LMFDB - Embedded newform 7935.2.a.bq.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7935,2,Mod(1,7935)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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

Newform invariants

comment:select newform

sage:traces = [15,0,-15,12,15,0,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.3612940039$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 21x^{13} + 172x^{11} - 696x^{9} + 1466x^{7} - 1583x^{5} + 803x^{3} - 11x^{2} - 143x + 11 $ x^15 - 21x^13 + 172x^11 - 696x^9 + 1466x^7 - 1583x^5 + 803x^3 - 11x^2 - 143x + 11
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 345)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.12733$ 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)

$f(q)$	$=$	\(q-2.12733 q^{2} -1.00000 q^{3} +2.52552 q^{4} +1.00000 q^{5} +2.12733 q^{6} -2.46529 q^{7} -1.11794 q^{8} +1.00000 q^{9} -2.12733 q^{10} -2.49782 q^{11} -2.52552 q^{12} +0.527315 q^{13} +5.24447 q^{14} -1.00000 q^{15} -2.67280 q^{16} -4.57109 q^{17} -2.12733 q^{18} -5.03906 q^{19} +2.52552 q^{20} +2.46529 q^{21} +5.31368 q^{22} +1.11794 q^{24} +1.00000 q^{25} -1.12177 q^{26} -1.00000 q^{27} -6.22613 q^{28} +1.30386 q^{29} +2.12733 q^{30} -1.05220 q^{31} +7.92181 q^{32} +2.49782 q^{33} +9.72420 q^{34} -2.46529 q^{35} +2.52552 q^{36} +4.73198 q^{37} +10.7197 q^{38} -0.527315 q^{39} -1.11794 q^{40} -2.46869 q^{41} -5.24447 q^{42} +12.2431 q^{43} -6.30828 q^{44} +1.00000 q^{45} +6.76385 q^{47} +2.67280 q^{48} -0.922350 q^{49} -2.12733 q^{50} +4.57109 q^{51} +1.33174 q^{52} +2.41092 q^{53} +2.12733 q^{54} -2.49782 q^{55} +2.75605 q^{56} +5.03906 q^{57} -2.77374 q^{58} +1.49746 q^{59} -2.52552 q^{60} +6.45669 q^{61} +2.23838 q^{62} -2.46529 q^{63} -11.5067 q^{64} +0.527315 q^{65} -5.31368 q^{66} +8.91145 q^{67} -11.5444 q^{68} +5.24447 q^{70} +2.83000 q^{71} -1.11794 q^{72} -14.8821 q^{73} -10.0665 q^{74} -1.00000 q^{75} -12.7262 q^{76} +6.15785 q^{77} +1.12177 q^{78} +15.2049 q^{79} -2.67280 q^{80} +1.00000 q^{81} +5.25171 q^{82} +0.703225 q^{83} +6.22613 q^{84} -4.57109 q^{85} -26.0450 q^{86} -1.30386 q^{87} +2.79242 q^{88} +7.10193 q^{89} -2.12733 q^{90} -1.29998 q^{91} +1.05220 q^{93} -14.3889 q^{94} -5.03906 q^{95} -7.92181 q^{96} -3.32670 q^{97} +1.96214 q^{98} -2.49782 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{3} + 12 q^{4} + 15 q^{5} + 5 q^{7} + 15 q^{9} - 13 q^{11} - 12 q^{12} - 24 q^{13} - 15 q^{14} - 15 q^{15} + 2 q^{16} - 2 q^{17} - 13 q^{19} + 12 q^{20} - 5 q^{21} + 9 q^{22} + 15 q^{25} - 9 q^{26}+ \cdots - 13 q^{99}+O(q^{100}) $ 15 * q - 15 * q^3 + 12 * q^4 + 15 * q^5 + 5 * q^7 + 15 * q^9 - 13 * q^11 - 12 * q^12 - 24 * q^13 - 15 * q^14 - 15 * q^15 + 2 * q^16 - 2 * q^17 - 13 * q^19 + 12 * q^20 - 5 * q^21 + 9 * q^22 + 15 * q^25 - 9 * q^26 - 15 * q^27 - q^28 - 3 * q^29 - 22 * q^31 + 13 * q^33 - q^34 + 5 * q^35 + 12 * q^36 + 6 * q^37 + 17 * q^38 + 24 * q^39 - 20 * q^41 + 15 * q^42 + 4 * q^43 + 18 * q^44 + 15 * q^45 + 7 * q^47 - 2 * q^48 - 10 * q^49 + 2 * q^51 - 55 * q^52 - 4 * q^53 - 13 * q^55 - 25 * q^56 + 13 * q^57 + 2 * q^58 + 9 * q^59 - 12 * q^60 - 13 * q^61 - 7 * q^62 + 5 * q^63 - 26 * q^64 - 24 * q^65 - 9 * q^66 + 32 * q^67 - 27 * q^68 - 15 * q^70 + 14 * q^71 - 43 * q^73 + 11 * q^74 - 15 * q^75 - 88 * q^76 - 21 * q^77 + 9 * q^78 - 33 * q^79 + 2 * q^80 + 15 * q^81 - 35 * q^82 + 12 * q^83 + q^84 - 2 * q^85 - 77 * q^86 + 3 * q^87 + 37 * q^88 - 29 * q^89 - 20 * q^91 + 22 * q^93 - 20 * q^94 - 13 * q^95 - 18 * q^97 - 19 * q^98 - 13 * q^99

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 $

$2$	−2.12733	−1.50425	−0.752123	−	0.659022i	$-0.770970\pi$
$2$	−2.12733	−1.50425	−0.752123	+	0.659022i	$0.770970\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.52552	1.26276
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.12733	0.868477
$7$	−2.46529	−0.931792	−0.465896	−	0.884840i	$-0.654268\pi$
$7$	−2.46529	−0.931792	−0.465896	+	0.884840i	$0.654268\pi$
$8$	−1.11794	−0.395253
$9$	1.00000	0.333333
$10$	−2.12733	−0.672720
$11$	−2.49782	−0.753121	−0.376561	−	0.926392i	$-0.622893\pi$
$11$	−2.49782	−0.753121	−0.376561	+	0.926392i	$0.622893\pi$
$12$	−2.52552	−0.729054
$13$	0.527315	0.146251	0.0731254	−	0.997323i	$-0.476703\pi$
$13$	0.527315	0.146251	0.0731254	+	0.997323i	$0.476703\pi$
$14$	5.24447	1.40164
$15$	−1.00000	−0.258199
$16$	−2.67280	−0.668201
$17$	−4.57109	−1.10865	−0.554326	−	0.832300i	$-0.687024\pi$
$17$	−4.57109	−1.10865	−0.554326	+	0.832300i	$0.687024\pi$
$18$	−2.12733	−0.501416
$19$	−5.03906	−1.15604	−0.578020	−	0.816023i	$-0.696174\pi$
$19$	−5.03906	−1.15604	−0.578020	+	0.816023i	$0.696174\pi$
$20$	2.52552	0.564722
$21$	2.46529	0.537970
$22$	5.31368	1.13288
$23$	0	0
$23$	0	0
$24$	1.11794	0.228199
$25$	1.00000	0.200000
$26$	−1.12177	−0.219997
$27$	−1.00000	−0.192450
$28$	−6.22613	−1.17663
$29$	1.30386	0.242122	0.121061	−	0.992645i	$-0.461370\pi$
$29$	1.30386	0.242122	0.121061	+	0.992645i	$0.461370\pi$
$30$	2.12733	0.388395
$31$	−1.05220	−0.188981	−0.0944905	−	0.995526i	$-0.530122\pi$
$31$	−1.05220	−0.188981	−0.0944905	+	0.995526i	$0.530122\pi$
$32$	7.92181	1.40039
$33$	2.49782	0.434815
$34$	9.72420	1.66769
$35$	−2.46529	−0.416710
$36$	2.52552	0.420919
$37$	4.73198	0.777932	0.388966	−	0.921252i	$-0.372832\pi$
$37$	4.73198	0.777932	0.388966	+	0.921252i	$0.372832\pi$
$38$	10.7197	1.73897
$39$	−0.527315	−0.0844380
$40$	−1.11794	−0.176762
$41$	−2.46869	−0.385545	−0.192772	−	0.981243i	$-0.561748\pi$
$41$	−2.46869	−0.385545	−0.192772	+	0.981243i	$0.561748\pi$
$42$	−5.24447	−0.809240
$43$	12.2431	1.86705	0.933526	−	0.358509i	$-0.116715\pi$
$43$	12.2431	1.86705	0.933526	+	0.358509i	$0.116715\pi$
$44$	−6.30828	−0.951009
$45$	1.00000	0.149071
$46$	0	0
$47$	6.76385	0.986608	0.493304	−	0.869857i	$-0.335789\pi$
$47$	6.76385	0.986608	0.493304	+	0.869857i	$0.335789\pi$
$48$	2.67280	0.385786
$49$	−0.922350	−0.131764
$50$	−2.12733	−0.300849
$51$	4.57109	0.640081
$52$	1.33174	0.184679
$53$	2.41092	0.331166	0.165583	−	0.986196i	$-0.447049\pi$
$53$	2.41092	0.331166	0.165583	+	0.986196i	$0.447049\pi$
$54$	2.12733	0.289492
$55$	−2.49782	−0.336806
$56$	2.75605	0.368293
$57$	5.03906	0.667439
$58$	−2.77374	−0.364210
$59$	1.49746	0.194953	0.0974764	−	0.995238i	$-0.468923\pi$
$59$	1.49746	0.194953	0.0974764	+	0.995238i	$0.468923\pi$
$60$	−2.52552	−0.326043
$61$	6.45669	0.826695	0.413347	−	0.910573i	$-0.364360\pi$
$61$	6.45669	0.826695	0.413347	+	0.910573i	$0.364360\pi$
$62$	2.23838	0.284274
$63$	−2.46529	−0.310597
$64$	−11.5067	−1.43833
$65$	0.527315	0.0654054
$66$	−5.31368	−0.654068
$67$	8.91145	1.08871	0.544354	−	0.838856i	$-0.316775\pi$
$67$	8.91145	1.08871	0.544354	+	0.838856i	$0.316775\pi$
$68$	−11.5444	−1.39996
$69$	0	0
$70$	5.24447	0.626834
$71$	2.83000	0.335859	0.167930	−	0.985799i	$-0.446292\pi$
$71$	2.83000	0.335859	0.167930	+	0.985799i	$0.446292\pi$
$72$	−1.11794	−0.131751
$73$	−14.8821	−1.74182	−0.870912	−	0.491440i	$-0.836471\pi$
$73$	−14.8821	−1.74182	−0.870912	+	0.491440i	$0.836471\pi$
$74$	−10.0665	−1.17020
$75$	−1.00000	−0.115470
$76$	−12.7262	−1.45980
$77$	6.15785	0.701752
$78$	1.12177	0.127016
$79$	15.2049	1.71068	0.855341	−	0.518066i	$-0.173348\pi$
$79$	15.2049	1.71068	0.855341	+	0.518066i	$0.173348\pi$
$80$	−2.67280	−0.298828
$81$	1.00000	0.111111
$82$	5.25171	0.579955
$83$	0.703225	0.0771889	0.0385945	−	0.999255i	$-0.487712\pi$
$83$	0.703225	0.0771889	0.0385945	+	0.999255i	$0.487712\pi$
$84$	6.22613	0.679326
$85$	−4.57109	−0.495804
$86$	−26.0450	−2.80851
$87$	−1.30386	−0.139789
$88$	2.79242	0.297673
$89$	7.10193	0.752803	0.376402	−	0.926457i	$-0.377161\pi$
$89$	7.10193	0.752803	0.376402	+	0.926457i	$0.377161\pi$
$90$	−2.12733	−0.224240
$91$	−1.29998	−0.136275
$92$	0	0
$93$	1.05220	0.109108
$94$	−14.3889	−1.48410
$95$	−5.03906	−0.516996
$96$	−7.92181	−0.808516
$97$	−3.32670	−0.337775	−0.168888	−	0.985635i	$-0.554018\pi$
$97$	−3.32670	−0.337775	−0.168888	+	0.985635i	$0.554018\pi$
$98$	1.96214	0.198206
$99$	−2.49782	−0.251040
$100$	2.52552	0.252552
$101$	−2.67750	−0.266421	−0.133210	−	0.991088i	$-0.542529\pi$
$101$	−2.67750	−0.266421	−0.133210	+	0.991088i	$0.542529\pi$
$102$	−9.72420	−0.962839
$103$	5.69796	0.561437	0.280719	−	0.959790i	$-0.409427\pi$
$103$	5.69796	0.561437	0.280719	+	0.959790i	$0.409427\pi$
$104$	−0.589508	−0.0578060
$105$	2.46529	0.240588
$106$	−5.12882	−0.498155
$107$	17.2402	1.66667	0.833335	−	0.552769i	$-0.186429\pi$
$107$	17.2402	1.66667	0.833335	+	0.552769i	$0.186429\pi$
$108$	−2.52552	−0.243018
$109$	−16.9758	−1.62599	−0.812995	−	0.582271i	$-0.802164\pi$
$109$	−16.9758	−1.62599	−0.812995	+	0.582271i	$0.802164\pi$
$110$	5.31368	0.506639
$111$	−4.73198	−0.449139
$112$	6.58923	0.622624
$113$	5.38102	0.506204	0.253102	−	0.967440i	$-0.418549\pi$
$113$	5.38102	0.506204	0.253102	+	0.967440i	$0.418549\pi$
$114$	−10.7197	−1.00399
$115$	0	0
$116$	3.29293	0.305741
$117$	0.527315	0.0487503
$118$	−3.18559	−0.293257
$119$	11.2691	1.03303
$120$	1.11794	0.102054
$121$	−4.76090	−0.432809
$122$	−13.7355	−1.24355
$123$	2.46869	0.222594
$124$	−2.65735	−0.238637
$125$	1.00000	0.0894427
$126$	5.24447	0.467215
$127$	−19.9557	−1.77078	−0.885390	−	0.464848i	$-0.846109\pi$
$127$	−19.9557	−1.77078	−0.885390	+	0.464848i	$0.846109\pi$
$128$	8.63481	0.763216
$129$	−12.2431	−1.07794
$130$	−1.12177	−0.0983858
$131$	−21.3624	−1.86644	−0.933220	−	0.359306i	$-0.883013\pi$
$131$	−21.3624	−1.86644	−0.933220	+	0.359306i	$0.883013\pi$
$132$	6.30828	0.549066
$133$	12.4227	1.07719
$134$	−18.9576	−1.63768
$135$	−1.00000	−0.0860663
$136$	5.11022	0.438198
$137$	11.7144	1.00083	0.500413	−	0.865787i	$-0.333182\pi$
$137$	11.7144	1.00083	0.500413	+	0.865787i	$0.333182\pi$
$138$	0	0
$139$	5.99314	0.508331	0.254166	−	0.967161i	$-0.418199\pi$
$139$	5.99314	0.508331	0.254166	+	0.967161i	$0.418199\pi$
$140$	−6.22613	−0.526204
$141$	−6.76385	−0.569619
$142$	−6.02033	−0.505215
$143$	−1.31714	−0.110145
$144$	−2.67280	−0.222734
$145$	1.30386	0.108280
$146$	31.6592	2.62013
$147$	0.922350	0.0760741
$148$	11.9507	0.982340
$149$	0.298095	0.0244209	0.0122104	−	0.999925i	$-0.496113\pi$
$149$	0.298095	0.0244209	0.0122104	+	0.999925i	$0.496113\pi$
$150$	2.12733	0.173695
$151$	−7.36031	−0.598974	−0.299487	−	0.954100i	$-0.596815\pi$
$151$	−7.36031	−0.598974	−0.299487	+	0.954100i	$0.596815\pi$
$152$	5.63338	0.456927
$153$	−4.57109	−0.369551
$154$	−13.0997	−1.05561
$155$	−1.05220	−0.0845149
$156$	−1.33174	−0.106625
$157$	14.3607	1.14611	0.573053	−	0.819518i	$-0.305759\pi$
$157$	14.3607	1.14611	0.573053	+	0.819518i	$0.305759\pi$
$158$	−32.3457	−2.57329
$159$	−2.41092	−0.191199
$160$	7.92181	0.626274
$161$	0	0
$162$	−2.12733	−0.167139
$163$	9.41408	0.737368	0.368684	−	0.929555i	$-0.379808\pi$
$163$	9.41408	0.737368	0.368684	+	0.929555i	$0.379808\pi$
$164$	−6.23472	−0.486850
$165$	2.49782	0.194455
$166$	−1.49599	−0.116111
$167$	20.1617	1.56016	0.780081	−	0.625679i	$-0.215178\pi$
$167$	20.1617	1.56016	0.780081	+	0.625679i	$0.215178\pi$
$168$	−2.75605	−0.212634
$169$	−12.7219	−0.978611
$170$	9.72420	0.745812
$171$	−5.03906	−0.385346
$172$	30.9201	2.35764
$173$	−11.9949	−0.911958	−0.455979	−	0.889991i	$-0.650711\pi$
$173$	−11.9949	−0.911958	−0.455979	+	0.889991i	$0.650711\pi$
$174$	2.77374	0.210277
$175$	−2.46529	−0.186358
$176$	6.67618	0.503236
$177$	−1.49746	−0.112556
$178$	−15.1081	−1.13240
$179$	4.08883	0.305613	0.152807	−	0.988256i	$-0.451169\pi$
$179$	4.08883	0.305613	0.152807	+	0.988256i	$0.451169\pi$
$180$	2.52552	0.188241
$181$	−15.6355	−1.16218	−0.581090	−	0.813839i	$-0.697374\pi$
$181$	−15.6355	−1.16218	−0.581090	+	0.813839i	$0.697374\pi$
$182$	2.76549	0.204992
$183$	−6.45669	−0.477292
$184$	0	0
$185$	4.73198	0.347902
$186$	−2.23838	−0.164126
$187$	11.4178	0.834949
$188$	17.0822	1.24585
$189$	2.46529	0.179323
$190$	10.7197	0.777690
$191$	22.2616	1.61079	0.805395	−	0.592738i	$-0.201953\pi$
$191$	22.2616	1.61079	0.805395	+	0.592738i	$0.201953\pi$
$192$	11.5067	0.830422
$193$	−4.76315	−0.342859	−0.171430	−	0.985196i	$-0.554839\pi$
$193$	−4.76315	−0.342859	−0.171430	+	0.985196i	$0.554839\pi$
$194$	7.07698	0.508097
$195$	−0.527315	−0.0377618
$196$	−2.32941	−0.166386
$197$	−13.7522	−0.979801	−0.489900	−	0.871778i	$-0.662967\pi$
$197$	−13.7522	−0.979801	−0.489900	+	0.871778i	$0.662967\pi$
$198$	5.31368	0.377627
$199$	−2.66387	−0.188836	−0.0944182	−	0.995533i	$-0.530099\pi$
$199$	−2.66387	−0.188836	−0.0944182	+	0.995533i	$0.530099\pi$
$200$	−1.11794	−0.0790505
$201$	−8.91145	−0.628565
$202$	5.69590	0.400762
$203$	−3.21440	−0.225607
$204$	11.5444	0.808267
$205$	−2.46869	−0.172421
$206$	−12.1214	−0.844540
$207$	0	0
$208$	−1.40941	−0.0977249
$209$	12.5867	0.870637
$210$	−5.24447	−0.361903
$211$	−1.70109	−0.117108	−0.0585539	−	0.998284i	$-0.518649\pi$
$211$	−1.70109	−0.117108	−0.0585539	+	0.998284i	$0.518649\pi$
$212$	6.08882	0.418182
$213$	−2.83000	−0.193908
$214$	−36.6754	−2.50708
$215$	12.2431	0.834971
$216$	1.11794	0.0760664
$217$	2.59398	0.176091
$218$	36.1131	2.44589
$219$	14.8821	1.00564
$220$	−6.30828	−0.425304
$221$	−2.41040	−0.162141
$222$	10.0665	0.675616
$223$	−25.3598	−1.69822	−0.849110	−	0.528216i	$-0.822861\pi$
$223$	−25.3598	−1.69822	−0.849110	+	0.528216i	$0.822861\pi$
$224$	−19.5295	−1.30487
$225$	1.00000	0.0666667
$226$	−11.4472	−0.761455
$227$	5.13230	0.340643	0.170321	−	0.985389i	$-0.445519\pi$
$227$	5.13230	0.340643	0.170321	+	0.985389i	$0.445519\pi$
$228$	12.7262	0.842814
$229$	−8.56535	−0.566014	−0.283007	−	0.959118i	$-0.591332\pi$
$229$	−8.56535	−0.566014	−0.283007	+	0.959118i	$0.591332\pi$
$230$	0	0
$231$	−6.15785	−0.405157
$232$	−1.45765	−0.0956991
$233$	−1.79157	−0.117370	−0.0586850	−	0.998277i	$-0.518691\pi$
$233$	−1.79157	−0.117370	−0.0586850	+	0.998277i	$0.518691\pi$
$234$	−1.12177	−0.0733324
$235$	6.76385	0.441225
$236$	3.78186	0.246178
$237$	−15.2049	−0.987663
$238$	−23.9730	−1.55394
$239$	4.62309	0.299043	0.149521	−	0.988759i	$-0.452227\pi$
$239$	4.62309	0.299043	0.149521	+	0.988759i	$0.452227\pi$
$240$	2.67280	0.172529
$241$	−21.1252	−1.36080	−0.680398	−	0.732843i	$-0.738193\pi$
$241$	−21.1252	−1.36080	−0.680398	+	0.732843i	$0.738193\pi$
$242$	10.1280	0.651051
$243$	−1.00000	−0.0641500
$244$	16.3065	1.04392
$245$	−0.922350	−0.0589267
$246$	−5.25171	−0.334837
$247$	−2.65717	−0.169072
$248$	1.17630	0.0746952
$249$	−0.703225	−0.0445651
$250$	−2.12733	−0.134544
$251$	−31.1876	−1.96854	−0.984272	−	0.176658i	$-0.943471\pi$
$251$	−31.1876	−1.96854	−0.984272	+	0.176658i	$0.943471\pi$
$252$	−6.22613	−0.392209
$253$	0	0
$254$	42.4522	2.66369
$255$	4.57109	0.286253
$256$	4.64428	0.290267
$257$	22.0231	1.37376	0.686880	−	0.726771i	$-0.258980\pi$
$257$	22.0231	1.37376	0.686880	+	0.726771i	$0.258980\pi$
$258$	26.0450	1.62149
$259$	−11.6657	−0.724871
$260$	1.33174	0.0825911
$261$	1.30386	0.0807072
$262$	45.4447	2.80759
$263$	23.4299	1.44475	0.722375	−	0.691502i	$-0.243051\pi$
$263$	23.4299	1.44475	0.722375	+	0.691502i	$0.243051\pi$
$264$	−2.79242	−0.171862
$265$	2.41092	0.148102
$266$	−26.4272	−1.62036
$267$	−7.10193	−0.434631
$268$	22.5060	1.37477
$269$	12.3997	0.756022	0.378011	−	0.925801i	$-0.376608\pi$
$269$	12.3997	0.756022	0.378011	+	0.925801i	$0.376608\pi$
$270$	2.12733	0.129465
$271$	25.3394	1.53926	0.769629	−	0.638491i	$-0.220441\pi$
$271$	25.3394	1.53926	0.769629	+	0.638491i	$0.220441\pi$
$272$	12.2176	0.740802
$273$	1.29998	0.0786786
$274$	−24.9203	−1.50549
$275$	−2.49782	−0.150624
$276$	0	0
$277$	−12.9940	−0.780736	−0.390368	−	0.920659i	$-0.627652\pi$
$277$	−12.9940	−0.780736	−0.390368	+	0.920659i	$0.627652\pi$
$278$	−12.7494	−0.764655
$279$	−1.05220	−0.0629937
$280$	2.75605	0.164706
$281$	−8.95711	−0.534337	−0.267168	−	0.963650i	$-0.586088\pi$
$281$	−8.95711	−0.534337	−0.267168	+	0.963650i	$0.586088\pi$
$282$	14.3889	0.856847
$283$	−15.5605	−0.924974	−0.462487	−	0.886626i	$-0.653043\pi$
$283$	−15.5605	−0.924974	−0.462487	+	0.886626i	$0.653043\pi$
$284$	7.14721	0.424109
$285$	5.03906	0.298488
$286$	2.80198	0.165685
$287$	6.08604	0.359248
$288$	7.92181	0.466797
$289$	3.89487	0.229110
$290$	−2.77374	−0.162880
$291$	3.32670	0.195015
$292$	−37.5851	−2.19950
$293$	−22.0424	−1.28773	−0.643865	−	0.765139i	$-0.722670\pi$
$293$	−22.0424	−1.28773	−0.643865	+	0.765139i	$0.722670\pi$
$294$	−1.96214	−0.114434
$295$	1.49746	0.0871855
$296$	−5.29008	−0.307480
$297$	2.49782	0.144938
$298$	−0.634145	−0.0367350
$299$	0	0
$300$	−2.52552	−0.145811
$301$	−30.1827	−1.73970
$302$	15.6578	0.901004
$303$	2.67750	0.153818
$304$	13.4684	0.772466
$305$	6.45669	0.369709
$306$	9.72420	0.555896
$307$	−14.2470	−0.813117	−0.406558	−	0.913625i	$-0.633271\pi$
$307$	−14.2470	−0.813117	−0.406558	+	0.913625i	$0.633271\pi$
$308$	15.5517	0.886143
$309$	−5.69796	−0.324146
$310$	2.23838	0.127131
$311$	−11.0558	−0.626920	−0.313460	−	0.949601i	$-0.601488\pi$
$311$	−11.0558	−0.626920	−0.313460	+	0.949601i	$0.601488\pi$
$312$	0.589508	0.0333743
$313$	18.0195	1.01852	0.509262	−	0.860612i	$-0.329919\pi$
$313$	18.0195	1.01852	0.509262	+	0.860612i	$0.329919\pi$
$314$	−30.5498	−1.72403
$315$	−2.46529	−0.138903
$316$	38.4001	2.16018
$317$	−20.1547	−1.13200	−0.565999	−	0.824406i	$-0.691510\pi$
$317$	−20.1547	−1.13200	−0.565999	+	0.824406i	$0.691510\pi$
$318$	5.12882	0.287610
$319$	−3.25682	−0.182347
$320$	−11.5067	−0.643242
$321$	−17.2402	−0.962252
$322$	0	0
$323$	23.0340	1.28165
$324$	2.52552	0.140306
$325$	0.527315	0.0292502
$326$	−20.0268	−1.10918
$327$	16.9758	0.938765
$328$	2.75986	0.152388
$329$	−16.6748	−0.919314
$330$	−5.31368	−0.292508
$331$	−1.48597	−0.0816760	−0.0408380	−	0.999166i	$-0.513003\pi$
$331$	−1.48597	−0.0816760	−0.0408380	+	0.999166i	$0.513003\pi$
$332$	1.77600	0.0974709
$333$	4.73198	0.259311
$334$	−42.8906	−2.34687
$335$	8.91145	0.486885
$336$	−6.58923	−0.359472
$337$	−9.72609	−0.529814	−0.264907	−	0.964274i	$-0.585341\pi$
$337$	−9.72609	−0.529814	−0.264907	+	0.964274i	$0.585341\pi$
$338$	27.0637	1.47207
$339$	−5.38102	−0.292257
$340$	−11.5444	−0.626081
$341$	2.62821	0.142326
$342$	10.7197	0.579656
$343$	19.5309	1.05457
$344$	−13.6871	−0.737957
$345$	0	0
$346$	25.5171	1.37181
$347$	33.8197	1.81554	0.907768	−	0.419474i	$-0.137785\pi$
$347$	33.8197	1.81554	0.907768	+	0.419474i	$0.137785\pi$
$348$	−3.29293	−0.176520
$349$	5.32711	0.285154	0.142577	−	0.989784i	$-0.454461\pi$
$349$	5.32711	0.285154	0.142577	+	0.989784i	$0.454461\pi$
$350$	5.24447	0.280329
$351$	−0.527315	−0.0281460
$352$	−19.7872	−1.05466
$353$	30.1157	1.60290	0.801448	−	0.598064i	$-0.204063\pi$
$353$	30.1157	1.60290	0.801448	+	0.598064i	$0.204063\pi$
$354$	3.18559	0.169312
$355$	2.83000	0.150201
$356$	17.9360	0.950608
$357$	−11.2691	−0.596422
$358$	−8.69826	−0.459718
$359$	12.1500	0.641252	0.320626	−	0.947206i	$-0.396107\pi$
$359$	12.1500	0.641252	0.320626	+	0.947206i	$0.396107\pi$
$360$	−1.11794	−0.0589208
$361$	6.39210	0.336426
$362$	33.2619	1.74821
$363$	4.76090	0.249882
$364$	−3.28313	−0.172083
$365$	−14.8821	−0.778967
$366$	13.7355	0.717965
$367$	29.2358	1.52610	0.763048	−	0.646342i	$-0.223702\pi$
$367$	29.2358	1.52610	0.763048	+	0.646342i	$0.223702\pi$
$368$	0	0
$369$	−2.46869	−0.128515
$370$	−10.0665	−0.523330
$371$	−5.94362	−0.308577
$372$	2.65735	0.137777
$373$	−8.21888	−0.425557	−0.212779	−	0.977100i	$-0.568251\pi$
$373$	−8.21888	−0.425557	−0.212779	+	0.977100i	$0.568251\pi$
$374$	−24.2893	−1.25597
$375$	−1.00000	−0.0516398
$376$	−7.56159	−0.389959
$377$	0.687547	0.0354105
$378$	−5.24447	−0.269747
$379$	−1.80972	−0.0929590	−0.0464795	−	0.998919i	$-0.514800\pi$
$379$	−1.80972	−0.0929590	−0.0464795	+	0.998919i	$0.514800\pi$
$380$	−12.7262	−0.652841
$381$	19.9557	1.02236
$382$	−47.3576	−2.42303
$383$	−28.7802	−1.47060	−0.735300	−	0.677742i	$-0.762959\pi$
$383$	−28.7802	−1.47060	−0.735300	+	0.677742i	$0.762959\pi$
$384$	−8.63481	−0.440643
$385$	6.15785	0.313833
$386$	10.1328	0.515745
$387$	12.2431	0.622351
$388$	−8.40163	−0.426528
$389$	−13.3390	−0.676315	−0.338158	−	0.941090i	$-0.609804\pi$
$389$	−13.3390	−0.676315	−0.338158	+	0.941090i	$0.609804\pi$
$390$	1.12177	0.0568031
$391$	0	0
$392$	1.03113	0.0520801
$393$	21.3624	1.07759
$394$	29.2553	1.47386
$395$	15.2049	0.765040
$396$	−6.30828	−0.317003
$397$	−25.6011	−1.28488	−0.642440	−	0.766336i	$-0.722078\pi$
$397$	−25.6011	−1.28488	−0.642440	+	0.766336i	$0.722078\pi$
$398$	5.66691	0.284057
$399$	−12.4227	−0.621915
$400$	−2.67280	−0.133640
$401$	28.9714	1.44676	0.723380	−	0.690450i	$-0.242587\pi$
$401$	28.9714	1.44676	0.723380	+	0.690450i	$0.242587\pi$
$402$	18.9576	0.945517
$403$	−0.554842	−0.0276386
$404$	−6.76206	−0.336425
$405$	1.00000	0.0496904
$406$	6.83808	0.339368
$407$	−11.8196	−0.585877
$408$	−5.11022	−0.252994
$409$	−15.5886	−0.770807	−0.385403	−	0.922748i	$-0.625938\pi$
$409$	−15.5886	−0.770807	−0.385403	+	0.922748i	$0.625938\pi$
$410$	5.25171	0.259364
$411$	−11.7144	−0.577827
$412$	14.3903	0.708959
$413$	−3.69167	−0.181655
$414$	0	0
$415$	0.703225	0.0345199
$416$	4.17729	0.204808
$417$	−5.99314	−0.293485
$418$	−26.7759	−1.30965
$419$	−8.71478	−0.425745	−0.212872	−	0.977080i	$-0.568282\pi$
$419$	−8.71478	−0.425745	−0.212872	+	0.977080i	$0.568282\pi$
$420$	6.22613	0.303804
$421$	−26.7715	−1.30476	−0.652381	−	0.757891i	$-0.726230\pi$
$421$	−26.7715	−1.30476	−0.652381	+	0.757891i	$0.726230\pi$
$422$	3.61877	0.176159
$423$	6.76385	0.328869
$424$	−2.69527	−0.130894
$425$	−4.57109	−0.221730
$426$	6.02033	0.291686
$427$	−15.9176	−0.770307
$428$	43.5403	2.10460
$429$	1.31714	0.0635920
$430$	−26.0450	−1.25600
$431$	14.1630	0.682206	0.341103	−	0.940026i	$-0.389199\pi$
$431$	14.1630	0.682206	0.341103	+	0.940026i	$0.389199\pi$
$432$	2.67280	0.128595
$433$	13.0542	0.627344	0.313672	−	0.949531i	$-0.398441\pi$
$433$	13.0542	0.627344	0.313672	+	0.949531i	$0.398441\pi$
$434$	−5.51824	−0.264884
$435$	−1.30386	−0.0625155
$436$	−42.8727	−2.05323
$437$	0	0
$438$	−31.6592	−1.51273
$439$	−4.92310	−0.234967	−0.117483	−	0.993075i	$-0.537483\pi$
$439$	−4.92310	−0.234967	−0.117483	+	0.993075i	$0.537483\pi$
$440$	2.79242	0.133123
$441$	−0.922350	−0.0439214
$442$	5.12772	0.243901
$443$	−30.3486	−1.44191	−0.720953	−	0.692984i	$-0.756295\pi$
$443$	−30.3486	−1.44191	−0.720953	+	0.692984i	$0.756295\pi$
$444$	−11.9507	−0.567154
$445$	7.10193	0.336664
$446$	53.9486	2.55454
$447$	−0.298095	−0.0140994
$448$	28.3672	1.34023
$449$	16.0629	0.758054	0.379027	−	0.925386i	$-0.376259\pi$
$449$	16.0629	0.758054	0.379027	+	0.925386i	$0.376259\pi$
$450$	−2.12733	−0.100283
$451$	6.16635	0.290362
$452$	13.5898	0.639213
$453$	7.36031	0.345818
$454$	−10.9181	−0.512411
$455$	−1.29998	−0.0609442
$456$	−5.63338	−0.263807
$457$	−10.1572	−0.475136	−0.237568	−	0.971371i	$-0.576350\pi$
$457$	−10.1572	−0.475136	−0.237568	+	0.971371i	$0.576350\pi$
$458$	18.2213	0.851425
$459$	4.57109	0.213360
$460$	0	0
$461$	−14.9033	−0.694116	−0.347058	−	0.937844i	$-0.612819\pi$
$461$	−14.9033	−0.694116	−0.347058	+	0.937844i	$0.612819\pi$
$462$	13.0997	0.609456
$463$	−26.4942	−1.23129	−0.615644	−	0.788024i	$-0.711104\pi$
$463$	−26.4942	−1.23129	−0.615644	+	0.788024i	$0.711104\pi$
$464$	−3.48497	−0.161786
$465$	1.05220	0.0487947
$466$	3.81126	0.176553
$467$	35.2818	1.63265	0.816323	−	0.577595i	$-0.196009\pi$
$467$	35.2818	1.63265	0.816323	+	0.577595i	$0.196009\pi$
$468$	1.33174	0.0615598
$469$	−21.9693	−1.01445
$470$	−14.3889	−0.663711
$471$	−14.3607	−0.661705
$472$	−1.67408	−0.0770556
$473$	−30.5810	−1.40612
$474$	32.3457	1.48569
$475$	−5.03906	−0.231208
$476$	28.4602	1.30447
$477$	2.41092	0.110389
$478$	−9.83481	−0.449834
$479$	−11.3638	−0.519225	−0.259613	−	0.965713i	$-0.583595\pi$
$479$	−11.3638	−0.519225	−0.259613	+	0.965713i	$0.583595\pi$
$480$	−7.92181	−0.361579
$481$	2.49524	0.113773
$482$	44.9403	2.04697
$483$	0	0
$484$	−12.0237	−0.546533
$485$	−3.32670	−0.151058
$486$	2.12733	0.0964975
$487$	32.1002	1.45460	0.727299	−	0.686321i	$-0.240775\pi$
$487$	32.1002	1.45460	0.727299	+	0.686321i	$0.240775\pi$
$488$	−7.21821	−0.326753
$489$	−9.41408	−0.425720
$490$	1.96214	0.0886404
$491$	29.2758	1.32120	0.660599	−	0.750739i	$-0.270302\pi$
$491$	29.2758	1.32120	0.660599	+	0.750739i	$0.270302\pi$
$492$	6.23472	0.281083
$493$	−5.96008	−0.268429
$494$	5.65267	0.254326
$495$	−2.49782	−0.112269
$496$	2.81233	0.126277
$497$	−6.97677	−0.312951
$498$	1.49599	0.0670368
$499$	29.6975	1.32944	0.664722	−	0.747091i	$-0.268550\pi$
$499$	29.6975	1.32944	0.664722	+	0.747091i	$0.268550\pi$
$500$	2.52552	0.112944
$501$	−20.1617	−0.900760
$502$	66.3462	2.96118
$503$	14.5310	0.647905	0.323953	−	0.946073i	$-0.394988\pi$
$503$	14.5310	0.647905	0.323953	+	0.946073i	$0.394988\pi$
$504$	2.75605	0.122764
$505$	−2.67750	−0.119147
$506$	0	0
$507$	12.7219	0.565001
$508$	−50.3984	−2.23607
$509$	−33.9297	−1.50391	−0.751954	−	0.659215i	$-0.770889\pi$
$509$	−33.9297	−1.50391	−0.751954	+	0.659215i	$0.770889\pi$
$510$	−9.72420	−0.430595
$511$	36.6888	1.62302
$512$	−27.1495	−1.19985
$513$	5.03906	0.222480
$514$	−46.8502	−2.06647
$515$	5.69796	0.251082
$516$	−30.9201	−1.36118
$517$	−16.8949	−0.743036
$518$	24.8167	1.09038
$519$	11.9949	0.526519
$520$	−0.589508	−0.0258516
$521$	14.3074	0.626819	0.313410	−	0.949618i	$-0.398529\pi$
$521$	14.3074	0.626819	0.313410	+	0.949618i	$0.398529\pi$
$522$	−2.77374	−0.121403
$523$	−15.2416	−0.666470	−0.333235	−	0.942844i	$-0.608140\pi$
$523$	−15.2416	−0.666470	−0.333235	+	0.942844i	$0.608140\pi$
$524$	−53.9510	−2.35686
$525$	2.46529	0.107594
$526$	−49.8430	−2.17326
$527$	4.80971	0.209514
$528$	−6.67618	−0.290543
$529$	0	0
$530$	−5.12882	−0.222782
$531$	1.49746	0.0649843
$532$	31.3738	1.36023
$533$	−1.30178	−0.0563863
$534$	15.1081	0.653792
$535$	17.2402	0.745357
$536$	−9.96249	−0.430314
$537$	−4.08883	−0.176446
$538$	−26.3782	−1.13724
$539$	2.30386	0.0992344
$540$	−2.52552	−0.108681
$541$	32.7950	1.40997	0.704984	−	0.709223i	$-0.250954\pi$
$541$	32.7950	1.40997	0.704984	+	0.709223i	$0.250954\pi$
$542$	−53.9052	−2.31542
$543$	15.6355	0.670986
$544$	−36.2113	−1.55255
$545$	−16.9758	−0.727164
$546$	−2.76549	−0.118352
$547$	−11.8157	−0.505205	−0.252602	−	0.967570i	$-0.581286\pi$
$547$	−11.8157	−0.505205	−0.252602	+	0.967570i	$0.581286\pi$
$548$	29.5848	1.26380
$549$	6.45669	0.275565
$550$	5.31368	0.226576
$551$	−6.57025	−0.279902
$552$	0	0
$553$	−37.4844	−1.59400
$554$	27.6425	1.17442
$555$	−4.73198	−0.200861
$556$	15.1358	0.641899
$557$	0.502448	0.0212894	0.0106447	−	0.999943i	$-0.496612\pi$
$557$	0.502448	0.0212894	0.0106447	+	0.999943i	$0.496612\pi$
$558$	2.23838	0.0947580
$559$	6.45596	0.273058
$560$	6.58923	0.278446
$561$	−11.4178	−0.482058
$562$	19.0547	0.803774
$563$	−27.8070	−1.17193	−0.585963	−	0.810338i	$-0.699283\pi$
$563$	−27.8070	−1.17193	−0.585963	+	0.810338i	$0.699283\pi$
$564$	−17.0822	−0.719290
$565$	5.38102	0.226381
$566$	33.1022	1.39139
$567$	−2.46529	−0.103532
$568$	−3.16378	−0.132749
$569$	−20.6645	−0.866301	−0.433150	−	0.901322i	$-0.642598\pi$
$569$	−20.6645	−0.866301	−0.433150	+	0.901322i	$0.642598\pi$
$570$	−10.7197	−0.449000
$571$	30.9692	1.29602	0.648011	−	0.761631i	$-0.275601\pi$
$571$	30.9692	1.29602	0.648011	+	0.761631i	$0.275601\pi$
$572$	−3.32645	−0.139086
$573$	−22.2616	−0.929990
$574$	−12.9470	−0.540397
$575$	0	0
$576$	−11.5067	−0.479444
$577$	12.1018	0.503805	0.251903	−	0.967753i	$-0.418944\pi$
$577$	12.1018	0.503805	0.251903	+	0.967753i	$0.418944\pi$
$578$	−8.28566	−0.344638
$579$	4.76315	0.197950
$580$	3.29293	0.136731
$581$	−1.73365	−0.0719240
$582$	−7.07698	−0.293350
$583$	−6.02205	−0.249408
$584$	16.6374	0.688460
$585$	0.527315	0.0218018
$586$	46.8914	1.93706
$587$	−24.7625	−1.02206	−0.511030	−	0.859563i	$-0.670736\pi$
$587$	−24.7625	−1.02206	−0.511030	+	0.859563i	$0.670736\pi$
$588$	2.32941	0.0960632
$589$	5.30211	0.218469
$590$	−3.18559	−0.131149
$591$	13.7522	0.565688
$592$	−12.6476	−0.519815
$593$	41.1220	1.68868	0.844339	−	0.535810i	$-0.179994\pi$
$593$	41.1220	1.68868	0.844339	+	0.535810i	$0.179994\pi$
$594$	−5.31368	−0.218023
$595$	11.2691	0.461986
$596$	0.752844	0.0308377
$597$	2.66387	0.109025
$598$	0	0
$599$	37.8782	1.54766	0.773830	−	0.633393i	$-0.218338\pi$
$599$	37.8782	1.54766	0.773830	+	0.633393i	$0.218338\pi$
$600$	1.11794	0.0456398
$601$	−40.8198	−1.66507	−0.832537	−	0.553970i	$-0.813112\pi$
$601$	−40.8198	−1.66507	−0.832537	+	0.553970i	$0.813112\pi$
$602$	64.2085	2.61694
$603$	8.91145	0.362902
$604$	−18.5886	−0.756359
$605$	−4.76090	−0.193558
$606$	−5.69590	−0.231380
$607$	−38.2591	−1.55289	−0.776445	−	0.630185i	$-0.782979\pi$
$607$	−38.2591	−1.55289	−0.776445	+	0.630185i	$0.782979\pi$
$608$	−39.9184	−1.61891
$609$	3.21440	0.130254
$610$	−13.7355	−0.556134
$611$	3.56668	0.144292
$612$	−11.5444	−0.466653
$613$	9.77228	0.394699	0.197349	−	0.980333i	$-0.436767\pi$
$613$	9.77228	0.394699	0.197349	+	0.980333i	$0.436767\pi$
$614$	30.3079	1.22313
$615$	2.46869	0.0995473
$616$	−6.88412	−0.277369
$617$	−23.8291	−0.959322	−0.479661	−	0.877454i	$-0.659240\pi$
$617$	−23.8291	−0.959322	−0.479661	+	0.877454i	$0.659240\pi$
$618$	12.1214	0.487595
$619$	−24.7664	−0.995444	−0.497722	−	0.867336i	$-0.665830\pi$
$619$	−24.7664	−0.995444	−0.497722	+	0.867336i	$0.665830\pi$
$620$	−2.65735	−0.106722
$621$	0	0
$622$	23.5194	0.943042
$623$	−17.5083	−0.701456
$624$	1.40941	0.0564215
$625$	1.00000	0.0400000
$626$	−38.3334	−1.53211
$627$	−12.5867	−0.502663
$628$	36.2681	1.44725
$629$	−21.6303	−0.862456
$630$	5.24447	0.208945
$631$	−32.6694	−1.30055	−0.650275	−	0.759699i	$-0.725346\pi$
$631$	−32.6694	−1.30055	−0.650275	+	0.759699i	$0.725346\pi$
$632$	−16.9982	−0.676151
$633$	1.70109	0.0676122
$634$	42.8755	1.70281
$635$	−19.9557	−0.791917
$636$	−6.08882	−0.241437
$637$	−0.486369	−0.0192706
$638$	6.92831	0.274295
$639$	2.83000	0.111953
$640$	8.63481	0.341321
$641$	−5.58700	−0.220673	−0.110337	−	0.993894i	$-0.535193\pi$
$641$	−5.58700	−0.220673	−0.110337	+	0.993894i	$0.535193\pi$
$642$	36.6754	1.44746
$643$	−22.4403	−0.884959	−0.442479	−	0.896779i	$-0.645901\pi$
$643$	−22.4403	−0.884959	−0.442479	+	0.896779i	$0.645901\pi$
$644$	0	0
$645$	−12.2431	−0.482071
$646$	−49.0008	−1.92791
$647$	−26.7563	−1.05190	−0.525948	−	0.850516i	$-0.676290\pi$
$647$	−26.7563	−1.05190	−0.525948	+	0.850516i	$0.676290\pi$
$648$	−1.11794	−0.0439169
$649$	−3.74039	−0.146823
$650$	−1.12177	−0.0439995
$651$	−2.59398	−0.101666
$652$	23.7754	0.931117
$653$	−33.9987	−1.33047	−0.665236	−	0.746633i	$-0.731669\pi$
$653$	−33.9987	−1.33047	−0.665236	+	0.746633i	$0.731669\pi$
$654$	−36.1131	−1.41213
$655$	−21.3624	−0.834697
$656$	6.59832	0.257621
$657$	−14.8821	−0.580608
$658$	35.4728	1.38287
$659$	11.9827	0.466778	0.233389	−	0.972383i	$-0.425018\pi$
$659$	11.9827	0.466778	0.233389	+	0.972383i	$0.425018\pi$
$660$	6.30828	0.245550
$661$	39.6610	1.54263	0.771317	−	0.636451i	$-0.219598\pi$
$661$	39.6610	1.54263	0.771317	+	0.636451i	$0.219598\pi$
$662$	3.16113	0.122861
$663$	2.41040	0.0936124
$664$	−0.786165	−0.0305091
$665$	12.4227	0.481733
$666$	−10.0665	−0.390067
$667$	0	0
$668$	50.9188	1.97011
$669$	25.3598	0.980468
$670$	−18.9576	−0.732394
$671$	−16.1277	−0.622601
$672$	19.5295	0.753369
$673$	−31.2265	−1.20369	−0.601847	−	0.798611i	$-0.705568\pi$
$673$	−31.2265	−1.20369	−0.601847	+	0.798611i	$0.705568\pi$
$674$	20.6906	0.796971
$675$	−1.00000	−0.0384900
$676$	−32.1295	−1.23575
$677$	−8.57586	−0.329597	−0.164799	−	0.986327i	$-0.552697\pi$
$677$	−8.57586	−0.329597	−0.164799	+	0.986327i	$0.552697\pi$
$678$	11.4472	0.439626
$679$	8.20128	0.314736
$680$	5.11022	0.195968
$681$	−5.13230	−0.196670
$682$	−5.59106	−0.214093
$683$	28.5484	1.09237	0.546187	−	0.837663i	$-0.316079\pi$
$683$	28.5484	1.09237	0.546187	+	0.837663i	$0.316079\pi$
$684$	−12.7262	−0.486599
$685$	11.7144	0.447583
$686$	−41.5486	−1.58633
$687$	8.56535	0.326788
$688$	−32.7233	−1.24757
$689$	1.27132	0.0484333
$690$	0	0
$691$	13.9817	0.531891	0.265945	−	0.963988i	$-0.414316\pi$
$691$	13.9817	0.531891	0.265945	+	0.963988i	$0.414316\pi$
$692$	−30.2934	−1.15158
$693$	6.15785	0.233917
$694$	−71.9455	−2.73101
$695$	5.99314	0.227333
$696$	1.45765	0.0552519
$697$	11.2846	0.427435
$698$	−11.3325	−0.428941
$699$	1.79157	0.0677636
$700$	−6.22613	−0.235325
$701$	−30.6388	−1.15721	−0.578606	−	0.815608i	$-0.696403\pi$
$701$	−30.6388	−1.15721	−0.578606	+	0.815608i	$0.696403\pi$
$702$	1.12177	0.0423385
$703$	−23.8447	−0.899320
$704$	28.7416	1.08324
$705$	−6.76385	−0.254741
$706$	−64.0659	−2.41115
$707$	6.60080	0.248249
$708$	−3.78186	−0.142131
$709$	−14.3909	−0.540463	−0.270232	−	0.962795i	$-0.587100\pi$
$709$	−14.3909	−0.540463	−0.270232	+	0.962795i	$0.587100\pi$
$710$	−6.02033	−0.225939
$711$	15.2049	0.570227
$712$	−7.93955	−0.297547
$713$	0	0
$714$	23.9730	0.897166
$715$	−1.31714	−0.0492582
$716$	10.3264	0.385915
$717$	−4.62309	−0.172652
$718$	−25.8470	−0.964601
$719$	−0.460699	−0.0171812	−0.00859058	−	0.999963i	$-0.502735\pi$
$719$	−0.460699	−0.0171812	−0.00859058	+	0.999963i	$0.502735\pi$
$720$	−2.67280	−0.0996095
$721$	−14.0471	−0.523142
$722$	−13.5981	−0.506068
$723$	21.1252	0.785656
$724$	−39.4878	−1.46755
$725$	1.30386	0.0484243
$726$	−10.1280	−0.375885
$727$	−49.1224	−1.82185	−0.910924	−	0.412573i	$-0.864630\pi$
$727$	−49.1224	−1.82185	−0.910924	+	0.412573i	$0.864630\pi$
$728$	1.45331	0.0538632
$729$	1.00000	0.0370370
$730$	31.6592	1.17176
$731$	−55.9642	−2.06991
$732$	−16.3065	−0.602705
$733$	−20.5312	−0.758338	−0.379169	−	0.925327i	$-0.623790\pi$
$733$	−20.5312	−0.758338	−0.379169	+	0.925327i	$0.623790\pi$
$734$	−62.1940	−2.29562
$735$	0.922350	0.0340214
$736$	0	0
$737$	−22.2592	−0.819928
$738$	5.25171	0.193318
$739$	−3.29136	−0.121075	−0.0605373	−	0.998166i	$-0.519281\pi$
$739$	−3.29136	−0.121075	−0.0605373	+	0.998166i	$0.519281\pi$
$740$	11.9507	0.439316
$741$	2.65717	0.0976136
$742$	12.6440	0.464176
$743$	34.4192	1.26272	0.631359	−	0.775491i	$-0.282498\pi$
$743$	34.4192	1.26272	0.631359	+	0.775491i	$0.282498\pi$
$744$	−1.17630	−0.0431253
$745$	0.298095	0.0109214
$746$	17.4842	0.640143
$747$	0.703225	0.0257296
$748$	28.8357	1.05434
$749$	−42.5020	−1.55299
$750$	2.12733	0.0776790
$751$	−20.0122	−0.730256	−0.365128	−	0.930957i	$-0.618975\pi$
$751$	−20.0122	−0.730256	−0.365128	+	0.930957i	$0.618975\pi$
$752$	−18.0784	−0.659252
$753$	31.1876	1.13654
$754$	−1.46264	−0.0532661
$755$	−7.36031	−0.267869
$756$	6.22613	0.226442
$757$	47.8177	1.73796	0.868981	−	0.494845i	$-0.164775\pi$
$757$	47.8177	1.73796	0.868981	+	0.494845i	$0.164775\pi$
$758$	3.84986	0.139833
$759$	0	0
$760$	5.63338	0.204344
$761$	−30.0234	−1.08835	−0.544173	−	0.838973i	$-0.683157\pi$
$761$	−30.0234	−1.08835	−0.544173	+	0.838973i	$0.683157\pi$
$762$	−42.4522	−1.53788
$763$	41.8503	1.51508
$764$	56.2219	2.03404
$765$	−4.57109	−0.165268
$766$	61.2249	2.21214
$767$	0.789633	0.0285120
$768$	−4.64428	−0.167586
$769$	−10.0441	−0.362199	−0.181100	−	0.983465i	$-0.557966\pi$
$769$	−10.0441	−0.362199	−0.181100	+	0.983465i	$0.557966\pi$
$770$	−13.0997	−0.472082
$771$	−22.0231	−0.793141
$772$	−12.0294	−0.432948
$773$	−12.5260	−0.450531	−0.225265	−	0.974297i	$-0.572325\pi$
$773$	−12.5260	−0.450531	−0.225265	+	0.974297i	$0.572325\pi$
$774$	−26.0450	−0.936169
$775$	−1.05220	−0.0377962
$776$	3.71906	0.133507
$777$	11.6657	0.418504
$778$	28.3764	1.01734
$779$	12.4399	0.445705
$780$	−1.33174	−0.0476840
$781$	−7.06883	−0.252943
$782$	0	0
$783$	−1.30386	−0.0465963
$784$	2.46526	0.0880449
$785$	14.3607	0.512554
$786$	−45.4447	−1.62096
$787$	−38.5204	−1.37311	−0.686553	−	0.727080i	$-0.740877\pi$
$787$	−38.5204	−1.37311	−0.686553	+	0.727080i	$0.740877\pi$
$788$	−34.7313	−1.23725
$789$	−23.4299	−0.834127
$790$	−32.3457	−1.15081
$791$	−13.2658	−0.471676
$792$	2.79242	0.0992243
$793$	3.40471	0.120905
$794$	54.4618	1.93278
$795$	−2.41092	−0.0855066
$796$	−6.72763	−0.238455
$797$	29.3631	1.04009	0.520047	−	0.854137i	$-0.325914\pi$
$797$	29.3631	1.04009	0.520047	+	0.854137i	$0.325914\pi$
$798$	26.4272	0.935513
$799$	−30.9182	−1.09381
$800$	7.92181	0.280078
$801$	7.10193	0.250934
$802$	−61.6315	−2.17629
$803$	37.1729	1.31180
$804$	−22.5060	−0.793726
$805$	0	0
$806$	1.18033	0.0415753
$807$	−12.3997	−0.436489
$808$	2.99329	0.105303
$809$	−28.1983	−0.991401	−0.495700	−	0.868494i	$-0.665089\pi$
$809$	−28.1983	−0.991401	−0.495700	+	0.868494i	$0.665089\pi$
$810$	−2.12733	−0.0747466
$811$	−20.7518	−0.728696	−0.364348	−	0.931263i	$-0.618708\pi$
$811$	−20.7518	−0.728696	−0.364348	+	0.931263i	$0.618708\pi$
$812$	−8.11802	−0.284887
$813$	−25.3394	−0.888691
$814$	25.1442	0.881304
$815$	9.41408	0.329761
$816$	−12.2176	−0.427702
$817$	−61.6936	−2.15839
$818$	33.1620	1.15948
$819$	−1.29998	−0.0454251
$820$	−6.23472	−0.217726
$821$	20.0232	0.698815	0.349407	−	0.936971i	$-0.386383\pi$
$821$	20.0232	0.698815	0.349407	+	0.936971i	$0.386383\pi$
$822$	24.9203	0.869194
$823$	−41.6999	−1.45357	−0.726784	−	0.686866i	$-0.758986\pi$
$823$	−41.6999	−1.45357	−0.726784	+	0.686866i	$0.758986\pi$
$824$	−6.37000	−0.221909
$825$	2.49782	0.0869629
$826$	7.85339	0.273255
$827$	37.3800	1.29983	0.649914	−	0.760008i	$-0.274805\pi$
$827$	37.3800	1.29983	0.649914	+	0.760008i	$0.274805\pi$
$828$	0	0
$829$	6.16093	0.213978	0.106989	−	0.994260i	$-0.465879\pi$
$829$	6.16093	0.213978	0.106989	+	0.994260i	$0.465879\pi$
$830$	−1.49599	−0.0519265
$831$	12.9940	0.450758
$832$	−6.06763	−0.210357
$833$	4.21614	0.146081
$834$	12.7494	0.441474
$835$	20.1617	0.697725
$836$	31.7878	1.09940
$837$	1.05220	0.0363694
$838$	18.5392	0.640425
$839$	−20.5683	−0.710097	−0.355048	−	0.934848i	$-0.615536\pi$
$839$	−20.5683	−0.710097	−0.355048	+	0.934848i	$0.615536\pi$
$840$	−2.75605	−0.0950928
$841$	−27.2999	−0.941377
$842$	56.9517	1.96268
$843$	8.95711	0.308499
$844$	−4.29613	−0.147879
$845$	−12.7219	−0.437648
$846$	−14.3889	−0.494701
$847$	11.7370	0.403288
$848$	−6.44392	−0.221285
$849$	15.5605	0.534034
$850$	9.72420	0.333537
$851$	0	0
$852$	−7.14721	−0.244859
$853$	50.0948	1.71521	0.857607	−	0.514306i	$-0.171951\pi$
$853$	50.0948	1.71521	0.857607	+	0.514306i	$0.171951\pi$
$854$	33.8619	1.15873
$855$	−5.03906	−0.172332
$856$	−19.2735	−0.658755
$857$	16.0780	0.549215	0.274608	−	0.961556i	$-0.411452\pi$
$857$	16.0780	0.549215	0.274608	+	0.961556i	$0.411452\pi$
$858$	−2.80198	−0.0956581
$859$	−37.4584	−1.27806	−0.639032	−	0.769180i	$-0.720665\pi$
$859$	−37.4584	−1.27806	−0.639032	+	0.769180i	$0.720665\pi$
$860$	30.9201	1.05437
$861$	−6.08604	−0.207412
$862$	−30.1292	−1.02621
$863$	15.6579	0.533000	0.266500	−	0.963835i	$-0.414133\pi$
$863$	15.6579	0.533000	0.266500	+	0.963835i	$0.414133\pi$
$864$	−7.92181	−0.269505
$865$	−11.9949	−0.407840
$866$	−27.7705	−0.943680
$867$	−3.89487	−0.132277
$868$	6.55114	0.222360
$869$	−37.9790	−1.28835
$870$	2.77374	0.0940387
$871$	4.69914	0.159224
$872$	18.9780	0.642676
$873$	−3.32670	−0.112592
$874$	0	0
$875$	−2.46529	−0.0833420
$876$	37.5851	1.26988
$877$	−8.95707	−0.302459	−0.151229	−	0.988499i	$-0.548323\pi$
$877$	−8.95707	−0.302459	−0.151229	+	0.988499i	$0.548323\pi$
$878$	10.4730	0.353448
$879$	22.0424	0.743472
$880$	6.67618	0.225054
$881$	8.15075	0.274606	0.137303	−	0.990529i	$-0.456157\pi$
$881$	8.15075	0.274606	0.137303	+	0.990529i	$0.456157\pi$
$882$	1.96214	0.0660686
$883$	−22.8366	−0.768513	−0.384257	−	0.923226i	$-0.625542\pi$
$883$	−22.8366	−0.768513	−0.384257	+	0.923226i	$0.625542\pi$
$884$	−6.08751	−0.204745
$885$	−1.49746	−0.0503366
$886$	64.5613	2.16898
$887$	−48.1787	−1.61768	−0.808841	−	0.588028i	$-0.799905\pi$
$887$	−48.1787	−1.61768	−0.808841	+	0.588028i	$0.799905\pi$
$888$	5.29008	0.177523
$889$	49.1965	1.65000
$890$	−15.1081	−0.506425
$891$	−2.49782	−0.0836801
$892$	−64.0467	−2.14444
$893$	−34.0834	−1.14056
$894$	0.634145	0.0212090
$895$	4.08883	0.136674
$896$	−21.2873	−0.711158
$897$	0	0
$898$	−34.1710	−1.14030
$899$	−1.37193	−0.0457564
$900$	2.52552	0.0841839
$901$	−11.0205	−0.367148
$902$	−13.1178	−0.436776
$903$	30.1827	1.00442
$904$	−6.01567	−0.200078
$905$	−15.6355	−0.519743
$906$	−15.6578	−0.520195
$907$	10.0557	0.333893	0.166946	−	0.985966i	$-0.446609\pi$
$907$	10.0557	0.333893	0.166946	+	0.985966i	$0.446609\pi$
$908$	12.9617	0.430149
$909$	−2.67750	−0.0888069
$910$	2.76549	0.0916751
$911$	48.6116	1.61057	0.805287	−	0.592885i	$-0.202011\pi$
$911$	48.6116	1.61057	0.805287	+	0.592885i	$0.202011\pi$
$912$	−13.4684	−0.445983
$913$	−1.75653	−0.0581326
$914$	21.6078	0.714722
$915$	−6.45669	−0.213452
$916$	−21.6319	−0.714739
$917$	52.6644	1.73913
$918$	−9.72420	−0.320946
$919$	−21.6332	−0.713613	−0.356806	−	0.934178i	$-0.616134\pi$
$919$	−21.6332	−0.713613	−0.356806	+	0.934178i	$0.616134\pi$
$920$	0	0
$921$	14.2470	0.469453
$922$	31.7042	1.04412
$923$	1.49230	0.0491197
$924$	−15.5517	−0.511615
$925$	4.73198	0.155586
$926$	56.3617	1.85216
$927$	5.69796	0.187146
$928$	10.3290	0.339065
$929$	−45.5745	−1.49525	−0.747626	−	0.664120i	$-0.768806\pi$
$929$	−45.5745	−1.49525	−0.747626	+	0.664120i	$0.768806\pi$
$930$	−2.23838	−0.0733992
$931$	4.64777	0.152325
$932$	−4.52465	−0.148210
$933$	11.0558	0.361952
$934$	−75.0559	−2.45590
$935$	11.4178	0.373401
$936$	−0.589508	−0.0192687
$937$	58.7410	1.91899	0.959493	−	0.281733i	$-0.0909093\pi$
$937$	58.7410	1.91899	0.959493	+	0.281733i	$0.0909093\pi$
$938$	46.7359	1.52598
$939$	−18.0195	−0.588045
$940$	17.0822	0.557160
$941$	−47.5586	−1.55037	−0.775183	−	0.631737i	$-0.782342\pi$
$941$	−47.5586	−1.55037	−0.775183	+	0.631737i	$0.782342\pi$
$942$	30.5498	0.995367
$943$	0	0
$944$	−4.00242	−0.130268
$945$	2.46529	0.0801959
$946$	65.0558	2.11515
$947$	1.02706	0.0333749	0.0166875	−	0.999861i	$-0.494688\pi$
$947$	1.02706	0.0333749	0.0166875	+	0.999861i	$0.494688\pi$
$948$	−38.4001	−1.24718
$949$	−7.84758	−0.254743
$950$	10.7197	0.347794
$951$	20.1547	0.653560
$952$	−12.5982	−0.408309
$953$	−37.6578	−1.21985	−0.609927	−	0.792457i	$-0.708801\pi$
$953$	−37.6578	−1.21985	−0.609927	+	0.792457i	$0.708801\pi$
$954$	−5.12882	−0.166052
$955$	22.2616	0.720368
$956$	11.6757	0.377618
$957$	3.25682	0.105278
$958$	24.1745	0.781042
$959$	−28.8793	−0.932561
$960$	11.5067	0.371376
$961$	−29.8929	−0.964286
$962$	−5.30819	−0.171143
$963$	17.2402	0.555556
$964$	−53.3521	−1.71836
$965$	−4.76315	−0.153331
$966$	0	0
$967$	−54.8151	−1.76273	−0.881367	−	0.472433i	$-0.843376\pi$
$967$	−54.8151	−1.76273	−0.881367	+	0.472433i	$0.843376\pi$
$968$	5.32241	0.171069
$969$	−23.0340	−0.739958
$970$	7.07698	0.227228
$971$	−35.4205	−1.13670	−0.568349	−	0.822788i	$-0.692418\pi$
$971$	−35.4205	−1.13670	−0.568349	+	0.822788i	$0.692418\pi$
$972$	−2.52552	−0.0810060
$973$	−14.7748	−0.473659
$974$	−68.2875	−2.18807
$975$	−0.527315	−0.0168876
$976$	−17.2575	−0.552398
$977$	3.63664	0.116347	0.0581733	−	0.998307i	$-0.481472\pi$
$977$	3.63664	0.116347	0.0581733	+	0.998307i	$0.481472\pi$
$978$	20.0268	0.640387
$979$	−17.7393	−0.566952
$980$	−2.32941	−0.0744102
$981$	−16.9758	−0.541996
$982$	−62.2792	−1.98741
$983$	−60.3421	−1.92461	−0.962307	−	0.271965i	$-0.912326\pi$
$983$	−60.3421	−1.92461	−0.962307	+	0.271965i	$0.912326\pi$
$984$	−2.75986	−0.0879810
$985$	−13.7522	−0.438180
$986$	12.6790	0.403783
$987$	16.6748	0.530766
$988$	−6.71072	−0.213497
$989$	0	0
$990$	5.31368	0.168880
$991$	−28.5119	−0.905710	−0.452855	−	0.891584i	$-0.649594\pi$
$991$	−28.5119	−0.905710	−0.452855	+	0.891584i	$0.649594\pi$
$992$	−8.33534	−0.264647
$993$	1.48597	0.0471557
$994$	14.8419	0.470755
$995$	−2.66387	−0.0844502
$996$	−1.77600	−0.0562749
$997$	4.71077	0.149192	0.0745959	−	0.997214i	$-0.476233\pi$
$997$	4.71077	0.149192	0.0745959	+	0.997214i	$0.476233\pi$
$998$	−63.1764	−1.99981
$999$	−4.73198	−0.149713

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bq.1.3		15
23.11	odd	22		345.2.m.a.121.1	✓	30
23.21	odd	22		345.2.m.a.211.1	yes	30
23.22	odd	2		7935.2.a.bp.1.3		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.a.121.1	✓	30	23.11	odd	22
345.2.m.a.211.1	yes	30	23.21	odd	22
7935.2.a.bp.1.3		15	23.22	odd	2
7935.2.a.bq.1.3		15	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q-2.12733 q^{2} -1.00000 q^{3} +2.52552 q^{4} +1.00000 q^{5} +2.12733 q^{6} -2.46529 q^{7} -1.11794 q^{8} +1.00000 q^{9} -2.12733 q^{10} -2.49782 q^{11} -2.52552 q^{12} +0.527315 q^{13} +5.24447 q^{14} -1.00000 q^{15} -2.67280 q^{16} -4.57109 q^{17} -2.12733 q^{18} -5.03906 q^{19} +2.52552 q^{20} +2.46529 q^{21} +5.31368 q^{22} +1.11794 q^{24} +1.00000 q^{25} -1.12177 q^{26} -1.00000 q^{27} -6.22613 q^{28} +1.30386 q^{29} +2.12733 q^{30} -1.05220 q^{31} +7.92181 q^{32} +2.49782 q^{33} +9.72420 q^{34} -2.46529 q^{35} +2.52552 q^{36} +4.73198 q^{37} +10.7197 q^{38} -0.527315 q^{39} -1.11794 q^{40} -2.46869 q^{41} -5.24447 q^{42} +12.2431 q^{43} -6.30828 q^{44} +1.00000 q^{45} +6.76385 q^{47} +2.67280 q^{48} -0.922350 q^{49} -2.12733 q^{50} +4.57109 q^{51} +1.33174 q^{52} +2.41092 q^{53} +2.12733 q^{54} -2.49782 q^{55} +2.75605 q^{56} +5.03906 q^{57} -2.77374 q^{58} +1.49746 q^{59} -2.52552 q^{60} +6.45669 q^{61} +2.23838 q^{62} -2.46529 q^{63} -11.5067 q^{64} +0.527315 q^{65} -5.31368 q^{66} +8.91145 q^{67} -11.5444 q^{68} +5.24447 q^{70} +2.83000 q^{71} -1.11794 q^{72} -14.8821 q^{73} -10.0665 q^{74} -1.00000 q^{75} -12.7262 q^{76} +6.15785 q^{77} +1.12177 q^{78} +15.2049 q^{79} -2.67280 q^{80} +1.00000 q^{81} +5.25171 q^{82} +0.703225 q^{83} +6.22613 q^{84} -4.57109 q^{85} -26.0450 q^{86} -1.30386 q^{87} +2.79242 q^{88} +7.10193 q^{89} -2.12733 q^{90} -1.29998 q^{91} +1.05220 q^{93} -14.3889 q^{94} -5.03906 q^{95} -7.92181 q^{96} -3.32670 q^{97} +1.96214 q^{98} -2.49782 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{3} + 12 q^{4} + 15 q^{5} + 5 q^{7} + 15 q^{9} - 13 q^{11} - 12 q^{12} - 24 q^{13} - 15 q^{14} - 15 q^{15} + 2 q^{16} - 2 q^{17} - 13 q^{19} + 12 q^{20} - 5 q^{21} + 9 q^{22} + 15 q^{25} - 9 q^{26}+ \cdots - 13 q^{99}+O(q^{100}) \) 15 * q - 15 * q^3 + 12 * q^4 + 15 * q^5 + 5 * q^7 + 15 * q^9 - 13 * q^11 - 12 * q^12 - 24 * q^13 - 15 * q^14 - 15 * q^15 + 2 * q^16 - 2 * q^17 - 13 * q^19 + 12 * q^20 - 5 * q^21 + 9 * q^22 + 15 * q^25 - 9 * q^26 - 15 * q^27 - q^28 - 3 * q^29 - 22 * q^31 + 13 * q^33 - q^34 + 5 * q^35 + 12 * q^36 + 6 * q^37 + 17 * q^38 + 24 * q^39 - 20 * q^41 + 15 * q^42 + 4 * q^43 + 18 * q^44 + 15 * q^45 + 7 * q^47 - 2 * q^48 - 10 * q^49 + 2 * q^51 - 55 * q^52 - 4 * q^53 - 13 * q^55 - 25 * q^56 + 13 * q^57 + 2 * q^58 + 9 * q^59 - 12 * q^60 - 13 * q^61 - 7 * q^62 + 5 * q^63 - 26 * q^64 - 24 * q^65 - 9 * q^66 + 32 * q^67 - 27 * q^68 - 15 * q^70 + 14 * q^71 - 43 * q^73 + 11 * q^74 - 15 * q^75 - 88 * q^76 - 21 * q^77 + 9 * q^78 - 33 * q^79 + 2 * q^80 + 15 * q^81 - 35 * q^82 + 12 * q^83 + q^84 - 2 * q^85 - 77 * q^86 + 3 * q^87 + 37 * q^88 - 29 * q^89 - 20 * q^91 + 22 * q^93 - 20 * q^94 - 13 * q^95 - 18 * q^97 - 19 * q^98 - 13 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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