LMFDB - Embedded newform 5819.2.a.o.1.16

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 = [18,2,-2,18,8] 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:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 2 x^{17} - 25 x^{16} + 48 x^{15} + 251 x^{14} - 460 x^{13} - 1295 x^{12} + 2248 x^{11} + \cdots - 39 $ x^18 - 2x^17 - 25x^16 + 48x^15 + 251x^14 - 460x^13 - 1295x^12 + 2248x^11 + 3649x^10 - 5930x^9 - 5548x^8 + 8236x^7 + 4387x^6 - 5508x^5 - 1902x^4 + 1554x^3 + 468x^2 - 132*x - 39
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Root			$2.24352$ 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)

$f(q)$	$=$	\(q+2.24352 q^{2} +2.33974 q^{3} +3.03336 q^{4} +4.11350 q^{5} +5.24923 q^{6} -1.26950 q^{7} +2.31836 q^{8} +2.47436 q^{9} +9.22871 q^{10} -1.00000 q^{11} +7.09726 q^{12} -5.17789 q^{13} -2.84813 q^{14} +9.62451 q^{15} -0.865449 q^{16} +5.76076 q^{17} +5.55127 q^{18} +5.14046 q^{19} +12.4777 q^{20} -2.97028 q^{21} -2.24352 q^{22} +5.42434 q^{24} +11.9209 q^{25} -11.6167 q^{26} -1.22986 q^{27} -3.85084 q^{28} +10.0462 q^{29} +21.5927 q^{30} -0.138232 q^{31} -6.57836 q^{32} -2.33974 q^{33} +12.9244 q^{34} -5.22207 q^{35} +7.50563 q^{36} -0.439152 q^{37} +11.5327 q^{38} -12.1149 q^{39} +9.53657 q^{40} -5.19984 q^{41} -6.66388 q^{42} +2.61480 q^{43} -3.03336 q^{44} +10.1783 q^{45} -7.83119 q^{47} -2.02492 q^{48} -5.38838 q^{49} +26.7447 q^{50} +13.4787 q^{51} -15.7064 q^{52} +1.53250 q^{53} -2.75920 q^{54} -4.11350 q^{55} -2.94315 q^{56} +12.0273 q^{57} +22.5387 q^{58} +4.18861 q^{59} +29.1946 q^{60} -2.39403 q^{61} -0.310126 q^{62} -3.14119 q^{63} -13.0278 q^{64} -21.2993 q^{65} -5.24923 q^{66} -12.0538 q^{67} +17.4745 q^{68} -11.7158 q^{70} -3.68996 q^{71} +5.73645 q^{72} -5.19238 q^{73} -0.985244 q^{74} +27.8918 q^{75} +15.5929 q^{76} +1.26950 q^{77} -27.1799 q^{78} +3.84426 q^{79} -3.56003 q^{80} -10.3006 q^{81} -11.6659 q^{82} -2.32289 q^{83} -9.00994 q^{84} +23.6969 q^{85} +5.86635 q^{86} +23.5054 q^{87} -2.31836 q^{88} +13.4702 q^{89} +22.8352 q^{90} +6.57331 q^{91} -0.323427 q^{93} -17.5694 q^{94} +21.1453 q^{95} -15.3916 q^{96} -9.73757 q^{97} -12.0889 q^{98} -2.47436 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{2} - 2 q^{3} + 18 q^{4} + 8 q^{5} - 6 q^{6} + 10 q^{7} + 6 q^{8} + 16 q^{9} + 12 q^{10} - 18 q^{11} + 10 q^{12} + 28 q^{14} + 8 q^{15} + 26 q^{16} - 20 q^{18} + 16 q^{19} + 40 q^{20} + 12 q^{21}+ \cdots - 16 q^{99}+O(q^{100}) $ 18 * q + 2 * q^2 - 2 * q^3 + 18 * q^4 + 8 * q^5 - 6 * q^6 + 10 * q^7 + 6 * q^8 + 16 * q^9 + 12 * q^10 - 18 * q^11 + 10 * q^12 + 28 * q^14 + 8 * q^15 + 26 * q^16 - 20 * q^18 + 16 * q^19 + 40 * q^20 + 12 * q^21 - 2 * q^22 + 26 * q^24 + 6 * q^25 - 20 * q^26 - 14 * q^27 + 32 * q^28 - 12 * q^29 + 14 * q^30 + 24 * q^32 + 2 * q^33 + 24 * q^34 + 2 * q^35 - 12 * q^36 + 36 * q^37 - 8 * q^38 - 10 * q^39 + 22 * q^40 + 6 * q^41 - 4 * q^42 + 20 * q^43 - 18 * q^44 - 16 * q^45 - 36 * q^47 + 28 * q^48 + 4 * q^49 + 52 * q^50 + 44 * q^51 - 16 * q^52 + 20 * q^53 - 8 * q^54 - 8 * q^55 + 40 * q^56 + 44 * q^57 + 2 * q^58 - 32 * q^59 + 88 * q^60 + 20 * q^61 + 2 * q^63 + 10 * q^64 - 40 * q^65 + 6 * q^66 - 12 * q^68 + 14 * q^70 - 28 * q^71 - 38 * q^72 - 16 * q^73 + 40 * q^74 + 16 * q^75 + 34 * q^76 - 10 * q^77 - 72 * q^78 + 40 * q^79 + 28 * q^80 + 18 * q^81 + 24 * q^82 + 32 * q^83 - 74 * q^84 - 12 * q^85 - 20 * q^86 + 46 * q^87 - 6 * q^88 + 88 * q^89 + 32 * q^90 - 32 * q^91 - 24 * q^93 - 22 * q^94 + 58 * q^95 + 10 * q^96 + 52 * q^97 + 82 * q^98 - 16 * 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 $

$2$	2.24352	1.58640	0.793202	−	0.608958i	$-0.208412\pi$
$2$	2.24352	1.58640	0.793202	+	0.608958i	$0.208412\pi$
$3$	2.33974	1.35085	0.675423	−	0.737430i	$-0.263961\pi$
$3$	2.33974	1.35085	0.675423	+	0.737430i	$0.263961\pi$
$4$	3.03336	1.51668
$5$	4.11350	1.83961	0.919807	−	0.392371i	$-0.128345\pi$
$5$	4.11350	1.83961	0.919807	+	0.392371i	$0.128345\pi$
$6$	5.24923	2.14299
$7$	−1.26950	−0.479824	−0.239912	−	0.970795i	$-0.577119\pi$
$7$	−1.26950	−0.479824	−0.239912	+	0.970795i	$0.577119\pi$
$8$	2.31836	0.819663
$9$	2.47436	0.824787
$10$	9.22871	2.91837
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	7.09726	2.04880
$13$	−5.17789	−1.43609	−0.718044	−	0.695998i	$-0.754962\pi$
$13$	−5.17789	−1.43609	−0.718044	+	0.695998i	$0.754962\pi$
$14$	−2.84813	−0.761195
$15$	9.62451	2.48504
$16$	−0.865449	−0.216362
$17$	5.76076	1.39719	0.698595	−	0.715518i	$-0.253809\pi$
$17$	5.76076	1.39719	0.698595	+	0.715518i	$0.253809\pi$
$18$	5.55127	1.30845
$19$	5.14046	1.17930	0.589651	−	0.807658i	$-0.299265\pi$
$19$	5.14046	1.17930	0.589651	+	0.807658i	$0.299265\pi$
$20$	12.4777	2.79011
$21$	−2.97028	−0.648169
$22$	−2.24352	−0.478319
$23$	0	0
$23$	0	0
$24$	5.42434	1.10724
$25$	11.9209	2.38418
$26$	−11.6167	−2.27822
$27$	−1.22986	−0.236686
$28$	−3.85084	−0.727740
$29$	10.0462	1.86553	0.932763	−	0.360491i	$-0.117391\pi$
$29$	10.0462	1.86553	0.932763	+	0.360491i	$0.117391\pi$
$30$	21.5927	3.94227
$31$	−0.138232	−0.0248272	−0.0124136	−	0.999923i	$-0.503951\pi$
$31$	−0.138232	−0.0248272	−0.0124136	+	0.999923i	$0.503951\pi$
$32$	−6.57836	−1.16290
$33$	−2.33974	−0.407296
$34$	12.9244	2.21651
$35$	−5.22207	−0.882692
$36$	7.50563	1.25094
$37$	−0.439152	−0.0721961	−0.0360981	−	0.999348i	$-0.511493\pi$
$37$	−0.439152	−0.0721961	−0.0360981	+	0.999348i	$0.511493\pi$
$38$	11.5327	1.87085
$39$	−12.1149	−1.93993
$40$	9.53657	1.50786
$41$	−5.19984	−0.812078	−0.406039	−	0.913856i	$-0.633090\pi$
$41$	−5.19984	−0.812078	−0.406039	+	0.913856i	$0.633090\pi$
$42$	−6.66388	−1.02826
$43$	2.61480	0.398754	0.199377	−	0.979923i	$-0.436108\pi$
$43$	2.61480	0.398754	0.199377	+	0.979923i	$0.436108\pi$
$44$	−3.03336	−0.457296
$45$	10.1783	1.51729
$46$	0	0
$47$	−7.83119	−1.14230	−0.571148	−	0.820847i	$-0.693502\pi$
$47$	−7.83119	−1.14230	−0.571148	+	0.820847i	$0.693502\pi$
$48$	−2.02492	−0.292272
$49$	−5.38838	−0.769769
$50$	26.7447	3.78228
$51$	13.4787	1.88739
$52$	−15.7064	−2.17809
$53$	1.53250	0.210505	0.105253	−	0.994446i	$-0.466435\pi$
$53$	1.53250	0.210505	0.105253	+	0.994446i	$0.466435\pi$
$54$	−2.75920	−0.375479
$55$	−4.11350	−0.554665
$56$	−2.94315	−0.393294
$57$	12.0273	1.59306
$58$	22.5387	2.95948
$59$	4.18861	0.545310	0.272655	−	0.962112i	$-0.412098\pi$
$59$	4.18861	0.545310	0.272655	+	0.962112i	$0.412098\pi$
$60$	29.1946	3.76901
$61$	−2.39403	−0.306524	−0.153262	−	0.988186i	$-0.548978\pi$
$61$	−2.39403	−0.306524	−0.153262	+	0.988186i	$0.548978\pi$
$62$	−0.310126	−0.0393861
$63$	−3.14119	−0.395753
$64$	−13.0278	−1.62847
$65$	−21.2993	−2.64185
$66$	−5.24923	−0.646136
$67$	−12.0538	−1.47260	−0.736300	−	0.676655i	$-0.763429\pi$
$67$	−12.0538	−1.47260	−0.736300	+	0.676655i	$0.763429\pi$
$68$	17.4745	2.11909
$69$	0	0
$70$	−11.7158	−1.40031
$71$	−3.68996	−0.437918	−0.218959	−	0.975734i	$-0.570266\pi$
$71$	−3.68996	−0.437918	−0.218959	+	0.975734i	$0.570266\pi$
$72$	5.73645	0.676048
$73$	−5.19238	−0.607722	−0.303861	−	0.952716i	$-0.598276\pi$
$73$	−5.19238	−0.607722	−0.303861	+	0.952716i	$0.598276\pi$
$74$	−0.985244	−0.114532
$75$	27.8918	3.22066
$76$	15.5929	1.78862
$77$	1.26950	0.144672
$78$	−27.1799	−3.07752
$79$	3.84426	0.432513	0.216256	−	0.976337i	$-0.430615\pi$
$79$	3.84426	0.432513	0.216256	+	0.976337i	$0.430615\pi$
$80$	−3.56003	−0.398023
$81$	−10.3006	−1.14451
$82$	−11.6659	−1.28828
$83$	−2.32289	−0.254970	−0.127485	−	0.991841i	$-0.540690\pi$
$83$	−2.32289	−0.254970	−0.127485	+	0.991841i	$0.540690\pi$
$84$	−9.00994	−0.983065
$85$	23.6969	2.57029
$86$	5.86635	0.632584
$87$	23.5054	2.52004
$88$	−2.31836	−0.247138
$89$	13.4702	1.42784	0.713921	−	0.700226i	$-0.246917\pi$
$89$	13.4702	1.42784	0.713921	+	0.700226i	$0.246917\pi$
$90$	22.8352	2.40704
$91$	6.57331	0.689070
$92$	0	0
$93$	−0.323427	−0.0335378
$94$	−17.5694	−1.81214
$95$	21.1453	2.16946
$96$	−15.3916	−1.57090
$97$	−9.73757	−0.988700	−0.494350	−	0.869263i	$-0.664594\pi$
$97$	−9.73757	−0.988700	−0.494350	+	0.869263i	$0.664594\pi$
$98$	−12.0889	−1.22116
$99$	−2.47436	−0.248683
$100$	36.1604	3.61604
$101$	−11.6842	−1.16262	−0.581311	−	0.813681i	$-0.697460\pi$
$101$	−11.6842	−1.16262	−0.581311	+	0.813681i	$0.697460\pi$
$102$	30.2396	2.99416
$103$	−6.21786	−0.612664	−0.306332	−	0.951925i	$-0.599102\pi$
$103$	−6.21786	−0.612664	−0.306332	+	0.951925i	$0.599102\pi$
$104$	−12.0042	−1.17711
$105$	−12.2183	−1.19238
$106$	3.43819	0.333947
$107$	2.12494	0.205426	0.102713	−	0.994711i	$-0.467248\pi$
$107$	2.12494	0.205426	0.102713	+	0.994711i	$0.467248\pi$
$108$	−3.73059	−0.358977
$109$	8.51932	0.816003	0.408002	−	0.912981i	$-0.366226\pi$
$109$	8.51932	0.816003	0.408002	+	0.912981i	$0.366226\pi$
$110$	−9.22871	−0.879923
$111$	−1.02750	−0.0975259
$112$	1.09868	0.103816
$113$	−8.24786	−0.775893	−0.387947	−	0.921682i	$-0.626816\pi$
$113$	−8.24786	−0.775893	−0.387947	+	0.921682i	$0.626816\pi$
$114$	26.9834	2.52723
$115$	0	0
$116$	30.4736	2.82940
$117$	−12.8120	−1.18447
$118$	9.39720	0.865082
$119$	−7.31326	−0.670405
$120$	22.3131	2.03689
$121$	1.00000	0.0909091
$122$	−5.37104	−0.486271
$123$	−12.1662	−1.09699
$124$	−0.419308	−0.0376550
$125$	28.4692	2.54636
$126$	−7.04731	−0.627824
$127$	−14.6998	−1.30439	−0.652196	−	0.758050i	$-0.726152\pi$
$127$	−14.6998	−1.30439	−0.652196	+	0.758050i	$0.726152\pi$
$128$	−16.0712	−1.42051
$129$	6.11794	0.538655
$130$	−47.7852	−4.19104
$131$	13.4794	1.17770	0.588852	−	0.808241i	$-0.299580\pi$
$131$	13.4794	1.17770	0.588852	+	0.808241i	$0.299580\pi$
$132$	−7.09726	−0.617737
$133$	−6.52579	−0.565858
$134$	−27.0428	−2.33614
$135$	−5.05901	−0.435411
$136$	13.3555	1.14522
$137$	−3.70059	−0.316163	−0.158082	−	0.987426i	$-0.550531\pi$
$137$	−3.70059	−0.316163	−0.158082	+	0.987426i	$0.550531\pi$
$138$	0	0
$139$	13.5566	1.14985	0.574927	−	0.818205i	$-0.305030\pi$
$139$	13.5566	1.14985	0.574927	+	0.818205i	$0.305030\pi$
$140$	−15.8404	−1.33876
$141$	−18.3229	−1.54307
$142$	−8.27848	−0.694715
$143$	5.17789	0.432997
$144$	−2.14143	−0.178453
$145$	41.3249	3.43185
$146$	−11.6492	−0.964093
$147$	−12.6074	−1.03984
$148$	−1.33211	−0.109498
$149$	−10.9764	−0.899223	−0.449612	−	0.893224i	$-0.648438\pi$
$149$	−10.9764	−0.899223	−0.449612	+	0.893224i	$0.648438\pi$
$150$	62.5756	5.10928
$151$	14.5257	1.18209	0.591044	−	0.806639i	$-0.298716\pi$
$151$	14.5257	1.18209	0.591044	+	0.806639i	$0.298716\pi$
$152$	11.9174	0.966630
$153$	14.2542	1.15238
$154$	2.84813	0.229509
$155$	−0.568619	−0.0456726
$156$	−36.7488	−2.94226
$157$	21.5134	1.71696	0.858479	−	0.512849i	$-0.171410\pi$
$157$	21.5134	1.71696	0.858479	+	0.512849i	$0.171410\pi$
$158$	8.62465	0.686140
$159$	3.58565	0.284361
$160$	−27.0601	−2.13929
$161$	0	0
$162$	−23.1096	−1.81566
$163$	−22.5485	−1.76614	−0.883068	−	0.469245i	$-0.844526\pi$
$163$	−22.5485	−1.76614	−0.883068	+	0.469245i	$0.844526\pi$
$164$	−15.7730	−1.23166
$165$	−9.62451	−0.749267
$166$	−5.21143	−0.404485
$167$	19.0163	1.47152	0.735762	−	0.677241i	$-0.236824\pi$
$167$	19.0163	1.47152	0.735762	+	0.677241i	$0.236824\pi$
$168$	−6.88618	−0.531280
$169$	13.8105	1.06235
$170$	53.1644	4.07752
$171$	12.7193	0.972673
$172$	7.93163	0.604781
$173$	8.29995	0.631033	0.315517	−	0.948920i	$-0.397822\pi$
$173$	8.29995	0.631033	0.315517	+	0.948920i	$0.397822\pi$
$174$	52.7346	3.99780
$175$	−15.1335	−1.14399
$176$	0.865449	0.0652357
$177$	9.80023	0.736630
$178$	30.2207	2.26514
$179$	0.759507	0.0567682	0.0283841	−	0.999597i	$-0.490964\pi$
$179$	0.759507	0.0567682	0.0283841	+	0.999597i	$0.490964\pi$
$180$	30.8744	2.30124
$181$	−0.389625	−0.0289606	−0.0144803	−	0.999895i	$-0.504609\pi$
$181$	−0.389625	−0.0289606	−0.0144803	+	0.999895i	$0.504609\pi$
$182$	14.7473	1.09314
$183$	−5.60140	−0.414067
$184$	0	0
$185$	−1.80645	−0.132813
$186$	−0.725613	−0.0532045
$187$	−5.76076	−0.421269
$188$	−23.7548	−1.73250
$189$	1.56130	0.113568
$190$	47.4398	3.44164
$191$	−25.7293	−1.86171	−0.930853	−	0.365394i	$-0.880934\pi$
$191$	−25.7293	−1.86171	−0.930853	+	0.365394i	$0.880934\pi$
$192$	−30.4815	−2.19981
$193$	0.00346159	0.000249171 0	0.000124586	−	1.00000i	$-0.499960\pi$
$193$	0.00346159	0.000249171 0	0.000124586		1.00000i	$0.499960\pi$
$194$	−21.8464	−1.56848
$195$	−49.8346	−3.56873
$196$	−16.3449	−1.16749
$197$	−2.88624	−0.205636	−0.102818	−	0.994700i	$-0.532786\pi$
$197$	−2.88624	−0.205636	−0.102818	+	0.994700i	$0.532786\pi$
$198$	−5.55127	−0.394511
$199$	−11.0110	−0.780550	−0.390275	−	0.920698i	$-0.627620\pi$
$199$	−11.0110	−0.780550	−0.390275	+	0.920698i	$0.627620\pi$
$200$	27.6369	1.95423
$201$	−28.2026	−1.98926
$202$	−26.2137	−1.84439
$203$	−12.7536	−0.895124
$204$	40.8856	2.86256
$205$	−21.3896	−1.49391
$206$	−13.9499	−0.971933
$207$	0	0
$208$	4.48120	0.310715
$209$	−5.14046	−0.355573
$210$	−27.4119	−1.89160
$211$	3.22795	0.222221	0.111110	−	0.993808i	$-0.464559\pi$
$211$	3.22795	0.222221	0.111110	+	0.993808i	$0.464559\pi$
$212$	4.64863	0.319269
$213$	−8.63353	−0.591560
$214$	4.76734	0.325889
$215$	10.7560	0.733553
$216$	−2.85124	−0.194003
$217$	0.175485	0.0119127
$218$	19.1132	1.29451
$219$	−12.1488	−0.820939
$220$	−12.4777	−0.841249
$221$	−29.8286	−2.00649
$222$	−2.30521	−0.154716
$223$	−17.9624	−1.20285	−0.601425	−	0.798929i	$-0.705400\pi$
$223$	−17.9624	−1.20285	−0.601425	+	0.798929i	$0.705400\pi$
$224$	8.35120	0.557988
$225$	29.4966	1.96644
$226$	−18.5042	−1.23088
$227$	−19.8097	−1.31481	−0.657407	−	0.753536i	$-0.728347\pi$
$227$	−19.8097	−1.31481	−0.657407	+	0.753536i	$0.728347\pi$
$228$	36.4831	2.41616
$229$	26.6173	1.75892	0.879460	−	0.475973i	$-0.157904\pi$
$229$	26.6173	1.75892	0.879460	+	0.475973i	$0.157904\pi$
$230$	0	0
$231$	2.97028	0.195430
$232$	23.2906	1.52910
$233$	22.4717	1.47217	0.736085	−	0.676889i	$-0.236672\pi$
$233$	22.4717	1.47217	0.736085	+	0.676889i	$0.236672\pi$
$234$	−28.7438	−1.87904
$235$	−32.2136	−2.10138
$236$	12.7055	0.827061
$237$	8.99455	0.584259
$238$	−16.4074	−1.06353
$239$	8.73635	0.565107	0.282554	−	0.959252i	$-0.408818\pi$
$239$	8.73635	0.565107	0.282554	+	0.959252i	$0.408818\pi$
$240$	−8.32952	−0.537668
$241$	5.63342	0.362881	0.181440	−	0.983402i	$-0.441924\pi$
$241$	5.63342	0.362881	0.181440	+	0.983402i	$0.441924\pi$
$242$	2.24352	0.144219
$243$	−20.4112	−1.30938
$244$	−7.26196	−0.464899
$245$	−22.1651	−1.41608
$246$	−27.2952	−1.74028
$247$	−26.6167	−1.69358
$248$	−0.320472	−0.0203500
$249$	−5.43494	−0.344425
$250$	63.8710	4.03956
$251$	8.92961	0.563632	0.281816	−	0.959468i	$-0.409063\pi$
$251$	8.92961	0.563632	0.281816	+	0.959468i	$0.409063\pi$
$252$	−9.52836	−0.600230
$253$	0	0
$254$	−32.9791	−2.06929
$255$	55.4445	3.47207
$256$	−10.0006	−0.625035
$257$	−2.28069	−0.142266	−0.0711329	−	0.997467i	$-0.522661\pi$
$257$	−2.28069	−0.142266	−0.0711329	+	0.997467i	$0.522661\pi$
$258$	13.7257	0.854525
$259$	0.557502	0.0346415
$260$	−64.6083	−4.00684
$261$	24.8578	1.53866
$262$	30.2413	1.86832
$263$	8.94548	0.551602	0.275801	−	0.961215i	$-0.411057\pi$
$263$	8.94548	0.551602	0.275801	+	0.961215i	$0.411057\pi$
$264$	−5.42434	−0.333845
$265$	6.30396	0.387249
$266$	−14.6407	−0.897679
$267$	31.5168	1.92880
$268$	−36.5634	−2.23346
$269$	−2.06038	−0.125624	−0.0628118	−	0.998025i	$-0.520007\pi$
$269$	−2.06038	−0.125624	−0.0628118	+	0.998025i	$0.520007\pi$
$270$	−11.3500	−0.690737
$271$	9.88178	0.600276	0.300138	−	0.953896i	$-0.402967\pi$
$271$	9.88178	0.600276	0.300138	+	0.953896i	$0.402967\pi$
$272$	−4.98564	−0.302299
$273$	15.3798	0.930828
$274$	−8.30234	−0.501563
$275$	−11.9209	−0.718858
$276$	0	0
$277$	−14.3719	−0.863525	−0.431762	−	0.901987i	$-0.642108\pi$
$277$	−14.3719	−0.863525	−0.431762	+	0.901987i	$0.642108\pi$
$278$	30.4144	1.82413
$279$	−0.342037	−0.0204772
$280$	−12.1066	−0.723510
$281$	5.10541	0.304563	0.152282	−	0.988337i	$-0.451338\pi$
$281$	5.10541	0.304563	0.152282	+	0.988337i	$0.451338\pi$
$282$	−41.1077	−2.44793
$283$	−16.4834	−0.979836	−0.489918	−	0.871768i	$-0.662973\pi$
$283$	−16.4834	−0.979836	−0.489918	+	0.871768i	$0.662973\pi$
$284$	−11.1930	−0.664181
$285$	49.4744	2.93061
$286$	11.6167	0.686908
$287$	6.60117	0.389655
$288$	−16.2772	−0.959146
$289$	16.1864	0.952139
$290$	92.7131	5.44430
$291$	−22.7833	−1.33558
$292$	−15.7503	−0.921719
$293$	−18.1277	−1.05903	−0.529515	−	0.848300i	$-0.677626\pi$
$293$	−18.1277	−1.05903	−0.529515	+	0.848300i	$0.677626\pi$
$294$	−28.2849	−1.64961
$295$	17.2298	1.00316
$296$	−1.01811	−0.0591765
$297$	1.22986	0.0713634
$298$	−24.6258	−1.42653
$299$	0	0
$300$	84.6058	4.88472
$301$	−3.31948	−0.191332
$302$	32.5887	1.87527
$303$	−27.3380	−1.57052
$304$	−4.44880	−0.255156
$305$	−9.84785	−0.563886
$306$	31.9795	1.82815
$307$	−22.3135	−1.27350	−0.636749	−	0.771071i	$-0.719721\pi$
$307$	−22.3135	−1.27350	−0.636749	+	0.771071i	$0.719721\pi$
$308$	3.85084	0.219422
$309$	−14.5481	−0.827615
$310$	−1.27570	−0.0724552
$311$	−33.0099	−1.87182	−0.935911	−	0.352237i	$-0.885421\pi$
$311$	−33.0099	−1.87182	−0.935911	+	0.352237i	$0.885421\pi$
$312$	−28.0866	−1.59009
$313$	−12.4217	−0.702117	−0.351059	−	0.936353i	$-0.614178\pi$
$313$	−12.4217	−0.702117	−0.351059	+	0.936353i	$0.614178\pi$
$314$	48.2657	2.72379
$315$	−12.9213	−0.728033
$316$	11.6610	0.655983
$317$	−0.0312776	−0.00175672	−0.000878362	−	1.00000i	$-0.500280\pi$
$317$	−0.0312776	−0.00175672	−0.000878362		1.00000i	$0.500280\pi$
$318$	8.04446	0.451111
$319$	−10.0462	−0.562477
$320$	−53.5897	−2.99576
$321$	4.97180	0.277499
$322$	0	0
$323$	29.6129	1.64771
$324$	−31.2455	−1.73586
$325$	−61.7251	−3.42389
$326$	−50.5879	−2.80181
$327$	19.9330	1.10230
$328$	−12.0551	−0.665631
$329$	9.94166	0.548101
$330$	−21.5927	−1.18864
$331$	−34.1674	−1.87801	−0.939004	−	0.343905i	$-0.888250\pi$
$331$	−34.1674	−1.87801	−0.939004	+	0.343905i	$0.888250\pi$
$332$	−7.04615	−0.386708
$333$	−1.08662	−0.0595464
$334$	42.6633	2.33443
$335$	−49.5831	−2.70902
$336$	2.57063	0.140239
$337$	−12.6987	−0.691744	−0.345872	−	0.938282i	$-0.612417\pi$
$337$	−12.6987	−0.691744	−0.345872	+	0.938282i	$0.612417\pi$
$338$	30.9841	1.68531
$339$	−19.2978	−1.04811
$340$	71.8812	3.89831
$341$	0.138232	0.00748570
$342$	28.5360	1.54305
$343$	15.7270	0.849178
$344$	6.06205	0.326844
$345$	0	0
$346$	18.6211	1.00107
$347$	1.21840	0.0654071	0.0327035	−	0.999465i	$-0.489588\pi$
$347$	1.21840	0.0654071	0.0327035	+	0.999465i	$0.489588\pi$
$348$	71.3002	3.82209
$349$	−9.18540	−0.491683	−0.245842	−	0.969310i	$-0.579064\pi$
$349$	−9.18540	−0.491683	−0.245842	+	0.969310i	$0.579064\pi$
$350$	−33.9523	−1.81483
$351$	6.36805	0.339902
$352$	6.57836	0.350628
$353$	3.50470	0.186537	0.0932683	−	0.995641i	$-0.470269\pi$
$353$	3.50470	0.186537	0.0932683	+	0.995641i	$0.470269\pi$
$354$	21.9870	1.16859
$355$	−15.1787	−0.805600
$356$	40.8601	2.16558
$357$	−17.1111	−0.905615
$358$	1.70397	0.0900574
$359$	35.3782	1.86719	0.933595	−	0.358330i	$-0.116654\pi$
$359$	35.3782	1.86719	0.933595	+	0.358330i	$0.116654\pi$
$360$	23.5969	1.24367
$361$	7.42429	0.390752
$362$	−0.874130	−0.0459433
$363$	2.33974	0.122804
$364$	19.9392	1.04510
$365$	−21.3589	−1.11797
$366$	−12.5668	−0.656878
$367$	16.9321	0.883847	0.441923	−	0.897053i	$-0.354296\pi$
$367$	16.9321	0.883847	0.441923	+	0.897053i	$0.354296\pi$
$368$	0	0
$369$	−12.8663	−0.669792
$370$	−4.05280	−0.210695
$371$	−1.94551	−0.101006
$372$	−0.981070	−0.0508661
$373$	16.5696	0.857944	0.428972	−	0.903318i	$-0.358876\pi$
$373$	16.5696	0.857944	0.428972	+	0.903318i	$0.358876\pi$
$374$	−12.9244	−0.668302
$375$	66.6103	3.43974
$376$	−18.1555	−0.936298
$377$	−52.0179	−2.67906
$378$	3.50279	0.180164
$379$	−9.50512	−0.488245	−0.244123	−	0.969744i	$-0.578500\pi$
$379$	−9.50512	−0.488245	−0.244123	+	0.969744i	$0.578500\pi$
$380$	64.1412	3.29038
$381$	−34.3935	−1.76203
$382$	−57.7240	−2.95342
$383$	22.3217	1.14059	0.570293	−	0.821442i	$-0.306830\pi$
$383$	22.3217	1.14059	0.570293	+	0.821442i	$0.306830\pi$
$384$	−37.6025	−1.91889
$385$	5.22207	0.266142
$386$	0.00776614	0.000395286 0
$387$	6.46996	0.328887
$388$	−29.5375	−1.49954
$389$	34.0539	1.72660	0.863301	−	0.504689i	$-0.168393\pi$
$389$	34.0539	1.72660	0.863301	+	0.504689i	$0.168393\pi$
$390$	−111.805	−5.66145
$391$	0	0
$392$	−12.4922	−0.630951
$393$	31.5383	1.59090
$394$	−6.47532	−0.326222
$395$	15.8134	0.795657
$396$	−7.50563	−0.377172
$397$	−13.3777	−0.671405	−0.335703	−	0.941968i	$-0.608974\pi$
$397$	−13.3777	−0.671405	−0.335703	+	0.941968i	$0.608974\pi$
$398$	−24.7034	−1.23827
$399$	−15.2686	−0.764387
$400$	−10.3169	−0.515847
$401$	15.9691	0.797460	0.398730	−	0.917068i	$-0.369451\pi$
$401$	15.9691	0.797460	0.398730	+	0.917068i	$0.369451\pi$
$402$	−63.2729	−3.15577
$403$	0.715751	0.0356541
$404$	−35.4424	−1.76333
$405$	−42.3716	−2.10546
$406$	−28.6128	−1.42003
$407$	0.439152	0.0217680
$408$	31.2483	1.54702
$409$	−5.55381	−0.274618	−0.137309	−	0.990528i	$-0.543845\pi$
$409$	−5.55381	−0.274618	−0.137309	+	0.990528i	$0.543845\pi$
$410$	−47.9878	−2.36995
$411$	−8.65841	−0.427088
$412$	−18.8610	−0.929215
$413$	−5.31742	−0.261653
$414$	0	0
$415$	−9.55520	−0.469046
$416$	34.0620	1.67003
$417$	31.7188	1.55328
$418$	−11.5327	−0.564082
$419$	−5.07582	−0.247970	−0.123985	−	0.992284i	$-0.539568\pi$
$419$	−5.07582	−0.247970	−0.123985	+	0.992284i	$0.539568\pi$
$420$	−37.0624	−1.80846
$421$	−24.7237	−1.20496	−0.602480	−	0.798134i	$-0.705821\pi$
$421$	−24.7237	−1.20496	−0.602480	+	0.798134i	$0.705821\pi$
$422$	7.24195	0.352532
$423$	−19.3772	−0.942151
$424$	3.55289	0.172544
$425$	68.6735	3.33115
$426$	−19.3695	−0.938453
$427$	3.03921	0.147078
$428$	6.44572	0.311565
$429$	12.1149	0.584912
$430$	24.1312	1.16371
$431$	19.2956	0.929437	0.464719	−	0.885458i	$-0.346155\pi$
$431$	19.2956	0.929437	0.464719	+	0.885458i	$0.346155\pi$
$432$	1.06438	0.0512098
$433$	8.85926	0.425749	0.212874	−	0.977080i	$-0.431717\pi$
$433$	8.85926	0.425749	0.212874	+	0.977080i	$0.431717\pi$
$434$	0.393704	0.0188984
$435$	96.6894	4.63590
$436$	25.8422	1.23762
$437$	0	0
$438$	−27.2560	−1.30234
$439$	2.69819	0.128777	0.0643887	−	0.997925i	$-0.479490\pi$
$439$	2.69819	0.128777	0.0643887	+	0.997925i	$0.479490\pi$
$440$	−9.53657	−0.454638
$441$	−13.3328	−0.634895
$442$	−66.9208	−3.18310
$443$	−2.59486	−0.123286	−0.0616428	−	0.998098i	$-0.519634\pi$
$443$	−2.59486	−0.123286	−0.0616428	+	0.998098i	$0.519634\pi$
$444$	−3.11678	−0.147916
$445$	55.4099	2.62668
$446$	−40.2989	−1.90821
$447$	−25.6819	−1.21471
$448$	16.5387	0.781379
$449$	33.6796	1.58944	0.794720	−	0.606976i	$-0.207618\pi$
$449$	33.6796	1.58944	0.794720	+	0.606976i	$0.207618\pi$
$450$	66.1761	3.11957
$451$	5.19984	0.244851
$452$	−25.0187	−1.17678
$453$	33.9864	1.59682
$454$	−44.4433	−2.08583
$455$	27.0393	1.26762
$456$	27.8836	1.30577
$457$	−35.8928	−1.67899	−0.839497	−	0.543365i	$-0.817150\pi$
$457$	−35.8928	−1.67899	−0.839497	+	0.543365i	$0.817150\pi$
$458$	59.7163	2.79036
$459$	−7.08490	−0.330695
$460$	0	0
$461$	18.8750	0.879098	0.439549	−	0.898219i	$-0.355138\pi$
$461$	18.8750	0.879098	0.439549	+	0.898219i	$0.355138\pi$
$462$	6.66388	0.310032
$463$	−22.5480	−1.04790	−0.523948	−	0.851750i	$-0.675541\pi$
$463$	−22.5480	−1.04790	−0.523948	+	0.851750i	$0.675541\pi$
$464$	−8.69444	−0.403629
$465$	−1.33042	−0.0616966
$466$	50.4156	2.33546
$467$	−9.37665	−0.433899	−0.216950	−	0.976183i	$-0.569611\pi$
$467$	−9.37665	−0.433899	−0.216950	+	0.976183i	$0.569611\pi$
$468$	−38.8633	−1.79646
$469$	15.3022	0.706589
$470$	−72.2717	−3.33365
$471$	50.3357	2.31935
$472$	9.71069	0.446971
$473$	−2.61480	−0.120229
$474$	20.1794	0.926870
$475$	61.2789	2.81167
$476$	−22.1837	−1.01679
$477$	3.79197	0.173622
$478$	19.6001	0.896489
$479$	19.2127	0.877850	0.438925	−	0.898524i	$-0.355359\pi$
$479$	19.2127	0.877850	0.438925	+	0.898524i	$0.355359\pi$
$480$	−63.3135	−2.88985
$481$	2.27388	0.103680
$482$	12.6387	0.575676
$483$	0	0
$484$	3.03336	0.137880
$485$	−40.0555	−1.81883
$486$	−45.7927	−2.07720
$487$	29.0830	1.31788	0.658938	−	0.752197i	$-0.271006\pi$
$487$	29.0830	1.31788	0.658938	+	0.752197i	$0.271006\pi$
$488$	−5.55022	−0.251247
$489$	−52.7576	−2.38578
$490$	−49.7278	−2.24647
$491$	4.75089	0.214405	0.107202	−	0.994237i	$-0.465811\pi$
$491$	4.75089	0.214405	0.107202	+	0.994237i	$0.465811\pi$
$492$	−36.9046	−1.66379
$493$	57.8735	2.60649
$494$	−59.7150	−2.68670
$495$	−10.1783	−0.457480
$496$	0.119633	0.00537168
$497$	4.68439	0.210124
$498$	−12.1934	−0.546398
$499$	33.8752	1.51646	0.758230	−	0.651987i	$-0.226064\pi$
$499$	33.8752	1.51646	0.758230	+	0.651987i	$0.226064\pi$
$500$	86.3572	3.86201
$501$	44.4930	1.98780
$502$	20.0337	0.894148
$503$	−4.93174	−0.219895	−0.109948	−	0.993937i	$-0.535068\pi$
$503$	−4.93174	−0.219895	−0.109948	+	0.993937i	$0.535068\pi$
$504$	−7.28241	−0.324384
$505$	−48.0630	−2.13878
$506$	0	0
$507$	32.3130	1.43507
$508$	−44.5896	−1.97835
$509$	40.7083	1.80436	0.902181	−	0.431358i	$-0.141965\pi$
$509$	40.7083	1.80436	0.902181	+	0.431358i	$0.141965\pi$
$510$	124.391	5.50811
$511$	6.59170	0.291600
$512$	9.70608	0.428952
$513$	−6.32202	−0.279124
$514$	−5.11677	−0.225691
$515$	−25.5772	−1.12706
$516$	18.5579	0.816967
$517$	7.83119	0.344415
$518$	1.25076	0.0549554
$519$	19.4197	0.852430
$520$	−49.3793	−2.16543
$521$	−35.2316	−1.54352	−0.771762	−	0.635911i	$-0.780624\pi$
$521$	−35.2316	−1.54352	−0.771762	+	0.635911i	$0.780624\pi$
$522$	55.7689	2.44094
$523$	−23.7044	−1.03652	−0.518260	−	0.855223i	$-0.673420\pi$
$523$	−23.7044	−1.03652	−0.518260	+	0.855223i	$0.673420\pi$
$524$	40.8880	1.78620
$525$	−35.4085	−1.54535
$526$	20.0693	0.875064
$527$	−0.796323	−0.0346884
$528$	2.02492	0.0881234
$529$	0	0
$530$	14.1430	0.614333
$531$	10.3641	0.449765
$532$	−19.7951	−0.858225
$533$	26.9242	1.16622
$534$	70.7084	3.05985
$535$	8.74096	0.377905
$536$	−27.9449	−1.20704
$537$	1.77705	0.0766852
$538$	−4.62250	−0.199290
$539$	5.38838	0.232094
$540$	−15.3458	−0.660378
$541$	−41.7025	−1.79293	−0.896465	−	0.443114i	$-0.853874\pi$
$541$	−41.7025	−1.79293	−0.896465	+	0.443114i	$0.853874\pi$
$542$	22.1699	0.952280
$543$	−0.911620	−0.0391214
$544$	−37.8964	−1.62479
$545$	35.0443	1.50113
$546$	34.5048	1.47667
$547$	−2.82101	−0.120618	−0.0603088	−	0.998180i	$-0.519209\pi$
$547$	−2.82101	−0.120618	−0.0603088	+	0.998180i	$0.519209\pi$
$548$	−11.2252	−0.479518
$549$	−5.92370	−0.252817
$550$	−26.7447	−1.14040
$551$	51.6419	2.20002
$552$	0	0
$553$	−4.88027	−0.207530
$554$	−32.2436	−1.36990
$555$	−4.22662	−0.179410
$556$	41.1220	1.74396
$557$	9.05227	0.383557	0.191778	−	0.981438i	$-0.438574\pi$
$557$	9.05227	0.383557	0.191778	+	0.981438i	$0.438574\pi$
$558$	−0.767364	−0.0324851
$559$	−13.5392	−0.572645
$560$	4.51944	0.190981
$561$	−13.4787	−0.569069
$562$	11.4541	0.483161
$563$	27.4113	1.15525	0.577624	−	0.816303i	$-0.303980\pi$
$563$	27.4113	1.15525	0.577624	+	0.816303i	$0.303980\pi$
$564$	−55.5800	−2.34034
$565$	−33.9276	−1.42734
$566$	−36.9808	−1.55442
$567$	13.0766	0.549165
$568$	−8.55465	−0.358945
$569$	17.5350	0.735104	0.367552	−	0.930003i	$-0.380196\pi$
$569$	17.5350	0.735104	0.367552	+	0.930003i	$0.380196\pi$
$570$	110.996	4.64913
$571$	1.65910	0.0694314	0.0347157	−	0.999397i	$-0.488947\pi$
$571$	1.65910	0.0694314	0.0347157	+	0.999397i	$0.488947\pi$
$572$	15.7064	0.656717
$573$	−60.1997	−2.51488
$574$	14.8098	0.618150
$575$	0	0
$576$	−32.2354	−1.34314
$577$	−3.98427	−0.165867	−0.0829337	−	0.996555i	$-0.526429\pi$
$577$	−3.98427	−0.165867	−0.0829337	+	0.996555i	$0.526429\pi$
$578$	36.3143	1.51048
$579$	0.00809921	0.000336592 0
$580$	125.353	5.20501
$581$	2.94889	0.122341
$582$	−51.1147	−2.11877
$583$	−1.53250	−0.0634698
$584$	−12.0378	−0.498127
$585$	−52.7021	−2.17896
$586$	−40.6697	−1.68005
$587$	−28.2027	−1.16405	−0.582025	−	0.813171i	$-0.697739\pi$
$587$	−28.2027	−1.16405	−0.582025	+	0.813171i	$0.697739\pi$
$588$	−38.2427	−1.57710
$589$	−0.710577	−0.0292788
$590$	38.6554	1.59142
$591$	−6.75303	−0.277783
$592$	0.380064	0.0156205
$593$	3.61432	0.148422	0.0742111	−	0.997243i	$-0.476356\pi$
$593$	3.61432	0.148422	0.0742111	+	0.997243i	$0.476356\pi$
$594$	2.75920	0.113211
$595$	−30.0831	−1.23329
$596$	−33.2954	−1.36383
$597$	−25.7629	−1.05440
$598$	0	0
$599$	−36.5117	−1.49183	−0.745913	−	0.666044i	$-0.767986\pi$
$599$	−36.5117	−1.49183	−0.745913	+	0.666044i	$0.767986\pi$
$600$	64.6631	2.63986
$601$	3.07562	0.125457	0.0627286	−	0.998031i	$-0.480020\pi$
$601$	3.07562	0.125457	0.0627286	+	0.998031i	$0.480020\pi$
$602$	−7.44730	−0.303529
$603$	−29.8253	−1.21458
$604$	44.0618	1.79285
$605$	4.11350	0.167238
$606$	−61.3331	−2.49149
$607$	−4.49119	−0.182292	−0.0911460	−	0.995838i	$-0.529053\pi$
$607$	−4.49119	−0.182292	−0.0911460	+	0.995838i	$0.529053\pi$
$608$	−33.8158	−1.37141
$609$	−29.8400	−1.20918
$610$	−22.0938	−0.894552
$611$	40.5490	1.64044
$612$	43.2381	1.74780
$613$	33.4772	1.35213	0.676065	−	0.736842i	$-0.263684\pi$
$613$	33.4772	1.35213	0.676065	+	0.736842i	$0.263684\pi$
$614$	−50.0606	−2.02028
$615$	−50.0459	−2.01804
$616$	2.94315	0.118583
$617$	15.5865	0.627487	0.313744	−	0.949508i	$-0.398417\pi$
$617$	15.5865	0.627487	0.313744	+	0.949508i	$0.398417\pi$
$618$	−32.6390	−1.31293
$619$	−12.1981	−0.490283	−0.245141	−	0.969487i	$-0.578834\pi$
$619$	−12.1981	−0.490283	−0.245141	+	0.969487i	$0.578834\pi$
$620$	−1.72483	−0.0692707
$621$	0	0
$622$	−74.0583	−2.96947
$623$	−17.1004	−0.685113
$624$	10.4848	0.419728
$625$	57.5035	2.30014
$626$	−27.8683	−1.11384
$627$	−12.0273	−0.480324
$628$	65.2579	2.60408
$629$	−2.52985	−0.100872
$630$	−28.9891	−1.15495
$631$	24.6470	0.981180	0.490590	−	0.871390i	$-0.336781\pi$
$631$	24.6470	0.981180	0.490590	+	0.871390i	$0.336781\pi$
$632$	8.91236	0.354515
$633$	7.55254	0.300186
$634$	−0.0701718	−0.00278688
$635$	−60.4675	−2.39958
$636$	10.8766	0.431284
$637$	27.9004	1.10546
$638$	−22.5387	−0.892316
$639$	−9.13029	−0.361189
$640$	−66.1091	−2.61319
$641$	11.1343	0.439778	0.219889	−	0.975525i	$-0.429430\pi$
$641$	11.1343	0.439778	0.219889	+	0.975525i	$0.429430\pi$
$642$	11.1543	0.440226
$643$	16.1309	0.636142	0.318071	−	0.948067i	$-0.396965\pi$
$643$	16.1309	0.636142	0.318071	+	0.948067i	$0.396965\pi$
$644$	0	0
$645$	25.1662	0.990917
$646$	66.4371	2.61393
$647$	−6.91331	−0.271790	−0.135895	−	0.990723i	$-0.543391\pi$
$647$	−6.91331	−0.271790	−0.135895	+	0.990723i	$0.543391\pi$
$648$	−23.8805	−0.938116
$649$	−4.18861	−0.164417
$650$	−138.481	−5.43168
$651$	0.410589	0.0160923
$652$	−68.3978	−2.67866
$653$	9.24594	0.361822	0.180911	−	0.983499i	$-0.442095\pi$
$653$	9.24594	0.361822	0.180911	+	0.983499i	$0.442095\pi$
$654$	44.7199	1.74869
$655$	55.4477	2.16652
$656$	4.50019	0.175703
$657$	−12.8478	−0.501241
$658$	22.3043	0.869510
$659$	6.62802	0.258191	0.129095	−	0.991632i	$-0.458793\pi$
$659$	6.62802	0.258191	0.129095	+	0.991632i	$0.458793\pi$
$660$	−29.1946	−1.13640
$661$	33.8343	1.31600	0.658001	−	0.753017i	$-0.271402\pi$
$661$	33.8343	1.31600	0.658001	+	0.753017i	$0.271402\pi$
$662$	−76.6550	−2.97928
$663$	−69.7910	−2.71046
$664$	−5.38528	−0.208989
$665$	−26.8438	−1.04096
$666$	−2.43785	−0.0944648
$667$	0	0
$668$	57.6832	2.23183
$669$	−42.0272	−1.62487
$670$	−111.241	−4.29760
$671$	2.39403	0.0924205
$672$	19.5396	0.753757
$673$	−2.79411	−0.107705	−0.0538524	−	0.998549i	$-0.517150\pi$
$673$	−2.79411	−0.107705	−0.0538524	+	0.998549i	$0.517150\pi$
$674$	−28.4898	−1.09739
$675$	−14.6610	−0.564302
$676$	41.8923	1.61124
$677$	−36.8561	−1.41650	−0.708248	−	0.705964i	$-0.750514\pi$
$677$	−36.8561	−1.41650	−0.708248	+	0.705964i	$0.750514\pi$
$678$	−43.2949	−1.66273
$679$	12.3618	0.474402
$680$	54.9379	2.10677
$681$	−46.3494	−1.77611
$682$	0.310126	0.0118753
$683$	−4.26427	−0.163168	−0.0815838	−	0.996666i	$-0.525998\pi$
$683$	−4.26427	−0.163168	−0.0815838	+	0.996666i	$0.525998\pi$
$684$	38.5824	1.47523
$685$	−15.2224	−0.581618
$686$	35.2838	1.34714
$687$	62.2774	2.37603
$688$	−2.26298	−0.0862752
$689$	−7.93513	−0.302304
$690$	0	0
$691$	25.3100	0.962839	0.481419	−	0.876490i	$-0.340121\pi$
$691$	25.3100	0.962839	0.481419	+	0.876490i	$0.340121\pi$
$692$	25.1767	0.957076
$693$	3.14119	0.119324
$694$	2.73350	0.103762
$695$	55.7650	2.11529
$696$	54.4938	2.06558
$697$	−29.9550	−1.13463
$698$	−20.6076	−0.780009
$699$	52.5779	1.98868
$700$	−45.9055	−1.73506
$701$	27.9680	1.05634	0.528169	−	0.849139i	$-0.322879\pi$
$701$	27.9680	1.05634	0.528169	+	0.849139i	$0.322879\pi$
$702$	14.2868	0.539221
$703$	−2.25744	−0.0851410
$704$	13.0278	0.491002
$705$	−75.3713	−2.83865
$706$	7.86285	0.295922
$707$	14.8331	0.557855
$708$	29.7276	1.11723
$709$	−27.2677	−1.02406	−0.512031	−	0.858967i	$-0.671107\pi$
$709$	−27.2677	−1.02406	−0.512031	+	0.858967i	$0.671107\pi$
$710$	−34.0535	−1.27801
$711$	9.51208	0.356731
$712$	31.2288	1.17035
$713$	0	0
$714$	−38.3890	−1.43667
$715$	21.2993	0.796547
$716$	2.30386	0.0860992
$717$	20.4407	0.763373
$718$	79.3715	2.96212
$719$	0.618322	0.0230595	0.0115298	−	0.999934i	$-0.496330\pi$
$719$	0.618322	0.0230595	0.0115298	+	0.999934i	$0.496330\pi$
$720$	−8.80879	−0.328284
$721$	7.89354	0.293971
$722$	16.6565	0.619891
$723$	13.1807	0.490196
$724$	−1.18187	−0.0439240
$725$	119.759	4.44775
$726$	5.24923	0.194817
$727$	−15.9522	−0.591636	−0.295818	−	0.955244i	$-0.595592\pi$
$727$	−15.9522	−0.591636	−0.295818	+	0.955244i	$0.595592\pi$
$728$	15.2393	0.564805
$729$	−16.8548	−0.624254
$730$	−47.9189	−1.77356
$731$	15.0632	0.557134
$732$	−16.9911	−0.628007
$733$	31.2434	1.15400	0.577000	−	0.816744i	$-0.304223\pi$
$733$	31.2434	1.15400	0.577000	+	0.816744i	$0.304223\pi$
$734$	37.9873	1.40214
$735$	−51.8605	−1.91290
$736$	0	0
$737$	12.0538	0.444006
$738$	−28.8657	−1.06256
$739$	6.43193	0.236602	0.118301	−	0.992978i	$-0.462255\pi$
$739$	6.43193	0.236602	0.118301	+	0.992978i	$0.462255\pi$
$740$	−5.47962	−0.201435
$741$	−62.2760	−2.28777
$742$	−4.36477	−0.160236
$743$	−17.8713	−0.655635	−0.327817	−	0.944741i	$-0.606313\pi$
$743$	−17.8713	−0.655635	−0.327817	+	0.944741i	$0.606313\pi$
$744$	−0.749819	−0.0274897
$745$	−45.1515	−1.65422
$746$	37.1743	1.36105
$747$	−5.74766	−0.210296
$748$	−17.4745	−0.638929
$749$	−2.69761	−0.0985684
$750$	149.441	5.45682
$751$	43.1909	1.57606	0.788030	−	0.615637i	$-0.211101\pi$
$751$	43.1909	1.57606	0.788030	+	0.615637i	$0.211101\pi$
$752$	6.77749	0.247150
$753$	20.8929	0.761380
$754$	−116.703	−4.25007
$755$	59.7517	2.17459
$756$	4.73597	0.172246
$757$	2.32299	0.0844306	0.0422153	−	0.999109i	$-0.486558\pi$
$757$	2.32299	0.0844306	0.0422153	+	0.999109i	$0.486558\pi$
$758$	−21.3249	−0.774555
$759$	0	0
$760$	49.0223	1.77823
$761$	−20.5101	−0.743491	−0.371745	−	0.928335i	$-0.621241\pi$
$761$	−20.5101	−0.743491	−0.371745	+	0.928335i	$0.621241\pi$
$762$	−77.1624	−2.79530
$763$	−10.8152	−0.391538
$764$	−78.0462	−2.82361
$765$	58.6347	2.11994
$766$	50.0791	1.80943
$767$	−21.6881	−0.783113
$768$	−23.3987	−0.844327
$769$	−26.8326	−0.967607	−0.483803	−	0.875177i	$-0.660745\pi$
$769$	−26.8326	−0.967607	−0.483803	+	0.875177i	$0.660745\pi$
$770$	11.7158	0.422208
$771$	−5.33622	−0.192179
$772$	0.0105003	0.000377913 0
$773$	21.3624	0.768353	0.384176	−	0.923260i	$-0.374485\pi$
$773$	21.3624	0.768353	0.384176	+	0.923260i	$0.374485\pi$
$774$	14.5155	0.521748
$775$	−1.64785	−0.0591927
$776$	−22.5752	−0.810401
$777$	1.30441	0.0467953
$778$	76.4005	2.73909
$779$	−26.7295	−0.957685
$780$	−151.166	−5.41262
$781$	3.68996	0.132037
$782$	0	0
$783$	−12.3553	−0.441543
$784$	4.66337	0.166549
$785$	88.4955	3.15854
$786$	70.7567	2.52381
$787$	−0.656433	−0.0233993	−0.0116997	−	0.999932i	$-0.503724\pi$
$787$	−0.656433	−0.0233993	−0.0116997	+	0.999932i	$0.503724\pi$
$788$	−8.75500	−0.311884
$789$	20.9301	0.745130
$790$	35.4775	1.26223
$791$	10.4706	0.372292
$792$	−5.73645	−0.203836
$793$	12.3960	0.440196
$794$	−30.0130	−1.06512
$795$	14.7496	0.523114
$796$	−33.4004	−1.18384
$797$	25.1336	0.890279	0.445139	−	0.895461i	$-0.353154\pi$
$797$	25.1336	0.890279	0.445139	+	0.895461i	$0.353154\pi$
$798$	−34.2554	−1.21263
$799$	−45.1136	−1.59600
$800$	−78.4200	−2.77257
$801$	33.3302	1.17767
$802$	35.8270	1.26509
$803$	5.19238	0.183235
$804$	−85.5486	−3.01707
$805$	0	0
$806$	1.60580	0.0565618
$807$	−4.82075	−0.169698
$808$	−27.0882	−0.952959
$809$	−8.43753	−0.296648	−0.148324	−	0.988939i	$-0.547388\pi$
$809$	−8.43753	−0.296648	−0.148324	+	0.988939i	$0.547388\pi$
$810$	−95.0614	−3.34012
$811$	−40.3635	−1.41735	−0.708676	−	0.705534i	$-0.750707\pi$
$811$	−40.3635	−1.41735	−0.708676	+	0.705534i	$0.750707\pi$
$812$	−38.6861	−1.35762
$813$	23.1208	0.810880
$814$	0.985244	0.0345328
$815$	−92.7534	−3.24901
$816$	−11.6651	−0.408360
$817$	13.4413	0.470251
$818$	−12.4601	−0.435656
$819$	16.2647	0.568336
$820$	−64.8822	−2.26578
$821$	26.8251	0.936204	0.468102	−	0.883675i	$-0.344938\pi$
$821$	26.8251	0.936204	0.468102	+	0.883675i	$0.344938\pi$
$822$	−19.4253	−0.677534
$823$	26.3320	0.917876	0.458938	−	0.888468i	$-0.348230\pi$
$823$	26.3320	0.917876	0.458938	+	0.888468i	$0.348230\pi$
$824$	−14.4152	−0.502178
$825$	−27.8918	−0.971067
$826$	−11.9297	−0.415088
$827$	1.52437	0.0530076	0.0265038	−	0.999649i	$-0.491563\pi$
$827$	1.52437	0.0530076	0.0265038	+	0.999649i	$0.491563\pi$
$828$	0	0
$829$	−48.9323	−1.69949	−0.849745	−	0.527194i	$-0.823244\pi$
$829$	−48.9323	−1.69949	−0.849745	+	0.527194i	$0.823244\pi$
$830$	−21.4372	−0.744097
$831$	−33.6265	−1.16649
$832$	67.4563	2.33863
$833$	−31.0412	−1.07551
$834$	71.1616	2.46413
$835$	78.2235	2.70703
$836$	−15.5929	−0.539290
$837$	0.170006	0.00587626
$838$	−11.3877	−0.393381
$839$	1.53217	0.0528963	0.0264482	−	0.999650i	$-0.491580\pi$
$839$	1.53217	0.0528963	0.0264482	+	0.999650i	$0.491580\pi$
$840$	−28.3263	−0.977351
$841$	71.9254	2.48019
$842$	−55.4680	−1.91155
$843$	11.9453	0.411419
$844$	9.79152	0.337038
$845$	56.8096	1.95431
$846$	−43.4730	−1.49463
$847$	−1.26950	−0.0436204
$848$	−1.32630	−0.0455454
$849$	−38.5668	−1.32361
$850$	154.070	5.28456
$851$	0	0
$852$	−26.1886	−0.897207
$853$	20.7396	0.710110	0.355055	−	0.934845i	$-0.384462\pi$
$853$	20.7396	0.710110	0.355055	+	0.934845i	$0.384462\pi$
$854$	6.81852	0.233325
$855$	52.3211	1.78934
$856$	4.92638	0.168380
$857$	51.0704	1.74453	0.872266	−	0.489033i	$-0.162650\pi$
$857$	51.0704	1.74453	0.872266	+	0.489033i	$0.162650\pi$
$858$	27.1799	0.927908
$859$	24.0075	0.819124	0.409562	−	0.912282i	$-0.365682\pi$
$859$	24.0075	0.819124	0.409562	+	0.912282i	$0.365682\pi$
$860$	32.6268	1.11256
$861$	15.4450	0.526364
$862$	43.2900	1.47446
$863$	25.5164	0.868590	0.434295	−	0.900771i	$-0.356998\pi$
$863$	25.5164	0.868590	0.434295	+	0.900771i	$0.356998\pi$
$864$	8.09043	0.275242
$865$	34.1419	1.16086
$866$	19.8759	0.675410
$867$	37.8718	1.28619
$868$	0.532310	0.0180678
$869$	−3.84426	−0.130408
$870$	216.924	7.35441
$871$	62.4130	2.11478
$872$	19.7508	0.668848
$873$	−24.0943	−0.815467
$874$	0	0
$875$	−36.1415	−1.22181
$876$	−36.8516	−1.24510
$877$	18.2882	0.617549	0.308775	−	0.951135i	$-0.400081\pi$
$877$	18.2882	0.617549	0.308775	+	0.951135i	$0.400081\pi$
$878$	6.05342	0.204293
$879$	−42.4140	−1.43059
$880$	3.56003	0.120008
$881$	10.0066	0.337132	0.168566	−	0.985690i	$-0.446086\pi$
$881$	10.0066	0.337132	0.168566	+	0.985690i	$0.446086\pi$
$882$	−29.9123	−1.00720
$883$	−25.2300	−0.849057	−0.424528	−	0.905415i	$-0.639560\pi$
$883$	−25.2300	−0.849057	−0.424528	+	0.905415i	$0.639560\pi$
$884$	−90.4808	−3.04320
$885$	40.3133	1.35512
$886$	−5.82161	−0.195581
$887$	23.8744	0.801625	0.400813	−	0.916160i	$-0.368728\pi$
$887$	23.8744	0.801625	0.400813	+	0.916160i	$0.368728\pi$
$888$	−2.38211	−0.0799384
$889$	18.6613	0.625879
$890$	124.313	4.16698
$891$	10.3006	0.345084
$892$	−54.4864	−1.82434
$893$	−40.2559	−1.34711
$894$	−57.6178	−1.92703
$895$	3.12423	0.104432
$896$	20.4024	0.681596
$897$	0	0
$898$	75.5608	2.52150
$899$	−1.38870	−0.0463159
$900$	89.4739	2.98246
$901$	8.82838	0.294116
$902$	11.6659	0.388433
$903$	−7.76670	−0.258460
$904$	−19.1215	−0.635971
$905$	−1.60272	−0.0532764
$906$	76.2489	2.53320
$907$	12.8716	0.427394	0.213697	−	0.976900i	$-0.431449\pi$
$907$	12.8716	0.427394	0.213697	+	0.976900i	$0.431449\pi$
$908$	−60.0898	−1.99415
$909$	−28.9110	−0.958916
$910$	60.6631	2.01096
$911$	35.2266	1.16711	0.583555	−	0.812073i	$-0.301661\pi$
$911$	35.2266	1.16711	0.583555	+	0.812073i	$0.301661\pi$
$912$	−10.4090	−0.344677
$913$	2.32289	0.0768763
$914$	−80.5260	−2.66356
$915$	−23.0414	−0.761724
$916$	80.7398	2.66772
$917$	−17.1121	−0.565091
$918$	−15.8951	−0.524616
$919$	−7.21706	−0.238069	−0.119034	−	0.992890i	$-0.537980\pi$
$919$	−7.21706	−0.238069	−0.119034	+	0.992890i	$0.537980\pi$
$920$	0	0
$921$	−52.2076	−1.72030
$922$	42.3464	1.39461
$923$	19.1062	0.628888
$924$	9.00994	0.296405
$925$	−5.23509	−0.172129
$926$	−50.5868	−1.66239
$927$	−15.3852	−0.505317
$928$	−66.0873	−2.16942
$929$	53.8813	1.76779	0.883895	−	0.467686i	$-0.154912\pi$
$929$	53.8813	1.76779	0.883895	+	0.467686i	$0.154912\pi$
$930$	−2.98481	−0.0978758
$931$	−27.6987	−0.907789
$932$	68.1648	2.23281
$933$	−77.2345	−2.52854
$934$	−21.0366	−0.688340
$935$	−23.6969	−0.774972
$936$	−29.7027	−0.970864
$937$	−44.7379	−1.46152	−0.730761	−	0.682633i	$-0.760835\pi$
$937$	−44.7379	−1.46152	−0.730761	+	0.682633i	$0.760835\pi$
$938$	34.3307	1.12094
$939$	−29.0635	−0.948453
$940$	−97.7154	−3.18713
$941$	46.6574	1.52099	0.760494	−	0.649345i	$-0.224957\pi$
$941$	46.6574	1.52099	0.760494	+	0.649345i	$0.224957\pi$
$942$	112.929	3.67942
$943$	0	0
$944$	−3.62502	−0.117984
$945$	6.42240	0.208921
$946$	−5.86635	−0.190731
$947$	24.6900	0.802317	0.401159	−	0.916009i	$-0.368608\pi$
$947$	24.6900	0.802317	0.401159	+	0.916009i	$0.368608\pi$
$948$	27.2837	0.886133
$949$	26.8855	0.872742
$950$	137.480	4.46044
$951$	−0.0731813	−0.00237307
$952$	−16.9548	−0.549507
$953$	−10.4522	−0.338581	−0.169290	−	0.985566i	$-0.554148\pi$
$953$	−10.4522	−0.338581	−0.169290	+	0.985566i	$0.554148\pi$
$954$	8.50733	0.275435
$955$	−105.837	−3.42482
$956$	26.5005	0.857087
$957$	−23.5054	−0.759820
$958$	43.1039	1.39262
$959$	4.69789	0.151703
$960$	−125.386	−4.04681
$961$	−30.9809	−0.999384
$962$	5.10148	0.164478
$963$	5.25788	0.169433
$964$	17.0882	0.550374
$965$	0.0142393	0.000458379 0
$966$	0	0
$967$	3.99607	0.128505	0.0642524	−	0.997934i	$-0.479534\pi$
$967$	3.99607	0.128505	0.0642524	+	0.997934i	$0.479534\pi$
$968$	2.31836	0.0745148
$969$	69.2864	2.22580
$970$	−89.8651	−2.88540
$971$	−49.6389	−1.59299	−0.796493	−	0.604647i	$-0.793314\pi$
$971$	−49.6389	−1.59299	−0.796493	+	0.604647i	$0.793314\pi$
$972$	−61.9144	−1.98590
$973$	−17.2100	−0.551728
$974$	65.2481	2.09068
$975$	−144.420	−4.62516
$976$	2.07191	0.0663203
$977$	31.9209	1.02124	0.510619	−	0.859807i	$-0.329416\pi$
$977$	31.9209	1.02124	0.510619	+	0.859807i	$0.329416\pi$
$978$	−118.362	−3.78481
$979$	−13.4702	−0.430511
$980$	−67.2348	−2.14774
$981$	21.0799	0.673029
$982$	10.6587	0.340133
$983$	−31.9754	−1.01986	−0.509929	−	0.860217i	$-0.670328\pi$
$983$	−31.9754	−1.01986	−0.509929	+	0.860217i	$0.670328\pi$
$984$	−28.2057	−0.899165
$985$	−11.8726	−0.378291
$986$	129.840	4.13495
$987$	23.2608	0.740401
$988$	−80.7380	−2.56862
$989$	0	0
$990$	−22.8352	−0.725749
$991$	−16.2458	−0.516066	−0.258033	−	0.966136i	$-0.583074\pi$
$991$	−16.2458	−0.516066	−0.258033	+	0.966136i	$0.583074\pi$
$992$	0.909342	0.0288716
$993$	−79.9426	−2.53690
$994$	10.5095	0.333341
$995$	−45.2938	−1.43591
$996$	−16.4861	−0.522383
$997$	43.2306	1.36913	0.684563	−	0.728954i	$-0.259993\pi$
$997$	43.2306	1.36913	0.684563	+	0.728954i	$0.259993\pi$
$998$	75.9994	2.40572
$999$	0.540093	0.0170878

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5819.2.a.o.1.16	yes	18
23.22	odd	2		5819.2.a.n.1.16	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5819.2.a.n.1.16	✓	18	23.22	odd	2
5819.2.a.o.1.16	yes	18	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+2.24352 q^{2} +2.33974 q^{3} +3.03336 q^{4} +4.11350 q^{5} +5.24923 q^{6} -1.26950 q^{7} +2.31836 q^{8} +2.47436 q^{9} +9.22871 q^{10} -1.00000 q^{11} +7.09726 q^{12} -5.17789 q^{13} -2.84813 q^{14} +9.62451 q^{15} -0.865449 q^{16} +5.76076 q^{17} +5.55127 q^{18} +5.14046 q^{19} +12.4777 q^{20} -2.97028 q^{21} -2.24352 q^{22} +5.42434 q^{24} +11.9209 q^{25} -11.6167 q^{26} -1.22986 q^{27} -3.85084 q^{28} +10.0462 q^{29} +21.5927 q^{30} -0.138232 q^{31} -6.57836 q^{32} -2.33974 q^{33} +12.9244 q^{34} -5.22207 q^{35} +7.50563 q^{36} -0.439152 q^{37} +11.5327 q^{38} -12.1149 q^{39} +9.53657 q^{40} -5.19984 q^{41} -6.66388 q^{42} +2.61480 q^{43} -3.03336 q^{44} +10.1783 q^{45} -7.83119 q^{47} -2.02492 q^{48} -5.38838 q^{49} +26.7447 q^{50} +13.4787 q^{51} -15.7064 q^{52} +1.53250 q^{53} -2.75920 q^{54} -4.11350 q^{55} -2.94315 q^{56} +12.0273 q^{57} +22.5387 q^{58} +4.18861 q^{59} +29.1946 q^{60} -2.39403 q^{61} -0.310126 q^{62} -3.14119 q^{63} -13.0278 q^{64} -21.2993 q^{65} -5.24923 q^{66} -12.0538 q^{67} +17.4745 q^{68} -11.7158 q^{70} -3.68996 q^{71} +5.73645 q^{72} -5.19238 q^{73} -0.985244 q^{74} +27.8918 q^{75} +15.5929 q^{76} +1.26950 q^{77} -27.1799 q^{78} +3.84426 q^{79} -3.56003 q^{80} -10.3006 q^{81} -11.6659 q^{82} -2.32289 q^{83} -9.00994 q^{84} +23.6969 q^{85} +5.86635 q^{86} +23.5054 q^{87} -2.31836 q^{88} +13.4702 q^{89} +22.8352 q^{90} +6.57331 q^{91} -0.323427 q^{93} -17.5694 q^{94} +21.1453 q^{95} -15.3916 q^{96} -9.73757 q^{97} -12.0889 q^{98} -2.47436 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{2} - 2 q^{3} + 18 q^{4} + 8 q^{5} - 6 q^{6} + 10 q^{7} + 6 q^{8} + 16 q^{9} + 12 q^{10} - 18 q^{11} + 10 q^{12} + 28 q^{14} + 8 q^{15} + 26 q^{16} - 20 q^{18} + 16 q^{19} + 40 q^{20} + 12 q^{21}+ \cdots - 16 q^{99}+O(q^{100}) \) 18 * q + 2 * q^2 - 2 * q^3 + 18 * q^4 + 8 * q^5 - 6 * q^6 + 10 * q^7 + 6 * q^8 + 16 * q^9 + 12 * q^10 - 18 * q^11 + 10 * q^12 + 28 * q^14 + 8 * q^15 + 26 * q^16 - 20 * q^18 + 16 * q^19 + 40 * q^20 + 12 * q^21 - 2 * q^22 + 26 * q^24 + 6 * q^25 - 20 * q^26 - 14 * q^27 + 32 * q^28 - 12 * q^29 + 14 * q^30 + 24 * q^32 + 2 * q^33 + 24 * q^34 + 2 * q^35 - 12 * q^36 + 36 * q^37 - 8 * q^38 - 10 * q^39 + 22 * q^40 + 6 * q^41 - 4 * q^42 + 20 * q^43 - 18 * q^44 - 16 * q^45 - 36 * q^47 + 28 * q^48 + 4 * q^49 + 52 * q^50 + 44 * q^51 - 16 * q^52 + 20 * q^53 - 8 * q^54 - 8 * q^55 + 40 * q^56 + 44 * q^57 + 2 * q^58 - 32 * q^59 + 88 * q^60 + 20 * q^61 + 2 * q^63 + 10 * q^64 - 40 * q^65 + 6 * q^66 - 12 * q^68 + 14 * q^70 - 28 * q^71 - 38 * q^72 - 16 * q^73 + 40 * q^74 + 16 * q^75 + 34 * q^76 - 10 * q^77 - 72 * q^78 + 40 * q^79 + 28 * q^80 + 18 * q^81 + 24 * q^82 + 32 * q^83 - 74 * q^84 - 12 * q^85 - 20 * q^86 + 46 * q^87 - 6 * q^88 + 88 * q^89 + 32 * q^90 - 32 * q^91 - 24 * q^93 - 22 * q^94 + 58 * q^95 + 10 * q^96 + 52 * q^97 + 82 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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