LMFDB - Embedded newform 931.2.a.q.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(1,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("931.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.a (trivial)

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:	yes
Analytic conductor:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 13x^{8} + 24x^{7} + 57x^{6} - 98x^{5} - 93x^{4} + 152x^{3} + 39x^{2} - 58x - 7 $ x^10 - 2x^9 - 13x^8 + 24x^7 + 57x^6 - 98x^5 - 93x^4 + 152x^3 + 39x^2 - 58*x - 7
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.686476$ of defining polynomial
Character	$\chi$	$=$	931.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.686476 q^{2} -1.12233 q^{3} -1.52875 q^{4} -0.737311 q^{5} -0.770452 q^{6} -2.42240 q^{8} -1.74038 q^{9} +O(q^{10})$	\(q+0.686476 q^{2} -1.12233 q^{3} -1.52875 q^{4} -0.737311 q^{5} -0.770452 q^{6} -2.42240 q^{8} -1.74038 q^{9} -0.506146 q^{10} -3.34916 q^{11} +1.71576 q^{12} +5.80244 q^{13} +0.827506 q^{15} +1.39458 q^{16} +2.86261 q^{17} -1.19473 q^{18} +1.00000 q^{19} +1.12716 q^{20} -2.29912 q^{22} +4.18979 q^{23} +2.71873 q^{24} -4.45637 q^{25} +3.98324 q^{26} +5.32027 q^{27} +2.54285 q^{29} +0.568063 q^{30} -1.17478 q^{31} +5.80215 q^{32} +3.75886 q^{33} +1.96512 q^{34} +2.66060 q^{36} +7.94572 q^{37} +0.686476 q^{38} -6.51225 q^{39} +1.78606 q^{40} +3.49997 q^{41} -5.07745 q^{43} +5.12003 q^{44} +1.28320 q^{45} +2.87619 q^{46} +3.81695 q^{47} -1.56518 q^{48} -3.05919 q^{50} -3.21280 q^{51} -8.87049 q^{52} +10.4581 q^{53} +3.65223 q^{54} +2.46937 q^{55} -1.12233 q^{57} +1.74561 q^{58} +8.12045 q^{59} -1.26505 q^{60} -14.1824 q^{61} -0.806460 q^{62} +1.19388 q^{64} -4.27820 q^{65} +2.58037 q^{66} -7.74347 q^{67} -4.37622 q^{68} -4.70233 q^{69} -8.44741 q^{71} +4.21589 q^{72} +11.7621 q^{73} +5.45455 q^{74} +5.00152 q^{75} -1.52875 q^{76} -4.47051 q^{78} +4.17426 q^{79} -1.02824 q^{80} -0.749967 q^{81} +2.40265 q^{82} +5.31324 q^{83} -2.11064 q^{85} -3.48554 q^{86} -2.85392 q^{87} +8.11300 q^{88} +10.3986 q^{89} +0.880884 q^{90} -6.40515 q^{92} +1.31849 q^{93} +2.62025 q^{94} -0.737311 q^{95} -6.51193 q^{96} +5.89822 q^{97} +5.82879 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} + 4 q^{3} + 10 q^{4} + 16 q^{5} + 8 q^{6} - 6 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 2 * q^2 + 4 * q^3 + 10 * q^4 + 16 * q^5 + 8 * q^6 - 6 * q^8 + 10 * q^9	$ 10 q - 2 q^{2} + 4 q^{3} + 10 q^{4} + 16 q^{5} + 8 q^{6} - 6 q^{8} + 10 q^{9} - 12 q^{10} + 12 q^{12} + 12 q^{13} + 2 q^{16} + 16 q^{17} + 2 q^{18} + 10 q^{19} + 32 q^{20} + 4 q^{22} + 12 q^{23} - 8 q^{24} + 14 q^{25} + 24 q^{26} + 16 q^{27} - 12 q^{29} - 12 q^{30} + 8 q^{31} - 34 q^{32} - 4 q^{33} + 16 q^{34} - 6 q^{36} + 4 q^{37} - 2 q^{38} - 4 q^{39} - 20 q^{40} + 40 q^{41} + 4 q^{43} - 20 q^{44} + 24 q^{45} - 32 q^{46} + 16 q^{47} + 12 q^{48} - 34 q^{50} - 28 q^{51} - 40 q^{52} + 8 q^{54} + 16 q^{55} + 4 q^{57} - 8 q^{58} + 36 q^{59} + 32 q^{60} + 16 q^{61} - 16 q^{62} + 18 q^{64} + 8 q^{65} + 8 q^{66} - 28 q^{67} + 40 q^{68} + 48 q^{69} - 12 q^{71} + 34 q^{72} + 24 q^{74} - 32 q^{75} + 10 q^{76} + 28 q^{78} - 8 q^{79} + 8 q^{80} + 14 q^{81} - 8 q^{82} + 40 q^{85} - 52 q^{86} - 8 q^{87} - 4 q^{88} + 48 q^{89} - 64 q^{90} + 28 q^{92} + 40 q^{93} - 36 q^{94} + 16 q^{95} - 8 q^{96} - 16 q^{97} - 8 q^{99}+O(q^{100}) $ 10 * q - 2 * q^2 + 4 * q^3 + 10 * q^4 + 16 * q^5 + 8 * q^6 - 6 * q^8 + 10 * q^9 - 12 * q^10 + 12 * q^12 + 12 * q^13 + 2 * q^16 + 16 * q^17 + 2 * q^18 + 10 * q^19 + 32 * q^20 + 4 * q^22 + 12 * q^23 - 8 * q^24 + 14 * q^25 + 24 * q^26 + 16 * q^27 - 12 * q^29 - 12 * q^30 + 8 * q^31 - 34 * q^32 - 4 * q^33 + 16 * q^34 - 6 * q^36 + 4 * q^37 - 2 * q^38 - 4 * q^39 - 20 * q^40 + 40 * q^41 + 4 * q^43 - 20 * q^44 + 24 * q^45 - 32 * q^46 + 16 * q^47 + 12 * q^48 - 34 * q^50 - 28 * q^51 - 40 * q^52 + 8 * q^54 + 16 * q^55 + 4 * q^57 - 8 * q^58 + 36 * q^59 + 32 * q^60 + 16 * q^61 - 16 * q^62 + 18 * q^64 + 8 * q^65 + 8 * q^66 - 28 * q^67 + 40 * q^68 + 48 * q^69 - 12 * q^71 + 34 * q^72 + 24 * q^74 - 32 * q^75 + 10 * q^76 + 28 * q^78 - 8 * q^79 + 8 * q^80 + 14 * q^81 - 8 * q^82 + 40 * q^85 - 52 * q^86 - 8 * q^87 - 4 * q^88 + 48 * q^89 - 64 * q^90 + 28 * q^92 + 40 * q^93 - 36 * q^94 + 16 * q^95 - 8 * q^96 - 16 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	0.686476	0.485412	0.242706	−	0.970100i	$-0.421965\pi$
$2$	0.686476	0.485412	0.242706	+	0.970100i	$0.421965\pi$
$3$	−1.12233	−0.647978	−0.323989	−	0.946061i	$-0.605024\pi$
$3$	−1.12233	−0.647978	−0.323989	+	0.946061i	$0.605024\pi$
$4$	−1.52875	−0.764375
$5$	−0.737311	−0.329735	−0.164868	−	0.986316i	$-0.552720\pi$
$5$	−0.737311	−0.329735	−0.164868	+	0.986316i	$0.552720\pi$
$6$	−0.770452	−0.314536
$7$	0	0
$7$	0	0
$8$	−2.42240	−0.856449
$9$	−1.74038	−0.580125
$10$	−0.506146	−0.160057
$11$	−3.34916	−1.00981	−0.504904	−	0.863175i	$-0.668472\pi$
$11$	−3.34916	−1.00981	−0.504904	+	0.863175i	$0.668472\pi$
$12$	1.71576	0.495298
$13$	5.80244	1.60931	0.804654	−	0.593744i	$-0.202351\pi$
$13$	5.80244	1.60931	0.804654	+	0.593744i	$0.202351\pi$
$14$	0	0
$15$	0.827506	0.213661
$16$	1.39458	0.348645
$17$	2.86261	0.694286	0.347143	−	0.937812i	$-0.387152\pi$
$17$	2.86261	0.694286	0.347143	+	0.937812i	$0.387152\pi$
$18$	−1.19473	−0.281600
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	1.12716	0.252042
$21$	0	0
$22$	−2.29912	−0.490173
$23$	4.18979	0.873632	0.436816	−	0.899551i	$-0.356106\pi$
$23$	4.18979	0.873632	0.436816	+	0.899551i	$0.356106\pi$
$24$	2.71873	0.554959
$25$	−4.45637	−0.891275
$26$	3.98324	0.781177
$27$	5.32027	1.02389
$28$	0	0
$29$	2.54285	0.472196	0.236098	−	0.971729i	$-0.424131\pi$
$29$	2.54285	0.472196	0.236098	+	0.971729i	$0.424131\pi$
$30$	0.568063	0.103714
$31$	−1.17478	−0.210997	−0.105499	−	0.994419i	$-0.533644\pi$
$31$	−1.17478	−0.210997	−0.105499	+	0.994419i	$0.533644\pi$
$32$	5.80215	1.02569
$33$	3.75886	0.654333
$34$	1.96512	0.337014
$35$	0	0
$36$	2.66060	0.443433
$37$	7.94572	1.30627	0.653134	−	0.757242i	$-0.273454\pi$
$37$	7.94572	1.30627	0.653134	+	0.757242i	$0.273454\pi$
$38$	0.686476	0.111361
$39$	−6.51225	−1.04280
$40$	1.78606	0.282401
$41$	3.49997	0.546604	0.273302	−	0.961928i	$-0.411884\pi$
$41$	3.49997	0.546604	0.273302	+	0.961928i	$0.411884\pi$
$42$	0	0
$43$	−5.07745	−0.774303	−0.387152	−	0.922016i	$-0.626541\pi$
$43$	−5.07745	−0.774303	−0.387152	+	0.922016i	$0.626541\pi$
$44$	5.12003	0.771873
$45$	1.28320	0.191288
$46$	2.87619	0.424071
$47$	3.81695	0.556760	0.278380	−	0.960471i	$-0.410203\pi$
$47$	3.81695	0.556760	0.278380	+	0.960471i	$0.410203\pi$
$48$	−1.56518	−0.225914
$49$	0	0
$50$	−3.05919	−0.432635
$51$	−3.21280	−0.449882
$52$	−8.87049	−1.23012
$53$	10.4581	1.43653	0.718264	−	0.695771i	$-0.244937\pi$
$53$	10.4581	1.43653	0.718264	+	0.695771i	$0.244937\pi$
$54$	3.65223	0.497006
$55$	2.46937	0.332970
$56$	0	0
$57$	−1.12233	−0.148656
$58$	1.74561	0.229210
$59$	8.12045	1.05719	0.528596	−	0.848874i	$-0.322719\pi$
$59$	8.12045	1.05719	0.528596	+	0.848874i	$0.322719\pi$
$60$	−1.26505	−0.163317
$61$	−14.1824	−1.81587	−0.907934	−	0.419113i	$-0.862341\pi$
$61$	−14.1824	−1.81587	−0.907934	+	0.419113i	$0.862341\pi$
$62$	−0.806460	−0.102421
$63$	0	0
$64$	1.19388	0.149234
$65$	−4.27820	−0.530646
$66$	2.58037	0.317621
$67$	−7.74347	−0.946015	−0.473008	−	0.881058i	$-0.656832\pi$
$67$	−7.74347	−0.946015	−0.473008	+	0.881058i	$0.656832\pi$
$68$	−4.37622	−0.530695
$69$	−4.70233	−0.566094
$70$	0	0
$71$	−8.44741	−1.00252	−0.501262	−	0.865296i	$-0.667131\pi$
$71$	−8.44741	−1.00252	−0.501262	+	0.865296i	$0.667131\pi$
$72$	4.21589	0.496847
$73$	11.7621	1.37665	0.688324	−	0.725403i	$-0.258347\pi$
$73$	11.7621	1.37665	0.688324	+	0.725403i	$0.258347\pi$
$74$	5.45455	0.634078
$75$	5.00152	0.577526
$76$	−1.52875	−0.175360
$77$	0	0
$78$	−4.47051	−0.506185
$79$	4.17426	0.469641	0.234821	−	0.972039i	$-0.424550\pi$
$79$	4.17426	0.469641	0.234821	+	0.972039i	$0.424550\pi$
$80$	−1.02824	−0.114961
$81$	−0.749967	−0.0833297
$82$	2.40265	0.265328
$83$	5.31324	0.583204	0.291602	−	0.956540i	$-0.405812\pi$
$83$	5.31324	0.583204	0.291602	+	0.956540i	$0.405812\pi$
$84$	0	0
$85$	−2.11064	−0.228931
$86$	−3.48554	−0.375856
$87$	−2.85392	−0.305972
$88$	8.11300	0.864849
$89$	10.3986	1.10224	0.551122	−	0.834425i	$-0.314200\pi$
$89$	10.3986	1.10224	0.551122	+	0.834425i	$0.314200\pi$
$90$	0.880884	0.0928533
$91$	0	0
$92$	−6.40515	−0.667783
$93$	1.31849	0.136721
$94$	2.62025	0.270258
$95$	−0.737311	−0.0756465
$96$	−6.51193	−0.664621
$97$	5.89822	0.598874	0.299437	−	0.954116i	$-0.403201\pi$
$97$	5.89822	0.598874	0.299437	+	0.954116i	$0.403201\pi$
$98$	0	0
$99$	5.82879	0.585815
$100$	6.81268	0.681268
$101$	−5.10873	−0.508338	−0.254169	−	0.967160i	$-0.581802\pi$
$101$	−5.10873	−0.508338	−0.254169	+	0.967160i	$0.581802\pi$
$102$	−2.20551	−0.218378
$103$	−0.571239	−0.0562859	−0.0281429	−	0.999604i	$-0.508959\pi$
$103$	−0.571239	−0.0562859	−0.0281429	+	0.999604i	$0.508959\pi$
$104$	−14.0558	−1.37829
$105$	0	0
$106$	7.17922	0.697307
$107$	11.4507	1.10698	0.553491	−	0.832855i	$-0.313295\pi$
$107$	11.4507	1.10698	0.553491	+	0.832855i	$0.313295\pi$
$108$	−8.13336	−0.782633
$109$	−14.0634	−1.34703	−0.673516	−	0.739172i	$-0.735217\pi$
$109$	−14.0634	−1.34703	−0.673516	+	0.739172i	$0.735217\pi$
$110$	1.69516	0.161627
$111$	−8.91772	−0.846432
$112$	0	0
$113$	10.1153	0.951569	0.475784	−	0.879562i	$-0.342164\pi$
$113$	10.1153	0.951569	0.475784	+	0.879562i	$0.342164\pi$
$114$	−0.770452	−0.0721595
$115$	−3.08918	−0.288067
$116$	−3.88739	−0.360935
$117$	−10.0984	−0.933600
$118$	5.57449	0.513173
$119$	0	0
$120$	−2.00455	−0.182990
$121$	0.216848	0.0197135
$122$	−9.73586	−0.881444
$123$	−3.92813	−0.354187
$124$	1.79595	0.161281
$125$	6.97229	0.623620
$126$	0	0
$127$	8.27740	0.734500	0.367250	−	0.930122i	$-0.380299\pi$
$127$	8.27740	0.734500	0.367250	+	0.930122i	$0.380299\pi$
$128$	−10.7847	−0.953245
$129$	5.69857	0.501731
$130$	−2.93688	−0.257582
$131$	−3.78190	−0.330427	−0.165213	−	0.986258i	$-0.552831\pi$
$131$	−3.78190	−0.330427	−0.165213	+	0.986258i	$0.552831\pi$
$132$	−5.74636	−0.500156
$133$	0	0
$134$	−5.31570	−0.459207
$135$	−3.92269	−0.337611
$136$	−6.93440	−0.594620
$137$	17.9551	1.53401	0.767004	−	0.641642i	$-0.221747\pi$
$137$	17.9551	1.53401	0.767004	+	0.641642i	$0.221747\pi$
$138$	−3.22803	−0.274789
$139$	−11.5916	−0.983189	−0.491594	−	0.870824i	$-0.663586\pi$
$139$	−11.5916	−0.983189	−0.491594	+	0.870824i	$0.663586\pi$
$140$	0	0
$141$	−4.28388	−0.360768
$142$	−5.79894	−0.486636
$143$	−19.4333	−1.62509
$144$	−2.42709	−0.202258
$145$	−1.87487	−0.155700
$146$	8.07439	0.668241
$147$	0	0
$148$	−12.1470	−0.998479
$149$	−21.4354	−1.75606	−0.878029	−	0.478608i	$-0.841141\pi$
$149$	−21.4354	−1.75606	−0.878029	+	0.478608i	$0.841141\pi$
$150$	3.43342	0.280338
$151$	−1.15980	−0.0943831	−0.0471915	−	0.998886i	$-0.515027\pi$
$151$	−1.15980	−0.0943831	−0.0471915	+	0.998886i	$0.515027\pi$
$152$	−2.42240	−0.196483
$153$	−4.98202	−0.402773
$154$	0	0
$155$	0.866180	0.0695733
$156$	9.95561	0.797087
$157$	9.43694	0.753149	0.376575	−	0.926386i	$-0.377102\pi$
$157$	9.43694	0.753149	0.376575	+	0.926386i	$0.377102\pi$
$158$	2.86553	0.227969
$159$	−11.7374	−0.930837
$160$	−4.27799	−0.338205
$161$	0	0
$162$	−0.514834	−0.0404492
$163$	−8.09938	−0.634392	−0.317196	−	0.948360i	$-0.602741\pi$
$163$	−8.09938	−0.634392	−0.317196	+	0.948360i	$0.602741\pi$
$164$	−5.35059	−0.417811
$165$	−2.77145	−0.215757
$166$	3.64741	0.283094
$167$	−15.4515	−1.19568	−0.597838	−	0.801617i	$-0.703973\pi$
$167$	−15.4515	−1.19568	−0.597838	+	0.801617i	$0.703973\pi$
$168$	0	0
$169$	20.6683	1.58987
$170$	−1.44890	−0.111126
$171$	−1.74038	−0.133090
$172$	7.76215	0.591858
$173$	4.97743	0.378427	0.189213	−	0.981936i	$-0.439406\pi$
$173$	4.97743	0.378427	0.189213	+	0.981936i	$0.439406\pi$
$174$	−1.95915	−0.148523
$175$	0	0
$176$	−4.67067	−0.352065
$177$	−9.11382	−0.685037
$178$	7.13835	0.535042
$179$	8.51156	0.636184	0.318092	−	0.948060i	$-0.396958\pi$
$179$	8.51156	0.636184	0.318092	+	0.948060i	$0.396958\pi$
$180$	−1.96169	−0.146216
$181$	10.0417	0.746393	0.373197	−	0.927752i	$-0.378262\pi$
$181$	10.0417	0.746393	0.373197	+	0.927752i	$0.378262\pi$
$182$	0	0
$183$	15.9173	1.17664
$184$	−10.1494	−0.748221
$185$	−5.85846	−0.430723
$186$	0.905114	0.0663662
$187$	−9.58734	−0.701096
$188$	−5.83517	−0.425574
$189$	0	0
$190$	−0.506146	−0.0367197
$191$	−18.2302	−1.31909	−0.659547	−	0.751664i	$-0.729252\pi$
$191$	−18.2302	−1.31909	−0.659547	+	0.751664i	$0.729252\pi$
$192$	−1.33992	−0.0967005
$193$	−1.42018	−0.102227	−0.0511135	−	0.998693i	$-0.516277\pi$
$193$	−1.42018	−0.102227	−0.0511135	+	0.998693i	$0.516277\pi$
$194$	4.04899	0.290700
$195$	4.80155	0.343846
$196$	0	0
$197$	−4.61982	−0.329149	−0.164574	−	0.986365i	$-0.552625\pi$
$197$	−4.61982	−0.329149	−0.164574	+	0.986365i	$0.552625\pi$
$198$	4.00132	0.284362
$199$	9.15609	0.649058	0.324529	−	0.945876i	$-0.394794\pi$
$199$	9.15609	0.649058	0.324529	+	0.945876i	$0.394794\pi$
$200$	10.7951	0.763331
$201$	8.69072	0.612996
$202$	−3.50702	−0.246753
$203$	0	0
$204$	4.91157	0.343878
$205$	−2.58057	−0.180235
$206$	−0.392142	−0.0273218
$207$	−7.29181	−0.506816
$208$	8.09197	0.561077
$209$	−3.34916	−0.231666
$210$	0	0
$211$	20.9803	1.44434	0.722170	−	0.691716i	$-0.243145\pi$
$211$	20.9803	1.44434	0.722170	+	0.691716i	$0.243145\pi$
$212$	−15.9878	−1.09805
$213$	9.48078	0.649612
$214$	7.86064	0.537342
$215$	3.74366	0.255315
$216$	−12.8878	−0.876905
$217$	0	0
$218$	−9.65421	−0.653865
$219$	−13.2009	−0.892037
$220$	−3.77505	−0.254514
$221$	16.6101	1.11732
$222$	−6.12180	−0.410868
$223$	6.39580	0.428294	0.214147	−	0.976801i	$-0.431303\pi$
$223$	6.39580	0.428294	0.214147	+	0.976801i	$0.431303\pi$
$224$	0	0
$225$	7.75576	0.517051
$226$	6.94392	0.461903
$227$	26.7953	1.77847	0.889233	−	0.457454i	$-0.151239\pi$
$227$	26.7953	1.77847	0.889233	+	0.457454i	$0.151239\pi$
$228$	1.71576	0.113629
$229$	16.3882	1.08296	0.541482	−	0.840713i	$-0.317864\pi$
$229$	16.3882	1.08296	0.541482	+	0.840713i	$0.317864\pi$
$230$	−2.12065	−0.139831
$231$	0	0
$232$	−6.15982	−0.404412
$233$	−2.30334	−0.150897	−0.0754485	−	0.997150i	$-0.524039\pi$
$233$	−2.30334	−0.150897	−0.0754485	+	0.997150i	$0.524039\pi$
$234$	−6.93233	−0.453180
$235$	−2.81428	−0.183583
$236$	−12.4141	−0.808092
$237$	−4.68490	−0.304317
$238$	0	0
$239$	20.7062	1.33937	0.669685	−	0.742645i	$-0.266429\pi$
$239$	20.7062	1.33937	0.669685	+	0.742645i	$0.266429\pi$
$240$	1.15402	0.0744919
$241$	−29.2355	−1.88322	−0.941612	−	0.336700i	$-0.890689\pi$
$241$	−29.2355	−1.88322	−0.941612	+	0.336700i	$0.890689\pi$
$242$	0.148861	0.00956914
$243$	−15.1191	−0.969890
$244$	21.6813	1.38800
$245$	0	0
$246$	−2.69656	−0.171927
$247$	5.80244	0.369200
$248$	2.84580	0.180708
$249$	−5.96321	−0.377903
$250$	4.78631	0.302713
$251$	−13.9307	−0.879298	−0.439649	−	0.898170i	$-0.644897\pi$
$251$	−13.9307	−0.879298	−0.439649	+	0.898170i	$0.644897\pi$
$252$	0	0
$253$	−14.0323	−0.882201
$254$	5.68224	0.356535
$255$	2.36883	0.148342
$256$	−9.79121	−0.611951
$257$	8.86800	0.553171	0.276585	−	0.960989i	$-0.410797\pi$
$257$	8.86800	0.553171	0.276585	+	0.960989i	$0.410797\pi$
$258$	3.91193	0.243546
$259$	0	0
$260$	6.54030	0.405612
$261$	−4.42552	−0.273933
$262$	−2.59619	−0.160393
$263$	−27.0146	−1.66579	−0.832896	−	0.553429i	$-0.813319\pi$
$263$	−27.0146	−1.66579	−0.832896	+	0.553429i	$0.813319\pi$
$264$	−9.10547	−0.560403
$265$	−7.71085	−0.473674
$266$	0	0
$267$	−11.6706	−0.714229
$268$	11.8378	0.723111
$269$	26.6791	1.62665	0.813327	−	0.581807i	$-0.197654\pi$
$269$	26.6791	1.62665	0.813327	+	0.581807i	$0.197654\pi$
$270$	−2.69283	−0.163880
$271$	−28.4788	−1.72996	−0.864981	−	0.501805i	$-0.832669\pi$
$271$	−28.4788	−1.72996	−0.864981	+	0.501805i	$0.832669\pi$
$272$	3.99215	0.242059
$273$	0	0
$274$	12.3257	0.744626
$275$	14.9251	0.900017
$276$	7.18869	0.432708
$277$	23.6179	1.41906	0.709532	−	0.704674i	$-0.248907\pi$
$277$	23.6179	1.41906	0.709532	+	0.704674i	$0.248907\pi$
$278$	−7.95737	−0.477251
$279$	2.04456	0.122405
$280$	0	0
$281$	8.77803	0.523653	0.261827	−	0.965115i	$-0.415675\pi$
$281$	8.77803	0.523653	0.261827	+	0.965115i	$0.415675\pi$
$282$	−2.94078	−0.175121
$283$	28.7769	1.71061	0.855306	−	0.518124i	$-0.173369\pi$
$283$	28.7769	1.71061	0.855306	+	0.518124i	$0.173369\pi$
$284$	12.9140	0.766304
$285$	0.827506	0.0490172
$286$	−13.3405	−0.788839
$287$	0	0
$288$	−10.0979	−0.595026
$289$	−8.80544	−0.517967
$290$	−1.28706	−0.0755785
$291$	−6.61975	−0.388057
$292$	−17.9813	−1.05228
$293$	19.7329	1.15281	0.576405	−	0.817164i	$-0.304455\pi$
$293$	19.7329	1.15281	0.576405	+	0.817164i	$0.304455\pi$
$294$	0	0
$295$	−5.98729	−0.348594
$296$	−19.2477	−1.11875
$297$	−17.8184	−1.03393
$298$	−14.7149	−0.852411
$299$	24.3110	1.40594
$300$	−7.64608	−0.441447
$301$	0	0
$302$	−0.796174	−0.0458147
$303$	5.73368	0.329391
$304$	1.39458	0.0799847
$305$	10.4568	0.598756
$306$	−3.42004	−0.195511
$307$	−20.4156	−1.16518	−0.582590	−	0.812766i	$-0.697961\pi$
$307$	−20.4156	−1.16518	−0.582590	+	0.812766i	$0.697961\pi$
$308$	0	0
$309$	0.641119	0.0364720
$310$	0.594612	0.0337717
$311$	22.9063	1.29890	0.649450	−	0.760405i	$-0.274999\pi$
$311$	22.9063	1.29890	0.649450	+	0.760405i	$0.274999\pi$
$312$	15.7753	0.893100
$313$	11.6039	0.655889	0.327944	−	0.944697i	$-0.393644\pi$
$313$	11.6039	0.655889	0.327944	+	0.944697i	$0.393644\pi$
$314$	6.47823	0.365588
$315$	0	0
$316$	−6.38141	−0.358982
$317$	−9.66648	−0.542924	−0.271462	−	0.962449i	$-0.587507\pi$
$317$	−9.66648	−0.542924	−0.271462	+	0.962449i	$0.587507\pi$
$318$	−8.05745	−0.451839
$319$	−8.51642	−0.476828
$320$	−0.880257	−0.0492079
$321$	−12.8515	−0.717300
$322$	0	0
$323$	2.86261	0.159280
$324$	1.14651	0.0636952
$325$	−25.8578	−1.43433
$326$	−5.56003	−0.307941
$327$	15.7838	0.872847
$328$	−8.47835	−0.468138
$329$	0	0
$330$	−1.90253	−0.104731
$331$	14.3179	0.786981	0.393491	−	0.919329i	$-0.371267\pi$
$331$	14.3179	0.786981	0.393491	+	0.919329i	$0.371267\pi$
$332$	−8.12262	−0.445786
$333$	−13.8285	−0.757799
$334$	−10.6071	−0.580395
$335$	5.70934	0.311935
$336$	0	0
$337$	−18.8493	−1.02679	−0.513394	−	0.858153i	$-0.671612\pi$
$337$	−18.8493	−1.02679	−0.513394	+	0.858153i	$0.671612\pi$
$338$	14.1883	0.771742
$339$	−11.3527	−0.616595
$340$	3.22664	0.174989
$341$	3.93453	0.213067
$342$	−1.19473	−0.0646034
$343$	0	0
$344$	12.2996	0.663151
$345$	3.46708	0.186661
$346$	3.41688	0.183693
$347$	17.7226	0.951400	0.475700	−	0.879608i	$-0.342195\pi$
$347$	17.7226	0.951400	0.475700	+	0.879608i	$0.342195\pi$
$348$	4.36293	0.233878
$349$	12.7635	0.683216	0.341608	−	0.939843i	$-0.389029\pi$
$349$	12.7635	0.683216	0.341608	+	0.939843i	$0.389029\pi$
$350$	0	0
$351$	30.8705	1.64775
$352$	−19.4323	−1.03575
$353$	28.8038	1.53307	0.766535	−	0.642202i	$-0.221979\pi$
$353$	28.8038	1.53307	0.766535	+	0.642202i	$0.221979\pi$
$354$	−6.25642	−0.332525
$355$	6.22837	0.330567
$356$	−15.8968	−0.842528
$357$	0	0
$358$	5.84298	0.308811
$359$	31.8151	1.67914	0.839568	−	0.543255i	$-0.182808\pi$
$359$	31.8151	1.67914	0.839568	+	0.543255i	$0.182808\pi$
$360$	−3.10842	−0.163828
$361$	1.00000	0.0526316
$362$	6.89338	0.362308
$363$	−0.243375	−0.0127739
$364$	0	0
$365$	−8.67231	−0.453930
$366$	10.9269	0.571156
$367$	−33.1711	−1.73152	−0.865759	−	0.500461i	$-0.833164\pi$
$367$	−33.1711	−1.73152	−0.865759	+	0.500461i	$0.833164\pi$
$368$	5.84300	0.304587
$369$	−6.09127	−0.317099
$370$	−4.02169	−0.209078
$371$	0	0
$372$	−2.01565	−0.104507
$373$	20.3121	1.05172	0.525861	−	0.850571i	$-0.323743\pi$
$373$	20.3121	1.05172	0.525861	+	0.850571i	$0.323743\pi$
$374$	−6.58148	−0.340320
$375$	−7.82520	−0.404092
$376$	−9.24620	−0.476836
$377$	14.7548	0.759909
$378$	0	0
$379$	14.6458	0.752302	0.376151	−	0.926558i	$-0.377247\pi$
$379$	14.6458	0.752302	0.376151	+	0.926558i	$0.377247\pi$
$380$	1.12716	0.0578223
$381$	−9.28997	−0.475940
$382$	−12.5146	−0.640303
$383$	−4.67315	−0.238787	−0.119393	−	0.992847i	$-0.538095\pi$
$383$	−4.67315	−0.238787	−0.119393	+	0.992847i	$0.538095\pi$
$384$	12.1040	0.617681
$385$	0	0
$386$	−0.974922	−0.0496222
$387$	8.83666	0.449193
$388$	−9.01691	−0.457764
$389$	23.3385	1.18331	0.591653	−	0.806192i	$-0.298475\pi$
$389$	23.3385	1.18331	0.591653	+	0.806192i	$0.298475\pi$
$390$	3.29615	0.166907
$391$	11.9938	0.606550
$392$	0	0
$393$	4.24455	0.214109
$394$	−3.17140	−0.159773
$395$	−3.07773	−0.154857
$396$	−8.91077	−0.447783
$397$	1.61422	0.0810156	0.0405078	−	0.999179i	$-0.487102\pi$
$397$	1.61422	0.0810156	0.0405078	+	0.999179i	$0.487102\pi$
$398$	6.28544	0.315060
$399$	0	0
$400$	−6.21477	−0.310739
$401$	−22.4797	−1.12258	−0.561291	−	0.827619i	$-0.689695\pi$
$401$	−22.4797	−1.12258	−0.561291	+	0.827619i	$0.689695\pi$
$402$	5.96597	0.297556
$403$	−6.81661	−0.339559
$404$	7.80998	0.388561
$405$	0.552959	0.0274767
$406$	0	0
$407$	−26.6115	−1.31908
$408$	7.78269	0.385300
$409$	−6.18380	−0.305769	−0.152885	−	0.988244i	$-0.548856\pi$
$409$	−6.18380	−0.305769	−0.152885	+	0.988244i	$0.548856\pi$
$410$	−1.77150	−0.0874881
$411$	−20.1516	−0.994003
$412$	0.873283	0.0430235
$413$	0	0
$414$	−5.00565	−0.246014
$415$	−3.91751	−0.192303
$416$	33.6666	1.65064
$417$	13.0096	0.637084
$418$	−2.29912	−0.112453
$419$	24.7746	1.21032	0.605160	−	0.796104i	$-0.293109\pi$
$419$	24.7746	1.21032	0.605160	+	0.796104i	$0.293109\pi$
$420$	0	0
$421$	−18.1474	−0.884448	−0.442224	−	0.896905i	$-0.645810\pi$
$421$	−18.1474	−0.884448	−0.442224	+	0.896905i	$0.645810\pi$
$422$	14.4024	0.701100
$423$	−6.64293	−0.322990
$424$	−25.3337	−1.23031
$425$	−12.7569	−0.618799
$426$	6.50833	0.315330
$427$	0	0
$428$	−17.5053	−0.846150
$429$	21.8106	1.05302
$430$	2.56993	0.123933
$431$	−31.5441	−1.51943	−0.759713	−	0.650259i	$-0.774661\pi$
$431$	−31.5441	−1.51943	−0.759713	+	0.650259i	$0.774661\pi$
$432$	7.41954	0.356973
$433$	−4.98774	−0.239695	−0.119848	−	0.992792i	$-0.538241\pi$
$433$	−4.98774	−0.239695	−0.119848	+	0.992792i	$0.538241\pi$
$434$	0	0
$435$	2.10423	0.100890
$436$	21.4995	1.02964
$437$	4.18979	0.200425
$438$	−9.06213	−0.433005
$439$	7.43067	0.354646	0.177323	−	0.984153i	$-0.443256\pi$
$439$	7.43067	0.354646	0.177323	+	0.984153i	$0.443256\pi$
$440$	−5.98181	−0.285171
$441$	0	0
$442$	11.4025	0.542360
$443$	−35.0602	−1.66576	−0.832880	−	0.553454i	$-0.813310\pi$
$443$	−35.0602	−1.66576	−0.832880	+	0.553454i	$0.813310\pi$
$444$	13.6330	0.646992
$445$	−7.66696	−0.363449
$446$	4.39056	0.207899
$447$	24.0576	1.13789
$448$	0	0
$449$	−22.9020	−1.08081	−0.540405	−	0.841405i	$-0.681729\pi$
$449$	−22.9020	−1.08081	−0.540405	+	0.841405i	$0.681729\pi$
$450$	5.32414	0.250983
$451$	−11.7220	−0.551966
$452$	−15.4638	−0.727356
$453$	1.30168	0.0611581
$454$	18.3943	0.863288
$455$	0	0
$456$	2.71873	0.127316
$457$	0.364297	0.0170411	0.00852055	−	0.999964i	$-0.497288\pi$
$457$	0.364297	0.0170411	0.00852055	+	0.999964i	$0.497288\pi$
$458$	11.2501	0.525683
$459$	15.2299	0.710869
$460$	4.72258	0.220192
$461$	27.1050	1.26241	0.631203	−	0.775618i	$-0.282562\pi$
$461$	27.1050	1.26241	0.631203	+	0.775618i	$0.282562\pi$
$462$	0	0
$463$	−30.4371	−1.41453	−0.707266	−	0.706948i	$-0.750072\pi$
$463$	−30.4371	−1.41453	−0.707266	+	0.706948i	$0.750072\pi$
$464$	3.54622	0.164629
$465$	−0.972140	−0.0450819
$466$	−1.58119	−0.0732472
$467$	25.5824	1.18381	0.591907	−	0.806006i	$-0.298375\pi$
$467$	25.5824	1.18381	0.591907	+	0.806006i	$0.298375\pi$
$468$	15.4380	0.713621
$469$	0	0
$470$	−1.93194	−0.0891136
$471$	−10.5914	−0.488024
$472$	−19.6710	−0.905431
$473$	17.0052	0.781898
$474$	−3.21607	−0.147719
$475$	−4.45637	−0.204472
$476$	0	0
$477$	−18.2010	−0.833366
$478$	14.2143	0.650146
$479$	−17.3211	−0.791421	−0.395710	−	0.918375i	$-0.629502\pi$
$479$	−17.3211	−0.791421	−0.395710	+	0.918375i	$0.629502\pi$
$480$	4.80131	0.219149
$481$	46.1046	2.10219
$482$	−20.0695	−0.914139
$483$	0	0
$484$	−0.331507	−0.0150685
$485$	−4.34882	−0.197470
$486$	−10.3789	−0.470796
$487$	13.4673	0.610261	0.305130	−	0.952311i	$-0.401300\pi$
$487$	13.4673	0.610261	0.305130	+	0.952311i	$0.401300\pi$
$488$	34.3554	1.55520
$489$	9.09017	0.411072
$490$	0	0
$491$	−30.7396	−1.38726	−0.693630	−	0.720331i	$-0.743990\pi$
$491$	−30.7396	−1.38726	−0.693630	+	0.720331i	$0.743990\pi$
$492$	6.00513	0.270732
$493$	7.27921	0.327839
$494$	3.98324	0.179214
$495$	−4.29763	−0.193164
$496$	−1.63833	−0.0735632
$497$	0	0
$498$	−4.09360	−0.183438
$499$	21.6005	0.966971	0.483485	−	0.875353i	$-0.339371\pi$
$499$	21.6005	0.966971	0.483485	+	0.875353i	$0.339371\pi$
$500$	−10.6589	−0.476680
$501$	17.3417	0.774771
$502$	−9.56309	−0.426822
$503$	−10.8811	−0.485162	−0.242581	−	0.970131i	$-0.577994\pi$
$503$	−10.8811	−0.485162	−0.242581	+	0.970131i	$0.577994\pi$
$504$	0	0
$505$	3.76672	0.167617
$506$	−9.63281	−0.428231
$507$	−23.1967	−1.03020
$508$	−12.6541	−0.561434
$509$	27.5836	1.22262	0.611310	−	0.791391i	$-0.290643\pi$
$509$	27.5836	1.22262	0.611310	+	0.791391i	$0.290643\pi$
$510$	1.62614	0.0720069
$511$	0	0
$512$	14.8480	0.656197
$513$	5.32027	0.234895
$514$	6.08767	0.268516
$515$	0.421181	0.0185594
$516$	−8.71169	−0.383511
$517$	−12.7836	−0.562221
$518$	0	0
$519$	−5.58632	−0.245212
$520$	10.3635	0.454471
$521$	19.8330	0.868898	0.434449	−	0.900696i	$-0.356943\pi$
$521$	19.8330	0.868898	0.434449	+	0.900696i	$0.356943\pi$
$522$	−3.03801	−0.132970
$523$	−10.3744	−0.453641	−0.226820	−	0.973937i	$-0.572833\pi$
$523$	−10.3744	−0.453641	−0.226820	+	0.973937i	$0.572833\pi$
$524$	5.78159	0.252570
$525$	0	0
$526$	−18.5449	−0.808595
$527$	−3.36295	−0.146492
$528$	5.24203	0.228130
$529$	−5.44566	−0.236768
$530$	−5.29331	−0.229927
$531$	−14.1326	−0.613304
$532$	0	0
$533$	20.3084	0.879654
$534$	−8.01159	−0.346695
$535$	−8.44273	−0.365011
$536$	18.7578	0.810213
$537$	−9.55278	−0.412233
$538$	18.3146	0.789597
$539$	0	0
$540$	5.99681	0.258062
$541$	40.4895	1.74078	0.870391	−	0.492362i	$-0.163866\pi$
$541$	40.4895	1.74078	0.870391	+	0.492362i	$0.163866\pi$
$542$	−19.5500	−0.839743
$543$	−11.2701	−0.483646
$544$	16.6093	0.712119
$545$	10.3691	0.444164
$546$	0	0
$547$	−24.2768	−1.03800	−0.519000	−	0.854774i	$-0.673696\pi$
$547$	−24.2768	−1.03800	−0.519000	+	0.854774i	$0.673696\pi$
$548$	−27.4489	−1.17256
$549$	24.6827	1.05343
$550$	10.2457	0.436879
$551$	2.54285	0.108329
$552$	11.3909	0.484830
$553$	0	0
$554$	16.2131	0.688830
$555$	6.57513	0.279099
$556$	17.7207	0.751525
$557$	11.8566	0.502382	0.251191	−	0.967938i	$-0.419178\pi$
$557$	11.8566	0.502382	0.251191	+	0.967938i	$0.419178\pi$
$558$	1.40354	0.0594167
$559$	−29.4616	−1.24609
$560$	0	0
$561$	10.7602	0.454294
$562$	6.02591	0.254188
$563$	20.8339	0.878045	0.439022	−	0.898476i	$-0.355325\pi$
$563$	20.8339	0.878045	0.439022	+	0.898476i	$0.355325\pi$
$564$	6.54899	0.275762
$565$	−7.45813	−0.313766
$566$	19.7547	0.830351
$567$	0	0
$568$	20.4630	0.858609
$569$	11.0310	0.462445	0.231222	−	0.972901i	$-0.425727\pi$
$569$	11.0310	0.462445	0.231222	+	0.972901i	$0.425727\pi$
$570$	0.568063	0.0237935
$571$	−33.0119	−1.38151	−0.690753	−	0.723090i	$-0.742721\pi$
$571$	−33.0119	−1.38151	−0.690753	+	0.723090i	$0.742721\pi$
$572$	29.7086	1.24218
$573$	20.4603	0.854743
$574$	0	0
$575$	−18.6713	−0.778646
$576$	−2.07779	−0.0865746
$577$	39.5495	1.64647	0.823234	−	0.567702i	$-0.192167\pi$
$577$	39.5495	1.64647	0.823234	+	0.567702i	$0.192167\pi$
$578$	−6.04472	−0.251427
$579$	1.59391	0.0662408
$580$	2.86621	0.119013
$581$	0	0
$582$	−4.54430	−0.188367
$583$	−35.0257	−1.45062
$584$	−28.4925	−1.17903
$585$	7.44568	0.307841
$586$	13.5462	0.559588
$587$	−31.0722	−1.28249	−0.641243	−	0.767338i	$-0.721581\pi$
$587$	−31.0722	−1.28249	−0.641243	+	0.767338i	$0.721581\pi$
$588$	0	0
$589$	−1.17478	−0.0484061
$590$	−4.11013	−0.169211
$591$	5.18497	0.213281
$592$	11.0809	0.455424
$593$	−6.91212	−0.283847	−0.141923	−	0.989878i	$-0.545329\pi$
$593$	−6.91212	−0.283847	−0.141923	+	0.989878i	$0.545329\pi$
$594$	−12.2319	−0.501881
$595$	0	0
$596$	32.7694	1.34229
$597$	−10.2762	−0.420575
$598$	16.6889	0.682461
$599$	−23.9395	−0.978140	−0.489070	−	0.872245i	$-0.662664\pi$
$599$	−23.9395	−0.978140	−0.489070	+	0.872245i	$0.662664\pi$
$600$	−12.1157	−0.494621
$601$	−38.4019	−1.56645	−0.783223	−	0.621741i	$-0.786426\pi$
$601$	−38.4019	−1.56645	−0.783223	+	0.621741i	$0.786426\pi$
$602$	0	0
$603$	13.4765	0.548807
$604$	1.77304	0.0721441
$605$	−0.159884	−0.00650022
$606$	3.93603	0.159890
$607$	−42.4164	−1.72163	−0.860815	−	0.508919i	$-0.830045\pi$
$607$	−42.4164	−1.72163	−0.860815	+	0.508919i	$0.830045\pi$
$608$	5.80215	0.235308
$609$	0	0
$610$	7.17836	0.290643
$611$	22.1476	0.895998
$612$	7.61627	0.307870
$613$	−12.4504	−0.502867	−0.251433	−	0.967875i	$-0.580902\pi$
$613$	−12.4504	−0.502867	−0.251433	+	0.967875i	$0.580902\pi$
$614$	−14.0148	−0.565592
$615$	2.89625	0.116788
$616$	0	0
$617$	−18.4958	−0.744611	−0.372305	−	0.928110i	$-0.621433\pi$
$617$	−18.4958	−0.744611	−0.372305	+	0.928110i	$0.621433\pi$
$618$	0.440113	0.0177039
$619$	−33.6143	−1.35107	−0.675536	−	0.737327i	$-0.736088\pi$
$619$	−33.6143	−1.35107	−0.675536	+	0.737327i	$0.736088\pi$
$620$	−1.32417	−0.0531801
$621$	22.2908	0.894499
$622$	15.7247	0.630501
$623$	0	0
$624$	−9.08186	−0.363566
$625$	17.1411	0.685645
$626$	7.96577	0.318376
$627$	3.75886	0.150114
$628$	−14.4267	−0.575689
$629$	22.7455	0.906923
$630$	0	0
$631$	25.0077	0.995540	0.497770	−	0.867309i	$-0.334152\pi$
$631$	25.0077	0.995540	0.497770	+	0.867309i	$0.334152\pi$
$632$	−10.1117	−0.402224
$633$	−23.5468	−0.935900
$634$	−6.63581	−0.263542
$635$	−6.10302	−0.242191
$636$	17.9436	0.711509
$637$	0	0
$638$	−5.84631	−0.231458
$639$	14.7017	0.581589
$640$	7.95170	0.314319
$641$	5.78643	0.228550	0.114275	−	0.993449i	$-0.463545\pi$
$641$	5.78643	0.228550	0.114275	+	0.993449i	$0.463545\pi$
$642$	−8.82223	−0.348186
$643$	25.9958	1.02518	0.512588	−	0.858635i	$-0.328687\pi$
$643$	25.9958	1.02518	0.512588	+	0.858635i	$0.328687\pi$
$644$	0	0
$645$	−4.20162	−0.165439
$646$	1.96512	0.0773164
$647$	−21.4019	−0.841395	−0.420698	−	0.907201i	$-0.638215\pi$
$647$	−21.4019	−0.841395	−0.420698	+	0.907201i	$0.638215\pi$
$648$	1.81672	0.0713676
$649$	−27.1966	−1.06756
$650$	−17.7508	−0.696243
$651$	0	0
$652$	12.3819	0.484914
$653$	14.0178	0.548557	0.274279	−	0.961650i	$-0.411561\pi$
$653$	14.0178	0.548557	0.274279	+	0.961650i	$0.411561\pi$
$654$	10.8352	0.423690
$655$	2.78844	0.108953
$656$	4.88100	0.190571
$657$	−20.4704	−0.798628
$658$	0	0
$659$	18.2916	0.712541	0.356271	−	0.934383i	$-0.384048\pi$
$659$	18.2916	0.712541	0.356271	+	0.934383i	$0.384048\pi$
$660$	4.23685	0.164919
$661$	12.2215	0.475361	0.237680	−	0.971343i	$-0.423613\pi$
$661$	12.2215	0.475361	0.237680	+	0.971343i	$0.423613\pi$
$662$	9.82887	0.382010
$663$	−18.6421	−0.723998
$664$	−12.8708	−0.499484
$665$	0	0
$666$	−9.49296	−0.367845
$667$	10.6540	0.412525
$668$	23.6216	0.913945
$669$	−7.17819	−0.277525
$670$	3.91933	0.151417
$671$	47.4990	1.83368
$672$	0	0
$673$	8.95741	0.345283	0.172641	−	0.984985i	$-0.444770\pi$
$673$	8.95741	0.345283	0.172641	+	0.984985i	$0.444770\pi$
$674$	−12.9396	−0.498415
$675$	−23.7091	−0.912563
$676$	−31.5967	−1.21526
$677$	25.7173	0.988397	0.494199	−	0.869349i	$-0.335462\pi$
$677$	25.7173	0.988397	0.494199	+	0.869349i	$0.335462\pi$
$678$	−7.79337	−0.299303
$679$	0	0
$680$	5.11281	0.196067
$681$	−30.0732	−1.15241
$682$	2.70096	0.103425
$683$	−42.1332	−1.61218	−0.806092	−	0.591791i	$-0.798421\pi$
$683$	−42.1332	−1.61218	−0.806092	+	0.591791i	$0.798421\pi$
$684$	2.66060	0.101731
$685$	−13.2385	−0.505817
$686$	0	0
$687$	−18.3930	−0.701736
$688$	−7.08091	−0.269957
$689$	60.6824	2.31181
$690$	2.38006	0.0906075
$691$	−30.6212	−1.16489	−0.582443	−	0.812872i	$-0.697903\pi$
$691$	−30.6212	−1.16489	−0.582443	+	0.812872i	$0.697903\pi$
$692$	−7.60925	−0.289260
$693$	0	0
$694$	12.1662	0.461821
$695$	8.54663	0.324192
$696$	6.91335	0.262050
$697$	10.0191	0.379500
$698$	8.76185	0.331641
$699$	2.58511	0.0977779
$700$	0	0
$701$	−21.9503	−0.829053	−0.414526	−	0.910037i	$-0.636053\pi$
$701$	−21.9503	−0.829053	−0.414526	+	0.910037i	$0.636053\pi$
$702$	21.1919	0.799836
$703$	7.94572	0.299678
$704$	−3.99847	−0.150698
$705$	3.15855	0.118958
$706$	19.7731	0.744171
$707$	0	0
$708$	13.9328	0.523625
$709$	−29.0631	−1.09149	−0.545744	−	0.837952i	$-0.683753\pi$
$709$	−29.0631	−1.09149	−0.545744	+	0.837952i	$0.683753\pi$
$710$	4.27562	0.160461
$711$	−7.26479	−0.272451
$712$	−25.1895	−0.944015
$713$	−4.92209	−0.184334
$714$	0	0
$715$	14.3284	0.535851
$716$	−13.0121	−0.486283
$717$	−23.2391	−0.867882
$718$	21.8403	0.815072
$719$	16.7994	0.626513	0.313257	−	0.949669i	$-0.398580\pi$
$719$	16.7994	0.626513	0.313257	+	0.949669i	$0.398580\pi$
$720$	1.78952	0.0666916
$721$	0	0
$722$	0.686476	0.0255480
$723$	32.8119	1.22029
$724$	−15.3512	−0.570525
$725$	−11.3319	−0.420856
$726$	−0.167071	−0.00620059
$727$	−50.5218	−1.87375	−0.936874	−	0.349667i	$-0.886295\pi$
$727$	−50.5218	−1.87375	−0.936874	+	0.349667i	$0.886295\pi$
$728$	0	0
$729$	19.2185	0.711796
$730$	−5.95333	−0.220343
$731$	−14.5348	−0.537588
$732$	−24.3336	−0.899396
$733$	7.34681	0.271361	0.135680	−	0.990753i	$-0.456678\pi$
$733$	7.34681	0.271361	0.135680	+	0.990753i	$0.456678\pi$
$734$	−22.7712	−0.840499
$735$	0	0
$736$	24.3098	0.896071
$737$	25.9341	0.955294
$738$	−4.18151	−0.153924
$739$	42.0322	1.54618	0.773091	−	0.634296i	$-0.218710\pi$
$739$	42.0322	1.54618	0.773091	+	0.634296i	$0.218710\pi$
$740$	8.95613	0.329234
$741$	−6.51225	−0.239234
$742$	0	0
$743$	−10.5335	−0.386436	−0.193218	−	0.981156i	$-0.561893\pi$
$743$	−10.5335	−0.386436	−0.193218	+	0.981156i	$0.561893\pi$
$744$	−3.19392	−0.117095
$745$	15.8046	0.579034
$746$	13.9438	0.510518
$747$	−9.24703	−0.338331
$748$	14.6567	0.535900
$749$	0	0
$750$	−5.37181	−0.196151
$751$	−16.7715	−0.612000	−0.306000	−	0.952032i	$-0.598991\pi$
$751$	−16.7715	−0.612000	−0.306000	+	0.952032i	$0.598991\pi$
$752$	5.32305	0.194112
$753$	15.6348	0.569765
$754$	10.1288	0.368869
$755$	0.855132	0.0311214
$756$	0	0
$757$	4.08764	0.148568	0.0742839	−	0.997237i	$-0.476333\pi$
$757$	4.08764	0.148568	0.0742839	+	0.997237i	$0.476333\pi$
$758$	10.0540	0.365176
$759$	15.7488	0.571646
$760$	1.78606	0.0647873
$761$	−30.9787	−1.12298	−0.561489	−	0.827484i	$-0.689771\pi$
$761$	−30.9787	−1.12298	−0.561489	+	0.827484i	$0.689771\pi$
$762$	−6.37734	−0.231027
$763$	0	0
$764$	27.8695	1.00828
$765$	3.67330	0.132808
$766$	−3.20801	−0.115910
$767$	47.1184	1.70135
$768$	10.9890	0.396530
$769$	7.37298	0.265877	0.132938	−	0.991124i	$-0.457559\pi$
$769$	7.37298	0.265877	0.132938	+	0.991124i	$0.457559\pi$
$770$	0	0
$771$	−9.95282	−0.358442
$772$	2.17111	0.0781399
$773$	−45.1725	−1.62474	−0.812371	−	0.583142i	$-0.801823\pi$
$773$	−45.1725	−1.62474	−0.812371	+	0.583142i	$0.801823\pi$
$774$	6.06616	0.218043
$775$	5.23527	0.188056
$776$	−14.2879	−0.512905
$777$	0	0
$778$	16.0213	0.574391
$779$	3.49997	0.125400
$780$	−7.34038	−0.262828
$781$	28.2917	1.01236
$782$	8.23342	0.294427
$783$	13.5287	0.483475
$784$	0	0
$785$	−6.95795	−0.248340
$786$	2.91378	0.103931
$787$	10.3352	0.368409	0.184204	−	0.982888i	$-0.441029\pi$
$787$	10.3352	0.368409	0.184204	+	0.982888i	$0.441029\pi$
$788$	7.06256	0.251593
$789$	30.3193	1.07940
$790$	−2.11279	−0.0751696
$791$	0	0
$792$	−14.1197	−0.501721
$793$	−82.2924	−2.92229
$794$	1.10813	0.0393259
$795$	8.65412	0.306930
$796$	−13.9974	−0.496124
$797$	−25.7955	−0.913724	−0.456862	−	0.889538i	$-0.651027\pi$
$797$	−25.7955	−0.913724	−0.456862	+	0.889538i	$0.651027\pi$
$798$	0	0
$799$	10.9265	0.386550
$800$	−25.8565	−0.914167
$801$	−18.0974	−0.639440
$802$	−15.4318	−0.544914
$803$	−39.3931	−1.39015
$804$	−13.2860	−0.468559
$805$	0	0
$806$	−4.67944	−0.164826
$807$	−29.9428	−1.05404
$808$	12.3754	0.435365
$809$	−21.1284	−0.742836	−0.371418	−	0.928466i	$-0.621128\pi$
$809$	−21.1284	−0.742836	−0.371418	+	0.928466i	$0.621128\pi$
$810$	0.379593	0.0133375
$811$	27.4486	0.963850	0.481925	−	0.876212i	$-0.339938\pi$
$811$	27.4486	0.963850	0.481925	+	0.876212i	$0.339938\pi$
$812$	0	0
$813$	31.9626	1.12098
$814$	−18.2681	−0.640297
$815$	5.97176	0.209182
$816$	−4.48051	−0.156849
$817$	−5.07745	−0.177637
$818$	−4.24503	−0.148424
$819$	0	0
$820$	3.94505	0.137767
$821$	17.9475	0.626372	0.313186	−	0.949692i	$-0.398604\pi$
$821$	17.9475	0.626372	0.313186	+	0.949692i	$0.398604\pi$
$822$	−13.8336	−0.482501
$823$	−2.76484	−0.0963762	−0.0481881	−	0.998838i	$-0.515345\pi$
$823$	−2.76484	−0.0963762	−0.0481881	+	0.998838i	$0.515345\pi$
$824$	1.38377	0.0482060
$825$	−16.7509	−0.583191
$826$	0	0
$827$	−32.5020	−1.13020	−0.565102	−	0.825021i	$-0.691163\pi$
$827$	−32.5020	−1.13020	−0.565102	+	0.825021i	$0.691163\pi$
$828$	11.1474	0.387397
$829$	26.6147	0.924368	0.462184	−	0.886784i	$-0.347066\pi$
$829$	26.6147	0.924368	0.462184	+	0.886784i	$0.347066\pi$
$830$	−2.68927	−0.0933461
$831$	−26.5071	−0.919521
$832$	6.92739	0.240164
$833$	0	0
$834$	8.93079	0.309248
$835$	11.3926	0.394257
$836$	5.12003	0.177080
$837$	−6.25016	−0.216037
$838$	17.0072	0.587504
$839$	−0.317154	−0.0109494	−0.00547469	−	0.999985i	$-0.501743\pi$
$839$	−0.317154	−0.0109494	−0.00547469	+	0.999985i	$0.501743\pi$
$840$	0	0
$841$	−22.5339	−0.777031
$842$	−12.4577	−0.429321
$843$	−9.85185	−0.339316
$844$	−32.0736	−1.10402
$845$	−15.2390	−0.524237
$846$	−4.56021	−0.156783
$847$	0	0
$848$	14.5846	0.500838
$849$	−32.2972	−1.10844
$850$	−8.75729	−0.300372
$851$	33.2909	1.14120
$852$	−14.4938	−0.496548
$853$	−32.2536	−1.10434	−0.552172	−	0.833730i	$-0.686201\pi$
$853$	−32.2536	−1.10434	−0.552172	+	0.833730i	$0.686201\pi$
$854$	0	0
$855$	1.28320	0.0438844
$856$	−27.7382	−0.948073
$857$	−11.8823	−0.405892	−0.202946	−	0.979190i	$-0.565052\pi$
$857$	−11.8823	−0.405892	−0.202946	+	0.979190i	$0.565052\pi$
$858$	14.9724	0.511150
$859$	−54.9400	−1.87453	−0.937265	−	0.348618i	$-0.886651\pi$
$859$	−54.9400	−1.87453	−0.937265	+	0.348618i	$0.886651\pi$
$860$	−5.72312	−0.195157
$861$	0	0
$862$	−21.6543	−0.737547
$863$	0.889348	0.0302738	0.0151369	−	0.999885i	$-0.495182\pi$
$863$	0.889348	0.0302738	0.0151369	+	0.999885i	$0.495182\pi$
$864$	30.8690	1.05018
$865$	−3.66991	−0.124781
$866$	−3.42396	−0.116351
$867$	9.88261	0.335631
$868$	0	0
$869$	−13.9803	−0.474248
$870$	1.44450	0.0489732
$871$	−44.9310	−1.52243
$872$	34.0673	1.15366
$873$	−10.2651	−0.347422
$874$	2.87619	0.0972886
$875$	0	0
$876$	20.1810	0.681851
$877$	−8.87710	−0.299759	−0.149879	−	0.988704i	$-0.547888\pi$
$877$	−8.87710	−0.299759	−0.149879	+	0.988704i	$0.547888\pi$
$878$	5.10097	0.172150
$879$	−22.1469	−0.746995
$880$	3.44373	0.116088
$881$	−15.3973	−0.518749	−0.259375	−	0.965777i	$-0.583516\pi$
$881$	−15.3973	−0.518749	−0.259375	+	0.965777i	$0.583516\pi$
$882$	0	0
$883$	58.5802	1.97138	0.985691	−	0.168564i	$-0.0539131\pi$
$883$	58.5802	1.97138	0.985691	+	0.168564i	$0.0539131\pi$
$884$	−25.3928	−0.854051
$885$	6.71972	0.225881
$886$	−24.0680	−0.808579
$887$	41.7908	1.40320	0.701599	−	0.712572i	$-0.252470\pi$
$887$	41.7908	1.40320	0.701599	+	0.712572i	$0.252470\pi$
$888$	21.6023	0.724926
$889$	0	0
$890$	−5.26319	−0.176422
$891$	2.51176	0.0841470
$892$	−9.77758	−0.327378
$893$	3.81695	0.127729
$894$	16.5150	0.552343
$895$	−6.27566	−0.209772
$896$	0	0
$897$	−27.2850	−0.911019
$898$	−15.7216	−0.524638
$899$	−2.98730	−0.0996321
$900$	−11.8566	−0.395221
$901$	29.9374	0.997361
$902$	−8.04685	−0.267931
$903$	0	0
$904$	−24.5034	−0.814970
$905$	−7.40385	−0.246112
$906$	0.893570	0.0296869
$907$	−13.0455	−0.433170	−0.216585	−	0.976264i	$-0.569492\pi$
$907$	−13.0455	−0.433170	−0.216585	+	0.976264i	$0.569492\pi$
$908$	−40.9633	−1.35942
$909$	8.89111	0.294900
$910$	0	0
$911$	11.6612	0.386354	0.193177	−	0.981164i	$-0.438121\pi$
$911$	11.6612	0.386354	0.193177	+	0.981164i	$0.438121\pi$
$912$	−1.56518	−0.0518283
$913$	−17.7949	−0.588924
$914$	0.250081	0.00827195
$915$	−11.7360	−0.387980
$916$	−25.0535	−0.827791
$917$	0	0
$918$	10.4549	0.345064
$919$	−23.9441	−0.789845	−0.394922	−	0.918715i	$-0.629228\pi$
$919$	−23.9441	−0.789845	−0.394922	+	0.918715i	$0.629228\pi$
$920$	7.48323	0.246715
$921$	22.9130	0.755010
$922$	18.6069	0.612787
$923$	−49.0156	−1.61337
$924$	0	0
$925$	−35.4091	−1.16424
$926$	−20.8943	−0.686630
$927$	0.994171	0.0326529
$928$	14.7540	0.484325
$929$	−2.43386	−0.0798524	−0.0399262	−	0.999203i	$-0.512712\pi$
$929$	−2.43386	−0.0798524	−0.0399262	+	0.999203i	$0.512712\pi$
$930$	−0.667351	−0.0218833
$931$	0	0
$932$	3.52124	0.115342
$933$	−25.7085	−0.841658
$934$	17.5617	0.574637
$935$	7.06885	0.231176
$936$	24.4625	0.799580
$937$	−27.5464	−0.899903	−0.449952	−	0.893053i	$-0.648559\pi$
$937$	−27.5464	−0.899903	−0.449952	+	0.893053i	$0.648559\pi$
$938$	0	0
$939$	−13.0234	−0.425001
$940$	4.30233	0.140327
$941$	−55.1026	−1.79629	−0.898147	−	0.439695i	$-0.855087\pi$
$941$	−55.1026	−1.79629	−0.898147	+	0.439695i	$0.855087\pi$
$942$	−7.27071	−0.236893
$943$	14.6642	0.477531
$944$	11.3246	0.368585
$945$	0	0
$946$	11.6736	0.379543
$947$	41.4293	1.34627	0.673136	−	0.739518i	$-0.264947\pi$
$947$	41.4293	1.34627	0.673136	+	0.739518i	$0.264947\pi$
$948$	7.16205	0.232612
$949$	68.2488	2.21545
$950$	−3.05919	−0.0992533
$951$	10.8490	0.351802
$952$	0	0
$953$	43.6193	1.41297	0.706485	−	0.707728i	$-0.250280\pi$
$953$	43.6193	1.41297	0.706485	+	0.707728i	$0.250280\pi$
$954$	−12.4945	−0.404525
$955$	13.4413	0.434952
$956$	−31.6546	−1.02378
$957$	9.55823	0.308974
$958$	−11.8905	−0.384165
$959$	0	0
$960$	0.987939	0.0318856
$961$	−29.6199	−0.955480
$962$	31.6497	1.02043
$963$	−19.9285	−0.642188
$964$	44.6938	1.43949
$965$	1.04712	0.0337079
$966$	0	0
$967$	11.5018	0.369874	0.184937	−	0.982750i	$-0.440792\pi$
$967$	11.5018	0.369874	0.184937	+	0.982750i	$0.440792\pi$
$968$	−0.525293	−0.0168836
$969$	−3.21280	−0.103210
$970$	−2.98536	−0.0958542
$971$	−56.2215	−1.80424	−0.902118	−	0.431490i	$-0.857988\pi$
$971$	−56.2215	−1.80424	−0.902118	+	0.431490i	$0.857988\pi$
$972$	23.1133	0.741360
$973$	0	0
$974$	9.24496	0.296228
$975$	29.0210	0.929417
$976$	−19.7785	−0.633094
$977$	12.0362	0.385074	0.192537	−	0.981290i	$-0.438329\pi$
$977$	12.0362	0.385074	0.192537	+	0.981290i	$0.438329\pi$
$978$	6.24018	0.199539
$979$	−34.8264	−1.11306
$980$	0	0
$981$	24.4756	0.781447
$982$	−21.1020	−0.673393
$983$	−34.2740	−1.09317	−0.546585	−	0.837404i	$-0.684072\pi$
$983$	−34.2740	−1.09317	−0.546585	+	0.837404i	$0.684072\pi$
$984$	9.51550	0.303343
$985$	3.40625	0.108532
$986$	4.99700	0.159137
$987$	0	0
$988$	−8.87049	−0.282208
$989$	−21.2734	−0.676456
$990$	−2.95022	−0.0937641
$991$	23.2287	0.737883	0.368941	−	0.929453i	$-0.379720\pi$
$991$	23.2287	0.737883	0.368941	+	0.929453i	$0.379720\pi$
$992$	−6.81627	−0.216417
$993$	−16.0694	−0.509946
$994$	0	0
$995$	−6.75088	−0.214017
$996$	9.11626	0.288860
$997$	−27.7014	−0.877313	−0.438656	−	0.898655i	$-0.644545\pi$
$997$	−27.7014	−0.877313	−0.438656	+	0.898655i	$0.644545\pi$
$998$	14.8282	0.469379
$999$	42.2733	1.33747

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.a.q.1.7	yes	10
3.2	odd	2		8379.2.a.cs.1.4		10
7.2	even	3		931.2.f.q.704.4		20
7.3	odd	6		931.2.f.r.324.4		20
7.4	even	3		931.2.f.q.324.4		20
7.5	odd	6		931.2.f.r.704.4		20
7.6	odd	2		931.2.a.p.1.7	✓	10
21.20	even	2		8379.2.a.ct.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
931.2.a.p.1.7	✓	10	7.6	odd	2
931.2.a.q.1.7	yes	10	1.1	even	1	trivial
931.2.f.q.324.4		20	7.4	even	3
931.2.f.q.704.4		20	7.2	even	3
931.2.f.r.324.4		20	7.3	odd	6
931.2.f.r.704.4		20	7.5	odd	6
8379.2.a.cs.1.4		10	3.2	odd	2
8379.2.a.ct.1.4		10	21.20	even	2

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:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.a (trivial)

\(f(q)\)	\(=\)	\(q+0.686476 q^{2} -1.12233 q^{3} -1.52875 q^{4} -0.737311 q^{5} -0.770452 q^{6} -2.42240 q^{8} -1.74038 q^{9} +O(q^{10})\)	\(q+0.686476 q^{2} -1.12233 q^{3} -1.52875 q^{4} -0.737311 q^{5} -0.770452 q^{6} -2.42240 q^{8} -1.74038 q^{9} -0.506146 q^{10} -3.34916 q^{11} +1.71576 q^{12} +5.80244 q^{13} +0.827506 q^{15} +1.39458 q^{16} +2.86261 q^{17} -1.19473 q^{18} +1.00000 q^{19} +1.12716 q^{20} -2.29912 q^{22} +4.18979 q^{23} +2.71873 q^{24} -4.45637 q^{25} +3.98324 q^{26} +5.32027 q^{27} +2.54285 q^{29} +0.568063 q^{30} -1.17478 q^{31} +5.80215 q^{32} +3.75886 q^{33} +1.96512 q^{34} +2.66060 q^{36} +7.94572 q^{37} +0.686476 q^{38} -6.51225 q^{39} +1.78606 q^{40} +3.49997 q^{41} -5.07745 q^{43} +5.12003 q^{44} +1.28320 q^{45} +2.87619 q^{46} +3.81695 q^{47} -1.56518 q^{48} -3.05919 q^{50} -3.21280 q^{51} -8.87049 q^{52} +10.4581 q^{53} +3.65223 q^{54} +2.46937 q^{55} -1.12233 q^{57} +1.74561 q^{58} +8.12045 q^{59} -1.26505 q^{60} -14.1824 q^{61} -0.806460 q^{62} +1.19388 q^{64} -4.27820 q^{65} +2.58037 q^{66} -7.74347 q^{67} -4.37622 q^{68} -4.70233 q^{69} -8.44741 q^{71} +4.21589 q^{72} +11.7621 q^{73} +5.45455 q^{74} +5.00152 q^{75} -1.52875 q^{76} -4.47051 q^{78} +4.17426 q^{79} -1.02824 q^{80} -0.749967 q^{81} +2.40265 q^{82} +5.31324 q^{83} -2.11064 q^{85} -3.48554 q^{86} -2.85392 q^{87} +8.11300 q^{88} +10.3986 q^{89} +0.880884 q^{90} -6.40515 q^{92} +1.31849 q^{93} +2.62025 q^{94} -0.737311 q^{95} -6.51193 q^{96} +5.89822 q^{97} +5.82879 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} + 4 q^{3} + 10 q^{4} + 16 q^{5} + 8 q^{6} - 6 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 2 * q^2 + 4 * q^3 + 10 * q^4 + 16 * q^5 + 8 * q^6 - 6 * q^8 + 10 * q^9	\( 10 q - 2 q^{2} + 4 q^{3} + 10 q^{4} + 16 q^{5} + 8 q^{6} - 6 q^{8} + 10 q^{9} - 12 q^{10} + 12 q^{12} + 12 q^{13} + 2 q^{16} + 16 q^{17} + 2 q^{18} + 10 q^{19} + 32 q^{20} + 4 q^{22} + 12 q^{23} - 8 q^{24} + 14 q^{25} + 24 q^{26} + 16 q^{27} - 12 q^{29} - 12 q^{30} + 8 q^{31} - 34 q^{32} - 4 q^{33} + 16 q^{34} - 6 q^{36} + 4 q^{37} - 2 q^{38} - 4 q^{39} - 20 q^{40} + 40 q^{41} + 4 q^{43} - 20 q^{44} + 24 q^{45} - 32 q^{46} + 16 q^{47} + 12 q^{48} - 34 q^{50} - 28 q^{51} - 40 q^{52} + 8 q^{54} + 16 q^{55} + 4 q^{57} - 8 q^{58} + 36 q^{59} + 32 q^{60} + 16 q^{61} - 16 q^{62} + 18 q^{64} + 8 q^{65} + 8 q^{66} - 28 q^{67} + 40 q^{68} + 48 q^{69} - 12 q^{71} + 34 q^{72} + 24 q^{74} - 32 q^{75} + 10 q^{76} + 28 q^{78} - 8 q^{79} + 8 q^{80} + 14 q^{81} - 8 q^{82} + 40 q^{85} - 52 q^{86} - 8 q^{87} - 4 q^{88} + 48 q^{89} - 64 q^{90} + 28 q^{92} + 40 q^{93} - 36 q^{94} + 16 q^{95} - 8 q^{96} - 16 q^{97} - 8 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 + 4 * q^3 + 10 * q^4 + 16 * q^5 + 8 * q^6 - 6 * q^8 + 10 * q^9 - 12 * q^10 + 12 * q^12 + 12 * q^13 + 2 * q^16 + 16 * q^17 + 2 * q^18 + 10 * q^19 + 32 * q^20 + 4 * q^22 + 12 * q^23 - 8 * q^24 + 14 * q^25 + 24 * q^26 + 16 * q^27 - 12 * q^29 - 12 * q^30 + 8 * q^31 - 34 * q^32 - 4 * q^33 + 16 * q^34 - 6 * q^36 + 4 * q^37 - 2 * q^38 - 4 * q^39 - 20 * q^40 + 40 * q^41 + 4 * q^43 - 20 * q^44 + 24 * q^45 - 32 * q^46 + 16 * q^47 + 12 * q^48 - 34 * q^50 - 28 * q^51 - 40 * q^52 + 8 * q^54 + 16 * q^55 + 4 * q^57 - 8 * q^58 + 36 * q^59 + 32 * q^60 + 16 * q^61 - 16 * q^62 + 18 * q^64 + 8 * q^65 + 8 * q^66 - 28 * q^67 + 40 * q^68 + 48 * q^69 - 12 * q^71 + 34 * q^72 + 24 * q^74 - 32 * q^75 + 10 * q^76 + 28 * q^78 - 8 * q^79 + 8 * q^80 + 14 * q^81 - 8 * q^82 + 40 * q^85 - 52 * q^86 - 8 * q^87 - 4 * q^88 + 48 * q^89 - 64 * q^90 + 28 * q^92 + 40 * q^93 - 36 * q^94 + 16 * q^95 - 8 * q^96 - 16 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more