LMFDB - Embedded newform 13.9.d.a.5.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [13,9,Mod(5,13)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("13.5"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	13.d (of order $4$, degree $2$, 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:	$5.29592193079$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 2 x^{17} + 2 x^{16} + 3828 x^{15} + 1204401 x^{14} + 47082 x^{13} + 4823826 x^{12} + \cdots + 18\!\cdots\!48 $ x^18 - 2x^17 + 2x^16 + 3828x^15 + 1204401x^14 + 47082x^13 + 4823826x^12 + 3014328096x^11 + 324100560576x^10 + 1243720573056x^9 + 2594493183360x^8 + 67426704543744x^7 + 16374511738433536x^6 + 38893585626849280x^5 + 61002122197950464x^4 + 4754717719118610432x^3 + 119869629126769115136x^2 + 658222091640736579584*x + 1807198057923881730048
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{2}\cdot 13^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.2
Root			$18.0289 + 18.0289i$ of defining polynomial
Character	$\chi$	$=$	13.5
Dual form			13.9.d.a.8.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-18.0289 + 18.0289i) q^{2} +107.999 q^{3} -394.083i q^{4} +(706.041 - 706.041i) q^{5} +(-1947.10 + 1947.10i) q^{6} +(1701.26 + 1701.26i) q^{7} +(2489.49 + 2489.49i) q^{8} +5102.69 q^{9} +25458.3i q^{10} +(5801.81 + 5801.81i) q^{11} -42560.4i q^{12} +(-16499.4 - 23313.1i) q^{13} -61343.7 q^{14} +(76251.4 - 76251.4i) q^{15} +11119.7 q^{16} +134321. i q^{17} +(-91995.9 + 91995.9i) q^{18} +(84022.1 - 84022.1i) q^{19} +(-278239. - 278239. i) q^{20} +(183733. + 183733. i) q^{21} -209201. q^{22} +136494. i q^{23} +(268861. + 268861. i) q^{24} -606362. i q^{25} +(717776. + 122845. i) q^{26} -157496. q^{27} +(670437. - 670437. i) q^{28} -958731. q^{29} +2.74946e6i q^{30} +(484682. - 484682. i) q^{31} +(-837786. + 837786. i) q^{32} +(626587. + 626587. i) q^{33} +(-2.42165e6 - 2.42165e6i) q^{34} +2.40232e6 q^{35} -2.01088e6i q^{36} +(-1.25356e6 - 1.25356e6i) q^{37} +3.02965e6i q^{38} +(-1.78191e6 - 2.51778e6i) q^{39} +3.51536e6 q^{40} +(687708. - 687708. i) q^{41} -6.62503e6 q^{42} +3.17073e6i q^{43} +(2.28640e6 - 2.28640e6i) q^{44} +(3.60270e6 - 3.60270e6i) q^{45} +(-2.46084e6 - 2.46084e6i) q^{46} +(-507919. - 507919. i) q^{47} +1.20091e6 q^{48} +23757.9i q^{49} +(1.09320e7 + 1.09320e7i) q^{50} +1.45064e7i q^{51} +(-9.18731e6 + 6.50212e6i) q^{52} -8.75734e6 q^{53} +(2.83948e6 - 2.83948e6i) q^{54} +8.19263e6 q^{55} +8.47053e6i q^{56} +(9.07426e6 - 9.07426e6i) q^{57} +(1.72849e7 - 1.72849e7i) q^{58} +(-3.35500e6 - 3.35500e6i) q^{59} +(-3.00494e7 - 3.00494e7i) q^{60} +3.53900e6 q^{61} +1.74766e7i q^{62} +(8.68099e6 + 8.68099e6i) q^{63} -2.73621e7i q^{64} +(-2.81092e7 - 4.81079e6i) q^{65} -2.25934e7 q^{66} +(-4.45919e6 + 4.45919e6i) q^{67} +5.29335e7 q^{68} +1.47412e7i q^{69} +(-4.33111e7 + 4.33111e7i) q^{70} +(-7.29718e6 + 7.29718e6i) q^{71} +(1.27031e7 + 1.27031e7i) q^{72} +(8.69469e6 + 8.69469e6i) q^{73} +4.52008e7 q^{74} -6.54862e7i q^{75} +(-3.31117e7 - 3.31117e7i) q^{76} +1.97408e7i q^{77} +(7.75187e7 + 1.32670e7i) q^{78} -5.57116e7 q^{79} +(7.85098e6 - 7.85098e6i) q^{80} -5.04880e7 q^{81} +2.47972e7i q^{82} +(-3.21832e6 + 3.21832e6i) q^{83} +(7.24062e7 - 7.24062e7i) q^{84} +(9.48358e7 + 9.48358e7i) q^{85} +(-5.71648e7 - 5.71648e7i) q^{86} -1.03542e8 q^{87} +2.88871e7i q^{88} +(4.69400e7 + 4.69400e7i) q^{89} +1.29906e8i q^{90} +(1.15920e7 - 6.77313e7i) q^{91} +5.37901e7 q^{92} +(5.23449e7 - 5.23449e7i) q^{93} +1.83144e7 q^{94} -1.18646e8i q^{95} +(-9.04797e7 + 9.04797e7i) q^{96} +(-5.15911e7 + 5.15911e7i) q^{97} +(-428329. - 428329. i) q^{98} +(2.96048e7 + 2.96048e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} - 4 q^{3} + 166 q^{5} + 2720 q^{6} + 5308 q^{7} + 10464 q^{8} + 39362 q^{9} - 31556 q^{11} + 71300 q^{13} - 110260 q^{14} + 121124 q^{15} - 522860 q^{16} - 308962 q^{18} + 100288 q^{19} + 736268 q^{20}+ \cdots - 1125076336 q^{99}+O(q^{100}) $ 18 * q - 2 * q^2 - 4 * q^3 + 166 * q^5 + 2720 * q^6 + 5308 * q^7 + 10464 * q^8 + 39362 * q^9 - 31556 * q^11 + 71300 * q^13 - 110260 * q^14 + 121124 * q^15 - 522860 * q^16 - 308962 * q^18 + 100288 * q^19 + 736268 * q^20 + 279416 * q^21 - 977312 * q^22 - 986232 * q^24 + 2952238 * q^26 + 364916 * q^27 + 4497084 * q^28 - 2479024 * q^29 - 1892664 * q^31 + 947212 * q^32 + 1368644 * q^33 - 531576 * q^34 - 2918284 * q^35 - 8343978 * q^37 - 1101268 * q^39 - 12691908 * q^40 + 1140178 * q^41 + 15137212 * q^42 - 3867188 * q^44 + 6565370 * q^45 + 2006148 * q^46 - 13368572 * q^47 - 10106716 * q^48 + 37369598 * q^50 - 14821220 * q^52 + 50561348 * q^53 - 4995928 * q^54 + 76994128 * q^55 - 34755760 * q^57 + 22505716 * q^58 + 2127976 * q^59 - 161134196 * q^60 - 52016516 * q^61 - 15210112 * q^63 + 10413082 * q^65 - 51097328 * q^66 + 960292 * q^67 + 283187508 * q^68 - 166635032 * q^70 + 67412140 * q^71 + 96846900 * q^72 - 145213226 * q^73 - 233620024 * q^74 - 150533640 * q^76 + 212071160 * q^78 - 76829120 * q^79 + 524889520 * q^80 + 293280674 * q^81 - 241951556 * q^83 + 345496184 * q^84 + 260737764 * q^85 - 579480384 * q^86 - 618300656 * q^87 - 89187110 * q^89 + 232660948 * q^91 - 122690376 * q^92 + 669553400 * q^93 + 1069637380 * q^94 - 1324092400 * q^96 + 331183146 * q^97 + 588677614 * q^98 - 1125076336 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−18.0289	+	18.0289i	−1.12681	+	1.12681i	−0.136114	+	0.990693i	$0.543461\pi$
$2$	−18.0289	+	18.0289i	−1.12681	+	1.12681i	−0.990693	+	0.136114i	$0.956539\pi$
$3$	107.999			1.33332			0.666658	−	0.745364i	$-0.267724\pi$
$3$	107.999			1.33332			0.666658	+	0.745364i	$0.267724\pi$
$4$		−	394.083i		−	1.53939i
$5$	706.041	−	706.041i	1.12967	−	1.12967i	0.139434	−	0.990231i	$-0.455472\pi$
$5$	706.041	−	706.041i	1.12967	−	1.12967i	0.990231	−	0.139434i	$-0.0445283\pi$
$6$	−1947.10	+	1947.10i	−1.50239	+	1.50239i
$7$	1701.26	+	1701.26i	0.708562	+	0.708562i	0.966233	−	0.257670i	$-0.0829549\pi$
$7$	1701.26	+	1701.26i	0.708562	+	0.708562i	−0.257670	+	0.966233i	$0.582955\pi$
$8$	2489.49	+	2489.49i	0.607786	+	0.607786i
$9$	5102.69			0.777730
$10$			25458.3i			2.54583i
$11$	5801.81	+	5801.81i	0.396271	+	0.396271i	0.876916	−	0.480644i	$-0.159597\pi$
$11$	5801.81	+	5801.81i	0.396271	+	0.396271i	−0.480644	+	0.876916i	$0.659597\pi$
$12$		−	42560.4i		−	2.05249i
$13$	−16499.4	−	23313.1i	−0.577689	−	0.816257i
$13$	−16499.4	−	23313.1i	−0.577689	−	0.816257i
$14$	−61343.7			−1.59683
$15$	76251.4	−	76251.4i	1.50620	−	1.50620i
$16$	11119.7			0.169674
$17$			134321.i			1.60823i	0.594477	+	0.804113i	$0.297359\pi$
$17$			134321.i			1.60823i	−0.594477	+	0.804113i	$0.702641\pi$
$18$	−91995.9	+	91995.9i	−0.876351	+	0.876351i
$19$	84022.1	−	84022.1i	0.644732	−	0.644732i	−0.306983	−	0.951715i	$-0.599320\pi$
$19$	84022.1	−	84022.1i	0.644732	−	0.644732i	0.951715	+	0.306983i	$0.0993196\pi$
$20$	−278239.	−	278239.i	−1.73899	−	1.73899i
$21$	183733.	+	183733.i	0.944737	+	0.944737i
$22$	−209201.			−0.893043
$23$			136494.i			0.487757i	0.969806	+	0.243878i	$0.0784198\pi$
$23$			136494.i			0.487757i	−0.969806	+	0.243878i	$0.921580\pi$
$24$	268861.	+	268861.i	0.810370	+	0.810370i
$25$		−	606362.i		−	1.55229i
$26$	717776.	+	122845.i	1.57071	+	0.268821i
$27$	−157496.			−0.296356
$28$	670437.	−	670437.i	1.09075	−	1.09075i
$29$	−958731.			−1.35552			−0.677758	−	0.735285i	$-0.737048\pi$
$29$	−958731.			−1.35552			−0.677758	+	0.735285i	$0.737048\pi$
$30$			2.74946e6i			3.39439i
$31$	484682.	−	484682.i	0.524819	−	0.524819i	−0.394204	−	0.919023i	$-0.628980\pi$
$31$	484682.	−	484682.i	0.524819	−	0.524819i	0.919023	+	0.394204i	$0.128980\pi$
$32$	−837786.	+	837786.i	−0.798975	+	0.798975i
$33$	626587.	+	626587.i	0.528355	+	0.528355i
$34$	−2.42165e6	−	2.42165e6i	−1.81216	−	1.81216i
$35$	2.40232e6			1.60088
$36$		−	2.01088e6i		−	1.19723i
$37$	−1.25356e6	−	1.25356e6i	−0.668867	−	0.668867i	0.288587	−	0.957454i	$-0.406815\pi$
$37$	−1.25356e6	−	1.25356e6i	−0.668867	−	0.668867i	−0.957454	+	0.288587i	$0.906815\pi$
$38$			3.02965e6i			1.45298i
$39$	−1.78191e6	−	2.51778e6i	−0.770241	−	1.08833i
$40$	3.51536e6			1.37319
$41$	687708.	−	687708.i	0.243371	−	0.243371i	−0.574872	−	0.818243i	$-0.694948\pi$
$41$	687708.	−	687708.i	0.243371	−	0.243371i	0.818243	+	0.574872i	$0.194948\pi$
$42$	−6.62503e6			−2.12907
$43$			3.17073e6i			0.927439i	0.885982	+	0.463720i	$0.153486\pi$
$43$			3.17073e6i			0.927439i	−0.885982	+	0.463720i	$0.846514\pi$
$44$	2.28640e6	−	2.28640e6i	0.610015	−	0.610015i
$45$	3.60270e6	−	3.60270e6i	0.878574	−	0.878574i
$46$	−2.46084e6	−	2.46084e6i	−0.549608	−	0.549608i
$47$	−507919.	−	507919.i	−0.104089	−	0.104089i	0.653145	−	0.757233i	$-0.273449\pi$
$47$	−507919.	−	507919.i	−0.104089	−	0.104089i	−0.757233	+	0.653145i	$0.773449\pi$
$48$	1.20091e6			0.226228
$49$			23757.9i			0.00412120i
$50$	1.09320e7	+	1.09320e7i	1.74913	+	1.74913i
$51$			1.45064e7i			2.14427i
$52$	−9.18731e6	+	6.50212e6i	−1.25654	+	0.889287i
$53$	−8.75734e6			−1.10986			−0.554931	−	0.831896i	$-0.687255\pi$
$53$	−8.75734e6			−1.10986			−0.554931	+	0.831896i	$0.687255\pi$
$54$	2.83948e6	−	2.83948e6i	0.333936	−	0.333936i
$55$	8.19263e6			0.895308
$56$			8.47053e6i			0.861308i
$57$	9.07426e6	−	9.07426e6i	0.859630	−	0.859630i
$58$	1.72849e7	−	1.72849e7i	1.52741	−	1.52741i
$59$	−3.35500e6	−	3.35500e6i	−0.276875	−	0.276875i	0.554985	−	0.831860i	$-0.312724\pi$
$59$	−3.35500e6	−	3.35500e6i	−0.276875	−	0.276875i	−0.831860	+	0.554985i	$0.812724\pi$
$60$	−3.00494e7	−	3.00494e7i	−2.31863	−	2.31863i
$61$	3.53900e6			0.255600			0.127800	−	0.991800i	$-0.459208\pi$
$61$	3.53900e6			0.255600			0.127800	+	0.991800i	$0.459208\pi$
$62$			1.74766e7i			1.18274i
$63$	8.68099e6	+	8.68099e6i	0.551070	+	0.551070i
$64$		−	2.73621e7i		−	1.63091i
$65$	−2.81092e7	−	4.81079e6i	−1.57469	−	0.269503i
$66$	−2.25934e7			−1.19071
$67$	−4.45919e6	+	4.45919e6i	−0.221287	+	0.221287i	−0.809040	−	0.587753i	$-0.800013\pi$
$67$	−4.45919e6	+	4.45919e6i	−0.221287	+	0.221287i	0.587753	+	0.809040i	$0.300013\pi$
$68$	5.29335e7			2.47568
$69$			1.47412e7i			0.650334i
$70$	−4.33111e7	+	4.33111e7i	−1.80388	+	1.80388i
$71$	−7.29718e6	+	7.29718e6i	−0.287158	+	0.287158i	−0.835956	−	0.548797i	$-0.815086\pi$
$71$	−7.29718e6	+	7.29718e6i	−0.287158	+	0.287158i	0.548797	+	0.835956i	$0.315086\pi$
$72$	1.27031e7	+	1.27031e7i	0.472693	+	0.472693i
$73$	8.69469e6	+	8.69469e6i	0.306170	+	0.306170i	0.843422	−	0.537252i	$-0.180538\pi$
$73$	8.69469e6	+	8.69469e6i	0.306170	+	0.306170i	−0.537252	+	0.843422i	$0.680538\pi$
$74$	4.52008e7			1.50737
$75$		−	6.54862e7i		−	2.06969i
$76$	−3.31117e7	−	3.31117e7i	−0.992492	−	0.992492i
$77$			1.97408e7i			0.561566i
$78$	7.75187e7	+	1.32670e7i	2.09425	+	0.358423i
$79$	−5.57116e7			−1.43033			−0.715167	−	0.698954i	$-0.753649\pi$
$79$	−5.57116e7			−1.43033			−0.715167	+	0.698954i	$0.753649\pi$
$80$	7.85098e6	−	7.85098e6i	0.191674	−	0.191674i
$81$	−5.04880e7			−1.17287
$82$			2.47972e7i			0.548464i
$83$	−3.21832e6	+	3.21832e6i	−0.0678136	+	0.0678136i	−0.740200	−	0.672387i	$-0.765269\pi$
$83$	−3.21832e6	+	3.21832e6i	−0.0678136	+	0.0678136i	0.672387	+	0.740200i	$0.265269\pi$
$84$	7.24062e7	−	7.24062e7i	1.45432	−	1.45432i
$85$	9.48358e7	+	9.48358e7i	1.81676	+	1.81676i
$86$	−5.71648e7	−	5.71648e7i	−1.04505	−	1.04505i
$87$	−1.03542e8			−1.80733
$88$			2.88871e7i			0.481696i
$89$	4.69400e7	+	4.69400e7i	0.748141	+	0.748141i	0.974130	−	0.225989i	$-0.0725613\pi$
$89$	4.69400e7	+	4.69400e7i	0.748141	+	0.748141i	−0.225989	+	0.974130i	$0.572561\pi$
$90$			1.29906e8i			1.97997i
$91$	1.15920e7	−	6.77313e7i	0.169041	−	0.987698i
$92$	5.37901e7			0.750847
$93$	5.23449e7	−	5.23449e7i	0.699750	−	0.699750i
$94$	1.83144e7			0.234575
$95$		−	1.18646e8i		−	1.45666i
$96$	−9.04797e7	+	9.04797e7i	−1.06529	+	1.06529i
$97$	−5.15911e7	+	5.15911e7i	−0.582757	+	0.582757i	−0.935660	−	0.352903i	$-0.885195\pi$
$97$	−5.15911e7	+	5.15911e7i	−0.582757	+	0.582757i	0.352903	+	0.935660i	$0.385195\pi$
$98$	−428329.	−	428329.i	−0.00464379	−	0.00464379i
$99$	2.96048e7	+	2.96048e7i	0.308192	+	0.308192i
$100$	−2.38957e8			−2.38957
$101$			1.34398e8i			1.29154i	0.763531	+	0.645771i	$0.223464\pi$
$101$			1.34398e8i			1.29154i	−0.763531	+	0.645771i	$0.776536\pi$
$102$	−2.61535e8	−	2.61535e8i	−2.41618	−	2.41618i
$103$		−	1.40184e8i		−	1.24552i	−0.782415	−	0.622758i	$-0.786012\pi$
$103$		−	1.40184e8i		−	1.24552i	0.782415	−	0.622758i	$-0.213988\pi$
$104$	1.69628e7	−	9.91128e7i	0.144999	−	0.847220i
$105$	2.59447e8			2.13447
$106$	1.57885e8	−	1.57885e8i	1.25060	−	1.25060i
$107$	2.20841e8			1.68479			0.842394	−	0.538863i	$-0.181146\pi$
$107$	2.20841e8			1.68479			0.842394	+	0.538863i	$0.181146\pi$
$108$			6.20665e7i			0.456207i
$109$	3.84233e7	−	3.84233e7i	0.272200	−	0.272200i	−0.557785	−	0.829985i	$-0.688349\pi$
$109$	3.84233e7	−	3.84233e7i	0.272200	−	0.272200i	0.829985	+	0.557785i	$0.188349\pi$
$110$	−1.47704e8	+	1.47704e8i	−1.00884	+	1.00884i
$111$	−1.35383e8	−	1.35383e8i	−0.891811	−	0.891811i
$112$	1.89175e7	+	1.89175e7i	0.120224	+	0.120224i
$113$	1.23741e7			0.0758924			0.0379462	−	0.999280i	$-0.487918\pi$
$113$	1.23741e7			0.0758924			0.0379462	+	0.999280i	$0.487918\pi$
$114$			3.27198e8i			1.93728i
$115$	9.63706e7	+	9.63706e7i	0.551002	+	0.551002i
$116$			3.77820e8i			2.08667i
$117$	−8.41911e7	−	1.18960e8i	−0.449286	−	0.634828i
$118$	1.20974e8			0.623970
$119$	−2.28514e8	+	2.28514e8i	−1.13953	+	1.13953i
$120$	3.79654e8			1.83089
$121$		−	1.47037e8i		−	0.685938i
$122$	−6.38043e7	+	6.38043e7i	−0.288012	+	0.288012i
$123$	7.42714e7	−	7.42714e7i	0.324490	−	0.324490i
$124$	−1.91005e8	−	1.91005e8i	−0.807900	−	0.807900i
$125$	−1.52319e8	−	1.52319e8i	−0.623900	−	0.623900i
$126$	−3.13017e8			−1.24190
$127$			5.22219e7i			0.200742i	0.994950	+	0.100371i	$0.0320029\pi$
$127$			5.22219e7i			0.200742i	−0.994950	+	0.100371i	$0.967997\pi$
$128$	2.78835e8	+	2.78835e8i	1.03874	+	1.03874i
$129$			3.42434e8i			1.23657i
$130$	5.93512e8	−	4.20046e8i	2.07805	−	1.47070i
$131$	−3.48669e8			−1.18394			−0.591968	−	0.805961i	$-0.701649\pi$
$131$	−3.48669e8			−1.18394			−0.591968	+	0.805961i	$0.701649\pi$
$132$	2.46927e8	−	2.46927e8i	0.813343	−	0.813343i
$133$	2.85886e8			0.913665
$134$		−	1.60789e8i		−	0.498696i
$135$	−1.11198e8	+	1.11198e8i	−0.334783	+	0.334783i
$136$	−3.34390e8	+	3.34390e8i	−0.977456	+	0.977456i
$137$	−1.37365e8	−	1.37365e8i	−0.389937	−	0.389937i	0.484728	−	0.874665i	$-0.338919\pi$
$137$	−1.37365e8	−	1.37365e8i	−0.389937	−	0.389937i	−0.874665	+	0.484728i	$0.838919\pi$
$138$	−2.65768e8	−	2.65768e8i	−0.732800	−	0.732800i
$139$	1.43378e7			0.0384081			0.0192040	−	0.999816i	$-0.493887\pi$
$139$	1.43378e7			0.0384081			0.0192040	+	0.999816i	$0.493887\pi$
$140$		−	9.46712e8i		−	2.46437i
$141$	−5.48545e7	−	5.48545e7i	−0.138783	−	0.138783i
$142$		−	2.63120e8i		−	0.647144i
$143$	3.95322e7	−	2.30984e8i	0.0945380	−	0.552381i
$144$	5.67405e7			0.131960
$145$	−6.76903e8	+	6.76903e8i	−1.53128	+	1.53128i
$146$	−3.13511e8			−0.689989
$147$			2.56582e6i			0.00549486i
$148$	−4.94009e8	+	4.94009e8i	−1.02965	+	1.02965i
$149$	3.31091e8	−	3.31091e8i	0.671742	−	0.671742i	−0.286376	−	0.958117i	$-0.592450\pi$
$149$	3.31091e8	−	3.31091e8i	0.671742	−	0.671742i	0.958117	+	0.286376i	$0.0924505\pi$
$150$	1.18065e9	+	1.18065e9i	2.33214	+	2.33214i
$151$	−5.37699e7	−	5.37699e7i	−0.103426	−	0.103426i	0.653500	−	0.756926i	$-0.273300\pi$
$151$	−5.37699e7	−	5.37699e7i	−0.103426	−	0.103426i	−0.756926	+	0.653500i	$0.773300\pi$
$152$	4.18344e8			0.783717
$153$			6.85396e8i			1.25077i
$154$	−3.55904e8	−	3.55904e8i	−0.632776	−	0.632776i
$155$		−	6.84410e8i		−	1.18574i
$156$	−9.92216e8	+	7.02220e8i	−1.67536	+	1.18570i
$157$	1.02886e9			1.69339			0.846695	−	0.532079i	$-0.178589\pi$
$157$	1.02886e9			1.69339			0.846695	+	0.532079i	$0.178589\pi$
$158$	1.00442e9	−	1.00442e9i	1.61171	−	1.61171i
$159$	−9.45780e8			−1.47980
$160$			1.18302e9i			1.80515i
$161$	−2.32212e8	+	2.32212e8i	−0.345606	+	0.345606i
$162$	9.10244e8	−	9.10244e8i	1.32159	−	1.32159i
$163$	−1.25745e7	−	1.25745e7i	−0.0178131	−	0.0178131i	0.698144	−	0.715957i	$-0.254009\pi$
$163$	−1.25745e7	−	1.25745e7i	−0.0178131	−	0.0178131i	−0.715957	+	0.698144i	$0.754009\pi$
$164$	−2.71014e8	−	2.71014e8i	−0.374642	−	0.374642i
$165$	8.84792e8			1.19373
$166$		−	1.16046e8i		−	0.152826i
$167$	3.77091e8	+	3.77091e8i	0.484820	+	0.484820i	0.906667	−	0.421847i	$-0.138618\pi$
$167$	3.77091e8	+	3.77091e8i	0.484820	+	0.484820i	−0.421847	+	0.906667i	$0.638618\pi$
$168$			9.14805e8i			1.14840i
$169$	−2.71273e8	+	7.69303e8i	−0.332552	+	0.943085i
$170$	−3.41957e9			−4.09427
$171$	4.28738e8	−	4.28738e8i	0.501427	−	0.501427i
$172$	1.24953e9			1.42769
$173$		−	1.73349e8i		−	0.193525i	−0.995307	−	0.0967626i	$-0.969151\pi$
$173$		−	1.73349e8i		−	0.193525i	0.995307	−	0.0967626i	$-0.0308488\pi$
$174$	1.86674e9	−	1.86674e9i	2.03651	−	2.03651i
$175$	1.03158e9	−	1.03158e9i	1.09989	−	1.09989i
$176$	6.45146e7	+	6.45146e7i	0.0672368	+	0.0672368i
$177$	−3.62335e8	−	3.62335e8i	−0.369162	−	0.369162i
$178$	−1.69256e9			−1.68602
$179$			9.54514e8i			0.929759i	0.885374	+	0.464879i	$0.153902\pi$
$179$			9.54514e8i			0.929759i	−0.885374	+	0.464879i	$0.846098\pi$
$180$	−1.41977e9	−	1.41977e9i	−1.35247	−	1.35247i
$181$			1.88245e8i			0.175391i	0.996147	+	0.0876957i	$0.0279503\pi$
$181$			1.88245e8i			0.175391i	−0.996147	+	0.0876957i	$0.972050\pi$
$182$	1.01213e9	+	1.43011e9i	0.922468	+	1.30342i
$183$	3.82207e8			0.340796
$184$	−3.39801e8	+	3.39801e8i	−0.296452	+	0.296452i
$185$	−1.77014e9			−1.51119
$186$			1.88744e9i			1.57697i
$187$	−7.79303e8	+	7.79303e8i	−0.637294	+	0.637294i
$188$	−2.00162e8	+	2.00162e8i	−0.160233	+	0.160233i
$189$	−2.67941e8	−	2.67941e8i	−0.209987	−	0.209987i
$190$	2.13906e9	+	2.13906e9i	1.64138	+	1.64138i
$191$	2.55263e8			0.191802			0.0959011	−	0.995391i	$-0.469427\pi$
$191$	2.55263e8			0.191802			0.0959011	+	0.995391i	$0.469427\pi$
$192$		−	2.95507e9i		−	2.17451i
$193$	1.53214e9	+	1.53214e9i	1.10425	+	1.10425i	0.993892	+	0.110360i	$0.0352005\pi$
$193$	1.53214e9	+	1.53214e9i	1.10425	+	1.10425i	0.110360	+	0.993892i	$0.464800\pi$
$194$		−	1.86026e9i		−	1.31331i
$195$	−3.03576e9	−	5.19559e8i	−2.09956	−	0.359332i
$196$	9.36259e6			0.00634412
$197$	8.98261e8	−	8.98261e8i	0.596400	−	0.596400i	−0.342953	−	0.939353i	$-0.611427\pi$
$197$	8.98261e8	−	8.98261e8i	0.596400	−	0.596400i	0.939353	+	0.342953i	$0.111427\pi$
$198$	−1.06748e9			−0.694546
$199$		−	2.75599e9i		−	1.75738i	−0.477393	−	0.878690i	$-0.658418\pi$
$199$		−	2.75599e9i		−	1.75738i	0.477393	−	0.878690i	$-0.341582\pi$
$200$	1.50953e9	−	1.50953e9i	0.943458	−	0.943458i
$201$	−4.81586e8	+	4.81586e8i	−0.295046	+	0.295046i
$202$	−2.42306e9	−	2.42306e9i	−1.45532	−	1.45532i
$203$	−1.63105e9	−	1.63105e9i	−0.960468	−	0.960468i
$204$	5.71674e9			3.30087
$205$		−	9.71099e8i		−	0.549855i
$206$	2.52736e9	+	2.52736e9i	1.40346	+	1.40346i
$207$			6.96488e8i			0.379343i
$208$	−1.83468e8	−	2.59236e8i	−0.0980185	−	0.138497i
$209$	9.74960e8			0.510977
$210$	−4.67754e9	+	4.67754e9i	−2.40514	+	2.40514i
$211$	1.56783e9			0.790986			0.395493	−	0.918469i	$-0.370574\pi$
$211$	1.56783e9			0.790986			0.395493	+	0.918469i	$0.370574\pi$
$212$			3.45112e9i			1.70851i
$213$	−7.88084e8	+	7.88084e8i	−0.382873	+	0.382873i
$214$	−3.98153e9	+	3.98153e9i	−1.89843	+	1.89843i
$215$	2.23867e9	+	2.23867e9i	1.04770	+	1.04770i
$216$	−3.92084e8	−	3.92084e8i	−0.180121	−	0.180121i
$217$	1.64914e9			0.743734
$218$			1.38546e9i			0.613435i
$219$	9.39014e8	+	9.39014e8i	0.408221	+	0.408221i
$220$		−	3.22858e9i		−	1.37823i
$221$	3.13143e9	−	2.21620e9i	1.31273	−	0.929054i
$222$	4.88162e9			2.00980
$223$	1.60070e8	−	1.60070e8i	0.0647278	−	0.0647278i	−0.674002	−	0.738730i	$-0.735426\pi$
$223$	1.60070e8	−	1.60070e8i	0.0647278	−	0.0647278i	0.738730	+	0.674002i	$0.235426\pi$
$224$	−2.85058e9			−1.13225
$225$		−	3.09408e9i		−	1.20726i
$226$	−2.23091e8	+	2.23091e8i	−0.0855161	+	0.0855161i
$227$	−9.32258e8	+	9.32258e8i	−0.351102	+	0.351102i	−0.860519	−	0.509418i	$-0.829861\pi$
$227$	−9.32258e8	+	9.32258e8i	−0.351102	+	0.351102i	0.509418	+	0.860519i	$0.329861\pi$
$228$	−3.57601e9	−	3.57601e9i	−1.32330	−	1.32330i
$229$	2.70819e9	+	2.70819e9i	0.984774	+	0.984774i	0.999886	−	0.0151117i	$-0.00481040\pi$
$229$	2.70819e9	+	2.70819e9i	0.984774	+	0.984774i	−0.0151117	+	0.999886i	$0.504810\pi$
$230$	−3.47491e9			−1.24175
$231$			2.13197e9i			0.748745i
$232$	−2.38675e9	−	2.38675e9i	−0.823863	−	0.823863i
$233$		−	7.96832e8i		−	0.270360i	−0.990821	−	0.135180i	$-0.956839\pi$
$233$		−	7.96832e8i		−	0.270360i	0.990821	−	0.135180i	$-0.0431613\pi$
$234$	3.66258e9	+	6.26838e8i	1.22159	+	0.209070i
$235$	−7.17223e8			−0.235170
$236$	−1.32215e9	+	1.32215e9i	−0.426218	+	0.426218i
$237$	−6.01677e9			−1.90709
$238$		−	8.23972e9i		−	2.56806i
$239$	3.81412e9	−	3.81412e9i	1.16897	−	1.16897i	0.186518	−	0.982452i	$-0.440280\pi$
$239$	3.81412e9	−	3.81412e9i	1.16897	−	1.16897i	0.982452	−	0.186518i	$-0.0597202\pi$
$240$	8.47895e8	−	8.47895e8i	0.255562	−	0.255562i
$241$	−2.16281e9	−	2.16281e9i	−0.641135	−	0.641135i	0.309699	−	0.950835i	$-0.399772\pi$
$241$	−2.16281e9	−	2.16281e9i	−0.641135	−	0.641135i	−0.950835	+	0.309699i	$0.899772\pi$
$242$	2.65091e9	+	2.65091e9i	0.772920	+	0.772920i
$243$	−4.41930e9			−1.26744
$244$		−	1.39466e9i		−	0.393468i
$245$	1.67740e7	+	1.67740e7i	0.00465557	+	0.00465557i
$246$			2.67807e9i			0.731275i
$247$	−3.34513e9	−	5.72506e8i	−0.898721	−	0.153813i
$248$	2.41322e9			0.637955
$249$	−3.47574e8	+	3.47574e8i	−0.0904169	+	0.0904169i
$250$	5.49230e9			1.40603
$251$			2.83257e9i			0.713651i	0.934171	+	0.356825i	$0.116141\pi$
$251$			2.83257e9i			0.713651i	−0.934171	+	0.356825i	$0.883859\pi$
$252$	3.42103e9	−	3.42103e9i	0.848310	−	0.848310i
$253$	−7.91914e8	+	7.91914e8i	−0.193284	+	0.193284i
$254$	−9.41504e8	−	9.41504e8i	−0.226197	−	0.226197i
$255$	1.02421e10	+	1.02421e10i	2.42231	+	2.42231i
$256$	−3.04950e9			−0.710017
$257$			2.21483e9i			0.507700i	0.967244	+	0.253850i	$0.0816970\pi$
$257$			2.21483e9i			0.507700i	−0.967244	+	0.253850i	$0.918303\pi$
$258$	−6.17372e9	−	6.17372e9i	−1.39337	−	1.39337i
$259$		−	4.26528e9i		−	0.947868i
$260$	−1.89585e9	+	1.10774e10i	−0.414869	+	2.42406i
$261$	−4.89210e9			−1.05423
$262$	6.28613e9	−	6.28613e9i	1.33407	−	1.33407i
$263$	3.78189e8			0.0790471			0.0395235	−	0.999219i	$-0.487416\pi$
$263$	3.78189e8			0.0790471			0.0395235	+	0.999219i	$0.487416\pi$
$264$			3.11976e9i			0.642253i
$265$	−6.18304e9	+	6.18304e9i	−1.25377	+	1.25377i
$266$	−5.15422e9	+	5.15422e9i	−1.02952	+	1.02952i
$267$	5.06946e9	+	5.06946e9i	0.997508	+	0.997508i
$268$	1.75729e9	+	1.75729e9i	0.340647	+	0.340647i
$269$	9.08136e8			0.173437			0.0867185	−	0.996233i	$-0.472362\pi$
$269$	9.08136e8			0.173437			0.0867185	+	0.996233i	$0.472362\pi$
$270$		−	4.00958e9i		−	0.754472i
$271$	−4.72790e9	−	4.72790e9i	−0.876579	−	0.876579i	0.116600	−	0.993179i	$-0.462801\pi$
$271$	−4.72790e9	−	4.72790e9i	−0.876579	−	0.876579i	−0.993179	+	0.116600i	$0.962801\pi$
$272$			1.49361e9i			0.272874i
$273$	1.25192e9	−	7.31488e9i	0.225385	−	1.31691i
$274$	4.95309e9			0.878767
$275$	3.51800e9	−	3.51800e9i	0.615127	−	0.615127i
$276$	5.80926e9			1.00112
$277$		−	1.59344e8i		−	0.0270655i	−0.999908	−	0.0135328i	$-0.995692\pi$
$277$		−	1.59344e8i		−	0.0270655i	0.999908	−	0.0135328i	$-0.00430775\pi$
$278$	−2.58494e8	+	2.58494e8i	−0.0432785	+	0.0432785i
$279$	2.47318e9	−	2.47318e9i	0.408168	−	0.408168i
$280$	5.98054e9	+	5.98054e9i	0.972990	+	0.972990i
$281$	−8.53572e9	−	8.53572e9i	−1.36904	−	1.36904i	−0.861818	−	0.507217i	$-0.830674\pi$
$281$	−8.53572e9	−	8.53572e9i	−1.36904	−	1.36904i	−0.507217	−	0.861818i	$-0.669326\pi$
$282$	1.97793e9			0.312763
$283$			1.14991e10i			1.79275i	0.443298	+	0.896374i	$0.353808\pi$
$283$			1.14991e10i			1.79275i	−0.443298	+	0.896374i	$0.646192\pi$
$284$	2.87569e9	+	2.87569e9i	0.442048	+	0.442048i
$285$		−	1.28136e10i		−	1.94219i
$286$	3.45168e9	+	4.87712e9i	0.515901	+	0.728953i
$287$	2.33994e9			0.344887
$288$	−4.27496e9	+	4.27496e9i	−0.621387	+	0.621387i
$289$	−1.10663e10			−1.58639
$290$		−	2.44077e10i		−	3.45091i
$291$	−5.57176e9	+	5.57176e9i	−0.776999	+	0.776999i
$292$	3.42643e9	−	3.42643e9i	0.471314	−	0.471314i
$293$	9.30877e9	+	9.30877e9i	1.26305	+	1.26305i	0.949605	+	0.313448i	$0.101484\pi$
$293$	9.30877e9	+	9.30877e9i	1.26305	+	1.26305i	0.313448	+	0.949605i	$0.398516\pi$
$294$	−4.62589e7	−	4.62589e7i	−0.00619164	−	0.00619164i
$295$	−4.73753e9			−0.625552
$296$		−	6.24147e9i		−	0.813056i
$297$	−9.13761e8	−	9.13761e8i	−0.117438	−	0.117438i
$298$			1.19384e10i			1.51385i
$299$	3.18211e9	−	2.25207e9i	0.398135	−	0.281772i
$300$	−2.58070e10			−3.18605
$301$	−5.39423e9	+	5.39423e9i	−0.657149	+	0.657149i
$302$	1.93882e9			0.233083
$303$			1.45148e10i			1.72203i
$304$	9.34303e8	−	9.34303e8i	0.109394	−	0.109394i
$305$	2.49868e9	−	2.49868e9i	0.288743	−	0.288743i
$306$	−1.23569e10	−	1.23569e10i	−1.40937	−	1.40937i
$307$	−3.72592e9	−	3.72592e9i	−0.419450	−	0.419450i	0.465564	−	0.885014i	$-0.345851\pi$
$307$	−3.72592e9	−	3.72592e9i	−0.419450	−	0.419450i	−0.885014	+	0.465564i	$0.845851\pi$
$308$	7.77950e9			0.864468
$309$		−	1.51397e10i		−	1.66067i
$310$	1.23392e10	+	1.23392e10i	1.33610	+	1.33610i
$311$		−	5.30331e9i		−	0.566898i	−0.958987	−	0.283449i	$-0.908521\pi$
$311$		−	5.30331e9i		−	0.566898i	0.958987	−	0.283449i	$-0.0914787\pi$
$312$	1.83196e9	−	1.07040e10i	0.193329	−	1.12961i
$313$	1.14891e10			1.19704			0.598521	−	0.801107i	$-0.295755\pi$
$313$	1.14891e10			1.19704			0.598521	+	0.801107i	$0.295755\pi$
$314$	−1.85492e10	+	1.85492e10i	−1.90812	+	1.90812i
$315$	1.22583e10			1.24505
$316$			2.19550e10i			2.20184i
$317$	3.70571e9	−	3.70571e9i	0.366973	−	0.366973i	−0.499399	−	0.866372i	$-0.666446\pi$
$317$	3.70571e9	−	3.70571e9i	0.366973	−	0.366973i	0.866372	+	0.499399i	$0.166446\pi$
$318$	1.70514e10	−	1.70514e10i	1.66744	−	1.66744i
$319$	−5.56238e9	−	5.56238e9i	−0.537152	−	0.537152i
$320$	−1.93187e10	−	1.93187e10i	−1.84238	−	1.84238i
$321$	2.38505e10			2.24635
$322$		−	8.37306e9i		−	0.778863i
$323$	1.12859e10	+	1.12859e10i	1.03687	+	1.03687i
$324$			1.98965e10i			1.80550i
$325$	−1.41362e10	+	1.00046e10i	−1.26707	+	0.896739i
$326$	4.53408e8			0.0401438
$327$	4.14966e9	−	4.14966e9i	0.362929	−	0.362929i
$328$	3.42408e9			0.295835
$329$		−	1.72820e9i		−	0.147506i
$330$	−1.59518e10	+	1.59518e10i	−1.34510	+	1.34510i
$331$	8.91506e8	−	8.91506e8i	0.0742698	−	0.0742698i	−0.668996	−	0.743266i	$-0.733276\pi$
$331$	8.91506e8	−	8.91506e8i	0.0742698	−	0.0742698i	0.743266	+	0.668996i	$0.233276\pi$
$332$	1.26829e9	+	1.26829e9i	0.104391	+	0.104391i
$333$	−6.39655e9	−	6.39655e9i	−0.520198	−	0.520198i
$334$	−1.35971e10			−1.09260
$335$			6.29674e9i			0.499961i
$336$	2.04307e9	+	2.04307e9i	0.160297	+	0.160297i
$337$		−	2.86060e8i		−	0.0221788i	−0.999939	−	0.0110894i	$-0.996470\pi$
$337$		−	2.86060e8i		−	0.0221788i	0.999939	−	0.0110894i	$-0.00352993\pi$
$338$	−8.97895e9	−	1.87605e10i	−0.687953	−	1.43740i
$339$	1.33638e9			0.101189
$340$	3.73732e10	−	3.73732e10i	2.79669	−	2.79669i
$341$	5.62406e9			0.415942
$342$			1.54594e10i			1.13002i
$343$	9.76700e9	−	9.76700e9i	0.705642	−	0.705642i
$344$	−7.89350e9	+	7.89350e9i	−0.563684	+	0.563684i
$345$	1.04079e10	+	1.04079e10i	0.734659	+	0.734659i
$346$	3.12530e9	+	3.12530e9i	0.218065	+	0.218065i
$347$	−2.29430e10			−1.58246			−0.791230	−	0.611519i	$-0.790559\pi$
$347$	−2.29430e10			−1.58246			−0.791230	+	0.611519i	$0.790559\pi$
$348$			4.08040e10i			2.78218i
$349$	−8.38687e9	−	8.38687e9i	−0.565325	−	0.565325i	0.365490	−	0.930815i	$-0.380901\pi$
$349$	−8.38687e9	−	8.38687e9i	−0.565325	−	0.565325i	−0.930815	+	0.365490i	$0.880901\pi$
$350$			3.71965e10i			2.47873i
$351$	2.59858e9	+	3.67172e9i	0.171202	+	0.241903i
$352$	−9.72135e9			−0.633222
$353$	1.24878e10	−	1.24878e10i	0.804245	−	0.804245i	−0.179511	−	0.983756i	$-0.557452\pi$
$353$	1.24878e10	−	1.24878e10i	0.804245	−	0.804245i	0.983756	+	0.179511i	$0.0574516\pi$
$354$	1.30650e10			0.831948
$355$			1.03042e10i			0.648786i
$356$	1.84983e10	−	1.84983e10i	1.15168	−	1.15168i
$357$	−2.46792e10	+	2.46792e10i	−1.51935	+	1.51935i
$358$	−1.72088e10	−	1.72088e10i	−1.04766	−	1.04766i
$359$	−1.89252e10	−	1.89252e10i	−1.13936	−	1.13936i	−0.988564	−	0.150799i	$-0.951815\pi$
$359$	−1.89252e10	−	1.89252e10i	−1.13936	−	1.13936i	−0.150799	−	0.988564i	$-0.548185\pi$
$360$	1.79378e10			1.06797
$361$			2.86415e9i			0.168642i
$362$	−3.39385e9	−	3.39385e9i	−0.197632	−	0.197632i
$363$		−	1.58798e10i		−	0.914572i
$364$	−2.66918e10	−	4.56820e9i	−1.52045	−	0.260219i
$365$	1.22776e10			0.691739
$366$	−6.89077e9	+	6.89077e9i	−0.384011	+	0.384011i
$367$	6.23990e9			0.343964			0.171982	−	0.985100i	$-0.444983\pi$
$367$	6.23990e9			0.343964			0.171982	+	0.985100i	$0.444983\pi$
$368$			1.51778e9i			0.0827595i
$369$	3.50916e9	−	3.50916e9i	0.189277	−	0.189277i
$370$	3.19136e10	−	3.19136e10i	1.70282	−	1.70282i
$371$	−1.48985e10	−	1.48985e10i	−0.786406	−	0.786406i
$372$	−2.06282e10	−	2.06282e10i	−1.07719	−	1.07719i
$373$	−2.96446e9			−0.153148			−0.0765739	−	0.997064i	$-0.524398\pi$
$373$	−2.96446e9			−0.153148			−0.0765739	+	0.997064i	$0.524398\pi$
$374$		−	2.81000e10i		−	1.43621i
$375$	−1.64503e10	−	1.64503e10i	−0.831855	−	0.831855i
$376$		−	2.52892e9i		−	0.126527i
$377$	1.58185e10	+	2.23510e10i	0.783066	+	1.10645i
$378$	9.66137e9			0.473229
$379$	1.71245e10	−	1.71245e10i	0.829970	−	0.829970i	−0.157542	−	0.987512i	$-0.550357\pi$
$379$	1.71245e10	−	1.71245e10i	0.829970	−	0.829970i	0.987512	+	0.157542i	$0.0503571\pi$
$380$	−4.67564e10			−2.24237
$381$			5.63989e9i			0.267652i
$382$	−4.60211e9	+	4.60211e9i	−0.216124	+	0.216124i
$383$	1.46047e10	−	1.46047e10i	0.678732	−	0.678732i	−0.280982	−	0.959713i	$-0.590660\pi$
$383$	1.46047e10	−	1.46047e10i	0.678732	−	0.678732i	0.959713	+	0.280982i	$0.0906600\pi$
$384$	3.01138e10	+	3.01138e10i	1.38497	+	1.38497i
$385$	1.39378e10	+	1.39378e10i	0.634382	+	0.634382i
$386$	−5.52455e10			−2.48856
$387$			1.61792e10i			0.721297i
$388$	2.03312e10	+	2.03312e10i	0.897089	+	0.897089i
$389$			2.88195e10i			1.25860i	0.777162	+	0.629301i	$0.216659\pi$
$389$			2.88195e10i			1.25860i	−0.777162	+	0.629301i	$0.783341\pi$
$390$	6.40985e10	−	4.53643e10i	2.77070	−	1.96090i
$391$	−1.83340e10			−0.784423
$392$	−5.91450e7	+	5.91450e7i	−0.00250480	+	0.00250480i
$393$	−3.76558e10			−1.57856
$394$			3.23893e10i			1.34406i
$395$	−3.93347e10	+	3.93347e10i	−1.61580	+	1.61580i
$396$	1.16668e10	−	1.16668e10i	0.474427	−	0.474427i
$397$	1.55229e10	+	1.55229e10i	0.624902	+	0.624902i	0.946781	−	0.321879i	$-0.104314\pi$
$397$	1.55229e10	+	1.55229e10i	0.624902	+	0.624902i	−0.321879	+	0.946781i	$0.604314\pi$
$398$	4.96875e10	+	4.96875e10i	1.98023	+	1.98023i
$399$	3.08753e10			1.21820
$400$		−	6.74258e9i		−	0.263382i
$401$	−2.81886e10	−	2.81886e10i	−1.09017	−	1.09017i	−0.995509	−	0.0946646i	$-0.969822\pi$
$401$	−2.81886e10	−	2.81886e10i	−1.09017	−	1.09017i	−0.0946646	−	0.995509i	$-0.530178\pi$
$402$		−	1.73649e10i		−	0.664919i
$403$	−1.92964e10	−	3.30251e9i	−0.731570	−	0.125205i
$404$	5.29642e10			1.98818
$405$	−3.56466e10	+	3.56466e10i	−1.32495	+	1.32495i
$406$	5.88121e10			2.16452
$407$		−	1.45459e10i		−	0.530106i
$408$	−3.61136e10	+	3.61136e10i	−1.30326	+	1.30326i
$409$	−1.87784e10	+	1.87784e10i	−0.671066	+	0.671066i	−0.957962	−	0.286896i	$-0.907377\pi$
$409$	−1.87784e10	+	1.87784e10i	−0.671066	+	0.671066i	0.286896	+	0.957962i	$0.407377\pi$
$410$	1.75079e10	+	1.75079e10i	0.619581	+	0.619581i
$411$	−1.48352e10	−	1.48352e10i	−0.519909	−	0.519909i
$412$	−5.52441e10			−1.91733
$413$		−	1.14154e10i		−	0.392367i
$414$	−1.25569e10	−	1.25569e10i	−0.427446	−	0.427446i
$415$			4.54453e9i			0.153213i
$416$	3.33543e10	+	5.70847e9i	1.11373	+	0.190610i
$417$	1.54846e9			0.0512101
$418$	−1.75775e10	+	1.75775e10i	−0.575773	+	0.575773i
$419$	5.34767e10			1.73503			0.867517	−	0.497407i	$-0.165714\pi$
$419$	5.34767e10			1.73503			0.867517	+	0.497407i	$0.165714\pi$
$420$		−	1.02244e11i		−	3.28578i
$421$	2.38177e10	−	2.38177e10i	0.758180	−	0.758180i	−0.217811	−	0.975991i	$-0.569892\pi$
$421$	2.38177e10	−	2.38177e10i	0.758180	−	0.758180i	0.975991	+	0.217811i	$0.0698916\pi$
$422$	−2.82663e10	+	2.82663e10i	−0.891289	+	0.891289i
$423$	−2.59175e9	−	2.59175e9i	−0.0809528	−	0.0809528i
$424$	−2.18013e10	−	2.18013e10i	−0.674558	−	0.674558i
$425$	8.14470e10			2.49643
$426$		−	2.84166e10i		−	0.862847i
$427$	6.02075e9	+	6.02075e9i	0.181109	+	0.181109i
$428$		−	8.70298e10i		−	2.59354i
$429$	4.26942e9	−	2.49460e10i	0.126049	−	0.736498i
$430$	−8.07214e10			−2.36110
$431$	3.39333e10	−	3.39333e10i	0.983370	−	0.983370i	−0.0164943	−	0.999864i	$-0.505251\pi$
$431$	3.39333e10	−	3.39333e10i	0.983370	−	0.983370i	0.999864	+	0.0164943i	$0.00525054\pi$
$432$	−1.75131e9			−0.0502838
$433$		−	6.21384e10i		−	1.76770i	−0.467771	−	0.883849i	$-0.654943\pi$
$433$		−	6.21384e10i		−	1.76770i	0.467771	−	0.883849i	$-0.345057\pi$
$434$	−2.97321e10	+	2.97321e10i	−0.838045	+	0.838045i
$435$	−7.31046e10	+	7.31046e10i	−2.04168	+	2.04168i
$436$	−1.51420e10	−	1.51420e10i	−0.419022	−	0.419022i
$437$	1.14685e10	+	1.14685e10i	0.314472	+	0.314472i
$438$	−3.38588e10			−0.919973
$439$			7.19465e10i			1.93710i	0.248822	+	0.968549i	$0.419957\pi$
$439$			7.19465e10i			1.93710i	−0.248822	+	0.968549i	$0.580043\pi$
$440$	2.03955e10	+	2.03955e10i	0.544155	+	0.544155i
$441$			1.21229e8i			0.00320518i
$442$	−1.65006e10	+	9.64121e10i	−0.432325	+	2.52605i
$443$	−2.02774e10			−0.526499			−0.263249	−	0.964728i	$-0.584794\pi$
$443$	−2.02774e10			−0.526499			−0.263249	+	0.964728i	$0.584794\pi$
$444$	−5.33522e10	+	5.33522e10i	−1.37284	+	1.37284i
$445$	6.62832e10			1.69030
$446$			5.77178e9i			0.145871i
$447$	3.57574e10	−	3.57574e10i	0.895644	−	0.895644i
$448$	4.65500e10	−	4.65500e10i	1.15560	−	1.15560i
$449$	7.54656e9	+	7.54656e9i	0.185679	+	0.185679i	0.793825	−	0.608146i	$-0.208086\pi$
$449$	7.54656e9	+	7.54656e9i	0.185679	+	0.185679i	−0.608146	+	0.793825i	$0.708086\pi$
$450$	5.57828e10	+	5.57828e10i	1.36035	+	1.36035i
$451$	7.97990e9			0.192882
$452$		−	4.87641e9i		−	0.116828i
$453$	−5.80707e9	−	5.80707e9i	−0.137900	−	0.137900i
$454$		−	3.36152e10i		−	0.791247i
$455$	−3.96367e10	−	5.60055e10i	−0.924808	−	1.30673i
$456$	4.51806e10			1.04494
$457$	−7.97853e9	+	7.97853e9i	−0.182919	+	0.182919i	−0.792626	−	0.609708i	$-0.791287\pi$
$457$	−7.97853e9	+	7.97853e9i	−0.182919	+	0.182919i	0.609708	+	0.792626i	$0.291287\pi$
$458$	−9.76513e10			−2.21930
$459$		−	2.11549e10i		−	0.476608i
$460$	3.79780e10	−	3.79780e10i	0.848206	−	0.848206i
$461$	−3.37578e10	+	3.37578e10i	−0.747430	+	0.747430i	−0.973996	−	0.226565i	$-0.927250\pi$
$461$	−3.37578e10	+	3.37578e10i	−0.747430	+	0.747430i	0.226565	+	0.973996i	$0.427250\pi$
$462$	−3.84371e10	−	3.84371e10i	−0.843691	−	0.843691i
$463$	2.56807e9	+	2.56807e9i	0.0558835	+	0.0558835i	0.734496	−	0.678613i	$-0.237419\pi$
$463$	2.56807e9	+	2.56807e9i	0.0558835	+	0.0558835i	−0.678613	+	0.734496i	$0.737419\pi$
$464$	−1.06608e10			−0.229995
$465$		−	7.39153e10i		−	1.58097i
$466$	1.43660e10	+	1.43660e10i	0.304644	+	0.304644i
$467$			6.24287e10i			1.31255i	0.754521	+	0.656276i	$0.227869\pi$
$467$			6.24287e10i			1.31255i	−0.754521	+	0.656276i	$0.772131\pi$
$468$	−4.68800e10	+	3.31783e10i	−0.977246	+	0.691625i
$469$	−1.51725e10			−0.313592
$470$	1.29307e10	−	1.29307e10i	0.264992	−	0.264992i
$471$	1.11115e11			2.25782
$472$		−	1.67045e10i		−	0.336561i
$473$	−1.83960e10	+	1.83960e10i	−0.367518	+	0.367518i
$474$	1.08476e11	−	1.08476e11i	2.14892	−	2.14892i
$475$	−5.09478e10	−	5.09478e10i	−1.00081	−	1.00081i
$476$	9.00536e10	+	9.00536e10i	1.75418	+	1.75418i
$477$	−4.46860e10			−0.863173
$478$			1.37529e11i			2.63441i
$479$	−5.07009e10	−	5.07009e10i	−0.963104	−	0.963104i	0.0362388	−	0.999343i	$-0.488462\pi$
$479$	−5.07009e10	−	5.07009e10i	−0.963104	−	0.963104i	−0.999343	+	0.0362388i	$0.988462\pi$
$480$			1.27765e11i			2.40683i
$481$	−8.54149e9	+	4.99075e10i	−0.159571	+	0.932365i
$482$	7.79861e10			1.44487
$483$	−2.50786e10	+	2.50786e10i	−0.460802	+	0.460802i
$484$	−5.79448e10			−1.05592
$485$			7.28508e10i			1.31664i
$486$	7.96752e10	−	7.96752e10i	1.42816	−	1.42816i
$487$	−1.81769e10	+	1.81769e10i	−0.323150	+	0.323150i	−0.849974	−	0.526824i	$-0.823383\pi$
$487$	−1.81769e10	+	1.81769e10i	−0.323150	+	0.323150i	0.526824	+	0.849974i	$0.323383\pi$
$488$	8.81030e9	+	8.81030e9i	0.155350	+	0.155350i
$489$	−1.35802e9	−	1.35802e9i	−0.0237505	−	0.0237505i
$490$	−6.04835e8			−0.0104919
$491$		−	1.13568e11i		−	1.95402i	−0.213184	−	0.977012i	$-0.568383\pi$
$491$		−	1.13568e11i		−	1.95402i	0.213184	−	0.977012i	$-0.431617\pi$
$492$	−2.92691e10	−	2.92691e10i	−0.499516	−	0.499516i
$493$		−	1.28777e11i		−	2.17998i
$494$	7.06307e10	−	4.99873e10i	1.18600	−	0.839367i
$495$	4.18044e10			0.696308
$496$	5.38953e9	−	5.38953e9i	0.0890480	−	0.0890480i
$497$	−2.48288e10			−0.406939
$498$		−	1.25328e10i		−	0.203765i
$499$	5.85848e9	−	5.85848e9i	0.0944894	−	0.0944894i	−0.658282	−	0.752771i	$-0.728717\pi$
$499$	5.85848e9	−	5.85848e9i	0.0944894	−	0.0944894i	0.752771	+	0.658282i	$0.228717\pi$
$500$	−6.00265e10	+	6.00265e10i	−0.960423	+	0.960423i
$501$	4.07253e10	+	4.07253e10i	0.646417	+	0.646417i
$502$	−5.10682e10	−	5.10682e10i	−0.804147	−	0.804147i
$503$	8.18123e10			1.27805			0.639023	−	0.769188i	$-0.279339\pi$
$503$	8.18123e10			1.27805			0.639023	+	0.769188i	$0.279339\pi$
$504$			4.32224e10i			0.669865i
$505$	9.48908e10	+	9.48908e10i	1.45901	+	1.45901i
$506$		−	2.85547e10i		−	0.435588i
$507$	−2.92971e10	+	8.30836e10i	−0.443397	+	1.25743i
$508$	2.05798e10			0.309019
$509$	−6.63020e10	+	6.63020e10i	−0.987770	+	0.987770i	−0.999926	−	0.0121563i	$-0.996130\pi$
$509$	−6.63020e10	+	6.63020e10i	−0.987770	+	0.987770i	0.0121563	+	0.999926i	$0.496130\pi$
$510$	−3.69309e11			−5.45895
$511$			2.95838e10i			0.433881i
$512$	−1.64027e10	+	1.64027e10i	−0.238690	+	0.238690i
$513$	−1.32331e10	+	1.32331e10i	−0.191070	+	0.191070i
$514$	−3.99309e10	−	3.99309e10i	−0.572080	−	0.572080i
$515$	−9.89755e10	−	9.89755e10i	−1.40702	−	1.40702i
$516$	1.34948e11			1.90356
$517$		−	5.89370e9i		−	0.0824946i
$518$	7.68983e10	+	7.68983e10i	1.06806	+	1.06806i
$519$		−	1.87215e10i		−	0.258030i
$520$	−5.80012e10	−	8.19541e10i	−0.793275	−	1.12088i
$521$	−8.77167e9			−0.119051			−0.0595253	−	0.998227i	$-0.518959\pi$
$521$	−8.77167e9			−0.119051			−0.0595253	+	0.998227i	$0.518959\pi$
$522$	8.81993e10	−	8.81993e10i	1.18791	−	1.18791i
$523$	−8.20061e10			−1.09607			−0.548037	−	0.836454i	$-0.684625\pi$
$523$	−8.20061e10			−1.09607			−0.548037	+	0.836454i	$0.684625\pi$
$524$			1.37405e11i			1.82254i
$525$	1.11409e11	−	1.11409e11i	1.46650	−	1.46650i
$526$	−6.81834e9	+	6.81834e9i	−0.0890708	+	0.0890708i
$527$	6.51027e10	+	6.51027e10i	0.844028	+	0.844028i
$528$	6.96748e9	+	6.96748e9i	0.0896479	+	0.0896479i
$529$	5.96803e10			0.762093
$530$		−	2.22947e11i		−	2.82552i
$531$	−1.71195e10	−	1.71195e10i	−0.215334	−	0.215334i
$532$		−	1.12663e11i		−	1.40648i
$533$	−2.73794e10	−	4.68588e9i	−0.339246	−	0.0580607i
$534$	−1.82794e11			−2.24800
$535$	1.55923e11	−	1.55923e11i	1.90325	−	1.90325i
$536$	−2.22022e10			−0.268990
$537$			1.03086e11i			1.23966i
$538$	−1.63727e10	+	1.63727e10i	−0.195430	+	0.195430i
$539$	−1.37839e8	+	1.37839e8i	−0.00163311	+	0.00163311i
$540$	4.38215e10	+	4.38215e10i	0.515361	+	0.515361i
$541$	6.06619e10	+	6.06619e10i	0.708153	+	0.708153i	0.966147	−	0.257994i	$-0.0830614\pi$
$541$	6.06619e10	+	6.06619e10i	0.708153	+	0.708153i	−0.257994	+	0.966147i	$0.583061\pi$
$542$	1.70478e11			1.97547
$543$			2.03302e10i			0.233852i
$544$	−1.12532e11	−	1.12532e11i	−1.28493	−	1.28493i
$545$		−	5.42569e10i		−	0.614991i
$546$	1.09309e11	+	1.54450e11i	1.22994	+	1.73787i
$547$	1.54001e10			0.172018			0.0860090	−	0.996294i	$-0.472589\pi$
$547$	1.54001e10			0.172018			0.0860090	+	0.996294i	$0.472589\pi$
$548$	−5.41333e10	+	5.41333e10i	−0.600264	+	0.600264i
$549$	1.80584e10			0.198788
$550$			1.26851e11i			1.38626i
$551$	−8.05546e10	+	8.05546e10i	−0.873944	+	0.873944i
$552$	−3.66980e10	+	3.66980e10i	−0.395263	+	0.395263i
$553$	−9.47798e10	−	9.47798e10i	−1.01348	−	1.01348i
$554$	2.87280e9	+	2.87280e9i	0.0304976	+	0.0304976i
$555$	−1.91172e11			−2.01490
$556$		−	5.65027e9i		−	0.0591249i
$557$	4.93168e10	+	4.93168e10i	0.512359	+	0.512359i	0.915248	−	0.402890i	$-0.131994\pi$
$557$	4.93168e10	+	4.93168e10i	0.512359	+	0.512359i	−0.402890	+	0.915248i	$0.631994\pi$
$558$			8.91774e10i			0.919852i
$559$	7.39196e10	−	5.23150e10i	0.757029	−	0.535771i
$560$	2.67131e10			0.271627
$561$	−8.41636e10	+	8.41636e10i	−0.849714	+	0.849714i
$562$	3.07779e11			3.08528
$563$			5.82242e10i			0.579522i	0.957099	+	0.289761i	$0.0935758\pi$
$563$			5.82242e10i			0.579522i	−0.957099	+	0.289761i	$0.906424\pi$
$564$	−2.16172e10	+	2.16172e10i	−0.213641	+	0.213641i
$565$	8.73659e9	−	8.73659e9i	0.0857330	−	0.0857330i
$566$	−2.07317e11	−	2.07317e11i	−2.02008	−	2.02008i
$567$	−8.58932e10	−	8.58932e10i	−0.831049	−	0.831049i
$568$	−3.63325e10			−0.349061
$569$			1.06030e11i			1.01154i	0.862669	+	0.505768i	$0.168791\pi$
$569$			1.06030e11i			1.01154i	−0.862669	+	0.505768i	$0.831209\pi$
$570$	2.31015e11	+	2.31015e11i	2.18847	+	2.18847i
$571$			9.54463e10i			0.897872i	0.893564	+	0.448936i	$0.148197\pi$
$571$			9.54463e10i			0.897872i	−0.893564	+	0.448936i	$0.851803\pi$
$572$	−9.10271e10	−	1.55790e10i	−0.850328	−	0.145531i
$573$	2.75680e10			0.255733
$574$	−4.21865e10	+	4.21865e10i	−0.388621	+	0.388621i
$575$	8.27650e10			0.757139
$576$		−	1.39620e11i		−	1.26841i
$577$	−8.36851e9	+	8.36851e9i	−0.0754997	+	0.0754997i	−0.743848	−	0.668349i	$-0.767001\pi$
$577$	−8.36851e9	+	8.36851e9i	−0.0754997	+	0.0754997i	0.668349	+	0.743848i	$0.267001\pi$
$578$	1.99513e11	−	1.99513e11i	1.78756	−	1.78756i
$579$	1.65468e11	+	1.65468e11i	1.47232	+	1.47232i
$580$	2.66756e11	+	2.66756e11i	2.35723	+	2.35723i
$581$	−1.09504e10			−0.0961003
$582$		−	2.00906e11i		−	1.75106i
$583$	−5.08084e10	−	5.08084e10i	−0.439807	−	0.439807i
$584$			4.32907e10i			0.372171i
$585$	−1.43433e11	−	2.45480e10i	−1.22469	−	0.209600i
$586$	−3.35654e11			−2.84643
$587$	−1.12403e11	+	1.12403e11i	−0.946731	+	0.946731i	−0.998651	−	0.0519204i	$-0.983466\pi$
$587$	−1.12403e11	+	1.12403e11i	−0.946731	+	0.946731i	0.0519204	+	0.998651i	$0.483466\pi$
$588$	1.01115e9			0.00845871
$589$		−	8.14479e10i		−	0.676735i
$590$	8.54125e10	−	8.54125e10i	0.704877	−	0.704877i
$591$	9.70109e10	−	9.70109e10i	0.795189	−	0.795189i
$592$	−1.39393e10	−	1.39393e10i	−0.113489	−	0.113489i
$593$	−8.34367e10	−	8.34367e10i	−0.674743	−	0.674743i	0.284063	−	0.958806i	$-0.408318\pi$
$593$	−8.34367e10	−	8.34367e10i	−0.674743	−	0.674743i	−0.958806	+	0.284063i	$0.908318\pi$
$594$	3.29482e10			0.264659
$595$			3.22681e11i			2.57457i
$596$	−1.30477e11	−	1.30477e11i	−1.03407	−	1.03407i
$597$		−	2.97643e11i		−	2.34314i
$598$	−1.67676e10	+	9.79723e10i	−0.131119	+	0.766123i
$599$	2.58135e10			0.200512			0.100256	−	0.994962i	$-0.468034\pi$
$599$	2.58135e10			0.200512			0.100256	+	0.994962i	$0.468034\pi$
$600$	1.63027e11	−	1.63027e11i	1.25793	−	1.25793i
$601$	−1.14049e11			−0.874162			−0.437081	−	0.899422i	$-0.643988\pi$
$601$	−1.14049e11			−0.874162			−0.437081	+	0.899422i	$0.643988\pi$
$602$		−	1.94504e11i		−	1.48096i
$603$	−2.27538e10	+	2.27538e10i	−0.172102	+	0.172102i
$604$	−2.11898e10	+	2.11898e10i	−0.159213	+	0.159213i
$605$	−1.03814e11	−	1.03814e11i	−0.774880	−	0.774880i
$606$	−2.61687e11	−	2.61687e11i	−1.94040	−	1.94040i
$607$	−1.31365e9			−0.00967668			−0.00483834	−	0.999988i	$-0.501540\pi$
$607$	−1.31365e9			−0.00967668			−0.00483834	+	0.999988i	$0.501540\pi$
$608$			1.40785e11i			1.03025i
$609$	−1.76151e11	−	1.76151e11i	−1.28061	−	1.28061i
$610$			9.00969e10i			0.650715i
$611$	−3.46084e9	+	2.02215e10i	−0.0248323	+	0.145094i
$612$	2.70103e11			1.92541
$613$	6.67181e10	−	6.67181e10i	0.472500	−	0.472500i	−0.430223	−	0.902723i	$-0.641565\pi$
$613$	6.67181e10	−	6.67181e10i	0.472500	−	0.472500i	0.902723	+	0.430223i	$0.141565\pi$
$614$	1.34349e11			0.945278
$615$		−	1.04877e11i		−	0.733130i
$616$	−4.91444e10	+	4.91444e10i	−0.341312	+	0.341312i
$617$	−1.24710e11	+	1.24710e11i	−0.860519	+	0.860519i	−0.991398	−	0.130880i	$-0.958220\pi$
$617$	−1.24710e11	+	1.24710e11i	−0.860519	+	0.860519i	0.130880	+	0.991398i	$0.458220\pi$
$618$	2.72951e11	+	2.72951e11i	1.87125	+	1.87125i
$619$	5.75160e10	+	5.75160e10i	0.391766	+	0.391766i	0.875316	−	0.483551i	$-0.160653\pi$
$619$	5.75160e10	+	5.75160e10i	0.391766	+	0.391766i	−0.483551	+	0.875316i	$0.660653\pi$
$620$	−2.69714e11			−1.82531
$621$		−	2.14973e10i		−	0.144550i
$622$	9.56128e10	+	9.56128e10i	0.638785	+	0.638785i
$623$			1.59714e11i			1.06021i
$624$	−1.98143e10	−	2.79971e10i	−0.130690	−	0.184661i
$625$	2.17730e10			0.142692
$626$	−2.07136e11	+	2.07136e11i	−1.34884	+	1.34884i
$627$	1.05294e11			0.681294
$628$		−	4.05456e11i		−	2.60678i
$629$	1.68380e11	−	1.68380e11i	1.07569	−	1.07569i
$630$	−2.21003e11	+	2.21003e11i	−1.40293	+	1.40293i
$631$	1.45885e11	+	1.45885e11i	0.920223	+	0.920223i	0.997045	−	0.0768214i	$-0.0244771\pi$
$631$	1.45885e11	+	1.45885e11i	0.920223	+	0.920223i	−0.0768214	+	0.997045i	$0.524477\pi$
$632$	−1.38693e11	−	1.38693e11i	−0.869336	−	0.869336i
$633$	1.69323e11			1.05463
$634$			1.33620e11i			0.827015i
$635$	3.68708e10	+	3.68708e10i	0.226771	+	0.226771i
$636$			3.72716e11i			2.27798i
$637$	5.53871e8	−	3.91990e8i	0.00336396	−	0.00238077i
$638$	2.00567e11			1.21053
$639$	−3.72352e10	+	3.72352e10i	−0.223332	+	0.223332i
$640$	3.93738e11			2.34686
$641$		−	5.42742e10i		−	0.321486i	−0.986996	−	0.160743i	$-0.948611\pi$
$641$		−	5.42742e10i		−	0.321486i	0.986996	−	0.160743i	$-0.0513890\pi$
$642$	−4.29999e11	+	4.29999e11i	−2.53121	+	2.53121i
$643$	1.17827e11	−	1.17827e11i	0.689287	−	0.689287i	−0.272787	−	0.962074i	$-0.587946\pi$
$643$	1.17827e11	−	1.17827e11i	0.689287	−	0.689287i	0.962074	+	0.272787i	$0.0879456\pi$
$644$	9.15109e10	+	9.15109e10i	0.532022	+	0.532022i
$645$	2.41773e11	+	2.41773e11i	1.39691	+	1.39691i
$646$	−4.06945e11			−2.33671
$647$		−	2.59864e11i		−	1.48296i	−0.670977	−	0.741479i	$-0.734125\pi$
$647$		−	2.59864e11i		−	1.48296i	0.670977	−	0.741479i	$-0.265875\pi$
$648$	−1.25689e11	−	1.25689e11i	−0.712851	−	0.712851i
$649$		−	3.89301e10i		−	0.219435i
$650$	7.44884e10	−	4.35232e11i	0.417287	−	2.43819i
$651$	1.78104e11			0.991632
$652$	−4.95539e9	+	4.95539e9i	−0.0274212	+	0.0274212i
$653$	−2.92048e11			−1.60621			−0.803105	−	0.595838i	$-0.796820\pi$
$653$	−2.92048e11			−1.60621			−0.803105	+	0.595838i	$0.796820\pi$
$654$			1.49628e11i			0.817902i
$655$	−2.46175e11	+	2.46175e11i	−1.33745	+	1.33745i
$656$	7.64713e9	−	7.64713e9i	0.0412936	−	0.0412936i
$657$	4.43663e10	+	4.43663e10i	0.238117	+	0.238117i
$658$	3.11576e10	+	3.11576e10i	0.166211	+	0.166211i
$659$	1.68819e11			0.895115			0.447557	−	0.894255i	$-0.352294\pi$
$659$	1.68819e11			0.895115			0.447557	+	0.894255i	$0.352294\pi$
$660$		−	3.48682e11i		−	1.83761i
$661$	−1.99672e11	−	1.99672e11i	−1.04595	−	1.04595i	−0.998892	−	0.0470593i	$-0.985015\pi$
$661$	−1.99672e11	−	1.99672e11i	−1.04595	−	1.04595i	−0.0470593	−	0.998892i	$-0.514985\pi$
$662$			3.21458e10i			0.167375i
$663$	3.38190e11	−	2.39347e11i	1.75028	−	1.23872i
$664$	−1.60239e10			−0.0824323
$665$	2.01847e11	−	2.01847e11i	1.03214	−	1.03214i
$666$	2.30646e11			1.17233
$667$		−	1.30861e11i		−	0.661162i
$668$	1.48605e11	−	1.48605e11i	0.746325	−	0.746325i
$669$	1.72873e10	−	1.72873e10i	0.0863025	−	0.0863025i
$670$	−1.13523e11	−	1.13523e11i	−0.563360	−	0.563360i
$671$	2.05326e10	+	2.05326e10i	0.101287	+	0.101287i
$672$	−3.07859e11			−1.50964
$673$			1.11564e11i			0.543828i	0.962321	+	0.271914i	$0.0876567\pi$
$673$			1.11564e11i			0.543828i	−0.962321	+	0.271914i	$0.912343\pi$
$674$	5.15735e9	+	5.15735e9i	0.0249912	+	0.0249912i
$675$			9.54995e10i			0.460030i
$676$	3.03170e11	+	1.06904e11i	1.45177	+	0.511926i
$677$	−2.36899e10			−0.112774			−0.0563869	−	0.998409i	$-0.517958\pi$
$677$	−2.36899e10			−0.112774			−0.0563869	+	0.998409i	$0.517958\pi$
$678$	−2.40935e10	+	2.40935e10i	−0.114020	+	0.114020i
$679$	−1.75539e11			−0.825840
$680$			4.72186e11i			2.20840i
$681$	−1.00683e11	+	1.00683e11i	−0.468129	+	0.468129i
$682$	−1.01396e11	+	1.01396e11i	−0.468686	+	0.468686i
$683$	−1.10040e11	−	1.10040e11i	−0.505673	−	0.505673i	0.407522	−	0.913195i	$-0.366393\pi$
$683$	−1.10040e11	−	1.10040e11i	−0.505673	−	0.505673i	−0.913195	+	0.407522i	$0.866393\pi$
$684$	−1.68958e11	−	1.68958e11i	−0.771890	−	0.771890i
$685$	−1.93971e11			−0.880996
$686$			3.52177e11i			1.59025i
$687$	2.92480e11	+	2.92480e11i	1.31301	+	1.31301i
$688$			3.52577e10i			0.157362i
$689$	1.44491e11	+	2.04161e11i	0.641155	+	0.905933i
$690$	−3.75286e11			−1.65564
$691$	9.26218e10	−	9.26218e10i	0.406257	−	0.406257i	−0.474174	−	0.880431i	$-0.657253\pi$
$691$	9.26218e10	−	9.26218e10i	0.406257	−	0.406257i	0.880431	+	0.474174i	$0.157253\pi$
$692$	−6.83140e10			−0.297910
$693$			1.00731e11i			0.436747i
$694$	4.13638e11	−	4.13638e11i	1.78313	−	1.78313i
$695$	1.01231e10	−	1.01231e10i	0.0433883	−	0.0433883i
$696$	−2.57766e11	−	2.57766e11i	−1.09847	−	1.09847i
$697$	9.23733e10	+	9.23733e10i	0.391395	+	0.391395i
$698$	3.02412e11			1.27402
$699$		−	8.60567e10i		−	0.360476i
$700$	−4.06528e11	−	4.06528e11i	−1.69316	−	1.69316i
$701$			9.17227e10i			0.379844i	0.981799	+	0.189922i	$0.0608234\pi$
$701$			9.17227e10i			0.379844i	−0.981799	+	0.189922i	$0.939177\pi$
$702$	−1.13047e11	−	1.93475e10i	−0.465489	−	0.0796668i
$703$	−2.10654e11			−0.862480
$704$	1.58750e11	−	1.58750e11i	0.646282	−	0.646282i
$705$	−7.74590e10			−0.313556
$706$			4.50284e11i			1.81246i
$707$	−2.28646e11	+	2.28646e11i	−0.915138	+	0.915138i
$708$	−1.42790e11	+	1.42790e11i	−0.568283	+	0.568283i
$709$	−7.57204e10	−	7.57204e10i	−0.299659	−	0.299659i	0.541221	−	0.840880i	$-0.317962\pi$
$709$	−7.57204e10	−	7.57204e10i	−0.299659	−	0.299659i	−0.840880	+	0.541221i	$0.817962\pi$
$710$	−1.85774e11	−	1.85774e11i	−0.731056	−	0.731056i
$711$	−2.84279e11			−1.11241
$712$			2.33713e11i			0.909419i
$713$	6.61563e10	+	6.61563e10i	0.255984	+	0.255984i
$714$		−	8.89878e11i		−	3.42403i
$715$	−1.35173e11	−	1.90996e11i	−0.517209	−	0.730802i
$716$	3.76158e11			1.43126
$717$	4.11920e11	−	4.11920e11i	1.55860	−	1.55860i
$718$	6.82401e11			2.56769
$719$			1.51493e11i			0.566861i	0.958993	+	0.283430i	$0.0914725\pi$
$719$			1.51493e11i			0.566861i	−0.958993	+	0.283430i	$0.908528\pi$
$720$	4.00611e10	−	4.00611e10i	0.149071	−	0.149071i
$721$	2.38489e11	−	2.38489e11i	0.882526	−	0.882526i
$722$	−5.16375e10	−	5.16375e10i	−0.190028	−	0.190028i
$723$	−2.33580e11	−	2.33580e11i	−0.854836	−	0.854836i
$724$	7.41841e10			0.269995
$725$			5.81338e11i			2.10415i
$726$	2.86295e11	+	2.86295e11i	1.03055	+	1.03055i
$727$		−	3.09159e11i		−	1.10674i	−0.832937	−	0.553368i	$-0.813342\pi$
$727$		−	3.09159e11i		−	1.10674i	0.832937	−	0.553368i	$-0.186658\pi$
$728$	1.97475e11	−	1.39758e11i	0.703049	−	0.497568i
$729$	−1.46026e11			−0.517037
$730$	−2.21352e11	+	2.21352e11i	−0.779456	+	0.779456i
$731$	−4.25895e11			−1.49153
$732$		−	1.50621e11i		−	0.524617i
$733$	−3.53287e11	+	3.53287e11i	−1.22380	+	1.22380i	−0.257533	+	0.966269i	$0.582910\pi$
$733$	−3.53287e11	+	3.53287e11i	−1.22380	+	1.22380i	−0.966269	+	0.257533i	$0.917090\pi$
$734$	−1.12499e11	+	1.12499e11i	−0.387581	+	0.387581i
$735$	1.81157e9	+	1.81157e9i	0.00620735	+	0.00620735i
$736$	−1.14353e11	−	1.14353e11i	−0.389705	−	0.389705i
$737$	−5.17427e10			−0.175380
$738$			1.26533e11i			0.426557i
$739$	1.74930e11	+	1.74930e11i	0.586524	+	0.586524i	0.936688	−	0.350164i	$-0.113874\pi$
$739$	1.74930e11	+	1.74930e11i	0.586524	+	0.586524i	−0.350164	+	0.936688i	$0.613874\pi$
$740$			6.97581e11i			2.32631i
$741$	−3.61269e11	−	6.18299e10i	−1.19828	−	0.205081i
$742$	5.37208e11			1.77226
$743$	1.82265e11	−	1.82265e11i	0.598066	−	0.598066i	−0.341732	−	0.939798i	$-0.611013\pi$
$743$	1.82265e11	−	1.82265e11i	0.598066	−	0.598066i	0.939798	+	0.341732i	$0.111013\pi$
$744$	2.60624e11			0.850595
$745$		−	4.67528e11i		−	1.51769i
$746$	5.34461e10	−	5.34461e10i	0.172568	−	0.172568i
$747$	−1.64221e10	+	1.64221e10i	−0.0527407	+	0.0527407i
$748$	3.07110e11	+	3.07110e11i	0.981042	+	0.981042i
$749$	3.75708e11	+	3.75708e11i	1.19378	+	1.19378i
$750$	5.93160e11			1.87468
$751$		−	4.21734e11i		−	1.32580i	−0.748706	−	0.662902i	$-0.769325\pi$
$751$		−	4.21734e11i		−	1.32580i	0.748706	−	0.662902i	$-0.230675\pi$
$752$	−5.64792e9	−	5.64792e9i	−0.0176611	−	0.0176611i
$753$			3.05913e11i			0.951522i
$754$	−6.88154e11	−	1.17775e11i	−2.12912	−	0.364391i
$755$	−7.59274e10			−0.233674
$756$	−1.05591e11	+	1.05591e11i	−0.323251	+	0.323251i
$757$	−1.34616e11			−0.409932			−0.204966	−	0.978769i	$-0.565708\pi$
$757$	−1.34616e11			−0.409932			−0.204966	+	0.978769i	$0.565708\pi$
$758$			6.17474e11i			1.87043i
$759$	−8.55256e10	+	8.55256e10i	−0.257709	+	0.257709i
$760$	2.95368e11	−	2.95368e11i	0.885338	−	0.885338i
$761$	2.98532e9	+	2.98532e9i	0.00890126	+	0.00890126i	0.711543	−	0.702642i	$-0.247996\pi$
$761$	2.98532e9	+	2.98532e9i	0.00890126	+	0.00890126i	−0.702642	+	0.711543i	$0.747996\pi$
$762$	−1.01681e11	−	1.01681e11i	−0.301592	−	0.301592i
$763$	1.30736e11			0.385742
$764$		−	1.00595e11i		−	0.295258i
$765$	4.83917e11	+	4.83917e11i	1.41295	+	1.41295i
$766$			5.26614e11i			1.52960i
$767$	−2.28601e10	+	1.33571e11i	−0.0660537	+	0.385949i
$768$	−3.29342e11			−0.946677
$769$	−4.30116e11	+	4.30116e11i	−1.22993	+	1.22993i	−0.265939	+	0.963990i	$0.585682\pi$
$769$	−4.30116e11	+	4.30116e11i	−1.22993	+	1.22993i	−0.963990	+	0.265939i	$0.914318\pi$
$770$	−5.02566e11			−1.42965
$771$			2.39198e11i			0.676925i
$772$	6.03789e11	−	6.03789e11i	1.69987	−	1.69987i
$773$	8.08122e10	−	8.08122e10i	0.226339	−	0.226339i	−0.584823	−	0.811161i	$-0.698836\pi$
$773$	8.08122e10	−	8.08122e10i	0.226339	−	0.226339i	0.811161	+	0.584823i	$0.198836\pi$
$774$	−2.91694e11	−	2.91694e11i	−0.812763	−	0.812763i
$775$	−2.93893e11	−	2.93893e11i	−0.814670	−	0.814670i
$776$	−2.56871e11			−0.708383
$777$		−	4.60644e11i		−	1.26381i
$778$	−5.19585e11	−	5.19585e11i	−1.41820	−	1.41820i
$779$		−	1.15565e11i		−	0.313818i
$780$	−2.04749e11	+	1.19634e12i	−0.553152	+	3.23204i
$781$	−8.46736e10			−0.227585
$782$	3.30542e11	−	3.30542e11i	0.883893	−	0.883893i
$783$	1.50996e11			0.401716
$784$			2.64181e8i			0.000699259i
$785$	7.26416e11	−	7.26416e11i	1.91296	−	1.91296i
$786$	6.78893e11	−	6.78893e11i	1.77873	−	1.77873i
$787$	3.45600e11	+	3.45600e11i	0.900896	+	0.900896i	0.995514	−	0.0946180i	$-0.0301630\pi$
$787$	3.45600e11	+	3.45600e11i	0.900896	+	0.900896i	−0.0946180	+	0.995514i	$0.530163\pi$
$788$	−3.53990e11	−	3.53990e11i	−0.918091	−	0.918091i
$789$	4.08439e10			0.105395
$790$		−	1.41832e12i		−	3.64138i
$791$	2.10515e10	+	2.10515e10i	0.0537745	+	0.0537745i
$792$			1.47402e11i			0.374629i
$793$	−5.83912e10	−	8.25052e10i	−0.147657	−	0.208636i
$794$	−5.59724e11			−1.40829
$795$	−6.67760e11	+	6.67760e11i	−1.67167	+	1.67167i
$796$	−1.08609e12			−2.70529
$797$		−	3.23312e11i		−	0.801287i	−0.916234	−	0.400644i	$-0.868787\pi$
$797$		−	3.23312e11i		−	0.801287i	0.916234	−	0.400644i	$-0.131213\pi$
$798$	−5.56648e11	+	5.56648e11i	−1.37268	+	1.37268i
$799$	6.82240e10	−	6.82240e10i	0.167398	−	0.167398i
$800$	5.08002e11	+	5.08002e11i	1.24024	+	1.24024i
$801$	2.39520e11	+	2.39520e11i	0.581852	+	0.581852i
$802$	1.01642e12			2.45683
$803$			1.00890e11i			0.242653i
$804$	1.89785e11	+	1.89785e11i	0.454190	+	0.454190i
$805$			3.27902e11i			0.780838i
$806$	4.07433e11	−	2.88352e11i	0.965420	−	0.683255i
$807$	9.80774e10			0.231246
$808$	−3.34584e11	+	3.34584e11i	−0.784981	+	0.784981i
$809$	6.43334e10			0.150190			0.0750952	−	0.997176i	$-0.476074\pi$
$809$	6.43334e10			0.150190			0.0750952	+	0.997176i	$0.476074\pi$
$810$		−	1.28534e12i		−	2.98592i
$811$	1.97439e11	−	1.97439e11i	0.456404	−	0.456404i	−0.441069	−	0.897473i	$-0.645401\pi$
$811$	1.97439e11	−	1.97439e11i	0.456404	−	0.456404i	0.897473	+	0.441069i	$0.145401\pi$
$812$	−6.42769e11	+	6.42769e11i	−1.47853	+	1.47853i
$813$	−5.10606e11	−	5.10606e11i	−1.16876	−	1.16876i
$814$	2.62247e11	+	2.62247e11i	0.597327	+	0.597327i
$815$	−1.77562e10			−0.0402457
$816$			1.61308e11i			0.363826i
$817$	2.66411e11	+	2.66411e11i	0.597949	+	0.597949i
$818$		−	6.77108e11i		−	1.51232i
$819$	5.91502e10	−	3.45612e11i	0.131468	−	0.768162i
$820$	−3.82694e11			−0.846440
$821$	−2.21288e11	+	2.21288e11i	−0.487063	+	0.487063i	−0.907378	−	0.420315i	$-0.861919\pi$
$821$	−2.21288e11	+	2.21288e11i	−0.487063	+	0.487063i	0.420315	+	0.907378i	$0.361919\pi$
$822$	5.34926e11			1.17167
$823$			2.35397e11i			0.513101i	0.966531	+	0.256550i	$0.0825859\pi$
$823$			2.35397e11i			0.513101i	−0.966531	+	0.256550i	$0.917414\pi$
$824$	3.48986e11	−	3.48986e11i	0.757006	−	0.757006i
$825$	3.79939e11	−	3.79939e11i	0.820158	−	0.820158i
$826$	2.05808e11	+	2.05808e11i	0.442121	+	0.442121i
$827$	−5.32581e11	−	5.32581e11i	−1.13858	−	1.13858i	−0.988705	−	0.149874i	$-0.952113\pi$
$827$	−5.32581e11	−	5.32581e11i	−1.13858	−	1.13858i	−0.149874	−	0.988705i	$-0.547887\pi$
$828$	2.74474e11			0.583956
$829$			7.96173e11i			1.68574i	0.538121	+	0.842868i	$0.319134\pi$
$829$			7.96173e11i			1.68574i	−0.538121	+	0.842868i	$0.680866\pi$
$830$	−8.19329e10	−	8.19329e10i	−0.172642	−	0.172642i
$831$		−	1.72089e10i		−	0.0360869i
$832$	−6.37896e11	+	4.51457e11i	−1.33124	+	0.942156i
$833$	−3.19117e9			−0.00662782
$834$	−2.79170e10	+	2.79170e10i	−0.0577039	+	0.0577039i
$835$	5.32483e11			1.09537
$836$		−	3.84215e11i		−	0.786592i
$837$	−7.63353e10	+	7.63353e10i	−0.155533	+	0.155533i
$838$	−9.64126e11	+	9.64126e11i	−1.95505	+	1.95505i
$839$	7.78054e10	+	7.78054e10i	0.157023	+	0.157023i	0.781246	−	0.624223i	$-0.214584\pi$
$839$	7.78054e10	+	7.78054e10i	0.157023	+	0.157023i	−0.624223	+	0.781246i	$0.714584\pi$
$840$	6.45890e11	+	6.45890e11i	1.29730	+	1.29730i
$841$	4.18919e11			0.837425
$842$			8.58816e11i			1.70864i
$843$	−9.21845e11	−	9.21845e11i	−1.82536	−	1.82536i
$844$		−	6.17855e11i		−	1.21763i
$845$	3.51630e11	+	7.34689e11i	0.689698	+	1.44104i
$846$	9.34529e10			0.182436
$847$	2.50148e11	−	2.50148e11i	0.486030	−	0.486030i
$848$	−9.73793e10			−0.188314
$849$			1.24189e12i			2.39030i
$850$	−1.46840e12	+	1.46840e12i	−2.81299	+	2.81299i
$851$	1.71105e11	−	1.71105e11i	0.326245	−	0.326245i
$852$	3.10571e11	+	3.10571e11i	0.589389	+	0.589389i
$853$	−4.02094e10	−	4.02094e10i	−0.0759506	−	0.0759506i	0.668111	−	0.744062i	$-0.267103\pi$
$853$	−4.02094e10	−	4.02094e10i	−0.0759506	−	0.0759506i	−0.744062	+	0.668111i	$0.767103\pi$
$854$	−2.17095e11			−0.408149
$855$		−	6.05413e11i		−	1.13289i
$856$	5.49782e11	+	5.49782e11i	1.02399	+	1.02399i
$857$		−	8.03555e11i		−	1.48968i	−0.667245	−	0.744839i	$-0.732526\pi$
$857$		−	8.03555e11i		−	1.48968i	0.667245	−	0.744839i	$-0.267474\pi$
$858$	3.72776e11	+	5.26722e11i	0.687858	+	0.971924i
$859$	6.03941e11			1.10923			0.554615	−	0.832107i	$-0.312866\pi$
$859$	6.03941e11			1.10923			0.554615	+	0.832107i	$0.312866\pi$
$860$	8.82220e11	−	8.82220e11i	1.61281	−	1.61281i
$861$	2.52710e11			0.459843
$862$			1.22356e12i			2.21614i
$863$	7.14366e11	−	7.14366e11i	1.28789	−	1.28789i	0.351818	−	0.936068i	$-0.385564\pi$
$863$	7.14366e11	−	7.14366e11i	1.28789	−	1.28789i	0.936068	−	0.351818i	$-0.114436\pi$
$864$	1.31948e11	−	1.31948e11i	0.236781	−	0.236781i
$865$	−1.22392e11	−	1.22392e11i	−0.218619	−	0.218619i
$866$	1.12029e12	+	1.12029e12i	1.99186	+	1.99186i
$867$	−1.19514e12			−2.11516
$868$		−	6.49897e11i		−	1.14490i
$869$	−3.23228e11	−	3.23228e11i	−0.566800	−	0.566800i
$870$		−	2.63599e12i		−	4.60116i
$871$	1.77531e11	+	3.03838e10i	0.308462	+	0.0527922i
$872$	1.91309e11			0.330879
$873$	−2.63253e11	+	2.63253e11i	−0.453228	+	0.453228i
$874$	−4.13530e11			−0.708699
$875$		−	5.18269e11i		−	0.884144i
$876$	3.70049e11	−	3.70049e11i	0.628410	−	0.628410i
$877$	5.61395e11	−	5.61395e11i	0.949008	−	0.949008i	−0.0497532	−	0.998762i	$-0.515843\pi$
$877$	5.61395e11	−	5.61395e11i	0.949008	−	0.949008i	0.998762	+	0.0497532i	$0.0158435\pi$
$878$	−1.29712e12	−	1.29712e12i	−2.18274	−	2.18274i
$879$	1.00533e12	+	1.00533e12i	1.68405	+	1.68405i
$880$	9.10998e10			0.151910
$881$		−	1.38278e11i		−	0.229536i	−0.993392	−	0.114768i	$-0.963388\pi$
$881$		−	1.38278e11i		−	0.229536i	0.993392	−	0.114768i	$-0.0366125\pi$
$882$	−2.18563e9	−	2.18563e9i	−0.00361162	−	0.00361162i
$883$			6.30093e11i			1.03648i	0.855235	+	0.518241i	$0.173413\pi$
$883$			6.30093e11i			1.03648i	−0.855235	+	0.518241i	$0.826587\pi$
$884$	−8.73369e11	−	1.23405e12i	−1.43017	−	2.02079i
$885$	−5.11646e11			−0.834059
$886$	3.65579e11	−	3.65579e11i	0.593263	−	0.593263i
$887$	−7.83211e11			−1.26527			−0.632637	−	0.774449i	$-0.718027\pi$
$887$	−7.83211e11			−1.26527			−0.632637	+	0.774449i	$0.718027\pi$
$888$		−	6.74070e11i		−	1.08406i
$889$	−8.88429e10	+	8.88429e10i	−0.142238	+	0.142238i
$890$	−1.19501e12	+	1.19501e12i	−1.90464	+	1.90464i
$891$	−2.92922e11	−	2.92922e11i	−0.464773	−	0.464773i
$892$	−6.30809e10	−	6.30809e10i	−0.0996411	−	0.0996411i
$893$	−8.53528e10			−0.134218
$894$			1.28933e12i			2.01844i
$895$	6.73926e11	+	6.73926e11i	1.05032	+	1.05032i
$896$			9.48742e11i			1.47203i
$897$	3.43663e11	−	2.43220e11i	0.530840	−	0.375690i
$898$	−2.72112e11			−0.418450
$899$	−4.64679e11	+	4.64679e11i	−0.711401	+	0.711401i
$900$	−1.21932e12			−1.85844
$901$		−	1.17629e12i		−	1.78491i
$902$	−1.43869e11	+	1.43869e11i	−0.217341	+	0.217341i
$903$	−5.82569e11	+	5.82569e11i	−0.876186	+	0.876186i
$904$	3.08051e10	+	3.08051e10i	0.0461263	+	0.0461263i
$905$	1.32908e11	+	1.32908e11i	0.198134	+	0.198134i
$906$	2.09390e11			0.310773
$907$		−	4.86298e10i		−	0.0718577i	−0.999354	−	0.0359288i	$-0.988561\pi$
$907$		−	4.86298e10i		−	0.0718577i	0.999354	−	0.0359288i	$-0.0114390\pi$
$908$	3.67387e11	+	3.67387e11i	0.540481	+	0.540481i
$909$			6.85793e11i			1.00447i
$910$	1.72432e12	+	2.95112e11i	2.51451	+	0.430349i
$911$	5.89747e10			0.0856234			0.0428117	−	0.999083i	$-0.486368\pi$
$911$	5.89747e10			0.0856234			0.0428117	+	0.999083i	$0.486368\pi$
$912$	1.00903e11	−	1.00903e11i	0.145857	−	0.145857i
$913$	−3.73442e10			−0.0537452
$914$		−	2.87688e11i		−	0.412228i
$915$	2.69854e11	−	2.69854e11i	0.384985	−	0.384985i
$916$	1.06725e12	−	1.06725e12i	1.51595	−	1.51595i
$917$	−5.93177e11	−	5.93177e11i	−0.838893	−	0.838893i
$918$	3.81401e11	+	3.81401e11i	0.537045	+	0.537045i
$919$	−1.20228e12			−1.68556			−0.842781	−	0.538257i	$-0.819083\pi$
$919$	−1.20228e12			−1.68556			−0.842781	+	0.538257i	$0.819083\pi$
$920$			4.79827e11i			0.669782i
$921$	−4.02394e11	−	4.02394e11i	−0.559259	−	0.559259i
$922$		−	1.21723e12i		−	1.68442i
$923$	2.90519e11	+	4.97212e10i	0.400283	+	0.0685070i
$924$	8.40175e11			1.15261
$925$	−7.60114e11	+	7.60114e11i	−1.03827	+	1.03827i
$926$	−9.25992e10			−0.125940
$927$		−	7.15314e11i		−	0.968675i
$928$	8.03211e11	−	8.03211e11i	1.08302	−	1.08302i
$929$	−5.36726e11	+	5.36726e11i	−0.720593	+	0.720593i	−0.968726	−	0.248133i	$-0.920183\pi$
$929$	−5.36726e11	+	5.36726e11i	−0.720593	+	0.720593i	0.248133	+	0.968726i	$0.420183\pi$
$930$	1.33261e12	+	1.33261e12i	1.78144	+	1.78144i
$931$	1.99619e9	+	1.99619e9i	0.00265707	+	0.00265707i
$932$	−3.14018e11			−0.416189
$933$		−	5.72749e11i		−	0.755854i
$934$	−1.12552e12	−	1.12552e12i	−1.47899	−	1.47899i
$935$			1.10044e12i			1.43986i
$936$	8.65558e10	−	5.05741e11i	0.112770	−	0.658908i
$937$	5.61778e11			0.728796			0.364398	−	0.931243i	$-0.381275\pi$
$937$	5.61778e11			0.728796			0.364398	+	0.931243i	$0.381275\pi$
$938$	2.73543e11	−	2.73543e11i	0.353357	−	0.353357i
$939$	1.24081e12			1.59603
$940$			2.82646e11i			0.362018i
$941$	−5.81505e11	+	5.81505e11i	−0.741643	+	0.741643i	−0.972894	−	0.231251i	$-0.925718\pi$
$941$	−5.81505e11	+	5.81505e11i	−0.741643	+	0.741643i	0.231251	+	0.972894i	$0.425718\pi$
$942$	−2.00329e12	+	2.00329e12i	−2.54413	+	2.54413i
$943$	9.38682e10	+	9.38682e10i	0.118706	+	0.118706i
$944$	−3.73066e10	−	3.73066e10i	−0.0469784	−	0.0469784i
$945$	−3.78355e11			−0.474430
$946$		−	6.63319e11i		−	0.828243i
$947$	5.95719e11	+	5.95719e11i	0.740698	+	0.740698i	0.972712	−	0.232014i	$-0.0745316\pi$
$947$	5.95719e11	+	5.95719e11i	0.740698	+	0.740698i	−0.232014	+	0.972712i	$0.574532\pi$
$948$			2.37111e12i			2.93574i
$949$	5.92435e10	−	3.46157e11i	0.0730426	−	0.426784i
$950$	1.83707e12			2.25544
$951$	4.00211e11	−	4.00211e11i	0.489291	−	0.489291i
$952$	−1.13777e12			−1.38518
$953$			5.10820e11i			0.619293i	0.950852	+	0.309646i	$0.100211\pi$
$953$			5.10820e11i			0.619293i	−0.950852	+	0.309646i	$0.899789\pi$
$954$	8.05639e11	−	8.05639e11i	0.972629	−	0.972629i
$955$	1.80226e11	−	1.80226e11i	0.216672	−	0.216672i
$956$	−1.50308e12	−	1.50308e12i	−1.79950	−	1.79950i
$957$	−6.00728e11	−	6.00728e11i	−0.716194	−	0.716194i
$958$	1.82816e12			2.17047
$959$		−	4.67387e11i		−	0.552589i
$960$	−2.08640e12	−	2.08640e12i	−2.45647	−	2.45647i
$961$			3.83058e11i			0.449129i
$962$	−7.45785e11	−	1.05377e12i	−0.870789	−	1.23040i
$963$	1.12688e12			1.31031
$964$	−8.52326e11	+	8.52326e11i	−0.986956	+	0.986956i
$965$	2.16350e12			2.49487
$966$		−	9.04279e11i		−	1.03847i
$967$	−3.84454e11	+	3.84454e11i	−0.439682	+	0.439682i	−0.891905	−	0.452223i	$-0.850631\pi$
$967$	−3.84454e11	+	3.84454e11i	−0.439682	+	0.439682i	0.452223	+	0.891905i	$0.350631\pi$
$968$	3.66047e11	−	3.66047e11i	0.416903	−	0.416903i
$969$	1.21886e12	+	1.21886e12i	1.38248	+	1.38248i
$970$	−1.31342e12	−	1.31342e12i	−1.48360	−	1.48360i
$971$	5.37749e11			0.604926			0.302463	−	0.953161i	$-0.402191\pi$
$971$	5.37749e11			0.604926			0.302463	+	0.953161i	$0.402191\pi$
$972$			1.74157e12i			1.95109i
$973$	2.43922e10	+	2.43922e10i	0.0272145	+	0.0272145i
$974$		−	6.55419e11i		−	0.728255i
$975$	−1.52669e12	+	1.08048e12i	−1.68940	+	1.19564i
$976$	3.93527e10			0.0433686
$977$	−8.39362e10	+	8.39362e10i	−0.0921237	+	0.0921237i	−0.751667	−	0.659543i	$-0.770750\pi$
$977$	−8.39362e10	+	8.39362e10i	−0.0921237	+	0.0921237i	0.659543	+	0.751667i	$0.270750\pi$
$978$	4.89674e10			0.0535244
$979$			5.44674e11i			0.592934i
$980$	6.61037e9	−	6.61037e9i	0.00716673	−	0.00716673i
$981$	1.96062e11	−	1.96062e11i	0.211698	−	0.211698i
$982$	2.04751e12	+	2.04751e12i	2.20181	+	2.20181i
$983$	2.54267e11	+	2.54267e11i	0.272318	+	0.272318i	0.830033	−	0.557715i	$-0.188322\pi$
$983$	2.54267e11	+	2.54267e11i	0.272318	+	0.272318i	−0.557715	+	0.830033i	$0.688322\pi$
$984$	3.69796e11			0.394441
$985$		−	1.26842e12i		−	1.34746i
$986$	2.32172e12	+	2.32172e12i	2.45641	+	2.45641i
$987$		−	1.86643e11i		−	0.196673i
$988$	−2.25615e11	+	1.31826e12i	−0.236778	+	1.38348i
$989$	−4.32787e11			−0.452365
$990$	−7.53688e11	+	7.53688e11i	−0.784604	+	0.784604i
$991$	−1.73726e12			−1.80123			−0.900615	−	0.434617i	$-0.856884\pi$
$991$	−1.73726e12			−1.80123			−0.900615	+	0.434617i	$0.856884\pi$
$992$			8.12119e11i			0.838635i
$993$	9.62813e10	−	9.62813e10i	0.0990251	−	0.0990251i
$994$	4.47635e11	−	4.47635e11i	0.458542	−	0.458542i
$995$	−1.94584e12	−	1.94584e12i	−1.98525	−	1.98525i
$996$	1.36973e11	+	1.36973e11i	0.139187	+	0.139187i
$997$	1.32018e12			1.33614			0.668072	−	0.744096i	$-0.267120\pi$
$997$	1.32018e12			1.33614			0.668072	+	0.744096i	$0.267120\pi$
$998$			2.11244e11i			0.212943i
$999$	1.97431e11	+	1.97431e11i	0.198223	+	0.198223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.9.d.a.5.2	✓	18
3.2	odd	2		117.9.j.a.109.8		18
13.8	odd	4	inner	13.9.d.a.8.2	yes	18
39.8	even	4		117.9.j.a.73.8		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.9.d.a.5.2	✓	18	1.1	even	1	trivial
13.9.d.a.8.2	yes	18	13.8	odd	4	inner
117.9.j.a.73.8		18	39.8	even	4
117.9.j.a.109.8		18	3.2	odd	2

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:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	13.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-18.0289 + 18.0289i) q^{2} +107.999 q^{3} -394.083i q^{4} +(706.041 - 706.041i) q^{5} +(-1947.10 + 1947.10i) q^{6} +(1701.26 + 1701.26i) q^{7} +(2489.49 + 2489.49i) q^{8} +5102.69 q^{9} +25458.3i q^{10} +(5801.81 + 5801.81i) q^{11} -42560.4i q^{12} +(-16499.4 - 23313.1i) q^{13} -61343.7 q^{14} +(76251.4 - 76251.4i) q^{15} +11119.7 q^{16} +134321. i q^{17} +(-91995.9 + 91995.9i) q^{18} +(84022.1 - 84022.1i) q^{19} +(-278239. - 278239. i) q^{20} +(183733. + 183733. i) q^{21} -209201. q^{22} +136494. i q^{23} +(268861. + 268861. i) q^{24} -606362. i q^{25} +(717776. + 122845. i) q^{26} -157496. q^{27} +(670437. - 670437. i) q^{28} -958731. q^{29} +2.74946e6i q^{30} +(484682. - 484682. i) q^{31} +(-837786. + 837786. i) q^{32} +(626587. + 626587. i) q^{33} +(-2.42165e6 - 2.42165e6i) q^{34} +2.40232e6 q^{35} -2.01088e6i q^{36} +(-1.25356e6 - 1.25356e6i) q^{37} +3.02965e6i q^{38} +(-1.78191e6 - 2.51778e6i) q^{39} +3.51536e6 q^{40} +(687708. - 687708. i) q^{41} -6.62503e6 q^{42} +3.17073e6i q^{43} +(2.28640e6 - 2.28640e6i) q^{44} +(3.60270e6 - 3.60270e6i) q^{45} +(-2.46084e6 - 2.46084e6i) q^{46} +(-507919. - 507919. i) q^{47} +1.20091e6 q^{48} +23757.9i q^{49} +(1.09320e7 + 1.09320e7i) q^{50} +1.45064e7i q^{51} +(-9.18731e6 + 6.50212e6i) q^{52} -8.75734e6 q^{53} +(2.83948e6 - 2.83948e6i) q^{54} +8.19263e6 q^{55} +8.47053e6i q^{56} +(9.07426e6 - 9.07426e6i) q^{57} +(1.72849e7 - 1.72849e7i) q^{58} +(-3.35500e6 - 3.35500e6i) q^{59} +(-3.00494e7 - 3.00494e7i) q^{60} +3.53900e6 q^{61} +1.74766e7i q^{62} +(8.68099e6 + 8.68099e6i) q^{63} -2.73621e7i q^{64} +(-2.81092e7 - 4.81079e6i) q^{65} -2.25934e7 q^{66} +(-4.45919e6 + 4.45919e6i) q^{67} +5.29335e7 q^{68} +1.47412e7i q^{69} +(-4.33111e7 + 4.33111e7i) q^{70} +(-7.29718e6 + 7.29718e6i) q^{71} +(1.27031e7 + 1.27031e7i) q^{72} +(8.69469e6 + 8.69469e6i) q^{73} +4.52008e7 q^{74} -6.54862e7i q^{75} +(-3.31117e7 - 3.31117e7i) q^{76} +1.97408e7i q^{77} +(7.75187e7 + 1.32670e7i) q^{78} -5.57116e7 q^{79} +(7.85098e6 - 7.85098e6i) q^{80} -5.04880e7 q^{81} +2.47972e7i q^{82} +(-3.21832e6 + 3.21832e6i) q^{83} +(7.24062e7 - 7.24062e7i) q^{84} +(9.48358e7 + 9.48358e7i) q^{85} +(-5.71648e7 - 5.71648e7i) q^{86} -1.03542e8 q^{87} +2.88871e7i q^{88} +(4.69400e7 + 4.69400e7i) q^{89} +1.29906e8i q^{90} +(1.15920e7 - 6.77313e7i) q^{91} +5.37901e7 q^{92} +(5.23449e7 - 5.23449e7i) q^{93} +1.83144e7 q^{94} -1.18646e8i q^{95} +(-9.04797e7 + 9.04797e7i) q^{96} +(-5.15911e7 + 5.15911e7i) q^{97} +(-428329. - 428329. i) q^{98} +(2.96048e7 + 2.96048e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} - 4 q^{3} + 166 q^{5} + 2720 q^{6} + 5308 q^{7} + 10464 q^{8} + 39362 q^{9} - 31556 q^{11} + 71300 q^{13} - 110260 q^{14} + 121124 q^{15} - 522860 q^{16} - 308962 q^{18} + 100288 q^{19} + 736268 q^{20}+ \cdots - 1125076336 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 - 4 * q^3 + 166 * q^5 + 2720 * q^6 + 5308 * q^7 + 10464 * q^8 + 39362 * q^9 - 31556 * q^11 + 71300 * q^13 - 110260 * q^14 + 121124 * q^15 - 522860 * q^16 - 308962 * q^18 + 100288 * q^19 + 736268 * q^20 + 279416 * q^21 - 977312 * q^22 - 986232 * q^24 + 2952238 * q^26 + 364916 * q^27 + 4497084 * q^28 - 2479024 * q^29 - 1892664 * q^31 + 947212 * q^32 + 1368644 * q^33 - 531576 * q^34 - 2918284 * q^35 - 8343978 * q^37 - 1101268 * q^39 - 12691908 * q^40 + 1140178 * q^41 + 15137212 * q^42 - 3867188 * q^44 + 6565370 * q^45 + 2006148 * q^46 - 13368572 * q^47 - 10106716 * q^48 + 37369598 * q^50 - 14821220 * q^52 + 50561348 * q^53 - 4995928 * q^54 + 76994128 * q^55 - 34755760 * q^57 + 22505716 * q^58 + 2127976 * q^59 - 161134196 * q^60 - 52016516 * q^61 - 15210112 * q^63 + 10413082 * q^65 - 51097328 * q^66 + 960292 * q^67 + 283187508 * q^68 - 166635032 * q^70 + 67412140 * q^71 + 96846900 * q^72 - 145213226 * q^73 - 233620024 * q^74 - 150533640 * q^76 + 212071160 * q^78 - 76829120 * q^79 + 524889520 * q^80 + 293280674 * q^81 - 241951556 * q^83 + 345496184 * q^84 + 260737764 * q^85 - 579480384 * q^86 - 618300656 * q^87 - 89187110 * q^89 + 232660948 * q^91 - 122690376 * q^92 + 669553400 * q^93 + 1069637380 * q^94 - 1324092400 * q^96 + 331183146 * q^97 + 588677614 * q^98 - 1125076336 * q^99

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