LMFDB - Embedded newform 5819.2.a.e.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5819,2,Mod(1,5819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5819, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5819.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 5819 = 11 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5819.a (trivial)

Newform invariants

comment:select newform

sage:traces = [6,3,7,5,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$46.4649489362$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.8639957.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 4x^{4} + 10x^{3} + 6x^{2} - 7x - 2 $ x^6 - 3x^5 - 4x^4 + 10x^3 + 6x^2 - 7*x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 253)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.255514$ of defining polynomial
Character	$\chi$	$=$	5819.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.25551 q^{2} +0.646163 q^{3} -0.423685 q^{4} -4.04297 q^{5} +0.811267 q^{6} -0.798084 q^{7} -3.04297 q^{8} -2.58247 q^{9} -5.07601 q^{10} -1.00000 q^{11} -0.273769 q^{12} -3.19289 q^{13} -1.00201 q^{14} -2.61242 q^{15} -2.97312 q^{16} -0.503752 q^{17} -3.24233 q^{18} -3.98359 q^{19} +1.71294 q^{20} -0.515693 q^{21} -1.25551 q^{22} -1.96625 q^{24} +11.3456 q^{25} -4.00871 q^{26} -3.60719 q^{27} +0.338136 q^{28} -6.16897 q^{29} -3.27993 q^{30} -3.28168 q^{31} +2.35314 q^{32} -0.646163 q^{33} -0.632468 q^{34} +3.22663 q^{35} +1.09415 q^{36} -5.17919 q^{37} -5.00145 q^{38} -2.06312 q^{39} +12.3026 q^{40} -11.8209 q^{41} -0.647459 q^{42} +7.08974 q^{43} +0.423685 q^{44} +10.4409 q^{45} +1.22773 q^{47} -1.92112 q^{48} -6.36306 q^{49} +14.2446 q^{50} -0.325506 q^{51} +1.35278 q^{52} +3.00201 q^{53} -4.52888 q^{54} +4.04297 q^{55} +2.42855 q^{56} -2.57405 q^{57} -7.74523 q^{58} +9.03304 q^{59} +1.10684 q^{60} -2.63648 q^{61} -4.12020 q^{62} +2.06103 q^{63} +8.90065 q^{64} +12.9087 q^{65} -0.811267 q^{66} -8.99026 q^{67} +0.213432 q^{68} +4.05108 q^{70} +9.80465 q^{71} +7.85839 q^{72} +1.31433 q^{73} -6.50255 q^{74} +7.33111 q^{75} +1.68779 q^{76} +0.798084 q^{77} -2.59028 q^{78} -15.6898 q^{79} +12.0202 q^{80} +5.41659 q^{81} -14.8413 q^{82} +2.92233 q^{83} +0.218491 q^{84} +2.03665 q^{85} +8.90127 q^{86} -3.98616 q^{87} +3.04297 q^{88} -6.20642 q^{89} +13.1086 q^{90} +2.54819 q^{91} -2.12050 q^{93} +1.54144 q^{94} +16.1055 q^{95} +1.52051 q^{96} +15.3359 q^{97} -7.98891 q^{98} +2.58247 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 7 q^{3} + 5 q^{4} - 3 q^{5} + 3 q^{6} + q^{7} + 3 q^{8} + 9 q^{9} + 6 q^{10} - 6 q^{11} + 11 q^{12} - 3 q^{13} + 8 q^{14} - 10 q^{15} - q^{16} - 5 q^{17} - 11 q^{18} - q^{19} + 7 q^{20}+ \cdots - 9 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 + 7 * q^3 + 5 * q^4 - 3 * q^5 + 3 * q^6 + q^7 + 3 * q^8 + 9 * q^9 + 6 * q^10 - 6 * q^11 + 11 * q^12 - 3 * q^13 + 8 * q^14 - 10 * q^15 - q^16 - 5 * q^17 - 11 * q^18 - q^19 + 7 * q^20 + 15 * q^21 - 3 * q^22 - 3 * q^24 + 3 * q^25 + 15 * q^26 + 16 * q^27 + 6 * q^29 + 25 * q^30 - 8 * q^31 - 6 * q^32 - 7 * q^33 + 6 * q^34 + 12 * q^35 - 8 * q^36 - 2 * q^37 - 9 * q^38 + q^39 + 30 * q^40 - 2 * q^41 + 31 * q^42 - 10 * q^43 - 5 * q^44 - 3 * q^45 + 14 * q^47 + 6 * q^48 - 5 * q^49 + 9 * q^50 + 24 * q^51 - 11 * q^52 + 4 * q^53 - 13 * q^54 + 3 * q^55 + 13 * q^56 + 19 * q^57 - 6 * q^58 + 39 * q^59 + 21 * q^60 + 22 * q^61 + 35 * q^63 - 33 * q^64 + 16 * q^65 - 3 * q^66 - 8 * q^67 - 17 * q^68 + 19 * q^70 + 18 * q^71 + 6 * q^72 - 9 * q^73 - 15 * q^74 + 6 * q^75 + 25 * q^76 - q^77 + 20 * q^78 + 15 * q^79 + 16 * q^80 + 18 * q^81 - 8 * q^82 - 43 * q^83 + 4 * q^84 - 21 * q^85 + 55 * q^86 - 28 * q^87 - 3 * q^88 - 17 * q^89 + 37 * q^90 + 9 * q^91 + 27 * q^93 + 63 * q^94 - 21 * q^95 + 26 * q^96 - 19 * q^97 + 34 * 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 $

$2$	1.25551	0.887782	0.443891	−	0.896081i	$-0.353598\pi$
$2$	1.25551	0.887782	0.443891	+	0.896081i	$0.353598\pi$
$3$	0.646163	0.373062	0.186531	−	0.982449i	$-0.440275\pi$
$3$	0.646163	0.373062	0.186531	+	0.982449i	$0.440275\pi$
$4$	−0.423685	−0.211842
$5$	−4.04297	−1.80807	−0.904036	−	0.427457i	$-0.859409\pi$
$5$	−4.04297	−1.80807	−0.904036	+	0.427457i	$0.859409\pi$
$6$	0.811267	0.331198
$7$	−0.798084	−0.301647	−0.150824	−	0.988561i	$-0.548193\pi$
$7$	−0.798084	−0.301647	−0.150824	+	0.988561i	$0.548193\pi$
$8$	−3.04297	−1.07585
$9$	−2.58247	−0.860824
$10$	−5.07601	−1.60517
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.273769	−0.0790304
$13$	−3.19289	−0.885547	−0.442774	−	0.896633i	$-0.646005\pi$
$13$	−3.19289	−0.885547	−0.442774	+	0.896633i	$0.646005\pi$
$14$	−1.00201	−0.267797
$15$	−2.61242	−0.674523
$16$	−2.97312	−0.743281
$17$	−0.503752	−0.122178	−0.0610889	−	0.998132i	$-0.519457\pi$
$17$	−0.503752	−0.122178	−0.0610889	+	0.998132i	$0.519457\pi$
$18$	−3.24233	−0.764225
$19$	−3.98359	−0.913898	−0.456949	−	0.889493i	$-0.651058\pi$
$19$	−3.98359	−0.913898	−0.456949	+	0.889493i	$0.651058\pi$
$20$	1.71294	0.383026
$21$	−0.515693	−0.112533
$22$	−1.25551	−0.267676
$23$	0	0
$23$	0	0
$24$	−1.96625	−0.401360
$25$	11.3456	2.26912
$26$	−4.00871	−0.786173
$27$	−3.60719	−0.694204
$28$	0.338136	0.0639017
$29$	−6.16897	−1.14555	−0.572774	−	0.819713i	$-0.694133\pi$
$29$	−6.16897	−1.14555	−0.572774	+	0.819713i	$0.694133\pi$
$30$	−3.27993	−0.598830
$31$	−3.28168	−0.589407	−0.294704	−	0.955589i	$-0.595221\pi$
$31$	−3.28168	−0.589407	−0.294704	+	0.955589i	$0.595221\pi$
$32$	2.35314	0.415981
$33$	−0.646163	−0.112483
$34$	−0.632468	−0.108467
$35$	3.22663	0.545400
$36$	1.09415	0.182359
$37$	−5.17919	−0.851454	−0.425727	−	0.904852i	$-0.639982\pi$
$37$	−5.17919	−0.851454	−0.425727	+	0.904852i	$0.639982\pi$
$38$	−5.00145	−0.811343
$39$	−2.06312	−0.330364
$40$	12.3026	1.94522
$41$	−11.8209	−1.84611	−0.923056	−	0.384666i	$-0.874317\pi$
$41$	−11.8209	−1.84611	−0.923056	+	0.384666i	$0.874317\pi$
$42$	−0.647459	−0.0999051
$43$	7.08974	1.08118	0.540588	−	0.841288i	$-0.318202\pi$
$43$	7.08974	1.08118	0.540588	+	0.841288i	$0.318202\pi$
$44$	0.423685	0.0638728
$45$	10.4409	1.55643
$46$	0	0
$47$	1.22773	0.179083	0.0895416	−	0.995983i	$-0.471460\pi$
$47$	1.22773	0.179083	0.0895416	+	0.995983i	$0.471460\pi$
$48$	−1.92112	−0.277290
$49$	−6.36306	−0.909009
$50$	14.2446	2.01449
$51$	−0.325506	−0.0455800
$52$	1.35278	0.187596
$53$	3.00201	0.412357	0.206179	−	0.978514i	$-0.433897\pi$
$53$	3.00201	0.412357	0.206179	+	0.978514i	$0.433897\pi$
$54$	−4.52888	−0.616302
$55$	4.04297	0.545154
$56$	2.42855	0.324528
$57$	−2.57405	−0.340941
$58$	−7.74523	−1.01700
$59$	9.03304	1.17600	0.588001	−	0.808861i	$-0.299915\pi$
$59$	9.03304	1.17600	0.588001	+	0.808861i	$0.299915\pi$
$60$	1.10684	0.142893
$61$	−2.63648	−0.337567	−0.168783	−	0.985653i	$-0.553984\pi$
$61$	−2.63648	−0.337567	−0.168783	+	0.985653i	$0.553984\pi$
$62$	−4.12020	−0.523266
$63$	2.06103	0.259666
$64$	8.90065	1.11258
$65$	12.9087	1.60113
$66$	−0.811267	−0.0998600
$67$	−8.99026	−1.09834	−0.549168	−	0.835712i	$-0.685055\pi$
$67$	−8.99026	−1.09834	−0.549168	+	0.835712i	$0.685055\pi$
$68$	0.213432	0.0258824
$69$	0	0
$70$	4.05108	0.484197
$71$	9.80465	1.16360	0.581799	−	0.813333i	$-0.302349\pi$
$71$	9.80465	1.16360	0.581799	+	0.813333i	$0.302349\pi$
$72$	7.85839	0.926120
$73$	1.31433	0.153830	0.0769151	−	0.997038i	$-0.475493\pi$
$73$	1.31433	0.153830	0.0769151	+	0.997038i	$0.475493\pi$
$74$	−6.50255	−0.755906
$75$	7.33111	0.846524
$76$	1.68779	0.193602
$77$	0.798084	0.0909501
$78$	−2.59028	−0.293292
$79$	−15.6898	−1.76524	−0.882618	−	0.470091i	$-0.844221\pi$
$79$	−15.6898	−1.76524	−0.882618	+	0.470091i	$0.844221\pi$
$80$	12.0202	1.34390
$81$	5.41659	0.601843
$82$	−14.8413	−1.63895
$83$	2.92233	0.320767	0.160384	−	0.987055i	$-0.448727\pi$
$83$	2.92233	0.320767	0.160384	+	0.987055i	$0.448727\pi$
$84$	0.218491	0.0238393
$85$	2.03665	0.220906
$86$	8.90127	0.959849
$87$	−3.98616	−0.427361
$88$	3.04297	0.324382
$89$	−6.20642	−0.657879	−0.328940	−	0.944351i	$-0.606691\pi$
$89$	−6.20642	−0.657879	−0.328940	+	0.944351i	$0.606691\pi$
$90$	13.1086	1.38177
$91$	2.54819	0.267123
$92$	0	0
$93$	−2.12050	−0.219886
$94$	1.54144	0.158987
$95$	16.1055	1.65239
$96$	1.52051	0.155187
$97$	15.3359	1.55712	0.778561	−	0.627569i	$-0.215950\pi$
$97$	15.3359	1.55712	0.778561	+	0.627569i	$0.215950\pi$
$98$	−7.98891	−0.807002
$99$	2.58247	0.259548
$100$	−4.80696	−0.480696
$101$	−5.69653	−0.566826	−0.283413	−	0.958998i	$-0.591467\pi$
$101$	−5.69653	−0.566826	−0.283413	+	0.958998i	$0.591467\pi$
$102$	−0.408677	−0.0404651
$103$	−0.992886	−0.0978319	−0.0489160	−	0.998803i	$-0.515577\pi$
$103$	−0.992886	−0.0978319	−0.0489160	+	0.998803i	$0.515577\pi$
$104$	9.71585	0.952718
$105$	2.08493	0.203468
$106$	3.76906	0.366084
$107$	5.98921	0.578999	0.289500	−	0.957178i	$-0.406511\pi$
$107$	5.98921	0.578999	0.289500	+	0.957178i	$0.406511\pi$
$108$	1.52831	0.147062
$109$	15.3585	1.47108	0.735541	−	0.677480i	$-0.236928\pi$
$109$	15.3585	1.47108	0.735541	+	0.677480i	$0.236928\pi$
$110$	5.07601	0.483978
$111$	−3.34660	−0.317645
$112$	2.37280	0.224209
$113$	−15.7470	−1.48135	−0.740675	−	0.671863i	$-0.765494\pi$
$113$	−15.7470	−1.48135	−0.740675	+	0.671863i	$0.765494\pi$
$114$	−3.23175	−0.302681
$115$	0	0
$116$	2.61370	0.242676
$117$	8.24554	0.762301
$118$	11.3411	1.04403
$119$	0.402037	0.0368546
$120$	7.94951	0.725688
$121$	1.00000	0.0909091
$122$	−3.31014	−0.299686
$123$	−7.63822	−0.688715
$124$	1.39040	0.124861
$125$	−25.6551	−2.29466
$126$	2.58765	0.230526
$127$	9.06863	0.804710	0.402355	−	0.915484i	$-0.368192\pi$
$127$	9.06863	0.804710	0.402355	+	0.915484i	$0.368192\pi$
$128$	6.46860	0.571749
$129$	4.58113	0.403346
$130$	16.2071	1.42146
$131$	10.9241	0.954442	0.477221	−	0.878783i	$-0.341644\pi$
$131$	10.9241	0.954442	0.477221	+	0.878783i	$0.341644\pi$
$132$	0.273769	0.0238286
$133$	3.17924	0.275675
$134$	−11.2874	−0.975083
$135$	14.5838	1.25517
$136$	1.53290	0.131445
$137$	−22.4269	−1.91606	−0.958029	−	0.286672i	$-0.907451\pi$
$137$	−22.4269	−1.91606	−0.958029	+	0.286672i	$0.907451\pi$
$138$	0	0
$139$	−0.760327	−0.0644901	−0.0322451	−	0.999480i	$-0.510266\pi$
$139$	−0.760327	−0.0644901	−0.0322451	+	0.999480i	$0.510266\pi$
$140$	−1.36707	−0.115539
$141$	0.793315	0.0668092
$142$	12.3099	1.03302
$143$	3.19289	0.267002
$144$	7.67801	0.639834
$145$	24.9410	2.07123
$146$	1.65015	0.136568
$147$	−4.11158	−0.339117
$148$	2.19434	0.180374
$149$	−5.59496	−0.458357	−0.229179	−	0.973384i	$-0.573604\pi$
$149$	−5.59496	−0.458357	−0.229179	+	0.973384i	$0.573604\pi$
$150$	9.20431	0.751529
$151$	7.13755	0.580845	0.290423	−	0.956898i	$-0.406204\pi$
$151$	7.13755	0.580845	0.290423	+	0.956898i	$0.406204\pi$
$152$	12.1219	0.983219
$153$	1.30093	0.105174
$154$	1.00201	0.0807439
$155$	13.2677	1.06569
$156$	0.874114	0.0699851
$157$	18.8473	1.50418	0.752090	−	0.659061i	$-0.229046\pi$
$157$	18.8473	1.50418	0.752090	+	0.659061i	$0.229046\pi$
$158$	−19.6987	−1.56715
$159$	1.93979	0.153835
$160$	−9.51369	−0.752123
$161$	0	0
$162$	6.80060	0.534306
$163$	−19.5160	−1.52861	−0.764305	−	0.644854i	$-0.776918\pi$
$163$	−19.5160	−1.52861	−0.764305	+	0.644854i	$0.776918\pi$
$164$	5.00833	0.391084
$165$	2.61242	0.203376
$166$	3.66903	0.284772
$167$	20.5303	1.58868	0.794342	−	0.607471i	$-0.207816\pi$
$167$	20.5303	1.58868	0.794342	+	0.607471i	$0.207816\pi$
$168$	1.56924	0.121069
$169$	−2.80548	−0.215806
$170$	2.55705	0.196117
$171$	10.2875	0.786706
$172$	−3.00381	−0.229039
$173$	4.67283	0.355268	0.177634	−	0.984097i	$-0.443156\pi$
$173$	4.67283	0.355268	0.177634	+	0.984097i	$0.443156\pi$
$174$	−5.00468	−0.379404
$175$	−9.05475	−0.684475
$176$	2.97312	0.224108
$177$	5.83681	0.438722
$178$	−7.79225	−0.584054
$179$	−4.68491	−0.350166	−0.175083	−	0.984554i	$-0.556019\pi$
$179$	−4.68491	−0.350166	−0.175083	+	0.984554i	$0.556019\pi$
$180$	−4.42363	−0.329718
$181$	−10.2400	−0.761133	−0.380566	−	0.924754i	$-0.624271\pi$
$181$	−10.2400	−0.761133	−0.380566	+	0.924754i	$0.624271\pi$
$182$	3.19929	0.237147
$183$	−1.70360	−0.125933
$184$	0	0
$185$	20.9393	1.53949
$186$	−2.66232	−0.195211
$187$	0.503752	0.0368380
$188$	−0.520171	−0.0379374
$189$	2.87884	0.209405
$190$	20.2207	1.46697
$191$	6.39892	0.463009	0.231505	−	0.972834i	$-0.425635\pi$
$191$	6.39892	0.463009	0.231505	+	0.972834i	$0.425635\pi$
$192$	5.75127	0.415062
$193$	2.17363	0.156462	0.0782308	−	0.996935i	$-0.475073\pi$
$193$	2.17363	0.156462	0.0782308	+	0.996935i	$0.475073\pi$
$194$	19.2544	1.38238
$195$	8.34115	0.597322
$196$	2.69593	0.192566
$197$	−9.15789	−0.652473	−0.326236	−	0.945288i	$-0.605781\pi$
$197$	−9.15789	−0.652473	−0.326236	+	0.945288i	$0.605781\pi$
$198$	3.24233	0.230422
$199$	−7.01847	−0.497526	−0.248763	−	0.968564i	$-0.580024\pi$
$199$	−7.01847	−0.497526	−0.248763	+	0.968564i	$0.580024\pi$
$200$	−34.5243	−2.44124
$201$	−5.80917	−0.409748
$202$	−7.15208	−0.503218
$203$	4.92336	0.345552
$204$	0.137912	0.00965576
$205$	47.7915	3.33790
$206$	−1.24658	−0.0868535
$207$	0	0
$208$	9.49284	0.658210
$209$	3.98359	0.275551
$210$	2.61766	0.180636
$211$	−14.4490	−0.994707	−0.497354	−	0.867548i	$-0.665695\pi$
$211$	−14.4490	−0.994707	−0.497354	+	0.867548i	$0.665695\pi$
$212$	−1.27190	−0.0873547
$213$	6.33540	0.434095
$214$	7.51954	0.514025
$215$	−28.6636	−1.95484
$216$	10.9766	0.746861
$217$	2.61906	0.177793
$218$	19.2829	1.30600
$219$	0.849268	0.0573882
$220$	−1.71294	−0.115487
$221$	1.60842	0.108194
$222$	−4.20170	−0.282000
$223$	24.2905	1.62661	0.813305	−	0.581838i	$-0.197666\pi$
$223$	24.2905	1.62661	0.813305	+	0.581838i	$0.197666\pi$
$224$	−1.87801	−0.125480
$225$	−29.2997	−1.95331
$226$	−19.7705	−1.31512
$227$	−21.5364	−1.42942	−0.714709	−	0.699422i	$-0.753441\pi$
$227$	−21.5364	−1.42942	−0.714709	+	0.699422i	$0.753441\pi$
$228$	1.09058	0.0722257
$229$	−6.71062	−0.443450	−0.221725	−	0.975109i	$-0.571169\pi$
$229$	−6.71062	−0.443450	−0.221725	+	0.975109i	$0.571169\pi$
$230$	0	0
$231$	0.515693	0.0339301
$232$	18.7720	1.23244
$233$	−15.0861	−0.988326	−0.494163	−	0.869369i	$-0.664525\pi$
$233$	−15.0861	−0.988326	−0.494163	+	0.869369i	$0.664525\pi$
$234$	10.3524	0.676757
$235$	−4.96369	−0.323795
$236$	−3.82716	−0.249127
$237$	−10.1381	−0.658543
$238$	0.504763	0.0327189
$239$	−30.6490	−1.98252	−0.991260	−	0.131919i	$-0.957886\pi$
$239$	−30.6490	−1.98252	−0.991260	+	0.131919i	$0.957886\pi$
$240$	7.76704	0.501360
$241$	13.3710	0.861301	0.430651	−	0.902519i	$-0.358284\pi$
$241$	13.3710	0.861301	0.430651	+	0.902519i	$0.358284\pi$
$242$	1.25551	0.0807075
$243$	14.3216	0.918729
$244$	1.11704	0.0715109
$245$	25.7257	1.64355
$246$	−9.58989	−0.611429
$247$	12.7191	0.809300
$248$	9.98606	0.634115
$249$	1.88830	0.119666
$250$	−32.2103	−2.03716
$251$	−25.4838	−1.60852	−0.804262	−	0.594276i	$-0.797439\pi$
$251$	−25.4838	−1.60852	−0.804262	+	0.594276i	$0.797439\pi$
$252$	−0.873227	−0.0550081
$253$	0	0
$254$	11.3858	0.714408
$255$	1.31601	0.0824118
$256$	−9.67988	−0.604992
$257$	−14.1016	−0.879634	−0.439817	−	0.898087i	$-0.644957\pi$
$257$	−14.1016	−0.879634	−0.439817	+	0.898087i	$0.644957\pi$
$258$	5.75167	0.358083
$259$	4.13343	0.256839
$260$	−5.46923	−0.339187
$261$	15.9312	0.986117
$262$	13.7153	0.847337
$263$	10.5011	0.647527	0.323764	−	0.946138i	$-0.395052\pi$
$263$	10.5011	0.647527	0.323764	+	0.946138i	$0.395052\pi$
$264$	1.96625	0.121015
$265$	−12.1370	−0.745571
$266$	3.99158	0.244739
$267$	−4.01036	−0.245430
$268$	3.80903	0.232674
$269$	20.5718	1.25429	0.627143	−	0.778904i	$-0.284224\pi$
$269$	20.5718	1.25429	0.627143	+	0.778904i	$0.284224\pi$
$270$	18.3101	1.11432
$271$	−28.7365	−1.74562	−0.872810	−	0.488060i	$-0.837705\pi$
$271$	−28.7365	−1.74562	−0.872810	+	0.488060i	$0.837705\pi$
$272$	1.49772	0.0908124
$273$	1.64655	0.0996536
$274$	−28.1573	−1.70104
$275$	−11.3456	−0.684166
$276$	0	0
$277$	−13.7543	−0.826416	−0.413208	−	0.910637i	$-0.635592\pi$
$277$	−13.7543	−0.826416	−0.413208	+	0.910637i	$0.635592\pi$
$278$	−0.954601	−0.0572532
$279$	8.47486	0.507376
$280$	−9.81854	−0.586770
$281$	−7.54904	−0.450338	−0.225169	−	0.974320i	$-0.572293\pi$
$281$	−7.54904	−0.450338	−0.225169	+	0.974320i	$0.572293\pi$
$282$	0.996019	0.0593120
$283$	27.0020	1.60510	0.802551	−	0.596584i	$-0.203476\pi$
$283$	27.0020	1.60510	0.802551	+	0.596584i	$0.203476\pi$
$284$	−4.15408	−0.246499
$285$	10.4068	0.616446
$286$	4.00871	0.237040
$287$	9.43406	0.556875
$288$	−6.07693	−0.358086
$289$	−16.7462	−0.985073
$290$	31.3137	1.83881
$291$	9.90947	0.580903
$292$	−0.556859	−0.0325877
$293$	10.4872	0.612666	0.306333	−	0.951924i	$-0.400898\pi$
$293$	10.4872	0.612666	0.306333	+	0.951924i	$0.400898\pi$
$294$	−5.16214	−0.301062
$295$	−36.5203	−2.12629
$296$	15.7601	0.916038
$297$	3.60719	0.209310
$298$	−7.02455	−0.406921
$299$	0	0
$300$	−3.10608	−0.179330
$301$	−5.65821	−0.326134
$302$	8.96129	0.515664
$303$	−3.68089	−0.211462
$304$	11.8437	0.679283
$305$	10.6592	0.610345
$306$	1.63333	0.0933714
$307$	19.2068	1.09619	0.548096	−	0.836415i	$-0.315353\pi$
$307$	19.2068	1.09619	0.548096	+	0.836415i	$0.315353\pi$
$308$	−0.338136	−0.0192671
$309$	−0.641566	−0.0364974
$310$	16.6578	0.946101
$311$	−16.6171	−0.942270	−0.471135	−	0.882061i	$-0.656155\pi$
$311$	−16.6171	−0.942270	−0.471135	+	0.882061i	$0.656155\pi$
$312$	6.27803	0.355423
$313$	−20.8071	−1.17609	−0.588044	−	0.808829i	$-0.700102\pi$
$313$	−20.8071	−1.17609	−0.588044	+	0.808829i	$0.700102\pi$
$314$	23.6631	1.33538
$315$	−8.33269	−0.469494
$316$	6.64751	0.373952
$317$	−0.842442	−0.0473163	−0.0236581	−	0.999720i	$-0.507531\pi$
$317$	−0.842442	−0.0473163	−0.0236581	+	0.999720i	$0.507531\pi$
$318$	2.43543	0.136572
$319$	6.16897	0.345396
$320$	−35.9851	−2.01163
$321$	3.87001	0.216003
$322$	0	0
$323$	2.00674	0.111658
$324$	−2.29492	−0.127496
$325$	−36.2252	−2.00941
$326$	−24.5026	−1.35707
$327$	9.92412	0.548805
$328$	35.9706	1.98614
$329$	−0.979834	−0.0540200
$330$	3.27993	0.180554
$331$	−10.2249	−0.562014	−0.281007	−	0.959706i	$-0.590668\pi$
$331$	−10.2249	−0.562014	−0.281007	+	0.959706i	$0.590668\pi$
$332$	−1.23815	−0.0679521
$333$	13.3751	0.732952
$334$	25.7761	1.41041
$335$	36.3473	1.98587
$336$	1.53322	0.0836438
$337$	−29.3644	−1.59958	−0.799791	−	0.600279i	$-0.795056\pi$
$337$	−29.3644	−1.59958	−0.799791	+	0.600279i	$0.795056\pi$
$338$	−3.52232	−0.191589
$339$	−10.1751	−0.552636
$340$	−0.862899	−0.0467973
$341$	3.28168	0.177713
$342$	12.9161	0.698424
$343$	10.6648	0.575848
$344$	−21.5739	−1.16318
$345$	0	0
$346$	5.86680	0.315401
$347$	24.9778	1.34088	0.670438	−	0.741965i	$-0.266106\pi$
$347$	24.9778	1.34088	0.670438	+	0.741965i	$0.266106\pi$
$348$	1.68887	0.0905332
$349$	−30.7570	−1.64638	−0.823191	−	0.567764i	$-0.807808\pi$
$349$	−30.7570	−1.64638	−0.823191	+	0.567764i	$0.807808\pi$
$350$	−11.3684	−0.607665
$351$	11.5173	0.614750
$352$	−2.35314	−0.125423
$353$	−18.1605	−0.966588	−0.483294	−	0.875458i	$-0.660560\pi$
$353$	−18.1605	−0.966588	−0.483294	+	0.875458i	$0.660560\pi$
$354$	7.32820	0.389490
$355$	−39.6399	−2.10387
$356$	2.62956	0.139367
$357$	0.259781	0.0137491
$358$	−5.88197	−0.310872
$359$	0.950635	0.0501726	0.0250863	−	0.999685i	$-0.492014\pi$
$359$	0.950635	0.0501726	0.0250863	+	0.999685i	$0.492014\pi$
$360$	−31.7712	−1.67449
$361$	−3.13102	−0.164790
$362$	−12.8565	−0.675720
$363$	0.646163	0.0339148
$364$	−1.07963	−0.0565879
$365$	−5.31378	−0.278136
$366$	−2.13889	−0.111801
$367$	28.6929	1.49776	0.748878	−	0.662708i	$-0.230593\pi$
$367$	28.6929	1.49776	0.748878	+	0.662708i	$0.230593\pi$
$368$	0	0
$369$	30.5271	1.58918
$370$	26.2896	1.36673
$371$	−2.39585	−0.124387
$372$	0.898424	0.0465811
$373$	−8.58485	−0.444507	−0.222253	−	0.974989i	$-0.571341\pi$
$373$	−8.58485	−0.444507	−0.222253	+	0.974989i	$0.571341\pi$
$374$	0.632468	0.0327041
$375$	−16.5774	−0.856052
$376$	−3.73595	−0.192667
$377$	19.6968	1.01444
$378$	3.61442	0.185906
$379$	−10.0573	−0.516610	−0.258305	−	0.966063i	$-0.583164\pi$
$379$	−10.0573	−0.516610	−0.258305	+	0.966063i	$0.583164\pi$
$380$	−6.82366	−0.350047
$381$	5.85981	0.300207
$382$	8.03393	0.411052
$383$	19.3152	0.986963	0.493481	−	0.869756i	$-0.335724\pi$
$383$	19.3152	0.986963	0.493481	+	0.869756i	$0.335724\pi$
$384$	4.17977	0.213298
$385$	−3.22663	−0.164444
$386$	2.72903	0.138904
$387$	−18.3091	−0.930702
$388$	−6.49757	−0.329864
$389$	−15.0719	−0.764178	−0.382089	−	0.924126i	$-0.624795\pi$
$389$	−15.0719	−0.764178	−0.382089	+	0.924126i	$0.624795\pi$
$390$	10.4724	0.530292
$391$	0	0
$392$	19.3626	0.977959
$393$	7.05874	0.356066
$394$	−11.4979	−0.579254
$395$	63.4332	3.19167
$396$	−1.09415	−0.0549833
$397$	12.9854	0.651720	0.325860	−	0.945418i	$-0.394346\pi$
$397$	12.9854	0.651720	0.325860	+	0.945418i	$0.394346\pi$
$398$	−8.81179	−0.441695
$399$	2.05431	0.102844
$400$	−33.7319	−1.68659
$401$	12.3840	0.618429	0.309214	−	0.950992i	$-0.399934\pi$
$401$	12.3840	0.618429	0.309214	+	0.950992i	$0.399934\pi$
$402$	−7.29350	−0.363767
$403$	10.4780	0.521948
$404$	2.41353	0.120078
$405$	−21.8991	−1.08818
$406$	6.18134	0.306775
$407$	5.17919	0.256723
$408$	0.990505	0.0490373
$409$	−0.984934	−0.0487019	−0.0243509	−	0.999703i	$-0.507752\pi$
$409$	−0.984934	−0.0487019	−0.0243509	+	0.999703i	$0.507752\pi$
$410$	60.0029	2.96333
$411$	−14.4914	−0.714809
$412$	0.420670	0.0207249
$413$	−7.20912	−0.354738
$414$	0	0
$415$	−11.8149	−0.579970
$416$	−7.51332	−0.368371
$417$	−0.491295	−0.0240588
$418$	5.00145	0.244629
$419$	12.0822	0.590255	0.295127	−	0.955458i	$-0.404638\pi$
$419$	12.0822	0.590255	0.295127	+	0.955458i	$0.404638\pi$
$420$	−0.883352	−0.0431032
$421$	37.5161	1.82842	0.914210	−	0.405240i	$-0.132812\pi$
$421$	37.5161	1.82842	0.914210	+	0.405240i	$0.132812\pi$
$422$	−18.1409	−0.883083
$423$	−3.17059	−0.154159
$424$	−9.13501	−0.443635
$425$	−5.71537	−0.277236
$426$	7.95419	0.385382
$427$	2.10413	0.101826
$428$	−2.53754	−0.122657
$429$	2.06312	0.0996086
$430$	−35.9876	−1.73547
$431$	8.43869	0.406478	0.203239	−	0.979129i	$-0.434853\pi$
$431$	8.43869	0.406478	0.203239	+	0.979129i	$0.434853\pi$
$432$	10.7246	0.515988
$433$	−8.74254	−0.420140	−0.210070	−	0.977686i	$-0.567369\pi$
$433$	−8.74254	−0.420140	−0.210070	+	0.977686i	$0.567369\pi$
$434$	3.28826	0.157842
$435$	16.1159	0.772700
$436$	−6.50718	−0.311637
$437$	0	0
$438$	1.06627	0.0509483
$439$	2.75687	0.131578	0.0657891	−	0.997834i	$-0.479044\pi$
$439$	2.75687	0.131578	0.0657891	+	0.997834i	$0.479044\pi$
$440$	−12.3026	−0.586505
$441$	16.4324	0.782497
$442$	2.01940	0.0960529
$443$	0.793474	0.0376991	0.0188496	−	0.999822i	$-0.494000\pi$
$443$	0.793474	0.0376991	0.0188496	+	0.999822i	$0.494000\pi$
$444$	1.41790	0.0672907
$445$	25.0924	1.18949
$446$	30.4970	1.44408
$447$	−3.61526	−0.170996
$448$	−7.10347	−0.335607
$449$	−38.9043	−1.83601	−0.918003	−	0.396574i	$-0.870199\pi$
$449$	−38.9043	−1.83601	−0.918003	+	0.396574i	$0.870199\pi$
$450$	−36.7862	−1.73412
$451$	11.8209	0.556624
$452$	6.67175	0.313813
$453$	4.61202	0.216692
$454$	−27.0392	−1.26901
$455$	−10.3023	−0.482977
$456$	7.83275	0.366802
$457$	−4.02954	−0.188494	−0.0942470	−	0.995549i	$-0.530044\pi$
$457$	−4.02954	−0.188494	−0.0942470	+	0.995549i	$0.530044\pi$
$458$	−8.42528	−0.393688
$459$	1.81713	0.0848163
$460$	0	0
$461$	−8.05034	−0.374942	−0.187471	−	0.982270i	$-0.560029\pi$
$461$	−8.05034	−0.374942	−0.187471	+	0.982270i	$0.560029\pi$
$462$	0.647459	0.0301225
$463$	−3.83757	−0.178347	−0.0891735	−	0.996016i	$-0.528423\pi$
$463$	−3.83757	−0.178347	−0.0891735	+	0.996016i	$0.528423\pi$
$464$	18.3411	0.851464
$465$	8.57312	0.397569
$466$	−18.9409	−0.877418
$467$	−32.1096	−1.48585	−0.742927	−	0.669372i	$-0.766563\pi$
$467$	−32.1096	−1.48585	−0.742927	+	0.669372i	$0.766563\pi$
$468$	−3.49351	−0.161487
$469$	7.17498	0.331310
$470$	−6.23198	−0.287460
$471$	12.1784	0.561153
$472$	−27.4873	−1.26520
$473$	−7.08974	−0.325987
$474$	−12.7286	−0.584643
$475$	−45.1962	−2.07375
$476$	−0.170337	−0.00780737
$477$	−7.75260	−0.354967
$478$	−38.4803	−1.76005
$479$	41.4512	1.89395	0.946976	−	0.321305i	$-0.104121\pi$
$479$	41.4512	1.89395	0.946976	+	0.321305i	$0.104121\pi$
$480$	−6.14739	−0.280589
$481$	16.5366	0.754002
$482$	16.7875	0.764648
$483$	0	0
$484$	−0.423685	−0.0192584
$485$	−62.0024	−2.81539
$486$	17.9809	0.815631
$487$	21.7836	0.987109	0.493554	−	0.869715i	$-0.335697\pi$
$487$	21.7836	0.987109	0.493554	+	0.869715i	$0.335697\pi$
$488$	8.02273	0.363172
$489$	−12.6105	−0.570267
$490$	32.2989	1.45912
$491$	16.5105	0.745110	0.372555	−	0.928010i	$-0.378482\pi$
$491$	16.5105	0.745110	0.372555	+	0.928010i	$0.378482\pi$
$492$	3.23619	0.145899
$493$	3.10763	0.139961
$494$	15.9691	0.718482
$495$	−10.4409	−0.469282
$496$	9.75684	0.438095
$497$	−7.82494	−0.350996
$498$	2.37079	0.106238
$499$	−5.88608	−0.263497	−0.131748	−	0.991283i	$-0.542059\pi$
$499$	−5.88608	−0.263497	−0.131748	+	0.991283i	$0.542059\pi$
$500$	10.8697	0.486106
$501$	13.2659	0.592678
$502$	−31.9953	−1.42802
$503$	−25.4624	−1.13531	−0.567656	−	0.823266i	$-0.692150\pi$
$503$	−25.4624	−1.13531	−0.567656	+	0.823266i	$0.692150\pi$
$504$	−6.27166	−0.279362
$505$	23.0309	1.02486
$506$	0	0
$507$	−1.81280	−0.0805093
$508$	−3.84224	−0.170472
$509$	−37.9786	−1.68337	−0.841687	−	0.539966i	$-0.818437\pi$
$509$	−37.9786	−1.68337	−0.841687	+	0.539966i	$0.818437\pi$
$510$	1.65227	0.0731638
$511$	−1.04894	−0.0464025
$512$	−25.0904	−1.10885
$513$	14.3696	0.634431
$514$	−17.7048	−0.780924
$515$	4.01421	0.176887
$516$	−1.94095	−0.0854457
$517$	−1.22773	−0.0539956
$518$	5.18958	0.228017
$519$	3.01941	0.132537
$520$	−39.2809	−1.72258
$521$	−30.5870	−1.34004	−0.670020	−	0.742343i	$-0.733714\pi$
$521$	−30.5870	−1.34004	−0.670020	+	0.742343i	$0.733714\pi$
$522$	20.0018	0.875457
$523$	2.66147	0.116378	0.0581890	−	0.998306i	$-0.481467\pi$
$523$	2.66147	0.116378	0.0581890	+	0.998306i	$0.481467\pi$
$524$	−4.62837	−0.202191
$525$	−5.85084	−0.255352
$526$	13.1843	0.574863
$527$	1.65315	0.0720125
$528$	1.92112	0.0836061
$529$	0	0
$530$	−15.2382	−0.661905
$531$	−23.3276	−1.01233
$532$	−1.34699	−0.0583996
$533$	37.7427	1.63482
$534$	−5.03506	−0.217888
$535$	−24.2142	−1.04687
$536$	27.3571	1.18165
$537$	−3.02721	−0.130634
$538$	25.8282	1.11353
$539$	6.36306	0.274076
$540$	−6.17891	−0.265898
$541$	41.1086	1.76740	0.883698	−	0.468058i	$-0.155046\pi$
$541$	41.1086	1.76740	0.883698	+	0.468058i	$0.155046\pi$
$542$	−36.0791	−1.54973
$543$	−6.61670	−0.283950
$544$	−1.18540	−0.0508236
$545$	−62.0941	−2.65982
$546$	2.06726	0.0884707
$547$	−7.10820	−0.303925	−0.151962	−	0.988386i	$-0.548559\pi$
$547$	−7.10820	−0.303925	−0.151962	+	0.988386i	$0.548559\pi$
$548$	9.50192	0.405902
$549$	6.80864	0.290586
$550$	−14.2446	−0.607390
$551$	24.5746	1.04691
$552$	0	0
$553$	12.5217	0.532479
$554$	−17.2687	−0.733678
$555$	13.5302	0.574325
$556$	0.322139	0.0136617
$557$	17.5181	0.742265	0.371133	−	0.928580i	$-0.378970\pi$
$557$	17.5181	0.742265	0.371133	+	0.928580i	$0.378970\pi$
$558$	10.6403	0.450440
$559$	−22.6367	−0.957432
$560$	−9.59317	−0.405385
$561$	0.325506	0.0137429
$562$	−9.47793	−0.399802
$563$	−32.5836	−1.37324	−0.686618	−	0.727019i	$-0.740905\pi$
$563$	−32.5836	−1.37324	−0.686618	+	0.727019i	$0.740905\pi$
$564$	−0.336115	−0.0141530
$565$	63.6645	2.67839
$566$	33.9014	1.42498
$567$	−4.32289	−0.181544
$568$	−29.8353	−1.25186
$569$	−42.5643	−1.78439	−0.892194	−	0.451653i	$-0.850835\pi$
$569$	−42.5643	−1.78439	−0.892194	+	0.451653i	$0.850835\pi$
$570$	13.0659	0.547270
$571$	3.70786	0.155169	0.0775845	−	0.996986i	$-0.475279\pi$
$571$	3.70786	0.155169	0.0775845	+	0.996986i	$0.475279\pi$
$572$	−1.35278	−0.0565624
$573$	4.13474	0.172731
$574$	11.8446	0.494384
$575$	0	0
$576$	−22.9857	−0.957737
$577$	−6.75679	−0.281289	−0.140644	−	0.990060i	$-0.544917\pi$
$577$	−6.75679	−0.281289	−0.140644	+	0.990060i	$0.544917\pi$
$578$	−21.0251	−0.874530
$579$	1.40452	0.0583700
$580$	−10.5671	−0.438775
$581$	−2.33227	−0.0967587
$582$	12.4415	0.515716
$583$	−3.00201	−0.124330
$584$	−3.99945	−0.165498
$585$	−33.3365	−1.37829
$586$	13.1668	0.543915
$587$	3.71910	0.153504	0.0767519	−	0.997050i	$-0.475545\pi$
$587$	3.71910	0.153504	0.0767519	+	0.997050i	$0.475545\pi$
$588$	1.74201	0.0718393
$589$	13.0729	0.538658
$590$	−45.8517	−1.88769
$591$	−5.91749	−0.243413
$592$	15.3984	0.632869
$593$	22.6333	0.929439	0.464719	−	0.885458i	$-0.346155\pi$
$593$	22.6333	0.929439	0.464719	+	0.885458i	$0.346155\pi$
$594$	4.52888	0.185822
$595$	−1.62542	−0.0666358
$596$	2.37050	0.0970994
$597$	−4.53508	−0.185608
$598$	0	0
$599$	−30.4468	−1.24402	−0.622010	−	0.783009i	$-0.713684\pi$
$599$	−30.4468	−1.24402	−0.622010	+	0.783009i	$0.713684\pi$
$600$	−22.3084	−0.910735
$601$	11.3551	0.463186	0.231593	−	0.972813i	$-0.425606\pi$
$601$	11.3551	0.463186	0.231593	+	0.972813i	$0.425606\pi$
$602$	−7.10396	−0.289536
$603$	23.2171	0.945474
$604$	−3.02407	−0.123048
$605$	−4.04297	−0.164370
$606$	−4.62141	−0.187732
$607$	9.14323	0.371112	0.185556	−	0.982634i	$-0.440591\pi$
$607$	9.14323	0.371112	0.185556	+	0.982634i	$0.440591\pi$
$608$	−9.37396	−0.380164
$609$	3.18129	0.128912
$610$	13.3828	0.541853
$611$	−3.92001	−0.158587
$612$	−0.551182	−0.0222802
$613$	3.40904	0.137690	0.0688449	−	0.997627i	$-0.478069\pi$
$613$	3.40904	0.137690	0.0688449	+	0.997627i	$0.478069\pi$
$614$	24.1145	0.973180
$615$	30.8811	1.24525
$616$	−2.42855	−0.0978489
$617$	−1.68640	−0.0678919	−0.0339460	−	0.999424i	$-0.510807\pi$
$617$	−1.68640	−0.0678919	−0.0339460	+	0.999424i	$0.510807\pi$
$618$	−0.805495	−0.0324018
$619$	7.71276	0.310002	0.155001	−	0.987914i	$-0.450462\pi$
$619$	7.71276	0.310002	0.155001	+	0.987914i	$0.450462\pi$
$620$	−5.62134	−0.225758
$621$	0	0
$622$	−20.8630	−0.836530
$623$	4.95324	0.198448
$624$	6.13392	0.245553
$625$	46.9947	1.87979
$626$	−26.1237	−1.04411
$627$	2.57405	0.102798
$628$	−7.98532	−0.318649
$629$	2.60903	0.104029
$630$	−10.4618	−0.416808
$631$	39.9860	1.59182	0.795908	−	0.605417i	$-0.206994\pi$
$631$	39.9860	1.59182	0.795908	+	0.605417i	$0.206994\pi$
$632$	47.7435	1.89913
$633$	−9.33638	−0.371088
$634$	−1.05770	−0.0420065
$635$	−36.6642	−1.45497
$636$	−0.821857	−0.0325888
$637$	20.3165	0.804970
$638$	7.74523	0.306637
$639$	−25.3202	−1.00165
$640$	−26.1524	−1.03376
$641$	8.13445	0.321291	0.160646	−	0.987012i	$-0.448642\pi$
$641$	8.13445	0.321291	0.160646	+	0.987012i	$0.448642\pi$
$642$	4.85885	0.191764
$643$	29.6220	1.16818	0.584088	−	0.811690i	$-0.301452\pi$
$643$	29.6220	1.16818	0.584088	+	0.811690i	$0.301452\pi$
$644$	0	0
$645$	−18.5214	−0.729278
$646$	2.51949	0.0991281
$647$	18.3325	0.720727	0.360363	−	0.932812i	$-0.382653\pi$
$647$	18.3325	0.720727	0.360363	+	0.932812i	$0.382653\pi$
$648$	−16.4825	−0.647494
$649$	−9.03304	−0.354578
$650$	−45.4813	−1.78392
$651$	1.69234	0.0663280
$652$	8.26863	0.323824
$653$	−4.41518	−0.172779	−0.0863896	−	0.996261i	$-0.527533\pi$
$653$	−4.41518	−0.172779	−0.0863896	+	0.996261i	$0.527533\pi$
$654$	12.4599	0.487220
$655$	−44.1657	−1.72570
$656$	35.1449	1.37218
$657$	−3.39421	−0.132421
$658$	−1.23020	−0.0479580
$659$	10.5431	0.410703	0.205351	−	0.978688i	$-0.434166\pi$
$659$	10.5431	0.410703	0.205351	+	0.978688i	$0.434166\pi$
$660$	−1.10684	−0.0430837
$661$	10.2501	0.398681	0.199341	−	0.979930i	$-0.436120\pi$
$661$	10.2501	0.398681	0.199341	+	0.979930i	$0.436120\pi$
$662$	−12.8376	−0.498946
$663$	1.03930	0.0403632
$664$	−8.89256	−0.345098
$665$	−12.8536	−0.498440
$666$	16.7927	0.650702
$667$	0	0
$668$	−8.69838	−0.336550
$669$	15.6956	0.606827
$670$	45.6346	1.76302
$671$	2.63648	0.101780
$672$	−1.21350	−0.0468117
$673$	29.0456	1.11962	0.559812	−	0.828620i	$-0.310873\pi$
$673$	29.0456	1.11962	0.559812	+	0.828620i	$0.310873\pi$
$674$	−36.8674	−1.42008
$675$	−40.9257	−1.57523
$676$	1.18864	0.0457169
$677$	−21.8323	−0.839084	−0.419542	−	0.907736i	$-0.637809\pi$
$677$	−21.8323	−0.839084	−0.419542	+	0.907736i	$0.637809\pi$
$678$	−12.7750	−0.490621
$679$	−12.2393	−0.469702
$680$	−6.19748	−0.237663
$681$	−13.9160	−0.533262
$682$	4.12020	0.157771
$683$	48.4518	1.85396	0.926979	−	0.375114i	$-0.122396\pi$
$683$	48.4518	1.85396	0.926979	+	0.375114i	$0.122396\pi$
$684$	−4.35866	−0.166658
$685$	90.6712	3.46437
$686$	13.3899	0.511227
$687$	−4.33616	−0.165435
$688$	−21.0787	−0.803617
$689$	−9.58506	−0.365162
$690$	0	0
$691$	23.0694	0.877601	0.438800	−	0.898585i	$-0.355404\pi$
$691$	23.0694	0.877601	0.438800	+	0.898585i	$0.355404\pi$
$692$	−1.97980	−0.0752609
$693$	−2.06103	−0.0782921
$694$	31.3599	1.19041
$695$	3.07398	0.116603
$696$	12.1298	0.459778
$697$	5.95480	0.225554
$698$	−38.6158	−1.46163
$699$	−9.74811	−0.368707
$700$	3.83636	0.145001
$701$	−35.6219	−1.34542	−0.672711	−	0.739905i	$-0.734870\pi$
$701$	−35.6219	−1.34542	−0.672711	+	0.739905i	$0.734870\pi$
$702$	14.4602	0.545764
$703$	20.6318	0.778142
$704$	−8.90065	−0.335456
$705$	−3.20735	−0.120796
$706$	−22.8008	−0.858120
$707$	4.54631	0.170982
$708$	−2.47297	−0.0929398
$709$	−21.1768	−0.795312	−0.397656	−	0.917534i	$-0.630176\pi$
$709$	−21.1768	−0.795312	−0.397656	+	0.917534i	$0.630176\pi$
$710$	−49.7685	−1.86778
$711$	40.5184	1.51956
$712$	18.8859	0.707781
$713$	0	0
$714$	0.326159	0.0122062
$715$	−12.9087	−0.482759
$716$	1.98492	0.0741801
$717$	−19.8043	−0.739604
$718$	1.19354	0.0445424
$719$	−47.0596	−1.75503	−0.877513	−	0.479553i	$-0.840799\pi$
$719$	−47.0596	−1.75503	−0.877513	+	0.479553i	$0.840799\pi$
$720$	−31.0420	−1.15687
$721$	0.792406	0.0295108
$722$	−3.93104	−0.146298
$723$	8.63984	0.321319
$724$	4.33853	0.161240
$725$	−69.9907	−2.59939
$726$	0.811267	0.0301089
$727$	34.5022	1.27961	0.639807	−	0.768535i	$-0.279014\pi$
$727$	34.5022	1.27961	0.639807	+	0.768535i	$0.279014\pi$
$728$	−7.75407	−0.287385
$729$	−6.99570	−0.259100
$730$	−6.67152	−0.246924
$731$	−3.57147	−0.132096
$732$	0.721787	0.0266780
$733$	19.9498	0.736863	0.368431	−	0.929655i	$-0.379895\pi$
$733$	19.9498	0.736863	0.368431	+	0.929655i	$0.379895\pi$
$734$	36.0243	1.32968
$735$	16.6230	0.613148
$736$	0	0
$737$	8.99026	0.331160
$738$	38.3272	1.41084
$739$	9.42242	0.346609	0.173305	−	0.984868i	$-0.444555\pi$
$739$	9.42242	0.346609	0.173305	+	0.984868i	$0.444555\pi$
$740$	−8.87166	−0.326129
$741$	8.21864	0.301919
$742$	−3.00803	−0.110428
$743$	−7.25579	−0.266189	−0.133095	−	0.991103i	$-0.542491\pi$
$743$	−7.25579	−0.266189	−0.133095	+	0.991103i	$0.542491\pi$
$744$	6.45262	0.236565
$745$	22.6203	0.828742
$746$	−10.7784	−0.394625
$747$	−7.54684	−0.276124
$748$	−0.213432	−0.00780385
$749$	−4.77990	−0.174654
$750$	−20.8131	−0.759988
$751$	18.9612	0.691904	0.345952	−	0.938252i	$-0.387556\pi$
$751$	18.9612	0.691904	0.345952	+	0.938252i	$0.387556\pi$
$752$	−3.65020	−0.133109
$753$	−16.4667	−0.600079
$754$	24.7296	0.900600
$755$	−28.8569	−1.05021
$756$	−1.21972	−0.0443608
$757$	8.51568	0.309508	0.154754	−	0.987953i	$-0.450542\pi$
$757$	8.51568	0.309508	0.154754	+	0.987953i	$0.450542\pi$
$758$	−12.6271	−0.458637
$759$	0	0
$760$	−49.0086	−1.77773
$761$	−3.63058	−0.131609	−0.0658043	−	0.997833i	$-0.520961\pi$
$761$	−3.63058	−0.131609	−0.0658043	+	0.997833i	$0.520961\pi$
$762$	7.35707	0.266519
$763$	−12.2574	−0.443748
$764$	−2.71112	−0.0980850
$765$	−5.25961	−0.190161
$766$	24.2506	0.876208
$767$	−28.8414	−1.04140
$768$	−6.25478	−0.225700
$769$	11.1413	0.401764	0.200882	−	0.979615i	$-0.435619\pi$
$769$	11.1413	0.401764	0.200882	+	0.979615i	$0.435619\pi$
$770$	−4.05108	−0.145991
$771$	−9.11194	−0.328158
$772$	−0.920935	−0.0331452
$773$	−40.1436	−1.44387	−0.721933	−	0.691963i	$-0.756746\pi$
$773$	−40.1436	−1.44387	−0.721933	+	0.691963i	$0.756746\pi$
$774$	−22.9873	−0.826261
$775$	−37.2327	−1.33744
$776$	−46.6666	−1.67523
$777$	2.67087	0.0958169
$778$	−18.9230	−0.678424
$779$	47.0895	1.68716
$780$	−3.53402	−0.126538
$781$	−9.80465	−0.350838
$782$	0	0
$783$	22.2526	0.795244
$784$	18.9182	0.675649
$785$	−76.1991	−2.71966
$786$	8.86235	0.316109
$787$	32.1916	1.14751	0.573754	−	0.819028i	$-0.305487\pi$
$787$	32.1916	1.14751	0.573754	+	0.819028i	$0.305487\pi$
$788$	3.88006	0.138221
$789$	6.78544	0.241568
$790$	79.6413	2.83351
$791$	12.5674	0.446846
$792$	−7.85839	−0.279236
$793$	8.41798	0.298931
$794$	16.3034	0.578585
$795$	−7.84249	−0.278145
$796$	2.97362	0.105397
$797$	10.4731	0.370977	0.185489	−	0.982646i	$-0.440613\pi$
$797$	10.4731	0.370977	0.185489	+	0.982646i	$0.440613\pi$
$798$	2.57921	0.0913031
$799$	−0.618473	−0.0218800
$800$	26.6978	0.943911
$801$	16.0279	0.566318
$802$	15.5483	0.549030
$803$	−1.31433	−0.0463815
$804$	2.46126	0.0868018
$805$	0	0
$806$	13.1553	0.463376
$807$	13.2928	0.467927
$808$	17.3344	0.609821
$809$	−2.51048	−0.0882637	−0.0441318	−	0.999026i	$-0.514052\pi$
$809$	−2.51048	−0.0882637	−0.0441318	+	0.999026i	$0.514052\pi$
$810$	−27.4946	−0.966063
$811$	−28.1415	−0.988183	−0.494091	−	0.869410i	$-0.664499\pi$
$811$	−28.1415	−0.988183	−0.494091	+	0.869410i	$0.664499\pi$
$812$	−2.08595	−0.0732025
$813$	−18.5685	−0.651225
$814$	6.50255	0.227914
$815$	78.9026	2.76384
$816$	0.967769	0.0338787
$817$	−28.2426	−0.988084
$818$	−1.23660	−0.0432367
$819$	−6.58064	−0.229946
$820$	−20.2485	−0.707109
$821$	9.55356	0.333421	0.166711	−	0.986006i	$-0.446685\pi$
$821$	9.55356	0.333421	0.166711	+	0.986006i	$0.446685\pi$
$822$	−18.1942	−0.634595
$823$	−38.7711	−1.35147	−0.675737	−	0.737143i	$-0.736174\pi$
$823$	−38.7711	−1.35147	−0.675737	+	0.737143i	$0.736174\pi$
$824$	3.02132	0.105253
$825$	−7.33111	−0.255237
$826$	−9.05116	−0.314930
$827$	−28.9099	−1.00530	−0.502648	−	0.864491i	$-0.667641\pi$
$827$	−28.9099	−1.00530	−0.502648	+	0.864491i	$0.667641\pi$
$828$	0	0
$829$	−13.0709	−0.453972	−0.226986	−	0.973898i	$-0.572887\pi$
$829$	−13.0709	−0.453972	−0.226986	+	0.973898i	$0.572887\pi$
$830$	−14.8338	−0.514887
$831$	−8.88752	−0.308305
$832$	−28.4187	−0.985243
$833$	3.20541	0.111061
$834$	−0.616828	−0.0213590
$835$	−83.0034	−2.87245
$836$	−1.68779	−0.0583733
$837$	11.8376	0.409169
$838$	15.1694	0.524018
$839$	9.03560	0.311944	0.155972	−	0.987762i	$-0.450149\pi$
$839$	9.03560	0.311944	0.155972	+	0.987762i	$0.450149\pi$
$840$	−6.34438	−0.218902
$841$	9.05619	0.312282
$842$	47.1019	1.62324
$843$	−4.87791	−0.168004
$844$	6.12180	0.210721
$845$	11.3425	0.390193
$846$	−3.98072	−0.136860
$847$	−0.798084	−0.0274225
$848$	−8.92533	−0.306497
$849$	17.4477	0.598803
$850$	−7.17573	−0.246126
$851$	0	0
$852$	−2.68421	−0.0919596
$853$	−13.4429	−0.460275	−0.230137	−	0.973158i	$-0.573918\pi$
$853$	−13.4429	−0.460275	−0.230137	+	0.973158i	$0.573918\pi$
$854$	2.64177	0.0903995
$855$	−41.5921	−1.42242
$856$	−18.2250	−0.622918
$857$	40.8692	1.39607	0.698033	−	0.716065i	$-0.254059\pi$
$857$	40.8692	1.39607	0.698033	+	0.716065i	$0.254059\pi$
$858$	2.59028	0.0884308
$859$	33.6168	1.14699	0.573495	−	0.819209i	$-0.305587\pi$
$859$	33.6168	1.14699	0.573495	+	0.819209i	$0.305587\pi$
$860$	12.1443	0.414118
$861$	6.09594	0.207749
$862$	10.5949	0.360864
$863$	6.28825	0.214055	0.107027	−	0.994256i	$-0.465867\pi$
$863$	6.28825	0.214055	0.107027	+	0.994256i	$0.465867\pi$
$864$	−8.48823	−0.288775
$865$	−18.8921	−0.642351
$866$	−10.9764	−0.372993
$867$	−10.8208	−0.367494
$868$	−1.10965	−0.0376641
$869$	15.6898	0.532239
$870$	20.2338	0.685989
$871$	28.7049	0.972627
$872$	−46.7356	−1.58267
$873$	−39.6045	−1.34041
$874$	0	0
$875$	20.4749	0.692179
$876$	−0.359822	−0.0121573
$877$	−46.4269	−1.56773	−0.783863	−	0.620934i	$-0.786754\pi$
$877$	−46.4269	−1.56773	−0.783863	+	0.620934i	$0.786754\pi$
$878$	3.46129	0.116813
$879$	6.77642	0.228563
$880$	−12.0202	−0.405202
$881$	6.31123	0.212631	0.106315	−	0.994332i	$-0.466095\pi$
$881$	6.31123	0.212631	0.106315	+	0.994332i	$0.466095\pi$
$882$	20.6312	0.694687
$883$	33.7642	1.13625	0.568127	−	0.822941i	$-0.307668\pi$
$883$	33.7642	1.13625	0.568127	+	0.822941i	$0.307668\pi$
$884$	−0.681464	−0.0229201
$885$	−23.5981	−0.793240
$886$	0.996218	0.0334686
$887$	14.5976	0.490139	0.245069	−	0.969506i	$-0.421189\pi$
$887$	14.5976	0.490139	0.245069	+	0.969506i	$0.421189\pi$
$888$	10.1836	0.341739
$889$	−7.23753	−0.242739
$890$	31.5038	1.05601
$891$	−5.41659	−0.181463
$892$	−10.2915	−0.344585
$893$	−4.89078	−0.163664
$894$	−4.53901	−0.151807
$895$	18.9409	0.633126
$896$	−5.16249	−0.172467
$897$	0	0
$898$	−48.8448	−1.62997
$899$	20.2446	0.675195
$900$	12.4138	0.413795
$901$	−1.51227	−0.0503809
$902$	14.8413	0.494161
$903$	−3.65613	−0.121668
$904$	47.9176	1.59371
$905$	41.4000	1.37618
$906$	5.79046	0.192375
$907$	48.0826	1.59656	0.798278	−	0.602290i	$-0.205745\pi$
$907$	48.0826	1.59656	0.798278	+	0.602290i	$0.205745\pi$
$908$	9.12462	0.302811
$909$	14.7111	0.487938
$910$	−12.9346	−0.428779
$911$	28.6152	0.948065	0.474033	−	0.880507i	$-0.342798\pi$
$911$	28.6152	0.948065	0.474033	+	0.880507i	$0.342798\pi$
$912$	7.65296	0.253415
$913$	−2.92233	−0.0967150
$914$	−5.05915	−0.167342
$915$	6.88759	0.227697
$916$	2.84319	0.0939416
$917$	−8.71834	−0.287905
$918$	2.28143	0.0752984
$919$	−8.89355	−0.293371	−0.146686	−	0.989183i	$-0.546861\pi$
$919$	−8.89355	−0.293371	−0.146686	+	0.989183i	$0.546861\pi$
$920$	0	0
$921$	12.4108	0.408948
$922$	−10.1073	−0.332866
$923$	−31.3051	−1.03042
$924$	−0.218491	−0.00718782
$925$	−58.7610	−1.93205
$926$	−4.81812	−0.158333
$927$	2.56410	0.0842161
$928$	−14.5165	−0.476526
$929$	−18.1893	−0.596771	−0.298385	−	0.954445i	$-0.596448\pi$
$929$	−18.1893	−0.596771	−0.298385	+	0.954445i	$0.596448\pi$
$930$	10.7637	0.352955
$931$	25.3478	0.830741
$932$	6.39176	0.209369
$933$	−10.7374	−0.351525
$934$	−40.3140	−1.31912
$935$	−2.03665	−0.0666057
$936$	−25.0909	−0.820123
$937$	−33.3478	−1.08943	−0.544713	−	0.838623i	$-0.683361\pi$
$937$	−33.3478	−1.08943	−0.544713	+	0.838623i	$0.683361\pi$
$938$	9.00829	0.294131
$939$	−13.4448	−0.438755
$940$	2.10304	0.0685935
$941$	−29.2596	−0.953836	−0.476918	−	0.878948i	$-0.658246\pi$
$941$	−29.2596	−0.953836	−0.476918	+	0.878948i	$0.658246\pi$
$942$	15.2902	0.498182
$943$	0	0
$944$	−26.8563	−0.874099
$945$	−11.6391	−0.378619
$946$	−8.90127	−0.289405
$947$	34.5660	1.12324	0.561621	−	0.827394i	$-0.310178\pi$
$947$	34.5660	1.12324	0.561621	+	0.827394i	$0.310178\pi$
$948$	4.29537	0.139507
$949$	−4.19649	−0.136224
$950$	−56.7445	−1.84103
$951$	−0.544355	−0.0176519
$952$	−1.22339	−0.0396502
$953$	−28.4736	−0.922350	−0.461175	−	0.887309i	$-0.652572\pi$
$953$	−28.4736	−0.922350	−0.461175	+	0.887309i	$0.652572\pi$
$954$	−9.73350	−0.315134
$955$	−25.8706	−0.837154
$956$	12.9855	0.419982
$957$	3.98616	0.128854
$958$	52.0425	1.68142
$959$	17.8985	0.577974
$960$	−23.2522	−0.750462
$961$	−20.2306	−0.652599
$962$	20.7619	0.669390
$963$	−15.4670	−0.498417
$964$	−5.66508	−0.182460
$965$	−8.78794	−0.282894
$966$	0	0
$967$	−10.9313	−0.351526	−0.175763	−	0.984433i	$-0.556239\pi$
$967$	−10.9313	−0.351526	−0.175763	+	0.984433i	$0.556239\pi$
$968$	−3.04297	−0.0978048
$969$	1.29668	0.0416554
$970$	−77.8449	−2.49945
$971$	7.59300	0.243671	0.121835	−	0.992550i	$-0.461122\pi$
$971$	7.59300	0.243671	0.121835	+	0.992550i	$0.461122\pi$
$972$	−6.06782	−0.194626
$973$	0.606805	0.0194533
$974$	27.3496	0.876338
$975$	−23.4074	−0.749637
$976$	7.83858	0.250907
$977$	−23.0302	−0.736802	−0.368401	−	0.929667i	$-0.620095\pi$
$977$	−23.0302	−0.736802	−0.368401	+	0.929667i	$0.620095\pi$
$978$	−15.8327	−0.506273
$979$	6.20642	0.198358
$980$	−10.8996	−0.348174
$981$	−39.6630	−1.26634
$982$	20.7292	0.661496
$983$	−21.6864	−0.691688	−0.345844	−	0.938292i	$-0.612407\pi$
$983$	−21.6864	−0.691688	−0.345844	+	0.938292i	$0.612407\pi$
$984$	23.2429	0.740956
$985$	37.0251	1.17972
$986$	3.90168	0.124255
$987$	−0.633133	−0.0201528
$988$	−5.38890	−0.171444
$989$	0	0
$990$	−13.1086	−0.416620
$991$	32.0034	1.01662	0.508310	−	0.861174i	$-0.330270\pi$
$991$	32.0034	1.01662	0.508310	+	0.861174i	$0.330270\pi$
$992$	−7.72227	−0.245182
$993$	−6.60698	−0.209666
$994$	−9.82432	−0.311608
$995$	28.3755	0.899563
$996$	−0.800044	−0.0253504
$997$	−44.7240	−1.41642	−0.708211	−	0.706001i	$-0.750498\pi$
$997$	−44.7240	−1.41642	−0.708211	+	0.706001i	$0.750498\pi$
$998$	−7.39005	−0.233928
$999$	18.6823	0.591082

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5819.2.a.e.1.4		6
23.22	odd	2		253.2.a.d.1.4	✓	6
69.68	even	2		2277.2.a.m.1.3		6
92.91	even	2		4048.2.a.bc.1.4		6
115.114	odd	2		6325.2.a.m.1.3		6
253.252	even	2		2783.2.a.h.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.2.a.d.1.4	✓	6	23.22	odd	2
2277.2.a.m.1.3		6	69.68	even	2
2783.2.a.h.1.3		6	253.252	even	2
4048.2.a.bc.1.4		6	92.91	even	2
5819.2.a.e.1.4		6	1.1	even	1	trivial
6325.2.a.m.1.3		6	115.114	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5819 = 11 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5819.a (trivial)

\(f(q)\)	\(=\)	\(q+1.25551 q^{2} +0.646163 q^{3} -0.423685 q^{4} -4.04297 q^{5} +0.811267 q^{6} -0.798084 q^{7} -3.04297 q^{8} -2.58247 q^{9} -5.07601 q^{10} -1.00000 q^{11} -0.273769 q^{12} -3.19289 q^{13} -1.00201 q^{14} -2.61242 q^{15} -2.97312 q^{16} -0.503752 q^{17} -3.24233 q^{18} -3.98359 q^{19} +1.71294 q^{20} -0.515693 q^{21} -1.25551 q^{22} -1.96625 q^{24} +11.3456 q^{25} -4.00871 q^{26} -3.60719 q^{27} +0.338136 q^{28} -6.16897 q^{29} -3.27993 q^{30} -3.28168 q^{31} +2.35314 q^{32} -0.646163 q^{33} -0.632468 q^{34} +3.22663 q^{35} +1.09415 q^{36} -5.17919 q^{37} -5.00145 q^{38} -2.06312 q^{39} +12.3026 q^{40} -11.8209 q^{41} -0.647459 q^{42} +7.08974 q^{43} +0.423685 q^{44} +10.4409 q^{45} +1.22773 q^{47} -1.92112 q^{48} -6.36306 q^{49} +14.2446 q^{50} -0.325506 q^{51} +1.35278 q^{52} +3.00201 q^{53} -4.52888 q^{54} +4.04297 q^{55} +2.42855 q^{56} -2.57405 q^{57} -7.74523 q^{58} +9.03304 q^{59} +1.10684 q^{60} -2.63648 q^{61} -4.12020 q^{62} +2.06103 q^{63} +8.90065 q^{64} +12.9087 q^{65} -0.811267 q^{66} -8.99026 q^{67} +0.213432 q^{68} +4.05108 q^{70} +9.80465 q^{71} +7.85839 q^{72} +1.31433 q^{73} -6.50255 q^{74} +7.33111 q^{75} +1.68779 q^{76} +0.798084 q^{77} -2.59028 q^{78} -15.6898 q^{79} +12.0202 q^{80} +5.41659 q^{81} -14.8413 q^{82} +2.92233 q^{83} +0.218491 q^{84} +2.03665 q^{85} +8.90127 q^{86} -3.98616 q^{87} +3.04297 q^{88} -6.20642 q^{89} +13.1086 q^{90} +2.54819 q^{91} -2.12050 q^{93} +1.54144 q^{94} +16.1055 q^{95} +1.52051 q^{96} +15.3359 q^{97} -7.98891 q^{98} +2.58247 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 7 q^{3} + 5 q^{4} - 3 q^{5} + 3 q^{6} + q^{7} + 3 q^{8} + 9 q^{9} + 6 q^{10} - 6 q^{11} + 11 q^{12} - 3 q^{13} + 8 q^{14} - 10 q^{15} - q^{16} - 5 q^{17} - 11 q^{18} - q^{19} + 7 q^{20}+ \cdots - 9 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 + 7 * q^3 + 5 * q^4 - 3 * q^5 + 3 * q^6 + q^7 + 3 * q^8 + 9 * q^9 + 6 * q^10 - 6 * q^11 + 11 * q^12 - 3 * q^13 + 8 * q^14 - 10 * q^15 - q^16 - 5 * q^17 - 11 * q^18 - q^19 + 7 * q^20 + 15 * q^21 - 3 * q^22 - 3 * q^24 + 3 * q^25 + 15 * q^26 + 16 * q^27 + 6 * q^29 + 25 * q^30 - 8 * q^31 - 6 * q^32 - 7 * q^33 + 6 * q^34 + 12 * q^35 - 8 * q^36 - 2 * q^37 - 9 * q^38 + q^39 + 30 * q^40 - 2 * q^41 + 31 * q^42 - 10 * q^43 - 5 * q^44 - 3 * q^45 + 14 * q^47 + 6 * q^48 - 5 * q^49 + 9 * q^50 + 24 * q^51 - 11 * q^52 + 4 * q^53 - 13 * q^54 + 3 * q^55 + 13 * q^56 + 19 * q^57 - 6 * q^58 + 39 * q^59 + 21 * q^60 + 22 * q^61 + 35 * q^63 - 33 * q^64 + 16 * q^65 - 3 * q^66 - 8 * q^67 - 17 * q^68 + 19 * q^70 + 18 * q^71 + 6 * q^72 - 9 * q^73 - 15 * q^74 + 6 * q^75 + 25 * q^76 - q^77 + 20 * q^78 + 15 * q^79 + 16 * q^80 + 18 * q^81 - 8 * q^82 - 43 * q^83 + 4 * q^84 - 21 * q^85 + 55 * q^86 - 28 * q^87 - 3 * q^88 - 17 * q^89 + 37 * q^90 + 9 * q^91 + 27 * q^93 + 63 * q^94 - 21 * q^95 + 26 * q^96 - 19 * q^97 + 34 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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