LMFDB - Embedded newform 666.2.bs.a.17.1

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

Embedding invariants

Embedding label			17.1
Character	$\chi$	$=$	666.17
Dual form			666.2.bs.a.431.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.573576 + 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(-0.980582 + 0.0857898i) q^{5} +(1.16963 + 0.981439i) q^{7} +(0.965926 + 0.258819i) q^{8} +O(q^{10})$	\(q+(-0.573576 + 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(-0.980582 + 0.0857898i) q^{5} +(1.16963 + 0.981439i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.492164 - 0.852453i) q^{10} +(-3.02784 - 5.24438i) q^{11} +(-1.58099 - 0.737228i) q^{13} +(-1.47482 + 0.395177i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(-7.17231 + 3.34450i) q^{17} +(2.99110 - 2.09439i) q^{19} +(0.415995 + 0.892104i) q^{20} +(6.03265 + 0.527788i) q^{22} +(0.211307 + 0.788610i) q^{23} +(-3.96986 + 0.699993i) q^{25} +(1.51072 - 0.872215i) q^{26} +(0.522213 - 1.43477i) q^{28} +(0.314145 - 1.17240i) q^{29} +(0.312140 - 0.312140i) q^{31} +(-0.0871557 - 0.996195i) q^{32} +(1.37421 - 7.79354i) q^{34} +(-1.23112 - 0.862038i) q^{35} +(-1.29697 - 5.94288i) q^{37} +3.65146i q^{38} +(-0.969373 - 0.170927i) q^{40} +(8.84597 - 3.21967i) q^{41} +(-4.57591 - 4.57591i) q^{43} +(-3.89252 + 4.63893i) q^{44} +(-0.767192 - 0.279235i) q^{46} +(-11.5245 - 6.65366i) q^{47} +(-0.810718 - 4.59781i) q^{49} +(1.70362 - 3.65342i) q^{50} +(-0.152037 + 1.73779i) q^{52} +(-7.93317 - 9.45438i) q^{53} +(3.41896 + 4.88279i) q^{55} +(0.875764 + 1.25072i) q^{56} +(0.780191 + 0.929796i) q^{58} +(-0.977451 + 11.1723i) q^{59} +(3.22828 - 6.92307i) q^{61} +(0.0766540 + 0.434726i) q^{62} +(0.866025 + 0.500000i) q^{64} +(1.61354 + 0.587280i) q^{65} +(-3.99253 + 4.75812i) q^{67} +(5.59588 + 5.59588i) q^{68} +(1.41228 - 0.514028i) q^{70} +(7.37567 + 1.30053i) q^{71} +8.51548i q^{73} +(5.61204 + 2.34629i) q^{74} +(-2.99110 - 2.09439i) q^{76} +(1.60557 - 9.10565i) q^{77} +(-0.00716907 - 0.0819428i) q^{79} +(0.696025 - 0.696025i) q^{80} +(-2.43644 + 9.09293i) q^{82} +(0.0951748 - 0.261491i) q^{83} +(6.74611 - 3.89487i) q^{85} +(6.37299 - 1.12373i) q^{86} +(-1.56733 - 5.84935i) q^{88} +(9.92117 + 0.867990i) q^{89} +(-1.12564 - 2.41393i) q^{91} +(0.668779 - 0.468284i) q^{92} +(12.0605 - 5.62392i) q^{94} +(-2.75334 + 2.31033i) q^{95} +(-7.26572 + 1.94684i) q^{97} +(4.23131 + 1.97309i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−0.980582	+	0.0857898i	−0.438529	+	0.0383664i	−0.304283	−	0.952582i	$-0.598417\pi$
$5$	−0.980582	+	0.0857898i	−0.438529	+	0.0383664i	−0.134246	+	0.990948i	$0.542861\pi$
$6$		0			0
$7$	1.16963	+	0.981439i	0.442080	+	0.370949i	0.836487	−	0.547987i	$-0.184606\pi$
$7$	1.16963	+	0.981439i	0.442080	+	0.370949i	−0.394407	+	0.918936i	$0.629050\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$		0			0
$10$	0.492164	−	0.852453i	0.155636	−	0.269569i
$11$	−3.02784	−	5.24438i	−0.912930	−	1.58124i	−0.809905	−	0.586562i	$-0.800481\pi$
$11$	−3.02784	−	5.24438i	−0.912930	−	1.58124i	−0.103025	−	0.994679i	$-0.532852\pi$
$12$		0			0
$13$	−1.58099	−	0.737228i	−0.438488	−	0.204470i	0.190822	−	0.981625i	$-0.438885\pi$
$13$	−1.58099	−	0.737228i	−0.438488	−	0.204470i	−0.629310	+	0.777154i	$0.716662\pi$
$14$	−1.47482	+	0.395177i	−0.394163	+	0.105616i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	−7.17231	+	3.34450i	−1.73954	+	0.811161i	−0.750982	+	0.660323i	$0.770419\pi$
$17$	−7.17231	+	3.34450i	−1.73954	+	0.811161i	−0.988559	+	0.150838i	$0.951803\pi$
$18$		0			0
$19$	2.99110	−	2.09439i	0.686205	−	0.480486i	−0.177736	−	0.984078i	$-0.556877\pi$
$19$	2.99110	−	2.09439i	0.686205	−	0.480486i	0.863942	+	0.503592i	$0.167988\pi$
$20$	0.415995	+	0.892104i	0.0930193	+	0.199480i
$21$		0			0
$22$	6.03265	+	0.527788i	1.28616	+	0.112525i
$23$	0.211307	+	0.788610i	0.0440606	+	0.164436i	0.984451	−	0.175662i	$-0.0562064\pi$
$23$	0.211307	+	0.788610i	0.0440606	+	0.164436i	−0.940390	+	0.340098i	$0.889540\pi$
$24$		0			0
$25$	−3.96986	+	0.699993i	−0.793972	+	0.139999i
$26$	1.51072	−	0.872215i	0.296277	−	0.171055i
$27$		0			0
$28$	0.522213	−	1.43477i	0.0986889	−	0.271146i
$29$	0.314145	−	1.17240i	0.0583352	−	0.217710i	−0.930605	−	0.366025i	$-0.880718\pi$
$29$	0.314145	−	1.17240i	0.0583352	−	0.217710i	0.988940	+	0.148315i	$0.0473850\pi$
$30$		0			0
$31$	0.312140	−	0.312140i	0.0560620	−	0.0560620i	−0.678520	−	0.734582i	$-0.737378\pi$
$31$	0.312140	−	0.312140i	0.0560620	−	0.0560620i	0.734582	+	0.678520i	$0.237378\pi$
$32$	−0.0871557	−	0.996195i	−0.0154071	−	0.176104i
$33$		0			0
$34$	1.37421	−	7.79354i	0.235675	−	1.33658i
$35$	−1.23112	−	0.862038i	−0.208097	−	0.145711i
$36$		0			0
$37$	−1.29697	−	5.94288i	−0.213220	−	0.977004i
$37$	−1.29697	−	5.94288i	−0.213220	−	0.977004i
$38$			3.65146i			0.592345i
$39$		0			0
$40$	−0.969373	−	0.170927i	−0.153271	−	0.0270259i
$41$	8.84597	−	3.21967i	1.38151	−	0.502828i	0.458874	−	0.888501i	$-0.348253\pi$
$41$	8.84597	−	3.21967i	1.38151	−	0.502828i	0.922635	+	0.385673i	$0.126031\pi$
$42$		0			0
$43$	−4.57591	−	4.57591i	−0.697819	−	0.697819i	0.266121	−	0.963940i	$-0.414258\pi$
$43$	−4.57591	−	4.57591i	−0.697819	−	0.697819i	−0.963940	+	0.266121i	$0.914258\pi$
$44$	−3.89252	+	4.63893i	−0.586820	+	0.699345i
$45$		0			0
$46$	−0.767192	−	0.279235i	−0.113116	−	0.0411710i
$47$	−11.5245	−	6.65366i	−1.68102	−	0.970536i	−0.960987	−	0.276594i	$-0.910794\pi$
$47$	−11.5245	−	6.65366i	−1.68102	−	0.970536i	−0.720031	−	0.693942i	$-0.755872\pi$
$48$		0			0
$49$	−0.810718	−	4.59781i	−0.115817	−	0.656830i
$50$	1.70362	−	3.65342i	0.240928	−	0.516671i
$51$		0			0
$52$	−0.152037	+	1.73779i	−0.0210838	+	0.240988i
$53$	−7.93317	−	9.45438i	−1.08970	−	1.29866i	−0.951294	−	0.308285i	$-0.900245\pi$
$53$	−7.93317	−	9.45438i	−1.08970	−	1.29866i	−0.138411	−	0.990375i	$-0.544199\pi$
$54$		0			0
$55$	3.41896	+	4.88279i	0.461013	+	0.658395i
$56$	0.875764	+	1.25072i	0.117029	+	0.167135i
$57$		0			0
$58$	0.780191	+	0.929796i	0.102444	+	0.122088i
$59$	−0.977451	+	11.1723i	−0.127253	+	1.45451i	0.617183	+	0.786819i	$0.288274\pi$
$59$	−0.977451	+	11.1723i	−0.127253	+	1.45451i	−0.744437	+	0.667693i	$0.767282\pi$
$60$		0			0
$61$	3.22828	−	6.92307i	0.413339	−	0.886408i	−0.583877	−	0.811842i	$-0.698465\pi$
$61$	3.22828	−	6.92307i	0.413339	−	0.886408i	0.997216	−	0.0745661i	$-0.0237572\pi$
$62$	0.0766540	+	0.434726i	0.00973506	+	0.0552103i
$63$		0			0
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	1.61354	+	0.587280i	0.200135	+	0.0728431i
$66$		0			0
$67$	−3.99253	+	4.75812i	−0.487765	+	0.581296i	−0.952648	−	0.304076i	$-0.901652\pi$
$67$	−3.99253	+	4.75812i	−0.487765	+	0.581296i	0.464882	+	0.885373i	$0.346097\pi$
$68$	5.59588	+	5.59588i	0.678600	+	0.678600i
$69$		0			0
$70$	1.41228	−	0.514028i	0.168800	−	0.0614381i
$71$	7.37567	+	1.30053i	0.875331	+	0.154344i	0.593223	−	0.805038i	$-0.297855\pi$
$71$	7.37567	+	1.30053i	0.875331	+	0.154344i	0.282108	+	0.959383i	$0.408966\pi$
$72$		0			0
$73$			8.51548i			0.996662i	0.866987	+	0.498331i	$0.166054\pi$
$73$			8.51548i			0.996662i	−0.866987	+	0.498331i	$0.833946\pi$
$74$	5.61204	+	2.34629i	0.652386	+	0.272750i
$75$		0			0
$76$	−2.99110	−	2.09439i	−0.343103	−	0.240243i
$77$	1.60557	−	9.10565i	0.182972	−	1.03768i
$78$		0			0
$79$	−0.00716907	−	0.0819428i	−0.000806583	−	0.00921929i	0.995781	−	0.0917645i	$-0.0292507\pi$
$79$	−0.00716907	−	0.0819428i	−0.000806583	−	0.00921929i	−0.996587	+	0.0825452i	$0.973695\pi$
$80$	0.696025	−	0.696025i	0.0778179	−	0.0778179i
$81$		0			0
$82$	−2.43644	+	9.09293i	−0.269060	+	1.00415i
$83$	0.0951748	−	0.261491i	0.0104468	−	0.0287023i	−0.934360	−	0.356331i	$-0.884027\pi$
$83$	0.0951748	−	0.261491i	0.0104468	−	0.0287023i	0.944806	+	0.327629i	$0.106250\pi$
$84$		0			0
$85$	6.74611	−	3.89487i	0.731718	−	0.422458i
$86$	6.37299	−	1.12373i	0.687218	−	0.121175i
$87$		0			0
$88$	−1.56733	−	5.84935i	−0.167078	−	0.623542i
$89$	9.92117	+	0.867990i	1.05164	+	0.0920068i	0.599847	−	0.800115i	$-0.295228\pi$
$89$	9.92117	+	0.867990i	1.05164	+	0.0920068i	0.451795	+	0.892122i	$0.350784\pi$
$90$		0			0
$91$	−1.12564	−	2.41393i	−0.117999	−	0.253049i
$92$	0.668779	−	0.468284i	0.0697251	−	0.0488220i
$93$		0			0
$94$	12.0605	−	5.62392i	1.24395	−	0.580063i
$95$	−2.75334	+	2.31033i	−0.282487	+	0.237035i
$96$		0			0
$97$	−7.26572	+	1.94684i	−0.737722	+	0.197672i	−0.608065	−	0.793887i	$-0.708054\pi$
$97$	−7.26572	+	1.94684i	−0.737722	+	0.197672i	−0.129656	+	0.991559i	$0.541387\pi$
$98$	4.23131	+	1.97309i	0.427427	+	0.199313i
$99$		0			0
$100$	2.01555	+	3.49103i	0.201555	+	0.349103i
$101$	3.47385	−	6.01688i	0.345661	−	0.598702i	−0.639813	−	0.768531i	$-0.720988\pi$
$101$	3.47385	−	6.01688i	0.345661	−	0.598702i	0.985474	+	0.169829i	$0.0543214\pi$
$102$		0			0
$103$	6.01896	+	1.61278i	0.593066	+	0.158912i	0.542854	−	0.839827i	$-0.317344\pi$
$103$	6.01896	+	1.61278i	0.593066	+	0.158912i	0.0502118	+	0.998739i	$0.484010\pi$
$104$	−1.33631	−	1.12130i	−0.131036	−	0.109952i
$105$		0			0
$106$	12.2949	−	1.07566i	1.19418	−	0.104477i
$107$	2.81945	+	7.74636i	0.272566	+	0.748869i	0.998154	+	0.0607394i	$0.0193459\pi$
$107$	2.81945	+	7.74636i	0.272566	+	0.748869i	−0.725588	+	0.688130i	$0.758432\pi$
$108$		0			0
$109$	−10.2084	+	14.5790i	−0.977783	+	1.39642i	−0.0605072	+	0.998168i	$0.519272\pi$
$109$	−10.2084	+	14.5790i	−0.977783	+	1.39642i	−0.917276	+	0.398252i	$0.869617\pi$
$110$	−5.96078			−0.568338
$111$		0			0
$112$	−1.52685			−0.144274
$113$	2.86810	−	4.09607i	0.269808	−	0.385326i	−0.661269	−	0.750149i	$-0.729982\pi$
$113$	2.86810	−	4.09607i	0.269808	−	0.385326i	0.931077	+	0.364823i	$0.118871\pi$
$114$		0			0
$115$	−0.274859	−	0.755168i	−0.0256307	−	0.0704198i
$116$	−1.20914	+	0.105786i	−0.112266	+	0.00982202i
$117$		0			0
$118$	−8.59119	−	7.20886i	−0.790883	−	0.663629i
$119$	−11.6714	−	3.12734i	−1.06991	−	0.286683i
$120$		0			0
$121$	−12.8357	+	22.2321i	−1.16688	+	2.02110i
$122$	3.81938	+	6.61536i	0.345790	+	0.598927i
$123$		0			0
$124$	−0.400074	−	0.186557i	−0.0359277	−	0.0167534i
$125$	8.58665	−	2.30079i	0.768014	−	0.205789i
$126$		0			0
$127$	−12.5650	+	10.5433i	−1.11496	+	0.935563i	−0.998339	−	0.0576136i	$-0.981651\pi$
$127$	−12.5650	+	10.5433i	−1.11496	+	0.935563i	−0.116621	+	0.993176i	$0.537206\pi$
$128$	−0.906308	+	0.422618i	−0.0801070	+	0.0373545i
$129$		0			0
$130$	−1.40656	+	0.984883i	−0.123363	+	0.0863799i
$131$	−0.709934	−	1.52246i	−0.0620273	−	0.133018i	0.872851	−	0.487988i	$-0.162269\pi$
$131$	−0.709934	−	1.52246i	−0.0620273	−	0.133018i	−0.934878	+	0.354970i	$0.884491\pi$
$132$		0			0
$133$	5.55401	+	0.485913i	0.481593	+	0.0421340i
$134$	−1.60760	−	5.99963i	−0.138875	−	0.518289i
$135$		0			0
$136$	−7.79354	+	1.37421i	−0.668290	+	0.117838i
$137$	1.25569	−	0.724975i	0.107281	−	0.0619388i	−0.445399	−	0.895332i	$-0.646938\pi$
$137$	1.25569	−	0.724975i	0.107281	−	0.0619388i	0.552681	+	0.833393i	$0.313605\pi$
$138$		0			0
$139$	2.22338	−	6.10870i	0.188585	−	0.518133i	−0.808983	−	0.587832i	$-0.799982\pi$
$139$	2.22338	−	6.10870i	0.188585	−	0.518133i	0.997568	+	0.0696990i	$0.0222039\pi$
$140$	−0.388984	+	1.45171i	−0.0328751	+	0.122692i
$141$		0			0
$142$	−5.29584	+	5.29584i	−0.444417	+	0.444417i
$143$	0.920690	+	10.5235i	0.0769919	+	0.880022i
$144$		0			0
$145$	−0.207464	+	1.17659i	−0.0172290	+	0.0977104i
$146$	−6.97547	−	4.88428i	−0.577294	−	0.404226i
$147$		0			0
$148$	−5.14090	+	3.25134i	−0.422579	+	0.267258i
$149$			7.47001i			0.611967i	0.952037	+	0.305984i	$0.0989853\pi$
$149$			7.47001i			0.611967i	−0.952037	+	0.305984i	$0.901015\pi$
$150$		0			0
$151$	10.0724	+	1.77603i	0.819676	+	0.144531i	0.567735	−	0.823211i	$-0.307820\pi$
$151$	10.0724	+	1.77603i	0.819676	+	0.144531i	0.251941	+	0.967742i	$0.418931\pi$
$152$	3.43125	−	1.24887i	0.278311	−	0.101297i
$153$		0			0
$154$	6.53799	+	6.53799i	0.526846	+	0.526846i
$155$	−0.279300	+	0.332857i	−0.0224339	+	0.0267357i
$156$		0			0
$157$	−6.97750	−	2.53960i	−0.556865	−	0.202682i	0.0482292	−	0.998836i	$-0.484642\pi$
$157$	−6.97750	−	2.53960i	−0.556865	−	0.202682i	−0.605094	+	0.796154i	$0.706864\pi$
$158$	0.0712357	+	0.0411279i	0.00566720	+	0.00327196i
$159$		0			0
$160$	0.170927	+	0.969373i	0.0135129	+	0.0766357i
$161$	−0.526820	+	1.12977i	−0.0415192	+	0.0890383i
$162$		0			0
$163$	0.420877	−	4.81064i	0.0329656	−	0.376799i	−0.961735	−	0.273982i	$-0.911659\pi$
$163$	0.420877	−	4.81064i	0.0329656	−	0.376799i	0.994700	−	0.102816i	$-0.0327854\pi$
$164$	−6.05100	−	7.21130i	−0.472504	−	0.563108i
$165$		0			0
$166$	0.159611	+	0.227947i	0.0123882	+	0.0176922i
$167$	2.87228	+	4.10205i	0.222264	+	0.317426i	0.914761	−	0.403994i	$-0.132378\pi$
$167$	2.87228	+	4.10205i	0.222264	+	0.317426i	−0.692497	+	0.721420i	$0.743490\pi$
$168$		0			0
$169$	−6.40021	−	7.62748i	−0.492324	−	0.586729i
$170$	−0.678920	+	7.76009i	−0.0520708	+	0.595172i
$171$		0			0
$172$	−2.73489	+	5.86500i	−0.208534	+	0.447202i
$173$	−0.560433	−	3.17837i	−0.0426089	−	0.241647i	0.956063	−	0.293160i	$-0.0947068\pi$
$173$	−0.560433	−	3.17837i	−0.0426089	−	0.241647i	−0.998672	+	0.0515128i	$0.983596\pi$
$174$		0			0
$175$	−5.33028	−	3.07744i	−0.402931	−	0.232632i
$176$	5.69049	+	2.07117i	0.428937	+	0.156120i
$177$		0			0
$178$	−6.40157	+	7.62909i	−0.479818	+	0.571825i
$179$	11.0818	+	11.0818i	0.828289	+	0.828289i	0.987280	−	0.158991i	$-0.0508241\pi$
$179$	11.0818	+	11.0818i	0.828289	+	0.828289i	−0.158991	+	0.987280i	$0.550824\pi$
$180$		0			0
$181$	8.99844	−	3.27516i	0.668849	−	0.243441i	0.0147965	−	0.999891i	$-0.495290\pi$
$181$	8.99844	−	3.27516i	0.668849	−	0.243441i	0.654052	+	0.756450i	$0.273068\pi$
$182$	2.62302	+	0.462508i	0.194431	+	0.0342834i
$183$		0			0
$184$			0.816429i			0.0601879i
$185$	1.78162	+	5.71622i	0.130987	+	0.420265i
$186$		0			0
$187$	39.2565	+	27.4877i	2.87072	+	2.01010i
$188$	−2.31079	+	13.1052i	−0.168532	+	0.955791i
$189$		0			0
$190$	−0.313258	−	3.58055i	−0.0227261	−	0.259761i
$191$	−12.9234	+	12.9234i	−0.935102	+	0.935102i	−0.998019	−	0.0629166i	$-0.979960\pi$
$191$	−12.9234	+	12.9234i	−0.935102	+	0.935102i	0.0629166	+	0.998019i	$0.479960\pi$
$192$		0			0
$193$	3.03191	−	11.3153i	0.218242	−	0.814490i	−0.766758	−	0.641936i	$-0.778131\pi$
$193$	3.03191	−	11.3153i	0.218242	−	0.814490i	0.985000	−	0.172554i	$-0.0552019\pi$
$194$	2.57268	−	7.06839i	0.184708	−	0.507481i
$195$		0			0
$196$	−4.04324	+	2.33437i	−0.288803	+	0.166741i
$197$	11.1073	−	1.95852i	0.791364	−	0.139539i	0.236667	−	0.971591i	$-0.423945\pi$
$197$	11.1073	−	1.95852i	0.791364	−	0.139539i	0.554698	+	0.832052i	$0.312834\pi$
$198$		0			0
$199$	5.71993	+	21.3471i	0.405475	+	1.51325i	0.803178	+	0.595739i	$0.203141\pi$
$199$	5.71993	+	21.3471i	0.405475	+	1.51325i	−0.397703	+	0.917514i	$0.630192\pi$
$200$	−4.01576	−	0.351333i	−0.283957	−	0.0248430i
$201$		0			0
$202$	2.93622	+	6.29675i	0.206592	+	0.443038i
$203$	1.51808	−	1.06297i	0.106548	−	0.0746058i
$204$		0			0
$205$	−8.39799	+	3.91605i	−0.586541	+	0.273508i
$206$	−4.77344	+	4.00539i	−0.332581	+	0.279069i
$207$		0			0
$208$	1.68499	−	0.451492i	0.116833	−	0.0313053i
$209$	−20.0404	−	9.34498i	−1.38622	−	0.646406i
$210$		0			0
$211$	−1.27177	−	2.20277i	−0.0875524	−	0.151645i	0.818924	−	0.573903i	$-0.194571\pi$
$211$	−1.27177	−	2.20277i	−0.0875524	−	0.151645i	−0.906476	+	0.422257i	$0.861238\pi$
$212$	−6.17091	+	10.6883i	−0.423820	+	0.734078i
$213$		0			0
$214$	−7.96262	−	2.13358i	−0.544313	−	0.145848i
$215$	4.87961	+	4.09448i	0.332787	+	0.279241i
$216$		0			0
$217$	0.671435	−	0.0587430i	0.0455800	−	0.00398773i
$218$	−6.08718	−	16.7244i	−0.412276	−	1.13272i
$219$		0			0
$220$	3.41896	−	4.88279i	0.230506	−	0.329197i
$221$	13.8050			0.928626
$222$		0			0
$223$	−15.0865			−1.01027			−0.505134	−	0.863041i	$-0.668557\pi$
$223$	−15.0865			−1.01027			−0.505134	+	0.863041i	$0.668557\pi$
$224$	0.875764	−	1.25072i	0.0585144	−	0.0835673i
$225$		0			0
$226$	1.71023	+	4.69882i	0.113763	+	0.312561i
$227$	12.0674	−	1.05576i	0.800941	−	0.0700732i	0.320667	−	0.947192i	$-0.396093\pi$
$227$	12.0674	−	1.05576i	0.800941	−	0.0700732i	0.480274	+	0.877119i	$0.340537\pi$
$228$		0			0
$229$	−17.3680	−	14.5735i	−1.14771	−	0.963045i	−0.148048	−	0.988980i	$-0.547299\pi$
$229$	−17.3680	−	14.5735i	−1.14771	−	0.963045i	−0.999664	+	0.0259356i	$0.991744\pi$
$230$	0.776250	+	0.207996i	0.0511844	+	0.0137148i
$231$		0			0
$232$	0.606881	−	1.05115i	0.0398437	−	0.0690113i
$233$	−10.2423	−	17.7402i	−0.670997	−	1.16220i	−0.977622	−	0.210371i	$-0.932533\pi$
$233$	−10.2423	−	17.7402i	−0.670997	−	1.16220i	0.306624	−	0.951831i	$-0.400800\pi$
$234$		0			0
$235$	11.8715	+	5.53577i	0.774412	+	0.361114i
$236$	10.8329	−	2.90265i	0.705159	−	0.188947i
$237$		0			0
$238$	9.25620	−	7.76688i	0.599991	−	0.503452i
$239$	−12.2403	+	5.70775i	−0.791759	+	0.369203i	−0.776049	−	0.630673i	$-0.782779\pi$
$239$	−12.2403	+	5.70775i	−0.791759	+	0.369203i	−0.0157108	+	0.999877i	$0.505001\pi$
$240$		0			0
$241$	5.14569	−	3.60305i	0.331463	−	0.232093i	−0.395983	−	0.918258i	$-0.629596\pi$
$241$	5.14569	−	3.60305i	0.331463	−	0.232093i	0.727446	+	0.686165i	$0.240707\pi$
$242$	−10.8492	−	23.2662i	−0.697413	−	1.49561i
$243$		0			0
$244$	−7.60969	−	0.665762i	−0.487161	−	0.0426210i
$245$	1.18942	+	4.43897i	0.0759892	+	0.283596i
$246$		0			0
$247$	−6.27295	+	1.10609i	−0.399138	+	0.0703788i
$248$	0.382292	−	0.220716i	0.0242756	−	0.0140155i
$249$		0			0
$250$	−3.04041	+	8.35345i	−0.192292	+	0.528319i
$251$	5.04274	−	18.8198i	0.318295	−	1.18789i	−0.602588	−	0.798053i	$-0.705864\pi$
$251$	5.04274	−	18.8198i	0.318295	−	1.18789i	0.920883	−	0.389840i	$-0.127470\pi$
$252$		0			0
$253$	3.49596	−	3.49596i	0.219789	−	0.219789i
$254$	−1.42956	−	16.3400i	−0.0896988	−	1.02526i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	16.9969	+	11.9014i	1.06024	+	0.742388i	0.967390	−	0.253292i	$-0.0815133\pi$
$257$	16.9969	+	11.9014i	1.06024	+	0.742388i	0.0928503	+	0.995680i	$0.470402\pi$
$258$		0			0
$259$	4.31560	−	8.22389i	0.268159	−	0.511008i
$260$		−	1.71709i		−	0.106489i
$261$		0			0
$262$	1.65433	+	0.291703i	0.102205	+	0.0180214i
$263$	−25.3902	+	9.24126i	−1.56562	+	0.569841i	−0.972016	−	0.234913i	$-0.924519\pi$
$263$	−25.3902	+	9.24126i	−1.56562	+	0.569841i	−0.593608	+	0.804754i	$0.702297\pi$
$264$		0			0
$265$	8.59021	+	8.59021i	0.527693	+	0.527693i
$266$	−3.58368	+	4.27087i	−0.219730	+	0.261864i
$267$		0			0
$268$	5.83669	+	2.12438i	0.356533	+	0.129767i
$269$	2.88940	+	1.66819i	0.176170	+	0.101712i	0.585492	−	0.810678i	$-0.300901\pi$
$269$	2.88940	+	1.66819i	0.176170	+	0.101712i	−0.409322	+	0.912390i	$0.634235\pi$
$270$		0			0
$271$	−2.30713	−	13.0844i	−0.140148	−	0.794819i	−0.971136	−	0.238528i	$-0.923335\pi$
$271$	−2.30713	−	13.0844i	−0.140148	−	0.794819i	0.830987	−	0.556291i	$-0.187776\pi$
$272$	3.34450	−	7.17231i	0.202790	−	0.434885i
$273$		0			0
$274$	−0.126372	+	1.44443i	−0.00763438	+	0.0872614i
$275$	15.6911	+	18.7000i	0.946212	+	1.12765i
$276$		0			0
$277$	−11.9768	−	17.1046i	−0.719615	−	1.02772i	−0.997741	−	0.0671725i	$-0.978602\pi$
$277$	−11.9768	−	17.1046i	−0.719615	−	1.02772i	0.278126	−	0.960545i	$-0.410287\pi$
$278$	3.72867	+	5.32509i	0.223631	+	0.319378i
$279$		0			0
$280$	−0.966057	−	1.15130i	−0.0577330	−	0.0688035i
$281$	0.465800	−	5.32412i	0.0277873	−	0.317610i	−0.969562	−	0.244846i	$-0.921262\pi$
$281$	0.465800	−	5.32412i	0.0277873	−	0.317610i	0.997349	−	0.0727639i	$-0.0231820\pi$
$282$		0			0
$283$	−8.48893	+	18.2046i	−0.504614	+	1.08215i	0.474764	+	0.880113i	$0.342533\pi$
$283$	−8.48893	+	18.2046i	−0.504614	+	1.08215i	−0.979378	+	0.202036i	$0.935244\pi$
$284$	−1.30053	−	7.37567i	−0.0771722	−	0.437665i
$285$		0			0
$286$	−9.14846	−	5.28186i	−0.540960	−	0.312323i
$287$	13.5065	+	4.91595i	0.797261	+	0.290179i
$288$		0			0
$289$	29.3289	−	34.9528i	1.72523	−	2.05605i
$290$	−0.844808	−	0.844808i	−0.0496089	−	0.0496089i
$291$		0			0
$292$	8.00194	−	2.91247i	0.468278	−	0.170439i
$293$	1.95100	+	0.344014i	0.113979	+	0.0200975i	0.230347	−	0.973109i	$-0.426014\pi$
$293$	1.95100	+	0.344014i	0.113979	+	0.0200975i	−0.116368	+	0.993206i	$0.537125\pi$
$294$		0			0
$295$		−	11.0392i		−	0.642729i
$296$	0.285359	−	6.07607i	0.0165862	−	0.353164i
$297$		0			0
$298$	−6.11908	−	4.28462i	−0.354469	−	0.248202i
$299$	0.247310	−	1.40257i	0.0143023	−	0.0811125i
$300$		0			0
$301$	−0.861160	−	9.84310i	−0.0496364	−	0.567347i
$302$	−7.23210	+	7.23210i	−0.416161	+	0.416161i
$303$		0			0
$304$	−0.945067	+	3.52704i	−0.0542033	+	0.202290i
$305$	−2.57166	+	7.06559i	−0.147253	+	0.404574i
$306$		0			0
$307$	9.48030	−	5.47345i	0.541069	−	0.312386i	−0.204443	−	0.978878i	$-0.565538\pi$
$307$	9.48030	−	5.47345i	0.541069	−	0.312386i	0.745512	+	0.666492i	$0.232205\pi$
$308$	−9.10565	+	1.60557i	−0.518842	+	0.0914859i
$309$		0			0
$310$	−0.112461	−	0.419708i	−0.00638733	−	0.0238378i
$311$	−12.4693	−	1.09092i	−0.707070	−	0.0618606i	−0.272052	−	0.962282i	$-0.587702\pi$
$311$	−12.4693	−	1.09092i	−0.707070	−	0.0618606i	−0.435018	+	0.900422i	$0.643258\pi$
$312$		0			0
$313$	−12.1833	−	26.1271i	−0.688640	−	1.47679i	−0.869833	−	0.493346i	$-0.835774\pi$
$313$	−12.1833	−	26.1271i	−0.688640	−	1.47679i	0.181194	−	0.983447i	$-0.442004\pi$
$314$	6.08245	−	4.25897i	0.343252	−	0.240348i
$315$		0			0
$316$	−0.0745491	+	0.0347628i	−0.00419372	+	0.00195556i
$317$	−2.15708	+	1.81001i	−0.121154	+	0.101660i	−0.701352	−	0.712816i	$-0.747420\pi$
$317$	−2.15708	+	1.81001i	−0.121154	+	0.101660i	0.580198	+	0.814476i	$0.302975\pi$
$318$		0			0
$319$	−7.09972	+	1.90236i	−0.397508	+	0.106512i
$320$	−0.892104	−	0.415995i	−0.0498701	−	0.0232548i
$321$		0			0
$322$	−0.623281	−	1.07955i	−0.0347341	−	0.0601612i
$323$	−14.4484	+	25.0254i	−0.803930	+	1.39245i
$324$		0			0
$325$	6.79236	+	1.82001i	0.376773	+	0.100956i
$326$	3.69924	+	3.10403i	0.204882	+	0.171917i
$327$		0			0
$328$	9.37787	−	0.820457i	0.517806	−	0.0453022i
$329$	−6.94925	−	19.0929i	−0.383125	−	1.05263i
$330$		0			0
$331$	18.4501	−	26.3494i	1.01411	−	1.44830i	0.124144	−	0.992264i	$-0.460381\pi$
$331$	18.4501	−	26.3494i	1.01411	−	1.44830i	0.889964	−	0.456032i	$-0.150730\pi$
$332$	−0.278272			−0.0152722
$333$		0			0
$334$	−5.00768			−0.274008
$335$	3.50681	−	5.00824i	0.191597	−	0.273629i
$336$		0			0
$337$	0.123390	+	0.339012i	0.00672150	+	0.0184672i	0.943008	−	0.332770i	$-0.107983\pi$
$337$	0.123390	+	0.339012i	0.00672150	+	0.0184672i	−0.936287	+	0.351237i	$0.885761\pi$
$338$	9.91907	−	0.867806i	0.539526	−	0.0472024i
$339$		0			0
$340$	−5.96728	−	5.00715i	−0.323621	−	0.271551i
$341$	−2.58209	−	0.691869i	−0.139828	−	0.0374668i
$342$		0			0
$343$	8.90819	−	15.4294i	0.480997	−	0.833111i
$344$	−3.23565	−	5.60432i	−0.174455	−	0.302164i
$345$		0			0
$346$	2.92502	+	1.36396i	0.157250	+	0.0733269i
$347$	24.4355	−	6.54748i	1.31177	−	0.351487i	0.465881	−	0.884848i	$-0.345738\pi$
$347$	24.4355	−	6.54748i	1.31177	−	0.351487i	0.845888	+	0.533360i	$0.179071\pi$
$348$		0			0
$349$	3.73895	−	3.13735i	0.200141	−	0.167939i	−0.537209	−	0.843449i	$-0.680521\pi$
$349$	3.73895	−	3.13735i	0.200141	−	0.167939i	0.737350	+	0.675511i	$0.236077\pi$
$350$	5.57821	−	2.60116i	0.298168	−	0.139038i
$351$		0			0
$352$	−4.96053	+	3.47340i	−0.264397	+	0.185133i
$353$	−11.8230	−	25.3546i	−0.629277	−	1.34949i	−0.919712	−	0.392595i	$-0.871578\pi$
$353$	−11.8230	−	25.3546i	−0.629277	−	1.34949i	0.290434	−	0.956895i	$-0.406200\pi$
$354$		0			0
$355$	−7.34402	−	0.642518i	−0.389780	−	0.0341013i
$356$	−2.57760	−	9.61972i	−0.136612	−	0.509844i
$357$		0			0
$358$	−15.4339	+	2.72141i	−0.815705	+	0.143831i
$359$	6.61627	−	3.81990i	0.349193	−	0.201607i	−0.315137	−	0.949046i	$-0.602050\pi$
$359$	6.61627	−	3.81990i	0.349193	−	0.201607i	0.664330	+	0.747439i	$0.268717\pi$
$360$		0			0
$361$	−1.93818	+	5.32509i	−0.102009	+	0.280268i
$362$	−2.47843	+	9.24964i	−0.130264	+	0.486150i
$363$		0			0
$364$	−1.88336	+	1.88336i	−0.0987151	+	0.0987151i
$365$	−0.730541	−	8.35013i	−0.0382383	−	0.437066i
$366$		0			0
$367$	−2.73554	+	15.5140i	−0.142794	+	0.809824i	0.826318	+	0.563203i	$0.190431\pi$
$367$	−2.73554	+	15.5140i	−0.142794	+	0.809824i	−0.969112	+	0.246621i	$0.920680\pi$
$368$	−0.668779	−	0.468284i	−0.0348625	−	0.0244110i
$369$		0			0
$370$	−5.70435	−	1.81927i	−0.296555	−	0.0945794i
$371$		−	18.8441i		−	0.978336i
$372$		0			0
$373$	3.58277	+	0.631738i	0.185509	+	0.0327102i	0.265631	−	0.964075i	$-0.414420\pi$
$373$	3.58277	+	0.631738i	0.185509	+	0.0327102i	−0.0801219	+	0.996785i	$0.525531\pi$
$374$	−45.0332	+	16.3907i	−2.32861	+	0.847545i
$375$		0			0
$376$	−9.40970	−	9.40970i	−0.485268	−	0.485268i
$377$	−1.36099	+	1.62196i	−0.0700945	+	0.0835354i
$378$		0			0
$379$	15.3773	+	5.59687i	0.789878	+	0.287492i	0.705285	−	0.708924i	$-0.250819\pi$
$379$	15.3773	+	5.59687i	0.789878	+	0.287492i	0.0845927	+	0.996416i	$0.473041\pi$
$380$	3.11270	+	1.79712i	0.159678	+	0.0921901i
$381$		0			0
$382$	−3.17366	−	17.9987i	−0.162379	−	0.920896i
$383$	−2.01740	+	4.32632i	−0.103084	+	0.221065i	−0.951084	−	0.308931i	$-0.900029\pi$
$383$	−2.01740	+	4.32632i	−0.103084	+	0.221065i	0.848000	+	0.529996i	$0.177807\pi$
$384$		0			0
$385$	−0.793222	+	9.06657i	−0.0404264	+	0.462075i
$386$	7.52988	+	8.97376i	0.383261	+	0.456753i
$387$		0			0
$388$	4.31446	+	6.16168i	0.219033	+	0.312812i
$389$	3.11915	+	4.45460i	0.158147	+	0.225857i	0.890404	−	0.455171i	$-0.150422\pi$
$389$	3.11915	+	4.45460i	0.158147	+	0.225857i	−0.732257	+	0.681028i	$0.761533\pi$
$390$		0			0
$391$	−4.15307	−	4.94943i	−0.210030	−	0.250304i
$392$	0.406907	−	4.65097i	0.0205519	−	0.234909i
$393$		0			0
$394$	−4.76658	+	10.2220i	−0.240137	+	0.514975i
$395$	0.0140597	+	0.0797366i	0.000707421	+	0.00401199i
$396$		0			0
$397$	19.2315	+	11.1033i	0.965201	+	0.557259i	0.897770	−	0.440465i	$-0.145186\pi$
$397$	19.2315	+	11.1033i	0.965201	+	0.557259i	0.0674309	+	0.997724i	$0.478520\pi$
$398$	−20.7673	−	7.55868i	−1.04097	−	0.378883i
$399$		0			0
$400$	2.59114	−	3.08800i	0.129557	−	0.154400i
$401$	24.8404	+	24.8404i	1.24047	+	1.24047i	0.959806	+	0.280665i	$0.0905551\pi$
$401$	24.8404	+	24.8404i	1.24047	+	1.24047i	0.280665	+	0.959806i	$0.409445\pi$
$402$		0			0
$403$	−0.723609	+	0.263372i	−0.0360455	+	0.0131195i
$404$	−6.84215	−	1.20646i	−0.340410	−	0.0600234i
$405$		0			0
$406$			1.85323i			0.0919743i
$407$	−27.2397	+	24.7959i	−1.35022	+	1.22909i
$408$		0			0
$409$	−10.1620	−	7.11549i	−0.502477	−	0.351838i	0.294694	−	0.955592i	$-0.404782\pi$
$409$	−10.1620	−	7.11549i	−0.502477	−	0.351838i	−0.797171	+	0.603753i	$0.793671\pi$
$410$	1.60905	−	9.12538i	0.0794653	−	0.450670i
$411$		0			0
$412$	−0.543092	−	6.20757i	−0.0267562	−	0.305825i
$413$	−12.1082	+	12.1082i	−0.595806	+	0.595806i
$414$		0			0
$415$	−0.0708934	+	0.264578i	−0.00348002	+	0.0129876i
$416$	−0.596630	+	1.63923i	−0.0292522	+	0.0803698i
$417$		0			0
$418$	19.1496	−	11.0561i	0.936640	−	0.540769i
$419$	−33.6752	+	5.93784i	−1.64514	+	0.290083i	−0.918052	−	0.396461i	$-0.870238\pi$
$419$	−33.6752	+	5.93784i	−1.64514	+	0.290083i	−0.727089	+	0.686544i	$0.759127\pi$
$420$		0			0
$421$	2.22301	+	8.29640i	0.108343	+	0.404342i	0.998703	−	0.0509155i	$-0.0162139\pi$
$421$	2.22301	+	8.29640i	0.108343	+	0.404342i	−0.890360	+	0.455257i	$0.849547\pi$
$422$	2.53387	+	0.221685i	0.123347	+	0.0107914i
$423$		0			0
$424$	−5.21588	−	11.1855i	−0.253306	−	0.543215i
$425$	26.1319	−	18.2978i	1.26758	−	0.887572i
$426$		0			0
$427$	10.5705	−	4.92909i	0.511541	−	0.238535i
$428$	6.31489	−	5.29883i	0.305242	−	0.256128i
$429$		0			0
$430$	−6.15284	+	1.64865i	−0.296716	+	0.0795048i
$431$	−8.80790	−	4.10719i	−0.424262	−	0.197836i	0.198748	−	0.980051i	$-0.436312\pi$
$431$	−8.80790	−	4.10719i	−0.424262	−	0.197836i	−0.623010	+	0.782214i	$0.714090\pi$
$432$		0			0
$433$	−1.16067	−	2.01034i	−0.0557781	−	0.0966106i	0.836788	−	0.547527i	$-0.184431\pi$
$433$	−1.16067	−	2.01034i	−0.0557781	−	0.0966106i	−0.892566	+	0.450916i	$0.851097\pi$
$434$	−0.337000	+	0.583701i	−0.0161765	+	0.0280186i
$435$		0			0
$436$	17.1913	+	4.60639i	0.823313	+	0.220606i
$437$	2.28370	+	1.91625i	0.109244	+	0.0916667i
$438$		0			0
$439$	30.0362	−	2.62783i	1.43355	−	0.125420i	0.656248	−	0.754545i	$-0.272143\pi$
$439$	30.0362	−	2.62783i	1.43355	−	0.125420i	0.777304	+	0.629126i	$0.216587\pi$
$440$	2.03871	+	5.60130i	0.0971916	+	0.267032i
$441$		0			0
$442$	−7.91823	+	11.3084i	−0.376632	+	0.537886i
$443$	14.5868			0.693037			0.346519	−	0.938043i	$-0.387364\pi$
$443$	14.5868			0.693037			0.346519	+	0.938043i	$0.387364\pi$
$444$		0			0
$445$	−9.80299			−0.464706
$446$	8.65327	−	12.3581i	0.409744	−	0.585175i
$447$		0			0
$448$	0.522213	+	1.43477i	0.0246722	+	0.0677864i
$449$	−13.1170	+	1.14759i	−0.619032	+	0.0541583i	−0.392358	−	0.919813i	$-0.628341\pi$
$449$	−13.1170	+	1.14759i	−0.619032	+	0.0541583i	−0.226674	+	0.973971i	$0.572785\pi$
$450$		0			0
$451$	−43.6694	−	36.6430i	−2.05631	−	1.72545i
$452$	−4.82999	−	1.29419i	−0.227184	−	0.0608737i
$453$		0			0
$454$	−6.05674	+	10.4906i	−0.284257	+	0.492348i
$455$	1.31087	+	2.27049i	0.0614544	+	0.106442i
$456$		0			0
$457$	−2.11792	−	0.987603i	−0.0990722	−	0.0461981i	0.372450	−	0.928052i	$-0.378518\pi$
$457$	−2.11792	−	0.987603i	−0.0990722	−	0.0461981i	−0.471523	+	0.881854i	$0.656295\pi$
$458$	21.8998	−	5.86804i	1.02331	−	0.274195i
$459$		0			0
$460$	−0.615619	+	0.516565i	−0.0287034	+	0.0240850i
$461$	21.7782	−	10.1554i	1.01431	−	0.472982i	0.156902	−	0.987614i	$-0.449849\pi$
$461$	21.7782	−	10.1554i	1.01431	−	0.472982i	0.857411	+	0.514632i	$0.172072\pi$
$462$		0			0
$463$	12.7977	−	8.96103i	0.594758	−	0.416454i	−0.237066	−	0.971494i	$-0.576186\pi$
$463$	12.7977	−	8.96103i	0.594758	−	0.416454i	0.831824	+	0.555039i	$0.187297\pi$
$464$	0.512958	+	1.10004i	0.0238135	+	0.0510682i
$465$		0			0
$466$	20.4067	+	1.78536i	0.945323	+	0.0827050i
$467$	3.84533	+	14.3510i	0.177940	+	0.664083i	0.996032	+	0.0889949i	$0.0283655\pi$
$467$	3.84533	+	14.3510i	0.177940	+	0.664083i	−0.818092	+	0.575088i	$0.804968\pi$
$468$		0			0
$469$	−9.33960	+	1.64682i	−0.431263	+	0.0760432i
$470$	−11.3439	+	6.54938i	−0.523253	+	0.302100i
$471$		0			0
$472$	−3.83575	+	10.5386i	−0.176555	+	0.485081i
$473$	−10.1427	+	37.8529i	−0.466360	+	1.74048i
$474$		0			0
$475$	−10.4082	+	10.4082i	−0.477560	+	0.477560i
$476$	1.05311	+	12.0371i	0.0482693	+	0.551721i
$477$		0			0
$478$	2.34524	−	13.3005i	0.107269	−	0.608351i
$479$	−21.9877	−	15.3960i	−1.00464	−	0.703459i	−0.0492478	−	0.998787i	$-0.515682\pi$
$479$	−21.9877	−	15.3960i	−1.00464	−	0.703459i	−0.955396	+	0.295327i	$0.904571\pi$
$480$		0			0
$481$	−2.33077	+	10.3518i	−0.106274	+	0.472002i
$482$			6.28172i			0.286125i
$483$		0			0
$484$	25.2814	+	4.45779i	1.14915	+	0.202627i
$485$	6.95761	−	2.53236i	0.315929	−	0.114989i
$486$		0			0
$487$	15.9768	+	15.9768i	0.723977	+	0.723977i	0.969413	−	0.245435i	$-0.0789310\pi$
$487$	15.9768	+	15.9768i	0.723977	+	0.723977i	−0.245435	+	0.969413i	$0.578931\pi$
$488$	4.91010	−	5.85163i	0.222270	−	0.264891i
$489$		0			0
$490$	−4.31842	−	1.57178i	−0.195086	−	0.0710056i
$491$	−17.6071	−	10.1655i	−0.794598	−	0.458761i	0.0469809	−	0.998896i	$-0.485040\pi$
$491$	−17.6071	−	10.1655i	−0.794598	−	0.458761i	−0.841579	+	0.540135i	$0.818373\pi$
$492$		0			0
$493$	1.66797	+	9.45950i	0.0751214	+	0.426035i
$494$	2.69196	−	5.77292i	0.121117	−	0.259736i
$495$		0			0
$496$	−0.0384734	+	0.439753i	−0.00172751	+	0.0197455i
$497$	7.35044	+	8.75991i	0.329712	+	0.392936i
$498$		0			0
$499$	−17.6846	−	25.2562i	−0.791671	−	1.13062i	−0.988653	−	0.150216i	$-0.952003\pi$
$499$	−17.6846	−	25.2562i	−0.791671	−	1.13062i	0.196982	−	0.980407i	$-0.436886\pi$
$500$	−5.09884	−	7.28190i	−0.228027	−	0.325656i
$501$		0			0
$502$	12.5239	+	14.9253i	0.558967	+	0.666151i
$503$	3.36949	−	38.5134i	0.150238	−	1.71723i	−0.430039	−	0.902810i	$-0.641500\pi$
$503$	3.36949	−	38.5134i	0.150238	−	1.71723i	0.580277	−	0.814419i	$-0.302944\pi$
$504$		0			0
$505$	−2.89021	+	6.19807i	−0.128612	+	0.275810i
$506$	0.858523	+	4.86893i	0.0381660	+	0.216450i
$507$		0			0
$508$	14.2049	+	8.20120i	0.630240	+	0.363869i
$509$	2.11147	+	0.768514i	0.0935895	+	0.0340638i	0.388391	−	0.921495i	$-0.373031\pi$
$509$	2.11147	+	0.768514i	0.0935895	+	0.0340638i	−0.294801	+	0.955559i	$0.595253\pi$
$510$		0			0
$511$	−8.35742	+	9.95999i	−0.369711	+	0.440604i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	−19.4981	+	7.09672i	−0.860024	+	0.313023i
$515$	−6.04044	−	1.06509i	−0.266174	−	0.0469336i
$516$		0			0
$517$			80.5850i			3.54412i
$518$	4.26129	+	8.25216i	0.187230	+	0.362579i
$519$		0			0
$520$	1.40656	+	0.984883i	0.0616817	+	0.0431900i
$521$	5.04735	−	28.6250i	0.221128	−	1.25408i	−0.648821	−	0.760941i	$-0.724738\pi$
$521$	5.04735	−	28.6250i	0.221128	−	1.25408i	0.869949	−	0.493141i	$-0.164151\pi$
$522$		0			0
$523$	−0.175420	−	2.00506i	−0.00767059	−	0.0876753i	0.991394	−	0.130909i	$-0.0417896\pi$
$523$	−0.175420	−	2.00506i	−0.00767059	−	0.0876753i	−0.999065	+	0.0432337i	$0.986234\pi$
$524$	−1.18783	+	1.18783i	−0.0518907	+	0.0518907i
$525$		0			0
$526$	6.99320	−	26.0990i	0.304918	−	1.13797i
$527$	−1.19481	+	3.28272i	−0.0520468	+	0.142997i
$528$		0			0
$529$	19.3413	−	11.1667i	0.840927	−	0.485510i
$530$	−11.9638	+	2.10955i	−0.519676	+	0.0916328i
$531$		0			0
$532$	−1.44297	−	5.38525i	−0.0625608	−	0.233480i
$533$	−16.3590	−	1.43123i	−0.708589	−	0.0619935i
$534$		0			0
$535$	−3.42926	−	7.35406i	−0.148260	−	0.317944i
$536$	−5.08798	+	3.56264i	−0.219767	+	0.153883i
$537$		0			0
$538$	−3.02379	+	1.41002i	−0.130365	+	0.0607902i
$539$	−21.6579	+	18.1732i	−0.932873	+	0.782773i
$540$		0			0
$541$	−33.0514	+	8.85609i	−1.42099	+	0.380753i	−0.885835	−	0.464001i	$-0.846413\pi$
$541$	−33.0514	+	8.85609i	−1.42099	+	0.380753i	−0.535155	+	0.844754i	$0.679747\pi$
$542$	12.0414	+	5.61500i	0.517223	+	0.241185i
$543$		0			0
$544$	3.95688	+	6.85352i	0.169650	+	0.293842i
$545$	8.75940	−	15.1717i	0.375211	−	0.649885i
$546$		0			0
$547$	36.9027	+	9.88804i	1.57784	+	0.422782i	0.938258	−	0.345937i	$-0.112439\pi$
$547$	36.9027	+	9.88804i	1.57784	+	0.422782i	0.639586	+	0.768719i	$0.279106\pi$
$548$	−1.11073	−	0.932010i	−0.0474479	−	0.0398135i
$549$		0			0
$550$	−24.3182	+	2.12757i	−1.03693	+	0.0907197i
$551$	−1.51583	−	4.16472i	−0.0645767	−	0.177423i
$552$		0			0
$553$	0.0720367	−	0.102879i	0.00306331	−	0.00437486i
$554$	20.8809			0.887144
$555$		0			0
$556$	−6.50074			−0.275693
$557$	−18.8529	+	26.9247i	−0.798822	+	1.14084i	0.188495	+	0.982074i	$0.439639\pi$
$557$	−18.8529	+	26.9247i	−0.798822	+	1.14084i	−0.987317	+	0.158761i	$0.949250\pi$
$558$		0			0
$559$	3.86098	+	10.6080i	0.163302	+	0.448669i
$560$	1.49720	−	0.130988i	0.0632682	−	0.00553525i
$561$		0			0
$562$	4.09409	+	3.43535i	0.172699	+	0.144911i
$563$	37.9953	+	10.1808i	1.60131	+	0.429070i	0.945439	−	0.325800i	$-0.105634\pi$
$563$	37.9953	+	10.1808i	1.60131	+	0.429070i	0.655874	+	0.754871i	$0.272300\pi$
$564$		0			0
$565$	−2.46100	+	4.26258i	−0.103535	+	0.179328i
$566$	−10.0433	−	17.3954i	−0.422149	−	0.731184i
$567$		0			0
$568$	6.78775	+	3.16518i	0.284808	+	0.132808i
$569$	−9.96167	+	2.66922i	−0.417615	+	0.111900i	−0.461507	−	0.887137i	$-0.652691\pi$
$569$	−9.96167	+	2.66922i	−0.417615	+	0.111900i	0.0438919	+	0.999036i	$0.486024\pi$
$570$		0			0
$571$	−6.09096	+	5.11092i	−0.254899	+	0.213885i	−0.761278	−	0.648425i	$-0.775428\pi$
$571$	−6.09096	+	5.11092i	−0.254899	+	0.213885i	0.506380	+	0.862311i	$0.330983\pi$
$572$	9.57399	−	4.46443i	0.400309	−	0.186667i
$573$		0			0
$574$	−11.7739	+	8.24417i	−0.491433	+	0.344105i
$575$	−1.39088	−	2.98275i	−0.0580038	−	0.124389i
$576$		0			0
$577$	−25.3040	−	2.21381i	−1.05342	−	0.0921622i	−0.452732	−	0.891647i	$-0.649551\pi$
$577$	−25.3040	−	2.21381i	−1.05342	−	0.0921622i	−0.600687	+	0.799484i	$0.705106\pi$
$578$	11.8093	+	44.0730i	0.491203	+	1.83319i
$579$		0			0
$580$	1.17659	−	0.207464i	0.0488552	−	0.00861449i
$581$	0.367957	−	0.212440i	0.0152654	−	0.00881349i
$582$		0			0
$583$	−25.5620	+	70.2310i	−1.05867	+	2.90867i
$584$	−2.20397	+	8.22532i	−0.0912009	+	0.340366i
$585$		0			0
$586$	−1.40085	+	1.40085i	−0.0578685	+	0.0578685i
$587$	−0.574609	−	6.56781i	−0.0237166	−	0.271082i	−0.998789	−	0.0491960i	$-0.984334\pi$
$587$	−0.574609	−	6.56781i	−0.0237166	−	0.271082i	0.975073	−	0.221886i	$-0.0712214\pi$
$588$		0			0
$589$	0.279899	−	1.58738i	0.0115330	−	0.0654070i
$590$	9.04281	+	6.33184i	0.372286	+	0.260678i
$591$		0			0
$592$	4.81355	+	3.71884i	0.197836	+	0.152843i
$593$		−	22.2709i		−	0.914557i	−0.889324	−	0.457278i	$-0.848824\pi$
$593$		−	22.2709i		−	0.914557i	0.889324	−	0.457278i	$-0.151176\pi$
$594$		0			0
$595$	11.7130	+	2.06533i	0.480188	+	0.0846701i
$596$	7.01952	−	2.55489i	0.287531	−	0.104653i
$597$		0			0
$598$	1.00706	+	1.00706i	0.0411819	+	0.0411819i
$599$	21.9309	−	26.1363i	0.896073	−	1.06790i	−0.101256	−	0.994860i	$-0.532286\pi$
$599$	21.9309	−	26.1363i	0.896073	−	1.06790i	0.997329	−	0.0730382i	$-0.0232695\pi$
$600$		0			0
$601$	11.3481	+	4.13038i	0.462899	+	0.168482i	0.562933	−	0.826502i	$-0.309673\pi$
$601$	11.3481	+	4.13038i	0.462899	+	0.168482i	−0.100034	+	0.994984i	$0.531895\pi$
$602$	8.55694	+	4.94035i	0.348755	+	0.201354i
$603$		0			0
$604$	−1.77603	−	10.0724i	−0.0722655	−	0.409838i
$605$	10.6792	−	22.9015i	0.434170	−	0.931080i
$606$		0			0
$607$	−2.08749	+	23.8601i	−0.0847286	+	0.968452i	0.828227	+	0.560393i	$0.189350\pi$
$607$	−2.08749	+	23.8601i	−0.0847286	+	0.968452i	−0.912955	+	0.408059i	$0.866206\pi$
$608$	−2.34711	−	2.79718i	−0.0951880	−	0.113441i
$609$		0			0
$610$	−4.31275	−	6.15924i	−0.174618	−	0.249380i
$611$	13.3148	+	19.0155i	0.538660	+	0.769287i
$612$		0			0
$613$	−23.8073	−	28.3725i	−0.961569	−	1.14595i	−0.989235	−	0.146336i	$-0.953252\pi$
$613$	−23.8073	−	28.3725i	−0.961569	−	1.14595i	0.0276655	−	0.999617i	$-0.491193\pi$
$614$	−0.954086	+	10.9053i	−0.0385038	+	0.440100i
$615$		0			0
$616$	3.90758	−	8.37983i	0.157441	−	0.337633i
$617$	−0.734106	−	4.16332i	−0.0295540	−	0.167609i	0.966459	−	0.256823i	$-0.0826757\pi$
$617$	−0.734106	−	4.16332i	−0.0295540	−	0.167609i	−0.996012	+	0.0892138i	$0.971565\pi$
$618$		0			0
$619$	−32.9750	−	19.0381i	−1.32538	−	0.765208i	−0.340797	−	0.940137i	$-0.610697\pi$
$619$	−32.9750	−	19.0381i	−1.32538	−	0.765208i	−0.984581	+	0.174929i	$0.944030\pi$
$620$	0.408310	+	0.148613i	0.0163981	+	0.00596842i
$621$		0			0
$622$	8.04574	−	9.58854i	0.322605	−	0.384465i
$623$	10.7523	+	10.7523i	0.430780	+	0.430780i
$624$		0			0
$625$	10.7174	−	3.90083i	0.428698	−	0.156033i
$626$	28.3901	+	5.00595i	1.13470	+	0.200078i
$627$		0			0
$628$			7.42530i			0.296302i
$629$	29.1782	+	38.2865i	1.16341	+	1.52658i
$630$		0			0
$631$	−3.54096	−	2.47941i	−0.140963	−	0.0987037i	0.500968	−	0.865466i	$-0.332978\pi$
$631$	−3.54096	−	2.47941i	−0.140963	−	0.0987037i	−0.641931	+	0.766762i	$0.721866\pi$
$632$	0.0142836	−	0.0810062i	0.000568170	−	0.00322225i
$633$		0			0
$634$	−0.245419	−	2.80515i	−0.00974684	−	0.111407i
$635$	11.4165	−	11.4165i	0.453049	−	0.453049i
$636$		0			0
$637$	−2.10790	+	7.86678i	−0.0835179	+	0.311693i
$638$	2.51391	−	6.90690i	0.0995265	−	0.273447i
$639$		0			0
$640$	0.852453	−	0.492164i	0.0336961	−	0.0194545i
$641$	−16.7324	+	2.95037i	−0.660888	+	0.116532i	−0.494025	−	0.869448i	$-0.664475\pi$
$641$	−16.7324	+	2.95037i	−0.660888	+	0.116532i	−0.166863	+	0.985980i	$0.553364\pi$
$642$		0			0
$643$	4.02232	+	15.0115i	0.158625	+	0.591995i	0.998768	+	0.0496304i	$0.0158043\pi$
$643$	4.02232	+	15.0115i	0.158625	+	0.591995i	−0.840143	+	0.542365i	$0.817529\pi$
$644$	1.24182	+	0.108645i	0.0489345	+	0.00428122i
$645$		0			0
$646$	−12.2123	−	26.1894i	−0.480487	−	1.03041i
$647$	13.3815	−	9.36984i	0.526082	−	0.368366i	−0.280159	−	0.959953i	$-0.590387\pi$
$647$	13.3815	−	9.36984i	0.526082	−	0.368366i	0.806241	+	0.591587i	$0.201498\pi$
$648$		0			0
$649$	61.5515	−	28.7019i	2.41611	−	1.12665i
$650$	−5.38680	+	4.52007i	−0.211288	+	0.177292i
$651$		0			0
$652$	−4.66448	+	1.24984i	−0.182675	+	0.0489476i
$653$	−22.8518	−	10.6560i	−0.894260	−	0.417000i	−0.0795243	−	0.996833i	$-0.525340\pi$
$653$	−22.8518	−	10.6560i	−0.894260	−	0.417000i	−0.814736	+	0.579833i	$0.803118\pi$
$654$		0			0
$655$	0.826760	+	1.43199i	0.0323042	+	0.0559525i
$656$	−4.70684	+	8.15249i	−0.183771	+	0.318301i
$657$		0			0
$658$	19.6259	+	5.25875i	0.765098	+	0.205007i
$659$	22.5572	+	18.9277i	0.878703	+	0.737319i	0.965912	−	0.258871i	$-0.0833504\pi$
$659$	22.5572	+	18.9277i	0.878703	+	0.737319i	−0.0872092	+	0.996190i	$0.527795\pi$
$660$		0			0
$661$	0.303779	−	0.0265772i	0.0118156	−	0.00103373i	−0.0812464	−	0.996694i	$-0.525890\pi$
$661$	0.303779	−	0.0265772i	0.0118156	−	0.00103373i	0.0930620	+	0.995660i	$0.470335\pi$
$662$	11.0017	+	30.2268i	0.427592	+	1.17480i
$663$		0			0
$664$	0.159611	−	0.227947i	0.00619409	−	0.00884608i
$665$	−5.48784			−0.212809
$666$		0			0
$667$	0.990951			0.0383698
$668$	2.87228	−	4.10205i	0.111132	−	0.158713i
$669$		0			0
$670$	2.09109	+	5.74522i	0.0807858	+	0.221957i
$671$	−46.0819	+	4.03165i	−1.77897	+	0.155640i
$672$		0			0
$673$	−6.45489	−	5.41629i	−0.248818	−	0.208783i	0.509845	−	0.860266i	$-0.329703\pi$
$673$	−6.45489	−	5.41629i	−0.248818	−	0.208783i	−0.758663	+	0.651483i	$0.774147\pi$
$674$	−0.348476	−	0.0933739i	−0.0134228	−	0.00359663i
$675$		0			0
$676$	−4.97848	+	8.62298i	−0.191480	+	0.331653i
$677$	−20.9549	−	36.2949i	−0.805361	−	1.39493i	−0.916047	−	0.401070i	$-0.868638\pi$
$677$	−20.9549	−	36.2949i	−0.805361	−	1.39493i	0.110687	−	0.993855i	$-0.464695\pi$
$678$		0			0
$679$	−10.4089	−	4.85376i	−0.399458	−	0.186270i
$680$	7.52431	−	2.01613i	0.288544	−	0.0773151i
$681$		0			0
$682$	2.04777	−	1.71829i	0.0784133	−	0.0657966i
$683$	−11.7794	+	5.49281i	−0.450725	+	0.210176i	−0.634707	−	0.772753i	$-0.718879\pi$
$683$	−11.7794	+	5.49281i	−0.450725	+	0.210176i	0.183982	+	0.982930i	$0.441101\pi$
$684$		0			0
$685$	−1.16912	+	0.818623i	−0.0446696	+	0.0312780i
$686$	7.52953	+	16.1471i	0.287479	+	0.616500i
$687$		0			0
$688$	6.44668	+	0.564012i	0.245777	+	0.0215027i
$689$	5.57223	+	20.7959i	0.212285	+	0.792259i
$690$		0			0
$691$	−12.5441	+	2.21187i	−0.477202	+	0.0841435i	−0.407075	−	0.913395i	$-0.633451\pi$
$691$	−12.5441	+	2.21187i	−0.477202	+	0.0841435i	−0.0701264	+	0.997538i	$0.522340\pi$
$692$	−2.79501	+	1.61370i	−0.106250	+	0.0613437i
$693$		0			0
$694$	−8.65227	+	23.7719i	−0.328436	+	0.902369i
$695$	−1.65615	+	6.18082i	−0.0628212	+	0.234452i
$696$		0			0
$697$	−52.6779	+	52.6779i	−1.99532	+	1.99532i
$698$	0.425394	+	4.86228i	0.0161014	+	0.184040i
$699$		0			0
$700$	−1.06878	+	6.06137i	−0.0403962	+	0.229098i
$701$	13.2016	+	9.24385i	0.498617	+	0.349135i	0.795675	−	0.605724i	$-0.207116\pi$
$701$	13.2016	+	9.24385i	0.498617	+	0.349135i	−0.297058	+	0.954860i	$0.596005\pi$
$702$		0			0
$703$	−16.3261	−	15.0594i	−0.615750	−	0.567976i
$704$		−	6.05569i		−	0.228232i
$705$		0			0
$706$	27.5507	+	4.85793i	1.03688	+	0.182831i
$707$	9.96833	−	3.62818i	0.374898	−	0.136452i
$708$		0			0
$709$	−12.9475	−	12.9475i	−0.486252	−	0.486252i	0.420869	−	0.907121i	$-0.361725\pi$
$709$	−12.9475	−	12.9475i	−0.486252	−	0.486252i	−0.907121	+	0.420869i	$0.861725\pi$
$710$	4.73868	−	5.64733i	0.177839	−	0.211941i
$711$		0			0
$712$	9.35847	+	3.40620i	0.350723	+	0.127653i
$713$	0.312114	+	0.180199i	0.0116888	+	0.00674851i
$714$		0			0
$715$	−1.80562	−	10.2402i	−0.0675265	−	0.382962i
$716$	6.62326	−	14.2036i	0.247523	−	0.530814i
$717$		0			0
$718$	−0.665853	+	7.61074i	−0.0248494	+	0.284030i
$719$	−19.3068	−	23.0089i	−0.720020	−	0.858087i	0.274612	−	0.961555i	$-0.411450\pi$
$719$	−19.3068	−	23.0089i	−0.720020	−	0.858087i	−0.994633	+	0.103468i	$0.967006\pi$
$720$		0			0
$721$	5.45714	+	7.79360i	0.203234	+	0.290249i
$722$	−3.25037	−	4.64201i	−0.120966	−	0.172758i
$723$		0			0
$724$	−6.15529	−	7.33559i	−0.228760	−	0.272625i
$725$	−0.426435	+	4.87418i	−0.0158374	+	0.181022i
$726$		0			0
$727$	−12.8824	+	27.6264i	−0.477781	+	1.02461i	0.508732	+	0.860925i	$0.330114\pi$
$727$	−12.8824	+	27.6264i	−0.477781	+	1.02461i	−0.986513	+	0.163680i	$0.947663\pi$
$728$	−0.462508	−	2.62302i	−0.0171417	−	0.0972154i
$729$		0			0
$730$	7.25904	+	4.19101i	0.268669	+	0.155116i
$731$	48.1239	+	17.5157i	1.77993	+	0.647841i
$732$		0			0
$733$	17.1370	−	20.4230i	0.632968	−	0.754342i	−0.350274	−	0.936647i	$-0.613912\pi$
$733$	17.1370	−	20.4230i	0.632968	−	0.754342i	0.983242	+	0.182305i	$0.0583560\pi$
$734$	−11.1393	−	11.1393i	−0.411158	−	0.411158i
$735$		0			0
$736$	0.767192	−	0.279235i	0.0282791	−	0.0102927i
$737$	37.0421	+	6.53153i	1.36446	+	0.240592i
$738$		0			0
$739$		−	30.0980i		−	1.10717i	−0.832792	−	0.553586i	$-0.813259\pi$
$739$		−	30.0980i		−	1.10717i	0.832792	−	0.553586i	$-0.186741\pi$
$740$	4.76214	−	3.62924i	0.175060	−	0.133413i
$741$		0			0
$742$	15.4362	+	10.8085i	0.566680	+	0.396793i
$743$	5.99726	−	34.0121i	0.220018	−	1.24778i	−0.651965	−	0.758249i	$-0.726055\pi$
$743$	5.99726	−	34.0121i	0.220018	−	1.24778i	0.871983	−	0.489536i	$-0.162834\pi$
$744$		0			0
$745$	−0.640851	−	7.32496i	−0.0234790	−	0.268366i
$746$	−2.57248	+	2.57248i	−0.0941852	+	0.0941852i
$747$		0			0
$748$	12.4035	−	46.2904i	0.453516	−	1.69254i
$749$	−4.30486	+	11.8275i	−0.157296	+	0.432168i
$750$		0			0
$751$	−41.0185	+	23.6820i	−1.49679	+	0.864170i	−0.999993	−	0.00369842i	$-0.998823\pi$
$751$	−41.0185	+	23.6820i	−1.49679	+	0.864170i	−0.496794	+	0.867869i	$0.665489\pi$
$752$	13.1052	−	2.31079i	0.477896	−	0.0842659i
$753$		0			0
$754$	−0.548004	−	2.04518i	−0.0199571	−	0.0744810i
$755$	−10.0291	−	0.877435i	−0.364997	−	0.0319331i
$756$		0			0
$757$	19.9562	+	42.7962i	0.725321	+	1.55546i	0.827992	+	0.560740i	$0.189483\pi$
$757$	19.9562	+	42.7962i	0.725321	+	1.55546i	−0.102671	+	0.994715i	$0.532739\pi$
$758$	−13.4047	+	9.38610i	−0.486882	+	0.340918i
$759$		0			0
$760$	−3.25748	+	1.51899i	−0.118161	+	0.0550995i
$761$	−25.1687	+	21.1191i	−0.912366	+	0.765566i	−0.972568	−	0.232620i	$-0.925270\pi$
$761$	−25.1687	+	21.1191i	−0.912366	+	0.765566i	0.0602014	+	0.998186i	$0.480826\pi$
$762$		0			0
$763$	−26.2485	+	7.03326i	−0.950259	+	0.254621i
$764$	16.5640	+	7.72394i	0.599266	+	0.279442i
$765$		0			0
$766$	−2.38678	−	4.13403i	−0.0862380	−	0.149369i
$767$	9.78189	−	16.9427i	0.353204	−	0.611767i
$768$		0			0
$769$	−8.04522	−	2.15571i	−0.290118	−	0.0777369i	0.110825	−	0.993840i	$-0.464651\pi$
$769$	−8.04522	−	2.15571i	−0.290118	−	0.0777369i	−0.400943	+	0.916103i	$0.631317\pi$
$770$	−6.97193	−	5.85014i	−0.251251	−	0.210824i
$771$		0			0
$772$	−11.6698	+	1.02098i	−0.420007	+	0.0367458i
$773$	−4.44004	−	12.1989i	−0.159697	−	0.438764i	0.833877	−	0.551951i	$-0.186116\pi$
$773$	−4.44004	−	12.1989i	−0.159697	−	0.438764i	−0.993574	+	0.113187i	$0.963894\pi$
$774$		0			0
$775$	−1.02066	+	1.45765i	−0.0366630	+	0.0523602i
$776$	−7.52202			−0.270025
$777$		0			0
$778$	−5.43807			−0.194964
$779$	19.7159	−	28.1573i	0.706397	−	1.00884i
$780$		0			0
$781$	−15.5119	−	42.6186i	−0.555060	−	1.52501i
$782$	6.43644	−	0.563116i	0.230167	−	0.0201370i
$783$		0			0
$784$	3.57646	+	3.00101i	0.127731	+	0.107179i

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)

\(f(q)\)	\(=\)	\(q+(-0.573576 + 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(-0.980582 + 0.0857898i) q^{5} +(1.16963 + 0.981439i) q^{7} +(0.965926 + 0.258819i) q^{8} +O(q^{10})\)	\(q+(-0.573576 + 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(-0.980582 + 0.0857898i) q^{5} +(1.16963 + 0.981439i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.492164 - 0.852453i) q^{10} +(-3.02784 - 5.24438i) q^{11} +(-1.58099 - 0.737228i) q^{13} +(-1.47482 + 0.395177i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(-7.17231 + 3.34450i) q^{17} +(2.99110 - 2.09439i) q^{19} +(0.415995 + 0.892104i) q^{20} +(6.03265 + 0.527788i) q^{22} +(0.211307 + 0.788610i) q^{23} +(-3.96986 + 0.699993i) q^{25} +(1.51072 - 0.872215i) q^{26} +(0.522213 - 1.43477i) q^{28} +(0.314145 - 1.17240i) q^{29} +(0.312140 - 0.312140i) q^{31} +(-0.0871557 - 0.996195i) q^{32} +(1.37421 - 7.79354i) q^{34} +(-1.23112 - 0.862038i) q^{35} +(-1.29697 - 5.94288i) q^{37} +3.65146i q^{38} +(-0.969373 - 0.170927i) q^{40} +(8.84597 - 3.21967i) q^{41} +(-4.57591 - 4.57591i) q^{43} +(-3.89252 + 4.63893i) q^{44} +(-0.767192 - 0.279235i) q^{46} +(-11.5245 - 6.65366i) q^{47} +(-0.810718 - 4.59781i) q^{49} +(1.70362 - 3.65342i) q^{50} +(-0.152037 + 1.73779i) q^{52} +(-7.93317 - 9.45438i) q^{53} +(3.41896 + 4.88279i) q^{55} +(0.875764 + 1.25072i) q^{56} +(0.780191 + 0.929796i) q^{58} +(-0.977451 + 11.1723i) q^{59} +(3.22828 - 6.92307i) q^{61} +(0.0766540 + 0.434726i) q^{62} +(0.866025 + 0.500000i) q^{64} +(1.61354 + 0.587280i) q^{65} +(-3.99253 + 4.75812i) q^{67} +(5.59588 + 5.59588i) q^{68} +(1.41228 - 0.514028i) q^{70} +(7.37567 + 1.30053i) q^{71} +8.51548i q^{73} +(5.61204 + 2.34629i) q^{74} +(-2.99110 - 2.09439i) q^{76} +(1.60557 - 9.10565i) q^{77} +(-0.00716907 - 0.0819428i) q^{79} +(0.696025 - 0.696025i) q^{80} +(-2.43644 + 9.09293i) q^{82} +(0.0951748 - 0.261491i) q^{83} +(6.74611 - 3.89487i) q^{85} +(6.37299 - 1.12373i) q^{86} +(-1.56733 - 5.84935i) q^{88} +(9.92117 + 0.867990i) q^{89} +(-1.12564 - 2.41393i) q^{91} +(0.668779 - 0.468284i) q^{92} +(12.0605 - 5.62392i) q^{94} +(-2.75334 + 2.31033i) q^{95} +(-7.26572 + 1.94684i) q^{97} +(4.23131 + 1.97309i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more