LMFDB - Embedded newform 3381.2.a.r.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3381,2,Mod(1,3381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3381, 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("3381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3381 = 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3381.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:	$26.9974209234$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 483)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	3381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.618034 q^{2} +1.00000 q^{3} -1.61803 q^{4} -1.61803 q^{5} +0.618034 q^{6} -2.23607 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.618034 q^{2} +1.00000 q^{3} -1.61803 q^{4} -1.61803 q^{5} +0.618034 q^{6} -2.23607 q^{8} +1.00000 q^{9} -1.00000 q^{10} -2.23607 q^{11} -1.61803 q^{12} +4.61803 q^{13} -1.61803 q^{15} +1.85410 q^{16} +6.70820 q^{17} +0.618034 q^{18} -5.47214 q^{19} +2.61803 q^{20} -1.38197 q^{22} -1.00000 q^{23} -2.23607 q^{24} -2.38197 q^{25} +2.85410 q^{26} +1.00000 q^{27} -3.76393 q^{29} -1.00000 q^{30} +6.70820 q^{31} +5.61803 q^{32} -2.23607 q^{33} +4.14590 q^{34} -1.61803 q^{36} -11.0000 q^{37} -3.38197 q^{38} +4.61803 q^{39} +3.61803 q^{40} -7.47214 q^{41} +0.618034 q^{43} +3.61803 q^{44} -1.61803 q^{45} -0.618034 q^{46} +2.76393 q^{47} +1.85410 q^{48} -1.47214 q^{50} +6.70820 q^{51} -7.47214 q^{52} -1.90983 q^{53} +0.618034 q^{54} +3.61803 q^{55} -5.47214 q^{57} -2.32624 q^{58} -11.6180 q^{59} +2.61803 q^{60} -1.85410 q^{61} +4.14590 q^{62} -0.236068 q^{64} -7.47214 q^{65} -1.38197 q^{66} +6.09017 q^{67} -10.8541 q^{68} -1.00000 q^{69} +6.61803 q^{71} -2.23607 q^{72} -0.708204 q^{73} -6.79837 q^{74} -2.38197 q^{75} +8.85410 q^{76} +2.85410 q^{78} -0.527864 q^{79} -3.00000 q^{80} +1.00000 q^{81} -4.61803 q^{82} -13.1803 q^{83} -10.8541 q^{85} +0.381966 q^{86} -3.76393 q^{87} +5.00000 q^{88} -9.38197 q^{89} -1.00000 q^{90} +1.61803 q^{92} +6.70820 q^{93} +1.70820 q^{94} +8.85410 q^{95} +5.61803 q^{96} +16.4164 q^{97} -2.23607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 2 q^{3} - q^{4} - q^{5} - q^{6} + 2 q^{9}+O(q^{10}) $ 2 * q - q^2 + 2 * q^3 - q^4 - q^5 - q^6 + 2 * q^9	$ 2 q - q^{2} + 2 q^{3} - q^{4} - q^{5} - q^{6} + 2 q^{9} - 2 q^{10} - q^{12} + 7 q^{13} - q^{15} - 3 q^{16} - q^{18} - 2 q^{19} + 3 q^{20} - 5 q^{22} - 2 q^{23} - 7 q^{25} - q^{26} + 2 q^{27} - 12 q^{29} - 2 q^{30} + 9 q^{32} + 15 q^{34} - q^{36} - 22 q^{37} - 9 q^{38} + 7 q^{39} + 5 q^{40} - 6 q^{41} - q^{43} + 5 q^{44} - q^{45} + q^{46} + 10 q^{47} - 3 q^{48} + 6 q^{50} - 6 q^{52} - 15 q^{53} - q^{54} + 5 q^{55} - 2 q^{57} + 11 q^{58} - 21 q^{59} + 3 q^{60} + 3 q^{61} + 15 q^{62} + 4 q^{64} - 6 q^{65} - 5 q^{66} + q^{67} - 15 q^{68} - 2 q^{69} + 11 q^{71} + 12 q^{73} + 11 q^{74} - 7 q^{75} + 11 q^{76} - q^{78} - 10 q^{79} - 6 q^{80} + 2 q^{81} - 7 q^{82} - 4 q^{83} - 15 q^{85} + 3 q^{86} - 12 q^{87} + 10 q^{88} - 21 q^{89} - 2 q^{90} + q^{92} - 10 q^{94} + 11 q^{95} + 9 q^{96} + 6 q^{97}+O(q^{100}) $ 2 * q - q^2 + 2 * q^3 - q^4 - q^5 - q^6 + 2 * q^9 - 2 * q^10 - q^12 + 7 * q^13 - q^15 - 3 * q^16 - q^18 - 2 * q^19 + 3 * q^20 - 5 * q^22 - 2 * q^23 - 7 * q^25 - q^26 + 2 * q^27 - 12 * q^29 - 2 * q^30 + 9 * q^32 + 15 * q^34 - q^36 - 22 * q^37 - 9 * q^38 + 7 * q^39 + 5 * q^40 - 6 * q^41 - q^43 + 5 * q^44 - q^45 + q^46 + 10 * q^47 - 3 * q^48 + 6 * q^50 - 6 * q^52 - 15 * q^53 - q^54 + 5 * q^55 - 2 * q^57 + 11 * q^58 - 21 * q^59 + 3 * q^60 + 3 * q^61 + 15 * q^62 + 4 * q^64 - 6 * q^65 - 5 * q^66 + q^67 - 15 * q^68 - 2 * q^69 + 11 * q^71 + 12 * q^73 + 11 * q^74 - 7 * q^75 + 11 * q^76 - q^78 - 10 * q^79 - 6 * q^80 + 2 * q^81 - 7 * q^82 - 4 * q^83 - 15 * q^85 + 3 * q^86 - 12 * q^87 + 10 * q^88 - 21 * q^89 - 2 * q^90 + q^92 - 10 * q^94 + 11 * q^95 + 9 * q^96 + 6 * q^97

Display 100 coefficients 10 coefficients

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 $

$2$	0.618034	0.437016	0.218508	−	0.975835i	$-0.429881\pi$
$2$	0.618034	0.437016	0.218508	+	0.975835i	$0.429881\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.61803	−0.809017
$5$	−1.61803	−0.723607	−0.361803	−	0.932254i	$-0.617839\pi$
$5$	−1.61803	−0.723607	−0.361803	+	0.932254i	$0.617839\pi$
$6$	0.618034	0.252311
$7$	0	0
$7$	0	0
$8$	−2.23607	−0.790569
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	−2.23607	−0.674200	−0.337100	−	0.941469i	$-0.609446\pi$
$11$	−2.23607	−0.674200	−0.337100	+	0.941469i	$0.609446\pi$
$12$	−1.61803	−0.467086
$13$	4.61803	1.28081	0.640406	−	0.768036i	$-0.278766\pi$
$13$	4.61803	1.28081	0.640406	+	0.768036i	$0.278766\pi$
$14$	0	0
$15$	−1.61803	−0.417775
$16$	1.85410	0.463525
$17$	6.70820	1.62698	0.813489	−	0.581580i	$-0.197565\pi$
$17$	6.70820	1.62698	0.813489	+	0.581580i	$0.197565\pi$
$18$	0.618034	0.145672
$19$	−5.47214	−1.25539	−0.627697	−	0.778458i	$-0.716002\pi$
$19$	−5.47214	−1.25539	−0.627697	+	0.778458i	$0.716002\pi$
$20$	2.61803	0.585410
$21$	0	0
$22$	−1.38197	−0.294636
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−2.23607	−0.456435
$25$	−2.38197	−0.476393
$26$	2.85410	0.559735
$27$	1.00000	0.192450
$28$	0	0
$29$	−3.76393	−0.698945	−0.349472	−	0.936947i	$-0.613639\pi$
$29$	−3.76393	−0.698945	−0.349472	+	0.936947i	$0.613639\pi$
$30$	−1.00000	−0.182574
$31$	6.70820	1.20483	0.602414	−	0.798183i	$-0.294205\pi$
$31$	6.70820	1.20483	0.602414	+	0.798183i	$0.294205\pi$
$32$	5.61803	0.993137
$33$	−2.23607	−0.389249
$34$	4.14590	0.711016
$35$	0	0
$36$	−1.61803	−0.269672
$37$	−11.0000	−1.80839	−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−11.0000	−1.80839	−0.904194	+	0.427121i	$0.859528\pi$
$38$	−3.38197	−0.548627
$39$	4.61803	0.739477
$40$	3.61803	0.572061
$41$	−7.47214	−1.16695	−0.583476	−	0.812131i	$-0.698308\pi$
$41$	−7.47214	−1.16695	−0.583476	+	0.812131i	$0.698308\pi$
$42$	0	0
$43$	0.618034	0.0942493	0.0471246	−	0.998889i	$-0.484994\pi$
$43$	0.618034	0.0942493	0.0471246	+	0.998889i	$0.484994\pi$
$44$	3.61803	0.545439
$45$	−1.61803	−0.241202
$46$	−0.618034	−0.0911241
$47$	2.76393	0.403161	0.201580	−	0.979472i	$-0.435392\pi$
$47$	2.76393	0.403161	0.201580	+	0.979472i	$0.435392\pi$
$48$	1.85410	0.267617
$49$	0	0
$50$	−1.47214	−0.208191
$51$	6.70820	0.939336
$52$	−7.47214	−1.03620
$53$	−1.90983	−0.262335	−0.131168	−	0.991360i	$-0.541873\pi$
$53$	−1.90983	−0.262335	−0.131168	+	0.991360i	$0.541873\pi$
$54$	0.618034	0.0841038
$55$	3.61803	0.487856
$56$	0	0
$57$	−5.47214	−0.724802
$58$	−2.32624	−0.305450
$59$	−11.6180	−1.51254	−0.756270	−	0.654260i	$-0.772980\pi$
$59$	−11.6180	−1.51254	−0.756270	+	0.654260i	$0.772980\pi$
$60$	2.61803	0.337987
$61$	−1.85410	−0.237393	−0.118697	−	0.992931i	$-0.537872\pi$
$61$	−1.85410	−0.237393	−0.118697	+	0.992931i	$0.537872\pi$
$62$	4.14590	0.526530
$63$	0	0
$64$	−0.236068	−0.0295085
$65$	−7.47214	−0.926804
$66$	−1.38197	−0.170108
$67$	6.09017	0.744033	0.372016	−	0.928226i	$-0.378667\pi$
$67$	6.09017	0.744033	0.372016	+	0.928226i	$0.378667\pi$
$68$	−10.8541	−1.31625
$69$	−1.00000	−0.120386
$70$	0	0
$71$	6.61803	0.785416	0.392708	−	0.919663i	$-0.371538\pi$
$71$	6.61803	0.785416	0.392708	+	0.919663i	$0.371538\pi$
$72$	−2.23607	−0.263523
$73$	−0.708204	−0.0828890	−0.0414445	−	0.999141i	$-0.513196\pi$
$73$	−0.708204	−0.0828890	−0.0414445	+	0.999141i	$0.513196\pi$
$74$	−6.79837	−0.790295
$75$	−2.38197	−0.275046
$76$	8.85410	1.01564
$77$	0	0
$78$	2.85410	0.323163
$79$	−0.527864	−0.0593893	−0.0296947	−	0.999559i	$-0.509453\pi$
$79$	−0.527864	−0.0593893	−0.0296947	+	0.999559i	$0.509453\pi$
$80$	−3.00000	−0.335410
$81$	1.00000	0.111111
$82$	−4.61803	−0.509977
$83$	−13.1803	−1.44673	−0.723365	−	0.690466i	$-0.757406\pi$
$83$	−13.1803	−1.44673	−0.723365	+	0.690466i	$0.757406\pi$
$84$	0	0
$85$	−10.8541	−1.17729
$86$	0.381966	0.0411885
$87$	−3.76393	−0.403536
$88$	5.00000	0.533002
$89$	−9.38197	−0.994486	−0.497243	−	0.867611i	$-0.665654\pi$
$89$	−9.38197	−0.994486	−0.497243	+	0.867611i	$0.665654\pi$
$90$	−1.00000	−0.105409
$91$	0	0
$92$	1.61803	0.168692
$93$	6.70820	0.695608
$94$	1.70820	0.176188
$95$	8.85410	0.908412
$96$	5.61803	0.573388
$97$	16.4164	1.66683	0.833417	−	0.552645i	$-0.186381\pi$
$97$	16.4164	1.66683	0.833417	+	0.552645i	$0.186381\pi$
$98$	0	0
$99$	−2.23607	−0.224733
$100$	3.85410	0.385410
$101$	−10.8541	−1.08002	−0.540012	−	0.841657i	$-0.681580\pi$
$101$	−10.8541	−1.08002	−0.540012	+	0.841657i	$0.681580\pi$
$102$	4.14590	0.410505
$103$	−19.4164	−1.91316	−0.956578	−	0.291477i	$-0.905853\pi$
$103$	−19.4164	−1.91316	−0.956578	+	0.291477i	$0.905853\pi$
$104$	−10.3262	−1.01257
$105$	0	0
$106$	−1.18034	−0.114645
$107$	−12.3262	−1.19162	−0.595811	−	0.803125i	$-0.703169\pi$
$107$	−12.3262	−1.19162	−0.595811	+	0.803125i	$0.703169\pi$
$108$	−1.61803	−0.155695
$109$	−14.2705	−1.36687	−0.683433	−	0.730013i	$-0.739514\pi$
$109$	−14.2705	−1.36687	−0.683433	+	0.730013i	$0.739514\pi$
$110$	2.23607	0.213201
$111$	−11.0000	−1.04407
$112$	0	0
$113$	−12.0902	−1.13735	−0.568674	−	0.822563i	$-0.692543\pi$
$113$	−12.0902	−1.13735	−0.568674	+	0.822563i	$0.692543\pi$
$114$	−3.38197	−0.316750
$115$	1.61803	0.150882
$116$	6.09017	0.565458
$117$	4.61803	0.426937
$118$	−7.18034	−0.661004
$119$	0	0
$120$	3.61803	0.330280
$121$	−6.00000	−0.545455
$122$	−1.14590	−0.103745
$123$	−7.47214	−0.673740
$124$	−10.8541	−0.974727
$125$	11.9443	1.06833
$126$	0	0
$127$	−11.2705	−1.00010	−0.500048	−	0.865998i	$-0.666684\pi$
$127$	−11.2705	−1.00010	−0.500048	+	0.865998i	$0.666684\pi$
$128$	−11.3820	−1.00603
$129$	0.618034	0.0544149
$130$	−4.61803	−0.405028
$131$	7.18034	0.627349	0.313675	−	0.949531i	$-0.398440\pi$
$131$	7.18034	0.627349	0.313675	+	0.949531i	$0.398440\pi$
$132$	3.61803	0.314909
$133$	0	0
$134$	3.76393	0.325154
$135$	−1.61803	−0.139258
$136$	−15.0000	−1.28624
$137$	10.4164	0.889934	0.444967	−	0.895547i	$-0.353215\pi$
$137$	10.4164	0.889934	0.444967	+	0.895547i	$0.353215\pi$
$138$	−0.618034	−0.0526105
$139$	13.6180	1.15507	0.577533	−	0.816367i	$-0.304015\pi$
$139$	13.6180	1.15507	0.577533	+	0.816367i	$0.304015\pi$
$140$	0	0
$141$	2.76393	0.232765
$142$	4.09017	0.343239
$143$	−10.3262	−0.863523
$144$	1.85410	0.154508
$145$	6.09017	0.505761
$146$	−0.437694	−0.0362238
$147$	0	0
$148$	17.7984	1.46302
$149$	−14.7639	−1.20951	−0.604754	−	0.796412i	$-0.706729\pi$
$149$	−14.7639	−1.20951	−0.604754	+	0.796412i	$0.706729\pi$
$150$	−1.47214	−0.120199
$151$	−10.7639	−0.875956	−0.437978	−	0.898986i	$-0.644305\pi$
$151$	−10.7639	−0.875956	−0.437978	+	0.898986i	$0.644305\pi$
$152$	12.2361	0.992476
$153$	6.70820	0.542326
$154$	0	0
$155$	−10.8541	−0.871822
$156$	−7.47214	−0.598250
$157$	13.7082	1.09403	0.547017	−	0.837122i	$-0.315763\pi$
$157$	13.7082	1.09403	0.547017	+	0.837122i	$0.315763\pi$
$158$	−0.326238	−0.0259541
$159$	−1.90983	−0.151459
$160$	−9.09017	−0.718641
$161$	0	0
$162$	0.618034	0.0485573
$163$	1.61803	0.126734	0.0633671	−	0.997990i	$-0.479816\pi$
$163$	1.61803	0.126734	0.0633671	+	0.997990i	$0.479816\pi$
$164$	12.0902	0.944084
$165$	3.61803	0.281664
$166$	−8.14590	−0.632244
$167$	−15.1803	−1.17469	−0.587345	−	0.809337i	$-0.699827\pi$
$167$	−15.1803	−1.17469	−0.587345	+	0.809337i	$0.699827\pi$
$168$	0	0
$169$	8.32624	0.640480
$170$	−6.70820	−0.514496
$171$	−5.47214	−0.418465
$172$	−1.00000	−0.0762493
$173$	−5.47214	−0.416039	−0.208019	−	0.978125i	$-0.566702\pi$
$173$	−5.47214	−0.416039	−0.208019	+	0.978125i	$0.566702\pi$
$174$	−2.32624	−0.176352
$175$	0	0
$176$	−4.14590	−0.312509
$177$	−11.6180	−0.873265
$178$	−5.79837	−0.434606
$179$	−4.85410	−0.362813	−0.181406	−	0.983408i	$-0.558065\pi$
$179$	−4.85410	−0.362813	−0.181406	+	0.983408i	$0.558065\pi$
$180$	2.61803	0.195137
$181$	−15.9443	−1.18513	−0.592564	−	0.805523i	$-0.701884\pi$
$181$	−15.9443	−1.18513	−0.592564	+	0.805523i	$0.701884\pi$
$182$	0	0
$183$	−1.85410	−0.137059
$184$	2.23607	0.164845
$185$	17.7984	1.30856
$186$	4.14590	0.303992
$187$	−15.0000	−1.09691
$188$	−4.47214	−0.326164
$189$	0	0
$190$	5.47214	0.396990
$191$	−6.18034	−0.447194	−0.223597	−	0.974682i	$-0.571780\pi$
$191$	−6.18034	−0.447194	−0.223597	+	0.974682i	$0.571780\pi$
$192$	−0.236068	−0.0170367
$193$	21.7082	1.56259	0.781295	−	0.624161i	$-0.214559\pi$
$193$	21.7082	1.56259	0.781295	+	0.624161i	$0.214559\pi$
$194$	10.1459	0.728433
$195$	−7.47214	−0.535091
$196$	0	0
$197$	12.5066	0.891057	0.445528	−	0.895268i	$-0.353016\pi$
$197$	12.5066	0.891057	0.445528	+	0.895268i	$0.353016\pi$
$198$	−1.38197	−0.0982120
$199$	18.0902	1.28238	0.641189	−	0.767383i	$-0.278441\pi$
$199$	18.0902	1.28238	0.641189	+	0.767383i	$0.278441\pi$
$200$	5.32624	0.376622
$201$	6.09017	0.429567
$202$	−6.70820	−0.471988
$203$	0	0
$204$	−10.8541	−0.759939
$205$	12.0902	0.844414
$206$	−12.0000	−0.836080
$207$	−1.00000	−0.0695048
$208$	8.56231	0.593689
$209$	12.2361	0.846387
$210$	0	0
$211$	−16.4164	−1.13015	−0.565076	−	0.825039i	$-0.691153\pi$
$211$	−16.4164	−1.13015	−0.565076	+	0.825039i	$0.691153\pi$
$212$	3.09017	0.212234
$213$	6.61803	0.453460
$214$	−7.61803	−0.520758
$215$	−1.00000	−0.0681994
$216$	−2.23607	−0.152145
$217$	0	0
$218$	−8.81966	−0.597343
$219$	−0.708204	−0.0478560
$220$	−5.85410	−0.394683
$221$	30.9787	2.08385
$222$	−6.79837	−0.456277
$223$	11.1459	0.746385	0.373192	−	0.927754i	$-0.378263\pi$
$223$	11.1459	0.746385	0.373192	+	0.927754i	$0.378263\pi$
$224$	0	0
$225$	−2.38197	−0.158798
$226$	−7.47214	−0.497039
$227$	−8.67376	−0.575698	−0.287849	−	0.957676i	$-0.592940\pi$
$227$	−8.67376	−0.575698	−0.287849	+	0.957676i	$0.592940\pi$
$228$	8.85410	0.586377
$229$	0.673762	0.0445235	0.0222617	−	0.999752i	$-0.492913\pi$
$229$	0.673762	0.0445235	0.0222617	+	0.999752i	$0.492913\pi$
$230$	1.00000	0.0659380
$231$	0	0
$232$	8.41641	0.552564
$233$	0.0901699	0.00590723	0.00295361	−	0.999996i	$-0.499060\pi$
$233$	0.0901699	0.00590723	0.00295361	+	0.999996i	$0.499060\pi$
$234$	2.85410	0.186578
$235$	−4.47214	−0.291730
$236$	18.7984	1.22367
$237$	−0.527864	−0.0342885
$238$	0	0
$239$	19.7984	1.28065	0.640325	−	0.768104i	$-0.278800\pi$
$239$	19.7984	1.28065	0.640325	+	0.768104i	$0.278800\pi$
$240$	−3.00000	−0.193649
$241$	11.0000	0.708572	0.354286	−	0.935137i	$-0.384724\pi$
$241$	11.0000	0.708572	0.354286	+	0.935137i	$0.384724\pi$
$242$	−3.70820	−0.238372
$243$	1.00000	0.0641500
$244$	3.00000	0.192055
$245$	0	0
$246$	−4.61803	−0.294435
$247$	−25.2705	−1.60792
$248$	−15.0000	−0.952501
$249$	−13.1803	−0.835270
$250$	7.38197	0.466877
$251$	17.1246	1.08090	0.540448	−	0.841377i	$-0.318255\pi$
$251$	17.1246	1.08090	0.540448	+	0.841377i	$0.318255\pi$
$252$	0	0
$253$	2.23607	0.140580
$254$	−6.96556	−0.437058
$255$	−10.8541	−0.679710
$256$	−6.56231	−0.410144
$257$	−1.23607	−0.0771038	−0.0385519	−	0.999257i	$-0.512274\pi$
$257$	−1.23607	−0.0771038	−0.0385519	+	0.999257i	$0.512274\pi$
$258$	0.381966	0.0237802
$259$	0	0
$260$	12.0902	0.749801
$261$	−3.76393	−0.232982
$262$	4.43769	0.274162
$263$	−17.9443	−1.10649	−0.553246	−	0.833018i	$-0.686611\pi$
$263$	−17.9443	−1.10649	−0.553246	+	0.833018i	$0.686611\pi$
$264$	5.00000	0.307729
$265$	3.09017	0.189828
$266$	0	0
$267$	−9.38197	−0.574167
$268$	−9.85410	−0.601935
$269$	20.9098	1.27489	0.637447	−	0.770494i	$-0.279990\pi$
$269$	20.9098	1.27489	0.637447	+	0.770494i	$0.279990\pi$
$270$	−1.00000	−0.0608581
$271$	−4.05573	−0.246368	−0.123184	−	0.992384i	$-0.539311\pi$
$271$	−4.05573	−0.246368	−0.123184	+	0.992384i	$0.539311\pi$
$272$	12.4377	0.754146
$273$	0	0
$274$	6.43769	0.388915
$275$	5.32624	0.321184
$276$	1.61803	0.0973942
$277$	−29.2705	−1.75869	−0.879347	−	0.476181i	$-0.842021\pi$
$277$	−29.2705	−1.75869	−0.879347	+	0.476181i	$0.842021\pi$
$278$	8.41641	0.504783
$279$	6.70820	0.401610
$280$	0	0
$281$	9.70820	0.579143	0.289571	−	0.957156i	$-0.406487\pi$
$281$	9.70820	0.579143	0.289571	+	0.957156i	$0.406487\pi$
$282$	1.70820	0.101722
$283$	−25.2148	−1.49886	−0.749432	−	0.662082i	$-0.769673\pi$
$283$	−25.2148	−1.49886	−0.749432	+	0.662082i	$0.769673\pi$
$284$	−10.7082	−0.635415
$285$	8.85410	0.524472
$286$	−6.38197	−0.377374
$287$	0	0
$288$	5.61803	0.331046
$289$	28.0000	1.64706
$290$	3.76393	0.221026
$291$	16.4164	0.962347
$292$	1.14590	0.0670586
$293$	−12.0000	−0.701047	−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000	−0.701047	−0.350524	+	0.936554i	$0.613996\pi$
$294$	0	0
$295$	18.7984	1.09448
$296$	24.5967	1.42966
$297$	−2.23607	−0.129750
$298$	−9.12461	−0.528575
$299$	−4.61803	−0.267068
$300$	3.85410	0.222517
$301$	0	0
$302$	−6.65248	−0.382807
$303$	−10.8541	−0.623552
$304$	−10.1459	−0.581907
$305$	3.00000	0.171780
$306$	4.14590	0.237005
$307$	24.1246	1.37686	0.688432	−	0.725301i	$-0.258299\pi$
$307$	24.1246	1.37686	0.688432	+	0.725301i	$0.258299\pi$
$308$	0	0
$309$	−19.4164	−1.10456
$310$	−6.70820	−0.381000
$311$	0.326238	0.0184993	0.00924963	−	0.999957i	$-0.497056\pi$
$311$	0.326238	0.0184993	0.00924963	+	0.999957i	$0.497056\pi$
$312$	−10.3262	−0.584608
$313$	−6.47214	−0.365827	−0.182913	−	0.983129i	$-0.558553\pi$
$313$	−6.47214	−0.365827	−0.182913	+	0.983129i	$0.558553\pi$
$314$	8.47214	0.478110
$315$	0	0
$316$	0.854102	0.0480470
$317$	−23.5066	−1.32026	−0.660130	−	0.751151i	$-0.729499\pi$
$317$	−23.5066	−1.32026	−0.660130	+	0.751151i	$0.729499\pi$
$318$	−1.18034	−0.0661902
$319$	8.41641	0.471228
$320$	0.381966	0.0213525
$321$	−12.3262	−0.687984
$322$	0	0
$323$	−36.7082	−2.04250
$324$	−1.61803	−0.0898908
$325$	−11.0000	−0.610170
$326$	1.00000	0.0553849
$327$	−14.2705	−0.789161
$328$	16.7082	0.922556
$329$	0	0
$330$	2.23607	0.123091
$331$	13.4164	0.737432	0.368716	−	0.929542i	$-0.379797\pi$
$331$	13.4164	0.737432	0.368716	+	0.929542i	$0.379797\pi$
$332$	21.3262	1.17043
$333$	−11.0000	−0.602796
$334$	−9.38197	−0.513358
$335$	−9.85410	−0.538387
$336$	0	0
$337$	30.5066	1.66180	0.830900	−	0.556422i	$-0.187826\pi$
$337$	30.5066	1.66180	0.830900	+	0.556422i	$0.187826\pi$
$338$	5.14590	0.279900
$339$	−12.0902	−0.656648
$340$	17.5623	0.952450
$341$	−15.0000	−0.812296
$342$	−3.38197	−0.182876
$343$	0	0
$344$	−1.38197	−0.0745106
$345$	1.61803	0.0871120
$346$	−3.38197	−0.181816
$347$	−17.1803	−0.922289	−0.461144	−	0.887325i	$-0.652561\pi$
$347$	−17.1803	−0.922289	−0.461144	+	0.887325i	$0.652561\pi$
$348$	6.09017	0.326467
$349$	5.14590	0.275454	0.137727	−	0.990470i	$-0.456020\pi$
$349$	5.14590	0.275454	0.137727	+	0.990470i	$0.456020\pi$
$350$	0	0
$351$	4.61803	0.246492
$352$	−12.5623	−0.669573
$353$	32.3050	1.71942	0.859710	−	0.510783i	$-0.170645\pi$
$353$	32.3050	1.71942	0.859710	+	0.510783i	$0.170645\pi$
$354$	−7.18034	−0.381631
$355$	−10.7082	−0.568332
$356$	15.1803	0.804556
$357$	0	0
$358$	−3.00000	−0.158555
$359$	11.9098	0.628577	0.314288	−	0.949328i	$-0.398234\pi$
$359$	11.9098	0.628577	0.314288	+	0.949328i	$0.398234\pi$
$360$	3.61803	0.190687
$361$	10.9443	0.576014
$362$	−9.85410	−0.517920
$363$	−6.00000	−0.314918
$364$	0	0
$365$	1.14590	0.0599790
$366$	−1.14590	−0.0598970
$367$	−4.14590	−0.216414	−0.108207	−	0.994128i	$-0.534511\pi$
$367$	−4.14590	−0.216414	−0.108207	+	0.994128i	$0.534511\pi$
$368$	−1.85410	−0.0966517
$369$	−7.47214	−0.388984
$370$	11.0000	0.571863
$371$	0	0
$372$	−10.8541	−0.562759
$373$	−2.41641	−0.125117	−0.0625584	−	0.998041i	$-0.519926\pi$
$373$	−2.41641	−0.125117	−0.0625584	+	0.998041i	$0.519926\pi$
$374$	−9.27051	−0.479367
$375$	11.9443	0.616800
$376$	−6.18034	−0.318727
$377$	−17.3820	−0.895217
$378$	0	0
$379$	−19.4164	−0.997354	−0.498677	−	0.866788i	$-0.666181\pi$
$379$	−19.4164	−0.997354	−0.498677	+	0.866788i	$0.666181\pi$
$380$	−14.3262	−0.734920
$381$	−11.2705	−0.577406
$382$	−3.81966	−0.195431
$383$	−12.7082	−0.649359	−0.324679	−	0.945824i	$-0.605256\pi$
$383$	−12.7082	−0.649359	−0.324679	+	0.945824i	$0.605256\pi$
$384$	−11.3820	−0.580834
$385$	0	0
$386$	13.4164	0.682877
$387$	0.618034	0.0314164
$388$	−26.5623	−1.34850
$389$	18.7082	0.948544	0.474272	−	0.880378i	$-0.342711\pi$
$389$	18.7082	0.948544	0.474272	+	0.880378i	$0.342711\pi$
$390$	−4.61803	−0.233843
$391$	−6.70820	−0.339248
$392$	0	0
$393$	7.18034	0.362200
$394$	7.72949	0.389406
$395$	0.854102	0.0429745
$396$	3.61803	0.181813
$397$	36.0689	1.81025	0.905123	−	0.425150i	$-0.139779\pi$
$397$	36.0689	1.81025	0.905123	+	0.425150i	$0.139779\pi$
$398$	11.1803	0.560420
$399$	0	0
$400$	−4.41641	−0.220820
$401$	10.8197	0.540308	0.270154	−	0.962817i	$-0.412925\pi$
$401$	10.8197	0.540308	0.270154	+	0.962817i	$0.412925\pi$
$402$	3.76393	0.187728
$403$	30.9787	1.54316
$404$	17.5623	0.873757
$405$	−1.61803	−0.0804008
$406$	0	0
$407$	24.5967	1.21922
$408$	−15.0000	−0.742611
$409$	20.4164	1.00953	0.504763	−	0.863258i	$-0.331580\pi$
$409$	20.4164	1.00953	0.504763	+	0.863258i	$0.331580\pi$
$410$	7.47214	0.369022
$411$	10.4164	0.513804
$412$	31.4164	1.54778
$413$	0	0
$414$	−0.618034	−0.0303747
$415$	21.3262	1.04686
$416$	25.9443	1.27202
$417$	13.6180	0.666878
$418$	7.56231	0.369884
$419$	−31.3262	−1.53039	−0.765193	−	0.643800i	$-0.777357\pi$
$419$	−31.3262	−1.53039	−0.765193	+	0.643800i	$0.777357\pi$
$420$	0	0
$421$	23.2705	1.13414	0.567068	−	0.823671i	$-0.308078\pi$
$421$	23.2705	1.13414	0.567068	+	0.823671i	$0.308078\pi$
$422$	−10.1459	−0.493895
$423$	2.76393	0.134387
$424$	4.27051	0.207394
$425$	−15.9787	−0.775081
$426$	4.09017	0.198169
$427$	0	0
$428$	19.9443	0.964043
$429$	−10.3262	−0.498555
$430$	−0.618034	−0.0298042
$431$	16.3262	0.786407	0.393204	−	0.919451i	$-0.371367\pi$
$431$	16.3262	0.786407	0.393204	+	0.919451i	$0.371367\pi$
$432$	1.85410	0.0892055
$433$	21.1246	1.01518	0.507592	−	0.861598i	$-0.330536\pi$
$433$	21.1246	1.01518	0.507592	+	0.861598i	$0.330536\pi$
$434$	0	0
$435$	6.09017	0.292001
$436$	23.0902	1.10582
$437$	5.47214	0.261768
$438$	−0.437694	−0.0209138
$439$	7.65248	0.365233	0.182616	−	0.983184i	$-0.441543\pi$
$439$	7.65248	0.365233	0.182616	+	0.983184i	$0.441543\pi$
$440$	−8.09017	−0.385684
$441$	0	0
$442$	19.1459	0.910678
$443$	−18.4721	−0.877638	−0.438819	−	0.898576i	$-0.644603\pi$
$443$	−18.4721	−0.877638	−0.438819	+	0.898576i	$0.644603\pi$
$444$	17.7984	0.844673
$445$	15.1803	0.719617
$446$	6.88854	0.326182
$447$	−14.7639	−0.698310
$448$	0	0
$449$	−38.5623	−1.81987	−0.909934	−	0.414753i	$-0.863868\pi$
$449$	−38.5623	−1.81987	−0.909934	+	0.414753i	$0.863868\pi$
$450$	−1.47214	−0.0693972
$451$	16.7082	0.786759
$452$	19.5623	0.920133
$453$	−10.7639	−0.505734
$454$	−5.36068	−0.251589
$455$	0	0
$456$	12.2361	0.573006
$457$	1.32624	0.0620388	0.0310194	−	0.999519i	$-0.490125\pi$
$457$	1.32624	0.0620388	0.0310194	+	0.999519i	$0.490125\pi$
$458$	0.416408	0.0194575
$459$	6.70820	0.313112
$460$	−2.61803	−0.122066
$461$	30.4508	1.41824	0.709119	−	0.705089i	$-0.249093\pi$
$461$	30.4508	1.41824	0.709119	+	0.705089i	$0.249093\pi$
$462$	0	0
$463$	30.7082	1.42713	0.713566	−	0.700588i	$-0.247079\pi$
$463$	30.7082	1.42713	0.713566	+	0.700588i	$0.247079\pi$
$464$	−6.97871	−0.323979
$465$	−10.8541	−0.503347
$466$	0.0557281	0.00258155
$467$	−7.18034	−0.332267	−0.166133	−	0.986103i	$-0.553128\pi$
$467$	−7.18034	−0.332267	−0.166133	+	0.986103i	$0.553128\pi$
$468$	−7.47214	−0.345400
$469$	0	0
$470$	−2.76393	−0.127491
$471$	13.7082	0.631641
$472$	25.9787	1.19577
$473$	−1.38197	−0.0635429
$474$	−0.326238	−0.0149846
$475$	13.0344	0.598061
$476$	0	0
$477$	−1.90983	−0.0874451
$478$	12.2361	0.559665
$479$	−21.0000	−0.959514	−0.479757	−	0.877401i	$-0.659275\pi$
$479$	−21.0000	−0.959514	−0.479757	+	0.877401i	$0.659275\pi$
$480$	−9.09017	−0.414908
$481$	−50.7984	−2.31621
$482$	6.79837	0.309657
$483$	0	0
$484$	9.70820	0.441282
$485$	−26.5623	−1.20613
$486$	0.618034	0.0280346
$487$	−42.7082	−1.93529	−0.967647	−	0.252309i	$-0.918810\pi$
$487$	−42.7082	−1.93529	−0.967647	+	0.252309i	$0.918810\pi$
$488$	4.14590	0.187676
$489$	1.61803	0.0731700
$490$	0	0
$491$	−14.7984	−0.667841	−0.333921	−	0.942601i	$-0.608372\pi$
$491$	−14.7984	−0.667841	−0.333921	+	0.942601i	$0.608372\pi$
$492$	12.0902	0.545067
$493$	−25.2492	−1.13717
$494$	−15.6180	−0.702689
$495$	3.61803	0.162619
$496$	12.4377	0.558469
$497$	0	0
$498$	−8.14590	−0.365026
$499$	35.3951	1.58450	0.792252	−	0.610195i	$-0.208909\pi$
$499$	35.3951	1.58450	0.792252	+	0.610195i	$0.208909\pi$
$500$	−19.3262	−0.864296
$501$	−15.1803	−0.678208
$502$	10.5836	0.472369
$503$	−20.6738	−0.921797	−0.460899	−	0.887453i	$-0.652473\pi$
$503$	−20.6738	−0.921797	−0.460899	+	0.887453i	$0.652473\pi$
$504$	0	0
$505$	17.5623	0.781512
$506$	1.38197	0.0614359
$507$	8.32624	0.369781
$508$	18.2361	0.809095
$509$	−33.5967	−1.48915	−0.744575	−	0.667539i	$-0.767348\pi$
$509$	−33.5967	−1.48915	−0.744575	+	0.667539i	$0.767348\pi$
$510$	−6.70820	−0.297044
$511$	0	0
$512$	18.7082	0.826794
$513$	−5.47214	−0.241601
$514$	−0.763932	−0.0336956
$515$	31.4164	1.38437
$516$	−1.00000	−0.0440225
$517$	−6.18034	−0.271811
$518$	0	0
$519$	−5.47214	−0.240200
$520$	16.7082	0.732703
$521$	−12.4721	−0.546414	−0.273207	−	0.961955i	$-0.588084\pi$
$521$	−12.4721	−0.546414	−0.273207	+	0.961955i	$0.588084\pi$
$522$	−2.32624	−0.101817
$523$	5.41641	0.236843	0.118421	−	0.992963i	$-0.462217\pi$
$523$	5.41641	0.236843	0.118421	+	0.992963i	$0.462217\pi$
$524$	−11.6180	−0.507536
$525$	0	0
$526$	−11.0902	−0.483554
$527$	45.0000	1.96023
$528$	−4.14590	−0.180427
$529$	1.00000	0.0434783
$530$	1.90983	0.0829577
$531$	−11.6180	−0.504180
$532$	0	0
$533$	−34.5066	−1.49465
$534$	−5.79837	−0.250920
$535$	19.9443	0.862266
$536$	−13.6180	−0.588209
$537$	−4.85410	−0.209470
$538$	12.9230	0.557149
$539$	0	0
$540$	2.61803	0.112662
$541$	35.1246	1.51013	0.755063	−	0.655653i	$-0.227606\pi$
$541$	35.1246	1.51013	0.755063	+	0.655653i	$0.227606\pi$
$542$	−2.50658	−0.107667
$543$	−15.9443	−0.684234
$544$	37.6869	1.61581
$545$	23.0902	0.989074
$546$	0	0
$547$	−11.7984	−0.504462	−0.252231	−	0.967667i	$-0.581164\pi$
$547$	−11.7984	−0.504462	−0.252231	+	0.967667i	$0.581164\pi$
$548$	−16.8541	−0.719972
$549$	−1.85410	−0.0791311
$550$	3.29180	0.140363
$551$	20.5967	0.877451
$552$	2.23607	0.0951734
$553$	0	0
$554$	−18.0902	−0.768578
$555$	17.7984	0.755499
$556$	−22.0344	−0.934468
$557$	−28.1803	−1.19404	−0.597020	−	0.802227i	$-0.703649\pi$
$557$	−28.1803	−1.19404	−0.597020	+	0.802227i	$0.703649\pi$
$558$	4.14590	0.175510
$559$	2.85410	0.120716
$560$	0	0
$561$	−15.0000	−0.633300
$562$	6.00000	0.253095
$563$	−14.5066	−0.611379	−0.305690	−	0.952131i	$-0.598887\pi$
$563$	−14.5066	−0.611379	−0.305690	+	0.952131i	$0.598887\pi$
$564$	−4.47214	−0.188311
$565$	19.5623	0.822992
$566$	−15.5836	−0.655027
$567$	0	0
$568$	−14.7984	−0.620926
$569$	28.3607	1.18894	0.594471	−	0.804117i	$-0.297362\pi$
$569$	28.3607	1.18894	0.594471	+	0.804117i	$0.297362\pi$
$570$	5.47214	0.229203
$571$	−17.5836	−0.735850	−0.367925	−	0.929855i	$-0.619932\pi$
$571$	−17.5836	−0.735850	−0.367925	+	0.929855i	$0.619932\pi$
$572$	16.7082	0.698605
$573$	−6.18034	−0.258187
$574$	0	0
$575$	2.38197	0.0993348
$576$	−0.236068	−0.00983617
$577$	−16.8328	−0.700759	−0.350380	−	0.936608i	$-0.613947\pi$
$577$	−16.8328	−0.700759	−0.350380	+	0.936608i	$0.613947\pi$
$578$	17.3050	0.719791
$579$	21.7082	0.902162
$580$	−9.85410	−0.409169
$581$	0	0
$582$	10.1459	0.420561
$583$	4.27051	0.176866
$584$	1.58359	0.0655295
$585$	−7.47214	−0.308935
$586$	−7.41641	−0.306369
$587$	1.96556	0.0811273	0.0405636	−	0.999177i	$-0.487085\pi$
$587$	1.96556	0.0811273	0.0405636	+	0.999177i	$0.487085\pi$
$588$	0	0
$589$	−36.7082	−1.51254
$590$	11.6180	0.478307
$591$	12.5066	0.514452
$592$	−20.3951	−0.838234
$593$	−26.0689	−1.07052	−0.535260	−	0.844687i	$-0.679787\pi$
$593$	−26.0689	−1.07052	−0.535260	+	0.844687i	$0.679787\pi$
$594$	−1.38197	−0.0567028
$595$	0	0
$596$	23.8885	0.978513
$597$	18.0902	0.740381
$598$	−2.85410	−0.116713
$599$	22.5066	0.919594	0.459797	−	0.888024i	$-0.347922\pi$
$599$	22.5066	0.919594	0.459797	+	0.888024i	$0.347922\pi$
$600$	5.32624	0.217443
$601$	−12.0902	−0.493168	−0.246584	−	0.969121i	$-0.579308\pi$
$601$	−12.0902	−0.493168	−0.246584	+	0.969121i	$0.579308\pi$
$602$	0	0
$603$	6.09017	0.248011
$604$	17.4164	0.708664
$605$	9.70820	0.394695
$606$	−6.70820	−0.272502
$607$	9.20163	0.373482	0.186741	−	0.982409i	$-0.440207\pi$
$607$	9.20163	0.373482	0.186741	+	0.982409i	$0.440207\pi$
$608$	−30.7426	−1.24678
$609$	0	0
$610$	1.85410	0.0750704
$611$	12.7639	0.516373
$612$	−10.8541	−0.438751
$613$	19.6525	0.793756	0.396878	−	0.917871i	$-0.370094\pi$
$613$	19.6525	0.793756	0.396878	+	0.917871i	$0.370094\pi$
$614$	14.9098	0.601712
$615$	12.0902	0.487523
$616$	0	0
$617$	−18.3262	−0.737787	−0.368893	−	0.929472i	$-0.620263\pi$
$617$	−18.3262	−0.737787	−0.368893	+	0.929472i	$0.620263\pi$
$618$	−12.0000	−0.482711
$619$	17.3820	0.698640	0.349320	−	0.937003i	$-0.386413\pi$
$619$	17.3820	0.698640	0.349320	+	0.937003i	$0.386413\pi$
$620$	17.5623	0.705319
$621$	−1.00000	−0.0401286
$622$	0.201626	0.00808447
$623$	0	0
$624$	8.56231	0.342767
$625$	−7.41641	−0.296656
$626$	−4.00000	−0.159872
$627$	12.2361	0.488661
$628$	−22.1803	−0.885092
$629$	−73.7902	−2.94221
$630$	0	0
$631$	−24.1246	−0.960386	−0.480193	−	0.877163i	$-0.659433\pi$
$631$	−24.1246	−0.960386	−0.480193	+	0.877163i	$0.659433\pi$
$632$	1.18034	0.0469514
$633$	−16.4164	−0.652494
$634$	−14.5279	−0.576975
$635$	18.2361	0.723676
$636$	3.09017	0.122533
$637$	0	0
$638$	5.20163	0.205934
$639$	6.61803	0.261805
$640$	18.4164	0.727972
$641$	−6.79837	−0.268520	−0.134260	−	0.990946i	$-0.542866\pi$
$641$	−6.79837	−0.268520	−0.134260	+	0.990946i	$0.542866\pi$
$642$	−7.61803	−0.300660
$643$	−34.9787	−1.37943	−0.689713	−	0.724083i	$-0.742263\pi$
$643$	−34.9787	−1.37943	−0.689713	+	0.724083i	$0.742263\pi$
$644$	0	0
$645$	−1.00000	−0.0393750
$646$	−22.6869	−0.892605
$647$	−5.03444	−0.197924	−0.0989622	−	0.995091i	$-0.531552\pi$
$647$	−5.03444	−0.197924	−0.0989622	+	0.995091i	$0.531552\pi$
$648$	−2.23607	−0.0878410
$649$	25.9787	1.01975
$650$	−6.79837	−0.266654
$651$	0	0
$652$	−2.61803	−0.102530
$653$	−14.7426	−0.576924	−0.288462	−	0.957491i	$-0.593144\pi$
$653$	−14.7426	−0.576924	−0.288462	+	0.957491i	$0.593144\pi$
$654$	−8.81966	−0.344876
$655$	−11.6180	−0.453954
$656$	−13.8541	−0.540912
$657$	−0.708204	−0.0276297
$658$	0	0
$659$	−21.6525	−0.843461	−0.421730	−	0.906721i	$-0.638577\pi$
$659$	−21.6525	−0.843461	−0.421730	+	0.906721i	$0.638577\pi$
$660$	−5.85410	−0.227871
$661$	12.4164	0.482942	0.241471	−	0.970408i	$-0.422370\pi$
$661$	12.4164	0.482942	0.241471	+	0.970408i	$0.422370\pi$
$662$	8.29180	0.322270
$663$	30.9787	1.20311
$664$	29.4721	1.14374
$665$	0	0
$666$	−6.79837	−0.263432
$667$	3.76393	0.145740
$668$	24.5623	0.950344
$669$	11.1459	0.430925
$670$	−6.09017	−0.235284
$671$	4.14590	0.160051
$672$	0	0
$673$	−14.4164	−0.555712	−0.277856	−	0.960623i	$-0.589624\pi$
$673$	−14.4164	−0.555712	−0.277856	+	0.960623i	$0.589624\pi$
$674$	18.8541	0.726233
$675$	−2.38197	−0.0916819
$676$	−13.4721	−0.518159
$677$	43.7426	1.68117	0.840583	−	0.541682i	$-0.182212\pi$
$677$	43.7426	1.68117	0.840583	+	0.541682i	$0.182212\pi$
$678$	−7.47214	−0.286966
$679$	0	0
$680$	24.2705	0.930732
$681$	−8.67376	−0.332379
$682$	−9.27051	−0.354986
$683$	−50.0132	−1.91370	−0.956850	−	0.290582i	$-0.906151\pi$
$683$	−50.0132	−1.91370	−0.956850	+	0.290582i	$0.906151\pi$
$684$	8.85410	0.338545
$685$	−16.8541	−0.643962
$686$	0	0
$687$	0.673762	0.0257056
$688$	1.14590	0.0436870
$689$	−8.81966	−0.336002
$690$	1.00000	0.0380693
$691$	41.2705	1.57000	0.785002	−	0.619493i	$-0.212662\pi$
$691$	41.2705	1.57000	0.785002	+	0.619493i	$0.212662\pi$
$692$	8.85410	0.336582
$693$	0	0
$694$	−10.6180	−0.403055
$695$	−22.0344	−0.835814
$696$	8.41641	0.319023
$697$	−50.1246	−1.89861
$698$	3.18034	0.120378
$699$	0.0901699	0.00341054
$700$	0	0
$701$	−18.4508	−0.696879	−0.348439	−	0.937331i	$-0.613288\pi$
$701$	−18.4508	−0.696879	−0.348439	+	0.937331i	$0.613288\pi$
$702$	2.85410	0.107721
$703$	60.1935	2.27024
$704$	0.527864	0.0198946
$705$	−4.47214	−0.168430
$706$	19.9656	0.751414
$707$	0	0
$708$	18.7984	0.706486
$709$	17.5623	0.659566	0.329783	−	0.944057i	$-0.393024\pi$
$709$	17.5623	0.659566	0.329783	+	0.944057i	$0.393024\pi$
$710$	−6.61803	−0.248370
$711$	−0.527864	−0.0197964
$712$	20.9787	0.786211
$713$	−6.70820	−0.251224
$714$	0	0
$715$	16.7082	0.624851
$716$	7.85410	0.293522
$717$	19.7984	0.739384
$718$	7.36068	0.274698
$719$	3.00000	0.111881	0.0559406	−	0.998434i	$-0.482184\pi$
$719$	3.00000	0.111881	0.0559406	+	0.998434i	$0.482184\pi$
$720$	−3.00000	−0.111803
$721$	0	0
$722$	6.76393	0.251727
$723$	11.0000	0.409094
$724$	25.7984	0.958789
$725$	8.96556	0.332972
$726$	−3.70820	−0.137624
$727$	16.8885	0.626361	0.313181	−	0.949694i	$-0.398605\pi$
$727$	16.8885	0.626361	0.313181	+	0.949694i	$0.398605\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0.708204	0.0262118
$731$	4.14590	0.153342
$732$	3.00000	0.110883
$733$	23.5967	0.871566	0.435783	−	0.900052i	$-0.356472\pi$
$733$	23.5967	0.871566	0.435783	+	0.900052i	$0.356472\pi$
$734$	−2.56231	−0.0945764
$735$	0	0
$736$	−5.61803	−0.207083
$737$	−13.6180	−0.501627
$738$	−4.61803	−0.169992
$739$	−35.2492	−1.29666	−0.648332	−	0.761358i	$-0.724533\pi$
$739$	−35.2492	−1.29666	−0.648332	+	0.761358i	$0.724533\pi$
$740$	−28.7984	−1.05865
$741$	−25.2705	−0.928335
$742$	0	0
$743$	27.3262	1.00250	0.501251	−	0.865302i	$-0.332873\pi$
$743$	27.3262	1.00250	0.501251	+	0.865302i	$0.332873\pi$
$744$	−15.0000	−0.549927
$745$	23.8885	0.875209
$746$	−1.49342	−0.0546781
$747$	−13.1803	−0.482243
$748$	24.2705	0.887418
$749$	0	0
$750$	7.38197	0.269551
$751$	−13.9787	−0.510091	−0.255045	−	0.966929i	$-0.582090\pi$
$751$	−13.9787	−0.510091	−0.255045	+	0.966929i	$0.582090\pi$
$752$	5.12461	0.186875
$753$	17.1246	0.624056
$754$	−10.7426	−0.391224
$755$	17.4164	0.633848
$756$	0	0
$757$	−17.0000	−0.617876	−0.308938	−	0.951082i	$-0.599973\pi$
$757$	−17.0000	−0.617876	−0.308938	+	0.951082i	$0.599973\pi$
$758$	−12.0000	−0.435860
$759$	2.23607	0.0811641
$760$	−19.7984	−0.718163
$761$	5.52786	0.200385	0.100192	−	0.994968i	$-0.468054\pi$
$761$	5.52786	0.200385	0.100192	+	0.994968i	$0.468054\pi$
$762$	−6.96556	−0.252336
$763$	0	0
$764$	10.0000	0.361787
$765$	−10.8541	−0.392431
$766$	−7.85410	−0.283780
$767$	−53.6525	−1.93728
$768$	−6.56231	−0.236797
$769$	−28.7639	−1.03725	−0.518627	−	0.855001i	$-0.673557\pi$
$769$	−28.7639	−1.03725	−0.518627	+	0.855001i	$0.673557\pi$
$770$	0	0
$771$	−1.23607	−0.0445159
$772$	−35.1246	−1.26416
$773$	2.05573	0.0739394	0.0369697	−	0.999316i	$-0.488229\pi$
$773$	2.05573	0.0739394	0.0369697	+	0.999316i	$0.488229\pi$
$774$	0.381966	0.0137295
$775$	−15.9787	−0.573972
$776$	−36.7082	−1.31775
$777$	0	0
$778$	11.5623	0.414529
$779$	40.8885	1.46498
$780$	12.0902	0.432898
$781$	−14.7984	−0.529527
$782$	−4.14590	−0.148257
$783$	−3.76393	−0.134512
$784$	0	0
$785$	−22.1803	−0.791650
$786$	4.43769	0.158287
$787$	−47.5755	−1.69588	−0.847941	−	0.530091i	$-0.822158\pi$
$787$	−47.5755	−1.69588	−0.847941	+	0.530091i	$0.822158\pi$
$788$	−20.2361	−0.720880
$789$	−17.9443	−0.638833
$790$	0.527864	0.0187806
$791$	0	0
$792$	5.00000	0.177667
$793$	−8.56231	−0.304056
$794$	22.2918	0.791106
$795$	3.09017	0.109597
$796$	−29.2705	−1.03747
$797$	−21.8197	−0.772892	−0.386446	−	0.922312i	$-0.626297\pi$
$797$	−21.8197	−0.772892	−0.386446	+	0.922312i	$0.626297\pi$
$798$	0	0
$799$	18.5410	0.655934
$800$	−13.3820	−0.473124
$801$	−9.38197	−0.331495
$802$	6.68692	0.236123
$803$	1.58359	0.0558838
$804$	−9.85410	−0.347527
$805$	0	0
$806$	19.1459	0.674385
$807$	20.9098	0.736061
$808$	24.2705	0.853834
$809$	−29.5623	−1.03936	−0.519678	−	0.854362i	$-0.673948\pi$
$809$	−29.5623	−1.03936	−0.519678	+	0.854362i	$0.673948\pi$
$810$	−1.00000	−0.0351364
$811$	−17.4721	−0.613530	−0.306765	−	0.951785i	$-0.599247\pi$
$811$	−17.4721	−0.613530	−0.306765	+	0.951785i	$0.599247\pi$
$812$	0	0
$813$	−4.05573	−0.142241
$814$	15.2016	0.532817
$815$	−2.61803	−0.0917057
$816$	12.4377	0.435406
$817$	−3.38197	−0.118320
$818$	12.6180	0.441179
$819$	0	0
$820$	−19.5623	−0.683145
$821$	11.1246	0.388252	0.194126	−	0.980977i	$-0.437813\pi$
$821$	11.1246	0.388252	0.194126	+	0.980977i	$0.437813\pi$
$822$	6.43769	0.224540
$823$	−33.1459	−1.15539	−0.577697	−	0.816252i	$-0.696048\pi$
$823$	−33.1459	−1.15539	−0.577697	+	0.816252i	$0.696048\pi$
$824$	43.4164	1.51248
$825$	5.32624	0.185436
$826$	0	0
$827$	23.2148	0.807257	0.403629	−	0.914923i	$-0.367749\pi$
$827$	23.2148	0.807257	0.403629	+	0.914923i	$0.367749\pi$
$828$	1.61803	0.0562306
$829$	3.58359	0.124463	0.0622316	−	0.998062i	$-0.480178\pi$
$829$	3.58359	0.124463	0.0622316	+	0.998062i	$0.480178\pi$
$830$	13.1803	0.457496
$831$	−29.2705	−1.01538
$832$	−1.09017	−0.0377948
$833$	0	0
$834$	8.41641	0.291436
$835$	24.5623	0.850014
$836$	−19.7984	−0.684741
$837$	6.70820	0.231869
$838$	−19.3607	−0.668804
$839$	25.7426	0.888735	0.444367	−	0.895845i	$-0.353428\pi$
$839$	25.7426	0.888735	0.444367	+	0.895845i	$0.353428\pi$
$840$	0	0
$841$	−14.8328	−0.511476
$842$	14.3820	0.495635
$843$	9.70820	0.334368
$844$	26.5623	0.914312
$845$	−13.4721	−0.463456
$846$	1.70820	0.0587293
$847$	0	0
$848$	−3.54102	−0.121599
$849$	−25.2148	−0.865369
$850$	−9.87539	−0.338723
$851$	11.0000	0.377075
$852$	−10.7082	−0.366857
$853$	6.87539	0.235409	0.117704	−	0.993049i	$-0.462446\pi$
$853$	6.87539	0.235409	0.117704	+	0.993049i	$0.462446\pi$
$854$	0	0
$855$	8.85410	0.302804
$856$	27.5623	0.942060
$857$	−26.2918	−0.898111	−0.449055	−	0.893504i	$-0.648239\pi$
$857$	−26.2918	−0.898111	−0.449055	+	0.893504i	$0.648239\pi$
$858$	−6.38197	−0.217877
$859$	14.0000	0.477674	0.238837	−	0.971060i	$-0.423234\pi$
$859$	14.0000	0.477674	0.238837	+	0.971060i	$0.423234\pi$
$860$	1.61803	0.0551745
$861$	0	0
$862$	10.0902	0.343673
$863$	50.0689	1.70436	0.852182	−	0.523245i	$-0.175279\pi$
$863$	50.0689	1.70436	0.852182	+	0.523245i	$0.175279\pi$
$864$	5.61803	0.191129
$865$	8.85410	0.301048
$866$	13.0557	0.443652
$867$	28.0000	0.950930
$868$	0	0
$869$	1.18034	0.0400403
$870$	3.76393	0.127609
$871$	28.1246	0.952966
$872$	31.9098	1.08060
$873$	16.4164	0.555611
$874$	3.38197	0.114397
$875$	0	0
$876$	1.14590	0.0387163
$877$	43.4164	1.46607	0.733034	−	0.680192i	$-0.238104\pi$
$877$	43.4164	1.46607	0.733034	+	0.680192i	$0.238104\pi$
$878$	4.72949	0.159613
$879$	−12.0000	−0.404750
$880$	6.70820	0.226134
$881$	−24.1803	−0.814656	−0.407328	−	0.913282i	$-0.633539\pi$
$881$	−24.1803	−0.814656	−0.407328	+	0.913282i	$0.633539\pi$
$882$	0	0
$883$	−15.0902	−0.507825	−0.253912	−	0.967227i	$-0.581717\pi$
$883$	−15.0902	−0.507825	−0.253912	+	0.967227i	$0.581717\pi$
$884$	−50.1246	−1.68587
$885$	18.7984	0.631900
$886$	−11.4164	−0.383542
$887$	14.7984	0.496881	0.248440	−	0.968647i	$-0.420082\pi$
$887$	14.7984	0.496881	0.248440	+	0.968647i	$0.420082\pi$
$888$	24.5967	0.825413
$889$	0	0
$890$	9.38197	0.314484
$891$	−2.23607	−0.0749111
$892$	−18.0344	−0.603838
$893$	−15.1246	−0.506126
$894$	−9.12461	−0.305173
$895$	7.85410	0.262534
$896$	0	0
$897$	−4.61803	−0.154192
$898$	−23.8328	−0.795311
$899$	−25.2492	−0.842109
$900$	3.85410	0.128470
$901$	−12.8115	−0.426814
$902$	10.3262	0.343826
$903$	0	0
$904$	27.0344	0.899152
$905$	25.7984	0.857567
$906$	−6.65248	−0.221014
$907$	2.02129	0.0671157	0.0335579	−	0.999437i	$-0.489316\pi$
$907$	2.02129	0.0671157	0.0335579	+	0.999437i	$0.489316\pi$
$908$	14.0344	0.465749
$909$	−10.8541	−0.360008
$910$	0	0
$911$	41.5967	1.37816	0.689081	−	0.724684i	$-0.258014\pi$
$911$	41.5967	1.37816	0.689081	+	0.724684i	$0.258014\pi$
$912$	−10.1459	−0.335964
$913$	29.4721	0.975385
$914$	0.819660	0.0271119
$915$	3.00000	0.0991769
$916$	−1.09017	−0.0360202
$917$	0	0
$918$	4.14590	0.136835
$919$	−9.87539	−0.325759	−0.162879	−	0.986646i	$-0.552078\pi$
$919$	−9.87539	−0.325759	−0.162879	+	0.986646i	$0.552078\pi$
$920$	−3.61803	−0.119283
$921$	24.1246	0.794933
$922$	18.8197	0.619792
$923$	30.5623	1.00597
$924$	0	0
$925$	26.2016	0.861504
$926$	18.9787	0.623679
$927$	−19.4164	−0.637719
$928$	−21.1459	−0.694148
$929$	−40.0902	−1.31532	−0.657658	−	0.753317i	$-0.728453\pi$
$929$	−40.0902	−1.31532	−0.657658	+	0.753317i	$0.728453\pi$
$930$	−6.70820	−0.219971
$931$	0	0
$932$	−0.145898	−0.00477905
$933$	0.326238	0.0106806
$934$	−4.43769	−0.145206
$935$	24.2705	0.793731
$936$	−10.3262	−0.337524
$937$	10.7082	0.349822	0.174911	−	0.984584i	$-0.444036\pi$
$937$	10.7082	0.349822	0.174911	+	0.984584i	$0.444036\pi$
$938$	0	0
$939$	−6.47214	−0.211210
$940$	7.23607	0.236015
$941$	32.9443	1.07395	0.536976	−	0.843597i	$-0.319566\pi$
$941$	32.9443	1.07395	0.536976	+	0.843597i	$0.319566\pi$
$942$	8.47214	0.276037
$943$	7.47214	0.243326
$944$	−21.5410	−0.701100
$945$	0	0
$946$	−0.854102	−0.0277693
$947$	−1.05573	−0.0343066	−0.0171533	−	0.999853i	$-0.505460\pi$
$947$	−1.05573	−0.0343066	−0.0171533	+	0.999853i	$0.505460\pi$
$948$	0.854102	0.0277399
$949$	−3.27051	−0.106165
$950$	8.05573	0.261362
$951$	−23.5066	−0.762253
$952$	0	0
$953$	−57.1591	−1.85156	−0.925782	−	0.378059i	$-0.876592\pi$
$953$	−57.1591	−1.85156	−0.925782	+	0.378059i	$0.876592\pi$
$954$	−1.18034	−0.0382149
$955$	10.0000	0.323592
$956$	−32.0344	−1.03607
$957$	8.41641	0.272064
$958$	−12.9787	−0.419323
$959$	0	0
$960$	0.381966	0.0123279
$961$	14.0000	0.451613
$962$	−31.3951	−1.01222
$963$	−12.3262	−0.397207
$964$	−17.7984	−0.573247
$965$	−35.1246	−1.13070
$966$	0	0
$967$	5.63932	0.181348	0.0906742	−	0.995881i	$-0.471098\pi$
$967$	5.63932	0.181348	0.0906742	+	0.995881i	$0.471098\pi$
$968$	13.4164	0.431220
$969$	−36.7082	−1.17924
$970$	−16.4164	−0.527099
$971$	−40.6869	−1.30571	−0.652853	−	0.757485i	$-0.726428\pi$
$971$	−40.6869	−1.30571	−0.652853	+	0.757485i	$0.726428\pi$
$972$	−1.61803	−0.0518985
$973$	0	0
$974$	−26.3951	−0.845754
$975$	−11.0000	−0.352282
$976$	−3.43769	−0.110038
$977$	25.2016	0.806271	0.403136	−	0.915140i	$-0.367920\pi$
$977$	25.2016	0.806271	0.403136	+	0.915140i	$0.367920\pi$
$978$	1.00000	0.0319765
$979$	20.9787	0.670483
$980$	0	0
$981$	−14.2705	−0.455622
$982$	−9.14590	−0.291857
$983$	56.5967	1.80516	0.902578	−	0.430526i	$-0.141672\pi$
$983$	56.5967	1.80516	0.902578	+	0.430526i	$0.141672\pi$
$984$	16.7082	0.532638
$985$	−20.2361	−0.644775
$986$	−15.6049	−0.496961
$987$	0	0
$988$	40.8885	1.30084
$989$	−0.618034	−0.0196523
$990$	2.23607	0.0710669
$991$	60.5755	1.92424	0.962121	−	0.272621i	$-0.0878905\pi$
$991$	60.5755	1.92424	0.962121	+	0.272621i	$0.0878905\pi$
$992$	37.6869	1.19656
$993$	13.4164	0.425757
$994$	0	0
$995$	−29.2705	−0.927938
$996$	21.3262	0.675748
$997$	31.7214	1.00463	0.502313	−	0.864686i	$-0.332483\pi$
$997$	31.7214	1.00463	0.502313	+	0.864686i	$0.332483\pi$
$998$	21.8754	0.692453
$999$	−11.0000	−0.348025

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.r.1.2		2
7.6	odd	2		483.2.a.d.1.2	✓	2
21.20	even	2		1449.2.a.h.1.1		2
28.27	even	2		7728.2.a.bn.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.a.d.1.2	✓	2	7.6	odd	2
1449.2.a.h.1.1		2	21.20	even	2
3381.2.a.r.1.2		2	1.1	even	1	trivial
7728.2.a.bn.1.2		2	28.27	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:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q+0.618034 q^{2} +1.00000 q^{3} -1.61803 q^{4} -1.61803 q^{5} +0.618034 q^{6} -2.23607 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.618034 q^{2} +1.00000 q^{3} -1.61803 q^{4} -1.61803 q^{5} +0.618034 q^{6} -2.23607 q^{8} +1.00000 q^{9} -1.00000 q^{10} -2.23607 q^{11} -1.61803 q^{12} +4.61803 q^{13} -1.61803 q^{15} +1.85410 q^{16} +6.70820 q^{17} +0.618034 q^{18} -5.47214 q^{19} +2.61803 q^{20} -1.38197 q^{22} -1.00000 q^{23} -2.23607 q^{24} -2.38197 q^{25} +2.85410 q^{26} +1.00000 q^{27} -3.76393 q^{29} -1.00000 q^{30} +6.70820 q^{31} +5.61803 q^{32} -2.23607 q^{33} +4.14590 q^{34} -1.61803 q^{36} -11.0000 q^{37} -3.38197 q^{38} +4.61803 q^{39} +3.61803 q^{40} -7.47214 q^{41} +0.618034 q^{43} +3.61803 q^{44} -1.61803 q^{45} -0.618034 q^{46} +2.76393 q^{47} +1.85410 q^{48} -1.47214 q^{50} +6.70820 q^{51} -7.47214 q^{52} -1.90983 q^{53} +0.618034 q^{54} +3.61803 q^{55} -5.47214 q^{57} -2.32624 q^{58} -11.6180 q^{59} +2.61803 q^{60} -1.85410 q^{61} +4.14590 q^{62} -0.236068 q^{64} -7.47214 q^{65} -1.38197 q^{66} +6.09017 q^{67} -10.8541 q^{68} -1.00000 q^{69} +6.61803 q^{71} -2.23607 q^{72} -0.708204 q^{73} -6.79837 q^{74} -2.38197 q^{75} +8.85410 q^{76} +2.85410 q^{78} -0.527864 q^{79} -3.00000 q^{80} +1.00000 q^{81} -4.61803 q^{82} -13.1803 q^{83} -10.8541 q^{85} +0.381966 q^{86} -3.76393 q^{87} +5.00000 q^{88} -9.38197 q^{89} -1.00000 q^{90} +1.61803 q^{92} +6.70820 q^{93} +1.70820 q^{94} +8.85410 q^{95} +5.61803 q^{96} +16.4164 q^{97} -2.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 2 q^{3} - q^{4} - q^{5} - q^{6} + 2 q^{9}+O(q^{10}) \) 2 * q - q^2 + 2 * q^3 - q^4 - q^5 - q^6 + 2 * q^9	\( 2 q - q^{2} + 2 q^{3} - q^{4} - q^{5} - q^{6} + 2 q^{9} - 2 q^{10} - q^{12} + 7 q^{13} - q^{15} - 3 q^{16} - q^{18} - 2 q^{19} + 3 q^{20} - 5 q^{22} - 2 q^{23} - 7 q^{25} - q^{26} + 2 q^{27} - 12 q^{29} - 2 q^{30} + 9 q^{32} + 15 q^{34} - q^{36} - 22 q^{37} - 9 q^{38} + 7 q^{39} + 5 q^{40} - 6 q^{41} - q^{43} + 5 q^{44} - q^{45} + q^{46} + 10 q^{47} - 3 q^{48} + 6 q^{50} - 6 q^{52} - 15 q^{53} - q^{54} + 5 q^{55} - 2 q^{57} + 11 q^{58} - 21 q^{59} + 3 q^{60} + 3 q^{61} + 15 q^{62} + 4 q^{64} - 6 q^{65} - 5 q^{66} + q^{67} - 15 q^{68} - 2 q^{69} + 11 q^{71} + 12 q^{73} + 11 q^{74} - 7 q^{75} + 11 q^{76} - q^{78} - 10 q^{79} - 6 q^{80} + 2 q^{81} - 7 q^{82} - 4 q^{83} - 15 q^{85} + 3 q^{86} - 12 q^{87} + 10 q^{88} - 21 q^{89} - 2 q^{90} + q^{92} - 10 q^{94} + 11 q^{95} + 9 q^{96} + 6 q^{97}+O(q^{100}) \) 2 * q - q^2 + 2 * q^3 - q^4 - q^5 - q^6 + 2 * q^9 - 2 * q^10 - q^12 + 7 * q^13 - q^15 - 3 * q^16 - q^18 - 2 * q^19 + 3 * q^20 - 5 * q^22 - 2 * q^23 - 7 * q^25 - q^26 + 2 * q^27 - 12 * q^29 - 2 * q^30 + 9 * q^32 + 15 * q^34 - q^36 - 22 * q^37 - 9 * q^38 + 7 * q^39 + 5 * q^40 - 6 * q^41 - q^43 + 5 * q^44 - q^45 + q^46 + 10 * q^47 - 3 * q^48 + 6 * q^50 - 6 * q^52 - 15 * q^53 - q^54 + 5 * q^55 - 2 * q^57 + 11 * q^58 - 21 * q^59 + 3 * q^60 + 3 * q^61 + 15 * q^62 + 4 * q^64 - 6 * q^65 - 5 * q^66 + q^67 - 15 * q^68 - 2 * q^69 + 11 * q^71 + 12 * q^73 + 11 * q^74 - 7 * q^75 + 11 * q^76 - q^78 - 10 * q^79 - 6 * q^80 + 2 * q^81 - 7 * q^82 - 4 * q^83 - 15 * q^85 + 3 * q^86 - 12 * q^87 + 10 * q^88 - 21 * q^89 - 2 * q^90 + q^92 - 10 * q^94 + 11 * q^95 + 9 * q^96 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more