LMFDB - Embedded newform 770.2.m.f.43.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(43,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("770.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.m (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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.14
Character	$\chi$	$=$	770.43
Dual form			770.2.m.f.197.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.129076 + 0.129076i) q^{3} +1.00000i q^{4} +(-1.76845 - 1.36842i) q^{5} +0.182542i q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} -2.96668i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.129076 + 0.129076i) q^{3} +1.00000i q^{4} +(-1.76845 - 1.36842i) q^{5} +0.182542i q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} -2.96668i q^{9} +(-0.282869 - 2.21810i) q^{10} +(-1.31499 - 3.04480i) q^{11} +(-0.129076 + 0.129076i) q^{12} +(2.63858 - 2.63858i) q^{13} +1.00000i q^{14} +(-0.0516353 - 0.404896i) q^{15} -1.00000 q^{16} +(-3.32632 - 3.32632i) q^{17} +(2.09776 - 2.09776i) q^{18} +2.52561 q^{19} +(1.36842 - 1.76845i) q^{20} +0.182542i q^{21} +(1.22316 - 3.08284i) q^{22} +(-1.90680 - 1.90680i) q^{23} -0.182542 q^{24} +(1.25486 + 4.83997i) q^{25} +3.73152 q^{26} +(0.770158 - 0.770158i) q^{27} +(-0.707107 + 0.707107i) q^{28} +0.802541 q^{29} +(0.249793 - 0.322817i) q^{30} +9.02473 q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.223278 - 0.562746i) q^{33} -4.70413i q^{34} +(-0.282869 - 2.21810i) q^{35} +2.96668 q^{36} +(-7.49723 + 7.49723i) q^{37} +(1.78587 + 1.78587i) q^{38} +0.681157 q^{39} +(2.21810 - 0.282869i) q^{40} -5.93687i q^{41} +(-0.129076 + 0.129076i) q^{42} +(7.13123 - 7.13123i) q^{43} +(3.04480 - 1.31499i) q^{44} +(-4.05966 + 5.24644i) q^{45} -2.69662i q^{46} +(1.82629 - 1.82629i) q^{47} +(-0.129076 - 0.129076i) q^{48} +1.00000i q^{49} +(-2.53505 + 4.30970i) q^{50} -0.858699i q^{51} +(2.63858 + 2.63858i) q^{52} +(-0.115350 - 0.115350i) q^{53} +1.08917 q^{54} +(-1.84106 + 7.18404i) q^{55} -1.00000 q^{56} +(0.325996 + 0.325996i) q^{57} +(0.567482 + 0.567482i) q^{58} -2.90454i q^{59} +(0.404896 - 0.0516353i) q^{60} -6.91475i q^{61} +(6.38145 + 6.38145i) q^{62} +(2.09776 - 2.09776i) q^{63} -1.00000i q^{64} +(-8.27689 + 1.05553i) q^{65} +(0.555803 - 0.240040i) q^{66} +(-11.2286 + 11.2286i) q^{67} +(3.32632 - 3.32632i) q^{68} -0.492246i q^{69} +(1.36842 - 1.76845i) q^{70} -0.437972 q^{71} +(2.09776 + 2.09776i) q^{72} +(7.08040 - 7.08040i) q^{73} -10.6027 q^{74} +(-0.462753 + 0.786700i) q^{75} +2.52561i q^{76} +(1.22316 - 3.08284i) q^{77} +(0.481651 + 0.481651i) q^{78} -7.19398 q^{79} +(1.76845 + 1.36842i) q^{80} -8.70122 q^{81} +(4.19800 - 4.19800i) q^{82} +(-5.44560 + 5.44560i) q^{83} -0.182542 q^{84} +(1.33065 + 10.4342i) q^{85} +10.0851 q^{86} +(0.103589 + 0.103589i) q^{87} +(3.08284 + 1.22316i) q^{88} -2.70652i q^{89} +(-6.58040 + 0.839180i) q^{90} +3.73152 q^{91} +(1.90680 - 1.90680i) q^{92} +(1.16488 + 1.16488i) q^{93} +2.58276 q^{94} +(-4.46642 - 3.45609i) q^{95} -0.182542i q^{96} +(1.36133 - 1.36133i) q^{97} +(-0.707107 + 0.707107i) q^{98} +(-9.03294 + 3.90114i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{3}+O(q^{10}) $ 36 * q - 4 * q^3	$ 36 q - 4 q^{3} + 12 q^{11} + 4 q^{12} - 4 q^{15} - 36 q^{16} - 12 q^{20} - 12 q^{22} + 4 q^{23} + 12 q^{25} + 24 q^{26} + 56 q^{27} + 8 q^{31} - 44 q^{33} - 44 q^{36} - 28 q^{37} + 16 q^{38} + 4 q^{42} - 44 q^{45} + 12 q^{47} + 4 q^{48} + 28 q^{53} + 40 q^{55} - 36 q^{56} - 24 q^{58} + 12 q^{60} + 24 q^{66} + 12 q^{67} - 12 q^{70} - 112 q^{71} - 52 q^{75} - 12 q^{77} + 48 q^{78} + 4 q^{81} + 40 q^{82} + 32 q^{86} - 12 q^{88} + 24 q^{91} - 4 q^{92} - 80 q^{93} + 100 q^{97}+O(q^{100}) $ 36 * q - 4 * q^3 + 12 * q^11 + 4 * q^12 - 4 * q^15 - 36 * q^16 - 12 * q^20 - 12 * q^22 + 4 * q^23 + 12 * q^25 + 24 * q^26 + 56 * q^27 + 8 * q^31 - 44 * q^33 - 44 * q^36 - 28 * q^37 + 16 * q^38 + 4 * q^42 - 44 * q^45 + 12 * q^47 + 4 * q^48 + 28 * q^53 + 40 * q^55 - 36 * q^56 - 24 * q^58 + 12 * q^60 + 24 * q^66 + 12 * q^67 - 12 * q^70 - 112 * q^71 - 52 * q^75 - 12 * q^77 + 48 * q^78 + 4 * q^81 + 40 * q^82 + 32 * q^86 - 12 * q^88 + 24 * q^91 - 4 * q^92 - 80 * q^93 + 100 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.129076	+	0.129076i	0.0745223	+	0.0745223i	0.743386	−	0.668863i	$-0.233219\pi$
$3$	0.129076	+	0.129076i	0.0745223	+	0.0745223i	−0.668863	+	0.743386i	$0.733219\pi$
$4$			1.00000i			0.500000i
$5$	−1.76845	−	1.36842i	−0.790877	−	0.611975i
$5$	−1.76845	−	1.36842i	−0.790877	−	0.611975i
$6$			0.182542i			0.0745223i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		−	2.96668i		−	0.988893i
$10$	−0.282869	−	2.21810i	−0.0894509	−	0.701426i
$11$	−1.31499	−	3.04480i	−0.396484	−	0.918042i
$11$	−1.31499	−	3.04480i	−0.396484	−	0.918042i
$12$	−0.129076	+	0.129076i	−0.0372612	+	0.0372612i
$13$	2.63858	−	2.63858i	0.731810	−	0.731810i	−0.239168	−	0.970978i	$-0.576875\pi$
$13$	2.63858	−	2.63858i	0.731810	−	0.731810i	0.970978	+	0.239168i	$0.0768746\pi$
$14$			1.00000i			0.267261i
$15$	−0.0516353	−	0.404896i	−0.0133322	−	0.104544i
$16$	−1.00000			−0.250000
$17$	−3.32632	−	3.32632i	−0.806751	−	0.806751i	0.177390	−	0.984141i	$-0.443235\pi$
$17$	−3.32632	−	3.32632i	−0.806751	−	0.806751i	−0.984141	+	0.177390i	$0.943235\pi$
$18$	2.09776	−	2.09776i	0.494446	−	0.494446i
$19$	2.52561			0.579414			0.289707	−	0.957115i	$-0.406442\pi$
$19$	2.52561			0.579414			0.289707	+	0.957115i	$0.406442\pi$
$20$	1.36842	−	1.76845i	0.305988	−	0.395438i
$21$			0.182542i			0.0398339i
$22$	1.22316	−	3.08284i	0.260779	−	0.657263i
$23$	−1.90680	−	1.90680i	−0.397596	−	0.397596i	0.479789	−	0.877384i	$-0.340713\pi$
$23$	−1.90680	−	1.90680i	−0.397596	−	0.397596i	−0.877384	+	0.479789i	$0.840713\pi$
$24$	−0.182542			−0.0372612
$25$	1.25486	+	4.83997i	0.250973	+	0.967994i
$26$	3.73152			0.731810
$27$	0.770158	−	0.770158i	0.148217	−	0.148217i
$28$	−0.707107	+	0.707107i	−0.133631	+	0.133631i
$29$	0.802541			0.149028			0.0745141	−	0.997220i	$-0.476259\pi$
$29$	0.802541			0.149028			0.0745141	+	0.997220i	$0.476259\pi$
$30$	0.249793	−	0.322817i	0.0456058	−	0.0589380i
$31$	9.02473			1.62089			0.810445	−	0.585815i	$-0.199226\pi$
$31$	9.02473			1.62089			0.810445	+	0.585815i	$0.199226\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	0.223278	−	0.562746i	0.0388677	−	0.0979615i
$34$		−	4.70413i		−	0.806751i
$35$	−0.282869	−	2.21810i	−0.0478135	−	0.374928i
$36$	2.96668			0.494446
$37$	−7.49723	+	7.49723i	−1.23254	+	1.23254i	−0.269551	+	0.962986i	$0.586875\pi$
$37$	−7.49723	+	7.49723i	−1.23254	+	1.23254i	−0.962986	+	0.269551i	$0.913125\pi$
$38$	1.78587	+	1.78587i	0.289707	+	0.289707i
$39$	0.681157			0.109072
$40$	2.21810	−	0.282869i	0.350713	−	0.0447254i
$41$		−	5.93687i		−	0.927184i	−0.886049	−	0.463592i	$-0.846560\pi$
$41$		−	5.93687i		−	0.927184i	0.886049	−	0.463592i	$-0.153440\pi$
$42$	−0.129076	+	0.129076i	−0.0199169	+	0.0199169i
$43$	7.13123	−	7.13123i	1.08750	−	1.08750i	0.0917175	−	0.995785i	$-0.470764\pi$
$43$	7.13123	−	7.13123i	1.08750	−	1.08750i	0.995785	−	0.0917175i	$-0.0292357\pi$
$44$	3.04480	−	1.31499i	0.459021	−	0.198242i
$45$	−4.05966	+	5.24644i	−0.605178	+	0.782093i
$46$		−	2.69662i		−	0.397596i
$47$	1.82629	−	1.82629i	0.266391	−	0.266391i	−0.561253	−	0.827644i	$-0.689681\pi$
$47$	1.82629	−	1.82629i	0.266391	−	0.266391i	0.827644	+	0.561253i	$0.189681\pi$
$48$	−0.129076	−	0.129076i	−0.0186306	−	0.0186306i
$49$			1.00000i			0.142857i
$50$	−2.53505	+	4.30970i	−0.358511	+	0.609483i
$51$		−	0.858699i		−	0.120242i
$52$	2.63858	+	2.63858i	0.365905	+	0.365905i
$53$	−0.115350	−	0.115350i	−0.0158445	−	0.0158445i	0.699140	−	0.714985i	$-0.253566\pi$
$53$	−0.115350	−	0.115350i	−0.0158445	−	0.0158445i	−0.714985	+	0.699140i	$0.753566\pi$
$54$	1.08917			0.148217
$55$	−1.84106	+	7.18404i	−0.248249	+	0.968696i
$56$	−1.00000			−0.133631
$57$	0.325996	+	0.325996i	0.0431793	+	0.0431793i
$58$	0.567482	+	0.567482i	0.0745141	+	0.0745141i
$59$		−	2.90454i		−	0.378139i	−0.981964	−	0.189069i	$-0.939453\pi$
$59$		−	2.90454i		−	0.378139i	0.981964	−	0.189069i	$-0.0605471\pi$
$60$	0.404896	−	0.0516353i	0.0522719	−	0.00666609i
$61$		−	6.91475i		−	0.885343i	−0.896684	−	0.442672i	$-0.854031\pi$
$61$		−	6.91475i		−	0.885343i	0.896684	−	0.442672i	$-0.145969\pi$
$62$	6.38145	+	6.38145i	0.810445	+	0.810445i
$63$	2.09776	−	2.09776i	0.264293	−	0.264293i
$64$		−	1.00000i		−	0.125000i
$65$	−8.27689	+	1.05553i	−1.02662	+	0.130922i
$66$	0.555803	−	0.240040i	0.0684146	−	0.0295469i
$67$	−11.2286	+	11.2286i	−1.37179	+	1.37179i	−0.514007	+	0.857786i	$0.671840\pi$
$67$	−11.2286	+	11.2286i	−1.37179	+	1.37179i	−0.857786	+	0.514007i	$0.828160\pi$
$68$	3.32632	−	3.32632i	0.403375	−	0.403375i
$69$		−	0.492246i		−	0.0592595i
$70$	1.36842	−	1.76845i	0.163557	−	0.211371i
$71$	−0.437972			−0.0519777			−0.0259888	−	0.999662i	$-0.508273\pi$
$71$	−0.437972			−0.0519777			−0.0259888	+	0.999662i	$0.508273\pi$
$72$	2.09776	+	2.09776i	0.247223	+	0.247223i
$73$	7.08040	−	7.08040i	0.828698	−	0.828698i	−0.158639	−	0.987337i	$-0.550710\pi$
$73$	7.08040	−	7.08040i	0.828698	−	0.828698i	0.987337	+	0.158639i	$0.0507105\pi$
$74$	−10.6027			−1.23254
$75$	−0.462753	+	0.786700i	−0.0534341	+	0.0908402i
$76$			2.52561i			0.289707i
$77$	1.22316	−	3.08284i	0.139392	−	0.351322i
$78$	0.481651	+	0.481651i	0.0545362	+	0.0545362i
$79$	−7.19398			−0.809386			−0.404693	−	0.914453i	$-0.632622\pi$
$79$	−7.19398			−0.809386			−0.404693	+	0.914453i	$0.632622\pi$
$80$	1.76845	+	1.36842i	0.197719	+	0.152994i
$81$	−8.70122			−0.966802
$82$	4.19800	−	4.19800i	0.463592	−	0.463592i
$83$	−5.44560	+	5.44560i	−0.597732	+	0.597732i	−0.939709	−	0.341976i	$-0.888904\pi$
$83$	−5.44560	+	5.44560i	−0.597732	+	0.597732i	0.341976	+	0.939709i	$0.388904\pi$
$84$	−0.182542			−0.0199169
$85$	1.33065	+	10.4342i	0.144329	+	1.13175i
$86$	10.0851			1.08750
$87$	0.103589	+	0.103589i	0.0111059	+	0.0111059i
$88$	3.08284	+	1.22316i	0.328631	+	0.130390i
$89$		−	2.70652i		−	0.286891i	−0.989658	−	0.143445i	$-0.954182\pi$
$89$		−	2.70652i		−	0.286891i	0.989658	−	0.143445i	$-0.0458181\pi$
$90$	−6.58040	+	0.839180i	−0.693635	+	0.0884574i
$91$	3.73152			0.391169
$92$	1.90680	−	1.90680i	0.198798	−	0.198798i
$93$	1.16488	+	1.16488i	0.120792	+	0.120792i
$94$	2.58276			0.266391
$95$	−4.46642	−	3.45609i	−0.458245	−	0.354587i
$96$		−	0.182542i		−	0.0186306i
$97$	1.36133	−	1.36133i	0.138222	−	0.138222i	−0.634610	−	0.772832i	$-0.718839\pi$
$97$	1.36133	−	1.36133i	0.138222	−	0.138222i	0.772832	+	0.634610i	$0.218839\pi$
$98$	−0.707107	+	0.707107i	−0.0714286	+	0.0714286i
$99$	−9.03294	+	3.90114i	−0.907845	+	0.392080i
$100$	−4.83997	+	1.25486i	−0.483997	+	0.125486i
$101$			14.0838i			1.40139i	0.713460	+	0.700696i	$0.247127\pi$
$101$			14.0838i			1.40139i	−0.713460	+	0.700696i	$0.752873\pi$
$102$	0.607192	−	0.607192i	0.0601210	−	0.0601210i
$103$	−4.89183	−	4.89183i	−0.482007	−	0.482007i	0.423765	−	0.905772i	$-0.360708\pi$
$103$	−4.89183	−	4.89183i	−0.482007	−	0.482007i	−0.905772	+	0.423765i	$0.860708\pi$
$104$			3.73152i			0.365905i
$105$	0.249793	−	0.322817i	0.0243773	−	0.0315037i
$106$		−	0.163130i		−	0.0158445i
$107$	5.96299	+	5.96299i	0.576464	+	0.576464i	0.933927	−	0.357463i	$-0.116358\pi$
$107$	5.96299	+	5.96299i	0.576464	+	0.576464i	−0.357463	+	0.933927i	$0.616358\pi$
$108$	0.770158	+	0.770158i	0.0741085	+	0.0741085i
$109$	3.47984			0.333308			0.166654	−	0.986015i	$-0.446704\pi$
$109$	3.47984			0.333308			0.166654	+	0.986015i	$0.446704\pi$
$110$	−6.38172	+	3.77806i	−0.608473	+	0.360224i
$111$	−1.93543			−0.183703
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$	14.1659	+	14.1659i	1.33262	+	1.33262i	0.903021	+	0.429597i	$0.141344\pi$
$113$	14.1659	+	14.1659i	1.33262	+	1.33262i	0.429597	+	0.903021i	$0.358656\pi$
$114$			0.461029i			0.0431793i
$115$	0.762790	+	5.98139i	0.0711306	+	0.557768i
$116$			0.802541i			0.0745141i
$117$	−7.82782	−	7.82782i	−0.723682	−	0.723682i
$118$	2.05382	−	2.05382i	0.189069	−	0.189069i
$119$		−	4.70413i		−	0.431227i
$120$	0.322817	+	0.249793i	0.0294690	+	0.0228029i
$121$	−7.54162	+	8.00775i	−0.685602	+	0.727977i
$122$	4.88947	−	4.88947i	0.442672	−	0.442672i
$123$	0.766311	−	0.766311i	0.0690959	−	0.0690959i
$124$			9.02473i			0.810445i
$125$	4.40393	−	10.2764i	0.393900	−	0.919153i
$126$	2.96668			0.264293
$127$	9.58442	+	9.58442i	0.850480	+	0.850480i	0.990192	−	0.139712i	$-0.0446177\pi$
$127$	9.58442	+	9.58442i	0.850480	+	0.850480i	−0.139712	+	0.990192i	$0.544618\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	1.84095			0.162086
$130$	−6.59902	−	5.10627i	−0.578772	−	0.447850i
$131$		−	5.46796i		−	0.477738i	−0.971052	−	0.238869i	$-0.923223\pi$
$131$		−	5.46796i		−	0.477738i	0.971052	−	0.238869i	$-0.0767766\pi$
$132$	0.562746	+	0.223278i	0.0489807	+	0.0194339i
$133$	1.78587	+	1.78587i	0.154855	+	0.154855i
$134$	−15.8797			−1.37179
$135$	−2.41589	+	0.308091i	−0.207926	+	0.0265163i
$136$	4.70413			0.403375
$137$	−8.95658	+	8.95658i	−0.765212	+	0.765212i	−0.977259	−	0.212047i	$-0.931987\pi$
$137$	−8.95658	+	8.95658i	−0.765212	+	0.765212i	0.212047	+	0.977259i	$0.431987\pi$
$138$	0.348071	−	0.348071i	0.0296297	−	0.0296297i
$139$	8.79364			0.745867			0.372933	−	0.927858i	$-0.378352\pi$
$139$	8.79364			0.745867			0.372933	+	0.927858i	$0.378352\pi$
$140$	2.21810	−	0.282869i	0.187464	−	0.0239068i
$141$	0.471461			0.0397042
$142$	−0.309693	−	0.309693i	−0.0259888	−	0.0259888i
$143$	−11.5036	−	4.56425i	−0.961983	−	0.381682i
$144$			2.96668i			0.247223i
$145$	−1.41926	−	1.09821i	−0.117863	−	0.0912015i
$146$	10.0132			0.828698
$147$	−0.129076	+	0.129076i	−0.0106460	+	0.0106460i
$148$	−7.49723	−	7.49723i	−0.616268	−	0.616268i
$149$	−14.3990			−1.17961			−0.589806	−	0.807545i	$-0.700796\pi$
$149$	−14.3990			−1.17961			−0.589806	+	0.807545i	$0.700796\pi$
$150$	−0.883496	+	0.229065i	−0.0721372	+	0.0187031i
$151$		−	17.3562i		−	1.41242i	−0.708000	−	0.706212i	$-0.750402\pi$
$151$		−	17.3562i		−	1.41242i	0.708000	−	0.706212i	$-0.249598\pi$
$152$	−1.78587	+	1.78587i	−0.144854	+	0.144854i
$153$	−9.86812	+	9.86812i	−0.797790	+	0.797790i
$154$	3.04480	−	1.31499i	0.245357	−	0.105965i
$155$	−15.9598	−	12.3496i	−1.28192	−	0.991944i
$156$			0.681157i			0.0545362i
$157$	−1.10318	+	1.10318i	−0.0880430	+	0.0880430i	−0.749757	−	0.661714i	$-0.769829\pi$
$157$	−1.10318	+	1.10318i	−0.0880430	+	0.0880430i	0.661714	+	0.749757i	$0.269829\pi$
$158$	−5.08691	−	5.08691i	−0.404693	−	0.404693i
$159$		−	0.0297779i		−	0.00236154i
$160$	0.282869	+	2.21810i	0.0223627	+	0.175357i
$161$		−	2.69662i		−	0.212524i
$162$	−6.15269	−	6.15269i	−0.483401	−	0.483401i
$163$	−8.39822	−	8.39822i	−0.657800	−	0.657800i	0.297059	−	0.954859i	$-0.403994\pi$
$163$	−8.39822	−	8.39822i	−0.657800	−	0.657800i	−0.954859	+	0.297059i	$0.903994\pi$
$164$	5.93687			0.463592
$165$	−1.16493	+	0.689653i	−0.0906896	+	0.0536894i
$166$	−7.70124			−0.597732
$167$	13.9026	+	13.9026i	1.07581	+	1.07581i	0.996880	+	0.0789333i	$0.0251514\pi$
$167$	13.9026	+	13.9026i	1.07581	+	1.07581i	0.0789333	+	0.996880i	$0.474849\pi$
$168$	−0.129076	−	0.129076i	−0.00995846	−	0.00995846i
$169$		−	0.924212i		−	0.0710932i
$170$	−6.43721	+	8.31903i	−0.493712	+	0.638041i
$171$		−	7.49266i		−	0.572978i
$172$	7.13123	+	7.13123i	0.543751	+	0.543751i
$173$	−1.44923	+	1.44923i	−0.110183	+	0.110183i	−0.760049	−	0.649866i	$-0.774825\pi$
$173$	−1.44923	+	1.44923i	−0.110183	+	0.110183i	0.649866	+	0.760049i	$0.274825\pi$
$174$			0.146497i			0.0111059i
$175$	−2.53505	+	4.30970i	−0.191632	+	0.325783i
$176$	1.31499	+	3.04480i	0.0991209	+	0.229510i
$177$	0.374908	−	0.374908i	0.0281798	−	0.0281798i
$178$	1.91380	−	1.91380i	0.143445	−	0.143445i
$179$		−	17.9885i		−	1.34452i	−0.740315	−	0.672260i	$-0.765324\pi$
$179$		−	17.9885i		−	1.34452i	0.740315	−	0.672260i	$-0.234676\pi$
$180$	−5.24644	−	4.05966i	−0.391046	−	0.302589i
$181$	13.2699			0.986342			0.493171	−	0.869932i	$-0.335838\pi$
$181$	13.2699			0.986342			0.493171	+	0.869932i	$0.335838\pi$
$182$	2.63858	+	2.63858i	0.195585	+	0.195585i
$183$	0.892532	−	0.892532i	0.0659778	−	0.0659778i
$184$	2.69662			0.198798
$185$	23.5179	−	2.99917i	1.72907	−	0.220503i
$186$			1.64739i			0.120792i
$187$	−5.75391	+	14.5020i	−0.420768	+	1.06049i
$188$	1.82629	+	1.82629i	0.133196	+	0.133196i
$189$	1.08917			0.0792253
$190$	−0.714415	−	5.60206i	−0.0518291	−	0.406416i
$191$	10.3337			0.747721			0.373860	−	0.927485i	$-0.378034\pi$
$191$	10.3337			0.747721			0.373860	+	0.927485i	$0.378034\pi$
$192$	0.129076	−	0.129076i	0.00931529	−	0.00931529i
$193$	−1.38232	+	1.38232i	−0.0995018	+	0.0995018i	−0.755105	−	0.655604i	$-0.772414\pi$
$193$	−1.38232	+	1.38232i	−0.0995018	+	0.0995018i	0.655604	+	0.755105i	$0.272414\pi$
$194$	1.92521			0.138222
$195$	−1.20460	−	0.932108i	−0.0862629	−	0.0667496i
$196$	−1.00000			−0.0714286
$197$	13.4283	+	13.4283i	0.956728	+	0.956728i	0.999102	−	0.0423739i	$-0.0134921\pi$
$197$	13.4283	+	13.4283i	0.956728	+	0.956728i	−0.0423739	+	0.999102i	$0.513492\pi$
$198$	−9.14578	−	3.62873i	−0.649962	−	0.257883i
$199$		−	27.4823i		−	1.94817i	−0.226183	−	0.974085i	$-0.572625\pi$
$199$		−	27.4823i		−	1.94817i	0.226183	−	0.974085i	$-0.427375\pi$
$200$	−4.30970	−	2.53505i	−0.304742	−	0.179255i
$201$	−2.89870			−0.204458
$202$	−9.95876	+	9.95876i	−0.700696	+	0.700696i
$203$	0.567482	+	0.567482i	0.0398294	+	0.0398294i
$204$	0.858699			0.0601210
$205$	−8.12413	+	10.4991i	−0.567414	+	0.733288i
$206$		−	6.91810i		−	0.482007i
$207$	−5.65687	+	5.65687i	−0.393179	+	0.393179i
$208$	−2.63858	+	2.63858i	−0.182953	+	0.182953i
$209$	−3.32114	−	7.68997i	−0.229728	−	0.531926i
$210$	0.404896	−	0.0516353i	0.0279405	−	0.00356317i
$211$			10.6730i			0.734761i	0.930071	+	0.367380i	$0.119745\pi$
$211$			10.6730i			0.734761i	−0.930071	+	0.367380i	$0.880255\pi$
$212$	0.115350	−	0.115350i	0.00792227	−	0.00792227i
$213$	−0.0565318	−	0.0565318i	−0.00387350	−	0.00387350i
$214$			8.43294i			0.576464i
$215$	−22.3698	+	2.85275i	−1.52561	+	0.194556i
$216$			1.08917i			0.0741085i
$217$	6.38145	+	6.38145i	0.433201	+	0.433201i
$218$	2.46062	+	2.46062i	0.166654	+	0.166654i
$219$	1.82783			0.123513
$220$	−7.18404	−	1.84106i	−0.484348	−	0.124125i
$221$	−17.5535			−1.18078
$222$	−1.36856	−	1.36856i	−0.0918515	−	0.0918515i
$223$	10.1950	+	10.1950i	0.682708	+	0.682708i	0.960610	−	0.277901i	$-0.0896388\pi$
$223$	10.1950	+	10.1950i	0.682708	+	0.682708i	−0.277901	+	0.960610i	$0.589639\pi$
$224$		−	1.00000i		−	0.0668153i
$225$	14.3586	−	3.72278i	0.957242	−	0.248185i
$226$			20.0336i			1.33262i
$227$	2.92799	+	2.92799i	0.194337	+	0.194337i	0.797567	−	0.603230i	$-0.206120\pi$
$227$	2.92799	+	2.92799i	0.194337	+	0.194337i	−0.603230	+	0.797567i	$0.706120\pi$
$228$	−0.325996	+	0.325996i	−0.0215896	+	0.0215896i
$229$			21.9446i			1.45014i	0.688676	+	0.725069i	$0.258192\pi$
$229$			21.9446i			1.45014i	−0.688676	+	0.725069i	$0.741808\pi$
$230$	−3.69011	+	4.76886i	−0.243319	+	0.314449i
$231$	0.555803	−	0.240040i	0.0365691	−	0.0157935i
$232$	−0.567482	+	0.567482i	−0.0372570	+	0.0372570i
$233$	2.56907	−	2.56907i	0.168305	−	0.168305i	−0.617929	−	0.786234i	$-0.712028\pi$
$233$	2.56907	−	2.56907i	0.168305	−	0.168305i	0.786234	+	0.617929i	$0.212028\pi$
$234$		−	11.0702i		−	0.723682i
$235$	−5.72882	+	0.730581i	−0.373707	+	0.0476578i
$236$	2.90454			0.189069
$237$	−0.928574	−	0.928574i	−0.0603173	−	0.0603173i
$238$	3.32632	−	3.32632i	0.215613	−	0.215613i
$239$	25.3178			1.63767			0.818836	−	0.574027i	$-0.194620\pi$
$239$	25.3178			1.63767			0.818836	+	0.574027i	$0.194620\pi$
$240$	0.0516353	+	0.404896i	0.00333304	+	0.0261359i
$241$			9.90945i			0.638324i	0.947700	+	0.319162i	$0.103401\pi$
$241$			9.90945i			0.638324i	−0.947700	+	0.319162i	$0.896599\pi$
$242$	−10.9951	+	0.329602i	−0.706789	+	0.0211876i
$243$	−3.43360	−	3.43360i	−0.220265	−	0.220265i
$244$	6.91475			0.442672
$245$	1.36842	−	1.76845i	0.0874250	−	0.112982i
$246$	1.08373			0.0690959
$247$	6.66402	−	6.66402i	0.424021	−	0.424021i
$248$	−6.38145	+	6.38145i	−0.405222	+	0.405222i
$249$	−1.40580			−0.0890888
$250$	10.3806	−	4.15249i	0.656527	−	0.262627i
$251$	−17.4289			−1.10010			−0.550052	−	0.835131i	$-0.685392\pi$
$251$	−17.4289			−1.10010			−0.550052	+	0.835131i	$0.685392\pi$
$252$	2.09776	+	2.09776i	0.132146	+	0.132146i
$253$	−3.29841	+	8.31325i	−0.207369	+	0.522650i
$254$			13.5544i			0.850480i
$255$	−1.17506	+	1.51857i	−0.0735851	+	0.0950966i
$256$	1.00000			0.0625000
$257$	−10.9146	+	10.9146i	−0.680834	+	0.680834i	−0.960188	−	0.279354i	$-0.909880\pi$
$257$	−10.9146	+	10.9146i	−0.680834	+	0.680834i	0.279354	+	0.960188i	$0.409880\pi$
$258$	1.30175	+	1.30175i	0.0810432	+	0.0810432i
$259$	−10.6027			−0.658819
$260$	−1.05553	−	8.27689i	−0.0654611	−	0.513311i
$261$		−	2.38088i		−	0.147373i
$262$	3.86643	−	3.86643i	0.238869	−	0.238869i
$263$	13.5025	−	13.5025i	0.832598	−	0.832598i	−0.155273	−	0.987872i	$-0.549626\pi$
$263$	13.5025	−	13.5025i	0.832598	−	0.832598i	0.987872	+	0.155273i	$0.0496258\pi$
$264$	0.240040	+	0.555803i	0.0147734	+	0.0342073i
$265$	0.0461442	+	0.361838i	0.00283462	+	0.0222276i
$266$			2.52561i			0.154855i
$267$	0.349348	−	0.349348i	0.0213798	−	0.0213798i
$268$	−11.2286	−	11.2286i	−0.685897	−	0.685897i
$269$			8.86635i			0.540591i	0.962777	+	0.270296i	$0.0871214\pi$
$269$			8.86635i			0.540591i	−0.962777	+	0.270296i	$0.912879\pi$
$270$	−1.92614	−	1.49044i	−0.117221	−	0.0907051i
$271$		−	5.23825i		−	0.318201i	−0.987262	−	0.159100i	$-0.949141\pi$
$271$		−	5.23825i		−	0.318201i	0.987262	−	0.159100i	$-0.0508594\pi$
$272$	3.32632	+	3.32632i	0.201688	+	0.201688i
$273$	0.481651	+	0.481651i	0.0291508	+	0.0291508i
$274$	−12.6665			−0.765212
$275$	13.0866	−	10.1853i	0.789153	−	0.614197i
$276$	0.492246			0.0296297
$277$	10.0587	+	10.0587i	0.604371	+	0.604371i	0.941469	−	0.337098i	$-0.109446\pi$
$277$	10.0587	+	10.0587i	0.604371	+	0.604371i	−0.337098	+	0.941469i	$0.609446\pi$
$278$	6.21804	+	6.21804i	0.372933	+	0.372933i
$279$		−	26.7735i		−	1.60289i
$280$	1.76845	+	1.36842i	0.105685	+	0.0817786i
$281$		−	32.9319i		−	1.96455i	−0.187441	−	0.982276i	$-0.560019\pi$
$281$		−	32.9319i		−	1.96455i	0.187441	−	0.982276i	$-0.439981\pi$
$282$	0.333373	+	0.333373i	0.0198521	+	0.0198521i
$283$	1.69887	−	1.69887i	0.100987	−	0.100987i	−0.654808	−	0.755795i	$-0.727251\pi$
$283$	1.69887	−	1.69887i	0.100987	−	0.100987i	0.755795	+	0.654808i	$0.227251\pi$
$284$		−	0.437972i		−	0.0259888i
$285$	−0.130410	−	1.02261i	−0.00772485	−	0.0605741i
$286$	−4.90690	−	11.3617i	−0.290151	−	0.671833i
$287$	4.19800	−	4.19800i	0.247800	−	0.247800i
$288$	−2.09776	+	2.09776i	−0.123612	+	0.123612i
$289$			5.12880i			0.301694i
$290$	−0.227014	−	1.78012i	−0.0133307	−	0.104532i
$291$	0.351431			0.0206013
$292$	7.08040	+	7.08040i	0.414349	+	0.414349i
$293$	−3.25333	+	3.25333i	−0.190062	+	0.190062i	−0.795723	−	0.605661i	$-0.792909\pi$
$293$	−3.25333	+	3.25333i	−0.190062	+	0.190062i	0.605661	+	0.795723i	$0.292909\pi$
$294$	−0.182542			−0.0106460
$295$	−3.97462	+	5.13655i	−0.231412	+	0.299061i
$296$		−	10.6027i		−	0.616268i
$297$	−3.35772	−	1.33223i	−0.194835	−	0.0773038i
$298$	−10.1816	−	10.1816i	−0.589806	−	0.589806i
$299$	−10.0625			−0.581929
$300$	−0.786700	−	0.462753i	−0.0454201	−	0.0267170i
$301$	10.0851			0.581295
$302$	12.2727	−	12.2727i	0.706212	−	0.706212i
$303$	−1.81789	+	1.81789i	−0.104435	+	0.104435i
$304$	−2.52561			−0.144854
$305$	−9.46227	+	12.2284i	−0.541808	+	0.700198i
$306$	−13.9556			−0.797790
$307$	−16.6031	−	16.6031i	−0.947591	−	0.947591i	0.0511021	−	0.998693i	$-0.483727\pi$
$307$	−16.6031	−	16.6031i	−0.947591	−	0.947591i	−0.998693	+	0.0511021i	$0.983727\pi$
$308$	3.08284	+	1.22316i	0.175661	+	0.0696962i
$309$		−	1.26284i		−	0.0718405i
$310$	−2.55281	−	20.0178i	−0.144990	−	1.13693i
$311$	33.0199			1.87238			0.936192	−	0.351489i	$-0.114324\pi$
$311$	33.0199			1.87238			0.936192	+	0.351489i	$0.114324\pi$
$312$	−0.481651	+	0.481651i	−0.0272681	+	0.0272681i
$313$	16.2927	+	16.2927i	0.920916	+	0.920916i	0.997094	−	0.0761781i	$-0.0242718\pi$
$313$	16.2927	+	16.2927i	0.920916	+	0.920916i	−0.0761781	+	0.997094i	$0.524272\pi$
$314$	−1.56013			−0.0880430
$315$	−6.58040	+	0.839180i	−0.370764	+	0.0472824i
$316$		−	7.19398i		−	0.404693i
$317$	6.24196	−	6.24196i	0.350583	−	0.350583i	−0.509743	−	0.860327i	$-0.670260\pi$
$317$	6.24196	−	6.24196i	0.350583	−	0.350583i	0.860327	+	0.509743i	$0.170260\pi$
$318$	0.0210562	−	0.0210562i	0.00118077	−	0.00118077i
$319$	−1.05533	−	2.44358i	−0.0590872	−	0.136814i
$320$	−1.36842	+	1.76845i	−0.0764969	+	0.0988596i
$321$			1.53936i			0.0859189i
$322$	1.90680	−	1.90680i	0.106262	−	0.106262i
$323$	−8.40098	−	8.40098i	−0.467443	−	0.467443i
$324$		−	8.70122i		−	0.483401i
$325$	16.0817	+	9.45959i	0.892053	+	0.524724i
$326$		−	11.8769i		−	0.657800i
$327$	0.449166	+	0.449166i	0.0248389	+	0.0248389i
$328$	4.19800	+	4.19800i	0.231796	+	0.231796i
$329$	2.58276			0.142392
$330$	−1.31139	−	0.336071i	−0.0721895	−	0.0185001i
$331$	−14.4363			−0.793491			−0.396745	−	0.917929i	$-0.629860\pi$
$331$	−14.4363			−0.793491			−0.396745	+	0.917929i	$0.629860\pi$
$332$	−5.44560	−	5.44560i	−0.298866	−	0.298866i
$333$	22.2419	+	22.2419i	1.21885	+	1.21885i
$334$			19.6612i			1.07581i
$335$	35.2227	−	4.49186i	1.92442	−	0.245416i
$336$		−	0.182542i		−	0.00995846i
$337$	8.85604	+	8.85604i	0.482419	+	0.482419i	0.905904	−	0.423484i	$-0.139193\pi$
$337$	8.85604	+	8.85604i	0.482419	+	0.482419i	−0.423484	+	0.905904i	$0.639193\pi$
$338$	0.653516	−	0.653516i	0.0355466	−	0.0355466i
$339$			3.65697i			0.198620i
$340$	−10.4342	+	1.33065i	−0.565876	+	0.0721646i
$341$	−11.8674	−	27.4785i	−0.642656	−	1.48804i
$342$	5.29811	−	5.29811i	0.286489	−	0.286489i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$			10.0851i			0.543751i
$345$	−0.673599	+	0.870515i	−0.0362653	+	0.0468670i
$346$	−2.04953			−0.110183
$347$	−19.2809	−	19.2809i	−1.03506	−	1.03506i	−0.999363	−	0.0356924i	$-0.988636\pi$
$347$	−19.2809	−	19.2809i	−1.03506	−	1.03506i	−0.0356924	−	0.999363i	$-0.511364\pi$
$348$	−0.103589	+	0.103589i	−0.00555296	+	0.00555296i
$349$	−9.84866			−0.527187			−0.263593	−	0.964634i	$-0.584908\pi$
$349$	−9.84866			−0.527187			−0.263593	+	0.964634i	$0.584908\pi$
$350$	−4.83997	+	1.25486i	−0.258707	+	0.0670753i
$351$		−	4.06425i		−	0.216933i
$352$	−1.22316	+	3.08284i	−0.0651948	+	0.164316i
$353$	18.3248	+	18.3248i	0.975329	+	0.975329i	0.999703	−	0.0243739i	$-0.00775923\pi$
$353$	18.3248	+	18.3248i	0.975329	+	0.975329i	−0.0243739	+	0.999703i	$0.507759\pi$
$354$	0.530199			0.0281798
$355$	0.774533	+	0.599328i	0.0411079	+	0.0318090i
$356$	2.70652			0.143445
$357$	0.607192	−	0.607192i	0.0321360	−	0.0321360i
$358$	12.7198	−	12.7198i	0.672260	−	0.672260i
$359$	13.3058			0.702253			0.351127	−	0.936328i	$-0.385799\pi$
$359$	13.3058			0.702253			0.351127	+	0.936328i	$0.385799\pi$
$360$	−0.839180	−	6.58040i	−0.0442287	−	0.346818i
$361$	−12.6213			−0.664279
$362$	9.38322	+	9.38322i	0.493171	+	0.493171i
$363$	−2.00706	+	0.0601661i	−0.105343	+	0.00315790i
$364$			3.73152i			0.195585i
$365$	−22.2103	+	2.83242i	−1.16254	+	0.148256i
$366$	1.26223			0.0659778
$367$	−1.34080	+	1.34080i	−0.0699890	+	0.0699890i	−0.741235	−	0.671246i	$-0.765759\pi$
$367$	−1.34080	+	1.34080i	−0.0699890	+	0.0699890i	0.671246	+	0.741235i	$0.265759\pi$
$368$	1.90680	+	1.90680i	0.0993989	+	0.0993989i
$369$	−17.6128			−0.916886
$370$	18.7504	+	14.5089i	0.974785	+	0.754282i
$371$		−	0.163130i		−	0.00846926i
$372$	−1.16488	+	1.16488i	−0.0603962	+	0.0603962i
$373$	11.3278	−	11.3278i	0.586533	−	0.586533i	−0.350158	−	0.936691i	$-0.613872\pi$
$373$	11.3278	−	11.3278i	0.586533	−	0.586533i	0.936691	+	0.350158i	$0.113872\pi$
$374$	−14.3231	+	6.18587i	−0.740631	+	0.319863i
$375$	1.89489	−	0.758003i	0.0978518	−	0.0391431i
$376$			2.58276i			0.133196i
$377$	2.11757	−	2.11757i	0.109060	−	0.109060i
$378$	0.770158	+	0.770158i	0.0396126	+	0.0396126i
$379$			12.1378i			0.623478i	0.950168	+	0.311739i	$0.100911\pi$
$379$			12.1378i			0.623478i	−0.950168	+	0.311739i	$0.899089\pi$
$380$	3.45609	−	4.46642i	0.177294	−	0.229123i
$381$			2.47425i			0.126760i
$382$	7.30703	+	7.30703i	0.373860	+	0.373860i
$383$	−5.83677	−	5.83677i	−0.298245	−	0.298245i	0.542081	−	0.840326i	$-0.317637\pi$
$383$	−5.83677	−	5.83677i	−0.298245	−	0.298245i	−0.840326	+	0.542081i	$0.817637\pi$
$384$	0.182542			0.00931529
$385$	−6.38172	+	3.77806i	−0.325242	+	0.192548i
$386$	−1.95490			−0.0995018
$387$	−21.1561	−	21.1561i	−1.07542	−	1.07542i
$388$	1.36133	+	1.36133i	0.0691111	+	0.0691111i
$389$			10.3990i			0.527249i	0.964625	+	0.263625i	$0.0849180\pi$
$389$			10.3990i			0.527249i	−0.964625	+	0.263625i	$0.915082\pi$
$390$	−0.192678	−	1.51088i	−0.00975663	−	0.0765062i
$391$			12.6853i			0.641521i
$392$	−0.707107	−	0.707107i	−0.0357143	−	0.0357143i
$393$	0.705784	−	0.705784i	0.0356021	−	0.0356021i
$394$			18.9905i			0.956728i
$395$	12.7222	+	9.84438i	0.640125	+	0.495324i
$396$	−3.90114	−	9.03294i	−0.196040	−	0.453923i
$397$	12.2428	−	12.2428i	0.614448	−	0.614448i	−0.329654	−	0.944102i	$-0.606932\pi$
$397$	12.2428	−	12.2428i	0.614448	−	0.614448i	0.944102	+	0.329654i	$0.106932\pi$
$398$	19.4329	−	19.4329i	0.974085	−	0.974085i
$399$			0.461029i			0.0230803i
$400$	−1.25486	−	4.83997i	−0.0627432	−	0.241999i
$401$	15.6050			0.779276			0.389638	−	0.920968i	$-0.372600\pi$
$401$	15.6050			0.779276			0.389638	+	0.920968i	$0.372600\pi$
$402$	−2.04969	−	2.04969i	−0.102229	−	0.102229i
$403$	23.8125	−	23.8125i	1.18618	−	1.18618i
$404$	−14.0838			−0.700696
$405$	15.3877	+	11.9069i	0.764621	+	0.591659i
$406$			0.802541i			0.0398294i
$407$	32.6863	+	12.9688i	1.62020	+	0.642840i
$408$	0.607192	+	0.607192i	0.0300605	+	0.0300605i
$409$	26.6689			1.31869			0.659346	−	0.751840i	$-0.270833\pi$
$409$	26.6689			1.31869			0.659346	+	0.751840i	$0.270833\pi$
$410$	−13.1686	+	1.67935i	−0.650351	+	0.0829374i
$411$	−2.31217			−0.114051
$412$	4.89183	−	4.89183i	0.241003	−	0.241003i
$413$	2.05382	−	2.05382i	0.101062	−	0.101062i
$414$	−8.00002			−0.393179
$415$	17.0822	−	2.17844i	0.838530	−	0.106935i
$416$	−3.73152			−0.182953
$417$	1.13505	+	1.13505i	0.0555837	+	0.0555837i
$418$	3.08923	−	7.78603i	0.151099	−	0.380827i
$419$		−	12.7649i		−	0.623606i	−0.950147	−	0.311803i	$-0.899067\pi$
$419$		−	12.7649i		−	0.623606i	0.950147	−	0.311803i	$-0.100933\pi$
$420$	0.322817	+	0.249793i	0.0157518	+	0.0121887i
$421$	20.4419			0.996279			0.498140	−	0.867097i	$-0.334017\pi$
$421$	20.4419			0.996279			0.498140	+	0.867097i	$0.334017\pi$
$422$	−7.54696	+	7.54696i	−0.367380	+	0.367380i
$423$	−5.41800	−	5.41800i	−0.263432	−	0.263432i
$424$	0.163130			0.00792227
$425$	11.9252	−	20.2734i	0.578458	−	0.983403i
$426$		−	0.0799480i		−	0.00387350i
$427$	4.88947	−	4.88947i	0.236618	−	0.236618i
$428$	−5.96299	+	5.96299i	−0.288232	+	0.288232i
$429$	−0.895713	−	2.07399i	−0.0432454	−	0.100133i
$430$	−17.8350	−	13.8006i	−0.860081	−	0.665525i
$431$			7.48786i			0.360678i	0.983605	+	0.180339i	$0.0577194\pi$
$431$			7.48786i			0.360678i	−0.983605	+	0.180339i	$0.942281\pi$
$432$	−0.770158	+	0.770158i	−0.0370542	+	0.0370542i
$433$	24.2677	+	24.2677i	1.16623	+	1.16623i	0.983086	+	0.183144i	$0.0586275\pi$
$433$	24.2677	+	24.2677i	1.16623	+	1.16623i	0.183144	+	0.983086i	$0.441373\pi$
$434$			9.02473i			0.433201i
$435$	−0.0414394	−	0.324946i	−0.00198687	−	0.0155800i
$436$			3.47984i			0.166654i
$437$	−4.81583	−	4.81583i	−0.230372	−	0.230372i
$438$	1.29247	+	1.29247i	0.0617565	+	0.0617565i
$439$	6.46700			0.308653			0.154326	−	0.988020i	$-0.450679\pi$
$439$	6.46700			0.308653			0.154326	+	0.988020i	$0.450679\pi$
$440$	−3.77806	−	6.38172i	−0.180112	−	0.304236i
$441$	2.96668			0.141270
$442$	−12.4122	−	12.4122i	−0.590389	−	0.590389i
$443$	14.4339	+	14.4339i	0.685774	+	0.685774i	0.961295	−	0.275521i	$-0.0888505\pi$
$443$	14.4339	+	14.4339i	0.685774	+	0.685774i	−0.275521	+	0.961295i	$0.588850\pi$
$444$		−	1.93543i		−	0.0918515i
$445$	−3.70365	+	4.78636i	−0.175570	+	0.226895i
$446$			14.4179i			0.682708i
$447$	−1.85857	−	1.85857i	−0.0879074	−	0.0879074i
$448$	0.707107	−	0.707107i	0.0334077	−	0.0334077i
$449$			2.35252i			0.111022i	0.998458	+	0.0555112i	$0.0176789\pi$
$449$			2.35252i			0.111022i	−0.998458	+	0.0555112i	$0.982321\pi$
$450$	12.7855	+	7.52069i	0.602714	+	0.354529i
$451$	−18.0766	+	7.80691i	−0.851194	+	0.367613i
$452$	−14.1659	+	14.1659i	−0.666309	+	0.666309i
$453$	2.24027	−	2.24027i	0.105257	−	0.105257i
$454$			4.14080i			0.194337i
$455$	−6.59902	−	5.10627i	−0.309367	−	0.239386i
$456$	−0.461029			−0.0215896
$457$	−5.97848	−	5.97848i	−0.279662	−	0.279662i	0.553312	−	0.832974i	$-0.313364\pi$
$457$	−5.97848	−	5.97848i	−0.279662	−	0.279662i	−0.832974	+	0.553312i	$0.813364\pi$
$458$	−15.5172	+	15.5172i	−0.725069	+	0.725069i
$459$	−5.12358			−0.239148
$460$	−5.98139	+	0.762790i	−0.278884	+	0.0355653i
$461$		−	39.8490i		−	1.85595i	−0.372640	−	0.927976i	$-0.621547\pi$
$461$		−	39.8490i		−	1.85595i	0.372640	−	0.927976i	$-0.378453\pi$
$462$	0.562746	+	0.223278i	0.0261813	+	0.0103878i
$463$	−9.78810	−	9.78810i	−0.454891	−	0.454891i	0.442083	−	0.896974i	$-0.354240\pi$
$463$	−9.78810	−	9.78810i	−0.454891	−	0.454891i	−0.896974	+	0.442083i	$0.854240\pi$
$464$	−0.802541			−0.0372570
$465$	−0.465995	−	3.65408i	−0.0216100	−	0.169454i
$466$	3.63321			0.168305
$467$	14.7602	−	14.7602i	0.683019	−	0.683019i	−0.277660	−	0.960679i	$-0.589559\pi$
$467$	14.7602	−	14.7602i	0.683019	−	0.683019i	0.960679	+	0.277660i	$0.0895590\pi$
$468$	7.82782	−	7.82782i	0.361841	−	0.361841i
$469$	−15.8797			−0.733254
$470$	−4.56749	−	3.53429i	−0.210683	−	0.163025i
$471$	−0.284788			−0.0131223
$472$	2.05382	+	2.05382i	0.0945347	+	0.0945347i
$473$	−31.0907	−	12.3357i	−1.42955	−	0.567196i
$474$		−	1.31320i		−	0.0603173i
$475$	3.16929	+	12.2239i	0.145417	+	0.560869i
$476$	4.70413			0.215613
$477$	−0.342206	+	0.342206i	−0.0156686	+	0.0156686i
$478$	17.9024	+	17.9024i	0.818836	+	0.818836i
$479$	40.9378			1.87050			0.935248	−	0.353993i	$-0.115176\pi$
$479$	40.9378			1.87050			0.935248	+	0.353993i	$0.115176\pi$
$480$	−0.249793	+	0.322817i	−0.0114015	+	0.0147345i
$481$			39.5641i			1.80397i
$482$	−7.00704	+	7.00704i	−0.319162	+	0.319162i
$483$	0.348071	−	0.348071i	0.0158378	−	0.0158378i
$484$	−8.00775	−	7.54162i	−0.363988	−	0.342801i
$485$	−4.27032	+	0.544582i	−0.193905	+	0.0247282i
$486$		−	4.85584i		−	0.220265i
$487$	−10.6084	+	10.6084i	−0.480715	+	0.480715i	−0.905360	−	0.424645i	$-0.860399\pi$
$487$	−10.6084	+	10.6084i	−0.480715	+	0.480715i	0.424645	+	0.905360i	$0.360399\pi$
$488$	4.88947	+	4.88947i	0.221336	+	0.221336i
$489$		−	2.16803i		−	0.0980415i
$490$	2.21810	−	0.282869i	0.100204	−	0.0127787i
$491$			17.5960i			0.794095i	0.917798	+	0.397047i	$0.129965\pi$
$491$			17.5960i			0.794095i	−0.917798	+	0.397047i	$0.870035\pi$
$492$	0.766311	+	0.766311i	0.0345479	+	0.0345479i
$493$	−2.66951	−	2.66951i	−0.120229	−	0.120229i
$494$	9.42434			0.424021
$495$	21.3127	+	5.46185i	0.957937	+	0.245492i
$496$	−9.02473			−0.405222
$497$	−0.309693	−	0.309693i	−0.0138916	−	0.0138916i
$498$	−0.994049	−	0.994049i	−0.0445444	−	0.0445444i
$499$			26.9280i			1.20546i	0.797945	+	0.602731i	$0.205921\pi$
$499$			26.9280i			1.20546i	−0.797945	+	0.602731i	$0.794079\pi$
$500$	10.2764	+	4.40393i	0.459577	+	0.196950i
$501$			3.58899i			0.160344i
$502$	−12.3241	−	12.3241i	−0.550052	−	0.550052i
$503$	−0.939750	+	0.939750i	−0.0419014	+	0.0419014i	−0.727747	−	0.685846i	$-0.759433\pi$
$503$	−0.939750	+	0.939750i	−0.0419014	+	0.0419014i	0.685846	+	0.727747i	$0.259433\pi$
$504$			2.96668i			0.132146i
$505$	19.2725	−	24.9066i	0.857617	−	1.10833i
$506$	−8.21068	+	3.54603i	−0.365009	+	0.157640i
$507$	0.119294	−	0.119294i	0.00529803	−	0.00529803i
$508$	−9.58442	+	9.58442i	−0.425240	+	0.425240i
$509$		−	21.0066i		−	0.931103i	−0.885021	−	0.465551i	$-0.845856\pi$
$509$		−	21.0066i		−	0.931103i	0.885021	−	0.465551i	$-0.154144\pi$
$510$	−1.90468	+	0.242899i	−0.0843408	+	0.0107557i
$511$	10.0132			0.442958
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	1.94512	−	1.94512i	0.0858790	−	0.0858790i
$514$	−15.4356			−0.680834
$515$	1.95691	+	15.3451i	0.0862319	+	0.676184i
$516$			1.84095i			0.0810432i
$517$	−7.96221	−	3.15913i	−0.350178	−	0.138938i
$518$	−7.49723	−	7.49723i	−0.329409	−	0.329409i
$519$	−0.374124			−0.0164222
$520$	5.10627	−	6.59902i	0.223925	−	0.289386i
$521$	−33.7336			−1.47789			−0.738947	−	0.673763i	$-0.764677\pi$
$521$	−33.7336			−1.47789			−0.738947	+	0.673763i	$0.764677\pi$
$522$	1.68354	−	1.68354i	0.0736864	−	0.0736864i
$523$	2.01631	−	2.01631i	0.0881669	−	0.0881669i	−0.661648	−	0.749815i	$-0.730143\pi$
$523$	2.01631	−	2.01631i	0.0881669	−	0.0881669i	0.749815	+	0.661648i	$0.230143\pi$
$524$	5.46796			0.238869
$525$	−0.883496	+	0.229065i	−0.0385589	+	0.00999721i
$526$	19.0954			0.832598
$527$	−30.0191	−	30.0191i	−1.30765	−	1.30765i
$528$	−0.223278	+	0.562746i	−0.00971693	+	0.0244904i
$529$		−	15.7282i		−	0.683835i
$530$	−0.223229	+	0.288487i	−0.00969647	+	0.0125311i
$531$	−8.61683			−0.373939
$532$	−1.78587	+	1.78587i	−0.0774275	+	0.0774275i
$533$	−15.6649	−	15.6649i	−0.678523	−	0.678523i
$534$	0.494053			0.0213798
$535$	−2.38541	−	18.7051i	−0.103130	−	0.808694i
$536$		−	15.8797i		−	0.685897i
$537$	2.32189	−	2.32189i	0.100197	−	0.100197i
$538$	−6.26946	+	6.26946i	−0.270296	+	0.270296i
$539$	3.04480	−	1.31499i	0.131149	−	0.0566405i
$540$	−0.308091	−	2.41589i	−0.0132581	−	0.103963i
$541$		−	13.8187i		−	0.594113i	−0.954860	−	0.297057i	$-0.903995\pi$
$541$		−	13.8187i		−	0.594113i	0.954860	−	0.297057i	$-0.0960050\pi$
$542$	3.70400	−	3.70400i	0.159100	−	0.159100i
$543$	1.71283	+	1.71283i	0.0735045	+	0.0735045i
$544$			4.70413i			0.201688i
$545$	−6.15394	−	4.76188i	−0.263606	−	0.203977i
$546$			0.681157i			0.0291508i
$547$	7.97431	+	7.97431i	0.340957	+	0.340957i	0.856727	−	0.515770i	$-0.172494\pi$
$547$	7.97431	+	7.97431i	0.340957	+	0.340957i	−0.515770	+	0.856727i	$0.672494\pi$
$548$	−8.95658	−	8.95658i	−0.382606	−	0.382606i
$549$	−20.5139			−0.875510
$550$	16.4557	+	2.05153i	0.701675	+	0.0874777i
$551$	2.02690			0.0863490
$552$	0.348071	+	0.348071i	0.0148149	+	0.0148149i
$553$	−5.08691	−	5.08691i	−0.216318	−	0.216318i
$554$			14.2252i			0.604371i
$555$	3.42272	+	2.64848i	0.145286	+	0.112422i
$556$			8.79364i			0.372933i
$557$	2.55770	+	2.55770i	0.108373	+	0.108373i	0.759214	−	0.650841i	$-0.225584\pi$
$557$	2.55770	+	2.55770i	0.108373	+	0.108373i	−0.650841	+	0.759214i	$0.725584\pi$
$558$	18.9317	−	18.9317i	0.801443	−	0.801443i
$559$		−	37.6327i		−	1.59169i
$560$	0.282869	+	2.21810i	0.0119534	+	0.0937320i
$561$	−2.61457	+	1.12918i	−0.110387	+	0.0476739i
$562$	23.2864	−	23.2864i	0.982276	−	0.982276i
$563$	−20.5478	+	20.5478i	−0.865984	+	0.865984i	−0.992025	−	0.126041i	$-0.959773\pi$
$563$	−20.5478	+	20.5478i	−0.865984	+	0.865984i	0.126041	+	0.992025i	$0.459773\pi$
$564$			0.471461i			0.0198521i
$565$	−5.66689	−	44.4367i	−0.238408	−	1.86947i
$566$	2.40256			0.100987
$567$	−6.15269	−	6.15269i	−0.258389	−	0.258389i
$568$	0.309693	−	0.309693i	0.0129944	−	0.0129944i
$569$	−17.2466			−0.723016			−0.361508	−	0.932369i	$-0.617738\pi$
$569$	−17.2466			−0.723016			−0.361508	+	0.932369i	$0.617738\pi$
$570$	0.630880	−	0.815308i	0.0264246	−	0.0341495i
$571$		−	5.24776i		−	0.219612i	−0.993953	−	0.109806i	$-0.964977\pi$
$571$		−	5.24776i		−	0.219612i	0.993953	−	0.109806i	$-0.0350229\pi$
$572$	4.56425	−	11.5036i	0.190841	−	0.480992i
$573$	1.33384	+	1.33384i	0.0557219	+	0.0557219i
$574$	5.93687			0.247800
$575$	6.83609	−	11.6216i	0.285085	−	0.484656i
$576$	−2.96668			−0.123612
$577$	24.4412	−	24.4412i	1.01750	−	1.01750i	0.0176579	−	0.999844i	$-0.494379\pi$
$577$	24.4412	−	24.4412i	1.01750	−	1.01750i	0.999844	−	0.0176579i	$-0.00562098\pi$
$578$	−3.62661	+	3.62661i	−0.150847	+	0.150847i
$579$	−0.356851			−0.0148302
$580$	1.09821	−	1.41926i	0.0456008	−	0.0589315i
$581$	−7.70124			−0.319501
$582$	0.248499	+	0.248499i	0.0103006	+	0.0103006i
$583$	−0.199534	+	0.502902i	−0.00826385	+	0.0208281i
$584$			10.0132i			0.414349i
$585$	3.13141	+	24.5549i	0.129468	+	1.01522i
$586$	−4.60091			−0.190062
$587$	−17.0410	+	17.0410i	−0.703358	+	0.703358i	−0.965130	−	0.261772i	$-0.915693\pi$
$587$	−17.0410	+	17.0410i	−0.703358	+	0.703358i	0.261772	+	0.965130i	$0.415693\pi$
$588$	−0.129076	−	0.129076i	−0.00532302	−	0.00532302i
$589$	22.7929			0.939166
$590$	−6.44257	+	0.821603i	−0.265236	+	0.0338249i
$591$			3.46656i			0.142595i
$592$	7.49723	−	7.49723i	0.308134	−	0.308134i
$593$	−25.0268	+	25.0268i	−1.02773	+	1.02773i	−0.0281209	+	0.999605i	$0.508952\pi$
$593$	−25.0268	+	25.0268i	−1.02773	+	1.02773i	−0.999605	+	0.0281209i	$0.991048\pi$
$594$	−1.43224	−	3.31630i	−0.0587656	−	0.136069i
$595$	−6.43721	+	8.31903i	−0.263900	+	0.341047i
$596$		−	14.3990i		−	0.589806i
$597$	3.54732	−	3.54732i	0.145182	−	0.145182i
$598$	−7.11526	−	7.11526i	−0.290965	−	0.290965i
$599$		−	10.8984i		−	0.445295i	−0.974899	−	0.222648i	$-0.928530\pi$
$599$		−	10.8984i		−	0.445295i	0.974899	−	0.222648i	$-0.0714699\pi$
$600$	−0.229065	−	0.883496i	−0.00935154	−	0.0360686i
$601$			5.18350i			0.211439i	0.994396	+	0.105720i	$0.0337146\pi$
$601$			5.18350i			0.211439i	−0.994396	+	0.105720i	$0.966285\pi$
$602$	7.13123	+	7.13123i	0.290647	+	0.290647i
$603$	33.3117	+	33.3117i	1.35656	+	1.35656i
$604$	17.3562			0.706212
$605$	24.2950	−	3.84125i	0.987730	−	0.156169i
$606$	−2.57088			−0.104435
$607$	7.31991	+	7.31991i	0.297106	+	0.297106i	0.839879	−	0.542773i	$-0.182626\pi$
$607$	7.31991	+	7.31991i	0.297106	+	0.297106i	−0.542773	+	0.839879i	$0.682626\pi$
$608$	−1.78587	−	1.78587i	−0.0724268	−	0.0724268i
$609$			0.146497i			0.00593637i
$610$	−15.3376	+	1.95597i	−0.621003	+	0.0791948i
$611$		−	9.63760i		−	0.389896i
$612$	−9.86812	−	9.86812i	−0.398895	−	0.398895i
$613$	−31.4119	+	31.4119i	−1.26871	+	1.26871i	−0.321959	+	0.946753i	$0.604341\pi$
$613$	−31.4119	+	31.4119i	−1.26871	+	1.26871i	−0.946753	+	0.321959i	$0.895659\pi$
$614$		−	23.4804i		−	0.947591i
$615$	−2.40382	+	0.306552i	−0.0969313	+	0.0123614i
$616$	1.31499	+	3.04480i	0.0529823	+	0.122679i
$617$	−32.1276	+	32.1276i	−1.29341	+	1.29341i	−0.360746	+	0.932664i	$0.617478\pi$
$617$	−32.1276	+	32.1276i	−1.29341	+	1.29341i	−0.932664	+	0.360746i	$0.882522\pi$
$618$	0.892964	−	0.892964i	0.0359203	−	0.0359203i
$619$			23.5449i			0.946349i	0.880969	+	0.473175i	$0.156892\pi$
$619$			23.5449i			0.946349i	−0.880969	+	0.473175i	$0.843108\pi$
$620$	12.3496	−	15.9598i	0.495972	−	0.640962i
$621$	−2.93708			−0.117861
$622$	23.3486	+	23.3486i	0.936192	+	0.936192i
$623$	1.91380	−	1.91380i	0.0766748	−	0.0766748i
$624$	−0.681157			−0.0272681
$625$	−21.8506	+	12.1470i	−0.874025	+	0.485880i
$626$			23.0413i			0.920916i
$627$	0.563913	−	1.42128i	0.0225205	−	0.0567603i
$628$	−1.10318	−	1.10318i	−0.0440215	−	0.0440215i
$629$	49.8764			1.98870
$630$	−5.24644	−	4.05966i	−0.209023	−	0.161741i
$631$	7.13944			0.284217			0.142108	−	0.989851i	$-0.454612\pi$
$631$	7.13944			0.284217			0.142108	+	0.989851i	$0.454612\pi$
$632$	5.08691	−	5.08691i	0.202347	−	0.202347i
$633$	−1.37763	+	1.37763i	−0.0547561	+	0.0547561i
$634$	8.82746			0.350583
$635$	−3.83412	−	30.0651i	−0.152152	−	1.19310i
$636$	0.0297779			0.00118077
$637$	2.63858	+	2.63858i	0.104544	+	0.104544i
$638$	0.981638	−	2.47410i	0.0388634	−	0.0979506i
$639$			1.29932i			0.0514003i
$640$	−2.21810	+	0.282869i	−0.0876783	+	0.0111814i
$641$	−0.566376			−0.0223705			−0.0111853	−	0.999937i	$-0.503560\pi$
$641$	−0.566376			−0.0223705			−0.0111853	+	0.999937i	$0.503560\pi$
$642$	−1.08849	+	1.08849i	−0.0429594	+	0.0429594i
$643$	−1.99142	−	1.99142i	−0.0785341	−	0.0785341i	0.666749	−	0.745283i	$-0.267685\pi$
$643$	−1.99142	−	1.99142i	−0.0785341	−	0.0785341i	−0.745283	+	0.666749i	$0.767685\pi$
$644$	2.69662			0.106262
$645$	−3.25563	−	2.51919i	−0.128190	−	0.0991929i
$646$		−	11.8808i		−	0.467443i
$647$	−7.99793	+	7.99793i	−0.314431	+	0.314431i	−0.846623	−	0.532192i	$-0.821368\pi$
$647$	−7.99793	+	7.99793i	−0.314431	+	0.314431i	0.532192	+	0.846623i	$0.321368\pi$
$648$	6.15269	−	6.15269i	0.241700	−	0.241700i
$649$	−8.84374	+	3.81943i	−0.347147	+	0.149926i
$650$	4.68254	+	18.0604i	0.183665	+	0.708388i
$651$			1.64739i			0.0645663i
$652$	8.39822	−	8.39822i	0.328900	−	0.328900i
$653$	−7.72049	−	7.72049i	−0.302126	−	0.302126i	0.539719	−	0.841845i	$-0.318530\pi$
$653$	−7.72049	−	7.72049i	−0.302126	−	0.302126i	−0.841845	+	0.539719i	$0.818530\pi$
$654$			0.635216i			0.0248389i
$655$	−7.48245	+	9.66983i	−0.292364	+	0.377832i
$656$			5.93687i			0.231796i
$657$	−21.0053	−	21.0053i	−0.819494	−	0.819494i
$658$	1.82629	+	1.82629i	0.0711960	+	0.0711960i
$659$	−21.7876			−0.848726			−0.424363	−	0.905492i	$-0.639502\pi$
$659$	−21.7876			−0.848726			−0.424363	+	0.905492i	$0.639502\pi$
$660$	−0.689653	−	1.16493i	−0.0268447	−	0.0453448i
$661$	−29.3456			−1.14141			−0.570705	−	0.821155i	$-0.693330\pi$
$661$	−29.3456			−1.14141			−0.570705	+	0.821155i	$0.693330\pi$
$662$	−10.2080	−	10.2080i	−0.396745	−	0.396745i
$663$	−2.26575	−	2.26575i	−0.0879943	−	0.0879943i
$664$		−	7.70124i		−	0.298866i
$665$	−0.714415	−	5.60206i	−0.0277038	−	0.217239i
$666$			31.4548i			1.21885i
$667$	−1.53029	−	1.53029i	−0.0592529	−	0.0592529i
$668$	−13.9026	+	13.9026i	−0.537907	+	0.537907i
$669$			2.63187i			0.101754i
$670$	28.0824	+	21.7300i	1.08492	+	0.839503i
$671$	−21.0540	+	9.09281i	−0.812782	+	0.351024i
$672$	0.129076	−	0.129076i	0.00497923	−	0.00497923i
$673$	17.8150	−	17.8150i	0.686717	−	0.686717i	−0.274788	−	0.961505i	$-0.588608\pi$
$673$	17.8150	−	17.8150i	0.686717	−	0.686717i	0.961505	+	0.274788i	$0.0886075\pi$
$674$			12.5243i			0.482419i
$675$	4.69398	+	2.76110i	0.180672	+	0.106275i
$676$	0.924212			0.0355466
$677$	−12.1009	−	12.1009i	−0.465074	−	0.465074i	0.435241	−	0.900314i	$-0.356663\pi$
$677$	−12.1009	−	12.1009i	−0.465074	−	0.465074i	−0.900314	+	0.435241i	$0.856663\pi$
$678$	−2.58587	+	2.58587i	−0.0993098	+	0.0993098i
$679$	1.92521			0.0738828
$680$	−8.31903	−	6.43721i	−0.319020	−	0.246856i
$681$			0.755869i			0.0289650i
$682$	11.0387	−	27.8218i	0.422694	−	1.06535i
$683$	−13.2824	−	13.2824i	−0.508237	−	0.508237i	0.405748	−	0.913985i	$-0.367011\pi$
$683$	−13.2824	−	13.2824i	−0.508237	−	0.508237i	−0.913985	+	0.405748i	$0.867011\pi$
$684$	7.49266			0.286489
$685$	28.0956	−	3.58296i	1.07348	−	0.136898i
$686$	−1.00000			−0.0381802
$687$	−2.83253	+	2.83253i	−0.108068	+	0.108068i
$688$	−7.13123	+	7.13123i	−0.271876	+	0.271876i
$689$	−0.608721			−0.0231904
$690$	−1.09185	+	0.139241i	−0.0415662	+	0.00530082i
$691$	−21.6423			−0.823312			−0.411656	−	0.911339i	$-0.635050\pi$
$691$	−21.6423			−0.823312			−0.411656	+	0.911339i	$0.635050\pi$
$692$	−1.44923	−	1.44923i	−0.0550916	−	0.0550916i
$693$	−9.14578	−	3.62873i	−0.347419	−	0.137844i
$694$		−	27.2674i		−	1.03506i
$695$	−15.5512	−	12.0334i	−0.589889	−	0.456452i
$696$	−0.146497			−0.00555296
$697$	−19.7479	+	19.7479i	−0.748007	+	0.748007i
$698$	−6.96405	−	6.96405i	−0.263593	−	0.263593i
$699$	0.663213			0.0250850
$700$	−4.30970	−	2.53505i	−0.162891	−	0.0958160i
$701$			10.8734i			0.410684i	0.978690	+	0.205342i	$0.0658307\pi$
$701$			10.8734i			0.410684i	−0.978690	+	0.205342i	$0.934169\pi$
$702$	2.87386	−	2.87386i	0.108467	−	0.108467i
$703$	−18.9351	+	18.9351i	−0.714149	+	0.714149i
$704$	−3.04480	+	1.31499i	−0.114755	+	0.0495604i
$705$	−0.833757	−	0.645155i	−0.0314011	−	0.0242980i
$706$			25.9151i			0.975329i
$707$	−9.95876	+	9.95876i	−0.374538	+	0.374538i
$708$	0.374908	+	0.374908i	0.0140899	+	0.0140899i
$709$			34.3597i			1.29040i	0.764012	+	0.645202i	$0.223227\pi$
$709$			34.3597i			1.29040i	−0.764012	+	0.645202i	$0.776773\pi$
$710$	0.123888	+	0.971466i	0.00464945	+	0.0364585i
$711$			21.3422i			0.800396i
$712$	1.91380	+	1.91380i	0.0717227	+	0.0717227i
$713$	−17.2084	−	17.2084i	−0.644458	−	0.644458i
$714$	0.858699			0.0321360
$715$	14.0979	+	23.8135i	0.527231	+	0.890573i
$716$	17.9885			0.672260
$717$	3.26793	+	3.26793i	0.122043	+	0.122043i
$718$	9.40862	+	9.40862i	0.351127	+	0.351127i
$719$		−	24.3944i		−	0.909756i	−0.890554	−	0.454878i	$-0.849683\pi$
$719$		−	24.3944i		−	0.909756i	0.890554	−	0.454878i	$-0.150317\pi$
$720$	4.05966	−	5.24644i	0.151294	−	0.195523i
$721$		−	6.91810i		−	0.257643i
$722$	−8.92461	−	8.92461i	−0.332140	−	0.332140i
$723$	−1.27908	+	1.27908i	−0.0475694	+	0.0475694i
$724$			13.2699i			0.493171i
$725$	1.00708	+	3.88428i	0.0374020	+	0.144258i
$726$	−1.46175	−	1.37666i	−0.0542505	−	0.0510926i
$727$	−6.83073	+	6.83073i	−0.253338	+	0.253338i	−0.822338	−	0.569000i	$-0.807330\pi$
$727$	−6.83073	+	6.83073i	−0.253338	+	0.253338i	0.569000	+	0.822338i	$0.307330\pi$
$728$	−2.63858	+	2.63858i	−0.0977923	+	0.0977923i
$729$			25.2173i			0.933973i
$730$	−17.7079	−	13.7022i	−0.655398	−	0.507143i
$731$	−47.4415			−1.75469
$732$	0.892532	+	0.892532i	0.0329889	+	0.0329889i
$733$	−28.0405	+	28.0405i	−1.03570	+	1.03570i	−0.0363592	+	0.999339i	$0.511576\pi$
$733$	−28.0405	+	28.0405i	−1.03570	+	1.03570i	−0.999339	+	0.0363592i	$0.988424\pi$
$734$	−1.89617			−0.0699890
$735$	0.404896	−	0.0516353i	0.0149348	−	0.00190460i
$736$			2.69662i			0.0993989i
$737$	48.9544	+	19.4234i	1.80326	+	0.715470i
$738$	−12.4541	−	12.4541i	−0.458443	−	0.458443i
$739$	31.0880			1.14359			0.571795	−	0.820397i	$-0.306247\pi$
$739$	31.0880			1.14359			0.571795	+	0.820397i	$0.306247\pi$
$740$	2.99917	+	23.5179i	0.110252	+	0.864533i
$741$	1.72034			0.0631981
$742$	0.115350	−	0.115350i	0.00423463	−	0.00423463i
$743$	−11.1460	+	11.1460i	−0.408908	+	0.408908i	−0.881358	−	0.472450i	$-0.843370\pi$
$743$	−11.1460	+	11.1460i	−0.408908	+	0.408908i	0.472450	+	0.881358i	$0.343370\pi$
$744$	−1.64739			−0.0603962
$745$	25.4640	+	19.7039i	0.932928	+	0.721893i
$746$	16.0200			0.586533
$747$	16.1554	+	16.1554i	0.591093	+	0.591093i
$748$	−14.5020	−	5.75391i	−0.530247	−	0.210384i
$749$			8.43294i			0.308133i
$750$	1.87588	+	0.803901i	0.0684974	+	0.0293543i
$751$	17.5918			0.641933			0.320967	−	0.947091i	$-0.395992\pi$
$751$	17.5918			0.641933			0.320967	+	0.947091i	$0.395992\pi$
$752$	−1.82629	+	1.82629i	−0.0665978	+	0.0665978i
$753$	−2.24966	−	2.24966i	−0.0819822	−	0.0819822i
$754$	2.99469			0.109060
$755$	−23.7505	+	30.6936i	−0.864369	+	1.11705i
$756$			1.08917i			0.0396126i
$757$	18.9842	−	18.9842i	0.689994	−	0.689994i	−0.272236	−	0.962230i	$-0.587763\pi$
$757$	18.9842	−	18.9842i	0.689994	−	0.689994i	0.962230	+	0.272236i	$0.0877632\pi$
$758$	−8.58274	+	8.58274i	−0.311739	+	0.311739i
$759$	−1.49879	+	0.647298i	−0.0544027	+	0.0234954i
$760$	5.60206	−	0.714415i	0.203208	−	0.0259146i
$761$			22.8315i			0.827641i	0.910358	+	0.413821i	$0.135806\pi$
$761$			22.8315i			0.827641i	−0.910358	+	0.413821i	$0.864194\pi$
$762$	−1.74956	+	1.74956i	−0.0633798	+	0.0633798i
$763$	2.46062	+	2.46062i	0.0890804	+	0.0890804i
$764$			10.3337i			0.373860i
$765$	30.9550	−	3.94761i	1.11918	−	0.142726i
$766$		−	8.25444i		−	0.298245i
$767$	−7.66386	−	7.66386i	−0.276726	−	0.276726i
$768$	0.129076	+	0.129076i	0.00465764	+	0.00465764i
$769$	−44.4205			−1.60185			−0.800923	−	0.598768i	$-0.795657\pi$
$769$	−44.4205			−1.60185			−0.800923	+	0.598768i	$0.795657\pi$
$770$	−7.18404	−	1.84106i	−0.258895	−	0.0663474i
$771$	−2.81764			−0.101475
$772$	−1.38232	−	1.38232i	−0.0497509	−	0.0497509i
$773$	16.5857	+	16.5857i	0.596546	+	0.596546i	0.939392	−	0.342846i	$-0.111391\pi$
$773$	16.5857	+	16.5857i	0.596546	+	0.596546i	−0.342846	+	0.939392i	$0.611391\pi$
$774$		−	29.9192i		−	1.07542i
$775$	11.3248	+	43.6794i	0.406799	+	1.56901i
$776$			1.92521i			0.0691111i
$777$	−1.36856	−	1.36856i	−0.0490967	−	0.0490967i
$778$	−7.35319	+	7.35319i	−0.263625	+	0.263625i
$779$		−	14.9942i		−	0.537223i
$780$	0.932108	−	1.20460i	0.0333748	−	0.0431314i
$781$	0.575927	+	1.33354i	0.0206083	+	0.0477177i
$782$	−8.96984	+	8.96984i	−0.320761	+	0.320761i
$783$	0.618083	−	0.618083i	0.0220885	−	0.0220885i
$784$		−	1.00000i		−	0.0357143i
$785$	3.46052	−	0.441310i	0.123511	−	0.0157510i
$786$	0.998130			0.0356021
$787$	−31.2025	−	31.2025i	−1.11225	−	1.11225i	−0.992846	−	0.119403i	$-0.961902\pi$
$787$	−31.2025	−	31.2025i	−1.11225	−	1.11225i	−0.119403	−	0.992846i	$-0.538098\pi$
$788$	−13.4283	+	13.4283i	−0.478364	+	0.478364i
$789$	3.48570			0.124094
$790$	2.03495	+	15.9570i	0.0724003	+	0.567725i
$791$			20.0336i			0.712314i
$792$	3.62873	−	9.14578i	0.128941	−	0.324981i
$793$	−18.2451	−	18.2451i	−0.647904	−	0.647904i
$794$	17.3139			0.614448
$795$	−0.0407487	+	0.0526609i	−0.00144521	+	0.00186769i
$796$	27.4823			0.974085
$797$	−33.8426	+	33.8426i	−1.19877	+	1.19877i	−0.224232	+	0.974536i	$0.571987\pi$
$797$	−33.8426	+	33.8426i	−1.19877	+	1.19877i	−0.974536	+	0.224232i	$0.928013\pi$
$798$	−0.325996	+	0.325996i	−0.0115401	+	0.0115401i
$799$	−12.1496			−0.429823
$800$	2.53505	−	4.30970i	0.0896277	−	0.152371i
$801$	−8.02938			−0.283704
$802$	11.0344	+	11.0344i	0.389638	+	0.389638i
$803$	−30.8690	−	12.2478i	−1.08934	−	0.432214i
$804$		−	2.89870i		−	0.102229i
$805$	−3.69011	+	4.76886i	−0.130059	+	0.168080i
$806$	33.6759			1.18618
$807$	−1.14444	+	1.14444i	−0.0402861	+	0.0402861i
$808$	−9.95876	−	9.95876i	−0.350348	−	0.350348i
$809$	−10.6003			−0.372686			−0.186343	−	0.982485i	$-0.559664\pi$
$809$	−10.6003			−0.372686			−0.186343	+	0.982485i	$0.559664\pi$
$810$	2.46130	+	19.3002i	0.0864813	+	0.678140i
$811$		−	33.6012i		−	1.17990i	−0.807441	−	0.589949i	$-0.799148\pi$
$811$		−	33.6012i		−	1.17990i	0.807441	−	0.589949i	$-0.200852\pi$
$812$	−0.567482	+	0.567482i	−0.0199147	+	0.0199147i
$813$	0.676134	−	0.676134i	0.0237131	−	0.0237131i
$814$	13.9424	+	32.2831i	0.488681	+	1.13152i
$815$	3.35960	+	26.3442i	0.117682	+	0.922796i
$816$			0.858699i			0.0300605i
$817$	18.0107	−	18.0107i	0.630114	−	0.630114i
$818$	18.8577	+	18.8577i	0.659346	+	0.659346i
$819$		−	11.0702i		−	0.386824i
$820$	−10.4991	−	8.12413i	−0.366644	−	0.283707i
$821$			40.4153i			1.41050i	0.708957	+	0.705251i	$0.249166\pi$
$821$			40.4153i			1.41050i	−0.708957	+	0.705251i	$0.750834\pi$
$822$	−1.63495	−	1.63495i	−0.0570254	−	0.0570254i
$823$	28.0225	+	28.0225i	0.976802	+	0.976802i	0.999737	−	0.0229354i	$-0.00730121\pi$
$823$	28.0225	+	28.0225i	0.976802	+	0.976802i	−0.0229354	+	0.999737i	$0.507301\pi$
$824$	6.91810			0.241003
$825$	3.00386	+	0.374490i	0.104581	+	0.0130381i
$826$	2.90454			0.101062
$827$	−9.02909	−	9.02909i	−0.313972	−	0.313972i	0.532474	−	0.846446i	$-0.321262\pi$
$827$	−9.02909	−	9.02909i	−0.313972	−	0.313972i	−0.846446	+	0.532474i	$0.821262\pi$
$828$	−5.65687	−	5.65687i	−0.196590	−	0.196590i
$829$		−	13.4934i		−	0.468644i	−0.972159	−	0.234322i	$-0.924713\pi$
$829$		−	13.4934i		−	0.468644i	0.972159	−	0.234322i	$-0.0752869\pi$
$830$	13.6193	+	10.5385i	0.472733	+	0.365797i
$831$			2.59669i			0.0900783i
$832$	−2.63858	−	2.63858i	−0.0914763	−	0.0914763i
$833$	3.32632	−	3.32632i	0.115250	−	0.115250i
$834$			1.60521i			0.0555837i
$835$	−5.56154	−	43.6106i	−0.192465	−	1.50921i
$836$	7.68997	−	3.32114i	0.265963	−	0.114864i
$837$	6.95046	−	6.95046i	0.240243	−	0.240243i
$838$	9.02615	−	9.02615i	0.311803	−	0.311803i
$839$		−	30.7455i		−	1.06145i	−0.847543	−	0.530727i	$-0.821919\pi$
$839$		−	30.7455i		−	1.06145i	0.847543	−	0.530727i	$-0.178081\pi$
$840$	0.0516353	+	0.404896i	0.00178159	+	0.0139703i
$841$	−28.3559			−0.977791
$842$	14.4546	+	14.4546i	0.498140	+	0.498140i
$843$	4.25073	−	4.25073i	0.146403	−	0.146403i
$844$	−10.6730			−0.367380
$845$	−1.26471	+	1.63443i	−0.0435073	+	0.0562260i
$846$		−	7.66221i		−	0.263432i
$847$	−10.9951	+	0.329602i	−0.377795	+	0.0113253i
$848$	0.115350	+	0.115350i	0.00396114	+	0.00396114i
$849$	0.438568			0.0150516
$850$	22.7678	−	5.90304i	0.780930	−	0.202473i
$851$	28.5915			0.980102
$852$	0.0565318	−	0.0565318i	0.00193675	−	0.00193675i
$853$	31.2962	−	31.2962i	1.07156	−	1.07156i	0.0743282	−	0.997234i	$-0.476319\pi$
$853$	31.2962	−	31.2962i	1.07156	−	1.07156i	0.997234	−	0.0743282i	$-0.0236812\pi$
$854$	6.91475			0.236618
$855$	−10.2531	+	13.2504i	−0.350649	+	0.453155i
$856$	−8.43294			−0.288232
$857$	−7.13087	−	7.13087i	−0.243586	−	0.243586i	0.574746	−	0.818332i	$-0.305101\pi$
$857$	−7.13087	−	7.13087i	−0.243586	−	0.243586i	−0.818332	+	0.574746i	$0.805101\pi$
$858$	0.833166	−	2.09990i	0.0284438	−	0.0716892i
$859$			32.3987i			1.10543i	0.833371	+	0.552714i	$0.186408\pi$
$859$			32.3987i			1.10543i	−0.833371	+	0.552714i	$0.813592\pi$
$860$	−2.85275	−	22.3698i	−0.0972781	−	0.762803i
$861$	1.08373			0.0369333
$862$	−5.29472	+	5.29472i	−0.180339	+	0.180339i
$863$	−23.9736	−	23.9736i	−0.816072	−	0.816072i	0.169465	−	0.985536i	$-0.445796\pi$
$863$	−23.9736	−	23.9736i	−0.816072	−	0.816072i	−0.985536	+	0.169465i	$0.945796\pi$
$864$	−1.08917			−0.0370542
$865$	4.54606	−	0.579746i	0.154571	−	0.0197120i
$866$			34.3197i			1.16623i
$867$	−0.662008	+	0.662008i	−0.0224830	+	0.0224830i
$868$	−6.38145	+	6.38145i	−0.216600	+	0.216600i
$869$	9.45999	+	21.9042i	0.320908	+	0.743051i
$870$	0.200469	−	0.259074i	0.00679655	−	0.00878342i
$871$			59.2552i			2.00779i
$872$	−2.46062	+	2.46062i	−0.0833271	+	0.0833271i
$873$	−4.03863	−	4.03863i	−0.136687	−	0.136687i
$874$		−	6.81062i		−	0.230372i
$875$	10.3806	−	4.15249i	0.350928	−	0.140380i
$876$			1.82783i			0.0617565i
$877$	5.42601	+	5.42601i	0.183223	+	0.183223i	0.792759	−	0.609536i	$-0.208644\pi$
$877$	5.42601	+	5.42601i	0.183223	+	0.183223i	−0.609536	+	0.792759i	$0.708644\pi$
$878$	4.57286	+	4.57286i	0.154326	+	0.154326i
$879$	−0.839858			−0.0283277
$880$	1.84106	−	7.18404i	0.0620623	−	0.242174i
$881$	−37.3228			−1.25744			−0.628719	−	0.777633i	$-0.716420\pi$
$881$	−37.3228			−1.25744			−0.628719	+	0.777633i	$0.716420\pi$
$882$	2.09776	+	2.09776i	0.0706352	+	0.0706352i
$883$	−38.4920	−	38.4920i	−1.29536	−	1.29536i	−0.931425	−	0.363934i	$-0.881433\pi$
$883$	−38.4920	−	38.4920i	−1.29536	−	1.29536i	−0.363934	−	0.931425i	$-0.618567\pi$
$884$		−	17.5535i		−	0.590389i
$885$	−1.17604	+	0.149977i	−0.0395321	+	0.00504141i
$886$			20.4126i			0.685774i
$887$	−21.5968	−	21.5968i	−0.725149	−	0.725149i	0.244500	−	0.969649i	$-0.421376\pi$
$887$	−21.5968	−	21.5968i	−0.725149	−	0.725149i	−0.969649	+	0.244500i	$0.921376\pi$
$888$	1.36856	−	1.36856i	0.0459258	−	0.0459258i
$889$			13.5544i			0.454601i
$890$	−6.00335	+	0.765590i	−0.201233	+	0.0256626i
$891$	11.4420	+	26.4935i	0.383321	+	0.887565i
$892$	−10.1950	+	10.1950i	−0.341354	+	0.341354i
$893$	4.61248	−	4.61248i	0.154351	−	0.154351i
$894$		−	2.62842i		−	0.0879074i
$895$	−24.6157	+	31.8118i	−0.822813	+	1.06335i
$896$	1.00000			0.0334077
$897$	−1.29883	−	1.29883i	−0.0433667	−	0.0433667i
$898$	−1.66349	+	1.66349i	−0.0555112	+	0.0555112i
$899$	7.24272			0.241558
$900$	3.72278	+	14.3586i	0.124093	+	0.478621i
$901$			0.767382i			0.0255652i
$902$	−18.3024	−	7.26176i	−0.609403	−	0.241790i
$903$	1.30175	+	1.30175i	0.0433194	+	0.0433194i
$904$	−20.0336			−0.666309
$905$	−23.4672	−	18.1587i	−0.780075	−	0.603617i
$906$	3.16822			0.105257
$907$	32.9281	−	32.9281i	1.09336	−	1.09336i	0.0981926	−	0.995167i	$-0.468694\pi$
$907$	32.9281	−	32.9281i	1.09336	−	1.09336i	0.995167	−	0.0981926i	$-0.0313061\pi$
$908$	−2.92799	+	2.92799i	−0.0971687	+	0.0971687i
$909$	41.7821			1.38583
$910$	−1.05553	−	8.27689i	−0.0349904	−	0.274376i
$911$	38.9173			1.28939			0.644694	−	0.764441i	$-0.276985\pi$
$911$	38.9173			1.28939			0.644694	+	0.764441i	$0.276985\pi$
$912$	−0.325996	−	0.325996i	−0.0107948	−	0.0107948i
$913$	23.7417	+	9.41987i	0.785734	+	0.311752i
$914$		−	8.45485i		−	0.279662i
$915$	−2.79976	+	0.357045i	−0.0925572	+	0.0118036i
$916$	−21.9446			−0.725069
$917$	3.86643	−	3.86643i	0.127681	−	0.127681i
$918$	−3.62292	−	3.62292i	−0.119574	−	0.119574i
$919$	8.79680			0.290180			0.145090	−	0.989418i	$-0.453653\pi$
$919$	8.79680			0.290180			0.145090	+	0.989418i	$0.453653\pi$
$920$	−4.76886	−	3.69011i	−0.157225	−	0.121659i
$921$		−	4.28615i		−	0.141233i
$922$	28.1775	−	28.1775i	0.927976	−	0.927976i
$923$	−1.15562	+	1.15562i	−0.0380378	+	0.0380378i
$924$	0.240040	+	0.555803i	0.00789673	+	0.0182846i
$925$	−45.6944	−	26.8784i	−1.50242	−	0.883755i
$926$		−	13.8425i		−	0.454891i
$927$	−14.5125	+	14.5125i	−0.476653	+	0.476653i
$928$	−0.567482	−	0.567482i	−0.0186285	−	0.0186285i
$929$			58.5821i			1.92202i	0.276520	+	0.961008i	$0.410819\pi$
$929$			58.5821i			1.92202i	−0.276520	+	0.961008i	$0.589181\pi$
$930$	2.25432	−	2.91333i	0.0739220	−	0.0955319i
$931$			2.52561i			0.0827734i
$932$	2.56907	+	2.56907i	0.0841527	+	0.0841527i
$933$	4.26209	+	4.26209i	0.139534	+	0.139534i
$934$	20.8740			0.683019
$935$	30.0204	−	17.7725i	0.981772	−	0.581221i
$936$	11.0702			0.361841
$937$	−38.1501	−	38.1501i	−1.24631	−	1.24631i	−0.957338	−	0.288970i	$-0.906687\pi$
$937$	−38.1501	−	38.1501i	−1.24631	−	1.24631i	−0.288970	−	0.957338i	$-0.593313\pi$
$938$	−11.2286	−	11.2286i	−0.366627	−	0.366627i
$939$			4.20600i			0.137258i
$940$	−0.730581	−	5.72882i	−0.0238289	−	0.186854i
$941$		−	45.4027i		−	1.48009i	−0.672560	−	0.740043i	$-0.734805\pi$
$941$		−	45.4027i		−	1.48009i	0.672560	−	0.740043i	$-0.265195\pi$
$942$	−0.201375	−	0.201375i	−0.00656117	−	0.00656117i
$943$	−11.3204	+	11.3204i	−0.368644	+	0.368644i
$944$			2.90454i			0.0945347i
$945$	−1.92614	−	1.49044i	−0.0626574	−	0.0484839i
$946$	−13.2618	−	30.7071i	−0.431177	−	0.998373i
$947$	5.30331	−	5.30331i	0.172334	−	0.172334i	−0.615670	−	0.788004i	$-0.711114\pi$
$947$	5.30331	−	5.30331i	0.172334	−	0.172334i	0.788004	+	0.615670i	$0.211114\pi$
$948$	0.928574	−	0.928574i	0.0301587	−	0.0301587i
$949$		−	37.3644i		−	1.21290i
$950$	−6.40255	+	10.8846i	−0.207726	+	0.353143i
$951$	1.61138			0.0522526
$952$	3.32632	+	3.32632i	0.107807	+	0.107807i
$953$	2.91992	−	2.91992i	0.0945855	−	0.0945855i	−0.658231	−	0.752816i	$-0.728695\pi$
$953$	2.91992	−	2.91992i	0.0945855	−	0.0945855i	0.752816	+	0.658231i	$0.228695\pi$
$954$	−0.483953			−0.0156686
$955$	−18.2747	−	14.1408i	−0.591355	−	0.457586i
$956$			25.3178i			0.818836i
$957$	0.179190	−	0.451627i	0.00579239	−	0.0145990i
$958$	28.9474	+	28.9474i	0.935248	+	0.935248i
$959$	−12.6665			−0.409023
$960$	−0.404896	+	0.0516353i	−0.0130680	+	0.00166652i
$961$	50.4457			1.62728
$962$	−27.9760	+	27.9760i	−0.901983	+	0.901983i
$963$	17.6903	−	17.6903i	0.570061	−	0.570061i
$964$	−9.90945			−0.319162
$965$	4.33617	−	0.552980i	0.139586	−	0.0178010i
$966$	0.492246			0.0158378
$967$	0.498266	+	0.498266i	0.0160232	+	0.0160232i	0.715073	−	0.699050i	$-0.246393\pi$
$967$	0.498266	+	0.498266i	0.0160232	+	0.0160232i	−0.699050	+	0.715073i	$0.746393\pi$
$968$	−0.329602	−	10.9951i	−0.0105938	−	0.353395i
$969$		−	2.16874i		−	0.0696699i
$970$	−3.40465	−	2.63449i	−0.109317	−	0.0845885i
$971$	33.9986			1.09107			0.545534	−	0.838089i	$-0.316327\pi$
$971$	33.9986			1.09107			0.545534	+	0.838089i	$0.316327\pi$
$972$	3.43360	−	3.43360i	0.110133	−	0.110133i
$973$	6.21804	+	6.21804i	0.199341	+	0.199341i
$974$	−15.0026			−0.480715
$975$	0.854759	+	3.29678i	0.0273742	+	0.105581i
$976$			6.91475i			0.221336i
$977$	21.3991	−	21.3991i	0.684617	−	0.684617i	−0.276420	−	0.961037i	$-0.589148\pi$
$977$	21.3991	−	21.3991i	0.684617	−	0.684617i	0.961037	+	0.276420i	$0.0891482\pi$
$978$	1.53303	−	1.53303i	0.0490208	−	0.0490208i
$979$	−8.24082	+	3.55904i	−0.263378	+	0.113747i
$980$	1.76845	+	1.36842i	0.0564912	+	0.0437125i
$981$		−	10.3236i		−	0.329606i
$982$	−12.4422	+	12.4422i	−0.397047	+	0.397047i
$983$	5.86960	+	5.86960i	0.187211	+	0.187211i	0.794489	−	0.607278i	$-0.207739\pi$
$983$	5.86960	+	5.86960i	0.187211	+	0.187211i	−0.607278	+	0.794489i	$0.707739\pi$
$984$			1.08373i			0.0345479i
$985$	−5.37182	−	42.1229i	−0.171160	−	1.34215i
$986$		−	3.77525i		−	0.120229i
$987$	0.333373	+	0.333373i	0.0106114	+	0.0106114i
$988$	6.66402	+	6.66402i	0.212011	+	0.212011i
$989$	−27.1957			−0.864773
$990$	11.2083	+	18.9325i	0.356222	+	0.601714i
$991$	52.3641			1.66340			0.831701	−	0.555224i	$-0.187368\pi$
$991$	52.3641			1.66340			0.831701	+	0.555224i	$0.187368\pi$
$992$	−6.38145	−	6.38145i	−0.202611	−	0.202611i
$993$	−1.86339	−	1.86339i	−0.0591328	−	0.0591328i
$994$		−	0.437972i		−	0.0138916i
$995$	−37.6073	+	48.6012i	−1.19223	+	1.54076i
$996$		−	1.40580i		−	0.0445444i
$997$	−40.0907	−	40.0907i	−1.26968	−	1.26968i	−0.946251	−	0.323434i	$-0.895163\pi$
$997$	−40.0907	−	40.0907i	−1.26968	−	1.26968i	−0.323434	−	0.946251i	$-0.604837\pi$
$998$	−19.0409	+	19.0409i	−0.602731	+	0.602731i
$999$			11.5481i			0.365366i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.m.f.43.14	yes	36
5.2	odd	4	inner	770.2.m.f.197.5	yes	36
11.10	odd	2	inner	770.2.m.f.43.5	✓	36
55.32	even	4	inner	770.2.m.f.197.14	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.m.f.43.5	✓	36	11.10	odd	2	inner
770.2.m.f.43.14	yes	36	1.1	even	1	trivial
770.2.m.f.197.5	yes	36	5.2	odd	4	inner
770.2.m.f.197.14	yes	36	55.32	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.129076 + 0.129076i) q^{3} +1.00000i q^{4} +(-1.76845 - 1.36842i) q^{5} +0.182542i q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} -2.96668i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.129076 + 0.129076i) q^{3} +1.00000i q^{4} +(-1.76845 - 1.36842i) q^{5} +0.182542i q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} -2.96668i q^{9} +(-0.282869 - 2.21810i) q^{10} +(-1.31499 - 3.04480i) q^{11} +(-0.129076 + 0.129076i) q^{12} +(2.63858 - 2.63858i) q^{13} +1.00000i q^{14} +(-0.0516353 - 0.404896i) q^{15} -1.00000 q^{16} +(-3.32632 - 3.32632i) q^{17} +(2.09776 - 2.09776i) q^{18} +2.52561 q^{19} +(1.36842 - 1.76845i) q^{20} +0.182542i q^{21} +(1.22316 - 3.08284i) q^{22} +(-1.90680 - 1.90680i) q^{23} -0.182542 q^{24} +(1.25486 + 4.83997i) q^{25} +3.73152 q^{26} +(0.770158 - 0.770158i) q^{27} +(-0.707107 + 0.707107i) q^{28} +0.802541 q^{29} +(0.249793 - 0.322817i) q^{30} +9.02473 q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.223278 - 0.562746i) q^{33} -4.70413i q^{34} +(-0.282869 - 2.21810i) q^{35} +2.96668 q^{36} +(-7.49723 + 7.49723i) q^{37} +(1.78587 + 1.78587i) q^{38} +0.681157 q^{39} +(2.21810 - 0.282869i) q^{40} -5.93687i q^{41} +(-0.129076 + 0.129076i) q^{42} +(7.13123 - 7.13123i) q^{43} +(3.04480 - 1.31499i) q^{44} +(-4.05966 + 5.24644i) q^{45} -2.69662i q^{46} +(1.82629 - 1.82629i) q^{47} +(-0.129076 - 0.129076i) q^{48} +1.00000i q^{49} +(-2.53505 + 4.30970i) q^{50} -0.858699i q^{51} +(2.63858 + 2.63858i) q^{52} +(-0.115350 - 0.115350i) q^{53} +1.08917 q^{54} +(-1.84106 + 7.18404i) q^{55} -1.00000 q^{56} +(0.325996 + 0.325996i) q^{57} +(0.567482 + 0.567482i) q^{58} -2.90454i q^{59} +(0.404896 - 0.0516353i) q^{60} -6.91475i q^{61} +(6.38145 + 6.38145i) q^{62} +(2.09776 - 2.09776i) q^{63} -1.00000i q^{64} +(-8.27689 + 1.05553i) q^{65} +(0.555803 - 0.240040i) q^{66} +(-11.2286 + 11.2286i) q^{67} +(3.32632 - 3.32632i) q^{68} -0.492246i q^{69} +(1.36842 - 1.76845i) q^{70} -0.437972 q^{71} +(2.09776 + 2.09776i) q^{72} +(7.08040 - 7.08040i) q^{73} -10.6027 q^{74} +(-0.462753 + 0.786700i) q^{75} +2.52561i q^{76} +(1.22316 - 3.08284i) q^{77} +(0.481651 + 0.481651i) q^{78} -7.19398 q^{79} +(1.76845 + 1.36842i) q^{80} -8.70122 q^{81} +(4.19800 - 4.19800i) q^{82} +(-5.44560 + 5.44560i) q^{83} -0.182542 q^{84} +(1.33065 + 10.4342i) q^{85} +10.0851 q^{86} +(0.103589 + 0.103589i) q^{87} +(3.08284 + 1.22316i) q^{88} -2.70652i q^{89} +(-6.58040 + 0.839180i) q^{90} +3.73152 q^{91} +(1.90680 - 1.90680i) q^{92} +(1.16488 + 1.16488i) q^{93} +2.58276 q^{94} +(-4.46642 - 3.45609i) q^{95} -0.182542i q^{96} +(1.36133 - 1.36133i) q^{97} +(-0.707107 + 0.707107i) q^{98} +(-9.03294 + 3.90114i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{3}+O(q^{10}) \) 36 * q - 4 * q^3	\( 36 q - 4 q^{3} + 12 q^{11} + 4 q^{12} - 4 q^{15} - 36 q^{16} - 12 q^{20} - 12 q^{22} + 4 q^{23} + 12 q^{25} + 24 q^{26} + 56 q^{27} + 8 q^{31} - 44 q^{33} - 44 q^{36} - 28 q^{37} + 16 q^{38} + 4 q^{42} - 44 q^{45} + 12 q^{47} + 4 q^{48} + 28 q^{53} + 40 q^{55} - 36 q^{56} - 24 q^{58} + 12 q^{60} + 24 q^{66} + 12 q^{67} - 12 q^{70} - 112 q^{71} - 52 q^{75} - 12 q^{77} + 48 q^{78} + 4 q^{81} + 40 q^{82} + 32 q^{86} - 12 q^{88} + 24 q^{91} - 4 q^{92} - 80 q^{93} + 100 q^{97}+O(q^{100}) \) 36 * q - 4 * q^3 + 12 * q^11 + 4 * q^12 - 4 * q^15 - 36 * q^16 - 12 * q^20 - 12 * q^22 + 4 * q^23 + 12 * q^25 + 24 * q^26 + 56 * q^27 + 8 * q^31 - 44 * q^33 - 44 * q^36 - 28 * q^37 + 16 * q^38 + 4 * q^42 - 44 * q^45 + 12 * q^47 + 4 * q^48 + 28 * q^53 + 40 * q^55 - 36 * q^56 - 24 * q^58 + 12 * q^60 + 24 * q^66 + 12 * q^67 - 12 * q^70 - 112 * q^71 - 52 * q^75 - 12 * q^77 + 48 * q^78 + 4 * q^81 + 40 * q^82 + 32 * q^86 - 12 * q^88 + 24 * q^91 - 4 * q^92 - 80 * q^93 + 100 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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