LMFDB - Embedded newform 1849.2.a.q.1.2

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:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 27 x^{18} + 300 x^{16} - 1775 x^{14} + 6037 x^{12} - 11859 x^{10} + 12809 x^{8} - 6823 x^{6} + \cdots + 1 $ x^20 - 27x^18 + 300x^16 - 1775x^14 + 6037x^12 - 11859x^10 + 12809x^8 - 6823x^6 + 1500x^4 - 75*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.42479$ 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)

$f(q)$	$=$	$q-2.42479 q^{2} +1.86133 q^{3} +3.87962 q^{4} -2.06206 q^{5} -4.51334 q^{6} +4.60517 q^{7} -4.55770 q^{8} +0.464543 q^{9} +O(q^{10})$	\(q-2.42479 q^{2} +1.86133 q^{3} +3.87962 q^{4} -2.06206 q^{5} -4.51334 q^{6} +4.60517 q^{7} -4.55770 q^{8} +0.464543 q^{9} +5.00007 q^{10} -2.98545 q^{11} +7.22125 q^{12} +0.123227 q^{13} -11.1666 q^{14} -3.83817 q^{15} +3.29223 q^{16} -1.25388 q^{17} -1.12642 q^{18} +1.44166 q^{19} -8.00002 q^{20} +8.57173 q^{21} +7.23911 q^{22} -5.31489 q^{23} -8.48338 q^{24} -0.747908 q^{25} -0.298799 q^{26} -4.71932 q^{27} +17.8663 q^{28} -0.662535 q^{29} +9.30677 q^{30} -9.01329 q^{31} +1.13241 q^{32} -5.55691 q^{33} +3.04039 q^{34} -9.49613 q^{35} +1.80225 q^{36} -6.93889 q^{37} -3.49574 q^{38} +0.229365 q^{39} +9.39825 q^{40} +4.47699 q^{41} -20.7847 q^{42} -11.5824 q^{44} -0.957917 q^{45} +12.8875 q^{46} -0.503650 q^{47} +6.12793 q^{48} +14.2076 q^{49} +1.81352 q^{50} -2.33388 q^{51} +0.478073 q^{52} -2.70494 q^{53} +11.4434 q^{54} +6.15618 q^{55} -20.9890 q^{56} +2.68341 q^{57} +1.60651 q^{58} -8.70352 q^{59} -14.8907 q^{60} +2.85382 q^{61} +21.8554 q^{62} +2.13930 q^{63} -9.33034 q^{64} -0.254101 q^{65} +13.4744 q^{66} -8.40578 q^{67} -4.86457 q^{68} -9.89275 q^{69} +23.0262 q^{70} -12.3620 q^{71} -2.11725 q^{72} +0.0416763 q^{73} +16.8254 q^{74} -1.39210 q^{75} +5.59312 q^{76} -13.7485 q^{77} -0.556163 q^{78} +4.41776 q^{79} -6.78878 q^{80} -10.1778 q^{81} -10.8558 q^{82} +4.42847 q^{83} +33.2551 q^{84} +2.58557 q^{85} -1.23319 q^{87} +13.6068 q^{88} +12.9619 q^{89} +2.32275 q^{90} +0.567479 q^{91} -20.6198 q^{92} -16.7767 q^{93} +1.22125 q^{94} -2.97280 q^{95} +2.10780 q^{96} -2.27033 q^{97} -34.4504 q^{98} -1.38687 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 14 q^{4} - 32 q^{6} - 6 q^{9}+O(q^{10}) $ 20 * q + 14 * q^4 - 32 * q^6 - 6 * q^9	$ 20 q + 14 q^{4} - 32 q^{6} - 6 q^{9} + 12 q^{10} - 20 q^{11} + 6 q^{13} - 34 q^{14} - 34 q^{15} + 14 q^{16} - 8 q^{17} + 12 q^{21} - 46 q^{23} + 2 q^{24} + 20 q^{25} - 38 q^{31} - 76 q^{35} - 46 q^{36} - 68 q^{38} - 64 q^{40} - 56 q^{41} - 58 q^{44} - 24 q^{47} - 20 q^{49} - 20 q^{52} - 42 q^{53} + 66 q^{54} - 46 q^{56} + 2 q^{57} + 12 q^{58} - 90 q^{59} + 18 q^{60} - 28 q^{64} + 76 q^{66} - 62 q^{67} - 54 q^{68} + 24 q^{74} - 36 q^{78} - 10 q^{79} - 48 q^{81} - 68 q^{83} + 70 q^{84} - 12 q^{87} + 58 q^{90} - 8 q^{92} - 42 q^{95} - 22 q^{96} - 44 q^{97} - 38 q^{99}+O(q^{100}) $ 20 * q + 14 * q^4 - 32 * q^6 - 6 * q^9 + 12 * q^10 - 20 * q^11 + 6 * q^13 - 34 * q^14 - 34 * q^15 + 14 * q^16 - 8 * q^17 + 12 * q^21 - 46 * q^23 + 2 * q^24 + 20 * q^25 - 38 * q^31 - 76 * q^35 - 46 * q^36 - 68 * q^38 - 64 * q^40 - 56 * q^41 - 58 * q^44 - 24 * q^47 - 20 * q^49 - 20 * q^52 - 42 * q^53 + 66 * q^54 - 46 * q^56 + 2 * q^57 + 12 * q^58 - 90 * q^59 + 18 * q^60 - 28 * q^64 + 76 * q^66 - 62 * q^67 - 54 * q^68 + 24 * q^74 - 36 * q^78 - 10 * q^79 - 48 * q^81 - 68 * q^83 + 70 * q^84 - 12 * q^87 + 58 * q^90 - 8 * q^92 - 42 * q^95 - 22 * q^96 - 44 * q^97 - 38 * 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 $

$2$	−2.42479	−1.71459	−0.857294	−	0.514827i	$-0.827856\pi$
$2$	−2.42479	−1.71459	−0.857294	+	0.514827i	$0.827856\pi$
$3$	1.86133	1.07464	0.537319	−	0.843379i	$-0.319437\pi$
$3$	1.86133	1.07464	0.537319	+	0.843379i	$0.319437\pi$
$4$	3.87962	1.93981
$5$	−2.06206	−0.922181	−0.461091	−	0.887353i	$-0.652542\pi$
$5$	−2.06206	−0.922181	−0.461091	+	0.887353i	$0.652542\pi$
$6$	−4.51334	−1.84256
$7$	4.60517	1.74059	0.870295	−	0.492531i	$-0.163928\pi$
$7$	4.60517	1.74059	0.870295	+	0.492531i	$0.163928\pi$
$8$	−4.55770	−1.61139
$9$	0.464543	0.154848
$10$	5.00007	1.58116
$11$	−2.98545	−0.900148	−0.450074	−	0.892991i	$-0.648602\pi$
$11$	−2.98545	−0.900148	−0.450074	+	0.892991i	$0.648602\pi$
$12$	7.22125	2.08460
$13$	0.123227	0.0341769	0.0170885	−	0.999854i	$-0.494560\pi$
$13$	0.123227	0.0341769	0.0170885	+	0.999854i	$0.494560\pi$
$14$	−11.1666	−2.98439
$15$	−3.83817	−0.991011
$16$	3.29223	0.823058
$17$	−1.25388	−0.304110	−0.152055	−	0.988372i	$-0.548589\pi$
$17$	−1.25388	−0.304110	−0.152055	+	0.988372i	$0.548589\pi$
$18$	−1.12642	−0.265500
$19$	1.44166	0.330741	0.165370	−	0.986232i	$-0.447118\pi$
$19$	1.44166	0.330741	0.165370	+	0.986232i	$0.447118\pi$
$20$	−8.00002	−1.78886
$21$	8.57173	1.87050
$22$	7.23911	1.54338
$23$	−5.31489	−1.10823	−0.554115	−	0.832440i	$-0.686943\pi$
$23$	−5.31489	−1.10823	−0.554115	+	0.832440i	$0.686943\pi$
$24$	−8.48338	−1.73166
$25$	−0.747908	−0.149582
$26$	−0.298799	−0.0585993
$27$	−4.71932	−0.908233
$28$	17.8663	3.37642
$29$	−0.662535	−0.123030	−0.0615148	−	0.998106i	$-0.519593\pi$
$29$	−0.662535	−0.123030	−0.0615148	+	0.998106i	$0.519593\pi$
$30$	9.30677	1.69918
$31$	−9.01329	−1.61884	−0.809418	−	0.587234i	$-0.800217\pi$
$31$	−9.01329	−1.61884	−0.809418	+	0.587234i	$0.800217\pi$
$32$	1.13241	0.200185
$33$	−5.55691	−0.967334
$34$	3.04039	0.521423
$35$	−9.49613	−1.60514
$36$	1.80225	0.300376
$37$	−6.93889	−1.14075	−0.570373	−	0.821386i	$-0.693201\pi$
$37$	−6.93889	−1.14075	−0.570373	+	0.821386i	$0.693201\pi$
$38$	−3.49574	−0.567084
$39$	0.229365	0.0367278
$40$	9.39825	1.48599
$41$	4.47699	0.699189	0.349594	−	0.936901i	$-0.386319\pi$
$41$	4.47699	0.699189	0.349594	+	0.936901i	$0.386319\pi$
$42$	−20.7847	−3.20715
$43$	0	0
$43$	0	0
$44$	−11.5824	−1.74612
$45$	−0.957917	−0.142798
$46$	12.8875	1.90016
$47$	−0.503650	−0.0734649	−0.0367325	−	0.999325i	$-0.511695\pi$
$47$	−0.503650	−0.0734649	−0.0367325	+	0.999325i	$0.511695\pi$
$48$	6.12793	0.884490
$49$	14.2076	2.02965
$50$	1.81352	0.256471
$51$	−2.33388	−0.326808
$52$	0.478073	0.0662968
$53$	−2.70494	−0.371552	−0.185776	−	0.982592i	$-0.559480\pi$
$53$	−2.70494	−0.371552	−0.185776	+	0.982592i	$0.559480\pi$
$54$	11.4434	1.55725
$55$	6.15618	0.830100
$56$	−20.9890	−2.80477
$57$	2.68341	0.355427
$58$	1.60651	0.210945
$59$	−8.70352	−1.13310	−0.566551	−	0.824027i	$-0.691722\pi$
$59$	−8.70352	−1.13310	−0.566551	+	0.824027i	$0.691722\pi$
$60$	−14.8907	−1.92238
$61$	2.85382	0.365394	0.182697	−	0.983169i	$-0.441517\pi$
$61$	2.85382	0.365394	0.182697	+	0.983169i	$0.441517\pi$
$62$	21.8554	2.77564
$63$	2.13930	0.269527
$64$	−9.33034	−1.16629
$65$	−0.254101	−0.0315173
$66$	13.4744	1.65858
$67$	−8.40578	−1.02693	−0.513465	−	0.858111i	$-0.671638\pi$
$67$	−8.40578	−1.02693	−0.513465	+	0.858111i	$0.671638\pi$
$68$	−4.86457	−0.589916
$69$	−9.89275	−1.19095
$70$	23.0262	2.75215
$71$	−12.3620	−1.46710	−0.733552	−	0.679633i	$-0.762139\pi$
$71$	−12.3620	−1.46710	−0.733552	+	0.679633i	$0.762139\pi$
$72$	−2.11725	−0.249520
$73$	0.0416763	0.00487784	0.00243892	−	0.999997i	$-0.499224\pi$
$73$	0.0416763	0.00487784	0.00243892	+	0.999997i	$0.499224\pi$
$74$	16.8254	1.95591
$75$	−1.39210	−0.160746
$76$	5.59312	0.641574
$77$	−13.7485	−1.56679
$78$	−0.556163	−0.0629731
$79$	4.41776	0.497036	0.248518	−	0.968627i	$-0.420056\pi$
$79$	4.41776	0.497036	0.248518	+	0.968627i	$0.420056\pi$
$80$	−6.78878	−0.759009
$81$	−10.1778	−1.13087
$82$	−10.8558	−1.19882
$83$	4.42847	0.486088	0.243044	−	0.970015i	$-0.421854\pi$
$83$	4.42847	0.486088	0.243044	+	0.970015i	$0.421854\pi$
$84$	33.2551	3.62843
$85$	2.58557	0.280444
$86$	0	0
$87$	−1.23319	−0.132212
$88$	13.6068	1.45049
$89$	12.9619	1.37396	0.686981	−	0.726675i	$-0.258936\pi$
$89$	12.9619	1.37396	0.686981	+	0.726675i	$0.258936\pi$
$90$	2.32275	0.244839
$91$	0.567479	0.0594880
$92$	−20.6198	−2.14976
$93$	−16.7767	−1.73966
$94$	1.22125	0.125962
$95$	−2.97280	−0.305003
$96$	2.10780	0.215126
$97$	−2.27033	−0.230517	−0.115258	−	0.993336i	$-0.536770\pi$
$97$	−2.27033	−0.230517	−0.115258	+	0.993336i	$0.536770\pi$
$98$	−34.4504	−3.48002
$99$	−1.38687	−0.139386
$100$	−2.90160	−0.290160
$101$	1.94485	0.193520	0.0967598	−	0.995308i	$-0.469152\pi$
$101$	1.94485	0.193520	0.0967598	+	0.995308i	$0.469152\pi$
$102$	5.65917	0.560341
$103$	16.6130	1.63693	0.818465	−	0.574556i	$-0.194825\pi$
$103$	16.6130	1.63693	0.818465	+	0.574556i	$0.194825\pi$
$104$	−0.561630	−0.0550723
$105$	−17.6754	−1.72494
$106$	6.55892	0.637059
$107$	−0.721544	−0.0697543	−0.0348771	−	0.999392i	$-0.511104\pi$
$107$	−0.721544	−0.0697543	−0.0348771	+	0.999392i	$0.511104\pi$
$108$	−18.3092	−1.76180
$109$	10.3091	0.987431	0.493716	−	0.869623i	$-0.335638\pi$
$109$	10.3091	0.987431	0.493716	+	0.869623i	$0.335638\pi$
$110$	−14.9275	−1.42328
$111$	−12.9155	−1.22589
$112$	15.1613	1.43261
$113$	−13.2740	−1.24871	−0.624355	−	0.781141i	$-0.714638\pi$
$113$	−13.2740	−1.24871	−0.624355	+	0.781141i	$0.714638\pi$
$114$	−6.50672	−0.609410
$115$	10.9596	1.02199
$116$	−2.57039	−0.238654
$117$	0.0572441	0.00529222
$118$	21.1042	1.94280
$119$	−5.77431	−0.529330
$120$	17.4932	1.59691
$121$	−2.08707	−0.189734
$122$	−6.91993	−0.626501
$123$	8.33316	0.751375
$124$	−34.9682	−3.14024
$125$	11.8525	1.06012
$126$	−5.18736	−0.462127
$127$	−21.5868	−1.91552	−0.957758	−	0.287576i	$-0.907151\pi$
$127$	−21.5868	−1.91552	−0.957758	+	0.287576i	$0.907151\pi$
$128$	20.3593	1.79953
$129$	0	0
$130$	0.616142	0.0540392
$131$	16.0452	1.40188	0.700938	−	0.713223i	$-0.252765\pi$
$131$	16.0452	1.40188	0.700938	+	0.713223i	$0.252765\pi$
$132$	−21.5587	−1.87645
$133$	6.63911	0.575684
$134$	20.3823	1.76076
$135$	9.73152	0.837556
$136$	5.71479	0.490039
$137$	−8.42498	−0.719795	−0.359897	−	0.932992i	$-0.617188\pi$
$137$	−8.42498	−0.719795	−0.359897	+	0.932992i	$0.617188\pi$
$138$	23.9879	2.04198
$139$	8.89492	0.754458	0.377229	−	0.926120i	$-0.376877\pi$
$139$	8.89492	0.754458	0.377229	+	0.926120i	$0.376877\pi$
$140$	−36.8414	−3.11367
$141$	−0.937459	−0.0789483
$142$	29.9754	2.51548
$143$	−0.367887	−0.0307643
$144$	1.52939	0.127449
$145$	1.36619	0.113456
$146$	−0.101056	−0.00836348
$147$	26.4450	2.18114
$148$	−26.9203	−2.21283
$149$	19.2850	1.57989	0.789944	−	0.613179i	$-0.210110\pi$
$149$	19.2850	1.57989	0.789944	+	0.613179i	$0.210110\pi$
$150$	3.37556	0.275613
$151$	−20.9791	−1.70726	−0.853628	−	0.520884i	$-0.825603\pi$
$151$	−20.9791	−1.70726	−0.853628	+	0.520884i	$0.825603\pi$
$152$	−6.57067	−0.532952
$153$	−0.582480	−0.0470907
$154$	33.3373	2.68640
$155$	18.5860	1.49286
$156$	0.889851	0.0712451
$157$	12.5430	1.00104	0.500519	−	0.865726i	$-0.333143\pi$
$157$	12.5430	1.00104	0.500519	+	0.865726i	$0.333143\pi$
$158$	−10.7121	−0.852213
$159$	−5.03478	−0.399284
$160$	−2.33511	−0.184606
$161$	−24.4759	−1.92897
$162$	24.6791	1.93898
$163$	0.587733	0.0460348	0.0230174	−	0.999735i	$-0.492673\pi$
$163$	0.587733	0.0460348	0.0230174	+	0.999735i	$0.492673\pi$
$164$	17.3691	1.35630
$165$	11.4587	0.892057
$166$	−10.7381	−0.833440
$167$	14.0650	1.08839	0.544193	−	0.838960i	$-0.316836\pi$
$167$	14.0650	1.08839	0.544193	+	0.838960i	$0.316836\pi$
$168$	−39.0674	−3.01411
$169$	−12.9848	−0.998832
$170$	−6.26947	−0.480846
$171$	0.669716	0.0512145
$172$	0	0
$173$	−2.70635	−0.205760	−0.102880	−	0.994694i	$-0.532806\pi$
$173$	−2.70635	−0.205760	−0.102880	+	0.994694i	$0.532806\pi$
$174$	2.99024	0.226690
$175$	−3.44424	−0.260360
$176$	−9.82880	−0.740874
$177$	−16.2001	−1.21767
$178$	−31.4300	−2.35578
$179$	−7.51482	−0.561684	−0.280842	−	0.959754i	$-0.590614\pi$
$179$	−7.51482	−0.561684	−0.280842	+	0.959754i	$0.590614\pi$
$180$	−3.71636	−0.277001
$181$	−9.27855	−0.689669	−0.344835	−	0.938663i	$-0.612065\pi$
$181$	−9.27855	−0.689669	−0.344835	+	0.938663i	$0.612065\pi$
$182$	−1.37602	−0.101997
$183$	5.31190	0.392667
$184$	24.2237	1.78579
$185$	14.3084	1.05197
$186$	40.6800	2.98280
$187$	3.74339	0.273744
$188$	−1.95397	−0.142508
$189$	−21.7332	−1.58086
$190$	7.20842	0.522954
$191$	7.36149	0.532659	0.266329	−	0.963882i	$-0.414189\pi$
$191$	7.36149	0.532659	0.266329	+	0.963882i	$0.414189\pi$
$192$	−17.3668	−1.25334
$193$	−8.66728	−0.623884	−0.311942	−	0.950101i	$-0.600979\pi$
$193$	−8.66728	−0.623884	−0.311942	+	0.950101i	$0.600979\pi$
$194$	5.50507	0.395241
$195$	−0.472965	−0.0338697
$196$	55.1200	3.93715
$197$	−9.56530	−0.681499	−0.340750	−	0.940154i	$-0.610681\pi$
$197$	−9.56530	−0.681499	−0.340750	+	0.940154i	$0.610681\pi$
$198$	3.36288	0.238989
$199$	−11.6099	−0.823005	−0.411502	−	0.911409i	$-0.634996\pi$
$199$	−11.6099	−0.823005	−0.411502	+	0.911409i	$0.634996\pi$
$200$	3.40874	0.241034
$201$	−15.6459	−1.10358
$202$	−4.71585	−0.331806
$203$	−3.05108	−0.214144
$204$	−9.05456	−0.633946
$205$	−9.23183	−0.644779
$206$	−40.2832	−2.80666
$207$	−2.46900	−0.171607
$208$	0.405691	0.0281296
$209$	−4.30402	−0.297715
$210$	42.8593	2.95757
$211$	−25.8375	−1.77873	−0.889363	−	0.457202i	$-0.848852\pi$
$211$	−25.8375	−1.77873	−0.889363	+	0.457202i	$0.848852\pi$
$212$	−10.4942	−0.720741
$213$	−23.0098	−1.57661
$214$	1.74960	0.119600
$215$	0	0
$216$	21.5092	1.46352
$217$	−41.5077	−2.81773
$218$	−24.9974	−1.69304
$219$	0.0775732	0.00524191
$220$	23.8837	1.61024
$221$	−0.154511	−0.0103935
$222$	31.3175	2.10190
$223$	19.2346	1.28804	0.644020	−	0.765008i	$-0.277265\pi$
$223$	19.2346	1.28804	0.644020	+	0.765008i	$0.277265\pi$
$224$	5.21496	0.348439
$225$	−0.347436	−0.0231624
$226$	32.1866	2.14102
$227$	−10.7731	−0.715034	−0.357517	−	0.933907i	$-0.616377\pi$
$227$	−10.7731	−0.715034	−0.357517	+	0.933907i	$0.616377\pi$
$228$	10.4106	0.689461
$229$	−15.6604	−1.03487	−0.517434	−	0.855723i	$-0.673113\pi$
$229$	−15.6604	−1.03487	−0.517434	+	0.855723i	$0.673113\pi$
$230$	−26.5748	−1.75229
$231$	−25.5905	−1.68373
$232$	3.01963	0.198249
$233$	−23.1417	−1.51606	−0.758030	−	0.652220i	$-0.773838\pi$
$233$	−23.1417	−1.51606	−0.758030	+	0.652220i	$0.773838\pi$
$234$	−0.138805	−0.00907398
$235$	1.03856	0.0677480
$236$	−33.7664	−2.19800
$237$	8.22290	0.534134
$238$	14.0015	0.907583
$239$	5.91394	0.382541	0.191270	−	0.981537i	$-0.438739\pi$
$239$	5.91394	0.382541	0.191270	+	0.981537i	$0.438739\pi$
$240$	−12.6362	−0.815660
$241$	24.2122	1.55964	0.779822	−	0.626001i	$-0.215309\pi$
$241$	24.2122	1.55964	0.779822	+	0.626001i	$0.215309\pi$
$242$	5.06072	0.325315
$243$	−4.78633	−0.307043
$244$	11.0717	0.708796
$245$	−29.2969	−1.87171
$246$	−20.2062	−1.28830
$247$	0.177651	0.0113037
$248$	41.0799	2.60857
$249$	8.24284	0.522369
$250$	−28.7399	−1.81767
$251$	14.6583	0.925222	0.462611	−	0.886561i	$-0.346913\pi$
$251$	14.6583	0.925222	0.462611	+	0.886561i	$0.346913\pi$
$252$	8.29968	0.522831
$253$	15.8673	0.997571
$254$	52.3435	3.28432
$255$	4.81259	0.301376
$256$	−30.7065	−1.91915
$257$	−21.5725	−1.34565	−0.672827	−	0.739800i	$-0.734920\pi$
$257$	−21.5725	−1.34565	−0.672827	+	0.739800i	$0.734920\pi$
$258$	0	0
$259$	−31.9547	−1.98557
$260$	−0.985815	−0.0611377
$261$	−0.307776	−0.0190509
$262$	−38.9063	−2.40364
$263$	−17.0465	−1.05113	−0.525566	−	0.850753i	$-0.676146\pi$
$263$	−17.0465	−1.05113	−0.525566	+	0.850753i	$0.676146\pi$
$264$	25.3267	1.55875
$265$	5.57775	0.342638
$266$	−16.0985	−0.987060
$267$	24.1264	1.47651
$268$	−32.6113	−1.99205
$269$	−26.8513	−1.63715	−0.818576	−	0.574398i	$-0.805236\pi$
$269$	−26.8513	−1.63715	−0.818576	+	0.574398i	$0.805236\pi$
$270$	−23.5969	−1.43606
$271$	−9.45285	−0.574220	−0.287110	−	0.957898i	$-0.592694\pi$
$271$	−9.45285	−0.574220	−0.287110	+	0.957898i	$0.592694\pi$
$272$	−4.12805	−0.250300
$273$	1.05627	0.0639281
$274$	20.4288	1.23415
$275$	2.23284	0.134646
$276$	−38.3801	−2.31021
$277$	−8.49600	−0.510475	−0.255238	−	0.966878i	$-0.582154\pi$
$277$	−8.49600	−0.510475	−0.255238	+	0.966878i	$0.582154\pi$
$278$	−21.5684	−1.29358
$279$	−4.18707	−0.250673
$280$	43.2805	2.58651
$281$	7.19738	0.429359	0.214680	−	0.976685i	$-0.431129\pi$
$281$	7.19738	0.429359	0.214680	+	0.976685i	$0.431129\pi$
$282$	2.27314	0.135364
$283$	−12.5754	−0.747533	−0.373766	−	0.927523i	$-0.621934\pi$
$283$	−12.5754	−0.747533	−0.373766	+	0.927523i	$0.621934\pi$
$284$	−47.9601	−2.84591
$285$	−5.53336	−0.327768
$286$	0.892051	0.0527481
$287$	20.6173	1.21700
$288$	0.526056	0.0309981
$289$	−15.4278	−0.907517
$290$	−3.31272	−0.194530
$291$	−4.22582	−0.247722
$292$	0.161688	0.00946209
$293$	−4.77025	−0.278681	−0.139341	−	0.990245i	$-0.544498\pi$
$293$	−4.77025	−0.278681	−0.139341	+	0.990245i	$0.544498\pi$
$294$	−64.1236	−3.73976
$295$	17.9472	1.04493
$296$	31.6254	1.83819
$297$	14.0893	0.817544
$298$	−46.7621	−2.70886
$299$	−0.654936	−0.0378759
$300$	−5.40084	−0.311817
$301$	0	0
$302$	50.8700	2.92724
$303$	3.62000	0.207964
$304$	4.74629	0.272219
$305$	−5.88475	−0.336960
$306$	1.41239	0.0807412
$307$	−6.71168	−0.383056	−0.191528	−	0.981487i	$-0.561344\pi$
$307$	−6.71168	−0.383056	−0.191528	+	0.981487i	$0.561344\pi$
$308$	−53.3391	−3.03927
$309$	30.9223	1.75911
$310$	−45.0671	−2.55964
$311$	−15.5506	−0.881794	−0.440897	−	0.897558i	$-0.645340\pi$
$311$	−15.5506	−0.881794	−0.440897	+	0.897558i	$0.645340\pi$
$312$	−1.04538	−0.0591829
$313$	−5.32980	−0.301258	−0.150629	−	0.988590i	$-0.548130\pi$
$313$	−5.32980	−0.301258	−0.150629	+	0.988590i	$0.548130\pi$
$314$	−30.4141	−1.71637
$315$	−4.41137	−0.248552
$316$	17.1392	0.964157
$317$	31.2570	1.75557	0.877783	−	0.479059i	$-0.159022\pi$
$317$	31.2570	1.75557	0.877783	+	0.479059i	$0.159022\pi$
$318$	12.2083	0.684608
$319$	1.97797	0.110745
$320$	19.2397	1.07553
$321$	−1.34303	−0.0749606
$322$	59.3491	3.30740
$323$	−1.80767	−0.100581
$324$	−39.4861	−2.19367
$325$	−0.0921622	−0.00511224
$326$	−1.42513	−0.0789308
$327$	19.1886	1.06113
$328$	−20.4048	−1.12667
$329$	−2.31939	−0.127872
$330$	−27.7849	−1.52951
$331$	13.7249	0.754388	0.377194	−	0.926134i	$-0.376889\pi$
$331$	13.7249	0.754388	0.377194	+	0.926134i	$0.376889\pi$
$332$	17.1808	0.942919
$333$	−3.22341	−0.176642
$334$	−34.1048	−1.86613
$335$	17.3332	0.947015
$336$	28.2201	1.53953
$337$	18.3416	0.999131	0.499565	−	0.866276i	$-0.333493\pi$
$337$	18.3416	0.999131	0.499565	+	0.866276i	$0.333493\pi$
$338$	31.4855	1.71259
$339$	−24.7072	−1.34191
$340$	10.0310	0.544009
$341$	26.9088	1.45719
$342$	−1.62392	−0.0878117
$343$	33.1921	1.79220
$344$	0	0
$345$	20.3994	1.09827
$346$	6.56234	0.352794
$347$	21.4357	1.15073	0.575365	−	0.817896i	$-0.304860\pi$
$347$	21.4357	1.15073	0.575365	+	0.817896i	$0.304860\pi$
$348$	−4.78433	−0.256467
$349$	−9.04654	−0.484250	−0.242125	−	0.970245i	$-0.577844\pi$
$349$	−9.04654	−0.484250	−0.242125	+	0.970245i	$0.577844\pi$
$350$	8.35158	0.446411
$351$	−0.581546	−0.0310406
$352$	−3.38077	−0.180196
$353$	2.51765	0.134001	0.0670005	−	0.997753i	$-0.478657\pi$
$353$	2.51765	0.134001	0.0670005	+	0.997753i	$0.478657\pi$
$354$	39.2819	2.08781
$355$	25.4913	1.35294
$356$	50.2874	2.66523
$357$	−10.7479	−0.568839
$358$	18.2219	0.963056
$359$	20.0330	1.05730	0.528650	−	0.848840i	$-0.322698\pi$
$359$	20.0330	1.05730	0.528650	+	0.848840i	$0.322698\pi$
$360$	4.36590	0.230103
$361$	−16.9216	−0.890611
$362$	22.4986	1.18250
$363$	−3.88472	−0.203895
$364$	2.20161	0.115396
$365$	−0.0859390	−0.00449825
$366$	−12.8803	−0.673262
$367$	−2.13298	−0.111341	−0.0556703	−	0.998449i	$-0.517730\pi$
$367$	−2.13298	−0.111341	−0.0556703	+	0.998449i	$0.517730\pi$
$368$	−17.4978	−0.912138
$369$	2.07976	0.108268
$370$	−34.6949	−1.80370
$371$	−12.4567	−0.646720
$372$	−65.0873	−3.37462
$373$	19.8294	1.02673	0.513363	−	0.858171i	$-0.328399\pi$
$373$	19.8294	1.02673	0.513363	+	0.858171i	$0.328399\pi$
$374$	−9.07694	−0.469358
$375$	22.0615	1.13925
$376$	2.29549	0.118381
$377$	−0.0816419	−0.00420477
$378$	52.6986	2.71053
$379$	11.2148	0.576065	0.288033	−	0.957621i	$-0.406999\pi$
$379$	11.2148	0.576065	0.288033	+	0.957621i	$0.406999\pi$
$380$	−11.5333	−0.591648
$381$	−40.1801	−2.05849
$382$	−17.8501	−0.913291
$383$	−2.82949	−0.144580	−0.0722902	−	0.997384i	$-0.523031\pi$
$383$	−2.82949	−0.144580	−0.0722902	+	0.997384i	$0.523031\pi$
$384$	37.8954	1.93384
$385$	28.3503	1.44486
$386$	21.0164	1.06970
$387$	0	0
$388$	−8.80801	−0.447159
$389$	−18.3907	−0.932445	−0.466222	−	0.884668i	$-0.654385\pi$
$389$	−18.3907	−0.932445	−0.466222	+	0.884668i	$0.654385\pi$
$390$	1.14684	0.0580726
$391$	6.66421	0.337024
$392$	−64.7538	−3.27056
$393$	29.8654	1.50651
$394$	23.1939	1.16849
$395$	−9.10968	−0.458358
$396$	−5.38054	−0.270383
$397$	23.0706	1.15788	0.578940	−	0.815370i	$-0.303466\pi$
$397$	23.0706	1.15788	0.578940	+	0.815370i	$0.303466\pi$
$398$	28.1516	1.41111
$399$	12.3576	0.618652
$400$	−2.46229	−0.123114
$401$	0.932235	0.0465536	0.0232768	−	0.999729i	$-0.492590\pi$
$401$	0.932235	0.0465536	0.0232768	+	0.999729i	$0.492590\pi$
$402$	37.9381	1.89218
$403$	−1.11068	−0.0553268
$404$	7.54528	0.375392
$405$	20.9873	1.04287
$406$	7.39825	0.367169
$407$	20.7157	1.02684
$408$	10.6371	0.526615
$409$	16.2686	0.804428	0.402214	−	0.915546i	$-0.368241\pi$
$409$	16.2686	0.804428	0.402214	+	0.915546i	$0.368241\pi$
$410$	22.3853	1.10553
$411$	−15.6817	−0.773519
$412$	64.4523	3.17534
$413$	−40.0812	−1.97227
$414$	5.98681	0.294235
$415$	−9.13177	−0.448261
$416$	0.139544	0.00684169
$417$	16.5564	0.810769
$418$	10.4364	0.510459
$419$	21.9978	1.07466	0.537331	−	0.843371i	$-0.319432\pi$
$419$	21.9978	1.07466	0.537331	+	0.843371i	$0.319432\pi$
$420$	−68.5740	−3.34607
$421$	−7.18600	−0.350224	−0.175112	−	0.984548i	$-0.556029\pi$
$421$	−7.18600	−0.350224	−0.175112	+	0.984548i	$0.556029\pi$
$422$	62.6506	3.04978
$423$	−0.233967	−0.0113759
$424$	12.3283	0.598715
$425$	0.937784	0.0454892
$426$	55.7941	2.70323
$427$	13.1423	0.636002
$428$	−2.79932	−0.135310
$429$	−0.684759	−0.0330605
$430$	0	0
$431$	−9.73440	−0.468890	−0.234445	−	0.972129i	$-0.575327\pi$
$431$	−9.73440	−0.468890	−0.234445	+	0.972129i	$0.575327\pi$
$432$	−15.5371	−0.747529
$433$	0.282643	0.0135830	0.00679149	−	0.999977i	$-0.497838\pi$
$433$	0.282643	0.0135830	0.00679149	+	0.999977i	$0.497838\pi$
$434$	100.648	4.83124
$435$	2.54292	0.121924
$436$	39.9954	1.91543
$437$	−7.66228	−0.366537
$438$	−0.188099	−0.00898772
$439$	−14.9719	−0.714571	−0.357285	−	0.933995i	$-0.616298\pi$
$439$	−14.9719	−0.714571	−0.357285	+	0.933995i	$0.616298\pi$
$440$	−28.0580	−1.33761
$441$	6.60004	0.314287
$442$	0.374657	0.0178206
$443$	11.6273	0.552428	0.276214	−	0.961096i	$-0.410920\pi$
$443$	11.6273	0.552428	0.276214	+	0.961096i	$0.410920\pi$
$444$	−50.1075	−2.37799
$445$	−26.7283	−1.26704
$446$	−46.6398	−2.20846
$447$	35.8957	1.69781
$448$	−42.9678	−2.03004
$449$	−21.3172	−1.00602	−0.503010	−	0.864281i	$-0.667774\pi$
$449$	−21.3172	−1.00602	−0.503010	+	0.864281i	$0.667774\pi$
$450$	0.842460	0.0397140
$451$	−13.3659	−0.629374
$452$	−51.4980	−2.42226
$453$	−39.0490	−1.83468
$454$	26.1225	1.22599
$455$	−1.17018	−0.0548587
$456$	−12.2302	−0.572731
$457$	25.0730	1.17287	0.586434	−	0.809997i	$-0.300531\pi$
$457$	25.0730	1.17287	0.586434	+	0.809997i	$0.300531\pi$
$458$	37.9732	1.77437
$459$	5.91744	0.276202
$460$	42.5192	1.98247
$461$	24.8420	1.15701	0.578504	−	0.815679i	$-0.303637\pi$
$461$	24.8420	1.15701	0.578504	+	0.815679i	$0.303637\pi$
$462$	62.0517	2.88691
$463$	4.18953	0.194704	0.0973521	−	0.995250i	$-0.468963\pi$
$463$	4.18953	0.194704	0.0973521	+	0.995250i	$0.468963\pi$
$464$	−2.18122	−0.101261
$465$	34.5946	1.60428
$466$	56.1137	2.59942
$467$	12.8507	0.594662	0.297331	−	0.954775i	$-0.403904\pi$
$467$	12.8507	0.594662	0.297331	+	0.954775i	$0.403904\pi$
$468$	0.222086	0.0102659
$469$	−38.7100	−1.78746
$470$	−2.51829	−0.116160
$471$	23.3466	1.07575
$472$	39.6680	1.82587
$473$	0	0
$474$	−19.9388	−0.915820
$475$	−1.07823	−0.0494727
$476$	−22.4022	−1.02680
$477$	−1.25656	−0.0575340
$478$	−14.3401	−0.655900
$479$	−8.94220	−0.408580	−0.204290	−	0.978910i	$-0.565489\pi$
$479$	−8.94220	−0.408580	−0.204290	+	0.978910i	$0.565489\pi$
$480$	−4.34640	−0.198385
$481$	−0.855055	−0.0389872
$482$	−58.7096	−2.67415
$483$	−45.5578	−2.07295
$484$	−8.09705	−0.368048
$485$	4.68155	0.212578
$486$	11.6059	0.526453
$487$	4.40451	0.199588	0.0997938	−	0.995008i	$-0.468182\pi$
$487$	4.40451	0.199588	0.0997938	+	0.995008i	$0.468182\pi$
$488$	−13.0069	−0.588793
$489$	1.09396	0.0494708
$490$	71.0389	3.20921
$491$	5.06045	0.228375	0.114187	−	0.993459i	$-0.463574\pi$
$491$	5.06045	0.228375	0.114187	+	0.993459i	$0.463574\pi$
$492$	32.3295	1.45753
$493$	0.830736	0.0374145
$494$	−0.430768	−0.0193812
$495$	2.85981	0.128539
$496$	−29.6739	−1.33240
$497$	−56.9293	−2.55363
$498$	−19.9872	−0.895647
$499$	−20.4862	−0.917089	−0.458544	−	0.888672i	$-0.651629\pi$
$499$	−20.4862	−0.917089	−0.458544	+	0.888672i	$0.651629\pi$
$500$	45.9834	2.05644
$501$	26.1796	1.16962
$502$	−35.5433	−1.58638
$503$	25.5685	1.14004	0.570022	−	0.821629i	$-0.306935\pi$
$503$	25.5685	1.14004	0.570022	+	0.821629i	$0.306935\pi$
$504$	−9.75029	−0.434312
$505$	−4.01039	−0.178460
$506$	−38.4750	−1.71042
$507$	−24.1690	−1.07338
$508$	−83.7485	−3.71574
$509$	−42.0909	−1.86565	−0.932824	−	0.360334i	$-0.882663\pi$
$509$	−42.0909	−1.86565	−0.932824	+	0.360334i	$0.882663\pi$
$510$	−11.6695	−0.516736
$511$	0.191926	0.00849032
$512$	33.7382	1.49103
$513$	−6.80367	−0.300389
$514$	52.3088	2.30724
$515$	−34.2571	−1.50955
$516$	0	0
$517$	1.50362	0.0661293
$518$	77.4836	3.40444
$519$	−5.03741	−0.221118
$520$	1.15811	0.0507867
$521$	30.1744	1.32197	0.660983	−	0.750401i	$-0.270140\pi$
$521$	30.1744	1.32197	0.660983	+	0.750401i	$0.270140\pi$
$522$	0.746294	0.0326644
$523$	32.4102	1.41720	0.708600	−	0.705610i	$-0.249327\pi$
$523$	32.4102	1.41720	0.708600	+	0.705610i	$0.249327\pi$
$524$	62.2493	2.71937
$525$	−6.41087	−0.279793
$526$	41.3342	1.80226
$527$	11.3016	0.492303
$528$	−18.2946	−0.796172
$529$	5.24802	0.228175
$530$	−13.5249	−0.587484
$531$	−4.04316	−0.175458
$532$	25.7572	1.11672
$533$	0.551685	0.0238961
$534$	−58.5016	−2.53161
$535$	1.48787	0.0643261
$536$	38.3110	1.65478
$537$	−13.9875	−0.603607
$538$	65.1088	2.80704
$539$	−42.4160	−1.82699
$540$	37.7546	1.62470
$541$	8.75723	0.376503	0.188251	−	0.982121i	$-0.439718\pi$
$541$	8.75723	0.376503	0.188251	+	0.982121i	$0.439718\pi$
$542$	22.9212	0.984550
$543$	−17.2704	−0.741145
$544$	−1.41991	−0.0608781
$545$	−21.2579	−0.910590
$546$	−2.56123	−0.109610
$547$	36.3491	1.55417	0.777087	−	0.629393i	$-0.216696\pi$
$547$	36.3491	1.55417	0.777087	+	0.629393i	$0.216696\pi$
$548$	−32.6858	−1.39627
$549$	1.32572	0.0565805
$550$	−5.41419	−0.230862
$551$	−0.955153	−0.0406909
$552$	45.0882	1.91908
$553$	20.3445	0.865137
$554$	20.6011	0.875255
$555$	26.6326	1.13049
$556$	34.5090	1.46351
$557$	3.85895	0.163509	0.0817544	−	0.996653i	$-0.473948\pi$
$557$	3.85895	0.163509	0.0817544	+	0.996653i	$0.473948\pi$
$558$	10.1528	0.429801
$559$	0	0
$560$	−31.2635	−1.32112
$561$	6.96768	0.294175
$562$	−17.4521	−0.736174
$563$	−45.5375	−1.91918	−0.959589	−	0.281405i	$-0.909200\pi$
$563$	−45.5375	−1.91918	−0.959589	+	0.281405i	$0.909200\pi$
$564$	−3.63699	−0.153145
$565$	27.3717	1.15154
$566$	30.4929	1.28171
$567$	−46.8706	−1.96838
$568$	56.3425	2.36408
$569$	−0.676782	−0.0283722	−0.0141861	−	0.999899i	$-0.504516\pi$
$569$	−0.676782	−0.0283722	−0.0141861	+	0.999899i	$0.504516\pi$
$570$	13.4172	0.561987
$571$	37.9090	1.58644	0.793222	−	0.608933i	$-0.208402\pi$
$571$	37.9090	1.58644	0.793222	+	0.608933i	$0.208402\pi$
$572$	−1.42726	−0.0596769
$573$	13.7022	0.572416
$574$	−49.9927	−2.08666
$575$	3.97505	0.165771
$576$	−4.33435	−0.180598
$577$	6.46860	0.269292	0.134646	−	0.990894i	$-0.457010\pi$
$577$	6.46860	0.269292	0.134646	+	0.990894i	$0.457010\pi$
$578$	37.4092	1.55602
$579$	−16.1326	−0.670450
$580$	5.30029	0.220083
$581$	20.3938	0.846079
$582$	10.2467	0.424741
$583$	8.07547	0.334452
$584$	−0.189948	−0.00786010
$585$	−0.118041	−0.00488039
$586$	11.5669	0.477823
$587$	−4.14398	−0.171040	−0.0855202	−	0.996336i	$-0.527255\pi$
$587$	−4.14398	−0.171040	−0.0855202	+	0.996336i	$0.527255\pi$
$588$	102.596	4.23101
$589$	−12.9941	−0.535414
$590$	−43.5182	−1.79162
$591$	−17.8042	−0.732365
$592$	−22.8444	−0.938900
$593$	16.6451	0.683531	0.341765	−	0.939785i	$-0.388975\pi$
$593$	16.6451	0.683531	0.341765	+	0.939785i	$0.388975\pi$
$594$	−34.1636	−1.40175
$595$	11.9070	0.488138
$596$	74.8185	3.06469
$597$	−21.6099	−0.884433
$598$	1.58808	0.0649416
$599$	−27.4365	−1.12102	−0.560512	−	0.828146i	$-0.689396\pi$
$599$	−27.4365	−1.12102	−0.560512	+	0.828146i	$0.689396\pi$
$600$	6.34479	0.259025
$601$	20.0328	0.817153	0.408577	−	0.912724i	$-0.366025\pi$
$601$	20.0328	0.817153	0.408577	+	0.912724i	$0.366025\pi$
$602$	0	0
$603$	−3.90485	−0.159018
$604$	−81.3910	−3.31175
$605$	4.30367	0.174969
$606$	−8.77775	−0.356572
$607$	15.4891	0.628685	0.314342	−	0.949310i	$-0.398216\pi$
$607$	15.4891	0.628685	0.314342	+	0.949310i	$0.398216\pi$
$608$	1.63256	0.0662091
$609$	−5.67907	−0.230127
$610$	14.2693	0.577747
$611$	−0.0620631	−0.00251081
$612$	−2.25980	−0.0913471
$613$	−37.7845	−1.52610	−0.763050	−	0.646339i	$-0.776299\pi$
$613$	−37.7845	−1.52610	−0.763050	+	0.646339i	$0.776299\pi$
$614$	16.2744	0.656783
$615$	−17.1835	−0.692904
$616$	62.6616	2.52471
$617$	22.1526	0.891832	0.445916	−	0.895075i	$-0.352878\pi$
$617$	22.1526	0.891832	0.445916	+	0.895075i	$0.352878\pi$
$618$	−74.9802	−3.01615
$619$	−27.6758	−1.11238	−0.556192	−	0.831054i	$-0.687738\pi$
$619$	−27.6758	−1.11238	−0.556192	+	0.831054i	$0.687738\pi$
$620$	72.1065	2.89587
$621$	25.0826	1.00653
$622$	37.7070	1.51191
$623$	59.6919	2.39150
$624$	0.755124	0.0302291
$625$	−20.7011	−0.828044
$626$	12.9237	0.516534
$627$	−8.01120	−0.319936
$628$	48.6620	1.94182
$629$	8.70050	0.346912
$630$	10.6967	0.426165
$631$	9.62168	0.383033	0.191516	−	0.981489i	$-0.438659\pi$
$631$	9.62168	0.383033	0.191516	+	0.981489i	$0.438659\pi$
$632$	−20.1348	−0.800920
$633$	−48.0920	−1.91149
$634$	−75.7917	−3.01007
$635$	44.5132	1.76645
$636$	−19.5331	−0.774536
$637$	1.75075	0.0693673
$638$	−4.79616	−0.189882
$639$	−5.74271	−0.227178
$640$	−41.9821	−1.65949
$641$	−12.8885	−0.509063	−0.254532	−	0.967064i	$-0.581921\pi$
$641$	−12.8885	−0.509063	−0.254532	+	0.967064i	$0.581921\pi$
$642$	3.25657	0.128527
$643$	−14.0965	−0.555910	−0.277955	−	0.960594i	$-0.589657\pi$
$643$	−14.0965	−0.555910	−0.277955	+	0.960594i	$0.589657\pi$
$644$	−94.9575	−3.74185
$645$	0	0
$646$	4.38322	0.172456
$647$	23.0238	0.905160	0.452580	−	0.891724i	$-0.350504\pi$
$647$	23.0238	0.905160	0.452580	+	0.891724i	$0.350504\pi$
$648$	46.3875	1.82227
$649$	25.9839	1.01996
$650$	0.223474	0.00876538
$651$	−77.2595	−3.02804
$652$	2.28018	0.0892989
$653$	26.7495	1.04679	0.523393	−	0.852091i	$-0.324666\pi$
$653$	26.7495	1.04679	0.523393	+	0.852091i	$0.324666\pi$
$654$	−46.5284	−1.81940
$655$	−33.0862	−1.29278
$656$	14.7393	0.575473
$657$	0.0193604	0.000755323 0
$658$	5.62405	0.219248
$659$	−1.55494	−0.0605720	−0.0302860	−	0.999541i	$-0.509642\pi$
$659$	−1.55494	−0.0605720	−0.0302860	+	0.999541i	$0.509642\pi$
$660$	44.4554	1.73042
$661$	34.1499	1.32828	0.664139	−	0.747609i	$-0.268798\pi$
$661$	34.1499	1.32828	0.664139	+	0.747609i	$0.268798\pi$
$662$	−33.2800	−1.29346
$663$	−0.287596	−0.0111693
$664$	−20.1836	−0.783277
$665$	−13.6902	−0.530885
$666$	7.81611	0.302868
$667$	3.52130	0.136345
$668$	54.5670	2.11126
$669$	35.8018	1.38418
$670$	−42.0295	−1.62374
$671$	−8.51995	−0.328909
$672$	9.70675	0.374446
$673$	−42.7826	−1.64915	−0.824574	−	0.565753i	$-0.808585\pi$
$673$	−42.7826	−1.64915	−0.824574	+	0.565753i	$0.808585\pi$
$674$	−44.4746	−1.71310
$675$	3.52962	0.135855
$676$	−50.3762	−1.93755
$677$	1.36870	0.0526033	0.0263016	−	0.999654i	$-0.491627\pi$
$677$	1.36870	0.0526033	0.0263016	+	0.999654i	$0.491627\pi$
$678$	59.9099	2.30083
$679$	−10.4552	−0.401235
$680$	−11.7842	−0.451905
$681$	−20.0522	−0.768403
$682$	−65.2482	−2.49848
$683$	30.7603	1.17701	0.588506	−	0.808493i	$-0.299716\pi$
$683$	30.7603	1.17701	0.588506	+	0.808493i	$0.299716\pi$
$684$	2.59825	0.0993464
$685$	17.3728	0.663781
$686$	−80.4840	−3.07289
$687$	−29.1492	−1.11211
$688$	0	0
$689$	−0.333321	−0.0126985
$690$	−49.4644	−1.88308
$691$	17.3600	0.660407	0.330203	−	0.943910i	$-0.392883\pi$
$691$	17.3600	0.660407	0.330203	+	0.943910i	$0.392883\pi$
$692$	−10.4996	−0.399136
$693$	−6.38678	−0.242614
$694$	−51.9772	−1.97303
$695$	−18.3419	−0.695747
$696$	5.62053	0.213046
$697$	−5.61360	−0.212630
$698$	21.9360	0.830289
$699$	−43.0742	−1.62922
$700$	−13.3624	−0.505050
$701$	−36.8641	−1.39234	−0.696168	−	0.717879i	$-0.745113\pi$
$701$	−36.8641	−1.39234	−0.696168	+	0.717879i	$0.745113\pi$
$702$	1.41013	0.0532218
$703$	−10.0035	−0.377291
$704$	27.8553	1.04984
$705$	1.93310	0.0728046
$706$	−6.10478	−0.229756
$707$	8.95635	0.336838
$708$	−62.8503	−2.36206
$709$	−10.7553	−0.403926	−0.201963	−	0.979393i	$-0.564732\pi$
$709$	−10.7553	−0.403926	−0.201963	+	0.979393i	$0.564732\pi$
$710$	−61.8111	−2.31973
$711$	2.05224	0.0769650
$712$	−59.0766	−2.21399
$713$	47.9046	1.79404
$714$	26.0614	0.975324
$715$	0.758606	0.0283702
$716$	−29.1547	−1.08956
$717$	11.0078	0.411093
$718$	−48.5759	−1.81283
$719$	−53.2366	−1.98539	−0.992695	−	0.120655i	$-0.961501\pi$
$719$	−53.2366	−1.98539	−0.992695	+	0.120655i	$0.961501\pi$
$720$	−3.15368	−0.117531
$721$	76.5058	2.84922
$722$	41.0314	1.52703
$723$	45.0668	1.67605
$724$	−35.9973	−1.33783
$725$	0.495515	0.0184030
$726$	9.41965	0.349596
$727$	−26.5096	−0.983188	−0.491594	−	0.870824i	$-0.663586\pi$
$727$	−26.5096	−0.983188	−0.491594	+	0.870824i	$0.663586\pi$
$728$	−2.58640	−0.0958584
$729$	21.6246	0.800909
$730$	0.208384	0.00771265
$731$	0	0
$732$	20.6082	0.761700
$733$	21.5567	0.796216	0.398108	−	0.917339i	$-0.369667\pi$
$733$	21.5567	0.796216	0.398108	+	0.917339i	$0.369667\pi$
$734$	5.17203	0.190903
$735$	−54.5311	−2.01141
$736$	−6.01866	−0.221851
$737$	25.0951	0.924388
$738$	−5.04298	−0.185635
$739$	22.4669	0.826459	0.413230	−	0.910627i	$-0.364401\pi$
$739$	22.4669	0.826459	0.413230	+	0.910627i	$0.364401\pi$
$740$	55.5112	2.04063
$741$	0.330668	0.0121474
$742$	30.2049	1.10886
$743$	30.2176	1.10858	0.554288	−	0.832325i	$-0.312991\pi$
$743$	30.2176	1.10858	0.554288	+	0.832325i	$0.312991\pi$
$744$	76.4631	2.80327
$745$	−39.7668	−1.45694
$746$	−48.0822	−1.76041
$747$	2.05722	0.0752696
$748$	14.5229	0.531011
$749$	−3.32283	−0.121414
$750$	−53.4945	−1.95334
$751$	−33.5572	−1.22452	−0.612260	−	0.790656i	$-0.709739\pi$
$751$	−33.5572	−1.22452	−0.612260	+	0.790656i	$0.709739\pi$
$752$	−1.65813	−0.0604659
$753$	27.2839	0.994280
$754$	0.197965	0.00720945
$755$	43.2602	1.57440
$756$	−84.3168	−3.06657
$757$	24.5782	0.893308	0.446654	−	0.894707i	$-0.352615\pi$
$757$	24.5782	0.893308	0.446654	+	0.894707i	$0.352615\pi$
$758$	−27.1935	−0.987714
$759$	29.5343	1.07203
$760$	13.5491	0.491478
$761$	14.2312	0.515880	0.257940	−	0.966161i	$-0.416956\pi$
$761$	14.2312	0.515880	0.257940	+	0.966161i	$0.416956\pi$
$762$	97.4284	3.52946
$763$	47.4751	1.71871
$764$	28.5598	1.03326
$765$	1.20111	0.0434262
$766$	6.86094	0.247896
$767$	−1.07251	−0.0387259
$768$	−57.1548	−2.06240
$769$	10.4173	0.375656	0.187828	−	0.982202i	$-0.439855\pi$
$769$	10.4173	0.375656	0.187828	+	0.982202i	$0.439855\pi$
$770$	−68.7435	−2.47734
$771$	−40.1534	−1.44609
$772$	−33.6258	−1.21022
$773$	34.3108	1.23407	0.617037	−	0.786934i	$-0.288333\pi$
$773$	34.3108	1.23407	0.617037	+	0.786934i	$0.288333\pi$
$774$	0	0
$775$	6.74112	0.242148
$776$	10.3475	0.371452
$777$	−59.4783	−2.13377
$778$	44.5936	1.59876
$779$	6.45432	0.231250
$780$	−1.83493	−0.0657009
$781$	36.9063	1.32061
$782$	−16.1593	−0.577857
$783$	3.12671	0.111740
$784$	46.7746	1.67052
$785$	−25.8644	−0.923138
$786$	−72.4174	−2.58304
$787$	29.3889	1.04760	0.523801	−	0.851841i	$-0.324514\pi$
$787$	29.3889	1.04760	0.523801	+	0.851841i	$0.324514\pi$
$788$	−37.1098	−1.32198
$789$	−31.7291	−1.12959
$790$	22.0891	0.785895
$791$	−61.1289	−2.17349
$792$	6.32095	0.224605
$793$	0.351667	0.0124880
$794$	−55.9414	−1.98529
$795$	10.3820	0.368212
$796$	−45.0421	−1.59647
$797$	33.7673	1.19610	0.598050	−	0.801459i	$-0.295943\pi$
$797$	33.7673	1.19610	0.598050	+	0.801459i	$0.295943\pi$
$798$	−29.9645	−1.06073
$799$	0.631515	0.0223414
$800$	−0.846942	−0.0299439
$801$	6.02138	0.212755
$802$	−2.26048	−0.0798203
$803$	−0.124423	−0.00439078
$804$	−60.7002	−2.14073
$805$	50.4709	1.77886
$806$	2.69316	0.0948626
$807$	−49.9791	−1.75935
$808$	−8.86403	−0.311836
$809$	−13.8564	−0.487166	−0.243583	−	0.969880i	$-0.578323\pi$
$809$	−13.8564	−0.487166	−0.243583	+	0.969880i	$0.578323\pi$
$810$	−50.8899	−1.78809
$811$	13.9232	0.488910	0.244455	−	0.969661i	$-0.421391\pi$
$811$	13.9232	0.488910	0.244455	+	0.969661i	$0.421391\pi$
$812$	−11.8371	−0.415399
$813$	−17.5949	−0.617079
$814$	−50.2313	−1.76061
$815$	−1.21194	−0.0424525
$816$	−7.68366	−0.268982
$817$	0	0
$818$	−39.4479	−1.37926
$819$	0.263619	0.00921159
$820$	−35.8160	−1.25075
$821$	−42.9130	−1.49767	−0.748837	−	0.662754i	$-0.769387\pi$
$821$	−42.9130	−1.49767	−0.748837	+	0.662754i	$0.769387\pi$
$822$	38.0248	1.32627
$823$	−40.0286	−1.39531	−0.697655	−	0.716434i	$-0.745773\pi$
$823$	−40.0286	−1.39531	−0.697655	+	0.716434i	$0.745773\pi$
$824$	−75.7172	−2.63773
$825$	4.15606	0.144695
$826$	97.1885	3.38162
$827$	−15.0346	−0.522804	−0.261402	−	0.965230i	$-0.584185\pi$
$827$	−15.0346	−0.522804	−0.261402	+	0.965230i	$0.584185\pi$
$828$	−9.57878	−0.332885
$829$	−40.6021	−1.41017	−0.705085	−	0.709123i	$-0.749091\pi$
$829$	−40.6021	−1.41017	−0.705085	+	0.709123i	$0.749091\pi$
$830$	22.1427	0.768583
$831$	−15.8139	−0.548577
$832$	−1.14975	−0.0398603
$833$	−17.8145	−0.617237
$834$	−40.1458	−1.39014
$835$	−29.0029	−1.00369
$836$	−16.6980	−0.577512
$837$	42.5366	1.47028
$838$	−53.3401	−1.84260
$839$	−38.6878	−1.33565	−0.667826	−	0.744318i	$-0.732775\pi$
$839$	−38.6878	−1.33565	−0.667826	+	0.744318i	$0.732775\pi$
$840$	80.5593	2.77956
$841$	−28.5610	−0.984864
$842$	17.4246	0.600490
$843$	13.3967	0.461406
$844$	−100.240	−3.45039
$845$	26.7755	0.921104
$846$	0.567323	0.0195050
$847$	−9.61131	−0.330249
$848$	−8.90529	−0.305809
$849$	−23.4070	−0.803327
$850$	−2.27393	−0.0779953
$851$	36.8794	1.26421
$852$	−89.2694	−3.05832
$853$	−5.00362	−0.171321	−0.0856604	−	0.996324i	$-0.527300\pi$
$853$	−5.00362	−0.171321	−0.0856604	+	0.996324i	$0.527300\pi$
$854$	−31.8674	−1.09048
$855$	−1.38099	−0.0472290
$856$	3.28858	0.112401
$857$	21.2085	0.724468	0.362234	−	0.932087i	$-0.382014\pi$
$857$	21.2085	0.724468	0.362234	+	0.932087i	$0.382014\pi$
$858$	1.66040	0.0566851
$859$	−14.6261	−0.499035	−0.249518	−	0.968370i	$-0.580272\pi$
$859$	−14.6261	−0.499035	−0.249518	+	0.968370i	$0.580272\pi$
$860$	0	0
$861$	38.3756	1.30784
$862$	23.6039	0.803952
$863$	−33.0612	−1.12542	−0.562708	−	0.826656i	$-0.690241\pi$
$863$	−33.0612	−1.12542	−0.562708	+	0.826656i	$0.690241\pi$
$864$	−5.34422	−0.181814
$865$	5.58066	0.189748
$866$	−0.685352	−0.0232892
$867$	−28.7162	−0.975253
$868$	−161.034	−5.46586
$869$	−13.1890	−0.447406
$870$	−6.16606	−0.209049
$871$	−1.03582	−0.0350973
$872$	−46.9857	−1.59114
$873$	−1.05467	−0.0356950
$874$	18.5795	0.628460
$875$	54.5829	1.84524
$876$	0.300955	0.0101683
$877$	42.8883	1.44824	0.724118	−	0.689676i	$-0.242247\pi$
$877$	42.8883	1.44824	0.724118	+	0.689676i	$0.242247\pi$
$878$	36.3038	1.22519
$879$	−8.87901	−0.299482
$880$	20.2676	0.683220
$881$	−33.0092	−1.11211	−0.556054	−	0.831146i	$-0.687685\pi$
$881$	−33.0092	−1.11211	−0.556054	+	0.831146i	$0.687685\pi$
$882$	−16.0037	−0.538873
$883$	1.11250	0.0374387	0.0187194	−	0.999825i	$-0.494041\pi$
$883$	1.11250	0.0374387	0.0187194	+	0.999825i	$0.494041\pi$
$884$	−0.599444	−0.0201615
$885$	33.4056	1.12292
$886$	−28.1937	−0.947186
$887$	−1.00581	−0.0337718	−0.0168859	−	0.999857i	$-0.505375\pi$
$887$	−1.00581	−0.0337718	−0.0168859	+	0.999857i	$0.505375\pi$
$888$	58.8652	1.97539
$889$	−99.4107	−3.33413
$890$	64.8106	2.17246
$891$	30.3854	1.01795
$892$	74.6228	2.49856
$893$	−0.726095	−0.0242978
$894$	−87.0397	−2.91104
$895$	15.4960	0.517974
$896$	93.7580	3.13224
$897$	−1.21905	−0.0407029
$898$	51.6898	1.72491
$899$	5.97162	0.199165
$900$	−1.34792	−0.0449307
$901$	3.39166	0.112993
$902$	32.4094	1.07912
$903$	0	0
$904$	60.4988	2.01216
$905$	19.1329	0.636000
$906$	94.6858	3.14572
$907$	33.6844	1.11847	0.559236	−	0.829009i	$-0.311095\pi$
$907$	33.6844	1.11847	0.559236	+	0.829009i	$0.311095\pi$
$908$	−41.7955	−1.38703
$909$	0.903466	0.0299661
$910$	2.83744	0.0940601
$911$	−20.8025	−0.689216	−0.344608	−	0.938747i	$-0.611988\pi$
$911$	−20.8025	−0.689216	−0.344608	+	0.938747i	$0.611988\pi$
$912$	8.83441	0.292537
$913$	−13.2210	−0.437551
$914$	−60.7970	−2.01098
$915$	−10.9535	−0.362110
$916$	−60.7565	−2.00745
$917$	73.8908	2.44009
$918$	−14.3486	−0.473573
$919$	−23.4343	−0.773027	−0.386513	−	0.922284i	$-0.626321\pi$
$919$	−23.4343	−0.773027	−0.386513	+	0.922284i	$0.626321\pi$
$920$	−49.9506	−1.64682
$921$	−12.4926	−0.411646
$922$	−60.2368	−1.98379
$923$	−1.52333	−0.0501411
$924$	−99.2815	−3.26612
$925$	5.18965	0.170635
$926$	−10.1588	−0.333837
$927$	7.71747	0.253475
$928$	−0.750264	−0.0246286
$929$	56.9853	1.86963	0.934814	−	0.355138i	$-0.115566\pi$
$929$	56.9853	1.86963	0.934814	+	0.355138i	$0.115566\pi$
$930$	−83.8847	−2.75069
$931$	20.4826	0.671289
$932$	−89.7809	−2.94087
$933$	−28.9448	−0.947610
$934$	−31.1604	−1.01960
$935$	−7.71909	−0.252441
$936$	−0.260901	−0.00852783
$937$	0.389455	0.0127229	0.00636147	−	0.999980i	$-0.497975\pi$
$937$	0.389455	0.0127229	0.00636147	+	0.999980i	$0.497975\pi$
$938$	93.8638	3.06476
$939$	−9.92051	−0.323744
$940$	4.02921	0.131418
$941$	−27.6314	−0.900757	−0.450379	−	0.892838i	$-0.648711\pi$
$941$	−27.6314	−0.900757	−0.450379	+	0.892838i	$0.648711\pi$
$942$	−56.6106	−1.84447
$943$	−23.7947	−0.774863
$944$	−28.6540	−0.932608
$945$	44.8153	1.45784
$946$	0	0
$947$	0.817723	0.0265724	0.0132862	−	0.999912i	$-0.495771\pi$
$947$	0.817723	0.0265724	0.0132862	+	0.999912i	$0.495771\pi$
$948$	31.9017	1.03612
$949$	0.00513563	0.000166710 0
$950$	2.61449	0.0848253
$951$	58.1795	1.88660
$952$	26.3176	0.852957
$953$	−5.17189	−0.167534	−0.0837669	−	0.996485i	$-0.526695\pi$
$953$	−5.17189	−0.167534	−0.0837669	+	0.996485i	$0.526695\pi$
$954$	3.04690	0.0986472
$955$	−15.1798	−0.491208
$956$	22.9439	0.742057
$957$	3.68164	0.119011
$958$	21.6830	0.700546
$959$	−38.7985	−1.25287
$960$	35.8114	1.15581
$961$	50.2394	1.62063
$962$	2.07333	0.0668469
$963$	−0.335189	−0.0108013
$964$	93.9342	3.02542
$965$	17.8724	0.575334
$966$	110.468	3.55426
$967$	−28.5314	−0.917507	−0.458754	−	0.888563i	$-0.651704\pi$
$967$	−28.5314	−0.917507	−0.458754	+	0.888563i	$0.651704\pi$
$968$	9.51224	0.305735
$969$	−3.36467	−0.108089
$970$	−11.3518	−0.364484
$971$	17.5477	0.563134	0.281567	−	0.959542i	$-0.409146\pi$
$971$	17.5477	0.563134	0.281567	+	0.959542i	$0.409146\pi$
$972$	−18.5692	−0.595606
$973$	40.9626	1.31320
$974$	−10.6800	−0.342210
$975$	−0.171544	−0.00549381
$976$	9.39544	0.300741
$977$	−3.13374	−0.100257	−0.0501287	−	0.998743i	$-0.515963\pi$
$977$	−3.13374	−0.100257	−0.0501287	+	0.998743i	$0.515963\pi$
$978$	−2.65264	−0.0848220
$979$	−38.6972	−1.23677
$980$	−113.661	−3.63076
$981$	4.78902	0.152902
$982$	−12.2705	−0.391569
$983$	−40.0531	−1.27750	−0.638748	−	0.769416i	$-0.720547\pi$
$983$	−40.0531	−1.27750	−0.638748	+	0.769416i	$0.720547\pi$
$984$	−37.9800	−1.21076
$985$	19.7242	0.628466
$986$	−2.01436	−0.0641504
$987$	−4.31715	−0.137417
$988$	0.689221	0.0219270
$989$	0	0
$990$	−6.93446	−0.220392
$991$	8.16301	0.259307	0.129653	−	0.991559i	$-0.458614\pi$
$991$	8.16301	0.259307	0.129653	+	0.991559i	$0.458614\pi$
$992$	−10.2068	−0.324066
$993$	25.5465	0.810695
$994$	138.042	4.37842
$995$	23.9403	0.758960
$996$	31.9791	1.01330
$997$	−24.6344	−0.780180	−0.390090	−	0.920777i	$-0.627556\pi$
$997$	−24.6344	−0.780180	−0.390090	+	0.920777i	$0.627556\pi$
$998$	49.6748	1.57243
$999$	32.7468	1.03606

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.q.1.2	✓	20
43.42	odd	2	inner	1849.2.a.q.1.19	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.2.a.q.1.2	✓	20	1.1	even	1	trivial
1849.2.a.q.1.19	yes	20	43.42	odd	2	inner

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)

\(f(q)\)	\(=\)	\(q-2.42479 q^{2} +1.86133 q^{3} +3.87962 q^{4} -2.06206 q^{5} -4.51334 q^{6} +4.60517 q^{7} -4.55770 q^{8} +0.464543 q^{9} +O(q^{10})\)	\(q-2.42479 q^{2} +1.86133 q^{3} +3.87962 q^{4} -2.06206 q^{5} -4.51334 q^{6} +4.60517 q^{7} -4.55770 q^{8} +0.464543 q^{9} +5.00007 q^{10} -2.98545 q^{11} +7.22125 q^{12} +0.123227 q^{13} -11.1666 q^{14} -3.83817 q^{15} +3.29223 q^{16} -1.25388 q^{17} -1.12642 q^{18} +1.44166 q^{19} -8.00002 q^{20} +8.57173 q^{21} +7.23911 q^{22} -5.31489 q^{23} -8.48338 q^{24} -0.747908 q^{25} -0.298799 q^{26} -4.71932 q^{27} +17.8663 q^{28} -0.662535 q^{29} +9.30677 q^{30} -9.01329 q^{31} +1.13241 q^{32} -5.55691 q^{33} +3.04039 q^{34} -9.49613 q^{35} +1.80225 q^{36} -6.93889 q^{37} -3.49574 q^{38} +0.229365 q^{39} +9.39825 q^{40} +4.47699 q^{41} -20.7847 q^{42} -11.5824 q^{44} -0.957917 q^{45} +12.8875 q^{46} -0.503650 q^{47} +6.12793 q^{48} +14.2076 q^{49} +1.81352 q^{50} -2.33388 q^{51} +0.478073 q^{52} -2.70494 q^{53} +11.4434 q^{54} +6.15618 q^{55} -20.9890 q^{56} +2.68341 q^{57} +1.60651 q^{58} -8.70352 q^{59} -14.8907 q^{60} +2.85382 q^{61} +21.8554 q^{62} +2.13930 q^{63} -9.33034 q^{64} -0.254101 q^{65} +13.4744 q^{66} -8.40578 q^{67} -4.86457 q^{68} -9.89275 q^{69} +23.0262 q^{70} -12.3620 q^{71} -2.11725 q^{72} +0.0416763 q^{73} +16.8254 q^{74} -1.39210 q^{75} +5.59312 q^{76} -13.7485 q^{77} -0.556163 q^{78} +4.41776 q^{79} -6.78878 q^{80} -10.1778 q^{81} -10.8558 q^{82} +4.42847 q^{83} +33.2551 q^{84} +2.58557 q^{85} -1.23319 q^{87} +13.6068 q^{88} +12.9619 q^{89} +2.32275 q^{90} +0.567479 q^{91} -20.6198 q^{92} -16.7767 q^{93} +1.22125 q^{94} -2.97280 q^{95} +2.10780 q^{96} -2.27033 q^{97} -34.4504 q^{98} -1.38687 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 14 q^{4} - 32 q^{6} - 6 q^{9}+O(q^{10}) \) 20 * q + 14 * q^4 - 32 * q^6 - 6 * q^9	\( 20 q + 14 q^{4} - 32 q^{6} - 6 q^{9} + 12 q^{10} - 20 q^{11} + 6 q^{13} - 34 q^{14} - 34 q^{15} + 14 q^{16} - 8 q^{17} + 12 q^{21} - 46 q^{23} + 2 q^{24} + 20 q^{25} - 38 q^{31} - 76 q^{35} - 46 q^{36} - 68 q^{38} - 64 q^{40} - 56 q^{41} - 58 q^{44} - 24 q^{47} - 20 q^{49} - 20 q^{52} - 42 q^{53} + 66 q^{54} - 46 q^{56} + 2 q^{57} + 12 q^{58} - 90 q^{59} + 18 q^{60} - 28 q^{64} + 76 q^{66} - 62 q^{67} - 54 q^{68} + 24 q^{74} - 36 q^{78} - 10 q^{79} - 48 q^{81} - 68 q^{83} + 70 q^{84} - 12 q^{87} + 58 q^{90} - 8 q^{92} - 42 q^{95} - 22 q^{96} - 44 q^{97} - 38 q^{99}+O(q^{100}) \) 20 * q + 14 * q^4 - 32 * q^6 - 6 * q^9 + 12 * q^10 - 20 * q^11 + 6 * q^13 - 34 * q^14 - 34 * q^15 + 14 * q^16 - 8 * q^17 + 12 * q^21 - 46 * q^23 + 2 * q^24 + 20 * q^25 - 38 * q^31 - 76 * q^35 - 46 * q^36 - 68 * q^38 - 64 * q^40 - 56 * q^41 - 58 * q^44 - 24 * q^47 - 20 * q^49 - 20 * q^52 - 42 * q^53 + 66 * q^54 - 46 * q^56 + 2 * q^57 + 12 * q^58 - 90 * q^59 + 18 * q^60 - 28 * q^64 + 76 * q^66 - 62 * q^67 - 54 * q^68 + 24 * q^74 - 36 * q^78 - 10 * q^79 - 48 * q^81 - 68 * q^83 + 70 * q^84 - 12 * q^87 + 58 * q^90 - 8 * q^92 - 42 * q^95 - 22 * q^96 - 44 * q^97 - 38 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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