LMFDB - Embedded newform 966.2.bf.a.11.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(11,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 44, 27]))

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

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

chi := DirichletCharacter("966.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.bf (of order $66$, degree $20$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$1280$
Relative dimension:	$64$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			11.7
Character	$\chi$	$=$	966.11
Dual form			966.2.bf.a.527.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.458227 + 0.888835i) q^{2} +(-1.24755 - 1.20151i) q^{3} +(-0.580057 - 0.814576i) q^{4} +(2.79695 + 2.66688i) q^{5} +(1.63960 - 0.558302i) q^{6} +(2.62506 - 0.330282i) q^{7} +(0.989821 - 0.142315i) q^{8} +(0.112753 + 2.99788i) q^{9} +O(q^{10})$	\(q+(-0.458227 + 0.888835i) q^{2} +(-1.24755 - 1.20151i) q^{3} +(-0.580057 - 0.814576i) q^{4} +(2.79695 + 2.66688i) q^{5} +(1.63960 - 0.558302i) q^{6} +(2.62506 - 0.330282i) q^{7} +(0.989821 - 0.142315i) q^{8} +(0.112753 + 2.99788i) q^{9} +(-3.65206 + 1.26399i) q^{10} +(5.50003 - 2.83546i) q^{11} +(-0.255071 + 1.71317i) q^{12} +(-0.719336 + 0.830158i) q^{13} +(-0.909304 + 2.48459i) q^{14} +(-0.285042 - 6.68762i) q^{15} +(-0.327068 + 0.945001i) q^{16} +(3.09962 + 0.295978i) q^{17} +(-2.71629 - 1.27349i) q^{18} +(-0.241903 - 2.53333i) q^{19} +(0.549991 - 3.82527i) q^{20} +(-3.67172 - 2.74198i) q^{21} +6.18791i q^{22} +(-4.74995 - 0.661825i) q^{23} +(-1.40584 - 1.01173i) q^{24} +(0.472735 + 9.92393i) q^{25} +(-0.408255 - 1.01977i) q^{26} +(3.46132 - 3.87547i) q^{27} +(-1.79172 - 1.94672i) q^{28} +(-4.41506 + 2.01629i) q^{29} +(6.07481 + 2.81109i) q^{30} +(-1.92958 - 0.772486i) q^{31} +(-0.690079 - 0.723734i) q^{32} +(-10.2684 - 3.07096i) q^{33} +(-1.68341 + 2.61943i) q^{34} +(8.22296 + 6.07694i) q^{35} +(2.37660 - 1.83079i) q^{36} +(-3.86603 + 0.937888i) q^{37} +(2.36256 + 0.945825i) q^{38} +(1.89485 - 0.171374i) q^{39} +(3.14802 + 2.24169i) q^{40} +(-1.74347 - 5.93771i) q^{41} +(4.11965 - 2.00710i) q^{42} +(4.15646 + 0.597609i) q^{43} +(-5.50003 - 2.83546i) q^{44} +(-7.67964 + 8.68561i) q^{45} +(2.76480 - 3.91865i) q^{46} +(6.58168 - 3.79994i) q^{47} +(1.54346 - 0.785959i) q^{48} +(6.78183 - 1.73402i) q^{49} +(-9.03736 - 4.12722i) q^{50} +(-3.51131 - 4.09347i) q^{51} +(1.09348 + 0.104415i) q^{52} +(11.6858 - 2.25224i) q^{53} +(1.85859 + 4.85238i) q^{54} +(22.9452 + 6.73731i) q^{55} +(2.55133 - 0.700504i) q^{56} +(-2.74203 + 3.45109i) q^{57} +(0.230947 - 4.84818i) q^{58} +(-7.76665 + 2.68806i) q^{59} +(-5.28224 + 4.11139i) q^{60} +(0.303171 + 0.385513i) q^{61} +(1.57080 - 1.36110i) q^{62} +(1.28613 + 7.83236i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-4.22588 + 0.403523i) q^{65} +(7.43483 - 7.71971i) q^{66} +(0.919068 - 0.0437806i) q^{67} +(-1.55686 - 2.69656i) q^{68} +(5.13060 + 6.53276i) q^{69} +(-9.16938 + 4.52425i) q^{70} +(3.10729 + 4.83504i) q^{71} +(0.538248 + 2.95132i) q^{72} +(3.63908 + 5.11038i) q^{73} +(0.937888 - 3.86603i) q^{74} +(11.3339 - 12.9486i) q^{75} +(-1.92327 + 1.66652i) q^{76} +(13.5014 - 9.25981i) q^{77} +(-0.715947 + 1.76274i) q^{78} +(-3.17104 + 16.4529i) q^{79} +(-3.43500 + 1.77087i) q^{80} +(-8.97457 + 0.676039i) q^{81} +(6.07655 + 1.17116i) q^{82} +(-0.204545 - 0.0600598i) q^{83} +(-0.103749 + 4.58140i) q^{84} +(7.88014 + 9.09417i) q^{85} +(-2.43578 + 3.42057i) q^{86} +(7.93059 + 2.78931i) q^{87} +(5.04052 - 3.58934i) q^{88} +(-8.12864 + 3.25422i) q^{89} +(-4.20107 - 10.8059i) q^{90} +(-1.61411 + 2.41679i) q^{91} +(2.21613 + 4.25309i) q^{92} +(1.47909 + 3.28212i) q^{93} +(0.361617 + 7.59127i) q^{94} +(6.07949 - 7.73070i) q^{95} +(-0.00866609 + 1.73203i) q^{96} +(0.0909583 + 0.309775i) q^{97} +(-1.56636 + 6.82250i) q^{98} +(9.12053 + 16.1687i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1280 q - 64 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) $ 1280 * q - 64 * q^4 - 8 * q^6 + 4 * q^9	$ 1280 q - 64 q^{4} - 8 q^{6} + 4 q^{9} + 64 q^{16} + 44 q^{18} - 132 q^{21} - 4 q^{24} + 72 q^{25} + 108 q^{27} + 44 q^{30} + 8 q^{36} + 44 q^{37} - 4 q^{39} - 88 q^{43} - 12 q^{46} + 60 q^{49} - 48 q^{54} + 96 q^{55} + 44 q^{58} - 176 q^{61} - 110 q^{63} + 128 q^{64} + 56 q^{69} - 120 q^{70} + 44 q^{72} + 40 q^{73} - 268 q^{75} + 16 q^{78} + 88 q^{79} + 8 q^{81} - 56 q^{82} - 22 q^{84} + 64 q^{85} - 42 q^{87} - 32 q^{93} + 8 q^{94} + 4 q^{96} + 132 q^{99}+O(q^{100}) $ 1280 * q - 64 * q^4 - 8 * q^6 + 4 * q^9 + 64 * q^16 + 44 * q^18 - 132 * q^21 - 4 * q^24 + 72 * q^25 + 108 * q^27 + 44 * q^30 + 8 * q^36 + 44 * q^37 - 4 * q^39 - 88 * q^43 - 12 * q^46 + 60 * q^49 - 48 * q^54 + 96 * q^55 + 44 * q^58 - 176 * q^61 - 110 * q^63 + 128 * q^64 + 56 * q^69 - 120 * q^70 + 44 * q^72 + 40 * q^73 - 268 * q^75 + 16 * q^78 + 88 * q^79 + 8 * q^81 - 56 * q^82 - 22 * q^84 + 64 * q^85 - 42 * q^87 - 32 * q^93 + 8 * q^94 + 4 * q^96 + 132 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{22}\right)$

Coefficient data

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

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

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

$2$	−0.458227	+	0.888835i	−0.324015	+	0.628502i
$2$	−0.458227	+	0.888835i	−0.324015	+	0.628502i
$3$	−1.24755	−	1.20151i	−0.720272	−	0.693691i
$3$	−1.24755	−	1.20151i	−0.720272	−	0.693691i
$4$	−0.580057	−	0.814576i	−0.290028	−	0.407288i
$5$	2.79695	+	2.66688i	1.25083	+	1.19267i	0.972685	+	0.232128i	$0.0745690\pi$
$5$	2.79695	+	2.66688i	1.25083	+	1.19267i	0.278148	+	0.960538i	$0.410280\pi$
$6$	1.63960	−	0.558302i	0.669365	−	0.227926i
$7$	2.62506	−	0.330282i	0.992178	−	0.124835i
$7$	2.62506	−	0.330282i	0.992178	−	0.124835i
$8$	0.989821	−	0.142315i	0.349955	−	0.0503159i
$9$	0.112753	+	2.99788i	0.0375843	+	0.999293i
$10$	−3.65206	+	1.26399i	−1.15488	+	0.399708i
$11$	5.50003	−	2.83546i	1.65832	−	0.854925i	0.664093	−	0.747650i	$-0.268818\pi$
$11$	5.50003	−	2.83546i	1.65832	−	0.854925i	0.994229	−	0.107275i	$-0.0342124\pi$
$12$	−0.255071	+	1.71317i	−0.0736327	+	0.494548i
$13$	−0.719336	+	0.830158i	−0.199508	+	0.230244i	−0.846684	−	0.532096i	$-0.821404\pi$
$13$	−0.719336	+	0.830158i	−0.199508	+	0.230244i	0.647176	+	0.762341i	$0.275950\pi$
$14$	−0.909304	+	2.48459i	−0.243022	+	0.664034i
$15$	−0.285042	−	6.68762i	−0.0735975	−	1.72674i
$16$	−0.327068	+	0.945001i	−0.0817670	+	0.236250i
$17$	3.09962	+	0.295978i	0.751769	+	0.0717852i	0.463904	−	0.885886i	$-0.346448\pi$
$17$	3.09962	+	0.295978i	0.751769	+	0.0717852i	0.287865	+	0.957671i	$0.407054\pi$
$18$	−2.71629	−	1.27349i	−0.640235	−	0.300164i
$19$	−0.241903	−	2.53333i	−0.0554964	−	0.581185i	−0.979862	−	0.199676i	$-0.936011\pi$
$19$	−0.241903	−	2.53333i	−0.0554964	−	0.581185i	0.924365	−	0.381508i	$-0.124595\pi$
$20$	0.549991	−	3.82527i	0.122982	−	0.855356i
$21$	−3.67172	−	2.74198i	−0.801235	−	0.598350i
$22$			6.18791i			1.31927i
$23$	−4.74995	−	0.661825i	−0.990432	−	0.138000i
$23$	−4.74995	−	0.661825i	−0.990432	−	0.138000i
$24$	−1.40584	−	1.01173i	−0.286966	−	0.206519i
$25$	0.472735	+	9.92393i	0.0945470	+	1.98479i
$26$	−0.408255	−	1.01977i	−0.0800654	−	0.199994i
$27$	3.46132	−	3.87547i	0.666130	−	0.745835i
$28$	−1.79172	−	1.94672i	−0.338603	−	0.367896i
$29$	−4.41506	+	2.01629i	−0.819856	+	0.374416i	−0.780769	−	0.624820i	$-0.785172\pi$
$29$	−4.41506	+	2.01629i	−0.819856	+	0.374416i	−0.0390874	+	0.999236i	$0.512445\pi$
$30$	6.07481	+	2.81109i	1.10910	+	0.513233i
$31$	−1.92958	−	0.772486i	−0.346562	−	0.138743i	0.191850	−	0.981424i	$-0.438551\pi$
$31$	−1.92958	−	0.772486i	−0.346562	−	0.138743i	−0.538412	+	0.842682i	$0.680976\pi$
$32$	−0.690079	−	0.723734i	−0.121990	−	0.127939i
$33$	−10.2684	−	3.07096i	−1.78750	−	0.534586i
$34$	−1.68341	+	2.61943i	−0.288702	+	0.449229i
$35$	8.22296	+	6.07694i	1.38993	+	1.02719i
$36$	2.37660	−	1.83079i	0.396100	−	0.305131i
$37$	−3.86603	+	0.937888i	−0.635571	+	0.154188i	−0.540583	−	0.841291i	$-0.681796\pi$
$37$	−3.86603	+	0.937888i	−0.635571	+	0.154188i	−0.0949879	+	0.995478i	$0.530281\pi$
$38$	2.36256	+	0.945825i	0.383257	+	0.153433i
$39$	1.89485	−	0.171374i	0.303419	−	0.0274417i
$40$	3.14802	+	2.24169i	0.497745	+	0.354443i
$41$	−1.74347	−	5.93771i	−0.272284	−	0.927315i	−0.976171	−	0.217003i	$-0.930372\pi$
$41$	−1.74347	−	5.93771i	−0.272284	−	0.927315i	0.703887	−	0.710312i	$-0.251446\pi$
$42$	4.11965	−	2.00710i	0.635676	−	0.309703i
$43$	4.15646	+	0.597609i	0.633854	+	0.0911345i	0.451750	−	0.892145i	$-0.350800\pi$
$43$	4.15646	+	0.597609i	0.633854	+	0.0911345i	0.182105	+	0.983279i	$0.441709\pi$
$44$	−5.50003	−	2.83546i	−0.829161	−	0.427462i
$45$	−7.67964	+	8.68561i	−1.14481	+	1.29477i
$46$	2.76480	−	3.91865i	0.407648	−	0.577774i
$47$	6.58168	−	3.79994i	0.960037	−	0.554278i	0.0638527	−	0.997959i	$-0.479661\pi$
$47$	6.58168	−	3.79994i	0.960037	−	0.554278i	0.896184	+	0.443682i	$0.146328\pi$
$48$	1.54346	−	0.785959i	0.222779	−	0.113443i
$49$	6.78183	−	1.73402i	0.968833	−	0.247717i
$50$	−9.03736	−	4.12722i	−1.27808	−	0.583678i
$51$	−3.51131	−	4.09347i	−0.491682	−	0.573201i
$52$	1.09348	+	0.104415i	0.151639	+	0.0144797i
$53$	11.6858	−	2.25224i	1.60516	−	0.309369i	0.693545	−	0.720413i	$-0.256048\pi$
$53$	11.6858	−	2.25224i	1.60516	−	0.309369i	0.911616	+	0.411043i	$0.134836\pi$
$54$	1.85859	+	4.85238i	0.252922	+	0.660326i
$55$	22.9452	+	6.73731i	3.09392	+	0.908458i
$56$	2.55133	−	0.700504i	0.340936	−	0.0936088i
$57$	−2.74203	+	3.45109i	−0.363190	+	0.457109i
$58$	0.230947	−	4.84818i	0.0303249	−	0.636597i
$59$	−7.76665	+	2.68806i	−1.01113	+	0.349956i	−0.781892	−	0.623414i	$-0.785745\pi$
$59$	−7.76665	+	2.68806i	−1.01113	+	0.349956i	−0.229239	+	0.973370i	$0.573624\pi$
$60$	−5.28224	+	4.11139i	−0.681934	+	0.530778i
$61$	0.303171	+	0.385513i	0.0388170	+	0.0493599i	0.805074	−	0.593174i	$-0.202125\pi$
$61$	0.303171	+	0.385513i	0.0388170	+	0.0493599i	−0.766257	+	0.642534i	$0.777883\pi$
$62$	1.57080	−	1.36110i	0.199491	−	0.172860i
$63$	1.28613	+	7.83236i	0.162037	+	0.986785i
$64$	0.959493	−	0.281733i	0.119937	−	0.0352166i
$65$	−4.22588	+	0.403523i	−0.524156	+	0.0500508i
$66$	7.43483	−	7.71971i	0.915164	−	0.950231i
$67$	0.919068	−	0.0437806i	0.112282	−	0.00534865i	0.00863428	−	0.999963i	$-0.497252\pi$
$67$	0.919068	−	0.0437806i	0.112282	−	0.00534865i	0.103648	+	0.994614i	$0.466949\pi$
$68$	−1.55686	−	2.69656i	−0.188797	−	0.327006i
$69$	5.13060	+	6.53276i	0.617651	+	0.786452i
$70$	−9.16938	+	4.52425i	−1.09595	+	0.540751i
$71$	3.10729	+	4.83504i	0.368768	+	0.573813i	0.975201	−	0.221321i	$-0.0710368\pi$
$71$	3.10729	+	4.83504i	0.368768	+	0.573813i	−0.606434	+	0.795134i	$0.707400\pi$
$72$	0.538248	+	2.95132i	0.0634331	+	0.347816i
$73$	3.63908	+	5.11038i	0.425922	+	0.598124i	0.970652	−	0.240487i	$-0.0773072\pi$
$73$	3.63908	+	5.11038i	0.425922	+	0.598124i	−0.544730	+	0.838612i	$0.683368\pi$
$74$	0.937888	−	3.86603i	0.109027	−	0.449417i
$75$	11.3339	−	12.9486i	1.30873	−	1.49517i
$76$	−1.92327	+	1.66652i	−0.220614	+	0.191163i
$77$	13.5014	−	9.25981i	1.53863	−	1.05525i
$78$	−0.715947	+	1.76274i	−0.0810651	+	0.199591i
$79$	−3.17104	+	16.4529i	−0.356770	+	1.85110i	0.149550	+	0.988754i	$0.452218\pi$
$79$	−3.17104	+	16.4529i	−0.356770	+	1.85110i	−0.506320	+	0.862346i	$0.668995\pi$
$80$	−3.43500	+	1.77087i	−0.384045	+	0.197989i
$81$	−8.97457	+	0.676039i	−0.997175	+	0.0751154i
$82$	6.07655	+	1.17116i	0.671043	+	0.129333i
$83$	−0.204545	−	0.0600598i	−0.0224517	−	0.00659242i	0.270487	−	0.962724i	$-0.412815\pi$
$83$	−0.204545	−	0.0600598i	−0.0224517	−	0.00659242i	−0.292939	+	0.956131i	$0.594633\pi$
$84$	−0.103749	+	4.58140i	−0.0113199	+	0.499872i
$85$	7.88014	+	9.09417i	0.854722	+	0.986401i
$86$	−2.43578	+	3.42057i	−0.262657	+	0.368849i
$87$	7.93059	+	2.78931i	0.850249	+	0.299046i
$88$	5.04052	−	3.58934i	0.537321	−	0.382625i
$89$	−8.12864	+	3.25422i	−0.861634	+	0.344946i	−0.760037	−	0.649879i	$-0.774819\pi$
$89$	−8.12864	+	3.25422i	−0.861634	+	0.344946i	−0.101597	+	0.994826i	$0.532395\pi$
$90$	−4.20107	−	10.8059i	−0.442831	−	1.13904i
$91$	−1.61411	+	2.41679i	−0.169205	+	0.253349i
$92$	2.21613	+	4.25309i	0.231048	+	0.443415i
$93$	1.47909	+	3.28212i	0.153375	+	0.340340i
$94$	0.361617	+	7.59127i	0.0372979	+	0.782979i
$95$	6.07949	−	7.73070i	0.623743	−	0.793154i
$96$	−0.00866609	+	1.73203i	−0.000884479	+	0.176774i
$97$	0.0909583	+	0.309775i	0.00923541	+	0.0314529i	0.963982	−	0.265968i	$-0.0856916\pi$
$97$	0.0909583	+	0.309775i	0.00923541	+	0.0314529i	−0.954746	+	0.297421i	$0.903873\pi$
$98$	−1.56636	+	6.82250i	−0.158226	+	0.689177i
$99$	9.12053	+	16.1687i	0.916647	+	1.62502i
$100$	7.80958	−	6.14152i	0.780958	−	0.614152i
$101$	−1.89610	−	1.98858i	−0.188669	−	0.197871i	0.622605	−	0.782536i	$-0.286074\pi$
$101$	−1.89610	−	1.98858i	−0.188669	−	0.197871i	−0.811275	+	0.584665i	$0.801226\pi$
$102$	5.24740	−	1.24524i	0.519570	−	0.123297i
$103$	−19.2583	−	0.917386i	−1.89758	−	0.0903927i	−0.933911	−	0.357505i	$-0.883628\pi$
$103$	−19.2583	−	0.917386i	−1.89758	−	0.0903927i	−0.963665	+	0.267112i	$0.913931\pi$
$104$	−0.593871	+	0.924081i	−0.0582338	+	0.0906136i
$105$	−2.95705	−	17.4612i	−0.288579	−	1.70404i
$106$	−3.35285	+	11.4187i	−0.325657	+	1.10909i
$107$	8.43048	−	6.62980i	0.815005	−	0.640927i	−0.121103	−	0.992640i	$-0.538643\pi$
$107$	8.43048	−	6.62980i	0.815005	−	0.640927i	0.936108	+	0.351713i	$0.114401\pi$
$108$	−5.16463	−	0.571509i	−0.496967	−	0.0549935i
$109$	−0.268581	+	2.81271i	−0.0257254	+	0.269408i	0.973453	+	0.228886i	$0.0735083\pi$
$109$	−0.268581	+	2.81271i	−0.0257254	+	0.269408i	−0.999179	+	0.0405224i	$0.987098\pi$
$110$	−16.5024	+	17.3073i	−1.57345	+	1.65018i
$111$	5.94994	+	3.47501i	0.564743	+	0.329833i
$112$	−0.546455	+	2.58870i	−0.0516351	+	0.244610i
$113$	11.8539	−	7.61806i	1.11512	−	0.716647i	0.152721	−	0.988269i	$-0.451196\pi$
$113$	11.8539	−	7.61806i	1.11512	−	0.716647i	0.962404	+	0.271622i	$0.0875601\pi$
$114$	−1.81099	−	4.01859i	−0.169614	−	0.376376i
$115$	−11.5203	−	14.5186i	−1.07428	−	1.35387i
$116$	4.20341	+	2.42684i	0.390277	+	0.225326i
$117$	−2.56982	−	2.06288i	−0.237580	−	0.190713i
$118$	1.16964	−	8.13501i	0.107674	−	0.748889i
$119$	8.23444	−	0.246790i	0.754850	−	0.0226232i
$120$	−1.23389	−	6.57899i	−0.112638	−	0.600577i
$121$	15.8299	−	22.2300i	1.43908	−	2.02091i
$122$	−0.481579	+	0.0928167i	−0.0436001	+	0.00840323i
$123$	−4.95915	+	9.50238i	−0.447152	+	0.856800i
$124$	0.490016	+	2.01987i	0.0440047	+	0.181390i
$125$	−12.4899	+	14.4141i	−1.11713	+	1.28923i
$126$	−7.55102	−	2.44584i	−0.672698	−	0.217893i
$127$	−11.5047	−	7.39364i	−1.02088	−	0.656079i	−0.0806928	−	0.996739i	$-0.525713\pi$
$127$	−11.5047	−	7.39364i	−1.02088	−	0.656079i	−0.940187	+	0.340660i	$0.889350\pi$
$128$	−0.189251	+	0.981929i	−0.0167276	+	0.0867911i
$129$	−4.46735	−	5.73957i	−0.393328	−	0.505341i
$130$	1.57775	−	3.94102i	0.138377	−	0.345650i
$131$	11.6939	+	4.04731i	1.02170	+	0.353615i	0.786011	−	0.618212i	$-0.212143\pi$
$131$	11.6939	+	4.04731i	1.02170	+	0.353615i	0.235693	+	0.971828i	$0.424264\pi$
$132$	3.45472	+	10.1457i	0.300695	+	0.883071i
$133$	−1.47172	−	6.57022i	−0.127614	−	0.569710i
$134$	−0.382227	+	0.836961i	−0.0330194	+	0.0723024i
$135$	20.0166	−	1.60857i	1.72275	−	0.138444i
$136$	3.11020	−	0.148157i	0.266697	−	0.0127043i
$137$	−3.12970	+	5.42079i	−0.267388	+	0.463130i	−0.968186	−	0.250230i	$-0.919494\pi$
$137$	−3.12970	+	5.42079i	−0.267388	+	0.463130i	0.700799	+	0.713359i	$0.252827\pi$
$138$	−8.15753	+	1.56677i	−0.694415	+	0.133373i
$139$	−14.4800			−1.22818			−0.614088	−	0.789238i	$-0.710476\pi$
$139$	−14.4800			−1.22818			−0.614088	+	0.789238i	$0.710476\pi$
$140$	0.180339	−	10.2232i	0.0152414	−	0.864018i
$141$	−12.7766	−	3.16735i	−1.07599	−	0.266739i
$142$	−5.72140	+	0.546327i	−0.480129	+	0.0458468i
$143$	−1.60249	+	6.60555i	−0.134007	+	0.552384i
$144$	−2.86988	−	0.873959i	−0.239156	−	0.0728299i
$145$	−17.7259	−	6.13500i	−1.47206	−	0.509484i
$146$	−6.20981	+	0.892835i	−0.513927	+	0.0738916i
$147$	−10.5441	−	5.98516i	−0.869662	−	0.493647i
$148$	3.00650	+	2.60515i	0.247133	+	0.214142i
$149$	0.353035	−	7.41112i	0.0289218	−	0.607143i	−0.937159	−	0.348903i	$-0.886554\pi$
$149$	0.353035	−	7.41112i	0.0289218	−	0.607143i	0.966081	−	0.258240i	$-0.0831426\pi$
$150$	6.31565	+	16.0074i	0.515670	+	1.30700i
$151$	−2.88711	−	8.34176i	−0.234950	−	0.678843i	−0.999416	−	0.0341788i	$-0.989118\pi$
$151$	−2.88711	−	8.34176i	−0.234950	−	0.678843i	0.764466	−	0.644664i	$-0.223003\pi$
$152$	−0.599971	−	2.47311i	−0.0486641	−	0.200596i
$153$	−0.537816	+	9.32567i	−0.0434798	+	0.753936i
$154$	2.04375	+	16.2436i	0.164690	+	1.30895i
$155$	−3.33680	−	7.30656i	−0.268018	−	0.586877i
$156$	−1.23872	−	1.44409i	−0.0991767	−	0.115620i
$157$	−13.2887	+	9.46286i	−1.06056	+	0.755218i	−0.970593	−	0.240727i	$-0.922614\pi$
$157$	−13.2887	+	9.46286i	−1.06056	+	0.755218i	−0.0899628	+	0.995945i	$0.528675\pi$
$158$	−13.1709	−	10.3577i	−1.04782	−	0.824015i
$159$	−17.2846	−	11.2308i	−1.37076	−	0.890656i
$160$		−	3.86461i		−	0.305524i
$161$	−12.6875	−	0.168505i	−0.999912	−	0.0132800i
$162$	3.51150	−	8.28670i	0.275890	−	0.651064i
$163$	13.7114	+	7.06870i	1.07396	+	0.553663i	0.902130	−	0.431464i	$-0.142003\pi$
$163$	13.7114	+	7.06870i	1.07396	+	0.553663i	0.171826	+	0.985127i	$0.445033\pi$
$164$	−3.82541	+	4.86440i	−0.298714	+	0.379846i
$165$	−20.5303	−	35.9739i	−1.59828	−	2.80057i
$166$	0.147111	−	0.154286i	0.0114180	−	0.0119749i
$167$	5.85868	−	2.67557i	0.453358	−	0.207042i	−0.175631	−	0.984456i	$-0.556196\pi$
$167$	5.85868	−	2.67557i	0.453358	−	0.207042i	0.628989	+	0.777414i	$0.283469\pi$
$168$	−4.02457	−	2.19153i	−0.310502	−	0.169081i
$169$	1.67837	+	11.6734i	0.129106	+	0.897950i
$170$	−11.6941	+	2.83696i	−0.896897	+	0.217585i
$171$	7.56733	−	1.01084i	0.578688	−	0.0773006i
$172$	−1.92419	−	3.73240i	−0.146718	−	0.284593i
$173$	−9.57465	−	0.456097i	−0.727947	−	0.0346764i	−0.319663	−	0.947531i	$-0.603570\pi$
$173$	−9.57465	−	0.456097i	−0.727947	−	0.0346764i	−0.408284	+	0.912855i	$0.633873\pi$
$174$	−6.11325	+	5.77085i	−0.463444	+	0.437487i
$175$	4.51865	+	25.8947i	0.341578	+	1.95746i
$176$	0.880631	+	6.12493i	0.0663801	+	0.461684i
$177$	12.9190	+	5.97821i	0.971051	+	0.449350i
$178$	0.832296	−	8.71619i	0.0623832	−	0.653306i
$179$	17.6739	+	4.28763i	1.32101	+	0.320473i	0.833439	−	0.552612i	$-0.186369\pi$
$179$	17.6739	+	4.28763i	1.32101	+	0.320473i	0.487568	+	0.873085i	$0.337884\pi$
$180$	11.5297	+	1.21750i	0.859374	+	0.0907469i
$181$	−0.778196	−	0.111888i	−0.0578428	−	0.00831655i	0.113333	−	0.993557i	$-0.463847\pi$
$181$	−0.778196	−	0.111888i	−0.0578428	−	0.00831655i	−0.171175	+	0.985241i	$0.554757\pi$
$182$	−1.40850	−	2.54212i	−0.104405	−	0.188434i
$183$	0.0849772	−	0.845208i	0.00628169	−	0.0624796i
$184$	−4.79579	+	0.0208996i	−0.353550	+	0.00154074i
$185$	−13.3143	−	7.68703i	−0.978888	−	0.565161i
$186$	−3.59502	−	0.189285i	−0.263600	−	0.0138790i
$187$	17.8873	−	7.16098i	1.30805	−	0.523663i
$188$	−6.91309	−	3.15710i	−0.504189	−	0.230255i
$189$	7.80614	−	11.3165i	0.567813	−	0.823157i
$190$	4.08554	+	8.94608i	0.296396	+	0.649017i
$191$	−4.00339	+	11.5670i	−0.289675	+	0.836961i	0.702453	+	0.711731i	$0.252088\pi$
$191$	−4.00339	+	11.5670i	−0.289675	+	0.836961i	−0.992128	+	0.125231i	$0.960033\pi$
$192$	−1.53552	−	0.801364i	−0.110816	−	0.0578335i
$193$	−3.51231	+	3.34898i	−0.252821	+	0.241065i	−0.805882	−	0.592076i	$-0.798308\pi$
$193$	−3.51231	+	3.34898i	−0.252821	+	0.241065i	0.553060	+	0.833141i	$0.313460\pi$
$194$	−0.317019	−	0.0611004i	−0.0227606	−	0.00438675i
$195$	5.75683	+	4.57402i	0.412255	+	0.327552i
$196$	−5.34633	−	4.51849i	−0.381881	−	0.322749i
$197$	−18.4267	−	15.9669i	−1.31285	−	1.13759i	−0.980946	−	0.194278i	$-0.937764\pi$
$197$	−18.4267	−	15.9669i	−1.31285	−	1.13759i	−0.331904	−	0.943313i	$-0.607691\pi$
$198$	−18.5506	+	0.697704i	−1.31833	+	0.0495837i
$199$	3.30723	−	8.26107i	0.234444	−	0.585612i	−0.763762	−	0.645499i	$-0.776650\pi$
$199$	3.30723	−	8.26107i	0.234444	−	0.585612i	0.998205	+	0.0598865i	$0.0190739\pi$
$200$	1.88025	+	9.75564i	0.132953	+	0.689828i
$201$	−1.19918	−	1.04965i	−0.0845839	−	0.0740366i
$202$	2.63636	−	0.774106i	0.185494	−	0.0544659i
$203$	−10.9238	+	6.75109i	−0.766703	+	0.473834i
$204$	−1.29768	+	5.23467i	−0.0908561	+	0.366501i
$205$	10.9588	−	21.2571i	0.765396	−	1.48466i
$206$	9.64007	−	16.6971i	0.671655	−	1.16334i
$207$	1.44850	−	14.3144i	0.100678	−	0.994919i
$208$	−0.549228	−	0.951292i	−0.0380821	−	0.0659602i
$209$	−8.51363	−	13.2475i	−0.588900	−	0.916346i
$210$	16.8752	+	5.37287i	1.16450	+	0.370763i
$211$	−8.31423	+	18.2056i	−0.572375	+	1.25333i	0.373148	+	0.927772i	$0.378278\pi$
$211$	−8.31423	+	18.2056i	−0.572375	+	1.25333i	−0.945523	+	0.325555i	$0.894449\pi$
$212$	−8.61302	−	8.21250i	−0.591545	−	0.564037i
$213$	1.93285	−	9.76538i	0.132436	−	0.669113i
$214$	2.02973	+	10.5313i	0.138750	+	0.719902i
$215$	10.0316	+	12.7563i	0.684153	+	0.869971i
$216$	2.87455	−	4.32862i	0.195588	−	0.294526i
$217$	−5.32039	−	1.39051i	−0.361171	−	0.0943943i
$218$	−2.37696	−	1.52758i	−0.160988	−	0.103461i
$219$	1.60023	−	10.7478i	0.108134	−	0.726271i
$220$	−7.82145	−	22.5986i	−0.527322	−	1.52360i
$221$	−2.47538	+	2.36027i	−0.166512	+	0.158769i
$222$	−5.81513	+	3.69618i	−0.390286	+	0.248071i
$223$	−9.42013	−	10.8714i	−0.630819	−	0.728004i	0.346905	−	0.937900i	$-0.387233\pi$
$223$	−9.42013	−	10.8714i	−0.630819	−	0.728004i	−0.977724	+	0.209897i	$0.932687\pi$
$224$	−2.05053	−	1.67192i	−0.137007	−	0.111710i
$225$	−29.6975	+	2.53615i	−1.97983	+	0.169077i
$226$	1.33942	+	14.0270i	0.0890966	+	0.933062i
$227$	1.76857	+	1.39082i	0.117384	+	0.0923121i	0.675126	−	0.737703i	$-0.264089\pi$
$227$	1.76857	+	1.39082i	0.117384	+	0.0923121i	−0.557741	+	0.830015i	$0.688332\pi$
$228$	4.40171	+	0.231758i	0.291510	+	0.0153486i
$229$	−23.4264	+	13.5252i	−1.54806	+	0.893772i	−0.549769	+	0.835317i	$0.685284\pi$
$229$	−23.4264	+	13.5252i	−1.54806	+	0.893772i	−0.998290	+	0.0584552i	$0.981383\pi$
$230$	18.1836	−	3.58686i	1.19899	−	0.236510i
$231$	−27.9694	−	4.66998i	−1.84025	−	0.307262i
$232$	−4.08317	+	2.62410i	−0.268073	+	0.172280i
$233$	4.00258	+	9.99797i	0.262218	+	0.654989i	0.999794	−	0.0202747i	$-0.00645409\pi$
$233$	4.00258	+	9.99797i	0.262218	+	0.654989i	−0.737576	+	0.675264i	$0.764030\pi$
$234$	3.01112	−	1.33888i	0.196843	−	0.0875255i
$235$	28.5426	+	6.92436i	1.86191	+	0.451696i
$236$	6.69473	+	4.76729i	0.435790	+	0.310324i
$237$	23.7244	−	16.7158i	1.54106	−	1.08581i
$238$	−3.55388	+	7.43215i	−0.230364	+	0.481754i
$239$	7.61902	−	25.9480i	0.492834	−	1.67844i	−0.218706	−	0.975791i	$-0.570183\pi$
$239$	7.61902	−	25.9480i	0.492834	−	1.67844i	0.711539	−	0.702646i	$-0.247998\pi$
$240$	6.41304	+	1.91794i	0.413960	+	0.123803i
$241$	6.57548	+	12.7547i	0.423564	+	0.821600i	0.999990	+	0.00445033i	$0.00141659\pi$
$241$	6.57548	+	12.7547i	0.423564	+	0.821600i	−0.576426	+	0.817149i	$0.695553\pi$
$242$	12.5051	+	24.2565i	0.803858	+	1.55927i
$243$	12.0085	+	9.93964i	0.770344	+	0.637628i
$244$	0.138173	−	0.470575i	0.00884564	−	0.0301255i
$245$	23.5928	+	13.2364i	1.50729	+	0.845642i
$246$	−6.17363	−	8.76211i	−0.393617	−	0.558652i
$247$	2.27707	+	1.62149i	0.144887	+	0.103173i
$248$	−2.01987	−	0.490016i	−0.128262	−	0.0311160i
$249$	0.183017	+	0.320690i	0.0115982	+	0.0203229i
$250$	−7.08855	−	17.7063i	−0.448319	−	1.11985i
$251$	−5.92150	+	3.80552i	−0.373762	+	0.240202i	−0.714013	−	0.700133i	$-0.753124\pi$
$251$	−5.92150	+	3.80552i	−0.373762	+	0.240202i	0.340251	+	0.940335i	$0.389488\pi$
$252$	5.63403	−	5.59086i	0.354910	−	0.352191i
$253$	−28.0014	+	9.82824i	−1.76044	+	0.617896i
$254$	11.8435	−	6.83785i	0.743127	−	0.429045i
$255$	1.09587	−	20.8135i	0.0686259	−	1.30339i
$256$	−0.786053	−	0.618159i	−0.0491283	−	0.0386349i
$257$	−0.597719	−	6.25959i	−0.0372847	−	0.390463i	−0.994782	−	0.102021i	$-0.967469\pi$
$257$	−0.597719	−	6.25959i	−0.0372847	−	0.390463i	0.957498	−	0.288441i	$-0.0931370\pi$
$258$	7.14859	−	1.34072i	0.445052	−	0.0834695i
$259$	−9.83877	+	3.73889i	−0.611351	+	0.232323i
$260$	2.77995	+	3.20824i	0.172405	+	0.198966i
$261$	−6.54241	−	13.0085i	−0.404965	−	0.805205i
$262$	−8.95586	+	8.53940i	−0.553295	+	0.527566i
$263$	7.36269	+	21.2731i	0.454003	+	1.31176i	0.907333	+	0.420413i	$0.138115\pi$
$263$	7.36269	+	21.2731i	0.454003	+	1.31176i	−0.453330	+	0.891343i	$0.649764\pi$
$264$	−10.6009	−	1.57836i	−0.652441	−	0.0971412i
$265$	38.6909	+	24.8651i	2.37676	+	1.52745i
$266$	6.51423	+	1.70253i	0.399413	+	0.104389i
$267$	14.0508	+	5.70684i	0.859898	+	0.349253i
$268$	−0.568774	−	0.723255i	−0.0347434	−	0.0441798i
$269$	−1.69438	−	8.79129i	−0.103308	−	0.536015i	−0.996300	−	0.0859417i	$-0.972610\pi$
$269$	−1.69438	−	8.79129i	−0.103308	−	0.536015i	0.892992	−	0.450073i	$-0.148602\pi$
$270$	−7.74236	+	18.5285i	−0.471185	+	1.12761i
$271$	−20.8929	−	19.9213i	−1.26915	−	1.21013i	−0.966394	−	0.257066i	$-0.917244\pi$
$271$	−20.8929	−	19.9213i	−1.26915	−	1.21013i	−0.302757	−	0.953068i	$-0.597907\pi$
$272$	−1.29349	+	2.83234i	−0.0784292	+	0.171736i
$273$	4.91748	−	1.07570i	0.297620	−	0.0651043i
$274$	−3.38408	−	5.26574i	−0.204440	−	0.318115i
$275$	30.7390	+	53.2415i	1.85363	+	3.21058i
$276$	2.34539	−	7.96863i	0.141176	−	0.479655i
$277$	15.1120	−	26.1748i	0.907995	−	1.57269i	0.0911490	−	0.995837i	$-0.470946\pi$
$277$	15.1120	−	26.1748i	0.907995	−	1.57269i	0.816846	−	0.576856i	$-0.195721\pi$
$278$	6.63511	−	12.8703i	0.397947	−	0.771910i
$279$	2.09826	−	5.87174i	0.125619	−	0.351532i
$280$	9.00410	+	4.84483i	0.538098	+	0.289534i
$281$	−2.69150	+	0.790295i	−0.160561	+	0.0471451i	−0.361025	−	0.932556i	$-0.617573\pi$
$281$	−2.69150	+	0.790295i	−0.160561	+	0.0471451i	0.200464	+	0.979701i	$0.435755\pi$
$282$	8.66984	−	9.90495i	0.516281	−	0.589831i
$283$	−2.30053	−	11.9363i	−0.136752	−	0.709539i	−0.983976	−	0.178302i	$-0.942940\pi$
$283$	−2.30053	−	11.9363i	−0.136752	−	0.709539i	0.847223	−	0.531237i	$-0.178273\pi$
$284$	2.13610	−	5.33572i	0.126754	−	0.316617i
$285$	−16.8730	+	2.33986i	−0.999469	+	0.138601i
$286$	−5.13694	−	4.45119i	−0.303754	−	0.263204i
$287$	−6.53782	−	15.0110i	−0.385915	−	0.886070i
$288$	2.09186	−	2.15038i	0.123264	−	0.126712i
$289$	−7.17273	−	1.38243i	−0.421925	−	0.0813194i
$290$	13.5755	−	12.9442i	0.797180	−	0.760109i
$291$	0.258723	−	0.495747i	0.0151666	−	0.0290612i
$292$	2.05191	−	5.92862i	0.120079	−	0.346946i
$293$	−0.137347	−	0.300747i	−0.00802387	−	0.0175698i	0.905578	−	0.424181i	$-0.139438\pi$
$293$	−0.137347	−	0.300747i	−0.00802387	−	0.0175698i	−0.913602	+	0.406611i	$0.866711\pi$
$294$	10.1514	−	6.62941i	0.592042	−	0.386635i
$295$	−28.8917	−	13.1944i	−1.68214	−	0.768206i
$296$	−3.69320	+	1.47854i	−0.214663	+	0.0859381i
$297$	8.04858	−	31.1297i	0.467026	−	1.80633i
$298$	6.42550	+	3.70976i	0.372219	+	0.214901i
$299$	3.96623	−	3.46713i	0.229373	−	0.200509i
$300$	−17.1219	−	1.72144i	−0.988535	−	0.0993872i
$301$	11.1083	+	0.195952i	0.640273	+	0.0112945i
$302$	8.73740	+	1.25625i	0.502781	+	0.0722890i
$303$	−0.0238115	+	4.75903i	−0.00136793	+	0.273399i
$304$	2.47311	+	0.599971i	0.141843	+	0.0344107i
$305$	−0.180166	+	1.88678i	−0.0103163	+	0.108037i
$306$	−8.04255	−	4.75130i	−0.459762	−	0.271614i
$307$	−2.55401	−	17.7635i	−0.145765	−	1.01382i	−0.923053	−	0.384672i	$-0.874314\pi$
$307$	−2.55401	−	17.7635i	−0.145765	−	1.01382i	0.777288	−	0.629144i	$-0.216595\pi$
$308$	−15.3744	−	5.62669i	−0.876037	−	0.320610i
$309$	22.9234	+	24.2835i	1.30407	+	1.38144i
$310$	8.02334	+	0.382199i	0.455695	+	0.0217074i
$311$	−11.6760	−	22.6483i	−0.662085	−	1.28427i	−0.945610	−	0.325302i	$-0.894534\pi$
$311$	−11.6760	−	22.6483i	−0.662085	−	1.28427i	0.283525	−	0.958965i	$-0.408496\pi$
$312$	1.85117	−	0.439294i	0.104802	−	0.0248701i
$313$	26.4308	−	6.41205i	1.49396	−	0.362431i	0.596171	−	0.802858i	$-0.296688\pi$
$313$	26.4308	−	6.41205i	1.49396	−	0.362431i	0.897788	+	0.440427i	$0.145173\pi$
$314$	−2.32168	−	16.1476i	−0.131020	−	0.911263i
$315$	−17.2908	+	25.3367i	−0.974224	+	1.42756i
$316$	15.2416	−	6.96058i	0.857404	−	0.391563i
$317$	−8.92178	+	9.35689i	−0.501097	+	0.525536i	−0.924896	−	0.380221i	$-0.875848\pi$
$317$	−8.92178	+	9.35689i	−0.501097	+	0.525536i	0.423799	+	0.905756i	$0.360696\pi$
$318$	17.9026	−	10.2170i	1.00393	−	0.572939i
$319$	−18.5659	+	23.6084i	−1.03949	+	1.32182i
$320$	3.43500	+	1.77087i	0.192022	+	0.0989944i
$321$	−18.4832	−	1.85830i	−1.03163	−	0.103720i
$322$	5.96350	−	11.1998i	0.332333	−	0.624143i
$323$		−	7.92395i		−	0.440900i
$324$	5.75645	+	6.91833i	0.319803	+	0.384352i
$325$	−8.57849	−	6.74620i	−0.475849	−	0.374212i
$326$	−12.5658	+	8.94808i	−0.695956	+	0.495588i
$327$	3.71456	−	3.18628i	0.205416	−	0.176202i
$328$	−2.57075	−	5.62915i	−0.141946	−	0.310818i
$329$	16.0222	−	12.1489i	0.883334	−	0.669788i
$330$	41.3824	−	1.76381i	2.27803	−	0.0970947i
$331$	3.39396	+	13.9901i	0.186549	+	0.768966i	0.985794	+	0.167960i	$0.0537179\pi$
$331$	3.39396	+	13.9901i	0.186549	+	0.768966i	−0.799245	+	0.601006i	$0.794767\pi$
$332$	0.0697244	+	0.201455i	0.00382662	+	0.0110563i
$333$	−3.24758	−	11.4841i	−0.177966	−	0.629327i
$334$	−0.306461	+	6.43341i	−0.0167688	+	0.352021i
$335$	2.68734	+	2.32859i	0.146825	+	0.127225i
$336$	3.79208	−	2.57296i	0.206875	−	0.140367i
$337$	−9.01720	+	1.29648i	−0.491198	+	0.0706236i	−0.383463	−	0.923556i	$-0.625269\pi$
$337$	−9.01720	+	1.29648i	−0.491198	+	0.0706236i	−0.107735	+	0.994180i	$0.534360\pi$
$338$	−11.1448	−	3.85724i	−0.606195	−	0.209806i
$339$	−23.9415	−	4.73871i	−1.30033	−	0.257372i
$340$	2.83696	−	11.6941i	0.153856	−	0.634202i
$341$	−12.8031	+	1.22255i	−0.693327	+	0.0662047i
$342$	−2.56908	+	7.18930i	−0.138920	+	0.388753i
$343$	17.2300	−	6.79180i	0.930330	−	0.366723i
$344$	4.19920			0.226406
$345$	−3.07210	+	31.9545i	−0.165396	+	1.72037i
$346$	4.79276	−	8.30130i	0.257660	−	0.446280i
$347$	−5.16416	+	0.245999i	−0.277227	+	0.0132059i	−0.185735	−	0.982600i	$-0.559467\pi$
$347$	−5.16416	+	0.245999i	−0.277227	+	0.0132059i	−0.0914918	+	0.995806i	$0.529164\pi$
$348$	−2.32809	−	8.07803i	−0.124798	−	0.433028i
$349$	−11.2143	+	24.5559i	−0.600287	+	1.31445i	0.328735	+	0.944422i	$0.393378\pi$
$349$	−11.2143	+	24.5559i	−0.600287	+	1.31445i	−0.929022	+	0.370024i	$0.879350\pi$
$350$	−25.0867	−	7.84932i	−1.34094	−	0.419564i
$351$	0.727407	+	5.66121i	0.0388261	+	0.302173i
$352$	−5.84758	−	2.02387i	−0.311677	−	0.107872i
$353$	6.13601	−	15.3270i	0.326587	−	0.815774i	−0.670670	−	0.741756i	$-0.733993\pi$
$353$	6.13601	−	15.3270i	0.326587	−	0.815774i	0.997257	−	0.0740184i	$-0.0235824\pi$
$354$	−11.2335	+	8.74349i	−0.597052	+	0.464711i
$355$	−4.20356	+	21.8101i	−0.223102	+	1.15756i
$356$	7.36588	+	4.73377i	0.390391	+	0.250889i
$357$	−10.5694	−	9.58587i	−0.559391	−	0.507338i
$358$	−11.9096	+	13.7445i	−0.629444	+	0.726417i
$359$	0.253684	+	1.04570i	0.0133890	+	0.0551900i	0.978114	−	0.208069i	$-0.0667178\pi$
$359$	0.253684	+	1.04570i	0.0133890	+	0.0551900i	−0.964725	+	0.263259i	$0.915203\pi$
$360$	−6.36538	+	9.69013i	−0.335485	+	0.510715i
$361$	12.2974	−	2.37013i	0.647233	−	0.124744i
$362$	0.456040	−	0.640418i	0.0239689	−	0.0336596i
$363$	−46.4580	+	8.71320i	−2.43841	+	0.457324i
$364$	2.90494	−	0.0870626i	0.152260	−	0.00456332i
$365$	−3.45046	+	23.9985i	−0.180605	+	1.25614i
$366$	0.712312	+	0.462828i	0.0372332	+	0.0241924i
$367$	−17.4871	−	10.0962i	−0.912822	−	0.527018i	−0.0314836	−	0.999504i	$-0.510023\pi$
$367$	−17.4871	−	10.0962i	−0.912822	−	0.527018i	−0.881338	+	0.472486i	$0.843357\pi$
$368$	2.17898	−	4.27224i	0.113587	−	0.222706i
$369$	17.6040	−	5.89621i	0.916426	−	0.306944i
$370$	12.9335	−	8.31184i	0.672379	−	0.432112i
$371$	29.9319	−	9.77186i	1.55398	−	0.507329i
$372$	1.81558	−	3.10865i	0.0941333	−	0.161176i
$373$	1.99356	−	2.09079i	0.103223	−	0.108257i	−0.670096	−	0.742275i	$-0.733747\pi$
$373$	1.99356	−	2.09079i	0.103223	−	0.108257i	0.773318	+	0.634018i	$0.218595\pi$
$374$	−1.83149	+	19.1802i	−0.0947039	+	0.991784i
$375$	32.9003	−	2.97557i	1.69897	−	0.153658i
$376$	5.97390	−	4.69793i	0.308081	−	0.242277i
$377$	1.50207	−	5.11559i	0.0773607	−	0.263466i
$378$	6.48156	+	12.1239i	0.333375	+	0.623587i
$379$	−1.29062	+	2.00825i	−0.0662949	+	0.103157i	−0.872818	−	0.488045i	$-0.837710\pi$
$379$	−1.29062	+	2.00825i	−0.0662949	+	0.103157i	0.806523	+	0.591202i	$0.201346\pi$
$380$	−9.82370	−	0.467960i	−0.503945	−	0.0240059i
$381$	5.46918	+	23.0470i	0.280194	+	1.18073i
$382$	−8.44673	−	8.85868i	−0.432172	−	0.453249i
$383$	26.5210	−	20.8563i	1.35516	−	1.06571i	0.364230	−	0.931309i	$-0.381332\pi$
$383$	26.5210	−	20.8563i	1.35516	−	1.06571i	0.990927	−	0.134399i	$-0.0429103\pi$
$384$	1.41590	−	0.997616i	0.0722546	−	0.0509094i
$385$	62.4575	+	10.1074i	3.18313	+	0.515122i
$386$	−1.36726	−	4.65645i	−0.0695916	−	0.237007i
$387$	−1.32291	+	12.5280i	−0.0672472	+	0.636832i
$388$	0.199575	−	0.253780i	0.0101319	−	0.0128837i
$389$	1.24096	+	26.0509i	0.0629189	+	1.32083i	0.780851	+	0.624718i	$0.214786\pi$
$389$	1.24096	+	26.0509i	0.0629189	+	1.32083i	−0.717932	+	0.696113i	$0.754911\pi$
$390$	−6.70348	+	3.02093i	−0.339444	+	0.152971i
$391$	−14.5272	−	3.45729i	−0.734670	−	0.174843i
$392$	6.46602	−	2.68152i	0.326583	−	0.135437i
$393$	−9.72587	−	19.0996i	−0.490605	−	0.963446i
$394$	22.6355	−	9.06190i	1.14036	−	0.456532i
$395$	−52.7473	+	37.5612i	−2.65401	+	1.88991i
$396$	7.88024	−	16.8081i	0.395997	−	0.844641i
$397$	−15.3447	+	21.5487i	−0.770131	+	1.08150i	0.224135	+	0.974558i	$0.428044\pi$
$397$	−15.3447	+	21.5487i	−0.770131	+	1.08150i	−0.994266	+	0.106939i	$0.965895\pi$
$398$	5.82727	+	6.72503i	0.292095	+	0.337095i
$399$	−6.05814	+	9.96495i	−0.303286	+	0.498872i
$400$	−9.53274	−	2.79906i	−0.476637	−	0.139953i
$401$	−0.785358	−	0.151365i	−0.0392189	−	0.00755882i	0.169604	−	0.985512i	$-0.445751\pi$
$401$	−0.785358	−	0.151365i	−0.0392189	−	0.00755882i	−0.208823	+	0.977953i	$0.566963\pi$
$402$	1.48246	−	0.584900i	0.0739386	−	0.0291722i
$403$	2.02930	−	1.04618i	0.101087	−	0.0521138i
$404$	−0.519999	+	2.69801i	−0.0258709	+	0.134231i
$405$	−26.9043	−	22.0433i	−1.33689	−	1.09534i
$406$	−0.995017	−	12.8030i	−0.0493818	−	0.635403i
$407$	−18.6039	+	16.1204i	−0.922163	+	0.799059i
$408$	−4.05813	−	3.55209i	−0.200907	−	0.175855i
$409$	0.156882	−	0.646677i	0.00775733	−	0.0319761i	−0.967801	−	0.251715i	$-0.919005\pi$
$409$	0.156882	−	0.646677i	0.00775733	−	0.0319761i	0.975559	+	0.219739i	$0.0705206\pi$
$410$	13.8725	+	19.4811i	0.685112	+	0.962105i
$411$	10.4176	−	3.00234i	0.513861	−	0.148095i
$412$	10.4236	+	16.2195i	0.513535	+	0.799077i
$413$	−19.5001	+	9.62149i	−0.959535	+	0.473443i
$414$	12.0594	+	7.84671i	0.592687	+	0.385645i
$415$	−0.411929	−	0.713481i	−0.0202208	−	0.0350234i
$416$	1.09721	−	0.0522667i	0.0537953	−	0.00256258i
$417$	18.0645	+	17.3978i	0.884621	+	0.851975i
$418$	15.6760	−	1.49688i	0.766738	−	0.0732146i
$419$	−18.5576	+	5.44901i	−0.906599	+	0.266202i	−0.701609	−	0.712562i	$-0.747535\pi$
$419$	−18.5576	+	5.44901i	−0.906599	+	0.266202i	−0.204991	+	0.978764i	$0.565716\pi$
$420$	−12.5082	+	12.5373i	−0.610340	+	0.611755i
$421$	−2.97184	+	2.57511i	−0.144839	+	0.125503i	−0.724267	−	0.689520i	$-0.757821\pi$
$421$	−2.97184	+	2.57511i	−0.144839	+	0.125503i	0.579428	+	0.815023i	$0.303276\pi$
$422$	−12.3720	−	15.7323i	−0.602260	−	0.765836i
$423$	12.1339	+	19.3026i	0.589968	+	0.938527i
$424$	11.2463	−	3.89237i	0.546168	−	0.189030i
$425$	−1.47197	+	30.9004i	−0.0714008	+	1.49889i
$426$	7.79413	+	6.19274i	0.377627	+	0.300039i
$427$	0.923168	+	0.911861i	0.0446752	+	0.0441281i
$428$	−10.2906	−	3.02160i	−0.497416	−	0.146055i
$429$	9.93581	−	6.31534i	0.479705	−	0.304907i
$430$	−15.9350	+	3.07122i	−0.768454	+	0.148107i
$431$	−33.7508	−	3.22281i	−1.62572	−	0.155237i	−0.757986	−	0.652271i	$-0.773816\pi$
$431$	−33.7508	−	3.22281i	−1.62572	−	0.155237i	−0.867731	+	0.497034i	$0.834422\pi$
$432$	2.53024	+	4.53849i	0.121736	+	0.218358i
$433$	−8.37492	−	3.82470i	−0.402473	−	0.183803i	0.203885	−	0.978995i	$-0.434643\pi$
$433$	−8.37492	−	3.82470i	−0.402473	−	0.183803i	−0.606358	+	0.795191i	$0.707370\pi$
$434$	3.67388	−	4.09178i	0.176352	−	0.196412i
$435$	14.7427	+	28.9515i	0.706857	+	1.38812i
$436$	2.44695	−	1.41275i	0.117188	−	0.0676585i
$437$	−0.527590	+	12.1933i	−0.0252380	+	0.583283i
$438$	8.81978	+	6.34728i	0.421426	+	0.303285i
$439$	−3.55788	−	1.83421i	−0.169808	−	0.0875423i	0.371227	−	0.928542i	$-0.378937\pi$
$439$	−3.55788	−	1.83421i	−0.169808	−	0.0875423i	−0.541035	+	0.841000i	$0.681967\pi$
$440$	23.6704	+	3.40329i	1.12844	+	0.162246i
$441$	5.96304	+	20.1356i	0.283954	+	0.958838i
$442$	−0.963607	−	3.28174i	−0.0458341	−	0.156097i
$443$	15.3176	+	10.9076i	0.727761	+	0.518236i	0.882845	−	0.469665i	$-0.155625\pi$
$443$	15.3176	+	10.9076i	0.727761	+	0.518236i	−0.155083	+	0.987901i	$0.549565\pi$
$444$	−0.620646	−	6.86238i	−0.0294545	−	0.325674i
$445$	−31.4140	−	12.5763i	−1.48917	−	0.596172i
$446$	13.9795	−	3.39138i	0.661946	−	0.160586i
$447$	−9.34496	+	8.82156i	−0.442001	+	0.417245i
$448$	2.42567	−	1.05647i	0.114602	−	0.0499134i
$449$	−19.0333	+	29.6164i	−0.898236	+	1.39768i	0.0192076	+	0.999816i	$0.493886\pi$
$449$	−19.0333	+	29.6164i	−0.898236	+	1.39768i	−0.917443	+	0.397866i	$0.869751\pi$
$450$	11.3539	−	27.5583i	0.535230	−	1.29911i
$451$	−26.4253	−	27.7141i	−1.24432	−	1.30500i
$452$	−13.0815	−	5.23702i	−0.615300	−	0.246329i
$453$	−6.42089	+	13.8756i	−0.301680	+	0.651934i
$454$	−2.04662	+	0.934660i	−0.0960526	+	0.0438657i
$455$	−10.9599	+	2.45500i	−0.513808	+	0.115092i
$456$	−2.22297	+	3.80620i	−0.104100	+	0.178242i
$457$	1.29117	+	3.22519i	0.0603985	+	0.150868i	0.955497	−	0.294999i	$-0.0953195\pi$
$457$	1.29117	+	3.22519i	0.0603985	+	0.150868i	−0.895099	+	0.445868i	$0.852895\pi$
$458$	−1.28711	−	27.0198i	−0.0601428	−	1.26255i
$459$	11.8758	−	10.9880i	0.554316	−	0.512878i
$460$	−5.14409	+	17.8058i	−0.239844	+	0.830201i
$461$		−	2.74216i		−	0.127715i	−0.997959	−	0.0638576i	$-0.979660\pi$
$461$		−	2.74216i		−	0.127715i	0.997959	−	0.0638576i	$-0.0203404\pi$
$462$	16.9672	−	22.7203i	0.789383	−	1.05704i
$463$	4.21789	−	29.3361i	0.196022	−	1.36336i	−0.619663	−	0.784868i	$-0.712731\pi$
$463$	4.21789	−	29.3361i	0.196022	−	1.36336i	0.815685	−	0.578496i	$-0.196360\pi$
$464$	−0.461371	−	4.83170i	−0.0214186	−	0.224306i
$465$	−4.61609	+	13.1245i	−0.214066	+	0.608633i
$466$	−10.7206	−	1.02370i	−0.496624	−	0.0474219i
$467$	0.540495	−	1.56166i	0.0250111	−	0.0722649i	−0.931804	−	0.362961i	$-0.881766\pi$
$467$	0.540495	−	1.56166i	0.0250111	−	0.0722649i	0.956815	+	0.290696i	$0.0938869\pi$
$468$	−0.189730	+	3.28990i	−0.00877029	+	0.152076i
$469$	2.39814	−	0.418478i	0.110736	−	0.0193235i
$470$	−19.2336	+	22.1968i	−0.887180	+	1.02386i
$471$	27.9480	+	4.16115i	1.28778	+	0.191736i
$472$	−7.30504	+	3.76601i	−0.336242	+	0.173345i
$473$	24.5552	−	8.49863i	1.12905	−	0.390767i
$474$	3.98645	+	28.7467i	0.183104	+	1.32038i
$475$	25.0262	−	3.59822i	1.14828	−	0.165098i
$476$	−4.97747	−	6.56442i	−0.228142	−	0.300880i
$477$	8.06956	+	34.7785i	0.369480	+	1.59240i
$478$	19.5723	+	18.6621i	0.895215	+	0.853586i
$479$	3.81465	+	5.35693i	0.174296	+	0.244764i	0.892478	−	0.451091i	$-0.148965\pi$
$479$	3.81465	+	5.35693i	0.174296	+	0.244764i	−0.718182	+	0.695855i	$0.755026\pi$
$480$	−4.64336	+	4.82128i	−0.211939	+	0.220060i
$481$	2.00238	−	3.88407i	0.0913006	−	0.177098i
$482$	−14.3499			−0.653618
$483$	15.6258	+	15.4543i	0.710996	+	0.703196i
$484$	−27.2902			−1.24046
$485$	−0.571730	+	1.10900i	−0.0259609	+	0.0503571i
$486$	−14.3373	+	6.11896i	−0.650353	+	0.277561i
$487$	−2.97074	−	4.17182i	−0.134617	−	0.189043i	0.741765	−	0.670660i	$-0.233989\pi$
$487$	−2.97074	−	4.17182i	−0.134617	−	0.189043i	−0.876382	+	0.481617i	$0.840050\pi$
$488$	0.354949	+	0.338443i	0.0160678	+	0.0153206i
$489$	−8.61248	−	25.2929i	−0.389470	−	1.14378i
$490$	−22.5758	+	14.9049i	−1.01987	+	0.673334i
$491$	24.3447	−	3.50023i	1.09866	−	0.157963i	0.430943	−	0.902379i	$-0.358181\pi$
$491$	24.3447	−	3.50023i	1.09866	−	0.157963i	0.667716	+	0.744416i	$0.267272\pi$
$492$	10.6170	−	1.47231i	0.478651	−	0.0663770i
$493$	−14.2818	+	4.94298i	−0.643220	+	0.222621i
$494$	−2.48466	+	1.28093i	−0.111790	+	0.0576317i
$495$	−17.6105	+	69.5465i	−0.791533	+	3.12588i
$496$	1.36110	−	1.57080i	0.0611153	−	0.0705309i
$497$	9.75373	+	11.6660i	0.437515	+	0.523290i
$498$	−0.368904	+	0.0157235i	−0.0165310	+	0.000704588i
$499$	−2.08617	+	6.02760i	−0.0933899	+	0.269832i	−0.982015	−	0.188801i	$-0.939540\pi$
$499$	−2.08617	+	6.02760i	−0.0933899	+	0.269832i	0.888625	+	0.458634i	$0.151661\pi$
$500$	18.9862	+	1.81296i	0.849088	+	0.0810781i
$501$	−10.5237	−	3.70135i	−0.470164	−	0.165364i
$502$	−0.669090	−	7.00702i	−0.0298629	−	0.312739i
$503$	−3.87742	+	26.9681i	−0.172886	+	1.20245i	0.699863	+	0.714277i	$0.253244\pi$
$503$	−3.87742	+	26.9681i	−0.172886	+	1.20245i	−0.872749	+	0.488169i	$0.837665\pi$
$504$	2.38770	+	7.56960i	0.106357	+	0.337177i
$505$		−	10.6186i		−	0.472523i
$506$	4.09531	−	29.3922i	0.182059	−	1.30664i
$507$	11.9318	−	16.5797i	0.529909	−	0.736328i
$508$	0.650716	+	13.6602i	0.0288708	+	0.606074i
$509$	3.07654	+	7.68484i	0.136365	+	0.340624i	0.980795	−	0.195043i	$-0.0624845\pi$
$509$	3.07654	+	7.68484i	0.136365	+	0.340624i	−0.844429	+	0.535667i	$0.820060\pi$
$510$	17.9976	+	10.5113i	0.796947	+	0.465450i
$511$	11.2407	+	12.2131i	0.497257	+	0.540275i
$512$	0.909632	−	0.415415i	0.0402004	−	0.0183589i
$513$	−10.6551	−	7.83115i	−0.470436	−	0.345754i
$514$	5.83764	+	2.33704i	0.257487	+	0.103082i
$515$	−51.4179	−	53.9255i	−2.26574	−	2.37624i
$516$	−2.08400	+	6.96828i	−0.0917429	+	0.306761i
$517$	25.4249	−	39.5619i	1.11819	−	1.73993i
$518$	1.18513	−	10.4583i	0.0520716	−	0.459512i
$519$	11.3968	+	12.0730i	0.500266	+	0.529947i
$520$	−4.12544	+	1.00082i	−0.180913	+	0.0438889i
$521$	−32.6032	−	13.0524i	−1.42837	−	0.571834i	−0.476733	−	0.879048i	$-0.658179\pi$
$521$	−32.6032	−	13.0524i	−1.42837	−	0.571834i	−0.951640	+	0.307214i	$0.900603\pi$
$522$	14.5603	+	0.145707i	0.637287	+	0.00637740i
$523$	−22.3590	−	15.9218i	−0.977689	−	0.696210i	−0.0248522	−	0.999691i	$-0.507912\pi$
$523$	−22.3590	−	15.9218i	−0.977689	−	0.696210i	−0.952837	+	0.303482i	$0.901851\pi$
$524$	−3.48631	−	11.8733i	−0.152300	−	0.518686i
$525$	25.4755	−	37.7341i	1.11184	−	1.64685i
$526$	−22.2821	−	3.20368i	−0.971544	−	0.139687i
$527$	−5.75232	−	2.96553i	−0.250575	−	0.129180i
$528$	6.26052	−	8.69923i	0.272454	−	0.378585i
$529$	22.1240	+	6.28726i	0.961912	+	0.273359i
$530$	−39.8302	+	22.9960i	−1.73011	+	0.998882i
$531$	−8.93420	−	22.9804i	−0.387711	−	0.997264i
$532$	−4.49826	+	5.00993i	−0.195024	+	0.217208i
$533$	6.18338	+	2.82386i	0.267832	+	0.122315i
$534$	−11.5109	+	9.87386i	−0.498126	+	0.427284i
$535$	41.2605	+	3.93990i	1.78385	+	0.170337i
$536$	0.903482	−	0.174132i	0.0390245	−	0.00752135i
$537$	−16.8974	−	26.5843i	−0.729175	−	1.14720i
$538$	8.59042	+	2.52238i	0.370359	+	0.108747i
$539$	32.3835	−	28.7668i	1.39486	−	1.23907i
$540$	−12.9210	−	15.3719i	−0.556033	−	0.661503i
$541$	1.27445	−	26.7540i	0.0547929	−	1.15024i	−0.789286	−	0.614026i	$-0.789549\pi$
$541$	1.27445	−	26.7540i	0.0547929	−	1.15024i	0.844079	−	0.536219i	$-0.180148\pi$
$542$	27.2804	−	9.44185i	1.17179	−	0.405562i
$543$	0.836403	+	1.07459i	0.0358935	+	0.0461153i
$544$	−1.92478	−	2.44755i	−0.0825241	−	0.104938i
$545$	−8.25237	+	7.15072i	−0.353493	+	0.306303i
$546$	−1.29720	+	4.86375i	−0.0555151	+	0.208149i
$547$	42.9734	−	12.6181i	1.83741	−	0.539512i	0.837434	−	0.546539i	$-0.184055\pi$
$547$	42.9734	−	12.6181i	1.83741	−	0.539512i	0.999975	+	0.00702649i	$0.00223662\pi$
$548$	6.23105	−	0.594993i	0.266177	−	0.0254168i
$549$	−1.12154	+	0.952337i	−0.0478661	+	0.0406448i
$550$	−61.4084	+	2.92524i	−2.61846	+	0.124733i
$551$	6.17594	+	10.6970i	0.263104	+	0.455709i
$552$	6.00809	+	5.73611i	0.255721	+	0.244145i
$553$	−2.89006	+	44.2372i	−0.122898	+	1.88116i
$554$	16.3404	+	25.4261i	0.694236	+	1.08025i
$555$	7.37422	+	25.5872i	0.313018	+	1.08612i
$556$	8.39921	+	11.7950i	0.356206	+	0.500221i
$557$	2.34729	−	9.67568i	0.0994581	−	0.409972i	−0.900218	−	0.435440i	$-0.856593\pi$
$557$	2.34729	−	9.67568i	0.0994581	−	0.409972i	0.999676	+	0.0254687i	$0.00810780\pi$
$558$	4.25754	+	4.55559i	0.180236	+	0.192854i
$559$	−3.48600	+	3.02064i	−0.147442	+	0.127759i
$560$	−8.43218	+	5.78314i	−0.356325	+	0.244382i
$561$	−30.9192	−	12.5580i	−1.30541	−	0.530201i
$562$	0.530874	−	2.75443i	0.0223936	−	0.116189i
$563$	22.4012	−	11.5486i	0.944099	−	0.486717i	0.0837862	−	0.996484i	$-0.473299\pi$
$563$	22.4012	−	11.5486i	0.944099	−	0.486717i	0.860312	+	0.509767i	$0.170268\pi$
$564$	4.83112	+	12.2448i	0.203427	+	0.515598i
$565$	53.4713	+	10.3058i	2.24956	+	0.433566i
$566$	11.6636	+	3.42473i	0.490256	+	0.143952i
$567$	−23.3355	+	4.73878i	−0.979997	+	0.199010i
$568$	3.76376	+	4.34361i	0.157924	+	0.182254i
$569$	20.0059	−	28.0944i	0.838693	−	1.17778i	−0.143453	−	0.989657i	$-0.545821\pi$
$569$	20.0059	−	28.0944i	0.838693	−	1.17778i	0.982146	−	0.188122i	$-0.0602400\pi$
$570$	5.65189	−	16.0695i	0.236732	−	0.673077i
$571$	−22.6992	+	16.1640i	−0.949933	+	0.676444i	−0.946211	−	0.323549i	$-0.895124\pi$
$571$	−22.6992	+	16.1640i	−0.949933	+	0.676444i	−0.00372161	+	0.999993i	$0.501185\pi$
$572$	6.31026	−	2.52625i	0.263845	−	0.105628i
$573$	18.8923	−	9.62032i	0.789238	−	0.401895i
$574$	16.3381	+	1.06738i	0.681939	+	0.0445517i
$575$	4.32244	−	47.4510i	0.180258	−	1.97884i
$576$	0.952786	+	2.84468i	0.0396994	+	0.118528i
$577$	−0.529425	−	11.1140i	−0.0220403	−	0.462682i	−0.982729	−	0.185053i	$-0.940754\pi$
$577$	−0.529425	−	11.1140i	−0.0220403	−	0.462682i	0.960688	−	0.277629i	$-0.0895486\pi$
$578$	4.51549	−	5.74191i	0.187819	−	0.238832i
$579$	8.40560	+	0.0420568i	0.349325	+	0.00174782i
$580$	5.28461	+	17.9977i	0.219432	+	0.747316i
$581$	−0.556778	−	0.0901027i	−0.0230990	−	0.00373809i
$582$	0.322084	+	0.457127i	0.0133508	+	0.0189485i
$583$	57.8859	−	45.5219i	2.39739	−	1.88533i
$584$	4.32932	+	4.54046i	0.179149	+	0.187886i
$585$	−1.68619	−	12.6232i	−0.0697155	−	0.521905i
$586$	0.330250	+	0.0157318i	0.0136425	+	0.000649873i
$587$	6.97400	−	10.8517i	0.287848	−	0.447900i	−0.666973	−	0.745082i	$-0.732410\pi$
$587$	6.97400	−	10.8517i	0.287848	−	0.447900i	0.954821	+	0.297182i	$0.0960468\pi$
$588$	1.24081	+	12.0607i	0.0511701	+	0.497375i
$589$	−1.49019	+	5.07511i	−0.0614021	+	0.209116i
$590$	24.9665	−	19.6339i	1.02786	−	0.808315i
$591$	3.80392	+	42.0593i	0.156472	+	1.73009i
$592$	0.378149	−	3.96015i	0.0155418	−	0.162761i
$593$	14.0696	−	14.7558i	0.577771	−	0.605949i	−0.368380	−	0.929675i	$-0.620087\pi$
$593$	14.0696	−	14.7558i	0.577771	−	0.605949i	0.946151	+	0.323727i	$0.104936\pi$
$594$	23.9811	+	21.4183i	0.983956	+	0.878804i
$595$	23.6895	+	21.2700i	0.971173	+	0.871986i
$596$	−6.24170	+	4.01130i	−0.255670	+	0.164309i
$597$	−14.0517	+	6.33241i	−0.575097	+	0.259168i
$598$	1.26428	+	5.11406i	0.0517002	+	0.209129i
$599$	−33.6100	−	19.4047i	−1.37327	−	0.792856i	−0.381930	−	0.924191i	$-0.624740\pi$
$599$	−33.6100	−	19.4047i	−1.37327	−	0.792856i	−0.991338	+	0.131335i	$0.958074\pi$
$600$	9.37579	−	14.4298i	0.382765	−	0.589093i
$601$	2.69789	−	18.7642i	0.110049	−	0.765408i	−0.857819	−	0.513951i	$-0.828181\pi$
$601$	2.69789	−	18.7642i	0.110049	−	0.765408i	0.967869	−	0.251457i	$-0.0809097\pi$
$602$	−5.26430	+	9.78368i	−0.214557	+	0.398753i
$603$	0.234876	+	2.75032i	0.00956491	+	0.112002i
$604$	−5.12031	+	7.19047i	−0.208342	+	0.292576i
$605$	103.560	−	19.9596i	4.21032	−	0.811472i
$606$	−4.21909	−	2.20188i	−0.171389	−	0.0894453i
$607$	0.523373	+	2.15737i	0.0212430	+	0.0875650i	0.981446	−	0.191737i	$-0.0614121\pi$
$607$	0.523373	+	2.15737i	0.0212430	+	0.0875650i	−0.960203	+	0.279302i	$0.909897\pi$
$608$	−1.66652	+	1.92327i	−0.0675864	+	0.0779988i
$609$	21.7395	+	4.70277i	0.880929	+	0.190566i
$610$	−1.59448	−	1.02471i	−0.0645587	−	0.0414893i
$611$	−1.57989	+	8.19727i	−0.0639157	+	0.331626i
$612$	7.90843	−	4.97133i	0.319679	−	0.200954i
$613$	5.19676	−	12.9809i	0.209895	−	0.524293i	−0.785640	−	0.618684i	$-0.787666\pi$
$613$	5.19676	−	12.9809i	0.209895	−	0.524293i	0.995535	+	0.0943909i	$0.0300903\pi$
$614$	16.9591	+	5.86962i	0.684415	+	0.236878i
$615$	−39.2122	+	13.3522i	−1.58119	+	0.538411i
$616$	12.0462	−	11.0870i	0.485353	−	0.446708i
$617$	−5.02147	+	10.9955i	−0.202157	+	0.442662i	−0.983373	−	0.181599i	$-0.941873\pi$
$617$	−5.02147	+	10.9955i	−0.202157	+	0.442662i	0.781216	+	0.624261i	$0.214600\pi$
$618$	−32.0882	+	9.24779i	−1.29077	+	0.372001i
$619$	−30.6142	+	1.45834i	−1.23049	+	0.0586155i	−0.652730	−	0.757591i	$-0.726376\pi$
$619$	−30.6142	+	1.45834i	−1.23049	+	0.0586155i	−0.577760	+	0.816206i	$0.696073\pi$
$620$	−4.01622	+	6.95630i	−0.161295	+	0.279372i
$621$	−19.0059	+	16.1175i	−0.762682	+	0.646773i
$622$	25.4809			1.02169
$623$	−20.2633	+	11.2272i	−0.811833	+	0.449810i
$624$	−0.457796	+	1.84668i	−0.0183265	+	0.0739266i
$625$	−23.9232	+	2.28438i	−0.956926	+	0.0913754i
$626$	−6.41205	+	26.4308i	−0.256277	+	1.05639i
$627$	−5.29578	+	26.7560i	−0.211493	+	1.06853i
$628$	15.4164	+	5.33568i	0.615183	+	0.212917i
$629$	−12.2608	+	1.76284i	−0.488871	+	0.0702891i
$630$	−14.5970	−	26.9786i	−0.581560	−	1.07485i
$631$	−29.2353	−	25.3326i	−1.16384	−	1.00847i	−0.999757	−	0.0220264i	$-0.992988\pi$
$631$	−29.2353	−	25.3326i	−1.16384	−	1.00847i	−0.164083	−	0.986447i	$-0.552466\pi$
$632$	−0.797270	+	16.7368i	−0.0317137	+	0.665752i
$633$	32.2466	−	12.7228i	1.28169	−	0.505685i
$634$	−4.22854	−	12.2176i	−0.167937	−	0.485222i
$635$	−12.4601	−	51.3614i	−0.494466	−	2.03821i
$636$	0.877768	+	20.5941i	0.0348058	+	0.816610i
$637$	−3.43891	+	6.87733i	−0.136254	+	0.272490i
$638$	−12.4766	−	27.3200i	−0.493954	−	1.08161i
$639$	−14.1445	+	9.86045i	−0.559548	+	0.390073i
$640$	−3.14802	+	2.24169i	−0.124436	+	0.0886106i
$641$	−2.83085	−	2.22620i	−0.111812	−	0.0879297i	0.560688	−	0.828027i	$-0.310537\pi$
$641$	−2.83085	−	2.22620i	−0.111812	−	0.0879297i	−0.672499	+	0.740098i	$0.734779\pi$
$642$	10.1212	−	15.5770i	0.399452	−	0.614775i
$643$			35.8548i			1.41397i	0.707226	+	0.706987i	$0.249946\pi$
$643$			35.8548i			1.41397i	−0.707226	+	0.706987i	$0.750054\pi$
$644$	7.22219	+	10.4326i	0.284594	+	0.411104i
$645$	2.81182	−	27.9672i	0.110715	−	1.10121i
$646$	7.04309	+	3.63096i	0.277107	+	0.142858i
$647$	−12.3294	+	15.6781i	−0.484719	+	0.616371i	−0.965479	−	0.260482i	$-0.916119\pi$
$647$	−12.3294	+	15.6781i	−0.484719	+	0.616371i	0.480759	+	0.876853i	$0.340361\pi$
$648$	−8.78702	+	1.94637i	−0.345187	+	0.0764607i
$649$	−35.0949	+	36.8065i	−1.37760	+	1.44478i
$650$	9.92715	−	4.53358i	0.389375	−	0.177822i
$651$	4.96672	+	8.12722i	0.194661	+	0.318531i
$652$	−2.19538	−	15.2692i	−0.0859776	−	0.597988i
$653$	−29.5366	+	7.16551i	−1.15586	+	0.280408i	−0.767468	−	0.641087i	$-0.778484\pi$
$653$	−29.5366	+	7.16551i	−1.15586	+	0.280408i	−0.388390	+	0.921495i	$0.626969\pi$
$654$	1.12997	+	4.76167i	0.0441854	+	0.186196i
$655$	21.9136	+	42.5065i	0.856236	+	1.66087i
$656$	6.18138	+	0.294455i	0.241342	+	0.0114965i
$657$	−14.9100	+	11.4857i	−0.581694	+	0.448101i
$658$	3.45652	+	19.8081i	0.134749	+	0.772198i
$659$	5.55968	+	38.6684i	0.216574	+	1.50631i	0.750554	+	0.660809i	$0.229787\pi$
$659$	5.55968	+	38.6684i	0.216574	+	1.50631i	−0.533980	+	0.845497i	$0.679304\pi$
$660$	−17.3948	+	37.5904i	−0.677091	+	1.46320i
$661$	2.20332	−	23.0742i	0.0856991	−	0.897482i	−0.845743	−	0.533591i	$-0.820842\pi$
$661$	2.20332	−	23.0742i	0.0856991	−	0.897482i	0.931442	−	0.363891i	$-0.118552\pi$
$662$	−13.9901	−	3.39396i	−0.543741	−	0.131910i
$663$	5.92404	+	0.0296405i	0.230071	+	0.00115114i
$664$	−0.211010	−	0.0303387i	−0.00818878	−	0.00117737i
$665$	13.4057	−	22.3015i	0.519850	−	0.864814i
$666$	11.6956	+	2.37577i	0.453197	+	0.0920593i
$667$	22.3057	−	6.65528i	0.863681	−	0.257693i
$668$	−5.57782	−	3.22035i	−0.215812	−	0.124599i
$669$	−1.31003	+	24.8810i	−0.0506487	+	0.961955i
$670$	−3.30115	+	1.32158i	−0.127534	+	0.0510571i
$671$	2.76056	+	1.26070i	0.106570	+	0.0486690i
$672$	0.549309	+	4.54953i	0.0211900	+	0.175502i
$673$	1.63632	+	3.58303i	0.0630753	+	0.138116i	0.938544	−	0.345158i	$-0.112175\pi$
$673$	1.63632	+	3.58303i	0.0630753	+	0.138116i	−0.875469	+	0.483274i	$0.839447\pi$
$674$	2.97956	−	8.60888i	0.114768	−	0.331602i
$675$	40.0962	+	32.5178i	1.54330	+	1.25161i
$676$	8.53528	−	8.13837i	0.328280	−	0.313014i
$677$	26.9185	+	5.18811i	1.03456	+	0.199395i	0.678142	−	0.734931i	$-0.262786\pi$
$677$	26.9185	+	5.18811i	1.03456	+	0.199395i	0.356419	+	0.934326i	$0.383998\pi$
$678$	15.1826	−	19.1087i	0.583084	−	0.733864i
$679$	0.341084	+	0.783136i	0.0130896	+	0.0300540i
$680$	9.09417	+	7.88014i	0.348746	+	0.302190i
$681$	−0.535296	−	3.86007i	−0.0205126	−	0.147918i
$682$	4.78008	−	11.9401i	0.183039	−	0.457208i
$683$	4.68501	+	24.3082i	0.179267	+	0.930126i	0.954446	+	0.298384i	$0.0964476\pi$
$683$	4.68501	+	24.3082i	0.179267	+	0.930126i	−0.775179	+	0.631742i	$0.782340\pi$
$684$	−5.21289	−	5.57782i	−0.199320	−	0.213273i
$685$	−23.2102	+	6.81514i	−0.886817	+	0.260393i
$686$	−1.85843	+	18.4268i	−0.0709551	+	0.703538i
$687$	45.4762	+	11.2736i	1.73503	+	0.430116i
$688$	−1.92419	+	3.73240i	−0.0733589	+	0.142296i
$689$	−6.53627	+	11.3211i	−0.249012	+	0.431301i
$690$	−26.9946	−	17.3730i	−1.02767	−	0.661378i
$691$	5.19983	+	9.00637i	0.197811	+	0.342618i	0.947818	−	0.318811i	$-0.103283\pi$
$691$	5.19983	+	9.00637i	0.197811	+	0.342618i	−0.750008	+	0.661429i	$0.769950\pi$
$692$	5.18232	+	8.06384i	0.197002	+	0.306541i
$693$	29.2821	+	39.4315i	1.11234	+	1.49788i
$694$	2.14770	−	4.70281i	0.0815257	−	0.178516i
$695$	−40.4997	−	38.6164i	−1.53624	−	1.46480i
$696$	8.24683	+	1.63228i	0.312595	+	0.0618715i
$697$	−3.64667	−	18.9207i	−0.138127	−	0.716673i
$698$	−16.6874	−	21.2198i	−0.631629	−	0.803182i
$699$	7.01924	−	17.2821i	0.265492	−	0.653669i
$700$	18.4722	−	18.7012i	0.698182	−	0.706839i
$701$	−20.8141	−	13.3764i	−0.786137	−	0.505220i	0.0849281	−	0.996387i	$-0.472934\pi$
$701$	−20.8141	−	13.3764i	−0.786137	−	0.505220i	−0.871065	+	0.491167i	$0.836570\pi$
$702$	−5.36520	−	1.94757i	−0.202496	−	0.0735063i
$703$	3.31118	+	9.56703i	0.124884	+	0.360827i
$704$	4.47840	−	4.27015i	0.168786	−	0.160937i
$705$	−27.2886	−	42.9327i	−1.02775	−	1.61694i
$706$	10.8115	+	12.4771i	0.406896	+	0.469583i
$707$	−5.63417	−	4.59388i	−0.211895	−	0.172771i
$708$	−2.62405	−	13.9912i	−0.0986178	−	0.525822i
$709$	−0.606189	−	6.34829i	−0.0227659	−	0.238415i	−0.999692	−	0.0248356i	$-0.992094\pi$
$709$	−0.606189	−	6.34829i	−0.0227659	−	0.238415i	0.976926	−	0.213580i	$-0.0685123\pi$
$710$	−17.4594	−	13.7303i	−0.655241	−	0.515287i
$711$	−49.6815	−	7.65129i	−1.86320	−	0.286946i
$712$	−7.58278	+	4.37792i	−0.284177	+	0.164070i
$713$	8.65414	+	4.94631i	0.324100	+	0.185241i
$714$	13.3634	−	5.00194i	0.500114	−	0.187193i
$715$	−22.0983	+	14.2017i	−0.826430	+	0.531114i
$716$	−6.75925	−	16.8838i	−0.252605	−	0.630977i
$717$	−40.6819	+	23.2171i	−1.51929	+	0.867057i
$718$	−1.04570	−	0.253684i	−0.0390252	−	0.00946742i
$719$	7.04361	+	5.01574i	0.262682	+	0.187055i	0.703808	−	0.710390i	$-0.251481\pi$
$719$	7.04361	+	5.01574i	0.262682	+	0.187055i	−0.441126	+	0.897445i	$0.645421\pi$
$720$	−5.69615	−	10.0980i	−0.212283	−	0.376332i
$721$	−50.8571	+	3.95248i	−1.89402	+	0.147198i
$722$	−3.52835	+	12.0164i	−0.131311	+	0.447206i
$723$	7.12160	−	23.8125i	0.264855	−	0.885598i
$724$	0.360257	+	0.698801i	0.0133888	+	0.0259707i
$725$	−22.0967	−	42.8616i	−0.820650	−	1.59184i
$726$	13.5437	−	45.2862i	0.502654	−	1.68073i
$727$	14.1139	−	48.0675i	0.523456	−	1.78273i	−0.0933758	−	0.995631i	$-0.529766\pi$
$727$	14.1139	−	48.0675i	0.523456	−	1.78273i	0.616831	−	0.787095i	$-0.288416\pi$
$728$	−1.25374	+	2.62191i	−0.0464665	+	0.0971744i
$729$	−3.03859	−	26.8285i	−0.112540	−	0.993647i
$730$	−19.7496	−	14.0636i	−0.730965	−	0.520518i
$731$	12.7066	+	3.08258i	0.469970	+	0.114013i
$732$	−0.737778	+	0.421049i	−0.0272691	+	0.0155624i
$733$	−1.90644	−	4.76205i	−0.0704158	−	0.175890i	0.888985	−	0.457936i	$-0.151411\pi$
$733$	−1.90644	−	4.76205i	−0.0704158	−	0.175890i	−0.959401	+	0.282046i	$0.908987\pi$
$734$	16.9869	−	10.9168i	0.626999	−	0.402948i
$735$	−13.5296	−	44.8600i	−0.499045	−	1.65469i
$736$	2.79885	+	3.89441i	0.103167	+	0.143550i
$737$	4.93076	−	2.84678i	0.181627	−	0.104862i
$738$	−2.82585	+	18.3488i	−0.104021	+	0.675430i
$739$	15.8570	+	12.4701i	0.583308	+	0.458719i	0.865688	−	0.500584i	$-0.166881\pi$
$739$	15.8570	+	12.4701i	0.583308	+	0.458719i	−0.282380	+	0.959303i	$0.591124\pi$
$740$	1.46140	+	15.3044i	0.0537220	+	0.562602i
$741$	−0.892515	−	4.75881i	−0.0327874	−	0.174819i
$742$	−5.03000	+	31.0822i	−0.184657	+	1.14106i
$743$	−23.6083	−	27.2454i	−0.866104	−	0.999537i	−0.999964	−	0.00853698i	$-0.997283\pi$
$743$	−23.6083	−	27.2454i	−0.866104	−	0.999537i	0.133860	−	0.991000i	$-0.457263\pi$
$744$	1.93113	+	3.03821i	0.0707987	+	0.111386i
$745$	20.7520	−	19.7870i	0.760296	−	0.724940i
$746$	0.944863	+	2.73000i	0.0345939	+	0.0999525i
$747$	0.156989	−	0.619973i	0.00574393	−	0.0226836i
$748$	−16.2088	−	10.4168i	−0.592652	−	0.380874i
$749$	19.9408	−	20.1880i	0.728620	−	0.737654i
$750$	−12.4310	+	30.6065i	−0.453917	+	1.11759i
$751$	−12.5993	−	16.0213i	−0.459754	−	0.584625i	0.499803	−	0.866139i	$-0.333406\pi$
$751$	−12.5993	−	16.0213i	−0.459754	−	0.584625i	−0.959557	+	0.281514i	$0.909163\pi$
$752$	1.43829	+	7.46253i	0.0524489	+	0.272131i
$753$	11.9597	+	2.36717i	0.435836	+	0.0862644i
$754$	3.85863	+	3.67919i	0.140523	+	0.133988i
$755$	14.1714	−	31.0311i	0.515750	−	1.12934i
$756$	−13.7462	+	0.205540i	−0.499944	+	0.00747542i
$757$	0.639827	+	0.995590i	0.0232549	+	0.0361853i	0.852686	−	0.522423i	$-0.174972\pi$
$757$	0.639827	+	0.995590i	0.0232549	+	0.0361853i	−0.829432	+	0.558608i	$0.811335\pi$
$758$	−1.19361	−	2.06739i	−0.0433537	−	0.0750909i
$759$	46.7419	+	21.3828i	1.69662	+	0.776145i
$760$	4.91742	−	8.51722i	0.178374	−	0.308952i
$761$	−4.01452	+	7.78708i	−0.145526	+	0.282281i	−0.950321	−	0.311272i	$-0.899245\pi$
$761$	−4.01452	+	7.78708i	−0.145526	+	0.282281i	0.804795	+	0.593553i	$0.202275\pi$
$762$	−22.9911	−	5.69953i	−0.832879	−	0.206472i
$763$	0.223946	+	7.47222i	0.00810740	+	0.270512i
$764$	11.7444	−	3.44847i	0.424898	−	0.124761i
$765$	−26.3747	+	24.6491i	−0.953580	+	0.891191i
$766$	6.38522	+	33.1297i	0.230707	+	1.19702i
$767$	3.35531	−	8.38117i	0.121153	−	0.302626i
$768$	0.237916	+	1.71563i	0.00858504	+	0.0619076i
$769$	−14.8141	−	12.8365i	−0.534211	−	0.462896i	0.345491	−	0.938422i	$-0.387712\pi$
$769$	−14.8141	−	12.8365i	−0.534211	−	0.462896i	−0.879702	+	0.475526i	$0.842258\pi$
$770$	−37.6035	+	50.8830i	−1.35514	+	1.83369i
$771$	−6.77527	+	8.52731i	−0.244005	+	0.307103i
$772$	4.76533	+	0.918443i	0.171508	+	0.0330555i
$773$	7.13502	−	6.80323i	0.256629	−	0.244695i	−0.550832	−	0.834616i	$-0.685690\pi$
$773$	7.13502	−	6.80323i	0.256629	−	0.244695i	0.807461	+	0.589921i	$0.200841\pi$
$774$	−10.5291	−	6.91649i	−0.378461	−	0.248608i
$775$	6.75392	−	19.5142i	0.242608	−	0.700970i
$776$	0.134118	+	0.293678i	0.00481456	+	0.0105424i
$777$	16.7666	+	7.15693i	0.601500	+	0.256753i
$778$	−23.7236	−	10.8342i	−0.850531	−	0.388425i
$779$	−14.6204	+	5.85313i	−0.523830	+	0.209710i
$780$	0.386600	−	7.34256i	0.0138425	−	0.262906i
$781$	30.7998	+	17.7823i	1.10210	+	0.636299i
$782$	9.72969	−	11.3280i	0.347933	−	0.405090i
$783$	−7.46784	+	24.0895i	−0.266879	+	0.860887i
$784$	−0.579472	+	6.97597i	−0.0206954	+	0.249142i
$785$	−62.4042	−	8.97237i	−2.22730	−	0.320238i
$786$	21.4330	+	0.107239i	0.764491	+	0.00382508i
$787$	−34.3158	−	8.32491i	−1.22322	−	0.296751i	−0.428400	−	0.903589i	$-0.640922\pi$
$787$	−34.3158	−	8.32491i	−1.22322	−	0.296751i	−0.794825	+	0.606838i	$0.792438\pi$
$788$	−2.31766	+	24.2717i	−0.0825633	+	0.864642i
$789$	16.3745	−	35.3855i	0.582948	−	1.25976i
$790$	−9.21550	−	64.0952i	−0.327873	−	2.28041i
$791$	28.6011	−	23.9130i	1.01694	−	0.850248i
$792$	11.3287	+	14.7062i	0.402549	+	0.522561i
$793$	−0.538119	−	0.0256337i	−0.0191092	−	0.000910281i
$794$	−12.1219	−	23.5131i	−0.430189	−	0.834450i
$795$	−18.3931	−	77.5079i	−0.652336	−	2.74892i
$796$	−8.64766	+	2.09790i	−0.306508	+	0.0743580i
$797$	7.31547	+	50.8802i	0.259127	+	1.80227i	0.539078	+	0.842256i	$0.318773\pi$
$797$	7.31547	+	50.8802i	0.259127	+	1.80227i	−0.279951	+	0.960014i	$0.590318\pi$
$798$	−6.08120	−	9.95089i	−0.215272	−	0.352258i
$799$	21.5254	−	9.83034i	0.761515	−	0.347772i
$800$	6.85606	−	7.19043i	0.242398	−	0.254220i
$801$	−10.6723	−	24.0018i	−0.377087	−	0.848061i
$802$	0.494411	−	0.628694i	0.0174582	−	0.0222000i
$803$	34.5054	+	17.7887i	1.21767	+	0.627751i
$804$	−0.159424	+	1.58568i	−0.00562246	+	0.0559227i
$805$	−35.0368	−	34.3073i	−1.23488	−	1.20917i
$806$			2.28310i			0.0804188i
$807$	−8.44899	+	13.0034i	−0.297419	+	0.457740i
$808$	−2.15981	−	1.69849i	−0.0759818	−	0.0597528i
$809$	4.89500	−	3.48571i	0.172099	−	0.122551i	−0.490762	−	0.871294i	$-0.663282\pi$
$809$	4.89500	−	3.48571i	0.172099	−	0.122551i	0.662861	+	0.748743i	$0.269342\pi$
$810$	31.9211	−	13.8127i	1.12159	−	0.485329i
$811$	6.33591	+	13.8737i	0.222484	+	0.487172i	0.987653	−	0.156657i	$-0.0500719\pi$
$811$	6.33591	+	13.8737i	0.222484	+	0.487172i	−0.765169	+	0.643830i	$0.777345\pi$
$812$	11.8357	+	4.98228i	0.415352	+	0.174844i
$813$	2.12923	+	49.9558i	0.0746753	+	1.75203i
$814$	−5.80357	−	23.9226i	−0.203415	−	0.838488i
$815$	19.4986	+	56.3374i	0.683005	+	1.97341i
$816$	5.01677	−	1.97935i	0.175622	−	0.0692910i
$817$	0.508476	−	10.6742i	0.0177893	−	0.373444i
$818$	0.502902	+	0.435767i	0.0175836	+	0.0152362i
$819$	−7.42726	−	4.56641i	−0.259529	−	0.159563i
$820$	−23.6722	+	3.40356i	−0.826671	+	0.118857i
$821$	29.7786	+	10.3065i	1.03928	+	0.359699i	0.792821	−	0.609455i	$-0.208612\pi$
$821$	29.7786	+	10.3065i	1.03928	+	0.359699i	0.246460	+	0.969153i	$0.420733\pi$
$822$	−2.10502	+	10.6353i	−0.0734211	+	0.370947i
$823$	11.8903	−	49.0127i	0.414471	−	1.70847i	−0.256119	−	0.966645i	$-0.582444\pi$
$823$	11.8903	−	49.0127i	0.414471	−	1.70847i	0.670590	−	0.741828i	$-0.266041\pi$
$824$	−19.1928	+	1.83269i	−0.668614	+	0.0638449i
$825$	25.6218	−	103.355i	0.892036	−	3.59834i
$826$	0.383518	−	21.7412i	0.0133443	−	0.756472i
$827$	35.1757			1.22318			0.611590	−	0.791175i	$-0.290530\pi$
$827$	35.1757			1.22318			0.611590	+	0.791175i	$0.290530\pi$
$828$	−12.5004	+	7.12325i	−0.434418	+	0.247550i
$829$	−20.5411	+	35.5783i	−0.713423	+	1.23568i	0.250142	+	0.968209i	$0.419523\pi$
$829$	−20.5411	+	35.5783i	−0.713423	+	1.23568i	−0.963565	+	0.267475i	$0.913811\pi$
$830$	0.822924	−	0.0392007i	0.0285641	−	0.00136068i
$831$	−50.3023	+	14.4971i	−1.74497	+	0.502899i
$832$	−0.456315	+	0.999191i	−0.0158199	+	0.0346407i
$833$	21.5343	−	3.36752i	0.746121	−	0.116678i
$834$	−23.7414	+	8.08419i	−0.822098	+	0.279933i
$835$	23.5218	+	8.14099i	0.814007	+	0.281730i
$836$	−5.85268	+	14.6193i	−0.202419	+	0.505618i
$837$	−9.67263	+	4.80421i	−0.334335	+	0.166058i
$838$	3.66032	−	18.9916i	0.126444	−	0.656052i
$839$	−39.0985	−	25.1271i	−1.34983	−	0.867483i	−0.352175	−	0.935934i	$-0.614558\pi$
$839$	−39.0985	−	25.1271i	−1.34983	−	0.867483i	−0.997654	+	0.0684514i	$0.978194\pi$
$840$	−5.41195	−	16.8627i	−0.186730	−	0.581817i
$841$	−3.56363	+	4.11265i	−0.122884	+	0.141815i
$842$	−0.927076	−	3.82146i	−0.0319492	−	0.131696i
$843$	4.30732	+	2.24793i	0.148352	+	0.0774228i
$844$	19.6526	−	3.78773i	0.676470	−	0.130379i
$845$	−26.4372	+	37.1258i	−0.909466	+	1.27717i
$846$	−22.7169	+	1.94002i	−0.781024	+	0.0666992i
$847$	34.2122	−	63.5832i	1.17554	−	2.18474i
$848$	−1.69366	+	11.7797i	−0.0581606	+	0.404516i
$849$	−11.4715	+	17.6552i	−0.393702	+	0.605925i
$850$	−26.7908	−	15.4677i	−0.918919	−	0.530538i
$851$	18.9841	−	1.89629i	0.650768	−	0.0650039i
$852$	−9.07580	+	4.09003i	−0.310932	+	0.140122i
$853$	−40.3962	+	25.9611i	−1.38314	+	0.888891i	−0.999403	−	0.0345512i	$-0.989000\pi$
$853$	−40.3962	+	25.9611i	−1.38314	+	0.888891i	−0.383738	+	0.923442i	$0.625363\pi$
$854$	−1.23351	+	0.402705i	−0.0422100	+	0.0137803i
$855$	23.8612	+	17.3539i	0.816036	+	0.593492i
$856$	7.40115	−	7.76210i	0.252966	−	0.265303i
$857$	−3.01273	+	31.5507i	−0.102913	+	1.07775i	0.785548	+	0.618800i	$0.212381\pi$
$857$	−3.01273	+	31.5507i	−0.102913	+	1.07775i	−0.888461	+	0.458952i	$0.848225\pi$
$858$	1.06044	+	11.7252i	0.0362030	+	0.400290i
$859$	19.1632	−	15.0701i	0.653841	−	0.514186i	−0.235239	−	0.971937i	$-0.575587\pi$
$859$	19.1632	−	15.0701i	0.653841	−	0.514186i	0.889080	+	0.457751i	$0.151345\pi$
$860$	4.57203	−	15.5709i	0.155905	−	0.530964i
$861$	−9.87958	+	26.5822i	−0.336695	+	0.905918i
$862$	18.3300	−	28.5221i	0.624324	−	0.971466i
$863$	−15.9885	−	0.761625i	−0.544254	−	0.0259260i	−0.226345	−	0.974047i	$-0.572678\pi$
$863$	−15.9885	−	0.761625i	−0.544254	−	0.0259260i	−0.317909	+	0.948121i	$0.602981\pi$
$864$	−5.19339	+	0.169311i	−0.176683	+	0.00576008i
$865$	−25.5634	−	26.8102i	−0.869183	−	0.911573i
$866$	7.23714	−	5.69135i	0.245928	−	0.193400i
$867$	7.28732	+	10.3427i	0.247490	+	0.351258i
$868$	1.95345	+	5.14044i	0.0663043	+	0.174478i
$869$	29.2109	+	99.4831i	0.990911	+	3.37473i
$870$	−32.4886	−	0.162555i	−1.10147	−	0.00551112i
$871$	−0.624774	+	0.794464i	−0.0211697	+	0.0269194i
$872$	0.134443	+	2.82230i	0.00455280	+	0.0955751i
$873$	−0.918414	+	0.307610i	−0.0310836	+	0.0104110i
$874$	−10.5960	−	6.05621i	−0.358416	−	0.204854i
$875$	−28.0259	+	41.9629i	−0.947447	+	1.41860i
$876$	−9.68315	+	4.93084i	−0.327163	+	0.166598i
$877$	−15.7266	+	6.29597i	−0.531049	+	0.212600i	−0.621661	−	0.783286i	$-0.713542\pi$
$877$	−15.7266	+	6.29597i	−0.531049	+	0.212600i	0.0906124	+	0.995886i	$0.471118\pi$
$878$	3.26063	−	2.32188i	0.110041	−	0.0783598i
$879$	−0.190004	+	0.540220i	−0.00640867	+	0.0182212i
$880$	−13.8714	+	19.4796i	−0.467604	+	0.656658i
$881$	13.1612	+	15.1888i	0.443411	+	0.511723i	0.932826	−	0.360328i	$-0.117335\pi$
$881$	13.1612	+	15.1888i	0.443411	+	0.511723i	−0.489415	+	0.872051i	$0.662790\pi$
$882$	−20.6297	−	3.92650i	−0.694637	−	0.132212i
$883$	31.4119	+	9.22336i	1.05709	+	0.310391i	0.763680	−	0.645595i	$-0.223390\pi$
$883$	31.4119	+	9.22336i	1.05709	+	0.310391i	0.293414	+	0.955985i	$0.405209\pi$
$884$	3.35848	+	0.647294i	0.112958	+	0.0217709i
$885$	20.1906	+	51.1742i	0.678698	+	1.72020i
$886$	−16.7140	+	8.61667i	−0.561518	+	0.289483i
$887$	8.26160	−	42.8653i	0.277397	−	1.43927i	−0.529363	−	0.848395i	$-0.677569\pi$
$887$	8.26160	−	42.8653i	0.277397	−	1.43927i	0.806760	−	0.590879i	$-0.201219\pi$
$888$	6.38392	+	2.59287i	0.214230	+	0.0870111i
$889$	−32.6425	−	15.6089i	−1.09480	−	0.523506i
$890$	25.5730	−	22.1591i	0.857208	−	0.742775i
$891$	−47.4436	+	29.1653i	−1.58942	+	0.977075i
$892$	−3.39138	+	13.9795i	−0.113552	+	0.468067i
$893$	−11.2186	−	15.7543i	−0.375416	−	0.527198i
$894$	−3.55881	−	12.3484i	−0.119024	−	0.412992i
$895$	37.9983	+	59.1265i	1.27014	+	1.97638i
$896$	−0.172482	+	2.64012i	−0.00576221	+	0.0882003i
$897$	−9.11385	−	0.440043i	−0.304303	−	0.0146926i
$898$	−17.6025	−	30.4884i	−0.587403	−	1.01741i
$899$	10.0768	−	0.480015i	0.336079	−	0.0160094i
$900$	19.2921	+	22.7197i	0.643070	+	0.757324i
$901$	36.8880	−	3.52238i	1.22892	−	0.117348i
$902$	36.7420	−	10.7884i	1.22338	−	0.359216i
$903$	−13.6227	−	13.5912i	−0.453336	−	0.452287i
$904$	10.6491	−	9.22752i	0.354184	−	0.306903i
$905$	−1.87818	−	2.38830i	−0.0624329	−	0.0793898i
$906$	−9.39094	−	12.0653i	−0.311993	−	0.400843i
$907$	4.94268	−	1.71068i	0.164119	−	0.0568021i	−0.243773	−	0.969832i	$-0.578385\pi$
$907$	4.94268	−	1.71068i	0.164119	−	0.0568021i	0.407892	+	0.913030i	$0.366264\pi$
$908$	0.107057	−	2.24739i	0.00355280	−	0.0745824i
$909$	5.74773	−	5.90851i	0.190640	−	0.195973i
$910$	2.84002	−	10.8665i	0.0941458	−	0.360221i
$911$	22.5080	+	6.60896i	0.745725	+	0.218965i	0.632452	−	0.774599i	$-0.282049\pi$
$911$	22.5080	+	6.60896i	0.745725	+	0.218965i	0.113272	+	0.993564i	$0.463867\pi$
$912$	−2.36446	−	3.71996i	−0.0782950	−	0.123180i
$913$	−1.29530	+	0.249649i	−0.0428682	+	0.00826216i
$914$	−3.45832	−	0.330229i	−0.114391	−	0.0109230i
$915$	2.49175	−	2.13738i	0.0823747	−	0.0706596i
$916$	24.6060	+	11.2372i	0.813004	+	0.371286i
$917$	32.0340	+	6.76212i	1.05786	+	0.223305i
$918$	4.32473	+	15.5907i	0.142738	+	0.514569i
$919$	−13.0012	+	7.50623i	−0.428869	+	0.247608i	−0.698865	−	0.715254i	$-0.746311\pi$
$919$	−13.0012	+	7.50623i	−0.428869	+	0.247608i	0.269996	+	0.962862i	$0.412978\pi$
$920$	−13.4693	−	12.7313i	−0.444070	−	0.419740i
$921$	−18.1568	+	25.2295i	−0.598286	+	0.831340i
$922$	2.43733	+	1.25653i	0.0802693	+	0.0413817i
$923$	−6.24903	−	0.898475i	−0.205689	−	0.0295737i
$924$	12.4198	+	25.4920i	0.408581	+	0.838626i
$925$	−11.1351	−	37.9228i	−0.366121	−	1.24690i
$926$	24.1422	+	17.1916i	0.793362	+	0.564951i
$927$	0.578786	−	57.8375i	0.0190098	−	1.89963i
$928$	4.50600	+	1.80393i	0.147917	+	0.0592169i
$929$	−9.02927	+	2.19048i	−0.296241	+	0.0718672i	−0.381125	−	0.924524i	$-0.624463\pi$
$929$	−9.02927	+	2.19048i	−0.296241	+	0.0718672i	0.0848840	+	0.996391i	$0.472948\pi$
$930$	−9.55029	−	10.1169i	−0.313166	−	0.331747i
$931$	−6.03337	−	16.7611i	−0.197736	−	0.549323i
$932$	5.82238	−	9.05980i	0.190718	−	0.296764i
$933$	−12.6457	+	42.2836i	−0.414003	+	1.38430i
$934$	1.14039	+	1.19600i	0.0373146	+	0.0391344i
$935$	69.1272	+	27.6744i	2.26070	+	0.905049i
$936$	−2.83724	−	1.67616i	−0.0927382	−	0.0547870i
$937$	−39.6800	+	18.1212i	−1.29629	+	0.591995i	−0.939615	−	0.342234i	$-0.888816\pi$
$937$	−39.6800	+	18.1212i	−1.29629	+	0.591995i	−0.356674	+	0.934229i	$0.616089\pi$
$938$	−0.726935	+	2.32331i	−0.0237353	+	0.0758588i
$939$	−40.6779	−	23.7575i	−1.32747	−	0.775298i
$940$	−10.9159	−	27.2667i	−0.356038	−	0.889340i
$941$	−0.0925166	−	1.94216i	−0.00301596	−	0.0633127i	0.996858	−	0.0792144i	$-0.0252412\pi$
$941$	−0.0925166	−	1.94216i	−0.00301596	−	0.0633127i	−0.999874	+	0.0159017i	$0.994938\pi$
$942$	−16.5051	+	22.9345i	−0.537765	+	0.747245i
$943$	4.35166	+	29.3577i	0.141710	+	0.956018i
$944$		−	8.21867i		−	0.267495i
$945$	52.0133	−	10.8337i	1.69199	−	0.352420i
$946$	−3.69795	+	25.7198i	−0.120231	+	0.836223i
$947$	−4.02614	−	42.1636i	−0.130832	−	1.37013i	−0.787668	−	0.616101i	$-0.788711\pi$
$947$	−4.02614	−	42.1636i	−0.130832	−	1.37013i	0.656836	−	0.754034i	$-0.271895\pi$
$948$	−27.3778	−	9.62920i	−0.889189	−	0.312742i
$949$	−6.86014	−	0.655064i	−0.222690	−	0.0212643i
$950$	−8.26944	+	23.8930i	−0.268296	+	0.775190i
$951$	22.3727	−	0.953577i	0.725486	−	0.0309219i
$952$	8.11550	−	1.41616i	0.263025	−	0.0458980i
$953$	1.10908	−	1.27995i	0.0359268	−	0.0414617i	−0.737502	−	0.675345i	$-0.763995\pi$
$953$	1.10908	−	1.27995i	0.0359268	−	0.0414617i	0.773429	+	0.633883i	$0.218540\pi$
$954$	−34.6101	−	8.76394i	−1.12054	−	0.283743i
$955$	−42.0452	+	21.6758i	−1.36055	+	0.701413i
$956$	−25.5561	+	8.84505i	−0.826543	+	0.286069i
$957$	51.5275	−	7.14558i	1.66565	−	0.230984i
$958$	−6.50940	+	0.935911i	−0.210309	+	0.0302379i
$959$	−6.42523	+	15.2636i	−0.207482	+	0.492886i
$960$	−2.15762	−	6.33642i	−0.0696368	−	0.204507i
$961$	−19.3092	−	18.4113i	−0.622878	−	0.593913i
$962$	2.53476	+	3.55957i	0.0817239	+	0.114765i
$963$	20.8259	+	24.5260i	0.671105	+	0.790340i
$964$	6.57548	−	12.7547i	0.211782	−	0.410800i
$965$	−18.7551			−0.603747
$966$	−20.8965	+	6.80715i	−0.672333	+	0.219016i
$967$	15.1934			0.488588			0.244294	−	0.969701i	$-0.421444\pi$
$967$	15.1934			0.488588			0.244294	+	0.969701i	$0.421444\pi$
$968$	12.5051	−	24.2565i	0.401929	−	0.779634i
$969$	−9.52070	+	9.88551i	−0.305849	+	0.317568i
$970$	−0.723738	−	1.01635i	−0.0232378	−	0.0326329i
$971$	−32.8540	−	31.3263i	−1.05434	−	1.00531i	−0.999977	−	0.00678602i	$-0.997840\pi$
$971$	−32.8540	−	31.3263i	−1.05434	−	1.00531i	−0.0543592	−	0.998521i	$-0.517312\pi$
$972$	1.13099	−	15.5474i	0.0362765	−	0.498682i
$973$	−38.0107	+	4.78247i	−1.21857	+	0.153319i
$974$	5.06933	−	0.728860i	0.162432	−	0.0233542i
$975$	2.59646	+	18.7233i	0.0831533	+	0.599627i
$976$	−0.463468	+	0.160408i	−0.0148352	+	0.00513453i
$977$	2.57379	−	1.32688i	0.0823429	−	0.0424507i	−0.416563	−	0.909107i	$-0.636766\pi$
$977$	2.57379	−	1.32688i	0.0823429	−	0.0424507i	0.498906	+	0.866656i	$0.333735\pi$
$978$	26.4277	+	3.93478i	0.845063	+	0.125820i
$979$	−35.4806	+	40.9468i	−1.13396	+	1.30866i
$980$	−2.90314	−	26.8960i	−0.0927373	−	0.859162i
$981$	−8.46244	−	0.488033i	−0.270185	−	0.0155817i
$982$	−8.04424	+	23.2423i	−0.256702	+	0.741692i
$983$	−12.5409	−	1.19751i	−0.399992	−	0.0381946i	−0.106878	−	0.994272i	$-0.534086\pi$
$983$	−12.5409	−	1.19751i	−0.399992	−	0.0381946i	−0.293114	+	0.956077i	$0.594692\pi$
$984$	−3.55635	+	10.1114i	−0.113372	+	0.322340i
$985$	−8.95685	−	93.8004i	−0.285389	−	2.98873i
$986$	2.15080	−	14.9592i	0.0684956	−	0.476397i
$987$	−34.5855	−	4.09457i	−1.10087	−	0.130332i
$988$		−	2.79541i		−	0.0889337i
$989$	−19.3475	−	5.58946i	−0.615213	−	0.177734i
$990$	−53.7458	−	47.5209i	−1.70815	−	1.51031i
$991$	0.00817463	+	0.171607i	0.000259676	+	0.00545127i	0.998993	−	0.0448561i	$-0.0142829\pi$
$991$	0.00817463	+	0.171607i	0.000259676	+	0.00545127i	−0.998734	+	0.0503074i	$0.983980\pi$
$992$	0.772486	+	1.92958i	0.0245265	+	0.0612642i
$993$	12.5751	−	21.5312i	0.399059	−	0.683272i
$994$	−14.8385	+	3.32381i	−0.470650	+	0.105425i
$995$	31.2815	−	14.2858i	0.991690	−	0.452890i
$996$	0.155066	−	0.335100i	0.00491345	−	0.0106180i
$997$	−0.222826	−	0.0892060i	−0.00705697	−	0.00282518i	0.368131	−	0.929774i	$-0.379998\pi$
$997$	−0.222826	−	0.0892060i	−0.00705697	−	0.00282518i	−0.375188	+	0.926949i	$0.622422\pi$
$998$	−4.40161	−	4.61627i	−0.139330	−	0.146125i
$999$	−9.74678	+	18.2290i	−0.308375	+	0.576741i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.bf.a.11.7	✓	1280
3.2	odd	2	inner	966.2.bf.a.11.40	yes	1280
7.2	even	3	inner	966.2.bf.a.149.61	yes	1280
21.2	odd	6	inner	966.2.bf.a.149.28	yes	1280
23.21	odd	22	inner	966.2.bf.a.389.28	yes	1280
69.44	even	22	inner	966.2.bf.a.389.61	yes	1280
161.44	odd	66	inner	966.2.bf.a.527.40	yes	1280
483.44	even	66	inner	966.2.bf.a.527.7	yes	1280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.bf.a.11.7	✓	1280	1.1	even	1	trivial
966.2.bf.a.11.40	yes	1280	3.2	odd	2	inner
966.2.bf.a.149.28	yes	1280	21.2	odd	6	inner
966.2.bf.a.149.61	yes	1280	7.2	even	3	inner
966.2.bf.a.389.28	yes	1280	23.21	odd	22	inner
966.2.bf.a.389.61	yes	1280	69.44	even	22	inner
966.2.bf.a.527.7	yes	1280	483.44	even	66	inner
966.2.bf.a.527.40	yes	1280	161.44	odd	66	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.bf (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.458227 + 0.888835i) q^{2} +(-1.24755 - 1.20151i) q^{3} +(-0.580057 - 0.814576i) q^{4} +(2.79695 + 2.66688i) q^{5} +(1.63960 - 0.558302i) q^{6} +(2.62506 - 0.330282i) q^{7} +(0.989821 - 0.142315i) q^{8} +(0.112753 + 2.99788i) q^{9} +O(q^{10})\)	\(q+(-0.458227 + 0.888835i) q^{2} +(-1.24755 - 1.20151i) q^{3} +(-0.580057 - 0.814576i) q^{4} +(2.79695 + 2.66688i) q^{5} +(1.63960 - 0.558302i) q^{6} +(2.62506 - 0.330282i) q^{7} +(0.989821 - 0.142315i) q^{8} +(0.112753 + 2.99788i) q^{9} +(-3.65206 + 1.26399i) q^{10} +(5.50003 - 2.83546i) q^{11} +(-0.255071 + 1.71317i) q^{12} +(-0.719336 + 0.830158i) q^{13} +(-0.909304 + 2.48459i) q^{14} +(-0.285042 - 6.68762i) q^{15} +(-0.327068 + 0.945001i) q^{16} +(3.09962 + 0.295978i) q^{17} +(-2.71629 - 1.27349i) q^{18} +(-0.241903 - 2.53333i) q^{19} +(0.549991 - 3.82527i) q^{20} +(-3.67172 - 2.74198i) q^{21} +6.18791i q^{22} +(-4.74995 - 0.661825i) q^{23} +(-1.40584 - 1.01173i) q^{24} +(0.472735 + 9.92393i) q^{25} +(-0.408255 - 1.01977i) q^{26} +(3.46132 - 3.87547i) q^{27} +(-1.79172 - 1.94672i) q^{28} +(-4.41506 + 2.01629i) q^{29} +(6.07481 + 2.81109i) q^{30} +(-1.92958 - 0.772486i) q^{31} +(-0.690079 - 0.723734i) q^{32} +(-10.2684 - 3.07096i) q^{33} +(-1.68341 + 2.61943i) q^{34} +(8.22296 + 6.07694i) q^{35} +(2.37660 - 1.83079i) q^{36} +(-3.86603 + 0.937888i) q^{37} +(2.36256 + 0.945825i) q^{38} +(1.89485 - 0.171374i) q^{39} +(3.14802 + 2.24169i) q^{40} +(-1.74347 - 5.93771i) q^{41} +(4.11965 - 2.00710i) q^{42} +(4.15646 + 0.597609i) q^{43} +(-5.50003 - 2.83546i) q^{44} +(-7.67964 + 8.68561i) q^{45} +(2.76480 - 3.91865i) q^{46} +(6.58168 - 3.79994i) q^{47} +(1.54346 - 0.785959i) q^{48} +(6.78183 - 1.73402i) q^{49} +(-9.03736 - 4.12722i) q^{50} +(-3.51131 - 4.09347i) q^{51} +(1.09348 + 0.104415i) q^{52} +(11.6858 - 2.25224i) q^{53} +(1.85859 + 4.85238i) q^{54} +(22.9452 + 6.73731i) q^{55} +(2.55133 - 0.700504i) q^{56} +(-2.74203 + 3.45109i) q^{57} +(0.230947 - 4.84818i) q^{58} +(-7.76665 + 2.68806i) q^{59} +(-5.28224 + 4.11139i) q^{60} +(0.303171 + 0.385513i) q^{61} +(1.57080 - 1.36110i) q^{62} +(1.28613 + 7.83236i) q^{63} +(0.959493 - 0.281733i) q^{64} +(-4.22588 + 0.403523i) q^{65} +(7.43483 - 7.71971i) q^{66} +(0.919068 - 0.0437806i) q^{67} +(-1.55686 - 2.69656i) q^{68} +(5.13060 + 6.53276i) q^{69} +(-9.16938 + 4.52425i) q^{70} +(3.10729 + 4.83504i) q^{71} +(0.538248 + 2.95132i) q^{72} +(3.63908 + 5.11038i) q^{73} +(0.937888 - 3.86603i) q^{74} +(11.3339 - 12.9486i) q^{75} +(-1.92327 + 1.66652i) q^{76} +(13.5014 - 9.25981i) q^{77} +(-0.715947 + 1.76274i) q^{78} +(-3.17104 + 16.4529i) q^{79} +(-3.43500 + 1.77087i) q^{80} +(-8.97457 + 0.676039i) q^{81} +(6.07655 + 1.17116i) q^{82} +(-0.204545 - 0.0600598i) q^{83} +(-0.103749 + 4.58140i) q^{84} +(7.88014 + 9.09417i) q^{85} +(-2.43578 + 3.42057i) q^{86} +(7.93059 + 2.78931i) q^{87} +(5.04052 - 3.58934i) q^{88} +(-8.12864 + 3.25422i) q^{89} +(-4.20107 - 10.8059i) q^{90} +(-1.61411 + 2.41679i) q^{91} +(2.21613 + 4.25309i) q^{92} +(1.47909 + 3.28212i) q^{93} +(0.361617 + 7.59127i) q^{94} +(6.07949 - 7.73070i) q^{95} +(-0.00866609 + 1.73203i) q^{96} +(0.0909583 + 0.309775i) q^{97} +(-1.56636 + 6.82250i) q^{98} +(9.12053 + 16.1687i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1280 q - 64 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) \) 1280 * q - 64 * q^4 - 8 * q^6 + 4 * q^9	\( 1280 q - 64 q^{4} - 8 q^{6} + 4 q^{9} + 64 q^{16} + 44 q^{18} - 132 q^{21} - 4 q^{24} + 72 q^{25} + 108 q^{27} + 44 q^{30} + 8 q^{36} + 44 q^{37} - 4 q^{39} - 88 q^{43} - 12 q^{46} + 60 q^{49} - 48 q^{54} + 96 q^{55} + 44 q^{58} - 176 q^{61} - 110 q^{63} + 128 q^{64} + 56 q^{69} - 120 q^{70} + 44 q^{72} + 40 q^{73} - 268 q^{75} + 16 q^{78} + 88 q^{79} + 8 q^{81} - 56 q^{82} - 22 q^{84} + 64 q^{85} - 42 q^{87} - 32 q^{93} + 8 q^{94} + 4 q^{96} + 132 q^{99}+O(q^{100}) \) 1280 * q - 64 * q^4 - 8 * q^6 + 4 * q^9 + 64 * q^16 + 44 * q^18 - 132 * q^21 - 4 * q^24 + 72 * q^25 + 108 * q^27 + 44 * q^30 + 8 * q^36 + 44 * q^37 - 4 * q^39 - 88 * q^43 - 12 * q^46 + 60 * q^49 - 48 * q^54 + 96 * q^55 + 44 * q^58 - 176 * q^61 - 110 * q^63 + 128 * q^64 + 56 * q^69 - 120 * q^70 + 44 * q^72 + 40 * q^73 - 268 * q^75 + 16 * q^78 + 88 * q^79 + 8 * q^81 - 56 * q^82 - 22 * q^84 + 64 * q^85 - 42 * q^87 - 32 * q^93 + 8 * q^94 + 4 * q^96 + 132 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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