LMFDB - Embedded newform 49.10.c.h.30.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [49,10,Mod(18,49)] 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("49.18"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(49, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	49.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,66,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$25.2367559720$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 5242 x^{14} + 24024 x^{13} + 10505991 x^{12} - 53910056 x^{11} + \cdots + 89\!\cdots\!16 $ x^16 - 4x^15 - 5242x^14 + 24024x^13 + 10505991x^12 - 53910056x^11 - 9779568598x^10 + 54819837928x^9 + 3963633390800x^8 - 23235313319744x^7 - 467753893701144x^6 + 2306370917243232x^5 + 26209670720799040x^4 - 90637606103367168x^3 - 744297532540383840x^2 + 1282950647298147456*x + 8963293398458481216
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6}\cdot 7^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			30.3
Root			$-6.41022 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	49.30
Dual form			49.10.c.h.18.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.14844 - 1.98916i) q^{2} +(-129.061 - 223.541i) q^{3} +(253.362 + 438.836i) q^{4} +(486.452 - 842.560i) q^{5} -592.877 q^{6} +2339.89 q^{8} +(-23472.1 + 40654.8i) q^{9} +(-1117.32 - 1935.26i) q^{10} +(21020.6 + 36408.7i) q^{11} +(65398.4 - 113273. i) q^{12} -151604. q^{13} -251128. q^{15} +(-127034. + 220030. i) q^{16} +(171136. + 296415. i) q^{17} +(53912.6 + 93379.4i) q^{18} +(-203488. + 352452. i) q^{19} +492994. q^{20} +96563.6 q^{22} +(1.14471e6 - 1.98270e6i) q^{23} +(-301989. - 523061. i) q^{24} +(503291. + 871725. i) q^{25} +(-174109. + 301565. i) q^{26} +7.03671e6 q^{27} +2.39735e6 q^{29} +(-288406. + 499535. i) q^{30} +(2.95097e6 + 5.11123e6i) q^{31} +(890795. + 1.54290e6i) q^{32} +(5.42588e6 - 9.39789e6i) q^{33} +786157. q^{34} -2.37877e7 q^{36} +(-974418. + 1.68774e6i) q^{37} +(467389. + 809541. i) q^{38} +(1.95662e7 + 3.38897e7i) q^{39} +(1.13825e6 - 1.97150e6i) q^{40} -1.25171e6 q^{41} -8.53275e6 q^{43} +(-1.06516e7 + 1.84492e7i) q^{44} +(2.28361e7 + 3.95533e7i) q^{45} +(-2.62927e6 - 4.55402e6i) q^{46} +(2.97343e6 - 5.15013e6i) q^{47} +6.55807e7 q^{48} +2.31200e6 q^{50} +(4.41739e7 - 7.65114e7i) q^{51} +(-3.84108e7 - 6.65294e7i) q^{52} +(3.01631e6 + 5.22439e6i) q^{53} +(8.08125e6 - 1.39971e7i) q^{54} +4.09020e7 q^{55} +1.05050e8 q^{57} +(2.75322e6 - 4.76871e6i) q^{58} +(3.71000e7 + 6.42590e7i) q^{59} +(-6.36264e7 - 1.10204e8i) q^{60} +(-2.53092e7 + 4.38368e7i) q^{61} +1.35561e7 q^{62} -1.25991e8 q^{64} +(-7.37482e7 + 1.27736e8i) q^{65} +(-1.24626e7 - 2.15859e7i) q^{66} +(5.00939e7 + 8.67652e7i) q^{67} +(-8.67185e7 + 1.50201e8i) q^{68} -5.90951e8 q^{69} +5.12492e7 q^{71} +(-5.49221e7 + 9.51279e7i) q^{72} +(-1.54723e8 - 2.67988e8i) q^{73} +(2.23813e6 + 3.87655e6i) q^{74} +(1.29911e8 - 2.25012e8i) q^{75} -2.06225e8 q^{76} +8.98826e7 q^{78} +(-4.60906e7 + 7.98313e7i) q^{79} +(1.23592e8 + 2.14068e8i) q^{80} +(-4.46165e8 - 7.72781e8i) q^{81} +(-1.43751e6 + 2.48985e6i) q^{82} +2.52452e8 q^{83} +3.32997e8 q^{85} +(-9.79936e6 + 1.69730e7i) q^{86} +(-3.09405e8 - 5.35905e8i) q^{87} +(4.91858e7 + 8.51923e7i) q^{88} +(-4.15826e8 + 7.20232e8i) q^{89} +1.04904e8 q^{90} +1.16011e9 q^{92} +(7.61711e8 - 1.31932e9i) q^{93} +(-6.82962e6 - 1.18292e7i) q^{94} +(1.97975e8 + 3.42902e8i) q^{95} +(2.29934e8 - 3.98258e8i) q^{96} +5.95209e8 q^{97} -1.97358e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 66 q^{2} - 1706 q^{4} - 117084 q^{8} - 27940 q^{9} + 82092 q^{11} - 164672 q^{15} - 1569570 q^{16} + 307774 q^{18} - 2600152 q^{22} + 2388480 q^{23} + 6191476 q^{25} - 36887784 q^{29} + 16703832 q^{30}+ \cdots - 6259461064 q^{99}+O(q^{100}) $ 16 * q + 66 * q^2 - 1706 * q^4 - 117084 * q^8 - 27940 * q^9 + 82092 * q^11 - 164672 * q^15 - 1569570 * q^16 + 307774 * q^18 - 2600152 * q^22 + 2388480 * q^23 + 6191476 * q^25 - 36887784 * q^29 + 16703832 * q^30 + 66365310 * q^32 - 163874260 * q^36 + 8944484 * q^37 + 128986088 * q^39 - 72060264 * q^43 + 20548980 * q^44 + 151133592 * q^46 - 358848780 * q^50 + 192522580 * q^51 + 140198712 * q^53 + 112011672 * q^57 - 407992572 * q^58 - 748541080 * q^60 + 1606537220 * q^64 + 69983508 * q^65 - 459952056 * q^67 + 431701008 * q^71 - 1088280558 * q^72 - 1222590060 * q^74 + 2845895808 * q^78 + 792601400 * q^79 - 1704517060 * q^81 - 736682888 * q^85 + 812465940 * q^86 - 1818979932 * q^88 + 5226574128 * q^92 + 2571584104 * q^93 + 3568335216 * q^95 - 6259461064 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.14844	−	1.98916i	0.0507544	−	0.0879093i	−0.839532	−	0.543310i	$-0.817171\pi$
$2$	1.14844	−	1.98916i	0.0507544	−	0.0879093i	0.890286	+	0.455401i	$0.150504\pi$
$3$	−129.061	−	223.541i	−0.919920	−	1.59335i	−0.799534	−	0.600621i	$-0.794920\pi$
$3$	−129.061	−	223.541i	−0.919920	−	1.59335i	−0.120386	−	0.992727i	$-0.538413\pi$
$4$	253.362	+	438.836i	0.494848	+	0.857102i
$5$	486.452	−	842.560i	0.348077	−	0.602887i	−0.637831	−	0.770176i	$-0.720168\pi$
$5$	486.452	−	842.560i	0.348077	−	0.602887i	0.985908	+	0.167289i	$0.0535015\pi$
$6$	−592.877			−0.186760
$7$		0			0
$7$		0			0
$8$	2339.89			0.201972
$9$	−23472.1	+	40654.8i	−1.19250	+	2.06548i
$10$	−1117.32	−	1935.26i	−0.0353329	−	0.0611984i
$11$	21020.6	+	36408.7i	0.432890	+	0.749787i	0.997121	−	0.0758301i	$-0.0241607\pi$
$11$	21020.6	+	36408.7i	0.432890	+	0.749787i	−0.564231	+	0.825617i	$0.690827\pi$
$12$	65398.4	−	113273.i	0.910441	−	1.57693i
$13$	−151604.			−1.47220			−0.736099	−	0.676874i	$-0.763334\pi$
$13$	−151604.			−1.47220			−0.736099	+	0.676874i	$0.763334\pi$
$14$		0			0
$15$	−251128.			−1.28081
$16$	−127034.	+	220030.i	−0.484597	+	0.839347i
$17$	171136.	+	296415.i	0.496958	+	0.860757i	0.999994	−	0.00350855i	$-0.00111681\pi$
$17$	171136.	+	296415.i	0.496958	+	0.860757i	−0.503035	+	0.864266i	$0.667783\pi$
$18$	53912.6	+	93379.4i	0.121050	+	0.209664i
$19$	−203488.	+	352452.i	−0.358218	+	0.620452i	−0.987663	−	0.156593i	$-0.949949\pi$
$19$	−203488.	+	352452.i	−0.358218	+	0.620452i	0.629445	+	0.777045i	$0.283282\pi$
$20$	492994.			0.688981
$21$		0			0
$22$	96563.6			0.0878843
$23$	1.14471e6	−	1.98270e6i	0.852944	−	1.47734i	−0.0255956	−	0.999672i	$-0.508148\pi$
$23$	1.14471e6	−	1.98270e6i	0.852944	−	1.47734i	0.878539	−	0.477670i	$-0.158518\pi$
$24$	−301989.	−	523061.i	−0.185798	−	0.321811i
$25$	503291.	+	871725.i	0.257685	+	0.446323i
$26$	−174109.	+	301565.i	−0.0747205	+	0.129420i
$27$	7.03671e6			2.54820
$28$		0			0
$29$	2.39735e6			0.629420			0.314710	−	0.949188i	$-0.398093\pi$
$29$	2.39735e6			0.629420			0.314710	+	0.949188i	$0.398093\pi$
$30$	−288406.	+	499535.i	−0.0650069	+	0.112595i
$31$	2.95097e6	+	5.11123e6i	0.573901	+	0.994025i	0.996160	+	0.0875502i	$0.0279038\pi$
$31$	2.95097e6	+	5.11123e6i	0.573901	+	0.994025i	−0.422259	+	0.906475i	$0.638763\pi$
$32$	890795.	+	1.54290e6i	0.150177	+	0.260114i
$33$	5.42588e6	−	9.39789e6i	0.796447	−	1.37949i
$34$	786157.			0.100891
$35$		0			0
$36$	−2.37877e7			−2.36043
$37$	−974418.	+	1.68774e6i	−0.0854747	+	0.148047i	−0.905593	−	0.424147i	$-0.860574\pi$
$37$	−974418.	+	1.68774e6i	−0.0854747	+	0.148047i	0.820119	+	0.572193i	$0.193907\pi$
$38$	467389.	+	809541.i	0.0363623	+	0.0629814i
$39$	1.95662e7	+	3.38897e7i	1.35430	+	2.34572i
$40$	1.13825e6	−	1.97150e6i	0.0703017	−	0.121766i
$41$	−1.25171e6			−0.0691793			−0.0345896	−	0.999402i	$-0.511012\pi$
$41$	−1.25171e6			−0.0691793			−0.0345896	+	0.999402i	$0.511012\pi$
$42$		0			0
$43$	−8.53275e6			−0.380611			−0.190305	−	0.981725i	$-0.560948\pi$
$43$	−8.53275e6			−0.380611			−0.190305	+	0.981725i	$0.560948\pi$
$44$	−1.06516e7	+	1.84492e7i	−0.428429	+	0.742061i
$45$	2.28361e7	+	3.95533e7i	0.830167	+	1.43789i
$46$	−2.62927e6	−	4.55402e6i	−0.0865814	−	0.149963i
$47$	2.97343e6	−	5.15013e6i	0.0888827	−	0.153949i	−0.818156	−	0.574996i	$-0.805004\pi$
$47$	2.97343e6	−	5.15013e6i	0.0888827	−	0.153949i	0.907039	+	0.421046i	$0.138337\pi$
$48$	6.55807e7			1.78316
$49$		0			0
$50$	2.31200e6			0.0523146
$51$	4.41739e7	−	7.65114e7i	0.914324	−	1.58366i
$52$	−3.84108e7	−	6.65294e7i	−0.728514	−	1.26182i
$53$	3.01631e6	+	5.22439e6i	0.0525090	+	0.0909483i	0.891085	−	0.453836i	$-0.149945\pi$
$53$	3.01631e6	+	5.22439e6i	0.0525090	+	0.0909483i	−0.838576	+	0.544784i	$0.816612\pi$
$54$	8.08125e6	−	1.39971e7i	0.129332	−	0.224010i
$55$	4.09020e7			0.602716
$56$		0			0
$57$	1.05050e8			1.31813
$58$	2.75322e6	−	4.76871e6i	0.0319459	−	0.0553319i
$59$	3.71000e7	+	6.42590e7i	0.398602	+	0.690399i	0.993554	−	0.113363i	$-0.0361622\pi$
$59$	3.71000e7	+	6.42590e7i	0.398602	+	0.690399i	−0.594952	+	0.803761i	$0.702829\pi$
$60$	−6.36264e7	−	1.10204e8i	−0.633807	−	1.09779i
$61$	−2.53092e7	+	4.38368e7i	−0.234042	+	0.405372i	−0.958994	−	0.283427i	$-0.908529\pi$
$61$	−2.53092e7	+	4.38368e7i	−0.234042	+	0.405372i	0.724952	+	0.688799i	$0.241862\pi$
$62$	1.35561e7			0.116512
$63$		0			0
$64$	−1.25991e8			−0.938705
$65$	−7.37482e7	+	1.27736e8i	−0.512438	+	0.887569i
$66$	−1.24626e7	−	2.15859e7i	−0.0808465	−	0.140030i
$67$	5.00939e7	+	8.67652e7i	0.303702	+	0.526028i	0.976972	−	0.213370i	$-0.0684438\pi$
$67$	5.00939e7	+	8.67652e7i	0.303702	+	0.526028i	−0.673269	+	0.739397i	$0.735111\pi$
$68$	−8.67185e7	+	1.50201e8i	−0.491838	+	0.851888i
$69$	−5.90951e8			−3.13856
$70$		0			0
$71$	5.12492e7			0.239345			0.119673	−	0.992813i	$-0.461816\pi$
$71$	5.12492e7			0.239345			0.119673	+	0.992813i	$0.461816\pi$
$72$	−5.49221e7	+	9.51279e7i	−0.240852	+	0.417169i
$73$	−1.54723e8	−	2.67988e8i	−0.637679	−	1.10449i	−0.985941	−	0.167095i	$-0.946561\pi$
$73$	−1.54723e8	−	2.67988e8i	−0.637679	−	1.10449i	0.348262	−	0.937397i	$-0.386772\pi$
$74$	2.23813e6	+	3.87655e6i	0.00867644	+	0.0150280i
$75$	1.29911e8	−	2.25012e8i	0.474099	−	0.821163i
$76$	−2.06225e8			−0.709055
$77$		0			0
$78$	8.98826e7			0.274948
$79$	−4.60906e7	+	7.98313e7i	−0.133135	+	0.230596i	−0.924883	−	0.380251i	$-0.875838\pi$
$79$	−4.60906e7	+	7.98313e7i	−0.133135	+	0.230596i	0.791749	+	0.610847i	$0.209171\pi$
$80$	1.23592e8	+	2.14068e8i	0.337354	+	0.584314i
$81$	−4.46165e8	−	7.72781e8i	−1.15163	−	1.99468i
$82$	−1.43751e6	+	2.48985e6i	−0.00351115	+	0.00608150i
$83$	2.52452e8			0.583886			0.291943	−	0.956436i	$-0.405698\pi$
$83$	2.52452e8			0.583886			0.291943	+	0.956436i	$0.405698\pi$
$84$		0			0
$85$	3.32997e8			0.691919
$86$	−9.79936e6	+	1.69730e7i	−0.0193177	+	0.0334592i
$87$	−3.09405e8	−	5.35905e8i	−0.579016	−	1.00288i
$88$	4.91858e7	+	8.51923e7i	0.0874315	+	0.151436i
$89$	−4.15826e8	+	7.20232e8i	−0.702517	+	1.21680i	0.265063	+	0.964231i	$0.414607\pi$
$89$	−4.15826e8	+	7.20232e8i	−0.702517	+	1.21680i	−0.967580	+	0.252564i	$0.918726\pi$
$90$	1.04904e8			0.168539
$91$		0			0
$92$	1.16011e9			1.68831
$93$	7.61711e8	−	1.31932e9i	1.05589	−	1.82885i
$94$	−6.82962e6	−	1.18292e7i	−0.00902238	−	0.0156272i
$95$	1.97975e8	+	3.42902e8i	0.249375	+	0.431930i
$96$	2.29934e8	−	3.98258e8i	0.276301	−	0.478568i
$97$	5.95209e8			0.682648			0.341324	−	0.939946i	$-0.389125\pi$
$97$	5.95209e8			0.682648			0.341324	+	0.939946i	$0.389125\pi$
$98$		0			0
$99$	−1.97358e9			−2.06489
$100$	−2.55030e8	+	4.41724e8i	−0.255030	+	0.441724i
$101$	−1.37110e7	−	2.37482e7i	−0.0131106	−	0.0227083i	0.859396	−	0.511311i	$-0.170840\pi$
$101$	−1.37110e7	−	2.37482e7i	−0.0131106	−	0.0227083i	−0.872506	+	0.488603i	$0.837507\pi$
$102$	−1.01462e8	−	1.75738e8i	−0.0928120	−	0.160755i
$103$	−2.88490e8	+	4.99680e8i	−0.252559	+	0.437446i	−0.964230	−	0.265068i	$-0.914606\pi$
$103$	−2.88490e8	+	4.99680e8i	−0.252559	+	0.437446i	0.711670	+	0.702514i	$0.247939\pi$
$104$	−3.54737e8			−0.297342
$105$		0			0
$106$	1.38562e7			0.0106603
$107$	−1.01701e9	+	1.76151e9i	−0.750062	+	1.29915i	0.197730	+	0.980257i	$0.436643\pi$
$107$	−1.01701e9	+	1.76151e9i	−0.750062	+	1.29915i	−0.947792	+	0.318889i	$0.896690\pi$
$108$	1.78284e9	+	3.08796e9i	1.26097	+	2.18406i
$109$	1.09627e9	+	1.89880e9i	0.743874	+	1.28843i	0.950719	+	0.310054i	$0.100347\pi$
$109$	1.09627e9	+	1.89880e9i	0.743874	+	1.28843i	−0.206845	+	0.978374i	$0.566319\pi$
$110$	4.69736e7	−	8.13606e7i	0.0305905	−	0.0529843i
$111$	5.03038e8			0.314519
$112$		0			0
$113$	−2.12853e9			−1.22808			−0.614040	−	0.789275i	$-0.710457\pi$
$113$	−2.12853e9			−1.22808			−0.614040	+	0.789275i	$0.710457\pi$
$114$	1.20643e8	−	2.08961e8i	0.0669009	−	0.115876i
$115$	−1.11369e9	−	1.92898e9i	−0.593780	−	1.02846i
$116$	6.07398e8	+	1.05204e9i	0.311467	+	0.539477i
$117$	3.55846e9	−	6.16344e9i	1.75560	−	3.04079i
$118$	1.70429e8			0.0809233
$119$		0			0
$120$	−5.87613e8			−0.258688
$121$	2.95246e8	−	5.11381e8i	0.125213	−	0.216876i
$122$	5.81322e7	+	1.00688e8i	0.0237573	+	0.0411489i
$123$	1.61547e8	+	2.79808e8i	0.0636394	+	0.110227i
$124$	−1.49533e9	+	2.58998e9i	−0.567987	+	0.983783i
$125$	2.87951e9			1.05493
$126$		0			0
$127$	2.97800e9			1.01580			0.507900	−	0.861416i	$-0.330422\pi$
$127$	2.97800e9			1.01580			0.507900	+	0.861416i	$0.330422\pi$
$128$	−6.00780e8	+	1.04058e9i	−0.197820	+	0.342635i
$129$	1.10125e9	+	1.90741e9i	0.350131	+	0.606445i
$130$	1.69391e8	+	2.93394e8i	0.0520170	+	0.0900961i
$131$	−2.45606e9	+	4.25402e9i	−0.728648	+	1.26206i	0.228806	+	0.973472i	$0.426518\pi$
$131$	−2.45606e9	+	4.25402e9i	−0.728648	+	1.26206i	−0.957455	+	0.288584i	$0.906815\pi$
$132$	5.49885e9			1.57648
$133$		0			0
$134$	2.30120e8			0.0616570
$135$	3.42302e9	−	5.92885e9i	0.886968	−	1.53627i
$136$	4.00439e8	+	6.93580e8i	0.100372	+	0.173849i
$137$	1.27904e9	+	2.21537e9i	0.310200	+	0.537283i	0.978406	−	0.206694i	$-0.0662705\pi$
$137$	1.27904e9	+	2.21537e9i	0.310200	+	0.537283i	−0.668205	+	0.743977i	$0.732937\pi$
$138$	−6.78673e8	+	1.17550e9i	−0.159296	+	0.275909i
$139$	−3.28332e9			−0.746012			−0.373006	−	0.927829i	$-0.621673\pi$
$139$	−3.28332e9			−0.746012			−0.373006	+	0.927829i	$0.621673\pi$
$140$		0			0
$141$	−1.53502e9			−0.327060
$142$	5.88568e7	−	1.01943e8i	0.0121478	−	0.0210407i
$143$	−3.18680e9	−	5.51971e9i	−0.637299	−	1.10383i
$144$	−5.96351e9	−	1.03291e10i	−1.15577	−	2.00185i
$145$	1.16620e9	−	2.01991e9i	0.219087	−	0.379469i
$146$	−7.10761e8			−0.129460
$147$		0			0
$148$	−9.87523e8			−0.169188
$149$	3.30704e9	−	5.72796e9i	0.549669	−	0.952054i	−0.448629	−	0.893718i	$-0.648087\pi$
$149$	3.30704e9	−	5.72796e9i	0.549669	−	0.952054i	0.998297	−	0.0583355i	$-0.0185793\pi$
$150$	−2.98390e8	−	5.16826e8i	−0.0481252	−	0.0833554i
$151$	2.34531e9	+	4.06219e9i	0.367116	+	0.635864i	0.989113	−	0.147156i	$-0.0470118\pi$
$151$	2.34531e9	+	4.06219e9i	0.367116	+	0.635864i	−0.621997	+	0.783019i	$0.713679\pi$
$152$	−4.76140e8	+	8.24699e8i	−0.0723500	+	0.125314i
$153$	−1.60676e10			−2.37050
$154$		0			0
$155$	5.74202e9			0.799047
$156$	−9.91467e9	+	1.71727e10i	−1.34035	+	2.32155i
$157$	2.44743e9	+	4.23906e9i	0.321485	+	0.556829i	0.980795	−	0.195043i	$-0.0624846\pi$
$157$	2.44743e9	+	4.23906e9i	0.321485	+	0.556829i	−0.659309	+	0.751872i	$0.729151\pi$
$158$	1.05865e8	+	1.83363e8i	0.0135143	+	0.0234075i
$159$	7.78576e8	−	1.34853e9i	0.0966082	−	0.167330i
$160$	1.73332e9			0.209092
$161$		0			0
$162$	−2.04958e9			−0.233801
$163$	−6.11577e9	+	1.05928e10i	−0.678590	+	1.17535i	0.296816	+	0.954935i	$0.404075\pi$
$163$	−6.11577e9	+	1.05928e10i	−0.678590	+	1.17535i	−0.975406	+	0.220417i	$0.929258\pi$
$164$	−3.17136e8	−	5.49295e8i	−0.0342332	−	0.0592937i
$165$	−5.27886e9	−	9.14325e9i	−0.554450	−	0.960335i
$166$	2.89927e8	−	5.02168e8i	0.0296348	−	0.0513290i
$167$	−1.29106e10			−1.28447			−0.642234	−	0.766509i	$-0.721992\pi$
$167$	−1.29106e10			−1.28447			−0.642234	+	0.766509i	$0.721992\pi$
$168$		0			0
$169$	1.23793e10			1.16736
$170$	3.82428e8	−	6.62385e8i	0.0351180	−	0.0608261i
$171$	−9.55257e9	−	1.65455e10i	−0.854354	−	1.47978i
$172$	−2.16188e9	−	3.74448e9i	−0.188344	−	0.326222i
$173$	3.90017e9	−	6.75529e9i	0.331036	−	0.573372i	−0.651679	−	0.758495i	$-0.725935\pi$
$173$	3.90017e9	−	6.75529e9i	0.331036	−	0.573372i	0.982715	+	0.185123i	$0.0592684\pi$
$174$	−1.42133e9			−0.117551
$175$		0			0
$176$	−1.06813e10			−0.839108
$177$	9.57633e9	−	1.65867e10i	0.733363	−	1.27022i
$178$	9.55105e8	+	1.65429e9i	0.0713117	+	0.123516i
$179$	5.24434e9	+	9.08347e9i	0.381814	+	0.661322i	0.991322	−	0.131458i	$-0.0419660\pi$
$179$	5.24434e9	+	9.08347e9i	0.381814	+	0.661322i	−0.609507	+	0.792781i	$0.708633\pi$
$180$	−1.15716e10	+	2.00426e10i	−0.821613	+	1.42308i
$181$	7.08232e9			0.490481			0.245240	−	0.969462i	$-0.421133\pi$
$181$	7.08232e9			0.490481			0.245240	+	0.969462i	$0.421133\pi$
$182$		0			0
$183$	1.30657e10			0.861199
$184$	2.67850e9	−	4.63930e9i	0.172271	−	0.298381i
$185$	9.48016e8	+	1.64201e9i	0.0595036	+	0.103063i
$186$	−1.74956e9	−	3.03033e9i	−0.107182	−	0.185644i
$187$	−7.19473e9	+	1.24616e10i	−0.430256	+	0.745226i
$188$	3.01342e9			0.175934
$189$		0			0
$190$	9.09449e8			0.0506276
$191$	9.87174e9	−	1.70984e10i	0.536715	−	0.929617i	−0.462363	−	0.886691i	$-0.652998\pi$
$191$	9.87174e9	−	1.70984e10i	0.536715	−	0.929617i	0.999078	−	0.0429269i	$-0.0136682\pi$
$192$	1.62605e10	+	2.81641e10i	0.863534	+	1.49568i
$193$	−1.68337e10	−	2.91567e10i	−0.873314	−	1.51262i	−0.858548	−	0.512733i	$-0.828633\pi$
$193$	−1.68337e10	−	2.91567e10i	−0.873314	−	1.51262i	−0.0147660	−	0.999891i	$-0.504700\pi$
$194$	6.83563e8	−	1.18397e9i	0.0346474	−	0.0600111i
$195$	3.80721e10			1.88561
$196$		0			0
$197$	−3.47614e10			−1.64437			−0.822185	−	0.569220i	$-0.807245\pi$
$197$	−3.47614e10			−1.64437			−0.822185	+	0.569220i	$0.807245\pi$
$198$	−2.26655e9	+	3.92577e9i	−0.104802	+	0.181523i
$199$	−8.95627e9	−	1.55127e10i	−0.404845	−	0.701211i	0.589459	−	0.807798i	$-0.299341\pi$
$199$	−8.95627e9	−	1.55127e10i	−0.404845	−	0.701211i	−0.994303	+	0.106587i	$0.966008\pi$
$200$	1.17765e9	+	2.03974e9i	0.0520451	+	0.0901447i
$201$	1.29304e10	−	2.23960e10i	0.558764	−	0.967807i
$202$	−6.29852e7			−0.00266169
$203$		0			0
$204$	4.47680e10			1.80981
$205$	−6.08897e8	+	1.05464e9i	−0.0240797	+	0.0417073i
$206$	6.62628e8	+	1.14771e9i	0.0256370	+	0.0444046i
$207$	5.37375e10	+	9.30760e10i	2.03428	+	3.52347i
$208$	1.92589e10	−	3.33574e10i	0.713422	−	1.23568i
$209$	−1.71097e10			−0.620276
$210$		0			0
$211$	−5.08291e10			−1.76539			−0.882696	−	0.469945i	$-0.844274\pi$
$211$	−5.08291e10			−1.76539			−0.882696	+	0.469945i	$0.844274\pi$
$212$	−1.52844e9	+	2.64733e9i	−0.0519680	+	0.0900112i
$213$	−6.61429e9	−	1.14563e10i	−0.220178	−	0.381360i
$214$	2.33595e9	+	4.04598e9i	0.0761380	+	0.131875i
$215$	−4.15077e9	+	7.18935e9i	−0.132482	+	0.229465i
$216$	1.64651e10			0.514664
$217$		0			0
$218$	5.03602e9			0.151020
$219$	−3.99374e10	+	6.91737e10i	−1.17323	+	2.03209i
$220$	1.03630e10	+	1.79493e10i	0.298253	+	0.516589i
$221$	−2.59449e10	−	4.49378e10i	−0.731621	−	1.26720i
$222$	5.77710e8	−	1.00062e9i	0.0159633	−	0.0276492i
$223$	1.48248e10			0.401436			0.200718	−	0.979649i	$-0.435672\pi$
$223$	1.48248e10			0.401436			0.200718	+	0.979649i	$0.435672\pi$
$224$		0			0
$225$	−4.72531e10			−1.22916
$226$	−2.44449e9	+	4.23399e9i	−0.0623306	+	0.107960i
$227$	3.55990e10	+	6.16594e10i	0.889861	+	1.54128i	0.840039	+	0.542526i	$0.182532\pi$
$227$	3.55990e10	+	6.16594e10i	0.889861	+	1.54128i	0.0498216	+	0.998758i	$0.484135\pi$
$228$	2.66156e10	+	4.60996e10i	0.652273	+	1.12977i
$229$	2.87930e10	−	4.98710e10i	0.691875	−	1.19836i	−0.279348	−	0.960190i	$-0.590118\pi$
$229$	2.87930e10	−	4.98710e10i	0.691875	−	1.19836i	0.971223	−	0.238172i	$-0.0765483\pi$
$230$	−5.11605e9			−0.120548
$231$		0			0
$232$	5.60954e9			0.127125
$233$	2.58931e10	−	4.48482e10i	0.575549	−	0.996881i	−0.420432	−	0.907324i	$-0.638122\pi$
$233$	2.58931e10	−	4.48482e10i	0.575549	−	0.996881i	0.995982	−	0.0895570i	$-0.0285451\pi$
$234$	−8.17338e9	−	1.41567e10i	−0.178209	−	0.308667i
$235$	−2.89286e9	−	5.01058e9i	−0.0618760	−	0.107172i
$236$	−1.87994e10	+	3.25616e10i	−0.394495	+	0.683285i
$237$	2.37940e10			0.489892
$238$		0			0
$239$	1.49198e10			0.295782			0.147891	−	0.989004i	$-0.452751\pi$
$239$	1.49198e10			0.295782			0.147891	+	0.989004i	$0.452751\pi$
$240$	3.19019e10	−	5.52557e10i	0.620677	−	1.07504i
$241$	−2.02765e10	−	3.51199e10i	−0.387183	−	0.670621i	0.604886	−	0.796312i	$-0.293219\pi$
$241$	−2.02765e10	−	3.51199e10i	−0.387183	−	0.670621i	−0.992069	+	0.125691i	$0.959885\pi$
$242$	−6.78146e8	−	1.17458e9i	−0.0127103	−	0.0220148i
$243$	−4.59134e10	+	7.95244e10i	−0.844717	+	1.46309i
$244$	−2.56495e10			−0.463261
$245$		0			0
$246$	7.42109e8			0.0129199
$247$	3.08496e10	−	5.34331e10i	0.527368	−	0.913428i
$248$	6.90494e9	+	1.19597e10i	0.115912	+	0.200765i
$249$	−3.25818e10	−	5.64333e10i	−0.537128	−	0.930333i
$250$	3.30695e9	−	5.72781e9i	0.0535424	−	0.0927382i
$251$	2.61634e10			0.416066			0.208033	−	0.978122i	$-0.433294\pi$
$251$	2.61634e10			0.416066			0.208033	+	0.978122i	$0.433294\pi$
$252$		0			0
$253$	9.62498e10			1.47692
$254$	3.42006e9	−	5.92372e9i	0.0515563	−	0.0892982i
$255$	−4.29770e10	−	7.44383e10i	−0.636510	−	1.10247i
$256$	−3.08738e10	−	5.34749e10i	−0.449272	−	0.778162i
$257$	−1.39752e10	+	2.42058e10i	−0.199829	+	0.346114i	−0.948473	−	0.316858i	$-0.897372\pi$
$257$	−1.39752e10	+	2.42058e10i	−0.199829	+	0.346114i	0.748644	+	0.662973i	$0.230705\pi$
$258$	5.05887e9			0.0710828
$259$		0			0
$260$	−7.47400e10			−1.01432
$261$	−5.62708e10	+	9.74638e10i	−0.750586	+	1.30005i
$262$	5.64128e9	+	9.77099e9i	0.0739643	+	0.128110i
$263$	−1.75270e10	−	3.03576e10i	−0.225895	−	0.391262i	0.730693	−	0.682707i	$-0.239197\pi$
$263$	−1.75270e10	−	3.03576e10i	−0.225895	−	0.391262i	−0.956588	+	0.291445i	$0.905864\pi$
$264$	1.26960e10	−	2.19900e10i	0.160860	−	0.278618i
$265$	5.86916e9			0.0731087
$266$		0			0
$267$	2.14668e11			2.58504
$268$	−2.53838e10	+	4.39660e10i	−0.300573	+	0.520608i
$269$	5.65451e10	+	9.79391e10i	0.658431	+	1.14044i	0.981022	+	0.193897i	$0.0621127\pi$
$269$	5.65451e10	+	9.79391e10i	0.658431	+	1.14044i	−0.322591	+	0.946538i	$0.604554\pi$
$270$	−7.86229e9	−	1.36179e10i	−0.0900351	−	0.155945i
$271$	−5.76329e9	+	9.98230e9i	−0.0649095	+	0.112427i	−0.896654	−	0.442732i	$-0.854009\pi$
$271$	−5.76329e9	+	9.98230e9i	−0.0649095	+	0.112427i	0.831744	+	0.555159i	$0.187343\pi$
$272$	−8.69603e10			−0.963298
$273$		0			0
$274$	5.87562e9			0.0629762
$275$	−2.11589e10	+	3.66483e10i	−0.223098	+	0.386417i
$276$	−1.49725e11	−	2.59331e11i	−1.55311	−	2.69007i
$277$	3.08863e10	+	5.34966e10i	0.315215	+	0.545968i	0.979483	−	0.201526i	$-0.0645902\pi$
$277$	3.08863e10	+	5.34966e10i	0.315215	+	0.545968i	−0.664268	+	0.747494i	$0.731257\pi$
$278$	−3.77070e9	+	6.53104e9i	−0.0378634	+	0.0655814i
$279$	−2.77061e11			−2.73752
$280$		0			0
$281$	−1.96493e11			−1.88005			−0.940026	−	0.341104i	$-0.889199\pi$
$281$	−1.96493e11			−1.88005			−0.940026	+	0.341104i	$0.889199\pi$
$282$	−1.76288e9	+	3.05339e9i	−0.0165997	+	0.0287516i
$283$	3.44971e10	+	5.97507e10i	0.319701	+	0.553738i	0.980425	−	0.196890i	$-0.0630843\pi$
$283$	3.44971e10	+	5.97507e10i	0.319701	+	0.553738i	−0.660725	+	0.750628i	$0.729751\pi$
$284$	1.29846e10	+	2.24900e10i	0.118440	+	0.205143i
$285$	5.11017e10	−	8.85107e10i	0.458810	−	0.794683i
$286$	−1.46394e10			−0.129383
$287$		0			0
$288$	−8.36352e10			−0.716346
$289$	7.19193e8	−	1.24568e9i	0.00606464	−	0.0105043i
$290$	−2.67862e9	−	4.63950e9i	−0.0222392	−	0.0385195i
$291$	−7.68183e10	−	1.33053e11i	−0.627981	−	1.08770i
$292$	7.84019e10	−	1.35796e11i	0.631108	−	1.09311i
$293$	−1.00405e11			−0.795887			−0.397944	−	0.917410i	$-0.630276\pi$
$293$	−1.00405e11			−0.795887			−0.397944	+	0.917410i	$0.630276\pi$
$294$		0			0
$295$	7.21894e10			0.554976
$296$	−2.28003e9	+	3.94913e9i	−0.0172635	+	0.0299012i
$297$	1.47916e11	+	2.56197e11i	1.10309	+	1.91060i
$298$	−7.59588e9	−	1.31565e10i	−0.0557962	−	0.0966419i
$299$	−1.73543e11	+	3.00585e11i	−1.25570	+	2.17494i
$300$	1.31658e11			0.938427
$301$		0			0
$302$	1.07738e10			0.0745311
$303$	−3.53912e9	+	6.12994e9i	−0.0241215	+	0.0417796i
$304$	−5.16999e10	−	8.95469e10i	−0.347183	−	0.601339i
$305$	2.46234e10	+	4.26490e10i	0.162929	+	0.282202i
$306$	−1.84527e10	+	3.19611e10i	−0.120313	+	0.208389i
$307$	1.52467e11			0.979612			0.489806	−	0.871831i	$-0.337068\pi$
$307$	1.52467e11			0.979612			0.489806	+	0.871831i	$0.337068\pi$
$308$		0			0
$309$	1.48932e11			0.929337
$310$	6.59438e9	−	1.14218e10i	0.0405552	−	0.0702436i
$311$	−5.38186e10	−	9.32166e10i	−0.326220	−	0.565030i	0.655538	−	0.755162i	$-0.272442\pi$
$311$	−5.38186e10	−	9.32166e10i	−0.326220	−	0.565030i	−0.981759	+	0.190132i	$0.939108\pi$
$312$	4.57828e10	+	7.92981e10i	0.273531	+	0.473770i
$313$	−3.73541e9	+	6.46991e9i	−0.0219983	+	0.0381021i	−0.876815	−	0.480828i	$-0.840336\pi$
$313$	−3.73541e9	+	6.46991e9i	−0.0219983	+	0.0381021i	0.854817	+	0.518930i	$0.173669\pi$
$314$	1.12429e10			0.0652672
$315$		0			0
$316$	−4.67105e10			−0.263525
$317$	8.14322e10	−	1.41045e11i	0.452929	−	0.784495i	−0.545638	−	0.838021i	$-0.683713\pi$
$317$	8.14322e10	−	1.41045e11i	0.452929	−	0.784495i	0.998566	+	0.0535257i	$0.0170459\pi$
$318$	−1.78830e9	−	3.09742e9i	−0.00980659	−	0.0169855i
$319$	5.03936e10	+	8.72843e10i	0.272469	+	0.471931i
$320$	−6.12886e10	+	1.06155e11i	−0.326742	+	0.565933i
$321$	5.25025e11			2.75999
$322$		0			0
$323$	−1.39296e11			−0.712079
$324$	2.26083e11	−	3.91587e11i	1.13976	−	1.97413i
$325$	−7.63010e10	−	1.32157e11i	−0.379363	−	0.657076i
$326$	1.40472e10	+	2.43305e10i	0.0688829	+	0.119309i
$327$	2.82973e11	−	4.90123e11i	1.36861	−	2.37050i
$328$	−2.92886e9			−0.0139723
$329$		0			0
$330$	−2.42499e10			−0.112563
$331$	−1.48919e11	+	2.57936e11i	−0.681908	+	1.18110i	0.292490	+	0.956268i	$0.405516\pi$
$331$	−1.48919e11	+	2.57936e11i	−0.681908	+	1.18110i	−0.974398	+	0.224830i	$0.927817\pi$
$332$	6.39618e10	+	1.10785e11i	0.288935	+	0.500449i
$333$	−4.57432e10	−	7.92296e10i	−0.203858	−	0.353092i
$334$	−1.48271e10	+	2.56813e10i	−0.0651924	+	0.112917i
$335$	9.74731e10			0.422847
$336$		0			0
$337$	3.90243e11			1.64816			0.824082	−	0.566471i	$-0.191692\pi$
$337$	3.90243e11			1.64816			0.824082	+	0.566471i	$0.191692\pi$
$338$	1.42169e10	−	2.46244e10i	0.0592489	−	0.102622i
$339$	2.74711e11	+	4.75813e11i	1.12974	+	1.95676i
$340$	8.43689e10	+	1.46131e11i	0.342395	+	0.593045i
$341$	−1.24062e11	+	2.14882e11i	−0.496871	+	0.860606i
$342$	−4.38823e10			−0.173449
$343$		0			0
$344$	−1.99657e10			−0.0768726
$345$	−2.87469e11	+	4.97912e11i	−1.09246	+	1.89220i
$346$	−8.95823e9	−	1.55161e10i	−0.0336031	−	0.0582023i
$347$	1.22486e11	+	2.12152e11i	0.453528	+	0.785534i	0.998602	−	0.0528539i	$-0.0168318\pi$
$347$	1.22486e11	+	2.12152e11i	0.453528	+	0.785534i	−0.545074	+	0.838388i	$0.683498\pi$
$348$	1.56783e11	−	2.71556e11i	0.573050	−	0.992551i
$349$	1.04110e11			0.375646			0.187823	−	0.982203i	$-0.439857\pi$
$349$	1.04110e11			0.375646			0.187823	+	0.982203i	$0.439857\pi$
$350$		0			0
$351$	−1.06679e12			−3.75145
$352$	−3.74500e10	+	6.48653e10i	−0.130020	+	0.225201i
$353$	−6.64052e10	−	1.15017e11i	−0.227623	−	0.394254i	0.729480	−	0.684002i	$-0.239762\pi$
$353$	−6.64052e10	−	1.15017e11i	−0.227623	−	0.394254i	−0.957103	+	0.289747i	$0.906429\pi$
$354$	−2.19957e10	−	3.80977e10i	−0.0744429	−	0.128939i
$355$	2.49303e10	−	4.31806e10i	0.0833106	−	0.144298i
$356$	−4.21419e11			−1.39056
$357$		0			0
$358$	2.40913e10			0.0775151
$359$	2.46058e11	−	4.26185e11i	0.781831	−	1.35417i	−0.149044	−	0.988831i	$-0.547619\pi$
$359$	2.46058e11	−	4.26185e11i	0.781831	−	1.35417i	0.930874	−	0.365340i	$-0.119047\pi$
$360$	5.34340e10	+	9.25503e10i	0.167670	+	0.290413i
$361$	7.85290e10	+	1.36016e11i	0.243359	+	0.421511i
$362$	8.13363e9	−	1.40879e10i	0.0248941	−	0.0431178i
$363$	−1.52419e11			−0.460744
$364$		0			0
$365$	−3.01061e11			−0.887845
$366$	1.50052e10	−	2.59898e10i	0.0437097	−	0.0757074i
$367$	−2.83216e10	−	4.90544e10i	−0.0814930	−	0.141150i	0.822398	−	0.568912i	$-0.192635\pi$
$367$	−2.83216e10	−	4.90544e10i	−0.0814930	−	0.141150i	−0.903891	+	0.427762i	$0.859302\pi$
$368$	2.90835e11	+	5.03741e11i	0.826668	+	1.43183i
$369$	2.93802e10	−	5.08880e10i	0.0824966	−	0.142888i
$370$	4.35497e9			0.0120803
$371$		0			0
$372$	7.71955e11			2.09001
$373$	−1.50720e11	+	2.61055e11i	−0.403164	+	0.698301i	−0.994106	−	0.108413i	$-0.965423\pi$
$373$	−1.50720e11	+	2.61055e11i	−0.403164	+	0.698301i	0.590942	+	0.806714i	$0.298756\pi$
$374$	1.65255e10	+	2.86229e10i	0.0436748	+	0.0756470i
$375$	−3.71633e11	−	6.43688e11i	−0.970451	−	1.68087i
$376$	6.95750e9	−	1.20507e10i	0.0179518	−	0.0310934i
$377$	−3.63448e11			−0.926630
$378$		0			0
$379$	7.40526e10			0.184359			0.0921795	−	0.995742i	$-0.470617\pi$
$379$	7.40526e10			0.184359			0.0921795	+	0.995742i	$0.470617\pi$
$380$	−1.00319e11	+	1.73757e11i	−0.246806	+	0.427480i
$381$	−3.84344e11	−	6.65704e11i	−0.934454	−	1.61852i
$382$	−2.26742e10	−	3.92729e10i	−0.0544813	−	0.0943644i
$383$	−3.77448e11	+	6.53759e11i	−0.896318	+	1.55247i	−0.0641539	+	0.997940i	$0.520435\pi$
$383$	−3.77448e11	+	6.53759e11i	−0.896318	+	1.55247i	−0.832164	+	0.554529i	$0.812898\pi$
$384$	3.10150e11			0.727915
$385$		0			0
$386$	−7.73299e10			−0.177298
$387$	2.00281e11	−	3.46897e11i	0.453880	−	0.786143i
$388$	1.50803e11	+	2.61199e11i	0.337807	+	0.585099i
$389$	3.30773e10	+	5.72915e10i	0.0732413	+	0.126858i	0.900320	−	0.435228i	$-0.143332\pi$
$389$	3.30773e10	+	5.72915e10i	0.0732413	+	0.126858i	−0.827079	+	0.562086i	$0.809999\pi$
$390$	4.37236e10	−	7.57315e10i	0.0957029	−	0.165762i
$391$	7.83603e11			1.69551
$392$		0			0
$393$	1.26793e12			2.68119
$394$	−3.99215e10	+	6.91460e10i	−0.0834591	+	0.144555i
$395$	4.48418e10	+	7.76683e10i	0.0926821	+	0.160530i
$396$	−5.00032e11	−	8.66080e11i	−1.02181	−	1.76982i
$397$	−1.39608e11	+	2.41808e11i	−0.282068	+	0.488555i	−0.971894	−	0.235420i	$-0.924354\pi$
$397$	−1.39608e11	+	2.41808e11i	−0.282068	+	0.488555i	0.689826	+	0.723975i	$0.257687\pi$
$398$	−4.11430e10			−0.0821907
$399$		0			0
$400$	−2.55741e11			−0.499493
$401$	2.65648e11	−	4.60115e11i	0.513046	−	0.888622i	−0.486839	−	0.873492i	$-0.661850\pi$
$401$	2.65648e11	−	4.60115e11i	0.513046	−	0.888622i	0.999886	−	0.0151306i	$-0.00481642\pi$
$402$	−2.96995e10	−	5.14411e10i	−0.0567195	−	0.0982410i
$403$	−4.47379e11	−	7.74883e11i	−0.844895	−	1.46340i
$404$	6.94771e9	−	1.20338e10i	0.0129755	−	0.0224743i
$405$	−8.68152e11			−1.60342
$406$		0			0
$407$	−8.19313e10			−0.148004
$408$	1.03362e11	−	1.79028e11i	0.184668	−	0.319854i
$409$	−3.78291e11	−	6.55219e11i	−0.668453	−	1.15779i	−0.978337	−	0.207020i	$-0.933624\pi$
$409$	−3.78291e11	−	6.55219e11i	−0.668453	−	1.15779i	0.309884	−	0.950774i	$-0.399710\pi$
$410$	1.39856e9	+	2.42239e9i	0.00244430	+	0.00423366i
$411$	3.30149e11	−	5.71836e11i	0.570719	−	0.988514i
$412$	−2.92370e11			−0.499914
$413$		0			0
$414$	2.46857e11			0.412995
$415$	1.22806e11	−	2.12706e11i	0.203237	−	0.352017i
$416$	−1.35048e11	−	2.33910e11i	−0.221090	−	0.382939i
$417$	4.23748e11	+	7.33954e11i	0.686271	+	1.18866i
$418$	−1.96495e10	+	3.40340e10i	−0.0314818	+	0.0545280i
$419$	−6.70372e11			−1.06256			−0.531279	−	0.847197i	$-0.678288\pi$
$419$	−6.70372e11			−1.06256			−0.531279	+	0.847197i	$0.678288\pi$
$420$		0			0
$421$	4.12181e11			0.639468			0.319734	−	0.947507i	$-0.396407\pi$
$421$	4.12181e11			0.639468			0.319734	+	0.947507i	$0.396407\pi$
$422$	−5.83742e10	+	1.01107e11i	−0.0896015	+	0.155194i
$423$	1.39585e11	+	2.41768e11i	0.211986	+	0.367171i
$424$	7.05783e9	+	1.22245e10i	0.0106053	+	0.0183690i
$425$	−1.72262e11	+	2.98366e11i	−0.256117	+	0.443608i
$426$	−3.03845e10			−0.0447001
$427$		0			0
$428$	−1.03069e12			−1.48467
$429$	−8.22585e11	+	1.42476e12i	−1.17253	+	2.03088i
$430$	9.53385e9	+	1.65131e10i	0.0134481	+	0.0232928i
$431$	−1.98046e11	−	3.43026e11i	−0.276451	−	0.478828i	0.694049	−	0.719928i	$-0.255825\pi$
$431$	−1.98046e11	−	3.43026e11i	−0.276451	−	0.478828i	−0.970500	+	0.241100i	$0.922492\pi$
$432$	−8.93903e11	+	1.54828e12i	−1.23485	+	2.13882i
$433$	−6.70903e10			−0.0917201			−0.0458600	−	0.998948i	$-0.514603\pi$
$433$	−6.70903e10			−0.0917201			−0.0458600	+	0.998948i	$0.514603\pi$
$434$		0			0
$435$	−6.02043e11			−0.806168
$436$	−5.55508e11	+	9.62168e11i	−0.736209	+	1.27515i
$437$	4.65870e11	+	8.06911e11i	0.611080	+	1.05842i
$438$	9.17317e10	+	1.58884e11i	0.119093	+	0.206275i
$439$	5.63506e11	−	9.76021e11i	0.724116	−	1.25421i	−0.235221	−	0.971942i	$-0.575581\pi$
$439$	5.63506e11	−	9.76021e11i	0.724116	−	1.25421i	0.959337	−	0.282264i	$-0.0910854\pi$
$440$	9.57062e10			0.121732
$441$		0			0
$442$	−1.19185e11			−0.148532
$443$	2.95671e11	−	5.12116e11i	0.364747	−	0.631760i	−0.623989	−	0.781433i	$-0.714489\pi$
$443$	2.95671e11	−	5.12116e11i	0.364747	−	0.631760i	0.988735	+	0.149674i	$0.0478223\pi$
$444$	1.27451e11	+	2.20751e11i	0.155639	+	0.269575i
$445$	4.04559e11	+	7.00717e11i	0.489060	+	0.847077i
$446$	1.70254e10	−	2.94889e10i	0.0203747	−	0.0352900i
$447$	−1.70724e12			−2.02260
$448$		0			0
$449$	8.30465e10			0.0964302			0.0482151	−	0.998837i	$-0.484647\pi$
$449$	8.30465e10			0.0964302			0.0482151	+	0.998837i	$0.484647\pi$
$450$	−5.42674e10	+	9.39940e10i	−0.0623854	+	0.108055i
$451$	−2.63116e10	−	4.55731e10i	−0.0299470	−	0.0518697i
$452$	−5.39289e11	−	9.34076e11i	−0.607713	−	1.05259i
$453$	6.05376e11	−	1.04854e12i	0.675435	−	1.16989i
$454$	1.63534e11			0.180658
$455$		0			0
$456$	2.45805e11			0.266225
$457$	7.31950e11	−	1.26777e12i	0.784980	−	1.35963i	−0.144031	−	0.989573i	$-0.546006\pi$
$457$	7.31950e11	−	1.26777e12i	0.784980	−	1.35963i	0.929011	−	0.370052i	$-0.120660\pi$
$458$	−6.61342e10	−	1.14548e11i	−0.0702314	−	0.121644i
$459$	1.20423e12	+	2.08579e12i	1.26635	+	2.19338i
$460$	5.64336e11	−	9.77459e11i	0.587662	−	1.01786i
$461$	1.37860e12			1.42162			0.710809	−	0.703385i	$-0.248329\pi$
$461$	1.37860e12			1.42162			0.710809	+	0.703385i	$0.248329\pi$
$462$		0			0
$463$	2.81332e11			0.284515			0.142258	−	0.989830i	$-0.454564\pi$
$463$	2.81332e11			0.284515			0.142258	+	0.989830i	$0.454564\pi$
$464$	−3.04545e11	+	5.27488e11i	−0.305015	+	0.528302i
$465$	−7.41072e11	−	1.28357e12i	−0.735059	−	1.27316i
$466$	−5.94735e10	−	1.03011e11i	−0.0584234	−	0.101192i
$467$	−3.91879e11	+	6.78754e11i	−0.381264	+	0.660368i	−0.991243	−	0.132049i	$-0.957844\pi$
$467$	−3.91879e11	+	6.78754e11i	−0.381264	+	0.660368i	0.609979	+	0.792417i	$0.291178\pi$
$468$	3.60632e12			3.47502
$469$		0			0
$470$	−1.32891e10			−0.0125619
$471$	6.31735e11	−	1.09420e12i	0.591481	−	1.02448i
$472$	8.68099e10	+	1.50359e11i	0.0805063	+	0.139441i
$473$	−1.79363e11	−	3.10666e11i	−0.164762	−	0.285377i
$474$	2.73261e10	−	4.73302e10i	0.0248642	−	0.0430661i
$475$	−4.09655e11			−0.369230
$476$		0			0
$477$	−2.83196e11			−0.250469
$478$	1.71345e10	−	2.96779e10i	0.0150123	−	0.0260020i
$479$	9.20728e11	+	1.59475e12i	0.799138	+	1.38415i	0.920178	+	0.391500i	$0.128044\pi$
$479$	9.20728e11	+	1.59475e12i	0.799138	+	1.38415i	−0.121041	+	0.992648i	$0.538623\pi$
$480$	−2.23704e11	−	3.87467e11i	−0.192348	−	0.333157i
$481$	1.47726e11	−	2.55869e11i	0.125836	−	0.217954i
$482$	−9.31456e10			−0.0786051
$483$		0			0
$484$	2.99217e11			0.247846
$485$	2.89541e11	−	5.01499e11i	0.237614	−	0.411559i
$486$	1.05458e11	+	1.82658e11i	0.0857463	+	0.148517i
$487$	−6.14264e11	−	1.06394e12i	−0.494851	−	0.857107i	0.505131	−	0.863042i	$-0.331444\pi$
$487$	−6.14264e11	−	1.06394e12i	−0.494851	−	0.857107i	−0.999982	+	0.00593530i	$0.998111\pi$
$488$	−5.92207e10	+	1.02573e11i	−0.0472699	+	0.0818738i
$489$	3.15724e12			2.49699
$490$		0			0
$491$	−4.92920e11			−0.382745			−0.191372	−	0.981517i	$-0.561294\pi$
$491$	−4.92920e11			−0.382745			−0.191372	+	0.981517i	$0.561294\pi$
$492$	−8.18598e10	+	1.41785e11i	−0.0629836	+	0.109091i
$493$	4.10272e11	+	7.10612e11i	0.312796	+	0.541778i
$494$	−7.08580e10	−	1.22730e11i	−0.0535325	−	0.0927211i
$495$	−9.60055e11	+	1.66286e12i	−0.718741	+	1.24490i
$496$	−1.49950e12			−1.11244
$497$		0			0
$498$	−1.49673e11			−0.109047
$499$	9.54629e11	−	1.65347e12i	0.689259	−	1.19383i	−0.282819	−	0.959173i	$-0.591270\pi$
$499$	9.54629e11	−	1.65347e12i	0.689259	−	1.19383i	0.972078	−	0.234658i	$-0.0753969\pi$
$500$	7.29559e11	+	1.26363e12i	0.522030	+	0.904183i
$501$	1.66626e12	+	2.88605e12i	1.18161	+	2.04660i
$502$	3.00471e10	−	5.20431e10i	0.0211172	−	0.0365760i
$503$	−3.80479e11			−0.265017			−0.132509	−	0.991182i	$-0.542303\pi$
$503$	−3.80479e11			−0.265017			−0.132509	+	0.991182i	$0.542303\pi$
$504$		0			0
$505$	−2.66790e10			−0.0182540
$506$	1.10537e11	−	1.91456e11i	0.0749604	−	0.129835i
$507$	−1.59769e12	−	2.76728e12i	−1.07388	−	1.86002i
$508$	7.54513e11	+	1.30685e12i	0.502666	+	0.870644i
$509$	1.10937e12	−	1.92148e12i	0.732563	−	1.26884i	−0.223222	−	0.974768i	$-0.571657\pi$
$509$	1.10937e12	−	1.92148e12i	0.732563	−	1.26884i	0.955784	−	0.294068i	$-0.0950093\pi$
$510$	−1.97426e11			−0.129223
$511$		0			0
$512$	−7.57026e11			−0.486851
$513$	−1.43189e12	+	2.48010e12i	−0.912810	+	1.58103i
$514$	3.20994e10	+	5.55978e10i	0.0202844	+	0.0351337i
$515$	2.80673e11	+	4.86141e11i	0.175820	+	0.304530i
$516$	−5.58028e11	+	9.66533e11i	−0.346523	+	0.600196i
$517$	2.50012e11			0.153906
$518$		0			0
$519$	−2.01344e12			−1.21811
$520$	−1.72563e11	+	2.98887e11i	−0.103498	+	0.179264i
$521$	−6.50050e11	−	1.12592e12i	−0.386525	−	0.669480i	0.605455	−	0.795880i	$-0.292991\pi$
$521$	−6.50050e11	−	1.12592e12i	−0.386525	−	0.669480i	−0.991979	+	0.126399i	$0.959658\pi$
$522$	1.29247e11	+	2.23863e11i	0.0761912	+	0.131967i
$523$	9.59819e10	−	1.66246e11i	0.0560960	−	0.0971611i	−0.836614	−	0.547793i	$-0.815468\pi$
$523$	9.59819e10	−	1.66246e11i	0.0560960	−	0.0971611i	0.892710	+	0.450632i	$0.148801\pi$
$524$	−2.48909e12			−1.44228
$525$		0			0
$526$	−8.05149e10			−0.0458607
$527$	−1.01003e12	+	1.74942e12i	−0.570410	+	0.987978i
$528$	1.37854e12	+	2.38771e12i	0.771912	+	1.33699i
$529$	−1.72015e12	−	2.97938e12i	−0.955026	−	1.65415i
$530$	6.74038e9	−	1.16747e10i	0.00371059	−	0.00642693i
$531$	−3.48325e12			−1.90134
$532$		0			0
$533$	1.89764e11			0.101846
$534$	2.46534e11	−	4.27009e11i	0.131202	−	0.227249i
$535$	9.89452e11	+	1.71378e12i	0.522159	+	0.904405i
$536$	1.17214e11	+	2.03021e11i	0.0613393	+	0.106243i
$537$	1.35368e12	−	2.34465e12i	0.702477	−	1.21673i
$538$	2.59755e11			0.133673
$539$		0			0
$540$	3.46906e12			1.75566
$541$	−4.38801e11	+	7.60026e11i	−0.220232	+	0.381453i	−0.954878	−	0.296997i	$-0.904015\pi$
$541$	−4.38801e11	+	7.60026e11i	−0.220232	+	0.381453i	0.734646	+	0.678450i	$0.237348\pi$
$542$	1.32376e10	+	2.29282e10i	0.00658889	+	0.0114123i
$543$	−9.14053e11	−	1.58319e12i	−0.451203	−	0.781506i
$544$	−3.04893e11	+	5.28091e11i	−0.149263	+	0.258532i
$545$	2.13314e12			1.03570
$546$		0			0
$547$	−1.07234e12			−0.512140			−0.256070	−	0.966658i	$-0.582428\pi$
$547$	−1.07234e12			−0.512140			−0.256070	+	0.966658i	$0.582428\pi$
$548$	−6.48122e11	+	1.12258e12i	−0.307004	+	0.531747i
$549$	−1.18812e12	−	2.05788e12i	−0.558192	−	0.966817i
$550$	4.85995e10	+	8.41769e10i	0.0226464	+	0.0392248i
$551$	−4.87832e11	+	8.44950e11i	−0.225470	+	0.390525i
$552$	−1.38276e12			−0.633901
$553$		0			0
$554$	1.41884e11			0.0639942
$555$	2.44704e11	−	4.23840e11i	0.109477	−	0.189620i
$556$	−8.31868e11	−	1.44084e12i	−0.369163	−	0.639408i
$557$	−1.77420e12	−	3.07300e12i	−0.781006	−	1.35274i	−0.931356	−	0.364109i	$-0.881374\pi$
$557$	−1.77420e12	−	3.07300e12i	−0.781006	−	1.35274i	0.150351	−	0.988633i	$-0.451960\pi$
$558$	−3.18189e11	+	5.51119e11i	−0.138941	+	0.240653i
$559$	1.29360e12			0.560334
$560$		0			0
$561$	3.71424e12			1.58320
$562$	−2.25661e11	+	3.90857e11i	−0.0954209	+	0.165274i
$563$	−1.87089e12	−	3.24047e12i	−0.784801	−	1.35931i	−0.929118	−	0.369783i	$-0.879432\pi$
$563$	−1.87089e12	−	3.24047e12i	−0.784801	−	1.35931i	0.144317	−	0.989531i	$-0.453901\pi$
$564$	−3.88915e11	−	6.73621e11i	−0.161845	−	0.280324i
$565$	−1.03543e12	+	1.79342e12i	−0.427467	+	0.740394i
$566$	1.58472e11			0.0649049
$567$		0			0
$568$	1.19918e11			0.0483410
$569$	1.72898e12	−	2.99468e12i	0.691487	−	1.19769i	−0.279864	−	0.960040i	$-0.590289\pi$
$569$	1.72898e12	−	2.99468e12i	0.691487	−	1.19769i	0.971351	−	0.237651i	$-0.0763774\pi$
$570$	−1.17375e11	−	2.03299e11i	−0.0465733	−	0.0806673i
$571$	1.67025e12	+	2.89296e12i	0.657537	+	1.13889i	0.981251	+	0.192732i	$0.0617349\pi$
$571$	1.67025e12	+	2.89296e12i	0.657537	+	1.13889i	−0.323715	+	0.946155i	$0.604932\pi$
$572$	1.61483e12	−	2.79697e12i	0.630732	−	1.09246i
$573$	−5.09623e12			−1.97494
$574$		0			0
$575$	2.30449e12			0.879163
$576$	2.95727e12	−	5.12214e12i	1.11941	−	1.93888i
$577$	−1.02686e12	−	1.77858e12i	−0.385675	−	0.668009i	0.606187	−	0.795322i	$-0.292698\pi$
$577$	−1.02686e12	−	1.77858e12i	−0.385675	−	0.668009i	−0.991863	+	0.127313i	$0.959365\pi$
$578$	−1.65190e9	−	2.86118e9i	−0.000615615	−	0.00106628i
$579$	−4.34514e12	+	7.52601e12i	−1.60676	+	2.78299i
$580$	1.18188e12			0.433658
$581$		0			0
$582$	−3.52886e11			−0.127491
$583$	−1.26809e11	+	2.19639e11i	−0.0454612	+	0.0787411i
$584$	−3.62035e11	−	6.27063e11i	−0.128793	−	0.223076i
$585$	−3.46205e12	−	5.99644e12i	−1.22217	−	2.11686i
$586$	−1.15309e11	+	1.99722e11i	−0.0403948	+	0.0699659i
$587$	3.97715e12			1.38261			0.691306	−	0.722563i	$-0.257036\pi$
$587$	3.97715e12			1.38261			0.691306	+	0.722563i	$0.257036\pi$
$588$		0			0
$589$	−2.40195e12			−0.822327
$590$	8.29054e10	−	1.43596e11i	0.0281675	−	0.0487876i
$591$	4.48635e12	+	7.77059e12i	1.51269	+	2.62005i
$592$	−2.47569e11	−	4.28802e11i	−0.0828416	−	0.143486i
$593$	1.90284e11	−	3.29582e11i	0.0631912	−	0.109450i	−0.832699	−	0.553726i	$-0.813206\pi$
$593$	1.90284e11	−	3.29582e11i	0.0631912	−	0.109450i	0.895890	+	0.444276i	$0.146539\pi$
$594$	6.79490e11			0.223946
$595$		0			0
$596$	3.35151e12			1.08801
$597$	−2.31181e12	+	4.00418e12i	−0.744849	+	1.29012i
$598$	3.98608e11	+	6.90409e11i	0.127465	+	0.220776i
$599$	2.49476e12	+	4.32105e12i	0.791786	+	1.37141i	0.924860	+	0.380308i	$0.124182\pi$
$599$	2.49476e12	+	4.32105e12i	0.791786	+	1.37141i	−0.133074	+	0.991106i	$0.542485\pi$
$600$	3.03977e11	−	5.26503e11i	0.0957546	−	0.165852i
$601$	−4.94216e12			−1.54519			−0.772595	−	0.634900i	$-0.781041\pi$
$601$	−4.94216e12			−1.54519			−0.772595	+	0.634900i	$0.781041\pi$
$602$		0			0
$603$	−4.70323e12			−1.44867
$604$	−1.18842e12	+	2.05841e12i	−0.363333	+	0.629312i
$605$	−2.87246e11	−	4.97525e11i	−0.0871677	−	0.150979i
$606$	8.12895e9	+	1.40798e10i	0.00244854	+	0.00424100i
$607$	−1.03273e12	+	1.78875e12i	−0.308773	+	0.534810i	−0.978094	−	0.208163i	$-0.933252\pi$
$607$	−1.03273e12	+	1.78875e12i	−0.308773	+	0.534810i	0.669321	+	0.742973i	$0.266585\pi$
$608$	−7.25065e11			−0.215184
$609$		0			0
$610$	1.13114e11			0.0330775
$611$	−4.50784e11	+	7.80781e11i	−0.130853	+	0.226644i
$612$	−4.07093e12	−	7.05105e12i	−1.17304	−	2.03176i
$613$	−6.65987e11	−	1.15352e12i	−0.190499	−	0.329955i	0.754916	−	0.655821i	$-0.227677\pi$
$613$	−6.65987e11	−	1.15352e12i	−0.190499	−	0.329955i	−0.945416	+	0.325866i	$0.894344\pi$
$614$	1.75100e11	−	3.03282e11i	0.0497197	−	0.0861170i
$615$	3.14340e11			0.0886056
$616$		0			0
$617$	2.58004e12			0.716709			0.358355	−	0.933586i	$-0.383338\pi$
$617$	2.58004e12			0.716709			0.358355	+	0.933586i	$0.383338\pi$
$618$	1.71039e11	−	2.96249e11i	0.0471680	−	0.0816974i
$619$	−6.70531e11	−	1.16139e12i	−0.183574	−	0.317959i	0.759521	−	0.650483i	$-0.225433\pi$
$619$	−6.70531e11	−	1.16139e12i	−0.183574	−	0.317959i	−0.943095	+	0.332523i	$0.892100\pi$
$620$	1.45481e12	+	2.51981e12i	0.395407	+	0.684864i
$621$	8.05500e12	−	1.39517e13i	2.17347	−	3.76456i
$622$	−2.47230e11			−0.0662285
$623$		0			0
$624$	−9.94231e12			−2.62517
$625$	4.17756e11	−	7.23574e11i	0.109512	−	0.189681i
$626$	8.57980e9	+	1.48606e10i	0.00223302	+	0.00386770i
$627$	2.20820e12	+	3.82472e12i	0.570604	+	0.988315i
$628$	−1.24017e12	+	2.14804e12i	−0.318173	+	0.551091i
$629$	−6.67030e11			−0.169910
$630$		0			0
$631$	2.51284e12			0.631004			0.315502	−	0.948925i	$-0.397827\pi$
$631$	2.51284e12			0.631004			0.315502	+	0.948925i	$0.397827\pi$
$632$	−1.07847e11	+	1.86797e11i	−0.0268894	+	0.0465738i
$633$	6.56006e12	+	1.13624e13i	1.62402	+	2.81288i
$634$	−1.87040e11	−	3.23964e11i	−0.0459763	−	0.0796332i
$635$	1.44866e12	−	2.50915e12i	0.353576	−	0.612412i
$636$	7.89047e11			0.191225
$637$		0			0
$638$	2.31497e11			0.0553161
$639$	−1.20293e12	+	2.08353e12i	−0.285420	+	0.494363i
$640$	5.84502e11	+	1.01239e12i	0.137713	+	0.238527i
$641$	1.75990e12	+	3.04823e12i	0.411743	+	0.713160i	0.995080	−	0.0990702i	$-0.0315868\pi$
$641$	1.75990e12	+	3.04823e12i	0.411743	+	0.713160i	−0.583338	+	0.812230i	$0.698254\pi$
$642$	6.02961e11	−	1.04436e12i	0.140082	−	0.242629i
$643$	4.14156e12			0.955464			0.477732	−	0.878506i	$-0.341459\pi$
$643$	4.14156e12			0.955464			0.477732	+	0.878506i	$0.341459\pi$
$644$		0			0
$645$	2.14282e12			0.487490
$646$	−1.59974e11	+	2.77082e11i	−0.0361411	+	0.0625983i
$647$	−1.27316e12	−	2.20517e12i	−0.285636	−	0.494735i	0.687127	−	0.726537i	$-0.258871\pi$
$647$	−1.27316e12	−	2.20517e12i	−0.285636	−	0.494735i	−0.972763	+	0.231801i	$0.925538\pi$
$648$	−1.04398e12	−	1.80822e12i	−0.232597	−	0.402870i
$649$	−1.55972e12	+	2.70152e12i	−0.345101	+	0.597733i
$650$	−3.50509e11			−0.0770174
$651$		0			0
$652$	−6.19802e12			−1.34319
$653$	−3.87564e12	+	6.71281e12i	−0.834131	+	1.44476i	0.0606043	+	0.998162i	$0.480697\pi$
$653$	−3.87564e12	+	6.71281e12i	−0.834131	+	1.44476i	−0.894736	+	0.446596i	$0.852636\pi$
$654$	−6.49955e11	−	1.12576e12i	−0.138926	−	0.240627i
$655$	2.38951e12	+	4.13876e12i	0.507252	+	0.878585i
$656$	1.59010e11	−	2.75413e11i	0.0335241	−	0.0580654i
$657$	1.45267e13			3.04174
$658$		0			0
$659$	4.73942e12			0.978906			0.489453	−	0.872030i	$-0.337196\pi$
$659$	4.73942e12			0.978906			0.489453	+	0.872030i	$0.337196\pi$
$660$	2.67493e12	−	4.63311e12i	0.548737	−	0.950440i
$661$	1.52360e12	+	2.63894e12i	0.310430	+	0.537680i	0.978455	−	0.206458i	$-0.0661938\pi$
$661$	1.52360e12	+	2.63894e12i	0.310430	+	0.537680i	−0.668026	+	0.744138i	$0.732860\pi$
$662$	3.42051e11	+	5.92449e11i	0.0692197	+	0.119892i
$663$	−6.69695e12	+	1.15995e13i	−1.34606	+	2.33145i
$664$	5.90711e11			0.117928
$665$		0			0
$666$	−2.10134e11			−0.0413868
$667$	2.74427e12	−	4.75322e12i	0.536860	−	0.929869i
$668$	−3.27106e12	−	5.66565e12i	−0.635616	−	1.10092i
$669$	−1.91330e12	−	3.31394e12i	−0.369289	−	0.639627i
$670$	1.11942e11	−	1.93890e11i	0.0214614	−	0.0371722i
$671$	−2.12805e12			−0.405257
$672$		0			0
$673$	4.36982e12			0.821100			0.410550	−	0.911838i	$-0.365337\pi$
$673$	4.36982e12			0.821100			0.410550	+	0.911838i	$0.365337\pi$
$674$	4.48171e11	−	7.76255e11i	0.0836516	−	0.144889i
$675$	3.54151e12	+	6.13408e12i	0.656631	+	1.13732i
$676$	3.13645e12	+	5.43249e12i	0.577668	+	1.00055i
$677$	1.93293e12	−	3.34794e12i	0.353645	−	0.612531i	−0.633240	−	0.773955i	$-0.718275\pi$
$677$	1.93293e12	−	3.34794e12i	0.353645	−	0.612531i	0.986885	+	0.161424i	$0.0516088\pi$
$678$	1.26196e12			0.229356
$679$		0			0
$680$	7.79177e11			0.139748
$681$	9.18891e12	−	1.59157e13i	1.63720	−	2.83572i
$682$	2.84956e11	+	4.93558e11i	0.0504369	+	0.0873592i
$683$	−2.43432e12	−	4.21636e12i	−0.428040	−	0.741387i	0.568659	−	0.822573i	$-0.307462\pi$
$683$	−2.43432e12	−	4.21636e12i	−0.428040	−	0.741387i	−0.996699	+	0.0811865i	$0.974129\pi$
$684$	4.84052e12	−	8.38403e12i	0.845551	−	1.46454i
$685$	2.48877e12			0.431895
$686$		0			0
$687$	−1.48642e13			−2.54588
$688$	1.08395e12	−	1.87746e12i	0.184443	−	0.319464i
$689$	−4.57284e11	−	7.92040e11i	−0.0773036	−	0.133894i
$690$	6.60284e11	+	1.14365e12i	0.110894	+	0.192075i
$691$	−4.67097e12	+	8.09035e12i	−0.779391	+	1.34995i	0.152902	+	0.988241i	$0.451138\pi$
$691$	−4.67097e12	+	8.09035e12i	−0.779391	+	1.34995i	−0.932293	+	0.361704i	$0.882195\pi$
$692$	3.95262e12			0.655251
$693$		0			0
$694$	5.62673e11			0.0920743
$695$	−1.59718e12	+	2.76639e12i	−0.259670	+	0.449761i
$696$	−7.23974e11	−	1.25396e12i	−0.116945	−	0.202554i
$697$	−2.14212e11	−	3.71026e11i	−0.0343792	−	0.0595466i
$698$	1.19565e11	−	2.07092e11i	0.0190657	−	0.0330228i
$699$	−1.33672e13			−2.11784
$700$		0			0
$701$	5.21727e12			0.816042			0.408021	−	0.912973i	$-0.366219\pi$
$701$	5.21727e12			0.816042			0.408021	+	0.912973i	$0.366219\pi$
$702$	−1.22515e12	+	2.12202e12i	−0.190403	+	0.329787i
$703$	−3.96565e11	−	6.86871e11i	−0.0612372	−	0.106066i
$704$	−2.64840e12	−	4.58716e12i	−0.406356	−	0.703829i
$705$	−7.46712e11	+	1.29334e12i	−0.113842	+	0.197180i
$706$	−3.05050e11			−0.0462115
$707$		0			0
$708$	9.70511e12			1.45161
$709$	−6.04877e12	+	1.04768e13i	−0.898998	+	1.55711i	−0.0702213	+	0.997531i	$0.522371\pi$
$709$	−6.04877e12	+	1.04768e13i	−0.898998	+	1.55711i	−0.828777	+	0.559579i	$0.810963\pi$
$710$	−5.72620e10	−	9.91807e10i	−0.00845676	−	0.0146475i
$711$	−2.16368e12	−	3.74761e12i	−0.317527	−	0.549973i
$712$	−9.72989e11	+	1.68527e12i	−0.141889	+	0.245758i
$713$	1.35120e13			1.95802
$714$		0			0
$715$	−6.20091e12			−0.887316
$716$	−2.65744e12	+	4.60281e12i	−0.377880	+	0.654508i
$717$	−1.92557e12	−	3.33518e12i	−0.272096	−	0.471284i
$718$	−5.65167e11	−	9.78898e11i	−0.0793628	−	0.137460i
$719$	4.20588e12	−	7.28480e12i	0.586917	−	1.01657i	−0.407716	−	0.913109i	$-0.633675\pi$
$719$	4.20588e12	−	7.28480e12i	0.586917	−	1.01657i	0.994633	−	0.103462i	$-0.0329920\pi$
$720$	−1.16039e13			−1.60919
$721$		0			0
$722$	3.60744e11			0.0494062
$723$	−5.23382e12	+	9.06524e12i	−0.712355	+	1.23383i
$724$	1.79439e12	+	3.10798e12i	0.242713	+	0.420392i
$725$	1.20656e12	+	2.08983e12i	0.162192	+	0.280925i
$726$	−1.75045e11	+	3.03186e11i	−0.0233848	+	0.0405037i
$727$	−1.42529e13			−1.89234			−0.946171	−	0.323668i	$-0.895084\pi$
$727$	−1.42529e13			−1.89234			−0.946171	+	0.323668i	$0.895084\pi$
$728$		0			0
$729$	6.13882e12			0.805028
$730$	−3.45751e11	+	5.98859e11i	−0.0450621	+	0.0780498i
$731$	−1.46026e12	−	2.52924e12i	−0.189148	−	0.327613i
$732$	3.31036e12	+	5.73371e12i	0.426163	+	0.738135i
$733$	6.28751e12	−	1.08903e13i	0.804472	−	1.39339i	−0.112175	−	0.993688i	$-0.535782\pi$
$733$	6.28751e12	−	1.08903e13i	0.804472	−	1.39339i	0.916647	−	0.399698i	$-0.130885\pi$
$734$	−1.30103e11			−0.0165445
$735$		0			0
$736$	4.07881e12			0.512370
$737$	−2.10600e12	+	3.64770e12i	−0.262939	+	0.455424i
$738$	−6.74829e10	−	1.16884e11i	−0.00837414	−	0.0145044i
$739$	−2.25106e12	−	3.89895e12i	−0.277643	−	0.480892i	0.693155	−	0.720788i	$-0.256220\pi$
$739$	−2.25106e12	−	3.89895e12i	−0.277643	−	0.480892i	−0.970799	+	0.239896i	$0.922887\pi$
$740$	−4.80383e11	+	8.32047e11i	−0.0588904	+	0.102001i
$741$	−1.59260e13			−1.94055
$742$		0			0
$743$	−2.21147e12			−0.266214			−0.133107	−	0.991102i	$-0.542495\pi$
$743$	−2.21147e12			−0.266214			−0.133107	+	0.991102i	$0.542495\pi$
$744$	1.78232e12	−	3.08707e12i	0.213259	−	0.369376i
$745$	−3.21743e12	−	5.57276e12i	−0.382654	−	0.662776i
$746$	3.46187e11	+	5.99613e11i	0.0409247	+	0.0708837i
$747$	−5.92558e12	+	1.02634e13i	−0.696286	+	1.20600i
$748$	−7.29149e12			−0.851646
$749$		0			0
$750$	−1.70720e12			−0.197019
$751$	5.74532e12	−	9.95118e12i	0.659074	−	1.14155i	−0.321781	−	0.946814i	$-0.604282\pi$
$751$	5.74532e12	−	9.95118e12i	0.659074	−	1.14155i	0.980856	−	0.194736i	$-0.0623851\pi$
$752$	7.55454e11	+	1.30849e12i	0.0861446	+	0.149207i
$753$	−3.37667e12	−	5.84857e12i	−0.382747	−	0.662937i
$754$	−4.17399e11	+	7.22957e11i	−0.0470306	+	0.0814594i
$755$	4.56352e12			0.511139
$756$		0			0
$757$	−1.01163e13			−1.11967			−0.559834	−	0.828604i	$-0.689135\pi$
$757$	−1.01163e13			−1.11967			−0.559834	+	0.828604i	$0.689135\pi$
$758$	8.50452e10	−	1.47303e11i	0.00935703	−	0.0162069i
$759$	−1.24221e13	−	2.15157e13i	−1.35865	−	2.35325i
$760$	4.63239e11	+	8.02353e11i	0.0503667	+	0.0872378i
$761$	−8.30801e11	+	1.43899e12i	−0.0897978	+	0.155534i	−0.907426	−	0.420213i	$-0.861955\pi$
$761$	−8.30801e11	+	1.43899e12i	−0.0897978	+	0.155534i	0.817628	+	0.575747i	$0.195289\pi$
$762$	−1.76559e12			−0.189711
$763$		0			0
$764$	1.00045e13			1.06237
$765$	−7.81613e12	+	1.35379e13i	−0.825117	+	1.42914i
$766$	8.66954e11	+	1.50161e12i	0.0909843	+	0.157589i
$767$	−5.62451e12	−	9.74193e12i	−0.586820	−	1.01640i
$768$	−7.96920e12	+	1.38031e13i	−0.826589	+	1.43169i
$769$	6.69555e12			0.690427			0.345213	−	0.938524i	$-0.387807\pi$
$769$	6.69555e12			0.690427			0.345213	+	0.938524i	$0.387807\pi$
$770$		0			0
$771$	7.21463e12			0.735308
$772$	8.53002e12	−	1.47744e13i	0.864315	−	1.49704i
$773$	6.45950e12	+	1.11882e13i	0.650716	+	1.12707i	0.982950	+	0.183875i	$0.0588643\pi$
$773$	6.45950e12	+	1.11882e13i	0.650716	+	1.12707i	−0.332234	+	0.943197i	$0.607802\pi$
$774$	−4.60023e11	−	7.96783e11i	−0.0460728	−	0.0798005i
$775$	−2.97039e12	+	5.14487e12i	−0.295771	+	0.512291i
$776$	1.39272e12			0.137876
$777$		0			0
$778$	1.51949e11			0.0148693
$779$	2.54708e11	−	4.41167e11i	0.0247813	−	0.0429224i
$780$	9.64603e12	+	1.67074e13i	0.933089	+	1.61616i
$781$	1.07729e12	+	1.86592e12i	0.103610	+	0.179458i
$782$	8.99922e11	−	1.55871e12i	0.0860547	−	0.149051i
$783$	1.68695e13			1.60388
$784$		0			0
$785$	4.76222e12			0.447606
$786$	1.45614e12	−	2.52211e12i	0.136082	−	0.235702i
$787$	6.07603e12	+	1.05240e13i	0.564590	+	0.977899i	0.997088	+	0.0762639i	$0.0242991\pi$
$787$	6.07603e12	+	1.05240e13i	0.564590	+	0.977899i	−0.432497	+	0.901635i	$0.642368\pi$
$788$	−8.80723e12	−	1.52546e13i	−0.813713	−	1.40939i
$789$	−4.52411e12	+	7.83599e12i	−0.415610	+	0.719858i
$790$	2.05993e11			0.0188161
$791$		0			0
$792$	−4.61797e12			−0.417050
$793$	3.83697e12	−	6.64583e12i	0.344556	−	0.596788i
$794$	3.20664e11	+	5.55406e11i	0.0286324	+	0.0495927i
$795$	−7.57480e11	−	1.31199e12i	−0.0672542	−	0.116488i
$796$	4.53836e12	−	7.86067e12i	0.400673	−	0.693986i
$797$	−1.01984e13			−0.895306			−0.447653	−	0.894207i	$-0.647740\pi$
$797$	−1.01984e13			−0.895306			−0.447653	+	0.894207i	$0.647740\pi$
$798$		0			0
$799$	2.03544e12			0.176684
$800$	−8.96658e11	+	1.55306e12i	−0.0773966	+	0.134055i
$801$	−1.95206e13	−	3.38107e13i	−1.67551	−	2.90207i
$802$	−6.10162e11	−	1.05683e12i	−0.0520788	−	0.0902031i
$803$	6.50472e12	−	1.12665e13i	0.552089	−	0.956246i
$804$	1.31042e13			1.10601
$805$		0			0
$806$	−2.05515e12			−0.171529
$807$	1.45956e13	−	2.52803e13i	1.21141	−	2.09822i
$808$	−3.20823e10	−	5.55682e10i	−0.00264798	−	0.00458643i
$809$	3.69491e12	+	6.39976e12i	0.303274	+	0.525286i	0.976876	−	0.213809i	$-0.0685870\pi$
$809$	3.69491e12	+	6.39976e12i	0.303274	+	0.525286i	−0.673602	+	0.739095i	$0.735254\pi$
$810$	−9.97023e11	+	1.72689e12i	−0.0813809	+	0.140956i
$811$	−5.15025e12			−0.418056			−0.209028	−	0.977910i	$-0.567030\pi$
$811$	−5.15025e12			−0.418056			−0.209028	+	0.977910i	$0.567030\pi$
$812$		0			0
$813$	2.97527e12			0.238846
$814$	−9.40933e10	+	1.62974e11i	−0.00751188	+	0.0130110i
$815$	5.95006e12	+	1.03058e13i	0.472403	+	0.818226i
$816$	1.12232e13	+	1.94391e13i	0.886157	+	1.53487i
$817$	1.73631e12	−	3.00738e12i	0.136342	−	0.236151i
$818$	−1.73778e12			−0.135708
$819$		0			0
$820$	−6.17085e11			−0.0476632
$821$	−3.38894e12	+	5.86981e12i	−0.260327	+	0.450900i	−0.966329	−	0.257310i	$-0.917164\pi$
$821$	−3.38894e12	+	5.86981e12i	−0.260327	+	0.450900i	0.706002	+	0.708210i	$0.250497\pi$
$822$	−7.58315e11	−	1.31344e12i	−0.0579331	−	0.100343i
$823$	4.23808e12	+	7.34057e12i	0.322011	+	0.557739i	0.980903	−	0.194499i	$-0.0623080\pi$
$823$	4.23808e12	+	7.34057e12i	0.322011	+	0.557739i	−0.658892	+	0.752237i	$0.728975\pi$
$824$	−6.75036e11	+	1.16920e12i	−0.0510099	+	0.0883517i
$825$	1.09232e13			0.820930
$826$		0			0
$827$	−9.70886e12			−0.721761			−0.360880	−	0.932612i	$-0.617524\pi$
$827$	−9.70886e12			−0.721761			−0.360880	+	0.932612i	$0.617524\pi$
$828$	−2.72301e13	+	4.71639e13i	−2.01332	+	3.48717i
$829$	−3.38675e11	−	5.86601e11i	−0.0249050	−	0.0431368i	0.853304	−	0.521413i	$-0.174595\pi$
$829$	−3.38675e11	−	5.86601e11i	−0.0249050	−	0.0431368i	−0.878209	+	0.478277i	$0.841262\pi$
$830$	−2.82071e11	−	4.88561e11i	−0.0206304	−	0.0357329i
$831$	7.97243e12	−	1.38087e13i	0.579944	−	1.00449i
$832$	1.91007e13			1.38196
$833$		0			0
$834$	1.94660e12			0.139325
$835$	−6.28040e12	+	1.08780e13i	−0.447093	+	0.774389i
$836$	−4.33496e12	−	7.50837e12i	−0.306942	−	0.531640i
$837$	2.07651e13	+	3.59662e13i	1.46241	+	2.53297i
$838$	−7.69883e11	+	1.33348e12i	−0.0539295	+	0.0934087i
$839$	−5.39522e12			−0.375907			−0.187953	−	0.982178i	$-0.560185\pi$
$839$	−5.39522e12			−0.375907			−0.187953	+	0.982178i	$0.560185\pi$
$840$		0			0
$841$	−8.75986e12			−0.603831
$842$	4.73366e11	−	8.19894e11i	0.0324558	−	0.0562151i
$843$	2.53597e13	+	4.39242e13i	1.72950	+	2.99558i
$844$	−1.28782e13	−	2.23056e13i	−0.873601	−	1.51312i
$845$	6.02195e12	−	1.04303e13i	0.406333	−	0.703789i
$846$	6.41221e11			0.0430369
$847$		0			0
$848$	−1.53270e12			−0.101783
$849$	8.90447e12	−	1.54230e13i	0.588198	−	1.01879i
$850$	3.95666e11	+	6.85313e11i	0.0259982	+	0.0450302i
$851$	2.23085e12	+	3.86395e12i	0.145810	+	0.252551i
$852$	3.35162e12	−	5.80518e12i	0.217910	−	0.377431i
$853$	−1.31884e13			−0.852946			−0.426473	−	0.904500i	$-0.640244\pi$
$853$	−1.31884e13			−0.852946			−0.426473	+	0.904500i	$0.640244\pi$
$854$		0			0
$855$	−1.85875e13			−1.18952
$856$	−2.37969e12	+	4.12174e12i	−0.151491	+	0.262391i
$857$	−3.94669e12	−	6.83587e12i	−0.249930	−	0.432892i	0.713576	−	0.700578i	$-0.247074\pi$
$857$	−3.94669e12	−	6.83587e12i	−0.249930	−	0.432892i	−0.963506	+	0.267686i	$0.913741\pi$
$858$	1.88938e12	+	3.27251e12i	0.119022	+	0.206152i
$859$	5.33619e12	−	9.24256e12i	0.334397	−	0.579193i	−0.648972	−	0.760812i	$-0.724801\pi$
$859$	5.33619e12	−	9.24256e12i	0.334397	−	0.579193i	0.983369	+	0.181620i	$0.0581340\pi$
$860$	−4.20660e12			−0.262233
$861$		0			0
$862$	−9.09778e11			−0.0561245
$863$	8.19087e12	−	1.41870e13i	0.502668	−	0.870647i	−0.497327	−	0.867563i	$-0.665685\pi$
$863$	8.19087e12	−	1.41870e13i	0.502668	−	0.870647i	0.999995	−	0.00308390i	$-0.000981639\pi$
$864$	6.26827e12	+	1.08570e13i	0.382680	+	0.662821i
$865$	−3.79449e12	−	6.57225e12i	−0.230452	−	0.399155i
$866$	−7.70493e10	+	1.33453e11i	−0.00465520	+	0.00806304i
$867$	−3.71280e11			−0.0223159
$868$		0			0
$869$	−3.87540e12			−0.230530
$870$	−6.91411e11	+	1.19756e12i	−0.0409166	+	0.0708697i
$871$	−7.59444e12	−	1.31540e13i	−0.447110	−	0.774417i
$872$	2.56516e12	+	4.44299e12i	0.150242	+	0.260226i
$873$	−1.39708e13	+	2.41981e13i	−0.814061	+	1.40999i
$874$	2.14010e12			0.124060
$875$		0			0
$876$	−4.04746e13			−2.32227
$877$	−6.19139e12	+	1.07238e13i	−0.353419	+	0.612140i	−0.986846	−	0.161662i	$-0.948314\pi$
$877$	−6.19139e12	+	1.07238e13i	−0.353419	+	0.612140i	0.633427	+	0.773803i	$0.281648\pi$
$878$	−1.29431e12	−	2.24181e12i	−0.0735042	−	0.127313i
$879$	1.29584e13	+	2.24446e13i	0.732152	+	1.26812i
$880$	−5.19595e12	+	8.99965e12i	−0.292074	+	0.505887i
$881$	1.81283e13			1.01383			0.506917	−	0.861995i	$-0.330785\pi$
$881$	1.81283e13			1.01383			0.506917	+	0.861995i	$0.330785\pi$
$882$		0			0
$883$	2.19803e12			0.121678			0.0608389	−	0.998148i	$-0.480622\pi$
$883$	2.19803e12			0.121678			0.0608389	+	0.998148i	$0.480622\pi$
$884$	1.31469e13	−	2.27711e13i	0.724082	−	1.25415i
$885$	−9.31685e12	−	1.61373e13i	−0.510534	−	0.884270i
$886$	−6.79121e11	−	1.17627e12i	−0.0370250	−	0.0641292i
$887$	1.15986e13	−	2.00894e13i	0.629144	−	1.08971i	−0.358580	−	0.933499i	$-0.616739\pi$
$887$	1.15986e13	−	2.00894e13i	0.629144	−	1.08971i	0.987724	−	0.156210i	$-0.0499277\pi$
$888$	1.17705e12			0.0635241
$889$		0			0
$890$	1.85845e12			0.0992879
$891$	1.87573e13	−	3.24886e13i	0.997058	−	1.72695i
$892$	3.75604e12	+	6.50565e12i	0.198650	+	0.344072i
$893$	1.21011e12	+	2.09598e12i	0.0636788	+	0.110295i
$894$	−1.96067e12	+	3.39597e12i	−0.102656	+	0.177806i
$895$	1.02045e13			0.531603
$896$		0			0
$897$	8.95906e13			4.62058
$898$	9.53741e10	−	1.65193e11i	0.00489426	−	0.00847711i
$899$	7.07450e12	+	1.22534e13i	0.361225	+	0.625659i
$900$	−1.19721e13	−	2.07364e13i	−0.608248	−	1.05352i
$901$	−1.03239e12	+	1.78816e12i	−0.0521896	+	0.0903950i
$902$	−1.20869e11			−0.00607977
$903$		0			0
$904$	−4.98053e12			−0.248038
$905$	3.44521e12	−	5.96728e12i	0.170725	−	0.295704i
$906$	−1.39048e12	−	2.40838e12i	−0.0685626	−	0.118754i
$907$	−1.14165e13	−	1.97739e13i	−0.560144	−	0.970198i	−0.997483	−	0.0709016i	$-0.977412\pi$
$907$	−1.14165e13	−	1.97739e13i	−0.560144	−	0.970198i	0.437339	−	0.899297i	$-0.355921\pi$
$908$	−1.80389e13	+	3.12443e13i	−0.880692	+	1.52540i
$909$	1.28730e12			0.0625380
$910$		0			0
$911$	−1.50436e13			−0.723635			−0.361818	−	0.932249i	$-0.617844\pi$
$911$	−1.50436e13			−0.723635			−0.361818	+	0.932249i	$0.617844\pi$
$912$	−1.33449e13	+	2.31140e13i	−0.638761	+	1.10637i
$913$	5.30669e12	+	9.19145e12i	0.252758	+	0.437790i
$914$	−1.68120e12	−	2.91193e12i	−0.0796825	−	0.138014i
$915$	6.35585e12	−	1.10087e13i	0.299764	−	0.519206i
$916$	2.91802e13			1.36949
$917$		0			0
$918$	5.53196e12			0.257091
$919$	−3.26371e12	+	5.65291e12i	−0.150936	+	0.261428i	−0.931572	−	0.363558i	$-0.881562\pi$
$919$	−3.26371e12	+	5.65291e12i	−0.150936	+	0.261428i	0.780636	+	0.624986i	$0.214895\pi$
$920$	−2.60592e12	−	4.51359e12i	−0.119927	−	0.207719i
$921$	−1.96776e13	−	3.40826e13i	−0.901165	−	1.56086i
$922$	1.58324e12	−	2.74225e12i	0.0721534	−	0.124973i
$923$	−7.76960e12			−0.352363
$924$		0			0
$925$	−1.96166e12			−0.0881022
$926$	3.23094e11	−	5.59615e11i	0.0144404	−	0.0250115i
$927$	−1.35429e13	−	2.34570e13i	−0.602356	−	1.04331i
$928$	2.13555e12	+	3.69888e12i	0.0945243	+	0.163721i
$929$	−1.47379e13	+	2.55268e13i	−0.649179	+	1.12441i	0.334141	+	0.942523i	$0.391554\pi$
$929$	−1.47379e13	+	2.55268e13i	−0.649179	+	1.12441i	−0.983319	+	0.181887i	$0.941779\pi$
$930$	−3.40431e12			−0.149230
$931$		0			0
$932$	2.62413e13			1.13924
$933$	−1.38918e13	+	2.40613e13i	−0.600193	+	1.03956i
$934$	9.00100e11	+	1.55902e12i	0.0387017	+	0.0670333i
$935$	6.99979e12	+	1.21240e13i	0.299525	+	0.518792i
$936$	8.32642e12	−	1.44218e13i	0.354582	−	0.614154i
$937$	−2.74410e13			−1.16298			−0.581489	−	0.813554i	$-0.697530\pi$
$937$	−2.74410e13			−1.16298			−0.581489	+	0.813554i	$0.697530\pi$
$938$		0			0
$939$	1.92838e12			0.0809465
$940$	1.46588e12	−	2.53899e12i	0.0612385	−	0.106068i
$941$	−2.07530e13	−	3.59453e13i	−0.862837	−	1.49448i	−0.869179	−	0.494497i	$-0.835352\pi$
$941$	−2.07530e13	−	3.59453e13i	−0.862837	−	1.49448i	0.00634284	−	0.999980i	$-0.497981\pi$
$942$	−1.45102e12	−	2.51324e12i	−0.0600406	−	0.103993i
$943$	−1.43284e12	+	2.48176e12i	−0.0590060	+	0.102201i
$944$	−1.88519e13			−0.772645
$945$		0			0
$946$	−8.23952e11			−0.0334497
$947$	1.75346e12	−	3.03708e12i	0.0708469	−	0.122710i	−0.828426	−	0.560099i	$-0.810763\pi$
$947$	1.75346e12	−	3.03708e12i	0.0708469	−	0.122710i	0.899273	+	0.437388i	$0.144096\pi$
$948$	6.02851e12	+	1.04417e13i	0.242422	+	0.419888i
$949$	2.34566e13	+	4.06281e13i	0.938789	+	1.62603i
$950$	−4.70465e11	+	8.14869e11i	−0.0187401	+	0.0324587i
$951$	−4.20390e13			−1.66663
$952$		0			0
$953$	−4.44833e13			−1.74695			−0.873473	−	0.486873i	$-0.838138\pi$
$953$	−4.44833e13			−1.74695			−0.873473	+	0.486873i	$0.838138\pi$
$954$	−3.25234e11	+	5.63322e11i	−0.0127124	+	0.0220185i
$955$	−9.60426e12	−	1.66351e13i	−0.373636	−	0.647157i
$956$	3.78011e12	+	6.54735e12i	0.146367	+	0.253516i
$957$	1.30077e13	−	2.25300e13i	0.501300	−	0.868277i
$958$	4.22961e12			0.162239
$959$		0			0
$960$	3.16399e13			1.20230
$961$	−4.19661e12	+	7.26874e12i	−0.158724	+	0.274918i
$962$	−3.39309e11	−	5.87701e11i	−0.0127734	−	0.0221242i
$963$	−4.77426e13	−	8.26925e13i	−1.78891	−	3.09848i
$964$	1.02746e13	−	1.77961e13i	0.383194	−	0.663711i
$965$	−3.27551e13			−1.21592
$966$		0			0
$967$	3.17722e13			1.16850			0.584250	−	0.811574i	$-0.301389\pi$
$967$	3.17722e13			1.16850			0.584250	+	0.811574i	$0.301389\pi$
$968$	6.90844e11	−	1.19658e12i	0.0252895	−	0.0438028i
$969$	1.79777e13	+	3.11383e13i	0.655055	+	1.13459i
$970$	−6.65041e11	−	1.15189e12i	−0.0241199	−	0.0417769i
$971$	−6.88757e12	+	1.19296e13i	−0.248645	+	0.430666i	−0.963150	−	0.268964i	$-0.913319\pi$
$971$	−6.88757e12	+	1.19296e13i	−0.248645	+	0.430666i	0.714505	+	0.699630i	$0.246652\pi$
$972$	−4.65309e13			−1.67203
$973$		0			0
$974$	−2.82178e12			−0.100464
$975$	−1.96950e13	+	3.41127e13i	−0.697967	+	1.20891i
$976$	−6.43026e12	−	1.11375e13i	−0.226832	−	0.392885i
$977$	8.84757e12	+	1.53244e13i	0.310669	+	0.538095i	0.978507	−	0.206212i	$-0.0661135\pi$
$977$	8.84757e12	+	1.53244e13i	0.310669	+	0.538095i	−0.667838	+	0.744307i	$0.732780\pi$
$978$	3.62590e12	−	6.28025e12i	0.126733	−	0.219509i
$979$	−3.49636e13			−1.21645
$980$		0			0
$981$	−1.02927e14			−3.54829
$982$	−5.66089e11	+	9.80496e11i	−0.0194260	+	0.0336468i
$983$	2.17289e13	+	3.76356e13i	0.742246	+	1.28561i	0.951471	+	0.307740i	$0.0995726\pi$
$983$	2.17289e13	+	3.76356e13i	0.742246	+	1.28561i	−0.209225	+	0.977868i	$0.567094\pi$
$984$	3.78002e11	+	6.54719e11i	0.0128534	+	0.0222627i
$985$	−1.69098e13	+	2.92886e13i	−0.572367	+	0.991369i
$986$	1.88469e12			0.0635031
$987$		0			0
$988$	3.12645e13			1.04387
$989$	−9.76753e12	+	1.69179e13i	−0.324639	+	0.562292i
$990$	2.20513e12	+	3.81940e12i	0.0729586	+	0.126368i
$991$	−1.44026e12	−	2.49460e12i	−0.0474362	−	0.0821619i	0.841332	−	0.540518i	$-0.181772\pi$
$991$	−1.44026e12	−	2.49460e12i	−0.0474362	−	0.0821619i	−0.888769	+	0.458356i	$0.848438\pi$
$992$	−5.25741e12	+	9.10611e12i	−0.172373	+	0.298559i
$993$	7.68789e13			2.50920
$994$		0			0
$995$	−1.74272e13			−0.563668
$996$	1.65100e13	−	2.85961e13i	0.531593	−	0.920747i
$997$	4.99423e12	+	8.65025e12i	0.160081	+	0.277269i	0.934898	−	0.354918i	$-0.115491\pi$
$997$	4.99423e12	+	8.65025e12i	0.160081	+	0.277269i	−0.774816	+	0.632186i	$0.782158\pi$
$998$	−2.19267e12	−	3.79782e12i	−0.0699659	−	0.121184i
$999$	−6.85670e12	+	1.18761e13i	−0.217806	+	0.377251i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.10.c.h.30.3		16
7.2	even	3		49.10.a.g.1.6	yes	8
7.3	odd	6	inner	49.10.c.h.18.4		16
7.4	even	3	inner	49.10.c.h.18.3		16
7.5	odd	6		49.10.a.g.1.5	✓	8
7.6	odd	2	inner	49.10.c.h.30.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.10.a.g.1.5	✓	8	7.5	odd	6
49.10.a.g.1.6	yes	8	7.2	even	3
49.10.c.h.18.3		16	7.4	even	3	inner
49.10.c.h.18.4		16	7.3	odd	6	inner
49.10.c.h.30.3		16	1.1	even	1	trivial
49.10.c.h.30.4		16	7.6	odd	2	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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	49.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.14844 - 1.98916i) q^{2} +(-129.061 - 223.541i) q^{3} +(253.362 + 438.836i) q^{4} +(486.452 - 842.560i) q^{5} -592.877 q^{6} +2339.89 q^{8} +(-23472.1 + 40654.8i) q^{9} +(-1117.32 - 1935.26i) q^{10} +(21020.6 + 36408.7i) q^{11} +(65398.4 - 113273. i) q^{12} -151604. q^{13} -251128. q^{15} +(-127034. + 220030. i) q^{16} +(171136. + 296415. i) q^{17} +(53912.6 + 93379.4i) q^{18} +(-203488. + 352452. i) q^{19} +492994. q^{20} +96563.6 q^{22} +(1.14471e6 - 1.98270e6i) q^{23} +(-301989. - 523061. i) q^{24} +(503291. + 871725. i) q^{25} +(-174109. + 301565. i) q^{26} +7.03671e6 q^{27} +2.39735e6 q^{29} +(-288406. + 499535. i) q^{30} +(2.95097e6 + 5.11123e6i) q^{31} +(890795. + 1.54290e6i) q^{32} +(5.42588e6 - 9.39789e6i) q^{33} +786157. q^{34} -2.37877e7 q^{36} +(-974418. + 1.68774e6i) q^{37} +(467389. + 809541. i) q^{38} +(1.95662e7 + 3.38897e7i) q^{39} +(1.13825e6 - 1.97150e6i) q^{40} -1.25171e6 q^{41} -8.53275e6 q^{43} +(-1.06516e7 + 1.84492e7i) q^{44} +(2.28361e7 + 3.95533e7i) q^{45} +(-2.62927e6 - 4.55402e6i) q^{46} +(2.97343e6 - 5.15013e6i) q^{47} +6.55807e7 q^{48} +2.31200e6 q^{50} +(4.41739e7 - 7.65114e7i) q^{51} +(-3.84108e7 - 6.65294e7i) q^{52} +(3.01631e6 + 5.22439e6i) q^{53} +(8.08125e6 - 1.39971e7i) q^{54} +4.09020e7 q^{55} +1.05050e8 q^{57} +(2.75322e6 - 4.76871e6i) q^{58} +(3.71000e7 + 6.42590e7i) q^{59} +(-6.36264e7 - 1.10204e8i) q^{60} +(-2.53092e7 + 4.38368e7i) q^{61} +1.35561e7 q^{62} -1.25991e8 q^{64} +(-7.37482e7 + 1.27736e8i) q^{65} +(-1.24626e7 - 2.15859e7i) q^{66} +(5.00939e7 + 8.67652e7i) q^{67} +(-8.67185e7 + 1.50201e8i) q^{68} -5.90951e8 q^{69} +5.12492e7 q^{71} +(-5.49221e7 + 9.51279e7i) q^{72} +(-1.54723e8 - 2.67988e8i) q^{73} +(2.23813e6 + 3.87655e6i) q^{74} +(1.29911e8 - 2.25012e8i) q^{75} -2.06225e8 q^{76} +8.98826e7 q^{78} +(-4.60906e7 + 7.98313e7i) q^{79} +(1.23592e8 + 2.14068e8i) q^{80} +(-4.46165e8 - 7.72781e8i) q^{81} +(-1.43751e6 + 2.48985e6i) q^{82} +2.52452e8 q^{83} +3.32997e8 q^{85} +(-9.79936e6 + 1.69730e7i) q^{86} +(-3.09405e8 - 5.35905e8i) q^{87} +(4.91858e7 + 8.51923e7i) q^{88} +(-4.15826e8 + 7.20232e8i) q^{89} +1.04904e8 q^{90} +1.16011e9 q^{92} +(7.61711e8 - 1.31932e9i) q^{93} +(-6.82962e6 - 1.18292e7i) q^{94} +(1.97975e8 + 3.42902e8i) q^{95} +(2.29934e8 - 3.98258e8i) q^{96} +5.95209e8 q^{97} -1.97358e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 66 q^{2} - 1706 q^{4} - 117084 q^{8} - 27940 q^{9} + 82092 q^{11} - 164672 q^{15} - 1569570 q^{16} + 307774 q^{18} - 2600152 q^{22} + 2388480 q^{23} + 6191476 q^{25} - 36887784 q^{29} + 16703832 q^{30}+ \cdots - 6259461064 q^{99}+O(q^{100}) \) 16 * q + 66 * q^2 - 1706 * q^4 - 117084 * q^8 - 27940 * q^9 + 82092 * q^11 - 164672 * q^15 - 1569570 * q^16 + 307774 * q^18 - 2600152 * q^22 + 2388480 * q^23 + 6191476 * q^25 - 36887784 * q^29 + 16703832 * q^30 + 66365310 * q^32 - 163874260 * q^36 + 8944484 * q^37 + 128986088 * q^39 - 72060264 * q^43 + 20548980 * q^44 + 151133592 * q^46 - 358848780 * q^50 + 192522580 * q^51 + 140198712 * q^53 + 112011672 * q^57 - 407992572 * q^58 - 748541080 * q^60 + 1606537220 * q^64 + 69983508 * q^65 - 459952056 * q^67 + 431701008 * q^71 - 1088280558 * q^72 - 1222590060 * q^74 + 2845895808 * q^78 + 792601400 * q^79 - 1704517060 * q^81 - 736682888 * q^85 + 812465940 * q^86 - 1818979932 * q^88 + 5226574128 * q^92 + 2571584104 * q^93 + 3568335216 * q^95 - 6259461064 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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