LMFDB - Embedded newform 3467.2.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3467,2,Mod(1,3467)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3467, 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("3467.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3467 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3467.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:	$27.6841343808$
Analytic rank:	$1$
Dimension:	$126$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	3467.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.57298 q^{2} -0.267298 q^{3} +4.62023 q^{4} -2.52986 q^{5} +0.687753 q^{6} -4.69728 q^{7} -6.74181 q^{8} -2.92855 q^{9} +6.50927 q^{10} +2.79951 q^{11} -1.23498 q^{12} -0.845941 q^{13} +12.0860 q^{14} +0.676226 q^{15} +8.10608 q^{16} +1.31976 q^{17} +7.53511 q^{18} +1.33224 q^{19} -11.6885 q^{20} +1.25557 q^{21} -7.20309 q^{22} -3.57006 q^{23} +1.80207 q^{24} +1.40017 q^{25} +2.17659 q^{26} +1.58469 q^{27} -21.7025 q^{28} +1.37347 q^{29} -1.73992 q^{30} +1.03261 q^{31} -7.37317 q^{32} -0.748304 q^{33} -3.39573 q^{34} +11.8834 q^{35} -13.5306 q^{36} -0.724634 q^{37} -3.42783 q^{38} +0.226118 q^{39} +17.0558 q^{40} +5.41760 q^{41} -3.23057 q^{42} -0.534970 q^{43} +12.9344 q^{44} +7.40881 q^{45} +9.18571 q^{46} -1.25775 q^{47} -2.16674 q^{48} +15.0645 q^{49} -3.60262 q^{50} -0.352771 q^{51} -3.90845 q^{52} -0.284928 q^{53} -4.07738 q^{54} -7.08236 q^{55} +31.6682 q^{56} -0.356105 q^{57} -3.53390 q^{58} +7.91289 q^{59} +3.12432 q^{60} +0.836999 q^{61} -2.65687 q^{62} +13.7562 q^{63} +2.75888 q^{64} +2.14011 q^{65} +1.92537 q^{66} +5.21884 q^{67} +6.09762 q^{68} +0.954271 q^{69} -30.5759 q^{70} +3.40604 q^{71} +19.7437 q^{72} +3.28626 q^{73} +1.86447 q^{74} -0.374263 q^{75} +6.15526 q^{76} -13.1501 q^{77} -0.581799 q^{78} +10.5036 q^{79} -20.5072 q^{80} +8.36207 q^{81} -13.9394 q^{82} +4.21855 q^{83} +5.80104 q^{84} -3.33881 q^{85} +1.37647 q^{86} -0.367125 q^{87} -18.8738 q^{88} +8.09001 q^{89} -19.0627 q^{90} +3.97362 q^{91} -16.4945 q^{92} -0.276014 q^{93} +3.23617 q^{94} -3.37038 q^{95} +1.97083 q^{96} -9.95203 q^{97} -38.7605 q^{98} -8.19852 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 126 q - 11 q^{2} - 25 q^{3} + 99 q^{4} - 32 q^{5} - 15 q^{6} - 27 q^{7} - 27 q^{8} + 93 q^{9} - 46 q^{10} - 6 q^{11} - 67 q^{12} - 137 q^{13} - 17 q^{14} - 15 q^{15} + 49 q^{16} - 30 q^{17} - 37 q^{18}+ \cdots + 9 q^{99}+O(q^{100}) $ 126 * q - 11 * q^2 - 25 * q^3 + 99 * q^4 - 32 * q^5 - 15 * q^6 - 27 * q^7 - 27 * q^8 + 93 * q^9 - 46 * q^10 - 6 * q^11 - 67 * q^12 - 137 * q^13 - 17 * q^14 - 15 * q^15 + 49 * q^16 - 30 * q^17 - 37 * q^18 - 39 * q^19 - 46 * q^20 - 54 * q^21 - 55 * q^22 - 35 * q^23 - 27 * q^24 + 26 * q^25 - 14 * q^26 - 88 * q^27 - 63 * q^28 - 31 * q^29 - 5 * q^30 - 64 * q^31 - 60 * q^32 - 100 * q^33 - 47 * q^34 - 38 * q^35 + 44 * q^36 - 148 * q^37 - 51 * q^38 + 7 * q^39 - 128 * q^40 - 28 * q^41 - 38 * q^42 - 68 * q^43 - 8 * q^44 - 137 * q^45 - 43 * q^46 - 51 * q^47 - 117 * q^48 + 3 * q^49 - 8 * q^50 - 30 * q^51 - 232 * q^52 - 112 * q^53 - 30 * q^54 - 96 * q^55 - 28 * q^56 - 47 * q^57 - 74 * q^58 - 38 * q^59 - 22 * q^60 - 124 * q^61 - 49 * q^62 - 69 * q^63 - 37 * q^64 - 13 * q^65 - 34 * q^66 - 125 * q^67 - 40 * q^68 - 150 * q^69 - 81 * q^70 - 26 * q^71 - 97 * q^72 - 154 * q^73 + 8 * q^74 - 80 * q^75 - 66 * q^76 - 130 * q^77 - 33 * q^78 - 45 * q^79 - 21 * q^80 + 22 * q^81 - 145 * q^82 - 63 * q^83 - 55 * q^84 - 134 * q^85 - 27 * q^86 - 87 * q^87 - 131 * q^88 - 47 * q^89 - 46 * q^90 - 56 * q^91 - 52 * q^92 - 130 * q^93 - 63 * q^94 + q^95 - 15 * q^96 - 204 * q^97 + 4 * q^98 + 9 * q^99

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 $

$2$	−2.57298	−1.81937	−0.909686	−	0.415296i	$-0.863678\pi$
$2$	−2.57298	−1.81937	−0.909686	+	0.415296i	$0.863678\pi$
$3$	−0.267298	−0.154325	−0.0771623	−	0.997019i	$-0.524586\pi$
$3$	−0.267298	−0.154325	−0.0771623	+	0.997019i	$0.524586\pi$
$4$	4.62023	2.31012
$5$	−2.52986	−1.13139	−0.565693	−	0.824616i	$-0.691391\pi$
$5$	−2.52986	−1.13139	−0.565693	+	0.824616i	$0.691391\pi$
$6$	0.687753	0.280774
$7$	−4.69728	−1.77541	−0.887703	−	0.460417i	$-0.847700\pi$
$7$	−4.69728	−1.77541	−0.887703	+	0.460417i	$0.847700\pi$
$8$	−6.74181	−2.38359
$9$	−2.92855	−0.976184
$10$	6.50927	2.05841
$11$	2.79951	0.844085	0.422042	−	0.906576i	$-0.361313\pi$
$11$	2.79951	0.844085	0.422042	+	0.906576i	$0.361313\pi$
$12$	−1.23498	−0.356508
$13$	−0.845941	−0.234622	−0.117311	−	0.993095i	$-0.537427\pi$
$13$	−0.845941	−0.234622	−0.117311	+	0.993095i	$0.537427\pi$
$14$	12.0860	3.23012
$15$	0.676226	0.174601
$16$	8.10608	2.02652
$17$	1.31976	0.320090	0.160045	−	0.987110i	$-0.448836\pi$
$17$	1.31976	0.320090	0.160045	+	0.987110i	$0.448836\pi$
$18$	7.53511	1.77604
$19$	1.33224	0.305637	0.152818	−	0.988254i	$-0.451165\pi$
$19$	1.33224	0.305637	0.152818	+	0.988254i	$0.451165\pi$
$20$	−11.6885	−2.61363
$21$	1.25557	0.273989
$22$	−7.20309	−1.53570
$23$	−3.57006	−0.744410	−0.372205	−	0.928151i	$-0.621398\pi$
$23$	−3.57006	−0.744410	−0.372205	+	0.928151i	$0.621398\pi$
$24$	1.80207	0.367846
$25$	1.40017	0.280034
$26$	2.17659	0.426865
$27$	1.58469	0.304974
$28$	−21.7025	−4.10139
$29$	1.37347	0.255046	0.127523	−	0.991836i	$-0.459297\pi$
$29$	1.37347	0.255046	0.127523	+	0.991836i	$0.459297\pi$
$30$	−1.73992	−0.317664
$31$	1.03261	0.185461	0.0927307	−	0.995691i	$-0.470440\pi$
$31$	1.03261	0.185461	0.0927307	+	0.995691i	$0.470440\pi$
$32$	−7.37317	−1.30340
$33$	−0.748304	−0.130263
$34$	−3.39573	−0.582363
$35$	11.8834	2.00867
$36$	−13.5306	−2.25510
$37$	−0.724634	−0.119129	−0.0595646	−	0.998224i	$-0.518971\pi$
$37$	−0.724634	−0.119129	−0.0595646	+	0.998224i	$0.518971\pi$
$38$	−3.42783	−0.556067
$39$	0.226118	0.0362079
$40$	17.0558	2.69676
$41$	5.41760	0.846087	0.423044	−	0.906109i	$-0.360962\pi$
$41$	5.41760	0.846087	0.423044	+	0.906109i	$0.360962\pi$
$42$	−3.23057	−0.498488
$43$	−0.534970	−0.0815822	−0.0407911	−	0.999168i	$-0.512988\pi$
$43$	−0.534970	−0.0815822	−0.0407911	+	0.999168i	$0.512988\pi$
$44$	12.9344	1.94993
$45$	7.40881	1.10444
$46$	9.18571	1.35436
$47$	−1.25775	−0.183462	−0.0917308	−	0.995784i	$-0.529240\pi$
$47$	−1.25775	−0.183462	−0.0917308	+	0.995784i	$0.529240\pi$
$48$	−2.16674	−0.312742
$49$	15.0645	2.15206
$50$	−3.60262	−0.509487
$51$	−0.352771	−0.0493978
$52$	−3.90845	−0.542004
$53$	−0.284928	−0.0391379	−0.0195690	−	0.999809i	$-0.506229\pi$
$53$	−0.284928	−0.0391379	−0.0195690	+	0.999809i	$0.506229\pi$
$54$	−4.07738	−0.554861
$55$	−7.08236	−0.954986
$56$	31.6682	4.23184
$57$	−0.356105	−0.0471673
$58$	−3.53390	−0.464024
$59$	7.91289	1.03017	0.515085	−	0.857139i	$-0.327760\pi$
$59$	7.91289	1.03017	0.515085	+	0.857139i	$0.327760\pi$
$60$	3.12432	0.403348
$61$	0.836999	0.107167	0.0535834	−	0.998563i	$-0.482936\pi$
$61$	0.836999	0.107167	0.0535834	+	0.998563i	$0.482936\pi$
$62$	−2.65687	−0.337423
$63$	13.7562	1.73312
$64$	2.75888	0.344859
$65$	2.14011	0.265448
$66$	1.92537	0.236997
$67$	5.21884	0.637582	0.318791	−	0.947825i	$-0.396723\pi$
$67$	5.21884	0.637582	0.318791	+	0.947825i	$0.396723\pi$
$68$	6.09762	0.739445
$69$	0.954271	0.114881
$70$	−30.5759	−3.65452
$71$	3.40604	0.404222	0.202111	−	0.979363i	$-0.435220\pi$
$71$	3.40604	0.404222	0.202111	+	0.979363i	$0.435220\pi$
$72$	19.7437	2.32682
$73$	3.28626	0.384628	0.192314	−	0.981333i	$-0.438401\pi$
$73$	3.28626	0.384628	0.192314	+	0.981333i	$0.438401\pi$
$74$	1.86447	0.216740
$75$	−0.374263	−0.0432162
$76$	6.15526	0.706056
$77$	−13.1501	−1.49859
$78$	−0.581799	−0.0658757
$79$	10.5036	1.18175	0.590876	−	0.806763i	$-0.298782\pi$
$79$	10.5036	1.18175	0.590876	+	0.806763i	$0.298782\pi$
$80$	−20.5072	−2.29278
$81$	8.36207	0.929119
$82$	−13.9394	−1.53935
$83$	4.21855	0.463046	0.231523	−	0.972829i	$-0.425629\pi$
$83$	4.21855	0.463046	0.231523	+	0.972829i	$0.425629\pi$
$84$	5.80104	0.632946
$85$	−3.33881	−0.362145
$86$	1.37647	0.148428
$87$	−0.367125	−0.0393599
$88$	−18.8738	−2.01195
$89$	8.09001	0.857540	0.428770	−	0.903414i	$-0.358947\pi$
$89$	8.09001	0.857540	0.428770	+	0.903414i	$0.358947\pi$
$90$	−19.0627	−2.00939
$91$	3.97362	0.416549
$92$	−16.4945	−1.71967
$93$	−0.276014	−0.0286213
$94$	3.23617	0.333785
$95$	−3.37038	−0.345793
$96$	1.97083	0.201147
$97$	−9.95203	−1.01048	−0.505238	−	0.862980i	$-0.668595\pi$
$97$	−9.95203	−1.01048	−0.505238	+	0.862980i	$0.668595\pi$
$98$	−38.7605	−3.91541
$99$	−8.19852	−0.823982
$100$	6.46912	0.646912
$101$	6.67004	0.663694	0.331847	−	0.943333i	$-0.392328\pi$
$101$	6.67004	0.663694	0.331847	+	0.943333i	$0.392328\pi$
$102$	0.907672	0.0898729
$103$	−11.5692	−1.13995	−0.569975	−	0.821662i	$-0.693047\pi$
$103$	−11.5692	−1.13995	−0.569975	+	0.821662i	$0.693047\pi$
$104$	5.70317	0.559242
$105$	−3.17642	−0.309987
$106$	0.733115	0.0712065
$107$	−5.77135	−0.557937	−0.278969	−	0.960300i	$-0.589993\pi$
$107$	−5.77135	−0.557937	−0.278969	+	0.960300i	$0.589993\pi$
$108$	7.32164	0.704525
$109$	−19.2901	−1.84766	−0.923828	−	0.382808i	$-0.874957\pi$
$109$	−19.2901	−1.84766	−0.923828	+	0.382808i	$0.874957\pi$
$110$	18.2228	1.73747
$111$	0.193693	0.0183846
$112$	−38.0765	−3.59789
$113$	2.42982	0.228578	0.114289	−	0.993448i	$-0.463541\pi$
$113$	2.42982	0.228578	0.114289	+	0.993448i	$0.463541\pi$
$114$	0.916252	0.0858148
$115$	9.03175	0.842215
$116$	6.34573	0.589186
$117$	2.47738	0.229034
$118$	−20.3597	−1.87426
$119$	−6.19931	−0.568289
$120$	−4.55898	−0.416176
$121$	−3.16273	−0.287521
$122$	−2.15358	−0.194976
$123$	−1.44811	−0.130572
$124$	4.77088	0.428437
$125$	9.10705	0.814559
$126$	−35.3945	−3.15319
$127$	−13.0228	−1.15559	−0.577795	−	0.816182i	$-0.696087\pi$
$127$	−13.0228	−1.15559	−0.577795	+	0.816182i	$0.696087\pi$
$128$	7.64781	0.675977
$129$	0.142996	0.0125901
$130$	−5.50646	−0.482949
$131$	−5.60575	−0.489777	−0.244888	−	0.969551i	$-0.578751\pi$
$131$	−5.60575	−0.489777	−0.244888	+	0.969551i	$0.578751\pi$
$132$	−3.45734	−0.300923
$133$	−6.25791	−0.542629
$134$	−13.4280	−1.16000
$135$	−4.00904	−0.345043
$136$	−8.89760	−0.762963
$137$	12.7239	1.08707	0.543537	−	0.839385i	$-0.317085\pi$
$137$	12.7239	1.08707	0.543537	+	0.839385i	$0.317085\pi$
$138$	−2.45532	−0.209011
$139$	−10.7613	−0.912760	−0.456380	−	0.889785i	$-0.650854\pi$
$139$	−10.7613	−0.912760	−0.456380	+	0.889785i	$0.650854\pi$
$140$	54.9043	4.64026
$141$	0.336194	0.0283126
$142$	−8.76367	−0.735431
$143$	−2.36822	−0.198041
$144$	−23.7391	−1.97826
$145$	−3.47467	−0.288556
$146$	−8.45549	−0.699782
$147$	−4.02670	−0.332117
$148$	−3.34798	−0.275202
$149$	−14.4679	−1.18526	−0.592629	−	0.805475i	$-0.701910\pi$
$149$	−14.4679	−1.18526	−0.592629	+	0.805475i	$0.701910\pi$
$150$	0.962972	0.0786263
$151$	2.88090	0.234444	0.117222	−	0.993106i	$-0.462601\pi$
$151$	2.88090	0.234444	0.117222	+	0.993106i	$0.462601\pi$
$152$	−8.98170	−0.728512
$153$	−3.86500	−0.312467
$154$	33.8350	2.72650
$155$	−2.61234	−0.209828
$156$	1.04472	0.0836445
$157$	23.5441	1.87903	0.939513	−	0.342514i	$-0.111278\pi$
$157$	23.5441	1.87903	0.939513	+	0.342514i	$0.111278\pi$
$158$	−27.0257	−2.15005
$159$	0.0761608	0.00603995
$160$	18.6531	1.47465
$161$	16.7696	1.32163
$162$	−21.5154	−1.69041
$163$	7.95112	0.622780	0.311390	−	0.950282i	$-0.399206\pi$
$163$	7.95112	0.622780	0.311390	+	0.950282i	$0.399206\pi$
$164$	25.0306	1.95456
$165$	1.89310	0.147378
$166$	−10.8543	−0.842454
$167$	14.3539	1.11074	0.555368	−	0.831605i	$-0.312577\pi$
$167$	14.3539	1.11074	0.555368	+	0.831605i	$0.312577\pi$
$168$	−8.46484	−0.653077
$169$	−12.2844	−0.944953
$170$	8.59071	0.658877
$171$	−3.90153	−0.298358
$172$	−2.47169	−0.188464
$173$	19.3322	1.46980	0.734899	−	0.678177i	$-0.237230\pi$
$173$	19.3322	1.46980	0.734899	+	0.678177i	$0.237230\pi$
$174$	0.944605	0.0716103
$175$	−6.57700	−0.497174
$176$	22.6931	1.71055
$177$	−2.11510	−0.158981
$178$	−20.8155	−1.56018
$179$	6.61842	0.494684	0.247342	−	0.968928i	$-0.420443\pi$
$179$	6.61842	0.494684	0.247342	+	0.968928i	$0.420443\pi$
$180$	34.2304	2.55139
$181$	−10.3000	−0.765590	−0.382795	−	0.923833i	$-0.625038\pi$
$181$	−10.3000	−0.765590	−0.382795	+	0.923833i	$0.625038\pi$
$182$	−10.2241	−0.757858
$183$	−0.223728	−0.0165385
$184$	24.0687	1.77437
$185$	1.83322	0.134781
$186$	0.710178	0.0520727
$187$	3.69470	0.270183
$188$	−5.81109	−0.423818
$189$	−7.44374	−0.541452
$190$	8.67191	0.629127
$191$	12.0209	0.869802	0.434901	−	0.900478i	$-0.356783\pi$
$191$	12.0209	0.869802	0.434901	+	0.900478i	$0.356783\pi$
$192$	−0.737442	−0.0532203
$193$	6.45540	0.464670	0.232335	−	0.972636i	$-0.425363\pi$
$193$	6.45540	0.464670	0.232335	+	0.972636i	$0.425363\pi$
$194$	25.6064	1.83843
$195$	−0.572047	−0.0409652
$196$	69.6013	4.97152
$197$	−7.83932	−0.558529	−0.279264	−	0.960214i	$-0.590091\pi$
$197$	−7.83932	−0.558529	−0.279264	+	0.960214i	$0.590091\pi$
$198$	21.0946	1.49913
$199$	−8.40486	−0.595805	−0.297902	−	0.954596i	$-0.596287\pi$
$199$	−8.40486	−0.595805	−0.297902	+	0.954596i	$0.596287\pi$
$200$	−9.43969	−0.667487
$201$	−1.39498	−0.0983946
$202$	−17.1619	−1.20751
$203$	−6.45156	−0.452810
$204$	−1.62988	−0.114115
$205$	−13.7058	−0.957251
$206$	29.7674	2.07399
$207$	10.4551	0.726681
$208$	−6.85727	−0.475466
$209$	3.72962	0.257983
$210$	8.17287	0.563982
$211$	14.9324	1.02799	0.513995	−	0.857793i	$-0.328165\pi$
$211$	14.9324	1.02799	0.513995	+	0.857793i	$0.328165\pi$
$212$	−1.31644	−0.0904132
$213$	−0.910427	−0.0623814
$214$	14.8496	1.01510
$215$	1.35340	0.0923009
$216$	−10.6837	−0.726932
$217$	−4.85044	−0.329269
$218$	49.6331	3.36157
$219$	−0.878412	−0.0593576
$220$	−32.7222	−2.20613
$221$	−1.11644	−0.0751001
$222$	−0.498369	−0.0334484
$223$	−24.0638	−1.61143	−0.805717	−	0.592301i	$-0.798220\pi$
$223$	−24.0638	−1.61143	−0.805717	+	0.592301i	$0.798220\pi$
$224$	34.6339	2.31407
$225$	−4.10048	−0.273365
$226$	−6.25187	−0.415868
$227$	21.5212	1.42841	0.714205	−	0.699937i	$-0.246788\pi$
$227$	21.5212	1.42841	0.714205	+	0.699937i	$0.246788\pi$
$228$	−1.64529	−0.108962
$229$	−0.0944420	−0.00624091	−0.00312045	−	0.999995i	$-0.500993\pi$
$229$	−0.0944420	−0.00624091	−0.00312045	+	0.999995i	$0.500993\pi$
$230$	−23.2385	−1.53230
$231$	3.51500	0.231270
$232$	−9.25964	−0.607925
$233$	−10.3362	−0.677147	−0.338574	−	0.940940i	$-0.609944\pi$
$233$	−10.3362	−0.677147	−0.338574	+	0.940940i	$0.609944\pi$
$234$	−6.37426	−0.416698
$235$	3.18193	0.207566
$236$	36.5594	2.37981
$237$	−2.80760	−0.182373
$238$	15.9507	1.03393
$239$	−12.5888	−0.814302	−0.407151	−	0.913361i	$-0.633478\pi$
$239$	−12.5888	−0.814302	−0.407151	+	0.913361i	$0.633478\pi$
$240$	5.48154	0.353832
$241$	−13.0254	−0.839043	−0.419521	−	0.907745i	$-0.637802\pi$
$241$	−13.0254	−0.839043	−0.419521	+	0.907745i	$0.637802\pi$
$242$	8.13764	0.523107
$243$	−6.98924	−0.448360
$244$	3.86713	0.247568
$245$	−38.1109	−2.43482
$246$	3.72597	0.237559
$247$	−1.12700	−0.0717091
$248$	−6.96163	−0.442064
$249$	−1.12761	−0.0714594
$250$	−23.4323	−1.48199
$251$	−3.12325	−0.197138	−0.0985689	−	0.995130i	$-0.531426\pi$
$251$	−3.12325	−0.197138	−0.0985689	+	0.995130i	$0.531426\pi$
$252$	63.5570	4.00371
$253$	−9.99444	−0.628345
$254$	33.5075	2.10245
$255$	0.892459	0.0558879
$256$	−25.1954	−1.57471
$257$	−22.5085	−1.40404	−0.702019	−	0.712158i	$-0.747718\pi$
$257$	−22.5085	−1.40404	−0.702019	+	0.712158i	$0.747718\pi$
$258$	−0.367927	−0.0229061
$259$	3.40381	0.211503
$260$	9.88780	0.613216
$261$	−4.02227	−0.248972
$262$	14.4235	0.891086
$263$	−1.87846	−0.115831	−0.0579153	−	0.998322i	$-0.518445\pi$
$263$	−1.87846	−0.115831	−0.0579153	+	0.998322i	$0.518445\pi$
$264$	5.04492	0.310494
$265$	0.720828	0.0442801
$266$	16.1015	0.987245
$267$	−2.16245	−0.132340
$268$	24.1122	1.47289
$269$	12.3945	0.755704	0.377852	−	0.925866i	$-0.376663\pi$
$269$	12.3945	0.755704	0.377852	+	0.925866i	$0.376663\pi$
$270$	10.3152	0.627762
$271$	−13.2452	−0.804586	−0.402293	−	0.915511i	$-0.631787\pi$
$271$	−13.2452	−0.804586	−0.402293	+	0.915511i	$0.631787\pi$
$272$	10.6981	0.648668
$273$	−1.06214	−0.0642838
$274$	−32.7383	−1.97779
$275$	3.91980	0.236373
$276$	4.40896	0.265388
$277$	−24.8771	−1.49472	−0.747361	−	0.664418i	$-0.768680\pi$
$277$	−24.8771	−1.49472	−0.747361	+	0.664418i	$0.768680\pi$
$278$	27.6886	1.66065
$279$	−3.02404	−0.181044
$280$	−80.1159	−4.78784
$281$	21.4496	1.27958	0.639789	−	0.768551i	$-0.279022\pi$
$281$	21.4496	1.27958	0.639789	+	0.768551i	$0.279022\pi$
$282$	−0.865021	−0.0515112
$283$	0.524168	0.0311586	0.0155793	−	0.999879i	$-0.495041\pi$
$283$	0.524168	0.0311586	0.0155793	+	0.999879i	$0.495041\pi$
$284$	15.7367	0.933800
$285$	0.900895	0.0533644
$286$	6.09339	0.360310
$287$	−25.4480	−1.50215
$288$	21.5927	1.27236
$289$	−15.2582	−0.897542
$290$	8.94026	0.524990
$291$	2.66016	0.155941
$292$	15.1833	0.888535
$293$	−6.44780	−0.376684	−0.188342	−	0.982103i	$-0.560311\pi$
$293$	−6.44780	−0.376684	−0.188342	+	0.982103i	$0.560311\pi$
$294$	10.3606	0.604244
$295$	−20.0185	−1.16552
$296$	4.88534	0.283955
$297$	4.43636	0.257424
$298$	37.2257	2.15643
$299$	3.02007	0.174655
$300$	−1.72918	−0.0998344
$301$	2.51291	0.144841
$302$	−7.41250	−0.426541
$303$	−1.78289	−0.102424
$304$	10.7992	0.619379
$305$	−2.11749	−0.121247
$306$	9.94457	0.568493
$307$	−8.24294	−0.470449	−0.235225	−	0.971941i	$-0.575583\pi$
$307$	−8.24294	−0.470449	−0.235225	+	0.971941i	$0.575583\pi$
$308$	−60.7565	−3.46192
$309$	3.09243	0.175922
$310$	6.72151	0.381756
$311$	−15.3960	−0.873026	−0.436513	−	0.899698i	$-0.643787\pi$
$311$	−15.3960	−0.873026	−0.436513	+	0.899698i	$0.643787\pi$
$312$	−1.52445	−0.0863048
$313$	7.06827	0.399522	0.199761	−	0.979845i	$-0.435983\pi$
$313$	7.06827	0.399522	0.199761	+	0.979845i	$0.435983\pi$
$314$	−60.5786	−3.41865
$315$	−34.8013	−1.96083
$316$	48.5292	2.72998
$317$	3.85503	0.216520	0.108260	−	0.994123i	$-0.465472\pi$
$317$	3.85503	0.216520	0.108260	+	0.994123i	$0.465472\pi$
$318$	−0.195960	−0.0109889
$319$	3.84504	0.215281
$320$	−6.97956	−0.390169
$321$	1.54267	0.0861035
$322$	−43.1479	−2.40454
$323$	1.75824	0.0978313
$324$	38.6347	2.14637
$325$	−1.18446	−0.0657022
$326$	−20.4581	−1.13307
$327$	5.15621	0.285139
$328$	−36.5244	−2.01672
$329$	5.90800	0.325719
$330$	−4.87092	−0.268135
$331$	22.2558	1.22329	0.611646	−	0.791132i	$-0.290508\pi$
$331$	22.2558	1.22329	0.611646	+	0.791132i	$0.290508\pi$
$332$	19.4907	1.06969
$333$	2.12213	0.116292
$334$	−36.9323	−2.02084
$335$	−13.2029	−0.721352
$336$	10.1778	0.555244
$337$	−6.44302	−0.350973	−0.175487	−	0.984482i	$-0.556150\pi$
$337$	−6.44302	−0.350973	−0.175487	+	0.984482i	$0.556150\pi$
$338$	31.6075	1.71922
$339$	−0.649485	−0.0352752
$340$	−15.4261	−0.836598
$341$	2.89079	0.156545
$342$	10.0386	0.542824
$343$	−37.8810	−2.04538
$344$	3.60667	0.194458
$345$	−2.41417	−0.129975
$346$	−49.7413	−2.67411
$347$	−18.0765	−0.970395	−0.485198	−	0.874404i	$-0.661252\pi$
$347$	−18.0765	−0.970395	−0.485198	+	0.874404i	$0.661252\pi$
$348$	−1.69620	−0.0909260
$349$	29.3099	1.56892	0.784462	−	0.620176i	$-0.212939\pi$
$349$	29.3099	1.56892	0.784462	+	0.620176i	$0.212939\pi$
$350$	16.9225	0.904546
$351$	−1.34056	−0.0715535
$352$	−20.6413	−1.10018
$353$	0.370212	0.0197044	0.00985221	−	0.999951i	$-0.496864\pi$
$353$	0.370212	0.0197044	0.00985221	+	0.999951i	$0.496864\pi$
$354$	5.44211	0.289245
$355$	−8.61678	−0.457331
$356$	37.3777	1.98102
$357$	1.65706	0.0877010
$358$	−17.0291	−0.900015
$359$	−16.6909	−0.880910	−0.440455	−	0.897775i	$-0.645183\pi$
$359$	−16.6909	−0.880910	−0.440455	+	0.897775i	$0.645183\pi$
$360$	−49.9488	−2.63253
$361$	−17.2251	−0.906586
$362$	26.5016	1.39289
$363$	0.845391	0.0443715
$364$	18.3591	0.962277
$365$	−8.31377	−0.435163
$366$	0.575648	0.0300896
$367$	−26.9194	−1.40518	−0.702591	−	0.711594i	$-0.747974\pi$
$367$	−26.9194	−1.40518	−0.702591	+	0.711594i	$0.747974\pi$
$368$	−28.9392	−1.50856
$369$	−15.8657	−0.825937
$370$	−4.71684	−0.245217
$371$	1.33839	0.0694857
$372$	−1.27525	−0.0661184
$373$	4.49431	0.232706	0.116353	−	0.993208i	$-0.462880\pi$
$373$	4.49431	0.232706	0.116353	+	0.993208i	$0.462880\pi$
$374$	−9.50639	−0.491564
$375$	−2.43430	−0.125707
$376$	8.47950	0.437297
$377$	−1.16187	−0.0598394
$378$	19.1526	0.985103
$379$	0.409629	0.0210412	0.0105206	−	0.999945i	$-0.496651\pi$
$379$	0.409629	0.0210412	0.0105206	+	0.999945i	$0.496651\pi$
$380$	−15.5719	−0.798822
$381$	3.48098	0.178336
$382$	−30.9296	−1.58249
$383$	−18.8474	−0.963057	−0.481529	−	0.876430i	$-0.659918\pi$
$383$	−18.8474	−0.963057	−0.481529	+	0.876430i	$0.659918\pi$
$384$	−2.04424	−0.104320
$385$	33.2679	1.69549
$386$	−16.6096	−0.845407
$387$	1.56669	0.0796392
$388$	−45.9807	−2.33431
$389$	−3.55161	−0.180074	−0.0900369	−	0.995938i	$-0.528698\pi$
$389$	−3.55161	−0.180074	−0.0900369	+	0.995938i	$0.528698\pi$
$390$	1.47187	0.0745309
$391$	−4.71165	−0.238278
$392$	−101.562	−5.12964
$393$	1.49841	0.0755846
$394$	20.1704	1.01617
$395$	−26.5727	−1.33702
$396$	−37.8791	−1.90349
$397$	25.2533	1.26743	0.633714	−	0.773568i	$-0.281530\pi$
$397$	25.2533	1.26743	0.633714	+	0.773568i	$0.281530\pi$
$398$	21.6256	1.08399
$399$	1.67273	0.0837410
$400$	11.3499	0.567495
$401$	−4.56437	−0.227934	−0.113967	−	0.993485i	$-0.536356\pi$
$401$	−4.56437	−0.227934	−0.113967	+	0.993485i	$0.536356\pi$
$402$	3.58927	0.179016
$403$	−0.873524	−0.0435133
$404$	30.8171	1.53321
$405$	−21.1548	−1.05119
$406$	16.5997	0.823831
$407$	−2.02862	−0.100555
$408$	2.37831	0.117744
$409$	21.7957	1.07773	0.538864	−	0.842393i	$-0.318854\pi$
$409$	21.7957	1.07773	0.538864	+	0.842393i	$0.318854\pi$
$410$	35.2646	1.74160
$411$	−3.40107	−0.167762
$412$	−53.4525	−2.63341
$413$	−37.1690	−1.82897
$414$	−26.9008	−1.32210
$415$	−10.6723	−0.523884
$416$	6.23727	0.305807
$417$	2.87647	0.140861
$418$	−9.59625	−0.469368
$419$	−3.73732	−0.182580	−0.0912900	−	0.995824i	$-0.529099\pi$
$419$	−3.73732	−0.182580	−0.0912900	+	0.995824i	$0.529099\pi$
$420$	−14.6758	−0.716106
$421$	−9.02554	−0.439878	−0.219939	−	0.975514i	$-0.570586\pi$
$421$	−9.02554	−0.439878	−0.219939	+	0.975514i	$0.570586\pi$
$422$	−38.4208	−1.87030
$423$	3.68338	0.179092
$424$	1.92093	0.0932887
$425$	1.84790	0.0896362
$426$	2.34251	0.113495
$427$	−3.93162	−0.190264
$428$	−26.6650	−1.28890
$429$	0.633022	0.0305626
$430$	−3.48227	−0.167930
$431$	5.76457	0.277669	0.138835	−	0.990316i	$-0.455664\pi$
$431$	5.76457	0.277669	0.138835	+	0.990316i	$0.455664\pi$
$432$	12.8456	0.618035
$433$	−3.87037	−0.185998	−0.0929991	−	0.995666i	$-0.529645\pi$
$433$	−3.87037	−0.185998	−0.0929991	+	0.995666i	$0.529645\pi$
$434$	12.4801	0.599063
$435$	0.928773	0.0445313
$436$	−89.1247	−4.26830
$437$	−4.75618	−0.227519
$438$	2.26014	0.107994
$439$	−3.96639	−0.189305	−0.0946527	−	0.995510i	$-0.530174\pi$
$439$	−3.96639	−0.189305	−0.0946527	+	0.995510i	$0.530174\pi$
$440$	47.7479	2.27629
$441$	−44.1170	−2.10081
$442$	2.87259	0.136635
$443$	34.0826	1.61931	0.809657	−	0.586903i	$-0.199653\pi$
$443$	34.0826	1.61931	0.809657	+	0.586903i	$0.199653\pi$
$444$	0.894908	0.0424705
$445$	−20.4666	−0.970209
$446$	61.9158	2.93180
$447$	3.86725	0.182915
$448$	−12.9592	−0.612265
$449$	−12.6231	−0.595719	−0.297860	−	0.954610i	$-0.596273\pi$
$449$	−12.6231	−0.595719	−0.297860	+	0.954610i	$0.596273\pi$
$450$	10.5504	0.497353
$451$	15.1666	0.714169
$452$	11.2263	0.528041
$453$	−0.770059	−0.0361805
$454$	−55.3736	−2.59881
$455$	−10.0527	−0.471278
$456$	2.40079	0.112427
$457$	0.184920	0.00865021	0.00432510	−	0.999991i	$-0.498623\pi$
$457$	0.184920	0.00865021	0.00432510	+	0.999991i	$0.498623\pi$
$458$	0.242998	0.0113545
$459$	2.09142	0.0976191
$460$	41.7288	1.94561
$461$	−22.5469	−1.05011	−0.525057	−	0.851067i	$-0.675956\pi$
$461$	−22.5469	−1.05011	−0.525057	+	0.851067i	$0.675956\pi$
$462$	−9.04402	−0.420766
$463$	−9.45723	−0.439515	−0.219757	−	0.975555i	$-0.570527\pi$
$463$	−9.45723	−0.439515	−0.219757	+	0.975555i	$0.570527\pi$
$464$	11.1334	0.516856
$465$	0.698274	0.0323817
$466$	26.5949	1.23198
$467$	−24.0534	−1.11306	−0.556529	−	0.830828i	$-0.687867\pi$
$467$	−24.0534	−1.11306	−0.556529	+	0.830828i	$0.687867\pi$
$468$	11.4461	0.529095
$469$	−24.5143	−1.13197
$470$	−8.18703	−0.377640
$471$	−6.29330	−0.289980
$472$	−53.3471	−2.45550
$473$	−1.49766	−0.0688623
$474$	7.22391	0.331805
$475$	1.86536	0.0855888
$476$	−28.6422	−1.31281
$477$	0.834428	0.0382058
$478$	32.3908	1.48152
$479$	−0.307276	−0.0140398	−0.00701990	−	0.999975i	$-0.502235\pi$
$479$	−0.307276	−0.0140398	−0.00701990	+	0.999975i	$0.502235\pi$
$480$	−4.98593	−0.227575
$481$	0.612998	0.0279503
$482$	33.5142	1.52653
$483$	−4.48248	−0.203960
$484$	−14.6125	−0.664206
$485$	25.1772	1.14324
$486$	17.9832	0.815733
$487$	18.5161	0.839045	0.419523	−	0.907745i	$-0.362198\pi$
$487$	18.5161	0.839045	0.419523	+	0.907745i	$0.362198\pi$
$488$	−5.64288	−0.255441
$489$	−2.12532	−0.0961102
$490$	98.0586	4.42984
$491$	9.04023	0.407980	0.203990	−	0.978973i	$-0.434609\pi$
$491$	9.04023	0.407980	0.203990	+	0.978973i	$0.434609\pi$
$492$	−6.69063	−0.301637
$493$	1.81265	0.0816377
$494$	2.89974	0.130466
$495$	20.7411	0.932242
$496$	8.37038	0.375841
$497$	−15.9991	−0.717658
$498$	2.90132	0.130011
$499$	1.51577	0.0678552	0.0339276	−	0.999424i	$-0.489198\pi$
$499$	1.51577	0.0678552	0.0339276	+	0.999424i	$0.489198\pi$
$500$	42.0767	1.88173
$501$	−3.83676	−0.171414
$502$	8.03606	0.358667
$503$	−3.11024	−0.138679	−0.0693395	−	0.997593i	$-0.522089\pi$
$503$	−3.11024	−0.138679	−0.0693395	+	0.997593i	$0.522089\pi$
$504$	−92.7419	−4.13105
$505$	−16.8742	−0.750894
$506$	25.7155	1.14319
$507$	3.28359	0.145829
$508$	−60.1686	−2.66955
$509$	32.7834	1.45310	0.726549	−	0.687115i	$-0.241123\pi$
$509$	32.7834	1.45310	0.726549	+	0.687115i	$0.241123\pi$
$510$	−2.29628	−0.101681
$511$	−15.4365	−0.682871
$512$	49.5317	2.18901
$513$	2.11119	0.0932112
$514$	57.9138	2.55447
$515$	29.2685	1.28972
$516$	0.660677	0.0290847
$517$	−3.52109	−0.154857
$518$	−8.75794	−0.384802
$519$	−5.16745	−0.226826
$520$	−14.4282	−0.632719
$521$	9.94376	0.435644	0.217822	−	0.975989i	$-0.430105\pi$
$521$	9.94376	0.435644	0.217822	+	0.975989i	$0.430105\pi$
$522$	10.3492	0.452973
$523$	24.4641	1.06974	0.534871	−	0.844934i	$-0.320360\pi$
$523$	24.4641	1.06974	0.534871	+	0.844934i	$0.320360\pi$
$524$	−25.8999	−1.13144
$525$	1.75802	0.0767263
$526$	4.83323	0.210739
$527$	1.36280	0.0593643
$528$	−6.06581	−0.263981
$529$	−10.2546	−0.445854
$530$	−1.85468	−0.0805620
$531$	−23.1733	−1.00564
$532$	−28.9130	−1.25354
$533$	−4.58297	−0.198511
$534$	5.56393	0.240775
$535$	14.6007	0.631243
$536$	−35.1844	−1.51973
$537$	−1.76909	−0.0763420
$538$	−31.8907	−1.37491
$539$	42.1731	1.81653
$540$	−18.5227	−0.797090
$541$	31.4615	1.35264	0.676319	−	0.736609i	$-0.263574\pi$
$541$	31.4615	1.35264	0.676319	+	0.736609i	$0.263574\pi$
$542$	34.0795	1.46384
$543$	2.75316	0.118149
$544$	−9.73085	−0.417207
$545$	48.8012	2.09041
$546$	2.73287	0.116956
$547$	0.198099	0.00847011	0.00423506	−	0.999991i	$-0.498652\pi$
$547$	0.198099	0.00847011	0.00423506	+	0.999991i	$0.498652\pi$
$548$	58.7873	2.51127
$549$	−2.45119	−0.104614
$550$	−10.0856	−0.430050
$551$	1.82979	0.0779515
$552$	−6.43351	−0.273829
$553$	−49.3385	−2.09809
$554$	64.0084	2.71946
$555$	−0.490016	−0.0208000
$556$	−49.7196	−2.10858
$557$	−40.8865	−1.73242	−0.866209	−	0.499682i	$-0.833450\pi$
$557$	−40.8865	−1.73242	−0.866209	+	0.499682i	$0.833450\pi$
$558$	7.78080	0.329387
$559$	0.452553	0.0191410
$560$	96.3281	4.07061
$561$	−0.987586	−0.0416959
$562$	−55.1895	−2.32803
$563$	−6.04687	−0.254845	−0.127423	−	0.991849i	$-0.540670\pi$
$563$	−6.04687	−0.254845	−0.127423	+	0.991849i	$0.540670\pi$
$564$	1.55329	0.0654055
$565$	−6.14708	−0.258610
$566$	−1.34867	−0.0566890
$567$	−39.2790	−1.64956
$568$	−22.9628	−0.963499
$569$	19.5894	0.821231	0.410615	−	0.911809i	$-0.365314\pi$
$569$	19.5894	0.821231	0.410615	+	0.911809i	$0.365314\pi$
$570$	−2.31799	−0.0970897
$571$	22.7557	0.952298	0.476149	−	0.879365i	$-0.342032\pi$
$571$	22.7557	0.952298	0.476149	+	0.879365i	$0.342032\pi$
$572$	−10.9417	−0.457497
$573$	−3.21316	−0.134232
$574$	65.4772	2.73297
$575$	−4.99870	−0.208460
$576$	−8.07951	−0.336646
$577$	−34.5065	−1.43653	−0.718263	−	0.695772i	$-0.755062\pi$
$577$	−34.5065	−1.43653	−0.718263	+	0.695772i	$0.755062\pi$
$578$	39.2591	1.63296
$579$	−1.72552	−0.0717100
$580$	−16.0538	−0.666597
$581$	−19.8157	−0.822095
$582$	−6.84453	−0.283715
$583$	−0.797661	−0.0330357
$584$	−22.1554	−0.916795
$585$	−6.26742	−0.259126
$586$	16.5901	0.685329
$587$	−21.0558	−0.869066	−0.434533	−	0.900656i	$-0.643086\pi$
$587$	−21.0558	−0.869066	−0.434533	+	0.900656i	$0.643086\pi$
$588$	−18.6043	−0.767228
$589$	1.37568	0.0566838
$590$	51.5071	2.12051
$591$	2.09544	0.0861947
$592$	−5.87394	−0.241418
$593$	−21.4973	−0.882788	−0.441394	−	0.897313i	$-0.645516\pi$
$593$	−21.4973	−0.882788	−0.441394	+	0.897313i	$0.645516\pi$
$594$	−11.4147	−0.468350
$595$	15.6834	0.642955
$596$	−66.8451	−2.73808
$597$	2.24660	0.0919474
$598$	−7.77057	−0.317762
$599$	−25.2689	−1.03246	−0.516230	−	0.856450i	$-0.672665\pi$
$599$	−25.2689	−1.03246	−0.516230	+	0.856450i	$0.672665\pi$
$600$	2.52321	0.103010
$601$	−13.1092	−0.534735	−0.267367	−	0.963595i	$-0.586154\pi$
$601$	−13.1092	−0.534735	−0.267367	+	0.963595i	$0.586154\pi$
$602$	−6.46566	−0.263521
$603$	−15.2836	−0.622398
$604$	13.3104	0.541593
$605$	8.00125	0.325297
$606$	4.58734	0.186348
$607$	19.4556	0.789678	0.394839	−	0.918750i	$-0.370800\pi$
$607$	19.4556	0.789678	0.394839	+	0.918750i	$0.370800\pi$
$608$	−9.82283	−0.398368
$609$	1.72449	0.0698798
$610$	5.44825	0.220593
$611$	1.06398	0.0430441
$612$	−17.8572	−0.721834
$613$	−24.8842	−1.00506	−0.502532	−	0.864559i	$-0.667598\pi$
$613$	−24.8842	−1.00506	−0.502532	+	0.864559i	$0.667598\pi$
$614$	21.2089	0.855922
$615$	3.66352	0.147727
$616$	88.6554	3.57203
$617$	−15.9052	−0.640318	−0.320159	−	0.947364i	$-0.603736\pi$
$617$	−15.9052	−0.640318	−0.320159	+	0.947364i	$0.603736\pi$
$618$	−7.95676	−0.320068
$619$	2.42098	0.0973074	0.0486537	−	0.998816i	$-0.484507\pi$
$619$	2.42098	0.0973074	0.0486537	+	0.998816i	$0.484507\pi$
$620$	−12.0696	−0.484728
$621$	−5.65745	−0.227026
$622$	39.6136	1.58836
$623$	−38.0011	−1.52248
$624$	1.83293	0.0733761
$625$	−30.0404	−1.20162
$626$	−18.1865	−0.726880
$627$	−0.996921	−0.0398132
$628$	108.779	4.34077
$629$	−0.956347	−0.0381320
$630$	89.5430	3.56748
$631$	31.9022	1.27001	0.635003	−	0.772510i	$-0.280999\pi$
$631$	31.9022	1.27001	0.635003	+	0.772510i	$0.280999\pi$
$632$	−70.8135	−2.81681
$633$	−3.99141	−0.158644
$634$	−9.91893	−0.393931
$635$	32.9459	1.30742
$636$	0.351881	0.0139530
$637$	−12.7436	−0.504922
$638$	−9.89320	−0.391676
$639$	−9.97475	−0.394595
$640$	−19.3479	−0.764791
$641$	−7.73367	−0.305461	−0.152731	−	0.988268i	$-0.548807\pi$
$641$	−7.73367	−0.305461	−0.152731	+	0.988268i	$0.548807\pi$
$642$	−3.96926	−0.156654
$643$	21.8973	0.863545	0.431773	−	0.901982i	$-0.357888\pi$
$643$	21.8973	0.863545	0.431773	+	0.901982i	$0.357888\pi$
$644$	77.4794	3.05312
$645$	−0.361761	−0.0142443
$646$	−4.52393	−0.177991
$647$	15.8153	0.621765	0.310883	−	0.950448i	$-0.399375\pi$
$647$	15.8153	0.621765	0.310883	+	0.950448i	$0.399375\pi$
$648$	−56.3755	−2.21464
$649$	22.1522	0.869551
$650$	3.04760	0.119537
$651$	1.29651	0.0508144
$652$	36.7360	1.43869
$653$	29.8603	1.16853	0.584263	−	0.811565i	$-0.301384\pi$
$653$	29.8603	1.16853	0.584263	+	0.811565i	$0.301384\pi$
$654$	−13.2668	−0.518774
$655$	14.1817	0.554127
$656$	43.9155	1.71461
$657$	−9.62399	−0.375468
$658$	−15.2012	−0.592604
$659$	3.39858	0.132390	0.0661950	−	0.997807i	$-0.478914\pi$
$659$	3.39858	0.132390	0.0661950	+	0.997807i	$0.478914\pi$
$660$	8.74657	0.340460
$661$	25.5485	0.993722	0.496861	−	0.867830i	$-0.334486\pi$
$661$	25.5485	0.993722	0.496861	+	0.867830i	$0.334486\pi$
$662$	−57.2638	−2.22562
$663$	0.298423	0.0115898
$664$	−28.4407	−1.10371
$665$	15.8316	0.613923
$666$	−5.46020	−0.211578
$667$	−4.90336	−0.189859
$668$	66.3182	2.56593
$669$	6.43222	0.248684
$670$	33.9708	1.31241
$671$	2.34319	0.0904578
$672$	−9.25756	−0.357118
$673$	−7.17539	−0.276591	−0.138296	−	0.990391i	$-0.544162\pi$
$673$	−7.17539	−0.276591	−0.138296	+	0.990391i	$0.544162\pi$
$674$	16.5778	0.638551
$675$	2.21884	0.0854031
$676$	−56.7567	−2.18295
$677$	−21.0547	−0.809199	−0.404600	−	0.914494i	$-0.632589\pi$
$677$	−21.0547	−0.809199	−0.404600	+	0.914494i	$0.632589\pi$
$678$	1.67111	0.0641787
$679$	46.7475	1.79400
$680$	22.5096	0.863205
$681$	−5.75257	−0.220439
$682$	−7.43795	−0.284814
$683$	−49.9962	−1.91305	−0.956526	−	0.291648i	$-0.905796\pi$
$683$	−49.9962	−1.91305	−0.956526	+	0.291648i	$0.905796\pi$
$684$	−18.0260	−0.689241
$685$	−32.1896	−1.22990
$686$	97.4671	3.72131
$687$	0.0252442	0.000963125 0
$688$	−4.33651	−0.165328
$689$	0.241033	0.00918262
$690$	6.21161	0.236472
$691$	−9.82064	−0.373595	−0.186797	−	0.982398i	$-0.559811\pi$
$691$	−9.82064	−0.373595	−0.186797	+	0.982398i	$0.559811\pi$
$692$	89.3191	3.39540
$693$	38.5107	1.46290
$694$	46.5104	1.76551
$695$	27.2245	1.03268
$696$	2.47508	0.0938178
$697$	7.14996	0.270824
$698$	−75.4139	−2.85446
$699$	2.76285	0.104500
$700$	−30.3873	−1.14853
$701$	−2.51625	−0.0950374	−0.0475187	−	0.998870i	$-0.515131\pi$
$701$	−2.51625	−0.0950374	−0.0475187	+	0.998870i	$0.515131\pi$
$702$	3.44922	0.130183
$703$	−0.965387	−0.0364102
$704$	7.72351	0.291091
$705$	−0.850523	−0.0320325
$706$	−0.952550	−0.0358497
$707$	−31.3310	−1.17833
$708$	−9.77225	−0.367264
$709$	14.9029	0.559690	0.279845	−	0.960045i	$-0.409717\pi$
$709$	14.9029	0.559690	0.279845	+	0.960045i	$0.409717\pi$
$710$	22.1708	0.832056
$711$	−30.7604	−1.15361
$712$	−54.5413	−2.04402
$713$	−3.68647	−0.138059
$714$	−4.26359	−0.159561
$715$	5.99126	0.224061
$716$	30.5787	1.14278
$717$	3.36496	0.125667
$718$	42.9453	1.60270
$719$	−47.4673	−1.77023	−0.885117	−	0.465369i	$-0.845922\pi$
$719$	−47.4673	−1.77023	−0.885117	+	0.465369i	$0.845922\pi$
$720$	60.0564	2.23817
$721$	54.3439	2.02387
$722$	44.3200	1.64942
$723$	3.48168	0.129485
$724$	−47.5882	−1.76860
$725$	1.92309	0.0714217
$726$	−2.17518	−0.0807284
$727$	−6.61402	−0.245300	−0.122650	−	0.992450i	$-0.539139\pi$
$727$	−6.61402	−0.245300	−0.122650	+	0.992450i	$0.539139\pi$
$728$	−26.7894	−0.992882
$729$	−23.2180	−0.859926
$730$	21.3912	0.791723
$731$	−0.706035	−0.0261136
$732$	−1.03368	−0.0382058
$733$	−6.43009	−0.237501	−0.118750	−	0.992924i	$-0.537889\pi$
$733$	−6.43009	−0.237501	−0.118750	+	0.992924i	$0.537889\pi$
$734$	69.2631	2.55655
$735$	10.1870	0.375752
$736$	26.3227	0.970268
$737$	14.6102	0.538174
$738$	40.8222	1.50269
$739$	43.0339	1.58303	0.791514	−	0.611151i	$-0.209293\pi$
$739$	43.0339	1.58303	0.791514	+	0.611151i	$0.209293\pi$
$740$	8.46990	0.311360
$741$	0.301244	0.0110665
$742$	−3.44365	−0.126420
$743$	33.2061	1.21821	0.609107	−	0.793088i	$-0.291528\pi$
$743$	33.2061	1.21821	0.609107	+	0.793088i	$0.291528\pi$
$744$	1.86083	0.0682213
$745$	36.6018	1.34098
$746$	−11.5638	−0.423380
$747$	−12.3542	−0.452018
$748$	17.0704	0.624154
$749$	27.1097	0.990565
$750$	6.26340	0.228707
$751$	−5.23324	−0.190964	−0.0954818	−	0.995431i	$-0.530439\pi$
$751$	−5.23324	−0.190964	−0.0954818	+	0.995431i	$0.530439\pi$
$752$	−10.1954	−0.371789
$753$	0.834839	0.0304232
$754$	2.98947	0.108870
$755$	−7.28826	−0.265247
$756$	−34.3918	−1.25082
$757$	−49.1075	−1.78484	−0.892420	−	0.451205i	$-0.850994\pi$
$757$	−49.1075	−1.78484	−0.892420	+	0.451205i	$0.850994\pi$
$758$	−1.05397	−0.0382818
$759$	2.67150	0.0969691
$760$	22.7224	0.824229
$761$	41.4278	1.50176	0.750879	−	0.660440i	$-0.229630\pi$
$761$	41.4278	1.50176	0.750879	+	0.660440i	$0.229630\pi$
$762$	−8.95650	−0.324460
$763$	90.6110	3.28034
$764$	55.5394	2.00934
$765$	9.77789	0.353520
$766$	48.4940	1.75216
$767$	−6.69384	−0.241700
$768$	6.73469	0.243017
$769$	−42.8857	−1.54650	−0.773248	−	0.634103i	$-0.781369\pi$
$769$	−42.8857	−1.54650	−0.773248	+	0.634103i	$0.781369\pi$
$770$	−85.5976	−3.08472
$771$	6.01647	0.216678
$772$	29.8254	1.07344
$773$	15.2446	0.548310	0.274155	−	0.961685i	$-0.411602\pi$
$773$	15.2446	0.548310	0.274155	+	0.961685i	$0.411602\pi$
$774$	−4.03106	−0.144893
$775$	1.44583	0.0519356
$776$	67.0946	2.40856
$777$	−0.909832	−0.0326400
$778$	9.13822	0.327621
$779$	7.21755	0.258595
$780$	−2.64299	−0.0946343
$781$	9.53524	0.341198
$782$	12.1230	0.433517
$783$	2.17652	0.0777824
$784$	122.114	4.36120
$785$	−59.5632	−2.12590
$786$	−3.85537	−0.137517
$787$	30.3788	1.08289	0.541444	−	0.840737i	$-0.317878\pi$
$787$	30.3788	1.08289	0.541444	+	0.840737i	$0.317878\pi$
$788$	−36.2195	−1.29027
$789$	0.502108	0.0178755
$790$	68.3710	2.43253
$791$	−11.4135	−0.405818
$792$	55.2728	1.96403
$793$	−0.708052	−0.0251437
$794$	−64.9763	−2.30592
$795$	−0.192676	−0.00683351
$796$	−38.8324	−1.37638
$797$	−16.1164	−0.570872	−0.285436	−	0.958398i	$-0.592138\pi$
$797$	−16.1164	−0.570872	−0.285436	+	0.958398i	$0.592138\pi$
$798$	−4.30389	−0.152356
$799$	−1.65993	−0.0587242
$800$	−10.3237	−0.364998
$801$	−23.6920	−0.837117
$802$	11.7440	0.414697
$803$	9.19994	0.324659
$804$	−6.44515	−0.227303
$805$	−42.4247	−1.49527
$806$	2.24756	0.0791669
$807$	−3.31302	−0.116624
$808$	−44.9681	−1.58197
$809$	−4.04964	−0.142378	−0.0711889	−	0.997463i	$-0.522679\pi$
$809$	−4.04964	−0.142378	−0.0711889	+	0.997463i	$0.522679\pi$
$810$	54.4310	1.91251
$811$	45.3378	1.59202	0.796012	−	0.605281i	$-0.206939\pi$
$811$	45.3378	1.59202	0.796012	+	0.605281i	$0.206939\pi$
$812$	−29.8077	−1.04604
$813$	3.54040	0.124167
$814$	5.21961	0.182947
$815$	−20.1152	−0.704604
$816$	−2.85959	−0.100106
$817$	−0.712709	−0.0249345
$818$	−56.0799	−1.96079
$819$	−11.6370	−0.406628
$820$	−63.3238	−2.21136
$821$	−6.05568	−0.211345	−0.105672	−	0.994401i	$-0.533699\pi$
$821$	−6.05568	−0.211345	−0.105672	+	0.994401i	$0.533699\pi$
$822$	8.75088	0.305222
$823$	50.3726	1.75588	0.877940	−	0.478771i	$-0.158917\pi$
$823$	50.3726	1.75588	0.877940	+	0.478771i	$0.158917\pi$
$824$	77.9974	2.71717
$825$	−1.04775	−0.0364781
$826$	95.6353	3.32758
$827$	4.48512	0.155963	0.0779815	−	0.996955i	$-0.475152\pi$
$827$	4.48512	0.155963	0.0779815	+	0.996955i	$0.475152\pi$
$828$	48.3051	1.67872
$829$	−44.7396	−1.55387	−0.776935	−	0.629581i	$-0.783227\pi$
$829$	−44.7396	−1.55387	−0.776935	+	0.629581i	$0.783227\pi$
$830$	27.4597	0.953140
$831$	6.64961	0.230672
$832$	−2.33385	−0.0809116
$833$	19.8815	0.688854
$834$	−7.40111	−0.256279
$835$	−36.3132	−1.25667
$836$	17.2317	0.595972
$837$	1.63636	0.0565609
$838$	9.61606	0.332181
$839$	11.9351	0.412045	0.206022	−	0.978547i	$-0.433948\pi$
$839$	11.9351	0.412045	0.206022	+	0.978547i	$0.433948\pi$
$840$	21.4148	0.738882
$841$	−27.1136	−0.934951
$842$	23.2225	0.800301
$843$	−5.73344	−0.197470
$844$	68.9912	2.37478
$845$	31.0777	1.06911
$846$	−9.47728	−0.325836
$847$	14.8562	0.510466
$848$	−2.30965	−0.0793138
$849$	−0.140109	−0.00480853
$850$	−4.75460	−0.163082
$851$	2.58699	0.0886809
$852$	−4.20638	−0.144108
$853$	−9.59589	−0.328557	−0.164278	−	0.986414i	$-0.552530\pi$
$853$	−9.59589	−0.328557	−0.164278	+	0.986414i	$0.552530\pi$
$854$	10.1160	0.346162
$855$	9.87032	0.337558
$856$	38.9093	1.32989
$857$	34.8563	1.19067	0.595335	−	0.803478i	$-0.297019\pi$
$857$	34.8563	1.19067	0.595335	+	0.803478i	$0.297019\pi$
$858$	−1.62875	−0.0556047
$859$	−36.9109	−1.25938	−0.629691	−	0.776845i	$-0.716819\pi$
$859$	−36.9109	−1.25938	−0.629691	+	0.776845i	$0.716819\pi$
$860$	6.25301	0.213226
$861$	6.80220	0.231818
$862$	−14.8321	−0.505184
$863$	26.9297	0.916697	0.458349	−	0.888773i	$-0.348441\pi$
$863$	26.9297	0.916697	0.458349	+	0.888773i	$0.348441\pi$
$864$	−11.6842	−0.397504
$865$	−48.9076	−1.66291
$866$	9.95840	0.338400
$867$	4.07849	0.138513
$868$	−22.4102	−0.760650
$869$	29.4051	0.997498
$870$	−2.38972	−0.0810189
$871$	−4.41483	−0.149591
$872$	130.050	4.40405
$873$	29.1450	0.986410
$874$	12.2376	0.413942
$875$	−42.7784	−1.44617
$876$	−4.05847	−0.137123
$877$	31.0035	1.04691	0.523457	−	0.852052i	$-0.324642\pi$
$877$	31.0035	1.04691	0.523457	+	0.852052i	$0.324642\pi$
$878$	10.2054	0.344417
$879$	1.72348	0.0581317
$880$	−57.4102	−1.93530
$881$	−51.2301	−1.72598	−0.862992	−	0.505217i	$-0.831412\pi$
$881$	−51.2301	−1.72598	−0.862992	+	0.505217i	$0.831412\pi$
$882$	113.512	3.82216
$883$	−4.11038	−0.138325	−0.0691627	−	0.997605i	$-0.522033\pi$
$883$	−4.11038	−0.138325	−0.0691627	+	0.997605i	$0.522033\pi$
$884$	−5.15823	−0.173490
$885$	5.35090	0.179868
$886$	−87.6939	−2.94614
$887$	4.14975	0.139335	0.0696675	−	0.997570i	$-0.477806\pi$
$887$	4.14975	0.139335	0.0696675	+	0.997570i	$0.477806\pi$
$888$	−1.30584	−0.0438212
$889$	61.1720	2.05164
$890$	52.6601	1.76517
$891$	23.4097	0.784255
$892$	−111.180	−3.72260
$893$	−1.67562	−0.0560726
$894$	−9.95035	−0.332790
$895$	−16.7437	−0.559679
$896$	−35.9239	−1.20013
$897$	−0.807258	−0.0269536
$898$	32.4789	1.08383
$899$	1.41825	0.0473012
$900$	−18.9451	−0.631505
$901$	−0.376038	−0.0125277
$902$	−39.0235	−1.29934
$903$	−0.671695	−0.0223526
$904$	−16.3814	−0.544836
$905$	26.0574	0.866178
$906$	1.98135	0.0658258
$907$	−25.8159	−0.857204	−0.428602	−	0.903493i	$-0.640994\pi$
$907$	−25.8159	−0.857204	−0.428602	+	0.903493i	$0.640994\pi$
$908$	99.4328	3.29979
$909$	−19.5336	−0.647887
$910$	25.8654	0.857430
$911$	0.601945	0.0199433	0.00997166	−	0.999950i	$-0.496826\pi$
$911$	0.601945	0.0199433	0.00997166	+	0.999950i	$0.496826\pi$
$912$	−2.88662	−0.0955854
$913$	11.8099	0.390850
$914$	−0.475797	−0.0157380
$915$	0.566000	0.0187114
$916$	−0.436344	−0.0144172
$917$	26.3318	0.869552
$918$	−5.38118	−0.177605
$919$	11.1047	0.366312	0.183156	−	0.983084i	$-0.441369\pi$
$919$	11.1047	0.366312	0.183156	+	0.983084i	$0.441369\pi$
$920$	−60.8903	−2.00749
$921$	2.20332	0.0726019
$922$	58.0127	1.91055
$923$	−2.88131	−0.0948394
$924$	16.2401	0.534260
$925$	−1.01461	−0.0333602
$926$	24.3333	0.799641
$927$	33.8811	1.11280
$928$	−10.1268	−0.332429
$929$	−29.4207	−0.965261	−0.482630	−	0.875824i	$-0.660319\pi$
$929$	−29.4207	−0.965261	−0.482630	+	0.875824i	$0.660319\pi$
$930$	−1.79665	−0.0589144
$931$	20.0695	0.657750
$932$	−47.7557	−1.56429
$933$	4.11532	0.134729
$934$	61.8889	2.02507
$935$	−9.34705	−0.305681
$936$	−16.7020	−0.545923
$937$	22.2978	0.728437	0.364219	−	0.931314i	$-0.381336\pi$
$937$	22.2978	0.728437	0.364219	+	0.931314i	$0.381336\pi$
$938$	63.0749	2.05947
$939$	−1.88933	−0.0616561
$940$	14.7012	0.479501
$941$	23.1099	0.753361	0.376680	−	0.926343i	$-0.377065\pi$
$941$	23.1099	0.753361	0.376680	+	0.926343i	$0.377065\pi$
$942$	16.1925	0.527581
$943$	−19.3412	−0.629836
$944$	64.1425	2.08766
$945$	18.8316	0.612591
$946$	3.85344	0.125286
$947$	32.0189	1.04047	0.520237	−	0.854022i	$-0.325844\pi$
$947$	32.0189	1.04047	0.520237	+	0.854022i	$0.325844\pi$
$948$	−12.9718	−0.421304
$949$	−2.77999	−0.0902422
$950$	−4.79955	−0.155718
$951$	−1.03044	−0.0334144
$952$	41.7945	1.35457
$953$	31.3512	1.01557	0.507783	−	0.861485i	$-0.330465\pi$
$953$	31.3512	1.01557	0.507783	+	0.861485i	$0.330465\pi$
$954$	−2.14697	−0.0695106
$955$	−30.4112	−0.984082
$956$	−58.1632	−1.88113
$957$	−1.02777	−0.0332231
$958$	0.790616	0.0255436
$959$	−59.7676	−1.93000
$960$	1.86562	0.0602127
$961$	−29.9337	−0.965604
$962$	−1.57723	−0.0508520
$963$	16.9017	0.544650
$964$	−60.1806	−1.93829
$965$	−16.3312	−0.525721
$966$	11.5333	0.371079
$967$	−48.1343	−1.54790	−0.773948	−	0.633249i	$-0.781721\pi$
$967$	−48.1343	−1.54790	−0.773948	+	0.633249i	$0.781721\pi$
$968$	21.3225	0.685331
$969$	−0.469975	−0.0150978
$970$	−64.7804	−2.07997
$971$	−26.5876	−0.853237	−0.426618	−	0.904432i	$-0.640295\pi$
$971$	−26.5876	−0.853237	−0.426618	+	0.904432i	$0.640295\pi$
$972$	−32.2919	−1.03576
$973$	50.5488	1.62052
$974$	−47.6416	−1.52654
$975$	0.316605	0.0101395
$976$	6.78478	0.217175
$977$	9.54244	0.305290	0.152645	−	0.988281i	$-0.451221\pi$
$977$	9.54244	0.305290	0.152645	+	0.988281i	$0.451221\pi$
$978$	5.46840	0.174860
$979$	22.6481	0.723836
$980$	−176.081	−5.62471
$981$	56.4920	1.80365
$982$	−23.2603	−0.742267
$983$	16.8963	0.538909	0.269454	−	0.963013i	$-0.413157\pi$
$983$	16.8963	0.538909	0.269454	+	0.963013i	$0.413157\pi$
$984$	9.76291	0.311230
$985$	19.8324	0.631912
$986$	−4.66392	−0.148529
$987$	−1.57920	−0.0502664
$988$	−5.20699	−0.165656
$989$	1.90988	0.0607306
$990$	−53.3664	−1.69609
$991$	3.44238	0.109351	0.0546754	−	0.998504i	$-0.482588\pi$
$991$	3.44238	0.109351	0.0546754	+	0.998504i	$0.482588\pi$
$992$	−7.61358	−0.241731
$993$	−5.94894	−0.188784
$994$	41.1654	1.30569
$995$	21.2631	0.674085
$996$	−5.20982	−0.165080
$997$	−15.6959	−0.497096	−0.248548	−	0.968620i	$-0.579953\pi$
$997$	−15.6959	−0.497096	−0.248548	+	0.968620i	$0.579953\pi$
$998$	−3.90005	−0.123454
$999$	−1.14832	−0.0363313

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3467.2.a.b.1.7	✓	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3467.2.a.b.1.7	✓	126	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:	\( N \)	\(=\)	\( 3467 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3467.a (trivial)

\(f(q)\)	\(=\)	\(q-2.57298 q^{2} -0.267298 q^{3} +4.62023 q^{4} -2.52986 q^{5} +0.687753 q^{6} -4.69728 q^{7} -6.74181 q^{8} -2.92855 q^{9} +6.50927 q^{10} +2.79951 q^{11} -1.23498 q^{12} -0.845941 q^{13} +12.0860 q^{14} +0.676226 q^{15} +8.10608 q^{16} +1.31976 q^{17} +7.53511 q^{18} +1.33224 q^{19} -11.6885 q^{20} +1.25557 q^{21} -7.20309 q^{22} -3.57006 q^{23} +1.80207 q^{24} +1.40017 q^{25} +2.17659 q^{26} +1.58469 q^{27} -21.7025 q^{28} +1.37347 q^{29} -1.73992 q^{30} +1.03261 q^{31} -7.37317 q^{32} -0.748304 q^{33} -3.39573 q^{34} +11.8834 q^{35} -13.5306 q^{36} -0.724634 q^{37} -3.42783 q^{38} +0.226118 q^{39} +17.0558 q^{40} +5.41760 q^{41} -3.23057 q^{42} -0.534970 q^{43} +12.9344 q^{44} +7.40881 q^{45} +9.18571 q^{46} -1.25775 q^{47} -2.16674 q^{48} +15.0645 q^{49} -3.60262 q^{50} -0.352771 q^{51} -3.90845 q^{52} -0.284928 q^{53} -4.07738 q^{54} -7.08236 q^{55} +31.6682 q^{56} -0.356105 q^{57} -3.53390 q^{58} +7.91289 q^{59} +3.12432 q^{60} +0.836999 q^{61} -2.65687 q^{62} +13.7562 q^{63} +2.75888 q^{64} +2.14011 q^{65} +1.92537 q^{66} +5.21884 q^{67} +6.09762 q^{68} +0.954271 q^{69} -30.5759 q^{70} +3.40604 q^{71} +19.7437 q^{72} +3.28626 q^{73} +1.86447 q^{74} -0.374263 q^{75} +6.15526 q^{76} -13.1501 q^{77} -0.581799 q^{78} +10.5036 q^{79} -20.5072 q^{80} +8.36207 q^{81} -13.9394 q^{82} +4.21855 q^{83} +5.80104 q^{84} -3.33881 q^{85} +1.37647 q^{86} -0.367125 q^{87} -18.8738 q^{88} +8.09001 q^{89} -19.0627 q^{90} +3.97362 q^{91} -16.4945 q^{92} -0.276014 q^{93} +3.23617 q^{94} -3.37038 q^{95} +1.97083 q^{96} -9.95203 q^{97} -38.7605 q^{98} -8.19852 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q - 11 q^{2} - 25 q^{3} + 99 q^{4} - 32 q^{5} - 15 q^{6} - 27 q^{7} - 27 q^{8} + 93 q^{9} - 46 q^{10} - 6 q^{11} - 67 q^{12} - 137 q^{13} - 17 q^{14} - 15 q^{15} + 49 q^{16} - 30 q^{17} - 37 q^{18}+ \cdots + 9 q^{99}+O(q^{100}) \) 126 * q - 11 * q^2 - 25 * q^3 + 99 * q^4 - 32 * q^5 - 15 * q^6 - 27 * q^7 - 27 * q^8 + 93 * q^9 - 46 * q^10 - 6 * q^11 - 67 * q^12 - 137 * q^13 - 17 * q^14 - 15 * q^15 + 49 * q^16 - 30 * q^17 - 37 * q^18 - 39 * q^19 - 46 * q^20 - 54 * q^21 - 55 * q^22 - 35 * q^23 - 27 * q^24 + 26 * q^25 - 14 * q^26 - 88 * q^27 - 63 * q^28 - 31 * q^29 - 5 * q^30 - 64 * q^31 - 60 * q^32 - 100 * q^33 - 47 * q^34 - 38 * q^35 + 44 * q^36 - 148 * q^37 - 51 * q^38 + 7 * q^39 - 128 * q^40 - 28 * q^41 - 38 * q^42 - 68 * q^43 - 8 * q^44 - 137 * q^45 - 43 * q^46 - 51 * q^47 - 117 * q^48 + 3 * q^49 - 8 * q^50 - 30 * q^51 - 232 * q^52 - 112 * q^53 - 30 * q^54 - 96 * q^55 - 28 * q^56 - 47 * q^57 - 74 * q^58 - 38 * q^59 - 22 * q^60 - 124 * q^61 - 49 * q^62 - 69 * q^63 - 37 * q^64 - 13 * q^65 - 34 * q^66 - 125 * q^67 - 40 * q^68 - 150 * q^69 - 81 * q^70 - 26 * q^71 - 97 * q^72 - 154 * q^73 + 8 * q^74 - 80 * q^75 - 66 * q^76 - 130 * q^77 - 33 * q^78 - 45 * q^79 - 21 * q^80 + 22 * q^81 - 145 * q^82 - 63 * q^83 - 55 * q^84 - 134 * q^85 - 27 * q^86 - 87 * q^87 - 131 * q^88 - 47 * q^89 - 46 * q^90 - 56 * q^91 - 52 * q^92 - 130 * q^93 - 63 * q^94 + q^95 - 15 * q^96 - 204 * q^97 + 4 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more