LMFDB - Embedded newform 666.2.bs.b.557.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(17,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 7]))

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

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

chi := DirichletCharacter("666.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.bs (of order $36$, degree $12$, 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:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			557.8
Character	$\chi$	$=$	666.557
Dual form			666.2.bs.b.611.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0871557 - 0.996195i) q^{2} +(-0.984808 - 0.173648i) q^{4} +(3.66235 + 1.70778i) q^{5} +(-0.294498 + 0.107188i) q^{7} +(-0.258819 + 0.965926i) q^{8} +O(q^{10})$	\(q+(0.0871557 - 0.996195i) q^{2} +(-0.984808 - 0.173648i) q^{4} +(3.66235 + 1.70778i) q^{5} +(-0.294498 + 0.107188i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(2.02048 - 3.49957i) q^{10} +(-0.875768 - 1.51687i) q^{11} +(1.84986 + 2.64187i) q^{13} +(0.0811133 + 0.302719i) q^{14} +(0.939693 + 0.342020i) q^{16} +(-0.590940 + 0.843949i) q^{17} +(5.81418 - 0.508675i) q^{19} +(-3.31015 - 2.31779i) q^{20} +(-1.58743 + 0.740231i) q^{22} +(-2.42008 + 0.648460i) q^{23} +(7.28233 + 8.67874i) q^{25} +(2.79304 - 1.61256i) q^{26} +(0.308637 - 0.0544210i) q^{28} +(-2.34207 - 0.627556i) q^{29} +(0.925955 + 0.925955i) q^{31} +(0.422618 - 0.906308i) q^{32} +(0.789234 + 0.662246i) q^{34} +(-1.26161 - 0.110376i) q^{35} +(5.99877 + 1.00737i) q^{37} -5.83639i q^{38} +(-2.59747 + 3.09555i) q^{40} +(-0.370837 + 2.10312i) q^{41} +(4.14796 - 4.14796i) q^{43} +(0.599060 + 1.64590i) q^{44} +(0.435068 + 2.46739i) q^{46} +(-3.98978 - 2.30350i) q^{47} +(-5.28707 + 4.43638i) q^{49} +(9.28041 - 6.49821i) q^{50} +(-1.36300 - 2.92296i) q^{52} +(2.72394 - 7.48397i) q^{53} +(-0.616877 - 7.05093i) q^{55} +(-0.0273144 - 0.312205i) q^{56} +(-0.829292 + 2.27846i) q^{58} +(0.432400 + 0.927286i) q^{59} +(0.131194 - 0.0918629i) q^{61} +(1.00313 - 0.841729i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(2.26309 + 12.8346i) q^{65} +(-5.46909 - 15.0262i) q^{67} +(0.728512 - 0.728512i) q^{68} +(-0.219912 + 1.24719i) q^{70} +(8.74807 - 10.4255i) q^{71} -11.4937i q^{73} +(1.52636 - 5.88814i) q^{74} +(-5.81418 - 0.508675i) q^{76} +(0.420503 + 0.352844i) q^{77} +(-0.448415 + 0.961629i) q^{79} +(2.85738 + 2.85738i) q^{80} +(2.06280 + 0.552725i) q^{82} +(-8.03449 + 1.41670i) q^{83} +(-3.60550 + 2.08164i) q^{85} +(-3.77066 - 4.49370i) q^{86} +(1.69185 - 0.453331i) q^{88} +(-12.5101 + 5.83354i) q^{89} +(-0.827957 - 0.579742i) q^{91} +(2.49592 - 0.218365i) q^{92} +(-2.64247 + 3.77383i) q^{94} +(22.1622 + 8.06640i) q^{95} +(2.88852 + 10.7801i) q^{97} +(3.95870 + 5.65361i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82} - 108 q^{85} - 24 q^{88} + 216 q^{91} - 60 q^{94} + 24 q^{97}+O(q^{100}) $ 96 * q - 12 * q^13 + 24 * q^19 + 12 * q^22 + 48 * q^31 + 72 * q^34 + 24 * q^37 + 72 * q^43 + 60 * q^46 + 12 * q^52 - 60 * q^55 + 12 * q^58 - 120 * q^61 + 36 * q^67 + 12 * q^70 - 24 * q^76 + 60 * q^79 + 96 * q^82 - 108 * q^85 - 24 * q^88 + 216 * q^91 - 60 * q^94 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{1}{36}\right)$

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 $

$2$	0.0871557	−	0.996195i	0.0616284	−	0.704416i
$2$	0.0871557	−	0.996195i	0.0616284	−	0.704416i
$3$		0			0
$3$		0			0
$4$	−0.984808	−	0.173648i	−0.492404	−	0.0868241i
$5$	3.66235	+	1.70778i	1.63785	+	0.763742i	0.999980	−	0.00640061i	$-0.00203739\pi$
$5$	3.66235	+	1.70778i	1.63785	+	0.763742i	0.637871	+	0.770143i	$0.279815\pi$
$6$		0			0
$7$	−0.294498	+	0.107188i	−0.111310	+	0.0405134i	−0.397075	−	0.917786i	$-0.629975\pi$
$7$	−0.294498	+	0.107188i	−0.111310	+	0.0405134i	0.285765	+	0.958300i	$0.407752\pi$
$8$	−0.258819	+	0.965926i	−0.0915064	+	0.341506i
$9$		0			0
$10$	2.02048	−	3.49957i	0.638931	−	1.10666i
$11$	−0.875768	−	1.51687i	−0.264054	−	0.457355i	0.703261	−	0.710931i	$-0.251726\pi$
$11$	−0.875768	−	1.51687i	−0.264054	−	0.457355i	−0.967315	+	0.253577i	$0.918393\pi$
$12$		0			0
$13$	1.84986	+	2.64187i	0.513058	+	0.732723i	0.989188	−	0.146652i	$-0.0468496\pi$
$13$	1.84986	+	2.64187i	0.513058	+	0.732723i	−0.476130	+	0.879375i	$0.657961\pi$
$14$	0.0811133	+	0.302719i	0.0216784	+	0.0809051i
$15$		0			0
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	−0.590940	+	0.843949i	−0.143324	+	0.204688i	−0.884395	−	0.466738i	$-0.845429\pi$
$17$	−0.590940	+	0.843949i	−0.143324	+	0.204688i	0.741072	+	0.671426i	$0.234318\pi$
$18$		0			0
$19$	5.81418	−	0.508675i	1.33386	−	0.116698i	0.602190	−	0.798353i	$-0.294295\pi$
$19$	5.81418	−	0.508675i	1.33386	−	0.116698i	0.731674	+	0.681655i	$0.238739\pi$
$20$	−3.31015	−	2.31779i	−0.740173	−	0.518275i
$21$		0			0
$22$	−1.58743	+	0.740231i	−0.338441	+	0.157818i
$23$	−2.42008	+	0.648460i	−0.504623	+	0.135213i	−0.502144	−	0.864784i	$-0.667455\pi$
$23$	−2.42008	+	0.648460i	−0.504623	+	0.135213i	−0.00247802	+	0.999997i	$0.500789\pi$
$24$		0			0
$25$	7.28233	+	8.67874i	1.45647	+	1.73575i
$26$	2.79304	−	1.61256i	0.547761	−	0.316250i
$27$		0			0
$28$	0.308637	−	0.0544210i	0.0583268	−	0.0102846i
$29$	−2.34207	−	0.627556i	−0.434911	−	0.116534i	0.0347193	−	0.999397i	$-0.488946\pi$
$29$	−2.34207	−	0.627556i	−0.434911	−	0.116534i	−0.469631	+	0.882863i	$0.655613\pi$
$30$		0			0
$31$	0.925955	+	0.925955i	0.166306	+	0.166306i	0.785354	−	0.619047i	$-0.212481\pi$
$31$	0.925955	+	0.925955i	0.166306	+	0.166306i	−0.619047	+	0.785354i	$0.712481\pi$
$32$	0.422618	−	0.906308i	0.0747091	−	0.160214i
$33$		0			0
$34$	0.789234	+	0.662246i	0.135352	+	0.113574i
$35$	−1.26161	−	0.110376i	−0.213250	−	0.0186570i
$36$		0			0
$37$	5.99877	+	1.00737i	0.986191	+	0.165610i
$37$	5.99877	+	1.00737i	0.986191	+	0.165610i
$38$		−	5.83639i		−	0.946787i
$39$		0			0
$40$	−2.59747	+	3.09555i	−0.410697	+	0.489449i
$41$	−0.370837	+	2.10312i	−0.0579150	+	0.328453i	−0.999976	−	0.00699040i	$-0.997775\pi$
$41$	−0.370837	+	2.10312i	−0.0579150	+	0.328453i	0.942061	+	0.335443i	$0.108886\pi$
$42$		0			0
$43$	4.14796	−	4.14796i	0.632559	−	0.632559i	−0.316151	−	0.948709i	$-0.602390\pi$
$43$	4.14796	−	4.14796i	0.632559	−	0.632559i	0.948709	+	0.316151i	$0.102390\pi$
$44$	0.599060	+	1.64590i	0.0903117	+	0.248129i
$45$		0			0
$46$	0.435068	+	2.46739i	0.0641473	+	0.363797i
$47$	−3.98978	−	2.30350i	−0.581969	−	0.336000i	0.179946	−	0.983676i	$-0.442408\pi$
$47$	−3.98978	−	2.30350i	−0.581969	−	0.336000i	−0.761916	+	0.647676i	$0.775741\pi$
$48$		0			0
$49$	−5.28707	+	4.43638i	−0.755296	+	0.633769i
$50$	9.28041	−	6.49821i	1.31245	−	0.918986i
$51$		0			0
$52$	−1.36300	−	2.92296i	−0.189014	−	0.405342i
$53$	2.72394	−	7.48397i	0.374162	−	1.02800i	−0.599573	−	0.800320i	$-0.704663\pi$
$53$	2.72394	−	7.48397i	0.374162	−	1.02800i	0.973735	−	0.227683i	$-0.0731149\pi$
$54$		0			0
$55$	−0.616877	−	7.05093i	−0.0831797	−	0.950748i
$56$	−0.0273144	−	0.312205i	−0.00365004	−	0.0417202i
$57$		0			0
$58$	−0.829292	+	2.27846i	−0.108891	+	0.299177i
$59$	0.432400	+	0.927286i	0.0562937	+	0.120722i	0.932442	−	0.361319i	$-0.117673\pi$
$59$	0.432400	+	0.927286i	0.0562937	+	0.120722i	−0.876149	+	0.482041i	$0.839896\pi$
$60$		0			0
$61$	0.131194	−	0.0918629i	0.0167976	−	0.0117618i	−0.565147	−	0.824990i	$-0.691181\pi$
$61$	0.131194	−	0.0918629i	0.0167976	−	0.0117618i	0.581945	+	0.813228i	$0.302292\pi$
$62$	1.00313	−	0.841729i	0.127398	−	0.106900i
$63$		0			0
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	2.26309	+	12.8346i	0.280701	+	1.59194i
$66$		0			0
$67$	−5.46909	−	15.0262i	−0.668156	−	1.83574i	−0.535406	−	0.844595i	$-0.679841\pi$
$67$	−5.46909	−	15.0262i	−0.668156	−	1.83574i	−0.132750	−	0.991150i	$-0.542381\pi$
$68$	0.728512	−	0.728512i	0.0883451	−	0.0883451i
$69$		0			0
$70$	−0.219912	+	1.24719i	−0.0262846	+	0.149067i
$71$	8.74807	−	10.4255i	1.03821	−	1.23729i	0.0673223	−	0.997731i	$-0.478554\pi$
$71$	8.74807	−	10.4255i	1.03821	−	1.23729i	0.970883	−	0.239554i	$-0.0770011\pi$
$72$		0			0
$73$		−	11.4937i		−	1.34524i	−0.739987	−	0.672621i	$-0.765169\pi$
$73$		−	11.4937i		−	1.34524i	0.739987	−	0.672621i	$-0.234831\pi$
$74$	1.52636	−	5.88814i	0.177436	−	0.684483i
$75$		0			0
$76$	−5.81418	−	0.508675i	−0.666932	−	0.0583490i
$77$	0.420503	+	0.352844i	0.0479207	+	0.0402103i
$78$		0			0
$79$	−0.448415	+	0.961629i	−0.0504506	+	0.108192i	−0.929917	−	0.367769i	$-0.880122\pi$
$79$	−0.448415	+	0.961629i	−0.0504506	+	0.108192i	0.879467	+	0.475961i	$0.157900\pi$
$80$	2.85738	+	2.85738i	0.319465	+	0.319465i
$81$		0			0
$82$	2.06280	+	0.552725i	0.227798	+	0.0610383i
$83$	−8.03449	+	1.41670i	−0.881900	+	0.155503i	−0.596219	−	0.802822i	$-0.703331\pi$
$83$	−8.03449	+	1.41670i	−0.881900	+	0.155503i	−0.285681	+	0.958325i	$0.592220\pi$
$84$		0			0
$85$	−3.60550	+	2.08164i	−0.391072	+	0.225785i
$86$	−3.77066	−	4.49370i	−0.406601	−	0.484568i
$87$		0			0
$88$	1.69185	−	0.453331i	0.180352	−	0.0483252i
$89$	−12.5101	+	5.83354i	−1.32606	+	0.618354i	−0.951157	−	0.308708i	$-0.900103\pi$
$89$	−12.5101	+	5.83354i	−1.32606	+	0.618354i	−0.374907	+	0.927062i	$0.622326\pi$
$90$		0			0
$91$	−0.827957	−	0.579742i	−0.0867935	−	0.0607734i
$92$	2.49592	−	0.218365i	0.260218	−	0.0227661i
$93$		0			0
$94$	−2.64247	+	3.77383i	−0.272550	+	0.389241i
$95$	22.1622	+	8.06640i	2.27380	+	0.827595i
$96$		0			0
$97$	2.88852	+	10.7801i	0.293285	+	1.09455i	0.942570	+	0.334009i	$0.108401\pi$
$97$	2.88852	+	10.7801i	0.293285	+	1.09455i	−0.649285	+	0.760545i	$0.724932\pi$
$98$	3.95870	+	5.65361i	0.399889	+	0.571101i
$99$		0			0
$100$	−5.66464	−	9.81145i	−0.566464	−	0.981145i
$101$	−3.85019	+	6.66872i	−0.383108	+	0.663562i	−0.991505	−	0.130071i	$-0.958480\pi$
$101$	−3.85019	+	6.66872i	−0.383108	+	0.663562i	0.608397	+	0.793633i	$0.291813\pi$
$102$		0			0
$103$	−5.13479	+	19.1633i	−0.505946	+	1.88822i	−0.0488373	+	0.998807i	$0.515552\pi$
$103$	−5.13479	+	19.1633i	−0.505946	+	1.88822i	−0.457109	+	0.889411i	$0.651115\pi$
$104$	−3.03063	+	1.10306i	−0.297178	+	0.108164i
$105$		0			0
$106$	−7.21809	−	3.36585i	−0.701083	−	0.326920i
$107$	−16.2662	−	2.86817i	−1.57251	−	0.277277i	−0.681695	−	0.731636i	$-0.738757\pi$
$107$	−16.2662	−	2.86817i	−1.57251	−	0.277277i	−0.890818	+	0.454360i	$0.849868\pi$
$108$		0			0
$109$	−1.12456	+	12.8538i	−0.107713	+	1.23117i	0.729380	+	0.684109i	$0.239809\pi$
$109$	−1.12456	+	12.8538i	−0.107713	+	1.23117i	−0.837093	+	0.547060i	$0.815747\pi$
$110$	−7.07787			−0.674848
$111$		0			0
$112$	−0.313398			−0.0296133
$113$	1.19803	−	13.6936i	0.112701	−	1.28818i	−0.703617	−	0.710579i	$-0.748433\pi$
$113$	1.19803	−	13.6936i	0.112701	−	1.28818i	0.816318	−	0.577602i	$-0.196012\pi$
$114$		0			0
$115$	−9.97061	−	1.75809i	−0.929764	−	0.163943i
$116$	2.19751	+	1.02472i	0.204034	+	0.0951427i
$117$		0			0
$118$	0.961443	−	0.349937i	0.0885080	−	0.0322143i
$119$	0.0835688	−	0.311883i	0.00766074	−	0.0285903i
$120$		0			0
$121$	3.96606	−	6.86942i	0.360551	−	0.624493i
$122$	−0.0800790	−	0.138701i	−0.00725001	−	0.0125574i
$123$		0			0
$124$	−0.751097	−	1.07268i	−0.0674505	−	0.0963293i
$125$	6.61965	+	24.7049i	0.592079	+	2.20967i
$126$		0			0
$127$	−7.99824	−	2.91112i	−0.709729	−	0.258320i	−0.0381699	−	0.999271i	$-0.512153\pi$
$127$	−7.99824	−	2.91112i	−0.709729	−	0.258320i	−0.671559	+	0.740951i	$0.734375\pi$
$128$	−0.573576	+	0.819152i	−0.0506975	+	0.0724035i
$129$		0			0
$130$	12.9830	−	1.13587i	1.13868	−	0.0996220i
$131$	−5.93708	−	4.15719i	−0.518725	−	0.363215i	0.284704	−	0.958615i	$-0.408105\pi$
$131$	−5.93708	−	4.15719i	−0.518725	−	0.363215i	−0.803429	+	0.595400i	$0.796994\pi$
$132$		0			0
$133$	−1.65774	+	0.773016i	−0.143744	+	0.0670290i
$134$	−15.4457	+	4.13866i	−1.33431	+	0.357526i
$135$		0			0
$136$	−0.662246	−	0.789234i	−0.0567871	−	0.0676762i
$137$	−12.4532	+	7.18988i	−1.06395	+	0.614273i	−0.926523	−	0.376239i	$-0.877217\pi$
$137$	−12.4532	+	7.18988i	−1.06395	+	0.614273i	−0.137429	+	0.990512i	$0.543884\pi$
$138$		0			0
$139$	4.78219	−	0.843229i	0.405620	−	0.0715217i	0.0328839	−	0.999459i	$-0.489531\pi$
$139$	4.78219	−	0.843229i	0.405620	−	0.0715217i	0.372736	+	0.927937i	$0.378420\pi$
$140$	1.22327	+	0.327775i	0.103385	+	0.0277020i
$141$		0			0
$142$	−9.62343	−	9.62343i	−0.807580	−	0.807580i
$143$	2.38734	−	5.11967i	0.199639	−	0.428128i
$144$		0			0
$145$	−7.50574	−	6.29806i	−0.623318	−	0.523026i
$146$	−11.4500	−	1.00175i	−0.947610	−	0.0829051i
$147$		0			0
$148$	−5.73270	−	2.03374i	−0.471225	−	0.167172i
$149$		−	1.17334i		−	0.0961241i	−0.998844	−	0.0480620i	$-0.984695\pi$
$149$		−	1.17334i		−	0.0961241i	0.998844	−	0.0480620i	$-0.0153045\pi$
$150$		0			0
$151$	−0.451815	+	0.538453i	−0.0367682	+	0.0438187i	−0.784115	−	0.620615i	$-0.786883\pi$
$151$	−0.451815	+	0.538453i	−0.0367682	+	0.0438187i	0.747347	+	0.664434i	$0.231327\pi$
$152$	−1.01348	+	5.74772i	−0.0822040	+	0.466202i
$153$		0			0
$154$	0.388150	−	0.388150i	0.0312780	−	0.0312780i
$155$	1.80984	+	4.97249i	0.145370	+	0.399400i
$156$		0			0
$157$	−1.01497	−	5.75619i	−0.0810036	−	0.459394i	−0.998148	−	0.0608382i	$-0.980623\pi$
$157$	−1.01497	−	5.75619i	−0.0810036	−	0.459394i	0.917144	−	0.398556i	$-0.130488\pi$
$158$	0.918888	+	0.530520i	0.0731028	+	0.0422059i
$159$		0			0
$160$	3.09555	−	2.59747i	0.244725	−	0.205348i
$161$	0.643202	−	0.450375i	0.0506914	−	0.0354945i
$162$		0			0
$163$	7.98612	+	17.1263i	0.625521	+	1.34143i	0.922295	+	0.386487i	$0.126312\pi$
$163$	7.98612	+	17.1263i	0.625521	+	1.34143i	−0.296774	+	0.954948i	$0.595911\pi$
$164$	0.730407	−	2.00678i	0.0570352	−	0.156703i
$165$		0			0
$166$	0.711055	+	8.12739i	0.0551885	+	0.630808i
$167$	2.15983	+	24.6870i	0.167133	+	1.91034i	0.366512	+	0.930413i	$0.380552\pi$
$167$	2.15983	+	24.6870i	0.167133	+	1.91034i	−0.199379	+	0.979922i	$0.563893\pi$
$168$		0			0
$169$	0.888752	−	2.44183i	0.0683656	−	0.187833i
$170$	1.75948	+	3.77321i	0.134946	+	0.289392i
$171$		0			0
$172$	−4.80523	+	3.36466i	−0.366396	+	0.256553i
$173$	−7.73952	+	6.49423i	−0.588425	+	0.493747i	−0.887702	−	0.460419i	$-0.847699\pi$
$173$	−7.73952	+	6.49423i	−0.588425	+	0.493747i	0.299277	+	0.954166i	$0.403255\pi$
$174$		0			0
$175$	−3.07489	−	1.77529i	−0.232440	−	0.134199i
$176$	−0.304151	−	1.72493i	−0.0229262	−	0.130021i
$177$		0			0
$178$	4.72102	+	12.9709i	0.353855	+	0.972209i
$179$	15.9537	−	15.9537i	1.19244	−	1.19244i	0.216057	−	0.976381i	$-0.430680\pi$
$179$	15.9537	−	15.9537i	1.19244	−	1.19244i	0.976381	−	0.216057i	$-0.0693197\pi$
$180$		0			0
$181$	2.79647	−	15.8595i	0.207860	−	1.17883i	−0.685016	−	0.728528i	$-0.740205\pi$
$181$	2.79647	−	15.8595i	0.207860	−	1.17883i	0.892876	−	0.450303i	$-0.148684\pi$
$182$	−0.649697	+	0.774278i	−0.0481587	+	0.0573933i
$183$		0			0
$184$		−	2.50546i		−	0.184705i
$185$	20.2492	+	13.9339i	1.48875	+	1.02444i
$186$		0			0
$187$	1.79769	+	0.157277i	0.131460	+	0.0115013i
$188$	3.52917	+	2.96132i	0.257391	+	0.215977i
$189$		0			0
$190$	9.96727	−	21.3749i	0.723102	−	1.55070i
$191$	4.91016	+	4.91016i	0.355287	+	0.355287i	0.862072	−	0.506785i	$-0.169166\pi$
$191$	4.91016	+	4.91016i	0.355287	+	0.355287i	−0.506785	+	0.862072i	$0.669166\pi$
$192$		0			0
$193$	7.21131	+	1.93226i	0.519081	+	0.139087i	0.508842	−	0.860860i	$-0.330074\pi$
$193$	7.21131	+	1.93226i	0.519081	+	0.139087i	0.0102397	+	0.999948i	$0.496741\pi$
$194$	10.9908	−	1.93798i	0.789096	−	0.139139i
$195$		0			0
$196$	5.97712	−	3.45089i	0.426937	−	0.246492i
$197$	−14.2648	−	17.0001i	−1.01632	−	1.21121i	−0.977276	−	0.211971i	$-0.932012\pi$
$197$	−14.2648	−	17.0001i	−1.01632	−	1.21121i	−0.0390483	−	0.999237i	$-0.512433\pi$
$198$		0			0
$199$	−14.2006	+	3.80504i	−1.00665	+	0.269732i	−0.724230	−	0.689558i	$-0.757805\pi$
$199$	−14.2006	+	3.80504i	−1.00665	+	0.269732i	−0.282423	+	0.959290i	$0.591138\pi$
$200$	−10.2678	+	4.78796i	−0.726045	+	0.338560i
$201$		0			0
$202$	6.30778	+	4.41675i	0.443814	+	0.310762i
$203$	0.757001	−	0.0662290i	0.0531310	−	0.00464836i
$204$		0			0
$205$	−4.94980	+	7.06905i	−0.345709	+	0.493724i
$206$	18.6429	+	6.78545i	1.29891	+	0.472765i
$207$		0			0
$208$	0.834725	+	3.11524i	0.0578778	+	0.216003i
$209$	−5.86347	−	8.37390i	−0.405584	−	0.579235i
$210$		0			0
$211$	−13.2618	−	22.9700i	−0.912977	−	1.58132i	−0.809836	−	0.586656i	$-0.800444\pi$
$211$	−13.2618	−	22.9700i	−0.912977	−	1.58132i	−0.103141	−	0.994667i	$-0.532889\pi$
$212$	−3.98214	+	6.89727i	−0.273494	+	0.473706i
$213$		0			0
$214$	−4.27495	+	15.9543i	−0.292230	+	1.09062i
$215$	22.2751	−	8.10747i	1.51915	−	0.552925i
$216$		0			0
$217$	−0.371943	−	0.173440i	−0.0252491	−	0.0117739i
$218$	12.7069	+	2.24056i	0.860617	+	0.151750i
$219$		0			0
$220$	−0.616877	+	7.05093i	−0.0415898	+	0.475374i
$221$	−3.32276			−0.223513
$222$		0			0
$223$	−17.1123			−1.14592			−0.572962	−	0.819582i	$-0.694206\pi$
$223$	−17.1123			−1.14592			−0.572962	+	0.819582i	$0.694206\pi$
$224$	−0.0273144	+	0.312205i	−0.00182502	+	0.0208601i
$225$		0			0
$226$	−13.5370	−	2.38695i	−0.900470	−	0.158777i
$227$	−10.2733	−	4.79050i	−0.681860	−	0.317957i	0.0506464	−	0.998717i	$-0.483872\pi$
$227$	−10.2733	−	4.79050i	−0.681860	−	0.317957i	−0.732506	+	0.680760i	$0.761650\pi$
$228$		0			0
$229$	19.2576	−	7.00919i	1.27258	−	0.463180i	0.384606	−	0.923081i	$-0.374337\pi$
$229$	19.2576	−	7.00919i	1.27258	−	0.463180i	0.887970	+	0.459901i	$0.152115\pi$
$230$	−2.62039	+	9.77944i	−0.172784	+	0.644837i
$231$		0			0
$232$	1.21234	−	2.09984i	0.0795943	−	0.137861i
$233$	6.61145	+	11.4514i	0.433131	+	0.750205i	0.997141	−	0.0755632i	$-0.0240755\pi$
$233$	6.61145	+	11.4514i	0.433131	+	0.750205i	−0.564010	+	0.825768i	$0.690742\pi$
$234$		0			0
$235$	−10.6781	−	15.2499i	−0.696561	−	0.994793i
$236$	−0.264810	−	0.988284i	−0.0172377	−	0.0643318i
$237$		0			0
$238$	−0.303413	−	0.110433i	−0.0196673	−	0.00715832i
$239$	10.0129	−	14.2999i	0.647678	−	0.924981i	−0.352262	−	0.935901i	$-0.614587\pi$
$239$	10.0129	−	14.2999i	0.647678	−	0.924981i	0.999940	+	0.0109208i	$0.00347627\pi$
$240$		0			0
$241$	−15.6164	+	1.36625i	−1.00594	+	0.0880082i	−0.578200	−	0.815895i	$-0.696245\pi$
$241$	−15.6164	+	1.36625i	−1.00594	+	0.0880082i	−0.427738	+	0.903903i	$0.640689\pi$
$242$	−6.49762	−	4.54968i	−0.417683	−	0.292465i
$243$		0			0
$244$	−0.145152	+	0.0676857i	−0.00929243	+	0.00433313i
$245$	−26.9394	+	7.21840i	−1.72110	+	0.461167i
$246$		0			0
$247$	12.0993	+	14.4193i	0.769858	+	0.917481i
$248$	−1.13406	+	0.654749i	−0.0720128	+	0.0415766i
$249$		0			0
$250$	25.1878	−	4.44129i	1.59302	−	0.280892i
$251$	−3.37176	−	0.903459i	−0.212823	−	0.0570258i	0.150832	−	0.988559i	$-0.451805\pi$
$251$	−3.37176	−	0.903459i	−0.212823	−	0.0570258i	−0.363655	+	0.931534i	$0.618471\pi$
$252$		0			0
$253$	3.10306	+	3.10306i	0.195088	+	0.195088i
$254$	−3.59714	+	7.71408i	−0.225704	+	0.484025i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−21.6111	−	1.89072i	−1.34806	−	0.117940i	−0.609854	−	0.792514i	$-0.708772\pi$
$257$	−21.6111	−	1.89072i	−1.34806	−	0.117940i	−0.738208	+	0.674574i	$0.764327\pi$
$258$		0			0
$259$	−1.87460	+	0.346331i	−0.116482	+	0.0215199i
$260$		−	13.0326i		−	0.808247i
$261$		0			0
$262$	−4.65882	+	5.55217i	−0.287823	+	0.343014i
$263$	4.61211	−	26.1566i	0.284395	−	1.61288i	−0.423044	−	0.906109i	$-0.639039\pi$
$263$	4.61211	−	26.1566i	0.284395	−	1.61288i	0.707439	−	0.706774i	$-0.249850\pi$
$264$		0			0
$265$	22.7570	−	22.7570i	1.39795	−	1.39795i
$266$	0.625593	+	1.71880i	0.0383576	+	0.105387i
$267$		0			0
$268$	2.77673	+	15.7476i	0.169616	+	0.961940i
$269$	14.0963	+	8.13848i	0.859465	+	0.496212i	0.863833	−	0.503778i	$-0.168057\pi$
$269$	14.0963	+	8.13848i	0.859465	+	0.496212i	−0.00436832	+	0.999990i	$0.501390\pi$
$270$		0			0
$271$	−10.8508	+	9.10492i	−0.659140	+	0.553084i	−0.909829	−	0.414983i	$-0.863787\pi$
$271$	−10.8508	+	9.10492i	−0.659140	+	0.553084i	0.250689	+	0.968068i	$0.419343\pi$
$272$	−0.843949	+	0.590940i	−0.0511719	+	0.0358310i
$273$		0			0
$274$	6.07715	+	13.0325i	0.367134	+	0.787321i
$275$	6.78693	−	18.6469i	0.409267	−	1.12445i
$276$		0			0
$277$	−1.93687	−	22.1386i	−0.116375	−	1.33018i	−0.799849	−	0.600202i	$-0.795087\pi$
$277$	−1.93687	−	22.1386i	−0.116375	−	1.33018i	0.683473	−	0.729975i	$-0.260469\pi$
$278$	−0.423225	−	4.83748i	−0.0253833	−	0.290133i
$279$		0			0
$280$	0.433143	−	1.19005i	0.0258852	−	0.0711191i
$281$	−10.5355	−	22.5933i	−0.628492	−	1.34781i	−0.920256	−	0.391316i	$-0.872020\pi$
$281$	−10.5355	−	22.5933i	−0.628492	−	1.34781i	0.291764	−	0.956490i	$-0.405758\pi$
$282$		0			0
$283$	1.47386	−	1.03201i	0.0876118	−	0.0613464i	−0.528950	−	0.848653i	$-0.677414\pi$
$283$	1.47386	−	1.03201i	0.0876118	−	0.0613464i	0.616562	+	0.787307i	$0.288525\pi$
$284$	−10.4255	+	8.74807i	−0.618643	+	0.519103i
$285$		0			0
$286$	−4.89212	−	2.82446i	−0.289277	−	0.167014i
$287$	−0.116220	−	0.659114i	−0.00686023	−	0.0389063i
$288$		0			0
$289$	5.45130	+	14.9773i	0.320665	+	0.881019i
$290$	−6.92827	+	6.92827i	−0.406842	+	0.406842i
$291$		0			0
$292$	−1.99587	+	11.3191i	−0.116799	+	0.662402i
$293$	−4.15142	+	4.94747i	−0.242528	+	0.289034i	−0.873553	−	0.486729i	$-0.838190\pi$
$293$	−4.15142	+	4.94747i	−0.242528	+	0.289034i	0.631025	+	0.775763i	$0.282635\pi$
$294$		0			0
$295$			4.13449i			0.240719i
$296$	−2.52564	+	5.53364i	−0.146800	+	0.321636i
$297$		0			0
$298$	−1.16888	−	0.102264i	−0.0677113	−	0.00592397i
$299$	−6.18996	−	5.19399i	−0.357975	−	0.300376i
$300$		0			0
$301$	−0.776952	+	1.66618i	−0.0447828	+	0.0960370i
$302$	0.497025	+	0.497025i	0.0286006	+	0.0286006i
$303$		0			0
$304$	5.63752	+	1.51057i	0.323334	+	0.0866371i
$305$	0.637359	−	0.112384i	0.0364950	−	0.00643506i
$306$		0			0
$307$	−1.76388	+	1.01838i	−0.100670	+	0.0581218i	−0.549490	−	0.835500i	$-0.685178\pi$
$307$	−1.76388	+	1.01838i	−0.100670	+	0.0581218i	0.448820	+	0.893622i	$0.351845\pi$
$308$	−0.352844	−	0.420503i	−0.0201051	−	0.0239604i
$309$		0			0
$310$	5.11131	−	1.36957i	0.290303	−	0.0777864i
$311$	−1.45635	+	0.679106i	−0.0825819	+	0.0385086i	−0.463470	−	0.886112i	$-0.653396\pi$
$311$	−1.45635	+	0.679106i	−0.0825819	+	0.0385086i	0.380888	+	0.924621i	$0.375618\pi$
$312$		0			0
$313$	4.27359	+	2.99240i	0.241557	+	0.169140i	0.688086	−	0.725629i	$-0.258451\pi$
$313$	4.27359	+	2.99240i	0.241557	+	0.169140i	−0.446529	+	0.894769i	$0.647340\pi$
$314$	−5.82275	+	0.509424i	−0.328597	+	0.0287485i
$315$		0			0
$316$	0.608588	−	0.869154i	0.0342357	−	0.0488937i
$317$	7.73134	+	2.81398i	0.434235	+	0.158049i	0.549883	−	0.835242i	$-0.314672\pi$
$317$	7.73134	+	2.81398i	0.434235	+	0.158049i	−0.115648	+	0.993290i	$0.536894\pi$
$318$		0			0
$319$	1.09919	+	4.10222i	0.0615426	+	0.229680i
$320$	−2.31779	−	3.31015i	−0.129569	−	0.185043i
$321$		0			0
$322$	−0.392602	−	0.680007i	−0.0218789	−	0.0378953i
$323$	−3.00653	+	5.20747i	−0.167288	+	0.289751i
$324$		0			0
$325$	−9.45684	+	35.2934i	−0.524571	+	1.95773i
$326$	17.7572	−	6.46308i	0.983478	−	0.357957i
$327$		0			0
$328$	−1.93548	−	0.902529i	−0.106869	−	0.0498339i
$329$	1.42189	+	0.250717i	0.0783913	+	0.0138225i
$330$		0			0
$331$	−2.45856	+	28.1015i	−0.135135	+	1.54460i	0.561685	+	0.827351i	$0.310153\pi$
$331$	−2.45856	+	28.1015i	−0.135135	+	1.54460i	−0.696819	+	0.717247i	$0.745402\pi$
$332$	8.15844			0.447752
$333$		0			0
$334$	24.7813			1.35597
$335$	5.63175	−	64.3712i	0.307695	−	3.51697i
$336$		0			0
$337$	−22.6775	−	3.99865i	−1.23532	−	0.217820i	−0.482412	−	0.875945i	$-0.660239\pi$
$337$	−22.6775	−	3.99865i	−1.23532	−	0.217820i	−0.752909	+	0.658124i	$0.771350\pi$
$338$	−2.35508	−	1.09819i	−0.128099	−	0.0597336i
$339$		0			0
$340$	3.91220	−	1.42392i	0.212169	−	0.0772232i
$341$	0.593636	−	2.21548i	0.0321472	−	0.119975i
$342$		0			0
$343$	2.17839	−	3.77309i	0.117622	−	0.203728i
$344$	2.93305	+	5.08020i	0.158140	+	0.273906i
$345$		0			0
$346$	5.79497	+	8.27608i	0.311540	+	0.444925i
$347$	6.39126	+	23.8525i	0.343101	+	1.28047i	0.894815	+	0.446437i	$0.147307\pi$
$347$	6.39126	+	23.8525i	0.343101	+	1.28047i	−0.551714	+	0.834033i	$0.686026\pi$
$348$		0			0
$349$	25.1954	+	9.17038i	1.34868	+	0.490879i	0.912535	−	0.408998i	$-0.134122\pi$
$349$	25.1954	+	9.17038i	1.34868	+	0.490879i	0.436144	+	0.899877i	$0.356344\pi$
$350$	−2.03653	+	2.90846i	−0.108857	+	0.155464i
$351$		0			0
$352$	−1.74487	+	0.152656i	−0.0930019	+	0.00813661i
$353$	12.3033	+	8.61485i	0.654837	+	0.458522i	0.853184	−	0.521610i	$-0.174668\pi$
$353$	12.3033	+	8.61485i	0.654837	+	0.458522i	−0.198347	+	0.980132i	$0.563557\pi$
$354$		0			0
$355$	49.8430	−	23.2422i	2.64539	−	1.23357i
$356$	13.3330	−	3.57256i	0.706647	−	0.189346i
$357$		0			0
$358$	−14.5026	−	17.2835i	−0.766484	−	0.913460i
$359$	23.5938	−	13.6219i	1.24523	−	0.718935i	0.275077	−	0.961422i	$-0.411296\pi$
$359$	23.5938	−	13.6219i	1.24523	−	0.718935i	0.970155	+	0.242487i	$0.0779632\pi$
$360$		0			0
$361$	14.8346	−	2.61574i	0.780768	−	0.137670i
$362$	−15.5555	−	4.16808i	−0.817577	−	0.219069i
$363$		0			0
$364$	0.714707	+	0.714707i	0.0374608	+	0.0374608i
$365$	19.6288	−	42.0941i	1.02742	−	2.20330i
$366$		0			0
$367$	−13.5860	−	11.4000i	−0.709185	−	0.595077i	0.215185	−	0.976573i	$-0.430964\pi$
$367$	−13.5860	−	11.4000i	−0.709185	−	0.595077i	−0.924370	+	0.381496i	$0.875409\pi$
$368$	−2.49592	−	0.218365i	−0.130109	−	0.0113831i
$369$		0			0
$370$	15.6457	−	18.9577i	0.813382	−	0.985565i
$371$			2.49599i			0.129585i
$372$		0			0
$373$	9.42680	−	11.2344i	0.488101	−	0.581696i	−0.464632	−	0.885504i	$-0.653813\pi$
$373$	9.42680	−	11.2344i	0.488101	−	0.581696i	0.952733	+	0.303807i	$0.0982579\pi$
$374$	0.313358	−	1.77714i	0.0162034	−	0.0918938i
$375$		0			0
$376$	3.25764	−	3.25764i	0.168000	−	0.168000i
$377$	−2.67458	−	7.34834i	−0.137748	−	0.378459i
$378$		0			0
$379$	−0.762761	−	4.32583i	−0.0391804	−	0.222203i	0.958930	−	0.283641i	$-0.0915425\pi$
$379$	−0.762761	−	4.32583i	−0.0391804	−	0.222203i	−0.998111	+	0.0614380i	$0.980431\pi$
$380$	−20.4248	−	11.7923i	−1.04777	−	0.604931i
$381$		0			0
$382$	5.31943	−	4.46353i	0.272166	−	0.228374i
$383$	4.43745	−	3.10714i	0.226743	−	0.158767i	−0.454685	−	0.890652i	$-0.650248\pi$
$383$	4.43745	−	3.10714i	0.226743	−	0.158767i	0.681428	+	0.731885i	$0.261359\pi$
$384$		0			0
$385$	0.937447	+	2.01036i	0.0477767	+	0.102458i
$386$	2.55342	−	7.01546i	0.129966	−	0.357077i
$387$		0			0
$388$	−0.972692	−	11.1179i	−0.0493809	−	0.564427i
$389$	0.979381	+	11.1944i	0.0496566	+	0.567578i	0.979746	+	0.200244i	$0.0641736\pi$
$389$	0.979381	+	11.1944i	0.0496566	+	0.567578i	−0.930089	+	0.367333i	$0.880271\pi$
$390$		0			0
$391$	0.882857	−	2.42563i	0.0446480	−	0.122669i
$392$	−2.91682	−	6.25514i	−0.147322	−	0.315932i
$393$		0			0
$394$	−18.1787	+	12.7289i	−0.915829	+	0.641270i
$395$	−3.28450	+	2.75602i	−0.165261	+	0.138671i
$396$		0			0
$397$	−2.68748	−	1.55162i	−0.134881	−	0.0778736i	0.431041	−	0.902332i	$-0.358146\pi$
$397$	−2.68748	−	1.55162i	−0.134881	−	0.0778736i	−0.565922	+	0.824459i	$0.691480\pi$
$398$	2.55289	+	14.4782i	0.127965	+	0.725726i
$399$		0			0
$400$	3.87484	+	10.6460i	0.193742	+	0.532302i
$401$	25.4721	−	25.4721i	1.27201	−	1.27201i	0.326984	−	0.945030i	$-0.393968\pi$
$401$	25.4721	−	25.4721i	1.27201	−	1.27201i	0.945030	−	0.326984i	$-0.106032\pi$
$402$		0			0
$403$	−0.733369	+	4.15914i	−0.0365317	+	0.207182i
$404$	4.94971	−	5.89883i	0.246257	−	0.293478i
$405$		0			0
$406$		−	0.759892i		−	0.0377128i
$407$	−3.72548	−	9.98159i	−0.184665	−	0.494769i
$408$		0			0
$409$	−0.121186	−	0.0106024i	−0.00599227	−	0.000524256i	0.0841592	−	0.996452i	$-0.473180\pi$
$409$	−0.121186	−	0.0106024i	−0.00599227	−	0.000524256i	−0.0901515	+	0.995928i	$0.528735\pi$
$410$	6.61075	+	5.54708i	0.326482	+	0.273951i
$411$		0			0
$412$	8.38446	−	17.9805i	0.413073	−	0.885837i
$413$	−0.226735	−	0.226735i	−0.0111569	−	0.0111569i
$414$		0			0
$415$	−31.8445	−	8.53271i	−1.56318	−	0.418854i
$416$	3.17613	−	0.560038i	0.155723	−	0.0274581i
$417$		0			0
$418$	−8.85307	+	5.11132i	−0.433018	+	0.250003i
$419$	14.6325	+	17.4383i	0.714844	+	0.851918i	0.994119	−	0.108293i	$-0.0345385\pi$
$419$	14.6325	+	17.4383i	0.714844	+	0.851918i	−0.279275	+	0.960211i	$0.590094\pi$
$420$		0			0
$421$	16.8669	−	4.51948i	0.822045	−	0.220266i	0.176804	−	0.984246i	$-0.443424\pi$
$421$	16.8669	−	4.51948i	0.822045	−	0.220266i	0.645240	+	0.763980i	$0.276757\pi$
$422$	−24.0385	+	11.2093i	−1.17017	+	0.545661i
$423$		0			0
$424$	6.52395	+	4.56812i	0.316831	+	0.221848i
$425$	−11.6278	+	1.01730i	−0.564033	+	0.0493465i
$426$		0			0
$427$	−0.0287896	+	0.0411158i	−0.00139323	+	0.00198974i
$428$	15.5210	+	5.64919i	0.750238	+	0.273064i
$429$		0			0
$430$	−6.13522	−	22.8969i	−0.295866	−	1.10419i
$431$	13.6040	+	19.4285i	0.655281	+	0.935838i	0.999996	−	0.00286932i	$-0.000913335\pi$
$431$	13.6040	+	19.4285i	0.655281	+	0.935838i	−0.344715	+	0.938707i	$0.612024\pi$
$432$		0			0
$433$	18.6294	+	32.2671i	0.895273	+	1.55066i	0.833466	+	0.552570i	$0.186353\pi$
$433$	18.6294	+	32.2671i	0.895273	+	1.55066i	0.0618070	+	0.998088i	$0.480314\pi$
$434$	−0.205197	+	0.355412i	−0.00984977	+	0.0170603i
$435$		0			0
$436$	3.33951	−	12.4632i	0.159934	−	0.596880i
$437$	−13.7410	+	5.00130i	−0.657319	+	0.239245i
$438$		0			0
$439$	−7.37435	−	3.43872i	−0.351959	−	0.164121i	0.238595	−	0.971119i	$-0.423313\pi$
$439$	−7.37435	−	3.43872i	−0.351959	−	0.164121i	−0.590554	+	0.806998i	$0.701091\pi$
$440$	6.97034	+	1.22906i	0.332298	+	0.0585931i
$441$		0			0
$442$	−0.289598	+	3.31012i	−0.0137748	+	0.157446i
$443$	−13.8127			−0.656259			−0.328130	−	0.944633i	$-0.606418\pi$
$443$	−13.8127			−0.656259			−0.328130	+	0.944633i	$0.606418\pi$
$444$		0			0
$445$	−55.7786			−2.64416
$446$	−1.49143	+	17.0472i	−0.0706214	+	0.807207i
$447$		0			0
$448$	0.308637	+	0.0544210i	0.0145817	+	0.00257115i
$449$	14.8097	+	6.90586i	0.698912	+	0.325908i	0.739395	−	0.673272i	$-0.235112\pi$
$449$	14.8097	+	6.90586i	0.698912	+	0.325908i	−0.0404829	+	0.999180i	$0.512890\pi$
$450$		0			0
$451$	3.51494	−	1.27933i	0.165512	−	0.0602414i
$452$	−3.55769	+	13.2775i	−0.167340	+	0.624521i
$453$		0			0
$454$	−5.66764	+	9.81664i	−0.265996	+	0.460718i
$455$	−2.04219	−	3.53718i	−0.0957395	−	0.165826i
$456$		0			0
$457$	−3.10859	−	4.43953i	−0.145414	−	0.207672i	0.739837	−	0.672786i	$-0.234902\pi$
$457$	−3.10859	−	4.43953i	−0.145414	−	0.207672i	−0.885251	+	0.465113i	$0.846014\pi$
$458$	−5.30411	−	19.7952i	−0.247845	−	0.924969i
$459$		0			0
$460$	9.51385	+	3.46276i	0.443585	+	0.161452i
$461$	−2.14790	+	3.06752i	−0.100038	+	0.142869i	−0.866050	−	0.499957i	$-0.833349\pi$
$461$	−2.14790	+	3.06752i	−0.100038	+	0.142869i	0.766013	+	0.642826i	$0.222238\pi$
$462$		0			0
$463$	20.6921	−	1.81032i	0.961642	−	0.0841328i	0.404489	−	0.914543i	$-0.367449\pi$
$463$	20.6921	−	1.81032i	0.961642	−	0.0841328i	0.557153	+	0.830410i	$0.311894\pi$
$464$	−1.98619	−	1.39074i	−0.0922065	−	0.0645637i
$465$		0			0
$466$	11.9840	−	5.58824i	0.555149	−	0.258870i
$467$	−7.39003	+	1.98015i	−0.341970	+	0.0916305i	−0.425717	−	0.904857i	$-0.639978\pi$
$467$	−7.39003	+	1.98015i	−0.341970	+	0.0916305i	0.0837469	+	0.996487i	$0.473311\pi$
$468$		0			0
$469$	3.22127	+	3.83896i	0.148744	+	0.177267i
$470$	−16.1225	+	9.30833i	−0.743676	+	0.429361i
$471$		0			0
$472$	−1.00760	+	0.177668i	−0.0463787	+	0.00817781i
$473$	−9.92459	−	2.65929i	−0.456333	−	0.122274i
$474$		0			0
$475$	46.7554	+	46.7554i	2.14529	+	2.14529i
$476$	−0.136457	+	0.292633i	−0.00625450	+	0.0134128i
$477$		0			0
$478$	−13.3728	−	11.2211i	−0.611656	−	0.513240i
$479$	0.917985	+	0.0803133i	0.0419438	+	0.00366961i	0.108108	−	0.994139i	$-0.465521\pi$
$479$	0.917985	+	0.0803133i	0.0419438	+	0.00366961i	−0.0661645	+	0.997809i	$0.521076\pi$
$480$		0			0
$481$	8.43553	+	17.7115i	0.384627	+	0.807573i
$482$			15.6760i			0.714023i
$483$		0			0
$484$	−5.09867	+	6.07636i	−0.231758	+	0.276198i
$485$	−7.83128	+	44.4134i	−0.355600	+	2.01671i
$486$		0			0
$487$	21.8338	−	21.8338i	0.989385	−	0.989385i	−0.0105593	−	0.999944i	$-0.503361\pi$
$487$	21.8338	−	21.8338i	0.989385	−	0.989385i	0.999944	+	0.0105593i	$0.00336121\pi$
$488$	0.0547773	+	0.150499i	0.00247965	+	0.00681278i
$489$		0			0
$490$	4.84301	+	27.4661i	0.218785	+	1.24079i
$491$	2.71120	+	1.56531i	0.122355	+	0.0706416i	0.559928	−	0.828541i	$-0.310829\pi$
$491$	2.71120	+	1.56531i	0.122355	+	0.0706416i	−0.437574	+	0.899183i	$0.644162\pi$
$492$		0			0
$493$	1.91365	−	1.60574i	0.0861863	−	0.0723189i
$494$	15.4190	−	10.7965i	0.693733	−	0.485757i
$495$		0			0
$496$	0.553418	+	1.18681i	0.0248492	+	0.0532893i
$497$	−1.45879	+	4.00799i	−0.0654357	+	0.179783i
$498$		0			0
$499$	−1.81759	−	20.7751i	−0.0813664	−	0.930022i	−0.921687	−	0.387933i	$-0.873189\pi$
$499$	−1.81759	−	20.7751i	−0.0813664	−	0.930022i	0.840321	−	0.542089i	$-0.182366\pi$
$500$	−2.22913	−	25.4790i	−0.0996895	−	1.13946i
$501$		0			0
$502$	−1.19389	+	3.28018i	−0.0532859	+	0.146402i
$503$	−3.11236	−	6.67447i	−0.138773	−	0.297600i	0.824623	−	0.565683i	$-0.191388\pi$
$503$	−3.11236	−	6.67447i	−0.138773	−	0.297600i	−0.963396	+	0.268083i	$0.913610\pi$
$504$		0			0
$505$	−25.4894	+	17.8479i	−1.13426	+	0.794220i
$506$	3.36170	−	2.82081i	0.149446	−	0.125400i
$507$		0			0
$508$	7.37122	+	4.25577i	0.327045	+	0.188819i
$509$	−3.70917	−	21.0358i	−0.164406	−	0.932394i	−0.949675	−	0.313238i	$-0.898586\pi$
$509$	−3.70917	−	21.0358i	−0.164406	−	0.932394i	0.785268	−	0.619156i	$-0.212525\pi$
$510$		0			0
$511$	1.23200	+	3.38488i	0.0545003	+	0.149738i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	−3.76706	+	21.3640i	−0.166158	+	0.942328i
$515$	−51.5321	+	61.4136i	−2.27078	+	2.70621i
$516$		0			0
$517$			8.06932i			0.354888i
$518$	0.181630	+	1.89765i	0.00798038	+	0.0833781i
$519$		0			0
$520$	−12.9830	−	1.13587i	−0.569342	−	0.0498110i
$521$	11.1679	+	9.37098i	0.489275	+	0.410550i	0.853766	−	0.520656i	$-0.174313\pi$
$521$	11.1679	+	9.37098i	0.489275	+	0.410550i	−0.364492	+	0.931207i	$0.618757\pi$
$522$		0			0
$523$	−1.60056	+	3.43241i	−0.0699875	+	0.150089i	−0.938189	−	0.346123i	$-0.887498\pi$
$523$	−1.60056	+	3.43241i	−0.0699875	+	0.150089i	0.868202	+	0.496211i	$0.165276\pi$
$524$	5.12499	+	5.12499i	0.223886	+	0.223886i
$525$		0			0
$526$	−25.6551	−	6.87425i	−1.11861	−	0.299732i
$527$	−1.32864	+	0.234276i	−0.0578766	+	0.0102052i
$528$		0			0
$529$	−14.4823	+	8.36135i	−0.629664	+	0.363537i
$530$	−20.6870	−	24.6538i	−0.898586	−	1.07089i
$531$		0			0
$532$	1.76679	−	0.473409i	0.0765999	−	0.0205249i
$533$	−6.24218	+	2.91077i	−0.270379	+	0.126080i
$534$		0			0
$535$	−54.6743	−	38.2833i	−2.36377	−	1.65513i
$536$	15.9297	−	1.39367i	0.688059	−	0.0601973i
$537$		0			0
$538$	9.33609	−	13.3333i	0.402507	−	0.574840i
$539$	11.3597	+	4.13458i	0.489296	+	0.178089i
$540$		0			0
$541$	4.66754	+	17.4195i	0.200673	+	0.748923i	0.990725	+	0.135883i	$0.0433870\pi$
$541$	4.66754	+	17.4195i	0.200673	+	0.748923i	−0.790052	+	0.613040i	$0.789946\pi$
$542$	8.12456	+	11.6031i	0.348980	+	0.498395i
$543$		0			0
$544$	0.515136	+	0.892241i	0.0220863	+	0.0382545i
$545$	−26.0700	+	45.1545i	−1.11671	+	1.93421i
$546$		0			0
$547$	−0.783509	+	2.92410i	−0.0335004	+	0.125025i	−0.980651	−	0.195764i	$-0.937281\pi$
$547$	−0.783509	+	2.92410i	−0.0335004	+	0.125025i	0.947151	+	0.320789i	$0.103948\pi$
$548$	13.5125	−	4.91816i	0.577227	−	0.210094i
$549$		0			0
$550$	−17.9845	−	8.38629i	−0.766860	−	0.357592i
$551$	−13.9364	−	2.45737i	−0.593712	−	0.104687i
$552$		0			0
$553$	0.0289817	−	0.331262i	0.00123243	−	0.0140867i
$554$	−22.2231			−0.944170
$555$		0			0
$556$	−4.85596			−0.205939
$557$	−0.227391	+	2.59909i	−0.00963485	+	0.110127i	−0.999489	−	0.0319591i	$-0.989825\pi$
$557$	−0.227391	+	2.59909i	−0.00963485	+	0.110127i	0.989854	+	0.142086i	$0.0453809\pi$
$558$		0			0
$559$	18.6315	+	3.28524i	0.788030	+	0.138951i
$560$	−1.14777	−	0.535215i	−0.0485022	−	0.0226169i
$561$		0			0
$562$	−23.4256	+	8.52622i	−0.988149	+	0.359657i
$563$	−8.62275	+	32.1805i	−0.363406	+	1.35625i	0.506164	+	0.862437i	$0.331063\pi$
$563$	−8.62275	+	32.1805i	−0.363406	+	1.35625i	−0.869569	+	0.493811i	$0.835604\pi$
$564$		0			0
$565$	27.7732	−	48.1046i	1.16843	−	2.02377i
$566$	−0.899625	−	1.55820i	−0.0378140	−	0.0654958i
$567$		0			0
$568$	7.80614	+	11.1483i	0.327538	+	0.467773i
$569$	−1.56364	−	5.83560i	−0.0655514	−	0.244641i	0.925374	−	0.379056i	$-0.123751\pi$
$569$	−1.56364	−	5.83560i	−0.0655514	−	0.244641i	−0.990925	+	0.134415i	$0.957085\pi$
$570$		0			0
$571$	−18.7956	−	6.84105i	−0.786572	−	0.286289i	−0.0826618	−	0.996578i	$-0.526342\pi$
$571$	−18.7956	−	6.84105i	−0.786572	−	0.286289i	−0.703910	+	0.710289i	$0.748564\pi$
$572$	−3.24009	+	4.62733i	−0.135475	+	0.193478i
$573$		0			0
$574$	−0.666735	+	0.0583318i	−0.0278290	+	0.00243472i
$575$	−23.2517	−	16.2810i	−0.969661	−	0.678964i
$576$		0			0
$577$	26.7644	−	12.4805i	1.11422	−	0.519568i	0.223764	−	0.974643i	$-0.428165\pi$
$577$	26.7644	−	12.4805i	1.11422	−	0.519568i	0.890453	+	0.455075i	$0.150388\pi$
$578$	15.3954	−	4.12520i	0.640366	−	0.171586i
$579$		0			0
$580$	6.29806	+	7.50574i	0.261513	+	0.311659i
$581$	2.21429	−	1.27842i	0.0918640	−	0.0530377i
$582$		0			0
$583$	−13.7378	+	2.42234i	−0.568961	+	0.100323i
$584$	11.1021	+	2.97480i	0.459409	+	0.123098i
$585$		0			0
$586$	4.56682	+	4.56682i	0.188654	+	0.188654i
$587$	−4.39523	+	9.42560i	−0.181410	+	0.389036i	−0.975893	−	0.218252i	$-0.929965\pi$
$587$	−4.39523	+	9.42560i	−0.181410	+	0.389036i	0.794482	+	0.607288i	$0.207742\pi$
$588$		0			0
$589$	5.85468	+	4.91266i	0.241238	+	0.202423i
$590$	4.11875	+	0.360344i	0.169566	+	0.0148351i
$591$		0			0
$592$	5.29246	+	2.99832i	0.217519	+	0.123230i
$593$			28.4921i			1.17003i	0.811022	+	0.585016i	$0.198912\pi$
$593$			28.4921i			1.17003i	−0.811022	+	0.585016i	$0.801088\pi$
$594$		0			0
$595$	0.838685	−	0.999506i	0.0343827	−	0.0409757i
$596$	−0.203749	+	1.15552i	−0.00834588	+	0.0473319i
$597$		0			0
$598$	−5.71372	+	5.71372i	−0.233651	+	0.233651i
$599$	−4.43933	−	12.1970i	−0.181386	−	0.498354i	0.815360	−	0.578954i	$-0.196539\pi$
$599$	−4.43933	−	12.1970i	−0.181386	−	0.498354i	−0.996747	+	0.0805993i	$0.974317\pi$
$600$		0			0
$601$	−8.34511	−	47.3275i	−0.340404	−	1.93053i	−0.365424	−	0.930841i	$-0.619076\pi$
$601$	−8.34511	−	47.3275i	−0.340404	−	1.93053i	0.0250202	−	0.999687i	$-0.492035\pi$
$602$	1.59212	+	0.919213i	0.0648901	+	0.0374643i
$603$		0			0
$604$	0.538453	−	0.451815i	0.0219093	−	0.0183841i
$605$	26.2566	−	18.3850i	1.06748	−	0.747458i
$606$		0			0
$607$	−17.4240	−	37.3659i	−0.707219	−	1.51664i	−0.849944	−	0.526873i	$-0.823364\pi$
$607$	−17.4240	−	37.3659i	−0.707219	−	1.51664i	0.142726	−	0.989762i	$-0.454413\pi$
$608$	1.99616	−	5.48441i	0.0809551	−	0.222422i
$609$		0			0
$610$	−0.0564064	−	0.644728i	−0.00228383	−	0.0261043i
$611$	−1.29498	−	14.8016i	−0.0523891	−	0.598810i
$612$		0			0
$613$	−5.00311	+	13.7459i	−0.202074	+	0.555193i	−0.998791	−	0.0491591i	$-0.984346\pi$
$613$	−5.00311	+	13.7459i	−0.202074	+	0.555193i	0.796717	+	0.604352i	$0.206568\pi$
$614$	0.860769	+	1.84593i	0.0347378	+	0.0744955i
$615$		0			0
$616$	−0.449655	+	0.314852i	−0.0181171	+	0.0126857i
$617$	3.19202	−	2.67842i	0.128506	−	0.107829i	−0.576270	−	0.817260i	$-0.695492\pi$
$617$	3.19202	−	2.67842i	0.128506	−	0.107829i	0.704775	+	0.709431i	$0.251048\pi$
$618$		0			0
$619$	−8.32867	−	4.80856i	−0.334758	−	0.193272i	0.323194	−	0.946333i	$-0.395243\pi$
$619$	−8.32867	−	4.80856i	−0.334758	−	0.193272i	−0.657951	+	0.753060i	$0.728577\pi$
$620$	−0.918880	−	5.21123i	−0.0369031	−	0.209288i
$621$		0			0
$622$	0.549593	+	1.50999i	0.0220367	+	0.0605452i
$623$	3.05890	−	3.05890i	0.122552	−	0.122552i
$624$		0			0
$625$	−8.11047	+	45.9968i	−0.324419	+	1.83987i
$626$	3.35348	−	3.99652i	0.134032	−	0.159733i
$627$		0			0
$628$			5.84499i			0.233240i
$629$	−4.39508	+	4.46736i	−0.175243	+	0.178125i
$630$		0			0
$631$	−10.7081	−	0.936833i	−0.426281	−	0.0372947i	−0.128003	−	0.991774i	$-0.540857\pi$
$631$	−10.7081	−	0.936833i	−0.426281	−	0.0372947i	−0.298278	+	0.954479i	$0.596412\pi$
$632$	−0.812804	−	0.682024i	−0.0323316	−	0.0271294i
$633$		0			0
$634$	3.47710	−	7.45666i	0.138093	−	0.296142i
$635$	−24.3208	−	24.3208i	−0.965140	−	0.965140i
$636$		0			0
$637$	−21.5007	−	5.76109i	−0.851888	−	0.228263i
$638$	4.18241	−	0.737471i	0.165583	−	0.0291968i
$639$		0			0
$640$	−3.49957	+	2.02048i	−0.138333	+	0.0798663i
$641$	23.8550	+	28.4293i	0.942216	+	1.12289i	0.992264	+	0.124143i	$0.0396180\pi$
$641$	23.8550	+	28.4293i	0.942216	+	1.12289i	−0.0500484	+	0.998747i	$0.515938\pi$
$642$		0			0
$643$	−22.4858	+	6.02506i	−0.886755	+	0.237605i	−0.673319	−	0.739352i	$-0.735132\pi$
$643$	−22.4858	+	6.02506i	−0.886755	+	0.237605i	−0.213436	+	0.976957i	$0.568465\pi$
$644$	−0.711637	+	0.331842i	−0.0280424	+	0.0130764i
$645$		0			0
$646$	4.92562	+	3.44895i	0.193796	+	0.135697i
$647$	−31.4432	+	2.75092i	−1.23616	+	0.108150i	−0.686432	−	0.727194i	$-0.740824\pi$
$647$	−31.4432	+	2.75092i	−1.23616	+	0.108150i	−0.549728	+	0.835344i	$0.685269\pi$
$648$		0			0
$649$	1.02789	−	1.46798i	0.0403483	−	0.0576234i
$650$	34.3349	+	12.4969i	1.34673	+	0.490168i
$651$		0			0
$652$	−4.89084	−	18.2529i	−0.191540	−	0.714838i
$653$	3.88391	+	5.54680i	0.151989	+	0.217063i	0.887925	−	0.459988i	$-0.152146\pi$
$653$	3.88391	+	5.54680i	0.151989	+	0.217063i	−0.735936	+	0.677051i	$0.763257\pi$
$654$		0			0
$655$	−14.6441	−	25.3643i	−0.572192	−	0.991065i
$656$	−1.06778	+	1.84945i	−0.0416899	+	0.0722091i
$657$		0			0
$658$	0.373689	−	1.39463i	0.0145679	−	0.0543682i
$659$	38.6771	−	14.0773i	1.50665	−	0.548374i	0.548875	−	0.835905i	$-0.315056\pi$
$659$	38.6771	−	14.0773i	1.50665	−	0.548374i	0.957772	+	0.287530i	$0.0928342\pi$
$660$		0			0
$661$	15.8222	+	7.37804i	0.615414	+	0.286972i	0.705222	−	0.708987i	$-0.250847\pi$
$661$	15.8222	+	7.37804i	0.615414	+	0.286972i	−0.0898076	+	0.995959i	$0.528625\pi$
$662$	27.7803	+	4.89841i	1.07971	+	0.190382i
$663$		0			0
$664$	0.711055	−	8.12739i	0.0275943	−	0.315404i
$665$	−7.39135			−0.286624
$666$		0			0
$667$	6.07495			0.235223
$668$	2.15983	−	24.6870i	0.0835664	−	0.955168i
$669$		0			0
$670$	−63.6354	−	11.2206i	−2.45845	−	0.433491i
$671$	−0.254240	−	0.118554i	−0.00981481	−	0.00457672i
$672$		0			0
$673$	8.98287	−	3.26950i	0.346264	−	0.126030i	−0.163033	−	0.986621i	$-0.552128\pi$
$673$	8.98287	−	3.26950i	0.346264	−	0.126030i	0.509297	+	0.860591i	$0.329905\pi$
$674$	−5.95991	+	22.2427i	−0.229567	+	0.856756i
$675$		0			0
$676$	−1.29927	+	2.25040i	−0.0499719	+	0.0865538i
$677$	13.3132	+	23.0591i	0.511667	+	0.886234i	0.999909	+	0.0135252i	$0.00430533\pi$
$677$	13.3132	+	23.0591i	0.511667	+	0.886234i	−0.488241	+	0.872709i	$0.662361\pi$
$678$		0			0
$679$	−2.00616	−	2.86510i	−0.0769895	−	0.109952i
$680$	−1.07754	−	4.02142i	−0.0413216	−	0.154214i
$681$		0			0
$682$	−2.15531	−	0.784468i	−0.0825311	−	0.0300388i
$683$	−1.76416	+	2.51949i	−0.0675039	+	0.0964056i	−0.851485	−	0.524380i	$-0.824297\pi$
$683$	−1.76416	+	2.51949i	−0.0675039	+	0.0964056i	0.783981	+	0.620785i	$0.213186\pi$
$684$		0			0
$685$	−57.8868	+	5.06443i	−2.21174	+	0.193502i
$686$	−3.56887	−	2.49895i	−0.136260	−	0.0954104i
$687$		0			0
$688$	5.31650	−	2.47912i	0.202690	−	0.0945157i
$689$	24.8106	−	6.64798i	0.945209	−	0.253268i
$690$		0			0
$691$	11.4621	+	13.6600i	0.436039	+	0.519651i	0.938654	−	0.344859i	$-0.112073\pi$
$691$	11.4621	+	13.6600i	0.436039	+	0.519651i	−0.502616	+	0.864510i	$0.667629\pi$
$692$	8.74965	−	5.05161i	0.332612	−	0.192034i
$693$		0			0
$694$	24.3188	−	4.28806i	0.923128	−	0.162772i
$695$	18.9541	+	5.07873i	0.718969	+	0.192647i
$696$		0			0
$697$	−1.55579	−	1.55579i	−0.0589296	−	0.0589296i
$698$	11.3314	−	24.3003i	0.428900	−	0.919779i
$699$		0			0
$700$	2.71990	+	2.28227i	0.102802	+	0.0862615i
$701$	28.8141	+	2.52091i	1.08829	+	0.0952133i	0.617152	−	0.786844i	$-0.288287\pi$
$701$	28.8141	+	2.52091i	1.08829	+	0.0952133i	0.471142	+	0.882058i	$0.343842\pi$
$702$		0			0
$703$	35.3903	+	2.80560i	1.33477	+	0.105815i
$704$			1.75154i			0.0660135i
$705$		0			0
$706$	9.65437	−	11.5056i	0.363347	−	0.433020i
$707$	0.419062	−	2.37662i	0.0157604	−	0.0893819i
$708$		0			0
$709$	0.829801	−	0.829801i	0.0311638	−	0.0311638i	−0.691353	−	0.722517i	$-0.742985\pi$
$709$	0.829801	−	0.829801i	0.0311638	−	0.0311638i	0.722517	+	0.691353i	$0.242985\pi$
$710$	−18.8096	−	51.6790i	−0.705913	−	1.93948i
$711$		0			0
$712$	−2.39692	−	13.5936i	−0.0898285	−	0.509443i
$713$	−2.84133	−	1.64045i	−0.106409	−	0.0614351i
$714$		0			0
$715$	17.4865	−	14.6729i	0.653959	−	0.548737i
$716$	−18.4817	+	12.9410i	−0.690693	+	0.483629i
$717$		0			0
$718$	−11.5137	−	24.6912i	−0.429688	−	0.921468i
$719$	−8.63325	+	23.7197i	−0.321966	+	0.884594i	0.668110	+	0.744062i	$0.267104\pi$
$719$	−8.63325	+	23.7197i	−0.321966	+	0.884594i	−0.990076	+	0.140532i	$0.955119\pi$
$720$		0			0
$721$	−0.541900	−	6.19394i	−0.0201814	−	0.230674i
$722$	−1.31287	−	15.0061i	−0.0488598	−	0.558470i
$723$		0			0
$724$	−5.50796	+	15.1330i	−0.204702	+	0.562414i
$725$	−11.6093	−	24.8963i	−0.431159	−	0.924624i
$726$		0			0
$727$	−0.559460	+	0.391738i	−0.0207492	+	0.0145288i	−0.583905	−	0.811822i	$-0.698476\pi$
$727$	−0.559460	+	0.391738i	−0.0207492	+	0.0145288i	0.563156	+	0.826351i	$0.309587\pi$
$728$	0.774278	−	0.649697i	0.0286967	−	0.0240794i
$729$		0			0
$730$	−40.2231	−	23.2228i	−1.48873	−	0.859516i
$731$	1.04947	+	5.95187i	0.0388162	+	0.220138i
$732$		0			0
$733$	2.99002	+	8.21501i	0.110439	+	0.303428i	0.982584	−	0.185819i	$-0.0594938\pi$
$733$	2.99002	+	8.21501i	0.110439	+	0.303428i	−0.872145	+	0.489247i	$0.837272\pi$
$734$	−12.5408	+	12.5408i	−0.462888	+	0.462888i
$735$		0			0
$736$	−0.435068	+	2.46739i	−0.0160368	+	0.0909493i
$737$	−18.0032	+	21.4554i	−0.663157	+	0.790320i
$738$		0			0
$739$			28.5466i			1.05010i	0.851071	+	0.525051i	$0.175954\pi$
$739$			28.5466i			1.05010i	−0.851071	+	0.525051i	$0.824046\pi$
$740$	−17.5220	−	17.2385i	−0.644120	−	0.633698i
$741$		0			0
$742$	2.48649	+	0.217540i	0.0912819	+	0.00798613i
$743$	16.8230	+	14.1161i	0.617174	+	0.517871i	0.896914	−	0.442205i	$-0.145804\pi$
$743$	16.8230	+	14.1161i	0.617174	+	0.517871i	−0.279740	+	0.960076i	$0.590248\pi$
$744$		0			0
$745$	2.00381	−	4.29719i	0.0734140	−	0.157437i
$746$	−10.3701	−	10.3701i	−0.379675	−	0.379675i
$747$		0			0
$748$	−1.74307	−	0.467054i	−0.0637329	−	0.0170772i
$749$	5.09779	−	0.898879i	0.186269	−	0.0328443i
$750$		0			0
$751$	16.9423	−	9.78162i	0.618232	−	0.356937i	−0.157948	−	0.987447i	$-0.550488\pi$
$751$	16.9423	−	9.78162i	0.618232	−	0.356937i	0.776180	+	0.630511i	$0.217155\pi$
$752$	−2.96132	−	3.52917i	−0.107988	−	0.128695i
$753$		0			0
$754$	−7.55348	+	2.02395i	−0.275081	+	0.0737079i
$755$	−2.57426	+	1.20040i	−0.0936870	+	0.0436870i
$756$		0			0
$757$	18.6066	+	13.0285i	0.676269	+	0.473529i	0.860564	−	0.509342i	$-0.170111\pi$
$757$	18.6066	+	13.0285i	0.676269	+	0.473529i	−0.184295	+	0.982871i	$0.559000\pi$
$758$	−4.37585	+	0.382837i	−0.158938	+	0.0139053i
$759$		0			0
$760$	−13.5276	+	19.3193i	−0.490696	+	0.700786i
$761$	−28.8549	−	10.5023i	−1.04599	−	0.380709i	−0.238841	−	0.971059i	$-0.576768\pi$
$761$	−28.8549	−	10.5023i	−1.04599	−	0.380709i	−0.807147	+	0.590350i	$0.798990\pi$
$762$		0			0
$763$	−1.04660	−	3.90595i	−0.0378893	−	0.141405i
$764$	−3.98293	−	5.68821i	−0.144097	−	0.205792i
$765$		0			0
$766$	−2.70857	−	4.69137i	−0.0978644	−	0.169506i
$767$	−1.64989	+	2.85769i	−0.0595741	+	0.103185i
$768$		0			0
$769$	−10.4223	+	38.8967i	−0.375839	+	1.40265i	0.476276	+	0.879296i	$0.341986\pi$
$769$	−10.4223	+	38.8967i	−0.375839	+	1.40265i	−0.852115	+	0.523355i	$0.824680\pi$
$770$	2.08442	−	0.758665i	0.0751171	−	0.0273404i
$771$		0			0
$772$	−6.76622	−	3.15514i	−0.243522	−	0.113556i
$773$	−17.6601	−	3.11395i	−0.635189	−	0.112001i	−0.153224	−	0.988191i	$-0.548966\pi$
$773$	−17.6601	−	3.11395i	−0.635189	−	0.112001i	−0.481965	+	0.876191i	$0.660077\pi$
$774$		0			0
$775$	−1.29301	+	14.7792i	−0.0464465	+	0.530886i
$776$	−11.1604			−0.400634
$777$		0			0
$778$	11.2371			0.402871
$779$	−1.08631	+	12.4166i	−0.0389211	+	0.444870i
$780$		0			0
$781$	−23.4755	−	4.13937i	−0.840020	−	0.148118i
$782$	−2.33945	−	1.09090i	−0.0836586	−	0.0390107i
$783$		0			0
$784$	−6.48555	+	2.36055i	−0.231627	+	0.0843053i
$785$	6.11313	−	22.8145i	0.218187	−	0.814285i
$786$		0			0
$787$	−7.44633	+	12.8974i	−0.265433	+	0.459744i	−0.967677	−	0.252193i	$-0.918848\pi$
$787$	−7.44633	+	12.8974i	−0.265433	+	0.459744i	0.702244	+	0.711936i	$0.252182\pi$
$788$	11.0960	+	19.2189i	0.395280	+	0.684645i
$789$		0			0
$790$	2.45927	+	3.51221i	0.0874970	+	0.124959i
$791$	1.11497	+	4.16114i	0.0396439	+	0.147953i
$792$		0			0
$793$	0.485380	+	0.176664i	0.0172363	+	0.00627352i
$794$	−1.77994	+	2.54202i	−0.0631679	+	0.0902131i
$795$		0			0
$796$	14.6456	−	1.28132i	0.519099	−	0.0454153i
$797$	16.3333	+	11.4367i	0.578555	+	0.405108i	0.825898	−	0.563820i	$-0.190669\pi$
$797$	16.3333	+	11.4367i	0.578555	+	0.405108i	−0.247343	+	0.968928i	$0.579558\pi$
$798$		0			0
$799$	4.30176	−	2.00594i	0.152185	−	0.0709651i
$800$	10.9433	−	2.93224i	0.386902	−	0.103670i
$801$		0			0
$802$	−23.1551	−	27.5952i	−0.817635	−	0.974419i
$803$	−17.4346	+	10.0659i	−0.615252	+	0.355216i
$804$		0			0
$805$	3.12477	−	0.550981i	0.110134	−	0.0194195i
$806$	4.07940	+	1.09307i	0.143691	+	0.0385018i
$807$		0			0
$808$	−5.44499	−	5.44499i	−0.191554	−	0.191554i
$809$	11.0839	−	23.7695i	0.389690	−	0.835693i	−0.609393	−	0.792869i	$-0.708587\pi$
$809$	11.0839	−	23.7695i	0.389690	−	0.835693i	0.999083	−	0.0428242i	$-0.0136355\pi$
$810$		0			0
$811$	27.0775	+	22.7207i	0.950819	+	0.797832i	0.979435	−	0.201759i	$-0.0646657\pi$
$811$	27.0775	+	22.7207i	0.950819	+	0.797832i	−0.0286164	+	0.999590i	$0.509110\pi$
$812$	−0.757001	−	0.0662290i	−0.0265655	−	0.00232418i
$813$		0			0
$814$	−10.2683	+	2.84135i	−0.359904	+	0.0995891i
$815$			76.3609i			2.67481i
$816$		0			0
$817$	22.0070	−	26.2270i	0.769929	−	0.917566i
$818$	−0.0211241	+	0.119801i	−0.000738588	+	0.00418874i
$819$		0			0
$820$	6.10213	−	6.10213i	0.213096	−	0.213096i
$821$	−15.6204	−	42.9166i	−0.545154	−	1.49780i	−0.840179	−	0.542309i	$-0.817550\pi$
$821$	−15.6204	−	42.9166i	−0.545154	−	1.49780i	0.295025	−	0.955490i	$-0.404672\pi$
$822$		0			0
$823$	2.60357	+	14.7656i	0.0907549	+	0.514696i	0.995966	+	0.0897339i	$0.0286016\pi$
$823$	2.60357	+	14.7656i	0.0907549	+	0.514696i	−0.905211	+	0.424963i	$0.860287\pi$
$824$	−17.1814	−	9.91966i	−0.598541	−	0.345568i
$825$		0			0
$826$	−0.245634	+	0.206111i	−0.00854669	+	0.00717152i
$827$	−35.6153	+	24.9381i	−1.23846	+	0.867182i	−0.994717	−	0.102657i	$-0.967266\pi$
$827$	−35.6153	+	24.9381i	−1.23846	+	0.867182i	−0.243747	+	0.969839i	$0.578377\pi$
$828$		0			0
$829$	−8.51185	−	18.2537i	−0.295629	−	0.633978i	0.701251	−	0.712915i	$-0.252625\pi$
$829$	−8.51185	−	18.2537i	−0.295629	−	0.633978i	−0.996880	+	0.0789367i	$0.974847\pi$
$830$	−11.2757	+	30.9796i	−0.391384	+	1.07532i
$831$		0			0
$832$	−0.281089	−	3.21286i	−0.00974499	−	0.111386i
$833$	−0.619739	−	7.08365i	−0.0214727	−	0.245434i
$834$		0			0
$835$	−34.2499	+	94.1008i	−1.18527	+	3.25649i
$836$	4.32027	+	9.26486i	0.149420	+	0.320432i
$837$		0			0
$838$	18.6473	−	13.0570i	0.644159	−	0.451045i
$839$	13.2259	−	11.0978i	0.456607	−	0.383139i	−0.385274	−	0.922802i	$-0.625893\pi$
$839$	13.2259	−	11.0978i	0.456607	−	0.383139i	0.841881	+	0.539663i	$0.181448\pi$
$840$		0			0
$841$	−20.0233	−	11.5604i	−0.690458	−	0.398636i
$842$	−3.03224	−	17.1967i	−0.104498	−	0.592636i
$843$		0			0
$844$	9.07158	+	24.9240i	0.312257	+	0.857918i
$845$	7.42502	−	7.42502i	0.255428	−	0.255428i
$846$		0			0
$847$	−0.431674	+	2.44814i	−0.0148325	+	0.0841192i
$848$	5.11934	−	6.10099i	0.175799	−	0.209509i
$849$		0			0
$850$			11.6722i			0.400355i
$851$	−15.1708	+	1.45204i	−0.520047	+	0.0497754i
$852$		0			0
$853$	0.0642643	+	0.00562239i	0.00220037	+	0.000192507i	0.0882559	−	0.996098i	$-0.471871\pi$
$853$	0.0642643	+	0.00562239i	0.00220037	+	0.000192507i	−0.0860555	+	0.996290i	$0.527426\pi$
$854$	0.0384502	+	0.0322636i	0.00131574	+	0.00110404i
$855$		0			0
$856$	6.98044	−	14.9696i	0.238587	−	0.511651i
$857$	−26.4642	−	26.4642i	−0.903998	−	0.903998i	0.0917808	−	0.995779i	$-0.470744\pi$
$857$	−26.4642	−	26.4642i	−0.903998	−	0.903998i	−0.995779	+	0.0917808i	$0.970744\pi$
$858$		0			0
$859$	−11.4826	−	3.07676i	−0.391782	−	0.104978i	0.0575496	−	0.998343i	$-0.481671\pi$
$859$	−11.4826	−	3.07676i	−0.391782	−	0.104978i	−0.449332	+	0.893365i	$0.648338\pi$
$860$	−23.3445	+	4.11627i	−0.796042	+	0.140364i
$861$		0			0
$862$	20.5402	−	11.8589i	0.699603	−	0.403916i
$863$	−2.31209	−	2.75544i	−0.0787045	−	0.0937964i	0.725255	−	0.688480i	$-0.241722\pi$
$863$	−2.31209	−	2.75544i	−0.0787045	−	0.0937964i	−0.803960	+	0.594684i	$0.797277\pi$
$864$		0			0
$865$	−39.4355	+	10.5667i	−1.34085	+	0.359279i
$866$	33.7680	−	15.7463i	1.14748	−	0.535080i
$867$		0			0
$868$	0.336175	+	0.235392i	0.0114105	+	0.00798973i
$869$	1.85138	−	0.161975i	0.0628037	−	0.00549461i
$870$		0			0
$871$	29.5803	−	42.2450i	1.00229	−	1.43142i
$872$	−12.1247	−	4.41305i	−0.410596	−	0.149445i
$873$		0			0
$874$	3.78466	+	14.1246i	0.128018	+	0.477770i
$875$	−4.59754	−	6.56597i	−0.155425	−	0.221970i
$876$		0			0
$877$	−19.0667	−	33.0245i	−0.643836	−	1.11516i	−0.984569	−	0.174997i	$-0.944008\pi$
$877$	−19.0667	−	33.0245i	−0.643836	−	1.11516i	0.340733	−	0.940160i	$-0.389325\pi$
$878$	−4.06835	+	7.04659i	−0.137300	+	0.237811i
$879$		0			0
$880$	1.83189	−	6.83670i	0.0617529	−	0.230465i
$881$	19.4881	−	7.09310i	0.656572	−	0.238973i	0.00781619	−	0.999969i	$-0.497512\pi$
$881$	19.4881	−	7.09310i	0.656572	−	0.238973i	0.648756	+	0.760997i	$0.275290\pi$
$882$		0			0
$883$	43.7825	+	20.4161i	1.47340	+	0.687057i	0.982859	−	0.184361i	$-0.0590215\pi$
$883$	43.7825	+	20.4161i	1.47340	+	0.687057i	0.490541	+	0.871418i	$0.336799\pi$
$884$	3.27228	+	0.576991i	0.110059	+	0.0194063i
$885$		0			0
$886$	−1.20385	+	13.7601i	−0.0404442	+	0.462279i
$887$	4.29206			0.144113			0.0720566	−	0.997401i	$-0.477044\pi$
$887$	4.29206			0.144113			0.0720566	+	0.997401i	$0.477044\pi$
$888$		0			0
$889$	2.66750			0.0894651
$890$	−4.86142	+	55.5663i	−0.162955	+	1.86259i
$891$		0			0
$892$	16.8523	+	2.97152i	0.564257	+	0.0994937i
$893$	−24.3690	−	11.3635i	−0.815479	−	0.380264i
$894$		0			0
$895$	85.6735	−	31.1826i	2.86375	−	1.04232i
$896$	0.0811133	−	0.302719i	0.00270981	−	0.0101131i
$897$		0			0
$898$	8.17033	−	14.1514i	0.272648	−	0.472239i
$899$	−1.58756	−	2.74974i	−0.0529482	−	0.0917089i
$900$		0			0
$901$	4.70641	+	6.72145i	0.156793	+	0.223924i
$902$	−0.968118	−	3.61306i	−0.0322348	−	0.120302i
$903$		0			0
$904$	12.9169	+	4.70136i	0.429609	+	0.156365i
$905$	37.3262	−	53.3074i	1.24077	−	1.77200i
$906$		0			0
$907$	−30.3538	+	2.65562i	−1.00788	+	0.0881783i	−0.579123	−	0.815240i	$-0.696605\pi$
$907$	−30.3538	+	2.65562i	−1.00788	+	0.0881783i	−0.428759	+	0.903419i	$0.641049\pi$
$908$	9.28532	+	6.50165i	0.308144	+	0.215765i
$909$		0			0
$910$	−3.70171	+	1.72614i	−0.122711	+	0.0572209i
$911$	−17.3137	+	4.63920i	−0.573630	+	0.153704i	−0.533961	−	0.845509i	$-0.679297\pi$
$911$	−17.3137	+	4.63920i	−0.573630	+	0.153704i	−0.0396690	+	0.999213i	$0.512630\pi$
$912$		0			0
$913$	9.18530	+	10.9466i	0.303989	+	0.362280i
$914$	−4.69356	+	2.70983i	−0.155249	+	0.0896332i
$915$		0			0
$916$	−20.1821	+	3.55866i	−0.666837	+	0.117581i
$917$	2.19406	+	0.587896i	0.0724542	+	0.0194140i
$918$		0			0
$919$	22.1656	+	22.1656i	0.731176	+	0.731176i	0.970853	−	0.239677i	$-0.0770415\pi$
$919$	22.1656	+	22.1656i	0.731176	+	0.731176i	−0.239677	+	0.970853i	$0.577042\pi$
$920$	4.27877	−	9.17585i	0.141067	−	0.302519i
$921$		0			0
$922$	2.86865	+	2.40708i	0.0944738	+	0.0792730i
$923$	43.7257	+	3.82550i	1.43925	+	0.125918i
$924$		0			0
$925$	34.9423	+	59.3977i	1.14890	+	1.95298i
$926$		−	20.7711i		−	0.682581i
$927$		0			0
$928$	−1.55856	+	1.85742i	−0.0511622	+	0.0609728i
$929$	−2.32904	+	13.2086i	−0.0764132	+	0.433361i	0.922468	+	0.386073i	$0.126169\pi$
$929$	−2.32904	+	13.2086i	−0.0764132	+	0.433361i	−0.998881	+	0.0472874i	$0.984942\pi$
$930$		0			0
$931$	−28.4833	+	28.4833i	−0.933503	+	0.933503i
$932$	−4.52250	−	12.4255i	−0.148139	−	0.407010i
$933$		0			0
$934$	1.32853	+	7.53449i	0.0434709	+	0.246536i
$935$	6.31517	+	3.64606i	0.206528	+	0.119239i
$936$		0			0
$937$	16.8627	−	14.1495i	0.550880	−	0.462243i	−0.324359	−	0.945934i	$-0.605148\pi$
$937$	16.8627	−	14.1495i	0.550880	−	0.462243i	0.875239	+	0.483691i	$0.160704\pi$
$938$	4.10510	−	2.87443i	0.134036	−	0.0938533i
$939$		0			0
$940$	7.86774	+	16.8724i	0.256617	+	0.550318i
$941$	−1.66861	+	4.58447i	−0.0543951	+	0.149449i	−0.963914	−	0.266212i	$-0.914228\pi$
$941$	−1.66861	+	4.58447i	−0.0543951	+	0.149449i	0.909519	+	0.415662i	$0.136450\pi$
$942$		0			0
$943$	−0.466333	−	5.33021i	−0.0151859	−	0.173575i
$944$	0.0891731	+	1.01925i	0.00290234	+	0.0331739i
$945$		0			0
$946$	−3.51415	+	9.65505i	−0.114255	+	0.313913i
$947$	20.8015	+	44.6090i	0.675959	+	1.44960i	0.882093	+	0.471075i	$0.156134\pi$
$947$	20.8015	+	44.6090i	0.675959	+	1.44960i	−0.206135	+	0.978524i	$0.566088\pi$
$948$		0			0
$949$	30.3650	−	21.2618i	0.985690	−	0.690187i
$950$	50.6525	−	42.5025i	1.64338	−	1.37896i
$951$		0			0
$952$	0.279627	+	0.161442i	0.00906275	+	0.00523238i
$953$	−9.77644	−	55.4449i	−0.316690	−	1.79604i	−0.562583	−	0.826741i	$-0.690192\pi$
$953$	−9.77644	−	55.4449i	−0.316690	−	1.79604i	0.245893	−	0.969297i	$-0.420919\pi$
$954$		0			0
$955$	9.59724	+	26.3682i	0.310559	+	0.853255i
$956$	−12.3439	+	12.3439i	−0.399230	+	0.399230i
$957$		0			0
$958$	0.160015	−	0.907492i	0.00516986	−	0.0293197i
$959$	2.89678	−	3.45224i	0.0935418	−	0.111479i
$960$		0			0
$961$		−	29.2852i		−	0.944684i
$962$	18.3793	−	6.85978i	0.592571	−	0.221168i
$963$		0			0
$964$	15.6164	+	1.36625i	0.502969	+	0.0440041i
$965$	23.1104	+	19.3919i	0.743951	+	0.624249i
$966$		0			0
$967$	21.4989	−	46.1045i	0.691357	−	1.48262i	−0.175716	−	0.984441i	$-0.556224\pi$
$967$	21.4989	−	46.1045i	0.691357	−	1.48262i	0.867074	−	0.498180i	$-0.165998\pi$
$968$	5.60886	+	5.60886i	0.180276	+	0.180276i
$969$		0			0
$970$	43.5619	+	11.6724i	1.39869	+	0.374777i
$971$	54.2677	−	9.56886i	1.74153	−	0.307079i	0.789654	−	0.613552i	$-0.210260\pi$
$971$	54.2677	−	9.56886i	1.74153	−	0.307079i	0.951880	+	0.306472i	$0.0991487\pi$
$972$		0			0
$973$	−1.31796	+	0.760924i	−0.0422518	+	0.0243941i
$974$	−19.8478	−	23.6537i	−0.635964	−	0.757913i
$975$		0			0
$976$	0.154701	−	0.0414519i	0.00495185	−	0.00132684i
$977$	−23.7018	+	11.0523i	−0.758286	+	0.353595i	−0.763004	−	0.646394i	$-0.776276\pi$
$977$	−23.7018	+	11.0523i	−0.758286	+	0.353595i	0.00471738	+	0.999989i	$0.498498\pi$
$978$		0			0
$979$	19.8047	+	13.8674i	0.632959	+	0.443203i
$980$	27.7836	−	2.43075i	0.887516	−	0.0776476i
$981$		0			0
$982$	1.79565	−	2.56446i	0.0573016	−	0.0818351i
$983$	47.4957	+	17.2870i	1.51488	+	0.551371i	0.959863	−	0.280469i	$-0.0904899\pi$
$983$	47.4957	+	17.2870i	1.51488	+	0.551371i	0.555016	+	0.831840i	$0.312712\pi$
$984$		0			0
$985$	−23.2101	−	86.6214i	−0.739537	−	2.75999i
$986$	−1.43284	−	2.04631i	−0.0456311	−	0.0651679i
$987$		0			0
$988$	−9.41156	−	16.3013i	−0.299422	−	0.518613i
$989$	−7.34864	+	12.7282i	−0.233673	+	0.404734i
$990$		0			0
$991$	−10.2293	+	38.1762i	−0.324944	+	1.21271i	0.589424	+	0.807824i	$0.299355\pi$
$991$	−10.2293	+	38.1762i	−0.324944	+	1.21271i	−0.914368	+	0.404883i	$0.867312\pi$
$992$	1.23053	−	0.447875i	0.0390692	−	0.0142200i
$993$		0			0
$994$	3.86560	+	1.80256i	0.122609	+	0.0571737i
$995$	−58.5056	−	10.3161i	−1.85475	−	0.327043i
$996$		0			0
$997$	1.75339	−	20.0413i	0.0555304	−	0.634715i	−0.916527	−	0.399972i	$-0.869020\pi$
$997$	1.75339	−	20.0413i	0.0555304	−	0.634715i	0.972058	−	0.234743i	$-0.0754247\pi$
$998$	−20.8545			−0.660137
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.bs.b.557.8	yes	96
3.2	odd	2	inner	666.2.bs.b.557.1	✓	96
37.19	odd	36	inner	666.2.bs.b.611.1	yes	96
111.56	even	36	inner	666.2.bs.b.611.8	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.bs.b.557.1	✓	96	3.2	odd	2	inner
666.2.bs.b.557.8	yes	96	1.1	even	1	trivial
666.2.bs.b.611.1	yes	96	37.19	odd	36	inner
666.2.bs.b.611.8	yes	96	111.56	even	36	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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.bs (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0871557 - 0.996195i) q^{2} +(-0.984808 - 0.173648i) q^{4} +(3.66235 + 1.70778i) q^{5} +(-0.294498 + 0.107188i) q^{7} +(-0.258819 + 0.965926i) q^{8} +O(q^{10})\)	\(q+(0.0871557 - 0.996195i) q^{2} +(-0.984808 - 0.173648i) q^{4} +(3.66235 + 1.70778i) q^{5} +(-0.294498 + 0.107188i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(2.02048 - 3.49957i) q^{10} +(-0.875768 - 1.51687i) q^{11} +(1.84986 + 2.64187i) q^{13} +(0.0811133 + 0.302719i) q^{14} +(0.939693 + 0.342020i) q^{16} +(-0.590940 + 0.843949i) q^{17} +(5.81418 - 0.508675i) q^{19} +(-3.31015 - 2.31779i) q^{20} +(-1.58743 + 0.740231i) q^{22} +(-2.42008 + 0.648460i) q^{23} +(7.28233 + 8.67874i) q^{25} +(2.79304 - 1.61256i) q^{26} +(0.308637 - 0.0544210i) q^{28} +(-2.34207 - 0.627556i) q^{29} +(0.925955 + 0.925955i) q^{31} +(0.422618 - 0.906308i) q^{32} +(0.789234 + 0.662246i) q^{34} +(-1.26161 - 0.110376i) q^{35} +(5.99877 + 1.00737i) q^{37} -5.83639i q^{38} +(-2.59747 + 3.09555i) q^{40} +(-0.370837 + 2.10312i) q^{41} +(4.14796 - 4.14796i) q^{43} +(0.599060 + 1.64590i) q^{44} +(0.435068 + 2.46739i) q^{46} +(-3.98978 - 2.30350i) q^{47} +(-5.28707 + 4.43638i) q^{49} +(9.28041 - 6.49821i) q^{50} +(-1.36300 - 2.92296i) q^{52} +(2.72394 - 7.48397i) q^{53} +(-0.616877 - 7.05093i) q^{55} +(-0.0273144 - 0.312205i) q^{56} +(-0.829292 + 2.27846i) q^{58} +(0.432400 + 0.927286i) q^{59} +(0.131194 - 0.0918629i) q^{61} +(1.00313 - 0.841729i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(2.26309 + 12.8346i) q^{65} +(-5.46909 - 15.0262i) q^{67} +(0.728512 - 0.728512i) q^{68} +(-0.219912 + 1.24719i) q^{70} +(8.74807 - 10.4255i) q^{71} -11.4937i q^{73} +(1.52636 - 5.88814i) q^{74} +(-5.81418 - 0.508675i) q^{76} +(0.420503 + 0.352844i) q^{77} +(-0.448415 + 0.961629i) q^{79} +(2.85738 + 2.85738i) q^{80} +(2.06280 + 0.552725i) q^{82} +(-8.03449 + 1.41670i) q^{83} +(-3.60550 + 2.08164i) q^{85} +(-3.77066 - 4.49370i) q^{86} +(1.69185 - 0.453331i) q^{88} +(-12.5101 + 5.83354i) q^{89} +(-0.827957 - 0.579742i) q^{91} +(2.49592 - 0.218365i) q^{92} +(-2.64247 + 3.77383i) q^{94} +(22.1622 + 8.06640i) q^{95} +(2.88852 + 10.7801i) q^{97} +(3.95870 + 5.65361i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82} - 108 q^{85} - 24 q^{88} + 216 q^{91} - 60 q^{94} + 24 q^{97}+O(q^{100}) \) 96 * q - 12 * q^13 + 24 * q^19 + 12 * q^22 + 48 * q^31 + 72 * q^34 + 24 * q^37 + 72 * q^43 + 60 * q^46 + 12 * q^52 - 60 * q^55 + 12 * q^58 - 120 * q^61 + 36 * q^67 + 12 * q^70 - 24 * q^76 + 60 * q^79 + 96 * q^82 - 108 * q^85 - 24 * q^88 + 216 * q^91 - 60 * q^94 + 24 * q^97

Introduction

L-functions

Modular forms

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Database

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