LMFDB - Embedded newform 4598.2.a.ca.1.3

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			1.3
Root			$0.313242$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.16972 q^{3} +1.00000 q^{4} +1.79068 q^{5} -2.16972 q^{6} +4.71351 q^{7} +1.00000 q^{8} +1.70770 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.16972 q^{3} +1.00000 q^{4} +1.79068 q^{5} -2.16972 q^{6} +4.71351 q^{7} +1.00000 q^{8} +1.70770 q^{9} +1.79068 q^{10} -2.16972 q^{12} +6.85893 q^{13} +4.71351 q^{14} -3.88529 q^{15} +1.00000 q^{16} -0.0921150 q^{17} +1.70770 q^{18} -1.00000 q^{19} +1.79068 q^{20} -10.2270 q^{21} +4.91452 q^{23} -2.16972 q^{24} -1.79346 q^{25} +6.85893 q^{26} +2.80392 q^{27} +4.71351 q^{28} -3.20492 q^{29} -3.88529 q^{30} +7.12135 q^{31} +1.00000 q^{32} -0.0921150 q^{34} +8.44039 q^{35} +1.70770 q^{36} +5.91321 q^{37} -1.00000 q^{38} -14.8820 q^{39} +1.79068 q^{40} +3.60439 q^{41} -10.2270 q^{42} -7.91031 q^{43} +3.05796 q^{45} +4.91452 q^{46} +2.78042 q^{47} -2.16972 q^{48} +15.2172 q^{49} -1.79346 q^{50} +0.199864 q^{51} +6.85893 q^{52} -7.27887 q^{53} +2.80392 q^{54} +4.71351 q^{56} +2.16972 q^{57} -3.20492 q^{58} +8.16245 q^{59} -3.88529 q^{60} -12.1233 q^{61} +7.12135 q^{62} +8.04928 q^{63} +1.00000 q^{64} +12.2822 q^{65} -10.7693 q^{67} -0.0921150 q^{68} -10.6631 q^{69} +8.44039 q^{70} -10.7649 q^{71} +1.70770 q^{72} +5.87074 q^{73} +5.91321 q^{74} +3.89131 q^{75} -1.00000 q^{76} -14.8820 q^{78} -14.0112 q^{79} +1.79068 q^{80} -11.2069 q^{81} +3.60439 q^{82} -2.00717 q^{83} -10.2270 q^{84} -0.164949 q^{85} -7.91031 q^{86} +6.95380 q^{87} -9.13077 q^{89} +3.05796 q^{90} +32.3296 q^{91} +4.91452 q^{92} -15.4514 q^{93} +2.78042 q^{94} -1.79068 q^{95} -2.16972 q^{96} -12.2285 q^{97} +15.2172 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.16972	−1.25269	−0.626346	−	0.779546i	$-0.715450\pi$
$3$	−2.16972	−1.25269	−0.626346	+	0.779546i	$0.715450\pi$
$4$	1.00000	0.500000
$5$	1.79068	0.800817	0.400409	−	0.916337i	$-0.368868\pi$
$5$	1.79068	0.800817	0.400409	+	0.916337i	$0.368868\pi$
$6$	−2.16972	−0.885786
$7$	4.71351	1.78154	0.890769	−	0.454456i	$-0.150166\pi$
$7$	4.71351	1.78154	0.890769	+	0.454456i	$0.150166\pi$
$8$	1.00000	0.353553
$9$	1.70770	0.569235
$10$	1.79068	0.566263
$11$	0	0
$11$	0	0
$12$	−2.16972	−0.626346
$13$	6.85893	1.90232	0.951162	−	0.308692i	$-0.0998913\pi$
$13$	6.85893	1.90232	0.951162	+	0.308692i	$0.0998913\pi$
$14$	4.71351	1.25974
$15$	−3.88529	−1.00318
$16$	1.00000	0.250000
$17$	−0.0921150	−0.0223412	−0.0111706	−	0.999938i	$-0.503556\pi$
$17$	−0.0921150	−0.0223412	−0.0111706	+	0.999938i	$0.503556\pi$
$18$	1.70770	0.402510
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	1.79068	0.400409
$21$	−10.2270	−2.23172
$22$	0	0
$23$	4.91452	1.02475	0.512374	−	0.858763i	$-0.328766\pi$
$23$	4.91452	1.02475	0.512374	+	0.858763i	$0.328766\pi$
$24$	−2.16972	−0.442893
$25$	−1.79346	−0.358692
$26$	6.85893	1.34515
$27$	2.80392	0.539616
$28$	4.71351	0.890769
$29$	−3.20492	−0.595139	−0.297570	−	0.954700i	$-0.596176\pi$
$29$	−3.20492	−0.595139	−0.297570	+	0.954700i	$0.596176\pi$
$30$	−3.88529	−0.709353
$31$	7.12135	1.27903	0.639516	−	0.768777i	$-0.279135\pi$
$31$	7.12135	1.27903	0.639516	+	0.768777i	$0.279135\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−0.0921150	−0.0157976
$35$	8.44039	1.42669
$36$	1.70770	0.284617
$37$	5.91321	0.972126	0.486063	−	0.873924i	$-0.338433\pi$
$37$	5.91321	0.972126	0.486063	+	0.873924i	$0.338433\pi$
$38$	−1.00000	−0.162221
$39$	−14.8820	−2.38302
$40$	1.79068	0.283132
$41$	3.60439	0.562910	0.281455	−	0.959574i	$-0.409183\pi$
$41$	3.60439	0.562910	0.281455	+	0.959574i	$0.409183\pi$
$42$	−10.2270	−1.57806
$43$	−7.91031	−1.20631	−0.603156	−	0.797624i	$-0.706090\pi$
$43$	−7.91031	−1.20631	−0.603156	+	0.797624i	$0.706090\pi$
$44$	0	0
$45$	3.05796	0.455853
$46$	4.91452	0.724606
$47$	2.78042	0.405566	0.202783	−	0.979224i	$-0.435001\pi$
$47$	2.78042	0.405566	0.202783	+	0.979224i	$0.435001\pi$
$48$	−2.16972	−0.313173
$49$	15.2172	2.17388
$50$	−1.79346	−0.253634
$51$	0.199864	0.0279866
$52$	6.85893	0.951162
$53$	−7.27887	−0.999830	−0.499915	−	0.866075i	$-0.666635\pi$
$53$	−7.27887	−0.999830	−0.499915	+	0.866075i	$0.666635\pi$
$54$	2.80392	0.381566
$55$	0	0
$56$	4.71351	0.629869
$57$	2.16972	0.287387
$58$	−3.20492	−0.420827
$59$	8.16245	1.06266	0.531330	−	0.847165i	$-0.321692\pi$
$59$	8.16245	1.06266	0.531330	+	0.847165i	$0.321692\pi$
$60$	−3.88529	−0.501588
$61$	−12.1233	−1.55223	−0.776113	−	0.630593i	$-0.782812\pi$
$61$	−12.1233	−1.55223	−0.776113	+	0.630593i	$0.782812\pi$
$62$	7.12135	0.904413
$63$	8.04928	1.01411
$64$	1.00000	0.125000
$65$	12.2822	1.52341
$66$	0	0
$67$	−10.7693	−1.31568	−0.657841	−	0.753157i	$-0.728530\pi$
$67$	−10.7693	−1.31568	−0.657841	+	0.753157i	$0.728530\pi$
$68$	−0.0921150	−0.0111706
$69$	−10.6631	−1.28369
$70$	8.44039	1.00882
$71$	−10.7649	−1.27755	−0.638777	−	0.769392i	$-0.720560\pi$
$71$	−10.7649	−1.27755	−0.638777	+	0.769392i	$0.720560\pi$
$72$	1.70770	0.201255
$73$	5.87074	0.687118	0.343559	−	0.939131i	$-0.388367\pi$
$73$	5.87074	0.687118	0.343559	+	0.939131i	$0.388367\pi$
$74$	5.91321	0.687397
$75$	3.89131	0.449330
$76$	−1.00000	−0.114708
$77$	0	0
$78$	−14.8820	−1.68505
$79$	−14.0112	−1.57638	−0.788192	−	0.615429i	$-0.788983\pi$
$79$	−14.0112	−1.57638	−0.788192	+	0.615429i	$0.788983\pi$
$80$	1.79068	0.200204
$81$	−11.2069	−1.24521
$82$	3.60439	0.398038
$83$	−2.00717	−0.220316	−0.110158	−	0.993914i	$-0.535136\pi$
$83$	−2.00717	−0.220316	−0.110158	+	0.993914i	$0.535136\pi$
$84$	−10.2270	−1.11586
$85$	−0.164949	−0.0178912
$86$	−7.91031	−0.852991
$87$	6.95380	0.745526
$88$	0	0
$89$	−9.13077	−0.967860	−0.483930	−	0.875107i	$-0.660791\pi$
$89$	−9.13077	−0.967860	−0.483930	+	0.875107i	$0.660791\pi$
$90$	3.05796	0.322337
$91$	32.3296	3.38906
$92$	4.91452	0.512374
$93$	−15.4514	−1.60223
$94$	2.78042	0.286779
$95$	−1.79068	−0.183720
$96$	−2.16972	−0.221447
$97$	−12.2285	−1.24162	−0.620810	−	0.783961i	$-0.713196\pi$
$97$	−12.2285	−1.24162	−0.620810	+	0.783961i	$0.713196\pi$
$98$	15.2172	1.53716
$99$	0	0
$100$	−1.79346	−0.179346
$101$	8.27651	0.823543	0.411772	−	0.911287i	$-0.364910\pi$
$101$	8.27651	0.823543	0.411772	+	0.911287i	$0.364910\pi$
$102$	0.199864	0.0197895
$103$	5.44199	0.536215	0.268108	−	0.963389i	$-0.413602\pi$
$103$	5.44199	0.536215	0.268108	+	0.963389i	$0.413602\pi$
$104$	6.85893	0.672573
$105$	−18.3133	−1.78720
$106$	−7.27887	−0.706986
$107$	−2.04132	−0.197342	−0.0986711	−	0.995120i	$-0.531459\pi$
$107$	−2.04132	−0.197342	−0.0986711	+	0.995120i	$0.531459\pi$
$108$	2.80392	0.269808
$109$	3.04609	0.291762	0.145881	−	0.989302i	$-0.453398\pi$
$109$	3.04609	0.291762	0.145881	+	0.989302i	$0.453398\pi$
$110$	0	0
$111$	−12.8300	−1.21777
$112$	4.71351	0.445385
$113$	−8.44342	−0.794290	−0.397145	−	0.917756i	$-0.629999\pi$
$113$	−8.44342	−0.794290	−0.397145	+	0.917756i	$0.629999\pi$
$114$	2.16972	0.203213
$115$	8.80033	0.820635
$116$	−3.20492	−0.297570
$117$	11.7130	1.08287
$118$	8.16245	0.751414
$119$	−0.434185	−0.0398016
$120$	−3.88529	−0.354676
$121$	0	0
$122$	−12.1233	−1.09759
$123$	−7.82052	−0.705153
$124$	7.12135	0.639516
$125$	−12.1649	−1.08806
$126$	8.04928	0.717087
$127$	2.30183	0.204254	0.102127	−	0.994771i	$-0.467435\pi$
$127$	2.30183	0.204254	0.102127	+	0.994771i	$0.467435\pi$
$128$	1.00000	0.0883883
$129$	17.1632	1.51114
$130$	12.2822	1.07722
$131$	10.0556	0.878559	0.439279	−	0.898350i	$-0.355234\pi$
$131$	10.0556	0.878559	0.439279	+	0.898350i	$0.355234\pi$
$132$	0	0
$133$	−4.71351	−0.408713
$134$	−10.7693	−0.930328
$135$	5.02094	0.432133
$136$	−0.0921150	−0.00789879
$137$	6.88151	0.587927	0.293963	−	0.955817i	$-0.405026\pi$
$137$	6.88151	0.587927	0.293963	+	0.955817i	$0.405026\pi$
$138$	−10.6631	−0.907707
$139$	4.86849	0.412940	0.206470	−	0.978453i	$-0.433802\pi$
$139$	4.86849	0.412940	0.206470	+	0.978453i	$0.433802\pi$
$140$	8.44039	0.713343
$141$	−6.03275	−0.508049
$142$	−10.7649	−0.903368
$143$	0	0
$144$	1.70770	0.142309
$145$	−5.73900	−0.476598
$146$	5.87074	0.485866
$147$	−33.0170	−2.72320
$148$	5.91321	0.486063
$149$	−2.23956	−0.183472	−0.0917360	−	0.995783i	$-0.529242\pi$
$149$	−2.23956	−0.183472	−0.0917360	+	0.995783i	$0.529242\pi$
$150$	3.89131	0.317725
$151$	5.64230	0.459164	0.229582	−	0.973289i	$-0.426264\pi$
$151$	5.64230	0.459164	0.229582	+	0.973289i	$0.426264\pi$
$152$	−1.00000	−0.0811107
$153$	−0.157305	−0.0127174
$154$	0	0
$155$	12.7521	1.02427
$156$	−14.8820	−1.19151
$157$	−9.99933	−0.798033	−0.399017	−	0.916944i	$-0.630648\pi$
$157$	−9.99933	−0.798033	−0.399017	+	0.916944i	$0.630648\pi$
$158$	−14.0112	−1.11467
$159$	15.7931	1.25248
$160$	1.79068	0.141566
$161$	23.1646	1.82563
$162$	−11.2069	−0.880494
$163$	−0.409669	−0.0320878	−0.0160439	−	0.999871i	$-0.505107\pi$
$163$	−0.409669	−0.0320878	−0.0160439	+	0.999871i	$0.505107\pi$
$164$	3.60439	0.281455
$165$	0	0
$166$	−2.00717	−0.155787
$167$	−16.0215	−1.23978	−0.619890	−	0.784688i	$-0.712823\pi$
$167$	−16.0215	−1.23978	−0.619890	+	0.784688i	$0.712823\pi$
$168$	−10.2270	−0.789031
$169$	34.0449	2.61884
$170$	−0.164949	−0.0126510
$171$	−1.70770	−0.130591
$172$	−7.91031	−0.603156
$173$	−19.1119	−1.45305	−0.726525	−	0.687140i	$-0.758866\pi$
$173$	−19.1119	−1.45305	−0.726525	+	0.687140i	$0.758866\pi$
$174$	6.95380	0.527166
$175$	−8.45349	−0.639024
$176$	0	0
$177$	−17.7103	−1.33119
$178$	−9.13077	−0.684380
$179$	−13.1233	−0.980884	−0.490442	−	0.871474i	$-0.663165\pi$
$179$	−13.1233	−0.980884	−0.490442	+	0.871474i	$0.663165\pi$
$180$	3.05796	0.227927
$181$	13.2670	0.986131	0.493065	−	0.869992i	$-0.335876\pi$
$181$	13.2670	0.986131	0.493065	+	0.869992i	$0.335876\pi$
$182$	32.3296	2.39643
$183$	26.3042	1.94446
$184$	4.91452	0.362303
$185$	10.5887	0.778495
$186$	−15.4514	−1.13295
$187$	0	0
$188$	2.78042	0.202783
$189$	13.2163	0.961346
$190$	−1.79068	−0.129910
$191$	21.7784	1.57583	0.787913	−	0.615786i	$-0.211162\pi$
$191$	21.7784	1.57583	0.787913	+	0.615786i	$0.211162\pi$
$192$	−2.16972	−0.156586
$193$	1.51828	0.109288	0.0546441	−	0.998506i	$-0.482598\pi$
$193$	1.51828	0.109288	0.0546441	+	0.998506i	$0.482598\pi$
$194$	−12.2285	−0.877957
$195$	−26.6489	−1.90837
$196$	15.2172	1.08694
$197$	−12.8759	−0.917370	−0.458685	−	0.888599i	$-0.651679\pi$
$197$	−12.8759	−0.917370	−0.458685	+	0.888599i	$0.651679\pi$
$198$	0	0
$199$	10.2537	0.726864	0.363432	−	0.931621i	$-0.381605\pi$
$199$	10.2537	0.726864	0.363432	+	0.931621i	$0.381605\pi$
$200$	−1.79346	−0.126817
$201$	23.3665	1.64814
$202$	8.27651	0.582333
$203$	−15.1064	−1.06026
$204$	0.199864	0.0139933
$205$	6.45431	0.450788
$206$	5.44199	0.379161
$207$	8.39254	0.583322
$208$	6.85893	0.475581
$209$	0	0
$210$	−18.3133	−1.26374
$211$	17.0419	1.17321	0.586606	−	0.809872i	$-0.300464\pi$
$211$	17.0419	1.17321	0.586606	+	0.809872i	$0.300464\pi$
$212$	−7.27887	−0.499915
$213$	23.3568	1.60038
$214$	−2.04132	−0.139542
$215$	−14.1648	−0.966034
$216$	2.80392	0.190783
$217$	33.5666	2.27865
$218$	3.04609	0.206307
$219$	−12.7379	−0.860747
$220$	0	0
$221$	−0.631810	−0.0425001
$222$	−12.8300	−0.861096
$223$	−5.94172	−0.397887	−0.198943	−	0.980011i	$-0.563751\pi$
$223$	−5.94172	−0.397887	−0.198943	+	0.980011i	$0.563751\pi$
$224$	4.71351	0.314934
$225$	−3.06270	−0.204180
$226$	−8.44342	−0.561648
$227$	15.8465	1.05177	0.525885	−	0.850556i	$-0.323734\pi$
$227$	15.8465	1.05177	0.525885	+	0.850556i	$0.323734\pi$
$228$	2.16972	0.143694
$229$	9.11568	0.602381	0.301191	−	0.953564i	$-0.402616\pi$
$229$	9.11568	0.602381	0.301191	+	0.953564i	$0.402616\pi$
$230$	8.80033	0.580277
$231$	0	0
$232$	−3.20492	−0.210414
$233$	−6.54893	−0.429035	−0.214517	−	0.976720i	$-0.568818\pi$
$233$	−6.54893	−0.429035	−0.214517	+	0.976720i	$0.568818\pi$
$234$	11.7130	0.765704
$235$	4.97885	0.324784
$236$	8.16245	0.531330
$237$	30.4005	1.97472
$238$	−0.434185	−0.0281440
$239$	17.7292	1.14681	0.573403	−	0.819274i	$-0.305623\pi$
$239$	17.7292	1.14681	0.573403	+	0.819274i	$0.305623\pi$
$240$	−3.88529	−0.250794
$241$	8.44210	0.543804	0.271902	−	0.962325i	$-0.412347\pi$
$241$	8.44210	0.543804	0.271902	+	0.962325i	$0.412347\pi$
$242$	0	0
$243$	15.9040	1.02024
$244$	−12.1233	−0.776113
$245$	27.2491	1.74088
$246$	−7.82052	−0.498618
$247$	−6.85893	−0.436423
$248$	7.12135	0.452206
$249$	4.35501	0.275988
$250$	−12.1649	−0.769377
$251$	20.8841	1.31819	0.659096	−	0.752059i	$-0.270939\pi$
$251$	20.8841	1.31819	0.659096	+	0.752059i	$0.270939\pi$
$252$	8.04928	0.507057
$253$	0	0
$254$	2.30183	0.144430
$255$	0.357893	0.0224121
$256$	1.00000	0.0625000
$257$	−25.8644	−1.61338	−0.806689	−	0.590976i	$-0.798743\pi$
$257$	−25.8644	−1.61338	−0.806689	+	0.590976i	$0.798743\pi$
$258$	17.1632	1.06853
$259$	27.8720	1.73188
$260$	12.2822	0.761707
$261$	−5.47306	−0.338774
$262$	10.0556	0.621235
$263$	31.2182	1.92500	0.962498	−	0.271287i	$-0.0874494\pi$
$263$	31.2182	1.92500	0.962498	+	0.271287i	$0.0874494\pi$
$264$	0	0
$265$	−13.0341	−0.800681
$266$	−4.71351	−0.289004
$267$	19.8113	1.21243
$268$	−10.7693	−0.657841
$269$	−21.4948	−1.31056	−0.655281	−	0.755385i	$-0.727450\pi$
$269$	−21.4948	−1.31056	−0.655281	+	0.755385i	$0.727450\pi$
$270$	5.02094	0.305564
$271$	−3.54899	−0.215586	−0.107793	−	0.994173i	$-0.534378\pi$
$271$	−3.54899	−0.215586	−0.107793	+	0.994173i	$0.534378\pi$
$272$	−0.0921150	−0.00558529
$273$	−70.1463	−4.24545
$274$	6.88151	0.415727
$275$	0	0
$276$	−10.6631	−0.641846
$277$	16.2532	0.976562	0.488281	−	0.872686i	$-0.337624\pi$
$277$	16.2532	0.976562	0.488281	+	0.872686i	$0.337624\pi$
$278$	4.86849	0.291992
$279$	12.1612	0.728070
$280$	8.44039	0.504410
$281$	−4.48610	−0.267618	−0.133809	−	0.991007i	$-0.542721\pi$
$281$	−4.48610	−0.267618	−0.133809	+	0.991007i	$0.542721\pi$
$282$	−6.03275	−0.359245
$283$	17.6314	1.04808	0.524038	−	0.851695i	$-0.324425\pi$
$283$	17.6314	1.04808	0.524038	+	0.851695i	$0.324425\pi$
$284$	−10.7649	−0.638777
$285$	3.88529	0.230144
$286$	0	0
$287$	16.9893	1.00285
$288$	1.70770	0.100627
$289$	−16.9915	−0.999501
$290$	−5.73900	−0.337005
$291$	26.5325	1.55537
$292$	5.87074	0.343559
$293$	−15.3404	−0.896198	−0.448099	−	0.893984i	$-0.647899\pi$
$293$	−15.3404	−0.896198	−0.448099	+	0.893984i	$0.647899\pi$
$294$	−33.0170	−1.92559
$295$	14.6163	0.850997
$296$	5.91321	0.343698
$297$	0	0
$298$	−2.23956	−0.129734
$299$	33.7083	1.94940
$300$	3.89131	0.224665
$301$	−37.2853	−2.14909
$302$	5.64230	0.324678
$303$	−17.9577	−1.03165
$304$	−1.00000	−0.0573539
$305$	−21.7089	−1.24305
$306$	−0.157305	−0.00899254
$307$	−19.5442	−1.11545	−0.557724	−	0.830027i	$-0.688325\pi$
$307$	−19.5442	−1.11545	−0.557724	+	0.830027i	$0.688325\pi$
$308$	0	0
$309$	−11.8076	−0.671712
$310$	12.7521	0.724269
$311$	−8.61145	−0.488311	−0.244155	−	0.969736i	$-0.578511\pi$
$311$	−8.61145	−0.488311	−0.244155	+	0.969736i	$0.578511\pi$
$312$	−14.8820	−0.842526
$313$	−2.89185	−0.163457	−0.0817284	−	0.996655i	$-0.526044\pi$
$313$	−2.89185	−0.163457	−0.0817284	+	0.996655i	$0.526044\pi$
$314$	−9.99933	−0.564295
$315$	14.4137	0.812120
$316$	−14.0112	−0.788192
$317$	−25.6747	−1.44203	−0.721017	−	0.692917i	$-0.756325\pi$
$317$	−25.6747	−1.44203	−0.721017	+	0.692917i	$0.756325\pi$
$318$	15.7931	0.885635
$319$	0	0
$320$	1.79068	0.100102
$321$	4.42911	0.247209
$322$	23.1646	1.29091
$323$	0.0921150	0.00512541
$324$	−11.2069	−0.622603
$325$	−12.3012	−0.682349
$326$	−0.409669	−0.0226895
$327$	−6.60917	−0.365488
$328$	3.60439	0.199019
$329$	13.1055	0.722532
$330$	0	0
$331$	0.669770	0.0368139	0.0184069	−	0.999831i	$-0.494141\pi$
$331$	0.669770	0.0368139	0.0184069	+	0.999831i	$0.494141\pi$
$332$	−2.00717	−0.110158
$333$	10.0980	0.553368
$334$	−16.0215	−0.876657
$335$	−19.2844	−1.05362
$336$	−10.2270	−0.557929
$337$	28.8260	1.57025	0.785126	−	0.619336i	$-0.212598\pi$
$337$	28.8260	1.57025	0.785126	+	0.619336i	$0.212598\pi$
$338$	34.0449	1.85180
$339$	18.3199	0.995000
$340$	−0.164949	−0.00894559
$341$	0	0
$342$	−1.70770	−0.0923421
$343$	38.7316	2.09131
$344$	−7.91031	−0.426495
$345$	−19.0943	−1.02800
$346$	−19.1119	−1.02746
$347$	−21.1062	−1.13304	−0.566520	−	0.824048i	$-0.691711\pi$
$347$	−21.1062	−1.13304	−0.566520	+	0.824048i	$0.691711\pi$
$348$	6.95380	0.372763
$349$	−6.85687	−0.367040	−0.183520	−	0.983016i	$-0.558749\pi$
$349$	−6.85687	−0.367040	−0.183520	+	0.983016i	$0.558749\pi$
$350$	−8.45349	−0.451858
$351$	19.2319	1.02652
$352$	0	0
$353$	18.5941	0.989666	0.494833	−	0.868988i	$-0.335229\pi$
$353$	18.5941	0.989666	0.494833	+	0.868988i	$0.335229\pi$
$354$	−17.7103	−0.941290
$355$	−19.2765	−1.02309
$356$	−9.13077	−0.483930
$357$	0.942061	0.0498592
$358$	−13.1233	−0.693590
$359$	−30.3200	−1.60023	−0.800115	−	0.599846i	$-0.795228\pi$
$359$	−30.3200	−1.60023	−0.800115	+	0.599846i	$0.795228\pi$
$360$	3.05796	0.161168
$361$	1.00000	0.0526316
$362$	13.2670	0.697300
$363$	0	0
$364$	32.3296	1.69453
$365$	10.5126	0.550256
$366$	26.3042	1.37494
$367$	14.2904	0.745952	0.372976	−	0.927841i	$-0.378337\pi$
$367$	14.2904	0.745952	0.372976	+	0.927841i	$0.378337\pi$
$368$	4.91452	0.256187
$369$	6.15523	0.320428
$370$	10.5887	0.550479
$371$	−34.3090	−1.78123
$372$	−15.4514	−0.801117
$373$	23.0852	1.19530	0.597652	−	0.801755i	$-0.296100\pi$
$373$	23.0852	1.19530	0.597652	+	0.801755i	$0.296100\pi$
$374$	0	0
$375$	26.3945	1.36301
$376$	2.78042	0.143389
$377$	−21.9823	−1.13215
$378$	13.2163	0.679774
$379$	−18.1805	−0.933869	−0.466935	−	0.884292i	$-0.654642\pi$
$379$	−18.1805	−0.933869	−0.466935	+	0.884292i	$0.654642\pi$
$380$	−1.79068	−0.0918600
$381$	−4.99434	−0.255868
$382$	21.7784	1.11428
$383$	28.2689	1.44447	0.722236	−	0.691647i	$-0.243114\pi$
$383$	28.2689	1.44447	0.722236	+	0.691647i	$0.243114\pi$
$384$	−2.16972	−0.110723
$385$	0	0
$386$	1.51828	0.0772785
$387$	−13.5085	−0.686674
$388$	−12.2285	−0.620810
$389$	−29.3433	−1.48777	−0.743883	−	0.668310i	$-0.767018\pi$
$389$	−29.3433	−1.48777	−0.743883	+	0.668310i	$0.767018\pi$
$390$	−26.6489	−1.34942
$391$	−0.452701	−0.0228941
$392$	15.2172	0.768582
$393$	−21.8178	−1.10056
$394$	−12.8759	−0.648678
$395$	−25.0896	−1.26240
$396$	0	0
$397$	2.08500	0.104643	0.0523216	−	0.998630i	$-0.483338\pi$
$397$	2.08500	0.104643	0.0523216	+	0.998630i	$0.483338\pi$
$398$	10.2537	0.513970
$399$	10.2270	0.511991
$400$	−1.79346	−0.0896730
$401$	11.5326	0.575912	0.287956	−	0.957644i	$-0.407024\pi$
$401$	11.5326	0.575912	0.287956	+	0.957644i	$0.407024\pi$
$402$	23.3665	1.16541
$403$	48.8448	2.43313
$404$	8.27651	0.411772
$405$	−20.0679	−0.997183
$406$	−15.1064	−0.749720
$407$	0	0
$408$	0.199864	0.00989475
$409$	−0.732331	−0.0362114	−0.0181057	−	0.999836i	$-0.505764\pi$
$409$	−0.732331	−0.0362114	−0.0181057	+	0.999836i	$0.505764\pi$
$410$	6.45431	0.318755
$411$	−14.9310	−0.736491
$412$	5.44199	0.268108
$413$	38.4738	1.89317
$414$	8.39254	0.412471
$415$	−3.59421	−0.176433
$416$	6.85893	0.336287
$417$	−10.5633	−0.517286
$418$	0	0
$419$	13.2156	0.645623	0.322812	−	0.946463i	$-0.395372\pi$
$419$	13.2156	0.645623	0.322812	+	0.946463i	$0.395372\pi$
$420$	−18.3133	−0.893599
$421$	10.4159	0.507641	0.253821	−	0.967251i	$-0.418313\pi$
$421$	10.4159	0.507641	0.253821	+	0.967251i	$0.418313\pi$
$422$	17.0419	0.829586
$423$	4.74814	0.230862
$424$	−7.27887	−0.353493
$425$	0.165205	0.00801360
$426$	23.3568	1.13164
$427$	−57.1432	−2.76535
$428$	−2.04132	−0.0986711
$429$	0	0
$430$	−14.1648	−0.683089
$431$	−11.2971	−0.544162	−0.272081	−	0.962274i	$-0.587712\pi$
$431$	−11.2971	−0.544162	−0.272081	+	0.962274i	$0.587712\pi$
$432$	2.80392	0.134904
$433$	−22.2278	−1.06820	−0.534099	−	0.845422i	$-0.679349\pi$
$433$	−22.2278	−1.06820	−0.534099	+	0.845422i	$0.679349\pi$
$434$	33.5666	1.61125
$435$	12.4520	0.597030
$436$	3.04609	0.145881
$437$	−4.91452	−0.235093
$438$	−12.7379	−0.608640
$439$	25.2534	1.20528	0.602641	−	0.798013i	$-0.294115\pi$
$439$	25.2534	1.20528	0.602641	+	0.798013i	$0.294115\pi$
$440$	0	0
$441$	25.9864	1.23745
$442$	−0.631810	−0.0300521
$443$	−4.17037	−0.198140	−0.0990701	−	0.995080i	$-0.531587\pi$
$443$	−4.17037	−0.198140	−0.0990701	+	0.995080i	$0.531587\pi$
$444$	−12.8300	−0.608887
$445$	−16.3503	−0.775078
$446$	−5.94172	−0.281348
$447$	4.85923	0.229834
$448$	4.71351	0.222692
$449$	−8.57443	−0.404652	−0.202326	−	0.979318i	$-0.564850\pi$
$449$	−8.57443	−0.404652	−0.202326	+	0.979318i	$0.564850\pi$
$450$	−3.06270	−0.144377
$451$	0	0
$452$	−8.44342	−0.397145
$453$	−12.2422	−0.575190
$454$	15.8465	0.743713
$455$	57.8920	2.71402
$456$	2.16972	0.101607
$457$	−12.0184	−0.562196	−0.281098	−	0.959679i	$-0.590699\pi$
$457$	−12.0184	−0.562196	−0.281098	+	0.959679i	$0.590699\pi$
$458$	9.11568	0.425948
$459$	−0.258283	−0.0120556
$460$	8.80033	0.410318
$461$	3.00764	0.140080	0.0700398	−	0.997544i	$-0.477687\pi$
$461$	3.00764	0.140080	0.0700398	+	0.997544i	$0.477687\pi$
$462$	0	0
$463$	20.2752	0.942270	0.471135	−	0.882061i	$-0.343844\pi$
$463$	20.2752	0.942270	0.471135	+	0.882061i	$0.343844\pi$
$464$	−3.20492	−0.148785
$465$	−27.6685	−1.28310
$466$	−6.54893	−0.303373
$467$	−21.4276	−0.991551	−0.495775	−	0.868451i	$-0.665116\pi$
$467$	−21.4276	−0.991551	−0.495775	+	0.868451i	$0.665116\pi$
$468$	11.7130	0.541435
$469$	−50.7613	−2.34394
$470$	4.97885	0.229657
$471$	21.6958	0.999689
$472$	8.16245	0.375707
$473$	0	0
$474$	30.4005	1.39634
$475$	1.79346	0.0822896
$476$	−0.434185	−0.0199008
$477$	−12.4302	−0.569138
$478$	17.7292	0.810914
$479$	27.0080	1.23403	0.617014	−	0.786953i	$-0.288342\pi$
$479$	27.0080	1.23403	0.617014	+	0.786953i	$0.288342\pi$
$480$	−3.88529	−0.177338
$481$	40.5583	1.84930
$482$	8.44210	0.384527
$483$	−50.2608	−2.28695
$484$	0	0
$485$	−21.8974	−0.994310
$486$	15.9040	0.721421
$487$	−2.39969	−0.108741	−0.0543703	−	0.998521i	$-0.517315\pi$
$487$	−2.39969	−0.108741	−0.0543703	+	0.998521i	$0.517315\pi$
$488$	−12.1233	−0.548795
$489$	0.888869	0.0401960
$490$	27.2491	1.23099
$491$	−13.2476	−0.597855	−0.298927	−	0.954276i	$-0.596629\pi$
$491$	−13.2476	−0.597855	−0.298927	+	0.954276i	$0.596629\pi$
$492$	−7.82052	−0.352576
$493$	0.295221	0.0132961
$494$	−6.85893	−0.308598
$495$	0	0
$496$	7.12135	0.319758
$497$	−50.7403	−2.27601
$498$	4.35501	0.195153
$499$	29.5161	1.32132	0.660662	−	0.750684i	$-0.270276\pi$
$499$	29.5161	1.32132	0.660662	+	0.750684i	$0.270276\pi$
$500$	−12.1649	−0.544032
$501$	34.7622	1.55306
$502$	20.8841	0.932102
$503$	29.9767	1.33660	0.668298	−	0.743894i	$-0.267023\pi$
$503$	29.9767	1.33660	0.668298	+	0.743894i	$0.267023\pi$
$504$	8.04928	0.358543
$505$	14.8206	0.659508
$506$	0	0
$507$	−73.8680	−3.28059
$508$	2.30183	0.102127
$509$	−26.9725	−1.19553	−0.597767	−	0.801670i	$-0.703945\pi$
$509$	−26.9725	−1.19553	−0.597767	+	0.801670i	$0.703945\pi$
$510$	0.357893	0.0158478
$511$	27.6718	1.22413
$512$	1.00000	0.0441942
$513$	−2.80392	−0.123796
$514$	−25.8644	−1.14083
$515$	9.74487	0.429410
$516$	17.1632	0.755568
$517$	0	0
$518$	27.8720	1.22462
$519$	41.4675	1.82022
$520$	12.2822	0.538608
$521$	−33.9575	−1.48771	−0.743853	−	0.668343i	$-0.767004\pi$
$521$	−33.9575	−1.48771	−0.743853	+	0.668343i	$0.767004\pi$
$522$	−5.47306	−0.239549
$523$	−37.1435	−1.62417	−0.812086	−	0.583537i	$-0.801668\pi$
$523$	−37.1435	−1.62417	−0.812086	+	0.583537i	$0.801668\pi$
$524$	10.0556	0.439279
$525$	18.3417	0.800499
$526$	31.2182	1.36118
$527$	−0.655983	−0.0285751
$528$	0	0
$529$	1.15247	0.0501074
$530$	−13.0341	−0.566167
$531$	13.9391	0.604903
$532$	−4.71351	−0.204356
$533$	24.7222	1.07084
$534$	19.8113	0.857317
$535$	−3.65536	−0.158035
$536$	−10.7693	−0.465164
$537$	28.4740	1.22874
$538$	−21.4948	−0.926707
$539$	0	0
$540$	5.02094	0.216067
$541$	7.29113	0.313470	0.156735	−	0.987641i	$-0.449903\pi$
$541$	7.29113	0.313470	0.156735	+	0.987641i	$0.449903\pi$
$542$	−3.54899	−0.152442
$543$	−28.7858	−1.23532
$544$	−0.0921150	−0.00394940
$545$	5.45457	0.233648
$546$	−70.1463	−3.00199
$547$	23.2315	0.993305	0.496653	−	0.867949i	$-0.334562\pi$
$547$	23.2315	0.993305	0.496653	+	0.867949i	$0.334562\pi$
$548$	6.88151	0.293963
$549$	−20.7030	−0.883582
$550$	0	0
$551$	3.20492	0.136534
$552$	−10.6631	−0.453854
$553$	−66.0420	−2.80839
$554$	16.2532	0.690534
$555$	−22.9745	−0.975214
$556$	4.86849	0.206470
$557$	−16.4141	−0.695488	−0.347744	−	0.937590i	$-0.613052\pi$
$557$	−16.4141	−0.695488	−0.347744	+	0.937590i	$0.613052\pi$
$558$	12.1612	0.514823
$559$	−54.2562	−2.29479
$560$	8.44039	0.356672
$561$	0	0
$562$	−4.48610	−0.189235
$563$	−18.2878	−0.770738	−0.385369	−	0.922763i	$-0.625926\pi$
$563$	−18.2878	−0.770738	−0.385369	+	0.922763i	$0.625926\pi$
$564$	−6.03275	−0.254025
$565$	−15.1195	−0.636081
$566$	17.6314	0.741102
$567$	−52.8236	−2.21838
$568$	−10.7649	−0.451684
$569$	−21.6509	−0.907653	−0.453827	−	0.891090i	$-0.649941\pi$
$569$	−21.6509	−0.907653	−0.453827	+	0.891090i	$0.649941\pi$
$570$	3.88529	0.162737
$571$	19.4212	0.812751	0.406375	−	0.913706i	$-0.366793\pi$
$571$	19.4212	0.812751	0.406375	+	0.913706i	$0.366793\pi$
$572$	0	0
$573$	−47.2530	−1.97402
$574$	16.9893	0.709120
$575$	−8.81399	−0.367569
$576$	1.70770	0.0711544
$577$	36.7379	1.52942	0.764710	−	0.644374i	$-0.222882\pi$
$577$	36.7379	1.52942	0.764710	+	0.644374i	$0.222882\pi$
$578$	−16.9915	−0.706754
$579$	−3.29425	−0.136904
$580$	−5.73900	−0.238299
$581$	−9.46083	−0.392501
$582$	26.5325	1.09981
$583$	0	0
$584$	5.87074	0.242933
$585$	20.9743	0.867180
$586$	−15.3404	−0.633708
$587$	−1.43056	−0.0590455	−0.0295227	−	0.999564i	$-0.509399\pi$
$587$	−1.43056	−0.0590455	−0.0295227	+	0.999564i	$0.509399\pi$
$588$	−33.0170	−1.36160
$589$	−7.12135	−0.293430
$590$	14.6163	0.601745
$591$	27.9372	1.14918
$592$	5.91321	0.243031
$593$	−43.4676	−1.78500	−0.892499	−	0.451049i	$-0.851050\pi$
$593$	−43.4676	−1.78500	−0.892499	+	0.451049i	$0.851050\pi$
$594$	0	0
$595$	−0.777486	−0.0318738
$596$	−2.23956	−0.0917360
$597$	−22.2477	−0.910536
$598$	33.7083	1.37844
$599$	−44.8745	−1.83352	−0.916760	−	0.399438i	$-0.869205\pi$
$599$	−44.8745	−1.83352	−0.916760	+	0.399438i	$0.869205\pi$
$600$	3.89131	0.158862
$601$	3.54973	0.144796	0.0723982	−	0.997376i	$-0.476935\pi$
$601$	3.54973	0.144796	0.0723982	+	0.997376i	$0.476935\pi$
$602$	−37.2853	−1.51964
$603$	−18.3908	−0.748932
$604$	5.64230	0.229582
$605$	0	0
$606$	−17.9577	−0.729484
$607$	30.0909	1.22135	0.610677	−	0.791880i	$-0.290898\pi$
$607$	30.0909	1.22135	0.610677	+	0.791880i	$0.290898\pi$
$608$	−1.00000	−0.0405554
$609$	32.7768	1.32818
$610$	−21.7089	−0.878969
$611$	19.0707	0.771518
$612$	−0.157305	−0.00635869
$613$	39.3882	1.59088	0.795438	−	0.606035i	$-0.207241\pi$
$613$	39.3882	1.59088	0.795438	+	0.606035i	$0.207241\pi$
$614$	−19.5442	−0.788740
$615$	−14.0041	−0.564698
$616$	0	0
$617$	−2.17245	−0.0874597	−0.0437299	−	0.999043i	$-0.513924\pi$
$617$	−2.17245	−0.0874597	−0.0437299	+	0.999043i	$0.513924\pi$
$618$	−11.8076	−0.474972
$619$	−33.8487	−1.36049	−0.680247	−	0.732983i	$-0.738128\pi$
$619$	−33.8487	−1.36049	−0.680247	+	0.732983i	$0.738128\pi$
$620$	12.7521	0.512136
$621$	13.7799	0.552970
$622$	−8.61145	−0.345288
$623$	−43.0379	−1.72428
$624$	−14.8820	−0.595756
$625$	−12.8162	−0.512648
$626$	−2.89185	−0.115581
$627$	0	0
$628$	−9.99933	−0.399017
$629$	−0.544695	−0.0217184
$630$	14.4137	0.574255
$631$	−8.31449	−0.330995	−0.165497	−	0.986210i	$-0.552923\pi$
$631$	−8.31449	−0.330995	−0.165497	+	0.986210i	$0.552923\pi$
$632$	−14.0112	−0.557336
$633$	−36.9762	−1.46967
$634$	−25.6747	−1.01967
$635$	4.12184	0.163570
$636$	15.7931	0.626239
$637$	104.373	4.13542
$638$	0	0
$639$	−18.3832	−0.727229
$640$	1.79068	0.0707829
$641$	20.4422	0.807420	0.403710	−	0.914887i	$-0.367721\pi$
$641$	20.4422	0.807420	0.403710	+	0.914887i	$0.367721\pi$
$642$	4.42911	0.174803
$643$	21.3255	0.840997	0.420498	−	0.907293i	$-0.361855\pi$
$643$	21.3255	0.840997	0.420498	+	0.907293i	$0.361855\pi$
$644$	23.1646	0.912814
$645$	30.7338	1.21014
$646$	0.0921150	0.00362422
$647$	−7.25276	−0.285135	−0.142568	−	0.989785i	$-0.545536\pi$
$647$	−7.25276	−0.285135	−0.142568	+	0.989785i	$0.545536\pi$
$648$	−11.2069	−0.440247
$649$	0	0
$650$	−12.3012	−0.482493
$651$	−72.8302	−2.85444
$652$	−0.409669	−0.0160439
$653$	21.6393	0.846813	0.423406	−	0.905940i	$-0.360834\pi$
$653$	21.6393	0.846813	0.423406	+	0.905940i	$0.360834\pi$
$654$	−6.60917	−0.258439
$655$	18.0063	0.703565
$656$	3.60439	0.140728
$657$	10.0255	0.391132
$658$	13.1055	0.510907
$659$	−13.1333	−0.511602	−0.255801	−	0.966729i	$-0.582339\pi$
$659$	−13.1333	−0.511602	−0.255801	+	0.966729i	$0.582339\pi$
$660$	0	0
$661$	9.99561	0.388784	0.194392	−	0.980924i	$-0.437727\pi$
$661$	9.99561	0.388784	0.194392	+	0.980924i	$0.437727\pi$
$662$	0.669770	0.0260314
$663$	1.37085	0.0532395
$664$	−2.00717	−0.0778934
$665$	−8.44039	−0.327304
$666$	10.0980	0.391290
$667$	−15.7506	−0.609868
$668$	−16.0215	−0.619890
$669$	12.8919	0.498429
$670$	−19.2844	−0.745022
$671$	0	0
$672$	−10.2270	−0.394516
$673$	38.8948	1.49929	0.749643	−	0.661843i	$-0.230225\pi$
$673$	38.8948	1.49929	0.749643	+	0.661843i	$0.230225\pi$
$674$	28.8260	1.11034
$675$	−5.02873	−0.193556
$676$	34.0449	1.30942
$677$	8.87662	0.341156	0.170578	−	0.985344i	$-0.445436\pi$
$677$	8.87662	0.341156	0.170578	+	0.985344i	$0.445436\pi$
$678$	18.3199	0.703572
$679$	−57.6393	−2.21199
$680$	−0.164949	−0.00632549
$681$	−34.3826	−1.31754
$682$	0	0
$683$	15.0170	0.574610	0.287305	−	0.957839i	$-0.407241\pi$
$683$	15.0170	0.574610	0.287305	+	0.957839i	$0.407241\pi$
$684$	−1.70770	−0.0652957
$685$	12.3226	0.470822
$686$	38.7316	1.47878
$687$	−19.7785	−0.754597
$688$	−7.91031	−0.301578
$689$	−49.9252	−1.90200
$690$	−19.0943	−0.726908
$691$	−14.3240	−0.544909	−0.272454	−	0.962169i	$-0.587835\pi$
$691$	−14.3240	−0.544909	−0.272454	+	0.962169i	$0.587835\pi$
$692$	−19.1119	−0.726525
$693$	0	0
$694$	−21.1062	−0.801180
$695$	8.71791	0.330689
$696$	6.95380	0.263583
$697$	−0.332018	−0.0125761
$698$	−6.85687	−0.259536
$699$	14.2094	0.537448
$700$	−8.45349	−0.319512
$701$	20.3007	0.766746	0.383373	−	0.923594i	$-0.374762\pi$
$701$	20.3007	0.766746	0.383373	+	0.923594i	$0.374762\pi$
$702$	19.2319	0.725862
$703$	−5.91321	−0.223021
$704$	0	0
$705$	−10.8027	−0.406854
$706$	18.5941	0.699800
$707$	39.0114	1.46717
$708$	−17.7103	−0.665593
$709$	5.24688	0.197051	0.0985254	−	0.995135i	$-0.468587\pi$
$709$	5.24688	0.197051	0.0985254	+	0.995135i	$0.468587\pi$
$710$	−19.2765	−0.723432
$711$	−23.9270	−0.897333
$712$	−9.13077	−0.342190
$713$	34.9980	1.31069
$714$	0.942061	0.0352558
$715$	0	0
$716$	−13.1233	−0.490442
$717$	−38.4674	−1.43659
$718$	−30.3200	−1.13153
$719$	16.9522	0.632210	0.316105	−	0.948724i	$-0.397625\pi$
$719$	16.9522	0.632210	0.316105	+	0.948724i	$0.397625\pi$
$720$	3.05796	0.113963
$721$	25.6509	0.955288
$722$	1.00000	0.0372161
$723$	−18.3170	−0.681218
$724$	13.2670	0.493065
$725$	5.74790	0.213472
$726$	0	0
$727$	−27.7361	−1.02867	−0.514337	−	0.857588i	$-0.671962\pi$
$727$	−27.7361	−1.02867	−0.514337	+	0.857588i	$0.671962\pi$
$728$	32.3296	1.19821
$729$	−0.886776	−0.0328436
$730$	10.5126	0.389090
$731$	0.728658	0.0269504
$732$	26.3042	0.972230
$733$	−30.2108	−1.11586	−0.557932	−	0.829887i	$-0.688405\pi$
$733$	−30.2108	−1.11586	−0.557932	+	0.829887i	$0.688405\pi$
$734$	14.2904	0.527468
$735$	−59.1230	−2.18078
$736$	4.91452	0.181151
$737$	0	0
$738$	6.15523	0.226577
$739$	−24.3407	−0.895388	−0.447694	−	0.894187i	$-0.647755\pi$
$739$	−24.3407	−0.895388	−0.447694	+	0.894187i	$0.647755\pi$
$740$	10.5887	0.389247
$741$	14.8820	0.546703
$742$	−34.3090	−1.25952
$743$	38.4189	1.40945	0.704726	−	0.709479i	$-0.251070\pi$
$743$	38.4189	1.40945	0.704726	+	0.709479i	$0.251070\pi$
$744$	−15.4514	−0.566475
$745$	−4.01034	−0.146927
$746$	23.0852	0.845208
$747$	−3.42766	−0.125412
$748$	0	0
$749$	−9.62180	−0.351573
$750$	26.3945	0.963792
$751$	−16.0680	−0.586329	−0.293165	−	0.956062i	$-0.594708\pi$
$751$	−16.0680	−0.586329	−0.293165	+	0.956062i	$0.594708\pi$
$752$	2.78042	0.101392
$753$	−45.3127	−1.65129
$754$	−21.9823	−0.800549
$755$	10.1036	0.367706
$756$	13.2163	0.480673
$757$	−25.3469	−0.921249	−0.460624	−	0.887595i	$-0.652374\pi$
$757$	−25.3469	−0.921249	−0.460624	+	0.887595i	$0.652374\pi$
$758$	−18.1805	−0.660345
$759$	0	0
$760$	−1.79068	−0.0649548
$761$	−32.6283	−1.18277	−0.591387	−	0.806388i	$-0.701420\pi$
$761$	−32.6283	−1.18277	−0.591387	+	0.806388i	$0.701420\pi$
$762$	−4.99434	−0.180926
$763$	14.3578	0.519786
$764$	21.7784	0.787913
$765$	−0.281684	−0.0101843
$766$	28.2689	1.02140
$767$	55.9856	2.02152
$768$	−2.16972	−0.0782932
$769$	−2.15033	−0.0775430	−0.0387715	−	0.999248i	$-0.512344\pi$
$769$	−2.15033	−0.0775430	−0.0387715	+	0.999248i	$0.512344\pi$
$770$	0	0
$771$	56.1186	2.02106
$772$	1.51828	0.0546441
$773$	−14.9822	−0.538873	−0.269437	−	0.963018i	$-0.586837\pi$
$773$	−14.9822	−0.538873	−0.269437	+	0.963018i	$0.586837\pi$
$774$	−13.5085	−0.485552
$775$	−12.7719	−0.458779
$776$	−12.2285	−0.438979
$777$	−60.4745	−2.16951
$778$	−29.3433	−1.05201
$779$	−3.60439	−0.129140
$780$	−26.6489	−0.954183
$781$	0	0
$782$	−0.452701	−0.0161885
$783$	−8.98636	−0.321146
$784$	15.2172	0.543470
$785$	−17.9056	−0.639079
$786$	−21.8178	−0.778216
$787$	−26.7872	−0.954862	−0.477431	−	0.878669i	$-0.658432\pi$
$787$	−26.7872	−0.954862	−0.477431	+	0.878669i	$0.658432\pi$
$788$	−12.8759	−0.458685
$789$	−67.7349	−2.41143
$790$	−25.0896	−0.892649
$791$	−39.7981	−1.41506
$792$	0	0
$793$	−83.1527	−2.95284
$794$	2.08500	0.0739939
$795$	28.2805	1.00301
$796$	10.2537	0.363432
$797$	−13.1749	−0.466680	−0.233340	−	0.972395i	$-0.574966\pi$
$797$	−13.1749	−0.466680	−0.233340	+	0.972395i	$0.574966\pi$
$798$	10.2270	0.362032
$799$	−0.256118	−0.00906082
$800$	−1.79346	−0.0634084
$801$	−15.5927	−0.550939
$802$	11.5326	0.407231
$803$	0	0
$804$	23.3665	0.824072
$805$	41.4804	1.46199
$806$	48.8448	1.72049
$807$	46.6378	1.64173
$808$	8.27651	0.291167
$809$	9.38383	0.329918	0.164959	−	0.986300i	$-0.447251\pi$
$809$	9.38383	0.329918	0.164959	+	0.986300i	$0.447251\pi$
$810$	−20.0679	−0.705115
$811$	−48.8891	−1.71673	−0.858365	−	0.513040i	$-0.828519\pi$
$811$	−48.8891	−1.71673	−0.858365	+	0.513040i	$0.828519\pi$
$812$	−15.1064	−0.530132
$813$	7.70033	0.270062
$814$	0	0
$815$	−0.733587	−0.0256964
$816$	0.199864	0.00699664
$817$	7.91031	0.276747
$818$	−0.732331	−0.0256053
$819$	55.2094	1.92917
$820$	6.45431	0.225394
$821$	26.7466	0.933464	0.466732	−	0.884399i	$-0.345431\pi$
$821$	26.7466	0.933464	0.466732	+	0.884399i	$0.345431\pi$
$822$	−14.9310	−0.520778
$823$	−35.7683	−1.24680	−0.623401	−	0.781902i	$-0.714250\pi$
$823$	−35.7683	−1.24680	−0.623401	+	0.781902i	$0.714250\pi$
$824$	5.44199	0.189581
$825$	0	0
$826$	38.4738	1.33867
$827$	0.0391128	0.00136009	0.000680043	−	1.00000i	$-0.499784\pi$
$827$	0.0391128	0.00136009	0.000680043		1.00000i	$0.499784\pi$
$828$	8.39254	0.291661
$829$	19.3214	0.671061	0.335530	−	0.942029i	$-0.391084\pi$
$829$	19.3214	0.671061	0.335530	+	0.942029i	$0.391084\pi$
$830$	−3.59421	−0.124757
$831$	−35.2650	−1.22333
$832$	6.85893	0.237791
$833$	−1.40173	−0.0485670
$834$	−10.5633	−0.365776
$835$	−28.6894	−0.992837
$836$	0	0
$837$	19.9677	0.690186
$838$	13.2156	0.456524
$839$	−26.0734	−0.900153	−0.450076	−	0.892990i	$-0.648603\pi$
$839$	−26.0734	−0.900153	−0.450076	+	0.892990i	$0.648603\pi$
$840$	−18.3133	−0.631870
$841$	−18.7285	−0.645809
$842$	10.4159	0.358957
$843$	9.73360	0.335243
$844$	17.0419	0.586606
$845$	60.9635	2.09721
$846$	4.74814	0.163244
$847$	0	0
$848$	−7.27887	−0.249957
$849$	−38.2552	−1.31292
$850$	0.165205	0.00566647
$851$	29.0606	0.996183
$852$	23.3568	0.800191
$853$	−5.34676	−0.183070	−0.0915348	−	0.995802i	$-0.529177\pi$
$853$	−5.34676	−0.183070	−0.0915348	+	0.995802i	$0.529177\pi$
$854$	−57.1432	−1.95540
$855$	−3.05796	−0.104580
$856$	−2.04132	−0.0697710
$857$	34.3568	1.17361	0.586803	−	0.809730i	$-0.300386\pi$
$857$	34.3568	1.17361	0.586803	+	0.809730i	$0.300386\pi$
$858$	0	0
$859$	18.8263	0.642346	0.321173	−	0.947021i	$-0.395923\pi$
$859$	18.8263	0.642346	0.321173	+	0.947021i	$0.395923\pi$
$860$	−14.1648	−0.483017
$861$	−36.8621	−1.25626
$862$	−11.2971	−0.384781
$863$	−28.2448	−0.961465	−0.480733	−	0.876867i	$-0.659629\pi$
$863$	−28.2448	−0.961465	−0.480733	+	0.876867i	$0.659629\pi$
$864$	2.80392	0.0953914
$865$	−34.2233	−1.16363
$866$	−22.2278	−0.755330
$867$	36.8669	1.25207
$868$	33.5666	1.13932
$869$	0	0
$870$	12.4520	0.422164
$871$	−73.8660	−2.50285
$872$	3.04609	0.103154
$873$	−20.8827	−0.706773
$874$	−4.91452	−0.166236
$875$	−57.3395	−1.93843
$876$	−12.7379	−0.430374
$877$	−10.8785	−0.367342	−0.183671	−	0.982988i	$-0.558798\pi$
$877$	−10.8785	−0.367342	−0.183671	+	0.982988i	$0.558798\pi$
$878$	25.2534	0.852263
$879$	33.2845	1.12266
$880$	0	0
$881$	29.2426	0.985208	0.492604	−	0.870254i	$-0.336045\pi$
$881$	29.2426	0.985208	0.492604	+	0.870254i	$0.336045\pi$
$882$	25.9864	0.875008
$883$	−1.27176	−0.0427982	−0.0213991	−	0.999771i	$-0.506812\pi$
$883$	−1.27176	−0.0427982	−0.0213991	+	0.999771i	$0.506812\pi$
$884$	−0.631810	−0.0212501
$885$	−31.7134	−1.06604
$886$	−4.17037	−0.140106
$887$	15.3988	0.517040	0.258520	−	0.966006i	$-0.416765\pi$
$887$	15.3988	0.517040	0.258520	+	0.966006i	$0.416765\pi$
$888$	−12.8300	−0.430548
$889$	10.8497	0.363887
$890$	−16.3503	−0.548063
$891$	0	0
$892$	−5.94172	−0.198943
$893$	−2.78042	−0.0930432
$894$	4.85923	0.162517
$895$	−23.4997	−0.785509
$896$	4.71351	0.157467
$897$	−73.1377	−2.44200
$898$	−8.57443	−0.286132
$899$	−22.8234	−0.761203
$900$	−3.06270	−0.102090
$901$	0.670493	0.0223374
$902$	0	0
$903$	80.8989	2.69215
$904$	−8.44342	−0.280824
$905$	23.7570	0.789710
$906$	−12.2422	−0.406721
$907$	−15.6666	−0.520199	−0.260100	−	0.965582i	$-0.583755\pi$
$907$	−15.6666	−0.520199	−0.260100	+	0.965582i	$0.583755\pi$
$908$	15.8465	0.525885
$909$	14.1338	0.468790
$910$	57.8920	1.91910
$911$	28.9989	0.960777	0.480388	−	0.877056i	$-0.340496\pi$
$911$	28.9989	0.960777	0.480388	+	0.877056i	$0.340496\pi$
$912$	2.16972	0.0718468
$913$	0	0
$914$	−12.0184	−0.397533
$915$	47.1024	1.55716
$916$	9.11568	0.301191
$917$	47.3970	1.56519
$918$	−0.258283	−0.00852462
$919$	2.61788	0.0863559	0.0431780	−	0.999067i	$-0.486252\pi$
$919$	2.61788	0.0863559	0.0431780	+	0.999067i	$0.486252\pi$
$920$	8.80033	0.290138
$921$	42.4056	1.39731
$922$	3.00764	0.0990513
$923$	−73.8355	−2.43032
$924$	0	0
$925$	−10.6051	−0.348694
$926$	20.2752	0.666285
$927$	9.29331	0.305232
$928$	−3.20492	−0.105207
$929$	−47.3803	−1.55450	−0.777248	−	0.629194i	$-0.783385\pi$
$929$	−47.3803	−1.55450	−0.777248	+	0.629194i	$0.783385\pi$
$930$	−27.6685	−0.907286
$931$	−15.2172	−0.498722
$932$	−6.54893	−0.214517
$933$	18.6845	0.611702
$934$	−21.4276	−0.701132
$935$	0	0
$936$	11.7130	0.382852
$937$	4.77951	0.156140	0.0780699	−	0.996948i	$-0.475124\pi$
$937$	4.77951	0.156140	0.0780699	+	0.996948i	$0.475124\pi$
$938$	−50.7613	−1.65741
$939$	6.27451	0.204761
$940$	4.97885	0.162392
$941$	26.9885	0.879800	0.439900	−	0.898047i	$-0.355014\pi$
$941$	26.9885	0.879800	0.439900	+	0.898047i	$0.355014\pi$
$942$	21.6958	0.706887
$943$	17.7138	0.576841
$944$	8.16245	0.265665
$945$	23.6662	0.769862
$946$	0	0
$947$	−7.94684	−0.258238	−0.129119	−	0.991629i	$-0.541215\pi$
$947$	−7.94684	−0.258238	−0.129119	+	0.991629i	$0.541215\pi$
$948$	30.4005	0.987362
$949$	40.2670	1.30712
$950$	1.79346	0.0581875
$951$	55.7070	1.80642
$952$	−0.434185	−0.0140720
$953$	−26.6307	−0.862653	−0.431326	−	0.902196i	$-0.641954\pi$
$953$	−26.6307	−0.862653	−0.431326	+	0.902196i	$0.641954\pi$
$954$	−12.4302	−0.402441
$955$	38.9981	1.26195
$956$	17.7292	0.573403
$957$	0	0
$958$	27.0080	0.872589
$959$	32.4360	1.04741
$960$	−3.88529	−0.125397
$961$	19.7137	0.635925
$962$	40.5583	1.30765
$963$	−3.48598	−0.112334
$964$	8.44210	0.271902
$965$	2.71876	0.0875199
$966$	−50.2608	−1.61712
$967$	−37.0849	−1.19257	−0.596284	−	0.802773i	$-0.703357\pi$
$967$	−37.0849	−1.19257	−0.596284	+	0.802773i	$0.703357\pi$
$968$	0	0
$969$	−0.199864	−0.00642056
$970$	−21.8974	−0.703083
$971$	5.36878	0.172292	0.0861462	−	0.996283i	$-0.472545\pi$
$971$	5.36878	0.172292	0.0861462	+	0.996283i	$0.472545\pi$
$972$	15.9040	0.510122
$973$	22.9476	0.735668
$974$	−2.39969	−0.0768912
$975$	26.6902	0.854772
$976$	−12.1233	−0.388057
$977$	−8.63945	−0.276401	−0.138200	−	0.990404i	$-0.544132\pi$
$977$	−8.63945	−0.276401	−0.138200	+	0.990404i	$0.544132\pi$
$978$	0.888869	0.0284229
$979$	0	0
$980$	27.2491	0.870440
$981$	5.20182	0.166081
$982$	−13.2476	−0.422747
$983$	−32.7340	−1.04405	−0.522026	−	0.852930i	$-0.674824\pi$
$983$	−32.7340	−1.04405	−0.522026	+	0.852930i	$0.674824\pi$
$984$	−7.82052	−0.249309
$985$	−23.0566	−0.734645
$986$	0.295221	0.00940177
$987$	−28.4354	−0.905109
$988$	−6.85893	−0.218212
$989$	−38.8753	−1.23616
$990$	0	0
$991$	33.6052	1.06750	0.533752	−	0.845641i	$-0.320782\pi$
$991$	33.6052	1.06750	0.533752	+	0.845641i	$0.320782\pi$
$992$	7.12135	0.226103
$993$	−1.45322	−0.0461164
$994$	−50.7403	−1.60938
$995$	18.3611	0.582085
$996$	4.35501	0.137994
$997$	−9.43019	−0.298657	−0.149329	−	0.988788i	$-0.547711\pi$
$997$	−9.43019	−0.298657	−0.149329	+	0.988788i	$0.547711\pi$
$998$	29.5161	0.934317
$999$	16.5802	0.524574

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.ca.1.3		8
11.5	even	5		418.2.f.f.267.2	yes	16
11.9	even	5		418.2.f.f.191.2	✓	16
11.10	odd	2		4598.2.a.bx.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.f.191.2	✓	16	11.9	even	5
418.2.f.f.267.2	yes	16	11.5	even	5
4598.2.a.bx.1.3		8	11.10	odd	2
4598.2.a.ca.1.3		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.16972 q^{3} +1.00000 q^{4} +1.79068 q^{5} -2.16972 q^{6} +4.71351 q^{7} +1.00000 q^{8} +1.70770 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.16972 q^{3} +1.00000 q^{4} +1.79068 q^{5} -2.16972 q^{6} +4.71351 q^{7} +1.00000 q^{8} +1.70770 q^{9} +1.79068 q^{10} -2.16972 q^{12} +6.85893 q^{13} +4.71351 q^{14} -3.88529 q^{15} +1.00000 q^{16} -0.0921150 q^{17} +1.70770 q^{18} -1.00000 q^{19} +1.79068 q^{20} -10.2270 q^{21} +4.91452 q^{23} -2.16972 q^{24} -1.79346 q^{25} +6.85893 q^{26} +2.80392 q^{27} +4.71351 q^{28} -3.20492 q^{29} -3.88529 q^{30} +7.12135 q^{31} +1.00000 q^{32} -0.0921150 q^{34} +8.44039 q^{35} +1.70770 q^{36} +5.91321 q^{37} -1.00000 q^{38} -14.8820 q^{39} +1.79068 q^{40} +3.60439 q^{41} -10.2270 q^{42} -7.91031 q^{43} +3.05796 q^{45} +4.91452 q^{46} +2.78042 q^{47} -2.16972 q^{48} +15.2172 q^{49} -1.79346 q^{50} +0.199864 q^{51} +6.85893 q^{52} -7.27887 q^{53} +2.80392 q^{54} +4.71351 q^{56} +2.16972 q^{57} -3.20492 q^{58} +8.16245 q^{59} -3.88529 q^{60} -12.1233 q^{61} +7.12135 q^{62} +8.04928 q^{63} +1.00000 q^{64} +12.2822 q^{65} -10.7693 q^{67} -0.0921150 q^{68} -10.6631 q^{69} +8.44039 q^{70} -10.7649 q^{71} +1.70770 q^{72} +5.87074 q^{73} +5.91321 q^{74} +3.89131 q^{75} -1.00000 q^{76} -14.8820 q^{78} -14.0112 q^{79} +1.79068 q^{80} -11.2069 q^{81} +3.60439 q^{82} -2.00717 q^{83} -10.2270 q^{84} -0.164949 q^{85} -7.91031 q^{86} +6.95380 q^{87} -9.13077 q^{89} +3.05796 q^{90} +32.3296 q^{91} +4.91452 q^{92} -15.4514 q^{93} +2.78042 q^{94} -1.79068 q^{95} -2.16972 q^{96} -12.2285 q^{97} +15.2172 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{4} + 2 q^{5} + 8 q^{7} + 8 q^{8} + 20 q^{9}+O(q^{10}) \) 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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