LMFDB - Embedded newform 1614.2.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1614,2,Mod(1,1614)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1614, 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("1614.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1614 = 2 \cdot 3 \cdot 269 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1614.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:	$12.8878548862$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 33x^{6} + 352x^{4} - 18x^{3} - 1229x^{2} + 178x + 108 $ x^8 - 33x^6 + 352x^4 - 18x^3 - 1229x^2 + 178*x + 108
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-3.24183$ of defining polynomial
Character	$\chi$	$=$	1614.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.24183 q^{5} -1.00000 q^{6} +0.788032 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.24183 q^{10} -3.71321 q^{11} +1.00000 q^{12} -4.56367 q^{13} -0.788032 q^{14} -3.24183 q^{15} +1.00000 q^{16} +6.73472 q^{17} -1.00000 q^{18} +0.264723 q^{19} -3.24183 q^{20} +0.788032 q^{21} +3.71321 q^{22} -4.99945 q^{23} -1.00000 q^{24} +5.50946 q^{25} +4.56367 q^{26} +1.00000 q^{27} +0.788032 q^{28} +2.15583 q^{29} +3.24183 q^{30} +9.33164 q^{31} -1.00000 q^{32} -3.71321 q^{33} -6.73472 q^{34} -2.55467 q^{35} +1.00000 q^{36} +10.4700 q^{37} -0.264723 q^{38} -4.56367 q^{39} +3.24183 q^{40} +10.0262 q^{41} -0.788032 q^{42} +1.64774 q^{43} -3.71321 q^{44} -3.24183 q^{45} +4.99945 q^{46} -2.72055 q^{47} +1.00000 q^{48} -6.37901 q^{49} -5.50946 q^{50} +6.73472 q^{51} -4.56367 q^{52} -9.63165 q^{53} -1.00000 q^{54} +12.0376 q^{55} -0.788032 q^{56} +0.264723 q^{57} -2.15583 q^{58} -13.8386 q^{59} -3.24183 q^{60} +9.36822 q^{61} -9.33164 q^{62} +0.788032 q^{63} +1.00000 q^{64} +14.7946 q^{65} +3.71321 q^{66} +14.7199 q^{67} +6.73472 q^{68} -4.99945 q^{69} +2.55467 q^{70} +14.4817 q^{71} -1.00000 q^{72} +5.06594 q^{73} -10.4700 q^{74} +5.50946 q^{75} +0.264723 q^{76} -2.92613 q^{77} +4.56367 q^{78} +4.20572 q^{79} -3.24183 q^{80} +1.00000 q^{81} -10.0262 q^{82} +1.30785 q^{83} +0.788032 q^{84} -21.8328 q^{85} -1.64774 q^{86} +2.15583 q^{87} +3.71321 q^{88} +7.12840 q^{89} +3.24183 q^{90} -3.59632 q^{91} -4.99945 q^{92} +9.33164 q^{93} +2.72055 q^{94} -0.858187 q^{95} -1.00000 q^{96} +4.67710 q^{97} +6.37901 q^{98} -3.71321 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{3} + 8 q^{4} - 8 q^{6} + 9 q^{7} - 8 q^{8} + 8 q^{9} + 8 q^{11} + 8 q^{12} - 3 q^{13} - 9 q^{14} + 8 q^{16} + 8 q^{17} - 8 q^{18} + 18 q^{19} + 9 q^{21} - 8 q^{22} - 10 q^{23} - 8 q^{24}+ \cdots + 8 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 - 8 * q^6 + 9 * q^7 - 8 * q^8 + 8 * q^9 + 8 * q^11 + 8 * q^12 - 3 * q^13 - 9 * q^14 + 8 * q^16 + 8 * q^17 - 8 * q^18 + 18 * q^19 + 9 * q^21 - 8 * q^22 - 10 * q^23 - 8 * q^24 + 26 * q^25 + 3 * q^26 + 8 * q^27 + 9 * q^28 - 9 * q^29 + 18 * q^31 - 8 * q^32 + 8 * q^33 - 8 * q^34 + 9 * q^35 + 8 * q^36 + 22 * q^37 - 18 * q^38 - 3 * q^39 - q^41 - 9 * q^42 + 14 * q^43 + 8 * q^44 + 10 * q^46 + 6 * q^47 + 8 * q^48 + 29 * q^49 - 26 * q^50 + 8 * q^51 - 3 * q^52 - 3 * q^53 - 8 * q^54 + 17 * q^55 - 9 * q^56 + 18 * q^57 + 9 * q^58 + q^59 + 18 * q^61 - 18 * q^62 + 9 * q^63 + 8 * q^64 - 14 * q^65 - 8 * q^66 + 30 * q^67 + 8 * q^68 - 10 * q^69 - 9 * q^70 - 5 * q^71 - 8 * q^72 + 15 * q^73 - 22 * q^74 + 26 * q^75 + 18 * q^76 - 20 * q^77 + 3 * q^78 + 21 * q^79 + 8 * q^81 + q^82 - 11 * q^83 + 9 * q^84 + 18 * q^85 - 14 * q^86 - 9 * q^87 - 8 * q^88 + 22 * q^89 + 53 * q^91 - 10 * q^92 + 18 * q^93 - 6 * q^94 - 9 * q^95 - 8 * q^96 + 13 * q^97 - 29 * q^98 + 8 * q^99

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−3.24183	−1.44979	−0.724895	−	0.688859i	$-0.758112\pi$
$5$	−3.24183	−1.44979	−0.724895	+	0.688859i	$0.758112\pi$
$6$	−1.00000	−0.408248
$7$	0.788032	0.297848	0.148924	−	0.988849i	$-0.452419\pi$
$7$	0.788032	0.297848	0.148924	+	0.988849i	$0.452419\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.24183	1.02516
$11$	−3.71321	−1.11958	−0.559788	−	0.828636i	$-0.689117\pi$
$11$	−3.71321	−1.11958	−0.559788	+	0.828636i	$0.689117\pi$
$12$	1.00000	0.288675
$13$	−4.56367	−1.26573	−0.632867	−	0.774260i	$-0.718122\pi$
$13$	−4.56367	−1.26573	−0.632867	+	0.774260i	$0.718122\pi$
$14$	−0.788032	−0.210610
$15$	−3.24183	−0.837037
$16$	1.00000	0.250000
$17$	6.73472	1.63341	0.816705	−	0.577055i	$-0.195798\pi$
$17$	6.73472	1.63341	0.816705	+	0.577055i	$0.195798\pi$
$18$	−1.00000	−0.235702
$19$	0.264723	0.0607316	0.0303658	−	0.999539i	$-0.490333\pi$
$19$	0.264723	0.0607316	0.0303658	+	0.999539i	$0.490333\pi$
$20$	−3.24183	−0.724895
$21$	0.788032	0.171963
$22$	3.71321	0.791659
$23$	−4.99945	−1.04246	−0.521228	−	0.853417i	$-0.674526\pi$
$23$	−4.99945	−1.04246	−0.521228	+	0.853417i	$0.674526\pi$
$24$	−1.00000	−0.204124
$25$	5.50946	1.10189
$26$	4.56367	0.895009
$27$	1.00000	0.192450
$28$	0.788032	0.148924
$29$	2.15583	0.400327	0.200163	−	0.979763i	$-0.435853\pi$
$29$	2.15583	0.400327	0.200163	+	0.979763i	$0.435853\pi$
$30$	3.24183	0.591875
$31$	9.33164	1.67601	0.838006	−	0.545661i	$-0.183721\pi$
$31$	9.33164	1.67601	0.838006	+	0.545661i	$0.183721\pi$
$32$	−1.00000	−0.176777
$33$	−3.71321	−0.646387
$34$	−6.73472	−1.15500
$35$	−2.55467	−0.431818
$36$	1.00000	0.166667
$37$	10.4700	1.72126	0.860629	−	0.509233i	$-0.170071\pi$
$37$	10.4700	1.72126	0.860629	+	0.509233i	$0.170071\pi$
$38$	−0.264723	−0.0429437
$39$	−4.56367	−0.730772
$40$	3.24183	0.512578
$41$	10.0262	1.56584	0.782918	−	0.622125i	$-0.213730\pi$
$41$	10.0262	1.56584	0.782918	+	0.622125i	$0.213730\pi$
$42$	−0.788032	−0.121596
$43$	1.64774	0.251278	0.125639	−	0.992076i	$-0.459902\pi$
$43$	1.64774	0.251278	0.125639	+	0.992076i	$0.459902\pi$
$44$	−3.71321	−0.559788
$45$	−3.24183	−0.483264
$46$	4.99945	0.737128
$47$	−2.72055	−0.396834	−0.198417	−	0.980118i	$-0.563580\pi$
$47$	−2.72055	−0.396834	−0.198417	+	0.980118i	$0.563580\pi$
$48$	1.00000	0.144338
$49$	−6.37901	−0.911286
$50$	−5.50946	−0.779156
$51$	6.73472	0.943050
$52$	−4.56367	−0.632867
$53$	−9.63165	−1.32301	−0.661504	−	0.749941i	$-0.730082\pi$
$53$	−9.63165	−1.32301	−0.661504	+	0.749941i	$0.730082\pi$
$54$	−1.00000	−0.136083
$55$	12.0376	1.62315
$56$	−0.788032	−0.105305
$57$	0.264723	0.0350634
$58$	−2.15583	−0.283074
$59$	−13.8386	−1.80163	−0.900814	−	0.434204i	$-0.857030\pi$
$59$	−13.8386	−1.80163	−0.900814	+	0.434204i	$0.857030\pi$
$60$	−3.24183	−0.418519
$61$	9.36822	1.19948	0.599739	−	0.800196i	$-0.295271\pi$
$61$	9.36822	1.19948	0.599739	+	0.800196i	$0.295271\pi$
$62$	−9.33164	−1.18512
$63$	0.788032	0.0992827
$64$	1.00000	0.125000
$65$	14.7946	1.83505
$66$	3.71321	0.457065
$67$	14.7199	1.79833	0.899163	−	0.437615i	$-0.144177\pi$
$67$	14.7199	1.79833	0.899163	+	0.437615i	$0.144177\pi$
$68$	6.73472	0.816705
$69$	−4.99945	−0.601862
$70$	2.55467	0.305341
$71$	14.4817	1.71866	0.859328	−	0.511425i	$-0.170882\pi$
$71$	14.4817	1.71866	0.859328	+	0.511425i	$0.170882\pi$
$72$	−1.00000	−0.117851
$73$	5.06594	0.592924	0.296462	−	0.955045i	$-0.404193\pi$
$73$	5.06594	0.592924	0.296462	+	0.955045i	$0.404193\pi$
$74$	−10.4700	−1.21711
$75$	5.50946	0.636178
$76$	0.264723	0.0303658
$77$	−2.92613	−0.333463
$78$	4.56367	0.516734
$79$	4.20572	0.473181	0.236590	−	0.971609i	$-0.423970\pi$
$79$	4.20572	0.473181	0.236590	+	0.971609i	$0.423970\pi$
$80$	−3.24183	−0.362448
$81$	1.00000	0.111111
$82$	−10.0262	−1.10721
$83$	1.30785	0.143555	0.0717774	−	0.997421i	$-0.477133\pi$
$83$	1.30785	0.143555	0.0717774	+	0.997421i	$0.477133\pi$
$84$	0.788032	0.0859814
$85$	−21.8328	−2.36810
$86$	−1.64774	−0.177681
$87$	2.15583	0.231129
$88$	3.71321	0.395830
$89$	7.12840	0.755609	0.377804	−	0.925885i	$-0.376679\pi$
$89$	7.12840	0.755609	0.377804	+	0.925885i	$0.376679\pi$
$90$	3.24183	0.341719
$91$	−3.59632	−0.376997
$92$	−4.99945	−0.521228
$93$	9.33164	0.967646
$94$	2.72055	0.280604
$95$	−0.858187	−0.0880481
$96$	−1.00000	−0.102062
$97$	4.67710	0.474888	0.237444	−	0.971401i	$-0.423690\pi$
$97$	4.67710	0.474888	0.237444	+	0.971401i	$0.423690\pi$
$98$	6.37901	0.644377
$99$	−3.71321	−0.373192
$100$	5.50946	0.550946
$101$	−9.10834	−0.906313	−0.453157	−	0.891431i	$-0.649702\pi$
$101$	−9.10834	−0.906313	−0.453157	+	0.891431i	$0.649702\pi$
$102$	−6.73472	−0.666837
$103$	−7.42243	−0.731354	−0.365677	−	0.930742i	$-0.619162\pi$
$103$	−7.42243	−0.731354	−0.365677	+	0.930742i	$0.619162\pi$
$104$	4.56367	0.447505
$105$	−2.55467	−0.249310
$106$	9.63165	0.935508
$107$	15.4018	1.48895	0.744474	−	0.667652i	$-0.232700\pi$
$107$	15.4018	1.48895	0.744474	+	0.667652i	$0.232700\pi$
$108$	1.00000	0.0962250
$109$	5.10716	0.489177	0.244589	−	0.969627i	$-0.421347\pi$
$109$	5.10716	0.489177	0.244589	+	0.969627i	$0.421347\pi$
$110$	−12.0376	−1.14774
$111$	10.4700	0.993768
$112$	0.788032	0.0744620
$113$	−14.8298	−1.39507	−0.697535	−	0.716551i	$-0.745720\pi$
$113$	−14.8298	−1.39507	−0.697535	+	0.716551i	$0.745720\pi$
$114$	−0.264723	−0.0247936
$115$	16.2074	1.51134
$116$	2.15583	0.200163
$117$	−4.56367	−0.421911
$118$	13.8386	1.27394
$119$	5.30718	0.486508
$120$	3.24183	0.295937
$121$	2.78793	0.253448
$122$	−9.36822	−0.848159
$123$	10.0262	0.904036
$124$	9.33164	0.838006
$125$	−1.65160	−0.147723
$126$	−0.788032	−0.0702035
$127$	−10.0825	−0.894673	−0.447337	−	0.894366i	$-0.647627\pi$
$127$	−10.0825	−0.894673	−0.447337	+	0.894366i	$0.647627\pi$
$128$	−1.00000	−0.0883883
$129$	1.64774	0.145076
$130$	−14.7946	−1.29758
$131$	−3.81000	−0.332881	−0.166440	−	0.986052i	$-0.553227\pi$
$131$	−3.81000	−0.332881	−0.166440	+	0.986052i	$0.553227\pi$
$132$	−3.71321	−0.323193
$133$	0.208610	0.0180888
$134$	−14.7199	−1.27161
$135$	−3.24183	−0.279012
$136$	−6.73472	−0.577498
$137$	16.2799	1.39088	0.695441	−	0.718583i	$-0.255209\pi$
$137$	16.2799	1.39088	0.695441	+	0.718583i	$0.255209\pi$
$138$	4.99945	0.425581
$139$	9.94125	0.843206	0.421603	−	0.906780i	$-0.361468\pi$
$139$	9.94125	0.843206	0.421603	+	0.906780i	$0.361468\pi$
$140$	−2.55467	−0.215909
$141$	−2.72055	−0.229112
$142$	−14.4817	−1.21527
$143$	16.9459	1.41708
$144$	1.00000	0.0833333
$145$	−6.98882	−0.580390
$146$	−5.06594	−0.419260
$147$	−6.37901	−0.526131
$148$	10.4700	0.860629
$149$	2.19925	0.180170	0.0900848	−	0.995934i	$-0.471286\pi$
$149$	2.19925	0.180170	0.0900848	+	0.995934i	$0.471286\pi$
$150$	−5.50946	−0.449846
$151$	−18.2565	−1.48570	−0.742848	−	0.669460i	$-0.766525\pi$
$151$	−18.2565	−1.48570	−0.742848	+	0.669460i	$0.766525\pi$
$152$	−0.264723	−0.0214719
$153$	6.73472	0.544470
$154$	2.92613	0.235794
$155$	−30.2516	−2.42987
$156$	−4.56367	−0.365386
$157$	−21.7925	−1.73923	−0.869615	−	0.493731i	$-0.835633\pi$
$157$	−21.7925	−1.73923	−0.869615	+	0.493731i	$0.835633\pi$
$158$	−4.20572	−0.334589
$159$	−9.63165	−0.763839
$160$	3.24183	0.256289
$161$	−3.93972	−0.310494
$162$	−1.00000	−0.0785674
$163$	7.45439	0.583873	0.291937	−	0.956438i	$-0.405700\pi$
$163$	7.45439	0.583873	0.291937	+	0.956438i	$0.405700\pi$
$164$	10.0262	0.782918
$165$	12.0376	0.937126
$166$	−1.30785	−0.101509
$167$	23.7891	1.84085	0.920426	−	0.390917i	$-0.127842\pi$
$167$	23.7891	1.84085	0.920426	+	0.390917i	$0.127842\pi$
$168$	−0.788032	−0.0607980
$169$	7.82709	0.602084
$170$	21.8328	1.67450
$171$	0.264723	0.0202439
$172$	1.64774	0.125639
$173$	21.3001	1.61942	0.809709	−	0.586832i	$-0.199625\pi$
$173$	21.3001	1.61942	0.809709	+	0.586832i	$0.199625\pi$
$174$	−2.15583	−0.163433
$175$	4.34164	0.328197
$176$	−3.71321	−0.279894
$177$	−13.8386	−1.04017
$178$	−7.12840	−0.534296
$179$	15.4981	1.15839	0.579193	−	0.815191i	$-0.303368\pi$
$179$	15.4981	1.15839	0.579193	+	0.815191i	$0.303368\pi$
$180$	−3.24183	−0.241632
$181$	−7.50942	−0.558171	−0.279085	−	0.960266i	$-0.590031\pi$
$181$	−7.50942	−0.558171	−0.279085	+	0.960266i	$0.590031\pi$
$182$	3.59632	0.266577
$183$	9.36822	0.692519
$184$	4.99945	0.368564
$185$	−33.9420	−2.49546
$186$	−9.33164	−0.684229
$187$	−25.0074	−1.82873
$188$	−2.72055	−0.198417
$189$	0.788032	0.0573209
$190$	0.858187	0.0622594
$191$	12.6057	0.912114	0.456057	−	0.889951i	$-0.349261\pi$
$191$	12.6057	0.912114	0.456057	+	0.889951i	$0.349261\pi$
$192$	1.00000	0.0721688
$193$	19.3091	1.38990	0.694951	−	0.719057i	$-0.255426\pi$
$193$	19.3091	1.38990	0.694951	+	0.719057i	$0.255426\pi$
$194$	−4.67710	−0.335796
$195$	14.7946	1.05947
$196$	−6.37901	−0.455643
$197$	−14.3110	−1.01962	−0.509809	−	0.860288i	$-0.670284\pi$
$197$	−14.3110	−1.01962	−0.509809	+	0.860288i	$0.670284\pi$
$198$	3.71321	0.263886
$199$	−17.8313	−1.26402	−0.632012	−	0.774958i	$-0.717771\pi$
$199$	−17.8313	−1.26402	−0.632012	+	0.774958i	$0.717771\pi$
$200$	−5.50946	−0.389578
$201$	14.7199	1.03826
$202$	9.10834	0.640860
$203$	1.69886	0.119237
$204$	6.73472	0.471525
$205$	−32.5034	−2.27013
$206$	7.42243	0.517145
$207$	−4.99945	−0.347485
$208$	−4.56367	−0.316434
$209$	−0.982972	−0.0679936
$210$	2.55467	0.176289
$211$	21.9781	1.51304	0.756518	−	0.653972i	$-0.226899\pi$
$211$	21.9781	1.51304	0.756518	+	0.653972i	$0.226899\pi$
$212$	−9.63165	−0.661504
$213$	14.4817	0.992266
$214$	−15.4018	−1.05285
$215$	−5.34170	−0.364301
$216$	−1.00000	−0.0680414
$217$	7.35363	0.499197
$218$	−5.10716	−0.345900
$219$	5.06594	0.342325
$220$	12.0376	0.811575
$221$	−30.7351	−2.06746
$222$	−10.4700	−0.702700
$223$	−5.97781	−0.400303	−0.200152	−	0.979765i	$-0.564144\pi$
$223$	−5.97781	−0.400303	−0.200152	+	0.979765i	$0.564144\pi$
$224$	−0.788032	−0.0526526
$225$	5.50946	0.367298
$226$	14.8298	0.986464
$227$	−24.6256	−1.63446	−0.817230	−	0.576311i	$-0.804492\pi$
$227$	−24.6256	−1.63446	−0.817230	+	0.576311i	$0.804492\pi$
$228$	0.264723	0.0175317
$229$	−0.638337	−0.0421825	−0.0210912	−	0.999778i	$-0.506714\pi$
$229$	−0.638337	−0.0421825	−0.0210912	+	0.999778i	$0.506714\pi$
$230$	−16.2074	−1.06868
$231$	−2.92613	−0.192525
$232$	−2.15583	−0.141537
$233$	22.3358	1.46327	0.731635	−	0.681697i	$-0.238758\pi$
$233$	22.3358	1.46327	0.731635	+	0.681697i	$0.238758\pi$
$234$	4.56367	0.298336
$235$	8.81958	0.575326
$236$	−13.8386	−0.900814
$237$	4.20572	0.273191
$238$	−5.30718	−0.344013
$239$	13.6030	0.879904	0.439952	−	0.898021i	$-0.354996\pi$
$239$	13.6030	0.879904	0.439952	+	0.898021i	$0.354996\pi$
$240$	−3.24183	−0.209259
$241$	9.10154	0.586282	0.293141	−	0.956069i	$-0.405299\pi$
$241$	9.10154	0.586282	0.293141	+	0.956069i	$0.405299\pi$
$242$	−2.78793	−0.179215
$243$	1.00000	0.0641500
$244$	9.36822	0.599739
$245$	20.6797	1.32117
$246$	−10.0262	−0.639250
$247$	−1.20811	−0.0768701
$248$	−9.33164	−0.592560
$249$	1.30785	0.0828814
$250$	1.65160	0.104456
$251$	20.2994	1.28129	0.640643	−	0.767839i	$-0.278668\pi$
$251$	20.2994	1.28129	0.640643	+	0.767839i	$0.278668\pi$
$252$	0.788032	0.0496414
$253$	18.5640	1.16711
$254$	10.0825	0.632629
$255$	−21.8328	−1.36722
$256$	1.00000	0.0625000
$257$	29.5408	1.84270	0.921352	−	0.388729i	$-0.127086\pi$
$257$	29.5408	1.84270	0.921352	+	0.388729i	$0.127086\pi$
$258$	−1.64774	−0.102584
$259$	8.25070	0.512673
$260$	14.7946	0.917525
$261$	2.15583	0.133442
$262$	3.81000	0.235382
$263$	−20.8720	−1.28702	−0.643511	−	0.765437i	$-0.722523\pi$
$263$	−20.8720	−1.28702	−0.643511	+	0.765437i	$0.722523\pi$
$264$	3.71321	0.228532
$265$	31.2242	1.91809
$266$	−0.208610	−0.0127907
$267$	7.12840	0.436251
$268$	14.7199	0.899163
$269$	−1.00000	−0.0609711
$269$	−1.00000	−0.0609711
$270$	3.24183	0.197292
$271$	−4.95607	−0.301060	−0.150530	−	0.988605i	$-0.548098\pi$
$271$	−4.95607	−0.301060	−0.150530	+	0.988605i	$0.548098\pi$
$272$	6.73472	0.408353
$273$	−3.59632	−0.217659
$274$	−16.2799	−0.983502
$275$	−20.4578	−1.23365
$276$	−4.99945	−0.300931
$277$	−13.4047	−0.805408	−0.402704	−	0.915330i	$-0.631930\pi$
$277$	−13.4047	−0.805408	−0.402704	+	0.915330i	$0.631930\pi$
$278$	−9.94125	−0.596237
$279$	9.33164	0.558671
$280$	2.55467	0.152671
$281$	−15.3640	−0.916538	−0.458269	−	0.888814i	$-0.651530\pi$
$281$	−15.3640	−0.916538	−0.458269	+	0.888814i	$0.651530\pi$
$282$	2.72055	0.162007
$283$	−29.1980	−1.73564	−0.867822	−	0.496876i	$-0.834480\pi$
$283$	−29.1980	−1.73564	−0.867822	+	0.496876i	$0.834480\pi$
$284$	14.4817	0.859328
$285$	−0.858187	−0.0508346
$286$	−16.9459	−1.00203
$287$	7.90100	0.466381
$288$	−1.00000	−0.0589256
$289$	28.3565	1.66803
$290$	6.98882	0.410398
$291$	4.67710	0.274177
$292$	5.06594	0.296462
$293$	−15.7324	−0.919094	−0.459547	−	0.888153i	$-0.651988\pi$
$293$	−15.7324	−0.919094	−0.459547	+	0.888153i	$0.651988\pi$
$294$	6.37901	0.372031
$295$	44.8623	2.61198
$296$	−10.4700	−0.608556
$297$	−3.71321	−0.215462
$298$	−2.19925	−0.127399
$299$	22.8158	1.31947
$300$	5.50946	0.318089
$301$	1.29847	0.0748428
$302$	18.2565	1.05055
$303$	−9.10834	−0.523260
$304$	0.264723	0.0151829
$305$	−30.3702	−1.73899
$306$	−6.73472	−0.384998
$307$	13.2383	0.755551	0.377776	−	0.925897i	$-0.376689\pi$
$307$	13.2383	0.755551	0.377776	+	0.925897i	$0.376689\pi$
$308$	−2.92613	−0.166732
$309$	−7.42243	−0.422247
$310$	30.2516	1.71818
$311$	0.988862	0.0560732	0.0280366	−	0.999607i	$-0.491074\pi$
$311$	0.988862	0.0560732	0.0280366	+	0.999607i	$0.491074\pi$
$312$	4.56367	0.258367
$313$	10.8424	0.612851	0.306426	−	0.951895i	$-0.400867\pi$
$313$	10.8424	0.612851	0.306426	+	0.951895i	$0.400867\pi$
$314$	21.7925	1.22982
$315$	−2.55467	−0.143939
$316$	4.20572	0.236590
$317$	1.55022	0.0870688	0.0435344	−	0.999052i	$-0.486138\pi$
$317$	1.55022	0.0870688	0.0435344	+	0.999052i	$0.486138\pi$
$318$	9.63165	0.540116
$319$	−8.00504	−0.448196
$320$	−3.24183	−0.181224
$321$	15.4018	0.859644
$322$	3.93972	0.219552
$323$	1.78284	0.0991996
$324$	1.00000	0.0555556
$325$	−25.1434	−1.39470
$326$	−7.45439	−0.412861
$327$	5.10716	0.282426
$328$	−10.0262	−0.553607
$329$	−2.14388	−0.118196
$330$	−12.0376	−0.662648
$331$	8.69747	0.478056	0.239028	−	0.971013i	$-0.423171\pi$
$331$	8.69747	0.478056	0.239028	+	0.971013i	$0.423171\pi$
$332$	1.30785	0.0717774
$333$	10.4700	0.573752
$334$	−23.7891	−1.30168
$335$	−47.7195	−2.60720
$336$	0.788032	0.0429907
$337$	7.56563	0.412126	0.206063	−	0.978539i	$-0.433935\pi$
$337$	7.56563	0.412126	0.206063	+	0.978539i	$0.433935\pi$
$338$	−7.82709	−0.425737
$339$	−14.8298	−0.805444
$340$	−21.8328	−1.18405
$341$	−34.6503	−1.87642
$342$	−0.264723	−0.0143146
$343$	−10.5431	−0.569273
$344$	−1.64774	−0.0888403
$345$	16.2074	0.872575
$346$	−21.3001	−1.14510
$347$	−23.9341	−1.28485	−0.642426	−	0.766348i	$-0.722072\pi$
$347$	−23.9341	−1.28485	−0.642426	+	0.766348i	$0.722072\pi$
$348$	2.15583	0.115564
$349$	−20.8227	−1.11462	−0.557308	−	0.830306i	$-0.688166\pi$
$349$	−20.8227	−1.11462	−0.557308	+	0.830306i	$0.688166\pi$
$350$	−4.34164	−0.232070
$351$	−4.56367	−0.243591
$352$	3.71321	0.197915
$353$	−15.0592	−0.801521	−0.400760	−	0.916183i	$-0.631254\pi$
$353$	−15.0592	−0.801521	−0.400760	+	0.916183i	$0.631254\pi$
$354$	13.8386	0.735512
$355$	−46.9471	−2.49169
$356$	7.12840	0.377804
$357$	5.30718	0.280886
$358$	−15.4981	−0.819102
$359$	−5.38757	−0.284345	−0.142173	−	0.989842i	$-0.545409\pi$
$359$	−5.38757	−0.284345	−0.142173	+	0.989842i	$0.545409\pi$
$360$	3.24183	0.170859
$361$	−18.9299	−0.996312
$362$	7.50942	0.394686
$363$	2.78793	0.146328
$364$	−3.59632	−0.188498
$365$	−16.4229	−0.859615
$366$	−9.36822	−0.489685
$367$	11.6957	0.610509	0.305255	−	0.952271i	$-0.401258\pi$
$367$	11.6957	0.610509	0.305255	+	0.952271i	$0.401258\pi$
$368$	−4.99945	−0.260614
$369$	10.0262	0.521945
$370$	33.9420	1.76456
$371$	−7.59005	−0.394056
$372$	9.33164	0.483823
$373$	−5.57113	−0.288462	−0.144231	−	0.989544i	$-0.546071\pi$
$373$	−5.57113	−0.288462	−0.144231	+	0.989544i	$0.546071\pi$
$374$	25.0074	1.29310
$375$	−1.65160	−0.0852882
$376$	2.72055	0.140302
$377$	−9.83848	−0.506708
$378$	−0.788032	−0.0405320
$379$	−26.4889	−1.36064	−0.680322	−	0.732913i	$-0.738160\pi$
$379$	−26.4889	−1.36064	−0.680322	+	0.732913i	$0.738160\pi$
$380$	−0.858187	−0.0440241
$381$	−10.0825	−0.516540
$382$	−12.6057	−0.644962
$383$	−9.63095	−0.492118	−0.246059	−	0.969255i	$-0.579136\pi$
$383$	−9.63095	−0.492118	−0.246059	+	0.969255i	$0.579136\pi$
$384$	−1.00000	−0.0510310
$385$	9.48602	0.483452
$386$	−19.3091	−0.982809
$387$	1.64774	0.0837595
$388$	4.67710	0.237444
$389$	−24.4142	−1.23785	−0.618923	−	0.785451i	$-0.712431\pi$
$389$	−24.4142	−1.23785	−0.618923	+	0.785451i	$0.712431\pi$
$390$	−14.7946	−0.749156
$391$	−33.6699	−1.70276
$392$	6.37901	0.322188
$393$	−3.81000	−0.192189
$394$	14.3110	0.720979
$395$	−13.6342	−0.686013
$396$	−3.71321	−0.186596
$397$	−4.91361	−0.246607	−0.123304	−	0.992369i	$-0.539349\pi$
$397$	−4.91361	−0.246607	−0.123304	+	0.992369i	$0.539349\pi$
$398$	17.8313	0.893800
$399$	0.208610	0.0104436
$400$	5.50946	0.275473
$401$	30.0274	1.49950	0.749749	−	0.661723i	$-0.230174\pi$
$401$	30.0274	1.49950	0.749749	+	0.661723i	$0.230174\pi$
$402$	−14.7199	−0.734163
$403$	−42.5865	−2.12139
$404$	−9.10834	−0.453157
$405$	−3.24183	−0.161088
$406$	−1.69886	−0.0843130
$407$	−38.8773	−1.92708
$408$	−6.73472	−0.333418
$409$	3.62462	0.179226	0.0896129	−	0.995977i	$-0.471437\pi$
$409$	3.62462	0.179226	0.0896129	+	0.995977i	$0.471437\pi$
$410$	32.5034	1.60523
$411$	16.2799	0.803026
$412$	−7.42243	−0.365677
$413$	−10.9052	−0.536612
$414$	4.99945	0.245709
$415$	−4.23982	−0.208124
$416$	4.56367	0.223752
$417$	9.94125	0.486825
$418$	0.982972	0.0480787
$419$	−17.4582	−0.852887	−0.426443	−	0.904514i	$-0.640234\pi$
$419$	−17.4582	−0.852887	−0.426443	+	0.904514i	$0.640234\pi$
$420$	−2.55467	−0.124655
$421$	30.3284	1.47812	0.739058	−	0.673641i	$-0.235271\pi$
$421$	30.3284	1.47812	0.739058	+	0.673641i	$0.235271\pi$
$422$	−21.9781	−1.06988
$423$	−2.72055	−0.132278
$424$	9.63165	0.467754
$425$	37.1047	1.79984
$426$	−14.4817	−0.701638
$427$	7.38246	0.357262
$428$	15.4018	0.744474
$429$	16.9459	0.818154
$430$	5.34170	0.257600
$431$	21.5434	1.03771	0.518854	−	0.854863i	$-0.326359\pi$
$431$	21.5434	1.03771	0.518854	+	0.854863i	$0.326359\pi$
$432$	1.00000	0.0481125
$433$	16.3157	0.784083	0.392041	−	0.919948i	$-0.371769\pi$
$433$	16.3157	0.784083	0.392041	+	0.919948i	$0.371769\pi$
$434$	−7.35363	−0.352986
$435$	−6.98882	−0.335088
$436$	5.10716	0.244589
$437$	−1.32347	−0.0633101
$438$	−5.06594	−0.242060
$439$	−13.5738	−0.647842	−0.323921	−	0.946084i	$-0.605001\pi$
$439$	−13.5738	−0.647842	−0.323921	+	0.946084i	$0.605001\pi$
$440$	−12.0376	−0.573870
$441$	−6.37901	−0.303762
$442$	30.7351	1.46192
$443$	−6.63518	−0.315247	−0.157623	−	0.987499i	$-0.550383\pi$
$443$	−6.63518	−0.315247	−0.157623	+	0.987499i	$0.550383\pi$
$444$	10.4700	0.496884
$445$	−23.1091	−1.09547
$446$	5.97781	0.283057
$447$	2.19925	0.104021
$448$	0.788032	0.0372310
$449$	−9.47509	−0.447157	−0.223578	−	0.974686i	$-0.571774\pi$
$449$	−9.47509	−0.447157	−0.223578	+	0.974686i	$0.571774\pi$
$450$	−5.50946	−0.259719
$451$	−37.2296	−1.75307
$452$	−14.8298	−0.697535
$453$	−18.2565	−0.857767
$454$	24.6256	1.15574
$455$	11.6587	0.546566
$456$	−0.264723	−0.0123968
$457$	−16.5364	−0.773540	−0.386770	−	0.922176i	$-0.626409\pi$
$457$	−16.5364	−0.773540	−0.386770	+	0.922176i	$0.626409\pi$
$458$	0.638337	0.0298275
$459$	6.73472	0.314350
$460$	16.2074	0.755672
$461$	36.0311	1.67814	0.839068	−	0.544027i	$-0.183101\pi$
$461$	36.0311	1.67814	0.839068	+	0.544027i	$0.183101\pi$
$462$	2.92613	0.136136
$463$	−22.1663	−1.03016	−0.515078	−	0.857144i	$-0.672237\pi$
$463$	−22.1663	−1.03016	−0.515078	+	0.857144i	$0.672237\pi$
$464$	2.15583	0.100082
$465$	−30.2516	−1.40288
$466$	−22.3358	−1.03469
$467$	−9.92491	−0.459270	−0.229635	−	0.973277i	$-0.573753\pi$
$467$	−9.92491	−0.459270	−0.229635	+	0.973277i	$0.573753\pi$
$468$	−4.56367	−0.210956
$469$	11.5998	0.535628
$470$	−8.81958	−0.406817
$471$	−21.7925	−1.00414
$472$	13.8386	0.636972
$473$	−6.11842	−0.281325
$474$	−4.20572	−0.193175
$475$	1.45848	0.0669197
$476$	5.30718	0.243254
$477$	−9.63165	−0.441003
$478$	−13.6030	−0.622186
$479$	34.4376	1.57349	0.786747	−	0.617276i	$-0.211764\pi$
$479$	34.4376	1.57349	0.786747	+	0.617276i	$0.211764\pi$
$480$	3.24183	0.147969
$481$	−47.7816	−2.17865
$482$	−9.10154	−0.414564
$483$	−3.93972	−0.179264
$484$	2.78793	0.126724
$485$	−15.1624	−0.688488
$486$	−1.00000	−0.0453609
$487$	7.07833	0.320750	0.160375	−	0.987056i	$-0.448730\pi$
$487$	7.07833	0.320750	0.160375	+	0.987056i	$0.448730\pi$
$488$	−9.36822	−0.424080
$489$	7.45439	0.337099
$490$	−20.6797	−0.934212
$491$	−10.6411	−0.480226	−0.240113	−	0.970745i	$-0.577185\pi$
$491$	−10.6411	−0.480226	−0.240113	+	0.970745i	$0.577185\pi$
$492$	10.0262	0.452018
$493$	14.5189	0.653898
$494$	1.20811	0.0543554
$495$	12.0376	0.541050
$496$	9.33164	0.419003
$497$	11.4120	0.511899
$498$	−1.30785	−0.0586060
$499$	−33.9900	−1.52160	−0.760801	−	0.648985i	$-0.775194\pi$
$499$	−33.9900	−1.52160	−0.760801	+	0.648985i	$0.775194\pi$
$500$	−1.65160	−0.0738617
$501$	23.7891	1.06282
$502$	−20.2994	−0.906005
$503$	−18.5083	−0.825242	−0.412621	−	0.910903i	$-0.635387\pi$
$503$	−18.5083	−0.825242	−0.412621	+	0.910903i	$0.635387\pi$
$504$	−0.788032	−0.0351017
$505$	29.5277	1.31396
$506$	−18.5640	−0.825270
$507$	7.82709	0.347613
$508$	−10.0825	−0.447337
$509$	21.7092	0.962246	0.481123	−	0.876653i	$-0.340229\pi$
$509$	21.7092	0.962246	0.481123	+	0.876653i	$0.340229\pi$
$510$	21.8328	0.966774
$511$	3.99213	0.176601
$512$	−1.00000	−0.0441942
$513$	0.264723	0.0116878
$514$	−29.5408	−1.30299
$515$	24.0623	1.06031
$516$	1.64774	0.0725378
$517$	10.1020	0.444285
$518$	−8.25070	−0.362515
$519$	21.3001	0.934972
$520$	−14.7946	−0.648788
$521$	34.1532	1.49628	0.748139	−	0.663542i	$-0.230948\pi$
$521$	34.1532	1.49628	0.748139	+	0.663542i	$0.230948\pi$
$522$	−2.15583	−0.0943580
$523$	−29.4256	−1.28669	−0.643347	−	0.765575i	$-0.722455\pi$
$523$	−29.4256	−1.28669	−0.643347	+	0.765575i	$0.722455\pi$
$524$	−3.81000	−0.166440
$525$	4.34164	0.189485
$526$	20.8720	0.910061
$527$	62.8460	2.73762
$528$	−3.71321	−0.161597
$529$	1.99445	0.0867153
$530$	−31.2242	−1.35629
$531$	−13.8386	−0.600543
$532$	0.208610	0.00904440
$533$	−45.7565	−1.98193
$534$	−7.12840	−0.308476
$535$	−49.9300	−2.15866
$536$	−14.7199	−0.635804
$537$	15.4981	0.668794
$538$	1.00000	0.0431131
$539$	23.6866	1.02025
$540$	−3.24183	−0.139506
$541$	24.5585	1.05585	0.527926	−	0.849290i	$-0.322970\pi$
$541$	24.5585	1.05585	0.527926	+	0.849290i	$0.322970\pi$
$542$	4.95607	0.212881
$543$	−7.50942	−0.322260
$544$	−6.73472	−0.288749
$545$	−16.5565	−0.709204
$546$	3.59632	0.153908
$547$	−21.9377	−0.937988	−0.468994	−	0.883201i	$-0.655383\pi$
$547$	−21.9377	−0.937988	−0.468994	+	0.883201i	$0.655383\pi$
$548$	16.2799	0.695441
$549$	9.36822	0.399826
$550$	20.4578	0.872324
$551$	0.570697	0.0243125
$552$	4.99945	0.212791
$553$	3.31424	0.140936
$554$	13.4047	0.569509
$555$	−33.9420	−1.44076
$556$	9.94125	0.421603
$557$	−28.7962	−1.22013	−0.610067	−	0.792350i	$-0.708857\pi$
$557$	−28.7962	−1.22013	−0.610067	+	0.792350i	$0.708857\pi$
$558$	−9.33164	−0.395040
$559$	−7.51975	−0.318052
$560$	−2.55467	−0.107954
$561$	−25.0074	−1.05581
$562$	15.3640	0.648090
$563$	7.64634	0.322255	0.161127	−	0.986934i	$-0.448487\pi$
$563$	7.64634	0.322255	0.161127	+	0.986934i	$0.448487\pi$
$564$	−2.72055	−0.114556
$565$	48.0757	2.02256
$566$	29.1980	1.22729
$567$	0.788032	0.0330942
$568$	−14.4817	−0.607637
$569$	26.1305	1.09545	0.547724	−	0.836659i	$-0.315495\pi$
$569$	26.1305	1.09545	0.547724	+	0.836659i	$0.315495\pi$
$570$	0.858187	0.0359455
$571$	31.1296	1.30273	0.651366	−	0.758764i	$-0.274196\pi$
$571$	31.1296	1.30273	0.651366	+	0.758764i	$0.274196\pi$
$572$	16.9459	0.708542
$573$	12.6057	0.526609
$574$	−7.90100	−0.329782
$575$	−27.5443	−1.14868
$576$	1.00000	0.0416667
$577$	15.5734	0.648329	0.324165	−	0.946001i	$-0.394917\pi$
$577$	15.5734	0.648329	0.324165	+	0.946001i	$0.394917\pi$
$578$	−28.3565	−1.17947
$579$	19.3091	0.802460
$580$	−6.98882	−0.290195
$581$	1.03063	0.0427575
$582$	−4.67710	−0.193872
$583$	35.7643	1.48121
$584$	−5.06594	−0.209630
$585$	14.7946	0.611683
$586$	15.7324	0.649898
$587$	46.6362	1.92488	0.962442	−	0.271489i	$-0.0875160\pi$
$587$	46.6362	1.92488	0.962442	+	0.271489i	$0.0875160\pi$
$588$	−6.37901	−0.263066
$589$	2.47030	0.101787
$590$	−44.8623	−1.84695
$591$	−14.3110	−0.588677
$592$	10.4700	0.430314
$593$	−15.3034	−0.628436	−0.314218	−	0.949351i	$-0.601742\pi$
$593$	−15.3034	−0.628436	−0.314218	+	0.949351i	$0.601742\pi$
$594$	3.71321	0.152355
$595$	−17.2050	−0.705335
$596$	2.19925	0.0900848
$597$	−17.8313	−0.729785
$598$	−22.8158	−0.933008
$599$	−16.1321	−0.659138	−0.329569	−	0.944131i	$-0.606903\pi$
$599$	−16.1321	−0.659138	−0.329569	+	0.944131i	$0.606903\pi$
$600$	−5.50946	−0.224923
$601$	−9.05954	−0.369546	−0.184773	−	0.982781i	$-0.559155\pi$
$601$	−9.05954	−0.369546	−0.184773	+	0.982781i	$0.559155\pi$
$602$	−1.29847	−0.0529219
$603$	14.7199	0.599442
$604$	−18.2565	−0.742848
$605$	−9.03800	−0.367447
$606$	9.10834	0.370001
$607$	−4.64018	−0.188339	−0.0941696	−	0.995556i	$-0.530020\pi$
$607$	−4.64018	−0.188339	−0.0941696	+	0.995556i	$0.530020\pi$
$608$	−0.264723	−0.0107359
$609$	1.69886	0.0688413
$610$	30.3702	1.22965
$611$	12.4157	0.502286
$612$	6.73472	0.272235
$613$	25.9966	1.04999	0.524997	−	0.851104i	$-0.324066\pi$
$613$	25.9966	1.04999	0.524997	+	0.851104i	$0.324066\pi$
$614$	−13.2383	−0.534256
$615$	−32.5034	−1.31066
$616$	2.92613	0.117897
$617$	−38.3931	−1.54565	−0.772824	−	0.634620i	$-0.781156\pi$
$617$	−38.3931	−1.54565	−0.772824	+	0.634620i	$0.781156\pi$
$618$	7.42243	0.298574
$619$	−9.23910	−0.371351	−0.185675	−	0.982611i	$-0.559447\pi$
$619$	−9.23910	−0.371351	−0.185675	+	0.982611i	$0.559447\pi$
$620$	−30.2516	−1.21493
$621$	−4.99945	−0.200621
$622$	−0.988862	−0.0396498
$623$	5.61741	0.225057
$624$	−4.56367	−0.182693
$625$	−22.1931	−0.887725
$626$	−10.8424	−0.433351
$627$	−0.982972	−0.0392561
$628$	−21.7925	−0.869615
$629$	70.5125	2.81152
$630$	2.55467	0.101780
$631$	−12.5492	−0.499574	−0.249787	−	0.968301i	$-0.580361\pi$
$631$	−12.5492	−0.499574	−0.249787	+	0.968301i	$0.580361\pi$
$632$	−4.20572	−0.167295
$633$	21.9781	0.873552
$634$	−1.55022	−0.0615669
$635$	32.6856	1.29709
$636$	−9.63165	−0.381920
$637$	29.1117	1.15345
$638$	8.00504	0.316922
$639$	14.4817	0.572885
$640$	3.24183	0.128145
$641$	3.02513	0.119485	0.0597427	−	0.998214i	$-0.480972\pi$
$641$	3.02513	0.119485	0.0597427	+	0.998214i	$0.480972\pi$
$642$	−15.4018	−0.607860
$643$	−7.68781	−0.303178	−0.151589	−	0.988444i	$-0.548439\pi$
$643$	−7.68781	−0.303178	−0.151589	+	0.988444i	$0.548439\pi$
$644$	−3.93972	−0.155247
$645$	−5.34170	−0.210329
$646$	−1.78284	−0.0701447
$647$	7.92807	0.311685	0.155842	−	0.987782i	$-0.450191\pi$
$647$	7.92807	0.311685	0.155842	+	0.987782i	$0.450191\pi$
$648$	−1.00000	−0.0392837
$649$	51.3855	2.01706
$650$	25.1434	0.986205
$651$	7.35363	0.288212
$652$	7.45439	0.291937
$653$	3.09574	0.121146	0.0605728	−	0.998164i	$-0.480707\pi$
$653$	3.09574	0.121146	0.0605728	+	0.998164i	$0.480707\pi$
$654$	−5.10716	−0.199706
$655$	12.3514	0.482608
$656$	10.0262	0.391459
$657$	5.06594	0.197641
$658$	2.14388	0.0835773
$659$	18.4579	0.719016	0.359508	−	0.933142i	$-0.382945\pi$
$659$	18.4579	0.719016	0.359508	+	0.933142i	$0.382945\pi$
$660$	12.0376	0.468563
$661$	19.8458	0.771913	0.385957	−	0.922517i	$-0.373871\pi$
$661$	19.8458	0.771913	0.385957	+	0.922517i	$0.373871\pi$
$662$	−8.69747	−0.338037
$663$	−30.7351	−1.19365
$664$	−1.30785	−0.0507543
$665$	−0.676279	−0.0262250
$666$	−10.4700	−0.405704
$667$	−10.7779	−0.417323
$668$	23.7891	0.920426
$669$	−5.97781	−0.231115
$670$	47.7195	1.84357
$671$	−34.7862	−1.34291
$672$	−0.788032	−0.0303990
$673$	35.8330	1.38126	0.690631	−	0.723207i	$-0.257333\pi$
$673$	35.8330	1.38126	0.690631	+	0.723207i	$0.257333\pi$
$674$	−7.56563	−0.291417
$675$	5.50946	0.212059
$676$	7.82709	0.301042
$677$	−24.0269	−0.923427	−0.461714	−	0.887029i	$-0.652765\pi$
$677$	−24.0269	−0.923427	−0.461714	+	0.887029i	$0.652765\pi$
$678$	14.8298	0.569535
$679$	3.68571	0.141444
$680$	21.8328	0.837251
$681$	−24.6256	−0.943656
$682$	34.6503	1.32683
$683$	−27.3594	−1.04688	−0.523440	−	0.852063i	$-0.675352\pi$
$683$	−27.3594	−1.04688	−0.523440	+	0.852063i	$0.675352\pi$
$684$	0.264723	0.0101219
$685$	−52.7765	−2.01649
$686$	10.5431	0.402537
$687$	−0.638337	−0.0243541
$688$	1.64774	0.0628196
$689$	43.9557	1.67458
$690$	−16.2074	−0.617003
$691$	32.5316	1.23756	0.618779	−	0.785565i	$-0.287627\pi$
$691$	32.5316	1.23756	0.618779	+	0.785565i	$0.287627\pi$
$692$	21.3001	0.809709
$693$	−2.92613	−0.111154
$694$	23.9341	0.908528
$695$	−32.2279	−1.22247
$696$	−2.15583	−0.0817164
$697$	67.5240	2.55765
$698$	20.8227	0.788153
$699$	22.3358	0.844819
$700$	4.34164	0.164098
$701$	29.7680	1.12432	0.562161	−	0.827028i	$-0.309970\pi$
$701$	29.7680	1.12432	0.562161	+	0.827028i	$0.309970\pi$
$702$	4.56367	0.172245
$703$	2.77165	0.104535
$704$	−3.71321	−0.139947
$705$	8.81958	0.332165
$706$	15.0592	0.566761
$707$	−7.17766	−0.269944
$708$	−13.8386	−0.520085
$709$	42.7612	1.60593	0.802965	−	0.596026i	$-0.203254\pi$
$709$	42.7612	1.60593	0.802965	+	0.596026i	$0.203254\pi$
$710$	46.9471	1.76189
$711$	4.20572	0.157727
$712$	−7.12840	−0.267148
$713$	−46.6530	−1.74717
$714$	−5.30718	−0.198616
$715$	−54.9356	−2.05448
$716$	15.4981	0.579193
$717$	13.6030	0.508013
$718$	5.38757	0.201062
$719$	−19.6263	−0.731936	−0.365968	−	0.930627i	$-0.619262\pi$
$719$	−19.6263	−0.731936	−0.365968	+	0.930627i	$0.619262\pi$
$720$	−3.24183	−0.120816
$721$	−5.84911	−0.217832
$722$	18.9299	0.704499
$723$	9.10154	0.338490
$724$	−7.50942	−0.279085
$725$	11.8774	0.441117
$726$	−2.78793	−0.103470
$727$	−8.61161	−0.319387	−0.159693	−	0.987167i	$-0.551051\pi$
$727$	−8.61161	−0.319387	−0.159693	+	0.987167i	$0.551051\pi$
$728$	3.59632	0.133288
$729$	1.00000	0.0370370
$730$	16.4229	0.607840
$731$	11.0971	0.410441
$732$	9.36822	0.346260
$733$	6.38328	0.235772	0.117886	−	0.993027i	$-0.462388\pi$
$733$	6.38328	0.235772	0.117886	+	0.993027i	$0.462388\pi$
$734$	−11.6957	−0.431695
$735$	20.6797	0.762781
$736$	4.99945	0.184282
$737$	−54.6582	−2.01336
$738$	−10.0262	−0.369071
$739$	13.0171	0.478841	0.239420	−	0.970916i	$-0.423043\pi$
$739$	13.0171	0.478841	0.239420	+	0.970916i	$0.423043\pi$
$740$	−33.9420	−1.24773
$741$	−1.20811	−0.0443810
$742$	7.59005	0.278639
$743$	27.7669	1.01867	0.509334	−	0.860569i	$-0.329892\pi$
$743$	27.7669	1.01867	0.509334	+	0.860569i	$0.329892\pi$
$744$	−9.33164	−0.342115
$745$	−7.12960	−0.261208
$746$	5.57113	0.203973
$747$	1.30785	0.0478516
$748$	−25.0074	−0.914363
$749$	12.1371	0.443480
$750$	1.65160	0.0603079
$751$	−24.4403	−0.891839	−0.445920	−	0.895073i	$-0.647123\pi$
$751$	−24.4403	−0.891839	−0.445920	+	0.895073i	$0.647123\pi$
$752$	−2.72055	−0.0992084
$753$	20.2994	0.739750
$754$	9.83848	0.358296
$755$	59.1846	2.15395
$756$	0.788032	0.0286605
$757$	−36.4296	−1.32406	−0.662029	−	0.749478i	$-0.730304\pi$
$757$	−36.4296	−1.32406	−0.662029	+	0.749478i	$0.730304\pi$
$758$	26.4889	0.962121
$759$	18.5640	0.673830
$760$	0.858187	0.0311297
$761$	−8.24382	−0.298838	−0.149419	−	0.988774i	$-0.547740\pi$
$761$	−8.24382	−0.298838	−0.149419	+	0.988774i	$0.547740\pi$
$762$	10.0825	0.365249
$763$	4.02461	0.145700
$764$	12.6057	0.456057
$765$	−21.8328	−0.789368
$766$	9.63095	0.347980
$767$	63.1547	2.28038
$768$	1.00000	0.0360844
$769$	−21.9280	−0.790744	−0.395372	−	0.918521i	$-0.629384\pi$
$769$	−21.9280	−0.790744	−0.395372	+	0.918521i	$0.629384\pi$
$770$	−9.48602	−0.341852
$771$	29.5408	1.06389
$772$	19.3091	0.694951
$773$	14.0498	0.505337	0.252668	−	0.967553i	$-0.418692\pi$
$773$	14.0498	0.505337	0.252668	+	0.967553i	$0.418692\pi$
$774$	−1.64774	−0.0592269
$775$	51.4123	1.84679
$776$	−4.67710	−0.167898
$777$	8.25070	0.295992
$778$	24.4142	0.875290
$779$	2.65418	0.0950958
$780$	14.7946	0.529733
$781$	−53.7734	−1.92416
$782$	33.6699	1.20403
$783$	2.15583	0.0770429
$784$	−6.37901	−0.227822
$785$	70.6475	2.52152
$786$	3.81000	0.135898
$787$	−37.6158	−1.34086	−0.670429	−	0.741973i	$-0.733890\pi$
$787$	−37.6158	−1.34086	−0.670429	+	0.741973i	$0.733890\pi$
$788$	−14.3110	−0.509809
$789$	−20.8720	−0.743062
$790$	13.6342	0.485084
$791$	−11.6864	−0.415519
$792$	3.71321	0.131943
$793$	−42.7535	−1.51822
$794$	4.91361	0.174377
$795$	31.2242	1.10741
$796$	−17.8313	−0.632012
$797$	42.9565	1.52160	0.760798	−	0.648988i	$-0.224808\pi$
$797$	42.9565	1.52160	0.760798	+	0.648988i	$0.224808\pi$
$798$	−0.208610	−0.00738472
$799$	−18.3222	−0.648192
$800$	−5.50946	−0.194789
$801$	7.12840	0.251870
$802$	−30.0274	−1.06030
$803$	−18.8109	−0.663823
$804$	14.7199	0.519132
$805$	12.7719	0.450151
$806$	42.5865	1.50005
$807$	−1.00000	−0.0352017
$808$	9.10834	0.320430
$809$	18.4410	0.648352	0.324176	−	0.945997i	$-0.394913\pi$
$809$	18.4410	0.648352	0.324176	+	0.945997i	$0.394913\pi$
$810$	3.24183	0.113906
$811$	44.0833	1.54797	0.773987	−	0.633201i	$-0.218259\pi$
$811$	44.0833	1.54797	0.773987	+	0.633201i	$0.218259\pi$
$812$	1.69886	0.0596183
$813$	−4.95607	−0.173817
$814$	38.8773	1.36265
$815$	−24.1659	−0.846494
$816$	6.73472	0.235762
$817$	0.436195	0.0152605
$818$	−3.62462	−0.126732
$819$	−3.59632	−0.125666
$820$	−32.5034	−1.13507
$821$	32.4550	1.13269	0.566344	−	0.824169i	$-0.308357\pi$
$821$	32.4550	1.13269	0.566344	+	0.824169i	$0.308357\pi$
$822$	−16.2799	−0.567825
$823$	29.9978	1.04566	0.522829	−	0.852438i	$-0.324877\pi$
$823$	29.9978	1.04566	0.522829	+	0.852438i	$0.324877\pi$
$824$	7.42243	0.258573
$825$	−20.4578	−0.712249
$826$	10.9052	0.379442
$827$	8.12753	0.282622	0.141311	−	0.989965i	$-0.454868\pi$
$827$	8.12753	0.282622	0.141311	+	0.989965i	$0.454868\pi$
$828$	−4.99945	−0.173743
$829$	24.1830	0.839909	0.419954	−	0.907545i	$-0.362046\pi$
$829$	24.1830	0.839909	0.419954	+	0.907545i	$0.362046\pi$
$830$	4.23982	0.147166
$831$	−13.4047	−0.465002
$832$	−4.56367	−0.158217
$833$	−42.9608	−1.48850
$834$	−9.94125	−0.344237
$835$	−77.1201	−2.66885
$836$	−0.982972	−0.0339968
$837$	9.33164	0.322549
$838$	17.4582	0.603082
$839$	−7.89858	−0.272689	−0.136345	−	0.990661i	$-0.543535\pi$
$839$	−7.89858	−0.272689	−0.136345	+	0.990661i	$0.543535\pi$
$840$	2.55467	0.0881444
$841$	−24.3524	−0.839738
$842$	−30.3284	−1.04519
$843$	−15.3640	−0.529163
$844$	21.9781	0.756518
$845$	−25.3741	−0.872895
$846$	2.72055	0.0935346
$847$	2.19698	0.0754891
$848$	−9.63165	−0.330752
$849$	−29.1980	−1.00207
$850$	−37.1047	−1.27268
$851$	−52.3442	−1.79434
$852$	14.4817	0.496133
$853$	48.7105	1.66781	0.833907	−	0.551904i	$-0.186099\pi$
$853$	48.7105	1.66781	0.833907	+	0.551904i	$0.186099\pi$
$854$	−7.38246	−0.252623
$855$	−0.858187	−0.0293494
$856$	−15.4018	−0.526423
$857$	32.2924	1.10309	0.551543	−	0.834146i	$-0.314039\pi$
$857$	32.2924	1.10309	0.551543	+	0.834146i	$0.314039\pi$
$858$	−16.9459	−0.578522
$859$	39.4010	1.34435	0.672173	−	0.740394i	$-0.265361\pi$
$859$	39.4010	1.34435	0.672173	+	0.740394i	$0.265361\pi$
$860$	−5.34170	−0.182151
$861$	7.90100	0.269265
$862$	−21.5434	−0.733770
$863$	−12.3482	−0.420339	−0.210169	−	0.977665i	$-0.567402\pi$
$863$	−12.3482	−0.420339	−0.210169	+	0.977665i	$0.567402\pi$
$864$	−1.00000	−0.0340207
$865$	−69.0514	−2.34782
$866$	−16.3157	−0.554430
$867$	28.3565	0.963037
$868$	7.35363	0.249599
$869$	−15.6167	−0.529761
$870$	6.98882	0.236943
$871$	−67.1769	−2.27620
$872$	−5.10716	−0.172950
$873$	4.67710	0.158296
$874$	1.32347	0.0447670
$875$	−1.30151	−0.0439992
$876$	5.06594	0.171162
$877$	20.8690	0.704697	0.352349	−	0.935869i	$-0.385383\pi$
$877$	20.8690	0.704697	0.352349	+	0.935869i	$0.385383\pi$
$878$	13.5738	0.458093
$879$	−15.7324	−0.530639
$880$	12.0376	0.405787
$881$	40.4750	1.36364	0.681819	−	0.731521i	$-0.261189\pi$
$881$	40.4750	1.36364	0.681819	+	0.731521i	$0.261189\pi$
$882$	6.37901	0.214792
$883$	−2.38651	−0.0803126	−0.0401563	−	0.999193i	$-0.512786\pi$
$883$	−2.38651	−0.0803126	−0.0401563	+	0.999193i	$0.512786\pi$
$884$	−30.7351	−1.03373
$885$	44.8623	1.50803
$886$	6.63518	0.222913
$887$	23.7608	0.797811	0.398905	−	0.916992i	$-0.369390\pi$
$887$	23.7608	0.797811	0.398905	+	0.916992i	$0.369390\pi$
$888$	−10.4700	−0.351350
$889$	−7.94530	−0.266477
$890$	23.1091	0.774617
$891$	−3.71321	−0.124397
$892$	−5.97781	−0.200152
$893$	−0.720193	−0.0241004
$894$	−2.19925	−0.0735539
$895$	−50.2423	−1.67942
$896$	−0.788032	−0.0263263
$897$	22.8158	0.761798
$898$	9.47509	0.316188
$899$	20.1174	0.670953
$900$	5.50946	0.183649
$901$	−64.8665	−2.16102
$902$	37.2296	1.23961
$903$	1.29847	0.0432105
$904$	14.8298	0.493232
$905$	24.3443	0.809231
$906$	18.2565	0.606533
$907$	12.0737	0.400900	0.200450	−	0.979704i	$-0.435760\pi$
$907$	12.0737	0.400900	0.200450	+	0.979704i	$0.435760\pi$
$908$	−24.6256	−0.817230
$909$	−9.10834	−0.302104
$910$	−11.6587	−0.386481
$911$	17.1151	0.567047	0.283524	−	0.958965i	$-0.408497\pi$
$911$	17.1151	0.567047	0.283524	+	0.958965i	$0.408497\pi$
$912$	0.264723	0.00876585
$913$	−4.85631	−0.160720
$914$	16.5364	0.546976
$915$	−30.3702	−1.00401
$916$	−0.638337	−0.0210912
$917$	−3.00240	−0.0991480
$918$	−6.73472	−0.222279
$919$	21.9454	0.723911	0.361956	−	0.932195i	$-0.382109\pi$
$919$	21.9454	0.723911	0.361956	+	0.932195i	$0.382109\pi$
$920$	−16.2074	−0.534341
$921$	13.2383	0.436218
$922$	−36.0311	−1.18662
$923$	−66.0895	−2.17536
$924$	−2.92613	−0.0962626
$925$	57.6841	1.89664
$926$	22.1663	0.728430
$927$	−7.42243	−0.243785
$928$	−2.15583	−0.0707685
$929$	21.5639	0.707489	0.353744	−	0.935342i	$-0.384908\pi$
$929$	21.5639	0.707489	0.353744	+	0.935342i	$0.384908\pi$
$930$	30.2516	0.991989
$931$	−1.68867	−0.0553439
$932$	22.3358	0.731635
$933$	0.988862	0.0323739
$934$	9.92491	0.324753
$935$	81.0699	2.65127
$936$	4.56367	0.149168
$937$	5.66686	0.185128	0.0925641	−	0.995707i	$-0.470494\pi$
$937$	5.66686	0.185128	0.0925641	+	0.995707i	$0.470494\pi$
$938$	−11.5998	−0.378746
$939$	10.8424	0.353830
$940$	8.81958	0.287663
$941$	41.6995	1.35937	0.679683	−	0.733506i	$-0.262117\pi$
$941$	41.6995	1.35937	0.679683	+	0.733506i	$0.262117\pi$
$942$	21.7925	0.710037
$943$	−50.1257	−1.63232
$944$	−13.8386	−0.450407
$945$	−2.55467	−0.0831033
$946$	6.11842	0.198927
$947$	−32.8763	−1.06834	−0.534168	−	0.845378i	$-0.679375\pi$
$947$	−32.8763	−1.06834	−0.534168	+	0.845378i	$0.679375\pi$
$948$	4.20572	0.136595
$949$	−23.1193	−0.750484
$950$	−1.45848	−0.0473194
$951$	1.55022	0.0502692
$952$	−5.30718	−0.172007
$953$	−31.0422	−1.00556	−0.502778	−	0.864415i	$-0.667689\pi$
$953$	−31.0422	−1.00556	−0.502778	+	0.864415i	$0.667689\pi$
$954$	9.63165	0.311836
$955$	−40.8654	−1.32237
$956$	13.6030	0.439952
$957$	−8.00504	−0.258766
$958$	−34.4376	−1.11263
$959$	12.8291	0.414272
$960$	−3.24183	−0.104630
$961$	56.0795	1.80902
$962$	47.7816	1.54054
$963$	15.4018	0.496316
$964$	9.10154	0.293141
$965$	−62.5969	−2.01507
$966$	3.93972	0.126759
$967$	−2.30245	−0.0740417	−0.0370208	−	0.999314i	$-0.511787\pi$
$967$	−2.30245	−0.0740417	−0.0370208	+	0.999314i	$0.511787\pi$
$968$	−2.78793	−0.0896075
$969$	1.78284	0.0572729
$970$	15.1624	0.486834
$971$	9.76703	0.313439	0.156720	−	0.987643i	$-0.449908\pi$
$971$	9.76703	0.313439	0.156720	+	0.987643i	$0.449908\pi$
$972$	1.00000	0.0320750
$973$	7.83403	0.251147
$974$	−7.07833	−0.226804
$975$	−25.1434	−0.805233
$976$	9.36822	0.299870
$977$	1.66403	0.0532369	0.0266185	−	0.999646i	$-0.491526\pi$
$977$	1.66403	0.0532369	0.0266185	+	0.999646i	$0.491526\pi$
$978$	−7.45439	−0.238365
$979$	−26.4692	−0.845961
$980$	20.6797	0.660587
$981$	5.10716	0.163059
$982$	10.6411	0.339571
$983$	−29.4908	−0.940611	−0.470306	−	0.882504i	$-0.655856\pi$
$983$	−29.4908	−0.940611	−0.470306	+	0.882504i	$0.655856\pi$
$984$	−10.0262	−0.319625
$985$	46.3939	1.47823
$986$	−14.5189	−0.462376
$987$	−2.14388	−0.0682406
$988$	−1.20811	−0.0384350
$989$	−8.23780	−0.261947
$990$	−12.0376	−0.382580
$991$	−40.9572	−1.30105	−0.650525	−	0.759485i	$-0.725451\pi$
$991$	−40.9572	−1.30105	−0.650525	+	0.759485i	$0.725451\pi$
$992$	−9.33164	−0.296280
$993$	8.69747	0.276006
$994$	−11.4120	−0.361967
$995$	57.8059	1.83257
$996$	1.30785	0.0414407
$997$	5.40962	0.171324	0.0856622	−	0.996324i	$-0.472699\pi$
$997$	5.40962	0.171324	0.0856622	+	0.996324i	$0.472699\pi$
$998$	33.9900	1.07594
$999$	10.4700	0.331256

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1614.2.a.i.1.2	✓	8
3.2	odd	2		4842.2.a.q.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1614.2.a.i.1.2	✓	8	1.1	even	1	trivial
4842.2.a.q.1.7		8	3.2	odd	2

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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:	\( N \)	\(=\)	\( 1614 = 2 \cdot 3 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1614.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.24183 q^{5} -1.00000 q^{6} +0.788032 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.24183 q^{10} -3.71321 q^{11} +1.00000 q^{12} -4.56367 q^{13} -0.788032 q^{14} -3.24183 q^{15} +1.00000 q^{16} +6.73472 q^{17} -1.00000 q^{18} +0.264723 q^{19} -3.24183 q^{20} +0.788032 q^{21} +3.71321 q^{22} -4.99945 q^{23} -1.00000 q^{24} +5.50946 q^{25} +4.56367 q^{26} +1.00000 q^{27} +0.788032 q^{28} +2.15583 q^{29} +3.24183 q^{30} +9.33164 q^{31} -1.00000 q^{32} -3.71321 q^{33} -6.73472 q^{34} -2.55467 q^{35} +1.00000 q^{36} +10.4700 q^{37} -0.264723 q^{38} -4.56367 q^{39} +3.24183 q^{40} +10.0262 q^{41} -0.788032 q^{42} +1.64774 q^{43} -3.71321 q^{44} -3.24183 q^{45} +4.99945 q^{46} -2.72055 q^{47} +1.00000 q^{48} -6.37901 q^{49} -5.50946 q^{50} +6.73472 q^{51} -4.56367 q^{52} -9.63165 q^{53} -1.00000 q^{54} +12.0376 q^{55} -0.788032 q^{56} +0.264723 q^{57} -2.15583 q^{58} -13.8386 q^{59} -3.24183 q^{60} +9.36822 q^{61} -9.33164 q^{62} +0.788032 q^{63} +1.00000 q^{64} +14.7946 q^{65} +3.71321 q^{66} +14.7199 q^{67} +6.73472 q^{68} -4.99945 q^{69} +2.55467 q^{70} +14.4817 q^{71} -1.00000 q^{72} +5.06594 q^{73} -10.4700 q^{74} +5.50946 q^{75} +0.264723 q^{76} -2.92613 q^{77} +4.56367 q^{78} +4.20572 q^{79} -3.24183 q^{80} +1.00000 q^{81} -10.0262 q^{82} +1.30785 q^{83} +0.788032 q^{84} -21.8328 q^{85} -1.64774 q^{86} +2.15583 q^{87} +3.71321 q^{88} +7.12840 q^{89} +3.24183 q^{90} -3.59632 q^{91} -4.99945 q^{92} +9.33164 q^{93} +2.72055 q^{94} -0.858187 q^{95} -1.00000 q^{96} +4.67710 q^{97} +6.37901 q^{98} -3.71321 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{3} + 8 q^{4} - 8 q^{6} + 9 q^{7} - 8 q^{8} + 8 q^{9} + 8 q^{11} + 8 q^{12} - 3 q^{13} - 9 q^{14} + 8 q^{16} + 8 q^{17} - 8 q^{18} + 18 q^{19} + 9 q^{21} - 8 q^{22} - 10 q^{23} - 8 q^{24}+ \cdots + 8 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 - 8 * q^6 + 9 * q^7 - 8 * q^8 + 8 * q^9 + 8 * q^11 + 8 * q^12 - 3 * q^13 - 9 * q^14 + 8 * q^16 + 8 * q^17 - 8 * q^18 + 18 * q^19 + 9 * q^21 - 8 * q^22 - 10 * q^23 - 8 * q^24 + 26 * q^25 + 3 * q^26 + 8 * q^27 + 9 * q^28 - 9 * q^29 + 18 * q^31 - 8 * q^32 + 8 * q^33 - 8 * q^34 + 9 * q^35 + 8 * q^36 + 22 * q^37 - 18 * q^38 - 3 * q^39 - q^41 - 9 * q^42 + 14 * q^43 + 8 * q^44 + 10 * q^46 + 6 * q^47 + 8 * q^48 + 29 * q^49 - 26 * q^50 + 8 * q^51 - 3 * q^52 - 3 * q^53 - 8 * q^54 + 17 * q^55 - 9 * q^56 + 18 * q^57 + 9 * q^58 + q^59 + 18 * q^61 - 18 * q^62 + 9 * q^63 + 8 * q^64 - 14 * q^65 - 8 * q^66 + 30 * q^67 + 8 * q^68 - 10 * q^69 - 9 * q^70 - 5 * q^71 - 8 * q^72 + 15 * q^73 - 22 * q^74 + 26 * q^75 + 18 * q^76 - 20 * q^77 + 3 * q^78 + 21 * q^79 + 8 * q^81 + q^82 - 11 * q^83 + 9 * q^84 + 18 * q^85 - 14 * q^86 - 9 * q^87 - 8 * q^88 + 22 * q^89 + 53 * q^91 - 10 * q^92 + 18 * q^93 - 6 * q^94 - 9 * q^95 - 8 * q^96 + 13 * q^97 - 29 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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