LMFDB - Embedded newform 7935.2.a.bi.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7935,2,Mod(1,7935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7935, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("7935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.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:	$63.3612940039$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 12x^{6} - 2x^{5} + 44x^{4} + 12x^{3} - 50x^{2} - 8x + 16 $ x^8 - 12x^6 - 2x^5 + 44x^4 + 12x^3 - 50x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$2.20023$ of defining polynomial
Character	$\chi$	$=$	7935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.20023 q^{2} +1.00000 q^{3} +2.84101 q^{4} +1.00000 q^{5} +2.20023 q^{6} -2.98493 q^{7} +1.85042 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.20023 q^{2} +1.00000 q^{3} +2.84101 q^{4} +1.00000 q^{5} +2.20023 q^{6} -2.98493 q^{7} +1.85042 q^{8} +1.00000 q^{9} +2.20023 q^{10} +6.44370 q^{11} +2.84101 q^{12} -4.24946 q^{13} -6.56754 q^{14} +1.00000 q^{15} -1.61068 q^{16} +3.96969 q^{17} +2.20023 q^{18} +3.04923 q^{19} +2.84101 q^{20} -2.98493 q^{21} +14.1776 q^{22} +1.85042 q^{24} +1.00000 q^{25} -9.34978 q^{26} +1.00000 q^{27} -8.48022 q^{28} +7.28597 q^{29} +2.20023 q^{30} +5.33265 q^{31} -7.24470 q^{32} +6.44370 q^{33} +8.73422 q^{34} -2.98493 q^{35} +2.84101 q^{36} +0.662130 q^{37} +6.70900 q^{38} -4.24946 q^{39} +1.85042 q^{40} +6.40844 q^{41} -6.56754 q^{42} -1.19671 q^{43} +18.3066 q^{44} +1.00000 q^{45} -7.91384 q^{47} -1.61068 q^{48} +1.90982 q^{49} +2.20023 q^{50} +3.96969 q^{51} -12.0727 q^{52} +8.59949 q^{53} +2.20023 q^{54} +6.44370 q^{55} -5.52337 q^{56} +3.04923 q^{57} +16.0308 q^{58} -5.35639 q^{59} +2.84101 q^{60} +1.72571 q^{61} +11.7330 q^{62} -2.98493 q^{63} -12.7186 q^{64} -4.24946 q^{65} +14.1776 q^{66} +7.36506 q^{67} +11.2779 q^{68} -6.56754 q^{70} -11.4088 q^{71} +1.85042 q^{72} -13.1973 q^{73} +1.45684 q^{74} +1.00000 q^{75} +8.66288 q^{76} -19.2340 q^{77} -9.34978 q^{78} -11.0556 q^{79} -1.61068 q^{80} +1.00000 q^{81} +14.1001 q^{82} -12.1542 q^{83} -8.48022 q^{84} +3.96969 q^{85} -2.63304 q^{86} +7.28597 q^{87} +11.9235 q^{88} +16.3537 q^{89} +2.20023 q^{90} +12.6843 q^{91} +5.33265 q^{93} -17.4123 q^{94} +3.04923 q^{95} -7.24470 q^{96} +9.07635 q^{97} +4.20204 q^{98} +6.44370 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} + 8 q^{4} + 8 q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^3 + 8 * q^4 + 8 * q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9	$ 8 q + 8 q^{3} + 8 q^{4} + 8 q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9} + 12 q^{11} + 8 q^{12} + 4 q^{13} + 8 q^{15} + 20 q^{17} + 4 q^{19} + 8 q^{20} + 6 q^{21} + 14 q^{22} + 6 q^{24} + 8 q^{25} - 22 q^{26} + 8 q^{27} - 8 q^{28} + 2 q^{31} + 12 q^{32} + 12 q^{33} + 8 q^{34} + 6 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{38} + 4 q^{39} + 6 q^{40} + 28 q^{41} + 4 q^{43} + 54 q^{44} + 8 q^{45} - 12 q^{47} + 14 q^{49} + 20 q^{51} - 22 q^{52} + 6 q^{53} + 12 q^{55} - 24 q^{56} + 4 q^{57} + 32 q^{58} + 2 q^{59} + 8 q^{60} + 32 q^{61} - 24 q^{62} + 6 q^{63} - 8 q^{64} + 4 q^{65} + 14 q^{66} + 32 q^{67} + 34 q^{68} + 2 q^{71} + 6 q^{72} - 2 q^{73} + 6 q^{74} + 8 q^{75} + 24 q^{76} - 30 q^{77} - 22 q^{78} - 36 q^{79} + 8 q^{81} + 16 q^{82} + 10 q^{83} - 8 q^{84} + 20 q^{85} + 50 q^{86} + 6 q^{88} + 42 q^{89} + 4 q^{91} + 2 q^{93} - 40 q^{94} + 4 q^{95} + 12 q^{96} + 16 q^{97} + 12 q^{99}+O(q^{100}) $ 8 * q + 8 * q^3 + 8 * q^4 + 8 * q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9 + 12 * q^11 + 8 * q^12 + 4 * q^13 + 8 * q^15 + 20 * q^17 + 4 * q^19 + 8 * q^20 + 6 * q^21 + 14 * q^22 + 6 * q^24 + 8 * q^25 - 22 * q^26 + 8 * q^27 - 8 * q^28 + 2 * q^31 + 12 * q^32 + 12 * q^33 + 8 * q^34 + 6 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^38 + 4 * q^39 + 6 * q^40 + 28 * q^41 + 4 * q^43 + 54 * q^44 + 8 * q^45 - 12 * q^47 + 14 * q^49 + 20 * q^51 - 22 * q^52 + 6 * q^53 + 12 * q^55 - 24 * q^56 + 4 * q^57 + 32 * q^58 + 2 * q^59 + 8 * q^60 + 32 * q^61 - 24 * q^62 + 6 * q^63 - 8 * q^64 + 4 * q^65 + 14 * q^66 + 32 * q^67 + 34 * q^68 + 2 * q^71 + 6 * q^72 - 2 * q^73 + 6 * q^74 + 8 * q^75 + 24 * q^76 - 30 * q^77 - 22 * q^78 - 36 * q^79 + 8 * q^81 + 16 * q^82 + 10 * q^83 - 8 * q^84 + 20 * q^85 + 50 * q^86 + 6 * q^88 + 42 * q^89 + 4 * q^91 + 2 * q^93 - 40 * q^94 + 4 * q^95 + 12 * q^96 + 16 * q^97 + 12 * 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 $

$2$	2.20023	1.55580	0.777899	−	0.628390i	$-0.216286\pi$
$2$	2.20023	1.55580	0.777899	+	0.628390i	$0.216286\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.84101	1.42051
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.20023	0.898240
$7$	−2.98493	−1.12820	−0.564099	−	0.825707i	$-0.690776\pi$
$7$	−2.98493	−1.12820	−0.564099	+	0.825707i	$0.690776\pi$
$8$	1.85042	0.654221
$9$	1.00000	0.333333
$10$	2.20023	0.695774
$11$	6.44370	1.94285	0.971425	−	0.237346i	$-0.0762777\pi$
$11$	6.44370	1.94285	0.971425	+	0.237346i	$0.0762777\pi$
$12$	2.84101	0.820129
$13$	−4.24946	−1.17859	−0.589293	−	0.807919i	$-0.700594\pi$
$13$	−4.24946	−1.17859	−0.589293	+	0.807919i	$0.700594\pi$
$14$	−6.56754	−1.75525
$15$	1.00000	0.258199
$16$	−1.61068	−0.402670
$17$	3.96969	0.962791	0.481395	−	0.876504i	$-0.340130\pi$
$17$	3.96969	0.962791	0.481395	+	0.876504i	$0.340130\pi$
$18$	2.20023	0.518599
$19$	3.04923	0.699540	0.349770	−	0.936836i	$-0.386260\pi$
$19$	3.04923	0.699540	0.349770	+	0.936836i	$0.386260\pi$
$20$	2.84101	0.635269
$21$	−2.98493	−0.651366
$22$	14.1776	3.02268
$23$	0	0
$23$	0	0
$24$	1.85042	0.377715
$25$	1.00000	0.200000
$26$	−9.34978	−1.83364
$27$	1.00000	0.192450
$28$	−8.48022	−1.60261
$29$	7.28597	1.35297	0.676486	−	0.736456i	$-0.263502\pi$
$29$	7.28597	1.35297	0.676486	+	0.736456i	$0.263502\pi$
$30$	2.20023	0.401705
$31$	5.33265	0.957771	0.478886	−	0.877877i	$-0.341041\pi$
$31$	5.33265	0.957771	0.478886	+	0.877877i	$0.341041\pi$
$32$	−7.24470	−1.28069
$33$	6.44370	1.12171
$34$	8.73422	1.49791
$35$	−2.98493	−0.504546
$36$	2.84101	0.473502
$37$	0.662130	0.108853	0.0544267	−	0.998518i	$-0.482667\pi$
$37$	0.662130	0.108853	0.0544267	+	0.998518i	$0.482667\pi$
$38$	6.70900	1.08834
$39$	−4.24946	−0.680457
$40$	1.85042	0.292577
$41$	6.40844	1.00083	0.500415	−	0.865785i	$-0.333181\pi$
$41$	6.40844	1.00083	0.500415	+	0.865785i	$0.333181\pi$
$42$	−6.56754	−1.01339
$43$	−1.19671	−0.182496	−0.0912482	−	0.995828i	$-0.529086\pi$
$43$	−1.19671	−0.182496	−0.0912482	+	0.995828i	$0.529086\pi$
$44$	18.3066	2.75983
$45$	1.00000	0.149071
$46$	0	0
$47$	−7.91384	−1.15435	−0.577176	−	0.816620i	$-0.695845\pi$
$47$	−7.91384	−1.15435	−0.577176	+	0.816620i	$0.695845\pi$
$48$	−1.61068	−0.232482
$49$	1.90982	0.272831
$50$	2.20023	0.311159
$51$	3.96969	0.555867
$52$	−12.0727	−1.67419
$53$	8.59949	1.18123	0.590616	−	0.806953i	$-0.298885\pi$
$53$	8.59949	1.18123	0.590616	+	0.806953i	$0.298885\pi$
$54$	2.20023	0.299413
$55$	6.44370	0.868869
$56$	−5.52337	−0.738091
$57$	3.04923	0.403880
$58$	16.0308	2.10495
$59$	−5.35639	−0.697343	−0.348671	−	0.937245i	$-0.613367\pi$
$59$	−5.35639	−0.697343	−0.348671	+	0.937245i	$0.613367\pi$
$60$	2.84101	0.366773
$61$	1.72571	0.220954	0.110477	−	0.993879i	$-0.464762\pi$
$61$	1.72571	0.220954	0.110477	+	0.993879i	$0.464762\pi$
$62$	11.7330	1.49010
$63$	−2.98493	−0.376066
$64$	−12.7186	−1.58983
$65$	−4.24946	−0.527080
$66$	14.1776	1.74515
$67$	7.36506	0.899785	0.449892	−	0.893083i	$-0.351462\pi$
$67$	7.36506	0.899785	0.449892	+	0.893083i	$0.351462\pi$
$68$	11.2779	1.36765
$69$	0	0
$70$	−6.56754	−0.784971
$71$	−11.4088	−1.35398	−0.676989	−	0.735993i	$-0.736715\pi$
$71$	−11.4088	−1.35398	−0.676989	+	0.735993i	$0.736715\pi$
$72$	1.85042	0.218074
$73$	−13.1973	−1.54463	−0.772316	−	0.635238i	$-0.780902\pi$
$73$	−13.1973	−1.54463	−0.772316	+	0.635238i	$0.780902\pi$
$74$	1.45684	0.169354
$75$	1.00000	0.115470
$76$	8.66288	0.993701
$77$	−19.2340	−2.19192
$78$	−9.34978	−1.05865
$79$	−11.0556	−1.24385	−0.621924	−	0.783077i	$-0.713649\pi$
$79$	−11.0556	−1.24385	−0.621924	+	0.783077i	$0.713649\pi$
$80$	−1.61068	−0.180079
$81$	1.00000	0.111111
$82$	14.1001	1.55709
$83$	−12.1542	−1.33410	−0.667050	−	0.745013i	$-0.732443\pi$
$83$	−12.1542	−1.33410	−0.667050	+	0.745013i	$0.732443\pi$
$84$	−8.48022	−0.925268
$85$	3.96969	0.430573
$86$	−2.63304	−0.283928
$87$	7.28597	0.781138
$88$	11.9235	1.27105
$89$	16.3537	1.73349	0.866744	−	0.498753i	$-0.166208\pi$
$89$	16.3537	1.73349	0.866744	+	0.498753i	$0.166208\pi$
$90$	2.20023	0.231925
$91$	12.6843	1.32968
$92$	0	0
$93$	5.33265	0.552970
$94$	−17.4123	−1.79594
$95$	3.04923	0.312844
$96$	−7.24470	−0.739409
$97$	9.07635	0.921564	0.460782	−	0.887513i	$-0.347569\pi$
$97$	9.07635	0.921564	0.460782	+	0.887513i	$0.347569\pi$
$98$	4.20204	0.424470
$99$	6.44370	0.647617
$100$	2.84101	0.284101
$101$	16.6716	1.65888	0.829442	−	0.558593i	$-0.188659\pi$
$101$	16.6716	1.65888	0.829442	+	0.558593i	$0.188659\pi$
$102$	8.73422	0.864817
$103$	18.0356	1.77710	0.888551	−	0.458777i	$-0.151712\pi$
$103$	18.0356	1.77710	0.888551	+	0.458777i	$0.151712\pi$
$104$	−7.86326	−0.771056
$105$	−2.98493	−0.291300
$106$	18.9209	1.83776
$107$	16.5202	1.59707	0.798533	−	0.601951i	$-0.205610\pi$
$107$	16.5202	1.59707	0.798533	+	0.601951i	$0.205610\pi$
$108$	2.84101	0.273376
$109$	−1.54932	−0.148398	−0.0741990	−	0.997243i	$-0.523640\pi$
$109$	−1.54932	−0.148398	−0.0741990	+	0.997243i	$0.523640\pi$
$110$	14.1776	1.35178
$111$	0.662130	0.0628466
$112$	4.80777	0.454292
$113$	3.90931	0.367757	0.183878	−	0.982949i	$-0.441135\pi$
$113$	3.90931	0.367757	0.183878	+	0.982949i	$0.441135\pi$
$114$	6.70900	0.628355
$115$	0	0
$116$	20.6995	1.92190
$117$	−4.24946	−0.392862
$118$	−11.7853	−1.08492
$119$	−11.8492	−1.08622
$120$	1.85042	0.168919
$121$	30.5213	2.77467
$122$	3.79695	0.343760
$123$	6.40844	0.577830
$124$	15.1501	1.36052
$125$	1.00000	0.0894427
$126$	−6.56754	−0.585083
$127$	−0.818786	−0.0726555	−0.0363278	−	0.999340i	$-0.511566\pi$
$127$	−0.818786	−0.0726555	−0.0363278	+	0.999340i	$0.511566\pi$
$128$	−13.4945	−1.19276
$129$	−1.19671	−0.105364
$130$	−9.34978	−0.820030
$131$	15.5034	1.35454	0.677269	−	0.735736i	$-0.263164\pi$
$131$	15.5034	1.35454	0.677269	+	0.735736i	$0.263164\pi$
$132$	18.3066	1.59339
$133$	−9.10173	−0.789220
$134$	16.2048	1.39988
$135$	1.00000	0.0860663
$136$	7.34558	0.629878
$137$	0.224833	0.0192088	0.00960439	−	0.999954i	$-0.496943\pi$
$137$	0.224833	0.0192088	0.00960439	+	0.999954i	$0.496943\pi$
$138$	0	0
$139$	13.1888	1.11866	0.559328	−	0.828946i	$-0.311059\pi$
$139$	13.1888	1.11866	0.559328	+	0.828946i	$0.311059\pi$
$140$	−8.48022	−0.716710
$141$	−7.91384	−0.666465
$142$	−25.1020	−2.10651
$143$	−27.3822	−2.28982
$144$	−1.61068	−0.134223
$145$	7.28597	0.605067
$146$	−29.0372	−2.40313
$147$	1.90982	0.157519
$148$	1.88112	0.154627
$149$	−1.82024	−0.149120	−0.0745600	−	0.997217i	$-0.523755\pi$
$149$	−1.82024	−0.149120	−0.0745600	+	0.997217i	$0.523755\pi$
$150$	2.20023	0.179648
$151$	−11.2010	−0.911525	−0.455763	−	0.890101i	$-0.650633\pi$
$151$	−11.2010	−0.911525	−0.455763	+	0.890101i	$0.650633\pi$
$152$	5.64234	0.457654
$153$	3.96969	0.320930
$154$	−42.3193	−3.41018
$155$	5.33265	0.428328
$156$	−12.0727	−0.966593
$157$	−2.78268	−0.222082	−0.111041	−	0.993816i	$-0.535418\pi$
$157$	−2.78268	−0.222082	−0.111041	+	0.993816i	$0.535418\pi$
$158$	−24.3248	−1.93518
$159$	8.59949	0.681984
$160$	−7.24470	−0.572744
$161$	0	0
$162$	2.20023	0.172866
$163$	10.6313	0.832706	0.416353	−	0.909203i	$-0.363308\pi$
$163$	10.6313	0.832706	0.416353	+	0.909203i	$0.363308\pi$
$164$	18.2065	1.42169
$165$	6.44370	0.501642
$166$	−26.7421	−2.07559
$167$	−6.91507	−0.535104	−0.267552	−	0.963543i	$-0.586215\pi$
$167$	−6.91507	−0.535104	−0.267552	+	0.963543i	$0.586215\pi$
$168$	−5.52337	−0.426137
$169$	5.05787	0.389067
$170$	8.73422	0.669884
$171$	3.04923	0.233180
$172$	−3.39986	−0.259237
$173$	−16.0537	−1.22054	−0.610270	−	0.792194i	$-0.708939\pi$
$173$	−16.0537	−1.22054	−0.610270	+	0.792194i	$0.708939\pi$
$174$	16.0308	1.21529
$175$	−2.98493	−0.225640
$176$	−10.3787	−0.782327
$177$	−5.35639	−0.402611
$178$	35.9819	2.69696
$179$	0.801801	0.0599294	0.0299647	−	0.999551i	$-0.490461\pi$
$179$	0.801801	0.0599294	0.0299647	+	0.999551i	$0.490461\pi$
$180$	2.84101	0.211756
$181$	−1.12038	−0.0832770	−0.0416385	−	0.999133i	$-0.513258\pi$
$181$	−1.12038	−0.0832770	−0.0416385	+	0.999133i	$0.513258\pi$
$182$	27.9085	2.06871
$183$	1.72571	0.127568
$184$	0	0
$185$	0.662130	0.0486808
$186$	11.7330	0.860309
$187$	25.5795	1.87056
$188$	−22.4833	−1.63976
$189$	−2.98493	−0.217122
$190$	6.70900	0.486722
$191$	−19.9341	−1.44238	−0.721190	−	0.692737i	$-0.756405\pi$
$191$	−19.9341	−1.44238	−0.721190	+	0.692737i	$0.756405\pi$
$192$	−12.7186	−0.917889
$193$	19.8286	1.42730	0.713648	−	0.700505i	$-0.247042\pi$
$193$	19.8286	1.42730	0.713648	+	0.700505i	$0.247042\pi$
$194$	19.9701	1.43377
$195$	−4.24946	−0.304310
$196$	5.42582	0.387558
$197$	−8.09748	−0.576922	−0.288461	−	0.957492i	$-0.593143\pi$
$197$	−8.09748	−0.576922	−0.288461	+	0.957492i	$0.593143\pi$
$198$	14.1776	1.00756
$199$	1.80725	0.128113	0.0640564	−	0.997946i	$-0.479596\pi$
$199$	1.80725	0.128113	0.0640564	+	0.997946i	$0.479596\pi$
$200$	1.85042	0.130844
$201$	7.36506	0.519491
$202$	36.6813	2.58089
$203$	−21.7481	−1.52642
$204$	11.2779	0.789613
$205$	6.40844	0.447585
$206$	39.6825	2.76481
$207$	0	0
$208$	6.84451	0.474582
$209$	19.6483	1.35910
$210$	−6.56754	−0.453203
$211$	1.79135	0.123321	0.0616607	−	0.998097i	$-0.480360\pi$
$211$	1.79135	0.123321	0.0616607	+	0.998097i	$0.480360\pi$
$212$	24.4313	1.67795
$213$	−11.4088	−0.781719
$214$	36.3482	2.48471
$215$	−1.19671	−0.0816149
$216$	1.85042	0.125905
$217$	−15.9176	−1.08056
$218$	−3.40886	−0.230877
$219$	−13.1973	−0.891794
$220$	18.3066	1.23423
$221$	−16.8690	−1.13473
$222$	1.45684	0.0977765
$223$	−7.94401	−0.531971	−0.265985	−	0.963977i	$-0.585697\pi$
$223$	−7.94401	−0.531971	−0.265985	+	0.963977i	$0.585697\pi$
$224$	21.6249	1.44488
$225$	1.00000	0.0666667
$226$	8.60138	0.572155
$227$	17.2522	1.14507	0.572533	−	0.819882i	$-0.305961\pi$
$227$	17.2522	1.14507	0.572533	+	0.819882i	$0.305961\pi$
$228$	8.66288	0.573713
$229$	−9.06521	−0.599046	−0.299523	−	0.954089i	$-0.596827\pi$
$229$	−9.06521	−0.599046	−0.299523	+	0.954089i	$0.596827\pi$
$230$	0	0
$231$	−19.2340	−1.26551
$232$	13.4821	0.885142
$233$	−12.6066	−0.825888	−0.412944	−	0.910756i	$-0.635500\pi$
$233$	−12.6066	−0.825888	−0.412944	+	0.910756i	$0.635500\pi$
$234$	−9.34978	−0.611214
$235$	−7.91384	−0.516242
$236$	−15.2176	−0.990579
$237$	−11.0556	−0.718136
$238$	−26.0711	−1.68994
$239$	−24.5752	−1.58964	−0.794819	−	0.606846i	$-0.792434\pi$
$239$	−24.5752	−1.58964	−0.794819	+	0.606846i	$0.792434\pi$
$240$	−1.61068	−0.103969
$241$	−8.03493	−0.517576	−0.258788	−	0.965934i	$-0.583323\pi$
$241$	−8.03493	−0.517576	−0.258788	+	0.965934i	$0.583323\pi$
$242$	67.1539	4.31682
$243$	1.00000	0.0641500
$244$	4.90276	0.313867
$245$	1.90982	0.122014
$246$	14.1001	0.898986
$247$	−12.9575	−0.824469
$248$	9.86761	0.626594
$249$	−12.1542	−0.770243
$250$	2.20023	0.139155
$251$	−27.4420	−1.73212	−0.866061	−	0.499939i	$-0.833356\pi$
$251$	−27.4420	−1.73212	−0.866061	+	0.499939i	$0.833356\pi$
$252$	−8.48022	−0.534204
$253$	0	0
$254$	−1.80152	−0.113037
$255$	3.96969	0.248591
$256$	−4.25379	−0.265862
$257$	−13.7118	−0.855320	−0.427660	−	0.903940i	$-0.640662\pi$
$257$	−13.7118	−0.855320	−0.427660	+	0.903940i	$0.640662\pi$
$258$	−2.63304	−0.163926
$259$	−1.97641	−0.122808
$260$	−12.0727	−0.748720
$261$	7.28597	0.450990
$262$	34.1110	2.10739
$263$	−19.9430	−1.22974	−0.614870	−	0.788628i	$-0.710792\pi$
$263$	−19.9430	−1.22974	−0.614870	+	0.788628i	$0.710792\pi$
$264$	11.9235	0.733843
$265$	8.59949	0.528263
$266$	−20.0259	−1.22787
$267$	16.3537	1.00083
$268$	20.9242	1.27815
$269$	−1.51198	−0.0921872	−0.0460936	−	0.998937i	$-0.514677\pi$
$269$	−1.51198	−0.0921872	−0.0460936	+	0.998937i	$0.514677\pi$
$270$	2.20023	0.133902
$271$	5.07064	0.308020	0.154010	−	0.988069i	$-0.450781\pi$
$271$	5.07064	0.308020	0.154010	+	0.988069i	$0.450781\pi$
$272$	−6.39390	−0.387687
$273$	12.6843	0.767691
$274$	0.494684	0.0298850
$275$	6.44370	0.388570
$276$	0	0
$277$	20.1372	1.20993	0.604965	−	0.796252i	$-0.293187\pi$
$277$	20.1372	1.20993	0.604965	+	0.796252i	$0.293187\pi$
$278$	29.0183	1.74040
$279$	5.33265	0.319257
$280$	−5.52337	−0.330084
$281$	−21.2356	−1.26681	−0.633405	−	0.773820i	$-0.718343\pi$
$281$	−21.2356	−1.26681	−0.633405	+	0.773820i	$0.718343\pi$
$282$	−17.4123	−1.03688
$283$	−13.0446	−0.775419	−0.387709	−	0.921782i	$-0.626734\pi$
$283$	−13.0446	−0.775419	−0.387709	+	0.921782i	$0.626734\pi$
$284$	−32.4126	−1.92333
$285$	3.04923	0.180621
$286$	−60.2472	−3.56249
$287$	−19.1288	−1.12914
$288$	−7.24470	−0.426898
$289$	−1.24158	−0.0730342
$290$	16.0308	0.941362
$291$	9.07635	0.532065
$292$	−37.4938	−2.19416
$293$	−3.29241	−0.192345	−0.0961724	−	0.995365i	$-0.530660\pi$
$293$	−3.29241	−0.192345	−0.0961724	+	0.995365i	$0.530660\pi$
$294$	4.20204	0.245068
$295$	−5.35639	−0.311861
$296$	1.22522	0.0712142
$297$	6.44370	0.373902
$298$	−4.00495	−0.232000
$299$	0	0
$300$	2.84101	0.164026
$301$	3.57210	0.205892
$302$	−24.6448	−1.41815
$303$	16.6716	0.957757
$304$	−4.91133	−0.281684
$305$	1.72571	0.0988138
$306$	8.73422	0.499302
$307$	32.2659	1.84151	0.920755	−	0.390141i	$-0.127574\pi$
$307$	32.2659	1.84151	0.920755	+	0.390141i	$0.127574\pi$
$308$	−54.6441	−3.11363
$309$	18.0356	1.02601
$310$	11.7330	0.666392
$311$	1.21234	0.0687457	0.0343729	−	0.999409i	$-0.489057\pi$
$311$	1.21234	0.0687457	0.0343729	+	0.999409i	$0.489057\pi$
$312$	−7.86326	−0.445170
$313$	−2.24782	−0.127054	−0.0635271	−	0.997980i	$-0.520235\pi$
$313$	−2.24782	−0.127054	−0.0635271	+	0.997980i	$0.520235\pi$
$314$	−6.12253	−0.345514
$315$	−2.98493	−0.168182
$316$	−31.4090	−1.76689
$317$	5.28720	0.296959	0.148479	−	0.988916i	$-0.452562\pi$
$317$	5.28720	0.296959	0.148479	+	0.988916i	$0.452562\pi$
$318$	18.9209	1.06103
$319$	46.9487	2.62862
$320$	−12.7186	−0.710994
$321$	16.5202	0.922067
$322$	0	0
$323$	12.1045	0.673511
$324$	2.84101	0.157834
$325$	−4.24946	−0.235717
$326$	23.3913	1.29552
$327$	−1.54932	−0.0856777
$328$	11.8583	0.654765
$329$	23.6223	1.30234
$330$	14.1776	0.780453
$331$	19.5471	1.07440	0.537202	−	0.843454i	$-0.319481\pi$
$331$	19.5471	1.07440	0.537202	+	0.843454i	$0.319481\pi$
$332$	−34.5303	−1.89510
$333$	0.662130	0.0362845
$334$	−15.2147	−0.832513
$335$	7.36506	0.402396
$336$	4.80777	0.262285
$337$	−20.4467	−1.11381	−0.556903	−	0.830578i	$-0.688010\pi$
$337$	−20.4467	−1.11381	−0.556903	+	0.830578i	$0.688010\pi$
$338$	11.1285	0.605310
$339$	3.90931	0.212325
$340$	11.2779	0.611631
$341$	34.3620	1.86081
$342$	6.70900	0.362781
$343$	15.1938	0.820390
$344$	−2.21441	−0.119393
$345$	0	0
$346$	−35.3218	−1.89891
$347$	−25.8418	−1.38726	−0.693629	−	0.720333i	$-0.743989\pi$
$347$	−25.8418	−1.38726	−0.693629	+	0.720333i	$0.743989\pi$
$348$	20.6995	1.10961
$349$	12.4468	0.666262	0.333131	−	0.942881i	$-0.391895\pi$
$349$	12.4468	0.666262	0.333131	+	0.942881i	$0.391895\pi$
$350$	−6.56754	−0.351050
$351$	−4.24946	−0.226819
$352$	−46.6827	−2.48820
$353$	−36.6985	−1.95326	−0.976631	−	0.214921i	$-0.931051\pi$
$353$	−36.6985	−1.95326	−0.976631	+	0.214921i	$0.931051\pi$
$354$	−11.7853	−0.626381
$355$	−11.4088	−0.605517
$356$	46.4610	2.46243
$357$	−11.8492	−0.627129
$358$	1.76415	0.0932380
$359$	0.313641	0.0165533	0.00827666	−	0.999966i	$-0.497365\pi$
$359$	0.313641	0.0165533	0.00827666	+	0.999966i	$0.497365\pi$
$360$	1.85042	0.0975255
$361$	−9.70222	−0.510643
$362$	−2.46509	−0.129562
$363$	30.5213	1.60195
$364$	36.0363	1.88882
$365$	−13.1973	−0.690780
$366$	3.79695	0.198470
$367$	−13.2930	−0.693889	−0.346945	−	0.937886i	$-0.612781\pi$
$367$	−13.2930	−0.693889	−0.346945	+	0.937886i	$0.612781\pi$
$368$	0	0
$369$	6.40844	0.333610
$370$	1.45684	0.0757374
$371$	−25.6689	−1.33266
$372$	15.1501	0.785496
$373$	−31.3976	−1.62571	−0.812853	−	0.582469i	$-0.802087\pi$
$373$	−31.3976	−1.62571	−0.812853	+	0.582469i	$0.802087\pi$
$374$	56.2808	2.91021
$375$	1.00000	0.0516398
$376$	−14.6439	−0.755201
$377$	−30.9614	−1.59459
$378$	−6.56754	−0.337798
$379$	−23.3481	−1.19931	−0.599655	−	0.800259i	$-0.704695\pi$
$379$	−23.3481	−1.19931	−0.599655	+	0.800259i	$0.704695\pi$
$380$	8.66288	0.444397
$381$	−0.818786	−0.0419477
$382$	−43.8596	−2.24405
$383$	−4.89774	−0.250263	−0.125132	−	0.992140i	$-0.539935\pi$
$383$	−4.89774	−0.250263	−0.125132	+	0.992140i	$0.539935\pi$
$384$	−13.4945	−0.688640
$385$	−19.2340	−0.980256
$386$	43.6275	2.22058
$387$	−1.19671	−0.0608322
$388$	25.7860	1.30909
$389$	−30.3328	−1.53793	−0.768967	−	0.639288i	$-0.779229\pi$
$389$	−30.3328	−1.53793	−0.768967	+	0.639288i	$0.779229\pi$
$390$	−9.34978	−0.473444
$391$	0	0
$392$	3.53396	0.178492
$393$	15.5034	0.782042
$394$	−17.8163	−0.897573
$395$	−11.0556	−0.556266
$396$	18.3066	0.919943
$397$	−21.7528	−1.09174	−0.545870	−	0.837870i	$-0.683801\pi$
$397$	−21.7528	−1.09174	−0.545870	+	0.837870i	$0.683801\pi$
$398$	3.97637	0.199318
$399$	−9.10173	−0.455657
$400$	−1.61068	−0.0805340
$401$	28.0752	1.40201	0.701004	−	0.713158i	$-0.252736\pi$
$401$	28.0752	1.40201	0.701004	+	0.713158i	$0.252736\pi$
$402$	16.2048	0.808223
$403$	−22.6608	−1.12882
$404$	47.3641	2.35645
$405$	1.00000	0.0496904
$406$	−47.8509	−2.37480
$407$	4.26657	0.211486
$408$	7.34558	0.363660
$409$	1.79479	0.0887466	0.0443733	−	0.999015i	$-0.485871\pi$
$409$	1.79479	0.0887466	0.0443733	+	0.999015i	$0.485871\pi$
$410$	14.1001	0.696352
$411$	0.224833	0.0110902
$412$	51.2394	2.52438
$413$	15.9885	0.786741
$414$	0	0
$415$	−12.1542	−0.596628
$416$	30.7860	1.50941
$417$	13.1888	0.645856
$418$	43.2308	2.11449
$419$	18.7418	0.915595	0.457798	−	0.889056i	$-0.348638\pi$
$419$	18.7418	0.915595	0.457798	+	0.889056i	$0.348638\pi$
$420$	−8.48022	−0.413793
$421$	−10.0807	−0.491305	−0.245652	−	0.969358i	$-0.579002\pi$
$421$	−10.0807	−0.491305	−0.245652	+	0.969358i	$0.579002\pi$
$422$	3.94138	0.191863
$423$	−7.91384	−0.384784
$424$	15.9126	0.772786
$425$	3.96969	0.192558
$426$	−25.1020	−1.21620
$427$	−5.15112	−0.249280
$428$	46.9340	2.26864
$429$	−27.3822	−1.32203
$430$	−2.63304	−0.126976
$431$	9.46857	0.456085	0.228042	−	0.973651i	$-0.426767\pi$
$431$	9.46857	0.456085	0.228042	+	0.973651i	$0.426767\pi$
$432$	−1.61068	−0.0774939
$433$	5.88839	0.282978	0.141489	−	0.989940i	$-0.454811\pi$
$433$	5.88839	0.282978	0.141489	+	0.989940i	$0.454811\pi$
$434$	−35.0223	−1.68113
$435$	7.28597	0.349336
$436$	−4.40164	−0.210800
$437$	0	0
$438$	−29.0372	−1.38745
$439$	7.07763	0.337797	0.168898	−	0.985633i	$-0.445979\pi$
$439$	7.07763	0.337797	0.168898	+	0.985633i	$0.445979\pi$
$440$	11.9235	0.568432
$441$	1.90982	0.0909438
$442$	−37.1157	−1.76541
$443$	−6.03178	−0.286579	−0.143289	−	0.989681i	$-0.545768\pi$
$443$	−6.03178	−0.286579	−0.143289	+	0.989681i	$0.545768\pi$
$444$	1.88112	0.0892739
$445$	16.3537	0.775240
$446$	−17.4787	−0.827638
$447$	−1.82024	−0.0860944
$448$	37.9643	1.79364
$449$	−14.3953	−0.679358	−0.339679	−	0.940541i	$-0.610318\pi$
$449$	−14.3953	−0.679358	−0.339679	+	0.940541i	$0.610318\pi$
$450$	2.20023	0.103720
$451$	41.2941	1.94446
$452$	11.1064	0.522401
$453$	−11.2010	−0.526269
$454$	37.9587	1.78149
$455$	12.6843	0.594651
$456$	5.64234	0.264227
$457$	−16.3695	−0.765733	−0.382867	−	0.923804i	$-0.625063\pi$
$457$	−16.3695	−0.765733	−0.382867	+	0.923804i	$0.625063\pi$
$458$	−19.9455	−0.931994
$459$	3.96969	0.185289
$460$	0	0
$461$	9.35754	0.435824	0.217912	−	0.975968i	$-0.430075\pi$
$461$	9.35754	0.435824	0.217912	+	0.975968i	$0.430075\pi$
$462$	−42.3193	−1.96887
$463$	−18.0440	−0.838578	−0.419289	−	0.907853i	$-0.637721\pi$
$463$	−18.0440	−0.838578	−0.419289	+	0.907853i	$0.637721\pi$
$464$	−11.7354	−0.544801
$465$	5.33265	0.247296
$466$	−27.7375	−1.28491
$467$	−37.2822	−1.72521	−0.862607	−	0.505875i	$-0.831170\pi$
$467$	−37.2822	−1.72521	−0.862607	+	0.505875i	$0.831170\pi$
$468$	−12.0727	−0.558063
$469$	−21.9842	−1.01514
$470$	−17.4123	−0.803168
$471$	−2.78268	−0.128219
$472$	−9.91155	−0.456216
$473$	−7.71124	−0.354563
$474$	−24.3248	−1.11727
$475$	3.04923	0.139908
$476$	−33.6638	−1.54298
$477$	8.59949	0.393744
$478$	−54.0711	−2.47316
$479$	18.7360	0.856068	0.428034	−	0.903763i	$-0.359206\pi$
$479$	18.7360	0.856068	0.428034	+	0.903763i	$0.359206\pi$
$480$	−7.24470	−0.330674
$481$	−2.81369	−0.128293
$482$	−17.6787	−0.805243
$483$	0	0
$484$	86.7114	3.94143
$485$	9.07635	0.412136
$486$	2.20023	0.0998044
$487$	−29.9958	−1.35924	−0.679620	−	0.733565i	$-0.737855\pi$
$487$	−29.9958	−1.35924	−0.679620	+	0.733565i	$0.737855\pi$
$488$	3.19328	0.144553
$489$	10.6313	0.480763
$490$	4.20204	0.189829
$491$	2.73940	0.123628	0.0618138	−	0.998088i	$-0.480312\pi$
$491$	2.73940	0.123628	0.0618138	+	0.998088i	$0.480312\pi$
$492$	18.2065	0.820811
$493$	28.9230	1.30263
$494$	−28.5096	−1.28271
$495$	6.44370	0.289623
$496$	−8.58918	−0.385666
$497$	34.0545	1.52756
$498$	−26.7421	−1.19834
$499$	28.9863	1.29761	0.648803	−	0.760956i	$-0.275270\pi$
$499$	28.9863	1.29761	0.648803	+	0.760956i	$0.275270\pi$
$500$	2.84101	0.127054
$501$	−6.91507	−0.308942
$502$	−60.3786	−2.69483
$503$	−0.855040	−0.0381244	−0.0190622	−	0.999818i	$-0.506068\pi$
$503$	−0.855040	−0.0381244	−0.0190622	+	0.999818i	$0.506068\pi$
$504$	−5.52337	−0.246030
$505$	16.6716	0.741875
$506$	0	0
$507$	5.05787	0.224628
$508$	−2.32618	−0.103208
$509$	−8.78942	−0.389584	−0.194792	−	0.980845i	$-0.562403\pi$
$509$	−8.78942	−0.389584	−0.194792	+	0.980845i	$0.562403\pi$
$510$	8.73422	0.386758
$511$	39.3932	1.74265
$512$	17.6297	0.779132
$513$	3.04923	0.134627
$514$	−30.1692	−1.33070
$515$	18.0356	0.794744
$516$	−3.39986	−0.149671
$517$	−50.9944	−2.24273
$518$	−4.34856	−0.191065
$519$	−16.0537	−0.704679
$520$	−7.86326	−0.344827
$521$	23.1128	1.01259	0.506295	−	0.862360i	$-0.331015\pi$
$521$	23.1128	1.01259	0.506295	+	0.862360i	$0.331015\pi$
$522$	16.0308	0.701650
$523$	−32.5906	−1.42509	−0.712544	−	0.701627i	$-0.752457\pi$
$523$	−32.5906	−1.42509	−0.712544	+	0.701627i	$0.752457\pi$
$524$	44.0453	1.92413
$525$	−2.98493	−0.130273
$526$	−43.8793	−1.91323
$527$	21.1689	0.922133
$528$	−10.3787	−0.451677
$529$	0	0
$530$	18.9209	0.821870
$531$	−5.35639	−0.232448
$532$	−25.8581	−1.12109
$533$	−27.2324	−1.17957
$534$	35.9819	1.55709
$535$	16.5202	0.714230
$536$	13.6284	0.588658
$537$	0.801801	0.0346003
$538$	−3.32671	−0.143425
$539$	12.3063	0.530070
$540$	2.84101	0.122258
$541$	−41.4469	−1.78194	−0.890970	−	0.454062i	$-0.849975\pi$
$541$	−41.4469	−1.78194	−0.890970	+	0.454062i	$0.849975\pi$
$542$	11.1566	0.479216
$543$	−1.12038	−0.0480800
$544$	−28.7592	−1.23304
$545$	−1.54932	−0.0663656
$546$	27.9085	1.19437
$547$	13.6956	0.585583	0.292792	−	0.956176i	$-0.405416\pi$
$547$	13.6956	0.585583	0.292792	+	0.956176i	$0.405416\pi$
$548$	0.638753	0.0272862
$549$	1.72571	0.0736514
$550$	14.1776	0.604536
$551$	22.2166	0.946458
$552$	0	0
$553$	33.0001	1.40331
$554$	44.3066	1.88241
$555$	0.662130	0.0281058
$556$	37.4694	1.58906
$557$	17.0238	0.721322	0.360661	−	0.932697i	$-0.382551\pi$
$557$	17.0238	0.721322	0.360661	+	0.932697i	$0.382551\pi$
$558$	11.7330	0.496699
$559$	5.08536	0.215088
$560$	4.80777	0.203165
$561$	25.5795	1.07997
$562$	−46.7232	−1.97090
$563$	−10.2793	−0.433219	−0.216609	−	0.976258i	$-0.569500\pi$
$563$	−10.2793	−0.433219	−0.216609	+	0.976258i	$0.569500\pi$
$564$	−22.4833	−0.946717
$565$	3.90931	0.164466
$566$	−28.7010	−1.20639
$567$	−2.98493	−0.125355
$568$	−21.1111	−0.885801
$569$	−28.8558	−1.20970	−0.604848	−	0.796341i	$-0.706766\pi$
$569$	−28.8558	−1.20970	−0.604848	+	0.796341i	$0.706766\pi$
$570$	6.70900	0.281009
$571$	0.834390	0.0349181	0.0174591	−	0.999848i	$-0.494442\pi$
$571$	0.834390	0.0349181	0.0174591	+	0.999848i	$0.494442\pi$
$572$	−77.7932	−3.25270
$573$	−19.9341	−0.832759
$574$	−42.0877	−1.75671
$575$	0	0
$576$	−12.7186	−0.529943
$577$	−1.15193	−0.0479557	−0.0239778	−	0.999712i	$-0.507633\pi$
$577$	−1.15193	−0.0479557	−0.0239778	+	0.999712i	$0.507633\pi$
$578$	−2.73176	−0.113626
$579$	19.8286	0.824049
$580$	20.6995	0.859501
$581$	36.2796	1.50513
$582$	19.9701	0.827785
$583$	55.4126	2.29496
$584$	−24.4206	−1.01053
$585$	−4.24946	−0.175693
$586$	−7.24406	−0.299250
$587$	−12.1966	−0.503406	−0.251703	−	0.967805i	$-0.580991\pi$
$587$	−12.1966	−0.503406	−0.251703	+	0.967805i	$0.580991\pi$
$588$	5.42582	0.223757
$589$	16.2604	0.670000
$590$	−11.7853	−0.485193
$591$	−8.09748	−0.333086
$592$	−1.06648	−0.0438320
$593$	−24.6728	−1.01319	−0.506596	−	0.862184i	$-0.669096\pi$
$593$	−24.6728	−1.01319	−0.506596	+	0.862184i	$0.669096\pi$
$594$	14.1776	0.581715
$595$	−11.8492	−0.485772
$596$	−5.17132	−0.211826
$597$	1.80725	0.0739659
$598$	0	0
$599$	20.6672	0.844438	0.422219	−	0.906494i	$-0.361251\pi$
$599$	20.6672	0.844438	0.422219	+	0.906494i	$0.361251\pi$
$600$	1.85042	0.0755429
$601$	−6.45704	−0.263388	−0.131694	−	0.991290i	$-0.542042\pi$
$601$	−6.45704	−0.263388	−0.131694	+	0.991290i	$0.542042\pi$
$602$	7.85943	0.320327
$603$	7.36506	0.299928
$604$	−31.8222	−1.29483
$605$	30.5213	1.24087
$606$	36.6813	1.49008
$607$	−12.6377	−0.512949	−0.256474	−	0.966551i	$-0.582561\pi$
$607$	−12.6377	−0.512949	−0.256474	+	0.966551i	$0.582561\pi$
$608$	−22.0907	−0.895897
$609$	−21.7481	−0.881279
$610$	3.79695	0.153734
$611$	33.6295	1.36050
$612$	11.2779	0.455883
$613$	−23.6730	−0.956145	−0.478073	−	0.878320i	$-0.658664\pi$
$613$	−23.6730	−0.956145	−0.478073	+	0.878320i	$0.658664\pi$
$614$	70.9923	2.86502
$615$	6.40844	0.258413
$616$	−35.5910	−1.43400
$617$	−48.5551	−1.95475	−0.977377	−	0.211503i	$-0.932164\pi$
$617$	−48.5551	−1.95475	−0.977377	+	0.211503i	$0.932164\pi$
$618$	39.6825	1.59626
$619$	24.2760	0.975735	0.487868	−	0.872918i	$-0.337775\pi$
$619$	24.2760	0.975735	0.487868	+	0.872918i	$0.337775\pi$
$620$	15.1501	0.608443
$621$	0	0
$622$	2.66744	0.106954
$623$	−48.8147	−1.95572
$624$	6.84451	0.274000
$625$	1.00000	0.0400000
$626$	−4.94571	−0.197671
$627$	19.6483	0.784678
$628$	−7.90561	−0.315468
$629$	2.62845	0.104803
$630$	−6.56754	−0.261657
$631$	26.1596	1.04140	0.520698	−	0.853741i	$-0.325672\pi$
$631$	26.1596	1.04140	0.520698	+	0.853741i	$0.325672\pi$
$632$	−20.4574	−0.813752
$633$	1.79135	0.0711997
$634$	11.6331	0.462007
$635$	−0.818786	−0.0324925
$636$	24.4313	0.968762
$637$	−8.11569	−0.321555
$638$	103.298	4.08960
$639$	−11.4088	−0.451326
$640$	−13.4945	−0.533418
$641$	−3.04101	−0.120113	−0.0600564	−	0.998195i	$-0.519128\pi$
$641$	−3.04101	−0.120113	−0.0600564	+	0.998195i	$0.519128\pi$
$642$	36.3482	1.43455
$643$	−4.25352	−0.167742	−0.0838712	−	0.996477i	$-0.526728\pi$
$643$	−4.25352	−0.167742	−0.0838712	+	0.996477i	$0.526728\pi$
$644$	0	0
$645$	−1.19671	−0.0471204
$646$	26.6326	1.04785
$647$	−36.2799	−1.42631	−0.713156	−	0.701006i	$-0.752735\pi$
$647$	−36.2799	−1.42631	−0.713156	+	0.701006i	$0.752735\pi$
$648$	1.85042	0.0726912
$649$	−34.5150	−1.35483
$650$	−9.34978	−0.366728
$651$	−15.9176	−0.623859
$652$	30.2036	1.18286
$653$	−33.2942	−1.30290	−0.651451	−	0.758691i	$-0.725839\pi$
$653$	−33.2942	−1.30290	−0.651451	+	0.758691i	$0.725839\pi$
$654$	−3.40886	−0.133297
$655$	15.5034	0.605767
$656$	−10.3220	−0.403005
$657$	−13.1973	−0.514877
$658$	51.9744	2.02617
$659$	49.1934	1.91630	0.958151	−	0.286262i	$-0.0924128\pi$
$659$	49.1934	1.91630	0.958151	+	0.286262i	$0.0924128\pi$
$660$	18.3066	0.712585
$661$	7.92555	0.308268	0.154134	−	0.988050i	$-0.450741\pi$
$661$	7.92555	0.308268	0.154134	+	0.988050i	$0.450741\pi$
$662$	43.0080	1.67155
$663$	−16.8690	−0.655138
$664$	−22.4904	−0.872796
$665$	−9.10173	−0.352950
$666$	1.45684	0.0564513
$667$	0	0
$668$	−19.6458	−0.760118
$669$	−7.94401	−0.307133
$670$	16.2048	0.626047
$671$	11.1200	0.429281
$672$	21.6249	0.834200
$673$	15.5045	0.597655	0.298828	−	0.954307i	$-0.403404\pi$
$673$	15.5045	0.597655	0.298828	+	0.954307i	$0.403404\pi$
$674$	−44.9875	−1.73286
$675$	1.00000	0.0384900
$676$	14.3695	0.552672
$677$	29.4723	1.13271	0.566356	−	0.824161i	$-0.308353\pi$
$677$	29.4723	1.13271	0.566356	+	0.824161i	$0.308353\pi$
$678$	8.60138	0.330334
$679$	−27.0923	−1.03971
$680$	7.34558	0.281690
$681$	17.2522	0.661104
$682$	75.6043	2.89504
$683$	−7.12997	−0.272821	−0.136410	−	0.990652i	$-0.543557\pi$
$683$	−7.12997	−0.272821	−0.136410	+	0.990652i	$0.543557\pi$
$684$	8.66288	0.331234
$685$	0.224833	0.00859043
$686$	33.4299	1.27636
$687$	−9.06521	−0.345859
$688$	1.92752	0.0734859
$689$	−36.5432	−1.39218
$690$	0	0
$691$	−44.3599	−1.68753	−0.843766	−	0.536712i	$-0.819666\pi$
$691$	−44.3599	−1.68753	−0.843766	+	0.536712i	$0.819666\pi$
$692$	−45.6087	−1.73378
$693$	−19.2340	−0.730640
$694$	−56.8578	−2.15829
$695$	13.1888	0.500278
$696$	13.4821	0.511037
$697$	25.4395	0.963591
$698$	27.3858	1.03657
$699$	−12.6066	−0.476827
$700$	−8.48022	−0.320522
$701$	43.4065	1.63944	0.819721	−	0.572763i	$-0.194129\pi$
$701$	43.4065	1.63944	0.819721	+	0.572763i	$0.194129\pi$
$702$	−9.34978	−0.352885
$703$	2.01898	0.0761474
$704$	−81.9552	−3.08880
$705$	−7.91384	−0.298052
$706$	−80.7451	−3.03888
$707$	−49.7635	−1.87155
$708$	−15.2176	−0.571911
$709$	45.3305	1.70242	0.851211	−	0.524824i	$-0.175869\pi$
$709$	45.3305	1.70242	0.851211	+	0.524824i	$0.175869\pi$
$710$	−25.1020	−0.942062
$711$	−11.0556	−0.414616
$712$	30.2612	1.13408
$713$	0	0
$714$	−26.0711	−0.975685
$715$	−27.3822	−1.02404
$716$	2.27793	0.0851301
$717$	−24.5752	−0.917778
$718$	0.690081	0.0257536
$719$	8.42194	0.314085	0.157043	−	0.987592i	$-0.449804\pi$
$719$	8.42194	0.314085	0.157043	+	0.987592i	$0.449804\pi$
$720$	−1.61068	−0.0600265
$721$	−53.8351	−2.00492
$722$	−21.3471	−0.794457
$723$	−8.03493	−0.298822
$724$	−3.18301	−0.118295
$725$	7.28597	0.270594
$726$	67.1539	2.49232
$727$	29.9170	1.10956	0.554780	−	0.831997i	$-0.312802\pi$
$727$	29.9170	1.10956	0.554780	+	0.831997i	$0.312802\pi$
$728$	23.4713	0.869904
$729$	1.00000	0.0370370
$730$	−29.0372	−1.07471
$731$	−4.75056	−0.175706
$732$	4.90276	0.181211
$733$	0.483801	0.0178696	0.00893480	−	0.999960i	$-0.497156\pi$
$733$	0.483801	0.0178696	0.00893480	+	0.999960i	$0.497156\pi$
$734$	−29.2477	−1.07955
$735$	1.90982	0.0704447
$736$	0	0
$737$	47.4583	1.74815
$738$	14.1001	0.519030
$739$	−43.3670	−1.59528	−0.797641	−	0.603133i	$-0.793919\pi$
$739$	−43.3670	−1.59528	−0.797641	+	0.603133i	$0.793919\pi$
$740$	1.88112	0.0691513
$741$	−12.9575	−0.476007
$742$	−56.4775	−2.07335
$743$	19.2658	0.706795	0.353398	−	0.935473i	$-0.385026\pi$
$743$	19.2658	0.706795	0.353398	+	0.935473i	$0.385026\pi$
$744$	9.86761	0.361764
$745$	−1.82024	−0.0666885
$746$	−69.0819	−2.52927
$747$	−12.1542	−0.444700
$748$	72.6716	2.65714
$749$	−49.3116	−1.80181
$750$	2.20023	0.0803410
$751$	13.1407	0.479509	0.239755	−	0.970834i	$-0.422933\pi$
$751$	13.1407	0.479509	0.239755	+	0.970834i	$0.422933\pi$
$752$	12.7467	0.464823
$753$	−27.4420	−1.00004
$754$	−68.1222	−2.48087
$755$	−11.2010	−0.407647
$756$	−8.48022	−0.308423
$757$	−9.68966	−0.352177	−0.176088	−	0.984374i	$-0.556344\pi$
$757$	−9.68966	−0.352177	−0.176088	+	0.984374i	$0.556344\pi$
$758$	−51.3711	−1.86588
$759$	0	0
$760$	5.64234	0.204669
$761$	−11.8792	−0.430622	−0.215311	−	0.976546i	$-0.569077\pi$
$761$	−11.8792	−0.430622	−0.215311	+	0.976546i	$0.569077\pi$
$762$	−1.80152	−0.0652621
$763$	4.62462	0.167422
$764$	−56.6330	−2.04891
$765$	3.96969	0.143524
$766$	−10.7762	−0.389359
$767$	22.7617	0.821879
$768$	−4.25379	−0.153496
$769$	−9.11032	−0.328526	−0.164263	−	0.986417i	$-0.552525\pi$
$769$	−9.11032	−0.328526	−0.164263	+	0.986417i	$0.552525\pi$
$770$	−42.3193	−1.52508
$771$	−13.7118	−0.493819
$772$	56.3333	2.02748
$773$	6.31734	0.227219	0.113609	−	0.993525i	$-0.463759\pi$
$773$	6.31734	0.227219	0.113609	+	0.993525i	$0.463759\pi$
$774$	−2.63304	−0.0946425
$775$	5.33265	0.191554
$776$	16.7950	0.602906
$777$	−1.97641	−0.0709034
$778$	−66.7392	−2.39272
$779$	19.5408	0.700122
$780$	−12.0727	−0.432274
$781$	−73.5151	−2.63058
$782$	0	0
$783$	7.28597	0.260379
$784$	−3.07611	−0.109861
$785$	−2.78268	−0.0993180
$786$	34.1110	1.21670
$787$	14.5381	0.518226	0.259113	−	0.965847i	$-0.416570\pi$
$787$	14.5381	0.518226	0.259113	+	0.965847i	$0.416570\pi$
$788$	−23.0050	−0.819520
$789$	−19.9430	−0.709991
$790$	−24.3248	−0.865437
$791$	−11.6690	−0.414903
$792$	11.9235	0.423684
$793$	−7.33332	−0.260414
$794$	−47.8611	−1.69853
$795$	8.59949	0.304993
$796$	5.13443	0.181985
$797$	42.6149	1.50950	0.754748	−	0.656015i	$-0.227759\pi$
$797$	42.6149	1.50950	0.754748	+	0.656015i	$0.227759\pi$
$798$	−20.0259	−0.708909
$799$	−31.4155	−1.11140
$800$	−7.24470	−0.256139
$801$	16.3537	0.577830
$802$	61.7718	2.18124
$803$	−85.0398	−3.00099
$804$	20.9242	0.737940
$805$	0	0
$806$	−49.8591	−1.75621
$807$	−1.51198	−0.0532243
$808$	30.8493	1.08528
$809$	−43.0345	−1.51301	−0.756506	−	0.653987i	$-0.773095\pi$
$809$	−43.0345	−1.51301	−0.756506	+	0.653987i	$0.773095\pi$
$810$	2.20023	0.0773082
$811$	39.3273	1.38097	0.690484	−	0.723348i	$-0.257398\pi$
$811$	39.3273	1.38097	0.690484	+	0.723348i	$0.257398\pi$
$812$	−61.7867	−2.16829
$813$	5.07064	0.177835
$814$	9.38743	0.329029
$815$	10.6313	0.372397
$816$	−6.39390	−0.223831
$817$	−3.64904	−0.127664
$818$	3.94895	0.138072
$819$	12.6843	0.443227
$820$	18.2065	0.635797
$821$	53.6986	1.87409	0.937046	−	0.349205i	$-0.113548\pi$
$821$	53.6986	1.87409	0.937046	+	0.349205i	$0.113548\pi$
$822$	0.494684	0.0172541
$823$	−34.1992	−1.19211	−0.596055	−	0.802944i	$-0.703266\pi$
$823$	−34.1992	−1.19211	−0.596055	+	0.802944i	$0.703266\pi$
$824$	33.3734	1.16262
$825$	6.44370	0.224341
$826$	35.1783	1.22401
$827$	28.0588	0.975701	0.487850	−	0.872927i	$-0.337781\pi$
$827$	28.0588	0.975701	0.487850	+	0.872927i	$0.337781\pi$
$828$	0	0
$829$	−1.79519	−0.0623494	−0.0311747	−	0.999514i	$-0.509925\pi$
$829$	−1.79519	−0.0623494	−0.0311747	+	0.999514i	$0.509925\pi$
$830$	−26.7421	−0.928232
$831$	20.1372	0.698553
$832$	54.0473	1.87375
$833$	7.58138	0.262679
$834$	29.0183	1.00482
$835$	−6.91507	−0.239306
$836$	55.8211	1.93061
$837$	5.33265	0.184323
$838$	41.2362	1.42448
$839$	31.3681	1.08295	0.541473	−	0.840718i	$-0.317867\pi$
$839$	31.3681	1.08295	0.541473	+	0.840718i	$0.317867\pi$
$840$	−5.52337	−0.190574
$841$	24.0854	0.830532
$842$	−22.1799	−0.764371
$843$	−21.2356	−0.731394
$844$	5.08924	0.175179
$845$	5.05787	0.173996
$846$	−17.4123	−0.598646
$847$	−91.1041	−3.13037
$848$	−13.8510	−0.475646
$849$	−13.0446	−0.447688
$850$	8.73422	0.299581
$851$	0	0
$852$	−32.4126	−1.11044
$853$	24.9888	0.855600	0.427800	−	0.903874i	$-0.359289\pi$
$853$	24.9888	0.855600	0.427800	+	0.903874i	$0.359289\pi$
$854$	−11.3337	−0.387830
$855$	3.04923	0.104281
$856$	30.5692	1.04483
$857$	18.5698	0.634334	0.317167	−	0.948370i	$-0.397268\pi$
$857$	18.5698	0.634334	0.317167	+	0.948370i	$0.397268\pi$
$858$	−60.2472	−2.05681
$859$	−42.6346	−1.45467	−0.727337	−	0.686280i	$-0.759242\pi$
$859$	−42.6346	−1.45467	−0.727337	+	0.686280i	$0.759242\pi$
$860$	−3.39986	−0.115934
$861$	−19.1288	−0.651907
$862$	20.8330	0.709576
$863$	−30.9965	−1.05513	−0.527567	−	0.849514i	$-0.676896\pi$
$863$	−30.9965	−1.05513	−0.527567	+	0.849514i	$0.676896\pi$
$864$	−7.24470	−0.246470
$865$	−16.0537	−0.545842
$866$	12.9558	0.440257
$867$	−1.24158	−0.0421663
$868$	−45.2220	−1.53494
$869$	−71.2388	−2.41661
$870$	16.0308	0.543496
$871$	−31.2975	−1.06047
$872$	−2.86689	−0.0970852
$873$	9.07635	0.307188
$874$	0	0
$875$	−2.98493	−0.100909
$876$	−37.4938	−1.26680
$877$	6.83731	0.230880	0.115440	−	0.993314i	$-0.463172\pi$
$877$	6.83731	0.230880	0.115440	+	0.993314i	$0.463172\pi$
$878$	15.5724	0.525543
$879$	−3.29241	−0.111050
$880$	−10.3787	−0.349867
$881$	0.857708	0.0288969	0.0144485	−	0.999896i	$-0.495401\pi$
$881$	0.857708	0.0288969	0.0144485	+	0.999896i	$0.495401\pi$
$882$	4.20204	0.141490
$883$	−14.2301	−0.478882	−0.239441	−	0.970911i	$-0.576964\pi$
$883$	−14.2301	−0.478882	−0.239441	+	0.970911i	$0.576964\pi$
$884$	−47.9250	−1.61189
$885$	−5.35639	−0.180053
$886$	−13.2713	−0.445858
$887$	5.41750	0.181902	0.0909509	−	0.995855i	$-0.471009\pi$
$887$	5.41750	0.181902	0.0909509	+	0.995855i	$0.471009\pi$
$888$	1.22522	0.0411156
$889$	2.44402	0.0819699
$890$	35.9819	1.20612
$891$	6.44370	0.215872
$892$	−22.5690	−0.755667
$893$	−24.1311	−0.807516
$894$	−4.00495	−0.133945
$895$	0.801801	0.0268013
$896$	40.2803	1.34567
$897$	0	0
$898$	−31.6730	−1.05694
$899$	38.8535	1.29584
$900$	2.84101	0.0947004
$901$	34.1373	1.13728
$902$	90.8566	3.02519
$903$	3.57210	0.118872
$904$	7.23385	0.240594
$905$	−1.12038	−0.0372426
$906$	−24.6448	−0.818769
$907$	29.4442	0.977677	0.488839	−	0.872374i	$-0.337421\pi$
$907$	29.4442	0.977677	0.488839	+	0.872374i	$0.337421\pi$
$908$	49.0136	1.62657
$909$	16.6716	0.552961
$910$	27.9085	0.925156
$911$	−21.6834	−0.718403	−0.359202	−	0.933260i	$-0.616951\pi$
$911$	−21.6834	−0.718403	−0.359202	+	0.933260i	$0.616951\pi$
$912$	−4.91133	−0.162630
$913$	−78.3183	−2.59196
$914$	−36.0167	−1.19133
$915$	1.72571	0.0570502
$916$	−25.7543	−0.850948
$917$	−46.2766	−1.52819
$918$	8.73422	0.288272
$919$	−20.8418	−0.687509	−0.343755	−	0.939060i	$-0.611699\pi$
$919$	−20.8418	−0.687509	−0.343755	+	0.939060i	$0.611699\pi$
$920$	0	0
$921$	32.2659	1.06320
$922$	20.5887	0.678054
$923$	48.4813	1.59578
$924$	−54.6441	−1.79766
$925$	0.662130	0.0217707
$926$	−39.7010	−1.30466
$927$	18.0356	0.592367
$928$	−52.7847	−1.73274
$929$	34.2351	1.12322	0.561608	−	0.827404i	$-0.310183\pi$
$929$	34.2351	1.12322	0.561608	+	0.827404i	$0.310183\pi$
$930$	11.7330	0.384742
$931$	5.82347	0.190857
$932$	−35.8156	−1.17318
$933$	1.21234	0.0396904
$934$	−82.0294	−2.68408
$935$	25.5795	0.836539
$936$	−7.86326	−0.257019
$937$	24.8731	0.812569	0.406285	−	0.913747i	$-0.366824\pi$
$937$	24.8731	0.812569	0.406285	+	0.913747i	$0.366824\pi$
$938$	−48.3703	−1.57935
$939$	−2.24782	−0.0733548
$940$	−22.4833	−0.733324
$941$	33.9028	1.10520	0.552601	−	0.833446i	$-0.313635\pi$
$941$	33.9028	1.10520	0.552601	+	0.833446i	$0.313635\pi$
$942$	−6.12253	−0.199483
$943$	0	0
$944$	8.62743	0.280799
$945$	−2.98493	−0.0970998
$946$	−16.9665	−0.551629
$947$	40.9684	1.33129	0.665647	−	0.746266i	$-0.268155\pi$
$947$	40.9684	1.33129	0.665647	+	0.746266i	$0.268155\pi$
$948$	−31.4090	−1.02012
$949$	56.0815	1.82048
$950$	6.70900	0.217669
$951$	5.28720	0.171449
$952$	−21.9260	−0.710627
$953$	−9.35690	−0.303100	−0.151550	−	0.988450i	$-0.548426\pi$
$953$	−9.35690	−0.303100	−0.151550	+	0.988450i	$0.548426\pi$
$954$	18.9209	0.612586
$955$	−19.9341	−0.645052
$956$	−69.8185	−2.25809
$957$	46.9487	1.51763
$958$	41.2234	1.33187
$959$	−0.671112	−0.0216713
$960$	−12.7186	−0.410492
$961$	−2.56289	−0.0826740
$962$	−6.19077	−0.199598
$963$	16.5202	0.532355
$964$	−22.8273	−0.735219
$965$	19.8286	0.638306
$966$	0	0
$967$	11.2493	0.361752	0.180876	−	0.983506i	$-0.442107\pi$
$967$	11.2493	0.361752	0.180876	+	0.983506i	$0.442107\pi$
$968$	56.4772	1.81525
$969$	12.1045	0.388852
$970$	19.9701	0.641200
$971$	−55.9483	−1.79547	−0.897734	−	0.440539i	$-0.854787\pi$
$971$	−55.9483	−1.79547	−0.897734	+	0.440539i	$0.854787\pi$
$972$	2.84101	0.0911255
$973$	−39.3675	−1.26207
$974$	−65.9976	−2.11470
$975$	−4.24946	−0.136091
$976$	−2.77956	−0.0889717
$977$	30.7772	0.984649	0.492324	−	0.870412i	$-0.336147\pi$
$977$	30.7772	0.984649	0.492324	+	0.870412i	$0.336147\pi$
$978$	23.3913	0.747970
$979$	105.378	3.36791
$980$	5.42582	0.173321
$981$	−1.54932	−0.0494660
$982$	6.02732	0.192339
$983$	26.1557	0.834239	0.417119	−	0.908852i	$-0.363040\pi$
$983$	26.1557	0.834239	0.417119	+	0.908852i	$0.363040\pi$
$984$	11.8583	0.378029
$985$	−8.09748	−0.258007
$986$	63.6373	2.02663
$987$	23.6223	0.751905
$988$	−36.8125	−1.17116
$989$	0	0
$990$	14.1776	0.450595
$991$	−22.8364	−0.725421	−0.362711	−	0.931902i	$-0.618149\pi$
$991$	−22.8364	−0.725421	−0.362711	+	0.931902i	$0.618149\pi$
$992$	−38.6334	−1.22661
$993$	19.5471	0.620307
$994$	74.9278	2.37657
$995$	1.80725	0.0572938
$996$	−34.5303	−1.09413
$997$	49.8349	1.57829	0.789144	−	0.614208i	$-0.210525\pi$
$997$	49.8349	1.57829	0.789144	+	0.614208i	$0.210525\pi$
$998$	63.7766	2.01881
$999$	0.662130	0.0209489

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bi.1.7	yes	8
23.22	odd	2		7935.2.a.bh.1.7	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7935.2.a.bh.1.7	✓	8	23.22	odd	2
7935.2.a.bi.1.7	yes	8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q+2.20023 q^{2} +1.00000 q^{3} +2.84101 q^{4} +1.00000 q^{5} +2.20023 q^{6} -2.98493 q^{7} +1.85042 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.20023 q^{2} +1.00000 q^{3} +2.84101 q^{4} +1.00000 q^{5} +2.20023 q^{6} -2.98493 q^{7} +1.85042 q^{8} +1.00000 q^{9} +2.20023 q^{10} +6.44370 q^{11} +2.84101 q^{12} -4.24946 q^{13} -6.56754 q^{14} +1.00000 q^{15} -1.61068 q^{16} +3.96969 q^{17} +2.20023 q^{18} +3.04923 q^{19} +2.84101 q^{20} -2.98493 q^{21} +14.1776 q^{22} +1.85042 q^{24} +1.00000 q^{25} -9.34978 q^{26} +1.00000 q^{27} -8.48022 q^{28} +7.28597 q^{29} +2.20023 q^{30} +5.33265 q^{31} -7.24470 q^{32} +6.44370 q^{33} +8.73422 q^{34} -2.98493 q^{35} +2.84101 q^{36} +0.662130 q^{37} +6.70900 q^{38} -4.24946 q^{39} +1.85042 q^{40} +6.40844 q^{41} -6.56754 q^{42} -1.19671 q^{43} +18.3066 q^{44} +1.00000 q^{45} -7.91384 q^{47} -1.61068 q^{48} +1.90982 q^{49} +2.20023 q^{50} +3.96969 q^{51} -12.0727 q^{52} +8.59949 q^{53} +2.20023 q^{54} +6.44370 q^{55} -5.52337 q^{56} +3.04923 q^{57} +16.0308 q^{58} -5.35639 q^{59} +2.84101 q^{60} +1.72571 q^{61} +11.7330 q^{62} -2.98493 q^{63} -12.7186 q^{64} -4.24946 q^{65} +14.1776 q^{66} +7.36506 q^{67} +11.2779 q^{68} -6.56754 q^{70} -11.4088 q^{71} +1.85042 q^{72} -13.1973 q^{73} +1.45684 q^{74} +1.00000 q^{75} +8.66288 q^{76} -19.2340 q^{77} -9.34978 q^{78} -11.0556 q^{79} -1.61068 q^{80} +1.00000 q^{81} +14.1001 q^{82} -12.1542 q^{83} -8.48022 q^{84} +3.96969 q^{85} -2.63304 q^{86} +7.28597 q^{87} +11.9235 q^{88} +16.3537 q^{89} +2.20023 q^{90} +12.6843 q^{91} +5.33265 q^{93} -17.4123 q^{94} +3.04923 q^{95} -7.24470 q^{96} +9.07635 q^{97} +4.20204 q^{98} +6.44370 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} + 8 q^{4} + 8 q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^3 + 8 * q^4 + 8 * q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9	\( 8 q + 8 q^{3} + 8 q^{4} + 8 q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9} + 12 q^{11} + 8 q^{12} + 4 q^{13} + 8 q^{15} + 20 q^{17} + 4 q^{19} + 8 q^{20} + 6 q^{21} + 14 q^{22} + 6 q^{24} + 8 q^{25} - 22 q^{26} + 8 q^{27} - 8 q^{28} + 2 q^{31} + 12 q^{32} + 12 q^{33} + 8 q^{34} + 6 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{38} + 4 q^{39} + 6 q^{40} + 28 q^{41} + 4 q^{43} + 54 q^{44} + 8 q^{45} - 12 q^{47} + 14 q^{49} + 20 q^{51} - 22 q^{52} + 6 q^{53} + 12 q^{55} - 24 q^{56} + 4 q^{57} + 32 q^{58} + 2 q^{59} + 8 q^{60} + 32 q^{61} - 24 q^{62} + 6 q^{63} - 8 q^{64} + 4 q^{65} + 14 q^{66} + 32 q^{67} + 34 q^{68} + 2 q^{71} + 6 q^{72} - 2 q^{73} + 6 q^{74} + 8 q^{75} + 24 q^{76} - 30 q^{77} - 22 q^{78} - 36 q^{79} + 8 q^{81} + 16 q^{82} + 10 q^{83} - 8 q^{84} + 20 q^{85} + 50 q^{86} + 6 q^{88} + 42 q^{89} + 4 q^{91} + 2 q^{93} - 40 q^{94} + 4 q^{95} + 12 q^{96} + 16 q^{97} + 12 q^{99}+O(q^{100}) \) 8 * q + 8 * q^3 + 8 * q^4 + 8 * q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9 + 12 * q^11 + 8 * q^12 + 4 * q^13 + 8 * q^15 + 20 * q^17 + 4 * q^19 + 8 * q^20 + 6 * q^21 + 14 * q^22 + 6 * q^24 + 8 * q^25 - 22 * q^26 + 8 * q^27 - 8 * q^28 + 2 * q^31 + 12 * q^32 + 12 * q^33 + 8 * q^34 + 6 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^38 + 4 * q^39 + 6 * q^40 + 28 * q^41 + 4 * q^43 + 54 * q^44 + 8 * q^45 - 12 * q^47 + 14 * q^49 + 20 * q^51 - 22 * q^52 + 6 * q^53 + 12 * q^55 - 24 * q^56 + 4 * q^57 + 32 * q^58 + 2 * q^59 + 8 * q^60 + 32 * q^61 - 24 * q^62 + 6 * q^63 - 8 * q^64 + 4 * q^65 + 14 * q^66 + 32 * q^67 + 34 * q^68 + 2 * q^71 + 6 * q^72 - 2 * q^73 + 6 * q^74 + 8 * q^75 + 24 * q^76 - 30 * q^77 - 22 * q^78 - 36 * q^79 + 8 * q^81 + 16 * q^82 + 10 * q^83 - 8 * q^84 + 20 * q^85 + 50 * q^86 + 6 * q^88 + 42 * q^89 + 4 * q^91 + 2 * q^93 - 40 * q^94 + 4 * q^95 + 12 * q^96 + 16 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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