LMFDB - Embedded newform 666.2.bs.b.557.1

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			557.1
Character	$\chi$	$=$	666.557
Dual form			666.2.bs.b.611.1

$q$-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	−0.637871	−	0.770143i	$-0.720185\pi$
$5$	−3.66235	−	1.70778i	−1.63785	−	0.763742i	−0.999980	+	0.00640061i	$0.997963\pi$
$6$		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	0.967315	−	0.253577i	$-0.0816070\pi$
$11$	0.875768	+	1.51687i	0.264054	+	0.457355i	−0.703261	+	0.710931i	$0.748274\pi$
$12$		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	−0.741072	−	0.671426i	$-0.765682\pi$
$17$	0.590940	−	0.843949i	0.143324	−	0.204688i	0.884395	+	0.466738i	$0.154571\pi$
$18$		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	0.00247802	−	0.999997i	$-0.499211\pi$
$23$	2.42008	−	0.648460i	0.504623	−	0.135213i	0.502144	+	0.864784i	$0.332545\pi$
$24$		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	0.469631	−	0.882863i	$-0.344387\pi$
$29$	2.34207	+	0.627556i	0.434911	+	0.116534i	−0.0347193	+	0.999397i	$0.511054\pi$
$30$		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	−0.942061	−	0.335443i	$-0.891114\pi$
$41$	0.370837	−	2.10312i	0.0579150	−	0.328453i	0.999976	+	0.00699040i	$0.00222513\pi$
$42$		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	0.761916	−	0.647676i	$-0.224259\pi$
$47$	3.98978	+	2.30350i	0.581969	+	0.336000i	−0.179946	+	0.983676i	$0.557592\pi$
$48$		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	$0.295337\pi$
$53$	−2.72394	+	7.48397i	−0.374162	+	1.02800i	−0.973735	+	0.227683i	$0.926885\pi$
$54$		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	0.876149	−	0.482041i	$-0.160104\pi$
$59$	−0.432400	−	0.927286i	−0.0562937	−	0.120722i	−0.932442	+	0.361319i	$0.882327\pi$
$60$		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	$0.521446\pi$
$71$	−8.74807	+	10.4255i	−1.03821	+	1.23729i	−0.970883	+	0.239554i	$0.922999\pi$
$72$		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	0.285681	−	0.958325i	$-0.407780\pi$
$83$	8.03449	−	1.41670i	0.881900	−	0.155503i	0.596219	+	0.802822i	$0.296669\pi$
$84$		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	0.374907	−	0.927062i	$-0.377674\pi$
$89$	12.5101	−	5.83354i	1.32606	−	0.618354i	0.951157	+	0.308708i	$0.0998967\pi$
$90$		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	−0.608397	−	0.793633i	$-0.708187\pi$
$101$	3.85019	−	6.66872i	0.383108	−	0.663562i	0.991505	+	0.130071i	$0.0415204\pi$
$102$		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	0.890818	−	0.454360i	$-0.150132\pi$
$107$	16.2662	+	2.86817i	1.57251	+	0.277277i	0.681695	+	0.731636i	$0.261243\pi$
$108$		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	$0.251567\pi$
$113$	−1.19803	+	13.6936i	−0.112701	+	1.28818i	−0.816318	+	0.577602i	$0.803988\pi$
$114$		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	0.803429	−	0.595400i	$-0.203006\pi$
$131$	5.93708	+	4.15719i	0.518725	+	0.363215i	−0.284704	+	0.958615i	$0.591895\pi$
$132$		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	0.137429	−	0.990512i	$-0.456116\pi$
$137$	12.4532	−	7.18988i	1.06395	−	0.614273i	0.926523	+	0.376239i	$0.122783\pi$
$138$		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	$0.0153045\pi$
$149$			1.17334i			0.0961241i	−0.998844	+	0.0480620i	$0.984695\pi$
$150$		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	$-0.619448\pi$
$167$	−2.15983	−	24.6870i	−0.167133	−	1.91034i	0.199379	−	0.979922i	$-0.436107\pi$
$168$		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	−0.299277	−	0.954166i	$-0.596745\pi$
$173$	7.73952	−	6.49423i	0.588425	−	0.493747i	0.887702	+	0.460419i	$0.152301\pi$
$174$		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	$0.569320\pi$
$179$	−15.9537	+	15.9537i	−1.19244	+	1.19244i	−0.976381	+	0.216057i	$0.930680\pi$
$180$		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	0.506785	−	0.862072i	$-0.330834\pi$
$191$	−4.91016	−	4.91016i	−0.355287	−	0.355287i	−0.862072	+	0.506785i	$0.830834\pi$
$192$		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	$0.0679882\pi$
$197$	14.2648	+	17.0001i	1.01632	+	1.21121i	0.0390483	+	0.999237i	$0.487567\pi$
$198$		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	0.732506	−	0.680760i	$-0.238350\pi$
$227$	10.2733	+	4.79050i	0.681860	+	0.317957i	−0.0506464	+	0.998717i	$0.516128\pi$
$228$		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	0.564010	−	0.825768i	$-0.309258\pi$
$233$	−6.61145	−	11.4514i	−0.433131	−	0.750205i	−0.997141	+	0.0755632i	$0.975925\pi$
$234$		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	−0.999940	−	0.0109208i	$-0.996524\pi$
$239$	−10.0129	+	14.2999i	−0.647678	+	0.924981i	0.352262	+	0.935901i	$0.385413\pi$
$240$		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	0.363655	−	0.931534i	$-0.381529\pi$
$251$	3.37176	+	0.903459i	0.212823	+	0.0570258i	−0.150832	+	0.988559i	$0.548195\pi$
$252$		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	0.738208	−	0.674574i	$-0.235673\pi$
$257$	21.6111	+	1.89072i	1.34806	+	0.117940i	0.609854	+	0.792514i	$0.291228\pi$
$258$		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	$0.360961\pi$
$263$	−4.61211	+	26.1566i	−0.284395	+	1.61288i	−0.707439	+	0.706774i	$0.750150\pi$
$264$		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	0.00436832	−	0.999990i	$-0.498610\pi$
$269$	−14.0963	−	8.13848i	−0.859465	−	0.496212i	−0.863833	+	0.503778i	$0.831943\pi$
$270$		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	$0.127980\pi$
$281$	10.5355	+	22.5933i	0.628492	+	1.34781i	−0.291764	+	0.956490i	$0.594242\pi$
$282$		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	−0.631025	−	0.775763i	$-0.717365\pi$
$293$	4.15142	−	4.94747i	0.242528	−	0.289034i	0.873553	+	0.486729i	$0.161810\pi$
$294$		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	−0.380888	−	0.924621i	$-0.624382\pi$
$311$	1.45635	−	0.679106i	0.0825819	−	0.0385086i	0.463470	+	0.886112i	$0.346604\pi$
$312$		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	0.115648	−	0.993290i	$-0.463106\pi$
$317$	−7.73134	−	2.81398i	−0.434235	−	0.158049i	−0.549883	+	0.835242i	$0.685328\pi$
$318$		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	$-0.852693\pi$
$347$	−6.39126	−	23.8525i	−0.343101	−	1.28047i	0.551714	−	0.834033i	$-0.313974\pi$
$348$		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	0.198347	−	0.980132i	$-0.436443\pi$
$353$	−12.3033	−	8.61485i	−0.654837	−	0.458522i	−0.853184	+	0.521610i	$0.825332\pi$
$354$		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	−0.970155	−	0.242487i	$-0.922037\pi$
$359$	−23.5938	+	13.6219i	−1.24523	+	0.718935i	−0.275077	+	0.961422i	$0.588704\pi$
$360$		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	−0.681428	−	0.731885i	$-0.738641\pi$
$383$	−4.43745	+	3.10714i	−0.226743	+	0.158767i	0.454685	+	0.890652i	$0.349752\pi$
$384$		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	$-0.935826\pi$
$389$	−0.979381	−	11.1944i	−0.0496566	−	0.567578i	0.930089	−	0.367333i	$-0.119729\pi$
$390$		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	$0.606032\pi$
$401$	−25.4721	+	25.4721i	−1.27201	+	1.27201i	−0.945030	+	0.326984i	$0.893968\pi$
$402$		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	0.279275	−	0.960211i	$-0.409906\pi$
$419$	−14.6325	−	17.4383i	−0.714844	−	0.851918i	−0.994119	+	0.108293i	$0.965461\pi$
$420$		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	0.344715	−	0.938707i	$-0.387976\pi$
$431$	−13.6040	−	19.4285i	−0.655281	−	0.935838i	−0.999996	+	0.00286932i	$0.999087\pi$
$432$		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	$-0.393582\pi$
$443$	13.8127			0.656259			0.328130	+	0.944633i	$0.393582\pi$
$444$		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	0.0404829	−	0.999180i	$-0.487110\pi$
$449$	−14.8097	−	6.90586i	−0.698912	−	0.325908i	−0.739395	+	0.673272i	$0.764888\pi$
$450$		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	−0.766013	−	0.642826i	$-0.777762\pi$
$461$	2.14790	−	3.06752i	0.100038	−	0.142869i	0.866050	+	0.499957i	$0.166651\pi$
$462$		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	−0.0837469	−	0.996487i	$-0.526689\pi$
$467$	7.39003	−	1.98015i	0.341970	−	0.0916305i	0.425717	+	0.904857i	$0.360022\pi$
$468$		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	0.0661645	−	0.997809i	$-0.478924\pi$
$479$	−0.917985	−	0.0803133i	−0.0419438	−	0.00366961i	−0.108108	+	0.994139i	$0.534479\pi$
$480$		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	0.437574	−	0.899183i	$-0.355838\pi$
$491$	−2.71120	−	1.56531i	−0.122355	−	0.0706416i	−0.559928	+	0.828541i	$0.689171\pi$
$492$		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	0.963396	−	0.268083i	$-0.0863902\pi$
$503$	3.11236	+	6.67447i	0.138773	+	0.297600i	−0.824623	+	0.565683i	$0.808612\pi$
$504$		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	$0.101414\pi$
$509$	3.70917	+	21.0358i	0.164406	+	0.932394i	−0.785268	+	0.619156i	$0.787475\pi$
$510$		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	0.364492	−	0.931207i	$-0.381243\pi$
$521$	−11.1679	−	9.37098i	−0.489275	−	0.410550i	−0.853766	+	0.520656i	$0.825687\pi$
$522$		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	−0.989854	−	0.142086i	$-0.954619\pi$
$557$	0.227391	−	2.59909i	0.00963485	−	0.110127i	0.999489	+	0.0319591i	$0.0101746\pi$
$558$		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	$-0.668937\pi$
$563$	8.62275	−	32.1805i	0.363406	−	1.35625i	0.869569	−	0.493811i	$-0.164396\pi$
$564$		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	0.990925	−	0.134415i	$-0.0429155\pi$
$569$	1.56364	+	5.83560i	0.0655514	+	0.244641i	−0.925374	+	0.379056i	$0.876249\pi$
$570$		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	−0.794482	−	0.607288i	$-0.792258\pi$
$587$	4.39523	−	9.42560i	0.181410	−	0.389036i	0.975893	+	0.218252i	$0.0700353\pi$
$588$		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	$-0.801088\pi$
$593$		−	28.4921i		−	1.17003i	0.811022	−	0.585016i	$-0.198912\pi$
$594$		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	0.996747	−	0.0805993i	$-0.0256834\pi$
$599$	4.43933	+	12.1970i	0.181386	+	0.498354i	−0.815360	+	0.578954i	$0.803461\pi$
$600$		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	−0.704775	−	0.709431i	$-0.748952\pi$
$617$	−3.19202	+	2.67842i	−0.128506	+	0.107829i	0.576270	+	0.817260i	$0.304508\pi$
$618$		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	$-0.960382\pi$
$641$	−23.8550	−	28.4293i	−0.942216	−	1.12289i	0.0500484	−	0.998747i	$-0.484062\pi$
$642$		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	0.549728	−	0.835344i	$-0.314731\pi$
$647$	31.4432	−	2.75092i	1.23616	−	0.108150i	0.686432	+	0.727194i	$0.259176\pi$
$648$		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	0.735936	−	0.677051i	$-0.236743\pi$
$653$	−3.88391	−	5.54680i	−0.151989	−	0.217063i	−0.887925	+	0.459988i	$0.847854\pi$
$654$		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	−0.957772	−	0.287530i	$-0.907166\pi$
$659$	−38.6771	+	14.0773i	−1.50665	+	0.548374i	−0.548875	+	0.835905i	$0.684944\pi$
$660$		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	$-0.995695\pi$
$677$	−13.3132	−	23.0591i	−0.511667	−	0.886234i	0.488241	−	0.872709i	$-0.337639\pi$
$678$		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	−0.783981	−	0.620785i	$-0.786814\pi$
$683$	1.76416	−	2.51949i	0.0675039	−	0.0964056i	0.851485	+	0.524380i	$0.175703\pi$
$684$		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	−0.471142	−	0.882058i	$-0.656158\pi$
$701$	−28.8141	−	2.52091i	−1.08829	−	0.0952133i	−0.617152	+	0.786844i	$0.711713\pi$
$702$		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	$-0.732896\pi$
$719$	8.63325	−	23.7197i	0.321966	−	0.884594i	0.990076	−	0.140532i	$-0.0448813\pi$
$720$		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	0.279740	−	0.960076i	$-0.409752\pi$
$743$	−16.8230	−	14.1161i	−0.617174	−	0.517871i	−0.896914	+	0.442205i	$0.854196\pi$
$744$		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	0.807147	−	0.590350i	$-0.201010\pi$
$761$	28.8549	+	10.5023i	1.04599	+	0.380709i	0.238841	+	0.971059i	$0.423232\pi$
$762$		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	0.481965	−	0.876191i	$-0.339923\pi$
$773$	17.6601	+	3.11395i	0.635189	+	0.112001i	0.153224	+	0.988191i	$0.451034\pi$
$774$		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

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

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