LMFDB - Embedded newform 1849.2.a.m.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,2,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1849.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:	$14.7643393337$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{44})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 11x^{8} + 44x^{6} - 77x^{4} + 55x^{2} - 11 $ x^10 - 11x^8 + 44x^6 - 77x^4 + 55x^2 - 11
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$1.51150$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.51150 q^{2} +2.59278 q^{3} +0.284630 q^{4} -2.07496 q^{5} +3.91899 q^{6} -3.84858 q^{7} -2.59278 q^{8} +3.72251 q^{9} +O(q^{10})$	\(q+1.51150 q^{2} +2.59278 q^{3} +0.284630 q^{4} -2.07496 q^{5} +3.91899 q^{6} -3.84858 q^{7} -2.59278 q^{8} +3.72251 q^{9} -3.13631 q^{10} +1.14055 q^{11} +0.737982 q^{12} -5.25380 q^{13} -5.81712 q^{14} -5.37993 q^{15} -4.48825 q^{16} +2.41316 q^{17} +5.62657 q^{18} +2.85087 q^{19} -0.590596 q^{20} -9.97852 q^{21} +1.72394 q^{22} -3.59946 q^{23} -6.72251 q^{24} -0.694523 q^{25} -7.94111 q^{26} +1.87332 q^{27} -1.09542 q^{28} -4.93883 q^{29} -8.13176 q^{30} -4.98021 q^{31} -1.59842 q^{32} +2.95720 q^{33} +3.64750 q^{34} +7.98567 q^{35} +1.05954 q^{36} +9.93421 q^{37} +4.30909 q^{38} -13.6219 q^{39} +5.37993 q^{40} -7.03092 q^{41} -15.0825 q^{42} +0.324635 q^{44} -7.72408 q^{45} -5.44058 q^{46} -0.413795 q^{47} -11.6370 q^{48} +7.81157 q^{49} -1.04977 q^{50} +6.25681 q^{51} -1.49539 q^{52} +6.20009 q^{53} +2.83152 q^{54} -2.36660 q^{55} +9.97852 q^{56} +7.39169 q^{57} -7.46504 q^{58} -9.98383 q^{59} -1.53129 q^{60} -11.5300 q^{61} -7.52759 q^{62} -14.3264 q^{63} +6.56048 q^{64} +10.9014 q^{65} +4.46981 q^{66} +2.69318 q^{67} +0.686858 q^{68} -9.33261 q^{69} +12.0703 q^{70} +11.9359 q^{71} -9.65166 q^{72} +0.792034 q^{73} +15.0156 q^{74} -1.80075 q^{75} +0.811443 q^{76} -4.38950 q^{77} -20.5896 q^{78} +5.43676 q^{79} +9.31295 q^{80} -6.31044 q^{81} -10.6272 q^{82} +0.475365 q^{83} -2.84018 q^{84} -5.00723 q^{85} -12.8053 q^{87} -2.95720 q^{88} +4.99089 q^{89} -11.6749 q^{90} +20.2197 q^{91} -1.02451 q^{92} -12.9126 q^{93} -0.625450 q^{94} -5.91546 q^{95} -4.14435 q^{96} -0.449409 q^{97} +11.8072 q^{98} +4.24572 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{4} + 22 q^{6} + 14 q^{9}+O(q^{10}) $ 10 * q + 2 * q^4 + 22 * q^6 + 14 * q^9	$ 10 q + 2 q^{4} + 22 q^{6} + 14 q^{9} - 22 q^{10} - 10 q^{11} - 14 q^{13} - 22 q^{14} - 22 q^{15} - 26 q^{16} - 16 q^{17} - 44 q^{21} - 18 q^{23} - 44 q^{24} - 6 q^{25} - 2 q^{31} - 28 q^{36} - 22 q^{38} + 22 q^{40} - 2 q^{44} - 18 q^{47} + 18 q^{49} + 28 q^{52} + 2 q^{53} + 44 q^{56} - 22 q^{57} - 22 q^{58} + 14 q^{59} + 8 q^{64} - 22 q^{66} + 26 q^{67} + 32 q^{68} + 44 q^{74} - 44 q^{78} - 56 q^{79} + 2 q^{81} - 38 q^{83} - 22 q^{87} - 22 q^{90} - 74 q^{92} + 22 q^{96} + 34 q^{97} - 36 q^{99}+O(q^{100}) $ 10 * q + 2 * q^4 + 22 * q^6 + 14 * q^9 - 22 * q^10 - 10 * q^11 - 14 * q^13 - 22 * q^14 - 22 * q^15 - 26 * q^16 - 16 * q^17 - 44 * q^21 - 18 * q^23 - 44 * q^24 - 6 * q^25 - 2 * q^31 - 28 * q^36 - 22 * q^38 + 22 * q^40 - 2 * q^44 - 18 * q^47 + 18 * q^49 + 28 * q^52 + 2 * q^53 + 44 * q^56 - 22 * q^57 - 22 * q^58 + 14 * q^59 + 8 * q^64 - 22 * q^66 + 26 * q^67 + 32 * q^68 + 44 * q^74 - 44 * q^78 - 56 * q^79 + 2 * q^81 - 38 * q^83 - 22 * q^87 - 22 * q^90 - 74 * q^92 + 22 * q^96 + 34 * q^97 - 36 * 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 $

$2$	1.51150	1.06879	0.534396	−	0.845234i	$-0.320539\pi$
$2$	1.51150	1.06879	0.534396	+	0.845234i	$0.320539\pi$
$3$	2.59278	1.49694	0.748471	−	0.663167i	$-0.230788\pi$
$3$	2.59278	1.49694	0.748471	+	0.663167i	$0.230788\pi$
$4$	0.284630	0.142315
$5$	−2.07496	−0.927952	−0.463976	−	0.885848i	$-0.653578\pi$
$5$	−2.07496	−0.927952	−0.463976	+	0.885848i	$0.653578\pi$
$6$	3.91899	1.59992
$7$	−3.84858	−1.45463	−0.727313	−	0.686306i	$-0.759231\pi$
$7$	−3.84858	−1.45463	−0.727313	+	0.686306i	$0.759231\pi$
$8$	−2.59278	−0.916686
$9$	3.72251	1.24084
$10$	−3.13631	−0.991787
$11$	1.14055	0.343889	0.171945	−	0.985107i	$-0.444995\pi$
$11$	1.14055	0.343889	0.171945	+	0.985107i	$0.444995\pi$
$12$	0.737982	0.213037
$13$	−5.25380	−1.45714	−0.728571	−	0.684970i	$-0.759815\pi$
$13$	−5.25380	−1.45714	−0.728571	+	0.684970i	$0.759815\pi$
$14$	−5.81712	−1.55469
$15$	−5.37993	−1.38909
$16$	−4.48825	−1.12206
$17$	2.41316	0.585278	0.292639	−	0.956223i	$-0.405467\pi$
$17$	2.41316	0.585278	0.292639	+	0.956223i	$0.405467\pi$
$18$	5.62657	1.32620
$19$	2.85087	0.654035	0.327018	−	0.945018i	$-0.393956\pi$
$19$	2.85087	0.654035	0.327018	+	0.945018i	$0.393956\pi$
$20$	−0.590596	−0.132061
$21$	−9.97852	−2.17749
$22$	1.72394	0.367546
$23$	−3.59946	−0.750539	−0.375270	−	0.926916i	$-0.622450\pi$
$23$	−3.59946	−0.750539	−0.375270	+	0.926916i	$0.622450\pi$
$24$	−6.72251	−1.37223
$25$	−0.694523	−0.138905
$26$	−7.94111	−1.55738
$27$	1.87332	0.360520
$28$	−1.09542	−0.207015
$29$	−4.93883	−0.917118	−0.458559	−	0.888664i	$-0.651634\pi$
$29$	−4.93883	−0.917118	−0.458559	+	0.888664i	$0.651634\pi$
$30$	−8.13176	−1.48465
$31$	−4.98021	−0.894473	−0.447236	−	0.894416i	$-0.647592\pi$
$31$	−4.98021	−0.894473	−0.447236	+	0.894416i	$0.647592\pi$
$32$	−1.59842	−0.282563
$33$	2.95720	0.514782
$34$	3.64750	0.625541
$35$	7.98567	1.34982
$36$	1.05954	0.176590
$37$	9.93421	1.63317	0.816587	−	0.577222i	$-0.195863\pi$
$37$	9.93421	1.63317	0.816587	+	0.577222i	$0.195863\pi$
$38$	4.30909	0.699027
$39$	−13.6219	−2.18126
$40$	5.37993	0.850641
$41$	−7.03092	−1.09805	−0.549023	−	0.835808i	$-0.685000\pi$
$41$	−7.03092	−1.09805	−0.549023	+	0.835808i	$0.685000\pi$
$42$	−15.0825	−2.32728
$43$	0	0
$43$	0	0
$44$	0.324635	0.0489405
$45$	−7.72408	−1.15144
$46$	−5.44058	−0.802170
$47$	−0.413795	−0.0603581	−0.0301791	−	0.999545i	$-0.509608\pi$
$47$	−0.413795	−0.0603581	−0.0301791	+	0.999545i	$0.509608\pi$
$48$	−11.6370	−1.67966
$49$	7.81157	1.11594
$50$	−1.04977	−0.148460
$51$	6.25681	0.876128
$52$	−1.49539	−0.207373
$53$	6.20009	0.851648	0.425824	−	0.904806i	$-0.359984\pi$
$53$	6.20009	0.851648	0.425824	+	0.904806i	$0.359984\pi$
$54$	2.83152	0.385320
$55$	−2.36660	−0.319113
$56$	9.97852	1.33344
$57$	7.39169	0.979053
$58$	−7.46504	−0.980207
$59$	−9.98383	−1.29978	−0.649892	−	0.760027i	$-0.725186\pi$
$59$	−9.98383	−1.29978	−0.649892	+	0.760027i	$0.725186\pi$
$60$	−1.53129	−0.197688
$61$	−11.5300	−1.47626	−0.738131	−	0.674658i	$-0.764291\pi$
$61$	−11.5300	−1.47626	−0.738131	+	0.674658i	$0.764291\pi$
$62$	−7.52759	−0.956004
$63$	−14.3264	−1.80495
$64$	6.56048	0.820061
$65$	10.9014	1.35216
$66$	4.46981	0.550195
$67$	2.69318	0.329024	0.164512	−	0.986375i	$-0.447395\pi$
$67$	2.69318	0.329024	0.164512	+	0.986375i	$0.447395\pi$
$68$	0.686858	0.0832938
$69$	−9.33261	−1.12351
$70$	12.0703	1.44268
$71$	11.9359	1.41653	0.708267	−	0.705944i	$-0.249477\pi$
$71$	11.9359	1.41653	0.708267	+	0.705944i	$0.249477\pi$
$72$	−9.65166	−1.13746
$73$	0.792034	0.0927006	0.0463503	−	0.998925i	$-0.485241\pi$
$73$	0.792034	0.0927006	0.0463503	+	0.998925i	$0.485241\pi$
$74$	15.0156	1.74552
$75$	−1.80075	−0.207932
$76$	0.811443	0.0930789
$77$	−4.38950	−0.500230
$78$	−20.5896	−2.33131
$79$	5.43676	0.611684	0.305842	−	0.952082i	$-0.401062\pi$
$79$	5.43676	0.611684	0.305842	+	0.952082i	$0.401062\pi$
$80$	9.31295	1.04122
$81$	−6.31044	−0.701160
$82$	−10.6272	−1.17358
$83$	0.475365	0.0521781	0.0260890	−	0.999660i	$-0.491695\pi$
$83$	0.475365	0.0521781	0.0260890	+	0.999660i	$0.491695\pi$
$84$	−2.84018	−0.309889
$85$	−5.00723	−0.543110
$86$	0	0
$87$	−12.8053	−1.37287
$88$	−2.95720	−0.315239
$89$	4.99089	0.529034	0.264517	−	0.964381i	$-0.414788\pi$
$89$	4.99089	0.529034	0.264517	+	0.964381i	$0.414788\pi$
$90$	−11.6749	−1.23065
$91$	20.2197	2.11960
$92$	−1.02451	−0.106813
$93$	−12.9126	−1.33897
$94$	−0.625450	−0.0645102
$95$	−5.91546	−0.606913
$96$	−4.14435	−0.422981
$97$	−0.449409	−0.0456305	−0.0228153	−	0.999740i	$-0.507263\pi$
$97$	−0.449409	−0.0456305	−0.0228153	+	0.999740i	$0.507263\pi$
$98$	11.8072	1.19270
$99$	4.24572	0.426711
$100$	−0.197682	−0.0197682
$101$	2.25114	0.223996	0.111998	−	0.993708i	$-0.464275\pi$
$101$	2.25114	0.223996	0.111998	+	0.993708i	$0.464275\pi$
$102$	9.45716	0.936398
$103$	−5.22094	−0.514434	−0.257217	−	0.966354i	$-0.582806\pi$
$103$	−5.22094	−0.514434	−0.257217	+	0.966354i	$0.582806\pi$
$104$	13.6219	1.33574
$105$	20.7051	2.02061
$106$	9.37143	0.910234
$107$	2.61046	0.252363	0.126182	−	0.992007i	$-0.459728\pi$
$107$	2.61046	0.252363	0.126182	+	0.992007i	$0.459728\pi$
$108$	0.533201	0.0513073
$109$	−2.24294	−0.214834	−0.107417	−	0.994214i	$-0.534258\pi$
$109$	−2.24294	−0.214834	−0.107417	+	0.994214i	$0.534258\pi$
$110$	−3.57712	−0.341065
$111$	25.7572	2.44477
$112$	17.2734	1.63218
$113$	5.06332	0.476317	0.238159	−	0.971226i	$-0.423456\pi$
$113$	5.06332	0.476317	0.238159	+	0.971226i	$0.423456\pi$
$114$	11.1725	1.04640
$115$	7.46875	0.696465
$116$	−1.40574	−0.130519
$117$	−19.5573	−1.80808
$118$	−15.0905	−1.38920
$119$	−9.28726	−0.851361
$120$	13.9490	1.27336
$121$	−9.69914	−0.881740
$122$	−17.4275	−1.57782
$123$	−18.2296	−1.64371
$124$	−1.41752	−0.127297
$125$	11.8159	1.05685
$126$	−21.6543	−1.92912
$127$	−15.6782	−1.39122	−0.695608	−	0.718421i	$-0.744865\pi$
$127$	−15.6782	−1.39122	−0.695608	+	0.718421i	$0.744865\pi$
$128$	13.1130	1.15904
$129$	0	0
$130$	16.4775	1.44517
$131$	14.2937	1.24885	0.624424	−	0.781085i	$-0.285334\pi$
$131$	14.2937	1.24885	0.624424	+	0.781085i	$0.285334\pi$
$132$	0.841707	0.0732612
$133$	−10.9718	−0.951377
$134$	4.07073	0.351658
$135$	−3.88706	−0.334545
$136$	−6.25681	−0.536517
$137$	6.37776	0.544889	0.272444	−	0.962172i	$-0.412168\pi$
$137$	6.37776	0.544889	0.272444	+	0.962172i	$0.412168\pi$
$138$	−14.1062	−1.20080
$139$	1.37437	0.116572	0.0582862	−	0.998300i	$-0.481436\pi$
$139$	1.37437	0.116572	0.0582862	+	0.998300i	$0.481436\pi$
$140$	2.27296	0.192100
$141$	−1.07288	−0.0903527
$142$	18.0412	1.51398
$143$	−5.99223	−0.501095
$144$	−16.7075	−1.39230
$145$	10.2479	0.851041
$146$	1.19716	0.0990776
$147$	20.2537	1.67050
$148$	2.82757	0.232425
$149$	−13.5842	−1.11286	−0.556431	−	0.830894i	$-0.687830\pi$
$149$	−13.5842	−1.11286	−0.556431	+	0.830894i	$0.687830\pi$
$150$	−2.72183	−0.222236
$151$	−6.10134	−0.496520	−0.248260	−	0.968693i	$-0.579859\pi$
$151$	−6.10134	−0.496520	−0.248260	+	0.968693i	$0.579859\pi$
$152$	−7.39169	−0.599545
$153$	8.98304	0.726235
$154$	−6.63473	−0.534642
$155$	10.3338	0.830028
$156$	−3.87721	−0.310425
$157$	−11.6447	−0.929348	−0.464674	−	0.885482i	$-0.653828\pi$
$157$	−11.6447	−0.929348	−0.464674	+	0.885482i	$0.653828\pi$
$158$	8.21766	0.653762
$159$	16.0755	1.27487
$160$	3.31666	0.262205
$161$	13.8528	1.09175
$162$	−9.53822	−0.749394
$163$	−18.2005	−1.42557	−0.712785	−	0.701382i	$-0.752567\pi$
$163$	−18.2005	−1.42557	−0.712785	+	0.701382i	$0.752567\pi$
$164$	−2.00121	−0.156268
$165$	−6.13608	−0.477694
$166$	0.718513	0.0557675
$167$	−17.1857	−1.32987	−0.664933	−	0.746903i	$-0.731540\pi$
$167$	−17.1857	−1.32987	−0.664933	+	0.746903i	$0.731540\pi$
$168$	25.8721	1.99608
$169$	14.6024	1.12326
$170$	−7.56843	−0.580472
$171$	10.6124	0.811551
$172$	0	0
$173$	20.0629	1.52535	0.762677	−	0.646779i	$-0.223884\pi$
$173$	20.0629	1.52535	0.762677	+	0.646779i	$0.223884\pi$
$174$	−19.3552	−1.46731
$175$	2.67293	0.202054
$176$	−5.11907	−0.385865
$177$	−25.8859	−1.94570
$178$	7.54373	0.565427
$179$	11.8493	0.885656	0.442828	−	0.896607i	$-0.353975\pi$
$179$	11.8493	0.885656	0.442828	+	0.896607i	$0.353975\pi$
$180$	−2.19850	−0.163867
$181$	−12.1219	−0.901015	−0.450507	−	0.892773i	$-0.648757\pi$
$181$	−12.1219	−0.901015	−0.450507	+	0.892773i	$0.648757\pi$
$182$	30.5620	2.26541
$183$	−29.8947	−2.20988
$184$	9.33261	0.688009
$185$	−20.6131	−1.51551
$186$	−19.5174	−1.43108
$187$	2.75234	0.201271
$188$	−0.117778	−0.00858986
$189$	−7.20960	−0.524422
$190$	−8.94121	−0.648664
$191$	22.7262	1.64441	0.822205	−	0.569191i	$-0.192744\pi$
$191$	22.7262	1.64441	0.822205	+	0.569191i	$0.192744\pi$
$192$	17.0099	1.22758
$193$	18.1362	1.30547	0.652736	−	0.757585i	$-0.273621\pi$
$193$	18.1362	1.30547	0.652736	+	0.757585i	$0.273621\pi$
$194$	−0.679281	−0.0487695
$195$	28.2651	2.02410
$196$	2.22340	0.158815
$197$	0.996294	0.0709830	0.0354915	−	0.999370i	$-0.488700\pi$
$197$	0.996294	0.0709830	0.0354915	+	0.999370i	$0.488700\pi$
$198$	6.41740	0.456065
$199$	5.44229	0.385794	0.192897	−	0.981219i	$-0.438212\pi$
$199$	5.44229	0.385794	0.192897	+	0.981219i	$0.438212\pi$
$200$	1.80075	0.127332
$201$	6.98281	0.492530
$202$	3.40259	0.239405
$203$	19.0075	1.33406
$204$	1.78087	0.124686
$205$	14.5889	1.01893
$206$	−7.89144	−0.549823
$207$	−13.3990	−0.931297
$208$	23.5803	1.63500
$209$	3.25157	0.224916
$210$	31.2957	2.15961
$211$	6.46515	0.445079	0.222540	−	0.974924i	$-0.428565\pi$
$211$	6.46515	0.445079	0.222540	+	0.974924i	$0.428565\pi$
$212$	1.76473	0.121202
$213$	30.9473	2.12047
$214$	3.94571	0.269723
$215$	0	0
$216$	−4.85710	−0.330484
$217$	19.1667	1.30112
$218$	−3.39020	−0.229613
$219$	2.05357	0.138767
$220$	−0.673606	−0.0454145
$221$	−12.6783	−0.852834
$222$	38.9320	2.61295
$223$	21.0841	1.41190	0.705948	−	0.708264i	$-0.250521\pi$
$223$	21.0841	1.41190	0.705948	+	0.708264i	$0.250521\pi$
$224$	6.15164	0.411024
$225$	−2.58537	−0.172358
$226$	7.65320	0.509084
$227$	−22.5140	−1.49431	−0.747154	−	0.664651i	$-0.768580\pi$
$227$	−22.5140	−1.49431	−0.747154	+	0.664651i	$0.768580\pi$
$228$	2.10389	0.139334
$229$	13.2596	0.876221	0.438110	−	0.898921i	$-0.355648\pi$
$229$	13.2596	0.876221	0.438110	+	0.898921i	$0.355648\pi$
$230$	11.2890	0.744375
$231$	−11.3810	−0.748816
$232$	12.8053	0.840709
$233$	−19.6060	−1.28443	−0.642217	−	0.766523i	$-0.721985\pi$
$233$	−19.6060	−1.28443	−0.642217	+	0.766523i	$0.721985\pi$
$234$	−29.5609	−1.93246
$235$	0.858609	0.0560095
$236$	−2.84169	−0.184978
$237$	14.0963	0.915655
$238$	−14.0377	−0.909928
$239$	−0.628848	−0.0406768	−0.0203384	−	0.999793i	$-0.506474\pi$
$239$	−0.628848	−0.0406768	−0.0203384	+	0.999793i	$0.506474\pi$
$240$	24.1464	1.55865
$241$	−17.6727	−1.13840	−0.569201	−	0.822199i	$-0.692747\pi$
$241$	−17.6727	−1.13840	−0.569201	+	0.822199i	$0.692747\pi$
$242$	−14.6602	−0.942396
$243$	−21.9815	−1.41012
$244$	−3.28177	−0.210094
$245$	−16.2087	−1.03554
$246$	−27.5541	−1.75678
$247$	−14.9779	−0.953022
$248$	12.9126	0.819951
$249$	1.23252	0.0781076
$250$	17.8598	1.12955
$251$	−16.0825	−1.01512	−0.507561	−	0.861616i	$-0.669453\pi$
$251$	−16.0825	−1.01512	−0.507561	+	0.861616i	$0.669453\pi$
$252$	−4.07771	−0.256872
$253$	−4.10537	−0.258102
$254$	−23.6976	−1.48692
$255$	−12.9827	−0.813005
$256$	6.69932	0.418708
$257$	−6.06652	−0.378419	−0.189210	−	0.981937i	$-0.560593\pi$
$257$	−6.06652	−0.378419	−0.189210	+	0.981937i	$0.560593\pi$
$258$	0	0
$259$	−38.2326	−2.37566
$260$	3.10287	0.192432
$261$	−18.3849	−1.13799
$262$	21.6050	1.33476
$263$	−10.6911	−0.659244	−0.329622	−	0.944113i	$-0.606921\pi$
$263$	−10.6911	−0.659244	−0.329622	+	0.944113i	$0.606921\pi$
$264$	−7.66737	−0.471894
$265$	−12.8650	−0.790288
$266$	−16.5839	−1.01682
$267$	12.9403	0.791933
$268$	0.766558	0.0468250
$269$	−3.58984	−0.218876	−0.109438	−	0.993994i	$-0.534905\pi$
$269$	−3.58984	−0.218876	−0.109438	+	0.993994i	$0.534905\pi$
$270$	−5.87529	−0.357559
$271$	8.87322	0.539010	0.269505	−	0.962999i	$-0.413140\pi$
$271$	8.87322	0.539010	0.269505	+	0.962999i	$0.413140\pi$
$272$	−10.8309	−0.656718
$273$	52.4252	3.17291
$274$	9.63998	0.582372
$275$	−0.792140	−0.0477678
$276$	−2.65634	−0.159893
$277$	−25.4980	−1.53203	−0.766013	−	0.642825i	$-0.777762\pi$
$277$	−25.4980	−1.53203	−0.766013	+	0.642825i	$0.777762\pi$
$278$	2.07736	0.124592
$279$	−18.5389	−1.10989
$280$	−20.7051	−1.23737
$281$	−7.74692	−0.462142	−0.231071	−	0.972937i	$-0.574223\pi$
$281$	−7.74692	−0.462142	−0.231071	+	0.972937i	$0.574223\pi$
$282$	−1.62165	−0.0965681
$283$	−27.4543	−1.63199	−0.815994	−	0.578060i	$-0.803810\pi$
$283$	−27.4543	−1.63199	−0.815994	+	0.578060i	$0.803810\pi$
$284$	3.39732	0.201594
$285$	−15.3375	−0.908514
$286$	−9.05725	−0.535566
$287$	27.0591	1.59725
$288$	−5.95013	−0.350615
$289$	−11.1766	−0.657449
$290$	15.4897	0.909586
$291$	−1.16522	−0.0683063
$292$	0.225436	0.0131927
$293$	−9.07706	−0.530287	−0.265144	−	0.964209i	$-0.585419\pi$
$293$	−9.07706	−0.530287	−0.265144	+	0.964209i	$0.585419\pi$
$294$	30.6134	1.78541
$295$	20.7161	1.20614
$296$	−25.7572	−1.49711
$297$	2.13661	0.123979
$298$	−20.5325	−1.18942
$299$	18.9108	1.09364
$300$	−0.512546	−0.0295919
$301$	0	0
$302$	−9.22218	−0.530677
$303$	5.83670	0.335310
$304$	−12.7954	−0.733867
$305$	23.9243	1.36990
$306$	13.5779	0.776194
$307$	−17.0027	−0.970394	−0.485197	−	0.874405i	$-0.661252\pi$
$307$	−17.0027	−0.970394	−0.485197	+	0.874405i	$0.661252\pi$
$308$	−1.24938	−0.0711902
$309$	−13.5367	−0.770078
$310$	15.6195	0.887126
$311$	−23.6872	−1.34318	−0.671588	−	0.740925i	$-0.734387\pi$
$311$	−23.6872	−1.34318	−0.671588	+	0.740925i	$0.734387\pi$
$312$	35.3187	1.99953
$313$	25.1858	1.42359	0.711793	−	0.702389i	$-0.247883\pi$
$313$	25.1858	1.42359	0.711793	+	0.702389i	$0.247883\pi$
$314$	−17.6010	−0.993279
$315$	29.7267	1.67491
$316$	1.54746	0.0870517
$317$	−26.6132	−1.49475	−0.747374	−	0.664403i	$-0.768686\pi$
$317$	−26.6132	−1.49475	−0.747374	+	0.664403i	$0.768686\pi$
$318$	24.2981	1.36257
$319$	−5.63299	−0.315387
$320$	−13.6128	−0.760977
$321$	6.76836	0.377773
$322$	20.9385	1.16686
$323$	6.87963	0.382793
$324$	−1.79614	−0.0997855
$325$	3.64889	0.202404
$326$	−27.5100	−1.52364
$327$	−5.81544	−0.321595
$328$	18.2296	1.00656
$329$	1.59252	0.0877985
$330$	−9.27469	−0.510555
$331$	−3.38262	−0.185925	−0.0929627	−	0.995670i	$-0.529634\pi$
$331$	−3.38262	−0.185925	−0.0929627	+	0.995670i	$0.529634\pi$
$332$	0.135303	0.00742571
$333$	36.9802	2.02650
$334$	−25.9761	−1.42135
$335$	−5.58824	−0.305318
$336$	44.7861	2.44328
$337$	1.86078	0.101363	0.0506815	−	0.998715i	$-0.483861\pi$
$337$	1.86078	0.101363	0.0506815	+	0.998715i	$0.483861\pi$
$338$	22.0715	1.20053
$339$	13.1281	0.713019
$340$	−1.42521	−0.0772927
$341$	−5.68019	−0.307599
$342$	16.0406	0.867379
$343$	−3.12337	−0.168646
$344$	0	0
$345$	19.3648	1.04257
$346$	30.3251	1.63029
$347$	−6.30643	−0.338547	−0.169273	−	0.985569i	$-0.554142\pi$
$347$	−6.30643	−0.338547	−0.169273	+	0.985569i	$0.554142\pi$
$348$	−3.64477	−0.195380
$349$	26.3252	1.40915	0.704577	−	0.709627i	$-0.251137\pi$
$349$	26.3252	1.40915	0.704577	+	0.709627i	$0.251137\pi$
$350$	4.04013	0.215954
$351$	−9.84202	−0.525328
$352$	−1.82308	−0.0971703
$353$	25.1412	1.33813	0.669064	−	0.743205i	$-0.266695\pi$
$353$	25.1412	1.33813	0.669064	+	0.743205i	$0.266695\pi$
$354$	−39.1265	−2.07955
$355$	−24.7666	−1.31448
$356$	1.42056	0.0752894
$357$	−24.0798	−1.27444
$358$	17.9102	0.946581
$359$	−36.1352	−1.90714	−0.953571	−	0.301169i	$-0.902623\pi$
$359$	−36.1352	−1.90714	−0.953571	+	0.301169i	$0.902623\pi$
$360$	20.0268	1.05551
$361$	−10.8725	−0.572238
$362$	−18.3223	−0.962997
$363$	−25.1477	−1.31991
$364$	5.75512	0.301650
$365$	−1.64344	−0.0860217
$366$	−45.1858	−2.36190
$367$	−16.8220	−0.878104	−0.439052	−	0.898462i	$-0.644686\pi$
$367$	−16.8220	−0.878104	−0.439052	+	0.898462i	$0.644686\pi$
$368$	16.1553	0.842151
$369$	−26.1727	−1.36250
$370$	−31.1567	−1.61976
$371$	−23.8615	−1.23883
$372$	−3.67531	−0.190556
$373$	−28.6489	−1.48338	−0.741691	−	0.670742i	$-0.765976\pi$
$373$	−28.6489	−1.48338	−0.741691	+	0.670742i	$0.765976\pi$
$374$	4.16016	0.215117
$375$	30.6361	1.58204
$376$	1.07288	0.0553295
$377$	25.9476	1.33637
$378$	−10.8973	−0.560497
$379$	26.1255	1.34197	0.670987	−	0.741469i	$-0.265870\pi$
$379$	26.1255	1.34197	0.670987	+	0.741469i	$0.265870\pi$
$380$	−1.68372	−0.0863728
$381$	−40.6502	−2.08257
$382$	34.3506	1.75753
$383$	6.54617	0.334494	0.167247	−	0.985915i	$-0.446512\pi$
$383$	6.54617	0.334494	0.167247	+	0.985915i	$0.446512\pi$
$384$	33.9991	1.73501
$385$	9.10806	0.464190
$386$	27.4129	1.39528
$387$	0	0
$388$	−0.127915	−0.00649390
$389$	−21.2054	−1.07515	−0.537577	−	0.843215i	$-0.680660\pi$
$389$	−21.2054	−1.07515	−0.537577	+	0.843215i	$0.680660\pi$
$390$	42.7226	2.16334
$391$	−8.68609	−0.439275
$392$	−20.2537	−1.02297
$393$	37.0605	1.86946
$394$	1.50590	0.0758660
$395$	−11.2811	−0.567613
$396$	1.20846	0.0607272
$397$	−23.4637	−1.17761	−0.588804	−	0.808276i	$-0.700401\pi$
$397$	−23.4637	−1.17761	−0.588804	+	0.808276i	$0.700401\pi$
$398$	8.22602	0.412333
$399$	−28.4475	−1.42416
$400$	3.11719	0.155860
$401$	−36.6744	−1.83143	−0.915716	−	0.401827i	$-0.868375\pi$
$401$	−36.6744	−1.83143	−0.915716	+	0.401827i	$0.868375\pi$
$402$	10.5545	0.526411
$403$	26.1650	1.30337
$404$	0.640740	0.0318780
$405$	13.0939	0.650643
$406$	28.7298	1.42584
$407$	11.3305	0.561631
$408$	−16.2225	−0.803135
$409$	9.38589	0.464103	0.232051	−	0.972704i	$-0.425456\pi$
$409$	9.38589	0.464103	0.232051	+	0.972704i	$0.425456\pi$
$410$	22.0511	1.08903
$411$	16.5361	0.815667
$412$	−1.48603	−0.0732116
$413$	38.4236	1.89070
$414$	−20.2526	−0.995362
$415$	−0.986365	−0.0484187
$416$	8.39776	0.411734
$417$	3.56343	0.174502
$418$	4.91474	0.240388
$419$	−11.1881	−0.546576	−0.273288	−	0.961932i	$-0.588111\pi$
$419$	−11.1881	−0.546576	−0.273288	+	0.961932i	$0.588111\pi$
$420$	5.89328	0.287563
$421$	12.3808	0.603404	0.301702	−	0.953402i	$-0.402445\pi$
$421$	12.3808	0.603404	0.301702	+	0.953402i	$0.402445\pi$
$422$	9.77207	0.475697
$423$	−1.54036	−0.0748946
$424$	−16.0755	−0.780694
$425$	−1.67600	−0.0812979
$426$	46.7768	2.26634
$427$	44.3740	2.14741
$428$	0.743015	0.0359150
$429$	−15.5365	−0.750111
$430$	0	0
$431$	7.23483	0.348490	0.174245	−	0.984702i	$-0.444252\pi$
$431$	7.23483	0.348490	0.174245	+	0.984702i	$0.444252\pi$
$432$	−8.40790	−0.404525
$433$	−11.5087	−0.553071	−0.276535	−	0.961004i	$-0.589186\pi$
$433$	−11.5087	−0.553071	−0.276535	+	0.961004i	$0.589186\pi$
$434$	28.9705	1.39063
$435$	26.5705	1.27396
$436$	−0.638406	−0.0305741
$437$	−10.2616	−0.490879
$438$	3.10397	0.148313
$439$	26.3662	1.25839	0.629194	−	0.777248i	$-0.283385\pi$
$439$	26.3662	1.25839	0.629194	+	0.777248i	$0.283385\pi$
$440$	6.13608	0.292526
$441$	29.0786	1.38470
$442$	−19.1632	−0.911501
$443$	8.46587	0.402226	0.201113	−	0.979568i	$-0.435544\pi$
$443$	8.46587	0.402226	0.201113	+	0.979568i	$0.435544\pi$
$444$	7.33127	0.347927
$445$	−10.3559	−0.490918
$446$	31.8686	1.50902
$447$	−35.2209	−1.66589
$448$	−25.2485	−1.19288
$449$	19.4386	0.917364	0.458682	−	0.888601i	$-0.348322\pi$
$449$	19.4386	0.917364	0.458682	+	0.888601i	$0.348322\pi$
$450$	−3.90779	−0.184215
$451$	−8.01913	−0.377606
$452$	1.44117	0.0677870
$453$	−15.8194	−0.743263
$454$	−34.0299	−1.59710
$455$	−41.9551	−1.96688
$456$	−19.1650	−0.897485
$457$	−0.0607795	−0.00284315	−0.00142157	−	0.999999i	$-0.500453\pi$
$457$	−0.0607795	−0.00284315	−0.00142157	+	0.999999i	$0.500453\pi$
$458$	20.0419	0.936497
$459$	4.52062	0.211004
$460$	2.12583	0.0991173
$461$	−23.6403	−1.10104	−0.550520	−	0.834822i	$-0.685571\pi$
$461$	−23.6403	−1.10104	−0.550520	+	0.834822i	$0.685571\pi$
$462$	−17.2024	−0.800328
$463$	8.07628	0.375337	0.187668	−	0.982232i	$-0.439907\pi$
$463$	8.07628	0.375337	0.187668	+	0.982232i	$0.439907\pi$
$464$	22.1667	1.02906
$465$	26.7932	1.24250
$466$	−29.6345	−1.37279
$467$	−34.6454	−1.60320	−0.801598	−	0.597863i	$-0.796017\pi$
$467$	−34.6454	−1.60320	−0.801598	+	0.597863i	$0.796017\pi$
$468$	−5.56660	−0.257316
$469$	−10.3649	−0.478607
$470$	1.29779	0.0598624
$471$	−30.1922	−1.39118
$472$	25.8859	1.19149
$473$	0	0
$474$	21.3066	0.978644
$475$	−1.98000	−0.0908485
$476$	−2.64343	−0.121161
$477$	23.0799	1.05676
$478$	−0.950503	−0.0434750
$479$	−36.1230	−1.65050	−0.825252	−	0.564765i	$-0.808967\pi$
$479$	−36.1230	−1.65050	−0.825252	+	0.564765i	$0.808967\pi$
$480$	8.59937	0.392506
$481$	−52.1924	−2.37977
$482$	−26.7123	−1.21671
$483$	35.9173	1.63429
$484$	−2.76066	−0.125485
$485$	0.932507	0.0423430
$486$	−33.2251	−1.50712
$487$	28.1907	1.27744	0.638721	−	0.769438i	$-0.279464\pi$
$487$	28.1907	1.27744	0.638721	+	0.769438i	$0.279464\pi$
$488$	29.8947	1.35327
$489$	−47.1898	−2.13400
$490$	−24.4995	−1.10677
$491$	24.9230	1.12476	0.562379	−	0.826880i	$-0.309886\pi$
$491$	24.9230	1.12476	0.562379	+	0.826880i	$0.309886\pi$
$492$	−5.18869	−0.233924
$493$	−11.9182	−0.536769
$494$	−22.6391	−1.01858
$495$	−8.80971	−0.395967
$496$	22.3524	1.00365
$497$	−45.9364	−2.06053
$498$	1.86295	0.0834807
$499$	22.6517	1.01403	0.507015	−	0.861937i	$-0.330749\pi$
$499$	22.6517	1.01403	0.507015	+	0.861937i	$0.330749\pi$
$500$	3.36317	0.150405
$501$	−44.5587	−1.99073
$502$	−24.3088	−1.08495
$503$	11.4515	0.510595	0.255298	−	0.966863i	$-0.417827\pi$
$503$	11.4515	0.510595	0.255298	+	0.966863i	$0.417827\pi$
$504$	37.1452	1.65458
$505$	−4.67103	−0.207858
$506$	−6.20526	−0.275858
$507$	37.8608	1.68146
$508$	−4.46248	−0.197991
$509$	−25.4043	−1.12603	−0.563014	−	0.826448i	$-0.690358\pi$
$509$	−25.4043	−1.12603	−0.563014	+	0.826448i	$0.690358\pi$
$510$	−19.6233	−0.868933
$511$	−3.04821	−0.134845
$512$	−16.1000	−0.711525
$513$	5.34058	0.235793
$514$	−9.16954	−0.404451
$515$	10.8333	0.477370
$516$	0	0
$517$	−0.471954	−0.0207565
$518$	−57.7886	−2.53908
$519$	52.0187	2.28337
$520$	−28.2651	−1.23950
$521$	22.8126	0.999439	0.499720	−	0.866187i	$-0.333436\pi$
$521$	22.8126	0.999439	0.499720	+	0.866187i	$0.333436\pi$
$522$	−27.7887	−1.21628
$523$	41.7500	1.82560	0.912801	−	0.408404i	$-0.133915\pi$
$523$	41.7500	1.82560	0.912801	+	0.408404i	$0.133915\pi$
$524$	4.06842	0.177730
$525$	6.93032	0.302464
$526$	−16.1596	−0.704594
$527$	−12.0181	−0.523516
$528$	−13.2726	−0.577617
$529$	−10.0439	−0.436691
$530$	−19.4454	−0.844653
$531$	−37.1649	−1.61282
$532$	−3.12290	−0.135395
$533$	36.9390	1.60001
$534$	19.5592	0.846411
$535$	−5.41662	−0.234181
$536$	−6.98281	−0.301612
$537$	30.7226	1.32578
$538$	−5.42604	−0.233933
$539$	8.90949	0.383759
$540$	−1.10637	−0.0476107
$541$	44.0065	1.89199	0.945994	−	0.324185i	$-0.105090\pi$
$541$	44.0065	1.89199	0.945994	+	0.324185i	$0.105090\pi$
$542$	13.4119	0.576089
$543$	−31.4295	−1.34877
$544$	−3.85724	−0.165378
$545$	4.65401	0.199356
$546$	79.2406	3.39118
$547$	3.33172	0.142454	0.0712271	−	0.997460i	$-0.477308\pi$
$547$	3.33172	0.142454	0.0712271	+	0.997460i	$0.477308\pi$
$548$	1.81530	0.0775458
$549$	−42.9204	−1.83180
$550$	−1.19732	−0.0510538
$551$	−14.0800	−0.599827
$552$	24.1974	1.02991
$553$	−20.9238	−0.889771
$554$	−38.5402	−1.63742
$555$	−53.4453	−2.26863
$556$	0.391186	0.0165900
$557$	−24.9762	−1.05828	−0.529138	−	0.848536i	$-0.677485\pi$
$557$	−24.9762	−1.05828	−0.529138	+	0.848536i	$0.677485\pi$
$558$	−28.0215	−1.18625
$559$	0	0
$560$	−35.8416	−1.51459
$561$	7.13621	0.301291
$562$	−11.7095	−0.493934
$563$	20.6022	0.868278	0.434139	−	0.900846i	$-0.357053\pi$
$563$	20.6022	0.868278	0.434139	+	0.900846i	$0.357053\pi$
$564$	−0.305373	−0.0128585
$565$	−10.5062	−0.441999
$566$	−41.4972	−1.74426
$567$	24.2862	1.01993
$568$	−30.9473	−1.29852
$569$	36.7111	1.53901	0.769504	−	0.638642i	$-0.220503\pi$
$569$	36.7111	1.53901	0.769504	+	0.638642i	$0.220503\pi$
$570$	−23.1826	−0.971012
$571$	38.1856	1.59802	0.799009	−	0.601319i	$-0.205358\pi$
$571$	38.1856	1.59802	0.799009	+	0.601319i	$0.205358\pi$
$572$	−1.70557	−0.0713133
$573$	58.9241	2.46159
$574$	40.8997	1.70712
$575$	2.49991	0.104253
$576$	24.4215	1.01756
$577$	−20.7354	−0.863228	−0.431614	−	0.902058i	$-0.642056\pi$
$577$	−20.7354	−0.863228	−0.431614	+	0.902058i	$0.642056\pi$
$578$	−16.8935	−0.702676
$579$	47.0232	1.95422
$580$	2.91686	0.121116
$581$	−1.82948	−0.0758996
$582$	−1.76123	−0.0730052
$583$	7.07152	0.292872
$584$	−2.05357	−0.0849774
$585$	40.5808	1.67781
$586$	−13.7200	−0.566767
$587$	43.6927	1.80339	0.901694	−	0.432374i	$-0.142324\pi$
$587$	43.6927	1.80339	0.901694	+	0.432374i	$0.142324\pi$
$588$	5.76480	0.237736
$589$	−14.1980	−0.585016
$590$	31.3123	1.28911
$591$	2.58317	0.106258
$592$	−44.5872	−1.83252
$593$	3.03902	0.124798	0.0623989	−	0.998051i	$-0.480125\pi$
$593$	3.03902	0.124798	0.0623989	+	0.998051i	$0.480125\pi$
$594$	3.22949	0.132508
$595$	19.2707	0.790023
$596$	−3.86647	−0.158377
$597$	14.1107	0.577511
$598$	28.5837	1.16888
$599$	−15.0885	−0.616498	−0.308249	−	0.951306i	$-0.599743\pi$
$599$	−15.0885	−0.616498	−0.308249	+	0.951306i	$0.599743\pi$
$600$	4.66894	0.190609
$601$	−36.6486	−1.49493	−0.747464	−	0.664303i	$-0.768729\pi$
$601$	−36.6486	−1.49493	−0.747464	+	0.664303i	$0.768729\pi$
$602$	0	0
$603$	10.0254	0.408265
$604$	−1.73662	−0.0706622
$605$	20.1254	0.818213
$606$	8.82217	0.358376
$607$	8.92342	0.362190	0.181095	−	0.983466i	$-0.442036\pi$
$607$	8.92342	0.362190	0.181095	+	0.983466i	$0.442036\pi$
$608$	−4.55688	−0.184806
$609$	49.2822	1.99702
$610$	36.1615	1.46414
$611$	2.17399	0.0879504
$612$	2.55684	0.103354
$613$	42.6254	1.72163	0.860813	−	0.508922i	$-0.169956\pi$
$613$	42.6254	1.72163	0.860813	+	0.508922i	$0.169956\pi$
$614$	−25.6995	−1.03715
$615$	37.8258	1.52528
$616$	11.3810	0.458554
$617$	16.0336	0.645488	0.322744	−	0.946486i	$-0.395395\pi$
$617$	16.0336	0.645488	0.322744	+	0.946486i	$0.395395\pi$
$618$	−20.4608	−0.823053
$619$	−16.5204	−0.664011	−0.332005	−	0.943278i	$-0.607725\pi$
$619$	−16.5204	−0.664011	−0.332005	+	0.943278i	$0.607725\pi$
$620$	2.94130	0.118125
$621$	−6.74293	−0.270584
$622$	−35.8031	−1.43557
$623$	−19.2079	−0.769546
$624$	61.1387	2.44750
$625$	−21.0450	−0.841801
$626$	38.0683	1.52152
$627$	8.43060	0.336686
$628$	−3.31443	−0.132260
$629$	23.9729	0.955862
$630$	44.9319	1.79013
$631$	−13.3904	−0.533063	−0.266531	−	0.963826i	$-0.585878\pi$
$631$	−13.3904	−0.533063	−0.266531	+	0.963826i	$0.585878\pi$
$632$	−14.0963	−0.560722
$633$	16.7627	0.666258
$634$	−40.2259	−1.59757
$635$	32.5317	1.29098
$636$	4.57556	0.181433
$637$	−41.0404	−1.62608
$638$	−8.51426	−0.337083
$639$	44.4317	1.75769
$640$	−27.2090	−1.07553
$641$	1.00308	0.0396192	0.0198096	−	0.999804i	$-0.493694\pi$
$641$	1.00308	0.0396192	0.0198096	+	0.999804i	$0.493694\pi$
$642$	10.2304	0.403760
$643$	19.2801	0.760332	0.380166	−	0.924918i	$-0.375867\pi$
$643$	19.2801	0.760332	0.380166	+	0.924918i	$0.375867\pi$
$644$	3.94292	0.155373
$645$	0	0
$646$	10.3985	0.409125
$647$	−28.1175	−1.10541	−0.552706	−	0.833376i	$-0.686405\pi$
$647$	−28.1175	−1.10541	−0.552706	+	0.833376i	$0.686405\pi$
$648$	16.3616	0.642744
$649$	−11.3871	−0.446982
$650$	5.51529	0.216327
$651$	49.6952	1.94771
$652$	−5.18039	−0.202880
$653$	−11.8795	−0.464883	−0.232441	−	0.972610i	$-0.574671\pi$
$653$	−11.8795	−0.464883	−0.232441	+	0.972610i	$0.574671\pi$
$654$	−8.79003	−0.343718
$655$	−29.6590	−1.15887
$656$	31.5565	1.23207
$657$	2.94836	0.115026
$658$	2.40709	0.0938383
$659$	−26.8353	−1.04536	−0.522678	−	0.852530i	$-0.675067\pi$
$659$	−26.8353	−1.04536	−0.522678	+	0.852530i	$0.675067\pi$
$660$	−1.74651	−0.0679829
$661$	28.7038	1.11645	0.558225	−	0.829690i	$-0.311483\pi$
$661$	28.7038	1.11645	0.558225	+	0.829690i	$0.311483\pi$
$662$	−5.11282	−0.198715
$663$	−32.8720	−1.27664
$664$	−1.23252	−0.0478309
$665$	22.7661	0.882832
$666$	55.8956	2.16591
$667$	17.7771	0.688333
$668$	−4.89155	−0.189260
$669$	54.6665	2.11353
$670$	−8.44662	−0.326322
$671$	−13.1505	−0.507670
$672$	15.9498	0.615279
$673$	25.3446	0.976963	0.488482	−	0.872574i	$-0.337551\pi$
$673$	25.3446	0.976963	0.488482	+	0.872574i	$0.337551\pi$
$674$	2.81256	0.108336
$675$	−1.30106	−0.0500779
$676$	4.15628	0.159857
$677$	15.2830	0.587374	0.293687	−	0.955902i	$-0.405118\pi$
$677$	15.2830	0.587374	0.293687	+	0.955902i	$0.405118\pi$
$678$	19.8431	0.762069
$679$	1.72959	0.0663754
$680$	12.9827	0.497862
$681$	−58.3739	−2.23689
$682$	−8.58560	−0.328760
$683$	27.5073	1.05254	0.526269	−	0.850318i	$-0.323590\pi$
$683$	27.5073	1.05254	0.526269	+	0.850318i	$0.323590\pi$
$684$	3.02061	0.115496
$685$	−13.2336	−0.505631
$686$	−4.72098	−0.180248
$687$	34.3793	1.31165
$688$	0	0
$689$	−32.5740	−1.24097
$690$	29.2699	1.11429
$691$	−6.78089	−0.257957	−0.128979	−	0.991647i	$-0.541170\pi$
$691$	−6.78089	−0.257957	−0.128979	+	0.991647i	$0.541170\pi$
$692$	5.71050	0.217081
$693$	−16.3400	−0.620704
$694$	−9.53216	−0.361836
$695$	−2.85176	−0.108174
$696$	33.2013	1.25849
$697$	−16.9668	−0.642662
$698$	39.7905	1.50609
$699$	−50.8342	−1.92272
$700$	0.760795	0.0287553
$701$	12.9567	0.489368	0.244684	−	0.969603i	$-0.421316\pi$
$701$	12.9567	0.489368	0.244684	+	0.969603i	$0.421316\pi$
$702$	−14.8762	−0.561466
$703$	28.3212	1.06815
$704$	7.48257	0.282010
$705$	2.22618	0.0838430
$706$	38.0008	1.43018
$707$	−8.66368	−0.325831
$708$	−7.36789	−0.276902
$709$	2.57997	0.0968928	0.0484464	−	0.998826i	$-0.484573\pi$
$709$	2.57997	0.0968928	0.0484464	+	0.998826i	$0.484573\pi$
$710$	−37.4347	−1.40490
$711$	20.2384	0.759000
$712$	−12.9403	−0.484958
$713$	17.9261	0.671337
$714$	−36.3966	−1.36211
$715$	12.4337	0.464993
$716$	3.37265	0.126042
$717$	−1.63046	−0.0608908
$718$	−54.6183	−2.03834
$719$	−4.22744	−0.157657	−0.0788284	−	0.996888i	$-0.525118\pi$
$719$	−4.22744	−0.157657	−0.0788284	+	0.996888i	$0.525118\pi$
$720$	34.6676	1.29198
$721$	20.0932	0.748309
$722$	−16.4338	−0.611603
$723$	−45.8215	−1.70412
$724$	−3.45026	−0.128228
$725$	3.43013	0.127392
$726$	−38.0108	−1.41071
$727$	−6.01827	−0.223205	−0.111603	−	0.993753i	$-0.535598\pi$
$727$	−6.01827	−0.223205	−0.111603	+	0.993753i	$0.535598\pi$
$728$	−52.4252	−1.94301
$729$	−38.0620	−1.40970
$730$	−2.48406	−0.0919393
$731$	0	0
$732$	−8.50891	−0.314498
$733$	−3.91945	−0.144768	−0.0723842	−	0.997377i	$-0.523061\pi$
$733$	−3.91945	−0.144768	−0.0723842	+	0.997377i	$0.523061\pi$
$734$	−25.4265	−0.938510
$735$	−42.0257	−1.55014
$736$	5.75344	0.212075
$737$	3.07171	0.113148
$738$	−39.5600	−1.45622
$739$	−13.4708	−0.495532	−0.247766	−	0.968820i	$-0.579696\pi$
$739$	−13.4708	−0.495532	−0.247766	+	0.968820i	$0.579696\pi$
$740$	−5.86711	−0.215679
$741$	−38.8344	−1.42662
$742$	−36.0667	−1.32405
$743$	1.02791	0.0377102	0.0188551	−	0.999822i	$-0.493998\pi$
$743$	1.02791	0.0377102	0.0188551	+	0.999822i	$0.493998\pi$
$744$	33.4795	1.22742
$745$	28.1868	1.03268
$746$	−43.3027	−1.58543
$747$	1.76955	0.0647445
$748$	0.783397	0.0286438
$749$	−10.0466	−0.367094
$750$	46.3065	1.69087
$751$	2.11014	0.0770002	0.0385001	−	0.999259i	$-0.487742\pi$
$751$	2.11014	0.0770002	0.0385001	+	0.999259i	$0.487742\pi$
$752$	1.85721	0.0677255
$753$	−41.6985	−1.51958
$754$	39.2198	1.42830
$755$	12.6601	0.460747
$756$	−2.05207	−0.0746330
$757$	−23.3366	−0.848184	−0.424092	−	0.905619i	$-0.639407\pi$
$757$	−23.3366	−0.848184	−0.424092	+	0.905619i	$0.639407\pi$
$758$	39.4886	1.43429
$759$	−10.6443	−0.386364
$760$	15.3375	0.556349
$761$	−27.1981	−0.985931	−0.492966	−	0.870049i	$-0.664087\pi$
$761$	−27.1981	−0.985931	−0.492966	+	0.870049i	$0.664087\pi$
$762$	−61.4427	−2.22583
$763$	8.63212	0.312504
$764$	6.46855	0.234024
$765$	−18.6395	−0.673912
$766$	9.89453	0.357504
$767$	52.4530	1.89397
$768$	17.3699	0.626781
$769$	41.4100	1.49328	0.746641	−	0.665227i	$-0.231665\pi$
$769$	41.4100	1.49328	0.746641	+	0.665227i	$0.231665\pi$
$770$	13.7668	0.496122
$771$	−15.7292	−0.566472
$772$	5.16210	0.185788
$773$	15.2245	0.547586	0.273793	−	0.961789i	$-0.411722\pi$
$773$	15.2245	0.547586	0.273793	+	0.961789i	$0.411722\pi$
$774$	0	0
$775$	3.45887	0.124246
$776$	1.16522	0.0418289
$777$	−99.1288	−3.55623
$778$	−32.0519	−1.14912
$779$	−20.0443	−0.718160
$780$	8.04507	0.288060
$781$	13.6135	0.487131
$782$	−13.1290	−0.469493
$783$	−9.25199	−0.330639
$784$	−35.0602	−1.25215
$785$	24.1623	0.862391
$786$	56.0169	1.99806
$787$	14.6735	0.523055	0.261528	−	0.965196i	$-0.415774\pi$
$787$	14.6735	0.523055	0.261528	+	0.965196i	$0.415774\pi$
$788$	0.283575	0.0101019
$789$	−27.7198	−0.986850
$790$	−17.0514	−0.606660
$791$	−19.4866	−0.692863
$792$	−11.0082	−0.391160
$793$	60.5761	2.15112
$794$	−35.4653	−1.25862
$795$	−33.3560	−1.18302
$796$	1.54904	0.0549042
$797$	11.2903	0.399924	0.199962	−	0.979804i	$-0.435918\pi$
$797$	11.2903	0.399924	0.199962	+	0.979804i	$0.435918\pi$
$798$	−42.9984	−1.52213
$799$	−0.998554	−0.0353263
$800$	1.11014	0.0392493
$801$	18.5787	0.656445
$802$	−55.4333	−1.95742
$803$	0.903356	0.0318787
$804$	1.98752	0.0700943
$805$	−28.7441	−1.01310
$806$	39.5484	1.39303
$807$	−9.30766	−0.327645
$808$	−5.83670	−0.205335
$809$	−10.0618	−0.353754	−0.176877	−	0.984233i	$-0.556599\pi$
$809$	−10.0618	−0.353754	−0.176877	+	0.984233i	$0.556599\pi$
$810$	19.7915	0.695402
$811$	19.4538	0.683115	0.341558	−	0.939861i	$-0.389046\pi$
$811$	19.4538	0.683115	0.341558	+	0.939861i	$0.389046\pi$
$812$	5.41009	0.189857
$813$	23.0063	0.806867
$814$	17.1260	0.600266
$815$	37.7653	1.32286
$816$	−28.0821	−0.983070
$817$	0	0
$818$	14.1868	0.496029
$819$	75.2679	2.63007
$820$	4.15244	0.145009
$821$	−18.8222	−0.656899	−0.328450	−	0.944521i	$-0.606526\pi$
$821$	−18.8222	−0.656899	−0.328450	+	0.944521i	$0.606526\pi$
$822$	24.9944	0.871778
$823$	19.3723	0.675277	0.337639	−	0.941276i	$-0.390372\pi$
$823$	19.3723	0.675277	0.337639	+	0.941276i	$0.390372\pi$
$824$	13.5367	0.471575
$825$	−2.05384	−0.0715057
$826$	58.0772	2.02076
$827$	40.8592	1.42082	0.710408	−	0.703791i	$-0.248511\pi$
$827$	40.8592	1.42082	0.710408	+	0.703791i	$0.248511\pi$
$828$	−3.81376	−0.132537
$829$	−28.7556	−0.998723	−0.499361	−	0.866394i	$-0.666432\pi$
$829$	−28.7556	−0.998723	−0.499361	+	0.866394i	$0.666432\pi$
$830$	−1.49089	−0.0517495
$831$	−66.1107	−2.29336
$832$	−34.4675	−1.19494
$833$	18.8506	0.653134
$834$	5.38613	0.186506
$835$	35.6596	1.23405
$836$	0.925493	0.0320088
$837$	−9.32951	−0.322475
$838$	−16.9109	−0.584176
$839$	16.5235	0.570456	0.285228	−	0.958460i	$-0.407931\pi$
$839$	16.5235	0.570456	0.285228	+	0.958460i	$0.407931\pi$
$840$	−53.6837	−1.85226
$841$	−4.60796	−0.158895
$842$	18.7136	0.644913
$843$	−20.0861	−0.691801
$844$	1.84017	0.0633414
$845$	−30.2995	−1.04233
$846$	−2.32825	−0.0800467
$847$	37.3279	1.28260
$848$	−27.8275	−0.955601
$849$	−71.1830	−2.44299
$850$	−2.53327	−0.0868905
$851$	−35.7578	−1.22576
$852$	8.80851	0.301775
$853$	6.69541	0.229246	0.114623	−	0.993409i	$-0.463434\pi$
$853$	6.69541	0.229246	0.114623	+	0.993409i	$0.463434\pi$
$854$	67.0713	2.29513
$855$	−22.0204	−0.753081
$856$	−6.76836	−0.231338
$857$	−1.67478	−0.0572095	−0.0286048	−	0.999591i	$-0.509106\pi$
$857$	−1.67478	−0.0572095	−0.0286048	+	0.999591i	$0.509106\pi$
$858$	−23.4835	−0.801712
$859$	−17.4988	−0.597052	−0.298526	−	0.954401i	$-0.596495\pi$
$859$	−17.4988	−0.597052	−0.298526	+	0.954401i	$0.596495\pi$
$860$	0	0
$861$	70.1582	2.39098
$862$	10.9354	0.372463
$863$	25.9534	0.883464	0.441732	−	0.897147i	$-0.354364\pi$
$863$	25.9534	0.883464	0.441732	+	0.897147i	$0.354364\pi$
$864$	−2.99434	−0.101870
$865$	−41.6298	−1.41546
$866$	−17.3953	−0.591117
$867$	−28.9786	−0.984164
$868$	5.45542	0.185169
$869$	6.20091	0.210351
$870$	40.1614	1.36160
$871$	−14.1494	−0.479434
$872$	5.81544	0.196936
$873$	−1.67293	−0.0566201
$874$	−15.5104	−0.524647
$875$	−45.4746	−1.53732
$876$	0.584507	0.0197487
$877$	33.5156	1.13174	0.565871	−	0.824494i	$-0.308540\pi$
$877$	33.5156	1.13174	0.565871	+	0.824494i	$0.308540\pi$
$878$	39.8524	1.34495
$879$	−23.5348	−0.793810
$880$	10.6219	0.358064
$881$	12.0919	0.407385	0.203692	−	0.979035i	$-0.434706\pi$
$881$	12.0919	0.407385	0.203692	+	0.979035i	$0.434706\pi$
$882$	43.9524	1.47995
$883$	−47.1779	−1.58766	−0.793832	−	0.608137i	$-0.791917\pi$
$883$	−47.1779	−1.58766	−0.793832	+	0.608137i	$0.791917\pi$
$884$	−3.60862	−0.121371
$885$	53.7123	1.80552
$886$	12.7962	0.429895
$887$	−47.3565	−1.59008	−0.795038	−	0.606560i	$-0.792549\pi$
$887$	−47.3565	−1.59008	−0.795038	+	0.606560i	$0.792549\pi$
$888$	−66.7829	−2.24109
$889$	60.3388	2.02370
$890$	−15.6530	−0.524689
$891$	−7.19738	−0.241121
$892$	6.00116	0.200934
$893$	−1.17968	−0.0394763
$894$	−53.2364	−1.78049
$895$	−24.5868	−0.821846
$896$	−50.4664	−1.68597
$897$	49.0317	1.63712
$898$	29.3814	0.980470
$899$	24.5964	0.820337
$900$	−0.735873	−0.0245291
$901$	14.9618	0.498451
$902$	−12.1209	−0.403582
$903$	0	0
$904$	−13.1281	−0.436633
$905$	25.1525	0.836099
$906$	−23.9111	−0.794393
$907$	−7.07267	−0.234844	−0.117422	−	0.993082i	$-0.537463\pi$
$907$	−7.07267	−0.234844	−0.117422	+	0.993082i	$0.537463\pi$
$908$	−6.40816	−0.212662
$909$	8.37988	0.277943
$910$	−63.4151	−2.10219
$911$	−1.06989	−0.0354470	−0.0177235	−	0.999843i	$-0.505642\pi$
$911$	−1.06989	−0.0354470	−0.0177235	+	0.999843i	$0.505642\pi$
$912$	−33.1757	−1.09856
$913$	0.542178	0.0179435
$914$	−0.0918682	−0.00303873
$915$	62.0304	2.05066
$916$	3.77408	0.124699
$917$	−55.0106	−1.81661
$918$	6.83291	0.225520
$919$	28.3194	0.934169	0.467085	−	0.884213i	$-0.345304\pi$
$919$	28.3194	0.934169	0.467085	+	0.884213i	$0.345304\pi$
$920$	−19.3648	−0.638440
$921$	−44.0842	−1.45262
$922$	−35.7324	−1.17678
$923$	−62.7090	−2.06409
$924$	−3.23938	−0.106568
$925$	−6.89954	−0.226856
$926$	12.2073	0.401157
$927$	−19.4350	−0.638329
$928$	7.89431	0.259143
$929$	51.4477	1.68795	0.843973	−	0.536386i	$-0.180211\pi$
$929$	51.4477	1.68795	0.843973	+	0.536386i	$0.180211\pi$
$930$	40.4979	1.32798
$931$	22.2698	0.729863
$932$	−5.58046	−0.182794
$933$	−61.4156	−2.01066
$934$	−52.3665	−1.71348
$935$	−5.71100	−0.186770
$936$	50.7079	1.65744
$937$	−13.7754	−0.450024	−0.225012	−	0.974356i	$-0.572242\pi$
$937$	−13.7754	−0.450024	−0.225012	+	0.974356i	$0.572242\pi$
$938$	−15.6665	−0.511531
$939$	65.3013	2.13103
$940$	0.244386	0.00797098
$941$	19.0844	0.622134	0.311067	−	0.950388i	$-0.399314\pi$
$941$	19.0844	0.622134	0.311067	+	0.950388i	$0.399314\pi$
$942$	−45.6354	−1.48688
$943$	25.3075	0.824126
$944$	44.8099	1.45844
$945$	14.9597	0.486638
$946$	0	0
$947$	−13.0250	−0.423256	−0.211628	−	0.977350i	$-0.567877\pi$
$947$	−13.0250	−0.423256	−0.211628	+	0.977350i	$0.567877\pi$
$948$	4.01224	0.130311
$949$	−4.16119	−0.135078
$950$	−2.99276	−0.0970981
$951$	−69.0023	−2.23755
$952$	24.0798	0.780432
$953$	−34.7613	−1.12603	−0.563014	−	0.826447i	$-0.690358\pi$
$953$	−34.7613	−1.12603	−0.563014	+	0.826447i	$0.690358\pi$
$954$	34.8853	1.12945
$955$	−47.1561	−1.52593
$956$	−0.178989	−0.00578891
$957$	−14.6051	−0.472116
$958$	−54.6000	−1.76404
$959$	−24.5453	−0.792610
$960$	−35.2949	−1.13914
$961$	−6.19749	−0.199919
$962$	−78.8887	−2.54347
$963$	9.71748	0.313141
$964$	−5.03019	−0.162011
$965$	−37.6320	−1.21142
$966$	54.2890	1.74672
$967$	−17.3530	−0.558036	−0.279018	−	0.960286i	$-0.590009\pi$
$967$	−17.3530	−0.558036	−0.279018	+	0.960286i	$0.590009\pi$
$968$	25.1477	0.808279
$969$	17.8374	0.573019
$970$	1.40948	0.0452558
$971$	−25.5522	−0.820008	−0.410004	−	0.912084i	$-0.634473\pi$
$971$	−25.5522	−0.820008	−0.410004	+	0.912084i	$0.634473\pi$
$972$	−6.25660	−0.200680
$973$	−5.28936	−0.169569
$974$	42.6102	1.36532
$975$	9.46076	0.302987
$976$	51.7493	1.65646
$977$	39.9500	1.27812	0.639058	−	0.769159i	$-0.279325\pi$
$977$	39.9500	1.27812	0.639058	+	0.769159i	$0.279325\pi$
$978$	−71.3274	−2.28080
$979$	5.69237	0.181929
$980$	−4.61348	−0.147372
$981$	−8.34936	−0.266574
$982$	37.6710	1.20213
$983$	−20.2158	−0.644783	−0.322392	−	0.946606i	$-0.604487\pi$
$983$	−20.2158	−0.644783	−0.322392	+	0.946606i	$0.604487\pi$
$984$	47.2654	1.50677
$985$	−2.06727	−0.0658688
$986$	−18.0144	−0.573694
$987$	4.12906	0.131429
$988$	−4.26316	−0.135629
$989$	0	0
$990$	−13.3159	−0.423206
$991$	34.5588	1.09780	0.548899	−	0.835889i	$-0.315047\pi$
$991$	34.5588	1.09780	0.548899	+	0.835889i	$0.315047\pi$
$992$	7.96046	0.252745
$993$	−8.77038	−0.278320
$994$	−69.4328	−2.20228
$995$	−11.2926	−0.357998
$996$	0.350811	0.0111159
$997$	32.2082	1.02004	0.510022	−	0.860161i	$-0.329637\pi$
$997$	32.2082	1.02004	0.510022	+	0.860161i	$0.329637\pi$
$998$	34.2380	1.08379
$999$	18.6099	0.588792

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.m.1.8	yes	10
43.42	odd	2	inner	1849.2.a.m.1.3	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.2.a.m.1.3	✓	10	43.42	odd	2	inner
1849.2.a.m.1.8	yes	10	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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q+1.51150 q^{2} +2.59278 q^{3} +0.284630 q^{4} -2.07496 q^{5} +3.91899 q^{6} -3.84858 q^{7} -2.59278 q^{8} +3.72251 q^{9} +O(q^{10})\)	\(q+1.51150 q^{2} +2.59278 q^{3} +0.284630 q^{4} -2.07496 q^{5} +3.91899 q^{6} -3.84858 q^{7} -2.59278 q^{8} +3.72251 q^{9} -3.13631 q^{10} +1.14055 q^{11} +0.737982 q^{12} -5.25380 q^{13} -5.81712 q^{14} -5.37993 q^{15} -4.48825 q^{16} +2.41316 q^{17} +5.62657 q^{18} +2.85087 q^{19} -0.590596 q^{20} -9.97852 q^{21} +1.72394 q^{22} -3.59946 q^{23} -6.72251 q^{24} -0.694523 q^{25} -7.94111 q^{26} +1.87332 q^{27} -1.09542 q^{28} -4.93883 q^{29} -8.13176 q^{30} -4.98021 q^{31} -1.59842 q^{32} +2.95720 q^{33} +3.64750 q^{34} +7.98567 q^{35} +1.05954 q^{36} +9.93421 q^{37} +4.30909 q^{38} -13.6219 q^{39} +5.37993 q^{40} -7.03092 q^{41} -15.0825 q^{42} +0.324635 q^{44} -7.72408 q^{45} -5.44058 q^{46} -0.413795 q^{47} -11.6370 q^{48} +7.81157 q^{49} -1.04977 q^{50} +6.25681 q^{51} -1.49539 q^{52} +6.20009 q^{53} +2.83152 q^{54} -2.36660 q^{55} +9.97852 q^{56} +7.39169 q^{57} -7.46504 q^{58} -9.98383 q^{59} -1.53129 q^{60} -11.5300 q^{61} -7.52759 q^{62} -14.3264 q^{63} +6.56048 q^{64} +10.9014 q^{65} +4.46981 q^{66} +2.69318 q^{67} +0.686858 q^{68} -9.33261 q^{69} +12.0703 q^{70} +11.9359 q^{71} -9.65166 q^{72} +0.792034 q^{73} +15.0156 q^{74} -1.80075 q^{75} +0.811443 q^{76} -4.38950 q^{77} -20.5896 q^{78} +5.43676 q^{79} +9.31295 q^{80} -6.31044 q^{81} -10.6272 q^{82} +0.475365 q^{83} -2.84018 q^{84} -5.00723 q^{85} -12.8053 q^{87} -2.95720 q^{88} +4.99089 q^{89} -11.6749 q^{90} +20.2197 q^{91} -1.02451 q^{92} -12.9126 q^{93} -0.625450 q^{94} -5.91546 q^{95} -4.14435 q^{96} -0.449409 q^{97} +11.8072 q^{98} +4.24572 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{4} + 22 q^{6} + 14 q^{9}+O(q^{10}) \) 10 * q + 2 * q^4 + 22 * q^6 + 14 * q^9	\( 10 q + 2 q^{4} + 22 q^{6} + 14 q^{9} - 22 q^{10} - 10 q^{11} - 14 q^{13} - 22 q^{14} - 22 q^{15} - 26 q^{16} - 16 q^{17} - 44 q^{21} - 18 q^{23} - 44 q^{24} - 6 q^{25} - 2 q^{31} - 28 q^{36} - 22 q^{38} + 22 q^{40} - 2 q^{44} - 18 q^{47} + 18 q^{49} + 28 q^{52} + 2 q^{53} + 44 q^{56} - 22 q^{57} - 22 q^{58} + 14 q^{59} + 8 q^{64} - 22 q^{66} + 26 q^{67} + 32 q^{68} + 44 q^{74} - 44 q^{78} - 56 q^{79} + 2 q^{81} - 38 q^{83} - 22 q^{87} - 22 q^{90} - 74 q^{92} + 22 q^{96} + 34 q^{97} - 36 q^{99}+O(q^{100}) \) 10 * q + 2 * q^4 + 22 * q^6 + 14 * q^9 - 22 * q^10 - 10 * q^11 - 14 * q^13 - 22 * q^14 - 22 * q^15 - 26 * q^16 - 16 * q^17 - 44 * q^21 - 18 * q^23 - 44 * q^24 - 6 * q^25 - 2 * q^31 - 28 * q^36 - 22 * q^38 + 22 * q^40 - 2 * q^44 - 18 * q^47 + 18 * q^49 + 28 * q^52 + 2 * q^53 + 44 * q^56 - 22 * q^57 - 22 * q^58 + 14 * q^59 + 8 * q^64 - 22 * q^66 + 26 * q^67 + 32 * q^68 + 44 * q^74 - 44 * q^78 - 56 * q^79 + 2 * q^81 - 38 * q^83 - 22 * q^87 - 22 * q^90 - 74 * q^92 + 22 * q^96 + 34 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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