LMFDB - Embedded newform 5819.2.a.o.1.14

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			1.14
Root			$1.65948$ 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)

$f(q)$	$=$	\(q+1.65948 q^{2} -1.50381 q^{3} +0.753868 q^{4} +3.61083 q^{5} -2.49554 q^{6} -1.22717 q^{7} -2.06793 q^{8} -0.738551 q^{9} +5.99209 q^{10} -1.00000 q^{11} -1.13367 q^{12} -0.261302 q^{13} -2.03646 q^{14} -5.43001 q^{15} -4.93942 q^{16} -2.31448 q^{17} -1.22561 q^{18} -5.38737 q^{19} +2.72209 q^{20} +1.84543 q^{21} -1.65948 q^{22} +3.10978 q^{24} +8.03810 q^{25} -0.433625 q^{26} +5.62208 q^{27} -0.925121 q^{28} +5.59693 q^{29} -9.01098 q^{30} +3.25729 q^{31} -4.06100 q^{32} +1.50381 q^{33} -3.84083 q^{34} -4.43109 q^{35} -0.556769 q^{36} +6.59357 q^{37} -8.94022 q^{38} +0.392949 q^{39} -7.46694 q^{40} +12.0171 q^{41} +3.06245 q^{42} -2.22896 q^{43} -0.753868 q^{44} -2.66678 q^{45} -6.33332 q^{47} +7.42796 q^{48} -5.49406 q^{49} +13.3390 q^{50} +3.48054 q^{51} -0.196987 q^{52} +10.3180 q^{53} +9.32971 q^{54} -3.61083 q^{55} +2.53769 q^{56} +8.10159 q^{57} +9.28798 q^{58} -1.16731 q^{59} -4.09351 q^{60} +12.7076 q^{61} +5.40540 q^{62} +0.906325 q^{63} +3.13970 q^{64} -0.943517 q^{65} +2.49554 q^{66} +6.81171 q^{67} -1.74481 q^{68} -7.35330 q^{70} +7.18668 q^{71} +1.52727 q^{72} +8.73391 q^{73} +10.9419 q^{74} -12.0878 q^{75} -4.06136 q^{76} +1.22717 q^{77} +0.652090 q^{78} +3.54440 q^{79} -17.8354 q^{80} -6.23889 q^{81} +19.9421 q^{82} +9.08846 q^{83} +1.39121 q^{84} -8.35720 q^{85} -3.69891 q^{86} -8.41673 q^{87} +2.06793 q^{88} +15.5343 q^{89} -4.42547 q^{90} +0.320661 q^{91} -4.89835 q^{93} -10.5100 q^{94} -19.4529 q^{95} +6.10698 q^{96} -4.43488 q^{97} -9.11728 q^{98} +0.738551 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.65948	1.17343	0.586714	−	0.809794i	$-0.300421\pi$
$2$	1.65948	1.17343	0.586714	+	0.809794i	$0.300421\pi$
$3$	−1.50381	−0.868226	−0.434113	−	0.900858i	$-0.642938\pi$
$3$	−1.50381	−0.868226	−0.434113	+	0.900858i	$0.642938\pi$
$4$	0.753868	0.376934
$5$	3.61083	1.61481	0.807406	−	0.589996i	$-0.200871\pi$
$5$	3.61083	1.61481	0.807406	+	0.589996i	$0.200871\pi$
$6$	−2.49554	−1.01880
$7$	−1.22717	−0.463825	−0.231913	−	0.972737i	$-0.574498\pi$
$7$	−1.22717	−0.463825	−0.231913	+	0.972737i	$0.574498\pi$
$8$	−2.06793	−0.731124
$9$	−0.738551	−0.246184
$10$	5.99209	1.89487
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.13367	−0.327264
$13$	−0.261302	−0.0724721	−0.0362361	−	0.999343i	$-0.511537\pi$
$13$	−0.261302	−0.0724721	−0.0362361	+	0.999343i	$0.511537\pi$
$14$	−2.03646	−0.544266
$15$	−5.43001	−1.40202
$16$	−4.93942	−1.23485
$17$	−2.31448	−0.561344	−0.280672	−	0.959804i	$-0.590557\pi$
$17$	−2.31448	−0.561344	−0.280672	+	0.959804i	$0.590557\pi$
$18$	−1.22561	−0.288879
$19$	−5.38737	−1.23595	−0.617973	−	0.786199i	$-0.712046\pi$
$19$	−5.38737	−1.23595	−0.617973	+	0.786199i	$0.712046\pi$
$20$	2.72209	0.608677
$21$	1.84543	0.402705
$22$	−1.65948	−0.353802
$23$	0	0
$23$	0	0
$24$	3.10978	0.634780
$25$	8.03810	1.60762
$26$	−0.433625	−0.0850408
$27$	5.62208	1.08197
$28$	−0.925121	−0.174831
$29$	5.59693	1.03932	0.519662	−	0.854372i	$-0.326058\pi$
$29$	5.59693	1.03932	0.519662	+	0.854372i	$0.326058\pi$
$30$	−9.01098	−1.64517
$31$	3.25729	0.585026	0.292513	−	0.956262i	$-0.405509\pi$
$31$	3.25729	0.585026	0.292513	+	0.956262i	$0.405509\pi$
$32$	−4.06100	−0.717890
$33$	1.50381	0.261780
$34$	−3.84083	−0.658697
$35$	−4.43109	−0.748991
$36$	−0.556769	−0.0927949
$37$	6.59357	1.08398	0.541988	−	0.840386i	$-0.317672\pi$
$37$	6.59357	1.08398	0.541988	+	0.840386i	$0.317672\pi$
$38$	−8.94022	−1.45029
$39$	0.392949	0.0629222
$40$	−7.46694	−1.18063
$41$	12.0171	1.87675	0.938375	−	0.345618i	$-0.112331\pi$
$41$	12.0171	1.87675	0.938375	+	0.345618i	$0.112331\pi$
$42$	3.06245	0.472546
$43$	−2.22896	−0.339913	−0.169957	−	0.985452i	$-0.554363\pi$
$43$	−2.22896	−0.339913	−0.169957	+	0.985452i	$0.554363\pi$
$44$	−0.753868	−0.113650
$45$	−2.66678	−0.397540
$46$	0	0
$47$	−6.33332	−0.923809	−0.461905	−	0.886930i	$-0.652834\pi$
$47$	−6.33332	−0.923809	−0.461905	+	0.886930i	$0.652834\pi$
$48$	7.42796	1.07213
$49$	−5.49406	−0.784866
$50$	13.3390	1.88643
$51$	3.48054	0.487373
$52$	−0.196987	−0.0273172
$53$	10.3180	1.41728	0.708642	−	0.705569i	$-0.249308\pi$
$53$	10.3180	1.41728	0.708642	+	0.705569i	$0.249308\pi$
$54$	9.32971	1.26961
$55$	−3.61083	−0.486884
$56$	2.53769	0.339114
$57$	8.10159	1.07308
$58$	9.28798	1.21957
$59$	−1.16731	−0.151971	−0.0759856	−	0.997109i	$-0.524210\pi$
$59$	−1.16731	−0.151971	−0.0759856	+	0.997109i	$0.524210\pi$
$60$	−4.09351	−0.528470
$61$	12.7076	1.62705	0.813523	−	0.581533i	$-0.197547\pi$
$61$	12.7076	1.62705	0.813523	+	0.581533i	$0.197547\pi$
$62$	5.40540	0.686486
$63$	0.906325	0.114186
$64$	3.13970	0.392463
$65$	−0.943517	−0.117029
$66$	2.49554	0.307180
$67$	6.81171	0.832183	0.416092	−	0.909323i	$-0.363400\pi$
$67$	6.81171	0.832183	0.416092	+	0.909323i	$0.363400\pi$
$68$	−1.74481	−0.211590
$69$	0	0
$70$	−7.35330	−0.878887
$71$	7.18668	0.852902	0.426451	−	0.904511i	$-0.359764\pi$
$71$	7.18668	0.852902	0.426451	+	0.904511i	$0.359764\pi$
$72$	1.52727	0.179991
$73$	8.73391	1.02223	0.511113	−	0.859513i	$-0.329233\pi$
$73$	8.73391	1.02223	0.511113	+	0.859513i	$0.329233\pi$
$74$	10.9419	1.27197
$75$	−12.0878	−1.39578
$76$	−4.06136	−0.465870
$77$	1.22717	0.139849
$78$	0.652090	0.0738346
$79$	3.54440	0.398776	0.199388	−	0.979921i	$-0.436105\pi$
$79$	3.54440	0.398776	0.199388	+	0.979921i	$0.436105\pi$
$80$	−17.8354	−1.99406
$81$	−6.23889	−0.693210
$82$	19.9421	2.20223
$83$	9.08846	0.997588	0.498794	−	0.866721i	$-0.333776\pi$
$83$	9.08846	0.997588	0.498794	+	0.866721i	$0.333776\pi$
$84$	1.39121	0.151793
$85$	−8.35720	−0.906465
$86$	−3.69891	−0.398864
$87$	−8.41673	−0.902368
$88$	2.06793	0.220442
$89$	15.5343	1.64664	0.823319	−	0.567579i	$-0.192120\pi$
$89$	15.5343	1.64664	0.823319	+	0.567579i	$0.192120\pi$
$90$	−4.42547	−0.466485
$91$	0.320661	0.0336144
$92$	0	0
$93$	−4.89835	−0.507935
$94$	−10.5100	−1.08402
$95$	−19.4529	−1.99582
$96$	6.10698	0.623291
$97$	−4.43488	−0.450294	−0.225147	−	0.974325i	$-0.572286\pi$
$97$	−4.43488	−0.450294	−0.225147	+	0.974325i	$0.572286\pi$
$98$	−9.11728	−0.920984
$99$	0.738551	0.0742271
$100$	6.05966	0.605966
$101$	−2.94301	−0.292841	−0.146420	−	0.989222i	$-0.546775\pi$
$101$	−2.94301	−0.292841	−0.146420	+	0.989222i	$0.546775\pi$
$102$	5.77588	0.571898
$103$	9.75473	0.961162	0.480581	−	0.876950i	$-0.340426\pi$
$103$	9.75473	0.961162	0.480581	+	0.876950i	$0.340426\pi$
$104$	0.540354	0.0529861
$105$	6.66352	0.650293
$106$	17.1225	1.66308
$107$	−6.47389	−0.625854	−0.312927	−	0.949777i	$-0.601310\pi$
$107$	−6.47389	−0.625854	−0.312927	+	0.949777i	$0.601310\pi$
$108$	4.23830	0.407831
$109$	−0.495246	−0.0474360	−0.0237180	−	0.999719i	$-0.507550\pi$
$109$	−0.495246	−0.0474360	−0.0237180	+	0.999719i	$0.507550\pi$
$110$	−5.99209	−0.571324
$111$	−9.91548	−0.941136
$112$	6.06149	0.572757
$113$	−6.48075	−0.609658	−0.304829	−	0.952407i	$-0.598599\pi$
$113$	−6.48075	−0.609658	−0.304829	+	0.952407i	$0.598599\pi$
$114$	13.4444	1.25918
$115$	0	0
$116$	4.21934	0.391756
$117$	0.192985	0.0178414
$118$	−1.93713	−0.178327
$119$	2.84025	0.260366
$120$	11.2289	1.02505
$121$	1.00000	0.0909091
$122$	21.0880	1.90922
$123$	−18.0714	−1.62944
$124$	2.45556	0.220516
$125$	10.9701	0.981192
$126$	1.50403	0.133989
$127$	−16.1595	−1.43392	−0.716962	−	0.697112i	$-0.754468\pi$
$127$	−16.1595	−1.43392	−0.716962	+	0.697112i	$0.754468\pi$
$128$	13.3323	1.17842
$129$	3.35193	0.295121
$130$	−1.56575	−0.137325
$131$	12.9820	1.13424	0.567120	−	0.823635i	$-0.308058\pi$
$131$	12.9820	1.13424	0.567120	+	0.823635i	$0.308058\pi$
$132$	1.13367	0.0986737
$133$	6.61120	0.573263
$134$	11.3039	0.976507
$135$	20.3004	1.74718
$136$	4.78618	0.410412
$137$	−15.8701	−1.35588	−0.677938	−	0.735119i	$-0.737126\pi$
$137$	−15.8701	−1.35588	−0.677938	+	0.735119i	$0.737126\pi$
$138$	0	0
$139$	−13.3735	−1.13433	−0.567165	−	0.823604i	$-0.691960\pi$
$139$	−13.3735	−1.13433	−0.567165	+	0.823604i	$0.691960\pi$
$140$	−3.34045	−0.282320
$141$	9.52412	0.802075
$142$	11.9261	1.00082
$143$	0.261302	0.0218512
$144$	3.64801	0.304001
$145$	20.2096	1.67831
$146$	14.4937	1.19951
$147$	8.26203	0.681441
$148$	4.97068	0.408587
$149$	14.7333	1.20700	0.603498	−	0.797365i	$-0.293773\pi$
$149$	14.7333	1.20700	0.603498	+	0.797365i	$0.293773\pi$
$150$	−20.0594	−1.63784
$151$	7.16752	0.583285	0.291642	−	0.956527i	$-0.405798\pi$
$151$	7.16752	0.583285	0.291642	+	0.956527i	$0.405798\pi$
$152$	11.1407	0.903630
$153$	1.70936	0.138194
$154$	2.03646	0.164102
$155$	11.7615	0.944707
$156$	0.296231	0.0237175
$157$	−21.6027	−1.72408	−0.862042	−	0.506837i	$-0.830814\pi$
$157$	−21.6027	−1.72408	−0.862042	+	0.506837i	$0.830814\pi$
$158$	5.88185	0.467935
$159$	−15.5163	−1.23052
$160$	−14.6636	−1.15926
$161$	0	0
$162$	−10.3533	−0.813432
$163$	−9.28152	−0.726985	−0.363493	−	0.931597i	$-0.618416\pi$
$163$	−9.28152	−0.726985	−0.363493	+	0.931597i	$0.618416\pi$
$164$	9.05928	0.707411
$165$	5.43001	0.422726
$166$	15.0821	1.17060
$167$	11.5039	0.890197	0.445099	−	0.895482i	$-0.353169\pi$
$167$	11.5039	0.890197	0.445099	+	0.895482i	$0.353169\pi$
$168$	−3.81621	−0.294427
$169$	−12.9317	−0.994748
$170$	−13.8686	−1.06367
$171$	3.97884	0.304270
$172$	−1.68034	−0.128125
$173$	−16.5378	−1.25735	−0.628674	−	0.777669i	$-0.716402\pi$
$173$	−16.5378	−1.25735	−0.628674	+	0.777669i	$0.716402\pi$
$174$	−13.9674	−1.05886
$175$	−9.86408	−0.745655
$176$	4.93942	0.372323
$177$	1.75542	0.131945
$178$	25.7789	1.93221
$179$	−24.0810	−1.79990	−0.899951	−	0.435991i	$-0.856398\pi$
$179$	−24.0810	−1.79990	−0.899951	+	0.435991i	$0.856398\pi$
$180$	−2.01040	−0.149846
$181$	−11.1797	−0.830981	−0.415491	−	0.909597i	$-0.636390\pi$
$181$	−11.1797	−0.830981	−0.415491	+	0.909597i	$0.636390\pi$
$182$	0.532130	0.0394441
$183$	−19.1099	−1.41264
$184$	0	0
$185$	23.8083	1.75042
$186$	−8.12870	−0.596025
$187$	2.31448	0.169252
$188$	−4.77448	−0.348215
$189$	−6.89922	−0.501845
$190$	−32.2816	−2.34195
$191$	−3.49949	−0.253214	−0.126607	−	0.991953i	$-0.540409\pi$
$191$	−3.49949	−0.253214	−0.126607	+	0.991953i	$0.540409\pi$
$192$	−4.72152	−0.340746
$193$	21.7972	1.56900	0.784499	−	0.620130i	$-0.212920\pi$
$193$	21.7972	1.56900	0.784499	+	0.620130i	$0.212920\pi$
$194$	−7.35958	−0.528387
$195$	1.41887	0.101608
$196$	−4.14180	−0.295843
$197$	18.5531	1.32185	0.660925	−	0.750452i	$-0.270164\pi$
$197$	18.5531	1.32185	0.660925	+	0.750452i	$0.270164\pi$
$198$	1.22561	0.0871002
$199$	16.2533	1.15217	0.576083	−	0.817391i	$-0.304580\pi$
$199$	16.2533	1.15217	0.576083	+	0.817391i	$0.304580\pi$
$200$	−16.6222	−1.17537
$201$	−10.2435	−0.722523
$202$	−4.88386	−0.343628
$203$	−6.86836	−0.482065
$204$	2.62387	0.183708
$205$	43.3916	3.03060
$206$	16.1878	1.12785
$207$	0	0
$208$	1.29068	0.0894925
$209$	5.38737	0.372652
$210$	11.0580	0.763073
$211$	−6.99965	−0.481875	−0.240938	−	0.970541i	$-0.577455\pi$
$211$	−6.99965	−0.481875	−0.240938	+	0.970541i	$0.577455\pi$
$212$	7.77839	0.534222
$213$	−10.8074	−0.740511
$214$	−10.7433	−0.734395
$215$	−8.04839	−0.548896
$216$	−11.6261	−0.791053
$217$	−3.99723	−0.271350
$218$	−0.821850	−0.0556627
$219$	−13.1342	−0.887524
$220$	−2.72209	−0.183523
$221$	0.604778	0.0406818
$222$	−16.4545	−1.10436
$223$	3.12105	0.209001	0.104500	−	0.994525i	$-0.466676\pi$
$223$	3.12105	0.209001	0.104500	+	0.994525i	$0.466676\pi$
$224$	4.98352	0.332975
$225$	−5.93654	−0.395770
$226$	−10.7547	−0.715389
$227$	−19.8734	−1.31905	−0.659523	−	0.751684i	$-0.729242\pi$
$227$	−19.8734	−1.31905	−0.659523	+	0.751684i	$0.729242\pi$
$228$	6.10752	0.404481
$229$	21.3844	1.41312	0.706560	−	0.707653i	$-0.250246\pi$
$229$	21.3844	1.41312	0.706560	+	0.707653i	$0.250246\pi$
$230$	0	0
$231$	−1.84543	−0.121420
$232$	−11.5741	−0.759874
$233$	9.25101	0.606054	0.303027	−	0.952982i	$-0.402003\pi$
$233$	9.25101	0.606054	0.303027	+	0.952982i	$0.402003\pi$
$234$	0.320254	0.0209357
$235$	−22.8685	−1.49178
$236$	−0.879999	−0.0572831
$237$	−5.33011	−0.346228
$238$	4.71334	0.305520
$239$	13.3912	0.866204	0.433102	−	0.901345i	$-0.357419\pi$
$239$	13.3912	0.866204	0.433102	+	0.901345i	$0.357419\pi$
$240$	26.8211	1.73129
$241$	−17.2886	−1.11365	−0.556827	−	0.830628i	$-0.687981\pi$
$241$	−17.2886	−1.11365	−0.556827	+	0.830628i	$0.687981\pi$
$242$	1.65948	0.106675
$243$	−7.48411	−0.480106
$244$	9.57987	0.613288
$245$	−19.8381	−1.26741
$246$	−29.9891	−1.91204
$247$	1.40773	0.0895717
$248$	−6.73584	−0.427726
$249$	−13.6673	−0.866132
$250$	18.2046	1.15136
$251$	20.4006	1.28767	0.643837	−	0.765163i	$-0.277342\pi$
$251$	20.4006	1.28767	0.643837	+	0.765163i	$0.277342\pi$
$252$	0.683249	0.0430406
$253$	0	0
$254$	−26.8163	−1.68261
$255$	12.5677	0.787017
$256$	15.8452	0.990325
$257$	−24.2625	−1.51345	−0.756726	−	0.653732i	$-0.773202\pi$
$257$	−24.2625	−1.51345	−0.756726	+	0.653732i	$0.773202\pi$
$258$	5.56246	0.346304
$259$	−8.09140	−0.502775
$260$	−0.711287	−0.0441121
$261$	−4.13362	−0.255864
$262$	21.5433	1.33095
$263$	13.9784	0.861945	0.430973	−	0.902365i	$-0.358171\pi$
$263$	13.9784	0.861945	0.430973	+	0.902365i	$0.358171\pi$
$264$	−3.10978	−0.191394
$265$	37.2565	2.28865
$266$	10.9711	0.672684
$267$	−23.3607	−1.42965
$268$	5.13513	0.313678
$269$	−4.12554	−0.251539	−0.125769	−	0.992060i	$-0.540140\pi$
$269$	−4.12554	−0.251539	−0.125769	+	0.992060i	$0.540140\pi$
$270$	33.6880	2.05019
$271$	−23.8044	−1.44602	−0.723008	−	0.690840i	$-0.757241\pi$
$271$	−23.8044	−1.44602	−0.723008	+	0.690840i	$0.757241\pi$
$272$	11.4322	0.693178
$273$	−0.482214	−0.0291849
$274$	−26.3361	−1.59102
$275$	−8.03810	−0.484716
$276$	0	0
$277$	−8.46281	−0.508481	−0.254241	−	0.967141i	$-0.581826\pi$
$277$	−8.46281	−0.508481	−0.254241	+	0.967141i	$0.581826\pi$
$278$	−22.1931	−1.33105
$279$	−2.40567	−0.144024
$280$	9.16318	0.547605
$281$	5.68815	0.339326	0.169663	−	0.985502i	$-0.445732\pi$
$281$	5.68815	0.339326	0.169663	+	0.985502i	$0.445732\pi$
$282$	15.8051	0.941178
$283$	24.9590	1.48366	0.741829	−	0.670589i	$-0.233958\pi$
$283$	24.9590	1.48366	0.741829	+	0.670589i	$0.233958\pi$
$284$	5.41780	0.321487
$285$	29.2535	1.73283
$286$	0.433625	0.0256408
$287$	−14.7469	−0.870485
$288$	2.99925	0.176733
$289$	−11.6432	−0.684893
$290$	33.5373	1.96938
$291$	6.66922	0.390957
$292$	6.58421	0.385312
$293$	12.8962	0.753407	0.376703	−	0.926334i	$-0.377058\pi$
$293$	12.8962	0.753407	0.376703	+	0.926334i	$0.377058\pi$
$294$	13.7107	0.799622
$295$	−4.21497	−0.245405
$296$	−13.6350	−0.792520
$297$	−5.62208	−0.326226
$298$	24.4495	1.41632
$299$	0	0
$300$	−9.11259	−0.526115
$301$	2.73530	0.157660
$302$	11.8943	0.684443
$303$	4.42574	0.254252
$304$	26.6105	1.52621
$305$	45.8851	2.62737
$306$	2.83665	0.162160
$307$	23.0234	1.31401	0.657007	−	0.753884i	$-0.271822\pi$
$307$	23.0234	1.31401	0.657007	+	0.753884i	$0.271822\pi$
$308$	0.925121	0.0527137
$309$	−14.6693	−0.834506
$310$	19.5180	1.10855
$311$	−29.2156	−1.65666	−0.828331	−	0.560239i	$-0.810709\pi$
$311$	−29.2156	−1.65666	−0.828331	+	0.560239i	$0.810709\pi$
$312$	−0.812590	−0.0460039
$313$	32.8856	1.85880	0.929401	−	0.369070i	$-0.120324\pi$
$313$	32.8856	1.85880	0.929401	+	0.369070i	$0.120324\pi$
$314$	−35.8492	−2.02309
$315$	3.27258	0.184389
$316$	2.67201	0.150312
$317$	8.97457	0.504062	0.252031	−	0.967719i	$-0.418902\pi$
$317$	8.97457	0.504062	0.252031	+	0.967719i	$0.418902\pi$
$318$	−25.7490	−1.44393
$319$	−5.59693	−0.313368
$320$	11.3369	0.633753
$321$	9.73550	0.543383
$322$	0	0
$323$	12.4690	0.693791
$324$	−4.70330	−0.261294
$325$	−2.10037	−0.116508
$326$	−15.4025	−0.853065
$327$	0.744757	0.0411851
$328$	−24.8505	−1.37214
$329$	7.77203	0.428486
$330$	9.01098	0.496038
$331$	23.1573	1.27284	0.636420	−	0.771343i	$-0.280415\pi$
$331$	23.1573	1.27284	0.636420	+	0.771343i	$0.280415\pi$
$332$	6.85149	0.376025
$333$	−4.86968	−0.266857
$334$	19.0904	1.04458
$335$	24.5959	1.34382
$336$	−9.11534	−0.497282
$337$	3.94062	0.214659	0.107330	−	0.994223i	$-0.465770\pi$
$337$	3.94062	0.214659	0.107330	+	0.994223i	$0.465770\pi$
$338$	−21.4599	−1.16727
$339$	9.74582	0.529321
$340$	−6.30022	−0.341677
$341$	−3.25729	−0.176392
$342$	6.60281	0.357039
$343$	15.3323	0.827866
$344$	4.60933	0.248518
$345$	0	0
$346$	−27.4442	−1.47541
$347$	26.9065	1.44442	0.722209	−	0.691675i	$-0.243127\pi$
$347$	26.9065	1.44442	0.722209	+	0.691675i	$0.243127\pi$
$348$	−6.34510	−0.340133
$349$	9.61839	0.514861	0.257430	−	0.966297i	$-0.417124\pi$
$349$	9.61839	0.514861	0.257430	+	0.966297i	$0.417124\pi$
$350$	−16.3692	−0.874972
$351$	−1.46906	−0.0784126
$352$	4.06100	0.216452
$353$	2.56552	0.136549	0.0682744	−	0.997667i	$-0.478251\pi$
$353$	2.56552	0.136549	0.0682744	+	0.997667i	$0.478251\pi$
$354$	2.91308	0.154828
$355$	25.9499	1.37728
$356$	11.7108	0.620673
$357$	−4.27121	−0.226056
$358$	−39.9620	−2.11206
$359$	12.7579	0.673337	0.336669	−	0.941623i	$-0.390700\pi$
$359$	12.7579	0.673337	0.336669	+	0.941623i	$0.390700\pi$
$360$	5.51472	0.290651
$361$	10.0237	0.527565
$362$	−18.5525	−0.975097
$363$	−1.50381	−0.0789296
$364$	0.241736	0.0126704
$365$	31.5367	1.65070
$366$	−31.7124	−1.65764
$367$	25.1126	1.31087	0.655433	−	0.755253i	$-0.272486\pi$
$367$	25.1126	1.31087	0.655433	+	0.755253i	$0.272486\pi$
$368$	0	0
$369$	−8.87522	−0.462025
$370$	39.5093	2.05399
$371$	−12.6619	−0.657372
$372$	−3.69270	−0.191458
$373$	−13.6744	−0.708035	−0.354017	−	0.935239i	$-0.615185\pi$
$373$	−13.6744	−0.708035	−0.354017	+	0.935239i	$0.615185\pi$
$374$	3.84083	0.198605
$375$	−16.4969	−0.851896
$376$	13.0969	0.675419
$377$	−1.46249	−0.0753220
$378$	−11.4491	−0.588879
$379$	6.70712	0.344522	0.172261	−	0.985051i	$-0.444893\pi$
$379$	6.70712	0.344522	0.172261	+	0.985051i	$0.444893\pi$
$380$	−14.6649	−0.752293
$381$	24.3009	1.24497
$382$	−5.80733	−0.297129
$383$	−26.0432	−1.33074	−0.665372	−	0.746512i	$-0.731727\pi$
$383$	−26.0432	−1.33074	−0.665372	+	0.746512i	$0.731727\pi$
$384$	−20.0492	−1.02313
$385$	4.43109	0.225829
$386$	36.1720	1.84111
$387$	1.64620	0.0836810
$388$	−3.34331	−0.169731
$389$	32.6351	1.65466	0.827332	−	0.561713i	$-0.189857\pi$
$389$	32.6351	1.65466	0.827332	+	0.561713i	$0.189857\pi$
$390$	2.35459	0.119229
$391$	0	0
$392$	11.3613	0.573834
$393$	−19.5224	−0.984776
$394$	30.7884	1.55110
$395$	12.7982	0.643949
$396$	0.556769	0.0279787
$397$	−19.9695	−1.00224	−0.501120	−	0.865378i	$-0.667079\pi$
$397$	−19.9695	−1.00224	−0.501120	+	0.865378i	$0.667079\pi$
$398$	26.9720	1.35198
$399$	−9.94199	−0.497722
$400$	−39.7035	−1.98518
$401$	−9.36083	−0.467458	−0.233729	−	0.972302i	$-0.575093\pi$
$401$	−9.36083	−0.467458	−0.233729	+	0.972302i	$0.575093\pi$
$402$	−16.9989	−0.847829
$403$	−0.851135	−0.0423981
$404$	−2.21864	−0.110382
$405$	−22.5276	−1.11940
$406$	−11.3979	−0.565668
$407$	−6.59357	−0.326831
$408$	−7.19752	−0.356330
$409$	1.43798	0.0711036	0.0355518	−	0.999368i	$-0.488681\pi$
$409$	1.43798	0.0711036	0.0355518	+	0.999368i	$0.488681\pi$
$410$	72.0074	3.55619
$411$	23.8657	1.17721
$412$	7.35377	0.362294
$413$	1.43249	0.0704881
$414$	0	0
$415$	32.8169	1.61092
$416$	1.06115	0.0520270
$417$	20.1113	0.984854
$418$	8.94022	0.437280
$419$	−1.58881	−0.0776182	−0.0388091	−	0.999247i	$-0.512356\pi$
$419$	−1.58881	−0.0776182	−0.0388091	+	0.999247i	$0.512356\pi$
$420$	5.02341	0.245118
$421$	9.26391	0.451495	0.225748	−	0.974186i	$-0.427518\pi$
$421$	9.26391	0.451495	0.225748	+	0.974186i	$0.427518\pi$
$422$	−11.6158	−0.565446
$423$	4.67748	0.227427
$424$	−21.3369	−1.03621
$425$	−18.6040	−0.902428
$426$	−17.9347	−0.868937
$427$	−15.5944	−0.754665
$428$	−4.88045	−0.235906
$429$	−0.392949	−0.0189717
$430$	−13.3561	−0.644090
$431$	9.66062	0.465336	0.232668	−	0.972556i	$-0.425255\pi$
$431$	9.66062	0.465336	0.232668	+	0.972556i	$0.425255\pi$
$432$	−27.7698	−1.33607
$433$	−5.83436	−0.280382	−0.140191	−	0.990125i	$-0.544772\pi$
$433$	−5.83436	−0.280382	−0.140191	+	0.990125i	$0.544772\pi$
$434$	−6.63332	−0.318410
$435$	−30.3914	−1.45716
$436$	−0.373350	−0.0178802
$437$	0	0
$438$	−21.7958	−1.04145
$439$	−33.1940	−1.58426	−0.792131	−	0.610351i	$-0.791028\pi$
$439$	−33.1940	−1.58426	−0.792131	+	0.610351i	$0.791028\pi$
$440$	7.46694	0.355973
$441$	4.05764	0.193221
$442$	1.00362	0.0477371
$443$	−10.5814	−0.502739	−0.251369	−	0.967891i	$-0.580881\pi$
$443$	−10.5814	−0.502739	−0.251369	+	0.967891i	$0.580881\pi$
$444$	−7.47496	−0.354746
$445$	56.0919	2.65901
$446$	5.17931	0.245247
$447$	−22.1560	−1.04794
$448$	−3.85293	−0.182034
$449$	35.6265	1.68132	0.840660	−	0.541563i	$-0.182167\pi$
$449$	35.6265	1.68132	0.840660	+	0.541563i	$0.182167\pi$
$450$	−9.85156	−0.464407
$451$	−12.0171	−0.565862
$452$	−4.88563	−0.229801
$453$	−10.7786	−0.506423
$454$	−32.9795	−1.54781
$455$	1.15785	0.0542809
$456$	−16.7535	−0.784555
$457$	−3.18967	−0.149206	−0.0746032	−	0.997213i	$-0.523769\pi$
$457$	−3.18967	−0.149206	−0.0746032	+	0.997213i	$0.523769\pi$
$458$	35.4869	1.65819
$459$	−13.0122	−0.607357
$460$	0	0
$461$	−11.0291	−0.513674	−0.256837	−	0.966455i	$-0.582680\pi$
$461$	−11.0291	−0.513674	−0.256837	+	0.966455i	$0.582680\pi$
$462$	−3.06245	−0.142478
$463$	35.3750	1.64402	0.822009	−	0.569475i	$-0.192854\pi$
$463$	35.3750	1.64402	0.822009	+	0.569475i	$0.192854\pi$
$464$	−27.6456	−1.28341
$465$	−17.6871	−0.820219
$466$	15.3518	0.711160
$467$	−16.4405	−0.760775	−0.380387	−	0.924827i	$-0.624209\pi$
$467$	−16.4405	−0.760775	−0.380387	+	0.924827i	$0.624209\pi$
$468$	0.145485	0.00672504
$469$	−8.35911	−0.385988
$470$	−37.9498	−1.75050
$471$	32.4864	1.49689
$472$	2.41392	0.111110
$473$	2.22896	0.102488
$474$	−8.84520	−0.406273
$475$	−43.3042	−1.98693
$476$	2.14117	0.0981406
$477$	−7.62035	−0.348912
$478$	22.2224	1.01643
$479$	17.3631	0.793342	0.396671	−	0.917961i	$-0.370165\pi$
$479$	17.3631	0.793342	0.396671	+	0.917961i	$0.370165\pi$
$480$	22.0513	1.00650
$481$	−1.72291	−0.0785580
$482$	−28.6900	−1.30679
$483$	0	0
$484$	0.753868	0.0342667
$485$	−16.0136	−0.727140
$486$	−12.4197	−0.563370
$487$	−3.65322	−0.165543	−0.0827717	−	0.996569i	$-0.526377\pi$
$487$	−3.65322	−0.165543	−0.0827717	+	0.996569i	$0.526377\pi$
$488$	−26.2785	−1.18957
$489$	13.9577	0.631187
$490$	−32.9209	−1.48722
$491$	−12.5694	−0.567251	−0.283626	−	0.958935i	$-0.591537\pi$
$491$	−12.5694	−0.567251	−0.283626	+	0.958935i	$0.591537\pi$
$492$	−13.6234	−0.614192
$493$	−12.9540	−0.583418
$494$	2.33610	0.105106
$495$	2.66678	0.119863
$496$	−16.0891	−0.722422
$497$	−8.81925	−0.395597
$498$	−22.6806	−1.01634
$499$	−14.9934	−0.671197	−0.335598	−	0.942005i	$-0.608938\pi$
$499$	−14.9934	−0.671197	−0.335598	+	0.942005i	$0.608938\pi$
$500$	8.26997	0.369844
$501$	−17.2997	−0.772892
$502$	33.8543	1.51099
$503$	41.1688	1.83563	0.917813	−	0.397012i	$-0.129953\pi$
$503$	41.1688	1.83563	0.917813	+	0.397012i	$0.129953\pi$
$504$	−1.87422	−0.0834842
$505$	−10.6267	−0.472883
$506$	0	0
$507$	19.4469	0.863666
$508$	−12.1821	−0.540494
$509$	−9.72276	−0.430954	−0.215477	−	0.976509i	$-0.569131\pi$
$509$	−9.72276	−0.430954	−0.215477	+	0.976509i	$0.569131\pi$
$510$	20.8557	0.923508
$511$	−10.7180	−0.474135
$512$	−0.369770	−0.0163417
$513$	−30.2882	−1.33726
$514$	−40.2631	−1.77593
$515$	35.2227	1.55210
$516$	2.52691	0.111241
$517$	6.33332	0.278539
$518$	−13.4275	−0.589971
$519$	24.8698	1.09166
$520$	1.95113	0.0855626
$521$	29.0991	1.27485	0.637427	−	0.770511i	$-0.279999\pi$
$521$	29.0991	1.27485	0.637427	+	0.770511i	$0.279999\pi$
$522$	−6.85965	−0.300239
$523$	−18.7217	−0.818641	−0.409320	−	0.912391i	$-0.634234\pi$
$523$	−18.7217	−0.818641	−0.409320	+	0.912391i	$0.634234\pi$
$524$	9.78668	0.427533
$525$	14.8337	0.647397
$526$	23.1969	1.01143
$527$	−7.53893	−0.328401
$528$	−7.42796	−0.323260
$529$	0	0
$530$	61.8263	2.68556
$531$	0.862120	0.0374128
$532$	4.98397	0.216082
$533$	−3.14008	−0.136012
$534$	−38.7666	−1.67760
$535$	−23.3761	−1.01064
$536$	−14.0861	−0.608429
$537$	36.2134	1.56272
$538$	−6.84624	−0.295162
$539$	5.49406	0.236646
$540$	15.3038	0.658570
$541$	6.35560	0.273248	0.136624	−	0.990623i	$-0.456375\pi$
$541$	6.35560	0.273248	0.136624	+	0.990623i	$0.456375\pi$
$542$	−39.5029	−1.69680
$543$	16.8122	0.721479
$544$	9.39910	0.402983
$545$	−1.78825	−0.0766002
$546$	−0.800223	−0.0342464
$547$	−5.81838	−0.248776	−0.124388	−	0.992234i	$-0.539697\pi$
$547$	−5.81838	−0.248776	−0.124388	+	0.992234i	$0.539697\pi$
$548$	−11.9640	−0.511075
$549$	−9.38523	−0.400552
$550$	−13.3390	−0.568779
$551$	−30.1527	−1.28455
$552$	0	0
$553$	−4.34957	−0.184962
$554$	−14.0439	−0.596666
$555$	−35.8031	−1.51976
$556$	−10.0819	−0.427567
$557$	7.56062	0.320354	0.160177	−	0.987088i	$-0.448794\pi$
$557$	7.56062	0.320354	0.160177	+	0.987088i	$0.448794\pi$
$558$	−3.99216	−0.169002
$559$	0.582431	0.0246342
$560$	21.8870	0.924895
$561$	−3.48054	−0.146949
$562$	9.43936	0.398175
$563$	−14.4117	−0.607382	−0.303691	−	0.952771i	$-0.598219\pi$
$563$	−14.4117	−0.607382	−0.303691	+	0.952771i	$0.598219\pi$
$564$	7.17992	0.302329
$565$	−23.4009	−0.984483
$566$	41.4189	1.74097
$567$	7.65616	0.321528
$568$	−14.8615	−0.623576
$569$	7.66093	0.321163	0.160581	−	0.987023i	$-0.448663\pi$
$569$	7.66093	0.321163	0.160581	+	0.987023i	$0.448663\pi$
$570$	48.5455	2.03335
$571$	35.0411	1.46643	0.733213	−	0.679999i	$-0.238020\pi$
$571$	35.0411	1.46643	0.733213	+	0.679999i	$0.238020\pi$
$572$	0.196987	0.00823644
$573$	5.26258	0.219847
$574$	−24.4722	−1.02145
$575$	0	0
$576$	−2.31883	−0.0966178
$577$	−41.6118	−1.73232	−0.866161	−	0.499766i	$-0.833419\pi$
$577$	−41.6118	−1.73232	−0.866161	+	0.499766i	$0.833419\pi$
$578$	−19.3216	−0.803673
$579$	−32.7789	−1.36225
$580$	15.2353	0.632613
$581$	−11.1530	−0.462706
$582$	11.0674	0.458760
$583$	−10.3180	−0.427327
$584$	−18.0611	−0.747374
$585$	0.696835	0.0288106
$586$	21.4010	0.884069
$587$	1.89646	0.0782752	0.0391376	−	0.999234i	$-0.487539\pi$
$587$	1.89646	0.0782752	0.0391376	+	0.999234i	$0.487539\pi$
$588$	6.22848	0.256858
$589$	−17.5482	−0.723061
$590$	−6.99465	−0.287965
$591$	−27.9003	−1.14766
$592$	−32.5684	−1.33855
$593$	20.6381	0.847504	0.423752	−	0.905778i	$-0.360713\pi$
$593$	20.6381	0.847504	0.423752	+	0.905778i	$0.360713\pi$
$594$	−9.32971	−0.382803
$595$	10.2557	0.420442
$596$	11.1069	0.454957
$597$	−24.4419	−1.00034
$598$	0	0
$599$	37.7532	1.54256	0.771278	−	0.636499i	$-0.219618\pi$
$599$	37.7532	1.54256	0.771278	+	0.636499i	$0.219618\pi$
$600$	24.9967	1.02049
$601$	−28.1039	−1.14638	−0.573190	−	0.819422i	$-0.694294\pi$
$601$	−28.1039	−1.14638	−0.573190	+	0.819422i	$0.694294\pi$
$602$	4.53918	0.185003
$603$	−5.03080	−0.204870
$604$	5.40336	0.219860
$605$	3.61083	0.146801
$606$	7.34441	0.298346
$607$	−31.7222	−1.28756	−0.643782	−	0.765209i	$-0.722636\pi$
$607$	−31.7222	−1.28756	−0.643782	+	0.765209i	$0.722636\pi$
$608$	21.8781	0.887274
$609$	10.3287	0.418541
$610$	76.1453	3.08303
$611$	1.65491	0.0669504
$612$	1.28863	0.0520899
$613$	33.9107	1.36964	0.684820	−	0.728712i	$-0.259881\pi$
$613$	33.9107	1.36964	0.684820	+	0.728712i	$0.259881\pi$
$614$	38.2068	1.54190
$615$	−65.2528	−2.63125
$616$	−2.53769	−0.102247
$617$	−41.8698	−1.68562	−0.842808	−	0.538215i	$-0.819099\pi$
$617$	−41.8698	−1.68562	−0.842808	+	0.538215i	$0.819099\pi$
$618$	−24.3433	−0.979233
$619$	−39.9272	−1.60481	−0.802405	−	0.596779i	$-0.796447\pi$
$619$	−39.9272	−1.60481	−0.802405	+	0.596779i	$0.796447\pi$
$620$	8.86662	0.356092
$621$	0	0
$622$	−48.4826	−1.94397
$623$	−19.0632	−0.763752
$624$	−1.94094	−0.0776997
$625$	−0.579475	−0.0231790
$626$	54.5729	2.18117
$627$	−8.10159	−0.323546
$628$	−16.2856	−0.649865
$629$	−15.2607	−0.608483
$630$	5.43078	0.216368
$631$	−10.1103	−0.402485	−0.201243	−	0.979541i	$-0.564498\pi$
$631$	−10.1103	−0.402485	−0.201243	+	0.979541i	$0.564498\pi$
$632$	−7.32957	−0.291555
$633$	10.5261	0.418377
$634$	14.8931	0.591480
$635$	−58.3492	−2.31552
$636$	−11.6972	−0.463825
$637$	1.43561	0.0568809
$638$	−9.28798	−0.367715
$639$	−5.30773	−0.209970
$640$	48.1405	1.90292
$641$	4.22253	0.166780	0.0833899	−	0.996517i	$-0.473425\pi$
$641$	4.22253	0.166780	0.0833899	+	0.996517i	$0.473425\pi$
$642$	16.1559	0.637621
$643$	19.7176	0.777587	0.388793	−	0.921325i	$-0.372892\pi$
$643$	19.7176	0.777587	0.388793	+	0.921325i	$0.372892\pi$
$644$	0	0
$645$	12.1033	0.476566
$646$	20.6920	0.814114
$647$	2.48402	0.0976567	0.0488284	−	0.998807i	$-0.484451\pi$
$647$	2.48402	0.0976567	0.0488284	+	0.998807i	$0.484451\pi$
$648$	12.9016	0.506822
$649$	1.16731	0.0458210
$650$	−3.48552	−0.136713
$651$	6.01109	0.235593
$652$	−6.99704	−0.274025
$653$	16.0793	0.629232	0.314616	−	0.949219i	$-0.398124\pi$
$653$	16.0793	0.629232	0.314616	+	0.949219i	$0.398124\pi$
$654$	1.23591	0.0483278
$655$	46.8757	1.83158
$656$	−59.3573	−2.31751
$657$	−6.45043	−0.251655
$658$	12.8975	0.502798
$659$	34.5728	1.34677	0.673383	−	0.739294i	$-0.264841\pi$
$659$	34.5728	1.34677	0.673383	+	0.739294i	$0.264841\pi$
$660$	4.09351	0.159340
$661$	1.72585	0.0671276	0.0335638	−	0.999437i	$-0.489314\pi$
$661$	1.72585	0.0671276	0.0335638	+	0.999437i	$0.489314\pi$
$662$	38.4290	1.49359
$663$	−0.909472	−0.0353210
$664$	−18.7943	−0.729360
$665$	23.8719	0.925713
$666$	−8.08113	−0.313138
$667$	0	0
$668$	8.67240	0.335545
$669$	−4.69347	−0.181460
$670$	40.8164	1.57688
$671$	−12.7076	−0.490573
$672$	−7.49428	−0.289098
$673$	28.7328	1.10757	0.553785	−	0.832660i	$-0.313183\pi$
$673$	28.7328	1.10757	0.553785	+	0.832660i	$0.313183\pi$
$674$	6.53938	0.251887
$675$	45.1908	1.73939
$676$	−9.74880	−0.374954
$677$	−28.2216	−1.08464	−0.542321	−	0.840171i	$-0.682454\pi$
$677$	−28.2216	−1.08464	−0.542321	+	0.840171i	$0.682454\pi$
$678$	16.1730	0.621120
$679$	5.44233	0.208858
$680$	17.2821	0.662738
$681$	29.8859	1.14523
$682$	−5.40540	−0.206983
$683$	−42.9010	−1.64156	−0.820780	−	0.571244i	$-0.806461\pi$
$683$	−42.9010	−1.64156	−0.820780	+	0.571244i	$0.806461\pi$
$684$	2.99952	0.114690
$685$	−57.3043	−2.18948
$686$	25.4436	0.971441
$687$	−32.1581	−1.22691
$688$	11.0098	0.419743
$689$	−2.69611	−0.102713
$690$	0	0
$691$	−30.2650	−1.15133	−0.575667	−	0.817684i	$-0.695257\pi$
$691$	−30.2650	−1.15133	−0.575667	+	0.817684i	$0.695257\pi$
$692$	−12.4673	−0.473937
$693$	−0.906325	−0.0344284
$694$	44.6508	1.69492
$695$	−48.2896	−1.83173
$696$	17.4052	0.659742
$697$	−27.8133	−1.05350
$698$	15.9615	0.604152
$699$	−13.9118	−0.526192
$700$	−7.43621	−0.281062
$701$	−5.81299	−0.219553	−0.109777	−	0.993956i	$-0.535014\pi$
$701$	−5.81299	−0.219553	−0.109777	+	0.993956i	$0.535014\pi$
$702$	−2.43787	−0.0920115
$703$	−35.5220	−1.33974
$704$	−3.13970	−0.118332
$705$	34.3900	1.29520
$706$	4.25742	0.160230
$707$	3.61157	0.135827
$708$	1.32335	0.0497347
$709$	−27.6343	−1.03783	−0.518914	−	0.854827i	$-0.673663\pi$
$709$	−27.6343	−1.03783	−0.518914	+	0.854827i	$0.673663\pi$
$710$	43.0632	1.61613
$711$	−2.61772	−0.0981721
$712$	−32.1239	−1.20390
$713$	0	0
$714$	−7.08797	−0.265261
$715$	0.943517	0.0352855
$716$	−18.1539	−0.678444
$717$	−20.1378	−0.752061
$718$	21.1715	0.790113
$719$	0.140300	0.00523232	0.00261616	−	0.999997i	$-0.499167\pi$
$719$	0.140300	0.00523232	0.00261616	+	0.999997i	$0.499167\pi$
$720$	13.1724	0.490905
$721$	−11.9707	−0.445811
$722$	16.6342	0.619059
$723$	25.9987	0.966903
$724$	−8.42802	−0.313225
$725$	44.9887	1.67084
$726$	−2.49554	−0.0926183
$727$	−1.23728	−0.0458882	−0.0229441	−	0.999737i	$-0.507304\pi$
$727$	−1.23728	−0.0458882	−0.0229441	+	0.999737i	$0.507304\pi$
$728$	−0.663104	−0.0245763
$729$	29.9714	1.11005
$730$	52.3344	1.93698
$731$	5.15888	0.190808
$732$	−14.4063	−0.532473
$733$	11.2573	0.415798	0.207899	−	0.978150i	$-0.433338\pi$
$733$	11.2573	0.415798	0.207899	+	0.978150i	$0.433338\pi$
$734$	41.6738	1.53821
$735$	29.8328	1.10040
$736$	0	0
$737$	−6.81171	−0.250913
$738$	−14.7282	−0.542153
$739$	15.4480	0.568263	0.284132	−	0.958785i	$-0.408295\pi$
$739$	15.4480	0.568263	0.284132	+	0.958785i	$0.408295\pi$
$740$	17.9483	0.659792
$741$	−2.11696	−0.0777685
$742$	−21.0121	−0.771379
$743$	39.6903	1.45610	0.728048	−	0.685526i	$-0.240428\pi$
$743$	39.6903	1.45610	0.728048	+	0.685526i	$0.240428\pi$
$744$	10.1294	0.371363
$745$	53.1993	1.94907
$746$	−22.6924	−0.830828
$747$	−6.71229	−0.245590
$748$	1.74481	0.0637966
$749$	7.94453	0.290287
$750$	−27.3762	−0.999639
$751$	−46.4677	−1.69563	−0.847815	−	0.530292i	$-0.822082\pi$
$751$	−46.4677	−1.69563	−0.847815	+	0.530292i	$0.822082\pi$
$752$	31.2829	1.14077
$753$	−30.6786	−1.11799
$754$	−2.42697	−0.0883849
$755$	25.8807	0.941896
$756$	−5.20110	−0.189162
$757$	23.2626	0.845494	0.422747	−	0.906248i	$-0.361066\pi$
$757$	23.2626	0.845494	0.422747	+	0.906248i	$0.361066\pi$
$758$	11.1303	0.404272
$759$	0	0
$760$	40.2272	1.45919
$761$	47.4948	1.72168	0.860842	−	0.508872i	$-0.169937\pi$
$761$	47.4948	1.72168	0.860842	+	0.508872i	$0.169937\pi$
$762$	40.3267	1.46088
$763$	0.607749	0.0220020
$764$	−2.63815	−0.0954451
$765$	6.17221	0.223157
$766$	−43.2181	−1.56153
$767$	0.305021	0.0110137
$768$	−23.8282	−0.859826
$769$	2.72132	0.0981333	0.0490666	−	0.998796i	$-0.484375\pi$
$769$	2.72132	0.0981333	0.0490666	+	0.998796i	$0.484375\pi$
$770$	7.35330	0.264994
$771$	36.4862	1.31402
$772$	16.4322	0.591409
$773$	−11.0335	−0.396848	−0.198424	−	0.980116i	$-0.563582\pi$
$773$	−11.0335	−0.396848	−0.198424	+	0.980116i	$0.563582\pi$
$774$	2.73183	0.0981937
$775$	26.1824	0.940499
$776$	9.17102	0.329220
$777$	12.1679	0.436523
$778$	54.1572	1.94163
$779$	−64.7404	−2.31956
$780$	1.06964	0.0382993
$781$	−7.18668	−0.257160
$782$	0	0
$783$	31.4664	1.12452
$784$	27.1375	0.969196
$785$	−78.0037	−2.78407
$786$	−32.3970	−1.15556
$787$	23.3791	0.833374	0.416687	−	0.909050i	$-0.363191\pi$
$787$	23.3791	0.833374	0.416687	+	0.909050i	$0.363191\pi$
$788$	13.9865	0.498250
$789$	−21.0209	−0.748363
$790$	21.2384	0.755627
$791$	7.95296	0.282775
$792$	−1.52727	−0.0542692
$793$	−3.32053	−0.117915
$794$	−33.1389	−1.17606
$795$	−56.0267	−1.98706
$796$	12.2528	0.434291
$797$	2.29001	0.0811165	0.0405582	−	0.999177i	$-0.487086\pi$
$797$	2.29001	0.0811165	0.0405582	+	0.999177i	$0.487086\pi$
$798$	−16.4985	−0.584041
$799$	14.6583	0.518575
$800$	−32.6427	−1.15409
$801$	−11.4729	−0.405375
$802$	−15.5341	−0.548528
$803$	−8.73391	−0.308213
$804$	−7.72227	−0.272343
$805$	0	0
$806$	−1.41244	−0.0497511
$807$	6.20403	0.218392
$808$	6.08594	0.214103
$809$	21.0789	0.741093	0.370546	−	0.928814i	$-0.379170\pi$
$809$	21.0789	0.741093	0.370546	+	0.928814i	$0.379170\pi$
$810$	−37.3840	−1.31354
$811$	1.57138	0.0551787	0.0275893	−	0.999619i	$-0.491217\pi$
$811$	1.57138	0.0551787	0.0275893	+	0.999619i	$0.491217\pi$
$812$	−5.17784	−0.181706
$813$	35.7974	1.25547
$814$	−10.9419	−0.383513
$815$	−33.5140	−1.17394
$816$	−17.1919	−0.601835
$817$	12.0082	0.420115
$818$	2.38630	0.0834350
$819$	−0.236824	−0.00827531
$820$	32.7115	1.14234
$821$	−11.5678	−0.403718	−0.201859	−	0.979415i	$-0.564698\pi$
$821$	−11.5678	−0.403718	−0.201859	+	0.979415i	$0.564698\pi$
$822$	39.6045	1.38137
$823$	−47.2465	−1.64691	−0.823454	−	0.567383i	$-0.807956\pi$
$823$	−47.2465	−1.64691	−0.823454	+	0.567383i	$0.807956\pi$
$824$	−20.1721	−0.702728
$825$	12.0878	0.420843
$826$	2.37718	0.0827127
$827$	−34.2977	−1.19265	−0.596325	−	0.802743i	$-0.703373\pi$
$827$	−34.2977	−1.19265	−0.596325	+	0.802743i	$0.703373\pi$
$828$	0	0
$829$	5.77394	0.200537	0.100269	−	0.994960i	$-0.468030\pi$
$829$	5.77394	0.200537	0.100269	+	0.994960i	$0.468030\pi$
$830$	54.4589	1.89030
$831$	12.7265	0.441477
$832$	−0.820410	−0.0284426
$833$	12.7159	0.440580
$834$	33.3743	1.15566
$835$	41.5386	1.43750
$836$	4.06136	0.140465
$837$	18.3127	0.632980
$838$	−2.63659	−0.0910794
$839$	−16.3933	−0.565959	−0.282979	−	0.959126i	$-0.591323\pi$
$839$	−16.3933	−0.565959	−0.282979	+	0.959126i	$0.591323\pi$
$840$	−13.7797	−0.475445
$841$	2.32563	0.0801940
$842$	15.3733	0.529797
$843$	−8.55390	−0.294612
$844$	−5.27680	−0.181635
$845$	−46.6943	−1.60633
$846$	7.76217	0.266869
$847$	−1.22717	−0.0421659
$848$	−50.9648	−1.75014
$849$	−37.5336	−1.28815
$850$	−30.8730	−1.05893
$851$	0	0
$852$	−8.14735	−0.279124
$853$	20.2698	0.694024	0.347012	−	0.937861i	$-0.387196\pi$
$853$	20.2698	0.694024	0.347012	+	0.937861i	$0.387196\pi$
$854$	−25.8785	−0.885545
$855$	14.3669	0.491339
$856$	13.3875	0.457577
$857$	33.6350	1.14895	0.574474	−	0.818523i	$-0.305207\pi$
$857$	33.6350	1.14895	0.574474	+	0.818523i	$0.305207\pi$
$858$	−0.652090	−0.0222620
$859$	−3.47103	−0.118430	−0.0592150	−	0.998245i	$-0.518860\pi$
$859$	−3.47103	−0.118430	−0.0592150	+	0.998245i	$0.518860\pi$
$860$	−6.06742	−0.206897
$861$	22.1766	0.755777
$862$	16.0316	0.546038
$863$	43.7807	1.49031	0.745157	−	0.666890i	$-0.232375\pi$
$863$	43.7807	1.49031	0.745157	+	0.666890i	$0.232375\pi$
$864$	−22.8312	−0.776735
$865$	−59.7153	−2.03038
$866$	−9.68200	−0.329008
$867$	17.5091	0.594642
$868$	−3.01338	−0.102281
$869$	−3.54440	−0.120236
$870$	−50.4338	−1.70987
$871$	−1.77991	−0.0603101
$872$	1.02413	0.0346815
$873$	3.27538	0.110855
$874$	0	0
$875$	−13.4621	−0.455102
$876$	−9.90141	−0.334538
$877$	−24.3526	−0.822329	−0.411164	−	0.911561i	$-0.634878\pi$
$877$	−24.3526	−0.822329	−0.411164	+	0.911561i	$0.634878\pi$
$878$	−55.0847	−1.85902
$879$	−19.3935	−0.654127
$880$	17.8354	0.601231
$881$	−37.4048	−1.26020	−0.630099	−	0.776514i	$-0.716986\pi$
$881$	−37.4048	−1.26020	−0.630099	+	0.776514i	$0.716986\pi$
$882$	6.73357	0.226731
$883$	34.5573	1.16295	0.581474	−	0.813565i	$-0.302476\pi$
$883$	34.5573	1.16295	0.581474	+	0.813565i	$0.302476\pi$
$884$	0.455923	0.0153343
$885$	6.33852	0.213067
$886$	−17.5596	−0.589928
$887$	12.6855	0.425938	0.212969	−	0.977059i	$-0.431687\pi$
$887$	12.6855	0.425938	0.212969	+	0.977059i	$0.431687\pi$
$888$	20.5045	0.688087
$889$	19.8304	0.665090
$890$	93.0833	3.12016
$891$	6.23889	0.209011
$892$	2.35286	0.0787794
$893$	34.1199	1.14178
$894$	−36.7675	−1.22969
$895$	−86.9526	−2.90650
$896$	−16.3609	−0.546579
$897$	0	0
$898$	59.1215	1.97291
$899$	18.2308	0.608031
$900$	−4.47537	−0.149179
$901$	−23.8808	−0.795583
$902$	−19.9421	−0.663998
$903$	−4.11338	−0.136885
$904$	13.4017	0.445735
$905$	−40.3680	−1.34188
$906$	−17.8869	−0.594251
$907$	24.0158	0.797432	0.398716	−	0.917074i	$-0.369456\pi$
$907$	24.0158	0.797432	0.398716	+	0.917074i	$0.369456\pi$
$908$	−14.9819	−0.497193
$909$	2.17356	0.0720926
$910$	1.92143	0.0636948
$911$	−11.6748	−0.386803	−0.193401	−	0.981120i	$-0.561952\pi$
$911$	−11.6748	−0.386803	−0.193401	+	0.981120i	$0.561952\pi$
$912$	−40.0171	−1.32510
$913$	−9.08846	−0.300784
$914$	−5.29318	−0.175083
$915$	−69.0025	−2.28115
$916$	16.1210	0.532652
$917$	−15.9310	−0.526089
$918$	−21.5934	−0.712690
$919$	37.0295	1.22149	0.610745	−	0.791827i	$-0.290870\pi$
$919$	37.0295	1.22149	0.610745	+	0.791827i	$0.290870\pi$
$920$	0	0
$921$	−34.6228	−1.14086
$922$	−18.3025	−0.602760
$923$	−1.87789	−0.0618116
$924$	−1.39121	−0.0457674
$925$	52.9997	1.74262
$926$	58.7041	1.92914
$927$	−7.20436	−0.236622
$928$	−22.7291	−0.746120
$929$	57.6308	1.89080	0.945402	−	0.325906i	$-0.105669\pi$
$929$	57.6308	1.89080	0.945402	+	0.325906i	$0.105669\pi$
$930$	−29.3513	−0.962469
$931$	29.5985	0.970053
$932$	6.97403	0.228442
$933$	43.9347	1.43836
$934$	−27.2826	−0.892715
$935$	8.35720	0.273310
$936$	−0.399079	−0.0130443
$937$	13.8380	0.452066	0.226033	−	0.974120i	$-0.427424\pi$
$937$	13.8380	0.452066	0.226033	+	0.974120i	$0.427424\pi$
$938$	−13.8718	−0.452929
$939$	−49.4537	−1.61386
$940$	−17.2398	−0.562302
$941$	4.13711	0.134866	0.0674329	−	0.997724i	$-0.478519\pi$
$941$	4.13711	0.134866	0.0674329	+	0.997724i	$0.478519\pi$
$942$	53.9105	1.75650
$943$	0	0
$944$	5.76585	0.187662
$945$	−24.9119	−0.810385
$946$	3.69891	0.120262
$947$	−37.6578	−1.22371	−0.611857	−	0.790968i	$-0.709577\pi$
$947$	−37.6578	−1.22371	−0.611857	+	0.790968i	$0.709577\pi$
$948$	−4.01820	−0.130505
$949$	−2.28219	−0.0740829
$950$	−71.8624	−2.33152
$951$	−13.4961	−0.437640
$952$	−5.87344	−0.190359
$953$	3.53082	0.114374	0.0571872	−	0.998363i	$-0.481787\pi$
$953$	3.53082	0.114374	0.0571872	+	0.998363i	$0.481787\pi$
$954$	−12.6458	−0.409423
$955$	−12.6361	−0.408894
$956$	10.0952	0.326501
$957$	8.41673	0.272074
$958$	28.8137	0.930929
$959$	19.4753	0.628889
$960$	−17.0486	−0.550241
$961$	−20.3901	−0.657745
$962$	−2.85913	−0.0921822
$963$	4.78129	0.154075
$964$	−13.0333	−0.419774
$965$	78.7061	2.53364
$966$	0	0
$967$	−40.5667	−1.30454	−0.652268	−	0.757989i	$-0.726182\pi$
$967$	−40.5667	−1.30454	−0.652268	+	0.757989i	$0.726182\pi$
$968$	−2.06793	−0.0664658
$969$	−18.7510	−0.602368
$970$	−26.5742	−0.853246
$971$	27.8461	0.893625	0.446812	−	0.894628i	$-0.352559\pi$
$971$	27.8461	0.893625	0.446812	+	0.894628i	$0.352559\pi$
$972$	−5.64203	−0.180968
$973$	16.4116	0.526131
$974$	−6.06244	−0.194253
$975$	3.15856	0.101155
$976$	−62.7683	−2.00916
$977$	−8.54673	−0.273434	−0.136717	−	0.990610i	$-0.543655\pi$
$977$	−8.54673	−0.273434	−0.136717	+	0.990610i	$0.543655\pi$
$978$	23.1624	0.740653
$979$	−15.5343	−0.496480
$980$	−14.9553	−0.477730
$981$	0.365764	0.0116780
$982$	−20.8587	−0.665628
$983$	53.4892	1.70604	0.853020	−	0.521878i	$-0.174768\pi$
$983$	53.4892	1.70604	0.853020	+	0.521878i	$0.174768\pi$
$984$	37.3704	1.19132
$985$	66.9919	2.13454
$986$	−21.4969	−0.684599
$987$	−11.6877	−0.372023
$988$	1.06124	0.0337626
$989$	0	0
$990$	4.42547	0.140651
$991$	−37.9262	−1.20476	−0.602382	−	0.798208i	$-0.705782\pi$
$991$	−37.9262	−1.20476	−0.602382	+	0.798208i	$0.705782\pi$
$992$	−13.2278	−0.419984
$993$	−34.8242	−1.10511
$994$	−14.6354	−0.464205
$995$	58.6880	1.86053
$996$	−10.3034	−0.326474
$997$	−41.4058	−1.31134	−0.655668	−	0.755049i	$-0.727613\pi$
$997$	−41.4058	−1.31134	−0.655668	+	0.755049i	$0.727613\pi$
$998$	−24.8812	−0.787601
$999$	37.0695	1.17283

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5819.2.a.o.1.14	yes	18
23.22	odd	2		5819.2.a.n.1.14	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5819.2.a.n.1.14	✓	18	23.22	odd	2
5819.2.a.o.1.14	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)

\(f(q)\)	\(=\)	\(q+1.65948 q^{2} -1.50381 q^{3} +0.753868 q^{4} +3.61083 q^{5} -2.49554 q^{6} -1.22717 q^{7} -2.06793 q^{8} -0.738551 q^{9} +5.99209 q^{10} -1.00000 q^{11} -1.13367 q^{12} -0.261302 q^{13} -2.03646 q^{14} -5.43001 q^{15} -4.93942 q^{16} -2.31448 q^{17} -1.22561 q^{18} -5.38737 q^{19} +2.72209 q^{20} +1.84543 q^{21} -1.65948 q^{22} +3.10978 q^{24} +8.03810 q^{25} -0.433625 q^{26} +5.62208 q^{27} -0.925121 q^{28} +5.59693 q^{29} -9.01098 q^{30} +3.25729 q^{31} -4.06100 q^{32} +1.50381 q^{33} -3.84083 q^{34} -4.43109 q^{35} -0.556769 q^{36} +6.59357 q^{37} -8.94022 q^{38} +0.392949 q^{39} -7.46694 q^{40} +12.0171 q^{41} +3.06245 q^{42} -2.22896 q^{43} -0.753868 q^{44} -2.66678 q^{45} -6.33332 q^{47} +7.42796 q^{48} -5.49406 q^{49} +13.3390 q^{50} +3.48054 q^{51} -0.196987 q^{52} +10.3180 q^{53} +9.32971 q^{54} -3.61083 q^{55} +2.53769 q^{56} +8.10159 q^{57} +9.28798 q^{58} -1.16731 q^{59} -4.09351 q^{60} +12.7076 q^{61} +5.40540 q^{62} +0.906325 q^{63} +3.13970 q^{64} -0.943517 q^{65} +2.49554 q^{66} +6.81171 q^{67} -1.74481 q^{68} -7.35330 q^{70} +7.18668 q^{71} +1.52727 q^{72} +8.73391 q^{73} +10.9419 q^{74} -12.0878 q^{75} -4.06136 q^{76} +1.22717 q^{77} +0.652090 q^{78} +3.54440 q^{79} -17.8354 q^{80} -6.23889 q^{81} +19.9421 q^{82} +9.08846 q^{83} +1.39121 q^{84} -8.35720 q^{85} -3.69891 q^{86} -8.41673 q^{87} +2.06793 q^{88} +15.5343 q^{89} -4.42547 q^{90} +0.320661 q^{91} -4.89835 q^{93} -10.5100 q^{94} -19.4529 q^{95} +6.10698 q^{96} -4.43488 q^{97} -9.11728 q^{98} +0.738551 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{2} - 2 q^{3} + 18 q^{4} + 8 q^{5} - 6 q^{6} + 10 q^{7} + 6 q^{8} + 16 q^{9} + 12 q^{10} - 18 q^{11} + 10 q^{12} + 28 q^{14} + 8 q^{15} + 26 q^{16} - 20 q^{18} + 16 q^{19} + 40 q^{20} + 12 q^{21}+ \cdots - 16 q^{99}+O(q^{100}) \) 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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