LMFDB - Embedded newform 2883.2.a.n.1.7

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,-5,8,5,-6] 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:	$1$
Dimension:	$8$
Coefficient field:	8.8.1697203125.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 5x^{6} + 12x^{5} + 9x^{4} - 12x^{3} - 5x^{2} + 3x + 1 $ x^8 - 3x^7 - 5x^6 + 12x^5 + 9x^4 - 12x^3 - 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
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			1.7
Root			$1.77306$ 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)

$f(q)$	$=$	\(q+0.773055 q^{2} +1.00000 q^{3} -1.40239 q^{4} -1.75478 q^{5} +0.773055 q^{6} +1.30487 q^{7} -2.63023 q^{8} +1.00000 q^{9} -1.35654 q^{10} +0.697276 q^{11} -1.40239 q^{12} -3.01220 q^{13} +1.00873 q^{14} -1.75478 q^{15} +0.771457 q^{16} +4.35161 q^{17} +0.773055 q^{18} +3.38600 q^{19} +2.46087 q^{20} +1.30487 q^{21} +0.539033 q^{22} -4.50106 q^{23} -2.63023 q^{24} -1.92076 q^{25} -2.32860 q^{26} +1.00000 q^{27} -1.82992 q^{28} -3.70329 q^{29} -1.35654 q^{30} +5.85684 q^{32} +0.697276 q^{33} +3.36404 q^{34} -2.28975 q^{35} -1.40239 q^{36} -10.5634 q^{37} +2.61756 q^{38} -3.01220 q^{39} +4.61547 q^{40} -4.60973 q^{41} +1.00873 q^{42} +5.22158 q^{43} -0.977850 q^{44} -1.75478 q^{45} -3.47957 q^{46} -4.89455 q^{47} +0.771457 q^{48} -5.29733 q^{49} -1.48485 q^{50} +4.35161 q^{51} +4.22426 q^{52} +13.7088 q^{53} +0.773055 q^{54} -1.22356 q^{55} -3.43210 q^{56} +3.38600 q^{57} -2.86285 q^{58} -4.66377 q^{59} +2.46087 q^{60} -13.2621 q^{61} +1.30487 q^{63} +2.98475 q^{64} +5.28574 q^{65} +0.539033 q^{66} -4.86707 q^{67} -6.10264 q^{68} -4.50106 q^{69} -1.77010 q^{70} -14.1021 q^{71} -2.63023 q^{72} +10.0283 q^{73} -8.16612 q^{74} -1.92076 q^{75} -4.74847 q^{76} +0.909852 q^{77} -2.32860 q^{78} -11.6809 q^{79} -1.35374 q^{80} +1.00000 q^{81} -3.56358 q^{82} +0.0923387 q^{83} -1.82992 q^{84} -7.63611 q^{85} +4.03657 q^{86} -3.70329 q^{87} -1.83400 q^{88} -6.43167 q^{89} -1.35654 q^{90} -3.93051 q^{91} +6.31222 q^{92} -3.78376 q^{94} -5.94167 q^{95} +5.85684 q^{96} +2.36201 q^{97} -4.09513 q^{98} +0.697276 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{2} + 8 q^{3} + 5 q^{4} - 6 q^{5} - 5 q^{6} - 6 q^{7} + 8 q^{9} + q^{10} + 5 q^{12} - 12 q^{13} - 3 q^{14} - 6 q^{15} + 3 q^{16} - 2 q^{17} - 5 q^{18} - 8 q^{19} - 5 q^{20} - 6 q^{21} - 4 q^{22}+ \cdots + 32 q^{98}+O(q^{100}) $ 8 * q - 5 * q^2 + 8 * q^3 + 5 * q^4 - 6 * q^5 - 5 * q^6 - 6 * q^7 + 8 * q^9 + q^10 + 5 * q^12 - 12 * q^13 - 3 * q^14 - 6 * q^15 + 3 * q^16 - 2 * q^17 - 5 * q^18 - 8 * q^19 - 5 * q^20 - 6 * q^21 - 4 * q^22 - 4 * q^23 - 12 * q^25 + 18 * q^26 + 8 * q^27 - 15 * q^28 + 6 * q^29 + q^30 - 17 * q^34 + 9 * q^35 + 5 * q^36 - 8 * q^37 - 7 * q^38 - 12 * q^39 + 13 * q^40 - 20 * q^41 - 3 * q^42 - 14 * q^43 - 25 * q^44 - 6 * q^45 - 9 * q^46 + 6 * q^47 + 3 * q^48 - 20 * q^49 + 6 * q^50 - 2 * q^51 - 30 * q^52 + 30 * q^53 - 5 * q^54 - 19 * q^55 + 6 * q^56 - 8 * q^57 - 19 * q^58 - 20 * q^59 - 5 * q^60 - 13 * q^61 - 6 * q^63 - 26 * q^64 + 27 * q^65 - 4 * q^66 + 32 * q^67 + 15 * q^68 - 4 * q^69 - 6 * q^70 - 17 * q^71 + 12 * q^73 + 10 * q^74 - 12 * q^75 - 20 * q^76 - 18 * q^77 + 18 * q^78 - 30 * q^79 - 21 * q^80 + 8 * q^81 - 23 * q^82 - 12 * q^83 - 15 * q^84 - 28 * q^85 + 46 * q^86 + 6 * q^87 - 22 * q^88 - 6 * q^89 + q^90 + 15 * q^91 + 70 * q^92 + 44 * q^94 - 36 * q^95 - 39 * q^97 + 32 * 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 $

$2$	0.773055	0.546633	0.273316	−	0.961924i	$-0.411879\pi$
$2$	0.773055	0.546633	0.273316	+	0.961924i	$0.411879\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.40239	−0.701193
$5$	−1.75478	−0.784760	−0.392380	−	0.919803i	$-0.628348\pi$
$5$	−1.75478	−0.784760	−0.392380	+	0.919803i	$0.628348\pi$
$6$	0.773055	0.315598
$7$	1.30487	0.493193	0.246596	−	0.969118i	$-0.420688\pi$
$7$	1.30487	0.493193	0.246596	+	0.969118i	$0.420688\pi$
$8$	−2.63023	−0.929927
$9$	1.00000	0.333333
$10$	−1.35654	−0.428975
$11$	0.697276	0.210237	0.105118	−	0.994460i	$-0.466478\pi$
$11$	0.697276	0.210237	0.105118	+	0.994460i	$0.466478\pi$
$12$	−1.40239	−0.404834
$13$	−3.01220	−0.835433	−0.417717	−	0.908577i	$-0.637170\pi$
$13$	−3.01220	−0.835433	−0.417717	+	0.908577i	$0.637170\pi$
$14$	1.00873	0.269595
$15$	−1.75478	−0.453081
$16$	0.771457	0.192864
$17$	4.35161	1.05542	0.527711	−	0.849424i	$-0.323051\pi$
$17$	4.35161	1.05542	0.527711	+	0.849424i	$0.323051\pi$
$18$	0.773055	0.182211
$19$	3.38600	0.776801	0.388400	−	0.921491i	$-0.373028\pi$
$19$	3.38600	0.776801	0.388400	+	0.921491i	$0.373028\pi$
$20$	2.46087	0.550268
$21$	1.30487	0.284745
$22$	0.539033	0.114922
$23$	−4.50106	−0.938536	−0.469268	−	0.883056i	$-0.655482\pi$
$23$	−4.50106	−0.938536	−0.469268	+	0.883056i	$0.655482\pi$
$24$	−2.63023	−0.536894
$25$	−1.92076	−0.384152
$26$	−2.32860	−0.456675
$27$	1.00000	0.192450
$28$	−1.82992	−0.345823
$29$	−3.70329	−0.687684	−0.343842	−	0.939027i	$-0.611728\pi$
$29$	−3.70329	−0.687684	−0.343842	+	0.939027i	$0.611728\pi$
$30$	−1.35654	−0.247669
$31$	0	0
$31$	0	0
$32$	5.85684	1.03535
$33$	0.697276	0.121380
$34$	3.36404	0.576928
$35$	−2.28975	−0.387038
$36$	−1.40239	−0.233731
$37$	−10.5634	−1.73662	−0.868310	−	0.496023i	$-0.834793\pi$
$37$	−10.5634	−1.73662	−0.868310	+	0.496023i	$0.834793\pi$
$38$	2.61756	0.424625
$39$	−3.01220	−0.482338
$40$	4.61547	0.729770
$41$	−4.60973	−0.719919	−0.359960	−	0.932968i	$-0.617210\pi$
$41$	−4.60973	−0.719919	−0.359960	+	0.932968i	$0.617210\pi$
$42$	1.00873	0.155651
$43$	5.22158	0.796283	0.398142	−	0.917324i	$-0.369655\pi$
$43$	5.22158	0.796283	0.398142	+	0.917324i	$0.369655\pi$
$44$	−0.977850	−0.147416
$45$	−1.75478	−0.261587
$46$	−3.47957	−0.513034
$47$	−4.89455	−0.713944	−0.356972	−	0.934115i	$-0.616191\pi$
$47$	−4.89455	−0.713944	−0.356972	+	0.934115i	$0.616191\pi$
$48$	0.771457	0.111350
$49$	−5.29733	−0.756761
$50$	−1.48485	−0.209990
$51$	4.35161	0.609348
$52$	4.22426	0.585800
$53$	13.7088	1.88305	0.941523	−	0.336948i	$-0.109395\pi$
$53$	13.7088	1.88305	0.941523	+	0.336948i	$0.109395\pi$
$54$	0.773055	0.105199
$55$	−1.22356	−0.164985
$56$	−3.43210	−0.458633
$57$	3.38600	0.448486
$58$	−2.86285	−0.375911
$59$	−4.66377	−0.607171	−0.303585	−	0.952804i	$-0.598184\pi$
$59$	−4.66377	−0.607171	−0.303585	+	0.952804i	$0.598184\pi$
$60$	2.46087	0.317697
$61$	−13.2621	−1.69804	−0.849021	−	0.528359i	$-0.822808\pi$
$61$	−13.2621	−1.69804	−0.849021	+	0.528359i	$0.822808\pi$
$62$	0	0
$63$	1.30487	0.164398
$64$	2.98475	0.373094
$65$	5.28574	0.655615
$66$	0.539033	0.0663504
$67$	−4.86707	−0.594607	−0.297304	−	0.954783i	$-0.596087\pi$
$67$	−4.86707	−0.594607	−0.297304	+	0.954783i	$0.596087\pi$
$68$	−6.10264	−0.740054
$69$	−4.50106	−0.541864
$70$	−1.77010	−0.211568
$71$	−14.1021	−1.67361	−0.836804	−	0.547502i	$-0.815579\pi$
$71$	−14.1021	−1.67361	−0.836804	+	0.547502i	$0.815579\pi$
$72$	−2.63023	−0.309976
$73$	10.0283	1.17372	0.586861	−	0.809688i	$-0.300363\pi$
$73$	10.0283	1.17372	0.586861	+	0.809688i	$0.300363\pi$
$74$	−8.16612	−0.949293
$75$	−1.92076	−0.221790
$76$	−4.74847	−0.544687
$77$	0.909852	0.103687
$78$	−2.32860	−0.263661
$79$	−11.6809	−1.31421	−0.657103	−	0.753801i	$-0.728218\pi$
$79$	−11.6809	−1.31421	−0.657103	+	0.753801i	$0.728218\pi$
$80$	−1.35374	−0.151352
$81$	1.00000	0.111111
$82$	−3.56358	−0.393531
$83$	0.0923387	0.0101355	0.00506775	−	0.999987i	$-0.498387\pi$
$83$	0.0923387	0.0101355	0.00506775	+	0.999987i	$0.498387\pi$
$84$	−1.82992	−0.199661
$85$	−7.63611	−0.828252
$86$	4.03657	0.435274
$87$	−3.70329	−0.397035
$88$	−1.83400	−0.195505
$89$	−6.43167	−0.681755	−0.340878	−	0.940108i	$-0.610724\pi$
$89$	−6.43167	−0.681755	−0.340878	+	0.940108i	$0.610724\pi$
$90$	−1.35654	−0.142992
$91$	−3.93051	−0.412030
$92$	6.31222	0.658095
$93$	0	0
$94$	−3.78376	−0.390265
$95$	−5.94167	−0.609602
$96$	5.85684	0.597761
$97$	2.36201	0.239826	0.119913	−	0.992784i	$-0.461738\pi$
$97$	2.36201	0.239826	0.119913	+	0.992784i	$0.461738\pi$
$98$	−4.09513	−0.413670
$99$	0.697276	0.0700789
$100$	2.69364	0.269364
$101$	−4.27380	−0.425259	−0.212629	−	0.977133i	$-0.568203\pi$
$101$	−4.27380	−0.425259	−0.212629	+	0.977133i	$0.568203\pi$
$102$	3.36404	0.333089
$103$	−6.02603	−0.593762	−0.296881	−	0.954914i	$-0.595947\pi$
$103$	−6.02603	−0.593762	−0.296881	+	0.954914i	$0.595947\pi$
$104$	7.92278	0.776892
$105$	−2.28975	−0.223456
$106$	10.5976	1.02933
$107$	−13.8422	−1.33817	−0.669086	−	0.743185i	$-0.733314\pi$
$107$	−13.8422	−1.33817	−0.669086	+	0.743185i	$0.733314\pi$
$108$	−1.40239	−0.134945
$109$	−16.7473	−1.60410	−0.802052	−	0.597254i	$-0.796258\pi$
$109$	−16.7473	−1.60410	−0.802052	+	0.597254i	$0.796258\pi$
$110$	−0.945883	−0.0901864
$111$	−10.5634	−1.00264
$112$	1.00665	0.0951193
$113$	19.8589	1.86817	0.934085	−	0.357050i	$-0.116218\pi$
$113$	19.8589	1.86817	0.934085	+	0.357050i	$0.116218\pi$
$114$	2.61756	0.245157
$115$	7.89836	0.736526
$116$	5.19344	0.482199
$117$	−3.01220	−0.278478
$118$	−3.60535	−0.331899
$119$	5.67827	0.520526
$120$	4.61547	0.421333
$121$	−10.5138	−0.955801
$122$	−10.2524	−0.928205
$123$	−4.60973	−0.415646
$124$	0	0
$125$	12.1444	1.08623
$126$	1.00873	0.0898651
$127$	6.60604	0.586191	0.293096	−	0.956083i	$-0.405315\pi$
$127$	6.60604	0.586191	0.293096	+	0.956083i	$0.405315\pi$
$128$	−9.40631	−0.831408
$129$	5.22158	0.459734
$130$	4.08617	0.358380
$131$	−4.88867	−0.427125	−0.213563	−	0.976929i	$-0.568507\pi$
$131$	−4.88867	−0.427125	−0.213563	+	0.976929i	$0.568507\pi$
$132$	−0.977850	−0.0851109
$133$	4.41827	0.383113
$134$	−3.76251	−0.325032
$135$	−1.75478	−0.151027
$136$	−11.4458	−0.981465
$137$	13.2554	1.13248	0.566242	−	0.824239i	$-0.308397\pi$
$137$	13.2554	1.13248	0.566242	+	0.824239i	$0.308397\pi$
$138$	−3.47957	−0.296200
$139$	0.0599152	0.00508194	0.00254097	−	0.999997i	$-0.499191\pi$
$139$	0.0599152	0.00508194	0.00254097	+	0.999997i	$0.499191\pi$
$140$	3.21111	0.271388
$141$	−4.89455	−0.412196
$142$	−10.9017	−0.914849
$143$	−2.10033	−0.175639
$144$	0.771457	0.0642881
$145$	6.49845	0.539667
$146$	7.75242	0.641595
$147$	−5.29733	−0.436916
$148$	14.8140	1.21771
$149$	1.10616	0.0906198	0.0453099	−	0.998973i	$-0.485572\pi$
$149$	1.10616	0.0906198	0.0453099	+	0.998973i	$0.485572\pi$
$150$	−1.48485	−0.121238
$151$	6.50260	0.529174	0.264587	−	0.964362i	$-0.414764\pi$
$151$	6.50260	0.529174	0.264587	+	0.964362i	$0.414764\pi$
$152$	−8.90596	−0.722368
$153$	4.35161	0.351807
$154$	0.703365	0.0566788
$155$	0	0
$156$	4.22426	0.338212
$157$	−11.6972	−0.933535	−0.466767	−	0.884380i	$-0.654581\pi$
$157$	−11.6972	−0.933535	−0.466767	+	0.884380i	$0.654581\pi$
$158$	−9.02999	−0.718387
$159$	13.7088	1.08718
$160$	−10.2775	−0.812504
$161$	−5.87328	−0.462879
$162$	0.773055	0.0607370
$163$	−3.09341	−0.242294	−0.121147	−	0.992635i	$-0.538657\pi$
$163$	−3.09341	−0.242294	−0.121147	+	0.992635i	$0.538657\pi$
$164$	6.46462	0.504802
$165$	−1.22356	−0.0952543
$166$	0.0713829	0.00554039
$167$	−11.1412	−0.862132	−0.431066	−	0.902320i	$-0.641862\pi$
$167$	−11.1412	−0.862132	−0.431066	+	0.902320i	$0.641862\pi$
$168$	−3.43210	−0.264792
$169$	−3.92666	−0.302051
$170$	−5.90313	−0.452750
$171$	3.38600	0.258934
$172$	−7.32267	−0.558348
$173$	−2.70512	−0.205666	−0.102833	−	0.994699i	$-0.532791\pi$
$173$	−2.70512	−0.205666	−0.102833	+	0.994699i	$0.532791\pi$
$174$	−2.86285	−0.217032
$175$	−2.50633	−0.189461
$176$	0.537919	0.0405471
$177$	−4.66377	−0.350550
$178$	−4.97203	−0.372670
$179$	24.1722	1.80672	0.903359	−	0.428886i	$-0.141094\pi$
$179$	24.1722	1.80672	0.903359	+	0.428886i	$0.141094\pi$
$180$	2.46087	0.183423
$181$	8.56648	0.636742	0.318371	−	0.947966i	$-0.396864\pi$
$181$	8.56648	0.636742	0.318371	+	0.947966i	$0.396864\pi$
$182$	−3.03850	−0.225229
$183$	−13.2621	−0.980365
$184$	11.8388	0.872770
$185$	18.5365	1.36283
$186$	0	0
$187$	3.03428	0.221888
$188$	6.86405	0.500613
$189$	1.30487	0.0949150
$190$	−4.59324	−0.333228
$191$	23.4530	1.69700	0.848498	−	0.529198i	$-0.177507\pi$
$191$	23.4530	1.69700	0.848498	+	0.529198i	$0.177507\pi$
$192$	2.98475	0.215406
$193$	−1.53696	−0.110633	−0.0553164	−	0.998469i	$-0.517617\pi$
$193$	−1.53696	−0.110633	−0.0553164	+	0.998469i	$0.517617\pi$
$194$	1.82597	0.131097
$195$	5.28574	0.378519
$196$	7.42890	0.530635
$197$	0.944824	0.0673159	0.0336580	−	0.999433i	$-0.489284\pi$
$197$	0.944824	0.0673159	0.0336580	+	0.999433i	$0.489284\pi$
$198$	0.539033	0.0383074
$199$	−13.9360	−0.987899	−0.493950	−	0.869491i	$-0.664447\pi$
$199$	−13.9360	−0.987899	−0.493950	+	0.869491i	$0.664447\pi$
$200$	5.05204	0.357233
$201$	−4.86707	−0.343297
$202$	−3.30388	−0.232460
$203$	−4.83230	−0.339161
$204$	−6.10264	−0.427270
$205$	8.08905	0.564964
$206$	−4.65845	−0.324570
$207$	−4.50106	−0.312845
$208$	−2.32378	−0.161125
$209$	2.36097	0.163312
$210$	−1.77010	−0.122149
$211$	−3.16978	−0.218217	−0.109108	−	0.994030i	$-0.534800\pi$
$211$	−3.16978	−0.218217	−0.109108	+	0.994030i	$0.534800\pi$
$212$	−19.2250	−1.32038
$213$	−14.1021	−0.966258
$214$	−10.7008	−0.731489
$215$	−9.16271	−0.624892
$216$	−2.63023	−0.178965
$217$	0	0
$218$	−12.9466	−0.876855
$219$	10.0283	0.677649
$220$	1.71591	0.115687
$221$	−13.1079	−0.881734
$222$	−8.16612	−0.548074
$223$	8.52766	0.571054	0.285527	−	0.958371i	$-0.407831\pi$
$223$	8.52766	0.571054	0.285527	+	0.958371i	$0.407831\pi$
$224$	7.64239	0.510629
$225$	−1.92076	−0.128051
$226$	15.3520	1.02120
$227$	−28.1360	−1.86745	−0.933726	−	0.357989i	$-0.883462\pi$
$227$	−28.1360	−1.86745	−0.933726	+	0.357989i	$0.883462\pi$
$228$	−4.74847	−0.314475
$229$	4.42919	0.292689	0.146344	−	0.989234i	$-0.453249\pi$
$229$	4.42919	0.292689	0.146344	+	0.989234i	$0.453249\pi$
$230$	6.10587	0.402609
$231$	0.909852	0.0598638
$232$	9.74052	0.639496
$233$	0.0478018	0.00313160	0.00156580	−	0.999999i	$-0.499502\pi$
$233$	0.0478018	0.00313160	0.00156580	+	0.999999i	$0.499502\pi$
$234$	−2.32860	−0.152225
$235$	8.58885	0.560275
$236$	6.54040	0.425744
$237$	−11.6809	−0.758757
$238$	4.38961	0.284536
$239$	14.8152	0.958318	0.479159	−	0.877728i	$-0.340942\pi$
$239$	14.8152	0.958318	0.479159	+	0.877728i	$0.340942\pi$
$240$	−1.35374	−0.0873832
$241$	5.07946	0.327197	0.163598	−	0.986527i	$-0.447690\pi$
$241$	5.07946	0.327197	0.163598	+	0.986527i	$0.447690\pi$
$242$	−8.12775	−0.522472
$243$	1.00000	0.0641500
$244$	18.5986	1.19066
$245$	9.29563	0.593876
$246$	−3.56358	−0.227205
$247$	−10.1993	−0.648965
$248$	0	0
$249$	0.0923387	0.00585173
$250$	9.38828	0.593767
$251$	8.30207	0.524022	0.262011	−	0.965065i	$-0.415614\pi$
$251$	8.30207	0.524022	0.262011	+	0.965065i	$0.415614\pi$
$252$	−1.82992	−0.115274
$253$	−3.13848	−0.197315
$254$	5.10683	0.320431
$255$	−7.63611	−0.478192
$256$	−13.2411	−0.827568
$257$	−17.7288	−1.10589	−0.552946	−	0.833217i	$-0.686496\pi$
$257$	−17.7288	−1.10589	−0.552946	+	0.833217i	$0.686496\pi$
$258$	4.03657	0.251306
$259$	−13.7839	−0.856488
$260$	−7.41264	−0.459712
$261$	−3.70329	−0.229228
$262$	−3.77921	−0.233481
$263$	−1.24321	−0.0766598	−0.0383299	−	0.999265i	$-0.512204\pi$
$263$	−1.24321	−0.0766598	−0.0383299	+	0.999265i	$0.512204\pi$
$264$	−1.83400	−0.112875
$265$	−24.0559	−1.47774
$266$	3.41557	0.209422
$267$	−6.43167	−0.393612
$268$	6.82551	0.416934
$269$	−19.7286	−1.20288	−0.601438	−	0.798920i	$-0.705405\pi$
$269$	−19.7286	−1.20288	−0.601438	+	0.798920i	$0.705405\pi$
$270$	−1.35654	−0.0825564
$271$	−14.0605	−0.854116	−0.427058	−	0.904224i	$-0.640450\pi$
$271$	−14.0605	−0.854116	−0.427058	+	0.904224i	$0.640450\pi$
$272$	3.35708	0.203553
$273$	−3.93051	−0.237885
$274$	10.2472	0.619053
$275$	−1.33930	−0.0807628
$276$	6.31222	0.379951
$277$	−9.57269	−0.575167	−0.287584	−	0.957756i	$-0.592852\pi$
$277$	−9.57269	−0.575167	−0.287584	+	0.957756i	$0.592852\pi$
$278$	0.0463178	0.00277796
$279$	0	0
$280$	6.02257	0.359917
$281$	−0.746512	−0.0445332	−0.0222666	−	0.999752i	$-0.507088\pi$
$281$	−0.746512	−0.0445332	−0.0222666	+	0.999752i	$0.507088\pi$
$282$	−3.78376	−0.225320
$283$	30.0863	1.78844	0.894222	−	0.447624i	$-0.147730\pi$
$283$	30.0863	1.78844	0.894222	+	0.447624i	$0.147730\pi$
$284$	19.7766	1.17352
$285$	−5.94167	−0.351954
$286$	−1.62367	−0.0960099
$287$	−6.01508	−0.355059
$288$	5.85684	0.345118
$289$	1.93653	0.113914
$290$	5.02366	0.295000
$291$	2.36201	0.138464
$292$	−14.0635	−0.823006
$293$	17.6615	1.03180	0.515898	−	0.856650i	$-0.327458\pi$
$293$	17.6615	1.03180	0.515898	+	0.856650i	$0.327458\pi$
$294$	−4.09513	−0.238833
$295$	8.18387	0.476483
$296$	27.7843	1.61493
$297$	0.697276	0.0404601
$298$	0.855119	0.0495357
$299$	13.5581	0.784084
$300$	2.69364	0.155518
$301$	6.81346	0.392721
$302$	5.02687	0.289264
$303$	−4.27380	−0.245523
$304$	2.61215	0.149817
$305$	23.2721	1.33256
$306$	3.36404	0.192309
$307$	30.6165	1.74737	0.873687	−	0.486489i	$-0.161723\pi$
$307$	30.6165	1.74737	0.873687	+	0.486489i	$0.161723\pi$
$308$	−1.27596	−0.0727047
$309$	−6.02603	−0.342809
$310$	0	0
$311$	−27.1240	−1.53806	−0.769030	−	0.639213i	$-0.779260\pi$
$311$	−27.1240	−1.53806	−0.769030	+	0.639213i	$0.779260\pi$
$312$	7.92278	0.448539
$313$	25.4615	1.43917	0.719586	−	0.694403i	$-0.244332\pi$
$313$	25.4615	1.43917	0.719586	+	0.694403i	$0.244332\pi$
$314$	−9.04255	−0.510301
$315$	−2.28975	−0.129013
$316$	16.3811	0.921511
$317$	21.4972	1.20740	0.603700	−	0.797211i	$-0.293692\pi$
$317$	21.4972	1.20740	0.603700	+	0.797211i	$0.293692\pi$
$318$	10.5976	0.594287
$319$	−2.58222	−0.144576
$320$	−5.23757	−0.292789
$321$	−13.8422	−0.772594
$322$	−4.54037	−0.253025
$323$	14.7345	0.819852
$324$	−1.40239	−0.0779103
$325$	5.78570	0.320933
$326$	−2.39137	−0.132446
$327$	−16.7473	−0.926130
$328$	12.1247	0.669473
$329$	−6.38673	−0.352112
$330$	−0.945883	−0.0520691
$331$	13.1974	0.725393	0.362696	−	0.931907i	$-0.381856\pi$
$331$	13.1974	0.725393	0.362696	+	0.931907i	$0.381856\pi$
$332$	−0.129495	−0.00710693
$333$	−10.5634	−0.578873
$334$	−8.61277	−0.471270
$335$	8.54062	0.466624
$336$	1.00665	0.0549171
$337$	2.21139	0.120462	0.0602311	−	0.998184i	$-0.480816\pi$
$337$	2.21139	0.120462	0.0602311	+	0.998184i	$0.480816\pi$
$338$	−3.03553	−0.165111
$339$	19.8589	1.07859
$340$	10.7088	0.580765
$341$	0	0
$342$	2.61756	0.141542
$343$	−16.0464	−0.866422
$344$	−13.7340	−0.740486
$345$	7.89836	0.425233
$346$	−2.09121	−0.112424
$347$	−7.78395	−0.417864	−0.208932	−	0.977930i	$-0.566999\pi$
$347$	−7.78395	−0.417864	−0.208932	+	0.977930i	$0.566999\pi$
$348$	5.19344	0.278398
$349$	16.4768	0.881982	0.440991	−	0.897512i	$-0.354627\pi$
$349$	16.4768	0.881982	0.440991	+	0.897512i	$0.354627\pi$
$350$	−1.93753	−0.103565
$351$	−3.01220	−0.160779
$352$	4.08384	0.217669
$353$	32.0848	1.70770	0.853850	−	0.520519i	$-0.174262\pi$
$353$	32.0848	1.70770	0.853850	+	0.520519i	$0.174262\pi$
$354$	−3.60535	−0.191622
$355$	24.7460	1.31338
$356$	9.01968	0.478042
$357$	5.67827	0.300526
$358$	18.6865	0.987611
$359$	27.9610	1.47572	0.737862	−	0.674951i	$-0.235835\pi$
$359$	27.9610	1.47572	0.737862	+	0.674951i	$0.235835\pi$
$360$	4.61547	0.243257
$361$	−7.53503	−0.396580
$362$	6.62236	0.348064
$363$	−10.5138	−0.551832
$364$	5.51209	0.288912
$365$	−17.5974	−0.921091
$366$	−10.2524	−0.535900
$367$	−16.2554	−0.848525	−0.424262	−	0.905539i	$-0.639467\pi$
$367$	−16.2554	−0.848525	−0.424262	+	0.905539i	$0.639467\pi$
$368$	−3.47237	−0.181010
$369$	−4.60973	−0.239973
$370$	14.3297	0.744967
$371$	17.8881	0.928705
$372$	0	0
$373$	14.4593	0.748674	0.374337	−	0.927293i	$-0.377870\pi$
$373$	14.4593	0.748674	0.374337	+	0.927293i	$0.377870\pi$
$374$	2.34566	0.121291
$375$	12.1444	0.627133
$376$	12.8738	0.663916
$377$	11.1550	0.574514
$378$	1.00873	0.0518836
$379$	−17.5005	−0.898938	−0.449469	−	0.893296i	$-0.648387\pi$
$379$	−17.5005	−0.898938	−0.449469	+	0.893296i	$0.648387\pi$
$380$	8.33251	0.427449
$381$	6.60604	0.338438
$382$	18.1304	0.927634
$383$	−12.0938	−0.617965	−0.308983	−	0.951068i	$-0.599989\pi$
$383$	−12.0938	−0.617965	−0.308983	+	0.951068i	$0.599989\pi$
$384$	−9.40631	−0.480014
$385$	−1.59659	−0.0813696
$386$	−1.18816	−0.0604755
$387$	5.22158	0.265428
$388$	−3.31245	−0.168164
$389$	7.97101	0.404146	0.202073	−	0.979370i	$-0.435232\pi$
$389$	7.97101	0.404146	0.202073	+	0.979370i	$0.435232\pi$
$390$	4.08617	0.206911
$391$	−19.5869	−0.990551
$392$	13.9332	0.703733
$393$	−4.88867	−0.246601
$394$	0.730401	0.0367971
$395$	20.4974	1.03134
$396$	−0.977850	−0.0491388
$397$	−19.4337	−0.975348	−0.487674	−	0.873026i	$-0.662155\pi$
$397$	−19.4337	−0.975348	−0.487674	+	0.873026i	$0.662155\pi$
$398$	−10.7733	−0.540018
$399$	4.41827	0.221190
$400$	−1.48178	−0.0740891
$401$	−6.49266	−0.324228	−0.162114	−	0.986772i	$-0.551831\pi$
$401$	−6.49266	−0.324228	−0.162114	+	0.986772i	$0.551831\pi$
$402$	−3.76251	−0.187657
$403$	0	0
$404$	5.99351	0.298188
$405$	−1.75478	−0.0871956
$406$	−3.73563	−0.185396
$407$	−7.36564	−0.365101
$408$	−11.4458	−0.566649
$409$	−10.5829	−0.523291	−0.261646	−	0.965164i	$-0.584265\pi$
$409$	−10.5829	−0.523291	−0.261646	+	0.965164i	$0.584265\pi$
$410$	6.25328	0.308828
$411$	13.2554	0.653840
$412$	8.45082	0.416342
$413$	−6.08559	−0.299452
$414$	−3.47957	−0.171011
$415$	−0.162034	−0.00795393
$416$	−17.6420	−0.864969
$417$	0.0599152	0.00293406
$418$	1.82516	0.0892717
$419$	−24.0990	−1.17731	−0.588656	−	0.808384i	$-0.700343\pi$
$419$	−24.0990	−1.17731	−0.588656	+	0.808384i	$0.700343\pi$
$420$	3.21111	0.156686
$421$	16.6514	0.811540	0.405770	−	0.913975i	$-0.367003\pi$
$421$	16.6514	0.811540	0.405770	+	0.913975i	$0.367003\pi$
$422$	−2.45042	−0.119284
$423$	−4.89455	−0.237981
$424$	−36.0573	−1.75110
$425$	−8.35839	−0.405442
$426$	−10.9017	−0.528188
$427$	−17.3053	−0.837462
$428$	19.4120	0.938317
$429$	−2.10033	−0.101405
$430$	−7.08328	−0.341586
$431$	38.4425	1.85171	0.925855	−	0.377878i	$-0.123346\pi$
$431$	38.4425	1.85171	0.925855	+	0.377878i	$0.123346\pi$
$432$	0.771457	0.0371167
$433$	−26.0635	−1.25253	−0.626265	−	0.779610i	$-0.715417\pi$
$433$	−26.0635	−1.25253	−0.626265	+	0.779610i	$0.715417\pi$
$434$	0	0
$435$	6.49845	0.311577
$436$	23.4862	1.12479
$437$	−15.2406	−0.729055
$438$	7.75242	0.370425
$439$	0.979258	0.0467374	0.0233687	−	0.999727i	$-0.492561\pi$
$439$	0.979258	0.0467374	0.0233687	+	0.999727i	$0.492561\pi$
$440$	3.21826	0.153424
$441$	−5.29733	−0.252254
$442$	−10.1331	−0.481985
$443$	−19.3542	−0.919547	−0.459774	−	0.888036i	$-0.652069\pi$
$443$	−19.3542	−0.919547	−0.459774	+	0.888036i	$0.652069\pi$
$444$	14.8140	0.703042
$445$	11.2861	0.535014
$446$	6.59235	0.312157
$447$	1.10616	0.0523194
$448$	3.89469	0.184007
$449$	2.57427	0.121488	0.0607438	−	0.998153i	$-0.480653\pi$
$449$	2.57427	0.121488	0.0607438	+	0.998153i	$0.480653\pi$
$450$	−1.48485	−0.0699966
$451$	−3.21426	−0.151353
$452$	−27.8499	−1.30995
$453$	6.50260	0.305519
$454$	−21.7507	−1.02081
$455$	6.89717	0.323344
$456$	−8.90596	−0.417060
$457$	30.3760	1.42093	0.710465	−	0.703733i	$-0.248485\pi$
$457$	30.3760	1.42093	0.710465	+	0.703733i	$0.248485\pi$
$458$	3.42401	0.159993
$459$	4.35161	0.203116
$460$	−11.0765	−0.516446
$461$	−5.65416	−0.263340	−0.131670	−	0.991294i	$-0.542034\pi$
$461$	−5.65416	−0.263340	−0.131670	+	0.991294i	$0.542034\pi$
$462$	0.703365	0.0327235
$463$	1.17124	0.0544321	0.0272160	−	0.999630i	$-0.491336\pi$
$463$	1.17124	0.0544321	0.0272160	+	0.999630i	$0.491336\pi$
$464$	−2.85693	−0.132630
$465$	0	0
$466$	0.0369534	0.00171183
$467$	−27.7924	−1.28608	−0.643039	−	0.765833i	$-0.722327\pi$
$467$	−27.7924	−1.28608	−0.643039	+	0.765833i	$0.722327\pi$
$468$	4.22426	0.195267
$469$	−6.35087	−0.293256
$470$	6.63966	0.306264
$471$	−11.6972	−0.538977
$472$	12.2668	0.564625
$473$	3.64088	0.167408
$474$	−9.02999	−0.414761
$475$	−6.50368	−0.298409
$476$	−7.96312	−0.364989
$477$	13.7088	0.627682
$478$	11.4530	0.523848
$479$	25.0606	1.14505	0.572524	−	0.819888i	$-0.305964\pi$
$479$	25.0606	1.14505	0.572524	+	0.819888i	$0.305964\pi$
$480$	−10.2775	−0.469099
$481$	31.8192	1.45083
$482$	3.92670	0.178856
$483$	−5.87328	−0.267243
$484$	14.7444	0.670201
$485$	−4.14481	−0.188206
$486$	0.773055	0.0350665
$487$	−35.7351	−1.61931	−0.809655	−	0.586906i	$-0.800346\pi$
$487$	−35.7351	−1.61931	−0.809655	+	0.586906i	$0.800346\pi$
$488$	34.8825	1.57906
$489$	−3.09341	−0.139889
$490$	7.18603	0.324632
$491$	−7.75165	−0.349827	−0.174913	−	0.984584i	$-0.555965\pi$
$491$	−7.75165	−0.349827	−0.174913	+	0.984584i	$0.555965\pi$
$492$	6.46462	0.291448
$493$	−16.1153	−0.725796
$494$	−7.88461	−0.354746
$495$	−1.22356	−0.0549951
$496$	0	0
$497$	−18.4013	−0.825412
$498$	0.0713829	0.00319875
$499$	−31.4079	−1.40601	−0.703005	−	0.711185i	$-0.748159\pi$
$499$	−31.4079	−1.40601	−0.703005	+	0.711185i	$0.748159\pi$
$500$	−17.0311	−0.761655
$501$	−11.1412	−0.497752
$502$	6.41796	0.286447
$503$	26.8130	1.19553	0.597766	−	0.801671i	$-0.296055\pi$
$503$	26.8130	1.19553	0.597766	+	0.801671i	$0.296055\pi$
$504$	−3.43210	−0.152878
$505$	7.49956	0.333726
$506$	−2.42622	−0.107859
$507$	−3.92666	−0.174389
$508$	−9.26422	−0.411033
$509$	21.1073	0.935564	0.467782	−	0.883844i	$-0.345053\pi$
$509$	21.1073	0.935564	0.467782	+	0.883844i	$0.345053\pi$
$510$	−5.90313	−0.261395
$511$	13.0856	0.578871
$512$	8.57652	0.379032
$513$	3.38600	0.149495
$514$	−13.7053	−0.604516
$515$	10.5743	0.465961
$516$	−7.32267	−0.322363
$517$	−3.41286	−0.150097
$518$	−10.6557	−0.468184
$519$	−2.70512	−0.118741
$520$	−13.9027	−0.609674
$521$	26.9948	1.18266	0.591332	−	0.806428i	$-0.298602\pi$
$521$	26.9948	1.18266	0.591332	+	0.806428i	$0.298602\pi$
$522$	−2.86285	−0.125304
$523$	4.43450	0.193907	0.0969535	−	0.995289i	$-0.469090\pi$
$523$	4.43450	0.193907	0.0969535	+	0.995289i	$0.469090\pi$
$524$	6.85581	0.299497
$525$	−2.50633	−0.109385
$526$	−0.961072	−0.0419047
$527$	0	0
$528$	0.537919	0.0234099
$529$	−2.74046	−0.119150
$530$	−18.5965	−0.807781
$531$	−4.66377	−0.202390
$532$	−6.19612	−0.268636
$533$	13.8854	0.601444
$534$	−4.97203	−0.215161
$535$	24.2899	1.05014
$536$	12.8015	0.552941
$537$	24.1722	1.04311
$538$	−15.2513	−0.657531
$539$	−3.69370	−0.159099
$540$	2.46087	0.105899
$541$	−33.0353	−1.42030	−0.710150	−	0.704050i	$-0.751373\pi$
$541$	−33.0353	−1.42030	−0.710150	+	0.704050i	$0.751373\pi$
$542$	−10.8696	−0.466887
$543$	8.56648	0.367623
$544$	25.4867	1.09273
$545$	29.3878	1.25884
$546$	−3.03850	−0.130036
$547$	−36.9117	−1.57823	−0.789115	−	0.614245i	$-0.789461\pi$
$547$	−36.9117	−1.57823	−0.789115	+	0.614245i	$0.789461\pi$
$548$	−18.5892	−0.794090
$549$	−13.2621	−0.566014
$550$	−1.03535	−0.0441475
$551$	−12.5393	−0.534194
$552$	11.8388	0.503894
$553$	−15.2420	−0.648156
$554$	−7.40022	−0.314405
$555$	18.5365	0.786830
$556$	−0.0840243	−0.00356342
$557$	45.3487	1.92149	0.960744	−	0.277437i	$-0.0894850\pi$
$557$	45.3487	1.92149	0.960744	+	0.277437i	$0.0894850\pi$
$558$	0	0
$559$	−15.7284	−0.665242
$560$	−1.76644	−0.0746458
$561$	3.03428	0.128107
$562$	−0.577095	−0.0243433
$563$	−6.00705	−0.253167	−0.126584	−	0.991956i	$-0.540401\pi$
$563$	−6.00705	−0.253167	−0.126584	+	0.991956i	$0.540401\pi$
$564$	6.86405	0.289029
$565$	−34.8480	−1.46607
$566$	23.2584	0.977622
$567$	1.30487	0.0547992
$568$	37.0917	1.55633
$569$	43.7995	1.83617	0.918086	−	0.396381i	$-0.129734\pi$
$569$	43.7995	1.83617	0.918086	+	0.396381i	$0.129734\pi$
$570$	−4.59324	−0.192390
$571$	−24.7649	−1.03638	−0.518190	−	0.855265i	$-0.673394\pi$
$571$	−24.7649	−1.03638	−0.518190	+	0.855265i	$0.673394\pi$
$572$	2.94548	0.123157
$573$	23.4530	0.979762
$574$	−4.64999	−0.194087
$575$	8.64545	0.360540
$576$	2.98475	0.124365
$577$	−23.1812	−0.965045	−0.482523	−	0.875883i	$-0.660279\pi$
$577$	−23.1812	−0.965045	−0.482523	+	0.875883i	$0.660279\pi$
$578$	1.49705	0.0622690
$579$	−1.53696	−0.0638739
$580$	−9.11334	−0.378411
$581$	0.120490	0.00499875
$582$	1.82597	0.0756887
$583$	9.55881	0.395885
$584$	−26.3767	−1.09148
$585$	5.28574	0.218538
$586$	13.6533	0.564014
$587$	17.5502	0.724374	0.362187	−	0.932106i	$-0.382030\pi$
$587$	17.5502	0.724374	0.362187	+	0.932106i	$0.382030\pi$
$588$	7.42890	0.306362
$589$	0	0
$590$	6.32658	0.260461
$591$	0.944824	0.0388649
$592$	−8.14924	−0.334932
$593$	−11.4099	−0.468549	−0.234275	−	0.972170i	$-0.575271\pi$
$593$	−11.4099	−0.468549	−0.234275	+	0.972170i	$0.575271\pi$
$594$	0.539033	0.0221168
$595$	−9.96410	−0.408488
$596$	−1.55126	−0.0635420
$597$	−13.9360	−0.570364
$598$	10.4811	0.428606
$599$	22.9201	0.936490	0.468245	−	0.883599i	$-0.344886\pi$
$599$	22.9201	0.936490	0.468245	+	0.883599i	$0.344886\pi$
$600$	5.05204	0.206249
$601$	31.1666	1.27131	0.635655	−	0.771973i	$-0.280730\pi$
$601$	31.1666	1.27131	0.635655	+	0.771973i	$0.280730\pi$
$602$	5.26718	0.214674
$603$	−4.86707	−0.198202
$604$	−9.11915	−0.371053
$605$	18.4494	0.750074
$606$	−3.30388	−0.134211
$607$	−33.0843	−1.34285	−0.671426	−	0.741072i	$-0.734318\pi$
$607$	−33.0843	−1.34285	−0.671426	+	0.741072i	$0.734318\pi$
$608$	19.8312	0.804263
$609$	−4.83230	−0.195815
$610$	17.9906	0.728418
$611$	14.7434	0.596453
$612$	−6.10264	−0.246685
$613$	−24.3138	−0.982026	−0.491013	−	0.871152i	$-0.663373\pi$
$613$	−24.3138	−0.982026	−0.491013	+	0.871152i	$0.663373\pi$
$614$	23.6682	0.955171
$615$	8.08905	0.326182
$616$	−2.39312	−0.0964216
$617$	−3.75808	−0.151295	−0.0756474	−	0.997135i	$-0.524102\pi$
$617$	−3.75808	−0.151295	−0.0756474	+	0.997135i	$0.524102\pi$
$618$	−4.65845	−0.187390
$619$	−10.1016	−0.406017	−0.203009	−	0.979177i	$-0.565072\pi$
$619$	−10.1016	−0.406017	−0.203009	+	0.979177i	$0.565072\pi$
$620$	0	0
$621$	−4.50106	−0.180621
$622$	−20.9683	−0.840753
$623$	−8.39246	−0.336237
$624$	−2.32378	−0.0930257
$625$	−11.7069	−0.468276
$626$	19.6832	0.786698
$627$	2.36097	0.0942883
$628$	16.4039	0.654588
$629$	−45.9680	−1.83286
$630$	−1.77010	−0.0705225
$631$	−29.7072	−1.18263	−0.591313	−	0.806442i	$-0.701390\pi$
$631$	−29.7072	−1.18263	−0.591313	+	0.806442i	$0.701390\pi$
$632$	30.7235	1.22212
$633$	−3.16978	−0.125988
$634$	16.6185	0.660005
$635$	−11.5921	−0.460020
$636$	−19.2250	−0.762321
$637$	15.9566	0.632223
$638$	−1.99620	−0.0790302
$639$	−14.1021	−0.557870
$640$	16.5060	0.652456
$641$	44.6653	1.76417	0.882087	−	0.471087i	$-0.156138\pi$
$641$	44.6653	1.76417	0.882087	+	0.471087i	$0.156138\pi$
$642$	−10.7008	−0.422325
$643$	−3.77464	−0.148857	−0.0744286	−	0.997226i	$-0.523713\pi$
$643$	−3.77464	−0.148857	−0.0744286	+	0.997226i	$0.523713\pi$
$644$	8.23660	0.324567
$645$	−9.16271	−0.360781
$646$	11.3906	0.448158
$647$	32.6232	1.28255	0.641274	−	0.767312i	$-0.278406\pi$
$647$	32.6232	1.28255	0.641274	+	0.767312i	$0.278406\pi$
$648$	−2.63023	−0.103325
$649$	−3.25193	−0.127650
$650$	4.47267	0.175432
$651$	0	0
$652$	4.33815	0.169895
$653$	−17.6023	−0.688832	−0.344416	−	0.938817i	$-0.611923\pi$
$653$	−17.6023	−0.688832	−0.344416	+	0.938817i	$0.611923\pi$
$654$	−12.9466	−0.506253
$655$	8.57853	0.335191
$656$	−3.55621	−0.138847
$657$	10.0283	0.391241
$658$	−4.93730	−0.192476
$659$	−15.6139	−0.608233	−0.304116	−	0.952635i	$-0.598361\pi$
$659$	−15.6139	−0.608233	−0.304116	+	0.952635i	$0.598361\pi$
$660$	1.71591	0.0667917
$661$	7.50294	0.291831	0.145915	−	0.989297i	$-0.453387\pi$
$661$	7.50294	0.291831	0.145915	+	0.989297i	$0.453387\pi$
$662$	10.2023	0.396523
$663$	−13.1079	−0.509069
$664$	−0.242872	−0.00942527
$665$	−7.75308	−0.300651
$666$	−8.16612	−0.316431
$667$	16.6687	0.645416
$668$	15.6243	0.604521
$669$	8.52766	0.329698
$670$	6.60237	0.255072
$671$	−9.24737	−0.356991
$672$	7.64239	0.294812
$673$	−33.5710	−1.29407	−0.647034	−	0.762461i	$-0.723991\pi$
$673$	−33.5710	−1.29407	−0.647034	+	0.762461i	$0.723991\pi$
$674$	1.70953	0.0658485
$675$	−1.92076	−0.0739300
$676$	5.50670	0.211796
$677$	43.7099	1.67991	0.839955	−	0.542656i	$-0.182581\pi$
$677$	43.7099	1.67991	0.839955	+	0.542656i	$0.182581\pi$
$678$	15.3520	0.589592
$679$	3.08211	0.118280
$680$	20.0847	0.770215
$681$	−28.1360	−1.07817
$682$	0	0
$683$	−20.1917	−0.772615	−0.386307	−	0.922370i	$-0.626250\pi$
$683$	−20.1917	−0.772615	−0.386307	+	0.922370i	$0.626250\pi$
$684$	−4.74847	−0.181562
$685$	−23.2603	−0.888729
$686$	−12.4047	−0.473614
$687$	4.42919	0.168984
$688$	4.02822	0.153575
$689$	−41.2936	−1.57316
$690$	6.10587	0.232446
$691$	−35.6758	−1.35717	−0.678586	−	0.734521i	$-0.737407\pi$
$691$	−35.6758	−1.35717	−0.678586	+	0.734521i	$0.737407\pi$
$692$	3.79362	0.144212
$693$	0.909852	0.0345624
$694$	−6.01742	−0.228418
$695$	−0.105138	−0.00398811
$696$	9.74052	0.369213
$697$	−20.0598	−0.759818
$698$	12.7375	0.482120
$699$	0.0478018	0.00180803
$700$	3.51484	0.132849
$701$	−20.6555	−0.780147	−0.390074	−	0.920784i	$-0.627550\pi$
$701$	−20.6555	−0.780147	−0.390074	+	0.920784i	$0.627550\pi$
$702$	−2.32860	−0.0878872
$703$	−35.7678	−1.34901
$704$	2.08119	0.0784379
$705$	8.58885	0.323475
$706$	24.8033	0.933484
$707$	−5.57673	−0.209734
$708$	6.54040	0.245803
$709$	−18.3550	−0.689335	−0.344667	−	0.938725i	$-0.612008\pi$
$709$	−18.3550	−0.689335	−0.344667	+	0.938725i	$0.612008\pi$
$710$	19.1300	0.717937
$711$	−11.6809	−0.438068
$712$	16.9168	0.633983
$713$	0	0
$714$	4.38961	0.164277
$715$	3.68562	0.137834
$716$	−33.8988	−1.26686
$717$	14.8152	0.553285
$718$	21.6154	0.806679
$719$	−5.83120	−0.217467	−0.108733	−	0.994071i	$-0.534680\pi$
$719$	−5.83120	−0.217467	−0.108733	+	0.994071i	$0.534680\pi$
$720$	−1.35374	−0.0504507
$721$	−7.86316	−0.292839
$722$	−5.82499	−0.216784
$723$	5.07946	0.188907
$724$	−12.0135	−0.446479
$725$	7.11313	0.264175
$726$	−8.12775	−0.301649
$727$	−4.98495	−0.184882	−0.0924408	−	0.995718i	$-0.529467\pi$
$727$	−4.98495	−0.184882	−0.0924408	+	0.995718i	$0.529467\pi$
$728$	10.3382	0.383158
$729$	1.00000	0.0370370
$730$	−13.6038	−0.503498
$731$	22.7223	0.840414
$732$	18.5986	0.687425
$733$	9.71555	0.358852	0.179426	−	0.983771i	$-0.442576\pi$
$733$	9.71555	0.358852	0.179426	+	0.983771i	$0.442576\pi$
$734$	−12.5663	−0.463831
$735$	9.29563	0.342874
$736$	−26.3620	−0.971716
$737$	−3.39369	−0.125008
$738$	−3.56358	−0.131177
$739$	26.3659	0.969885	0.484943	−	0.874546i	$-0.338841\pi$
$739$	26.3659	0.969885	0.484943	+	0.874546i	$0.338841\pi$
$740$	−25.9953	−0.955606
$741$	−10.1993	−0.374680
$742$	13.8285	0.507660
$743$	−23.1796	−0.850376	−0.425188	−	0.905105i	$-0.639792\pi$
$743$	−23.1796	−0.850376	−0.425188	+	0.905105i	$0.639792\pi$
$744$	0	0
$745$	−1.94106	−0.0711148
$746$	11.1778	0.409250
$747$	0.0923387	0.00337850
$748$	−4.25523	−0.155586
$749$	−18.0622	−0.659977
$750$	9.38828	0.342812
$751$	4.17694	0.152419	0.0762093	−	0.997092i	$-0.475718\pi$
$751$	4.17694	0.152419	0.0762093	+	0.997092i	$0.475718\pi$
$752$	−3.77594	−0.137694
$753$	8.30207	0.302544
$754$	8.62347	0.314048
$755$	−11.4106	−0.415275
$756$	−1.82992	−0.0665537
$757$	17.7945	0.646753	0.323376	−	0.946270i	$-0.395182\pi$
$757$	17.7945	0.646753	0.323376	+	0.946270i	$0.395182\pi$
$758$	−13.5288	−0.491389
$759$	−3.13848	−0.113920
$760$	15.6280	0.566886
$761$	33.1196	1.20059	0.600293	−	0.799780i	$-0.295051\pi$
$761$	33.1196	1.20059	0.600293	+	0.799780i	$0.295051\pi$
$762$	5.10683	0.185001
$763$	−21.8530	−0.791132
$764$	−32.8901	−1.18992
$765$	−7.63611	−0.276084
$766$	−9.34919	−0.337800
$767$	14.0482	0.507251
$768$	−13.2411	−0.477797
$769$	13.6473	0.492135	0.246067	−	0.969253i	$-0.420862\pi$
$769$	13.6473	0.492135	0.246067	+	0.969253i	$0.420862\pi$
$770$	−1.23425	−0.0444793
$771$	−17.7288	−0.638487
$772$	2.15541	0.0775750
$773$	−24.9319	−0.896738	−0.448369	−	0.893849i	$-0.647995\pi$
$773$	−24.9319	−0.896738	−0.448369	+	0.893849i	$0.647995\pi$
$774$	4.03657	0.145091
$775$	0	0
$776$	−6.21264	−0.223021
$777$	−13.7839	−0.494494
$778$	6.16203	0.220919
$779$	−15.6085	−0.559234
$780$	−7.41264	−0.265415
$781$	−9.83304	−0.351854
$782$	−15.1417	−0.541467
$783$	−3.70329	−0.132345
$784$	−4.08666	−0.145952
$785$	20.5259	0.732601
$786$	−3.77921	−0.134800
$787$	22.6198	0.806310	0.403155	−	0.915132i	$-0.367914\pi$
$787$	22.6198	0.806310	0.403155	+	0.915132i	$0.367914\pi$
$788$	−1.32501	−0.0472015
$789$	−1.24321	−0.0442596
$790$	15.8456	0.563762
$791$	25.9132	0.921368
$792$	−1.83400	−0.0651683
$793$	39.9482	1.41860
$794$	−15.0233	−0.533157
$795$	−24.0559	−0.853173
$796$	19.5437	0.692708
$797$	0.459299	0.0162692	0.00813460	−	0.999967i	$-0.497411\pi$
$797$	0.459299	0.0162692	0.00813460	+	0.999967i	$0.497411\pi$
$798$	3.41557	0.120910
$799$	−21.2992	−0.753512
$800$	−11.2496	−0.397733
$801$	−6.43167	−0.227252
$802$	−5.01919	−0.177234
$803$	6.99249	0.246760
$804$	6.82551	0.240717
$805$	10.3063	0.363249
$806$	0	0
$807$	−19.7286	−0.694481
$808$	11.2411	0.395460
$809$	2.44846	0.0860834	0.0430417	−	0.999073i	$-0.486295\pi$
$809$	2.44846	0.0860834	0.0430417	+	0.999073i	$0.486295\pi$
$810$	−1.35654	−0.0476639
$811$	55.6918	1.95560	0.977802	−	0.209530i	$-0.0671934\pi$
$811$	55.6918	1.95560	0.977802	+	0.209530i	$0.0671934\pi$
$812$	6.77674	0.237817
$813$	−14.0605	−0.493124
$814$	−5.69404	−0.199576
$815$	5.42824	0.190143
$816$	3.35708	0.117521
$817$	17.6803	0.618554
$818$	−8.18117	−0.286048
$819$	−3.93051	−0.137343
$820$	−11.3440	−0.396149
$821$	11.6067	0.405076	0.202538	−	0.979274i	$-0.435081\pi$
$821$	11.6067	0.405076	0.202538	+	0.979274i	$0.435081\pi$
$822$	10.2472	0.357410
$823$	−0.0981262	−0.00342046	−0.00171023	−	0.999999i	$-0.500544\pi$
$823$	−0.0981262	−0.00342046	−0.00171023	+	0.999999i	$0.500544\pi$
$824$	15.8499	0.552156
$825$	−1.33930	−0.0466284
$826$	−4.70449	−0.163690
$827$	2.94776	0.102504	0.0512519	−	0.998686i	$-0.483679\pi$
$827$	2.94776	0.102504	0.0512519	+	0.998686i	$0.483679\pi$
$828$	6.31222	0.219365
$829$	−11.5569	−0.401389	−0.200695	−	0.979654i	$-0.564320\pi$
$829$	−11.5569	−0.401389	−0.200695	+	0.979654i	$0.564320\pi$
$830$	−0.125261	−0.00434788
$831$	−9.57269	−0.332073
$832$	−8.99065	−0.311695
$833$	−23.0519	−0.798702
$834$	0.0463178	0.00160385
$835$	19.5503	0.676567
$836$	−3.31100	−0.114513
$837$	0	0
$838$	−18.6298	−0.643557
$839$	1.17000	0.0403928	0.0201964	−	0.999796i	$-0.493571\pi$
$839$	1.17000	0.0403928	0.0201964	+	0.999796i	$0.493571\pi$
$840$	6.02257	0.207798
$841$	−15.2856	−0.527091
$842$	12.8725	0.443614
$843$	−0.746512	−0.0257112
$844$	4.44526	0.153012
$845$	6.89042	0.237038
$846$	−3.78376	−0.130088
$847$	−13.7191	−0.471394
$848$	10.5757	0.363172
$849$	30.0863	1.03256
$850$	−6.46150	−0.221628
$851$	47.5467	1.62988
$852$	19.7766	0.677534
$853$	16.6400	0.569743	0.284872	−	0.958566i	$-0.408049\pi$
$853$	16.6400	0.569743	0.284872	+	0.958566i	$0.408049\pi$
$854$	−13.3780	−0.457784
$855$	−5.94167	−0.203201
$856$	36.4081	1.24440
$857$	24.3272	0.831001	0.415500	−	0.909593i	$-0.363606\pi$
$857$	24.3272	0.831001	0.415500	+	0.909593i	$0.363606\pi$
$858$	−1.62367	−0.0554313
$859$	−3.57607	−0.122014	−0.0610070	−	0.998137i	$-0.519431\pi$
$859$	−3.57607	−0.122014	−0.0610070	+	0.998137i	$0.519431\pi$
$860$	12.8497	0.438169
$861$	−6.01508	−0.204993
$862$	29.7182	1.01221
$863$	15.7085	0.534723	0.267362	−	0.963596i	$-0.413848\pi$
$863$	15.7085	0.534723	0.267362	+	0.963596i	$0.413848\pi$
$864$	5.85684	0.199254
$865$	4.74688	0.161399
$866$	−20.1485	−0.684674
$867$	1.93653	0.0657682
$868$	0	0
$869$	−8.14482	−0.276294
$870$	5.02366	0.170318
$871$	14.6606	0.496755
$872$	44.0494	1.49170
$873$	2.36201	0.0799420
$874$	−11.7818	−0.398525
$875$	15.8468	0.535719
$876$	−14.0635	−0.475163
$877$	−37.4703	−1.26528	−0.632641	−	0.774445i	$-0.718029\pi$
$877$	−37.4703	−1.26528	−0.632641	+	0.774445i	$0.718029\pi$
$878$	0.757020	0.0255482
$879$	17.6615	0.595708
$880$	−0.943927	−0.0318198
$881$	0.261197	0.00879994	0.00439997	−	0.999990i	$-0.498599\pi$
$881$	0.261197	0.00879994	0.00439997	+	0.999990i	$0.498599\pi$
$882$	−4.09513	−0.137890
$883$	−37.1782	−1.25115	−0.625573	−	0.780165i	$-0.715135\pi$
$883$	−37.1782	−1.25115	−0.625573	+	0.780165i	$0.715135\pi$
$884$	18.3824	0.618266
$885$	8.18387	0.275098
$886$	−14.9619	−0.502654
$887$	−14.8602	−0.498955	−0.249478	−	0.968381i	$-0.580259\pi$
$887$	−14.8602	−0.498955	−0.249478	+	0.968381i	$0.580259\pi$
$888$	27.7843	0.932380
$889$	8.61999	0.289105
$890$	8.72481	0.292456
$891$	0.697276	0.0233596
$892$	−11.9591	−0.400419
$893$	−16.5729	−0.554592
$894$	0.855119	0.0285995
$895$	−42.4169	−1.41784
$896$	−12.2740	−0.410044
$897$	13.5581	0.452691
$898$	1.99006	0.0664090
$899$	0	0
$900$	2.69364	0.0897881
$901$	59.6553	1.98741
$902$	−2.48480	−0.0827347
$903$	6.81346	0.226738
$904$	−52.2336	−1.73726
$905$	−15.0323	−0.499689
$906$	5.02687	0.167006
$907$	21.5541	0.715693	0.357847	−	0.933780i	$-0.383511\pi$
$907$	21.5541	0.715693	0.357847	+	0.933780i	$0.383511\pi$
$908$	39.4575	1.30944
$909$	−4.27380	−0.141753
$910$	5.33190	0.176751
$911$	9.42479	0.312257	0.156129	−	0.987737i	$-0.450099\pi$
$911$	9.42479	0.312257	0.156129	+	0.987737i	$0.450099\pi$
$912$	2.61215	0.0864970
$913$	0.0643856	0.00213085
$914$	23.4823	0.776726
$915$	23.2721	0.769352
$916$	−6.21143	−0.205231
$917$	−6.37906	−0.210655
$918$	3.36404	0.111030
$919$	17.3908	0.573669	0.286835	−	0.957980i	$-0.407397\pi$
$919$	17.3908	0.573669	0.286835	+	0.957980i	$0.407397\pi$
$920$	−20.7745	−0.684915
$921$	30.6165	1.00885
$922$	−4.37098	−0.143950
$923$	42.4782	1.39819
$924$	−1.27596	−0.0419761
$925$	20.2898	0.667125
$926$	0.905432	0.0297543
$927$	−6.02603	−0.197921
$928$	−21.6896	−0.711996
$929$	−4.65072	−0.152585	−0.0762926	−	0.997085i	$-0.524308\pi$
$929$	−4.65072	−0.152585	−0.0762926	+	0.997085i	$0.524308\pi$
$930$	0	0
$931$	−17.9367	−0.587853
$932$	−0.0670365	−0.00219586
$933$	−27.1240	−0.887999
$934$	−21.4851	−0.703013
$935$	−5.32448	−0.174129
$936$	7.92278	0.258964
$937$	16.8302	0.549819	0.274909	−	0.961470i	$-0.411352\pi$
$937$	16.8302	0.549819	0.274909	+	0.961470i	$0.411352\pi$
$938$	−4.90957	−0.160303
$939$	25.4615	0.830906
$940$	−12.0449	−0.392861
$941$	−24.8551	−0.810254	−0.405127	−	0.914260i	$-0.632773\pi$
$941$	−24.8551	−0.810254	−0.405127	+	0.914260i	$0.632773\pi$
$942$	−9.04255	−0.294622
$943$	20.7487	0.675670
$944$	−3.59789	−0.117102
$945$	−2.28975	−0.0744855
$946$	2.81460	0.0915107
$947$	−13.2606	−0.430912	−0.215456	−	0.976514i	$-0.569124\pi$
$947$	−13.2606	−0.430912	−0.215456	+	0.976514i	$0.569124\pi$
$948$	16.3811	0.532035
$949$	−30.2072	−0.980567
$950$	−5.02770	−0.163120
$951$	21.4972	0.697093
$952$	−14.9352	−0.484051
$953$	−47.2097	−1.52927	−0.764637	−	0.644461i	$-0.777082\pi$
$953$	−47.2097	−1.52927	−0.764637	+	0.644461i	$0.777082\pi$
$954$	10.5976	0.343111
$955$	−41.1547	−1.33174
$956$	−20.7767	−0.671965
$957$	−2.58222	−0.0834712
$958$	19.3732	0.625920
$959$	17.2965	0.558533
$960$	−5.23757	−0.169042
$961$	0	0
$962$	24.5980	0.793071
$963$	−13.8422	−0.446057
$964$	−7.12336	−0.229428
$965$	2.69702	0.0868203
$966$	−4.54037	−0.146084
$967$	25.9297	0.833842	0.416921	−	0.908943i	$-0.363109\pi$
$967$	25.9297	0.833842	0.416921	+	0.908943i	$0.363109\pi$
$968$	27.6537	0.888825
$969$	14.7345	0.473342
$970$	−3.20416	−0.102880
$971$	34.7397	1.11485	0.557426	−	0.830227i	$-0.311789\pi$
$971$	34.7397	1.11485	0.557426	+	0.830227i	$0.311789\pi$
$972$	−1.40239	−0.0449815
$973$	0.0781813	0.00250638
$974$	−27.6252	−0.885168
$975$	5.78570	0.185291
$976$	−10.2312	−0.327492
$977$	−30.9102	−0.988905	−0.494452	−	0.869205i	$-0.664631\pi$
$977$	−30.9102	−0.988905	−0.494452	+	0.869205i	$0.664631\pi$
$978$	−2.39137	−0.0764677
$979$	−4.48465	−0.143330
$980$	−13.0361	−0.416421
$981$	−16.7473	−0.534701
$982$	−5.99245	−0.191227
$983$	−25.0053	−0.797546	−0.398773	−	0.917050i	$-0.630564\pi$
$983$	−25.0053	−0.797546	−0.398773	+	0.917050i	$0.630564\pi$
$984$	12.1247	0.386520
$985$	−1.65796	−0.0528269
$986$	−12.4580	−0.396744
$987$	−6.38673	−0.203292
$988$	14.3033	0.455050
$989$	−23.5026	−0.747341
$990$	−0.945883	−0.0300621
$991$	37.3608	1.18680	0.593402	−	0.804906i	$-0.297784\pi$
$991$	37.3608	1.18680	0.593402	+	0.804906i	$0.297784\pi$
$992$	0	0
$993$	13.1974	0.418806
$994$	−14.2252	−0.451197
$995$	24.4546	0.775264
$996$	−0.129495	−0.00410319
$997$	−44.6107	−1.41284	−0.706418	−	0.707795i	$-0.749690\pi$
$997$	−44.6107	−1.41284	−0.706418	+	0.707795i	$0.749690\pi$
$998$	−24.2800	−0.768571
$999$	−10.5634	−0.334213

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2883.2.a.n.1.7		8
3.2	odd	2		8649.2.a.bi.1.2		8
31.12	odd	30		93.2.m.a.82.2	yes	16
31.13	odd	30		93.2.m.a.76.2	✓	16
31.30	odd	2		2883.2.a.m.1.7		8
93.44	even	30		279.2.y.b.262.1		16
93.74	even	30		279.2.y.b.82.1		16
93.92	even	2		8649.2.a.bj.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.m.a.76.2	✓	16	31.13	odd	30
93.2.m.a.82.2	yes	16	31.12	odd	30
279.2.y.b.82.1		16	93.74	even	30
279.2.y.b.262.1		16	93.44	even	30
2883.2.a.m.1.7		8	31.30	odd	2
2883.2.a.n.1.7		8	1.1	even	1	trivial
8649.2.a.bi.1.2		8	3.2	odd	2
8649.2.a.bj.1.2		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)

\(f(q)\)	\(=\)	\(q+0.773055 q^{2} +1.00000 q^{3} -1.40239 q^{4} -1.75478 q^{5} +0.773055 q^{6} +1.30487 q^{7} -2.63023 q^{8} +1.00000 q^{9} -1.35654 q^{10} +0.697276 q^{11} -1.40239 q^{12} -3.01220 q^{13} +1.00873 q^{14} -1.75478 q^{15} +0.771457 q^{16} +4.35161 q^{17} +0.773055 q^{18} +3.38600 q^{19} +2.46087 q^{20} +1.30487 q^{21} +0.539033 q^{22} -4.50106 q^{23} -2.63023 q^{24} -1.92076 q^{25} -2.32860 q^{26} +1.00000 q^{27} -1.82992 q^{28} -3.70329 q^{29} -1.35654 q^{30} +5.85684 q^{32} +0.697276 q^{33} +3.36404 q^{34} -2.28975 q^{35} -1.40239 q^{36} -10.5634 q^{37} +2.61756 q^{38} -3.01220 q^{39} +4.61547 q^{40} -4.60973 q^{41} +1.00873 q^{42} +5.22158 q^{43} -0.977850 q^{44} -1.75478 q^{45} -3.47957 q^{46} -4.89455 q^{47} +0.771457 q^{48} -5.29733 q^{49} -1.48485 q^{50} +4.35161 q^{51} +4.22426 q^{52} +13.7088 q^{53} +0.773055 q^{54} -1.22356 q^{55} -3.43210 q^{56} +3.38600 q^{57} -2.86285 q^{58} -4.66377 q^{59} +2.46087 q^{60} -13.2621 q^{61} +1.30487 q^{63} +2.98475 q^{64} +5.28574 q^{65} +0.539033 q^{66} -4.86707 q^{67} -6.10264 q^{68} -4.50106 q^{69} -1.77010 q^{70} -14.1021 q^{71} -2.63023 q^{72} +10.0283 q^{73} -8.16612 q^{74} -1.92076 q^{75} -4.74847 q^{76} +0.909852 q^{77} -2.32860 q^{78} -11.6809 q^{79} -1.35374 q^{80} +1.00000 q^{81} -3.56358 q^{82} +0.0923387 q^{83} -1.82992 q^{84} -7.63611 q^{85} +4.03657 q^{86} -3.70329 q^{87} -1.83400 q^{88} -6.43167 q^{89} -1.35654 q^{90} -3.93051 q^{91} +6.31222 q^{92} -3.78376 q^{94} -5.94167 q^{95} +5.85684 q^{96} +2.36201 q^{97} -4.09513 q^{98} +0.697276 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{2} + 8 q^{3} + 5 q^{4} - 6 q^{5} - 5 q^{6} - 6 q^{7} + 8 q^{9} + q^{10} + 5 q^{12} - 12 q^{13} - 3 q^{14} - 6 q^{15} + 3 q^{16} - 2 q^{17} - 5 q^{18} - 8 q^{19} - 5 q^{20} - 6 q^{21} - 4 q^{22}+ \cdots + 32 q^{98}+O(q^{100}) \) 8 * q - 5 * q^2 + 8 * q^3 + 5 * q^4 - 6 * q^5 - 5 * q^6 - 6 * q^7 + 8 * q^9 + q^10 + 5 * q^12 - 12 * q^13 - 3 * q^14 - 6 * q^15 + 3 * q^16 - 2 * q^17 - 5 * q^18 - 8 * q^19 - 5 * q^20 - 6 * q^21 - 4 * q^22 - 4 * q^23 - 12 * q^25 + 18 * q^26 + 8 * q^27 - 15 * q^28 + 6 * q^29 + q^30 - 17 * q^34 + 9 * q^35 + 5 * q^36 - 8 * q^37 - 7 * q^38 - 12 * q^39 + 13 * q^40 - 20 * q^41 - 3 * q^42 - 14 * q^43 - 25 * q^44 - 6 * q^45 - 9 * q^46 + 6 * q^47 + 3 * q^48 - 20 * q^49 + 6 * q^50 - 2 * q^51 - 30 * q^52 + 30 * q^53 - 5 * q^54 - 19 * q^55 + 6 * q^56 - 8 * q^57 - 19 * q^58 - 20 * q^59 - 5 * q^60 - 13 * q^61 - 6 * q^63 - 26 * q^64 + 27 * q^65 - 4 * q^66 + 32 * q^67 + 15 * q^68 - 4 * q^69 - 6 * q^70 - 17 * q^71 + 12 * q^73 + 10 * q^74 - 12 * q^75 - 20 * q^76 - 18 * q^77 + 18 * q^78 - 30 * q^79 - 21 * q^80 + 8 * q^81 - 23 * q^82 - 12 * q^83 - 15 * q^84 - 28 * q^85 + 46 * q^86 + 6 * q^87 - 22 * q^88 - 6 * q^89 + q^90 + 15 * q^91 + 70 * q^92 + 44 * q^94 - 36 * q^95 - 39 * q^97 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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