LMFDB - Embedded newform 930.2.j.g.497.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [930,2,Mod(497,930)] 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("930.497"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(930, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,-4,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			497.14
Character	$\chi$	$=$	930.497
Dual form			930.2.j.g.683.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{2} +(-1.46789 + 0.919406i) q^{3} -1.00000i q^{4} +(-2.22068 - 0.261841i) q^{5} +(-0.387835 + 1.68807i) q^{6} +(3.32500 + 3.32500i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.30939 - 2.69917i) q^{9} +(-1.75541 + 1.38511i) q^{10} -3.28280i q^{11} +(0.919406 + 1.46789i) q^{12} +(-1.75323 + 1.75323i) q^{13} +4.70226 q^{14} +(3.50045 - 1.65736i) q^{15} -1.00000 q^{16} +(-5.45143 + 5.45143i) q^{17} +(-0.982724 - 2.83448i) q^{18} +0.692195i q^{19} +(-0.261841 + 2.22068i) q^{20} +(-7.93774 - 1.82370i) q^{21} +(-2.32129 - 2.32129i) q^{22} +(-1.40350 - 1.40350i) q^{23} +(1.68807 + 0.387835i) q^{24} +(4.86288 + 1.16293i) q^{25} +2.47944i q^{26} +(0.559598 + 5.16593i) q^{27} +(3.32500 - 3.32500i) q^{28} -1.76926 q^{29} +(1.30327 - 3.64712i) q^{30} +1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.01823 + 4.81878i) q^{33} +7.70948i q^{34} +(-6.51315 - 8.25439i) q^{35} +(-2.69917 - 1.30939i) q^{36} +(2.58318 + 2.58318i) q^{37} +(0.489456 + 0.489456i) q^{38} +(0.961614 - 4.18547i) q^{39} +(1.38511 + 1.75541i) q^{40} +6.83679i q^{41} +(-6.90238 + 4.32328i) q^{42} +(-8.40397 + 8.40397i) q^{43} -3.28280 q^{44} +(-3.61449 + 5.65115i) q^{45} -1.98485 q^{46} +(-8.79496 + 8.79496i) q^{47} +(1.46789 - 0.919406i) q^{48} +15.1112i q^{49} +(4.26089 - 2.61626i) q^{50} +(2.99001 - 13.0142i) q^{51} +(1.75323 + 1.75323i) q^{52} +(4.69421 + 4.69421i) q^{53} +(4.04856 + 3.25717i) q^{54} +(-0.859572 + 7.29007i) q^{55} -4.70226i q^{56} +(-0.636408 - 1.01606i) q^{57} +(-1.25105 + 1.25105i) q^{58} +6.39908 q^{59} +(-1.65736 - 3.50045i) q^{60} -12.2460 q^{61} +(0.707107 - 0.707107i) q^{62} +(13.3284 - 4.62102i) q^{63} +1.00000i q^{64} +(4.35244 - 3.43430i) q^{65} +(5.54160 + 1.27319i) q^{66} +(-7.69460 - 7.69460i) q^{67} +(5.45143 + 5.45143i) q^{68} +(3.35056 + 0.769793i) q^{69} +(-10.4422 - 1.23124i) q^{70} -0.464287i q^{71} +(-2.83448 + 0.982724i) q^{72} +(4.31841 - 4.31841i) q^{73} +3.65317 q^{74} +(-8.20736 + 2.76390i) q^{75} +0.692195 q^{76} +(10.9153 - 10.9153i) q^{77} +(-2.27961 - 3.63954i) q^{78} +14.1021i q^{79} +(2.22068 + 0.261841i) q^{80} +(-5.57101 - 7.06851i) q^{81} +(4.83434 + 4.83434i) q^{82} +(0.133755 + 0.133755i) q^{83} +(-1.82370 + 7.93774i) q^{84} +(13.5333 - 10.6785i) q^{85} +11.8850i q^{86} +(2.59707 - 1.62666i) q^{87} +(-2.32129 + 2.32129i) q^{88} +5.90070 q^{89} +(1.44014 + 6.55179i) q^{90} -11.6590 q^{91} +(-1.40350 + 1.40350i) q^{92} +(-1.46789 + 0.919406i) q^{93} +12.4379i q^{94} +(0.181245 - 1.53715i) q^{95} +(0.387835 - 1.68807i) q^{96} +(-2.86345 - 2.86345i) q^{97} +(10.6852 + 10.6852i) q^{98} +(-8.86084 - 4.29846i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} - 8 q^{7} + 8 q^{10} + 4 q^{12} - 20 q^{13} - 44 q^{15} - 40 q^{16} + 16 q^{18} - 32 q^{21} - 4 q^{22} + 8 q^{25} + 8 q^{27} - 8 q^{28} - 4 q^{30} + 40 q^{31} + 48 q^{33} + 64 q^{37} - 4 q^{40}+ \cdots - 52 q^{97}+O(q^{100}) $ 40 * q - 4 * q^3 - 8 * q^7 + 8 * q^10 + 4 * q^12 - 20 * q^13 - 44 * q^15 - 40 * q^16 + 16 * q^18 - 32 * q^21 - 4 * q^22 + 8 * q^25 + 8 * q^27 - 8 * q^28 - 4 * q^30 + 40 * q^31 + 48 * q^33 + 64 * q^37 - 4 * q^40 - 20 * q^42 - 48 * q^43 - 4 * q^45 - 80 * q^46 + 4 * q^48 + 48 * q^51 + 20 * q^52 + 164 * q^55 + 40 * q^57 + 56 * q^58 + 24 * q^60 - 128 * q^61 + 56 * q^63 + 8 * q^66 - 4 * q^67 - 56 * q^70 - 16 * q^72 - 48 * q^73 - 48 * q^75 - 40 * q^76 - 36 * q^78 - 24 * q^81 - 16 * q^82 - 56 * q^85 - 12 * q^87 - 4 * q^88 - 28 * q^90 - 32 * q^91 - 4 * q^93 - 52 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−1.46789	+	0.919406i	−0.847485	+	0.530819i
$3$	−1.46789	+	0.919406i	−0.847485	+	0.530819i
$4$		−	1.00000i		−	0.500000i
$5$	−2.22068	−	0.261841i	−0.993120	−	0.117099i
$5$	−2.22068	−	0.261841i	−0.993120	−	0.117099i
$6$	−0.387835	+	1.68807i	−0.158333	+	0.689152i
$7$	3.32500	+	3.32500i	1.25673	+	1.25673i	0.952645	+	0.304086i	$0.0983510\pi$
$7$	3.32500	+	3.32500i	1.25673	+	1.25673i	0.304086	+	0.952645i	$0.401649\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	1.30939	−	2.69917i	0.436462	−	0.899723i
$10$	−1.75541	+	1.38511i	−0.555110	+	0.438011i
$11$		−	3.28280i		−	0.989802i	−0.868949	−	0.494901i	$-0.835204\pi$
$11$		−	3.28280i		−	0.989802i	0.868949	−	0.494901i	$-0.164796\pi$
$12$	0.919406	+	1.46789i	0.265410	+	0.423743i
$13$	−1.75323	+	1.75323i	−0.486258	+	0.486258i	−0.907123	−	0.420865i	$-0.861727\pi$
$13$	−1.75323	+	1.75323i	−0.486258	+	0.486258i	0.420865	+	0.907123i	$0.361727\pi$
$14$	4.70226			1.25673
$15$	3.50045	−	1.65736i	0.903813	−	0.427928i
$16$	−1.00000			−0.250000
$17$	−5.45143	+	5.45143i	−1.32217	+	1.32217i	−0.410146	+	0.912020i	$0.634522\pi$
$17$	−5.45143	+	5.45143i	−1.32217	+	1.32217i	−0.912020	+	0.410146i	$0.865478\pi$
$18$	−0.982724	−	2.83448i	−0.231630	−	0.668092i
$19$			0.692195i			0.158800i	0.996843	+	0.0794002i	$0.0253005\pi$
$19$			0.692195i			0.158800i	−0.996843	+	0.0794002i	$0.974700\pi$
$20$	−0.261841	+	2.22068i	−0.0585494	+	0.496560i
$21$	−7.93774	−	1.82370i	−1.73216	−	0.397964i
$22$	−2.32129	−	2.32129i	−0.494901	−	0.494901i
$23$	−1.40350	−	1.40350i	−0.292650	−	0.292650i	0.545476	−	0.838126i	$-0.316349\pi$
$23$	−1.40350	−	1.40350i	−0.292650	−	0.292650i	−0.838126	+	0.545476i	$0.816349\pi$
$24$	1.68807	+	0.387835i	0.344576	+	0.0791665i
$25$	4.86288	+	1.16293i	0.972576	+	0.232586i
$26$			2.47944i			0.486258i
$27$	0.559598	+	5.16593i	0.107695	+	0.994184i
$28$	3.32500	−	3.32500i	0.628365	−	0.628365i
$29$	−1.76926			−0.328543			−0.164271	−	0.986415i	$-0.552527\pi$
$29$	−1.76926			−0.328543			−0.164271	+	0.986415i	$0.552527\pi$
$30$	1.30327	−	3.64712i	0.237943	−	0.665870i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	3.01823	+	4.81878i	0.525406	+	0.838843i
$34$			7.70948i			1.32217i
$35$	−6.51315	−	8.25439i	−1.10092	−	1.39525i
$36$	−2.69917	−	1.30939i	−0.449861	−	0.218231i
$37$	2.58318	+	2.58318i	0.424672	+	0.424672i	0.886809	−	0.462137i	$-0.152917\pi$
$37$	2.58318	+	2.58318i	0.424672	+	0.424672i	−0.462137	+	0.886809i	$0.652917\pi$
$38$	0.489456	+	0.489456i	0.0794002	+	0.0794002i
$39$	0.961614	−	4.18547i	0.153981	−	0.670212i
$40$	1.38511	+	1.75541i	0.219005	+	0.277555i
$41$			6.83679i			1.06773i	0.845571	+	0.533863i	$0.179260\pi$
$41$			6.83679i			1.06773i	−0.845571	+	0.533863i	$0.820740\pi$
$42$	−6.90238	+	4.32328i	−1.06506	+	0.667097i
$43$	−8.40397	+	8.40397i	−1.28159	+	1.28159i	−0.341831	+	0.939761i	$0.611047\pi$
$43$	−8.40397	+	8.40397i	−1.28159	+	1.28159i	−0.939761	+	0.341831i	$0.888953\pi$
$44$	−3.28280			−0.494901
$45$	−3.61449	+	5.65115i	−0.538816	+	0.842424i
$46$	−1.98485			−0.292650
$47$	−8.79496	+	8.79496i	−1.28288	+	1.28288i	−0.343853	+	0.939023i	$0.611732\pi$
$47$	−8.79496	+	8.79496i	−1.28288	+	1.28288i	−0.939023	+	0.343853i	$0.888268\pi$
$48$	1.46789	−	0.919406i	0.211871	−	0.132705i
$49$			15.1112i			2.15874i
$50$	4.26089	−	2.61626i	0.602581	−	0.369995i
$51$	2.99001	−	13.0142i	0.418685	−	1.82235i
$52$	1.75323	+	1.75323i	0.243129	+	0.243129i
$53$	4.69421	+	4.69421i	0.644800	+	0.644800i	0.951731	−	0.306932i	$-0.0993024\pi$
$53$	4.69421	+	4.69421i	0.644800	+	0.644800i	−0.306932	+	0.951731i	$0.599302\pi$
$54$	4.04856	+	3.25717i	0.550939	+	0.443245i
$55$	−0.859572	+	7.29007i	−0.115905	+	0.982993i
$56$		−	4.70226i		−	0.628365i
$57$	−0.636408	−	1.01606i	−0.0842943	−	0.134581i
$58$	−1.25105	+	1.25105i	−0.164271	+	0.164271i
$59$	6.39908			0.833089			0.416545	−	0.909115i	$-0.363241\pi$
$59$	6.39908			0.833089			0.416545	+	0.909115i	$0.363241\pi$
$60$	−1.65736	−	3.50045i	−0.213964	−	0.451906i
$61$	−12.2460			−1.56794			−0.783969	−	0.620800i	$-0.786808\pi$
$61$	−12.2460			−1.56794			−0.783969	+	0.620800i	$0.786808\pi$
$62$	0.707107	−	0.707107i	0.0898027	−	0.0898027i
$63$	13.3284	−	4.62102i	1.67922	−	0.582194i
$64$			1.00000i			0.125000i
$65$	4.35244	−	3.43430i	0.539853	−	0.425973i
$66$	5.54160	+	1.27319i	0.682124	+	0.156718i
$67$	−7.69460	−	7.69460i	−0.940046	−	0.940046i	0.0582561	−	0.998302i	$-0.481446\pi$
$67$	−7.69460	−	7.69460i	−0.940046	−	0.940046i	−0.998302	+	0.0582561i	$0.981446\pi$
$68$	5.45143	+	5.45143i	0.661083	+	0.661083i
$69$	3.35056	+	0.769793i	0.403360	+	0.0926722i
$70$	−10.4422	−	1.23124i	−1.24808	−	0.147162i
$71$		−	0.464287i		−	0.0551007i	−0.999620	−	0.0275504i	$-0.991229\pi$
$71$		−	0.464287i		−	0.0551007i	0.999620	−	0.0275504i	$-0.00877067\pi$
$72$	−2.83448	+	0.982724i	−0.334046	+	0.115815i
$73$	4.31841	−	4.31841i	0.505432	−	0.505432i	−0.407689	−	0.913121i	$-0.633665\pi$
$73$	4.31841	−	4.31841i	0.505432	−	0.505432i	0.913121	+	0.407689i	$0.133665\pi$
$74$	3.65317			0.424672
$75$	−8.20736	+	2.76390i	−0.947705	+	0.319148i
$76$	0.692195			0.0794002
$77$	10.9153	−	10.9153i	1.24391	−	1.24391i
$78$	−2.27961	−	3.63954i	−0.258115	−	0.412097i
$79$			14.1021i			1.58661i	0.608827	+	0.793303i	$0.291641\pi$
$79$			14.1021i			1.58661i	−0.608827	+	0.793303i	$0.708359\pi$
$80$	2.22068	+	0.261841i	0.248280	+	0.0292747i
$81$	−5.57101	−	7.06851i	−0.619002	−	0.785390i
$82$	4.83434	+	4.83434i	0.533863	+	0.533863i
$83$	0.133755	+	0.133755i	0.0146815	+	0.0146815i	0.714409	−	0.699728i	$-0.246695\pi$
$83$	0.133755	+	0.133755i	0.0146815	+	0.0146815i	−0.699728	+	0.714409i	$0.746695\pi$
$84$	−1.82370	+	7.93774i	−0.198982	+	0.866079i
$85$	13.5333	−	10.6785i	1.46789	−	1.15825i
$86$			11.8850i			1.28159i
$87$	2.59707	−	1.62666i	0.278435	−	0.174397i
$88$	−2.32129	+	2.32129i	−0.247451	+	0.247451i
$89$	5.90070			0.625472			0.312736	−	0.949840i	$-0.398754\pi$
$89$	5.90070			0.625472			0.312736	+	0.949840i	$0.398754\pi$
$90$	1.44014	+	6.55179i	0.151804	+	0.690620i
$91$	−11.6590			−1.22219
$92$	−1.40350	+	1.40350i	−0.146325	+	0.146325i
$93$	−1.46789	+	0.919406i	−0.152213	+	0.0953379i
$94$			12.4379i			1.28288i
$95$	0.181245	−	1.53715i	0.0185953	−	0.157708i
$96$	0.387835	−	1.68807i	0.0395833	−	0.172288i
$97$	−2.86345	−	2.86345i	−0.290739	−	0.290739i	0.546633	−	0.837372i	$-0.315909\pi$
$97$	−2.86345	−	2.86345i	−0.290739	−	0.290739i	−0.837372	+	0.546633i	$0.815909\pi$
$98$	10.6852	+	10.6852i	1.07937	+	1.07937i
$99$	−8.86084	−	4.29846i	−0.890547	−	0.432011i
$100$	1.16293	−	4.86288i	0.116293	−	0.486288i
$101$		−	6.75989i		−	0.672634i	−0.941749	−	0.336317i	$-0.890819\pi$
$101$		−	6.75989i		−	0.672634i	0.941749	−	0.336317i	$-0.109181\pi$
$102$	−7.08814	−	11.3167i	−0.701831	−	1.12052i
$103$	3.47102	−	3.47102i	0.342010	−	0.342010i	−0.515113	−	0.857122i	$-0.672250\pi$
$103$	3.47102	−	3.47102i	0.342010	−	0.342010i	0.857122	+	0.515113i	$0.172250\pi$
$104$	2.47944			0.243129
$105$	17.1497	+	6.12829i	1.67364	+	0.598060i
$106$	6.63862			0.644800
$107$	8.41957	−	8.41957i	0.813950	−	0.813950i	−0.171273	−	0.985224i	$-0.554788\pi$
$107$	8.41957	−	8.41957i	0.813950	−	0.813950i	0.985224	+	0.171273i	$0.0547882\pi$
$108$	5.16593	−	0.559598i	0.497092	−	0.0538474i
$109$		−	13.8823i		−	1.32968i	−0.746984	−	0.664842i	$-0.768499\pi$
$109$		−	13.8823i		−	1.32968i	0.746984	−	0.664842i	$-0.231501\pi$
$110$	4.54705	+	5.76267i	0.433544	+	0.549449i
$111$	−6.16681	−	1.41683i	−0.585327	−	0.134479i
$112$	−3.32500	−	3.32500i	−0.314183	−	0.314183i
$113$	−2.35475	−	2.35475i	−0.221516	−	0.221516i	0.587621	−	0.809137i	$-0.300065\pi$
$113$	−2.35475	−	2.35475i	−0.221516	−	0.221516i	−0.809137	+	0.587621i	$0.800065\pi$
$114$	−1.16847	−	0.268457i	−0.109438	−	0.0251433i
$115$	2.74923	+	3.48422i	0.256367	+	0.324905i
$116$			1.76926i			0.164271i
$117$	2.43661	+	7.02791i	0.225264	+	0.649731i
$118$	4.52483	−	4.52483i	0.416545	−	0.416545i
$119$	−36.2520			−3.32321
$120$	−3.64712	−	1.30327i	−0.332935	−	0.118971i
$121$	0.223207			0.0202915
$122$	−8.65922	+	8.65922i	−0.783969	+	0.783969i
$123$	−6.28578	−	10.0356i	−0.566770	−	0.904883i
$124$		−	1.00000i		−	0.0898027i
$125$	−10.4944	−	3.85581i	−0.938649	−	0.344874i
$126$	6.15707	−	12.6922i	0.548515	−	1.13071i
$127$	−1.08839	−	1.08839i	−0.0965788	−	0.0965788i	0.657167	−	0.753745i	$-0.271755\pi$
$127$	−1.08839	−	1.08839i	−0.0965788	−	0.0965788i	−0.753745	+	0.657167i	$0.771755\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	4.60942	−	20.0627i	0.405837	−	1.76642i
$130$	0.649219	−	5.50605i	0.0569403	−	0.482913i
$131$			9.40510i			0.821728i	0.911697	+	0.410864i	$0.134773\pi$
$131$			9.40510i			0.821728i	−0.911697	+	0.410864i	$0.865227\pi$
$132$	4.81878	−	3.01823i	0.419421	−	0.262703i
$133$	−2.30154	+	2.30154i	−0.199569	+	0.199569i
$134$	−10.8818			−0.940046
$135$	0.109961	−	11.6184i	0.00946392	−	0.999955i
$136$	7.70948			0.661083
$137$	10.0062	−	10.0062i	0.854887	−	0.854887i	−0.135843	−	0.990730i	$-0.543374\pi$
$137$	10.0062	−	10.0062i	0.854887	−	0.854887i	0.990730	+	0.135843i	$0.0433744\pi$
$138$	2.91353	−	1.82488i	0.248016	−	0.155344i
$139$		−	15.0644i		−	1.27774i	−0.769314	−	0.638871i	$-0.779402\pi$
$139$		−	15.0644i		−	1.27774i	0.769314	−	0.638871i	$-0.220598\pi$
$140$	−8.25439	+	6.51315i	−0.697623	+	0.550461i
$141$	4.82387	−	20.9961i	0.406243	−	1.76819i
$142$	−0.328301	−	0.328301i	−0.0275504	−	0.0275504i
$143$	5.75550	+	5.75550i	0.481300	+	0.481300i
$144$	−1.30939	+	2.69917i	−0.109116	+	0.224931i
$145$	3.92896	+	0.463264i	0.326282	+	0.0384720i
$146$		−	6.10715i		−	0.505432i
$147$	−13.8933	−	22.1815i	−1.14590	−	1.82950i
$148$	2.58318	−	2.58318i	0.212336	−	0.212336i
$149$	5.94580			0.487099			0.243550	−	0.969888i	$-0.421688\pi$
$149$	5.94580			0.487099			0.243550	+	0.969888i	$0.421688\pi$
$150$	−3.84911	+	7.75786i	−0.314278	+	0.633427i
$151$	−6.40300			−0.521069			−0.260534	−	0.965465i	$-0.583899\pi$
$151$	−6.40300			−0.521069			−0.260534	+	0.965465i	$0.583899\pi$
$152$	0.489456	−	0.489456i	0.0397001	−	0.0397001i
$153$	7.57629	+	21.8523i	0.612507	+	1.76666i
$154$		−	15.4366i		−	1.24391i
$155$	−2.22068	−	0.261841i	−0.178370	−	0.0210316i
$156$	−4.18547	−	0.961614i	−0.335106	−	0.0769907i
$157$	14.6111	+	14.6111i	1.16610	+	1.16610i	0.983117	+	0.182979i	$0.0585742\pi$
$157$	14.6111	+	14.6111i	1.16610	+	1.16610i	0.182979	+	0.983117i	$0.441426\pi$
$158$	9.97167	+	9.97167i	0.793303	+	0.793303i
$159$	−11.2065	−	2.57469i	−0.888730	−	0.204186i
$160$	1.75541	−	1.38511i	0.138777	−	0.109503i
$161$		−	9.33325i		−	0.735563i
$162$	−8.93749	−	1.05889i	−0.702196	−	0.0831941i
$163$	5.40211	−	5.40211i	0.423126	−	0.423126i	−0.463153	−	0.886279i	$-0.653282\pi$
$163$	5.40211	−	5.40211i	0.423126	−	0.423126i	0.886279	+	0.463153i	$0.153282\pi$
$164$	6.83679			0.533863
$165$	−5.44078	−	11.4913i	−0.423564	−	0.894596i
$166$	0.189158			0.0146815
$167$	−4.23326	+	4.23326i	−0.327580	+	0.327580i	−0.851665	−	0.524086i	$-0.824407\pi$
$167$	−4.23326	+	4.23326i	−0.327580	+	0.327580i	0.524086	+	0.851665i	$0.324407\pi$
$168$	4.32328	+	6.90238i	0.333548	+	0.532530i
$169$			6.85238i			0.527106i
$170$	2.01866	−	17.1203i	0.154824	−	1.31307i
$171$	1.86835	+	0.906350i	0.142876	+	0.0693103i
$172$	8.40397	+	8.40397i	0.640796	+	0.640796i
$173$	−4.73722	−	4.73722i	−0.360164	−	0.360164i	0.503709	−	0.863873i	$-0.331968\pi$
$173$	−4.73722	−	4.73722i	−0.360164	−	0.360164i	−0.863873	+	0.503709i	$0.831968\pi$
$174$	0.686180	−	2.98663i	0.0520192	−	0.226416i
$175$	12.3023	+	20.0358i	0.929967	+	1.51456i
$176$			3.28280i			0.247451i
$177$	−9.39313	+	5.88335i	−0.706031	+	0.442220i
$178$	4.17242	−	4.17242i	0.312736	−	0.312736i
$179$	−6.44508			−0.481728			−0.240864	−	0.970559i	$-0.577431\pi$
$179$	−6.44508			−0.481728			−0.240864	+	0.970559i	$0.577431\pi$
$180$	5.65115	+	3.61449i	0.421212	+	0.269408i
$181$	−7.98162			−0.593269			−0.296635	−	0.954991i	$-0.595864\pi$
$181$	−7.98162			−0.593269			−0.296635	+	0.954991i	$0.595864\pi$
$182$	−8.24413	+	8.24413i	−0.611096	+	0.611096i
$183$	17.9757	−	11.2590i	1.32880	−	0.832292i
$184$			1.98485i			0.146325i
$185$	−5.06004	−	6.41281i	−0.372022	−	0.471479i
$186$	−0.387835	+	1.68807i	−0.0284374	+	0.123775i
$187$	17.8960	+	17.8960i	1.30868	+	1.30868i
$188$	8.79496	+	8.79496i	0.641438	+	0.641438i
$189$	−15.3160	+	19.0374i	−1.11408	+	1.38476i
$190$	−0.958767	−	1.21509i	−0.0695563	−	0.0881516i
$191$			11.8393i			0.856663i	0.903622	+	0.428332i	$0.140899\pi$
$191$			11.8393i			0.856663i	−0.903622	+	0.428332i	$0.859101\pi$
$192$	−0.919406	−	1.46789i	−0.0663524	−	0.105936i
$193$	−2.13271	+	2.13271i	−0.153516	+	0.153516i	−0.779686	−	0.626170i	$-0.784621\pi$
$193$	−2.13271	+	2.13271i	−0.153516	+	0.153516i	0.626170	+	0.779686i	$0.284621\pi$
$194$	−4.04953			−0.290739
$195$	−3.23137	+	9.04282i	−0.231403	+	0.647570i
$196$	15.1112			1.07937
$197$	−11.2892	+	11.2892i	−0.804322	+	0.804322i	−0.983768	−	0.179446i	$-0.942569\pi$
$197$	−11.2892	+	11.2892i	−0.804322	+	0.804322i	0.179446	+	0.983768i	$0.442569\pi$
$198$	−9.30503	+	3.22609i	−0.661279	+	0.229268i
$199$			10.3463i			0.733428i	0.930334	+	0.366714i	$0.119517\pi$
$199$			10.3463i			0.733428i	−0.930334	+	0.366714i	$0.880483\pi$
$200$	−2.61626	−	4.26089i	−0.184997	−	0.301291i
$201$	18.3693	+	4.22035i	1.29567	+	0.297681i
$202$	−4.77997	−	4.77997i	−0.336317	−	0.336317i
$203$	−5.88277	−	5.88277i	−0.412890	−	0.412890i
$204$	−13.0142	−	2.99001i	−0.911173	−	0.209342i
$205$	1.79015	−	15.1823i	0.125030	−	1.06038i
$206$		−	4.90876i		−	0.342010i
$207$	−5.62600	+	1.95056i	−0.391034	+	0.135573i
$208$	1.75323	−	1.75323i	0.121565	−	0.121565i
$209$	2.27234			0.157181
$210$	16.4600	−	7.79331i	1.13585	−	0.537790i
$211$	18.1832			1.25178			0.625892	−	0.779910i	$-0.284735\pi$
$211$	18.1832			1.25178			0.625892	+	0.779910i	$0.284735\pi$
$212$	4.69421	−	4.69421i	0.322400	−	0.322400i
$213$	0.426868	+	0.681521i	0.0292485	+	0.0466971i
$214$		−	11.9071i		−	0.813950i
$215$	20.8631	−	16.4621i	1.42285	−	1.12270i
$216$	3.25717	−	4.04856i	0.221622	−	0.275470i
$217$	3.32500	+	3.32500i	0.225715	+	0.225715i
$218$	−9.81628	−	9.81628i	−0.664842	−	0.664842i
$219$	−2.36857	+	10.3093i	−0.160053	+	0.696639i
$220$	7.29007	+	0.859572i	0.491496	+	0.0579523i
$221$		−	19.1152i		−	1.28583i
$222$	−5.36244	+	3.35874i	−0.359903	+	0.225424i
$223$	10.8799	−	10.8799i	0.728575	−	0.728575i	−0.241761	−	0.970336i	$-0.577725\pi$
$223$	10.8799	−	10.8799i	0.728575	−	0.728575i	0.970336	+	0.241761i	$0.0777249\pi$
$224$	−4.70226			−0.314183
$225$	9.50634	−	11.6030i	0.633756	−	0.773533i
$226$	−3.33011			−0.221516
$227$	−13.1663	+	13.1663i	−0.873878	+	0.873878i	−0.992893	−	0.119015i	$-0.962026\pi$
$227$	−13.1663	+	13.1663i	−0.873878	+	0.873878i	0.119015	+	0.992893i	$0.462026\pi$
$228$	−1.01606	+	0.636408i	−0.0672905	+	0.0421471i
$229$		−	13.0668i		−	0.863480i	−0.901998	−	0.431740i	$-0.857900\pi$
$229$		−	13.0668i		−	0.863480i	0.901998	−	0.431740i	$-0.142100\pi$
$230$	4.40772	+	0.519714i	0.290636	+	0.0342689i
$231$	−5.98685	+	26.0580i	−0.393906	+	1.71449i
$232$	1.25105	+	1.25105i	0.0821357	+	0.0821357i
$233$	18.9563	+	18.9563i	1.24187	+	1.24187i	0.959224	+	0.282645i	$0.0912119\pi$
$233$	18.9563	+	18.9563i	1.24187	+	1.24187i	0.282645	+	0.959224i	$0.408788\pi$
$234$	6.69243	+	3.24655i	0.437498	+	0.212233i
$235$	21.8337	−	17.2279i	1.42427	−	1.12383i
$236$		−	6.39908i		−	0.416545i
$237$	−12.9655	−	20.7002i	−0.842201	−	1.34463i
$238$	−25.6340	+	25.6340i	−1.66161	+	1.66161i
$239$	−9.47761			−0.613056			−0.306528	−	0.951862i	$-0.599167\pi$
$239$	−9.47761			−0.613056			−0.306528	+	0.951862i	$0.599167\pi$
$240$	−3.50045	+	1.65736i	−0.225953	+	0.106982i
$241$	3.05724			0.196934			0.0984669	−	0.995140i	$-0.468606\pi$
$241$	3.05724			0.196934			0.0984669	+	0.995140i	$0.468606\pi$
$242$	0.157831	−	0.157831i	0.0101458	−	0.0101458i
$243$	14.6764	+	5.25375i	0.941495	+	0.337028i
$244$			12.2460i			0.783969i
$245$	3.95673	−	33.5572i	0.252786	−	2.14389i
$246$	−11.5410	−	2.65155i	−0.735826	−	0.169056i
$247$	−1.21358	−	1.21358i	−0.0772180	−	0.0772180i
$248$	−0.707107	−	0.707107i	−0.0449013	−	0.0449013i
$249$	−0.319312	−	0.0733620i	−0.0202356	−	0.00464913i
$250$	−10.1471	+	4.69421i	−0.641761	+	0.296888i
$251$			3.91167i			0.246902i	0.992351	+	0.123451i	$0.0393962\pi$
$251$			3.91167i			0.246902i	−0.992351	+	0.123451i	$0.960604\pi$
$252$	−4.62102	−	13.3284i	−0.291097	−	0.839612i
$253$	−4.60741	+	4.60741i	−0.289665	+	0.289665i
$254$	−1.53921			−0.0965788
$255$	−10.0475	+	28.1174i	−0.629199	+	1.76078i
$256$	1.00000			0.0625000
$257$	13.3355	−	13.3355i	0.831844	−	0.831844i	−0.155925	−	0.987769i	$-0.549836\pi$
$257$	13.3355	−	13.3355i	0.831844	−	0.831844i	0.987769	+	0.155925i	$0.0498358\pi$
$258$	−10.9271	−	17.4458i	−0.680294	−	1.08613i
$259$			17.1781i			1.06740i
$260$	−3.43430	−	4.35244i	−0.212986	−	0.269927i
$261$	−2.31664	+	4.77552i	−0.143396	+	0.295597i
$262$	6.65041	+	6.65041i	0.410864	+	0.410864i
$263$	−4.50623	−	4.50623i	−0.277866	−	0.277866i	0.554390	−	0.832257i	$-0.312951\pi$
$263$	−4.50623	−	4.50623i	−0.277866	−	0.277866i	−0.832257	+	0.554390i	$0.812951\pi$
$264$	1.27319	−	5.54160i	0.0783592	−	0.341062i
$265$	−9.19523	−	11.6535i	−0.564858	−	0.715869i
$266$			3.25488i			0.199569i
$267$	−8.66156	+	5.42513i	−0.530079	+	0.332013i
$268$	−7.69460	+	7.69460i	−0.470023	+	0.470023i
$269$	18.3284			1.11750			0.558751	−	0.829335i	$-0.311281\pi$
$269$	18.3284			1.11750			0.558751	+	0.829335i	$0.311281\pi$
$270$	−8.13772	−	8.29322i	−0.495246	−	0.504710i
$271$	−8.68904			−0.527821			−0.263911	−	0.964547i	$-0.585012\pi$
$271$	−8.68904			−0.527821			−0.263911	+	0.964547i	$0.585012\pi$
$272$	5.45143	−	5.45143i	0.330541	−	0.330541i
$273$	17.1140	−	10.7193i	1.03579	−	0.648762i
$274$		−	14.1509i		−	0.854887i
$275$	3.81768	−	15.9639i	0.230215	−	0.962658i
$276$	0.769793	−	3.35056i	0.0463361	−	0.201680i
$277$	11.3984	+	11.3984i	0.684864	+	0.684864i	0.961092	−	0.276228i	$-0.0890845\pi$
$277$	11.3984	+	11.3984i	0.684864	+	0.684864i	−0.276228	+	0.961092i	$0.589084\pi$
$278$	−10.6521	−	10.6521i	−0.638871	−	0.638871i
$279$	1.30939	−	2.69917i	0.0783909	−	0.161595i
$280$	−1.23124	+	10.4422i	−0.0735808	+	0.624042i
$281$			21.0945i			1.25839i	0.777246	+	0.629197i	$0.216616\pi$
$281$			21.0945i			1.25839i	−0.777246	+	0.629197i	$0.783384\pi$
$282$	−11.4355	−	18.2575i	−0.680975	−	1.08722i
$283$	3.92085	−	3.92085i	0.233070	−	0.233070i	−0.580903	−	0.813973i	$-0.697300\pi$
$283$	3.92085	−	3.92085i	0.233070	−	0.233070i	0.813973	+	0.580903i	$0.197300\pi$
$284$	−0.464287			−0.0275504
$285$	1.14721	+	2.42299i	0.0679551	+	0.143526i
$286$	8.13951			0.481300
$287$	−22.7323	+	22.7323i	−1.34184	+	1.34184i
$288$	0.982724	+	2.83448i	0.0579076	+	0.167023i
$289$		−	42.4362i		−	2.49624i
$290$	3.10577	−	2.45062i	0.182377	−	0.143905i
$291$	6.83590	+	1.57055i	0.400727	+	0.0920673i
$292$	−4.31841	−	4.31841i	−0.252716	−	0.252716i
$293$	−0.969611	−	0.969611i	−0.0566453	−	0.0566453i	0.678217	−	0.734862i	$-0.262753\pi$
$293$	−0.969611	−	0.969611i	−0.0566453	−	0.0566453i	−0.734862	+	0.678217i	$0.762753\pi$
$294$	−25.5088	−	5.86066i	−1.48770	−	0.341800i
$295$	−14.2103	−	1.67554i	−0.827358	−	0.0975538i
$296$		−	3.65317i		−	0.212336i
$297$	16.9587	−	1.83705i	0.984046	−	0.106597i
$298$	4.20432	−	4.20432i	0.243550	−	0.243550i
$299$	4.92131			0.284607
$300$	2.76390	+	8.20736i	0.159574	+	0.473852i
$301$	−55.8863			−3.22123
$302$	−4.52760	+	4.52760i	−0.260534	+	0.260534i
$303$	6.21508	+	9.92276i	0.357047	+	0.570048i
$304$		−	0.692195i		−	0.0397001i
$305$	27.1945	+	3.20650i	1.55715	+	0.183604i
$306$	20.8092	+	10.0947i	1.18958	+	0.577075i
$307$	−20.8384	−	20.8384i	−1.18931	−	1.18931i	−0.977258	−	0.212051i	$-0.931986\pi$
$307$	−20.8384	−	20.8384i	−1.18931	−	1.18931i	−0.212051	−	0.977258i	$-0.568014\pi$
$308$	−10.9153	−	10.9153i	−0.621957	−	0.621957i
$309$	−1.90379	+	8.28634i	−0.108303	+	0.471393i
$310$	−1.75541	+	1.38511i	−0.0997006	+	0.0786690i
$311$			4.95516i			0.280981i	0.990082	+	0.140491i	$0.0448680\pi$
$311$			4.95516i			0.280981i	−0.990082	+	0.140491i	$0.955132\pi$
$312$	−3.63954	+	2.27961i	−0.206048	+	0.129058i
$313$	16.2076	−	16.2076i	0.916105	−	0.916105i	−0.0806380	−	0.996743i	$-0.525696\pi$
$313$	16.2076	−	16.2076i	0.916105	−	0.916105i	0.996743	+	0.0806380i	$0.0256958\pi$
$314$	20.6633			1.16610
$315$	−30.8082	+	6.77190i	−1.73585	+	0.381553i
$316$	14.1021			0.793303
$317$	−21.8647	+	21.8647i	−1.22804	+	1.22804i	−0.263342	+	0.964703i	$0.584825\pi$
$317$	−21.8647	+	21.8647i	−1.22804	+	1.22804i	−0.964703	+	0.263342i	$0.915175\pi$
$318$	−9.74474	+	6.10358i	−0.546458	+	0.342272i
$319$			5.80812i			0.325192i
$320$	0.261841	−	2.22068i	0.0146374	−	0.124140i
$321$	−4.61798	+	20.1000i	−0.257750	+	1.12187i
$322$	−6.59961	−	6.59961i	−0.367782	−	0.367782i
$323$	−3.77345	−	3.77345i	−0.209960	−	0.209960i
$324$	−7.06851	+	5.57101i	−0.392695	+	0.309501i
$325$	−10.5646	+	6.48685i	−0.586020	+	0.359826i
$326$		−	7.63974i		−	0.423126i
$327$	12.7635	+	20.3777i	0.705822	+	1.12689i
$328$	4.83434	−	4.83434i	0.266932	−	0.266932i
$329$	−58.4864			−3.22446
$330$	−11.9728	−	4.27836i	−0.659080	−	0.235516i
$331$	−24.4498			−1.34388			−0.671941	−	0.740605i	$-0.734539\pi$
$331$	−24.4498			−1.34388			−0.671941	+	0.740605i	$0.734539\pi$
$332$	0.133755	−	0.133755i	0.00734075	−	0.00734075i
$333$	10.3548	−	3.59006i	0.567440	−	0.196734i
$334$			5.98673i			0.327580i
$335$	15.0725	+	19.1021i	0.823500	+	1.04366i
$336$	7.93774	+	1.82370i	0.433039	+	0.0994910i
$337$	−3.67711	−	3.67711i	−0.200305	−	0.200305i	0.599826	−	0.800131i	$-0.295237\pi$
$337$	−3.67711	−	3.67711i	−0.200305	−	0.200305i	−0.800131	+	0.599826i	$0.795237\pi$
$338$	4.84536	+	4.84536i	0.263553	+	0.263553i
$339$	5.62147	+	1.29154i	0.305316	+	0.0701466i
$340$	−10.6785	−	13.5333i	−0.579123	−	0.733947i
$341$		−	3.28280i		−	0.177774i
$342$	1.96201	−	0.680236i	0.106093	−	0.0367830i
$343$	−26.9697	+	26.9697i	−1.45623	+	1.45623i
$344$	11.8850			0.640796
$345$	−7.23898	−	2.58678i	−0.389733	−	0.139268i
$346$	−6.69944			−0.360164
$347$	−7.32880	+	7.32880i	−0.393430	+	0.393430i	−0.875908	−	0.482478i	$-0.839737\pi$
$347$	−7.32880	+	7.32880i	−0.393430	+	0.393430i	0.482478	+	0.875908i	$0.339737\pi$
$348$	−1.62666	−	2.59707i	−0.0871984	−	0.139218i
$349$			8.20510i			0.439209i	0.975589	+	0.219605i	$0.0704767\pi$
$349$			8.20510i			0.439209i	−0.975589	+	0.219605i	$0.929523\pi$
$350$	22.8665	+	5.46840i	1.22227	+	0.292298i
$351$	−10.0382	−	8.07596i	−0.535798	−	0.431063i
$352$	2.32129	+	2.32129i	0.123725	+	0.123725i
$353$	−20.2340	−	20.2340i	−1.07695	−	1.07695i	−0.996781	−	0.0801685i	$-0.974454\pi$
$353$	−20.2340	−	20.2340i	−1.07695	−	1.07695i	−0.0801685	−	0.996781i	$-0.525546\pi$
$354$	−2.48179	+	10.8021i	−0.131906	+	0.574125i
$355$	−0.121569	+	1.03104i	−0.00645223	+	0.0547217i
$356$		−	5.90070i		−	0.312736i
$357$	53.2138	−	33.3303i	2.81637	−	1.76402i
$358$	−4.55736	+	4.55736i	−0.240864	+	0.240864i
$359$	17.0753			0.901197			0.450599	−	0.892727i	$-0.351211\pi$
$359$	17.0753			0.901197			0.450599	+	0.892727i	$0.351211\pi$
$360$	6.55179	−	1.44014i	0.345310	−	0.0759019i
$361$	18.5209			0.974782
$362$	−5.64386	+	5.64386i	−0.296635	+	0.296635i
$363$	−0.327642	+	0.205218i	−0.0171968	+	0.0107711i
$364$			11.6590i			0.611096i
$365$	−10.7206	+	8.45909i	−0.561140	+	0.442769i
$366$	4.74942	−	20.6721i	0.248256	−	1.08055i
$367$	12.9439	+	12.9439i	0.675666	+	0.675666i	0.959016	−	0.283351i	$-0.0914461\pi$
$367$	12.9439	+	12.9439i	0.675666	+	0.675666i	−0.283351	+	0.959016i	$0.591446\pi$
$368$	1.40350	+	1.40350i	0.0731624	+	0.0731624i
$369$	18.4536	+	8.95200i	0.960658	+	0.466022i
$370$	−8.11253	−	0.956549i	−0.421750	−	0.0497286i
$371$			31.2165i			1.62068i
$372$	0.919406	+	1.46789i	0.0476690	+	0.0761064i
$373$	12.4763	−	12.4763i	0.646001	−	0.646001i	−0.306023	−	0.952024i	$-0.598999\pi$
$373$	12.4763	−	12.4763i	0.646001	−	0.646001i	0.952024	+	0.306023i	$0.0989986\pi$
$374$	25.3087			1.30868
$375$	18.9497	−	3.98874i	0.978557	−	0.205977i
$376$	12.4379			0.641438
$377$	3.10191	−	3.10191i	0.159757	−	0.159757i
$378$	2.63137	+	24.2915i	0.135343	+	1.24942i
$379$		−	6.64627i		−	0.341396i	−0.985323	−	0.170698i	$-0.945398\pi$
$379$		−	6.64627i		−	0.341396i	0.985323	−	0.170698i	$-0.0546023\pi$
$380$	−1.53715	−	0.181245i	−0.0788539	−	0.00929767i
$381$	2.59830	+	0.596961i	0.133115	+	0.0305832i
$382$	8.37167	+	8.37167i	0.428332	+	0.428332i
$383$	−26.2660	−	26.2660i	−1.34213	−	1.34213i	−0.893936	−	0.448194i	$-0.852067\pi$
$383$	−26.2660	−	26.2660i	−1.34213	−	1.34213i	−0.448194	−	0.893936i	$-0.647933\pi$
$384$	−1.68807	−	0.387835i	−0.0861440	−	0.0197916i
$385$	−27.0975	+	21.3814i	−1.38102	+	1.08970i
$386$			3.01611i			0.153516i
$387$	11.6797	+	33.6878i	0.593711	+	1.71244i
$388$	−2.86345	+	2.86345i	−0.145370	+	0.145370i
$389$	13.7614			0.697729			0.348865	−	0.937173i	$-0.386567\pi$
$389$	13.7614			0.697729			0.348865	+	0.937173i	$0.386567\pi$
$390$	4.10932	+	8.67916i	0.208083	+	0.439487i
$391$	15.3021			0.773863
$392$	10.6852	−	10.6852i	0.539686	−	0.539686i
$393$	−8.64710	−	13.8056i	−0.436189	−	0.696402i
$394$			15.9653i			0.804322i
$395$	3.69250	−	31.3162i	0.185790	−	1.57569i
$396$	−4.29846	+	8.86084i	−0.216006	+	0.445274i
$397$	13.9257	+	13.9257i	0.698913	+	0.698913i	0.964176	−	0.265263i	$-0.0854588\pi$
$397$	13.9257	+	13.9257i	0.698913	+	0.698913i	−0.265263	+	0.964176i	$0.585459\pi$
$398$	7.31593	+	7.31593i	0.366714	+	0.366714i
$399$	1.26236	−	5.49446i	0.0631968	−	0.275067i
$400$	−4.86288	−	1.16293i	−0.243144	−	0.0581466i
$401$			11.6209i			0.580319i	0.956978	+	0.290159i	$0.0937083\pi$
$401$			11.6209i			0.580319i	−0.956978	+	0.290159i	$0.906292\pi$
$402$	15.9733	−	10.0048i	0.796675	−	0.498994i
$403$	−1.75323	+	1.75323i	−0.0873346	+	0.0873346i
$404$	−6.75989			−0.336317
$405$	10.5206	+	17.1556i	0.522775	+	0.852471i
$406$	−8.31950			−0.412890
$407$	8.48007	−	8.48007i	0.420341	−	0.420341i
$408$	−11.3167	+	7.08814i	−0.560258	+	0.350915i
$409$			4.76046i			0.235390i	0.993050	+	0.117695i	$0.0375505\pi$
$409$			4.76046i			0.235390i	−0.993050	+	0.117695i	$0.962450\pi$
$410$	−9.46971	−	12.0014i	−0.467676	−	0.592705i
$411$	−5.48822	+	23.8877i	−0.270714	+	1.17829i
$412$	−3.47102	−	3.47102i	−0.171005	−	0.171005i
$413$	21.2769	+	21.2769i	1.04697	+	1.04697i
$414$	−2.59893	+	5.35743i	−0.127730	+	0.263303i
$415$	−0.262005	−	0.332050i	−0.0128613	−	0.0162997i
$416$		−	2.47944i		−	0.121565i
$417$	13.8503	+	22.1128i	0.678250	+	1.08287i
$418$	1.60679	−	1.60679i	0.0785905	−	0.0785905i
$419$	14.2106			0.694233			0.347116	−	0.937822i	$-0.387161\pi$
$419$	14.2106			0.694233			0.347116	+	0.937822i	$0.387161\pi$
$420$	6.12829	−	17.1497i	0.299030	−	0.836820i
$421$	10.4874			0.511124			0.255562	−	0.966793i	$-0.417740\pi$
$421$	10.4874			0.511124			0.255562	+	0.966793i	$0.417740\pi$
$422$	12.8575	−	12.8575i	0.625892	−	0.625892i
$423$	12.2231	+	35.2551i	0.594306	+	1.71416i
$424$		−	6.63862i		−	0.322400i
$425$	−32.8493	+	20.1700i	−1.59342	+	0.978388i
$426$	0.783750	+	0.180067i	0.0379728	+	0.00872427i
$427$	−40.7179	−	40.7179i	−1.97048	−	1.97048i
$428$	−8.41957	−	8.41957i	−0.406975	−	0.406975i
$429$	−13.7401	−	3.15679i	−0.663377	−	0.152411i
$430$	3.11198	−	26.3928i	0.150073	−	1.27278i
$431$		−	17.2169i		−	0.829308i	−0.909979	−	0.414654i	$-0.863903\pi$
$431$		−	17.2169i		−	0.829308i	0.909979	−	0.414654i	$-0.136097\pi$
$432$	−0.559598	−	5.16593i	−0.0269237	−	0.248546i
$433$	6.64429	−	6.64429i	0.319304	−	0.319304i	−0.529196	−	0.848500i	$-0.677506\pi$
$433$	6.64429	−	6.64429i	0.319304	−	0.319304i	0.848500	+	0.529196i	$0.177506\pi$
$434$	4.70226			0.225715
$435$	−6.19320	+	2.93229i	−0.296941	+	0.140593i
$436$	−13.8823			−0.664842
$437$	0.971494	−	0.971494i	0.0464729	−	0.0464729i
$438$	5.61495	+	8.96461i	0.268293	+	0.428346i
$439$			10.2028i			0.486952i	0.969907	+	0.243476i	$0.0782877\pi$
$439$			10.2028i			0.486952i	−0.969907	+	0.243476i	$0.921712\pi$
$440$	5.76267	−	4.54705i	0.274724	−	0.216772i
$441$	40.7877	+	19.7864i	1.94227	+	0.942210i
$442$	−13.5165	−	13.5165i	−0.642914	−	0.642914i
$443$	−18.3421	−	18.3421i	−0.871459	−	0.871459i	0.121173	−	0.992631i	$-0.461334\pi$
$443$	−18.3421	−	18.3421i	−0.871459	−	0.871459i	−0.992631	+	0.121173i	$0.961334\pi$
$444$	−1.41683	+	6.16681i	−0.0672396	+	0.292664i
$445$	−13.1036	−	1.54504i	−0.621169	−	0.0732421i
$446$		−	15.3866i		−	0.728575i
$447$	−8.72777	+	5.46661i	−0.412809	+	0.258562i
$448$	−3.32500	+	3.32500i	−0.157091	+	0.157091i
$449$	10.8779			0.513362			0.256681	−	0.966496i	$-0.417371\pi$
$449$	10.8779			0.513362			0.256681	+	0.966496i	$0.417371\pi$
$450$	−1.48256	−	14.9266i	−0.0698887	−	0.703644i
$451$	22.4438			1.05684
$452$	−2.35475	+	2.35475i	−0.110758	+	0.110758i
$453$	9.39888	−	5.88695i	0.441598	−	0.276593i
$454$			18.6200i			0.873878i
$455$	25.8909	+	3.05279i	1.21378	+	0.143117i
$456$	−0.268457	+	1.16847i	−0.0125717	+	0.0547188i
$457$	27.7591	+	27.7591i	1.29851	+	1.29851i	0.929373	+	0.369142i	$0.120348\pi$
$457$	27.7591	+	27.7591i	1.29851	+	1.29851i	0.369142	+	0.929373i	$0.379652\pi$
$458$	−9.23964	−	9.23964i	−0.431740	−	0.431740i
$459$	−31.2123	−	25.1111i	−1.45687	−	1.17209i
$460$	3.48422	−	2.74923i	0.162453	−	0.128184i
$461$			16.4636i			0.766785i	0.923585	+	0.383393i	$0.125244\pi$
$461$			16.4636i			0.766785i	−0.923585	+	0.383393i	$0.874756\pi$
$462$	14.1925	+	22.6592i	0.660294	+	1.05420i
$463$	−0.440640	+	0.440640i	−0.0204783	+	0.0204783i	−0.717272	−	0.696793i	$-0.754609\pi$
$463$	−0.440640	+	0.440640i	−0.0204783	+	0.0204783i	0.696793	+	0.717272i	$0.254609\pi$
$464$	1.76926			0.0821357
$465$	3.50045	−	1.65736i	0.162330	−	0.0768581i
$466$	26.8083			1.24187
$467$	−8.06166	+	8.06166i	−0.373049	+	0.373049i	−0.868587	−	0.495537i	$-0.834971\pi$
$467$	−8.06166	+	8.06166i	−0.373049	+	0.373049i	0.495537	+	0.868587i	$0.334971\pi$
$468$	7.02791	−	2.43661i	0.324865	−	0.112632i
$469$		−	51.1691i		−	2.36277i
$470$	3.25676	−	27.6208i	0.150223	−	1.27405i
$471$	−34.8811	−	8.01394i	−1.60724	−	0.369263i
$472$	−4.52483	−	4.52483i	−0.208272	−	0.208272i
$473$	27.5886	+	27.5886i	1.26852	+	1.26852i
$474$	−23.8053	−	5.46928i	−1.09341	−	0.251212i
$475$	−0.804975	+	3.36606i	−0.0369348	+	0.154445i
$476$			36.2520i			1.66161i
$477$	18.8170	−	6.52393i	0.861571	−	0.298710i
$478$	−6.70168	+	6.70168i	−0.306528	+	0.306528i
$479$	−17.8680			−0.816409			−0.408204	−	0.912891i	$-0.633845\pi$
$479$	−17.8680			−0.816409			−0.408204	+	0.912891i	$0.633845\pi$
$480$	−1.30327	+	3.64712i	−0.0594857	+	0.166468i
$481$	−9.05781			−0.413001
$482$	2.16179	−	2.16179i	0.0984669	−	0.0984669i
$483$	8.58105	+	13.7002i	0.390451	+	0.623379i
$484$		−	0.223207i		−	0.0101458i
$485$	5.60905	+	7.10859i	0.254694	+	0.322784i
$486$	14.0928	−	6.66285i	0.639261	−	0.302233i
$487$	0.0845231	+	0.0845231i	0.00383011	+	0.00383011i	0.709019	−	0.705189i	$-0.249138\pi$
$487$	0.0845231	+	0.0845231i	0.00383011	+	0.00383011i	−0.705189	+	0.709019i	$0.749138\pi$
$488$	8.65922	+	8.65922i	0.391985	+	0.391985i
$489$	−2.96296	+	12.8964i	−0.133990	+	0.583196i
$490$	−20.9307	−	26.5264i	−0.945553	−	1.19834i
$491$		−	30.9417i		−	1.39638i	−0.715913	−	0.698190i	$-0.753989\pi$
$491$		−	30.9417i		−	1.39638i	0.715913	−	0.698190i	$-0.246011\pi$
$492$	−10.0356	+	6.28578i	−0.452441	+	0.283385i
$493$	9.64498	−	9.64498i	0.434388	−	0.434388i
$494$	−1.71626			−0.0772180
$495$	18.5516	+	11.8656i	0.833833	+	0.533321i
$496$	−1.00000			−0.0449013
$497$	1.54375	−	1.54375i	0.0692468	−	0.0692468i
$498$	−0.277662	+	0.173913i	−0.0124423	+	0.00779322i
$499$			37.7934i			1.69187i	0.533289	+	0.845933i	$0.320956\pi$
$499$			37.7934i			1.69187i	−0.533289	+	0.845933i	$0.679044\pi$
$500$	−3.85581	+	10.4944i	−0.172437	+	0.469325i
$501$	2.32187	−	10.1060i	0.103733	−	0.451504i
$502$	2.76597	+	2.76597i	0.123451	+	0.123451i
$503$	9.29282	+	9.29282i	0.414346	+	0.414346i	0.883250	−	0.468903i	$-0.155351\pi$
$503$	9.29282	+	9.29282i	0.414346	+	0.414346i	−0.468903	+	0.883250i	$0.655351\pi$
$504$	−12.6922	−	6.15707i	−0.565354	−	0.274258i
$505$	−1.77002	+	15.0116i	−0.0787647	+	0.668007i
$506$			6.51586i			0.289665i
$507$	−6.30011	−	10.0585i	−0.279798	−	0.446714i
$508$	−1.08839	+	1.08839i	−0.0482894	+	0.0482894i
$509$	25.9656			1.15091			0.575453	−	0.817835i	$-0.304826\pi$
$509$	25.9656			1.15091			0.575453	+	0.817835i	$0.304826\pi$
$510$	12.7774	+	26.9867i	0.565791	+	1.19499i
$511$	28.7174			1.27038
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−3.57583	+	0.387351i	−0.157877	+	0.0171020i
$514$		−	18.8592i		−	0.831844i
$515$	−8.61689	+	6.79918i	−0.379706	+	0.299608i
$516$	−20.0627	−	4.60942i	−0.883212	−	0.202918i
$517$	28.8721	+	28.8721i	1.26979	+	1.26979i
$518$	12.1468	+	12.1468i	0.533698	+	0.533698i
$519$	11.3091	+	2.59828i	0.496416	+	0.114052i
$520$	−5.50605	−	0.649219i	−0.241456	−	0.0284701i
$521$		−	29.2044i		−	1.27947i	−0.768596	−	0.639734i	$-0.779044\pi$
$521$		−	29.2044i		−	1.27947i	0.768596	−	0.639734i	$-0.220956\pi$
$522$	1.73869	+	5.01492i	0.0761004	+	0.219497i
$523$	−3.71048	+	3.71048i	−0.162248	+	0.162248i	−0.783562	−	0.621314i	$-0.786599\pi$
$523$	−3.71048	+	3.71048i	−0.162248	+	0.162248i	0.621314	+	0.783562i	$0.286599\pi$
$524$	9.40510			0.410864
$525$	−36.4794	−	18.0995i	−1.59209	−	0.789926i
$526$	−6.37278			−0.277866
$527$	−5.45143	+	5.45143i	−0.237468	+	0.237468i
$528$	−3.01823	−	4.81878i	−0.131351	−	0.209711i
$529$		−	19.0604i		−	0.828712i
$530$	−14.7423	−	1.73826i	−0.640364	−	0.0755053i
$531$	8.37887	−	17.2722i	0.363612	−	0.749549i
$532$	2.30154	+	2.30154i	0.0997846	+	0.0997846i
$533$	−11.9865	−	11.9865i	−0.519191	−	0.519191i
$534$	−2.28850	+	9.96079i	−0.0990329	+	0.431046i
$535$	−20.9018	+	16.4926i	−0.903663	+	0.713038i
$536$			10.8818i			0.470023i
$537$	9.46065	−	5.92564i	0.408257	−	0.255710i
$538$	12.9601	−	12.9601i	0.558751	−	0.558751i
$539$	49.6071			2.13673
$540$	−11.6184	−	0.109961i	−0.499978	−	0.00473196i
$541$	4.61784			0.198536			0.0992682	−	0.995061i	$-0.468350\pi$
$541$	4.61784			0.198536			0.0992682	+	0.995061i	$0.468350\pi$
$542$	−6.14408	+	6.14408i	−0.263911	+	0.263911i
$543$	11.7161	−	7.33835i	0.502787	−	0.314919i
$544$		−	7.70948i		−	0.330541i
$545$	−3.63496	+	30.8282i	−0.155704	+	1.32054i
$546$	4.52175	−	19.6812i	0.193513	−	0.842276i
$547$	−22.2626	−	22.2626i	−0.951880	−	0.951880i	0.0470143	−	0.998894i	$-0.485029\pi$
$547$	−22.2626	−	22.2626i	−0.951880	−	0.951880i	−0.998894	+	0.0470143i	$0.985029\pi$
$548$	−10.0062	−	10.0062i	−0.427444	−	0.427444i
$549$	−16.0347	+	33.0540i	−0.684346	+	1.41071i
$550$	−8.58866	−	13.9877i	−0.366222	−	0.596436i
$551$		−	1.22467i		−	0.0521727i
$552$	−1.82488	−	2.91353i	−0.0776720	−	0.124008i
$553$	−46.8893	+	46.8893i	−1.99394	+	1.99394i
$554$	16.1198			0.684864
$555$	13.3235	+	4.76105i	0.565553	+	0.202095i
$556$	−15.0644			−0.638871
$557$	9.01589	−	9.01589i	0.382016	−	0.382016i	−0.489812	−	0.871828i	$-0.662935\pi$
$557$	9.01589	−	9.01589i	0.382016	−	0.382016i	0.871828	+	0.489812i	$0.162935\pi$
$558$	−0.982724	−	2.83448i	−0.0416020	−	0.119993i
$559$		−	29.4682i		−	1.24637i
$560$	6.51315	+	8.25439i	0.275231	+	0.348812i
$561$	−42.7229	−	9.81561i	−1.80376	−	0.414415i
$562$	14.9161	+	14.9161i	0.629197	+	0.629197i
$563$	1.87451	+	1.87451i	0.0790013	+	0.0790013i	0.745503	−	0.666502i	$-0.232209\pi$
$563$	1.87451	+	1.87451i	0.0790013	+	0.0790013i	−0.666502	+	0.745503i	$0.732209\pi$
$564$	−20.9961	−	4.82387i	−0.884097	−	0.203122i
$565$	4.61258	+	5.84572i	0.194053	+	0.245931i
$566$		−	5.54492i		−	0.233070i
$567$	4.97916	−	42.0264i	0.209105	−	1.76494i
$568$	−0.328301	+	0.328301i	−0.0137752	+	0.0137752i
$569$	16.0543			0.673032			0.336516	−	0.941678i	$-0.390751\pi$
$569$	16.0543			0.673032			0.336516	+	0.941678i	$0.390751\pi$
$570$	2.52452	+	0.902113i	0.105740	+	0.0377854i
$571$	−37.6126			−1.57404			−0.787020	−	0.616928i	$-0.788377\pi$
$571$	−37.6126			−1.57404			−0.787020	+	0.616928i	$0.788377\pi$
$572$	5.75550	−	5.75550i	0.240650	−	0.240650i
$573$	−10.8851	−	17.3788i	−0.454733	−	0.726010i
$574$			32.1483i			1.34184i
$575$	−5.19287	−	8.45722i	−0.216558	−	0.352690i
$576$	2.69917	+	1.30939i	0.112465	+	0.0545578i
$577$	7.50694	+	7.50694i	0.312518	+	0.312518i	0.845884	−	0.533366i	$-0.179073\pi$
$577$	7.50694	+	7.50694i	0.312518	+	0.312518i	−0.533366	+	0.845884i	$0.679073\pi$
$578$	−30.0069	−	30.0069i	−1.24812	−	1.24812i
$579$	1.16975	−	5.09140i	0.0486132	−	0.211591i
$580$	0.463264	−	3.92896i	0.0192360	−	0.163141i
$581$			0.889468i			0.0369014i
$582$	5.94426	−	3.72316i	0.246397	−	0.154330i
$583$	15.4102	−	15.4102i	0.638224	−	0.638224i
$584$	−6.10715			−0.252716
$585$	−3.57074	−	16.2448i	−0.147632	−	0.671639i
$586$	−1.37124			−0.0566453
$587$	14.6910	−	14.6910i	0.606362	−	0.606362i	−0.335631	−	0.941993i	$-0.608950\pi$
$587$	14.6910	−	14.6910i	0.606362	−	0.606362i	0.941993	+	0.335631i	$0.108950\pi$
$588$	−22.1815	+	13.8933i	−0.914751	+	0.572951i
$589$			0.692195i			0.0285214i
$590$	−11.2330	+	8.86344i	−0.462456	+	0.364902i
$591$	6.19192	−	26.9506i	0.254701	−	1.10860i
$592$	−2.58318	−	2.58318i	−0.106168	−	0.106168i
$593$	−7.56492	−	7.56492i	−0.310654	−	0.310654i	0.534509	−	0.845163i	$-0.320497\pi$
$593$	−7.56492	−	7.56492i	−0.310654	−	0.310654i	−0.845163	+	0.534509i	$0.820497\pi$
$594$	10.6926	−	13.2906i	0.438725	−	0.545321i
$595$	80.5042	+	9.49225i	3.30035	+	0.389144i
$596$		−	5.94580i		−	0.243550i
$597$	−9.51243	−	15.1872i	−0.389318	−	0.621570i
$598$	3.47989	−	3.47989i	0.142303	−	0.142303i
$599$	12.9203			0.527908			0.263954	−	0.964535i	$-0.414973\pi$
$599$	12.9203			0.527908			0.263954	+	0.964535i	$0.414973\pi$
$600$	7.75786	+	3.84911i	0.316713	+	0.157139i
$601$	−41.2095			−1.68097			−0.840484	−	0.541836i	$-0.817730\pi$
$601$	−41.2095			−1.68097			−0.840484	+	0.541836i	$0.817730\pi$
$602$	−39.5176	+	39.5176i	−1.61062	+	1.61062i
$603$	−30.8442	+	10.6938i	−1.25607	+	0.435486i
$604$			6.40300i			0.260534i
$605$	−0.495672	−	0.0584447i	−0.0201519	−	0.00237611i
$606$	11.4112	+	2.62172i	0.463547	+	0.106500i
$607$	−2.11119	−	2.11119i	−0.0856904	−	0.0856904i	0.662962	−	0.748653i	$-0.269299\pi$
$607$	−2.11119	−	2.11119i	−0.0856904	−	0.0856904i	−0.748653	+	0.662962i	$0.769299\pi$
$608$	−0.489456	−	0.489456i	−0.0198500	−	0.0198500i
$609$	14.0439	+	3.22659i	0.569088	+	0.130748i
$610$	21.4967	−	16.9621i	0.870377	−	0.686774i
$611$		−	30.8392i		−	1.24762i
$612$	21.8523	−	7.57629i	0.883329	−	0.306254i
$613$	17.5846	−	17.5846i	0.710234	−	0.710234i	−0.256350	−	0.966584i	$-0.582520\pi$
$613$	17.5846	−	17.5846i	0.710234	−	0.710234i	0.966584	+	0.256350i	$0.0825199\pi$
$614$	−29.4699			−1.18931
$615$	11.3310	+	23.9318i	0.456910	+	0.965025i
$616$	−15.4366			−0.621957
$617$	−27.5043	+	27.5043i	−1.10728	+	1.10728i	−0.113776	+	0.993506i	$0.536295\pi$
$617$	−27.5043	+	27.5043i	−1.10728	+	1.10728i	−0.993506	+	0.113776i	$0.963705\pi$
$618$	4.51314	+	7.20551i	0.181545	+	0.289848i
$619$			22.6242i			0.909343i	0.890659	+	0.454672i	$0.150243\pi$
$619$			22.6242i			0.909343i	−0.890659	+	0.454672i	$0.849757\pi$
$620$	−0.261841	+	2.22068i	−0.0105158	+	0.0891848i
$621$	6.46498	−	8.03577i	0.259431	−	0.322464i
$622$	3.50382	+	3.50382i	0.140491	+	0.140491i
$623$	19.6198	+	19.6198i	0.786050	+	0.786050i
$624$	−0.961614	+	4.18547i	−0.0384954	+	0.167553i
$625$	22.2952	+	11.3104i	0.891807	+	0.452416i
$626$		−	22.9210i		−	0.916105i
$627$	−3.33554	+	2.08920i	−0.133209	+	0.0834346i
$628$	14.6111	−	14.6111i	0.583048	−	0.583048i
$629$	−28.1640			−1.12297
$630$	−16.9962	+	26.5731i	−0.677146	+	1.05870i
$631$	31.0396			1.23567			0.617833	−	0.786310i	$-0.288011\pi$
$631$	31.0396			1.23567			0.617833	+	0.786310i	$0.288011\pi$
$632$	9.97167	−	9.97167i	0.396652	−	0.396652i
$633$	−26.6909	+	16.7178i	−1.06087	+	0.664471i
$634$			30.9214i			1.22804i
$635$	2.13198	+	2.70195i	0.0846051	+	0.107224i
$636$	−2.57469	+	11.2065i	−0.102093	+	0.444365i
$637$	−26.4934	−	26.4934i	−1.04971	−	1.04971i
$638$	4.10696	+	4.10696i	0.162596	+	0.162596i
$639$	−1.25319	−	0.607931i	−0.0495754	−	0.0240494i
$640$	−1.38511	−	1.75541i	−0.0547513	−	0.0693887i
$641$			47.7083i			1.88436i	0.335101	+	0.942182i	$0.391230\pi$
$641$			47.7083i			1.88436i	−0.335101	+	0.942182i	$0.608770\pi$
$642$	10.9474	+	17.4782i	0.432060	+	0.689811i
$643$	−22.7231	+	22.7231i	−0.896111	+	0.896111i	−0.995090	−	0.0989784i	$-0.968443\pi$
$643$	−22.7231	+	22.7231i	−0.896111	+	0.896111i	0.0989784	+	0.995090i	$0.468443\pi$
$644$	−9.33325			−0.367782
$645$	−15.4893	+	43.3461i	−0.609891	+	1.70675i
$646$	−5.33646			−0.209960
$647$	−7.29186	+	7.29186i	−0.286673	+	0.286673i	−0.835763	−	0.549090i	$-0.814974\pi$
$647$	−7.29186	+	7.29186i	−0.286673	+	0.286673i	0.549090	+	0.835763i	$0.314974\pi$
$648$	−1.05889	+	8.93749i	−0.0415970	+	0.351098i
$649$		−	21.0069i		−	0.824594i
$650$	−2.88342	+	12.0572i	−0.113097	+	0.472923i
$651$	−7.93774	−	1.82370i	−0.311105	−	0.0714764i
$652$	−5.40211	−	5.40211i	−0.211563	−	0.211563i
$653$	26.6210	+	26.6210i	1.04176	+	1.04176i	0.999089	+	0.0426726i	$0.0135872\pi$
$653$	26.6210	+	26.6210i	1.04176	+	1.04176i	0.0426726	+	0.999089i	$0.486413\pi$
$654$	23.4343	+	5.38405i	0.916355	+	0.210533i
$655$	2.46264	−	20.8858i	0.0962233	−	0.816074i
$656$		−	6.83679i		−	0.266932i
$657$	−6.00165	−	17.3106i	−0.234146	−	0.675350i
$658$	−41.3561	+	41.3561i	−1.61223	+	1.61223i
$659$	−11.8724			−0.462485			−0.231242	−	0.972896i	$-0.574279\pi$
$659$	−11.8724			−0.462485			−0.231242	+	0.972896i	$0.574279\pi$
$660$	−11.4913	+	5.44078i	−0.447298	+	0.211782i
$661$	40.2044			1.56377			0.781885	−	0.623422i	$-0.214258\pi$
$661$	40.2044			1.56377			0.781885	+	0.623422i	$0.214258\pi$
$662$	−17.2886	+	17.2886i	−0.671941	+	0.671941i
$663$	17.5746	+	28.0590i	0.682542	+	1.08972i
$664$		−	0.189158i		−	0.00734075i
$665$	5.71364	−	4.50837i	0.221566	−	0.174827i
$666$	4.78341	−	9.86051i	0.185353	−	0.382087i
$667$	2.48315	+	2.48315i	0.0961479	+	0.0961479i
$668$	4.23326	+	4.23326i	0.163790	+	0.163790i
$669$	−5.96745	+	25.9736i	−0.230715	+	1.00420i
$670$	24.1651	+	2.84930i	0.933578	+	0.110078i
$671$			40.2012i			1.55195i
$672$	6.90238	−	4.32328i	0.266265	−	0.166774i
$673$	−21.8003	+	21.8003i	−0.840339	+	0.840339i	−0.988903	−	0.148564i	$-0.952535\pi$
$673$	−21.8003	+	21.8003i	−0.840339	+	0.840339i	0.148564	+	0.988903i	$0.452535\pi$
$674$	−5.20021			−0.200305
$675$	−3.28637	+	25.7721i	−0.126492	+	0.991968i
$676$	6.85238			0.263553
$677$	−3.94473	+	3.94473i	−0.151608	+	0.151608i	−0.778836	−	0.627228i	$-0.784190\pi$
$677$	−3.94473	+	3.94473i	−0.151608	+	0.151608i	0.627228	+	0.778836i	$0.284190\pi$
$678$	4.88823	−	3.06173i	0.187731	−	0.117585i
$679$		−	19.0419i		−	0.730762i
$680$	−17.1203	−	2.01866i	−0.656535	−	0.0774120i
$681$	7.22147	−	31.4318i	0.276727	−	1.20447i
$682$	−2.32129	−	2.32129i	−0.0888869	−	0.0888869i
$683$	−32.3268	−	32.3268i	−1.23695	−	1.23695i	−0.961241	−	0.275711i	$-0.911087\pi$
$683$	−32.3268	−	32.3268i	−1.23695	−	1.23695i	−0.275711	−	0.961241i	$-0.588913\pi$
$684$	0.906350	−	1.86835i	0.0346552	−	0.0714381i
$685$	−24.8406	+	19.6006i	−0.949112	+	0.748899i
$686$			38.1409i			1.45623i
$687$	12.0137	+	19.1806i	0.458352	+	0.731786i
$688$	8.40397	−	8.40397i	0.320398	−	0.320398i
$689$	−16.4601			−0.627078
$690$	−6.94786	+	3.28960i	−0.264501	+	0.125233i
$691$	9.29980			0.353781			0.176891	−	0.984231i	$-0.443396\pi$
$691$	9.29980			0.353781			0.176891	+	0.984231i	$0.443396\pi$
$692$	−4.73722	+	4.73722i	−0.180082	+	0.180082i
$693$	−15.1699	−	43.7546i	−0.576257	−	1.66210i
$694$			10.3645i			0.393430i
$695$	−3.94446	+	33.4532i	−0.149622	+	1.26895i
$696$	−2.98663	−	0.686180i	−0.113208	−	0.0260096i
$697$	−37.2703	−	37.2703i	−1.41171	−	1.41171i
$698$	5.80188	+	5.80188i	0.219605	+	0.219605i
$699$	−45.2543	−	10.3972i	−1.71167	−	0.393258i
$700$	20.0358	−	12.3023i	0.757282	−	0.464984i
$701$			31.4083i			1.18628i	0.805101	+	0.593138i	$0.202111\pi$
$701$			31.4083i			1.18628i	−0.805101	+	0.593138i	$0.797889\pi$
$702$	−12.8086	+	1.38749i	−0.483430	+	0.0523675i
$703$	−1.78806	+	1.78806i	−0.0674381	+	0.0674381i
$704$	3.28280			0.123725
$705$	−16.2100	+	45.3627i	−0.610502	+	1.70846i
$706$	−28.6153			−1.07695
$707$	22.4766	−	22.4766i	0.845320	−	0.845320i
$708$	5.88335	+	9.39313i	0.221110	+	0.353015i
$709$		−	37.3181i		−	1.40151i	−0.713403	−	0.700754i	$-0.752847\pi$
$709$		−	37.3181i		−	1.40151i	0.713403	−	0.700754i	$-0.247153\pi$
$710$	0.643089	+	0.815015i	0.0241347	+	0.0305869i
$711$	38.0639	+	18.4651i	1.42751	+	0.692494i
$712$	−4.17242	−	4.17242i	−0.156368	−	0.156368i
$713$	−1.40350	−	1.40350i	−0.0525614	−	0.0525614i
$714$	14.0598	−	61.1959i	0.526174	−	2.29020i
$715$	−11.2741	−	14.2882i	−0.421629	−	0.534348i
$716$			6.44508i			0.240864i
$717$	13.9121	−	8.71377i	0.519556	−	0.325422i
$718$	12.0740	−	12.0740i	0.450599	−	0.450599i
$719$	−31.3798			−1.17027			−0.585135	−	0.810936i	$-0.698958\pi$
$719$	−31.3798			−1.17027			−0.585135	+	0.810936i	$0.698958\pi$
$720$	3.61449	−	5.65115i	0.134704	−	0.210606i
$721$	23.0822			0.859628
$722$	13.0962	−	13.0962i	0.487391	−	0.487391i
$723$	−4.48768	+	2.81084i	−0.166899	+	0.104536i
$724$			7.98162i			0.296635i
$725$	−8.60368	−	2.05753i	−0.319533	−	0.0764146i
$726$	−0.0865674	+	0.376789i	−0.00321282	+	0.0139839i
$727$	−18.1035	−	18.1035i	−0.671423	−	0.671423i	0.286621	−	0.958044i	$-0.407468\pi$
$727$	−18.1035	−	18.1035i	−0.671423	−	0.671423i	−0.958044	+	0.286621i	$0.907468\pi$
$728$	8.24413	+	8.24413i	0.305548	+	0.305548i
$729$	−26.3737	+	5.78169i	−0.976804	+	0.214137i
$730$	−1.59910	+	13.5621i	−0.0591855	+	0.501954i
$731$		−	91.6272i		−	3.38896i
$732$	−11.2590	−	17.9757i	−0.416146	−	0.664402i
$733$	−33.3064	+	33.3064i	−1.23020	+	1.23020i	−0.266313	+	0.963887i	$0.585805\pi$
$733$	−33.3064	+	33.3064i	−1.23020	+	1.23020i	−0.963887	+	0.266313i	$0.914195\pi$
$734$	18.3054			0.675666
$735$	25.0447	+	52.8961i	0.923786	+	1.95110i
$736$	1.98485			0.0731624
$737$	−25.2599	+	25.2599i	−0.930459	+	0.930459i
$738$	19.3787	−	6.71867i	0.713340	−	0.247318i
$739$			12.6490i			0.465303i	0.972560	+	0.232651i	$0.0747401\pi$
$739$			12.6490i			0.465303i	−0.972560	+	0.232651i	$0.925260\pi$
$740$	−6.41281	+	5.06004i	−0.235740	+	0.186011i
$741$	2.89716	+	0.665624i	0.106430	+	0.0244523i
$742$	22.0734	+	22.0734i	0.810339	+	0.810339i
$743$	20.4531	+	20.4531i	0.750350	+	0.750350i	0.974544	−	0.224194i	$-0.0719750\pi$
$743$	20.4531	+	20.4531i	0.750350	+	0.750350i	−0.224194	+	0.974544i	$0.571975\pi$
$744$	1.68807	+	0.387835i	0.0618877	+	0.0142187i
$745$	−13.2038	−	1.55686i	−0.483748	−	0.0570388i
$746$		−	17.6442i		−	0.646001i
$747$	0.536163	−	0.185890i	0.0196172	−	0.00680136i
$748$	17.8960	−	17.8960i	0.654341	−	0.654341i
$749$	55.9900			2.04583
$750$	10.5790	−	16.2199i	0.386290	−	0.592267i
$751$	−18.7803			−0.685302			−0.342651	−	0.939463i	$-0.611325\pi$
$751$	−18.7803			−0.685302			−0.342651	+	0.939463i	$0.611325\pi$
$752$	8.79496	−	8.79496i	0.320719	−	0.320719i
$753$	−3.59641	−	5.74188i	−0.131060	−	0.209246i
$754$		−	4.38677i		−	0.159757i
$755$	14.2190	+	1.67657i	0.517484	+	0.0610165i
$756$	19.0374	+	15.3160i	0.692382	+	0.557039i
$757$	19.4350	+	19.4350i	0.706379	+	0.706379i	0.965772	−	0.259393i	$-0.0835225\pi$
$757$	19.4350	+	19.4350i	0.706379	+	0.706379i	−0.259393	+	0.965772i	$0.583522\pi$
$758$	−4.69962	−	4.69962i	−0.170698	−	0.170698i
$759$	2.52708	−	10.9992i	0.0917271	−	0.399247i
$760$	−1.21509	+	0.958767i	−0.0440758	+	0.0347781i
$761$			22.8166i			0.827100i	0.910481	+	0.413550i	$0.135711\pi$
$761$			22.8166i			0.827100i	−0.910481	+	0.413550i	$0.864289\pi$
$762$	2.25939	−	1.41516i	0.0818491	−	0.0512659i
$763$	46.1586	−	46.1586i	1.67106	−	1.67106i
$764$	11.8393			0.428332
$765$	−11.1027	−	50.5110i	−0.401420	−	1.82623i
$766$	−37.1457			−1.34213
$767$	−11.2191	+	11.2191i	−0.405096	+	0.405096i
$768$	−1.46789	+	0.919406i	−0.0529678	+	0.0331762i
$769$		−	52.0805i		−	1.87807i	−0.343822	−	0.939035i	$-0.611722\pi$
$769$		−	52.0805i		−	1.87807i	0.343822	−	0.939035i	$-0.388278\pi$
$770$	−4.04193	+	34.2798i	−0.145661	+	1.23536i
$771$	−7.31426	+	31.8357i	−0.263417	+	1.14653i
$772$	2.13271	+	2.13271i	0.0767579	+	0.0767579i
$773$	−4.50923	−	4.50923i	−0.162186	−	0.162186i	0.621349	−	0.783534i	$-0.286585\pi$
$773$	−4.50923	−	4.50923i	−0.162186	−	0.162186i	−0.783534	+	0.621349i	$0.786585\pi$
$774$	32.0796	+	15.5621i	1.15308	+	0.559367i
$775$	4.86288	+	1.16293i	0.174680	+	0.0417738i
$776$			4.04953i			0.145370i
$777$	−15.7937	−	25.2156i	−0.566595	−	0.904603i
$778$	9.73076	−	9.73076i	0.348865	−	0.348865i
$779$	−4.73239			−0.169555
$780$	9.04282	+	3.23137i	0.323785	+	0.115702i
$781$	−1.52416			−0.0545388
$782$	10.8202	−	10.8202i	0.386931	−	0.386931i
$783$	−0.990074	−	9.13986i	−0.0353823	−	0.326632i
$784$		−	15.1112i		−	0.539686i
$785$	−28.6209	−	36.2725i	−1.02153	−	1.29462i
$786$	−15.8765	−	3.64763i	−0.566295	−	0.130107i
$787$	−13.3071	−	13.3071i	−0.474348	−	0.474348i	0.428970	−	0.903319i	$-0.358877\pi$
$787$	−13.3071	−	13.3071i	−0.474348	−	0.474348i	−0.903319	+	0.428970i	$0.858877\pi$
$788$	11.2892	+	11.2892i	0.402161	+	0.402161i
$789$	10.7577	+	2.47159i	0.382984	+	0.0879908i
$790$	−19.5329	−	24.7549i	−0.694951	−	0.880741i
$791$		−	15.6591i		−	0.556772i
$792$	3.22609	+	9.30503i	0.114634	+	0.330640i
$793$	21.4700	−	21.4700i	0.762423	−	0.762423i
$794$	19.6940			0.698913
$795$	24.2119	+	8.65188i	0.858706	+	0.306851i
$796$	10.3463			0.366714
$797$	−0.522275	+	0.522275i	−0.0184999	+	0.0184999i	−0.716296	−	0.697796i	$-0.754164\pi$
$797$	−0.522275	+	0.522275i	−0.0184999	+	0.0184999i	0.697796	+	0.716296i	$0.254164\pi$
$798$	−2.99255	−	4.77779i	−0.105935	−	0.169132i
$799$		−	95.8902i		−	3.39235i
$800$	−4.26089	+	2.61626i	−0.150645	+	0.0924987i
$801$	7.72629	−	15.9270i	0.272995	−	0.562752i
$802$	8.21720	+	8.21720i	0.290159	+	0.290159i
$803$	−14.1765	−	14.1765i	−0.500277	−	0.500277i
$804$	4.22035	−	18.3693i	0.148840	−	0.647834i
$805$	−2.44383	+	20.7262i	−0.0861336	+	0.730503i
$806$			2.47944i			0.0873346i
$807$	−26.9040	+	16.8512i	−0.947066	+	0.593191i
$808$	−4.77997	+	4.77997i	−0.168159	+	0.168159i
$809$	3.01936			0.106155			0.0530774	−	0.998590i	$-0.483097\pi$
$809$	3.01936			0.106155			0.0530774	+	0.998590i	$0.483097\pi$
$810$	19.5701	+	4.69166i	0.687623	+	0.164848i
$811$	−1.93779			−0.0680450			−0.0340225	−	0.999421i	$-0.510832\pi$
$811$	−1.93779			−0.0680450			−0.0340225	+	0.999421i	$0.510832\pi$
$812$	−5.88277	+	5.88277i	−0.206445	+	0.206445i
$813$	12.7545	−	7.98875i	0.447321	−	0.280178i
$814$		−	11.9926i		−	0.420341i
$815$	−13.4109	+	10.5819i	−0.469763	+	0.370667i
$816$	−2.99001	+	13.0142i	−0.104671	+	0.455587i
$817$	−5.81718	−	5.81718i	−0.203517	−	0.203517i
$818$	3.36615	+	3.36615i	0.117695	+	0.117695i
$819$	−15.2661	+	31.4695i	−0.533440	+	1.09963i
$820$	−15.1823	−	1.79015i	−0.530191	−	0.0625148i
$821$			4.46040i			0.155669i	0.996966	+	0.0778345i	$0.0248006\pi$
$821$			4.46040i			0.155669i	−0.996966	+	0.0778345i	$0.975199\pi$
$822$	13.0104	+	20.7719i	0.453790	+	0.724504i
$823$	−3.65314	+	3.65314i	−0.127340	+	0.127340i	−0.767905	−	0.640564i	$-0.778701\pi$
$823$	−3.65314	+	3.65314i	−0.127340	+	0.127340i	0.640564	+	0.767905i	$0.278701\pi$
$824$	−4.90876			−0.171005
$825$	9.07335	+	26.9432i	0.315894	+	0.938040i
$826$	30.0901			1.04697
$827$	−26.8866	+	26.8866i	−0.934940	+	0.934940i	−0.998009	−	0.0630689i	$-0.979911\pi$
$827$	−26.8866	+	26.8866i	−0.934940	+	0.934940i	0.0630689	+	0.998009i	$0.479911\pi$
$828$	1.95056	+	5.62600i	0.0677865	+	0.195517i
$829$			30.7601i			1.06834i	0.845377	+	0.534171i	$0.179376\pi$
$829$			30.7601i			1.06834i	−0.845377	+	0.534171i	$0.820624\pi$
$830$	−0.420060	−	0.0495293i	−0.0145805	−	0.00171919i
$831$	−27.2113	−	6.25182i	−0.943951	−	0.216873i
$832$	−1.75323	−	1.75323i	−0.0607823	−	0.0607823i
$833$	−82.3777	−	82.3777i	−2.85422	−	2.85422i
$834$	25.4297	+	5.84248i	0.880558	+	0.202309i
$835$	10.5092	−	8.29229i	0.363685	−	0.286967i
$836$		−	2.27234i		−	0.0785905i
$837$	0.559598	+	5.16593i	0.0193426	+	0.178561i
$838$	10.0484	−	10.0484i	0.347116	−	0.347116i
$839$	16.0763			0.555015			0.277508	−	0.960723i	$-0.410492\pi$
$839$	16.0763			0.555015			0.277508	+	0.960723i	$0.410492\pi$
$840$	−7.79331	−	16.4600i	−0.268895	−	0.567925i
$841$	−25.8697			−0.892060
$842$	7.41570	−	7.41570i	0.255562	−	0.255562i
$843$	−19.3944	−	30.9644i	−0.667979	−	1.06647i
$844$		−	18.1832i		−	0.625892i
$845$	1.79423	−	15.2170i	0.0617235	−	0.523479i
$846$	33.5721	+	16.2861i	1.15423	+	0.559927i
$847$	0.742162	+	0.742162i	0.0255010	+	0.0255010i
$848$	−4.69421	−	4.69421i	−0.161200	−	0.161200i
$849$	−2.15051	+	9.36022i	−0.0738055	+	0.321242i
$850$	−8.96561	+	37.4903i	−0.307518	+	1.28591i
$851$		−	7.25098i		−	0.248560i
$852$	0.681521	−	0.426868i	0.0233485	−	0.0146243i
$853$	18.2352	−	18.2352i	0.624360	−	0.624360i	−0.322283	−	0.946643i	$-0.604450\pi$
$853$	18.2352	−	18.2352i	0.624360	−	0.624360i	0.946643	+	0.322283i	$0.104450\pi$
$854$	−57.5838			−1.97048
$855$	−3.91170	−	2.50193i	−0.133777	−	0.0855641i
$856$	−11.9071			−0.406975
$857$	−11.8899	+	11.8899i	−0.406150	+	0.406150i	−0.880394	−	0.474243i	$-0.842722\pi$
$857$	−11.8899	+	11.8899i	−0.406150	+	0.406150i	0.474243	+	0.880394i	$0.342722\pi$
$858$	−11.9479	+	7.48351i	−0.407894	+	0.255483i
$859$		−	25.0723i		−	0.855455i	−0.903908	−	0.427728i	$-0.859314\pi$
$859$		−	25.0723i		−	0.855455i	0.903908	−	0.427728i	$-0.140686\pi$
$860$	−16.4621	−	20.8631i	−0.561351	−	0.711424i
$861$	12.4682	−	54.2686i	0.424917	−	1.84947i
$862$	−12.1742	−	12.1742i	−0.414654	−	0.414654i
$863$	4.69846	+	4.69846i	0.159938	+	0.159938i	0.782539	−	0.622601i	$-0.213924\pi$
$863$	4.69846	+	4.69846i	0.159938	+	0.159938i	−0.622601	+	0.782539i	$0.713924\pi$
$864$	−4.04856	−	3.25717i	−0.137735	−	0.110811i
$865$	9.27947	+	11.7603i	0.315511	+	0.399861i
$866$		−	9.39644i		−	0.319304i
$867$	39.0160	+	62.2915i	1.32505	+	2.11553i
$868$	3.32500	−	3.32500i	0.112858	−	0.112858i
$869$	46.2943			1.57043
$870$	−2.30581	+	6.45270i	−0.0781743	+	0.218767i
$871$	26.9808			0.914210
$872$	−9.81628	+	9.81628i	−0.332421	+	0.332421i
$873$	−11.4783	+	3.97957i	−0.388482	+	0.134688i
$874$		−	1.37390i		−	0.0464729i
$875$	−22.0734	−	47.7144i	−0.746216	−	1.61304i
$876$	10.3093	+	2.36857i	0.348319	+	0.0800265i
$877$	2.09533	+	2.09533i	0.0707542	+	0.0707542i	0.741598	−	0.670844i	$-0.234068\pi$
$877$	2.09533	+	2.09533i	0.0707542	+	0.0707542i	−0.670844	+	0.741598i	$0.734068\pi$
$878$	7.21446	+	7.21446i	0.243476	+	0.243476i
$879$	2.31475	+	0.531814i	0.0780744	+	0.0179376i
$880$	0.859572	−	7.29007i	0.0289762	−	0.245748i
$881$		−	44.9655i		−	1.51493i	−0.652877	−	0.757464i	$-0.726438\pi$
$881$		−	44.9655i		−	1.51493i	0.652877	−	0.757464i	$-0.273562\pi$
$882$	42.8323	−	14.8501i	1.44224	−	0.500030i
$883$	−19.1284	+	19.1284i	−0.643721	+	0.643721i	−0.951468	−	0.307747i	$-0.900425\pi$
$883$	−19.1284	+	19.1284i	−0.643721	+	0.643721i	0.307747	+	0.951468i	$0.400425\pi$
$884$	−19.1152			−0.642914
$885$	22.3997	−	10.6056i	0.752957	−	0.356502i
$886$	−25.9396			−0.871459
$887$	27.9615	−	27.9615i	0.938856	−	0.938856i	−0.0593790	−	0.998236i	$-0.518912\pi$
$887$	27.9615	−	27.9615i	0.938856	−	0.938856i	0.998236	+	0.0593790i	$0.0189121\pi$
$888$	3.35874	+	5.36244i	0.112712	+	0.179952i
$889$		−	7.23777i		−	0.242747i
$890$	−10.3581	+	8.17312i	−0.347206	+	0.273964i
$891$	−23.2045	+	18.2885i	−0.777381	+	0.612689i
$892$	−10.8799	−	10.8799i	−0.364288	−	0.364288i
$893$	−6.08782	−	6.08782i	−0.203721	−	0.203721i
$894$	−2.30599	+	10.0369i	−0.0771239	+	0.335686i
$895$	14.3125	+	1.68759i	0.478414	+	0.0564097i
$896$			4.70226i			0.157091i
$897$	−7.22393	+	4.52468i	−0.241200	+	0.151075i
$898$	7.69186	−	7.69186i	0.256681	−	0.256681i
$899$	−1.76926			−0.0590080
$900$	−11.6030	−	9.50634i	−0.386767	−	0.316878i
$901$	−51.1803			−1.70506
$902$	15.8702	−	15.8702i	0.528419	−	0.528419i
$903$	82.0348	−	51.3822i	2.72995	−	1.70989i
$904$			3.33011i			0.110758i
$905$	17.7247	+	2.08991i	0.589188	+	0.0694711i
$906$	2.48331	−	10.8087i	0.0825024	−	0.359096i
$907$	32.7703	+	32.7703i	1.08812	+	1.08812i	0.995722	+	0.0923980i	$0.0294532\pi$
$907$	32.7703	+	32.7703i	1.08812	+	1.08812i	0.0923980	+	0.995722i	$0.470547\pi$
$908$	13.1663	+	13.1663i	0.436939	+	0.436939i
$909$	−18.2461	−	8.85131i	−0.605184	−	0.293579i
$910$	20.4663	−	16.1490i	0.678450	−	0.535333i
$911$			29.9209i			0.991322i	0.868516	+	0.495661i	$0.165074\pi$
$911$			29.9209i			0.991322i	−0.868516	+	0.495661i	$0.834926\pi$
$912$	0.636408	+	1.01606i	0.0210736	+	0.0336452i
$913$	0.439091	−	0.439091i	0.0145318	−	0.0145318i
$914$	39.2573			1.29851
$915$	−42.8665	+	20.2960i	−1.41712	+	0.670964i
$916$	−13.0668			−0.431740
$917$	−31.2719	+	31.2719i	−1.03269	+	1.03269i
$918$	−39.8267	+	4.31422i	−1.31448	+	0.142390i
$919$		−	33.2795i		−	1.09779i	−0.835892	−	0.548894i	$-0.815049\pi$
$919$		−	33.2795i		−	1.09779i	0.835892	−	0.548894i	$-0.184951\pi$
$920$	0.519714	−	4.40772i	0.0171345	−	0.145318i
$921$	49.7474	+	11.4295i	1.63923	+	0.376614i
$922$	11.6415	+	11.6415i	0.383393	+	0.383393i
$923$	0.814002	+	0.814002i	0.0267932	+	0.0267932i
$924$	26.0580	+	5.98685i	0.857246	+	0.196953i
$925$	9.55763	+	15.5658i	0.314253	+	0.511799i
$926$			0.623160i			0.0204783i
$927$	−4.82396	−	13.9138i	−0.158440	−	0.456988i
$928$	1.25105	−	1.25105i	0.0410678	−	0.0410678i
$929$	38.4284			1.26079			0.630397	−	0.776273i	$-0.282892\pi$
$929$	38.4284			1.26079			0.630397	+	0.776273i	$0.282892\pi$
$930$	1.30327	−	3.64712i	0.0427358	−	0.119594i
$931$	−10.4599			−0.342809
$932$	18.9563	−	18.9563i	0.620935	−	0.620935i
$933$	−4.55580	−	7.27361i	−0.149150	−	0.238127i
$934$			11.4009i			0.373049i
$935$	−35.0554	−	44.4272i	−1.14643	−	1.45292i
$936$	3.24655	−	6.69243i	0.106117	−	0.218749i
$937$	−0.944433	−	0.944433i	−0.0308533	−	0.0308533i	0.691512	−	0.722365i	$-0.256945\pi$
$937$	−0.944433	−	0.944433i	−0.0308533	−	0.0308533i	−0.722365	+	0.691512i	$0.756945\pi$
$938$	−36.1820	−	36.1820i	−1.18138	−	1.18138i
$939$	−8.88955	+	38.6922i	−0.290099	+	1.26267i
$940$	−17.2279	−	21.8337i	−0.561914	−	0.712137i
$941$			22.4152i			0.730715i	0.930867	+	0.365358i	$0.119053\pi$
$941$			22.4152i			0.730715i	−0.930867	+	0.365358i	$0.880947\pi$
$942$	−30.3314	+	18.9979i	−0.988249	+	0.618986i
$943$	9.59542	−	9.59542i	0.312470	−	0.312470i
$944$	−6.39908			−0.208272
$945$	38.9969	−	38.2656i	1.26857	−	1.24478i
$946$	39.0161			1.26852
$947$	9.85080	−	9.85080i	0.320108	−	0.320108i	−0.528701	−	0.848808i	$-0.677321\pi$
$947$	9.85080	−	9.85080i	0.320108	−	0.320108i	0.848808	+	0.528701i	$0.177321\pi$
$948$	−20.7002	+	12.9655i	−0.672313	+	0.421101i
$949$			15.1423i			0.491541i
$950$	1.81096	+	2.94937i	0.0587553	+	0.0956901i
$951$	11.9924	−	52.1975i	0.388880	−	1.69262i
$952$	25.6340	+	25.6340i	0.830803	+	0.830803i
$953$	2.28960	+	2.28960i	0.0741675	+	0.0741675i	0.743217	−	0.669050i	$-0.233299\pi$
$953$	2.28960	+	2.28960i	0.0741675	+	0.0741675i	−0.669050	+	0.743217i	$0.733299\pi$
$954$	8.69252	−	17.9187i	0.281431	−	0.580141i
$955$	3.10002	−	26.2914i	0.100314	−	0.850770i
$956$			9.47761i			0.306528i
$957$	−5.34002	−	8.52567i	−0.172618	−	0.275596i
$958$	−12.6346	+	12.6346i	−0.408204	+	0.408204i
$959$	66.5411			2.14873
$960$	1.65736	+	3.50045i	0.0534910	+	0.112977i
$961$	1.00000			0.0322581
$962$	−6.40484	+	6.40484i	−0.206500	+	0.206500i
$963$	−11.7014	−	33.7503i	−0.377071	−	1.08759i
$964$		−	3.05724i		−	0.0984669i
$965$	5.29450	−	4.17764i	0.170436	−	0.134483i
$966$	15.7552	+	3.61976i	0.506915	+	0.116464i
$967$	−23.1963	−	23.1963i	−0.745942	−	0.745942i	0.227773	−	0.973714i	$-0.426856\pi$
$967$	−23.1963	−	23.1963i	−0.745942	−	0.745942i	−0.973714	+	0.227773i	$0.926856\pi$
$968$	−0.157831	−	0.157831i	−0.00507288	−	0.00507288i
$969$	9.00833	+	2.06967i	0.289389	+	0.0664873i
$970$	8.99273	+	1.06033i	0.288739	+	0.0340452i
$971$			48.7177i			1.56342i	0.623640	+	0.781712i	$0.285653\pi$
$971$			48.7177i			1.56342i	−0.623640	+	0.781712i	$0.714347\pi$
$972$	5.25375	−	14.6764i	0.168514	−	0.470747i
$973$	50.0889	−	50.0889i	1.60578	−	1.60578i
$974$	0.119534			0.00383011
$975$	9.54363	−	19.2351i	0.305641	−	0.616018i
$976$	12.2460			0.391985
$977$	26.3158	−	26.3158i	0.841916	−	0.841916i	−0.147192	−	0.989108i	$-0.547024\pi$
$977$	26.3158	−	26.3158i	0.841916	−	0.841916i	0.989108	+	0.147192i	$0.0470236\pi$
$978$	7.02402	+	11.2143i	0.224603	+	0.358593i
$979$		−	19.3708i		−	0.619094i
$980$	−33.5572	−	3.95673i	−1.07195	−	0.126393i
$981$	−37.4707	−	18.1773i	−1.19635	−	0.580357i
$982$	−21.8791	−	21.8791i	−0.698190	−	0.698190i
$983$	3.44235	+	3.44235i	0.109794	+	0.109794i	0.759869	−	0.650076i	$-0.225263\pi$
$983$	3.44235	+	3.44235i	0.109794	+	0.109794i	−0.650076	+	0.759869i	$0.725263\pi$
$984$	−2.65155	+	11.5410i	−0.0845282	+	0.367913i
$985$	28.0257	−	22.1138i	0.892973	−	0.704603i
$986$		−	13.6401i		−	0.434388i
$987$	85.8515	−	53.7727i	2.73268	−	1.71161i
$988$	−1.21358	+	1.21358i	−0.0386090	+	0.0386090i
$989$	23.5899			0.750115
$990$	21.5082	−	4.72769i	0.683577	−	0.150256i
$991$	0.949046			0.0301475			0.0150737	−	0.999886i	$-0.495202\pi$
$991$	0.949046			0.0301475			0.0150737	+	0.999886i	$0.495202\pi$
$992$	−0.707107	+	0.707107i	−0.0224507	+	0.0224507i
$993$	35.8895	−	22.4793i	1.13892	−	0.713358i
$994$		−	2.18320i		−	0.0692468i
$995$	2.70908	−	22.9758i	0.0858836	−	0.728383i
$996$	−0.0733620	+	0.319312i	−0.00232457	+	0.0101178i
$997$	32.8743	+	32.8743i	1.04114	+	1.04114i	0.999117	+	0.0420237i	$0.0133805\pi$
$997$	32.8743	+	32.8743i	1.04114	+	1.04114i	0.0420237	+	0.999117i	$0.486619\pi$
$998$	26.7240	+	26.7240i	0.845933	+	0.845933i
$999$	−11.8990	+	14.7901i	−0.376467	+	0.467937i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.g.497.14	yes	40
3.2	odd	2	inner	930.2.j.g.497.3	✓	40
5.3	odd	4	inner	930.2.j.g.683.3	yes	40
15.8	even	4	inner	930.2.j.g.683.14	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.g.497.3	✓	40	3.2	odd	2	inner
930.2.j.g.497.14	yes	40	1.1	even	1	trivial
930.2.j.g.683.3	yes	40	5.3	odd	4	inner
930.2.j.g.683.14	yes	40	15.8	even	4	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-1.46789 + 0.919406i) q^{3} -1.00000i q^{4} +(-2.22068 - 0.261841i) q^{5} +(-0.387835 + 1.68807i) q^{6} +(3.32500 + 3.32500i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.30939 - 2.69917i) q^{9} +(-1.75541 + 1.38511i) q^{10} -3.28280i q^{11} +(0.919406 + 1.46789i) q^{12} +(-1.75323 + 1.75323i) q^{13} +4.70226 q^{14} +(3.50045 - 1.65736i) q^{15} -1.00000 q^{16} +(-5.45143 + 5.45143i) q^{17} +(-0.982724 - 2.83448i) q^{18} +0.692195i q^{19} +(-0.261841 + 2.22068i) q^{20} +(-7.93774 - 1.82370i) q^{21} +(-2.32129 - 2.32129i) q^{22} +(-1.40350 - 1.40350i) q^{23} +(1.68807 + 0.387835i) q^{24} +(4.86288 + 1.16293i) q^{25} +2.47944i q^{26} +(0.559598 + 5.16593i) q^{27} +(3.32500 - 3.32500i) q^{28} -1.76926 q^{29} +(1.30327 - 3.64712i) q^{30} +1.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.01823 + 4.81878i) q^{33} +7.70948i q^{34} +(-6.51315 - 8.25439i) q^{35} +(-2.69917 - 1.30939i) q^{36} +(2.58318 + 2.58318i) q^{37} +(0.489456 + 0.489456i) q^{38} +(0.961614 - 4.18547i) q^{39} +(1.38511 + 1.75541i) q^{40} +6.83679i q^{41} +(-6.90238 + 4.32328i) q^{42} +(-8.40397 + 8.40397i) q^{43} -3.28280 q^{44} +(-3.61449 + 5.65115i) q^{45} -1.98485 q^{46} +(-8.79496 + 8.79496i) q^{47} +(1.46789 - 0.919406i) q^{48} +15.1112i q^{49} +(4.26089 - 2.61626i) q^{50} +(2.99001 - 13.0142i) q^{51} +(1.75323 + 1.75323i) q^{52} +(4.69421 + 4.69421i) q^{53} +(4.04856 + 3.25717i) q^{54} +(-0.859572 + 7.29007i) q^{55} -4.70226i q^{56} +(-0.636408 - 1.01606i) q^{57} +(-1.25105 + 1.25105i) q^{58} +6.39908 q^{59} +(-1.65736 - 3.50045i) q^{60} -12.2460 q^{61} +(0.707107 - 0.707107i) q^{62} +(13.3284 - 4.62102i) q^{63} +1.00000i q^{64} +(4.35244 - 3.43430i) q^{65} +(5.54160 + 1.27319i) q^{66} +(-7.69460 - 7.69460i) q^{67} +(5.45143 + 5.45143i) q^{68} +(3.35056 + 0.769793i) q^{69} +(-10.4422 - 1.23124i) q^{70} -0.464287i q^{71} +(-2.83448 + 0.982724i) q^{72} +(4.31841 - 4.31841i) q^{73} +3.65317 q^{74} +(-8.20736 + 2.76390i) q^{75} +0.692195 q^{76} +(10.9153 - 10.9153i) q^{77} +(-2.27961 - 3.63954i) q^{78} +14.1021i q^{79} +(2.22068 + 0.261841i) q^{80} +(-5.57101 - 7.06851i) q^{81} +(4.83434 + 4.83434i) q^{82} +(0.133755 + 0.133755i) q^{83} +(-1.82370 + 7.93774i) q^{84} +(13.5333 - 10.6785i) q^{85} +11.8850i q^{86} +(2.59707 - 1.62666i) q^{87} +(-2.32129 + 2.32129i) q^{88} +5.90070 q^{89} +(1.44014 + 6.55179i) q^{90} -11.6590 q^{91} +(-1.40350 + 1.40350i) q^{92} +(-1.46789 + 0.919406i) q^{93} +12.4379i q^{94} +(0.181245 - 1.53715i) q^{95} +(0.387835 - 1.68807i) q^{96} +(-2.86345 - 2.86345i) q^{97} +(10.6852 + 10.6852i) q^{98} +(-8.86084 - 4.29846i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} - 8 q^{7} + 8 q^{10} + 4 q^{12} - 20 q^{13} - 44 q^{15} - 40 q^{16} + 16 q^{18} - 32 q^{21} - 4 q^{22} + 8 q^{25} + 8 q^{27} - 8 q^{28} - 4 q^{30} + 40 q^{31} + 48 q^{33} + 64 q^{37} - 4 q^{40}+ \cdots - 52 q^{97}+O(q^{100}) \) 40 * q - 4 * q^3 - 8 * q^7 + 8 * q^10 + 4 * q^12 - 20 * q^13 - 44 * q^15 - 40 * q^16 + 16 * q^18 - 32 * q^21 - 4 * q^22 + 8 * q^25 + 8 * q^27 - 8 * q^28 - 4 * q^30 + 40 * q^31 + 48 * q^33 + 64 * q^37 - 4 * q^40 - 20 * q^42 - 48 * q^43 - 4 * q^45 - 80 * q^46 + 4 * q^48 + 48 * q^51 + 20 * q^52 + 164 * q^55 + 40 * q^57 + 56 * q^58 + 24 * q^60 - 128 * q^61 + 56 * q^63 + 8 * q^66 - 4 * q^67 - 56 * q^70 - 16 * q^72 - 48 * q^73 - 48 * q^75 - 40 * q^76 - 36 * q^78 - 24 * q^81 - 16 * q^82 - 56 * q^85 - 12 * q^87 - 4 * q^88 - 28 * q^90 - 32 * q^91 - 4 * q^93 - 52 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more