LMFDB - Embedded newform 2883.2.a.o.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2883,2,Mod(1,2883)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2883, 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("2883.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2883 = 3 \cdot 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2883.a (trivial)

Newform invariants

comment:select newform

sage:traces = [8,1,-8,13,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$23.0208709027$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 14x^{6} + 10x^{5} + 62x^{4} - 31x^{3} - 82x^{2} + 42x + 9 $ x^8 - x^7 - 14x^6 + 10x^5 + 62x^4 - 31x^3 - 82x^2 + 42x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 93)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.67120$ of defining polynomial
Character	$\chi$	$=$	2883.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.67120 q^{2} -1.00000 q^{3} +0.792899 q^{4} +3.89560 q^{5} +1.67120 q^{6} +4.51364 q^{7} +2.01730 q^{8} +1.00000 q^{9} -6.51032 q^{10} -0.335097 q^{11} -0.792899 q^{12} +1.74603 q^{13} -7.54317 q^{14} -3.89560 q^{15} -4.95711 q^{16} +3.47039 q^{17} -1.67120 q^{18} +0.211855 q^{19} +3.08882 q^{20} -4.51364 q^{21} +0.560013 q^{22} -2.74271 q^{23} -2.01730 q^{24} +10.1757 q^{25} -2.91796 q^{26} -1.00000 q^{27} +3.57886 q^{28} +7.23800 q^{29} +6.51032 q^{30} +4.24970 q^{32} +0.335097 q^{33} -5.79970 q^{34} +17.5833 q^{35} +0.792899 q^{36} +7.41580 q^{37} -0.354051 q^{38} -1.74603 q^{39} +7.85861 q^{40} +6.51032 q^{41} +7.54317 q^{42} -3.05753 q^{43} -0.265698 q^{44} +3.89560 q^{45} +4.58361 q^{46} +3.33460 q^{47} +4.95711 q^{48} +13.3729 q^{49} -17.0056 q^{50} -3.47039 q^{51} +1.38442 q^{52} -12.1365 q^{53} +1.67120 q^{54} -1.30540 q^{55} +9.10537 q^{56} -0.211855 q^{57} -12.0961 q^{58} -1.37161 q^{59} -3.08882 q^{60} -3.58978 q^{61} +4.51364 q^{63} +2.81214 q^{64} +6.80184 q^{65} -0.560013 q^{66} -1.37225 q^{67} +2.75167 q^{68} +2.74271 q^{69} -29.3852 q^{70} -1.73742 q^{71} +2.01730 q^{72} -13.0174 q^{73} -12.3933 q^{74} -10.1757 q^{75} +0.167979 q^{76} -1.51250 q^{77} +2.91796 q^{78} -8.50919 q^{79} -19.3109 q^{80} +1.00000 q^{81} -10.8800 q^{82} +7.95742 q^{83} -3.57886 q^{84} +13.5193 q^{85} +5.10973 q^{86} -7.23800 q^{87} -0.675992 q^{88} +8.05400 q^{89} -6.51032 q^{90} +7.88094 q^{91} -2.17469 q^{92} -5.57278 q^{94} +0.825302 q^{95} -4.24970 q^{96} -3.44476 q^{97} -22.3488 q^{98} -0.335097 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 8 q^{3} + 13 q^{4} + 3 q^{5} - q^{6} - q^{7} + 9 q^{8} + 8 q^{9} + 6 q^{10} + 5 q^{11} - 13 q^{12} + 4 q^{13} + 3 q^{14} - 3 q^{15} + 19 q^{16} - 2 q^{17} + q^{18} - 7 q^{19} + q^{20}+ \cdots + 5 q^{99}+O(q^{100}) $ 8 * q + q^2 - 8 * q^3 + 13 * q^4 + 3 * q^5 - q^6 - q^7 + 9 * q^8 + 8 * q^9 + 6 * q^10 + 5 * q^11 - 13 * q^12 + 4 * q^13 + 3 * q^14 - 3 * q^15 + 19 * q^16 - 2 * q^17 + q^18 - 7 * q^19 + q^20 + q^21 + 9 * q^23 - 9 * q^24 + 15 * q^25 + 8 * q^26 - 8 * q^27 - 3 * q^28 + q^29 - 6 * q^30 + 54 * q^32 - 5 * q^33 - 48 * q^34 + 51 * q^35 + 13 * q^36 + 14 * q^37 - 16 * q^38 - 4 * q^39 + 59 * q^40 - 6 * q^41 - 3 * q^42 - 36 * q^43 + 27 * q^44 + 3 * q^45 + 3 * q^46 + 35 * q^47 - 19 * q^48 + 3 * q^49 - 37 * q^50 + 2 * q^51 + 46 * q^52 - 8 * q^53 - q^54 - 6 * q^55 + 52 * q^56 + 7 * q^57 - 52 * q^58 - 28 * q^59 - q^60 - q^63 + 17 * q^64 + 3 * q^65 + 30 * q^67 + 15 * q^68 - 9 * q^69 - 35 * q^70 - 6 * q^71 + 9 * q^72 + q^73 + 30 * q^74 - 15 * q^75 - 34 * q^76 - q^77 - 8 * q^78 - 36 * q^79 + 38 * q^80 + 8 * q^81 - 7 * q^82 + 22 * q^83 + 3 * q^84 - 8 * q^85 + 3 * q^86 - q^87 + 16 * q^88 + q^89 + 6 * q^90 + 6 * q^91 + 35 * q^92 + 37 * q^94 + 50 * q^95 - 54 * q^96 + 29 * q^97 - 41 * q^98 + 5 * 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 $

$2$	−1.67120	−1.18171	−0.590857	−	0.806776i	$-0.701210\pi$
$2$	−1.67120	−1.18171	−0.590857	+	0.806776i	$0.701210\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.792899	0.396449
$5$	3.89560	1.74217	0.871083	−	0.491136i	$-0.163418\pi$
$5$	3.89560	1.74217	0.871083	+	0.491136i	$0.163418\pi$
$6$	1.67120	0.682263
$7$	4.51364	1.70599	0.852997	−	0.521916i	$-0.174783\pi$
$7$	4.51364	1.70599	0.852997	+	0.521916i	$0.174783\pi$
$8$	2.01730	0.713225
$9$	1.00000	0.333333
$10$	−6.51032	−2.05874
$11$	−0.335097	−0.101035	−0.0505177	−	0.998723i	$-0.516087\pi$
$11$	−0.335097	−0.101035	−0.0505177	+	0.998723i	$0.516087\pi$
$12$	−0.792899	−0.228890
$13$	1.74603	0.484261	0.242131	−	0.970244i	$-0.422154\pi$
$13$	1.74603	0.484261	0.242131	+	0.970244i	$0.422154\pi$
$14$	−7.54317	−2.01600
$15$	−3.89560	−1.00584
$16$	−4.95711	−1.23928
$17$	3.47039	0.841693	0.420847	−	0.907132i	$-0.361733\pi$
$17$	3.47039	0.841693	0.420847	+	0.907132i	$0.361733\pi$
$18$	−1.67120	−0.393905
$19$	0.211855	0.0486028	0.0243014	−	0.999705i	$-0.492264\pi$
$19$	0.211855	0.0486028	0.0243014	+	0.999705i	$0.492264\pi$
$20$	3.08882	0.690681
$21$	−4.51364	−0.984956
$22$	0.560013	0.119395
$23$	−2.74271	−0.571895	−0.285947	−	0.958245i	$-0.592308\pi$
$23$	−2.74271	−0.571895	−0.285947	+	0.958245i	$0.592308\pi$
$24$	−2.01730	−0.411780
$25$	10.1757	2.03514
$26$	−2.91796	−0.572259
$27$	−1.00000	−0.192450
$28$	3.57886	0.676340
$29$	7.23800	1.34406	0.672031	−	0.740523i	$-0.265422\pi$
$29$	7.23800	1.34406	0.672031	+	0.740523i	$0.265422\pi$
$30$	6.51032	1.18862
$31$	0	0
$31$	0	0
$32$	4.24970	0.751247
$33$	0.335097	0.0583329
$34$	−5.79970	−0.994641
$35$	17.5833	2.97212
$36$	0.792899	0.132150
$37$	7.41580	1.21915	0.609575	−	0.792729i	$-0.291340\pi$
$37$	7.41580	1.21915	0.609575	+	0.792729i	$0.291340\pi$
$38$	−0.354051	−0.0574347
$39$	−1.74603	−0.279588
$40$	7.85861	1.24256
$41$	6.51032	1.01674	0.508370	−	0.861139i	$-0.330248\pi$
$41$	6.51032	1.01674	0.508370	+	0.861139i	$0.330248\pi$
$42$	7.54317	1.16394
$43$	−3.05753	−0.466269	−0.233134	−	0.972445i	$-0.574898\pi$
$43$	−3.05753	−0.466269	−0.233134	+	0.972445i	$0.574898\pi$
$44$	−0.265698	−0.0400555
$45$	3.89560	0.580722
$46$	4.58361	0.675816
$47$	3.33460	0.486402	0.243201	−	0.969976i	$-0.421803\pi$
$47$	3.33460	0.486402	0.243201	+	0.969976i	$0.421803\pi$
$48$	4.95711	0.715497
$49$	13.3729	1.91042
$50$	−17.0056	−2.40496
$51$	−3.47039	−0.485952
$52$	1.38442	0.191985
$53$	−12.1365	−1.66708	−0.833541	−	0.552458i	$-0.813690\pi$
$53$	−12.1365	−1.66708	−0.833541	+	0.552458i	$0.813690\pi$
$54$	1.67120	0.227421
$55$	−1.30540	−0.176021
$56$	9.10537	1.21676
$57$	−0.211855	−0.0280609
$58$	−12.0961	−1.58830
$59$	−1.37161	−0.178568	−0.0892842	−	0.996006i	$-0.528458\pi$
$59$	−1.37161	−0.178568	−0.0892842	+	0.996006i	$0.528458\pi$
$60$	−3.08882	−0.398765
$61$	−3.58978	−0.459624	−0.229812	−	0.973235i	$-0.573811\pi$
$61$	−3.58978	−0.459624	−0.229812	+	0.973235i	$0.573811\pi$
$62$	0	0
$63$	4.51364	0.568665
$64$	2.81214	0.351517
$65$	6.80184	0.843664
$66$	−0.560013	−0.0689328
$67$	−1.37225	−0.167647	−0.0838233	−	0.996481i	$-0.526713\pi$
$67$	−1.37225	−0.167647	−0.0838233	+	0.996481i	$0.526713\pi$
$68$	2.75167	0.333689
$69$	2.74271	0.330184
$70$	−29.3852	−3.51220
$71$	−1.73742	−0.206194	−0.103097	−	0.994671i	$-0.532875\pi$
$71$	−1.73742	−0.206194	−0.103097	+	0.994671i	$0.532875\pi$
$72$	2.01730	0.237742
$73$	−13.0174	−1.52357	−0.761784	−	0.647832i	$-0.775676\pi$
$73$	−13.0174	−1.52357	−0.761784	+	0.647832i	$0.775676\pi$
$74$	−12.3933	−1.44069
$75$	−10.1757	−1.17499
$76$	0.167979	0.0192686
$77$	−1.51250	−0.172366
$78$	2.91796	0.330394
$79$	−8.50919	−0.957358	−0.478679	−	0.877990i	$-0.658884\pi$
$79$	−8.50919	−0.957358	−0.478679	+	0.877990i	$0.658884\pi$
$80$	−19.3109	−2.15903
$81$	1.00000	0.111111
$82$	−10.8800	−1.20150
$83$	7.95742	0.873440	0.436720	−	0.899597i	$-0.356140\pi$
$83$	7.95742	0.873440	0.436720	+	0.899597i	$0.356140\pi$
$84$	−3.57886	−0.390485
$85$	13.5193	1.46637
$86$	5.10973	0.550997
$87$	−7.23800	−0.775995
$88$	−0.675992	−0.0720610
$89$	8.05400	0.853722	0.426861	−	0.904317i	$-0.359619\pi$
$89$	8.05400	0.853722	0.426861	+	0.904317i	$0.359619\pi$
$90$	−6.51032	−0.686248
$91$	7.88094	0.826147
$92$	−2.17469	−0.226727
$93$	0	0
$94$	−5.57278	−0.574788
$95$	0.825302	0.0846742
$96$	−4.24970	−0.433733
$97$	−3.44476	−0.349763	−0.174881	−	0.984589i	$-0.555954\pi$
$97$	−3.44476	−0.349763	−0.174881	+	0.984589i	$0.555954\pi$
$98$	−22.3488	−2.25757
$99$	−0.335097	−0.0336785
$100$	8.06831	0.806831
$101$	−0.632314	−0.0629176	−0.0314588	−	0.999505i	$-0.510015\pi$
$101$	−0.632314	−0.0629176	−0.0314588	+	0.999505i	$0.510015\pi$
$102$	5.79970	0.574256
$103$	1.08793	0.107197	0.0535985	−	0.998563i	$-0.482931\pi$
$103$	1.08793	0.107197	0.0535985	+	0.998563i	$0.482931\pi$
$104$	3.52227	0.345387
$105$	−17.5833	−1.71596
$106$	20.2825	1.97001
$107$	−7.97759	−0.771223	−0.385611	−	0.922661i	$-0.626009\pi$
$107$	−7.97759	−0.771223	−0.385611	+	0.922661i	$0.626009\pi$
$108$	−0.792899	−0.0762967
$109$	0.219454	0.0210198	0.0105099	−	0.999945i	$-0.496655\pi$
$109$	0.219454	0.0210198	0.0105099	+	0.999945i	$0.496655\pi$
$110$	2.18159	0.208006
$111$	−7.41580	−0.703876
$112$	−22.3746	−2.11420
$113$	−11.9252	−1.12183	−0.560916	−	0.827873i	$-0.689551\pi$
$113$	−11.9252	−1.12183	−0.560916	+	0.827873i	$0.689551\pi$
$114$	0.354051	0.0331599
$115$	−10.6845	−0.996336
$116$	5.73900	0.532853
$117$	1.74603	0.161420
$118$	2.29223	0.211017
$119$	15.6641	1.43592
$120$	−7.85861	−0.717390
$121$	−10.8877	−0.989792
$122$	5.99922	0.543144
$123$	−6.51032	−0.587016
$124$	0	0
$125$	20.1625	1.80339
$126$	−7.54317	−0.671999
$127$	−12.9672	−1.15065	−0.575324	−	0.817925i	$-0.695124\pi$
$127$	−12.9672	−1.15065	−0.575324	+	0.817925i	$0.695124\pi$
$128$	−13.1990	−1.16664
$129$	3.05753	0.269200
$130$	−11.3672	−0.996970
$131$	13.2669	1.15914	0.579568	−	0.814924i	$-0.303221\pi$
$131$	13.2669	1.15914	0.579568	+	0.814924i	$0.303221\pi$
$132$	0.265698	0.0231260
$133$	0.956236	0.0829161
$134$	2.29330	0.198111
$135$	−3.89560	−0.335280
$136$	7.00083	0.600316
$137$	10.5121	0.898109	0.449054	−	0.893504i	$-0.351761\pi$
$137$	10.5121	0.898109	0.449054	+	0.893504i	$0.351761\pi$
$138$	−4.58361	−0.390183
$139$	−23.4907	−1.99245	−0.996227	−	0.0867830i	$-0.972341\pi$
$139$	−23.4907	−1.99245	−0.996227	+	0.0867830i	$0.972341\pi$
$140$	13.9418	1.17830
$141$	−3.33460	−0.280824
$142$	2.90357	0.243662
$143$	−0.585089	−0.0489276
$144$	−4.95711	−0.413092
$145$	28.1963	2.34158
$146$	21.7546	1.80042
$147$	−13.3729	−1.10298
$148$	5.87998	0.483331
$149$	−10.6943	−0.876113	−0.438056	−	0.898948i	$-0.644333\pi$
$149$	−10.6943	−0.876113	−0.438056	+	0.898948i	$0.644333\pi$
$150$	17.0056	1.38850
$151$	−2.81490	−0.229073	−0.114537	−	0.993419i	$-0.536538\pi$
$151$	−2.81490	−0.229073	−0.114537	+	0.993419i	$0.536538\pi$
$152$	0.427376	0.0346647
$153$	3.47039	0.280564
$154$	2.52769	0.203687
$155$	0	0
$156$	−1.38442	−0.110843
$157$	14.6205	1.16684	0.583420	−	0.812171i	$-0.301714\pi$
$157$	14.6205	1.16684	0.583420	+	0.812171i	$0.301714\pi$
$158$	14.2205	1.13132
$159$	12.1365	0.962490
$160$	16.5551	1.30880
$161$	−12.3796	−0.975649
$162$	−1.67120	−0.131302
$163$	−17.2452	−1.35075	−0.675374	−	0.737476i	$-0.736018\pi$
$163$	−17.2452	−1.35075	−0.675374	+	0.737476i	$0.736018\pi$
$164$	5.16202	0.403086
$165$	1.30540	0.101626
$166$	−13.2984	−1.03216
$167$	0.408108	0.0315804	0.0157902	−	0.999875i	$-0.494974\pi$
$167$	0.408108	0.0315804	0.0157902	+	0.999875i	$0.494974\pi$
$168$	−9.10537	−0.702495
$169$	−9.95138	−0.765491
$170$	−22.5933	−1.73283
$171$	0.211855	0.0162009
$172$	−2.42431	−0.184852
$173$	3.74370	0.284628	0.142314	−	0.989822i	$-0.454546\pi$
$173$	3.74370	0.284628	0.142314	+	0.989822i	$0.454546\pi$
$174$	12.0961	0.917004
$175$	45.9295	3.47194
$176$	1.66111	0.125211
$177$	1.37161	0.103097
$178$	−13.4598	−1.00886
$179$	−1.83178	−0.136913	−0.0684567	−	0.997654i	$-0.521808\pi$
$179$	−1.83178	−0.136913	−0.0684567	+	0.997654i	$0.521808\pi$
$180$	3.08882	0.230227
$181$	11.5508	0.858565	0.429283	−	0.903170i	$-0.358766\pi$
$181$	11.5508	0.858565	0.429283	+	0.903170i	$0.358766\pi$
$182$	−13.1706	−0.976270
$183$	3.58978	0.265364
$184$	−5.53288	−0.407889
$185$	28.8890	2.12396
$186$	0	0
$187$	−1.16292	−0.0850409
$188$	2.64400	0.192834
$189$	−4.51364	−0.328319
$190$	−1.37924	−0.100061
$191$	−8.89041	−0.643287	−0.321644	−	0.946861i	$-0.604235\pi$
$191$	−8.89041	−0.643287	−0.321644	+	0.946861i	$0.604235\pi$
$192$	−2.81214	−0.202949
$193$	−11.3286	−0.815449	−0.407725	−	0.913105i	$-0.633678\pi$
$193$	−11.3286	−0.815449	−0.407725	+	0.913105i	$0.633678\pi$
$194$	5.75688	0.413320
$195$	−6.80184	−0.487090
$196$	10.6034	0.757383
$197$	13.9315	0.992579	0.496289	−	0.868157i	$-0.334696\pi$
$197$	13.9315	0.992579	0.496289	+	0.868157i	$0.334696\pi$
$198$	0.560013	0.0397984
$199$	−0.446722	−0.0316673	−0.0158336	−	0.999875i	$-0.505040\pi$
$199$	−0.446722	−0.0316673	−0.0158336	+	0.999875i	$0.505040\pi$
$200$	20.5275	1.45151
$201$	1.37225	0.0967909
$202$	1.05672	0.0743506
$203$	32.6697	2.29296
$204$	−2.75167	−0.192655
$205$	25.3616	1.77133
$206$	−1.81815	−0.126676
$207$	−2.74271	−0.190632
$208$	−8.65526	−0.600134
$209$	−0.0709919	−0.00491061
$210$	29.3852	2.02777
$211$	20.4011	1.40447	0.702234	−	0.711946i	$-0.252186\pi$
$211$	20.4011	1.40447	0.702234	+	0.711946i	$0.252186\pi$
$212$	−9.62304	−0.660913
$213$	1.73742	0.119046
$214$	13.3321	0.911365
$215$	−11.9109	−0.812318
$216$	−2.01730	−0.137260
$217$	0	0
$218$	−0.366750	−0.0248394
$219$	13.0174	0.879632
$220$	−1.03505	−0.0697833
$221$	6.05940	0.407599
$222$	12.3933	0.831781
$223$	−20.4372	−1.36857	−0.684287	−	0.729213i	$-0.739886\pi$
$223$	−20.4372	−1.36857	−0.684287	+	0.729213i	$0.739886\pi$
$224$	19.1816	1.28162
$225$	10.1757	0.678381
$226$	19.9294	1.32568
$227$	−12.1282	−0.804976	−0.402488	−	0.915425i	$-0.631854\pi$
$227$	−12.1282	−0.804976	−0.402488	+	0.915425i	$0.631854\pi$
$228$	−0.167979	−0.0111247
$229$	−23.5742	−1.55783	−0.778915	−	0.627130i	$-0.784230\pi$
$229$	−23.5742	−1.55783	−0.778915	+	0.627130i	$0.784230\pi$
$230$	17.8559	1.17738
$231$	1.51250	0.0995155
$232$	14.6012	0.958618
$233$	7.68952	0.503757	0.251879	−	0.967759i	$-0.418952\pi$
$233$	7.68952	0.503757	0.251879	+	0.967759i	$0.418952\pi$
$234$	−2.91796	−0.190753
$235$	12.9903	0.847393
$236$	−1.08755	−0.0707934
$237$	8.50919	0.552731
$238$	−26.1777	−1.69685
$239$	22.3543	1.44598	0.722990	−	0.690859i	$-0.242767\pi$
$239$	22.3543	1.44598	0.722990	+	0.690859i	$0.242767\pi$
$240$	19.3109	1.24651
$241$	−8.78690	−0.566014	−0.283007	−	0.959118i	$-0.591332\pi$
$241$	−8.78690	−0.566014	−0.283007	+	0.959118i	$0.591332\pi$
$242$	18.1955	1.16965
$243$	−1.00000	−0.0641500
$244$	−2.84633	−0.182218
$245$	52.0955	3.32826
$246$	10.8800	0.693685
$247$	0.369905	0.0235365
$248$	0	0
$249$	−7.95742	−0.504281
$250$	−33.6955	−2.13109
$251$	−9.27250	−0.585275	−0.292637	−	0.956223i	$-0.594533\pi$
$251$	−9.27250	−0.585275	−0.292637	+	0.956223i	$0.594533\pi$
$252$	3.57886	0.225447
$253$	0.919074	0.0577817
$254$	21.6707	1.35974
$255$	−13.5193	−0.846609
$256$	16.4339	1.02712
$257$	−2.03509	−0.126946	−0.0634729	−	0.997984i	$-0.520218\pi$
$257$	−2.03509	−0.126946	−0.0634729	+	0.997984i	$0.520218\pi$
$258$	−5.10973	−0.318118
$259$	33.4722	2.07986
$260$	5.39317	0.334470
$261$	7.23800	0.448021
$262$	−22.1716	−1.36977
$263$	29.6069	1.82564	0.912819	−	0.408364i	$-0.133900\pi$
$263$	29.6069	1.82564	0.912819	+	0.408364i	$0.133900\pi$
$264$	0.675992	0.0416044
$265$	−47.2791	−2.90433
$266$	−1.59806	−0.0979832
$267$	−8.05400	−0.492897
$268$	−1.08805	−0.0664634
$269$	20.6451	1.25875	0.629376	−	0.777101i	$-0.283311\pi$
$269$	20.6451	1.25875	0.629376	+	0.777101i	$0.283311\pi$
$270$	6.51032	0.396205
$271$	−6.46297	−0.392598	−0.196299	−	0.980544i	$-0.562892\pi$
$271$	−6.46297	−0.392598	−0.196299	+	0.980544i	$0.562892\pi$
$272$	−17.2031	−1.04309
$273$	−7.88094	−0.476976
$274$	−17.5678	−1.06131
$275$	−3.40985	−0.205622
$276$	2.17469	0.130901
$277$	−9.45301	−0.567976	−0.283988	−	0.958828i	$-0.591658\pi$
$277$	−9.45301	−0.567976	−0.283988	+	0.958828i	$0.591658\pi$
$278$	39.2576	2.35451
$279$	0	0
$280$	35.4709	2.11979
$281$	−2.27165	−0.135515	−0.0677575	−	0.997702i	$-0.521584\pi$
$281$	−2.27165	−0.135515	−0.0677575	+	0.997702i	$0.521584\pi$
$282$	5.57278	0.331854
$283$	−27.1242	−1.61237	−0.806183	−	0.591667i	$-0.798470\pi$
$283$	−27.1242	−1.61237	−0.806183	+	0.591667i	$0.798470\pi$
$284$	−1.37760	−0.0817454
$285$	−0.825302	−0.0488867
$286$	0.977799	0.0578184
$287$	29.3852	1.73455
$288$	4.24970	0.250416
$289$	−4.95640	−0.291553
$290$	−47.1216	−2.76708
$291$	3.44476	0.201936
$292$	−10.3215	−0.604017
$293$	9.17316	0.535902	0.267951	−	0.963433i	$-0.413653\pi$
$293$	9.17316	0.535902	0.267951	+	0.963433i	$0.413653\pi$
$294$	22.3488	1.30341
$295$	−5.34325	−0.311096
$296$	14.9599	0.869527
$297$	0.335097	0.0194443
$298$	17.8723	1.03532
$299$	−4.78885	−0.276947
$300$	−8.06831	−0.465824
$301$	−13.8006	−0.795452
$302$	4.70425	0.270699
$303$	0.632314	0.0363255
$304$	−1.05019	−0.0602324
$305$	−13.9843	−0.800741
$306$	−5.79970	−0.331547
$307$	−9.06925	−0.517609	−0.258805	−	0.965930i	$-0.583329\pi$
$307$	−9.06925	−0.517609	−0.258805	+	0.965930i	$0.583329\pi$
$308$	−1.19926	−0.0683344
$309$	−1.08793	−0.0618902
$310$	0	0
$311$	−11.8965	−0.674587	−0.337293	−	0.941400i	$-0.609511\pi$
$311$	−11.8965	−0.674587	−0.337293	+	0.941400i	$0.609511\pi$
$312$	−3.52227	−0.199409
$313$	15.6841	0.886516	0.443258	−	0.896394i	$-0.353823\pi$
$313$	15.6841	0.886516	0.443258	+	0.896394i	$0.353823\pi$
$314$	−24.4337	−1.37887
$315$	17.5833	0.990708
$316$	−6.74692	−0.379544
$317$	−15.0304	−0.844194	−0.422097	−	0.906551i	$-0.638706\pi$
$317$	−15.0304	−0.844194	−0.422097	+	0.906551i	$0.638706\pi$
$318$	−20.2825	−1.13739
$319$	−2.42543	−0.135798
$320$	10.9550	0.612401
$321$	7.97759	0.445266
$322$	20.6887	1.15294
$323$	0.735219	0.0409087
$324$	0.792899	0.0440499
$325$	17.7671	0.985541
$326$	28.8201	1.59620
$327$	−0.219454	−0.0121358
$328$	13.1333	0.725164
$329$	15.0512	0.829799
$330$	−2.18159	−0.120092
$331$	−13.5963	−0.747318	−0.373659	−	0.927566i	$-0.621897\pi$
$331$	−13.5963	−0.747318	−0.373659	+	0.927566i	$0.621897\pi$
$332$	6.30943	0.346275
$333$	7.41580	0.406383
$334$	−0.682029	−0.0373190
$335$	−5.34573	−0.292068
$336$	22.3746	1.22063
$337$	10.3562	0.564136	0.282068	−	0.959394i	$-0.408980\pi$
$337$	10.3562	0.564136	0.282068	+	0.959394i	$0.408980\pi$
$338$	16.6307	0.904592
$339$	11.9252	0.647689
$340$	10.7194	0.581341
$341$	0	0
$342$	−0.354051	−0.0191449
$343$	28.7650	1.55316
$344$	−6.16796	−0.332554
$345$	10.6845	0.575235
$346$	−6.25645	−0.336349
$347$	2.52600	0.135603	0.0678013	−	0.997699i	$-0.478402\pi$
$347$	2.52600	0.135603	0.0678013	+	0.997699i	$0.478402\pi$
$348$	−5.73900	−0.307643
$349$	34.8988	1.86809	0.934046	−	0.357153i	$-0.116252\pi$
$349$	34.8988	1.86809	0.934046	+	0.357153i	$0.116252\pi$
$350$	−76.7572	−4.10284
$351$	−1.74603	−0.0931962
$352$	−1.42406	−0.0759027
$353$	−9.14039	−0.486494	−0.243247	−	0.969964i	$-0.578213\pi$
$353$	−9.14039	−0.486494	−0.243247	+	0.969964i	$0.578213\pi$
$354$	−2.29223	−0.121831
$355$	−6.76830	−0.359224
$356$	6.38601	0.338458
$357$	−15.6641	−0.829031
$358$	3.06126	0.161793
$359$	−4.71581	−0.248891	−0.124445	−	0.992226i	$-0.539715\pi$
$359$	−4.71581	−0.248891	−0.124445	+	0.992226i	$0.539715\pi$
$360$	7.85861	0.414185
$361$	−18.9551	−0.997638
$362$	−19.3037	−1.01458
$363$	10.8877	0.571457
$364$	6.24879	0.327526
$365$	−50.7105	−2.65431
$366$	−5.99922	−0.313584
$367$	24.4353	1.27551	0.637756	−	0.770238i	$-0.279863\pi$
$367$	24.4353	1.27551	0.637756	+	0.770238i	$0.279863\pi$
$368$	13.5959	0.708736
$369$	6.51032	0.338914
$370$	−48.2792	−2.50992
$371$	−54.7799	−2.84403
$372$	0	0
$373$	−3.54248	−0.183422	−0.0917112	−	0.995786i	$-0.529234\pi$
$373$	−3.54248	−0.183422	−0.0917112	+	0.995786i	$0.529234\pi$
$374$	1.94346	0.100494
$375$	−20.1625	−1.04119
$376$	6.72691	0.346914
$377$	12.6378	0.650877
$378$	7.54317	0.387979
$379$	24.1617	1.24111	0.620553	−	0.784165i	$-0.286908\pi$
$379$	24.1617	1.24111	0.620553	+	0.784165i	$0.286908\pi$
$380$	0.654381	0.0335690
$381$	12.9672	0.664327
$382$	14.8576	0.760182
$383$	−1.18780	−0.0606935	−0.0303468	−	0.999539i	$-0.509661\pi$
$383$	−1.18780	−0.0606935	−0.0303468	+	0.999539i	$0.509661\pi$
$384$	13.1990	0.673560
$385$	−5.89212	−0.300290
$386$	18.9323	0.963628
$387$	−3.05753	−0.155423
$388$	−2.73135	−0.138663
$389$	−18.2656	−0.926102	−0.463051	−	0.886332i	$-0.653245\pi$
$389$	−18.2656	−0.926102	−0.463051	+	0.886332i	$0.653245\pi$
$390$	11.3672	0.575601
$391$	−9.51827	−0.481360
$392$	26.9772	1.36256
$393$	−13.2669	−0.669228
$394$	−23.2823	−1.17294
$395$	−33.1484	−1.66788
$396$	−0.265698	−0.0133518
$397$	−2.65218	−0.133109	−0.0665546	−	0.997783i	$-0.521201\pi$
$397$	−2.65218	−0.133109	−0.0665546	+	0.997783i	$0.521201\pi$
$398$	0.746560	0.0374217
$399$	−0.956236	−0.0478717
$400$	−50.4421	−2.52211
$401$	16.6033	0.829131	0.414566	−	0.910019i	$-0.363934\pi$
$401$	16.6033	0.829131	0.414566	+	0.910019i	$0.363934\pi$
$402$	−2.29330	−0.114379
$403$	0	0
$404$	−0.501361	−0.0249436
$405$	3.89560	0.193574
$406$	−54.5975	−2.70963
$407$	−2.48501	−0.123177
$408$	−7.00083	−0.346593
$409$	−25.6723	−1.26942	−0.634708	−	0.772752i	$-0.718880\pi$
$409$	−25.6723	−1.26942	−0.634708	+	0.772752i	$0.718880\pi$
$410$	−42.3842	−2.09321
$411$	−10.5121	−0.518523
$412$	0.862619	0.0424982
$413$	−6.19095	−0.304637
$414$	4.58361	0.225272
$415$	30.9989	1.52168
$416$	7.42010	0.363800
$417$	23.4907	1.15034
$418$	0.118641	0.00580294
$419$	31.1576	1.52215	0.761075	−	0.648664i	$-0.224672\pi$
$419$	31.1576	1.52215	0.761075	+	0.648664i	$0.224672\pi$
$420$	−13.9418	−0.680290
$421$	−30.5518	−1.48900	−0.744502	−	0.667620i	$-0.767313\pi$
$421$	−30.5518	−1.48900	−0.744502	+	0.667620i	$0.767313\pi$
$422$	−34.0942	−1.65968
$423$	3.33460	0.162134
$424$	−24.4831	−1.18900
$425$	35.3137	1.71297
$426$	−2.90357	−0.140679
$427$	−16.2029	−0.784115
$428$	−6.32542	−0.305751
$429$	0.585089	0.0282484
$430$	19.9055	0.959928
$431$	−36.6717	−1.76641	−0.883206	−	0.468986i	$-0.844620\pi$
$431$	−36.6717	−1.76641	−0.883206	+	0.468986i	$0.844620\pi$
$432$	4.95711	0.238499
$433$	13.7562	0.661083	0.330541	−	0.943791i	$-0.392769\pi$
$433$	13.7562	0.661083	0.330541	+	0.943791i	$0.392769\pi$
$434$	0	0
$435$	−28.1963	−1.35191
$436$	0.174004	0.00833330
$437$	−0.581057	−0.0277957
$438$	−21.7546	−1.03947
$439$	−5.74749	−0.274313	−0.137156	−	0.990549i	$-0.543796\pi$
$439$	−5.74749	−0.274313	−0.137156	+	0.990549i	$0.543796\pi$
$440$	−2.63340	−0.125542
$441$	13.3729	0.636805
$442$	−10.1265	−0.481666
$443$	32.0745	1.52390	0.761952	−	0.647633i	$-0.224241\pi$
$443$	32.0745	1.52390	0.761952	+	0.647633i	$0.224241\pi$
$444$	−5.87998	−0.279051
$445$	31.3752	1.48733
$446$	34.1545	1.61726
$447$	10.6943	0.505824
$448$	12.6930	0.599686
$449$	22.5738	1.06532	0.532662	−	0.846328i	$-0.321192\pi$
$449$	22.5738	1.06532	0.532662	+	0.846328i	$0.321192\pi$
$450$	−17.0056	−0.801653
$451$	−2.18159	−0.102727
$452$	−9.45550	−0.444749
$453$	2.81490	0.132256
$454$	20.2686	0.951252
$455$	30.7010	1.43929
$456$	−0.427376	−0.0200137
$457$	−8.28399	−0.387509	−0.193754	−	0.981050i	$-0.562066\pi$
$457$	−8.28399	−0.387509	−0.193754	+	0.981050i	$0.562066\pi$
$458$	39.3972	1.84091
$459$	−3.47039	−0.161984
$460$	−8.47173	−0.394997
$461$	15.7988	0.735822	0.367911	−	0.929861i	$-0.380073\pi$
$461$	15.7988	0.735822	0.367911	+	0.929861i	$0.380073\pi$
$462$	−2.52769	−0.117599
$463$	14.2339	0.661506	0.330753	−	0.943717i	$-0.392697\pi$
$463$	14.2339	0.661506	0.330753	+	0.943717i	$0.392697\pi$
$464$	−35.8795	−1.66567
$465$	0	0
$466$	−12.8507	−0.595298
$467$	26.2440	1.21443	0.607213	−	0.794539i	$-0.292287\pi$
$467$	26.2440	1.21443	0.607213	+	0.794539i	$0.292287\pi$
$468$	1.38442	0.0639951
$469$	−6.19382	−0.286004
$470$	−21.7093	−1.00138
$471$	−14.6205	−0.673675
$472$	−2.76695	−0.127359
$473$	1.02457	0.0471097
$474$	−14.2205	−0.653170
$475$	2.15577	0.0989137
$476$	12.4200	0.569271
$477$	−12.1365	−0.555694
$478$	−37.3584	−1.70874
$479$	−41.7540	−1.90779	−0.953895	−	0.300141i	$-0.902966\pi$
$479$	−41.7540	−1.90779	−0.953895	+	0.300141i	$0.902966\pi$
$480$	−16.5551	−0.755635
$481$	12.9482	0.590387
$482$	14.6846	0.668867
$483$	12.3796	0.563291
$484$	−8.63285	−0.392402
$485$	−13.4194	−0.609345
$486$	1.67120	0.0758070
$487$	34.5409	1.56520	0.782598	−	0.622527i	$-0.213894\pi$
$487$	34.5409	1.56520	0.782598	+	0.622527i	$0.213894\pi$
$488$	−7.24167	−0.327815
$489$	17.2452	0.779855
$490$	−87.0619	−3.93305
$491$	−13.4986	−0.609183	−0.304592	−	0.952483i	$-0.598520\pi$
$491$	−13.4986	−0.609183	−0.304592	+	0.952483i	$0.598520\pi$
$492$	−5.16202	−0.232722
$493$	25.1187	1.13129
$494$	−0.618184	−0.0278134
$495$	−1.30540	−0.0586735
$496$	0	0
$497$	−7.84208	−0.351766
$498$	13.2984	0.595916
$499$	37.7824	1.69137	0.845687	−	0.533679i	$-0.179191\pi$
$499$	37.7824	1.69137	0.845687	+	0.533679i	$0.179191\pi$
$500$	15.9868	0.714953
$501$	−0.408108	−0.0182329
$502$	15.4962	0.691628
$503$	5.37870	0.239824	0.119912	−	0.992785i	$-0.461739\pi$
$503$	5.37870	0.239824	0.119912	+	0.992785i	$0.461739\pi$
$504$	9.10537	0.405586
$505$	−2.46324	−0.109613
$506$	−1.53595	−0.0682814
$507$	9.95138	0.441956
$508$	−10.2816	−0.456174
$509$	18.4656	0.818475	0.409237	−	0.912428i	$-0.365795\pi$
$509$	18.4656	0.818475	0.409237	+	0.912428i	$0.365795\pi$
$510$	22.5933	1.00045
$511$	−58.7556	−2.59920
$512$	−1.06623	−0.0471210
$513$	−0.211855	−0.00935362
$514$	3.40104	0.150014
$515$	4.23815	0.186755
$516$	2.42431	0.106724
$517$	−1.11742	−0.0491439
$518$	−55.9387	−2.45780
$519$	−3.74370	−0.164330
$520$	13.7214	0.601722
$521$	−20.3286	−0.890610	−0.445305	−	0.895379i	$-0.646905\pi$
$521$	−20.3286	−0.890610	−0.445305	+	0.895379i	$0.646905\pi$
$522$	−12.0961	−0.529433
$523$	5.37216	0.234908	0.117454	−	0.993078i	$-0.462527\pi$
$523$	5.37216	0.234908	0.117454	+	0.993078i	$0.462527\pi$
$524$	10.5193	0.459539
$525$	−45.9295	−2.00453
$526$	−49.4789	−2.15738
$527$	0	0
$528$	−1.66111	−0.0722906
$529$	−15.4775	−0.672936
$530$	79.0127	3.43209
$531$	−1.37161	−0.0595228
$532$	0.758198	0.0328721
$533$	11.3672	0.492368
$534$	13.4598	0.582463
$535$	−31.0775	−1.34360
$536$	−2.76824	−0.119570
$537$	1.83178	0.0790470
$538$	−34.5020	−1.48748
$539$	−4.48122	−0.193020
$540$	−3.08882	−0.132922
$541$	29.3978	1.26391	0.631954	−	0.775006i	$-0.282253\pi$
$541$	29.3978	1.26391	0.631954	+	0.775006i	$0.282253\pi$
$542$	10.8009	0.463938
$543$	−11.5508	−0.495693
$544$	14.7481	0.632320
$545$	0.854904	0.0366200
$546$	13.1706	0.563650
$547$	−37.7150	−1.61258	−0.806288	−	0.591523i	$-0.798527\pi$
$547$	−37.7150	−1.61258	−0.806288	+	0.591523i	$0.798527\pi$
$548$	8.33502	0.356055
$549$	−3.58978	−0.153208
$550$	5.69853	0.242986
$551$	1.53340	0.0653252
$552$	5.53288	0.235495
$553$	−38.4074	−1.63325
$554$	15.7978	0.671186
$555$	−28.8890	−1.22627
$556$	−18.6257	−0.789907
$557$	−2.12741	−0.0901411	−0.0450706	−	0.998984i	$-0.514351\pi$
$557$	−2.12741	−0.0901411	−0.0450706	+	0.998984i	$0.514351\pi$
$558$	0	0
$559$	−5.33854	−0.225796
$560$	−87.1625	−3.68329
$561$	1.16292	0.0490984
$562$	3.79637	0.160140
$563$	−15.4591	−0.651523	−0.325761	−	0.945452i	$-0.605621\pi$
$563$	−15.4591	−0.651523	−0.325761	+	0.945452i	$0.605621\pi$
$564$	−2.64400	−0.111333
$565$	−46.4559	−1.95442
$566$	45.3299	1.90536
$567$	4.51364	0.189555
$568$	−3.50491	−0.147063
$569$	−43.4928	−1.82331	−0.911656	−	0.410954i	$-0.865196\pi$
$569$	−43.4928	−1.82331	−0.911656	+	0.410954i	$0.865196\pi$
$570$	1.37924	0.0577701
$571$	−9.60615	−0.402005	−0.201002	−	0.979591i	$-0.564420\pi$
$571$	−9.60615	−0.402005	−0.201002	+	0.979591i	$0.564420\pi$
$572$	−0.463916	−0.0193973
$573$	8.89041	0.371402
$574$	−49.1085	−2.04975
$575$	−27.9090	−1.16389
$576$	2.81214	0.117172
$577$	45.8418	1.90842	0.954210	−	0.299139i	$-0.0966993\pi$
$577$	45.8418	1.90842	0.954210	+	0.299139i	$0.0966993\pi$
$578$	8.28312	0.344532
$579$	11.3286	0.470800
$580$	22.3568	0.928318
$581$	35.9169	1.49008
$582$	−5.75688	−0.238630
$583$	4.06691	0.168434
$584$	−26.2600	−1.08665
$585$	6.80184	0.281221
$586$	−15.3302	−0.633283
$587$	0.304600	0.0125722	0.00628610	−	0.999980i	$-0.497999\pi$
$587$	0.304600	0.0125722	0.00628610	+	0.999980i	$0.497999\pi$
$588$	−10.6034	−0.437275
$589$	0	0
$590$	8.92962	0.367627
$591$	−13.9315	−0.573066
$592$	−36.7609	−1.51086
$593$	32.9188	1.35181	0.675906	−	0.736988i	$-0.263753\pi$
$593$	32.9188	1.35181	0.675906	+	0.736988i	$0.263753\pi$
$594$	−0.560013	−0.0229776
$595$	61.0210	2.50162
$596$	−8.47951	−0.347334
$597$	0.446722	0.0182831
$598$	8.00312	0.327272
$599$	0.464587	0.0189825	0.00949125	−	0.999955i	$-0.496979\pi$
$599$	0.464587	0.0189825	0.00949125	+	0.999955i	$0.496979\pi$
$600$	−20.5275	−0.838032
$601$	−4.23305	−0.172670	−0.0863349	−	0.996266i	$-0.527516\pi$
$601$	−4.23305	−0.172670	−0.0863349	+	0.996266i	$0.527516\pi$
$602$	23.0635	0.939997
$603$	−1.37225	−0.0558822
$604$	−2.23193	−0.0908160
$605$	−42.4142	−1.72438
$606$	−1.05672	−0.0429263
$607$	−16.3205	−0.662430	−0.331215	−	0.943555i	$-0.607459\pi$
$607$	−16.3205	−0.662430	−0.331215	+	0.943555i	$0.607459\pi$
$608$	0.900319	0.0365128
$609$	−32.6697	−1.32384
$610$	23.3706	0.946247
$611$	5.82232	0.235546
$612$	2.75167	0.111230
$613$	19.5044	0.787773	0.393887	−	0.919159i	$-0.371130\pi$
$613$	19.5044	0.787773	0.393887	+	0.919159i	$0.371130\pi$
$614$	15.1565	0.611666
$615$	−25.3616	−1.02268
$616$	−3.05118	−0.122936
$617$	−3.39753	−0.136779	−0.0683897	−	0.997659i	$-0.521786\pi$
$617$	−3.39753	−0.136779	−0.0683897	+	0.997659i	$0.521786\pi$
$618$	1.81815	0.0731366
$619$	26.4142	1.06168	0.530839	−	0.847473i	$-0.321877\pi$
$619$	26.4142	1.06168	0.530839	+	0.847473i	$0.321877\pi$
$620$	0	0
$621$	2.74271	0.110061
$622$	19.8813	0.797169
$623$	36.3528	1.45644
$624$	8.65526	0.346488
$625$	27.6666	1.10666
$626$	−26.2112	−1.04761
$627$	0.0709919	0.00283514
$628$	11.5925	0.462593
$629$	25.7357	1.02615
$630$	−29.3852	−1.17073
$631$	27.5230	1.09567	0.547836	−	0.836586i	$-0.315452\pi$
$631$	27.5230	1.09567	0.547836	+	0.836586i	$0.315452\pi$
$632$	−17.1656	−0.682811
$633$	−20.4011	−0.810870
$634$	25.1188	0.997596
$635$	−50.5149	−2.00462
$636$	9.62304	0.381579
$637$	23.3495	0.925141
$638$	4.05337	0.160474
$639$	−1.73742	−0.0687313
$640$	−51.4182	−2.03248
$641$	8.91667	0.352187	0.176094	−	0.984373i	$-0.443654\pi$
$641$	8.91667	0.352187	0.176094	+	0.984373i	$0.443654\pi$
$642$	−13.3321	−0.526177
$643$	12.6584	0.499199	0.249600	−	0.968349i	$-0.419701\pi$
$643$	12.6584	0.499199	0.249600	+	0.968349i	$0.419701\pi$
$644$	−9.81577	−0.386795
$645$	11.9109	0.468992
$646$	−1.22870	−0.0483424
$647$	29.0256	1.14111	0.570556	−	0.821259i	$-0.306728\pi$
$647$	29.0256	1.14111	0.570556	+	0.821259i	$0.306728\pi$
$648$	2.01730	0.0792472
$649$	0.459622	0.0180418
$650$	−29.6923	−1.16463
$651$	0	0
$652$	−13.6737	−0.535503
$653$	32.4706	1.27067	0.635337	−	0.772235i	$-0.280861\pi$
$653$	32.4706	1.27067	0.635337	+	0.772235i	$0.280861\pi$
$654$	0.366750	0.0143411
$655$	51.6826	2.01941
$656$	−32.2724	−1.26002
$657$	−13.0174	−0.507856
$658$	−25.1535	−0.980586
$659$	9.23568	0.359771	0.179886	−	0.983688i	$-0.442427\pi$
$659$	9.23568	0.359771	0.179886	+	0.983688i	$0.442427\pi$
$660$	1.03505	0.0402894
$661$	−21.1259	−0.821704	−0.410852	−	0.911702i	$-0.634769\pi$
$661$	−21.1259	−0.821704	−0.410852	+	0.911702i	$0.634769\pi$
$662$	22.7220	0.883116
$663$	−6.05940	−0.235328
$664$	16.0525	0.622959
$665$	3.72511	0.144454
$666$	−12.3933	−0.480229
$667$	−19.8517	−0.768662
$668$	0.323588	0.0125200
$669$	20.4372	0.790146
$670$	8.93377	0.345141
$671$	1.20292	0.0464383
$672$	−19.1816	−0.739946
$673$	−40.4793	−1.56036	−0.780181	−	0.625554i	$-0.784873\pi$
$673$	−40.4793	−1.56036	−0.780181	+	0.625554i	$0.784873\pi$
$674$	−17.3072	−0.666648
$675$	−10.1757	−0.391663
$676$	−7.89044	−0.303478
$677$	−16.5546	−0.636245	−0.318123	−	0.948050i	$-0.603052\pi$
$677$	−16.5546	−0.636245	−0.318123	+	0.948050i	$0.603052\pi$
$678$	−19.9294	−0.765384
$679$	−15.5484	−0.596693
$680$	27.2724	1.04585
$681$	12.1282	0.464753
$682$	0	0
$683$	−15.8493	−0.606455	−0.303228	−	0.952918i	$-0.598064\pi$
$683$	−15.8493	−0.606455	−0.303228	+	0.952918i	$0.598064\pi$
$684$	0.167979	0.00642285
$685$	40.9509	1.56465
$686$	−48.0719	−1.83540
$687$	23.5742	0.899413
$688$	15.1565	0.577836
$689$	−21.1907	−0.807303
$690$	−17.8559	−0.679763
$691$	0.273282	0.0103961	0.00519807	−	0.999986i	$-0.498345\pi$
$691$	0.273282	0.0103961	0.00519807	+	0.999986i	$0.498345\pi$
$692$	2.96837	0.112841
$693$	−1.51250	−0.0574553
$694$	−4.22144	−0.160244
$695$	−91.5104	−3.47119
$696$	−14.6012	−0.553458
$697$	22.5933	0.855784
$698$	−58.3228	−2.20755
$699$	−7.68952	−0.290845
$700$	36.4174	1.37645
$701$	−22.4179	−0.846711	−0.423356	−	0.905964i	$-0.639148\pi$
$701$	−22.4179	−0.846711	−0.423356	+	0.905964i	$0.639148\pi$
$702$	2.91796	0.110131
$703$	1.57107	0.0592541
$704$	−0.942338	−0.0355157
$705$	−12.9903	−0.489243
$706$	15.2754	0.574897
$707$	−2.85403	−0.107337
$708$	1.08755	0.0408726
$709$	−14.8070	−0.556090	−0.278045	−	0.960568i	$-0.589686\pi$
$709$	−14.8070	−0.556090	−0.278045	+	0.960568i	$0.589686\pi$
$710$	11.3112	0.424500
$711$	−8.50919	−0.319119
$712$	16.2474	0.608896
$713$	0	0
$714$	26.1777	0.979678
$715$	−2.27927	−0.0852400
$716$	−1.45241	−0.0542793
$717$	−22.3543	−0.834837
$718$	7.88105	0.294118
$719$	25.1086	0.936392	0.468196	−	0.883625i	$-0.344904\pi$
$719$	25.1086	0.936392	0.468196	+	0.883625i	$0.344904\pi$
$720$	−19.3109	−0.719676
$721$	4.91052	0.182877
$722$	31.6777	1.17892
$723$	8.78690	0.326788
$724$	9.15863	0.340378
$725$	73.6518	2.73536
$726$	−18.1955	−0.675299
$727$	1.32303	0.0490686	0.0245343	−	0.999699i	$-0.492190\pi$
$727$	1.32303	0.0490686	0.0245343	+	0.999699i	$0.492190\pi$
$728$	15.8983	0.589228
$729$	1.00000	0.0370370
$730$	84.7472	3.13663
$731$	−10.6108	−0.392455
$732$	2.84633	0.105203
$733$	21.3453	0.788408	0.394204	−	0.919023i	$-0.371020\pi$
$733$	21.3453	0.788408	0.394204	+	0.919023i	$0.371020\pi$
$734$	−40.8362	−1.50729
$735$	−52.0955	−1.92157
$736$	−11.6557	−0.429635
$737$	0.459836	0.0169383
$738$	−10.8800	−0.400499
$739$	22.1603	0.815178	0.407589	−	0.913165i	$-0.366370\pi$
$739$	22.1603	0.815178	0.407589	+	0.913165i	$0.366370\pi$
$740$	22.9060	0.842043
$741$	−0.369905	−0.0135888
$742$	91.5480	3.36083
$743$	29.6842	1.08901	0.544503	−	0.838759i	$-0.316718\pi$
$743$	29.6842	1.08901	0.544503	+	0.838759i	$0.316718\pi$
$744$	0	0
$745$	−41.6608	−1.52633
$746$	5.92018	0.216753
$747$	7.95742	0.291147
$748$	−0.922075	−0.0337144
$749$	−36.0079	−1.31570
$750$	33.6955	1.23039
$751$	15.5930	0.568996	0.284498	−	0.958677i	$-0.408173\pi$
$751$	15.5930	0.568996	0.284498	+	0.958677i	$0.408173\pi$
$752$	−16.5300	−0.602787
$753$	9.27250	0.337909
$754$	−21.1202	−0.769151
$755$	−10.9657	−0.399084
$756$	−3.57886	−0.130162
$757$	−21.2045	−0.770691	−0.385345	−	0.922772i	$-0.625918\pi$
$757$	−21.2045	−0.770691	−0.385345	+	0.922772i	$0.625918\pi$
$758$	−40.3790	−1.46663
$759$	−0.919074	−0.0333603
$760$	1.66488	0.0603917
$761$	24.4271	0.885481	0.442740	−	0.896650i	$-0.354006\pi$
$761$	24.4271	0.885481	0.442740	+	0.896650i	$0.354006\pi$
$762$	−21.6707	−0.785045
$763$	0.990533	0.0358597
$764$	−7.04920	−0.255031
$765$	13.5193	0.488790
$766$	1.98504	0.0717224
$767$	−2.39487	−0.0864738
$768$	−16.4339	−0.593007
$769$	23.9568	0.863903	0.431952	−	0.901897i	$-0.357825\pi$
$769$	23.9568	0.863903	0.431952	+	0.901897i	$0.357825\pi$
$770$	9.84689	0.354857
$771$	2.03509	0.0732921
$772$	−8.98242	−0.323284
$773$	−45.1977	−1.62565	−0.812825	−	0.582508i	$-0.802071\pi$
$773$	−45.1977	−1.62565	−0.812825	+	0.582508i	$0.802071\pi$
$774$	5.10973	0.183666
$775$	0	0
$776$	−6.94914	−0.249459
$777$	−33.4722	−1.20081
$778$	30.5254	1.09439
$779$	1.37924	0.0494165
$780$	−5.39317	−0.193106
$781$	0.582204	0.0208329
$782$	15.9069	0.568830
$783$	−7.23800	−0.258665
$784$	−66.2910	−2.36753
$785$	56.9555	2.03283
$786$	22.1716	0.790836
$787$	19.8996	0.709346	0.354673	−	0.934990i	$-0.384592\pi$
$787$	19.8996	0.709346	0.354673	+	0.934990i	$0.384592\pi$
$788$	11.0463	0.393507
$789$	−29.6069	−1.05403
$790$	55.3975	1.97095
$791$	−53.8261	−1.91384
$792$	−0.675992	−0.0240203
$793$	−6.26785	−0.222578
$794$	4.43232	0.157297
$795$	47.2791	1.67682
$796$	−0.354205	−0.0125545
$797$	41.1645	1.45812	0.729060	−	0.684449i	$-0.239957\pi$
$797$	41.1645	1.45812	0.729060	+	0.684449i	$0.239957\pi$
$798$	1.59806	0.0565706
$799$	11.5724	0.409401
$800$	43.2437	1.52890
$801$	8.05400	0.284574
$802$	−27.7474	−0.979796
$803$	4.36208	0.153934
$804$	1.08805	0.0383727
$805$	−48.2260	−1.69974
$806$	0	0
$807$	−20.6451	−0.726740
$808$	−1.27557	−0.0448744
$809$	−44.0715	−1.54947	−0.774736	−	0.632285i	$-0.782117\pi$
$809$	−44.0715	−1.54947	−0.774736	+	0.632285i	$0.782117\pi$
$810$	−6.51032	−0.228749
$811$	24.0093	0.843079	0.421539	−	0.906810i	$-0.361490\pi$
$811$	24.0093	0.843079	0.421539	+	0.906810i	$0.361490\pi$
$812$	25.9037	0.909043
$813$	6.46297	0.226666
$814$	4.15294	0.145561
$815$	−67.1804	−2.35323
$816$	17.2031	0.602229
$817$	−0.647752	−0.0226620
$818$	42.9035	1.50009
$819$	7.88094	0.275382
$820$	20.1092	0.702243
$821$	−41.8591	−1.46089	−0.730447	−	0.682970i	$-0.760688\pi$
$821$	−41.8591	−1.46089	−0.730447	+	0.682970i	$0.760688\pi$
$822$	17.5678	0.612746
$823$	−41.7357	−1.45481	−0.727407	−	0.686206i	$-0.759275\pi$
$823$	−41.7357	−1.45481	−0.727407	+	0.686206i	$0.759275\pi$
$824$	2.19469	0.0764555
$825$	3.40985	0.118716
$826$	10.3463	0.359994
$827$	−18.0321	−0.627039	−0.313520	−	0.949582i	$-0.601508\pi$
$827$	−18.0321	−0.627039	−0.313520	+	0.949582i	$0.601508\pi$
$828$	−2.17469	−0.0755758
$829$	−12.6733	−0.440162	−0.220081	−	0.975482i	$-0.570632\pi$
$829$	−12.6733	−0.440162	−0.220081	+	0.975482i	$0.570632\pi$
$830$	−51.8053	−1.79819
$831$	9.45301	0.327921
$832$	4.91007	0.170226
$833$	46.4092	1.60798
$834$	−39.2576	−1.35938
$835$	1.58983	0.0550182
$836$	−0.0562894	−0.00194681
$837$	0	0
$838$	−52.0705	−1.79875
$839$	−43.0991	−1.48795	−0.743974	−	0.668209i	$-0.767061\pi$
$839$	−43.0991	−1.48795	−0.743974	+	0.668209i	$0.767061\pi$
$840$	−35.4709	−1.22386
$841$	23.3886	0.806503
$842$	51.0581	1.75958
$843$	2.27165	0.0782397
$844$	16.1760	0.556800
$845$	−38.7666	−1.33361
$846$	−5.57278	−0.191596
$847$	−49.1432	−1.68858
$848$	60.1621	2.06598
$849$	27.1242	0.930900
$850$	−59.0161	−2.02424
$851$	−20.3394	−0.697225
$852$	1.37760	0.0471958
$853$	44.8847	1.53682	0.768411	−	0.639956i	$-0.221048\pi$
$853$	44.8847	1.53682	0.768411	+	0.639956i	$0.221048\pi$
$854$	27.0783	0.926600
$855$	0.825302	0.0282247
$856$	−16.0932	−0.550055
$857$	14.2215	0.485796	0.242898	−	0.970052i	$-0.421902\pi$
$857$	14.2215	0.485796	0.242898	+	0.970052i	$0.421902\pi$
$858$	−0.977799	−0.0333815
$859$	23.5553	0.803698	0.401849	−	0.915706i	$-0.368368\pi$
$859$	23.5553	0.803698	0.401849	+	0.915706i	$0.368368\pi$
$860$	−9.44415	−0.322043
$861$	−29.3852	−1.00144
$862$	61.2856	2.08739
$863$	−33.9831	−1.15680	−0.578400	−	0.815754i	$-0.696323\pi$
$863$	−33.9831	−1.15680	−0.578400	+	0.815754i	$0.696323\pi$
$864$	−4.24970	−0.144578
$865$	14.5840	0.495869
$866$	−22.9894	−0.781211
$867$	4.95640	0.168328
$868$	0	0
$869$	2.85140	0.0967272
$870$	47.1216	1.59757
$871$	−2.39598	−0.0811848
$872$	0.442704	0.0149919
$873$	−3.44476	−0.116588
$874$	0.971060	0.0328466
$875$	91.0062	3.07657
$876$	10.3215	0.348730
$877$	−42.3591	−1.43036	−0.715182	−	0.698938i	$-0.753656\pi$
$877$	−42.3591	−1.43036	−0.715182	+	0.698938i	$0.753656\pi$
$878$	9.60519	0.324160
$879$	−9.17316	−0.309403
$880$	6.47103	0.218138
$881$	33.4197	1.12594	0.562970	−	0.826478i	$-0.309659\pi$
$881$	33.4197	1.12594	0.562970	+	0.826478i	$0.309659\pi$
$882$	−22.3488	−0.752522
$883$	16.1834	0.544616	0.272308	−	0.962210i	$-0.412213\pi$
$883$	16.1834	0.544616	0.272308	+	0.962210i	$0.412213\pi$
$884$	4.80449	0.161593
$885$	5.34325	0.179611
$886$	−53.6028	−1.80082
$887$	−43.0207	−1.44449	−0.722247	−	0.691635i	$-0.756891\pi$
$887$	−43.0207	−1.44449	−0.722247	+	0.691635i	$0.756891\pi$
$888$	−14.9599	−0.502022
$889$	−58.5290	−1.96300
$890$	−52.4341	−1.75759
$891$	−0.335097	−0.0112262
$892$	−16.2046	−0.542570
$893$	0.706452	0.0236405
$894$	−17.8723	−0.597739
$895$	−7.13588	−0.238526
$896$	−59.5756	−1.99028
$897$	4.78885	0.159895
$898$	−37.7253	−1.25891
$899$	0	0
$900$	8.06831	0.268944
$901$	−42.1185	−1.40317
$902$	3.64586	0.121394
$903$	13.8006	0.459254
$904$	−24.0568	−0.800117
$905$	44.9974	1.49576
$906$	−4.70425	−0.156288
$907$	18.4721	0.613354	0.306677	−	0.951814i	$-0.400783\pi$
$907$	18.4721	0.613354	0.306677	+	0.951814i	$0.400783\pi$
$908$	−9.61642	−0.319132
$909$	−0.632314	−0.0209725
$910$	−51.3074	−1.70082
$911$	−20.8824	−0.691864	−0.345932	−	0.938260i	$-0.612437\pi$
$911$	−20.8824	−0.691864	−0.345932	+	0.938260i	$0.612437\pi$
$912$	1.05019	0.0347752
$913$	−2.66651	−0.0882485
$914$	13.8442	0.457925
$915$	13.9843	0.462308
$916$	−18.6920	−0.617601
$917$	59.8820	1.97748
$918$	5.79970	0.191419
$919$	−14.9218	−0.492225	−0.246112	−	0.969241i	$-0.579153\pi$
$919$	−14.9218	−0.492225	−0.246112	+	0.969241i	$0.579153\pi$
$920$	−21.5539	−0.710611
$921$	9.06925	0.298842
$922$	−26.4028	−0.869531
$923$	−3.03359	−0.0998518
$924$	1.19926	0.0394529
$925$	75.4610	2.48114
$926$	−23.7877	−0.781712
$927$	1.08793	0.0357323
$928$	30.7593	1.00972
$929$	19.8663	0.651793	0.325897	−	0.945405i	$-0.394334\pi$
$929$	19.8663	0.651793	0.325897	+	0.945405i	$0.394334\pi$
$930$	0	0
$931$	2.83312	0.0928516
$932$	6.09701	0.199714
$933$	11.8965	0.389473
$934$	−43.8588	−1.43511
$935$	−4.53026	−0.148155
$936$	3.52227	0.115129
$937$	10.1006	0.329973	0.164986	−	0.986296i	$-0.447242\pi$
$937$	10.1006	0.329973	0.164986	+	0.986296i	$0.447242\pi$
$938$	10.3511	0.337975
$939$	−15.6841	−0.511830
$940$	10.3000	0.335949
$941$	12.6891	0.413651	0.206826	−	0.978378i	$-0.433687\pi$
$941$	12.6891	0.413651	0.206826	+	0.978378i	$0.433687\pi$
$942$	24.4337	0.796092
$943$	−17.8559	−0.581469
$944$	6.79922	0.221296
$945$	−17.5833	−0.571986
$946$	−1.71226	−0.0556702
$947$	−16.6123	−0.539828	−0.269914	−	0.962884i	$-0.586995\pi$
$947$	−16.6123	−0.539828	−0.269914	+	0.962884i	$0.586995\pi$
$948$	6.74692	0.219130
$949$	−22.7287	−0.737805
$950$	−3.60272	−0.116888
$951$	15.0304	0.487396
$952$	31.5992	1.02414
$953$	55.2584	1.79000	0.894998	−	0.446070i	$-0.147177\pi$
$953$	55.2584	1.79000	0.894998	+	0.446070i	$0.147177\pi$
$954$	20.2825	0.656671
$955$	−34.6335	−1.12071
$956$	17.7247	0.573258
$957$	2.42543	0.0784030
$958$	69.7792	2.25446
$959$	47.4478	1.53217
$960$	−10.9550	−0.353570
$961$	0	0
$962$	−21.6390	−0.697669
$963$	−7.97759	−0.257074
$964$	−6.96712	−0.224396
$965$	−44.1316	−1.42065
$966$	−20.6887	−0.665649
$967$	44.8302	1.44164	0.720821	−	0.693121i	$-0.243765\pi$
$967$	44.8302	1.44164	0.720821	+	0.693121i	$0.243765\pi$
$968$	−21.9638	−0.705944
$969$	−0.735219	−0.0236186
$970$	22.4265	0.720072
$971$	−60.8757	−1.95360	−0.976798	−	0.214165i	$-0.931297\pi$
$971$	−60.8757	−1.95360	−0.976798	+	0.214165i	$0.931297\pi$
$972$	−0.792899	−0.0254322
$973$	−106.028	−3.39912
$974$	−57.7246	−1.84962
$975$	−17.7671	−0.569002
$976$	17.7949	0.569601
$977$	28.7783	0.920699	0.460349	−	0.887738i	$-0.347724\pi$
$977$	28.7783	0.920699	0.460349	+	0.887738i	$0.347724\pi$
$978$	−28.8201	−0.921566
$979$	−2.69887	−0.0862562
$980$	41.3065	1.31949
$981$	0.219454	0.00700661
$982$	22.5588	0.719881
$983$	−31.6935	−1.01086	−0.505432	−	0.862866i	$-0.668667\pi$
$983$	−31.6935	−1.01086	−0.505432	+	0.862866i	$0.668667\pi$
$984$	−13.1333	−0.418674
$985$	54.2716	1.72924
$986$	−41.9782	−1.33686
$987$	−15.0512	−0.479085
$988$	0.293297	0.00933102
$989$	8.38592	0.266657
$990$	2.18159	0.0693354
$991$	2.33148	0.0740618	0.0370309	−	0.999314i	$-0.488210\pi$
$991$	2.33148	0.0740618	0.0370309	+	0.999314i	$0.488210\pi$
$992$	0	0
$993$	13.5963	0.431464
$994$	13.1057	0.415686
$995$	−1.74025	−0.0551696
$996$	−6.30943	−0.199922
$997$	22.7279	0.719800	0.359900	−	0.932991i	$-0.382811\pi$
$997$	22.7279	0.719800	0.359900	+	0.932991i	$0.382811\pi$
$998$	−63.1419	−1.99872
$999$	−7.41580	−0.234625

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2883.2.a.o.1.3		8
3.2	odd	2		8649.2.a.bg.1.6		8
31.15	odd	10		93.2.f.b.70.2	yes	16
31.29	odd	10		93.2.f.b.4.2	✓	16
31.30	odd	2		2883.2.a.p.1.3		8
93.29	even	10		279.2.i.c.190.3		16
93.77	even	10		279.2.i.c.163.3		16
93.92	even	2		8649.2.a.bh.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.f.b.4.2	✓	16	31.29	odd	10
93.2.f.b.70.2	yes	16	31.15	odd	10
279.2.i.c.163.3		16	93.77	even	10
279.2.i.c.190.3		16	93.29	even	10
2883.2.a.o.1.3		8	1.1	even	1	trivial
2883.2.a.p.1.3		8	31.30	odd	2
8649.2.a.bg.1.6		8	3.2	odd	2
8649.2.a.bh.1.6		8	93.92	even	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:	\( N \)	\(=\)	\( 2883 = 3 \cdot 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2883.a (trivial)

\(f(q)\)	\(=\)	\(q-1.67120 q^{2} -1.00000 q^{3} +0.792899 q^{4} +3.89560 q^{5} +1.67120 q^{6} +4.51364 q^{7} +2.01730 q^{8} +1.00000 q^{9} -6.51032 q^{10} -0.335097 q^{11} -0.792899 q^{12} +1.74603 q^{13} -7.54317 q^{14} -3.89560 q^{15} -4.95711 q^{16} +3.47039 q^{17} -1.67120 q^{18} +0.211855 q^{19} +3.08882 q^{20} -4.51364 q^{21} +0.560013 q^{22} -2.74271 q^{23} -2.01730 q^{24} +10.1757 q^{25} -2.91796 q^{26} -1.00000 q^{27} +3.57886 q^{28} +7.23800 q^{29} +6.51032 q^{30} +4.24970 q^{32} +0.335097 q^{33} -5.79970 q^{34} +17.5833 q^{35} +0.792899 q^{36} +7.41580 q^{37} -0.354051 q^{38} -1.74603 q^{39} +7.85861 q^{40} +6.51032 q^{41} +7.54317 q^{42} -3.05753 q^{43} -0.265698 q^{44} +3.89560 q^{45} +4.58361 q^{46} +3.33460 q^{47} +4.95711 q^{48} +13.3729 q^{49} -17.0056 q^{50} -3.47039 q^{51} +1.38442 q^{52} -12.1365 q^{53} +1.67120 q^{54} -1.30540 q^{55} +9.10537 q^{56} -0.211855 q^{57} -12.0961 q^{58} -1.37161 q^{59} -3.08882 q^{60} -3.58978 q^{61} +4.51364 q^{63} +2.81214 q^{64} +6.80184 q^{65} -0.560013 q^{66} -1.37225 q^{67} +2.75167 q^{68} +2.74271 q^{69} -29.3852 q^{70} -1.73742 q^{71} +2.01730 q^{72} -13.0174 q^{73} -12.3933 q^{74} -10.1757 q^{75} +0.167979 q^{76} -1.51250 q^{77} +2.91796 q^{78} -8.50919 q^{79} -19.3109 q^{80} +1.00000 q^{81} -10.8800 q^{82} +7.95742 q^{83} -3.57886 q^{84} +13.5193 q^{85} +5.10973 q^{86} -7.23800 q^{87} -0.675992 q^{88} +8.05400 q^{89} -6.51032 q^{90} +7.88094 q^{91} -2.17469 q^{92} -5.57278 q^{94} +0.825302 q^{95} -4.24970 q^{96} -3.44476 q^{97} -22.3488 q^{98} -0.335097 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 8 q^{3} + 13 q^{4} + 3 q^{5} - q^{6} - q^{7} + 9 q^{8} + 8 q^{9} + 6 q^{10} + 5 q^{11} - 13 q^{12} + 4 q^{13} + 3 q^{14} - 3 q^{15} + 19 q^{16} - 2 q^{17} + q^{18} - 7 q^{19} + q^{20}+ \cdots + 5 q^{99}+O(q^{100}) \) 8 * q + q^2 - 8 * q^3 + 13 * q^4 + 3 * q^5 - q^6 - q^7 + 9 * q^8 + 8 * q^9 + 6 * q^10 + 5 * q^11 - 13 * q^12 + 4 * q^13 + 3 * q^14 - 3 * q^15 + 19 * q^16 - 2 * q^17 + q^18 - 7 * q^19 + q^20 + q^21 + 9 * q^23 - 9 * q^24 + 15 * q^25 + 8 * q^26 - 8 * q^27 - 3 * q^28 + q^29 - 6 * q^30 + 54 * q^32 - 5 * q^33 - 48 * q^34 + 51 * q^35 + 13 * q^36 + 14 * q^37 - 16 * q^38 - 4 * q^39 + 59 * q^40 - 6 * q^41 - 3 * q^42 - 36 * q^43 + 27 * q^44 + 3 * q^45 + 3 * q^46 + 35 * q^47 - 19 * q^48 + 3 * q^49 - 37 * q^50 + 2 * q^51 + 46 * q^52 - 8 * q^53 - q^54 - 6 * q^55 + 52 * q^56 + 7 * q^57 - 52 * q^58 - 28 * q^59 - q^60 - q^63 + 17 * q^64 + 3 * q^65 + 30 * q^67 + 15 * q^68 - 9 * q^69 - 35 * q^70 - 6 * q^71 + 9 * q^72 + q^73 + 30 * q^74 - 15 * q^75 - 34 * q^76 - q^77 - 8 * q^78 - 36 * q^79 + 38 * q^80 + 8 * q^81 - 7 * q^82 + 22 * q^83 + 3 * q^84 - 8 * q^85 + 3 * q^86 - q^87 + 16 * q^88 + q^89 + 6 * q^90 + 6 * q^91 + 35 * q^92 + 37 * q^94 + 50 * q^95 - 54 * q^96 + 29 * q^97 - 41 * q^98 + 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more