LMFDB - Embedded newform 2645.2.a.n.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2645,2,Mod(1,2645)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2645, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2645.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2645 = 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2645.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:	$21.1204313346$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\Q(\zeta_{22})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1 $ x^5 - x^4 - 4x^3 + 3x^2 + 3*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 115)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.30972$ of defining polynomial
Character	$\chi$	$=$	2645.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.22871 q^{2} -1.00000 q^{3} +2.96714 q^{4} -1.00000 q^{5} -2.22871 q^{6} +0.0881559 q^{7} +2.15546 q^{8} -2.00000 q^{9} -2.22871 q^{10} +2.44009 q^{11} -2.96714 q^{12} -3.60149 q^{13} +0.196474 q^{14} +1.00000 q^{15} -1.13037 q^{16} +3.38296 q^{17} -4.45741 q^{18} -2.86103 q^{19} -2.96714 q^{20} -0.0881559 q^{21} +5.43826 q^{22} -2.15546 q^{24} +1.00000 q^{25} -8.02667 q^{26} +5.00000 q^{27} +0.261571 q^{28} -7.44592 q^{29} +2.22871 q^{30} -1.72352 q^{31} -6.83020 q^{32} -2.44009 q^{33} +7.53964 q^{34} -0.0881559 q^{35} -5.93427 q^{36} +0.707778 q^{37} -6.37640 q^{38} +3.60149 q^{39} -2.15546 q^{40} -5.55113 q^{41} -0.196474 q^{42} -2.39725 q^{43} +7.24009 q^{44} +2.00000 q^{45} -11.6146 q^{47} +1.13037 q^{48} -6.99223 q^{49} +2.22871 q^{50} -3.38296 q^{51} -10.6861 q^{52} -10.3751 q^{53} +11.1435 q^{54} -2.44009 q^{55} +0.190017 q^{56} +2.86103 q^{57} -16.5948 q^{58} +11.5533 q^{59} +2.96714 q^{60} +4.06175 q^{61} -3.84121 q^{62} -0.176312 q^{63} -12.9618 q^{64} +3.60149 q^{65} -5.43826 q^{66} -12.2089 q^{67} +10.0377 q^{68} -0.196474 q^{70} +1.89679 q^{71} -4.31093 q^{72} -5.51637 q^{73} +1.57743 q^{74} -1.00000 q^{75} -8.48907 q^{76} +0.215109 q^{77} +8.02667 q^{78} +7.00855 q^{79} +1.13037 q^{80} +1.00000 q^{81} -12.3718 q^{82} +4.17259 q^{83} -0.261571 q^{84} -3.38296 q^{85} -5.34276 q^{86} +7.44592 q^{87} +5.25954 q^{88} -15.9469 q^{89} +4.45741 q^{90} -0.317493 q^{91} +1.72352 q^{93} -25.8855 q^{94} +2.86103 q^{95} +6.83020 q^{96} +14.3797 q^{97} -15.5836 q^{98} -4.88019 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 3 q^{2} - 5 q^{3} + 5 q^{4} - 5 q^{5} + 3 q^{6} - 3 q^{7} + 3 q^{8} - 10 q^{9} + 3 q^{10} + 4 q^{11} - 5 q^{12} + 4 q^{14} + 5 q^{15} - 3 q^{16} + 5 q^{17} + 6 q^{18} - q^{19} - 5 q^{20} + 3 q^{21}+ \cdots - 8 q^{99}+O(q^{100}) $ 5 * q - 3 * q^2 - 5 * q^3 + 5 * q^4 - 5 * q^5 + 3 * q^6 - 3 * q^7 + 3 * q^8 - 10 * q^9 + 3 * q^10 + 4 * q^11 - 5 * q^12 + 4 * q^14 + 5 * q^15 - 3 * q^16 + 5 * q^17 + 6 * q^18 - q^19 - 5 * q^20 + 3 * q^21 + 2 * q^22 - 3 * q^24 + 5 * q^25 - 11 * q^26 + 25 * q^27 - 3 * q^28 + q^29 - 3 * q^30 - 10 * q^31 - 2 * q^32 - 4 * q^33 + 8 * q^34 + 3 * q^35 - 10 * q^36 + q^37 + 5 * q^38 - 3 * q^40 - 8 * q^41 - 4 * q^42 + 24 * q^43 + 4 * q^44 + 10 * q^45 - 26 * q^47 + 3 * q^48 - 20 * q^49 - 3 * q^50 - 5 * q^51 - 11 * q^52 + 3 * q^53 - 15 * q^54 - 4 * q^55 + 7 * q^56 + q^57 - 27 * q^58 + 41 * q^59 + 5 * q^60 + 4 * q^61 + 17 * q^62 + 6 * q^63 - 17 * q^64 - 2 * q^66 - 23 * q^67 + 16 * q^68 - 4 * q^70 - 6 * q^72 - 17 * q^73 - 27 * q^74 - 5 * q^75 - 34 * q^76 + 2 * q^77 + 11 * q^78 - 13 * q^79 + 3 * q^80 + 5 * q^81 - 26 * q^82 + 19 * q^83 + 3 * q^84 - 5 * q^85 - 43 * q^86 - q^87 + 31 * q^88 - 32 * q^89 - 6 * q^90 - 11 * q^91 + 10 * q^93 - 2 * q^94 + q^95 + 2 * q^96 + 15 * q^97 + q^98 - 8 * 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 $

$2$	2.22871	1.57593	0.787967	−	0.615717i	$-0.211134\pi$
$2$	2.22871	1.57593	0.787967	+	0.615717i	$0.211134\pi$
$3$	−1.00000	−0.577350	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	2.96714	1.48357
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.22871	−0.909866
$7$	0.0881559	0.0333198	0.0166599	−	0.999861i	$-0.494697\pi$
$7$	0.0881559	0.0333198	0.0166599	+	0.999861i	$0.494697\pi$
$8$	2.15546	0.762072
$9$	−2.00000	−0.666667
$10$	−2.22871	−0.704779
$11$	2.44009	0.735716	0.367858	−	0.929882i	$-0.380091\pi$
$11$	2.44009	0.735716	0.367858	+	0.929882i	$0.380091\pi$
$12$	−2.96714	−0.856539
$13$	−3.60149	−0.998874	−0.499437	−	0.866350i	$-0.666460\pi$
$13$	−3.60149	−0.998874	−0.499437	+	0.866350i	$0.666460\pi$
$14$	0.196474	0.0525098
$15$	1.00000	0.258199
$16$	−1.13037	−0.282593
$17$	3.38296	0.820489	0.410245	−	0.911976i	$-0.365443\pi$
$17$	3.38296	0.820489	0.410245	+	0.911976i	$0.365443\pi$
$18$	−4.45741	−1.05062
$19$	−2.86103	−0.656366	−0.328183	−	0.944614i	$-0.606436\pi$
$19$	−2.86103	−0.656366	−0.328183	+	0.944614i	$0.606436\pi$
$20$	−2.96714	−0.663472
$21$	−0.0881559	−0.0192372
$22$	5.43826	1.15944
$23$	0	0
$23$	0	0
$24$	−2.15546	−0.439982
$25$	1.00000	0.200000
$26$	−8.02667	−1.57416
$27$	5.00000	0.962250
$28$	0.261571	0.0494322
$29$	−7.44592	−1.38267	−0.691336	−	0.722533i	$-0.742978\pi$
$29$	−7.44592	−1.38267	−0.691336	+	0.722533i	$0.742978\pi$
$30$	2.22871	0.406904
$31$	−1.72352	−0.309553	−0.154776	−	0.987950i	$-0.549466\pi$
$31$	−1.72352	−0.309553	−0.154776	+	0.987950i	$0.549466\pi$
$32$	−6.83020	−1.20742
$33$	−2.44009	−0.424766
$34$	7.53964	1.29304
$35$	−0.0881559	−0.0149011
$36$	−5.93427	−0.989046
$37$	0.707778	0.116358	0.0581790	−	0.998306i	$-0.481471\pi$
$37$	0.707778	0.116358	0.0581790	+	0.998306i	$0.481471\pi$
$38$	−6.37640	−1.03439
$39$	3.60149	0.576700
$40$	−2.15546	−0.340809
$41$	−5.55113	−0.866941	−0.433470	−	0.901168i	$-0.642711\pi$
$41$	−5.55113	−0.866941	−0.433470	+	0.901168i	$0.642711\pi$
$42$	−0.196474	−0.0303166
$43$	−2.39725	−0.365577	−0.182788	−	0.983152i	$-0.558512\pi$
$43$	−2.39725	−0.365577	−0.182788	+	0.983152i	$0.558512\pi$
$44$	7.24009	1.09149
$45$	2.00000	0.298142
$46$	0	0
$47$	−11.6146	−1.69416	−0.847079	−	0.531466i	$-0.821641\pi$
$47$	−11.6146	−1.69416	−0.847079	+	0.531466i	$0.821641\pi$
$48$	1.13037	0.163155
$49$	−6.99223	−0.998890
$50$	2.22871	0.315187
$51$	−3.38296	−0.473710
$52$	−10.6861	−1.48190
$53$	−10.3751	−1.42513	−0.712564	−	0.701607i	$-0.752466\pi$
$53$	−10.3751	−1.42513	−0.712564	+	0.701607i	$0.752466\pi$
$54$	11.1435	1.51644
$55$	−2.44009	−0.329022
$56$	0.190017	0.0253921
$57$	2.86103	0.378953
$58$	−16.5948	−2.17900
$59$	11.5533	1.50412	0.752059	−	0.659096i	$-0.229061\pi$
$59$	11.5533	1.50412	0.752059	+	0.659096i	$0.229061\pi$
$60$	2.96714	0.383056
$61$	4.06175	0.520054	0.260027	−	0.965601i	$-0.416269\pi$
$61$	4.06175	0.520054	0.260027	+	0.965601i	$0.416269\pi$
$62$	−3.84121	−0.487835
$63$	−0.176312	−0.0222132
$64$	−12.9618	−1.62022
$65$	3.60149	0.446710
$66$	−5.43826	−0.669403
$67$	−12.2089	−1.49156	−0.745778	−	0.666194i	$-0.767922\pi$
$67$	−12.2089	−1.49156	−0.745778	+	0.666194i	$0.767922\pi$
$68$	10.0377	1.21725
$69$	0	0
$70$	−0.196474	−0.0234831
$71$	1.89679	0.225108	0.112554	−	0.993646i	$-0.464097\pi$
$71$	1.89679	0.225108	0.112554	+	0.993646i	$0.464097\pi$
$72$	−4.31093	−0.508048
$73$	−5.51637	−0.645643	−0.322821	−	0.946460i	$-0.604631\pi$
$73$	−5.51637	−0.645643	−0.322821	+	0.946460i	$0.604631\pi$
$74$	1.57743	0.183373
$75$	−1.00000	−0.115470
$76$	−8.48907	−0.973763
$77$	0.215109	0.0245139
$78$	8.02667	0.908842
$79$	7.00855	0.788523	0.394261	−	0.918998i	$-0.371000\pi$
$79$	7.00855	0.788523	0.394261	+	0.918998i	$0.371000\pi$
$80$	1.13037	0.126380
$81$	1.00000	0.111111
$82$	−12.3718	−1.36624
$83$	4.17259	0.458001	0.229001	−	0.973426i	$-0.426454\pi$
$83$	4.17259	0.458001	0.229001	+	0.973426i	$0.426454\pi$
$84$	−0.261571	−0.0285397
$85$	−3.38296	−0.366934
$86$	−5.34276	−0.576125
$87$	7.44592	0.798287
$88$	5.25954	0.560669
$89$	−15.9469	−1.69036	−0.845182	−	0.534478i	$-0.820508\pi$
$89$	−15.9469	−1.69036	−0.845182	+	0.534478i	$0.820508\pi$
$90$	4.45741	0.469853
$91$	−0.317493	−0.0332823
$92$	0	0
$93$	1.72352	0.178720
$94$	−25.8855	−2.66988
$95$	2.86103	0.293536
$96$	6.83020	0.697104
$97$	14.3797	1.46003	0.730017	−	0.683429i	$-0.239512\pi$
$97$	14.3797	1.46003	0.730017	+	0.683429i	$0.239512\pi$
$98$	−15.5836	−1.57418
$99$	−4.88019	−0.490477
$100$	2.96714	0.296714
$101$	17.3832	1.72970	0.864848	−	0.502034i	$-0.167415\pi$
$101$	17.3832	1.72970	0.864848	+	0.502034i	$0.167415\pi$
$102$	−7.53964	−0.746535
$103$	1.16334	0.114628	0.0573138	−	0.998356i	$-0.481746\pi$
$103$	1.16334	0.114628	0.0573138	+	0.998356i	$0.481746\pi$
$104$	−7.76289	−0.761214
$105$	0.0881559	0.00860314
$106$	−23.1230	−2.24591
$107$	17.1503	1.65799	0.828993	−	0.559259i	$-0.188914\pi$
$107$	17.1503	1.65799	0.828993	+	0.559259i	$0.188914\pi$
$108$	14.8357	1.42756
$109$	2.61471	0.250444	0.125222	−	0.992129i	$-0.460036\pi$
$109$	2.61471	0.250444	0.125222	+	0.992129i	$0.460036\pi$
$110$	−5.43826	−0.518517
$111$	−0.707778	−0.0671793
$112$	−0.0996491	−0.00941595
$113$	−17.9160	−1.68539	−0.842696	−	0.538390i	$-0.819033\pi$
$113$	−17.9160	−1.68539	−0.842696	+	0.538390i	$0.819033\pi$
$114$	6.37640	0.597205
$115$	0	0
$116$	−22.0931	−2.05129
$117$	7.20299	0.665916
$118$	25.7490	2.37039
$119$	0.298228	0.0273385
$120$	2.15546	0.196766
$121$	−5.04594	−0.458722
$122$	9.05245	0.819570
$123$	5.55113	0.500529
$124$	−5.11391	−0.459242
$125$	−1.00000	−0.0894427
$126$	−0.392948	−0.0350065
$127$	2.99178	0.265477	0.132739	−	0.991151i	$-0.457623\pi$
$127$	2.99178	0.265477	0.132739	+	0.991151i	$0.457623\pi$
$128$	−15.2276	−1.34594
$129$	2.39725	0.211066
$130$	8.02667	0.703986
$131$	−13.4235	−1.17282	−0.586408	−	0.810016i	$-0.699458\pi$
$131$	−13.4235	−1.17282	−0.586408	+	0.810016i	$0.699458\pi$
$132$	−7.24009	−0.630169
$133$	−0.252217	−0.0218700
$134$	−27.2101	−2.35060
$135$	−5.00000	−0.430331
$136$	7.29186	0.625272
$137$	19.2932	1.64833	0.824165	−	0.566350i	$-0.191645\pi$
$137$	19.2932	1.64833	0.824165	+	0.566350i	$0.191645\pi$
$138$	0	0
$139$	15.4962	1.31437	0.657185	−	0.753729i	$-0.271747\pi$
$139$	15.4962	1.31437	0.657185	+	0.753729i	$0.271747\pi$
$140$	−0.261571	−0.0221068
$141$	11.6146	0.978123
$142$	4.22739	0.354755
$143$	−8.78798	−0.734888
$144$	2.26075	0.188396
$145$	7.44592	0.618350
$146$	−12.2944	−1.01749
$147$	6.99223	0.576709
$148$	2.10007	0.172625
$149$	−15.9525	−1.30688	−0.653440	−	0.756978i	$-0.726675\pi$
$149$	−15.9525	−1.30688	−0.653440	+	0.756978i	$0.726675\pi$
$150$	−2.22871	−0.181973
$151$	0.442267	0.0359912	0.0179956	−	0.999838i	$-0.494272\pi$
$151$	0.442267	0.0359912	0.0179956	+	0.999838i	$0.494272\pi$
$152$	−6.16685	−0.500198
$153$	−6.76593	−0.546993
$154$	0.479415	0.0386323
$155$	1.72352	0.138436
$156$	10.6861	0.855575
$157$	7.11870	0.568134	0.284067	−	0.958804i	$-0.408316\pi$
$157$	7.11870	0.568134	0.284067	+	0.958804i	$0.408316\pi$
$158$	15.6200	1.24266
$159$	10.3751	0.822798
$160$	6.83020	0.539975
$161$	0	0
$162$	2.22871	0.175104
$163$	−7.14635	−0.559745	−0.279872	−	0.960037i	$-0.590292\pi$
$163$	−7.14635	−0.559745	−0.279872	+	0.960037i	$0.590292\pi$
$164$	−16.4710	−1.28617
$165$	2.44009	0.189961
$166$	9.29948	0.721780
$167$	1.33264	0.103123	0.0515614	−	0.998670i	$-0.483580\pi$
$167$	1.33264	0.103123	0.0515614	+	0.998670i	$0.483580\pi$
$168$	−0.190017	−0.0146601
$169$	−0.0292481	−0.00224985
$170$	−7.53964	−0.578264
$171$	5.72206	0.437577
$172$	−7.11296	−0.542358
$173$	2.70076	0.205335	0.102667	−	0.994716i	$-0.467262\pi$
$173$	2.70076	0.205335	0.102667	+	0.994716i	$0.467262\pi$
$174$	16.5948	1.25805
$175$	0.0881559	0.00666396
$176$	−2.75822	−0.207908
$177$	−11.5533	−0.868402
$178$	−35.5409	−2.66390
$179$	−19.7880	−1.47902	−0.739512	−	0.673144i	$-0.764944\pi$
$179$	−19.7880	−1.47902	−0.739512	+	0.673144i	$0.764944\pi$
$180$	5.93427	0.442315
$181$	3.98546	0.296237	0.148118	−	0.988970i	$-0.452678\pi$
$181$	3.98546	0.296237	0.148118	+	0.988970i	$0.452678\pi$
$182$	−0.707599	−0.0524507
$183$	−4.06175	−0.300253
$184$	0	0
$185$	−0.707778	−0.0520369
$186$	3.84121	0.281651
$187$	8.25475	0.603647
$188$	−34.4620	−2.51340
$189$	0.440780	0.0320620
$190$	6.37640	0.462593
$191$	−5.97924	−0.432643	−0.216321	−	0.976322i	$-0.569406\pi$
$191$	−5.97924	−0.432643	−0.216321	+	0.976322i	$0.569406\pi$
$192$	12.9618	0.935435
$193$	10.0864	0.726035	0.363018	−	0.931782i	$-0.381746\pi$
$193$	10.0864	0.726035	0.363018	+	0.931782i	$0.381746\pi$
$194$	32.0481	2.30092
$195$	−3.60149	−0.257908
$196$	−20.7469	−1.48192
$197$	−5.11562	−0.364473	−0.182236	−	0.983255i	$-0.558334\pi$
$197$	−5.11562	−0.364473	−0.182236	+	0.983255i	$0.558334\pi$
$198$	−10.8765	−0.772960
$199$	26.5800	1.88420	0.942102	−	0.335327i	$-0.108847\pi$
$199$	26.5800	1.88420	0.942102	+	0.335327i	$0.108847\pi$
$200$	2.15546	0.152414
$201$	12.2089	0.861151
$202$	38.7421	2.72589
$203$	−0.656402	−0.0460704
$204$	−10.0377	−0.702781
$205$	5.55113	0.387708
$206$	2.59275	0.180646
$207$	0	0
$208$	4.07103	0.282275
$209$	−6.98119	−0.482899
$210$	0.196474	0.0135580
$211$	−14.7426	−1.01492	−0.507460	−	0.861675i	$-0.669416\pi$
$211$	−14.7426	−1.01492	−0.507460	+	0.861675i	$0.669416\pi$
$212$	−30.7843	−2.11427
$213$	−1.89679	−0.129966
$214$	38.2231	2.61288
$215$	2.39725	0.163491
$216$	10.7773	0.733304
$217$	−0.151938	−0.0103142
$218$	5.82742	0.394683
$219$	5.51637	0.372762
$220$	−7.24009	−0.488127
$221$	−12.1837	−0.819566
$222$	−1.57743	−0.105870
$223$	−1.01193	−0.0677637	−0.0338818	−	0.999426i	$-0.510787\pi$
$223$	−1.01193	−0.0677637	−0.0338818	+	0.999426i	$0.510787\pi$
$224$	−0.602123	−0.0402310
$225$	−2.00000	−0.133333
$226$	−39.9294	−2.65607
$227$	5.04227	0.334667	0.167334	−	0.985900i	$-0.446484\pi$
$227$	5.04227	0.334667	0.167334	+	0.985900i	$0.446484\pi$
$228$	8.48907	0.562202
$229$	−22.9504	−1.51661	−0.758304	−	0.651901i	$-0.773972\pi$
$229$	−22.9504	−1.51661	−0.758304	+	0.651901i	$0.773972\pi$
$230$	0	0
$231$	−0.215109	−0.0141531
$232$	−16.0494	−1.05370
$233$	21.5229	1.41001	0.705006	−	0.709201i	$-0.250944\pi$
$233$	21.5229	1.41001	0.705006	+	0.709201i	$0.250944\pi$
$234$	16.0533	1.04944
$235$	11.6146	0.757651
$236$	34.2803	2.23146
$237$	−7.00855	−0.455254
$238$	0.664664	0.0430837
$239$	−8.76977	−0.567269	−0.283634	−	0.958932i	$-0.591540\pi$
$239$	−8.76977	−0.567269	−0.283634	+	0.958932i	$0.591540\pi$
$240$	−1.13037	−0.0729653
$241$	8.81811	0.568024	0.284012	−	0.958821i	$-0.408334\pi$
$241$	8.81811	0.568024	0.284012	+	0.958821i	$0.408334\pi$
$242$	−11.2459	−0.722915
$243$	−16.0000	−1.02640
$244$	12.0518	0.771535
$245$	6.99223	0.446717
$246$	12.3718	0.788800
$247$	10.3040	0.655627
$248$	−3.71498	−0.235901
$249$	−4.17259	−0.264427
$250$	−2.22871	−0.140956
$251$	−5.89202	−0.371901	−0.185950	−	0.982559i	$-0.559536\pi$
$251$	−5.89202	−0.371901	−0.185950	+	0.982559i	$0.559536\pi$
$252$	−0.523141	−0.0329548
$253$	0	0
$254$	6.66780	0.418375
$255$	3.38296	0.211849
$256$	−8.01431	−0.500895
$257$	−7.71341	−0.481149	−0.240575	−	0.970631i	$-0.577336\pi$
$257$	−7.71341	−0.481149	−0.240575	+	0.970631i	$0.577336\pi$
$258$	5.34276	0.332626
$259$	0.0623948	0.00387703
$260$	10.6861	0.662725
$261$	14.8918	0.921782
$262$	−29.9170	−1.84828
$263$	22.3906	1.38067	0.690333	−	0.723492i	$-0.257464\pi$
$263$	22.3906	1.38067	0.690333	+	0.723492i	$0.257464\pi$
$264$	−5.25954	−0.323702
$265$	10.3751	0.637336
$266$	−0.562117	−0.0344656
$267$	15.9469	0.975932
$268$	−36.2255	−2.21283
$269$	9.26230	0.564732	0.282366	−	0.959307i	$-0.408881\pi$
$269$	9.26230	0.564732	0.282366	+	0.959307i	$0.408881\pi$
$270$	−11.1435	−0.678174
$271$	21.9586	1.33389	0.666944	−	0.745108i	$-0.267602\pi$
$271$	21.9586	1.33389	0.666944	+	0.745108i	$0.267602\pi$
$272$	−3.82401	−0.231865
$273$	0.317493	0.0192155
$274$	42.9989	2.59766
$275$	2.44009	0.147143
$276$	0	0
$277$	12.5089	0.751589	0.375795	−	0.926703i	$-0.377370\pi$
$277$	12.5089	0.751589	0.375795	+	0.926703i	$0.377370\pi$
$278$	34.5365	2.07136
$279$	3.44703	0.206368
$280$	−0.190017	−0.0113557
$281$	−24.5232	−1.46293	−0.731467	−	0.681877i	$-0.761164\pi$
$281$	−24.5232	−1.46293	−0.731467	+	0.681877i	$0.761164\pi$
$282$	25.8855	1.54146
$283$	−17.6658	−1.05012	−0.525061	−	0.851065i	$-0.675957\pi$
$283$	−17.6658	−1.05012	−0.525061	+	0.851065i	$0.675957\pi$
$284$	5.62804	0.333963
$285$	−2.86103	−0.169473
$286$	−19.5858	−1.15814
$287$	−0.489365	−0.0288863
$288$	13.6604	0.804947
$289$	−5.55555	−0.326797
$290$	16.5948	0.974479
$291$	−14.3797	−0.842951
$292$	−16.3678	−0.957855
$293$	8.49029	0.496008	0.248004	−	0.968759i	$-0.420225\pi$
$293$	8.49029	0.496008	0.248004	+	0.968759i	$0.420225\pi$
$294$	15.5836	0.908856
$295$	−11.5533	−0.672662
$296$	1.52559	0.0886732
$297$	12.2005	0.707943
$298$	−35.5535	−2.05956
$299$	0	0
$300$	−2.96714	−0.171308
$301$	−0.211332	−0.0121810
$302$	0.985683	0.0567197
$303$	−17.3832	−0.998641
$304$	3.23403	0.185484
$305$	−4.06175	−0.232575
$306$	−15.0793	−0.862025
$307$	−14.6797	−0.837813	−0.418906	−	0.908029i	$-0.637586\pi$
$307$	−14.6797	−0.837813	−0.418906	+	0.908029i	$0.637586\pi$
$308$	0.638257	0.0363681
$309$	−1.16334	−0.0661803
$310$	3.84121	0.218166
$311$	30.1760	1.71112	0.855561	−	0.517703i	$-0.173213\pi$
$311$	30.1760	1.71112	0.855561	+	0.517703i	$0.173213\pi$
$312$	7.76289	0.439487
$313$	−5.56602	−0.314610	−0.157305	−	0.987550i	$-0.550281\pi$
$313$	−5.56602	−0.314610	−0.157305	+	0.987550i	$0.550281\pi$
$314$	15.8655	0.895342
$315$	0.176312	0.00993405
$316$	20.7953	1.16983
$317$	2.81109	0.157887	0.0789434	−	0.996879i	$-0.474845\pi$
$317$	2.81109	0.157887	0.0789434	+	0.996879i	$0.474845\pi$
$318$	23.1230	1.29668
$319$	−18.1688	−1.01725
$320$	12.9618	0.724585
$321$	−17.1503	−0.957238
$322$	0	0
$323$	−9.67876	−0.538541
$324$	2.96714	0.164841
$325$	−3.60149	−0.199775
$326$	−15.9271	−0.882121
$327$	−2.61471	−0.144594
$328$	−11.9653	−0.660671
$329$	−1.02389	−0.0564490
$330$	5.43826	0.299366
$331$	−13.8531	−0.761435	−0.380717	−	0.924691i	$-0.624323\pi$
$331$	−13.8531	−0.761435	−0.380717	+	0.924691i	$0.624323\pi$
$332$	12.3806	0.679476
$333$	−1.41556	−0.0775720
$334$	2.97007	0.162515
$335$	12.2089	0.667045
$336$	0.0996491	0.00543630
$337$	21.5800	1.17554	0.587770	−	0.809028i	$-0.300006\pi$
$337$	21.5800	1.17554	0.587770	+	0.809028i	$0.300006\pi$
$338$	−0.0651854	−0.00354562
$339$	17.9160	0.973061
$340$	−10.0377	−0.544372
$341$	−4.20554	−0.227743
$342$	12.7528	0.689593
$343$	−1.23350	−0.0666026
$344$	−5.16718	−0.278596
$345$	0	0
$346$	6.01920	0.323594
$347$	18.9076	1.01501	0.507506	−	0.861648i	$-0.330567\pi$
$347$	18.9076	1.01501	0.507506	+	0.861648i	$0.330567\pi$
$348$	22.0931	1.18431
$349$	20.9290	1.12030	0.560152	−	0.828390i	$-0.310743\pi$
$349$	20.9290	1.12030	0.560152	+	0.828390i	$0.310743\pi$
$350$	0.196474	0.0105020
$351$	−18.0075	−0.961167
$352$	−16.6663	−0.888319
$353$	1.61202	0.0857993	0.0428996	−	0.999079i	$-0.486340\pi$
$353$	1.61202	0.0857993	0.0428996	+	0.999079i	$0.486340\pi$
$354$	−25.7490	−1.36854
$355$	−1.89679	−0.100671
$356$	−47.3165	−2.50777
$357$	−0.298228	−0.0157839
$358$	−44.1016	−2.33084
$359$	34.8162	1.83753	0.918764	−	0.394808i	$-0.129189\pi$
$359$	34.8162	1.83753	0.918764	+	0.394808i	$0.129189\pi$
$360$	4.31093	0.227206
$361$	−10.8145	−0.569184
$362$	8.88243	0.466850
$363$	5.04594	0.264843
$364$	−0.942045	−0.0493766
$365$	5.51637	0.288740
$366$	−9.05245	−0.473179
$367$	−22.6244	−1.18098	−0.590491	−	0.807044i	$-0.701066\pi$
$367$	−22.6244	−1.18098	−0.590491	+	0.807044i	$0.701066\pi$
$368$	0	0
$369$	11.1023	0.577961
$370$	−1.57743	−0.0820067
$371$	−0.914625	−0.0474850
$372$	5.11391	0.265144
$373$	10.7952	0.558955	0.279477	−	0.960152i	$-0.409839\pi$
$373$	10.7952	0.558955	0.279477	+	0.960152i	$0.409839\pi$
$374$	18.3974	0.951308
$375$	1.00000	0.0516398
$376$	−25.0348	−1.29107
$377$	26.8164	1.38112
$378$	0.982369	0.0505276
$379$	−3.68722	−0.189400	−0.0946999	−	0.995506i	$-0.530189\pi$
$379$	−3.68722	−0.189400	−0.0946999	+	0.995506i	$0.530189\pi$
$380$	8.48907	0.435480
$381$	−2.99178	−0.153273
$382$	−13.3260	−0.681816
$383$	−5.94274	−0.303660	−0.151830	−	0.988407i	$-0.548517\pi$
$383$	−5.94274	−0.303660	−0.151830	+	0.988407i	$0.548517\pi$
$384$	15.2276	0.777080
$385$	−0.215109	−0.0109630
$386$	22.4796	1.14418
$387$	4.79450	0.243718
$388$	42.6665	2.16606
$389$	6.64224	0.336775	0.168387	−	0.985721i	$-0.446144\pi$
$389$	6.64224	0.336775	0.168387	+	0.985721i	$0.446144\pi$
$390$	−8.02667	−0.406446
$391$	0	0
$392$	−15.0715	−0.761226
$393$	13.4235	0.677126
$394$	−11.4012	−0.574385
$395$	−7.00855	−0.352638
$396$	−14.4802	−0.727657
$397$	−4.55745	−0.228732	−0.114366	−	0.993439i	$-0.536484\pi$
$397$	−4.55745	−0.228732	−0.114366	+	0.993439i	$0.536484\pi$
$398$	59.2390	2.96938
$399$	0.252217	0.0126266
$400$	−1.13037	−0.0565187
$401$	−27.9113	−1.39382	−0.696912	−	0.717157i	$-0.745443\pi$
$401$	−27.9113	−1.39382	−0.696912	+	0.717157i	$0.745443\pi$
$402$	27.2101	1.35712
$403$	6.20723	0.309204
$404$	51.5784	2.56612
$405$	−1.00000	−0.0496904
$406$	−1.46293	−0.0726039
$407$	1.72705	0.0856065
$408$	−7.29186	−0.361001
$409$	8.11904	0.401461	0.200730	−	0.979647i	$-0.435668\pi$
$409$	8.11904	0.401461	0.200730	+	0.979647i	$0.435668\pi$
$410$	12.3718	0.611002
$411$	−19.2932	−0.951664
$412$	3.45180	0.170058
$413$	1.01850	0.0501169
$414$	0	0
$415$	−4.17259	−0.204824
$416$	24.5989	1.20606
$417$	−15.4962	−0.758852
$418$	−15.5590	−0.761017
$419$	−27.7342	−1.35490	−0.677452	−	0.735567i	$-0.736916\pi$
$419$	−27.7342	−1.35490	−0.677452	+	0.735567i	$0.736916\pi$
$420$	0.261571	0.0127633
$421$	−34.9538	−1.70355	−0.851773	−	0.523911i	$-0.824472\pi$
$421$	−34.9538	−1.70355	−0.851773	+	0.523911i	$0.824472\pi$
$422$	−32.8569	−1.59945
$423$	23.2291	1.12944
$424$	−22.3631	−1.08605
$425$	3.38296	0.164098
$426$	−4.22739	−0.204818
$427$	0.358067	0.0173281
$428$	50.8874	2.45973
$429$	8.78798	0.424288
$430$	5.34276	0.257651
$431$	−9.26697	−0.446374	−0.223187	−	0.974776i	$-0.571646\pi$
$431$	−9.26697	−0.446374	−0.223187	+	0.974776i	$0.571646\pi$
$432$	−5.65187	−0.271925
$433$	22.6284	1.08745	0.543726	−	0.839263i	$-0.317013\pi$
$433$	22.6284	1.08745	0.543726	+	0.839263i	$0.317013\pi$
$434$	−0.338626	−0.0162546
$435$	−7.44592	−0.357005
$436$	7.75820	0.371550
$437$	0	0
$438$	12.2944	0.587448
$439$	−18.4978	−0.882854	−0.441427	−	0.897297i	$-0.645528\pi$
$439$	−18.4978	−0.882854	−0.441427	+	0.897297i	$0.645528\pi$
$440$	−5.25954	−0.250739
$441$	13.9845	0.665927
$442$	−27.1540	−1.29158
$443$	−22.3789	−1.06325	−0.531627	−	0.846978i	$-0.678419\pi$
$443$	−22.3789	−1.06325	−0.531627	+	0.846978i	$0.678419\pi$
$444$	−2.10007	−0.0996651
$445$	15.9469	0.755954
$446$	−2.25529	−0.106791
$447$	15.9525	0.754528
$448$	−1.14266	−0.0539855
$449$	4.91420	0.231916	0.115958	−	0.993254i	$-0.463006\pi$
$449$	4.91420	0.231916	0.115958	+	0.993254i	$0.463006\pi$
$450$	−4.45741	−0.210125
$451$	−13.5453	−0.637822
$452$	−53.1591	−2.50039
$453$	−0.442267	−0.0207795
$454$	11.2378	0.527414
$455$	0.317493	0.0148843
$456$	6.16685	0.288789
$457$	11.5825	0.541808	0.270904	−	0.962606i	$-0.412677\pi$
$457$	11.5825	0.541808	0.270904	+	0.962606i	$0.412677\pi$
$458$	−51.1498	−2.39007
$459$	16.9148	0.789516
$460$	0	0
$461$	−15.5495	−0.724210	−0.362105	−	0.932137i	$-0.617942\pi$
$461$	−15.5495	−0.724210	−0.362105	+	0.932137i	$0.617942\pi$
$462$	−0.479415	−0.0223044
$463$	10.1271	0.470646	0.235323	−	0.971917i	$-0.424385\pi$
$463$	10.1271	0.470646	0.235323	+	0.971917i	$0.424385\pi$
$464$	8.41667	0.390734
$465$	−1.72352	−0.0799261
$466$	47.9683	2.22209
$467$	0.159849	0.00739693	0.00369847	−	0.999993i	$-0.498823\pi$
$467$	0.159849	0.00739693	0.00369847	+	0.999993i	$0.498823\pi$
$468$	21.3722	0.987932
$469$	−1.07629	−0.0496984
$470$	25.8855	1.19401
$471$	−7.11870	−0.328012
$472$	24.9028	1.14625
$473$	−5.84951	−0.268961
$474$	−15.6200	−0.717450
$475$	−2.86103	−0.131273
$476$	0.884884	0.0405586
$477$	20.7502	0.950085
$478$	−19.5452	−0.893979
$479$	5.87472	0.268423	0.134211	−	0.990953i	$-0.457150\pi$
$479$	5.87472	0.268423	0.134211	+	0.990953i	$0.457150\pi$
$480$	−6.83020	−0.311755
$481$	−2.54906	−0.116227
$482$	19.6530	0.895169
$483$	0	0
$484$	−14.9720	−0.680545
$485$	−14.3797	−0.652947
$486$	−35.6593	−1.61754
$487$	−6.93404	−0.314211	−0.157106	−	0.987582i	$-0.550216\pi$
$487$	−6.93404	−0.314211	−0.157106	+	0.987582i	$0.550216\pi$
$488$	8.75496	0.396318
$489$	7.14635	0.323169
$490$	15.5836	0.703997
$491$	−21.9565	−0.990883	−0.495442	−	0.868641i	$-0.664994\pi$
$491$	−21.9565	−0.990883	−0.495442	+	0.868641i	$0.664994\pi$
$492$	16.4710	0.742568
$493$	−25.1893	−1.13447
$494$	22.9646	1.03322
$495$	4.88019	0.219348
$496$	1.94822	0.0874775
$497$	0.167213	0.00750055
$498$	−9.29948	−0.416720
$499$	−28.4517	−1.27367	−0.636836	−	0.770999i	$-0.719757\pi$
$499$	−28.4517	−1.27367	−0.636836	+	0.770999i	$0.719757\pi$
$500$	−2.96714	−0.132694
$501$	−1.33264	−0.0595380
$502$	−13.1316	−0.586091
$503$	34.3525	1.53170	0.765850	−	0.643019i	$-0.222318\pi$
$503$	34.3525	1.53170	0.765850	+	0.643019i	$0.222318\pi$
$504$	−0.380034	−0.0169281
$505$	−17.3832	−0.773544
$506$	0	0
$507$	0.0292481	0.00129895
$508$	8.87701	0.393854
$509$	−6.88147	−0.305016	−0.152508	−	0.988302i	$-0.548735\pi$
$509$	−6.88147	−0.305016	−0.152508	+	0.988302i	$0.548735\pi$
$510$	7.53964	0.333861
$511$	−0.486301	−0.0215127
$512$	12.5936	0.556565
$513$	−14.3052	−0.631588
$514$	−17.1909	−0.758260
$515$	−1.16334	−0.0512630
$516$	7.11296	0.313131
$517$	−28.3406	−1.24642
$518$	0.139060	0.00610994
$519$	−2.70076	−0.118550
$520$	7.76289	0.340425
$521$	−5.51528	−0.241629	−0.120814	−	0.992675i	$-0.538551\pi$
$521$	−5.51528	−0.241629	−0.120814	+	0.992675i	$0.538551\pi$
$522$	33.1896	1.45267
$523$	−4.75922	−0.208106	−0.104053	−	0.994572i	$-0.533181\pi$
$523$	−4.75922	−0.208106	−0.104053	+	0.994572i	$0.533181\pi$
$524$	−39.8293	−1.73995
$525$	−0.0881559	−0.00384744
$526$	49.9022	2.17584
$527$	−5.83059	−0.253985
$528$	2.75822	0.120036
$529$	0	0
$530$	23.1230	1.00440
$531$	−23.1067	−1.00274
$532$	−0.748362	−0.0324456
$533$	19.9924	0.865965
$534$	35.5409	1.53801
$535$	−17.1503	−0.741474
$536$	−26.3159	−1.13667
$537$	19.7880	0.853915
$538$	20.6430	0.889981
$539$	−17.0617	−0.734899
$540$	−14.8357	−0.638426
$541$	−16.9095	−0.726997	−0.363499	−	0.931595i	$-0.618418\pi$
$541$	−16.9095	−0.726997	−0.363499	+	0.931595i	$0.618418\pi$
$542$	48.9392	2.10212
$543$	−3.98546	−0.171032
$544$	−23.1063	−0.990675
$545$	−2.61471	−0.112002
$546$	0.707599	0.0302824
$547$	−38.5686	−1.64907	−0.824537	−	0.565808i	$-0.808564\pi$
$547$	−38.5686	−1.64907	−0.824537	+	0.565808i	$0.808564\pi$
$548$	57.2456	2.44541
$549$	−8.12350	−0.346702
$550$	5.43826	0.231888
$551$	21.3030	0.907539
$552$	0	0
$553$	0.617845	0.0262734
$554$	27.8788	1.18445
$555$	0.707778	0.0300435
$556$	45.9793	1.94996
$557$	42.1360	1.78536	0.892680	−	0.450690i	$-0.148822\pi$
$557$	42.1360	1.78536	0.892680	+	0.450690i	$0.148822\pi$
$558$	7.68243	0.325223
$559$	8.63367	0.365165
$560$	0.0996491	0.00421094
$561$	−8.25475	−0.348516
$562$	−54.6551	−2.30549
$563$	−6.01962	−0.253697	−0.126848	−	0.991922i	$-0.540486\pi$
$563$	−6.01962	−0.253697	−0.126848	+	0.991922i	$0.540486\pi$
$564$	34.4620	1.45111
$565$	17.9160	0.753730
$566$	−39.3718	−1.65492
$567$	0.0881559	0.00370220
$568$	4.08847	0.171548
$569$	−17.4865	−0.733074	−0.366537	−	0.930404i	$-0.619457\pi$
$569$	−17.4865	−0.733074	−0.366537	+	0.930404i	$0.619457\pi$
$570$	−6.37640	−0.267078
$571$	13.1986	0.552346	0.276173	−	0.961108i	$-0.410934\pi$
$571$	13.1986	0.552346	0.276173	+	0.961108i	$0.410934\pi$
$572$	−26.0751	−1.09026
$573$	5.97924	0.249786
$574$	−1.09065	−0.0455229
$575$	0	0
$576$	25.9235	1.08015
$577$	−32.4864	−1.35242	−0.676212	−	0.736707i	$-0.736380\pi$
$577$	−32.4864	−1.35242	−0.676212	+	0.736707i	$0.736380\pi$
$578$	−12.3817	−0.515011
$579$	−10.0864	−0.419177
$580$	22.0931	0.917365
$581$	0.367839	0.0152605
$582$	−32.0481	−1.32844
$583$	−25.3162	−1.04849
$584$	−11.8903	−0.492026
$585$	−7.20299	−0.297807
$586$	18.9224	0.781676
$587$	−13.1715	−0.543644	−0.271822	−	0.962348i	$-0.587626\pi$
$587$	−13.1715	−0.543644	−0.271822	+	0.962348i	$0.587626\pi$
$588$	20.7469	0.855588
$589$	4.93103	0.203180
$590$	−25.7490	−1.06007
$591$	5.11562	0.210429
$592$	−0.800053	−0.0328820
$593$	31.5836	1.29698	0.648492	−	0.761222i	$-0.275400\pi$
$593$	31.5836	1.29698	0.648492	+	0.761222i	$0.275400\pi$
$594$	27.1913	1.11567
$595$	−0.298228	−0.0122262
$596$	−47.3333	−1.93885
$597$	−26.5800	−1.08785
$598$	0	0
$599$	−5.38162	−0.219887	−0.109943	−	0.993938i	$-0.535067\pi$
$599$	−5.38162	−0.219887	−0.109943	+	0.993938i	$0.535067\pi$
$600$	−2.15546	−0.0879965
$601$	33.8505	1.38079	0.690395	−	0.723433i	$-0.257437\pi$
$601$	33.8505	1.38079	0.690395	+	0.723433i	$0.257437\pi$
$602$	−0.470996	−0.0191964
$603$	24.4178	0.994371
$604$	1.31227	0.0533953
$605$	5.04594	0.205147
$606$	−38.7421	−1.57379
$607$	21.7913	0.884480	0.442240	−	0.896897i	$-0.354184\pi$
$607$	21.7913	0.884480	0.442240	+	0.896897i	$0.354184\pi$
$608$	19.5414	0.792509
$609$	0.656402	0.0265988
$610$	−9.05245	−0.366523
$611$	41.8298	1.69225
$612$	−20.0754	−0.811501
$613$	−6.78176	−0.273913	−0.136956	−	0.990577i	$-0.543732\pi$
$613$	−6.78176	−0.273913	−0.136956	+	0.990577i	$0.543732\pi$
$614$	−32.7167	−1.32034
$615$	−5.55113	−0.223843
$616$	0.463659	0.0186814
$617$	−32.2677	−1.29905	−0.649524	−	0.760341i	$-0.725032\pi$
$617$	−32.2677	−1.29905	−0.649524	+	0.760341i	$0.725032\pi$
$618$	−2.59275	−0.104296
$619$	−35.0977	−1.41069	−0.705347	−	0.708862i	$-0.749209\pi$
$619$	−35.0977	−1.41069	−0.705347	+	0.708862i	$0.749209\pi$
$620$	5.11391	0.205379
$621$	0	0
$622$	67.2534	2.69661
$623$	−1.40581	−0.0563226
$624$	−4.07103	−0.162972
$625$	1.00000	0.0400000
$626$	−12.4050	−0.495805
$627$	6.98119	0.278802
$628$	21.1222	0.842866
$629$	2.39439	0.0954705
$630$	0.392948	0.0156554
$631$	−13.0467	−0.519383	−0.259691	−	0.965692i	$-0.583621\pi$
$631$	−13.0467	−0.519383	−0.259691	+	0.965692i	$0.583621\pi$
$632$	15.1067	0.600911
$633$	14.7426	0.585964
$634$	6.26510	0.248819
$635$	−2.99178	−0.118725
$636$	30.7843	1.22068
$637$	25.1825	0.997765
$638$	−40.4928	−1.60313
$639$	−3.79358	−0.150072
$640$	15.2276	0.601924
$641$	−36.1324	−1.42715	−0.713573	−	0.700581i	$-0.752924\pi$
$641$	−36.1324	−1.42715	−0.713573	+	0.700581i	$0.752924\pi$
$642$	−38.2231	−1.50854
$643$	31.5510	1.24425	0.622126	−	0.782917i	$-0.286269\pi$
$643$	31.5510	1.24425	0.622126	+	0.782917i	$0.286269\pi$
$644$	0	0
$645$	−2.39725	−0.0943915
$646$	−21.5711	−0.848705
$647$	−13.8629	−0.545006	−0.272503	−	0.962155i	$-0.587851\pi$
$647$	−13.8629	−0.545006	−0.272503	+	0.962155i	$0.587851\pi$
$648$	2.15546	0.0846747
$649$	28.1912	1.10660
$650$	−8.02667	−0.314832
$651$	0.151938	0.00595493
$652$	−21.2042	−0.830420
$653$	−5.65494	−0.221295	−0.110647	−	0.993860i	$-0.535292\pi$
$653$	−5.65494	−0.221295	−0.110647	+	0.993860i	$0.535292\pi$
$654$	−5.82742	−0.227870
$655$	13.4235	0.524499
$656$	6.27485	0.244992
$657$	11.0327	0.430428
$658$	−2.28196	−0.0889600
$659$	29.2694	1.14017	0.570087	−	0.821584i	$-0.306910\pi$
$659$	29.2694	1.14017	0.570087	+	0.821584i	$0.306910\pi$
$660$	7.24009	0.281820
$661$	16.0655	0.624876	0.312438	−	0.949938i	$-0.398854\pi$
$661$	16.0655	0.624876	0.312438	+	0.949938i	$0.398854\pi$
$662$	−30.8745	−1.19997
$663$	12.1837	0.473177
$664$	8.99387	0.349030
$665$	0.252217	0.00978055
$666$	−3.15486	−0.122248
$667$	0	0
$668$	3.95413	0.152990
$669$	1.01193	0.0391234
$670$	27.2101	1.05122
$671$	9.91105	0.382612
$672$	0.602123	0.0232274
$673$	3.82334	0.147379	0.0736895	−	0.997281i	$-0.476523\pi$
$673$	3.82334	0.147379	0.0736895	+	0.997281i	$0.476523\pi$
$674$	48.0956	1.85257
$675$	5.00000	0.192450
$676$	−0.0867830	−0.00333781
$677$	16.4258	0.631296	0.315648	−	0.948876i	$-0.397778\pi$
$677$	16.4258	0.631296	0.315648	+	0.948876i	$0.397778\pi$
$678$	39.9294	1.53348
$679$	1.26765	0.0486481
$680$	−7.29186	−0.279630
$681$	−5.04227	−0.193220
$682$	−9.37292	−0.358908
$683$	7.36144	0.281678	0.140839	−	0.990033i	$-0.455020\pi$
$683$	7.36144	0.281678	0.140839	+	0.990033i	$0.455020\pi$
$684$	16.9781	0.649175
$685$	−19.2932	−0.737156
$686$	−2.74911	−0.104961
$687$	22.9504	0.875614
$688$	2.70978	0.103310
$689$	37.3658	1.42352
$690$	0	0
$691$	−9.67502	−0.368055	−0.184028	−	0.982921i	$-0.558914\pi$
$691$	−9.67502	−0.368055	−0.184028	+	0.982921i	$0.558914\pi$
$692$	8.01352	0.304628
$693$	−0.430218	−0.0163426
$694$	42.1395	1.59959
$695$	−15.4962	−0.587804
$696$	16.0494	0.608352
$697$	−18.7793	−0.711316
$698$	46.6446	1.76552
$699$	−21.5229	−0.814071
$700$	0.261571	0.00988644
$701$	42.5690	1.60781	0.803905	−	0.594758i	$-0.202752\pi$
$701$	42.5690	1.60781	0.803905	+	0.594758i	$0.202752\pi$
$702$	−40.1334	−1.51474
$703$	−2.02497	−0.0763734
$704$	−31.6279	−1.19202
$705$	−11.6146	−0.437430
$706$	3.59273	0.135214
$707$	1.53243	0.0576331
$708$	−34.2803	−1.28833
$709$	35.0710	1.31712	0.658559	−	0.752529i	$-0.271166\pi$
$709$	35.0710	1.31712	0.658559	+	0.752529i	$0.271166\pi$
$710$	−4.22739	−0.158651
$711$	−14.0171	−0.525682
$712$	−34.3729	−1.28818
$713$	0	0
$714$	−0.664664	−0.0248744
$715$	8.78798	0.328652
$716$	−58.7137	−2.19423
$717$	8.76977	0.327513
$718$	77.5951	2.89582
$719$	22.2022	0.828003	0.414001	−	0.910276i	$-0.364131\pi$
$719$	22.2022	0.828003	0.414001	+	0.910276i	$0.364131\pi$
$720$	−2.26075	−0.0842530
$721$	0.102556	0.00381937
$722$	−24.1024	−0.896997
$723$	−8.81811	−0.327949
$724$	11.8254	0.439488
$725$	−7.44592	−0.276535
$726$	11.2459	0.417375
$727$	0.698686	0.0259128	0.0129564	−	0.999916i	$-0.495876\pi$
$727$	0.698686	0.0259128	0.0129564	+	0.999916i	$0.495876\pi$
$728$	−0.684345	−0.0253635
$729$	13.0000	0.481481
$730$	12.2944	0.455036
$731$	−8.10980	−0.299952
$732$	−12.0518	−0.445446
$733$	−37.3028	−1.37781	−0.688905	−	0.724852i	$-0.741908\pi$
$733$	−37.3028	−1.37781	−0.688905	+	0.724852i	$0.741908\pi$
$734$	−50.4231	−1.86115
$735$	−6.99223	−0.257912
$736$	0	0
$737$	−29.7909	−1.09736
$738$	24.7437	0.910828
$739$	−24.5705	−0.903841	−0.451920	−	0.892058i	$-0.649261\pi$
$739$	−24.5705	−0.903841	−0.451920	+	0.892058i	$0.649261\pi$
$740$	−2.10007	−0.0772003
$741$	−10.3040	−0.378526
$742$	−2.03843	−0.0748332
$743$	41.3598	1.51735	0.758673	−	0.651472i	$-0.225848\pi$
$743$	41.3598	1.51735	0.758673	+	0.651472i	$0.225848\pi$
$744$	3.71498	0.136198
$745$	15.9525	0.584455
$746$	24.0594	0.880876
$747$	−8.34518	−0.305334
$748$	24.4930	0.895552
$749$	1.51190	0.0552438
$750$	2.22871	0.0813809
$751$	−40.9702	−1.49502	−0.747511	−	0.664249i	$-0.768751\pi$
$751$	−40.9702	−1.49502	−0.747511	+	0.664249i	$0.768751\pi$
$752$	13.1288	0.478758
$753$	5.89202	0.214717
$754$	59.7660	2.17655
$755$	−0.442267	−0.0160957
$756$	1.30785	0.0475662
$757$	9.98856	0.363040	0.181520	−	0.983387i	$-0.441898\pi$
$757$	9.98856	0.363040	0.181520	+	0.983387i	$0.441898\pi$
$758$	−8.21774	−0.298482
$759$	0	0
$760$	6.16685	0.223695
$761$	−16.8603	−0.611184	−0.305592	−	0.952163i	$-0.598854\pi$
$761$	−16.8603	−0.611184	−0.305592	+	0.952163i	$0.598854\pi$
$762$	−6.66780	−0.241549
$763$	0.230502	0.00834473
$764$	−17.7412	−0.641855
$765$	6.76593	0.244623
$766$	−13.2446	−0.478548
$767$	−41.6093	−1.50242
$768$	8.01431	0.289192
$769$	−43.7692	−1.57836	−0.789180	−	0.614162i	$-0.789494\pi$
$769$	−43.7692	−1.57836	−0.789180	+	0.614162i	$0.789494\pi$
$770$	−0.479415	−0.0172769
$771$	7.71341	0.277792
$772$	29.9277	1.07712
$773$	33.6293	1.20956	0.604780	−	0.796392i	$-0.293261\pi$
$773$	33.6293	1.20956	0.604780	+	0.796392i	$0.293261\pi$
$774$	10.6855	0.384083
$775$	−1.72352	−0.0619105
$776$	30.9949	1.11265
$777$	−0.0623948	−0.00223840
$778$	14.8036	0.530735
$779$	15.8820	0.569030
$780$	−10.6861	−0.382625
$781$	4.62835	0.165615
$782$	0	0
$783$	−37.2296	−1.33048
$784$	7.90383	0.282280
$785$	−7.11870	−0.254077
$786$	29.9170	1.06711
$787$	1.25077	0.0445850	0.0222925	−	0.999751i	$-0.492903\pi$
$787$	1.25077	0.0445850	0.0222925	+	0.999751i	$0.492903\pi$
$788$	−15.1787	−0.540721
$789$	−22.3906	−0.797128
$790$	−15.6200	−0.555735
$791$	−1.57940	−0.0561569
$792$	−10.5191	−0.373779
$793$	−14.6284	−0.519468
$794$	−10.1572	−0.360466
$795$	−10.3751	−0.367966
$796$	78.8664	2.79535
$797$	−12.2211	−0.432893	−0.216447	−	0.976294i	$-0.569447\pi$
$797$	−12.2211	−0.432893	−0.216447	+	0.976294i	$0.569447\pi$
$798$	0.562117	0.0198987
$799$	−39.2917	−1.39004
$800$	−6.83020	−0.241484
$801$	31.8937	1.12691
$802$	−62.2061	−2.19657
$803$	−13.4605	−0.475010
$804$	36.2255	1.27758
$805$	0	0
$806$	13.8341	0.487285
$807$	−9.26230	−0.326048
$808$	37.4689	1.31815
$809$	−26.8027	−0.942333	−0.471166	−	0.882044i	$-0.656167\pi$
$809$	−26.8027	−0.942333	−0.471166	+	0.882044i	$0.656167\pi$
$810$	−2.22871	−0.0783088
$811$	−39.5899	−1.39019	−0.695095	−	0.718918i	$-0.744638\pi$
$811$	−39.5899	−1.39019	−0.695095	+	0.718918i	$0.744638\pi$
$812$	−1.94763	−0.0683486
$813$	−21.9586	−0.770121
$814$	3.84908	0.134910
$815$	7.14635	0.250326
$816$	3.82401	0.133867
$817$	6.85860	0.239952
$818$	18.0950	0.632676
$819$	0.634986	0.0221882
$820$	16.4710	0.575191
$821$	−31.6627	−1.10504	−0.552518	−	0.833501i	$-0.686333\pi$
$821$	−31.6627	−1.10504	−0.552518	+	0.833501i	$0.686333\pi$
$822$	−42.9989	−1.49976
$823$	−46.9147	−1.63535	−0.817673	−	0.575683i	$-0.804736\pi$
$823$	−46.9147	−1.63535	−0.817673	+	0.575683i	$0.804736\pi$
$824$	2.50754	0.0873545
$825$	−2.44009	−0.0849532
$826$	2.26993	0.0789809
$827$	−24.2676	−0.843869	−0.421934	−	0.906626i	$-0.638649\pi$
$827$	−24.2676	−0.843869	−0.421934	+	0.906626i	$0.638649\pi$
$828$	0	0
$829$	−21.8597	−0.759220	−0.379610	−	0.925147i	$-0.623942\pi$
$829$	−21.8597	−0.759220	−0.379610	+	0.925147i	$0.623942\pi$
$830$	−9.29948	−0.322790
$831$	−12.5089	−0.433930
$832$	46.6817	1.61840
$833$	−23.6545	−0.819578
$834$	−34.5365	−1.19590
$835$	−1.33264	−0.0461179
$836$	−20.7141	−0.716413
$837$	−8.61758	−0.297867
$838$	−61.8114	−2.13524
$839$	−27.3006	−0.942522	−0.471261	−	0.881994i	$-0.656201\pi$
$839$	−27.3006	−0.942522	−0.471261	+	0.881994i	$0.656201\pi$
$840$	0.190017	0.00655621
$841$	26.4417	0.911784
$842$	−77.9019	−2.68468
$843$	24.5232	0.844625
$844$	−43.7432	−1.50570
$845$	0.0292481	0.00100616
$846$	51.7710	1.77992
$847$	−0.444829	−0.0152845
$848$	11.7277	0.402731
$849$	17.6658	0.606288
$850$	7.53964	0.258607
$851$	0	0
$852$	−5.62804	−0.192813
$853$	−28.1686	−0.964473	−0.482237	−	0.876041i	$-0.660175\pi$
$853$	−28.1686	−0.964473	−0.482237	+	0.876041i	$0.660175\pi$
$854$	0.798027	0.0273079
$855$	−5.72206	−0.195690
$856$	36.9669	1.26350
$857$	−11.2388	−0.383909	−0.191954	−	0.981404i	$-0.561483\pi$
$857$	−11.2388	−0.383909	−0.191954	+	0.981404i	$0.561483\pi$
$858$	19.5858	0.668650
$859$	−8.80436	−0.300401	−0.150200	−	0.988656i	$-0.547992\pi$
$859$	−8.80436	−0.300401	−0.150200	+	0.988656i	$0.547992\pi$
$860$	7.11296	0.242550
$861$	0.489365	0.0166775
$862$	−20.6534	−0.703457
$863$	−47.8623	−1.62925	−0.814626	−	0.579987i	$-0.803058\pi$
$863$	−47.8623	−1.62925	−0.814626	+	0.579987i	$0.803058\pi$
$864$	−34.1510	−1.16184
$865$	−2.70076	−0.0918285
$866$	50.4321	1.71375
$867$	5.55555	0.188677
$868$	−0.450821	−0.0153019
$869$	17.1015	0.580129
$870$	−16.5948	−0.562616
$871$	43.9703	1.48988
$872$	5.63591	0.190856
$873$	−28.7593	−0.973356
$874$	0	0
$875$	−0.0881559	−0.00298021
$876$	16.3678	0.553018
$877$	−47.1535	−1.59226	−0.796130	−	0.605125i	$-0.793123\pi$
$877$	−47.1535	−1.59226	−0.796130	+	0.605125i	$0.793123\pi$
$878$	−41.2263	−1.39132
$879$	−8.49029	−0.286370
$880$	2.75822	0.0929795
$881$	36.9722	1.24562	0.622812	−	0.782371i	$-0.285990\pi$
$881$	36.9722	1.24562	0.622812	+	0.782371i	$0.285990\pi$
$882$	31.1673	1.04946
$883$	−54.5603	−1.83610	−0.918050	−	0.396466i	$-0.870237\pi$
$883$	−54.5603	−1.83610	−0.918050	+	0.396466i	$0.870237\pi$
$884$	−36.1508	−1.21588
$885$	11.5533	0.388361
$886$	−49.8761	−1.67562
$887$	−14.1790	−0.476083	−0.238041	−	0.971255i	$-0.576505\pi$
$887$	−14.1790	−0.476083	−0.238041	+	0.971255i	$0.576505\pi$
$888$	−1.52559	−0.0511955
$889$	0.263743	0.00884565
$890$	35.5409	1.19133
$891$	2.44009	0.0817462
$892$	−3.00253	−0.100532
$893$	33.2296	1.11199
$894$	35.5535	1.18909
$895$	19.7880	0.661439
$896$	−1.34240	−0.0448465
$897$	0	0
$898$	10.9523	0.365484
$899$	12.8332	0.428010
$900$	−5.93427	−0.197809
$901$	−35.0985	−1.16930
$902$	−30.1885	−1.00517
$903$	0.211332	0.00703267
$904$	−38.6172	−1.28439
$905$	−3.98546	−0.132481
$906$	−0.985683	−0.0327471
$907$	49.8093	1.65389	0.826945	−	0.562283i	$-0.190077\pi$
$907$	49.8093	1.65389	0.826945	+	0.562283i	$0.190077\pi$
$908$	14.9611	0.496502
$909$	−34.7665	−1.15313
$910$	0.707599	0.0234567
$911$	−21.1307	−0.700092	−0.350046	−	0.936733i	$-0.613834\pi$
$911$	−21.1307	−0.700092	−0.350046	+	0.936733i	$0.613834\pi$
$912$	−3.23403	−0.107090
$913$	10.1815	0.336959
$914$	25.8141	0.853854
$915$	4.06175	0.134277
$916$	−68.0971	−2.24999
$917$	−1.18336	−0.0390780
$918$	37.6982	1.24423
$919$	−1.66022	−0.0547657	−0.0273829	−	0.999625i	$-0.508717\pi$
$919$	−1.66022	−0.0547657	−0.0273829	+	0.999625i	$0.508717\pi$
$920$	0	0
$921$	14.6797	0.483711
$922$	−34.6552	−1.14131
$923$	−6.83128	−0.224854
$924$	−0.638257	−0.0209971
$925$	0.707778	0.0232716
$926$	22.5703	0.741707
$927$	−2.32669	−0.0764184
$928$	50.8571	1.66947
$929$	29.1773	0.957275	0.478637	−	0.878013i	$-0.341131\pi$
$929$	29.1773	0.957275	0.478637	+	0.878013i	$0.341131\pi$
$930$	−3.84121	−0.125958
$931$	20.0050	0.655637
$932$	63.8614	2.09185
$933$	−30.1760	−0.987916
$934$	0.356257	0.0116571
$935$	−8.25475	−0.269959
$936$	15.5258	0.507476
$937$	18.4120	0.601495	0.300748	−	0.953704i	$-0.402764\pi$
$937$	18.4120	0.601495	0.300748	+	0.953704i	$0.402764\pi$
$938$	−2.39873	−0.0783214
$939$	5.56602	0.181640
$940$	34.4620	1.12403
$941$	43.3084	1.41181	0.705907	−	0.708304i	$-0.250539\pi$
$941$	43.3084	1.41181	0.705907	+	0.708304i	$0.250539\pi$
$942$	−15.8655	−0.516926
$943$	0	0
$944$	−13.0596	−0.425053
$945$	−0.440780	−0.0143386
$946$	−13.0368	−0.423865
$947$	−21.0783	−0.684951	−0.342476	−	0.939527i	$-0.611265\pi$
$947$	−21.0783	−0.684951	−0.342476	+	0.939527i	$0.611265\pi$
$948$	−20.7953	−0.675400
$949$	19.8672	0.644916
$950$	−6.37640	−0.206878
$951$	−2.81109	−0.0911559
$952$	0.642821	0.0208339
$953$	14.7442	0.477610	0.238805	−	0.971067i	$-0.423244\pi$
$953$	14.7442	0.477610	0.238805	+	0.971067i	$0.423244\pi$
$954$	46.2461	1.49727
$955$	5.97924	0.193484
$956$	−26.0211	−0.841582
$957$	18.1688	0.587312
$958$	13.0930	0.423017
$959$	1.70081	0.0549220
$960$	−12.9618	−0.418339
$961$	−28.0295	−0.904177
$962$	−5.68110	−0.183166
$963$	−34.3007	−1.10532
$964$	26.1645	0.842703
$965$	−10.0864	−0.324693
$966$	0	0
$967$	−25.3720	−0.815909	−0.407955	−	0.913002i	$-0.633758\pi$
$967$	−25.3720	−0.815909	−0.407955	+	0.913002i	$0.633758\pi$
$968$	−10.8763	−0.349579
$969$	9.67876	0.310927
$970$	−32.0481	−1.02900
$971$	−39.1100	−1.25510	−0.627549	−	0.778577i	$-0.715942\pi$
$971$	−39.1100	−1.25510	−0.627549	+	0.778577i	$0.715942\pi$
$972$	−47.4742	−1.52274
$973$	1.36608	0.0437945
$974$	−15.4539	−0.495176
$975$	3.60149	0.115340
$976$	−4.59129	−0.146964
$977$	−23.2542	−0.743967	−0.371984	−	0.928239i	$-0.621322\pi$
$977$	−23.2542	−0.743967	−0.371984	+	0.928239i	$0.621322\pi$
$978$	15.9271	0.509293
$979$	−38.9119	−1.24363
$980$	20.7469	0.662735
$981$	−5.22942	−0.166962
$982$	−48.9346	−1.56157
$983$	0.657692	0.0209771	0.0104886	−	0.999945i	$-0.496661\pi$
$983$	0.657692	0.0209771	0.0104886	+	0.999945i	$0.496661\pi$
$984$	11.9653	0.381439
$985$	5.11562	0.162997
$986$	−56.1395	−1.78785
$987$	1.02389	0.0325909
$988$	30.5733	0.972667
$989$	0	0
$990$	10.8765	0.345678
$991$	3.15685	0.100281	0.0501403	−	0.998742i	$-0.484033\pi$
$991$	3.15685	0.100281	0.0501403	+	0.998742i	$0.484033\pi$
$992$	11.7720	0.373760
$993$	13.8531	0.439614
$994$	0.372670	0.0118204
$995$	−26.5800	−0.842642
$996$	−12.3806	−0.392296
$997$	−8.80815	−0.278957	−0.139479	−	0.990225i	$-0.544543\pi$
$997$	−8.80815	−0.278957	−0.139479	+	0.990225i	$0.544543\pi$
$998$	−63.4105	−2.00722
$999$	3.53889	0.111966

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2645.2.a.n.1.5		5
23.2	even	11		115.2.g.a.96.1	yes	10
23.12	even	11		115.2.g.a.6.1	✓	10
23.22	odd	2		2645.2.a.o.1.5		5
115.2	odd	44		575.2.p.a.349.1		20
115.12	odd	44		575.2.p.a.374.2		20
115.48	odd	44		575.2.p.a.349.2		20
115.58	odd	44		575.2.p.a.374.1		20
115.94	even	22		575.2.k.a.326.1		10
115.104	even	22		575.2.k.a.351.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.a.6.1	✓	10	23.12	even	11
115.2.g.a.96.1	yes	10	23.2	even	11
575.2.k.a.326.1		10	115.94	even	22
575.2.k.a.351.1		10	115.104	even	22
575.2.p.a.349.1		20	115.2	odd	44
575.2.p.a.349.2		20	115.48	odd	44
575.2.p.a.374.1		20	115.58	odd	44
575.2.p.a.374.2		20	115.12	odd	44
2645.2.a.n.1.5		5	1.1	even	1	trivial
2645.2.a.o.1.5		5	23.22	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2645 = 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2645.a (trivial)

\(f(q)\)	\(=\)	\(q+2.22871 q^{2} -1.00000 q^{3} +2.96714 q^{4} -1.00000 q^{5} -2.22871 q^{6} +0.0881559 q^{7} +2.15546 q^{8} -2.00000 q^{9} -2.22871 q^{10} +2.44009 q^{11} -2.96714 q^{12} -3.60149 q^{13} +0.196474 q^{14} +1.00000 q^{15} -1.13037 q^{16} +3.38296 q^{17} -4.45741 q^{18} -2.86103 q^{19} -2.96714 q^{20} -0.0881559 q^{21} +5.43826 q^{22} -2.15546 q^{24} +1.00000 q^{25} -8.02667 q^{26} +5.00000 q^{27} +0.261571 q^{28} -7.44592 q^{29} +2.22871 q^{30} -1.72352 q^{31} -6.83020 q^{32} -2.44009 q^{33} +7.53964 q^{34} -0.0881559 q^{35} -5.93427 q^{36} +0.707778 q^{37} -6.37640 q^{38} +3.60149 q^{39} -2.15546 q^{40} -5.55113 q^{41} -0.196474 q^{42} -2.39725 q^{43} +7.24009 q^{44} +2.00000 q^{45} -11.6146 q^{47} +1.13037 q^{48} -6.99223 q^{49} +2.22871 q^{50} -3.38296 q^{51} -10.6861 q^{52} -10.3751 q^{53} +11.1435 q^{54} -2.44009 q^{55} +0.190017 q^{56} +2.86103 q^{57} -16.5948 q^{58} +11.5533 q^{59} +2.96714 q^{60} +4.06175 q^{61} -3.84121 q^{62} -0.176312 q^{63} -12.9618 q^{64} +3.60149 q^{65} -5.43826 q^{66} -12.2089 q^{67} +10.0377 q^{68} -0.196474 q^{70} +1.89679 q^{71} -4.31093 q^{72} -5.51637 q^{73} +1.57743 q^{74} -1.00000 q^{75} -8.48907 q^{76} +0.215109 q^{77} +8.02667 q^{78} +7.00855 q^{79} +1.13037 q^{80} +1.00000 q^{81} -12.3718 q^{82} +4.17259 q^{83} -0.261571 q^{84} -3.38296 q^{85} -5.34276 q^{86} +7.44592 q^{87} +5.25954 q^{88} -15.9469 q^{89} +4.45741 q^{90} -0.317493 q^{91} +1.72352 q^{93} -25.8855 q^{94} +2.86103 q^{95} +6.83020 q^{96} +14.3797 q^{97} -15.5836 q^{98} -4.88019 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 3 q^{2} - 5 q^{3} + 5 q^{4} - 5 q^{5} + 3 q^{6} - 3 q^{7} + 3 q^{8} - 10 q^{9} + 3 q^{10} + 4 q^{11} - 5 q^{12} + 4 q^{14} + 5 q^{15} - 3 q^{16} + 5 q^{17} + 6 q^{18} - q^{19} - 5 q^{20} + 3 q^{21}+ \cdots - 8 q^{99}+O(q^{100}) \) 5 * q - 3 * q^2 - 5 * q^3 + 5 * q^4 - 5 * q^5 + 3 * q^6 - 3 * q^7 + 3 * q^8 - 10 * q^9 + 3 * q^10 + 4 * q^11 - 5 * q^12 + 4 * q^14 + 5 * q^15 - 3 * q^16 + 5 * q^17 + 6 * q^18 - q^19 - 5 * q^20 + 3 * q^21 + 2 * q^22 - 3 * q^24 + 5 * q^25 - 11 * q^26 + 25 * q^27 - 3 * q^28 + q^29 - 3 * q^30 - 10 * q^31 - 2 * q^32 - 4 * q^33 + 8 * q^34 + 3 * q^35 - 10 * q^36 + q^37 + 5 * q^38 - 3 * q^40 - 8 * q^41 - 4 * q^42 + 24 * q^43 + 4 * q^44 + 10 * q^45 - 26 * q^47 + 3 * q^48 - 20 * q^49 - 3 * q^50 - 5 * q^51 - 11 * q^52 + 3 * q^53 - 15 * q^54 - 4 * q^55 + 7 * q^56 + q^57 - 27 * q^58 + 41 * q^59 + 5 * q^60 + 4 * q^61 + 17 * q^62 + 6 * q^63 - 17 * q^64 - 2 * q^66 - 23 * q^67 + 16 * q^68 - 4 * q^70 - 6 * q^72 - 17 * q^73 - 27 * q^74 - 5 * q^75 - 34 * q^76 + 2 * q^77 + 11 * q^78 - 13 * q^79 + 3 * q^80 + 5 * q^81 - 26 * q^82 + 19 * q^83 + 3 * q^84 - 5 * q^85 - 43 * q^86 - q^87 + 31 * q^88 - 32 * q^89 - 6 * q^90 - 11 * q^91 + 10 * q^93 - 2 * q^94 + q^95 + 2 * q^96 + 15 * q^97 + q^98 - 8 * q^99

Introduction

L-functions

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Varieties

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Representations

Groups

Database

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