LMFDB - Embedded newform 1875.2.b.e.1249.8

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 23x^{10} + 199x^{8} + 794x^{6} + 1399x^{4} + 783x^{2} + 81 $ x^12 + 23x^10 + 199x^8 + 794x^6 + 1399x^4 + 783*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1249.8
Root			$0.858825i$ of defining polynomial
Character	$\chi$	$=$	1875.1249
Dual form			1875.2.b.e.1249.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.858825i q^{2} +1.00000i q^{3} +1.26242 q^{4} -0.858825 q^{6} +3.88045i q^{7} +2.80185i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+0.858825i q^{2} +1.00000i q^{3} +1.26242 q^{4} -0.858825 q^{6} +3.88045i q^{7} +2.80185i q^{8} -1.00000 q^{9} -1.39825 q^{11} +1.26242i q^{12} -3.36204i q^{13} -3.33263 q^{14} +0.118543 q^{16} +3.11590i q^{17} -0.858825i q^{18} +2.70595 q^{19} -3.88045 q^{21} -1.20085i q^{22} +6.43989i q^{23} -2.80185 q^{24} +2.88740 q^{26} -1.00000i q^{27} +4.89876i q^{28} -8.26242 q^{29} -6.34027 q^{31} +5.70550i q^{32} -1.39825i q^{33} -2.67601 q^{34} -1.26242 q^{36} -7.49949i q^{37} +2.32394i q^{38} +3.36204 q^{39} +11.3783 q^{41} -3.33263i q^{42} +3.39725i q^{43} -1.76518 q^{44} -5.53074 q^{46} +8.38291i q^{47} +0.118543i q^{48} -8.05792 q^{49} -3.11590 q^{51} -4.24430i q^{52} -11.4431i q^{53} +0.858825 q^{54} -10.8724 q^{56} +2.70595i q^{57} -7.09597i q^{58} -7.64074 q^{59} +10.8219 q^{61} -5.44518i q^{62} -3.88045i q^{63} -4.66294 q^{64} +1.20085 q^{66} +3.54377i q^{67} +3.93358i q^{68} -6.43989 q^{69} +1.18356 q^{71} -2.80185i q^{72} -2.39461i q^{73} +6.44075 q^{74} +3.41605 q^{76} -5.42585i q^{77} +2.88740i q^{78} -10.6245 q^{79} +1.00000 q^{81} +9.77199i q^{82} -1.40894i q^{83} -4.89876 q^{84} -2.91764 q^{86} -8.26242i q^{87} -3.91769i q^{88} -4.62972 q^{89} +13.0462 q^{91} +8.12984i q^{92} -6.34027i q^{93} -7.19945 q^{94} -5.70550 q^{96} -1.51516i q^{97} -6.92034i q^{98} +1.39825 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 22 q^{4} - 2 q^{6} - 12 q^{9}+O(q^{10}) $ 12 * q - 22 * q^4 - 2 * q^6 - 12 * q^9	$ 12 q - 22 q^{4} - 2 q^{6} - 12 q^{9} + 8 q^{14} + 34 q^{16} + 4 q^{19} + 4 q^{21} + 12 q^{24} + 74 q^{26} - 62 q^{29} - 4 q^{31} - 74 q^{34} + 22 q^{36} + 66 q^{41} + 22 q^{44} - 24 q^{46} - 8 q^{49} - 4 q^{51} + 2 q^{54} - 60 q^{56} + 16 q^{59} + 68 q^{61} - 24 q^{64} - 18 q^{66} - 2 q^{69} - 6 q^{71} - 72 q^{74} + 54 q^{76} - 50 q^{79} + 12 q^{81} - 88 q^{84} - 60 q^{86} - 36 q^{89} + 56 q^{91} + 100 q^{94} - 66 q^{96}+O(q^{100}) $ 12 * q - 22 * q^4 - 2 * q^6 - 12 * q^9 + 8 * q^14 + 34 * q^16 + 4 * q^19 + 4 * q^21 + 12 * q^24 + 74 * q^26 - 62 * q^29 - 4 * q^31 - 74 * q^34 + 22 * q^36 + 66 * q^41 + 22 * q^44 - 24 * q^46 - 8 * q^49 - 4 * q^51 + 2 * q^54 - 60 * q^56 + 16 * q^59 + 68 * q^61 - 24 * q^64 - 18 * q^66 - 2 * q^69 - 6 * q^71 - 72 * q^74 + 54 * q^76 - 50 * q^79 + 12 * q^81 - 88 * q^84 - 60 * q^86 - 36 * q^89 + 56 * q^91 + 100 * q^94 - 66 * q^96

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 $

$2$	0.858825i	0.607281i	0.952787	+	0.303640i	$0.0982022\pi$
$2$	0.858825i	0.607281i	−0.952787	+	0.303640i	$0.901798\pi$
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	1.26242	0.631210
$5$	0	0
$5$	0	0
$6$	−0.858825	−0.350614
$7$	3.88045i	1.46667i	0.679865	+	0.733337i	$0.262038\pi$
$7$	3.88045i	1.46667i	−0.679865	+	0.733337i	$0.737962\pi$
$8$	2.80185i	0.990603i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−1.39825	−0.421589	−0.210794	−	0.977530i	$-0.567605\pi$
$11$	−1.39825	−0.421589	−0.210794	+	0.977530i	$0.567605\pi$
$12$	1.26242i	0.364429i
$13$	− 3.36204i	− 0.932461i	−0.884663	−	0.466230i	$-0.845612\pi$
$13$	− 3.36204i	− 0.932461i	0.884663	−	0.466230i	$-0.154388\pi$
$14$	−3.33263	−0.890683
$15$	0	0
$16$	0.118543	0.0296359
$17$	3.11590i	0.755717i	0.925863	+	0.377859i	$0.123339\pi$
$17$	3.11590i	0.755717i	−0.925863	+	0.377859i	$0.876661\pi$
$18$	− 0.858825i	− 0.202427i
$19$	2.70595	0.620788	0.310394	−	0.950608i	$-0.399539\pi$
$19$	2.70595	0.620788	0.310394	+	0.950608i	$0.399539\pi$
$20$	0	0
$21$	−3.88045	−0.846784
$22$	− 1.20085i	− 0.256023i
$23$	6.43989i	1.34281i	0.741091	+	0.671405i	$0.234309\pi$
$23$	6.43989i	1.34281i	−0.741091	+	0.671405i	$0.765691\pi$
$24$	−2.80185	−0.571925
$25$	0	0
$26$	2.88740	0.566266
$27$	− 1.00000i	− 0.192450i
$28$	4.89876i	0.925779i
$29$	−8.26242	−1.53429	−0.767146	−	0.641472i	$-0.778324\pi$
$29$	−8.26242	−1.53429	−0.767146	+	0.641472i	$0.778324\pi$
$30$	0	0
$31$	−6.34027	−1.13875	−0.569373	−	0.822079i	$-0.692814\pi$
$31$	−6.34027	−1.13875	−0.569373	+	0.822079i	$0.692814\pi$
$32$	5.70550i	1.00860i
$33$	− 1.39825i	− 0.243404i
$34$	−2.67601	−0.458933
$35$	0	0
$36$	−1.26242	−0.210403
$37$	− 7.49949i	− 1.23291i	−0.787391	−	0.616454i	$-0.788568\pi$
$37$	− 7.49949i	− 1.23291i	0.787391	−	0.616454i	$-0.211432\pi$
$38$	2.32394i	0.376993i
$39$	3.36204	0.538357
$40$	0	0
$41$	11.3783	1.77700	0.888498	−	0.458881i	$-0.151750\pi$
$41$	11.3783	1.77700	0.888498	+	0.458881i	$0.151750\pi$
$42$	− 3.33263i	− 0.514236i
$43$	3.39725i	0.518076i	0.965867	+	0.259038i	$0.0834054\pi$
$43$	3.39725i	0.518076i	−0.965867	+	0.259038i	$0.916595\pi$
$44$	−1.76518	−0.266111
$45$	0	0
$46$	−5.53074	−0.815463
$47$	8.38291i	1.22277i	0.791332	+	0.611387i	$0.209388\pi$
$47$	8.38291i	1.22277i	−0.791332	+	0.611387i	$0.790612\pi$
$48$	0.118543i	0.0171103i
$49$	−8.05792	−1.15113
$50$	0	0
$51$	−3.11590	−0.436314
$52$	− 4.24430i	− 0.588579i
$53$	− 11.4431i	− 1.57184i	−0.618330	−	0.785918i	$-0.712191\pi$
$53$	− 11.4431i	− 1.57184i	0.618330	−	0.785918i	$-0.287809\pi$
$54$	0.858825	0.116871
$55$	0	0
$56$	−10.8724	−1.45289
$57$	2.70595i	0.358412i
$58$	− 7.09597i	− 0.931747i
$59$	−7.64074	−0.994740	−0.497370	−	0.867539i	$-0.665701\pi$
$59$	−7.64074	−0.994740	−0.497370	+	0.867539i	$0.665701\pi$
$60$	0	0
$61$	10.8219	1.38560	0.692798	−	0.721132i	$-0.256378\pi$
$61$	10.8219	1.38560	0.692798	+	0.721132i	$0.256378\pi$
$62$	− 5.44518i	− 0.691539i
$63$	− 3.88045i	− 0.488891i
$64$	−4.66294	−0.582868
$65$	0	0
$66$	1.20085	0.147815
$67$	3.54377i	0.432940i	0.976289	+	0.216470i	$0.0694544\pi$
$67$	3.54377i	0.432940i	−0.976289	+	0.216470i	$0.930546\pi$
$68$	3.93358i	0.477016i
$69$	−6.43989	−0.775271
$70$	0	0
$71$	1.18356	0.140463	0.0702317	−	0.997531i	$-0.477626\pi$
$71$	1.18356	0.140463	0.0702317	+	0.997531i	$0.477626\pi$
$72$	− 2.80185i	− 0.330201i
$73$	− 2.39461i	− 0.280268i	−0.990133	−	0.140134i	$-0.955247\pi$
$73$	− 2.39461i	− 0.280268i	0.990133	−	0.140134i	$-0.0447533\pi$
$74$	6.44075	0.748722
$75$	0	0
$76$	3.41605	0.391847
$77$	− 5.42585i	− 0.618333i
$78$	2.88740i	0.326934i
$79$	−10.6245	−1.19534	−0.597672	−	0.801740i	$-0.703908\pi$
$79$	−10.6245	−1.19534	−0.597672	+	0.801740i	$0.703908\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	9.77199i	1.07914i
$83$	− 1.40894i	− 0.154651i	−0.997006	−	0.0773255i	$-0.975362\pi$
$83$	− 1.40894i	− 0.154651i	0.997006	−	0.0773255i	$-0.0246381\pi$
$84$	−4.89876	−0.534499
$85$	0	0
$86$	−2.91764	−0.314617
$87$	− 8.26242i	− 0.885824i
$88$	− 3.91769i	− 0.417627i
$89$	−4.62972	−0.490750	−0.245375	−	0.969428i	$-0.578911\pi$
$89$	−4.62972	−0.490750	−0.245375	+	0.969428i	$0.578911\pi$
$90$	0	0
$91$	13.0462	1.36762
$92$	8.12984i	0.847595i
$93$	− 6.34027i	− 0.657456i
$94$	−7.19945	−0.742567
$95$	0	0
$96$	−5.70550	−0.582315
$97$	− 1.51516i	− 0.153841i	−0.997037	−	0.0769204i	$-0.975491\pi$
$97$	− 1.51516i	− 0.153841i	0.997037	−	0.0769204i	$-0.0245087\pi$
$98$	− 6.92034i	− 0.699060i
$99$	1.39825	0.140530
$100$	0	0
$101$	17.2376	1.71521	0.857604	−	0.514310i	$-0.171952\pi$
$101$	17.2376	1.71521	0.857604	+	0.514310i	$0.171952\pi$
$102$	− 2.67601i	− 0.264965i
$103$	10.9905i	1.08292i	0.840726	+	0.541461i	$0.182129\pi$
$103$	10.9905i	1.08292i	−0.840726	+	0.541461i	$0.817871\pi$
$104$	9.41991	0.923698
$105$	0	0
$106$	9.82766	0.954546
$107$	6.80699i	0.658056i	0.944320	+	0.329028i	$0.106721\pi$
$107$	6.80699i	0.658056i	−0.944320	+	0.329028i	$0.893279\pi$
$108$	− 1.26242i	− 0.121476i
$109$	11.4451	1.09624	0.548121	−	0.836399i	$-0.315343\pi$
$109$	11.4451	1.09624	0.548121	+	0.836399i	$0.315343\pi$
$110$	0	0
$111$	7.49949	0.711820
$112$	0.460003i	0.0434662i
$113$	16.2686i	1.53042i	0.643781	+	0.765210i	$0.277365\pi$
$113$	16.2686i	1.53042i	−0.643781	+	0.765210i	$0.722635\pi$
$114$	−2.32394	−0.217657
$115$	0	0
$116$	−10.4306	−0.968461
$117$	3.36204i	0.310820i
$118$	− 6.56206i	− 0.604087i
$119$	−12.0911	−1.10839
$120$	0	0
$121$	−9.04489	−0.822263
$122$	9.29408i	0.841446i
$123$	11.3783i	1.02595i
$124$	−8.00409	−0.718788
$125$	0	0
$126$	3.33263	0.296894
$127$	− 16.2477i	− 1.44175i	−0.693065	−	0.720875i	$-0.743740\pi$
$127$	− 16.2477i	− 1.44175i	0.693065	−	0.720875i	$-0.256260\pi$
$128$	7.40636i	0.654636i
$129$	−3.39725	−0.299111
$130$	0	0
$131$	−15.3119	−1.33781	−0.668903	−	0.743349i	$-0.733236\pi$
$131$	−15.3119	−1.33781	−0.668903	+	0.743349i	$0.733236\pi$
$132$	− 1.76518i	− 0.153639i
$133$	10.5003i	0.910493i
$134$	−3.04348	−0.262916
$135$	0	0
$136$	−8.73028	−0.748615
$137$	6.86417i	0.586445i	0.956044	+	0.293223i	$0.0947277\pi$
$137$	6.86417i	0.586445i	−0.956044	+	0.293223i	$0.905272\pi$
$138$	− 5.53074i	− 0.470808i
$139$	−13.8225	−1.17241	−0.586203	−	0.810164i	$-0.699378\pi$
$139$	−13.8225	−1.17241	−0.586203	+	0.810164i	$0.699378\pi$
$140$	0	0
$141$	−8.38291	−0.705968
$142$	1.01647i	0.0853007i
$143$	4.70097i	0.393115i
$144$	−0.118543	−0.00987862
$145$	0	0
$146$	2.05655	0.170201
$147$	− 8.05792i	− 0.664606i
$148$	− 9.46751i	− 0.778224i
$149$	−7.09597	−0.581325	−0.290662	−	0.956826i	$-0.593876\pi$
$149$	−7.09597	−0.581325	−0.290662	+	0.956826i	$0.593876\pi$
$150$	0	0
$151$	19.1474	1.55819	0.779097	−	0.626903i	$-0.215678\pi$
$151$	19.1474	1.55819	0.779097	+	0.626903i	$0.215678\pi$
$152$	7.58166i	0.614954i
$153$	− 3.11590i	− 0.251906i
$154$	4.65986	0.375502
$155$	0	0
$156$	4.24430	0.339816
$157$	− 11.8114i	− 0.942653i	−0.881959	−	0.471326i	$-0.843775\pi$
$157$	− 11.8114i	− 0.942653i	0.881959	−	0.471326i	$-0.156225\pi$
$158$	− 9.12455i	− 0.725910i
$159$	11.4431	0.907500
$160$	0	0
$161$	−24.9897	−1.96946
$162$	0.858825i	0.0674757i
$163$	− 8.92635i	− 0.699165i	−0.936906	−	0.349583i	$-0.886323\pi$
$163$	− 8.92635i	− 0.699165i	0.936906	−	0.349583i	$-0.113677\pi$
$164$	14.3642	1.12166
$165$	0	0
$166$	1.21003	0.0939166
$167$	15.8114i	1.22352i	0.791042	+	0.611762i	$0.209539\pi$
$167$	15.8114i	1.22352i	−0.791042	+	0.611762i	$0.790461\pi$
$168$	− 10.8724i	− 0.838827i
$169$	1.69672	0.130517
$170$	0	0
$171$	−2.70595	−0.206929
$172$	4.28876i	0.327015i
$173$	− 16.3259i	− 1.24124i	−0.784112	−	0.620619i	$-0.786881\pi$
$173$	− 16.3259i	− 1.24124i	0.784112	−	0.620619i	$-0.213119\pi$
$174$	7.09597	0.537944
$175$	0	0
$176$	−0.165754	−0.0124942
$177$	− 7.64074i	− 0.574313i
$178$	− 3.97612i	− 0.298023i
$179$	0.852080	0.0636875	0.0318437	−	0.999493i	$-0.489862\pi$
$179$	0.852080	0.0636875	0.0318437	+	0.999493i	$0.489862\pi$
$180$	0	0
$181$	21.9643	1.63260	0.816298	−	0.577631i	$-0.196023\pi$
$181$	21.9643	1.63260	0.816298	+	0.577631i	$0.196023\pi$
$182$	11.2044i	0.830527i
$183$	10.8219i	0.799974i
$184$	−18.0436	−1.33019
$185$	0	0
$186$	5.44518	0.399260
$187$	− 4.35682i	− 0.318602i
$188$	10.5828i	0.771827i
$189$	3.88045	0.282261
$190$	0	0
$191$	−1.15408	−0.0835065	−0.0417532	−	0.999128i	$-0.513294\pi$
$191$	−1.15408	−0.0835065	−0.0417532	+	0.999128i	$0.513294\pi$
$192$	− 4.66294i	− 0.336519i
$193$	0.983419i	0.0707880i	0.999373	+	0.0353940i	$0.0112686\pi$
$193$	0.983419i	0.0707880i	−0.999373	+	0.0353940i	$0.988731\pi$
$194$	1.30125	0.0934246
$195$	0	0
$196$	−10.1725	−0.726606
$197$	− 7.40726i	− 0.527745i	−0.964558	−	0.263873i	$-0.915000\pi$
$197$	− 7.40726i	− 0.527745i	0.964558	−	0.263873i	$-0.0849999\pi$
$198$	1.20085i	0.0853410i
$199$	13.5887	0.963274	0.481637	−	0.876371i	$-0.340042\pi$
$199$	13.5887	0.963274	0.481637	+	0.876371i	$0.340042\pi$
$200$	0	0
$201$	−3.54377	−0.249958
$202$	14.8041i	1.04161i
$203$	− 32.0619i	− 2.25031i
$204$	−3.93358	−0.275405
$205$	0	0
$206$	−9.43888	−0.657638
$207$	− 6.43989i	− 0.447603i
$208$	− 0.398547i	− 0.0276343i
$209$	−3.78360	−0.261717
$210$	0	0
$211$	26.2982	1.81044	0.905221	−	0.424941i	$-0.139705\pi$
$211$	26.2982	1.81044	0.905221	+	0.424941i	$0.139705\pi$
$212$	− 14.4461i	− 0.992159i
$213$	1.18356i	0.0810965i
$214$	−5.84601	−0.399625
$215$	0	0
$216$	2.80185	0.190642
$217$	− 24.6031i	− 1.67017i
$218$	9.82934i	0.665727i
$219$	2.39461	0.161813
$220$	0	0
$221$	10.4758	0.704677
$222$	6.44075i	0.432275i
$223$	13.5470i	0.907176i	0.891212	+	0.453588i	$0.149856\pi$
$223$	13.5470i	0.907176i	−0.891212	+	0.453588i	$0.850144\pi$
$224$	−22.1399	−1.47929
$225$	0	0
$226$	−13.9719	−0.929395
$227$	0.265434i	0.0176175i	0.999961	+	0.00880874i	$0.00280395\pi$
$227$	0.265434i	0.0176175i	−0.999961	+	0.00880874i	$0.997196\pi$
$228$	3.41605i	0.226233i
$229$	−4.28115	−0.282906	−0.141453	−	0.989945i	$-0.545177\pi$
$229$	−4.28115	−0.282906	−0.141453	+	0.989945i	$0.545177\pi$
$230$	0	0
$231$	5.42585	0.356995
$232$	− 23.1500i	− 1.51987i
$233$	6.74720i	0.442024i	0.975271	+	0.221012i	$0.0709359\pi$
$233$	6.74720i	0.442024i	−0.975271	+	0.221012i	$0.929064\pi$
$234$	−2.88740	−0.188755
$235$	0	0
$236$	−9.64582	−0.627890
$237$	− 10.6245i	− 0.690133i
$238$	− 10.3841i	− 0.673104i
$239$	0.307310	0.0198782	0.00993912	−	0.999951i	$-0.496836\pi$
$239$	0.307310	0.0198782	0.00993912	+	0.999951i	$0.496836\pi$
$240$	0	0
$241$	−11.1233	−0.716513	−0.358256	−	0.933623i	$-0.616629\pi$
$241$	−11.1233	−0.716513	−0.358256	+	0.933623i	$0.616629\pi$
$242$	− 7.76798i	− 0.499344i
$243$	1.00000i	0.0641500i
$244$	13.6617	0.874602
$245$	0	0
$246$	−9.77199	−0.623039
$247$	− 9.09751i	− 0.578860i
$248$	− 17.7645i	− 1.12805i
$249$	1.40894	0.0892878
$250$	0	0
$251$	−20.5499	−1.29710	−0.648549	−	0.761173i	$-0.724624\pi$
$251$	−20.5499	−1.29710	−0.648549	+	0.761173i	$0.724624\pi$
$252$	− 4.89876i	− 0.308593i
$253$	− 9.00459i	− 0.566114i
$254$	13.9539	0.875548
$255$	0	0
$256$	−15.6866	−0.980415
$257$	− 2.43352i	− 0.151799i	−0.997115	−	0.0758996i	$-0.975817\pi$
$257$	− 2.43352i	− 0.151799i	0.997115	−	0.0758996i	$-0.0241828\pi$
$258$	− 2.91764i	− 0.181644i
$259$	29.1014	1.80827
$260$	0	0
$261$	8.26242	0.511431
$262$	− 13.1502i	− 0.812425i
$263$	20.1748i	1.24403i	0.783004	+	0.622017i	$0.213686\pi$
$263$	20.1748i	1.24403i	−0.783004	+	0.622017i	$0.786314\pi$
$264$	3.91769	0.241117
$265$	0	0
$266$	−9.01794	−0.552925
$267$	− 4.62972i	− 0.283334i
$268$	4.47372i	0.273276i
$269$	18.6834	1.13915	0.569574	−	0.821940i	$-0.307108\pi$
$269$	18.6834	1.13915	0.569574	+	0.821940i	$0.307108\pi$
$270$	0	0
$271$	7.61184	0.462387	0.231193	−	0.972908i	$-0.425737\pi$
$271$	7.61184	0.462387	0.231193	+	0.972908i	$0.425737\pi$
$272$	0.369370i	0.0223963i
$273$	13.0462i	0.789593i
$274$	−5.89512	−0.356137
$275$	0	0
$276$	−8.12984	−0.489359
$277$	− 8.17364i	− 0.491107i	−0.969383	−	0.245553i	$-0.921030\pi$
$277$	− 8.17364i	− 0.491107i	0.969383	−	0.245553i	$-0.0789696\pi$
$278$	− 11.8711i	− 0.711980i
$279$	6.34027	0.379582
$280$	0	0
$281$	14.8891	0.888211	0.444105	−	0.895975i	$-0.353522\pi$
$281$	14.8891	0.888211	0.444105	+	0.895975i	$0.353522\pi$
$282$	− 7.19945i	− 0.428721i
$283$	1.35203i	0.0803698i	0.999192	+	0.0401849i	$0.0127947\pi$
$283$	1.35203i	0.0803698i	−0.999192	+	0.0401849i	$0.987205\pi$
$284$	1.49416	0.0886618
$285$	0	0
$286$	−4.03731	−0.238731
$287$	44.1531i	2.60627i
$288$	− 5.70550i	− 0.336200i
$289$	7.29115	0.428891
$290$	0	0
$291$	1.51516	0.0888201
$292$	− 3.02300i	− 0.176908i
$293$	10.4773i	0.612091i	0.952017	+	0.306045i	$0.0990059\pi$
$293$	10.4773i	0.612091i	−0.952017	+	0.306045i	$0.900994\pi$
$294$	6.92034	0.403603
$295$	0	0
$296$	21.0124	1.22132
$297$	1.39825i	0.0811348i
$298$	− 6.09420i	− 0.353027i
$299$	21.6511	1.25212
$300$	0	0
$301$	−13.1829	−0.759848
$302$	16.4443i	0.946262i
$303$	17.2376i	0.990276i
$304$	0.320773	0.0183976
$305$	0	0
$306$	2.67601	0.152978
$307$	10.4991i	0.599216i	0.954062	+	0.299608i	$0.0968558\pi$
$307$	10.4991i	0.599216i	−0.954062	+	0.299608i	$0.903144\pi$
$308$	− 6.84971i	− 0.390298i
$309$	−10.9905	−0.625225
$310$	0	0
$311$	−4.68539	−0.265684	−0.132842	−	0.991137i	$-0.542410\pi$
$311$	−4.68539	−0.265684	−0.132842	+	0.991137i	$0.542410\pi$
$312$	9.41991i	0.533297i
$313$	17.2431i	0.974635i	0.873225	+	0.487317i	$0.162025\pi$
$313$	17.2431i	0.974635i	−0.873225	+	0.487317i	$0.837975\pi$
$314$	10.1439	0.572455
$315$	0	0
$316$	−13.4125	−0.754513
$317$	− 8.94648i	− 0.502484i	−0.967924	−	0.251242i	$-0.919161\pi$
$317$	− 8.94648i	− 0.502484i	0.967924	−	0.251242i	$-0.0808390\pi$
$318$	9.82766i	0.551108i
$319$	11.5529	0.646841
$320$	0	0
$321$	−6.80699	−0.379929
$322$	− 21.4618i	− 1.19602i
$323$	8.43148i	0.469140i
$324$	1.26242	0.0701344
$325$	0	0
$326$	7.66617	0.424590
$327$	11.4451i	0.632916i
$328$	31.8803i	1.76030i
$329$	−32.5295	−1.79341
$330$	0	0
$331$	12.0810	0.664034	0.332017	−	0.943273i	$-0.392271\pi$
$331$	12.0810	0.664034	0.332017	+	0.943273i	$0.392271\pi$
$332$	− 1.77867i	− 0.0976172i
$333$	7.49949i	0.410970i
$334$	−13.5792	−0.743022
$335$	0	0
$336$	−0.460003	−0.0250952
$337$	15.2014i	0.828074i	0.910260	+	0.414037i	$0.135882\pi$
$337$	15.2014i	0.828074i	−0.910260	+	0.414037i	$0.864118\pi$
$338$	1.45718i	0.0792603i
$339$	−16.2686	−0.883588
$340$	0	0
$341$	8.86530	0.480083
$342$	− 2.32394i	− 0.125664i
$343$	− 4.10522i	− 0.221661i
$344$	−9.51857	−0.513207
$345$	0	0
$346$	14.0211	0.753780
$347$	− 8.51395i	− 0.457053i	−0.973538	−	0.228526i	$-0.926609\pi$
$347$	− 8.51395i	− 0.457053i	0.973538	−	0.228526i	$-0.0733908\pi$
$348$	− 10.4306i	− 0.559141i
$349$	6.72703	0.360090	0.180045	−	0.983658i	$-0.442376\pi$
$349$	6.72703	0.360090	0.180045	+	0.983658i	$0.442376\pi$
$350$	0	0
$351$	−3.36204	−0.179452
$352$	− 7.97773i	− 0.425215i
$353$	− 13.3066i	− 0.708239i	−0.935200	−	0.354119i	$-0.884781\pi$
$353$	− 13.3066i	− 0.708239i	0.935200	−	0.354119i	$-0.115219\pi$
$354$	6.56206	0.348770
$355$	0	0
$356$	−5.84465	−0.309766
$357$	− 12.0911i	− 0.639930i
$358$	0.731788i	0.0386762i
$359$	27.1766	1.43433	0.717163	−	0.696905i	$-0.245440\pi$
$359$	27.1766	1.43433	0.717163	+	0.696905i	$0.245440\pi$
$360$	0	0
$361$	−11.6778	−0.614622
$362$	18.8635i	0.991445i
$363$	− 9.04489i	− 0.474734i
$364$	16.4698	0.863253
$365$	0	0
$366$	−9.29408	−0.485809
$367$	15.9939i	0.834877i	0.908705	+	0.417439i	$0.137072\pi$
$367$	15.9939i	0.834877i	−0.908705	+	0.417439i	$0.862928\pi$
$368$	0.763407i	0.0397953i
$369$	−11.3783	−0.592332
$370$	0	0
$371$	44.4046	2.30537
$372$	− 8.00409i	− 0.414992i
$373$	31.2294i	1.61700i	0.588497	+	0.808499i	$0.299720\pi$
$373$	31.2294i	1.61700i	−0.588497	+	0.808499i	$0.700280\pi$
$374$	3.74174	0.193481
$375$	0	0
$376$	−23.4876	−1.21128
$377$	27.7785i	1.43067i
$378$	3.33263i	0.171412i
$379$	32.2022	1.65412	0.827059	−	0.562115i	$-0.190012\pi$
$379$	32.2022	1.65412	0.827059	+	0.562115i	$0.190012\pi$
$380$	0	0
$381$	16.2477	0.832395
$382$	− 0.991154i	− 0.0507119i
$383$	19.4271i	0.992678i	0.868129	+	0.496339i	$0.165323\pi$
$383$	19.4271i	0.992678i	−0.868129	+	0.496339i	$0.834677\pi$
$384$	−7.40636	−0.377954
$385$	0	0
$386$	−0.844584	−0.0429882
$387$	− 3.39725i	− 0.172692i
$388$	− 1.91276i	− 0.0971059i
$389$	−7.87404	−0.399230	−0.199615	−	0.979874i	$-0.563969\pi$
$389$	−7.87404	−0.399230	−0.199615	+	0.979874i	$0.563969\pi$
$390$	0	0
$391$	−20.0661	−1.01478
$392$	− 22.5771i	− 1.14031i
$393$	− 15.3119i	− 0.772383i
$394$	6.36154	0.320490
$395$	0	0
$396$	1.76518	0.0887037
$397$	28.4801i	1.42938i	0.699443	+	0.714689i	$0.253432\pi$
$397$	28.4801i	1.42938i	−0.699443	+	0.714689i	$0.746568\pi$
$398$	11.6703i	0.584978i
$399$	−10.5003	−0.525674
$400$	0	0
$401$	23.2147	1.15929	0.579643	−	0.814870i	$-0.303192\pi$
$401$	23.2147	1.15929	0.579643	+	0.814870i	$0.303192\pi$
$402$	− 3.04348i	− 0.151795i
$403$	21.3162i	1.06184i
$404$	21.7611	1.08266
$405$	0	0
$406$	27.5356	1.36657
$407$	10.4862i	0.519781i
$408$	− 8.73028i	− 0.432213i
$409$	−4.32217	−0.213718	−0.106859	−	0.994274i	$-0.534079\pi$
$409$	−4.32217	−0.213718	−0.106859	+	0.994274i	$0.534079\pi$
$410$	0	0
$411$	−6.86417	−0.338584
$412$	13.8746i	0.683551i
$413$	− 29.6495i	− 1.45896i
$414$	5.53074	0.271821
$415$	0	0
$416$	19.1821	0.940480
$417$	− 13.8225i	− 0.676889i
$418$	− 3.24945i	− 0.158936i
$419$	1.96426	0.0959604	0.0479802	−	0.998848i	$-0.484722\pi$
$419$	1.96426	0.0959604	0.0479802	+	0.998848i	$0.484722\pi$
$420$	0	0
$421$	2.13023	0.103821	0.0519106	−	0.998652i	$-0.483469\pi$
$421$	2.13023	0.103821	0.0519106	+	0.998652i	$0.483469\pi$
$422$	22.5855i	1.09945i
$423$	− 8.38291i	− 0.407591i
$424$	32.0619	1.55707
$425$	0	0
$426$	−1.01647	−0.0492484
$427$	41.9937i	2.03222i
$428$	8.59328i	0.415372i
$429$	−4.70097	−0.226965
$430$	0	0
$431$	0.0662228	0.00318984	0.00159492	−	0.999999i	$-0.499492\pi$
$431$	0.0662228	0.00318984	0.00159492	+	0.999999i	$0.499492\pi$
$432$	− 0.118543i	− 0.00570343i
$433$	1.22844i	0.0590352i	0.999564	+	0.0295176i	$0.00939711\pi$
$433$	1.22844i	0.0590352i	−0.999564	+	0.0295176i	$0.990603\pi$
$434$	21.1298	1.01426
$435$	0	0
$436$	14.4485	0.691959
$437$	17.4260i	0.833600i
$438$	2.05655i	0.0982657i
$439$	37.8322	1.80563	0.902816	−	0.430028i	$-0.141496\pi$
$439$	37.8322	1.80563	0.902816	+	0.430028i	$0.141496\pi$
$440$	0	0
$441$	8.05792	0.383711
$442$	8.99686i	0.427937i
$443$	− 26.9171i	− 1.27887i	−0.768845	−	0.639435i	$-0.779168\pi$
$443$	− 26.9171i	− 1.27887i	0.768845	−	0.639435i	$-0.220832\pi$
$444$	9.46751	0.449308
$445$	0	0
$446$	−11.6345	−0.550910
$447$	− 7.09597i	− 0.335628i
$448$	− 18.0943i	− 0.854877i
$449$	25.3090	1.19440	0.597202	−	0.802091i	$-0.296279\pi$
$449$	25.3090	1.19440	0.597202	+	0.802091i	$0.296279\pi$
$450$	0	0
$451$	−15.9098	−0.749162
$452$	20.5378i	0.966016i
$453$	19.1474i	0.899624i
$454$	−0.227961	−0.0106988
$455$	0	0
$456$	−7.58166	−0.355044
$457$	− 38.0944i	− 1.78198i	−0.454023	−	0.890990i	$-0.650012\pi$
$457$	− 38.0944i	− 1.78198i	0.454023	−	0.890990i	$-0.349988\pi$
$458$	− 3.67676i	− 0.171804i
$459$	3.11590	0.145438
$460$	0	0
$461$	3.53623	0.164699	0.0823494	−	0.996604i	$-0.473758\pi$
$461$	3.53623	0.164699	0.0823494	+	0.996604i	$0.473758\pi$
$462$	4.65986i	0.216796i
$463$	− 23.7206i	− 1.10239i	−0.834377	−	0.551195i	$-0.814172\pi$
$463$	− 23.7206i	− 1.10239i	0.834377	−	0.551195i	$-0.185828\pi$
$464$	−0.979456	−0.0454701
$465$	0	0
$466$	−5.79466	−0.268433
$467$	19.0985i	0.883774i	0.897071	+	0.441887i	$0.145691\pi$
$467$	19.0985i	0.883774i	−0.897071	+	0.441887i	$0.854309\pi$
$468$	4.24430i	0.196193i
$469$	−13.7514	−0.634982
$470$	0	0
$471$	11.8114	0.544241
$472$	− 21.4082i	− 0.985392i
$473$	− 4.75021i	− 0.218415i
$474$	9.12455	0.419104
$475$	0	0
$476$	−15.2641	−0.699627
$477$	11.4431i	0.523946i
$478$	0.263926i	0.0120717i
$479$	−18.3034	−0.836302	−0.418151	−	0.908378i	$-0.637322\pi$
$479$	−18.3034	−0.836302	−0.418151	+	0.908378i	$0.637322\pi$
$480$	0	0
$481$	−25.2136	−1.14964
$482$	− 9.55294i	− 0.435124i
$483$	− 24.9897i	− 1.13707i
$484$	−11.4184	−0.519020
$485$	0	0
$486$	−0.858825	−0.0389571
$487$	− 7.01638i	− 0.317943i	−0.987283	−	0.158971i	$-0.949182\pi$
$487$	− 7.01638i	− 0.317943i	0.987283	−	0.158971i	$-0.0508177\pi$
$488$	30.3212i	1.37258i
$489$	8.92635	0.403663
$490$	0	0
$491$	−4.63076	−0.208983	−0.104492	−	0.994526i	$-0.533322\pi$
$491$	−4.63076	−0.208983	−0.104492	+	0.994526i	$0.533322\pi$
$492$	14.3642i	0.647589i
$493$	− 25.7449i	− 1.15949i
$494$	7.81316	0.351531
$495$	0	0
$496$	−0.751598	−0.0337477
$497$	4.59277i	0.206014i
$498$	1.21003i	0.0542228i
$499$	5.44561	0.243779	0.121890	−	0.992544i	$-0.461105\pi$
$499$	5.44561	0.243779	0.121890	+	0.992544i	$0.461105\pi$
$500$	0	0
$501$	−15.8114	−0.706401
$502$	− 17.6488i	− 0.787703i
$503$	− 17.2645i	− 0.769788i	−0.922961	−	0.384894i	$-0.874238\pi$
$503$	− 17.2645i	− 0.769788i	0.922961	−	0.384894i	$-0.125762\pi$
$504$	10.8724	0.484297
$505$	0	0
$506$	7.73336	0.343790
$507$	1.69672i	0.0753538i
$508$	− 20.5114i	− 0.910047i
$509$	10.1973	0.451989	0.225994	−	0.974129i	$-0.427437\pi$
$509$	10.1973	0.451989	0.225994	+	0.974129i	$0.427437\pi$
$510$	0	0
$511$	9.29217	0.411061
$512$	1.34063i	0.0592481i
$513$	− 2.70595i	− 0.119471i
$514$	2.08997	0.0921847
$515$	0	0
$516$	−4.28876	−0.188802
$517$	− 11.7214i	− 0.515508i
$518$	24.9930i	1.09813i
$519$	16.3259	0.716629
$520$	0	0
$521$	38.5575	1.68923	0.844617	−	0.535371i	$-0.179828\pi$
$521$	38.5575	1.68923	0.844617	+	0.535371i	$0.179828\pi$
$522$	7.09597i	0.310582i
$523$	6.40172i	0.279928i	0.990157	+	0.139964i	$0.0446987\pi$
$523$	6.40172i	0.279928i	−0.990157	+	0.139964i	$0.955301\pi$
$524$	−19.3300	−0.844437
$525$	0	0
$526$	−17.3266	−0.755478
$527$	− 19.7557i	− 0.860570i
$528$	− 0.165754i	− 0.00721350i
$529$	−18.4722	−0.803137
$530$	0	0
$531$	7.64074	0.331580
$532$	13.2558i	0.574712i
$533$	− 38.2543i	− 1.65698i
$534$	3.97612	0.172064
$535$	0	0
$536$	−9.92910	−0.428872
$537$	0.852080i	0.0367700i
$538$	16.0458i	0.691783i
$539$	11.2670	0.485304
$540$	0	0
$541$	28.7378	1.23553	0.617766	−	0.786362i	$-0.288038\pi$
$541$	28.7378	1.23553	0.617766	+	0.786362i	$0.288038\pi$
$542$	6.53724i	0.280799i
$543$	21.9643i	0.942580i
$544$	−17.7778	−0.762216
$545$	0	0
$546$	−11.2044	−0.479505
$547$	5.20272i	0.222452i	0.993795	+	0.111226i	$0.0354778\pi$
$547$	5.20272i	0.222452i	−0.993795	+	0.111226i	$0.964522\pi$
$548$	8.66546i	0.370170i
$549$	−10.8219	−0.461865
$550$	0	0
$551$	−22.3577	−0.952470
$552$	− 18.0436i	− 0.767986i
$553$	− 41.2277i	− 1.75318i
$554$	7.01973	0.298240
$555$	0	0
$556$	−17.4498	−0.740035
$557$	− 33.0079i	− 1.39859i	−0.714833	−	0.699296i	$-0.753497\pi$
$557$	− 33.0079i	− 1.39859i	0.714833	−	0.699296i	$-0.246503\pi$
$558$	5.44518i	0.230513i
$559$	11.4217	0.483085
$560$	0	0
$561$	4.35682	0.183945
$562$	12.7872i	0.539393i
$563$	− 15.1684i	− 0.639270i	−0.947541	−	0.319635i	$-0.896440\pi$
$563$	− 15.1684i	− 0.639270i	0.947541	−	0.319635i	$-0.103560\pi$
$564$	−10.5828	−0.445614
$565$	0	0
$566$	−1.16116	−0.0488070
$567$	3.88045i	0.162964i
$568$	3.31617i	0.139143i
$569$	29.5024	1.23681	0.618403	−	0.785861i	$-0.287780\pi$
$569$	29.5024	1.23681	0.618403	+	0.785861i	$0.287780\pi$
$570$	0	0
$571$	3.12393	0.130733	0.0653663	−	0.997861i	$-0.479178\pi$
$571$	3.12393	0.130733	0.0653663	+	0.997861i	$0.479178\pi$
$572$	5.93460i	0.248138i
$573$	− 1.15408i	− 0.0482125i
$574$	−37.9197	−1.58274
$575$	0	0
$576$	4.66294	0.194289
$577$	28.0748i	1.16877i	0.811476	+	0.584385i	$0.198664\pi$
$577$	28.0748i	1.16877i	−0.811476	+	0.584385i	$0.801336\pi$
$578$	6.26182i	0.260458i
$579$	−0.983419	−0.0408695
$580$	0	0
$581$	5.46732	0.226823
$582$	1.30125i	0.0539387i
$583$	16.0004i	0.662669i
$584$	6.70933	0.277634
$585$	0	0
$586$	−8.99817	−0.371711
$587$	− 35.9054i	− 1.48197i	−0.671520	−	0.740987i	$-0.734358\pi$
$587$	− 35.9054i	− 1.48197i	0.671520	−	0.740987i	$-0.265642\pi$
$588$	− 10.1725i	− 0.419506i
$589$	−17.1565	−0.706920
$590$	0	0
$591$	7.40726	0.304694
$592$	− 0.889016i	− 0.0365383i
$593$	15.3084i	0.628641i	0.949317	+	0.314321i	$0.101777\pi$
$593$	15.3084i	0.628641i	−0.949317	+	0.314321i	$0.898223\pi$
$594$	−1.20085	−0.0492716
$595$	0	0
$596$	−8.95810	−0.366938
$597$	13.5887i	0.556147i
$598$	18.5945i	0.760387i
$599$	16.2538	0.664114	0.332057	−	0.943259i	$-0.392257\pi$
$599$	16.2538	0.664114	0.332057	+	0.943259i	$0.392257\pi$
$600$	0	0
$601$	−0.233686	−0.00953223	−0.00476612	−	0.999989i	$-0.501517\pi$
$601$	−0.233686	−0.00953223	−0.00476612	+	0.999989i	$0.501517\pi$
$602$	− 11.3218i	− 0.461441i
$603$	− 3.54377i	− 0.144313i
$604$	24.1721	0.983548
$605$	0	0
$606$	−14.8041	−0.601376
$607$	− 10.6590i	− 0.432637i	−0.976323	−	0.216318i	$-0.930595\pi$
$607$	− 10.6590i	− 0.432637i	0.976323	−	0.216318i	$-0.0694049\pi$
$608$	15.4388i	0.626127i
$609$	32.0619	1.29922
$610$	0	0
$611$	28.1836	1.14019
$612$	− 3.93358i	− 0.159005i
$613$	− 17.9094i	− 0.723353i	−0.932304	−	0.361677i	$-0.882204\pi$
$613$	− 17.9094i	− 0.723353i	0.932304	−	0.361677i	$-0.117796\pi$
$614$	−9.01689	−0.363892
$615$	0	0
$616$	15.2024	0.612523
$617$	31.6418i	1.27385i	0.770925	+	0.636926i	$0.219794\pi$
$617$	31.6418i	1.27385i	−0.770925	+	0.636926i	$0.780206\pi$
$618$	− 9.43888i	− 0.379687i
$619$	−21.8317	−0.877488	−0.438744	−	0.898612i	$-0.644577\pi$
$619$	−21.8317	−0.877488	−0.438744	+	0.898612i	$0.644577\pi$
$620$	0	0
$621$	6.43989	0.258424
$622$	− 4.02393i	− 0.161345i
$623$	− 17.9654i	− 0.719769i
$624$	0.398547	0.0159547
$625$	0	0
$626$	−14.8088	−0.591877
$627$	− 3.78360i	− 0.151103i
$628$	− 14.9110i	− 0.595012i
$629$	23.3677	0.931730
$630$	0	0
$631$	1.62102	0.0645318	0.0322659	−	0.999479i	$-0.489728\pi$
$631$	1.62102	0.0645318	0.0322659	+	0.999479i	$0.489728\pi$
$632$	− 29.7681i	− 1.18411i
$633$	26.2982i	1.04526i
$634$	7.68346	0.305149
$635$	0	0
$636$	14.4461	0.572823
$637$	27.0910i	1.07339i
$638$	9.92196i	0.392814i
$639$	−1.18356	−0.0468211
$640$	0	0
$641$	4.53285	0.179037	0.0895183	−	0.995985i	$-0.471467\pi$
$641$	4.53285	0.179037	0.0895183	+	0.995985i	$0.471467\pi$
$642$	− 5.84601i	− 0.230724i
$643$	− 12.6562i	− 0.499111i	−0.968360	−	0.249556i	$-0.919715\pi$
$643$	− 12.6562i	− 0.499111i	0.968360	−	0.249556i	$-0.0802846\pi$
$644$	−31.5475	−1.24314
$645$	0	0
$646$	−7.24117	−0.284900
$647$	− 22.3268i	− 0.877757i	−0.898546	−	0.438879i	$-0.855376\pi$
$647$	− 22.3268i	− 0.877757i	0.898546	−	0.438879i	$-0.144624\pi$
$648$	2.80185i	0.110067i
$649$	10.6837	0.419371
$650$	0	0
$651$	24.6031	0.964273
$652$	− 11.2688i	− 0.441320i
$653$	29.7988i	1.16612i	0.812431	+	0.583058i	$0.198144\pi$
$653$	29.7988i	1.16612i	−0.812431	+	0.583058i	$0.801856\pi$
$654$	−9.82934	−0.384358
$655$	0	0
$656$	1.34883	0.0526628
$657$	2.39461i	0.0934226i
$658$	− 27.9371i	− 1.08910i
$659$	−50.2976	−1.95932	−0.979659	−	0.200671i	$-0.935688\pi$
$659$	−50.2976	−1.95932	−0.979659	+	0.200671i	$0.935688\pi$
$660$	0	0
$661$	−20.8701	−0.811753	−0.405877	−	0.913928i	$-0.633034\pi$
$661$	−20.8701	−0.811753	−0.405877	+	0.913928i	$0.633034\pi$
$662$	10.3755i	0.403255i
$663$	10.4758i	0.406845i
$664$	3.94763	0.153198
$665$	0	0
$666$	−6.44075	−0.249574
$667$	− 53.2091i	− 2.06026i
$668$	19.9606i	0.772300i
$669$	−13.5470	−0.523758
$670$	0	0
$671$	−15.1317	−0.584152
$672$	− 22.1399i	− 0.854067i
$673$	4.50092i	0.173498i	0.996230	+	0.0867488i	$0.0276478\pi$
$673$	4.50092i	0.173498i	−0.996230	+	0.0867488i	$0.972352\pi$
$674$	−13.0554	−0.502874
$675$	0	0
$676$	2.14197	0.0823834
$677$	− 13.5082i	− 0.519161i	−0.965721	−	0.259580i	$-0.916416\pi$
$677$	− 13.5082i	− 0.519161i	0.965721	−	0.259580i	$-0.0835843\pi$
$678$	− 13.9719i	− 0.536586i
$679$	5.87950	0.225634
$680$	0	0
$681$	−0.265434	−0.0101715
$682$	7.61374i	0.291545i
$683$	6.98466i	0.267261i	0.991031	+	0.133630i	$0.0426635\pi$
$683$	6.98466i	0.267261i	−0.991031	+	0.133630i	$0.957337\pi$
$684$	−3.41605	−0.130616
$685$	0	0
$686$	3.52566	0.134610
$687$	− 4.28115i	− 0.163336i
$688$	0.402722i	0.0153536i
$689$	−38.4723	−1.46568
$690$	0	0
$691$	−25.6891	−0.977261	−0.488630	−	0.872491i	$-0.662503\pi$
$691$	−25.6891	−0.977261	−0.488630	+	0.872491i	$0.662503\pi$
$692$	− 20.6102i	− 0.783482i
$693$	5.42585i	0.206111i
$694$	7.31200	0.277560
$695$	0	0
$696$	23.1500	0.877500
$697$	35.4537i	1.34291i
$698$	5.77734i	0.218676i
$699$	−6.74720	−0.255202
$700$	0	0
$701$	2.35830	0.0890717	0.0445358	−	0.999008i	$-0.485819\pi$
$701$	2.35830	0.0890717	0.0445358	+	0.999008i	$0.485819\pi$
$702$	− 2.88740i	− 0.108978i
$703$	− 20.2933i	− 0.765375i
$704$	6.51997	0.245731
$705$	0	0
$706$	11.4280	0.430100
$707$	66.8898i	2.51565i
$708$	− 9.64582i	− 0.362512i
$709$	−13.1277	−0.493022	−0.246511	−	0.969140i	$-0.579284\pi$
$709$	−13.1277	−0.493022	−0.246511	+	0.969140i	$0.579284\pi$
$710$	0	0
$711$	10.6245	0.398448
$712$	− 12.9718i	− 0.486138i
$713$	− 40.8306i	− 1.52912i
$714$	10.3841	0.388617
$715$	0	0
$716$	1.07568	0.0402002
$717$	0.307310i	0.0114767i
$718$	23.3399i	0.871039i
$719$	29.5306	1.10131	0.550653	−	0.834735i	$-0.314379\pi$
$719$	29.5306	1.10131	0.550653	+	0.834735i	$0.314379\pi$
$720$	0	0
$721$	−42.6480	−1.58829
$722$	− 10.0292i	− 0.373248i
$723$	− 11.1233i	− 0.413679i
$724$	27.7282	1.03051
$725$	0	0
$726$	7.76798	0.288297
$727$	− 45.2103i	− 1.67676i	−0.545089	−	0.838378i	$-0.683504\pi$
$727$	− 45.2103i	− 1.67676i	0.545089	−	0.838378i	$-0.316496\pi$
$728$	36.5535i	1.35476i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−10.5855	−0.391519
$732$	13.6617i	0.504952i
$733$	20.6475i	0.762633i	0.924444	+	0.381317i	$0.124529\pi$
$733$	20.6475i	0.762633i	−0.924444	+	0.381317i	$0.875471\pi$
$734$	−13.7360	−0.507005
$735$	0	0
$736$	−36.7428	−1.35436
$737$	− 4.95508i	− 0.182523i
$738$	− 9.77199i	− 0.359712i
$739$	−26.6229	−0.979339	−0.489670	−	0.871908i	$-0.662883\pi$
$739$	−26.6229	−0.979339	−0.489670	+	0.871908i	$0.662883\pi$
$740$	0	0
$741$	9.09751	0.334205
$742$	38.1358i	1.40001i
$743$	− 34.2594i	− 1.25686i	−0.777868	−	0.628428i	$-0.783699\pi$
$743$	− 34.2594i	− 1.25686i	0.777868	−	0.628428i	$-0.216301\pi$
$744$	17.7645	0.651277
$745$	0	0
$746$	−26.8206	−0.981972
$747$	1.40894i	0.0515503i
$748$	− 5.50013i	− 0.201105i
$749$	−26.4142	−0.965154
$750$	0	0
$751$	34.9423	1.27506	0.637531	−	0.770425i	$-0.279956\pi$
$751$	34.9423	1.27506	0.637531	+	0.770425i	$0.279956\pi$
$752$	0.993739i	0.0362380i
$753$	− 20.5499i	− 0.748880i
$754$	−23.8569	−0.868817
$755$	0	0
$756$	4.89876	0.178166
$757$	25.4445i	0.924796i	0.886673	+	0.462398i	$0.153011\pi$
$757$	25.4445i	0.924796i	−0.886673	+	0.462398i	$0.846989\pi$
$758$	27.6561i	1.00451i
$759$	9.00459	0.326846
$760$	0	0
$761$	−14.7352	−0.534149	−0.267075	−	0.963676i	$-0.586057\pi$
$761$	−14.7352	−0.534149	−0.267075	+	0.963676i	$0.586057\pi$
$762$	13.9539i	0.505498i
$763$	44.4122i	1.60783i
$764$	−1.45694	−0.0527101
$765$	0	0
$766$	−16.6845	−0.602834
$767$	25.6884i	0.927556i
$768$	− 15.6866i	− 0.566043i
$769$	−28.9603	−1.04434	−0.522168	−	0.852843i	$-0.674877\pi$
$769$	−28.9603	−1.04434	−0.522168	+	0.852843i	$0.674877\pi$
$770$	0	0
$771$	2.43352	0.0876413
$772$	1.24149i	0.0446821i
$773$	− 19.7129i	− 0.709022i	−0.935052	−	0.354511i	$-0.884647\pi$
$773$	− 19.7129i	− 0.709022i	0.935052	−	0.354511i	$-0.115353\pi$
$774$	2.91764	0.104872
$775$	0	0
$776$	4.24524	0.152395
$777$	29.1014i	1.04401i
$778$	− 6.76242i	− 0.242445i
$779$	30.7892	1.10314
$780$	0	0
$781$	−1.65492	−0.0592178
$782$	− 17.2332i	− 0.616259i
$783$	8.26242i	0.295275i
$784$	−0.955214	−0.0341148
$785$	0	0
$786$	13.1502	0.469054
$787$	− 18.0212i	− 0.642385i	−0.947014	−	0.321193i	$-0.895916\pi$
$787$	− 18.0212i	− 0.642385i	0.947014	−	0.321193i	$-0.104084\pi$
$788$	− 9.35107i	− 0.333118i
$789$	−20.1748	−0.718243
$790$	0	0
$791$	−63.1295	−2.24463
$792$	3.91769i	0.139209i
$793$	− 36.3835i	− 1.29201i
$794$	−24.4595	−0.868033
$795$	0	0
$796$	17.1546	0.608028
$797$	17.7479i	0.628663i	0.949313	+	0.314332i	$0.101780\pi$
$797$	17.7479i	0.628663i	−0.949313	+	0.314332i	$0.898220\pi$
$798$	− 9.01794i	− 0.319232i
$799$	−26.1203	−0.924071
$800$	0	0
$801$	4.62972	0.163583
$802$	19.9374i	0.704012i
$803$	3.34827i	0.118158i
$804$	−4.47372	−0.157776
$805$	0	0
$806$	−18.3069	−0.644833
$807$	18.6834i	0.657687i
$808$	48.2972i	1.69909i
$809$	−24.7020	−0.868477	−0.434238	−	0.900798i	$-0.642982\pi$
$809$	−24.7020	−0.868477	−0.434238	+	0.900798i	$0.642982\pi$
$810$	0	0
$811$	−13.6855	−0.480561	−0.240281	−	0.970703i	$-0.577239\pi$
$811$	−13.6855	−0.480561	−0.240281	+	0.970703i	$0.577239\pi$
$812$	− 40.4756i	− 1.42042i
$813$	7.61184i	0.266959i
$814$	−9.00579	−0.315653
$815$	0	0
$816$	−0.369370	−0.0129305
$817$	9.19279i	0.321615i
$818$	− 3.71199i	− 0.129787i
$819$	−13.0462	−0.455872
$820$	0	0
$821$	−56.1647	−1.96016	−0.980081	−	0.198600i	$-0.936360\pi$
$821$	−56.1647	−1.96016	−0.980081	+	0.198600i	$0.936360\pi$
$822$	− 5.89512i	− 0.205616i
$823$	15.1705i	0.528810i	0.964412	+	0.264405i	$0.0851755\pi$
$823$	15.1705i	0.528810i	−0.964412	+	0.264405i	$0.914825\pi$
$824$	−30.7936	−1.07275
$825$	0	0
$826$	25.4638	0.885998
$827$	− 12.2655i	− 0.426515i	−0.976996	−	0.213257i	$-0.931593\pi$
$827$	− 12.2655i	− 0.426515i	0.976996	−	0.213257i	$-0.0684073\pi$
$828$	− 8.12984i	− 0.282532i
$829$	−29.4191	−1.02177	−0.510884	−	0.859650i	$-0.670682\pi$
$829$	−29.4191	−1.02177	−0.510884	+	0.859650i	$0.670682\pi$
$830$	0	0
$831$	8.17364	0.283540
$832$	15.6770i	0.543501i
$833$	− 25.1077i	− 0.869930i
$834$	11.8711	0.411062
$835$	0	0
$836$	−4.77650	−0.165199
$837$	6.34027i	0.219152i
$838$	1.68696i	0.0582749i
$839$	7.01431	0.242161	0.121080	−	0.992643i	$-0.461364\pi$
$839$	7.01431	0.242161	0.121080	+	0.992643i	$0.461364\pi$
$840$	0	0
$841$	39.2676	1.35405
$842$	1.82950i	0.0630486i
$843$	14.8891i	0.512809i
$844$	33.1994	1.14277
$845$	0	0
$846$	7.19945	0.247522
$847$	− 35.0983i	− 1.20599i
$848$	− 1.35651i	− 0.0465827i
$849$	−1.35203	−0.0464015
$850$	0	0
$851$	48.2959	1.65556
$852$	1.49416i	0.0511889i
$853$	27.1094i	0.928208i	0.885781	+	0.464104i	$0.153624\pi$
$853$	27.1094i	0.928208i	−0.885781	+	0.464104i	$0.846376\pi$
$854$	−36.0652	−1.23413
$855$	0	0
$856$	−19.0721	−0.651872
$857$	− 5.19405i	− 0.177425i	−0.996057	−	0.0887127i	$-0.971725\pi$
$857$	− 5.19405i	− 0.177425i	0.996057	−	0.0887127i	$-0.0282753\pi$
$858$	− 4.03731i	− 0.137832i
$859$	15.2545	0.520478	0.260239	−	0.965544i	$-0.416199\pi$
$859$	15.2545	0.520478	0.260239	+	0.965544i	$0.416199\pi$
$860$	0	0
$861$	−44.1531	−1.50473
$862$	0.0568738i	0.00193713i
$863$	46.8290i	1.59408i	0.603929	+	0.797038i	$0.293601\pi$
$863$	46.8290i	1.59408i	−0.603929	+	0.797038i	$0.706399\pi$
$864$	5.70550	0.194105
$865$	0	0
$866$	−1.05502	−0.0358510
$867$	7.29115i	0.247621i
$868$	− 31.0595i	− 1.05423i
$869$	14.8557	0.503944
$870$	0	0
$871$	11.9143	0.403700
$872$	32.0674i	1.08594i
$873$	1.51516i	0.0512803i
$874$	−14.9659	−0.506229
$875$	0	0
$876$	3.02300	0.102138
$877$	− 0.979616i	− 0.0330793i	−0.999863	−	0.0165396i	$-0.994735\pi$
$877$	− 0.979616i	− 0.0330793i	0.999863	−	0.0165396i	$-0.00526497\pi$
$878$	32.4912i	1.09653i
$879$	−10.4773	−0.353391
$880$	0	0
$881$	39.0186	1.31457	0.657286	−	0.753641i	$-0.271704\pi$
$881$	39.0186	1.31457	0.657286	+	0.753641i	$0.271704\pi$
$882$	6.92034i	0.233020i
$883$	− 8.90989i	− 0.299842i	−0.988698	−	0.149921i	$-0.952098\pi$
$883$	− 8.90989i	− 0.299842i	0.988698	−	0.149921i	$-0.0479019\pi$
$884$	13.2248	0.444799
$885$	0	0
$886$	23.1171	0.776633
$887$	− 51.4215i	− 1.72656i	−0.504721	−	0.863282i	$-0.668405\pi$
$887$	− 51.4215i	− 1.72656i	0.504721	−	0.863282i	$-0.331595\pi$
$888$	21.0124i	0.705131i
$889$	63.0485	2.11458
$890$	0	0
$891$	−1.39825	−0.0468432
$892$	17.1020i	0.572618i
$893$	22.6838i	0.759083i
$894$	6.09420	0.203820
$895$	0	0
$896$	−28.7400	−0.960137
$897$	21.6511i	0.722910i
$898$	21.7360i	0.725339i
$899$	52.3860	1.74717
$900$	0	0
$901$	35.6557	1.18786
$902$	− 13.6637i	− 0.454952i
$903$	− 13.1829i	− 0.438698i
$904$	−45.5821	−1.51604
$905$	0	0
$906$	−16.4443	−0.546324
$907$	18.0057i	0.597871i	0.954273	+	0.298935i	$0.0966315\pi$
$907$	18.0057i	0.597871i	−0.954273	+	0.298935i	$0.903369\pi$
$908$	0.335089i	0.0111203i
$909$	−17.2376	−0.571736
$910$	0	0
$911$	42.3831	1.40421	0.702107	−	0.712071i	$-0.252243\pi$
$911$	42.3831	1.40421	0.702107	+	0.712071i	$0.252243\pi$
$912$	0.320773i	0.0106219i
$913$	1.97005i	0.0651991i
$914$	32.7164	1.08216
$915$	0	0
$916$	−5.40460	−0.178573
$917$	− 59.4171i	− 1.96213i
$918$	2.67601i	0.0883216i
$919$	−15.9252	−0.525325	−0.262662	−	0.964888i	$-0.584601\pi$
$919$	−15.9252	−0.525325	−0.262662	+	0.964888i	$0.584601\pi$
$920$	0	0
$921$	−10.4991	−0.345957
$922$	3.03700i	0.100018i
$923$	− 3.97919i	− 0.130977i
$924$	6.84971	0.225339
$925$	0	0
$926$	20.3718	0.669460
$927$	− 10.9905i	− 0.360974i
$928$	− 47.1413i	− 1.54749i
$929$	−7.47386	−0.245210	−0.122605	−	0.992456i	$-0.539125\pi$
$929$	−7.47386	−0.245210	−0.122605	+	0.992456i	$0.539125\pi$
$930$	0	0
$931$	−21.8043	−0.714609
$932$	8.51780i	0.279010i
$933$	− 4.68539i	− 0.153393i
$934$	−16.4023	−0.536699
$935$	0	0
$936$	−9.41991	−0.307899
$937$	− 26.3843i	− 0.861937i	−0.902367	−	0.430969i	$-0.858172\pi$
$937$	− 26.3843i	− 0.861937i	0.902367	−	0.430969i	$-0.141828\pi$
$938$	− 11.8101i	− 0.385612i
$939$	−17.2431	−0.562706
$940$	0	0
$941$	40.8626	1.33208	0.666041	−	0.745915i	$-0.267988\pi$
$941$	40.8626	1.33208	0.666041	+	0.745915i	$0.267988\pi$
$942$	10.1439i	0.330507i
$943$	73.2751i	2.38617i
$944$	−0.905760	−0.0294800
$945$	0	0
$946$	4.07960	0.132639
$947$	− 44.3060i	− 1.43975i	−0.694103	−	0.719876i	$-0.744199\pi$
$947$	− 44.3060i	− 1.43975i	0.694103	−	0.719876i	$-0.255801\pi$
$948$	− 13.4125i	− 0.435619i
$949$	−8.05076	−0.261339
$950$	0	0
$951$	8.94648	0.290109
$952$	− 33.8775i	− 1.09797i
$953$	21.0768i	0.682744i	0.939928	+	0.341372i	$0.110892\pi$
$953$	21.0768i	0.682744i	−0.939928	+	0.341372i	$0.889108\pi$
$954$	−9.82766	−0.318182
$955$	0	0
$956$	0.387954	0.0125473
$957$	11.5529i	0.373454i
$958$	− 15.7194i	− 0.507870i
$959$	−26.6361	−0.860124
$960$	0	0
$961$	9.19905	0.296744
$962$	− 21.6540i	− 0.698154i
$963$	− 6.80699i	− 0.219352i
$964$	−14.0422	−0.452270
$965$	0	0
$966$	21.4618	0.690521
$967$	9.34590i	0.300544i	0.988645	+	0.150272i	$0.0480149\pi$
$967$	9.34590i	0.300544i	−0.988645	+	0.150272i	$0.951985\pi$
$968$	− 25.3424i	− 0.814536i
$969$	−8.43148	−0.270858
$970$	0	0
$971$	−49.2708	−1.58118	−0.790588	−	0.612348i	$-0.790225\pi$
$971$	−49.2708	−1.58118	−0.790588	+	0.612348i	$0.790225\pi$
$972$	1.26242i	0.0404921i
$973$	− 53.6374i	− 1.71954i
$974$	6.02584	0.193080
$975$	0	0
$976$	1.28286	0.0410634
$977$	− 54.8767i	− 1.75566i	−0.478971	−	0.877830i	$-0.658990\pi$
$977$	− 54.8767i	− 1.75566i	0.478971	−	0.877830i	$-0.341010\pi$
$978$	7.66617i	0.245137i
$979$	6.47352	0.206895
$980$	0	0
$981$	−11.4451	−0.365414
$982$	− 3.97701i	− 0.126912i
$983$	15.9788i	0.509646i	0.966988	+	0.254823i	$0.0820172\pi$
$983$	15.9788i	0.509646i	−0.966988	+	0.254823i	$0.917983\pi$
$984$	−31.8803	−1.01631
$985$	0	0
$986$	22.1104	0.704137
$987$	− 32.5295i	− 1.03543i
$988$	− 11.4849i	− 0.365382i
$989$	−21.8779	−0.695677
$990$	0	0
$991$	−29.2757	−0.929973	−0.464986	−	0.885318i	$-0.653941\pi$
$991$	−29.2757	−0.929973	−0.464986	+	0.885318i	$0.653941\pi$
$992$	− 36.1744i	− 1.14854i
$993$	12.0810i	0.383380i
$994$	−3.94438	−0.125108
$995$	0	0
$996$	1.77867	0.0563593
$997$	− 19.6838i	− 0.623392i	−0.950182	−	0.311696i	$-0.899103\pi$
$997$	− 19.6838i	− 0.623392i	0.950182	−	0.311696i	$-0.100897\pi$
$998$	4.67683i	0.148042i
$999$	−7.49949	−0.237273

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.2.b.e.1249.8		12
5.2	odd	4		1875.2.a.i.1.3	✓	6
5.3	odd	4		1875.2.a.l.1.4	yes	6
5.4	even	2	inner	1875.2.b.e.1249.5		12
15.2	even	4		5625.2.a.r.1.4		6
15.8	even	4		5625.2.a.o.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1875.2.a.i.1.3	✓	6	5.2	odd	4
1875.2.a.l.1.4	yes	6	5.3	odd	4
1875.2.b.e.1249.5		12	5.4	even	2	inner
1875.2.b.e.1249.8		12	1.1	even	1	trivial
5625.2.a.o.1.3		6	15.8	even	4
5625.2.a.r.1.4		6	15.2	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)

\(f(q)\)	\(=\)	\(q+0.858825i q^{2} +1.00000i q^{3} +1.26242 q^{4} -0.858825 q^{6} +3.88045i q^{7} +2.80185i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+0.858825i q^{2} +1.00000i q^{3} +1.26242 q^{4} -0.858825 q^{6} +3.88045i q^{7} +2.80185i q^{8} -1.00000 q^{9} -1.39825 q^{11} +1.26242i q^{12} -3.36204i q^{13} -3.33263 q^{14} +0.118543 q^{16} +3.11590i q^{17} -0.858825i q^{18} +2.70595 q^{19} -3.88045 q^{21} -1.20085i q^{22} +6.43989i q^{23} -2.80185 q^{24} +2.88740 q^{26} -1.00000i q^{27} +4.89876i q^{28} -8.26242 q^{29} -6.34027 q^{31} +5.70550i q^{32} -1.39825i q^{33} -2.67601 q^{34} -1.26242 q^{36} -7.49949i q^{37} +2.32394i q^{38} +3.36204 q^{39} +11.3783 q^{41} -3.33263i q^{42} +3.39725i q^{43} -1.76518 q^{44} -5.53074 q^{46} +8.38291i q^{47} +0.118543i q^{48} -8.05792 q^{49} -3.11590 q^{51} -4.24430i q^{52} -11.4431i q^{53} +0.858825 q^{54} -10.8724 q^{56} +2.70595i q^{57} -7.09597i q^{58} -7.64074 q^{59} +10.8219 q^{61} -5.44518i q^{62} -3.88045i q^{63} -4.66294 q^{64} +1.20085 q^{66} +3.54377i q^{67} +3.93358i q^{68} -6.43989 q^{69} +1.18356 q^{71} -2.80185i q^{72} -2.39461i q^{73} +6.44075 q^{74} +3.41605 q^{76} -5.42585i q^{77} +2.88740i q^{78} -10.6245 q^{79} +1.00000 q^{81} +9.77199i q^{82} -1.40894i q^{83} -4.89876 q^{84} -2.91764 q^{86} -8.26242i q^{87} -3.91769i q^{88} -4.62972 q^{89} +13.0462 q^{91} +8.12984i q^{92} -6.34027i q^{93} -7.19945 q^{94} -5.70550 q^{96} -1.51516i q^{97} -6.92034i q^{98} +1.39825 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 22 q^{4} - 2 q^{6} - 12 q^{9}+O(q^{10}) \) 12 * q - 22 * q^4 - 2 * q^6 - 12 * q^9	\( 12 q - 22 q^{4} - 2 q^{6} - 12 q^{9} + 8 q^{14} + 34 q^{16} + 4 q^{19} + 4 q^{21} + 12 q^{24} + 74 q^{26} - 62 q^{29} - 4 q^{31} - 74 q^{34} + 22 q^{36} + 66 q^{41} + 22 q^{44} - 24 q^{46} - 8 q^{49} - 4 q^{51} + 2 q^{54} - 60 q^{56} + 16 q^{59} + 68 q^{61} - 24 q^{64} - 18 q^{66} - 2 q^{69} - 6 q^{71} - 72 q^{74} + 54 q^{76} - 50 q^{79} + 12 q^{81} - 88 q^{84} - 60 q^{86} - 36 q^{89} + 56 q^{91} + 100 q^{94} - 66 q^{96}+O(q^{100}) \) 12 * q - 22 * q^4 - 2 * q^6 - 12 * q^9 + 8 * q^14 + 34 * q^16 + 4 * q^19 + 4 * q^21 + 12 * q^24 + 74 * q^26 - 62 * q^29 - 4 * q^31 - 74 * q^34 + 22 * q^36 + 66 * q^41 + 22 * q^44 - 24 * q^46 - 8 * q^49 - 4 * q^51 + 2 * q^54 - 60 * q^56 + 16 * q^59 + 68 * q^61 - 24 * q^64 - 18 * q^66 - 2 * q^69 - 6 * q^71 - 72 * q^74 + 54 * q^76 - 50 * q^79 + 12 * q^81 - 88 * q^84 - 60 * q^86 - 36 * q^89 + 56 * q^91 + 100 * q^94 - 66 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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