LMFDB - Embedded newform 8670.2.a.by.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8670,2,Mod(1,8670)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8670, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8670.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8670.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$69.2302985525$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{16})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 4x^{2} + 2 $ x^4 - 4*x^2 + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 510)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.84776$ of defining polynomial
Character	$\chi$	$=$	8670.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +4.61313 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -5.10973 q^{11} -1.00000 q^{12} -3.23463 q^{13} +4.61313 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{18} -4.00000 q^{19} -1.00000 q^{20} -4.61313 q^{21} -5.10973 q^{22} +6.22784 q^{23} -1.00000 q^{24} +1.00000 q^{25} -3.23463 q^{26} -1.00000 q^{27} +4.61313 q^{28} -8.33598 q^{29} +1.00000 q^{30} +3.79724 q^{31} +1.00000 q^{32} +5.10973 q^{33} -4.61313 q^{35} +1.00000 q^{36} +7.49207 q^{37} -4.00000 q^{38} +3.23463 q^{39} -1.00000 q^{40} +9.56767 q^{41} -4.61313 q^{42} -8.25744 q^{43} -5.10973 q^{44} -1.00000 q^{45} +6.22784 q^{46} -12.4525 q^{47} -1.00000 q^{48} +14.2809 q^{49} +1.00000 q^{50} -3.23463 q^{52} -1.36595 q^{53} -1.00000 q^{54} +5.10973 q^{55} +4.61313 q^{56} +4.00000 q^{57} -8.33598 q^{58} +2.37170 q^{59} +1.00000 q^{60} +1.22625 q^{61} +3.79724 q^{62} +4.61313 q^{63} +1.00000 q^{64} +3.23463 q^{65} +5.10973 q^{66} +2.74444 q^{67} -6.22784 q^{69} -4.61313 q^{70} -9.09841 q^{71} +1.00000 q^{72} -9.20851 q^{73} +7.49207 q^{74} -1.00000 q^{75} -4.00000 q^{76} -23.5718 q^{77} +3.23463 q^{78} -3.61153 q^{79} -1.00000 q^{80} +1.00000 q^{81} +9.56767 q^{82} -11.2649 q^{83} -4.61313 q^{84} -8.25744 q^{86} +8.33598 q^{87} -5.10973 q^{88} -9.03188 q^{89} -1.00000 q^{90} -14.9218 q^{91} +6.22784 q^{92} -3.79724 q^{93} -12.4525 q^{94} +4.00000 q^{95} -1.00000 q^{96} -6.00416 q^{97} +14.2809 q^{98} -5.10973 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 8 q^{7} + 4 q^{8} + 4 q^{9} - 4 q^{10} - 4 q^{12} - 16 q^{13} + 8 q^{14} + 4 q^{15} + 4 q^{16} + 4 q^{18} - 16 q^{19} - 4 q^{20} - 8 q^{21} + 8 q^{23}+ \cdots + 4 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 8 * q^7 + 4 * q^8 + 4 * q^9 - 4 * q^10 - 4 * q^12 - 16 * q^13 + 8 * q^14 + 4 * q^15 + 4 * q^16 + 4 * q^18 - 16 * q^19 - 4 * q^20 - 8 * q^21 + 8 * q^23 - 4 * q^24 + 4 * q^25 - 16 * q^26 - 4 * q^27 + 8 * q^28 + 8 * q^29 + 4 * q^30 + 4 * q^32 - 8 * q^35 + 4 * q^36 + 16 * q^37 - 16 * q^38 + 16 * q^39 - 4 * q^40 - 8 * q^42 - 16 * q^43 - 4 * q^45 + 8 * q^46 - 8 * q^47 - 4 * q^48 + 4 * q^49 + 4 * q^50 - 16 * q^52 - 8 * q^53 - 4 * q^54 + 8 * q^56 + 16 * q^57 + 8 * q^58 - 24 * q^59 + 4 * q^60 - 16 * q^61 + 8 * q^63 + 4 * q^64 + 16 * q^65 - 8 * q^69 - 8 * q^70 + 8 * q^71 + 4 * q^72 - 16 * q^73 + 16 * q^74 - 4 * q^75 - 16 * q^76 - 16 * q^77 + 16 * q^78 - 4 * q^80 + 4 * q^81 - 32 * q^83 - 8 * q^84 - 16 * q^86 - 8 * q^87 - 24 * q^89 - 4 * q^90 - 24 * q^91 + 8 * q^92 - 8 * q^94 + 16 * q^95 - 4 * q^96 + 16 * q^97 + 4 * q^98

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.00000	−0.408248
$7$	4.61313	1.74360	0.871799	−	0.489864i	$-0.162954\pi$
$7$	4.61313	1.74360	0.871799	+	0.489864i	$0.162954\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	−5.10973	−1.54064	−0.770321	−	0.637656i	$-0.779904\pi$
$11$	−5.10973	−1.54064	−0.770321	+	0.637656i	$0.779904\pi$
$12$	−1.00000	−0.288675
$13$	−3.23463	−0.897126	−0.448563	−	0.893751i	$-0.648064\pi$
$13$	−3.23463	−0.897126	−0.448563	+	0.893751i	$0.648064\pi$
$14$	4.61313	1.23291
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	0	0
$17$	0	0
$18$	1.00000	0.235702
$19$	−4.00000	−0.917663	−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000	−0.917663	−0.458831	+	0.888523i	$0.651732\pi$
$20$	−1.00000	−0.223607
$21$	−4.61313	−1.00667
$22$	−5.10973	−1.08940
$23$	6.22784	1.29860	0.649298	−	0.760534i	$-0.275063\pi$
$23$	6.22784	1.29860	0.649298	+	0.760534i	$0.275063\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−3.23463	−0.634364
$27$	−1.00000	−0.192450
$28$	4.61313	0.871799
$29$	−8.33598	−1.54795	−0.773977	−	0.633214i	$-0.781735\pi$
$29$	−8.33598	−1.54795	−0.773977	+	0.633214i	$0.781735\pi$
$30$	1.00000	0.182574
$31$	3.79724	0.682005	0.341002	−	0.940062i	$-0.389234\pi$
$31$	3.79724	0.682005	0.341002	+	0.940062i	$0.389234\pi$
$32$	1.00000	0.176777
$33$	5.10973	0.889490
$34$	0	0
$35$	−4.61313	−0.779761
$36$	1.00000	0.166667
$37$	7.49207	1.23169	0.615844	−	0.787868i	$-0.288815\pi$
$37$	7.49207	1.23169	0.615844	+	0.787868i	$0.288815\pi$
$38$	−4.00000	−0.648886
$39$	3.23463	0.517956
$40$	−1.00000	−0.158114
$41$	9.56767	1.49422	0.747110	−	0.664701i	$-0.231441\pi$
$41$	9.56767	1.49422	0.747110	+	0.664701i	$0.231441\pi$
$42$	−4.61313	−0.711821
$43$	−8.25744	−1.25925	−0.629624	−	0.776900i	$-0.716791\pi$
$43$	−8.25744	−1.25925	−0.629624	+	0.776900i	$0.716791\pi$
$44$	−5.10973	−0.770321
$45$	−1.00000	−0.149071
$46$	6.22784	0.918246
$47$	−12.4525	−1.81638	−0.908192	−	0.418553i	$-0.862537\pi$
$47$	−12.4525	−1.81638	−0.908192	+	0.418553i	$0.862537\pi$
$48$	−1.00000	−0.144338
$49$	14.2809	2.04013
$50$	1.00000	0.141421
$51$	0	0
$52$	−3.23463	−0.448563
$53$	−1.36595	−0.187628	−0.0938138	−	0.995590i	$-0.529906\pi$
$53$	−1.36595	−0.187628	−0.0938138	+	0.995590i	$0.529906\pi$
$54$	−1.00000	−0.136083
$55$	5.10973	0.688996
$56$	4.61313	0.616455
$57$	4.00000	0.529813
$58$	−8.33598	−1.09457
$59$	2.37170	0.308770	0.154385	−	0.988011i	$-0.450660\pi$
$59$	2.37170	0.308770	0.154385	+	0.988011i	$0.450660\pi$
$60$	1.00000	0.129099
$61$	1.22625	0.157005	0.0785027	−	0.996914i	$-0.474986\pi$
$61$	1.22625	0.157005	0.0785027	+	0.996914i	$0.474986\pi$
$62$	3.79724	0.482250
$63$	4.61313	0.581199
$64$	1.00000	0.125000
$65$	3.23463	0.401207
$66$	5.10973	0.628964
$67$	2.74444	0.335287	0.167643	−	0.985848i	$-0.446384\pi$
$67$	2.74444	0.335287	0.167643	+	0.985848i	$0.446384\pi$
$68$	0	0
$69$	−6.22784	−0.749744
$70$	−4.61313	−0.551374
$71$	−9.09841	−1.07978	−0.539891	−	0.841735i	$-0.681535\pi$
$71$	−9.09841	−1.07978	−0.539891	+	0.841735i	$0.681535\pi$
$72$	1.00000	0.117851
$73$	−9.20851	−1.07777	−0.538887	−	0.842378i	$-0.681155\pi$
$73$	−9.20851	−1.07777	−0.538887	+	0.842378i	$0.681155\pi$
$74$	7.49207	0.870935
$75$	−1.00000	−0.115470
$76$	−4.00000	−0.458831
$77$	−23.5718	−2.68626
$78$	3.23463	0.366250
$79$	−3.61153	−0.406329	−0.203165	−	0.979145i	$-0.565123\pi$
$79$	−3.61153	−0.406329	−0.203165	+	0.979145i	$0.565123\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	9.56767	1.05657
$83$	−11.2649	−1.23649	−0.618243	−	0.785987i	$-0.712155\pi$
$83$	−11.2649	−1.23649	−0.618243	+	0.785987i	$0.712155\pi$
$84$	−4.61313	−0.503333
$85$	0	0
$86$	−8.25744	−0.890422
$87$	8.33598	0.893711
$88$	−5.10973	−0.544699
$89$	−9.03188	−0.957377	−0.478688	−	0.877985i	$-0.658888\pi$
$89$	−9.03188	−0.957377	−0.478688	+	0.877985i	$0.658888\pi$
$90$	−1.00000	−0.105409
$91$	−14.9218	−1.56423
$92$	6.22784	0.649298
$93$	−3.79724	−0.393756
$94$	−12.4525	−1.28438
$95$	4.00000	0.410391
$96$	−1.00000	−0.102062
$97$	−6.00416	−0.609630	−0.304815	−	0.952412i	$-0.598595\pi$
$97$	−6.00416	−0.609630	−0.304815	+	0.952412i	$0.598595\pi$
$98$	14.2809	1.44259
$99$	−5.10973	−0.513547
$100$	1.00000	0.100000
$101$	−6.96882	−0.693423	−0.346712	−	0.937972i	$-0.612702\pi$
$101$	−6.96882	−0.693423	−0.346712	+	0.937972i	$0.612702\pi$
$102$	0	0
$103$	−17.5854	−1.73274	−0.866371	−	0.499401i	$-0.833554\pi$
$103$	−17.5854	−1.73274	−0.866371	+	0.499401i	$0.833554\pi$
$104$	−3.23463	−0.317182
$105$	4.61313	0.450195
$106$	−1.36595	−0.132673
$107$	−2.78976	−0.269697	−0.134848	−	0.990866i	$-0.543055\pi$
$107$	−2.78976	−0.269697	−0.134848	+	0.990866i	$0.543055\pi$
$108$	−1.00000	−0.0962250
$109$	−15.1489	−1.45100	−0.725502	−	0.688220i	$-0.758392\pi$
$109$	−15.1489	−1.45100	−0.725502	+	0.688220i	$0.758392\pi$
$110$	5.10973	0.487194
$111$	−7.49207	−0.711116
$112$	4.61313	0.435899
$113$	2.34662	0.220751	0.110376	−	0.993890i	$-0.464795\pi$
$113$	2.34662	0.220751	0.110376	+	0.993890i	$0.464795\pi$
$114$	4.00000	0.374634
$115$	−6.22784	−0.580750
$116$	−8.33598	−0.773977
$117$	−3.23463	−0.299042
$118$	2.37170	0.218333
$119$	0	0
$120$	1.00000	0.0912871
$121$	15.1094	1.37358
$122$	1.22625	0.111020
$123$	−9.56767	−0.862688
$124$	3.79724	0.341002
$125$	−1.00000	−0.0894427
$126$	4.61313	0.410970
$127$	8.19438	0.727133	0.363567	−	0.931568i	$-0.381559\pi$
$127$	8.19438	0.727133	0.363567	+	0.931568i	$0.381559\pi$
$128$	1.00000	0.0883883
$129$	8.25744	0.727027
$130$	3.23463	0.283696
$131$	6.52076	0.569721	0.284861	−	0.958569i	$-0.408053\pi$
$131$	6.52076	0.569721	0.284861	+	0.958569i	$0.408053\pi$
$132$	5.10973	0.444745
$133$	−18.4525	−1.60003
$134$	2.74444	0.237084
$135$	1.00000	0.0860663
$136$	0	0
$137$	11.5076	0.983157	0.491578	−	0.870833i	$-0.336420\pi$
$137$	11.5076	0.983157	0.491578	+	0.870833i	$0.336420\pi$
$138$	−6.22784	−0.530149
$139$	21.1412	1.79318	0.896588	−	0.442866i	$-0.146038\pi$
$139$	21.1412	1.79318	0.896588	+	0.442866i	$0.146038\pi$
$140$	−4.61313	−0.389880
$141$	12.4525	1.04869
$142$	−9.09841	−0.763521
$143$	16.5281	1.38215
$144$	1.00000	0.0833333
$145$	8.33598	0.692266
$146$	−9.20851	−0.762102
$147$	−14.2809	−1.17787
$148$	7.49207	0.615844
$149$	−20.4592	−1.67608	−0.838040	−	0.545609i	$-0.816298\pi$
$149$	−20.4592	−1.67608	−0.838040	+	0.545609i	$0.816298\pi$
$150$	−1.00000	−0.0816497
$151$	15.2905	1.24433	0.622163	−	0.782888i	$-0.286254\pi$
$151$	15.2905	1.24433	0.622163	+	0.782888i	$0.286254\pi$
$152$	−4.00000	−0.324443
$153$	0	0
$154$	−23.5718	−1.89947
$155$	−3.79724	−0.305002
$156$	3.23463	0.258978
$157$	−1.82267	−0.145465	−0.0727325	−	0.997351i	$-0.523172\pi$
$157$	−1.82267	−0.145465	−0.0727325	+	0.997351i	$0.523172\pi$
$158$	−3.61153	−0.287318
$159$	1.36595	0.108327
$160$	−1.00000	−0.0790569
$161$	28.7298	2.26423
$162$	1.00000	0.0785674
$163$	7.77019	0.608608	0.304304	−	0.952575i	$-0.401576\pi$
$163$	7.77019	0.608608	0.304304	+	0.952575i	$0.401576\pi$
$164$	9.56767	0.747110
$165$	−5.10973	−0.397792
$166$	−11.2649	−0.874327
$167$	−4.87056	−0.376895	−0.188448	−	0.982083i	$-0.560346\pi$
$167$	−4.87056	−0.376895	−0.188448	+	0.982083i	$0.560346\pi$
$168$	−4.61313	−0.355910
$169$	−2.53715	−0.195165
$170$	0	0
$171$	−4.00000	−0.305888
$172$	−8.25744	−0.629624
$173$	0.867091	0.0659237	0.0329619	−	0.999457i	$-0.489506\pi$
$173$	0.867091	0.0659237	0.0329619	+	0.999457i	$0.489506\pi$
$174$	8.33598	0.631949
$175$	4.61313	0.348720
$176$	−5.10973	−0.385161
$177$	−2.37170	−0.178268
$178$	−9.03188	−0.676968
$179$	17.3691	1.29823	0.649113	−	0.760692i	$-0.275140\pi$
$179$	17.3691	1.29823	0.649113	+	0.760692i	$0.275140\pi$
$180$	−1.00000	−0.0745356
$181$	−6.20345	−0.461099	−0.230549	−	0.973061i	$-0.574052\pi$
$181$	−6.20345	−0.461099	−0.230549	+	0.973061i	$0.574052\pi$
$182$	−14.9218	−1.10608
$183$	−1.22625	−0.0906471
$184$	6.22784	0.459123
$185$	−7.49207	−0.550828
$186$	−3.79724	−0.278427
$187$	0	0
$188$	−12.4525	−0.908192
$189$	−4.61313	−0.335556
$190$	4.00000	0.290191
$191$	−2.35916	−0.170703	−0.0853514	−	0.996351i	$-0.527201\pi$
$191$	−2.35916	−0.170703	−0.0853514	+	0.996351i	$0.527201\pi$
$192$	−1.00000	−0.0721688
$193$	−1.54847	−0.111462	−0.0557308	−	0.998446i	$-0.517749\pi$
$193$	−1.54847	−0.111462	−0.0557308	+	0.998446i	$0.517749\pi$
$194$	−6.00416	−0.431074
$195$	−3.23463	−0.231637
$196$	14.2809	1.02007
$197$	4.95136	0.352770	0.176385	−	0.984321i	$-0.443560\pi$
$197$	4.95136	0.352770	0.176385	+	0.984321i	$0.443560\pi$
$198$	−5.10973	−0.363133
$199$	10.3508	0.733747	0.366874	−	0.930271i	$-0.380428\pi$
$199$	10.3508	0.733747	0.366874	+	0.930271i	$0.380428\pi$
$200$	1.00000	0.0707107
$201$	−2.74444	−0.193578
$202$	−6.96882	−0.490324
$203$	−38.4549	−2.69901
$204$	0	0
$205$	−9.56767	−0.668235
$206$	−17.5854	−1.22523
$207$	6.22784	0.432865
$208$	−3.23463	−0.224281
$209$	20.4389	1.41379
$210$	4.61313	0.318336
$211$	2.29541	0.158023	0.0790113	−	0.996874i	$-0.474824\pi$
$211$	2.29541	0.158023	0.0790113	+	0.996874i	$0.474824\pi$
$212$	−1.36595	−0.0938138
$213$	9.09841	0.623413
$214$	−2.78976	−0.190704
$215$	8.25744	0.563153
$216$	−1.00000	−0.0680414
$217$	17.5172	1.18914
$218$	−15.1489	−1.02601
$219$	9.20851	0.622254
$220$	5.10973	0.344498
$221$	0	0
$222$	−7.49207	−0.502835
$223$	−26.2446	−1.75747	−0.878733	−	0.477314i	$-0.841610\pi$
$223$	−26.2446	−1.75747	−0.878733	+	0.477314i	$0.841610\pi$
$224$	4.61313	0.308227
$225$	1.00000	0.0666667
$226$	2.34662	0.156095
$227$	−4.20026	−0.278781	−0.139391	−	0.990237i	$-0.544514\pi$
$227$	−4.20026	−0.278781	−0.139391	+	0.990237i	$0.544514\pi$
$228$	4.00000	0.264906
$229$	12.5954	0.832327	0.416163	−	0.909290i	$-0.363374\pi$
$229$	12.5954	0.832327	0.416163	+	0.909290i	$0.363374\pi$
$230$	−6.22784	−0.410652
$231$	23.5718	1.55091
$232$	−8.33598	−0.547284
$233$	−20.9134	−1.37008	−0.685041	−	0.728505i	$-0.740216\pi$
$233$	−20.9134	−1.37008	−0.685041	+	0.728505i	$0.740216\pi$
$234$	−3.23463	−0.211455
$235$	12.4525	0.812312
$236$	2.37170	0.154385
$237$	3.61153	0.234594
$238$	0	0
$239$	−24.2741	−1.57016	−0.785082	−	0.619392i	$-0.787379\pi$
$239$	−24.2741	−1.57016	−0.785082	+	0.619392i	$0.787379\pi$
$240$	1.00000	0.0645497
$241$	−5.86452	−0.377767	−0.188884	−	0.981999i	$-0.560487\pi$
$241$	−5.86452	−0.377767	−0.188884	+	0.981999i	$0.560487\pi$
$242$	15.1094	0.971266
$243$	−1.00000	−0.0641500
$244$	1.22625	0.0785027
$245$	−14.2809	−0.912375
$246$	−9.56767	−0.610013
$247$	12.9385	0.823259
$248$	3.79724	0.241125
$249$	11.2649	0.713885
$250$	−1.00000	−0.0632456
$251$	−3.18412	−0.200980	−0.100490	−	0.994938i	$-0.532041\pi$
$251$	−3.18412	−0.200980	−0.100490	+	0.994938i	$0.532041\pi$
$252$	4.61313	0.290600
$253$	−31.8226	−2.00067
$254$	8.19438	0.514161
$255$	0	0
$256$	1.00000	0.0625000
$257$	−10.8084	−0.674212	−0.337106	−	0.941467i	$-0.609448\pi$
$257$	−10.8084	−0.674212	−0.337106	+	0.941467i	$0.609448\pi$
$258$	8.25744	0.514086
$259$	34.5619	2.14757
$260$	3.23463	0.200603
$261$	−8.33598	−0.515984
$262$	6.52076	0.402854
$263$	−26.1440	−1.61211	−0.806055	−	0.591840i	$-0.798402\pi$
$263$	−26.1440	−1.61211	−0.806055	+	0.591840i	$0.798402\pi$
$264$	5.10973	0.314482
$265$	1.36595	0.0839096
$266$	−18.4525	−1.13140
$267$	9.03188	0.552742
$268$	2.74444	0.167643
$269$	12.8503	0.783498	0.391749	−	0.920072i	$-0.371870\pi$
$269$	12.8503	0.783498	0.391749	+	0.920072i	$0.371870\pi$
$270$	1.00000	0.0608581
$271$	6.64954	0.403931	0.201965	−	0.979393i	$-0.435267\pi$
$271$	6.64954	0.403931	0.201965	+	0.979393i	$0.435267\pi$
$272$	0	0
$273$	14.9218	0.903107
$274$	11.5076	0.695197
$275$	−5.10973	−0.308128
$276$	−6.22784	−0.374872
$277$	20.7370	1.24597	0.622983	−	0.782236i	$-0.285921\pi$
$277$	20.7370	1.24597	0.622983	+	0.782236i	$0.285921\pi$
$278$	21.1412	1.26797
$279$	3.79724	0.227335
$280$	−4.61313	−0.275687
$281$	−18.5104	−1.10424	−0.552118	−	0.833766i	$-0.686180\pi$
$281$	−18.5104	−1.10424	−0.552118	+	0.833766i	$0.686180\pi$
$282$	12.4525	0.741536
$283$	−31.8441	−1.89293	−0.946467	−	0.322801i	$-0.895375\pi$
$283$	−31.8441	−1.89293	−0.946467	+	0.322801i	$0.895375\pi$
$284$	−9.09841	−0.539891
$285$	−4.00000	−0.236940
$286$	16.5281	0.977327
$287$	44.1369	2.60532
$288$	1.00000	0.0589256
$289$	0	0
$290$	8.33598	0.489506
$291$	6.00416	0.351970
$292$	−9.20851	−0.538887
$293$	−0.145584	−0.00850509	−0.00425255	−	0.999991i	$-0.501354\pi$
$293$	−0.145584	−0.00850509	−0.00425255	+	0.999991i	$0.501354\pi$
$294$	−14.2809	−0.832881
$295$	−2.37170	−0.138086
$296$	7.49207	0.435468
$297$	5.10973	0.296497
$298$	−20.4592	−1.18517
$299$	−20.1448	−1.16500
$300$	−1.00000	−0.0577350
$301$	−38.0926	−2.19562
$302$	15.2905	0.879871
$303$	6.96882	0.400348
$304$	−4.00000	−0.229416
$305$	−1.22625	−0.0702150
$306$	0	0
$307$	−8.52742	−0.486685	−0.243343	−	0.969940i	$-0.578244\pi$
$307$	−8.52742	−0.486685	−0.243343	+	0.969940i	$0.578244\pi$
$308$	−23.5718	−1.34313
$309$	17.5854	1.00040
$310$	−3.79724	−0.215669
$311$	−4.12196	−0.233735	−0.116867	−	0.993148i	$-0.537285\pi$
$311$	−4.12196	−0.233735	−0.116867	+	0.993148i	$0.537285\pi$
$312$	3.23463	0.183125
$313$	13.4178	0.758422	0.379211	−	0.925310i	$-0.376196\pi$
$313$	13.4178	0.758422	0.379211	+	0.925310i	$0.376196\pi$
$314$	−1.82267	−0.102859
$315$	−4.61313	−0.259920
$316$	−3.61153	−0.203165
$317$	−17.5140	−0.983683	−0.491841	−	0.870685i	$-0.663676\pi$
$317$	−17.5140	−0.983683	−0.491841	+	0.870685i	$0.663676\pi$
$318$	1.36595	0.0765986
$319$	42.5946	2.38484
$320$	−1.00000	−0.0559017
$321$	2.78976	0.155709
$322$	28.7298	1.60105
$323$	0	0
$324$	1.00000	0.0555556
$325$	−3.23463	−0.179425
$326$	7.77019	0.430351
$327$	15.1489	0.837737
$328$	9.56767	0.528286
$329$	−57.4450	−3.16704
$330$	−5.10973	−0.281281
$331$	−10.7274	−0.589631	−0.294815	−	0.955554i	$-0.595258\pi$
$331$	−10.7274	−0.589631	−0.294815	+	0.955554i	$0.595258\pi$
$332$	−11.2649	−0.618243
$333$	7.49207	0.410563
$334$	−4.87056	−0.266505
$335$	−2.74444	−0.149945
$336$	−4.61313	−0.251667
$337$	6.87125	0.374301	0.187151	−	0.982331i	$-0.440075\pi$
$337$	6.87125	0.374301	0.187151	+	0.982331i	$0.440075\pi$
$338$	−2.53715	−0.138003
$339$	−2.34662	−0.127451
$340$	0	0
$341$	−19.4029	−1.05073
$342$	−4.00000	−0.216295
$343$	33.5879	1.81357
$344$	−8.25744	−0.445211
$345$	6.22784	0.335296
$346$	0.867091	0.0466151
$347$	−5.94532	−0.319162	−0.159581	−	0.987185i	$-0.551014\pi$
$347$	−5.94532	−0.319162	−0.159581	+	0.987185i	$0.551014\pi$
$348$	8.33598	0.446856
$349$	−15.6342	−0.836880	−0.418440	−	0.908244i	$-0.637423\pi$
$349$	−15.6342	−0.836880	−0.418440	+	0.908244i	$0.637423\pi$
$350$	4.61313	0.246582
$351$	3.23463	0.172652
$352$	−5.10973	−0.272350
$353$	−25.7425	−1.37014	−0.685068	−	0.728479i	$-0.740227\pi$
$353$	−25.7425	−1.37014	−0.685068	+	0.728479i	$0.740227\pi$
$354$	−2.37170	−0.126055
$355$	9.09841	0.482893
$356$	−9.03188	−0.478688
$357$	0	0
$358$	17.3691	0.917984
$359$	−1.57709	−0.0832355	−0.0416178	−	0.999134i	$-0.513251\pi$
$359$	−1.57709	−0.0832355	−0.0416178	+	0.999134i	$0.513251\pi$
$360$	−1.00000	−0.0527046
$361$	−3.00000	−0.157895
$362$	−6.20345	−0.326046
$363$	−15.1094	−0.793036
$364$	−14.9218	−0.782113
$365$	9.20851	0.481996
$366$	−1.22625	−0.0640972
$367$	3.82336	0.199578	0.0997890	−	0.995009i	$-0.468183\pi$
$367$	3.82336	0.199578	0.0997890	+	0.995009i	$0.468183\pi$
$368$	6.22784	0.324649
$369$	9.56767	0.498073
$370$	−7.49207	−0.389494
$371$	−6.30130	−0.327147
$372$	−3.79724	−0.196878
$373$	8.52742	0.441533	0.220766	−	0.975327i	$-0.429144\pi$
$373$	8.52742	0.441533	0.220766	+	0.975327i	$0.429144\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	−12.4525	−0.642189
$377$	26.9638	1.38871
$378$	−4.61313	−0.237274
$379$	−0.576186	−0.0295967	−0.0147983	−	0.999890i	$-0.504711\pi$
$379$	−0.576186	−0.0295967	−0.0147983	+	0.999890i	$0.504711\pi$
$380$	4.00000	0.205196
$381$	−8.19438	−0.419811
$382$	−2.35916	−0.120705
$383$	8.37146	0.427762	0.213881	−	0.976860i	$-0.431390\pi$
$383$	8.37146	0.427762	0.213881	+	0.976860i	$0.431390\pi$
$384$	−1.00000	−0.0510310
$385$	23.5718	1.20133
$386$	−1.54847	−0.0788152
$387$	−8.25744	−0.419749
$388$	−6.00416	−0.304815
$389$	−21.4213	−1.08610	−0.543052	−	0.839699i	$-0.682731\pi$
$389$	−21.4213	−1.08610	−0.543052	+	0.839699i	$0.682731\pi$
$390$	−3.23463	−0.163792
$391$	0	0
$392$	14.2809	0.721296
$393$	−6.52076	−0.328929
$394$	4.95136	0.249446
$395$	3.61153	0.181716
$396$	−5.10973	−0.256774
$397$	5.85389	0.293798	0.146899	−	0.989151i	$-0.453071\pi$
$397$	5.85389	0.293798	0.146899	+	0.989151i	$0.453071\pi$
$398$	10.3508	0.518838
$399$	18.4525	0.923781
$400$	1.00000	0.0500000
$401$	−13.4583	−0.672076	−0.336038	−	0.941848i	$-0.609087\pi$
$401$	−13.4583	−0.672076	−0.336038	+	0.941848i	$0.609087\pi$
$402$	−2.74444	−0.136880
$403$	−12.2827	−0.611844
$404$	−6.96882	−0.346712
$405$	−1.00000	−0.0496904
$406$	−38.4549	−1.90849
$407$	−38.2825	−1.89759
$408$	0	0
$409$	12.5762	0.621852	0.310926	−	0.950434i	$-0.399361\pi$
$409$	12.5762	0.621852	0.310926	+	0.950434i	$0.399361\pi$
$410$	−9.56767	−0.472514
$411$	−11.5076	−0.567626
$412$	−17.5854	−0.866371
$413$	10.9410	0.538370
$414$	6.22784	0.306082
$415$	11.2649	0.552973
$416$	−3.23463	−0.158591
$417$	−21.1412	−1.03529
$418$	20.4389	0.999701
$419$	5.94829	0.290593	0.145296	−	0.989388i	$-0.453586\pi$
$419$	5.94829	0.290593	0.145296	+	0.989388i	$0.453586\pi$
$420$	4.61313	0.225097
$421$	17.3255	0.844392	0.422196	−	0.906505i	$-0.361259\pi$
$421$	17.3255	0.844392	0.422196	+	0.906505i	$0.361259\pi$
$422$	2.29541	0.111739
$423$	−12.4525	−0.605461
$424$	−1.36595	−0.0663364
$425$	0	0
$426$	9.09841	0.440819
$427$	5.65685	0.273754
$428$	−2.78976	−0.134848
$429$	−16.5281	−0.797985
$430$	8.25744	0.398209
$431$	7.69968	0.370881	0.185440	−	0.982656i	$-0.440629\pi$
$431$	7.69968	0.370881	0.185440	+	0.982656i	$0.440629\pi$
$432$	−1.00000	−0.0481125
$433$	−37.3311	−1.79402	−0.897009	−	0.442012i	$-0.854265\pi$
$433$	−37.3311	−1.79402	−0.897009	+	0.442012i	$0.854265\pi$
$434$	17.5172	0.840850
$435$	−8.33598	−0.399680
$436$	−15.1489	−0.725502
$437$	−24.9114	−1.19167
$438$	9.20851	0.440000
$439$	−29.2516	−1.39610	−0.698052	−	0.716047i	$-0.745950\pi$
$439$	−29.2516	−1.39610	−0.698052	+	0.716047i	$0.745950\pi$
$440$	5.10973	0.243597
$441$	14.2809	0.680044
$442$	0	0
$443$	−9.66136	−0.459025	−0.229513	−	0.973306i	$-0.573713\pi$
$443$	−9.66136	−0.459025	−0.229513	+	0.973306i	$0.573713\pi$
$444$	−7.49207	−0.355558
$445$	9.03188	0.428152
$446$	−26.2446	−1.24272
$447$	20.4592	0.967685
$448$	4.61313	0.217950
$449$	−15.2994	−0.722024	−0.361012	−	0.932561i	$-0.617569\pi$
$449$	−15.2994	−0.722024	−0.361012	+	0.932561i	$0.617569\pi$
$450$	1.00000	0.0471405
$451$	−48.8882	−2.30206
$452$	2.34662	0.110376
$453$	−15.2905	−0.718412
$454$	−4.20026	−0.197128
$455$	14.9218	0.699543
$456$	4.00000	0.187317
$457$	31.6369	1.47991	0.739956	−	0.672655i	$-0.234846\pi$
$457$	31.6369	1.47991	0.739956	+	0.672655i	$0.234846\pi$
$458$	12.5954	0.588544
$459$	0	0
$460$	−6.22784	−0.290375
$461$	−15.2314	−0.709399	−0.354700	−	0.934980i	$-0.615417\pi$
$461$	−15.2314	−0.709399	−0.354700	+	0.934980i	$0.615417\pi$
$462$	23.5718	1.09666
$463$	26.4086	1.22731	0.613656	−	0.789574i	$-0.289698\pi$
$463$	26.4086	1.22731	0.613656	+	0.789574i	$0.289698\pi$
$464$	−8.33598	−0.386988
$465$	3.79724	0.176093
$466$	−20.9134	−0.968794
$467$	8.62955	0.399328	0.199664	−	0.979864i	$-0.436015\pi$
$467$	8.62955	0.399328	0.199664	+	0.979864i	$0.436015\pi$
$468$	−3.23463	−0.149521
$469$	12.6605	0.584606
$470$	12.4525	0.574391
$471$	1.82267	0.0839843
$472$	2.37170	0.109167
$473$	42.1933	1.94005
$474$	3.61153	0.165883
$475$	−4.00000	−0.183533
$476$	0	0
$477$	−1.36595	−0.0625425
$478$	−24.2741	−1.11027
$479$	−7.25731	−0.331595	−0.165797	−	0.986160i	$-0.553020\pi$
$479$	−7.25731	−0.331595	−0.165797	+	0.986160i	$0.553020\pi$
$480$	1.00000	0.0456435
$481$	−24.2341	−1.10498
$482$	−5.86452	−0.267122
$483$	−28.7298	−1.30725
$484$	15.1094	0.686789
$485$	6.00416	0.272635
$486$	−1.00000	−0.0453609
$487$	7.72095	0.349870	0.174935	−	0.984580i	$-0.444029\pi$
$487$	7.72095	0.349870	0.174935	+	0.984580i	$0.444029\pi$
$488$	1.22625	0.0555098
$489$	−7.77019	−0.351380
$490$	−14.2809	−0.645147
$491$	1.52235	0.0687028	0.0343514	−	0.999410i	$-0.489063\pi$
$491$	1.52235	0.0687028	0.0343514	+	0.999410i	$0.489063\pi$
$492$	−9.56767	−0.431344
$493$	0	0
$494$	12.9385	0.582132
$495$	5.10973	0.229665
$496$	3.79724	0.170501
$497$	−41.9721	−1.88271
$498$	11.2649	0.504793
$499$	10.9191	0.488805	0.244402	−	0.969674i	$-0.421408\pi$
$499$	10.9191	0.488805	0.244402	+	0.969674i	$0.421408\pi$
$500$	−1.00000	−0.0447214
$501$	4.87056	0.217601
$502$	−3.18412	−0.142114
$503$	7.69310	0.343019	0.171509	−	0.985183i	$-0.445136\pi$
$503$	7.69310	0.343019	0.171509	+	0.985183i	$0.445136\pi$
$504$	4.61313	0.205485
$505$	6.96882	0.310108
$506$	−31.8226	−1.41469
$507$	2.53715	0.112679
$508$	8.19438	0.363567
$509$	−10.6762	−0.473214	−0.236607	−	0.971605i	$-0.576035\pi$
$509$	−10.6762	−0.473214	−0.236607	+	0.971605i	$0.576035\pi$
$510$	0	0
$511$	−42.4800	−1.87921
$512$	1.00000	0.0441942
$513$	4.00000	0.176604
$514$	−10.8084	−0.476740
$515$	17.5854	0.774906
$516$	8.25744	0.363513
$517$	63.6290	2.79840
$518$	34.5619	1.51856
$519$	−0.867091	−0.0380611
$520$	3.23463	0.141848
$521$	−33.1918	−1.45416	−0.727078	−	0.686554i	$-0.759122\pi$
$521$	−33.1918	−1.45416	−0.727078	+	0.686554i	$0.759122\pi$
$522$	−8.33598	−0.364856
$523$	13.6526	0.596988	0.298494	−	0.954412i	$-0.403516\pi$
$523$	13.6526	0.596988	0.298494	+	0.954412i	$0.403516\pi$
$524$	6.52076	0.284861
$525$	−4.61313	−0.201333
$526$	−26.1440	−1.13993
$527$	0	0
$528$	5.10973	0.222373
$529$	15.7860	0.686350
$530$	1.36595	0.0593330
$531$	2.37170	0.102923
$532$	−18.4525	−0.800017
$533$	−30.9479	−1.34050
$534$	9.03188	0.390847
$535$	2.78976	0.120612
$536$	2.74444	0.118542
$537$	−17.3691	−0.749531
$538$	12.8503	0.554017
$539$	−72.9717	−3.14311
$540$	1.00000	0.0430331
$541$	19.9083	0.855927	0.427963	−	0.903796i	$-0.359231\pi$
$541$	19.9083	0.855927	0.427963	+	0.903796i	$0.359231\pi$
$542$	6.64954	0.285622
$543$	6.20345	0.266215
$544$	0	0
$545$	15.1489	0.648909
$546$	14.9218	0.638593
$547$	−23.9406	−1.02363	−0.511813	−	0.859097i	$-0.671026\pi$
$547$	−23.9406	−1.02363	−0.511813	+	0.859097i	$0.671026\pi$
$548$	11.5076	0.491578
$549$	1.22625	0.0523352
$550$	−5.10973	−0.217880
$551$	33.3439	1.42050
$552$	−6.22784	−0.265075
$553$	−16.6605	−0.708475
$554$	20.7370	0.881030
$555$	7.49207	0.318021
$556$	21.1412	0.896588
$557$	43.3001	1.83469	0.917343	−	0.398098i	$-0.130330\pi$
$557$	43.3001	1.83469	0.917343	+	0.398098i	$0.130330\pi$
$558$	3.79724	0.160750
$559$	26.7098	1.12970
$560$	−4.61313	−0.194940
$561$	0	0
$562$	−18.5104	−0.780813
$563$	7.33741	0.309235	0.154618	−	0.987974i	$-0.450585\pi$
$563$	7.33741	0.309235	0.154618	+	0.987974i	$0.450585\pi$
$564$	12.4525	0.524345
$565$	−2.34662	−0.0987229
$566$	−31.8441	−1.33851
$567$	4.61313	0.193733
$568$	−9.09841	−0.381761
$569$	35.8596	1.50331	0.751655	−	0.659556i	$-0.229256\pi$
$569$	35.8596	1.50331	0.751655	+	0.659556i	$0.229256\pi$
$570$	−4.00000	−0.167542
$571$	−38.3152	−1.60344	−0.801722	−	0.597698i	$-0.796082\pi$
$571$	−38.3152	−1.60344	−0.801722	+	0.597698i	$0.796082\pi$
$572$	16.5281	0.691075
$573$	2.35916	0.0985554
$574$	44.1369	1.84224
$575$	6.22784	0.259719
$576$	1.00000	0.0416667
$577$	−11.2911	−0.470053	−0.235026	−	0.971989i	$-0.575518\pi$
$577$	−11.2911	−0.470053	−0.235026	+	0.971989i	$0.575518\pi$
$578$	0	0
$579$	1.54847	0.0643523
$580$	8.33598	0.346133
$581$	−51.9665	−2.15593
$582$	6.00416	0.248881
$583$	6.97963	0.289067
$584$	−9.20851	−0.381051
$585$	3.23463	0.133736
$586$	−0.145584	−0.00601401
$587$	23.6916	0.977856	0.488928	−	0.872324i	$-0.337388\pi$
$587$	23.6916	0.977856	0.488928	+	0.872324i	$0.337388\pi$
$588$	−14.2809	−0.588936
$589$	−15.1890	−0.625851
$590$	−2.37170	−0.0976415
$591$	−4.95136	−0.203672
$592$	7.49207	0.307922
$593$	31.2409	1.28291	0.641456	−	0.767160i	$-0.278331\pi$
$593$	31.2409	1.28291	0.641456	+	0.767160i	$0.278331\pi$
$594$	5.10973	0.209655
$595$	0	0
$596$	−20.4592	−0.838040
$597$	−10.3508	−0.423629
$598$	−20.1448	−0.823782
$599$	−39.0402	−1.59514	−0.797570	−	0.603227i	$-0.793881\pi$
$599$	−39.0402	−1.59514	−0.797570	+	0.603227i	$0.793881\pi$
$600$	−1.00000	−0.0408248
$601$	15.1228	0.616872	0.308436	−	0.951245i	$-0.400194\pi$
$601$	15.1228	0.616872	0.308436	+	0.951245i	$0.400194\pi$
$602$	−38.0926	−1.55254
$603$	2.74444	0.111762
$604$	15.2905	0.622163
$605$	−15.1094	−0.614283
$606$	6.96882	0.283089
$607$	23.7589	0.964343	0.482171	−	0.876077i	$-0.339848\pi$
$607$	23.7589	0.964343	0.482171	+	0.876077i	$0.339848\pi$
$608$	−4.00000	−0.162221
$609$	38.4549	1.55827
$610$	−1.22625	−0.0496495
$611$	40.2793	1.62953
$612$	0	0
$613$	23.1238	0.933961	0.466980	−	0.884268i	$-0.345342\pi$
$613$	23.1238	0.933961	0.466980	+	0.884268i	$0.345342\pi$
$614$	−8.52742	−0.344139
$615$	9.56767	0.385806
$616$	−23.5718	−0.949736
$617$	1.44445	0.0581515	0.0290757	−	0.999577i	$-0.490744\pi$
$617$	1.44445	0.0581515	0.0290757	+	0.999577i	$0.490744\pi$
$618$	17.5854	0.707389
$619$	−4.81485	−0.193525	−0.0967626	−	0.995307i	$-0.530849\pi$
$619$	−4.81485	−0.193525	−0.0967626	+	0.995307i	$0.530849\pi$
$620$	−3.79724	−0.152501
$621$	−6.22784	−0.249915
$622$	−4.12196	−0.165275
$623$	−41.6652	−1.66928
$624$	3.23463	0.129489
$625$	1.00000	0.0400000
$626$	13.4178	0.536285
$627$	−20.4389	−0.816252
$628$	−1.82267	−0.0727325
$629$	0	0
$630$	−4.61313	−0.183791
$631$	27.8950	1.11048	0.555241	−	0.831690i	$-0.312626\pi$
$631$	27.8950	1.11048	0.555241	+	0.831690i	$0.312626\pi$
$632$	−3.61153	−0.143659
$633$	−2.29541	−0.0912344
$634$	−17.5140	−0.695569
$635$	−8.19438	−0.325184
$636$	1.36595	0.0541634
$637$	−46.1936	−1.83026
$638$	42.5946	1.68634
$639$	−9.09841	−0.359927
$640$	−1.00000	−0.0395285
$641$	18.3466	0.724646	0.362323	−	0.932053i	$-0.381984\pi$
$641$	18.3466	0.724646	0.362323	+	0.932053i	$0.381984\pi$
$642$	2.78976	0.110103
$643$	21.8339	0.861047	0.430523	−	0.902579i	$-0.358329\pi$
$643$	21.8339	0.861047	0.430523	+	0.902579i	$0.358329\pi$
$644$	28.7298	1.13211
$645$	−8.25744	−0.325136
$646$	0	0
$647$	11.9054	0.468049	0.234024	−	0.972231i	$-0.424810\pi$
$647$	11.9054	0.468049	0.234024	+	0.972231i	$0.424810\pi$
$648$	1.00000	0.0392837
$649$	−12.1188	−0.475703
$650$	−3.23463	−0.126873
$651$	−17.5172	−0.686552
$652$	7.77019	0.304304
$653$	2.10554	0.0823961	0.0411980	−	0.999151i	$-0.486883\pi$
$653$	2.10554	0.0823961	0.0411980	+	0.999151i	$0.486883\pi$
$654$	15.1489	0.592370
$655$	−6.52076	−0.254787
$656$	9.56767	0.373555
$657$	−9.20851	−0.359258
$658$	−57.4450	−2.23944
$659$	34.9841	1.36279	0.681393	−	0.731918i	$-0.261374\pi$
$659$	34.9841	1.36279	0.681393	+	0.731918i	$0.261374\pi$
$660$	−5.10973	−0.198896
$661$	23.6884	0.921372	0.460686	−	0.887563i	$-0.347603\pi$
$661$	23.6884	0.921372	0.460686	+	0.887563i	$0.347603\pi$
$662$	−10.7274	−0.416932
$663$	0	0
$664$	−11.2649	−0.437164
$665$	18.4525	0.715557
$666$	7.49207	0.290312
$667$	−51.9152	−2.01016
$668$	−4.87056	−0.188448
$669$	26.2446	1.01467
$670$	−2.74444	−0.106027
$671$	−6.26582	−0.241889
$672$	−4.61313	−0.177955
$673$	−27.6693	−1.06657	−0.533287	−	0.845934i	$-0.679044\pi$
$673$	−27.6693	−1.06657	−0.533287	+	0.845934i	$0.679044\pi$
$674$	6.87125	0.264671
$675$	−1.00000	−0.0384900
$676$	−2.53715	−0.0975826
$677$	−32.9178	−1.26514	−0.632568	−	0.774505i	$-0.717999\pi$
$677$	−32.9178	−1.26514	−0.632568	+	0.774505i	$0.717999\pi$
$678$	−2.34662	−0.0901213
$679$	−27.6980	−1.06295
$680$	0	0
$681$	4.20026	0.160954
$682$	−19.4029	−0.742975
$683$	32.8824	1.25821	0.629104	−	0.777321i	$-0.283422\pi$
$683$	32.8824	1.25821	0.629104	+	0.777321i	$0.283422\pi$
$684$	−4.00000	−0.152944
$685$	−11.5076	−0.439681
$686$	33.5879	1.28239
$687$	−12.5954	−0.480544
$688$	−8.25744	−0.314812
$689$	4.41834	0.168326
$690$	6.22784	0.237090
$691$	−35.2698	−1.34173	−0.670863	−	0.741581i	$-0.734076\pi$
$691$	−35.2698	−1.34173	−0.670863	+	0.741581i	$0.734076\pi$
$692$	0.867091	0.0329619
$693$	−23.5718	−0.895420
$694$	−5.94532	−0.225681
$695$	−21.1412	−0.801933
$696$	8.33598	0.315975
$697$	0	0
$698$	−15.6342	−0.591763
$699$	20.9134	0.791017
$700$	4.61313	0.174360
$701$	−22.1766	−0.837598	−0.418799	−	0.908079i	$-0.637549\pi$
$701$	−22.1766	−0.837598	−0.418799	+	0.908079i	$0.637549\pi$
$702$	3.23463	0.122083
$703$	−29.9683	−1.13028
$704$	−5.10973	−0.192580
$705$	−12.4525	−0.468988
$706$	−25.7425	−0.968832
$707$	−32.1480	−1.20905
$708$	−2.37170	−0.0891341
$709$	3.38860	0.127261	0.0636307	−	0.997974i	$-0.479732\pi$
$709$	3.38860	0.127261	0.0636307	+	0.997974i	$0.479732\pi$
$710$	9.09841	0.341457
$711$	−3.61153	−0.135443
$712$	−9.03188	−0.338484
$713$	23.6486	0.885648
$714$	0	0
$715$	−16.5281	−0.618116
$716$	17.3691	0.649113
$717$	24.2741	0.906534
$718$	−1.57709	−0.0588564
$719$	−33.0604	−1.23294	−0.616472	−	0.787377i	$-0.711439\pi$
$719$	−33.0604	−1.23294	−0.616472	+	0.787377i	$0.711439\pi$
$720$	−1.00000	−0.0372678
$721$	−81.1237	−3.02121
$722$	−3.00000	−0.111648
$723$	5.86452	0.218104
$724$	−6.20345	−0.230549
$725$	−8.33598	−0.309591
$726$	−15.1094	−0.560761
$727$	−27.6774	−1.02650	−0.513250	−	0.858239i	$-0.671559\pi$
$727$	−27.6774	−1.02650	−0.513250	+	0.858239i	$0.671559\pi$
$728$	−14.9218	−0.553038
$729$	1.00000	0.0370370
$730$	9.20851	0.340822
$731$	0	0
$732$	−1.22625	−0.0453236
$733$	−10.7508	−0.397090	−0.198545	−	0.980092i	$-0.563622\pi$
$733$	−10.7508	−0.397090	−0.198545	+	0.980092i	$0.563622\pi$
$734$	3.82336	0.141123
$735$	14.2809	0.526760
$736$	6.22784	0.229561
$737$	−14.0234	−0.516557
$738$	9.56767	0.352191
$739$	−16.4434	−0.604881	−0.302441	−	0.953168i	$-0.597801\pi$
$739$	−16.4434	−0.604881	−0.302441	+	0.953168i	$0.597801\pi$
$740$	−7.49207	−0.275414
$741$	−12.9385	−0.475309
$742$	−6.30130	−0.231328
$743$	19.1698	0.703271	0.351636	−	0.936137i	$-0.385626\pi$
$743$	19.1698	0.703271	0.351636	+	0.936137i	$0.385626\pi$
$744$	−3.79724	−0.139214
$745$	20.4592	0.749566
$746$	8.52742	0.312211
$747$	−11.2649	−0.412162
$748$	0	0
$749$	−12.8695	−0.470242
$750$	1.00000	0.0365148
$751$	5.47045	0.199620	0.0998099	−	0.995007i	$-0.468177\pi$
$751$	5.47045	0.199620	0.0998099	+	0.995007i	$0.468177\pi$
$752$	−12.4525	−0.454096
$753$	3.18412	0.116036
$754$	26.9638	0.981965
$755$	−15.2905	−0.556479
$756$	−4.61313	−0.167778
$757$	37.4980	1.36289	0.681444	−	0.731871i	$-0.261352\pi$
$757$	37.4980	1.36289	0.681444	+	0.731871i	$0.261352\pi$
$758$	−0.576186	−0.0209280
$759$	31.8226	1.15509
$760$	4.00000	0.145095
$761$	18.8762	0.684260	0.342130	−	0.939653i	$-0.388852\pi$
$761$	18.8762	0.684260	0.342130	+	0.939653i	$0.388852\pi$
$762$	−8.19438	−0.296851
$763$	−69.8839	−2.52997
$764$	−2.35916	−0.0853514
$765$	0	0
$766$	8.37146	0.302473
$767$	−7.67159	−0.277005
$768$	−1.00000	−0.0360844
$769$	24.5762	0.886240	0.443120	−	0.896462i	$-0.353872\pi$
$769$	24.5762	0.886240	0.443120	+	0.896462i	$0.353872\pi$
$770$	23.5718	0.849470
$771$	10.8084	0.389256
$772$	−1.54847	−0.0557308
$773$	46.9099	1.68723	0.843616	−	0.536948i	$-0.180423\pi$
$773$	46.9099	1.68723	0.843616	+	0.536948i	$0.180423\pi$
$774$	−8.25744	−0.296807
$775$	3.79724	0.136401
$776$	−6.00416	−0.215537
$777$	−34.5619	−1.23990
$778$	−21.4213	−0.767991
$779$	−38.2707	−1.37119
$780$	−3.23463	−0.115818
$781$	46.4904	1.66356
$782$	0	0
$783$	8.33598	0.297904
$784$	14.2809	0.510033
$785$	1.82267	0.0650540
$786$	−6.52076	−0.232588
$787$	−51.1538	−1.82344	−0.911718	−	0.410817i	$-0.865244\pi$
$787$	−51.1538	−1.82344	−0.911718	+	0.410817i	$0.865244\pi$
$788$	4.95136	0.176385
$789$	26.1440	0.930753
$790$	3.61153	0.128493
$791$	10.8252	0.384901
$792$	−5.10973	−0.181566
$793$	−3.96647	−0.140854
$794$	5.85389	0.207747
$795$	−1.36595	−0.0484452
$796$	10.3508	0.366874
$797$	27.8081	0.985012	0.492506	−	0.870309i	$-0.336081\pi$
$797$	27.8081	0.985012	0.492506	+	0.870309i	$0.336081\pi$
$798$	18.4525	0.653212
$799$	0	0
$800$	1.00000	0.0353553
$801$	−9.03188	−0.319126
$802$	−13.4583	−0.475230
$803$	47.0530	1.66047
$804$	−2.74444	−0.0967890
$805$	−28.7298	−1.01259
$806$	−12.2827	−0.432639
$807$	−12.8503	−0.452353
$808$	−6.96882	−0.245162
$809$	30.9200	1.08709	0.543545	−	0.839380i	$-0.317082\pi$
$809$	30.9200	1.08709	0.543545	+	0.839380i	$0.317082\pi$
$810$	−1.00000	−0.0351364
$811$	23.8544	0.837642	0.418821	−	0.908069i	$-0.362444\pi$
$811$	23.8544	0.837642	0.418821	+	0.908069i	$0.362444\pi$
$812$	−38.4549	−1.34950
$813$	−6.64954	−0.233209
$814$	−38.2825	−1.34180
$815$	−7.77019	−0.272178
$816$	0	0
$817$	33.0297	1.15556
$818$	12.5762	0.439716
$819$	−14.9218	−0.521409
$820$	−9.56767	−0.334118
$821$	39.7172	1.38614	0.693070	−	0.720870i	$-0.256258\pi$
$821$	39.7172	1.38614	0.693070	+	0.720870i	$0.256258\pi$
$822$	−11.5076	−0.401372
$823$	21.2067	0.739219	0.369610	−	0.929187i	$-0.379491\pi$
$823$	21.2067	0.739219	0.369610	+	0.929187i	$0.379491\pi$
$824$	−17.5854	−0.612617
$825$	5.10973	0.177898
$826$	10.9410	0.380685
$827$	−39.8777	−1.38668	−0.693342	−	0.720609i	$-0.743862\pi$
$827$	−39.8777	−1.38668	−0.693342	+	0.720609i	$0.743862\pi$
$828$	6.22784	0.216433
$829$	−20.7092	−0.719262	−0.359631	−	0.933095i	$-0.617097\pi$
$829$	−20.7092	−0.719262	−0.359631	+	0.933095i	$0.617097\pi$
$830$	11.2649	0.391011
$831$	−20.7370	−0.719358
$832$	−3.23463	−0.112141
$833$	0	0
$834$	−21.1412	−0.732061
$835$	4.87056	0.168553
$836$	20.4389	0.706895
$837$	−3.79724	−0.131252
$838$	5.94829	0.205480
$839$	28.1199	0.970806	0.485403	−	0.874290i	$-0.338673\pi$
$839$	28.1199	0.970806	0.485403	+	0.874290i	$0.338673\pi$
$840$	4.61313	0.159168
$841$	40.4886	1.39616
$842$	17.3255	0.597076
$843$	18.5104	0.637531
$844$	2.29541	0.0790113
$845$	2.53715	0.0872806
$846$	−12.4525	−0.428126
$847$	69.7014	2.39497
$848$	−1.36595	−0.0469069
$849$	31.8441	1.09289
$850$	0	0
$851$	46.6594	1.59947
$852$	9.09841	0.311706
$853$	−8.04433	−0.275433	−0.137716	−	0.990472i	$-0.543976\pi$
$853$	−8.04433	−0.275433	−0.137716	+	0.990472i	$0.543976\pi$
$854$	5.65685	0.193574
$855$	4.00000	0.136797
$856$	−2.78976	−0.0953521
$857$	−17.5356	−0.599004	−0.299502	−	0.954096i	$-0.596821\pi$
$857$	−17.5356	−0.599004	−0.299502	+	0.954096i	$0.596821\pi$
$858$	−16.5281	−0.564260
$859$	−41.4391	−1.41388	−0.706942	−	0.707272i	$-0.749926\pi$
$859$	−41.4391	−1.41388	−0.706942	+	0.707272i	$0.749926\pi$
$860$	8.25744	0.281576
$861$	−44.1369	−1.50418
$862$	7.69968	0.262252
$863$	−29.7790	−1.01369	−0.506844	−	0.862038i	$-0.669188\pi$
$863$	−29.7790	−1.01369	−0.506844	+	0.862038i	$0.669188\pi$
$864$	−1.00000	−0.0340207
$865$	−0.867091	−0.0294820
$866$	−37.3311	−1.26856
$867$	0	0
$868$	17.5172	0.594571
$869$	18.4540	0.626008
$870$	−8.33598	−0.282616
$871$	−8.87726	−0.300795
$872$	−15.1489	−0.513007
$873$	−6.00416	−0.203210
$874$	−24.9114	−0.842640
$875$	−4.61313	−0.155952
$876$	9.20851	0.311127
$877$	−35.6105	−1.20248	−0.601241	−	0.799068i	$-0.705327\pi$
$877$	−35.6105	−1.20248	−0.601241	+	0.799068i	$0.705327\pi$
$878$	−29.2516	−0.987195
$879$	0.145584	0.00491042
$880$	5.10973	0.172249
$881$	28.9124	0.974082	0.487041	−	0.873379i	$-0.338076\pi$
$881$	28.9124	0.974082	0.487041	+	0.873379i	$0.338076\pi$
$882$	14.2809	0.480864
$883$	−47.8658	−1.61081	−0.805406	−	0.592723i	$-0.798053\pi$
$883$	−47.8658	−1.61081	−0.805406	+	0.592723i	$0.798053\pi$
$884$	0	0
$885$	2.37170	0.0797240
$886$	−9.66136	−0.324580
$887$	−37.7401	−1.26719	−0.633594	−	0.773666i	$-0.718421\pi$
$887$	−37.7401	−1.26719	−0.633594	+	0.773666i	$0.718421\pi$
$888$	−7.49207	−0.251417
$889$	37.8017	1.26783
$890$	9.03188	0.302749
$891$	−5.10973	−0.171182
$892$	−26.2446	−0.878733
$893$	49.8100	1.66683
$894$	20.4592	0.684257
$895$	−17.3691	−0.580584
$896$	4.61313	0.154114
$897$	20.1448	0.672615
$898$	−15.2994	−0.510548
$899$	−31.6537	−1.05571
$900$	1.00000	0.0333333
$901$	0	0
$902$	−48.8882	−1.62780
$903$	38.0926	1.26764
$904$	2.34662	0.0780473
$905$	6.20345	0.206210
$906$	−15.2905	−0.507994
$907$	26.5445	0.881397	0.440698	−	0.897655i	$-0.354731\pi$
$907$	26.5445	0.881397	0.440698	+	0.897655i	$0.354731\pi$
$908$	−4.20026	−0.139391
$909$	−6.96882	−0.231141
$910$	14.9218	0.494652
$911$	13.2890	0.440285	0.220143	−	0.975468i	$-0.429348\pi$
$911$	13.2890	0.440285	0.220143	+	0.975468i	$0.429348\pi$
$912$	4.00000	0.132453
$913$	57.5607	1.90498
$914$	31.6369	1.04646
$915$	1.22625	0.0405386
$916$	12.5954	0.416163
$917$	30.0811	0.993365
$918$	0	0
$919$	−34.2273	−1.12905	−0.564527	−	0.825415i	$-0.690941\pi$
$919$	−34.2273	−1.12905	−0.564527	+	0.825415i	$0.690941\pi$
$920$	−6.22784	−0.205326
$921$	8.52742	0.280988
$922$	−15.2314	−0.501621
$923$	29.4300	0.968701
$924$	23.5718	0.775456
$925$	7.49207	0.246338
$926$	26.4086	0.867840
$927$	−17.5854	−0.577581
$928$	−8.33598	−0.273642
$929$	−16.5577	−0.543240	−0.271620	−	0.962405i	$-0.587559\pi$
$929$	−16.5577	−0.543240	−0.271620	+	0.962405i	$0.587559\pi$
$930$	3.79724	0.124516
$931$	−57.1237	−1.87215
$932$	−20.9134	−0.685041
$933$	4.12196	0.134947
$934$	8.62955	0.282367
$935$	0	0
$936$	−3.23463	−0.105727
$937$	29.2570	0.955783	0.477892	−	0.878419i	$-0.341401\pi$
$937$	29.2570	0.955783	0.477892	+	0.878419i	$0.341401\pi$
$938$	12.6605	0.413379
$939$	−13.4178	−0.437875
$940$	12.4525	0.406156
$941$	−22.9978	−0.749708	−0.374854	−	0.927084i	$-0.622307\pi$
$941$	−22.9978	−0.749708	−0.374854	+	0.927084i	$0.622307\pi$
$942$	1.82267	0.0593859
$943$	59.5860	1.94039
$944$	2.37170	0.0771924
$945$	4.61313	0.150065
$946$	42.1933	1.37182
$947$	−21.4516	−0.697083	−0.348542	−	0.937293i	$-0.613323\pi$
$947$	−21.4516	−0.697083	−0.348542	+	0.937293i	$0.613323\pi$
$948$	3.61153	0.117297
$949$	29.7862	0.966900
$950$	−4.00000	−0.129777
$951$	17.5140	0.567929
$952$	0	0
$953$	2.27834	0.0738026	0.0369013	−	0.999319i	$-0.488251\pi$
$953$	2.27834	0.0738026	0.0369013	+	0.999319i	$0.488251\pi$
$954$	−1.36595	−0.0442242
$955$	2.35916	0.0763407
$956$	−24.2741	−0.785082
$957$	−42.5946	−1.37689
$958$	−7.25731	−0.234473
$959$	53.0858	1.71423
$960$	1.00000	0.0322749
$961$	−16.5810	−0.534869
$962$	−24.2341	−0.781339
$963$	−2.78976	−0.0898989
$964$	−5.86452	−0.188884
$965$	1.54847	0.0498471
$966$	−28.7298	−0.924367
$967$	−28.4479	−0.914824	−0.457412	−	0.889255i	$-0.651224\pi$
$967$	−28.4479	−0.914824	−0.457412	+	0.889255i	$0.651224\pi$
$968$	15.1094	0.485633
$969$	0	0
$970$	6.00416	0.192782
$971$	−20.8966	−0.670605	−0.335302	−	0.942111i	$-0.608838\pi$
$971$	−20.8966	−0.670605	−0.335302	+	0.942111i	$0.608838\pi$
$972$	−1.00000	−0.0320750
$973$	97.5272	3.12658
$974$	7.72095	0.247395
$975$	3.23463	0.103591
$976$	1.22625	0.0392514
$977$	51.8216	1.65792	0.828961	−	0.559307i	$-0.188933\pi$
$977$	51.8216	1.65792	0.828961	+	0.559307i	$0.188933\pi$
$978$	−7.77019	−0.248463
$979$	46.1505	1.47498
$980$	−14.2809	−0.456188
$981$	−15.1489	−0.483668
$982$	1.52235	0.0485802
$983$	−34.0934	−1.08741	−0.543705	−	0.839277i	$-0.682979\pi$
$983$	−34.0934	−1.08741	−0.543705	+	0.839277i	$0.682979\pi$
$984$	−9.56767	−0.305006
$985$	−4.95136	−0.157764
$986$	0	0
$987$	57.4450	1.82849
$988$	12.9385	0.411630
$989$	−51.4260	−1.63525
$990$	5.10973	0.162398
$991$	−35.4046	−1.12467	−0.562333	−	0.826911i	$-0.690096\pi$
$991$	−35.4046	−1.12467	−0.562333	+	0.826911i	$0.690096\pi$
$992$	3.79724	0.120563
$993$	10.7274	0.340424
$994$	−41.9721	−1.33127
$995$	−10.3508	−0.328142
$996$	11.2649	0.356943
$997$	42.9269	1.35951	0.679754	−	0.733440i	$-0.262086\pi$
$997$	42.9269	1.35951	0.679754	+	0.733440i	$0.262086\pi$
$998$	10.9191	0.345637
$999$	−7.49207	−0.237039

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8670.2.a.by.1.4		4
17.5	odd	16		510.2.u.a.331.2	yes	8
17.7	odd	16		510.2.u.a.151.2	✓	8
17.16	even	2		8670.2.a.bz.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.u.a.151.2	✓	8	17.7	odd	16
510.2.u.a.331.2	yes	8	17.5	odd	16
8670.2.a.by.1.4		4	1.1	even	1	trivial
8670.2.a.bz.1.1		4	17.16	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8670.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +4.61313 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -5.10973 q^{11} -1.00000 q^{12} -3.23463 q^{13} +4.61313 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{18} -4.00000 q^{19} -1.00000 q^{20} -4.61313 q^{21} -5.10973 q^{22} +6.22784 q^{23} -1.00000 q^{24} +1.00000 q^{25} -3.23463 q^{26} -1.00000 q^{27} +4.61313 q^{28} -8.33598 q^{29} +1.00000 q^{30} +3.79724 q^{31} +1.00000 q^{32} +5.10973 q^{33} -4.61313 q^{35} +1.00000 q^{36} +7.49207 q^{37} -4.00000 q^{38} +3.23463 q^{39} -1.00000 q^{40} +9.56767 q^{41} -4.61313 q^{42} -8.25744 q^{43} -5.10973 q^{44} -1.00000 q^{45} +6.22784 q^{46} -12.4525 q^{47} -1.00000 q^{48} +14.2809 q^{49} +1.00000 q^{50} -3.23463 q^{52} -1.36595 q^{53} -1.00000 q^{54} +5.10973 q^{55} +4.61313 q^{56} +4.00000 q^{57} -8.33598 q^{58} +2.37170 q^{59} +1.00000 q^{60} +1.22625 q^{61} +3.79724 q^{62} +4.61313 q^{63} +1.00000 q^{64} +3.23463 q^{65} +5.10973 q^{66} +2.74444 q^{67} -6.22784 q^{69} -4.61313 q^{70} -9.09841 q^{71} +1.00000 q^{72} -9.20851 q^{73} +7.49207 q^{74} -1.00000 q^{75} -4.00000 q^{76} -23.5718 q^{77} +3.23463 q^{78} -3.61153 q^{79} -1.00000 q^{80} +1.00000 q^{81} +9.56767 q^{82} -11.2649 q^{83} -4.61313 q^{84} -8.25744 q^{86} +8.33598 q^{87} -5.10973 q^{88} -9.03188 q^{89} -1.00000 q^{90} -14.9218 q^{91} +6.22784 q^{92} -3.79724 q^{93} -12.4525 q^{94} +4.00000 q^{95} -1.00000 q^{96} -6.00416 q^{97} +14.2809 q^{98} -5.10973 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 8 q^{7} + 4 q^{8} + 4 q^{9} - 4 q^{10} - 4 q^{12} - 16 q^{13} + 8 q^{14} + 4 q^{15} + 4 q^{16} + 4 q^{18} - 16 q^{19} - 4 q^{20} - 8 q^{21} + 8 q^{23}+ \cdots + 4 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 8 * q^7 + 4 * q^8 + 4 * q^9 - 4 * q^10 - 4 * q^12 - 16 * q^13 + 8 * q^14 + 4 * q^15 + 4 * q^16 + 4 * q^18 - 16 * q^19 - 4 * q^20 - 8 * q^21 + 8 * q^23 - 4 * q^24 + 4 * q^25 - 16 * q^26 - 4 * q^27 + 8 * q^28 + 8 * q^29 + 4 * q^30 + 4 * q^32 - 8 * q^35 + 4 * q^36 + 16 * q^37 - 16 * q^38 + 16 * q^39 - 4 * q^40 - 8 * q^42 - 16 * q^43 - 4 * q^45 + 8 * q^46 - 8 * q^47 - 4 * q^48 + 4 * q^49 + 4 * q^50 - 16 * q^52 - 8 * q^53 - 4 * q^54 + 8 * q^56 + 16 * q^57 + 8 * q^58 - 24 * q^59 + 4 * q^60 - 16 * q^61 + 8 * q^63 + 4 * q^64 + 16 * q^65 - 8 * q^69 - 8 * q^70 + 8 * q^71 + 4 * q^72 - 16 * q^73 + 16 * q^74 - 4 * q^75 - 16 * q^76 - 16 * q^77 + 16 * q^78 - 4 * q^80 + 4 * q^81 - 32 * q^83 - 8 * q^84 - 16 * q^86 - 8 * q^87 - 24 * q^89 - 4 * q^90 - 24 * q^91 + 8 * q^92 - 8 * q^94 + 16 * q^95 - 4 * q^96 + 16 * q^97 + 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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