LMFDB - Embedded newform 1859.2.a.s.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,2,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, 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("1859.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1859.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:	$14.8441897358$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.603243 q^{2} -0.154529 q^{3} -1.63610 q^{4} -4.17643 q^{5} -0.0932187 q^{6} -2.73997 q^{7} -2.19345 q^{8} -2.97612 q^{9} +O(q^{10})$	\(q+0.603243 q^{2} -0.154529 q^{3} -1.63610 q^{4} -4.17643 q^{5} -0.0932187 q^{6} -2.73997 q^{7} -2.19345 q^{8} -2.97612 q^{9} -2.51940 q^{10} -1.00000 q^{11} +0.252825 q^{12} -1.65287 q^{14} +0.645380 q^{15} +1.94901 q^{16} -2.78947 q^{17} -1.79532 q^{18} -8.62913 q^{19} +6.83305 q^{20} +0.423406 q^{21} -0.603243 q^{22} -5.00464 q^{23} +0.338952 q^{24} +12.4426 q^{25} +0.923485 q^{27} +4.48287 q^{28} +5.70078 q^{29} +0.389321 q^{30} -6.49432 q^{31} +5.56263 q^{32} +0.154529 q^{33} -1.68273 q^{34} +11.4433 q^{35} +4.86923 q^{36} +3.15244 q^{37} -5.20546 q^{38} +9.16079 q^{40} -1.15203 q^{41} +0.255417 q^{42} -6.42524 q^{43} +1.63610 q^{44} +12.4296 q^{45} -3.01901 q^{46} +0.354093 q^{47} -0.301179 q^{48} +0.507462 q^{49} +7.50588 q^{50} +0.431055 q^{51} -11.4273 q^{53} +0.557086 q^{54} +4.17643 q^{55} +6.01000 q^{56} +1.33345 q^{57} +3.43895 q^{58} +3.55166 q^{59} -1.05591 q^{60} +9.99485 q^{61} -3.91765 q^{62} +8.15450 q^{63} -0.542409 q^{64} +0.0932187 q^{66} -8.44511 q^{67} +4.56385 q^{68} +0.773363 q^{69} +6.90310 q^{70} -5.99422 q^{71} +6.52797 q^{72} +4.94834 q^{73} +1.90169 q^{74} -1.92274 q^{75} +14.1181 q^{76} +2.73997 q^{77} -7.84360 q^{79} -8.13991 q^{80} +8.78566 q^{81} -0.694952 q^{82} -2.14414 q^{83} -0.692734 q^{84} +11.6500 q^{85} -3.87598 q^{86} -0.880937 q^{87} +2.19345 q^{88} -6.72386 q^{89} +7.49804 q^{90} +8.18808 q^{92} +1.00356 q^{93} +0.213604 q^{94} +36.0389 q^{95} -0.859589 q^{96} +10.5674 q^{97} +0.306123 q^{98} +2.97612 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9}+O(q^{10}) $ 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9	\( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9} + 18 q^{10} - 21 q^{11} + 23 q^{12} + 20 q^{14} - 16 q^{15} + 50 q^{16} + 16 q^{17} - 3 q^{18} + 11 q^{19} - 24 q^{20} + 5 q^{21} - 9 q^{23} + 54 q^{24} + 36 q^{25} + 11 q^{28} + 28 q^{29} + 21 q^{30} - 15 q^{31} + 61 q^{32} - 6 q^{33} + 6 q^{34} - 3 q^{35} + 45 q^{36} + 12 q^{37} + q^{38} + 55 q^{40} + 4 q^{41} - 34 q^{42} + 17 q^{43} - 32 q^{44} - 9 q^{45} - 11 q^{46} - 36 q^{47} + 24 q^{48} + 72 q^{49} + 9 q^{50} + 2 q^{51} + 19 q^{53} - q^{54} + 7 q^{55} + 44 q^{56} + 4 q^{57} + 33 q^{58} - 54 q^{59} - 64 q^{60} + 98 q^{61} - 29 q^{62} + 81 q^{63} + 63 q^{64} - 19 q^{66} - 25 q^{67} + 4 q^{68} + 89 q^{69} - 65 q^{70} - 37 q^{71} - 55 q^{72} - 8 q^{73} - 11 q^{74} + 24 q^{75} - 13 q^{76} + q^{77} + 24 q^{79} - 26 q^{80} + 81 q^{81} + 26 q^{82} + 34 q^{83} + 103 q^{84} + 11 q^{85} - 30 q^{86} + 32 q^{87} - 3 q^{88} - 6 q^{89} + 47 q^{90} - 80 q^{92} - 41 q^{93} + 40 q^{94} + 20 q^{95} + 98 q^{96} + 5 q^{98} - 33 q^{99}+O(q^{100}) \) 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9 + 18 * q^10 - 21 * q^11 + 23 * q^12 + 20 * q^14 - 16 * q^15 + 50 * q^16 + 16 * q^17 - 3 * q^18 + 11 * q^19 - 24 * q^20 + 5 * q^21 - 9 * q^23 + 54 * q^24 + 36 * q^25 + 11 * q^28 + 28 * q^29 + 21 * q^30 - 15 * q^31 + 61 * q^32 - 6 * q^33 + 6 * q^34 - 3 * q^35 + 45 * q^36 + 12 * q^37 + q^38 + 55 * q^40 + 4 * q^41 - 34 * q^42 + 17 * q^43 - 32 * q^44 - 9 * q^45 - 11 * q^46 - 36 * q^47 + 24 * q^48 + 72 * q^49 + 9 * q^50 + 2 * q^51 + 19 * q^53 - q^54 + 7 * q^55 + 44 * q^56 + 4 * q^57 + 33 * q^58 - 54 * q^59 - 64 * q^60 + 98 * q^61 - 29 * q^62 + 81 * q^63 + 63 * q^64 - 19 * q^66 - 25 * q^67 + 4 * q^68 + 89 * q^69 - 65 * q^70 - 37 * q^71 - 55 * q^72 - 8 * q^73 - 11 * q^74 + 24 * q^75 - 13 * q^76 + q^77 + 24 * q^79 - 26 * q^80 + 81 * q^81 + 26 * q^82 + 34 * q^83 + 103 * q^84 + 11 * q^85 - 30 * q^86 + 32 * q^87 - 3 * q^88 - 6 * q^89 + 47 * q^90 - 80 * q^92 - 41 * q^93 + 40 * q^94 + 20 * q^95 + 98 * q^96 + 5 * q^98 - 33 * q^99

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 $

$2$	0.603243	0.426557	0.213279	−	0.976991i	$-0.431586\pi$
$2$	0.603243	0.426557	0.213279	+	0.976991i	$0.431586\pi$
$3$	−0.154529	−0.0892175	−0.0446087	−	0.999005i	$-0.514204\pi$
$3$	−0.154529	−0.0892175	−0.0446087	+	0.999005i	$0.514204\pi$
$4$	−1.63610	−0.818049
$5$	−4.17643	−1.86776	−0.933878	−	0.357592i	$-0.883598\pi$
$5$	−4.17643	−1.86776	−0.933878	+	0.357592i	$0.883598\pi$
$6$	−0.0932187	−0.0380564
$7$	−2.73997	−1.03561	−0.517807	−	0.855498i	$-0.673251\pi$
$7$	−2.73997	−1.03561	−0.517807	+	0.855498i	$0.673251\pi$
$8$	−2.19345	−0.775502
$9$	−2.97612	−0.992040
$10$	−2.51940	−0.796705
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.252825	0.0729843
$13$	0	0
$13$	0	0
$14$	−1.65287	−0.441748
$15$	0.645380	0.166636
$16$	1.94901	0.487253
$17$	−2.78947	−0.676546	−0.338273	−	0.941048i	$-0.609843\pi$
$17$	−2.78947	−0.676546	−0.338273	+	0.941048i	$0.609843\pi$
$18$	−1.79532	−0.423162
$19$	−8.62913	−1.97966	−0.989829	−	0.142263i	$-0.954562\pi$
$19$	−8.62913	−1.97966	−0.989829	+	0.142263i	$0.954562\pi$
$20$	6.83305	1.52792
$21$	0.423406	0.0923948
$22$	−0.603243	−0.128612
$23$	−5.00464	−1.04354	−0.521769	−	0.853087i	$-0.674728\pi$
$23$	−5.00464	−1.04354	−0.521769	+	0.853087i	$0.674728\pi$
$24$	0.338952	0.0691883
$25$	12.4426	2.48851
$26$	0	0
$27$	0.923485	0.177725
$28$	4.48287	0.847182
$29$	5.70078	1.05861	0.529304	−	0.848432i	$-0.322453\pi$
$29$	5.70078	1.05861	0.529304	+	0.848432i	$0.322453\pi$
$30$	0.389321	0.0710800
$31$	−6.49432	−1.16641	−0.583207	−	0.812323i	$-0.698203\pi$
$31$	−6.49432	−1.16641	−0.583207	+	0.812323i	$0.698203\pi$
$32$	5.56263	0.983343
$33$	0.154529	0.0269001
$34$	−1.68273	−0.288586
$35$	11.4433	1.93427
$36$	4.86923	0.811538
$37$	3.15244	0.518258	0.259129	−	0.965843i	$-0.416565\pi$
$37$	3.15244	0.518258	0.259129	+	0.965843i	$0.416565\pi$
$38$	−5.20546	−0.844437
$39$	0	0
$40$	9.16079	1.44845
$41$	−1.15203	−0.179916	−0.0899582	−	0.995946i	$-0.528673\pi$
$41$	−1.15203	−0.179916	−0.0899582	+	0.995946i	$0.528673\pi$
$42$	0.255417	0.0394117
$43$	−6.42524	−0.979839	−0.489920	−	0.871768i	$-0.662974\pi$
$43$	−6.42524	−0.979839	−0.489920	+	0.871768i	$0.662974\pi$
$44$	1.63610	0.246651
$45$	12.4296	1.85289
$46$	−3.01901	−0.445129
$47$	0.354093	0.0516498	0.0258249	−	0.999666i	$-0.491779\pi$
$47$	0.354093	0.0516498	0.0258249	+	0.999666i	$0.491779\pi$
$48$	−0.301179	−0.0434715
$49$	0.507462	0.0724945
$50$	7.50588	1.06149
$51$	0.431055	0.0603598
$52$	0	0
$53$	−11.4273	−1.56966	−0.784829	−	0.619712i	$-0.787249\pi$
$53$	−11.4273	−1.56966	−0.784829	+	0.619712i	$0.787249\pi$
$54$	0.557086	0.0758098
$55$	4.17643	0.563149
$56$	6.01000	0.803120
$57$	1.33345	0.176620
$58$	3.43895	0.451557
$59$	3.55166	0.462387	0.231193	−	0.972908i	$-0.425737\pi$
$59$	3.55166	0.462387	0.231193	+	0.972908i	$0.425737\pi$
$60$	−1.05591	−0.136317
$61$	9.99485	1.27971	0.639855	−	0.768496i	$-0.278995\pi$
$61$	9.99485	1.27971	0.639855	+	0.768496i	$0.278995\pi$
$62$	−3.91765	−0.497543
$63$	8.15450	1.02737
$64$	−0.542409	−0.0678011
$65$	0	0
$66$	0.0932187	0.0114744
$67$	−8.44511	−1.03173	−0.515867	−	0.856668i	$-0.672530\pi$
$67$	−8.44511	−1.03173	−0.515867	+	0.856668i	$0.672530\pi$
$68$	4.56385	0.553448
$69$	0.773363	0.0931019
$70$	6.90310	0.825078
$71$	−5.99422	−0.711383	−0.355692	−	0.934603i	$-0.615755\pi$
$71$	−5.99422	−0.711383	−0.355692	+	0.934603i	$0.615755\pi$
$72$	6.52797	0.769329
$73$	4.94834	0.579160	0.289580	−	0.957154i	$-0.406484\pi$
$73$	4.94834	0.579160	0.289580	+	0.957154i	$0.406484\pi$
$74$	1.90169	0.221067
$75$	−1.92274	−0.222019
$76$	14.1181	1.61946
$77$	2.73997	0.312249
$78$	0	0
$79$	−7.84360	−0.882474	−0.441237	−	0.897391i	$-0.645460\pi$
$79$	−7.84360	−0.882474	−0.441237	+	0.897391i	$0.645460\pi$
$80$	−8.13991	−0.910070
$81$	8.78566	0.976184
$82$	−0.694952	−0.0767447
$83$	−2.14414	−0.235350	−0.117675	−	0.993052i	$-0.537544\pi$
$83$	−2.14414	−0.235350	−0.117675	+	0.993052i	$0.537544\pi$
$84$	−0.692734	−0.0755835
$85$	11.6500	1.26362
$86$	−3.87598	−0.417957
$87$	−0.880937	−0.0944463
$88$	2.19345	0.233823
$89$	−6.72386	−0.712727	−0.356364	−	0.934347i	$-0.615984\pi$
$89$	−6.72386	−0.712727	−0.356364	+	0.934347i	$0.615984\pi$
$90$	7.49804	0.790363
$91$	0	0
$92$	8.18808	0.853666
$93$	1.00356	0.104065
$94$	0.213604	0.0220316
$95$	36.0389	3.69752
$96$	−0.859589	−0.0877314
$97$	10.5674	1.07296	0.536481	−	0.843913i	$-0.319753\pi$
$97$	10.5674	1.07296	0.536481	+	0.843913i	$0.319753\pi$
$98$	0.306123	0.0309231
$99$	2.97612	0.299111
$100$	−20.3572	−2.03572
$101$	5.02737	0.500242	0.250121	−	0.968215i	$-0.419530\pi$
$101$	5.02737	0.500242	0.250121	+	0.968215i	$0.419530\pi$
$102$	0.260031	0.0257469
$103$	1.17627	0.115902	0.0579509	−	0.998319i	$-0.481543\pi$
$103$	1.17627	0.115902	0.0579509	+	0.998319i	$0.481543\pi$
$104$	0	0
$105$	−1.76833	−0.172571
$106$	−6.89343	−0.669549
$107$	−5.53162	−0.534762	−0.267381	−	0.963591i	$-0.586158\pi$
$107$	−5.53162	−0.534762	−0.267381	+	0.963591i	$0.586158\pi$
$108$	−1.51091	−0.145388
$109$	−17.4224	−1.66877	−0.834384	−	0.551184i	$-0.814176\pi$
$109$	−17.4224	−1.66877	−0.834384	+	0.551184i	$0.814176\pi$
$110$	2.51940	0.240215
$111$	−0.487144	−0.0462377
$112$	−5.34025	−0.504606
$113$	−2.29189	−0.215603	−0.107802	−	0.994172i	$-0.534381\pi$
$113$	−2.29189	−0.215603	−0.107802	+	0.994172i	$0.534381\pi$
$114$	0.804396	0.0753386
$115$	20.9015	1.94908
$116$	−9.32703	−0.865993
$117$	0	0
$118$	2.14251	0.197234
$119$	7.64308	0.700640
$120$	−1.41561	−0.129227
$121$	1.00000	0.0909091
$122$	6.02932	0.545869
$123$	0.178022	0.0160517
$124$	10.6253	0.954185
$125$	−31.0833	−2.78017
$126$	4.91914	0.438232
$127$	−3.76454	−0.334049	−0.167024	−	0.985953i	$-0.553416\pi$
$127$	−3.76454	−0.334049	−0.167024	+	0.985953i	$0.553416\pi$
$128$	−11.4525	−1.01226
$129$	0.992887	0.0874188
$130$	0	0
$131$	−4.42684	−0.386775	−0.193387	−	0.981122i	$-0.561947\pi$
$131$	−4.42684	−0.386775	−0.193387	+	0.981122i	$0.561947\pi$
$132$	−0.252825	−0.0220056
$133$	23.6436	2.05016
$134$	−5.09446	−0.440094
$135$	−3.85687	−0.331947
$136$	6.11857	0.524663
$137$	−11.9412	−1.02020	−0.510102	−	0.860114i	$-0.670392\pi$
$137$	−11.9412	−1.02020	−0.510102	+	0.860114i	$0.670392\pi$
$138$	0.466526	0.0397133
$139$	2.06266	0.174952	0.0874762	−	0.996167i	$-0.472120\pi$
$139$	2.06266	0.174952	0.0874762	+	0.996167i	$0.472120\pi$
$140$	−18.7224	−1.58233
$141$	−0.0547178	−0.00460807
$142$	−3.61597	−0.303446
$143$	0	0
$144$	−5.80050	−0.483375
$145$	−23.8089	−1.97722
$146$	2.98505	0.247045
$147$	−0.0784177	−0.00646778
$148$	−5.15770	−0.423960
$149$	−19.5995	−1.60566	−0.802828	−	0.596211i	$-0.796672\pi$
$149$	−19.5995	−1.60566	−0.802828	+	0.596211i	$0.796672\pi$
$150$	−1.15988	−0.0947037
$151$	5.91806	0.481605	0.240802	−	0.970574i	$-0.422589\pi$
$151$	5.91806	0.481605	0.240802	+	0.970574i	$0.422589\pi$
$152$	18.9276	1.53523
$153$	8.30181	0.671161
$154$	1.65287	0.133192
$155$	27.1231	2.17858
$156$	0	0
$157$	17.5345	1.39940	0.699702	−	0.714435i	$-0.253316\pi$
$157$	17.5345	1.39940	0.699702	+	0.714435i	$0.253316\pi$
$158$	−4.73160	−0.376426
$159$	1.76585	0.140041
$160$	−23.2319	−1.83664
$161$	13.7126	1.08070
$162$	5.29989	0.416398
$163$	−15.9728	−1.25108	−0.625542	−	0.780191i	$-0.715122\pi$
$163$	−15.9728	−1.25108	−0.625542	+	0.780191i	$0.715122\pi$
$164$	1.88483	0.147180
$165$	−0.645380	−0.0502428
$166$	−1.29344	−0.100390
$167$	−23.3488	−1.80678	−0.903391	−	0.428818i	$-0.858930\pi$
$167$	−23.3488	−1.80678	−0.903391	+	0.428818i	$0.858930\pi$
$168$	−0.928720	−0.0716523
$169$	0	0
$170$	7.02780	0.539008
$171$	25.6813	1.96390
$172$	10.5123	0.801556
$173$	−12.7004	−0.965593	−0.482797	−	0.875733i	$-0.660379\pi$
$173$	−12.7004	−0.965593	−0.482797	+	0.875733i	$0.660379\pi$
$174$	−0.531419	−0.0402868
$175$	−34.0923	−2.57713
$176$	−1.94901	−0.146912
$177$	−0.548835	−0.0412530
$178$	−4.05612	−0.304019
$179$	−6.78692	−0.507278	−0.253639	−	0.967299i	$-0.581628\pi$
$179$	−6.78692	−0.507278	−0.253639	+	0.967299i	$0.581628\pi$
$180$	−20.3360	−1.51575
$181$	−13.5531	−1.00739	−0.503696	−	0.863881i	$-0.668027\pi$
$181$	−13.5531	−1.00739	−0.503696	+	0.863881i	$0.668027\pi$
$182$	0	0
$183$	−1.54450	−0.114172
$184$	10.9774	0.809266
$185$	−13.1659	−0.967979
$186$	0.605392	0.0443895
$187$	2.78947	0.203986
$188$	−0.579332	−0.0422521
$189$	−2.53033	−0.184054
$190$	21.7402	1.57720
$191$	−5.48548	−0.396915	−0.198458	−	0.980109i	$-0.563593\pi$
$191$	−5.48548	−0.396915	−0.198458	+	0.980109i	$0.563593\pi$
$192$	0.0838180	0.00604904
$193$	5.20633	0.374760	0.187380	−	0.982287i	$-0.440000\pi$
$193$	5.20633	0.374760	0.187380	+	0.982287i	$0.440000\pi$
$194$	6.37474	0.457679
$195$	0	0
$196$	−0.830257	−0.0593041
$197$	18.8540	1.34329	0.671645	−	0.740873i	$-0.265588\pi$
$197$	18.8540	1.34329	0.671645	+	0.740873i	$0.265588\pi$
$198$	1.79532	0.127588
$199$	18.8110	1.33347	0.666737	−	0.745293i	$-0.267690\pi$
$199$	18.8110	1.33347	0.666737	+	0.745293i	$0.267690\pi$
$200$	−27.2921	−1.92984
$201$	1.30502	0.0920488
$202$	3.03273	0.213382
$203$	−15.6200	−1.09631
$204$	−0.705248	−0.0493772
$205$	4.81136	0.336040
$206$	0.709579	0.0494387
$207$	14.8944	1.03523
$208$	0	0
$209$	8.62913	0.596889
$210$	−1.06673	−0.0736114
$211$	−5.38555	−0.370757	−0.185378	−	0.982667i	$-0.559351\pi$
$211$	−5.38555	−0.370757	−0.185378	+	0.982667i	$0.559351\pi$
$212$	18.6962	1.28406
$213$	0.926282	0.0634678
$214$	−3.33691	−0.228107
$215$	26.8345	1.83010
$216$	−2.02562	−0.137826
$217$	17.7943	1.20795
$218$	−10.5100	−0.711825
$219$	−0.764664	−0.0516712
$220$	−6.83305	−0.460684
$221$	0	0
$222$	−0.293866	−0.0197230
$223$	8.25185	0.552585	0.276292	−	0.961074i	$-0.410894\pi$
$223$	8.25185	0.552585	0.276292	+	0.961074i	$0.410894\pi$
$224$	−15.2415	−1.01836
$225$	−37.0305	−2.46870
$226$	−1.38257	−0.0919671
$227$	15.4059	1.02252	0.511261	−	0.859425i	$-0.329178\pi$
$227$	15.4059	1.02252	0.511261	+	0.859425i	$0.329178\pi$
$228$	−2.18166	−0.144484
$229$	−0.144341	−0.00953833	−0.00476917	−	0.999989i	$-0.501518\pi$
$229$	−0.144341	−0.00953833	−0.00476917	+	0.999989i	$0.501518\pi$
$230$	12.6087	0.831392
$231$	−0.423406	−0.0278581
$232$	−12.5044	−0.820952
$233$	−23.1843	−1.51885	−0.759426	−	0.650593i	$-0.774520\pi$
$233$	−23.1843	−1.51885	−0.759426	+	0.650593i	$0.774520\pi$
$234$	0	0
$235$	−1.47885	−0.0964693
$236$	−5.81087	−0.378255
$237$	1.21207	0.0787321
$238$	4.61064	0.298863
$239$	10.4269	0.674461	0.337231	−	0.941422i	$-0.390510\pi$
$239$	10.4269	0.674461	0.337231	+	0.941422i	$0.390510\pi$
$240$	1.25785	0.0811941
$241$	−18.3629	−1.18286	−0.591431	−	0.806356i	$-0.701437\pi$
$241$	−18.3629	−1.18286	−0.591431	+	0.806356i	$0.701437\pi$
$242$	0.603243	0.0387779
$243$	−4.12810	−0.264818
$244$	−16.3526	−1.04687
$245$	−2.11938	−0.135402
$246$	0.107390	0.00684697
$247$	0	0
$248$	14.2450	0.904557
$249$	0.331333	0.0209973
$250$	−18.7508	−1.18590
$251$	−0.622813	−0.0393116	−0.0196558	−	0.999807i	$-0.506257\pi$
$251$	−0.622813	−0.0393116	−0.0196558	+	0.999807i	$0.506257\pi$
$252$	−13.3416	−0.840439
$253$	5.00464	0.314639
$254$	−2.27093	−0.142491
$255$	−1.80027	−0.112737
$256$	−5.82380	−0.363987
$257$	15.5574	0.970445	0.485222	−	0.874391i	$-0.338739\pi$
$257$	15.5574	0.970445	0.485222	+	0.874391i	$0.338739\pi$
$258$	0.598952	0.0372891
$259$	−8.63761	−0.536715
$260$	0	0
$261$	−16.9662	−1.05018
$262$	−2.67046	−0.164982
$263$	−5.12614	−0.316091	−0.158046	−	0.987432i	$-0.550519\pi$
$263$	−5.12614	−0.316091	−0.158046	+	0.987432i	$0.550519\pi$
$264$	−0.338952	−0.0208611
$265$	47.7252	2.93174
$266$	14.2628	0.874510
$267$	1.03903	0.0635877
$268$	13.8170	0.844010
$269$	9.02443	0.550229	0.275115	−	0.961411i	$-0.411284\pi$
$269$	9.02443	0.550229	0.275115	+	0.961411i	$0.411284\pi$
$270$	−2.32663	−0.141594
$271$	−2.54851	−0.154811	−0.0774054	−	0.997000i	$-0.524664\pi$
$271$	−2.54851	−0.154811	−0.0774054	+	0.997000i	$0.524664\pi$
$272$	−5.43672	−0.329649
$273$	0	0
$274$	−7.20343	−0.435175
$275$	−12.4426	−0.750314
$276$	−1.26530	−0.0761619
$277$	−9.42522	−0.566307	−0.283153	−	0.959075i	$-0.591381\pi$
$277$	−9.42522	−0.566307	−0.283153	+	0.959075i	$0.591381\pi$
$278$	1.24428	0.0746272
$279$	19.3279	1.15713
$280$	−25.1003	−1.50003
$281$	−11.0792	−0.660930	−0.330465	−	0.943818i	$-0.607206\pi$
$281$	−11.0792	−0.660930	−0.330465	+	0.943818i	$0.607206\pi$
$282$	−0.0330081	−0.00196560
$283$	−10.7080	−0.636522	−0.318261	−	0.948003i	$-0.603099\pi$
$283$	−10.7080	−0.636522	−0.318261	+	0.948003i	$0.603099\pi$
$284$	9.80713	0.581946
$285$	−5.56907	−0.329883
$286$	0	0
$287$	3.15653	0.186324
$288$	−16.5551	−0.975516
$289$	−9.21885	−0.542285
$290$	−14.3625	−0.843398
$291$	−1.63298	−0.0957269
$292$	−8.09597	−0.473781
$293$	−2.86960	−0.167644	−0.0838219	−	0.996481i	$-0.526713\pi$
$293$	−2.86960	−0.167644	−0.0838219	+	0.996481i	$0.526713\pi$
$294$	−0.0473049	−0.00275888
$295$	−14.8333	−0.863626
$296$	−6.91472	−0.401910
$297$	−0.923485	−0.0535860
$298$	−11.8233	−0.684904
$299$	0	0
$300$	3.14579	0.181622
$301$	17.6050	1.01473
$302$	3.57003	0.205432
$303$	−0.776876	−0.0446303
$304$	−16.8183	−0.964594
$305$	−41.7428	−2.39018
$306$	5.00801	0.286289
$307$	18.3260	1.04592	0.522959	−	0.852358i	$-0.324828\pi$
$307$	18.3260	1.04592	0.522959	+	0.852358i	$0.324828\pi$
$308$	−4.48287	−0.255435
$309$	−0.181769	−0.0103405
$310$	16.3618	0.929288
$311$	−7.08340	−0.401663	−0.200831	−	0.979626i	$-0.564364\pi$
$311$	−7.08340	−0.401663	−0.200831	+	0.979626i	$0.564364\pi$
$312$	0	0
$313$	−12.8140	−0.724290	−0.362145	−	0.932122i	$-0.617955\pi$
$313$	−12.8140	−0.724290	−0.362145	+	0.932122i	$0.617955\pi$
$314$	10.5776	0.596926
$315$	−34.0567	−1.91888
$316$	12.8329	0.721907
$317$	4.22486	0.237292	0.118646	−	0.992937i	$-0.462145\pi$
$317$	4.22486	0.237292	0.118646	+	0.992937i	$0.462145\pi$
$318$	1.06524	0.0597355
$319$	−5.70078	−0.319182
$320$	2.26533	0.126636
$321$	0.854798	0.0477101
$322$	8.27202	0.460981
$323$	24.0707	1.33933
$324$	−14.3742	−0.798566
$325$	0	0
$326$	−9.63546	−0.533659
$327$	2.69228	0.148883
$328$	2.52692	0.139526
$329$	−0.970207	−0.0534893
$330$	−0.389321	−0.0214314
$331$	6.06087	0.333136	0.166568	−	0.986030i	$-0.446732\pi$
$331$	6.06087	0.333136	0.166568	+	0.986030i	$0.446732\pi$
$332$	3.50803	0.192528
$333$	−9.38204	−0.514133
$334$	−14.0850	−0.770696
$335$	35.2704	1.92703
$336$	0.825224	0.0450197
$337$	19.9135	1.08476	0.542378	−	0.840135i	$-0.317524\pi$
$337$	19.9135	1.08476	0.542378	+	0.840135i	$0.317524\pi$
$338$	0	0
$339$	0.354165	0.0192356
$340$	−19.0606	−1.03371
$341$	6.49432	0.351687
$342$	15.4921	0.837716
$343$	17.7894	0.960537
$344$	14.0934	0.759867
$345$	−3.22989	−0.173892
$346$	−7.66142	−0.411881
$347$	−22.7608	−1.22187	−0.610933	−	0.791682i	$-0.709205\pi$
$347$	−22.7608	−1.22187	−0.610933	+	0.791682i	$0.709205\pi$
$348$	1.44130	0.0772617
$349$	0.661068	0.0353862	0.0176931	−	0.999843i	$-0.494368\pi$
$349$	0.661068	0.0353862	0.0176931	+	0.999843i	$0.494368\pi$
$350$	−20.5659	−1.09930
$351$	0	0
$352$	−5.56263	−0.296489
$353$	−8.10393	−0.431329	−0.215664	−	0.976468i	$-0.569192\pi$
$353$	−8.10393	−0.431329	−0.215664	+	0.976468i	$0.569192\pi$
$354$	−0.331081	−0.0175968
$355$	25.0344	1.32869
$356$	11.0009	0.583046
$357$	−1.18108	−0.0625094
$358$	−4.09416	−0.216383
$359$	27.2296	1.43712	0.718562	−	0.695463i	$-0.244801\pi$
$359$	27.2296	1.43712	0.718562	+	0.695463i	$0.244801\pi$
$360$	−27.2636	−1.43692
$361$	55.4619	2.91904
$362$	−8.17579	−0.429710
$363$	−0.154529	−0.00811068
$364$	0	0
$365$	−20.6664	−1.08173
$366$	−0.931707	−0.0487011
$367$	25.4037	1.32606	0.663032	−	0.748591i	$-0.269269\pi$
$367$	25.4037	1.32606	0.663032	+	0.748591i	$0.269269\pi$
$368$	−9.75410	−0.508468
$369$	3.42857	0.178484
$370$	−7.94226	−0.412898
$371$	31.3105	1.62556
$372$	−1.64193	−0.0851299
$373$	11.2123	0.580550	0.290275	−	0.956943i	$-0.406253\pi$
$373$	11.2123	0.580550	0.290275	+	0.956943i	$0.406253\pi$
$374$	1.68273	0.0870119
$375$	4.80328	0.248040
$376$	−0.776686	−0.0400545
$377$	0	0
$378$	−1.52640	−0.0785096
$379$	14.8480	0.762692	0.381346	−	0.924432i	$-0.375461\pi$
$379$	14.8480	0.762692	0.381346	+	0.924432i	$0.375461\pi$
$380$	−58.9632	−3.02475
$381$	0.581731	0.0298030
$382$	−3.30908	−0.169307
$383$	−18.2976	−0.934963	−0.467482	−	0.884003i	$-0.654839\pi$
$383$	−18.2976	−0.934963	−0.467482	+	0.884003i	$0.654839\pi$
$384$	1.76974	0.0903117
$385$	−11.4433	−0.583205
$386$	3.14068	0.159857
$387$	19.1223	0.972040
$388$	−17.2894	−0.877735
$389$	−3.21120	−0.162814	−0.0814072	−	0.996681i	$-0.525941\pi$
$389$	−3.21120	−0.162814	−0.0814072	+	0.996681i	$0.525941\pi$
$390$	0	0
$391$	13.9603	0.706002
$392$	−1.11309	−0.0562197
$393$	0.684076	0.0345071
$394$	11.3735	0.572990
$395$	32.7583	1.64825
$396$	−4.86923	−0.244688
$397$	3.70621	0.186010	0.0930048	−	0.995666i	$-0.470353\pi$
$397$	3.70621	0.186010	0.0930048	+	0.995666i	$0.470353\pi$
$398$	11.3476	0.568803
$399$	−3.65363	−0.182910
$400$	24.2507	1.21253
$401$	−30.6476	−1.53047	−0.765234	−	0.643752i	$-0.777377\pi$
$401$	−30.6476	−1.53047	−0.765234	+	0.643752i	$0.777377\pi$
$402$	0.787242	0.0392641
$403$	0	0
$404$	−8.22527	−0.409222
$405$	−36.6927	−1.82327
$406$	−9.42265	−0.467638
$407$	−3.15244	−0.156261
$408$	−0.945498	−0.0468091
$409$	6.59417	0.326061	0.163030	−	0.986621i	$-0.447873\pi$
$409$	6.59417	0.326061	0.163030	+	0.986621i	$0.447873\pi$
$410$	2.90242	0.143340
$411$	1.84526	0.0910200
$412$	−1.92450	−0.0948133
$413$	−9.73146	−0.478854
$414$	8.98494	0.441586
$415$	8.95486	0.439577
$416$	0	0
$417$	−0.318741	−0.0156088
$418$	5.20546	0.254607
$419$	−11.5675	−0.565110	−0.282555	−	0.959251i	$-0.591182\pi$
$419$	−11.5675	−0.565110	−0.282555	+	0.959251i	$0.591182\pi$
$420$	2.89315	0.141171
$421$	23.5795	1.14919	0.574596	−	0.818437i	$-0.305159\pi$
$421$	23.5795	1.14919	0.574596	+	0.818437i	$0.305159\pi$
$422$	−3.24880	−0.158149
$423$	−1.05382	−0.0512387
$424$	25.0652	1.21727
$425$	−34.7082	−1.68359
$426$	0.558773	0.0270726
$427$	−27.3856	−1.32528
$428$	9.05028	0.437462
$429$	0	0
$430$	16.1877	0.780642
$431$	18.9954	0.914974	0.457487	−	0.889216i	$-0.348750\pi$
$431$	18.9954	0.914974	0.457487	+	0.889216i	$0.348750\pi$
$432$	1.79988	0.0865970
$433$	−0.769340	−0.0369721	−0.0184860	−	0.999829i	$-0.505885\pi$
$433$	−0.769340	−0.0369721	−0.0184860	+	0.999829i	$0.505885\pi$
$434$	10.7343	0.515262
$435$	3.67917	0.176403
$436$	28.5048	1.36513
$437$	43.1857	2.06585
$438$	−0.461278	−0.0220407
$439$	−27.8529	−1.32935	−0.664674	−	0.747134i	$-0.731429\pi$
$439$	−27.8529	−1.32935	−0.664674	+	0.747134i	$0.731429\pi$
$440$	−9.16079	−0.436723
$441$	−1.51027	−0.0719175
$442$	0	0
$443$	−23.1471	−1.09975	−0.549876	−	0.835246i	$-0.685325\pi$
$443$	−23.1471	−1.09975	−0.549876	+	0.835246i	$0.685325\pi$
$444$	0.797015	0.0378247
$445$	28.0817	1.33120
$446$	4.97787	0.235709
$447$	3.02870	0.143253
$448$	1.48619	0.0702157
$449$	−11.5156	−0.543453	−0.271727	−	0.962374i	$-0.587595\pi$
$449$	−11.5156	−0.543453	−0.271727	+	0.962374i	$0.587595\pi$
$450$	−22.3384	−1.05304
$451$	1.15203	0.0542469
$452$	3.74976	0.176374
$453$	−0.914513	−0.0429675
$454$	9.29347	0.436164
$455$	0	0
$456$	−2.92486	−0.136969
$457$	−13.5305	−0.632928	−0.316464	−	0.948604i	$-0.602496\pi$
$457$	−13.5305	−0.632928	−0.316464	+	0.948604i	$0.602496\pi$
$458$	−0.0870728	−0.00406864
$459$	−2.57604	−0.120239
$460$	−34.1969	−1.59444
$461$	37.6661	1.75428	0.877142	−	0.480231i	$-0.159447\pi$
$461$	37.6661	1.75428	0.877142	+	0.480231i	$0.159447\pi$
$462$	−0.255417	−0.0118831
$463$	31.7879	1.47731	0.738655	−	0.674084i	$-0.235461\pi$
$463$	31.7879	1.47731	0.738655	+	0.674084i	$0.235461\pi$
$464$	11.1109	0.515810
$465$	−4.19131	−0.194367
$466$	−13.9858	−0.647877
$467$	−1.64872	−0.0762937	−0.0381469	−	0.999272i	$-0.512145\pi$
$467$	−1.64872	−0.0762937	−0.0381469	+	0.999272i	$0.512145\pi$
$468$	0	0
$469$	23.1394	1.06848
$470$	−0.892103	−0.0411497
$471$	−2.70959	−0.124851
$472$	−7.79039	−0.358582
$473$	6.42524	0.295433
$474$	0.731170	0.0335838
$475$	−107.368	−4.92640
$476$	−12.5048	−0.573158
$477$	34.0090	1.55716
$478$	6.28996	0.287696
$479$	12.5405	0.572988	0.286494	−	0.958082i	$-0.407510\pi$
$479$	12.5405	0.572988	0.286494	+	0.958082i	$0.407510\pi$
$480$	3.59001	0.163861
$481$	0	0
$482$	−11.0773	−0.504558
$483$	−2.11899	−0.0964176
$484$	−1.63610	−0.0743681
$485$	−44.1342	−2.00403
$486$	−2.49024	−0.112960
$487$	−31.0109	−1.40524	−0.702619	−	0.711566i	$-0.747986\pi$
$487$	−31.0109	−1.40524	−0.702619	+	0.711566i	$0.747986\pi$
$488$	−21.9232	−0.992417
$489$	2.46826	0.111619
$490$	−1.27850	−0.0577567
$491$	−0.580666	−0.0262051	−0.0131025	−	0.999914i	$-0.504171\pi$
$491$	−0.580666	−0.0262051	−0.0131025	+	0.999914i	$0.504171\pi$
$492$	−0.291261	−0.0131311
$493$	−15.9022	−0.716197
$494$	0	0
$495$	−12.4296	−0.558667
$496$	−12.6575	−0.568339
$497$	16.4240	0.736718
$498$	0.199874	0.00895657
$499$	−15.7550	−0.705291	−0.352645	−	0.935757i	$-0.614718\pi$
$499$	−15.7550	−0.705291	−0.352645	+	0.935757i	$0.614718\pi$
$500$	50.8553	2.27432
$501$	3.60807	0.161197
$502$	−0.375707	−0.0167686
$503$	−33.7223	−1.50360	−0.751801	−	0.659390i	$-0.770815\pi$
$503$	−33.7223	−1.50360	−0.751801	+	0.659390i	$0.770815\pi$
$504$	−17.8865	−0.796727
$505$	−20.9965	−0.934330
$506$	3.01901	0.134211
$507$	0	0
$508$	6.15915	0.273268
$509$	40.4825	1.79435	0.897177	−	0.441671i	$-0.145614\pi$
$509$	40.4825	1.79435	0.897177	+	0.441671i	$0.145614\pi$
$510$	−1.08600	−0.0480889
$511$	−13.5583	−0.599785
$512$	19.3918	0.857003
$513$	−7.96887	−0.351834
$514$	9.38490	0.413950
$515$	−4.91263	−0.216476
$516$	−1.62446	−0.0715129
$517$	−0.354093	−0.0155730
$518$	−5.21057	−0.228939
$519$	1.96258	0.0861478
$520$	0	0
$521$	28.6290	1.25426	0.627129	−	0.778915i	$-0.284230\pi$
$521$	28.6290	1.25426	0.627129	+	0.778915i	$0.284230\pi$
$522$	−10.2347	−0.447962
$523$	20.4531	0.894354	0.447177	−	0.894446i	$-0.352429\pi$
$523$	20.4531	0.894354	0.447177	+	0.894446i	$0.352429\pi$
$524$	7.24275	0.316401
$525$	5.26825	0.229925
$526$	−3.09231	−0.134831
$527$	18.1157	0.789134
$528$	0.301179	0.0131072
$529$	2.04639	0.0889736
$530$	28.7899	1.25055
$531$	−10.5702	−0.458706
$532$	−38.6832	−1.67713
$533$	0	0
$534$	0.626789	0.0271238
$535$	23.1024	0.998805
$536$	18.5239	0.800112
$537$	1.04878	0.0452581
$538$	5.44392	0.234704
$539$	−0.507462	−0.0218579
$540$	6.31022	0.271549
$541$	14.2756	0.613755	0.306878	−	0.951749i	$-0.400716\pi$
$541$	14.2756	0.613755	0.306878	+	0.951749i	$0.400716\pi$
$542$	−1.53737	−0.0660356
$543$	2.09434	0.0898769
$544$	−15.5168	−0.665277
$545$	72.7636	3.11685
$546$	0	0
$547$	24.9378	1.06626	0.533131	−	0.846032i	$-0.321015\pi$
$547$	24.9378	1.06626	0.533131	+	0.846032i	$0.321015\pi$
$548$	19.5369	0.834577
$549$	−29.7459	−1.26952
$550$	−7.50588	−0.320052
$551$	−49.1927	−2.09568
$552$	−1.69633	−0.0722007
$553$	21.4913	0.913902
$554$	−5.68570	−0.241562
$555$	2.03452	0.0863607
$556$	−3.37471	−0.143120
$557$	−29.6736	−1.25731	−0.628655	−	0.777684i	$-0.716394\pi$
$557$	−29.6736	−1.25731	−0.628655	+	0.777684i	$0.716394\pi$
$558$	11.6594	0.493582
$559$	0	0
$560$	22.3032	0.942480
$561$	−0.431055	−0.0181992
$562$	−6.68345	−0.281924
$563$	−31.5076	−1.32789	−0.663943	−	0.747783i	$-0.731118\pi$
$563$	−31.5076	−1.32789	−0.663943	+	0.747783i	$0.731118\pi$
$564$	0.0895237	0.00376963
$565$	9.57193	0.402694
$566$	−6.45950	−0.271513
$567$	−24.0725	−1.01095
$568$	13.1480	0.551679
$569$	−18.4812	−0.774774	−0.387387	−	0.921917i	$-0.626622\pi$
$569$	−18.4812	−0.774774	−0.387387	+	0.921917i	$0.626622\pi$
$570$	−3.35950	−0.140714
$571$	−15.2093	−0.636490	−0.318245	−	0.948009i	$-0.603093\pi$
$571$	−15.2093	−0.636490	−0.318245	+	0.948009i	$0.603093\pi$
$572$	0	0
$573$	0.847667	0.0354118
$574$	1.90415	0.0794778
$575$	−62.2705	−2.59686
$576$	1.61427	0.0672614
$577$	−35.3665	−1.47233	−0.736164	−	0.676803i	$-0.763365\pi$
$577$	−35.3665	−1.47233	−0.736164	+	0.676803i	$0.763365\pi$
$578$	−5.56120	−0.231316
$579$	−0.804531	−0.0334352
$580$	38.9537	1.61746
$581$	5.87489	0.243732
$582$	−0.985083	−0.0408330
$583$	11.4273	0.473270
$584$	−10.8539	−0.449139
$585$	0	0
$586$	−1.73107	−0.0715097
$587$	14.0192	0.578634	0.289317	−	0.957233i	$-0.406572\pi$
$587$	14.0192	0.578634	0.289317	+	0.957233i	$0.406572\pi$
$588$	0.128299	0.00529096
$589$	56.0403	2.30910
$590$	−8.94806	−0.368386
$591$	−2.91349	−0.119845
$592$	6.14414	0.252523
$593$	1.04938	0.0430927	0.0215464	−	0.999768i	$-0.493141\pi$
$593$	1.04938	0.0430927	0.0215464	+	0.999768i	$0.493141\pi$
$594$	−0.557086	−0.0228575
$595$	−31.9208	−1.30862
$596$	32.0667	1.31350
$597$	−2.90685	−0.118969
$598$	0	0
$599$	−36.6575	−1.49778	−0.748892	−	0.662692i	$-0.769414\pi$
$599$	−36.6575	−1.49778	−0.748892	+	0.662692i	$0.769414\pi$
$600$	4.21743	0.172176
$601$	−33.4890	−1.36604	−0.683022	−	0.730398i	$-0.739335\pi$
$601$	−33.4890	−1.36604	−0.683022	+	0.730398i	$0.739335\pi$
$602$	10.6201	0.432842
$603$	25.1337	1.02352
$604$	−9.68252	−0.393976
$605$	−4.17643	−0.169796
$606$	−0.468645	−0.0190374
$607$	−28.9078	−1.17333	−0.586666	−	0.809829i	$-0.699560\pi$
$607$	−28.9078	−1.17333	−0.586666	+	0.809829i	$0.699560\pi$
$608$	−48.0006	−1.94668
$609$	2.41374	0.0978098
$610$	−25.1810	−1.01955
$611$	0	0
$612$	−13.5826	−0.549043
$613$	25.7244	1.03900	0.519498	−	0.854471i	$-0.326119\pi$
$613$	25.7244	1.03900	0.519498	+	0.854471i	$0.326119\pi$
$614$	11.0550	0.446144
$615$	−0.743496	−0.0299806
$616$	−6.01000	−0.242150
$617$	−27.9072	−1.12350	−0.561751	−	0.827307i	$-0.689872\pi$
$617$	−27.9072	−1.12350	−0.561751	+	0.827307i	$0.689872\pi$
$618$	−0.109651	−0.00441080
$619$	−17.2993	−0.695316	−0.347658	−	0.937621i	$-0.613023\pi$
$619$	−17.2993	−0.695316	−0.347658	+	0.937621i	$0.613023\pi$
$620$	−44.3760	−1.78218
$621$	−4.62171	−0.185463
$622$	−4.27301	−0.171332
$623$	18.4232	0.738110
$624$	0	0
$625$	67.6044	2.70418
$626$	−7.72995	−0.308951
$627$	−1.33345	−0.0532530
$628$	−28.6881	−1.14478
$629$	−8.79364	−0.350625
$630$	−20.5444	−0.818510
$631$	−28.5282	−1.13569	−0.567845	−	0.823135i	$-0.692223\pi$
$631$	−28.5282	−1.13569	−0.567845	+	0.823135i	$0.692223\pi$
$632$	17.2046	0.684361
$633$	0.832225	0.0330780
$634$	2.54862	0.101219
$635$	15.7223	0.623921
$636$	−2.88910	−0.114560
$637$	0	0
$638$	−3.43895	−0.136149
$639$	17.8395	0.705721
$640$	47.8304	1.89066
$641$	3.46631	0.136911	0.0684555	−	0.997654i	$-0.478193\pi$
$641$	3.46631	0.136911	0.0684555	+	0.997654i	$0.478193\pi$
$642$	0.515651	0.0203511
$643$	39.9565	1.57573	0.787866	−	0.615847i	$-0.211186\pi$
$643$	39.9565	1.57573	0.787866	+	0.615847i	$0.211186\pi$
$644$	−22.4351	−0.884068
$645$	−4.14672	−0.163277
$646$	14.5205	0.571301
$647$	−19.7561	−0.776694	−0.388347	−	0.921513i	$-0.626954\pi$
$647$	−19.7561	−0.776694	−0.388347	+	0.921513i	$0.626954\pi$
$648$	−19.2709	−0.757033
$649$	−3.55166	−0.139415
$650$	0	0
$651$	−2.74974	−0.107771
$652$	26.1330	1.02345
$653$	23.2622	0.910319	0.455159	−	0.890410i	$-0.349582\pi$
$653$	23.2622	0.910319	0.455159	+	0.890410i	$0.349582\pi$
$654$	1.62410	0.0635072
$655$	18.4884	0.722401
$656$	−2.24532	−0.0876649
$657$	−14.7269	−0.574550
$658$	−0.585271	−0.0228162
$659$	−21.9368	−0.854538	−0.427269	−	0.904125i	$-0.640524\pi$
$659$	−21.9368	−0.854538	−0.427269	+	0.904125i	$0.640524\pi$
$660$	1.05591	0.0411011
$661$	25.6652	0.998259	0.499129	−	0.866527i	$-0.333653\pi$
$661$	25.6652	0.998259	0.499129	+	0.866527i	$0.333653\pi$
$662$	3.65618	0.142101
$663$	0	0
$664$	4.70307	0.182514
$665$	−98.7458	−3.82920
$666$	−5.65965	−0.219307
$667$	−28.5303	−1.10470
$668$	38.2009	1.47804
$669$	−1.27515	−0.0493002
$670$	21.2766	0.821988
$671$	−9.99485	−0.385847
$672$	2.35525	0.0908558
$673$	−2.40531	−0.0927179	−0.0463589	−	0.998925i	$-0.514762\pi$
$673$	−2.40531	−0.0927179	−0.0463589	+	0.998925i	$0.514762\pi$
$674$	12.0127	0.462710
$675$	11.4905	0.442270
$676$	0	0
$677$	−32.8859	−1.26391	−0.631955	−	0.775005i	$-0.717747\pi$
$677$	−32.8859	−1.26391	−0.631955	+	0.775005i	$0.717747\pi$
$678$	0.213647	0.00820508
$679$	−28.9545	−1.11117
$680$	−25.5538	−0.979942
$681$	−2.38065	−0.0912269
$682$	3.91765	0.150015
$683$	15.4703	0.591954	0.295977	−	0.955195i	$-0.404355\pi$
$683$	15.4703	0.591954	0.295977	+	0.955195i	$0.404355\pi$
$684$	−42.0172	−1.60657
$685$	49.8715	1.90549
$686$	10.7313	0.409724
$687$	0.0223049	0.000850986 0
$688$	−12.5229	−0.477430
$689$	0	0
$690$	−1.94841	−0.0741747
$691$	18.4742	0.702791	0.351396	−	0.936227i	$-0.385707\pi$
$691$	18.4742	0.702791	0.351396	+	0.936227i	$0.385707\pi$
$692$	20.7791	0.789902
$693$	−8.15450	−0.309764
$694$	−13.7303	−0.521196
$695$	−8.61455	−0.326769
$696$	1.93229	0.0732433
$697$	3.21355	0.121722
$698$	0.398785	0.0150942
$699$	3.58265	0.135508
$700$	55.7783	2.10822
$701$	42.1518	1.59205	0.796026	−	0.605262i	$-0.206932\pi$
$701$	42.1518	1.59205	0.796026	+	0.605262i	$0.206932\pi$
$702$	0	0
$703$	−27.2028	−1.02597
$704$	0.542409	0.0204428
$705$	0.228525	0.00860675
$706$	−4.88864	−0.183986
$707$	−13.7749	−0.518057
$708$	0.897948	0.0337470
$709$	−38.6700	−1.45228	−0.726141	−	0.687546i	$-0.758688\pi$
$709$	−38.6700	−1.45228	−0.726141	+	0.687546i	$0.758688\pi$
$710$	15.1018	0.566762
$711$	23.3435	0.875450
$712$	14.7484	0.552721
$713$	32.5017	1.21720
$714$	−0.712478	−0.0266638
$715$	0	0
$716$	11.1041	0.414978
$717$	−1.61126	−0.0601737
$718$	16.4261	0.613015
$719$	−12.4070	−0.462704	−0.231352	−	0.972870i	$-0.574315\pi$
$719$	−12.4070	−0.462704	−0.231352	+	0.972870i	$0.574315\pi$
$720$	24.2254	0.902826
$721$	−3.22296	−0.120029
$722$	33.4570	1.24514
$723$	2.83761	0.105532
$724$	22.1741	0.824095
$725$	70.9322	2.63436
$726$	−0.0932187	−0.00345967
$727$	−38.2088	−1.41708	−0.708542	−	0.705668i	$-0.750647\pi$
$727$	−38.2088	−1.41708	−0.708542	+	0.705668i	$0.750647\pi$
$728$	0	0
$729$	−25.7191	−0.952558
$730$	−12.4669	−0.461419
$731$	17.9230	0.662907
$732$	2.52695	0.0933987
$733$	7.45535	0.275370	0.137685	−	0.990476i	$-0.456034\pi$
$733$	7.45535	0.275370	0.137685	+	0.990476i	$0.456034\pi$
$734$	15.3246	0.565642
$735$	0.327506	0.0120802
$736$	−27.8389	−1.02616
$737$	8.44511	0.311080
$738$	2.06826	0.0761338
$739$	−13.1243	−0.482784	−0.241392	−	0.970428i	$-0.577604\pi$
$739$	−13.1243	−0.482784	−0.241392	+	0.970428i	$0.577604\pi$
$740$	21.5408	0.791854
$741$	0	0
$742$	18.8878	0.693394
$743$	−14.4180	−0.528945	−0.264473	−	0.964393i	$-0.585198\pi$
$743$	−14.4180	−0.528945	−0.264473	+	0.964393i	$0.585198\pi$
$744$	−2.20127	−0.0807023
$745$	81.8560	2.99897
$746$	6.76373	0.247638
$747$	6.38122	0.233477
$748$	−4.56385	−0.166871
$749$	15.1565	0.553807
$750$	2.89754	0.105803
$751$	15.4568	0.564025	0.282012	−	0.959411i	$-0.408998\pi$
$751$	15.4568	0.564025	0.282012	+	0.959411i	$0.408998\pi$
$752$	0.690133	0.0251665
$753$	0.0962428	0.00350728
$754$	0	0
$755$	−24.7163	−0.899520
$756$	4.13986	0.150565
$757$	−37.8175	−1.37450	−0.687250	−	0.726421i	$-0.741182\pi$
$757$	−37.8175	−1.37450	−0.687250	+	0.726421i	$0.741182\pi$
$758$	8.95697	0.325332
$759$	−0.773363	−0.0280713
$760$	−79.0496	−2.86743
$761$	13.7020	0.496697	0.248349	−	0.968671i	$-0.420112\pi$
$761$	13.7020	0.496697	0.248349	+	0.968671i	$0.420112\pi$
$762$	0.350925	0.0127127
$763$	47.7371	1.72820
$764$	8.97478	0.324696
$765$	−34.6719	−1.25357
$766$	−11.0379	−0.398815
$767$	0	0
$768$	0.899947	0.0324740
$769$	−28.6385	−1.03273	−0.516365	−	0.856369i	$-0.672715\pi$
$769$	−28.6385	−1.03273	−0.516365	+	0.856369i	$0.672715\pi$
$770$	−6.90310	−0.248770
$771$	−2.40407	−0.0865806
$772$	−8.51807	−0.306572
$773$	−4.43381	−0.159473	−0.0797366	−	0.996816i	$-0.525408\pi$
$773$	−4.43381	−0.159473	−0.0797366	+	0.996816i	$0.525408\pi$
$774$	11.5354	0.414631
$775$	−80.8060	−2.90264
$776$	−23.1792	−0.832084
$777$	1.33476	0.0478843
$778$	−1.93713	−0.0694496
$779$	9.94099	0.356173
$780$	0	0
$781$	5.99422	0.214490
$782$	8.42145	0.301150
$783$	5.26458	0.188141
$784$	0.989049	0.0353232
$785$	−73.2315	−2.61374
$786$	0.412664	0.0147192
$787$	55.4317	1.97593	0.987964	−	0.154686i	$-0.0494365\pi$
$787$	55.4317	1.97593	0.987964	+	0.154686i	$0.0494365\pi$
$788$	−30.8469	−1.09888
$789$	0.792138	0.0282009
$790$	19.7612	0.703071
$791$	6.27973	0.223282
$792$	−6.52797	−0.231961
$793$	0	0
$794$	2.23575	0.0793437
$795$	−7.37494	−0.261562
$796$	−30.7766	−1.09085
$797$	−15.6093	−0.552910	−0.276455	−	0.961027i	$-0.589160\pi$
$797$	−15.6093	−0.552910	−0.276455	+	0.961027i	$0.589160\pi$
$798$	−2.20402	−0.0780216
$799$	−0.987734	−0.0349435
$800$	69.2133	2.44706
$801$	20.0110	0.707054
$802$	−18.4880	−0.652832
$803$	−4.94834	−0.174623
$804$	−2.13514	−0.0753004
$805$	−57.2696	−2.01849
$806$	0	0
$807$	−1.39454	−0.0490901
$808$	−11.0273	−0.387939
$809$	48.9142	1.71973	0.859867	−	0.510519i	$-0.170547\pi$
$809$	48.9142	1.71973	0.859867	+	0.510519i	$0.170547\pi$
$810$	−22.1346	−0.777730
$811$	3.66769	0.128790	0.0643951	−	0.997924i	$-0.479488\pi$
$811$	3.66769	0.128790	0.0643951	+	0.997924i	$0.479488\pi$
$812$	25.5558	0.896834
$813$	0.393819	0.0138118
$814$	−1.90169	−0.0666541
$815$	66.7091	2.33672
$816$	0.840131	0.0294105
$817$	55.4442	1.93975
$818$	3.97789	0.139084
$819$	0	0
$820$	−7.87186	−0.274897
$821$	54.7264	1.90996	0.954982	−	0.296665i	$-0.0958746\pi$
$821$	54.7264	1.90996	0.954982	+	0.296665i	$0.0958746\pi$
$822$	1.11314	0.0388252
$823$	42.9535	1.49727	0.748633	−	0.662985i	$-0.230711\pi$
$823$	42.9535	1.49727	0.748633	+	0.662985i	$0.230711\pi$
$824$	−2.58010	−0.0898820
$825$	1.92274	0.0669412
$826$	−5.87044	−0.204259
$827$	−30.4806	−1.05991	−0.529957	−	0.848024i	$-0.677792\pi$
$827$	−30.4806	−1.05991	−0.529957	+	0.848024i	$0.677792\pi$
$828$	−24.3687	−0.846871
$829$	9.56411	0.332175	0.166088	−	0.986111i	$-0.446887\pi$
$829$	9.56411	0.332175	0.166088	+	0.986111i	$0.446887\pi$
$830$	5.40195	0.187505
$831$	1.45647	0.0505245
$832$	0	0
$833$	−1.41555	−0.0490459
$834$	−0.192278	−0.00665805
$835$	97.5145	3.37463
$836$	−14.1181	−0.488285
$837$	−5.99741	−0.207301
$838$	−6.97803	−0.241052
$839$	13.6849	0.472456	0.236228	−	0.971698i	$-0.424089\pi$
$839$	13.6849	0.472456	0.236228	+	0.971698i	$0.424089\pi$
$840$	3.87873	0.133829
$841$	3.49886	0.120650
$842$	14.2241	0.490196
$843$	1.71206	0.0589665
$844$	8.81129	0.303297
$845$	0	0
$846$	−0.635712	−0.0218562
$847$	−2.73997	−0.0941466
$848$	−22.2719	−0.764821
$849$	1.65469	0.0567889
$850$	−20.9375	−0.718149
$851$	−15.7768	−0.540822
$852$	−1.51549	−0.0519198
$853$	48.2728	1.65283	0.826415	−	0.563061i	$-0.190376\pi$
$853$	48.2728	1.65283	0.826415	+	0.563061i	$0.190376\pi$
$854$	−16.5202	−0.565309
$855$	−107.256	−3.66809
$856$	12.1333	0.414709
$857$	−0.574419	−0.0196218	−0.00981090	−	0.999952i	$-0.503123\pi$
$857$	−0.574419	−0.0196218	−0.00981090	+	0.999952i	$0.503123\pi$
$858$	0	0
$859$	−56.0203	−1.91139	−0.955694	−	0.294361i	$-0.904893\pi$
$859$	−56.0203	−1.91139	−0.955694	+	0.294361i	$0.904893\pi$
$860$	−43.9039	−1.49711
$861$	−0.487776	−0.0166233
$862$	11.4588	0.390289
$863$	24.3871	0.830146	0.415073	−	0.909788i	$-0.363756\pi$
$863$	24.3871	0.830146	0.415073	+	0.909788i	$0.363756\pi$
$864$	5.13701	0.174764
$865$	53.0423	1.80349
$866$	−0.464099	−0.0157707
$867$	1.42458	0.0483813
$868$	−29.1132	−0.988166
$869$	7.84360	0.266076
$870$	2.21943	0.0752458
$871$	0	0
$872$	38.2153	1.29413
$873$	−31.4500	−1.06442
$874$	26.0514	0.881203
$875$	85.1675	2.87919
$876$	1.25106	0.0422696
$877$	−11.9636	−0.403982	−0.201991	−	0.979387i	$-0.564741\pi$
$877$	−11.9636	−0.403982	−0.201991	+	0.979387i	$0.564741\pi$
$878$	−16.8021	−0.567043
$879$	0.443437	0.0149568
$880$	8.13991	0.274396
$881$	−15.1233	−0.509516	−0.254758	−	0.967005i	$-0.581996\pi$
$881$	−15.1233	−0.509516	−0.254758	+	0.967005i	$0.581996\pi$
$882$	−0.911058	−0.0306769
$883$	−24.3493	−0.819418	−0.409709	−	0.912216i	$-0.634370\pi$
$883$	−24.3493	−0.819418	−0.409709	+	0.912216i	$0.634370\pi$
$884$	0	0
$885$	2.29217	0.0770505
$886$	−13.9633	−0.469107
$887$	−28.5969	−0.960190	−0.480095	−	0.877217i	$-0.659398\pi$
$887$	−28.5969	−0.960190	−0.480095	+	0.877217i	$0.659398\pi$
$888$	1.06853	0.0358574
$889$	10.3147	0.345945
$890$	16.9401	0.567833
$891$	−8.78566	−0.294331
$892$	−13.5008	−0.452041
$893$	−3.05552	−0.102249
$894$	1.82704	0.0611054
$895$	28.3451	0.947472
$896$	31.3795	1.04831
$897$	0	0
$898$	−6.94669	−0.231814
$899$	−37.0227	−1.23478
$900$	60.5856	2.01952
$901$	31.8761	1.06195
$902$	0.694952	0.0231394
$903$	−2.72048	−0.0905320
$904$	5.02716	0.167201
$905$	56.6034	1.88156
$906$	−0.551673	−0.0183281
$907$	54.8751	1.82210	0.911049	−	0.412297i	$-0.135273\pi$
$907$	54.8751	1.82210	0.911049	+	0.412297i	$0.135273\pi$
$908$	−25.2055	−0.836473
$909$	−14.9621	−0.496260
$910$	0	0
$911$	4.35325	0.144229	0.0721147	−	0.997396i	$-0.477025\pi$
$911$	4.35325	0.144229	0.0721147	+	0.997396i	$0.477025\pi$
$912$	2.59892	0.0860587
$913$	2.14414	0.0709607
$914$	−8.16215	−0.269980
$915$	6.45048	0.213246
$916$	0.236156	0.00780282
$917$	12.1294	0.400549
$918$	−1.55398	−0.0512888
$919$	−4.16367	−0.137347	−0.0686734	−	0.997639i	$-0.521877\pi$
$919$	−4.16367	−0.137347	−0.0686734	+	0.997639i	$0.521877\pi$
$920$	−45.8464	−1.51151
$921$	−2.83190	−0.0933142
$922$	22.7218	0.748303
$923$	0	0
$924$	0.692734	0.0227893
$925$	39.2244	1.28969
$926$	19.1758	0.630157
$927$	−3.50074	−0.114979
$928$	31.7113	1.04097
$929$	22.1678	0.727303	0.363652	−	0.931535i	$-0.381530\pi$
$929$	22.1678	0.727303	0.363652	+	0.931535i	$0.381530\pi$
$930$	−2.52838	−0.0829087
$931$	−4.37895	−0.143514
$932$	37.9318	1.24250
$933$	1.09459	0.0358353
$934$	−0.994579	−0.0325436
$935$	−11.6500	−0.380997
$936$	0	0
$937$	23.2278	0.758819	0.379409	−	0.925229i	$-0.376127\pi$
$937$	23.2278	0.758819	0.379409	+	0.925229i	$0.376127\pi$
$938$	13.9587	0.455767
$939$	1.98014	0.0646193
$940$	2.41954	0.0789166
$941$	−33.9577	−1.10699	−0.553495	−	0.832852i	$-0.686706\pi$
$941$	−33.9577	−1.10699	−0.553495	+	0.832852i	$0.686706\pi$
$942$	−1.63454	−0.0532562
$943$	5.76548	0.187750
$944$	6.92223	0.225299
$945$	10.5677	0.343768
$946$	3.87598	0.126019
$947$	32.5647	1.05821	0.529106	−	0.848556i	$-0.322527\pi$
$947$	32.5647	1.05821	0.529106	+	0.848556i	$0.322527\pi$
$948$	−1.98306	−0.0644068
$949$	0	0
$950$	−64.7692	−2.10139
$951$	−0.652864	−0.0211706
$952$	−16.7647	−0.543348
$953$	−40.2221	−1.30292	−0.651461	−	0.758682i	$-0.725843\pi$
$953$	−40.2221	−1.30292	−0.651461	+	0.758682i	$0.725843\pi$
$954$	20.5157	0.664220
$955$	22.9097	0.741341
$956$	−17.0595	−0.551742
$957$	0.880937	0.0284766
$958$	7.56495	0.244412
$959$	32.7185	1.05654
$960$	−0.350060	−0.0112981
$961$	11.1762	0.360524
$962$	0	0
$963$	16.4628	0.530506
$964$	30.0436	0.967639
$965$	−21.7439	−0.699960
$966$	−1.27827	−0.0411276
$967$	28.2981	0.910006	0.455003	−	0.890490i	$-0.349638\pi$
$967$	28.2981	0.910006	0.455003	+	0.890490i	$0.349638\pi$
$968$	−2.19345	−0.0705002
$969$	−3.71963	−0.119492
$970$	−26.6236	−0.854833
$971$	−32.0941	−1.02995	−0.514974	−	0.857206i	$-0.672198\pi$
$971$	−32.0941	−1.02995	−0.514974	+	0.857206i	$0.672198\pi$
$972$	6.75397	0.216634
$973$	−5.65164	−0.181183
$974$	−18.7071	−0.599415
$975$	0	0
$976$	19.4801	0.623542
$977$	−33.9087	−1.08484	−0.542418	−	0.840109i	$-0.682491\pi$
$977$	−33.9087	−1.08484	−0.542418	+	0.840109i	$0.682491\pi$
$978$	1.48896	0.0476117
$979$	6.72386	0.214895
$980$	3.46751	0.110766
$981$	51.8513	1.65548
$982$	−0.350283	−0.0111780
$983$	−37.3803	−1.19225	−0.596124	−	0.802893i	$-0.703293\pi$
$983$	−37.3803	−1.19225	−0.596124	+	0.802893i	$0.703293\pi$
$984$	−0.390482	−0.0124481
$985$	−78.7423	−2.50894
$986$	−9.59286	−0.305499
$987$	0.149925	0.00477218
$988$	0	0
$989$	32.1560	1.02250
$990$	−7.49804	−0.238303
$991$	12.5110	0.397424	0.198712	−	0.980058i	$-0.436324\pi$
$991$	12.5110	0.397424	0.198712	+	0.980058i	$0.436324\pi$
$992$	−36.1255	−1.14699
$993$	−0.936582	−0.0297215
$994$	9.90767	0.314252
$995$	−78.5627	−2.49060
$996$	−0.542093	−0.0171769
$997$	60.2994	1.90970	0.954851	−	0.297086i	$-0.0960148\pi$
$997$	60.2994	1.90970	0.954851	+	0.297086i	$0.0960148\pi$
$998$	−9.50410	−0.300847
$999$	2.91123	0.0921073

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.s.1.13	✓	21
13.12	even	2		1859.2.a.t.1.9	yes	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.2.a.s.1.13	✓	21	1.1	even	1	trivial
1859.2.a.t.1.9	yes	21	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q+0.603243 q^{2} -0.154529 q^{3} -1.63610 q^{4} -4.17643 q^{5} -0.0932187 q^{6} -2.73997 q^{7} -2.19345 q^{8} -2.97612 q^{9} +O(q^{10})\)	\(q+0.603243 q^{2} -0.154529 q^{3} -1.63610 q^{4} -4.17643 q^{5} -0.0932187 q^{6} -2.73997 q^{7} -2.19345 q^{8} -2.97612 q^{9} -2.51940 q^{10} -1.00000 q^{11} +0.252825 q^{12} -1.65287 q^{14} +0.645380 q^{15} +1.94901 q^{16} -2.78947 q^{17} -1.79532 q^{18} -8.62913 q^{19} +6.83305 q^{20} +0.423406 q^{21} -0.603243 q^{22} -5.00464 q^{23} +0.338952 q^{24} +12.4426 q^{25} +0.923485 q^{27} +4.48287 q^{28} +5.70078 q^{29} +0.389321 q^{30} -6.49432 q^{31} +5.56263 q^{32} +0.154529 q^{33} -1.68273 q^{34} +11.4433 q^{35} +4.86923 q^{36} +3.15244 q^{37} -5.20546 q^{38} +9.16079 q^{40} -1.15203 q^{41} +0.255417 q^{42} -6.42524 q^{43} +1.63610 q^{44} +12.4296 q^{45} -3.01901 q^{46} +0.354093 q^{47} -0.301179 q^{48} +0.507462 q^{49} +7.50588 q^{50} +0.431055 q^{51} -11.4273 q^{53} +0.557086 q^{54} +4.17643 q^{55} +6.01000 q^{56} +1.33345 q^{57} +3.43895 q^{58} +3.55166 q^{59} -1.05591 q^{60} +9.99485 q^{61} -3.91765 q^{62} +8.15450 q^{63} -0.542409 q^{64} +0.0932187 q^{66} -8.44511 q^{67} +4.56385 q^{68} +0.773363 q^{69} +6.90310 q^{70} -5.99422 q^{71} +6.52797 q^{72} +4.94834 q^{73} +1.90169 q^{74} -1.92274 q^{75} +14.1181 q^{76} +2.73997 q^{77} -7.84360 q^{79} -8.13991 q^{80} +8.78566 q^{81} -0.694952 q^{82} -2.14414 q^{83} -0.692734 q^{84} +11.6500 q^{85} -3.87598 q^{86} -0.880937 q^{87} +2.19345 q^{88} -6.72386 q^{89} +7.49804 q^{90} +8.18808 q^{92} +1.00356 q^{93} +0.213604 q^{94} +36.0389 q^{95} -0.859589 q^{96} +10.5674 q^{97} +0.306123 q^{98} +2.97612 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9}+O(q^{10}) \) 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9	\( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9} + 18 q^{10} - 21 q^{11} + 23 q^{12} + 20 q^{14} - 16 q^{15} + 50 q^{16} + 16 q^{17} - 3 q^{18} + 11 q^{19} - 24 q^{20} + 5 q^{21} - 9 q^{23} + 54 q^{24} + 36 q^{25} + 11 q^{28} + 28 q^{29} + 21 q^{30} - 15 q^{31} + 61 q^{32} - 6 q^{33} + 6 q^{34} - 3 q^{35} + 45 q^{36} + 12 q^{37} + q^{38} + 55 q^{40} + 4 q^{41} - 34 q^{42} + 17 q^{43} - 32 q^{44} - 9 q^{45} - 11 q^{46} - 36 q^{47} + 24 q^{48} + 72 q^{49} + 9 q^{50} + 2 q^{51} + 19 q^{53} - q^{54} + 7 q^{55} + 44 q^{56} + 4 q^{57} + 33 q^{58} - 54 q^{59} - 64 q^{60} + 98 q^{61} - 29 q^{62} + 81 q^{63} + 63 q^{64} - 19 q^{66} - 25 q^{67} + 4 q^{68} + 89 q^{69} - 65 q^{70} - 37 q^{71} - 55 q^{72} - 8 q^{73} - 11 q^{74} + 24 q^{75} - 13 q^{76} + q^{77} + 24 q^{79} - 26 q^{80} + 81 q^{81} + 26 q^{82} + 34 q^{83} + 103 q^{84} + 11 q^{85} - 30 q^{86} + 32 q^{87} - 3 q^{88} - 6 q^{89} + 47 q^{90} - 80 q^{92} - 41 q^{93} + 40 q^{94} + 20 q^{95} + 98 q^{96} + 5 q^{98} - 33 q^{99}+O(q^{100}) \) 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9 + 18 * q^10 - 21 * q^11 + 23 * q^12 + 20 * q^14 - 16 * q^15 + 50 * q^16 + 16 * q^17 - 3 * q^18 + 11 * q^19 - 24 * q^20 + 5 * q^21 - 9 * q^23 + 54 * q^24 + 36 * q^25 + 11 * q^28 + 28 * q^29 + 21 * q^30 - 15 * q^31 + 61 * q^32 - 6 * q^33 + 6 * q^34 - 3 * q^35 + 45 * q^36 + 12 * q^37 + q^38 + 55 * q^40 + 4 * q^41 - 34 * q^42 + 17 * q^43 - 32 * q^44 - 9 * q^45 - 11 * q^46 - 36 * q^47 + 24 * q^48 + 72 * q^49 + 9 * q^50 + 2 * q^51 + 19 * q^53 - q^54 + 7 * q^55 + 44 * q^56 + 4 * q^57 + 33 * q^58 - 54 * q^59 - 64 * q^60 + 98 * q^61 - 29 * q^62 + 81 * q^63 + 63 * q^64 - 19 * q^66 - 25 * q^67 + 4 * q^68 + 89 * q^69 - 65 * q^70 - 37 * q^71 - 55 * q^72 - 8 * q^73 - 11 * q^74 + 24 * q^75 - 13 * q^76 + q^77 + 24 * q^79 - 26 * q^80 + 81 * q^81 + 26 * q^82 + 34 * q^83 + 103 * q^84 + 11 * q^85 - 30 * q^86 + 32 * q^87 - 3 * q^88 - 6 * q^89 + 47 * q^90 - 80 * q^92 - 41 * q^93 + 40 * q^94 + 20 * q^95 + 98 * q^96 + 5 * q^98 - 33 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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