LMFDB - Embedded newform 7935.2.a.bp.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("7935.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7935, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			1.2
Root			$-2.38025$ of defining polynomial
Character	$\chi$	$=$	7935.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.38025 q^{2} -1.00000 q^{3} +3.66560 q^{4} -1.00000 q^{5} +2.38025 q^{6} -3.58597 q^{7} -3.96455 q^{8} +1.00000 q^{9} +2.38025 q^{10} -3.63349 q^{11} -3.66560 q^{12} -2.93707 q^{13} +8.53551 q^{14} +1.00000 q^{15} +2.10543 q^{16} +4.41210 q^{17} -2.38025 q^{18} +5.72464 q^{19} -3.66560 q^{20} +3.58597 q^{21} +8.64862 q^{22} +3.96455 q^{24} +1.00000 q^{25} +6.99097 q^{26} -1.00000 q^{27} -13.1447 q^{28} -1.14829 q^{29} -2.38025 q^{30} -5.61839 q^{31} +2.91765 q^{32} +3.63349 q^{33} -10.5019 q^{34} +3.58597 q^{35} +3.66560 q^{36} -5.52584 q^{37} -13.6261 q^{38} +2.93707 q^{39} +3.96455 q^{40} -2.65154 q^{41} -8.53551 q^{42} -3.19321 q^{43} -13.3189 q^{44} -1.00000 q^{45} +5.24866 q^{47} -2.10543 q^{48} +5.85917 q^{49} -2.38025 q^{50} -4.41210 q^{51} -10.7661 q^{52} -12.2199 q^{53} +2.38025 q^{54} +3.63349 q^{55} +14.2168 q^{56} -5.72464 q^{57} +2.73322 q^{58} -6.96614 q^{59} +3.66560 q^{60} +12.2913 q^{61} +13.3732 q^{62} -3.58597 q^{63} -11.1556 q^{64} +2.93707 q^{65} -8.64862 q^{66} -9.68589 q^{67} +16.1730 q^{68} -8.53551 q^{70} +13.3823 q^{71} -3.96455 q^{72} -5.72287 q^{73} +13.1529 q^{74} -1.00000 q^{75} +20.9842 q^{76} +13.0296 q^{77} -6.99097 q^{78} +11.7785 q^{79} -2.10543 q^{80} +1.00000 q^{81} +6.31133 q^{82} +15.9126 q^{83} +13.1447 q^{84} -4.41210 q^{85} +7.60065 q^{86} +1.14829 q^{87} +14.4052 q^{88} +9.75994 q^{89} +2.38025 q^{90} +10.5322 q^{91} +5.61839 q^{93} -12.4931 q^{94} -5.72464 q^{95} -2.91765 q^{96} +4.06707 q^{97} -13.9463 q^{98} -3.63349 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{3} + 12 q^{4} - 15 q^{5} - 5 q^{7} + 15 q^{9} + 13 q^{11} - 12 q^{12} - 24 q^{13} + 15 q^{14} + 15 q^{15} + 2 q^{16} + 2 q^{17} + 13 q^{19} - 12 q^{20} + 5 q^{21} - 9 q^{22} + 15 q^{25} - 9 q^{26}+ \cdots + 13 q^{99}+O(q^{100}) $ 15 * q - 15 * q^3 + 12 * q^4 - 15 * q^5 - 5 * q^7 + 15 * q^9 + 13 * q^11 - 12 * q^12 - 24 * q^13 + 15 * q^14 + 15 * q^15 + 2 * q^16 + 2 * q^17 + 13 * q^19 - 12 * q^20 + 5 * q^21 - 9 * q^22 + 15 * q^25 - 9 * q^26 - 15 * q^27 + q^28 - 3 * q^29 - 22 * q^31 - 13 * q^33 + q^34 + 5 * q^35 + 12 * q^36 - 6 * q^37 - 17 * q^38 + 24 * q^39 - 20 * q^41 - 15 * q^42 - 4 * q^43 - 18 * q^44 - 15 * q^45 + 7 * q^47 - 2 * q^48 - 10 * q^49 - 2 * q^51 - 55 * q^52 + 4 * q^53 - 13 * q^55 + 25 * q^56 - 13 * q^57 + 2 * q^58 + 9 * q^59 + 12 * q^60 + 13 * q^61 - 7 * q^62 - 5 * q^63 - 26 * q^64 + 24 * q^65 + 9 * q^66 - 32 * q^67 + 27 * q^68 - 15 * q^70 + 14 * q^71 - 43 * q^73 - 11 * q^74 - 15 * q^75 + 88 * q^76 - 21 * q^77 + 9 * q^78 + 33 * q^79 - 2 * q^80 + 15 * q^81 - 35 * q^82 - 12 * q^83 - q^84 - 2 * q^85 + 77 * q^86 + 3 * q^87 - 37 * q^88 + 29 * q^89 + 20 * q^91 + 22 * q^93 - 20 * q^94 - 13 * q^95 + 18 * q^97 - 19 * q^98 + 13 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.38025	−1.68309	−0.841546	−	0.540185i	$-0.818354\pi$
$2$	−2.38025	−1.68309	−0.841546	+	0.540185i	$0.818354\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.66560	1.83280
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.38025	0.971734
$7$	−3.58597	−1.35537	−0.677684	−	0.735353i	$-0.737016\pi$
$7$	−3.58597	−1.35537	−0.677684	+	0.735353i	$0.737016\pi$
$8$	−3.96455	−1.40168
$9$	1.00000	0.333333
$10$	2.38025	0.752702
$11$	−3.63349	−1.09554	−0.547769	−	0.836630i	$-0.684523\pi$
$11$	−3.63349	−1.09554	−0.547769	+	0.836630i	$0.684523\pi$
$12$	−3.66560	−1.05817
$13$	−2.93707	−0.814597	−0.407298	−	0.913295i	$-0.633529\pi$
$13$	−2.93707	−0.814597	−0.407298	+	0.913295i	$0.633529\pi$
$14$	8.53551	2.28121
$15$	1.00000	0.258199
$16$	2.10543	0.526358
$17$	4.41210	1.07009	0.535045	−	0.844823i	$-0.320295\pi$
$17$	4.41210	1.07009	0.535045	+	0.844823i	$0.320295\pi$
$18$	−2.38025	−0.561031
$19$	5.72464	1.31332	0.656661	−	0.754186i	$-0.271968\pi$
$19$	5.72464	1.31332	0.656661	+	0.754186i	$0.271968\pi$
$20$	−3.66560	−0.819653
$21$	3.58597	0.782522
$22$	8.64862	1.84389
$23$	0	0
$23$	0	0
$24$	3.96455	0.809261
$25$	1.00000	0.200000
$26$	6.99097	1.37104
$27$	−1.00000	−0.192450
$28$	−13.1447	−2.48412
$29$	−1.14829	−0.213232	−0.106616	−	0.994300i	$-0.534002\pi$
$29$	−1.14829	−0.213232	−0.106616	+	0.994300i	$0.534002\pi$
$30$	−2.38025	−0.434573
$31$	−5.61839	−1.00909	−0.504546	−	0.863385i	$-0.668340\pi$
$31$	−5.61839	−1.00909	−0.504546	+	0.863385i	$0.668340\pi$
$32$	2.91765	0.515772
$33$	3.63349	0.632509
$34$	−10.5019	−1.80106
$35$	3.58597	0.606139
$36$	3.66560	0.610934
$37$	−5.52584	−0.908443	−0.454222	−	0.890889i	$-0.650083\pi$
$37$	−5.52584	−0.908443	−0.454222	+	0.890889i	$0.650083\pi$
$38$	−13.6261	−2.21044
$39$	2.93707	0.470308
$40$	3.96455	0.626851
$41$	−2.65154	−0.414101	−0.207050	−	0.978330i	$-0.566386\pi$
$41$	−2.65154	−0.414101	−0.207050	+	0.978330i	$0.566386\pi$
$42$	−8.53551	−1.31706
$43$	−3.19321	−0.486960	−0.243480	−	0.969906i	$-0.578289\pi$
$43$	−3.19321	−0.486960	−0.243480	+	0.969906i	$0.578289\pi$
$44$	−13.3189	−2.00790
$45$	−1.00000	−0.149071
$46$	0	0
$47$	5.24866	0.765595	0.382798	−	0.923832i	$-0.374961\pi$
$47$	5.24866	0.765595	0.382798	+	0.923832i	$0.374961\pi$
$48$	−2.10543	−0.303893
$49$	5.85917	0.837024
$50$	−2.38025	−0.336619
$51$	−4.41210	−0.617817
$52$	−10.7661	−1.49299
$53$	−12.2199	−1.67854	−0.839269	−	0.543716i	$-0.817017\pi$
$53$	−12.2199	−1.67854	−0.839269	+	0.543716i	$0.817017\pi$
$54$	2.38025	0.323911
$55$	3.63349	0.489940
$56$	14.2168	1.89979
$57$	−5.72464	−0.758247
$58$	2.73322	0.358890
$59$	−6.96614	−0.906914	−0.453457	−	0.891278i	$-0.649809\pi$
$59$	−6.96614	−0.906914	−0.453457	+	0.891278i	$0.649809\pi$
$60$	3.66560	0.473227
$61$	12.2913	1.57374	0.786870	−	0.617119i	$-0.211700\pi$
$61$	12.2913	1.57374	0.786870	+	0.617119i	$0.211700\pi$
$62$	13.3732	1.69840
$63$	−3.58597	−0.451790
$64$	−11.1556	−1.39445
$65$	2.93707	0.364299
$66$	−8.64862	−1.06457
$67$	−9.68589	−1.18332	−0.591660	−	0.806187i	$-0.701527\pi$
$67$	−9.68589	−1.18332	−0.591660	+	0.806187i	$0.701527\pi$
$68$	16.1730	1.96126
$69$	0	0
$70$	−8.53551	−1.02019
$71$	13.3823	1.58819	0.794094	−	0.607794i	$-0.207945\pi$
$71$	13.3823	1.58819	0.794094	+	0.607794i	$0.207945\pi$
$72$	−3.96455	−0.467227
$73$	−5.72287	−0.669811	−0.334905	−	0.942252i	$-0.608704\pi$
$73$	−5.72287	−0.669811	−0.334905	+	0.942252i	$0.608704\pi$
$74$	13.1529	1.52899
$75$	−1.00000	−0.115470
$76$	20.9842	2.40706
$77$	13.0296	1.48486
$78$	−6.99097	−0.791571
$79$	11.7785	1.32519	0.662594	−	0.748979i	$-0.269456\pi$
$79$	11.7785	1.32519	0.662594	+	0.748979i	$0.269456\pi$
$80$	−2.10543	−0.235394
$81$	1.00000	0.111111
$82$	6.31133	0.696970
$83$	15.9126	1.74664	0.873320	−	0.487148i	$-0.161963\pi$
$83$	15.9126	1.74664	0.873320	+	0.487148i	$0.161963\pi$
$84$	13.1447	1.43421
$85$	−4.41210	−0.478559
$86$	7.60065	0.819599
$87$	1.14829	0.123110
$88$	14.4052	1.53559
$89$	9.75994	1.03455	0.517276	−	0.855819i	$-0.326946\pi$
$89$	9.75994	1.03455	0.517276	+	0.855819i	$0.326946\pi$
$90$	2.38025	0.250901
$91$	10.5322	1.10408
$92$	0	0
$93$	5.61839	0.582600
$94$	−12.4931	−1.28857
$95$	−5.72464	−0.587336
$96$	−2.91765	−0.297781
$97$	4.06707	0.412949	0.206474	−	0.978452i	$-0.433801\pi$
$97$	4.06707	0.412949	0.206474	+	0.978452i	$0.433801\pi$
$98$	−13.9463	−1.40879
$99$	−3.63349	−0.365179
$100$	3.66560	0.366560
$101$	8.24732	0.820639	0.410320	−	0.911942i	$-0.365417\pi$
$101$	8.24732	0.820639	0.410320	+	0.911942i	$0.365417\pi$
$102$	10.5019	1.03984
$103$	−1.74169	−0.171614	−0.0858071	−	0.996312i	$-0.527347\pi$
$103$	−1.74169	−0.171614	−0.0858071	+	0.996312i	$0.527347\pi$
$104$	11.6442	1.14180
$105$	−3.58597	−0.349955
$106$	29.0865	2.82513
$107$	11.4479	1.10671	0.553353	−	0.832947i	$-0.313348\pi$
$107$	11.4479	1.10671	0.553353	+	0.832947i	$0.313348\pi$
$108$	−3.66560	−0.352723
$109$	−0.811222	−0.0777010	−0.0388505	−	0.999245i	$-0.512370\pi$
$109$	−0.811222	−0.0777010	−0.0388505	+	0.999245i	$0.512370\pi$
$110$	−8.64862	−0.824614
$111$	5.52584	0.524490
$112$	−7.55001	−0.713409
$113$	−18.0028	−1.69356	−0.846778	−	0.531946i	$-0.821461\pi$
$113$	−18.0028	−1.69356	−0.846778	+	0.531946i	$0.821461\pi$
$114$	13.6261	1.27620
$115$	0	0
$116$	−4.20918	−0.390812
$117$	−2.93707	−0.271532
$118$	16.5812	1.52642
$119$	−15.8216	−1.45037
$120$	−3.96455	−0.361912
$121$	2.20224	0.200204
$122$	−29.2564	−2.64875
$123$	2.65154	0.239081
$124$	−20.5948	−1.84947
$125$	−1.00000	−0.0894427
$126$	8.53551	0.760404
$127$	−11.6887	−1.03720	−0.518600	−	0.855017i	$-0.673547\pi$
$127$	−11.6887	−1.03720	−0.518600	+	0.855017i	$0.673547\pi$
$128$	20.7178	1.83122
$129$	3.19321	0.281146
$130$	−6.99097	−0.613149
$131$	11.2344	0.981550	0.490775	−	0.871286i	$-0.336714\pi$
$131$	11.2344	0.981550	0.490775	+	0.871286i	$0.336714\pi$
$132$	13.3189	1.15926
$133$	−20.5284	−1.78004
$134$	23.0549	1.99164
$135$	1.00000	0.0860663
$136$	−17.4920	−1.49993
$137$	2.53113	0.216249	0.108124	−	0.994137i	$-0.465516\pi$
$137$	2.53113	0.216249	0.108124	+	0.994137i	$0.465516\pi$
$138$	0	0
$139$	−1.91330	−0.162284	−0.0811420	−	0.996703i	$-0.525857\pi$
$139$	−1.91330	−0.162284	−0.0811420	+	0.996703i	$0.525857\pi$
$140$	13.1447	1.11093
$141$	−5.24866	−0.442017
$142$	−31.8533	−2.67307
$143$	10.6718	0.892422
$144$	2.10543	0.175453
$145$	1.14829	0.0953604
$146$	13.6219	1.12735
$147$	−5.85917	−0.483256
$148$	−20.2555	−1.66499
$149$	15.6701	1.28374	0.641871	−	0.766813i	$-0.278158\pi$
$149$	15.6701	1.28374	0.641871	+	0.766813i	$0.278158\pi$
$150$	2.38025	0.194347
$151$	16.5747	1.34883	0.674416	−	0.738352i	$-0.264395\pi$
$151$	16.5747	1.34883	0.674416	+	0.738352i	$0.264395\pi$
$152$	−22.6956	−1.84086
$153$	4.41210	0.356697
$154$	−31.0137	−2.49915
$155$	5.61839	0.451280
$156$	10.7661	0.861980
$157$	−0.909266	−0.0725673	−0.0362836	−	0.999342i	$-0.511552\pi$
$157$	−0.909266	−0.0725673	−0.0362836	+	0.999342i	$0.511552\pi$
$158$	−28.0359	−2.23041
$159$	12.2199	0.969104
$160$	−2.91765	−0.230660
$161$	0	0
$162$	−2.38025	−0.187010
$163$	−18.4287	−1.44345	−0.721723	−	0.692182i	$-0.756649\pi$
$163$	−18.4287	−1.44345	−0.721723	+	0.692182i	$0.756649\pi$
$164$	−9.71949	−0.758964
$165$	−3.63349	−0.282867
$166$	−37.8761	−2.93976
$167$	3.57771	0.276852	0.138426	−	0.990373i	$-0.455796\pi$
$167$	3.57771	0.276852	0.138426	+	0.990373i	$0.455796\pi$
$168$	−14.2168	−1.09685
$169$	−4.37361	−0.336432
$170$	10.5019	0.805459
$171$	5.72464	0.437774
$172$	−11.7050	−0.892501
$173$	14.4080	1.09542	0.547710	−	0.836668i	$-0.315500\pi$
$173$	14.4080	1.09542	0.547710	+	0.836668i	$0.315500\pi$
$174$	−2.73322	−0.207205
$175$	−3.58597	−0.271074
$176$	−7.65006	−0.576645
$177$	6.96614	0.523607
$178$	−23.2311	−1.74125
$179$	14.9968	1.12092	0.560458	−	0.828183i	$-0.310625\pi$
$179$	14.9968	1.12092	0.560458	+	0.828183i	$0.310625\pi$
$180$	−3.66560	−0.273218
$181$	19.9742	1.48467	0.742335	−	0.670029i	$-0.233718\pi$
$181$	19.9742	1.48467	0.742335	+	0.670029i	$0.233718\pi$
$182$	−25.0694	−1.85827
$183$	−12.2913	−0.908599
$184$	0	0
$185$	5.52584	0.406268
$186$	−13.3732	−0.980570
$187$	−16.0313	−1.17233
$188$	19.2395	1.40318
$189$	3.58597	0.260841
$190$	13.6261	0.988540
$191$	13.0360	0.943249	0.471624	−	0.881800i	$-0.343668\pi$
$191$	13.0360	0.943249	0.471624	+	0.881800i	$0.343668\pi$
$192$	11.1556	0.805086
$193$	−17.8715	−1.28642	−0.643209	−	0.765690i	$-0.722397\pi$
$193$	−17.8715	−1.28642	−0.643209	+	0.765690i	$0.722397\pi$
$194$	−9.68066	−0.695031
$195$	−2.93707	−0.210328
$196$	21.4774	1.53410
$197$	−6.21319	−0.442671	−0.221336	−	0.975198i	$-0.571042\pi$
$197$	−6.21319	−0.442671	−0.221336	+	0.975198i	$0.571042\pi$
$198$	8.64862	0.614631
$199$	14.8319	1.05140	0.525701	−	0.850669i	$-0.323803\pi$
$199$	14.8319	1.05140	0.525701	+	0.850669i	$0.323803\pi$
$200$	−3.96455	−0.280336
$201$	9.68589	0.683190
$202$	−19.6307	−1.38121
$203$	4.11773	0.289008
$204$	−16.1730	−1.13234
$205$	2.65154	0.185192
$206$	4.14567	0.288843
$207$	0	0
$208$	−6.18380	−0.428769
$209$	−20.8004	−1.43879
$210$	8.53551	0.589006
$211$	3.02940	0.208553	0.104276	−	0.994548i	$-0.466747\pi$
$211$	3.02940	0.208553	0.104276	+	0.994548i	$0.466747\pi$
$212$	−44.7934	−3.07643
$213$	−13.3823	−0.916941
$214$	−27.2488	−1.86269
$215$	3.19321	0.217775
$216$	3.96455	0.269754
$217$	20.1474	1.36769
$218$	1.93091	0.130778
$219$	5.72287	0.386715
$220$	13.3189	0.897962
$221$	−12.9586	−0.871692
$222$	−13.1529	−0.882765
$223$	22.6453	1.51644	0.758221	−	0.651997i	$-0.226069\pi$
$223$	22.6453	1.51644	0.758221	+	0.651997i	$0.226069\pi$
$224$	−10.4626	−0.699061
$225$	1.00000	0.0666667
$226$	42.8511	2.85041
$227$	16.5074	1.09563	0.547816	−	0.836599i	$-0.315460\pi$
$227$	16.5074	1.09563	0.547816	+	0.836599i	$0.315460\pi$
$228$	−20.9842	−1.38972
$229$	−12.5550	−0.829660	−0.414830	−	0.909899i	$-0.636159\pi$
$229$	−12.5550	−0.829660	−0.414830	+	0.909899i	$0.636159\pi$
$230$	0	0
$231$	−13.0296	−0.857283
$232$	4.55246	0.298884
$233$	11.4665	0.751194	0.375597	−	0.926783i	$-0.377438\pi$
$233$	11.4665	0.751194	0.375597	+	0.926783i	$0.377438\pi$
$234$	6.99097	0.457014
$235$	−5.24866	−0.342385
$236$	−25.5351	−1.66219
$237$	−11.7785	−0.765097
$238$	37.6595	2.44110
$239$	−24.4642	−1.58246	−0.791230	−	0.611518i	$-0.790559\pi$
$239$	−24.4642	−1.58246	−0.791230	+	0.611518i	$0.790559\pi$
$240$	2.10543	0.135905
$241$	−8.74326	−0.563203	−0.281602	−	0.959531i	$-0.590866\pi$
$241$	−8.74326	−0.563203	−0.281602	+	0.959531i	$0.590866\pi$
$242$	−5.24190	−0.336962
$243$	−1.00000	−0.0641500
$244$	45.0550	2.88435
$245$	−5.85917	−0.374328
$246$	−6.31133	−0.402396
$247$	−16.8137	−1.06983
$248$	22.2744	1.41443
$249$	−15.9126	−1.00842
$250$	2.38025	0.150540
$251$	−7.66078	−0.483544	−0.241772	−	0.970333i	$-0.577729\pi$
$251$	−7.66078	−0.483544	−0.241772	+	0.970333i	$0.577729\pi$
$252$	−13.1447	−0.828040
$253$	0	0
$254$	27.8220	1.74571
$255$	4.41210	0.276296
$256$	−27.0025	−1.68766
$257$	11.0444	0.688930	0.344465	−	0.938799i	$-0.388060\pi$
$257$	11.0444	0.688930	0.344465	+	0.938799i	$0.388060\pi$
$258$	−7.60065	−0.473196
$259$	19.8155	1.23128
$260$	10.7661	0.667687
$261$	−1.14829	−0.0710774
$262$	−26.7406	−1.65204
$263$	−2.93105	−0.180736	−0.0903681	−	0.995908i	$-0.528804\pi$
$263$	−2.93105	−0.180736	−0.0903681	+	0.995908i	$0.528804\pi$
$264$	−14.4052	−0.886576
$265$	12.2199	0.750665
$266$	48.8627	2.99597
$267$	−9.75994	−0.597299
$268$	−35.5046	−2.16879
$269$	15.4122	0.939701	0.469850	−	0.882746i	$-0.344308\pi$
$269$	15.4122	0.939701	0.469850	+	0.882746i	$0.344308\pi$
$270$	−2.38025	−0.144858
$271$	−30.0420	−1.82492	−0.912461	−	0.409164i	$-0.865821\pi$
$271$	−30.0420	−1.82492	−0.912461	+	0.409164i	$0.865821\pi$
$272$	9.28936	0.563250
$273$	−10.5322	−0.637440
$274$	−6.02472	−0.363967
$275$	−3.63349	−0.219108
$276$	0	0
$277$	−30.8208	−1.85184	−0.925920	−	0.377720i	$-0.876708\pi$
$277$	−30.8208	−1.85184	−0.925920	+	0.377720i	$0.876708\pi$
$278$	4.55414	0.273139
$279$	−5.61839	−0.336364
$280$	−14.2168	−0.849614
$281$	−15.5785	−0.929335	−0.464667	−	0.885485i	$-0.653826\pi$
$281$	−15.5785	−0.929335	−0.464667	+	0.885485i	$0.653826\pi$
$282$	12.4931	0.743955
$283$	28.0832	1.66937	0.834686	−	0.550726i	$-0.185649\pi$
$283$	28.0832	1.66937	0.834686	+	0.550726i	$0.185649\pi$
$284$	49.0542	2.91083
$285$	5.72464	0.339098
$286$	−25.4016	−1.50203
$287$	9.50834	0.561259
$288$	2.91765	0.171924
$289$	2.46659	0.145094
$290$	−2.73322	−0.160500
$291$	−4.06707	−0.238416
$292$	−20.9777	−1.22763
$293$	19.3355	1.12959	0.564797	−	0.825230i	$-0.308955\pi$
$293$	19.3355	1.12959	0.564797	+	0.825230i	$0.308955\pi$
$294$	13.9463	0.813365
$295$	6.96614	0.405584
$296$	21.9075	1.27335
$297$	3.63349	0.210836
$298$	−37.2987	−2.16066
$299$	0	0
$300$	−3.66560	−0.211634
$301$	11.4508	0.660010
$302$	−39.4520	−2.27021
$303$	−8.24732	−0.473796
$304$	12.0528	0.691277
$305$	−12.2913	−0.703798
$306$	−10.5019	−0.600354
$307$	16.2209	0.925774	0.462887	−	0.886417i	$-0.346814\pi$
$307$	16.2209	0.925774	0.462887	+	0.886417i	$0.346814\pi$
$308$	47.7612	2.72145
$309$	1.74169	0.0990815
$310$	−13.3732	−0.759546
$311$	−19.6405	−1.11371	−0.556856	−	0.830609i	$-0.687993\pi$
$311$	−19.6405	−1.11371	−0.556856	+	0.830609i	$0.687993\pi$
$312$	−11.6442	−0.659221
$313$	−18.8540	−1.06569	−0.532846	−	0.846212i	$-0.678878\pi$
$313$	−18.8540	−1.06569	−0.532846	+	0.846212i	$0.678878\pi$
$314$	2.16428	0.122137
$315$	3.58597	0.202046
$316$	43.1754	2.42880
$317$	10.4645	0.587744	0.293872	−	0.955845i	$-0.405056\pi$
$317$	10.4645	0.587744	0.293872	+	0.955845i	$0.405056\pi$
$318$	−29.0865	−1.63109
$319$	4.17230	0.233604
$320$	11.1556	0.623617
$321$	−11.4479	−0.638957
$322$	0	0
$323$	25.2577	1.40537
$324$	3.66560	0.203645
$325$	−2.93707	−0.162919
$326$	43.8649	2.42945
$327$	0.811222	0.0448607
$328$	10.5122	0.580437
$329$	−18.8215	−1.03766
$330$	8.64862	0.476091
$331$	−20.7116	−1.13841	−0.569207	−	0.822194i	$-0.692750\pi$
$331$	−20.7116	−1.13841	−0.569207	+	0.822194i	$0.692750\pi$
$332$	58.3294	3.20124
$333$	−5.52584	−0.302814
$334$	−8.51586	−0.465967
$335$	9.68589	0.529197
$336$	7.55001	0.411887
$337$	−11.1566	−0.607739	−0.303869	−	0.952714i	$-0.598279\pi$
$337$	−11.1566	−0.607739	−0.303869	+	0.952714i	$0.598279\pi$
$338$	10.4103	0.566246
$339$	18.0028	0.977775
$340$	−16.1730	−0.877103
$341$	20.4144	1.10550
$342$	−13.6261	−0.736814
$343$	4.09099	0.220893
$344$	12.6596	0.682562
$345$	0	0
$346$	−34.2947	−1.84369
$347$	2.71634	0.145821	0.0729103	−	0.997338i	$-0.476771\pi$
$347$	2.71634	0.145821	0.0729103	+	0.997338i	$0.476771\pi$
$348$	4.20918	0.225636
$349$	10.3190	0.552365	0.276182	−	0.961105i	$-0.410931\pi$
$349$	10.3190	0.552365	0.276182	+	0.961105i	$0.410931\pi$
$350$	8.53551	0.456242
$351$	2.93707	0.156769
$352$	−10.6012	−0.565048
$353$	−25.6033	−1.36273	−0.681363	−	0.731945i	$-0.738613\pi$
$353$	−25.6033	−1.36273	−0.681363	+	0.731945i	$0.738613\pi$
$354$	−16.5812	−0.881279
$355$	−13.3823	−0.710260
$356$	35.7760	1.89613
$357$	15.8216	0.837370
$358$	−35.6963	−1.88661
$359$	35.3977	1.86822	0.934109	−	0.356987i	$-0.116196\pi$
$359$	35.3977	1.86822	0.934109	+	0.356987i	$0.116196\pi$
$360$	3.96455	0.208950
$361$	13.7715	0.724816
$362$	−47.5436	−2.49884
$363$	−2.20224	−0.115588
$364$	38.6070	2.02356
$365$	5.72287	0.299548
$366$	29.2564	1.52926
$367$	20.5613	1.07329	0.536645	−	0.843808i	$-0.319691\pi$
$367$	20.5613	1.07329	0.536645	+	0.843808i	$0.319691\pi$
$368$	0	0
$369$	−2.65154	−0.138034
$370$	−13.1529	−0.683787
$371$	43.8203	2.27504
$372$	20.5948	1.06779
$373$	27.3218	1.41467	0.707334	−	0.706879i	$-0.249897\pi$
$373$	27.3218	1.41467	0.707334	+	0.706879i	$0.249897\pi$
$374$	38.1586	1.97313
$375$	1.00000	0.0516398
$376$	−20.8086	−1.07312
$377$	3.37261	0.173698
$378$	−8.53551	−0.439019
$379$	22.6686	1.16441	0.582203	−	0.813043i	$-0.302191\pi$
$379$	22.6686	1.16441	0.582203	+	0.813043i	$0.302191\pi$
$380$	−20.9842	−1.07647
$381$	11.6887	0.598828
$382$	−31.0289	−1.58758
$383$	−27.8115	−1.42110	−0.710551	−	0.703646i	$-0.751554\pi$
$383$	−27.8115	−1.42110	−0.710551	+	0.703646i	$0.751554\pi$
$384$	−20.7178	−1.05725
$385$	−13.0296	−0.664049
$386$	42.5387	2.16516
$387$	−3.19321	−0.162320
$388$	14.9083	0.756853
$389$	7.90037	0.400565	0.200282	−	0.979738i	$-0.435814\pi$
$389$	7.90037	0.400565	0.200282	+	0.979738i	$0.435814\pi$
$390$	6.99097	0.354002
$391$	0	0
$392$	−23.2290	−1.17324
$393$	−11.2344	−0.566698
$394$	14.7890	0.745057
$395$	−11.7785	−0.592642
$396$	−13.3189	−0.669301
$397$	18.4083	0.923886	0.461943	−	0.886910i	$-0.347153\pi$
$397$	18.4083	0.923886	0.461943	+	0.886910i	$0.347153\pi$
$398$	−35.3036	−1.76961
$399$	20.5284	1.02770
$400$	2.10543	0.105272
$401$	−8.97443	−0.448162	−0.224081	−	0.974571i	$-0.571938\pi$
$401$	−8.97443	−0.448162	−0.224081	+	0.974571i	$0.571938\pi$
$402$	−23.0549	−1.14987
$403$	16.5016	0.822004
$404$	30.2314	1.50407
$405$	−1.00000	−0.0496904
$406$	−9.80125	−0.486428
$407$	20.0781	0.995234
$408$	17.4920	0.865982
$409$	11.6137	0.574258	0.287129	−	0.957892i	$-0.407299\pi$
$409$	11.6137	0.574258	0.287129	+	0.957892i	$0.407299\pi$
$410$	−6.31133	−0.311695
$411$	−2.53113	−0.124851
$412$	−6.38436	−0.314535
$413$	24.9803	1.22920
$414$	0	0
$415$	−15.9126	−0.781121
$416$	−8.56934	−0.420146
$417$	1.91330	0.0936947
$418$	49.5102	2.42163
$419$	−11.9648	−0.584520	−0.292260	−	0.956339i	$-0.594407\pi$
$419$	−11.9648	−0.584520	−0.292260	+	0.956339i	$0.594407\pi$
$420$	−13.1447	−0.641397
$421$	−24.8002	−1.20869	−0.604344	−	0.796724i	$-0.706565\pi$
$421$	−24.8002	−1.20869	−0.604344	+	0.796724i	$0.706565\pi$
$422$	−7.21075	−0.351014
$423$	5.24866	0.255198
$424$	48.4466	2.35277
$425$	4.41210	0.214018
$426$	31.8533	1.54330
$427$	−44.0762	−2.13300
$428$	41.9633	2.02837
$429$	−10.6718	−0.515240
$430$	−7.60065	−0.366536
$431$	2.14074	0.103116	0.0515580	−	0.998670i	$-0.483581\pi$
$431$	2.14074	0.103116	0.0515580	+	0.998670i	$0.483581\pi$
$432$	−2.10543	−0.101298
$433$	5.29063	0.254251	0.127126	−	0.991887i	$-0.459425\pi$
$433$	5.29063	0.254251	0.127126	+	0.991887i	$0.459425\pi$
$434$	−47.9558	−2.30195
$435$	−1.14829	−0.0550563
$436$	−2.97362	−0.142410
$437$	0	0
$438$	−13.6219	−0.650878
$439$	−29.2822	−1.39756	−0.698782	−	0.715335i	$-0.746274\pi$
$439$	−29.2822	−1.39756	−0.698782	+	0.715335i	$0.746274\pi$
$440$	−14.4052	−0.686739
$441$	5.85917	0.279008
$442$	30.8448	1.46714
$443$	−6.46498	−0.307160	−0.153580	−	0.988136i	$-0.549080\pi$
$443$	−6.46498	−0.307160	−0.153580	+	0.988136i	$0.549080\pi$
$444$	20.2555	0.961285
$445$	−9.75994	−0.462665
$446$	−53.9016	−2.55231
$447$	−15.6701	−0.741169
$448$	40.0036	1.88999
$449$	−30.2072	−1.42557	−0.712784	−	0.701384i	$-0.752566\pi$
$449$	−30.2072	−1.42557	−0.712784	+	0.701384i	$0.752566\pi$
$450$	−2.38025	−0.112206
$451$	9.63434	0.453663
$452$	−65.9909	−3.10395
$453$	−16.5747	−0.778748
$454$	−39.2917	−1.84405
$455$	−10.5322	−0.493759
$456$	22.6956	1.06282
$457$	−16.3135	−0.763115	−0.381558	−	0.924345i	$-0.624612\pi$
$457$	−16.3135	−0.763115	−0.381558	+	0.924345i	$0.624612\pi$
$458$	29.8842	1.39639
$459$	−4.41210	−0.205939
$460$	0	0
$461$	−29.2881	−1.36408	−0.682041	−	0.731314i	$-0.738908\pi$
$461$	−29.2881	−1.36408	−0.682041	+	0.731314i	$0.738908\pi$
$462$	31.0137	1.44289
$463$	17.8260	0.828447	0.414223	−	0.910175i	$-0.364053\pi$
$463$	17.8260	0.828447	0.414223	+	0.910175i	$0.364053\pi$
$464$	−2.41765	−0.112236
$465$	−5.61839	−0.260547
$466$	−27.2931	−1.26433
$467$	3.34540	0.154807	0.0774034	−	0.997000i	$-0.475337\pi$
$467$	3.34540	0.154807	0.0774034	+	0.997000i	$0.475337\pi$
$468$	−10.7661	−0.497665
$469$	34.7333	1.60384
$470$	12.4931	0.576265
$471$	0.909266	0.0418967
$472$	27.6176	1.27120
$473$	11.6025	0.533483
$474$	28.0359	1.28773
$475$	5.72464	0.262664
$476$	−57.9958	−2.65823
$477$	−12.2199	−0.559513
$478$	58.2311	2.66343
$479$	−7.77932	−0.355446	−0.177723	−	0.984081i	$-0.556873\pi$
$479$	−7.77932	−0.355446	−0.177723	+	0.984081i	$0.556873\pi$
$480$	2.91765	0.133172
$481$	16.2298	0.740015
$482$	20.8112	0.947923
$483$	0	0
$484$	8.07255	0.366934
$485$	−4.06707	−0.184676
$486$	2.38025	0.107970
$487$	14.6546	0.664063	0.332031	−	0.943268i	$-0.392266\pi$
$487$	14.6546	0.664063	0.332031	+	0.943268i	$0.392266\pi$
$488$	−48.7295	−2.20588
$489$	18.4287	0.833374
$490$	13.9463	0.630029
$491$	19.1331	0.863465	0.431732	−	0.902002i	$-0.357903\pi$
$491$	19.1331	0.863465	0.431732	+	0.902002i	$0.357903\pi$
$492$	9.71949	0.438188
$493$	−5.06637	−0.228178
$494$	40.0208	1.80062
$495$	3.63349	0.163313
$496$	−11.8291	−0.531144
$497$	−47.9886	−2.15258
$498$	37.8761	1.69727
$499$	13.2692	0.594009	0.297005	−	0.954876i	$-0.404012\pi$
$499$	13.2692	0.594009	0.297005	+	0.954876i	$0.404012\pi$
$500$	−3.66560	−0.163931
$501$	−3.57771	−0.159840
$502$	18.2346	0.813849
$503$	7.24929	0.323230	0.161615	−	0.986854i	$-0.448330\pi$
$503$	7.24929	0.323230	0.161615	+	0.986854i	$0.448330\pi$
$504$	14.2168	0.633265
$505$	−8.24732	−0.367001
$506$	0	0
$507$	4.37361	0.194239
$508$	−42.8460	−1.90098
$509$	−0.978533	−0.0433727	−0.0216864	−	0.999765i	$-0.506904\pi$
$509$	−0.978533	−0.0433727	−0.0216864	+	0.999765i	$0.506904\pi$
$510$	−10.5019	−0.465032
$511$	20.5220	0.907840
$512$	22.8371	1.00927
$513$	−5.72464	−0.252749
$514$	−26.2884	−1.15953
$515$	1.74169	0.0767482
$516$	11.7050	0.515285
$517$	−19.0709	−0.838739
$518$	−47.1659	−2.07235
$519$	−14.4080	−0.632441
$520$	−11.6442	−0.510631
$521$	21.7844	0.954391	0.477196	−	0.878797i	$-0.341653\pi$
$521$	21.7844	0.954391	0.477196	+	0.878797i	$0.341653\pi$
$522$	2.73322	0.119630
$523$	−13.0832	−0.572087	−0.286043	−	0.958217i	$-0.592340\pi$
$523$	−13.0832	−0.572087	−0.286043	+	0.958217i	$0.592340\pi$
$524$	41.1807	1.79899
$525$	3.58597	0.156504
$526$	6.97664	0.304196
$527$	−24.7889	−1.07982
$528$	7.65006	0.332926
$529$	0	0
$530$	−29.0865	−1.26344
$531$	−6.96614	−0.302305
$532$	−75.2488	−3.26245
$533$	7.78776	0.337325
$534$	23.2311	1.00531
$535$	−11.4479	−0.494934
$536$	38.4002	1.65864
$537$	−14.9968	−0.647161
$538$	−36.6850	−1.58160
$539$	−21.2892	−0.916992
$540$	3.66560	0.157742
$541$	−18.2621	−0.785150	−0.392575	−	0.919720i	$-0.628416\pi$
$541$	−18.2621	−0.785150	−0.392575	+	0.919720i	$0.628416\pi$
$542$	71.5076	3.07151
$543$	−19.9742	−0.857175
$544$	12.8729	0.551923
$545$	0.811222	0.0347489
$546$	25.0694	1.07287
$547$	−23.4198	−1.00136	−0.500679	−	0.865633i	$-0.666916\pi$
$547$	−23.4198	−1.00136	−0.500679	+	0.865633i	$0.666916\pi$
$548$	9.27810	0.396341
$549$	12.2913	0.524580
$550$	8.64862	0.368778
$551$	−6.57355	−0.280043
$552$	0	0
$553$	−42.2374	−1.79612
$554$	73.3612	3.11682
$555$	−5.52584	−0.234559
$556$	−7.01340	−0.297434
$557$	−8.40016	−0.355926	−0.177963	−	0.984037i	$-0.556951\pi$
$557$	−8.40016	−0.355926	−0.177963	+	0.984037i	$0.556951\pi$
$558$	13.3732	0.566132
$559$	9.37868	0.396676
$560$	7.55001	0.319046
$561$	16.0313	0.676842
$562$	37.0807	1.56416
$563$	6.75021	0.284487	0.142244	−	0.989832i	$-0.454568\pi$
$563$	6.75021	0.284487	0.142244	+	0.989832i	$0.454568\pi$
$564$	−19.2395	−0.810129
$565$	18.0028	0.757382
$566$	−66.8451	−2.80971
$567$	−3.58597	−0.150597
$568$	−53.0549	−2.22613
$569$	4.37193	0.183281	0.0916403	−	0.995792i	$-0.470789\pi$
$569$	4.37193	0.183281	0.0916403	+	0.995792i	$0.470789\pi$
$570$	−13.6261	−0.570734
$571$	−42.8773	−1.79436	−0.897179	−	0.441667i	$-0.854387\pi$
$571$	−42.8773	−1.79436	−0.897179	+	0.441667i	$0.854387\pi$
$572$	39.1186	1.63563
$573$	−13.0360	−0.544585
$574$	−22.6322	−0.944651
$575$	0	0
$576$	−11.1556	−0.464817
$577$	2.84454	0.118420	0.0592099	−	0.998246i	$-0.481142\pi$
$577$	2.84454	0.118420	0.0592099	+	0.998246i	$0.481142\pi$
$578$	−5.87112	−0.244206
$579$	17.8715	0.742714
$580$	4.20918	0.174777
$581$	−57.0622	−2.36734
$582$	9.68066	0.401276
$583$	44.4010	1.83890
$584$	22.6886	0.938861
$585$	2.93707	0.121433
$586$	−46.0234	−1.90121
$587$	11.8741	0.490097	0.245048	−	0.969511i	$-0.421196\pi$
$587$	11.8741	0.490097	0.245048	+	0.969511i	$0.421196\pi$
$588$	−21.4774	−0.885712
$589$	−32.1633	−1.32526
$590$	−16.5812	−0.682636
$591$	6.21319	0.255576
$592$	−11.6343	−0.478166
$593$	−40.2544	−1.65305	−0.826524	−	0.562901i	$-0.809685\pi$
$593$	−40.2544	−1.65305	−0.826524	+	0.562901i	$0.809685\pi$
$594$	−8.64862	−0.354857
$595$	15.8216	0.648624
$596$	57.4402	2.35284
$597$	−14.8319	−0.607027
$598$	0	0
$599$	−24.7275	−1.01034	−0.505168	−	0.863021i	$-0.668570\pi$
$599$	−24.7275	−1.01034	−0.505168	+	0.863021i	$0.668570\pi$
$600$	3.96455	0.161852
$601$	−10.3375	−0.421675	−0.210837	−	0.977521i	$-0.567619\pi$
$601$	−10.3375	−0.421675	−0.210837	+	0.977521i	$0.567619\pi$
$602$	−27.2557	−1.11086
$603$	−9.68589	−0.394440
$604$	60.7563	2.47214
$605$	−2.20224	−0.0895340
$606$	19.6307	0.797443
$607$	8.74395	0.354906	0.177453	−	0.984129i	$-0.443214\pi$
$607$	8.74395	0.354906	0.177453	+	0.984129i	$0.443214\pi$
$608$	16.7025	0.677375
$609$	−4.11773	−0.166859
$610$	29.2564	1.18456
$611$	−15.4157	−0.623652
$612$	16.1730	0.653754
$613$	−18.7613	−0.757762	−0.378881	−	0.925445i	$-0.623691\pi$
$613$	−18.7613	−0.757762	−0.378881	+	0.925445i	$0.623691\pi$
$614$	−38.6098	−1.55816
$615$	−2.65154	−0.106920
$616$	−51.6564	−2.08130
$617$	−39.0264	−1.57114	−0.785571	−	0.618772i	$-0.787631\pi$
$617$	−39.0264	−1.57114	−0.785571	+	0.618772i	$0.787631\pi$
$618$	−4.14567	−0.166763
$619$	−5.12363	−0.205936	−0.102968	−	0.994685i	$-0.532834\pi$
$619$	−5.12363	−0.205936	−0.102968	+	0.994685i	$0.532834\pi$
$620$	20.5948	0.827106
$621$	0	0
$622$	46.7494	1.87448
$623$	−34.9988	−1.40220
$624$	6.18380	0.247550
$625$	1.00000	0.0400000
$626$	44.8773	1.79366
$627$	20.8004	0.830689
$628$	−3.33301	−0.133001
$629$	−24.3806	−0.972116
$630$	−8.53551	−0.340063
$631$	−25.6571	−1.02139	−0.510697	−	0.859761i	$-0.670612\pi$
$631$	−25.6571	−1.02139	−0.510697	+	0.859761i	$0.670612\pi$
$632$	−46.6966	−1.85749
$633$	−3.02940	−0.120408
$634$	−24.9081	−0.989228
$635$	11.6887	0.463850
$636$	44.7934	1.77618
$637$	−17.2088	−0.681837
$638$	−9.93113	−0.393177
$639$	13.3823	0.529396
$640$	−20.7178	−0.818945
$641$	14.1150	0.557509	0.278754	−	0.960362i	$-0.410078\pi$
$641$	14.1150	0.557509	0.278754	+	0.960362i	$0.410078\pi$
$642$	27.2488	1.07542
$643$	50.0605	1.97420	0.987098	−	0.160120i	$-0.0511880\pi$
$643$	50.0605	1.97420	0.987098	+	0.160120i	$0.0511880\pi$
$644$	0	0
$645$	−3.19321	−0.125733
$646$	−60.1196	−2.36537
$647$	22.4669	0.883265	0.441632	−	0.897196i	$-0.354400\pi$
$647$	22.4669	0.883265	0.441632	+	0.897196i	$0.354400\pi$
$648$	−3.96455	−0.155742
$649$	25.3114	0.993559
$650$	6.99097	0.274208
$651$	−20.1474	−0.789638
$652$	−67.5522	−2.64555
$653$	8.53473	0.333990	0.166995	−	0.985958i	$-0.446594\pi$
$653$	8.53473	0.333990	0.166995	+	0.985958i	$0.446594\pi$
$654$	−1.93091	−0.0755047
$655$	−11.2344	−0.438963
$656$	−5.58263	−0.217965
$657$	−5.72287	−0.223270
$658$	44.8000	1.74648
$659$	−22.9183	−0.892772	−0.446386	−	0.894841i	$-0.647289\pi$
$659$	−22.9183	−0.892772	−0.446386	+	0.894841i	$0.647289\pi$
$660$	−13.3189	−0.518438
$661$	37.0411	1.44073	0.720365	−	0.693595i	$-0.243974\pi$
$661$	37.0411	1.44073	0.720365	+	0.693595i	$0.243974\pi$
$662$	49.2989	1.91606
$663$	12.9586	0.503272
$664$	−63.0865	−2.44823
$665$	20.5284	0.796056
$666$	13.1529	0.509665
$667$	0	0
$668$	13.1145	0.507414
$669$	−22.6453	−0.875519
$670$	−23.0549	−0.890687
$671$	−44.6603	−1.72409
$672$	10.4626	0.403603
$673$	−4.38512	−0.169034	−0.0845169	−	0.996422i	$-0.526935\pi$
$673$	−4.38512	−0.169034	−0.0845169	+	0.996422i	$0.526935\pi$
$674$	26.5555	1.02288
$675$	−1.00000	−0.0384900
$676$	−16.0319	−0.616613
$677$	32.6379	1.25438	0.627188	−	0.778868i	$-0.284206\pi$
$677$	32.6379	1.25438	0.627188	+	0.778868i	$0.284206\pi$
$678$	−42.8511	−1.64569
$679$	−14.5844	−0.559698
$680$	17.4920	0.670787
$681$	−16.5074	−0.632563
$682$	−48.5913	−1.86066
$683$	43.4624	1.66304	0.831522	−	0.555493i	$-0.187470\pi$
$683$	43.4624	1.66304	0.831522	+	0.555493i	$0.187470\pi$
$684$	20.9842	0.802353
$685$	−2.53113	−0.0967093
$686$	−9.73759	−0.371783
$687$	12.5550	0.479005
$688$	−6.72308	−0.256315
$689$	35.8908	1.36733
$690$	0	0
$691$	−8.02389	−0.305243	−0.152622	−	0.988285i	$-0.548772\pi$
$691$	−8.02389	−0.305243	−0.152622	+	0.988285i	$0.548772\pi$
$692$	52.8140	2.00769
$693$	13.0296	0.494953
$694$	−6.46557	−0.245430
$695$	1.91330	0.0725756
$696$	−4.55246	−0.172561
$697$	−11.6988	−0.443125
$698$	−24.5619	−0.929681
$699$	−11.4665	−0.433702
$700$	−13.1447	−0.496824
$701$	−12.6846	−0.479092	−0.239546	−	0.970885i	$-0.576999\pi$
$701$	−12.6846	−0.479092	−0.239546	+	0.970885i	$0.576999\pi$
$702$	−6.99097	−0.263857
$703$	−31.6335	−1.19308
$704$	40.5337	1.52767
$705$	5.24866	0.197676
$706$	60.9423	2.29360
$707$	−29.5746	−1.11227
$708$	25.5351	0.959667
$709$	−2.31097	−0.0867901	−0.0433951	−	0.999058i	$-0.513817\pi$
$709$	−2.31097	−0.0867901	−0.0433951	+	0.999058i	$0.513817\pi$
$710$	31.8533	1.19543
$711$	11.7785	0.441729
$712$	−38.6938	−1.45011
$713$	0	0
$714$	−37.6595	−1.40937
$715$	−10.6718	−0.399103
$716$	54.9724	2.05442
$717$	24.4642	0.913634
$718$	−84.2554	−3.14439
$719$	−30.3933	−1.13348	−0.566740	−	0.823897i	$-0.691796\pi$
$719$	−30.3933	−1.13348	−0.566740	+	0.823897i	$0.691796\pi$
$720$	−2.10543	−0.0784648
$721$	6.24566	0.232600
$722$	−32.7797	−1.21993
$723$	8.74326	0.325166
$724$	73.2174	2.72110
$725$	−1.14829	−0.0426465
$726$	5.24190	0.194545
$727$	−53.0907	−1.96903	−0.984513	−	0.175310i	$-0.943907\pi$
$727$	−53.0907	−1.96903	−0.984513	+	0.175310i	$0.943907\pi$
$728$	−41.7556	−1.54757
$729$	1.00000	0.0370370
$730$	−13.6219	−0.504168
$731$	−14.0888	−0.521091
$732$	−45.0550	−1.66528
$733$	−7.32557	−0.270576	−0.135288	−	0.990806i	$-0.543196\pi$
$733$	−7.32557	−0.270576	−0.135288	+	0.990806i	$0.543196\pi$
$734$	−48.9411	−1.80645
$735$	5.85917	0.216119
$736$	0	0
$737$	35.1936	1.29637
$738$	6.31133	0.232323
$739$	−23.0475	−0.847815	−0.423907	−	0.905705i	$-0.639342\pi$
$739$	−23.0475	−0.847815	−0.423907	+	0.905705i	$0.639342\pi$
$740$	20.2555	0.744608
$741$	16.8137	0.617666
$742$	−104.303	−3.82910
$743$	24.1990	0.887775	0.443888	−	0.896082i	$-0.353599\pi$
$743$	24.1990	0.887775	0.443888	+	0.896082i	$0.353599\pi$
$744$	−22.2744	−0.816619
$745$	−15.6701	−0.574107
$746$	−65.0328	−2.38102
$747$	15.9126	0.582213
$748$	−58.7644	−2.14864
$749$	−41.0517	−1.49999
$750$	−2.38025	−0.0869145
$751$	−17.2941	−0.631070	−0.315535	−	0.948914i	$-0.602184\pi$
$751$	−17.2941	−0.631070	−0.315535	+	0.948914i	$0.602184\pi$
$752$	11.0507	0.402977
$753$	7.66078	0.279174
$754$	−8.02767	−0.292350
$755$	−16.5747	−0.603216
$756$	13.1447	0.478069
$757$	35.8735	1.30384	0.651922	−	0.758286i	$-0.273963\pi$
$757$	35.8735	1.30384	0.651922	+	0.758286i	$0.273963\pi$
$758$	−53.9569	−1.95980
$759$	0	0
$760$	22.6956	0.823257
$761$	−2.82917	−0.102557	−0.0512786	−	0.998684i	$-0.516330\pi$
$761$	−2.82917	−0.102557	−0.0512786	+	0.998684i	$0.516330\pi$
$762$	−27.8220	−1.00788
$763$	2.90902	0.105313
$764$	47.7846	1.72879
$765$	−4.41210	−0.159520
$766$	66.1984	2.39185
$767$	20.4600	0.738769
$768$	27.0025	0.974369
$769$	−43.6469	−1.57395	−0.786974	−	0.616986i	$-0.788353\pi$
$769$	−43.6469	−1.57395	−0.786974	+	0.616986i	$0.788353\pi$
$770$	31.0137	1.11766
$771$	−11.0444	−0.397754
$772$	−65.5098	−2.35775
$773$	−5.95708	−0.214261	−0.107131	−	0.994245i	$-0.534166\pi$
$773$	−5.95708	−0.214261	−0.107131	+	0.994245i	$0.534166\pi$
$774$	7.60065	0.273200
$775$	−5.61839	−0.201819
$776$	−16.1241	−0.578822
$777$	−19.8155	−0.710877
$778$	−18.8049	−0.674187
$779$	−15.1791	−0.543848
$780$	−10.7661	−0.385489
$781$	−48.6245	−1.73992
$782$	0	0
$783$	1.14829	0.0410366
$784$	12.3361	0.440574
$785$	0.909266	0.0324531
$786$	26.7406	0.953806
$787$	−0.336463	−0.0119936	−0.00599680	−	0.999982i	$-0.501909\pi$
$787$	−0.336463	−0.0119936	−0.00599680	+	0.999982i	$0.501909\pi$
$788$	−22.7751	−0.811329
$789$	2.93105	0.104348
$790$	28.0359	0.997471
$791$	64.5573	2.29539
$792$	14.4052	0.511865
$793$	−36.1004	−1.28196
$794$	−43.8164	−1.55498
$795$	−12.2199	−0.433397
$796$	54.3677	1.92701
$797$	17.7832	0.629914	0.314957	−	0.949106i	$-0.398010\pi$
$797$	17.7832	0.629914	0.314957	+	0.949106i	$0.398010\pi$
$798$	−48.8627	−1.72972
$799$	23.1576	0.819256
$800$	2.91765	0.103154
$801$	9.75994	0.344850
$802$	21.3614	0.754298
$803$	20.7940	0.733803
$804$	35.5046	1.25215
$805$	0	0
$806$	−39.2780	−1.38351
$807$	−15.4122	−0.542536
$808$	−32.6969	−1.15027
$809$	1.66209	0.0584361	0.0292180	−	0.999573i	$-0.490698\pi$
$809$	1.66209	0.0584361	0.0292180	+	0.999573i	$0.490698\pi$
$810$	2.38025	0.0836335
$811$	29.4020	1.03244	0.516222	−	0.856455i	$-0.327338\pi$
$811$	29.4020	1.03244	0.516222	+	0.856455i	$0.327338\pi$
$812$	15.0940	0.529695
$813$	30.0420	1.05362
$814$	−47.7909	−1.67507
$815$	18.4287	0.645529
$816$	−9.28936	−0.325193
$817$	−18.2800	−0.639536
$818$	−27.6434	−0.966530
$819$	10.5322	0.368026
$820$	9.71949	0.339419
$821$	−21.3203	−0.744085	−0.372042	−	0.928216i	$-0.621342\pi$
$821$	−21.3203	−0.744085	−0.372042	+	0.928216i	$0.621342\pi$
$822$	6.02472	0.210136
$823$	45.7702	1.59545	0.797725	−	0.603022i	$-0.206037\pi$
$823$	45.7702	1.59545	0.797725	+	0.603022i	$0.206037\pi$
$824$	6.90504	0.240548
$825$	3.63349	0.126502
$826$	−59.4595	−2.06886
$827$	−22.9208	−0.797036	−0.398518	−	0.917161i	$-0.630475\pi$
$827$	−22.9208	−0.797036	−0.398518	+	0.917161i	$0.630475\pi$
$828$	0	0
$829$	41.1449	1.42902	0.714512	−	0.699624i	$-0.246649\pi$
$829$	41.1449	1.42902	0.714512	+	0.699624i	$0.246649\pi$
$830$	37.8761	1.31470
$831$	30.8208	1.06916
$832$	32.7648	1.13591
$833$	25.8512	0.895691
$834$	−4.55414	−0.157697
$835$	−3.57771	−0.123812
$836$	−76.2460	−2.63702
$837$	5.61839	0.194200
$838$	28.4793	0.983801
$839$	32.6345	1.12667	0.563334	−	0.826229i	$-0.309518\pi$
$839$	32.6345	1.12667	0.563334	+	0.826229i	$0.309518\pi$
$840$	14.2168	0.490525
$841$	−27.6814	−0.954532
$842$	59.0307	2.03433
$843$	15.5785	0.536552
$844$	11.1046	0.382236
$845$	4.37361	0.150457
$846$	−12.4931	−0.429523
$847$	−7.89718	−0.271350
$848$	−25.7282	−0.883511
$849$	−28.0832	−0.963813
$850$	−10.5019	−0.360212
$851$	0	0
$852$	−49.0542	−1.68057
$853$	−38.9675	−1.33422	−0.667111	−	0.744958i	$-0.732470\pi$
$853$	−38.9675	−1.33422	−0.667111	+	0.744958i	$0.732470\pi$
$854$	104.913	3.59003
$855$	−5.72464	−0.195779
$856$	−45.3856	−1.55125
$857$	−50.4424	−1.72308	−0.861539	−	0.507692i	$-0.830499\pi$
$857$	−50.4424	−1.72308	−0.861539	+	0.507692i	$0.830499\pi$
$858$	25.4016	0.867197
$859$	−39.2113	−1.33787	−0.668937	−	0.743319i	$-0.733250\pi$
$859$	−39.2113	−1.33787	−0.668937	+	0.743319i	$0.733250\pi$
$860$	11.7050	0.399138
$861$	−9.50834	−0.324043
$862$	−5.09551	−0.173554
$863$	−44.4673	−1.51369	−0.756843	−	0.653597i	$-0.773259\pi$
$863$	−44.4673	−1.51369	−0.756843	+	0.653597i	$0.773259\pi$
$864$	−2.91765	−0.0992604
$865$	−14.4080	−0.489887
$866$	−12.5930	−0.427928
$867$	−2.46659	−0.0837699
$868$	73.8522	2.50671
$869$	−42.7971	−1.45179
$870$	2.73322	0.0926649
$871$	28.4482	0.963929
$872$	3.21613	0.108912
$873$	4.06707	0.137650
$874$	0	0
$875$	3.58597	0.121228
$876$	20.9777	0.708772
$877$	−50.3971	−1.70179	−0.850895	−	0.525336i	$-0.823940\pi$
$877$	−50.3971	−1.70179	−0.850895	+	0.525336i	$0.823940\pi$
$878$	69.6990	2.35223
$879$	−19.3355	−0.652171
$880$	7.65006	0.257883
$881$	13.6569	0.460112	0.230056	−	0.973177i	$-0.426109\pi$
$881$	13.6569	0.460112	0.230056	+	0.973177i	$0.426109\pi$
$882$	−13.9463	−0.469596
$883$	−36.2215	−1.21895	−0.609475	−	0.792806i	$-0.708620\pi$
$883$	−36.2215	−1.21895	−0.609475	+	0.792806i	$0.708620\pi$
$884$	−47.5012	−1.59764
$885$	−6.96614	−0.234164
$886$	15.3883	0.516979
$887$	4.84300	0.162612	0.0813060	−	0.996689i	$-0.474091\pi$
$887$	4.84300	0.162612	0.0813060	+	0.996689i	$0.474091\pi$
$888$	−21.9075	−0.735167
$889$	41.9152	1.40579
$890$	23.2311	0.778709
$891$	−3.63349	−0.121726
$892$	83.0087	2.77934
$893$	30.0467	1.00547
$894$	37.2987	1.24746
$895$	−14.9968	−0.501289
$896$	−74.2935	−2.48197
$897$	0	0
$898$	71.9009	2.39936
$899$	6.45155	0.215171
$900$	3.66560	0.122187
$901$	−53.9156	−1.79619
$902$	−22.9322	−0.763557
$903$	−11.4508	−0.381057
$904$	71.3728	2.37383
$905$	−19.9742	−0.663965
$906$	39.4520	1.31071
$907$	49.3404	1.63832	0.819161	−	0.573563i	$-0.194439\pi$
$907$	49.3404	1.63832	0.819161	+	0.573563i	$0.194439\pi$
$908$	60.5094	2.00807
$909$	8.24732	0.273546
$910$	25.0694	0.831042
$911$	10.3345	0.342398	0.171199	−	0.985236i	$-0.445236\pi$
$911$	10.3345	0.342398	0.171199	+	0.985236i	$0.445236\pi$
$912$	−12.0528	−0.399109
$913$	−57.8184	−1.91351
$914$	38.8304	1.28439
$915$	12.2913	0.406338
$916$	−46.0218	−1.52060
$917$	−40.2860	−1.33036
$918$	10.5019	0.346614
$919$	−12.2091	−0.402739	−0.201370	−	0.979515i	$-0.564539\pi$
$919$	−12.2091	−0.402739	−0.201370	+	0.979515i	$0.564539\pi$
$920$	0	0
$921$	−16.2209	−0.534496
$922$	69.7130	2.29588
$923$	−39.3048	−1.29373
$924$	−47.7612	−1.57123
$925$	−5.52584	−0.181689
$926$	−42.4305	−1.39435
$927$	−1.74169	−0.0572047
$928$	−3.35031	−0.109979
$929$	−5.26773	−0.172829	−0.0864144	−	0.996259i	$-0.527541\pi$
$929$	−5.26773	−0.172829	−0.0864144	+	0.996259i	$0.527541\pi$
$930$	13.3732	0.438524
$931$	33.5416	1.09928
$932$	42.0315	1.37679
$933$	19.6405	0.643002
$934$	−7.96290	−0.260554
$935$	16.0313	0.524280
$936$	11.6442	0.380602
$937$	−0.358566	−0.0117138	−0.00585692	−	0.999983i	$-0.501864\pi$
$937$	−0.358566	−0.0117138	−0.00585692	+	0.999983i	$0.501864\pi$
$938$	−82.6740	−2.69940
$939$	18.8540	0.615278
$940$	−19.2395	−0.627523
$941$	−49.3538	−1.60889	−0.804444	−	0.594029i	$-0.797537\pi$
$941$	−49.3538	−1.60889	−0.804444	+	0.594029i	$0.797537\pi$
$942$	−2.16428	−0.0705161
$943$	0	0
$944$	−14.6667	−0.477361
$945$	−3.58597	−0.116652
$946$	−27.6169	−0.897902
$947$	−14.2553	−0.463234	−0.231617	−	0.972807i	$-0.574402\pi$
$947$	−14.2553	−0.463234	−0.231617	+	0.972807i	$0.574402\pi$
$948$	−43.1754	−1.40227
$949$	16.8085	0.545626
$950$	−13.6261	−0.442089
$951$	−10.4645	−0.339334
$952$	62.7257	2.03295
$953$	−26.9773	−0.873882	−0.436941	−	0.899490i	$-0.643938\pi$
$953$	−26.9773	−0.873882	−0.436941	+	0.899490i	$0.643938\pi$
$954$	29.0865	0.941712
$955$	−13.0360	−0.421834
$956$	−89.6762	−2.90033
$957$	−4.17230	−0.134871
$958$	18.5168	0.598249
$959$	−9.07654	−0.293097
$960$	−11.1556	−0.360045
$961$	0.566312	0.0182681
$962$	−38.6310	−1.24551
$963$	11.4479	0.368902
$964$	−32.0493	−1.03224
$965$	17.8715	0.575304
$966$	0	0
$967$	−13.7176	−0.441129	−0.220564	−	0.975372i	$-0.570790\pi$
$967$	−13.7176	−0.441129	−0.220564	+	0.975372i	$0.570790\pi$
$968$	−8.73091	−0.280622
$969$	−25.2577	−0.811393
$970$	9.68066	0.310827
$971$	−2.66371	−0.0854826	−0.0427413	−	0.999086i	$-0.513609\pi$
$971$	−2.66371	−0.0854826	−0.0427413	+	0.999086i	$0.513609\pi$
$972$	−3.66560	−0.117574
$973$	6.86103	0.219955
$974$	−34.8816	−1.11768
$975$	2.93707	0.0940615
$976$	25.8785	0.828350
$977$	−26.8051	−0.857570	−0.428785	−	0.903406i	$-0.641058\pi$
$977$	−26.8051	−0.857570	−0.428785	+	0.903406i	$0.641058\pi$
$978$	−43.8649	−1.40265
$979$	−35.4626	−1.13339
$980$	−21.4774	−0.686069
$981$	−0.811222	−0.0259003
$982$	−45.5416	−1.45329
$983$	37.7012	1.20248	0.601240	−	0.799068i	$-0.294673\pi$
$983$	37.7012	1.20248	0.601240	+	0.799068i	$0.294673\pi$
$984$	−10.5122	−0.335116
$985$	6.21319	0.197969
$986$	12.0592	0.384044
$987$	18.8215	0.599096
$988$	−61.6322	−1.96078
$989$	0	0
$990$	−8.64862	−0.274871
$991$	42.5042	1.35019	0.675095	−	0.737731i	$-0.264103\pi$
$991$	42.5042	1.35019	0.675095	+	0.737731i	$0.264103\pi$
$992$	−16.3925	−0.520462
$993$	20.7116	0.657264
$994$	114.225	3.62299
$995$	−14.8319	−0.470201
$996$	−58.3294	−1.84824
$997$	24.4453	0.774190	0.387095	−	0.922040i	$-0.373479\pi$
$997$	24.4453	0.774190	0.387095	+	0.922040i	$0.373479\pi$
$998$	−31.5840	−0.999773
$999$	5.52584	0.174830

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bp.1.2		15
23.9	even	11		345.2.m.a.196.1	✓	30
23.18	even	11		345.2.m.a.301.1	yes	30
23.22	odd	2		7935.2.a.bq.1.2		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.a.196.1	✓	30	23.9	even	11
345.2.m.a.301.1	yes	30	23.18	even	11
7935.2.a.bp.1.2		15	1.1	even	1	trivial
7935.2.a.bq.1.2		15	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:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q-2.38025 q^{2} -1.00000 q^{3} +3.66560 q^{4} -1.00000 q^{5} +2.38025 q^{6} -3.58597 q^{7} -3.96455 q^{8} +1.00000 q^{9} +2.38025 q^{10} -3.63349 q^{11} -3.66560 q^{12} -2.93707 q^{13} +8.53551 q^{14} +1.00000 q^{15} +2.10543 q^{16} +4.41210 q^{17} -2.38025 q^{18} +5.72464 q^{19} -3.66560 q^{20} +3.58597 q^{21} +8.64862 q^{22} +3.96455 q^{24} +1.00000 q^{25} +6.99097 q^{26} -1.00000 q^{27} -13.1447 q^{28} -1.14829 q^{29} -2.38025 q^{30} -5.61839 q^{31} +2.91765 q^{32} +3.63349 q^{33} -10.5019 q^{34} +3.58597 q^{35} +3.66560 q^{36} -5.52584 q^{37} -13.6261 q^{38} +2.93707 q^{39} +3.96455 q^{40} -2.65154 q^{41} -8.53551 q^{42} -3.19321 q^{43} -13.3189 q^{44} -1.00000 q^{45} +5.24866 q^{47} -2.10543 q^{48} +5.85917 q^{49} -2.38025 q^{50} -4.41210 q^{51} -10.7661 q^{52} -12.2199 q^{53} +2.38025 q^{54} +3.63349 q^{55} +14.2168 q^{56} -5.72464 q^{57} +2.73322 q^{58} -6.96614 q^{59} +3.66560 q^{60} +12.2913 q^{61} +13.3732 q^{62} -3.58597 q^{63} -11.1556 q^{64} +2.93707 q^{65} -8.64862 q^{66} -9.68589 q^{67} +16.1730 q^{68} -8.53551 q^{70} +13.3823 q^{71} -3.96455 q^{72} -5.72287 q^{73} +13.1529 q^{74} -1.00000 q^{75} +20.9842 q^{76} +13.0296 q^{77} -6.99097 q^{78} +11.7785 q^{79} -2.10543 q^{80} +1.00000 q^{81} +6.31133 q^{82} +15.9126 q^{83} +13.1447 q^{84} -4.41210 q^{85} +7.60065 q^{86} +1.14829 q^{87} +14.4052 q^{88} +9.75994 q^{89} +2.38025 q^{90} +10.5322 q^{91} +5.61839 q^{93} -12.4931 q^{94} -5.72464 q^{95} -2.91765 q^{96} +4.06707 q^{97} -13.9463 q^{98} -3.63349 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{3} + 12 q^{4} - 15 q^{5} - 5 q^{7} + 15 q^{9} + 13 q^{11} - 12 q^{12} - 24 q^{13} + 15 q^{14} + 15 q^{15} + 2 q^{16} + 2 q^{17} + 13 q^{19} - 12 q^{20} + 5 q^{21} - 9 q^{22} + 15 q^{25} - 9 q^{26}+ \cdots + 13 q^{99}+O(q^{100}) \) 15 * q - 15 * q^3 + 12 * q^4 - 15 * q^5 - 5 * q^7 + 15 * q^9 + 13 * q^11 - 12 * q^12 - 24 * q^13 + 15 * q^14 + 15 * q^15 + 2 * q^16 + 2 * q^17 + 13 * q^19 - 12 * q^20 + 5 * q^21 - 9 * q^22 + 15 * q^25 - 9 * q^26 - 15 * q^27 + q^28 - 3 * q^29 - 22 * q^31 - 13 * q^33 + q^34 + 5 * q^35 + 12 * q^36 - 6 * q^37 - 17 * q^38 + 24 * q^39 - 20 * q^41 - 15 * q^42 - 4 * q^43 - 18 * q^44 - 15 * q^45 + 7 * q^47 - 2 * q^48 - 10 * q^49 - 2 * q^51 - 55 * q^52 + 4 * q^53 - 13 * q^55 + 25 * q^56 - 13 * q^57 + 2 * q^58 + 9 * q^59 + 12 * q^60 + 13 * q^61 - 7 * q^62 - 5 * q^63 - 26 * q^64 + 24 * q^65 + 9 * q^66 - 32 * q^67 + 27 * q^68 - 15 * q^70 + 14 * q^71 - 43 * q^73 - 11 * q^74 - 15 * q^75 + 88 * q^76 - 21 * q^77 + 9 * q^78 + 33 * q^79 - 2 * q^80 + 15 * q^81 - 35 * q^82 - 12 * q^83 - q^84 - 2 * q^85 + 77 * q^86 + 3 * q^87 - 37 * q^88 + 29 * q^89 + 20 * q^91 + 22 * q^93 - 20 * q^94 - 13 * q^95 + 18 * q^97 - 19 * q^98 + 13 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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