LMFDB - Embedded newform 495.2.n.a.136.1

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			136.1
Root			$0.418926 + 1.28932i$ of defining polynomial
Character	$\chi$	$=$	495.136
Dual form			495.2.n.a.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.90578 - 1.38463i) q^{2} +(1.09676 + 3.37549i) q^{4} +(0.809017 - 0.587785i) q^{5} +(0.0598032 + 0.184055i) q^{7} +(1.12773 - 3.47080i) q^{8} +O(q^{10})$	\(q+(-1.90578 - 1.38463i) q^{2} +(1.09676 + 3.37549i) q^{4} +(0.809017 - 0.587785i) q^{5} +(0.0598032 + 0.184055i) q^{7} +(1.12773 - 3.47080i) q^{8} -2.35567 q^{10} +(1.96213 + 2.67395i) q^{11} +(-0.787747 - 0.572331i) q^{13} +(0.140877 - 0.433574i) q^{14} +(-1.21225 + 0.880754i) q^{16} +(-2.16469 + 1.57274i) q^{17} +(-1.71480 + 5.27760i) q^{19} +(2.87136 + 2.08617i) q^{20} +(-0.0369604 - 7.81280i) q^{22} +4.80040 q^{23} +(0.309017 - 0.951057i) q^{25} +(0.708805 + 2.18148i) q^{26} +(-0.555687 + 0.403730i) q^{28} +(3.12657 + 9.62260i) q^{29} +(2.02685 + 1.47259i) q^{31} -3.76902 q^{32} +6.30309 q^{34} +(0.156567 + 0.113752i) q^{35} +(1.76516 + 5.43260i) q^{37} +(10.5756 - 7.68359i) q^{38} +(-1.12773 - 3.47080i) q^{40} +(2.55823 - 7.87342i) q^{41} +5.11353 q^{43} +(-6.87391 + 9.55586i) q^{44} +(-9.14851 - 6.64678i) q^{46} +(3.35354 - 10.3211i) q^{47} +(5.63282 - 4.09248i) q^{49} +(-1.90578 + 1.38463i) q^{50} +(1.06793 - 3.28674i) q^{52} +(-7.51479 - 5.45981i) q^{53} +(3.15911 + 1.00996i) q^{55} +0.706260 q^{56} +(7.36518 - 22.6677i) q^{58} +(3.46656 + 10.6690i) q^{59} +(-0.975693 + 0.708883i) q^{61} +(-1.82374 - 5.61288i) q^{62} +(9.60743 + 6.98021i) q^{64} -0.973708 q^{65} +3.25922 q^{67} +(-7.68293 - 5.58197i) q^{68} +(-0.140877 - 0.433574i) q^{70} +(4.84664 - 3.52129i) q^{71} +(1.02168 + 3.14442i) q^{73} +(4.15814 - 12.7974i) q^{74} -19.6952 q^{76} +(-0.374813 + 0.521052i) q^{77} +(-8.21389 - 5.96774i) q^{79} +(-0.463040 + 1.42509i) q^{80} +(-15.7772 + 11.4628i) q^{82} +(6.72704 - 4.88748i) q^{83} +(-0.826838 + 2.54475i) q^{85} +(-9.74527 - 7.08035i) q^{86} +(11.4935 - 3.79468i) q^{88} -7.34270 q^{89} +(0.0582308 - 0.179216i) q^{91} +(5.26490 + 16.2037i) q^{92} +(-20.6821 + 15.0264i) q^{94} +(1.71480 + 5.27760i) q^{95} +(12.8248 + 9.31774i) q^{97} -16.4015 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 2 q^{4} + 2 q^{5} + 3 q^{7} + q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 + 2 * q^4 + 2 * q^5 + 3 * q^7 + q^8	$ 8 q - 4 q^{2} + 2 q^{4} + 2 q^{5} + 3 q^{7} + q^{8} - 6 q^{10} - 3 q^{11} - 4 q^{13} + 4 q^{14} - 12 q^{16} + 2 q^{19} + 3 q^{20} + 9 q^{22} + 6 q^{23} - 2 q^{25} - 2 q^{26} - 11 q^{28} - 10 q^{29} + 19 q^{31} - 12 q^{32} - 6 q^{34} - 3 q^{35} - q^{37} + 20 q^{38} - q^{40} + 9 q^{41} - 17 q^{44} - 22 q^{46} + 19 q^{47} + q^{49} - 4 q^{50} - 2 q^{52} - 25 q^{53} + 3 q^{55} + 16 q^{56} - 12 q^{58} - 13 q^{59} + 13 q^{61} - 35 q^{62} + 39 q^{64} + 14 q^{65} + 2 q^{67} - 19 q^{68} - 4 q^{70} + 11 q^{71} - 7 q^{73} + 43 q^{74} - 38 q^{76} + 7 q^{77} - 22 q^{79} - 13 q^{80} - 35 q^{82} + 21 q^{83} + 10 q^{85} - 20 q^{86} + 59 q^{88} + 20 q^{89} - 11 q^{91} + 28 q^{92} - 35 q^{94} - 2 q^{95} + 31 q^{97} - 22 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 + 2 * q^4 + 2 * q^5 + 3 * q^7 + q^8 - 6 * q^10 - 3 * q^11 - 4 * q^13 + 4 * q^14 - 12 * q^16 + 2 * q^19 + 3 * q^20 + 9 * q^22 + 6 * q^23 - 2 * q^25 - 2 * q^26 - 11 * q^28 - 10 * q^29 + 19 * q^31 - 12 * q^32 - 6 * q^34 - 3 * q^35 - q^37 + 20 * q^38 - q^40 + 9 * q^41 - 17 * q^44 - 22 * q^46 + 19 * q^47 + q^49 - 4 * q^50 - 2 * q^52 - 25 * q^53 + 3 * q^55 + 16 * q^56 - 12 * q^58 - 13 * q^59 + 13 * q^61 - 35 * q^62 + 39 * q^64 + 14 * q^65 + 2 * q^67 - 19 * q^68 - 4 * q^70 + 11 * q^71 - 7 * q^73 + 43 * q^74 - 38 * q^76 + 7 * q^77 - 22 * q^79 - 13 * q^80 - 35 * q^82 + 21 * q^83 + 10 * q^85 - 20 * q^86 + 59 * q^88 + 20 * q^89 - 11 * q^91 + 28 * q^92 - 35 * q^94 - 2 * q^95 + 31 * q^97 - 22 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.90578	−	1.38463i	−1.34759	−	0.979082i	−0.999128	−	0.0417590i	$-0.986704\pi$
$2$	−1.90578	−	1.38463i	−1.34759	−	0.979082i	−0.348463	−	0.937323i	$-0.613296\pi$
$3$		0			0
$3$		0			0
$4$	1.09676	+	3.37549i	0.548382	+	1.68775i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$		0			0
$7$	0.0598032	+	0.184055i	0.0226035	+	0.0695663i	0.961722	−	0.274027i	$-0.0883558\pi$
$7$	0.0598032	+	0.184055i	0.0226035	+	0.0695663i	−0.939119	+	0.343593i	$0.888356\pi$
$8$	1.12773	−	3.47080i	0.398713	−	1.22711i
$9$		0			0
$10$	−2.35567			−0.744930
$11$	1.96213	+	2.67395i	0.591606	+	0.806227i
$11$	1.96213	+	2.67395i	0.591606	+	0.806227i
$12$		0			0
$13$	−0.787747	−	0.572331i	−0.218482	−	0.158736i	0.473161	−	0.880976i	$-0.343113\pi$
$13$	−0.787747	−	0.572331i	−0.218482	−	0.158736i	−0.691643	+	0.722240i	$0.743113\pi$
$14$	0.140877	−	0.433574i	0.0376509	−	0.115878i
$15$		0			0
$16$	−1.21225	+	0.880754i	−0.303063	+	0.220188i
$17$	−2.16469	+	1.57274i	−0.525015	+	0.381446i	−0.818490	−	0.574521i	$-0.805188\pi$
$17$	−2.16469	+	1.57274i	−0.525015	+	0.381446i	0.293475	+	0.955967i	$0.405188\pi$
$18$		0			0
$19$	−1.71480	+	5.27760i	−0.393402	+	1.21077i	0.536798	+	0.843711i	$0.319634\pi$
$19$	−1.71480	+	5.27760i	−0.393402	+	1.21077i	−0.930199	+	0.367055i	$0.880366\pi$
$20$	2.87136	+	2.08617i	0.642057	+	0.466481i
$21$		0			0
$22$	−0.0369604	−	7.81280i	−0.00787998	−	1.66569i
$23$	4.80040			1.00095			0.500476	−	0.865750i	$-0.333158\pi$
$23$	4.80040			1.00095			0.500476	+	0.865750i	$0.333158\pi$
$24$		0			0
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	0.708805	+	2.18148i	0.139008	+	0.427823i
$27$		0			0
$28$	−0.555687	+	0.403730i	−0.105015	+	0.0762978i
$29$	3.12657	+	9.62260i	0.580590	+	1.78687i	0.616303	+	0.787509i	$0.288630\pi$
$29$	3.12657	+	9.62260i	0.580590	+	1.78687i	−0.0357132	+	0.999362i	$0.511370\pi$
$30$		0			0
$31$	2.02685	+	1.47259i	0.364033	+	0.264486i	0.754732	−	0.656033i	$-0.227767\pi$
$31$	2.02685	+	1.47259i	0.364033	+	0.264486i	−0.390699	+	0.920518i	$0.627767\pi$
$32$	−3.76902			−0.666275
$33$		0			0
$34$	6.30309			1.08097
$35$	0.156567	+	0.113752i	0.0264646	+	0.0192277i
$36$		0			0
$37$	1.76516	+	5.43260i	0.290190	+	0.893114i	0.984795	+	0.173722i	$0.0555794\pi$
$37$	1.76516	+	5.43260i	0.290190	+	0.893114i	−0.694604	+	0.719392i	$0.744421\pi$
$38$	10.5756	−	7.68359i	1.71558	−	1.24644i
$39$		0			0
$40$	−1.12773	−	3.47080i	−0.178310	−	0.548781i
$41$	2.55823	−	7.87342i	0.399529	−	1.22962i	−0.525850	−	0.850577i	$-0.676253\pi$
$41$	2.55823	−	7.87342i	0.399529	−	1.22962i	0.925378	−	0.379045i	$-0.123747\pi$
$42$		0			0
$43$	5.11353			0.779807			0.389903	−	0.920856i	$-0.372508\pi$
$43$	5.11353			0.779807			0.389903	+	0.920856i	$0.372508\pi$
$44$	−6.87391	+	9.55586i	−1.03628	+	1.44060i
$45$		0			0
$46$	−9.14851	−	6.64678i	−1.34887	−	0.980014i
$47$	3.35354	−	10.3211i	0.489164	−	1.50549i	−0.336693	−	0.941614i	$-0.609308\pi$
$47$	3.35354	−	10.3211i	0.489164	−	1.50549i	0.825857	−	0.563879i	$-0.190692\pi$
$48$		0			0
$49$	5.63282	−	4.09248i	0.804688	−	0.584640i
$50$	−1.90578	+	1.38463i	−0.269518	+	0.195816i
$51$		0			0
$52$	1.06793	−	3.28674i	0.148095	−	0.455789i
$53$	−7.51479	−	5.45981i	−1.03224	−	0.749963i	−0.0634803	−	0.997983i	$-0.520220\pi$
$53$	−7.51479	−	5.45981i	−1.03224	−	0.749963i	−0.968755	+	0.248020i	$0.920220\pi$
$54$		0			0
$55$	3.15911	+	1.00996i	0.425974	+	0.136183i
$56$	0.706260			0.0943780
$57$		0			0
$58$	7.36518	−	22.6677i	0.967096	−	2.97642i
$59$	3.46656	+	10.6690i	0.451307	+	1.38898i	0.875416	+	0.483369i	$0.160587\pi$
$59$	3.46656	+	10.6690i	0.451307	+	1.38898i	−0.424109	+	0.905611i	$0.639413\pi$
$60$		0			0
$61$	−0.975693	+	0.708883i	−0.124925	+	0.0907631i	−0.648493	−	0.761221i	$-0.724600\pi$
$61$	−0.975693	+	0.708883i	−0.124925	+	0.0907631i	0.523568	+	0.851984i	$0.324600\pi$
$62$	−1.82374	−	5.61288i	−0.231615	−	0.712836i
$63$		0			0
$64$	9.60743	+	6.98021i	1.20093	+	0.872526i
$65$	−0.973708			−0.120774
$66$		0			0
$67$	3.25922			0.398176			0.199088	−	0.979982i	$-0.436202\pi$
$67$	3.25922			0.398176			0.199088	+	0.979982i	$0.436202\pi$
$68$	−7.68293	−	5.58197i	−0.931692	−	0.676914i
$69$		0			0
$70$	−0.140877	−	0.433574i	−0.0168380	−	0.0518220i
$71$	4.84664	−	3.52129i	0.575191	−	0.417901i	−0.261796	−	0.965123i	$-0.584315\pi$
$71$	4.84664	−	3.52129i	0.575191	−	0.417901i	0.836987	+	0.547222i	$0.184315\pi$
$72$		0			0
$73$	1.02168	+	3.14442i	0.119579	+	0.368026i	0.992875	−	0.119165i	$-0.0380216\pi$
$73$	1.02168	+	3.14442i	0.119579	+	0.368026i	−0.873296	+	0.487191i	$0.838022\pi$
$74$	4.15814	−	12.7974i	0.483374	−	1.48767i
$75$		0			0
$76$	−19.6952			−2.25920
$77$	−0.374813	+	0.521052i	−0.0427139	+	0.0593794i
$78$		0			0
$79$	−8.21389	−	5.96774i	−0.924135	−	0.671423i	0.0204147	−	0.999792i	$-0.493501\pi$
$79$	−8.21389	−	5.96774i	−0.924135	−	0.671423i	−0.944550	+	0.328368i	$0.893501\pi$
$80$	−0.463040	+	1.42509i	−0.0517694	+	0.159330i
$81$		0			0
$82$	−15.7772	+	11.4628i	−1.74230	+	1.26586i
$83$	6.72704	−	4.88748i	0.738388	−	0.536471i	−0.153818	−	0.988099i	$-0.549157\pi$
$83$	6.72704	−	4.88748i	0.738388	−	0.536471i	0.892206	+	0.451629i	$0.149157\pi$
$84$		0			0
$85$	−0.826838	+	2.54475i	−0.0896832	+	0.276017i
$86$	−9.74527	−	7.08035i	−1.05086	−	0.763494i
$87$		0			0
$88$	11.4935	−	3.79468i	1.22521	−	0.404514i
$89$	−7.34270			−0.778325			−0.389163	−	0.921169i	$-0.627236\pi$
$89$	−7.34270			−0.778325			−0.389163	+	0.921169i	$0.627236\pi$
$90$		0			0
$91$	0.0582308	−	0.179216i	0.00610425	−	0.0187869i
$92$	5.26490	+	16.2037i	0.548904	+	1.68935i
$93$		0			0
$94$	−20.6821	+	15.0264i	−2.13319	+	1.54986i
$95$	1.71480	+	5.27760i	0.175935	+	0.541471i
$96$		0			0
$97$	12.8248	+	9.31774i	1.30216	+	0.946074i	0.999974	−	0.00717602i	$-0.00228422\pi$
$97$	12.8248	+	9.31774i	1.30216	+	0.946074i	0.302184	+	0.953250i	$0.402284\pi$
$98$	−16.4015			−1.65680
$99$		0			0
$100$	3.54920			0.354920
$101$	10.6460	+	7.73475i	1.05931	+	0.769636i	0.973961	−	0.226715i	$-0.0727985\pi$
$101$	10.6460	+	7.73475i	1.05931	+	0.769636i	0.0853519	+	0.996351i	$0.472799\pi$
$102$		0			0
$103$	1.23525	+	3.80172i	0.121713	+	0.374595i	0.993288	−	0.115668i	$-0.0369009\pi$
$103$	1.23525	+	3.80172i	0.121713	+	0.374595i	−0.871575	+	0.490263i	$0.836901\pi$
$104$	−2.87481	+	2.08867i	−0.281899	+	0.204811i
$105$		0			0
$106$	6.76171	+	20.8104i	0.656755	+	2.02129i
$107$	−1.51011	+	4.64764i	−0.145988	+	0.449304i	−0.997137	−	0.0756201i	$-0.975906\pi$
$107$	−1.51011	+	4.64764i	−0.145988	+	0.449304i	0.851149	+	0.524924i	$0.175906\pi$
$108$		0			0
$109$	−7.51977			−0.720263			−0.360131	−	0.932902i	$-0.617268\pi$
$109$	−7.51977			−0.720263			−0.360131	+	0.932902i	$0.617268\pi$
$110$	−4.62215	−	6.29896i	−0.440705	−	0.600583i
$111$		0			0
$112$	−0.234604	−	0.170450i	−0.0221680	−	0.0161060i
$113$	−6.24947	+	19.2339i	−0.587901	+	1.80937i	−0.000604375		1.00000i	$0.500192\pi$
$113$	−6.24947	+	19.2339i	−0.587901	+	1.80937i	−0.587296	+	0.809372i	$0.699808\pi$
$114$		0			0
$115$	3.88361	−	2.82160i	0.362148	−	0.263116i
$116$	−29.0519	+	21.1074i	−2.69740	+	1.95978i
$117$		0			0
$118$	8.16608	−	25.1326i	0.751748	−	2.31364i
$119$	−0.418926	−	0.304368i	−0.0384029	−	0.0279014i
$120$		0			0
$121$	−3.30005	+	10.4933i	−0.300005	+	0.953938i
$122$	2.84100			0.257212
$123$		0			0
$124$	−2.74775	+	8.45670i	−0.246755	+	0.759434i
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$		0			0
$127$	−5.74419	+	4.17340i	−0.509715	+	0.370329i	−0.812715	−	0.582661i	$-0.802012\pi$
$127$	−5.74419	+	4.17340i	−0.509715	+	0.370329i	0.303001	+	0.952990i	$0.402012\pi$
$128$	−6.31526	−	19.4364i	−0.558196	−	1.71795i
$129$		0			0
$130$	1.85567	+	1.34823i	0.162753	+	0.118247i
$131$	2.50024			0.218447			0.109223	−	0.994017i	$-0.465164\pi$
$131$	2.50024			0.218447			0.109223	+	0.994017i	$0.465164\pi$
$132$		0			0
$133$	−1.07392			−0.0931207
$134$	−6.21135	−	4.51281i	−0.536579	−	0.389847i
$135$		0			0
$136$	3.01748	+	9.28684i	0.258746	+	0.796340i
$137$	−12.3734	+	8.98981i	−1.05713	+	0.768052i	−0.973556	−	0.228450i	$-0.926634\pi$
$137$	−12.3734	+	8.98981i	−1.05713	+	0.768052i	−0.0835766	+	0.996501i	$0.526634\pi$
$138$		0			0
$139$	−6.07484	−	18.6964i	−0.515261	−	1.58581i	−0.782806	−	0.622266i	$-0.786212\pi$
$139$	−6.07484	−	18.6964i	−0.515261	−	1.58581i	0.267544	−	0.963546i	$-0.413788\pi$
$140$	−0.212253	+	0.653249i	−0.0179387	+	0.0552096i
$141$		0			0
$142$	−14.1123			−1.18428
$143$	−0.0152774	−	3.22939i	−0.00127756	−	0.270055i
$144$		0			0
$145$	8.18547	+	5.94709i	0.679766	+	0.493879i
$146$	2.40675	−	7.40722i	0.199184	−	0.613026i
$147$		0			0
$148$	−16.4017	+	11.9166i	−1.34821	+	0.979535i
$149$	−8.19771	+	5.95599i	−0.671583	+	0.487933i	−0.870555	−	0.492072i	$-0.836240\pi$
$149$	−8.19771	+	5.95599i	−0.671583	+	0.487933i	0.198972	+	0.980005i	$0.436240\pi$
$150$		0			0
$151$	3.69682	−	11.3776i	0.300843	−	0.925899i	−0.680353	−	0.732884i	$-0.738174\pi$
$151$	3.69682	−	11.3776i	0.300843	−	0.925899i	0.981196	−	0.193015i	$-0.0618264\pi$
$152$	16.3837	+	11.9034i	1.32889	+	0.965496i
$153$		0			0
$154$	1.43578	−	0.474033i	0.115698	−	0.0381987i
$155$	2.50533			0.201233
$156$		0			0
$157$	−0.811494	+	2.49752i	−0.0647643	+	0.199324i	−0.978202	−	0.207654i	$-0.933417\pi$
$157$	−0.811494	+	2.49752i	−0.0647643	+	0.199324i	0.913438	+	0.406978i	$0.133417\pi$
$158$	7.39076	+	22.7464i	0.587977	+	1.80961i
$159$		0			0
$160$	−3.04920	+	2.21537i	−0.241061	+	0.175141i
$161$	0.287079	+	0.883539i	0.0226250	+	0.0696326i
$162$		0			0
$163$	−19.1927	−	13.9443i	−1.50329	−	1.09220i	−0.969049	−	0.246868i	$-0.920598\pi$
$163$	−19.1927	−	13.9443i	−1.50329	−	1.09220i	−0.534238	−	0.845334i	$-0.679402\pi$
$164$	29.3825			2.29438
$165$		0			0
$166$	−19.5876			−1.52029
$167$	2.82488	+	2.05240i	0.218596	+	0.158819i	0.691694	−	0.722190i	$-0.256865\pi$
$167$	2.82488	+	2.05240i	0.218596	+	0.158819i	−0.473098	+	0.881010i	$0.656865\pi$
$168$		0			0
$169$	−3.72424	−	11.4620i	−0.286480	−	0.881695i
$170$	5.09931	−	3.70486i	0.391099	−	0.284150i
$171$		0			0
$172$	5.60834	+	17.2607i	0.427632	+	1.31612i
$173$	6.29145	−	19.3631i	0.478330	−	1.47215i	−0.363083	−	0.931757i	$-0.618276\pi$
$173$	6.29145	−	19.3631i	0.478330	−	1.47215i	0.841413	−	0.540392i	$-0.181724\pi$
$174$		0			0
$175$	0.193527			0.0146293
$176$	−4.73370	−	1.51335i	−0.356816	−	0.114073i
$177$		0			0
$178$	13.9936	+	10.1669i	1.04886	+	0.762044i
$179$	−1.19008	+	3.66268i	−0.0889506	+	0.273762i	−0.985630	−	0.168919i	$-0.945972\pi$
$179$	−1.19008	+	3.66268i	−0.0889506	+	0.273762i	0.896679	+	0.442681i	$0.145972\pi$
$180$		0			0
$181$	14.2509	−	10.3539i	1.05926	−	0.769599i	0.0853107	−	0.996354i	$-0.472812\pi$
$181$	14.2509	−	10.3539i	1.05926	−	0.769599i	0.973952	+	0.226755i	$0.0728117\pi$
$182$	−0.359123	+	0.260918i	−0.0266200	+	0.0193406i
$183$		0			0
$184$	5.41356	−	16.6612i	0.399093	−	1.22828i
$185$	4.62125	+	3.35753i	0.339761	+	0.246851i
$186$		0			0
$187$	−8.45285	−	2.70236i	−0.618134	−	0.197616i
$188$	38.5170			2.80914
$189$		0			0
$190$	4.03950	−	12.4323i	0.293056	−	0.901935i
$191$	−0.128891	−	0.396685i	−0.00932620	−	0.0287031i	0.946285	−	0.323333i	$-0.104804\pi$
$191$	−0.128891	−	0.396685i	−0.00932620	−	0.0287031i	−0.955611	+	0.294630i	$0.904804\pi$
$192$		0			0
$193$	−9.46269	+	6.87505i	−0.681140	+	0.494877i	−0.873736	−	0.486401i	$-0.838309\pi$
$193$	−9.46269	+	6.87505i	−0.681140	+	0.494877i	0.192596	+	0.981278i	$0.438309\pi$
$194$	−11.5396	−	35.5151i	−0.828493	−	2.54984i
$195$		0			0
$196$	19.9920	+	14.5250i	1.42800	+	1.03750i
$197$	−21.5958			−1.53864			−0.769320	−	0.638863i	$-0.779405\pi$
$197$	−21.5958			−1.53864			−0.769320	+	0.638863i	$0.779405\pi$
$198$		0			0
$199$	7.76028			0.550111			0.275056	−	0.961428i	$-0.411304\pi$
$199$	7.76028			0.550111			0.275056	+	0.961428i	$0.411304\pi$
$200$	−2.95244	−	2.14507i	−0.208769	−	0.151679i
$201$		0			0
$202$	−9.57911	−	29.4815i	−0.673984	−	2.07431i
$203$	−1.58411	+	1.15092i	−0.111183	+	0.0807790i
$204$		0			0
$205$	−2.55823	−	7.87342i	−0.178675	−	0.549904i
$206$	2.90986	−	8.95561i	0.202739	−	0.623967i
$207$		0			0
$208$	1.45903			0.101166
$209$	−17.4767	+	5.77008i	−1.20889	+	0.399125i
$210$		0			0
$211$	10.1173	+	7.35065i	0.696504	+	0.506040i	0.878792	−	0.477205i	$-0.158350\pi$
$211$	10.1173	+	7.35065i	0.696504	+	0.506040i	−0.182288	+	0.983245i	$0.558350\pi$
$212$	10.1876	−	31.3542i	0.699687	−	2.15342i
$213$		0			0
$214$	9.31320	−	6.76644i	0.636637	−	0.462544i
$215$	4.13694	−	3.00566i	0.282137	−	0.204984i
$216$		0			0
$217$	−0.149826	+	0.461118i	−0.0101709	+	0.0313027i
$218$	14.3310	+	10.4121i	0.970619	+	0.705196i
$219$		0			0
$220$	0.0556868	+	11.7712i	0.00375440	+	0.793617i
$221$	2.60536			0.175255
$222$		0			0
$223$	−1.66118	+	5.11257i	−0.111241	+	0.342363i	−0.991144	−	0.132789i	$-0.957607\pi$
$223$	−1.66118	+	5.11257i	−0.111241	+	0.342363i	0.879904	+	0.475152i	$0.157607\pi$
$224$	−0.225399	−	0.693708i	−0.0150601	−	0.0463503i
$225$		0			0
$226$	38.5419	−	28.0024i	2.56377	−	1.86269i
$227$	6.72202	+	20.6882i	0.446156	+	1.37313i	0.881211	+	0.472723i	$0.156729\pi$
$227$	6.72202	+	20.6882i	0.446156	+	1.37313i	−0.435055	+	0.900404i	$0.643271\pi$
$228$		0			0
$229$	−2.16068	−	1.56983i	−0.142782	−	0.103737i	0.514101	−	0.857730i	$-0.328126\pi$
$229$	−2.16068	−	1.56983i	−0.142782	−	0.103737i	−0.656883	+	0.753992i	$0.728126\pi$
$230$	−11.3082			−0.745639
$231$		0			0
$232$	36.9240			2.42418
$233$	−4.63323	−	3.36624i	−0.303533	−	0.220530i	0.425584	−	0.904919i	$-0.360069\pi$
$233$	−4.63323	−	3.36624i	−0.303533	−	0.220530i	−0.729117	+	0.684389i	$0.760069\pi$
$234$		0			0
$235$	−3.35354	−	10.3211i	−0.218761	−	0.673277i
$236$	−32.2110	+	23.4027i	−2.09676	+	1.52338i
$237$		0			0
$238$	0.376945	+	1.16012i	0.0244337	+	0.0751992i
$239$	7.53013	−	23.1754i	0.487084	−	1.49909i	−0.341857	−	0.939752i	$-0.611056\pi$
$239$	7.53013	−	23.1754i	0.487084	−	1.49909i	0.828940	−	0.559337i	$-0.188944\pi$
$240$		0			0
$241$	−16.7082			−1.07627			−0.538135	−	0.842859i	$-0.680871\pi$
$241$	−16.7082			−1.07627			−0.538135	+	0.842859i	$0.680871\pi$
$242$	20.8185	−	15.4286i	1.33827	−	0.991788i
$243$		0			0
$244$	−3.46293	−	2.51597i	−0.221691	−	0.161068i
$245$	2.15155	−	6.62178i	0.137457	−	0.423050i
$246$		0			0
$247$	4.37136	−	3.17598i	0.278143	−	0.202083i
$248$	7.39682	−	5.37410i	0.469698	−	0.341256i
$249$		0			0
$250$	−0.727943	+	2.24038i	−0.0460392	+	0.141694i
$251$	−13.0239	−	9.46240i	−0.822060	−	0.597262i	0.0952418	−	0.995454i	$-0.469638\pi$
$251$	−13.0239	−	9.46240i	−0.822060	−	0.597262i	−0.917302	+	0.398193i	$0.869638\pi$
$252$		0			0
$253$	9.41903	+	12.8360i	0.592169	+	0.806995i
$254$	16.7258			1.04947
$255$		0			0
$256$	−7.53728	+	23.1974i	−0.471080	+	1.44984i
$257$	−1.84445	−	5.67662i	−0.115053	−	0.354098i	0.876905	−	0.480664i	$-0.159604\pi$
$257$	−1.84445	−	5.67662i	−0.115053	−	0.354098i	−0.991958	+	0.126566i	$0.959604\pi$
$258$		0			0
$259$	−0.894336	+	0.649773i	−0.0555713	+	0.0403749i
$260$	−1.06793	−	3.28674i	−0.0662301	−	0.203835i
$261$		0			0
$262$	−4.76490	−	3.46191i	−0.294377	−	0.213877i
$263$	0.451149			0.0278190			0.0139095	−	0.999903i	$-0.495572\pi$
$263$	0.451149			0.0278190			0.0139095	+	0.999903i	$0.495572\pi$
$264$		0			0
$265$	−9.28879			−0.570606
$266$	2.04666	+	1.48698i	0.125489	+	0.0911728i
$267$		0			0
$268$	3.57459	+	11.0015i	0.218353	+	0.672021i
$269$	11.9085	−	8.65203i	0.726074	−	0.527524i	−0.162245	−	0.986751i	$-0.551873\pi$
$269$	11.9085	−	8.65203i	0.726074	−	0.527524i	0.888319	+	0.459227i	$0.151873\pi$
$270$		0			0
$271$	1.36829	+	4.21115i	0.0831175	+	0.255809i	0.983975	−	0.178305i	$-0.0570614\pi$
$271$	1.36829	+	4.21115i	0.0831175	+	0.255809i	−0.900858	+	0.434114i	$0.857061\pi$
$272$	1.23896	−	3.81312i	0.0751228	−	0.231204i
$273$		0			0
$274$	36.0286			2.17657
$275$	3.14941	−	1.03980i	0.189917	−	0.0627025i
$276$		0			0
$277$	0.0746965	+	0.0542702i	0.00448808	+	0.00326078i	0.590027	−	0.807383i	$-0.299117\pi$
$277$	0.0746965	+	0.0542702i	0.00448808	+	0.00326078i	−0.585539	+	0.810644i	$0.699117\pi$
$278$	−14.3104	+	44.0427i	−0.858278	+	2.64151i
$279$		0			0
$280$	0.571377	−	0.415129i	0.0341463	−	0.0248087i
$281$	4.19314	−	3.04650i	0.250142	−	0.181739i	−0.455648	−	0.890160i	$-0.650592\pi$
$281$	4.19314	−	3.04650i	0.250142	−	0.181739i	0.705790	+	0.708421i	$0.250592\pi$
$282$		0			0
$283$	0.483496	−	1.48805i	0.0287408	−	0.0884552i	−0.935657	−	0.352910i	$-0.885192\pi$
$283$	0.483496	−	1.48805i	0.0287408	−	0.0884552i	0.964398	+	0.264455i	$0.0851921\pi$
$284$	17.2017	+	12.4978i	1.02073	+	0.741607i
$285$		0			0
$286$	−4.44240	+	6.17566i	−0.262684	+	0.365174i
$287$	1.60214			0.0945710
$288$		0			0
$289$	−3.04091	+	9.35897i	−0.178877	+	0.550527i
$290$	−7.36518	−	22.6677i	−0.432498	−	1.33109i
$291$		0			0
$292$	−9.49341	+	6.89736i	−0.555560	+	0.403638i
$293$	7.15592	+	22.0236i	0.418053	+	1.28664i	0.909491	+	0.415723i	$0.136471\pi$
$293$	7.15592	+	22.0236i	0.418053	+	1.28664i	−0.491438	+	0.870912i	$0.663529\pi$
$294$		0			0
$295$	9.07556	+	6.59378i	0.528400	+	0.383905i
$296$	20.8461			1.21165
$297$		0			0
$298$	23.8699			1.38274
$299$	−3.78150	−	2.74742i	−0.218690	−	0.158887i
$300$		0			0
$301$	0.305805	+	0.941172i	0.0176263	+	0.0542483i
$302$	−22.7991	+	16.5646i	−1.31194	+	0.953183i
$303$		0			0
$304$	−2.56950	−	7.90811i	−0.147371	−	0.453561i
$305$	−0.372682	+	1.14700i	−0.0213397	+	0.0656768i
$306$		0			0
$307$	−7.72480			−0.440878			−0.220439	−	0.975401i	$-0.570749\pi$
$307$	−7.72480			−0.440878			−0.220439	+	0.975401i	$0.570749\pi$
$308$	−2.16989	−	0.693708i	−0.123641	−	0.0395277i
$309$		0			0
$310$	−4.77460	−	3.46895i	−0.271179	−	0.197023i
$311$	5.90867	−	18.1850i	0.335050	−	1.03118i	−0.631647	−	0.775256i	$-0.717621\pi$
$311$	5.90867	−	18.1850i	0.335050	−	1.03118i	0.966697	−	0.255922i	$-0.0823790\pi$
$312$		0			0
$313$	−2.34863	+	1.70638i	−0.132752	+	0.0964503i	−0.652180	−	0.758064i	$-0.726145\pi$
$313$	−2.34863	+	1.70638i	−0.132752	+	0.0964503i	0.519427	+	0.854515i	$0.326145\pi$
$314$	5.00468	−	3.63611i	0.282430	−	0.205198i
$315$		0			0
$316$	11.1354	−	34.2711i	0.626413	−	1.92790i
$317$	1.82962	+	1.32930i	0.102762	+	0.0746607i	0.637979	−	0.770053i	$-0.279770\pi$
$317$	1.82962	+	1.32930i	0.102762	+	0.0746607i	−0.535218	+	0.844714i	$0.679770\pi$
$318$		0			0
$319$	−19.5956	+	27.2411i	−1.09714	+	1.52521i
$320$	11.8754			0.663857
$321$		0			0
$322$	0.676265	−	2.08133i	0.0376868	−	0.115988i
$323$	−4.58829	−	14.1213i	−0.255299	−	0.785731i
$324$		0			0
$325$	−0.787747	+	0.572331i	−0.0436963	+	0.0317472i
$326$	17.2693	+	53.1496i	0.956460	+	2.94368i
$327$		0			0
$328$	−24.4421	−	17.7582i	−1.34959	−	0.980533i
$329$	2.10021			0.115788
$330$		0			0
$331$	6.02336			0.331074			0.165537	−	0.986204i	$-0.447064\pi$
$331$	6.02336			0.331074			0.165537	+	0.986204i	$0.447064\pi$
$332$	23.8756	+	17.3466i	1.31034	+	0.952021i
$333$		0			0
$334$	−2.54179	−	7.82284i	−0.139081	−	0.428047i
$335$	2.63676	−	1.91572i	0.144062	−	0.104667i
$336$		0			0
$337$	−4.50076	−	13.8519i	−0.245172	−	0.754562i	−0.995608	−	0.0936187i	$-0.970157\pi$
$337$	−4.50076	−	13.8519i	−0.245172	−	0.754562i	0.750436	−	0.660943i	$-0.229843\pi$
$338$	−8.77310	+	27.0008i	−0.477193	+	1.46865i
$339$		0			0
$340$	−9.49662			−0.515026
$341$	0.0393084	+	8.30913i	0.00212867	+	0.449965i
$342$		0			0
$343$	2.18607	+	1.58827i	0.118037	+	0.0857587i
$344$	5.76669	−	17.7480i	0.310919	−	0.956911i
$345$		0			0
$346$	−38.8009	+	28.1905i	−2.08595	+	1.51553i
$347$	23.3281	−	16.9489i	1.25232	−	0.909863i	0.253965	−	0.967213i	$-0.418265\pi$
$347$	23.3281	−	16.9489i	1.25232	−	0.909863i	0.998354	+	0.0573506i	$0.0182653\pi$
$348$		0			0
$349$	−0.504421	+	1.55245i	−0.0270010	+	0.0831006i	−0.963649	−	0.267172i	$-0.913911\pi$
$349$	−0.504421	+	1.55245i	−0.0270010	+	0.0831006i	0.936648	+	0.350272i	$0.113911\pi$
$350$	−0.368820	−	0.267964i	−0.0197143	−	0.0143233i
$351$		0			0
$352$	−7.39533	−	10.0782i	−0.394172	−	0.537169i
$353$	−24.9297			−1.32687			−0.663437	−	0.748232i	$-0.730903\pi$
$353$	−24.9297			−1.32687			−0.663437	+	0.748232i	$0.730903\pi$
$354$		0			0
$355$	1.85125	−	5.69757i	0.0982543	−	0.302396i
$356$	−8.05321	−	24.7852i	−0.426819	−	1.31361i
$357$		0			0
$358$	7.33949	−	5.33245i	0.387904	−	0.281829i
$359$	−8.78874	−	27.0489i	−0.463852	−	1.42759i	−0.860421	−	0.509584i	$-0.829799\pi$
$359$	−8.78874	−	27.0489i	−0.463852	−	1.42759i	0.396569	−	0.918005i	$-0.370201\pi$
$360$		0			0
$361$	−9.54125	−	6.93213i	−0.502171	−	0.364849i
$362$	−41.4955			−2.18095
$363$		0			0
$364$	0.668808			0.0350550
$365$	2.67480	+	1.94336i	0.140005	+	0.101720i
$366$		0			0
$367$	−3.22653	−	9.93023i	−0.168423	−	0.518354i	0.830849	−	0.556498i	$-0.187855\pi$
$367$	−3.22653	−	9.93023i	−0.168423	−	0.518354i	−0.999272	+	0.0381442i	$0.987855\pi$
$368$	−5.81930	+	4.22797i	−0.303352	+	0.220398i
$369$		0			0
$370$	−4.15814	−	12.7974i	−0.216171	−	0.665307i
$371$	0.555499	−	1.70965i	0.0288401	−	0.0887606i
$372$		0			0
$373$	−2.81747			−0.145883			−0.0729416	−	0.997336i	$-0.523239\pi$
$373$	−2.81747			−0.145883			−0.0729416	+	0.997336i	$0.523239\pi$
$374$	12.3675	+	16.8542i	0.639509	+	0.871508i
$375$		0			0
$376$	−32.0407	−	23.2789i	−1.65237	−	1.20052i
$377$	3.04437	−	9.36960i	0.156793	−	0.482559i
$378$		0			0
$379$	−7.22711	+	5.25080i	−0.371231	+	0.269715i	−0.757721	−	0.652578i	$-0.773687\pi$
$379$	−7.22711	+	5.25080i	−0.371231	+	0.269715i	0.386490	+	0.922294i	$0.373687\pi$
$380$	−15.9338	+	11.5766i	−0.817386	+	0.593865i
$381$		0			0
$382$	−0.303625	+	0.934460i	−0.0155348	+	0.0478111i
$383$	−6.90317	−	5.01545i	−0.352736	−	0.256278i	0.397280	−	0.917697i	$-0.369954\pi$
$383$	−6.90317	−	5.01545i	−0.352736	−	0.256278i	−0.750016	+	0.661420i	$0.769954\pi$
$384$		0			0
$385$	0.00303643	+	0.641850i	0.000154751	+	0.0327117i
$386$	27.5532			1.40242
$387$		0			0
$388$	−17.3862	+	53.5093i	−0.882651	+	2.71652i
$389$	−3.63890	−	11.1994i	−0.184500	−	0.567832i	0.815440	−	0.578842i	$-0.196495\pi$
$389$	−3.63890	−	11.1994i	−0.184500	−	0.567832i	−0.999939	+	0.0110104i	$0.996495\pi$
$390$		0			0
$391$	−10.3914	+	7.54978i	−0.525515	+	0.381809i
$392$	−7.85188	−	24.1656i	−0.396580	−	1.22055i
$393$		0			0
$394$	41.1569	+	29.9023i	2.07346	+	1.50645i
$395$	−10.1529			−0.510849
$396$		0			0
$397$	−1.41214			−0.0708735			−0.0354368	−	0.999372i	$-0.511282\pi$
$397$	−1.41214			−0.0708735			−0.0354368	+	0.999372i	$0.511282\pi$
$398$	−14.7894	−	10.7451i	−0.741325	−	0.538604i
$399$		0			0
$400$	0.463040	+	1.42509i	0.0231520	+	0.0712545i
$401$	6.84361	−	4.97217i	0.341753	−	0.248298i	−0.403648	−	0.914914i	$-0.632258\pi$
$401$	6.84361	−	4.97217i	0.341753	−	0.248298i	0.745401	+	0.666616i	$0.232258\pi$
$402$		0			0
$403$	−0.753833	−	2.32006i	−0.0375511	−	0.115570i
$404$	−14.4325	+	44.4185i	−0.718042	+	2.20991i
$405$		0			0
$406$	4.61257			0.228918
$407$	−11.0630	+	15.3794i	−0.548375	+	0.762331i
$408$		0			0
$409$	−8.19172	−	5.95163i	−0.405054	−	0.294289i	0.366542	−	0.930401i	$-0.380542\pi$
$409$	−8.19172	−	5.95163i	−0.405054	−	0.294289i	−0.771597	+	0.636112i	$0.780542\pi$
$410$	−6.02636	+	18.5472i	−0.297621	+	0.915982i
$411$		0			0
$412$	−11.4779	+	8.33918i	−0.565475	+	0.410842i
$413$	−1.75637	+	1.27608i	−0.0864252	+	0.0627915i
$414$		0			0
$415$	2.56950	−	7.90811i	0.126132	−	0.388194i
$416$	2.96903	+	2.15713i	0.145569	+	0.105762i
$417$		0			0
$418$	41.2962	+	13.2023i	2.01987	+	0.645746i
$419$	−32.8019			−1.60248			−0.801240	−	0.598343i	$-0.795826\pi$
$419$	−32.8019			−1.60248			−0.801240	+	0.598343i	$0.795826\pi$
$420$		0			0
$421$	−4.36619	+	13.4377i	−0.212795	+	0.654915i	0.786508	+	0.617580i	$0.211887\pi$
$421$	−4.36619	+	13.4377i	−0.212795	+	0.654915i	−0.999303	+	0.0373351i	$0.988113\pi$
$422$	−9.10342	−	28.0175i	−0.443148	−	1.36387i
$423$		0			0
$424$	−27.4246	+	19.9251i	−1.33185	+	0.967649i
$425$	0.826838	+	2.54475i	0.0401076	+	0.123438i
$426$		0			0
$427$	−0.188823	−	0.137188i	−0.00913779	−	0.00663899i
$428$	−17.3443			−0.838368
$429$		0			0
$430$	−12.0458			−0.580901
$431$	15.4569	+	11.2301i	0.744531	+	0.540933i	0.894127	−	0.447814i	$-0.147797\pi$
$431$	15.4569	+	11.2301i	0.744531	+	0.540933i	−0.149596	+	0.988747i	$0.547797\pi$
$432$		0			0
$433$	4.67235	+	14.3800i	0.224539	+	0.691059i	0.998338	+	0.0576283i	$0.0183538\pi$
$433$	4.67235	+	14.3800i	0.224539	+	0.691059i	−0.773799	+	0.633431i	$0.781646\pi$
$434$	0.924015	−	0.671336i	0.0443541	−	0.0322252i
$435$		0			0
$436$	−8.24740	−	25.3829i	−0.394979	−	1.21562i
$437$	−8.23171	+	25.3346i	−0.393776	+	1.21192i
$438$		0			0
$439$	37.1642			1.77375			0.886876	−	0.462008i	$-0.152871\pi$
$439$	37.1642			1.77375			0.886876	+	0.462008i	$0.152871\pi$
$440$	7.06799	−	9.82567i	0.336953	−	0.468421i
$441$		0			0
$442$	−4.96524	−	3.60746i	−0.236172	−	0.171589i
$443$	0.853040	−	2.62539i	0.0405291	−	0.124736i	−0.928745	−	0.370720i	$-0.879111\pi$
$443$	0.853040	−	2.62539i	0.0405291	−	0.124736i	0.969274	+	0.245984i	$0.0791110\pi$
$444$		0			0
$445$	−5.94037	+	4.31593i	−0.281601	+	0.204595i
$446$	10.2449	−	7.44333i	0.485108	−	0.352452i
$447$		0			0
$448$	−0.710189	+	2.18574i	−0.0335533	+	0.103266i
$449$	−14.4540	−	10.5015i	−0.682127	−	0.495594i	0.191936	−	0.981408i	$-0.438524\pi$
$449$	−14.4540	−	10.5015i	−0.682127	−	0.495594i	−0.874063	+	0.485813i	$0.838524\pi$
$450$		0			0
$451$	26.0728	−	8.60813i	1.22772	−	0.405341i
$452$	−71.7780			−3.37615
$453$		0			0
$454$	15.8349	−	48.7348i	0.743168	−	2.28724i
$455$	−0.0582308	−	0.179216i	−0.00272990	−	0.00840178i
$456$		0			0
$457$	17.1205	−	12.4388i	0.800864	−	0.581862i	−0.110304	−	0.993898i	$-0.535182\pi$
$457$	17.1205	−	12.4388i	0.800864	−	0.581862i	0.911167	+	0.412036i	$0.135182\pi$
$458$	1.94416	+	5.98350i	0.0908444	+	0.279590i
$459$		0			0
$460$	13.7837	+	10.0144i	0.642668	+	0.466926i
$461$	34.3476			1.59973			0.799864	−	0.600181i	$-0.204905\pi$
$461$	34.3476			1.59973			0.799864	+	0.600181i	$0.204905\pi$
$462$		0			0
$463$	10.4516			0.485727			0.242864	−	0.970060i	$-0.421913\pi$
$463$	10.4516			0.485727			0.242864	+	0.970060i	$0.421913\pi$
$464$	−12.2653	−	8.91129i	−0.569404	−	0.413696i
$465$		0			0
$466$	4.16892	+	12.8306i	0.193122	+	0.594367i
$467$	23.9820	−	17.4239i	1.10975	−	0.806284i	0.127129	−	0.991886i	$-0.459424\pi$
$467$	23.9820	−	17.4239i	1.10975	−	0.806284i	0.982625	+	0.185602i	$0.0594236\pi$
$468$		0			0
$469$	0.194911	+	0.599875i	0.00900017	+	0.0276997i
$470$	−7.89985	+	24.3133i	−0.364393	+	1.12149i
$471$		0			0
$472$	40.9392			1.88438
$473$	10.0334	+	13.6734i	0.461338	+	0.628701i
$474$		0			0
$475$	4.48940	+	3.26174i	0.205988	+	0.149659i
$476$	0.567928	−	1.74790i	0.0260309	−	0.0801150i
$477$		0			0
$478$	−46.4401	+	33.7407i	−2.12412	+	1.54326i
$479$	−10.6941	+	7.76971i	−0.488625	+	0.355007i	−0.804655	−	0.593742i	$-0.797650\pi$
$479$	−10.6941	+	7.76971i	−0.488625	+	0.355007i	0.316030	+	0.948749i	$0.397650\pi$
$480$		0			0
$481$	1.71875	−	5.28977i	0.0783682	−	0.241193i
$482$	31.8422	+	23.1347i	1.45037	+	1.05376i
$483$		0			0
$484$	−39.0395	+	0.369380i	−1.77452	+	0.0167900i
$485$	15.8523			0.719816
$486$		0			0
$487$	−13.1325	+	40.4176i	−0.595089	+	1.83150i	−0.0408075	+	0.999167i	$0.512993\pi$
$487$	−13.1325	+	40.4176i	−0.595089	+	1.83150i	−0.554282	+	0.832329i	$0.687007\pi$
$488$	1.36007	+	4.18586i	0.0615675	+	0.189485i
$489$		0			0
$490$	−13.2691	+	9.64056i	−0.599436	+	0.435516i
$491$	4.86568	+	14.9750i	0.219585	+	0.675813i	0.998796	+	0.0490515i	$0.0156198\pi$
$491$	4.86568	+	14.9750i	0.219585	+	0.675813i	−0.779211	+	0.626761i	$0.784380\pi$
$492$		0			0
$493$	−21.9019	−	15.9127i	−0.986412	−	0.716670i
$494$	−12.7284			−0.572679
$495$		0			0
$496$	−3.75405			−0.168562
$497$	0.937957	+	0.681466i	0.0420731	+	0.0305679i
$498$		0			0
$499$	−10.3607	−	31.8869i	−0.463808	−	1.42746i	−0.860475	−	0.509493i	$-0.829833\pi$
$499$	−10.3607	−	31.8869i	−0.463808	−	1.42746i	0.396666	−	0.917963i	$-0.370167\pi$
$500$	2.87136	−	2.08617i	0.128411	−	0.0932963i
$501$		0			0
$502$	11.7187	+	36.0665i	0.523032	+	1.60973i
$503$	7.05063	−	21.6996i	0.314372	−	0.967537i	−0.661640	−	0.749821i	$-0.730139\pi$
$503$	7.05063	−	21.6996i	0.314372	−	0.967537i	0.976012	−	0.217716i	$-0.0698606\pi$
$504$		0			0
$505$	13.1591			0.585574
$506$	−0.177425	−	37.5046i	−0.00788749	−	1.66728i
$507$		0			0
$508$	−20.3873	−	14.8122i	−0.904540	−	0.657187i
$509$	−12.2731	+	37.7727i	−0.543996	+	1.67425i	0.179370	+	0.983782i	$0.442594\pi$
$509$	−12.2731	+	37.7727i	−0.543996	+	1.67425i	−0.723365	+	0.690465i	$0.757406\pi$
$510$		0			0
$511$	−0.517646	+	0.376092i	−0.0228993	+	0.0166373i
$512$	13.4170	−	9.74805i	0.592955	−	0.430807i
$513$		0			0
$514$	−4.34491	+	13.3723i	−0.191646	+	0.589826i
$515$	3.23394	+	2.34959i	0.142504	+	0.103535i
$516$		0			0
$517$	34.1784	−	11.2843i	1.50316	−	0.496281i
$518$	2.60410			0.114418
$519$		0			0
$520$	−1.09808	+	3.37955i	−0.0481540	+	0.148203i
$521$	−7.88005	−	24.2523i	−0.345231	−	1.06251i	−0.961460	−	0.274945i	$-0.911340\pi$
$521$	−7.88005	−	24.2523i	−0.345231	−	1.06251i	0.616229	−	0.787567i	$-0.288660\pi$
$522$		0			0
$523$	12.4835	−	9.06977i	0.545864	−	0.396593i	−0.280394	−	0.959885i	$-0.590465\pi$
$523$	12.4835	−	9.06977i	0.545864	−	0.396593i	0.826258	+	0.563291i	$0.190465\pi$
$524$	2.74217	+	8.43953i	0.119792	+	0.368683i
$525$		0			0
$526$	−0.859791	−	0.624675i	−0.0374887	−	0.0272371i
$527$	−6.70351			−0.292010
$528$		0			0
$529$	0.0438407			0.00190612
$530$	17.7024	+	12.8615i	0.768943	+	0.558669i
$531$		0			0
$532$	−1.17784	−	3.62501i	−0.0510657	−	0.157164i
$533$	−6.52145	+	4.73811i	−0.282475	+	0.205230i
$534$		0			0
$535$	1.51011	+	4.64764i	0.0652877	+	0.200935i
$536$	3.67552	−	11.3121i	0.158758	−	0.488607i
$537$		0			0
$538$	−34.6749			−1.49494
$539$	21.9955	+	7.03189i	0.947411	+	0.302885i
$540$		0			0
$541$	−22.3294	−	16.2233i	−0.960018	−	0.697494i	−0.00686309	−	0.999976i	$-0.502185\pi$
$541$	−22.3294	−	16.2233i	−0.960018	−	0.697494i	−0.953155	+	0.302483i	$0.902185\pi$
$542$	3.22324	−	9.92010i	0.138450	−	0.426105i
$543$		0			0
$544$	8.15877	−	5.92769i	0.349804	−	0.254148i
$545$	−6.08362	+	4.42001i	−0.260594	+	0.189332i
$546$		0			0
$547$	9.50800	−	29.2626i	0.406533	−	1.25118i	−0.513076	−	0.858343i	$-0.671494\pi$
$547$	9.50800	−	29.2626i	0.406533	−	1.25118i	0.919608	−	0.392836i	$-0.128506\pi$
$548$	−43.9157	−	31.9067i	−1.87599	−	1.36298i
$549$		0			0
$550$	−7.44184	−	2.37914i	−0.317321	−	0.101447i
$551$	−56.1457			−2.39189
$552$		0			0
$553$	0.607177	−	1.86870i	0.0258198	−	0.0794652i
$554$	−0.0672109	−	0.206854i	−0.00285552	−	0.00878838i
$555$		0			0
$556$	56.4470	−	41.0112i	2.39389	−	1.73926i
$557$	4.30642	+	13.2538i	0.182469	+	0.561582i	0.999896	−	0.0144509i	$-0.00460003\pi$
$557$	4.30642	+	13.2538i	0.182469	+	0.561582i	−0.817427	+	0.576033i	$0.804600\pi$
$558$		0			0
$559$	−4.02817	−	2.92664i	−0.170373	−	0.123783i
$560$	−0.289986			−0.0122542
$561$		0			0
$562$	−12.2095			−0.515026
$563$	4.72456	+	3.43259i	0.199117	+	0.144667i	0.682876	−	0.730534i	$-0.260729\pi$
$563$	4.72456	+	3.43259i	0.199117	+	0.144667i	−0.483759	+	0.875201i	$0.660729\pi$
$564$		0			0
$565$	6.24947	+	19.2339i	0.262917	+	0.809176i
$566$	−2.98183	+	2.16643i	−0.125336	+	0.0910618i
$567$		0			0
$568$	−6.75599	−	20.7928i	−0.283475	−	0.872447i
$569$	1.68536	−	5.18701i	0.0706540	−	0.217451i	−0.909494	−	0.415716i	$-0.863531\pi$
$569$	1.68536	−	5.18701i	0.0706540	−	0.217451i	0.980148	+	0.198266i	$0.0635309\pi$
$570$		0			0
$571$	40.2894			1.68606			0.843030	−	0.537866i	$-0.180770\pi$
$571$	40.2894			1.68606			0.843030	+	0.537866i	$0.180770\pi$
$572$	10.8840	−	3.59344i	0.455084	−	0.150249i
$573$		0			0
$574$	−3.05332	−	2.21837i	−0.127443	−	0.0925928i
$575$	1.48341	−	4.56545i	0.0618623	−	0.190392i
$576$		0			0
$577$	19.2737	−	14.0032i	0.802374	−	0.582959i	−0.109236	−	0.994016i	$-0.534840\pi$
$577$	19.2737	−	14.0032i	0.802374	−	0.582959i	0.911610	+	0.411057i	$0.134840\pi$
$578$	18.7540	−	13.6256i	0.780065	−	0.566750i
$579$		0			0
$580$	−11.0968	+	34.1525i	−0.460771	+	1.41811i
$581$	1.30186	+	0.945860i	0.0540104	+	0.0392409i
$582$		0			0
$583$	−0.145740	−	30.8071i	−0.00603595	−	1.27590i
$584$	12.0658			0.499287
$585$		0			0
$586$	16.8570	−	51.8805i	0.696357	−	2.14317i
$587$	−6.05919	−	18.6483i	−0.250090	−	0.769697i	−0.994758	−	0.102262i	$-0.967392\pi$
$587$	−6.05919	−	18.6483i	−0.250090	−	0.769697i	0.744668	−	0.667435i	$-0.232608\pi$
$588$		0			0
$589$	−11.2474	+	8.17172i	−0.463441	+	0.336710i
$590$	−8.16608	−	25.1326i	−0.336192	−	1.03469i
$591$		0			0
$592$	−6.92460	−	5.03102i	−0.284599	−	0.206774i
$593$	−3.31095			−0.135964			−0.0679822	−	0.997687i	$-0.521656\pi$
$593$	−3.31095			−0.135964			−0.0679822	+	0.997687i	$0.521656\pi$
$594$		0			0
$595$	−0.517822			−0.0212286
$596$	−29.0953	−	21.1390i	−1.19179	−	0.865887i
$597$		0			0
$598$	3.40255	+	10.4720i	0.139140	+	0.428230i
$599$	25.9460	−	18.8509i	1.06012	−	0.770225i	0.0860126	−	0.996294i	$-0.472587\pi$
$599$	25.9460	−	18.8509i	1.06012	−	0.770225i	0.974111	+	0.226069i	$0.0725875\pi$
$600$		0			0
$601$	−9.05125	−	27.8569i	−0.369208	−	1.13631i	−0.947304	−	0.320337i	$-0.896204\pi$
$601$	−9.05125	−	27.8569i	−0.369208	−	1.13631i	0.578095	−	0.815969i	$-0.303796\pi$
$602$	0.720378	−	2.21710i	0.0293604	−	0.0903621i
$603$		0			0
$604$	42.4596			1.72766
$605$	3.49802	+	10.4290i	0.142215	+	0.423999i
$606$		0			0
$607$	31.6169	+	22.9710i	1.28329	+	0.932364i	0.999647	−	0.0265657i	$-0.00845712\pi$
$607$	31.6169	+	22.9710i	1.28329	+	0.932364i	0.283642	+	0.958930i	$0.408457\pi$
$608$	6.46311	−	19.8914i	0.262114	−	0.806703i
$609$		0			0
$610$	2.29842	−	1.66990i	0.0930601	−	0.0676121i
$611$	−8.54886	+	6.21111i	−0.345850	+	0.251275i
$612$		0			0
$613$	−3.93452	+	12.1092i	−0.158914	+	0.489086i	−0.998536	−	0.0540840i	$-0.982776\pi$
$613$	−3.93452	+	12.1092i	−0.158914	+	0.489086i	0.839623	+	0.543170i	$0.182776\pi$
$614$	14.7218	+	10.6960i	0.594123	+	0.431655i
$615$		0			0
$616$	1.38578	+	1.88851i	0.0558346	+	0.0760901i
$617$	8.97789			0.361436			0.180718	−	0.983535i	$-0.442158\pi$
$617$	8.97789			0.361436			0.180718	+	0.983535i	$0.442158\pi$
$618$		0			0
$619$	−6.86392	+	21.1250i	−0.275884	+	0.849084i	0.713100	+	0.701062i	$0.247290\pi$
$619$	−6.86392	+	21.1250i	−0.275884	+	0.849084i	−0.988984	+	0.148022i	$0.952710\pi$
$620$	2.74775	+	8.45670i	0.110352	+	0.339629i
$621$		0			0
$622$	−36.4402	+	26.4753i	−1.46112	+	1.06156i
$623$	−0.439117	−	1.35146i	−0.0175928	−	0.0541452i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	6.83868			0.273329
$627$		0			0
$628$	−9.32038			−0.371924
$629$	−12.3651	−	8.98377i	−0.493029	−	0.358206i
$630$		0			0
$631$	8.27153	+	25.4572i	0.329285	+	1.01343i	0.969469	+	0.245213i	$0.0788578\pi$
$631$	8.27153	+	25.4572i	0.329285	+	1.01343i	−0.640185	+	0.768221i	$0.721142\pi$
$632$	−29.9759	+	21.7788i	−1.19238	+	0.866313i
$633$		0			0
$634$	−1.64627	−	5.06670i	−0.0653817	−	0.201224i
$635$	−2.19409	+	6.75270i	−0.0870697	+	0.267973i
$636$		0			0
$637$	−6.77949			−0.268613
$638$	75.0639	−	24.7829i	2.97181	−	0.981166i
$639$		0			0
$640$	−16.5336	−	12.0123i	−0.653547	−	0.474830i
$641$	−4.65770	+	14.3349i	−0.183968	+	0.566195i	−0.999929	−	0.0119117i	$-0.996208\pi$
$641$	−4.65770	+	14.3349i	−0.183968	+	0.566195i	0.815961	+	0.578107i	$0.196208\pi$
$642$		0			0
$643$	31.7840	−	23.0925i	1.25344	−	0.910678i	0.255024	−	0.966935i	$-0.417917\pi$
$643$	31.7840	−	23.0925i	1.25344	−	0.910678i	0.998416	+	0.0562569i	$0.0179166\pi$
$644$	−2.66752	+	1.93807i	−0.105115	+	0.0763705i
$645$		0			0
$646$	−10.8085	+	33.2652i	−0.425256	+	1.30880i
$647$	19.2656	+	13.9973i	0.757408	+	0.550289i	0.898114	−	0.439762i	$-0.144937\pi$
$647$	19.2656	+	13.9973i	0.757408	+	0.550289i	−0.140706	+	0.990051i	$0.544937\pi$
$648$		0			0
$649$	−21.7265	+	30.2033i	−0.852838	+	1.18559i
$650$	2.29374			0.0899679
$651$		0			0
$652$	26.0190	−	80.0784i	1.01898	−	3.13611i
$653$	−2.13331	−	6.56566i	−0.0834829	−	0.256934i	0.900599	−	0.434652i	$-0.143129\pi$
$653$	−2.13331	−	6.56566i	−0.0834829	−	0.256934i	−0.984081	+	0.177718i	$0.943129\pi$
$654$		0			0
$655$	2.02273	−	1.46960i	0.0790348	−	0.0574221i
$656$	3.83332	+	11.7978i	0.149666	+	0.460625i
$657$		0			0
$658$	−4.00254	−	2.90802i	−0.156035	−	0.113366i
$659$	20.3718			0.793571			0.396786	−	0.917911i	$-0.370126\pi$
$659$	20.3718			0.793571			0.396786	+	0.917911i	$0.370126\pi$
$660$		0			0
$661$	−19.7451			−0.767994			−0.383997	−	0.923334i	$-0.625453\pi$
$661$	−19.7451			−0.767994			−0.383997	+	0.923334i	$0.625453\pi$
$662$	−11.4792	−	8.34013i	−0.446152	−	0.324148i
$663$		0			0
$664$	−9.37717	−	28.8600i	−0.363905	−	1.11998i
$665$	−0.868820	+	0.631235i	−0.0336914	+	0.0244782i
$666$		0			0
$667$	15.0088	+	46.1923i	0.581143	+	1.78857i
$668$	−3.82962	+	11.7864i	−0.148172	+	0.456028i
$669$		0			0
$670$	−7.67765			−0.296613
$671$	−3.80996	−	1.21803i	−0.147082	−	0.0470217i
$672$		0			0
$673$	−29.6207	−	21.5207i	−1.14180	−	0.829563i	−0.154427	−	0.988004i	$-0.549353\pi$
$673$	−29.6207	−	21.5207i	−1.14180	−	0.829563i	−0.987368	+	0.158441i	$0.949353\pi$
$674$	−10.6023	+	32.6306i	−0.408386	+	1.25688i
$675$		0			0
$676$	34.6054	−	25.1423i	1.33098	−	0.967011i
$677$	5.96357	−	4.33279i	0.229199	−	0.166523i	−0.467259	−	0.884120i	$-0.654758\pi$
$677$	5.96357	−	4.33279i	0.229199	−	0.166523i	0.696458	+	0.717598i	$0.254758\pi$
$678$		0			0
$679$	−0.948017	+	2.91770i	−0.0363816	+	0.111971i
$680$	7.89985	+	5.73958i	0.302946	+	0.220103i
$681$		0			0
$682$	11.4302	−	15.8898i	0.437684	−	0.608452i
$683$	−24.5651			−0.939959			−0.469979	−	0.882677i	$-0.655739\pi$
$683$	−24.5651			−0.939959			−0.469979	+	0.882677i	$0.655739\pi$
$684$		0			0
$685$	−4.72622	+	14.5458i	−0.180580	+	0.555767i
$686$	−1.96700	−	6.05380i	−0.0751004	−	0.231135i
$687$		0			0
$688$	−6.19890	+	4.50376i	−0.236331	+	0.171704i
$689$	2.79492	+	8.60189i	0.106478	+	0.327706i
$690$		0			0
$691$	−24.1439	−	17.5416i	−0.918479	−	0.667314i	0.0246662	−	0.999696i	$-0.492148\pi$
$691$	−24.1439	−	17.5416i	−0.918479	−	0.667314i	−0.943145	+	0.332382i	$0.892148\pi$
$692$	72.2602			2.74692
$693$		0			0
$694$	−67.9262			−2.57844
$695$	−15.9041	−	11.5550i	−0.603279	−	0.438308i
$696$		0			0
$697$	6.84507	+	21.0670i	0.259276	+	0.797968i
$698$	3.11088	−	2.26019i	0.117749	−	0.0855494i
$699$		0			0
$700$	0.212253	+	0.653249i	0.00802243	+	0.0246905i
$701$	4.45569	−	13.7132i	0.168289	−	0.517940i	−0.830975	−	0.556310i	$-0.812217\pi$
$701$	4.45569	−	13.7132i	0.168289	−	0.517940i	0.999264	+	0.0383701i	$0.0122166\pi$
$702$		0			0
$703$	−31.6980			−1.19551
$704$	0.186325	+	39.3859i	0.00702238	+	1.48441i
$705$		0			0
$706$	47.5106	+	34.5184i	1.78808	+	1.29912i
$707$	−0.786958	+	2.42201i	−0.0295966	+	0.0910890i
$708$		0			0
$709$	36.0084	−	26.1616i	1.35232	−	0.982520i	0.353430	−	0.935461i	$-0.385015\pi$
$709$	36.0084	−	26.1616i	1.35232	−	0.982520i	0.998892	−	0.0470585i	$-0.0149847\pi$
$710$	−11.4171	+	8.29502i	−0.428477	+	0.311307i
$711$		0			0
$712$	−8.28059	+	25.4850i	−0.310328	+	0.955093i
$713$	9.72970	+	7.06904i	0.364380	+	0.264738i
$714$		0			0
$715$	−1.91055	−	2.60365i	−0.0714504	−	0.0973710i
$716$	−13.6686			−0.510819
$717$		0			0
$718$	−20.7034	+	63.7185i	−0.772644	+	2.37795i
$719$	−1.11044	−	3.41758i	−0.0414124	−	0.127454i	0.928213	−	0.372050i	$-0.121345\pi$
$719$	−1.11044	−	3.41758i	−0.0414124	−	0.127454i	−0.969625	+	0.244595i	$0.921345\pi$
$720$		0			0
$721$	−0.625854	+	0.454710i	−0.0233080	+	0.0169343i
$722$	8.58510	+	26.4222i	0.319504	+	0.983333i
$723$		0			0
$724$	50.5794	+	36.7481i	1.87977	+	1.36573i
$725$	10.1178			0.375766
$726$		0			0
$727$	−39.0846			−1.44957			−0.724784	−	0.688976i	$-0.758060\pi$
$727$	−39.0846			−1.44957			−0.724784	+	0.688976i	$0.758060\pi$
$728$	−0.556354	−	0.404215i	−0.0206199	−	0.0149812i
$729$		0			0
$730$	−2.40675	−	7.40722i	−0.0890779	−	0.274154i
$731$	−11.0692	+	8.04226i	−0.409410	+	0.297454i
$732$		0			0
$733$	11.6519	+	35.8610i	0.430374	+	1.32455i	0.897753	+	0.440498i	$0.145198\pi$
$733$	11.6519	+	35.8610i	0.430374	+	1.32455i	−0.467379	+	0.884057i	$0.654802\pi$
$734$	−7.60065	+	23.3924i	−0.280545	+	0.863429i
$735$		0			0
$736$	−18.0928			−0.666910
$737$	6.39502	+	8.71499i	0.235564	+	0.321021i
$738$		0			0
$739$	−12.0806	−	8.77706i	−0.444392	−	0.322869i	0.342986	−	0.939341i	$-0.388562\pi$
$739$	−12.0806	−	8.77706i	−0.444392	−	0.322869i	−0.787377	+	0.616471i	$0.788562\pi$
$740$	−6.26490	+	19.2814i	−0.230302	+	0.708798i
$741$		0			0
$742$	−3.42589	+	2.48906i	−0.125768	+	0.0913761i
$743$	10.8149	−	7.85749i	0.396760	−	0.288263i	−0.371460	−	0.928449i	$-0.621143\pi$
$743$	10.8149	−	7.85749i	0.396760	−	0.288263i	0.768220	+	0.640186i	$0.221143\pi$
$744$		0			0
$745$	−3.13125	+	9.63699i	−0.114720	+	0.353072i
$746$	5.36949	+	3.90116i	0.196591	+	0.142832i
$747$		0			0
$748$	−0.149001	−	31.4964i	−0.00544803	−	1.15162i
$749$	−0.945731			−0.0345563
$750$		0			0
$751$	12.5045	−	38.4849i	0.456296	−	1.40434i	−0.413310	−	0.910590i	$-0.635627\pi$
$751$	12.5045	−	38.4849i	0.456296	−	1.40434i	0.869606	−	0.493745i	$-0.164373\pi$
$752$	5.02504	+	15.4655i	0.183244	+	0.563968i
$753$		0			0
$754$	−18.7753	+	13.6411i	−0.683757	+	0.496779i
$755$	−3.69682	−	11.3776i	−0.134541	−	0.414075i
$756$		0			0
$757$	6.90704	+	5.01826i	0.251040	+	0.182392i	0.706188	−	0.708025i	$-0.250413\pi$
$757$	6.90704	+	5.01826i	0.251040	+	0.182392i	−0.455147	+	0.890416i	$0.650413\pi$
$758$	21.0437			0.764341
$759$		0			0
$760$	20.2513			0.734593
$761$	−17.2162	−	12.5083i	−0.624089	−	0.453427i	0.230259	−	0.973129i	$-0.426043\pi$
$761$	−17.2162	−	12.5083i	−0.624089	−	0.453427i	−0.854347	+	0.519703i	$0.826043\pi$
$762$		0			0
$763$	−0.449706	−	1.38405i	−0.0162804	−	0.0501060i
$764$	1.19764	−	0.870139i	0.0433292	−	0.0314805i
$765$		0			0
$766$	6.21139	+	19.1167i	0.224427	+	0.690714i
$767$	3.37541	−	10.3885i	0.121879	−	0.375105i
$768$		0			0
$769$	−24.4717			−0.882471			−0.441235	−	0.897391i	$-0.645460\pi$
$769$	−24.4717			−0.882471			−0.441235	+	0.897391i	$0.645460\pi$
$770$	0.882938	−	1.22743i	0.0318189	−	0.0442335i
$771$		0			0
$772$	−33.5850	−	24.4009i	−1.20875	−	0.878209i
$773$	−4.21721	+	12.9792i	−0.151682	+	0.466830i	−0.997810	−	0.0661505i	$-0.978928\pi$
$773$	−4.21721	+	12.9792i	−0.151682	+	0.466830i	0.846127	+	0.532981i	$0.178928\pi$
$774$		0			0
$775$	2.02685	−	1.47259i	0.0728066	−	0.0528971i
$776$	46.8029	−	34.0043i	1.68013	−	1.22068i
$777$		0			0
$778$	−8.57207	+	26.3821i	−0.307324	+	0.945845i
$779$	37.1660	+	27.0027i	1.33161	+	0.967471i
$780$		0			0
$781$	18.9255	+	6.05045i	0.677209	+	0.216502i
$782$	30.2574			1.08200
$783$		0			0
$784$	−3.22394	+	9.92225i	−0.115141	+	0.354366i
$785$	0.811494	+	2.49752i	0.0289635	+	0.0891404i
$786$		0			0
$787$	6.03291	−	4.38317i	0.215050	−	0.156243i	−0.475046	−	0.879961i	$-0.657568\pi$
$787$	6.03291	−	4.38317i	0.215050	−	0.156243i	0.690096	+	0.723718i	$0.257568\pi$
$788$	−23.6855	−	72.8966i	−0.843762	−	2.59683i
$789$		0			0
$790$	19.3493	+	14.0581i	0.688416	+	0.500163i
$791$	−3.91383			−0.139160
$792$		0			0
$793$	1.17431			0.0417011
$794$	2.69124	+	1.95530i	0.0955085	+	0.0693910i
$795$		0			0
$796$	8.51119	+	26.1947i	0.301671	+	0.928448i
$797$	9.73624	−	7.07379i	0.344875	−	0.250567i	−0.401841	−	0.915710i	$-0.631629\pi$
$797$	9.73624	−	7.07379i	0.344875	−	0.250567i	0.746716	+	0.665143i	$0.231629\pi$
$798$		0			0
$799$	8.97309	+	27.6163i	0.317445	+	0.976996i
$800$	−1.16469	+	3.58455i	−0.0411781	+	0.126733i
$801$		0			0
$802$	−19.9270			−0.703648
$803$	−6.40334	+	8.90170i	−0.225969	+	0.314134i
$804$		0			0
$805$	0.751583	+	0.546057i	0.0264898	+	0.0192460i
$806$	−1.77579	+	5.46531i	−0.0625494	+	0.192507i
$807$		0			0
$808$	38.8515	−	28.2273i	1.36679	−	0.993033i
$809$	−40.4782	+	29.4091i	−1.42314	+	1.03397i	−0.431892	+	0.901925i	$0.642154\pi$
$809$	−40.4782	+	29.4091i	−1.42314	+	1.03397i	−0.991244	+	0.132044i	$0.957846\pi$
$810$		0			0
$811$	−3.46678	+	10.6697i	−0.121735	+	0.374663i	−0.993292	−	0.115632i	$-0.963111\pi$
$811$	−3.46678	+	10.6697i	−0.121735	+	0.374663i	0.871557	+	0.490294i	$0.163111\pi$
$812$	−5.62233	−	4.08486i	−0.197305	−	0.143350i
$813$		0			0
$814$	42.3786	−	13.9916i	1.48537	−	0.490406i
$815$	−23.7235			−0.830997
$816$		0			0
$817$	−8.76867	+	26.9872i	−0.306777	+	0.944163i
$818$	7.37080	+	22.6850i	0.257714	+	0.793163i
$819$		0			0
$820$	23.7709	−	17.2706i	0.830116	−	0.603114i
$821$	−2.27969	−	7.01616i	−0.0795617	−	0.244866i	0.903362	−	0.428879i	$-0.141091\pi$
$821$	−2.27969	−	7.01616i	−0.0795617	−	0.244866i	−0.982924	+	0.184013i	$0.941091\pi$
$822$		0			0
$823$	−28.8318	−	20.9475i	−1.00501	−	0.730184i	−0.0418554	−	0.999124i	$-0.513327\pi$
$823$	−28.8318	−	20.9475i	−1.00501	−	0.730184i	−0.963157	+	0.268939i	$0.913327\pi$
$824$	14.5880			0.508198
$825$		0			0
$826$	5.11414			0.177944
$827$	−40.8789	−	29.7003i	−1.42150	−	1.03278i	−0.991522	−	0.129940i	$-0.958522\pi$
$827$	−40.8789	−	29.7003i	−1.42150	−	1.03278i	−0.429977	−	0.902840i	$-0.641478\pi$
$828$		0			0
$829$	−1.89888	−	5.84416i	−0.0659509	−	0.202976i	0.912651	−	0.408741i	$-0.134032\pi$
$829$	−1.89888	−	5.84416i	−0.0659509	−	0.202976i	−0.978602	+	0.205765i	$0.934032\pi$
$830$	−15.8467	+	11.5133i	−0.550047	+	0.399633i
$831$		0			0
$832$	−3.57323	−	10.9973i	−0.123879	−	0.381262i
$833$	−5.75690	+	17.7179i	−0.199465	+	0.613890i
$834$		0			0
$835$	3.49175			0.120837
$836$	−38.6447	−	52.6641i	−1.33655	−	1.82143i
$837$		0			0
$838$	62.5133	+	45.4186i	2.15949	+	1.56896i
$839$	11.5953	−	35.6865i	0.400312	−	1.23204i	−0.524434	−	0.851451i	$-0.675723\pi$
$839$	11.5953	−	35.6865i	0.400312	−	1.23204i	0.924746	−	0.380584i	$-0.124277\pi$
$840$		0			0
$841$	−59.3574	+	43.1257i	−2.04681	+	1.48709i
$842$	26.9273	−	19.5638i	0.927976	−	0.674214i
$843$		0			0
$844$	−13.7158	+	42.2128i	−0.472116	+	1.45302i
$845$	−9.75019	−	7.08392i	−0.335417	−	0.243694i
$846$		0			0
$847$	−2.12870	+	0.0201412i	−0.0731431	+	0.000692058i
$848$	13.9186			0.477966
$849$		0			0
$850$	1.94776	−	5.99460i	0.0668077	−	0.205613i
$851$	8.47347	+	26.0787i	0.290467	+	0.893965i
$852$		0			0
$853$	21.8533	−	15.8774i	0.748244	−	0.543631i	−0.147038	−	0.989131i	$-0.546974\pi$
$853$	21.8533	−	15.8774i	0.748244	−	0.543631i	0.895282	+	0.445500i	$0.146974\pi$
$854$	0.169901	+	0.522900i	0.00581388	+	0.0178933i
$855$		0			0
$856$	14.4280	+	10.4826i	0.493140	+	0.358287i
$857$	2.51515			0.0859159			0.0429580	−	0.999077i	$-0.486322\pi$
$857$	2.51515			0.0859159			0.0429580	+	0.999077i	$0.486322\pi$
$858$		0			0
$859$	6.70885			0.228903			0.114451	−	0.993429i	$-0.463489\pi$
$859$	6.70885			0.228903			0.114451	+	0.993429i	$0.463489\pi$
$860$	14.6828	+	10.6677i	0.500680	+	0.363765i
$861$		0			0
$862$	−13.9079	−	42.8041i	−0.473705	−	1.45791i
$863$	−2.67577	+	1.94406i	−0.0910844	+	0.0661767i	−0.632395	−	0.774646i	$-0.717928\pi$
$863$	−2.67577	+	1.94406i	−0.0910844	+	0.0661767i	0.541311	+	0.840822i	$0.317928\pi$
$864$		0			0
$865$	−6.29145	−	19.3631i	−0.213916	−	0.658365i
$866$	11.0065	−	33.8746i	0.374017	−	1.15111i
$867$		0			0
$868$	−1.72082			−0.0584086
$869$	−0.159299	−	33.6731i	−0.00540384	−	1.14228i
$870$		0			0
$871$	−2.56744	−	1.86535i	−0.0869942	−	0.0632050i
$872$	−8.48027	+	26.0996i	−0.287178	+	0.883844i
$873$		0			0
$874$	50.7669	−	36.8843i	1.71722	−	1.24763i
$875$	0.156567	−	0.113752i	0.00529292	−	0.00384553i
$876$		0			0
$877$	9.91956	−	30.5293i	0.334960	−	1.03090i	−0.631782	−	0.775146i	$-0.717676\pi$
$877$	9.91956	−	30.5293i	0.334960	−	1.03090i	0.966742	−	0.255754i	$-0.0823238\pi$
$878$	−70.8269	−	51.4587i	−2.39029	−	1.73665i
$879$		0			0
$880$	−4.71917	+	1.55807i	−0.159083	+	0.0525226i
$881$	35.2547			1.18776			0.593881	−	0.804553i	$-0.297595\pi$
$881$	35.2547			1.18776			0.593881	+	0.804553i	$0.297595\pi$
$882$		0			0
$883$	−0.140866	+	0.433541i	−0.00474052	+	0.0145898i	−0.953399	−	0.301713i	$-0.902442\pi$
$883$	−0.140866	+	0.433541i	−0.00474052	+	0.0145898i	0.948658	+	0.316303i	$0.102442\pi$
$884$	2.85746	+	8.79436i	0.0961068	+	0.295786i
$885$		0			0
$886$	−5.26090	+	3.82226i	−0.176743	+	0.128411i
$887$	0.556725	+	1.71342i	0.0186930	+	0.0575312i	0.959968	−	0.280110i	$-0.0903710\pi$
$887$	0.556725	+	1.71342i	0.0186930	+	0.0575312i	−0.941275	+	0.337641i	$0.890371\pi$
$888$		0			0
$889$	−1.11166	−	0.807666i	−0.0372838	−	0.0270882i
$890$	17.2970			0.579797
$891$		0			0
$892$	−19.0794			−0.638824
$893$	48.7203	+	35.3973i	1.63036	+	1.18453i
$894$		0			0
$895$	1.19008	+	3.66268i	0.0397799	+	0.122430i
$896$	3.19970	−	2.32471i	0.106894	−	0.0776633i
$897$		0			0
$898$	13.0055	+	40.0269i	0.434001	+	1.33572i
$899$	−7.83308	+	24.1077i	−0.261248	+	0.804038i
$900$		0			0
$901$	24.8541			0.828009
$902$	−61.6080	−	19.6959i	−2.05132	−	0.655803i
$903$		0			0
$904$	59.7092	+	43.3813i	1.98590	+	1.44284i
$905$	5.44337	−	16.7530i	0.180944	−	0.556887i
$906$		0			0
$907$	28.5962	−	20.7764i	0.949522	−	0.689868i	−0.00117159	−	0.999999i	$-0.500373\pi$
$907$	28.5962	−	20.7764i	0.949522	−	0.689868i	0.950694	+	0.310131i	$0.100373\pi$
$908$	−62.4605	+	45.3802i	−2.07282	+	1.50600i
$909$		0			0
$910$	−0.137173	+	0.422175i	−0.00454724	+	0.0139950i
$911$	−1.33388	−	0.969123i	−0.0441935	−	0.0321085i	0.565469	−	0.824769i	$-0.308695\pi$
$911$	−1.33388	−	0.969123i	−0.0441935	−	0.0321085i	−0.609663	+	0.792661i	$0.708695\pi$
$912$		0			0
$913$	26.2682	+	8.39789i	0.869352	+	0.277930i
$914$	−49.8511			−1.64893
$915$		0			0
$916$	2.92918	−	9.01510i	0.0967829	−	0.297867i
$917$	0.149522	+	0.460182i	0.00493765	+	0.0151965i
$918$		0			0
$919$	0.258068	−	0.187498i	0.00851288	−	0.00618497i	−0.583521	−	0.812098i	$-0.698325\pi$
$919$	0.258068	−	0.187498i	0.00851288	−	0.00618497i	0.592034	+	0.805913i	$0.298325\pi$
$920$	−5.41356	−	16.6612i	−0.178480	−	0.549304i
$921$		0			0
$922$	−65.4590	−	47.5588i	−2.15578	−	1.56626i
$923$	−5.83327			−0.192005
$924$		0			0
$925$	5.71217			0.187815
$926$	−19.9185	−	14.4716i	−0.654561	−	0.475567i
$927$		0			0
$928$	−11.7841	−	36.2678i	−0.386832	−	1.19055i
$929$	45.4270	−	33.0046i	1.49041	−	1.08285i	0.516400	−	0.856347i	$-0.327272\pi$
$929$	45.4270	−	33.0046i	1.49041	−	1.08285i	0.974011	−	0.226500i	$-0.0727283\pi$
$930$		0			0
$931$	11.9394	+	36.7456i	0.391297	+	1.20429i
$932$	6.28115	−	19.3314i	0.205746	−	0.633221i
$933$		0			0
$934$	−69.8301			−2.28491
$935$	−8.42690	+	2.78221i	−0.275589	+	0.0909880i
$936$		0			0
$937$	−29.8061	−	21.6554i	−0.973724	−	0.707452i	−0.0174269	−	0.999848i	$-0.505547\pi$
$937$	−29.8061	−	21.6554i	−0.973724	−	0.707452i	−0.956297	+	0.292396i	$0.905547\pi$
$938$	0.459148	−	1.41311i	0.0149917	−	0.0461397i
$939$		0			0
$940$	31.1609	−	22.6397i	1.01636	−	0.738426i
$941$	−12.3865	+	8.99929i	−0.403787	+	0.293368i	−0.771082	−	0.636736i	$-0.780284\pi$
$941$	−12.3865	+	8.99929i	−0.403787	+	0.293368i	0.367295	+	0.930105i	$0.380284\pi$
$942$		0			0
$943$	12.2805	−	37.7956i	0.399909	−	1.23079i
$944$	−13.5991	−	9.88030i	−0.442612	−	0.321576i
$945$		0			0
$946$	−0.188998	−	39.9510i	−0.00614486	−	1.29892i
$947$	22.6654			0.736526			0.368263	−	0.929722i	$-0.379953\pi$
$947$	22.6654			0.736526			0.368263	+	0.929722i	$0.379953\pi$
$948$		0			0
$949$	0.994821	−	3.06174i	0.0322933	−	0.0993884i
$950$	−4.03950	−	12.4323i	−0.131059	−	0.403358i
$951$		0			0
$952$	−1.52884	+	1.11076i	−0.0495499	+	0.0360001i
$953$	−12.1544	−	37.4074i	−0.393719	−	1.21174i	−0.929955	−	0.367675i	$-0.880154\pi$
$953$	−12.1544	−	37.4074i	−0.393719	−	1.21174i	0.536235	−	0.844069i	$-0.319846\pi$
$954$		0			0
$955$	−0.337440	−	0.245165i	−0.0109193	−	0.00793334i
$956$	86.4870			2.79719
$957$		0			0
$958$	31.1388			1.00605
$959$	−2.39459	−	1.73977i	−0.0773254	−	0.0561802i
$960$		0			0
$961$	−7.63993	−	23.5133i	−0.246449	−	0.758493i
$962$	−10.5999	+	7.70130i	−0.341756	+	0.248300i
$963$		0			0
$964$	−18.3249	−	56.3984i	−0.590207	−	1.81647i
$965$	−3.61443	+	11.1241i	−0.116353	+	0.358096i
$966$		0			0
$967$	3.06103			0.0984360			0.0492180	−	0.998788i	$-0.484327\pi$
$967$	3.06103			0.0984360			0.0492180	+	0.998788i	$0.484327\pi$
$968$	32.6986	+	23.2875i	1.05097	+	0.748487i
$969$		0			0
$970$	−30.2110	−	21.9496i	−0.970016	−	0.704758i
$971$	−9.90043	+	30.4704i	−0.317720	+	0.977841i	0.656900	+	0.753977i	$0.271867\pi$
$971$	−9.90043	+	30.4704i	−0.317720	+	0.977841i	−0.974620	+	0.223864i	$0.928133\pi$
$972$		0			0
$973$	3.07788	−	2.23621i	0.0986724	−	0.0716897i
$974$	80.9911	−	58.8434i	2.59512	−	1.88547i
$975$		0			0
$976$	0.558436	−	1.71869i	0.0178751	−	0.0550139i
$977$	−43.0366	−	31.2679i	−1.37686	−	1.00035i	−0.997166	−	0.0752388i	$-0.976028\pi$
$977$	−43.0366	−	31.2679i	−1.37686	−	1.00035i	−0.379697	−	0.925111i	$-0.623972\pi$
$978$		0			0
$979$	−14.4074	−	19.6340i	−0.460462	−	0.627507i
$980$	24.7115			0.789379
$981$		0			0
$982$	11.4619	−	35.2762i	0.365765	−	1.12571i
$983$	7.57104	+	23.3013i	0.241479	+	0.743195i	0.996196	+	0.0871446i	$0.0277742\pi$
$983$	7.57104	+	23.3013i	0.241479	+	0.743195i	−0.754717	+	0.656051i	$0.772226\pi$
$984$		0			0
$985$	−17.4714	+	12.6937i	−0.556685	+	0.404456i
$986$	19.7071	+	60.6521i	0.627601	+	1.93156i
$987$		0			0
$988$	15.5149	+	11.2722i	0.493593	+	0.358616i
$989$	24.5470			0.780549
$990$		0			0
$991$	−6.34819			−0.201657			−0.100828	−	0.994904i	$-0.532149\pi$
$991$	−6.34819			−0.201657			−0.100828	+	0.994904i	$0.532149\pi$
$992$	−7.63924	−	5.55023i	−0.242546	−	0.176220i
$993$		0			0
$994$	−0.843962	−	2.59745i	−0.0267689	−	0.0823861i
$995$	6.27820	−	4.56138i	0.199032	−	0.144605i
$996$		0			0
$997$	−8.01777	−	24.6761i	−0.253925	−	0.781501i	−0.994040	−	0.109020i	$-0.965229\pi$
$997$	−8.01777	−	24.6761i	−0.253925	−	0.781501i	0.740114	−	0.672481i	$-0.234771\pi$
$998$	−24.4064	+	75.1152i	−0.772572	+	2.37773i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.a.136.1		8
3.2	odd	2		165.2.m.d.136.2	yes	8
11.3	even	5	inner	495.2.n.a.91.1		8
11.5	even	5		5445.2.a.bt.1.4		4
11.6	odd	10		5445.2.a.bf.1.1		4
15.2	even	4		825.2.bx.f.499.1		16
15.8	even	4		825.2.bx.f.499.4		16
15.14	odd	2		825.2.n.g.301.1		8
33.5	odd	10		1815.2.a.p.1.1		4
33.14	odd	10		165.2.m.d.91.2	✓	8
33.17	even	10		1815.2.a.w.1.4		4
165.14	odd	10		825.2.n.g.751.1		8
165.47	even	20		825.2.bx.f.124.4		16
165.104	odd	10		9075.2.a.di.1.4		4
165.113	even	20		825.2.bx.f.124.1		16
165.149	even	10		9075.2.a.cm.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.d.91.2	✓	8	33.14	odd	10
165.2.m.d.136.2	yes	8	3.2	odd	2
495.2.n.a.91.1		8	11.3	even	5	inner
495.2.n.a.136.1		8	1.1	even	1	trivial
825.2.n.g.301.1		8	15.14	odd	2
825.2.n.g.751.1		8	165.14	odd	10
825.2.bx.f.124.1		16	165.113	even	20
825.2.bx.f.124.4		16	165.47	even	20
825.2.bx.f.499.1		16	15.2	even	4
825.2.bx.f.499.4		16	15.8	even	4
1815.2.a.p.1.1		4	33.5	odd	10
1815.2.a.w.1.4		4	33.17	even	10
5445.2.a.bf.1.1		4	11.6	odd	10
5445.2.a.bt.1.4		4	11.5	even	5
9075.2.a.cm.1.1		4	165.149	even	10
9075.2.a.di.1.4		4	165.104	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)

\(f(q)\)	\(=\)	\(q+(-1.90578 - 1.38463i) q^{2} +(1.09676 + 3.37549i) q^{4} +(0.809017 - 0.587785i) q^{5} +(0.0598032 + 0.184055i) q^{7} +(1.12773 - 3.47080i) q^{8} +O(q^{10})\)	\(q+(-1.90578 - 1.38463i) q^{2} +(1.09676 + 3.37549i) q^{4} +(0.809017 - 0.587785i) q^{5} +(0.0598032 + 0.184055i) q^{7} +(1.12773 - 3.47080i) q^{8} -2.35567 q^{10} +(1.96213 + 2.67395i) q^{11} +(-0.787747 - 0.572331i) q^{13} +(0.140877 - 0.433574i) q^{14} +(-1.21225 + 0.880754i) q^{16} +(-2.16469 + 1.57274i) q^{17} +(-1.71480 + 5.27760i) q^{19} +(2.87136 + 2.08617i) q^{20} +(-0.0369604 - 7.81280i) q^{22} +4.80040 q^{23} +(0.309017 - 0.951057i) q^{25} +(0.708805 + 2.18148i) q^{26} +(-0.555687 + 0.403730i) q^{28} +(3.12657 + 9.62260i) q^{29} +(2.02685 + 1.47259i) q^{31} -3.76902 q^{32} +6.30309 q^{34} +(0.156567 + 0.113752i) q^{35} +(1.76516 + 5.43260i) q^{37} +(10.5756 - 7.68359i) q^{38} +(-1.12773 - 3.47080i) q^{40} +(2.55823 - 7.87342i) q^{41} +5.11353 q^{43} +(-6.87391 + 9.55586i) q^{44} +(-9.14851 - 6.64678i) q^{46} +(3.35354 - 10.3211i) q^{47} +(5.63282 - 4.09248i) q^{49} +(-1.90578 + 1.38463i) q^{50} +(1.06793 - 3.28674i) q^{52} +(-7.51479 - 5.45981i) q^{53} +(3.15911 + 1.00996i) q^{55} +0.706260 q^{56} +(7.36518 - 22.6677i) q^{58} +(3.46656 + 10.6690i) q^{59} +(-0.975693 + 0.708883i) q^{61} +(-1.82374 - 5.61288i) q^{62} +(9.60743 + 6.98021i) q^{64} -0.973708 q^{65} +3.25922 q^{67} +(-7.68293 - 5.58197i) q^{68} +(-0.140877 - 0.433574i) q^{70} +(4.84664 - 3.52129i) q^{71} +(1.02168 + 3.14442i) q^{73} +(4.15814 - 12.7974i) q^{74} -19.6952 q^{76} +(-0.374813 + 0.521052i) q^{77} +(-8.21389 - 5.96774i) q^{79} +(-0.463040 + 1.42509i) q^{80} +(-15.7772 + 11.4628i) q^{82} +(6.72704 - 4.88748i) q^{83} +(-0.826838 + 2.54475i) q^{85} +(-9.74527 - 7.08035i) q^{86} +(11.4935 - 3.79468i) q^{88} -7.34270 q^{89} +(0.0582308 - 0.179216i) q^{91} +(5.26490 + 16.2037i) q^{92} +(-20.6821 + 15.0264i) q^{94} +(1.71480 + 5.27760i) q^{95} +(12.8248 + 9.31774i) q^{97} -16.4015 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 2 q^{4} + 2 q^{5} + 3 q^{7} + q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 + 2 * q^4 + 2 * q^5 + 3 * q^7 + q^8	\( 8 q - 4 q^{2} + 2 q^{4} + 2 q^{5} + 3 q^{7} + q^{8} - 6 q^{10} - 3 q^{11} - 4 q^{13} + 4 q^{14} - 12 q^{16} + 2 q^{19} + 3 q^{20} + 9 q^{22} + 6 q^{23} - 2 q^{25} - 2 q^{26} - 11 q^{28} - 10 q^{29} + 19 q^{31} - 12 q^{32} - 6 q^{34} - 3 q^{35} - q^{37} + 20 q^{38} - q^{40} + 9 q^{41} - 17 q^{44} - 22 q^{46} + 19 q^{47} + q^{49} - 4 q^{50} - 2 q^{52} - 25 q^{53} + 3 q^{55} + 16 q^{56} - 12 q^{58} - 13 q^{59} + 13 q^{61} - 35 q^{62} + 39 q^{64} + 14 q^{65} + 2 q^{67} - 19 q^{68} - 4 q^{70} + 11 q^{71} - 7 q^{73} + 43 q^{74} - 38 q^{76} + 7 q^{77} - 22 q^{79} - 13 q^{80} - 35 q^{82} + 21 q^{83} + 10 q^{85} - 20 q^{86} + 59 q^{88} + 20 q^{89} - 11 q^{91} + 28 q^{92} - 35 q^{94} - 2 q^{95} + 31 q^{97} - 22 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 + 2 * q^4 + 2 * q^5 + 3 * q^7 + q^8 - 6 * q^10 - 3 * q^11 - 4 * q^13 + 4 * q^14 - 12 * q^16 + 2 * q^19 + 3 * q^20 + 9 * q^22 + 6 * q^23 - 2 * q^25 - 2 * q^26 - 11 * q^28 - 10 * q^29 + 19 * q^31 - 12 * q^32 - 6 * q^34 - 3 * q^35 - q^37 + 20 * q^38 - q^40 + 9 * q^41 - 17 * q^44 - 22 * q^46 + 19 * q^47 + q^49 - 4 * q^50 - 2 * q^52 - 25 * q^53 + 3 * q^55 + 16 * q^56 - 12 * q^58 - 13 * q^59 + 13 * q^61 - 35 * q^62 + 39 * q^64 + 14 * q^65 + 2 * q^67 - 19 * q^68 - 4 * q^70 + 11 * q^71 - 7 * q^73 + 43 * q^74 - 38 * q^76 + 7 * q^77 - 22 * q^79 - 13 * q^80 - 35 * q^82 + 21 * q^83 + 10 * q^85 - 20 * q^86 + 59 * q^88 + 20 * q^89 - 11 * q^91 + 28 * q^92 - 35 * q^94 - 2 * q^95 + 31 * q^97 - 22 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more