LMFDB - Embedded newform 429.2.j.a.122.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(122,429)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("429.122");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			122.15
Character	$\chi$	$=$	429.122
Dual form			429.2.j.a.320.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.943039 - 0.943039i) q^{2} +(-1.40657 - 1.01073i) q^{3} -0.221356i q^{4} +(-0.0801747 - 0.0801747i) q^{5} +(0.373288 + 2.27960i) q^{6} +(-3.37063 - 3.37063i) q^{7} +(-2.09482 + 2.09482i) q^{8} +(0.956852 + 2.84331i) q^{9} +O(q^{10})$	\(q+(-0.943039 - 0.943039i) q^{2} +(-1.40657 - 1.01073i) q^{3} -0.221356i q^{4} +(-0.0801747 - 0.0801747i) q^{5} +(0.373288 + 2.27960i) q^{6} +(-3.37063 - 3.37063i) q^{7} +(-2.09482 + 2.09482i) q^{8} +(0.956852 + 2.84331i) q^{9} +0.151216i q^{10} +(-0.707107 + 0.707107i) q^{11} +(-0.223731 + 0.311351i) q^{12} +(2.49995 - 2.59812i) q^{13} +6.35727i q^{14} +(0.0317360 + 0.193806i) q^{15} +3.50829 q^{16} -2.91900 q^{17} +(1.77901 - 3.58370i) q^{18} +(-3.82164 + 3.82164i) q^{19} +(-0.0177471 + 0.0177471i) q^{20} +(1.33422 + 8.14781i) q^{21} +1.33366 q^{22} +4.33611 q^{23} +(5.06381 - 0.829206i) q^{24} -4.98714i q^{25} +(-4.80768 + 0.0925794i) q^{26} +(1.52795 - 4.96643i) q^{27} +(-0.746109 + 0.746109i) q^{28} +4.56539i q^{29} +(0.152838 - 0.212695i) q^{30} +(-1.09767 + 1.09767i) q^{31} +(0.881195 + 0.881195i) q^{32} +(1.70929 - 0.279898i) q^{33} +(2.75273 + 2.75273i) q^{34} +0.540479i q^{35} +(0.629384 - 0.211805i) q^{36} +(4.52465 + 4.52465i) q^{37} +7.20791 q^{38} +(-6.14234 + 1.12765i) q^{39} +0.335904 q^{40} +(2.23148 + 2.23148i) q^{41} +(6.42548 - 8.94192i) q^{42} -5.27579i q^{43} +(0.156522 + 0.156522i) q^{44} +(0.151247 - 0.304677i) q^{45} +(-4.08912 - 4.08912i) q^{46} +(-5.87235 + 5.87235i) q^{47} +(-4.93464 - 3.54593i) q^{48} +15.7223i q^{49} +(-4.70307 + 4.70307i) q^{50} +(4.10576 + 2.95032i) q^{51} +(-0.575109 - 0.553379i) q^{52} +3.15558i q^{53} +(-6.12444 + 3.24262i) q^{54} +0.113384 q^{55} +14.1218 q^{56} +(9.23803 - 1.51274i) q^{57} +(4.30534 - 4.30534i) q^{58} +(-4.51242 + 4.51242i) q^{59} +(0.0429000 - 0.00702495i) q^{60} -2.90645 q^{61} +2.07028 q^{62} +(6.35857 - 12.8090i) q^{63} -8.67858i q^{64} +(-0.408737 + 0.00787086i) q^{65} +(-1.87588 - 1.34797i) q^{66} +(-0.192651 + 0.192651i) q^{67} +0.646137i q^{68} +(-6.09902 - 4.38264i) q^{69} +(0.509693 - 0.509693i) q^{70} +(-11.1160 - 11.1160i) q^{71} +(-7.96068 - 3.95181i) q^{72} +(-2.10299 - 2.10299i) q^{73} -8.53385i q^{74} +(-5.04065 + 7.01474i) q^{75} +(0.845942 + 0.845942i) q^{76} +4.76679 q^{77} +(6.85589 + 4.72905i) q^{78} -9.65956 q^{79} +(-0.281276 - 0.281276i) q^{80} +(-7.16887 + 5.44126i) q^{81} -4.20875i q^{82} +(-11.0419 - 11.0419i) q^{83} +(1.80356 - 0.295336i) q^{84} +(0.234030 + 0.234030i) q^{85} +(-4.97527 + 4.97527i) q^{86} +(4.61437 - 6.42152i) q^{87} -2.96253i q^{88} +(10.4812 - 10.4812i) q^{89} +(-0.429954 + 0.144691i) q^{90} +(-17.1837 + 0.330900i) q^{91} -0.959823i q^{92} +(2.65338 - 0.434496i) q^{93} +11.0757 q^{94} +0.612798 q^{95} +(-0.348809 - 2.13011i) q^{96} +(-8.53028 + 8.53028i) q^{97} +(14.8268 - 14.8268i) q^{98} +(-2.68712 - 1.33393i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{6} - 16 q^{7}+O(q^{10}) $ 96 * q + 12 * q^6 - 16 * q^7	$ 96 q + 12 q^{6} - 16 q^{7} + 16 q^{13} - 16 q^{15} - 120 q^{16} - 28 q^{18} - 24 q^{19} + 24 q^{24} - 24 q^{27} + 56 q^{28} + 48 q^{31} - 16 q^{34} - 16 q^{37} + 80 q^{40} + 52 q^{42} + 4 q^{45} - 56 q^{46} + 28 q^{48} + 4 q^{54} + 4 q^{57} + 48 q^{58} + 4 q^{60} - 96 q^{61} - 36 q^{63} + 20 q^{66} - 16 q^{67} + 48 q^{70} - 16 q^{72} - 16 q^{73} - 88 q^{76} + 80 q^{78} + 16 q^{79} + 32 q^{81} + 52 q^{84} - 8 q^{85} - 48 q^{87} - 16 q^{91} - 36 q^{93} - 16 q^{94} - 108 q^{96} - 48 q^{97}+O(q^{100}) $ 96 * q + 12 * q^6 - 16 * q^7 + 16 * q^13 - 16 * q^15 - 120 * q^16 - 28 * q^18 - 24 * q^19 + 24 * q^24 - 24 * q^27 + 56 * q^28 + 48 * q^31 - 16 * q^34 - 16 * q^37 + 80 * q^40 + 52 * q^42 + 4 * q^45 - 56 * q^46 + 28 * q^48 + 4 * q^54 + 4 * q^57 + 48 * q^58 + 4 * q^60 - 96 * q^61 - 36 * q^63 + 20 * q^66 - 16 * q^67 + 48 * q^70 - 16 * q^72 - 16 * q^73 - 88 * q^76 + 80 * q^78 + 16 * q^79 + 32 * q^81 + 52 * q^84 - 8 * q^85 - 48 * q^87 - 16 * q^91 - 36 * q^93 - 16 * q^94 - 108 * q^96 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	−0.943039	−	0.943039i	−0.666829	−	0.666829i	0.290152	−	0.956981i	$-0.406294\pi$
$2$	−0.943039	−	0.943039i	−0.666829	−	0.666829i	−0.956981	+	0.290152i	$0.906294\pi$
$3$	−1.40657	−	1.01073i	−0.812081	−	0.583545i
$3$	−1.40657	−	1.01073i	−0.812081	−	0.583545i
$4$		−	0.221356i		−	0.110678i
$5$	−0.0801747	−	0.0801747i	−0.0358552	−	0.0358552i	0.688952	−	0.724807i	$-0.258071\pi$
$5$	−0.0801747	−	0.0801747i	−0.0358552	−	0.0358552i	−0.724807	+	0.688952i	$0.758071\pi$
$6$	0.373288	+	2.27960i	0.152394	+	0.930644i
$7$	−3.37063	−	3.37063i	−1.27398	−	1.27398i	−0.943982	−	0.329997i	$-0.892952\pi$
$7$	−3.37063	−	3.37063i	−1.27398	−	1.27398i	−0.329997	−	0.943982i	$-0.607048\pi$
$8$	−2.09482	+	2.09482i	−0.740632	+	0.740632i
$9$	0.956852	+	2.84331i	0.318951	+	0.947771i
$10$			0.151216i			0.0478186i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$12$	−0.223731	+	0.311351i	−0.0645855	+	0.0898794i
$13$	2.49995	−	2.59812i	0.693362	−	0.720590i
$13$	2.49995	−	2.59812i	0.693362	−	0.720590i
$14$			6.35727i			1.69905i
$15$	0.0317360	+	0.193806i	0.00819421	+	0.0500405i
$16$	3.50829			0.877073
$17$	−2.91900			−0.707961			−0.353981	−	0.935253i	$-0.615172\pi$
$17$	−2.91900			−0.707961			−0.353981	+	0.935253i	$0.615172\pi$
$18$	1.77901	−	3.58370i	0.419316	−	0.844687i
$19$	−3.82164	+	3.82164i	−0.876744	+	0.876744i	−0.993196	−	0.116452i	$-0.962848\pi$
$19$	−3.82164	+	3.82164i	−0.876744	+	0.876744i	0.116452	+	0.993196i	$0.462848\pi$
$20$	−0.0177471	+	0.0177471i	−0.00396838	+	0.00396838i
$21$	1.33422	+	8.14781i	0.291150	+	1.77800i
$22$	1.33366			0.284337
$23$	4.33611			0.904142			0.452071	−	0.891982i	$-0.350685\pi$
$23$	4.33611			0.904142			0.452071	+	0.891982i	$0.350685\pi$
$24$	5.06381	−	0.829206i	1.03365	−	0.169261i
$25$		−	4.98714i		−	0.997429i
$26$	−4.80768	+	0.0925794i	−0.942864	+	0.0181563i
$27$	1.52795	−	4.96643i	0.294054	−	0.955789i
$28$	−0.746109	+	0.746109i	−0.141001	+	0.141001i
$29$			4.56539i			0.847771i	0.905716	+	0.423886i	$0.139334\pi$
$29$			4.56539i			0.847771i	−0.905716	+	0.423886i	$0.860666\pi$
$30$	0.152838	−	0.212695i	0.0279043	−	0.0388326i
$31$	−1.09767	+	1.09767i	−0.197147	+	0.197147i	−0.798776	−	0.601629i	$-0.794519\pi$
$31$	−1.09767	+	1.09767i	−0.197147	+	0.197147i	0.601629	+	0.798776i	$0.294519\pi$
$32$	0.881195	+	0.881195i	0.155775	+	0.155775i
$33$	1.70929	−	0.279898i	0.297548	−	0.0487240i
$34$	2.75273	+	2.75273i	0.472089	+	0.472089i
$35$			0.540479i			0.0913576i
$36$	0.629384	−	0.211805i	0.104897	−	0.0353008i
$37$	4.52465	+	4.52465i	0.743849	+	0.743849i	0.973316	−	0.229468i	$-0.0736985\pi$
$37$	4.52465	+	4.52465i	0.743849	+	0.743849i	−0.229468	+	0.973316i	$0.573699\pi$
$38$	7.20791			1.16928
$39$	−6.14234	+	1.12765i	−0.983562	+	0.180569i
$40$	0.335904			0.0531111
$41$	2.23148	+	2.23148i	0.348499	+	0.348499i	0.859550	−	0.511051i	$-0.170744\pi$
$41$	2.23148	+	2.23148i	0.348499	+	0.348499i	−0.511051	+	0.859550i	$0.670744\pi$
$42$	6.42548	−	8.94192i	0.991474	−	1.37977i
$43$		−	5.27579i		−	0.804550i	−0.915519	−	0.402275i	$-0.868220\pi$
$43$		−	5.27579i		−	0.804550i	0.915519	−	0.402275i	$-0.131780\pi$
$44$	0.156522	+	0.156522i	0.0235966	+	0.0235966i
$45$	0.151247	−	0.304677i	0.0225465	−	0.0454186i
$46$	−4.08912	−	4.08912i	−0.602908	−	0.602908i
$47$	−5.87235	+	5.87235i	−0.856570	+	0.856570i	−0.990932	−	0.134363i	$-0.957101\pi$
$47$	−5.87235	+	5.87235i	−0.856570	+	0.856570i	0.134363	+	0.990932i	$0.457101\pi$
$48$	−4.93464	−	3.54593i	−0.712254	−	0.511811i
$49$			15.7223i			2.24605i
$50$	−4.70307	+	4.70307i	−0.665115	+	0.665115i
$51$	4.10576	+	2.95032i	0.574922	+	0.413127i
$52$	−0.575109	−	0.553379i	−0.0797533	−	0.0767398i
$53$			3.15558i			0.433452i	0.976232	+	0.216726i	$0.0695378\pi$
$53$			3.15558i			0.433452i	−0.976232	+	0.216726i	$0.930462\pi$
$54$	−6.12444	+	3.24262i	−0.833431	+	0.441264i
$55$	0.113384			0.0152887
$56$	14.1218			1.88710
$57$	9.23803	−	1.51274i	1.22361	−	0.200367i
$58$	4.30534	−	4.30534i	0.565319	−	0.565319i
$59$	−4.51242	+	4.51242i	−0.587467	+	0.587467i	−0.936945	−	0.349478i	$-0.886359\pi$
$59$	−4.51242	+	4.51242i	−0.587467	+	0.587467i	0.349478	+	0.936945i	$0.386359\pi$
$60$	0.0429000	−	0.00702495i	0.00553837	−	0.000906917i
$61$	−2.90645			−0.372133			−0.186067	−	0.982537i	$-0.559574\pi$
$61$	−2.90645			−0.372133			−0.186067	+	0.982537i	$0.559574\pi$
$62$	2.07028			0.262926
$63$	6.35857	−	12.8090i	0.801105	−	1.61378i
$64$		−	8.67858i		−	1.08482i
$65$	−0.408737	+	0.00787086i	−0.0506975	+	0.000976260i
$66$	−1.87588	−	1.34797i	−0.230905	−	0.165923i
$67$	−0.192651	+	0.192651i	−0.0235360	+	0.0235360i	−0.718777	−	0.695241i	$-0.755298\pi$
$67$	−0.192651	+	0.192651i	−0.0235360	+	0.0235360i	0.695241	+	0.718777i	$0.255298\pi$
$68$			0.646137i			0.0783556i
$69$	−6.09902	−	4.38264i	−0.734236	−	0.527607i
$70$	0.509693	−	0.509693i	0.0609199	−	0.0609199i
$71$	−11.1160	−	11.1160i	−1.31922	−	1.31922i	−0.914391	−	0.404833i	$-0.867330\pi$
$71$	−11.1160	−	11.1160i	−1.31922	−	1.31922i	−0.404833	−	0.914391i	$-0.632670\pi$
$72$	−7.96068	−	3.95181i	−0.938175	−	0.465725i
$73$	−2.10299	−	2.10299i	−0.246137	−	0.246137i	0.573246	−	0.819383i	$-0.305684\pi$
$73$	−2.10299	−	2.10299i	−0.246137	−	0.246137i	−0.819383	+	0.573246i	$0.805684\pi$
$74$		−	8.53385i		−	0.992040i
$75$	−5.04065	+	7.01474i	−0.582045	+	0.809993i
$76$	0.845942	+	0.845942i	0.0970362	+	0.0970362i
$77$	4.76679			0.543227
$78$	6.85589	+	4.72905i	0.776277	+	0.535459i
$79$	−9.65956			−1.08679			−0.543393	−	0.839478i	$-0.682861\pi$
$79$	−9.65956			−1.08679			−0.543393	+	0.839478i	$0.682861\pi$
$80$	−0.281276	−	0.281276i	−0.0314476	−	0.0314476i
$81$	−7.16887	+	5.44126i	−0.796541	+	0.604584i
$82$		−	4.20875i		−	0.464779i
$83$	−11.0419	−	11.0419i	−1.21200	−	1.21200i	−0.970367	−	0.241637i	$-0.922316\pi$
$83$	−11.0419	−	11.0419i	−1.21200	−	1.21200i	−0.241637	−	0.970367i	$-0.577684\pi$
$84$	1.80356	−	0.295336i	0.196785	−	0.0322239i
$85$	0.234030	+	0.234030i	0.0253841	+	0.0253841i
$86$	−4.97527	+	4.97527i	−0.536498	+	0.536498i
$87$	4.61437	−	6.42152i	0.494713	−	0.688459i
$88$		−	2.96253i		−	0.315807i
$89$	10.4812	−	10.4812i	1.11101	−	1.11101i	0.117992	−	0.993014i	$-0.462354\pi$
$89$	10.4812	−	10.4812i	1.11101	−	1.11101i	0.993014	−	0.117992i	$-0.0376459\pi$
$90$	−0.429954	+	0.144691i	−0.0453211	+	0.0152518i
$91$	−17.1837	+	0.330900i	−1.80134	+	0.0346877i
$92$		−	0.959823i		−	0.100068i
$93$	2.65338	−	0.434496i	0.275143	−	0.0450551i
$94$	11.0757			1.14237
$95$	0.612798			0.0628717
$96$	−0.348809	−	2.13011i	−0.0356001	−	0.217403i
$97$	−8.53028	+	8.53028i	−0.866119	+	0.866119i	−0.992040	−	0.125922i	$-0.959811\pi$
$97$	−8.53028	+	8.53028i	−0.866119	+	0.866119i	0.125922	+	0.992040i	$0.459811\pi$
$98$	14.8268	−	14.8268i	1.49773	−	1.49773i
$99$	−2.68712	−	1.33393i	−0.270066	−	0.134065i
$100$	−1.10393			−0.110393
$101$	−14.4845			−1.44126			−0.720629	−	0.693321i	$-0.756147\pi$
$101$	−14.4845			−1.44126			−0.720629	+	0.693321i	$0.756147\pi$
$102$	−1.08963	−	6.65416i	−0.107889	−	0.658860i
$103$			5.51938i			0.543841i	0.962320	+	0.271920i	$0.0876587\pi$
$103$			5.51938i			0.543841i	−0.962320	+	0.271920i	$0.912341\pi$
$104$	0.205652	+	10.6796i	0.0201658	+	1.04722i
$105$	0.546278	−	0.760219i	0.0533113	−	0.0741898i
$106$	2.97583	−	2.97583i	0.289038	−	0.289038i
$107$			3.14527i			0.304064i	0.988376	+	0.152032i	$0.0485817\pi$
$107$			3.14527i			0.304064i	−0.988376	+	0.152032i	$0.951418\pi$
$108$	−1.09935	−	0.338220i	−0.105785	−	0.0325452i
$109$	−3.52544	+	3.52544i	−0.337676	+	0.337676i	−0.855492	−	0.517816i	$-0.826745\pi$
$109$	−3.52544	+	3.52544i	−0.337676	+	0.337676i	0.517816	+	0.855492i	$0.326745\pi$
$110$	−0.106926	−	0.106926i	−0.0101950	−	0.0101950i
$111$	−1.79102	−	10.9374i	−0.169996	−	1.03813i
$112$	−11.8252	−	11.8252i	−1.11737	−	1.11737i
$113$		−	6.79886i		−	0.639583i	−0.947488	−	0.319791i	$-0.896387\pi$
$113$		−	6.79886i		−	0.639583i	0.947488	−	0.319791i	$-0.103613\pi$
$114$	−10.1384	−	7.28524i	−0.949547	−	0.682326i
$115$	−0.347647	−	0.347647i	−0.0324182	−	0.0324182i
$116$	1.01057			0.0938295
$117$	9.77936	+	4.62213i	0.904102	+	0.427316i
$118$	8.51077			0.783480
$119$	9.83887	+	9.83887i	0.901928	+	0.901928i
$120$	−0.472471	−	0.339508i	−0.0431305	−	0.0309927i
$121$		−	1.00000i		−	0.0909091i
$122$	2.74090	+	2.74090i	0.248149	+	0.248149i
$123$	−0.883301	−	5.39415i	−0.0796446	−	0.486374i
$124$	0.242975	+	0.242975i	0.0218198	+	0.0218198i
$125$	−0.800716	+	0.800716i	−0.0716183	+	0.0716183i
$126$	−18.0757	+	6.08297i	−1.61031	+	0.541914i
$127$		−	2.08099i		−	0.184658i	−0.995729	−	0.0923288i	$-0.970569\pi$
$127$		−	2.08099i		−	0.184658i	0.995729	−	0.0923288i	$-0.0294311\pi$
$128$	−6.42185	+	6.42185i	−0.567617	+	0.567617i
$129$	−5.33240	+	7.42074i	−0.469491	+	0.653360i
$130$	0.392877	+	0.378032i	0.0344576	+	0.0331556i
$131$		−	0.0507579i		−	0.00443474i	−0.999998	−	0.00221737i	$-0.999294\pi$
$131$		−	0.0507579i		−	0.00443474i	0.999998	−	0.00221737i	$-0.000705811\pi$
$132$	−0.0619570	−	0.378360i	−0.00539267	−	0.0329320i
$133$	25.7627			2.23391
$134$	0.363354			0.0313890
$135$	−0.520684	+	0.275679i	−0.0448134	+	0.0237267i
$136$	6.11479	−	6.11479i	0.524339	−	0.524339i
$137$	−11.3919	+	11.3919i	−0.973277	+	0.973277i	−0.999652	−	0.0263756i	$-0.991603\pi$
$137$	−11.3919	+	11.3919i	−0.973277	+	0.973277i	0.0263756	+	0.999652i	$0.491603\pi$
$138$	1.61862	+	9.88461i	0.137786	+	0.841434i
$139$	2.20453			0.186986			0.0934928	−	0.995620i	$-0.470197\pi$
$139$	2.20453			0.186986			0.0934928	+	0.995620i	$0.470197\pi$
$140$	0.119638			0.0101113
$141$	14.1952	−	2.32448i	1.19545	−	0.195757i
$142$			20.9656i			1.75939i
$143$	0.0694177	+	3.60488i	0.00580500	+	0.301455i
$144$	3.35691	+	9.97517i	0.279743	+	0.831264i
$145$	0.366029	−	0.366029i	0.0303970	−	0.0303970i
$146$			3.96641i			0.328263i
$147$	15.8910	−	22.1145i	1.31067	−	1.82397i
$148$	1.00156	−	1.00156i	0.0823276	−	0.0823276i
$149$	−2.87212	−	2.87212i	−0.235293	−	0.235293i	0.579605	−	0.814898i	$-0.303207\pi$
$149$	−2.87212	−	2.87212i	−0.235293	−	0.235293i	−0.814898	+	0.579605i	$0.803207\pi$
$150$	11.3687	−	1.86164i	0.928251	−	0.152003i
$151$	11.3439	+	11.3439i	0.923150	+	0.923150i	0.997251	−	0.0741004i	$-0.0236085\pi$
$151$	11.3439	+	11.3439i	0.923150	+	0.923150i	−0.0741004	+	0.997251i	$0.523609\pi$
$152$		−	16.0113i		−	1.29869i
$153$	−2.79305	−	8.29963i	−0.225805	−	0.670985i
$154$	−4.49527	−	4.49527i	−0.362239	−	0.362239i
$155$	0.176010			0.0141375
$156$	0.249613	+	1.35964i	0.0199850	+	0.108859i
$157$	14.0178			1.11874			0.559371	−	0.828917i	$-0.311043\pi$
$157$	14.0178			1.11874			0.559371	+	0.828917i	$0.311043\pi$
$158$	9.10934	+	9.10934i	0.724700	+	0.724700i
$159$	3.18944	−	4.43853i	0.252939	−	0.351998i
$160$		−	0.141299i		−	0.0111707i
$161$	−14.6154	−	14.6154i	−1.15186	−	1.15186i
$162$	11.8918	+	1.62920i	0.934311	+	0.128002i
$163$	−2.03406	−	2.03406i	−0.159320	−	0.159320i	0.622946	−	0.782265i	$-0.285936\pi$
$163$	−2.03406	−	2.03406i	−0.159320	−	0.159320i	−0.782265	+	0.622946i	$0.785936\pi$
$164$	0.493952	−	0.493952i	0.0385711	−	0.0385711i
$165$	−0.159482	−	0.114601i	−0.0124157	−	0.00892166i
$166$			20.8258i			1.61640i
$167$	−10.7126	+	10.7126i	−0.828966	+	0.828966i	−0.987374	−	0.158407i	$-0.949364\pi$
$167$	−10.7126	+	10.7126i	−0.828966	+	0.828966i	0.158407	+	0.987374i	$0.449364\pi$
$168$	−19.8632	−	14.2733i	−1.53248	−	1.10121i
$169$	−0.500485	−	12.9904i	−0.0384988	−	0.999259i
$170$		−	0.441399i		−	0.0338537i
$171$	−14.5229	−	7.20938i	−1.11059	−	0.551315i
$172$	−1.16783			−0.0890459
$173$	−19.2078			−1.46034			−0.730171	−	0.683264i	$-0.760560\pi$
$173$	−19.2078			−1.46034			−0.730171	+	0.683264i	$0.760560\pi$
$174$	−10.4073	+	1.70421i	−0.788973	+	0.129196i
$175$	−16.8098	+	16.8098i	−1.27070	+	1.27070i
$176$	−2.48074	+	2.48074i	−0.186992	+	0.186992i
$177$	10.9078	−	1.78618i	0.819884	−	0.134257i
$178$	−19.7684			−1.48170
$179$	21.8587			1.63379			0.816897	−	0.576784i	$-0.195692\pi$
$179$	21.8587			1.63379			0.816897	+	0.576784i	$0.195692\pi$
$180$	−0.0674420	−	0.0334793i	−0.00502683	−	0.00249540i
$181$			7.35093i			0.546391i	0.961959	+	0.273195i	$0.0880805\pi$
$181$			7.35093i			0.546391i	−0.961959	+	0.273195i	$0.911919\pi$
$182$	16.5170	+	15.8929i	1.22432	+	1.17806i
$183$	4.08812	+	2.93764i	0.302202	+	0.217157i
$184$	−9.08339	+	9.08339i	−0.669637	+	0.669637i
$185$		−	0.725526i		−	0.0533417i
$186$	−2.91199	−	2.09250i	−0.213518	−	0.153429i
$187$	2.06404	−	2.06404i	0.150938	−	0.150938i
$188$	1.29988	+	1.29988i	0.0948033	+	0.0948033i
$189$	−21.8901	+	11.5898i	−1.59227	+	0.843037i
$190$	−0.577892	−	0.577892i	−0.0419247	−	0.0419247i
$191$		−	12.4236i		−	0.898942i	−0.893295	−	0.449471i	$-0.851612\pi$
$191$		−	12.4236i		−	0.898942i	0.893295	−	0.449471i	$-0.148388\pi$
$192$	−8.77170	+	12.2070i	−0.633043	+	0.880964i
$193$	−12.0631	−	12.0631i	−0.868323	−	0.868323i	0.123964	−	0.992287i	$-0.460439\pi$
$193$	−12.0631	−	12.0631i	−0.868323	−	0.868323i	−0.992287	+	0.123964i	$0.960439\pi$
$194$	16.0888			1.15511
$195$	0.582870	+	0.402051i	0.0417402	+	0.0287915i
$196$	3.48023			0.248588
$197$	−0.975031	−	0.975031i	−0.0694681	−	0.0694681i	0.671519	−	0.740987i	$-0.265642\pi$
$197$	−0.975031	−	0.975031i	−0.0694681	−	0.0694681i	−0.740987	+	0.671519i	$0.765642\pi$
$198$	1.27611	+	3.79201i	0.0906894	+	0.269486i
$199$		−	6.05654i		−	0.429337i	−0.976687	−	0.214668i	$-0.931133\pi$
$199$		−	6.05654i		−	0.429337i	0.976687	−	0.214668i	$-0.0688671\pi$
$200$	10.4472	+	10.4472i	0.738728	+	0.738728i
$201$	0.465693	−	0.0762580i	0.0328475	−	0.00537883i
$202$	13.6594	+	13.6594i	0.961072	+	0.961072i
$203$	15.3882	−	15.3882i	1.08004	−	1.08004i
$204$	0.653070	−	0.908834i	0.0457240	−	0.0636311i
$205$		−	0.357817i		−	0.0249910i
$206$	5.20499	−	5.20499i	0.362649	−	0.362649i
$207$	4.14902	+	12.3289i	0.288377	+	0.856920i
$208$	8.77056	−	9.11497i	0.608129	−	0.632009i
$209$		−	5.40461i		−	0.373845i
$210$	−1.23208	+	0.201755i	−0.0850214	+	0.0139224i
$211$	13.4088			0.923100			0.461550	−	0.887114i	$-0.347294\pi$
$211$	13.4088			0.923100			0.461550	+	0.887114i	$0.347294\pi$
$212$	0.698505			0.0479735
$213$	4.40010	+	26.8706i	0.301490	+	1.84114i
$214$	2.96611	−	2.96611i	0.202759	−	0.202759i
$215$	−0.422985	+	0.422985i	−0.0288473	+	0.0288473i
$216$	7.20301	+	13.6046i	0.490103	+	0.925674i
$217$	7.39966			0.502322
$218$	6.64926			0.450345
$219$	0.832441	+	5.08356i	0.0562511	+	0.343515i
$220$		−	0.0250982i		−	0.00169212i
$221$	−7.29736	+	7.58392i	−0.490873	+	0.510149i
$222$	−8.62541	+	12.0034i	−0.578900	+	0.805617i
$223$	6.58341	−	6.58341i	0.440858	−	0.440858i	−0.451442	−	0.892300i	$-0.649090\pi$
$223$	6.58341	−	6.58341i	0.440858	−	0.440858i	0.892300	+	0.451442i	$0.149090\pi$
$224$		−	5.94037i		−	0.396908i
$225$	14.1800	−	4.77196i	0.945334	−	0.318130i
$226$	−6.41159	+	6.41159i	−0.426493	+	0.426493i
$227$	−3.55224	−	3.55224i	−0.235770	−	0.235770i	0.579326	−	0.815096i	$-0.303316\pi$
$227$	−3.55224	−	3.55224i	−0.235770	−	0.235770i	−0.815096	+	0.579326i	$0.803316\pi$
$228$	−0.334854	−	2.04489i	−0.0221762	−	0.135426i
$229$	6.35787	+	6.35787i	0.420140	+	0.420140i	0.885252	−	0.465112i	$-0.153986\pi$
$229$	6.35787	+	6.35787i	0.420140	+	0.420140i	−0.465112	+	0.885252i	$0.653986\pi$
$230$			0.655688i			0.0432348i
$231$	−6.70481	−	4.81794i	−0.441144	−	0.316997i
$232$	−9.56369	−	9.56369i	−0.627887	−	0.627887i
$233$	−0.291016			−0.0190651			−0.00953254	−	0.999955i	$-0.503034\pi$
$233$	−0.291016			−0.0190651			−0.00953254	+	0.999955i	$0.503034\pi$
$234$	−4.86347	−	13.5812i	−0.317935	−	0.887829i
$235$	0.941627			0.0614250
$236$	0.998850	+	0.998850i	0.0650196	+	0.0650196i
$237$	13.5868	+	9.76321i	0.882558	+	0.634188i
$238$		−	18.5569i		−	1.20286i
$239$	−3.13568	−	3.13568i	−0.202831	−	0.202831i	0.598381	−	0.801212i	$-0.295811\pi$
$239$	−3.13568	−	3.13568i	−0.202831	−	0.202831i	−0.801212	+	0.598381i	$0.795811\pi$
$240$	0.111339	+	0.679927i	0.00718691	+	0.0438891i
$241$	20.5774	+	20.5774i	1.32550	+	1.32550i	0.909247	+	0.416257i	$0.136658\pi$
$241$	20.5774	+	20.5774i	1.32550	+	1.32550i	0.416257	+	0.909247i	$0.363342\pi$
$242$	−0.943039	+	0.943039i	−0.0606208	+	0.0606208i
$243$	15.5831	−	0.407699i	0.999658	−	0.0261539i
$244$			0.643360i			0.0411869i
$245$	1.26053	−	1.26053i	0.0805325	−	0.0805325i
$246$	−4.25391	+	5.91988i	−0.271219	+	0.377438i
$247$	0.375176	+	19.4830i	0.0238719	+	1.23967i
$248$		−	4.59884i		−	0.292027i
$249$	4.37077	+	26.6915i	0.276986	+	1.69150i
$250$	1.51021			0.0955143
$251$	12.3335			0.778482			0.389241	−	0.921136i	$-0.372737\pi$
$251$	12.3335			0.778482			0.389241	+	0.921136i	$0.372737\pi$
$252$	−2.83534	−	1.40751i	−0.178609	−	0.0886645i
$253$	−3.06609	+	3.06609i	−0.192764	+	0.192764i
$254$	−1.96245	+	1.96245i	−0.123135	+	0.123135i
$255$	−0.0926374	−	0.565719i	−0.00580118	−	0.0354267i
$256$	−5.24506			−0.327816
$257$	−24.3094			−1.51638			−0.758189	−	0.652035i	$-0.773916\pi$
$257$	−24.3094			−1.51638			−0.758189	+	0.652035i	$0.773916\pi$
$258$	12.0267	−	1.96939i	0.748750	−	0.122609i
$259$		−	30.5019i		−	1.89530i
$260$	0.00174226	+	0.0904762i	0.000108050	+	0.00561110i
$261$	−12.9808	+	4.36840i	−0.803493	+	0.270397i
$262$	−0.0478667	+	0.0478667i	−0.00295721	+	0.00295721i
$263$			31.7363i			1.95695i	0.206376	+	0.978473i	$0.433833\pi$
$263$			31.7363i			1.95695i	−0.206376	+	0.978473i	$0.566167\pi$
$264$	−2.99432	+	4.16699i	−0.184287	+	0.256461i
$265$	0.252998	−	0.252998i	0.0155415	−	0.0155415i
$266$	−24.2952	−	24.2952i	−1.48963	−	1.48963i
$267$	−25.3362	+	4.14884i	−1.55055	+	0.253905i
$268$	0.0426443	+	0.0426443i	0.00260492	+	0.00260492i
$269$			8.53059i			0.520119i	0.965593	+	0.260060i	$0.0837422\pi$
$269$			8.53059i			0.520119i	−0.965593	+	0.260060i	$0.916258\pi$
$270$	0.751002	+	0.231050i	0.0457045	+	0.0140612i
$271$	9.33317	+	9.33317i	0.566950	+	0.566950i	0.931273	−	0.364323i	$-0.118700\pi$
$271$	9.33317	+	9.33317i	0.566950	+	0.566950i	−0.364323	+	0.931273i	$0.618700\pi$
$272$	−10.2407			−0.620933
$273$	24.5045	+	16.9027i	1.48308	+	1.02300i
$274$	21.4860			1.29802
$275$	3.52644	+	3.52644i	0.212653	+	0.212653i
$276$	−0.970122	+	1.35005i	−0.0583945	+	0.0812637i
$277$		−	18.7505i		−	1.12661i	−0.826250	−	0.563304i	$-0.809530\pi$
$277$		−	18.7505i		−	1.12661i	0.826250	−	0.563304i	$-0.190470\pi$
$278$	−2.07895	−	2.07895i	−0.124687	−	0.124687i
$279$	−4.17132	−	2.07071i	−0.249730	−	0.123970i
$280$	−1.13221	−	1.13221i	−0.0676624	−	0.0676624i
$281$	−5.46090	+	5.46090i	−0.325770	+	0.325770i	−0.850975	−	0.525206i	$-0.823988\pi$
$281$	−5.46090	+	5.46090i	−0.325770	+	0.325770i	0.525206	+	0.850975i	$0.323988\pi$
$282$	−15.5787	−	11.1945i	−0.927698	−	0.666625i
$283$		−	26.5958i		−	1.58095i	−0.612492	−	0.790477i	$-0.709833\pi$
$283$		−	26.5958i		−	1.58095i	0.612492	−	0.790477i	$-0.290167\pi$
$284$	−2.46058	+	2.46058i	−0.146009	+	0.146009i
$285$	−0.861940	−	0.619373i	−0.0510569	−	0.0366885i
$286$	3.33408	−	3.46501i	0.197148	−	0.204890i
$287$		−	15.0430i		−	0.887961i
$288$	−1.66234	+	3.34869i	−0.0979544	+	0.197323i
$289$	−8.47945			−0.498791
$290$	−0.690359			−0.0405393
$291$	20.6202	−	3.37659i	1.20878	−	0.197939i
$292$	−0.465510	+	0.465510i	−0.0272419	+	0.0272419i
$293$	13.0999	−	13.0999i	0.765307	−	0.765307i	−0.211969	−	0.977276i	$-0.567988\pi$
$293$	13.0999	−	13.0999i	0.765307	−	0.765307i	0.977276	+	0.211969i	$0.0679877\pi$
$294$	−35.8407	+	5.86896i	−2.09027	+	0.342285i
$295$	0.723564			0.0421275
$296$	−18.9567			−1.10184
$297$	2.43137	+	4.59221i	0.141082	+	0.266467i
$298$			5.41704i			0.313800i
$299$	10.8401	−	11.2658i	0.626897	−	0.651515i
$300$	1.55275	+	1.11578i	0.0896483	+	0.0644194i
$301$	−17.7827	+	17.7827i	−1.02498	+	1.02498i
$302$		−	21.3954i		−	1.23117i
$303$	20.3733	+	14.6399i	1.17042	+	0.841039i
$304$	−13.4074	+	13.4074i	−0.768968	+	0.768968i
$305$	0.233024	+	0.233024i	0.0133429	+	0.0133429i
$306$	−5.19292	+	10.4608i	−0.296859	+	0.598006i
$307$	−20.1180	−	20.1180i	−1.14820	−	1.14820i	−0.986907	−	0.161290i	$-0.948435\pi$
$307$	−20.1180	−	20.1180i	−1.14820	−	1.14820i	−0.161290	−	0.986907i	$-0.551565\pi$
$308$		−	1.05516i		−	0.0601231i
$309$	5.57860	−	7.76337i	0.317356	−	0.441643i
$310$	−0.165985	−	0.165985i	−0.00942729	−	0.00942729i
$311$	−1.78359			−0.101138			−0.0505690	−	0.998721i	$-0.516103\pi$
$311$	−1.78359			−0.101138			−0.0505690	+	0.998721i	$0.516103\pi$
$312$	10.5049	−	15.2294i	0.594723	−	0.862193i
$313$	3.53269			0.199680			0.0998398	−	0.995004i	$-0.468167\pi$
$313$	3.53269			0.199680			0.0998398	+	0.995004i	$0.468167\pi$
$314$	−13.2193	−	13.2193i	−0.746010	−	0.746010i
$315$	−1.53675	+	0.517158i	−0.0865861	+	0.0291386i
$316$			2.13820i			0.120283i
$317$	−16.5529	−	16.5529i	−0.929703	−	0.929703i	0.0679835	−	0.997686i	$-0.478343\pi$
$317$	−16.5529	−	16.5529i	−0.929703	−	0.929703i	−0.997686	+	0.0679835i	$0.978343\pi$
$318$	−7.19347	+	1.17794i	−0.403390	+	0.0660557i
$319$	−3.22822	−	3.22822i	−0.180745	−	0.180745i
$320$	−0.695803	+	0.695803i	−0.0388966	+	0.0388966i
$321$	3.17901	−	4.42402i	0.177435	−	0.246925i
$322$			27.5659i			1.53618i
$323$	11.1554	−	11.1554i	0.620701	−	0.620701i
$324$	1.20445	+	1.58687i	0.0669141	+	0.0881595i
$325$	−12.9572	−	12.4676i	−0.718737	−	0.691579i
$326$			3.83639i			0.212478i
$327$	8.52203	−	1.39550i	0.471270	−	0.0771711i
$328$	−9.34913			−0.516219
$329$	39.5870			2.18250
$330$	0.0423250	+	0.258471i	0.00232991	+	0.0142284i
$331$	−19.1895	+	19.1895i	−1.05475	+	1.05475i	−0.0563368	+	0.998412i	$0.517942\pi$
$331$	−19.1895	+	19.1895i	−1.05475	+	1.05475i	−0.998412	+	0.0563368i	$0.982058\pi$
$332$	−2.44418	+	2.44418i	−0.134142	+	0.134142i
$333$	−8.53559	+	17.1944i	−0.467748	+	0.942249i
$334$	20.2048			1.10556
$335$	0.0308914			0.00168778
$336$	4.68082	+	28.5849i	0.255360	+	1.55943i
$337$		−	11.1547i		−	0.607633i	−0.952731	−	0.303817i	$-0.901739\pi$
$337$		−	11.1547i		−	0.607633i	0.952731	−	0.303817i	$-0.0982610\pi$
$338$	−11.7784	+	12.7224i	−0.640663	+	0.692007i
$339$	−6.87181	+	9.56304i	−0.373225	+	0.519393i
$340$	0.0518039	−	0.0518039i	0.00280946	−	0.00280946i
$341$		−	1.55234i		−	0.0840637i
$342$	6.89690	+	20.4943i	0.372942	+	1.10821i
$343$	29.3997	−	29.3997i	1.58744	−	1.58744i
$344$	11.0519	+	11.0519i	0.595876	+	0.595876i
$345$	0.137611	+	0.840364i	0.00740872	+	0.0452437i
$346$	18.1137	+	18.1137i	0.973799	+	0.973799i
$347$			0.852060i			0.0457410i	0.999738	+	0.0228705i	$0.00728054\pi$
$347$			0.852060i			0.0457410i	−0.999738	+	0.0228705i	$0.992719\pi$
$348$	−1.42144	−	1.02142i	−0.0761971	−	0.0547537i
$349$	−24.5208	−	24.5208i	−1.31257	−	1.31257i	−0.919518	−	0.393048i	$-0.871420\pi$
$349$	−24.5208	−	24.5208i	−1.31257	−	1.31257i	−0.393048	−	0.919518i	$-0.628580\pi$
$350$	31.7046			1.69468
$351$	−9.08359	−	16.3856i	−0.484846	−	0.874599i
$352$	−1.24620			−0.0664226
$353$	−7.23803	−	7.23803i	−0.385242	−	0.385242i	0.487745	−	0.872986i	$-0.337820\pi$
$353$	−7.23803	−	7.23803i	−0.385242	−	0.385242i	−0.872986	+	0.487745i	$0.837820\pi$
$354$	−11.9710	−	8.60209i	−0.636249	−	0.457196i
$355$			1.78244i			0.0946021i
$356$	−2.32008	−	2.32008i	−0.122964	−	0.122964i
$357$	−3.89458	−	23.7835i	−0.206123	−	1.25875i
$358$	−20.6136	−	20.6136i	−1.08946	−	1.08946i
$359$	−15.7889	+	15.7889i	−0.833307	+	0.833307i	−0.987968	−	0.154660i	$-0.950572\pi$
$359$	−15.7889	+	15.7889i	−0.833307	+	0.833307i	0.154660	+	0.987968i	$0.450572\pi$
$360$	0.321410	+	0.955080i	0.0169398	+	0.0503372i
$361$		−	10.2098i		−	0.537360i
$362$	6.93222	−	6.93222i	0.364349	−	0.364349i
$363$	−1.01073	+	1.40657i	−0.0530495	+	0.0738255i
$364$	0.0732465	+	3.80372i	0.00383916	+	0.199369i
$365$			0.337214i			0.0176506i
$366$	−1.08495	−	6.62556i	−0.0567110	−	0.346324i
$367$	−35.8840			−1.87313			−0.936564	−	0.350497i	$-0.886013\pi$
$367$	−35.8840			−1.87313			−0.936564	+	0.350497i	$0.886013\pi$
$368$	15.2123			0.792998
$369$	−4.20961	+	8.48001i	−0.219143	+	0.441451i
$370$	−0.684199	+	0.684199i	−0.0355698	+	0.0355698i
$371$	10.6363	−	10.6363i	0.552209	−	0.552209i
$372$	−0.0961781	−	0.587342i	−0.00498660	−	0.0304523i
$373$	33.6755			1.74365			0.871825	−	0.489817i	$-0.162936\pi$
$373$	33.6755			1.74365			0.871825	+	0.489817i	$0.162936\pi$
$374$	−3.89295			−0.201299
$375$	1.93557	−	0.316952i	0.0999523	−	0.0163673i
$376$		−	24.6031i		−	1.26881i
$377$	11.8614	+	11.4132i	0.610895	+	0.587812i
$378$	31.5729	+	9.71358i	1.62394	+	0.499613i
$379$	14.2458	−	14.2458i	0.731756	−	0.731756i	−0.239212	−	0.970967i	$-0.576889\pi$
$379$	14.2458	−	14.2458i	0.731756	−	0.731756i	0.970967	+	0.239212i	$0.0768889\pi$
$380$		−	0.135646i		−	0.00695851i
$381$	−2.10331	+	2.92704i	−0.107756	+	0.149957i
$382$	−11.7160	+	11.7160i	−0.599441	+	0.599441i
$383$	1.02513	+	1.02513i	0.0523815	+	0.0523815i	0.732812	−	0.680431i	$-0.238207\pi$
$383$	1.02513	+	1.02513i	0.0523815	+	0.0523815i	−0.680431	+	0.732812i	$0.738207\pi$
$384$	15.5235	−	2.54200i	0.792181	−	0.129721i
$385$	−0.382176	−	0.382176i	−0.0194775	−	0.0194775i
$386$			22.7520i			1.15805i
$387$	15.0007	−	5.04815i	0.762530	−	0.256612i
$388$	1.88823	+	1.88823i	0.0958601	+	0.0958601i
$389$	26.8828			1.36301			0.681506	−	0.731813i	$-0.261325\pi$
$389$	26.8828			1.36301			0.681506	+	0.731813i	$0.261325\pi$
$390$	−0.170519	−	0.928819i	−0.00863457	−	0.0470326i
$391$	−12.6571			−0.640097
$392$	−32.9355	−	32.9355i	−1.66349	−	1.66349i
$393$	−0.0513025	+	0.0713943i	−0.00258787	+	0.00360137i
$394$			1.83898i			0.0926467i
$395$	0.774453	+	0.774453i	0.0389670	+	0.0389670i
$396$	−0.295273	+	0.594810i	−0.0148380	+	0.0298903i
$397$	−11.1710	−	11.1710i	−0.560659	−	0.560659i	0.368836	−	0.929495i	$-0.379756\pi$
$397$	−11.1710	−	11.1710i	−0.560659	−	0.560659i	−0.929495	+	0.368836i	$0.879756\pi$
$398$	−5.71155	+	5.71155i	−0.286294	+	0.286294i
$399$	−36.2369	−	26.0391i	−1.81411	−	1.30359i
$400$		−	17.4963i		−	0.874817i
$401$	18.7546	−	18.7546i	0.936560	−	0.936560i	−0.0615439	−	0.998104i	$-0.519602\pi$
$401$	18.7546	−	18.7546i	0.936560	−	0.936560i	0.998104	+	0.0615439i	$0.0196024\pi$
$402$	−0.511081	−	0.367253i	−0.0254904	−	0.0183169i
$403$	0.107759	+	5.59599i	0.00536788	+	0.278756i
$404$			3.20622i			0.159515i
$405$	1.01101	+	0.138511i	0.0502377	+	0.00688265i
$406$	−29.0234			−1.44041
$407$	−6.39883			−0.317178
$408$	−14.7813	+	2.42045i	−0.731781	+	0.119830i
$409$	−19.4214	+	19.4214i	−0.960326	+	0.960326i	−0.999242	−	0.0389167i	$-0.987609\pi$
$409$	−19.4214	+	19.4214i	−0.960326	+	0.960326i	0.0389167	+	0.999242i	$0.487609\pi$
$410$	−0.337435	+	0.337435i	−0.0166647	+	0.0166647i
$411$	27.5376	−	4.50933i	1.35833	−	0.222429i
$412$	1.22175			0.0601911
$413$	30.4194			1.49684
$414$	7.71397	−	15.5393i	0.379121	−	0.763717i
$415$			1.77056i			0.0869133i
$416$	4.49240	−	0.0865082i	0.220258	−	0.00424141i
$417$	−3.10081	−	2.22818i	−0.151847	−	0.109114i
$418$	−5.09676	+	5.09676i	−0.249291	+	0.249291i
$419$		−	9.65185i		−	0.471524i	−0.971811	−	0.235762i	$-0.924241\pi$
$419$		−	9.65185i		−	0.471524i	0.971811	−	0.235762i	$-0.0757586\pi$
$420$	−0.168279	−	0.120922i	−0.00821116	−	0.00590038i
$421$	8.50694	−	8.50694i	0.414603	−	0.414603i	−0.468736	−	0.883339i	$-0.655290\pi$
$421$	8.50694	−	8.50694i	0.414603	−	0.414603i	0.883339	+	0.468736i	$0.155290\pi$
$422$	−12.6450	−	12.6450i	−0.615550	−	0.615550i
$423$	−22.3159	−	11.0780i	−1.08504	−	0.538629i
$424$	−6.61038	−	6.61038i	−0.321029	−	0.321029i
$425$			14.5575i			0.706141i
$426$	21.1905	−	29.4895i	1.02669	−	1.42877i
$427$	9.79659	+	9.79659i	0.474090	+	0.474090i
$428$	0.696222			0.0336532
$429$	3.54592	−	5.14067i	0.171199	−	0.248194i
$430$	0.797782			0.0384725
$431$	−28.1988	−	28.1988i	−1.35829	−	1.35829i	−0.876025	−	0.482266i	$-0.839814\pi$
$431$	−28.1988	−	28.1988i	−1.35829	−	1.35829i	−0.482266	−	0.876025i	$-0.660186\pi$
$432$	5.36048	−	17.4237i	0.257906	−	0.838296i
$433$			23.4642i			1.12762i	0.825905	+	0.563809i	$0.190665\pi$
$433$			23.4642i			1.12762i	−0.825905	+	0.563809i	$0.809335\pi$
$434$	−6.97817	−	6.97817i	−0.334963	−	0.334963i
$435$	−0.884799	+	0.144887i	−0.0424229	+	0.00694681i
$436$	0.780377	+	0.780377i	0.0373733	+	0.0373733i
$437$	−16.5711	+	16.5711i	−0.792701	+	0.792701i
$438$	4.00897	−	5.57902i	0.191556	−	0.266576i
$439$		−	6.74876i		−	0.322101i	−0.986946	−	0.161050i	$-0.948512\pi$
$439$		−	6.74876i		−	0.322101i	0.986946	−	0.161050i	$-0.0514882\pi$
$440$	−0.237520	+	0.237520i	−0.0113233	+	0.0113233i
$441$	−44.7035	+	15.0439i	−2.12874	+	0.716378i
$442$	14.0336	−	0.270239i	0.667511	−	0.0128540i
$443$			19.9123i			0.946063i	0.881046	+	0.473031i	$0.156840\pi$
$443$			19.9123i			0.946063i	−0.881046	+	0.473031i	$0.843160\pi$
$444$	−2.42106	+	0.396453i	−0.114898	+	0.0188148i
$445$	−1.68066			−0.0796708
$446$	−12.4168			−0.587954
$447$	1.13689	+	6.94275i	0.0537729	+	0.328381i
$448$	−29.2523	+	29.2523i	−1.38204	+	1.38204i
$449$	26.5130	−	26.5130i	1.25123	−	1.25123i	0.296055	−	0.955171i	$-0.404329\pi$
$449$	26.5130	−	26.5130i	1.25123	−	1.25123i	0.955171	−	0.296055i	$-0.0956713\pi$
$450$	−17.8724	−	8.87217i	−0.842515	−	0.418238i
$451$	−3.15579			−0.148601
$452$	−1.50497			−0.0707877
$453$	−4.49031	−	27.4215i	−0.210973	−	1.28837i
$454$			6.69979i			0.314437i
$455$	1.40423	+	1.35117i	0.0658314	+	0.0633439i
$456$	−16.1831	+	22.5210i	−0.757844	+	1.05464i
$457$	8.74604	−	8.74604i	0.409123	−	0.409123i	−0.472310	−	0.881433i	$-0.656580\pi$
$457$	8.74604	−	8.74604i	0.409123	−	0.409123i	0.881433	+	0.472310i	$0.156580\pi$
$458$		−	11.9914i		−	0.560323i
$459$	−4.46008	+	14.4970i	−0.208178	+	0.676661i
$460$	−0.0769535	+	0.0769535i	−0.00358798	+	0.00358798i
$461$	9.66438	+	9.66438i	0.450115	+	0.450115i	0.895393	−	0.445278i	$-0.146895\pi$
$461$	9.66438	+	9.66438i	0.450115	+	0.450115i	−0.445278	+	0.895393i	$0.646895\pi$
$462$	1.77939	+	10.8664i	0.0827847	+	0.505551i
$463$	16.1617	+	16.1617i	0.751096	+	0.751096i	0.974684	−	0.223588i	$-0.0717769\pi$
$463$	16.1617	+	16.1617i	0.751096	+	0.751096i	−0.223588	+	0.974684i	$0.571777\pi$
$464$			16.0167i			0.743557i
$465$	−0.247570	−	0.177899i	−0.0114808	−	0.00824986i
$466$	0.274439	+	0.274439i	0.0127132	+	0.0127132i
$467$	−9.11751			−0.421908			−0.210954	−	0.977496i	$-0.567657\pi$
$467$	−9.11751			−0.421908			−0.210954	+	0.977496i	$0.567657\pi$
$468$	1.02313	−	2.16472i	0.0472944	−	0.100064i
$469$	1.29871			0.0599688
$470$	−0.887991	−	0.887991i	−0.0409600	−	0.0409600i
$471$	−19.7170	−	14.1682i	−0.908510	−	0.652837i
$472$		−	18.9055i		−	0.870194i
$473$	3.73055	+	3.73055i	0.171531	+	0.171531i
$474$	−3.60580	−	22.0200i	−0.165620	−	1.01141i
$475$	19.0591	+	19.0591i	0.874490	+	0.874490i
$476$	2.17789	−	2.17789i	0.0998234	−	0.0998234i
$477$	−8.97230	+	3.01942i	−0.410813	+	0.138250i
$478$			5.91414i			0.270507i
$479$	−7.64089	+	7.64089i	−0.349121	+	0.349121i	−0.859782	−	0.510661i	$-0.829401\pi$
$479$	−7.64089	+	7.64089i	−0.349121	+	0.349121i	0.510661	+	0.859782i	$0.329401\pi$
$480$	−0.142815	+	0.198747i	−0.00651859	+	0.00907150i
$481$	23.0670	−	0.444192i	1.05177	−	0.0202534i
$482$		−	38.8105i		−	1.76777i
$483$	5.78531	+	35.3298i	0.263241	+	1.60756i
$484$	−0.221356			−0.0100616
$485$	1.36783			0.0621098
$486$	−15.0800	−	14.3110i	−0.684041	−	0.649161i
$487$	−1.97522	+	1.97522i	−0.0895059	+	0.0895059i	−0.750442	−	0.660936i	$-0.770159\pi$
$487$	−1.97522	+	1.97522i	−0.0895059	+	0.0895059i	0.660936	+	0.750442i	$0.270159\pi$
$488$	6.08851	−	6.08851i	0.275614	−	0.275614i
$489$	0.805152	+	4.91691i	0.0364102	+	0.222350i
$490$	−2.37746			−0.107403
$491$	27.1439			1.22499			0.612494	−	0.790475i	$-0.290166\pi$
$491$	27.1439			1.22499			0.612494	+	0.790475i	$0.290166\pi$
$492$	−1.19403	+	0.195524i	−0.0538309	+	0.00881489i
$493$		−	13.3264i		−	0.600189i
$494$	18.0194	−	18.7270i	0.810732	−	0.842569i
$495$	0.108492	+	0.322387i	0.00487635	+	0.0144902i
$496$	−3.85093	+	3.85093i	−0.172912	+	0.172912i
$497$			74.9357i			3.36133i
$498$	21.0493	−	29.2929i	0.943241	−	1.31265i
$499$	−15.7750	+	15.7750i	−0.706185	+	0.706185i	−0.965731	−	0.259546i	$-0.916427\pi$
$499$	−15.7750	+	15.7750i	−0.706185	+	0.706185i	0.259546	+	0.965731i	$0.416427\pi$
$500$	0.177243	+	0.177243i	0.00792655	+	0.00792655i
$501$	25.8955	−	4.24043i	1.15693	−	0.189449i
$502$	−11.6309	−	11.6309i	−0.519115	−	0.519115i
$503$		−	28.5910i		−	1.27481i	−0.770529	−	0.637405i	$-0.780008\pi$
$503$		−	28.5910i		−	1.27481i	0.770529	−	0.637405i	$-0.219992\pi$
$504$	13.5124	+	40.1526i	0.601892	+	1.78854i
$505$	1.16129	+	1.16129i	0.0516766	+	0.0516766i
$506$	5.78289			0.257081
$507$	−12.4258	+	18.7776i	−0.551848	+	0.833945i
$508$	−0.460638			−0.0204375
$509$	−24.3579	−	24.3579i	−1.07965	−	1.07965i	−0.996541	−	0.0831058i	$-0.973516\pi$
$509$	−24.3579	−	24.3579i	−1.07965	−	1.07965i	−0.0831058	−	0.996541i	$-0.526484\pi$
$510$	−0.446135	+	0.620856i	−0.0197552	+	0.0274920i
$511$			14.1768i			0.627147i
$512$	17.7900	+	17.7900i	0.786214	+	0.786214i
$513$	13.1406	+	24.8191i	0.580173	+	1.09579i
$514$	22.9247	+	22.9247i	1.01117	+	1.01117i
$515$	0.442515	−	0.442515i	0.0194995	−	0.0194995i
$516$	1.64262	+	1.18036i	0.0723125	+	0.0519623i
$517$		−	8.30475i		−	0.365243i
$518$	−28.7645	+	28.7645i	−1.26384	+	1.26384i
$519$	27.0170	+	19.4139i	1.18592	+	0.852176i
$520$	0.839744	−	0.872720i	0.0368252	−	0.0382713i
$521$		−	8.76606i		−	0.384048i	−0.981390	−	0.192024i	$-0.938495\pi$
$521$		−	8.76606i		−	0.384048i	0.981390	−	0.192024i	$-0.0615051\pi$
$522$	16.3610	+	8.12186i	0.716101	+	0.355484i
$523$	−7.95164			−0.347701			−0.173851	−	0.984772i	$-0.555621\pi$
$523$	−7.95164			−0.347701			−0.173851	+	0.984772i	$0.555621\pi$
$524$	−0.0112356			−0.000490827
$525$	40.6343	−	6.65393i	1.77343	−	0.290401i
$526$	29.9286	−	29.9286i	1.30495	−	1.30495i
$527$	3.20409	−	3.20409i	0.139572	−	0.139572i
$528$	5.99667	−	0.981964i	0.260972	−	0.0427345i
$529$	−4.19813			−0.182528
$530$	−0.477173			−0.0207271
$531$	−17.1479	−	8.51251i	−0.744157	−	0.369411i
$532$		−	5.70272i		−	0.247244i
$533$	11.3763	−	0.219068i	0.492761	−	0.00948888i
$534$	27.8055	+	19.9805i	1.20326	+	0.864641i
$535$	0.252171	−	0.252171i	0.0109023	−	0.0109023i
$536$		−	0.807139i		−	0.0348631i
$537$	−30.7456	−	22.0932i	−1.32677	−	0.953392i
$538$	8.04468	−	8.04468i	0.346831	−	0.346831i
$539$	−11.1174	−	11.1174i	−0.478859	−	0.478859i
$540$	0.0610231	+	0.115256i	0.00262602	+	0.00495985i
$541$	23.6194	+	23.6194i	1.01548	+	1.01548i	0.999878	+	0.0156011i	$0.00496620\pi$
$541$	23.6194	+	23.6194i	1.01548	+	1.01548i	0.0156011	+	0.999878i	$0.495034\pi$
$542$		−	17.6031i		−	0.756117i
$543$	7.42981	−	10.3396i	0.318844	−	0.443713i
$544$	−2.57221	−	2.57221i	−0.110283	−	0.110283i
$545$	0.565303			0.0242149
$546$	−7.16881	−	39.0486i	−0.306797	−	1.67112i
$547$	32.7961			1.40226			0.701129	−	0.713034i	$-0.252680\pi$
$547$	32.7961			1.40226			0.701129	+	0.713034i	$0.252680\pi$
$548$	2.52166	+	2.52166i	0.107720	+	0.107720i
$549$	−2.78105	−	8.26396i	−0.118692	−	0.352697i
$550$		−	6.65115i		−	0.283606i
$551$	−17.4473	−	17.4473i	−0.743278	−	0.743278i
$552$	21.9572	−	3.59553i	0.934562	−	0.153036i
$553$	32.5588	+	32.5588i	1.38454	+	1.38454i
$554$	−17.6824	+	17.6824i	−0.751255	+	0.751255i
$555$	−0.733310	+	1.02050i	−0.0311273	+	0.0433178i
$556$		−	0.487985i		−	0.0206952i
$557$	−6.40503	+	6.40503i	−0.271390	+	0.271390i	−0.829659	−	0.558270i	$-0.811465\pi$
$557$	−6.40503	+	6.40503i	−0.271390	+	0.271390i	0.558270	+	0.829659i	$0.311465\pi$
$558$	1.98096	+	5.88647i	0.0838605	+	0.249194i
$559$	−13.7071	−	13.1892i	−0.579751	−	0.557844i
$560$			1.89616i			0.0801273i
$561$	−4.98940	+	0.817022i	−0.210653	+	0.0344947i
$562$	10.2997			0.434466
$563$	−22.8645			−0.963622			−0.481811	−	0.876275i	$-0.660021\pi$
$563$	−22.8645			−0.963622			−0.481811	+	0.876275i	$0.660021\pi$
$564$	−0.514538	−	3.14219i	−0.0216660	−	0.132310i
$565$	−0.545097	+	0.545097i	−0.0229324	+	0.0229324i
$566$	−25.0808	+	25.0808i	−1.05423	+	1.05423i
$567$	42.5041	+	5.82314i	1.78500	+	0.244549i
$568$	46.5720			1.95412
$569$	−10.6053			−0.444597			−0.222299	−	0.974979i	$-0.571356\pi$
$569$	−10.6053			−0.444597			−0.222299	+	0.974979i	$0.571356\pi$
$570$	0.228750	+	1.39694i	0.00958130	+	0.0585112i
$571$		−	22.5756i		−	0.944761i	−0.881395	−	0.472380i	$-0.843395\pi$
$571$		−	22.5756i		−	0.944761i	0.881395	−	0.472380i	$-0.156605\pi$
$572$	0.797961	−	0.0153660i	0.0333644	−	0.000642484i
$573$	−12.5569	+	17.4746i	−0.524573	+	0.730014i
$574$	−14.1861	+	14.1861i	−0.592118	+	0.592118i
$575$		−	21.6248i		−	0.901817i
$576$	24.6759	−	8.30412i	1.02816	−	0.346005i
$577$	−14.9129	+	14.9129i	−0.620830	+	0.620830i	−0.945744	−	0.324913i	$-0.894665\pi$
$577$	−14.9129	+	14.9129i	−0.620830	+	0.620830i	0.324913	+	0.945744i	$0.394665\pi$
$578$	7.99645	+	7.99645i	0.332608	+	0.332608i
$579$	4.77502	+	29.1601i	0.198443	+	1.21185i
$580$	−0.0810225	−	0.0810225i	−0.00336428	−	0.00336428i
$581$			74.4362i			3.08814i
$582$	−22.6299	−	16.2614i	−0.938040	−	0.674056i
$583$	−2.23133	−	2.23133i	−0.0924123	−	0.0924123i
$584$	8.81081			0.364594
$585$	−0.413480	−	1.15464i	−0.0170953	−	0.0477383i
$586$	−24.7075			−1.02066
$587$	16.9874	+	16.9874i	0.701146	+	0.701146i	0.964657	−	0.263510i	$-0.0848804\pi$
$587$	16.9874	+	16.9874i	0.701146	+	0.701146i	−0.263510	+	0.964657i	$0.584880\pi$
$588$	−4.89516	−	3.51757i	−0.201873	−	0.145062i
$589$		−	8.38977i		−	0.345695i
$590$	−0.682349	−	0.682349i	−0.0280919	−	0.0280919i
$591$	0.385952	+	2.35694i	0.0158760	+	0.0969515i
$592$	15.8738	+	15.8738i	0.652409	+	0.652409i
$593$	2.34044	−	2.34044i	0.0961104	−	0.0961104i	−0.657417	−	0.753527i	$-0.728351\pi$
$593$	2.34044	−	2.34044i	0.0961104	−	0.0961104i	0.753527	+	0.657417i	$0.228351\pi$
$594$	2.03776	−	6.62351i	0.0836103	−	0.271766i
$595$		−	1.57766i		−	0.0646776i
$596$	−0.635760	+	0.635760i	−0.0260417	+	0.0260417i
$597$	−6.12153	+	8.51892i	−0.250537	+	0.348656i
$598$	−20.8466	+	0.401435i	−0.852483	+	0.0164159i
$599$			36.5552i			1.49360i	0.665046	+	0.746802i	$0.268412\pi$
$599$			36.5552i			1.49360i	−0.665046	+	0.746802i	$0.731588\pi$
$600$	−4.13537	−	25.2539i	−0.168826	−	1.03099i
$601$	−27.6167			−1.12651			−0.563254	−	0.826284i	$-0.690451\pi$
$601$	−27.6167			−1.12651			−0.563254	+	0.826284i	$0.690451\pi$
$602$	33.5396			1.36697
$603$	−0.732104	−	0.363428i	−0.0298136	−	0.0147999i
$604$	2.51103	−	2.51103i	0.102172	−	0.102172i
$605$	−0.0801747	+	0.0801747i	−0.00325957	+	0.00325957i
$606$	−5.40688	−	33.0188i	−0.219640	−	1.34130i
$607$	−39.6008			−1.60735			−0.803673	−	0.595072i	$-0.797124\pi$
$607$	−39.6008			−1.60735			−0.803673	+	0.595072i	$0.797124\pi$
$608$	−6.73522			−0.273149
$609$	−37.1979	+	6.09122i	−1.50734	+	0.246829i
$610$		−	0.439502i		−	0.0177949i
$611$	0.576496	+	29.9377i	0.0233225	+	1.21115i
$612$	−1.83717	+	0.618257i	−0.0742632	+	0.0249916i
$613$	14.3902	−	14.3902i	0.581215	−	0.581215i	−0.354022	−	0.935237i	$-0.615186\pi$
$613$	14.3902	−	14.3902i	0.581215	−	0.581215i	0.935237	+	0.354022i	$0.115186\pi$
$614$			37.9442i			1.53130i
$615$	−0.361656	+	0.503293i	−0.0145834	+	0.0202947i
$616$	−9.98560	+	9.98560i	−0.402331	+	0.402331i
$617$	−15.4618	−	15.4618i	−0.622467	−	0.622467i	0.323695	−	0.946162i	$-0.395075\pi$
$617$	−15.4618	−	15.4618i	−0.622467	−	0.622467i	−0.946162	+	0.323695i	$0.895075\pi$
$618$	−12.5820	+	2.06032i	−0.506122	+	0.0828783i
$619$	12.7503	+	12.7503i	0.512479	+	0.512479i	0.915285	−	0.402807i	$-0.131965\pi$
$619$	12.7503	+	12.7503i	0.512479	+	0.512479i	−0.402807	+	0.915285i	$0.631965\pi$
$620$		−	0.0389609i		−	0.00156471i
$621$	6.62535	−	21.5350i	0.265866	−	0.864169i
$622$	1.68199	+	1.68199i	0.0674418	+	0.0674418i
$623$	−70.6567			−2.83080
$624$	−21.5491	+	3.95614i	−0.862655	+	0.158372i
$625$	−24.8073			−0.992293
$626$	−3.33147	−	3.33147i	−0.133152	−	0.133152i
$627$	−5.46260	+	7.60194i	−0.218155	+	0.303592i
$628$		−	3.10292i		−	0.123820i
$629$	−13.2075	−	13.2075i	−0.526616	−	0.526616i
$630$	1.93692	+	0.961516i	0.0771686	+	0.0383077i
$631$	2.55432	+	2.55432i	0.101686	+	0.101686i	0.756119	−	0.654434i	$-0.227093\pi$
$631$	2.55432	+	2.55432i	0.101686	+	0.101686i	−0.654434	+	0.756119i	$0.727093\pi$
$632$	20.2351	−	20.2351i	0.804909	−	0.804909i
$633$	−18.8604	−	13.5527i	−0.749632	−	0.538670i
$634$			31.2200i			1.23991i
$635$	−0.166842	+	0.166842i	−0.00662094	+	0.00662094i
$636$	−0.982493	−	0.706000i	−0.0389584	−	0.0279947i
$637$	40.8485	+	39.3050i	1.61848	+	1.55732i
$638$			6.08867i			0.241053i
$639$	20.9699	−	42.2425i	0.829555	−	1.67109i
$640$	1.02974			0.0407040
$641$	−19.8000			−0.782053			−0.391027	−	0.920379i	$-0.627880\pi$
$641$	−19.8000			−0.782053			−0.391027	+	0.920379i	$0.627880\pi$
$642$	−7.16995	+	1.17409i	−0.282976	+	0.0463377i
$643$	2.94579	−	2.94579i	0.116170	−	0.116170i	−0.646632	−	0.762802i	$-0.723823\pi$
$643$	2.94579	−	2.94579i	0.116170	−	0.116170i	0.762802	+	0.646632i	$0.223823\pi$
$644$	−3.23521	+	3.23521i	−0.127485	+	0.127485i
$645$	1.02248	−	0.167433i	0.0402601	−	0.00659265i
$646$	−21.0399			−0.827803
$647$	−25.3178			−0.995346			−0.497673	−	0.867365i	$-0.665812\pi$
$647$	−25.3178			−0.995346			−0.497673	+	0.867365i	$0.665812\pi$
$648$	3.61904	−	26.4160i	0.142169	−	1.03772i
$649$		−	6.38153i		−	0.250497i
$650$	0.461707	+	23.9766i	0.0181096	+	0.940440i
$651$	−10.4081	−	7.47906i	−0.407926	−	0.293127i
$652$	−0.450250	+	0.450250i	−0.0176331	+	0.0176331i
$653$			20.2785i			0.793559i	0.917914	+	0.396780i	$0.129872\pi$
$653$			20.2785i			0.793559i	−0.917914	+	0.396780i	$0.870128\pi$
$654$	−9.35262	−	6.72060i	−0.365716	−	0.262796i
$655$	−0.00406950	+	0.00406950i	−0.000159009	+	0.000159009i
$656$	7.82869	+	7.82869i	0.305659	+	0.305659i
$657$	3.96722	−	7.99173i	0.154776	−	0.311787i
$658$	−37.3321	−	37.3321i	−1.45536	−	1.45536i
$659$			27.2390i			1.06108i	0.847660	+	0.530540i	$0.178011\pi$
$659$			27.2390i			1.06108i	−0.847660	+	0.530540i	$0.821989\pi$
$660$	−0.0253675	+	0.0353023i	−0.000987430	+	0.00137414i
$661$	−13.0843	−	13.0843i	−0.508922	−	0.508922i	0.405274	−	0.914195i	$-0.367176\pi$
$661$	−13.0843	−	13.0843i	−0.508922	−	0.508922i	−0.914195	+	0.405274i	$0.867176\pi$
$662$	36.1928			1.40667
$663$	17.9295	−	3.29162i	0.696324	−	0.127836i
$664$	46.2616			1.79530
$665$	−2.06552	−	2.06552i	−0.0800973	−	0.0800973i
$666$	24.2644	−	8.16563i	0.940227	−	0.316412i
$667$			19.7960i			0.766506i
$668$	2.37130	+	2.37130i	0.0917482	+	0.0917482i
$669$	−15.9140	+	2.60595i	−0.615273	+	0.100752i
$670$	−0.0291318	−	0.0291318i	−0.00112546	−	0.00112546i
$671$	2.05517	−	2.05517i	0.0793391	−	0.0793391i
$672$	−6.00411	+	8.35552i	−0.231614	+	0.322321i
$673$		−	5.18311i		−	0.199794i	−0.994998	−	0.0998970i	$-0.968149\pi$
$673$		−	5.18311i		−	0.199794i	0.994998	−	0.0998970i	$-0.0318513\pi$
$674$	−10.5193	+	10.5193i	−0.405187	+	0.405187i
$675$	−24.7683	−	7.62009i	−0.953331	−	0.293297i
$676$	−2.87549	+	0.110785i	−0.110596	+	0.00426097i
$677$		−	46.8438i		−	1.80035i	−0.435525	−	0.900177i	$-0.643437\pi$
$677$		−	46.8438i		−	1.80035i	0.435525	−	0.900177i	$-0.356563\pi$
$678$	15.4987	−	2.53794i	0.595224	−	0.0974689i
$679$	57.5049			2.20683
$680$	−0.980503			−0.0376006
$681$	1.40610	+	8.58680i	0.0538820	+	0.329047i
$682$	−1.46391	+	1.46391i	−0.0560561	+	0.0560561i
$683$	31.2783	−	31.2783i	1.19683	−	1.19683i	0.221720	−	0.975110i	$-0.428833\pi$
$683$	31.2783	−	31.2783i	1.19683	−	1.19683i	0.975110	−	0.221720i	$-0.0711669\pi$
$684$	−1.59584	+	3.21472i	−0.0610183	+	0.122918i
$685$	1.82669			0.0697941
$686$	−55.4502			−2.11710
$687$	−2.51667	−	15.3688i	−0.0960171	−	0.586358i
$688$		−	18.5090i		−	0.705649i
$689$	8.19858	+	7.88879i	0.312341	+	0.300539i
$690$	0.662724	−	0.922269i	0.0252295	−	0.0351102i
$691$	19.8462	−	19.8462i	0.754986	−	0.754986i	−0.220419	−	0.975405i	$-0.570743\pi$
$691$	19.8462	−	19.8462i	0.754986	−	0.754986i	0.975405	+	0.220419i	$0.0707426\pi$
$692$			4.25176i			0.161628i
$693$	4.56111	+	13.5535i	0.173262	+	0.514855i
$694$	0.803526	−	0.803526i	0.0305014	−	0.0305014i
$695$	−0.176747	−	0.176747i	−0.00670441	−	0.00670441i
$696$	3.78565	+	23.1183i	0.143495	+	0.876295i
$697$	−6.51370	−	6.51370i	−0.246724	−	0.246724i
$698$			46.2481i			1.75051i
$699$	0.409333	+	0.294138i	0.0154824	+	0.0111253i
$700$	3.72095	+	3.72095i	0.140639	+	0.140639i
$701$	1.93167			0.0729580			0.0364790	−	0.999334i	$-0.488386\pi$
$701$	1.93167			0.0729580			0.0364790	+	0.999334i	$0.488386\pi$
$702$	−6.88609	+	24.0184i	−0.259899	+	0.906518i
$703$	−34.5832			−1.30433
$704$	6.13669	+	6.13669i	0.231285	+	0.231285i
$705$	−1.32446	−	0.951731i	−0.0498821	−	0.0358442i
$706$			13.6515i			0.513781i
$707$	48.8218	+	48.8218i	1.83613	+	1.83613i
$708$	−0.395380	−	2.41451i	−0.0148593	−	0.0907430i
$709$	−34.4814	−	34.4814i	−1.29498	−	1.29498i	−0.931670	−	0.363305i	$-0.881648\pi$
$709$	−34.4814	−	34.4814i	−1.29498	−	1.29498i	−0.363305	−	0.931670i	$-0.618352\pi$
$710$	1.68091	−	1.68091i	0.0630834	−	0.0630834i
$711$	−9.24277	−	27.4652i	−0.346631	−	1.03002i
$712$			43.9126i			1.64570i
$713$	−4.75961	+	4.75961i	−0.178249	+	0.178249i
$714$	−18.7560	+	26.1015i	−0.701925	+	0.976822i
$715$	0.283455	−	0.294586i	0.0106006	−	0.0110169i
$716$		−	4.83854i		−	0.180825i
$717$	1.24122	+	7.57987i	0.0463541	+	0.283076i
$718$	29.7791			1.11135
$719$	−35.9943			−1.34236			−0.671180	−	0.741295i	$-0.734212\pi$
$719$	−35.9943			−1.34236			−0.671180	+	0.741295i	$0.734212\pi$
$720$	0.530617	−	1.06890i	0.0197749	−	0.0398354i
$721$	18.6038	−	18.6038i	0.692842	−	0.692842i
$722$	−9.62828	+	9.62828i	−0.358328	+	0.358328i
$723$	−8.14525	−	49.7415i	−0.302925	−	1.84991i
$724$	1.62717			0.0604733
$725$	22.7682			0.845592
$726$	2.27960	−	0.373288i	0.0846040	−	0.0138540i
$727$			5.51236i			0.204442i	0.994762	+	0.102221i	$0.0325949\pi$
$727$			5.51236i			0.204442i	−0.994762	+	0.102221i	$0.967405\pi$
$728$	35.3037	−	36.6901i	1.30844	−	1.35982i
$729$	−22.3308	−	15.1769i	−0.827065	−	0.562106i
$730$	0.318006	−	0.318006i	0.0117699	−	0.0117699i
$731$			15.4000i			0.569590i
$732$	0.650263	−	0.904928i	0.0240344	−	0.0334471i
$733$	2.33753	−	2.33753i	0.0863387	−	0.0863387i	−0.662618	−	0.748957i	$-0.730555\pi$
$733$	2.33753	−	2.33753i	0.0863387	−	0.0863387i	0.748957	+	0.662618i	$0.230555\pi$
$734$	33.8400	+	33.8400i	1.24906	+	1.24906i
$735$	−3.04708	+	0.498964i	−0.112393	+	0.0184046i
$736$	3.82096	+	3.82096i	0.140843	+	0.140843i
$737$		−	0.272449i		−	0.0100358i
$738$	11.9668	−	4.02715i	0.440504	−	0.148241i
$739$	17.0372	+	17.0372i	0.626722	+	0.626722i	0.947242	−	0.320520i	$-0.103858\pi$
$739$	17.0372	+	17.0372i	0.626722	+	0.626722i	−0.320520	+	0.947242i	$0.603858\pi$
$740$	−0.160599			−0.00590375
$741$	19.1643	−	27.7833i	0.704019	−	1.02065i
$742$	−20.0609			−0.736458
$743$	29.3368	+	29.3368i	1.07626	+	1.07626i	0.996841	+	0.0794222i	$0.0253075\pi$
$743$	29.3368	+	29.3368i	1.07626	+	1.07626i	0.0794222	+	0.996841i	$0.474692\pi$
$744$	−4.64818	+	6.46857i	−0.170411	+	0.237149i
$745$			0.460542i			0.0168730i
$746$	−31.7573	−	31.7573i	−1.16272	−	1.16272i
$747$	20.8301	−	41.9610i	0.762133	−	1.53527i
$748$	−0.456888	−	0.456888i	−0.0167055	−	0.0167055i
$749$	10.6015	−	10.6015i	0.387372	−	0.387372i
$750$	−2.12421	−	1.52642i	−0.0775653	−	0.0557369i
$751$			5.37008i			0.195957i	0.995189	+	0.0979786i	$0.0312377\pi$
$751$			5.37008i			0.195957i	−0.995189	+	0.0979786i	$0.968762\pi$
$752$	−20.6019	+	20.6019i	−0.751274	+	0.751274i
$753$	−17.3478	−	12.4658i	−0.632191	−	0.454279i
$754$	−0.422661	−	21.9489i	−0.0153924	−	0.799333i
$755$		−	1.81898i		−	0.0661995i
$756$	2.56548	+	4.84551i	0.0933055	+	0.176229i
$757$	−28.2595			−1.02711			−0.513555	−	0.858057i	$-0.671672\pi$
$757$	−28.2595			−1.02711			−0.513555	+	0.858057i	$0.671672\pi$
$758$	−26.8686			−0.975912
$759$	7.41165	−	1.21367i	0.269026	−	0.0440534i
$760$	−1.28370	+	1.28370i	−0.0465648	+	0.0465648i
$761$	8.57287	−	8.57287i	0.310766	−	0.310766i	−0.534440	−	0.845206i	$-0.679477\pi$
$761$	8.57287	−	8.57287i	0.310766	−	0.310766i	0.845206	+	0.534440i	$0.179477\pi$
$762$	4.74382	−	0.776808i	0.171851	−	0.0281408i
$763$	23.7659			0.860385
$764$	−2.75004			−0.0994930
$765$	−0.441489	+	0.889352i	−0.0159621	+	0.0321546i
$766$		−	1.93347i		−	0.0698590i
$767$	0.442991	+	23.0047i	0.0159955	+	0.830650i
$768$	7.37752	+	5.30134i	0.266213	+	0.191296i
$769$	−14.8656	+	14.8656i	−0.536069	+	0.536069i	−0.922372	−	0.386303i	$-0.873752\pi$
$769$	−14.8656	+	14.8656i	−0.536069	+	0.536069i	0.386303	+	0.922372i	$0.373752\pi$
$770$			0.720814i			0.0259763i
$771$	34.1927	+	24.5702i	1.23142	+	0.884875i
$772$	−2.67024	+	2.67024i	−0.0961041	+	0.0961041i
$773$	0.247459	+	0.247459i	0.00890047	+	0.00890047i	0.711543	−	0.702643i	$-0.247997\pi$
$773$	0.247459	+	0.247459i	0.00890047	+	0.00890047i	−0.702643	+	0.711543i	$0.747997\pi$
$774$	−18.9069	−	9.38567i	−0.679593	−	0.337361i
$775$	5.47422	+	5.47422i	0.196640	+	0.196640i
$776$		−	35.7389i		−	1.28295i
$777$	−30.8292	+	42.9029i	−1.10599	+	1.53913i
$778$	−25.3515	−	25.3515i	−0.908896	−	0.908896i
$779$	−17.0558			−0.611089
$780$	0.0889964	−	0.129022i	0.00318658	−	0.00461972i
$781$	15.7204			0.562519
$782$	11.9361	+	11.9361i	0.426836	+	0.426836i
$783$	22.6737	+	6.97567i	0.810290	+	0.249290i
$784$			55.1585i			1.96995i
$785$	−1.12387	−	1.12387i	−0.0401128	−	0.0401128i
$786$	0.115708	−	0.0189473i	0.00412716	−	0.000675829i
$787$	3.69619	+	3.69619i	0.131755	+	0.131755i	0.769909	−	0.638154i	$-0.220302\pi$
$787$	3.69619	+	3.69619i	0.131755	+	0.131755i	−0.638154	+	0.769909i	$0.720302\pi$
$788$	−0.215829	+	0.215829i	−0.00768858	+	0.00768858i
$789$	32.0768	−	44.6392i	1.14197	−	1.58920i
$790$		−	1.46068i		−	0.0519686i
$791$	−22.9165	+	22.9165i	−0.814815	+	0.814815i
$792$	8.42340	−	2.83470i	0.299313	−	0.100727i
$793$	−7.26599	+	7.55132i	−0.258023	+	0.268155i
$794$			21.0695i			0.747727i
$795$	−0.611570	+	0.100146i	−0.0216901	+	0.00355180i
$796$	−1.34065			−0.0475181
$797$	−5.15453			−0.182583			−0.0912915	−	0.995824i	$-0.529099\pi$
$797$	−5.15453			−0.182583			−0.0912915	+	0.995824i	$0.529099\pi$
$798$	9.61691	+	58.7287i	0.340435	+	2.07897i
$799$	17.1414	−	17.1414i	0.606418	−	0.606418i
$800$	4.39465	−	4.39465i	0.155374	−	0.155374i
$801$	39.8304	+	19.7724i	1.40734	+	0.698624i
$802$	−35.3726			−1.24905
$803$	2.97408			0.104953
$804$	−0.0168801	−	0.103084i	−0.000595317	−	0.00363549i
$805$			2.34358i			0.0826003i
$806$	5.17561	−	5.37885i	0.182303	−	0.189462i
$807$	8.62212	−	11.9988i	0.303513	−	0.422379i
$808$	30.3424	−	30.3424i	1.06744	−	1.06744i
$809$		−	11.0521i		−	0.388572i	−0.980945	−	0.194286i	$-0.937761\pi$
$809$		−	11.0521i		−	0.388572i	0.980945	−	0.194286i	$-0.0622390\pi$
$810$	−0.822804	−	1.08405i	−0.0289104	−	0.0380895i
$811$	4.15172	−	4.15172i	0.145787	−	0.145787i	−0.630446	−	0.776233i	$-0.717128\pi$
$811$	4.15172	−	4.15172i	0.145787	−	0.145787i	0.776233	+	0.630446i	$0.217128\pi$
$812$	−3.40628	−	3.40628i	−0.119537	−	0.119537i
$813$	−3.69440	−	22.5610i	−0.129568	−	0.791250i
$814$	6.03434	+	6.03434i	0.211504	+	0.211504i
$815$			0.326160i			0.0114249i
$816$	14.4042	+	10.3506i	0.504248	+	0.362343i
$817$	20.1622	+	20.1622i	0.705385	+	0.705385i
$818$	36.6302			1.28075
$819$	−17.3831	−	48.5421i	−0.607416	−	1.69620i
$820$	−0.0792049			−0.00276595
$821$	4.10633	+	4.10633i	0.143312	+	0.143312i	0.775123	−	0.631811i	$-0.217688\pi$
$821$	4.10633	+	4.10633i	0.143312	+	0.143312i	−0.631811	+	0.775123i	$0.717688\pi$
$822$	−30.2215	−	21.7166i	−1.05410	−	0.757452i
$823$		−	1.64368i		−	0.0572951i	−0.999590	−	0.0286475i	$-0.990880\pi$
$823$		−	1.64368i		−	0.0572951i	0.999590	−	0.0286475i	$-0.00912005\pi$
$824$	−11.5621	−	11.5621i	−0.402786	−	0.402786i
$825$	−1.39589	−	8.52445i	−0.0485987	−	0.296783i
$826$	−28.6867	−	28.6867i	−0.998138	−	0.998138i
$827$	18.0992	−	18.0992i	0.629369	−	0.629369i	−0.318540	−	0.947909i	$-0.603193\pi$
$827$	18.0992	−	18.0992i	0.629369	−	0.629369i	0.947909	+	0.318540i	$0.103193\pi$
$828$	2.72908	−	0.918408i	0.0948420	−	0.0319169i
$829$		−	28.8114i		−	1.00066i	−0.865834	−	0.500331i	$-0.833212\pi$
$829$		−	28.8114i		−	1.00066i	0.865834	−	0.500331i	$-0.166788\pi$
$830$	1.66971	−	1.66971i	0.0579563	−	0.0579563i
$831$	−18.9517	+	26.3738i	−0.657427	+	0.914897i
$832$	−22.5480	−	21.6960i	−0.781712	−	0.752175i
$833$		−	45.8934i		−	1.59011i
$834$	0.822924	+	5.02544i	0.0284955	+	0.174017i
$835$	1.71776			0.0594456
$836$	−1.19634			−0.0413764
$837$	3.77430	+	7.12866i	0.130459	+	0.246402i
$838$	−9.10207	+	9.10207i	−0.314426	+	0.314426i
$839$	4.24437	−	4.24437i	0.146532	−	0.146532i	−0.630035	−	0.776567i	$-0.716959\pi$
$839$	4.24437	−	4.24437i	0.146532	−	0.146532i	0.776567	+	0.630035i	$0.216959\pi$
$840$	0.448169	+	2.73688i	0.0154633	+	0.0944314i
$841$	8.15723			0.281284
$842$	−16.0448			−0.552939
$843$	13.2006	−	2.16162i	0.454653	−	0.0744501i
$844$		−	2.96811i		−	0.102167i
$845$	−1.00137	+	1.08162i	−0.0344483	+	0.0372090i
$846$	10.5978	+	31.4917i	0.364360	+	1.08271i
$847$	−3.37063	+	3.37063i	−0.115816	+	0.115816i
$848$			11.0707i			0.380169i
$849$	−26.8811	+	37.4087i	−0.922558	+	1.28386i
$850$	13.7283	−	13.7283i	0.470875	−	0.470875i
$851$	19.6194	+	19.6194i	0.672545	+	0.672545i
$852$	5.94796	−	0.973987i	0.203774	−	0.0333683i
$853$	13.2140	+	13.2140i	0.452437	+	0.452437i	0.896163	−	0.443726i	$-0.146343\pi$
$853$	13.2140	+	13.2140i	0.452437	+	0.452437i	−0.443726	+	0.896163i	$0.646343\pi$
$854$		−	18.4771i		−	0.632274i
$855$	0.586356	+	1.74238i	0.0200530	+	0.0595880i
$856$	−6.58878	−	6.58878i	−0.225200	−	0.225200i
$857$	−7.99813			−0.273211			−0.136605	−	0.990626i	$-0.543619\pi$
$857$	−7.99813			−0.273211			−0.136605	+	0.990626i	$0.543619\pi$
$858$	−8.19179	+	1.50391i	−0.279663	+	0.0513425i
$859$	−0.845692			−0.0288546			−0.0144273	−	0.999896i	$-0.504593\pi$
$859$	−0.845692			−0.0288546			−0.0144273	+	0.999896i	$0.504593\pi$
$860$	0.0936301	+	0.0936301i	0.00319276	+	0.00319276i
$861$	−15.2044	+	21.1590i	−0.518165	+	0.721096i
$862$			53.1852i			1.81150i
$863$	−40.3613	−	40.3613i	−1.37392	−	1.37392i	−0.854555	−	0.519361i	$-0.826170\pi$
$863$	−40.3613	−	40.3613i	−1.37392	−	1.37392i	−0.519361	−	0.854555i	$-0.673830\pi$
$864$	5.72281	−	3.02997i	0.194694	−	0.103082i
$865$	1.53998	+	1.53998i	0.0523609	+	0.0523609i
$866$	22.1277	−	22.1277i	0.751929	−	0.751929i
$867$	11.9269	+	8.57043i	0.405059	+	0.291067i
$868$		−	1.63796i		−	0.0555959i
$869$	6.83034	−	6.83034i	0.231704	−	0.231704i
$870$	0.971034	+	0.697766i	0.0329211	+	0.0236565i
$871$	0.0189128	+	0.982147i	0.000640835	+	0.0332788i
$872$		−	14.7704i		−	0.500188i
$873$	−32.4165	−	16.0921i	−1.09713	−	0.544633i
$874$	31.2543			1.05719
$875$	5.39784			0.182480
$876$	1.12527	−	0.184265i	0.0380195	−	0.00622575i
$877$	−29.4517	+	29.4517i	−0.994514	+	0.994514i	−0.999985	−	0.00547057i	$-0.998259\pi$
$877$	−29.4517	+	29.4517i	−0.994514	+	0.994514i	0.00547057	+	0.999985i	$0.498259\pi$
$878$	−6.36434	+	6.36434i	−0.214786	+	0.214786i
$879$	−31.6664	+	5.18543i	−1.06808	+	0.174900i
$880$	0.397785			0.0134093
$881$	−28.0506			−0.945047			−0.472524	−	0.881318i	$-0.656657\pi$
$881$	−28.0506			−0.945047			−0.472524	+	0.881318i	$0.656657\pi$
$882$	56.3441	+	27.9701i	1.89721	+	0.941803i
$883$			10.7204i			0.360770i	0.983596	+	0.180385i	$0.0577343\pi$
$883$			10.7204i			0.360770i	−0.983596	+	0.180385i	$0.942266\pi$
$884$	1.67874	+	1.61531i	0.0564622	+	0.0543288i
$885$	−1.01774	−	0.731327i	−0.0342110	−	0.0245833i
$886$	18.7781	−	18.7781i	0.630862	−	0.630862i
$887$		−	4.95610i		−	0.166409i	−0.996532	−	0.0832047i	$-0.973484\pi$
$887$		−	4.95610i		−	0.166409i	0.996532	−	0.0832047i	$-0.0265155\pi$
$888$	26.6639	+	19.1601i	0.894780	+	0.642971i
$889$	−7.01424	+	7.01424i	−0.235250	+	0.235250i
$890$	1.58493	+	1.58493i	0.0531268	+	0.0531268i
$891$	1.22160	−	8.91671i	0.0409253	−	0.298721i
$892$	−1.45728	−	1.45728i	−0.0487932	−	0.0487932i
$893$		−	44.8840i		−	1.50198i
$894$	5.47516	−	7.61941i	0.183117	−	0.254831i
$895$	−1.75251	−	1.75251i	−0.0585800	−	0.0585800i
$896$	43.2914			1.44626
$897$	−26.6339	+	4.88964i	−0.889280	+	0.163260i
$898$	−50.0056			−1.66871
$899$	−5.01128	−	5.01128i	−0.167135	−	0.167135i
$900$	−1.05630	−	3.13883i	−0.0352100	−	0.104628i
$901$		−	9.21113i		−	0.306867i
$902$	2.97604	+	2.97604i	0.0990912	+	0.0990912i
$903$	42.9861	−	7.03905i	1.43049	−	0.234245i
$904$	14.2424	+	14.2424i	0.473696	+	0.473696i
$905$	0.589359	−	0.589359i	0.0195910	−	0.0195910i
$906$	−21.6250	+	30.0940i	−0.718441	+	0.999807i
$907$		−	3.51176i		−	0.116606i	−0.998299	−	0.0583031i	$-0.981431\pi$
$907$		−	3.51176i		−	0.116606i	0.998299	−	0.0583031i	$-0.0185690\pi$
$908$	−0.786308	+	0.786308i	−0.0260945	+	0.0260945i
$909$	−13.8595	−	41.1839i	−0.459690	−	1.36598i
$910$	−0.0500372	−	2.59845i	−0.00165872	−	0.0861378i
$911$			19.7821i			0.655411i	0.944780	+	0.327706i	$0.106275\pi$
$911$			19.7821i			0.655411i	−0.944780	+	0.327706i	$0.893725\pi$
$912$	32.4097	−	5.30714i	1.07319	−	0.175737i
$913$	15.6156			0.516800
$914$	−16.4957			−0.545630
$915$	−0.0922393	−	0.563288i	−0.00304934	−	0.0186217i
$916$	1.40735	−	1.40735i	0.0465002	−	0.0465002i
$917$	−0.171086	+	0.171086i	−0.00564977	+	0.00564977i
$918$	17.8772	−	9.46520i	0.590037	−	0.312398i
$919$	8.49997			0.280388			0.140194	−	0.990124i	$-0.455227\pi$
$919$	8.49997			0.280388			0.140194	+	0.990124i	$0.455227\pi$
$920$	1.45652			0.0480199
$921$	7.96344	+	48.6312i	0.262404	+	1.60245i
$922$		−	18.2278i		−	0.600300i
$923$	−56.6701	+	1.09127i	−1.86532	+	0.0359196i
$924$	−1.06648	+	1.48415i	−0.0350846	+	0.0488249i
$925$	22.5651	−	22.5651i	0.741936	−	0.741936i
$926$		−	30.4822i		−	1.00171i
$927$	−15.6933	+	5.28123i	−0.515437	+	0.173458i
$928$	−4.02300	+	4.02300i	−0.132061	+	0.132061i
$929$	−7.73253	−	7.73253i	−0.253696	−	0.253696i	0.568788	−	0.822484i	$-0.307412\pi$
$929$	−7.73253	−	7.73253i	−0.253696	−	0.253696i	−0.822484	+	0.568788i	$0.807412\pi$
$930$	0.0657026	+	0.401233i	0.00215447	+	0.0131570i
$931$	−60.0850	−	60.0850i	−1.96921	−	1.96921i
$932$			0.0644180i			0.00211008i
$933$	2.50873	+	1.80273i	0.0821322	+	0.0590186i
$934$	8.59816	+	8.59816i	0.281340	+	0.281340i
$935$	−0.330968			−0.0108238
$936$	−30.1686	+	10.8035i	−0.986091	+	0.353123i
$937$	−2.43490			−0.0795448			−0.0397724	−	0.999209i	$-0.512663\pi$
$937$	−2.43490			−0.0795448			−0.0397724	+	0.999209i	$0.512663\pi$
$938$	−1.22473	−	1.22473i	−0.0399889	−	0.0399889i
$939$	−4.96897	−	3.57060i	−0.162156	−	0.116522i
$940$		−	0.208435i		−	0.00679839i
$941$	13.1849	+	13.1849i	0.429816	+	0.429816i	0.888566	−	0.458750i	$-0.151703\pi$
$941$	13.1849	+	13.1849i	0.429816	+	0.429816i	−0.458750	+	0.888566i	$0.651703\pi$
$942$	5.23269	+	31.9550i	0.170490	+	1.04115i
$943$	9.67596	+	9.67596i	0.315093	+	0.315093i
$944$	−15.8309	+	15.8309i	−0.515251	+	0.515251i
$945$	2.68425	+	0.825823i	0.0873186	+	0.0268640i
$946$		−	7.03610i		−	0.228763i
$947$	10.3748	−	10.3748i	0.337135	−	0.337135i	−0.518153	−	0.855288i	$-0.673380\pi$
$947$	10.3748	−	10.3748i	0.337135	−	0.337135i	0.855288	+	0.518153i	$0.173380\pi$
$948$	2.16114	−	3.00752i	0.0701906	−	0.0976796i
$949$	−10.7212	+	0.206454i	−0.348026	+	0.00670178i
$950$		−	35.9469i		−	1.16627i
$951$	6.55223	+	40.0132i	0.212470	+	1.29752i
$952$	−41.2214			−1.33599
$953$	32.6737			1.05840			0.529202	−	0.848496i	$-0.322491\pi$
$953$	32.6737			1.05840			0.529202	+	0.848496i	$0.322491\pi$
$954$	11.3087	+	5.61380i	0.366131	+	0.181753i
$955$	−0.996061	+	0.996061i	−0.0322318	+	0.0322318i
$956$	−0.694102	+	0.694102i	−0.0224489	+	0.0224489i
$957$	1.27784	+	7.80355i	0.0413068	+	0.252253i
$958$	14.4113			0.465608
$959$	76.7959			2.47987
$960$	1.68196	−	0.275424i	0.0542851	−	0.00888926i
$961$			28.5903i			0.922266i
$962$	−22.1720	−	21.3342i	−0.714854	−	0.687843i
$963$	−8.94298	+	3.00955i	−0.288183	+	0.0969815i
$964$	4.55491	−	4.55491i	0.146704	−	0.146704i
$965$			1.93432i			0.0622678i
$966$	27.8616	−	38.7732i	0.896433	−	1.24751i
$967$	4.27105	−	4.27105i	0.137348	−	0.137348i	−0.635090	−	0.772438i	$-0.719037\pi$
$967$	4.27105	−	4.27105i	0.137348	−	0.137348i	0.772438	+	0.635090i	$0.219037\pi$
$968$	2.09482	+	2.09482i	0.0673302	+	0.0673302i
$969$	−26.9658	+	4.41569i	−0.866266	+	0.141852i
$970$	−1.28991	−	1.28991i	−0.0414166	−	0.0414166i
$971$		−	9.70612i		−	0.311484i	−0.987798	−	0.155742i	$-0.950223\pi$
$971$		−	9.70612i		−	0.311484i	0.987798	−	0.155742i	$-0.0497769\pi$
$972$	−0.0902464	−	3.44941i	−0.00289466	−	0.110640i
$973$	−7.43065	−	7.43065i	−0.238216	−	0.238216i
$974$	3.72542			0.119370
$975$	5.62378	+	30.6328i	0.180105	+	0.981033i
$976$	−10.1967			−0.326388
$977$	−15.6898	−	15.6898i	−0.501961	−	0.501961i	0.410086	−	0.912047i	$-0.365499\pi$
$977$	−15.6898	−	15.6898i	−0.501961	−	0.501961i	−0.912047	+	0.410086i	$0.865499\pi$
$978$	3.87755	−	5.39613i	0.123990	−	0.172549i
$979$			14.8227i			0.473735i
$980$	−0.279026	−	0.279026i	−0.00891316	−	0.00891316i
$981$	−13.3973	−	6.65061i	−0.427742	−	0.212338i
$982$	−25.5978	−	25.5978i	−0.816858	−	0.816858i
$983$	35.3665	−	35.3665i	1.12802	−	1.12802i	0.137516	−	0.990500i	$-0.456088\pi$
$983$	35.3665	−	35.3665i	1.12802	−	1.12802i	0.990500	−	0.137516i	$-0.0439119\pi$
$984$	13.1502	+	9.44944i	0.419212	+	0.301237i
$985$			0.156346i			0.00498159i
$986$	−12.5673	+	12.5673i	−0.400224	+	0.400224i
$987$	−55.6817	−	40.0118i	−1.77237	−	1.27359i
$988$	4.31267	−	0.0830473i	0.137204	−	0.00264209i
$989$		−	22.8764i		−	0.727428i
$990$	0.201711	−	0.406335i	0.00641080	−	0.0129142i
$991$	−2.99090			−0.0950090			−0.0475045	−	0.998871i	$-0.515127\pi$
$991$	−2.99090			−0.0950090			−0.0475045	+	0.998871i	$0.515127\pi$
$992$	−1.93452			−0.0614210
$993$	46.3866	−	7.59588i	1.47203	−	0.241048i
$994$	70.6673	−	70.6673i	2.24143	−	2.24143i
$995$	−0.485582	+	0.485582i	−0.0153940	+	0.0153940i
$996$	5.90831	−	0.967495i	0.187212	−	0.0306563i
$997$	−17.5839			−0.556886			−0.278443	−	0.960453i	$-0.589818\pi$
$997$	−17.5839			−0.556886			−0.278443	+	0.960453i	$0.589818\pi$
$998$	29.7528			0.941809
$999$	29.3848	−	15.5579i	0.929694	−	0.492231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.j.a.122.15	✓	96
3.2	odd	2	inner	429.2.j.a.122.34	yes	96
13.8	odd	4	inner	429.2.j.a.320.34	yes	96
39.8	even	4	inner	429.2.j.a.320.15	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.j.a.122.15	✓	96	1.1	even	1	trivial
429.2.j.a.122.34	yes	96	3.2	odd	2	inner
429.2.j.a.320.15	yes	96	39.8	even	4	inner
429.2.j.a.320.34	yes	96	13.8	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.943039 - 0.943039i) q^{2} +(-1.40657 - 1.01073i) q^{3} -0.221356i q^{4} +(-0.0801747 - 0.0801747i) q^{5} +(0.373288 + 2.27960i) q^{6} +(-3.37063 - 3.37063i) q^{7} +(-2.09482 + 2.09482i) q^{8} +(0.956852 + 2.84331i) q^{9} +O(q^{10})\)	\(q+(-0.943039 - 0.943039i) q^{2} +(-1.40657 - 1.01073i) q^{3} -0.221356i q^{4} +(-0.0801747 - 0.0801747i) q^{5} +(0.373288 + 2.27960i) q^{6} +(-3.37063 - 3.37063i) q^{7} +(-2.09482 + 2.09482i) q^{8} +(0.956852 + 2.84331i) q^{9} +0.151216i q^{10} +(-0.707107 + 0.707107i) q^{11} +(-0.223731 + 0.311351i) q^{12} +(2.49995 - 2.59812i) q^{13} +6.35727i q^{14} +(0.0317360 + 0.193806i) q^{15} +3.50829 q^{16} -2.91900 q^{17} +(1.77901 - 3.58370i) q^{18} +(-3.82164 + 3.82164i) q^{19} +(-0.0177471 + 0.0177471i) q^{20} +(1.33422 + 8.14781i) q^{21} +1.33366 q^{22} +4.33611 q^{23} +(5.06381 - 0.829206i) q^{24} -4.98714i q^{25} +(-4.80768 + 0.0925794i) q^{26} +(1.52795 - 4.96643i) q^{27} +(-0.746109 + 0.746109i) q^{28} +4.56539i q^{29} +(0.152838 - 0.212695i) q^{30} +(-1.09767 + 1.09767i) q^{31} +(0.881195 + 0.881195i) q^{32} +(1.70929 - 0.279898i) q^{33} +(2.75273 + 2.75273i) q^{34} +0.540479i q^{35} +(0.629384 - 0.211805i) q^{36} +(4.52465 + 4.52465i) q^{37} +7.20791 q^{38} +(-6.14234 + 1.12765i) q^{39} +0.335904 q^{40} +(2.23148 + 2.23148i) q^{41} +(6.42548 - 8.94192i) q^{42} -5.27579i q^{43} +(0.156522 + 0.156522i) q^{44} +(0.151247 - 0.304677i) q^{45} +(-4.08912 - 4.08912i) q^{46} +(-5.87235 + 5.87235i) q^{47} +(-4.93464 - 3.54593i) q^{48} +15.7223i q^{49} +(-4.70307 + 4.70307i) q^{50} +(4.10576 + 2.95032i) q^{51} +(-0.575109 - 0.553379i) q^{52} +3.15558i q^{53} +(-6.12444 + 3.24262i) q^{54} +0.113384 q^{55} +14.1218 q^{56} +(9.23803 - 1.51274i) q^{57} +(4.30534 - 4.30534i) q^{58} +(-4.51242 + 4.51242i) q^{59} +(0.0429000 - 0.00702495i) q^{60} -2.90645 q^{61} +2.07028 q^{62} +(6.35857 - 12.8090i) q^{63} -8.67858i q^{64} +(-0.408737 + 0.00787086i) q^{65} +(-1.87588 - 1.34797i) q^{66} +(-0.192651 + 0.192651i) q^{67} +0.646137i q^{68} +(-6.09902 - 4.38264i) q^{69} +(0.509693 - 0.509693i) q^{70} +(-11.1160 - 11.1160i) q^{71} +(-7.96068 - 3.95181i) q^{72} +(-2.10299 - 2.10299i) q^{73} -8.53385i q^{74} +(-5.04065 + 7.01474i) q^{75} +(0.845942 + 0.845942i) q^{76} +4.76679 q^{77} +(6.85589 + 4.72905i) q^{78} -9.65956 q^{79} +(-0.281276 - 0.281276i) q^{80} +(-7.16887 + 5.44126i) q^{81} -4.20875i q^{82} +(-11.0419 - 11.0419i) q^{83} +(1.80356 - 0.295336i) q^{84} +(0.234030 + 0.234030i) q^{85} +(-4.97527 + 4.97527i) q^{86} +(4.61437 - 6.42152i) q^{87} -2.96253i q^{88} +(10.4812 - 10.4812i) q^{89} +(-0.429954 + 0.144691i) q^{90} +(-17.1837 + 0.330900i) q^{91} -0.959823i q^{92} +(2.65338 - 0.434496i) q^{93} +11.0757 q^{94} +0.612798 q^{95} +(-0.348809 - 2.13011i) q^{96} +(-8.53028 + 8.53028i) q^{97} +(14.8268 - 14.8268i) q^{98} +(-2.68712 - 1.33393i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{6} - 16 q^{7}+O(q^{10}) \) 96 * q + 12 * q^6 - 16 * q^7	\( 96 q + 12 q^{6} - 16 q^{7} + 16 q^{13} - 16 q^{15} - 120 q^{16} - 28 q^{18} - 24 q^{19} + 24 q^{24} - 24 q^{27} + 56 q^{28} + 48 q^{31} - 16 q^{34} - 16 q^{37} + 80 q^{40} + 52 q^{42} + 4 q^{45} - 56 q^{46} + 28 q^{48} + 4 q^{54} + 4 q^{57} + 48 q^{58} + 4 q^{60} - 96 q^{61} - 36 q^{63} + 20 q^{66} - 16 q^{67} + 48 q^{70} - 16 q^{72} - 16 q^{73} - 88 q^{76} + 80 q^{78} + 16 q^{79} + 32 q^{81} + 52 q^{84} - 8 q^{85} - 48 q^{87} - 16 q^{91} - 36 q^{93} - 16 q^{94} - 108 q^{96} - 48 q^{97}+O(q^{100}) \) 96 * q + 12 * q^6 - 16 * q^7 + 16 * q^13 - 16 * q^15 - 120 * q^16 - 28 * q^18 - 24 * q^19 + 24 * q^24 - 24 * q^27 + 56 * q^28 + 48 * q^31 - 16 * q^34 - 16 * q^37 + 80 * q^40 + 52 * q^42 + 4 * q^45 - 56 * q^46 + 28 * q^48 + 4 * q^54 + 4 * q^57 + 48 * q^58 + 4 * q^60 - 96 * q^61 - 36 * q^63 + 20 * q^66 - 16 * q^67 + 48 * q^70 - 16 * q^72 - 16 * q^73 - 88 * q^76 + 80 * q^78 + 16 * q^79 + 32 * q^81 + 52 * q^84 - 8 * q^85 - 48 * q^87 - 16 * q^91 - 36 * q^93 - 16 * q^94 - 108 * q^96 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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