LMFDB - Embedded newform 71.10.g.a.2.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [71,10,Mod(2,71)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("71.2"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(71, base_ring=CyclotomicField(70)) chi = DirichletCharacter(H, H._module([6])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 71 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	71.g (of order $35$, degree $24$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$36.5675443676$
Analytic rank:	$0$
Dimension:	$1272$
Relative dimension:	$53$ over $\Q(\zeta_{35})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{35}]$

Embedding invariants

Embedding label			2.2
Character	$\chi$	$=$	71.2
Dual form			71.10.g.a.36.2

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.95578 + 43.5489i) q^{2} +(-130.482 - 113.998i) q^{3} +(-1382.74 - 124.449i) q^{4} +(729.287 + 2244.51i) q^{5} +(5219.69 - 5459.36i) q^{6} +(-9550.39 - 2635.74i) q^{7} +(5127.92 - 37855.8i) q^{8} +(1387.71 + 10244.5i) q^{9} +(-99172.4 + 27369.8i) q^{10} +(-4461.52 + 8290.89i) q^{11} +(166235. + 173868. i) q^{12} +(-65803.7 - 122284. i) q^{13} +(133462. - 410754. i) q^{14} +(160712. - 376005. i) q^{15} +(939147. + 170430. i) q^{16} +(289725. + 210497. i) q^{17} +(-448849. + 40397.1i) q^{18} +(-130929. - 306324. i) q^{19} +(-729086. - 3.19434e6i) q^{20} +(945679. + 1.43264e6i) q^{21} +(-352333. - 210509. i) q^{22} +(-573711. - 719411. i) q^{23} +(-4.98460e6 + 4.35491e6i) q^{24} +(-2.92588e6 + 2.12577e6i) q^{25} +(5.45401e6 - 2.62651e6i) q^{26} +(-891992. + 1.35131e6i) q^{27} +(1.28777e7 + 4.83307e6i) q^{28} +(2.97147e6 - 1.77537e6i) q^{29} +(1.60603e7 + 7.73422e6i) q^{30} +(-6.35989e6 + 1.15415e6i) q^{31} +(-4.90648e6 + 2.14967e7i) q^{32} +(1.52729e6 - 573203. i) q^{33} +(-9.73356e6 + 1.22055e7i) q^{34} +(-1.04902e6 - 2.33582e7i) q^{35} +(-643926. - 1.43381e7i) q^{36} +(-5.72130e6 + 7.17429e6i) q^{37} +(1.35961e7 - 5.10271e6i) q^{38} +(-5.35397e6 + 2.34573e7i) q^{39} +(8.87076e7 - 1.60981e7i) q^{40} +(9.10033e6 + 4.38249e6i) q^{41} +(-6.42395e7 + 3.83813e7i) q^{42} +(-2.43587e7 - 9.14199e6i) q^{43} +(7.20091e6 - 1.09089e7i) q^{44} +(-2.19818e7 + 1.05859e7i) q^{45} +(3.24516e7 - 2.35774e7i) q^{46} +(-3.19455e7 + 2.79100e7i) q^{47} +(-1.03113e8 - 1.29299e8i) q^{48} +(4.96213e7 + 2.96473e7i) q^{49} +(-8.68526e7 - 1.31576e8i) q^{50} +(-1.38074e7 - 6.04941e7i) q^{51} +(7.57712e7 + 1.77276e8i) q^{52} +(-3.16811e7 + 2.85135e6i) q^{53} +(-5.71035e7 - 4.14881e7i) q^{54} +(-2.18628e7 - 3.96751e6i) q^{55} +(-1.48752e8 + 3.48022e8i) q^{56} +(-1.78366e7 + 5.48953e7i) q^{57} +(7.15038e7 + 1.32876e8i) q^{58} +(2.05857e7 + 2.15309e7i) q^{59} +(-2.69017e8 + 4.99916e8i) q^{60} +(1.35560e8 - 3.74123e7i) q^{61} +(-3.78234e7 - 2.79223e8i) q^{62} +(1.37486e7 - 1.01496e8i) q^{63} +(-4.55474e8 - 1.25703e8i) q^{64} +(2.26478e8 - 2.36877e8i) q^{65} +(2.19753e7 + 6.76329e7i) q^{66} +(1.92690e8 + 1.73424e7i) q^{67} +(-3.74417e8 - 3.27119e8i) q^{68} +(-7.15291e6 + 1.59272e8i) q^{69} +1.01927e9 q^{70} +(-2.11723e8 - 3.19646e7i) q^{71} +3.94929e8 q^{72} +(1.75852e6 - 3.91564e7i) q^{73} +(-3.01242e8 - 2.63188e8i) q^{74} +(6.24107e8 + 5.61707e7i) q^{75} +(1.42919e8 + 4.39860e8i) q^{76} +(6.44619e7 - 6.74218e7i) q^{77} +(-1.01107e9 - 2.79036e8i) q^{78} +(4.66562e7 - 3.44430e8i) q^{79} +(3.02375e8 + 2.23222e9i) q^{80} +(4.66586e8 - 1.28770e8i) q^{81} +(-2.08651e8 + 3.87738e8i) q^{82} +(5.60316e8 + 5.86044e8i) q^{83} +(-1.12934e9 - 2.09866e9i) q^{84} +(-2.61172e8 + 8.03804e8i) q^{85} +(4.45763e8 - 1.04292e9i) q^{86} +(-5.90111e8 - 1.07089e8i) q^{87} +(2.90980e8 + 2.11409e8i) q^{88} +(-2.92314e8 + 2.63087e7i) q^{89} +(-4.18012e8 - 9.77987e8i) q^{90} +(3.06143e8 + 1.34130e9i) q^{91} +(7.03763e8 + 1.06616e9i) q^{92} +(9.61419e8 + 5.74421e8i) q^{93} +(-1.15297e9 - 1.44578e9i) q^{94} +(5.92063e8 - 5.17270e8i) q^{95} +(3.09079e9 - 2.24559e9i) q^{96} +(-4.09446e8 + 1.97179e8i) q^{97} +(-1.38816e9 + 2.10297e9i) q^{98} +(-9.11271e7 - 3.42006e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1272 q - 76 q^{2} - 395 q^{3} + 13542 q^{4} - 1610 q^{5} - 4334 q^{6} - 4827 q^{7} - 18627 q^{8} + 286810 q^{9} - 53448 q^{10} - 170685 q^{11} + 138323 q^{12} - 93291 q^{13} + 985964 q^{14} - 966194 q^{15}+ \cdots - 4074592265 q^{99}+O(q^{100}) $ 1272 * q - 76 * q^2 - 395 * q^3 + 13542 * q^4 - 1610 * q^5 - 4334 * q^6 - 4827 * q^7 - 18627 * q^8 + 286810 * q^9 - 53448 * q^10 - 170685 * q^11 + 138323 * q^12 - 93291 * q^13 + 985964 * q^14 - 966194 * q^15 + 4755334 * q^16 + 2558412 * q^17 - 2619769 * q^18 - 172269 * q^19 + 738120 * q^20 + 1797929 * q^21 + 3015622 * q^22 + 6635088 * q^23 + 4803145 * q^24 - 115100016 * q^25 + 19254293 * q^26 - 17686931 * q^27 + 15761532 * q^28 - 10052927 * q^29 + 62637435 * q^30 - 23748991 * q^31 + 10388192 * q^32 - 15097203 * q^33 + 33217854 * q^34 - 24823174 * q^35 + 27856812 * q^36 - 27156308 * q^37 - 43400577 * q^38 + 251072838 * q^39 - 129856160 * q^40 + 62087988 * q^41 - 91873950 * q^42 - 167299067 * q^43 + 60914131 * q^44 - 31536191 * q^45 - 50201490 * q^46 - 23317743 * q^47 + 10641329 * q^48 + 338745866 * q^49 + 303770229 * q^50 + 448039613 * q^51 - 979580293 * q^52 + 12085215 * q^53 - 182583505 * q^54 - 243892552 * q^55 + 30440435 * q^56 + 714581966 * q^57 - 244549660 * q^58 - 859013315 * q^59 - 1894499000 * q^60 - 876373921 * q^61 + 186553636 * q^62 - 196611021 * q^63 + 5528242635 * q^64 + 867018244 * q^65 + 2727701199 * q^66 - 286780089 * q^67 - 1689988351 * q^68 - 3073308182 * q^69 - 41489396 * q^70 - 2538053548 * q^71 - 6821388000 * q^72 + 128479023 * q^73 + 3282772334 * q^74 + 3407782757 * q^75 + 7133788844 * q^76 + 1087098389 * q^77 + 2715049934 * q^78 + 144243625 * q^79 - 7443877603 * q^80 - 4083269278 * q^81 - 10375744380 * q^82 + 1543773955 * q^83 - 4117054288 * q^84 + 7843382686 * q^85 + 3545751759 * q^86 + 5261609811 * q^87 - 818728797 * q^88 - 1369081479 * q^89 + 10041256259 * q^90 - 7299574322 * q^91 + 602797624 * q^92 - 2146129677 * q^93 - 683447510 * q^94 - 7007204038 * q^95 + 6601829126 * q^96 - 10081488030 * q^97 - 5942379880 * q^98 - 4074592265 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/71\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{3}{35}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.95578	+	43.5489i	−0.0864341	+	1.92461i	0.225037	+	0.974350i	$0.427750\pi$
$2$	−1.95578	+	43.5489i	−0.0864341	+	1.92461i	−0.311471	+	0.950256i	$0.600822\pi$
$3$	−130.482	−	113.998i	−0.930044	−	0.812555i	0.0524935	−	0.998621i	$-0.483283\pi$
$3$	−130.482	−	113.998i	−0.930044	−	0.812555i	−0.982537	+	0.186067i	$0.940426\pi$
$4$	−1382.74	−	124.449i	−2.70066	−	0.243064i
$5$	729.287	+	2244.51i	0.521835	+	1.60604i	0.770490	+	0.637452i	$0.220012\pi$
$5$	729.287	+	2244.51i	0.521835	+	1.60604i	−0.248655	+	0.968592i	$0.579988\pi$
$6$	5219.69	−	5459.36i	1.64423	−	1.71973i
$7$	−9550.39	−	2635.74i	−1.50342	−	0.414917i	−0.585166	−	0.810913i	$-0.698971\pi$
$7$	−9550.39	−	2635.74i	−1.50342	−	0.414917i	−0.918252	+	0.395996i	$0.870399\pi$
$8$	5127.92	−	37855.8i	0.442625	−	3.26759i
$9$	1387.71	+	10244.5i	0.0705028	+	0.520473i
$10$	−99172.4	+	27369.8i	−3.13611	+	0.865510i
$11$	−4461.52	+	8290.89i	−0.0918789	+	0.170740i	−0.922387	−	0.386267i	$-0.873764\pi$
$11$	−4461.52	+	8290.89i	−0.0918789	+	0.170740i	0.830508	+	0.557006i	$0.188050\pi$
$12$	166235.	+	173868.i	2.31423	+	2.42050i
$13$	−65803.7	−	122284.i	−0.639006	−	1.18747i	−0.969831	−	0.243780i	$-0.921613\pi$
$13$	−65803.7	−	122284.i	−0.639006	−	1.18747i	0.330824	−	0.943692i	$-0.392673\pi$
$14$	133462.	−	410754.i	0.928498	−	2.85762i
$15$	160712.	−	376005.i	0.819669	−	1.91771i
$16$	939147.	+	170430.i	3.58256	+	0.650139i
$17$	289725.	+	210497.i	0.841328	+	0.611261i	0.922741	−	0.385420i	$-0.125943\pi$
$17$	289725.	+	210497.i	0.841328	+	0.611261i	−0.0814133	+	0.996680i	$0.525943\pi$
$18$	−448849.	+	40397.1i	−1.00780	+	0.0907035i
$19$	−130929.	−	306324.i	−0.230486	−	0.539249i	0.763867	−	0.645374i	$-0.223299\pi$
$19$	−130929.	−	306324.i	−0.230486	−	0.539249i	−0.994353	+	0.106125i	$0.966156\pi$
$20$	−729086.	−	3.19434e6i	−1.01893	−	4.46422i
$21$	945679.	+	1.43264e6i	1.06110	+	1.60750i
$22$	−352333.	−	210509.i	−0.320665	−	0.191588i
$23$	−573711.	−	719411.i	−0.427482	−	0.536046i	0.520714	−	0.853731i	$-0.325666\pi$
$23$	−573711.	−	719411.i	−0.427482	−	0.536046i	−0.948196	+	0.317686i	$0.897094\pi$
$24$	−4.98460e6	+	4.35491e6i	−3.06676	+	2.67934i
$25$	−2.92588e6	+	2.12577e6i	−1.49805	+	1.08840i
$26$	5.45401e6	−	2.62651e6i	2.34065	−	1.12720i
$27$	−891992.	+	1.35131e6i	−0.323016	+	0.489349i
$28$	1.28777e7	+	4.83307e6i	3.95937	+	1.48598i
$29$	2.97147e6	−	1.77537e6i	0.780154	−	0.466120i	−0.0668130	−	0.997766i	$-0.521283\pi$
$29$	2.97147e6	−	1.77537e6i	0.780154	−	0.466120i	0.846967	+	0.531645i	$0.178426\pi$
$30$	1.60603e7	+	7.73422e6i	3.61999	+	1.74330i
$31$	−6.35989e6	+	1.15415e6i	−1.23686	+	0.224458i	−0.757311	−	0.653055i	$-0.773487\pi$
$31$	−6.35989e6	+	1.15415e6i	−1.23686	+	0.224458i	−0.479554	+	0.877513i	$0.659201\pi$
$32$	−4.90648e6	+	2.14967e7i	−0.827170	+	3.62407i
$33$	1.52729e6	−	573203.i	0.224187	−	0.0841386i
$34$	−9.73356e6	+	1.22055e7i	−1.24916	+	1.56639i
$35$	−1.04902e6	−	2.33582e7i	−0.118162	−	2.63107i
$36$	−643926.	−	1.43381e7i	−0.0638961	−	1.42276i
$37$	−5.72130e6	+	7.17429e6i	−0.501865	+	0.629319i	−0.966649	−	0.256105i	$-0.917561\pi$
$37$	−5.72130e6	+	7.17429e6i	−0.501865	+	0.629319i	0.464784	+	0.885424i	$0.346132\pi$
$38$	1.35961e7	−	5.10271e6i	1.05776	−	0.396986i
$39$	−5.35397e6	+	2.34573e7i	−0.370583	+	1.62363i
$40$	8.87076e7	−	1.60981e7i	5.47887	−	0.994269i
$41$	9.10033e6	+	4.38249e6i	0.502956	+	0.242211i	0.668117	−	0.744056i	$-0.267100\pi$
$41$	9.10033e6	+	4.38249e6i	0.502956	+	0.242211i	−0.165162	+	0.986266i	$0.552815\pi$
$42$	−6.42395e7	+	3.83813e7i	−3.18552	+	1.90326i
$43$	−2.43587e7	−	9.14199e6i	−1.08654	−	0.407786i	−0.257104	−	0.966384i	$-0.582768\pi$
$43$	−2.43587e7	−	9.14199e6i	−1.08654	−	0.407786i	−0.829439	+	0.558598i	$0.811340\pi$
$44$	7.20091e6	−	1.09089e7i	0.289634	−	0.438777i
$45$	−2.19818e7	+	1.05859e7i	−0.799111	+	0.384832i
$46$	3.24516e7	−	2.35774e7i	1.06863	−	0.776402i
$47$	−3.19455e7	+	2.79100e7i	−0.954926	+	0.834294i	−0.986258	−	0.165215i	$-0.947168\pi$
$47$	−3.19455e7	+	2.79100e7i	−0.954926	+	0.834294i	0.0313314	+	0.999509i	$0.490025\pi$
$48$	−1.03113e8	−	1.29299e8i	−2.80367	−	3.51569i
$49$	4.96213e7	+	2.96473e7i	1.22966	+	0.734689i
$50$	−8.68526e7	−	1.31576e8i	−1.96525	−	2.97723i
$51$	−1.38074e7	−	6.04941e7i	−0.285789	−	1.25212i
$52$	7.57712e7	+	1.77276e8i	1.43711	+	3.36228i
$53$	−3.16811e7	+	2.85135e6i	−0.551518	+	0.0496375i	−0.361894	−	0.932219i	$-0.617870\pi$
$53$	−3.16811e7	+	2.85135e6i	−0.551518	+	0.0496375i	−0.189624	+	0.981857i	$0.560727\pi$
$54$	−5.71035e7	−	4.14881e7i	−0.913883	−	0.663975i
$55$	−2.18628e7	−	3.96751e6i	−0.322161	−	0.0584636i
$56$	−1.48752e8	+	3.48022e8i	−2.02123	+	4.72890i
$57$	−1.78366e7	+	5.48953e7i	−0.223807	+	0.688808i
$58$	7.15038e7	+	1.32876e8i	0.829666	+	1.54178i
$59$	2.05857e7	+	2.15309e7i	0.221172	+	0.231328i	0.824067	−	0.566493i	$-0.191700\pi$
$59$	2.05857e7	+	2.15309e7i	0.221172	+	0.231328i	−0.602894	+	0.797821i	$0.705986\pi$
$60$	−2.69017e8	+	4.99916e8i	−2.67977	+	4.97986i
$61$	1.35560e8	−	3.74123e7i	1.25357	−	0.345963i	0.424663	−	0.905351i	$-0.360393\pi$
$61$	1.35560e8	−	3.74123e7i	1.25357	−	0.345963i	0.828906	+	0.559388i	$0.188964\pi$
$62$	−3.78234e7	−	2.79223e8i	−0.325085	−	2.39988i
$63$	1.37486e7	−	1.01496e8i	0.109958	−	0.811741i
$64$	−4.55474e8	−	1.25703e8i	−3.39354	−	0.936559i
$65$	2.26478e8	−	2.36877e8i	1.57368	−	1.64594i
$66$	2.19753e7	+	6.76329e7i	0.142556	+	0.438743i
$67$	1.92690e8	+	1.73424e7i	1.16821	+	0.105141i	0.656712	−	0.754141i	$-0.271947\pi$
$67$	1.92690e8	+	1.73424e7i	1.16821	+	0.105141i	0.511502	+	0.859282i	$0.329089\pi$
$68$	−3.74417e8	−	3.27119e8i	−2.12357	−	1.85530i
$69$	−7.15291e6	+	1.59272e8i	−0.0379893	+	0.845898i
$70$	1.01927e9			5.07399
$71$	−2.11723e8	−	3.19646e7i	−0.988795	−	0.149282i
$71$	−2.11723e8	−	3.19646e7i	−0.988795	−	0.149282i
$72$	3.94929e8			1.73190
$73$	1.75852e6	−	3.91564e7i	0.00724759	−	0.161380i	−0.992105	−	0.125408i	$-0.959976\pi$
$73$	1.75852e6	−	3.91564e7i	0.00724759	−	0.161380i	0.999353	−	0.0359718i	$-0.0114527\pi$
$74$	−3.01242e8	−	2.63188e8i	−1.16781	−	1.02029i
$75$	6.24107e8	+	5.61707e7i	2.27763	+	0.204991i
$76$	1.42919e8	+	4.39860e8i	0.491393	+	1.51235i
$77$	6.44619e7	−	6.74218e7i	0.208975	−	0.218571i
$78$	−1.01107e9	−	2.79036e8i	−3.09281	−	0.853562i
$79$	4.66562e7	−	3.44430e8i	0.134768	−	0.994898i	−0.789661	−	0.613544i	$-0.789743\pi$
$79$	4.66562e7	−	3.44430e8i	0.134768	−	0.994898i	0.924429	−	0.381354i	$-0.124542\pi$
$80$	3.02375e8	+	2.23222e9i	0.825356	+	6.09302i
$81$	4.66586e8	−	1.28770e8i	1.20434	−	0.332377i
$82$	−2.08651e8	+	3.87738e8i	−0.509633	+	0.947056i
$83$	5.60316e8	+	5.86044e8i	1.29593	+	1.35544i	0.899223	+	0.437490i	$0.144132\pi$
$83$	5.60316e8	+	5.86044e8i	1.29593	+	1.35544i	0.396706	+	0.917946i	$0.370153\pi$
$84$	−1.12934e9	−	2.09866e9i	−2.47495	−	4.59923i
$85$	−2.61172e8	+	8.03804e8i	−0.542677	+	1.67019i
$86$	4.45763e8	−	1.04292e9i	0.878742	−	2.05592i
$87$	−5.90111e8	−	1.07089e8i	−1.10433	−	0.200406i
$88$	2.90980e8	+	2.11409e8i	0.517239	+	0.375796i
$89$	−2.92314e8	+	2.63087e7i	−0.493849	+	0.0444472i	−0.333765	−	0.942656i	$-0.608319\pi$
$89$	−2.92314e8	+	2.63087e7i	−0.493849	+	0.0444472i	−0.160084	+	0.987103i	$0.551176\pi$
$90$	−4.18012e8	−	9.77987e8i	−0.671579	−	1.57124i
$91$	3.06143e8	+	1.34130e9i	0.467991	+	2.05040i
$92$	7.03763e8	+	1.06616e9i	1.02419	+	1.55158i
$93$	9.61419e8	+	5.74421e8i	1.33272	+	0.796264i
$94$	−1.15297e9	−	1.44578e9i	−1.52315	−	1.90997i
$95$	5.92063e8	−	5.17270e8i	0.745782	−	0.651570i
$96$	3.09079e9	−	2.24559e9i	3.71406	−	2.69842i
$97$	−4.09446e8	+	1.97179e8i	−0.469595	+	0.226145i	−0.653689	−	0.756764i	$-0.726779\pi$
$97$	−4.09446e8	+	1.97179e8i	−0.469595	+	0.226145i	0.184093	+	0.982909i	$0.441065\pi$
$98$	−1.38816e9	+	2.10297e9i	−1.52027	+	2.30311i
$99$	−9.11271e7	−	3.42006e7i	−0.0953430	−	0.0357828i
$100$	4.31027e9	−	2.57527e9i	4.31027	−	2.57527i
$101$	5.73521e8	+	2.76193e8i	0.548407	+	0.264099i	0.687505	−	0.726180i	$-0.258706\pi$
$101$	5.73521e8	+	2.76193e8i	0.548407	+	0.264099i	−0.139098	+	0.990279i	$0.544420\pi$
$102$	2.66145e9	−	4.82983e8i	2.43455	−	0.441805i
$103$	−2.96121e8	+	1.29739e9i	−0.259240	+	1.13580i	0.662827	+	0.748772i	$0.269356\pi$
$103$	−2.96121e8	+	1.29739e9i	−0.259240	+	1.13580i	−0.922067	+	0.387031i	$0.873501\pi$
$104$	−4.96658e9	+	1.86399e9i	−4.16301	+	1.56241i
$105$	−2.52592e9	+	3.16740e9i	−2.02800	+	2.54303i
$106$	−6.22118e7	−	1.38525e9i	−0.0478626	−	1.06574i
$107$	2.28503e7	+	5.08802e8i	0.0168525	+	0.375251i	0.989642	+	0.143559i	$0.0458547\pi$
$107$	2.28503e7	+	5.08802e8i	0.0168525	+	0.375251i	−0.972789	+	0.231692i	$0.925574\pi$
$108$	1.40156e9	−	1.75750e9i	0.991300	−	1.24305i
$109$	1.14838e9	−	4.30994e8i	0.779231	−	0.292450i	0.0701122	−	0.997539i	$-0.477664\pi$
$109$	1.14838e9	−	4.30994e8i	0.779231	−	0.292450i	0.709119	+	0.705089i	$0.249093\pi$
$110$	2.15539e8	−	9.44339e8i	0.140365	−	0.614980i
$111$	1.56438e9	−	2.83893e8i	0.978113	−	0.177501i
$112$	−8.52001e9	−	4.10302e9i	−5.11634	−	2.46390i
$113$	1.59186e9	−	9.51095e8i	0.918445	−	0.548745i	0.0258804	−	0.999665i	$-0.491761\pi$
$113$	1.59186e9	−	9.51095e8i	0.918445	−	0.548745i	0.892564	+	0.450920i	$0.148904\pi$
$114$	−2.35574e9	−	8.84125e8i	−1.30634	−	0.490277i
$115$	1.19633e9	−	1.81236e9i	0.637838	−	0.966283i
$116$	−4.32971e9	+	2.08508e9i	−2.22023	+	1.06921i
$117$	1.16142e9	−	8.43817e8i	0.572995	−	0.416305i
$118$	−9.77908e8	+	8.54372e8i	−0.464332	+	0.405675i
$119$	−2.21217e9	−	2.77397e9i	−1.01125	−	1.26806i
$120$	−1.34099e10	−	8.01202e9i	−5.90349	−	3.52717i
$121$	1.25015e9	+	1.89390e9i	0.530187	+	0.803199i
$122$	1.36413e9	+	5.97667e9i	0.557491	+	2.44253i
$123$	−6.87829e8	−	1.60926e9i	−0.270961	−	0.633945i
$124$	8.93770e9	−	8.04408e8i	3.39491	−	0.305547i
$125$	−3.17603e9	−	2.30752e9i	−1.16356	−	0.845378i
$126$	4.39316e9	+	7.97240e8i	1.55278	+	0.281788i
$127$	1.56403e9	−	3.65923e9i	0.533492	−	1.24817i	−0.408570	−	0.912727i	$-0.633972\pi$
$127$	1.56403e9	−	3.65923e9i	0.533492	−	1.24817i	0.942062	−	0.335440i	$-0.108885\pi$
$128$	2.87642e9	−	8.85271e9i	0.947125	−	2.91495i
$129$	2.13619e9	+	3.96971e9i	0.679183	+	1.26213i
$130$	9.87279e9	+	1.03261e10i	3.03176	+	3.17097i
$131$	2.29476e9	−	4.26438e9i	0.680795	−	1.26513i	−0.272229	−	0.962233i	$-0.587761\pi$
$131$	2.29476e9	−	4.26438e9i	0.680795	−	1.26513i	0.953024	−	0.302896i	$-0.0979535\pi$
$132$	−2.18318e9	+	6.02520e8i	−0.625903	+	0.172738i
$133$	4.43034e8	+	3.27061e9i	0.122773	+	0.906350i
$134$	−1.13210e9	+	8.35751e9i	−0.303329	+	2.23926i
$135$	−3.68356e9	−	1.01660e9i	−0.954476	−	0.263419i
$136$	9.45423e9	−	9.88835e9i	2.36974	−	2.47856i
$137$	−1.14465e9	−	3.52287e9i	−0.277607	−	0.854387i	−0.988518	−	0.151104i	$-0.951717\pi$
$137$	−1.14465e9	−	3.52287e9i	−0.277607	−	0.854387i	0.710911	−	0.703282i	$-0.248283\pi$
$138$	−6.92212e9	−	6.23002e8i	−1.62474	−	0.146229i
$139$	−4.95291e9	−	4.32722e9i	−1.12537	−	0.983202i	−0.125405	−	0.992106i	$-0.540023\pi$
$139$	−4.95291e9	−	4.32722e9i	−1.12537	−	0.983202i	−0.999960	+	0.00890339i	$0.997166\pi$
$140$	−1.45638e9	+	3.24288e10i	−0.320405	+	7.13436i
$141$	7.34999e9			1.56603
$142$	1.80611e9	−	9.15779e9i	0.372774	−	1.89014i
$143$	1.30743e9			0.261460
$144$	−4.42704e8	+	9.85757e9i	−0.0857990	+	1.91046i
$145$	6.15190e9	+	5.37475e9i	1.15572	+	1.00972i
$146$	1.70178e9	+	1.53163e8i	0.309967	+	0.0278975i
$147$	−3.09491e9	−	9.52517e9i	−0.546664	−	1.68246i
$148$	8.80390e9	−	9.20816e9i	1.50833	−	1.57759i
$149$	1.74680e9	+	4.82086e8i	0.290339	+	0.0801284i	0.408172	−	0.912905i	$-0.366166\pi$
$149$	1.74680e9	+	4.82086e8i	0.290339	+	0.0801284i	−0.117833	+	0.993033i	$0.537595\pi$
$150$	−3.66678e9	+	2.70693e10i	−0.591391	+	4.36582i
$151$	3.75980e8	+	2.77560e9i	0.0588530	+	0.434471i	0.996272	+	0.0862672i	$0.0274939\pi$
$151$	3.75980e8	+	2.77560e9i	0.0588530	+	0.434471i	−0.937419	+	0.348203i	$0.886792\pi$
$152$	−1.22675e10	+	3.38562e9i	−1.86406	+	0.514449i
$153$	−1.75438e9	+	3.26018e9i	−0.258829	+	0.480984i
$154$	2.81007e9	+	2.93910e9i	0.402600	+	0.421087i
$155$	−7.22869e9	−	1.34332e10i	−1.00593	−	1.86933i
$156$	1.03224e10	−	3.17690e10i	1.39546	−	4.29480i
$157$	−2.16176e9	+	5.05769e9i	−0.283961	+	0.664361i	−0.999411	−	0.0343033i	$-0.989079\pi$
$157$	−2.16176e9	+	5.05769e9i	−0.283961	+	0.664361i	0.715450	+	0.698664i	$0.246222\pi$
$158$	1.49083e10	+	2.70545e9i	1.90314	+	0.345369i
$159$	4.45885e9	+	3.23955e9i	0.553269	+	0.401973i
$160$	−5.18278e10	+	4.66459e9i	−6.25206	+	0.562696i
$161$	3.58298e9	+	8.38281e9i	0.420270	+	0.983270i
$162$	4.69523e9	+	2.05711e10i	0.535598	+	2.34661i
$163$	−7.73567e8	−	1.17190e9i	−0.0858329	−	0.130031i	0.789121	−	0.614238i	$-0.210537\pi$
$163$	−7.73567e8	−	1.17190e9i	−0.0858329	−	0.130031i	−0.874953	+	0.484207i	$0.839108\pi$
$164$	−1.20380e10	−	7.19236e9i	−1.29944	−	0.776380i
$165$	2.40040e9	+	3.01000e9i	0.252119	+	0.316147i
$166$	−2.66174e10	+	2.32549e10i	−2.72069	+	2.37700i
$167$	3.16493e9	−	2.29946e9i	0.314876	−	0.228771i	−0.419110	−	0.907936i	$-0.637658\pi$
$167$	3.16493e9	−	2.29946e9i	0.314876	−	0.228771i	0.733986	+	0.679165i	$0.237658\pi$
$168$	5.90832e10	−	2.84530e10i	5.72232	−	2.75573i
$169$	−4.78119e9	+	7.24320e9i	−0.450865	+	0.683031i
$170$	−3.44940e10	−	1.29458e10i	−3.16755	−	1.18880i
$171$	2.95643e9	−	1.76639e9i	0.264415	−	0.157980i
$172$	3.25441e10	+	1.56724e10i	2.83527	+	1.36539i
$173$	1.51753e10	−	2.75391e9i	1.28804	−	0.233745i	0.509028	−	0.860750i	$-0.330005\pi$
$173$	1.51753e10	−	2.75391e9i	1.28804	−	0.233745i	0.779015	+	0.627005i	$0.215719\pi$
$174$	5.81775e9	−	2.54892e10i	0.481153	−	2.10807i
$175$	3.35462e10	−	1.25901e10i	2.70379	−	1.01475i
$176$	−5.60304e9	+	7.02599e9i	−0.440166	+	0.551951i
$177$	−2.31561e8	−	5.15611e9i	−0.0177332	−	0.394860i
$178$	−5.74013e8	−	1.27814e10i	−0.0428580	−	0.954306i
$179$	4.50875e9	−	5.65379e9i	0.328260	−	0.411625i	−0.590126	−	0.807311i	$-0.700922\pi$
$179$	4.50875e9	−	5.65379e9i	0.328260	−	0.411625i	0.918386	+	0.395687i	$0.129493\pi$
$180$	3.17125e10	−	1.19019e10i	2.25167	−	0.845065i
$181$	3.00234e9	−	1.31541e10i	0.207925	−	0.910977i	−0.758021	−	0.652231i	$-0.773833\pi$
$181$	3.00234e9	−	1.31541e10i	0.207925	−	0.910977i	0.965945	−	0.258747i	$-0.0833094\pi$
$182$	−5.90107e10	+	1.07089e10i	−3.98667	+	0.723473i
$183$	−2.19530e10	−	1.05720e10i	−1.44699	−	0.696833i
$184$	−3.01758e10	+	1.80292e10i	−1.94079	+	1.15957i
$185$	−2.02753e10	−	7.60943e9i	−1.27261	−	0.477617i
$186$	−2.68957e10	+	4.07453e10i	−1.64769	+	2.49614i
$187$	−3.03782e9	+	1.46294e9i	−0.181667	+	0.0874861i
$188$	4.76457e10	−	3.46166e10i	2.78172	−	2.02104i
$189$	1.20806e10	−	1.05545e10i	0.688667	−	0.601671i
$190$	2.13686e10	+	2.67954e10i	1.18955	+	1.49165i
$191$	1.05503e10	+	6.30353e9i	0.573609	+	0.342715i	0.770232	−	0.637764i	$-0.220140\pi$
$191$	1.05503e10	+	6.30353e9i	0.573609	+	0.342715i	−0.196623	+	0.980479i	$0.562998\pi$
$192$	4.51010e10	+	6.83251e10i	2.39514	+	3.62848i
$193$	5.78006e8	+	2.53241e9i	0.0299864	+	0.131379i	0.987706	−	0.156326i	$-0.0499650\pi$
$193$	5.78006e8	+	2.53241e9i	0.0299864	+	0.131379i	−0.957719	+	0.287705i	$0.907108\pi$
$194$	−7.78612e9	−	1.82165e10i	−0.394651	−	0.923333i
$195$	−5.65548e10	+	5.09002e9i	−2.80100	+	0.252095i
$196$	−6.49237e10	−	4.71698e10i	−3.14232	−	2.28303i
$197$	1.06912e10	+	1.94017e9i	0.505742	+	0.0917786i	0.425430	−	0.904991i	$-0.360123\pi$
$197$	1.06912e10	+	1.94017e9i	0.505742	+	0.0917786i	0.0803116	+	0.996770i	$0.474408\pi$
$198$	1.66762e9	−	3.90159e9i	0.0771088	−	0.180405i
$199$	−1.07156e10	+	3.29791e10i	−0.484369	+	1.49073i	0.348524	+	0.937300i	$0.386683\pi$
$199$	−1.07156e10	+	3.29791e10i	−0.484369	+	1.49073i	−0.832893	+	0.553434i	$0.813317\pi$
$200$	6.54692e10	+	1.21662e11i	2.89336	+	5.37676i
$201$	−2.31655e10	−	2.42292e10i	−1.00106	−	1.04702i
$202$	−1.31496e10	+	2.44360e10i	−0.555687	+	1.03264i
$203$	−3.30581e10	+	9.12346e9i	−1.36630	+	0.377075i
$204$	1.15636e10	+	8.53659e10i	0.467474	+	3.45103i
$205$	−3.19981e9	+	2.36219e10i	−0.126541	+	0.934163i
$206$	−5.59207e10	−	1.54331e10i	−2.16357	−	0.597106i
$207$	6.57384e9	−	6.87570e9i	0.248858	−	0.260286i
$208$	−4.09585e10	−	1.26057e11i	−1.51726	−	4.66964i
$209$	3.12384e9	+	2.81151e8i	0.113248	+	0.0101925i
$210$	−1.32996e11	−	1.16196e11i	−4.71904	−	4.12290i
$211$	−4.83283e8	+	1.07611e10i	−0.0167854	+	0.373755i	0.972966	+	0.230950i	$0.0741835\pi$
$211$	−4.83283e8	+	1.07611e10i	−0.0167854	+	0.373755i	−0.989751	+	0.142805i	$0.954388\pi$
$212$	4.41616e10			1.50153
$213$	2.39821e10	+	2.83069e10i	0.798323	+	0.942288i
$214$	−2.22024e10			−0.723666
$215$	2.75481e9	−	6.13407e10i	0.0879264	−	1.95783i
$216$	4.65809e10	+	4.06965e10i	1.45602	+	1.27208i
$217$	6.37815e10	+	5.74044e9i	1.95266	+	0.175742i
$218$	1.65233e10	+	5.08536e10i	0.495499	+	1.52499i
$219$	−4.69322e9	+	4.90872e9i	−0.137871	+	0.144201i
$220$	2.97367e10	+	8.20682e9i	0.855837	+	0.236196i
$221$	6.67544e9	−	4.92801e10i	0.188241	−	1.38965i
$222$	9.30364e9	+	6.86822e10i	0.257078	+	1.89782i
$223$	1.72101e10	−	4.74968e9i	0.466027	−	0.128615i	−0.0251340	−	0.999684i	$-0.508001\pi$
$223$	1.72101e10	−	4.74968e9i	0.466027	−	0.128615i	0.491161	+	0.871069i	$0.336573\pi$
$224$	1.03518e11	−	1.92369e11i	2.74727	−	5.10528i
$225$	−2.58377e10	−	2.70241e10i	−0.672097	−	0.702958i
$226$	3.83057e10	+	7.11840e10i	0.976733	+	1.81507i
$227$	4.50307e9	−	1.38590e10i	0.112562	−	0.346430i	−0.878869	−	0.477064i	$-0.841701\pi$
$227$	4.50307e9	−	1.38590e10i	0.112562	−	0.346430i	0.991431	+	0.130633i	$0.0417011\pi$
$228$	3.14950e10	−	7.36861e10i	0.771852	−	1.80584i
$229$	−6.41496e10	−	1.16414e10i	−1.54147	−	0.279735i	−0.659740	−	0.751494i	$-0.729334\pi$
$229$	−6.41496e10	−	1.16414e10i	−1.54147	−	0.279735i	−0.881728	+	0.471759i	$0.843619\pi$
$230$	7.65864e10	+	5.56433e10i	1.80458	+	1.31111i
$231$	−1.60971e10	+	1.44876e9i	−0.371957	+	0.0334767i
$232$	−5.19707e10	−	1.21591e11i	−1.17777	−	2.75554i
$233$	6.68777e9	+	2.93010e10i	0.148655	+	0.651301i	0.993260	+	0.115910i	$0.0369784\pi$
$233$	6.68777e9	+	2.93010e10i	0.148655	+	0.651301i	−0.844605	+	0.535391i	$0.820164\pi$
$234$	3.44758e10	+	5.22286e10i	0.751698	+	1.13877i
$235$	−8.59418e10	−	5.13478e10i	−1.83823	−	1.09829i
$236$	−2.57851e10	−	3.23335e10i	−0.541084	−	0.678498i
$237$	−4.53521e10	+	3.96230e10i	−0.933749	+	0.815792i
$238$	1.25130e11	−	9.09121e10i	2.52793	−	1.83665i
$239$	−1.61140e10	+	7.76012e9i	−0.319458	+	0.153843i	−0.586740	−	0.809775i	$-0.699589\pi$
$239$	−1.61140e10	+	7.76012e9i	−0.319458	+	0.153843i	0.267282	+	0.963618i	$0.413875\pi$
$240$	2.15015e11	−	3.25734e11i	4.18330	−	6.33742i
$241$	3.94414e10	+	1.48026e10i	0.753141	+	0.282658i	0.698269	−	0.715835i	$-0.253954\pi$
$241$	3.94414e10	+	1.48026e10i	0.753141	+	0.282658i	0.0548713	+	0.998493i	$0.482525\pi$
$242$	−8.49222e10	+	5.07387e10i	−1.59167	+	0.950977i
$243$	−4.68465e10	−	2.25601e10i	−0.861884	−	0.415061i
$244$	−1.92100e11	+	3.48611e10i	−3.46956	+	0.629632i
$245$	−3.03557e10	+	1.32997e11i	−0.538261	+	2.35828i
$246$	7.14265e10	−	2.68068e10i	1.24352	−	0.466699i
$247$	−2.88428e10	+	3.61677e10i	−0.493062	+	0.618280i
$248$	1.10783e10	+	2.46677e11i	0.185969	+	4.14092i
$249$	−6.30281e9	−	1.40343e11i	−0.103905	−	2.31363i
$250$	1.06702e11	−	1.33800e11i	1.72759	−	2.16633i
$251$	1.01561e11	−	3.81164e10i	1.61508	−	0.606150i	0.629750	−	0.776798i	$-0.283158\pi$
$251$	1.01561e11	−	3.81164e10i	1.61508	−	0.606150i	0.985332	+	0.170648i	$0.0545861\pi$
$252$	−3.16418e10	+	1.38632e11i	−0.494264	+	2.16551i
$253$	8.52418e9	−	1.54691e9i	0.130801	−	0.0237368i
$254$	1.56296e11	+	7.52683e10i	2.35612	+	1.13465i
$255$	1.25710e11	−	7.51085e10i	1.86183	−	1.11239i
$256$	1.53405e11	+	5.75739e10i	2.23234	+	0.837810i
$257$	−2.90493e10	+	4.40079e10i	−0.415372	+	0.629262i	−0.980680	−	0.195618i	$-0.937329\pi$
$257$	−2.90493e10	+	4.40079e10i	−0.415372	+	0.629262i	0.565308	+	0.824880i	$0.308757\pi$
$258$	−1.77054e11	+	8.52649e10i	−2.48782	+	1.19807i
$259$	7.35502e10	−	5.34374e10i	1.01563	−	0.737898i
$260$	−3.42639e11	+	2.99354e11i	−4.65004	+	4.06261i
$261$	2.23113e10	+	2.79774e10i	0.297606	+	0.373186i
$262$	1.81221e11	+	1.08274e11i	2.37603	+	1.41961i
$263$	5.41736e10	+	8.20694e10i	0.698211	+	1.05774i	0.994711	+	0.102711i	$0.0327518\pi$
$263$	5.41736e10	+	8.20694e10i	0.698211	+	1.05774i	−0.296501	+	0.955033i	$0.595820\pi$
$264$	−1.38672e10	−	6.07563e10i	−0.175700	−	0.769792i
$265$	−2.95046e10	−	6.90293e10i	−0.367521	−	0.859859i
$266$	−1.43298e11	+	1.28970e10i	−1.75498	+	0.157951i
$267$	4.11407e10	+	2.98905e10i	0.495417	+	0.359941i
$268$	−2.64282e11	−	4.79601e10i	−3.12940	−	0.567902i
$269$	−5.80743e10	+	1.35872e11i	−0.676236	+	1.58213i	0.130651	+	0.991428i	$0.458293\pi$
$269$	−5.80743e10	+	1.35872e11i	−0.676236	+	1.58213i	−0.806887	+	0.590705i	$0.798850\pi$
$270$	5.14759e10	−	1.58426e11i	0.589477	−	1.81422i
$271$	−4.13867e10	−	7.69094e10i	−0.466122	−	0.866199i	−0.999790	−	0.0205051i	$-0.993473\pi$
$271$	−4.13867e10	−	7.69094e10i	−0.466122	−	0.866199i	0.533668	−	0.845694i	$-0.320813\pi$
$272$	2.36219e11	+	2.47066e11i	2.61671	+	2.73686i
$273$	1.12960e11	−	2.09914e11i	1.23081	−	2.28723i
$274$	1.55656e11	−	4.29583e10i	1.66835	−	0.460436i
$275$	−4.57070e9	−	3.37423e10i	−0.0481932	−	0.355777i
$276$	2.97118e10	−	2.19341e11i	0.308204	−	2.27525i
$277$	6.93163e10	+	1.91301e10i	0.707418	+	0.195235i	0.601189	−	0.799107i	$-0.294694\pi$
$277$	6.93163e10	+	1.91301e10i	0.707418	+	0.195235i	0.106229	+	0.994342i	$0.466122\pi$
$278$	1.98132e11	−	2.07230e11i	1.98955	−	2.08090i
$279$	−2.06493e10	−	6.35521e10i	−0.204027	−	0.627929i
$280$	−8.89623e11	−	8.00675e10i	−8.64957	−	0.778476i
$281$	−4.31545e9	−	3.77030e9i	−0.0412903	−	0.0360742i	0.637046	−	0.770826i	$-0.280156\pi$
$281$	−4.31545e9	−	3.77030e9i	−0.0412903	−	0.0360742i	−0.678337	+	0.734751i	$0.737299\pi$
$282$	−1.43750e10	+	3.20084e11i	−0.135359	+	3.01399i
$283$	−7.80867e10			−0.723666			−0.361833	−	0.932243i	$-0.617849\pi$
$283$	−7.80867e10			−0.723666			−0.361833	+	0.932243i	$0.617849\pi$
$284$	2.88780e11	+	7.05474e10i	2.63412	+	0.643500i
$285$	−1.36221e11			−1.22305
$286$	−2.55704e9	+	5.69369e10i	−0.0225990	+	0.503207i
$287$	−7.53606e10	−	6.58405e10i	−0.655655	−	0.572829i
$288$	−2.27031e11	−	2.04331e10i	−1.94455	−	0.175012i
$289$	2.98561e9	+	9.18877e9i	0.0251764	+	0.0774849i
$290$	−2.46096e11	+	2.57396e11i	−2.04321	+	2.13703i
$291$	7.59032e10	+	2.09479e10i	0.620500	+	0.171247i
$292$	−7.30454e9	+	5.39242e10i	−0.0587990	+	0.434071i
$293$	−2.94966e10	−	2.17753e11i	−0.233813	−	1.72608i	−0.603884	−	0.797072i	$-0.706381\pi$
$293$	−2.94966e10	−	2.17753e11i	−0.233813	−	1.72608i	0.370072	−	0.929003i	$-0.379333\pi$
$294$	4.20863e11	−	1.16151e11i	3.28532	−	0.906691i
$295$	−3.33136e10	+	6.19070e10i	−0.256108	+	0.475928i
$296$	2.42250e11	+	2.53374e11i	1.83422	+	1.91844i
$297$	−7.22393e9	−	1.34243e10i	−0.0538728	−	0.100112i
$298$	−2.44107e10	+	7.51283e10i	−0.179311	+	0.551862i
$299$	−5.02199e10	+	1.17495e11i	−0.363376	+	0.850160i
$300$	−8.55987e11	−	1.55339e11i	−6.10129	−	1.10722i
$301$	2.08539e11	+	1.51513e11i	1.46433	+	1.06390i
$302$	−1.21609e11	+	1.09451e10i	−0.841272	+	0.0757158i
$303$	−4.33483e10	−	1.01418e11i	−0.295448	−	0.691234i
$304$	−7.07549e10	−	3.09998e11i	−0.475144	−	2.08174i
$305$	1.82835e11	+	2.76983e11i	1.20979	+	1.83275i
$306$	−1.38546e11	−	8.27774e10i	−0.903333	−	0.539716i
$307$	−2.28462e10	−	2.86482e10i	−0.146788	−	0.184066i	0.703002	−	0.711188i	$-0.251843\pi$
$307$	−2.28462e10	−	2.86482e10i	−0.146788	−	0.184066i	−0.849790	+	0.527122i	$0.823271\pi$
$308$	−9.75245e10	+	8.52046e10i	−0.617498	+	0.539492i
$309$	1.86538e11	−	1.35528e11i	1.16401	−	0.845700i
$310$	5.99137e11	−	2.88529e11i	3.68467	−	1.77444i
$311$	6.79958e10	−	1.03009e11i	0.412155	−	0.624387i	−0.567904	−	0.823095i	$-0.692246\pi$
$311$	6.79958e10	−	1.03009e11i	0.412155	−	0.624387i	0.980059	+	0.198707i	$0.0636742\pi$
$312$	8.60539e11	+	3.22966e11i	5.14132	+	1.92957i
$313$	−1.93566e11	+	1.15650e11i	−1.13993	+	0.681079i	−0.953501	−	0.301389i	$-0.902550\pi$
$313$	−1.93566e11	+	1.15650e11i	−1.13993	+	0.681079i	−0.186433	+	0.982468i	$0.559693\pi$
$314$	−2.16029e11	−	1.04034e11i	−1.25409	−	0.603937i
$315$	2.37837e11	−	4.31610e10i	1.36107	−	0.246998i
$316$	−1.07377e11	+	4.70450e11i	−0.605787	+	2.65413i
$317$	−1.55455e11	+	5.83431e10i	−0.864643	+	0.324506i	−0.743992	−	0.668189i	$-0.767070\pi$
$317$	−1.55455e11	+	5.83431e10i	−0.864643	+	0.324506i	−0.120651	+	0.992695i	$0.538498\pi$
$318$	−1.49799e11	+	1.87842e11i	−0.821461	+	1.03008i
$319$	1.46214e9	+	3.25570e10i	0.00790551	+	0.176030i
$320$	−5.00294e10	−	1.11399e12i	−0.266717	−	5.93891i
$321$	5.50210e10	−	6.89941e10i	0.289238	−	0.362693i
$322$	−3.72069e11	+	1.39640e11i	−1.92873	+	0.723866i
$323$	2.65470e10	−	1.16310e11i	0.135707	−	0.594573i
$324$	−6.61192e11	+	1.19989e11i	−3.33330	+	0.604906i
$325$	4.52481e11	+	2.17903e11i	2.24970	+	1.08340i
$326$	5.25480e10	−	3.13960e10i	0.257678	−	0.153955i
$327$	−1.98975e11	−	7.46765e10i	−0.962351	−	0.361176i
$328$	2.12568e11	−	3.22027e11i	1.01407	−	1.53624i
$329$	3.78656e11	−	1.82351e11i	1.78182	−	0.858077i
$330$	−1.35777e11	+	9.86476e10i	−0.630250	+	0.457904i
$331$	−1.98967e11	+	1.73832e11i	−0.911076	+	0.795983i	−0.979452	−	0.201676i	$-0.935361\pi$
$331$	−1.98967e11	+	1.73832e11i	−0.911076	+	0.795983i	0.0683760	+	0.997660i	$0.478218\pi$
$332$	−7.01838e11	−	8.80077e11i	−3.17041	−	3.97557i
$333$	−8.14362e10	−	4.86559e10i	−0.362927	−	0.216838i
$334$	9.39487e10	+	1.42326e11i	0.413078	+	0.625786i
$335$	1.01601e11	+	4.45143e11i	0.440754	+	1.93107i
$336$	6.43967e11	+	1.50664e12i	2.75636	+	6.44884i
$337$	−2.84528e11	+	2.56080e10i	−1.20169	+	0.108154i	−0.672333	−	0.740249i	$-0.734708\pi$
$337$	−2.84528e11	+	2.56080e10i	−1.20169	+	0.108154i	−0.529352	+	0.848402i	$0.677565\pi$
$338$	−3.06082e11	−	2.22382e11i	−1.27559	−	0.926774i
$339$	−3.16132e11	−	5.73695e10i	−1.30008	−	0.235930i
$340$	4.61165e11	−	1.07895e12i	1.87155	−	4.37871i
$341$	1.88058e10	−	5.78784e10i	0.0753179	−	0.231805i
$342$	7.11420e10	+	1.32204e11i	0.281196	+	0.522549i
$343$	−1.19473e11	−	1.24959e11i	−0.466064	−	0.487464i
$344$	−4.70987e11	+	8.75240e11i	−1.81341	+	3.36988i
$345$	−3.62705e11	+	1.00100e11i	−1.37837	+	0.380407i
$346$	9.02502e10	+	6.66254e11i	0.338537	+	2.49918i
$347$	1.42568e10	−	1.05248e11i	0.0527885	−	0.389700i	−0.945210	−	0.326463i	$-0.894143\pi$
$347$	1.42568e10	−	1.05248e11i	0.0527885	−	0.389700i	0.997999	−	0.0632375i	$-0.0201426\pi$
$348$	8.02643e11	+	2.21515e11i	2.93370	+	0.809650i
$349$	2.50179e10	−	2.61666e10i	0.0902684	−	0.0944134i	−0.676117	−	0.736794i	$-0.736339\pi$
$349$	2.50179e10	−	2.61666e10i	0.0902684	−	0.0944134i	0.766386	+	0.642380i	$0.222053\pi$
$350$	4.82676e11	+	1.48552e12i	1.71929	+	5.29143i
$351$	2.23940e11	+	2.01549e10i	0.787497	+	0.0708760i
$352$	−1.56336e11	−	1.36587e11i	−0.542772	−	0.474206i
$353$	−1.68326e9	+	3.74806e10i	−0.00576984	+	0.128476i	0.994041	+	0.109010i	$0.0347680\pi$
$353$	−1.68326e9	+	3.74806e10i	−0.00576984	+	0.128476i	−0.999811	+	0.0194658i	$0.993803\pi$
$354$	2.24996e11			0.761482
$355$	−8.26621e10	−	4.98527e11i	−0.276235	−	1.66595i
$356$	4.07468e11			1.34452
$357$	−2.75808e10	+	6.14135e11i	−0.0898670	+	2.00105i
$358$	2.37398e11	+	2.07408e11i	0.763842	+	0.667349i
$359$	4.32344e11	+	3.89117e10i	1.37374	+	0.123639i	0.751782	−	0.659412i	$-0.229195\pi$
$359$	4.32344e11	+	3.89117e10i	1.37374	+	0.123639i	0.621958	+	0.783051i	$0.286337\pi$
$360$	2.88016e11	+	8.86423e11i	0.903766	+	2.78150i
$361$	1.46306e11	−	1.53024e11i	0.453397	−	0.474216i
$362$	5.66974e11	+	1.56475e11i	1.73530	+	0.478912i
$363$	5.27795e10	−	3.89634e11i	0.159546	−	1.17782i
$364$	−2.56392e11	−	1.89276e12i	−0.765506	−	5.65119i
$365$	8.91696e10	−	2.46092e10i	0.262966	−	0.0725739i
$366$	5.03335e11	−	9.35353e11i	1.46620	−	2.72465i
$367$	1.21516e11	+	1.27096e11i	0.349652	+	0.365708i	0.874109	−	0.485729i	$-0.161446\pi$
$367$	1.21516e11	+	1.27096e11i	0.349652	+	0.365708i	−0.524457	+	0.851437i	$0.675732\pi$
$368$	−4.16190e11	−	7.73411e11i	−1.18298	−	2.19834i
$369$	−3.22677e10	+	9.93096e10i	−0.0906043	+	0.278851i
$370$	3.71036e11	−	8.68082e11i	1.02922	−	2.40798i
$371$	3.10083e11	+	5.62717e10i	0.849757	+	0.154208i
$372$	−1.25791e12	−	9.13922e11i	−3.40569	−	2.47438i
$373$	−1.52885e11	+	1.37599e10i	−0.408955	+	0.0368066i	−0.292207	−	0.956355i	$-0.594390\pi$
$373$	−1.52885e11	+	1.37599e10i	−0.408955	+	0.0368066i	−0.116748	+	0.993162i	$0.537247\pi$
$374$	−5.77680e10	−	1.35155e11i	−0.152674	−	0.357198i
$375$	1.51360e11	+	6.63151e11i	0.395249	+	1.73170i
$376$	8.92740e11	+	1.35244e12i	2.30346	+	3.48959i
$377$	−4.12633e11	−	2.46537e11i	−1.05203	−	0.628558i
$378$	4.36009e11	+	5.46738e11i	1.09845	+	1.37742i
$379$	2.72702e11	−	2.38252e11i	0.678908	−	0.593144i	−0.247852	−	0.968798i	$-0.579725\pi$
$379$	2.72702e11	−	2.38252e11i	0.678908	−	0.593144i	0.926760	+	0.375654i	$0.122582\pi$
$380$	−8.83043e11	+	6.41568e11i	−2.17248	+	1.57840i
$381$	−6.21222e11	+	2.99165e11i	−1.51037	+	0.727358i
$382$	−2.95146e11	+	4.47126e11i	−0.709171	+	1.07435i
$383$	2.35812e11	+	8.85016e10i	0.559978	+	0.210163i	0.615283	−	0.788306i	$-0.289042\pi$
$383$	2.35812e11	+	8.85016e10i	0.559978	+	0.210163i	−0.0553053	+	0.998469i	$0.517613\pi$
$384$	−1.38451e12	+	8.27208e11i	−3.24942	+	1.94144i
$385$	1.98341e11	+	9.55158e10i	0.460085	+	0.221565i
$386$	−1.11414e11	+	2.02187e10i	−0.255445	+	0.0463564i
$387$	5.98520e10	−	2.62229e11i	0.135637	−	0.594266i
$388$	5.90696e11	−	2.21692e11i	1.32319	−	0.496600i
$389$	4.60215e11	−	5.77092e11i	1.01903	−	1.27783i	0.0589050	−	0.998264i	$-0.481239\pi$
$389$	4.60215e11	−	5.77092e11i	1.01903	−	1.27783i	0.960127	−	0.279563i	$-0.0901895\pi$
$390$	−1.11056e11	−	2.47285e12i	−0.243081	−	5.41261i
$391$	−1.47842e10	−	3.29196e11i	−0.0319891	−	0.712293i
$392$	1.37678e12	−	1.72642e12i	2.94494	−	3.69284i
$393$	−7.85555e11	+	2.94824e11i	−1.66115	+	0.623442i
$394$	−1.05402e11	+	4.61796e11i	−0.220351	+	0.965421i
$395$	8.07103e11	−	1.46468e11i	1.66818	−	0.302729i
$396$	1.21749e11	+	5.86311e10i	0.248792	+	0.119812i
$397$	−1.84461e11	+	1.10210e11i	−0.372689	+	0.222671i	−0.687014	−	0.726644i	$-0.741079\pi$
$397$	−1.84461e11	+	1.10210e11i	−0.372689	+	0.222671i	0.314325	+	0.949315i	$0.398222\pi$
$398$	−1.41525e12	−	5.31150e11i	−2.82721	−	1.06107i
$399$	3.15036e11	−	4.77259e11i	0.622274	−	0.942705i
$400$	−3.11012e12	+	1.49776e12i	−6.07446	+	2.92531i
$401$	7.13635e10	−	5.18486e10i	0.137824	−	0.100135i	−0.516737	−	0.856144i	$-0.672853\pi$
$401$	7.13635e10	−	5.18486e10i	0.137824	−	0.100135i	0.654561	+	0.756009i	$0.272853\pi$
$402$	1.10046e12	−	9.61443e11i	2.10163	−	1.83614i
$403$	5.59638e11	+	7.01764e11i	1.05690	+	1.32531i
$404$	−7.58658e11	−	4.53277e11i	−1.41687	−	0.846540i
$405$	6.29300e11	+	9.53349e11i	1.16228	+	1.76078i
$406$	−3.32662e11	−	1.45749e12i	−0.607625	−	2.66218i
$407$	−3.39555e10	−	7.94429e10i	−0.0613389	−	0.143509i
$408$	−2.36086e12	+	2.12481e11i	−4.21793	+	0.379620i
$409$	−9.86846e10	−	7.16985e10i	−0.174379	−	0.126694i	0.497172	−	0.867652i	$-0.334372\pi$
$409$	−9.86846e10	−	7.16985e10i	−0.174379	−	0.126694i	−0.671551	+	0.740958i	$0.734372\pi$
$410$	−1.02245e12	−	1.85547e11i	−1.78696	−	0.324285i
$411$	−2.52246e11	+	5.90158e11i	−0.436049	+	1.02019i
$412$	5.70916e11	−	1.75710e12i	0.976191	−	3.00441i
$413$	−1.39851e11	−	2.59887e11i	−0.236532	−	0.439551i
$414$	2.86572e11	+	2.99730e11i	0.479437	+	0.501452i
$415$	−9.06754e11	+	1.68503e12i	−1.50063	+	2.78863i
$416$	2.95156e12	−	8.14578e11i	4.83205	−	1.33356i
$417$	1.52967e11	+	1.12925e12i	0.247733	+	1.82884i
$418$	−1.83533e10	+	1.35490e11i	−0.0294051	+	0.217077i
$419$	9.80185e11	+	2.70514e11i	1.55362	+	0.428772i	0.934336	−	0.356394i	$-0.115994\pi$
$419$	9.80185e11	+	2.70514e11i	1.55362	+	0.428772i	0.619285	+	0.785166i	$0.287423\pi$
$420$	3.88686e12	−	4.06534e12i	6.09505	−	6.37492i
$421$	−8.51880e10	−	2.62182e11i	−0.132163	−	0.406755i	0.862975	−	0.505246i	$-0.168598\pi$
$421$	−8.51880e10	−	2.62182e11i	−0.132163	−	0.406755i	−0.995138	+	0.0984912i	$0.968598\pi$
$422$	−4.67690e11	−	4.20928e10i	−0.717880	−	0.0646104i
$423$	−3.30254e11	−	2.88534e11i	−0.501552	−	0.438193i
$424$	−5.45180e10	+	1.21394e12i	−0.0819206	+	1.82410i
$425$	−1.29517e12			−1.92564
$426$	−1.27964e12	+	9.89030e11i	−1.88254	+	1.45501i
$427$	−1.39326e12			−2.02818
$428$	3.17237e10	−	7.06384e11i	0.0456970	−	1.01752i
$429$	−1.70595e11	−	1.49044e11i	−0.243169	−	0.212450i
$430$	2.66593e12	+	2.39938e11i	3.76046	+	0.338447i
$431$	−1.55926e10	−	4.79892e10i	−0.0217657	−	0.0669878i	0.939584	−	0.342319i	$-0.111212\pi$
$431$	−1.55926e10	−	4.79892e10i	−0.0217657	−	0.0669878i	−0.961349	+	0.275331i	$0.911212\pi$
$432$	−1.06802e12	+	1.11706e12i	−1.47537	+	1.54312i
$433$	−1.42115e11	−	3.92214e10i	−0.194288	−	0.0536200i	0.167539	−	0.985866i	$-0.446418\pi$
$433$	−1.42115e11	−	3.92214e10i	−0.194288	−	0.0536200i	−0.361826	+	0.932245i	$0.617847\pi$
$434$	−3.74732e11	+	2.76638e12i	−0.507011	+	3.74290i
$435$	−1.89997e11	−	1.40261e12i	−0.254416	−	1.87817i
$436$	−1.64155e12	+	4.53038e11i	−2.17552	+	0.600407i
$437$	−1.45257e11	+	2.69933e11i	−0.190534	+	0.354071i
$438$	−2.04590e11	−	2.13985e11i	−0.265614	−	0.277811i
$439$	2.18068e11	+	4.05238e11i	0.280221	+	0.520738i	0.981334	−	0.192312i	$-0.0615987\pi$
$439$	2.18068e11	+	4.05238e11i	0.280221	+	0.520738i	−0.701113	+	0.713051i	$0.747313\pi$
$440$	−2.62304e11	+	8.07287e11i	−0.333632	+	1.02681i
$441$	−2.34861e11	+	5.49485e11i	−0.295691	+	0.691803i
$442$	2.13304e12	+	3.87089e11i	2.65826	+	0.482404i
$443$	−5.45499e11	−	3.96328e11i	−0.672941	−	0.488920i	0.198067	−	0.980188i	$-0.436534\pi$
$443$	−5.45499e11	−	3.96328e11i	−0.672941	−	0.488920i	−0.871008	+	0.491268i	$0.836534\pi$
$444$	−2.19846e12	+	1.97865e11i	−2.68470	+	0.241627i
$445$	−2.72231e11	−	6.36916e11i	−0.329092	−	0.769949i
$446$	1.73184e11	+	7.58769e11i	0.207253	+	0.908035i
$447$	−1.72968e11	−	2.62036e11i	−0.204919	−	0.310439i
$448$	4.01863e12	+	2.40102e12i	4.71332	+	2.81608i
$449$	−6.81055e10	−	8.54016e10i	−0.0790813	−	0.0991648i	0.740717	−	0.671817i	$-0.234486\pi$
$449$	−6.81055e10	−	8.54016e10i	−0.0790813	−	0.0991648i	−0.819798	+	0.572652i	$0.805915\pi$
$450$	1.22740e12	−	1.07235e12i	1.41101	−	1.23276i
$451$	−7.69360e10	+	5.58973e10i	−0.0875660	+	0.0636204i
$452$	−2.31950e12	+	1.11701e12i	−2.61379	+	1.25873i
$453$	2.67355e11	−	4.05025e11i	0.298295	−	0.451898i
$454$	5.94737e11	+	2.23209e11i	0.657013	+	0.246581i
$455$	−2.78730e12	+	1.66533e12i	−3.04882	+	1.82159i
$456$	1.98664e12	+	9.56716e11i	2.15168	+	1.03619i
$457$	1.07432e12	−	1.94961e11i	1.15216	−	0.209086i	0.431327	−	0.902196i	$-0.358045\pi$
$457$	1.07432e12	−	1.94961e11i	1.15216	−	0.209086i	0.720832	+	0.693109i	$0.243760\pi$
$458$	6.32434e11	−	2.77088e12i	0.671615	−	2.94254i
$459$	−5.42880e11	+	2.03746e11i	−0.570882	+	0.214256i
$460$	−1.87976e12	+	2.35714e12i	−1.95745	+	2.45457i
$461$	−1.86773e10	−	4.15883e11i	−0.0192602	−	0.428862i	−0.985338	−	0.170612i	$-0.945426\pi$
$461$	−1.86773e10	−	4.15883e11i	−0.0192602	−	0.428862i	0.966078	−	0.258250i	$-0.0831458\pi$
$462$	−3.16096e10	−	7.03842e11i	−0.0322797	−	0.718764i
$463$	6.15691e11	−	7.72052e11i	0.622656	−	0.780786i	−0.366059	−	0.930592i	$-0.619293\pi$
$463$	6.15691e11	−	7.72052e11i	0.622656	−	0.780786i	0.988716	+	0.149805i	$0.0478647\pi$
$464$	3.09323e12	−	1.16091e12i	3.09800	−	1.16270i
$465$	−5.88146e11	+	2.57684e12i	−0.583374	+	2.55593i
$466$	−1.28911e12	+	2.33938e11i	−1.26635	+	0.229808i
$467$	−4.84986e11	−	2.33557e11i	−0.471850	−	0.227231i	0.182819	−	0.983147i	$-0.441478\pi$
$467$	−4.84986e11	−	2.33557e11i	−0.471850	−	0.227231i	−0.654669	+	0.755916i	$0.727192\pi$
$468$	−1.71095e12	+	1.02224e12i	−1.64866	+	0.985026i
$469$	−1.79455e12	−	6.73507e11i	−1.71269	−	0.642783i
$470$	2.40422e12	−	3.64224e12i	2.27266	−	3.44293i
$471$	8.58638e11	−	4.13498e11i	0.803926	−	0.387150i
$472$	9.20632e11	−	6.68878e11i	0.853782	−	0.620309i
$473$	1.84472e11	−	1.61169e11i	0.169456	−	0.148049i
$474$	−1.63684e12	−	2.05253e12i	−1.48937	−	1.86761i
$475$	1.03426e12	+	6.17940e11i	0.932196	+	0.556961i
$476$	2.71363e12	+	4.11098e12i	2.42281	+	3.67040i
$477$	−7.31748e10	−	3.20600e11i	−0.0647185	−	0.283550i
$478$	−3.06429e11	−	7.16925e11i	−0.268475	−	0.628128i
$479$	1.11698e12	−	1.00530e11i	0.969472	−	0.0872541i	0.406430	−	0.913682i	$-0.366774\pi$
$479$	1.11698e12	−	1.00530e11i	0.969472	−	0.0872541i	0.563043	+	0.826428i	$0.309631\pi$
$480$	7.29433e12	+	5.29964e12i	6.27191	+	4.55681i
$481$	1.25378e12	+	2.27528e11i	1.06799	+	0.193812i
$482$	−7.21776e11	+	1.68868e12i	−0.609103	+	1.42507i
$483$	4.88112e11	−	1.50226e12i	0.408092	−	1.25598i
$484$	−1.49294e12	−	2.77435e12i	−1.23663	−	2.29804i
$485$	−7.41174e11	−	7.75208e11i	−0.608251	−	0.636180i
$486$	1.07409e12	−	1.99599e12i	0.873326	−	1.62291i
$487$	−8.26271e11	+	2.28036e11i	−0.665644	+	0.183706i	−0.582499	−	0.812831i	$-0.697925\pi$
$487$	−8.26271e11	+	2.28036e11i	−0.665644	+	0.183706i	−0.0831452	+	0.996537i	$0.526497\pi$
$488$	−7.21129e11	−	5.32359e12i	−0.575604	−	4.24928i
$489$	−3.26588e10	+	2.41097e11i	−0.0258292	+	0.190679i
$490$	−5.73250e12	−	1.58207e12i	−4.49223	−	1.23978i
$491$	3.52493e11	−	3.68679e11i	0.273706	−	0.286274i	−0.571627	−	0.820513i	$-0.693688\pi$
$491$	3.52493e11	−	3.68679e11i	0.273706	−	0.286274i	0.845333	+	0.534239i	$0.179402\pi$
$492$	7.50818e11	+	2.31078e12i	0.577686	+	1.77793i
$493$	1.23462e12	+	1.11118e11i	0.941287	+	0.0847173i
$494$	−1.51865e12	−	1.32681e12i	−1.14733	−	1.00239i
$495$	1.03059e10	−	2.29478e11i	0.00771545	−	0.171798i
$496$	−6.16958e12			−4.57707
$497$	1.93779e12	+	8.63322e11i	1.42463	+	0.634701i
$498$	6.12410e12			4.46180
$499$	−1.46037e10	+	3.25178e11i	−0.0105442	+	0.234784i	0.986800	+	0.161946i	$0.0517770\pi$
$499$	−1.46037e10	+	3.25178e11i	−0.0105442	+	0.234784i	−0.997344	+	0.0728379i	$0.976794\pi$
$500$	4.10446e12	+	3.58596e12i	2.93691	+	2.56590i
$501$	−6.75099e11	−	6.07600e10i	−0.478737	−	0.0430871i
$502$	1.46130e12	+	4.49741e12i	1.02700	+	3.16079i
$503$	8.48787e11	−	8.87761e11i	0.591211	−	0.618358i	−0.357725	−	0.933827i	$-0.616447\pi$
$503$	8.48787e11	−	8.87761e11i	0.591211	−	0.618358i	0.948936	+	0.315469i	$0.102162\pi$
$504$	−3.77172e12	−	1.04093e12i	−2.60377	−	0.718594i
$505$	−2.01658e11	+	1.48870e12i	−0.137976	+	1.01858i
$506$	5.06948e10	+	3.74244e11i	0.0343784	+	0.253792i
$507$	1.44957e12	−	4.00056e11i	0.974324	−	0.268896i
$508$	−2.61803e12	+	4.86511e12i	−1.74417	+	3.24120i
$509$	1.05180e12	+	1.10010e12i	0.694550	+	0.726442i	0.972177	−	0.234247i	$-0.0752623\pi$
$509$	1.05180e12	+	1.10010e12i	0.694550	+	0.726442i	−0.277627	+	0.960689i	$0.589548\pi$
$510$	3.02503e12	+	5.62144e12i	1.97999	+	3.67944i
$511$	−1.20001e11	+	3.69324e11i	−0.0778555	+	0.239615i
$512$	−9.34208e11	+	2.18569e12i	−0.600798	+	1.40564i
$513$	5.30726e11	+	9.63127e10i	0.338332	+	0.0613981i
$514$	−1.85968e12	−	1.35114e12i	−1.17518	−	0.853817i
$515$	−3.12797e12	+	2.81522e11i	−1.95943	+	0.176352i
$516$	−2.45977e12	−	5.75492e12i	−1.52747	−	3.57368i
$517$	−8.88730e10	−	3.89378e11i	−0.0547094	−	0.239698i
$518$	2.18329e12	+	3.30754e12i	1.33238	+	2.01846i
$519$	−2.29404e12	−	1.37063e12i	−1.38787	−	0.829212i
$520$	−7.80582e12	−	9.78819e12i	−4.68170	−	5.87066i
$521$	1.80450e12	−	1.57654e12i	1.07297	−	0.937423i	0.0747553	−	0.997202i	$-0.476182\pi$
$521$	1.80450e12	−	1.57654e12i	1.07297	−	0.937423i	0.998212	+	0.0597789i	$0.0190396\pi$
$522$	−1.26202e12	+	9.16912e11i	−0.743960	+	0.540518i
$523$	2.08169e12	−	1.00249e12i	1.21663	−	0.585899i	0.288260	−	0.957552i	$-0.406923\pi$
$523$	2.08169e12	−	1.00249e12i	1.21663	−	0.585899i	0.928372	+	0.371653i	$0.121209\pi$
$524$	−3.70375e12	+	5.61094e12i	−2.14610	+	3.25121i
$525$	−5.81241e12	−	2.18144e12i	−3.33918	−	1.25321i
$526$	−3.67998e12	+	2.19869e12i	−2.09609	+	1.25235i
$527$	−2.08556e12	−	1.00435e12i	−1.17781	−	0.567204i
$528$	1.53204e12	−	2.78025e11i	0.857865	−	0.155679i
$529$	2.12386e11	−	9.30526e11i	0.117917	−	0.516628i
$530$	3.06385e12	−	1.14988e12i	1.68666	−	0.633013i
$531$	−1.92006e11	+	2.40768e11i	−0.104807	+	0.131423i
$532$	−2.05577e11	−	4.57753e12i	−0.111269	−	2.47759i
$533$	−6.29282e10	−	1.40121e12i	−0.0337733	−	0.752020i
$534$	−1.38216e12	+	1.73317e12i	−0.735566	+	0.922371i
$535$	−1.12535e12	+	4.22350e11i	−0.593875	+	0.222885i
$536$	1.64461e12	−	7.20550e12i	0.860639	−	3.77071i
$537$	−1.23283e12	+	2.23726e11i	−0.639763	+	0.116100i
$538$	−5.80347e12	−	2.79480e12i	−2.98653	−	1.43824i
$539$	−4.67189e11	+	2.79133e11i	−0.238420	+	0.142450i
$540$	4.96688e12	+	1.86410e12i	2.51369	+	0.943404i
$541$	1.37988e12	−	2.09042e12i	0.692552	−	1.04917i	−0.302818	−	0.953049i	$-0.597927\pi$
$541$	1.37988e12	−	2.09042e12i	0.692552	−	1.04917i	0.995369	−	0.0961228i	$-0.0306441\pi$
$542$	3.43026e12	−	1.65193e12i	1.70738	−	0.822231i
$543$	−1.89129e12	+	1.37411e12i	−0.933598	+	0.678298i
$544$	−5.94652e12	+	5.19532e12i	−2.91117	+	2.54341i
$545$	1.80487e12	+	2.26324e12i	0.876319	+	1.09887i
$546$	8.92060e12	+	5.32981e12i	4.29563	+	2.56652i
$547$	−7.94599e11	−	1.20377e12i	−0.379494	−	0.574909i	0.593759	−	0.804643i	$-0.297643\pi$
$547$	−7.94599e11	−	1.20377e12i	−0.379494	−	0.574909i	−0.973254	+	0.229734i	$0.926215\pi$
$548$	1.14434e12	+	5.01366e12i	0.542052	+	2.37489i
$549$	5.71387e11	+	1.33683e12i	0.268445	+	0.628057i
$550$	1.47838e12	−	1.33056e11i	0.688895	−	0.0620017i
$551$	−9.32890e11	−	6.77785e11i	−0.431170	−	0.313263i
$552$	5.99269e12	+	1.08751e12i	2.74723	+	0.498550i
$553$	−1.35341e12	+	3.16646e12i	−0.615413	+	1.43983i
$554$	−9.68661e11	+	2.98123e12i	−0.436896	+	1.34463i
$555$	1.77809e12	+	3.30424e12i	0.795489	+	1.47827i
$556$	6.31006e12	+	6.59981e12i	2.80025	+	2.92883i
$557$	4.55067e11	−	8.45656e11i	0.200321	−	0.372259i	−0.760539	−	0.649292i	$-0.775065\pi$
$557$	4.55067e11	−	8.45656e11i	0.200321	−	0.372259i	0.960860	+	0.277033i	$0.0893511\pi$
$558$	2.80801e12	−	7.74960e11i	1.22615	−	0.338396i
$559$	4.84978e11	+	3.58025e12i	0.210072	+	1.55082i
$560$	2.99576e12	−	2.21156e13i	1.28724	−	9.50281i
$561$	5.63152e11	+	1.55420e11i	0.240045	+	0.0662482i
$562$	1.72632e11	−	1.80559e11i	0.0729976	−	0.0763495i
$563$	−2.11089e11	−	6.49665e11i	−0.0885479	−	0.272522i	0.896971	−	0.442090i	$-0.145763\pi$
$563$	−2.11089e11	−	6.49665e11i	−0.0885479	−	0.272522i	−0.985519	+	0.169568i	$0.945763\pi$
$564$	−1.01631e13	−	9.14697e11i	−4.22932	−	0.380646i
$565$	3.29567e12	+	2.87934e12i	1.36059	+	1.18871i
$566$	1.52721e11	−	3.40059e12i	0.0625495	−	1.39277i
$567$	−4.79548e12			−1.94854
$568$	−2.29574e12	+	7.85105e12i	−0.925457	+	3.16490i
$569$	2.61444e12			1.04562			0.522810	−	0.852449i	$-0.324884\pi$
$569$	2.61444e12			1.04562			0.522810	+	0.852449i	$0.324884\pi$
$570$	2.66419e11	−	5.93228e12i	0.105713	−	2.35388i
$571$	−2.72107e11	−	2.37732e11i	−0.107121	−	0.0935892i	0.602712	−	0.797959i	$-0.294087\pi$
$571$	−2.72107e11	−	2.37732e11i	−0.107121	−	0.0935892i	−0.709833	+	0.704370i	$0.751230\pi$
$572$	−1.80783e12	−	1.62707e11i	−0.706114	−	0.0635514i
$573$	−6.58032e11	−	2.02521e12i	−0.255006	−	0.784829i
$574$	3.01467e12	−	3.15310e12i	1.15914	−	1.21237i
$575$	3.20791e12	+	8.85327e11i	1.22382	+	0.337752i
$576$	6.55694e11	−	4.84052e12i	0.248199	−	1.83228i
$577$	−6.68786e11	−	4.93718e12i	−0.251186	−	1.85433i	−0.475370	−	0.879786i	$-0.657686\pi$
$577$	−6.68786e11	−	4.93718e12i	−0.251186	−	1.85433i	0.224184	−	0.974547i	$-0.428028\pi$
$578$	−4.06000e11	+	1.12049e11i	−0.151304	+	0.0417573i
$579$	2.13271e11	−	3.96324e11i	0.0788640	−	0.146554i
$580$	−7.83759e12	−	8.19748e12i	−2.87579	−	3.00784i
$581$	−3.80657e12	−	7.07379e12i	−1.38593	−	2.57549i
$582$	−1.06071e12	+	3.26453e12i	−0.383215	+	1.17942i
$583$	1.17706e11	−	2.75386e11i	0.0421978	−	0.0987265i
$584$	−1.47328e12	−	2.67361e11i	−0.524116	−	0.0951131i
$585$	2.74097e12	+	1.99143e12i	0.967614	+	0.703013i
$586$	9.54058e12	−	8.58668e11i	3.34222	−	0.300806i
$587$	1.19152e12	+	2.78769e12i	0.414218	+	0.969111i	0.988606	+	0.150528i	$0.0480974\pi$
$587$	1.19152e12	+	2.78769e12i	0.414218	+	0.969111i	−0.574388	+	0.818583i	$0.694760\pi$
$588$	3.09406e12	+	1.35560e13i	1.06741	+	4.67663i
$589$	1.18624e12	+	1.79707e12i	0.406119	+	0.615244i
$590$	−2.63083e12	−	1.57185e12i	−0.893836	−	0.534042i
$591$	−1.17383e12	−	1.47194e12i	−0.395787	−	0.496301i
$592$	−6.59586e12	+	5.76263e12i	−2.20711	+	1.92829i
$593$	−3.48044e12	+	2.52869e12i	−1.15581	+	0.839749i	−0.989243	−	0.146281i	$-0.953270\pi$
$593$	−3.48044e12	+	2.52869e12i	−1.15581	+	0.839749i	−0.166572	+	0.986029i	$0.553270\pi$
$594$	5.98742e11	−	2.88339e11i	0.197333	−	0.0950308i
$595$	4.61291e12	−	6.98826e12i	1.50886	−	2.28582i
$596$	−2.35537e12	−	8.83987e11i	−0.764631	−	0.286971i
$597$	5.15774e12	−	3.08161e12i	1.66179	−	0.992872i
$598$	−5.01857e12	−	2.41682e12i	−1.60481	−	0.772838i
$599$	−5.34956e11	+	9.70801e10i	−0.169784	+	0.0308113i	−0.262783	−	0.964855i	$-0.584640\pi$
$599$	−5.34956e11	+	9.70801e10i	−0.169784	+	0.0308113i	0.0929990	+	0.995666i	$0.470355\pi$
$600$	5.32676e12	−	2.33380e13i	1.67796	−	7.35163i
$601$	4.78971e12	−	1.79761e12i	1.49752	−	0.562030i	0.537824	−	0.843057i	$-0.319247\pi$
$601$	4.78971e12	−	1.79761e12i	1.49752	−	0.562030i	0.959700	+	0.281027i	$0.0906751\pi$
$602$	−7.00607e12	+	8.78533e12i	−2.17415	+	2.72630i
$603$	8.97335e10	+	1.99807e12i	0.0276393	+	0.615437i
$604$	−1.74463e11	−	3.88472e12i	−0.0533380	−	1.18766i
$605$	−3.33917e12	+	4.18718e12i	−1.01330	+	1.27064i
$606$	4.50144e12	−	1.68942e12i	1.35589	−	0.508874i
$607$	8.05874e10	−	3.53077e11i	0.0240945	−	0.105565i	−0.961451	−	0.274977i	$-0.911330\pi$
$607$	8.05874e10	−	3.53077e11i	0.0240945	−	0.105565i	0.985545	+	0.169412i	$0.0541869\pi$
$608$	7.22734e12	−	1.31157e12i	2.14493	−	0.389247i
$609$	5.35353e12	+	2.57812e12i	1.57711	+	0.759497i
$610$	−1.24199e13	+	7.42053e12i	−3.63189	+	2.16995i
$611$	5.51507e12	+	2.06984e12i	1.60090	+	0.600829i
$612$	2.83157e12	−	4.28965e12i	0.815918	−	1.23606i
$613$	−4.68669e12	+	2.25699e12i	−1.34059	+	0.645592i	−0.960220	−	0.279244i	$-0.909916\pi$
$613$	−4.68669e12	+	2.25699e12i	−1.34059	+	0.645592i	−0.380365	+	0.924836i	$0.624202\pi$
$614$	1.29228e12	−	9.38894e11i	0.366942	−	0.266599i
$615$	3.11037e12	−	2.71745e12i	0.876747	−	0.765991i
$616$	−2.22175e12	−	2.78599e12i	−0.621702	−	0.779590i
$617$	−4.33021e12	−	2.58718e12i	−1.20289	−	0.718693i	−0.235472	−	0.971881i	$-0.575664\pi$
$617$	−4.33021e12	−	2.58718e12i	−1.20289	−	0.718693i	−0.967417	+	0.253188i	$0.918521\pi$
$618$	5.53727e12	+	8.38860e12i	1.52703	+	2.31335i
$619$	1.16407e12	+	5.10011e12i	0.318691	+	1.39628i	0.839850	+	0.542818i	$0.182643\pi$
$619$	1.16407e12	+	5.10011e12i	0.318691	+	1.39628i	−0.521159	+	0.853460i	$0.674500\pi$
$620$	8.32365e12	+	1.94742e13i	2.26231	+	5.29293i
$621$	1.48389e12	−	1.33553e11i	0.400397	−	0.0360364i
$622$	4.35295e12	+	3.16260e12i	1.16608	+	0.847203i
$623$	2.86105e12	+	5.19204e11i	0.760904	+	0.138084i
$624$	−9.02599e12	+	2.11174e13i	−2.38322	+	5.57582i
$625$	6.80247e11	−	2.09358e12i	0.178323	−	0.548821i
$626$	−4.65787e12	−	8.65577e12i	−1.21228	−	2.25279i
$627$	−3.75553e11	−	3.92797e11i	−0.0970436	−	0.101500i
$628$	3.61857e12	−	6.72444e12i	0.928366	−	1.72519i
$629$	−3.16777e12	+	8.74249e11i	−0.806912	+	0.222693i
$630$	1.41445e12	+	1.04419e13i	0.357731	+	2.64088i
$631$	−8.12770e11	+	6.00011e12i	−0.204096	+	1.50670i	0.541726	+	0.840555i	$0.317771\pi$
$631$	−8.12770e11	+	6.00011e12i	−0.204096	+	1.50670i	−0.745822	+	0.666145i	$0.767943\pi$
$632$	−1.27994e13	−	3.53241e12i	−3.19127	−	0.880734i
$633$	1.28981e12	−	1.34904e12i	0.319307	−	0.333969i
$634$	−2.23674e12	−	6.88398e12i	−0.549811	−	1.69215i
$635$	9.35382e12	+	8.41859e11i	2.28301	+	0.205474i
$636$	−5.76227e12	−	5.03435e12i	−1.39649	−	1.22007i
$637$	3.60124e11	−	8.01878e12i	0.0866611	−	1.92966i
$638$	−1.42068e12			−0.339471
$639$	3.36501e10	−	2.21335e12i	0.00798421	−	0.525166i
$640$	2.19678e13			5.17578
$641$	−9.08024e10	+	2.02187e12i	−0.0212440	+	0.473034i	0.959969	+	0.280106i	$0.0903698\pi$
$641$	−9.08024e10	+	2.02187e12i	−0.0212440	+	0.473034i	−0.981213	+	0.192928i	$0.938202\pi$
$642$	2.89701e12	+	2.53104e12i	0.673041	+	0.588018i
$643$	5.06874e12	+	4.56195e11i	1.16937	+	0.105245i	0.657251	−	0.753672i	$-0.271719\pi$
$643$	5.06874e12	+	4.56195e11i	1.16937	+	0.105245i	0.512115	+	0.858917i	$0.328862\pi$
$644$	−3.91110e12	−	1.20371e13i	−0.896009	−	2.75763i
$645$	−7.35218e12	+	7.68978e12i	−1.67262	+	1.74942i
$646$	5.01324e12	+	1.38357e12i	1.13259	+	0.312575i
$647$	3.02295e11	−	2.23163e12i	0.0678207	−	0.500672i	−0.924898	−	0.380216i	$-0.875850\pi$
$647$	3.02295e11	−	2.23163e12i	0.0678207	−	0.500672i	0.992719	−	0.120457i	$-0.0384359\pi$
$648$	−2.48206e12	−	1.83233e13i	−0.553000	−	4.08241i
$649$	−2.70354e11	+	7.46129e10i	−0.0598179	+	0.0165087i
$650$	−1.03744e13	+	1.92788e13i	−2.27957	+	4.23615i
$651$	−7.66790e12	−	8.02000e12i	−1.67325	−	1.75009i
$652$	9.23799e11	+	1.71671e12i	0.200200	+	0.372033i
$653$	−1.68284e12	+	5.17925e12i	−0.362188	+	1.11470i	0.589536	+	0.807742i	$0.299311\pi$
$653$	−1.68284e12	+	5.17925e12i	−0.362188	+	1.11470i	−0.951723	+	0.306957i	$0.900689\pi$
$654$	3.64123e12	−	8.51908e12i	0.778302	−	1.82093i
$655$	1.12450e13	+	2.04067e12i	2.38711	+	0.433197i
$656$	7.79964e12	+	5.66677e12i	1.64440	+	1.19473i
$657$	4.03577e11	−	3.63226e10i	0.0845049	−	0.00760558i
$658$	7.20061e12	+	1.68467e13i	1.49745	+	3.50346i
$659$	−6.08329e10	−	2.66527e11i	−0.0125648	−	0.0550498i	0.968257	−	0.249957i	$-0.0804165\pi$
$659$	−6.08329e10	−	2.66527e11i	−0.0125648	−	0.0550498i	−0.980822	+	0.194907i	$0.937559\pi$
$660$	−2.94453e12	−	4.46077e12i	−0.604044	−	0.915087i
$661$	−1.94933e12	−	1.16467e12i	−0.397173	−	0.237300i	0.300400	−	0.953813i	$-0.402880\pi$
$661$	−1.94933e12	−	1.16467e12i	−0.397173	−	0.237300i	−0.697573	+	0.716513i	$0.745737\pi$
$662$	−7.18105e12	−	9.00476e12i	−1.45321	−	1.82226i
$663$	−6.48887e12	+	5.66915e12i	−1.30424	+	1.13948i
$664$	2.50584e13	−	1.82060e13i	5.00262	−	3.63462i
$665$	−7.01783e12	+	3.37961e12i	−1.39157	+	0.670145i
$666$	2.27818e12	−	3.45130e12i	0.448698	−	0.679748i
$667$	−2.98199e12	−	1.11916e12i	−0.583364	−	0.218940i
$668$	−4.66243e12	+	2.78567e12i	−0.905980	+	0.541298i
$669$	−2.78705e12	−	1.34217e12i	−0.537932	−	0.259055i
$670$	−1.95842e13	+	3.55400e12i	−3.75464	+	0.681367i
$671$	−2.94624e11	+	1.29083e12i	−0.0561069	+	0.245821i
$672$	−3.54370e13	+	1.32997e13i	−6.70340	+	2.51583i
$673$	3.85535e12	−	4.83446e12i	0.724430	−	0.908406i	−0.274150	−	0.961687i	$-0.588396\pi$
$673$	3.85535e12	−	4.83446e12i	0.724430	−	0.908406i	0.998580	+	0.0532808i	$0.0169678\pi$
$674$	−5.58724e11	−	1.24410e13i	−0.104286	−	2.32212i
$675$	−2.62721e11	−	5.84994e12i	−0.0487111	−	1.08464i
$676$	7.51255e12	−	9.42044e12i	1.38365	−	1.73505i
$677$	−2.35519e12	+	8.83918e11i	−0.430901	+	0.161720i	−0.557395	−	0.830248i	$-0.688199\pi$
$677$	−2.35519e12	+	8.83918e11i	−0.430901	+	0.161720i	0.126494	+	0.991967i	$0.459628\pi$
$678$	3.11666e12	−	1.36550e13i	0.566443	−	2.48175i
$679$	4.43008e12	−	8.03941e11i	0.799830	−	0.145148i
$680$	2.90894e13	+	1.40087e13i	5.21729	+	2.51251i
$681$	−2.16747e12	+	1.29500e12i	−0.386181	+	0.230732i
$682$	2.48376e12	+	9.32171e11i	0.439622	+	0.164993i
$683$	−5.08424e12	+	7.70229e12i	−0.893990	+	1.35434i	0.0408113	+	0.999167i	$0.487006\pi$
$683$	−5.08424e12	+	7.70229e12i	−0.893990	+	1.35434i	−0.934802	+	0.355171i	$0.884423\pi$
$684$	−4.30780e12	+	2.07453e12i	−0.752494	+	0.362382i
$685$	7.07236e12	−	5.13837e12i	1.22732	−	0.891698i
$686$	5.67547e12	−	4.95851e12i	0.978461	−	0.854855i
$687$	7.04324e12	+	8.83194e12i	1.20633	+	1.51269i
$688$	−2.13184e13	−	1.27371e13i	−3.62749	−	2.16732i
$689$	2.43341e12	+	3.68646e12i	0.411366	+	0.623193i
$690$	−3.64987e12	−	1.59911e13i	−0.612995	−	2.68571i
$691$	−1.88779e12	−	4.41671e12i	−0.314995	−	0.736967i	−0.999965	−	0.00839565i	$-0.997328\pi$
$691$	−1.88779e12	−	4.41671e12i	−0.314995	−	0.736967i	0.684970	−	0.728571i	$-0.259815\pi$
$692$	−2.13262e13	+	1.91940e12i	−3.53538	+	0.318190i
$693$	7.80155e11	+	5.66816e11i	0.128494	+	0.0933560i
$694$	4.55554e12	+	8.26709e11i	0.745457	+	0.135281i
$695$	6.10043e12	−	1.42727e13i	0.991811	−	2.32046i
$696$	−7.08000e12	+	2.17900e13i	−1.14365	+	3.51978i
$697$	1.71409e12	+	3.18531e12i	0.275097	+	0.511216i
$698$	1.09060e12	+	1.14068e12i	0.173906	+	0.181892i
$699$	2.46764e12	−	4.58564e12i	0.390962	−	0.726528i
$700$	−4.79525e13	+	1.32340e13i	−7.54866	+	2.08330i
$701$	6.46393e10	+	4.77187e11i	0.0101103	+	0.0746375i	0.995302	−	0.0968193i	$-0.0308669\pi$
$701$	6.46393e10	+	4.77187e11i	0.0101103	+	0.0746375i	−0.985192	+	0.171457i	$0.945153\pi$
$702$	−1.31570e12	+	9.71290e12i	−0.204475	+	1.50950i
$703$	2.94674e12	+	8.13249e11i	0.455033	+	0.125581i
$704$	3.07429e12	−	3.21546e12i	0.471703	−	0.493362i
$705$	5.36025e12	+	1.64972e13i	0.817211	+	2.51512i
$706$	−1.62895e12	−	1.46608e11i	−0.246766	−	0.0222093i
$707$	−4.74937e12	−	4.14940e12i	−0.714906	−	0.624595i
$708$	−3.21483e11	+	7.15838e12i	−0.0480849	+	1.07069i
$709$	−4.38339e12			−0.651481			−0.325741	−	0.945459i	$-0.605614\pi$
$709$	−4.38339e12			−0.651481			−0.325741	+	0.945459i	$0.605614\pi$
$710$	2.18720e13	−	2.62483e12i	3.23017	−	0.387649i
$711$	3.59324e12			0.527319
$712$	−5.03023e11	+	1.12007e13i	−0.0733547	+	1.63337i
$713$	4.47905e12	+	3.91323e12i	0.649057	+	0.567064i
$714$	−2.66909e13	−	2.40223e12i	−3.84346	−	0.345917i
$715$	9.53488e11	+	2.93454e12i	0.136439	+	0.419916i
$716$	−6.93803e12	+	7.25661e12i	−0.986570	+	1.03187i
$717$	2.98723e12	+	8.24422e11i	0.422116	+	0.116497i
$718$	−2.54013e12	+	1.87520e13i	−0.356694	+	2.63322i
$719$	−7.07271e11	−	5.22129e12i	−0.0986975	−	0.728614i	−0.970903	−	0.239474i	$-0.923025\pi$
$719$	−7.07271e11	−	5.22129e12i	−0.0986975	−	0.728614i	0.872205	−	0.489140i	$-0.162689\pi$
$720$	−2.24483e13	+	6.19534e12i	−3.11306	+	0.859150i
$721$	6.24765e12	−	1.16101e13i	0.861009	−	1.60002i
$722$	6.37786e12	+	6.67072e12i	0.873489	+	0.913598i
$723$	−3.45891e12	−	6.42772e12i	−0.470778	−	0.874853i
$724$	−5.78846e12	+	1.78150e13i	−0.782960	+	2.40970i
$725$	−4.92012e12	+	1.15112e13i	−0.661385	+	1.54739i
$726$	1.68649e13	+	3.06053e12i	2.25304	+	0.408866i
$727$	−1.04436e13	−	7.58775e12i	−1.38659	−	1.00741i	−0.996230	−	0.0867506i	$-0.972352\pi$
$727$	−1.04436e13	−	7.58775e12i	−1.38659	−	1.00741i	−0.390357	−	0.920664i	$-0.627648\pi$
$728$	5.23458e13	−	4.71121e12i	6.90702	−	0.621643i
$729$	−2.03616e11	−	4.76383e11i	−0.0267016	−	0.0624716i
$730$	8.97308e11	+	3.93136e12i	0.116947	+	0.512378i
$731$	−5.13296e12	−	7.77611e12i	−0.664875	−	1.00724i
$732$	2.90397e13	+	1.73504e13i	3.73845	+	2.23362i
$733$	−4.14862e12	−	5.20221e12i	−0.530806	−	0.665610i	0.442058	−	0.896987i	$-0.354249\pi$
$733$	−4.14862e12	−	5.20221e12i	−0.530806	−	0.665610i	−0.972864	+	0.231376i	$0.925677\pi$
$734$	−5.77254e12	+	5.04331e12i	−0.734065	+	0.641333i
$735$	1.91223e13	−	1.38932e13i	2.41684	−	1.75593i
$736$	1.82798e13	−	8.80311e12i	2.29627	−	1.10582i
$737$	−1.00347e12	+	1.52020e12i	−0.125286	+	0.189800i
$738$	−4.26171e12	−	1.59945e12i	−0.528847	−	0.198480i
$739$	5.81837e12	−	3.47631e12i	0.717631	−	0.428765i	−0.107131	−	0.994245i	$-0.534166\pi$
$739$	5.81837e12	−	3.47631e12i	0.717631	−	0.428765i	0.824762	+	0.565480i	$0.191309\pi$
$740$	2.70884e13	+	1.30451e13i	3.32079	+	1.59921i
$741$	7.88651e12	−	1.43119e12i	0.960955	−	0.174388i
$742$	−3.05702e12	+	1.33937e13i	−0.370238	+	1.62212i
$743$	−7.34491e12	+	2.75659e12i	−0.884172	+	0.331835i	−0.751821	−	0.659368i	$-0.770824\pi$
$743$	−7.34491e12	+	2.75659e12i	−0.884172	+	0.331835i	−0.132351	+	0.991203i	$0.542253\pi$
$744$	2.66753e13	−	3.34497e13i	3.19176	−	4.00234i
$745$	1.91869e11	+	4.27230e12i	0.0228193	+	0.508111i
$746$	−3.00219e11	−	6.68489e12i	−0.0354906	−	0.790259i
$747$	−5.22616e12	+	6.55339e12i	−0.614101	+	0.770058i
$748$	4.38258e12	−	1.64481e12i	0.511885	−	0.192114i
$749$	1.12284e12	−	4.91948e12i	0.130362	−	0.571151i
$750$	−2.91755e13	+	5.29457e12i	−3.36700	+	0.611020i
$751$	6.87575e12	+	3.31119e12i	0.788752	+	0.379843i	0.784485	−	0.620148i	$-0.212927\pi$
$751$	6.87575e12	+	3.31119e12i	0.788752	+	0.379843i	0.00426712	+	0.999991i	$0.498642\pi$
$752$	−3.47583e13	+	2.07671e13i	−3.96349	+	2.36808i
$753$	−1.75970e13	−	6.60427e12i	−1.99463	−	0.748596i
$754$	1.15434e13	−	1.74875e13i	1.30066	−	1.97041i
$755$	−5.95567e12	+	2.86810e12i	−0.667067	+	0.321243i
$756$	−1.80178e13	+	1.30907e13i	−2.00610	+	1.45752i
$757$	2.72562e12	−	2.38130e12i	0.301671	−	0.263562i	−0.493771	−	0.869592i	$-0.664382\pi$
$757$	2.72562e12	−	2.38130e12i	0.301671	−	0.263562i	0.795442	+	0.606030i	$0.207239\pi$
$758$	9.84227e12	+	1.23418e13i	1.08289	+	1.35790i
$759$	−1.28859e12	−	7.69899e11i	−0.140938	−	0.0842065i
$760$	−1.65456e13	−	2.50656e13i	−1.79896	−	2.72531i
$761$	1.27081e12	+	5.56778e12i	0.137357	+	0.601799i	0.996010	+	0.0892421i	$0.0284445\pi$
$761$	1.27081e12	+	5.56778e12i	0.137357	+	0.601799i	−0.858653	+	0.512557i	$0.828698\pi$
$762$	−1.18133e13	−	2.76386e13i	−1.26933	−	2.96974i
$763$	−1.21035e13	+	1.08933e12i	−1.29285	+	0.116359i
$764$	−1.38039e13	−	1.00291e13i	−1.46582	−	1.06498i
$765$	−8.59698e12	−	1.56012e12i	−0.907547	−	0.164696i
$766$	−4.31534e12	+	1.00962e13i	−0.452882	+	1.05957i
$767$	1.27827e12	−	3.93410e12i	0.133365	−	0.410456i
$768$	−1.34532e13	−	2.50002e13i	−1.39540	−	2.59310i
$769$	−7.81580e12	−	8.17468e12i	−0.805944	−	0.842951i	0.184217	−	0.982886i	$-0.441025\pi$
$769$	−7.81580e12	−	8.17468e12i	−0.805944	−	0.842951i	−0.990161	+	0.139934i	$0.955311\pi$
$770$	−4.54751e12	+	8.45069e12i	−0.466193	+	0.866332i
$771$	8.80722e12	−	2.43064e12i	0.897623	−	0.247728i
$772$	−4.84076e11	−	3.57359e12i	−0.0490496	−	0.362099i
$773$	1.15998e12	−	8.56329e12i	0.116853	−	0.862647i	−0.833729	−	0.552174i	$-0.813798\pi$
$773$	1.15998e12	−	8.56329e12i	0.116853	−	0.862647i	0.950582	−	0.310473i	$-0.100487\pi$
$774$	1.13027e13	+	3.11935e12i	1.13200	+	0.312413i
$775$	1.61548e13	−	1.68966e13i	1.60858	−	1.68245i
$776$	5.36476e12	+	1.65110e13i	0.531095	+	1.63454i
$777$	−1.56887e13	−	1.41201e12i	−1.54416	−	0.138977i
$778$	2.42316e13	+	2.11705e13i	2.37123	+	2.07168i
$779$	1.50963e11	−	3.36144e12i	0.0146876	−	0.327045i
$780$	7.88339e13			7.62583
$781$	1.20962e12	−	1.61276e12i	0.116338	−	0.155111i
$782$	1.43650e13			1.37365
$783$	−2.51451e11	+	5.59900e12i	−0.0239070	+	0.532332i
$784$	4.15489e13	+	3.63002e13i	3.92769	+	3.43152i
$785$	−1.29286e13	−	1.16360e12i	−1.21517	−	0.109368i
$786$	−1.13029e13	−	3.47866e13i	−1.05630	−	3.25095i
$787$	2.35578e12	−	2.46395e12i	0.218901	−	0.228953i	−0.604221	−	0.796816i	$-0.706516\pi$
$787$	2.35578e12	−	2.46395e12i	0.218901	−	0.228953i	0.823122	+	0.567864i	$0.192230\pi$
$788$	−1.45417e13	−	4.01326e12i	−1.34353	−	0.370791i
$789$	2.28712e12	−	1.68842e13i	0.210108	−	1.55108i
$790$	4.79998e12	+	3.54349e13i	0.438447	+	3.23675i
$791$	−1.77098e13	+	4.88758e12i	−1.60849	+	0.443915i
$792$	−1.76198e12	+	3.27431e12i	−0.159125	+	0.295704i
$793$	−1.34953e13	−	1.41149e13i	−1.21186	−	1.26751i
$794$	−4.43876e12	−	8.24859e12i	−0.396341	−	0.736525i
$795$	−4.01943e12	+	1.23705e13i	−0.356872	+	1.09834i
$796$	1.89210e13	−	4.42680e13i	1.67046	−	3.90824i
$797$	1.67938e13	+	3.04762e12i	1.47430	+	0.267546i	0.855418	−	0.517939i	$-0.173301\pi$
$797$	1.67938e13	+	3.04762e12i	1.47430	+	0.267546i	0.618881	+	0.785485i	$0.287586\pi$
$798$	2.01679e13	+	1.46529e13i	1.76055	+	1.27911i
$799$	−1.51304e13	+	1.36176e12i	−1.31338	+	0.118206i
$800$	−3.13413e13	−	7.33266e13i	−2.70528	−	6.32932i
$801$	−6.75165e11	−	2.95809e12i	−0.0579513	−	0.253901i
$802$	2.11838e12	+	3.20920e12i	0.180808	+	0.273913i
$803$	3.16796e11	+	1.89277e11i	0.0268881	+	0.0160649i
$804$	2.90165e13	+	3.63856e13i	2.44902	+	3.07098i
$805$	−1.62023e13	+	1.41555e13i	−1.35986	+	1.18808i
$806$	−3.16555e13	+	2.29991e13i	−2.64206	+	1.91957i
$807$	2.30667e13	−	1.11084e13i	1.91450	−	0.921974i
$808$	1.33965e13	−	2.02948e13i	1.10571	−	1.67507i
$809$	7.05596e12	+	2.64814e12i	0.579145	+	0.217357i	0.623718	−	0.781649i	$-0.285621\pi$
$809$	7.05596e12	+	2.64814e12i	0.579145	+	0.217357i	−0.0445729	+	0.999006i	$0.514193\pi$
$810$	−4.27480e13	+	2.55408e13i	−3.48926	+	2.08474i
$811$	−4.01701e12	−	1.93449e12i	−0.326069	−	0.157027i	0.263686	−	0.964608i	$-0.415062\pi$
$811$	−4.01701e12	−	1.93449e12i	−0.326069	−	0.157027i	−0.589755	+	0.807582i	$0.700776\pi$
$812$	4.68461e13	−	8.50132e12i	3.78157	−	0.686253i
$813$	−3.36734e12	+	1.47533e13i	−0.270321	+	1.18435i
$814$	3.52606e12	−	1.32335e12i	0.281501	−	0.105649i
$815$	2.06620e12	−	2.59094e12i	0.164045	−	0.205706i
$816$	−2.65715e12	−	5.91661e13i	−0.209803	−	4.67162i
$817$	3.88859e11	+	8.65861e12i	0.0305346	+	0.679906i
$818$	3.31539e12	−	4.15737e12i	0.258908	−	0.324660i
$819$	−1.33160e13	+	4.99760e12i	−1.03418	+	0.388136i
$820$	7.36421e12	−	3.22647e13i	0.568806	−	2.49210i
$821$	−5.29814e12	+	9.61471e11i	−0.406986	+	0.0738571i	−0.378189	−	0.925728i	$-0.623453\pi$
$821$	−5.29814e12	+	9.61471e11i	−0.406986	+	0.0738571i	−0.0287965	+	0.999585i	$0.509167\pi$
$822$	−2.52074e13	−	1.21392e13i	−1.92577	−	0.927402i
$823$	−1.63590e13	+	9.77404e12i	−1.24296	+	0.742634i	−0.975301	−	0.220880i	$-0.929107\pi$
$823$	−1.63590e13	+	9.77404e12i	−1.24296	+	0.742634i	−0.267659	+	0.963514i	$0.586250\pi$
$824$	4.75953e13	+	1.78628e13i	3.59659	+	1.34982i
$825$	−3.25017e12	+	4.92380e12i	−0.244266	+	0.370048i
$826$	1.15913e13	−	5.58208e12i	0.866407	−	0.417240i
$827$	3.84111e10	−	2.79073e10i	0.00285550	−	0.00207464i	−0.586357	−	0.810053i	$-0.699438\pi$
$827$	3.84111e10	−	2.79073e10i	0.00285550	−	0.00207464i	0.589212	+	0.807978i	$0.299438\pi$
$828$	−9.94557e12	+	8.68919e12i	−0.735349	+	0.642455i
$829$	−8.29291e12	−	1.03990e13i	−0.609834	−	0.764708i	0.377040	−	0.926197i	$-0.376942\pi$
$829$	−8.29291e12	−	1.03990e13i	−0.609834	−	0.764708i	−0.986874	+	0.161489i	$0.948370\pi$
$830$	−7.16078e13	−	4.27836e13i	−5.23731	−	3.12915i
$831$	−6.86370e12	−	1.03981e13i	−0.499291	−	0.756393i
$832$	1.46004e13	+	6.39687e13i	1.05636	+	4.62821i
$833$	8.13583e12	+	1.90347e13i	0.585463	+	1.36976i
$834$	−4.94765e13	+	4.45297e12i	−3.54121	+	0.318715i
$835$	7.46930e12	+	5.42677e12i	0.531730	+	0.386324i
$836$	−4.28447e12	−	7.77516e11i	−0.303367	−	0.0550530i
$837$	4.11336e12	−	9.62368e12i	0.289689	−	0.677761i
$838$	−1.36976e13	+	4.21569e13i	−0.959503	+	2.95305i
$839$	1.03470e13	+	1.92279e13i	0.720916	+	1.33969i	0.932086	+	0.362237i	$0.117987\pi$
$839$	1.03470e13	+	1.92279e13i	0.720916	+	1.33969i	−0.211171	+	0.977449i	$0.567728\pi$
$840$	1.06952e14	+	1.11863e14i	7.41193	+	7.75227i
$841$	−1.19679e12	+	2.22400e12i	−0.0824963	+	0.153304i
$842$	1.15843e13	−	3.19707e12i	0.794267	−	0.219204i
$843$	1.33279e11	+	9.83908e11i	0.00908948	+	0.0671012i
$844$	2.00746e12	−	1.48197e13i	0.136178	−	1.00531i
$845$	−1.97443e13	−	5.44909e12i	−1.33225	−	0.367679i
$846$	1.32112e13	−	1.38179e13i	0.886700	−	0.927416i
$847$	−6.94761e12	−	2.13826e13i	−0.463832	−	1.42753i
$848$	−3.02392e13	−	2.72158e12i	−2.00812	−	0.180734i
$849$	1.01889e13	+	8.90175e12i	0.673041	+	0.588018i
$850$	2.53307e12	−	5.64031e13i	0.166441	−	3.70610i
$851$	8.44364e12			0.551882
$852$	−2.96382e13	−	4.21256e13i	−1.92696	−	2.73885i
$853$	−2.38007e13			−1.53928			−0.769641	−	0.638477i	$-0.779565\pi$
$853$	−2.38007e13			−1.53928			−0.769641	+	0.638477i	$0.779565\pi$
$854$	2.72492e12	−	6.06750e13i	0.175304	−	3.90346i
$855$	6.12077e12	+	5.34756e12i	0.391704	+	0.342222i
$856$	1.93783e13	+	1.74408e12i	1.23363	+	0.111028i
$857$	8.11981e12	+	2.49902e13i	0.514200	+	1.58254i	0.784733	+	0.619834i	$0.212800\pi$
$857$	8.11981e12	+	2.49902e13i	0.514200	+	1.58254i	−0.270533	+	0.962711i	$0.587200\pi$
$858$	6.82435e12	−	7.13771e12i	0.429901	−	0.449641i
$859$	3.50360e12	+	9.66931e11i	0.219556	+	0.0605935i	0.374084	−	0.927395i	$-0.377957\pi$
$859$	3.50360e12	+	9.66931e11i	0.219556	+	0.0605935i	−0.154528	+	0.987988i	$0.549386\pi$
$860$	−1.14430e13	+	8.44753e13i	−0.713338	+	5.26607i
$861$	2.32745e12	+	1.71819e13i	0.144333	+	1.06551i
$862$	2.12037e12	−	5.85185e11i	0.130806	−	0.0361003i
$863$	1.33614e13	−	2.48296e13i	0.819978	−	1.52377i	−0.0315720	−	0.999501i	$-0.510051\pi$
$863$	1.33614e13	−	2.48296e13i	0.819978	−	1.52377i	0.851550	−	0.524273i	$-0.175663\pi$
$864$	−2.46721e13	−	2.58050e13i	−1.50624	−	1.57541i
$865$	1.72484e13	+	3.20528e13i	1.04755	+	1.94668i
$866$	1.98599e12	−	6.11226e12i	0.119991	−	0.369293i
$867$	6.57937e11	−	1.53932e12i	0.0395456	−	0.0925216i
$868$	−8.74787e13	−	1.58750e13i	−5.23075	−	0.949240i
$869$	2.64747e12	+	1.92350e12i	0.157486	+	0.114420i
$870$	6.14537e13	−	5.53094e12i	3.63674	−	0.327312i
$871$	−1.05590e13	−	2.47040e13i	−0.621644	−	1.45441i
$872$	−1.04268e13	−	4.56830e13i	−0.610701	−	2.67565i
$873$	−2.58818e12	−	3.92093e12i	−0.150810	−	0.228468i
$874$	−1.14712e13	−	6.85372e12i	−0.664978	−	0.397306i
$875$	2.42503e13	+	3.04089e13i	1.39856	+	1.75374i
$876$	7.10038e12	−	6.20341e12i	0.407392	−	0.355928i
$877$	−5.18688e12	+	3.76849e12i	−0.296079	+	0.215114i	−0.725900	−	0.687800i	$-0.758577\pi$
$877$	−5.18688e12	+	3.76849e12i	−0.296079	+	0.215114i	0.429821	+	0.902914i	$0.358577\pi$
$878$	−1.80741e13	+	8.70404e12i	−1.02644	+	0.494306i
$879$	−2.09747e13	+	3.17753e13i	−1.18507	+	1.79531i
$880$	−1.98562e13	−	7.45215e12i	−1.11615	−	0.418899i
$881$	2.59504e12	−	1.55047e12i	0.145129	−	0.0867103i	−0.438499	−	0.898732i	$-0.644490\pi$
$881$	2.59504e12	−	1.55047e12i	0.145129	−	0.0867103i	0.583628	+	0.812021i	$0.301633\pi$
$882$	−2.34701e13	−	1.13026e13i	−1.30589	−	0.628884i
$883$	−2.67349e12	+	4.85167e11i	−0.147998	+	0.0268577i	−0.252050	−	0.967714i	$-0.581105\pi$
$883$	−2.67349e12	+	4.85167e11i	−0.147998	+	0.0268577i	0.104052	+	0.994572i	$0.466819\pi$
$884$	−1.53632e13	+	6.73108e13i	−0.846151	+	3.70723i
$885$	1.14041e13	−	4.28003e12i	0.624908	−	0.234532i
$886$	1.83265e13	−	2.29807e13i	0.999144	−	1.25289i
$887$	−5.99771e11	−	1.33549e13i	−0.0325334	−	0.724412i	−0.947284	−	0.320394i	$-0.896185\pi$
$887$	−5.99771e11	−	1.33549e13i	−0.0325334	−	0.724412i	0.914751	−	0.404018i	$-0.132387\pi$
$888$	−2.72499e12	−	6.06767e13i	−0.147064	−	3.27464i
$889$	−2.45819e13	+	3.08247e13i	−1.31995	+	1.65516i
$890$	2.82694e13	−	1.06097e13i	1.51029	−	0.566823i
$891$	−1.01407e12	+	4.44292e12i	−0.0539036	+	0.236167i
$892$	−2.43881e13	+	4.42580e12i	−1.28984	+	0.234072i
$893$	1.27321e13	+	6.13145e12i	0.669990	+	0.322650i
$894$	1.17496e13	−	7.02008e12i	0.615185	−	0.367556i
$895$	1.59782e13	+	5.99672e12i	0.832385	+	0.312399i
$896$	−5.08043e13	+	7.69653e13i	−2.63339	+	3.98941i
$897$	1.99470e13	−	9.60599e12i	1.02876	−	0.495423i
$898$	3.85234e12	−	2.79889e12i	0.197689	−	0.143629i
$899$	−1.68492e13	+	1.47207e13i	−0.860321	+	0.751639i
$900$	3.23636e13	+	4.05827e13i	1.64424	+	2.06182i
$901$	−9.77901e12	−	5.84269e12i	−0.494349	−	0.295360i
$902$	−2.28379e12	−	3.45980e12i	−0.114875	−	0.174029i
$903$	−9.93835e12	−	4.35428e13i	−0.497416	−	2.17932i
$904$	−2.78415e13	−	6.51385e13i	−1.38655	−	3.24399i
$905$	3.17141e13	−	2.85432e12i	1.57157	−	0.141444i
$906$	1.71155e13	+	1.24351e13i	0.843942	+	0.613160i
$907$	3.67501e13	+	6.66916e12i	1.80312	+	0.327219i	0.973078	−	0.230477i	$-0.0740286\pi$
$907$	3.67501e13	+	6.66916e12i	1.80312	+	0.327219i	0.830046	+	0.557695i	$0.188314\pi$
$908$	−7.95130e12	+	1.86030e13i	−0.388197	+	0.908231i
$909$	−2.03357e12	+	6.25869e12i	−0.0987921	+	0.304051i
$910$	−6.70720e13	−	1.24641e14i	−3.24231	−	6.02523i
$911$	−1.37832e13	−	1.44161e13i	−0.663007	−	0.693451i	0.302700	−	0.953086i	$-0.402112\pi$
$911$	−1.37832e13	−	1.44161e13i	−0.663007	−	0.693451i	−0.965707	+	0.259635i	$0.916398\pi$
$912$	−2.61070e13	+	4.85149e13i	−1.24963	+	2.32219i
$913$	−7.35869e12	+	2.03087e12i	−0.350495	+	0.0967305i
$914$	6.38919e12	+	4.71669e13i	0.302822	+	2.23553i
$915$	7.71900e12	−	5.69840e13i	0.364054	−	2.68756i
$916$	8.72534e13	+	2.40804e13i	4.09499	+	1.13015i
$917$	−3.31556e13	+	3.46781e13i	−1.54844	+	1.61954i
$918$	−7.81116e12	−	2.40403e13i	−0.363014	−	1.11724i
$919$	2.46831e13	+	2.22152e12i	1.14151	+	0.102738i	0.644216	−	0.764844i	$-0.277184\pi$
$919$	2.46831e13	+	2.22152e12i	1.14151	+	0.102738i	0.497295	+	0.867581i	$0.334327\pi$
$920$	−6.24737e13	−	5.45816e13i	−2.87509	−	2.51189i
$921$	−2.84841e11	+	6.34248e12i	−0.0130447	+	0.290463i
$922$	1.81478e13			0.827055
$923$	1.00234e13	+	2.79937e13i	0.454578	+	1.26956i
$924$	2.24383e13			1.01267
$925$	1.48891e12	−	3.31533e13i	0.0668701	−	1.48898i
$926$	3.24178e13	+	2.83226e13i	1.44889	+	1.26585i
$927$	−1.37020e13	−	1.23320e12i	−0.609432	−	0.0548498i
$928$	2.35851e13	+	7.25876e13i	1.04393	+	3.21289i
$929$	−1.75831e12	+	1.83905e12i	−0.0774508	+	0.0810072i	−0.760384	−	0.649473i	$-0.774989\pi$
$929$	−1.75831e12	+	1.83905e12i	−0.0774508	+	0.0810072i	0.682934	+	0.730480i	$0.260704\pi$
$930$	−1.11068e14	−	3.06528e13i	−4.86873	−	1.34368i
$931$	2.58482e12	−	1.90819e13i	0.112760	−	0.832430i
$932$	−5.60096e12	−	4.13480e13i	−0.243159	−	1.79508i
$933$	−2.06151e13	+	5.68939e12i	−0.890671	+	0.245809i
$934$	1.11197e13	−	2.06638e13i	0.478114	−	0.888484i
$935$	−5.49903e12	−	5.75154e12i	−0.235307	−	0.246111i
$936$	−2.59878e13	−	4.82933e13i	−1.10669	−	2.05658i
$937$	2.88435e12	−	8.87713e12i	0.122242	−	0.376222i	−0.871146	−	0.491023i	$-0.836623\pi$
$937$	2.88435e12	−	8.87713e12i	0.122242	−	0.376222i	0.993389	+	0.114801i	$0.0366230\pi$
$938$	3.28402e13	−	7.68335e13i	1.38514	−	3.24069i
$939$	3.84407e13	+	6.97596e12i	1.61360	+	0.292826i
$940$	1.12445e14	+	8.16960e13i	4.69747	+	3.41291i
$941$	1.08616e12	−	9.77565e10i	0.0451588	−	0.00406436i	−0.0670369	−	0.997750i	$-0.521355\pi$
$941$	1.08616e12	−	9.77565e10i	0.0451588	−	0.00406436i	0.112196	+	0.993686i	$0.464212\pi$
$942$	1.63281e13	+	3.82014e13i	0.675625	+	1.58070i
$943$	−2.06815e12	−	9.06116e12i	−0.0851686	−	0.373148i
$944$	1.56635e13	+	2.37291e13i	0.641968	+	0.972540i
$945$	3.24999e13	+	1.94178e13i	1.32568	+	0.792057i
$946$	6.65792e12	+	8.34876e12i	0.270289	+	0.338932i
$947$	1.75619e13	−	1.53434e13i	0.709574	−	0.619936i	−0.225561	−	0.974229i	$-0.572421\pi$
$947$	1.75619e13	−	1.53434e13i	0.709574	−	0.619936i	0.935134	+	0.354293i	$0.115279\pi$
$948$	6.76412e13	−	4.91442e13i	2.72003	−	1.97622i
$949$	−4.90391e12	+	2.36160e12i	−0.196266	+	0.0945166i
$950$	−2.89334e13	+	4.38322e13i	−1.15250	+	1.74597i
$951$	2.69350e13	+	1.01089e13i	1.06783	+	0.400765i
$952$	−1.16355e14	+	6.95187e13i	−4.59111	+	2.74306i
$953$	2.86522e13	+	1.37982e13i	1.12523	+	0.541880i	0.901503	−	0.432773i	$-0.142465\pi$
$953$	2.86522e13	+	1.37982e13i	1.12523	+	0.541880i	0.223723	+	0.974653i	$0.428179\pi$
$954$	1.41049e13	−	2.55965e12i	0.551317	−	0.100049i
$955$	−6.45414e12	+	2.82774e13i	−0.251087	+	1.10008i
$956$	2.32473e13	−	8.72484e12i	0.900142	−	0.337829i
$957$	3.52066e12	−	4.41477e12i	0.135681	−	0.170139i
$958$	2.19340e12	+	4.88398e13i	0.0841342	+	1.87339i
$959$	1.64648e12	+	3.66618e13i	0.0628599	+	1.39968i
$960$	−1.20465e14	+	1.51058e14i	−4.57763	+	5.74017i
$961$	1.43625e13	−	5.39032e12i	0.543217	−	0.203873i
$962$	−1.23607e13	+	5.41557e13i	−0.465324	+	2.03872i
$963$	−5.18069e12	+	9.40157e11i	−0.194120	+	0.0352275i
$964$	−5.26951e13	−	2.53766e13i	−1.96527	−	0.946426i
$965$	−5.26250e12	+	3.14420e12i	−0.195352	+	0.116718i
$966$	6.44668e13	+	2.41948e13i	2.38199	+	0.893975i
$967$	1.94302e13	−	2.94355e13i	0.714592	−	1.08256i	−0.277942	−	0.960598i	$-0.589652\pi$
$967$	1.94302e13	−	2.94355e13i	0.714592	−	1.08256i	0.992535	−	0.121963i	$-0.0389190\pi$
$968$	7.81058e13	−	3.76138e13i	2.85920	−	1.37692i
$969$	−1.67230e13	+	1.21500e13i	−0.609337	+	0.442709i
$970$	3.52090e13	−	3.07612e13i	1.27697	−	1.11565i
$971$	3.30447e13	+	4.14367e13i	1.19293	+	1.49589i	0.824151	+	0.566370i	$0.191653\pi$
$971$	3.30447e13	+	4.14367e13i	1.19293	+	1.49589i	0.368780	+	0.929517i	$0.379776\pi$
$972$	6.19689e13	+	3.70247e13i	2.22677	+	1.33043i
$973$	3.58967e13	+	5.43812e13i	1.28395	+	1.94510i
$974$	−8.31472e12	−	3.64292e13i	−0.296028	−	1.29698i
$975$	−3.41998e13	−	8.00144e13i	−1.21200	−	2.83561i
$976$	1.33687e14	−	1.20321e13i	4.71591	−	0.424440i
$977$	1.78183e13	+	1.29457e13i	0.625662	+	0.454570i	0.854895	−	0.518802i	$-0.173622\pi$
$977$	1.78183e13	+	1.29457e13i	0.625662	+	0.454570i	−0.229233	+	0.973372i	$0.573622\pi$
$978$	−1.04356e13	−	1.89379e12i	−0.364749	−	0.0661921i
$979$	1.08604e12	−	2.54092e12i	0.0377854	−	0.0884033i
$980$	5.85254e13	−	1.80123e14i	2.02687	−	6.23808i
$981$	6.00892e12	+	1.11664e13i	0.207150	+	0.384950i
$982$	1.53662e13	+	1.60717e13i	0.527307	+	0.551520i
$983$	−1.54989e13	+	2.88017e13i	−0.529430	+	0.983846i	0.465668	+	0.884959i	$0.345814\pi$
$983$	−1.54989e13	+	2.88017e13i	−0.529430	+	0.983846i	−0.995099	+	0.0988870i	$0.968472\pi$
$984$	−6.44468e13	+	1.77862e13i	−2.19141	+	0.604790i
$985$	3.44223e12	+	2.54115e13i	0.116513	+	0.860137i
$986$	−7.25370e12	+	5.35489e13i	−0.244407	+	1.80428i
$987$	−7.01952e13	−	1.93727e13i	−2.35440	−	0.649774i
$988$	4.43831e13	−	4.64211e13i	1.48187	−	1.54992i
$989$	7.39803e12	+	2.27688e13i	0.245885	+	0.756758i
$990$	9.97335e12	+	8.97618e11i	0.329976	+	0.0296984i
$991$	−3.47678e13	−	3.03757e13i	−1.14511	−	1.00045i	−0.999939	−	0.0110413i	$-0.996485\pi$
$991$	−3.47678e13	−	3.03757e13i	−1.14511	−	1.00045i	−0.145166	−	0.989407i	$-0.546372\pi$
$992$	6.39426e12	−	1.42379e14i	0.209647	−	4.66815i
$993$	4.57780e13			1.49412
$994$	−4.13866e13	+	8.27000e13i	−1.34469	+	2.68700i
$995$	−8.18368e13			−2.64695
$996$	−8.75036e12	+	1.94842e14i	−0.281747	+	6.27358i
$997$	−6.55083e11	−	5.72329e11i	−0.0209975	−	0.0183450i	0.647376	−	0.762171i	$-0.275866\pi$
$997$	−6.55083e11	−	5.72329e11i	−0.0209975	−	0.0183450i	−0.668374	+	0.743826i	$0.733009\pi$
$998$	−1.41325e13	−	1.27195e12i	−0.450955	−	0.0405867i
$999$	−4.59133e12	−	1.41307e13i	−0.145846	−	0.448867i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	71.10.g.a.2.2	✓	1272
71.36	even	35	inner	71.10.g.a.36.2	yes	1272

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.10.g.a.2.2	✓	1272	1.1	even	1	trivial
71.10.g.a.36.2	yes	1272	71.36	even	35	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	71.g (of order \(35\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.95578 + 43.5489i) q^{2} +(-130.482 - 113.998i) q^{3} +(-1382.74 - 124.449i) q^{4} +(729.287 + 2244.51i) q^{5} +(5219.69 - 5459.36i) q^{6} +(-9550.39 - 2635.74i) q^{7} +(5127.92 - 37855.8i) q^{8} +(1387.71 + 10244.5i) q^{9} +(-99172.4 + 27369.8i) q^{10} +(-4461.52 + 8290.89i) q^{11} +(166235. + 173868. i) q^{12} +(-65803.7 - 122284. i) q^{13} +(133462. - 410754. i) q^{14} +(160712. - 376005. i) q^{15} +(939147. + 170430. i) q^{16} +(289725. + 210497. i) q^{17} +(-448849. + 40397.1i) q^{18} +(-130929. - 306324. i) q^{19} +(-729086. - 3.19434e6i) q^{20} +(945679. + 1.43264e6i) q^{21} +(-352333. - 210509. i) q^{22} +(-573711. - 719411. i) q^{23} +(-4.98460e6 + 4.35491e6i) q^{24} +(-2.92588e6 + 2.12577e6i) q^{25} +(5.45401e6 - 2.62651e6i) q^{26} +(-891992. + 1.35131e6i) q^{27} +(1.28777e7 + 4.83307e6i) q^{28} +(2.97147e6 - 1.77537e6i) q^{29} +(1.60603e7 + 7.73422e6i) q^{30} +(-6.35989e6 + 1.15415e6i) q^{31} +(-4.90648e6 + 2.14967e7i) q^{32} +(1.52729e6 - 573203. i) q^{33} +(-9.73356e6 + 1.22055e7i) q^{34} +(-1.04902e6 - 2.33582e7i) q^{35} +(-643926. - 1.43381e7i) q^{36} +(-5.72130e6 + 7.17429e6i) q^{37} +(1.35961e7 - 5.10271e6i) q^{38} +(-5.35397e6 + 2.34573e7i) q^{39} +(8.87076e7 - 1.60981e7i) q^{40} +(9.10033e6 + 4.38249e6i) q^{41} +(-6.42395e7 + 3.83813e7i) q^{42} +(-2.43587e7 - 9.14199e6i) q^{43} +(7.20091e6 - 1.09089e7i) q^{44} +(-2.19818e7 + 1.05859e7i) q^{45} +(3.24516e7 - 2.35774e7i) q^{46} +(-3.19455e7 + 2.79100e7i) q^{47} +(-1.03113e8 - 1.29299e8i) q^{48} +(4.96213e7 + 2.96473e7i) q^{49} +(-8.68526e7 - 1.31576e8i) q^{50} +(-1.38074e7 - 6.04941e7i) q^{51} +(7.57712e7 + 1.77276e8i) q^{52} +(-3.16811e7 + 2.85135e6i) q^{53} +(-5.71035e7 - 4.14881e7i) q^{54} +(-2.18628e7 - 3.96751e6i) q^{55} +(-1.48752e8 + 3.48022e8i) q^{56} +(-1.78366e7 + 5.48953e7i) q^{57} +(7.15038e7 + 1.32876e8i) q^{58} +(2.05857e7 + 2.15309e7i) q^{59} +(-2.69017e8 + 4.99916e8i) q^{60} +(1.35560e8 - 3.74123e7i) q^{61} +(-3.78234e7 - 2.79223e8i) q^{62} +(1.37486e7 - 1.01496e8i) q^{63} +(-4.55474e8 - 1.25703e8i) q^{64} +(2.26478e8 - 2.36877e8i) q^{65} +(2.19753e7 + 6.76329e7i) q^{66} +(1.92690e8 + 1.73424e7i) q^{67} +(-3.74417e8 - 3.27119e8i) q^{68} +(-7.15291e6 + 1.59272e8i) q^{69} +1.01927e9 q^{70} +(-2.11723e8 - 3.19646e7i) q^{71} +3.94929e8 q^{72} +(1.75852e6 - 3.91564e7i) q^{73} +(-3.01242e8 - 2.63188e8i) q^{74} +(6.24107e8 + 5.61707e7i) q^{75} +(1.42919e8 + 4.39860e8i) q^{76} +(6.44619e7 - 6.74218e7i) q^{77} +(-1.01107e9 - 2.79036e8i) q^{78} +(4.66562e7 - 3.44430e8i) q^{79} +(3.02375e8 + 2.23222e9i) q^{80} +(4.66586e8 - 1.28770e8i) q^{81} +(-2.08651e8 + 3.87738e8i) q^{82} +(5.60316e8 + 5.86044e8i) q^{83} +(-1.12934e9 - 2.09866e9i) q^{84} +(-2.61172e8 + 8.03804e8i) q^{85} +(4.45763e8 - 1.04292e9i) q^{86} +(-5.90111e8 - 1.07089e8i) q^{87} +(2.90980e8 + 2.11409e8i) q^{88} +(-2.92314e8 + 2.63087e7i) q^{89} +(-4.18012e8 - 9.77987e8i) q^{90} +(3.06143e8 + 1.34130e9i) q^{91} +(7.03763e8 + 1.06616e9i) q^{92} +(9.61419e8 + 5.74421e8i) q^{93} +(-1.15297e9 - 1.44578e9i) q^{94} +(5.92063e8 - 5.17270e8i) q^{95} +(3.09079e9 - 2.24559e9i) q^{96} +(-4.09446e8 + 1.97179e8i) q^{97} +(-1.38816e9 + 2.10297e9i) q^{98} +(-9.11271e7 - 3.42006e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1272 q - 76 q^{2} - 395 q^{3} + 13542 q^{4} - 1610 q^{5} - 4334 q^{6} - 4827 q^{7} - 18627 q^{8} + 286810 q^{9} - 53448 q^{10} - 170685 q^{11} + 138323 q^{12} - 93291 q^{13} + 985964 q^{14} - 966194 q^{15}+ \cdots - 4074592265 q^{99}+O(q^{100}) \) 1272 * q - 76 * q^2 - 395 * q^3 + 13542 * q^4 - 1610 * q^5 - 4334 * q^6 - 4827 * q^7 - 18627 * q^8 + 286810 * q^9 - 53448 * q^10 - 170685 * q^11 + 138323 * q^12 - 93291 * q^13 + 985964 * q^14 - 966194 * q^15 + 4755334 * q^16 + 2558412 * q^17 - 2619769 * q^18 - 172269 * q^19 + 738120 * q^20 + 1797929 * q^21 + 3015622 * q^22 + 6635088 * q^23 + 4803145 * q^24 - 115100016 * q^25 + 19254293 * q^26 - 17686931 * q^27 + 15761532 * q^28 - 10052927 * q^29 + 62637435 * q^30 - 23748991 * q^31 + 10388192 * q^32 - 15097203 * q^33 + 33217854 * q^34 - 24823174 * q^35 + 27856812 * q^36 - 27156308 * q^37 - 43400577 * q^38 + 251072838 * q^39 - 129856160 * q^40 + 62087988 * q^41 - 91873950 * q^42 - 167299067 * q^43 + 60914131 * q^44 - 31536191 * q^45 - 50201490 * q^46 - 23317743 * q^47 + 10641329 * q^48 + 338745866 * q^49 + 303770229 * q^50 + 448039613 * q^51 - 979580293 * q^52 + 12085215 * q^53 - 182583505 * q^54 - 243892552 * q^55 + 30440435 * q^56 + 714581966 * q^57 - 244549660 * q^58 - 859013315 * q^59 - 1894499000 * q^60 - 876373921 * q^61 + 186553636 * q^62 - 196611021 * q^63 + 5528242635 * q^64 + 867018244 * q^65 + 2727701199 * q^66 - 286780089 * q^67 - 1689988351 * q^68 - 3073308182 * q^69 - 41489396 * q^70 - 2538053548 * q^71 - 6821388000 * q^72 + 128479023 * q^73 + 3282772334 * q^74 + 3407782757 * q^75 + 7133788844 * q^76 + 1087098389 * q^77 + 2715049934 * q^78 + 144243625 * q^79 - 7443877603 * q^80 - 4083269278 * q^81 - 10375744380 * q^82 + 1543773955 * q^83 - 4117054288 * q^84 + 7843382686 * q^85 + 3545751759 * q^86 + 5261609811 * q^87 - 818728797 * q^88 - 1369081479 * q^89 + 10041256259 * q^90 - 7299574322 * q^91 + 602797624 * q^92 - 2146129677 * q^93 - 683447510 * q^94 - 7007204038 * q^95 + 6601829126 * q^96 - 10081488030 * q^97 - 5942379880 * q^98 - 4074592265 * q^99

Introduction

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