LMFDB - Embedded newform 429.2.j.a.122.16

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			122.16
Character	$\chi$	$=$	429.122
Dual form			429.2.j.a.320.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.786557 - 0.786557i) q^{2} +(-0.138475 - 1.72651i) q^{3} -0.762656i q^{4} +(-2.59877 - 2.59877i) q^{5} +(-1.24908 + 1.46691i) q^{6} +(1.66123 + 1.66123i) q^{7} +(-2.17299 + 2.17299i) q^{8} +(-2.96165 + 0.478155i) q^{9} +O(q^{10})$	\(q+(-0.786557 - 0.786557i) q^{2} +(-0.138475 - 1.72651i) q^{3} -0.762656i q^{4} +(-2.59877 - 2.59877i) q^{5} +(-1.24908 + 1.46691i) q^{6} +(1.66123 + 1.66123i) q^{7} +(-2.17299 + 2.17299i) q^{8} +(-2.96165 + 0.478155i) q^{9} +4.08816i q^{10} +(-0.707107 + 0.707107i) q^{11} +(-1.31673 + 0.105609i) q^{12} +(-2.30564 - 2.77200i) q^{13} -2.61330i q^{14} +(-4.12692 + 4.84665i) q^{15} +1.89305 q^{16} +0.227424 q^{17} +(2.70560 + 1.95341i) q^{18} +(3.47748 - 3.47748i) q^{19} +(-1.98196 + 1.98196i) q^{20} +(2.63809 - 3.09816i) q^{21} +1.11236 q^{22} +6.07423 q^{23} +(4.05258 + 3.45077i) q^{24} +8.50717i q^{25} +(-0.366819 + 3.99386i) q^{26} +(1.23565 + 5.04709i) q^{27} +(1.26695 - 1.26695i) q^{28} -3.16820i q^{29} +(7.05823 - 0.566106i) q^{30} +(-5.82470 + 5.82470i) q^{31} +(2.85698 + 2.85698i) q^{32} +(1.31874 + 1.12291i) q^{33} +(-0.178882 - 0.178882i) q^{34} -8.63429i q^{35} +(0.364668 + 2.25872i) q^{36} +(-6.11691 - 6.11691i) q^{37} -5.47048 q^{38} +(-4.46661 + 4.36456i) q^{39} +11.2942 q^{40} +(-2.60292 - 2.60292i) q^{41} +(-4.51189 + 0.361877i) q^{42} +0.246500i q^{43} +(0.539279 + 0.539279i) q^{44} +(8.93925 + 6.45402i) q^{45} +(-4.77773 - 4.77773i) q^{46} +(-6.19096 + 6.19096i) q^{47} +(-0.262139 - 3.26835i) q^{48} -1.48063i q^{49} +(6.69137 - 6.69137i) q^{50} +(-0.0314925 - 0.392649i) q^{51} +(-2.11408 + 1.75841i) q^{52} -5.98713i q^{53} +(2.99792 - 4.94174i) q^{54} +3.67521 q^{55} -7.21966 q^{56} +(-6.48544 - 5.52235i) q^{57} +(-2.49197 + 2.49197i) q^{58} +(-7.36078 + 7.36078i) q^{59} +(3.69632 + 3.14742i) q^{60} -10.4922 q^{61} +9.16292 q^{62} +(-5.71431 - 4.12565i) q^{63} -8.28045i q^{64} +(-1.21196 + 13.1956i) q^{65} +(-0.154034 - 1.92050i) q^{66} +(4.63058 - 4.63058i) q^{67} -0.173446i q^{68} +(-0.841127 - 10.4872i) q^{69} +(-6.79137 + 6.79137i) q^{70} +(2.55758 + 2.55758i) q^{71} +(5.39660 - 7.47465i) q^{72} +(4.26887 + 4.26887i) q^{73} +9.62261i q^{74} +(14.6877 - 1.17803i) q^{75} +(-2.65212 - 2.65212i) q^{76} -2.34933 q^{77} +(6.94622 + 0.0802664i) q^{78} +7.92269 q^{79} +(-4.91958 - 4.91958i) q^{80} +(8.54274 - 2.83225i) q^{81} +4.09469i q^{82} +(-2.99429 - 2.99429i) q^{83} +(-2.36283 - 2.01195i) q^{84} +(-0.591022 - 0.591022i) q^{85} +(0.193887 - 0.193887i) q^{86} +(-5.46992 + 0.438716i) q^{87} -3.07307i q^{88} +(-4.89478 + 4.89478i) q^{89} +(-1.95477 - 12.1077i) q^{90} +(0.774731 - 8.43514i) q^{91} -4.63255i q^{92} +(10.8630 + 9.24981i) q^{93} +9.73909 q^{94} -18.0743 q^{95} +(4.53698 - 5.32822i) q^{96} +(-6.93103 + 6.93103i) q^{97} +(-1.16460 + 1.16460i) q^{98} +(1.75610 - 2.43231i) 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 $

$2$	−0.786557	−	0.786557i	−0.556180	−	0.556180i	0.372038	−	0.928218i	$-0.378659\pi$
$2$	−0.786557	−	0.786557i	−0.556180	−	0.556180i	−0.928218	+	0.372038i	$0.878659\pi$
$3$	−0.138475	−	1.72651i	−0.0799484	−	0.996799i
$3$	−0.138475	−	1.72651i	−0.0799484	−	0.996799i
$4$		−	0.762656i		−	0.381328i
$5$	−2.59877	−	2.59877i	−1.16220	−	1.16220i	−0.983992	−	0.178211i	$-0.942969\pi$
$5$	−2.59877	−	2.59877i	−1.16220	−	1.16220i	−0.178211	−	0.983992i	$-0.557031\pi$
$6$	−1.24908	+	1.46691i	−0.509934	+	0.598865i
$7$	1.66123	+	1.66123i	0.627886	+	0.627886i	0.947536	−	0.319650i	$-0.103565\pi$
$7$	1.66123	+	1.66123i	0.627886	+	0.627886i	−0.319650	+	0.947536i	$0.603565\pi$
$8$	−2.17299	+	2.17299i	−0.768267	+	0.768267i
$9$	−2.96165	+	0.478155i	−0.987217	+	0.159385i
$10$			4.08816i			1.29279i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$12$	−1.31673	+	0.105609i	−0.380107	+	0.0304865i
$13$	−2.30564	−	2.77200i	−0.639471	−	0.768816i
$13$	−2.30564	−	2.77200i	−0.639471	−	0.768816i
$14$		−	2.61330i		−	0.698435i
$15$	−4.12692	+	4.84665i	−1.06557	+	1.25140i
$16$	1.89305			0.473261
$17$	0.227424			0.0551585			0.0275792	−	0.999620i	$-0.491220\pi$
$17$	0.227424			0.0551585			0.0275792	+	0.999620i	$0.491220\pi$
$18$	2.70560	+	1.95341i	0.637717	+	0.460423i
$19$	3.47748	−	3.47748i	0.797790	−	0.797790i	−0.184957	−	0.982747i	$-0.559215\pi$
$19$	3.47748	−	3.47748i	0.797790	−	0.797790i	0.982747	+	0.184957i	$0.0592146\pi$
$20$	−1.98196	+	1.98196i	−0.443180	+	0.443180i
$21$	2.63809	−	3.09816i	0.575677	−	0.676074i
$22$	1.11236			0.237156
$23$	6.07423			1.26656			0.633282	−	0.773921i	$-0.281707\pi$
$23$	6.07423			1.26656			0.633282	+	0.773921i	$0.281707\pi$
$24$	4.05258	+	3.45077i	0.827229	+	0.704386i
$25$			8.50717i			1.70143i
$26$	−0.366819	+	3.99386i	−0.0719391	+	0.783260i
$27$	1.23565	+	5.04709i	0.237801	+	0.971314i
$28$	1.26695	−	1.26695i	0.239430	−	0.239430i
$29$		−	3.16820i		−	0.588320i	−0.955756	−	0.294160i	$-0.904960\pi$
$29$		−	3.16820i		−	0.588320i	0.955756	−	0.294160i	$-0.0950399\pi$
$30$	7.05823	−	0.566106i	1.28865	−	0.103356i
$31$	−5.82470	+	5.82470i	−1.04615	+	1.04615i	−0.0472641	+	0.998882i	$0.515050\pi$
$31$	−5.82470	+	5.82470i	−1.04615	+	1.04615i	−0.998882	+	0.0472641i	$0.984950\pi$
$32$	2.85698	+	2.85698i	0.505048	+	0.505048i
$33$	1.31874	+	1.12291i	0.229563	+	0.195473i
$34$	−0.178882	−	0.178882i	−0.0306780	−	0.0306780i
$35$		−	8.63429i		−	1.45946i
$36$	0.364668	+	2.25872i	0.0607779	+	0.376453i
$37$	−6.11691	−	6.11691i	−1.00561	−	1.00561i	−0.999984	−	0.00563029i	$-0.998208\pi$
$37$	−6.11691	−	6.11691i	−1.00561	−	1.00561i	−0.00563029	−	0.999984i	$-0.501792\pi$
$38$	−5.47048			−0.887429
$39$	−4.46661	+	4.36456i	−0.715230	+	0.698889i
$40$	11.2942			1.78576
$41$	−2.60292	−	2.60292i	−0.406508	−	0.406508i	0.474011	−	0.880519i	$-0.342806\pi$
$41$	−2.60292	−	2.60292i	−0.406508	−	0.406508i	−0.880519	+	0.474011i	$0.842806\pi$
$42$	−4.51189	+	0.361877i	−0.696199	+	0.0558388i
$43$			0.246500i			0.0375909i	0.999823	+	0.0187955i	$0.00598313\pi$
$43$			0.246500i			0.0375909i	−0.999823	+	0.0187955i	$0.994017\pi$
$44$	0.539279	+	0.539279i	0.0812994	+	0.0812994i
$45$	8.93925	+	6.45402i	1.33258	+	0.962109i
$46$	−4.77773	−	4.77773i	−0.704438	−	0.704438i
$47$	−6.19096	+	6.19096i	−0.903045	+	0.903045i	−0.995698	−	0.0926539i	$-0.970465\pi$
$47$	−6.19096	+	6.19096i	−0.903045	+	0.903045i	0.0926539	+	0.995698i	$0.470465\pi$
$48$	−0.262139	−	3.26835i	−0.0378365	−	0.471746i
$49$		−	1.48063i		−	0.211519i
$50$	6.69137	−	6.69137i	0.946303	−	0.946303i
$51$	−0.0314925	−	0.392649i	−0.00440983	−	0.0549819i
$52$	−2.11408	+	1.75841i	−0.293171	+	0.243848i
$53$		−	5.98713i		−	0.822395i	−0.911546	−	0.411198i	$-0.865111\pi$
$53$		−	5.98713i		−	0.822395i	0.911546	−	0.411198i	$-0.134889\pi$
$54$	2.99792	−	4.94174i	0.407965	−	0.672485i
$55$	3.67521			0.495565
$56$	−7.21966			−0.964768
$57$	−6.48544	−	5.52235i	−0.859018	−	0.731454i
$58$	−2.49197	+	2.49197i	−0.327212	+	0.327212i
$59$	−7.36078	+	7.36078i	−0.958292	+	0.958292i	−0.999164	−	0.0408723i	$-0.986986\pi$
$59$	−7.36078	+	7.36078i	−0.958292	+	0.958292i	0.0408723	+	0.999164i	$0.486986\pi$
$60$	3.69632	+	3.14742i	0.477193	+	0.406330i
$61$	−10.4922			−1.34339			−0.671696	−	0.740827i	$-0.734434\pi$
$61$	−10.4922			−1.34339			−0.671696	+	0.740827i	$0.734434\pi$
$62$	9.16292			1.16369
$63$	−5.71431	−	4.12565i	−0.719935	−	0.519784i
$64$		−	8.28045i		−	1.03506i
$65$	−1.21196	+	13.1956i	−0.150325	+	1.63671i
$66$	−0.154034	−	1.92050i	−0.0189602	−	0.236397i
$67$	4.63058	−	4.63058i	0.565715	−	0.565715i	−0.365210	−	0.930925i	$-0.619003\pi$
$67$	4.63058	−	4.63058i	0.565715	−	0.565715i	0.930925	+	0.365210i	$0.119003\pi$
$68$		−	0.173446i		−	0.0210335i
$69$	−0.841127	−	10.4872i	−0.101260	−	1.26251i
$70$	−6.79137	+	6.79137i	−0.811723	+	0.811723i
$71$	2.55758	+	2.55758i	0.303529	+	0.303529i	0.842393	−	0.538864i	$-0.181146\pi$
$71$	2.55758	+	2.55758i	0.303529	+	0.303529i	−0.538864	+	0.842393i	$0.681146\pi$
$72$	5.39660	−	7.47465i	0.635995	−	0.880896i
$73$	4.26887	+	4.26887i	0.499634	+	0.499634i	0.911324	−	0.411690i	$-0.135061\pi$
$73$	4.26887	+	4.26887i	0.499634	+	0.499634i	−0.411690	+	0.911324i	$0.635061\pi$
$74$			9.62261i			1.11861i
$75$	14.6877	−	1.17803i	1.69599	−	0.136027i
$76$	−2.65212	−	2.65212i	−0.304219	−	0.304219i
$77$	−2.34933			−0.267731
$78$	6.94622	+	0.0802664i	0.786505	+	0.00908838i
$79$	7.92269			0.891372			0.445686	−	0.895189i	$-0.352960\pi$
$79$	7.92269			0.891372			0.445686	+	0.895189i	$0.352960\pi$
$80$	−4.91958	−	4.91958i	−0.550026	−	0.550026i
$81$	8.54274	−	2.83225i	0.949193	−	0.314695i
$82$			4.09469i			0.452183i
$83$	−2.99429	−	2.99429i	−0.328666	−	0.328666i	0.523413	−	0.852079i	$-0.324658\pi$
$83$	−2.99429	−	2.99429i	−0.328666	−	0.328666i	−0.852079	+	0.523413i	$0.824658\pi$
$84$	−2.36283	−	2.01195i	−0.257806	−	0.219522i
$85$	−0.591022	−	0.591022i	−0.0641053	−	0.0641053i
$86$	0.193887	−	0.193887i	0.0209073	−	0.0209073i
$87$	−5.46992	+	0.438716i	−0.586437	+	0.0470353i
$88$		−	3.07307i		−	0.327590i
$89$	−4.89478	+	4.89478i	−0.518845	+	0.518845i	−0.917222	−	0.398377i	$-0.869574\pi$
$89$	−4.89478	+	4.89478i	−0.518845	+	0.518845i	0.398377	+	0.917222i	$0.369574\pi$
$90$	−1.95477	−	12.1077i	−0.206051	−	1.27626i
$91$	0.774731	−	8.43514i	0.0812139	−	0.884243i
$92$		−	4.63255i		−	0.482976i
$93$	10.8630	+	9.24981i	1.12644	+	0.959160i
$94$	9.73909			1.00451
$95$	−18.0743			−1.85439
$96$	4.53698	−	5.32822i	0.463054	−	0.543810i
$97$	−6.93103	+	6.93103i	−0.703740	+	0.703740i	−0.965211	−	0.261471i	$-0.915792\pi$
$97$	−6.93103	+	6.93103i	−0.703740	+	0.703740i	0.261471	+	0.965211i	$0.415792\pi$
$98$	−1.16460	+	1.16460i	−0.117643	+	0.117643i
$99$	1.75610	−	2.43231i	0.176494	−	0.244456i
$100$	6.48804			0.648804
$101$	−6.20672			−0.617592			−0.308796	−	0.951128i	$-0.599926\pi$
$101$	−6.20672			−0.617592			−0.308796	+	0.951128i	$0.599926\pi$
$102$	−0.284070	+	0.333612i	−0.0281272	+	0.0330325i
$103$		−	8.43371i		−	0.830998i	−0.909594	−	0.415499i	$-0.863607\pi$
$103$		−	8.43371i		−	0.830998i	0.909594	−	0.415499i	$-0.136393\pi$
$104$	11.0337	+	1.01339i	1.08194	+	0.0993714i
$105$	−14.9072	+	1.19563i	−1.45479	+	0.116682i
$106$	−4.70922	+	4.70922i	−0.457400	+	0.457400i
$107$		−	16.6580i		−	1.61039i	−0.593013	−	0.805193i	$-0.702062\pi$
$107$		−	16.6580i		−	1.61039i	0.593013	−	0.805193i	$-0.297938\pi$
$108$	3.84920	−	0.942376i	0.370389	−	0.0906802i
$109$	3.19560	−	3.19560i	0.306083	−	0.306083i	−0.537305	−	0.843388i	$-0.680558\pi$
$109$	3.19560	−	3.19560i	0.306083	−	0.306083i	0.843388	+	0.537305i	$0.180558\pi$
$110$	−2.89076	−	2.89076i	−0.275623	−	0.275623i
$111$	−9.71385	+	11.4079i	−0.921998	+	1.08279i
$112$	3.14478	+	3.14478i	0.297154	+	0.297154i
$113$		−	15.5226i		−	1.46024i	−0.683318	−	0.730121i	$-0.739464\pi$
$113$		−	15.5226i		−	1.46024i	0.683318	−	0.730121i	$-0.260536\pi$
$114$	0.757523	+	9.44482i	0.0709485	+	0.884588i
$115$	−15.7855	−	15.7855i	−1.47201	−	1.47201i
$116$	−2.41625			−0.224343
$117$	8.15396	+	7.10725i	0.753834	+	0.657065i
$118$	11.5794			1.06597
$119$	0.377804	+	0.377804i	0.0346332	+	0.0346332i
$120$	−1.56396	−	19.4995i	−0.142769	−	1.78005i
$121$		−	1.00000i		−	0.0909091i
$122$	8.25273	+	8.25273i	0.747167	+	0.747167i
$123$	−4.13352	+	4.85440i	−0.372707	+	0.437706i
$124$	4.44224	+	4.44224i	0.398925	+	0.398925i
$125$	9.11431	−	9.11431i	0.815208	−	0.815208i
$126$	1.24956	+	7.73969i	0.111320	+	0.689507i
$127$		−	8.15520i		−	0.723657i	−0.932245	−	0.361829i	$-0.882153\pi$
$127$		−	8.15520i		−	0.723657i	0.932245	−	0.361829i	$-0.117847\pi$
$128$	−0.799081	+	0.799081i	−0.0706295	+	0.0706295i
$129$	0.425584	−	0.0341340i	0.0374706	−	0.00300533i
$130$	11.3324	−	9.42583i	0.993916	−	0.826700i
$131$			12.7260i			1.11187i	0.831225	+	0.555937i	$0.187640\pi$
$131$			12.7260i			1.11187i	−0.831225	+	0.555937i	$0.812360\pi$
$132$	0.856392	−	1.00575i	0.0745394	−	0.0875389i
$133$	11.5538			1.00184
$134$	−7.28443			−0.629279
$135$	9.90505	−	16.3274i	0.852491	−	1.40524i
$136$	−0.494190	+	0.494190i	−0.0423764	+	0.0423764i
$137$	9.53657	−	9.53657i	0.814764	−	0.814764i	−0.170580	−	0.985344i	$-0.554564\pi$
$137$	9.53657	−	9.53657i	0.814764	−	0.814764i	0.985344	+	0.170580i	$0.0545641\pi$
$138$	−7.58719	+	8.91038i	−0.645864	+	0.758502i
$139$	−8.47564			−0.718894			−0.359447	−	0.933165i	$-0.617035\pi$
$139$	−8.47564			−0.718894			−0.359447	+	0.933165i	$0.617035\pi$
$140$	−6.58499			−0.556533
$141$	11.5460	+	9.83144i	0.972351	+	0.827957i
$142$		−	4.02337i		−	0.337633i
$143$	3.59044	+	0.329766i	0.300248	+	0.0275764i
$144$	−5.60654	+	0.905169i	−0.467211	+	0.0754307i
$145$	−8.23342	+	8.23342i	−0.683748	+	0.683748i
$146$		−	6.71543i		−	0.555773i
$147$	−2.55632	+	0.205030i	−0.210842	+	0.0169106i
$148$	−4.66510	+	4.66510i	−0.383469	+	0.383469i
$149$	−11.8402	−	11.8402i	−0.969986	−	0.969986i	0.0295767	−	0.999563i	$-0.490584\pi$
$149$	−11.8402	−	11.8402i	−0.969986	−	0.969986i	−0.999563	+	0.0295767i	$0.990584\pi$
$150$	−12.4793	−	10.6261i	−1.01893	−	0.867619i
$151$	−3.73897	−	3.73897i	−0.304273	−	0.304273i	0.538410	−	0.842683i	$-0.319025\pi$
$151$	−3.73897	−	3.73897i	−0.304273	−	0.304273i	−0.842683	+	0.538410i	$0.819025\pi$
$152$			15.1131i			1.22583i
$153$	−0.673551	+	0.108744i	−0.0544533	+	0.00879143i
$154$	1.84789	+	1.84789i	0.148907	+	0.148907i
$155$	30.2740			2.43167
$156$	3.32866	+	3.40648i	0.266506	+	0.272737i
$157$	−18.3723			−1.46627			−0.733134	−	0.680084i	$-0.761943\pi$
$157$	−18.3723			−1.46627			−0.733134	+	0.680084i	$0.761943\pi$
$158$	−6.23165	−	6.23165i	−0.495763	−	0.495763i
$159$	−10.3368	+	0.829066i	−0.819763	+	0.0657492i
$160$		−	14.8493i		−	1.17394i
$161$	10.0907	+	10.0907i	0.795258	+	0.795258i
$162$	−8.94708	−	4.49162i	−0.702949	−	0.352895i
$163$	−5.59332	−	5.59332i	−0.438103	−	0.438103i	0.453270	−	0.891373i	$-0.350257\pi$
$163$	−5.59332	−	5.59332i	−0.438103	−	0.438103i	−0.891373	+	0.453270i	$0.850257\pi$
$164$	−1.98513	+	1.98513i	−0.155013	+	0.155013i
$165$	−0.508924	−	6.34527i	−0.0396196	−	0.493979i
$166$			4.71036i			0.365595i
$167$	14.2303	−	14.2303i	1.10118	−	1.10118i	0.106906	−	0.994269i	$-0.465906\pi$
$167$	14.2303	−	14.2303i	1.10118	−	1.10118i	0.994269	−	0.106906i	$-0.0340944\pi$
$168$	0.999740	+	12.4648i	0.0771316	+	0.961679i
$169$	−2.36801	+	12.7825i	−0.182155	+	0.983270i
$170$			0.929745i			0.0713082i
$171$	−8.63631	+	11.9619i	−0.660435	+	0.914747i
$172$	0.187995			0.0143345
$173$	10.8528			0.825124			0.412562	−	0.910929i	$-0.364634\pi$
$173$	10.8528			0.825124			0.412562	+	0.910929i	$0.364634\pi$
$174$	4.64748	+	3.95733i	0.352325	+	0.300004i
$175$	−14.1324	+	14.1324i	−1.06831	+	1.06831i
$176$	−1.33859	+	1.33859i	−0.100900	+	0.100900i
$177$	13.7277	+	11.6892i	1.03184	+	0.878611i
$178$	7.70005			0.577143
$179$	−3.26806			−0.244266			−0.122133	−	0.992514i	$-0.538973\pi$
$179$	−3.26806			−0.244266			−0.122133	+	0.992514i	$0.538973\pi$
$180$	4.92220	−	6.81757i	0.366879	−	0.508151i
$181$			9.34413i			0.694544i	0.937764	+	0.347272i	$0.112892\pi$
$181$			9.34413i			0.694544i	−0.937764	+	0.347272i	$0.887108\pi$
$182$	−7.24409	+	6.02535i	−0.536968	+	0.446629i
$183$	1.45291	+	18.1149i	0.107402	+	1.33909i
$184$	−13.1992	+	13.1992i	−0.973060	+	0.973060i
$185$			31.7929i			2.33746i
$186$	−1.26883	−	15.8198i	−0.0930353	−	1.15997i
$187$	−0.160813	+	0.160813i	−0.0117598	+	0.0117598i
$188$	4.72157	+	4.72157i	0.344356	+	0.344356i
$189$	−6.33168	+	10.4371i	−0.460562	+	0.759186i
$190$	14.2165	+	14.2165i	1.03137	+	1.03137i
$191$			4.36071i			0.315530i	0.987477	+	0.157765i	$0.0504289\pi$
$191$			4.36071i			0.315530i	−0.987477	+	0.157765i	$0.949571\pi$
$192$	−14.2963	+	1.14663i	−1.03174	+	0.0827511i
$193$	13.5489	+	13.5489i	0.975270	+	0.975270i	0.999702	−	0.0244313i	$-0.00777748\pi$
$193$	13.5489	+	13.5489i	0.975270	+	0.975270i	−0.0244313	+	0.999702i	$0.507777\pi$
$194$	10.9033			0.782812
$195$	22.9501	+	0.265198i	1.64349	+	0.0189912i
$196$	−1.12921			−0.0806580
$197$	14.0244	+	14.0244i	0.999195	+	0.999195i	1.00000		0.000804669i	$-0.000256134\pi$
$197$	14.0244	+	14.0244i	0.999195	+	0.999195i	−0.000804669		1.00000i	$0.500256\pi$
$198$	−3.29442	+	0.531880i	−0.234124	+	0.0377991i
$199$		−	21.1544i		−	1.49959i	−0.661668	−	0.749797i	$-0.730151\pi$
$199$		−	21.1544i		−	1.49959i	0.661668	−	0.749797i	$-0.269849\pi$
$200$	−18.4860	−	18.4860i	−1.30715	−	1.30715i
$201$	−8.63594	−	7.35351i	−0.609132	−	0.518676i
$202$	4.88194	+	4.88194i	0.343492	+	0.343492i
$203$	5.26311	−	5.26311i	0.369398	−	0.369398i
$204$	−0.299456	+	0.0240179i	−0.0209661	+	0.00168159i
$205$			13.5288i			0.944890i
$206$	−6.63359	+	6.63359i	−0.462184	+	0.462184i
$207$	−17.9897	+	2.90442i	−1.25037	+	0.201871i
$208$	−4.36469	−	5.24753i	−0.302637	−	0.363851i
$209$			4.91790i			0.340179i
$210$	12.6658	+	10.7849i	0.874021	+	0.744229i
$211$	17.0793			1.17579			0.587895	−	0.808937i	$-0.299957\pi$
$211$	17.0793			1.17579			0.587895	+	0.808937i	$0.299957\pi$
$212$	−4.56612			−0.313602
$213$	4.06152	−	4.76984i	0.278291	−	0.326824i
$214$	−13.1024	+	13.1024i	−0.895665	+	0.895665i
$215$	0.640596	−	0.640596i	0.0436883	−	0.0436883i
$216$	−13.6523	−	8.28222i	−0.928923	−	0.563533i
$217$	−19.3523			−1.31372
$218$	−5.02705			−0.340475
$219$	6.77911	−	7.96137i	0.458090	−	0.537980i
$220$		−	2.80292i		−	0.188973i
$221$	−0.524359	−	0.630421i	−0.0352722	−	0.0424067i
$222$	16.6135	−	1.33249i	1.11502	−	0.0894307i
$223$	11.1126	−	11.1126i	0.744154	−	0.744154i	−0.229221	−	0.973375i	$-0.573618\pi$
$223$	11.1126	−	11.1126i	0.744154	−	0.744154i	0.973375	+	0.229221i	$0.0736177\pi$
$224$			9.49222i			0.634225i
$225$	−4.06774	−	25.1952i	−0.271183	−	1.67968i
$226$	−12.2094	+	12.2094i	−0.812158	+	0.812158i
$227$	−19.0632	−	19.0632i	−1.26527	−	1.26527i	−0.948503	−	0.316769i	$-0.897402\pi$
$227$	−19.0632	−	19.0632i	−1.26527	−	1.26527i	−0.316769	−	0.948503i	$-0.602598\pi$
$228$	−4.21165	+	4.94616i	−0.278924	+	0.327567i
$229$	10.5183	+	10.5183i	0.695068	+	0.695068i	0.963343	−	0.268274i	$-0.0864534\pi$
$229$	10.5183	+	10.5183i	0.695068	+	0.695068i	−0.268274	+	0.963343i	$0.586453\pi$
$230$			24.8324i			1.63740i
$231$	0.325323	+	4.05614i	0.0214047	+	0.266874i
$232$	6.88446	+	6.88446i	0.451987	+	0.451987i
$233$	12.1195			0.793975			0.396987	−	0.917824i	$-0.370056\pi$
$233$	12.1195			0.793975			0.396987	+	0.917824i	$0.370056\pi$
$234$	−0.823295	−	12.0038i	−0.0538205	−	0.784714i
$235$	32.1777			2.09904
$236$	5.61374	+	5.61374i	0.365423	+	0.365423i
$237$	−1.09709	−	13.6786i	−0.0712638	−	0.888519i
$238$		−	0.594328i		−	0.0385246i
$239$	−15.2342	−	15.2342i	−0.985416	−	0.985416i	0.0144796	−	0.999895i	$-0.495391\pi$
$239$	−15.2342	−	15.2342i	−0.985416	−	0.985416i	−0.999895	+	0.0144796i	$0.995391\pi$
$240$	−7.81245	+	9.17493i	−0.504292	+	0.592239i
$241$	−6.65164	−	6.65164i	−0.428470	−	0.428470i	0.459637	−	0.888107i	$-0.347980\pi$
$241$	−6.65164	−	6.65164i	−0.428470	−	0.428470i	−0.888107	+	0.459637i	$0.847980\pi$
$242$	−0.786557	+	0.786557i	−0.0505618	+	0.0505618i
$243$	−6.07286	−	14.3569i	−0.389574	−	0.920995i
$244$			8.00195i			0.512272i
$245$	−3.84782	+	3.84782i	−0.245828	+	0.245828i
$246$	7.06951	−	0.567011i	0.450736	−	0.0361513i
$247$	−17.6574	−	1.62176i	−1.12352	−	0.103190i
$248$		−	25.3140i		−	1.60744i
$249$	−4.75503	+	5.58429i	−0.301337	+	0.353890i
$250$	−14.3378			−0.906805
$251$	14.8981			0.940361			0.470181	−	0.882570i	$-0.344189\pi$
$251$	14.8981			0.940361			0.470181	+	0.882570i	$0.344189\pi$
$252$	−3.14645	+	4.35805i	−0.198208	+	0.274531i
$253$	−4.29513	+	4.29513i	−0.270033	+	0.270033i
$254$	−6.41453	+	6.41453i	−0.402484	+	0.402484i
$255$	−0.938562	+	1.10225i	−0.0587750	+	0.0690253i
$256$	−15.3039			−0.956491
$257$	7.47531			0.466297			0.233149	−	0.972441i	$-0.425097\pi$
$257$	7.47531			0.466297			0.233149	+	0.972441i	$0.425097\pi$
$258$	−0.361595	−	0.307898i	−0.0225119	−	0.0191689i
$259$		−	20.3232i		−	1.26282i
$260$	10.0637	+	0.924308i	0.624125	+	0.0573232i
$261$	1.51489	+	9.38310i	0.0937694	+	0.580800i
$262$	10.0097	−	10.0097i	0.618402	−	0.618402i
$263$			2.70926i			0.167060i	0.996505	+	0.0835301i	$0.0266195\pi$
$263$			2.70926i			0.167060i	−0.996505	+	0.0835301i	$0.973381\pi$
$264$	−5.30567	+	0.425542i	−0.326541	+	0.0261903i
$265$	−15.5591	+	15.5591i	−0.955790	+	0.955790i
$266$	−9.08772	−	9.08772i	−0.557204	−	0.557204i
$267$	9.12867	+	7.77306i	0.558665	+	0.475704i
$268$	−3.53154	−	3.53154i	−0.215723	−	0.215723i
$269$			1.42683i			0.0869956i	0.999054	+	0.0434978i	$0.0138501\pi$
$269$			1.42683i			0.0869956i	−0.999054	+	0.0434978i	$0.986150\pi$
$270$	−20.6333	+	5.05153i	−1.25570	+	0.307427i
$271$	−10.7137	−	10.7137i	−0.650809	−	0.650809i	0.302379	−	0.953188i	$-0.402219\pi$
$271$	−10.7137	−	10.7137i	−0.650809	−	0.650809i	−0.953188	+	0.302379i	$0.902219\pi$
$272$	0.430524			0.0261044
$273$	−14.6706	−	0.169525i	−0.887905	−	0.0102601i
$274$	−15.0021			−0.906311
$275$	−6.01548	−	6.01548i	−0.362747	−	0.362747i
$276$	−7.99812	+	0.641491i	−0.481430	+	0.0386132i
$277$			14.4673i			0.869257i	0.900610	+	0.434628i	$0.143120\pi$
$277$			14.4673i			0.869257i	−0.900610	+	0.434628i	$0.856880\pi$
$278$	6.66658	+	6.66658i	0.399835	+	0.399835i
$279$	14.4656	−	20.0358i	0.866033	−	1.19951i
$280$	18.7622	+	18.7622i	1.12126	+	1.12126i
$281$	15.3890	−	15.3890i	0.918033	−	0.918033i	−0.0788534	−	0.996886i	$-0.525126\pi$
$281$	15.3890	−	15.3890i	0.918033	−	0.918033i	0.996886	+	0.0788534i	$0.0251259\pi$
$282$	−1.34862	−	16.8146i	−0.0803090	−	1.00130i
$283$			8.84864i			0.525997i	0.964796	+	0.262999i	$0.0847115\pi$
$283$			8.84864i			0.525997i	−0.964796	+	0.262999i	$0.915289\pi$
$284$	1.95055	−	1.95055i	0.115744	−	0.115744i
$285$	2.50284	+	31.2055i	0.148255	+	1.84845i
$286$	−2.56471	−	3.08347i	−0.151654	−	0.182329i
$287$		−	8.64810i		−	0.510481i
$288$	−9.82747	−	7.09531i	−0.579089	−	0.418095i
$289$	−16.9483			−0.996958
$290$	12.9521			0.760574
$291$	12.9262	+	11.0067i	0.757750	+	0.645224i
$292$	3.25568	−	3.25568i	0.190524	−	0.190524i
$293$	10.9028	−	10.9028i	0.636950	−	0.636950i	−0.312852	−	0.949802i	$-0.601284\pi$
$293$	10.9028	−	10.9028i	0.636950	−	0.636950i	0.949802	+	0.312852i	$0.101284\pi$
$294$	2.17196	+	1.84942i	0.126671	+	0.107861i
$295$	38.2579			2.22746
$296$	26.5839			1.54516
$297$	−4.44257	−	2.69510i	−0.257784	−	0.156385i
$298$			18.6260i			1.07897i
$299$	−14.0050	−	16.8378i	−0.809931	−	0.973755i
$300$	−0.898429	−	11.2016i	−0.0518708	−	0.646727i
$301$	−0.409493	+	0.409493i	−0.0236028	+	0.0236028i
$302$			5.88183i			0.338461i
$303$	0.859473	+	10.7159i	0.0493755	+	0.615615i
$304$	6.58303	−	6.58303i	0.377563	−	0.377563i
$305$	27.2668	+	27.2668i	1.56129	+	1.56129i
$306$	0.615319	+	0.444253i	0.0351755	+	0.0253962i
$307$	22.5181	+	22.5181i	1.28518	+	1.28518i	0.937681	+	0.347496i	$0.112968\pi$
$307$	22.5181	+	22.5181i	1.28518	+	1.28518i	0.347496	+	0.937681i	$0.387032\pi$
$308$			1.79173i			0.102093i
$309$	−14.5609	+	1.16786i	−0.828338	+	0.0664370i
$310$	−23.8123	−	23.8123i	−1.35245	−	1.35245i
$311$	−6.14032			−0.348186			−0.174093	−	0.984729i	$-0.555699\pi$
$311$	−6.14032			−0.348186			−0.174093	+	0.984729i	$0.555699\pi$
$312$	0.221748	−	19.1900i	0.0125540	−	1.08642i
$313$	23.9065			1.35128			0.675639	−	0.737233i	$-0.263868\pi$
$313$	23.9065			1.35128			0.675639	+	0.737233i	$0.263868\pi$
$314$	14.4509	+	14.4509i	0.815509	+	0.815509i
$315$	4.12853	+	25.5718i	0.232616	+	1.44081i
$316$		−	6.04228i		−	0.339905i
$317$	−6.87742	−	6.87742i	−0.386274	−	0.386274i	0.487082	−	0.873356i	$-0.338061\pi$
$317$	−6.87742	−	6.87742i	−0.386274	−	0.386274i	−0.873356	+	0.487082i	$0.838061\pi$
$318$	8.78260	+	7.47839i	0.492504	+	0.419367i
$319$	2.24026	+	2.24026i	0.125430	+	0.125430i
$320$	−21.5190	+	21.5190i	−1.20295	+	1.20295i
$321$	−28.7601	+	2.30671i	−1.60523	+	0.128748i
$322$		−	15.8738i		−	0.884613i
$323$	0.790864	−	0.790864i	0.0440048	−	0.0440048i
$324$	−2.16003	−	6.51517i	−0.120002	−	0.361954i
$325$	23.5819	−	19.6145i	1.30809	−	1.08802i
$326$			8.79894i			0.487328i
$327$	−5.95974	−	5.07472i	−0.329574	−	0.280633i
$328$	11.3122			0.624613
$329$	−20.5692			−1.13402
$330$	−4.59062	+	5.39122i	−0.252705	+	0.296777i
$331$	−12.8416	+	12.8416i	−0.705837	+	0.705837i	−0.965657	−	0.259820i	$-0.916337\pi$
$331$	−12.8416	+	12.8416i	−0.705837	+	0.705837i	0.259820	+	0.965657i	$0.416337\pi$
$332$	−2.28361	+	2.28361i	−0.125329	+	0.125329i
$333$	21.0410	+	15.1913i	1.15304	+	0.832479i
$334$	−22.3859			−1.22490
$335$	−24.0676			−1.31495
$336$	4.99402	−	5.86496i	0.272446	−	0.319960i
$337$		−	28.3421i		−	1.54389i	−0.635689	−	0.771945i	$-0.719284\pi$
$337$		−	28.3421i		−	1.54389i	0.635689	−	0.771945i	$-0.280716\pi$
$338$	11.9168	−	8.19160i	0.648186	−	0.445564i
$339$	−26.7999	+	2.14949i	−1.45557	+	0.116744i
$340$	−0.450746	+	0.450746i	−0.0244452	+	0.0244452i
$341$		−	8.23737i		−	0.446078i
$342$	16.2016	−	2.61574i	0.876085	−	0.141443i
$343$	14.0883	−	14.0883i	0.760695	−	0.760695i
$344$	−0.535642	−	0.535642i	−0.0288799	−	0.0288799i
$345$	−25.0679	+	29.4397i	−1.34961	+	1.58498i
$346$	−8.53636	−	8.53636i	−0.458918	−	0.458918i
$347$			13.2071i			0.708994i	0.935057	+	0.354497i	$0.115348\pi$
$347$			13.2071i			0.708994i	−0.935057	+	0.354497i	$0.884652\pi$
$348$	0.334589	+	4.17167i	0.0179359	+	0.223625i
$349$	−3.57395	−	3.57395i	−0.191309	−	0.191309i	0.604953	−	0.796262i	$-0.293192\pi$
$349$	−3.57395	−	3.57395i	−0.191309	−	0.191309i	−0.796262	+	0.604953i	$0.793192\pi$
$350$	22.2318			1.18834
$351$	11.1416	−	15.0620i	0.594694	−	0.803952i
$352$	−4.04039			−0.215353
$353$	11.4551	+	11.4551i	0.609692	+	0.609692i	0.942866	−	0.333174i	$-0.108120\pi$
$353$	11.4551	+	11.4551i	0.609692	+	0.609692i	−0.333174	+	0.942866i	$0.608120\pi$
$354$	−1.60345	−	19.9918i	−0.0852222	−	1.06255i
$355$		−	13.2931i		−	0.705525i
$356$	3.73303	+	3.73303i	0.197850	+	0.197850i
$357$	0.599964	−	0.704597i	0.0317535	−	0.0372912i
$358$	2.57051	+	2.57051i	0.135856	+	0.135856i
$359$	2.15361	−	2.15361i	0.113663	−	0.113663i	−0.647988	−	0.761651i	$-0.724389\pi$
$359$	2.15361	−	2.15361i	0.113663	−	0.113663i	0.761651	+	0.647988i	$0.224389\pi$
$360$	−33.4494	+	5.40036i	−1.76294	+	0.284624i
$361$		−	5.18579i		−	0.272936i
$362$	7.34969	−	7.34969i	0.386291	−	0.386291i
$363$	−1.72651	+	0.138475i	−0.0906181	+	0.00726804i
$364$	−6.43311	−	0.590853i	−0.337186	−	0.0309691i
$365$		−	22.1876i		−	1.16135i
$366$	13.1056	−	15.3912i	0.685041	−	0.804510i
$367$	−5.00133			−0.261067			−0.130534	−	0.991444i	$-0.541669\pi$
$367$	−5.00133			−0.261067			−0.130534	+	0.991444i	$0.541669\pi$
$368$	11.4988			0.599416
$369$	8.95354	+	6.46434i	0.466103	+	0.336520i
$370$	25.0069	−	25.0069i	1.30005	−	1.30005i
$371$	9.94599	−	9.94599i	0.516370	−	0.516370i
$372$	7.05442	−	8.28469i	0.365754	−	0.429541i
$373$	27.4406			1.42082			0.710411	−	0.703787i	$-0.248509\pi$
$373$	27.4406			1.42082			0.710411	+	0.703787i	$0.248509\pi$
$374$	0.252977			0.0130812
$375$	−16.9980	−	14.4738i	−0.877774	−	0.747424i
$376$		−	26.9058i		−	1.38756i
$377$	−8.78227	+	7.30475i	−0.452310	+	0.376214i
$378$	13.1896	−	3.22913i	0.678400	−	0.166089i
$379$	6.58280	−	6.58280i	0.338136	−	0.338136i	−0.517530	−	0.855665i	$-0.673148\pi$
$379$	6.58280	−	6.58280i	0.338136	−	0.338136i	0.855665	+	0.517530i	$0.173148\pi$
$380$			13.7845i			0.707129i
$381$	−14.0800	+	1.12929i	−0.721341	+	0.0578552i
$382$	3.42995	−	3.42995i	0.175492	−	0.175492i
$383$	18.7244	+	18.7244i	0.956771	+	0.956771i	0.999104	−	0.0423324i	$-0.0134789\pi$
$383$	18.7244	+	18.7244i	0.956771	+	0.956771i	−0.0423324	+	0.999104i	$0.513479\pi$
$384$	1.49027	+	1.26897i	0.0760501	+	0.0647567i
$385$	6.10537	+	6.10537i	0.311158	+	0.311158i
$386$		−	21.3139i		−	1.08485i
$387$	−0.117865	−	0.730047i	−0.00599143	−	0.0371104i
$388$	5.28599	+	5.28599i	0.268356	+	0.268356i
$389$	−3.42773			−0.173793			−0.0868963	−	0.996217i	$-0.527695\pi$
$389$	−3.42773			−0.173793			−0.0868963	+	0.996217i	$0.527695\pi$
$390$	−17.8430	−	18.2602i	−0.903516	−	0.924641i
$391$	1.38143			0.0698618
$392$	3.21739	+	3.21739i	0.162503	+	0.162503i
$393$	21.9715	−	1.76223i	1.10831	−	0.0888925i
$394$		−	22.0619i		−	1.11146i
$395$	−20.5892	−	20.5892i	−1.03596	−	1.03596i
$396$	−1.85501	−	1.33930i	−0.0932180	−	0.0673022i
$397$	−21.1003	−	21.1003i	−1.05899	−	1.05899i	−0.998147	−	0.0608449i	$-0.980620\pi$
$397$	−21.1003	−	21.1003i	−1.05899	−	1.05899i	−0.0608449	−	0.998147i	$-0.519380\pi$
$398$	−16.6391	+	16.6391i	−0.834044	+	0.834044i
$399$	−1.59991	−	19.9477i	−0.0800956	−	0.998635i
$400$			16.1045i			0.805223i
$401$	−13.6307	+	13.6307i	−0.680685	+	0.680685i	−0.960155	−	0.279470i	$-0.909841\pi$
$401$	−13.6307	+	13.6307i	−0.680685	+	0.680685i	0.279470	+	0.960155i	$0.409841\pi$
$402$	1.00871	+	12.5766i	0.0503098	+	0.627265i
$403$	29.5758	+	2.71641i	1.47327	+	0.135314i
$404$			4.73359i			0.235505i
$405$	−29.5609	−	14.8402i	−1.46889	−	0.737416i
$406$	−8.27948			−0.410903
$407$	8.65062			0.428795
$408$	0.921654	+	0.784789i	0.0456287	+	0.0388528i
$409$	−16.6210	+	16.6210i	−0.821856	+	0.821856i	−0.986374	−	0.164518i	$-0.947393\pi$
$409$	−16.6210	+	16.6210i	−0.821856	+	0.821856i	0.164518	+	0.986374i	$0.447393\pi$
$410$	10.6411	−	10.6411i	0.525529	−	0.525529i
$411$	−17.7855	−	15.1444i	−0.877295	−	0.747017i
$412$	−6.43202			−0.316883
$413$	−24.4559			−1.20340
$414$	16.4345	+	11.8655i	0.807710	+	0.583156i
$415$			15.5629i			0.763953i
$416$	1.33238	−	14.5068i	0.0653255	−	0.711253i
$417$	1.17366	+	14.6332i	0.0574745	+	0.716593i
$418$	3.86821	−	3.86821i	0.189200	−	0.189200i
$419$			20.6216i			1.00743i	0.863870	+	0.503716i	$0.168034\pi$
$419$			20.6216i			1.00743i	−0.863870	+	0.503716i	$0.831966\pi$
$420$	0.911855	+	11.3690i	0.0444940	+	0.554752i
$421$	−2.35083	+	2.35083i	−0.114573	+	0.114573i	−0.762069	−	0.647496i	$-0.775816\pi$
$421$	−2.35083	+	2.35083i	−0.114573	+	0.114573i	0.647496	+	0.762069i	$0.275816\pi$
$422$	−13.4339	−	13.4339i	−0.653951	−	0.653951i
$423$	15.3752	−	21.2957i	0.747569	−	1.03543i
$424$	13.0099	+	13.0099i	0.631819	+	0.631819i
$425$			1.93474i			0.0938484i
$426$	−6.94637	+	0.557135i	−0.336553	+	0.0269933i
$427$	−17.4300	−	17.4300i	−0.843496	−	0.843496i
$428$	−12.7043			−0.614085
$429$	0.0721586	−	6.24458i	0.00348385	−	0.301491i
$430$	−1.00773			−0.0485971
$431$	5.79611	+	5.79611i	0.279189	+	0.279189i	0.832785	−	0.553596i	$-0.186745\pi$
$431$	5.79611	+	5.79611i	0.279189	+	0.279189i	−0.553596	+	0.832785i	$0.686745\pi$
$432$	2.33914	+	9.55438i	0.112542	+	0.459685i
$433$		−	11.6924i		−	0.561899i	−0.959723	−	0.280950i	$-0.909351\pi$
$433$		−	11.6924i		−	0.561899i	0.959723	−	0.280950i	$-0.0906494\pi$
$434$	15.2217	+	15.2217i	0.730665	+	0.730665i
$435$	15.3552	+	13.0749i	0.736224	+	0.626895i
$436$	−2.43715	−	2.43715i	−0.116718	−	0.116718i
$437$	21.1230	−	21.1230i	1.01045	−	1.01045i
$438$	−11.5942	+	0.929917i	−0.553994	+	0.0444331i
$439$		−	18.7984i		−	0.897197i	−0.893733	−	0.448598i	$-0.851923\pi$
$439$		−	18.7984i		−	0.897197i	0.893733	−	0.448598i	$-0.148077\pi$
$440$	−7.98618	+	7.98618i	−0.380726	+	0.380726i
$441$	0.707971	+	4.38511i	0.0337129	+	0.208815i
$442$	−0.0834234	+	0.908300i	−0.00396805	+	0.0432034i
$443$		−	4.62780i		−	0.219873i	−0.993939	−	0.109937i	$-0.964935\pi$
$443$		−	4.62780i		−	0.219873i	0.993939	−	0.109937i	$-0.0350648\pi$
$444$	8.70032	+	7.40833i	0.412899	+	0.351584i
$445$	25.4408			1.20601
$446$	−17.4814			−0.827767
$447$	−18.8026	+	22.0817i	−0.889332	+	1.04443i
$448$	13.7557	−	13.7557i	0.649897	−	0.649897i
$449$	12.2665	−	12.2665i	0.578893	−	0.578893i	−0.355705	−	0.934598i	$-0.615759\pi$
$449$	12.2665	−	12.2665i	0.578893	−	0.578893i	0.934598	+	0.355705i	$0.115759\pi$
$450$	−16.6180	+	23.0170i	−0.783380	+	1.08503i
$451$	3.68109			0.173336
$452$	−11.8384			−0.556831
$453$	−5.93761	+	6.97311i	−0.278973	+	0.327626i
$454$			29.9887i			1.40744i
$455$	−23.9343	+	19.9076i	−1.12206	+	0.933283i
$456$	26.0928	−	2.09278i	1.22191	−	0.0980032i
$457$	15.8595	−	15.8595i	0.741878	−	0.741878i	−0.231061	−	0.972939i	$-0.574220\pi$
$457$	15.8595	−	15.8595i	0.741878	−	0.741878i	0.972939	+	0.231061i	$0.0742199\pi$
$458$		−	16.5465i		−	0.773166i
$459$	0.281017	+	1.14783i	0.0131167	+	0.0535762i
$460$	−12.0389	+	12.0389i	−0.561317	+	0.561317i
$461$	−14.7290	−	14.7290i	−0.685997	−	0.685997i	0.275348	−	0.961345i	$-0.411207\pi$
$461$	−14.7290	−	14.7290i	−0.685997	−	0.685997i	−0.961345	+	0.275348i	$0.911207\pi$
$462$	2.93450	−	3.44627i	0.136525	−	0.160335i
$463$	−26.5547	−	26.5547i	−1.23410	−	1.23410i	−0.962375	−	0.271725i	$-0.912406\pi$
$463$	−26.5547	−	26.5547i	−1.23410	−	1.23410i	−0.271725	−	0.962375i	$-0.587594\pi$
$464$		−	5.99755i		−	0.278429i
$465$	−4.19219	−	52.2683i	−0.194408	−	2.42389i
$466$	−9.53268	−	9.53268i	−0.441593	−	0.441593i
$467$	23.9475			1.10816			0.554079	−	0.832464i	$-0.313070\pi$
$467$	23.9475			1.10816			0.554079	+	0.832464i	$0.313070\pi$
$468$	5.42038	−	6.21866i	0.250557	−	0.287458i
$469$	15.3849			0.710409
$470$	−25.3096	−	25.3096i	−1.16745	−	1.16745i
$471$	2.54410	+	31.7199i	0.117226	+	1.46157i
$472$		−	31.9898i		−	1.47245i
$473$	−0.174302	−	0.174302i	−0.00801441	−	0.00801441i
$474$	−9.89605	+	11.6219i	−0.454541	+	0.533812i
$475$	29.5835	+	29.5835i	1.35739	+	1.35739i
$476$	0.288134	−	0.288134i	0.0132066	−	0.0132066i
$477$	2.86277	+	17.7318i	0.131077	+	0.811882i
$478$			23.9651i			1.09614i
$479$	−17.8427	+	17.8427i	−0.815255	+	0.815255i	−0.985416	−	0.170161i	$-0.945571\pi$
$479$	−17.8427	+	17.8427i	−0.815255	+	0.815255i	0.170161	+	0.985416i	$0.445571\pi$
$480$	−25.6374	+	2.05625i	−1.17018	+	0.0938545i
$481$	−2.85268	+	31.0595i	−0.130071	+	1.41619i
$482$			10.4638i			0.476613i
$483$	16.0243	−	18.8190i	0.729133	−	0.856292i
$484$	−0.762656			−0.0346662
$485$	36.0243			1.63578
$486$	−6.51587	+	16.0692i	−0.295566	+	0.728912i
$487$	−23.9070	+	23.9070i	−1.08333	+	1.08333i	−0.0871332	+	0.996197i	$0.527771\pi$
$487$	−23.9070	+	23.9070i	−1.08333	+	1.08333i	−0.996197	+	0.0871332i	$0.972229\pi$
$488$	22.7995	−	22.7995i	1.03208	−	1.03208i
$489$	−8.88238	+	10.4314i	−0.401675	+	0.471726i
$490$	6.05305			0.273449
$491$	19.8719			0.896805			0.448403	−	0.893832i	$-0.351993\pi$
$491$	19.8719			0.896805			0.448403	+	0.893832i	$0.351993\pi$
$492$	3.70223	+	3.15245i	0.166910	+	0.142124i
$493$		−	0.720526i		−	0.0324508i
$494$	12.6130	+	15.1642i	0.567485	+	0.682269i
$495$	−10.8847	+	1.75732i	−0.489230	+	0.0789856i
$496$	−11.0264	+	11.0264i	−0.495101	+	0.495101i
$497$			8.49746i			0.381163i
$498$	8.13246	−	0.652265i	0.364424	−	0.0292287i
$499$	7.49681	−	7.49681i	0.335603	−	0.335603i	−0.519106	−	0.854710i	$-0.673735\pi$
$499$	7.49681	−	7.49681i	0.335603	−	0.335603i	0.854710	+	0.519106i	$0.173735\pi$
$500$	−6.95108	−	6.95108i	−0.310862	−	0.310862i
$501$	−26.5393	−	22.5982i	−1.18569	−	1.00961i
$502$	−11.7182	−	11.7182i	−0.523010	−	0.523010i
$503$		−	22.3184i		−	0.995129i	−0.867427	−	0.497564i	$-0.834228\pi$
$503$		−	22.3184i		−	0.995129i	0.867427	−	0.497564i	$-0.165772\pi$
$504$	21.3821	−	3.45212i	0.952435	−	0.153769i
$505$	16.1298	+	16.1298i	0.717767	+	0.717767i
$506$	6.75673			0.300373
$507$	22.3970	+	2.31833i	0.994685	+	0.102961i
$508$	−6.21961			−0.275951
$509$	11.7737	+	11.7737i	0.521862	+	0.521862i	0.918133	−	0.396271i	$-0.129696\pi$
$509$	11.7737	+	11.7737i	0.521862	+	0.521862i	−0.396271	+	0.918133i	$0.629696\pi$
$510$	1.60521	−	0.128746i	0.0710800	−	0.00570098i
$511$			14.1832i			0.627426i
$512$	13.6355	+	13.6355i	0.602611	+	0.602611i
$513$	21.8481	+	13.2542i	0.964619	+	0.585189i
$514$	−5.87976	−	5.87976i	−0.259345	−	0.259345i
$515$	−21.9172	+	21.9172i	−0.965789	+	0.965789i
$516$	−0.0260325	−	0.324574i	−0.00114602	−	0.0142886i
$517$		−	8.75534i		−	0.385059i
$518$	−15.9854	+	15.9854i	−0.702356	+	0.702356i
$519$	−1.50284	−	18.7375i	−0.0659674	−	0.822483i
$520$	−26.0403	−	31.3075i	−1.14194	−	1.37292i
$521$		−	22.6448i		−	0.992089i	−0.868297	−	0.496044i	$-0.834785\pi$
$521$		−	22.6448i		−	0.992089i	0.868297	−	0.496044i	$-0.165215\pi$
$522$	6.18880	−	8.57190i	0.270876	−	0.375182i
$523$	16.9815			0.742551			0.371275	−	0.928523i	$-0.378921\pi$
$523$	16.9815			0.742551			0.371275	+	0.928523i	$0.378921\pi$
$524$	9.70553			0.423988
$525$	26.3566	+	22.4426i	1.15030	+	0.979477i
$526$	2.13099	−	2.13099i	0.0929155	−	0.0929155i
$527$	−1.32468	+	1.32468i	−0.0577038	+	0.0577038i
$528$	2.49644	+	2.12572i	0.108643	+	0.0925099i
$529$	13.8963			0.604187
$530$	24.4763			1.06318
$531$	18.2805	−	25.3196i	0.793304	−	1.09878i
$532$		−	8.81157i		−	0.382030i
$533$	−1.21390	+	13.2167i	−0.0525798	+	0.572480i
$534$	−1.06626	−	13.2942i	−0.0461416	−	0.575295i
$535$	−43.2902	+	43.2902i	−1.87160	+	1.87160i
$536$			20.1244i			0.869241i
$537$	0.452543	+	5.64232i	0.0195287	+	0.243484i
$538$	1.12229	−	1.12229i	0.0483852	−	0.0483852i
$539$	1.04696	+	1.04696i	0.0450960	+	0.0450960i
$540$	−12.4522	−	7.55414i	−0.535856	−	0.325078i
$541$	−30.1974	−	30.1974i	−1.29829	−	1.29829i	−0.929522	−	0.368767i	$-0.879780\pi$
$541$	−30.1974	−	30.1974i	−1.29829	−	1.29829i	−0.368767	−	0.929522i	$-0.620220\pi$
$542$			16.8538i			0.723934i
$543$	16.1327	−	1.29393i	0.692321	−	0.0555277i
$544$	0.649747	+	0.649747i	0.0278577	+	0.0278577i
$545$	−16.6093			−0.711462
$546$	11.4059	+	11.6726i	0.488129	+	0.499542i
$547$	−1.89198			−0.0808951			−0.0404475	−	0.999182i	$-0.512878\pi$
$547$	−1.89198			−0.0808951			−0.0404475	+	0.999182i	$0.512878\pi$
$548$	−7.27312	−	7.27312i	−0.310692	−	0.310692i
$549$	31.0743	−	5.01691i	1.32622	−	0.214116i
$550$			9.46303i			0.403505i
$551$	−11.0174	−	11.0174i	−0.469356	−	0.469356i
$552$	24.6163	+	20.9608i	1.04774	+	0.892150i
$553$	13.1614	+	13.1614i	0.559680	+	0.559680i
$554$	11.3794	−	11.3794i	0.483463	−	0.483463i
$555$	54.8906	−	4.40251i	2.32997	−	0.186876i
$556$			6.46399i			0.274134i
$557$	−2.62955	+	2.62955i	−0.111418	+	0.111418i	−0.760618	−	0.649200i	$-0.775104\pi$
$557$	−2.62955	+	2.62955i	−0.111418	+	0.111418i	0.649200	+	0.760618i	$0.275104\pi$
$558$	−27.1373	+	4.38129i	−1.14882	+	0.185475i
$559$	0.683300	−	0.568342i	0.0289005	−	0.0240383i
$560$		−	16.3451i		−	0.690707i
$561$	0.299914	+	0.255376i	0.0126624	+	0.0107820i
$562$	−24.2087			−1.02118
$563$	−15.1181			−0.637154			−0.318577	−	0.947897i	$-0.603205\pi$
$563$	−15.1181			−0.637154			−0.318577	+	0.947897i	$0.603205\pi$
$564$	7.49801	−	8.80564i	0.315723	−	0.370784i
$565$	−40.3396	+	40.3396i	−1.69710	+	1.69710i
$566$	6.95996	−	6.95996i	0.292549	−	0.292549i
$567$	18.8965	+	9.48642i	0.793577	+	0.398392i
$568$	−11.1152			−0.466383
$569$	−18.8785			−0.791428			−0.395714	−	0.918374i	$-0.629503\pi$
$569$	−18.8785			−0.791428			−0.395714	+	0.918374i	$0.629503\pi$
$570$	22.5762	−	26.5135i	0.945615	−	1.11053i
$571$			15.0142i			0.628325i	0.949369	+	0.314163i	$0.101724\pi$
$571$			15.0142i			0.628325i	−0.949369	+	0.314163i	$0.898276\pi$
$572$	0.251498	−	2.73827i	0.0105157	−	0.114493i
$573$	7.52880	−	0.603849i	0.314520	−	0.0252261i
$574$	−6.80222	+	6.80222i	−0.283919	+	0.283919i
$575$			51.6745i			2.15498i
$576$	3.95934	+	24.5238i	0.164973	+	1.02183i
$577$	−13.1599	+	13.1599i	−0.547855	+	0.547855i	−0.925820	−	0.377965i	$-0.876624\pi$
$577$	−13.1599	+	13.1599i	−0.547855	+	0.547855i	0.377965	+	0.925820i	$0.376624\pi$
$578$	13.3308	+	13.3308i	0.554488	+	0.554488i
$579$	21.5161	−	25.2684i	0.894177	−	1.05012i
$580$	6.27926	+	6.27926i	0.260732	+	0.260732i
$581$		−	9.94840i		−	0.412729i
$582$	−1.50983	−	18.8246i	−0.0625846	−	0.780306i
$583$	4.23354	+	4.23354i	0.175335	+	0.175335i
$584$	−18.5524			−0.767704
$585$	−2.72015	−	39.6603i	−0.112464	−	1.63975i
$586$	−17.1514			−0.708518
$587$	−15.0573	−	15.0573i	−0.621481	−	0.621481i	0.324429	−	0.945910i	$-0.394828\pi$
$587$	−15.0573	−	15.0573i	−0.621481	−	0.621481i	−0.945910	+	0.324429i	$0.894828\pi$
$588$	0.156367	+	1.94959i	0.00644848	+	0.0803998i
$589$			40.5106i			1.66921i
$590$	−30.0920	−	30.0920i	−1.23887	−	1.23887i
$591$	22.2711	−	26.1552i	0.916113	−	1.07588i
$592$	−11.5796	−	11.5796i	−0.475918	−	0.475918i
$593$	6.09308	−	6.09308i	0.250213	−	0.250213i	−0.570845	−	0.821058i	$-0.693384\pi$
$593$	6.09308	−	6.09308i	0.250213	−	0.250213i	0.821058	+	0.570845i	$0.193384\pi$
$594$	1.37449	+	5.61419i	0.0563960	+	0.230353i
$595$		−	1.96365i		−	0.0805017i
$596$	−9.02998	+	9.02998i	−0.369883	+	0.369883i
$597$	−36.5232	+	2.92935i	−1.49479	+	0.119890i
$598$	−2.22814	+	24.2596i	−0.0911155	+	0.992050i
$599$			24.7080i			1.00954i	0.863254	+	0.504771i	$0.168423\pi$
$599$			24.7080i			1.00954i	−0.863254	+	0.504771i	$0.831577\pi$
$600$	−29.3563	+	34.4760i	−1.19847	+	1.40748i
$601$	20.0857			0.819314			0.409657	−	0.912240i	$-0.365648\pi$
$601$	20.0857			0.819314			0.409657	+	0.912240i	$0.365648\pi$
$602$	0.644180			0.0262548
$603$	−11.5000	+	15.9283i	−0.468317	+	0.648650i
$604$	−2.85155	+	2.85155i	−0.116028	+	0.116028i
$605$	−2.59877	+	2.59877i	−0.105655	+	0.105655i
$606$	7.75267	−	9.10472i	0.314931	−	0.369854i
$607$	3.74243			0.151901			0.0759503	−	0.997112i	$-0.475801\pi$
$607$	3.74243			0.151901			0.0759503	+	0.997112i	$0.475801\pi$
$608$	19.8702			0.805845
$609$	−9.81560	−	8.35799i	−0.397748	−	0.338683i
$610$		−	42.8938i		−	1.73672i
$611$	31.4355	+	2.88722i	1.27175	+	0.116804i
$612$	0.0829342	+	0.513687i	0.00335242	+	0.0207646i
$613$	−1.37934	+	1.37934i	−0.0557109	+	0.0557109i	−0.734413	−	0.678702i	$-0.762543\pi$
$613$	−1.37934	+	1.37934i	−0.0557109	+	0.0557109i	0.678702	+	0.734413i	$0.262543\pi$
$614$		−	35.4236i		−	1.42958i
$615$	23.3575	−	1.87339i	0.941865	−	0.0755424i
$616$	5.10507	−	5.10507i	0.205689	−	0.205689i
$617$	−8.34653	−	8.34653i	−0.336019	−	0.336019i	0.518848	−	0.854867i	$-0.326361\pi$
$617$	−8.34653	−	8.34653i	−0.336019	−	0.336019i	−0.854867	+	0.518848i	$0.826361\pi$
$618$	12.3715	+	10.5344i	0.497656	+	0.423754i
$619$	26.2275	+	26.2275i	1.05417	+	1.05417i	0.998446	+	0.0557247i	$0.0177469\pi$
$619$	26.2275	+	26.2275i	1.05417	+	1.05417i	0.0557247	+	0.998446i	$0.482253\pi$
$620$		−	23.0887i		−	0.927263i
$621$	7.50563	+	30.6572i	0.301191	+	1.23023i
$622$	4.82972	+	4.82972i	0.193654	+	0.193654i
$623$	−16.2627			−0.651551
$624$	−8.45549	+	8.26231i	−0.338491	+	0.330757i
$625$	−4.83606			−0.193442
$626$	−18.8039	−	18.8039i	−0.751553	−	0.751553i
$627$	8.49079	−	0.681005i	0.339090	−	0.0271967i
$628$			14.0117i			0.559129i
$629$	−1.39113	−	1.39113i	−0.0554681	−	0.0554681i
$630$	16.8663	−	23.3610i	0.671970	−	0.930723i
$631$	−11.7369	−	11.7369i	−0.467238	−	0.467238i	0.433780	−	0.901019i	$-0.357179\pi$
$631$	−11.7369	−	11.7369i	−0.467238	−	0.467238i	−0.901019	+	0.433780i	$0.857179\pi$
$632$	−17.2159	+	17.2159i	−0.684811	+	0.684811i
$633$	−2.36506	−	29.4876i	−0.0940025	−	1.17203i
$634$			10.8190i			0.429676i
$635$	−21.1935	+	21.1935i	−0.841037	+	0.841037i
$636$	0.632292	+	7.88343i	0.0250720	+	0.312598i
$637$	−4.10432	+	3.41381i	−0.162619	+	0.135260i
$638$		−	3.52418i		−	0.139524i
$639$	−8.79758	−	6.35174i	−0.348027	−	0.251271i
$640$	4.15325			0.164172
$641$	−39.2854			−1.55168			−0.775841	−	0.630929i	$-0.782674\pi$
$641$	−39.2854			−1.55168			−0.775841	+	0.630929i	$0.782674\pi$
$642$	24.4358	+	20.8071i	0.964404	+	0.821191i
$643$	−22.6088	+	22.6088i	−0.891605	+	0.891605i	−0.994674	−	0.103069i	$-0.967134\pi$
$643$	−22.6088	+	22.6088i	−0.891605	+	0.891605i	0.103069	+	0.994674i	$0.467134\pi$
$644$	7.69572	−	7.69572i	0.303254	−	0.303254i
$645$	−1.19470	−	1.01729i	−0.0470413	−	0.0400556i
$646$	−1.24412			−0.0489492
$647$	−12.6484			−0.497259			−0.248629	−	0.968599i	$-0.579980\pi$
$647$	−12.6484			−0.497259			−0.248629	+	0.968599i	$0.579980\pi$
$648$	−12.4088	+	24.7177i	−0.487464	+	0.971003i
$649$		−	10.4097i		−	0.408617i
$650$	−33.9764	−	3.12059i	−1.33267	−	0.122400i
$651$	2.67981	+	33.4119i	0.105030	+	1.30952i
$652$	−4.26578	+	4.26578i	−0.167061	+	0.167061i
$653$		−	3.49826i		−	0.136897i	−0.997655	−	0.0684487i	$-0.978195\pi$
$653$		−	3.49826i		−	0.136897i	0.997655	−	0.0684487i	$-0.0218050\pi$
$654$	0.696119	+	8.67924i	0.0272204	+	0.339385i
$655$	33.0718	−	33.0718i	1.29222	−	1.29222i
$656$	−4.92745	−	4.92745i	−0.192384	−	0.192384i
$657$	−14.6841	−	10.6017i	−0.572881	−	0.413613i
$658$	16.1789	+	16.1789i	0.630718	+	0.630718i
$659$		−	7.26061i		−	0.282833i	−0.989950	−	0.141417i	$-0.954834\pi$
$659$		−	7.26061i		−	0.282833i	0.989950	−	0.141417i	$-0.0451657\pi$
$660$	−4.83926	+	0.388133i	−0.188368	+	0.0151081i
$661$	−6.00106	−	6.00106i	−0.233414	−	0.233414i	0.580702	−	0.814116i	$-0.302778\pi$
$661$	−6.00106	−	6.00106i	−0.233414	−	0.233414i	−0.814116	+	0.580702i	$0.802778\pi$
$662$	20.2013			0.785145
$663$	−1.01581	+	0.992607i	−0.0394510	+	0.0385497i
$664$	13.0131			0.505006
$665$	−30.0256	−	30.0256i	−1.16434	−	1.16434i
$666$	−4.60110	−	28.4988i	−0.178289	−	1.10431i
$667$		−	19.2444i		−	0.745146i
$668$	−10.8528	−	10.8528i	−0.419909	−	0.419909i
$669$	−20.7248	−	17.6471i	−0.801266	−	0.682278i
$670$	18.9305	+	18.9305i	0.731350	+	0.731350i
$671$	7.41912	−	7.41912i	0.286412	−	0.286412i
$672$	16.3884	−	1.31443i	0.632195	−	0.0507053i
$673$			24.2999i			0.936694i	0.883545	+	0.468347i	$0.155150\pi$
$673$			24.2999i			0.936694i	−0.883545	+	0.468347i	$0.844850\pi$
$674$	−22.2927	+	22.2927i	−0.858681	+	0.858681i
$675$	−42.9365	+	10.5119i	−1.65263	+	0.404603i
$676$	9.74865	+	1.80598i	0.374948	+	0.0694607i
$677$		−	22.1600i		−	0.851676i	−0.904799	−	0.425838i	$-0.859979\pi$
$677$		−	22.1600i		−	0.851676i	0.904799	−	0.425838i	$-0.140021\pi$
$678$	22.7703	+	19.3889i	0.874489	+	0.744627i
$679$	−23.0281			−0.883737
$680$	2.56857			0.0985000
$681$	−30.2730	+	35.5526i	−1.16006	+	1.36238i
$682$	−6.47916	+	6.47916i	−0.248100	+	0.248100i
$683$	23.0620	−	23.0620i	0.882444	−	0.882444i	−0.111338	−	0.993783i	$-0.535514\pi$
$683$	23.0620	−	23.0620i	0.882444	−	0.882444i	0.993783	+	0.111338i	$0.0355137\pi$
$684$	9.12278	+	6.58653i	0.348818	+	0.251842i
$685$	−49.5666			−1.89384
$686$	−22.1625			−0.846167
$687$	16.7034	−	19.6164i	0.637274	−	0.748413i
$688$			0.466636i			0.0177903i
$689$	−16.5963	+	13.8042i	−0.632270	+	0.525898i
$690$	42.8733	−	3.43866i	1.63216	−	0.130908i
$691$	25.2511	−	25.2511i	0.960599	−	0.960599i	−0.0386540	−	0.999253i	$-0.512307\pi$
$691$	25.2511	−	25.2511i	0.960599	−	0.960599i	0.999253	+	0.0386540i	$0.0123070\pi$
$692$		−	8.27696i		−	0.314643i
$693$	6.95790	−	1.12335i	0.264309	−	0.0426724i
$694$	10.3881	−	10.3881i	0.394328	−	0.394328i
$695$	22.0262	+	22.0262i	0.835502	+	0.835502i
$696$	10.9327	−	12.8394i	0.414405	−	0.486676i
$697$	−0.591967	−	0.591967i	−0.0224224	−	0.0224224i
$698$			5.62223i			0.212804i
$699$	−1.67824	−	20.9244i	−0.0634770	−	0.791433i
$700$	10.7781	+	10.7781i	0.407375	+	0.407375i
$701$	2.10522			0.0795131			0.0397565	−	0.999209i	$-0.487342\pi$
$701$	2.10522			0.0795131			0.0397565	+	0.999209i	$0.487342\pi$
$702$	−20.6107	+	3.08365i	−0.777899	+	0.116385i
$703$	−42.5429			−1.60454
$704$	5.85517	+	5.85517i	0.220675	+	0.220675i
$705$	−4.45580	−	55.5550i	−0.167815	−	2.09232i
$706$		−	18.0201i		−	0.678197i
$707$	−10.3108	−	10.3108i	−0.387777	−	0.387777i
$708$	8.91480	−	10.4695i	0.335039	−	0.393469i
$709$	−2.27572	−	2.27572i	−0.0854664	−	0.0854664i	0.663081	−	0.748548i	$-0.269248\pi$
$709$	−2.27572	−	2.27572i	−0.0854664	−	0.0854664i	−0.748548	+	0.663081i	$0.769248\pi$
$710$	−10.4558	+	10.4558i	−0.392399	+	0.392399i
$711$	−23.4642	+	3.78827i	−0.879977	+	0.142071i
$712$		−	21.2726i		−	0.797223i
$713$	−35.3806	+	35.3806i	−1.32501	+	1.32501i
$714$	−1.02611	+	0.0822995i	−0.0384013	+	0.00307998i
$715$	−8.47373	−	10.1877i	−0.316899	−	0.380998i
$716$			2.49240i			0.0931454i
$717$	−24.1923	+	28.4114i	−0.903479	+	1.06104i
$718$	−3.38788			−0.126435
$719$	16.1591			0.602632			0.301316	−	0.953524i	$-0.402574\pi$
$719$	16.1591			0.602632			0.301316	+	0.953524i	$0.402574\pi$
$720$	16.9224	+	12.2178i	0.630661	+	0.455329i
$721$	14.0103	−	14.0103i	0.521772	−	0.521772i
$722$	−4.07892	+	4.07892i	−0.151802	+	0.151802i
$723$	−10.5630	+	12.4052i	−0.392843	+	0.461354i
$724$	7.12635			0.264849
$725$	26.9524			1.00099
$726$	1.46691	+	1.24908i	0.0544423	+	0.0463576i
$727$			26.2792i			0.974642i	0.873223	+	0.487321i	$0.162026\pi$
$727$			26.2792i			0.974642i	−0.873223	+	0.487321i	$0.837974\pi$
$728$	16.6460	+	20.0129i	0.616941	+	0.741728i
$729$	−23.9463	+	12.4729i	−0.886901	+	0.461959i
$730$	−17.4518	+	17.4518i	−0.645921	+	0.645921i
$731$			0.0560601i			0.00207346i
$732$	13.8154	−	1.10807i	0.510633	−	0.0409554i
$733$	6.35193	−	6.35193i	0.234614	−	0.234614i	−0.580002	−	0.814615i	$-0.696948\pi$
$733$	6.35193	−	6.35193i	0.234614	−	0.234614i	0.814615	+	0.580002i	$0.196948\pi$
$734$	3.93383	+	3.93383i	0.145200	+	0.145200i
$735$	7.17610	+	6.11045i	0.264695	+	0.225387i
$736$	17.3540	+	17.3540i	0.639677	+	0.639677i
$737$			6.54863i			0.241222i
$738$	−1.95790	−	12.1270i	−0.0720712	−	0.446403i
$739$	20.6180	+	20.6180i	0.758446	+	0.758446i	0.976040	−	0.217593i	$-0.0698207\pi$
$739$	20.6180	+	20.6180i	0.758446	+	0.758446i	−0.217593	+	0.976040i	$0.569821\pi$
$740$	24.2470			0.891337
$741$	−0.354869	+	30.7103i	−0.0130364	+	1.12817i
$742$	−15.6462			−0.574390
$743$	−19.5186	−	19.5186i	−0.716067	−	0.716067i	0.251730	−	0.967797i	$-0.419000\pi$
$743$	−19.5186	−	19.5186i	−0.716067	−	0.716067i	−0.967797	+	0.251730i	$0.919000\pi$
$744$	−43.7048	+	3.50535i	−1.60229	+	0.128512i
$745$			61.5397i			2.25464i
$746$	−21.5836	−	21.5836i	−0.790232	−	0.790232i
$747$	10.2998	+	7.43630i	0.376849	+	0.272080i
$748$	0.122645	+	0.122645i	0.00448435	+	0.00448435i
$749$	27.6727	−	27.6727i	1.01114	−	1.01114i
$750$	1.98543	+	24.7544i	0.0724976	+	0.903902i
$751$			12.9894i			0.473991i	0.971511	+	0.236995i	$0.0761627\pi$
$751$			12.9894i			0.473991i	−0.971511	+	0.236995i	$0.923837\pi$
$752$	−11.7198	+	11.7198i	−0.427376	+	0.427376i
$753$	−2.06301	−	25.7217i	−0.0751804	−	0.937351i
$754$	12.6534	+	1.16216i	0.460808	+	0.0423232i
$755$			19.4334i			0.707255i
$756$	7.95990	+	4.82889i	0.289499	+	0.175625i
$757$	−7.56144			−0.274825			−0.137413	−	0.990514i	$-0.543879\pi$
$757$	−7.56144			−0.274825			−0.137413	+	0.990514i	$0.543879\pi$
$758$	−10.3555			−0.376129
$759$	8.01034	+	6.82080i	0.290757	+	0.247580i
$760$	39.2753	−	39.2753i	1.42466	−	1.42466i
$761$	28.1681	−	28.1681i	1.02109	−	1.02109i	0.0213202	−	0.999773i	$-0.493213\pi$
$761$	28.1681	−	28.1681i	1.02109	−	1.02109i	0.999773	−	0.0213202i	$-0.00678695\pi$
$762$	11.9630	+	10.1865i	0.433373	+	0.369017i
$763$	10.6173			0.384371
$764$	3.32572			0.120320
$765$	2.03300	+	1.46780i	0.0735033	+	0.0530684i
$766$		−	29.4556i		−	1.06427i
$767$	37.3755	+	3.43277i	1.34955	+	0.123950i
$768$	2.11920	+	26.4222i	0.0764700	+	0.953430i
$769$	37.2656	−	37.2656i	1.34383	−	1.34383i	0.451620	−	0.892211i	$-0.350846\pi$
$769$	37.2656	−	37.2656i	1.34383	−	1.34383i	0.892211	−	0.451620i	$-0.149154\pi$
$770$		−	9.60444i		−	0.346120i
$771$	−1.03514	−	12.9062i	−0.0372797	−	0.464805i
$772$	10.3331	−	10.3331i	0.371898	−	0.371898i
$773$	13.0615	+	13.0615i	0.469788	+	0.469788i	0.901846	−	0.432058i	$-0.142212\pi$
$773$	13.0615	+	13.0615i	0.469788	+	0.469788i	−0.432058	+	0.901846i	$0.642212\pi$
$774$	−0.481516	+	0.666932i	−0.0173077	+	0.0239724i
$775$	−49.5517	−	49.5517i	−1.77995	−	1.77995i
$776$		−	30.1221i		−	1.08132i
$777$	−35.0881	+	2.81425i	−1.25878	+	0.100961i
$778$	2.69610	+	2.69610i	0.0966600	+	0.0966600i
$779$	−18.1032			−0.648616
$780$	0.202255	−	17.5031i	0.00724189	−	0.626710i
$781$	−3.61697			−0.129425
$782$	−1.08657	−	1.08657i	−0.0388557	−	0.0388557i
$783$	15.9902	−	3.91479i	0.571444	−	0.139903i
$784$		−	2.80290i		−	0.100104i
$785$	47.7453	+	47.7453i	1.70410	+	1.70410i
$786$	−18.6679	−	15.8957i	−0.665862	−	0.566982i
$787$	11.4390	+	11.4390i	0.407756	+	0.407756i	0.880955	−	0.473199i	$-0.156901\pi$
$787$	11.4390	+	11.4390i	0.407756	+	0.407756i	−0.473199	+	0.880955i	$0.656901\pi$
$788$	10.6958	−	10.6958i	0.381021	−	0.381021i
$789$	4.67755	−	0.375164i	0.166525	−	0.0133562i
$790$			32.3892i			1.15236i
$791$	25.7866	−	25.7866i	0.916866	−	0.916866i
$792$	1.46940	+	9.10135i	0.0522129	+	0.323402i
$793$	24.1913	+	29.0845i	0.859059	+	1.03282i
$794$			33.1931i			1.17798i
$795$	29.0175	+	24.7084i	1.02914	+	0.876317i
$796$	−16.1335			−0.571837
$797$	−20.7469			−0.734894			−0.367447	−	0.930044i	$-0.619768\pi$
$797$	−20.7469			−0.734894			−0.367447	+	0.930044i	$0.619768\pi$
$798$	−14.4316	+	16.9484i	−0.510873	+	0.599968i
$799$	−1.40797	+	1.40797i	−0.0498105	+	0.0498105i
$800$	−24.3048	+	24.3048i	−0.859306	+	0.859306i
$801$	12.1562	−	16.8371i	0.429517	−	0.594909i
$802$	21.4427			0.757167
$803$	−6.03710			−0.213045
$804$	−5.60819	+	6.58625i	−0.197786	+	0.232279i
$805$		−	52.4467i		−	1.84850i
$806$	−21.1264	−	25.3996i	−0.744146	−	0.894664i
$807$	2.46344	−	0.197580i	0.0867171	−	0.00695516i
$808$	13.4871	−	13.4871i	0.474475	−	0.474475i
$809$			40.2218i			1.41412i	0.707152	+	0.707061i	$0.249980\pi$
$809$			40.2218i			1.41412i	−0.707152	+	0.707061i	$0.750020\pi$
$810$	11.5787	+	34.9240i	0.406834	+	1.22711i
$811$	20.0451	−	20.0451i	0.703879	−	0.703879i	−0.261362	−	0.965241i	$-0.584172\pi$
$811$	20.0451	−	20.0451i	0.703879	−	0.703879i	0.965241	+	0.261362i	$0.0841717\pi$
$812$	−4.01394	−	4.01394i	−0.140862	−	0.140862i
$813$	−17.0136	+	19.9808i	−0.596694	+	0.700757i
$814$	−6.80421	−	6.80421i	−0.238487	−	0.238487i
$815$			29.0715i			1.01833i
$816$	−0.0596167	−	0.743303i	−0.00208700	−	0.0260208i
$817$	0.857200	+	0.857200i	0.0299896	+	0.0299896i
$818$	26.1468			0.914200
$819$	1.73882	+	25.3524i	0.0607594	+	0.885883i
$820$	10.3178			0.360313
$821$	−31.0840	−	31.0840i	−1.08484	−	1.08484i	−0.996051	−	0.0887872i	$-0.971701\pi$
$821$	−31.0840	−	31.0840i	−1.08484	−	1.08484i	−0.0887872	−	0.996051i	$-0.528299\pi$
$822$	2.07741	+	25.9012i	0.0724581	+	0.903410i
$823$		−	13.5674i		−	0.472929i	−0.971640	−	0.236465i	$-0.924011\pi$
$823$		−	13.5674i		−	0.472929i	0.971640	−	0.236465i	$-0.0759888\pi$
$824$	18.3263	+	18.3263i	0.638428	+	0.638428i
$825$	−9.55277	+	11.2187i	−0.332585	+	0.390587i
$826$	19.2360	+	19.2360i	0.669305	+	0.669305i
$827$	−23.4919	+	23.4919i	−0.816892	+	0.816892i	−0.985656	−	0.168764i	$-0.946022\pi$
$827$	−23.4919	+	23.4919i	−0.816892	+	0.816892i	0.168764	+	0.985656i	$0.446022\pi$
$828$	2.21508	+	13.7200i	0.0769792	+	0.476802i
$829$			20.3800i			0.707826i	0.935278	+	0.353913i	$0.115149\pi$
$829$			20.3800i			0.707826i	−0.935278	+	0.353913i	$0.884851\pi$
$830$	12.2411	−	12.2411i	0.424895	−	0.424895i
$831$	24.9779	−	2.00336i	0.866474	−	0.0694957i
$832$	−22.9535	+	19.0918i	−0.795768	+	0.661888i
$833$		−	0.336731i		−	0.0116671i
$834$	10.5867	−	12.4330i	0.366589	−	0.430521i
$835$	−73.9625			−2.55958
$836$	3.75067			0.129720
$837$	−36.5951	−	22.2005i	−1.26491	−	0.767362i
$838$	16.2201	−	16.2201i	0.560313	−	0.560313i
$839$	−0.692297	+	0.692297i	−0.0239008	+	0.0239008i	−0.718956	−	0.695055i	$-0.755380\pi$
$839$	−0.692297	+	0.692297i	−0.0239008	+	0.0239008i	0.695055	+	0.718956i	$0.255380\pi$
$840$	29.7950	−	34.9912i	1.02802	−	1.20731i
$841$	18.9625			0.653879
$842$	3.69813			0.127446
$843$	−28.7003	−	24.4383i	−0.988489	−	0.841699i
$844$		−	13.0257i		−	0.448361i
$845$	39.3727	−	27.0648i	1.35446	−	0.931059i
$846$	−28.8438	+	4.65679i	−0.991669	+	0.160104i
$847$	1.66123	−	1.66123i	0.0570805	−	0.0570805i
$848$		−	11.3339i		−	0.389208i
$849$	15.2772	−	1.22531i	0.524314	−	0.0420526i
$850$	1.52178	−	1.52178i	0.0521966	−	0.0521966i
$851$	−37.1556	−	37.1556i	−1.27368	−	1.27368i
$852$	−3.63775	−	3.09754i	−0.124627	−	0.106120i
$853$	−28.9527	−	28.9527i	−0.991321	−	0.991321i	0.00864148	−	0.999963i	$-0.497249\pi$
$853$	−28.9527	−	28.9527i	−0.991321	−	0.991321i	−0.999963	+	0.00864148i	$0.997249\pi$
$854$			27.4194i			0.938271i
$855$	53.5298	−	8.64233i	1.83068	−	0.295561i
$856$	36.1975	+	36.1975i	1.23721	+	1.23721i
$857$	−2.73290			−0.0933541			−0.0466770	−	0.998910i	$-0.514863\pi$
$857$	−2.73290			−0.0933541			−0.0466770	+	0.998910i	$0.514863\pi$
$858$	−4.96848	+	4.85496i	−0.169621	+	0.165746i
$859$	7.31872			0.249712			0.124856	−	0.992175i	$-0.460153\pi$
$859$	7.31872			0.249712			0.124856	+	0.992175i	$0.460153\pi$
$860$	−0.488554	−	0.488554i	−0.0166596	−	0.0166596i
$861$	−14.9310	+	1.19754i	−0.508847	+	0.0408122i
$862$		−	9.11794i		−	0.310558i
$863$	−33.9429	−	33.9429i	−1.15543	−	1.15543i	−0.985447	−	0.169982i	$-0.945629\pi$
$863$	−33.9429	−	33.9429i	−1.15543	−	1.15543i	−0.169982	−	0.985447i	$-0.554371\pi$
$864$	−10.8892	+	17.9497i	−0.370459	+	0.610662i
$865$	−28.2039	−	28.2039i	−0.958962	−	0.958962i
$866$	−9.19672	+	9.19672i	−0.312517	+	0.312517i
$867$	2.34691	+	29.2613i	0.0797052	+	0.993766i
$868$			14.7592i			0.500958i
$869$	−5.60219	+	5.60219i	−0.190041	+	0.190041i
$870$	−1.79354	−	22.3619i	−0.0608067	−	0.758139i
$871$	−23.5125	−	2.15952i	−0.796689	−	0.0731724i
$872$			13.8880i			0.470307i
$873$	17.2132	−	23.8414i	0.582578	−	0.806909i
$874$	−33.2290			−1.12399
$875$	30.2819			1.02372
$876$	−6.07178	−	5.17013i	−0.205147	−	0.174682i
$877$	33.9677	−	33.9677i	1.14701	−	1.14701i	0.159871	−	0.987138i	$-0.448892\pi$
$877$	33.9677	−	33.9677i	1.14701	−	1.14701i	0.987138	−	0.159871i	$-0.0511078\pi$
$878$	−14.7860	+	14.7860i	−0.499003	+	0.499003i
$879$	−20.3336	−	17.3140i	−0.685835	−	0.583988i
$880$	6.95734			0.234532
$881$	−18.8457			−0.634928			−0.317464	−	0.948270i	$-0.602831\pi$
$881$	−18.8457			−0.634928			−0.317464	+	0.948270i	$0.602831\pi$
$882$	2.89228	−	4.00600i	0.0973882	−	0.134889i
$883$			58.1410i			1.95660i	0.207192	+	0.978300i	$0.433567\pi$
$883$			58.1410i			1.95660i	−0.207192	+	0.978300i	$0.566433\pi$
$884$	−0.480794	+	0.399905i	−0.0161708	+	0.0134503i
$885$	−5.29775	−	66.0525i	−0.178082	−	2.22033i
$886$	−3.64003	+	3.64003i	−0.122289	+	0.122289i
$887$			3.27775i			0.110056i	0.998485	+	0.0550281i	$0.0175248\pi$
$887$			3.27775i			0.110056i	−0.998485	+	0.0550281i	$0.982475\pi$
$888$	−3.68120	−	45.8974i	−0.123533	−	1.54021i
$889$	13.5477	−	13.5477i	0.454374	−	0.454374i
$890$	−20.0106	−	20.0106i	−0.670757	−	0.670757i
$891$	−4.03792	+	8.04333i	−0.135275	+	0.269462i
$892$	−8.47508	−	8.47508i	−0.283767	−	0.283767i
$893$			43.0579i			1.44088i
$894$	32.1579	−	2.57923i	1.07552	−	0.0862622i
$895$	8.49291	+	8.49291i	0.283887	+	0.283887i
$896$	−2.65491			−0.0886945
$897$	−27.1312	+	26.5114i	−0.905885	+	0.885189i
$898$	−19.2966			−0.643937
$899$	18.4538	+	18.4538i	0.615469	+	0.615469i
$900$	−19.2153	+	3.10229i	−0.640510	+	0.103410i
$901$		−	1.36162i		−	0.0453620i
$902$	−2.89538	−	2.89538i	−0.0964058	−	0.0964058i
$903$	0.763698	+	0.650289i	0.0254143	+	0.0216403i
$904$	33.7304	+	33.7304i	1.12186	+	1.12186i
$905$	24.2832	−	24.2832i	0.807201	−	0.807201i
$906$	10.1550	−	0.814485i	0.337378	−	0.0270595i
$907$			30.3230i			1.00686i	0.864036	+	0.503430i	$0.167929\pi$
$907$			30.3230i			1.00686i	−0.864036	+	0.503430i	$0.832071\pi$
$908$	−14.5387	+	14.5387i	−0.482483	+	0.482483i
$909$	18.3821	−	2.96777i	0.609697	−	0.0984348i
$910$	34.4842	+	3.16722i	1.14314	+	0.104992i
$911$		−	20.4902i		−	0.678869i	−0.940630	−	0.339435i	$-0.889764\pi$
$911$		−	20.4902i		−	0.678869i	0.940630	−	0.339435i	$-0.110236\pi$
$912$	−12.2772	−	10.4541i	−0.406540	−	0.346169i
$913$	4.23456			0.140144
$914$	−24.9489			−0.825235
$915$	43.3006	−	50.8521i	1.43147	−	1.68112i
$916$	8.02183	−	8.02183i	0.265049	−	0.265049i
$917$	−21.1408	+	21.1408i	−0.698130	+	0.698130i
$918$	0.681799	−	1.12387i	0.0225027	−	0.0370933i
$919$	−30.8117			−1.01638			−0.508191	−	0.861244i	$-0.669686\pi$
$919$	−30.8117			−1.01638			−0.508191	+	0.861244i	$0.669686\pi$
$920$	68.6034			2.26179
$921$	35.7595	−	41.9959i	1.17832	−	1.38381i
$922$			23.1704i			0.763075i
$923$	1.19275	−	12.9865i	0.0392600	−	0.427456i
$924$	3.09344	−	0.248110i	0.101767	−	0.00816221i
$925$	52.0376	−	52.0376i	1.71099	−	1.71099i
$926$			41.7735i			1.37276i
$927$	4.03262	+	24.9777i	0.132449	+	0.820375i
$928$	9.05151	−	9.05151i	0.297130	−	0.297130i
$929$	−3.22989	−	3.22989i	−0.105969	−	0.105969i	0.652134	−	0.758103i	$-0.273874\pi$
$929$	−3.22989	−	3.22989i	−0.105969	−	0.105969i	−0.758103	+	0.652134i	$0.773874\pi$
$930$	−37.8146	+	44.4094i	−1.23999	+	1.45624i
$931$	−5.14887	−	5.14887i	−0.168748	−	0.168748i
$932$		−	9.24301i		−	0.302765i
$933$	0.850280	+	10.6013i	0.0278369	+	0.347071i
$934$	−18.8361	−	18.8361i	−0.616336	−	0.616336i
$935$	0.835831			0.0273346
$936$	−33.1624	+	2.27448i	−1.08395	+	0.0743438i
$937$	27.7574			0.906794			0.453397	−	0.891309i	$-0.350212\pi$
$937$	27.7574			0.906794			0.453397	+	0.891309i	$0.350212\pi$
$938$	−12.1011	−	12.1011i	−0.395115	−	0.395115i
$939$	−3.31045	−	41.2748i	−0.108032	−	1.34695i
$940$		−	24.5405i		−	0.800423i
$941$	39.7161	+	39.7161i	1.29471	+	1.29471i	0.931841	+	0.362866i	$0.118202\pi$
$941$	39.7161	+	39.7161i	1.29471	+	1.29471i	0.362866	+	0.931841i	$0.381798\pi$
$942$	22.9484	−	26.9506i	0.747700	−	0.878097i
$943$	−15.8107	−	15.8107i	−0.514869	−	0.514869i
$944$	−13.9343	+	13.9343i	−0.453523	+	0.453523i
$945$	43.5781	−	10.6690i	1.41760	−	0.347062i
$946$			0.274197i			0.00891491i
$947$	6.41763	−	6.41763i	0.208545	−	0.208545i	−0.595104	−	0.803649i	$-0.702889\pi$
$947$	6.41763	−	6.41763i	0.208545	−	0.208545i	0.803649	+	0.595104i	$0.202889\pi$
$948$	−10.4320	+	0.836703i	−0.338817	+	0.0271749i
$949$	1.99083	−	21.6758i	0.0646251	−	0.703628i
$950$		−	46.5383i		−	1.50990i
$951$	−10.9216	+	12.8263i	−0.354156	+	0.415920i
$952$	−1.64192			−0.0532151
$953$	14.7492			0.477775			0.238887	−	0.971047i	$-0.423217\pi$
$953$	14.7492			0.477775			0.238887	+	0.971047i	$0.423217\pi$
$954$	11.6953	−	16.1988i	0.378650	−	0.524455i
$955$	11.3325	−	11.3325i	0.366710	−	0.366710i
$956$	−11.6184	+	11.6184i	−0.375766	+	0.375766i
$957$	3.55760	−	4.17804i	0.115001	−	0.135057i
$958$	28.0687			0.906857
$959$	31.6849			1.02316
$960$	40.1325	+	34.1728i	1.29527	+	1.10292i
$961$		−	36.8542i		−	1.18885i
$962$	26.6739	−	22.1863i	0.860001	−	0.715315i
$963$	7.96509	+	49.3351i	0.256671	+	1.58980i
$964$	−5.07291	+	5.07291i	−0.163388	+	0.163388i
$965$		−	70.4208i		−	2.26692i
$966$	−27.4062	+	2.19812i	−0.881782	+	0.0707234i
$967$	12.6743	−	12.6743i	0.407577	−	0.407577i	−0.473316	−	0.880893i	$-0.656943\pi$
$967$	12.6743	−	12.6743i	0.407577	−	0.407577i	0.880893	+	0.473316i	$0.156943\pi$
$968$	2.17299	+	2.17299i	0.0698424	+	0.0698424i
$969$	−1.47495	−	1.25592i	−0.0473821	−	0.0403459i
$970$	−28.3351	−	28.3351i	−0.909787	−	0.909787i
$971$			59.6230i			1.91339i	0.291088	+	0.956696i	$0.405983\pi$
$971$			59.6230i			1.91339i	−0.291088	+	0.956696i	$0.594017\pi$
$972$	−10.9494	+	4.63150i	−0.351201	+	0.148555i
$973$	−14.0800	−	14.0800i	−0.451384	−	0.451384i
$974$	37.6085			1.20505
$975$	−37.1301	−	37.9982i	−1.18911	−	1.21692i
$976$	−19.8622			−0.635775
$977$	29.8185	+	29.8185i	0.953978	+	0.953978i	0.998987	−	0.0450084i	$-0.0143315\pi$
$977$	29.8185	+	29.8185i	0.953978	+	0.953978i	−0.0450084	+	0.998987i	$0.514331\pi$
$978$	15.1914	−	1.21843i	0.485768	−	0.0389611i
$979$		−	6.92226i		−	0.221236i
$980$	2.93456	+	2.93456i	0.0937410	+	0.0937410i
$981$	−7.93627	+	10.9923i	−0.253385	+	0.350956i
$982$	−15.6304	−	15.6304i	−0.498785	−	0.498785i
$983$	19.7117	−	19.7117i	0.628705	−	0.628705i	−0.319037	−	0.947742i	$-0.603359\pi$
$983$	19.7117	−	19.7117i	0.628705	−	0.628705i	0.947742	+	0.319037i	$0.103359\pi$
$984$	−1.56646	−	19.5306i	−0.0499368	−	0.622614i
$985$		−	72.8921i		−	2.32254i
$986$	−0.566735	+	0.566735i	−0.0180485	+	0.0180485i
$987$	2.84832	+	35.5129i	0.0906629	+	1.13039i
$988$	−1.23684	+	13.4665i	−0.0393492	+	0.428428i
$989$			1.49730i			0.0476114i
$990$	9.94366	+	7.17919i	0.316030	+	0.228170i
$991$	17.5329			0.556951			0.278475	−	0.960443i	$-0.410171\pi$
$991$	17.5329			0.556951			0.278475	+	0.960443i	$0.410171\pi$
$992$	−33.2821			−1.05671
$993$	23.9493	+	20.3928i	0.760008	+	0.647147i
$994$	6.68374	−	6.68374i	0.211995	−	0.211995i
$995$	−54.9753	+	54.9753i	−1.74283	+	1.74283i
$996$	4.25889	+	3.62645i	0.134948	+	0.114908i
$997$	−17.4500			−0.552648			−0.276324	−	0.961065i	$-0.589116\pi$
$997$	−17.4500			−0.552648			−0.276324	+	0.961065i	$0.589116\pi$
$998$	−11.7933			−0.373312
$999$	23.3143	−	38.4310i	0.737631	−	1.21590i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.j.a.122.16	✓	96
3.2	odd	2	inner	429.2.j.a.122.33	yes	96
13.8	odd	4	inner	429.2.j.a.320.33	yes	96
39.8	even	4	inner	429.2.j.a.320.16	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.j.a.122.16	✓	96	1.1	even	1	trivial
429.2.j.a.122.33	yes	96	3.2	odd	2	inner
429.2.j.a.320.16	yes	96	39.8	even	4	inner
429.2.j.a.320.33	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)

\(f(q)\)	\(=\)	\(q+(-0.786557 - 0.786557i) q^{2} +(-0.138475 - 1.72651i) q^{3} -0.762656i q^{4} +(-2.59877 - 2.59877i) q^{5} +(-1.24908 + 1.46691i) q^{6} +(1.66123 + 1.66123i) q^{7} +(-2.17299 + 2.17299i) q^{8} +(-2.96165 + 0.478155i) q^{9} +O(q^{10})\)	\(q+(-0.786557 - 0.786557i) q^{2} +(-0.138475 - 1.72651i) q^{3} -0.762656i q^{4} +(-2.59877 - 2.59877i) q^{5} +(-1.24908 + 1.46691i) q^{6} +(1.66123 + 1.66123i) q^{7} +(-2.17299 + 2.17299i) q^{8} +(-2.96165 + 0.478155i) q^{9} +4.08816i q^{10} +(-0.707107 + 0.707107i) q^{11} +(-1.31673 + 0.105609i) q^{12} +(-2.30564 - 2.77200i) q^{13} -2.61330i q^{14} +(-4.12692 + 4.84665i) q^{15} +1.89305 q^{16} +0.227424 q^{17} +(2.70560 + 1.95341i) q^{18} +(3.47748 - 3.47748i) q^{19} +(-1.98196 + 1.98196i) q^{20} +(2.63809 - 3.09816i) q^{21} +1.11236 q^{22} +6.07423 q^{23} +(4.05258 + 3.45077i) q^{24} +8.50717i q^{25} +(-0.366819 + 3.99386i) q^{26} +(1.23565 + 5.04709i) q^{27} +(1.26695 - 1.26695i) q^{28} -3.16820i q^{29} +(7.05823 - 0.566106i) q^{30} +(-5.82470 + 5.82470i) q^{31} +(2.85698 + 2.85698i) q^{32} +(1.31874 + 1.12291i) q^{33} +(-0.178882 - 0.178882i) q^{34} -8.63429i q^{35} +(0.364668 + 2.25872i) q^{36} +(-6.11691 - 6.11691i) q^{37} -5.47048 q^{38} +(-4.46661 + 4.36456i) q^{39} +11.2942 q^{40} +(-2.60292 - 2.60292i) q^{41} +(-4.51189 + 0.361877i) q^{42} +0.246500i q^{43} +(0.539279 + 0.539279i) q^{44} +(8.93925 + 6.45402i) q^{45} +(-4.77773 - 4.77773i) q^{46} +(-6.19096 + 6.19096i) q^{47} +(-0.262139 - 3.26835i) q^{48} -1.48063i q^{49} +(6.69137 - 6.69137i) q^{50} +(-0.0314925 - 0.392649i) q^{51} +(-2.11408 + 1.75841i) q^{52} -5.98713i q^{53} +(2.99792 - 4.94174i) q^{54} +3.67521 q^{55} -7.21966 q^{56} +(-6.48544 - 5.52235i) q^{57} +(-2.49197 + 2.49197i) q^{58} +(-7.36078 + 7.36078i) q^{59} +(3.69632 + 3.14742i) q^{60} -10.4922 q^{61} +9.16292 q^{62} +(-5.71431 - 4.12565i) q^{63} -8.28045i q^{64} +(-1.21196 + 13.1956i) q^{65} +(-0.154034 - 1.92050i) q^{66} +(4.63058 - 4.63058i) q^{67} -0.173446i q^{68} +(-0.841127 - 10.4872i) q^{69} +(-6.79137 + 6.79137i) q^{70} +(2.55758 + 2.55758i) q^{71} +(5.39660 - 7.47465i) q^{72} +(4.26887 + 4.26887i) q^{73} +9.62261i q^{74} +(14.6877 - 1.17803i) q^{75} +(-2.65212 - 2.65212i) q^{76} -2.34933 q^{77} +(6.94622 + 0.0802664i) q^{78} +7.92269 q^{79} +(-4.91958 - 4.91958i) q^{80} +(8.54274 - 2.83225i) q^{81} +4.09469i q^{82} +(-2.99429 - 2.99429i) q^{83} +(-2.36283 - 2.01195i) q^{84} +(-0.591022 - 0.591022i) q^{85} +(0.193887 - 0.193887i) q^{86} +(-5.46992 + 0.438716i) q^{87} -3.07307i q^{88} +(-4.89478 + 4.89478i) q^{89} +(-1.95477 - 12.1077i) q^{90} +(0.774731 - 8.43514i) q^{91} -4.63255i q^{92} +(10.8630 + 9.24981i) q^{93} +9.73909 q^{94} -18.0743 q^{95} +(4.53698 - 5.32822i) q^{96} +(-6.93103 + 6.93103i) q^{97} +(-1.16460 + 1.16460i) q^{98} +(1.75610 - 2.43231i) 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

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