LMFDB - Embedded newform 671.2.f.a.538.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(538,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("671.538");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.f (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:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$60$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			538.6
Character	$\chi$	$=$	671.538
Dual form			671.2.f.a.560.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73598 - 1.73598i) q^{2} -2.48629i q^{3} +4.02728i q^{4} +3.17645i q^{5} +(-4.31616 + 4.31616i) q^{6} +(0.00734923 + 0.00734923i) q^{7} +(3.51933 - 3.51933i) q^{8} -3.18164 q^{9} +O(q^{10})$	\(q+(-1.73598 - 1.73598i) q^{2} -2.48629i q^{3} +4.02728i q^{4} +3.17645i q^{5} +(-4.31616 + 4.31616i) q^{6} +(0.00734923 + 0.00734923i) q^{7} +(3.51933 - 3.51933i) q^{8} -3.18164 q^{9} +(5.51426 - 5.51426i) q^{10} +(1.61196 - 2.89855i) q^{11} +10.0130 q^{12} -5.29957i q^{13} -0.0255163i q^{14} +7.89757 q^{15} -4.16443 q^{16} +(-0.0268583 + 0.0268583i) q^{17} +(5.52327 + 5.52327i) q^{18} -4.62686 q^{19} -12.7924 q^{20} +(0.0182723 - 0.0182723i) q^{21} +(-7.83017 + 2.23350i) q^{22} +(1.91902 - 1.91902i) q^{23} +(-8.75006 - 8.75006i) q^{24} -5.08981 q^{25} +(-9.19997 + 9.19997i) q^{26} +0.451602i q^{27} +(-0.0295974 + 0.0295974i) q^{28} +(-4.76083 + 4.76083i) q^{29} +(-13.7100 - 13.7100i) q^{30} +(1.49223 + 1.49223i) q^{31} +(0.190724 + 0.190724i) q^{32} +(-7.20664 - 4.00779i) q^{33} +0.0932511 q^{34} +(-0.0233445 + 0.0233445i) q^{35} -12.8133i q^{36} +(-5.74296 - 5.74296i) q^{37} +(8.03216 + 8.03216i) q^{38} -13.1763 q^{39} +(11.1790 + 11.1790i) q^{40} +1.13771 q^{41} -0.0634409 q^{42} +(1.28633 - 1.28633i) q^{43} +(11.6733 + 6.49180i) q^{44} -10.1063i q^{45} -6.66277 q^{46} +6.60444 q^{47} +10.3540i q^{48} -6.99989i q^{49} +(8.83584 + 8.83584i) q^{50} +(0.0667775 + 0.0667775i) q^{51} +21.3429 q^{52} +(-4.16097 + 4.16097i) q^{53} +(0.783973 - 0.783973i) q^{54} +(9.20709 + 5.12030i) q^{55} +0.0517287 q^{56} +11.5037i q^{57} +16.5295 q^{58} +(-9.99545 - 9.99545i) q^{59} +31.8057i q^{60} +(-6.46810 - 4.37763i) q^{61} -5.18098i q^{62} +(-0.0233826 - 0.0233826i) q^{63} +7.66666i q^{64} +16.8338 q^{65} +(5.55314 + 19.4681i) q^{66} +(-4.43100 - 4.43100i) q^{67} +(-0.108166 - 0.108166i) q^{68} +(-4.77124 - 4.77124i) q^{69} +0.0810512 q^{70} +(10.1042 + 10.1042i) q^{71} +(-11.1972 + 11.1972i) q^{72} -6.35682i q^{73} +19.9394i q^{74} +12.6548i q^{75} -18.6337i q^{76} +(0.0331488 - 0.00945547i) q^{77} +(22.8738 + 22.8738i) q^{78} +(-7.58446 - 7.58446i) q^{79} -13.2281i q^{80} -8.42210 q^{81} +(-1.97504 - 1.97504i) q^{82} +10.2076i q^{83} +(0.0735878 + 0.0735878i) q^{84} +(-0.0853139 - 0.0853139i) q^{85} -4.46610 q^{86} +(11.8368 + 11.8368i) q^{87} +(-4.52794 - 15.8739i) q^{88} +(-8.85305 - 8.85305i) q^{89} +(-17.5444 + 17.5444i) q^{90} +(0.0389478 - 0.0389478i) q^{91} +(7.72843 + 7.72843i) q^{92} +(3.71012 - 3.71012i) q^{93} +(-11.4652 - 11.4652i) q^{94} -14.6970i q^{95} +(0.474195 - 0.474195i) q^{96} -8.88752i q^{97} +(-12.1517 + 12.1517i) q^{98} +(-5.12866 + 9.22213i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 120 q^{9}+O(q^{10}) $ 120 * q - 120 * q^9	$ 120 q - 120 q^{9} - 4 q^{11} + 16 q^{12} + 16 q^{15} - 148 q^{16} + 56 q^{20} - 4 q^{22} - 4 q^{23} - 104 q^{25} + 40 q^{26} - 2 q^{33} - 8 q^{34} - 12 q^{37} + 20 q^{38} + 16 q^{42} - 10 q^{44} - 4 q^{53} + 50 q^{55} - 24 q^{56} + 64 q^{58} - 56 q^{67} + 68 q^{69} + 144 q^{70} - 12 q^{71} - 64 q^{77} + 84 q^{78} + 72 q^{81} + 40 q^{82} - 80 q^{86} + 4 q^{89} - 4 q^{91} + 4 q^{92} + 64 q^{93} + 24 q^{99}+O(q^{100}) $ 120 * q - 120 * q^9 - 4 * q^11 + 16 * q^12 + 16 * q^15 - 148 * q^16 + 56 * q^20 - 4 * q^22 - 4 * q^23 - 104 * q^25 + 40 * q^26 - 2 * q^33 - 8 * q^34 - 12 * q^37 + 20 * q^38 + 16 * q^42 - 10 * q^44 - 4 * q^53 + 50 * q^55 - 24 * q^56 + 64 * q^58 - 56 * q^67 + 68 * q^69 + 144 * q^70 - 12 * q^71 - 64 * q^77 + 84 * q^78 + 72 * q^81 + 40 * q^82 - 80 * q^86 + 4 * q^89 - 4 * q^91 + 4 * q^92 + 64 * q^93 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/671\mathbb{Z}\right)^\times$.

$n$	$123$	$551$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.73598	−	1.73598i	−1.22753	−	1.22753i	−0.964897	−	0.262629i	$-0.915410\pi$
$2$	−1.73598	−	1.73598i	−1.22753	−	1.22753i	−0.262629	−	0.964897i	$-0.584590\pi$
$3$		−	2.48629i		−	1.43546i	−0.696321	−	0.717730i	$-0.745181\pi$
$3$		−	2.48629i		−	1.43546i	0.696321	−	0.717730i	$-0.254819\pi$
$4$			4.02728i			2.01364i
$5$			3.17645i			1.42055i	0.703924	+	0.710275i	$0.251429\pi$
$5$			3.17645i			1.42055i	−0.703924	+	0.710275i	$0.748571\pi$
$6$	−4.31616	+	4.31616i	−1.76206	+	1.76206i
$7$	0.00734923	+	0.00734923i	0.00277775	+	0.00277775i	0.708494	−	0.705717i	$-0.249375\pi$
$7$	0.00734923	+	0.00734923i	0.00277775	+	0.00277775i	−0.705717	+	0.708494i	$0.749375\pi$
$8$	3.51933	−	3.51933i	1.24427	−	1.24427i
$9$	−3.18164			−1.06055
$10$	5.51426	−	5.51426i	1.74376	−	1.74376i
$11$	1.61196	−	2.89855i	0.486023	−	0.873946i
$11$	1.61196	−	2.89855i	0.486023	−	0.873946i
$12$	10.0130			2.89050
$13$		−	5.29957i		−	1.46984i	−0.678156	−	0.734918i	$-0.737221\pi$
$13$		−	5.29957i		−	1.46984i	0.678156	−	0.734918i	$-0.262779\pi$
$14$		−	0.0255163i		−	0.00681952i
$15$	7.89757			2.03914
$16$	−4.16443			−1.04111
$17$	−0.0268583	+	0.0268583i	−0.00651409	+	0.00651409i	−0.710356	−	0.703842i	$-0.751466\pi$
$17$	−0.0268583	+	0.0268583i	−0.00651409	+	0.00651409i	0.703842	+	0.710356i	$0.251466\pi$
$18$	5.52327	+	5.52327i	1.30185	+	1.30185i
$19$	−4.62686			−1.06148			−0.530738	−	0.847536i	$-0.678085\pi$
$19$	−4.62686			−1.06148			−0.530738	+	0.847536i	$0.678085\pi$
$20$	−12.7924			−2.86048
$21$	0.0182723	−	0.0182723i	0.00398735	−	0.00398735i
$22$	−7.83017	+	2.23350i	−1.66940	+	0.476185i
$23$	1.91902	−	1.91902i	0.400143	−	0.400143i	−0.478140	−	0.878283i	$-0.658689\pi$
$23$	1.91902	−	1.91902i	0.400143	−	0.400143i	0.878283	+	0.478140i	$0.158689\pi$
$24$	−8.75006	−	8.75006i	−1.78610	−	1.78610i
$25$	−5.08981			−1.01796
$26$	−9.19997	+	9.19997i	−1.80426	+	1.80426i
$27$			0.451602i			0.0869108i
$28$	−0.0295974	+	0.0295974i	−0.00559339	+	0.00559339i
$29$	−4.76083	+	4.76083i	−0.884064	+	0.884064i	−0.993945	−	0.109881i	$-0.964953\pi$
$29$	−4.76083	+	4.76083i	−0.884064	+	0.884064i	0.109881	+	0.993945i	$0.464953\pi$
$30$	−13.7100	−	13.7100i	−2.50310	−	2.50310i
$31$	1.49223	+	1.49223i	0.268013	+	0.268013i	0.828299	−	0.560286i	$-0.189309\pi$
$31$	1.49223	+	1.49223i	0.268013	+	0.268013i	−0.560286	+	0.828299i	$0.689309\pi$
$32$	0.190724	+	0.190724i	0.0337156	+	0.0337156i
$33$	−7.20664	−	4.00779i	−1.25451	−	0.697667i
$34$	0.0932511			0.0159924
$35$	−0.0233445	+	0.0233445i	−0.00394593	+	0.00394593i
$36$		−	12.8133i		−	2.13556i
$37$	−5.74296	−	5.74296i	−0.944137	−	0.944137i	0.0543834	−	0.998520i	$-0.482681\pi$
$37$	−5.74296	−	5.74296i	−0.944137	−	0.944137i	−0.998520	+	0.0543834i	$0.982681\pi$
$38$	8.03216	+	8.03216i	1.30299	+	1.30299i
$39$	−13.1763			−2.10989
$40$	11.1790	+	11.1790i	1.76755	+	1.76755i
$41$	1.13771			0.177680			0.0888399	−	0.996046i	$-0.471684\pi$
$41$	1.13771			0.177680			0.0888399	+	0.996046i	$0.471684\pi$
$42$	−0.0634409			−0.00978915
$43$	1.28633	−	1.28633i	0.196164	−	0.196164i	−0.602189	−	0.798353i	$-0.705705\pi$
$43$	1.28633	−	1.28633i	0.196164	−	0.196164i	0.798353	+	0.602189i	$0.205705\pi$
$44$	11.6733	+	6.49180i	1.75981	+	0.978676i
$45$		−	10.1063i		−	1.50656i
$46$	−6.66277			−0.982372
$47$	6.60444			0.963357			0.481678	−	0.876348i	$-0.340027\pi$
$47$	6.60444			0.963357			0.481678	+	0.876348i	$0.340027\pi$
$48$			10.3540i			1.49447i
$49$		−	6.99989i		−	0.999985i
$50$	8.83584	+	8.83584i	1.24958	+	1.24958i
$51$	0.0667775	+	0.0667775i	0.00935071	+	0.00935071i
$52$	21.3429			2.95972
$53$	−4.16097	+	4.16097i	−0.571553	+	0.571553i	−0.932562	−	0.361009i	$-0.882432\pi$
$53$	−4.16097	+	4.16097i	−0.571553	+	0.571553i	0.361009	+	0.932562i	$0.382432\pi$
$54$	0.783973	−	0.783973i	0.106685	−	0.106685i
$55$	9.20709	+	5.12030i	1.24148	+	0.690421i
$56$	0.0517287			0.00691254
$57$			11.5037i			1.52371i
$58$	16.5295			2.17042
$59$	−9.99545	−	9.99545i	−1.30130	−	1.30130i	−0.927518	−	0.373780i	$-0.878062\pi$
$59$	−9.99545	−	9.99545i	−1.30130	−	1.30130i	−0.373780	−	0.927518i	$-0.621938\pi$
$60$			31.8057i			4.10610i
$61$	−6.46810	−	4.37763i	−0.828155	−	0.560498i
$61$	−6.46810	−	4.37763i	−0.828155	−	0.560498i
$62$		−	5.18098i		−	0.657986i
$63$	−0.0233826	−	0.0233826i	−0.00294593	−	0.00294593i
$64$			7.66666i			0.958333i
$65$	16.8338			2.08798
$66$	5.55314	+	19.4681i	0.683544	+	2.39635i
$67$	−4.43100	−	4.43100i	−0.541333	−	0.541333i	0.382587	−	0.923920i	$-0.375033\pi$
$67$	−4.43100	−	4.43100i	−0.541333	−	0.541333i	−0.923920	+	0.382587i	$0.875033\pi$
$68$	−0.108166	−	0.108166i	−0.0131170	−	0.0131170i
$69$	−4.77124	−	4.77124i	−0.574389	−	0.574389i
$70$	0.0810512			0.00968747
$71$	10.1042	+	10.1042i	1.19915	+	1.19915i	0.974422	+	0.224728i	$0.0721492\pi$
$71$	10.1042	+	10.1042i	1.19915	+	1.19915i	0.224728	+	0.974422i	$0.427851\pi$
$72$	−11.1972	+	11.1972i	−1.31960	+	1.31960i
$73$		−	6.35682i		−	0.744010i	−0.928231	−	0.372005i	$-0.878670\pi$
$73$		−	6.35682i		−	0.744010i	0.928231	−	0.372005i	$-0.121330\pi$
$74$			19.9394i			2.31790i
$75$			12.6548i			1.46125i
$76$		−	18.6337i		−	2.13743i
$77$	0.0331488	−	0.00945547i	0.00377765	−	0.00107755i
$78$	22.8738	+	22.8738i	2.58995	+	2.58995i
$79$	−7.58446	−	7.58446i	−0.853319	−	0.853319i	0.137222	−	0.990540i	$-0.456183\pi$
$79$	−7.58446	−	7.58446i	−0.853319	−	0.853319i	−0.990540	+	0.137222i	$0.956183\pi$
$80$		−	13.2281i		−	1.47894i
$81$	−8.42210			−0.935789
$82$	−1.97504	−	1.97504i	−0.218107	−	0.218107i
$83$			10.2076i			1.12043i	0.828347	+	0.560215i	$0.189282\pi$
$83$			10.2076i			1.12043i	−0.828347	+	0.560215i	$0.810718\pi$
$84$	0.0735878	+	0.0735878i	0.00802909	+	0.00802909i
$85$	−0.0853139	−	0.0853139i	−0.00925359	−	0.00925359i
$86$	−4.46610			−0.481592
$87$	11.8368	+	11.8368i	1.26904	+	1.26904i
$88$	−4.52794	−	15.8739i	−0.482680	−	1.69217i
$89$	−8.85305	−	8.85305i	−0.938421	−	0.938421i	0.0597897	−	0.998211i	$-0.480957\pi$
$89$	−8.85305	−	8.85305i	−0.938421	−	0.938421i	−0.998211	+	0.0597897i	$0.980957\pi$
$90$	−17.5444	+	17.5444i	−1.84934	+	1.84934i
$91$	0.0389478	−	0.0389478i	0.00408284	−	0.00408284i
$92$	7.72843	+	7.72843i	0.805744	+	0.805744i
$93$	3.71012	−	3.71012i	0.384722	−	0.384722i
$94$	−11.4652	−	11.4652i	−1.18255	−	1.18255i
$95$		−	14.6970i		−	1.50788i
$96$	0.474195	−	0.474195i	0.0483973	−	0.0483973i
$97$		−	8.88752i		−	0.902391i	−0.892425	−	0.451195i	$-0.850998\pi$
$97$		−	8.88752i		−	0.902391i	0.892425	−	0.451195i	$-0.149002\pi$
$98$	−12.1517	+	12.1517i	−1.22751	+	1.22751i
$99$	−5.12866	+	9.22213i	−0.515450	+	0.926859i
$100$		−	20.4981i		−	2.04981i
$101$	8.49049	+	8.49049i	0.844835	+	0.844835i	0.989483	−	0.144648i	$-0.0462050\pi$
$101$	8.49049	+	8.49049i	0.844835	+	0.844835i	−0.144648	+	0.989483i	$0.546205\pi$
$102$		−	0.231849i		−	0.0229565i
$103$	14.4336			1.42219			0.711094	−	0.703097i	$-0.248200\pi$
$103$	14.4336			1.42219			0.711094	+	0.703097i	$0.248200\pi$
$104$	−18.6509	−	18.6509i	−1.82887	−	1.82887i
$105$	0.0580411	+	0.0580411i	0.00566423	+	0.00566423i
$106$	14.4467			1.40319
$107$	−6.69645			−0.647370			−0.323685	−	0.946165i	$-0.604922\pi$
$107$	−6.69645			−0.647370			−0.323685	+	0.946165i	$0.604922\pi$
$108$	−1.81873			−0.175007
$109$	−3.40131			−0.325787			−0.162893	−	0.986644i	$-0.552083\pi$
$109$	−3.40131			−0.325787			−0.162893	+	0.986644i	$0.552083\pi$
$110$	−7.09461	−	24.8721i	−0.676444	−	2.37146i
$111$	−14.2787	+	14.2787i	−1.35527	+	1.35527i
$112$	−0.0306053	−	0.0306053i	−0.00289193	−	0.00289193i
$113$		−	7.70896i		−	0.725198i	−0.931945	−	0.362599i	$-0.881889\pi$
$113$		−	7.70896i		−	0.725198i	0.931945	−	0.362599i	$-0.118111\pi$
$114$	19.9703	−	19.9703i	1.87039	−	1.87039i
$115$	6.09566	+	6.09566i	0.568423	+	0.568423i
$116$	−19.1732	−	19.1732i	−1.78019	−	1.78019i
$117$			16.8613i			1.55883i
$118$			34.7039i			3.19475i
$119$	−0.000394776	0		−3.61890e−5	0
$120$	27.7941	−	27.7941i	2.53724	−	2.53724i
$121$	−5.80319	−	9.34468i	−0.527562	−	0.849516i
$122$	3.62902	+	18.8280i	0.328556	+	1.70461i
$123$		−	2.82867i		−	0.255052i
$124$	−6.00964	+	6.00964i	−0.539682	+	0.539682i
$125$		−	0.285290i		−	0.0255172i
$126$			0.0811836i			0.00723241i
$127$	−11.2434			−0.997690			−0.498845	−	0.866691i	$-0.666242\pi$
$127$	−11.2434			−0.997690			−0.498845	+	0.866691i	$0.666242\pi$
$128$	13.6907	−	13.6907i	1.21009	−	1.21009i
$129$	−3.19819	−	3.19819i	−0.281585	−	0.281585i
$130$	−29.2232	−	29.2232i	−2.56304	−	2.56304i
$131$			13.4517i			1.17528i	0.809121	+	0.587642i	$0.199944\pi$
$131$			13.4517i			1.17528i	−0.809121	+	0.587642i	$0.800056\pi$
$132$	16.1405	−	29.0231i	1.40485	−	2.52614i
$133$	−0.0340039	−	0.0340039i	−0.00294851	−	0.00294851i
$134$			15.3843i			1.32900i
$135$	−1.43449			−0.123461
$136$			0.189046i			0.0162106i
$137$	13.0436			1.11439			0.557194	−	0.830383i	$-0.311878\pi$
$137$	13.0436			1.11439			0.557194	+	0.830383i	$0.311878\pi$
$138$			16.5656i			1.41016i
$139$	0.251462	−	0.251462i	0.0213287	−	0.0213287i	−0.696362	−	0.717691i	$-0.745199\pi$
$139$	0.251462	−	0.251462i	0.0213287	−	0.0213287i	0.717691	+	0.696362i	$0.245199\pi$
$140$	−0.0940147	−	0.0940147i	−0.00794569	−	0.00794569i
$141$		−	16.4206i		−	1.38286i
$142$		−	35.0815i		−	2.94397i
$143$	−15.3611	−	8.54268i	−1.28456	−	0.714375i
$144$	13.2497			1.10414
$145$	−15.1225	−	15.1225i	−1.25586	−	1.25586i
$146$	−11.0353	+	11.0353i	−0.913291	+	0.913291i
$147$	−17.4038			−1.43544
$148$	23.1285	−	23.1285i	1.90115	−	1.90115i
$149$	−2.09398			−0.171545			−0.0857727	−	0.996315i	$-0.527336\pi$
$149$	−2.09398			−0.171545			−0.0857727	+	0.996315i	$0.527336\pi$
$150$	21.9684	−	21.9684i	1.79372	−	1.79372i
$151$	8.83867	−	8.83867i	0.719281	−	0.719281i	−0.249177	−	0.968458i	$-0.580160\pi$
$151$	8.83867	−	8.83867i	0.719281	−	0.719281i	0.968458	+	0.249177i	$0.0801601\pi$
$152$	−16.2834	+	16.2834i	−1.32076	+	1.32076i
$153$	0.0854533	−	0.0854533i	0.00690849	−	0.00690849i
$154$	−0.0739603	−	0.0411312i	−0.00595989	−	0.00331445i
$155$	−4.74000	+	4.74000i	−0.380726	+	0.380726i
$156$		−	53.0645i		−	4.24856i
$157$	1.44041	+	1.44041i	0.114957	+	0.114957i	0.762245	−	0.647288i	$-0.224097\pi$
$157$	1.44041	+	1.44041i	0.114957	+	0.114957i	−0.647288	+	0.762245i	$0.724097\pi$
$158$			26.3330i			2.09494i
$159$	10.3454	+	10.3454i	0.820442	+	0.820442i
$160$	−0.605825	+	0.605825i	−0.0478946	+	0.0478946i
$161$	0.0282066			0.00222299
$162$	14.6206	+	14.6206i	1.14870	+	1.14870i
$163$			13.7160i			1.07432i	0.843481	+	0.537159i	$0.180503\pi$
$163$			13.7160i			1.07432i	−0.843481	+	0.537159i	$0.819497\pi$
$164$			4.58186i			0.357783i
$165$	12.7305	−	22.8915i	0.991071	−	1.78210i
$166$	17.7202	−	17.7202i	1.37536	−	1.37536i
$167$	10.8750			0.841530			0.420765	−	0.907170i	$-0.361762\pi$
$167$	10.8750			0.841530			0.420765	+	0.907170i	$0.361762\pi$
$168$		−	0.128613i		−	0.00992267i
$169$	−15.0854			−1.16042
$170$			0.296207i			0.0227180i
$171$	14.7210			1.12574
$172$	5.18042	+	5.18042i	0.395003	+	0.395003i
$173$	3.71196	+	3.71196i	0.282215	+	0.282215i	0.833992	−	0.551777i	$-0.186050\pi$
$173$	3.71196	+	3.71196i	0.282215	+	0.282215i	−0.551777	+	0.833992i	$0.686050\pi$
$174$		−	41.0970i		−	3.11556i
$175$	−0.0374062	−	0.0374062i	−0.00282765	−	0.00282765i
$176$	−6.71288	+	12.0708i	−0.506002	+	0.909871i
$177$	−24.8516	+	24.8516i	−1.86796	+	1.86796i
$178$			30.7375i			2.30387i
$179$	9.40918			0.703275			0.351638	−	0.936136i	$-0.385625\pi$
$179$	9.40918			0.703275			0.351638	+	0.936136i	$0.385625\pi$
$180$	40.7009			3.03367
$181$	0.792377	+	0.792377i	0.0588969	+	0.0588969i	0.735942	−	0.677045i	$-0.236740\pi$
$181$	0.792377	+	0.792377i	0.0588969	+	0.0588969i	−0.677045	+	0.735942i	$0.736740\pi$
$182$	−0.135225			−0.0100236
$183$	−10.8841	+	16.0816i	−0.804573	+	1.18878i
$184$		−	13.5073i		−	0.995772i
$185$	18.2422	−	18.2422i	1.34119	−	1.34119i
$186$	−12.8814			−0.944512
$187$	0.0345557	+	0.121144i	0.00252696	+	0.00885896i
$188$			26.5979i			1.93985i
$189$	−0.00331893	+	0.00331893i	−0.000241416	+	0.000241416i
$190$	−25.5137	+	25.5137i	−1.85096	+	1.85096i
$191$	−5.70641	−	5.70641i	−0.412901	−	0.412901i	0.469847	−	0.882748i	$-0.344309\pi$
$191$	−5.70641	−	5.70641i	−0.412901	−	0.412901i	−0.882748	+	0.469847i	$0.844309\pi$
$192$	19.0615			1.37565
$193$	10.8892	−	10.8892i	0.783818	−	0.783818i	−0.196655	−	0.980473i	$-0.563008\pi$
$193$	10.8892	−	10.8892i	0.783818	−	0.783818i	0.980473	+	0.196655i	$0.0630077\pi$
$194$	−15.4286	+	15.4286i	−1.10771	+	1.10771i
$195$		−	41.8537i		−	2.99721i
$196$	28.1905			2.01361
$197$	17.0525			1.21494			0.607469	−	0.794344i	$-0.292185\pi$
$197$	17.0525			1.21494			0.607469	+	0.794344i	$0.292185\pi$
$198$	24.9128	−	7.10620i	1.77047	−	0.505016i
$199$	20.1450			1.42804			0.714019	−	0.700126i	$-0.246873\pi$
$199$	20.1450			1.42804			0.714019	+	0.700126i	$0.246873\pi$
$200$	−17.9127	+	17.9127i	−1.26662	+	1.26662i
$201$	−11.0168	+	11.0168i	−0.777062	+	0.777062i
$202$		−	29.4787i		−	2.07411i
$203$	−0.0699769			−0.00491142
$204$	−0.268932	+	0.268932i	−0.0188290	+	0.0188290i
$205$			3.61386i			0.252403i
$206$	−25.0565	−	25.0565i	−1.74577	−	1.74577i
$207$	−6.10562	+	6.10562i	−0.424370	+	0.424370i
$208$			22.0697i			1.53026i
$209$	−7.45831	+	13.4112i	−0.515902	+	0.927672i
$210$		−	0.201517i		−	0.0139060i
$211$	6.83606	−	6.83606i	0.470614	−	0.470614i	−0.431500	−	0.902113i	$-0.642015\pi$
$211$	6.83606	−	6.83606i	0.470614	−	0.470614i	0.902113	+	0.431500i	$0.142015\pi$
$212$	−16.7574	−	16.7574i	−1.15090	−	1.15090i
$213$	25.1220	−	25.1220i	1.72133	−	1.72133i
$214$	11.6249	+	11.6249i	0.794663	+	0.794663i
$215$	4.08596	+	4.08596i	0.278660	+	0.278660i
$216$	1.58933	+	1.58933i	0.108140	+	0.108140i
$217$			0.0219335i			0.00148895i
$218$	5.90462	+	5.90462i	0.399911	+	0.399911i
$219$	−15.8049			−1.06800
$220$	−20.6209	+	37.0795i	−1.39026	+	2.49990i
$221$	0.142337	+	0.142337i	0.00957464	+	0.00957464i
$222$	49.5751			3.32726
$223$	−15.8894	+	15.8894i	−1.06403	+	1.06403i	−0.0662257	+	0.997805i	$0.521096\pi$
$223$	−15.8894	+	15.8894i	−1.06403	+	1.06403i	−0.997805	+	0.0662257i	$0.978904\pi$
$224$			0.00280335i			0.000187307i
$225$	16.1939			1.07960
$226$	−13.3826	+	13.3826i	−0.890200	+	0.890200i
$227$	−7.32522	−	7.32522i	−0.486192	−	0.486192i	0.420910	−	0.907102i	$-0.361711\pi$
$227$	−7.32522	−	7.32522i	−0.486192	−	0.486192i	−0.907102	+	0.420910i	$0.861711\pi$
$228$	−46.3287			−3.06819
$229$		−	12.0085i		−	0.793542i	−0.917918	−	0.396771i	$-0.870131\pi$
$229$		−	12.0085i		−	0.793542i	0.917918	−	0.396771i	$-0.129869\pi$
$230$		−	21.1639i		−	1.39551i
$231$	−0.0235090	−	0.0824175i	−0.00154678	−	0.00542267i
$232$			33.5098i			2.20003i
$233$	−16.6700	−	16.6700i	−1.09209	−	1.09209i	−0.995306	−	0.0967816i	$-0.969145\pi$
$233$	−16.6700	−	16.6700i	−1.09209	−	1.09209i	−0.0967816	−	0.995306i	$-0.530855\pi$
$234$	29.2710	−	29.2710i	1.91350	−	1.91350i
$235$			20.9787i			1.36850i
$236$	40.2545	−	40.2545i	2.62034	−	2.62034i
$237$	−18.8572	+	18.8572i	−1.22490	+	1.22490i
$238$	0.000685324	0	0.000685324i	4.44230e−5	0	4.44230e-5i
$239$			4.59417i			0.297172i	0.988899	+	0.148586i	$0.0474722\pi$
$239$			4.59417i			0.297172i	−0.988899	+	0.148586i	$0.952528\pi$
$240$	−32.8888			−2.12296
$241$			2.89567i			0.186526i	0.995641	+	0.0932631i	$0.0297298\pi$
$241$			2.89567i			0.186526i	−0.995641	+	0.0932631i	$0.970270\pi$
$242$	−6.14797	+	26.2965i	−0.395207	+	1.69040i
$243$			22.2946i			1.43020i
$244$	17.6300	−	26.0489i	1.12864	−	1.66761i
$245$	22.2348			1.42053
$246$	−4.91052	+	4.91052i	−0.313083	+	0.313083i
$247$			24.5204i			1.56019i
$248$	10.5033			0.666961
$249$	25.3791			1.60833
$250$	−0.495260	+	0.495260i	−0.0313230	+	0.0313230i
$251$	9.02764	−	9.02764i	0.569819	−	0.569819i	−0.362258	−	0.932078i	$-0.617994\pi$
$251$	9.02764	−	9.02764i	0.569819	−	0.569819i	0.932078	+	0.362258i	$0.117994\pi$
$252$	0.0941683	−	0.0941683i	0.00593204	−	0.00593204i
$253$	−2.46900	−	8.65575i	−0.155224	−	0.544182i
$254$	19.5183	+	19.5183i	1.22469	+	1.22469i
$255$	−0.212115	+	0.212115i	−0.0132832	+	0.0132832i
$256$	−32.2002			−2.01251
$257$	−27.3162			−1.70394			−0.851969	−	0.523592i	$-0.824592\pi$
$257$	−27.3162			−1.70394			−0.851969	+	0.523592i	$0.824592\pi$
$258$			11.1040i			0.691306i
$259$		−	0.0844127i		−	0.00524515i
$260$			67.7944i			4.20443i
$261$	15.1472	−	15.1472i	0.937590	−	0.937590i
$262$	23.3520	−	23.3520i	1.44269	−	1.44269i
$263$	−3.13762			−0.193474			−0.0967370	−	0.995310i	$-0.530841\pi$
$263$	−3.13762			−0.193474			−0.0967370	+	0.995310i	$0.530841\pi$
$264$	−39.4672	+	11.2578i	−2.42904	+	0.692868i
$265$	−13.2171	−	13.2171i	−0.811920	−	0.811920i
$266$			0.118060i			0.00723875i
$267$	−22.0112	+	22.0112i	−1.34707	+	1.34707i
$268$	17.8449	−	17.8449i	1.09005	−	1.09005i
$269$	−18.1883			−1.10896			−0.554479	−	0.832198i	$-0.687082\pi$
$269$	−18.1883			−1.10896			−0.554479	+	0.832198i	$0.687082\pi$
$270$	2.49025	+	2.49025i	0.151552	+	0.151552i
$271$	6.12423			0.372021			0.186010	−	0.982548i	$-0.440444\pi$
$271$	6.12423			0.372021			0.186010	+	0.982548i	$0.440444\pi$
$272$	0.111849	−	0.111849i	0.00678186	−	0.00678186i
$273$	−0.0968355	−	0.0968355i	−0.00586075	−	0.00586075i
$274$	−22.6434	−	22.6434i	−1.36794	−	1.36794i
$275$	−8.20456	+	14.7531i	−0.494754	+	0.889644i
$276$	19.2151	−	19.2151i	1.15661	−	1.15661i
$277$	−15.5723	−	15.5723i	−0.935651	−	0.935651i	0.0624002	−	0.998051i	$-0.480124\pi$
$277$	−15.5723	−	15.5723i	−0.935651	−	0.935651i	−0.998051	+	0.0624002i	$0.980124\pi$
$278$	−0.873069			−0.0523632
$279$	−4.74774	−	4.74774i	−0.284240	−	0.284240i
$280$			0.164313i			0.00981961i
$281$	20.3335	−	20.3335i	1.21299	−	1.21299i	0.242958	−	0.970037i	$-0.421882\pi$
$281$	20.3335	−	20.3335i	1.21299	−	1.21299i	0.970037	−	0.242958i	$-0.0781177\pi$
$282$	−28.5058	+	28.5058i	−1.69750	+	1.69750i
$283$	−1.23697			−0.0735301			−0.0367650	−	0.999324i	$-0.511705\pi$
$283$	−1.23697			−0.0735301			−0.0367650	+	0.999324i	$0.511705\pi$
$284$	−40.6925	+	40.6925i	−2.41465	+	2.41465i
$285$	−36.5410			−2.16450
$286$	11.8366	+	41.4965i	0.699914	+	2.45374i
$287$	0.00836127	+	0.00836127i	0.000493550	+	0.000493550i
$288$	−0.606814	−	0.606814i	−0.0357569	−	0.0357569i
$289$			16.9986i			0.999915i
$290$			52.5049i			3.08320i
$291$	−22.0969			−1.29535
$292$	25.6007			1.49817
$293$	20.9616			1.22459			0.612296	−	0.790628i	$-0.290246\pi$
$293$	20.9616			1.22459			0.612296	+	0.790628i	$0.290246\pi$
$294$	30.2126	+	30.2126i	1.76204	+	1.76204i
$295$	31.7500	−	31.7500i	1.84856	−	1.84856i
$296$	−40.4227			−2.34952
$297$	1.30899	+	0.727963i	0.0759553	+	0.0422407i
$298$	3.63511	+	3.63511i	0.210576	+	0.210576i
$299$	−10.1700	−	10.1700i	−0.588145	−	0.588145i
$300$	−50.9642			−2.94242
$301$	0.0189071			0.00108979
$302$	−30.6876			−1.76587
$303$	21.1098	−	21.1098i	1.21273	−	1.21273i
$304$	19.2682			1.10511
$305$	13.9053	−	20.5456i	0.796216	−	1.17644i
$306$	−0.296691			−0.0169607
$307$	9.77021	+	9.77021i	0.557615	+	0.557615i	0.928628	−	0.371013i	$-0.120989\pi$
$307$	9.77021	+	9.77021i	0.557615	+	0.557615i	−0.371013	+	0.928628i	$0.620989\pi$
$308$	0.0380798	+	0.133499i	0.00216980	+	0.00760684i
$309$		−	35.8862i		−	2.04149i
$310$	16.4571			0.934702
$311$	−17.1305	−	17.1305i	−0.971384	−	0.971384i	0.0282175	−	0.999602i	$-0.491017\pi$
$311$	−17.1305	−	17.1305i	−0.971384	−	0.971384i	−0.999602	+	0.0282175i	$0.991017\pi$
$312$	−46.3716	+	46.3716i	−2.62527	+	2.62527i
$313$	17.4152	+	17.4152i	0.984368	+	0.984368i	0.999880	−	0.0155118i	$-0.00493775\pi$
$313$	17.4152	+	17.4152i	0.984368	+	0.984368i	−0.0155118	+	0.999880i	$0.504938\pi$
$314$		−	5.00106i		−	0.282226i
$315$	0.0742736	−	0.0742736i	0.00418484	−	0.00418484i
$316$	30.5448	−	30.5448i	1.71828	−	1.71828i
$317$	5.23554			0.294057			0.147029	−	0.989132i	$-0.453029\pi$
$317$	5.23554			0.294057			0.147029	+	0.989132i	$0.453029\pi$
$318$		−	35.9188i		−	2.01423i
$319$	6.12525	+	21.4738i	0.342948	+	1.20230i
$320$	−24.3527			−1.36136
$321$			16.6493i			0.929274i
$322$	−0.0489663	−	0.0489663i	−0.00272878	−	0.00272878i
$323$	0.124270	−	0.124270i	0.00691455	−	0.00691455i
$324$		−	33.9181i		−	1.88434i
$325$			26.9738i			1.49624i
$326$	23.8107	−	23.8107i	1.31875	−	1.31875i
$327$			8.45665i			0.467654i
$328$	4.00396	−	4.00396i	0.221082	−	0.221082i
$329$	0.0485376	+	0.0485376i	0.00267596	+	0.00267596i
$330$	−61.8393	+	17.6393i	−3.40414	+	0.971009i
$331$	17.7279	−	17.7279i	0.974413	−	0.974413i	−0.0252681	−	0.999681i	$-0.508044\pi$
$331$	17.7279	−	17.7279i	0.974413	−	0.974413i	0.999681	+	0.0252681i	$0.00804395\pi$
$332$	−41.1089			−2.25614
$333$	18.2720	+	18.2720i	1.00130	+	1.00130i
$334$	−18.8788	−	18.8788i	−1.03300	−	1.03300i
$335$	14.0748	−	14.0748i	0.768991	−	0.768991i
$336$	−0.0760937	+	0.0760937i	−0.00415125	+	0.00415125i
$337$	11.3419	+	11.3419i	0.617834	+	0.617834i	0.944976	−	0.327141i	$-0.106085\pi$
$337$	11.3419	+	11.3419i	0.617834	+	0.617834i	−0.327141	+	0.944976i	$0.606085\pi$
$338$	26.1881	+	26.1881i	1.42444	+	1.42444i
$339$	−19.1667			−1.04099
$340$	0.343583	−	0.343583i	0.0186334	−	0.0186334i
$341$	6.73073	−	1.91990i	0.364489	−	0.103968i
$342$	−25.5554	−	25.5554i	−1.38188	−	1.38188i
$343$	0.102888	−	0.102888i	0.00555546	−	0.00555546i
$344$		−	9.05404i		−	0.488161i
$345$	15.1556	−	15.1556i	0.815949	−	0.815949i
$346$		−	12.8878i		−	0.692852i
$347$			19.3444i			1.03846i	0.854633	+	0.519232i	$0.173782\pi$
$347$			19.3444i			1.03846i	−0.854633	+	0.519232i	$0.826218\pi$
$348$	−47.6701	+	47.6701i	−2.55539	+	2.55539i
$349$	23.6851	+	23.6851i	1.26784	+	1.26784i	0.947204	+	0.320632i	$0.103895\pi$
$349$	23.6851	+	23.6851i	1.26784	+	1.26784i	0.320632	+	0.947204i	$0.396105\pi$
$350$			0.129873i			0.00694202i
$351$	2.39329			0.127745
$352$	0.860262	−	0.245384i	0.0458521	−	0.0130790i
$353$			5.72943i			0.304947i	0.988308	+	0.152473i	$0.0487238\pi$
$353$			5.72943i			0.304947i	−0.988308	+	0.152473i	$0.951276\pi$
$354$	86.2839			4.58594
$355$	−32.0955	+	32.0955i	−1.70345	+	1.70345i
$356$	35.6537	−	35.6537i	1.88964	−	1.88964i
$357$		0	0.000981526i		0	5.19479e-5i
$358$	−16.3342	−	16.3342i	−0.863288	−	0.863288i
$359$	11.4531	−	11.4531i	0.604472	−	0.604472i	−0.337024	−	0.941496i	$-0.609420\pi$
$359$	11.4531	−	11.4531i	0.604472	−	0.604472i	0.941496	+	0.337024i	$0.109420\pi$
$360$	−35.5674	−	35.5674i	−1.87456	−	1.87456i
$361$	2.40787			0.126730
$362$		−	2.75111i		−	0.144595i
$363$	−23.2336	+	14.4284i	−1.21945	+	0.757295i
$364$	0.156854	+	0.156854i	0.00822136	+	0.00822136i
$365$	20.1921			1.05690
$366$	46.8119	−	9.02279i	2.44690	−	0.471629i
$367$	31.4351			1.64090			0.820449	−	0.571719i	$-0.193723\pi$
$367$	31.4351			1.64090			0.820449	+	0.571719i	$0.193723\pi$
$368$	−7.99161	+	7.99161i	−0.416591	+	0.416591i
$369$	−3.61977			−0.188437
$370$	−63.3364			−3.29270
$371$	−0.0611599			−0.00317526
$372$	14.9417	+	14.9417i	0.774691	+	0.774691i
$373$	−17.8638	−	17.8638i	−0.924951	−	0.924951i	0.0724226	−	0.997374i	$-0.476927\pi$
$373$	−17.8638	−	17.8638i	−0.924951	−	0.924951i	−0.997374	+	0.0724226i	$0.976927\pi$
$374$	0.150317	−	0.270293i	0.00777269	−	0.0139765i
$375$	−0.709315			−0.0366289
$376$	23.2432	−	23.2432i	1.19868	−	1.19868i
$377$	25.2304	+	25.2304i	1.29943	+	1.29943i
$378$	0.0115232			0.000592690
$379$	−8.48815			−0.436007			−0.218003	−	0.975948i	$-0.569954\pi$
$379$	−8.48815			−0.436007			−0.218003	+	0.975948i	$0.569954\pi$
$380$	59.1889			3.03633
$381$			27.9543i			1.43214i
$382$			19.8125i			1.01369i
$383$	−9.12562	−	9.12562i	−0.466297	−	0.466297i	0.434415	−	0.900713i	$-0.356955\pi$
$383$	−9.12562	−	9.12562i	−0.466297	−	0.466297i	−0.900713	+	0.434415i	$0.856955\pi$
$384$	−34.0389	−	34.0389i	−1.73704	−	1.73704i
$385$	0.0300348	+	0.105295i	0.00153072	+	0.00536635i
$386$	−37.8068			−1.92431
$387$	−4.09264	+	4.09264i	−0.208041	+	0.208041i
$388$	35.7925			1.81709
$389$	−15.3327	+	15.3327i	−0.777399	+	0.777399i	−0.979388	−	0.201989i	$-0.935260\pi$
$389$	−15.3327	+	15.3327i	−0.777399	+	0.777399i	0.201989	+	0.979388i	$0.435260\pi$
$390$	−72.6574	+	72.6574i	−3.67915	+	3.67915i
$391$			0.103083i			0.00521313i
$392$	−24.6349	−	24.6349i	−1.24425	−	1.24425i
$393$	33.4449			1.68707
$394$	−29.6028	−	29.6028i	−1.49137	−	1.49137i
$395$	24.0916	−	24.0916i	1.21218	−	1.21218i
$396$	−37.1401	−	20.6546i	−1.86636	−	1.03793i
$397$	0.154129	+	0.154129i	0.00773552	+	0.00773552i	0.710964	−	0.703228i	$-0.248259\pi$
$397$	0.154129	+	0.154129i	0.00773552	+	0.00773552i	−0.703228	+	0.710964i	$0.748259\pi$
$398$	−34.9713	−	34.9713i	−1.75295	−	1.75295i
$399$	−0.0845436	+	0.0845436i	−0.00423247	+	0.00423247i
$400$	21.1962			1.05981
$401$	10.3282	+	10.3282i	0.515767	+	0.515767i	0.916288	−	0.400521i	$-0.131171\pi$
$401$	10.3282	+	10.3282i	0.515767	+	0.515767i	−0.400521	+	0.916288i	$0.631171\pi$
$402$	38.2498			1.90773
$403$	7.90819	−	7.90819i	0.393935	−	0.393935i
$404$	−34.1936	+	34.1936i	−1.70119	+	1.70119i
$405$		−	26.7523i		−	1.32933i
$406$	0.121479	+	0.121479i	0.00602889	+	0.00602889i
$407$	−25.9037	+	7.38885i	−1.28400	+	0.366252i
$408$	0.470023			0.0232696
$409$	−18.7576	+	18.7576i	−0.927505	+	0.927505i	−0.997544	−	0.0700388i	$-0.977688\pi$
$409$	−18.7576	+	18.7576i	−0.927505	+	0.927505i	0.0700388	+	0.997544i	$0.477688\pi$
$410$	6.27360	−	6.27360i	0.309831	−	0.309831i
$411$		−	32.4301i		−	1.59966i
$412$			58.1283i			2.86377i
$413$		−	0.146918i		−	0.00722936i
$414$	21.1985			1.04185
$415$	−32.4239			−1.59163
$416$	1.01076	−	1.01076i	0.0495563	−	0.0495563i
$417$	−0.625208	−	0.625208i	−0.0306166	−	0.0306166i
$418$	36.2291	−	10.3341i	1.77202	−	0.505458i
$419$	1.93896	−	1.93896i	0.0947244	−	0.0947244i	−0.658157	−	0.752881i	$-0.728664\pi$
$419$	1.93896	−	1.93896i	0.0947244	−	0.0947244i	0.752881	+	0.658157i	$0.228664\pi$
$420$	−0.233748	+	0.233748i	−0.0114057	+	0.0114057i
$421$	9.12896	−	9.12896i	0.444918	−	0.444918i	−0.448743	−	0.893661i	$-0.648128\pi$
$421$	9.12896	−	9.12896i	0.444918	−	0.444918i	0.893661	+	0.448743i	$0.148128\pi$
$422$	−23.7346			−1.15538
$423$	−21.0129			−1.02168
$424$			29.2876i			1.42233i
$425$	0.136704	−	0.136704i	0.00663110	−	0.00663110i
$426$	−87.2228			−4.22596
$427$	−0.0153633	−	0.0797078i	−0.000743484	−	0.00385733i
$428$		−	26.9685i		−	1.30357i
$429$	−21.2396	+	38.1921i	−1.02546	+	1.84393i
$430$		−	14.1863i		−	0.684126i
$431$	2.60315			0.125389			0.0626947	−	0.998033i	$-0.480031\pi$
$431$	2.60315			0.125389			0.0626947	+	0.998033i	$0.480031\pi$
$432$		−	1.88066i		−	0.0904834i
$433$	17.5910	+	17.5910i	0.845371	+	0.845371i	0.989551	−	0.144180i	$-0.0460545\pi$
$433$	17.5910	+	17.5910i	0.845371	+	0.845371i	−0.144180	+	0.989551i	$0.546055\pi$
$434$	0.0380763	−	0.0380763i	0.00182772	−	0.00182772i
$435$	−37.5990	+	37.5990i	−1.80273	+	1.80273i
$436$		−	13.6980i		−	0.656017i
$437$	−8.87904	+	8.87904i	−0.424742	+	0.424742i
$438$	27.4371	+	27.4371i	1.31099	+	1.31099i
$439$			34.7787i			1.65990i	0.557839	+	0.829949i	$0.311631\pi$
$439$			34.7787i			1.65990i	−0.557839	+	0.829949i	$0.688369\pi$
$440$	50.4227	−	14.3828i	2.40381	−	0.685671i
$441$			22.2711i			1.06053i
$442$		−	0.494190i		−	0.0235062i
$443$	12.7329			0.604960			0.302480	−	0.953156i	$-0.402185\pi$
$443$	12.7329			0.604960			0.302480	+	0.953156i	$0.402185\pi$
$444$	−57.5042	−	57.5042i	−2.72903	−	2.72903i
$445$	28.1212	−	28.1212i	1.33307	−	1.33307i
$446$	55.1674			2.61225
$447$			5.20624i			0.246247i
$448$	−0.0563441	+	0.0563441i	−0.00266201	+	0.00266201i
$449$	22.0350			1.03989			0.519947	−	0.854198i	$-0.325952\pi$
$449$	22.0350			1.03989			0.519947	+	0.854198i	$0.325952\pi$
$450$	−28.1124	−	28.1124i	−1.32523	−	1.32523i
$451$	1.83393	−	3.29770i	0.0863565	−	0.155282i
$452$	31.0462			1.46029
$453$	−21.9755	−	21.9755i	−1.03250	−	1.03250i
$454$			25.4329i			1.19363i
$455$	0.123716	+	0.123716i	0.00579987	+	0.00579987i
$456$	40.4854	+	40.4854i	1.89590	+	1.89590i
$457$	14.6250	+	14.6250i	0.684128	+	0.684128i	0.960928	−	0.276800i	$-0.0892738\pi$
$457$	14.6250	+	14.6250i	0.684128	+	0.684128i	−0.276800	+	0.960928i	$0.589274\pi$
$458$	−20.8465	+	20.8465i	−0.974093	+	0.974093i
$459$	−0.0121292	−	0.0121292i	−0.000566145	−	0.000566145i
$460$	−24.5489	+	24.5489i	−1.14460	+	1.14460i
$461$			39.2401i			1.82759i	0.406172	+	0.913797i	$0.366864\pi$
$461$			39.2401i			1.82759i	−0.406172	+	0.913797i	$0.633136\pi$
$462$	−0.102264	+	0.183887i	−0.00475776	+	0.00855519i
$463$		−	40.6012i		−	1.88690i	−0.331519	−	0.943449i	$-0.607561\pi$
$463$		−	40.6012i		−	1.88690i	0.331519	−	0.943449i	$-0.392439\pi$
$464$	19.8261	−	19.8261i	0.920405	−	0.920405i
$465$	11.7850	+	11.7850i	0.546517	+	0.546517i
$466$			57.8777i			2.68113i
$467$	−0.276779	+	0.276779i	−0.0128078	+	0.0128078i	−0.713482	−	0.700674i	$-0.752883\pi$
$467$	−0.276779	+	0.276779i	−0.0128078	+	0.0128078i	0.700674	+	0.713482i	$0.252883\pi$
$468$	−67.9052			−3.13892
$469$		−	0.0651289i		−	0.00300737i
$470$	36.4186	−	36.4186i	1.67987	−	1.67987i
$471$	3.58128	−	3.58128i	0.165017	−	0.165017i
$472$	−70.3545			−3.23833
$473$	−1.65498	−	5.80201i	−0.0760963	−	0.266777i
$474$	65.4715			3.00721
$475$	23.5499			1.08054
$476$		−	0.00158987i		−	7.28717e-5i
$477$	13.2387	−	13.2387i	0.606158	−	0.606158i
$478$	7.97541	−	7.97541i	0.364787	−	0.364787i
$479$	43.4139			1.98363			0.991815	−	0.127680i	$-0.0407529\pi$
$479$	43.4139			1.98363			0.991815	+	0.127680i	$0.0407529\pi$
$480$	1.50626	+	1.50626i	0.0687508	+	0.0687508i
$481$	−30.4352	+	30.4352i	−1.38773	+	1.38773i
$482$	5.02683	−	5.02683i	0.228966	−	0.228966i
$483$		−	0.0701299i		−	0.00319102i
$484$	37.6336	−	23.3711i	1.71062	−	1.06232i
$485$	28.2307			1.28189
$486$	38.7030	−	38.7030i	1.75561	−	1.75561i
$487$		−	34.8788i		−	1.58051i	−0.612778	−	0.790255i	$-0.709948\pi$
$487$		−	34.8788i		−	1.58051i	0.612778	−	0.790255i	$-0.290052\pi$
$488$	−38.1697	+	7.35704i	−1.72786	+	0.333037i
$489$	34.1019			1.54214
$490$	−38.5992	−	38.5992i	−1.74374	−	1.74374i
$491$	6.21391			0.280430			0.140215	−	0.990121i	$-0.455221\pi$
$491$	6.21391			0.280430			0.140215	+	0.990121i	$0.455221\pi$
$492$	11.3918			0.513583
$493$		−	0.255735i		−	0.0115177i
$494$	42.5670	−	42.5670i	1.91518	−	1.91518i
$495$	−29.2936	−	16.2909i	−1.31665	−	0.732223i
$496$	−6.21429	−	6.21429i	−0.279030	−	0.279030i
$497$			0.148516i			0.00666187i
$498$	−44.0577	−	44.0577i	−1.97427	−	1.97427i
$499$	16.3087	+	16.3087i	0.730080	+	0.730080i	0.970635	−	0.240556i	$-0.0773297\pi$
$499$	16.3087	+	16.3087i	0.730080	+	0.730080i	−0.240556	+	0.970635i	$0.577330\pi$
$500$	1.14894			0.0513824
$501$		−	27.0383i		−	1.20798i
$502$	−31.3437			−1.39894
$503$		−	24.7817i		−	1.10496i	−0.833526	−	0.552480i	$-0.813681\pi$
$503$		−	24.7817i		−	1.10496i	0.833526	−	0.552480i	$-0.186319\pi$
$504$	−0.164582			−0.00733106
$505$	−26.9696	+	26.9696i	−1.20013	+	1.20013i
$506$	−10.7401	+	19.3124i	−0.477456	+	0.858540i
$507$			37.5068i			1.66573i
$508$		−	45.2803i		−	2.00899i
$509$	−24.2404	−	24.2404i	−1.07444	−	1.07444i	−0.996997	−	0.0774419i	$-0.975325\pi$
$509$	−24.2404	−	24.2404i	−1.07444	−	1.07444i	−0.0774419	−	0.996997i	$-0.524675\pi$
$510$	0.736457			0.0326108
$511$	0.0467178	−	0.0467178i	0.00206667	−	0.00206667i
$512$	28.5177	+	28.5177i	1.26032	+	1.26032i
$513$		−	2.08950i		−	0.0922537i
$514$	47.4205	+	47.4205i	2.09163	+	2.09163i
$515$			45.8477i			2.02029i
$516$	12.8800	−	12.8800i	0.567011	−	0.567011i
$517$	10.6461	−	19.1433i	0.468214	−	0.841922i
$518$	−0.146539	+	0.146539i	−0.00643856	+	0.00643856i
$519$	9.22900	−	9.22900i	0.405108	−	0.405108i
$520$	59.2436	−	59.2436i	2.59800	−	2.59800i
$521$	20.9543	−	20.9543i	0.918024	−	0.918024i	−0.0788618	−	0.996886i	$-0.525129\pi$
$521$	20.9543	−	20.9543i	0.918024	−	0.918024i	0.996886	+	0.0788618i	$0.0251286\pi$
$522$	−52.5907			−2.30183
$523$	−12.1611	+	12.1611i	−0.531767	+	0.531767i	−0.921098	−	0.389331i	$-0.872706\pi$
$523$	−12.1611	+	12.1611i	−0.531767	+	0.531767i	0.389331	+	0.921098i	$0.372706\pi$
$524$	−54.1740			−2.36660
$525$	−0.0930028	+	0.0930028i	−0.00405897	+	0.00405897i
$526$	5.44686	+	5.44686i	0.237494	+	0.237494i
$527$	−0.0801576			−0.00349172
$528$	30.0115	+	16.6902i	1.30608	+	0.726346i
$529$			15.6347i			0.679771i
$530$			45.8893i			1.99331i
$531$	31.8019	+	31.8019i	1.38008	+	1.38008i
$532$	0.136943	−	0.136943i	0.00593724	−	0.00593724i
$533$		−	6.02935i		−	0.261160i
$534$	76.4223			3.30712
$535$		−	21.2709i		−	0.919621i
$536$	−31.1883			−1.34713
$537$		−	23.3939i		−	1.00952i
$538$	31.5745	+	31.5745i	1.36127	+	1.36127i
$539$	−20.2895	−	11.2835i	−0.873932	−	0.486016i
$540$		−	5.77709i		−	0.248606i
$541$	1.95287	+	1.95287i	0.0839605	+	0.0839605i	0.747840	−	0.663879i	$-0.231091\pi$
$541$	1.95287	+	1.95287i	0.0839605	+	0.0839605i	−0.663879	+	0.747840i	$0.731091\pi$
$542$	−10.6316	−	10.6316i	−0.456665	−	0.456665i
$543$	1.97008	−	1.97008i	0.0845442	−	0.0845442i
$544$	−0.0102450			−0.000439252
$545$		−	10.8041i		−	0.462796i
$546$			0.336210i			0.0143884i
$547$	29.5595	−	29.5595i	1.26387	−	1.26387i	0.314670	−	0.949201i	$-0.398106\pi$
$547$	29.5595	−	29.5595i	1.26387	−	1.26387i	0.949201	−	0.314670i	$-0.101894\pi$
$548$			52.5301i			2.24398i
$549$	20.5791	+	13.9280i	0.878297	+	0.594434i
$550$	39.8541	−	11.3681i	1.69938	−	0.484738i
$551$	22.0277	−	22.0277i	0.938412	−	0.938412i
$552$	−33.5831			−1.42939
$553$		−	0.111480i		−	0.00474061i
$554$			54.0667i			2.29707i
$555$	−45.3554	−	45.3554i	−1.92523	−	1.92523i
$556$	1.01271	+	1.01271i	0.0429484	+	0.0429484i
$557$	17.0911	−	17.0911i	0.724174	−	0.724174i	−0.245279	−	0.969453i	$-0.578880\pi$
$557$	17.0911	−	17.0911i	0.724174	−	0.724174i	0.969453	+	0.245279i	$0.0788795\pi$
$558$			16.4840i			0.697824i
$559$	−6.81700	−	6.81700i	−0.288328	−	0.288328i
$560$	0.0972162	−	0.0972162i	0.00410814	−	0.00410814i
$561$	0.301200	−	0.0859154i	0.0127167	−	0.00362735i
$562$	−70.5973			−2.97797
$563$	37.3213			1.57290			0.786452	−	0.617651i	$-0.211916\pi$
$563$	37.3213			1.57290			0.786452	+	0.617651i	$0.211916\pi$
$564$	66.1302			2.78458
$565$	24.4871			1.03018
$566$	2.14735	+	2.14735i	0.0902600	+	0.0902600i
$567$	−0.0618960	−	0.0618960i	−0.00259939	−	0.00259939i
$568$	71.1200			2.98413
$569$			24.2432i			1.01633i	0.861261	+	0.508163i	$0.169675\pi$
$569$			24.2432i			1.01633i	−0.861261	+	0.508163i	$0.830325\pi$
$570$	63.4345	+	63.4345i	2.65698	+	2.65698i
$571$			45.2250i			1.89261i	0.323281	+	0.946303i	$0.395214\pi$
$571$			45.2250i			1.89261i	−0.323281	+	0.946303i	$0.604786\pi$
$572$	34.4038	−	61.8633i	1.43849	−	2.58664i
$573$	−14.1878	+	14.1878i	−0.592703	+	0.592703i
$574$		−	0.0290300i		−	0.00121169i
$575$	−9.76745	+	9.76745i	−0.407331	+	0.407331i
$576$		−	24.3925i		−	1.01636i
$577$	−14.2075	−	14.2075i	−0.591467	−	0.591467i	0.346561	−	0.938027i	$-0.387349\pi$
$577$	−14.2075	−	14.2075i	−0.591467	−	0.591467i	−0.938027	+	0.346561i	$0.887349\pi$
$578$	29.5092	−	29.5092i	1.22742	−	1.22742i
$579$	−27.0736	−	27.0736i	−1.12514	−	1.12514i
$580$	60.9026	−	60.9026i	2.52884	−	2.52884i
$581$	−0.0750181	+	0.0750181i	−0.00311228	+	0.00311228i
$582$	38.3599	+	38.3599i	1.59007	+	1.59007i
$583$	5.35347	+	18.7681i	0.221718	+	0.777294i
$584$	−22.3717	−	22.3717i	−0.925749	−	0.925749i
$585$	−53.5590			−2.21439
$586$	−36.3891	−	36.3891i	−1.50322	−	1.50322i
$587$	8.46447	+	8.46447i	0.349366	+	0.349366i	0.859873	−	0.510507i	$-0.170542\pi$
$587$	8.46447	+	8.46447i	0.349366	+	0.349366i	−0.510507	+	0.859873i	$0.670542\pi$
$588$		−	70.0898i		−	2.89046i
$589$	−6.90436	−	6.90436i	−0.284489	−	0.284489i
$590$	−110.235			−4.53831
$591$		−	42.3974i		−	1.74399i
$592$	23.9161	+	23.9161i	0.982947	+	0.982947i
$593$	−11.8463	−	11.8463i	−0.486471	−	0.486471i	0.420720	−	0.907191i	$-0.361778\pi$
$593$	−11.8463	−	11.8463i	−0.486471	−	0.486471i	−0.907191	+	0.420720i	$0.861778\pi$
$594$	−1.00865	−	3.53612i	−0.0413856	−	0.145089i
$595$		−	0.00125398i		−	5.14083e-5i
$596$		−	8.43304i		−	0.345431i
$597$		−	50.0862i		−	2.04989i
$598$			35.3098i			1.44393i
$599$	−0.984815	+	0.984815i	−0.0402385	+	0.0402385i	−0.726940	−	0.686701i	$-0.759058\pi$
$599$	−0.984815	+	0.984815i	−0.0402385	+	0.0402385i	0.686701	+	0.726940i	$0.259058\pi$
$600$	44.5362	+	44.5362i	1.81818	+	1.81818i
$601$	−35.9873			−1.46795			−0.733977	−	0.679174i	$-0.762338\pi$
$601$	−35.9873			−1.46795			−0.733977	+	0.679174i	$0.762338\pi$
$602$	−0.0328224	−	0.0328224i	−0.00133774	−	0.00133774i
$603$	14.0978	+	14.0978i	0.574108	+	0.574108i
$604$	35.5958	+	35.5958i	1.44837	+	1.44837i
$605$	29.6829	−	18.4335i	1.20678	−	0.749429i
$606$	−73.2926			−2.97731
$607$		−	29.3610i		−	1.19173i	−0.803086	−	0.595863i	$-0.796810\pi$
$607$		−	29.3610i		−	1.19173i	0.803086	−	0.595863i	$-0.203190\pi$
$608$	−0.882454	−	0.882454i	−0.0357882	−	0.0357882i
$609$			0.173983i			0.00705014i
$610$	−59.8062	+	11.5274i	−2.42148	+	0.466730i
$611$		−	35.0007i		−	1.41598i
$612$	0.344144	+	0.344144i	0.0139112	+	0.0139112i
$613$	34.7764			1.40460			0.702302	−	0.711879i	$-0.252156\pi$
$613$	34.7764			1.40460			0.702302	+	0.711879i	$0.252156\pi$
$614$		−	33.9219i		−	1.36897i
$615$	8.98511			0.362314
$616$	0.0833845	−	0.149938i	0.00335966	−	0.00604118i
$617$	6.34379	−	6.34379i	0.255391	−	0.255391i	−0.567785	−	0.823177i	$-0.692200\pi$
$617$	6.34379	−	6.34379i	0.255391	−	0.255391i	0.823177	+	0.567785i	$0.192200\pi$
$618$	−62.2978	+	62.2978i	−2.50599	+	2.50599i
$619$	11.3174			0.454883			0.227442	−	0.973792i	$-0.426964\pi$
$619$	11.3174			0.454883			0.227442	+	0.973792i	$0.426964\pi$
$620$	−19.0893	−	19.0893i	−0.766645	−	0.766645i
$621$	0.866632	+	0.866632i	0.0347767	+	0.0347767i
$622$			59.4767i			2.38480i
$623$		−	0.130126i		−	0.00521340i
$624$	54.8716			2.19662
$625$	−24.5429			−0.981714
$626$		−	60.4652i		−	2.41667i
$627$	33.3441	+	18.5435i	1.33164	+	0.740557i
$628$	−5.80094	+	5.80094i	−0.231483	+	0.231483i
$629$	0.308492			0.0123004
$630$	−0.257875			−0.0102740
$631$	−4.77061	−	4.77061i	−0.189915	−	0.189915i	0.605744	−	0.795659i	$-0.292875\pi$
$631$	−4.77061	−	4.77061i	−0.189915	−	0.189915i	−0.795659	+	0.605744i	$0.792875\pi$
$632$	−53.3844			−2.12352
$633$	−16.9964	−	16.9964i	−0.675547	−	0.675547i
$634$	−9.08881	−	9.08881i	−0.360963	−	0.360963i
$635$		−	35.7140i		−	1.41727i
$636$	−41.6637	+	41.6637i	−1.65207	+	1.65207i
$637$	−37.0964			−1.46981
$638$	26.6448	−	47.9114i	1.05488	−	1.89683i
$639$	−32.1479	−	32.1479i	−1.27175	−	1.27175i
$640$	43.4876	+	43.4876i	1.71900	+	1.71900i
$641$	16.6041	+	16.6041i	0.655824	+	0.655824i	0.954389	−	0.298565i	$-0.0965081\pi$
$641$	16.6041	+	16.6041i	0.655824	+	0.655824i	−0.298565	+	0.954389i	$0.596508\pi$
$642$	28.9029	−	28.9029i	1.14071	−	1.14071i
$643$	−5.71586	+	5.71586i	−0.225411	+	0.225411i	−0.810773	−	0.585361i	$-0.800953\pi$
$643$	−5.71586	+	5.71586i	−0.225411	+	0.225411i	0.585361	+	0.810773i	$0.300953\pi$
$644$			0.113596i			0.00447631i
$645$	10.1589	−	10.1589i	0.400006	−	0.400006i
$646$	−0.431460			−0.0169756
$647$	−18.6580	−	18.6580i	−0.733520	−	0.733520i	0.237795	−	0.971315i	$-0.423575\pi$
$647$	−18.6580	−	18.6580i	−0.733520	−	0.733520i	−0.971315	+	0.237795i	$0.923575\pi$
$648$	−29.6401	+	29.6401i	−1.16437	+	1.16437i
$649$	−45.0846	+	12.8601i	−1.76972	+	0.504802i
$650$	46.8261	−	46.8261i	1.83667	−	1.83667i
$651$	0.0545331			0.00213732
$652$	−55.2381			−2.16329
$653$	−19.0990	−	19.0990i	−0.747402	−	0.747402i	0.226588	−	0.973991i	$-0.427243\pi$
$653$	−19.0990	−	19.0990i	−0.747402	−	0.747402i	−0.973991	+	0.226588i	$0.927243\pi$
$654$	14.6806	−	14.6806i	0.574057	−	0.574057i
$655$	−42.7288			−1.66955
$656$	−4.73789			−0.184984
$657$			20.2251i			0.789056i
$658$		−	0.168521i		−	0.00656963i
$659$	−35.1212			−1.36813			−0.684064	−	0.729422i	$-0.739789\pi$
$659$	−35.1212			−1.36813			−0.684064	+	0.729422i	$0.739789\pi$
$660$	92.1905	+	51.2695i	3.58851	+	1.99566i
$661$	−25.2570	+	25.2570i	−0.982382	+	0.982382i	−0.999847	−	0.0174651i	$-0.994440\pi$
$661$	−25.2570	+	25.2570i	−0.982382	+	0.982382i	0.0174651	+	0.999847i	$0.494440\pi$
$662$	−61.5506			−2.39223
$663$	0.353892	−	0.353892i	0.0137440	−	0.0137440i
$664$	35.9239	+	35.9239i	1.39412	+	1.39412i
$665$	0.108012	−	0.108012i	0.00418851	−	0.00418851i
$666$		−	63.4398i		−	2.45824i
$667$			18.2722i			0.707504i
$668$			43.7965i			1.69454i
$669$	39.5056	+	39.5056i	1.52737	+	1.52737i
$670$	−48.8674			−1.88791
$671$	−23.1151	+	11.6916i	−0.892348	+	0.451348i
$672$	0.00696994			0.000268871
$673$	6.92027	+	6.92027i	0.266757	+	0.266757i	0.827792	−	0.561035i	$-0.189597\pi$
$673$	6.92027	+	6.92027i	0.266757	+	0.266757i	−0.561035	+	0.827792i	$0.689597\pi$
$674$		−	39.3788i		−	1.51682i
$675$		−	2.29857i		−	0.0884720i
$676$		−	60.7533i		−	2.33666i
$677$	−24.3427	+	24.3427i	−0.935564	+	0.935564i	−0.998046	−	0.0624817i	$-0.980098\pi$
$677$	−24.3427	+	24.3427i	−0.935564	+	0.935564i	0.0624817	+	0.998046i	$0.480098\pi$
$678$	33.2731	+	33.2731i	1.27785	+	1.27785i
$679$	0.0653165	−	0.0653165i	0.00250662	−	0.00250662i
$680$	−0.600495			−0.0230279
$681$	−18.2126	+	18.2126i	−0.697909	+	0.697909i
$682$	−15.0173	−	8.35152i	−0.575044	−	0.319796i
$683$	−28.5702			−1.09321			−0.546605	−	0.837391i	$-0.684080\pi$
$683$	−28.5702			−1.09321			−0.546605	+	0.837391i	$0.684080\pi$
$684$			59.2856i			2.26684i
$685$			41.4322i			1.58304i
$686$	−0.357226			−0.0136389
$687$	−29.8565			−1.13910
$688$	−5.35683	+	5.35683i	−0.204227	+	0.204227i
$689$	22.0513	+	22.0513i	0.840089	+	0.840089i
$690$	−52.6197			−2.00320
$691$	−41.4039			−1.57508			−0.787538	−	0.616266i	$-0.788645\pi$
$691$	−41.4039			−1.57508			−0.787538	+	0.616266i	$0.788645\pi$
$692$	−14.9491	+	14.9491i	−0.568279	+	0.568279i
$693$	−0.105467	+	0.0300839i	−0.00400637	+	0.00114279i
$694$	33.5816	−	33.5816i	1.27474	−	1.27474i
$695$	0.798756	+	0.798756i	0.0302985	+	0.0302985i
$696$	83.3151			3.15805
$697$	−0.0305568	+	0.0305568i	−0.00115742	+	0.00115742i
$698$		−	82.2340i		−	3.11260i
$699$	−41.4464	+	41.4464i	−1.56765	+	1.56765i
$700$	0.150645	−	0.150645i	0.00569386	−	0.00569386i
$701$	−22.7231	−	22.7231i	−0.858238	−	0.858238i	0.132892	−	0.991130i	$-0.457574\pi$
$701$	−22.7231	−	22.7231i	−0.858238	−	0.858238i	−0.991130	+	0.132892i	$0.957574\pi$
$702$	−4.15472	−	4.15472i	−0.156810	−	0.156810i
$703$	26.5719	+	26.5719i	1.00218	+	1.00218i
$704$	22.2222	+	12.3583i	0.837531	+	0.465772i
$705$	52.1590			1.96442
$706$	9.94619	−	9.94619i	0.374330	−	0.374330i
$707$			0.124797i			0.00469348i
$708$	−100.084	−	100.084i	−3.76140	−	3.76140i
$709$	−10.5731	−	10.5731i	−0.397082	−	0.397082i	0.480121	−	0.877202i	$-0.340593\pi$
$709$	−10.5731	−	10.5731i	−0.397082	−	0.397082i	−0.877202	+	0.480121i	$0.840593\pi$
$710$	111.434			4.18206
$711$	24.1310	+	24.1310i	0.904983	+	0.904983i
$712$	−62.3135			−2.33530
$713$	5.72724			0.214487
$714$	0.00170391	−	0.00170391i	6.37674e−5	−	6.37674e-5i
$715$	27.1354	−	48.7936i	1.01481	−	1.82478i
$716$			37.8934i			1.41614i
$717$	11.4224			0.426579
$718$	−39.7648			−1.48401
$719$			9.08917i			0.338969i	0.985533	+	0.169484i	$0.0542102\pi$
$719$			9.08917i			0.338969i	−0.985533	+	0.169484i	$0.945790\pi$
$720$			42.0869i			1.56849i
$721$	0.106076	+	0.106076i	0.00395048	+	0.00395048i
$722$	−4.18003	−	4.18003i	−0.155565	−	0.155565i
$723$	7.19946			0.267751
$724$	−3.19113	+	3.19113i	−0.118597	+	0.118597i
$725$	24.2317	−	24.2317i	0.899944	−	0.899944i
$726$	65.3806	+	15.2856i	2.42650	+	0.567303i
$727$	−5.00780			−0.185729			−0.0928646	−	0.995679i	$-0.529602\pi$
$727$	−5.00780			−0.185729			−0.0928646	+	0.995679i	$0.529602\pi$
$728$		−	0.274140i		−	0.0101603i
$729$	30.1645			1.11720
$730$	−35.0532	−	35.0532i	−1.29738	−	1.29738i
$731$			0.0690973i			0.00255566i
$732$	−64.7650	−	43.8332i	−2.39378	−	1.62012i
$733$		−	31.4559i		−	1.16185i	−0.813957	−	0.580925i	$-0.802691\pi$
$733$		−	31.4559i		−	1.16185i	0.813957	−	0.580925i	$-0.197309\pi$
$734$	−54.5708	−	54.5708i	−2.01425	−	2.01425i
$735$		−	55.2821i		−	2.03911i
$736$	0.732006			0.0269821
$737$	−19.9861	+	5.70089i	−0.736196	+	0.209995i
$738$	6.28386	+	6.28386i	0.231312	+	0.231312i
$739$	32.2008	+	32.2008i	1.18453	+	1.18453i	0.978559	+	0.205967i	$0.0660339\pi$
$739$	32.2008	+	32.2008i	1.18453	+	1.18453i	0.205967	+	0.978559i	$0.433966\pi$
$740$	73.4665	+	73.4665i	2.70068	+	2.70068i
$741$	60.9648			2.23960
$742$	0.106173	+	0.106173i	0.00389772	+	0.00389772i
$743$	7.38142	−	7.38142i	0.270798	−	0.270798i	−0.558623	−	0.829421i	$-0.688670\pi$
$743$	7.38142	−	7.38142i	0.270798	−	0.270798i	0.829421	+	0.558623i	$0.188670\pi$
$744$		−	26.1143i		−	0.957395i
$745$		−	6.65141i		−	0.243689i
$746$			62.0225i			2.27080i
$747$		−	32.4769i		−	1.18827i
$748$	−0.487883	+	0.139165i	−0.0178388	+	0.00508839i
$749$	−0.0492138	−	0.0492138i	−0.00179823	−	0.00179823i
$750$	1.23136	+	1.23136i	0.0449629	+	0.0449629i
$751$			41.5823i			1.51736i	0.651464	+	0.758680i	$0.274155\pi$
$751$			41.5823i			1.51736i	−0.651464	+	0.758680i	$0.725845\pi$
$752$	−27.5037			−1.00296
$753$	−22.4453	−	22.4453i	−0.817953	−	0.817953i
$754$		−	87.5990i		−	3.19017i
$755$	28.0756	+	28.0756i	1.02177	+	1.02177i
$756$	−0.0133662	−	0.0133662i	−0.000486126	−	0.000486126i
$757$	25.5575			0.928902			0.464451	−	0.885599i	$-0.346252\pi$
$757$	25.5575			0.928902			0.464451	+	0.885599i	$0.346252\pi$
$758$	14.7353	+	14.7353i	0.535210	+	0.535210i
$759$	−21.5207	+	6.13864i	−0.781152	+	0.222818i
$760$	−51.7235	−	51.7235i	−1.87621	−	1.87621i
$761$	−4.79298	+	4.79298i	−0.173745	+	0.173745i	−0.788623	−	0.614877i	$-0.789205\pi$
$761$	−4.79298	+	4.79298i	−0.173745	+	0.173745i	0.614877	+	0.788623i	$0.289205\pi$
$762$	48.5283	−	48.5283i	1.75799	−	1.75799i
$763$	−0.0249970	−	0.0249970i	−0.000904954	−	0.000904954i
$764$	22.9813	−	22.9813i	0.831435	−	0.831435i
$765$	0.271438	+	0.271438i	0.00981385	+	0.00981385i
$766$			31.6838i			1.14478i
$767$	−52.9716	+	52.9716i	−1.91269	+	1.91269i
$768$			80.0590i			2.88888i
$769$	34.1502	−	34.1502i	1.23149	−	1.23149i	0.268098	−	0.963392i	$-0.413605\pi$
$769$	34.1502	−	34.1502i	1.23149	−	1.23149i	0.963392	−	0.268098i	$-0.0863950\pi$
$770$	0.130651	−	0.234931i	0.00470834	−	0.00846632i
$771$			67.9160i			2.44593i
$772$	43.8537	+	43.8537i	1.57833	+	1.57833i
$773$			27.6623i			0.994944i	0.867480	+	0.497472i	$0.165738\pi$
$773$			27.6623i			0.994944i	−0.867480	+	0.497472i	$0.834262\pi$
$774$	14.2095			0.510750
$775$	−7.59519	−	7.59519i	−0.272827	−	0.272827i
$776$	−31.2781	−	31.2781i	−1.12282	−	1.12282i
$777$	−0.209874			−0.00752920
$778$	53.2347			1.90855
$779$	−5.26401			−0.188603
$780$	168.557			6.03529
$781$	45.5751	−	13.0000i	1.63081	−	0.465177i
$782$	0.178951	−	0.178951i	0.00639926	−	0.00639926i
$783$	−2.15000	−	2.15000i	−0.0768347	−	0.0768347i
$784$			29.1505i			1.04109i
$785$	−4.57539	+	4.57539i	−0.163303	+	0.163303i
$786$	−58.0599	−	58.0599i	−2.07093	−	2.07093i
$787$	16.8151	+	16.8151i	0.599392	+	0.599392i	0.940151	−	0.340759i	$-0.110684\pi$
$787$	16.8151	+	16.8151i	0.599392	+	0.599392i	−0.340759	+	0.940151i	$0.610684\pi$
$788$			68.6750i			2.44645i
$789$			7.80104i			0.277724i
$790$	−83.6454			−2.97597
$791$	0.0566550	−	0.0566550i	0.00201442	−	0.00201442i
$792$	14.4063	+	50.5051i	0.511904	+	1.79462i
$793$	−23.1996	+	34.2781i	−0.823841	+	1.21725i
$794$		−	0.535131i		−	0.0189911i
$795$	−32.8615	+	32.8615i	−1.16548	+	1.16548i
$796$			81.1294i			2.87556i
$797$			43.2852i			1.53324i	0.642101	+	0.766620i	$0.278063\pi$
$797$			43.2852i			1.53324i	−0.642101	+	0.766620i	$0.721937\pi$
$798$	0.293533			0.0103909
$799$	−0.177384	+	0.177384i	−0.00627539	+	0.00627539i
$800$	−0.970750	−	0.970750i	−0.0343212	−	0.0343212i
$801$	28.1672	+	28.1672i	0.995239	+	0.995239i
$802$		−	35.8592i		−	1.26623i
$803$	−18.4256	−	10.2469i	−0.650224	−	0.361606i
$804$	−44.3675	−	44.3675i	−1.56472	−	1.56472i
$805$			0.0895969i			0.00315787i
$806$	−27.4570			−0.967131
$807$			45.2213i			1.59186i
$808$	59.7616			2.10241
$809$		−	2.02556i		−	0.0712150i	−0.999366	−	0.0356075i	$-0.988663\pi$
$809$		−	2.02556i		−	0.0712150i	0.999366	−	0.0356075i	$-0.0113366\pi$
$810$	−46.4416	+	46.4416i	−1.63179	+	1.63179i
$811$	−16.7320	−	16.7320i	−0.587540	−	0.587540i	0.349424	−	0.936965i	$-0.386377\pi$
$811$	−16.7320	−	16.7320i	−0.587540	−	0.587540i	−0.936965	+	0.349424i	$0.886377\pi$
$812$		−	0.281817i		−	0.00988983i
$813$		−	15.2266i		−	0.534021i
$814$	57.7953	+	32.1414i	2.02572	+	1.12656i
$815$	−43.5681			−1.52612
$816$	−0.278090	−	0.278090i	−0.00973509	−	0.00973509i
$817$	−5.95168	+	5.95168i	−0.208223	+	0.208223i
$818$	65.1259			2.27707
$819$	−0.123918	+	0.123918i	−0.00433003	+	0.00433003i
$820$	−14.5540			−0.508249
$821$	3.90359	−	3.90359i	0.136236	−	0.136236i	−0.635700	−	0.771936i	$-0.719288\pi$
$821$	3.90359	−	3.90359i	0.136236	−	0.136236i	0.771936	+	0.635700i	$0.219288\pi$
$822$	−56.2981	+	56.2981i	−1.96362	+	1.96362i
$823$	17.4068	−	17.4068i	0.606762	−	0.606762i	−0.335336	−	0.942099i	$-0.608850\pi$
$823$	17.4068	−	17.4068i	0.606762	−	0.606762i	0.942099	+	0.335336i	$0.108850\pi$
$824$	50.7966	−	50.7966i	1.76958	−	1.76958i
$825$	36.6804	+	20.3989i	1.27705	+	0.710199i
$826$	−0.255047	+	0.255047i	−0.00887422	+	0.00887422i
$827$		−	18.1909i		−	0.632558i	−0.948666	−	0.316279i	$-0.897566\pi$
$827$		−	18.1909i		−	0.632558i	0.948666	−	0.316279i	$-0.102434\pi$
$828$	−24.5890	−	24.5890i	−0.854528	−	0.854528i
$829$		−	10.2839i		−	0.357173i	−0.983924	−	0.178587i	$-0.942848\pi$
$829$		−	10.2839i		−	0.357173i	0.983924	−	0.178587i	$-0.0571525\pi$
$830$	56.2874	+	56.2874i	1.95376	+	1.95376i
$831$	−38.7173	+	38.7173i	−1.34309	+	1.34309i
$832$	40.6300			1.40859
$833$	0.188005	+	0.188005i	0.00651399	+	0.00651399i
$834$			2.17070i			0.0751652i
$835$			34.5437i			1.19544i
$836$	−54.0107	−	30.0367i	−1.86800	−	1.03884i
$837$	−0.673895	+	0.673895i	−0.0232932	+	0.0232932i
$838$	−6.73201			−0.232553
$839$			13.3423i			0.460626i	0.973117	+	0.230313i	$0.0739749\pi$
$839$			13.3423i			0.460626i	−0.973117	+	0.230313i	$0.926025\pi$
$840$	0.408531			0.0140957
$841$		−	16.3310i		−	0.563138i
$842$	−31.6955			−1.09230
$843$	−50.5550	−	50.5550i	−1.74121	−	1.74121i
$844$	27.5307	+	27.5307i	0.947647	+	0.947647i
$845$		−	47.9181i		−	1.64843i
$846$	36.4781	+	36.4781i	1.25414	+	1.25414i
$847$	0.0260273	−	0.111325i	0.000894307	−	0.00382518i
$848$	17.3280	−	17.3280i	0.595047	−	0.595047i
$849$			3.07546i			0.105549i
$850$	−0.474631			−0.0162797
$851$	−22.0417			−0.755579
$852$	101.173	+	101.173i	3.46614	+	3.46614i
$853$	−0.484542			−0.0165904			−0.00829521	−	0.999966i	$-0.502640\pi$
$853$	−0.484542			−0.0165904			−0.00829521	+	0.999966i	$0.502640\pi$
$854$	−0.111701	+	0.165042i	−0.00382233	+	0.00564762i
$855$			46.7605i			1.59917i
$856$	−23.5670	+	23.5670i	−0.805503	+	0.805503i
$857$	−8.77367			−0.299703			−0.149851	−	0.988709i	$-0.547880\pi$
$857$	−8.77367			−0.299703			−0.149851	+	0.988709i	$0.547880\pi$
$858$	103.172	−	29.4292i	3.52225	−	1.00470i
$859$			14.6432i			0.499619i	0.968295	+	0.249810i	$0.0803681\pi$
$859$			14.6432i			0.499619i	−0.968295	+	0.249810i	$0.919632\pi$
$860$	−16.4553	+	16.4553i	−0.561122	+	0.561122i
$861$	0.0207885	−	0.0207885i	0.000708471	−	0.000708471i
$862$	−4.51903	−	4.51903i	−0.153919	−	0.153919i
$863$	22.0136			0.749351			0.374675	−	0.927156i	$-0.377754\pi$
$863$	22.0136			0.749351			0.374675	+	0.927156i	$0.377754\pi$
$864$	−0.0861313	+	0.0861313i	−0.00293025	+	0.00293025i
$865$	−11.7908	+	11.7908i	−0.400901	+	0.400901i
$866$		−	61.0755i		−	2.07543i
$867$	42.2633			1.43534
$868$	−0.0883325			−0.00299820
$869$	−34.2098	+	9.75812i	−1.16049	+	0.331021i
$870$	130.542			4.42580
$871$	−23.4824	+	23.4824i	−0.795671	+	0.795671i
$872$	−11.9703	+	11.9703i	−0.405366	+	0.405366i
$873$			28.2769i			0.957027i
$874$	30.8277			1.04276
$875$	0.00209667	−	0.00209667i	7.08803e−5	−	7.08803e-5i
$876$		−	63.6508i		−	2.15056i
$877$	0.629687	+	0.629687i	0.0212630	+	0.0212630i	0.717658	−	0.696395i	$-0.245214\pi$
$877$	0.629687	+	0.629687i	0.0212630	+	0.0212630i	−0.696395	+	0.717658i	$0.745214\pi$
$878$	60.3753	−	60.3753i	2.03757	−	2.03757i
$879$		−	52.1167i		−	1.75785i
$880$	−38.3422	−	21.3231i	−1.29252	−	0.718801i
$881$		−	0.598592i		−	0.0201671i	−0.999949	−	0.0100835i	$-0.996790\pi$
$881$		−	0.598592i		−	0.0201671i	0.999949	−	0.0100835i	$-0.00320974\pi$
$882$	38.6623	−	38.6623i	1.30183	−	1.30183i
$883$	−33.3582	−	33.3582i	−1.12259	−	1.12259i	−0.991350	−	0.131243i	$-0.958103\pi$
$883$	−33.3582	−	33.3582i	−1.12259	−	1.12259i	−0.131243	−	0.991350i	$-0.541897\pi$
$884$	−0.573232	+	0.573232i	−0.0192799	+	0.0192799i
$885$	−78.9398	−	78.9398i	−2.65353	−	2.65353i
$886$	−22.1042	−	22.1042i	−0.742604	−	0.742604i
$887$	34.4481	+	34.4481i	1.15665	+	1.15665i	0.985191	+	0.171463i	$0.0548493\pi$
$887$	34.4481	+	34.4481i	1.15665	+	1.15665i	0.171463	+	0.985191i	$0.445151\pi$
$888$			100.503i			3.37264i
$889$	−0.0826303	−	0.0826303i	−0.00277133	−	0.00277133i
$890$	−97.6360			−3.27277
$891$	−13.5761	+	24.4119i	−0.454815	+	0.817829i
$892$	−63.9909	−	63.9909i	−2.14257	−	2.14257i
$893$	−30.5579			−1.02258
$894$	9.03794	−	9.03794i	0.302274	−	0.302274i
$895$			29.8878i			0.999038i
$896$	0.201232			0.00672268
$897$	−25.2855	+	25.2855i	−0.844258	+	0.844258i
$898$	−38.2524	−	38.2524i	−1.27650	−	1.27650i
$899$	−14.2085			−0.473881
$900$			65.2175i			2.17392i
$901$		−	0.223513i		−	0.00744629i
$902$	−8.90843	+	2.54107i	−0.296618	+	0.0846084i
$903$		−	0.0470085i		−	0.00156435i
$904$	−27.1304	−	27.1304i	−0.902342	−	0.902342i
$905$	−2.51694	+	2.51694i	−0.0836661	+	0.0836661i
$906$			76.2982i			2.53484i
$907$	0.354227	−	0.354227i	0.0117619	−	0.0117619i	−0.701201	−	0.712963i	$-0.747353\pi$
$907$	0.354227	−	0.354227i	0.0117619	−	0.0117619i	0.712963	+	0.701201i	$0.247353\pi$
$908$	29.5007	−	29.5007i	0.979015	−	0.979015i
$909$	−27.0137	−	27.0137i	−0.895986	−	0.895986i
$910$		−	0.429536i		−	0.0142390i
$911$	18.4544			0.611422			0.305711	−	0.952124i	$-0.401106\pi$
$911$	18.4544			0.611422			0.305711	+	0.952124i	$0.401106\pi$
$912$		−	47.9064i		−	1.58634i
$913$	29.5873	+	16.4542i	0.979196	+	0.544556i
$914$		−	50.7775i		−	1.67957i
$915$	−51.0823	−	34.5727i	−1.68873	−	1.14294i
$916$	48.3614			1.59791
$917$	−0.0988601	+	0.0988601i	−0.00326465	+	0.00326465i
$918$			0.0421123i			0.00138991i
$919$	−29.1607			−0.961922			−0.480961	−	0.876742i	$-0.659712\pi$
$919$	−29.1607			−0.961922			−0.480961	+	0.876742i	$0.659712\pi$
$920$	42.9052			1.41454
$921$	24.2916	−	24.2916i	0.800434	−	0.800434i
$922$	68.1202	−	68.1202i	2.24342	−	2.24342i
$923$	53.5480	−	53.5480i	1.76255	−	1.76255i
$924$	0.331918	−	0.0946775i	0.0109193	−	0.00311466i
$925$	29.2306	+	29.2306i	0.961096	+	0.961096i
$926$	−70.4830	+	70.4830i	−2.31622	+	2.31622i
$927$	−45.9226			−1.50829
$928$	−1.81601			−0.0596134
$929$		−	14.8474i		−	0.487128i	−0.969885	−	0.243564i	$-0.921683\pi$
$929$		−	14.8474i		−	0.487128i	0.969885	−	0.243564i	$-0.0783166\pi$
$930$		−	40.9172i		−	1.34173i
$931$			32.3875i			1.06146i
$932$	67.1347	−	67.1347i	2.19907	−	2.19907i
$933$	−42.5915	+	42.5915i	−1.39438	+	1.39438i
$934$	0.960969			0.0314439
$935$	−0.384809	+	0.109764i	−0.0125846	+	0.00358967i
$936$	59.3404	+	59.3404i	1.93960	+	1.93960i
$937$			26.8971i			0.878691i	0.898318	+	0.439345i	$0.144790\pi$
$937$			26.8971i			0.878691i	−0.898318	+	0.439345i	$0.855210\pi$
$938$	−0.113063	+	0.113063i	−0.00369163	+	0.00369163i
$939$	43.2993	−	43.2993i	1.41302	−	1.41302i
$940$	−84.4869			−2.75566
$941$	−9.07478	−	9.07478i	−0.295829	−	0.295829i	0.543548	−	0.839378i	$-0.317080\pi$
$941$	−9.07478	−	9.07478i	−0.295829	−	0.295829i	−0.839378	+	0.543548i	$0.817080\pi$
$942$	−12.4341			−0.405125
$943$	2.18328	−	2.18328i	0.0710973	−	0.0710973i
$944$	41.6253	+	41.6253i	1.35479	+	1.35479i
$945$	−0.0105424	−	0.0105424i	−0.000342944	−	0.000342944i
$946$	−7.19916	+	12.9452i	−0.234065	+	0.420885i
$947$	−29.4024	+	29.4024i	−0.955450	+	0.955450i	−0.999049	−	0.0435988i	$-0.986118\pi$
$947$	−29.4024	+	29.4024i	−0.955450	+	0.955450i	0.0435988	+	0.999049i	$0.486118\pi$
$948$	−75.9431	−	75.9431i	−2.46652	−	2.46652i
$949$	−33.6884			−1.09357
$950$	−40.8822	−	40.8822i	−1.32639	−	1.32639i
$951$		−	13.0171i		−	0.422107i
$952$	−0.00138934	+	0.00138934i	−4.50289e−5	+	4.50289e-5i
$953$	−26.6176	+	26.6176i	−0.862228	+	0.862228i	−0.991597	−	0.129369i	$-0.958705\pi$
$953$	−26.6176	+	26.6176i	−0.862228	+	0.862228i	0.129369	+	0.991597i	$0.458705\pi$
$954$	−45.9643			−1.48815
$955$	18.1261	−	18.1261i	0.586547	−	0.586547i
$956$	−18.5020			−0.598398
$957$	53.3900	−	15.2291i	1.72585	−	0.492288i
$958$	−75.3658	−	75.3658i	−2.43496	−	2.43496i
$959$	0.0958603	+	0.0958603i	0.00309549	+	0.00309549i
$960$			60.5480i			1.95418i
$961$		−	26.5465i		−	0.856338i
$962$	105.670			3.40694
$963$	21.3057			0.686565
$964$	−11.6617			−0.375597
$965$	34.5888	+	34.5888i	1.11345	+	1.11345i
$966$	−0.121744	+	0.121744i	−0.00391706	+	0.00391706i
$967$	−0.0277330			−0.000891833			−0.000445917	−	1.00000i	$-0.500142\pi$
$967$	−0.0277330			−0.000891833			−0.000445917		1.00000i	$0.500142\pi$
$968$	−53.3103	−	12.4637i	−1.71346	−	0.400597i
$969$	−0.308970	−	0.308970i	−0.00992555	−	0.00992555i
$970$	−49.0081	−	49.0081i	−1.57356	−	1.57356i
$971$	−11.2598			−0.361345			−0.180672	−	0.983543i	$-0.557827\pi$
$971$	−11.2598			−0.361345			−0.180672	+	0.983543i	$0.557827\pi$
$972$	−89.7865			−2.87990
$973$	0.00369611			0.000118492
$974$	−60.5490	+	60.5490i	−1.94012	+	1.94012i
$975$	67.0647			2.14779
$976$	26.9359	+	18.2303i	0.862198	+	0.583539i
$977$	−2.51462			−0.0804497			−0.0402248	−	0.999191i	$-0.512807\pi$
$977$	−2.51462			−0.0804497			−0.0402248	+	0.999191i	$0.512807\pi$
$978$	−59.2004	−	59.2004i	−1.89302	−	1.89302i
$979$	−39.9317	+	11.3903i	−1.27622	+	0.364035i
$980$			89.5457i			2.86043i
$981$	10.8217			0.345512
$982$	−10.7872	−	10.7872i	−0.344235	−	0.344235i
$983$	4.04237	−	4.04237i	0.128932	−	0.128932i	−0.639696	−	0.768628i	$-0.720940\pi$
$983$	4.04237	−	4.04237i	0.128932	−	0.128932i	0.768628	+	0.639696i	$0.220940\pi$
$984$	−9.95500	−	9.95500i	−0.317354	−	0.317354i
$985$			54.1662i			1.72588i
$986$	−0.443953	+	0.443953i	−0.0141383	+	0.0141383i
$987$	0.120679	−	0.120679i	0.00384124	−	0.00384124i
$988$	−98.7505			−3.14167
$989$		−	4.93699i		−	0.156987i
$990$	22.5725	+	79.1340i	0.717400	+	2.51504i
$991$	7.57524			0.240636			0.120318	−	0.992735i	$-0.461609\pi$
$991$	7.57524			0.240636			0.120318	+	0.992735i	$0.461609\pi$
$992$			0.569209i			0.0180724i
$993$	−44.0767	−	44.0767i	−1.39873	−	1.39873i
$994$	0.257822	−	0.257822i	0.00817762	−	0.00817762i
$995$			63.9894i			2.02860i
$996$			102.209i			3.23861i
$997$	30.9996	−	30.9996i	0.981768	−	0.981768i	−0.0180690	−	0.999837i	$-0.505752\pi$
$997$	30.9996	−	30.9996i	0.981768	−	0.981768i	0.999837	+	0.0180690i	$0.00575187\pi$
$998$		−	56.6234i		−	1.79238i
$999$	2.59353	−	2.59353i	0.0820557	−	0.0820557i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.f.a.538.6	✓	120
11.10	odd	2	inner	671.2.f.a.538.55	yes	120
61.11	odd	4	inner	671.2.f.a.560.55	yes	120
671.560	even	4	inner	671.2.f.a.560.6	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.f.a.538.6	✓	120	1.1	even	1	trivial
671.2.f.a.538.55	yes	120	11.10	odd	2	inner
671.2.f.a.560.6	yes	120	671.560	even	4	inner
671.2.f.a.560.55	yes	120	61.11	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73598 - 1.73598i) q^{2} -2.48629i q^{3} +4.02728i q^{4} +3.17645i q^{5} +(-4.31616 + 4.31616i) q^{6} +(0.00734923 + 0.00734923i) q^{7} +(3.51933 - 3.51933i) q^{8} -3.18164 q^{9} +O(q^{10})\)	\(q+(-1.73598 - 1.73598i) q^{2} -2.48629i q^{3} +4.02728i q^{4} +3.17645i q^{5} +(-4.31616 + 4.31616i) q^{6} +(0.00734923 + 0.00734923i) q^{7} +(3.51933 - 3.51933i) q^{8} -3.18164 q^{9} +(5.51426 - 5.51426i) q^{10} +(1.61196 - 2.89855i) q^{11} +10.0130 q^{12} -5.29957i q^{13} -0.0255163i q^{14} +7.89757 q^{15} -4.16443 q^{16} +(-0.0268583 + 0.0268583i) q^{17} +(5.52327 + 5.52327i) q^{18} -4.62686 q^{19} -12.7924 q^{20} +(0.0182723 - 0.0182723i) q^{21} +(-7.83017 + 2.23350i) q^{22} +(1.91902 - 1.91902i) q^{23} +(-8.75006 - 8.75006i) q^{24} -5.08981 q^{25} +(-9.19997 + 9.19997i) q^{26} +0.451602i q^{27} +(-0.0295974 + 0.0295974i) q^{28} +(-4.76083 + 4.76083i) q^{29} +(-13.7100 - 13.7100i) q^{30} +(1.49223 + 1.49223i) q^{31} +(0.190724 + 0.190724i) q^{32} +(-7.20664 - 4.00779i) q^{33} +0.0932511 q^{34} +(-0.0233445 + 0.0233445i) q^{35} -12.8133i q^{36} +(-5.74296 - 5.74296i) q^{37} +(8.03216 + 8.03216i) q^{38} -13.1763 q^{39} +(11.1790 + 11.1790i) q^{40} +1.13771 q^{41} -0.0634409 q^{42} +(1.28633 - 1.28633i) q^{43} +(11.6733 + 6.49180i) q^{44} -10.1063i q^{45} -6.66277 q^{46} +6.60444 q^{47} +10.3540i q^{48} -6.99989i q^{49} +(8.83584 + 8.83584i) q^{50} +(0.0667775 + 0.0667775i) q^{51} +21.3429 q^{52} +(-4.16097 + 4.16097i) q^{53} +(0.783973 - 0.783973i) q^{54} +(9.20709 + 5.12030i) q^{55} +0.0517287 q^{56} +11.5037i q^{57} +16.5295 q^{58} +(-9.99545 - 9.99545i) q^{59} +31.8057i q^{60} +(-6.46810 - 4.37763i) q^{61} -5.18098i q^{62} +(-0.0233826 - 0.0233826i) q^{63} +7.66666i q^{64} +16.8338 q^{65} +(5.55314 + 19.4681i) q^{66} +(-4.43100 - 4.43100i) q^{67} +(-0.108166 - 0.108166i) q^{68} +(-4.77124 - 4.77124i) q^{69} +0.0810512 q^{70} +(10.1042 + 10.1042i) q^{71} +(-11.1972 + 11.1972i) q^{72} -6.35682i q^{73} +19.9394i q^{74} +12.6548i q^{75} -18.6337i q^{76} +(0.0331488 - 0.00945547i) q^{77} +(22.8738 + 22.8738i) q^{78} +(-7.58446 - 7.58446i) q^{79} -13.2281i q^{80} -8.42210 q^{81} +(-1.97504 - 1.97504i) q^{82} +10.2076i q^{83} +(0.0735878 + 0.0735878i) q^{84} +(-0.0853139 - 0.0853139i) q^{85} -4.46610 q^{86} +(11.8368 + 11.8368i) q^{87} +(-4.52794 - 15.8739i) q^{88} +(-8.85305 - 8.85305i) q^{89} +(-17.5444 + 17.5444i) q^{90} +(0.0389478 - 0.0389478i) q^{91} +(7.72843 + 7.72843i) q^{92} +(3.71012 - 3.71012i) q^{93} +(-11.4652 - 11.4652i) q^{94} -14.6970i q^{95} +(0.474195 - 0.474195i) q^{96} -8.88752i q^{97} +(-12.1517 + 12.1517i) q^{98} +(-5.12866 + 9.22213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 120 q^{9}+O(q^{10}) \) 120 * q - 120 * q^9	\( 120 q - 120 q^{9} - 4 q^{11} + 16 q^{12} + 16 q^{15} - 148 q^{16} + 56 q^{20} - 4 q^{22} - 4 q^{23} - 104 q^{25} + 40 q^{26} - 2 q^{33} - 8 q^{34} - 12 q^{37} + 20 q^{38} + 16 q^{42} - 10 q^{44} - 4 q^{53} + 50 q^{55} - 24 q^{56} + 64 q^{58} - 56 q^{67} + 68 q^{69} + 144 q^{70} - 12 q^{71} - 64 q^{77} + 84 q^{78} + 72 q^{81} + 40 q^{82} - 80 q^{86} + 4 q^{89} - 4 q^{91} + 4 q^{92} + 64 q^{93} + 24 q^{99}+O(q^{100}) \) 120 * q - 120 * q^9 - 4 * q^11 + 16 * q^12 + 16 * q^15 - 148 * q^16 + 56 * q^20 - 4 * q^22 - 4 * q^23 - 104 * q^25 + 40 * q^26 - 2 * q^33 - 8 * q^34 - 12 * q^37 + 20 * q^38 + 16 * q^42 - 10 * q^44 - 4 * q^53 + 50 * q^55 - 24 * q^56 + 64 * q^58 - 56 * q^67 + 68 * q^69 + 144 * q^70 - 12 * q^71 - 64 * q^77 + 84 * q^78 + 72 * q^81 + 40 * q^82 - 80 * q^86 + 4 * q^89 - 4 * q^91 + 4 * q^92 + 64 * q^93 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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