LMFDB - Embedded newform 1875.2.b.a.1249.1

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			1249.1
Root			$-1.61803i$ of defining polynomial
Character	$\chi$	$=$	1875.1249
Dual form			1875.2.b.a.1249.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.61803i q^{2} +1.00000i q^{3} -0.618034 q^{4} +1.61803 q^{6} +2.00000i q^{7} -2.23607i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.61803i q^{2} +1.00000i q^{3} -0.618034 q^{4} +1.61803 q^{6} +2.00000i q^{7} -2.23607i q^{8} -1.00000 q^{9} -3.00000 q^{11} -0.618034i q^{12} -1.00000i q^{13} +3.23607 q^{14} -4.85410 q^{16} +4.23607i q^{17} +1.61803i q^{18} +6.70820 q^{19} -2.00000 q^{21} +4.85410i q^{22} +5.38197i q^{23} +2.23607 q^{24} -1.61803 q^{26} -1.00000i q^{27} -1.23607i q^{28} +3.61803 q^{29} +8.70820 q^{31} +3.38197i q^{32} -3.00000i q^{33} +6.85410 q^{34} +0.618034 q^{36} +2.00000i q^{37} -10.8541i q^{38} +1.00000 q^{39} -9.38197 q^{41} +3.23607i q^{42} -7.38197i q^{43} +1.85410 q^{44} +8.70820 q^{46} +4.76393i q^{47} -4.85410i q^{48} +3.00000 q^{49} -4.23607 q^{51} +0.618034i q^{52} +11.2361i q^{53} -1.61803 q^{54} +4.47214 q^{56} +6.70820i q^{57} -5.85410i q^{58} -3.94427 q^{59} +8.70820 q^{61} -14.0902i q^{62} -2.00000i q^{63} -4.23607 q^{64} -4.85410 q^{66} +13.1803i q^{67} -2.61803i q^{68} -5.38197 q^{69} +10.0902 q^{71} +2.23607i q^{72} +15.7082i q^{73} +3.23607 q^{74} -4.14590 q^{76} -6.00000i q^{77} -1.61803i q^{78} +9.14590 q^{79} +1.00000 q^{81} +15.1803i q^{82} +9.00000i q^{83} +1.23607 q^{84} -11.9443 q^{86} +3.61803i q^{87} +6.70820i q^{88} +11.1803 q^{89} +2.00000 q^{91} -3.32624i q^{92} +8.70820i q^{93} +7.70820 q^{94} -3.38197 q^{96} -3.85410i q^{97} -4.85410i q^{98} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	− 1.61803i	− 1.14412i	−0.820211	−	0.572061i	$-0.806144\pi$
$2$	− 1.61803i	− 1.14412i	0.820211	−	0.572061i	$-0.193856\pi$
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	−0.618034	−0.309017
$5$	0	0
$5$	0	0
$6$	1.61803	0.660560
$7$	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	$0.649385\pi$
$12$	− 0.618034i	− 0.178411i
$13$	− 1.00000i	− 0.277350i	−0.990338	−	0.138675i	$-0.955716\pi$
$13$	− 1.00000i	− 0.277350i	0.990338	−	0.138675i	$-0.0442844\pi$
$14$	3.23607	0.864876
$15$	0	0
$16$	−4.85410	−1.21353
$17$	4.23607i	1.02740i	0.857971	+	0.513699i	$0.171725\pi$
$17$	4.23607i	1.02740i	−0.857971	+	0.513699i	$0.828275\pi$
$18$	1.61803i	0.381374i
$19$	6.70820	1.53897	0.769484	−	0.638666i	$-0.220514\pi$
$19$	6.70820	1.53897	0.769484	+	0.638666i	$0.220514\pi$
$20$	0	0
$21$	−2.00000	−0.436436
$22$	4.85410i	1.03490i
$23$	5.38197i	1.12222i	0.827742	+	0.561109i	$0.189625\pi$
$23$	5.38197i	1.12222i	−0.827742	+	0.561109i	$0.810375\pi$
$24$	2.23607	0.456435
$25$	0	0
$26$	−1.61803	−0.317323
$27$	− 1.00000i	− 0.192450i
$28$	− 1.23607i	− 0.233595i
$29$	3.61803	0.671852	0.335926	−	0.941888i	$-0.390951\pi$
$29$	3.61803	0.671852	0.335926	+	0.941888i	$0.390951\pi$
$30$	0	0
$31$	8.70820	1.56404	0.782020	−	0.623254i	$-0.214190\pi$
$31$	8.70820	1.56404	0.782020	+	0.623254i	$0.214190\pi$
$32$	3.38197i	0.597853i
$33$	− 3.00000i	− 0.522233i
$34$	6.85410	1.17547
$35$	0	0
$36$	0.618034	0.103006
$37$	2.00000i	0.328798i	0.986394	+	0.164399i	$0.0525685\pi$
$37$	2.00000i	0.328798i	−0.986394	+	0.164399i	$0.947432\pi$
$38$	− 10.8541i	− 1.76077i
$39$	1.00000	0.160128
$40$	0	0
$41$	−9.38197	−1.46522	−0.732608	−	0.680650i	$-0.761697\pi$
$41$	−9.38197	−1.46522	−0.732608	+	0.680650i	$0.761697\pi$
$42$	3.23607i	0.499336i
$43$	− 7.38197i	− 1.12574i	−0.826546	−	0.562870i	$-0.809697\pi$
$43$	− 7.38197i	− 1.12574i	0.826546	−	0.562870i	$-0.190303\pi$
$44$	1.85410	0.279516
$45$	0	0
$46$	8.70820	1.28395
$47$	4.76393i	0.694891i	0.937700	+	0.347445i	$0.112951\pi$
$47$	4.76393i	0.694891i	−0.937700	+	0.347445i	$0.887049\pi$
$48$	− 4.85410i	− 0.700629i
$49$	3.00000	0.428571
$50$	0	0
$51$	−4.23607	−0.593168
$52$	0.618034i	0.0857059i
$53$	11.2361i	1.54339i	0.635991	+	0.771696i	$0.280591\pi$
$53$	11.2361i	1.54339i	−0.635991	+	0.771696i	$0.719409\pi$
$54$	−1.61803	−0.220187
$55$	0	0
$56$	4.47214	0.597614
$57$	6.70820i	0.888523i
$58$	− 5.85410i	− 0.768681i
$59$	−3.94427	−0.513500	−0.256750	−	0.966478i	$-0.582652\pi$
$59$	−3.94427	−0.513500	−0.256750	+	0.966478i	$0.582652\pi$
$60$	0	0
$61$	8.70820	1.11497	0.557486	−	0.830187i	$-0.311766\pi$
$61$	8.70820	1.11497	0.557486	+	0.830187i	$0.311766\pi$
$62$	− 14.0902i	− 1.78945i
$63$	− 2.00000i	− 0.251976i
$64$	−4.23607	−0.529508
$65$	0	0
$66$	−4.85410	−0.597499
$67$	13.1803i	1.61023i	0.593115	+	0.805117i	$0.297898\pi$
$67$	13.1803i	1.61023i	−0.593115	+	0.805117i	$0.702102\pi$
$68$	− 2.61803i	− 0.317483i
$69$	−5.38197	−0.647913
$70$	0	0
$71$	10.0902	1.19748	0.598741	−	0.800942i	$-0.295668\pi$
$71$	10.0902	1.19748	0.598741	+	0.800942i	$0.295668\pi$
$72$	2.23607i	0.263523i
$73$	15.7082i	1.83851i	0.393667	+	0.919253i	$0.371206\pi$
$73$	15.7082i	1.83851i	−0.393667	+	0.919253i	$0.628794\pi$
$74$	3.23607	0.376185
$75$	0	0
$76$	−4.14590	−0.475567
$77$	− 6.00000i	− 0.683763i
$78$	− 1.61803i	− 0.183206i
$79$	9.14590	1.02899	0.514497	−	0.857492i	$-0.327979\pi$
$79$	9.14590	1.02899	0.514497	+	0.857492i	$0.327979\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	15.1803i	1.67639i
$83$	9.00000i	0.987878i	0.869496	+	0.493939i	$0.164443\pi$
$83$	9.00000i	0.987878i	−0.869496	+	0.493939i	$0.835557\pi$
$84$	1.23607	0.134866
$85$	0	0
$86$	−11.9443	−1.28798
$87$	3.61803i	0.387894i
$88$	6.70820i	0.715097i
$89$	11.1803	1.18511	0.592557	−	0.805529i	$-0.298119\pi$
$89$	11.1803	1.18511	0.592557	+	0.805529i	$0.298119\pi$
$90$	0	0
$91$	2.00000	0.209657
$92$	− 3.32624i	− 0.346784i
$93$	8.70820i	0.902999i
$94$	7.70820	0.795041
$95$	0	0
$96$	−3.38197	−0.345170
$97$	− 3.85410i	− 0.391325i	−0.980671	−	0.195662i	$-0.937314\pi$
$97$	− 3.85410i	− 0.391325i	0.980671	−	0.195662i	$-0.0626857\pi$
$98$	− 4.85410i	− 0.490338i
$99$	3.00000	0.301511
$100$	0	0
$101$	−9.38197	−0.933541	−0.466770	−	0.884379i	$-0.654583\pi$
$101$	−9.38197	−0.933541	−0.466770	+	0.884379i	$0.654583\pi$
$102$	6.85410i	0.678657i
$103$	− 14.4164i	− 1.42049i	−0.703954	−	0.710245i	$-0.748584\pi$
$103$	− 14.4164i	− 1.42049i	0.703954	−	0.710245i	$-0.251416\pi$
$104$	−2.23607	−0.219265
$105$	0	0
$106$	18.1803	1.76583
$107$	1.14590i	0.110778i	0.998465	+	0.0553891i	$0.0176399\pi$
$107$	1.14590i	0.110778i	−0.998465	+	0.0553891i	$0.982360\pi$
$108$	0.618034i	0.0594703i
$109$	4.14590	0.397105	0.198553	−	0.980090i	$-0.436376\pi$
$109$	4.14590	0.397105	0.198553	+	0.980090i	$0.436376\pi$
$110$	0	0
$111$	−2.00000	−0.189832
$112$	− 9.70820i	− 0.917339i
$113$	− 3.76393i	− 0.354081i	−0.984204	−	0.177040i	$-0.943348\pi$
$113$	− 3.76393i	− 0.354081i	0.984204	−	0.177040i	$-0.0566523\pi$
$114$	10.8541	1.01658
$115$	0	0
$116$	−2.23607	−0.207614
$117$	1.00000i	0.0924500i
$118$	6.38197i	0.587508i
$119$	−8.47214	−0.776639
$120$	0	0
$121$	−2.00000	−0.181818
$122$	− 14.0902i	− 1.27566i
$123$	− 9.38197i	− 0.845943i
$124$	−5.38197	−0.483315
$125$	0	0
$126$	−3.23607	−0.288292
$127$	− 13.6525i	− 1.21146i	−0.795670	−	0.605731i	$-0.792881\pi$
$127$	− 13.6525i	− 1.21146i	0.795670	−	0.605731i	$-0.207119\pi$
$128$	13.6180i	1.20368i
$129$	7.38197	0.649946
$130$	0	0
$131$	−14.1803	−1.23894	−0.619471	−	0.785020i	$-0.712653\pi$
$131$	−14.1803	−1.23894	−0.619471	+	0.785020i	$0.712653\pi$
$132$	1.85410i	0.161379i
$133$	13.4164i	1.16335i
$134$	21.3262	1.84231
$135$	0	0
$136$	9.47214	0.812229
$137$	− 0.437694i	− 0.0373947i	−0.999825	−	0.0186974i	$-0.994048\pi$
$137$	− 0.437694i	− 0.0373947i	0.999825	−	0.0186974i	$-0.00595190\pi$
$138$	8.70820i	0.741292i
$139$	−13.4164	−1.13796	−0.568982	−	0.822350i	$-0.692663\pi$
$139$	−13.4164	−1.13796	−0.568982	+	0.822350i	$0.692663\pi$
$140$	0	0
$141$	−4.76393	−0.401195
$142$	− 16.3262i	− 1.37007i
$143$	3.00000i	0.250873i
$144$	4.85410	0.404508
$145$	0	0
$146$	25.4164	2.10348
$147$	3.00000i	0.247436i
$148$	− 1.23607i	− 0.101604i
$149$	13.0902	1.07239	0.536194	−	0.844095i	$-0.319861\pi$
$149$	13.0902	1.07239	0.536194	+	0.844095i	$0.319861\pi$
$150$	0	0
$151$	−6.61803	−0.538568	−0.269284	−	0.963061i	$-0.586787\pi$
$151$	−6.61803	−0.538568	−0.269284	+	0.963061i	$0.586787\pi$
$152$	− 15.0000i	− 1.21666i
$153$	− 4.23607i	− 0.342466i
$154$	−9.70820	−0.782309
$155$	0	0
$156$	−0.618034	−0.0494823
$157$	2.85410i	0.227782i	0.993493	+	0.113891i	$0.0363315\pi$
$157$	2.85410i	0.227782i	−0.993493	+	0.113891i	$0.963669\pi$
$158$	− 14.7984i	− 1.17730i
$159$	−11.2361	−0.891078
$160$	0	0
$161$	−10.7639	−0.848317
$162$	− 1.61803i	− 0.127125i
$163$	18.2705i	1.43106i	0.698584	+	0.715528i	$0.253814\pi$
$163$	18.2705i	1.43106i	−0.698584	+	0.715528i	$0.746186\pi$
$164$	5.79837	0.452777
$165$	0	0
$166$	14.5623	1.13025
$167$	− 17.7984i	− 1.37728i	−0.725104	−	0.688640i	$-0.758208\pi$
$167$	− 17.7984i	− 1.37728i	0.725104	−	0.688640i	$-0.241792\pi$
$168$	4.47214i	0.345033i
$169$	12.0000	0.923077
$170$	0	0
$171$	−6.70820	−0.512989
$172$	4.56231i	0.347873i
$173$	0.909830i	0.0691731i	0.999402	+	0.0345865i	$0.0110114\pi$
$173$	0.909830i	0.0691731i	−0.999402	+	0.0345865i	$0.988989\pi$
$174$	5.85410	0.443798
$175$	0	0
$176$	14.5623	1.09768
$177$	− 3.94427i	− 0.296470i
$178$	− 18.0902i	− 1.35592i
$179$	15.6525	1.16992	0.584960	−	0.811062i	$-0.301110\pi$
$179$	15.6525	1.16992	0.584960	+	0.811062i	$0.301110\pi$
$180$	0	0
$181$	−12.4721	−0.927047	−0.463523	−	0.886085i	$-0.653415\pi$
$181$	−12.4721	−0.927047	−0.463523	+	0.886085i	$0.653415\pi$
$182$	− 3.23607i	− 0.239873i
$183$	8.70820i	0.643729i
$184$	12.0344	0.887191
$185$	0	0
$186$	14.0902	1.03314
$187$	− 12.7082i	− 0.929316i
$188$	− 2.94427i	− 0.214733i
$189$	2.00000	0.145479
$190$	0	0
$191$	17.3262	1.25368	0.626841	−	0.779147i	$-0.284347\pi$
$191$	17.3262	1.25368	0.626841	+	0.779147i	$0.284347\pi$
$192$	− 4.23607i	− 0.305712i
$193$	− 11.0000i	− 0.791797i	−0.918294	−	0.395899i	$-0.870433\pi$
$193$	− 11.0000i	− 0.791797i	0.918294	−	0.395899i	$-0.129567\pi$
$194$	−6.23607	−0.447724
$195$	0	0
$196$	−1.85410	−0.132436
$197$	0.0901699i	0.00642434i	0.999995	+	0.00321217i	$0.00102247\pi$
$197$	0.0901699i	0.00642434i	−0.999995	+	0.00321217i	$0.998978\pi$
$198$	− 4.85410i	− 0.344966i
$199$	−11.7082	−0.829973	−0.414986	−	0.909828i	$-0.636214\pi$
$199$	−11.7082	−0.829973	−0.414986	+	0.909828i	$0.636214\pi$
$200$	0	0
$201$	−13.1803	−0.929669
$202$	15.1803i	1.06808i
$203$	7.23607i	0.507872i
$204$	2.61803	0.183299
$205$	0	0
$206$	−23.3262	−1.62522
$207$	− 5.38197i	− 0.374072i
$208$	4.85410i	0.336571i
$209$	−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	$0.532929\pi$
$212$	− 6.94427i	− 0.476935i
$213$	10.0902i	0.691367i
$214$	1.85410	0.126744
$215$	0	0
$216$	−2.23607	−0.152145
$217$	17.4164i	1.18230i
$218$	− 6.70820i	− 0.454337i
$219$	−15.7082	−1.06146
$220$	0	0
$221$	4.23607	0.284949
$222$	3.23607i	0.217191i
$223$	− 10.1459i	− 0.679420i	−0.940530	−	0.339710i	$-0.889671\pi$
$223$	− 10.1459i	− 0.679420i	0.940530	−	0.339710i	$-0.110329\pi$
$224$	−6.76393	−0.451934
$225$	0	0
$226$	−6.09017	−0.405112
$227$	− 5.76393i	− 0.382566i	−0.981535	−	0.191283i	$-0.938735\pi$
$227$	− 5.76393i	− 0.382566i	0.981535	−	0.191283i	$-0.0612648\pi$
$228$	− 4.14590i	− 0.274569i
$229$	16.1803	1.06923	0.534613	−	0.845097i	$-0.320457\pi$
$229$	16.1803	1.06923	0.534613	+	0.845097i	$0.320457\pi$
$230$	0	0
$231$	6.00000	0.394771
$232$	− 8.09017i	− 0.531146i
$233$	10.1803i	0.666936i	0.942761	+	0.333468i	$0.108219\pi$
$233$	10.1803i	0.666936i	−0.942761	+	0.333468i	$0.891781\pi$
$234$	1.61803	0.105774
$235$	0	0
$236$	2.43769	0.158680
$237$	9.14590i	0.594090i
$238$	13.7082i	0.888571i
$239$	−21.3820	−1.38308	−0.691542	−	0.722336i	$-0.743068\pi$
$239$	−21.3820	−1.38308	−0.691542	+	0.722336i	$0.743068\pi$
$240$	0	0
$241$	7.32624	0.471924	0.235962	−	0.971762i	$-0.424176\pi$
$241$	7.32624	0.471924	0.235962	+	0.971762i	$0.424176\pi$
$242$	3.23607i	0.208022i
$243$	1.00000i	0.0641500i
$244$	−5.38197	−0.344545
$245$	0	0
$246$	−15.1803	−0.967863
$247$	− 6.70820i	− 0.426833i
$248$	− 19.4721i	− 1.23648i
$249$	−9.00000	−0.570352
$250$	0	0
$251$	−18.9787	−1.19793	−0.598963	−	0.800777i	$-0.704420\pi$
$251$	−18.9787	−1.19793	−0.598963	+	0.800777i	$0.704420\pi$
$252$	1.23607i	0.0778650i
$253$	− 16.1459i	− 1.01508i
$254$	−22.0902	−1.38606
$255$	0	0
$256$	13.5623	0.847644
$257$	− 31.2148i	− 1.94712i	−0.228422	−	0.973562i	$-0.573356\pi$
$257$	− 31.2148i	− 1.94712i	0.228422	−	0.973562i	$-0.426644\pi$
$258$	− 11.9443i	− 0.743618i
$259$	−4.00000	−0.248548
$260$	0	0
$261$	−3.61803	−0.223951
$262$	22.9443i	1.41750i
$263$	− 12.5066i	− 0.771189i	−0.922668	−	0.385594i	$-0.873996\pi$
$263$	− 12.5066i	− 0.771189i	0.922668	−	0.385594i	$-0.126004\pi$
$264$	−6.70820	−0.412861
$265$	0	0
$266$	21.7082	1.33102
$267$	11.1803i	0.684226i
$268$	− 8.14590i	− 0.497590i
$269$	20.5279	1.25161	0.625803	−	0.779981i	$-0.284771\pi$
$269$	20.5279	1.25161	0.625803	+	0.779981i	$0.284771\pi$
$270$	0	0
$271$	−11.4164	−0.693497	−0.346749	−	0.937958i	$-0.612714\pi$
$271$	−11.4164	−0.693497	−0.346749	+	0.937958i	$0.612714\pi$
$272$	− 20.5623i	− 1.24677i
$273$	2.00000i	0.121046i
$274$	−0.708204	−0.0427842
$275$	0	0
$276$	3.32624	0.200216
$277$	13.0557i	0.784443i	0.919871	+	0.392221i	$0.128293\pi$
$277$	13.0557i	0.784443i	−0.919871	+	0.392221i	$0.871707\pi$
$278$	21.7082i	1.30197i
$279$	−8.70820	−0.521347
$280$	0	0
$281$	−14.1803	−0.845928	−0.422964	−	0.906146i	$-0.639010\pi$
$281$	−14.1803	−0.845928	−0.422964	+	0.906146i	$0.639010\pi$
$282$	7.70820i	0.459017i
$283$	2.29180i	0.136233i	0.997677	+	0.0681166i	$0.0216990\pi$
$283$	2.29180i	0.136233i	−0.997677	+	0.0681166i	$0.978301\pi$
$284$	−6.23607	−0.370043
$285$	0	0
$286$	4.85410	0.287029
$287$	− 18.7639i	− 1.10760i
$288$	− 3.38197i	− 0.199284i
$289$	−0.944272	−0.0555454
$290$	0	0
$291$	3.85410	0.225931
$292$	− 9.70820i	− 0.568130i
$293$	− 6.32624i	− 0.369583i	−0.982778	−	0.184791i	$-0.940839\pi$
$293$	− 6.32624i	− 0.369583i	0.982778	−	0.184791i	$-0.0591609\pi$
$294$	4.85410	0.283097
$295$	0	0
$296$	4.47214	0.259938
$297$	3.00000i	0.174078i
$298$	− 21.1803i	− 1.22694i
$299$	5.38197	0.311247
$300$	0	0
$301$	14.7639	0.850979
$302$	10.7082i	0.616188i
$303$	− 9.38197i	− 0.538980i
$304$	−32.5623	−1.86758
$305$	0	0
$306$	−6.85410	−0.391823
$307$	− 8.85410i	− 0.505330i	−0.967554	−	0.252665i	$-0.918693\pi$
$307$	− 8.85410i	− 0.505330i	0.967554	−	0.252665i	$-0.0813071\pi$
$308$	3.70820i	0.211295i
$309$	14.4164	0.820121
$310$	0	0
$311$	−13.5279	−0.767095	−0.383547	−	0.923521i	$-0.625298\pi$
$311$	−13.5279	−0.767095	−0.383547	+	0.923521i	$0.625298\pi$
$312$	− 2.23607i	− 0.126592i
$313$	2.29180i	0.129540i	0.997900	+	0.0647700i	$0.0206314\pi$
$313$	2.29180i	0.129540i	−0.997900	+	0.0647700i	$0.979369\pi$
$314$	4.61803	0.260611
$315$	0	0
$316$	−5.65248	−0.317977
$317$	− 20.5623i	− 1.15489i	−0.816428	−	0.577447i	$-0.804049\pi$
$317$	− 20.5623i	− 1.15489i	0.816428	−	0.577447i	$-0.195951\pi$
$318$	18.1803i	1.01950i
$319$	−10.8541	−0.607713
$320$	0	0
$321$	−1.14590	−0.0639578
$322$	17.4164i	0.970578i
$323$	28.4164i	1.58113i
$324$	−0.618034	−0.0343352
$325$	0	0
$326$	29.5623	1.63730
$327$	4.14590i	0.229269i
$328$	20.9787i	1.15836i
$329$	−9.52786	−0.525288
$330$	0	0
$331$	−30.6869	−1.68671	−0.843353	−	0.537360i	$-0.819422\pi$
$331$	−30.6869	−1.68671	−0.843353	+	0.537360i	$0.819422\pi$
$332$	− 5.56231i	− 0.305271i
$333$	− 2.00000i	− 0.109599i
$334$	−28.7984	−1.57578
$335$	0	0
$336$	9.70820	0.529626
$337$	33.1803i	1.80745i	0.428115	+	0.903724i	$0.359178\pi$
$337$	33.1803i	1.80745i	−0.428115	+	0.903724i	$0.640822\pi$
$338$	− 19.4164i	− 1.05611i
$339$	3.76393	0.204429
$340$	0	0
$341$	−26.1246	−1.41473
$342$	10.8541i	0.586923i
$343$	20.0000i	1.07990i
$344$	−16.5066	−0.889975
$345$	0	0
$346$	1.47214	0.0791425
$347$	− 12.2705i	− 0.658715i	−0.944205	−	0.329358i	$-0.893168\pi$
$347$	− 12.2705i	− 0.658715i	0.944205	−	0.329358i	$-0.106832\pi$
$348$	− 2.23607i	− 0.119866i
$349$	−7.23607	−0.387338	−0.193669	−	0.981067i	$-0.562039\pi$
$349$	−7.23607	−0.387338	−0.193669	+	0.981067i	$0.562039\pi$
$350$	0	0
$351$	−1.00000	−0.0533761
$352$	− 10.1459i	− 0.540778i
$353$	− 12.3820i	− 0.659026i	−0.944151	−	0.329513i	$-0.893116\pi$
$353$	− 12.3820i	− 0.659026i	0.944151	−	0.329513i	$-0.106884\pi$
$354$	−6.38197	−0.339198
$355$	0	0
$356$	−6.90983	−0.366220
$357$	− 8.47214i	− 0.448393i
$358$	− 25.3262i	− 1.33853i
$359$	−23.9443	−1.26373	−0.631865	−	0.775078i	$-0.717710\pi$
$359$	−23.9443	−1.26373	−0.631865	+	0.775078i	$0.717710\pi$
$360$	0	0
$361$	26.0000	1.36842
$362$	20.1803i	1.06066i
$363$	− 2.00000i	− 0.104973i
$364$	−1.23607	−0.0647876
$365$	0	0
$366$	14.0902	0.736505
$367$	12.5279i	0.653949i	0.945033	+	0.326975i	$0.106029\pi$
$367$	12.5279i	0.653949i	−0.945033	+	0.326975i	$0.893971\pi$
$368$	− 26.1246i	− 1.36184i
$369$	9.38197	0.488406
$370$	0	0
$371$	−22.4721	−1.16670
$372$	− 5.38197i	− 0.279042i
$373$	17.4164i	0.901787i	0.892578	+	0.450894i	$0.148895\pi$
$373$	17.4164i	0.901787i	−0.892578	+	0.450894i	$0.851105\pi$
$374$	−20.5623	−1.06325
$375$	0	0
$376$	10.6525	0.549359
$377$	− 3.61803i	− 0.186338i
$378$	− 3.23607i	− 0.166445i
$379$	13.6180	0.699511	0.349756	−	0.936841i	$-0.386265\pi$
$379$	13.6180	0.699511	0.349756	+	0.936841i	$0.386265\pi$
$380$	0	0
$381$	13.6525	0.699438
$382$	− 28.0344i	− 1.43437i
$383$	5.05573i	0.258336i	0.991623	+	0.129168i	$0.0412306\pi$
$383$	5.05573i	0.258336i	−0.991623	+	0.129168i	$0.958769\pi$
$384$	−13.6180	−0.694942
$385$	0	0
$386$	−17.7984	−0.905913
$387$	7.38197i	0.375246i
$388$	2.38197i	0.120926i
$389$	−0.652476	−0.0330818	−0.0165409	−	0.999863i	$-0.505265\pi$
$389$	−0.652476	−0.0330818	−0.0165409	+	0.999863i	$0.505265\pi$
$390$	0	0
$391$	−22.7984	−1.15296
$392$	− 6.70820i	− 0.338815i
$393$	− 14.1803i	− 0.715304i
$394$	0.145898	0.00735024
$395$	0	0
$396$	−1.85410	−0.0931721
$397$	2.52786i	0.126870i	0.997986	+	0.0634349i	$0.0202055\pi$
$397$	2.52786i	0.126870i	−0.997986	+	0.0634349i	$0.979794\pi$
$398$	18.9443i	0.949591i
$399$	−13.4164	−0.671660
$400$	0	0
$401$	36.2705	1.81126	0.905631	−	0.424066i	$-0.139397\pi$
$401$	36.2705	1.81126	0.905631	+	0.424066i	$0.139397\pi$
$402$	21.3262i	1.06366i
$403$	− 8.70820i	− 0.433787i
$404$	5.79837	0.288480
$405$	0	0
$406$	11.7082	0.581068
$407$	− 6.00000i	− 0.297409i
$408$	9.47214i	0.468941i
$409$	5.12461	0.253396	0.126698	−	0.991941i	$-0.459562\pi$
$409$	5.12461	0.253396	0.126698	+	0.991941i	$0.459562\pi$
$410$	0	0
$411$	0.437694	0.0215899
$412$	8.90983i	0.438956i
$413$	− 7.88854i	− 0.388170i
$414$	−8.70820	−0.427985
$415$	0	0
$416$	3.38197	0.165815
$417$	− 13.4164i	− 0.657004i
$418$	32.5623i	1.59267i
$419$	−0.326238	−0.0159378	−0.00796888	−	0.999968i	$-0.502537\pi$
$419$	−0.326238	−0.0159378	−0.00796888	+	0.999968i	$0.502537\pi$
$420$	0	0
$421$	−30.3607	−1.47969	−0.739844	−	0.672778i	$-0.765101\pi$
$421$	−30.3607	−1.47969	−0.739844	+	0.672778i	$0.765101\pi$
$422$	4.85410i	0.236294i
$423$	− 4.76393i	− 0.231630i
$424$	25.1246	1.22016
$425$	0	0
$426$	16.3262	0.791009
$427$	17.4164i	0.842839i
$428$	− 0.708204i	− 0.0342323i
$429$	−3.00000	−0.144841
$430$	0	0
$431$	29.7639	1.43368	0.716839	−	0.697239i	$-0.245588\pi$
$431$	29.7639	1.43368	0.716839	+	0.697239i	$0.245588\pi$
$432$	4.85410i	0.233543i
$433$	3.47214i	0.166860i	0.996514	+	0.0834301i	$0.0265875\pi$
$433$	3.47214i	0.166860i	−0.996514	+	0.0834301i	$0.973412\pi$
$434$	28.1803	1.35270
$435$	0	0
$436$	−2.56231	−0.122712
$437$	36.1033i	1.72706i
$438$	25.4164i	1.21444i
$439$	32.0344	1.52892	0.764460	−	0.644671i	$-0.223006\pi$
$439$	32.0344	1.52892	0.764460	+	0.644671i	$0.223006\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	− 6.85410i	− 0.326016i
$443$	− 19.4164i	− 0.922501i	−0.887270	−	0.461251i	$-0.847401\pi$
$443$	− 19.4164i	− 0.922501i	0.887270	−	0.461251i	$-0.152599\pi$
$444$	1.23607	0.0586612
$445$	0	0
$446$	−16.4164	−0.777339
$447$	13.0902i	0.619144i
$448$	− 8.47214i	− 0.400271i
$449$	−16.5066	−0.778994	−0.389497	−	0.921028i	$-0.627351\pi$
$449$	−16.5066	−0.778994	−0.389497	+	0.921028i	$0.627351\pi$
$450$	0	0
$451$	28.1459	1.32534
$452$	2.32624i	0.109417i
$453$	− 6.61803i	− 0.310942i
$454$	−9.32624	−0.437702
$455$	0	0
$456$	15.0000	0.702439
$457$	9.88854i	0.462567i	0.972886	+	0.231283i	$0.0742924\pi$
$457$	9.88854i	0.462567i	−0.972886	+	0.231283i	$0.925708\pi$
$458$	− 26.1803i	− 1.22333i
$459$	4.23607	0.197723
$460$	0	0
$461$	−19.1803	−0.893317	−0.446659	−	0.894704i	$-0.647386\pi$
$461$	−19.1803	−0.893317	−0.446659	+	0.894704i	$0.647386\pi$
$462$	− 9.70820i	− 0.451667i
$463$	− 33.6869i	− 1.56556i	−0.622296	−	0.782782i	$-0.713800\pi$
$463$	− 33.6869i	− 1.56556i	0.622296	−	0.782782i	$-0.286200\pi$
$464$	−17.5623	−0.815310
$465$	0	0
$466$	16.4721	0.763057
$467$	10.4164i	0.482014i	0.970523	+	0.241007i	$0.0774777\pi$
$467$	10.4164i	0.482014i	−0.970523	+	0.241007i	$0.922522\pi$
$468$	− 0.618034i	− 0.0285686i
$469$	−26.3607	−1.21722
$470$	0	0
$471$	−2.85410	−0.131510
$472$	8.81966i	0.405958i
$473$	22.1459i	1.01827i
$474$	14.7984	0.679712
$475$	0	0
$476$	5.23607	0.239995
$477$	− 11.2361i	− 0.514464i
$478$	34.5967i	1.58242i
$479$	−4.79837	−0.219243	−0.109622	−	0.993973i	$-0.534964\pi$
$479$	−4.79837	−0.219243	−0.109622	+	0.993973i	$0.534964\pi$
$480$	0	0
$481$	2.00000	0.0911922
$482$	− 11.8541i	− 0.539940i
$483$	− 10.7639i	− 0.489776i
$484$	1.23607	0.0561849
$485$	0	0
$486$	1.61803	0.0733955
$487$	− 16.6180i	− 0.753035i	−0.926410	−	0.376518i	$-0.877121\pi$
$487$	− 16.6180i	− 0.753035i	0.926410	−	0.376518i	$-0.122879\pi$
$488$	− 19.4721i	− 0.881462i
$489$	−18.2705	−0.826221
$490$	0	0
$491$	22.3262	1.00757	0.503785	−	0.863829i	$-0.331941\pi$
$491$	22.3262	1.00757	0.503785	+	0.863829i	$0.331941\pi$
$492$	5.79837i	0.261411i
$493$	15.3262i	0.690259i
$494$	−10.8541	−0.488349
$495$	0	0
$496$	−42.2705	−1.89800
$497$	20.1803i	0.905212i
$498$	14.5623i	0.652553i
$499$	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
$501$	17.7984	0.795173
$502$	30.7082i	1.37057i
$503$	− 3.96556i	− 0.176815i	−0.996084	−	0.0884077i	$-0.971822\pi$
$503$	− 3.96556i	− 0.176815i	0.996084	−	0.0884077i	$-0.0281778\pi$
$504$	−4.47214	−0.199205
$505$	0	0
$506$	−26.1246	−1.16138
$507$	12.0000i	0.532939i
$508$	8.43769i	0.374362i
$509$	−32.8885	−1.45776	−0.728880	−	0.684642i	$-0.759959\pi$
$509$	−32.8885	−1.45776	−0.728880	+	0.684642i	$0.759959\pi$
$510$	0	0
$511$	−31.4164	−1.38978
$512$	5.29180i	0.233867i
$513$	− 6.70820i	− 0.296174i
$514$	−50.5066	−2.22775
$515$	0	0
$516$	−4.56231	−0.200844
$517$	− 14.2918i	− 0.628552i
$518$	6.47214i	0.284369i
$519$	−0.909830	−0.0399371
$520$	0	0
$521$	40.0902	1.75638	0.878191	−	0.478310i	$-0.158750\pi$
$521$	40.0902	1.75638	0.878191	+	0.478310i	$0.158750\pi$
$522$	5.85410i	0.256227i
$523$	1.56231i	0.0683149i	0.999416	+	0.0341574i	$0.0108748\pi$
$523$	1.56231i	0.0683149i	−0.999416	+	0.0341574i	$0.989125\pi$
$524$	8.76393	0.382854
$525$	0	0
$526$	−20.2361	−0.882334
$527$	36.8885i	1.60689i
$528$	14.5623i	0.633743i
$529$	−5.96556	−0.259372
$530$	0	0
$531$	3.94427	0.171167
$532$	− 8.29180i	− 0.359495i
$533$	9.38197i	0.406378i
$534$	18.0902	0.782838
$535$	0	0
$536$	29.4721	1.27300
$537$	15.6525i	0.675454i
$538$	− 33.2148i	− 1.43199i
$539$	−9.00000	−0.387657
$540$	0	0
$541$	−26.2918	−1.13037	−0.565186	−	0.824963i	$-0.691196\pi$
$541$	−26.2918	−1.13037	−0.565186	+	0.824963i	$0.691196\pi$
$542$	18.4721i	0.793446i
$543$	− 12.4721i	− 0.535231i
$544$	−14.3262	−0.614232
$545$	0	0
$546$	3.23607	0.138491
$547$	− 24.7082i	− 1.05645i	−0.849106	−	0.528223i	$-0.822858\pi$
$547$	− 24.7082i	− 1.05645i	0.849106	−	0.528223i	$-0.177142\pi$
$548$	0.270510i	0.0115556i
$549$	−8.70820	−0.371657
$550$	0	0
$551$	24.2705	1.03396
$552$	12.0344i	0.512220i
$553$	18.2918i	0.777846i
$554$	21.1246	0.897499
$555$	0	0
$556$	8.29180	0.351650
$557$	37.6525i	1.59539i	0.603063	+	0.797693i	$0.293947\pi$
$557$	37.6525i	1.59539i	−0.603063	+	0.797693i	$0.706053\pi$
$558$	14.0902i	0.596484i
$559$	−7.38197	−0.312224
$560$	0	0
$561$	12.7082	0.536541
$562$	22.9443i	0.967846i
$563$	9.00000i	0.379305i	0.981851	+	0.189652i	$0.0607361\pi$
$563$	9.00000i	0.379305i	−0.981851	+	0.189652i	$0.939264\pi$
$564$	2.94427	0.123976
$565$	0	0
$566$	3.70820	0.155867
$567$	2.00000i	0.0839921i
$568$	− 22.5623i	− 0.946693i
$569$	10.8541	0.455028	0.227514	−	0.973775i	$-0.426940\pi$
$569$	10.8541	0.455028	0.227514	+	0.973775i	$0.426940\pi$
$570$	0	0
$571$	−38.1246	−1.59547	−0.797733	−	0.603011i	$-0.793967\pi$
$571$	−38.1246	−1.59547	−0.797733	+	0.603011i	$0.793967\pi$
$572$	− 1.85410i	− 0.0775239i
$573$	17.3262i	0.723814i
$574$	−30.3607	−1.26723
$575$	0	0
$576$	4.23607	0.176503
$577$	− 3.72949i	− 0.155261i	−0.996982	−	0.0776304i	$-0.975265\pi$
$577$	− 3.72949i	− 0.155261i	0.996982	−	0.0776304i	$-0.0247354\pi$
$578$	1.52786i	0.0635508i
$579$	11.0000	0.457144
$580$	0	0
$581$	−18.0000	−0.746766
$582$	− 6.23607i	− 0.258493i
$583$	− 33.7082i	− 1.39605i
$584$	35.1246	1.45347
$585$	0	0
$586$	−10.2361	−0.422848
$587$	− 39.3050i	− 1.62229i	−0.584846	−	0.811144i	$-0.698845\pi$
$587$	− 39.3050i	− 1.62229i	0.584846	−	0.811144i	$-0.301155\pi$
$588$	− 1.85410i	− 0.0764619i
$589$	58.4164	2.40701
$590$	0	0
$591$	−0.0901699	−0.00370910
$592$	− 9.70820i	− 0.399005i
$593$	17.6180i	0.723486i	0.932278	+	0.361743i	$0.117818\pi$
$593$	17.6180i	0.723486i	−0.932278	+	0.361743i	$0.882182\pi$
$594$	4.85410	0.199166
$595$	0	0
$596$	−8.09017	−0.331386
$597$	− 11.7082i	− 0.479185i
$598$	− 8.70820i	− 0.356105i
$599$	−39.2705	−1.60455	−0.802275	−	0.596955i	$-0.796377\pi$
$599$	−39.2705	−1.60455	−0.802275	+	0.596955i	$0.796377\pi$
$600$	0	0
$601$	−24.7082	−1.00787	−0.503934	−	0.863742i	$-0.668115\pi$
$601$	−24.7082	−1.00787	−0.503934	+	0.863742i	$0.668115\pi$
$602$	− 23.8885i	− 0.973624i
$603$	− 13.1803i	− 0.536745i
$604$	4.09017	0.166427
$605$	0	0
$606$	−15.1803	−0.616659
$607$	22.8541i	0.927619i	0.885935	+	0.463810i	$0.153518\pi$
$607$	22.8541i	0.927619i	−0.885935	+	0.463810i	$0.846482\pi$
$608$	22.6869i	0.920076i
$609$	−7.23607	−0.293220
$610$	0	0
$611$	4.76393	0.192728
$612$	2.61803i	0.105828i
$613$	− 5.87539i	− 0.237305i	−0.992936	−	0.118652i	$-0.962143\pi$
$613$	− 5.87539i	− 0.237305i	0.992936	−	0.118652i	$-0.0378574\pi$
$614$	−14.3262	−0.578160
$615$	0	0
$616$	−13.4164	−0.540562
$617$	− 25.2361i	− 1.01597i	−0.861367	−	0.507983i	$-0.830391\pi$
$617$	− 25.2361i	− 1.01597i	0.861367	−	0.507983i	$-0.169609\pi$
$618$	− 23.3262i	− 0.938319i
$619$	−34.2705	−1.37745	−0.688724	−	0.725024i	$-0.741829\pi$
$619$	−34.2705	−1.37745	−0.688724	+	0.725024i	$0.741829\pi$
$620$	0	0
$621$	5.38197	0.215971
$622$	21.8885i	0.877651i
$623$	22.3607i	0.895862i
$624$	−4.85410	−0.194320
$625$	0	0
$626$	3.70820	0.148210
$627$	− 20.1246i	− 0.803700i
$628$	− 1.76393i	− 0.0703886i
$629$	−8.47214	−0.337806
$630$	0	0
$631$	−10.7639	−0.428505	−0.214253	−	0.976778i	$-0.568732\pi$
$631$	−10.7639	−0.428505	−0.214253	+	0.976778i	$0.568732\pi$
$632$	− 20.4508i	− 0.813491i
$633$	− 3.00000i	− 0.119239i
$634$	−33.2705	−1.32134
$635$	0	0
$636$	6.94427	0.275358
$637$	− 3.00000i	− 0.118864i
$638$	17.5623i	0.695298i
$639$	−10.0902	−0.399161
$640$	0	0
$641$	−23.3262	−0.921331	−0.460666	−	0.887574i	$-0.652389\pi$
$641$	−23.3262	−0.921331	−0.460666	+	0.887574i	$0.652389\pi$
$642$	1.85410i	0.0731756i
$643$	5.90983i	0.233061i	0.993187	+	0.116530i	$0.0371773\pi$
$643$	5.90983i	0.233061i	−0.993187	+	0.116530i	$0.962823\pi$
$644$	6.65248	0.262144
$645$	0	0
$646$	45.9787	1.80901
$647$	19.0344i	0.748321i	0.927364	+	0.374161i	$0.122069\pi$
$647$	19.0344i	0.748321i	−0.927364	+	0.374161i	$0.877931\pi$
$648$	− 2.23607i	− 0.0878410i
$649$	11.8328	0.464479
$650$	0	0
$651$	−17.4164	−0.682603
$652$	− 11.2918i	− 0.442221i
$653$	29.6525i	1.16039i	0.814477	+	0.580196i	$0.197024\pi$
$653$	29.6525i	1.16039i	−0.814477	+	0.580196i	$0.802976\pi$
$654$	6.70820	0.262312
$655$	0	0
$656$	45.5410	1.77808
$657$	− 15.7082i	− 0.612835i
$658$	15.4164i	0.600994i
$659$	2.23607	0.0871048	0.0435524	−	0.999051i	$-0.486132\pi$
$659$	2.23607	0.0871048	0.0435524	+	0.999051i	$0.486132\pi$
$660$	0	0
$661$	4.88854	0.190142	0.0950712	−	0.995470i	$-0.469692\pi$
$661$	4.88854	0.190142	0.0950712	+	0.995470i	$0.469692\pi$
$662$	49.6525i	1.92980i
$663$	4.23607i	0.164515i
$664$	20.1246	0.780986
$665$	0	0
$666$	−3.23607	−0.125395
$667$	19.4721i	0.753964i
$668$	11.0000i	0.425603i
$669$	10.1459	0.392263
$670$	0	0
$671$	−26.1246	−1.00853
$672$	− 6.76393i	− 0.260924i
$673$	− 46.7771i	− 1.80312i	−0.432650	−	0.901562i	$-0.642421\pi$
$673$	− 46.7771i	− 1.80312i	0.432650	−	0.901562i	$-0.357579\pi$
$674$	53.6869	2.06794
$675$	0	0
$676$	−7.41641	−0.285246
$677$	44.8885i	1.72521i	0.505881	+	0.862603i	$0.331168\pi$
$677$	44.8885i	1.72521i	−0.505881	+	0.862603i	$0.668832\pi$
$678$	− 6.09017i	− 0.233892i
$679$	7.70820	0.295814
$680$	0	0
$681$	5.76393	0.220874
$682$	42.2705i	1.61862i
$683$	− 0.596748i	− 0.0228339i	−0.999935	−	0.0114170i	$-0.996366\pi$
$683$	− 0.596748i	− 0.0228339i	0.999935	−	0.0114170i	$-0.00363421\pi$
$684$	4.14590	0.158522
$685$	0	0
$686$	32.3607	1.23554
$687$	16.1803i	0.617318i
$688$	35.8328i	1.36611i
$689$	11.2361	0.428060
$690$	0	0
$691$	15.0902	0.574057	0.287029	−	0.957922i	$-0.407333\pi$
$691$	15.0902	0.574057	0.287029	+	0.957922i	$0.407333\pi$
$692$	− 0.562306i	− 0.0213757i
$693$	6.00000i	0.227921i
$694$	−19.8541	−0.753651
$695$	0	0
$696$	8.09017	0.306657
$697$	− 39.7426i	− 1.50536i
$698$	11.7082i	0.443162i
$699$	−10.1803	−0.385056
$700$	0	0
$701$	−48.6525	−1.83758	−0.918789	−	0.394748i	$-0.870832\pi$
$701$	−48.6525	−1.83758	−0.918789	+	0.394748i	$0.870832\pi$
$702$	1.61803i	0.0610688i
$703$	13.4164i	0.506009i
$704$	12.7082	0.478958
$705$	0	0
$706$	−20.0344	−0.754006
$707$	− 18.7639i	− 0.705690i
$708$	2.43769i	0.0916142i
$709$	5.20163	0.195351	0.0976756	−	0.995218i	$-0.468859\pi$
$709$	5.20163	0.195351	0.0976756	+	0.995218i	$0.468859\pi$
$710$	0	0
$711$	−9.14590	−0.342998
$712$	− 25.0000i	− 0.936915i
$713$	46.8673i	1.75519i
$714$	−13.7082	−0.513017
$715$	0	0
$716$	−9.67376	−0.361525
$717$	− 21.3820i	− 0.798524i
$718$	38.7426i	1.44586i
$719$	35.1246	1.30993	0.654963	−	0.755661i	$-0.272684\pi$
$719$	35.1246	1.30993	0.654963	+	0.755661i	$0.272684\pi$
$720$	0	0
$721$	28.8328	1.07379
$722$	− 42.0689i	− 1.56564i
$723$	7.32624i	0.272466i
$724$	7.70820	0.286473
$725$	0	0
$726$	−3.23607	−0.120102
$727$	14.4377i	0.535464i	0.963493	+	0.267732i	$0.0862743\pi$
$727$	14.4377i	0.535464i	−0.963493	+	0.267732i	$0.913726\pi$
$728$	− 4.47214i	− 0.165748i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	31.2705	1.15658
$732$	− 5.38197i	− 0.198923i
$733$	− 10.1459i	− 0.374747i	−0.982289	−	0.187374i	$-0.940002\pi$
$733$	− 10.1459i	− 0.374747i	0.982289	−	0.187374i	$-0.0599975\pi$
$734$	20.2705	0.748198
$735$	0	0
$736$	−18.2016	−0.670921
$737$	− 39.5410i	− 1.45651i
$738$	− 15.1803i	− 0.558796i
$739$	1.70820	0.0628373	0.0314186	−	0.999506i	$-0.489997\pi$
$739$	1.70820	0.0628373	0.0314186	+	0.999506i	$0.489997\pi$
$740$	0	0
$741$	6.70820	0.246432
$742$	36.3607i	1.33484i
$743$	− 16.5279i	− 0.606349i	−0.952935	−	0.303174i	$-0.901954\pi$
$743$	− 16.5279i	− 0.606349i	0.952935	−	0.303174i	$-0.0980464\pi$
$744$	19.4721	0.713883
$745$	0	0
$746$	28.1803	1.03176
$747$	− 9.00000i	− 0.329293i
$748$	7.85410i	0.287174i
$749$	−2.29180	−0.0837404
$750$	0	0
$751$	15.2918	0.558006	0.279003	−	0.960290i	$-0.409996\pi$
$751$	15.2918	0.558006	0.279003	+	0.960290i	$0.409996\pi$
$752$	− 23.1246i	− 0.843268i
$753$	− 18.9787i	− 0.691623i
$754$	−5.85410	−0.213194
$755$	0	0
$756$	−1.23607	−0.0449554
$757$	− 32.2705i	− 1.17289i	−0.809988	−	0.586446i	$-0.800527\pi$
$757$	− 32.2705i	− 1.17289i	0.809988	−	0.586446i	$-0.199473\pi$
$758$	− 22.0344i	− 0.800327i
$759$	16.1459	0.586059
$760$	0	0
$761$	3.18034	0.115287	0.0576436	−	0.998337i	$-0.481641\pi$
$761$	3.18034	0.115287	0.0576436	+	0.998337i	$0.481641\pi$
$762$	− 22.0902i	− 0.800242i
$763$	8.29180i	0.300183i
$764$	−10.7082	−0.387409
$765$	0	0
$766$	8.18034	0.295568
$767$	3.94427i	0.142419i
$768$	13.5623i	0.489388i
$769$	36.3050	1.30919	0.654595	−	0.755980i	$-0.272839\pi$
$769$	36.3050	1.30919	0.654595	+	0.755980i	$0.272839\pi$
$770$	0	0
$771$	31.2148	1.12417
$772$	6.79837i	0.244679i
$773$	− 41.7771i	− 1.50262i	−0.659951	−	0.751309i	$-0.729423\pi$
$773$	− 41.7771i	− 1.50262i	0.659951	−	0.751309i	$-0.270577\pi$
$774$	11.9443	0.429328
$775$	0	0
$776$	−8.61803	−0.309369
$777$	− 4.00000i	− 0.143499i
$778$	1.05573i	0.0378497i
$779$	−62.9361	−2.25492
$780$	0	0
$781$	−30.2705	−1.08316
$782$	36.8885i	1.31913i
$783$	− 3.61803i	− 0.129298i
$784$	−14.5623	−0.520082
$785$	0	0
$786$	−22.9443	−0.818395
$787$	− 17.1459i	− 0.611185i	−0.952162	−	0.305593i	$-0.901145\pi$
$787$	− 17.1459i	− 0.611185i	0.952162	−	0.305593i	$-0.0988546\pi$
$788$	− 0.0557281i	− 0.00198523i
$789$	12.5066	0.445246
$790$	0	0
$791$	7.52786	0.267660
$792$	− 6.70820i	− 0.238366i
$793$	− 8.70820i	− 0.309237i
$794$	4.09017	0.145155
$795$	0	0
$796$	7.23607	0.256476
$797$	30.0132i	1.06312i	0.847020	+	0.531560i	$0.178394\pi$
$797$	30.0132i	1.06312i	−0.847020	+	0.531560i	$0.821606\pi$
$798$	21.7082i	0.768462i
$799$	−20.1803	−0.713929
$800$	0	0
$801$	−11.1803	−0.395038
$802$	− 58.6869i	− 2.07231i
$803$	− 47.1246i	− 1.66299i
$804$	8.14590	0.287284
$805$	0	0
$806$	−14.0902	−0.496305
$807$	20.5279i	0.722615i
$808$	20.9787i	0.738029i
$809$	39.9230	1.40362	0.701809	−	0.712365i	$-0.252376\pi$
$809$	39.9230	1.40362	0.701809	+	0.712365i	$0.252376\pi$
$810$	0	0
$811$	−33.7771	−1.18607	−0.593037	−	0.805175i	$-0.702071\pi$
$811$	−33.7771	−1.18607	−0.593037	+	0.805175i	$0.702071\pi$
$812$	− 4.47214i	− 0.156941i
$813$	− 11.4164i	− 0.400391i
$814$	−9.70820	−0.340272
$815$	0	0
$816$	20.5623	0.719825
$817$	− 49.5197i	− 1.73248i
$818$	− 8.29180i	− 0.289916i
$819$	−2.00000	−0.0698857
$820$	0	0
$821$	5.94427	0.207457	0.103728	−	0.994606i	$-0.466923\pi$
$821$	5.94427	0.207457	0.103728	+	0.994606i	$0.466923\pi$
$822$	− 0.708204i	− 0.0247014i
$823$	− 28.5623i	− 0.995619i	−0.867286	−	0.497810i	$-0.834138\pi$
$823$	− 28.5623i	− 0.995619i	0.867286	−	0.497810i	$-0.165862\pi$
$824$	−32.2361	−1.12300
$825$	0	0
$826$	−12.7639	−0.444114
$827$	− 48.9787i	− 1.70316i	−0.524227	−	0.851578i	$-0.675646\pi$
$827$	− 48.9787i	− 1.70316i	0.524227	−	0.851578i	$-0.324354\pi$
$828$	3.32624i	0.115595i
$829$	50.1246	1.74090	0.870450	−	0.492257i	$-0.163828\pi$
$829$	50.1246	1.74090	0.870450	+	0.492257i	$0.163828\pi$
$830$	0	0
$831$	−13.0557	−0.452898
$832$	4.23607i	0.146859i
$833$	12.7082i	0.440313i
$834$	−21.7082	−0.751694
$835$	0	0
$836$	12.4377	0.430167
$837$	− 8.70820i	− 0.301000i
$838$	0.527864i	0.0182348i
$839$	3.21478	0.110987	0.0554933	−	0.998459i	$-0.482327\pi$
$839$	3.21478	0.110987	0.0554933	+	0.998459i	$0.482327\pi$
$840$	0	0
$841$	−15.9098	−0.548615
$842$	49.1246i	1.69295i
$843$	− 14.1803i	− 0.488397i
$844$	1.85410	0.0638208
$845$	0	0
$846$	−7.70820	−0.265014
$847$	− 4.00000i	− 0.137442i
$848$	− 54.5410i	− 1.87295i
$849$	−2.29180	−0.0786542
$850$	0	0
$851$	−10.7639	−0.368983
$852$	− 6.23607i	− 0.213644i
$853$	− 20.3951i	− 0.698316i	−0.937064	−	0.349158i	$-0.886468\pi$
$853$	− 20.3951i	− 0.698316i	0.937064	−	0.349158i	$-0.113532\pi$
$854$	28.1803	0.964311
$855$	0	0
$856$	2.56231	0.0875778
$857$	− 9.05573i	− 0.309338i	−0.987966	−	0.154669i	$-0.950569\pi$
$857$	− 9.05573i	− 0.309338i	0.987966	−	0.154669i	$-0.0494311\pi$
$858$	4.85410i	0.165716i
$859$	−15.1246	−0.516045	−0.258023	−	0.966139i	$-0.583071\pi$
$859$	−15.1246	−0.516045	−0.258023	+	0.966139i	$0.583071\pi$
$860$	0	0
$861$	18.7639	0.639473
$862$	− 48.1591i	− 1.64030i
$863$	13.0689i	0.444870i	0.974948	+	0.222435i	$0.0714005\pi$
$863$	13.0689i	0.444870i	−0.974948	+	0.222435i	$0.928599\pi$
$864$	3.38197	0.115057
$865$	0	0
$866$	5.61803	0.190909
$867$	− 0.944272i	− 0.0320692i
$868$	− 10.7639i	− 0.365352i
$869$	−27.4377	−0.930760
$870$	0	0
$871$	13.1803	0.446599
$872$	− 9.27051i	− 0.313939i
$873$	3.85410i	0.130442i
$874$	58.4164	1.97596
$875$	0	0
$876$	9.70820	0.328010
$877$	− 43.1246i	− 1.45621i	−0.685463	−	0.728107i	$-0.740400\pi$
$877$	− 43.1246i	− 1.45621i	0.685463	−	0.728107i	$-0.259600\pi$
$878$	− 51.8328i	− 1.74927i
$879$	6.32624	0.213379
$880$	0	0
$881$	15.0902	0.508401	0.254200	−	0.967152i	$-0.418188\pi$
$881$	15.0902	0.508401	0.254200	+	0.967152i	$0.418188\pi$
$882$	4.85410i	0.163446i
$883$	29.2016i	0.982713i	0.870959	+	0.491356i	$0.163499\pi$
$883$	29.2016i	0.982713i	−0.870959	+	0.491356i	$0.836501\pi$
$884$	−2.61803	−0.0880540
$885$	0	0
$886$	−31.4164	−1.05545
$887$	− 42.9230i	− 1.44121i	−0.693344	−	0.720606i	$-0.743864\pi$
$887$	− 42.9230i	− 1.44121i	0.693344	−	0.720606i	$-0.256136\pi$
$888$	4.47214i	0.150075i
$889$	27.3050	0.915779
$890$	0	0
$891$	−3.00000	−0.100504
$892$	6.27051i	0.209952i
$893$	31.9574i	1.06941i
$894$	21.1803	0.708377
$895$	0	0
$896$	−27.2361	−0.909893
$897$	5.38197i	0.179699i
$898$	26.7082i	0.891264i
$899$	31.5066	1.05080
$900$	0	0
$901$	−47.5967	−1.58568
$902$	− 45.5410i	− 1.51635i
$903$	14.7639i	0.491313i
$904$	−8.41641	−0.279926
$905$	0	0
$906$	−10.7082	−0.355756
$907$	17.0000i	0.564476i	0.959344	+	0.282238i	$0.0910767\pi$
$907$	17.0000i	0.564476i	−0.959344	+	0.282238i	$0.908923\pi$
$908$	3.56231i	0.118219i
$909$	9.38197	0.311180
$910$	0	0
$911$	14.8885	0.493279	0.246640	−	0.969107i	$-0.420674\pi$
$911$	14.8885	0.493279	0.246640	+	0.969107i	$0.420674\pi$
$912$	− 32.5623i	− 1.07825i
$913$	− 27.0000i	− 0.893570i
$914$	16.0000	0.529233
$915$	0	0
$916$	−10.0000	−0.330409
$917$	− 28.3607i	− 0.936552i
$918$	− 6.85410i	− 0.226219i
$919$	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
$921$	8.85410	0.291753
$922$	31.0344i	1.02206i
$923$	− 10.0902i	− 0.332122i
$924$	−3.70820	−0.121991
$925$	0	0
$926$	−54.5066	−1.79120
$927$	14.4164i	0.473497i
$928$	12.2361i	0.401669i
$929$	29.5967	0.971038	0.485519	−	0.874226i	$-0.338631\pi$
$929$	29.5967	0.971038	0.485519	+	0.874226i	$0.338631\pi$
$930$	0	0
$931$	20.1246	0.659558
$932$	− 6.29180i	− 0.206095i
$933$	− 13.5279i	− 0.442882i
$934$	16.8541	0.551483
$935$	0	0
$936$	2.23607	0.0730882
$937$	10.4164i	0.340289i	0.985419	+	0.170145i	$0.0544235\pi$
$937$	10.4164i	0.340289i	−0.985419	+	0.170145i	$0.945577\pi$
$938$	42.6525i	1.39265i
$939$	−2.29180	−0.0747899
$940$	0	0
$941$	57.9787	1.89005	0.945026	−	0.326995i	$-0.106036\pi$
$941$	57.9787	1.89005	0.945026	+	0.326995i	$0.106036\pi$
$942$	4.61803i	0.150464i
$943$	− 50.4934i	− 1.64429i
$944$	19.1459	0.623146
$945$	0	0
$946$	35.8328	1.16503
$947$	23.8328i	0.774462i	0.921983	+	0.387231i	$0.126568\pi$
$947$	23.8328i	0.774462i	−0.921983	+	0.387231i	$0.873432\pi$
$948$	− 5.65248i	− 0.183584i
$949$	15.7082	0.509910
$950$	0	0
$951$	20.5623	0.666778
$952$	18.9443i	0.613987i
$953$	− 42.0557i	− 1.36232i	−0.732135	−	0.681159i	$-0.761476\pi$
$953$	− 42.0557i	− 1.36232i	0.732135	−	0.681159i	$-0.238524\pi$
$954$	−18.1803	−0.588610
$955$	0	0
$956$	13.2148	0.427397
$957$	− 10.8541i	− 0.350863i
$958$	7.76393i	0.250841i
$959$	0.875388	0.0282678
$960$	0	0
$961$	44.8328	1.44622
$962$	− 3.23607i	− 0.104335i
$963$	− 1.14590i	− 0.0369260i
$964$	−4.52786	−0.145833
$965$	0	0
$966$	−17.4164	−0.560364
$967$	35.4164i	1.13891i	0.822021	+	0.569457i	$0.192847\pi$
$967$	35.4164i	1.13891i	−0.822021	+	0.569457i	$0.807153\pi$
$968$	4.47214i	0.143740i
$969$	−28.4164	−0.912867
$970$	0	0
$971$	29.8885	0.959169	0.479585	−	0.877496i	$-0.340787\pi$
$971$	29.8885	0.959169	0.479585	+	0.877496i	$0.340787\pi$
$972$	− 0.618034i	− 0.0198234i
$973$	− 26.8328i	− 0.860221i
$974$	−26.8885	−0.861565
$975$	0	0
$976$	−42.2705	−1.35305
$977$	37.6525i	1.20461i	0.798266	+	0.602305i	$0.205751\pi$
$977$	37.6525i	1.20461i	−0.798266	+	0.602305i	$0.794249\pi$
$978$	29.5623i	0.945298i
$979$	−33.5410	−1.07198
$980$	0	0
$981$	−4.14590	−0.132368
$982$	− 36.1246i	− 1.15278i
$983$	− 24.6180i	− 0.785193i	−0.919711	−	0.392597i	$-0.871577\pi$
$983$	− 24.6180i	− 0.785193i	0.919711	−	0.392597i	$-0.128423\pi$
$984$	−20.9787	−0.668777
$985$	0	0
$986$	24.7984	0.789741
$987$	− 9.52786i	− 0.303275i
$988$	4.14590i	0.131899i
$989$	39.7295	1.26332
$990$	0	0
$991$	32.0000	1.01651	0.508257	−	0.861206i	$-0.330290\pi$
$991$	32.0000	1.01651	0.508257	+	0.861206i	$0.330290\pi$
$992$	29.4508i	0.935065i
$993$	− 30.6869i	− 0.973820i
$994$	32.6525	1.03567
$995$	0	0
$996$	5.56231	0.176248
$997$	2.93112i	0.0928294i	0.998922	+	0.0464147i	$0.0147796\pi$
$997$	2.93112i	0.0928294i	−0.998922	+	0.0464147i	$0.985220\pi$
$998$	− 24.2705i	− 0.768270i
$999$	2.00000	0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.2.b.a.1249.1		4
5.2	odd	4		1875.2.a.c.1.2	yes	2
5.3	odd	4		1875.2.a.b.1.1	✓	2
5.4	even	2	inner	1875.2.b.a.1249.4		4
15.2	even	4		5625.2.a.b.1.1		2
15.8	even	4		5625.2.a.g.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1875.2.a.b.1.1	✓	2	5.3	odd	4
1875.2.a.c.1.2	yes	2	5.2	odd	4
1875.2.b.a.1249.1		4	1.1	even	1	trivial
1875.2.b.a.1249.4		4	5.4	even	2	inner
5625.2.a.b.1.1		2	15.2	even	4
5625.2.a.g.1.2		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)

\(f(q)\)	\(=\)	\(q-1.61803i q^{2} +1.00000i q^{3} -0.618034 q^{4} +1.61803 q^{6} +2.00000i q^{7} -2.23607i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.61803i q^{2} +1.00000i q^{3} -0.618034 q^{4} +1.61803 q^{6} +2.00000i q^{7} -2.23607i q^{8} -1.00000 q^{9} -3.00000 q^{11} -0.618034i q^{12} -1.00000i q^{13} +3.23607 q^{14} -4.85410 q^{16} +4.23607i q^{17} +1.61803i q^{18} +6.70820 q^{19} -2.00000 q^{21} +4.85410i q^{22} +5.38197i q^{23} +2.23607 q^{24} -1.61803 q^{26} -1.00000i q^{27} -1.23607i q^{28} +3.61803 q^{29} +8.70820 q^{31} +3.38197i q^{32} -3.00000i q^{33} +6.85410 q^{34} +0.618034 q^{36} +2.00000i q^{37} -10.8541i q^{38} +1.00000 q^{39} -9.38197 q^{41} +3.23607i q^{42} -7.38197i q^{43} +1.85410 q^{44} +8.70820 q^{46} +4.76393i q^{47} -4.85410i q^{48} +3.00000 q^{49} -4.23607 q^{51} +0.618034i q^{52} +11.2361i q^{53} -1.61803 q^{54} +4.47214 q^{56} +6.70820i q^{57} -5.85410i q^{58} -3.94427 q^{59} +8.70820 q^{61} -14.0902i q^{62} -2.00000i q^{63} -4.23607 q^{64} -4.85410 q^{66} +13.1803i q^{67} -2.61803i q^{68} -5.38197 q^{69} +10.0902 q^{71} +2.23607i q^{72} +15.7082i q^{73} +3.23607 q^{74} -4.14590 q^{76} -6.00000i q^{77} -1.61803i q^{78} +9.14590 q^{79} +1.00000 q^{81} +15.1803i q^{82} +9.00000i q^{83} +1.23607 q^{84} -11.9443 q^{86} +3.61803i q^{87} +6.70820i q^{88} +11.1803 q^{89} +2.00000 q^{91} -3.32624i q^{92} +8.70820i q^{93} +7.70820 q^{94} -3.38197 q^{96} -3.85410i q^{97} -4.85410i q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 2 q^{6} - 4 q^{9}+O(q^{10}) \) 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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