LMFDB - Embedded newform 616.2.bi.b.237.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [616,2,Mod(13,616)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(616, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 5, 1]))

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

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

chi := DirichletCharacter("616.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 616 = 2^{3} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	616.bi (of order $10$, 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:	$4.91878476451$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.37515625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - x^{6} + 3x^{5} - x^{4} + 6x^{3} - 4x^{2} - 8x + 16 $ x^8 - x^7 - x^6 + 3x^5 - x^4 + 6x^3 - 4x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{10}]$

Embedding invariants

Embedding label			237.1
Root			$-0.373058 - 1.36412i$ of defining polynomial
Character	$\chi$	$=$	616.237
Dual form			616.2.bi.b.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.373058 + 1.36412i) q^{2} +(-1.72166 - 1.01779i) q^{4} +(1.55513 + 2.14046i) q^{7} +(2.03067 - 1.96885i) q^{8} +(-0.927051 - 2.85317i) q^{9} +O(q^{10})$	\(q+(-0.373058 + 1.36412i) q^{2} +(-1.72166 - 1.01779i) q^{4} +(1.55513 + 2.14046i) q^{7} +(2.03067 - 1.96885i) q^{8} +(-0.927051 - 2.85317i) q^{9} +(1.89823 + 2.71970i) q^{11} +(-3.50000 + 1.32288i) q^{14} +(1.92819 + 3.50458i) q^{16} +(4.23791 - 0.200212i) q^{18} +(-4.41814 + 1.57480i) q^{22} +9.58240 q^{23} +(4.04508 + 2.93893i) q^{25} +(-0.498859 - 5.26794i) q^{28} +(-8.64279 + 6.27935i) q^{29} +(-5.50000 + 1.32288i) q^{32} +(-1.30788 + 5.85572i) q^{36} +(7.10547 + 9.77984i) q^{37} -8.74072 q^{43} +(-0.500000 - 6.61438i) q^{44} +(-3.57480 + 13.0716i) q^{46} +(-2.16312 + 6.65740i) q^{49} +(-5.51811 + 4.42160i) q^{50} +(5.93482 - 1.92834i) q^{53} +(7.37221 + 1.28474i) q^{56} +(-5.34154 - 14.1324i) q^{58} +(4.66540 - 6.42137i) q^{63} +(0.247258 - 7.99618i) q^{64} -1.10127i q^{67} +(3.08300 - 9.48849i) q^{71} +(-7.50000 - 3.96863i) q^{72} +(-15.9916 + 6.04427i) q^{74} +(-2.86940 + 8.29256i) q^{77} +(11.9015 - 3.86702i) q^{79} +(-7.28115 + 5.29007i) q^{81} +(3.26080 - 11.9234i) q^{86} +(9.20934 + 1.78549i) q^{88} +(-16.4976 - 9.75291i) q^{92} +(-8.27453 - 5.43435i) q^{98} +(6.00000 - 7.93725i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 3 q^{4} - 5 q^{8} + 6 q^{9}+O(q^{10}) $ 8 * q + q^2 + 3 * q^4 - 5 * q^8 + 6 * q^9	$ 8 q + q^{2} + 3 q^{4} - 5 q^{8} + 6 q^{9} + 4 q^{11} - 28 q^{14} - q^{16} - 3 q^{18} - 9 q^{22} + 16 q^{23} + 10 q^{25} - 7 q^{28} - 4 q^{29} - 44 q^{32} - 9 q^{36} + 30 q^{37} + 24 q^{43} - 4 q^{44} - 23 q^{46} + 14 q^{49} - 5 q^{50} + 50 q^{53} - 7 q^{56} + 2 q^{58} - 9 q^{64} + 48 q^{71} - 60 q^{72} - 28 q^{74} - 14 q^{77} + 40 q^{79} - 18 q^{81} - 12 q^{86} + 17 q^{88} - 24 q^{92} - 7 q^{98} + 48 q^{99}+O(q^{100}) $ 8 * q + q^2 + 3 * q^4 - 5 * q^8 + 6 * q^9 + 4 * q^11 - 28 * q^14 - q^16 - 3 * q^18 - 9 * q^22 + 16 * q^23 + 10 * q^25 - 7 * q^28 - 4 * q^29 - 44 * q^32 - 9 * q^36 + 30 * q^37 + 24 * q^43 - 4 * q^44 - 23 * q^46 + 14 * q^49 - 5 * q^50 + 50 * q^53 - 7 * q^56 + 2 * q^58 - 9 * q^64 + 48 * q^71 - 60 * q^72 - 28 * q^74 - 14 * q^77 + 40 * q^79 - 18 * q^81 - 12 * q^86 + 17 * q^88 - 24 * q^92 - 7 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/616\mathbb{Z}\right)^\times$.

$n$	$57$	$309$	$353$	$463$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$	$-1$	$1$

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 $

$2$	−0.373058	+	1.36412i	−0.263792	+	0.964580i
$2$	−0.373058	+	1.36412i	−0.263792	+	0.964580i
$3$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$3$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$4$	−1.72166	−	1.01779i	−0.860828	−	0.508897i
$5$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$5$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$6$		0			0
$7$	1.55513	+	2.14046i	0.587785	+	0.809017i
$7$	1.55513	+	2.14046i	0.587785	+	0.809017i
$8$	2.03067	−	1.96885i	0.717951	−	0.696094i
$9$	−0.927051	−	2.85317i	−0.309017	−	0.951057i
$10$		0			0
$11$	1.89823	+	2.71970i	0.572336	+	0.820019i
$11$	1.89823	+	2.71970i	0.572336	+	0.820019i
$12$		0			0
$13$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$13$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$14$	−3.50000	+	1.32288i	−0.935414	+	0.353553i
$15$		0			0
$16$	1.92819	+	3.50458i	0.482048	+	0.876145i
$17$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$17$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$18$	4.23791	−	0.200212i	0.998886	−	0.0471903i
$19$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$19$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$20$		0			0
$21$		0			0
$22$	−4.41814	+	1.57480i	−0.941951	+	0.335750i
$23$	9.58240			1.99807			0.999035	−	0.0439305i	$-0.0139880\pi$
$23$	9.58240			1.99807			0.999035	+	0.0439305i	$0.0139880\pi$
$24$		0			0
$25$	4.04508	+	2.93893i	0.809017	+	0.587785i
$26$		0			0
$27$		0			0
$28$	−0.498859	−	5.26794i	−0.0942755	−	0.995546i
$29$	−8.64279	+	6.27935i	−1.60492	+	1.16605i	−0.727793	+	0.685797i	$0.759454\pi$
$29$	−8.64279	+	6.27935i	−1.60492	+	1.16605i	−0.877132	+	0.480249i	$0.840546\pi$
$30$		0			0
$31$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$31$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$32$	−5.50000	+	1.32288i	−0.972272	+	0.233854i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−1.30788	+	5.85572i	−0.217979	+	0.975953i
$37$	7.10547	+	9.77984i	1.16813	+	1.60780i	0.674935	+	0.737878i	$0.264172\pi$
$37$	7.10547	+	9.77984i	1.16813	+	1.60780i	0.493197	+	0.869918i	$0.335828\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$41$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$42$		0			0
$43$	−8.74072			−1.33295			−0.666474	−	0.745528i	$-0.732197\pi$
$43$	−8.74072			−1.33295			−0.666474	+	0.745528i	$0.732197\pi$
$44$	−0.500000	−	6.61438i	−0.0753778	−	0.997155i
$45$		0			0
$46$	−3.57480	+	13.0716i	−0.527075	+	1.92730i
$47$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$47$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$48$		0			0
$49$	−2.16312	+	6.65740i	−0.309017	+	0.951057i
$50$	−5.51811	+	4.42160i	−0.780378	+	0.625308i
$51$		0			0
$52$		0			0
$53$	5.93482	−	1.92834i	0.815210	−	0.264878i	0.128407	−	0.991722i	$-0.459014\pi$
$53$	5.93482	−	1.92834i	0.815210	−	0.264878i	0.686803	+	0.726844i	$0.259014\pi$
$54$		0			0
$55$		0			0
$56$	7.37221	+	1.28474i	0.985153	+	0.171681i
$57$		0			0
$58$	−5.34154	−	14.1324i	−0.701378	−	1.85567i
$59$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$59$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$60$		0			0
$61$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$61$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$62$		0			0
$63$	4.66540	−	6.42137i	0.587785	−	0.809017i
$64$	0.247258	−	7.99618i	0.0309072	−	0.999522i
$65$		0			0
$66$		0			0
$67$		−	1.10127i		−	0.134541i	−0.997735	−	0.0672706i	$-0.978571\pi$
$67$		−	1.10127i		−	0.134541i	0.997735	−	0.0672706i	$-0.0214291\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.08300	−	9.48849i	0.365885	−	1.12608i	−0.583541	−	0.812084i	$-0.698333\pi$
$71$	3.08300	−	9.48849i	0.365885	−	1.12608i	0.949425	−	0.313993i	$-0.101667\pi$
$72$	−7.50000	−	3.96863i	−0.883883	−	0.467707i
$73$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$73$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$74$	−15.9916	+	6.04427i	−1.85899	+	0.702632i
$75$		0			0
$76$		0			0
$77$	−2.86940	+	8.29256i	−0.326998	+	0.945025i
$78$		0			0
$79$	11.9015	−	3.86702i	1.33902	−	0.435074i	0.450035	−	0.893011i	$-0.351411\pi$
$79$	11.9015	−	3.86702i	1.33902	−	0.435074i	0.888985	+	0.457937i	$0.151411\pi$
$80$		0			0
$81$	−7.28115	+	5.29007i	−0.809017	+	0.587785i
$82$		0			0
$83$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$83$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$84$		0			0
$85$		0			0
$86$	3.26080	−	11.9234i	0.351621	−	1.28573i
$87$		0			0
$88$	9.20934	+	1.78549i	0.981719	+	0.190334i
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$		0			0
$91$		0			0
$92$	−16.4976	−	9.75291i	−1.71999	−	1.01681i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$97$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$98$	−8.27453	−	5.43435i	−0.835853	−	0.548953i
$99$	6.00000	−	7.93725i	0.603023	−	0.797724i
$100$	−3.97302	−	9.17688i	−0.397302	−	0.917688i
$101$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$101$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$102$		0			0
$103$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$103$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$104$		0			0
$105$		0			0
$106$	0.416456	+	8.81520i	0.0404498	+	0.856207i
$107$	−10.5739	−	7.68240i	−1.02222	−	0.742685i	−0.0554821	−	0.998460i	$-0.517670\pi$
$107$	−10.5739	−	7.68240i	−1.02222	−	0.742685i	−0.966736	+	0.255774i	$0.917670\pi$
$108$		0			0
$109$	8.34177			0.798997			0.399498	−	0.916734i	$-0.369184\pi$
$109$	8.34177			0.798997			0.399498	+	0.916734i	$0.369184\pi$
$110$		0			0
$111$		0			0
$112$	−4.50281	+	9.57730i	−0.425475	+	0.904970i
$113$	−15.7856	−	11.4689i	−1.48498	−	1.07890i	−0.975909	−	0.218179i	$-0.929988\pi$
$113$	−15.7856	−	11.4689i	−1.48498	−	1.07890i	−0.509073	−	0.860724i	$-0.670012\pi$
$114$		0			0
$115$		0			0
$116$	21.2710	−	2.01430i	1.97496	−	0.187023i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−3.79348	+	10.3252i	−0.344862	+	0.938653i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	7.01907	+	8.75972i	0.625308	+	0.780378i
$127$	21.1584	+	6.87480i	1.87751	+	0.610040i	0.988297	+	0.152545i	$0.0487468\pi$
$127$	21.1584	+	6.87480i	1.87751	+	0.610040i	0.889212	+	0.457495i	$0.151253\pi$
$128$	10.8155	+	3.32033i	0.955966	+	0.293478i
$129$		0			0
$130$		0			0
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$		0			0
$133$		0			0
$134$	1.50226	+	0.410837i	0.129776	+	0.0354909i
$135$		0			0
$136$		0			0
$137$	6.34450	−	19.5264i	0.542047	−	1.66825i	−0.185861	−	0.982576i	$-0.559507\pi$
$137$	6.34450	−	19.5264i	0.542047	−	1.66825i	0.727909	−	0.685674i	$-0.240493\pi$
$138$		0			0
$139$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$139$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$140$		0			0
$141$		0			0
$142$	11.7933	+	7.74534i	0.989673	+	0.649975i
$143$		0			0
$144$	8.21163	−	8.75038i	0.684302	−	0.729199i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−2.27931	−	24.0694i	−0.187358	−	1.97849i
$149$	6.79837	−	20.9232i	0.556944	−	1.71410i	−0.133808	−	0.991007i	$-0.542720\pi$
$149$	6.79837	−	20.9232i	0.556944	−	1.71410i	0.690752	−	0.723092i	$-0.257280\pi$
$150$		0			0
$151$	−5.77554	+	7.94934i	−0.470007	+	0.646909i	−0.976546	−	0.215308i	$-0.930924\pi$
$151$	−5.77554	+	7.94934i	−0.470007	+	0.646909i	0.506540	+	0.862217i	$0.330924\pi$
$152$		0			0
$153$		0			0
$154$	−10.2416	−	7.00782i	−0.825292	−	0.564706i
$155$		0			0
$156$		0			0
$157$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$157$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$158$	0.835146	+	17.6777i	0.0664406	+	1.40636i
$159$		0			0
$160$		0			0
$161$	14.9019	+	20.5107i	1.17444	+	1.61647i
$162$	−4.50000	−	11.9059i	−0.353553	−	0.935414i
$163$	23.3945	−	7.60134i	1.83240	−	0.595383i	0.833307	−	0.552811i	$-0.186445\pi$
$163$	23.3945	−	7.60134i	1.83240	−	0.595383i	0.999093	−	0.0425718i	$-0.0135551\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$167$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$168$		0			0
$169$	−10.5172	+	7.64121i	−0.809017	+	0.587785i
$170$		0			0
$171$		0			0
$172$	15.0485	+	8.89625i	1.14744	+	0.678333i
$173$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$173$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$174$		0			0
$175$			13.2288i			1.00000i
$176$	−5.87125	+	11.8966i	−0.442562	+	0.896738i
$177$		0			0
$178$		0			0
$179$	13.9633	−	19.2188i	1.04366	−	1.43648i	0.149487	−	0.988764i	$-0.452238\pi$
$179$	13.9633	−	19.2188i	1.04366	−	1.43648i	0.894176	−	0.447715i	$-0.147762\pi$
$180$		0			0
$181$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$181$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$182$		0			0
$183$		0			0
$184$	19.4587	−	18.8663i	1.43452	−	1.39084i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−18.3570	+	13.3371i	−1.32826	+	0.965040i	−0.328474	+	0.944513i	$0.606534\pi$
$191$	−18.3570	+	13.3371i	−1.32826	+	0.965040i	−0.999789	+	0.0205267i	$0.993466\pi$
$192$		0			0
$193$	−22.5017	−	7.31124i	−1.61971	−	0.526275i	−0.647834	−	0.761781i	$-0.724325\pi$
$193$	−22.5017	−	7.31124i	−1.61971	−	0.526275i	−0.971873	+	0.235507i	$0.924325\pi$
$194$		0			0
$195$		0			0
$196$	10.5000	−	9.26013i	0.750000	−	0.661438i
$197$	−27.2550			−1.94184			−0.970918	−	0.239411i	$-0.923046\pi$
$197$	−27.2550			−1.94184			−0.970918	+	0.239411i	$0.923046\pi$
$198$	8.58903	+	11.1458i	0.610396	+	0.792097i
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	14.0005	−	1.99617i	0.989988	−	0.141151i
$201$		0			0
$202$		0			0
$203$	−26.8814	−	8.73429i	−1.88670	−	0.613027i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−8.88338	−	27.3402i	−0.617437	−	1.90028i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−1.80563	−	5.55715i	−0.124304	−	0.382570i	0.869469	−	0.493987i	$-0.164461\pi$
$211$	−1.80563	−	5.55715i	−0.124304	−	0.382570i	−0.993774	+	0.111417i	$0.964461\pi$
$212$	−12.1804	−	2.72049i	−0.836551	−	0.186844i
$213$		0			0
$214$	14.4244	−	11.5581i	0.986032	−	0.790097i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−3.11197	+	11.3792i	−0.210769	+	0.770696i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$223$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$224$	−11.3848	−	9.71527i	−0.760679	−	0.649129i
$225$	4.63525	−	14.2658i	0.309017	−	0.951057i
$226$	21.5339	−	17.2549i	1.43241	−	1.14778i
$227$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$227$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$228$		0			0
$229$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$229$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$230$		0			0
$231$		0			0
$232$	−5.18756	+	29.7677i	−0.340580	+	1.95434i
$233$	−20.1301	+	6.54066i	−1.31876	+	0.428493i	−0.882071	−	0.471117i	$-0.843851\pi$
$233$	−20.1301	+	6.54066i	−1.31876	+	0.428493i	−0.436694	+	0.899610i	$0.643851\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−4.13864	+	5.69636i	−0.267707	+	0.368467i	−0.921614	−	0.388108i	$-0.873129\pi$
$239$	−4.13864	+	5.69636i	−0.267707	+	0.368467i	0.653907	+	0.756575i	$0.273129\pi$
$240$		0			0
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$	−12.6696	−	9.02667i	−0.814434	−	0.580256i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$251$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$252$	−14.5678	+	6.30697i	−0.917688	+	0.397302i
$253$	18.1896	+	26.0612i	1.14357	+	1.63845i
$254$	−17.2714	+	26.2980i	−1.08370	+	1.65008i
$255$		0			0
$256$	−8.56415	+	13.5150i	−0.535259	+	0.844688i
$257$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$257$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$258$		0			0
$259$	−9.88338	+	30.4179i	−0.614123	+	1.89008i
$260$		0			0
$261$	25.9284	+	18.8381i	1.60492	+	1.16605i
$262$		0			0
$263$		−	32.0690i		−	1.97746i	−0.149718	−	0.988729i	$-0.547836\pi$
$263$		−	32.0690i		−	1.97746i	0.149718	−	0.988729i	$-0.452164\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−1.12086	+	1.89600i	−0.0684676	+	0.115817i
$269$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$269$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$270$		0			0
$271$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$271$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$272$		0			0
$273$		0			0
$274$	24.2695	+	15.9391i	1.46617	+	0.962919i
$275$	−0.314502	+	16.5801i	−0.0189652	+	0.999820i
$276$		0			0
$277$	−3.26675	−	10.0540i	−0.196280	−	0.604088i	−0.999959	−	0.00902525i	$-0.997127\pi$
$277$	−3.26675	−	10.0540i	−0.196280	−	0.604088i	0.803679	−	0.595063i	$-0.202873\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−17.2967	−	5.62003i	−1.03183	−	0.335263i	−0.256319	−	0.966592i	$-0.582510\pi$
$281$	−17.2967	−	5.62003i	−1.03183	−	0.335263i	−0.775515	+	0.631329i	$0.782510\pi$
$282$		0			0
$283$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$283$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$284$	−14.9652	+	13.1981i	−0.888020	+	0.783160i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	8.87317	+	14.4661i	0.522856	+	0.852421i
$289$	13.7533	+	9.99235i	0.809017	+	0.587785i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$293$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$294$		0			0
$295$		0			0
$296$	33.6839	+	5.87004i	1.95784	+	0.341189i
$297$		0			0
$298$	26.0057	+	17.0794i	1.50647	+	0.989383i
$299$		0			0
$300$		0			0
$301$	−13.5930	−	18.7091i	−0.783487	−	1.07838i
$302$	−8.68926	−	10.8441i	−0.500011	−	0.624008i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$	13.3802	−	11.3565i	0.762409	−	0.647095i
$309$		0			0
$310$		0			0
$311$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$311$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$312$		0			0
$313$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$313$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$314$		0			0
$315$		0			0
$316$	−24.4261	−	5.45556i	−1.37407	−	0.306899i
$317$	−33.8636	+	11.0029i	−1.90197	+	0.617986i	−0.947152	+	0.320786i	$0.896053\pi$
$317$	−33.8636	+	11.0029i	−1.90197	+	0.617986i	−0.954815	+	0.297200i	$0.903947\pi$
$318$		0			0
$319$	−33.4839	−	11.5861i	−1.87474	−	0.648698i
$320$		0			0
$321$		0			0
$322$	−33.5384	+	12.6763i	−1.86902	+	0.706424i
$323$		0			0
$324$	17.9198	−	1.69696i	0.995546	−	0.0942755i
$325$		0			0
$326$	1.64163	+	34.7487i	0.0909216	+	1.92455i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		−	25.4412i		−	1.39837i	−0.714939	−	0.699187i	$-0.753545\pi$
$331$		−	25.4412i		−	1.39837i	0.714939	−	0.699187i	$-0.246455\pi$
$332$		0			0
$333$	21.3164	−	29.3395i	1.16813	−	1.60780i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.299709	−	0.412514i	−0.0163262	−	0.0224711i	0.800776	−	0.598964i	$-0.204421\pi$
$337$	−0.299709	−	0.412514i	−0.0163262	−	0.0224711i	−0.817102	+	0.576493i	$0.804421\pi$
$338$	−6.50000	−	17.1974i	−0.353553	−	0.935414i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−17.6138	+	5.72307i	−0.951057	+	0.309017i
$344$	−17.7495	+	17.2092i	−0.956991	+	0.927856i
$345$		0			0
$346$		0			0
$347$	−10.5040	+	32.3279i	−0.563883	+	1.73545i	0.107366	+	0.994220i	$0.465758\pi$
$347$	−10.5040	+	32.3279i	−0.563883	+	1.73545i	−0.671248	+	0.741233i	$0.734242\pi$
$348$		0			0
$349$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$349$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$350$	−18.0456	−	4.93510i	−0.964580	−	0.263792i
$351$		0			0
$352$	−14.0381	−	12.4472i	−0.748231	−	0.663438i
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	21.0076	+	26.2173i	1.11029	+	1.38563i
$359$	20.3777	+	28.0476i	1.07550	+	1.48029i	0.864384	+	0.502832i	$0.167708\pi$
$359$	20.3777	+	28.0476i	1.07550	+	1.48029i	0.211112	+	0.977462i	$0.432292\pi$
$360$		0			0
$361$	5.87132	+	18.0701i	0.309017	+	0.951057i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$367$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$368$	18.4767	+	33.5823i	0.963165	+	1.75060i
$369$		0			0
$370$		0			0
$371$	13.3570	+	9.70440i	0.693459	+	0.503827i
$372$		0			0
$373$	−22.0000			−1.13912			−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000			−1.13912			−0.569558	+	0.821951i	$0.692886\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−21.7915	−	7.08050i	−1.11936	−	0.363701i	−0.309834	−	0.950791i	$-0.600274\pi$
$379$	−21.7915	−	7.08050i	−1.11936	−	0.363701i	−0.809522	+	0.587090i	$0.800274\pi$
$380$		0			0
$381$		0			0
$382$	−11.3452	−	30.0166i	−0.580472	−	1.53579i
$383$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$383$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$384$		0			0
$385$		0			0
$386$	18.3679	−	27.9675i	0.934900	−	1.42351i
$387$	8.10309	+	24.9388i	0.411903	+	1.26771i
$388$		0			0
$389$	8.09616	+	11.1434i	0.410492	+	0.564993i	0.963338	−	0.268290i	$-0.0864585\pi$
$389$	8.09616	+	11.1434i	0.410492	+	0.564993i	−0.552847	+	0.833283i	$0.686458\pi$
$390$		0			0
$391$		0			0
$392$	8.71483	+	17.7778i	0.440165	+	0.897917i
$393$		0			0
$394$	10.1677	−	37.1791i	0.512241	−	1.87306i
$395$		0			0
$396$	−18.4084	+	7.55845i	−0.925058	+	0.379826i
$397$		0			0			−	1.00000i	$-0.5\pi$
$397$		0			0				1.00000i	$0.5\pi$
$398$		0			0
$399$		0			0
$400$	−2.50000	+	19.8431i	−0.125000	+	0.992157i
$401$	4.65550	−	14.3282i	0.232484	−	0.715514i	−0.764961	−	0.644077i	$-0.777242\pi$
$401$	4.65550	−	14.3282i	0.232484	−	0.715514i	0.997445	−	0.0714367i	$-0.0227584\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	21.9429	−	33.4111i	1.08901	−	1.65816i
$407$	−13.1104	+	37.8890i	−0.649858	+	1.87809i
$408$		0			0
$409$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$409$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	40.6094	−	1.91851i	1.99584	−	0.0942895i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	6.11478	−	8.41627i	0.298016	−	0.410184i	−0.633581	−	0.773676i	$-0.718416\pi$
$421$	6.11478	−	8.41627i	0.298016	−	0.410184i	0.931597	+	0.363492i	$0.118416\pi$
$422$	8.25423	−	0.389954i	0.401810	−	0.0189827i
$423$		0			0
$424$	8.25506	−	15.6006i	0.400901	−	0.757632i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	10.3855	+	23.9885i	0.502004	+	1.15953i
$429$		0			0
$430$		0			0
$431$	−2.46842	+	0.802038i	−0.118900	+	0.0386328i	−0.367862	−	0.929880i	$-0.619910\pi$
$431$	−2.46842	+	0.802038i	−0.118900	+	0.0386328i	0.248963	+	0.968513i	$0.419910\pi$
$432$		0			0
$433$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$433$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$434$		0			0
$435$		0			0
$436$	−14.3617	−	8.49020i	−0.687798	−	0.406607i
$437$		0			0
$438$		0			0
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$		0			0
$441$	21.0000			1.00000
$442$		0			0
$443$	17.9082	−	24.6485i	0.850845	−	1.17109i	−0.132831	−	0.991139i	$-0.542407\pi$
$443$	17.9082	−	24.6485i	0.850845	−	1.17109i	0.983676	−	0.179949i	$-0.0575933\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	17.5000	−	11.9059i	0.826797	−	0.562500i
$449$	−7.18900	−	22.1255i	−0.339270	−	1.04417i	−0.964580	−	0.263790i	$-0.915028\pi$
$449$	−7.18900	−	22.1255i	−0.339270	−	1.04417i	0.625310	−	0.780376i	$-0.284972\pi$
$450$	17.7311	+	11.6450i	0.835853	+	0.548953i
$451$		0			0
$452$	15.5043	+	35.8119i	0.729263	+	1.68445i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	35.9252	+	11.6728i	1.68051	+	0.546031i	0.985011	−	0.172493i	$-0.0551823\pi$
$457$	35.9252	+	11.6728i	1.68051	+	0.546031i	0.695501	+	0.718525i	$0.255182\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$	2.73687			0.127193			0.0635967	−	0.997976i	$-0.479743\pi$
$463$	2.73687			0.127193			0.0635967	+	0.997976i	$0.479743\pi$
$464$	−38.6714	−	18.1815i	−1.79528	−	0.844056i
$465$		0			0
$466$	−1.41256	−	29.8999i	−0.0654356	−	1.38509i
$467$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$467$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$468$		0			0
$469$	2.35721	−	1.71262i	0.108846	−	0.0790813i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−16.5919	−	23.7721i	−0.762894	−	1.09304i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−11.0038	−	15.1454i	−0.503827	−	0.693459i
$478$	−6.22657	−	7.77069i	−0.284796	−	0.355423i
$479$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$479$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	17.0400	−	13.9154i	0.774545	−	0.632519i
$485$		0			0
$486$		0			0
$487$	−34.4997	−	25.0655i	−1.56333	−	1.13583i	−0.933210	−	0.359333i	$-0.883004\pi$
$487$	−34.4997	−	25.0655i	−1.56333	−	1.13583i	−0.630123	−	0.776495i	$-0.716996\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	35.5967	−	25.8626i	1.60646	−	1.16716i	0.733047	−	0.680178i	$-0.238097\pi$
$491$	35.5967	−	25.8626i	1.60646	−	1.16716i	0.873412	−	0.486983i	$-0.161903\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	25.1042	−	8.15685i	1.12608	−	0.365885i
$498$		0			0
$499$	15.3190	+	21.0848i	0.685772	+	0.943884i	0.999985	−	0.00546838i	$-0.00174065\pi$
$499$	15.3190	+	21.0848i	0.685772	+	0.943884i	−0.314213	+	0.949352i	$0.601741\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$503$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$504$	−3.16882	−	22.2252i	−0.141151	−	0.989988i
$505$		0			0
$506$	−42.3364	+	15.0904i	−1.88208	+	0.670851i
$507$		0			0
$508$	−29.4304	−	33.3710i	−1.30576	−	1.48060i
$509$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$509$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$510$		0			0
$511$		0			0
$512$	−15.2412	−	16.7244i	−0.673571	−	0.739122i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−37.8066	−	24.8298i	−1.66113	−	1.09096i
$519$		0			0
$520$		0			0
$521$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$521$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$522$	−35.3702	+	28.3417i	−1.54811	+	1.24048i
$523$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$523$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$524$		0			0
$525$		0			0
$526$	43.7460	+	11.9636i	1.90742	+	0.521638i
$527$		0			0
$528$		0			0
$529$	68.8225			2.99228
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−2.16823	−	2.23631i	−0.0936532	−	0.0965939i
$537$		0			0
$538$		0			0
$539$	−22.2122	+	6.75421i	−0.956746	+	0.290924i
$540$		0			0
$541$	−14.2668	−	43.9085i	−0.613376	−	1.88778i	−0.423238	−	0.906019i	$-0.639107\pi$
$541$	−14.2668	−	43.9085i	−0.613376	−	1.88778i	−0.190138	−	0.981757i	$-0.560893\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	35.5967	+	25.8626i	1.52201	+	1.10580i	0.960482	+	0.278343i	$0.0897853\pi$
$547$	35.5967	+	25.8626i	1.52201	+	1.10580i	0.561525	+	0.827460i	$0.310215\pi$
$548$	−30.7969	+	27.1603i	−1.31558	+	1.16023i
$549$		0			0
$550$	−22.5000	−	6.61438i	−0.959403	−	0.282038i
$551$		0			0
$552$		0			0
$553$	26.7856	+	19.4609i	1.13904	+	0.827560i
$554$	14.9336	−	0.705508i	0.634468	−	0.0299742i
$555$		0			0
$556$		0			0
$557$	19.6428	−	14.2713i	0.832292	−	0.604695i	−0.0879152	−	0.996128i	$-0.528020\pi$
$557$	19.6428	−	14.2713i	0.832292	−	0.604695i	0.920207	+	0.391433i	$0.128020\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	14.1191	−	21.4982i	0.595578	−	0.906846i
$563$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$563$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−22.6463	−	7.35824i	−0.951057	−	0.309017i
$568$	−12.4209	−	25.3380i	−0.521168	−	1.06316i
$569$	24.8821	−	34.2473i	1.04311	−	1.43572i	0.148483	−	0.988915i	$-0.452561\pi$
$569$	24.8821	−	34.2473i	1.04311	−	1.43572i	0.894630	−	0.446808i	$-0.147439\pi$
$570$		0			0
$571$	−24.7563			−1.03602			−0.518010	−	0.855374i	$-0.673327\pi$
$571$	−24.7563			−1.03602			−0.518010	+	0.855374i	$0.673327\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	38.7616	+	28.1620i	1.61647	+	1.17444i
$576$	−23.0437	+	6.70740i	−0.960153	+	0.279475i
$577$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$577$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$578$	−18.7616	+	15.0334i	−0.780378	+	0.625308i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	16.5101	+	12.4805i	0.683779	+	0.516888i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$587$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−20.5735	+	43.7591i	−0.845566	+	1.79849i
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$		0			0
$595$		0			0
$596$	−33.0000	+	29.1033i	−1.35173	+	1.19212i
$597$		0			0
$598$		0			0
$599$	−1.27212	+	3.91519i	−0.0519775	+	0.159970i	−0.973676	−	0.227937i	$-0.926802\pi$
$599$	−1.27212	+	3.91519i	−0.0519775	+	0.159970i	0.921698	+	0.387907i	$0.126802\pi$
$600$		0			0
$601$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$601$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$602$	30.5925	−	11.5629i	1.24686	−	0.471268i
$603$	−3.14210	+	1.02093i	−0.127956	+	0.0415755i
$604$	18.0343	−	7.80772i	0.733804	−	0.317692i
$605$		0			0
$606$		0			0
$607$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$607$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−14.9284	−	10.8461i	−0.602951	−	0.438069i	0.243974	−	0.969782i	$-0.421549\pi$
$613$	−14.9284	−	10.8461i	−0.602951	−	0.438069i	−0.846925	+	0.531712i	$0.821549\pi$
$614$		0			0
$615$		0			0
$616$	10.5000	+	22.4889i	0.423057	+	0.906103i
$617$	−32.2257			−1.29736			−0.648679	−	0.761062i	$-0.724678\pi$
$617$	−32.2257			−1.29736			−0.648679	+	0.761062i	$0.724678\pi$
$618$		0			0
$619$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$619$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	7.72542	+	23.7764i	0.309017	+	0.951057i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	12.1742	−	8.84507i	0.484647	−	0.352117i	−0.318475	−	0.947931i	$-0.603171\pi$
$631$	12.1742	−	8.84507i	0.484647	−	0.352117i	0.803122	+	0.595815i	$0.203171\pi$
$632$	16.5544	−	31.2849i	0.658498	−	1.24444i
$633$		0			0
$634$	−2.37626	−	50.2987i	−0.0943734	−	1.99762i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	28.2963	−	41.3538i	1.12026	−	1.63721i
$639$	−29.9304			−1.18403
$640$		0			0
$641$	−4.78557	−	3.47692i	−0.189019	−	0.137330i	0.489251	−	0.872143i	$-0.337270\pi$
$641$	−4.78557	−	3.47692i	−0.189019	−	0.137330i	−0.678270	+	0.734813i	$0.737270\pi$
$642$		0			0
$643$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$643$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$644$	−4.78027	−	50.4795i	−0.188369	−	1.98917i
$645$		0			0
$646$		0			0
$647$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$647$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$648$	−4.37028	+	25.0779i	−0.171681	+	0.985153i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−48.0139	−	10.7239i	−1.88037	−	0.419981i
$653$	22.3071	+	30.7031i	0.872944	+	1.20150i	0.978326	+	0.207072i	$0.0663936\pi$
$653$	22.3071	+	30.7031i	0.872944	+	1.20150i	−0.105382	+	0.994432i	$0.533606\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	44.0000			1.71400			0.856998	−	0.515319i	$-0.172327\pi$
$659$	44.0000			1.71400			0.856998	+	0.515319i	$0.172327\pi$
$660$		0			0
$661$		0			0			−	1.00000i	$-0.5\pi$
$661$		0			0				1.00000i	$0.5\pi$
$662$	34.7049	+	9.49105i	1.34884	+	0.368880i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	32.0704	+	40.0235i	1.24270	+	1.55088i
$667$	−82.8187	+	60.1713i	−3.20675	+	2.32984i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−14.6942	+	4.77443i	−0.566419	+	0.184041i	−0.578208	−	0.815890i	$-0.696248\pi$
$673$	−14.6942	+	4.77443i	−0.566419	+	0.184041i	0.0117883	+	0.999931i	$0.496248\pi$
$674$	0.674528	−	0.254948i	0.0259819	−	0.00982022i
$675$		0			0
$676$	25.8842	−	2.45116i	0.995546	−	0.0942755i
$677$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$677$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	26.2839i		−	1.00573i	−0.864366	−	0.502863i	$-0.832280\pi$
$683$		−	26.2839i		−	1.00573i	0.864366	−	0.502863i	$-0.167720\pi$
$684$		0			0
$685$		0			0
$686$	−1.23599	−	26.1624i	−0.0471903	−	0.998886i
$687$		0			0
$688$	−16.8538	−	30.6326i	−0.642545	−	1.16786i
$689$		0			0
$690$		0			0
$691$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$691$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$692$		0			0
$693$	26.3202	+	0.499256i	0.999820	+	0.0189652i
$694$	−40.1806	−	26.3889i	−1.52523	−	1.00171i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	13.4641	−	22.7754i	0.508897	−	0.860828i
$701$	23.8536	+	17.3306i	0.900937	+	0.654569i	0.938707	−	0.344717i	$-0.112025\pi$
$701$	23.8536	+	17.3306i	0.900937	+	0.654569i	−0.0377695	+	0.999286i	$0.512025\pi$
$702$		0			0
$703$		0			0
$704$	22.2165	−	14.5061i	0.837316	−	0.546718i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−10.1243	−	3.28958i	−0.380226	−	0.123543i	0.112667	−	0.993633i	$-0.464061\pi$
$709$	−10.1243	−	3.28958i	−0.380226	−	0.123543i	−0.492893	+	0.870090i	$0.664061\pi$
$710$		0			0
$711$	−22.0665	−	30.3720i	−0.827560	−	1.13904i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−43.6007	+	18.8764i	−1.62943	+	0.705444i
$717$		0			0
$718$	−45.8624	+	17.3343i	−1.71157	+	0.646912i
$719$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$719$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$720$		0			0
$721$		0			0
$722$	−26.8401	+	1.26801i	−0.998886	+	0.0471903i
$723$		0			0
$724$		0			0
$725$	−53.4154			−1.98380
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	21.8435	+	15.8702i	0.809017	+	0.587785i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$733$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$734$		0			0
$735$		0			0
$736$	−52.7032	+	12.6763i	−1.94267	+	0.467256i
$737$	2.99511	−	2.09045i	0.110326	−	0.0770028i
$738$		0			0
$739$	0.300157	+	0.923789i	0.0110415	+	0.0339821i	0.956425	−	0.291977i	$-0.0943129\pi$
$739$	0.300157	+	0.923789i	0.0110415	+	0.0339821i	−0.945384	+	0.325959i	$0.894313\pi$
$740$		0			0
$741$		0			0
$742$	−18.2209	+	14.6002i	−0.668911	+	0.535991i
$743$	25.2944	+	8.21865i	0.927962	+	0.301513i	0.733729	−	0.679442i	$-0.237778\pi$
$743$	25.2944	+	8.21865i	0.927962	+	0.301513i	0.194233	+	0.980955i	$0.437778\pi$
$744$		0			0
$745$		0			0
$746$	8.20728	−	30.0107i	0.300490	−	1.09877i
$747$		0			0
$748$		0			0
$749$		−	34.5802i		−	1.26353i
$750$		0			0
$751$	18.8351	+	13.6845i	0.687303	+	0.499355i	0.875772	−	0.482724i	$-0.160353\pi$
$751$	18.8351	+	13.6845i	0.687303	+	0.499355i	−0.188469	+	0.982079i	$0.560353\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−45.7332	+	14.8596i	−1.66220	+	0.540082i	−0.981332	−	0.192323i	$-0.938398\pi$
$757$	−45.7332	+	14.8596i	−1.66220	+	0.540082i	−0.680869	+	0.732405i	$0.738398\pi$
$758$	17.7882	−	27.0849i	0.646096	−	0.983767i
$759$		0			0
$760$		0			0
$761$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$761$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$762$		0			0
$763$	12.9726	+	17.8552i	0.469639	+	0.646402i
$764$	45.1788	−	4.27831i	1.63451	−	0.154784i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0			−	1.00000i	$-0.5\pi$
$769$		0			0				1.00000i	$0.5\pi$
$770$		0			0
$771$		0			0
$772$	31.2988	+	35.4895i	1.12647	+	1.27730i
$773$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$773$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$774$	−37.0424	+	1.74999i	−1.33146	+	0.0629022i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−18.2213	+	6.88700i	−0.653265	+	0.246911i
$779$		0			0
$780$		0			0
$781$	31.6580	−	9.62648i	1.13281	−	0.344462i
$782$		0			0
$783$		0			0
$784$	−27.5023	+	5.25591i	−0.982224	+	0.187711i
$785$		0			0
$786$		0			0
$787$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$787$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$788$	46.9237	+	27.7399i	1.67159	+	0.988195i
$789$		0			0
$790$		0			0
$791$		−	51.6240i		−	1.83554i
$792$	−3.44323	−	27.9311i	−0.122350	−	0.992487i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$797$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$798$		0			0
$799$		0			0
$800$	−26.1358	−	10.8130i	−0.924040	−	0.382296i
$801$		0			0
$802$	17.8086	+	11.6959i	0.628842	+	0.412997i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	11.3285	+	3.68085i	0.398289	+	0.129412i	0.501311	−	0.865267i	$-0.332851\pi$
$809$	11.3285	+	3.68085i	0.398289	+	0.129412i	−0.103022	+	0.994679i	$0.532851\pi$
$810$		0			0
$811$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$811$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$812$	37.3907	+	42.3971i	1.31216	+	1.48785i
$813$		0			0
$814$	−46.7943	−	32.0190i	−1.64014	−	1.12227i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−17.7984	+	12.9313i	−0.621168	+	0.451305i	−0.853329	−	0.521373i	$-0.825420\pi$
$821$	−17.7984	+	12.9313i	−0.621168	+	0.451305i	0.232162	+	0.972677i	$0.425420\pi$
$822$		0			0
$823$	10.9405	+	33.6713i	0.381361	+	1.17371i	0.939086	+	0.343683i	$0.111674\pi$
$823$	10.9405	+	33.6713i	0.381361	+	1.17371i	−0.557725	+	0.830026i	$0.688326\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−13.5967	−	41.8465i	−0.472805	−	1.45514i	−0.848895	−	0.528562i	$-0.822732\pi$
$827$	−13.5967	−	41.8465i	−0.472805	−	1.45514i	0.376090	−	0.926583i	$-0.377268\pi$
$828$	−12.5326	+	56.1119i	−0.435538	+	1.95002i
$829$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$829$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$839$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$840$		0			0
$841$	26.3060	−	80.9615i	0.907103	−	2.79178i
$842$	9.19964	+	11.4811i	0.317041	+	0.395663i
$843$		0			0
$844$	−2.54736	+	11.4052i	−0.0876839	+	0.392585i
$845$		0			0
$846$		0			0
$847$	−28.0000	+	7.93725i	−0.962091	+	0.272727i
$848$	18.2015	+	17.0808i	0.625042	+	0.586558i
$849$		0			0
$850$		0			0
$851$	68.0875	+	93.7143i	2.33401	+	3.21249i
$852$		0			0
$853$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$853$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$854$		0			0
$855$		0			0
$856$	−36.5976	+	5.21802i	−1.25088	+	0.178348i
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$		0			0			−	1.00000i	$-0.5\pi$
$859$		0			0				1.00000i	$0.5\pi$
$860$		0			0
$861$		0			0
$862$	−0.173213	−	3.66643i	−0.00589966	−	0.124879i
$863$	−2.47214	+	7.60845i	−0.0841525	+	0.258995i	−0.984275	−	0.176642i	$-0.943477\pi$
$863$	−2.47214	+	7.60845i	−0.0841525	+	0.258995i	0.900123	+	0.435636i	$0.143477\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	33.1088	+	25.0279i	1.12314	+	0.849013i
$870$		0			0
$871$		0			0
$872$	16.9394	−	16.4237i	0.573641	−	0.556177i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	36.9284	+	26.8300i	1.24698	+	0.905985i	0.998043	−	0.0625337i	$-0.0199181\pi$
$877$	36.9284	+	26.8300i	1.24698	+	0.905985i	0.248939	+	0.968519i	$0.419918\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−7.83422	+	28.6466i	−0.263792	+	0.964580i
$883$	34.2129	−	47.0901i	1.15136	−	1.58471i	0.412325	−	0.911037i	$-0.364717\pi$
$883$	34.2129	−	47.0901i	1.15136	−	1.58471i	0.739032	−	0.673670i	$-0.235283\pi$
$884$		0			0
$885$		0			0
$886$	26.9428	+	33.6243i	0.905161	+	1.12963i
$887$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$887$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$888$		0			0
$889$	18.1890	+	55.9800i	0.610040	+	1.87751i
$890$		0			0
$891$	−28.2086	−	9.76078i	−0.945025	−	0.326998i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	9.71255	+	28.3137i	0.324473	+	0.945895i
$897$		0			0
$898$	32.8638	−	1.55258i	1.09668	−	0.0518103i
$899$		0			0
$900$	−22.5000	+	19.8431i	−0.750000	+	0.661438i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−54.6358	+	7.78987i	−1.81716	+	0.259087i
$905$		0			0
$906$		0			0
$907$	−52.7154	−	17.1283i	−1.75039	−	0.568735i	−0.754252	−	0.656585i	$-0.772000\pi$
$907$	−52.7154	−	17.1283i	−1.75039	−	0.568735i	−0.996134	+	0.0878507i	$0.972000\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−4.94427	−	15.2169i	−0.163811	−	0.504159i	0.835136	−	0.550044i	$-0.185389\pi$
$911$	−4.94427	−	15.2169i	−0.163811	−	0.504159i	−0.998947	+	0.0458855i	$0.985389\pi$
$912$		0			0
$913$		0			0
$914$	−29.3254	+	44.6518i	−0.969996	+	1.47695i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	54.3023	+	17.6439i	1.79127	+	0.582019i	0.999582	−	0.0289084i	$-0.00920311\pi$
$919$	54.3023	+	17.6439i	1.79127	+	0.582019i	0.791687	+	0.610927i	$0.209203\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$			60.4427i			1.98734i
$926$	−1.02101	+	3.73343i	−0.0335526	+	0.122688i
$927$		0			0
$928$	39.2285	−	45.9698i	1.28774	−	1.50903i
$929$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$929$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$930$		0			0
$931$		0			0
$932$	41.3141	+	9.22751i	1.35329	+	0.302257i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$937$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$938$	1.45684	+	3.85443i	0.0475675	+	0.125852i
$939$		0			0
$940$		0			0
$941$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$941$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	38.6178	−	13.7649i	1.25557	−	0.447536i
$947$		−	58.2065i		−	1.89146i	−0.324956	−	0.945729i	$-0.605350\pi$
$947$		−	58.2065i		−	1.89146i	0.324956	−	0.945729i	$-0.394650\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−30.1035	−	41.4340i	−0.975149	−	1.34218i	−0.939402	−	0.342817i	$-0.888619\pi$
$953$	−30.1035	−	41.4340i	−0.975149	−	1.34218i	−0.0357473	−	0.999361i	$-0.511381\pi$
$954$	24.7652	−	9.36036i	0.801802	−	0.303053i
$955$		0			0
$956$	12.9230	−	5.59487i	0.417961	−	0.180951i
$957$		0			0
$958$		0			0
$959$	51.6619	−	16.7860i	1.66825	−	0.542047i
$960$		0			0
$961$	−25.0795	+	18.2213i	−0.809017	+	0.587785i
$962$		0			0
$963$	−12.1166	+	37.2911i	−0.390453	+	1.20169i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			15.0168i			0.482909i	0.970412	+	0.241454i	$0.0776244\pi$
$967$			15.0168i			0.482909i	−0.970412	+	0.241454i	$0.922376\pi$
$968$	12.6254	+	28.4359i	0.405797	+	0.913963i
$969$		0			0
$970$		0			0
$971$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$971$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$972$		0			0
$973$		0			0
$974$	47.0629	−	37.7109i	1.50799	−	1.20834i
$975$		0			0
$976$		0			0
$977$	3.81100	+	11.7290i	0.121925	+	0.375245i	0.993328	−	0.115321i	$-0.0367898\pi$
$977$	3.81100	+	11.7290i	0.121925	+	0.375245i	−0.871404	+	0.490567i	$0.836790\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−7.73325	−	23.8005i	−0.246904	−	0.759891i
$982$	22.0000	+	58.2065i	0.702048	+	1.85744i
$983$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$983$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−83.7571			−2.66332
$990$		0			0
$991$	−24.0000			−0.762385			−0.381193	−	0.924496i	$-0.624487\pi$
$991$	−24.0000			−0.762385			−0.381193	+	0.924496i	$0.624487\pi$
$992$		0			0
$993$		0			0
$994$	1.76160	+	37.2881i	0.0558746	+	1.18271i
$995$		0			0
$996$		0			0
$997$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$997$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$998$	−34.4771	+	13.0311i	−1.09135	+	0.412492i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	616.2.bi.b.237.1	yes	8
7.6	odd	2	CM	616.2.bi.b.237.1	yes	8
8.5	even	2		616.2.bi.a.237.1	yes	8
11.2	odd	10		616.2.bi.a.13.1	✓	8
56.13	odd	2		616.2.bi.a.237.1	yes	8
77.13	even	10		616.2.bi.a.13.1	✓	8
88.13	odd	10	inner	616.2.bi.b.13.1	yes	8
616.13	even	10	inner	616.2.bi.b.13.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.bi.a.13.1	✓	8	11.2	odd	10
616.2.bi.a.13.1	✓	8	77.13	even	10
616.2.bi.a.237.1	yes	8	8.5	even	2
616.2.bi.a.237.1	yes	8	56.13	odd	2
616.2.bi.b.13.1	yes	8	88.13	odd	10	inner
616.2.bi.b.13.1	yes	8	616.13	even	10	inner
616.2.bi.b.237.1	yes	8	1.1	even	1	trivial
616.2.bi.b.237.1	yes	8	7.6	odd	2	CM

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:	\( N \)	\(=\)	\( 616 = 2^{3} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	616.bi (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.373058 + 1.36412i) q^{2} +(-1.72166 - 1.01779i) q^{4} +(1.55513 + 2.14046i) q^{7} +(2.03067 - 1.96885i) q^{8} +(-0.927051 - 2.85317i) q^{9} +O(q^{10})\)	\(q+(-0.373058 + 1.36412i) q^{2} +(-1.72166 - 1.01779i) q^{4} +(1.55513 + 2.14046i) q^{7} +(2.03067 - 1.96885i) q^{8} +(-0.927051 - 2.85317i) q^{9} +(1.89823 + 2.71970i) q^{11} +(-3.50000 + 1.32288i) q^{14} +(1.92819 + 3.50458i) q^{16} +(4.23791 - 0.200212i) q^{18} +(-4.41814 + 1.57480i) q^{22} +9.58240 q^{23} +(4.04508 + 2.93893i) q^{25} +(-0.498859 - 5.26794i) q^{28} +(-8.64279 + 6.27935i) q^{29} +(-5.50000 + 1.32288i) q^{32} +(-1.30788 + 5.85572i) q^{36} +(7.10547 + 9.77984i) q^{37} -8.74072 q^{43} +(-0.500000 - 6.61438i) q^{44} +(-3.57480 + 13.0716i) q^{46} +(-2.16312 + 6.65740i) q^{49} +(-5.51811 + 4.42160i) q^{50} +(5.93482 - 1.92834i) q^{53} +(7.37221 + 1.28474i) q^{56} +(-5.34154 - 14.1324i) q^{58} +(4.66540 - 6.42137i) q^{63} +(0.247258 - 7.99618i) q^{64} -1.10127i q^{67} +(3.08300 - 9.48849i) q^{71} +(-7.50000 - 3.96863i) q^{72} +(-15.9916 + 6.04427i) q^{74} +(-2.86940 + 8.29256i) q^{77} +(11.9015 - 3.86702i) q^{79} +(-7.28115 + 5.29007i) q^{81} +(3.26080 - 11.9234i) q^{86} +(9.20934 + 1.78549i) q^{88} +(-16.4976 - 9.75291i) q^{92} +(-8.27453 - 5.43435i) q^{98} +(6.00000 - 7.93725i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 3 q^{4} - 5 q^{8} + 6 q^{9}+O(q^{10}) \) 8 * q + q^2 + 3 * q^4 - 5 * q^8 + 6 * q^9	\( 8 q + q^{2} + 3 q^{4} - 5 q^{8} + 6 q^{9} + 4 q^{11} - 28 q^{14} - q^{16} - 3 q^{18} - 9 q^{22} + 16 q^{23} + 10 q^{25} - 7 q^{28} - 4 q^{29} - 44 q^{32} - 9 q^{36} + 30 q^{37} + 24 q^{43} - 4 q^{44} - 23 q^{46} + 14 q^{49} - 5 q^{50} + 50 q^{53} - 7 q^{56} + 2 q^{58} - 9 q^{64} + 48 q^{71} - 60 q^{72} - 28 q^{74} - 14 q^{77} + 40 q^{79} - 18 q^{81} - 12 q^{86} + 17 q^{88} - 24 q^{92} - 7 q^{98} + 48 q^{99}+O(q^{100}) \) 8 * q + q^2 + 3 * q^4 - 5 * q^8 + 6 * q^9 + 4 * q^11 - 28 * q^14 - q^16 - 3 * q^18 - 9 * q^22 + 16 * q^23 + 10 * q^25 - 7 * q^28 - 4 * q^29 - 44 * q^32 - 9 * q^36 + 30 * q^37 + 24 * q^43 - 4 * q^44 - 23 * q^46 + 14 * q^49 - 5 * q^50 + 50 * q^53 - 7 * q^56 + 2 * q^58 - 9 * q^64 + 48 * q^71 - 60 * q^72 - 28 * q^74 - 14 * q^77 + 40 * q^79 - 18 * q^81 - 12 * q^86 + 17 * q^88 - 24 * q^92 - 7 * q^98 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more