LMFDB - Embedded newform 925.2.b.g.149.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [925,2,Mod(149,925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(925, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("925.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.b (of order $2$, degree $1$, not 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:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.8689006034944.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 2x^{8} + 10x^{7} + 26x^{6} - 4x^{5} + 6x^{4} + 22x^{3} + 25x^{2} + 10x + 2 $ x^10 - 2x^9 + 2x^8 + 10x^7 + 26x^6 - 4x^5 + 6x^4 + 22x^3 + 25x^2 + 10*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.1
Root			$-0.272959 - 0.272959i$ of defining polynomial
Character	$\chi$	$=$	925.149
Dual form			925.2.b.g.149.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66356i q^{2} +0.671838i q^{3} -5.09455 q^{4} +1.78948 q^{6} -0.305070i q^{7} +8.24252i q^{8} +2.54863 q^{9} +O(q^{10})$	\(q-2.66356i q^{2} +0.671838i q^{3} -5.09455 q^{4} +1.78948 q^{6} -0.305070i q^{7} +8.24252i q^{8} +2.54863 q^{9} +1.85927 q^{11} -3.42271i q^{12} -4.78120i q^{13} -0.812573 q^{14} +11.7653 q^{16} -2.54592i q^{17} -6.78844i q^{18} -8.13969 q^{19} +0.204958 q^{21} -4.95226i q^{22} -6.67080i q^{23} -5.53764 q^{24} -12.7350 q^{26} +3.72778i q^{27} +1.55420i q^{28} -0.374855 q^{29} -4.02477 q^{31} -14.8527i q^{32} +1.24913i q^{33} -6.78120 q^{34} -12.9841 q^{36} -1.00000i q^{37} +21.6806i q^{38} +3.21219 q^{39} +3.06337 q^{41} -0.545917i q^{42} -11.5328i q^{43} -9.47212 q^{44} -17.7681 q^{46} +4.13587i q^{47} +7.90441i q^{48} +6.90693 q^{49} +1.71044 q^{51} +24.3581i q^{52} +2.51559i q^{53} +9.92917 q^{54} +2.51455 q^{56} -5.46855i q^{57} +0.998448i q^{58} +2.62947 q^{59} -2.92264 q^{61} +10.7202i q^{62} -0.777512i q^{63} -16.0303 q^{64} +3.32712 q^{66} -8.57520i q^{67} +12.9703i q^{68} +4.48169 q^{69} -14.7798 q^{71} +21.0072i q^{72} +8.32984i q^{73} -2.66356 q^{74} +41.4681 q^{76} -0.567206i q^{77} -8.55587i q^{78} -8.41618 q^{79} +5.14143 q^{81} -8.15947i q^{82} -10.8444i q^{83} -1.04417 q^{84} -30.7182 q^{86} -0.251842i q^{87} +15.3250i q^{88} -17.7053 q^{89} -1.45860 q^{91} +33.9847i q^{92} -2.70399i q^{93} +11.0161 q^{94} +9.97858 q^{96} -13.6612i q^{97} -18.3970i q^{98} +4.73859 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 12 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) $ 10 * q - 12 * q^4 - 4 * q^6 - 4 * q^9	$ 10 q - 12 q^{4} - 4 q^{6} - 4 q^{9} + 14 q^{11} - 8 q^{14} + 16 q^{16} - 28 q^{19} - 18 q^{21} - 24 q^{24} - 40 q^{26} - 4 q^{29} + 16 q^{31} - 24 q^{34} - 72 q^{36} - 24 q^{39} - 18 q^{41} - 36 q^{44} - 56 q^{46} - 4 q^{49} + 20 q^{51} + 24 q^{54} - 28 q^{56} - 24 q^{59} + 24 q^{61} - 24 q^{64} - 20 q^{66} + 60 q^{69} + 26 q^{71} + 36 q^{76} - 72 q^{79} + 42 q^{81} - 60 q^{84} - 16 q^{86} + 32 q^{89} - 8 q^{91} - 40 q^{94} - 36 q^{99}+O(q^{100}) $ 10 * q - 12 * q^4 - 4 * q^6 - 4 * q^9 + 14 * q^11 - 8 * q^14 + 16 * q^16 - 28 * q^19 - 18 * q^21 - 24 * q^24 - 40 * q^26 - 4 * q^29 + 16 * q^31 - 24 * q^34 - 72 * q^36 - 24 * q^39 - 18 * q^41 - 36 * q^44 - 56 * q^46 - 4 * q^49 + 20 * q^51 + 24 * q^54 - 28 * q^56 - 24 * q^59 + 24 * q^61 - 24 * q^64 - 20 * q^66 + 60 * q^69 + 26 * q^71 + 36 * q^76 - 72 * q^79 + 42 * q^81 - 60 * q^84 - 16 * q^86 + 32 * q^89 - 8 * q^91 - 40 * q^94 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 2.66356i	− 1.88342i	−0.336424	−	0.941711i	$-0.609218\pi$
$2$	− 2.66356i	− 1.88342i	0.336424	−	0.941711i	$-0.390782\pi$
$3$	0.671838i	0.387886i	0.981013	+	0.193943i	$0.0621277\pi$
$3$	0.671838i	0.387886i	−0.981013	+	0.193943i	$0.937872\pi$
$4$	−5.09455	−2.54728
$5$	0	0
$5$	0	0
$6$	1.78948	0.730552
$7$	− 0.305070i	− 0.115306i	−0.998337	−	0.0576528i	$-0.981638\pi$
$7$	− 0.305070i	− 0.115306i	0.998337	−	0.0576528i	$-0.0183616\pi$
$8$	8.24252i	2.91417i
$9$	2.54863	0.849545
$10$	0	0
$11$	1.85927	0.560590	0.280295	−	0.959914i	$-0.409568\pi$
$11$	1.85927	0.560590	0.280295	+	0.959914i	$0.409568\pi$
$12$	− 3.42271i	− 0.988052i
$13$	− 4.78120i	− 1.32607i	−0.748590	−	0.663033i	$-0.769269\pi$
$13$	− 4.78120i	− 1.32607i	0.748590	−	0.663033i	$-0.230731\pi$
$14$	−0.812573	−0.217169
$15$	0	0
$16$	11.7653	2.94134
$17$	− 2.54592i	− 0.617476i	−0.951147	−	0.308738i	$-0.900093\pi$
$17$	− 2.54592i	− 0.617476i	0.951147	−	0.308738i	$-0.0999066\pi$
$18$	− 6.78844i	− 1.60005i
$19$	−8.13969	−1.86737	−0.933687	−	0.358091i	$-0.883428\pi$
$19$	−8.13969	−1.86737	−0.933687	+	0.358091i	$0.883428\pi$
$20$	0	0
$21$	0.204958	0.0447254
$22$	− 4.95226i	− 1.05583i
$23$	− 6.67080i	− 1.39096i	−0.718547	−	0.695479i	$-0.755192\pi$
$23$	− 6.67080i	− 1.39096i	0.718547	−	0.695479i	$-0.244808\pi$
$24$	−5.53764	−1.13037
$25$	0	0
$26$	−12.7350	−2.49754
$27$	3.72778i	0.717412i
$28$	1.55420i	0.293715i
$29$	−0.374855	−0.0696088	−0.0348044	−	0.999394i	$-0.511081\pi$
$29$	−0.374855	−0.0696088	−0.0348044	+	0.999394i	$0.511081\pi$
$30$	0	0
$31$	−4.02477	−0.722869	−0.361435	−	0.932397i	$-0.617713\pi$
$31$	−4.02477	−0.722869	−0.361435	+	0.932397i	$0.617713\pi$
$32$	− 14.8527i	− 2.62560i
$33$	1.24913i	0.217445i
$34$	−6.78120	−1.16297
$35$	0	0
$36$	−12.9841	−2.16402
$37$	− 1.00000i	− 0.164399i
$37$	− 1.00000i	− 0.164399i
$38$	21.6806i	3.51705i
$39$	3.21219	0.514363
$40$	0	0
$41$	3.06337	0.478418	0.239209	−	0.970968i	$-0.423112\pi$
$41$	3.06337	0.478418	0.239209	+	0.970968i	$0.423112\pi$
$42$	− 0.545917i	− 0.0842368i
$43$	− 11.5328i	− 1.75873i	−0.476146	−	0.879366i	$-0.657967\pi$
$43$	− 11.5328i	− 1.75873i	0.476146	−	0.879366i	$-0.342033\pi$
$44$	−9.47212	−1.42798
$45$	0	0
$46$	−17.7681	−2.61976
$47$	4.13587i	0.603279i	0.953422	+	0.301640i	$0.0975339\pi$
$47$	4.13587i	0.603279i	−0.953422	+	0.301640i	$0.902466\pi$
$48$	7.90441i	1.14090i
$49$	6.90693	0.986705
$50$	0	0
$51$	1.71044	0.239510
$52$	24.3581i	3.37786i
$53$	2.51559i	0.345543i	0.984962	+	0.172771i	$0.0552722\pi$
$53$	2.51559i	0.345543i	−0.984962	+	0.172771i	$0.944728\pi$
$54$	9.92917	1.35119
$55$	0	0
$56$	2.51455	0.336020
$57$	− 5.46855i	− 0.724328i
$58$	0.998448i	0.131103i
$59$	2.62947	0.342328	0.171164	−	0.985243i	$-0.445247\pi$
$59$	2.62947	0.342328	0.171164	+	0.985243i	$0.445247\pi$
$60$	0	0
$61$	−2.92264	−0.374205	−0.187103	−	0.982340i	$-0.559910\pi$
$61$	−2.92264	−0.374205	−0.187103	+	0.982340i	$0.559910\pi$
$62$	10.7202i	1.36147i
$63$	− 0.777512i	− 0.0979573i
$64$	−16.0303	−2.00378
$65$	0	0
$66$	3.32712	0.409540
$67$	− 8.57520i	− 1.04763i	−0.851833	−	0.523814i	$-0.824509\pi$
$67$	− 8.57520i	− 1.04763i	0.851833	−	0.523814i	$-0.175491\pi$
$68$	12.9703i	1.57288i
$69$	4.48169	0.539533
$70$	0	0
$71$	−14.7798	−1.75404	−0.877021	−	0.480452i	$-0.840473\pi$
$71$	−14.7798	−1.75404	−0.877021	+	0.480452i	$0.840473\pi$
$72$	21.0072i	2.47572i
$73$	8.32984i	0.974934i	0.873142	+	0.487467i	$0.162079\pi$
$73$	8.32984i	0.974934i	−0.873142	+	0.487467i	$0.837921\pi$
$74$	−2.66356	−0.309633
$75$	0	0
$76$	41.4681	4.75671
$77$	− 0.567206i	− 0.0646392i
$78$	− 8.55587i	− 0.968761i
$79$	−8.41618	−0.946894	−0.473447	−	0.880822i	$-0.656990\pi$
$79$	−8.41618	−0.946894	−0.473447	+	0.880822i	$0.656990\pi$
$80$	0	0
$81$	5.14143	0.571271
$82$	− 8.15947i	− 0.901063i
$83$	− 10.8444i	− 1.19033i	−0.803605	−	0.595163i	$-0.797088\pi$
$83$	− 10.8444i	− 1.19033i	0.803605	−	0.595163i	$-0.202912\pi$
$84$	−1.04417	−0.113928
$85$	0	0
$86$	−30.7182	−3.31243
$87$	− 0.251842i	− 0.0270003i
$88$	15.3250i	1.63365i
$89$	−17.7053	−1.87676	−0.938380	−	0.345605i	$-0.887674\pi$
$89$	−17.7053	−1.87676	−0.938380	+	0.345605i	$0.887674\pi$
$90$	0	0
$91$	−1.45860	−0.152903
$92$	33.9847i	3.54315i
$93$	− 2.70399i	− 0.280391i
$94$	11.0161	1.13623
$95$	0	0
$96$	9.97858	1.01843
$97$	− 13.6612i	− 1.38709i	−0.720415	−	0.693544i	$-0.756048\pi$
$97$	− 13.6612i	− 1.38709i	0.720415	−	0.693544i	$-0.243952\pi$
$98$	− 18.3970i	− 1.85838i
$99$	4.73859	0.476246
$100$	0	0
$101$	2.57981	0.256701	0.128350	−	0.991729i	$-0.459032\pi$
$101$	2.57981	0.256701	0.128350	+	0.991729i	$0.459032\pi$
$102$	− 4.55587i	− 0.451098i
$103$	8.31211i	0.819017i	0.912306	+	0.409509i	$0.134300\pi$
$103$	8.31211i	0.819017i	−0.912306	+	0.409509i	$0.865700\pi$
$104$	39.4092	3.86439
$105$	0	0
$106$	6.70042	0.650803
$107$	− 10.2766i	− 0.993477i	−0.867900	−	0.496739i	$-0.834531\pi$
$107$	− 10.2766i	− 0.993477i	0.867900	−	0.496739i	$-0.165469\pi$
$108$	− 18.9914i	− 1.82745i
$109$	19.7515	1.89185	0.945926	−	0.324384i	$-0.105157\pi$
$109$	19.7515	1.89185	0.945926	+	0.324384i	$0.105157\pi$
$110$	0	0
$111$	0.671838	0.0637680
$112$	− 3.58926i	− 0.339153i
$113$	0.193052i	0.0181608i	0.999959	+	0.00908039i	$0.00289042\pi$
$113$	0.193052i	0.0181608i	−0.999959	+	0.00908039i	$0.997110\pi$
$114$	−14.5658	−1.36421
$115$	0	0
$116$	1.90972	0.177313
$117$	− 12.1855i	− 1.12655i
$118$	− 7.00376i	− 0.644748i
$119$	−0.776683	−0.0711984
$120$	0	0
$121$	−7.54313	−0.685739
$122$	7.78462i	0.704786i
$123$	2.05809i	0.185572i
$124$	20.5044	1.84135
$125$	0	0
$126$	−2.07095	−0.184495
$127$	3.21589i	0.285364i	0.989769	+	0.142682i	$0.0455726\pi$
$127$	3.21589i	0.285364i	−0.989769	+	0.142682i	$0.954427\pi$
$128$	12.9922i	1.14836i
$129$	7.74816	0.682187
$130$	0	0
$131$	12.9029	1.12733	0.563664	−	0.826004i	$-0.309391\pi$
$131$	12.9029	1.12733	0.563664	+	0.826004i	$0.309391\pi$
$132$	− 6.36373i	− 0.553892i
$133$	2.48318i	0.215319i
$134$	−22.8406	−1.97312
$135$	0	0
$136$	20.9848	1.79943
$137$	− 6.77934i	− 0.579198i	−0.957148	−	0.289599i	$-0.906478\pi$
$137$	− 6.77934i	− 0.579198i	0.957148	−	0.289599i	$-0.0935219\pi$
$138$	− 11.9373i	− 1.01617i
$139$	6.06609	0.514519	0.257259	−	0.966342i	$-0.417181\pi$
$139$	6.06609	0.514519	0.257259	+	0.966342i	$0.417181\pi$
$140$	0	0
$141$	−2.77864	−0.234003
$142$	39.3669i	3.30360i
$143$	− 8.88952i	− 0.743379i
$144$	29.9856	2.49880
$145$	0	0
$146$	22.1870	1.83621
$147$	4.64034i	0.382729i
$148$	5.09455i	0.418769i
$149$	10.2822	0.842348	0.421174	−	0.906980i	$-0.361618\pi$
$149$	10.2822	0.842348	0.421174	+	0.906980i	$0.361618\pi$
$150$	0	0
$151$	11.1876	0.910430	0.455215	−	0.890382i	$-0.349562\pi$
$151$	11.1876	0.910430	0.455215	+	0.890382i	$0.349562\pi$
$152$	− 67.0916i	− 5.44185i
$153$	− 6.48861i	− 0.524573i
$154$	−1.51079	−0.121743
$155$	0	0
$156$	−16.3647	−1.31022
$157$	16.6402i	1.32804i	0.747716	+	0.664018i	$0.231150\pi$
$157$	16.6402i	1.32804i	−0.747716	+	0.664018i	$0.768850\pi$
$158$	22.4170i	1.78340i
$159$	−1.69007	−0.134031
$160$	0	0
$161$	−2.03506	−0.160385
$162$	− 13.6945i	− 1.07594i
$163$	11.1117i	0.870339i	0.900349	+	0.435169i	$0.143311\pi$
$163$	11.1117i	0.870339i	−0.900349	+	0.435169i	$0.856689\pi$
$164$	−15.6065	−1.21866
$165$	0	0
$166$	−28.8847	−2.24188
$167$	2.24836i	0.173983i	0.996209	+	0.0869915i	$0.0277253\pi$
$167$	2.24836i	0.173983i	−0.996209	+	0.0869915i	$0.972275\pi$
$168$	1.68937i	0.130338i
$169$	−9.85990	−0.758454
$170$	0	0
$171$	−20.7451	−1.58642
$172$	58.7543i	4.47998i
$173$	10.3774i	0.788981i	0.918900	+	0.394490i	$0.129079\pi$
$173$	10.3774i	0.788981i	−0.918900	+	0.394490i	$0.870921\pi$
$174$	−0.670796	−0.0508529
$175$	0	0
$176$	21.8749	1.64888
$177$	1.76658i	0.132784i
$178$	47.1592i	3.53473i
$179$	9.67455	0.723110	0.361555	−	0.932351i	$-0.382246\pi$
$179$	9.67455	0.723110	0.361555	+	0.932351i	$0.382246\pi$
$180$	0	0
$181$	22.1236	1.64443	0.822216	−	0.569175i	$-0.192737\pi$
$181$	22.1236	1.64443	0.822216	+	0.569175i	$0.192737\pi$
$182$	3.88507i	0.287981i
$183$	− 1.96354i	− 0.145149i
$184$	54.9842	4.05349
$185$	0	0
$186$	−7.20224	−0.528094
$187$	− 4.73354i	− 0.346150i
$188$	− 21.0704i	− 1.53672i
$189$	1.13724	0.0827217
$190$	0	0
$191$	13.4291	0.971695	0.485848	−	0.874043i	$-0.338511\pi$
$191$	13.4291	0.971695	0.485848	+	0.874043i	$0.338511\pi$
$192$	− 10.7697i	− 0.777239i
$193$	− 5.54030i	− 0.398799i	−0.979918	−	0.199400i	$-0.936101\pi$
$193$	− 5.54030i	− 0.398799i	0.979918	−	0.199400i	$-0.0638992\pi$
$194$	−36.3875	−2.61247
$195$	0	0
$196$	−35.1877	−2.51341
$197$	9.64388i	0.687098i	0.939135	+	0.343549i	$0.111629\pi$
$197$	9.64388i	0.687098i	−0.939135	+	0.343549i	$0.888371\pi$
$198$	− 12.6215i	− 0.896972i
$199$	−9.72036	−0.689058	−0.344529	−	0.938776i	$-0.611961\pi$
$199$	−9.72036	−0.689058	−0.344529	+	0.938776i	$0.611961\pi$
$200$	0	0
$201$	5.76115	0.406360
$202$	− 6.87149i	− 0.483476i
$203$	0.114357i	0.00802629i
$204$	−8.71394	−0.610098
$205$	0	0
$206$	22.1398	1.54255
$207$	− 17.0014i	− 1.18168i
$208$	− 56.2525i	− 3.90041i
$209$	−15.1338	−1.04683
$210$	0	0
$211$	18.2671	1.25756	0.628779	−	0.777584i	$-0.283555\pi$
$211$	18.2671	1.25756	0.628779	+	0.777584i	$0.283555\pi$
$212$	− 12.8158i	− 0.880193i
$213$	− 9.92964i	− 0.680368i
$214$	−27.3724	−1.87114
$215$	0	0
$216$	−30.7263	−2.09066
$217$	1.22784i	0.0833509i
$218$	− 52.6093i	− 3.56315i
$219$	−5.59630	−0.378163
$220$	0	0
$221$	−12.1725	−0.818814
$222$	− 1.78948i	− 0.120102i
$223$	3.90014i	0.261173i	0.991437	+	0.130586i	$0.0416860\pi$
$223$	3.90014i	0.261173i	−0.991437	+	0.130586i	$0.958314\pi$
$224$	−4.53110	−0.302747
$225$	0	0
$226$	0.514205	0.0342044
$227$	− 23.0180i	− 1.52776i	−0.645360	−	0.763878i	$-0.723293\pi$
$227$	− 23.0180i	− 1.52776i	0.645360	−	0.763878i	$-0.276707\pi$
$228$	27.8598i	1.84506i
$229$	24.9325	1.64758	0.823792	−	0.566893i	$-0.191855\pi$
$229$	24.9325	1.64758	0.823792	+	0.566893i	$0.191855\pi$
$230$	0	0
$231$	0.381071	0.0250726
$232$	− 3.08975i	− 0.202852i
$233$	− 27.1703i	− 1.77999i	−0.455974	−	0.889993i	$-0.650709\pi$
$233$	− 27.1703i	− 1.77999i	0.455974	−	0.889993i	$-0.349291\pi$
$234$	−32.4569	−2.12177
$235$	0	0
$236$	−13.3960	−0.872004
$237$	− 5.65431i	− 0.367287i
$238$	2.06874i	0.134097i
$239$	−11.4668	−0.741726	−0.370863	−	0.928688i	$-0.620938\pi$
$239$	−11.4668	−0.741726	−0.370863	+	0.928688i	$0.620938\pi$
$240$	0	0
$241$	−13.6581	−0.879797	−0.439898	−	0.898048i	$-0.644986\pi$
$241$	−13.6581	−0.879797	−0.439898	+	0.898048i	$0.644986\pi$
$242$	20.0916i	1.29154i
$243$	14.6376i	0.939000i
$244$	14.8895	0.953204
$245$	0	0
$246$	5.48184	0.349510
$247$	38.9175i	2.47626i
$248$	− 33.1742i	− 2.10657i
$249$	7.28567	0.461710
$250$	0	0
$251$	−6.65785	−0.420240	−0.210120	−	0.977676i	$-0.567385\pi$
$251$	−6.65785	−0.420240	−0.210120	+	0.977676i	$0.567385\pi$
$252$	3.96107i	0.249524i
$253$	− 12.4028i	− 0.779756i
$254$	8.56571	0.537461
$255$	0	0
$256$	2.54507	0.159067
$257$	− 11.5885i	− 0.722869i	−0.932398	−	0.361434i	$-0.882287\pi$
$257$	− 11.5885i	− 0.722869i	0.932398	−	0.361434i	$-0.117713\pi$
$258$	− 20.6377i	− 1.28485i
$259$	−0.305070	−0.0189561
$260$	0	0
$261$	−0.955368	−0.0591358
$262$	− 34.3675i	− 2.12323i
$263$	17.1403i	1.05692i	0.848959	+	0.528459i	$0.177230\pi$
$263$	17.1403i	1.05692i	−0.848959	+	0.528459i	$0.822770\pi$
$264$	−10.2959	−0.633671
$265$	0	0
$266$	6.61409	0.405536
$267$	− 11.8951i	− 0.727969i
$268$	43.6868i	2.66860i
$269$	2.00497	0.122245	0.0611225	−	0.998130i	$-0.480532\pi$
$269$	2.00497	0.122245	0.0611225	+	0.998130i	$0.480532\pi$
$270$	0	0
$271$	5.82824	0.354040	0.177020	−	0.984207i	$-0.443354\pi$
$271$	5.82824	0.354040	0.177020	+	0.984207i	$0.443354\pi$
$272$	− 29.9536i	− 1.81620i
$273$	− 0.979944i	− 0.0593089i
$274$	−18.0572	−1.09087
$275$	0	0
$276$	−22.8322	−1.37434
$277$	21.8323i	1.31177i	0.754859	+	0.655887i	$0.227705\pi$
$277$	21.8323i	1.31177i	−0.754859	+	0.655887i	$0.772295\pi$
$278$	− 16.1574i	− 0.969056i
$279$	−10.2577	−0.614110
$280$	0	0
$281$	3.56449	0.212640	0.106320	−	0.994332i	$-0.466093\pi$
$281$	3.56449	0.212640	0.106320	+	0.994332i	$0.466093\pi$
$282$	7.40107i	0.440727i
$283$	14.0437i	0.834812i	0.908720	+	0.417406i	$0.137061\pi$
$283$	14.0437i	0.834812i	−0.908720	+	0.417406i	$0.862939\pi$
$284$	75.2965	4.46803
$285$	0	0
$286$	−23.6778	−1.40010
$287$	− 0.934543i	− 0.0551643i
$288$	− 37.8540i	− 2.23057i
$289$	10.5183	0.618724
$290$	0	0
$291$	9.17813	0.538031
$292$	− 42.4368i	− 2.48342i
$293$	23.9496i	1.39915i	0.714558	+	0.699577i	$0.246628\pi$
$293$	23.9496i	1.39915i	−0.714558	+	0.699577i	$0.753372\pi$
$294$	12.3598	0.720839
$295$	0	0
$296$	8.24252	0.479087
$297$	6.93094i	0.402174i
$298$	− 27.3872i	− 1.58650i
$299$	−31.8944	−1.84450
$300$	0	0
$301$	−3.51831	−0.202792
$302$	− 29.7987i	− 1.71472i
$303$	1.73322i	0.0995707i
$304$	−95.7663	−5.49257
$305$	0	0
$306$	−17.2828	−0.987992
$307$	− 3.40442i	− 0.194301i	−0.995270	−	0.0971503i	$-0.969027\pi$
$307$	− 3.40442i	− 0.194301i	0.995270	−	0.0971503i	$-0.0309728\pi$
$308$	2.88966i	0.164654i
$309$	−5.58439	−0.317685
$310$	0	0
$311$	1.85014	0.104912	0.0524558	−	0.998623i	$-0.483295\pi$
$311$	1.85014	0.104912	0.0524558	+	0.998623i	$0.483295\pi$
$312$	26.4766i	1.49894i
$313$	24.8106i	1.40238i	0.712975	+	0.701189i	$0.247347\pi$
$313$	24.8106i	1.40238i	−0.712975	+	0.701189i	$0.752653\pi$
$314$	44.3223	2.50125
$315$	0	0
$316$	42.8766	2.41200
$317$	− 29.0459i	− 1.63138i	−0.578489	−	0.815690i	$-0.696358\pi$
$317$	− 29.0459i	− 1.63138i	0.578489	−	0.815690i	$-0.303642\pi$
$318$	4.50160i	0.252437i
$319$	−0.696955	−0.0390220
$320$	0	0
$321$	6.90422	0.385356
$322$	5.42051i	0.302073i
$323$	20.7230i	1.15306i
$324$	−26.1933	−1.45518
$325$	0	0
$326$	29.5968	1.63921
$327$	13.2698i	0.733822i
$328$	25.2499i	1.39419i
$329$	1.26173	0.0695615
$330$	0	0
$331$	−5.75347	−0.316239	−0.158120	−	0.987420i	$-0.550543\pi$
$331$	−5.75347	−0.316239	−0.158120	+	0.987420i	$0.550543\pi$
$332$	55.2473i	3.03209i
$333$	− 2.54863i	− 0.139664i
$334$	5.98863	0.327683
$335$	0	0
$336$	2.41140	0.131553
$337$	− 1.93856i	− 0.105600i	−0.998605	−	0.0528001i	$-0.983185\pi$
$337$	− 1.93856i	− 0.105600i	0.998605	−	0.0528001i	$-0.0168146\pi$
$338$	26.2624i	1.42849i
$339$	−0.129700	−0.00704431
$340$	0	0
$341$	−7.48311	−0.405233
$342$	55.2558i	2.98789i
$343$	− 4.24259i	− 0.229078i
$344$	95.0592	5.12525
$345$	0	0
$346$	27.6409	1.48598
$347$	21.1544i	1.13563i	0.823156	+	0.567815i	$0.192211\pi$
$347$	21.1544i	1.13563i	−0.823156	+	0.567815i	$0.807789\pi$
$348$	1.28302i	0.0687771i
$349$	16.4132	0.878577	0.439289	−	0.898346i	$-0.355231\pi$
$349$	16.4132	0.878577	0.439289	+	0.898346i	$0.355231\pi$
$350$	0	0
$351$	17.8233	0.951337
$352$	− 27.6150i	− 1.47189i
$353$	0.557505i	0.0296730i	0.999890	+	0.0148365i	$0.00472278\pi$
$353$	0.557505i	0.0296730i	−0.999890	+	0.0148365i	$0.995277\pi$
$354$	4.70539	0.250089
$355$	0	0
$356$	90.2007	4.78063
$357$	− 0.521805i	− 0.0276169i
$358$	− 25.7688i	− 1.36192i
$359$	−2.92356	−0.154299	−0.0771497	−	0.997020i	$-0.524582\pi$
$359$	−2.92356	−0.154299	−0.0771497	+	0.997020i	$0.524582\pi$
$360$	0	0
$361$	47.2546	2.48708
$362$	− 58.9275i	− 3.09716i
$363$	− 5.06776i	− 0.265989i
$364$	7.43092	0.389486
$365$	0	0
$366$	−5.23000	−0.273377
$367$	9.11824i	0.475968i	0.971269	+	0.237984i	$0.0764866\pi$
$367$	9.11824i	0.475968i	−0.971269	+	0.237984i	$0.923513\pi$
$368$	− 78.4842i	− 4.09127i
$369$	7.80741	0.406438
$370$	0	0
$371$	0.767431	0.0398430
$372$	13.7756i	0.714233i
$373$	− 14.0591i	− 0.727953i	−0.931408	−	0.363977i	$-0.881419\pi$
$373$	− 14.0591i	− 0.727953i	0.931408	−	0.363977i	$-0.118581\pi$
$374$	−12.6081	−0.651947
$375$	0	0
$376$	−34.0900	−1.75806
$377$	1.79226i	0.0923059i
$378$	− 3.02909i	− 0.155800i
$379$	−0.614911	−0.0315858	−0.0157929	−	0.999875i	$-0.505027\pi$
$379$	−0.614911	−0.0315858	−0.0157929	+	0.999875i	$0.505027\pi$
$380$	0	0
$381$	−2.16056	−0.110689
$382$	− 35.7692i	− 1.83011i
$383$	− 1.29749i	− 0.0662988i	−0.999450	−	0.0331494i	$-0.989446\pi$
$383$	− 1.29749i	− 0.0662988i	0.999450	−	0.0331494i	$-0.0105537\pi$
$384$	−8.72867	−0.445433
$385$	0	0
$386$	−14.7569	−0.751107
$387$	− 29.3928i	− 1.49412i
$388$	69.5978i	3.53329i
$389$	−31.3099	−1.58747	−0.793737	−	0.608261i	$-0.791867\pi$
$389$	−31.3099	−1.58747	−0.793737	+	0.608261i	$0.791867\pi$
$390$	0	0
$391$	−16.9833	−0.858882
$392$	56.9305i	2.87543i
$393$	8.66863i	0.437274i
$394$	25.6871	1.29410
$395$	0	0
$396$	−24.1410	−1.21313
$397$	− 6.53409i	− 0.327937i	−0.986466	−	0.163968i	$-0.947570\pi$
$397$	− 6.53409i	− 0.327937i	0.986466	−	0.163968i	$-0.0524295\pi$
$398$	25.8907i	1.29779i
$399$	−1.66829	−0.0835191
$400$	0	0
$401$	−9.19104	−0.458978	−0.229489	−	0.973311i	$-0.573706\pi$
$401$	−9.19104	−0.458978	−0.229489	+	0.973311i	$0.573706\pi$
$402$	− 15.3452i	− 0.765347i
$403$	19.2432i	0.958573i
$404$	−13.1430	−0.653888
$405$	0	0
$406$	0.304597	0.0151169
$407$	− 1.85927i	− 0.0921604i
$408$	14.0984i	0.697973i
$409$	34.8027	1.72088	0.860442	−	0.509549i	$-0.170188\pi$
$409$	34.8027	1.72088	0.860442	+	0.509549i	$0.170188\pi$
$410$	0	0
$411$	4.55462	0.224663
$412$	− 42.3465i	− 2.08626i
$413$	− 0.802174i	− 0.0394724i
$414$	−45.2843	−2.22560
$415$	0	0
$416$	−71.0136	−3.48173
$417$	4.07543i	0.199575i
$418$	40.3099i	1.97162i
$419$	13.4200	0.655608	0.327804	−	0.944746i	$-0.393691\pi$
$419$	13.4200	0.655608	0.327804	+	0.944746i	$0.393691\pi$
$420$	0	0
$421$	21.6891	1.05706	0.528532	−	0.848913i	$-0.322743\pi$
$421$	21.6891	1.05706	0.528532	+	0.848913i	$0.322743\pi$
$422$	− 48.6555i	− 2.36851i
$423$	10.5408i	0.512512i
$424$	−20.7348	−1.00697
$425$	0	0
$426$	−26.4482	−1.28142
$427$	0.891609i	0.0431480i
$428$	52.3547i	2.53066i
$429$	5.97232	0.288346
$430$	0	0
$431$	−21.5555	−1.03829	−0.519145	−	0.854686i	$-0.673750\pi$
$431$	−21.5555	−1.03829	−0.519145	+	0.854686i	$0.673750\pi$
$432$	43.8587i	2.11015i
$433$	7.21533i	0.346747i	0.984856	+	0.173373i	$0.0554667\pi$
$433$	7.21533i	0.346747i	−0.984856	+	0.173373i	$0.944533\pi$
$434$	3.27041	0.156985
$435$	0	0
$436$	−100.625	−4.81907
$437$	54.2982i	2.59744i
$438$	14.9061i	0.712240i
$439$	−11.6800	−0.557455	−0.278728	−	0.960370i	$-0.589913\pi$
$439$	−11.6800	−0.557455	−0.278728	+	0.960370i	$0.589913\pi$
$440$	0	0
$441$	17.6032	0.838250
$442$	32.4223i	1.54217i
$443$	2.79428i	0.132760i	0.997794	+	0.0663802i	$0.0211450\pi$
$443$	2.79428i	0.132760i	−0.997794	+	0.0663802i	$0.978855\pi$
$444$	−3.42271	−0.162435
$445$	0	0
$446$	10.3883	0.491898
$447$	6.90795i	0.326735i
$448$	4.89035i	0.231047i
$449$	27.3557	1.29099	0.645497	−	0.763763i	$-0.276650\pi$
$449$	27.3557	1.29099	0.645497	+	0.763763i	$0.276650\pi$
$450$	0	0
$451$	5.69562	0.268196
$452$	− 0.983512i	− 0.0462605i
$453$	7.51622i	0.353143i
$454$	−61.3097	−2.87741
$455$	0	0
$456$	45.0747	2.11082
$457$	32.6562i	1.52759i	0.645458	+	0.763796i	$0.276667\pi$
$457$	32.6562i	1.52759i	−0.645458	+	0.763796i	$0.723333\pi$
$458$	− 66.4091i	− 3.10309i
$459$	9.49063	0.442985
$460$	0	0
$461$	16.8322	0.783955	0.391977	−	0.919975i	$-0.371791\pi$
$461$	16.8322	0.783955	0.391977	+	0.919975i	$0.371791\pi$
$462$	− 1.01500i	− 0.0472223i
$463$	− 11.0460i	− 0.513353i	−0.966497	−	0.256676i	$-0.917373\pi$
$463$	− 11.0460i	− 0.513353i	0.966497	−	0.256676i	$-0.0826274\pi$
$464$	−4.41030	−0.204743
$465$	0	0
$466$	−72.3697	−3.35246
$467$	− 3.59552i	− 0.166381i	−0.996534	−	0.0831904i	$-0.973489\pi$
$467$	− 3.59552i	− 0.166381i	0.996534	−	0.0831904i	$-0.0265110\pi$
$468$	62.0798i	2.86964i
$469$	−2.61604	−0.120797
$470$	0	0
$471$	−11.1796	−0.515127
$472$	21.6735i	0.997603i
$473$	− 21.4425i	− 0.985927i
$474$	−15.0606	−0.691756
$475$	0	0
$476$	3.95685	0.181362
$477$	6.41132i	0.293554i
$478$	30.5425i	1.39698i
$479$	13.3049	0.607915	0.303958	−	0.952686i	$-0.401692\pi$
$479$	13.3049	0.607915	0.303958	+	0.952686i	$0.401692\pi$
$480$	0	0
$481$	−4.78120	−0.218004
$482$	36.3792i	1.65703i
$483$	− 1.36723i	− 0.0622112i
$484$	38.4289	1.74677
$485$	0	0
$486$	38.9880	1.76853
$487$	14.6228i	0.662624i	0.943521	+	0.331312i	$0.107491\pi$
$487$	14.6228i	0.662624i	−0.943521	+	0.331312i	$0.892509\pi$
$488$	− 24.0899i	− 1.09050i
$489$	−7.46529	−0.337592
$490$	0	0
$491$	−16.3252	−0.736745	−0.368373	−	0.929678i	$-0.620085\pi$
$491$	−16.3252	−0.736745	−0.368373	+	0.929678i	$0.620085\pi$
$492$	− 10.4850i	− 0.472702i
$493$	0.954350i	0.0429817i
$494$	103.659	4.66384
$495$	0	0
$496$	−47.3528	−2.12620
$497$	4.50888i	0.202251i
$498$	− 19.4058i	− 0.869595i
$499$	5.52070	0.247140	0.123570	−	0.992336i	$-0.460566\pi$
$499$	5.52070	0.247140	0.123570	+	0.992336i	$0.460566\pi$
$500$	0	0
$501$	−1.51053	−0.0674856
$502$	17.7336i	0.791488i
$503$	8.54778i	0.381127i	0.981675	+	0.190563i	$0.0610315\pi$
$503$	8.54778i	0.381127i	−0.981675	+	0.190563i	$0.938969\pi$
$504$	6.40866	0.285464
$505$	0	0
$506$	−33.0355	−1.46861
$507$	− 6.62425i	− 0.294193i
$508$	− 16.3835i	− 0.726901i
$509$	−28.9252	−1.28209	−0.641044	−	0.767505i	$-0.721498\pi$
$509$	−28.9252	−1.28209	−0.641044	+	0.767505i	$0.721498\pi$
$510$	0	0
$511$	2.54118	0.112415
$512$	19.2055i	0.848772i
$513$	− 30.3430i	− 1.33968i
$514$	−30.8666	−1.36147
$515$	0	0
$516$	−39.4734	−1.73772
$517$	7.68969i	0.338192i
$518$	0.812573i	0.0357024i
$519$	−6.97195	−0.306034
$520$	0	0
$521$	−7.22238	−0.316418	−0.158209	−	0.987406i	$-0.550572\pi$
$521$	−7.22238	−0.316418	−0.158209	+	0.987406i	$0.550572\pi$
$522$	2.54468i	0.111378i
$523$	− 17.6241i	− 0.770647i	−0.922782	−	0.385324i	$-0.874090\pi$
$523$	− 17.6241i	− 0.770647i	0.922782	−	0.385324i	$-0.125910\pi$
$524$	−65.7343	−2.87161
$525$	0	0
$526$	45.6543	1.99062
$527$	10.2467i	0.446354i
$528$	14.6964i	0.639578i
$529$	−21.4995	−0.934761
$530$	0	0
$531$	6.70156	0.290823
$532$	− 12.6507i	− 0.548476i
$533$	− 14.6466i	− 0.634415i
$534$	−31.6833	−1.37107
$535$	0	0
$536$	70.6813	3.05297
$537$	6.49973i	0.280484i
$538$	− 5.34035i	− 0.230239i
$539$	12.8418	0.553136
$540$	0	0
$541$	7.75499	0.333413	0.166707	−	0.986007i	$-0.446687\pi$
$541$	7.75499	0.333413	0.166707	+	0.986007i	$0.446687\pi$
$542$	− 15.5239i	− 0.666807i
$543$	14.8635i	0.637852i
$544$	−37.8136	−1.62125
$545$	0	0
$546$	−2.61014	−0.111704
$547$	− 13.7097i	− 0.586186i	−0.956084	−	0.293093i	$-0.905315\pi$
$547$	− 13.7097i	− 0.586186i	0.956084	−	0.293093i	$-0.0946846\pi$
$548$	34.5377i	1.47538i
$549$	−7.44873	−0.317904
$550$	0	0
$551$	3.05120	0.129986
$552$	36.9405i	1.57229i
$553$	2.56752i	0.109182i
$554$	58.1516	2.47062
$555$	0	0
$556$	−30.9040	−1.31062
$557$	− 18.5503i	− 0.786001i	−0.919538	−	0.393000i	$-0.871437\pi$
$557$	− 18.5503i	− 0.786001i	0.919538	−	0.393000i	$-0.128563\pi$
$558$	27.3219i	1.15663i
$559$	−55.1405	−2.33220
$560$	0	0
$561$	3.18017	0.134267
$562$	− 9.49423i	− 0.400490i
$563$	42.1208i	1.77518i	0.460635	+	0.887590i	$0.347622\pi$
$563$	42.1208i	1.77518i	−0.460635	+	0.887590i	$0.652378\pi$
$564$	14.1559	0.596071
$565$	0	0
$566$	37.4063	1.57230
$567$	− 1.56850i	− 0.0658707i
$568$	− 121.823i	− 5.11158i
$569$	−2.03727	−0.0854066	−0.0427033	−	0.999088i	$-0.513597\pi$
$569$	−2.03727	−0.0854066	−0.0427033	+	0.999088i	$0.513597\pi$
$570$	0	0
$571$	−8.16633	−0.341750	−0.170875	−	0.985293i	$-0.554659\pi$
$571$	−8.16633	−0.341750	−0.170875	+	0.985293i	$0.554659\pi$
$572$	45.2881i	1.89359i
$573$	9.02218i	0.376907i
$574$	−2.48921	−0.103898
$575$	0	0
$576$	−40.8553	−1.70230
$577$	9.12193i	0.379751i	0.981808	+	0.189875i	$0.0608084\pi$
$577$	9.12193i	0.379751i	−0.981808	+	0.189875i	$0.939192\pi$
$578$	− 28.0161i	− 1.16532i
$579$	3.72218	0.154689
$580$	0	0
$581$	−3.30830	−0.137251
$582$	− 24.4465i	− 1.01334i
$583$	4.67715i	0.193708i
$584$	−68.6589	−2.84112
$585$	0	0
$586$	63.7913	2.63519
$587$	10.4884i	0.432902i	0.976293	+	0.216451i	$0.0694482\pi$
$587$	10.4884i	0.432902i	−0.976293	+	0.216451i	$0.930552\pi$
$588$	− 23.6404i	− 0.974916i
$589$	32.7604	1.34987
$590$	0	0
$591$	−6.47913	−0.266516
$592$	− 11.7653i	− 0.483553i
$593$	5.23762i	0.215083i	0.994201	+	0.107542i	$0.0342979\pi$
$593$	5.23762i	0.215083i	−0.994201	+	0.107542i	$0.965702\pi$
$594$	18.4610	0.757463
$595$	0	0
$596$	−52.3830	−2.14569
$597$	− 6.53050i	− 0.267276i
$598$	84.9527i	3.47397i
$599$	−19.5578	−0.799108	−0.399554	−	0.916710i	$-0.630835\pi$
$599$	−19.5578	−0.799108	−0.399554	+	0.916710i	$0.630835\pi$
$600$	0	0
$601$	11.3565	0.463242	0.231621	−	0.972806i	$-0.425597\pi$
$601$	11.3565	0.463242	0.231621	+	0.972806i	$0.425597\pi$
$602$	9.37122i	0.381942i
$603$	− 21.8550i	− 0.890006i
$604$	−56.9955	−2.31912
$605$	0	0
$606$	4.61652	0.187534
$607$	− 27.7177i	− 1.12503i	−0.826788	−	0.562514i	$-0.809834\pi$
$607$	− 27.7177i	− 1.12503i	0.826788	−	0.562514i	$-0.190166\pi$
$608$	120.896i	4.90298i
$609$	−0.0768294	−0.00311328
$610$	0	0
$611$	19.7744	0.799989
$612$	33.0566i	1.33623i
$613$	− 17.1015i	− 0.690725i	−0.938469	−	0.345362i	$-0.887756\pi$
$613$	− 17.1015i	− 0.690725i	0.938469	−	0.345362i	$-0.112244\pi$
$614$	−9.06788	−0.365950
$615$	0	0
$616$	4.67521	0.188370
$617$	− 21.3110i	− 0.857950i	−0.903316	−	0.428975i	$-0.858875\pi$
$617$	− 21.3110i	− 0.857950i	0.903316	−	0.428975i	$-0.141125\pi$
$618$	14.8744i	0.598335i
$619$	−12.0242	−0.483292	−0.241646	−	0.970364i	$-0.577687\pi$
$619$	−12.0242	−0.483292	−0.241646	+	0.970364i	$0.577687\pi$
$620$	0	0
$621$	24.8673	0.997889
$622$	− 4.92795i	− 0.197593i
$623$	5.40137i	0.216401i
$624$	37.7926	1.51291
$625$	0	0
$626$	66.0845	2.64127
$627$	− 10.1675i	− 0.406051i
$628$	− 84.7746i	− 3.38287i
$629$	−2.54592	−0.101512
$630$	0	0
$631$	−33.0174	−1.31440	−0.657201	−	0.753715i	$-0.728260\pi$
$631$	−33.0174	−1.31440	−0.657201	+	0.753715i	$0.728260\pi$
$632$	− 69.3705i	− 2.75941i
$633$	12.2725i	0.487789i
$634$	−77.3655	−3.07258
$635$	0	0
$636$	8.61014	0.341414
$637$	− 33.0234i	− 1.30844i
$638$	1.85638i	0.0734948i
$639$	−37.6683	−1.49014
$640$	0	0
$641$	14.2676	0.563535	0.281767	−	0.959483i	$-0.409079\pi$
$641$	14.2676	0.563535	0.281767	+	0.959483i	$0.409079\pi$
$642$	− 18.3898i	− 0.725787i
$643$	− 22.5157i	− 0.887932i	−0.896044	−	0.443966i	$-0.853571\pi$
$643$	− 22.5157i	− 0.887932i	0.896044	−	0.443966i	$-0.146429\pi$
$644$	10.3677	0.408545
$645$	0	0
$646$	55.1969	2.17169
$647$	− 41.2531i	− 1.62183i	−0.585167	−	0.810913i	$-0.698971\pi$
$647$	− 41.2531i	− 1.62183i	0.585167	−	0.810913i	$-0.301029\pi$
$648$	42.3784i	1.66478i
$649$	4.88889	0.191906
$650$	0	0
$651$	−0.824907	−0.0323306
$652$	− 56.6093i	− 2.21699i
$653$	13.4063i	0.524628i	0.964983	+	0.262314i	$0.0844857\pi$
$653$	13.4063i	0.524628i	−0.964983	+	0.262314i	$0.915514\pi$
$654$	35.3449	1.38210
$655$	0	0
$656$	36.0416	1.40719
$657$	21.2297i	0.828250i
$658$	− 3.36070i	− 0.131014i
$659$	35.6948	1.39047	0.695236	−	0.718781i	$-0.255300\pi$
$659$	35.6948	1.39047	0.695236	+	0.718781i	$0.255300\pi$
$660$	0	0
$661$	−33.2215	−1.29217	−0.646084	−	0.763266i	$-0.723595\pi$
$661$	−33.2215	−1.29217	−0.646084	+	0.763266i	$0.723595\pi$
$662$	15.3247i	0.595612i
$663$	− 8.17798i	− 0.317606i
$664$	89.3851	3.46881
$665$	0	0
$666$	−6.78844	−0.263047
$667$	2.50058i	0.0968229i
$668$	− 11.4544i	− 0.443183i
$669$	−2.62026	−0.101305
$670$	0	0
$671$	−5.43396	−0.209776
$672$	− 3.04417i	− 0.117431i
$673$	− 34.4820i	− 1.32918i	−0.747206	−	0.664592i	$-0.768605\pi$
$673$	− 34.4820i	− 1.32918i	0.747206	−	0.664592i	$-0.231395\pi$
$674$	−5.16348	−0.198890
$675$	0	0
$676$	50.2317	1.93199
$677$	13.6122i	0.523158i	0.965182	+	0.261579i	$0.0842432\pi$
$677$	13.6122i	0.523158i	−0.965182	+	0.261579i	$0.915757\pi$
$678$	0.345462i	0.0132674i
$679$	−4.16763	−0.159939
$680$	0	0
$681$	15.4643	0.592595
$682$	19.9317i	0.763225i
$683$	22.3789i	0.856304i	0.903707	+	0.428152i	$0.140835\pi$
$683$	22.3789i	0.856304i	−0.903707	+	0.428152i	$0.859165\pi$
$684$	105.687	4.04104
$685$	0	0
$686$	−11.3004	−0.431451
$687$	16.7506i	0.639074i
$688$	− 135.687i	− 5.17302i
$689$	12.0275	0.458213
$690$	0	0
$691$	−24.7590	−0.941877	−0.470938	−	0.882166i	$-0.656085\pi$
$691$	−24.7590	−0.941877	−0.470938	+	0.882166i	$0.656085\pi$
$692$	− 52.8683i	− 2.00975i
$693$	− 1.44560i	− 0.0549139i
$694$	56.3461	2.13887
$695$	0	0
$696$	2.07581	0.0786834
$697$	− 7.79909i	− 0.295412i
$698$	− 43.7175i	− 1.65473i
$699$	18.2540	0.690431
$700$	0	0
$701$	4.21211	0.159089	0.0795446	−	0.996831i	$-0.474653\pi$
$701$	4.21211	0.159089	0.0795446	+	0.996831i	$0.474653\pi$
$702$	− 47.4734i	− 1.79177i
$703$	8.13969i	0.306994i
$704$	−29.8045	−1.12330
$705$	0	0
$706$	1.48495	0.0558868
$707$	− 0.787024i	− 0.0295991i
$708$	− 8.99993i	− 0.338238i
$709$	−27.8603	−1.04632	−0.523158	−	0.852236i	$-0.675246\pi$
$709$	−27.8603	−1.04632	−0.523158	+	0.852236i	$0.675246\pi$
$710$	0	0
$711$	−21.4498	−0.804429
$712$	− 145.936i	− 5.46920i
$713$	26.8484i	1.00548i
$714$	−1.38986	−0.0520142
$715$	0	0
$716$	−49.2875	−1.84196
$717$	− 7.70384i	− 0.287705i
$718$	7.78707i	0.290611i
$719$	16.3154	0.608460	0.304230	−	0.952599i	$-0.401601\pi$
$719$	16.3154	0.608460	0.304230	+	0.952599i	$0.401601\pi$
$720$	0	0
$721$	2.53578	0.0944373
$722$	− 125.865i	− 4.68423i
$723$	− 9.17604i	− 0.341261i
$724$	−112.710	−4.18882
$725$	0	0
$726$	−13.4983	−0.500968
$727$	33.2581i	1.23348i	0.787168	+	0.616738i	$0.211546\pi$
$727$	33.2581i	1.23348i	−0.787168	+	0.616738i	$0.788454\pi$
$728$	− 12.0226i	− 0.445586i
$729$	5.59024	0.207046
$730$	0	0
$731$	−29.3615	−1.08597
$732$	10.0033i	0.369734i
$733$	2.17580i	0.0803648i	0.999192	+	0.0401824i	$0.0127939\pi$
$733$	2.17580i	0.0803648i	−0.999192	+	0.0401824i	$0.987206\pi$
$734$	24.2870	0.896448
$735$	0	0
$736$	−99.0791	−3.65210
$737$	− 15.9436i	− 0.587289i
$738$	− 20.7955i	− 0.765493i
$739$	39.0865	1.43782	0.718910	−	0.695103i	$-0.244641\pi$
$739$	39.0865	1.43782	0.718910	+	0.695103i	$0.244641\pi$
$740$	0	0
$741$	−26.1463	−0.960507
$742$	− 2.04410i	− 0.0750412i
$743$	− 32.4833i	− 1.19170i	−0.803097	−	0.595848i	$-0.796816\pi$
$743$	− 32.4833i	− 1.19170i	0.803097	−	0.595848i	$-0.203184\pi$
$744$	22.2877	0.817107
$745$	0	0
$746$	−37.4473	−1.37104
$747$	− 27.6384i	− 1.01123i
$748$	24.1152i	0.881740i
$749$	−3.13509	−0.114554
$750$	0	0
$751$	33.0898	1.20747	0.603733	−	0.797187i	$-0.293679\pi$
$751$	33.0898	1.20747	0.603733	+	0.797187i	$0.293679\pi$
$752$	48.6600i	1.77445i
$753$	− 4.47299i	− 0.163005i
$754$	4.77378	0.173851
$755$	0	0
$756$	−5.79370	−0.210715
$757$	14.4706i	0.525942i	0.964804	+	0.262971i	$0.0847023\pi$
$757$	14.4706i	0.525942i	−0.964804	+	0.262971i	$0.915298\pi$
$758$	1.63785i	0.0594894i
$759$	8.33266	0.302456
$760$	0	0
$761$	−0.396943	−0.0143892	−0.00719459	−	0.999974i	$-0.502290\pi$
$761$	−0.396943	−0.0143892	−0.00719459	+	0.999974i	$0.502290\pi$
$762$	5.75477i	0.208473i
$763$	− 6.02559i	− 0.218141i
$764$	−68.4152	−2.47518
$765$	0	0
$766$	−3.45595	−0.124868
$767$	− 12.5720i	− 0.453950i
$768$	1.70987i	0.0616997i
$769$	40.3582	1.45535	0.727676	−	0.685921i	$-0.240600\pi$
$769$	40.3582	1.45535	0.727676	+	0.685921i	$0.240600\pi$
$770$	0	0
$771$	7.78557	0.280390
$772$	28.2253i	1.01585i
$773$	− 34.5410i	− 1.24236i	−0.783670	−	0.621178i	$-0.786655\pi$
$773$	− 34.5410i	− 1.24236i	0.783670	−	0.621178i	$-0.213345\pi$
$774$	−78.2895	−2.81406
$775$	0	0
$776$	112.603	4.04221
$777$	− 0.204958i	− 0.00735282i
$778$	83.3957i	2.98988i
$779$	−24.9349	−0.893386
$780$	0	0
$781$	−27.4796	−0.983298
$782$	45.2360i	1.61764i
$783$	− 1.39738i	− 0.0499382i
$784$	81.2625	2.90223
$785$	0	0
$786$	23.0894	0.823572
$787$	− 22.2006i	− 0.791365i	−0.918387	−	0.395682i	$-0.870508\pi$
$787$	− 22.2006i	− 0.791365i	0.918387	−	0.395682i	$-0.129492\pi$
$788$	− 49.1313i	− 1.75023i
$789$	−11.5155	−0.409963
$790$	0	0
$791$	0.0588943	0.00209404
$792$	39.0579i	1.38786i
$793$	13.9737i	0.496221i
$794$	−17.4039	−0.617643
$795$	0	0
$796$	49.5208	1.75522
$797$	21.1930i	0.750695i	0.926884	+	0.375348i	$0.122477\pi$
$797$	21.1930i	0.750695i	−0.926884	+	0.375348i	$0.877523\pi$
$798$	4.44360i	0.157302i
$799$	10.5296	0.372510
$800$	0	0
$801$	−45.1244	−1.59439
$802$	24.4809i	0.864450i
$803$	15.4874i	0.546538i
$804$	−29.3505	−1.03511
$805$	0	0
$806$	51.2555	1.80540
$807$	1.34701i	0.0474171i
$808$	21.2642i	0.748071i
$809$	−9.51326	−0.334468	−0.167234	−	0.985917i	$-0.553484\pi$
$809$	−9.51326	−0.334468	−0.167234	+	0.985917i	$0.553484\pi$
$810$	0	0
$811$	−31.4978	−1.10604	−0.553019	−	0.833169i	$-0.686524\pi$
$811$	−31.4978	−1.10604	−0.553019	+	0.833169i	$0.686524\pi$
$812$	− 0.582598i	− 0.0204452i
$813$	3.91563i	0.137327i
$814$	−4.95226	−0.173577
$815$	0	0
$816$	20.1240	0.704480
$817$	93.8733i	3.28421i
$818$	− 92.6991i	− 3.24115i
$819$	−3.71744	−0.129898
$820$	0	0
$821$	24.2852	0.847558	0.423779	−	0.905766i	$-0.360703\pi$
$821$	24.2852	0.847558	0.423779	+	0.905766i	$0.360703\pi$
$822$	− 12.1315i	− 0.423134i
$823$	23.7422i	0.827602i	0.910367	+	0.413801i	$0.135799\pi$
$823$	23.7422i	0.827602i	−0.910367	+	0.413801i	$0.864201\pi$
$824$	−68.5128	−2.38676
$825$	0	0
$826$	−2.13664	−0.0743431
$827$	− 30.7256i	− 1.06844i	−0.845347	−	0.534218i	$-0.820606\pi$
$827$	− 30.7256i	− 1.06844i	0.845347	−	0.534218i	$-0.179394\pi$
$828$	86.6146i	3.01006i
$829$	19.9615	0.693290	0.346645	−	0.937996i	$-0.387321\pi$
$829$	19.9615	0.693290	0.346645	+	0.937996i	$0.387321\pi$
$830$	0	0
$831$	−14.6678	−0.508819
$832$	76.6439i	2.65715i
$833$	− 17.5845i	− 0.609266i
$834$	10.8551	0.375883
$835$	0	0
$836$	77.1002	2.66656
$837$	− 15.0035i	− 0.518595i
$838$	− 35.7449i	− 1.23479i
$839$	−27.5692	−0.951796	−0.475898	−	0.879501i	$-0.657877\pi$
$839$	−27.5692	−0.951796	−0.475898	+	0.879501i	$0.657877\pi$
$840$	0	0
$841$	−28.8595	−0.995155
$842$	− 57.7703i	− 1.99090i
$843$	2.39476i	0.0824799i
$844$	−93.0626	−3.20335
$845$	0	0
$846$	28.0761	0.965277
$847$	2.30118i	0.0790696i
$848$	29.5968i	1.01636i
$849$	−9.43510	−0.323812
$850$	0	0
$851$	−6.67080	−0.228672
$852$	50.5871i	1.73308i
$853$	2.05731i	0.0704408i	0.999380	+	0.0352204i	$0.0112133\pi$
$853$	2.05731i	0.0704408i	−0.999380	+	0.0352204i	$0.988787\pi$
$854$	2.37485	0.0812659
$855$	0	0
$856$	84.7052	2.89516
$857$	− 2.81604i	− 0.0961942i	−0.998843	−	0.0480971i	$-0.984684\pi$
$857$	− 2.81604i	− 0.0961942i	0.998843	−	0.0480971i	$-0.0153157\pi$
$858$	− 15.9076i	− 0.543078i
$859$	9.11129	0.310873	0.155437	−	0.987846i	$-0.450322\pi$
$859$	9.11129	0.310873	0.155437	+	0.987846i	$0.450322\pi$
$860$	0	0
$861$	0.627862	0.0213975
$862$	57.4143i	1.95554i
$863$	9.48116i	0.322743i	0.986894	+	0.161371i	$0.0515917\pi$
$863$	9.48116i	0.322743i	−0.986894	+	0.161371i	$0.948408\pi$
$864$	55.3675	1.88364
$865$	0	0
$866$	19.2185	0.653070
$867$	7.06660i	0.239994i
$868$	− 6.25527i	− 0.212318i
$869$	−15.6479	−0.530819
$870$	0	0
$871$	−40.9998	−1.38922
$872$	162.802i	5.51318i
$873$	− 34.8175i	− 1.17839i
$874$	144.627	4.89207
$875$	0	0
$876$	28.5106	0.963285
$877$	5.35815i	0.180932i	0.995900	+	0.0904659i	$0.0288356\pi$
$877$	5.35815i	0.180932i	−0.995900	+	0.0904659i	$0.971164\pi$
$878$	31.1103i	1.04992i
$879$	−16.0903	−0.542712
$880$	0	0
$881$	−46.0547	−1.55162	−0.775812	−	0.630964i	$-0.782659\pi$
$881$	−46.0547	−1.55162	−0.775812	+	0.630964i	$0.782659\pi$
$882$	− 46.8873i	− 1.57878i
$883$	40.0651i	1.34830i	0.738595	+	0.674150i	$0.235490\pi$
$883$	40.0651i	1.34830i	−0.738595	+	0.674150i	$0.764510\pi$
$884$	62.0137	2.08574
$885$	0	0
$886$	7.44274	0.250044
$887$	27.6759i	0.929266i	0.885503	+	0.464633i	$0.153814\pi$
$887$	27.6759i	0.929266i	−0.885503	+	0.464633i	$0.846186\pi$
$888$	5.53764i	0.185831i
$889$	0.981072	0.0329041
$890$	0	0
$891$	9.55929	0.320248
$892$	− 19.8695i	− 0.665279i
$893$	− 33.6647i	− 1.12655i
$894$	18.3997	0.615379
$895$	0	0
$896$	3.96354	0.132413
$897$	− 21.4279i	− 0.715456i
$898$	− 72.8635i	− 2.43149i
$899$	1.50870	0.0503181
$900$	0	0
$901$	6.40448	0.213364
$902$	− 15.1706i	− 0.505127i
$903$	− 2.36373i	− 0.0786601i
$904$	−1.59123	−0.0529236
$905$	0	0
$906$	20.0199	0.665117
$907$	15.4980i	0.514603i	0.966331	+	0.257302i	$0.0828334\pi$
$907$	15.4980i	0.514603i	−0.966331	+	0.257302i	$0.917167\pi$
$908$	117.266i	3.89162i
$909$	6.57500	0.218079
$910$	0	0
$911$	−32.7886	−1.08633	−0.543167	−	0.839625i	$-0.682775\pi$
$911$	−32.7886	−1.08633	−0.543167	+	0.839625i	$0.682775\pi$
$912$	− 64.3394i	− 2.13049i
$913$	− 20.1626i	− 0.667284i
$914$	86.9817	2.87710
$915$	0	0
$916$	−127.020	−4.19685
$917$	− 3.93628i	− 0.129987i
$918$	− 25.2789i	− 0.834326i
$919$	0.940187	0.0310139	0.0155070	−	0.999880i	$-0.495064\pi$
$919$	0.940187	0.0310139	0.0155070	+	0.999880i	$0.495064\pi$
$920$	0	0
$921$	2.28722	0.0753665
$922$	− 44.8336i	− 1.47652i
$923$	70.6653i	2.32598i
$924$	−1.94138	−0.0638669
$925$	0	0
$926$	−29.4218	−0.966859
$927$	21.1845i	0.695791i
$928$	5.56759i	0.182765i
$929$	7.74285	0.254035	0.127017	−	0.991900i	$-0.459460\pi$
$929$	7.74285	0.254035	0.127017	+	0.991900i	$0.459460\pi$
$930$	0	0
$931$	−56.2203	−1.84255
$932$	138.421i	4.53411i
$933$	1.24299i	0.0406937i
$934$	−9.57688	−0.313365
$935$	0	0
$936$	100.440	3.28297
$937$	− 27.8977i	− 0.911377i	−0.890139	−	0.455689i	$-0.849393\pi$
$937$	− 27.8977i	− 0.911377i	0.890139	−	0.455689i	$-0.150607\pi$
$938$	6.96797i	0.227512i
$939$	−16.6687	−0.543963
$940$	0	0
$941$	−49.2272	−1.60476	−0.802380	−	0.596813i	$-0.796433\pi$
$941$	−49.2272	−1.60476	−0.802380	+	0.596813i	$0.796433\pi$
$942$	29.7774i	0.970200i
$943$	− 20.4351i	− 0.665459i
$944$	30.9367	1.00690
$945$	0	0
$946$	−57.1134	−1.85692
$947$	37.8698i	1.23060i	0.788291	+	0.615302i	$0.210966\pi$
$947$	37.8698i	1.23060i	−0.788291	+	0.615302i	$0.789034\pi$
$948$	28.8062i	0.935581i
$949$	39.8266	1.29283
$950$	0	0
$951$	19.5141	0.632789
$952$	− 6.40183i	− 0.207484i
$953$	− 33.5987i	− 1.08837i	−0.838965	−	0.544185i	$-0.816839\pi$
$953$	− 33.5987i	− 1.08837i	0.838965	−	0.544185i	$-0.183161\pi$
$954$	17.0769	0.552886
$955$	0	0
$956$	58.4183	1.88938
$957$	− 0.468241i	− 0.0151361i
$958$	− 35.4383i	− 1.14496i
$959$	−2.06817	−0.0667848
$960$	0	0
$961$	−14.8013	−0.477460
$962$	12.7350i	0.410593i
$963$	− 26.1913i	− 0.844003i
$964$	69.5820	2.24109
$965$	0	0
$966$	−3.64170	−0.117170
$967$	32.5035i	1.04524i	0.852565	+	0.522622i	$0.175046\pi$
$967$	32.5035i	1.04524i	−0.852565	+	0.522622i	$0.824954\pi$
$968$	− 62.1744i	− 1.99836i
$969$	−13.9225	−0.447255
$970$	0	0
$971$	−30.1776	−0.968445	−0.484223	−	0.874945i	$-0.660898\pi$
$971$	−30.1776	−0.968445	−0.484223	+	0.874945i	$0.660898\pi$
$972$	− 74.5718i	− 2.39189i
$973$	− 1.85058i	− 0.0593269i
$974$	38.9488	1.24800
$975$	0	0
$976$	−34.3858	−1.10066
$977$	− 41.4992i	− 1.32768i	−0.747876	−	0.663839i	$-0.768926\pi$
$977$	− 41.4992i	− 1.32768i	0.747876	−	0.663839i	$-0.231074\pi$
$978$	19.8842i	0.635828i
$979$	−32.9189	−1.05209
$980$	0	0
$981$	50.3394	1.60721
$982$	43.4831i	1.38760i
$983$	21.6389i	0.690173i	0.938571	+	0.345086i	$0.112150\pi$
$983$	21.6389i	0.690173i	−0.938571	+	0.345086i	$0.887850\pi$
$984$	−16.9638	−0.540788
$985$	0	0
$986$	2.54197	0.0809527
$987$	0.847679i	0.0269819i
$988$	− 198.267i	− 6.30772i
$989$	−76.9328	−2.44632
$990$	0	0
$991$	19.4143	0.616714	0.308357	−	0.951271i	$-0.400221\pi$
$991$	19.4143	0.616714	0.308357	+	0.951271i	$0.400221\pi$
$992$	59.7785i	1.89797i
$993$	− 3.86540i	− 0.122665i
$994$	12.0097	0.380924
$995$	0	0
$996$	−37.1172	−1.17610
$997$	− 10.2171i	− 0.323578i	−0.986825	−	0.161789i	$-0.948274\pi$
$997$	− 10.2171i	− 0.323578i	0.986825	−	0.161789i	$-0.0517264\pi$
$998$	− 14.7047i	− 0.465470i
$999$	3.72778	0.117942

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.b.g.149.1		10
5.2	odd	4		925.2.a.h.1.5		5
5.3	odd	4		185.2.a.d.1.1	✓	5
5.4	even	2	inner	925.2.b.g.149.10		10
15.2	even	4		8325.2.a.cc.1.1		5
15.8	even	4		1665.2.a.q.1.5		5
20.3	even	4		2960.2.a.ba.1.4		5
35.13	even	4		9065.2.a.j.1.1		5
185.73	odd	4		6845.2.a.g.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.a.d.1.1	✓	5	5.3	odd	4
925.2.a.h.1.5		5	5.2	odd	4
925.2.b.g.149.1		10	1.1	even	1	trivial
925.2.b.g.149.10		10	5.4	even	2	inner
1665.2.a.q.1.5		5	15.8	even	4
2960.2.a.ba.1.4		5	20.3	even	4
6845.2.a.g.1.5		5	185.73	odd	4
8325.2.a.cc.1.1		5	15.2	even	4
9065.2.a.j.1.1		5	35.13	even	4

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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.66356i q^{2} +0.671838i q^{3} -5.09455 q^{4} +1.78948 q^{6} -0.305070i q^{7} +8.24252i q^{8} +2.54863 q^{9} +O(q^{10})\)	\(q-2.66356i q^{2} +0.671838i q^{3} -5.09455 q^{4} +1.78948 q^{6} -0.305070i q^{7} +8.24252i q^{8} +2.54863 q^{9} +1.85927 q^{11} -3.42271i q^{12} -4.78120i q^{13} -0.812573 q^{14} +11.7653 q^{16} -2.54592i q^{17} -6.78844i q^{18} -8.13969 q^{19} +0.204958 q^{21} -4.95226i q^{22} -6.67080i q^{23} -5.53764 q^{24} -12.7350 q^{26} +3.72778i q^{27} +1.55420i q^{28} -0.374855 q^{29} -4.02477 q^{31} -14.8527i q^{32} +1.24913i q^{33} -6.78120 q^{34} -12.9841 q^{36} -1.00000i q^{37} +21.6806i q^{38} +3.21219 q^{39} +3.06337 q^{41} -0.545917i q^{42} -11.5328i q^{43} -9.47212 q^{44} -17.7681 q^{46} +4.13587i q^{47} +7.90441i q^{48} +6.90693 q^{49} +1.71044 q^{51} +24.3581i q^{52} +2.51559i q^{53} +9.92917 q^{54} +2.51455 q^{56} -5.46855i q^{57} +0.998448i q^{58} +2.62947 q^{59} -2.92264 q^{61} +10.7202i q^{62} -0.777512i q^{63} -16.0303 q^{64} +3.32712 q^{66} -8.57520i q^{67} +12.9703i q^{68} +4.48169 q^{69} -14.7798 q^{71} +21.0072i q^{72} +8.32984i q^{73} -2.66356 q^{74} +41.4681 q^{76} -0.567206i q^{77} -8.55587i q^{78} -8.41618 q^{79} +5.14143 q^{81} -8.15947i q^{82} -10.8444i q^{83} -1.04417 q^{84} -30.7182 q^{86} -0.251842i q^{87} +15.3250i q^{88} -17.7053 q^{89} -1.45860 q^{91} +33.9847i q^{92} -2.70399i q^{93} +11.0161 q^{94} +9.97858 q^{96} -13.6612i q^{97} -18.3970i q^{98} +4.73859 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 12 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) \) 10 * q - 12 * q^4 - 4 * q^6 - 4 * q^9	\( 10 q - 12 q^{4} - 4 q^{6} - 4 q^{9} + 14 q^{11} - 8 q^{14} + 16 q^{16} - 28 q^{19} - 18 q^{21} - 24 q^{24} - 40 q^{26} - 4 q^{29} + 16 q^{31} - 24 q^{34} - 72 q^{36} - 24 q^{39} - 18 q^{41} - 36 q^{44} - 56 q^{46} - 4 q^{49} + 20 q^{51} + 24 q^{54} - 28 q^{56} - 24 q^{59} + 24 q^{61} - 24 q^{64} - 20 q^{66} + 60 q^{69} + 26 q^{71} + 36 q^{76} - 72 q^{79} + 42 q^{81} - 60 q^{84} - 16 q^{86} + 32 q^{89} - 8 q^{91} - 40 q^{94} - 36 q^{99}+O(q^{100}) \) 10 * q - 12 * q^4 - 4 * q^6 - 4 * q^9 + 14 * q^11 - 8 * q^14 + 16 * q^16 - 28 * q^19 - 18 * q^21 - 24 * q^24 - 40 * q^26 - 4 * q^29 + 16 * q^31 - 24 * q^34 - 72 * q^36 - 24 * q^39 - 18 * q^41 - 36 * q^44 - 56 * q^46 - 4 * q^49 + 20 * q^51 + 24 * q^54 - 28 * q^56 - 24 * q^59 + 24 * q^61 - 24 * q^64 - 20 * q^66 + 60 * q^69 + 26 * q^71 + 36 * q^76 - 72 * q^79 + 42 * q^81 - 60 * q^84 - 16 * q^86 + 32 * q^89 - 8 * q^91 - 40 * q^94 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more