LMFDB - Embedded newform 666.2.bs.a.17.2

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:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			17.2
Character	$\chi$	$=$	666.17
Dual form			666.2.bs.a.431.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.573576 + 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(-0.718088 + 0.0628246i) q^{5} +(-2.07081 - 1.73762i) q^{7} +(0.965926 + 0.258819i) q^{8} +O(q^{10})$	\(q+(-0.573576 + 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(-0.718088 + 0.0628246i) q^{5} +(-2.07081 - 1.73762i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.360415 - 0.624258i) q^{10} +(2.14666 + 3.71813i) q^{11} +(0.0350998 + 0.0163673i) q^{13} +(2.61114 - 0.699652i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(-1.26227 + 0.588607i) q^{17} +(-1.15999 + 0.812232i) q^{19} +(0.304636 + 0.653295i) q^{20} +(-4.27699 - 0.374188i) q^{22} +(1.21793 + 4.54537i) q^{23} +(-4.41234 + 0.778014i) q^{25} +(-0.0335397 + 0.0193642i) q^{26} +(-0.924566 + 2.54022i) q^{28} +(-2.18568 + 8.15709i) q^{29} +(-3.19999 + 3.19999i) q^{31} +(-0.0871557 - 0.996195i) q^{32} +(0.241851 - 1.37160i) q^{34} +(1.59619 + 1.11766i) q^{35} +(6.02223 + 0.856003i) q^{37} -1.41608i q^{38} +(-0.709880 - 0.125171i) q^{40} +(-8.42883 + 3.06784i) q^{41} +(-0.673546 - 0.673546i) q^{43} +(2.75969 - 3.28888i) q^{44} +(-4.42192 - 1.60945i) q^{46} +(2.04440 + 1.18033i) q^{47} +(0.0534066 + 0.302884i) q^{49} +(1.89350 - 4.06062i) q^{50} +(0.00337540 - 0.0385810i) q^{52} +(-0.385452 - 0.459364i) q^{53} +(-1.77508 - 2.53508i) q^{55} +(-1.55052 - 2.21437i) q^{56} +(-5.42824 - 6.46912i) q^{58} +(0.273822 - 3.12980i) q^{59} +(-4.73693 + 10.1584i) q^{61} +(-0.785839 - 4.45671i) q^{62} +(0.866025 + 0.500000i) q^{64} +(-0.0262330 - 0.00954803i) q^{65} +(5.48130 - 6.53235i) q^{67} +(0.984832 + 0.984832i) q^{68} +(-1.83107 + 0.666456i) q^{70} +(0.759603 + 0.133939i) q^{71} +9.36628i q^{73} +(-4.15541 + 4.44214i) q^{74} +(1.15999 + 0.812232i) q^{76} +(2.01535 - 11.4296i) q^{77} +(-0.124024 - 1.41760i) q^{79} +(0.509704 - 0.509704i) q^{80} +(2.32155 - 8.66414i) q^{82} +(-2.84370 + 7.81299i) q^{83} +(0.869443 - 0.501973i) q^{85} +(0.938067 - 0.165407i) q^{86} +(1.11119 + 4.14703i) q^{88} +(-10.6799 - 0.934373i) q^{89} +(-0.0442449 - 0.0948835i) q^{91} +(3.85469 - 2.69909i) q^{92} +(-2.13949 + 0.997660i) q^{94} +(0.781945 - 0.656130i) q^{95} +(-2.87161 + 0.769446i) q^{97} +(-0.278741 - 0.129979i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q + 12 q^{13} - 24 q^{19} - 12 q^{22} + 72 q^{34} + 72 q^{37} + 24 q^{40} + 24 q^{43} + 36 q^{46} - 48 q^{49} - 12 q^{52} + 60 q^{55} + 120 q^{61} + 60 q^{67} - 60 q^{70} + 24 q^{76} - 12 q^{79} - 48 q^{82} + 108 q^{85} - 24 q^{88} - 168 q^{91} - 84 q^{94} - 264 q^{97}+O(q^{100}) $ 72 * q + 12 * q^13 - 24 * q^19 - 12 * q^22 + 72 * q^34 + 72 * q^37 + 24 * q^40 + 24 * q^43 + 36 * q^46 - 48 * q^49 - 12 * q^52 + 60 * q^55 + 120 * q^61 + 60 * q^67 - 60 * q^70 + 24 * q^76 - 12 * q^79 - 48 * q^82 + 108 * q^85 - 24 * q^88 - 168 * q^91 - 84 * q^94 - 264 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{7}{36}\right)$

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 $

$2$	−0.573576	+	0.819152i	−0.405580	+	0.579228i
$2$	−0.573576	+	0.819152i	−0.405580	+	0.579228i
$3$		0			0
$3$		0			0
$4$	−0.342020	−	0.939693i	−0.171010	−	0.469846i
$5$	−0.718088	+	0.0628246i	−0.321139	+	0.0280960i	−0.246586	−	0.969121i	$-0.579309\pi$
$5$	−0.718088	+	0.0628246i	−0.321139	+	0.0280960i	−0.0745532	+	0.997217i	$0.523753\pi$
$6$		0			0
$7$	−2.07081	−	1.73762i	−0.782692	−	0.656757i	0.161233	−	0.986916i	$-0.448453\pi$
$7$	−2.07081	−	1.73762i	−0.782692	−	0.656757i	−0.943925	+	0.330160i	$0.892897\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$		0			0
$10$	0.360415	−	0.624258i	0.113973	−	0.197408i
$11$	2.14666	+	3.71813i	0.647243	+	1.12106i	0.983779	+	0.179387i	$0.0574113\pi$
$11$	2.14666	+	3.71813i	0.647243	+	1.12106i	−0.336536	+	0.941671i	$0.609255\pi$
$12$		0			0
$13$	0.0350998	+	0.0163673i	0.00973493	+	0.00453947i	0.427480	−	0.904025i	$-0.359402\pi$
$13$	0.0350998	+	0.0163673i	0.00973493	+	0.00453947i	−0.417745	+	0.908564i	$0.637179\pi$
$14$	2.61114	−	0.699652i	0.697856	−	0.186990i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	−1.26227	+	0.588607i	−0.306146	+	0.142758i	−0.569620	−	0.821908i	$-0.692910\pi$
$17$	−1.26227	+	0.588607i	−0.306146	+	0.142758i	0.263474	+	0.964667i	$0.415132\pi$
$18$		0			0
$19$	−1.15999	+	0.812232i	−0.266119	+	0.186339i	−0.699018	−	0.715104i	$-0.746380\pi$
$19$	−1.15999	+	0.812232i	−0.266119	+	0.186339i	0.432899	+	0.901442i	$0.357491\pi$
$20$	0.304636	+	0.653295i	0.0681188	+	0.146081i
$21$		0			0
$22$	−4.27699	−	0.374188i	−0.911856	−	0.0797771i
$23$	1.21793	+	4.54537i	0.253955	+	0.947775i	0.968669	+	0.248357i	$0.0798906\pi$
$23$	1.21793	+	4.54537i	0.253955	+	0.947775i	−0.714713	+	0.699418i	$0.753443\pi$
$24$		0			0
$25$	−4.41234	+	0.778014i	−0.882467	+	0.155603i
$26$	−0.0335397	+	0.0193642i	−0.00657768	+	0.00379763i
$27$		0			0
$28$	−0.924566	+	2.54022i	−0.174726	+	0.480057i
$29$	−2.18568	+	8.15709i	−0.405871	+	1.51473i	0.396571	+	0.918004i	$0.370200\pi$
$29$	−2.18568	+	8.15709i	−0.405871	+	1.51473i	−0.802443	+	0.596729i	$0.796467\pi$
$30$		0			0
$31$	−3.19999	+	3.19999i	−0.574735	+	0.574735i	−0.933448	−	0.358713i	$-0.883216\pi$
$31$	−3.19999	+	3.19999i	−0.574735	+	0.574735i	0.358713	+	0.933448i	$0.383216\pi$
$32$	−0.0871557	−	0.996195i	−0.0154071	−	0.176104i
$33$		0			0
$34$	0.241851	−	1.37160i	0.0414771	−	0.235228i
$35$	1.59619	+	1.11766i	0.269805	+	0.188920i
$36$		0			0
$37$	6.02223	+	0.856003i	0.990049	+	0.140726i
$37$	6.02223	+	0.856003i	0.990049	+	0.140726i
$38$		−	1.41608i		−	0.229719i
$39$		0			0
$40$	−0.709880	−	0.125171i	−0.112242	−	0.0197913i
$41$	−8.42883	+	3.06784i	−1.31636	+	0.479117i	−0.902291	−	0.431128i	$-0.858116\pi$
$41$	−8.42883	+	3.06784i	−1.31636	+	0.479117i	−0.414071	+	0.910244i	$0.635894\pi$
$42$		0			0
$43$	−0.673546	−	0.673546i	−0.102715	−	0.102715i	0.653882	−	0.756597i	$-0.273139\pi$
$43$	−0.673546	−	0.673546i	−0.102715	−	0.102715i	−0.756597	+	0.653882i	$0.773139\pi$
$44$	2.75969	−	3.28888i	0.416040	−	0.495817i
$45$		0			0
$46$	−4.42192	−	1.60945i	−0.651977	−	0.237300i
$47$	2.04440	+	1.18033i	0.298206	+	0.172169i	0.641637	−	0.767009i	$-0.278256\pi$
$47$	2.04440	+	1.18033i	0.298206	+	0.172169i	−0.343431	+	0.939178i	$0.611589\pi$
$48$		0			0
$49$	0.0534066	+	0.302884i	0.00762951	+	0.0432691i
$50$	1.89350	−	4.06062i	0.267781	−	0.574259i
$51$		0			0
$52$	0.00337540	−	0.0385810i	0.000468083	−	0.00535022i
$53$	−0.385452	−	0.459364i	−0.0529459	−	0.0630985i	0.738922	−	0.673791i	$-0.235335\pi$
$53$	−0.385452	−	0.459364i	−0.0529459	−	0.0630985i	−0.791867	+	0.610693i	$0.790891\pi$
$54$		0			0
$55$	−1.77508	−	2.53508i	−0.239352	−	0.341830i
$56$	−1.55052	−	2.21437i	−0.207197	−	0.295908i
$57$		0			0
$58$	−5.42824	−	6.46912i	−0.712762	−	0.849437i
$59$	0.273822	−	3.12980i	0.0356486	−	0.407465i	−0.957315	−	0.289046i	$-0.906662\pi$
$59$	0.273822	−	3.12980i	0.0356486	−	0.407465i	0.992964	−	0.118419i	$-0.0377826\pi$
$60$		0			0
$61$	−4.73693	+	10.1584i	−0.606501	+	1.30065i	0.327997	+	0.944679i	$0.393626\pi$
$61$	−4.73693	+	10.1584i	−0.606501	+	1.30065i	−0.934498	+	0.355967i	$0.884151\pi$
$62$	−0.785839	−	4.45671i	−0.0998016	−	0.566003i
$63$		0			0
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	−0.0262330	−	0.00954803i	−0.00325380	−	0.00118429i
$66$		0			0
$67$	5.48130	−	6.53235i	0.669647	−	0.798054i	−0.319089	−	0.947725i	$-0.603377\pi$
$67$	5.48130	−	6.53235i	0.669647	−	0.798054i	0.988736	+	0.149671i	$0.0478213\pi$
$68$	0.984832	+	0.984832i	0.119428	+	0.119428i
$69$		0			0
$70$	−1.83107	+	0.666456i	−0.218855	+	0.0796567i
$71$	0.759603	+	0.133939i	0.0901483	+	0.0158956i	0.218540	−	0.975828i	$-0.429870\pi$
$71$	0.759603	+	0.133939i	0.0901483	+	0.0158956i	−0.128392	+	0.991723i	$0.540982\pi$
$72$		0			0
$73$			9.36628i			1.09624i	0.836400	+	0.548120i	$0.184656\pi$
$73$			9.36628i			1.09624i	−0.836400	+	0.548120i	$0.815344\pi$
$74$	−4.15541	+	4.44214i	−0.483056	+	0.516388i
$75$		0			0
$76$	1.15999	+	0.812232i	0.133060	+	0.0931694i
$77$	2.01535	−	11.4296i	0.229670	−	1.30252i
$78$		0			0
$79$	−0.124024	−	1.41760i	−0.0139538	−	0.159493i	0.986021	−	0.166622i	$-0.0532861\pi$
$79$	−0.124024	−	1.41760i	−0.0139538	−	0.159493i	−0.999975	+	0.00712971i	$0.997731\pi$
$80$	0.509704	−	0.509704i	0.0569867	−	0.0569867i
$81$		0			0
$82$	2.32155	−	8.66414i	0.256372	−	0.956794i
$83$	−2.84370	+	7.81299i	−0.312136	+	0.857588i	0.680089	+	0.733130i	$0.261941\pi$
$83$	−2.84370	+	7.81299i	−0.312136	+	0.857588i	−0.992225	+	0.124458i	$0.960281\pi$
$84$		0			0
$85$	0.869443	−	0.501973i	0.0943044	−	0.0544467i
$86$	0.938067	−	0.165407i	0.101154	−	0.0178362i
$87$		0			0
$88$	1.11119	+	4.14703i	0.118454	+	0.442075i
$89$	−10.6799	−	0.934373i	−1.13207	−	0.0990433i	−0.494315	−	0.869283i	$-0.664581\pi$
$89$	−10.6799	−	0.934373i	−1.13207	−	0.0990433i	−0.637755	+	0.770239i	$0.720137\pi$
$90$		0			0
$91$	−0.0442449	−	0.0948835i	−0.00463813	−	0.00994649i
$92$	3.85469	−	2.69909i	0.401880	−	0.281399i
$93$		0			0
$94$	−2.13949	+	0.997660i	−0.220671	+	0.102901i
$95$	0.781945	−	0.656130i	0.0802258	−	0.0673175i
$96$		0			0
$97$	−2.87161	+	0.769446i	−0.291568	+	0.0781254i	−0.401638	−	0.915798i	$-0.631559\pi$
$97$	−2.87161	+	0.769446i	−0.291568	+	0.0781254i	0.110070	+	0.993924i	$0.464892\pi$
$98$	−0.278741	−	0.129979i	−0.0281570	−	0.0131298i
$99$		0			0
$100$	2.24020	+	3.88014i	0.224020	+	0.388014i
$101$	−3.35666	+	5.81391i	−0.334000	+	0.578505i	−0.983292	−	0.182034i	$-0.941732\pi$
$101$	−3.35666	+	5.81391i	−0.334000	+	0.578505i	0.649292	+	0.760539i	$0.275065\pi$
$102$		0			0
$103$	9.58937	+	2.56946i	0.944869	+	0.253177i	0.698183	−	0.715919i	$-0.253992\pi$
$103$	9.58937	+	2.56946i	0.944869	+	0.253177i	0.246685	+	0.969096i	$0.420659\pi$
$104$	0.0296676	+	0.0248941i	0.00290915	+	0.00244107i
$105$		0			0
$106$	0.597375	−	0.0522635i	0.0580222	−	0.00507628i
$107$	−3.18517	−	8.75119i	−0.307922	−	0.846010i	−0.993061	−	0.117597i	$-0.962481\pi$
$107$	−3.18517	−	8.75119i	−0.307922	−	0.846010i	0.685139	−	0.728412i	$-0.259741\pi$
$108$		0			0
$109$	5.93207	−	8.47187i	0.568189	−	0.811458i	−0.427519	−	0.904006i	$-0.640612\pi$
$109$	5.93207	−	8.47187i	0.568189	−	0.811458i	0.995708	+	0.0925480i	$0.0295012\pi$
$110$	3.09476			0.295074
$111$		0			0
$112$	2.70325			0.255433
$113$	1.82365	−	2.60444i	0.171554	−	0.245005i	−0.724163	−	0.689629i	$-0.757774\pi$
$113$	1.82365	−	2.60444i	0.171554	−	0.245005i	0.895717	+	0.444624i	$0.146663\pi$
$114$		0			0
$115$	−1.16014	−	3.18746i	−0.108184	−	0.297232i
$116$	8.41270	−	0.736016i	0.781100	−	0.0683374i
$117$		0			0
$118$	2.40672	+	2.01948i	0.221557	+	0.185908i
$119$	3.63670	+	0.974450i	0.333375	+	0.0893277i
$120$		0			0
$121$	−3.71631	+	6.43684i	−0.337846	+	0.585167i
$122$	−5.60426	−	9.70686i	−0.507386	−	0.878818i
$123$		0			0
$124$	4.10147	+	1.91254i	0.368322	+	0.171752i
$125$	6.60091	−	1.76871i	0.590404	−	0.158198i
$126$		0			0
$127$	13.2744	−	11.1386i	1.17792	−	0.988389i	0.177926	−	0.984044i	$-0.443061\pi$
$127$	13.2744	−	11.1386i	1.17792	−	0.988389i	0.999991	−	0.00434519i	$-0.00138312\pi$
$128$	−0.906308	+	0.422618i	−0.0801070	+	0.0373545i
$129$		0			0
$130$	0.0228679	−	0.0160123i	0.00200565	−	0.00140437i
$131$	−7.18594	−	15.4103i	−0.627838	−	1.34640i	−0.920708	−	0.390252i	$-0.872388\pi$
$131$	−7.18594	−	15.4103i	−0.627838	−	1.34640i	0.292870	−	0.956152i	$-0.405390\pi$
$132$		0			0
$133$	3.81346	+	0.333634i	0.330669	+	0.0289298i
$134$	2.20705	+	8.23682i	0.190660	+	0.711553i
$135$		0			0
$136$	−1.37160	+	0.241851i	−0.117614	+	0.0207385i
$137$	−7.25301	+	4.18752i	−0.619666	+	0.357764i	−0.776739	−	0.629823i	$-0.783128\pi$
$137$	−7.25301	+	4.18752i	−0.619666	+	0.357764i	0.157073	+	0.987587i	$0.449794\pi$
$138$		0			0
$139$	−2.79536	+	7.68019i	−0.237099	+	0.651425i	0.762889	+	0.646530i	$0.223780\pi$
$139$	−2.79536	+	7.68019i	−0.237099	+	0.651425i	−0.999988	+	0.00489532i	$0.998442\pi$
$140$	0.504331	−	1.88219i	0.0426238	−	0.159074i
$141$		0			0
$142$	−0.545406	+	0.545406i	−0.0457695	+	0.0457695i
$143$	0.0144917	+	0.165641i	0.00121185	+	0.0138516i
$144$		0			0
$145$	1.05705	−	5.99482i	0.0877831	−	0.497843i
$146$	−7.67241	−	5.37228i	−0.634973	−	0.444613i
$147$		0			0
$148$	−1.25534	−	5.95182i	−0.103189	−	0.489236i
$149$		−	10.1731i		−	0.833417i	−0.909040	−	0.416708i	$-0.863184\pi$
$149$		−	10.1731i		−	0.833417i	0.909040	−	0.416708i	$-0.136816\pi$
$150$		0			0
$151$	16.5269	+	2.91414i	1.34494	+	0.237149i	0.799332	−	0.600890i	$-0.205187\pi$
$151$	16.5269	+	2.91414i	1.34494	+	0.237149i	0.545609	+	0.838040i	$0.316298\pi$
$152$	−1.33068	+	0.484329i	−0.107933	+	0.0392843i
$153$		0			0
$154$	8.20663	+	8.20663i	0.661309	+	0.661309i
$155$	2.09684	−	2.49891i	0.168422	−	0.200717i
$156$		0			0
$157$	22.5615	+	8.21170i	1.80060	+	0.655365i	0.998290	+	0.0584573i	$0.0186182\pi$
$157$	22.5615	+	8.21170i	1.80060	+	0.655365i	0.802310	+	0.596907i	$0.203604\pi$
$158$	1.23237	+	0.711508i	0.0980420	+	0.0566046i
$159$		0			0
$160$	0.125171	+	0.709880i	0.00989564	+	0.0561209i
$161$	5.37600	−	11.5289i	0.423689	−	0.908603i
$162$		0			0
$163$	0.660979	−	7.55502i	0.0517718	−	0.591755i	−0.925356	−	0.379100i	$-0.876234\pi$
$163$	0.660979	−	7.55502i	0.0517718	−	0.591755i	0.977127	−	0.212655i	$-0.0682109\pi$
$164$	5.76566	+	6.87125i	0.450222	+	0.536554i
$165$		0			0
$166$	−4.76895	−	6.81077i	−0.370142	−	0.528618i
$167$	12.3723	+	17.6695i	0.957398	+	1.36731i	0.929951	+	0.367683i	$0.119849\pi$
$167$	12.3723	+	17.6695i	0.957398	+	1.36731i	0.0274467	+	0.999623i	$0.491262\pi$
$168$		0			0
$169$	−8.35527	−	9.95743i	−0.642713	−	0.765956i
$170$	−0.0874997	+	1.00013i	−0.00671092	+	0.0767062i
$171$		0			0
$172$	−0.402560	+	0.863293i	−0.0306949	+	0.0658255i
$173$	0.812529	+	4.60808i	0.0617755	+	0.350346i	0.999991	+	0.00429404i	$0.00136684\pi$
$173$	0.812529	+	4.60808i	0.0617755	+	0.350346i	−0.938215	+	0.346052i	$0.887522\pi$
$174$		0			0
$175$	10.4890	+	6.05582i	0.792893	+	0.457777i
$176$	−4.03440	−	1.46840i	−0.304105	−	0.110685i
$177$		0			0
$178$	6.89115	−	8.21255i	0.516514	−	0.615557i
$179$	18.2887	+	18.2887i	1.36696	+	1.36696i	0.864737	+	0.502225i	$0.167485\pi$
$179$	18.2887	+	18.2887i	1.36696	+	1.36696i	0.502225	+	0.864737i	$0.332515\pi$
$180$		0			0
$181$	−2.37927	+	0.865985i	−0.176850	+	0.0643681i	−0.428928	−	0.903339i	$-0.641108\pi$
$181$	−2.37927	+	0.865985i	−0.176850	+	0.0643681i	0.252078	+	0.967707i	$0.418886\pi$
$182$	0.103102	+	0.0181796i	0.00764242	+	0.00134756i
$183$		0			0
$184$			4.70571i			0.346910i
$185$	−4.37827	−	0.236342i	−0.321897	−	0.0173762i
$186$		0			0
$187$	−4.89819	−	3.42975i	−0.358191	−	0.250808i
$188$	0.409925	−	2.32480i	0.0298969	−	0.169553i
$189$		0			0
$190$	0.0889648	+	1.01687i	0.00645418	+	0.0737717i
$191$	−0.163885	+	0.163885i	−0.0118583	+	0.0118583i	−0.713011	−	0.701153i	$-0.752669\pi$
$191$	−0.163885	+	0.163885i	−0.0118583	+	0.0118583i	0.701153	+	0.713011i	$0.252669\pi$
$192$		0			0
$193$	−4.08217	+	15.2349i	−0.293841	+	1.09663i	0.648292	+	0.761392i	$0.275484\pi$
$193$	−4.08217	+	15.2349i	−0.293841	+	1.09663i	−0.942133	+	0.335239i	$0.891183\pi$
$194$	1.01680	−	2.79362i	0.0730017	−	0.200571i
$195$		0			0
$196$	0.266351	−	0.153778i	0.0190251	−	0.0109841i
$197$	−0.409273	+	0.0721659i	−0.0291595	+	0.00514161i	−0.188209	−	0.982129i	$-0.560268\pi$
$197$	−0.409273	+	0.0721659i	−0.0291595	+	0.00514161i	0.159049	+	0.987271i	$0.449157\pi$
$198$		0			0
$199$	−0.265434	−	0.990613i	−0.0188161	−	0.0702227i	0.955879	−	0.293759i	$-0.0949064\pi$
$199$	−0.265434	−	0.990613i	−0.0188161	−	0.0702227i	−0.974696	+	0.223537i	$0.928240\pi$
$200$	−4.46335	−	0.390493i	−0.315607	−	0.0276120i
$201$		0			0
$202$	−2.83717	−	6.08434i	−0.199623	−	0.428092i
$203$	18.7000	−	13.0939i	1.31248	−	0.919011i
$204$		0			0
$205$	5.85991	−	2.73252i	0.409274	−	0.190847i
$206$	−7.60502	+	6.38137i	−0.529867	+	0.444611i
$207$		0			0
$208$	−0.0374087	+	0.0100236i	−0.00259383	+	0.000695014i
$209$	−5.51008	−	2.56939i	−0.381140	−	0.177729i
$210$		0			0
$211$	−5.73085	−	9.92613i	−0.394528	−	0.683343i	0.598513	−	0.801113i	$-0.295759\pi$
$211$	−5.73085	−	9.92613i	−0.394528	−	0.683343i	−0.993041	+	0.117771i	$0.962425\pi$
$212$	−0.299828	+	0.519318i	−0.0205923	+	0.0356669i
$213$		0			0
$214$	8.99550	+	2.41034i	0.614920	+	0.164767i
$215$	0.525981	+	0.441350i	0.0358716	+	0.0300998i
$216$		0			0
$217$	12.1869	−	1.06622i	0.827301	−	0.0723795i
$218$	3.53726	+	9.71854i	0.239573	+	0.658222i
$219$		0			0
$220$	−1.77508	+	2.53508i	−0.119676	+	0.170915i
$221$	−0.0539394			−0.00362836
$222$		0			0
$223$	−3.10179			−0.207711			−0.103856	−	0.994592i	$-0.533118\pi$
$223$	−3.10179			−0.207711			−0.103856	+	0.994592i	$0.533118\pi$
$224$	−1.55052	+	2.21437i	−0.103598	+	0.147954i
$225$		0			0
$226$	1.08743	+	2.98769i	0.0723348	+	0.198738i
$227$	−4.72486	+	0.413372i	−0.313600	+	0.0274365i	−0.242869	−	0.970059i	$-0.578089\pi$
$227$	−4.72486	+	0.413372i	−0.313600	+	0.0274365i	−0.0707307	+	0.997495i	$0.522533\pi$
$228$		0			0
$229$	−19.3753	−	16.2578i	−1.28035	−	1.07434i	−0.993195	−	0.116461i	$-0.962845\pi$
$229$	−19.3753	−	16.2578i	−1.28035	−	1.07434i	−0.287158	−	0.957883i	$-0.592711\pi$
$230$	3.27644	+	0.877920i	0.216042	+	0.0578883i
$231$		0			0
$232$	−4.22242	+	7.31344i	−0.277215	+	0.480151i
$233$	−5.20016	−	9.00695i	−0.340674	−	0.590065i	0.643884	−	0.765123i	$-0.277322\pi$
$233$	−5.20016	−	9.00695i	−0.340674	−	0.590065i	−0.984558	+	0.175058i	$0.943989\pi$
$234$		0			0
$235$	−1.54221	−	0.719144i	−0.100603	−	0.0469118i
$236$	−3.03470	+	0.813146i	−0.197542	+	0.0529313i
$237$		0			0
$238$	−2.88415	+	2.42009i	−0.186951	+	0.156871i
$239$	11.3149	−	5.27620i	0.731897	−	0.341289i	−0.0206863	−	0.999786i	$-0.506585\pi$
$239$	11.3149	−	5.27620i	0.731897	−	0.341289i	0.752584	+	0.658497i	$0.228807\pi$
$240$		0			0
$241$	−7.21834	+	5.05434i	−0.464974	+	0.325578i	−0.782478	−	0.622679i	$-0.786044\pi$
$241$	−7.21834	+	5.05434i	−0.464974	+	0.325578i	0.317503	+	0.948257i	$0.397155\pi$
$242$	−3.14116	−	6.73624i	−0.201921	−	0.433022i
$243$		0			0
$244$	11.1659	+	0.976887i	0.714821	+	0.0625388i
$245$	−0.0573792	−	0.214142i	−0.00366582	−	0.0136810i
$246$		0			0
$247$	−0.0540094	+	0.00952331i	−0.00343653	+	0.000605954i
$248$	−3.91917	+	2.26273i	−0.248867	+	0.143684i
$249$		0			0
$250$	−2.33729	+	6.42164i	−0.147823	+	0.406140i
$251$	2.12374	−	7.92590i	0.134049	−	0.500279i	−0.865951	−	0.500129i	$-0.833286\pi$
$251$	2.12374	−	7.92590i	0.134049	−	0.500279i	1.00000		0.000149336i	$-4.75350e-5\pi$
$252$		0			0
$253$	−14.2858	+	14.2858i	−0.898139	+	0.898139i
$254$	1.51028	+	17.2626i	0.0947636	+	1.08315i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−6.57242	−	4.60206i	−0.409976	−	0.287068i	0.350339	−	0.936623i	$-0.386067\pi$
$257$	−6.57242	−	4.60206i	−0.409976	−	0.287068i	−0.760315	+	0.649555i	$0.774955\pi$
$258$		0			0
$259$	−10.9835	−	12.2369i	−0.682481	−	0.760366i
$260$			0.0279166i			0.00173131i
$261$		0			0
$262$	16.7451	+	2.95261i	1.03451	+	0.182413i
$263$	−18.2632	+	6.64726i	−1.12616	+	0.409888i	−0.836896	−	0.547363i	$-0.815632\pi$
$263$	−18.2632	+	6.64726i	−1.12616	+	0.409888i	−0.289261	+	0.957250i	$0.593410\pi$
$264$		0			0
$265$	0.305648	+	0.305648i	0.0187758	+	0.0187758i
$266$	−2.46061	+	2.93244i	−0.150870	+	0.179799i
$267$		0			0
$268$	−8.01312	−	2.91654i	−0.489479	−	0.178156i
$269$	−17.0791	−	9.86062i	−1.04133	−	0.601212i	−0.121121	−	0.992638i	$-0.538649\pi$
$269$	−17.0791	−	9.86062i	−1.04133	−	0.601212i	−0.920210	+	0.391425i	$0.871982\pi$
$270$		0			0
$271$	−4.40413	−	24.9771i	−0.267532	−	1.51725i	−0.761727	−	0.647898i	$-0.775648\pi$
$271$	−4.40413	−	24.9771i	−0.267532	−	1.51725i	0.494195	−	0.869351i	$-0.335463\pi$
$272$	0.588607	−	1.26227i	0.0356895	−	0.0765365i
$273$		0			0
$274$	0.729934	−	8.34318i	0.0440969	−	0.504030i
$275$	−12.3645	−	14.7355i	−0.745610	−	0.888583i
$276$		0			0
$277$	−3.96790	−	5.66675i	−0.238408	−	0.340482i	0.682063	−	0.731294i	$-0.261083\pi$
$277$	−3.96790	−	5.66675i	−0.238408	−	0.340482i	−0.920471	+	0.390812i	$0.872194\pi$
$278$	−4.68789	−	6.69500i	−0.281161	−	0.401540i
$279$		0			0
$280$	1.25253	+	1.49270i	0.0748528	+	0.0892061i
$281$	−0.564702	+	6.45458i	−0.0336873	+	0.385048i	0.960571	+	0.278037i	$0.0896836\pi$
$281$	−0.564702	+	6.45458i	−0.0336873	+	0.385048i	−0.994258	+	0.107011i	$0.965872\pi$
$282$		0			0
$283$	−10.1227	+	21.7081i	−0.601729	+	1.29041i	0.335612	+	0.942000i	$0.391057\pi$
$283$	−10.1227	+	21.7081i	−0.601729	+	1.29041i	−0.937341	+	0.348413i	$0.886721\pi$
$284$	−0.133939	−	0.759603i	−0.00794779	−	0.0450742i
$285$		0			0
$286$	−0.143997	−	0.0831366i	−0.00851471	−	0.00491597i
$287$	22.7852	+	8.29315i	1.34497	+	0.489529i
$288$		0			0
$289$	−9.68052	+	11.5368i	−0.569442	+	0.678635i
$290$	4.30437	+	4.30437i	0.252761	+	0.252761i
$291$		0			0
$292$	8.80143	−	3.20346i	0.515064	−	0.187468i
$293$	13.7242	+	2.41994i	0.801775	+	0.141375i	0.559497	−	0.828832i	$-0.310994\pi$
$293$	13.7242	+	2.41994i	0.801775	+	0.141375i	0.242278	+	0.970207i	$0.422105\pi$
$294$		0			0
$295$			2.26467i			0.131854i
$296$	5.59548	+	2.38550i	0.325231	+	0.138655i
$297$		0			0
$298$	8.33335	+	5.83508i	0.482738	+	0.338017i
$299$	−0.0316464	+	0.179476i	−0.00183016	+	0.0103793i
$300$		0			0
$301$	0.224421	+	2.56515i	0.0129354	+	0.147853i
$302$	−11.8666	+	11.8666i	−0.682844	+	0.682844i
$303$		0			0
$304$	0.366509	−	1.36783i	0.0210207	−	0.0784505i
$305$	2.76333	−	7.59220i	0.158228	−	0.434728i
$306$		0			0
$307$	14.6235	−	8.44288i	0.834607	−	0.481860i	−0.0208206	−	0.999783i	$-0.506628\pi$
$307$	14.6235	−	8.44288i	0.834607	−	0.481860i	0.855427	+	0.517923i	$0.173295\pi$
$308$	−11.4296	+	2.01535i	−0.651262	+	0.114835i
$309$		0			0
$310$	0.844293	+	3.15094i	0.0479526	+	0.178962i
$311$	8.86433	+	0.775528i	0.502650	+	0.0439762i	0.335662	−	0.941983i	$-0.391040\pi$
$311$	8.86433	+	0.775528i	0.502650	+	0.0439762i	0.166988	+	0.985959i	$0.446596\pi$
$312$		0			0
$313$	−8.21984	−	17.6275i	−0.464613	−	0.996365i	−0.989411	−	0.145139i	$-0.953637\pi$
$313$	−8.21984	−	17.6275i	−0.464613	−	0.996365i	0.524799	−	0.851226i	$-0.324141\pi$
$314$	−19.6673	+	13.7712i	−1.10989	+	0.777155i
$315$		0			0
$316$	−1.28969	+	0.601393i	−0.0725508	+	0.0338310i
$317$	−17.2721	+	14.4930i	−0.970100	+	0.814011i	−0.982566	−	0.185912i	$-0.940476\pi$
$317$	−17.2721	+	14.4930i	−0.970100	+	0.814011i	0.0124662	+	0.999922i	$0.496032\pi$
$318$		0			0
$319$	−35.0210	+	9.38385i	−1.96080	+	0.525395i
$320$	−0.653295	−	0.304636i	−0.0365203	−	0.0170297i
$321$		0			0
$322$	6.36036	+	11.0165i	0.354449	+	0.613923i
$323$	0.986134	−	1.70803i	0.0548700	−	0.0950376i
$324$		0			0
$325$	−0.167606	−	0.0449099i	−0.00929711	−	0.00249115i
$326$	5.80959	+	4.87482i	0.321763	+	0.269992i
$327$		0			0
$328$	−8.93564	+	0.781767i	−0.493388	+	0.0431659i
$329$	−2.18259	−	5.99661i	−0.120330	−	0.330604i
$330$		0			0
$331$	−4.31602	+	6.16391i	−0.237230	+	0.338799i	−0.920060	−	0.391778i	$-0.871860\pi$
$331$	−4.31602	+	6.16391i	−0.237230	+	0.338799i	0.682830	+	0.730577i	$0.260749\pi$
$332$	8.31441			0.456313
$333$		0			0
$334$	−21.5705			−1.18028
$335$	−3.52566	+	5.03517i	−0.192627	+	0.275100i
$336$		0			0
$337$	−3.76826	−	10.3532i	−0.205270	−	0.563976i	0.793749	−	0.608245i	$-0.208126\pi$
$337$	−3.76826	−	10.3532i	−0.205270	−	0.563976i	−0.999020	+	0.0442695i	$0.985904\pi$
$338$	12.9490	−	1.13289i	0.704335	−	0.0616213i
$339$		0			0
$340$	−0.769068	−	0.645324i	−0.0417086	−	0.0349976i
$341$	−18.7672	−	5.02867i	−1.01630	−	0.272318i
$342$		0			0
$343$	−9.04567	+	15.6676i	−0.488420	+	0.845969i
$344$	−0.476269	−	0.824922i	−0.0256787	−	0.0444768i
$345$		0			0
$346$	−4.24077	−	1.97750i	−0.227985	−	0.106311i
$347$	19.7758	−	5.29892i	1.06162	−	0.284461i	0.314576	−	0.949232i	$-0.398138\pi$
$347$	19.7758	−	5.29892i	1.06162	−	0.284461i	0.747047	+	0.664772i	$0.231471\pi$
$348$		0			0
$349$	−20.4583	+	17.1665i	−1.09511	+	0.918903i	−0.997086	−	0.0762816i	$-0.975695\pi$
$349$	−20.4583	+	17.1665i	−1.09511	+	0.918903i	−0.0980196	+	0.995184i	$0.531251\pi$
$350$	−10.9769	+	5.11860i	−0.586739	+	0.273601i
$351$		0			0
$352$	3.51688	−	2.46255i	0.187451	−	0.131254i
$353$	1.23427	+	2.64689i	0.0656933	+	0.140880i	0.936413	−	0.350900i	$-0.114124\pi$
$353$	1.23427	+	2.64689i	0.0656933	+	0.140880i	−0.870720	+	0.491780i	$0.836347\pi$
$354$		0			0
$355$	−0.553877	−	0.0484579i	−0.0293967	−	0.00257188i
$356$	2.77473	+	10.3554i	0.147060	+	0.548837i
$357$		0			0
$358$	−25.4712	+	4.49126i	−1.34619	+	0.237370i
$359$	26.8112	−	15.4795i	1.41504	−	0.816975i	0.419184	−	0.907901i	$-0.362316\pi$
$359$	26.8112	−	15.4795i	1.41504	−	0.816975i	0.995858	+	0.0909267i	$0.0289829\pi$
$360$		0			0
$361$	−5.81253	+	15.9698i	−0.305923	+	0.840516i
$362$	0.655322	−	2.44570i	0.0344430	−	0.128543i
$363$		0			0
$364$	−0.0740287	+	0.0740287i	−0.00388016	+	0.00388016i
$365$	−0.588433	−	6.72581i	−0.0308000	−	0.352045i
$366$		0			0
$367$	1.71660	−	9.73534i	0.0896059	−	0.508180i	−0.906661	−	0.421859i	$-0.861378\pi$
$367$	1.71660	−	9.73534i	0.0896059	−	0.508180i	0.996267	−	0.0863214i	$-0.0275112\pi$
$368$	−3.85469	−	2.69909i	−0.200940	−	0.140700i
$369$		0			0
$370$	2.70487	−	3.45091i	0.140620	−	0.179404i
$371$			1.62102i			0.0841592i
$372$		0			0
$373$	3.04917	+	0.537652i	0.157880	+	0.0278386i	0.252030	−	0.967720i	$-0.418902\pi$
$373$	3.04917	+	0.537652i	0.157880	+	0.0278386i	−0.0941493	+	0.995558i	$0.530013\pi$
$374$	5.61897	−	2.04514i	0.290550	−	0.105752i
$375$		0			0
$376$	1.66924	+	1.66924i	0.0860846	+	0.0860846i
$377$	−0.210227	+	0.250538i	−0.0108272	+	0.0129034i
$378$		0			0
$379$	−25.9424	−	9.44226i	−1.33257	−	0.485016i	−0.425106	−	0.905144i	$-0.639763\pi$
$379$	−25.9424	−	9.44226i	−1.33257	−	0.485016i	−0.907465	+	0.420127i	$0.861985\pi$
$380$	−0.884001	−	0.510378i	−0.0453483	−	0.0261819i
$381$		0			0
$382$	−0.0402462	−	0.228247i	−0.00205917	−	0.0116782i
$383$	−4.97953	+	10.6786i	−0.254442	+	0.545653i	−0.991489	−	0.130189i	$-0.958442\pi$
$383$	−4.97953	+	10.6786i	−0.254442	+	0.545653i	0.737047	+	0.675841i	$0.236219\pi$
$384$		0			0
$385$	−0.729137	+	8.33407i	−0.0371603	+	0.424744i
$386$	−10.1382	−	12.0823i	−0.516023	−	0.614972i
$387$		0			0
$388$	1.70519	+	2.43527i	0.0865680	+	0.123632i
$389$	13.8852	+	19.8301i	0.704006	+	1.00543i	0.998757	+	0.0498511i	$0.0158747\pi$
$389$	13.8852	+	19.8301i	0.704006	+	1.00543i	−0.294750	+	0.955574i	$0.595236\pi$
$390$		0			0
$391$	−4.21279	−	5.02061i	−0.213050	−	0.253903i
$392$	−0.0268053	+	0.306386i	−0.00135387	+	0.0154748i
$393$		0			0
$394$	0.175635	−	0.376650i	0.00884835	−	0.0189753i
$395$	0.178120	+	1.01017i	0.00896221	+	0.0508272i
$396$		0			0
$397$	−12.1780	−	7.03099i	−0.611198	−	0.352875i	0.162236	−	0.986752i	$-0.448129\pi$
$397$	−12.1780	−	7.03099i	−0.611198	−	0.352875i	−0.773434	+	0.633877i	$0.781463\pi$
$398$	0.963709	+	0.350761i	0.0483064	+	0.0175821i
$399$		0			0
$400$	2.87995	−	3.43219i	0.143997	−	0.171609i
$401$	12.7350	+	12.7350i	0.635955	+	0.635955i	0.949555	−	0.313600i	$-0.101535\pi$
$401$	12.7350	+	12.7350i	0.635955	+	0.635955i	−0.313600	+	0.949555i	$0.601535\pi$
$402$		0			0
$403$	−0.164694	+	0.0599437i	−0.00820400	+	0.00298601i
$404$	6.61133	+	1.16576i	0.328926	+	0.0579985i
$405$		0			0
$406$			22.8285i			1.13296i
$407$	9.74496	+	24.2290i	0.483040	+	1.20099i
$408$		0			0
$409$	19.7209	+	13.8087i	0.975135	+	0.682797i	0.948476	−	0.316848i	$-0.102624\pi$
$409$	19.7209	+	13.8087i	0.975135	+	0.682797i	0.0266586	+	0.999645i	$0.491513\pi$
$410$	−1.12276	+	6.36746i	−0.0554489	+	0.314467i
$411$		0			0
$412$	−0.865251	−	9.88987i	−0.0426279	−	0.487239i
$413$	−6.00542	+	6.00542i	−0.295507	+	0.295507i
$414$		0			0
$415$	1.55118	−	5.78907i	0.0761443	−	0.284174i
$416$	0.0132459	−	0.0363927i	0.000649432	−	0.00178430i
$417$		0			0
$418$	5.26518	−	3.03985i	0.257528	−	0.148684i
$419$	−4.19000	+	0.738811i	−0.204695	+	0.0360933i	−0.275055	−	0.961428i	$-0.588696\pi$
$419$	−4.19000	+	0.738811i	−0.204695	+	0.0360933i	0.0703603	+	0.997522i	$0.477585\pi$
$420$		0			0
$421$	2.60289	+	9.71413i	0.126857	+	0.473438i	0.999899	−	0.0142075i	$-0.00452255\pi$
$421$	2.60289	+	9.71413i	0.126857	+	0.473438i	−0.873042	+	0.487645i	$0.837856\pi$
$422$	11.4181	+	0.998953i	0.555824	+	0.0486283i
$423$		0			0
$424$	−0.253426	−	0.543474i	−0.0123074	−	0.0263934i
$425$	5.11162	−	3.57920i	0.247950	−	0.173617i
$426$		0			0
$427$	27.4606	−	12.8051i	1.32891	−	0.619682i
$428$	−7.13404	+	5.98617i	−0.344837	+	0.289352i
$429$		0			0
$430$	−0.663223	+	0.177710i	−0.0319835	+	0.00856994i
$431$	−10.0279	−	4.67606i	−0.483025	−	0.225238i	0.165824	−	0.986155i	$-0.446972\pi$
$431$	−10.0279	−	4.67606i	−0.483025	−	0.225238i	−0.648849	+	0.760917i	$0.724749\pi$
$432$		0			0
$433$	−8.87524	−	15.3724i	−0.426517	−	0.738748i	0.570044	−	0.821614i	$-0.306926\pi$
$433$	−8.87524	−	15.3724i	−0.426517	−	0.738748i	−0.996561	+	0.0828656i	$0.973593\pi$
$434$	−6.11673	+	10.5945i	−0.293613	+	0.508552i
$435$		0			0
$436$	−9.98985	−	2.67677i	−0.478427	−	0.128194i
$437$	−5.10467	−	4.28333i	−0.244190	−	0.204899i
$438$		0			0
$439$	10.2965	−	0.900824i	0.491424	−	0.0429940i	0.161249	−	0.986914i	$-0.448448\pi$
$439$	10.2965	−	0.900824i	0.491424	−	0.0429940i	0.330175	+	0.943920i	$0.392892\pi$
$440$	−1.05847	−	2.90812i	−0.0504606	−	0.138639i
$441$		0			0
$442$	0.0309384	−	0.0441846i	0.00147159	−	0.00210165i
$443$	19.7759			0.939580			0.469790	−	0.882778i	$-0.344330\pi$
$443$	19.7759			0.939580			0.469790	+	0.882778i	$0.344330\pi$
$444$		0			0
$445$	7.72783			0.366334
$446$	1.77911	−	2.54084i	0.0842434	−	0.120312i
$447$		0			0
$448$	−0.924566	−	2.54022i	−0.0436816	−	0.120014i
$449$	−17.1146	+	1.49733i	−0.807686	+	0.0706633i	−0.483516	−	0.875336i	$-0.660640\pi$
$449$	−17.1146	+	1.49733i	−0.807686	+	0.0706633i	−0.324170	+	0.945999i	$0.605085\pi$
$450$		0			0
$451$	−29.5005	−	24.7538i	−1.38912	−	1.16561i
$452$	−3.07110	−	0.822898i	−0.144452	−	0.0387058i
$453$		0			0
$454$	2.37146	−	4.10748i	0.111298	−	0.192774i
$455$	0.0377327	+	0.0653550i	0.00176894	+	0.00306389i
$456$		0			0
$457$	36.0382	+	16.8049i	1.68579	+	0.786099i	0.998198	+	0.0600060i	$0.0191120\pi$
$457$	36.0382	+	16.8049i	1.68579	+	0.786099i	0.687597	+	0.726093i	$0.258666\pi$
$458$	24.4308	−	6.54621i	1.14158	−	0.305884i
$459$		0			0
$460$	−2.59844	+	2.18035i	−0.121153	+	0.101659i
$461$	−37.4798	+	17.4771i	−1.74561	+	0.813991i	−0.758959	+	0.651138i	$0.774292\pi$
$461$	−37.4798	+	17.4771i	−1.74561	+	0.813991i	−0.986650	+	0.162853i	$0.947930\pi$
$462$		0			0
$463$	31.8270	−	22.2855i	1.47913	−	1.03570i	0.492939	−	0.870064i	$-0.335922\pi$
$463$	31.8270	−	22.2855i	1.47913	−	1.03570i	0.986188	−	0.165632i	$-0.0529665\pi$
$464$	−3.56894	−	7.65362i	−0.165684	−	0.355310i
$465$		0			0
$466$	10.3608	+	0.906448i	0.479953	+	0.0419904i
$467$	−5.38963	−	20.1144i	−0.249403	−	0.930783i	−0.971119	−	0.238594i	$-0.923313\pi$
$467$	−5.38963	−	20.1144i	−0.249403	−	0.930783i	0.721717	−	0.692188i	$-0.243353\pi$
$468$		0			0
$469$	−22.7014	+	4.00288i	−1.04825	+	0.184836i
$470$	1.47366	−	0.850820i	0.0679750	−	0.0392454i
$471$		0			0
$472$	1.07454	−	2.95228i	0.0494599	−	0.135890i
$473$	1.05845	−	3.95021i	0.0486678	−	0.181631i
$474$		0			0
$475$	4.48633	−	4.48633i	0.205847	−	0.205847i
$476$	−0.328140	−	3.75066i	−0.0150403	−	0.171911i
$477$		0			0
$478$	−2.16792	+	12.2949i	−0.0991584	+	0.562355i
$479$	16.4408	+	11.5120i	0.751201	+	0.525996i	0.885328	−	0.464968i	$-0.153934\pi$
$479$	16.4408	+	11.5120i	0.751201	+	0.525996i	−0.134127	+	0.990964i	$0.542823\pi$
$480$		0			0
$481$	0.197369	+	0.128613i	0.00899923	+	0.00586426i
$482$		−	8.81197i		−	0.401374i
$483$		0			0
$484$	7.31970	+	1.29066i	0.332714	+	0.0586664i
$485$	2.01373	−	0.732938i	0.0914388	−	0.0332810i
$486$		0			0
$487$	10.4440	+	10.4440i	0.473261	+	0.473261i	0.902968	−	0.429708i	$-0.141383\pi$
$487$	10.4440	+	10.4440i	0.473261	+	0.473261i	−0.429708	+	0.902968i	$0.641383\pi$
$488$	−7.20470	+	8.58622i	−0.326141	+	0.388680i
$489$		0			0
$490$	0.208326	+	0.0758245i	0.00941121	+	0.00342540i
$491$	−19.9822	−	11.5367i	−0.901785	−	0.520646i	−0.0240064	−	0.999712i	$-0.507642\pi$
$491$	−19.9822	−	11.5367i	−0.901785	−	0.520646i	−0.877779	+	0.479066i	$0.840976\pi$
$492$		0			0
$493$	−2.04239	−	11.5830i	−0.0919846	−	0.521671i
$494$	0.0231775	−	0.0497042i	0.00104280	−	0.00223630i
$495$		0			0
$496$	0.394420	−	4.50825i	0.0177100	−	0.202426i
$497$	−1.34026	−	1.59726i	−0.0601189	−	0.0716469i
$498$		0			0
$499$	9.48381	+	13.5443i	0.424554	+	0.606326i	0.973265	−	0.229687i	$-0.0737701\pi$
$499$	9.48381	+	13.5443i	0.424554	+	0.606326i	−0.548711	+	0.836012i	$0.684881\pi$
$500$	−3.91969	−	5.59790i	−0.175294	−	0.250345i
$501$		0			0
$502$	5.27439	+	6.28578i	0.235408	+	0.280548i
$503$	−3.72021	+	42.5222i	−0.165876	+	1.89597i	0.223210	+	0.974770i	$0.428346\pi$
$503$	−3.72021	+	42.5222i	−0.165876	+	1.89597i	−0.389086	+	0.921201i	$0.627209\pi$
$504$		0			0
$505$	2.04512	−	4.38578i	0.0910067	−	0.195165i
$506$	−3.50824	−	19.8962i	−0.155960	−	0.884494i
$507$		0			0
$508$	−15.0070	−	8.66428i	−0.665827	−	0.384415i
$509$	18.5564	+	6.75400i	0.822500	+	0.299366i	0.718777	−	0.695241i	$-0.244702\pi$
$509$	18.5564	+	6.75400i	0.822500	+	0.299366i	0.103723	+	0.994606i	$0.466924\pi$
$510$		0			0
$511$	16.2750	−	19.3958i	0.719963	−	0.858019i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	7.53957	−	2.74418i	0.332556	−	0.121041i
$515$	−7.04744	−	1.24265i	−0.310547	−	0.0547578i
$516$		0			0
$517$			10.1351i			0.445741i
$518$	16.3238	−	1.97833i	0.717226	−	0.0869226i
$519$		0			0
$520$	−0.0228679	−	0.0160123i	−0.00100283	−	0.000702186i
$521$	4.14458	−	23.5051i	0.181577	−	1.02978i	−0.748697	−	0.662912i	$-0.769320\pi$
$521$	4.14458	−	23.5051i	0.181577	−	1.02978i	0.930275	−	0.366864i	$-0.119569\pi$
$522$		0			0
$523$	−2.11764	−	24.2048i	−0.0925981	−	1.05840i	−0.890308	−	0.455360i	$-0.849511\pi$
$523$	−2.11764	−	24.2048i	−0.0925981	−	1.05840i	0.797709	−	0.603042i	$-0.206045\pi$
$524$	−12.0232	+	12.0232i	−0.525236	+	0.525236i
$525$		0			0
$526$	5.03022	−	18.7730i	0.219328	−	0.818544i
$527$	2.15572	−	5.92279i	0.0939046	−	0.258001i
$528$		0			0
$529$	0.741561	−	0.428140i	0.0322418	−	0.0186148i
$530$	−0.425684	+	0.0750596i	−0.0184905	+	0.00326038i
$531$		0			0
$532$	−0.990766	−	3.69759i	−0.0429551	−	0.160311i
$533$	−0.346063	−	0.0302766i	−0.0149896	−	0.00131142i
$534$		0			0
$535$	2.83703	+	6.08402i	0.122655	+	0.263035i
$536$	6.98522	−	4.89111i	0.301716	−	0.211264i
$537$		0			0
$538$	17.8735	−	8.33455i	0.770582	−	0.359328i
$539$	−1.01151	+	0.848761i	−0.0435690	+	0.0365587i
$540$		0			0
$541$	−18.3170	+	4.90803i	−0.787510	+	0.211013i	−0.630093	−	0.776520i	$-0.716983\pi$
$541$	−18.3170	+	4.90803i	−0.787510	+	0.211013i	−0.157417	+	0.987532i	$0.550317\pi$
$542$	22.9861	+	10.7186i	0.987338	+	0.460403i
$543$		0			0
$544$	0.696381	+	1.20617i	0.0298571	+	0.0517140i
$545$	−3.72751	+	6.45623i	−0.159669	+	0.276555i
$546$		0			0
$547$	17.5071	+	4.69100i	0.748548	+	0.200573i	0.612874	−	0.790181i	$-0.290013\pi$
$547$	17.5071	+	4.69100i	0.748548	+	0.200573i	0.135674	+	0.990754i	$0.456680\pi$
$548$	6.41566	+	5.38338i	0.274063	+	0.229967i
$549$		0			0
$550$	19.1626	−	1.67651i	0.817097	−	0.0714867i
$551$	−4.09008	−	11.2374i	−0.174243	−	0.478729i
$552$		0			0
$553$	−2.20642	+	3.15109i	−0.0938264	+	0.133998i
$554$	6.91782			0.293910
$555$		0			0
$556$	8.17309			0.346616
$557$	7.83666	−	11.1919i	0.332050	−	0.474216i	−0.618060	−	0.786131i	$-0.712081\pi$
$557$	7.83666	−	11.1919i	0.332050	−	0.474216i	0.950110	+	0.311914i	$0.100970\pi$
$558$		0			0
$559$	−0.0126172	−	0.0346655i	−0.000533651	−	0.00146619i
$560$	−1.94117	+	0.169830i	−0.0820294	+	0.00717665i
$561$		0			0
$562$	−4.96338	−	4.16477i	−0.209368	−	0.175680i
$563$	−8.05397	−	2.15805i	−0.339434	−	0.0909512i	0.0850754	−	0.996375i	$-0.472887\pi$
$563$	−8.05397	−	2.15805i	−0.339434	−	0.0909512i	−0.424510	+	0.905423i	$0.639554\pi$
$564$		0			0
$565$	−1.14592	+	1.98479i	−0.0482091	+	0.0835006i
$566$	−11.9761	−	20.7433i	−0.503394	−	0.871904i
$567$		0			0
$568$	0.699054	+	0.325974i	0.0293317	+	0.0136776i
$569$	40.1145	−	10.7487i	1.68169	−	0.450607i	0.713465	−	0.700691i	$-0.247125\pi$
$569$	40.1145	−	10.7487i	1.68169	−	0.450607i	0.968224	+	0.250084i	$0.0804582\pi$
$570$		0			0
$571$	−27.7990	+	23.3261i	−1.16335	+	0.976168i	−0.999946	−	0.0103904i	$-0.996693\pi$
$571$	−27.7990	+	23.3261i	−1.16335	+	0.976168i	−0.163406	+	0.986559i	$0.552248\pi$
$572$	0.150695	−	0.0702701i	0.00630086	−	0.00293814i
$573$		0			0
$574$	−19.8624	+	13.9078i	−0.829041	+	0.580501i
$575$	−8.91026	−	19.1081i	−0.371584	−	0.796864i
$576$		0			0
$577$	43.0103	+	3.76291i	1.79054	+	0.156652i	0.933495	−	0.358590i	$-0.116742\pi$
$577$	43.0103	+	3.76291i	1.79054	+	0.156652i	0.857045	+	0.515241i	$0.172298\pi$
$578$	−3.89787	−	14.5470i	−0.162130	−	0.605077i
$579$		0			0
$580$	−5.99482	+	1.05705i	−0.248921	+	0.0438916i
$581$	19.4647	−	11.2380i	0.807533	−	0.466229i
$582$		0			0
$583$	0.880538	−	2.41926i	0.0364681	−	0.100195i
$584$	−2.42417	+	9.04713i	−0.100313	+	0.374373i
$585$		0			0
$586$	−9.85416	+	9.85416i	−0.407072	+	0.407072i
$587$	−3.51806	−	40.2116i	−0.145206	−	1.65971i	−0.623734	−	0.781636i	$-0.714385\pi$
$587$	−3.51806	−	40.2116i	−0.145206	−	1.65971i	0.478529	−	0.878072i	$-0.341170\pi$
$588$		0			0
$589$	1.11281	−	6.31108i	0.0458527	−	0.260043i
$590$	−1.85511	−	1.29896i	−0.0763738	−	0.0534775i
$591$		0			0
$592$	−5.16352	+	3.21528i	−0.212220	+	0.132147i
$593$			34.1575i			1.40268i	0.712827	+	0.701340i	$0.247415\pi$
$593$			34.1575i			1.40268i	−0.712827	+	0.701340i	$0.752585\pi$
$594$		0			0
$595$	−2.67269	−	0.471267i	−0.109570	−	0.0193201i
$596$	−9.55963	+	3.47942i	−0.391578	+	0.142523i
$597$		0			0
$598$	−0.128866	−	0.128866i	−0.00526973	−	0.00526973i
$599$	−22.3960	+	26.6906i	−0.915078	+	1.09055i	0.0805140	+	0.996753i	$0.474344\pi$
$599$	−22.3960	+	26.6906i	−0.915078	+	1.09055i	−0.995592	+	0.0937937i	$0.970101\pi$
$600$		0			0
$601$	32.7398	+	11.9163i	1.33549	+	0.486077i	0.908388	−	0.418129i	$-0.137314\pi$
$601$	32.7398	+	11.9163i	1.33549	+	0.486077i	0.427098	+	0.904206i	$0.359536\pi$
$602$	−2.22997	−	1.28747i	−0.0908868	−	0.0524735i
$603$		0			0
$604$	−2.91414	−	16.5269i	−0.118575	−	0.672471i
$605$	2.26425	−	4.85569i	0.0920547	−	0.197412i
$606$		0			0
$607$	−2.11297	+	24.1513i	−0.0857626	+	0.980271i	0.824397	+	0.566013i	$0.191515\pi$
$607$	−2.11297	+	24.1513i	−0.0857626	+	0.980271i	−0.910159	+	0.414259i	$0.864041\pi$
$608$	0.910241	+	1.08478i	0.0369151	+	0.0439937i
$609$		0			0
$610$	4.63418	+	6.61830i	0.187633	+	0.267967i
$611$	0.0524390	+	0.0748906i	0.00212145	+	0.00302975i
$612$		0			0
$613$	8.25283	+	9.83534i	0.333329	+	0.397246i	0.906511	−	0.422182i	$-0.138736\pi$
$613$	8.25283	+	9.83534i	0.333329	+	0.397246i	−0.573182	+	0.819428i	$0.694291\pi$
$614$	−1.47169	+	16.8215i	−0.0593926	+	0.678860i
$615$		0			0
$616$	4.90487	−	10.5185i	0.197623	−	0.423804i
$617$	0.996744	+	5.65281i	0.0401274	+	0.227574i	0.998276	−	0.0586983i	$-0.0186950\pi$
$617$	0.996744	+	5.65281i	0.0401274	+	0.227574i	−0.958148	+	0.286272i	$0.907584\pi$
$618$		0			0
$619$	6.45138	+	3.72470i	0.259303	+	0.149709i	0.624016	−	0.781411i	$-0.285500\pi$
$619$	6.45138	+	3.72470i	0.259303	+	0.149709i	−0.364714	+	0.931120i	$0.618833\pi$
$620$	−3.06537	−	1.11570i	−0.123108	−	0.0448077i
$621$		0			0
$622$	−5.71965	+	6.81641i	−0.229337	+	0.273313i
$623$	20.4925	+	20.4925i	0.821015	+	0.821015i
$624$		0			0
$625$	16.4221	−	5.97715i	0.656884	−	0.239086i
$626$	19.1543	+	3.37742i	0.765560	+	0.134989i
$627$		0			0
$628$		−	24.0094i		−	0.958079i
$629$	−8.10554	+	2.46422i	−0.323189	+	0.0982548i
$630$		0			0
$631$	34.6175	+	24.2394i	1.37810	+	0.964955i	0.999219	+	0.0395094i	$0.0125795\pi$
$631$	34.6175	+	24.2394i	1.37810	+	0.964955i	0.378880	+	0.925446i	$0.376309\pi$
$632$	0.247104	−	1.40140i	0.00982928	−	0.0557446i
$633$		0			0
$634$	−1.96512	−	22.4614i	−0.0780447	−	0.892056i
$635$	−8.83244	+	8.83244i	−0.350505	+	0.350505i
$636$		0			0
$637$	−0.00308283	+	0.0115053i	−0.000122146	+	0.000455856i
$638$	12.4004	−	34.0699i	0.490937	−	1.34884i
$639$		0			0
$640$	0.624258	−	0.360415i	0.0246760	−	0.0142467i
$641$	3.53559	−	0.623420i	0.139647	−	0.0246236i	−0.103387	−	0.994641i	$-0.532968\pi$
$641$	3.53559	−	0.623420i	0.139647	−	0.0246236i	0.243035	+	0.970018i	$0.421857\pi$
$642$		0			0
$643$	10.9454	+	40.8489i	0.431646	+	1.61092i	0.748968	+	0.662606i	$0.230550\pi$
$643$	10.9454	+	40.8489i	0.431646	+	1.61092i	−0.317322	+	0.948318i	$0.602784\pi$
$644$	−12.6723	−	1.10868i	−0.499359	−	0.0436882i
$645$		0			0
$646$	0.833516	+	1.78748i	0.0327943	+	0.0703275i
$647$	−10.5382	+	7.37894i	−0.414300	+	0.290096i	−0.762083	−	0.647479i	$-0.775823\pi$
$647$	−10.5382	+	7.37894i	−0.414300	+	0.290096i	0.347783	+	0.937575i	$0.386934\pi$
$648$		0			0
$649$	12.2248	−	5.70051i	0.479865	−	0.223765i
$650$	0.132923	−	0.111536i	0.00521367	−	0.00437479i
$651$		0			0
$652$	−7.32547	+	1.96285i	−0.286887	+	0.0768712i
$653$	−20.0068	−	9.32931i	−0.782926	−	0.365084i	−0.0103006	−	0.999947i	$-0.503279\pi$
$653$	−20.0068	−	9.32931i	−0.782926	−	0.365084i	−0.772625	+	0.634863i	$0.781057\pi$
$654$		0			0
$655$	6.12828	+	10.6145i	0.239452	+	0.414743i
$656$	4.48489	−	7.76805i	0.175105	−	0.303292i
$657$		0			0
$658$	6.16402	+	1.65164i	0.240299	+	0.0643878i
$659$	−4.14058	−	3.47436i	−0.161294	−	0.135342i	0.558569	−	0.829458i	$-0.311351\pi$
$659$	−4.14058	−	3.47436i	−0.161294	−	0.135342i	−0.719863	+	0.694117i	$0.755795\pi$
$660$		0			0
$661$	37.3375	−	3.26660i	1.45226	−	0.127056i	0.666461	−	0.745540i	$-0.267808\pi$
$661$	37.3375	−	3.26660i	1.45226	−	0.127056i	0.785798	+	0.618484i	$0.212253\pi$
$662$	−2.57361	−	7.07095i	−0.100026	−	0.274820i
$663$		0			0
$664$	−4.76895	+	6.81077i	−0.185071	+	0.264309i
$665$	−2.75936			−0.107003
$666$		0			0
$667$	−39.7390			−1.53870
$668$	12.3723	−	17.6695i	0.478699	−	0.683653i
$669$		0			0
$670$	−2.10233	−	5.77610i	−0.0812201	−	0.223150i
$671$	−47.9387	+	4.19409i	−1.85065	+	0.161911i
$672$		0			0
$673$	−32.0178	−	26.8661i	−1.23420	−	1.03561i	−0.997955	−	0.0639180i	$-0.979640\pi$
$673$	−32.0178	−	26.8661i	−1.23420	−	1.03561i	−0.236240	−	0.971695i	$-0.575915\pi$
$674$	10.6422	+	2.85158i	0.409924	+	0.109839i
$675$		0			0
$676$	−6.49925	+	11.2570i	−0.249971	+	0.432963i
$677$	−19.7100	−	34.1388i	−0.757518	−	1.31206i	−0.944113	−	0.329623i	$-0.893078\pi$
$677$	−19.7100	−	34.1388i	−0.757518	−	1.31206i	0.186594	−	0.982437i	$-0.440255\pi$
$678$		0			0
$679$	7.28356	+	3.39638i	0.279518	+	0.130341i
$680$	0.969738	−	0.259841i	0.0371878	−	0.00996443i
$681$		0			0
$682$	14.8837	−	12.4889i	0.569926	−	0.478225i
$683$	15.4128	−	7.18709i	0.589753	−	0.275006i	−0.104747	−	0.994499i	$-0.533403\pi$
$683$	15.4128	−	7.18709i	0.589753	−	0.275006i	0.694500	+	0.719492i	$0.255626\pi$
$684$		0			0
$685$	4.94522	−	3.46268i	0.188947	−	0.132302i
$686$	−7.64573	−	16.3963i	−0.291915	−	0.626015i
$687$		0			0
$688$	0.948913	+	0.0830192i	0.0361770	+	0.00316508i
$689$	−0.00601074	−	0.0224324i	−0.000228991	−	0.000854606i
$690$		0			0
$691$	8.02015	−	1.41417i	0.305101	−	0.0537975i	−0.0190017	−	0.999819i	$-0.506049\pi$
$691$	8.02015	−	1.41417i	0.305101	−	0.0537975i	0.324103	+	0.946022i	$0.394938\pi$
$692$	4.05228	−	2.33959i	0.154045	−	0.0889377i
$693$		0			0
$694$	−7.00233	+	19.2387i	−0.265805	+	0.730293i
$695$	1.52481	−	5.69067i	0.0578394	−	0.215859i
$696$		0			0
$697$	8.83372	−	8.83372i	0.334601	−	0.334601i
$698$	−2.32761	−	26.6047i	−0.0881015	−	1.00700i
$699$		0			0
$700$	2.10317	−	11.9276i	0.0794922	−	0.450822i
$701$	13.8128	+	9.67182i	0.521702	+	0.365299i	0.804569	−	0.593860i	$-0.202397\pi$
$701$	13.8128	+	9.67182i	0.521702	+	0.365299i	−0.282867	+	0.959159i	$0.591285\pi$
$702$		0			0
$703$	−7.68098	+	3.89849i	−0.289694	+	0.147035i
$704$			4.29332i			0.161811i
$705$		0			0
$706$	−2.87615	−	0.507143i	−0.108245	−	0.0190866i
$707$	17.0533	−	6.20691i	0.641357	−	0.233435i
$708$		0			0
$709$	−11.8507	−	11.8507i	−0.445064	−	0.445064i	0.448646	−	0.893710i	$-0.351906\pi$
$709$	−11.8507	−	11.8507i	−0.445064	−	0.445064i	−0.893710	+	0.448646i	$0.851906\pi$
$710$	0.357385	−	0.425915i	0.0134124	−	0.0159843i
$711$		0			0
$712$	−10.0742	−	3.66670i	−0.377546	−	0.137416i
$713$	−18.4425	−	10.6478i	−0.690676	−	0.398762i
$714$		0			0
$715$	−0.0208126	−	0.118034i	−0.000778347	−	0.00441422i
$716$	10.9307	−	23.4409i	0.408498	−	0.876026i
$717$		0			0
$718$	−2.69825	+	30.8411i	−0.100698	+	1.15098i
$719$	−1.15668	−	1.37848i	−0.0431370	−	0.0514086i	0.744045	−	0.668130i	$-0.232905\pi$
$719$	−1.15668	−	1.37848i	−0.0431370	−	0.0514086i	−0.787182	+	0.616721i	$0.788461\pi$
$720$		0			0
$721$	−15.3930	−	21.9835i	−0.573266	−	0.818708i
$722$	−9.74776	−	13.9213i	−0.362774	−	0.518095i
$723$		0			0
$724$	1.62752	+	1.93960i	0.0604863	+	0.0720847i
$725$	3.29765	−	37.6923i	0.122472	−	1.39986i
$726$		0			0
$727$	15.3139	−	32.8407i	0.567960	−	1.21800i	−0.387224	−	0.921985i	$-0.626566\pi$
$727$	15.3139	−	32.8407i	0.567960	−	1.21800i	0.955185	−	0.296010i	$-0.0956561\pi$
$728$	−0.0181796	−	0.103102i	−0.000673782	−	0.00382121i
$729$		0			0
$730$	5.84698	+	3.37575i	0.216406	+	0.124942i
$731$	1.24665	+	0.453744i	0.0461091	+	0.0167823i
$732$		0			0
$733$	24.6964	−	29.4320i	0.912182	−	1.08710i	−0.0837050	−	0.996491i	$-0.526675\pi$
$733$	24.6964	−	29.4320i	0.912182	−	1.08710i	0.995887	−	0.0906055i	$-0.0288802\pi$
$734$	6.99012	+	6.99012i	0.258010	+	0.258010i
$735$		0			0
$736$	4.42192	−	1.60945i	0.162994	−	0.0593250i
$737$	36.0546	+	6.35740i	1.32809	+	0.234178i
$738$		0			0
$739$			45.9953i			1.69196i	0.533211	+	0.845982i	$0.320985\pi$
$739$			45.9953i			1.69196i	−0.533211	+	0.845982i	$0.679015\pi$
$740$	1.27537	+	4.19506i	0.0468835	+	0.154214i
$741$		0			0
$742$	−1.32786	−	0.929780i	−0.0487474	−	0.0341333i
$743$	−0.372254	+	2.11116i	−0.0136567	+	0.0774508i	−0.990874	−	0.134788i	$-0.956965\pi$
$743$	−0.372254	+	2.11116i	−0.0136567	+	0.0774508i	0.977218	+	0.212239i	$0.0680756\pi$
$744$		0			0
$745$	0.639123	+	7.30521i	0.0234157	+	0.267642i
$746$	−2.18935	+	2.18935i	−0.0801579	+	0.0801579i
$747$		0			0
$748$	−1.54763	+	5.77583i	−0.0565869	+	0.211185i
$749$	−8.61032	+	23.6567i	−0.314614	+	0.864395i
$750$		0			0
$751$	23.4439	−	13.5354i	0.855481	−	0.493912i	−0.00701548	−	0.999975i	$-0.502233\pi$
$751$	23.4439	−	13.5354i	0.855481	−	0.493912i	0.862496	+	0.506063i	$0.168900\pi$
$752$	−2.32480	+	0.409925i	−0.0847767	+	0.0149484i
$753$		0			0
$754$	−0.0846479	−	0.315910i	−0.00308270	−	0.0115048i
$755$	−12.0509	−	1.05431i	−0.438576	−	0.0383704i
$756$		0			0
$757$	−12.5183	−	26.8457i	−0.454987	−	0.975723i	−0.991290	−	0.131697i	$-0.957957\pi$
$757$	−12.5183	−	26.8457i	−0.454987	−	0.975723i	0.536303	−	0.844026i	$-0.319820\pi$
$758$	22.6146	−	15.8349i	0.821399	−	0.575150i
$759$		0			0
$760$	0.925120	−	0.431390i	0.0335576	−	0.0156482i
$761$	−33.4303	+	28.0514i	−1.21185	+	1.01686i	−0.212637	+	0.977131i	$0.568205\pi$
$761$	−33.4303	+	28.0514i	−1.21185	+	1.01686i	−0.999210	+	0.0397296i	$0.987350\pi$
$762$		0			0
$763$	−27.0050	+	7.23598i	−0.977648	+	0.261960i
$764$	0.210054	+	0.0979496i	0.00759947	+	0.00354369i
$765$		0			0
$766$	−5.89128	−	10.2040i	−0.212861	−	0.368686i
$767$	0.0608375	−	0.105374i	0.00219671	−	0.00380482i
$768$		0			0
$769$	16.6847	+	4.47064i	0.601664	+	0.161215i	0.546779	−	0.837277i	$-0.315854\pi$
$769$	16.6847	+	4.47064i	0.601664	+	0.161215i	0.0548856	+	0.998493i	$0.482521\pi$
$770$	−6.40866	−	5.37750i	−0.230952	−	0.193792i
$771$		0			0
$772$	15.7123	−	1.37465i	0.565498	−	0.0494746i
$773$	3.90275	+	10.7227i	0.140372	+	0.385669i	0.989880	−	0.141907i	$-0.0453233\pi$
$773$	3.90275	+	10.7227i	0.140372	+	0.385669i	−0.849508	+	0.527576i	$0.823101\pi$
$774$		0			0
$775$	11.6298	−	16.6091i	0.417754	−	0.596615i
$776$	−2.97291			−0.106721
$777$		0			0
$778$	−24.2081			−0.867901
$779$	7.28554	−	10.4048i	0.261031	−	0.372792i
$780$		0			0
$781$	1.13261	+	3.11182i	0.0405280	+	0.111350i
$782$	6.52900	−	0.571214i	0.233477	−	0.0204266i
$783$		0			0
$784$	−0.235602	−	0.197693i

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)

\(f(q)\)	\(=\)	\(q+(-0.573576 + 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(-0.718088 + 0.0628246i) q^{5} +(-2.07081 - 1.73762i) q^{7} +(0.965926 + 0.258819i) q^{8} +O(q^{10})\)	\(q+(-0.573576 + 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(-0.718088 + 0.0628246i) q^{5} +(-2.07081 - 1.73762i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.360415 - 0.624258i) q^{10} +(2.14666 + 3.71813i) q^{11} +(0.0350998 + 0.0163673i) q^{13} +(2.61114 - 0.699652i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(-1.26227 + 0.588607i) q^{17} +(-1.15999 + 0.812232i) q^{19} +(0.304636 + 0.653295i) q^{20} +(-4.27699 - 0.374188i) q^{22} +(1.21793 + 4.54537i) q^{23} +(-4.41234 + 0.778014i) q^{25} +(-0.0335397 + 0.0193642i) q^{26} +(-0.924566 + 2.54022i) q^{28} +(-2.18568 + 8.15709i) q^{29} +(-3.19999 + 3.19999i) q^{31} +(-0.0871557 - 0.996195i) q^{32} +(0.241851 - 1.37160i) q^{34} +(1.59619 + 1.11766i) q^{35} +(6.02223 + 0.856003i) q^{37} -1.41608i q^{38} +(-0.709880 - 0.125171i) q^{40} +(-8.42883 + 3.06784i) q^{41} +(-0.673546 - 0.673546i) q^{43} +(2.75969 - 3.28888i) q^{44} +(-4.42192 - 1.60945i) q^{46} +(2.04440 + 1.18033i) q^{47} +(0.0534066 + 0.302884i) q^{49} +(1.89350 - 4.06062i) q^{50} +(0.00337540 - 0.0385810i) q^{52} +(-0.385452 - 0.459364i) q^{53} +(-1.77508 - 2.53508i) q^{55} +(-1.55052 - 2.21437i) q^{56} +(-5.42824 - 6.46912i) q^{58} +(0.273822 - 3.12980i) q^{59} +(-4.73693 + 10.1584i) q^{61} +(-0.785839 - 4.45671i) q^{62} +(0.866025 + 0.500000i) q^{64} +(-0.0262330 - 0.00954803i) q^{65} +(5.48130 - 6.53235i) q^{67} +(0.984832 + 0.984832i) q^{68} +(-1.83107 + 0.666456i) q^{70} +(0.759603 + 0.133939i) q^{71} +9.36628i q^{73} +(-4.15541 + 4.44214i) q^{74} +(1.15999 + 0.812232i) q^{76} +(2.01535 - 11.4296i) q^{77} +(-0.124024 - 1.41760i) q^{79} +(0.509704 - 0.509704i) q^{80} +(2.32155 - 8.66414i) q^{82} +(-2.84370 + 7.81299i) q^{83} +(0.869443 - 0.501973i) q^{85} +(0.938067 - 0.165407i) q^{86} +(1.11119 + 4.14703i) q^{88} +(-10.6799 - 0.934373i) q^{89} +(-0.0442449 - 0.0948835i) q^{91} +(3.85469 - 2.69909i) q^{92} +(-2.13949 + 0.997660i) q^{94} +(0.781945 - 0.656130i) q^{95} +(-2.87161 + 0.769446i) q^{97} +(-0.278741 - 0.129979i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q + 12 q^{13} - 24 q^{19} - 12 q^{22} + 72 q^{34} + 72 q^{37} + 24 q^{40} + 24 q^{43} + 36 q^{46} - 48 q^{49} - 12 q^{52} + 60 q^{55} + 120 q^{61} + 60 q^{67} - 60 q^{70} + 24 q^{76} - 12 q^{79} - 48 q^{82} + 108 q^{85} - 24 q^{88} - 168 q^{91} - 84 q^{94} - 264 q^{97}+O(q^{100}) \) 72 * q + 12 * q^13 - 24 * q^19 - 12 * q^22 + 72 * q^34 + 72 * q^37 + 24 * q^40 + 24 * q^43 + 36 * q^46 - 48 * q^49 - 12 * q^52 + 60 * q^55 + 120 * q^61 + 60 * q^67 - 60 * q^70 + 24 * q^76 - 12 * q^79 - 48 * q^82 + 108 * q^85 - 24 * q^88 - 168 * q^91 - 84 * q^94 - 264 * q^97

Introduction

L-functions

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