LMFDB - Embedded newform 2523.2.a.r.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2523,2,Mod(1,2523)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2523, 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("2523.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2523 = 3 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2523.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:	$20.1462564300$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4x^{8} - 6x^{7} + 33x^{6} + 6x^{5} - 90x^{4} + 21x^{3} + 84x^{2} - 36x - 8 $ x^9 - 4x^8 - 6x^7 + 33x^6 + 6x^5 - 90x^4 + 21x^3 + 84x^2 - 36x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 87)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.19178$ of defining polynomial
Character	$\chi$	$=$	2523.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.19178 q^{2} +1.00000 q^{3} +2.80388 q^{4} -2.39677 q^{5} -2.19178 q^{6} +1.35191 q^{7} -1.76193 q^{8} +1.00000 q^{9} +5.25319 q^{10} +3.50954 q^{11} +2.80388 q^{12} +6.03467 q^{13} -2.96308 q^{14} -2.39677 q^{15} -1.74601 q^{16} +3.05437 q^{17} -2.19178 q^{18} +5.63574 q^{19} -6.72027 q^{20} +1.35191 q^{21} -7.69212 q^{22} +1.01478 q^{23} -1.76193 q^{24} +0.744514 q^{25} -13.2266 q^{26} +1.00000 q^{27} +3.79059 q^{28} +5.25319 q^{30} +8.11166 q^{31} +7.35072 q^{32} +3.50954 q^{33} -6.69450 q^{34} -3.24021 q^{35} +2.80388 q^{36} +5.49645 q^{37} -12.3523 q^{38} +6.03467 q^{39} +4.22294 q^{40} -6.85782 q^{41} -2.96308 q^{42} -7.80197 q^{43} +9.84033 q^{44} -2.39677 q^{45} -2.22416 q^{46} -0.418254 q^{47} -1.74601 q^{48} -5.17235 q^{49} -1.63181 q^{50} +3.05437 q^{51} +16.9205 q^{52} -13.3425 q^{53} -2.19178 q^{54} -8.41156 q^{55} -2.38197 q^{56} +5.63574 q^{57} +3.56102 q^{59} -6.72027 q^{60} +7.20954 q^{61} -17.7790 q^{62} +1.35191 q^{63} -12.6191 q^{64} -14.4637 q^{65} -7.69212 q^{66} +8.31317 q^{67} +8.56410 q^{68} +1.01478 q^{69} +7.10182 q^{70} -9.78678 q^{71} -1.76193 q^{72} -0.303730 q^{73} -12.0470 q^{74} +0.744514 q^{75} +15.8019 q^{76} +4.74457 q^{77} -13.2266 q^{78} +4.00638 q^{79} +4.18478 q^{80} +1.00000 q^{81} +15.0308 q^{82} -4.31434 q^{83} +3.79059 q^{84} -7.32063 q^{85} +17.1002 q^{86} -6.18356 q^{88} +13.9924 q^{89} +5.25319 q^{90} +8.15831 q^{91} +2.84532 q^{92} +8.11166 q^{93} +0.916719 q^{94} -13.5076 q^{95} +7.35072 q^{96} -3.80357 q^{97} +11.3366 q^{98} +3.50954 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 5 q^{2} + 9 q^{3} + 11 q^{4} - 4 q^{5} + 5 q^{6} + 5 q^{7} + 24 q^{8} + 9 q^{9} - q^{11} + 11 q^{12} + q^{13} + 9 q^{14} - 4 q^{15} + 35 q^{16} + 2 q^{17} + 5 q^{18} + 9 q^{19} - 18 q^{20} + 5 q^{21}+ \cdots - q^{99}+O(q^{100}) $ 9 * q + 5 * q^2 + 9 * q^3 + 11 * q^4 - 4 * q^5 + 5 * q^6 + 5 * q^7 + 24 * q^8 + 9 * q^9 - q^11 + 11 * q^12 + q^13 + 9 * q^14 - 4 * q^15 + 35 * q^16 + 2 * q^17 + 5 * q^18 + 9 * q^19 - 18 * q^20 + 5 * q^21 - 4 * q^22 - 4 * q^23 + 24 * q^24 + q^25 - 8 * q^26 + 9 * q^27 + 40 * q^28 + 8 * q^31 + 43 * q^32 - q^33 - 4 * q^34 + 22 * q^35 + 11 * q^36 + 27 * q^37 - 30 * q^38 + q^39 - 29 * q^40 + 12 * q^41 + 9 * q^42 + 16 * q^43 + 37 * q^44 - 4 * q^45 - 22 * q^46 - 8 * q^47 + 35 * q^48 - 6 * q^49 - 7 * q^50 + 2 * q^51 + 33 * q^52 - 8 * q^53 + 5 * q^54 + 9 * q^55 + 40 * q^56 + 9 * q^57 - 16 * q^59 - 18 * q^60 + 21 * q^61 - 32 * q^62 + 5 * q^63 + 36 * q^64 - 31 * q^65 - 4 * q^66 + 3 * q^67 + 33 * q^68 - 4 * q^69 - 6 * q^70 - 33 * q^71 + 24 * q^72 + 3 * q^73 + 28 * q^74 + q^75 - 26 * q^76 + 24 * q^77 - 8 * q^78 + 3 * q^79 - 64 * q^80 + 9 * q^81 + 13 * q^82 + 13 * q^83 + 40 * q^84 + 6 * q^85 + 58 * q^86 + 27 * q^88 + 6 * q^89 + q^91 - 29 * q^92 + 8 * q^93 - 18 * q^94 + 48 * q^95 + 43 * q^96 + 4 * q^97 - 30 * q^98 - 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 $

$2$	−2.19178	−1.54982	−0.774910	−	0.632072i	$-0.782205\pi$
$2$	−2.19178	−1.54982	−0.774910	+	0.632072i	$0.782205\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.80388	1.40194
$5$	−2.39677	−1.07187	−0.535934	−	0.844260i	$-0.680041\pi$
$5$	−2.39677	−1.07187	−0.535934	+	0.844260i	$0.680041\pi$
$6$	−2.19178	−0.894789
$7$	1.35191	0.510973	0.255486	−	0.966813i	$-0.417764\pi$
$7$	1.35191	0.510973	0.255486	+	0.966813i	$0.417764\pi$
$8$	−1.76193	−0.622936
$9$	1.00000	0.333333
$10$	5.25319	1.66120
$11$	3.50954	1.05817	0.529083	−	0.848570i	$-0.322536\pi$
$11$	3.50954	1.05817	0.529083	+	0.848570i	$0.322536\pi$
$12$	2.80388	0.809411
$13$	6.03467	1.67372	0.836858	−	0.547420i	$-0.184390\pi$
$13$	6.03467	1.67372	0.836858	+	0.547420i	$0.184390\pi$
$14$	−2.96308	−0.791916
$15$	−2.39677	−0.618844
$16$	−1.74601	−0.436502
$17$	3.05437	0.740794	0.370397	−	0.928874i	$-0.379222\pi$
$17$	3.05437	0.740794	0.370397	+	0.928874i	$0.379222\pi$
$18$	−2.19178	−0.516607
$19$	5.63574	1.29293	0.646463	−	0.762945i	$-0.276247\pi$
$19$	5.63574	1.29293	0.646463	+	0.762945i	$0.276247\pi$
$20$	−6.72027	−1.50270
$21$	1.35191	0.295010
$22$	−7.69212	−1.63997
$23$	1.01478	0.211596	0.105798	−	0.994388i	$-0.466260\pi$
$23$	1.01478	0.211596	0.105798	+	0.994388i	$0.466260\pi$
$24$	−1.76193	−0.359653
$25$	0.744514	0.148903
$26$	−13.2266	−2.59396
$27$	1.00000	0.192450
$28$	3.79059	0.716354
$29$	0	0
$29$	0	0
$30$	5.25319	0.959096
$31$	8.11166	1.45690	0.728449	−	0.685100i	$-0.240242\pi$
$31$	8.11166	1.45690	0.728449	+	0.685100i	$0.240242\pi$
$32$	7.35072	1.29944
$33$	3.50954	0.610932
$34$	−6.69450	−1.14810
$35$	−3.24021	−0.547696
$36$	2.80388	0.467314
$37$	5.49645	0.903610	0.451805	−	0.892117i	$-0.350780\pi$
$37$	5.49645	0.903610	0.451805	+	0.892117i	$0.350780\pi$
$38$	−12.3523	−2.00380
$39$	6.03467	0.966320
$40$	4.22294	0.667706
$41$	−6.85782	−1.07101	−0.535506	−	0.844531i	$-0.679879\pi$
$41$	−6.85782	−1.07101	−0.535506	+	0.844531i	$0.679879\pi$
$42$	−2.96308	−0.457213
$43$	−7.80197	−1.18979	−0.594895	−	0.803804i	$-0.702806\pi$
$43$	−7.80197	−1.18979	−0.594895	+	0.803804i	$0.702806\pi$
$44$	9.84033	1.48349
$45$	−2.39677	−0.357290
$46$	−2.22416	−0.327935
$47$	−0.418254	−0.0610086	−0.0305043	−	0.999535i	$-0.509711\pi$
$47$	−0.418254	−0.0610086	−0.0305043	+	0.999535i	$0.509711\pi$
$48$	−1.74601	−0.252015
$49$	−5.17235	−0.738907
$50$	−1.63181	−0.230773
$51$	3.05437	0.427698
$52$	16.9205	2.34645
$53$	−13.3425	−1.83273	−0.916367	−	0.400340i	$-0.868892\pi$
$53$	−13.3425	−1.83273	−0.916367	+	0.400340i	$0.868892\pi$
$54$	−2.19178	−0.298263
$55$	−8.41156	−1.13421
$56$	−2.38197	−0.318304
$57$	5.63574	0.746471
$58$	0	0
$59$	3.56102	0.463606	0.231803	−	0.972763i	$-0.425538\pi$
$59$	3.56102	0.463606	0.231803	+	0.972763i	$0.425538\pi$
$60$	−6.72027	−0.867583
$61$	7.20954	0.923086	0.461543	−	0.887118i	$-0.347296\pi$
$61$	7.20954	0.923086	0.461543	+	0.887118i	$0.347296\pi$
$62$	−17.7790	−2.25793
$63$	1.35191	0.170324
$64$	−12.6191	−1.57739
$65$	−14.4637	−1.79400
$66$	−7.69212	−0.946835
$67$	8.31317	1.01562	0.507808	−	0.861471i	$-0.330456\pi$
$67$	8.31317	1.01562	0.507808	+	0.861471i	$0.330456\pi$
$68$	8.56410	1.03855
$69$	1.01478	0.122165
$70$	7.10182	0.848830
$71$	−9.78678	−1.16148	−0.580739	−	0.814090i	$-0.697236\pi$
$71$	−9.78678	−1.16148	−0.580739	+	0.814090i	$0.697236\pi$
$72$	−1.76193	−0.207645
$73$	−0.303730	−0.0355489	−0.0177745	−	0.999842i	$-0.505658\pi$
$73$	−0.303730	−0.0355489	−0.0177745	+	0.999842i	$0.505658\pi$
$74$	−12.0470	−1.40043
$75$	0.744514	0.0859691
$76$	15.8019	1.81261
$77$	4.74457	0.540694
$78$	−13.2266	−1.49762
$79$	4.00638	0.450753	0.225377	−	0.974272i	$-0.427639\pi$
$79$	4.00638	0.450753	0.225377	+	0.974272i	$0.427639\pi$
$80$	4.18478	0.467873
$81$	1.00000	0.111111
$82$	15.0308	1.65988
$83$	−4.31434	−0.473560	−0.236780	−	0.971563i	$-0.576092\pi$
$83$	−4.31434	−0.473560	−0.236780	+	0.971563i	$0.576092\pi$
$84$	3.79059	0.413587
$85$	−7.32063	−0.794034
$86$	17.1002	1.84396
$87$	0	0
$88$	−6.18356	−0.659170
$89$	13.9924	1.48320	0.741598	−	0.670844i	$-0.234068\pi$
$89$	13.9924	1.48320	0.741598	+	0.670844i	$0.234068\pi$
$90$	5.25319	0.553734
$91$	8.15831	0.855224
$92$	2.84532	0.296645
$93$	8.11166	0.841140
$94$	0.916719	0.0945523
$95$	−13.5076	−1.38585
$96$	7.35072	0.750230
$97$	−3.80357	−0.386194	−0.193097	−	0.981180i	$-0.561853\pi$
$97$	−3.80357	−0.386194	−0.193097	+	0.981180i	$0.561853\pi$
$98$	11.3366	1.14517
$99$	3.50954	0.352722
$100$	2.08753	0.208753
$101$	−0.0422219	−0.00420124	−0.00210062	−	0.999998i	$-0.500669\pi$
$101$	−0.0422219	−0.00420124	−0.00210062	+	0.999998i	$0.500669\pi$
$102$	−6.69450	−0.662854
$103$	11.7804	1.16075	0.580377	−	0.814348i	$-0.302905\pi$
$103$	11.7804	1.16075	0.580377	+	0.814348i	$0.302905\pi$
$104$	−10.6327	−1.04262
$105$	−3.24021	−0.316212
$106$	29.2438	2.84041
$107$	−6.26717	−0.605870	−0.302935	−	0.953011i	$-0.597967\pi$
$107$	−6.26717	−0.605870	−0.302935	+	0.953011i	$0.597967\pi$
$108$	2.80388	0.269804
$109$	−14.8073	−1.41828	−0.709141	−	0.705067i	$-0.750917\pi$
$109$	−14.8073	−1.41828	−0.709141	+	0.705067i	$0.750917\pi$
$110$	18.4363	1.75783
$111$	5.49645	0.521700
$112$	−2.36044	−0.223041
$113$	11.8933	1.11882	0.559411	−	0.828890i	$-0.311027\pi$
$113$	11.8933	1.11882	0.559411	+	0.828890i	$0.311027\pi$
$114$	−12.3523	−1.15690
$115$	−2.43219	−0.226803
$116$	0	0
$117$	6.03467	0.557905
$118$	−7.80497	−0.718506
$119$	4.12923	0.378526
$120$	4.22294	0.385500
$121$	1.31686	0.119714
$122$	−15.8017	−1.43062
$123$	−6.85782	−0.618349
$124$	22.7442	2.04249
$125$	10.1994	0.912265
$126$	−2.96308	−0.263972
$127$	−15.0938	−1.33935	−0.669677	−	0.742652i	$-0.733567\pi$
$127$	−15.0938	−1.33935	−0.669677	+	0.742652i	$0.733567\pi$
$128$	12.9568	1.14523
$129$	−7.80197	−0.686925
$130$	31.7012	2.78038
$131$	10.4468	0.912739	0.456369	−	0.889790i	$-0.349150\pi$
$131$	10.4468	0.912739	0.456369	+	0.889790i	$0.349150\pi$
$132$	9.84033	0.856491
$133$	7.61899	0.660650
$134$	−18.2206	−1.57402
$135$	−2.39677	−0.206281
$136$	−5.38159	−0.461468
$137$	−3.67212	−0.313731	−0.156865	−	0.987620i	$-0.550139\pi$
$137$	−3.67212	−0.313731	−0.156865	+	0.987620i	$0.550139\pi$
$138$	−2.22416	−0.189333
$139$	5.78134	0.490367	0.245183	−	0.969477i	$-0.421152\pi$
$139$	5.78134	0.490367	0.245183	+	0.969477i	$0.421152\pi$
$140$	−9.08518	−0.767838
$141$	−0.418254	−0.0352233
$142$	21.4504	1.80008
$143$	21.1789	1.77107
$144$	−1.74601	−0.145501
$145$	0	0
$146$	0.665709	0.0550944
$147$	−5.17235	−0.426608
$148$	15.4114	1.26681
$149$	−8.58416	−0.703242	−0.351621	−	0.936142i	$-0.614369\pi$
$149$	−8.58416	−0.703242	−0.351621	+	0.936142i	$0.614369\pi$
$150$	−1.63181	−0.133237
$151$	11.9406	0.971714	0.485857	−	0.874038i	$-0.338508\pi$
$151$	11.9406	0.971714	0.485857	+	0.874038i	$0.338508\pi$
$152$	−9.92977	−0.805411
$153$	3.05437	0.246931
$154$	−10.3990	−0.837978
$155$	−19.4418	−1.56160
$156$	16.9205	1.35472
$157$	−12.2535	−0.977936	−0.488968	−	0.872302i	$-0.662626\pi$
$157$	−12.2535	−0.977936	−0.488968	+	0.872302i	$0.662626\pi$
$158$	−8.78109	−0.698586
$159$	−13.3425	−1.05813
$160$	−17.6180	−1.39282
$161$	1.37189	0.108120
$162$	−2.19178	−0.172202
$163$	−7.93140	−0.621235	−0.310618	−	0.950535i	$-0.600536\pi$
$163$	−7.93140	−0.621235	−0.310618	+	0.950535i	$0.600536\pi$
$164$	−19.2285	−1.50150
$165$	−8.41156	−0.654839
$166$	9.45607	0.733933
$167$	12.9244	1.00012	0.500061	−	0.865990i	$-0.333311\pi$
$167$	12.9244	1.00012	0.500061	+	0.865990i	$0.333311\pi$
$168$	−2.38197	−0.183773
$169$	23.4172	1.80133
$170$	16.0452	1.23061
$171$	5.63574	0.430975
$172$	−21.8758	−1.66801
$173$	2.65357	0.201747	0.100874	−	0.994899i	$-0.467836\pi$
$173$	2.65357	0.201747	0.100874	+	0.994899i	$0.467836\pi$
$174$	0	0
$175$	1.00651	0.0760853
$176$	−6.12768	−0.461891
$177$	3.56102	0.267663
$178$	−30.6683	−2.29869
$179$	−13.3988	−1.00147	−0.500735	−	0.865601i	$-0.666937\pi$
$179$	−13.3988	−1.00147	−0.500735	+	0.865601i	$0.666937\pi$
$180$	−6.72027	−0.500899
$181$	1.51389	0.112527	0.0562634	−	0.998416i	$-0.482081\pi$
$181$	1.51389	0.112527	0.0562634	+	0.998416i	$0.482081\pi$
$182$	−17.8812	−1.32544
$183$	7.20954	0.532944
$184$	−1.78797	−0.131811
$185$	−13.1737	−0.968552
$186$	−17.7790	−1.30362
$187$	10.7194	0.783883
$188$	−1.17273	−0.0855305
$189$	1.35191	0.0983368
$190$	29.6056	2.14781
$191$	−11.6187	−0.840696	−0.420348	−	0.907363i	$-0.638092\pi$
$191$	−11.6187	−0.840696	−0.420348	+	0.907363i	$0.638092\pi$
$192$	−12.6191	−0.910706
$193$	−6.16179	−0.443536	−0.221768	−	0.975100i	$-0.571183\pi$
$193$	−6.16179	−0.443536	−0.221768	+	0.975100i	$0.571183\pi$
$194$	8.33658	0.598532
$195$	−14.4637	−1.03577
$196$	−14.5027	−1.03590
$197$	−2.52672	−0.180021	−0.0900107	−	0.995941i	$-0.528690\pi$
$197$	−2.52672	−0.180021	−0.0900107	+	0.995941i	$0.528690\pi$
$198$	−7.69212	−0.546655
$199$	13.2818	0.941524	0.470762	−	0.882260i	$-0.343979\pi$
$199$	13.2818	0.941524	0.470762	+	0.882260i	$0.343979\pi$
$200$	−1.31178	−0.0927570
$201$	8.31317	0.586366
$202$	0.0925410	0.00651116
$203$	0	0
$204$	8.56410	0.599607
$205$	16.4366	1.14798
$206$	−25.8199	−1.79896
$207$	1.01478	0.0705319
$208$	−10.5366	−0.730580
$209$	19.7788	1.36813
$210$	7.10182	0.490072
$211$	−8.30478	−0.571724	−0.285862	−	0.958271i	$-0.592280\pi$
$211$	−8.30478	−0.571724	−0.285862	+	0.958271i	$0.592280\pi$
$212$	−37.4108	−2.56938
$213$	−9.78678	−0.670579
$214$	13.7362	0.938990
$215$	18.6995	1.27530
$216$	−1.76193	−0.119884
$217$	10.9662	0.744435
$218$	32.4543	2.19808
$219$	−0.303730	−0.0205242
$220$	−23.5850	−1.59010
$221$	18.4321	1.23988
$222$	−12.0470	−0.808540
$223$	25.0119	1.67492	0.837461	−	0.546496i	$-0.184039\pi$
$223$	25.0119	1.67492	0.837461	+	0.546496i	$0.184039\pi$
$224$	9.93749	0.663977
$225$	0.744514	0.0496343
$226$	−26.0673	−1.73397
$227$	3.04387	0.202029	0.101014	−	0.994885i	$-0.467791\pi$
$227$	3.04387	0.202029	0.101014	+	0.994885i	$0.467791\pi$
$228$	15.8019	1.04651
$229$	−21.9086	−1.44776	−0.723879	−	0.689927i	$-0.757643\pi$
$229$	−21.9086	−1.44776	−0.723879	+	0.689927i	$0.757643\pi$
$230$	5.33082	0.351504
$231$	4.74457	0.312170
$232$	0	0
$233$	9.96464	0.652805	0.326403	−	0.945231i	$-0.394163\pi$
$233$	9.96464	0.652805	0.326403	+	0.945231i	$0.394163\pi$
$234$	−13.2266	−0.864653
$235$	1.00246	0.0653932
$236$	9.98469	0.649948
$237$	4.00638	0.260242
$238$	−9.05034	−0.586647
$239$	−7.78097	−0.503309	−0.251655	−	0.967817i	$-0.580975\pi$
$239$	−7.78097	−0.503309	−0.251655	+	0.967817i	$0.580975\pi$
$240$	4.18478	0.270127
$241$	−23.1891	−1.49374	−0.746872	−	0.664968i	$-0.768445\pi$
$241$	−23.1891	−1.49374	−0.746872	+	0.664968i	$0.768445\pi$
$242$	−2.88626	−0.185536
$243$	1.00000	0.0641500
$244$	20.2147	1.29411
$245$	12.3969	0.792011
$246$	15.0308	0.958329
$247$	34.0098	2.16399
$248$	−14.2922	−0.907555
$249$	−4.31434	−0.273410
$250$	−22.3549	−1.41385
$251$	1.18054	0.0745150	0.0372575	−	0.999306i	$-0.488138\pi$
$251$	1.18054	0.0745150	0.0372575	+	0.999306i	$0.488138\pi$
$252$	3.79059	0.238785
$253$	3.56140	0.223903
$254$	33.0821	2.07576
$255$	−7.32063	−0.458436
$256$	−3.16025	−0.197516
$257$	15.9745	0.996461	0.498231	−	0.867044i	$-0.333983\pi$
$257$	15.9745	0.996461	0.498231	+	0.867044i	$0.333983\pi$
$258$	17.1002	1.06461
$259$	7.43069	0.461720
$260$	−40.5546	−2.51509
$261$	0	0
$262$	−22.8970	−1.41458
$263$	14.6106	0.900927	0.450463	−	0.892795i	$-0.351259\pi$
$263$	14.6106	0.900927	0.450463	+	0.892795i	$0.351259\pi$
$264$	−6.18356	−0.380572
$265$	31.9789	1.96445
$266$	−16.6991	−1.02389
$267$	13.9924	0.856324
$268$	23.3091	1.42383
$269$	22.1146	1.34835	0.674174	−	0.738573i	$-0.264500\pi$
$269$	22.1146	1.34835	0.674174	+	0.738573i	$0.264500\pi$
$270$	5.25319	0.319699
$271$	−23.1151	−1.40414	−0.702072	−	0.712106i	$-0.747742\pi$
$271$	−23.1151	−1.40414	−0.702072	+	0.712106i	$0.747742\pi$
$272$	−5.33296	−0.323358
$273$	8.15831	0.493764
$274$	8.04847	0.486226
$275$	2.61290	0.157564
$276$	2.84532	0.171268
$277$	18.7130	1.12435	0.562177	−	0.827017i	$-0.309964\pi$
$277$	18.7130	1.12435	0.562177	+	0.827017i	$0.309964\pi$
$278$	−12.6714	−0.759980
$279$	8.11166	0.485633
$280$	5.70903	0.341180
$281$	−8.66587	−0.516962	−0.258481	−	0.966016i	$-0.583222\pi$
$281$	−8.66587	−0.516962	−0.258481	+	0.966016i	$0.583222\pi$
$282$	0.916719	0.0545898
$283$	5.58496	0.331991	0.165996	−	0.986126i	$-0.446916\pi$
$283$	5.58496	0.331991	0.165996	+	0.986126i	$0.446916\pi$
$284$	−27.4410	−1.62832
$285$	−13.5076	−0.800119
$286$	−46.4194	−2.74484
$287$	−9.27114	−0.547258
$288$	7.35072	0.433145
$289$	−7.67081	−0.451224
$290$	0	0
$291$	−3.80357	−0.222969
$292$	−0.851624	−0.0498375
$293$	−4.71899	−0.275686	−0.137843	−	0.990454i	$-0.544017\pi$
$293$	−4.71899	−0.275686	−0.137843	+	0.990454i	$0.544017\pi$
$294$	11.3366	0.661165
$295$	−8.53496	−0.496925
$296$	−9.68436	−0.562892
$297$	3.50954	0.203644
$298$	18.8146	1.08990
$299$	6.12385	0.354151
$300$	2.08753	0.120524
$301$	−10.5475	−0.607950
$302$	−26.1712	−1.50598
$303$	−0.0422219	−0.00242559
$304$	−9.84004	−0.564365
$305$	−17.2796	−0.989428
$306$	−6.69450	−0.382699
$307$	11.7362	0.669821	0.334910	−	0.942250i	$-0.391294\pi$
$307$	11.7362	0.669821	0.334910	+	0.942250i	$0.391294\pi$
$308$	13.3032	0.758021
$309$	11.7804	0.670161
$310$	42.6121	2.42020
$311$	16.8038	0.952858	0.476429	−	0.879213i	$-0.341931\pi$
$311$	16.8038	0.952858	0.476429	+	0.879213i	$0.341931\pi$
$312$	−10.6327	−0.601956
$313$	−11.9599	−0.676012	−0.338006	−	0.941144i	$-0.609752\pi$
$313$	−11.9599	−0.676012	−0.338006	+	0.941144i	$0.609752\pi$
$314$	26.8569	1.51562
$315$	−3.24021	−0.182565
$316$	11.2334	0.631929
$317$	−14.1360	−0.793954	−0.396977	−	0.917829i	$-0.629941\pi$
$317$	−14.1360	−0.793954	−0.396977	+	0.917829i	$0.629941\pi$
$318$	29.2438	1.63991
$319$	0	0
$320$	30.2451	1.69075
$321$	−6.26717	−0.349799
$322$	−3.00686	−0.167566
$323$	17.2136	0.957792
$324$	2.80388	0.155771
$325$	4.49290	0.249221
$326$	17.3839	0.962803
$327$	−14.8073	−0.818845
$328$	12.0830	0.667172
$329$	−0.565441	−0.0311737
$330$	18.4363	1.01488
$331$	23.0236	1.26549	0.632747	−	0.774359i	$-0.281927\pi$
$331$	23.0236	1.26549	0.632747	+	0.774359i	$0.281927\pi$
$332$	−12.0969	−0.663904
$333$	5.49645	0.301203
$334$	−28.3275	−1.55001
$335$	−19.9248	−1.08861
$336$	−2.36044	−0.128773
$337$	−2.55630	−0.139250	−0.0696252	−	0.997573i	$-0.522180\pi$
$337$	−2.55630	−0.139250	−0.0696252	+	0.997573i	$0.522180\pi$
$338$	−51.3253	−2.79173
$339$	11.8933	0.645953
$340$	−20.5262	−1.11319
$341$	28.4682	1.54164
$342$	−12.3523	−0.667934
$343$	−16.4559	−0.888534
$344$	13.7465	0.741163
$345$	−2.43219	−0.130945
$346$	−5.81604	−0.312672
$347$	−0.891885	−0.0478789	−0.0239394	−	0.999713i	$-0.507621\pi$
$347$	−0.891885	−0.0478789	−0.0239394	+	0.999713i	$0.507621\pi$
$348$	0	0
$349$	−0.755575	−0.0404450	−0.0202225	−	0.999796i	$-0.506437\pi$
$349$	−0.755575	−0.0404450	−0.0202225	+	0.999796i	$0.506437\pi$
$350$	−2.20605	−0.117919
$351$	6.03467	0.322107
$352$	25.7976	1.37502
$353$	19.2406	1.02407	0.512036	−	0.858964i	$-0.328891\pi$
$353$	19.2406	1.02407	0.512036	+	0.858964i	$0.328891\pi$
$354$	−7.80497	−0.414829
$355$	23.4567	1.24495
$356$	39.2332	2.07935
$357$	4.12923	0.218542
$358$	29.3671	1.55210
$359$	17.6146	0.929661	0.464830	−	0.885400i	$-0.346115\pi$
$359$	17.6146	0.929661	0.464830	+	0.885400i	$0.346115\pi$
$360$	4.22294	0.222569
$361$	12.7615	0.671658
$362$	−3.31812	−0.174396
$363$	1.31686	0.0691171
$364$	22.8750	1.19897
$365$	0.727972	0.0381038
$366$	−15.8017	−0.825967
$367$	3.79787	0.198247	0.0991235	−	0.995075i	$-0.468396\pi$
$367$	3.79787	0.198247	0.0991235	+	0.995075i	$0.468396\pi$
$368$	−1.77181	−0.0923620
$369$	−6.85782	−0.357004
$370$	28.8739	1.50108
$371$	−18.0378	−0.936477
$372$	22.7442	1.17923
$373$	−8.29264	−0.429377	−0.214688	−	0.976683i	$-0.568874\pi$
$373$	−8.29264	−0.429377	−0.214688	+	0.976683i	$0.568874\pi$
$374$	−23.4946	−1.21488
$375$	10.1994	0.526696
$376$	0.736934	0.0380045
$377$	0	0
$378$	−2.96308	−0.152404
$379$	−8.93238	−0.458826	−0.229413	−	0.973329i	$-0.573681\pi$
$379$	−8.93238	−0.458826	−0.229413	+	0.973329i	$0.573681\pi$
$380$	−37.8736	−1.94288
$381$	−15.0938	−0.773277
$382$	25.4655	1.30293
$383$	35.8530	1.83200	0.916001	−	0.401176i	$-0.131398\pi$
$383$	35.8530	1.83200	0.916001	+	0.401176i	$0.131398\pi$
$384$	12.9568	0.661201
$385$	−11.3717	−0.579553
$386$	13.5053	0.687400
$387$	−7.80197	−0.396596
$388$	−10.6648	−0.541422
$389$	11.3446	0.575194	0.287597	−	0.957752i	$-0.407144\pi$
$389$	11.3446	0.575194	0.287597	+	0.957752i	$0.407144\pi$
$390$	31.7012	1.60525
$391$	3.09951	0.156749
$392$	9.11331	0.460292
$393$	10.4468	0.526970
$394$	5.53800	0.279001
$395$	−9.60238	−0.483148
$396$	9.84033	0.494495
$397$	−24.1353	−1.21131	−0.605657	−	0.795726i	$-0.707090\pi$
$397$	−24.1353	−1.21131	−0.605657	+	0.795726i	$0.707090\pi$
$398$	−29.1108	−1.45919
$399$	7.61899	0.381427
$400$	−1.29993	−0.0649964
$401$	19.3564	0.966611	0.483305	−	0.875452i	$-0.339436\pi$
$401$	19.3564	0.966611	0.483305	+	0.875452i	$0.339436\pi$
$402$	−18.2206	−0.908761
$403$	48.9512	2.43843
$404$	−0.118385	−0.00588989
$405$	−2.39677	−0.119097
$406$	0	0
$407$	19.2900	0.956169
$408$	−5.38159	−0.266428
$409$	11.4459	0.565963	0.282981	−	0.959125i	$-0.408677\pi$
$409$	11.4459	0.565963	0.282981	+	0.959125i	$0.408677\pi$
$410$	−36.0254	−1.77917
$411$	−3.67212	−0.181132
$412$	33.0308	1.62731
$413$	4.81418	0.236890
$414$	−2.22416	−0.109312
$415$	10.3405	0.507595
$416$	44.3592	2.17489
$417$	5.78134	0.283113
$418$	−43.3508	−2.12036
$419$	−21.1185	−1.03171	−0.515854	−	0.856677i	$-0.672525\pi$
$419$	−21.1185	−1.03171	−0.515854	+	0.856677i	$0.672525\pi$
$420$	−9.08518	−0.443311
$421$	27.5131	1.34090	0.670452	−	0.741953i	$-0.266100\pi$
$421$	27.5131	1.34090	0.670452	+	0.741953i	$0.266100\pi$
$422$	18.2022	0.886070
$423$	−0.418254	−0.0203362
$424$	23.5086	1.14168
$425$	2.27402	0.110306
$426$	21.4504	1.03928
$427$	9.74662	0.471672
$428$	−17.5724	−0.849394
$429$	21.1789	1.02253
$430$	−40.9852	−1.97648
$431$	−1.94954	−0.0939060	−0.0469530	−	0.998897i	$-0.514951\pi$
$431$	−1.94954	−0.0939060	−0.0469530	+	0.998897i	$0.514951\pi$
$432$	−1.74601	−0.0840049
$433$	7.83478	0.376516	0.188258	−	0.982120i	$-0.439716\pi$
$433$	7.83478	0.376516	0.188258	+	0.982120i	$0.439716\pi$
$434$	−24.0355	−1.15374
$435$	0	0
$436$	−41.5179	−1.98835
$437$	5.71902	0.273578
$438$	0.665709	0.0318088
$439$	2.38989	0.114063	0.0570317	−	0.998372i	$-0.481836\pi$
$439$	2.38989	0.114063	0.0570317	+	0.998372i	$0.481836\pi$
$440$	14.8206	0.706544
$441$	−5.17235	−0.246302
$442$	−40.3991	−1.92159
$443$	38.3497	1.82205	0.911024	−	0.412354i	$-0.135293\pi$
$443$	38.3497	1.82205	0.911024	+	0.412354i	$0.135293\pi$
$444$	15.4114	0.731392
$445$	−33.5367	−1.58979
$446$	−54.8206	−2.59583
$447$	−8.58416	−0.406017
$448$	−17.0599	−0.806003
$449$	−31.3441	−1.47922	−0.739609	−	0.673037i	$-0.764990\pi$
$449$	−31.3441	−1.47922	−0.739609	+	0.673037i	$0.764990\pi$
$450$	−1.63181	−0.0769242
$451$	−24.0678	−1.13331
$452$	33.3473	1.56852
$453$	11.9406	0.561020
$454$	−6.67148	−0.313108
$455$	−19.5536	−0.916688
$456$	−9.92977	−0.465004
$457$	−32.2643	−1.50926	−0.754630	−	0.656151i	$-0.772183\pi$
$457$	−32.2643	−1.50926	−0.754630	+	0.656151i	$0.772183\pi$
$458$	48.0187	2.24376
$459$	3.05437	0.142566
$460$	−6.81957	−0.317964
$461$	−5.67806	−0.264454	−0.132227	−	0.991219i	$-0.542213\pi$
$461$	−5.67806	−0.264454	−0.132227	+	0.991219i	$0.542213\pi$
$462$	−10.3990	−0.483807
$463$	23.2339	1.07977	0.539886	−	0.841738i	$-0.318467\pi$
$463$	23.2339	1.07977	0.539886	+	0.841738i	$0.318467\pi$
$464$	0	0
$465$	−19.4418	−0.901592
$466$	−21.8403	−1.01173
$467$	12.0771	0.558861	0.279430	−	0.960166i	$-0.409854\pi$
$467$	12.0771	0.558861	0.279430	+	0.960166i	$0.409854\pi$
$468$	16.9205	0.782150
$469$	11.2386	0.518952
$470$	−2.19717	−0.101348
$471$	−12.2535	−0.564611
$472$	−6.27428	−0.288797
$473$	−27.3813	−1.25899
$474$	−8.78109	−0.403329
$475$	4.19588	0.192520
$476$	11.5779	0.530671
$477$	−13.3425	−0.610911
$478$	17.0541	0.780038
$479$	−30.5109	−1.39408	−0.697039	−	0.717033i	$-0.745500\pi$
$479$	−30.5109	−1.39408	−0.697039	+	0.717033i	$0.745500\pi$
$480$	−17.6180	−0.804148
$481$	33.1692	1.51239
$482$	50.8254	2.31503
$483$	1.37189	0.0624229
$484$	3.69231	0.167832
$485$	9.11630	0.413950
$486$	−2.19178	−0.0994210
$487$	−23.5248	−1.06601	−0.533005	−	0.846112i	$-0.678937\pi$
$487$	−23.5248	−1.06601	−0.533005	+	0.846112i	$0.678937\pi$
$488$	−12.7027	−0.575024
$489$	−7.93140	−0.358670
$490$	−27.1713	−1.22747
$491$	27.5887	1.24506	0.622531	−	0.782595i	$-0.286104\pi$
$491$	27.5887	1.24506	0.622531	+	0.782595i	$0.286104\pi$
$492$	−19.2285	−0.866889
$493$	0	0
$494$	−74.5419	−3.35380
$495$	−8.41156	−0.378072
$496$	−14.1630	−0.635939
$497$	−13.2308	−0.593483
$498$	9.45607	0.423737
$499$	−38.3679	−1.71758	−0.858791	−	0.512327i	$-0.828784\pi$
$499$	−38.3679	−1.71758	−0.858791	+	0.512327i	$0.828784\pi$
$500$	28.5980	1.27894
$501$	12.9244	0.577421
$502$	−2.58748	−0.115485
$503$	−4.95969	−0.221142	−0.110571	−	0.993868i	$-0.535268\pi$
$503$	−4.95969	−0.221142	−0.110571	+	0.993868i	$0.535268\pi$
$504$	−2.38197	−0.106101
$505$	0.101196	0.00450318
$506$	−7.80579	−0.347010
$507$	23.4172	1.04000
$508$	−42.3211	−1.87770
$509$	−16.4294	−0.728220	−0.364110	−	0.931356i	$-0.618627\pi$
$509$	−16.4294	−0.728220	−0.364110	+	0.931356i	$0.618627\pi$
$510$	16.0452	0.710493
$511$	−0.410615	−0.0181645
$512$	−18.9871	−0.839119
$513$	5.63574	0.248824
$514$	−35.0125	−1.54434
$515$	−28.2348	−1.24418
$516$	−21.8758	−0.963029
$517$	−1.46788	−0.0645572
$518$	−16.2864	−0.715583
$519$	2.65357	0.116479
$520$	25.4841	1.11755
$521$	−30.7040	−1.34517	−0.672583	−	0.740021i	$-0.734815\pi$
$521$	−30.7040	−1.34517	−0.672583	+	0.740021i	$0.734815\pi$
$522$	0	0
$523$	37.0601	1.62052	0.810262	−	0.586068i	$-0.199325\pi$
$523$	37.0601	1.62052	0.810262	+	0.586068i	$0.199325\pi$
$524$	29.2915	1.27961
$525$	1.00651	0.0439279
$526$	−32.0231	−1.39627
$527$	24.7760	1.07926
$528$	−6.12768	−0.266673
$529$	−21.9702	−0.955227
$530$	−70.0906	−3.04454
$531$	3.56102	0.154535
$532$	21.3628	0.926193
$533$	−41.3847	−1.79257
$534$	−30.6683	−1.32715
$535$	15.0210	0.649413
$536$	−14.6472	−0.632664
$537$	−13.3988	−0.578199
$538$	−48.4701	−2.08970
$539$	−18.1525	−0.781886
$540$	−6.72027	−0.289194
$541$	34.0254	1.46287	0.731434	−	0.681913i	$-0.238852\pi$
$541$	34.0254	1.46287	0.731434	+	0.681913i	$0.238852\pi$
$542$	50.6632	2.17617
$543$	1.51389	0.0649674
$544$	22.4518	0.962614
$545$	35.4897	1.52021
$546$	−17.8812	−0.765245
$547$	17.1964	0.735265	0.367633	−	0.929971i	$-0.380168\pi$
$547$	17.1964	0.735265	0.367633	+	0.929971i	$0.380168\pi$
$548$	−10.2962	−0.439832
$549$	7.20954	0.307695
$550$	−5.72689	−0.244196
$551$	0	0
$552$	−1.78797	−0.0761009
$553$	5.41626	0.230323
$554$	−41.0147	−1.74255
$555$	−13.1737	−0.559194
$556$	16.2102	0.687466
$557$	−29.6847	−1.25778	−0.628890	−	0.777494i	$-0.716490\pi$
$557$	−29.6847	−1.25778	−0.628890	+	0.777494i	$0.716490\pi$
$558$	−17.7790	−0.752643
$559$	−47.0823	−1.99137
$560$	5.65744	0.239070
$561$	10.7194	0.452575
$562$	18.9936	0.801198
$563$	−27.8621	−1.17425	−0.587125	−	0.809497i	$-0.699740\pi$
$563$	−27.8621	−1.17425	−0.587125	+	0.809497i	$0.699740\pi$
$564$	−1.17273	−0.0493810
$565$	−28.5054	−1.19923
$566$	−12.2410	−0.514527
$567$	1.35191	0.0567748
$568$	17.2436	0.723526
$569$	−9.78846	−0.410354	−0.205177	−	0.978725i	$-0.565777\pi$
$569$	−9.78846	−0.410354	−0.205177	+	0.978725i	$0.565777\pi$
$570$	29.6056	1.24004
$571$	−32.3247	−1.35275	−0.676374	−	0.736559i	$-0.736450\pi$
$571$	−32.3247	−1.35275	−0.676374	+	0.736559i	$0.736450\pi$
$572$	59.3831	2.48293
$573$	−11.6187	−0.485376
$574$	20.3203	0.848151
$575$	0.755516	0.0315072
$576$	−12.6191	−0.525796
$577$	−43.6057	−1.81533	−0.907664	−	0.419698i	$-0.862136\pi$
$577$	−43.6057	−1.81533	−0.907664	+	0.419698i	$0.862136\pi$
$578$	16.8127	0.699316
$579$	−6.16179	−0.256075
$580$	0	0
$581$	−5.83259	−0.241977
$582$	8.33658	0.345562
$583$	−46.8260	−1.93934
$584$	0.535152	0.0221447
$585$	−14.4637	−0.598001
$586$	10.3430	0.427264
$587$	−43.6633	−1.80218	−0.901088	−	0.433636i	$-0.857231\pi$
$587$	−43.6633	−1.80218	−0.901088	+	0.433636i	$0.857231\pi$
$588$	−14.5027	−0.598079
$589$	45.7152	1.88366
$590$	18.7067	0.770144
$591$	−2.52672	−0.103935
$592$	−9.59684	−0.394428
$593$	24.0076	0.985873	0.492937	−	0.870065i	$-0.335923\pi$
$593$	24.0076	0.985873	0.492937	+	0.870065i	$0.335923\pi$
$594$	−7.69212	−0.315612
$595$	−9.89682	−0.405730
$596$	−24.0690	−0.985904
$597$	13.2818	0.543589
$598$	−13.4221	−0.548870
$599$	3.63501	0.148522	0.0742612	−	0.997239i	$-0.476340\pi$
$599$	3.63501	0.148522	0.0742612	+	0.997239i	$0.476340\pi$
$600$	−1.31178	−0.0535533
$601$	−15.2601	−0.622474	−0.311237	−	0.950332i	$-0.600743\pi$
$601$	−15.2601	−0.622474	−0.311237	+	0.950332i	$0.600743\pi$
$602$	23.1178	0.942213
$603$	8.31317	0.338538
$604$	33.4801	1.36229
$605$	−3.15621	−0.128318
$606$	0.0925410	0.00375922
$607$	−2.89009	−0.117305	−0.0586526	−	0.998278i	$-0.518680\pi$
$607$	−2.89009	−0.117305	−0.0586526	+	0.998278i	$0.518680\pi$
$608$	41.4267	1.68007
$609$	0	0
$610$	37.8730	1.53343
$611$	−2.52402	−0.102111
$612$	8.56410	0.346183
$613$	−4.40402	−0.177877	−0.0889384	−	0.996037i	$-0.528347\pi$
$613$	−4.40402	−0.177877	−0.0889384	+	0.996037i	$0.528347\pi$
$614$	−25.7231	−1.03810
$615$	16.4366	0.662789
$616$	−8.35960	−0.336818
$617$	6.95938	0.280174	0.140087	−	0.990139i	$-0.455262\pi$
$617$	6.95938	0.280174	0.140087	+	0.990139i	$0.455262\pi$
$618$	−25.8199	−1.03863
$619$	13.1480	0.528461	0.264230	−	0.964460i	$-0.414882\pi$
$619$	13.1480	0.528461	0.264230	+	0.964460i	$0.414882\pi$
$620$	−54.5125	−2.18928
$621$	1.01478	0.0407216
$622$	−36.8302	−1.47676
$623$	18.9165	0.757873
$624$	−10.5366	−0.421801
$625$	−28.1683	−1.12673
$626$	26.2134	1.04770
$627$	19.7788	0.789890
$628$	−34.3574	−1.37101
$629$	16.7882	0.669389
$630$	7.10182	0.282943
$631$	−13.2938	−0.529217	−0.264609	−	0.964356i	$-0.585243\pi$
$631$	−13.2938	−0.529217	−0.264609	+	0.964356i	$0.585243\pi$
$632$	−7.05896	−0.280790
$633$	−8.30478	−0.330085
$634$	30.9828	1.23049
$635$	36.1763	1.43561
$636$	−37.4108	−1.48343
$637$	−31.2134	−1.23672
$638$	0	0
$639$	−9.78678	−0.387159
$640$	−31.0546	−1.22754
$641$	20.1373	0.795376	0.397688	−	0.917521i	$-0.369813\pi$
$641$	20.1373	0.795376	0.397688	+	0.917521i	$0.369813\pi$
$642$	13.7362	0.542126
$643$	44.1506	1.74113	0.870565	−	0.492053i	$-0.163753\pi$
$643$	44.1506	1.74113	0.870565	+	0.492053i	$0.163753\pi$
$644$	3.84660	0.151577
$645$	18.6995	0.736294
$646$	−37.7284	−1.48440
$647$	18.2323	0.716784	0.358392	−	0.933571i	$-0.383325\pi$
$647$	18.2323	0.716784	0.358392	+	0.933571i	$0.383325\pi$
$648$	−1.76193	−0.0692152
$649$	12.4976	0.490572
$650$	−9.84742	−0.386248
$651$	10.9662	0.429800
$652$	−22.2387	−0.870935
$653$	−15.1966	−0.594688	−0.297344	−	0.954770i	$-0.596101\pi$
$653$	−15.1966	−0.594688	−0.297344	+	0.954770i	$0.596101\pi$
$654$	32.4543	1.26906
$655$	−25.0385	−0.978336
$656$	11.9738	0.467499
$657$	−0.303730	−0.0118496
$658$	1.23932	0.0483137
$659$	−16.7811	−0.653699	−0.326849	−	0.945076i	$-0.605987\pi$
$659$	−16.7811	−0.653699	−0.326849	+	0.945076i	$0.605987\pi$
$660$	−23.5850	−0.918046
$661$	−1.34387	−0.0522705	−0.0261352	−	0.999658i	$-0.508320\pi$
$661$	−1.34387	−0.0522705	−0.0261352	+	0.999658i	$0.508320\pi$
$662$	−50.4627	−1.96129
$663$	18.4321	0.715844
$664$	7.60157	0.294998
$665$	−18.2610	−0.708131
$666$	−12.0470	−0.466811
$667$	0	0
$668$	36.2386	1.40211
$669$	25.0119	0.967017
$670$	43.6706	1.68714
$671$	25.3021	0.976778
$672$	9.93749	0.383347
$673$	11.9193	0.459457	0.229728	−	0.973255i	$-0.426216\pi$
$673$	11.9193	0.459457	0.229728	+	0.973255i	$0.426216\pi$
$674$	5.60283	0.215813
$675$	0.744514	0.0286564
$676$	65.6592	2.52535
$677$	16.2061	0.622850	0.311425	−	0.950271i	$-0.399194\pi$
$677$	16.2061	0.622850	0.311425	+	0.950271i	$0.399194\pi$
$678$	−26.0673	−1.00111
$679$	−5.14208	−0.197335
$680$	12.8984	0.494633
$681$	3.04387	0.116641
$682$	−62.3959	−2.38926
$683$	−28.8129	−1.10249	−0.551247	−	0.834342i	$-0.685848\pi$
$683$	−28.8129	−1.10249	−0.551247	+	0.834342i	$0.685848\pi$
$684$	15.8019	0.604202
$685$	8.80124	0.336278
$686$	36.0676	1.37707
$687$	−21.9086	−0.835864
$688$	13.6223	0.519345
$689$	−80.5176	−3.06747
$690$	5.33082	0.202941
$691$	−25.3535	−0.964492	−0.482246	−	0.876036i	$-0.660179\pi$
$691$	−25.3535	−0.964492	−0.482246	+	0.876036i	$0.660179\pi$
$692$	7.44031	0.282838
$693$	4.74457	0.180231
$694$	1.95481	0.0742037
$695$	−13.8566	−0.525609
$696$	0	0
$697$	−20.9463	−0.793399
$698$	1.65605	0.0626825
$699$	9.96464	0.376897
$700$	2.82215	0.106667
$701$	13.2108	0.498965	0.249482	−	0.968379i	$-0.419740\pi$
$701$	13.2108	0.498965	0.249482	+	0.968379i	$0.419740\pi$
$702$	−13.2266	−0.499207
$703$	30.9765	1.16830
$704$	−44.2873	−1.66914
$705$	1.00246	0.0377548
$706$	−42.1710	−1.58713
$707$	−0.0570801	−0.00214672
$708$	9.98469	0.375248
$709$	−35.6702	−1.33962	−0.669811	−	0.742532i	$-0.733625\pi$
$709$	−35.6702	−1.33962	−0.669811	+	0.742532i	$0.733625\pi$
$710$	−51.4118	−1.92945
$711$	4.00638	0.150251
$712$	−24.6537	−0.923937
$713$	8.23153	0.308273
$714$	−9.05034	−0.338701
$715$	−50.7610	−1.89835
$716$	−37.5685	−1.40400
$717$	−7.78097	−0.290586
$718$	−38.6072	−1.44081
$719$	2.02313	0.0754500	0.0377250	−	0.999288i	$-0.487989\pi$
$719$	2.02313	0.0754500	0.0377250	+	0.999288i	$0.487989\pi$
$720$	4.18478	0.155958
$721$	15.9260	0.593114
$722$	−27.9704	−1.04095
$723$	−23.1891	−0.862414
$724$	4.24478	0.157756
$725$	0	0
$726$	−2.88626	−0.107119
$727$	−10.5449	−0.391091	−0.195545	−	0.980695i	$-0.562648\pi$
$727$	−10.5449	−0.391091	−0.195545	+	0.980695i	$0.562648\pi$
$728$	−14.3744	−0.532750
$729$	1.00000	0.0370370
$730$	−1.59555	−0.0590540
$731$	−23.8301	−0.881389
$732$	20.2147	0.747156
$733$	−19.0185	−0.702464	−0.351232	−	0.936289i	$-0.614237\pi$
$733$	−19.0185	−0.702464	−0.351232	+	0.936289i	$0.614237\pi$
$734$	−8.32408	−0.307247
$735$	12.3969	0.457268
$736$	7.45934	0.274955
$737$	29.1754	1.07469
$738$	15.0308	0.553292
$739$	−43.0359	−1.58310	−0.791550	−	0.611104i	$-0.790726\pi$
$739$	−43.0359	−1.58310	−0.791550	+	0.611104i	$0.790726\pi$
$740$	−36.9376	−1.35785
$741$	34.0098	1.24938
$742$	39.5349	1.45137
$743$	−3.32534	−0.121995	−0.0609974	−	0.998138i	$-0.519428\pi$
$743$	−3.32534	−0.121995	−0.0609974	+	0.998138i	$0.519428\pi$
$744$	−14.2922	−0.523977
$745$	20.5743	0.753783
$746$	18.1756	0.665456
$747$	−4.31434	−0.157853
$748$	30.0560	1.09896
$749$	−8.47263	−0.309583
$750$	−22.3549	−0.816284
$751$	20.4786	0.747274	0.373637	−	0.927575i	$-0.378111\pi$
$751$	20.4786	0.747274	0.373637	+	0.927575i	$0.378111\pi$
$752$	0.730275	0.0266304
$753$	1.18054	0.0430212
$754$	0	0
$755$	−28.6190	−1.04155
$756$	3.79059	0.137862
$757$	−8.42636	−0.306261	−0.153131	−	0.988206i	$-0.548936\pi$
$757$	−8.42636	−0.306261	−0.153131	+	0.988206i	$0.548936\pi$
$758$	19.5778	0.711097
$759$	3.56140	0.129271
$760$	23.7994	0.863295
$761$	−26.1414	−0.947625	−0.473812	−	0.880626i	$-0.657123\pi$
$761$	−26.1414	−0.947625	−0.473812	+	0.880626i	$0.657123\pi$
$762$	33.0821	1.19844
$763$	−20.0181	−0.724703
$764$	−32.5773	−1.17861
$765$	−7.32063	−0.264678
$766$	−78.5817	−2.83927
$767$	21.4896	0.775945
$768$	−3.16025	−0.114036
$769$	41.1420	1.48362	0.741808	−	0.670612i	$-0.233968\pi$
$769$	41.1420	1.48362	0.741808	+	0.670612i	$0.233968\pi$
$770$	24.9241	0.898203
$771$	15.9745	0.575307
$772$	−17.2769	−0.621811
$773$	34.8669	1.25407	0.627037	−	0.778990i	$-0.284268\pi$
$773$	34.8669	1.25407	0.627037	+	0.778990i	$0.284268\pi$
$774$	17.1002	0.614653
$775$	6.03925	0.216936
$776$	6.70163	0.240575
$777$	7.43069	0.266574
$778$	−24.8648	−0.891446
$779$	−38.6489	−1.38474
$780$	−40.5546	−1.45209
$781$	−34.3471	−1.22904
$782$	−6.79343	−0.242932
$783$	0	0
$784$	9.03096	0.322534
$785$	29.3688	1.04822
$786$	−22.8970	−0.816708
$787$	15.9557	0.568759	0.284380	−	0.958712i	$-0.408212\pi$
$787$	15.9557	0.568759	0.284380	+	0.958712i	$0.408212\pi$
$788$	−7.08463	−0.252379
$789$	14.6106	0.520150
$790$	21.0463	0.748792
$791$	16.0786	0.571688
$792$	−6.18356	−0.219723
$793$	43.5072	1.54498
$794$	52.8991	1.87732
$795$	31.9789	1.13418
$796$	37.2407	1.31996
$797$	38.0735	1.34863	0.674316	−	0.738443i	$-0.264439\pi$
$797$	38.0735	1.34863	0.674316	+	0.738443i	$0.264439\pi$
$798$	−16.6991	−0.591143
$799$	−1.27750	−0.0451948
$800$	5.47271	0.193490
$801$	13.9924	0.494399
$802$	−42.4248	−1.49807
$803$	−1.06595	−0.0376167
$804$	23.3091	0.822050
$805$	−3.28810	−0.115890
$806$	−107.290	−3.77913
$807$	22.1146	0.778469
$808$	0.0743921	0.00261710
$809$	−52.1314	−1.83284	−0.916421	−	0.400216i	$-0.868935\pi$
$809$	−52.1314	−1.83284	−0.916421	+	0.400216i	$0.868935\pi$
$810$	5.25319	0.184578
$811$	6.35528	0.223164	0.111582	−	0.993755i	$-0.464408\pi$
$811$	6.35528	0.223164	0.111582	+	0.993755i	$0.464408\pi$
$812$	0	0
$813$	−23.1151	−0.810683
$814$	−42.2793	−1.48189
$815$	19.0098	0.665883
$816$	−5.33296	−0.186691
$817$	−43.9698	−1.53831
$818$	−25.0868	−0.877140
$819$	8.15831	0.285075
$820$	46.0864	1.60941
$821$	0.213766	0.00746047	0.00373024	−	0.999993i	$-0.498813\pi$
$821$	0.213766	0.00746047	0.00373024	+	0.999993i	$0.498813\pi$
$822$	8.04847	0.280723
$823$	25.4184	0.886029	0.443015	−	0.896514i	$-0.353909\pi$
$823$	25.4184	0.886029	0.443015	+	0.896514i	$0.353909\pi$
$824$	−20.7562	−0.723076
$825$	2.61290	0.0909695
$826$	−10.5516	−0.367137
$827$	39.3267	1.36752	0.683761	−	0.729706i	$-0.260343\pi$
$827$	39.3267	1.36752	0.683761	+	0.729706i	$0.260343\pi$
$828$	2.84532	0.0988816
$829$	2.14332	0.0744405	0.0372203	−	0.999307i	$-0.488150\pi$
$829$	2.14332	0.0744405	0.0372203	+	0.999307i	$0.488150\pi$
$830$	−22.6640	−0.786680
$831$	18.7130	0.649146
$832$	−76.1522	−2.64010
$833$	−15.7983	−0.547378
$834$	−12.6714	−0.438775
$835$	−30.9769	−1.07200
$836$	55.4575	1.91804
$837$	8.11166	0.280380
$838$	46.2871	1.59896
$839$	−15.6125	−0.539002	−0.269501	−	0.963000i	$-0.586859\pi$
$839$	−15.6125	−0.539002	−0.269501	+	0.963000i	$0.586859\pi$
$840$	5.70903	0.196980
$841$	0	0
$842$	−60.3025	−2.07816
$843$	−8.66587	−0.298468
$844$	−23.2856	−0.801524
$845$	−56.1257	−1.93078
$846$	0.916719	0.0315174
$847$	1.78027	0.0611708
$848$	23.2961	0.799992
$849$	5.58496	0.191675
$850$	−4.98415	−0.170955
$851$	5.57767	0.191200
$852$	−27.4410	−0.940112
$853$	36.4571	1.24827	0.624133	−	0.781318i	$-0.285452\pi$
$853$	36.4571	1.24827	0.624133	+	0.781318i	$0.285452\pi$
$854$	−21.3624	−0.731007
$855$	−13.5076	−0.461949
$856$	11.0423	0.377419
$857$	−0.490297	−0.0167482	−0.00837412	−	0.999965i	$-0.502666\pi$
$857$	−0.490297	−0.0167482	−0.00837412	+	0.999965i	$0.502666\pi$
$858$	−46.4194	−1.58473
$859$	−36.7217	−1.25293	−0.626465	−	0.779450i	$-0.715499\pi$
$859$	−36.7217	−1.25293	−0.626465	+	0.779450i	$0.715499\pi$
$860$	52.4313	1.78789
$861$	−9.27114	−0.315960
$862$	4.27295	0.145537
$863$	40.0757	1.36419	0.682096	−	0.731263i	$-0.261069\pi$
$863$	40.0757	1.36419	0.682096	+	0.731263i	$0.261069\pi$
$864$	7.35072	0.250077
$865$	−6.36001	−0.216247
$866$	−17.1721	−0.583531
$867$	−7.67081	−0.260514
$868$	30.7480	1.04365
$869$	14.0605	0.476971
$870$	0	0
$871$	50.1672	1.69985
$872$	26.0894	0.883499
$873$	−3.80357	−0.128731
$874$	−12.5348	−0.423996
$875$	13.7887	0.466143
$876$	−0.851624	−0.0287737
$877$	29.2270	0.986925	0.493463	−	0.869767i	$-0.335731\pi$
$877$	29.2270	0.986925	0.493463	+	0.869767i	$0.335731\pi$
$878$	−5.23811	−0.176778
$879$	−4.71899	−0.159168
$880$	14.6867	0.495087
$881$	23.3679	0.787285	0.393643	−	0.919264i	$-0.371215\pi$
$881$	23.3679	0.787285	0.393643	+	0.919264i	$0.371215\pi$
$882$	11.3366	0.381724
$883$	−22.0878	−0.743314	−0.371657	−	0.928370i	$-0.621210\pi$
$883$	−22.0878	−0.743314	−0.371657	+	0.928370i	$0.621210\pi$
$884$	51.6815	1.73824
$885$	−8.53496	−0.286900
$886$	−84.0539	−2.82384
$887$	16.2336	0.545072	0.272536	−	0.962146i	$-0.412138\pi$
$887$	16.2336	0.545072	0.272536	+	0.962146i	$0.412138\pi$
$888$	−9.68436	−0.324986
$889$	−20.4054	−0.684374
$890$	73.5049	2.46389
$891$	3.50954	0.117574
$892$	70.1305	2.34814
$893$	−2.35717	−0.0788796
$894$	18.8146	0.629253
$895$	32.1138	1.07344
$896$	17.5164	0.585183
$897$	6.12385	0.204469
$898$	68.6992	2.29252
$899$	0	0
$900$	2.08753	0.0695843
$901$	−40.7530	−1.35768
$902$	52.7512	1.75642
$903$	−10.5475	−0.351000
$904$	−20.9551	−0.696956
$905$	−3.62846	−0.120614
$906$	−26.1712	−0.869479
$907$	−3.44533	−0.114400	−0.0572002	−	0.998363i	$-0.518217\pi$
$907$	−3.44533	−0.114400	−0.0572002	+	0.998363i	$0.518217\pi$
$908$	8.53466	0.283233
$909$	−0.0422219	−0.00140041
$910$	42.8571	1.42070
$911$	−18.9945	−0.629315	−0.314658	−	0.949205i	$-0.601890\pi$
$911$	−18.9945	−0.629315	−0.314658	+	0.949205i	$0.601890\pi$
$912$	−9.84004	−0.325836
$913$	−15.1413	−0.501105
$914$	70.7161	2.33908
$915$	−17.2796	−0.571246
$916$	−61.4290	−2.02967
$917$	14.1231	0.466385
$918$	−6.69450	−0.220951
$919$	−16.7391	−0.552171	−0.276086	−	0.961133i	$-0.589037\pi$
$919$	−16.7391	−0.552171	−0.276086	+	0.961133i	$0.589037\pi$
$920$	4.28535	0.141284
$921$	11.7362	0.386721
$922$	12.4450	0.409856
$923$	−59.0600	−1.94398
$924$	13.3032	0.437644
$925$	4.09218	0.134550
$926$	−50.9236	−1.67345
$927$	11.7804	0.386918
$928$	0	0
$929$	−57.7025	−1.89316	−0.946578	−	0.322474i	$-0.895485\pi$
$929$	−57.7025	−1.89316	−0.946578	+	0.322474i	$0.895485\pi$
$930$	42.6121	1.39731
$931$	−29.1500	−0.955352
$932$	27.9397	0.915194
$933$	16.8038	0.550133
$934$	−26.4703	−0.866133
$935$	−25.6920	−0.840219
$936$	−10.6327	−0.347540
$937$	−40.1165	−1.31055	−0.655274	−	0.755391i	$-0.727447\pi$
$937$	−40.1165	−1.31055	−0.655274	+	0.755391i	$0.727447\pi$
$938$	−24.6326	−0.804282
$939$	−11.9599	−0.390296
$940$	2.81078	0.0916774
$941$	37.2722	1.21504	0.607520	−	0.794305i	$-0.292165\pi$
$941$	37.2722	1.21504	0.607520	+	0.794305i	$0.292165\pi$
$942$	26.8569	0.875046
$943$	−6.95916	−0.226622
$944$	−6.21758	−0.202365
$945$	−3.24021	−0.105404
$946$	60.0137	1.95121
$947$	−27.4624	−0.892408	−0.446204	−	0.894931i	$-0.647224\pi$
$947$	−27.4624	−0.892408	−0.446204	+	0.894931i	$0.647224\pi$
$948$	11.2334	0.364845
$949$	−1.83291	−0.0594988
$950$	−9.19644	−0.298372
$951$	−14.1360	−0.458390
$952$	−7.27541	−0.235797
$953$	2.42289	0.0784851	0.0392425	−	0.999230i	$-0.487506\pi$
$953$	2.42289	0.0784851	0.0392425	+	0.999230i	$0.487506\pi$
$954$	29.2438	0.946802
$955$	27.8473	0.901116
$956$	−21.8169	−0.705610
$957$	0	0
$958$	66.8731	2.16057
$959$	−4.96437	−0.160308
$960$	30.2451	0.976158
$961$	34.7991	1.12255
$962$	−72.6995	−2.34393
$963$	−6.26717	−0.201957
$964$	−65.0196	−2.09414
$965$	14.7684	0.475412
$966$	−3.00686	−0.0967443
$967$	37.8518	1.21723	0.608616	−	0.793465i	$-0.291725\pi$
$967$	37.8518	1.21723	0.608616	+	0.793465i	$0.291725\pi$
$968$	−2.32021	−0.0745744
$969$	17.2136	0.552981
$970$	−19.9809	−0.641548
$971$	−12.8802	−0.413346	−0.206673	−	0.978410i	$-0.566264\pi$
$971$	−12.8802	−0.413346	−0.206673	+	0.978410i	$0.566264\pi$
$972$	2.80388	0.0899346
$973$	7.81584	0.250564
$974$	51.5611	1.65212
$975$	4.49290	0.143888
$976$	−12.5879	−0.402929
$977$	1.41211	0.0451775	0.0225887	−	0.999745i	$-0.492809\pi$
$977$	1.41211	0.0451775	0.0225887	+	0.999745i	$0.492809\pi$
$978$	17.3839	0.555874
$979$	49.1070	1.56947
$980$	34.7595	1.11035
$981$	−14.8073	−0.472760
$982$	−60.4683	−1.92962
$983$	12.0413	0.384059	0.192030	−	0.981389i	$-0.438493\pi$
$983$	12.0413	0.384059	0.192030	+	0.981389i	$0.438493\pi$
$984$	12.0830	0.385192
$985$	6.05597	0.192959
$986$	0	0
$987$	−0.565441	−0.0179982
$988$	95.3595	3.03379
$989$	−7.91726	−0.251754
$990$	18.4363	0.585943
$991$	−44.9003	−1.42630	−0.713152	−	0.701009i	$-0.752733\pi$
$991$	−44.9003	−1.42630	−0.713152	+	0.701009i	$0.752733\pi$
$992$	59.6266	1.89315
$993$	23.0236	0.730633
$994$	28.9990	0.919792
$995$	−31.8335	−1.00919
$996$	−12.0969	−0.383305
$997$	18.2114	0.576762	0.288381	−	0.957516i	$-0.406883\pi$
$997$	18.2114	0.576762	0.288381	+	0.957516i	$0.406883\pi$
$998$	84.0938	2.66194
$999$	5.49645	0.173900

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2523.2.a.r.1.1		9
3.2	odd	2		7569.2.a.bj.1.9		9
29.23	even	7		87.2.g.a.7.3	✓	18
29.24	even	7		87.2.g.a.25.3	yes	18
29.28	even	2		2523.2.a.o.1.9		9
87.23	odd	14		261.2.k.c.181.1		18
87.53	odd	14		261.2.k.c.199.1		18
87.86	odd	2		7569.2.a.bm.1.1		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.g.a.7.3	✓	18	29.23	even	7
87.2.g.a.25.3	yes	18	29.24	even	7
261.2.k.c.181.1		18	87.23	odd	14
261.2.k.c.199.1		18	87.53	odd	14
2523.2.a.o.1.9		9	29.28	even	2
2523.2.a.r.1.1		9	1.1	even	1	trivial
7569.2.a.bj.1.9		9	3.2	odd	2
7569.2.a.bm.1.1		9	87.86	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 2523 = 3 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2523.a (trivial)

\(f(q)\)	\(=\)	\(q-2.19178 q^{2} +1.00000 q^{3} +2.80388 q^{4} -2.39677 q^{5} -2.19178 q^{6} +1.35191 q^{7} -1.76193 q^{8} +1.00000 q^{9} +5.25319 q^{10} +3.50954 q^{11} +2.80388 q^{12} +6.03467 q^{13} -2.96308 q^{14} -2.39677 q^{15} -1.74601 q^{16} +3.05437 q^{17} -2.19178 q^{18} +5.63574 q^{19} -6.72027 q^{20} +1.35191 q^{21} -7.69212 q^{22} +1.01478 q^{23} -1.76193 q^{24} +0.744514 q^{25} -13.2266 q^{26} +1.00000 q^{27} +3.79059 q^{28} +5.25319 q^{30} +8.11166 q^{31} +7.35072 q^{32} +3.50954 q^{33} -6.69450 q^{34} -3.24021 q^{35} +2.80388 q^{36} +5.49645 q^{37} -12.3523 q^{38} +6.03467 q^{39} +4.22294 q^{40} -6.85782 q^{41} -2.96308 q^{42} -7.80197 q^{43} +9.84033 q^{44} -2.39677 q^{45} -2.22416 q^{46} -0.418254 q^{47} -1.74601 q^{48} -5.17235 q^{49} -1.63181 q^{50} +3.05437 q^{51} +16.9205 q^{52} -13.3425 q^{53} -2.19178 q^{54} -8.41156 q^{55} -2.38197 q^{56} +5.63574 q^{57} +3.56102 q^{59} -6.72027 q^{60} +7.20954 q^{61} -17.7790 q^{62} +1.35191 q^{63} -12.6191 q^{64} -14.4637 q^{65} -7.69212 q^{66} +8.31317 q^{67} +8.56410 q^{68} +1.01478 q^{69} +7.10182 q^{70} -9.78678 q^{71} -1.76193 q^{72} -0.303730 q^{73} -12.0470 q^{74} +0.744514 q^{75} +15.8019 q^{76} +4.74457 q^{77} -13.2266 q^{78} +4.00638 q^{79} +4.18478 q^{80} +1.00000 q^{81} +15.0308 q^{82} -4.31434 q^{83} +3.79059 q^{84} -7.32063 q^{85} +17.1002 q^{86} -6.18356 q^{88} +13.9924 q^{89} +5.25319 q^{90} +8.15831 q^{91} +2.84532 q^{92} +8.11166 q^{93} +0.916719 q^{94} -13.5076 q^{95} +7.35072 q^{96} -3.80357 q^{97} +11.3366 q^{98} +3.50954 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 5 q^{2} + 9 q^{3} + 11 q^{4} - 4 q^{5} + 5 q^{6} + 5 q^{7} + 24 q^{8} + 9 q^{9} - q^{11} + 11 q^{12} + q^{13} + 9 q^{14} - 4 q^{15} + 35 q^{16} + 2 q^{17} + 5 q^{18} + 9 q^{19} - 18 q^{20} + 5 q^{21}+ \cdots - q^{99}+O(q^{100}) \) 9 * q + 5 * q^2 + 9 * q^3 + 11 * q^4 - 4 * q^5 + 5 * q^6 + 5 * q^7 + 24 * q^8 + 9 * q^9 - q^11 + 11 * q^12 + q^13 + 9 * q^14 - 4 * q^15 + 35 * q^16 + 2 * q^17 + 5 * q^18 + 9 * q^19 - 18 * q^20 + 5 * q^21 - 4 * q^22 - 4 * q^23 + 24 * q^24 + q^25 - 8 * q^26 + 9 * q^27 + 40 * q^28 + 8 * q^31 + 43 * q^32 - q^33 - 4 * q^34 + 22 * q^35 + 11 * q^36 + 27 * q^37 - 30 * q^38 + q^39 - 29 * q^40 + 12 * q^41 + 9 * q^42 + 16 * q^43 + 37 * q^44 - 4 * q^45 - 22 * q^46 - 8 * q^47 + 35 * q^48 - 6 * q^49 - 7 * q^50 + 2 * q^51 + 33 * q^52 - 8 * q^53 + 5 * q^54 + 9 * q^55 + 40 * q^56 + 9 * q^57 - 16 * q^59 - 18 * q^60 + 21 * q^61 - 32 * q^62 + 5 * q^63 + 36 * q^64 - 31 * q^65 - 4 * q^66 + 3 * q^67 + 33 * q^68 - 4 * q^69 - 6 * q^70 - 33 * q^71 + 24 * q^72 + 3 * q^73 + 28 * q^74 + q^75 - 26 * q^76 + 24 * q^77 - 8 * q^78 + 3 * q^79 - 64 * q^80 + 9 * q^81 + 13 * q^82 + 13 * q^83 + 40 * q^84 + 6 * q^85 + 58 * q^86 + 27 * q^88 + 6 * q^89 + q^91 - 29 * q^92 + 8 * q^93 - 18 * q^94 + 48 * q^95 + 43 * q^96 + 4 * q^97 - 30 * q^98 - q^99

Introduction

L-functions

Modular forms

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