LMFDB - Embedded newform 2783.2.a.g.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2783,2,Mod(1,2783)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2783.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2783, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2783 = 11^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2783.a (trivial)

Newform invariants

comment:select newform

sage:traces = [5,4,-5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$22.2223668825$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.170701.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 4x + 1 $ x^5 - x^4 - 6x^3 + 4x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 253)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.281423$ of defining polynomial
Character	$\chi$	$=$	2783.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.28142 q^{2} -3.27194 q^{3} -0.357954 q^{4} +3.80110 q^{5} -4.19274 q^{6} +1.85610 q^{7} -3.02154 q^{8} +7.70561 q^{9} +4.87082 q^{10} +1.17121 q^{12} +5.27194 q^{13} +2.37845 q^{14} -12.4370 q^{15} -3.15596 q^{16} +3.86848 q^{17} +9.87415 q^{18} -0.195412 q^{19} -1.36062 q^{20} -6.07305 q^{21} -1.00000 q^{23} +9.88630 q^{24} +9.44840 q^{25} +6.75559 q^{26} -15.3965 q^{27} -0.664399 q^{28} +4.42266 q^{29} -15.9371 q^{30} -2.08520 q^{31} +1.99896 q^{32} +4.95715 q^{34} +7.05522 q^{35} -2.75826 q^{36} -4.77980 q^{37} -0.250406 q^{38} -17.2495 q^{39} -11.4852 q^{40} +5.28296 q^{41} -7.78214 q^{42} -3.21324 q^{43} +29.2898 q^{45} -1.28142 q^{46} -2.30911 q^{47} +10.3261 q^{48} -3.55490 q^{49} +12.1074 q^{50} -12.6574 q^{51} -1.88712 q^{52} -0.819313 q^{53} -19.7294 q^{54} -5.60827 q^{56} +0.639378 q^{57} +5.66730 q^{58} -13.0628 q^{59} +4.45188 q^{60} -1.76409 q^{61} -2.67202 q^{62} +14.3024 q^{63} +8.87343 q^{64} +20.0392 q^{65} -0.481852 q^{67} -1.38474 q^{68} +3.27194 q^{69} +9.04073 q^{70} +12.8100 q^{71} -23.2828 q^{72} -1.48889 q^{73} -6.12494 q^{74} -30.9146 q^{75} +0.0699487 q^{76} -22.1039 q^{78} +11.3518 q^{79} -11.9961 q^{80} +27.2596 q^{81} +6.76970 q^{82} +15.8886 q^{83} +2.17387 q^{84} +14.7045 q^{85} -4.11752 q^{86} -14.4707 q^{87} +1.51554 q^{89} +37.5327 q^{90} +9.78524 q^{91} +0.357954 q^{92} +6.82264 q^{93} -2.95895 q^{94} -0.742782 q^{95} -6.54047 q^{96} -3.96654 q^{97} -4.55533 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 4 q^{2} - 5 q^{3} + 6 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} + 6 q^{8} + 4 q^{9} + 6 q^{10} + 3 q^{12} + 15 q^{13} + 4 q^{14} - 2 q^{15} + 8 q^{16} + 9 q^{17} - 6 q^{18} + 5 q^{19} - 17 q^{20} + 3 q^{21}+ \cdots + 33 q^{98}+O(q^{100}) $ 5 * q + 4 * q^2 - 5 * q^3 + 6 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 + 6 * q^8 + 4 * q^9 + 6 * q^10 + 3 * q^12 + 15 * q^13 + 4 * q^14 - 2 * q^15 + 8 * q^16 + 9 * q^17 - 6 * q^18 + 5 * q^19 - 17 * q^20 + 3 * q^21 - 5 * q^23 + 21 * q^24 + 12 * q^25 + 5 * q^26 - 20 * q^27 + 8 * q^29 - 37 * q^30 - 4 * q^31 + 31 * q^32 + 36 * q^34 + 20 * q^35 - 3 * q^36 + 8 * q^37 - 11 * q^38 - 29 * q^39 - 22 * q^40 + 6 * q^41 + q^42 + 8 * q^43 + 21 * q^45 - 4 * q^46 - 34 * q^47 + 46 * q^48 + 14 * q^49 - 22 * q^50 - 4 * q^51 + 9 * q^52 + 2 * q^53 - 27 * q^54 + 27 * q^56 - 7 * q^57 + 12 * q^58 - 13 * q^59 + 15 * q^60 - 18 * q^61 - 30 * q^62 + 7 * q^63 + 36 * q^64 - 4 * q^65 - 4 * q^67 + 43 * q^68 + 5 * q^69 + 11 * q^70 + 10 * q^71 - 31 * q^72 + 31 * q^73 - 19 * q^74 - 66 * q^75 - 27 * q^76 + 3 * q^79 + 2 * q^80 + 33 * q^81 - 10 * q^82 + 43 * q^83 + 26 * q^84 + 3 * q^85 - 15 * q^86 - 18 * q^87 + 15 * q^89 + 79 * q^90 + 3 * q^91 - 6 * q^92 - 9 * q^93 - 7 * q^94 - 3 * q^95 + 10 * q^96 + 17 * q^97 + 33 * q^98

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 $

$2$	1.28142	0.906103	0.453052	−	0.891484i	$-0.350335\pi$
$2$	1.28142	0.906103	0.453052	+	0.891484i	$0.350335\pi$
$3$	−3.27194	−1.88906	−0.944529	−	0.328429i	$-0.893481\pi$
$3$	−3.27194	−1.88906	−0.944529	+	0.328429i	$0.893481\pi$
$4$	−0.357954	−0.178977
$5$	3.80110	1.69991	0.849953	−	0.526859i	$-0.176630\pi$
$5$	3.80110	1.69991	0.849953	+	0.526859i	$0.176630\pi$
$6$	−4.19274	−1.71168
$7$	1.85610	0.701539	0.350770	−	0.936462i	$-0.385920\pi$
$7$	1.85610	0.701539	0.350770	+	0.936462i	$0.385920\pi$
$8$	−3.02154	−1.06827
$9$	7.70561	2.56854
$10$	4.87082	1.54029
$11$	0	0
$11$	0	0
$12$	1.17121	0.338098
$13$	5.27194	1.46217	0.731087	−	0.682284i	$-0.239013\pi$
$13$	5.27194	1.46217	0.731087	+	0.682284i	$0.239013\pi$
$14$	2.37845	0.635667
$15$	−12.4370	−3.21122
$16$	−3.15596	−0.788990
$17$	3.86848	0.938243	0.469122	−	0.883134i	$-0.344571\pi$
$17$	3.86848	0.938243	0.469122	+	0.883134i	$0.344571\pi$
$18$	9.87415	2.32736
$19$	−0.195412	−0.0448306	−0.0224153	−	0.999749i	$-0.507136\pi$
$19$	−0.195412	−0.0448306	−0.0224153	+	0.999749i	$0.507136\pi$
$20$	−1.36062	−0.304244
$21$	−6.07305	−1.32525
$22$	0	0
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	9.88630	2.01803
$25$	9.44840	1.88968
$26$	6.75559	1.32488
$27$	−15.3965	−2.96306
$28$	−0.664399	−0.125560
$29$	4.42266	0.821267	0.410633	−	0.911801i	$-0.365308\pi$
$29$	4.42266	0.821267	0.410633	+	0.911801i	$0.365308\pi$
$30$	−15.9371	−2.90970
$31$	−2.08520	−0.374512	−0.187256	−	0.982311i	$-0.559959\pi$
$31$	−2.08520	−0.374512	−0.187256	+	0.982311i	$0.559959\pi$
$32$	1.99896	0.353369
$33$	0	0
$34$	4.95715	0.850145
$35$	7.05522	1.19255
$36$	−2.75826	−0.459710
$37$	−4.77980	−0.785794	−0.392897	−	0.919583i	$-0.628527\pi$
$37$	−4.77980	−0.785794	−0.392897	+	0.919583i	$0.628527\pi$
$38$	−0.250406	−0.0406212
$39$	−17.2495	−2.76213
$40$	−11.4852	−1.81597
$41$	5.28296	0.825059	0.412530	−	0.910944i	$-0.364645\pi$
$41$	5.28296	0.825059	0.412530	+	0.910944i	$0.364645\pi$
$42$	−7.78214	−1.20081
$43$	−3.21324	−0.490014	−0.245007	−	0.969521i	$-0.578790\pi$
$43$	−3.21324	−0.490014	−0.245007	+	0.969521i	$0.578790\pi$
$44$	0	0
$45$	29.2898	4.36627
$46$	−1.28142	−0.188936
$47$	−2.30911	−0.336819	−0.168409	−	0.985717i	$-0.553863\pi$
$47$	−2.30911	−0.336819	−0.168409	+	0.985717i	$0.553863\pi$
$48$	10.3261	1.49045
$49$	−3.55490	−0.507843
$50$	12.1074	1.71224
$51$	−12.6574	−1.77240
$52$	−1.88712	−0.261696
$53$	−0.819313	−0.112541	−0.0562707	−	0.998416i	$-0.517921\pi$
$53$	−0.819313	−0.112541	−0.0562707	+	0.998416i	$0.517921\pi$
$54$	−19.7294	−2.68484
$55$	0	0
$56$	−5.60827	−0.749437
$57$	0.639378	0.0846876
$58$	5.66730	0.744152
$59$	−13.0628	−1.70063	−0.850313	−	0.526278i	$-0.823587\pi$
$59$	−13.0628	−1.70063	−0.850313	+	0.526278i	$0.823587\pi$
$60$	4.45188	0.574735
$61$	−1.76409	−0.225869	−0.112934	−	0.993602i	$-0.536025\pi$
$61$	−1.76409	−0.225869	−0.112934	+	0.993602i	$0.536025\pi$
$62$	−2.67202	−0.339347
$63$	14.3024	1.80193
$64$	8.87343	1.10918
$65$	20.0392	2.48556
$66$	0	0
$67$	−0.481852	−0.0588676	−0.0294338	−	0.999567i	$-0.509370\pi$
$67$	−0.481852	−0.0588676	−0.0294338	+	0.999567i	$0.509370\pi$
$68$	−1.38474	−0.167924
$69$	3.27194	0.393896
$70$	9.04073	1.08057
$71$	12.8100	1.52027	0.760134	−	0.649767i	$-0.225133\pi$
$71$	12.8100	1.52027	0.760134	+	0.649767i	$0.225133\pi$
$72$	−23.2828	−2.74390
$73$	−1.48889	−0.174262	−0.0871309	−	0.996197i	$-0.527770\pi$
$73$	−1.48889	−0.174262	−0.0871309	+	0.996197i	$0.527770\pi$
$74$	−6.12494	−0.712010
$75$	−30.9146	−3.56971
$76$	0.0699487	0.00802366
$77$	0	0
$78$	−22.1039	−2.50278
$79$	11.3518	1.27718	0.638589	−	0.769548i	$-0.279518\pi$
$79$	11.3518	1.27718	0.638589	+	0.769548i	$0.279518\pi$
$80$	−11.9961	−1.34121
$81$	27.2596	3.02885
$82$	6.76970	0.747589
$83$	15.8886	1.74401	0.872003	−	0.489501i	$-0.162821\pi$
$83$	15.8886	1.74401	0.872003	+	0.489501i	$0.162821\pi$
$84$	2.17387	0.237189
$85$	14.7045	1.59492
$86$	−4.11752	−0.444003
$87$	−14.4707	−1.55142
$88$	0	0
$89$	1.51554	0.160647	0.0803233	−	0.996769i	$-0.474405\pi$
$89$	1.51554	0.160647	0.0803233	+	0.996769i	$0.474405\pi$
$90$	37.5327	3.95629
$91$	9.78524	1.02577
$92$	0.357954	0.0373193
$93$	6.82264	0.707475
$94$	−2.95895	−0.305192
$95$	−0.742782	−0.0762079
$96$	−6.54047	−0.667534
$97$	−3.96654	−0.402742	−0.201371	−	0.979515i	$-0.564540\pi$
$97$	−3.96654	−0.402742	−0.201371	+	0.979515i	$0.564540\pi$
$98$	−4.55533	−0.460158
$99$	0	0
$100$	−3.38210	−0.338210
$101$	−6.46599	−0.643390	−0.321695	−	0.946843i	$-0.604253\pi$
$101$	−6.46599	−0.643390	−0.321695	+	0.946843i	$0.604253\pi$
$102$	−16.2195	−1.60597
$103$	16.7876	1.65413	0.827065	−	0.562106i	$-0.190009\pi$
$103$	16.7876	1.65413	0.827065	+	0.562106i	$0.190009\pi$
$104$	−15.9294	−1.56200
$105$	−23.0843	−2.25280
$106$	−1.04989	−0.101974
$107$	−5.73210	−0.554143	−0.277072	−	0.960849i	$-0.589364\pi$
$107$	−5.73210	−0.554143	−0.277072	+	0.960849i	$0.589364\pi$
$108$	5.51125	0.530320
$109$	−4.12494	−0.395098	−0.197549	−	0.980293i	$-0.563298\pi$
$109$	−4.12494	−0.395098	−0.197549	+	0.980293i	$0.563298\pi$
$110$	0	0
$111$	15.6392	1.48441
$112$	−5.85777	−0.553507
$113$	4.53730	0.426834	0.213417	−	0.976961i	$-0.431541\pi$
$113$	4.53730	0.426834	0.213417	+	0.976961i	$0.431541\pi$
$114$	0.819313	0.0767357
$115$	−3.80110	−0.354455
$116$	−1.58311	−0.146988
$117$	40.6236	3.75565
$118$	−16.7389	−1.54094
$119$	7.18027	0.658214
$120$	37.5789	3.43046
$121$	0	0
$122$	−2.26055	−0.204660
$123$	−17.2855	−1.55858
$124$	0.746405	0.0670292
$125$	16.9088	1.51237
$126$	18.3274	1.63273
$127$	13.7670	1.22163	0.610813	−	0.791775i	$-0.290843\pi$
$127$	13.7670	1.22163	0.610813	+	0.791775i	$0.290843\pi$
$128$	7.37271	0.651661
$129$	10.5135	0.925665
$130$	25.6787	2.25217
$131$	−6.96530	−0.608561	−0.304280	−	0.952583i	$-0.598416\pi$
$131$	−6.96530	−0.608561	−0.304280	+	0.952583i	$0.598416\pi$
$132$	0	0
$133$	−0.362704	−0.0314504
$134$	−0.617456	−0.0533401
$135$	−58.5237	−5.03692
$136$	−11.6887	−1.00230
$137$	−14.9495	−1.27723	−0.638613	−	0.769528i	$-0.720492\pi$
$137$	−14.9495	−1.27723	−0.638613	+	0.769528i	$0.720492\pi$
$138$	4.19274	0.356910
$139$	−8.06585	−0.684137	−0.342068	−	0.939675i	$-0.611127\pi$
$139$	−8.06585	−0.684137	−0.342068	+	0.939675i	$0.611127\pi$
$140$	−2.52545	−0.213439
$141$	7.55528	0.636270
$142$	16.4150	1.37752
$143$	0	0
$144$	−24.3186	−2.02655
$145$	16.8110	1.39608
$146$	−1.90790	−0.157899
$147$	11.6314	0.959344
$148$	1.71095	0.140639
$149$	19.1168	1.56611	0.783056	−	0.621951i	$-0.213660\pi$
$149$	19.1168	1.56611	0.783056	+	0.621951i	$0.213660\pi$
$150$	−39.6147	−3.23453
$151$	0.136973	0.0111467	0.00557333	−	0.999984i	$-0.498226\pi$
$151$	0.136973	0.0111467	0.00557333	+	0.999984i	$0.498226\pi$
$152$	0.590445	0.0478914
$153$	29.8090	2.40991
$154$	0	0
$155$	−7.92605	−0.636635
$156$	6.17454	0.494358
$157$	−0.0660065	−0.00526789	−0.00263395	−	0.999997i	$-0.500838\pi$
$157$	−0.0660065	−0.00526789	−0.00263395	+	0.999997i	$0.500838\pi$
$158$	14.5465	1.15725
$159$	2.68075	0.212597
$160$	7.59824	0.600693
$161$	−1.85610	−0.146281
$162$	34.9311	2.74445
$163$	16.7047	1.30841	0.654207	−	0.756316i	$-0.273003\pi$
$163$	16.7047	1.30841	0.654207	+	0.756316i	$0.273003\pi$
$164$	−1.89106	−0.147667
$165$	0	0
$166$	20.3601	1.58025
$167$	−12.4899	−0.966495	−0.483248	−	0.875484i	$-0.660543\pi$
$167$	−12.4899	−0.966495	−0.483248	+	0.875484i	$0.660543\pi$
$168$	18.3499	1.41573
$169$	14.7934	1.13795
$170$	18.8427	1.44517
$171$	−1.50577	−0.115149
$172$	1.15019	0.0877014
$173$	20.3094	1.54410	0.772048	−	0.635564i	$-0.219232\pi$
$173$	20.3094	1.54410	0.772048	+	0.635564i	$0.219232\pi$
$174$	−18.5431	−1.40575
$175$	17.5371	1.32568
$176$	0	0
$177$	42.7406	3.21258
$178$	1.94204	0.145562
$179$	3.24632	0.242641	0.121321	−	0.992613i	$-0.461287\pi$
$179$	3.24632	0.242641	0.121321	+	0.992613i	$0.461287\pi$
$180$	−10.4844	−0.781463
$181$	10.7943	0.802333	0.401167	−	0.916005i	$-0.368605\pi$
$181$	10.7943	0.802333	0.401167	+	0.916005i	$0.368605\pi$
$182$	12.5390	0.929455
$183$	5.77200	0.426679
$184$	3.02154	0.222751
$185$	−18.1685	−1.33578
$186$	8.74269	0.641045
$187$	0	0
$188$	0.826557	0.0602829
$189$	−28.5774	−2.07870
$190$	−0.951818	−0.0690522
$191$	14.7625	1.06817	0.534087	−	0.845429i	$-0.320655\pi$
$191$	14.7625	1.06817	0.534087	+	0.845429i	$0.320655\pi$
$192$	−29.0334	−2.09530
$193$	−10.4829	−0.754579	−0.377289	−	0.926095i	$-0.623144\pi$
$193$	−10.4829	−0.754579	−0.377289	+	0.926095i	$0.623144\pi$
$194$	−5.08282	−0.364925
$195$	−65.5672	−4.69536
$196$	1.27249	0.0908923
$197$	−6.05359	−0.431301	−0.215650	−	0.976471i	$-0.569187\pi$
$197$	−6.05359	−0.431301	−0.215650	+	0.976471i	$0.569187\pi$
$198$	0	0
$199$	7.18451	0.509297	0.254648	−	0.967034i	$-0.418040\pi$
$199$	7.18451	0.509297	0.254648	+	0.967034i	$0.418040\pi$
$200$	−28.5487	−2.01870
$201$	1.57659	0.111204
$202$	−8.28567	−0.582978
$203$	8.20889	0.576151
$204$	4.53078	0.317218
$205$	20.0811	1.40252
$206$	21.5120	1.49881
$207$	−7.70561	−0.535577
$208$	−16.6380	−1.15364
$209$	0	0
$210$	−29.5807	−2.04127
$211$	23.1873	1.59628	0.798140	−	0.602472i	$-0.205817\pi$
$211$	23.1873	1.59628	0.798140	+	0.602472i	$0.205817\pi$
$212$	0.293277	0.0201423
$213$	−41.9136	−2.87187
$214$	−7.34525	−0.502111
$215$	−12.2139	−0.832978
$216$	46.5211	3.16536
$217$	−3.87033	−0.262735
$218$	−5.28580	−0.357999
$219$	4.87157	0.329191
$220$	0	0
$221$	20.3944	1.37187
$222$	20.0405	1.34503
$223$	11.3673	0.761209	0.380605	−	0.924738i	$-0.375716\pi$
$223$	11.3673	0.761209	0.380605	+	0.924738i	$0.375716\pi$
$224$	3.71026	0.247902
$225$	72.8057	4.85371
$226$	5.81421	0.386755
$227$	25.1503	1.66929	0.834643	−	0.550791i	$-0.185674\pi$
$227$	25.1503	1.66929	0.834643	+	0.550791i	$0.185674\pi$
$228$	−0.228868	−0.0151572
$229$	−27.7272	−1.83227	−0.916133	−	0.400874i	$-0.868707\pi$
$229$	−27.7272	−1.83227	−0.916133	+	0.400874i	$0.868707\pi$
$230$	−4.87082	−0.321173
$231$	0	0
$232$	−13.3632	−0.877339
$233$	−25.1145	−1.64531	−0.822654	−	0.568543i	$-0.807507\pi$
$233$	−25.1145	−1.64531	−0.822654	+	0.568543i	$0.807507\pi$
$234$	52.0560	3.40301
$235$	−8.77718	−0.572560
$236$	4.67587	0.304373
$237$	−37.1425	−2.41266
$238$	9.20096	0.596410
$239$	−2.60259	−0.168348	−0.0841739	−	0.996451i	$-0.526825\pi$
$239$	−2.60259	−0.168348	−0.0841739	+	0.996451i	$0.526825\pi$
$240$	39.2507	2.53362
$241$	−22.7867	−1.46782	−0.733911	−	0.679246i	$-0.762307\pi$
$241$	−22.7867	−1.46782	−0.733911	+	0.679246i	$0.762307\pi$
$242$	0	0
$243$	−43.0025	−2.75861
$244$	0.631464	0.0404253
$245$	−13.5125	−0.863285
$246$	−22.1501	−1.41224
$247$	−1.03020	−0.0655502
$248$	6.30050	0.400082
$249$	−51.9868	−3.29453
$250$	21.6674	1.37036
$251$	7.91155	0.499373	0.249686	−	0.968327i	$-0.419672\pi$
$251$	7.91155	0.499373	0.249686	+	0.968327i	$0.419672\pi$
$252$	−5.11960	−0.322504
$253$	0	0
$254$	17.6414	1.10692
$255$	−48.1122	−3.01290
$256$	−8.29930	−0.518706
$257$	7.26003	0.452868	0.226434	−	0.974027i	$-0.427293\pi$
$257$	7.26003	0.452868	0.226434	+	0.974027i	$0.427293\pi$
$258$	13.4723	0.838748
$259$	−8.87177	−0.551265
$260$	−7.17312	−0.444858
$261$	34.0793	2.10946
$262$	−8.92549	−0.551419
$263$	−3.69770	−0.228010	−0.114005	−	0.993480i	$-0.536368\pi$
$263$	−3.69770	−0.228010	−0.114005	+	0.993480i	$0.536368\pi$
$264$	0	0
$265$	−3.11430	−0.191310
$266$	−0.464778	−0.0284973
$267$	−4.95875	−0.303471
$268$	0.172481	0.0105360
$269$	−31.9537	−1.94825	−0.974126	−	0.226005i	$-0.927433\pi$
$269$	−31.9537	−1.94825	−0.974126	+	0.226005i	$0.927433\pi$
$270$	−74.9936	−4.56397
$271$	−0.579921	−0.0352277	−0.0176138	−	0.999845i	$-0.505607\pi$
$271$	−0.579921	−0.0352277	−0.0176138	+	0.999845i	$0.505607\pi$
$272$	−12.2088	−0.740264
$273$	−32.0168	−1.93774
$274$	−19.1567	−1.15730
$275$	0	0
$276$	−1.17121	−0.0704984
$277$	−6.91340	−0.415386	−0.207693	−	0.978194i	$-0.566596\pi$
$277$	−6.91340	−0.415386	−0.207693	+	0.978194i	$0.566596\pi$
$278$	−10.3358	−0.619898
$279$	−16.0677	−0.961949
$280$	−21.3176	−1.27397
$281$	16.0724	0.958799	0.479399	−	0.877597i	$-0.340855\pi$
$281$	16.0724	0.958799	0.479399	+	0.877597i	$0.340855\pi$
$282$	9.68152	0.576526
$283$	−3.57436	−0.212473	−0.106237	−	0.994341i	$-0.533880\pi$
$283$	−3.57436	−0.212473	−0.106237	+	0.994341i	$0.533880\pi$
$284$	−4.58540	−0.272093
$285$	2.43034	0.143961
$286$	0	0
$287$	9.80569	0.578811
$288$	15.4032	0.907641
$289$	−2.03490	−0.119700
$290$	21.5420	1.26499
$291$	12.9783	0.760802
$292$	0.532956	0.0311889
$293$	14.7794	0.863422	0.431711	−	0.902012i	$-0.357910\pi$
$293$	14.7794	0.863422	0.431711	+	0.902012i	$0.357910\pi$
$294$	14.9048	0.869265
$295$	−49.6529	−2.89090
$296$	14.4423	0.839444
$297$	0	0
$298$	24.4968	1.41906
$299$	−5.27194	−0.304884
$300$	11.0660	0.638897
$301$	−5.96408	−0.343764
$302$	0.175520	0.0101000
$303$	21.1564	1.21540
$304$	0.616713	0.0353709
$305$	−6.70549	−0.383955
$306$	38.1979	2.18363
$307$	−8.71106	−0.497167	−0.248583	−	0.968611i	$-0.579965\pi$
$307$	−8.71106	−0.497167	−0.248583	+	0.968611i	$0.579965\pi$
$308$	0	0
$309$	−54.9281	−3.12475
$310$	−10.1566	−0.576857
$311$	−13.6516	−0.774113	−0.387057	−	0.922056i	$-0.626508\pi$
$311$	−13.6516	−0.774113	−0.387057	+	0.922056i	$0.626508\pi$
$312$	52.1200	2.95071
$313$	0.389578	0.0220202	0.0110101	−	0.999939i	$-0.496495\pi$
$313$	0.389578	0.0220202	0.0110101	+	0.999939i	$0.496495\pi$
$314$	−0.0845823	−0.00477326
$315$	54.3648	3.06311
$316$	−4.06343	−0.228586
$317$	2.69883	0.151582	0.0757908	−	0.997124i	$-0.475852\pi$
$317$	2.69883	0.151582	0.0757908	+	0.997124i	$0.475852\pi$
$318$	3.43517	0.192635
$319$	0	0
$320$	33.7288	1.88550
$321$	18.7551	1.04681
$322$	−2.37845	−0.132546
$323$	−0.755947	−0.0420620
$324$	−9.75771	−0.542095
$325$	49.8114	2.76304
$326$	21.4058	1.18556
$327$	13.4966	0.746362
$328$	−15.9627	−0.881390
$329$	−4.28594	−0.236291
$330$	0	0
$331$	−5.98910	−0.329191	−0.164595	−	0.986361i	$-0.552632\pi$
$331$	−5.98910	−0.329191	−0.164595	+	0.986361i	$0.552632\pi$
$332$	−5.68741	−0.312137
$333$	−36.8313	−2.01834
$334$	−16.0048	−0.875744
$335$	−1.83157	−0.100069
$336$	19.1663	1.04561
$337$	−1.52298	−0.0829622	−0.0414811	−	0.999139i	$-0.513208\pi$
$337$	−1.52298	−0.0829622	−0.0414811	+	0.999139i	$0.513208\pi$
$338$	18.9566	1.03110
$339$	−14.8458	−0.806313
$340$	−5.26353	−0.285455
$341$	0	0
$342$	−1.92953	−0.104337
$343$	−19.5909	−1.05781
$344$	9.70892	0.523470
$345$	12.4370	0.669586
$346$	26.0250	1.39911
$347$	4.67011	0.250705	0.125352	−	0.992112i	$-0.459994\pi$
$347$	4.67011	0.250705	0.125352	+	0.992112i	$0.459994\pi$
$348$	5.17985	0.277669
$349$	−9.40093	−0.503220	−0.251610	−	0.967829i	$-0.580960\pi$
$349$	−9.40093	−0.503220	−0.251610	+	0.967829i	$0.580960\pi$
$350$	22.4725	1.20121
$351$	−81.1695	−4.33251
$352$	0	0
$353$	21.2570	1.13140	0.565699	−	0.824612i	$-0.308607\pi$
$353$	21.2570	1.13140	0.565699	+	0.824612i	$0.308607\pi$
$354$	54.7688	2.91093
$355$	48.6921	2.58431
$356$	−0.542493	−0.0287521
$357$	−23.4934	−1.24340
$358$	4.15991	0.219858
$359$	−28.3775	−1.49771	−0.748855	−	0.662734i	$-0.769396\pi$
$359$	−28.3775	−1.49771	−0.748855	+	0.662734i	$0.769396\pi$
$360$	−88.5004	−4.66438
$361$	−18.9618	−0.997990
$362$	13.8321	0.726997
$363$	0	0
$364$	−3.50267	−0.183590
$365$	−5.65944	−0.296229
$366$	7.39638	0.386615
$367$	−8.92022	−0.465631	−0.232816	−	0.972521i	$-0.574794\pi$
$367$	−8.92022	−0.465631	−0.232816	+	0.972521i	$0.574794\pi$
$368$	3.15596	0.164516
$369$	40.7084	2.11920
$370$	−23.2815	−1.21035
$371$	−1.52073	−0.0789522
$372$	−2.44220	−0.126622
$373$	−27.2725	−1.41212	−0.706059	−	0.708153i	$-0.749529\pi$
$373$	−27.2725	−1.41212	−0.706059	+	0.708153i	$0.749529\pi$
$374$	0	0
$375$	−55.3247	−2.85696
$376$	6.97707	0.359815
$377$	23.3160	1.20084
$378$	−36.6198	−1.88352
$379$	−16.3560	−0.840152	−0.420076	−	0.907489i	$-0.637997\pi$
$379$	−16.3560	−0.840152	−0.420076	+	0.907489i	$0.637997\pi$
$380$	0.265882	0.0136395
$381$	−45.0450	−2.30772
$382$	18.9170	0.967876
$383$	−20.3313	−1.03888	−0.519439	−	0.854507i	$-0.673859\pi$
$383$	−20.3313	−1.03888	−0.519439	+	0.854507i	$0.673859\pi$
$384$	−24.1231	−1.23103
$385$	0	0
$386$	−13.4331	−0.683726
$387$	−24.7600	−1.25862
$388$	1.41984	0.0720816
$389$	−38.3557	−1.94471	−0.972355	−	0.233509i	$-0.924979\pi$
$389$	−38.3557	−1.94471	−0.972355	+	0.233509i	$0.924979\pi$
$390$	−84.0193	−4.25448
$391$	−3.86848	−0.195637
$392$	10.7413	0.542516
$393$	22.7901	1.14961
$394$	−7.75721	−0.390803
$395$	43.1494	2.17108
$396$	0	0
$397$	21.9251	1.10039	0.550195	−	0.835036i	$-0.314553\pi$
$397$	21.9251	1.10039	0.550195	+	0.835036i	$0.314553\pi$
$398$	9.20640	0.461475
$399$	1.18675	0.0594117
$400$	−29.8188	−1.49094
$401$	4.54119	0.226776	0.113388	−	0.993551i	$-0.463830\pi$
$401$	4.54119	0.226776	0.113388	+	0.993551i	$0.463830\pi$
$402$	2.02028	0.100762
$403$	−10.9930	−0.547602
$404$	2.31453	0.115152
$405$	103.617	5.14876
$406$	10.5191	0.522052
$407$	0	0
$408$	38.2449	1.89341
$409$	8.51157	0.420870	0.210435	−	0.977608i	$-0.432512\pi$
$409$	8.51157	0.420870	0.210435	+	0.977608i	$0.432512\pi$
$410$	25.7323	1.27083
$411$	48.9141	2.41275
$412$	−6.00919	−0.296052
$413$	−24.2458	−1.19306
$414$	−9.87415	−0.485288
$415$	60.3944	2.96465
$416$	10.5384	0.516687
$417$	26.3910	1.29237
$418$	0	0
$419$	−14.6838	−0.717351	−0.358675	−	0.933462i	$-0.616771\pi$
$419$	−14.6838	−0.717351	−0.358675	+	0.933462i	$0.616771\pi$
$420$	8.26312	0.403199
$421$	21.4822	1.04698	0.523489	−	0.852032i	$-0.324630\pi$
$421$	21.4822	1.04698	0.523489	+	0.852032i	$0.324630\pi$
$422$	29.7128	1.44639
$423$	−17.7931	−0.865131
$424$	2.47559	0.120225
$425$	36.5509	1.77298
$426$	−53.7090	−2.60221
$427$	−3.27432	−0.158456
$428$	2.05183	0.0991790
$429$	0	0
$430$	−15.6511	−0.754764
$431$	12.3258	0.593711	0.296856	−	0.954922i	$-0.404062\pi$
$431$	12.3258	0.593711	0.296856	+	0.954922i	$0.404062\pi$
$432$	48.5907	2.33782
$433$	4.18186	0.200968	0.100484	−	0.994939i	$-0.467961\pi$
$433$	4.18186	0.200968	0.100484	+	0.994939i	$0.467961\pi$
$434$	−4.95953	−0.238065
$435$	−55.0046	−2.63727
$436$	1.47654	0.0707135
$437$	0.195412	0.00934783
$438$	6.24255	0.298281
$439$	31.3602	1.49674	0.748370	−	0.663282i	$-0.230837\pi$
$439$	31.3602	1.49674	0.748370	+	0.663282i	$0.230837\pi$
$440$	0	0
$441$	−27.3927	−1.30441
$442$	26.1338	1.24306
$443$	−37.6486	−1.78874	−0.894370	−	0.447328i	$-0.852376\pi$
$443$	−37.6486	−1.78874	−0.894370	+	0.447328i	$0.852376\pi$
$444$	−5.59813	−0.265675
$445$	5.76072	0.273084
$446$	14.5663	0.689734
$447$	−62.5492	−2.95848
$448$	16.4700	0.778132
$449$	40.6798	1.91980	0.959899	−	0.280345i	$-0.0904490\pi$
$449$	40.6798	1.91980	0.959899	+	0.280345i	$0.0904490\pi$
$450$	93.2949	4.39796
$451$	0	0
$452$	−1.62415	−0.0763935
$453$	−0.448166	−0.0210567
$454$	32.2282	1.51255
$455$	37.1947	1.74372
$456$	−1.93190	−0.0904697
$457$	−30.7326	−1.43761	−0.718804	−	0.695213i	$-0.755310\pi$
$457$	−30.7326	−1.43761	−0.718804	+	0.695213i	$0.755310\pi$
$458$	−35.5303	−1.66022
$459$	−59.5610	−2.78007
$460$	1.36062	0.0634393
$461$	20.8666	0.971856	0.485928	−	0.873999i	$-0.338482\pi$
$461$	20.8666	0.971856	0.485928	+	0.873999i	$0.338482\pi$
$462$	0	0
$463$	23.2506	1.08055	0.540274	−	0.841489i	$-0.318321\pi$
$463$	23.2506	1.08055	0.540274	+	0.841489i	$0.318321\pi$
$464$	−13.9577	−0.647971
$465$	25.9336	1.20264
$466$	−32.1823	−1.49082
$467$	−13.0604	−0.604365	−0.302183	−	0.953250i	$-0.597715\pi$
$467$	−13.0604	−0.604365	−0.302183	+	0.953250i	$0.597715\pi$
$468$	−14.5414	−0.672176
$469$	−0.894364	−0.0412979
$470$	−11.2473	−0.518798
$471$	0.215970	0.00995135
$472$	39.4696	1.81674
$473$	0	0
$474$	−47.5952	−2.18612
$475$	−1.84633	−0.0847155
$476$	−2.57021	−0.117805
$477$	−6.31331	−0.289067
$478$	−3.33502	−0.152540
$479$	5.70788	0.260800	0.130400	−	0.991461i	$-0.458374\pi$
$479$	5.70788	0.260800	0.130400	+	0.991461i	$0.458374\pi$
$480$	−24.8610	−1.13474
$481$	−25.1988	−1.14897
$482$	−29.1994	−1.33000
$483$	6.07305	0.276333
$484$	0	0
$485$	−15.0772	−0.684623
$486$	−55.1044	−2.49959
$487$	23.0832	1.04600	0.523000	−	0.852333i	$-0.324813\pi$
$487$	23.0832	1.04600	0.523000	+	0.852333i	$0.324813\pi$
$488$	5.33027	0.241290
$489$	−54.6569	−2.47167
$490$	−17.3153	−0.782225
$491$	−15.6115	−0.704536	−0.352268	−	0.935899i	$-0.614589\pi$
$491$	−15.6115	−0.704536	−0.352268	+	0.935899i	$0.614589\pi$
$492$	6.18743	0.278951
$493$	17.1089	0.770548
$494$	−1.32012	−0.0593952
$495$	0	0
$496$	6.58079	0.295486
$497$	23.7766	1.06653
$498$	−66.6170	−2.98518
$499$	−8.07097	−0.361306	−0.180653	−	0.983547i	$-0.557821\pi$
$499$	−8.07097	−0.361306	−0.180653	+	0.983547i	$0.557821\pi$
$500$	−6.05259	−0.270680
$501$	40.8662	1.82577
$502$	10.1380	0.452483
$503$	34.6008	1.54277	0.771386	−	0.636367i	$-0.219564\pi$
$503$	34.6008	1.54277	0.771386	+	0.636367i	$0.219564\pi$
$504$	−43.2152	−1.92496
$505$	−24.5779	−1.09370
$506$	0	0
$507$	−48.4031	−2.14966
$508$	−4.92797	−0.218643
$509$	15.0158	0.665563	0.332781	−	0.943004i	$-0.392013\pi$
$509$	15.0158	0.665563	0.332781	+	0.943004i	$0.392013\pi$
$510$	−61.6521	−2.73000
$511$	−2.76353	−0.122251
$512$	−25.3803	−1.12166
$513$	3.00866	0.132836
$514$	9.30317	0.410345
$515$	63.8114	2.81187
$516$	−3.76336	−0.165673
$517$	0	0
$518$	−11.3685	−0.499503
$519$	−66.4513	−2.91689
$520$	−60.5492	−2.65526
$521$	−25.1881	−1.10351	−0.551755	−	0.834006i	$-0.686042\pi$
$521$	−25.1881	−1.10351	−0.551755	+	0.834006i	$0.686042\pi$
$522$	43.6700	1.91138
$523$	32.0155	1.39994	0.699970	−	0.714172i	$-0.253196\pi$
$523$	32.0155	1.39994	0.699970	+	0.714172i	$0.253196\pi$
$524$	2.49326	0.108919
$525$	−57.3806	−2.50429
$526$	−4.73832	−0.206601
$527$	−8.06653	−0.351383
$528$	0	0
$529$	1.00000	0.0434783
$530$	−3.99073	−0.173346
$531$	−100.657	−4.36812
$532$	0.129832	0.00562891
$533$	27.8514	1.20638
$534$	−6.35426	−0.274976
$535$	−21.7883	−0.941991
$536$	1.45593	0.0628867
$537$	−10.6218	−0.458363
$538$	−40.9462	−1.76532
$539$	0	0
$540$	20.9488	0.901494
$541$	14.2450	0.612439	0.306219	−	0.951961i	$-0.400936\pi$
$541$	14.2450	0.612439	0.306219	+	0.951961i	$0.400936\pi$
$542$	−0.743124	−0.0319199
$543$	−35.3183	−1.51565
$544$	7.73291	0.331546
$545$	−15.6793	−0.671629
$546$	−41.0270	−1.75579
$547$	−9.20117	−0.393414	−0.196707	−	0.980462i	$-0.563025\pi$
$547$	−9.20117	−0.393414	−0.196707	+	0.980462i	$0.563025\pi$
$548$	5.35126	0.228594
$549$	−13.5934	−0.580152
$550$	0	0
$551$	−0.864241	−0.0368179
$552$	−9.88630	−0.420789
$553$	21.0701	0.895990
$554$	−8.85900	−0.376383
$555$	59.4463	2.52336
$556$	2.88721	0.122445
$557$	17.4388	0.738907	0.369453	−	0.929249i	$-0.379545\pi$
$557$	17.4388	0.738907	0.369453	+	0.929249i	$0.379545\pi$
$558$	−20.5895	−0.871625
$559$	−16.9400	−0.716486
$560$	−22.2660	−0.940910
$561$	0	0
$562$	20.5955	0.868771
$563$	−7.12652	−0.300347	−0.150174	−	0.988660i	$-0.547983\pi$
$563$	−7.12652	−0.300347	−0.150174	+	0.988660i	$0.547983\pi$
$564$	−2.70445	−0.113878
$565$	17.2468	0.725577
$566$	−4.58026	−0.192523
$567$	50.5966	2.12486
$568$	−38.7059	−1.62406
$569$	−38.9361	−1.63229	−0.816143	−	0.577849i	$-0.803892\pi$
$569$	−38.9361	−1.63229	−0.816143	+	0.577849i	$0.803892\pi$
$570$	3.11430	0.130444
$571$	−29.3981	−1.23027	−0.615136	−	0.788421i	$-0.710899\pi$
$571$	−29.3981	−1.23027	−0.615136	+	0.788421i	$0.710899\pi$
$572$	0	0
$573$	−48.3020	−2.01784
$574$	12.5652	0.524463
$575$	−9.44840	−0.394025
$576$	68.3752	2.84897
$577$	−20.3394	−0.846740	−0.423370	−	0.905957i	$-0.639153\pi$
$577$	−20.3394	−0.846740	−0.423370	+	0.905957i	$0.639153\pi$
$578$	−2.60757	−0.108460
$579$	34.2996	1.42544
$580$	−6.01757	−0.249866
$581$	29.4909	1.22349
$582$	16.6307	0.689365
$583$	0	0
$584$	4.49875	0.186159
$585$	154.414	6.38425
$586$	18.9387	0.782350
$587$	0.714390	0.0294860	0.0147430	−	0.999891i	$-0.495307\pi$
$587$	0.714390	0.0294860	0.0147430	+	0.999891i	$0.495307\pi$
$588$	−4.16352	−0.171701
$589$	0.407473	0.0167896
$590$	−63.6264	−2.61946
$591$	19.8070	0.814752
$592$	15.0848	0.619983
$593$	3.17833	0.130518	0.0652592	−	0.997868i	$-0.479213\pi$
$593$	3.17833	0.130518	0.0652592	+	0.997868i	$0.479213\pi$
$594$	0	0
$595$	27.2930	1.11890
$596$	−6.84296	−0.280298
$597$	−23.5073	−0.962090
$598$	−6.75559	−0.276257
$599$	15.1347	0.618387	0.309194	−	0.950999i	$-0.399941\pi$
$599$	15.1347	0.618387	0.309194	+	0.950999i	$0.399941\pi$
$600$	93.4097	3.81343
$601$	29.8591	1.21798	0.608990	−	0.793178i	$-0.291575\pi$
$601$	29.8591	1.21798	0.608990	+	0.793178i	$0.291575\pi$
$602$	−7.64252	−0.311486
$603$	−3.71296	−0.151204
$604$	−0.0490299	−0.00199500
$605$	0	0
$606$	27.1102	1.10128
$607$	−33.7487	−1.36982	−0.684909	−	0.728629i	$-0.740158\pi$
$607$	−33.7487	−1.36982	−0.684909	+	0.728629i	$0.740158\pi$
$608$	−0.390620	−0.0158417
$609$	−26.8590	−1.08838
$610$	−8.59257	−0.347903
$611$	−12.1735	−0.492487
$612$	−10.6703	−0.431320
$613$	−35.5376	−1.43535	−0.717675	−	0.696378i	$-0.754794\pi$
$613$	−35.5376	−1.43535	−0.717675	+	0.696378i	$0.754794\pi$
$614$	−11.1626	−0.450484
$615$	−65.7041	−2.64945
$616$	0	0
$617$	−8.52643	−0.343261	−0.171631	−	0.985161i	$-0.554904\pi$
$617$	−8.52643	−0.343261	−0.171631	+	0.985161i	$0.554904\pi$
$618$	−70.3861	−2.83134
$619$	10.7185	0.430815	0.215407	−	0.976524i	$-0.430892\pi$
$619$	10.7185	0.430815	0.215407	+	0.976524i	$0.430892\pi$
$620$	2.83716	0.113943
$621$	15.3965	0.617840
$622$	−17.4935	−0.701426
$623$	2.81299	0.112700
$624$	54.4387	2.17929
$625$	17.0302	0.681208
$626$	0.499214	0.0199526
$627$	0	0
$628$	0.0236273	0.000942833 0
$629$	−18.4905	−0.737265
$630$	69.6643	2.77549
$631$	−5.06204	−0.201517	−0.100758	−	0.994911i	$-0.532127\pi$
$631$	−5.06204	−0.201517	−0.100758	+	0.994911i	$0.532127\pi$
$632$	−34.2999	−1.36438
$633$	−75.8676	−3.01547
$634$	3.45835	0.137349
$635$	52.3299	2.07665
$636$	−0.959585	−0.0380500
$637$	−18.7412	−0.742555
$638$	0	0
$639$	98.7089	3.90486
$640$	28.0244	1.10776
$641$	6.71512	0.265231	0.132616	−	0.991168i	$-0.457662\pi$
$641$	6.71512	0.265231	0.132616	+	0.991168i	$0.457662\pi$
$642$	24.0332	0.948516
$643$	10.3874	0.409638	0.204819	−	0.978800i	$-0.434339\pi$
$643$	10.3874	0.409638	0.204819	+	0.978800i	$0.434339\pi$
$644$	0.664399	0.0261810
$645$	39.9630	1.57354
$646$	−0.968688	−0.0381125
$647$	3.54279	0.139281	0.0696407	−	0.997572i	$-0.477815\pi$
$647$	3.54279	0.139281	0.0696407	+	0.997572i	$0.477815\pi$
$648$	−82.3660	−3.23564
$649$	0	0
$650$	63.8295	2.50360
$651$	12.6635	0.496321
$652$	−5.97952	−0.234176
$653$	29.8393	1.16770	0.583851	−	0.811861i	$-0.301545\pi$
$653$	29.8393	1.16770	0.583851	+	0.811861i	$0.301545\pi$
$654$	17.2948	0.676281
$655$	−26.4758	−1.03450
$656$	−16.6728	−0.650963
$657$	−11.4728	−0.447598
$658$	−5.49210	−0.214104
$659$	46.1786	1.79886	0.899432	−	0.437062i	$-0.143981\pi$
$659$	46.1786	1.79886	0.899432	+	0.437062i	$0.143981\pi$
$660$	0	0
$661$	−13.0358	−0.507032	−0.253516	−	0.967331i	$-0.581587\pi$
$661$	−13.0358	−0.507032	−0.253516	+	0.967331i	$0.581587\pi$
$662$	−7.67457	−0.298281
$663$	−66.7293	−2.59155
$664$	−48.0082	−1.86308
$665$	−1.37868	−0.0534628
$666$	−47.1964	−1.82882
$667$	−4.42266	−0.171246
$668$	4.47081	0.172981
$669$	−37.1931	−1.43797
$670$	−2.34702	−0.0906731
$671$	0	0
$672$	−12.1398	−0.468301
$673$	−1.49971	−0.0578097	−0.0289049	−	0.999582i	$-0.509202\pi$
$673$	−1.49971	−0.0578097	−0.0289049	+	0.999582i	$0.509202\pi$
$674$	−1.95159	−0.0751723
$675$	−145.472	−5.59923
$676$	−5.29536	−0.203668
$677$	−37.4924	−1.44095	−0.720474	−	0.693482i	$-0.756076\pi$
$677$	−37.4924	−1.44095	−0.720474	+	0.693482i	$0.756076\pi$
$678$	−19.0238	−0.730603
$679$	−7.36230	−0.282539
$680$	−44.4301	−1.70382
$681$	−82.2905	−3.15338
$682$	0	0
$683$	4.06400	0.155505	0.0777523	−	0.996973i	$-0.475226\pi$
$683$	4.06400	0.155505	0.0777523	+	0.996973i	$0.475226\pi$
$684$	0.538997	0.0206091
$685$	−56.8248	−2.17116
$686$	−25.1043	−0.958486
$687$	90.7219	3.46126
$688$	10.1408	0.386616
$689$	−4.31937	−0.164555
$690$	15.9371	0.606713
$691$	4.81991	0.183358	0.0916790	−	0.995789i	$-0.470777\pi$
$691$	4.81991	0.183358	0.0916790	+	0.995789i	$0.470777\pi$
$692$	−7.26985	−0.276358
$693$	0	0
$694$	5.98439	0.227164
$695$	−30.6591	−1.16297
$696$	43.7237	1.65734
$697$	20.4370	0.774106
$698$	−12.0466	−0.455970
$699$	82.1733	3.10808
$700$	−6.27750	−0.237267
$701$	−5.75429	−0.217337	−0.108668	−	0.994078i	$-0.534659\pi$
$701$	−5.75429	−0.217337	−0.108668	+	0.994078i	$0.534659\pi$
$702$	−104.012	−3.92570
$703$	0.934031	0.0352276
$704$	0	0
$705$	28.7184	1.08160
$706$	27.2393	1.02516
$707$	−12.0015	−0.451363
$708$	−15.2992	−0.574979
$709$	−12.4167	−0.466318	−0.233159	−	0.972439i	$-0.574906\pi$
$709$	−12.4167	−0.466318	−0.233159	+	0.972439i	$0.574906\pi$
$710$	62.3952	2.34165
$711$	87.4726	3.28048
$712$	−4.57925	−0.171615
$713$	2.08520	0.0780912
$714$	−30.1050	−1.12665
$715$	0	0
$716$	−1.16203	−0.0434272
$717$	8.51554	0.318019
$718$	−36.3636	−1.35708
$719$	−12.2243	−0.455888	−0.227944	−	0.973674i	$-0.573200\pi$
$719$	−12.2243	−0.455888	−0.227944	+	0.973674i	$0.573200\pi$
$720$	−92.4376	−3.44494
$721$	31.1594	1.16044
$722$	−24.2981	−0.904282
$723$	74.5569	2.77280
$724$	−3.86387	−0.143599
$725$	41.7870	1.55193
$726$	0	0
$727$	−25.2721	−0.937291	−0.468646	−	0.883386i	$-0.655258\pi$
$727$	−25.2721	−0.937291	−0.468646	+	0.883386i	$0.655258\pi$
$728$	−29.5665	−1.09581
$729$	58.9228	2.18233
$730$	−7.25214	−0.268414
$731$	−12.4303	−0.459752
$732$	−2.06611	−0.0763658
$733$	−2.34082	−0.0864600	−0.0432300	−	0.999065i	$-0.513765\pi$
$733$	−2.34082	−0.0864600	−0.0432300	+	0.999065i	$0.513765\pi$
$734$	−11.4306	−0.421910
$735$	44.2123	1.63079
$736$	−1.99896	−0.0736825
$737$	0	0
$738$	52.1647	1.92021
$739$	−17.6494	−0.649245	−0.324623	−	0.945844i	$-0.605237\pi$
$739$	−17.6494	−0.649245	−0.324623	+	0.945844i	$0.605237\pi$
$740$	6.50350	0.239073
$741$	3.37076	0.123828
$742$	−1.94869	−0.0715388
$743$	25.6263	0.940137	0.470069	−	0.882630i	$-0.344229\pi$
$743$	25.6263	0.940137	0.470069	+	0.882630i	$0.344229\pi$
$744$	−20.6149	−0.755778
$745$	72.6651	2.66224
$746$	−34.9476	−1.27952
$747$	122.432	4.47954
$748$	0	0
$749$	−10.6393	−0.388753
$750$	−70.8944	−2.58870
$751$	29.0528	1.06015	0.530077	−	0.847950i	$-0.322163\pi$
$751$	29.0528	1.06015	0.530077	+	0.847950i	$0.322163\pi$
$752$	7.28746	0.265746
$753$	−25.8861	−0.943344
$754$	29.8777	1.08808
$755$	0.520647	0.0189483
$756$	10.2294	0.372040
$757$	35.1534	1.27767	0.638837	−	0.769342i	$-0.279416\pi$
$757$	35.1534	1.27767	0.638837	+	0.769342i	$0.279416\pi$
$758$	−20.9590	−0.761264
$759$	0	0
$760$	2.24434	0.0814109
$761$	28.8811	1.04694	0.523469	−	0.852045i	$-0.324638\pi$
$761$	28.8811	1.04694	0.523469	+	0.852045i	$0.324638\pi$
$762$	−57.7217	−2.09104
$763$	−7.65630	−0.277177
$764$	−5.28429	−0.191179
$765$	113.307	4.09662
$766$	−26.0529	−0.941331
$767$	−68.8661	−2.48661
$768$	27.1548	0.979866
$769$	43.5547	1.57062	0.785311	−	0.619102i	$-0.212503\pi$
$769$	43.5547	1.57062	0.785311	+	0.619102i	$0.212503\pi$
$770$	0	0
$771$	−23.7544	−0.855494
$772$	3.75242	0.135052
$773$	31.2181	1.12284	0.561418	−	0.827532i	$-0.310256\pi$
$773$	31.2181	1.12284	0.561418	+	0.827532i	$0.310256\pi$
$774$	−31.7280	−1.14044
$775$	−19.7018	−0.707708
$776$	11.9851	0.430239
$777$	29.0279	1.04137
$778$	−49.1498	−1.76211
$779$	−1.03235	−0.0369879
$780$	23.4701	0.840363
$781$	0	0
$782$	−4.95715	−0.177267
$783$	−68.0935	−2.43346
$784$	11.2191	0.400683
$785$	−0.250898	−0.00895492
$786$	29.2037	1.04166
$787$	17.9596	0.640190	0.320095	−	0.947385i	$-0.396285\pi$
$787$	17.9596	0.640190	0.320095	+	0.947385i	$0.396285\pi$
$788$	2.16691	0.0771930
$789$	12.0987	0.430724
$790$	55.2926	1.96722
$791$	8.42168	0.299441
$792$	0	0
$793$	−9.30019	−0.330259
$794$	28.0954	0.997068
$795$	10.1898	0.361395
$796$	−2.57173	−0.0911525
$797$	−17.1452	−0.607315	−0.303657	−	0.952781i	$-0.598208\pi$
$797$	−17.1452	−0.607315	−0.303657	+	0.952781i	$0.598208\pi$
$798$	1.52073	0.0538331
$799$	−8.93274	−0.316018
$800$	18.8869	0.667753
$801$	11.6781	0.412627
$802$	5.81919	0.205483
$803$	0	0
$804$	−0.564348	−0.0199030
$805$	−7.05522	−0.248664
$806$	−14.0867	−0.496184
$807$	104.551	3.68036
$808$	19.5372	0.687318
$809$	−50.8251	−1.78692	−0.893458	−	0.449146i	$-0.851728\pi$
$809$	−50.8251	−1.78692	−0.893458	+	0.449146i	$0.851728\pi$
$810$	132.777	4.66531
$811$	25.5494	0.897162	0.448581	−	0.893742i	$-0.351930\pi$
$811$	25.5494	0.897162	0.448581	+	0.893742i	$0.351930\pi$
$812$	−2.93841	−0.103118
$813$	1.89747	0.0665471
$814$	0	0
$815$	63.4963	2.22418
$816$	39.9463	1.39840
$817$	0.627906	0.0219676
$818$	10.9069	0.381351
$819$	75.4013	2.63474
$820$	−7.18811	−0.251020
$821$	14.0095	0.488936	0.244468	−	0.969657i	$-0.421387\pi$
$821$	14.0095	0.488936	0.244468	+	0.969657i	$0.421387\pi$
$822$	62.6796	2.18620
$823$	−20.8927	−0.728273	−0.364136	−	0.931346i	$-0.618636\pi$
$823$	−20.8927	−0.728273	−0.364136	+	0.931346i	$0.618636\pi$
$824$	−50.7243	−1.76707
$825$	0	0
$826$	−31.0691	−1.08103
$827$	37.9506	1.31967	0.659836	−	0.751409i	$-0.270626\pi$
$827$	37.9506	1.31967	0.659836	+	0.751409i	$0.270626\pi$
$828$	2.75826	0.0958561
$829$	7.05288	0.244957	0.122478	−	0.992471i	$-0.460916\pi$
$829$	7.05288	0.244957	0.122478	+	0.992471i	$0.460916\pi$
$830$	77.3908	2.68627
$831$	22.6203	0.784688
$832$	46.7802	1.62181
$833$	−13.7520	−0.476480
$834$	33.8181	1.17102
$835$	−47.4753	−1.64295
$836$	0	0
$837$	32.1047	1.10970
$838$	−18.8162	−0.649994
$839$	−21.9542	−0.757942	−0.378971	−	0.925409i	$-0.623722\pi$
$839$	−21.9542	−0.757942	−0.378971	+	0.925409i	$0.623722\pi$
$840$	69.7501	2.40661
$841$	−9.44010	−0.325521
$842$	27.5278	0.948670
$843$	−52.5880	−1.81123
$844$	−8.30000	−0.285698
$845$	56.2312	1.93441
$846$	−22.8005	−0.783898
$847$	0	0
$848$	2.58572	0.0887940
$849$	11.6951	0.401374
$850$	46.8372	1.60650
$851$	4.77980	0.163849
$852$	15.0032	0.514000
$853$	−12.3263	−0.422043	−0.211022	−	0.977481i	$-0.567679\pi$
$853$	−12.3263	−0.422043	−0.211022	+	0.977481i	$0.567679\pi$
$854$	−4.19580	−0.143577
$855$	−5.72359	−0.195743
$856$	17.3198	0.591977
$857$	7.42600	0.253667	0.126834	−	0.991924i	$-0.459519\pi$
$857$	7.42600	0.253667	0.126834	+	0.991924i	$0.459519\pi$
$858$	0	0
$859$	−10.8222	−0.369247	−0.184624	−	0.982809i	$-0.559107\pi$
$859$	−10.8222	−0.369247	−0.184624	+	0.982809i	$0.559107\pi$
$860$	4.37200	0.149084
$861$	−32.0836	−1.09341
$862$	15.7945	0.537964
$863$	−29.5880	−1.00719	−0.503593	−	0.863941i	$-0.667989\pi$
$863$	−29.5880	−1.00719	−0.503593	+	0.863941i	$0.667989\pi$
$864$	−30.7769	−1.04705
$865$	77.1982	2.62482
$866$	5.35874	0.182097
$867$	6.65807	0.226120
$868$	1.38540	0.0470236
$869$	0	0
$870$	−70.4842	−2.38964
$871$	−2.54030	−0.0860746
$872$	12.4637	0.422073
$873$	−30.5647	−1.03446
$874$	0.250406	0.00847010
$875$	31.3844	1.06099
$876$	−1.74380	−0.0589176
$877$	20.6128	0.696045	0.348023	−	0.937486i	$-0.386853\pi$
$877$	20.6128	0.696045	0.348023	+	0.937486i	$0.386853\pi$
$878$	40.1856	1.35620
$879$	−48.3574	−1.63105
$880$	0	0
$881$	0.245259	0.00826298	0.00413149	−	0.999991i	$-0.498685\pi$
$881$	0.245259	0.00826298	0.00413149	+	0.999991i	$0.498685\pi$
$882$	−35.1016	−1.18193
$883$	−6.05542	−0.203781	−0.101891	−	0.994796i	$-0.532489\pi$
$883$	−6.05542	−0.203781	−0.101891	+	0.994796i	$0.532489\pi$
$884$	−7.30026	−0.245534
$885$	162.461	5.46108
$886$	−48.2438	−1.62078
$887$	1.26377	0.0424333	0.0212167	−	0.999775i	$-0.493246\pi$
$887$	1.26377	0.0424333	0.0212167	+	0.999775i	$0.493246\pi$
$888$	−47.2545	−1.58576
$889$	25.5530	0.857019
$890$	7.38191	0.247442
$891$	0	0
$892$	−4.06897	−0.136239
$893$	0.451229	0.0150998
$894$	−80.1520	−2.68068
$895$	12.3396	0.412467
$896$	13.6845	0.457166
$897$	17.2495	0.575944
$898$	52.1280	1.73954
$899$	−9.22211	−0.307574
$900$	−26.0611	−0.868704
$901$	−3.16949	−0.105591
$902$	0	0
$903$	19.5141	0.649390
$904$	−13.7096	−0.455976
$905$	41.0302	1.36389
$906$	−0.574291	−0.0190795
$907$	−13.9710	−0.463900	−0.231950	−	0.972728i	$-0.574511\pi$
$907$	−13.9710	−0.463900	−0.231950	+	0.972728i	$0.574511\pi$
$908$	−9.00267	−0.298764
$909$	−49.8244	−1.65257
$910$	47.6622	1.57999
$911$	−32.0863	−1.06307	−0.531533	−	0.847037i	$-0.678384\pi$
$911$	−32.0863	−1.06307	−0.531533	+	0.847037i	$0.678384\pi$
$912$	−2.01785	−0.0668177
$913$	0	0
$914$	−39.3814	−1.30262
$915$	21.9400	0.725314
$916$	9.92508	0.327934
$917$	−12.9283	−0.426929
$918$	−76.3228	−2.51903
$919$	−9.71485	−0.320463	−0.160232	−	0.987079i	$-0.551224\pi$
$919$	−9.71485	−0.320463	−0.160232	+	0.987079i	$0.551224\pi$
$920$	11.4852	0.378655
$921$	28.5021	0.939176
$922$	26.7390	0.880601
$923$	67.5336	2.22290
$924$	0	0
$925$	−45.1614	−1.48490
$926$	29.7939	0.979088
$927$	129.359	4.24870
$928$	8.84069	0.290210
$929$	−37.7506	−1.23856	−0.619279	−	0.785171i	$-0.712575\pi$
$929$	−37.7506	−1.23856	−0.619279	+	0.785171i	$0.712575\pi$
$930$	33.2319	1.08972
$931$	0.694671	0.0227669
$932$	8.98986	0.294473
$933$	44.6674	1.46234
$934$	−16.7360	−0.547617
$935$	0	0
$936$	−122.746	−4.01207
$937$	45.6896	1.49262	0.746308	−	0.665601i	$-0.231825\pi$
$937$	45.6896	1.49262	0.746308	+	0.665601i	$0.231825\pi$
$938$	−1.14606	−0.0374202
$939$	−1.27468	−0.0415975
$940$	3.14183	0.102475
$941$	−8.70849	−0.283889	−0.141944	−	0.989875i	$-0.545335\pi$
$941$	−8.70849	−0.283889	−0.141944	+	0.989875i	$0.545335\pi$
$942$	0.276748	0.00901695
$943$	−5.28296	−0.172037
$944$	41.2255	1.34178
$945$	−108.626	−3.53360
$946$	0	0
$947$	−54.0484	−1.75634	−0.878168	−	0.478352i	$-0.841234\pi$
$947$	−54.0484	−1.75634	−0.878168	+	0.478352i	$0.841234\pi$
$948$	13.2953	0.431812
$949$	−7.84936	−0.254801
$950$	−2.36593	−0.0767610
$951$	−8.83043	−0.286346
$952$	−21.6955	−0.703154
$953$	42.0502	1.36214	0.681069	−	0.732219i	$-0.261515\pi$
$953$	42.0502	1.36214	0.681069	+	0.732219i	$0.261515\pi$
$954$	−8.09003	−0.261924
$955$	56.1137	1.81580
$956$	0.931610	0.0301304
$957$	0	0
$958$	7.31421	0.236312
$959$	−27.7478	−0.896024
$960$	−110.359	−3.56182
$961$	−26.6520	−0.859741
$962$	−32.2903	−1.04108
$963$	−44.1694	−1.42334
$964$	8.15661	0.262707
$965$	−39.8468	−1.28271
$966$	7.78214	0.250386
$967$	17.3621	0.558328	0.279164	−	0.960243i	$-0.409943\pi$
$967$	17.3621	0.558328	0.279164	+	0.960243i	$0.409943\pi$
$968$	0	0
$969$	2.47342	0.0794576
$970$	−19.3203	−0.620339
$971$	−55.0793	−1.76758	−0.883789	−	0.467886i	$-0.845016\pi$
$971$	−55.0793	−1.76758	−0.883789	+	0.467886i	$0.845016\pi$
$972$	15.3929	0.493729
$973$	−14.9710	−0.479949
$974$	29.5793	0.947783
$975$	−162.980	−5.21954
$976$	5.56740	0.178208
$977$	−6.16086	−0.197103	−0.0985517	−	0.995132i	$-0.531421\pi$
$977$	−6.16086	−0.197103	−0.0985517	+	0.995132i	$0.531421\pi$
$978$	−70.0386	−2.23959
$979$	0	0
$980$	4.83688	0.154508
$981$	−31.7852	−1.01482
$982$	−20.0049	−0.638383
$983$	10.3104	0.328851	0.164425	−	0.986390i	$-0.447423\pi$
$983$	10.3104	0.328851	0.164425	+	0.986390i	$0.447423\pi$
$984$	52.2289	1.66500
$985$	−23.0103	−0.733170
$986$	21.9238	0.698196
$987$	14.0233	0.446368
$988$	0.368765	0.0117320
$989$	3.21324	0.102175
$990$	0	0
$991$	−15.1363	−0.480820	−0.240410	−	0.970671i	$-0.577282\pi$
$991$	−15.1363	−0.480820	−0.240410	+	0.970671i	$0.577282\pi$
$992$	−4.16821	−0.132341
$993$	19.5960	0.621860
$994$	30.4679	0.966383
$995$	27.3091	0.865756
$996$	18.6089	0.589645
$997$	10.2906	0.325907	0.162953	−	0.986634i	$-0.447898\pi$
$997$	10.2906	0.325907	0.162953	+	0.986634i	$0.447898\pi$
$998$	−10.3423	−0.327381
$999$	73.5921	2.32835

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2783.2.a.g.1.3		5
11.10	odd	2		253.2.a.c.1.3	✓	5
33.32	even	2		2277.2.a.l.1.3		5
44.43	even	2		4048.2.a.bb.1.5		5
55.54	odd	2		6325.2.a.l.1.3		5
253.252	even	2		5819.2.a.d.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.2.a.c.1.3	✓	5	11.10	odd	2
2277.2.a.l.1.3		5	33.32	even	2
2783.2.a.g.1.3		5	1.1	even	1	trivial
4048.2.a.bb.1.5		5	44.43	even	2
5819.2.a.d.1.3		5	253.252	even	2
6325.2.a.l.1.3		5	55.54	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2783 = 11^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2783.a (trivial)

\(f(q)\)	\(=\)	\(q+1.28142 q^{2} -3.27194 q^{3} -0.357954 q^{4} +3.80110 q^{5} -4.19274 q^{6} +1.85610 q^{7} -3.02154 q^{8} +7.70561 q^{9} +4.87082 q^{10} +1.17121 q^{12} +5.27194 q^{13} +2.37845 q^{14} -12.4370 q^{15} -3.15596 q^{16} +3.86848 q^{17} +9.87415 q^{18} -0.195412 q^{19} -1.36062 q^{20} -6.07305 q^{21} -1.00000 q^{23} +9.88630 q^{24} +9.44840 q^{25} +6.75559 q^{26} -15.3965 q^{27} -0.664399 q^{28} +4.42266 q^{29} -15.9371 q^{30} -2.08520 q^{31} +1.99896 q^{32} +4.95715 q^{34} +7.05522 q^{35} -2.75826 q^{36} -4.77980 q^{37} -0.250406 q^{38} -17.2495 q^{39} -11.4852 q^{40} +5.28296 q^{41} -7.78214 q^{42} -3.21324 q^{43} +29.2898 q^{45} -1.28142 q^{46} -2.30911 q^{47} +10.3261 q^{48} -3.55490 q^{49} +12.1074 q^{50} -12.6574 q^{51} -1.88712 q^{52} -0.819313 q^{53} -19.7294 q^{54} -5.60827 q^{56} +0.639378 q^{57} +5.66730 q^{58} -13.0628 q^{59} +4.45188 q^{60} -1.76409 q^{61} -2.67202 q^{62} +14.3024 q^{63} +8.87343 q^{64} +20.0392 q^{65} -0.481852 q^{67} -1.38474 q^{68} +3.27194 q^{69} +9.04073 q^{70} +12.8100 q^{71} -23.2828 q^{72} -1.48889 q^{73} -6.12494 q^{74} -30.9146 q^{75} +0.0699487 q^{76} -22.1039 q^{78} +11.3518 q^{79} -11.9961 q^{80} +27.2596 q^{81} +6.76970 q^{82} +15.8886 q^{83} +2.17387 q^{84} +14.7045 q^{85} -4.11752 q^{86} -14.4707 q^{87} +1.51554 q^{89} +37.5327 q^{90} +9.78524 q^{91} +0.357954 q^{92} +6.82264 q^{93} -2.95895 q^{94} -0.742782 q^{95} -6.54047 q^{96} -3.96654 q^{97} -4.55533 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 4 q^{2} - 5 q^{3} + 6 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} + 6 q^{8} + 4 q^{9} + 6 q^{10} + 3 q^{12} + 15 q^{13} + 4 q^{14} - 2 q^{15} + 8 q^{16} + 9 q^{17} - 6 q^{18} + 5 q^{19} - 17 q^{20} + 3 q^{21}+ \cdots + 33 q^{98}+O(q^{100}) \) 5 * q + 4 * q^2 - 5 * q^3 + 6 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 + 6 * q^8 + 4 * q^9 + 6 * q^10 + 3 * q^12 + 15 * q^13 + 4 * q^14 - 2 * q^15 + 8 * q^16 + 9 * q^17 - 6 * q^18 + 5 * q^19 - 17 * q^20 + 3 * q^21 - 5 * q^23 + 21 * q^24 + 12 * q^25 + 5 * q^26 - 20 * q^27 + 8 * q^29 - 37 * q^30 - 4 * q^31 + 31 * q^32 + 36 * q^34 + 20 * q^35 - 3 * q^36 + 8 * q^37 - 11 * q^38 - 29 * q^39 - 22 * q^40 + 6 * q^41 + q^42 + 8 * q^43 + 21 * q^45 - 4 * q^46 - 34 * q^47 + 46 * q^48 + 14 * q^49 - 22 * q^50 - 4 * q^51 + 9 * q^52 + 2 * q^53 - 27 * q^54 + 27 * q^56 - 7 * q^57 + 12 * q^58 - 13 * q^59 + 15 * q^60 - 18 * q^61 - 30 * q^62 + 7 * q^63 + 36 * q^64 - 4 * q^65 - 4 * q^67 + 43 * q^68 + 5 * q^69 + 11 * q^70 + 10 * q^71 - 31 * q^72 + 31 * q^73 - 19 * q^74 - 66 * q^75 - 27 * q^76 + 3 * q^79 + 2 * q^80 + 33 * q^81 - 10 * q^82 + 43 * q^83 + 26 * q^84 + 3 * q^85 - 15 * q^86 - 18 * q^87 + 15 * q^89 + 79 * q^90 + 3 * q^91 - 6 * q^92 - 9 * q^93 - 7 * q^94 - 3 * q^95 + 10 * q^96 + 17 * q^97 + 33 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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