LMFDB - Embedded newform 4598.2.a.ca.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4598,2,Mod(1,4598)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4598, 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("4598.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4598 = 2 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4598.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:	$36.7152148494$
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} - 2x^{7} - 10x^{6} + 16x^{5} + 26x^{4} - 32x^{3} - 16x^{2} + 20x - 4 $ x^8 - 2x^7 - 10x^6 + 16x^5 + 26x^4 - 32x^3 - 16x^2 + 20*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.04921$ of defining polynomial
Character	$\chi$	$=$	4598.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.90436 q^{3} +1.00000 q^{4} -2.98197 q^{5} -2.90436 q^{6} -2.79511 q^{7} +1.00000 q^{8} +5.43531 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.90436 q^{3} +1.00000 q^{4} -2.98197 q^{5} -2.90436 q^{6} -2.79511 q^{7} +1.00000 q^{8} +5.43531 q^{9} -2.98197 q^{10} -2.90436 q^{12} +6.11143 q^{13} -2.79511 q^{14} +8.66073 q^{15} +1.00000 q^{16} -5.07356 q^{17} +5.43531 q^{18} -1.00000 q^{19} -2.98197 q^{20} +8.11802 q^{21} -4.21811 q^{23} -2.90436 q^{24} +3.89217 q^{25} +6.11143 q^{26} -7.07303 q^{27} -2.79511 q^{28} -4.63883 q^{29} +8.66073 q^{30} -5.42466 q^{31} +1.00000 q^{32} -5.07356 q^{34} +8.33495 q^{35} +5.43531 q^{36} -8.46374 q^{37} -1.00000 q^{38} -17.7498 q^{39} -2.98197 q^{40} -7.19663 q^{41} +8.11802 q^{42} +2.90660 q^{43} -16.2080 q^{45} -4.21811 q^{46} -0.390888 q^{47} -2.90436 q^{48} +0.812652 q^{49} +3.89217 q^{50} +14.7354 q^{51} +6.11143 q^{52} -9.35865 q^{53} -7.07303 q^{54} -2.79511 q^{56} +2.90436 q^{57} -4.63883 q^{58} +11.2873 q^{59} +8.66073 q^{60} -5.43079 q^{61} -5.42466 q^{62} -15.1923 q^{63} +1.00000 q^{64} -18.2241 q^{65} +9.66167 q^{67} -5.07356 q^{68} +12.2509 q^{69} +8.33495 q^{70} +7.90690 q^{71} +5.43531 q^{72} -7.83239 q^{73} -8.46374 q^{74} -11.3043 q^{75} -1.00000 q^{76} -17.7498 q^{78} +1.49859 q^{79} -2.98197 q^{80} +4.23670 q^{81} -7.19663 q^{82} +5.64998 q^{83} +8.11802 q^{84} +15.1292 q^{85} +2.90660 q^{86} +13.4729 q^{87} -10.4849 q^{89} -16.2080 q^{90} -17.0821 q^{91} -4.21811 q^{92} +15.7552 q^{93} -0.390888 q^{94} +2.98197 q^{95} -2.90436 q^{96} +12.0521 q^{97} +0.812652 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{4} + 2 q^{5} + 8 q^{7} + 8 q^{8} + 20 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^4 + 2 * q^5 + 8 * q^7 + 8 * q^8 + 20 * q^9	$ 8 q + 8 q^{2} + 8 q^{4} + 2 q^{5} + 8 q^{7} + 8 q^{8} + 20 q^{9} + 2 q^{10} + 18 q^{13} + 8 q^{14} + 10 q^{15} + 8 q^{16} + 4 q^{17} + 20 q^{18} - 8 q^{19} + 2 q^{20} + 14 q^{21} + 12 q^{23} + 18 q^{26} - 24 q^{27} + 8 q^{28} + 14 q^{29} + 10 q^{30} - 2 q^{31} + 8 q^{32} + 4 q^{34} + 40 q^{35} + 20 q^{36} - 22 q^{37} - 8 q^{38} - 4 q^{39} + 2 q^{40} + 8 q^{41} + 14 q^{42} + 28 q^{43} - 28 q^{45} + 12 q^{46} + 6 q^{47} + 32 q^{49} - 12 q^{51} + 18 q^{52} - 24 q^{53} - 24 q^{54} + 8 q^{56} + 14 q^{58} + 46 q^{59} + 10 q^{60} - 24 q^{61} - 2 q^{62} + 30 q^{63} + 8 q^{64} - 16 q^{65} - 22 q^{67} + 4 q^{68} - 38 q^{69} + 40 q^{70} + 8 q^{71} + 20 q^{72} + 16 q^{73} - 22 q^{74} + 6 q^{75} - 8 q^{76} - 4 q^{78} + 4 q^{79} + 2 q^{80} + 28 q^{81} + 8 q^{82} + 12 q^{83} + 14 q^{84} + 48 q^{85} + 28 q^{86} + 42 q^{87} - 28 q^{89} - 28 q^{90} - 12 q^{91} + 12 q^{92} + 22 q^{93} + 6 q^{94} - 2 q^{95} - 22 q^{97} + 32 q^{98}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^4 + 2 * q^5 + 8 * q^7 + 8 * q^8 + 20 * q^9 + 2 * q^10 + 18 * q^13 + 8 * q^14 + 10 * q^15 + 8 * q^16 + 4 * q^17 + 20 * q^18 - 8 * q^19 + 2 * q^20 + 14 * q^21 + 12 * q^23 + 18 * q^26 - 24 * q^27 + 8 * q^28 + 14 * q^29 + 10 * q^30 - 2 * q^31 + 8 * q^32 + 4 * q^34 + 40 * q^35 + 20 * q^36 - 22 * q^37 - 8 * q^38 - 4 * q^39 + 2 * q^40 + 8 * q^41 + 14 * q^42 + 28 * q^43 - 28 * q^45 + 12 * q^46 + 6 * q^47 + 32 * q^49 - 12 * q^51 + 18 * q^52 - 24 * q^53 - 24 * q^54 + 8 * q^56 + 14 * q^58 + 46 * q^59 + 10 * q^60 - 24 * q^61 - 2 * q^62 + 30 * q^63 + 8 * q^64 - 16 * q^65 - 22 * q^67 + 4 * q^68 - 38 * q^69 + 40 * q^70 + 8 * q^71 + 20 * q^72 + 16 * q^73 - 22 * q^74 + 6 * q^75 - 8 * q^76 - 4 * q^78 + 4 * q^79 + 2 * q^80 + 28 * q^81 + 8 * q^82 + 12 * q^83 + 14 * q^84 + 48 * q^85 + 28 * q^86 + 42 * q^87 - 28 * q^89 - 28 * q^90 - 12 * q^91 + 12 * q^92 + 22 * q^93 + 6 * q^94 - 2 * q^95 - 22 * q^97 + 32 * q^98

Display 100 coefficients 10 coefficients

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
$3$	−2.90436	−1.67683	−0.838417	−	0.545029i	$-0.816518\pi$
$3$	−2.90436	−1.67683	−0.838417	+	0.545029i	$0.816518\pi$
$4$	1.00000	0.500000
$5$	−2.98197	−1.33358	−0.666790	−	0.745246i	$-0.732332\pi$
$5$	−2.98197	−1.33358	−0.666790	+	0.745246i	$0.732332\pi$
$6$	−2.90436	−1.18570
$7$	−2.79511	−1.05645	−0.528227	−	0.849103i	$-0.677143\pi$
$7$	−2.79511	−1.05645	−0.528227	+	0.849103i	$0.677143\pi$
$8$	1.00000	0.353553
$9$	5.43531	1.81177
$10$	−2.98197	−0.942983
$11$	0	0
$11$	0	0
$12$	−2.90436	−0.838417
$13$	6.11143	1.69501	0.847503	−	0.530791i	$-0.178105\pi$
$13$	6.11143	1.69501	0.847503	+	0.530791i	$0.178105\pi$
$14$	−2.79511	−0.747025
$15$	8.66073	2.23619
$16$	1.00000	0.250000
$17$	−5.07356	−1.23052	−0.615259	−	0.788325i	$-0.710949\pi$
$17$	−5.07356	−1.23052	−0.615259	+	0.788325i	$0.710949\pi$
$18$	5.43531	1.28112
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−2.98197	−0.666790
$21$	8.11802	1.77150
$22$	0	0
$23$	−4.21811	−0.879538	−0.439769	−	0.898111i	$-0.644940\pi$
$23$	−4.21811	−0.879538	−0.439769	+	0.898111i	$0.644940\pi$
$24$	−2.90436	−0.592850
$25$	3.89217	0.778433
$26$	6.11143	1.19855
$27$	−7.07303	−1.36121
$28$	−2.79511	−0.528227
$29$	−4.63883	−0.861410	−0.430705	−	0.902493i	$-0.641735\pi$
$29$	−4.63883	−0.861410	−0.430705	+	0.902493i	$0.641735\pi$
$30$	8.66073	1.58123
$31$	−5.42466	−0.974298	−0.487149	−	0.873319i	$-0.661963\pi$
$31$	−5.42466	−0.974298	−0.487149	+	0.873319i	$0.661963\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−5.07356	−0.870108
$35$	8.33495	1.40886
$36$	5.43531	0.905886
$37$	−8.46374	−1.39143	−0.695715	−	0.718318i	$-0.744913\pi$
$37$	−8.46374	−1.39143	−0.695715	+	0.718318i	$0.744913\pi$
$38$	−1.00000	−0.162221
$39$	−17.7498	−2.84224
$40$	−2.98197	−0.471491
$41$	−7.19663	−1.12393	−0.561963	−	0.827163i	$-0.689954\pi$
$41$	−7.19663	−1.12393	−0.561963	+	0.827163i	$0.689954\pi$
$42$	8.11802	1.25264
$43$	2.90660	0.443253	0.221626	−	0.975132i	$-0.428863\pi$
$43$	2.90660	0.443253	0.221626	+	0.975132i	$0.428863\pi$
$44$	0	0
$45$	−16.2080	−2.41614
$46$	−4.21811	−0.621927
$47$	−0.390888	−0.0570168	−0.0285084	−	0.999594i	$-0.509076\pi$
$47$	−0.390888	−0.0570168	−0.0285084	+	0.999594i	$0.509076\pi$
$48$	−2.90436	−0.419208
$49$	0.812652	0.116093
$50$	3.89217	0.550436
$51$	14.7354	2.06337
$52$	6.11143	0.847503
$53$	−9.35865	−1.28551	−0.642755	−	0.766072i	$-0.722209\pi$
$53$	−9.35865	−1.28551	−0.642755	+	0.766072i	$0.722209\pi$
$54$	−7.07303	−0.962518
$55$	0	0
$56$	−2.79511	−0.373513
$57$	2.90436	0.384692
$58$	−4.63883	−0.609109
$59$	11.2873	1.46948	0.734739	−	0.678350i	$-0.237304\pi$
$59$	11.2873	1.46948	0.734739	+	0.678350i	$0.237304\pi$
$60$	8.66073	1.11810
$61$	−5.43079	−0.695341	−0.347670	−	0.937617i	$-0.613027\pi$
$61$	−5.43079	−0.695341	−0.347670	+	0.937617i	$0.613027\pi$
$62$	−5.42466	−0.688933
$63$	−15.1923	−1.91405
$64$	1.00000	0.125000
$65$	−18.2241	−2.26042
$66$	0	0
$67$	9.66167	1.18036	0.590180	−	0.807272i	$-0.299057\pi$
$67$	9.66167	1.18036	0.590180	+	0.807272i	$0.299057\pi$
$68$	−5.07356	−0.615259
$69$	12.2509	1.47484
$70$	8.33495	0.996217
$71$	7.90690	0.938376	0.469188	−	0.883098i	$-0.344547\pi$
$71$	7.90690	0.938376	0.469188	+	0.883098i	$0.344547\pi$
$72$	5.43531	0.640558
$73$	−7.83239	−0.916712	−0.458356	−	0.888769i	$-0.651562\pi$
$73$	−7.83239	−0.916712	−0.458356	+	0.888769i	$0.651562\pi$
$74$	−8.46374	−0.983890
$75$	−11.3043	−1.30530
$76$	−1.00000	−0.114708
$77$	0	0
$78$	−17.7498	−2.00977
$79$	1.49859	0.168604	0.0843021	−	0.996440i	$-0.473134\pi$
$79$	1.49859	0.168604	0.0843021	+	0.996440i	$0.473134\pi$
$80$	−2.98197	−0.333395
$81$	4.23670	0.470745
$82$	−7.19663	−0.794735
$83$	5.64998	0.620166	0.310083	−	0.950710i	$-0.399643\pi$
$83$	5.64998	0.620166	0.310083	+	0.950710i	$0.399643\pi$
$84$	8.11802	0.885748
$85$	15.1292	1.64099
$86$	2.90660	0.313427
$87$	13.4729	1.44444
$88$	0	0
$89$	−10.4849	−1.11140	−0.555699	−	0.831383i	$-0.687549\pi$
$89$	−10.4849	−1.11140	−0.555699	+	0.831383i	$0.687549\pi$
$90$	−16.2080	−1.70847
$91$	−17.0821	−1.79069
$92$	−4.21811	−0.439769
$93$	15.7552	1.63374
$94$	−0.390888	−0.0403170
$95$	2.98197	0.305944
$96$	−2.90436	−0.296425
$97$	12.0521	1.22371	0.611855	−	0.790970i	$-0.290424\pi$
$97$	12.0521	1.22371	0.611855	+	0.790970i	$0.290424\pi$
$98$	0.812652	0.0820902
$99$	0	0
$100$	3.89217	0.389217
$101$	−19.8323	−1.97339	−0.986694	−	0.162587i	$-0.948016\pi$
$101$	−19.8323	−1.97339	−0.986694	+	0.162587i	$0.948016\pi$
$102$	14.7354	1.45903
$103$	2.49896	0.246230	0.123115	−	0.992392i	$-0.460712\pi$
$103$	2.49896	0.246230	0.123115	+	0.992392i	$0.460712\pi$
$104$	6.11143	0.599275
$105$	−24.2077	−2.36243
$106$	−9.35865	−0.908993
$107$	14.3794	1.39011	0.695053	−	0.718958i	$-0.255381\pi$
$107$	14.3794	1.39011	0.695053	+	0.718958i	$0.255381\pi$
$108$	−7.07303	−0.680603
$109$	12.2613	1.17442	0.587209	−	0.809436i	$-0.300227\pi$
$109$	12.2613	1.17442	0.587209	+	0.809436i	$0.300227\pi$
$110$	0	0
$111$	24.5818	2.33320
$112$	−2.79511	−0.264113
$113$	12.8432	1.20819	0.604093	−	0.796914i	$-0.293536\pi$
$113$	12.8432	1.20819	0.604093	+	0.796914i	$0.293536\pi$
$114$	2.90436	0.272018
$115$	12.5783	1.17293
$116$	−4.63883	−0.430705
$117$	33.2176	3.07096
$118$	11.2873	1.03908
$119$	14.1812	1.29998
$120$	8.66073	0.790613
$121$	0	0
$122$	−5.43079	−0.491680
$123$	20.9016	1.88464
$124$	−5.42466	−0.487149
$125$	3.30353	0.295476
$126$	−15.1923	−1.35344
$127$	−3.17023	−0.281313	−0.140656	−	0.990058i	$-0.544921\pi$
$127$	−3.17023	−0.281313	−0.140656	+	0.990058i	$0.544921\pi$
$128$	1.00000	0.0883883
$129$	−8.44183	−0.743261
$130$	−18.2241	−1.59836
$131$	−9.50622	−0.830562	−0.415281	−	0.909693i	$-0.636317\pi$
$131$	−9.50622	−0.830562	−0.415281	+	0.909693i	$0.636317\pi$
$132$	0	0
$133$	2.79511	0.242367
$134$	9.66167	0.834641
$135$	21.0916	1.81528
$136$	−5.07356	−0.435054
$137$	6.60928	0.564669	0.282334	−	0.959316i	$-0.408891\pi$
$137$	6.60928	0.564669	0.282334	+	0.959316i	$0.408891\pi$
$138$	12.2509	1.04287
$139$	−3.51361	−0.298021	−0.149010	−	0.988836i	$-0.547609\pi$
$139$	−3.51361	−0.298021	−0.149010	+	0.988836i	$0.547609\pi$
$140$	8.33495	0.704432
$141$	1.13528	0.0956077
$142$	7.90690	0.663532
$143$	0	0
$144$	5.43531	0.452943
$145$	13.8329	1.14876
$146$	−7.83239	−0.648214
$147$	−2.36023	−0.194669
$148$	−8.46374	−0.695715
$149$	−11.0768	−0.907446	−0.453723	−	0.891143i	$-0.649904\pi$
$149$	−11.0768	−0.907446	−0.453723	+	0.891143i	$0.649904\pi$
$150$	−11.3043	−0.922989
$151$	8.70404	0.708324	0.354162	−	0.935184i	$-0.384766\pi$
$151$	8.70404	0.708324	0.354162	+	0.935184i	$0.384766\pi$
$152$	−1.00000	−0.0811107
$153$	−27.5764	−2.22942
$154$	0	0
$155$	16.1762	1.29930
$156$	−17.7498	−1.42112
$157$	6.51081	0.519619	0.259810	−	0.965660i	$-0.416340\pi$
$157$	6.51081	0.519619	0.259810	+	0.965660i	$0.416340\pi$
$158$	1.49859	0.119221
$159$	27.1809	2.15559
$160$	−2.98197	−0.235746
$161$	11.7901	0.929190
$162$	4.23670	0.332867
$163$	7.98406	0.625360	0.312680	−	0.949859i	$-0.398773\pi$
$163$	7.98406	0.625360	0.312680	+	0.949859i	$0.398773\pi$
$164$	−7.19663	−0.561963
$165$	0	0
$166$	5.64998	0.438523
$167$	12.2491	0.947865	0.473932	−	0.880561i	$-0.342834\pi$
$167$	12.2491	0.947865	0.473932	+	0.880561i	$0.342834\pi$
$168$	8.11802	0.626318
$169$	24.3496	1.87305
$170$	15.1292	1.16036
$171$	−5.43531	−0.415649
$172$	2.90660	0.221626
$173$	−13.0541	−0.992485	−0.496242	−	0.868184i	$-0.665287\pi$
$173$	−13.0541	−0.992485	−0.496242	+	0.868184i	$0.665287\pi$
$174$	13.4729	1.02137
$175$	−10.8790	−0.822378
$176$	0	0
$177$	−32.7823	−2.46407
$178$	−10.4849	−0.785877
$179$	7.67488	0.573648	0.286824	−	0.957983i	$-0.407401\pi$
$179$	7.67488	0.573648	0.286824	+	0.957983i	$0.407401\pi$
$180$	−16.2080	−1.20807
$181$	−18.7816	−1.39603	−0.698014	−	0.716084i	$-0.745933\pi$
$181$	−18.7816	−1.39603	−0.698014	+	0.716084i	$0.745933\pi$
$182$	−17.0821	−1.26621
$183$	15.7730	1.16597
$184$	−4.21811	−0.310964
$185$	25.2387	1.85558
$186$	15.7552	1.15523
$187$	0	0
$188$	−0.390888	−0.0285084
$189$	19.7699	1.43805
$190$	2.98197	0.216335
$191$	−13.9700	−1.01083	−0.505417	−	0.862875i	$-0.668661\pi$
$191$	−13.9700	−1.01083	−0.505417	+	0.862875i	$0.668661\pi$
$192$	−2.90436	−0.209604
$193$	16.0205	1.15318	0.576592	−	0.817032i	$-0.304382\pi$
$193$	16.0205	1.15318	0.576592	+	0.817032i	$0.304382\pi$
$194$	12.0521	0.865294
$195$	52.9295	3.79036
$196$	0.812652	0.0580465
$197$	5.76542	0.410769	0.205384	−	0.978681i	$-0.434156\pi$
$197$	5.76542	0.410769	0.205384	+	0.978681i	$0.434156\pi$
$198$	0	0
$199$	14.0469	0.995757	0.497879	−	0.867247i	$-0.334113\pi$
$199$	14.0469	0.995757	0.497879	+	0.867247i	$0.334113\pi$
$200$	3.89217	0.275218
$201$	−28.0610	−1.97927
$202$	−19.8323	−1.39540
$203$	12.9661	0.910039
$204$	14.7354	1.03169
$205$	21.4602	1.49884
$206$	2.49896	0.174111
$207$	−22.9268	−1.59352
$208$	6.11143	0.423752
$209$	0	0
$210$	−24.2077	−1.67049
$211$	10.0453	0.691547	0.345774	−	0.938318i	$-0.387616\pi$
$211$	10.0453	0.691547	0.345774	+	0.938318i	$0.387616\pi$
$212$	−9.35865	−0.642755
$213$	−22.9645	−1.57350
$214$	14.3794	0.982954
$215$	−8.66741	−0.591113
$216$	−7.07303	−0.481259
$217$	15.1625	1.02930
$218$	12.2613	0.830439
$219$	22.7481	1.53717
$220$	0	0
$221$	−31.0067	−2.08574
$222$	24.5818	1.64982
$223$	14.8013	0.991170	0.495585	−	0.868560i	$-0.334954\pi$
$223$	14.8013	0.991170	0.495585	+	0.868560i	$0.334954\pi$
$224$	−2.79511	−0.186756
$225$	21.1552	1.41034
$226$	12.8432	0.854316
$227$	−6.67930	−0.443320	−0.221660	−	0.975124i	$-0.571148\pi$
$227$	−6.67930	−0.443320	−0.221660	+	0.975124i	$0.571148\pi$
$228$	2.90436	0.192346
$229$	−26.9028	−1.77779	−0.888894	−	0.458114i	$-0.848525\pi$
$229$	−26.9028	−1.77779	−0.888894	+	0.458114i	$0.848525\pi$
$230$	12.5783	0.829389
$231$	0	0
$232$	−4.63883	−0.304554
$233$	−11.2301	−0.735705	−0.367853	−	0.929884i	$-0.619907\pi$
$233$	−11.2301	−0.735705	−0.367853	+	0.929884i	$0.619907\pi$
$234$	33.2176	2.17150
$235$	1.16562	0.0760364
$236$	11.2873	0.734739
$237$	−4.35244	−0.282721
$238$	14.1812	0.919228
$239$	−22.9712	−1.48589	−0.742943	−	0.669355i	$-0.766571\pi$
$239$	−22.9712	−1.48589	−0.742943	+	0.669355i	$0.766571\pi$
$240$	8.66073	0.559048
$241$	20.5101	1.32117	0.660586	−	0.750750i	$-0.270308\pi$
$241$	20.5101	1.32117	0.660586	+	0.750750i	$0.270308\pi$
$242$	0	0
$243$	8.91419	0.571846
$244$	−5.43079	−0.347670
$245$	−2.42331	−0.154819
$246$	20.9016	1.33264
$247$	−6.11143	−0.388861
$248$	−5.42466	−0.344466
$249$	−16.4096	−1.03992
$250$	3.30353	0.208933
$251$	−18.0367	−1.13847	−0.569234	−	0.822175i	$-0.692760\pi$
$251$	−18.0367	−1.13847	−0.569234	+	0.822175i	$0.692760\pi$
$252$	−15.1923	−0.957026
$253$	0	0
$254$	−3.17023	−0.198918
$255$	−43.9407	−2.75167
$256$	1.00000	0.0625000
$257$	−2.67722	−0.167000	−0.0835000	−	0.996508i	$-0.526610\pi$
$257$	−2.67722	−0.167000	−0.0835000	+	0.996508i	$0.526610\pi$
$258$	−8.44183	−0.525565
$259$	23.6571	1.46998
$260$	−18.2241	−1.13021
$261$	−25.2135	−1.56068
$262$	−9.50622	−0.587296
$263$	28.4003	1.75124	0.875620	−	0.483000i	$-0.160453\pi$
$263$	28.4003	1.75124	0.875620	+	0.483000i	$0.160453\pi$
$264$	0	0
$265$	27.9073	1.71433
$266$	2.79511	0.171379
$267$	30.4520	1.86363
$268$	9.66167	0.590180
$269$	−14.2995	−0.871856	−0.435928	−	0.899982i	$-0.643580\pi$
$269$	−14.2995	−0.871856	−0.435928	+	0.899982i	$0.643580\pi$
$270$	21.0916	1.28359
$271$	−2.32789	−0.141409	−0.0707045	−	0.997497i	$-0.522525\pi$
$271$	−2.32789	−0.141409	−0.0707045	+	0.997497i	$0.522525\pi$
$272$	−5.07356	−0.307630
$273$	49.6127	3.00270
$274$	6.60928	0.399281
$275$	0	0
$276$	12.2509	0.737419
$277$	24.3190	1.46119	0.730595	−	0.682811i	$-0.239243\pi$
$277$	24.3190	1.46119	0.730595	+	0.682811i	$0.239243\pi$
$278$	−3.51361	−0.210733
$279$	−29.4847	−1.76521
$280$	8.33495	0.498109
$281$	−0.905794	−0.0540351	−0.0270176	−	0.999635i	$-0.508601\pi$
$281$	−0.905794	−0.0540351	−0.0270176	+	0.999635i	$0.508601\pi$
$282$	1.13528	0.0676049
$283$	−7.55703	−0.449219	−0.224609	−	0.974449i	$-0.572111\pi$
$283$	−7.55703	−0.449219	−0.224609	+	0.974449i	$0.572111\pi$
$284$	7.90690	0.469188
$285$	−8.66073	−0.513017
$286$	0	0
$287$	20.1154	1.18737
$288$	5.43531	0.320279
$289$	8.74098	0.514175
$290$	13.8329	0.812295
$291$	−35.0038	−2.05196
$292$	−7.83239	−0.458356
$293$	10.0010	0.584264	0.292132	−	0.956378i	$-0.405635\pi$
$293$	10.0010	0.584264	0.292132	+	0.956378i	$0.405635\pi$
$294$	−2.36023	−0.137652
$295$	−33.6584	−1.95967
$296$	−8.46374	−0.491945
$297$	0	0
$298$	−11.0768	−0.641661
$299$	−25.7787	−1.49082
$300$	−11.3043	−0.652652
$301$	−8.12428	−0.468276
$302$	8.70404	0.500861
$303$	57.6002	3.30904
$304$	−1.00000	−0.0573539
$305$	16.1945	0.927292
$306$	−27.5764	−1.57644
$307$	−12.3399	−0.704277	−0.352139	−	0.935948i	$-0.614545\pi$
$307$	−12.3399	−0.704277	−0.352139	+	0.935948i	$0.614545\pi$
$308$	0	0
$309$	−7.25789	−0.412887
$310$	16.1762	0.918746
$311$	7.05463	0.400031	0.200016	−	0.979793i	$-0.435901\pi$
$311$	7.05463	0.400031	0.200016	+	0.979793i	$0.435901\pi$
$312$	−17.7498	−1.00488
$313$	−1.13018	−0.0638815	−0.0319408	−	0.999490i	$-0.510169\pi$
$313$	−1.13018	−0.0638815	−0.0319408	+	0.999490i	$0.510169\pi$
$314$	6.51081	0.367426
$315$	45.3031	2.55254
$316$	1.49859	0.0843021
$317$	−26.5112	−1.48902	−0.744508	−	0.667613i	$-0.767316\pi$
$317$	−26.5112	−1.48902	−0.744508	+	0.667613i	$0.767316\pi$
$318$	27.1809	1.52423
$319$	0	0
$320$	−2.98197	−0.166697
$321$	−41.7629	−2.33098
$322$	11.7901	0.657037
$323$	5.07356	0.282300
$324$	4.23670	0.235372
$325$	23.7867	1.31945
$326$	7.98406	0.442196
$327$	−35.6112	−1.96930
$328$	−7.19663	−0.397368
$329$	1.09257	0.0602356
$330$	0	0
$331$	−8.29118	−0.455724	−0.227862	−	0.973693i	$-0.573174\pi$
$331$	−8.29118	−0.455724	−0.227862	+	0.973693i	$0.573174\pi$
$332$	5.64998	0.310083
$333$	−46.0031	−2.52095
$334$	12.2491	0.670242
$335$	−28.8108	−1.57410
$336$	8.11802	0.442874
$337$	34.0702	1.85592	0.927961	−	0.372678i	$-0.121560\pi$
$337$	34.0702	1.85592	0.927961	+	0.372678i	$0.121560\pi$
$338$	24.3496	1.32444
$339$	−37.3013	−2.02593
$340$	15.1292	0.820497
$341$	0	0
$342$	−5.43531	−0.293908
$343$	17.2943	0.933806
$344$	2.90660	0.156714
$345$	−36.5319	−1.96681
$346$	−13.0541	−0.701793
$347$	14.9781	0.804067	0.402033	−	0.915625i	$-0.368304\pi$
$347$	14.9781	0.804067	0.402033	+	0.915625i	$0.368304\pi$
$348$	13.4729	0.722221
$349$	16.9237	0.905906	0.452953	−	0.891534i	$-0.350370\pi$
$349$	16.9237	0.905906	0.452953	+	0.891534i	$0.350370\pi$
$350$	−10.8790	−0.581509
$351$	−43.2264	−2.30725
$352$	0	0
$353$	15.8601	0.844150	0.422075	−	0.906561i	$-0.361302\pi$
$353$	15.8601	0.844150	0.422075	+	0.906561i	$0.361302\pi$
$354$	−32.7823	−1.74236
$355$	−23.5782	−1.25140
$356$	−10.4849	−0.555699
$357$	−41.1872	−2.17986
$358$	7.67488	0.405630
$359$	−0.691621	−0.0365023	−0.0182512	−	0.999833i	$-0.505810\pi$
$359$	−0.691621	−0.0365023	−0.0182512	+	0.999833i	$0.505810\pi$
$360$	−16.2080	−0.854235
$361$	1.00000	0.0526316
$362$	−18.7816	−0.987141
$363$	0	0
$364$	−17.0821	−0.895347
$365$	23.3560	1.22251
$366$	15.7730	0.824466
$367$	−22.4739	−1.17313	−0.586564	−	0.809903i	$-0.699520\pi$
$367$	−22.4739	−1.17313	−0.586564	+	0.809903i	$0.699520\pi$
$368$	−4.21811	−0.219884
$369$	−39.1160	−2.03630
$370$	25.2387	1.31210
$371$	26.1585	1.35808
$372$	15.7552	0.816868
$373$	−2.36335	−0.122370	−0.0611849	−	0.998126i	$-0.519488\pi$
$373$	−2.36335	−0.122370	−0.0611849	+	0.998126i	$0.519488\pi$
$374$	0	0
$375$	−9.59464	−0.495465
$376$	−0.390888	−0.0201585
$377$	−28.3499	−1.46009
$378$	19.7699	1.01686
$379$	−6.44891	−0.331258	−0.165629	−	0.986188i	$-0.552965\pi$
$379$	−6.44891	−0.331258	−0.165629	+	0.986188i	$0.552965\pi$
$380$	2.98197	0.152972
$381$	9.20750	0.471715
$382$	−13.9700	−0.714768
$383$	14.8436	0.758473	0.379237	−	0.925300i	$-0.376187\pi$
$383$	14.8436	0.758473	0.379237	+	0.925300i	$0.376187\pi$
$384$	−2.90436	−0.148213
$385$	0	0
$386$	16.0205	0.815424
$387$	15.7983	0.803073
$388$	12.0521	0.611855
$389$	24.2763	1.23086	0.615428	−	0.788193i	$-0.288983\pi$
$389$	24.2763	1.23086	0.615428	+	0.788193i	$0.288983\pi$
$390$	52.9295	2.68019
$391$	21.4008	1.08229
$392$	0.812652	0.0410451
$393$	27.6095	1.39272
$394$	5.76542	0.290458
$395$	−4.46875	−0.224847
$396$	0	0
$397$	5.78039	0.290109	0.145055	−	0.989424i	$-0.453664\pi$
$397$	5.78039	0.290109	0.145055	+	0.989424i	$0.453664\pi$
$398$	14.0469	0.704107
$399$	−8.11802	−0.406409
$400$	3.89217	0.194608
$401$	39.0838	1.95175	0.975877	−	0.218322i	$-0.0700583\pi$
$401$	39.0838	1.95175	0.975877	+	0.218322i	$0.0700583\pi$
$402$	−28.0610	−1.39955
$403$	−33.1524	−1.65144
$404$	−19.8323	−0.986694
$405$	−12.6337	−0.627775
$406$	12.9661	0.643495
$407$	0	0
$408$	14.7354	0.729513
$409$	21.3472	1.05555	0.527777	−	0.849383i	$-0.323026\pi$
$409$	21.3472	1.05555	0.527777	+	0.849383i	$0.323026\pi$
$410$	21.4602	1.05984
$411$	−19.1957	−0.946856
$412$	2.49896	0.123115
$413$	−31.5492	−1.55244
$414$	−22.9268	−1.12679
$415$	−16.8481	−0.827040
$416$	6.11143	0.299638
$417$	10.2048	0.499731
$418$	0	0
$419$	0.718508	0.0351014	0.0175507	−	0.999846i	$-0.494413\pi$
$419$	0.718508	0.0351014	0.0175507	+	0.999846i	$0.494413\pi$
$420$	−24.2077	−1.18122
$421$	−15.3939	−0.750253	−0.375127	−	0.926974i	$-0.622401\pi$
$421$	−15.3939	−0.750253	−0.375127	+	0.926974i	$0.622401\pi$
$422$	10.0453	0.488998
$423$	−2.12460	−0.103301
$424$	−9.35865	−0.454496
$425$	−19.7471	−0.957877
$426$	−22.9645	−1.11263
$427$	15.1797	0.734595
$428$	14.3794	0.695053
$429$	0	0
$430$	−8.66741	−0.417980
$431$	7.69343	0.370579	0.185290	−	0.982684i	$-0.440678\pi$
$431$	7.69343	0.370579	0.185290	+	0.982684i	$0.440678\pi$
$432$	−7.07303	−0.340301
$433$	−22.0627	−1.06026	−0.530132	−	0.847915i	$-0.677858\pi$
$433$	−22.0627	−1.06026	−0.530132	+	0.847915i	$0.677858\pi$
$434$	15.1625	0.727825
$435$	−40.1757	−1.92628
$436$	12.2613	0.587209
$437$	4.21811	0.201780
$438$	22.7481	1.08695
$439$	7.27573	0.347251	0.173626	−	0.984812i	$-0.444452\pi$
$439$	7.27573	0.347251	0.173626	+	0.984812i	$0.444452\pi$
$440$	0	0
$441$	4.41702	0.210334
$442$	−31.0067	−1.47484
$443$	−16.3024	−0.774548	−0.387274	−	0.921965i	$-0.626583\pi$
$443$	−16.3024	−0.774548	−0.387274	+	0.921965i	$0.626583\pi$
$444$	24.5818	1.16660
$445$	31.2657	1.48214
$446$	14.8013	0.700863
$447$	32.1710	1.52164
$448$	−2.79511	−0.132057
$449$	11.6635	0.550434	0.275217	−	0.961382i	$-0.411250\pi$
$449$	11.6635	0.550434	0.275217	+	0.961382i	$0.411250\pi$
$450$	21.1552	0.997264
$451$	0	0
$452$	12.8432	0.604093
$453$	−25.2797	−1.18774
$454$	−6.67930	−0.313475
$455$	50.9385	2.38803
$456$	2.90436	0.136009
$457$	27.7473	1.29796	0.648982	−	0.760804i	$-0.275195\pi$
$457$	27.7473	1.29796	0.648982	+	0.760804i	$0.275195\pi$
$458$	−26.9028	−1.25709
$459$	35.8854	1.67499
$460$	12.5783	0.586467
$461$	27.3928	1.27581	0.637904	−	0.770116i	$-0.279802\pi$
$461$	27.3928	1.27581	0.637904	+	0.770116i	$0.279802\pi$
$462$	0	0
$463$	24.2856	1.12865	0.564324	−	0.825553i	$-0.309137\pi$
$463$	24.2856	1.12865	0.564324	+	0.825553i	$0.309137\pi$
$464$	−4.63883	−0.215352
$465$	−46.9815	−2.17872
$466$	−11.2301	−0.520222
$467$	−35.0167	−1.62038	−0.810190	−	0.586167i	$-0.800636\pi$
$467$	−35.0167	−1.62038	−0.810190	+	0.586167i	$0.800636\pi$
$468$	33.2176	1.53548
$469$	−27.0054	−1.24700
$470$	1.16562	0.0537659
$471$	−18.9098	−0.871315
$472$	11.2873	0.519539
$473$	0	0
$474$	−4.35244	−0.199914
$475$	−3.89217	−0.178585
$476$	14.1812	0.649992
$477$	−50.8672	−2.32905
$478$	−22.9712	−1.05068
$479$	2.25155	0.102876	0.0514380	−	0.998676i	$-0.483620\pi$
$479$	2.25155	0.102876	0.0514380	+	0.998676i	$0.483620\pi$
$480$	8.66073	0.395306
$481$	−51.7256	−2.35848
$482$	20.5101	0.934210
$483$	−34.2427	−1.55810
$484$	0	0
$485$	−35.9392	−1.63191
$486$	8.91419	0.404356
$487$	−27.2643	−1.23546	−0.617732	−	0.786389i	$-0.711948\pi$
$487$	−27.2643	−1.23546	−0.617732	+	0.786389i	$0.711948\pi$
$488$	−5.43079	−0.245840
$489$	−23.1886	−1.04862
$490$	−2.42331	−0.109474
$491$	−33.4935	−1.51154	−0.755770	−	0.654837i	$-0.772737\pi$
$491$	−33.4935	−1.51154	−0.755770	+	0.654837i	$0.772737\pi$
$492$	20.9016	0.942318
$493$	23.5354	1.05998
$494$	−6.11143	−0.274966
$495$	0	0
$496$	−5.42466	−0.243574
$497$	−22.1007	−0.991350
$498$	−16.4096	−0.735331
$499$	7.38895	0.330775	0.165387	−	0.986229i	$-0.447113\pi$
$499$	7.38895	0.330775	0.165387	+	0.986229i	$0.447113\pi$
$500$	3.30353	0.147738
$501$	−35.5758	−1.58941
$502$	−18.0367	−0.805019
$503$	−15.5147	−0.691765	−0.345882	−	0.938278i	$-0.612420\pi$
$503$	−15.5147	−0.691765	−0.345882	+	0.938278i	$0.612420\pi$
$504$	−15.1923	−0.676719
$505$	59.1394	2.63167
$506$	0	0
$507$	−70.7200	−3.14079
$508$	−3.17023	−0.140656
$509$	28.9373	1.28263	0.641313	−	0.767280i	$-0.278390\pi$
$509$	28.9373	1.28263	0.641313	+	0.767280i	$0.278390\pi$
$510$	−43.9407	−1.94573
$511$	21.8924	0.968464
$512$	1.00000	0.0441942
$513$	7.07303	0.312282
$514$	−2.67722	−0.118087
$515$	−7.45184	−0.328367
$516$	−8.44183	−0.371631
$517$	0	0
$518$	23.6571	1.03943
$519$	37.9138	1.66423
$520$	−18.2241	−0.799181
$521$	29.4920	1.29207	0.646035	−	0.763308i	$-0.276426\pi$
$521$	29.4920	1.29207	0.646035	+	0.763308i	$0.276426\pi$
$522$	−25.2135	−1.10357
$523$	−17.7597	−0.776579	−0.388289	−	0.921537i	$-0.626934\pi$
$523$	−17.7597	−0.776579	−0.388289	+	0.921537i	$0.626934\pi$
$524$	−9.50622	−0.415281
$525$	31.5967	1.37899
$526$	28.4003	1.23831
$527$	27.5223	1.19889
$528$	0	0
$529$	−5.20751	−0.226413
$530$	27.9073	1.21221
$531$	61.3499	2.66236
$532$	2.79511	0.121183
$533$	−43.9817	−1.90506
$534$	30.4520	1.31779
$535$	−42.8789	−1.85382
$536$	9.66167	0.417320
$537$	−22.2906	−0.961912
$538$	−14.2995	−0.616495
$539$	0	0
$540$	21.0916	0.907638
$541$	4.67242	0.200883	0.100442	−	0.994943i	$-0.467974\pi$
$541$	4.67242	0.200883	0.100442	+	0.994943i	$0.467974\pi$
$542$	−2.32789	−0.0999912
$543$	54.5487	2.34091
$544$	−5.07356	−0.217527
$545$	−36.5628	−1.56618
$546$	49.6127	2.12323
$547$	−7.63169	−0.326307	−0.163154	−	0.986601i	$-0.552167\pi$
$547$	−7.63169	−0.326307	−0.163154	+	0.986601i	$0.552167\pi$
$548$	6.60928	0.282334
$549$	−29.5180	−1.25980
$550$	0	0
$551$	4.63883	0.197621
$552$	12.2509	0.521434
$553$	−4.18872	−0.178122
$554$	24.3190	1.03322
$555$	−73.3022	−3.11150
$556$	−3.51361	−0.149010
$557$	22.5313	0.954684	0.477342	−	0.878718i	$-0.341600\pi$
$557$	22.5313	0.954684	0.477342	+	0.878718i	$0.341600\pi$
$558$	−29.4847	−1.24819
$559$	17.7635	0.751316
$560$	8.33495	0.352216
$561$	0	0
$562$	−0.905794	−0.0382086
$563$	−28.0615	−1.18265	−0.591325	−	0.806433i	$-0.701395\pi$
$563$	−28.0615	−1.18265	−0.591325	+	0.806433i	$0.701395\pi$
$564$	1.13528	0.0478039
$565$	−38.2981	−1.61121
$566$	−7.55703	−0.317646
$567$	−11.8421	−0.497319
$568$	7.90690	0.331766
$569$	8.33004	0.349214	0.174607	−	0.984638i	$-0.444135\pi$
$569$	8.33004	0.349214	0.174607	+	0.984638i	$0.444135\pi$
$570$	−8.66073	−0.362758
$571$	−9.67003	−0.404678	−0.202339	−	0.979316i	$-0.564854\pi$
$571$	−9.67003	−0.404678	−0.202339	+	0.979316i	$0.564854\pi$
$572$	0	0
$573$	40.5739	1.69500
$574$	20.1154	0.839600
$575$	−16.4176	−0.684662
$576$	5.43531	0.226471
$577$	−15.7453	−0.655487	−0.327743	−	0.944767i	$-0.606288\pi$
$577$	−15.7453	−0.655487	−0.327743	+	0.944767i	$0.606288\pi$
$578$	8.74098	0.363577
$579$	−46.5294	−1.93370
$580$	13.8329	0.574379
$581$	−15.7923	−0.655176
$582$	−35.0038	−1.45095
$583$	0	0
$584$	−7.83239	−0.324107
$585$	−99.0539	−4.09537
$586$	10.0010	0.413137
$587$	45.4128	1.87439	0.937193	−	0.348812i	$-0.113415\pi$
$587$	45.4128	1.87439	0.937193	+	0.348812i	$0.113415\pi$
$588$	−2.36023	−0.0973344
$589$	5.42466	0.223519
$590$	−33.6584	−1.38569
$591$	−16.7449	−0.688791
$592$	−8.46374	−0.347858
$593$	24.2199	0.994591	0.497295	−	0.867581i	$-0.334327\pi$
$593$	24.2199	0.994591	0.497295	+	0.867581i	$0.334327\pi$
$594$	0	0
$595$	−42.2878	−1.73363
$596$	−11.0768	−0.453723
$597$	−40.7972	−1.66972
$598$	−25.7787	−1.05417
$599$	34.3722	1.40441	0.702205	−	0.711974i	$-0.252199\pi$
$599$	34.3722	1.40441	0.702205	+	0.711974i	$0.252199\pi$
$600$	−11.3043	−0.461495
$601$	25.7994	1.05238	0.526190	−	0.850367i	$-0.323620\pi$
$601$	25.7994	1.05238	0.526190	+	0.850367i	$0.323620\pi$
$602$	−8.12428	−0.331121
$603$	52.5142	2.13854
$604$	8.70404	0.354162
$605$	0	0
$606$	57.6002	2.33985
$607$	24.8177	1.00732	0.503659	−	0.863902i	$-0.331987\pi$
$607$	24.8177	1.00732	0.503659	+	0.863902i	$0.331987\pi$
$608$	−1.00000	−0.0405554
$609$	−37.6581	−1.52598
$610$	16.1945	0.655695
$611$	−2.38888	−0.0966439
$612$	−27.5764	−1.11471
$613$	8.55329	0.345464	0.172732	−	0.984969i	$-0.444740\pi$
$613$	8.55329	0.345464	0.172732	+	0.984969i	$0.444740\pi$
$614$	−12.3399	−0.497999
$615$	−62.3281	−2.51331
$616$	0	0
$617$	−35.7109	−1.43766	−0.718832	−	0.695183i	$-0.755323\pi$
$617$	−35.7109	−1.43766	−0.718832	+	0.695183i	$0.755323\pi$
$618$	−7.25789	−0.291955
$619$	−3.75635	−0.150981	−0.0754903	−	0.997147i	$-0.524052\pi$
$619$	−3.75635	−0.150981	−0.0754903	+	0.997147i	$0.524052\pi$
$620$	16.1762	0.649652
$621$	29.8349	1.19723
$622$	7.05463	0.282865
$623$	29.3065	1.17414
$624$	−17.7498	−0.710561
$625$	−29.3119	−1.17247
$626$	−1.13018	−0.0451711
$627$	0	0
$628$	6.51081	0.259810
$629$	42.9413	1.71218
$630$	45.3031	1.80492
$631$	5.98590	0.238295	0.119148	−	0.992877i	$-0.461984\pi$
$631$	5.98590	0.238295	0.119148	+	0.992877i	$0.461984\pi$
$632$	1.49859	0.0596106
$633$	−29.1752	−1.15961
$634$	−26.5112	−1.05289
$635$	9.45355	0.375153
$636$	27.1809	1.07779
$637$	4.96646	0.196779
$638$	0	0
$639$	42.9765	1.70012
$640$	−2.98197	−0.117873
$641$	−3.80225	−0.150180	−0.0750899	−	0.997177i	$-0.523924\pi$
$641$	−3.80225	−0.150180	−0.0750899	+	0.997177i	$0.523924\pi$
$642$	−41.7629	−1.64825
$643$	18.9641	0.747873	0.373936	−	0.927454i	$-0.378008\pi$
$643$	18.9641	0.747873	0.373936	+	0.927454i	$0.378008\pi$
$644$	11.7901	0.464595
$645$	25.1733	0.991198
$646$	5.07356	0.199616
$647$	22.7844	0.895748	0.447874	−	0.894097i	$-0.352181\pi$
$647$	22.7844	0.895748	0.447874	+	0.894097i	$0.352181\pi$
$648$	4.23670	0.166433
$649$	0	0
$650$	23.7867	0.932992
$651$	−44.0375	−1.72597
$652$	7.98406	0.312680
$653$	−7.65713	−0.299647	−0.149823	−	0.988713i	$-0.547870\pi$
$653$	−7.65713	−0.299647	−0.149823	+	0.988713i	$0.547870\pi$
$654$	−35.6112	−1.39251
$655$	28.3473	1.10762
$656$	−7.19663	−0.280981
$657$	−42.5715	−1.66087
$658$	1.09257	0.0425930
$659$	−10.5305	−0.410208	−0.205104	−	0.978740i	$-0.565753\pi$
$659$	−10.5305	−0.410208	−0.205104	+	0.978740i	$0.565753\pi$
$660$	0	0
$661$	−15.0882	−0.586864	−0.293432	−	0.955980i	$-0.594797\pi$
$661$	−15.0882	−0.586864	−0.293432	+	0.955980i	$0.594797\pi$
$662$	−8.29118	−0.322246
$663$	90.0546	3.49743
$664$	5.64998	0.219262
$665$	−8.33495	−0.323216
$666$	−46.0031	−1.78258
$667$	19.5671	0.757642
$668$	12.2491	0.473932
$669$	−42.9884	−1.66203
$670$	−28.8108	−1.11306
$671$	0	0
$672$	8.11802	0.313159
$673$	5.77897	0.222763	0.111381	−	0.993778i	$-0.464472\pi$
$673$	5.77897	0.222763	0.111381	+	0.993778i	$0.464472\pi$
$674$	34.0702	1.31233
$675$	−27.5294	−1.05961
$676$	24.3496	0.936523
$677$	38.2792	1.47119	0.735594	−	0.677422i	$-0.236903\pi$
$677$	38.2792	1.47119	0.735594	+	0.677422i	$0.236903\pi$
$678$	−37.3013	−1.43255
$679$	−33.6871	−1.29279
$680$	15.1292	0.580179
$681$	19.3991	0.743375
$682$	0	0
$683$	7.48010	0.286218	0.143109	−	0.989707i	$-0.454290\pi$
$683$	7.48010	0.286218	0.143109	+	0.989707i	$0.454290\pi$
$684$	−5.43531	−0.207824
$685$	−19.7087	−0.753031
$686$	17.2943	0.660301
$687$	78.1355	2.98105
$688$	2.90660	0.110813
$689$	−57.1948	−2.17895
$690$	−36.5319	−1.39075
$691$	0.0245599	0.000934303 0	0.000467152	−	1.00000i	$-0.499851\pi$
$691$	0.0245599	0.000934303 0	0.000467152		1.00000i	$0.499851\pi$
$692$	−13.0541	−0.496242
$693$	0	0
$694$	14.9781	0.568561
$695$	10.4775	0.397434
$696$	13.4729	0.510687
$697$	36.5125	1.38301
$698$	16.9237	0.640572
$699$	32.6161	1.23366
$700$	−10.8790	−0.411189
$701$	29.3219	1.10747	0.553736	−	0.832692i	$-0.313202\pi$
$701$	29.3219	1.10747	0.553736	+	0.832692i	$0.313202\pi$
$702$	−43.2264	−1.63147
$703$	8.46374	0.319216
$704$	0	0
$705$	−3.38537	−0.127500
$706$	15.8601	0.596904
$707$	55.4335	2.08479
$708$	−32.7823	−1.23204
$709$	−43.8263	−1.64593	−0.822966	−	0.568090i	$-0.807683\pi$
$709$	−43.8263	−1.64593	−0.822966	+	0.568090i	$0.807683\pi$
$710$	−23.5782	−0.884872
$711$	8.14529	0.305472
$712$	−10.4849	−0.392939
$713$	22.8818	0.856932
$714$	−41.1872	−1.54139
$715$	0	0
$716$	7.67488	0.286824
$717$	66.7168	2.49158
$718$	−0.691621	−0.0258110
$719$	−0.326033	−0.0121590	−0.00607950	−	0.999982i	$-0.501935\pi$
$719$	−0.326033	−0.0121590	−0.00607950	+	0.999982i	$0.501935\pi$
$720$	−16.2080	−0.604035
$721$	−6.98488	−0.260130
$722$	1.00000	0.0372161
$723$	−59.5688	−2.21539
$724$	−18.7816	−0.698014
$725$	−18.0551	−0.670550
$726$	0	0
$727$	1.10590	0.0410155	0.0205077	−	0.999790i	$-0.493472\pi$
$727$	1.10590	0.0410155	0.0205077	+	0.999790i	$0.493472\pi$
$728$	−17.0821	−0.633106
$729$	−38.6001	−1.42963
$730$	23.3560	0.864444
$731$	−14.7468	−0.545431
$732$	15.7730	0.582986
$733$	−28.2624	−1.04390	−0.521948	−	0.852977i	$-0.674795\pi$
$733$	−28.2624	−1.04390	−0.521948	+	0.852977i	$0.674795\pi$
$734$	−22.4739	−0.829526
$735$	7.03816	0.259606
$736$	−4.21811	−0.155482
$737$	0	0
$738$	−39.1160	−1.43988
$739$	44.4511	1.63516	0.817580	−	0.575815i	$-0.195315\pi$
$739$	44.4511	1.63516	0.817580	+	0.575815i	$0.195315\pi$
$740$	25.2387	0.927792
$741$	17.7498	0.652055
$742$	26.1585	0.960308
$743$	22.3606	0.820331	0.410165	−	0.912011i	$-0.365471\pi$
$743$	22.3606	0.820331	0.410165	+	0.912011i	$0.365471\pi$
$744$	15.7552	0.577613
$745$	33.0307	1.21015
$746$	−2.36335	−0.0865285
$747$	30.7094	1.12360
$748$	0	0
$749$	−40.1920	−1.46858
$750$	−9.59464	−0.350347
$751$	36.8865	1.34601	0.673004	−	0.739639i	$-0.265004\pi$
$751$	36.8865	1.34601	0.673004	+	0.739639i	$0.265004\pi$
$752$	−0.390888	−0.0142542
$753$	52.3852	1.90902
$754$	−28.3499	−1.03244
$755$	−25.9552	−0.944607
$756$	19.7699	0.719025
$757$	−3.52812	−0.128232	−0.0641159	−	0.997942i	$-0.520423\pi$
$757$	−3.52812	−0.128232	−0.0641159	+	0.997942i	$0.520423\pi$
$758$	−6.44891	−0.234235
$759$	0	0
$760$	2.98197	0.108168
$761$	27.6451	1.00213	0.501067	−	0.865409i	$-0.332941\pi$
$761$	27.6451	1.00213	0.501067	+	0.865409i	$0.332941\pi$
$762$	9.20750	0.333553
$763$	−34.2716	−1.24072
$764$	−13.9700	−0.505417
$765$	82.2320	2.97311
$766$	14.8436	0.536322
$767$	68.9814	2.49078
$768$	−2.90436	−0.104802
$769$	−13.7325	−0.495205	−0.247603	−	0.968862i	$-0.579643\pi$
$769$	−13.7325	−0.495205	−0.247603	+	0.968862i	$0.579643\pi$
$770$	0	0
$771$	7.77560	0.280031
$772$	16.0205	0.576592
$773$	−1.06575	−0.0383325	−0.0191662	−	0.999816i	$-0.506101\pi$
$773$	−1.06575	−0.0383325	−0.0191662	+	0.999816i	$0.506101\pi$
$774$	15.7983	0.567858
$775$	−21.1137	−0.758426
$776$	12.0521	0.432647
$777$	−68.7088	−2.46491
$778$	24.2763	0.870347
$779$	7.19663	0.257846
$780$	52.9295	1.89518
$781$	0	0
$782$	21.4008	0.765293
$783$	32.8106	1.17256
$784$	0.812652	0.0290233
$785$	−19.4151	−0.692954
$786$	27.6095	0.984798
$787$	−47.0035	−1.67549	−0.837747	−	0.546059i	$-0.816128\pi$
$787$	−47.0035	−1.67549	−0.837747	+	0.546059i	$0.816128\pi$
$788$	5.76542	0.205384
$789$	−82.4849	−2.93654
$790$	−4.46875	−0.158991
$791$	−35.8982	−1.27639
$792$	0	0
$793$	−33.1899	−1.17861
$794$	5.78039	0.205138
$795$	−81.0528	−2.87465
$796$	14.0469	0.497879
$797$	−33.3638	−1.18181	−0.590904	−	0.806742i	$-0.701229\pi$
$797$	−33.3638	−1.18181	−0.590904	+	0.806742i	$0.701229\pi$
$798$	−8.11802	−0.287375
$799$	1.98319	0.0701602
$800$	3.89217	0.137609
$801$	−56.9888	−2.01360
$802$	39.0838	1.38010
$803$	0	0
$804$	−28.0610	−0.989634
$805$	−35.1578	−1.23915
$806$	−33.1524	−1.16775
$807$	41.5309	1.46196
$808$	−19.8323	−0.697698
$809$	−22.8269	−0.802551	−0.401276	−	0.915957i	$-0.631433\pi$
$809$	−22.8269	−0.802551	−0.401276	+	0.915957i	$0.631433\pi$
$810$	−12.6337	−0.443904
$811$	10.1707	0.357141	0.178571	−	0.983927i	$-0.442853\pi$
$811$	10.1707	0.357141	0.178571	+	0.983927i	$0.442853\pi$
$812$	12.9661	0.455020
$813$	6.76102	0.237119
$814$	0	0
$815$	−23.8083	−0.833967
$816$	14.7354	0.515844
$817$	−2.90660	−0.101689
$818$	21.3472	0.746389
$819$	−92.8468	−3.24433
$820$	21.4602	0.749422
$821$	−16.9023	−0.589894	−0.294947	−	0.955514i	$-0.595302\pi$
$821$	−16.9023	−0.589894	−0.294947	+	0.955514i	$0.595302\pi$
$822$	−19.1957	−0.669528
$823$	−21.0975	−0.735413	−0.367707	−	0.929942i	$-0.619857\pi$
$823$	−21.0975	−0.735413	−0.367707	+	0.929942i	$0.619857\pi$
$824$	2.49896	0.0870555
$825$	0	0
$826$	−31.5492	−1.09774
$827$	1.45713	0.0506692	0.0253346	−	0.999679i	$-0.491935\pi$
$827$	1.45713	0.0506692	0.0253346	+	0.999679i	$0.491935\pi$
$828$	−22.9268	−0.796761
$829$	42.4013	1.47266	0.736329	−	0.676624i	$-0.236558\pi$
$829$	42.4013	1.47266	0.736329	+	0.676624i	$0.236558\pi$
$830$	−16.8481	−0.584806
$831$	−70.6313	−2.45017
$832$	6.11143	0.211876
$833$	−4.12303	−0.142855
$834$	10.2048	0.353363
$835$	−36.5265	−1.26405
$836$	0	0
$837$	38.3688	1.32622
$838$	0.718508	0.0248205
$839$	−25.1324	−0.867669	−0.433834	−	0.900993i	$-0.642840\pi$
$839$	−25.1324	−0.867669	−0.433834	+	0.900993i	$0.642840\pi$
$840$	−24.2077	−0.835245
$841$	−7.48122	−0.257973
$842$	−15.3939	−0.530509
$843$	2.63075	0.0906079
$844$	10.0453	0.345774
$845$	−72.6098	−2.49785
$846$	−2.12460	−0.0730452
$847$	0	0
$848$	−9.35865	−0.321378
$849$	21.9483	0.753265
$850$	−19.7471	−0.677321
$851$	35.7010	1.22382
$852$	−22.9645	−0.786750
$853$	22.0836	0.756129	0.378065	−	0.925779i	$-0.376590\pi$
$853$	22.0836	0.756129	0.378065	+	0.925779i	$0.376590\pi$
$854$	15.1797	0.519437
$855$	16.2080	0.554301
$856$	14.3794	0.491477
$857$	−18.1127	−0.618717	−0.309358	−	0.950946i	$-0.600114\pi$
$857$	−18.1127	−0.618717	−0.309358	+	0.950946i	$0.600114\pi$
$858$	0	0
$859$	33.2794	1.13548	0.567739	−	0.823209i	$-0.307818\pi$
$859$	33.2794	1.13548	0.567739	+	0.823209i	$0.307818\pi$
$860$	−8.66741	−0.295556
$861$	−58.4224	−1.99103
$862$	7.69343	0.262039
$863$	−43.3013	−1.47399	−0.736997	−	0.675896i	$-0.763757\pi$
$863$	−43.3013	−1.47399	−0.736997	+	0.675896i	$0.763757\pi$
$864$	−7.07303	−0.240629
$865$	38.9270	1.32356
$866$	−22.0627	−0.749720
$867$	−25.3870	−0.862186
$868$	15.1625	0.514650
$869$	0	0
$870$	−40.1757	−1.36208
$871$	59.0466	2.00072
$872$	12.2613	0.415219
$873$	65.5072	2.21708
$874$	4.21811	0.142680
$875$	−9.23373	−0.312157
$876$	22.7481	0.768587
$877$	5.99853	0.202556	0.101278	−	0.994858i	$-0.467707\pi$
$877$	5.99853	0.202556	0.101278	+	0.994858i	$0.467707\pi$
$878$	7.27573	0.245544
$879$	−29.0465	−0.979714
$880$	0	0
$881$	13.9504	0.470002	0.235001	−	0.971995i	$-0.424491\pi$
$881$	13.9504	0.470002	0.235001	+	0.971995i	$0.424491\pi$
$882$	4.41702	0.148729
$883$	33.5479	1.12898	0.564488	−	0.825441i	$-0.309074\pi$
$883$	33.5479	1.12898	0.564488	+	0.825441i	$0.309074\pi$
$884$	−31.0067	−1.04287
$885$	97.7561	3.28603
$886$	−16.3024	−0.547688
$887$	24.5581	0.824579	0.412289	−	0.911053i	$-0.364729\pi$
$887$	24.5581	0.824579	0.412289	+	0.911053i	$0.364729\pi$
$888$	24.5818	0.824910
$889$	8.86116	0.297194
$890$	31.2657	1.04803
$891$	0	0
$892$	14.8013	0.495585
$893$	0.390888	0.0130806
$894$	32.1710	1.07596
$895$	−22.8863	−0.765005
$896$	−2.79511	−0.0933781
$897$	74.8707	2.49986
$898$	11.6635	0.389215
$899$	25.1641	0.839270
$900$	21.1552	0.705172
$901$	47.4817	1.58184
$902$	0	0
$903$	23.5958	0.785221
$904$	12.8432	0.427158
$905$	56.0063	1.86171
$906$	−25.2797	−0.839861
$907$	55.9670	1.85835	0.929177	−	0.369634i	$-0.120517\pi$
$907$	55.9670	1.85835	0.929177	+	0.369634i	$0.120517\pi$
$908$	−6.67930	−0.221660
$909$	−107.795	−3.57533
$910$	50.9385	1.68859
$911$	−9.32213	−0.308856	−0.154428	−	0.988004i	$-0.549353\pi$
$911$	−9.32213	−0.308856	−0.154428	+	0.988004i	$0.549353\pi$
$912$	2.90436	0.0961730
$913$	0	0
$914$	27.7473	0.917799
$915$	−47.0346	−1.55491
$916$	−26.9028	−0.888894
$917$	26.5710	0.877450
$918$	35.8854	1.18440
$919$	−3.40224	−0.112229	−0.0561147	−	0.998424i	$-0.517871\pi$
$919$	−3.40224	−0.112229	−0.0561147	+	0.998424i	$0.517871\pi$
$920$	12.5783	0.414695
$921$	35.8396	1.18096
$922$	27.3928	0.902132
$923$	48.3224	1.59055
$924$	0	0
$925$	−32.9423	−1.08314
$926$	24.2856	0.798075
$927$	13.5826	0.446113
$928$	−4.63883	−0.152277
$929$	−32.6345	−1.07070	−0.535351	−	0.844630i	$-0.679821\pi$
$929$	−32.6345	−1.07070	−0.535351	+	0.844630i	$0.679821\pi$
$930$	−46.9815	−1.54058
$931$	−0.812652	−0.0266336
$932$	−11.2301	−0.367853
$933$	−20.4892	−0.670786
$934$	−35.0167	−1.14578
$935$	0	0
$936$	33.2176	1.08575
$937$	−13.4953	−0.440872	−0.220436	−	0.975401i	$-0.570748\pi$
$937$	−13.4953	−0.440872	−0.220436	+	0.975401i	$0.570748\pi$
$938$	−27.0054	−0.881759
$939$	3.28245	0.107119
$940$	1.16562	0.0380182
$941$	−8.38407	−0.273313	−0.136656	−	0.990618i	$-0.543636\pi$
$941$	−8.38407	−0.273313	−0.136656	+	0.990618i	$0.543636\pi$
$942$	−18.9098	−0.616113
$943$	30.3562	0.988535
$944$	11.2873	0.367370
$945$	−58.9534	−1.91775
$946$	0	0
$947$	−30.3229	−0.985363	−0.492681	−	0.870210i	$-0.663983\pi$
$947$	−30.3229	−0.985363	−0.492681	+	0.870210i	$0.663983\pi$
$948$	−4.35244	−0.141361
$949$	−47.8671	−1.55383
$950$	−3.89217	−0.126279
$951$	76.9981	2.49683
$952$	14.1812	0.459614
$953$	43.7625	1.41761	0.708803	−	0.705406i	$-0.249235\pi$
$953$	43.7625	1.41761	0.708803	+	0.705406i	$0.249235\pi$
$954$	−50.8672	−1.64689
$955$	41.6582	1.34803
$956$	−22.9712	−0.742943
$957$	0	0
$958$	2.25155	0.0727444
$959$	−18.4737	−0.596546
$960$	8.66073	0.279524
$961$	−1.57305	−0.0507436
$962$	−51.7256	−1.66770
$963$	78.1564	2.51856
$964$	20.5101	0.660586
$965$	−47.7728	−1.53786
$966$	−34.2427	−1.10174
$967$	14.3123	0.460252	0.230126	−	0.973161i	$-0.426086\pi$
$967$	14.3123	0.460252	0.230126	+	0.973161i	$0.426086\pi$
$968$	0	0
$969$	−14.7354	−0.473371
$970$	−35.9392	−1.15394
$971$	−61.5503	−1.97524	−0.987622	−	0.156851i	$-0.949866\pi$
$971$	−61.5503	−1.97524	−0.987622	+	0.156851i	$0.949866\pi$
$972$	8.91419	0.285923
$973$	9.82094	0.314845
$974$	−27.2643	−0.873605
$975$	−69.0852	−2.21250
$976$	−5.43079	−0.173835
$977$	−33.8723	−1.08367	−0.541836	−	0.840484i	$-0.682271\pi$
$977$	−33.8723	−1.08367	−0.541836	+	0.840484i	$0.682271\pi$
$978$	−23.1886	−0.741490
$979$	0	0
$980$	−2.42331	−0.0774097
$981$	66.6439	2.12778
$982$	−33.4935	−1.06882
$983$	−10.1178	−0.322707	−0.161354	−	0.986897i	$-0.551586\pi$
$983$	−10.1178	−0.322707	−0.161354	+	0.986897i	$0.551586\pi$
$984$	20.9016	0.666319
$985$	−17.1923	−0.547793
$986$	23.5354	0.749519
$987$	−3.17323	−0.101005
$988$	−6.11143	−0.194431
$989$	−12.2604	−0.389858
$990$	0	0
$991$	51.8642	1.64752	0.823760	−	0.566939i	$-0.191872\pi$
$991$	51.8642	1.64752	0.823760	+	0.566939i	$0.191872\pi$
$992$	−5.42466	−0.172233
$993$	24.0806	0.764174
$994$	−22.1007	−0.700990
$995$	−41.8874	−1.32792
$996$	−16.4096	−0.519958
$997$	8.54170	0.270518	0.135259	−	0.990810i	$-0.456813\pi$
$997$	8.54170	0.270518	0.135259	+	0.990810i	$0.456813\pi$
$998$	7.38895	0.233893
$999$	59.8643	1.89402

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.ca.1.2		8
11.5	even	5		418.2.f.f.267.1	yes	16
11.9	even	5		418.2.f.f.191.1	✓	16
11.10	odd	2		4598.2.a.bx.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.f.191.1	✓	16	11.9	even	5
418.2.f.f.267.1	yes	16	11.5	even	5
4598.2.a.bx.1.2		8	11.10	odd	2
4598.2.a.ca.1.2		8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.90436 q^{3} +1.00000 q^{4} -2.98197 q^{5} -2.90436 q^{6} -2.79511 q^{7} +1.00000 q^{8} +5.43531 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.90436 q^{3} +1.00000 q^{4} -2.98197 q^{5} -2.90436 q^{6} -2.79511 q^{7} +1.00000 q^{8} +5.43531 q^{9} -2.98197 q^{10} -2.90436 q^{12} +6.11143 q^{13} -2.79511 q^{14} +8.66073 q^{15} +1.00000 q^{16} -5.07356 q^{17} +5.43531 q^{18} -1.00000 q^{19} -2.98197 q^{20} +8.11802 q^{21} -4.21811 q^{23} -2.90436 q^{24} +3.89217 q^{25} +6.11143 q^{26} -7.07303 q^{27} -2.79511 q^{28} -4.63883 q^{29} +8.66073 q^{30} -5.42466 q^{31} +1.00000 q^{32} -5.07356 q^{34} +8.33495 q^{35} +5.43531 q^{36} -8.46374 q^{37} -1.00000 q^{38} -17.7498 q^{39} -2.98197 q^{40} -7.19663 q^{41} +8.11802 q^{42} +2.90660 q^{43} -16.2080 q^{45} -4.21811 q^{46} -0.390888 q^{47} -2.90436 q^{48} +0.812652 q^{49} +3.89217 q^{50} +14.7354 q^{51} +6.11143 q^{52} -9.35865 q^{53} -7.07303 q^{54} -2.79511 q^{56} +2.90436 q^{57} -4.63883 q^{58} +11.2873 q^{59} +8.66073 q^{60} -5.43079 q^{61} -5.42466 q^{62} -15.1923 q^{63} +1.00000 q^{64} -18.2241 q^{65} +9.66167 q^{67} -5.07356 q^{68} +12.2509 q^{69} +8.33495 q^{70} +7.90690 q^{71} +5.43531 q^{72} -7.83239 q^{73} -8.46374 q^{74} -11.3043 q^{75} -1.00000 q^{76} -17.7498 q^{78} +1.49859 q^{79} -2.98197 q^{80} +4.23670 q^{81} -7.19663 q^{82} +5.64998 q^{83} +8.11802 q^{84} +15.1292 q^{85} +2.90660 q^{86} +13.4729 q^{87} -10.4849 q^{89} -16.2080 q^{90} -17.0821 q^{91} -4.21811 q^{92} +15.7552 q^{93} -0.390888 q^{94} +2.98197 q^{95} -2.90436 q^{96} +12.0521 q^{97} +0.812652 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{4} + 2 q^{5} + 8 q^{7} + 8 q^{8} + 20 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^4 + 2 * q^5 + 8 * q^7 + 8 * q^8 + 20 * q^9	\( 8 q + 8 q^{2} + 8 q^{4} + 2 q^{5} + 8 q^{7} + 8 q^{8} + 20 q^{9} + 2 q^{10} + 18 q^{13} + 8 q^{14} + 10 q^{15} + 8 q^{16} + 4 q^{17} + 20 q^{18} - 8 q^{19} + 2 q^{20} + 14 q^{21} + 12 q^{23} + 18 q^{26} - 24 q^{27} + 8 q^{28} + 14 q^{29} + 10 q^{30} - 2 q^{31} + 8 q^{32} + 4 q^{34} + 40 q^{35} + 20 q^{36} - 22 q^{37} - 8 q^{38} - 4 q^{39} + 2 q^{40} + 8 q^{41} + 14 q^{42} + 28 q^{43} - 28 q^{45} + 12 q^{46} + 6 q^{47} + 32 q^{49} - 12 q^{51} + 18 q^{52} - 24 q^{53} - 24 q^{54} + 8 q^{56} + 14 q^{58} + 46 q^{59} + 10 q^{60} - 24 q^{61} - 2 q^{62} + 30 q^{63} + 8 q^{64} - 16 q^{65} - 22 q^{67} + 4 q^{68} - 38 q^{69} + 40 q^{70} + 8 q^{71} + 20 q^{72} + 16 q^{73} - 22 q^{74} + 6 q^{75} - 8 q^{76} - 4 q^{78} + 4 q^{79} + 2 q^{80} + 28 q^{81} + 8 q^{82} + 12 q^{83} + 14 q^{84} + 48 q^{85} + 28 q^{86} + 42 q^{87} - 28 q^{89} - 28 q^{90} - 12 q^{91} + 12 q^{92} + 22 q^{93} + 6 q^{94} - 2 q^{95} - 22 q^{97} + 32 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^4 + 2 * q^5 + 8 * q^7 + 8 * q^8 + 20 * q^9 + 2 * q^10 + 18 * q^13 + 8 * q^14 + 10 * q^15 + 8 * q^16 + 4 * q^17 + 20 * q^18 - 8 * q^19 + 2 * q^20 + 14 * q^21 + 12 * q^23 + 18 * q^26 - 24 * q^27 + 8 * q^28 + 14 * q^29 + 10 * q^30 - 2 * q^31 + 8 * q^32 + 4 * q^34 + 40 * q^35 + 20 * q^36 - 22 * q^37 - 8 * q^38 - 4 * q^39 + 2 * q^40 + 8 * q^41 + 14 * q^42 + 28 * q^43 - 28 * q^45 + 12 * q^46 + 6 * q^47 + 32 * q^49 - 12 * q^51 + 18 * q^52 - 24 * q^53 - 24 * q^54 + 8 * q^56 + 14 * q^58 + 46 * q^59 + 10 * q^60 - 24 * q^61 - 2 * q^62 + 30 * q^63 + 8 * q^64 - 16 * q^65 - 22 * q^67 + 4 * q^68 - 38 * q^69 + 40 * q^70 + 8 * q^71 + 20 * q^72 + 16 * q^73 - 22 * q^74 + 6 * q^75 - 8 * q^76 - 4 * q^78 + 4 * q^79 + 2 * q^80 + 28 * q^81 + 8 * q^82 + 12 * q^83 + 14 * q^84 + 48 * q^85 + 28 * q^86 + 42 * q^87 - 28 * q^89 - 28 * q^90 - 12 * q^91 + 12 * q^92 + 22 * q^93 + 6 * q^94 - 2 * q^95 - 22 * q^97 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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