LMFDB - Embedded newform 495.2.n.h.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(91,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("495.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.n (of order $5$, degree $4$, 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:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 8 x^{13} + 47 x^{12} + 32 x^{11} + 171 x^{10} + 26 x^{9} + 360 x^{8} + \cdots + 1 $ x^16 - 2x^15 + 5x^14 - 8x^13 + 47x^12 + 32x^11 + 171x^10 + 26x^9 + 360x^8 - 172x^7 + 471x^6 - 430x^5 + 383x^4 + 70x^3 + 17x^2 + 4*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.2
Root			$-0.166559 - 0.121012i$ of defining polynomial
Character	$\chi$	$=$	495.361
Dual form			495.2.n.h.181.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.372637 + 1.14686i) q^{2} +(0.441609 + 0.320848i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-3.49122 - 2.53652i) q^{7} +(-2.48368 + 1.80450i) q^{8} +O(q^{10})$	\(q+(-0.372637 + 1.14686i) q^{2} +(0.441609 + 0.320848i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-3.49122 - 2.53652i) q^{7} +(-2.48368 + 1.80450i) q^{8} +1.20588 q^{10} +(-2.96210 - 1.49196i) q^{11} +(1.91048 - 5.87986i) q^{13} +(4.20999 - 3.05873i) q^{14} +(-0.806633 - 2.48256i) q^{16} +(0.248446 + 0.764638i) q^{17} +(1.51601 - 1.10144i) q^{19} +(0.168680 - 0.519143i) q^{20} +(2.81486 - 2.84115i) q^{22} -8.08431 q^{23} +(-0.809017 + 0.587785i) q^{25} +(6.03145 + 4.38210i) q^{26} +(-0.727918 - 2.24030i) q^{28} +(-0.857138 - 0.622747i) q^{29} +(-0.499089 + 1.53604i) q^{31} -2.99226 q^{32} -0.969511 q^{34} +(-1.33353 + 4.10418i) q^{35} +(4.48304 + 3.25712i) q^{37} +(0.698278 + 2.14908i) q^{38} +(2.48368 + 1.80450i) q^{40} +(4.08714 - 2.96948i) q^{41} -9.87101 q^{43} +(-0.829398 - 1.60925i) q^{44} +(3.01251 - 9.27156i) q^{46} +(10.5056 - 7.63280i) q^{47} +(3.59157 + 11.0537i) q^{49} +(-0.372637 - 1.14686i) q^{50} +(2.73023 - 1.98363i) q^{52} +(0.823336 - 2.53397i) q^{53} +(-0.503601 + 3.27817i) q^{55} +13.2482 q^{56} +(1.03360 - 0.750957i) q^{58} +(5.34734 + 3.88507i) q^{59} +(-1.65250 - 5.08587i) q^{61} +(-1.57564 - 1.14477i) q^{62} +(2.72829 - 8.39682i) q^{64} -6.18245 q^{65} -7.49018 q^{67} +(-0.135616 + 0.417384i) q^{68} +(-4.20999 - 3.05873i) q^{70} +(1.80140 + 5.54415i) q^{71} +(-3.88448 - 2.82224i) q^{73} +(-5.40600 + 3.92769i) q^{74} +1.02288 q^{76} +(6.55696 + 12.7222i) q^{77} +(-4.31076 + 13.2672i) q^{79} +(-2.11179 + 1.53431i) q^{80} +(1.88255 + 5.79391i) q^{82} +(-3.72575 - 11.4667i) q^{83} +(0.650440 - 0.472572i) q^{85} +(3.67830 - 11.3206i) q^{86} +(10.0491 - 1.63955i) q^{88} -12.7727 q^{89} +(-21.5843 + 15.6819i) q^{91} +(-3.57011 - 2.59383i) q^{92} +(4.83894 + 14.8927i) q^{94} +(-1.51601 - 1.10144i) q^{95} +(0.416434 - 1.28165i) q^{97} -14.0154 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} - 8 q^{4} + 4 q^{5} - 4 q^{7} + 6 q^{8}+O(q^{10}) $ 16 * q + 2 * q^2 - 8 * q^4 + 4 * q^5 - 4 * q^7 + 6 * q^8	$ 16 q + 2 q^{2} - 8 q^{4} + 4 q^{5} - 4 q^{7} + 6 q^{8} + 8 q^{10} - 4 q^{11} + 2 q^{13} + 22 q^{14} + 8 q^{16} + 4 q^{17} - 4 q^{19} - 2 q^{20} - 28 q^{22} - 8 q^{23} - 4 q^{25} - 6 q^{26} - 2 q^{28} + 26 q^{29} - 10 q^{31} - 56 q^{32} - 4 q^{34} + 4 q^{35} + 22 q^{37} + 30 q^{38} - 6 q^{40} + 6 q^{41} + 28 q^{43} - 68 q^{44} + 16 q^{46} + 20 q^{47} + 10 q^{49} + 2 q^{50} + 30 q^{52} - 14 q^{53} - 6 q^{55} - 68 q^{56} - 6 q^{58} + 16 q^{59} - 38 q^{61} + 20 q^{62} + 10 q^{64} - 12 q^{65} + 20 q^{67} + 48 q^{68} - 22 q^{70} + 54 q^{71} + 2 q^{73} - 28 q^{74} - 44 q^{76} - 34 q^{77} - 12 q^{79} + 22 q^{80} + 30 q^{82} + 28 q^{83} - 4 q^{85} - 74 q^{86} + 46 q^{88} - 76 q^{89} - 34 q^{91} + 8 q^{92} - 10 q^{94} + 4 q^{95} - 18 q^{97} - 8 q^{98}+O(q^{100}) $ 16 * q + 2 * q^2 - 8 * q^4 + 4 * q^5 - 4 * q^7 + 6 * q^8 + 8 * q^10 - 4 * q^11 + 2 * q^13 + 22 * q^14 + 8 * q^16 + 4 * q^17 - 4 * q^19 - 2 * q^20 - 28 * q^22 - 8 * q^23 - 4 * q^25 - 6 * q^26 - 2 * q^28 + 26 * q^29 - 10 * q^31 - 56 * q^32 - 4 * q^34 + 4 * q^35 + 22 * q^37 + 30 * q^38 - 6 * q^40 + 6 * q^41 + 28 * q^43 - 68 * q^44 + 16 * q^46 + 20 * q^47 + 10 * q^49 + 2 * q^50 + 30 * q^52 - 14 * q^53 - 6 * q^55 - 68 * q^56 - 6 * q^58 + 16 * q^59 - 38 * q^61 + 20 * q^62 + 10 * q^64 - 12 * q^65 + 20 * q^67 + 48 * q^68 - 22 * q^70 + 54 * q^71 + 2 * q^73 - 28 * q^74 - 44 * q^76 - 34 * q^77 - 12 * q^79 + 22 * q^80 + 30 * q^82 + 28 * q^83 - 4 * q^85 - 74 * q^86 + 46 * q^88 - 76 * q^89 - 34 * q^91 + 8 * q^92 - 10 * q^94 + 4 * q^95 - 18 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$1$

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 $

$2$	−0.372637	+	1.14686i	−0.263494	+	0.810951i	0.728543	+	0.685001i	$0.240198\pi$
$2$	−0.372637	+	1.14686i	−0.263494	+	0.810951i	−0.992037	+	0.125950i	$0.959802\pi$
$3$		0			0
$3$		0			0
$4$	0.441609	+	0.320848i	0.220805	+	0.160424i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$6$		0			0
$7$	−3.49122	−	2.53652i	−1.31956	−	0.958715i	−0.999938	−	0.0111694i	$-0.996445\pi$
$7$	−3.49122	−	2.53652i	−1.31956	−	0.958715i	−0.319620	−	0.947546i	$-0.603555\pi$
$8$	−2.48368	+	1.80450i	−0.878113	+	0.637986i
$9$		0			0
$10$	1.20588			0.381332
$11$	−2.96210	−	1.49196i	−0.893107	−	0.449844i
$11$	−2.96210	−	1.49196i	−0.893107	−	0.449844i
$12$		0			0
$13$	1.91048	−	5.87986i	0.529873	−	1.63078i	−0.224602	−	0.974451i	$-0.572108\pi$
$13$	1.91048	−	5.87986i	0.529873	−	1.63078i	0.754474	−	0.656329i	$-0.227892\pi$
$14$	4.20999	−	3.05873i	1.12517	−	0.817481i
$15$		0			0
$16$	−0.806633	−	2.48256i	−0.201658	−	0.620640i
$17$	0.248446	+	0.764638i	0.0602570	+	0.185452i	0.976654	−	0.214819i	$-0.0689161\pi$
$17$	0.248446	+	0.764638i	0.0602570	+	0.185452i	−0.916397	+	0.400271i	$0.868916\pi$
$18$		0			0
$19$	1.51601	−	1.10144i	0.347795	−	0.252688i	−0.400148	−	0.916450i	$-0.631041\pi$
$19$	1.51601	−	1.10144i	0.347795	−	0.252688i	0.747944	+	0.663762i	$0.231041\pi$
$20$	0.168680	−	0.519143i	0.0377179	−	0.116084i
$21$		0			0
$22$	2.81486	−	2.84115i	0.600129	−	0.605735i
$23$	−8.08431			−1.68570			−0.842848	−	0.538152i	$-0.819123\pi$
$23$	−8.08431			−1.68570			−0.842848	+	0.538152i	$0.819123\pi$
$24$		0			0
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	6.03145	+	4.38210i	1.18286	+	0.859401i
$27$		0			0
$28$	−0.727918	−	2.24030i	−0.137564	−	0.423377i
$29$	−0.857138	−	0.622747i	−0.159166	−	0.115641i	0.505351	−	0.862914i	$-0.331363\pi$
$29$	−0.857138	−	0.622747i	−0.159166	−	0.115641i	−0.664518	+	0.747273i	$0.731363\pi$
$30$		0			0
$31$	−0.499089	+	1.53604i	−0.0896391	+	0.275881i	−0.985820	−	0.167809i	$-0.946331\pi$
$31$	−0.499089	+	1.53604i	−0.0896391	+	0.275881i	0.896180	+	0.443690i	$0.146331\pi$
$32$	−2.99226			−0.528962
$33$		0			0
$34$	−0.969511			−0.166270
$35$	−1.33353	+	4.10418i	−0.225407	+	0.693733i
$36$		0			0
$37$	4.48304	+	3.25712i	0.737007	+	0.535467i	0.891772	−	0.452484i	$-0.149462\pi$
$37$	4.48304	+	3.25712i	0.737007	+	0.535467i	−0.154765	+	0.987951i	$0.549462\pi$
$38$	0.698278	+	2.14908i	0.113276	+	0.348627i
$39$		0			0
$40$	2.48368	+	1.80450i	0.392704	+	0.285316i
$41$	4.08714	−	2.96948i	0.638304	−	0.463755i	−0.220963	−	0.975282i	$-0.570920\pi$
$41$	4.08714	−	2.96948i	0.638304	−	0.463755i	0.859267	+	0.511527i	$0.170920\pi$
$42$		0			0
$43$	−9.87101			−1.50531			−0.752657	−	0.658412i	$-0.771228\pi$
$43$	−9.87101			−1.50531			−0.752657	+	0.658412i	$0.771228\pi$
$44$	−0.829398	−	1.60925i	−0.125037	−	0.242603i
$45$		0			0
$46$	3.01251	−	9.27156i	0.444171	−	1.36702i
$47$	10.5056	−	7.63280i	1.53241	−	1.11336i	0.577523	−	0.816375i	$-0.304020\pi$
$47$	10.5056	−	7.63280i	1.53241	−	1.11336i	0.954883	−	0.296983i	$-0.0959805\pi$
$48$		0			0
$49$	3.59157	+	11.0537i	0.513082	+	1.57910i
$50$	−0.372637	−	1.14686i	−0.0526988	−	0.162190i
$51$		0			0
$52$	2.73023	−	1.98363i	0.378614	−	0.275079i
$53$	0.823336	−	2.53397i	0.113094	−	0.348067i	−0.878451	−	0.477833i	$-0.841422\pi$
$53$	0.823336	−	2.53397i	0.113094	−	0.348067i	0.991545	+	0.129766i	$0.0414225\pi$
$54$		0			0
$55$	−0.503601	+	3.27817i	−0.0679055	+	0.442028i
$56$	13.2482			1.77037
$57$		0			0
$58$	1.03360	−	0.750957i	0.135719	−	0.0986054i
$59$	5.34734	+	3.88507i	0.696165	+	0.505793i	0.878681	−	0.477410i	$-0.158424\pi$
$59$	5.34734	+	3.88507i	0.696165	+	0.505793i	−0.182516	+	0.983203i	$0.558424\pi$
$60$		0			0
$61$	−1.65250	−	5.08587i	−0.211581	−	0.651178i	−0.999379	−	0.0352447i	$-0.988779\pi$
$61$	−1.65250	−	5.08587i	−0.211581	−	0.651178i	0.787798	−	0.615934i	$-0.211221\pi$
$62$	−1.57564	−	1.14477i	−0.200106	−	0.145386i
$63$		0			0
$64$	2.72829	−	8.39682i	0.341037	−	1.04960i
$65$	−6.18245			−0.766839
$66$		0			0
$67$	−7.49018			−0.915071			−0.457536	−	0.889191i	$-0.651268\pi$
$67$	−7.49018			−0.915071			−0.457536	+	0.889191i	$0.651268\pi$
$68$	−0.135616	+	0.417384i	−0.0164459	+	0.0506153i
$69$		0			0
$70$	−4.20999	−	3.05873i	−0.503190	−	0.365589i
$71$	1.80140	+	5.54415i	0.213787	+	0.657970i	0.999237	+	0.0390448i	$0.0124315\pi$
$71$	1.80140	+	5.54415i	0.213787	+	0.657970i	−0.785450	+	0.618925i	$0.787568\pi$
$72$		0			0
$73$	−3.88448	−	2.82224i	−0.454643	−	0.330318i	0.336783	−	0.941582i	$-0.390661\pi$
$73$	−3.88448	−	2.82224i	−0.454643	−	0.330318i	−0.791426	+	0.611265i	$0.790661\pi$
$74$	−5.40600	+	3.92769i	−0.628435	+	0.456584i
$75$		0			0
$76$	1.02288			0.117332
$77$	6.55696	+	12.7222i	0.747235	+	1.44983i
$78$		0			0
$79$	−4.31076	+	13.2672i	−0.484998	+	1.49267i	0.346985	+	0.937871i	$0.387206\pi$
$79$	−4.31076	+	13.2672i	−0.484998	+	1.49267i	−0.831983	+	0.554801i	$0.812794\pi$
$80$	−2.11179	+	1.53431i	−0.236106	+	0.171541i
$81$		0			0
$82$	1.88255	+	5.79391i	0.207893	+	0.639830i
$83$	−3.72575	−	11.4667i	−0.408954	−	1.25863i	−0.917548	−	0.397624i	$-0.869835\pi$
$83$	−3.72575	−	11.4667i	−0.408954	−	1.25863i	0.508595	−	0.861006i	$-0.330165\pi$
$84$		0			0
$85$	0.650440	−	0.472572i	0.0705501	−	0.0512576i
$86$	3.67830	−	11.3206i	0.396641	−	1.22074i
$87$		0			0
$88$	10.0491	−	1.63955i	1.07124	−	0.174777i
$89$	−12.7727			−1.35390			−0.676951	−	0.736028i	$-0.736699\pi$
$89$	−12.7727			−1.35390			−0.676951	+	0.736028i	$0.736699\pi$
$90$		0			0
$91$	−21.5843	+	15.6819i	−2.26265	+	1.64391i
$92$	−3.57011	−	2.59383i	−0.372209	−	0.270426i
$93$		0			0
$94$	4.83894	+	14.8927i	0.499099	+	1.53607i
$95$	−1.51601	−	1.10144i	−0.155539	−	0.113006i
$96$		0			0
$97$	0.416434	−	1.28165i	0.0422825	−	0.130132i	−0.927687	−	0.373359i	$-0.878206\pi$
$97$	0.416434	−	1.28165i	0.0422825	−	0.130132i	0.969969	+	0.243227i	$0.0782060\pi$
$98$	−14.0154			−1.41577
$99$		0			0
$100$	−0.545859			−0.0545859
$101$	2.60486	−	8.01692i	0.259193	−	0.797713i	−0.733782	−	0.679385i	$-0.762247\pi$
$101$	2.60486	−	8.01692i	0.259193	−	0.797713i	0.992975	−	0.118328i	$-0.0377535\pi$
$102$		0			0
$103$	8.00959	+	5.81931i	0.789208	+	0.573393i	0.907728	−	0.419558i	$-0.137815\pi$
$103$	8.00959	+	5.81931i	0.789208	+	0.573393i	−0.118520	+	0.992952i	$0.537815\pi$
$104$	5.86517	+	18.0511i	0.575127	+	1.77006i
$105$		0			0
$106$	2.59930	+	1.88850i	0.252466	+	0.183427i
$107$	6.60758	−	4.80069i	0.638779	−	0.464100i	−0.220652	−	0.975353i	$-0.570818\pi$
$107$	6.60758	−	4.80069i	0.638779	−	0.464100i	0.859430	+	0.511253i	$0.170818\pi$
$108$		0			0
$109$	13.4997			1.29303			0.646517	−	0.762900i	$-0.276225\pi$
$109$	13.4997			1.29303			0.646517	+	0.762900i	$0.276225\pi$
$110$	−3.57193	−	1.79912i	−0.340570	−	0.171540i
$111$		0			0
$112$	−3.48094	+	10.7132i	−0.328917	+	1.01230i
$113$	−10.9303	+	7.94132i	−1.02824	+	0.747057i	−0.967955	−	0.251125i	$-0.919200\pi$
$113$	−10.9303	+	7.94132i	−1.02824	+	0.747057i	−0.0602808	+	0.998181i	$0.519200\pi$
$114$		0			0
$115$	2.49819	+	7.68864i	0.232957	+	0.716969i
$116$	−0.178713	−	0.550022i	−0.0165931	−	0.0510682i
$117$		0			0
$118$	−6.44824	+	4.68492i	−0.593609	+	0.431282i
$119$	1.07214	−	3.29971i	0.0982830	−	0.302484i
$120$		0			0
$121$	6.54810	+	8.83869i	0.595281	+	0.803517i
$122$	6.44855			0.583824
$123$		0			0
$124$	−0.713237	+	0.518197i	−0.0640506	+	0.0465355i
$125$	0.809017	+	0.587785i	0.0723607	+	0.0525731i
$126$		0			0
$127$	−0.655154	−	2.01636i	−0.0581355	−	0.178923i	0.917772	−	0.397108i	$-0.129986\pi$
$127$	−0.655154	−	2.01636i	−0.0581355	−	0.178923i	−0.975907	+	0.218186i	$0.929986\pi$
$128$	3.77172	+	2.74031i	0.333376	+	0.242212i
$129$		0			0
$130$	2.30381	−	7.09039i	0.202057	−	0.621869i
$131$	−8.72324			−0.762153			−0.381076	−	0.924544i	$-0.624447\pi$
$131$	−8.72324			−0.762153			−0.381076	+	0.924544i	$0.624447\pi$
$132$		0			0
$133$	−8.08654			−0.701192
$134$	2.79112	−	8.59017i	0.241116	−	0.742078i
$135$		0			0
$136$	−1.99685	−	1.45079i	−0.171228	−	0.124405i
$137$	0.477068	+	1.46826i	0.0407587	+	0.125442i	0.969365	−	0.245623i	$-0.0789926\pi$
$137$	0.477068	+	1.46826i	0.0407587	+	0.125442i	−0.928607	+	0.371065i	$0.878993\pi$
$138$		0			0
$139$	−13.1046	−	9.52107i	−1.11152	−	0.807566i	−0.128617	−	0.991694i	$-0.541054\pi$
$139$	−13.1046	−	9.52107i	−1.11152	−	0.807566i	−0.982902	+	0.184128i	$0.941054\pi$
$140$	−1.90572	+	1.38458i	−0.161062	+	0.117019i
$141$		0			0
$142$	−7.02962			−0.589913
$143$	−14.4316	+	14.5664i	−1.20683	+	1.21810i
$144$		0			0
$145$	−0.327397	+	1.00763i	−0.0271889	+	0.0836788i
$146$	4.68420	−	3.40327i	0.387667	−	0.281657i
$147$		0			0
$148$	0.934712	+	2.87675i	0.0768329	+	0.236467i
$149$	−4.33189	−	13.3322i	−0.354883	−	1.09222i	−0.956078	−	0.293114i	$-0.905308\pi$
$149$	−4.33189	−	13.3322i	−0.354883	−	1.09222i	0.601195	−	0.799102i	$-0.294692\pi$
$150$		0			0
$151$	10.9906	−	7.98516i	0.894404	−	0.649823i	−0.0426183	−	0.999091i	$-0.513570\pi$
$151$	10.9906	−	7.98516i	0.894404	−	0.649823i	0.937023	+	0.349269i	$0.113570\pi$
$152$	−1.77772	+	5.47126i	−0.144192	+	0.443777i
$153$		0			0
$154$	−17.0339	+	2.77914i	−1.37263	+	0.223950i
$155$	1.61509			0.129727
$156$		0			0
$157$	3.54409	−	2.57493i	0.282849	−	0.205502i	−0.437310	−	0.899311i	$-0.644069\pi$
$157$	3.54409	−	2.57493i	0.282849	−	0.205502i	0.720159	+	0.693809i	$0.244069\pi$
$158$	−13.6092	−	9.88766i	−1.08269	−	0.786620i
$159$		0			0
$160$	0.924660	+	2.84581i	0.0731008	+	0.224981i
$161$	28.2241	+	20.5060i	2.22437	+	1.61610i
$162$		0			0
$163$	−1.44826	+	4.45729i	−0.113437	+	0.349122i	−0.991618	−	0.129206i	$-0.958757\pi$
$163$	−1.44826	+	4.45729i	−0.113437	+	0.349122i	0.878181	+	0.478328i	$0.158757\pi$
$164$	2.75767			0.215338
$165$		0			0
$166$	14.5390			1.12844
$167$	−0.509622	+	1.56846i	−0.0394358	+	0.121371i	−0.968836	−	0.247702i	$-0.920325\pi$
$167$	−0.509622	+	1.56846i	−0.0394358	+	0.121371i	0.929401	+	0.369073i	$0.120325\pi$
$168$		0			0
$169$	−20.4056	−	14.8255i	−1.56966	−	1.14043i
$170$	0.299595	+	0.922060i	0.0229779	+	0.0707188i
$171$		0			0
$172$	−4.35913	−	3.16709i	−0.332380	−	0.241489i
$173$	−13.4072	+	9.74090i	−1.01933	+	0.740587i	−0.966146	−	0.257998i	$-0.916937\pi$
$173$	−13.4072	+	9.74090i	−1.01933	+	0.740587i	−0.0531852	+	0.998585i	$0.516937\pi$
$174$		0			0
$175$	4.31539			0.326213
$176$	−1.31456	+	8.55707i	−0.0990886	+	0.645013i
$177$		0			0
$178$	4.75957	−	14.6485i	0.356745	−	1.09795i
$179$	14.2383	−	10.3447i	1.06422	−	0.773201i	0.0893553	−	0.996000i	$-0.471519\pi$
$179$	14.2383	−	10.3447i	1.06422	−	0.773201i	0.974864	+	0.222799i	$0.0715193\pi$
$180$		0			0
$181$	2.59782	+	7.99527i	0.193094	+	0.594284i	0.999994	+	0.00359434i	$0.00114412\pi$
$181$	2.59782	+	7.99527i	0.193094	+	0.594284i	−0.806899	+	0.590689i	$0.798856\pi$
$182$	−9.94183	−	30.5978i	−0.736937	−	2.26806i
$183$		0			0
$184$	20.0788	−	14.5881i	1.48023	−	1.07545i
$185$	1.71237	−	5.27013i	0.125896	−	0.387468i
$186$		0			0
$187$	0.404889	−	2.63561i	0.0296084	−	0.192735i
$188$	7.08835			0.516971
$189$		0			0
$190$	1.82812	−	1.32820i	0.132626	−	0.0963581i
$191$	−4.30212	−	3.12567i	−0.311290	−	0.226166i	0.421160	−	0.906987i	$-0.361623\pi$
$191$	−4.30212	−	3.12567i	−0.311290	−	0.226166i	−0.732450	+	0.680821i	$0.761623\pi$
$192$		0			0
$193$	4.72401	+	14.5390i	0.340042	+	1.04654i	0.964185	+	0.265231i	$0.0854483\pi$
$193$	4.72401	+	14.5390i	0.340042	+	1.04654i	−0.624143	+	0.781310i	$0.714552\pi$
$194$	1.31469	+	0.955181i	0.0943895	+	0.0685780i
$195$		0			0
$196$	−1.96049	+	6.03378i	−0.140035	+	0.430984i
$197$	1.69118			0.120492			0.0602458	−	0.998184i	$-0.480812\pi$
$197$	1.69118			0.120492			0.0602458	+	0.998184i	$0.480812\pi$
$198$		0			0
$199$	3.44855			0.244461			0.122230	−	0.992502i	$-0.460995\pi$
$199$	3.44855			0.244461			0.122230	+	0.992502i	$0.460995\pi$
$200$	0.948680	−	2.91974i	0.0670818	−	0.206457i
$201$		0			0
$202$	8.22360	+	5.97480i	0.578611	+	0.420385i
$203$	1.41285	+	4.34830i	0.0991624	+	0.305191i
$204$		0			0
$205$	−4.08714	−	2.96948i	−0.285458	−	0.207398i
$206$	−9.65858	+	7.01737i	−0.672945	+	0.488923i
$207$		0			0
$208$	−16.1382			−1.11898
$209$	−6.13387	+	1.00076i	−0.424289	+	0.0692241i
$210$		0			0
$211$	−0.121891	+	0.375140i	−0.00839129	+	0.0258257i	−0.955164	−	0.296076i	$-0.904322\pi$
$211$	−0.121891	+	0.375140i	−0.00839129	+	0.0258257i	0.946773	+	0.321901i	$0.104322\pi$
$212$	1.17661	−	0.854858i	0.0808100	−	0.0587119i
$213$		0			0
$214$	3.04348	+	9.36687i	0.208048	+	0.640306i
$215$	3.05031	+	9.38789i	0.208029	+	0.640249i
$216$		0			0
$217$	5.63863	−	4.09670i	0.382775	−	0.278102i
$218$	−5.03047	+	15.4822i	−0.340707	+	1.04859i
$219$		0			0
$220$	−1.27419	+	1.28609i	−0.0859057	+	0.0867082i
$221$	4.97062			0.334360
$222$		0			0
$223$	6.28724	−	4.56795i	0.421025	−	0.305893i	−0.357025	−	0.934095i	$-0.616209\pi$
$223$	6.28724	−	4.56795i	0.421025	−	0.305893i	0.778050	+	0.628202i	$0.216209\pi$
$224$	10.4467	+	7.58994i	0.697996	+	0.507124i
$225$		0			0
$226$	−5.03454	−	15.4947i	−0.334893	−	1.03069i
$227$	22.0993	+	16.0560i	1.46678	+	1.06568i	0.981531	+	0.191301i	$0.0612705\pi$
$227$	22.0993	+	16.0560i	1.46678	+	1.06568i	0.485248	+	0.874377i	$0.338729\pi$
$228$		0			0
$229$	4.81517	−	14.8196i	0.318195	−	0.979304i	−0.656224	−	0.754566i	$-0.727847\pi$
$229$	4.81517	−	14.8196i	0.318195	−	0.979304i	0.974419	−	0.224738i	$-0.0721526\pi$
$230$	−9.74869			−0.642810
$231$		0			0
$232$	3.25260			0.213544
$233$	8.61681	−	26.5198i	0.564506	−	1.73737i	−0.104908	−	0.994482i	$-0.533455\pi$
$233$	8.61681	−	26.5198i	0.564506	−	1.73737i	0.669414	−	0.742889i	$-0.266545\pi$
$234$		0			0
$235$	−10.5056	−	7.63280i	−0.685313	−	0.497909i
$236$	1.11492	+	3.43137i	0.0725750	+	0.223363i
$237$		0			0
$238$	3.38478	+	2.45919i	0.219403	+	0.159405i
$239$	15.1657	−	11.0185i	0.980988	−	0.712729i	0.0230587	−	0.999734i	$-0.492660\pi$
$239$	15.1657	−	11.0185i	0.980988	−	0.712729i	0.957929	+	0.287005i	$0.0926595\pi$
$240$		0			0
$241$	−11.0049			−0.708886			−0.354443	−	0.935078i	$-0.615329\pi$
$241$	−11.0049			−0.708886			−0.354443	+	0.935078i	$0.615329\pi$
$242$	−12.5768	+	4.21611i	−0.808466	+	0.271022i
$243$		0			0
$244$	0.902031	−	2.77617i	0.0577466	−	0.177726i
$245$	9.40286	−	6.83158i	0.600727	−	0.436454i
$246$		0			0
$247$	−3.58003	−	11.0182i	−0.227792	−	0.701070i
$248$	−1.53220	−	4.71563i	−0.0972949	−	0.299443i
$249$		0			0
$250$	−0.975576	+	0.708797i	−0.0617008	+	0.0448283i
$251$	7.20429	−	22.1725i	0.454731	−	1.39952i	−0.416721	−	0.909035i	$-0.636821\pi$
$251$	7.20429	−	22.1725i	0.454731	−	1.39952i	0.871451	−	0.490482i	$-0.163179\pi$
$252$		0			0
$253$	23.9466	+	12.0615i	1.50551	+	0.758299i
$254$	2.55661			0.160416
$255$		0			0
$256$	9.73730	−	7.07456i	0.608581	−	0.442160i
$257$	14.1360	+	10.2704i	0.881779	+	0.640650i	0.933721	−	0.358000i	$-0.116541\pi$
$257$	14.1360	+	10.2704i	0.881779	+	0.640650i	−0.0519427	+	0.998650i	$0.516541\pi$
$258$		0			0
$259$	−7.38954	−	22.7427i	−0.459164	−	1.41316i
$260$	−2.73023	−	1.98363i	−0.169322	−	0.123019i
$261$		0			0
$262$	3.25060	−	10.0043i	0.200823	−	0.618069i
$263$	−1.61187			−0.0993921			−0.0496961	−	0.998764i	$-0.515825\pi$
$263$	−1.61187			−0.0993921			−0.0496961	+	0.998764i	$0.515825\pi$
$264$		0			0
$265$	−2.66437			−0.163671
$266$	3.01334	−	9.27412i	0.184760	−	0.568633i
$267$		0			0
$268$	−3.30773	−	2.40321i	−0.202052	−	0.146799i
$269$	−2.52549	−	7.77266i	−0.153982	−	0.473908i	0.844074	−	0.536226i	$-0.180151\pi$
$269$	−2.52549	−	7.77266i	−0.153982	−	0.473908i	−0.998056	+	0.0623184i	$0.980151\pi$
$270$		0			0
$271$	−8.49430	−	6.17147i	−0.515992	−	0.374890i	0.299100	−	0.954222i	$-0.403314\pi$
$271$	−8.49430	−	6.17147i	−0.515992	−	0.374890i	−0.815092	+	0.579332i	$0.803314\pi$
$272$	1.69786	−	1.23356i	0.102948	−	0.0747958i
$273$		0			0
$274$	−1.86166			−0.112467
$275$	3.27334	−	0.534057i	0.197390	−	0.0322048i
$276$		0			0
$277$	2.75712	−	8.48554i	0.165659	−	0.509846i	−0.833425	−	0.552632i	$-0.813623\pi$
$277$	2.75712	−	8.48554i	0.165659	−	0.509846i	0.999084	+	0.0427860i	$0.0136234\pi$
$278$	15.8026	−	11.4812i	0.947775	−	0.688599i
$279$		0			0
$280$	−4.09392	−	12.5998i	−0.244659	−	0.752982i
$281$	−1.35769	−	4.17854i	−0.0809930	−	0.249271i	0.902358	−	0.430987i	$-0.141835\pi$
$281$	−1.35769	−	4.17854i	−0.0809930	−	0.249271i	−0.983351	+	0.181717i	$0.941835\pi$
$282$		0			0
$283$	−10.5211	+	7.64404i	−0.625416	+	0.454391i	−0.854809	−	0.518943i	$-0.826326\pi$
$283$	−10.5211	+	7.64404i	−0.625416	+	0.454391i	0.229393	+	0.973334i	$0.426326\pi$
$284$	−0.983313	+	3.02633i	−0.0583489	+	0.179579i
$285$		0			0
$286$	−11.3278	−	21.9789i	−0.669829	−	1.29964i
$287$	−21.8013			−1.28689
$288$		0			0
$289$	13.2303	−	9.61241i	0.778255	−	0.565436i
$290$	−1.03360	−	0.750957i	−0.0606953	−	0.0440977i
$291$		0			0
$292$	−0.809912	−	2.49265i	−0.0473965	−	0.145871i
$293$	12.5757	+	9.13679i	0.734681	+	0.533777i	0.891041	−	0.453923i	$-0.149976\pi$
$293$	12.5757	+	9.13679i	0.734681	+	0.533777i	−0.156360	+	0.987700i	$0.549976\pi$
$294$		0			0
$295$	2.04250	−	6.28618i	0.118919	−	0.365996i
$296$	−17.0119			−0.988796
$297$		0			0
$298$	16.9044			0.979243
$299$	−15.4449	+	47.5346i	−0.893204	+	2.74900i
$300$		0			0
$301$	34.4619	+	25.0380i	1.98635	+	1.44317i
$302$	5.06233	+	15.5802i	0.291304	+	0.896542i
$303$		0			0
$304$	−3.95726	−	2.87512i	−0.226964	−	0.164899i
$305$	−4.32630	+	3.14324i	−0.247723	+	0.179981i
$306$		0			0
$307$	8.76859			0.500450			0.250225	−	0.968188i	$-0.419495\pi$
$307$	8.76859			0.500450			0.250225	+	0.968188i	$0.419495\pi$
$308$	−1.18628	+	7.72203i	−0.0675945	+	0.440004i
$309$		0			0
$310$	−0.601841	+	1.85228i	−0.0341823	+	0.105202i
$311$	−1.41676	+	1.02934i	−0.0803370	+	0.0583682i	−0.627229	−	0.778835i	$-0.715811\pi$
$311$	−1.41676	+	1.02934i	−0.0803370	+	0.0583682i	0.546892	+	0.837203i	$0.315811\pi$
$312$		0			0
$313$	−5.41621	−	16.6694i	−0.306142	−	0.942209i	−0.979249	−	0.202663i	$-0.935040\pi$
$313$	−5.41621	−	16.6694i	−0.306142	−	0.942209i	0.673106	−	0.739546i	$-0.264960\pi$
$314$	1.63242	+	5.02408i	0.0921230	+	0.283525i
$315$		0			0
$316$	−6.16041	+	4.47580i	−0.346550	+	0.251783i
$317$	0.615520	−	1.89438i	0.0345711	−	0.106399i	−0.932282	−	0.361733i	$-0.882185\pi$
$317$	0.615520	−	1.89438i	0.0345711	−	0.106399i	0.966853	+	0.255334i	$0.0821853\pi$
$318$		0			0
$319$	1.60981	+	3.12346i	0.0901323	+	0.174880i
$320$	−8.82894			−0.493553
$321$		0			0
$322$	−34.0348	+	24.7278i	−1.89669	+	1.37802i
$323$	1.21885	+	0.885546i	0.0678186	+	0.0492731i
$324$		0			0
$325$	1.91048	+	5.87986i	0.105975	+	0.326156i
$326$	−4.57220	−	3.32190i	−0.253231	−	0.183983i
$327$		0			0
$328$	−4.79272	+	14.7505i	−0.264634	+	0.814458i
$329$	−56.0383			−3.08949
$330$		0			0
$331$	−10.3437			−0.568541			−0.284271	−	0.958744i	$-0.591751\pi$
$331$	−10.3437			−0.568541			−0.284271	+	0.958744i	$0.591751\pi$
$332$	2.03373	−	6.25918i	0.111616	−	0.343517i
$333$		0			0
$334$	−1.60889	−	1.16893i	−0.0880347	−	0.0639609i
$335$	2.31459	+	7.12359i	0.126460	+	0.389203i
$336$		0			0
$337$	16.6809	+	12.1194i	0.908667	+	0.660185i	0.940677	−	0.339303i	$-0.110191\pi$
$337$	16.6809	+	12.1194i	0.908667	+	0.660185i	−0.0320107	+	0.999488i	$0.510191\pi$
$338$	24.6067	−	17.8778i	1.33843	−	0.972423i
$339$		0			0
$340$	0.438864			0.0238007
$341$	3.77007	−	3.80528i	0.204161	−	0.206068i
$342$		0			0
$343$	6.16434	−	18.9719i	0.332843	−	1.02438i
$344$	24.5164	−	17.8122i	1.32184	−	0.960370i
$345$		0			0
$346$	−6.17542	−	19.0060i	−0.331992	−	1.02177i
$347$	−0.922028	−	2.83771i	−0.0494971	−	0.152336i	0.923253	−	0.384193i	$-0.125520\pi$
$347$	−0.922028	−	2.83771i	−0.0494971	−	0.152336i	−0.972750	+	0.231856i	$0.925520\pi$
$348$		0			0
$349$	−9.13355	+	6.63591i	−0.488908	+	0.355212i	−0.804764	−	0.593595i	$-0.797708\pi$
$349$	−9.13355	+	6.63591i	−0.488908	+	0.355212i	0.315857	+	0.948807i	$0.397708\pi$
$350$	−1.60807	+	4.94914i	−0.0859551	+	0.264542i
$351$		0			0
$352$	8.86339	+	4.46434i	0.472420	+	0.237950i
$353$	13.4952			0.718275			0.359137	−	0.933285i	$-0.383071\pi$
$353$	13.4952			0.718275			0.359137	+	0.933285i	$0.383071\pi$
$354$		0			0
$355$	4.71614	−	3.42647i	0.250307	−	0.181858i
$356$	−5.64054	−	4.09809i	−0.298948	−	0.217198i
$357$		0			0
$358$	6.55822	+	20.1841i	0.346613	+	1.06676i
$359$	−19.9818	−	14.5176i	−1.05460	−	0.766211i	−0.0815173	−	0.996672i	$-0.525977\pi$
$359$	−19.9818	−	14.5176i	−1.05460	−	0.766211i	−0.973082	+	0.230461i	$0.925977\pi$
$360$		0			0
$361$	−4.78623	+	14.7305i	−0.251907	+	0.775289i
$362$	−10.1375			−0.532814
$363$		0			0
$364$	−14.5633			−0.763327
$365$	−1.48374	+	4.56647i	−0.0776624	+	0.239020i
$366$		0			0
$367$	−5.13314	−	3.72944i	−0.267948	−	0.194675i	0.445696	−	0.895184i	$-0.352956\pi$
$367$	−5.13314	−	3.72944i	−0.267948	−	0.194675i	−0.713643	+	0.700509i	$0.752956\pi$
$368$	6.52107	+	20.0698i	0.339934	+	1.04621i
$369$		0			0
$370$	5.40600	+	3.92769i	0.281044	+	0.204191i
$371$	−9.30191	+	6.75823i	−0.482931	+	0.350870i
$372$		0			0
$373$	13.1832			0.682601			0.341301	−	0.939954i	$-0.389133\pi$
$373$	13.1832			0.682601			0.341301	+	0.939954i	$0.389133\pi$
$374$	2.87179	+	1.44647i	0.148497	+	0.0747954i
$375$		0			0
$376$	−12.3193	+	37.9148i	−0.635318	+	1.95531i
$377$	−5.29921	+	3.85010i	−0.272923	+	0.198290i
$378$		0			0
$379$	−5.72802	−	17.6290i	−0.294229	−	0.905543i	−0.983479	−	0.181020i	$-0.942060\pi$
$379$	−5.72802	−	17.6290i	−0.294229	−	0.905543i	0.689251	−	0.724523i	$-0.257940\pi$
$380$	−0.316086	−	0.972814i	−0.0162149	−	0.0499043i
$381$		0			0
$382$	5.18783	−	3.76918i	0.265432	−	0.192848i
$383$	8.77123	−	26.9951i	0.448189	−	1.37938i	−0.430760	−	0.902467i	$-0.641754\pi$
$383$	8.77123	−	26.9951i	0.448189	−	1.37938i	0.878949	−	0.476917i	$-0.158246\pi$
$384$		0			0
$385$	10.0733	−	10.1674i	0.513384	−	0.518180i
$386$	−18.4345			−0.938293
$387$		0			0
$388$	0.595116	−	0.432377i	0.0302125	−	0.0219506i
$389$	15.5100	+	11.2687i	0.786388	+	0.571344i	0.906889	−	0.421369i	$-0.138450\pi$
$389$	15.5100	+	11.2687i	0.786388	+	0.571344i	−0.120502	+	0.992713i	$0.538450\pi$
$390$		0			0
$391$	−2.00851	−	6.18157i	−0.101575	−	0.312615i
$392$	−28.8667	−	20.9729i	−1.45799	−	1.05929i
$393$		0			0
$394$	−0.630196	+	1.93954i	−0.0317488	+	0.0977127i
$395$	13.9499			0.701896
$396$		0			0
$397$	16.2455			0.815339			0.407670	−	0.913130i	$-0.366342\pi$
$397$	16.2455			0.815339			0.407670	+	0.913130i	$0.366342\pi$
$398$	−1.28505	+	3.95499i	−0.0644140	+	0.198246i
$399$		0			0
$400$	2.11179	+	1.53431i	0.105590	+	0.0767154i
$401$	3.80853	+	11.7215i	0.190189	+	0.585342i	0.999999	−	0.00135034i	$-0.000429826\pi$
$401$	3.80853	+	11.7215i	0.190189	+	0.585342i	−0.809810	+	0.586692i	$0.800430\pi$
$402$		0			0
$403$	8.07820	+	5.86915i	0.402404	+	0.292363i
$404$	3.72254	−	2.70458i	0.185203	−	0.134558i
$405$		0			0
$406$	−5.51336			−0.273623
$407$	−8.41972	−	16.3364i	−0.417350	−	0.809768i
$408$		0			0
$409$	−0.604903	+	1.86170i	−0.0299106	+	0.0920552i	−0.964897	−	0.262627i	$-0.915411\pi$
$409$	−0.604903	+	1.86170i	−0.0299106	+	0.0920552i	0.934987	+	0.354682i	$0.115411\pi$
$410$	4.92859	−	3.58083i	0.243406	−	0.176845i
$411$		0			0
$412$	1.67000	+	5.13972i	0.0822748	+	0.253216i
$413$	−8.81420	−	27.1273i	−0.433718	−	1.33485i
$414$		0			0
$415$	−9.75413	+	7.08679i	−0.478811	+	0.347877i
$416$	−5.71667	+	17.5941i	−0.280283	+	0.862621i
$417$		0			0
$418$	1.13797	−	7.40760i	0.0556602	−	0.362318i
$419$	−20.5776			−1.00528			−0.502640	−	0.864496i	$-0.667638\pi$
$419$	−20.5776			−1.00528			−0.502640	+	0.864496i	$0.667638\pi$
$420$		0			0
$421$	13.8507	−	10.0632i	0.675044	−	0.490448i	−0.196666	−	0.980471i	$-0.563011\pi$
$421$	13.8507	−	10.0632i	0.675044	−	0.490448i	0.871710	+	0.490022i	$0.163011\pi$
$422$	−0.384812	−	0.279582i	−0.0187324	−	0.0136098i
$423$		0			0
$424$	2.52764	+	7.77927i	0.122753	+	0.377795i
$425$	−0.650440	−	0.472572i	−0.0315510	−	0.0229231i
$426$		0			0
$427$	−7.13117	+	21.9475i	−0.345101	+	1.06211i
$428$	4.45826			0.215498
$429$		0			0
$430$	−11.9032			−0.574025
$431$	−3.27801	+	10.0887i	−0.157896	+	0.485955i	−0.998443	−	0.0557847i	$-0.982234\pi$
$431$	−3.27801	+	10.0887i	−0.157896	+	0.485955i	0.840547	+	0.541739i	$0.182234\pi$
$432$		0			0
$433$	−20.0848	−	14.5925i	−0.965215	−	0.701270i	−0.0108592	−	0.999941i	$-0.503457\pi$
$433$	−20.0848	−	14.5925i	−0.965215	−	0.701270i	−0.954356	+	0.298671i	$0.903457\pi$
$434$	2.59718	+	7.99329i	0.124668	+	0.383690i
$435$		0			0
$436$	5.96158	+	4.33134i	0.285508	+	0.207434i
$437$	−12.2559	+	8.90440i	−0.586277	+	0.425955i
$438$		0			0
$439$	6.78781			0.323965			0.161982	−	0.986794i	$-0.448211\pi$
$439$	6.78781			0.323965			0.161982	+	0.986794i	$0.448211\pi$
$440$	−4.66466	−	9.05066i	−0.222379	−	0.431473i
$441$		0			0
$442$	−1.85223	+	5.70059i	−0.0881018	+	0.271149i
$443$	−12.2566	+	8.90495i	−0.582329	+	0.423087i	−0.839563	−	0.543262i	$-0.817189\pi$
$443$	−12.2566	+	8.90495i	−0.582329	+	0.423087i	0.257234	+	0.966349i	$0.417189\pi$
$444$		0			0
$445$	3.94698	+	12.1476i	0.187105	+	0.575849i
$446$	2.89593	+	8.91276i	0.137126	+	0.422031i
$447$		0			0
$448$	−30.8238	+	22.3948i	−1.45629	+	1.05805i
$449$	5.54099	−	17.0534i	0.261495	−	0.804800i	−0.730985	−	0.682394i	$-0.760939\pi$
$449$	5.54099	−	17.0534i	0.261495	−	0.804800i	0.992480	−	0.122406i	$-0.0390611\pi$
$450$		0			0
$451$	−16.5369	+	2.69805i	−0.778691	+	0.127046i
$452$	−7.37488			−0.346885
$453$		0			0
$454$	−26.6490	+	19.3616i	−1.25070	+	0.908686i
$455$	21.5843	+	15.6819i	1.01189	+	0.735180i
$456$		0			0
$457$	−12.7310	−	39.1820i	−0.595531	−	1.83286i	−0.552063	−	0.833802i	$-0.686159\pi$
$457$	−12.7310	−	39.1820i	−0.595531	−	1.83286i	−0.0434679	−	0.999055i	$-0.513841\pi$
$458$	15.2016	+	11.0446i	0.710325	+	0.516081i
$459$		0			0
$460$	−1.36366	+	4.19691i	−0.0635809	+	0.195682i
$461$	−16.8145			−0.783128			−0.391564	−	0.920151i	$-0.628066\pi$
$461$	−16.8145			−0.783128			−0.391564	+	0.920151i	$0.628066\pi$
$462$		0			0
$463$	−35.7050			−1.65935			−0.829676	−	0.558245i	$-0.811475\pi$
$463$	−35.7050			−1.65935			−0.829676	+	0.558245i	$0.811475\pi$
$464$	−0.854612	+	2.63023i	−0.0396744	+	0.122105i
$465$		0			0
$466$	27.2035	+	19.7645i	1.26018	+	0.915573i
$467$	11.1095	+	34.1916i	0.514087	+	1.58220i	0.784936	+	0.619576i	$0.212696\pi$
$467$	11.1095	+	34.1916i	0.514087	+	1.58220i	−0.270849	+	0.962622i	$0.587304\pi$
$468$		0			0
$469$	26.1499	+	18.9990i	1.20749	+	0.877293i
$470$	12.6685	−	9.20422i	0.584355	−	0.424559i
$471$		0			0
$472$	−20.2917			−0.934000
$473$	29.2389	+	14.7272i	1.34441	+	0.677156i
$474$		0			0
$475$	−0.579062	+	1.78217i	−0.0265692	+	0.0817716i
$476$	1.53217	−	1.11319i	0.0702270	−	0.0510229i
$477$		0			0
$478$	6.98539	+	21.4988i	0.319504	+	0.983333i
$479$	4.29272	+	13.2116i	0.196139	+	0.603655i	0.999961	+	0.00878522i	$0.00279646\pi$
$479$	4.29272	+	13.2116i	0.196139	+	0.603655i	−0.803822	+	0.594870i	$0.797204\pi$
$480$		0			0
$481$	27.7162	−	20.1370i	1.26375	−	0.918167i
$482$	4.10082	−	12.6210i	0.186787	−	0.574872i
$483$		0			0
$484$	0.0558246	+	6.00419i	0.00253748	+	0.272918i
$485$	−1.34761			−0.0611918
$486$		0			0
$487$	11.3265	−	8.22916i	0.513251	−	0.372899i	−0.300804	−	0.953686i	$-0.597255\pi$
$487$	11.3265	−	8.22916i	0.513251	−	0.372899i	0.814055	+	0.580787i	$0.197255\pi$
$488$	13.2817	+	9.64972i	0.601234	+	0.436822i
$489$		0			0
$490$	4.33100	+	13.3294i	0.195655	+	0.602163i
$491$	−20.4259	−	14.8403i	−0.921806	−	0.669731i	0.0221670	−	0.999754i	$-0.492943\pi$
$491$	−20.4259	−	14.8403i	−0.921806	−	0.669731i	−0.943973	+	0.330023i	$0.892943\pi$
$492$		0			0
$493$	0.263224	−	0.810119i	0.0118550	−	0.0364859i
$494$	13.9703			0.628555
$495$		0			0
$496$	4.21590			0.189299
$497$	7.77376	−	23.9252i	0.348701	−	1.07319i
$498$		0			0
$499$	7.16997	+	5.20929i	0.320972	+	0.233200i	0.736590	−	0.676340i	$-0.236435\pi$
$499$	7.16997	+	5.20929i	0.320972	+	0.233200i	−0.415618	+	0.909539i	$0.636435\pi$
$500$	0.168680	+	0.519143i	0.00754359	+	0.0232168i
$501$		0			0
$502$	22.7441	+	16.5246i	1.01512	+	0.737528i
$503$	0.534909	−	0.388634i	0.0238504	−	0.0173283i	−0.575796	−	0.817593i	$-0.695308\pi$
$503$	0.534909	−	0.388634i	0.0238504	−	0.0173283i	0.599647	+	0.800265i	$0.295308\pi$
$504$		0			0
$505$	−8.42949			−0.375107
$506$	−22.7562	+	22.9687i	−1.01164	+	1.02108i
$507$		0			0
$508$	0.357621	−	1.10065i	0.0158669	−	0.0488333i
$509$	31.3224	−	22.7570i	1.38834	−	1.00869i	0.392295	−	0.919839i	$-0.371681\pi$
$509$	31.3224	−	22.7570i	1.38834	−	1.00869i	0.996045	−	0.0888492i	$-0.0283189\pi$
$510$		0			0
$511$	6.40290	+	19.7061i	0.283248	+	0.871747i
$512$	7.36638	+	22.6714i	0.325551	+	1.00194i
$513$		0			0
$514$	−17.0463	+	12.3848i	−0.751879	+	0.546272i
$515$	3.05939	−	9.41583i	0.134813	−	0.414911i
$516$		0			0
$517$	−42.5066	+	6.93510i	−1.86944	+	0.305005i
$518$	28.8362			1.26699
$519$		0			0
$520$	15.3552	−	11.1562i	0.673371	−	0.489233i
$521$	−19.8803	−	14.4439i	−0.870971	−	0.632797i	0.0598763	−	0.998206i	$-0.480929\pi$
$521$	−19.8803	−	14.4439i	−0.870971	−	0.632797i	−0.930847	+	0.365408i	$0.880929\pi$
$522$		0			0
$523$	10.4121	+	32.0453i	0.455291	+	1.40124i	0.870793	+	0.491650i	$0.163606\pi$
$523$	10.4121	+	32.0453i	0.455291	+	1.40124i	−0.415501	+	0.909593i	$0.636394\pi$
$524$	−3.85226	−	2.79883i	−0.168287	−	0.122268i
$525$		0			0
$526$	0.600642	−	1.84859i	0.0261892	−	0.0806021i
$527$	−1.29851			−0.0565640
$528$		0			0
$529$	42.3561			1.84157
$530$	0.992842	−	3.05565i	0.0431263	−	0.132729i
$531$		0			0
$532$	−3.57109	−	2.59455i	−0.154826	−	0.112488i
$533$	−9.65172	−	29.7050i	−0.418063	−	1.28666i
$534$		0			0
$535$	−6.60758	−	4.80069i	−0.285671	−	0.207552i
$536$	18.6032	−	13.5160i	0.803536	−	0.583803i
$537$		0			0
$538$	9.85523			0.424889
$539$	5.85314	−	38.1008i	0.252113	−	1.64112i
$540$		0			0
$541$	−2.53653	+	7.80665i	−0.109054	+	0.335634i	−0.990661	−	0.136351i	$-0.956462\pi$
$541$	−2.53653	+	7.80665i	−0.109054	+	0.335634i	0.881606	+	0.471985i	$0.156462\pi$
$542$	10.2431	−	7.44204i	0.439978	−	0.319663i
$543$		0			0
$544$	−0.743415	−	2.28800i	−0.0318737	−	0.0980971i
$545$	−4.17163	−	12.8390i	−0.178693	−	0.549960i
$546$		0			0
$547$	−28.3770	+	20.6171i	−1.21331	+	0.881523i	−0.995527	−	0.0944734i	$-0.969883\pi$
$547$	−28.3770	+	20.6171i	−1.21331	+	0.881523i	−0.217785	+	0.975997i	$0.569883\pi$
$548$	−0.260412	+	0.801465i	−0.0111242	+	0.0342369i
$549$		0			0
$550$	−0.607281	+	3.95307i	−0.0258945	+	0.168559i
$551$	−1.98534			−0.0845785
$552$		0			0
$553$	48.7022	−	35.3843i	2.07103	−	1.50469i
$554$	8.70430	+	6.32404i	0.369810	+	0.268683i
$555$		0			0
$556$	−2.73231	−	8.40918i	−0.115876	−	0.356629i
$557$	32.0476	+	23.2839i	1.35790	+	0.986572i	0.998575	+	0.0533600i	$0.0169931\pi$
$557$	32.0476	+	23.2839i	1.35790	+	0.986572i	0.359325	+	0.933212i	$0.383007\pi$
$558$		0			0
$559$	−18.8584	+	58.0402i	−0.797625	+	2.45484i
$560$	11.2645			0.476014
$561$		0			0
$562$	5.29812			0.223488
$563$	−6.69959	+	20.6192i	−0.282354	+	0.868996i	0.704825	+	0.709381i	$0.251025\pi$
$563$	−6.69959	+	20.6192i	−0.282354	+	0.868996i	−0.987179	+	0.159615i	$0.948975\pi$
$564$		0			0
$565$	10.9303	+	7.94132i	0.459841	+	0.334094i
$566$	−4.84607	−	14.9147i	−0.203696	−	0.626911i
$567$		0			0
$568$	−14.4785	−	10.5193i	−0.607505	−	0.441378i
$569$	−22.2187	+	16.1428i	−0.931457	+	0.676743i	−0.946349	−	0.323146i	$-0.895259\pi$
$569$	−22.2187	+	16.1428i	−0.931457	+	0.676743i	0.0148922	+	0.999889i	$0.495259\pi$
$570$		0			0
$571$	23.8306			0.997281			0.498641	−	0.866809i	$-0.333833\pi$
$571$	23.8306			0.997281			0.498641	+	0.866809i	$0.333833\pi$
$572$	−11.0467	+	1.80231i	−0.461886	+	0.0753582i
$573$		0			0
$574$	8.12395	−	25.0029i	0.339087	−	1.04360i
$575$	6.54034	−	4.75184i	0.272751	−	0.198165i
$576$		0			0
$577$	−4.96685	−	15.2864i	−0.206773	−	0.636381i	−0.999636	−	0.0269812i	$-0.991411\pi$
$577$	−4.96685	−	15.2864i	−0.206773	−	0.636381i	0.792863	−	0.609400i	$-0.208589\pi$
$578$	6.09395	+	18.7553i	0.253475	+	0.780116i
$579$		0			0
$580$	−0.467876	+	0.339932i	−0.0194275	+	0.0141149i
$581$	−16.0780	+	49.4831i	−0.667030	+	2.05291i
$582$		0			0
$583$	−6.21939	+	6.27748i	−0.257581	+	0.259987i
$584$	14.7405			0.609966
$585$		0			0
$586$	−15.1648	+	11.0178i	−0.626451	+	0.455143i
$587$	−14.3837	−	10.4504i	−0.593680	−	0.431334i	0.249950	−	0.968259i	$-0.419586\pi$
$587$	−14.3837	−	10.4504i	−0.593680	−	0.431334i	−0.843630	+	0.536925i	$0.819586\pi$
$588$		0			0
$589$	0.935237	+	2.87836i	0.0385358	+	0.118601i
$590$	6.44824	+	4.68492i	0.265470	+	0.192875i
$591$		0			0
$592$	4.46983	−	13.7567i	0.183709	−	0.565398i
$593$	20.2944			0.833389			0.416695	−	0.909046i	$-0.363188\pi$
$593$	20.2944			0.833389			0.416695	+	0.909046i	$0.363188\pi$
$594$		0			0
$595$	−3.46952			−0.142236
$596$	2.36460	−	7.27750i	0.0968579	−	0.298098i
$597$		0			0
$598$	−48.7601	−	35.4263i	−1.99395	−	1.44869i
$599$	−2.78334	−	8.56623i	−0.113724	−	0.350007i	0.877955	−	0.478744i	$-0.158908\pi$
$599$	−2.78334	−	8.56623i	−0.113724	−	0.350007i	−0.991679	+	0.128737i	$0.958908\pi$
$600$		0			0
$601$	−33.2571	−	24.1627i	−1.35659	−	0.985618i	−0.998654	−	0.0518711i	$-0.983481\pi$
$601$	−33.2571	−	24.1627i	−1.35659	−	0.985618i	−0.357933	−	0.933747i	$-0.616519\pi$
$602$	−41.5568	+	30.1928i	−1.69373	+	1.23057i
$603$		0			0
$604$	7.41558			0.301736
$605$	6.38262	−	8.95891i	0.259490	−	0.364232i
$606$		0			0
$607$	0.367905	−	1.13230i	0.0149328	−	0.0459585i	−0.943312	−	0.331906i	$-0.892308\pi$
$607$	0.367905	−	1.13230i	0.0149328	−	0.0459585i	0.958245	+	0.285948i	$0.0923083\pi$
$608$	−4.53629	+	3.29580i	−0.183971	+	0.133663i
$609$		0			0
$610$	−1.99271	−	6.13293i	−0.0806825	−	0.248315i
$611$	−24.8089	−	76.3540i	−1.00366	−	3.08895i
$612$		0			0
$613$	−0.110508	+	0.0802891i	−0.00446339	+	0.00324284i	−0.590015	−	0.807392i	$-0.700878\pi$
$613$	−0.110508	+	0.0802891i	−0.00446339	+	0.00324284i	0.585551	+	0.810635i	$0.300878\pi$
$614$	−3.26750	+	10.0563i	−0.131866	+	0.405840i
$615$		0			0
$616$	−39.2426	−	19.7658i	−1.58113	−	0.796389i
$617$	17.7011			0.712620			0.356310	−	0.934368i	$-0.384035\pi$
$617$	17.7011			0.712620			0.356310	+	0.934368i	$0.384035\pi$
$618$		0			0
$619$	5.73528	−	4.16693i	0.230521	−	0.167483i	−0.466529	−	0.884506i	$-0.654496\pi$
$619$	5.73528	−	4.16693i	0.230521	−	0.167483i	0.697050	+	0.717023i	$0.254496\pi$
$620$	0.713237	+	0.518197i	0.0286443	+	0.0208113i
$621$		0			0
$622$	−0.652565	−	2.00839i	−0.0261655	−	0.0805290i
$623$	44.5923	+	32.3982i	1.78655	+	1.29801i
$624$		0			0
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	21.1357			0.844752
$627$		0			0
$628$	2.39127			0.0954219
$629$	−1.37672	+	4.23712i	−0.0548936	+	0.168945i
$630$		0			0
$631$	−19.5299	−	14.1893i	−0.777473	−	0.564867i	0.126746	−	0.991935i	$-0.459547\pi$
$631$	−19.5299	−	14.1893i	−0.777473	−	0.564867i	−0.904220	+	0.427068i	$0.859547\pi$
$632$	−13.2340	−	40.7301i	−0.526421	−	1.62016i
$633$		0			0
$634$	1.94322	+	1.41183i	0.0771750	+	0.0560709i
$635$	−1.71521	+	1.24618i	−0.0680662	+	0.0494530i
$636$		0			0
$637$	71.8560			2.84704
$638$	−4.18204	+	0.682313i	−0.165568	+	0.0270130i
$639$		0			0
$640$	1.44067	−	4.43392i	0.0569474	−	0.175266i
$641$	−34.6422	+	25.1690i	−1.36828	+	0.994116i	−0.370415	+	0.928867i	$0.620784\pi$
$641$	−34.6422	+	25.1690i	−1.36828	+	0.994116i	−0.997869	+	0.0652496i	$0.979216\pi$
$642$		0			0
$643$	−10.5810	−	32.5651i	−0.417275	−	1.28424i	−0.910200	−	0.414169i	$-0.864072\pi$
$643$	−10.5810	−	32.5651i	−0.417275	−	1.28424i	0.492925	−	0.870072i	$-0.335928\pi$
$644$	5.88472	+	18.1113i	0.231890	+	0.713685i
$645$		0			0
$646$	−1.46978	+	1.06786i	−0.0578279	+	0.0420144i
$647$	3.36612	−	10.3598i	0.132336	−	0.407287i	−0.862830	−	0.505494i	$-0.831310\pi$
$647$	3.36612	−	10.3598i	0.132336	−	0.407287i	0.995166	+	0.0982061i	$0.0313104\pi$
$648$		0			0
$649$	−10.0430	−	19.4860i	−0.394222	−	0.764893i
$650$	−7.45528			−0.292420
$651$		0			0
$652$	−2.06968	+	1.50371i	−0.0810549	+	0.0588898i
$653$	−34.0195	−	24.7166i	−1.33129	−	0.967237i	−0.999717	−	0.0238064i	$-0.992421\pi$
$653$	−34.0195	−	24.7166i	−1.33129	−	0.967237i	−0.331571	−	0.943430i	$-0.607579\pi$
$654$		0			0
$655$	2.69563	+	8.29629i	0.105327	+	0.324163i
$656$	−10.6687	−	7.75129i	−0.416544	−	0.302637i
$657$		0			0
$658$	20.8819	−	64.2679i	0.814062	−	2.50543i
$659$	−0.425249			−0.0165654			−0.00828268	−	0.999966i	$-0.502636\pi$
$659$	−0.425249			−0.0165654			−0.00828268	+	0.999966i	$0.502636\pi$
$660$		0			0
$661$	−7.08477			−0.275565			−0.137783	−	0.990462i	$-0.543998\pi$
$661$	−7.08477			−0.275565			−0.137783	+	0.990462i	$0.543998\pi$
$662$	3.85444	−	11.8628i	0.149807	−	0.461059i
$663$		0			0
$664$	29.9451	+	21.7564i	1.16210	+	0.844312i
$665$	2.49888	+	7.69076i	0.0969024	+	0.298235i
$666$		0			0
$667$	6.92937	+	5.03448i	0.268306	+	0.194936i
$668$	−0.728290	+	0.529134i	−0.0281784	+	0.0204728i
$669$		0			0
$670$	−9.03224			−0.348946
$671$	−2.69305	+	17.5303i	−0.103964	+	0.676750i
$672$		0			0
$673$	−3.79575	+	11.6821i	−0.146315	+	0.450313i	−0.997178	−	0.0750760i	$-0.976080\pi$
$673$	−3.79575	+	11.6821i	−0.146315	+	0.450313i	0.850862	+	0.525389i	$0.176080\pi$
$674$	−20.1151	+	14.6145i	−0.774806	+	0.562929i
$675$		0			0
$676$	−4.25456	−	13.0942i	−0.163637	−	0.503623i
$677$	5.33859	+	16.4305i	0.205179	+	0.631475i	0.999706	+	0.0242467i	$0.00771873\pi$
$677$	5.33859	+	16.4305i	0.205179	+	0.631475i	−0.794527	+	0.607228i	$0.792281\pi$
$678$		0			0
$679$	−4.70480	+	3.41824i	−0.180554	+	0.131180i
$680$	−0.762728	+	2.34743i	−0.0292493	+	0.0900200i
$681$		0			0
$682$	2.95925	+	5.74172i	0.113316	+	0.219862i
$683$	26.8858			1.02876			0.514379	−	0.857563i	$-0.328022\pi$
$683$	26.8858			1.02876			0.514379	+	0.857563i	$0.328022\pi$
$684$		0			0
$685$	1.24898	−	0.907437i	0.0477211	−	0.0346714i
$686$	19.4610	+	14.1392i	0.743024	+	0.539838i
$687$		0			0
$688$	7.96228	+	24.5054i	0.303559	+	0.934259i
$689$	−13.3264	−	9.68220i	−0.507696	−	0.368862i
$690$		0			0
$691$	7.70472	−	23.7127i	0.293102	−	0.902074i	−0.690751	−	0.723093i	$-0.742720\pi$
$691$	7.70472	−	23.7127i	0.293102	−	0.902074i	0.983853	−	0.178981i	$-0.0572801\pi$
$692$	−9.04609			−0.343881
$693$		0			0
$694$	3.59803			0.136579
$695$	−5.00552	+	15.4054i	−0.189870	+	0.584361i
$696$		0			0
$697$	3.28601	+	2.38743i	0.124467	+	0.0904302i
$698$	−4.20695	−	12.9477i	−0.159235	−	0.490076i
$699$		0			0
$700$	1.90572	+	1.38458i	0.0720293	+	0.0523323i
$701$	−16.2387	+	11.7981i	−0.613325	+	0.445607i	−0.850584	−	0.525840i	$-0.823751\pi$
$701$	−16.2387	+	11.7981i	−0.613325	+	0.445607i	0.237258	+	0.971447i	$0.423751\pi$
$702$		0			0
$703$	10.3838			0.391634
$704$	−20.6092	+	20.8017i	−0.776740	+	0.783995i
$705$		0			0
$706$	−5.02879	+	15.4770i	−0.189261	+	0.582485i
$707$	−29.4292	+	21.3816i	−1.10680	+	0.804137i
$708$		0			0
$709$	−3.50289	−	10.7808i	−0.131554	−	0.404881i	0.863484	−	0.504376i	$-0.168277\pi$
$709$	−3.50289	−	10.7808i	−0.131554	−	0.404881i	−0.995038	+	0.0994949i	$0.968277\pi$
$710$	2.17227	+	6.68557i	0.0815240	+	0.250905i
$711$		0			0
$712$	31.7232	−	23.0483i	1.18888	−	0.863771i
$713$	4.03479	−	12.4178i	0.151104	−	0.465051i
$714$		0			0
$715$	18.3131	+	9.22399i	0.684869	+	0.344958i
$716$	9.60684			0.359025
$717$		0			0
$718$	24.0956	−	17.5065i	0.899240	−	0.653336i
$719$	−3.75010	−	2.72460i	−0.139855	−	0.101611i	0.515658	−	0.856795i	$-0.327548\pi$
$719$	−3.75010	−	2.72460i	−0.139855	−	0.101611i	−0.655513	+	0.755184i	$0.727548\pi$
$720$		0			0
$721$	−13.2025	−	40.6330i	−0.491685	−	1.51325i
$722$	−15.1103	−	10.9782i	−0.562345	−	0.408568i
$723$		0			0
$724$	−1.41804	+	4.36429i	−0.0527012	+	0.162198i
$725$	1.05948			0.0393481
$726$		0			0
$727$	−2.22651			−0.0825766			−0.0412883	−	0.999147i	$-0.513146\pi$
$727$	−2.22651			−0.0825766			−0.0412883	+	0.999147i	$0.513146\pi$
$728$	25.3105	−	77.8977i	0.938069	−	2.88708i
$729$		0			0
$730$	−4.68420	−	3.40327i	−0.173370	−	0.125961i
$731$	−2.45241	−	7.54775i	−0.0907057	−	0.279164i
$732$		0			0
$733$	24.6573	+	17.9145i	0.910737	+	0.661689i	0.941201	−	0.337847i	$-0.109699\pi$
$733$	24.6573	+	17.9145i	0.910737	+	0.661689i	−0.0304645	+	0.999536i	$0.509699\pi$
$734$	6.18994	−	4.49725i	0.228475	−	0.165997i
$735$		0			0
$736$	24.1904			0.891669
$737$	22.1867	+	11.1751i	0.817257	+	0.411639i
$738$		0			0
$739$	−2.84351	+	8.75141i	−0.104600	+	0.321926i	−0.989636	−	0.143596i	$-0.954133\pi$
$739$	−2.84351	+	8.75141i	−0.104600	+	0.321926i	0.885036	+	0.465522i	$0.154133\pi$
$740$	2.44711	−	1.77793i	0.0899575	−	0.0653579i
$741$		0			0
$742$	−4.28450	−	13.1863i	−0.157289	−	0.484086i
$743$	0.534297	+	1.64440i	0.0196014	+	0.0603270i	0.960379	−	0.278698i	$-0.0899029\pi$
$743$	0.534297	+	1.64440i	0.0196014	+	0.0603270i	−0.940777	+	0.339025i	$0.889903\pi$
$744$		0			0
$745$	−11.3410	+	8.23975i	−0.415504	+	0.301881i
$746$	−4.91255	+	15.1193i	−0.179861	+	0.553556i
$747$		0			0
$748$	1.02443	−	1.03400i	0.0374569	−	0.0378068i
$749$	−35.2456			−1.28785
$750$		0			0
$751$	−27.4077	+	19.9129i	−1.00012	+	0.726631i	−0.962114	−	0.272647i	$-0.912101\pi$
$751$	−27.4077	+	19.9129i	−1.00012	+	0.726631i	−0.0380072	+	0.999277i	$0.512101\pi$
$752$	−27.4231	−	19.9240i	−1.00002	−	0.726555i
$753$		0			0
$754$	−2.44084	−	7.51213i	−0.0888901	−	0.273576i
$755$	−10.9906	−	7.98516i	−0.399990	−	0.290610i
$756$		0			0
$757$	−8.30257	+	25.5527i	−0.301762	+	0.928728i	0.679104	+	0.734042i	$0.262369\pi$
$757$	−8.30257	+	25.5527i	−0.301762	+	0.928728i	−0.980866	+	0.194685i	$0.937631\pi$
$758$	22.3525			0.811879
$759$		0			0
$760$	5.75282			0.208677
$761$	−5.38966	+	16.5877i	−0.195375	+	0.601303i	0.804597	+	0.593821i	$0.202381\pi$
$761$	−5.38966	+	16.5877i	−0.195375	+	0.601303i	−0.999972	+	0.00748151i	$0.997619\pi$
$762$		0			0
$763$	−47.1304	−	34.2422i	−1.70623	−	1.23965i
$764$	−0.896990	−	2.76065i	−0.0324520	−	0.0998769i
$765$		0			0
$766$	27.6910	+	20.1187i	1.00052	+	0.726918i
$767$	33.0597	−	24.0193i	1.19372	−	0.867286i
$768$		0			0
$769$	−41.6485			−1.50188			−0.750942	−	0.660368i	$-0.770400\pi$
$769$	−41.6485			−1.50188			−0.750942	+	0.660368i	$0.770400\pi$
$770$	7.90689	+	15.3414i	0.284945	+	0.552867i
$771$		0			0
$772$	−2.57865	+	7.93626i	−0.0928075	+	0.285632i
$773$	−17.9209	+	13.0203i	−0.644570	+	0.468308i	−0.861417	−	0.507898i	$-0.830423\pi$
$773$	−17.9209	+	13.0203i	−0.644570	+	0.468308i	0.216847	+	0.976206i	$0.430423\pi$
$774$		0			0
$775$	−0.499089	−	1.53604i	−0.0179278	−	0.0551762i
$776$	1.27845	+	3.93466i	0.0458937	+	0.141246i
$777$		0			0
$778$	−18.7032	+	13.5886i	−0.670540	+	0.487176i
$779$	2.92541	−	9.00350i	0.104814	−	0.322584i
$780$		0			0
$781$	2.93572	−	19.1100i	0.105048	−	0.683809i
$782$	7.83783			0.280280
$783$		0			0
$784$	24.5445	−	17.8326i	0.876588	−	0.636879i
$785$	−3.54409	−	2.57493i	−0.126494	−	0.0919033i
$786$		0			0
$787$	−2.59956	−	8.00062i	−0.0926642	−	0.285191i	0.893974	−	0.448119i	$-0.147906\pi$
$787$	−2.59956	−	8.00062i	−0.0926642	−	0.285191i	−0.986638	+	0.162928i	$0.947906\pi$
$788$	0.746840	+	0.542611i	0.0266051	+	0.0193297i
$789$		0			0
$790$	−5.19825	+	15.9986i	−0.184945	+	0.569203i
$791$	58.3034			2.07303
$792$		0			0
$793$	−33.0612			−1.17404
$794$	−6.05368	+	18.6313i	−0.214837	+	0.661200i
$795$		0			0
$796$	1.52291	+	1.10646i	0.0539781	+	0.0392174i
$797$	−12.6460	−	38.9205i	−0.447945	−	1.37863i	−0.879221	−	0.476414i	$-0.841937\pi$
$797$	−12.6460	−	38.9205i	−0.447945	−	1.37863i	0.431276	−	0.902220i	$-0.358063\pi$
$798$		0			0
$799$	8.44641	+	6.13667i	0.298812	+	0.217100i
$800$	2.42079	−	1.75881i	0.0855879	−	0.0621832i
$801$		0			0
$802$	−14.8621			−0.524797
$803$	7.29554	+	14.1552i	0.257454	+	0.499528i
$804$		0			0
$805$	10.7807	−	33.1795i	0.379968	−	1.16942i
$806$	−9.74132	+	7.07748i	−0.343123	+	0.249294i
$807$		0			0
$808$	7.99689	+	24.6119i	0.281330	+	0.865844i
$809$	6.69688	+	20.6109i	0.235450	+	0.724640i	0.997061	+	0.0766060i	$0.0244084\pi$
$809$	6.69688	+	20.6109i	0.235450	+	0.724640i	−0.761612	+	0.648034i	$0.775592\pi$
$810$		0			0
$811$	44.0939	−	32.0361i	1.54835	−	1.12494i	0.603531	−	0.797339i	$-0.293760\pi$
$811$	44.0939	−	32.0361i	1.54835	−	1.12494i	0.944816	−	0.327601i	$-0.106240\pi$
$812$	−0.771215	+	2.37356i	−0.0270644	+	0.0832955i
$813$		0			0
$814$	21.8731	−	3.56866i	0.766651	−	0.125082i
$815$	4.68667			0.164167
$816$		0			0
$817$	−14.9645	+	10.8723i	−0.523542	+	0.380375i
$818$	−1.90970	−	1.38748i	−0.0667710	−	0.0485120i
$819$		0			0
$820$	−0.852167	−	2.62270i	−0.0297590	−	0.0915886i
$821$	14.5227	+	10.5513i	0.506845	+	0.368244i	0.811625	−	0.584178i	$-0.198583\pi$
$821$	14.5227	+	10.5513i	0.506845	+	0.368244i	−0.304780	+	0.952423i	$0.598583\pi$
$822$		0			0
$823$	10.8883	−	33.5106i	0.379541	−	1.16811i	−0.560822	−	0.827936i	$-0.689515\pi$
$823$	10.8883	−	33.5106i	0.379541	−	1.16811i	0.940363	−	0.340171i	$-0.110485\pi$
$824$	−30.3942			−1.05883
$825$		0			0
$826$	34.3957			1.19678
$827$	−12.3413	+	37.9826i	−0.429149	+	1.32079i	0.469816	+	0.882765i	$0.344320\pi$
$827$	−12.3413	+	37.9826i	−0.429149	+	1.32079i	−0.898965	+	0.438021i	$0.855680\pi$
$828$		0			0
$829$	36.8359	+	26.7629i	1.27936	+	0.929512i	0.999534	−	0.0305372i	$-0.00972181\pi$
$829$	36.8359	+	26.7629i	1.27936	+	0.929512i	0.279830	+	0.960049i	$0.409722\pi$
$830$	−4.49279	−	13.8274i	−0.155947	−	0.479956i
$831$		0			0
$832$	−44.1598	−	32.0840i	−1.53097	−	1.11231i
$833$	−7.55979	+	5.49251i	−0.261931	+	0.190304i
$834$		0			0
$835$	1.64917			0.0570720
$836$	−3.02987	−	1.52609i	−0.104790	−	0.0527811i
$837$		0			0
$838$	7.66795	−	23.5995i	0.264885	−	0.815232i
$839$	−14.5925	+	10.6021i	−0.503789	+	0.366024i	−0.810462	−	0.585791i	$-0.800784\pi$
$839$	−14.5925	+	10.6021i	−0.503789	+	0.366024i	0.306673	+	0.951815i	$0.400784\pi$
$840$		0			0
$841$	−8.61462	−	26.5131i	−0.297056	−	0.914244i
$842$	6.37971	+	19.6347i	0.219859	+	0.676658i
$843$		0			0
$844$	−0.174191	+	0.126557i	−0.00599590	+	0.00435628i
$845$	−7.79425	+	23.9882i	−0.268130	+	0.825220i
$846$		0			0
$847$	−0.441331	−	47.4672i	−0.0151643	−	1.63099i
$848$	−6.95486			−0.238831
$849$		0			0
$850$	0.784351	−	0.569864i	0.0269030	−	0.0195462i
$851$	−36.2423	−	26.3316i	−1.24237	−	0.902635i
$852$		0			0
$853$	−0.366815	−	1.12894i	−0.0125595	−	0.0386542i	0.944580	−	0.328280i	$-0.106469\pi$
$853$	−0.366815	−	1.12894i	−0.0125595	−	0.0386542i	−0.957140	+	0.289626i	$0.906469\pi$
$854$	−22.5133	−	16.3569i	−0.770390	−	0.559721i
$855$		0			0
$856$	−7.74827	+	23.8467i	−0.264830	+	0.815064i
$857$	5.59493			0.191119			0.0955597	−	0.995424i	$-0.469536\pi$
$857$	5.59493			0.191119			0.0955597	+	0.995424i	$0.469536\pi$
$858$		0			0
$859$	−18.5783			−0.633882			−0.316941	−	0.948445i	$-0.602656\pi$
$859$	−18.5783			−0.633882			−0.316941	+	0.948445i	$0.602656\pi$
$860$	−1.66504	+	5.12446i	−0.0567774	+	0.174743i
$861$		0			0
$862$	−10.3488	−	7.51882i	−0.352481	−	0.256092i
$863$	4.39573	+	13.5287i	0.149632	+	0.460521i	0.997578	−	0.0695631i	$-0.0221605\pi$
$863$	4.39573	+	13.5287i	0.149632	+	0.460521i	−0.847945	+	0.530084i	$0.822161\pi$
$864$		0			0
$865$	13.4072	+	9.74090i	0.455859	+	0.331201i
$866$	24.2198	−	17.5968i	0.823024	−	0.597962i
$867$		0			0
$868$	3.80449			0.129133
$869$	32.5630	−	32.8672i	1.10462	−	1.11494i
$870$		0			0
$871$	−14.3099	+	44.0412i	−0.484871	+	1.49228i
$872$	−33.5288	+	24.3601i	−1.13543	+	0.824938i
$873$		0			0
$874$	−5.64510	−	17.3738i	−0.190948	−	0.587679i
$875$	−1.33353	−	4.10418i	−0.0450815	−	0.138747i
$876$		0			0
$877$	15.0492	−	10.9339i	0.508177	−	0.369212i	−0.303955	−	0.952686i	$-0.598307\pi$
$877$	15.0492	−	10.9339i	0.508177	−	0.369212i	0.812131	+	0.583475i	$0.198307\pi$
$878$	−2.52939	+	7.78466i	−0.0853627	+	0.262719i
$879$		0			0
$880$	8.54448	−	1.39406i	0.288034	−	0.0469937i
$881$	−30.5201			−1.02825			−0.514124	−	0.857716i	$-0.671883\pi$
$881$	−30.5201			−1.02825			−0.514124	+	0.857716i	$0.671883\pi$
$882$		0			0
$883$	13.1770	−	9.57367i	0.443442	−	0.322180i	−0.343559	−	0.939131i	$-0.611633\pi$
$883$	13.1770	−	9.57367i	0.443442	−	0.322180i	0.787001	+	0.616952i	$0.211633\pi$
$884$	2.19507	+	1.59481i	0.0738282	+	0.0536393i
$885$		0			0
$886$	−5.64545	−	17.3749i	−0.189663	−	0.583721i
$887$	4.28172	+	3.11085i	0.143766	+	0.104452i	0.657344	−	0.753591i	$-0.271680\pi$
$887$	4.28172	+	3.11085i	0.143766	+	0.104452i	−0.513577	+	0.858043i	$0.671680\pi$
$888$		0			0
$889$	−2.82724	+	8.70136i	−0.0948226	+	0.291834i
$890$	−15.4023			−0.516286
$891$		0			0
$892$	4.24212			0.142037
$893$	7.51952	−	23.1427i	0.251631	−	0.774441i
$894$		0			0
$895$	−14.2383	−	10.3447i	−0.475934	−	0.345786i
$896$	−6.21704	−	19.1341i	−0.207697	−	0.639225i
$897$		0			0
$898$	17.4931	+	12.7095i	0.583751	+	0.424120i
$899$	1.38435	−	1.00579i	0.0461707	−	0.0335450i
$900$		0			0
$901$	2.14212			0.0713644
$902$	3.06797	−	19.9708i	0.102152	−	0.664956i
$903$		0			0
$904$	12.8172	−	39.4474i	0.426295	−	1.31200i
$905$	6.80118	−	4.94135i	0.226079	−	0.164256i
$906$		0			0
$907$	0.355631	+	1.09452i	0.0118085	+	0.0363429i	0.956787	−	0.290789i	$-0.0939178\pi$
$907$	0.355631	+	1.09452i	0.0118085	+	0.0363429i	−0.944979	+	0.327132i	$0.893918\pi$
$908$	4.60769	+	14.1810i	0.152911	+	0.470613i
$909$		0			0
$910$	−26.0280	+	18.9105i	−0.862821	+	0.626876i
$911$	7.56155	−	23.2721i	0.250525	−	0.771038i	−0.744153	−	0.668009i	$-0.767147\pi$
$911$	7.56155	−	23.2721i	0.250525	−	0.771038i	0.994678	−	0.103029i	$-0.0328533\pi$
$912$		0			0
$913$	−6.07180	+	39.5241i	−0.200947	+	1.30806i
$914$	49.6802			1.64328
$915$		0			0
$916$	6.88125	−	4.99952i	0.227363	−	0.165189i
$917$	30.4548	+	22.1267i	1.00570	+	0.730687i
$918$		0			0
$919$	−8.37953	−	25.7896i	−0.276415	−	0.850719i	−0.988841	−	0.148972i	$-0.952404\pi$
$919$	−8.37953	−	25.7896i	−0.276415	−	0.850719i	0.712426	−	0.701747i	$-0.247596\pi$
$920$	−20.0788	−	14.5881i	−0.661979	−	0.480956i
$921$		0			0
$922$	6.26569	−	19.2838i	0.206349	−	0.635078i
$923$	36.0404			1.18628
$924$		0			0
$925$	−5.54134			−0.182198
$926$	13.3050	−	40.9486i	0.437229	−	1.34565i
$927$		0			0
$928$	2.56478	+	1.86342i	0.0841931	+	0.0611698i
$929$	8.98153	+	27.6423i	0.294674	+	0.906915i	0.983331	+	0.181827i	$0.0582010\pi$
$929$	8.98153	+	27.6423i	0.294674	+	0.906915i	−0.688656	+	0.725088i	$0.741799\pi$
$930$		0			0
$931$	17.6199	+	12.8016i	0.577468	+	0.419555i
$932$	12.3141	−	8.94671i	0.403361	−	0.293059i
$933$		0			0
$934$	−43.3527			−1.41854
$935$	−2.63173	+	0.429375i	−0.0860667	+	0.0140421i
$936$		0			0
$937$	−18.4959	+	56.9244i	−0.604234	+	1.85964i	−0.102258	+	0.994758i	$0.532607\pi$
$937$	−18.4959	+	56.9244i	−0.604234	+	1.85964i	−0.501975	+	0.864882i	$0.667393\pi$
$938$	−31.5336	+	22.9105i	−1.02961	+	0.748054i
$939$		0			0
$940$	−2.19042	−	6.74143i	−0.0714437	−	0.219881i
$941$	9.33822	+	28.7401i	0.304417	+	0.936900i	0.979894	+	0.199519i	$0.0639379\pi$
$941$	9.33822	+	28.7401i	0.304417	+	0.936900i	−0.675477	+	0.737381i	$0.736062\pi$
$942$		0			0
$943$	−33.0417	+	24.0062i	−1.07599	+	0.781750i
$944$	5.33159	−	16.4089i	0.173528	−	0.534065i
$945$		0			0
$946$	−27.7855	+	28.0450i	−0.903384	+	0.911822i
$947$	38.6489			1.25592			0.627960	−	0.778245i	$-0.283890\pi$
$947$	38.6489			1.25592			0.627960	+	0.778245i	$0.283890\pi$
$948$		0			0
$949$	−24.0156	+	17.4483i	−0.779579	+	0.566397i
$950$	−1.82812	−	1.32820i	−0.0593119	−	0.0430926i
$951$		0			0
$952$	3.29147	+	10.1301i	0.106677	+	0.328318i
$953$	−36.1767	−	26.2839i	−1.17188	−	0.851419i	−0.180646	−	0.983548i	$-0.557819\pi$
$953$	−36.1767	−	26.2839i	−1.17188	−	0.851419i	−0.991233	+	0.132129i	$0.957819\pi$
$954$		0			0
$955$	−1.64326	+	5.05744i	−0.0531748	+	0.163655i
$956$	10.2326			0.330945
$957$		0			0
$958$	−16.7515			−0.541216
$959$	2.05873	−	6.33613i	0.0664800	−	0.204604i
$960$		0			0
$961$	22.9692	+	16.6881i	0.740942	+	0.538326i
$962$	12.7662	+	39.2903i	0.411599	+	1.26677i
$963$		0			0
$964$	−4.85985	−	3.53089i	−0.156525	−	0.113722i
$965$	12.3676	−	8.98561i	0.398128	−	0.289257i
$966$		0			0
$967$	−34.5876			−1.11226			−0.556131	−	0.831095i	$-0.687715\pi$
$967$	−34.5876			−1.11226			−0.556131	+	0.831095i	$0.687715\pi$
$968$	−32.2128	−	10.1364i	−1.03536	−	0.325797i
$969$		0			0
$970$	0.502168	−	1.54552i	0.0161237	−	0.0496235i
$971$	5.59187	−	4.06273i	0.179452	−	0.130379i	−0.494433	−	0.869216i	$-0.664624\pi$
$971$	5.59187	−	4.06273i	0.179452	−	0.130379i	0.673885	+	0.738836i	$0.264624\pi$
$972$		0			0
$973$	21.6008	+	66.4803i	0.692489	+	2.13126i
$974$	5.21702	+	16.0563i	0.167164	+	0.514478i
$975$		0			0
$976$	−11.2930	+	8.20486i	−0.361481	+	0.262631i
$977$	3.79043	−	11.6658i	0.121267	−	0.373220i	−0.871936	−	0.489620i	$-0.837135\pi$
$977$	3.79043	−	11.6658i	0.121267	−	0.373220i	0.993202	+	0.116400i	$0.0371354\pi$
$978$		0			0
$979$	37.8340	+	19.0564i	1.20918	+	0.609044i
$980$	6.34429			0.202661
$981$		0			0
$982$	24.6311	−	17.8955i	0.786009	−	0.571069i
$983$	0.130862	+	0.0950771i	0.00417386	+	0.00303249i	0.589870	−	0.807498i	$-0.299179\pi$
$983$	0.130862	+	0.0950771i	0.00417386	+	0.00303249i	−0.585696	+	0.810531i	$0.699179\pi$
$984$		0			0
$985$	−0.522603	−	1.60841i	−0.0166515	−	0.0512481i
$986$	0.831004	+	0.603760i	0.0264646	+	0.0192276i
$987$		0			0
$988$	1.95419	−	6.01438i	0.0621710	−	0.191343i
$989$	79.8003			2.53750
$990$		0			0
$991$	43.1252			1.36992			0.684958	−	0.728582i	$-0.259820\pi$
$991$	43.1252			1.36992			0.684958	+	0.728582i	$0.259820\pi$
$992$	1.49341	−	4.59623i	0.0474157	−	0.145931i
$993$		0			0
$994$	24.5420	+	17.8308i	0.778424	+	0.565558i
$995$	−1.06566	−	3.27976i	−0.0337837	−	0.103975i
$996$		0			0
$997$	1.19110	+	0.865386i	0.0377226	+	0.0274070i	0.606487	−	0.795094i	$-0.292578\pi$
$997$	1.19110	+	0.865386i	0.0377226	+	0.0274070i	−0.568764	+	0.822501i	$0.692578\pi$
$998$	−8.64610	+	6.28176i	−0.273688	+	0.198846i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.h.361.2	yes	16
3.2	odd	2		495.2.n.g.361.3	yes	16
11.4	even	5		5445.2.a.ca.1.4		8
11.5	even	5	inner	495.2.n.h.181.2	yes	16
11.7	odd	10		5445.2.a.cc.1.5		8
33.5	odd	10		495.2.n.g.181.3	✓	16
33.26	odd	10		5445.2.a.cd.1.5		8
33.29	even	10		5445.2.a.cb.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
495.2.n.g.181.3	✓	16	33.5	odd	10
495.2.n.g.361.3	yes	16	3.2	odd	2
495.2.n.h.181.2	yes	16	11.5	even	5	inner
495.2.n.h.361.2	yes	16	1.1	even	1	trivial
5445.2.a.ca.1.4		8	11.4	even	5
5445.2.a.cb.1.4		8	33.29	even	10
5445.2.a.cc.1.5		8	11.7	odd	10
5445.2.a.cd.1.5		8	33.26	odd	10

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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.372637 + 1.14686i) q^{2} +(0.441609 + 0.320848i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-3.49122 - 2.53652i) q^{7} +(-2.48368 + 1.80450i) q^{8} +O(q^{10})\)	\(q+(-0.372637 + 1.14686i) q^{2} +(0.441609 + 0.320848i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-3.49122 - 2.53652i) q^{7} +(-2.48368 + 1.80450i) q^{8} +1.20588 q^{10} +(-2.96210 - 1.49196i) q^{11} +(1.91048 - 5.87986i) q^{13} +(4.20999 - 3.05873i) q^{14} +(-0.806633 - 2.48256i) q^{16} +(0.248446 + 0.764638i) q^{17} +(1.51601 - 1.10144i) q^{19} +(0.168680 - 0.519143i) q^{20} +(2.81486 - 2.84115i) q^{22} -8.08431 q^{23} +(-0.809017 + 0.587785i) q^{25} +(6.03145 + 4.38210i) q^{26} +(-0.727918 - 2.24030i) q^{28} +(-0.857138 - 0.622747i) q^{29} +(-0.499089 + 1.53604i) q^{31} -2.99226 q^{32} -0.969511 q^{34} +(-1.33353 + 4.10418i) q^{35} +(4.48304 + 3.25712i) q^{37} +(0.698278 + 2.14908i) q^{38} +(2.48368 + 1.80450i) q^{40} +(4.08714 - 2.96948i) q^{41} -9.87101 q^{43} +(-0.829398 - 1.60925i) q^{44} +(3.01251 - 9.27156i) q^{46} +(10.5056 - 7.63280i) q^{47} +(3.59157 + 11.0537i) q^{49} +(-0.372637 - 1.14686i) q^{50} +(2.73023 - 1.98363i) q^{52} +(0.823336 - 2.53397i) q^{53} +(-0.503601 + 3.27817i) q^{55} +13.2482 q^{56} +(1.03360 - 0.750957i) q^{58} +(5.34734 + 3.88507i) q^{59} +(-1.65250 - 5.08587i) q^{61} +(-1.57564 - 1.14477i) q^{62} +(2.72829 - 8.39682i) q^{64} -6.18245 q^{65} -7.49018 q^{67} +(-0.135616 + 0.417384i) q^{68} +(-4.20999 - 3.05873i) q^{70} +(1.80140 + 5.54415i) q^{71} +(-3.88448 - 2.82224i) q^{73} +(-5.40600 + 3.92769i) q^{74} +1.02288 q^{76} +(6.55696 + 12.7222i) q^{77} +(-4.31076 + 13.2672i) q^{79} +(-2.11179 + 1.53431i) q^{80} +(1.88255 + 5.79391i) q^{82} +(-3.72575 - 11.4667i) q^{83} +(0.650440 - 0.472572i) q^{85} +(3.67830 - 11.3206i) q^{86} +(10.0491 - 1.63955i) q^{88} -12.7727 q^{89} +(-21.5843 + 15.6819i) q^{91} +(-3.57011 - 2.59383i) q^{92} +(4.83894 + 14.8927i) q^{94} +(-1.51601 - 1.10144i) q^{95} +(0.416434 - 1.28165i) q^{97} -14.0154 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} - 8 q^{4} + 4 q^{5} - 4 q^{7} + 6 q^{8}+O(q^{10}) \) 16 * q + 2 * q^2 - 8 * q^4 + 4 * q^5 - 4 * q^7 + 6 * q^8	\( 16 q + 2 q^{2} - 8 q^{4} + 4 q^{5} - 4 q^{7} + 6 q^{8} + 8 q^{10} - 4 q^{11} + 2 q^{13} + 22 q^{14} + 8 q^{16} + 4 q^{17} - 4 q^{19} - 2 q^{20} - 28 q^{22} - 8 q^{23} - 4 q^{25} - 6 q^{26} - 2 q^{28} + 26 q^{29} - 10 q^{31} - 56 q^{32} - 4 q^{34} + 4 q^{35} + 22 q^{37} + 30 q^{38} - 6 q^{40} + 6 q^{41} + 28 q^{43} - 68 q^{44} + 16 q^{46} + 20 q^{47} + 10 q^{49} + 2 q^{50} + 30 q^{52} - 14 q^{53} - 6 q^{55} - 68 q^{56} - 6 q^{58} + 16 q^{59} - 38 q^{61} + 20 q^{62} + 10 q^{64} - 12 q^{65} + 20 q^{67} + 48 q^{68} - 22 q^{70} + 54 q^{71} + 2 q^{73} - 28 q^{74} - 44 q^{76} - 34 q^{77} - 12 q^{79} + 22 q^{80} + 30 q^{82} + 28 q^{83} - 4 q^{85} - 74 q^{86} + 46 q^{88} - 76 q^{89} - 34 q^{91} + 8 q^{92} - 10 q^{94} + 4 q^{95} - 18 q^{97} - 8 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 - 8 * q^4 + 4 * q^5 - 4 * q^7 + 6 * q^8 + 8 * q^10 - 4 * q^11 + 2 * q^13 + 22 * q^14 + 8 * q^16 + 4 * q^17 - 4 * q^19 - 2 * q^20 - 28 * q^22 - 8 * q^23 - 4 * q^25 - 6 * q^26 - 2 * q^28 + 26 * q^29 - 10 * q^31 - 56 * q^32 - 4 * q^34 + 4 * q^35 + 22 * q^37 + 30 * q^38 - 6 * q^40 + 6 * q^41 + 28 * q^43 - 68 * q^44 + 16 * q^46 + 20 * q^47 + 10 * q^49 + 2 * q^50 + 30 * q^52 - 14 * q^53 - 6 * q^55 - 68 * q^56 - 6 * q^58 + 16 * q^59 - 38 * q^61 + 20 * q^62 + 10 * q^64 - 12 * q^65 + 20 * q^67 + 48 * q^68 - 22 * q^70 + 54 * q^71 + 2 * q^73 - 28 * q^74 - 44 * q^76 - 34 * q^77 - 12 * q^79 + 22 * q^80 + 30 * q^82 + 28 * q^83 - 4 * q^85 - 74 * q^86 + 46 * q^88 - 76 * q^89 - 34 * q^91 + 8 * q^92 - 10 * q^94 + 4 * q^95 - 18 * q^97 - 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more