LMFDB - Embedded newform 1875.2.b.a.1249.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1875,2,Mod(1249,1875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1875, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1875.1249");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1875 = 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1875.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:	$14.9719503790$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1249.3
Root			$0.618034i$ of defining polynomial
Character	$\chi$	$=$	1875.1249
Dual form			1875.2.b.a.1249.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.618034i q^{2} +1.00000i q^{3} +1.61803 q^{4} -0.618034 q^{6} +2.00000i q^{7} +2.23607i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+0.618034i q^{2} +1.00000i q^{3} +1.61803 q^{4} -0.618034 q^{6} +2.00000i q^{7} +2.23607i q^{8} -1.00000 q^{9} -3.00000 q^{11} +1.61803i q^{12} -1.00000i q^{13} -1.23607 q^{14} +1.85410 q^{16} -0.236068i q^{17} -0.618034i q^{18} -6.70820 q^{19} -2.00000 q^{21} -1.85410i q^{22} +7.61803i q^{23} -2.23607 q^{24} +0.618034 q^{26} -1.00000i q^{27} +3.23607i q^{28} +1.38197 q^{29} -4.70820 q^{31} +5.61803i q^{32} -3.00000i q^{33} +0.145898 q^{34} -1.61803 q^{36} +2.00000i q^{37} -4.14590i q^{38} +1.00000 q^{39} -11.6180 q^{41} -1.23607i q^{42} -9.61803i q^{43} -4.85410 q^{44} -4.70820 q^{46} +9.23607i q^{47} +1.85410i q^{48} +3.00000 q^{49} +0.236068 q^{51} -1.61803i q^{52} +6.76393i q^{53} +0.618034 q^{54} -4.47214 q^{56} -6.70820i q^{57} +0.854102i q^{58} +13.9443 q^{59} -4.70820 q^{61} -2.90983i q^{62} -2.00000i q^{63} +0.236068 q^{64} +1.85410 q^{66} -9.18034i q^{67} -0.381966i q^{68} -7.61803 q^{69} -1.09017 q^{71} -2.23607i q^{72} +2.29180i q^{73} -1.23607 q^{74} -10.8541 q^{76} -6.00000i q^{77} +0.618034i q^{78} +15.8541 q^{79} +1.00000 q^{81} -7.18034i q^{82} +9.00000i q^{83} -3.23607 q^{84} +5.94427 q^{86} +1.38197i q^{87} -6.70820i q^{88} -11.1803 q^{89} +2.00000 q^{91} +12.3262i q^{92} -4.70820i q^{93} -5.70820 q^{94} -5.61803 q^{96} +2.85410i q^{97} +1.85410i q^{98} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 2 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 2 * q^6 - 4 * q^9	$ 4 q + 2 q^{4} + 2 q^{6} - 4 q^{9} - 12 q^{11} + 4 q^{14} - 6 q^{16} - 8 q^{21} - 2 q^{26} + 10 q^{29} + 8 q^{31} + 14 q^{34} - 2 q^{36} + 4 q^{39} - 42 q^{41} - 6 q^{44} + 8 q^{46} + 12 q^{49} - 8 q^{51} - 2 q^{54} + 20 q^{59} + 8 q^{61} - 8 q^{64} - 6 q^{66} - 26 q^{69} + 18 q^{71} + 4 q^{74} - 30 q^{76} + 50 q^{79} + 4 q^{81} - 4 q^{84} - 12 q^{86} + 8 q^{91} + 4 q^{94} - 18 q^{96} + 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 + 2 * q^6 - 4 * q^9 - 12 * q^11 + 4 * q^14 - 6 * q^16 - 8 * q^21 - 2 * q^26 + 10 * q^29 + 8 * q^31 + 14 * q^34 - 2 * q^36 + 4 * q^39 - 42 * q^41 - 6 * q^44 + 8 * q^46 + 12 * q^49 - 8 * q^51 - 2 * q^54 + 20 * q^59 + 8 * q^61 - 8 * q^64 - 6 * q^66 - 26 * q^69 + 18 * q^71 + 4 * q^74 - 30 * q^76 + 50 * q^79 + 4 * q^81 - 4 * q^84 - 12 * q^86 + 8 * q^91 + 4 * q^94 - 18 * q^96 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1875\mathbb{Z}\right)^\times$.

$n$	$626$	$1252$
$\chi(n)$	$1$	$-1$

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 $

$2$	0.618034i	0.437016i	0.975835	+	0.218508i	$0.0701190\pi$
$2$	0.618034i	0.437016i	−0.975835	+	0.218508i	$0.929881\pi$
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	1.61803	0.809017
$5$	0	0
$5$	0	0
$6$	−0.618034	−0.252311
$7$	2.00000i	0.755929i	0.925820	+	0.377964i	$0.123376\pi$
$7$	2.00000i	0.755929i	−0.925820	+	0.377964i	$0.876624\pi$
$8$	2.23607i	0.790569i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	1.61803i	0.467086i
$13$	− 1.00000i	− 0.277350i	−0.990338	−	0.138675i	$-0.955716\pi$
$13$	− 1.00000i	− 0.277350i	0.990338	−	0.138675i	$-0.0442844\pi$
$14$	−1.23607	−0.330353
$15$	0	0
$16$	1.85410	0.463525
$17$	− 0.236068i	− 0.0572549i	−0.999590	−	0.0286274i	$-0.990886\pi$
$17$	− 0.236068i	− 0.0572549i	0.999590	−	0.0286274i	$-0.00911364\pi$
$18$	− 0.618034i	− 0.145672i
$19$	−6.70820	−1.53897	−0.769484	−	0.638666i	$-0.779486\pi$
$19$	−6.70820	−1.53897	−0.769484	+	0.638666i	$0.779486\pi$
$20$	0	0
$21$	−2.00000	−0.436436
$22$	− 1.85410i	− 0.395296i
$23$	7.61803i	1.58847i	0.607611	+	0.794235i	$0.292128\pi$
$23$	7.61803i	1.58847i	−0.607611	+	0.794235i	$0.707872\pi$
$24$	−2.23607	−0.456435
$25$	0	0
$26$	0.618034	0.121206
$27$	− 1.00000i	− 0.192450i
$28$	3.23607i	0.611559i
$29$	1.38197	0.256625	0.128312	−	0.991734i	$-0.459044\pi$
$29$	1.38197	0.256625	0.128312	+	0.991734i	$0.459044\pi$
$30$	0	0
$31$	−4.70820	−0.845618	−0.422809	−	0.906219i	$-0.638956\pi$
$31$	−4.70820	−0.845618	−0.422809	+	0.906219i	$0.638956\pi$
$32$	5.61803i	0.993137i
$33$	− 3.00000i	− 0.522233i
$34$	0.145898	0.0250213
$35$	0	0
$36$	−1.61803	−0.269672
$37$	2.00000i	0.328798i	0.986394	+	0.164399i	$0.0525685\pi$
$37$	2.00000i	0.328798i	−0.986394	+	0.164399i	$0.947432\pi$
$38$	− 4.14590i	− 0.672553i
$39$	1.00000	0.160128
$40$	0	0
$41$	−11.6180	−1.81443	−0.907216	−	0.420665i	$-0.861797\pi$
$41$	−11.6180	−1.81443	−0.907216	+	0.420665i	$0.861797\pi$
$42$	− 1.23607i	− 0.190729i
$43$	− 9.61803i	− 1.46674i	−0.679832	−	0.733368i	$-0.737947\pi$
$43$	− 9.61803i	− 1.46674i	0.679832	−	0.733368i	$-0.262053\pi$
$44$	−4.85410	−0.731783
$45$	0	0
$46$	−4.70820	−0.694187
$47$	9.23607i	1.34722i	0.739087	+	0.673609i	$0.235257\pi$
$47$	9.23607i	1.34722i	−0.739087	+	0.673609i	$0.764743\pi$
$48$	1.85410i	0.267617i
$49$	3.00000	0.428571
$50$	0	0
$51$	0.236068	0.0330561
$52$	− 1.61803i	− 0.224381i
$53$	6.76393i	0.929098i	0.885548	+	0.464549i	$0.153783\pi$
$53$	6.76393i	0.929098i	−0.885548	+	0.464549i	$0.846217\pi$
$54$	0.618034	0.0841038
$55$	0	0
$56$	−4.47214	−0.597614
$57$	− 6.70820i	− 0.888523i
$58$	0.854102i	0.112149i
$59$	13.9443	1.81539	0.907695	−	0.419631i	$-0.137841\pi$
$59$	13.9443	1.81539	0.907695	+	0.419631i	$0.137841\pi$
$60$	0	0
$61$	−4.70820	−0.602824	−0.301412	−	0.953494i	$-0.597458\pi$
$61$	−4.70820	−0.602824	−0.301412	+	0.953494i	$0.597458\pi$
$62$	− 2.90983i	− 0.369549i
$63$	− 2.00000i	− 0.251976i
$64$	0.236068	0.0295085
$65$	0	0
$66$	1.85410	0.228224
$67$	− 9.18034i	− 1.12156i	−0.827966	−	0.560779i	$-0.810502\pi$
$67$	− 9.18034i	− 1.12156i	0.827966	−	0.560779i	$-0.189498\pi$
$68$	− 0.381966i	− 0.0463202i
$69$	−7.61803	−0.917104
$70$	0	0
$71$	−1.09017	−0.129379	−0.0646897	−	0.997905i	$-0.520606\pi$
$71$	−1.09017	−0.129379	−0.0646897	+	0.997905i	$0.520606\pi$
$72$	− 2.23607i	− 0.263523i
$73$	2.29180i	0.268234i	0.990965	+	0.134117i	$0.0428199\pi$
$73$	2.29180i	0.268234i	−0.990965	+	0.134117i	$0.957180\pi$
$74$	−1.23607	−0.143690
$75$	0	0
$76$	−10.8541	−1.24505
$77$	− 6.00000i	− 0.683763i
$78$	0.618034i	0.0699786i
$79$	15.8541	1.78373	0.891863	−	0.452306i	$-0.149398\pi$
$79$	15.8541	1.78373	0.891863	+	0.452306i	$0.149398\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	− 7.18034i	− 0.792936i
$83$	9.00000i	0.987878i	0.869496	+	0.493939i	$0.164443\pi$
$83$	9.00000i	0.987878i	−0.869496	+	0.493939i	$0.835557\pi$
$84$	−3.23607	−0.353084
$85$	0	0
$86$	5.94427	0.640987
$87$	1.38197i	0.148162i
$88$	− 6.70820i	− 0.715097i
$89$	−11.1803	−1.18511	−0.592557	−	0.805529i	$-0.701881\pi$
$89$	−11.1803	−1.18511	−0.592557	+	0.805529i	$0.701881\pi$
$90$	0	0
$91$	2.00000	0.209657
$92$	12.3262i	1.28510i
$93$	− 4.70820i	− 0.488218i
$94$	−5.70820	−0.588756
$95$	0	0
$96$	−5.61803	−0.573388
$97$	2.85410i	0.289790i	0.989447	+	0.144895i	$0.0462845\pi$
$97$	2.85410i	0.289790i	−0.989447	+	0.144895i	$0.953716\pi$
$98$	1.85410i	0.187293i
$99$	3.00000	0.301511
$100$	0	0
$101$	−11.6180	−1.15604	−0.578019	−	0.816023i	$-0.696174\pi$
$101$	−11.6180	−1.15604	−0.578019	+	0.816023i	$0.696174\pi$
$102$	0.145898i	0.0144461i
$103$	12.4164i	1.22343i	0.791080	+	0.611713i	$0.209519\pi$
$103$	12.4164i	1.22343i	−0.791080	+	0.611713i	$0.790481\pi$
$104$	2.23607	0.219265
$105$	0	0
$106$	−4.18034	−0.406031
$107$	7.85410i	0.759285i	0.925133	+	0.379642i	$0.123953\pi$
$107$	7.85410i	0.759285i	−0.925133	+	0.379642i	$0.876047\pi$
$108$	− 1.61803i	− 0.155695i
$109$	10.8541	1.03963	0.519817	−	0.854278i	$-0.326000\pi$
$109$	10.8541	1.03963	0.519817	+	0.854278i	$0.326000\pi$
$110$	0	0
$111$	−2.00000	−0.189832
$112$	3.70820i	0.350392i
$113$	− 8.23607i	− 0.774784i	−0.921915	−	0.387392i	$-0.873376\pi$
$113$	− 8.23607i	− 0.774784i	0.921915	−	0.387392i	$-0.126624\pi$
$114$	4.14590	0.388299
$115$	0	0
$116$	2.23607	0.207614
$117$	1.00000i	0.0924500i
$118$	8.61803i	0.793354i
$119$	0.472136	0.0432806
$120$	0	0
$121$	−2.00000	−0.181818
$122$	− 2.90983i	− 0.263444i
$123$	− 11.6180i	− 1.04756i
$124$	−7.61803	−0.684120
$125$	0	0
$126$	1.23607	0.110118
$127$	17.6525i	1.56640i	0.621767	+	0.783202i	$0.286415\pi$
$127$	17.6525i	1.56640i	−0.621767	+	0.783202i	$0.713585\pi$
$128$	11.3820i	1.00603i
$129$	9.61803	0.846821
$130$	0	0
$131$	8.18034	0.714720	0.357360	−	0.933967i	$-0.383677\pi$
$131$	8.18034	0.714720	0.357360	+	0.933967i	$0.383677\pi$
$132$	− 4.85410i	− 0.422495i
$133$	− 13.4164i	− 1.16335i
$134$	5.67376	0.490138
$135$	0	0
$136$	0.527864	0.0452640
$137$	− 20.5623i	− 1.75676i	−0.477966	−	0.878378i	$-0.658626\pi$
$137$	− 20.5623i	− 1.75676i	0.477966	−	0.878378i	$-0.341374\pi$
$138$	− 4.70820i	− 0.400789i
$139$	13.4164	1.13796	0.568982	−	0.822350i	$-0.307337\pi$
$139$	13.4164	1.13796	0.568982	+	0.822350i	$0.307337\pi$
$140$	0	0
$141$	−9.23607	−0.777817
$142$	− 0.673762i	− 0.0565409i
$143$	3.00000i	0.250873i
$144$	−1.85410	−0.154508
$145$	0	0
$146$	−1.41641	−0.117223
$147$	3.00000i	0.247436i
$148$	3.23607i	0.266003i
$149$	1.90983	0.156459	0.0782297	−	0.996935i	$-0.475073\pi$
$149$	1.90983	0.156459	0.0782297	+	0.996935i	$0.475073\pi$
$150$	0	0
$151$	−4.38197	−0.356599	−0.178300	−	0.983976i	$-0.557060\pi$
$151$	−4.38197	−0.356599	−0.178300	+	0.983976i	$0.557060\pi$
$152$	− 15.0000i	− 1.21666i
$153$	0.236068i	0.0190850i
$154$	3.70820	0.298816
$155$	0	0
$156$	1.61803	0.129546
$157$	− 3.85410i	− 0.307591i	−0.988103	−	0.153795i	$-0.950850\pi$
$157$	− 3.85410i	− 0.307591i	0.988103	−	0.153795i	$-0.0491497\pi$
$158$	9.79837i	0.779517i
$159$	−6.76393	−0.536415
$160$	0	0
$161$	−15.2361	−1.20077
$162$	0.618034i	0.0485573i
$163$	− 15.2705i	− 1.19608i	−0.801467	−	0.598039i	$-0.795947\pi$
$163$	− 15.2705i	− 1.19608i	0.801467	−	0.598039i	$-0.204053\pi$
$164$	−18.7984	−1.46791
$165$	0	0
$166$	−5.56231	−0.431719
$167$	6.79837i	0.526074i	0.964786	+	0.263037i	$0.0847241\pi$
$167$	6.79837i	0.526074i	−0.964786	+	0.263037i	$0.915276\pi$
$168$	− 4.47214i	− 0.345033i
$169$	12.0000	0.923077
$170$	0	0
$171$	6.70820	0.512989
$172$	− 15.5623i	− 1.18661i
$173$	12.0902i	0.919199i	0.888126	+	0.459599i	$0.152007\pi$
$173$	12.0902i	0.919199i	−0.888126	+	0.459599i	$0.847993\pi$
$174$	−0.854102	−0.0647493
$175$	0	0
$176$	−5.56231	−0.419275
$177$	13.9443i	1.04812i
$178$	− 6.90983i	− 0.517914i
$179$	−15.6525	−1.16992	−0.584960	−	0.811062i	$-0.698890\pi$
$179$	−15.6525	−1.16992	−0.584960	+	0.811062i	$0.698890\pi$
$180$	0	0
$181$	−3.52786	−0.262224	−0.131112	−	0.991368i	$-0.541855\pi$
$181$	−3.52786	−0.262224	−0.131112	+	0.991368i	$0.541855\pi$
$182$	1.23607i	0.0916235i
$183$	− 4.70820i	− 0.348040i
$184$	−17.0344	−1.25580
$185$	0	0
$186$	2.90983	0.213359
$187$	0.708204i	0.0517890i
$188$	14.9443i	1.08992i
$189$	2.00000	0.145479
$190$	0	0
$191$	1.67376	0.121109	0.0605546	−	0.998165i	$-0.480713\pi$
$191$	1.67376	0.121109	0.0605546	+	0.998165i	$0.480713\pi$
$192$	0.236068i	0.0170367i
$193$	− 11.0000i	− 0.791797i	−0.918294	−	0.395899i	$-0.870433\pi$
$193$	− 11.0000i	− 0.791797i	0.918294	−	0.395899i	$-0.129567\pi$
$194$	−1.76393	−0.126643
$195$	0	0
$196$	4.85410	0.346722
$197$	− 11.0902i	− 0.790142i	−0.918651	−	0.395071i	$-0.870720\pi$
$197$	− 11.0902i	− 0.790142i	0.918651	−	0.395071i	$-0.129280\pi$
$198$	1.85410i	0.131765i
$199$	1.70820	0.121091	0.0605457	−	0.998165i	$-0.480716\pi$
$199$	1.70820	0.121091	0.0605457	+	0.998165i	$0.480716\pi$
$200$	0	0
$201$	9.18034	0.647531
$202$	− 7.18034i	− 0.505207i
$203$	2.76393i	0.193990i
$204$	0.381966	0.0267430
$205$	0	0
$206$	−7.67376	−0.534656
$207$	− 7.61803i	− 0.529490i
$208$	− 1.85410i	− 0.128559i
$209$	20.1246	1.39205
$210$	0	0
$211$	−3.00000	−0.206529	−0.103264	−	0.994654i	$-0.532929\pi$
$211$	−3.00000	−0.206529	−0.103264	+	0.994654i	$0.532929\pi$
$212$	10.9443i	0.751656i
$213$	− 1.09017i	− 0.0746972i
$214$	−4.85410	−0.331820
$215$	0	0
$216$	2.23607	0.152145
$217$	− 9.41641i	− 0.639227i
$218$	6.70820i	0.454337i
$219$	−2.29180	−0.154865
$220$	0	0
$221$	−0.236068	−0.0158797
$222$	− 1.23607i	− 0.0829595i
$223$	− 16.8541i	− 1.12863i	−0.825558	−	0.564317i	$-0.809140\pi$
$223$	− 16.8541i	− 1.12863i	0.825558	−	0.564317i	$-0.190860\pi$
$224$	−11.2361	−0.750741
$225$	0	0
$226$	5.09017	0.338593
$227$	− 10.2361i	− 0.679392i	−0.940535	−	0.339696i	$-0.889676\pi$
$227$	− 10.2361i	− 0.679392i	0.940535	−	0.339696i	$-0.110324\pi$
$228$	− 10.8541i	− 0.718830i
$229$	−6.18034	−0.408408	−0.204204	−	0.978928i	$-0.565461\pi$
$229$	−6.18034	−0.408408	−0.204204	+	0.978928i	$0.565461\pi$
$230$	0	0
$231$	6.00000	0.394771
$232$	3.09017i	0.202880i
$233$	− 12.1803i	− 0.797961i	−0.916959	−	0.398980i	$-0.869364\pi$
$233$	− 12.1803i	− 0.797961i	0.916959	−	0.398980i	$-0.130636\pi$
$234$	−0.618034	−0.0404021
$235$	0	0
$236$	22.5623	1.46868
$237$	15.8541i	1.02983i
$238$	0.291796i	0.0189143i
$239$	−23.6180	−1.52772	−0.763862	−	0.645380i	$-0.776699\pi$
$239$	−23.6180	−1.52772	−0.763862	+	0.645380i	$0.776699\pi$
$240$	0	0
$241$	−8.32624	−0.536340	−0.268170	−	0.963372i	$-0.586419\pi$
$241$	−8.32624	−0.536340	−0.268170	+	0.963372i	$0.586419\pi$
$242$	− 1.23607i	− 0.0794575i
$243$	1.00000i	0.0641500i
$244$	−7.61803	−0.487695
$245$	0	0
$246$	7.18034	0.457802
$247$	6.70820i	0.426833i
$248$	− 10.5279i	− 0.668520i
$249$	−9.00000	−0.570352
$250$	0	0
$251$	27.9787	1.76600	0.883000	−	0.469372i	$-0.155520\pi$
$251$	27.9787	1.76600	0.883000	+	0.469372i	$0.155520\pi$
$252$	− 3.23607i	− 0.203853i
$253$	− 22.8541i	− 1.43683i
$254$	−10.9098	−0.684544
$255$	0	0
$256$	−6.56231	−0.410144
$257$	20.2148i	1.26096i	0.776204	+	0.630482i	$0.217143\pi$
$257$	20.2148i	1.26096i	−0.776204	+	0.630482i	$0.782857\pi$
$258$	5.94427i	0.370074i
$259$	−4.00000	−0.248548
$260$	0	0
$261$	−1.38197	−0.0855415
$262$	5.05573i	0.312344i
$263$	25.5066i	1.57280i	0.617716	+	0.786401i	$0.288058\pi$
$263$	25.5066i	1.57280i	−0.617716	+	0.786401i	$0.711942\pi$
$264$	6.70820	0.412861
$265$	0	0
$266$	8.29180	0.508403
$267$	− 11.1803i	− 0.684226i
$268$	− 14.8541i	− 0.907359i
$269$	29.4721	1.79695	0.898474	−	0.439027i	$-0.144677\pi$
$269$	29.4721	1.79695	0.898474	+	0.439027i	$0.144677\pi$
$270$	0	0
$271$	15.4164	0.936480	0.468240	−	0.883601i	$-0.344888\pi$
$271$	15.4164	0.936480	0.468240	+	0.883601i	$0.344888\pi$
$272$	− 0.437694i	− 0.0265391i
$273$	2.00000i	0.121046i
$274$	12.7082	0.767731
$275$	0	0
$276$	−12.3262	−0.741952
$277$	30.9443i	1.85926i	0.368493	+	0.929631i	$0.379874\pi$
$277$	30.9443i	1.85926i	−0.368493	+	0.929631i	$0.620126\pi$
$278$	8.29180i	0.497309i
$279$	4.70820	0.281873
$280$	0	0
$281$	8.18034	0.487998	0.243999	−	0.969775i	$-0.421541\pi$
$281$	8.18034	0.487998	0.243999	+	0.969775i	$0.421541\pi$
$282$	− 5.70820i	− 0.339919i
$283$	15.7082i	0.933756i	0.884322	+	0.466878i	$0.154621\pi$
$283$	15.7082i	0.933756i	−0.884322	+	0.466878i	$0.845379\pi$
$284$	−1.76393	−0.104670
$285$	0	0
$286$	−1.85410	−0.109635
$287$	− 23.2361i	− 1.37158i
$288$	− 5.61803i	− 0.331046i
$289$	16.9443	0.996722
$290$	0	0
$291$	−2.85410	−0.167310
$292$	3.70820i	0.217006i
$293$	9.32624i	0.544845i	0.962178	+	0.272422i	$0.0878248\pi$
$293$	9.32624i	0.544845i	−0.962178	+	0.272422i	$0.912175\pi$
$294$	−1.85410	−0.108133
$295$	0	0
$296$	−4.47214	−0.259938
$297$	3.00000i	0.174078i
$298$	1.18034i	0.0683753i
$299$	7.61803	0.440562
$300$	0	0
$301$	19.2361	1.10875
$302$	− 2.70820i	− 0.155840i
$303$	− 11.6180i	− 0.667439i
$304$	−12.4377	−0.713351
$305$	0	0
$306$	−0.145898	−0.00834044
$307$	− 2.14590i	− 0.122473i	−0.998123	−	0.0612364i	$-0.980496\pi$
$307$	− 2.14590i	− 0.122473i	0.998123	−	0.0612364i	$-0.0195044\pi$
$308$	− 9.70820i	− 0.553176i
$309$	−12.4164	−0.706345
$310$	0	0
$311$	−22.4721	−1.27428	−0.637139	−	0.770749i	$-0.719882\pi$
$311$	−22.4721	−1.27428	−0.637139	+	0.770749i	$0.719882\pi$
$312$	2.23607i	0.126592i
$313$	15.7082i	0.887880i	0.896056	+	0.443940i	$0.146420\pi$
$313$	15.7082i	0.887880i	−0.896056	+	0.443940i	$0.853580\pi$
$314$	2.38197	0.134422
$315$	0	0
$316$	25.6525	1.44306
$317$	− 0.437694i	− 0.0245833i	−0.999924	−	0.0122917i	$-0.996087\pi$
$317$	− 0.437694i	− 0.0245833i	0.999924	−	0.0122917i	$-0.00391266\pi$
$318$	− 4.18034i	− 0.234422i
$319$	−4.14590	−0.232126
$320$	0	0
$321$	−7.85410	−0.438373
$322$	− 9.41641i	− 0.524756i
$323$	1.58359i	0.0881134i
$324$	1.61803	0.0898908
$325$	0	0
$326$	9.43769	0.522706
$327$	10.8541i	0.600233i
$328$	− 25.9787i	− 1.43443i
$329$	−18.4721	−1.01840
$330$	0	0
$331$	29.6869	1.63174	0.815870	−	0.578235i	$-0.196258\pi$
$331$	29.6869	1.63174	0.815870	+	0.578235i	$0.196258\pi$
$332$	14.5623i	0.799210i
$333$	− 2.00000i	− 0.109599i
$334$	−4.20163	−0.229903
$335$	0	0
$336$	−3.70820	−0.202299
$337$	10.8197i	0.589384i	0.955592	+	0.294692i	$0.0952171\pi$
$337$	10.8197i	0.589384i	−0.955592	+	0.294692i	$0.904783\pi$
$338$	7.41641i	0.403399i
$339$	8.23607	0.447322
$340$	0	0
$341$	14.1246	0.764891
$342$	4.14590i	0.224184i
$343$	20.0000i	1.07990i
$344$	21.5066	1.15956
$345$	0	0
$346$	−7.47214	−0.401705
$347$	21.2705i	1.14186i	0.820998	+	0.570930i	$0.193417\pi$
$347$	21.2705i	1.14186i	−0.820998	+	0.570930i	$0.806583\pi$
$348$	2.23607i	0.119866i
$349$	−2.76393	−0.147950	−0.0739749	−	0.997260i	$-0.523568\pi$
$349$	−2.76393	−0.147950	−0.0739749	+	0.997260i	$0.523568\pi$
$350$	0	0
$351$	−1.00000	−0.0533761
$352$	− 16.8541i	− 0.898327i
$353$	− 14.6180i	− 0.778039i	−0.921229	−	0.389020i	$-0.872814\pi$
$353$	− 14.6180i	− 0.778039i	0.921229	−	0.389020i	$-0.127186\pi$
$354$	−8.61803	−0.458043
$355$	0	0
$356$	−18.0902	−0.958777
$357$	0.472136i	0.0249881i
$358$	− 9.67376i	− 0.511274i
$359$	−6.05573	−0.319609	−0.159805	−	0.987149i	$-0.551086\pi$
$359$	−6.05573	−0.319609	−0.159805	+	0.987149i	$0.551086\pi$
$360$	0	0
$361$	26.0000	1.36842
$362$	− 2.18034i	− 0.114596i
$363$	− 2.00000i	− 0.104973i
$364$	3.23607	0.169616
$365$	0	0
$366$	2.90983	0.152099
$367$	21.4721i	1.12084i	0.828210	+	0.560418i	$0.189360\pi$
$367$	21.4721i	1.12084i	−0.828210	+	0.560418i	$0.810640\pi$
$368$	14.1246i	0.736296i
$369$	11.6180	0.604811
$370$	0	0
$371$	−13.5279	−0.702332
$372$	− 7.61803i	− 0.394977i
$373$	− 9.41641i	− 0.487563i	−0.969830	−	0.243782i	$-0.921612\pi$
$373$	− 9.41641i	− 0.487563i	0.969830	−	0.243782i	$-0.0783880\pi$
$374$	−0.437694	−0.0226326
$375$	0	0
$376$	−20.6525	−1.06507
$377$	− 1.38197i	− 0.0711749i
$378$	1.23607i	0.0635765i
$379$	11.3820	0.584652	0.292326	−	0.956319i	$-0.405571\pi$
$379$	11.3820	0.584652	0.292326	+	0.956319i	$0.405571\pi$
$380$	0	0
$381$	−17.6525	−0.904364
$382$	1.03444i	0.0529266i
$383$	22.9443i	1.17240i	0.810167	+	0.586199i	$0.199376\pi$
$383$	22.9443i	1.17240i	−0.810167	+	0.586199i	$0.800624\pi$
$384$	−11.3820	−0.580834
$385$	0	0
$386$	6.79837	0.346028
$387$	9.61803i	0.488912i
$388$	4.61803i	0.234445i
$389$	30.6525	1.55414	0.777071	−	0.629413i	$-0.216705\pi$
$389$	30.6525	1.55414	0.777071	+	0.629413i	$0.216705\pi$
$390$	0	0
$391$	1.79837	0.0909477
$392$	6.70820i	0.338815i
$393$	8.18034i	0.412644i
$394$	6.85410	0.345305
$395$	0	0
$396$	4.85410	0.243928
$397$	11.4721i	0.575770i	0.957665	+	0.287885i	$0.0929521\pi$
$397$	11.4721i	0.575770i	−0.957665	+	0.287885i	$0.907048\pi$
$398$	1.05573i	0.0529189i
$399$	13.4164	0.671660
$400$	0	0
$401$	2.72949	0.136304	0.0681521	−	0.997675i	$-0.478290\pi$
$401$	2.72949	0.136304	0.0681521	+	0.997675i	$0.478290\pi$
$402$	5.67376i	0.282982i
$403$	4.70820i	0.234532i
$404$	−18.7984	−0.935254
$405$	0	0
$406$	−1.70820	−0.0847767
$407$	− 6.00000i	− 0.297409i
$408$	0.527864i	0.0261332i
$409$	−35.1246	−1.73680	−0.868400	−	0.495864i	$-0.834851\pi$
$409$	−35.1246	−1.73680	−0.868400	+	0.495864i	$0.834851\pi$
$410$	0	0
$411$	20.5623	1.01426
$412$	20.0902i	0.989772i
$413$	27.8885i	1.37231i
$414$	4.70820	0.231396
$415$	0	0
$416$	5.61803	0.275447
$417$	13.4164i	0.657004i
$418$	12.4377i	0.608348i
$419$	15.3262	0.748736	0.374368	−	0.927280i	$-0.377860\pi$
$419$	15.3262	0.748736	0.374368	+	0.927280i	$0.377860\pi$
$420$	0	0
$421$	14.3607	0.699897	0.349948	−	0.936769i	$-0.386199\pi$
$421$	14.3607	0.699897	0.349948	+	0.936769i	$0.386199\pi$
$422$	− 1.85410i	− 0.0902563i
$423$	− 9.23607i	− 0.449073i
$424$	−15.1246	−0.734516
$425$	0	0
$426$	0.673762	0.0326439
$427$	− 9.41641i	− 0.455692i
$428$	12.7082i	0.614274i
$429$	−3.00000	−0.144841
$430$	0	0
$431$	34.2361	1.64909	0.824547	−	0.565794i	$-0.191430\pi$
$431$	34.2361	1.64909	0.824547	+	0.565794i	$0.191430\pi$
$432$	− 1.85410i	− 0.0892055i
$433$	− 5.47214i	− 0.262974i	−0.991318	−	0.131487i	$-0.958025\pi$
$433$	− 5.47214i	− 0.262974i	0.991318	−	0.131487i	$-0.0419752\pi$
$434$	5.81966	0.279353
$435$	0	0
$436$	17.5623	0.841082
$437$	− 51.1033i	− 2.44460i
$438$	− 1.41641i	− 0.0676786i
$439$	2.96556	0.141538	0.0707692	−	0.997493i	$-0.477455\pi$
$439$	2.96556	0.141538	0.0707692	+	0.997493i	$0.477455\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	− 0.145898i	− 0.00693966i
$443$	7.41641i	0.352364i	0.984358	+	0.176182i	$0.0563748\pi$
$443$	7.41641i	0.352364i	−0.984358	+	0.176182i	$0.943625\pi$
$444$	−3.23607	−0.153577
$445$	0	0
$446$	10.4164	0.493231
$447$	1.90983i	0.0903319i
$448$	0.472136i	0.0223063i
$449$	21.5066	1.01496	0.507479	−	0.861664i	$-0.330577\pi$
$449$	21.5066	1.01496	0.507479	+	0.861664i	$0.330577\pi$
$450$	0	0
$451$	34.8541	1.64122
$452$	− 13.3262i	− 0.626814i
$453$	− 4.38197i	− 0.205883i
$454$	6.32624	0.296905
$455$	0	0
$456$	15.0000	0.702439
$457$	− 25.8885i	− 1.21102i	−0.795840	−	0.605508i	$-0.792970\pi$
$457$	− 25.8885i	− 1.21102i	0.795840	−	0.605508i	$-0.207030\pi$
$458$	− 3.81966i	− 0.178481i
$459$	−0.236068	−0.0110187
$460$	0	0
$461$	3.18034	0.148123	0.0740616	−	0.997254i	$-0.476404\pi$
$461$	3.18034	0.148123	0.0740616	+	0.997254i	$0.476404\pi$
$462$	3.70820i	0.172521i
$463$	26.6869i	1.24025i	0.784505	+	0.620123i	$0.212917\pi$
$463$	26.6869i	1.24025i	−0.784505	+	0.620123i	$0.787083\pi$
$464$	2.56231	0.118952
$465$	0	0
$466$	7.52786	0.348722
$467$	− 16.4164i	− 0.759661i	−0.925056	−	0.379830i	$-0.875982\pi$
$467$	− 16.4164i	− 0.759661i	0.925056	−	0.379830i	$-0.124018\pi$
$468$	1.61803i	0.0747936i
$469$	18.3607	0.847817
$470$	0	0
$471$	3.85410	0.177588
$472$	31.1803i	1.43519i
$473$	28.8541i	1.32671i
$474$	−9.79837	−0.450054
$475$	0	0
$476$	0.763932	0.0350148
$477$	− 6.76393i	− 0.309699i
$478$	− 14.5967i	− 0.667640i
$479$	19.7984	0.904611	0.452305	−	0.891863i	$-0.350602\pi$
$479$	19.7984	0.904611	0.452305	+	0.891863i	$0.350602\pi$
$480$	0	0
$481$	2.00000	0.0911922
$482$	− 5.14590i	− 0.234389i
$483$	− 15.2361i	− 0.693265i
$484$	−3.23607	−0.147094
$485$	0	0
$486$	−0.618034	−0.0280346
$487$	− 14.3820i	− 0.651709i	−0.945420	−	0.325855i	$-0.894348\pi$
$487$	− 14.3820i	− 0.651709i	0.945420	−	0.325855i	$-0.105652\pi$
$488$	− 10.5279i	− 0.476574i
$489$	15.2705	0.690556
$490$	0	0
$491$	6.67376	0.301183	0.150591	−	0.988596i	$-0.451882\pi$
$491$	6.67376	0.301183	0.150591	+	0.988596i	$0.451882\pi$
$492$	− 18.7984i	− 0.847496i
$493$	− 0.326238i	− 0.0146930i
$494$	−4.14590	−0.186533
$495$	0	0
$496$	−8.72949	−0.391966
$497$	− 2.18034i	− 0.0978016i
$498$	− 5.56231i	− 0.249253i
$499$	15.0000	0.671492	0.335746	−	0.941953i	$-0.391012\pi$
$499$	15.0000	0.671492	0.335746	+	0.941953i	$0.391012\pi$
$500$	0	0
$501$	−6.79837	−0.303729
$502$	17.2918i	0.771771i
$503$	− 33.0344i	− 1.47293i	−0.676474	−	0.736466i	$-0.736493\pi$
$503$	− 33.0344i	− 1.47293i	0.676474	−	0.736466i	$-0.263507\pi$
$504$	4.47214	0.199205
$505$	0	0
$506$	14.1246	0.627916
$507$	12.0000i	0.532939i
$508$	28.5623i	1.26725i
$509$	2.88854	0.128032	0.0640162	−	0.997949i	$-0.479609\pi$
$509$	2.88854	0.128032	0.0640162	+	0.997949i	$0.479609\pi$
$510$	0	0
$511$	−4.58359	−0.202766
$512$	18.7082i	0.826794i
$513$	6.70820i	0.296174i
$514$	−12.4934	−0.551061
$515$	0	0
$516$	15.5623	0.685092
$517$	− 27.7082i	− 1.21861i
$518$	− 2.47214i	− 0.108619i
$519$	−12.0902	−0.530700
$520$	0	0
$521$	28.9098	1.26656	0.633281	−	0.773922i	$-0.281708\pi$
$521$	28.9098	1.26656	0.633281	+	0.773922i	$0.281708\pi$
$522$	− 0.854102i	− 0.0373830i
$523$	− 18.5623i	− 0.811673i	−0.913946	−	0.405836i	$-0.866980\pi$
$523$	− 18.5623i	− 0.811673i	0.913946	−	0.405836i	$-0.133020\pi$
$524$	13.2361	0.578220
$525$	0	0
$526$	−15.7639	−0.687340
$527$	1.11146i	0.0484158i
$528$	− 5.56231i	− 0.242068i
$529$	−35.0344	−1.52324
$530$	0	0
$531$	−13.9443	−0.605130
$532$	− 21.7082i	− 0.941170i
$533$	11.6180i	0.503233i
$534$	6.90983	0.299018
$535$	0	0
$536$	20.5279	0.886669
$537$	− 15.6525i	− 0.675454i
$538$	18.2148i	0.785295i
$539$	−9.00000	−0.387657
$540$	0	0
$541$	−39.7082	−1.70719	−0.853595	−	0.520938i	$-0.825582\pi$
$541$	−39.7082	−1.70719	−0.853595	+	0.520938i	$0.825582\pi$
$542$	9.52786i	0.409257i
$543$	− 3.52786i	− 0.151395i
$544$	1.32624	0.0568620
$545$	0	0
$546$	−1.23607	−0.0528988
$547$	− 11.2918i	− 0.482802i	−0.970425	−	0.241401i	$-0.922393\pi$
$547$	− 11.2918i	− 0.482802i	0.970425	−	0.241401i	$-0.0776070\pi$
$548$	− 33.2705i	− 1.42125i
$549$	4.70820	0.200941
$550$	0	0
$551$	−9.27051	−0.394937
$552$	− 17.0344i	− 0.725034i
$553$	31.7082i	1.34837i
$554$	−19.1246	−0.812527
$555$	0	0
$556$	21.7082	0.920633
$557$	6.34752i	0.268953i	0.990917	+	0.134477i	$0.0429353\pi$
$557$	6.34752i	0.268953i	−0.990917	+	0.134477i	$0.957065\pi$
$558$	2.90983i	0.123183i
$559$	−9.61803	−0.406799
$560$	0	0
$561$	−0.708204	−0.0299004
$562$	5.05573i	0.213263i
$563$	9.00000i	0.379305i	0.981851	+	0.189652i	$0.0607361\pi$
$563$	9.00000i	0.379305i	−0.981851	+	0.189652i	$0.939264\pi$
$564$	−14.9443	−0.629267
$565$	0	0
$566$	−9.70820	−0.408066
$567$	2.00000i	0.0839921i
$568$	− 2.43769i	− 0.102283i
$569$	4.14590	0.173805	0.0869025	−	0.996217i	$-0.472303\pi$
$569$	4.14590	0.173805	0.0869025	+	0.996217i	$0.472303\pi$
$570$	0	0
$571$	2.12461	0.0889122	0.0444561	−	0.999011i	$-0.485845\pi$
$571$	2.12461	0.0889122	0.0444561	+	0.999011i	$0.485845\pi$
$572$	4.85410i	0.202960i
$573$	1.67376i	0.0699224i
$574$	14.3607	0.599403
$575$	0	0
$576$	−0.236068	−0.00983617
$577$	− 37.2705i	− 1.55159i	−0.630984	−	0.775796i	$-0.717349\pi$
$577$	− 37.2705i	− 1.55159i	0.630984	−	0.775796i	$-0.282651\pi$
$578$	10.4721i	0.435583i
$579$	11.0000	0.457144
$580$	0	0
$581$	−18.0000	−0.746766
$582$	− 1.76393i	− 0.0731173i
$583$	− 20.2918i	− 0.840400i
$584$	−5.12461	−0.212058
$585$	0	0
$586$	−5.76393	−0.238106
$587$	23.3050i	0.961898i	0.876748	+	0.480949i	$0.159708\pi$
$587$	23.3050i	0.961898i	−0.876748	+	0.480949i	$0.840292\pi$
$588$	4.85410i	0.200180i
$589$	31.5836	1.30138
$590$	0	0
$591$	11.0902	0.456189
$592$	3.70820i	0.152406i
$593$	15.3820i	0.631662i	0.948816	+	0.315831i	$0.102283\pi$
$593$	15.3820i	0.631662i	−0.948816	+	0.315831i	$0.897717\pi$
$594$	−1.85410	−0.0760747
$595$	0	0
$596$	3.09017	0.126578
$597$	1.70820i	0.0699121i
$598$	4.70820i	0.192533i
$599$	−5.72949	−0.234101	−0.117050	−	0.993126i	$-0.537344\pi$
$599$	−5.72949	−0.234101	−0.117050	+	0.993126i	$0.537344\pi$
$600$	0	0
$601$	−11.2918	−0.460602	−0.230301	−	0.973119i	$-0.573971\pi$
$601$	−11.2918	−0.460602	−0.230301	+	0.973119i	$0.573971\pi$
$602$	11.8885i	0.484541i
$603$	9.18034i	0.373852i
$604$	−7.09017	−0.288495
$605$	0	0
$606$	7.18034	0.291681
$607$	16.1459i	0.655342i	0.944792	+	0.327671i	$0.106264\pi$
$607$	16.1459i	0.655342i	−0.944792	+	0.327671i	$0.893736\pi$
$608$	− 37.6869i	− 1.52841i
$609$	−2.76393	−0.112000
$610$	0	0
$611$	9.23607	0.373651
$612$	0.381966i	0.0154401i
$613$	− 46.1246i	− 1.86296i	−0.363798	−	0.931478i	$-0.618520\pi$
$613$	− 46.1246i	− 1.86296i	0.363798	−	0.931478i	$-0.381480\pi$
$614$	1.32624	0.0535226
$615$	0	0
$616$	13.4164	0.540562
$617$	− 20.7639i	− 0.835924i	−0.908464	−	0.417962i	$-0.862744\pi$
$617$	− 20.7639i	− 0.835924i	0.908464	−	0.417962i	$-0.137256\pi$
$618$	− 7.67376i	− 0.308684i
$619$	−0.729490	−0.0293207	−0.0146603	−	0.999893i	$-0.504667\pi$
$619$	−0.729490	−0.0293207	−0.0146603	+	0.999893i	$0.504667\pi$
$620$	0	0
$621$	7.61803	0.305701
$622$	− 13.8885i	− 0.556880i
$623$	− 22.3607i	− 0.895862i
$624$	1.85410	0.0742235
$625$	0	0
$626$	−9.70820	−0.388018
$627$	20.1246i	0.803700i
$628$	− 6.23607i	− 0.248846i
$629$	0.472136	0.0188253
$630$	0	0
$631$	−15.2361	−0.606538	−0.303269	−	0.952905i	$-0.598078\pi$
$631$	−15.2361	−0.606538	−0.303269	+	0.952905i	$0.598078\pi$
$632$	35.4508i	1.41016i
$633$	− 3.00000i	− 0.119239i
$634$	0.270510	0.0107433
$635$	0	0
$636$	−10.9443	−0.433969
$637$	− 3.00000i	− 0.118864i
$638$	− 2.56231i	− 0.101443i
$639$	1.09017	0.0431265
$640$	0	0
$641$	−7.67376	−0.303095	−0.151548	−	0.988450i	$-0.548426\pi$
$641$	−7.67376	−0.303095	−0.151548	+	0.988450i	$0.548426\pi$
$642$	− 4.85410i	− 0.191576i
$643$	17.0902i	0.673971i	0.941510	+	0.336985i	$0.109407\pi$
$643$	17.0902i	0.673971i	−0.941510	+	0.336985i	$0.890593\pi$
$644$	−24.6525	−0.971444
$645$	0	0
$646$	−0.978714	−0.0385070
$647$	− 10.0344i	− 0.394495i	−0.980354	−	0.197247i	$-0.936800\pi$
$647$	− 10.0344i	− 0.394495i	0.980354	−	0.197247i	$-0.0632002\pi$
$648$	2.23607i	0.0878410i
$649$	−41.8328	−1.64208
$650$	0	0
$651$	9.41641	0.369058
$652$	− 24.7082i	− 0.967648i
$653$	− 1.65248i	− 0.0646664i	−0.999477	−	0.0323332i	$-0.989706\pi$
$653$	− 1.65248i	− 0.0646664i	0.999477	−	0.0323332i	$-0.0102938\pi$
$654$	−6.70820	−0.262312
$655$	0	0
$656$	−21.5410	−0.841036
$657$	− 2.29180i	− 0.0894115i
$658$	− 11.4164i	− 0.445058i
$659$	−2.23607	−0.0871048	−0.0435524	−	0.999051i	$-0.513868\pi$
$659$	−2.23607	−0.0871048	−0.0435524	+	0.999051i	$0.513868\pi$
$660$	0	0
$661$	−30.8885	−1.20143	−0.600713	−	0.799465i	$-0.705116\pi$
$661$	−30.8885	−1.20143	−0.600713	+	0.799465i	$0.705116\pi$
$662$	18.3475i	0.713097i
$663$	− 0.236068i	− 0.00916812i
$664$	−20.1246	−0.780986
$665$	0	0
$666$	1.23607	0.0478967
$667$	10.5279i	0.407641i
$668$	11.0000i	0.425603i
$669$	16.8541	0.651617
$670$	0	0
$671$	14.1246	0.545275
$672$	− 11.2361i	− 0.433441i
$673$	24.7771i	0.955087i	0.878608	+	0.477543i	$0.158473\pi$
$673$	24.7771i	0.955087i	−0.878608	+	0.477543i	$0.841527\pi$
$674$	−6.68692	−0.257570
$675$	0	0
$676$	19.4164	0.746785
$677$	9.11146i	0.350182i	0.984552	+	0.175091i	$0.0560219\pi$
$677$	9.11146i	0.350182i	−0.984552	+	0.175091i	$0.943978\pi$
$678$	5.09017i	0.195487i
$679$	−5.70820	−0.219061
$680$	0	0
$681$	10.2361	0.392247
$682$	8.72949i	0.334269i
$683$	48.5967i	1.85950i	0.368188	+	0.929751i	$0.379978\pi$
$683$	48.5967i	1.85950i	−0.368188	+	0.929751i	$0.620022\pi$
$684$	10.8541	0.415017
$685$	0	0
$686$	−12.3607	−0.471933
$687$	− 6.18034i	− 0.235795i
$688$	− 17.8328i	− 0.679870i
$689$	6.76393	0.257685
$690$	0	0
$691$	3.90983	0.148737	0.0743685	−	0.997231i	$-0.476306\pi$
$691$	3.90983	0.148737	0.0743685	+	0.997231i	$0.476306\pi$
$692$	19.5623i	0.743647i
$693$	6.00000i	0.227921i
$694$	−13.1459	−0.499011
$695$	0	0
$696$	−3.09017	−0.117133
$697$	2.74265i	0.103885i
$698$	− 1.70820i	− 0.0646565i
$699$	12.1803	0.460703
$700$	0	0
$701$	−17.3475	−0.655207	−0.327603	−	0.944815i	$-0.606241\pi$
$701$	−17.3475	−0.655207	−0.327603	+	0.944815i	$0.606241\pi$
$702$	− 0.618034i	− 0.0233262i
$703$	− 13.4164i	− 0.506009i
$704$	−0.708204	−0.0266914
$705$	0	0
$706$	9.03444	0.340016
$707$	− 23.2361i	− 0.873882i
$708$	22.5623i	0.847943i
$709$	29.7984	1.11910	0.559551	−	0.828796i	$-0.310974\pi$
$709$	29.7984	1.11910	0.559551	+	0.828796i	$0.310974\pi$
$710$	0	0
$711$	−15.8541	−0.594575
$712$	− 25.0000i	− 0.936915i
$713$	− 35.8673i	− 1.34324i
$714$	−0.291796	−0.0109202
$715$	0	0
$716$	−25.3262	−0.946486
$717$	− 23.6180i	− 0.882032i
$718$	− 3.74265i	− 0.139674i
$719$	−5.12461	−0.191116	−0.0955579	−	0.995424i	$-0.530464\pi$
$719$	−5.12461	−0.191116	−0.0955579	+	0.995424i	$0.530464\pi$
$720$	0	0
$721$	−24.8328	−0.924822
$722$	16.0689i	0.598022i
$723$	− 8.32624i	− 0.309656i
$724$	−5.70820	−0.212144
$725$	0	0
$726$	1.23607	0.0458748
$727$	34.5623i	1.28184i	0.767606	+	0.640922i	$0.221448\pi$
$727$	34.5623i	1.28184i	−0.767606	+	0.640922i	$0.778552\pi$
$728$	4.47214i	0.165748i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−2.27051	−0.0839778
$732$	− 7.61803i	− 0.281571i
$733$	− 16.8541i	− 0.622520i	−0.950325	−	0.311260i	$-0.899249\pi$
$733$	− 16.8541i	− 0.622520i	0.950325	−	0.311260i	$-0.100751\pi$
$734$	−13.2705	−0.489823
$735$	0	0
$736$	−42.7984	−1.57757
$737$	27.5410i	1.01449i
$738$	7.18034i	0.264312i
$739$	−11.7082	−0.430693	−0.215347	−	0.976538i	$-0.569088\pi$
$739$	−11.7082	−0.430693	−0.215347	+	0.976538i	$0.569088\pi$
$740$	0	0
$741$	−6.70820	−0.246432
$742$	− 8.36068i	− 0.306930i
$743$	− 25.4721i	− 0.934482i	−0.884130	−	0.467241i	$-0.845248\pi$
$743$	− 25.4721i	− 0.934482i	0.884130	−	0.467241i	$-0.154752\pi$
$744$	10.5279	0.385970
$745$	0	0
$746$	5.81966	0.213073
$747$	− 9.00000i	− 0.329293i
$748$	1.14590i	0.0418982i
$749$	−15.7082	−0.573965
$750$	0	0
$751$	28.7082	1.04758	0.523789	−	0.851848i	$-0.324518\pi$
$751$	28.7082	1.04758	0.523789	+	0.851848i	$0.324518\pi$
$752$	17.1246i	0.624470i
$753$	27.9787i	1.01960i
$754$	0.854102	0.0311046
$755$	0	0
$756$	3.23607	0.117695
$757$	1.27051i	0.0461775i	0.999733	+	0.0230887i	$0.00735002\pi$
$757$	1.27051i	0.0461775i	−0.999733	+	0.0230887i	$0.992650\pi$
$758$	7.03444i	0.255502i
$759$	22.8541	0.829551
$760$	0	0
$761$	−19.1803	−0.695287	−0.347643	−	0.937627i	$-0.613018\pi$
$761$	−19.1803	−0.695287	−0.347643	+	0.937627i	$0.613018\pi$
$762$	− 10.9098i	− 0.395221i
$763$	21.7082i	0.785890i
$764$	2.70820	0.0979794
$765$	0	0
$766$	−14.1803	−0.512357
$767$	− 13.9443i	− 0.503498i
$768$	− 6.56231i	− 0.236797i
$769$	−26.3050	−0.948581	−0.474290	−	0.880368i	$-0.657295\pi$
$769$	−26.3050	−0.948581	−0.474290	+	0.880368i	$0.657295\pi$
$770$	0	0
$771$	−20.2148	−0.728018
$772$	− 17.7984i	− 0.640577i
$773$	29.7771i	1.07101i	0.844533	+	0.535504i	$0.179878\pi$
$773$	29.7771i	1.07101i	−0.844533	+	0.535504i	$0.820122\pi$
$774$	−5.94427	−0.213662
$775$	0	0
$776$	−6.38197	−0.229099
$777$	− 4.00000i	− 0.143499i
$778$	18.9443i	0.679185i
$779$	77.9361	2.79235
$780$	0	0
$781$	3.27051	0.117028
$782$	1.11146i	0.0397456i
$783$	− 1.38197i	− 0.0493874i
$784$	5.56231	0.198654
$785$	0	0
$786$	−5.05573	−0.180332
$787$	− 23.8541i	− 0.850307i	−0.905121	−	0.425153i	$-0.860220\pi$
$787$	− 23.8541i	− 0.850307i	0.905121	−	0.425153i	$-0.139780\pi$
$788$	− 17.9443i	− 0.639238i
$789$	−25.5066	−0.908058
$790$	0	0
$791$	16.4721	0.585682
$792$	6.70820i	0.238366i
$793$	4.70820i	0.167193i
$794$	−7.09017	−0.251621
$795$	0	0
$796$	2.76393	0.0979650
$797$	− 46.0132i	− 1.62987i	−0.579553	−	0.814935i	$-0.696773\pi$
$797$	− 46.0132i	− 1.62987i	0.579553	−	0.814935i	$-0.303227\pi$
$798$	8.29180i	0.293526i
$799$	2.18034	0.0771349
$800$	0	0
$801$	11.1803	0.395038
$802$	1.68692i	0.0595671i
$803$	− 6.87539i	− 0.242627i
$804$	14.8541	0.523864
$805$	0	0
$806$	−2.90983	−0.102494
$807$	29.4721i	1.03747i
$808$	− 25.9787i	− 0.913928i
$809$	−24.9230	−0.876246	−0.438123	−	0.898915i	$-0.644356\pi$
$809$	−24.9230	−0.876246	−0.438123	+	0.898915i	$0.644356\pi$
$810$	0	0
$811$	37.7771	1.32653	0.663266	−	0.748383i	$-0.269170\pi$
$811$	37.7771	1.32653	0.663266	+	0.748383i	$0.269170\pi$
$812$	4.47214i	0.156941i
$813$	15.4164i	0.540677i
$814$	3.70820	0.129972
$815$	0	0
$816$	0.437694	0.0153224
$817$	64.5197i	2.25726i
$818$	− 21.7082i	− 0.759010i
$819$	−2.00000	−0.0698857
$820$	0	0
$821$	−11.9443	−0.416858	−0.208429	−	0.978038i	$-0.566835\pi$
$821$	−11.9443	−0.416858	−0.208429	+	0.978038i	$0.566835\pi$
$822$	12.7082i	0.443250i
$823$	− 8.43769i	− 0.294120i	−0.989128	−	0.147060i	$-0.953019\pi$
$823$	− 8.43769i	− 0.294120i	0.989128	−	0.147060i	$-0.0469810\pi$
$824$	−27.7639	−0.967202
$825$	0	0
$826$	−17.2361	−0.599720
$827$	− 2.02129i	− 0.0702870i	−0.999382	−	0.0351435i	$-0.988811\pi$
$827$	− 2.02129i	− 0.0702870i	0.999382	−	0.0351435i	$-0.0111888\pi$
$828$	− 12.3262i	− 0.428366i
$829$	9.87539	0.342986	0.171493	−	0.985185i	$-0.445141\pi$
$829$	9.87539	0.342986	0.171493	+	0.985185i	$0.445141\pi$
$830$	0	0
$831$	−30.9443	−1.07344
$832$	− 0.236068i	− 0.00818418i
$833$	− 0.708204i	− 0.0245378i
$834$	−8.29180	−0.287121
$835$	0	0
$836$	32.5623	1.12619
$837$	4.70820i	0.162739i
$838$	9.47214i	0.327210i
$839$	−48.2148	−1.66456	−0.832280	−	0.554356i	$-0.812965\pi$
$839$	−48.2148	−1.66456	−0.832280	+	0.554356i	$0.812965\pi$
$840$	0	0
$841$	−27.0902	−0.934144
$842$	8.87539i	0.305866i
$843$	8.18034i	0.281746i
$844$	−4.85410	−0.167085
$845$	0	0
$846$	5.70820	0.196252
$847$	− 4.00000i	− 0.137442i
$848$	12.5410i	0.430660i
$849$	−15.7082	−0.539104
$850$	0	0
$851$	−15.2361	−0.522286
$852$	− 1.76393i	− 0.0604313i
$853$	53.3951i	1.82821i	0.405473	+	0.914107i	$0.367107\pi$
$853$	53.3951i	1.82821i	−0.405473	+	0.914107i	$0.632893\pi$
$854$	5.81966	0.199145
$855$	0	0
$856$	−17.5623	−0.600267
$857$	− 26.9443i	− 0.920399i	−0.887816	−	0.460199i	$-0.847778\pi$
$857$	− 26.9443i	− 0.920399i	0.887816	−	0.460199i	$-0.152222\pi$
$858$	− 1.85410i	− 0.0632980i
$859$	25.1246	0.857241	0.428620	−	0.903485i	$-0.359000\pi$
$859$	25.1246	0.857241	0.428620	+	0.903485i	$0.359000\pi$
$860$	0	0
$861$	23.2361	0.791883
$862$	21.1591i	0.720680i
$863$	− 45.0689i	− 1.53416i	−0.641550	−	0.767081i	$-0.721708\pi$
$863$	− 45.0689i	− 1.53416i	0.641550	−	0.767081i	$-0.278292\pi$
$864$	5.61803	0.191129
$865$	0	0
$866$	3.38197	0.114924
$867$	16.9443i	0.575458i
$868$	− 15.2361i	− 0.517146i
$869$	−47.5623	−1.61344
$870$	0	0
$871$	−9.18034	−0.311064
$872$	24.2705i	0.821903i
$873$	− 2.85410i	− 0.0965967i
$874$	31.5836	1.06833
$875$	0	0
$876$	−3.70820	−0.125289
$877$	− 2.87539i	− 0.0970950i	−0.998821	−	0.0485475i	$-0.984541\pi$
$877$	− 2.87539i	− 0.0970950i	0.998821	−	0.0485475i	$-0.0154592\pi$
$878$	1.83282i	0.0618545i
$879$	−9.32624	−0.314566
$880$	0	0
$881$	3.90983	0.131726	0.0658628	−	0.997829i	$-0.479020\pi$
$881$	3.90983	0.131726	0.0658628	+	0.997829i	$0.479020\pi$
$882$	− 1.85410i	− 0.0624309i
$883$	53.7984i	1.81046i	0.424923	+	0.905230i	$0.360301\pi$
$883$	53.7984i	1.81046i	−0.424923	+	0.905230i	$0.639699\pi$
$884$	−0.381966	−0.0128469
$885$	0	0
$886$	−4.58359	−0.153989
$887$	21.9230i	0.736102i	0.929806	+	0.368051i	$0.119975\pi$
$887$	21.9230i	0.736102i	−0.929806	+	0.368051i	$0.880025\pi$
$888$	− 4.47214i	− 0.150075i
$889$	−35.3050	−1.18409
$890$	0	0
$891$	−3.00000	−0.100504
$892$	− 27.2705i	− 0.913084i
$893$	− 61.9574i	− 2.07333i
$894$	−1.18034	−0.0394765
$895$	0	0
$896$	−22.7639	−0.760490
$897$	7.61803i	0.254359i
$898$	13.2918i	0.443553i
$899$	−6.50658	−0.217007
$900$	0	0
$901$	1.59675	0.0531954
$902$	21.5410i	0.717238i
$903$	19.2361i	0.640136i
$904$	18.4164	0.612521
$905$	0	0
$906$	2.70820	0.0899740
$907$	17.0000i	0.564476i	0.959344	+	0.282238i	$0.0910767\pi$
$907$	17.0000i	0.564476i	−0.959344	+	0.282238i	$0.908923\pi$
$908$	− 16.5623i	− 0.549639i
$909$	11.6180	0.385346
$910$	0	0
$911$	−20.8885	−0.692068	−0.346034	−	0.938222i	$-0.612472\pi$
$911$	−20.8885	−0.692068	−0.346034	+	0.938222i	$0.612472\pi$
$912$	− 12.4377i	− 0.411853i
$913$	− 27.0000i	− 0.893570i
$914$	16.0000	0.529233
$915$	0	0
$916$	−10.0000	−0.330409
$917$	16.3607i	0.540277i
$918$	− 0.145898i	− 0.00481535i
$919$	5.00000	0.164935	0.0824674	−	0.996594i	$-0.473720\pi$
$919$	5.00000	0.164935	0.0824674	+	0.996594i	$0.473720\pi$
$920$	0	0
$921$	2.14590	0.0707097
$922$	1.96556i	0.0647322i
$923$	1.09017i	0.0358834i
$924$	9.70820	0.319376
$925$	0	0
$926$	−16.4934	−0.542007
$927$	− 12.4164i	− 0.407808i
$928$	7.76393i	0.254864i
$929$	−19.5967	−0.642948	−0.321474	−	0.946918i	$-0.604178\pi$
$929$	−19.5967	−0.642948	−0.321474	+	0.946918i	$0.604178\pi$
$930$	0	0
$931$	−20.1246	−0.659558
$932$	− 19.7082i	− 0.645564i
$933$	− 22.4721i	− 0.735705i
$934$	10.1459	0.331984
$935$	0	0
$936$	−2.23607	−0.0730882
$937$	− 16.4164i	− 0.536301i	−0.963377	−	0.268150i	$-0.913588\pi$
$937$	− 16.4164i	− 0.536301i	0.963377	−	0.268150i	$-0.0864124\pi$
$938$	11.3475i	0.370510i
$939$	−15.7082	−0.512618
$940$	0	0
$941$	11.0213	0.359284	0.179642	−	0.983732i	$-0.442506\pi$
$941$	11.0213	0.359284	0.179642	+	0.983732i	$0.442506\pi$
$942$	2.38197i	0.0776086i
$943$	− 88.5066i	− 2.88217i
$944$	25.8541	0.841479
$945$	0	0
$946$	−17.8328	−0.579795
$947$	− 29.8328i	− 0.969436i	−0.874670	−	0.484718i	$-0.838922\pi$
$947$	− 29.8328i	− 0.969436i	0.874670	−	0.484718i	$-0.161078\pi$
$948$	25.6525i	0.833154i
$949$	2.29180	0.0743948
$950$	0	0
$951$	0.437694	0.0141932
$952$	1.05573i	0.0342163i
$953$	− 59.9443i	− 1.94179i	−0.239515	−	0.970893i	$-0.576988\pi$
$953$	− 59.9443i	− 1.94179i	0.239515	−	0.970893i	$-0.423012\pi$
$954$	4.18034	0.135344
$955$	0	0
$956$	−38.2148	−1.23595
$957$	− 4.14590i	− 0.134018i
$958$	12.2361i	0.395329i
$959$	41.1246	1.32798
$960$	0	0
$961$	−8.83282	−0.284930
$962$	1.23607i	0.0398524i
$963$	− 7.85410i	− 0.253095i
$964$	−13.4721	−0.433908
$965$	0	0
$966$	9.41641	0.302968
$967$	8.58359i	0.276030i	0.990430	+	0.138015i	$0.0440722\pi$
$967$	8.58359i	0.276030i	−0.990430	+	0.138015i	$0.955928\pi$
$968$	− 4.47214i	− 0.143740i
$969$	−1.58359	−0.0508723
$970$	0	0
$971$	−5.88854	−0.188972	−0.0944862	−	0.995526i	$-0.530121\pi$
$971$	−5.88854	−0.188972	−0.0944862	+	0.995526i	$0.530121\pi$
$972$	1.61803i	0.0518985i
$973$	26.8328i	0.860221i
$974$	8.88854	0.284807
$975$	0	0
$976$	−8.72949	−0.279424
$977$	6.34752i	0.203075i	0.994832	+	0.101538i	$0.0323762\pi$
$977$	6.34752i	0.203075i	−0.994832	+	0.101538i	$0.967624\pi$
$978$	9.43769i	0.301784i
$979$	33.5410	1.07198
$980$	0	0
$981$	−10.8541	−0.346545
$982$	4.12461i	0.131622i
$983$	− 22.3820i	− 0.713874i	−0.934128	−	0.356937i	$-0.883821\pi$
$983$	− 22.3820i	− 0.713874i	0.934128	−	0.356937i	$-0.116179\pi$
$984$	25.9787	0.828171
$985$	0	0
$986$	0.201626	0.00642108
$987$	− 18.4721i	− 0.587975i
$988$	10.8541i	0.345315i
$989$	73.2705	2.32987
$990$	0	0
$991$	32.0000	1.01651	0.508257	−	0.861206i	$-0.330290\pi$
$991$	32.0000	1.01651	0.508257	+	0.861206i	$0.330290\pi$
$992$	− 26.4508i	− 0.839815i
$993$	29.6869i	0.942086i
$994$	1.34752	0.0427409
$995$	0	0
$996$	−14.5623	−0.461424
$997$	61.0689i	1.93407i	0.254642	+	0.967035i	$0.418042\pi$
$997$	61.0689i	1.93407i	−0.254642	+	0.967035i	$0.581958\pi$
$998$	9.27051i	0.293453i
$999$	2.00000	0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.2.b.a.1249.3		4
5.2	odd	4		1875.2.a.c.1.1	yes	2
5.3	odd	4		1875.2.a.b.1.2	✓	2
5.4	even	2	inner	1875.2.b.a.1249.2		4
15.2	even	4		5625.2.a.b.1.2		2
15.8	even	4		5625.2.a.g.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1875.2.a.b.1.2	✓	2	5.3	odd	4
1875.2.a.c.1.1	yes	2	5.2	odd	4
1875.2.b.a.1249.2		4	5.4	even	2	inner
1875.2.b.a.1249.3		4	1.1	even	1	trivial
5625.2.a.b.1.2		2	15.2	even	4
5625.2.a.g.1.1		2	15.8	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:	\( N \)	\(=\)	\( 1875 = 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1875.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+0.618034i q^{2} +1.00000i q^{3} +1.61803 q^{4} -0.618034 q^{6} +2.00000i q^{7} +2.23607i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+0.618034i q^{2} +1.00000i q^{3} +1.61803 q^{4} -0.618034 q^{6} +2.00000i q^{7} +2.23607i q^{8} -1.00000 q^{9} -3.00000 q^{11} +1.61803i q^{12} -1.00000i q^{13} -1.23607 q^{14} +1.85410 q^{16} -0.236068i q^{17} -0.618034i q^{18} -6.70820 q^{19} -2.00000 q^{21} -1.85410i q^{22} +7.61803i q^{23} -2.23607 q^{24} +0.618034 q^{26} -1.00000i q^{27} +3.23607i q^{28} +1.38197 q^{29} -4.70820 q^{31} +5.61803i q^{32} -3.00000i q^{33} +0.145898 q^{34} -1.61803 q^{36} +2.00000i q^{37} -4.14590i q^{38} +1.00000 q^{39} -11.6180 q^{41} -1.23607i q^{42} -9.61803i q^{43} -4.85410 q^{44} -4.70820 q^{46} +9.23607i q^{47} +1.85410i q^{48} +3.00000 q^{49} +0.236068 q^{51} -1.61803i q^{52} +6.76393i q^{53} +0.618034 q^{54} -4.47214 q^{56} -6.70820i q^{57} +0.854102i q^{58} +13.9443 q^{59} -4.70820 q^{61} -2.90983i q^{62} -2.00000i q^{63} +0.236068 q^{64} +1.85410 q^{66} -9.18034i q^{67} -0.381966i q^{68} -7.61803 q^{69} -1.09017 q^{71} -2.23607i q^{72} +2.29180i q^{73} -1.23607 q^{74} -10.8541 q^{76} -6.00000i q^{77} +0.618034i q^{78} +15.8541 q^{79} +1.00000 q^{81} -7.18034i q^{82} +9.00000i q^{83} -3.23607 q^{84} +5.94427 q^{86} +1.38197i q^{87} -6.70820i q^{88} -11.1803 q^{89} +2.00000 q^{91} +12.3262i q^{92} -4.70820i q^{93} -5.70820 q^{94} -5.61803 q^{96} +2.85410i q^{97} +1.85410i q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 2 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 2 * q^6 - 4 * q^9	\( 4 q + 2 q^{4} + 2 q^{6} - 4 q^{9} - 12 q^{11} + 4 q^{14} - 6 q^{16} - 8 q^{21} - 2 q^{26} + 10 q^{29} + 8 q^{31} + 14 q^{34} - 2 q^{36} + 4 q^{39} - 42 q^{41} - 6 q^{44} + 8 q^{46} + 12 q^{49} - 8 q^{51} - 2 q^{54} + 20 q^{59} + 8 q^{61} - 8 q^{64} - 6 q^{66} - 26 q^{69} + 18 q^{71} + 4 q^{74} - 30 q^{76} + 50 q^{79} + 4 q^{81} - 4 q^{84} - 12 q^{86} + 8 q^{91} + 4 q^{94} - 18 q^{96} + 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 + 2 * q^6 - 4 * q^9 - 12 * q^11 + 4 * q^14 - 6 * q^16 - 8 * q^21 - 2 * q^26 + 10 * q^29 + 8 * q^31 + 14 * q^34 - 2 * q^36 + 4 * q^39 - 42 * q^41 - 6 * q^44 + 8 * q^46 + 12 * q^49 - 8 * q^51 - 2 * q^54 + 20 * q^59 + 8 * q^61 - 8 * q^64 - 6 * q^66 - 26 * q^69 + 18 * q^71 + 4 * q^74 - 30 * q^76 + 50 * q^79 + 4 * q^81 - 4 * q^84 - 12 * q^86 + 8 * q^91 + 4 * q^94 - 18 * q^96 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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