LMFDB - Embedded newform 5610.2.a.bu.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5610,2,Mod(1,5610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5610, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("5610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5610.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:	$44.7960755339$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	5610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.23607 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} -3.23607 q^{13} -1.23607 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +5.70820 q^{19} -1.00000 q^{20} +1.23607 q^{21} +1.00000 q^{22} -0.763932 q^{23} -1.00000 q^{24} +1.00000 q^{25} -3.23607 q^{26} -1.00000 q^{27} -1.23607 q^{28} +0.472136 q^{29} +1.00000 q^{30} -4.00000 q^{31} +1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +1.23607 q^{35} +1.00000 q^{36} -6.00000 q^{37} +5.70820 q^{38} +3.23607 q^{39} -1.00000 q^{40} +8.94427 q^{41} +1.23607 q^{42} +1.23607 q^{43} +1.00000 q^{44} -1.00000 q^{45} -0.763932 q^{46} -6.47214 q^{47} -1.00000 q^{48} -5.47214 q^{49} +1.00000 q^{50} +1.00000 q^{51} -3.23607 q^{52} -1.23607 q^{53} -1.00000 q^{54} -1.00000 q^{55} -1.23607 q^{56} -5.70820 q^{57} +0.472136 q^{58} +1.23607 q^{59} +1.00000 q^{60} +6.00000 q^{61} -4.00000 q^{62} -1.23607 q^{63} +1.00000 q^{64} +3.23607 q^{65} -1.00000 q^{66} +6.00000 q^{67} -1.00000 q^{68} +0.763932 q^{69} +1.23607 q^{70} -5.23607 q^{71} +1.00000 q^{72} -3.23607 q^{73} -6.00000 q^{74} -1.00000 q^{75} +5.70820 q^{76} -1.23607 q^{77} +3.23607 q^{78} -9.70820 q^{79} -1.00000 q^{80} +1.00000 q^{81} +8.94427 q^{82} -12.9443 q^{83} +1.23607 q^{84} +1.00000 q^{85} +1.23607 q^{86} -0.472136 q^{87} +1.00000 q^{88} +10.9443 q^{89} -1.00000 q^{90} +4.00000 q^{91} -0.763932 q^{92} +4.00000 q^{93} -6.47214 q^{94} -5.70820 q^{95} -1.00000 q^{96} -5.47214 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} - 2 q^{13} + 2 q^{14} + 2 q^{15} + 2 q^{16} - 2 q^{17} + 2 q^{18} - 2 q^{19} - 2 q^{20}+ \cdots + 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 - 2 * q^13 + 2 * q^14 + 2 * q^15 + 2 * q^16 - 2 * q^17 + 2 * q^18 - 2 * q^19 - 2 * q^20 - 2 * q^21 + 2 * q^22 - 6 * q^23 - 2 * q^24 + 2 * q^25 - 2 * q^26 - 2 * q^27 + 2 * q^28 - 8 * q^29 + 2 * q^30 - 8 * q^31 + 2 * q^32 - 2 * q^33 - 2 * q^34 - 2 * q^35 + 2 * q^36 - 12 * q^37 - 2 * q^38 + 2 * q^39 - 2 * q^40 - 2 * q^42 - 2 * q^43 + 2 * q^44 - 2 * q^45 - 6 * q^46 - 4 * q^47 - 2 * q^48 - 2 * q^49 + 2 * q^50 + 2 * q^51 - 2 * q^52 + 2 * q^53 - 2 * q^54 - 2 * q^55 + 2 * q^56 + 2 * q^57 - 8 * q^58 - 2 * q^59 + 2 * q^60 + 12 * q^61 - 8 * q^62 + 2 * q^63 + 2 * q^64 + 2 * q^65 - 2 * q^66 + 12 * q^67 - 2 * q^68 + 6 * q^69 - 2 * q^70 - 6 * q^71 + 2 * q^72 - 2 * q^73 - 12 * q^74 - 2 * q^75 - 2 * q^76 + 2 * q^77 + 2 * q^78 - 6 * q^79 - 2 * q^80 + 2 * q^81 - 8 * q^83 - 2 * q^84 + 2 * q^85 - 2 * q^86 + 8 * q^87 + 2 * q^88 + 4 * q^89 - 2 * q^90 + 8 * q^91 - 6 * q^92 + 8 * q^93 - 4 * q^94 + 2 * q^95 - 2 * q^96 - 2 * q^98 + 2 * q^99

Coefficient data

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

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

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

$2$	1.00000	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
$7$	−1.23607	−0.467190	−0.233595	−	0.972334i	$-0.575049\pi$
$7$	−1.23607	−0.467190	−0.233595	+	0.972334i	$0.575049\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	−3.23607	−0.897524	−0.448762	−	0.893651i	$-0.648135\pi$
$13$	−3.23607	−0.897524	−0.448762	+	0.893651i	$0.648135\pi$
$14$	−1.23607	−0.330353
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	5.70820	1.30955	0.654776	−	0.755823i	$-0.272763\pi$
$19$	5.70820	1.30955	0.654776	+	0.755823i	$0.272763\pi$
$20$	−1.00000	−0.223607
$21$	1.23607	0.269732
$22$	1.00000	0.213201
$23$	−0.763932	−0.159291	−0.0796454	−	0.996823i	$-0.525379\pi$
$23$	−0.763932	−0.159291	−0.0796454	+	0.996823i	$0.525379\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−3.23607	−0.634645
$27$	−1.00000	−0.192450
$28$	−1.23607	−0.233595
$29$	0.472136	0.0876734	0.0438367	−	0.999039i	$-0.486042\pi$
$29$	0.472136	0.0876734	0.0438367	+	0.999039i	$0.486042\pi$
$30$	1.00000	0.182574
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	−1.00000	−0.171499
$35$	1.23607	0.208934
$36$	1.00000	0.166667
$37$	−6.00000	−0.986394	−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000	−0.986394	−0.493197	+	0.869918i	$0.664172\pi$
$38$	5.70820	0.925993
$39$	3.23607	0.518186
$40$	−1.00000	−0.158114
$41$	8.94427	1.39686	0.698430	−	0.715678i	$-0.253882\pi$
$41$	8.94427	1.39686	0.698430	+	0.715678i	$0.253882\pi$
$42$	1.23607	0.190729
$43$	1.23607	0.188499	0.0942493	−	0.995549i	$-0.469955\pi$
$43$	1.23607	0.188499	0.0942493	+	0.995549i	$0.469955\pi$
$44$	1.00000	0.150756
$45$	−1.00000	−0.149071
$46$	−0.763932	−0.112636
$47$	−6.47214	−0.944058	−0.472029	−	0.881583i	$-0.656478\pi$
$47$	−6.47214	−0.944058	−0.472029	+	0.881583i	$0.656478\pi$
$48$	−1.00000	−0.144338
$49$	−5.47214	−0.781734
$50$	1.00000	0.141421
$51$	1.00000	0.140028
$52$	−3.23607	−0.448762
$53$	−1.23607	−0.169787	−0.0848935	−	0.996390i	$-0.527055\pi$
$53$	−1.23607	−0.169787	−0.0848935	+	0.996390i	$0.527055\pi$
$54$	−1.00000	−0.136083
$55$	−1.00000	−0.134840
$56$	−1.23607	−0.165177
$57$	−5.70820	−0.756070
$58$	0.472136	0.0619945
$59$	1.23607	0.160922	0.0804612	−	0.996758i	$-0.474361\pi$
$59$	1.23607	0.160922	0.0804612	+	0.996758i	$0.474361\pi$
$60$	1.00000	0.129099
$61$	6.00000	0.768221	0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000	0.768221	0.384111	+	0.923287i	$0.374508\pi$
$62$	−4.00000	−0.508001
$63$	−1.23607	−0.155730
$64$	1.00000	0.125000
$65$	3.23607	0.401385
$66$	−1.00000	−0.123091
$67$	6.00000	0.733017	0.366508	−	0.930415i	$-0.380553\pi$
$67$	6.00000	0.733017	0.366508	+	0.930415i	$0.380553\pi$
$68$	−1.00000	−0.121268
$69$	0.763932	0.0919666
$70$	1.23607	0.147738
$71$	−5.23607	−0.621407	−0.310703	−	0.950507i	$-0.600565\pi$
$71$	−5.23607	−0.621407	−0.310703	+	0.950507i	$0.600565\pi$
$72$	1.00000	0.117851
$73$	−3.23607	−0.378753	−0.189377	−	0.981905i	$-0.560647\pi$
$73$	−3.23607	−0.378753	−0.189377	+	0.981905i	$0.560647\pi$
$74$	−6.00000	−0.697486
$75$	−1.00000	−0.115470
$76$	5.70820	0.654776
$77$	−1.23607	−0.140863
$78$	3.23607	0.366413
$79$	−9.70820	−1.09226	−0.546129	−	0.837701i	$-0.683899\pi$
$79$	−9.70820	−1.09226	−0.546129	+	0.837701i	$0.683899\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	8.94427	0.987730
$83$	−12.9443	−1.42082	−0.710409	−	0.703789i	$-0.751490\pi$
$83$	−12.9443	−1.42082	−0.710409	+	0.703789i	$0.751490\pi$
$84$	1.23607	0.134866
$85$	1.00000	0.108465
$86$	1.23607	0.133289
$87$	−0.472136	−0.0506183
$88$	1.00000	0.106600
$89$	10.9443	1.16009	0.580045	−	0.814584i	$-0.303035\pi$
$89$	10.9443	1.16009	0.580045	+	0.814584i	$0.303035\pi$
$90$	−1.00000	−0.105409
$91$	4.00000	0.419314
$92$	−0.763932	−0.0796454
$93$	4.00000	0.414781
$94$	−6.47214	−0.667550
$95$	−5.70820	−0.585649
$96$	−1.00000	−0.102062
$97$	0	0		−	1.00000i	$-0.5\pi$
$97$	0	0			1.00000i	$0.5\pi$
$98$	−5.47214	−0.552769
$99$	1.00000	0.100504
$100$	1.00000	0.100000
$101$	−8.94427	−0.889988	−0.444994	−	0.895533i	$-0.646794\pi$
$101$	−8.94427	−0.889988	−0.444994	+	0.895533i	$0.646794\pi$
$102$	1.00000	0.0990148
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	−3.23607	−0.317323
$105$	−1.23607	−0.120628
$106$	−1.23607	−0.120058
$107$	−16.9443	−1.63806	−0.819032	−	0.573747i	$-0.805489\pi$
$107$	−16.9443	−1.63806	−0.819032	+	0.573747i	$0.805489\pi$
$108$	−1.00000	−0.0962250
$109$	−6.00000	−0.574696	−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000	−0.574696	−0.287348	+	0.957826i	$0.592774\pi$
$110$	−1.00000	−0.0953463
$111$	6.00000	0.569495
$112$	−1.23607	−0.116797
$113$	−10.7639	−1.01259	−0.506293	−	0.862362i	$-0.668984\pi$
$113$	−10.7639	−1.01259	−0.506293	+	0.862362i	$0.668984\pi$
$114$	−5.70820	−0.534622
$115$	0.763932	0.0712370
$116$	0.472136	0.0438367
$117$	−3.23607	−0.299175
$118$	1.23607	0.113789
$119$	1.23607	0.113310
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	6.00000	0.543214
$123$	−8.94427	−0.806478
$124$	−4.00000	−0.359211
$125$	−1.00000	−0.0894427
$126$	−1.23607	−0.110118
$127$	−12.0000	−1.06483	−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000	−1.06483	−0.532414	+	0.846484i	$0.678715\pi$
$128$	1.00000	0.0883883
$129$	−1.23607	−0.108830
$130$	3.23607	0.283822
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	−1.00000	−0.0870388
$133$	−7.05573	−0.611809
$134$	6.00000	0.518321
$135$	1.00000	0.0860663
$136$	−1.00000	−0.0857493
$137$	19.8885	1.69919	0.849596	−	0.527433i	$-0.176846\pi$
$137$	19.8885	1.69919	0.849596	+	0.527433i	$0.176846\pi$
$138$	0.763932	0.0650302
$139$	8.00000	0.678551	0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000	0.678551	0.339276	+	0.940687i	$0.389818\pi$
$140$	1.23607	0.104467
$141$	6.47214	0.545052
$142$	−5.23607	−0.439401
$143$	−3.23607	−0.270614
$144$	1.00000	0.0833333
$145$	−0.472136	−0.0392088
$146$	−3.23607	−0.267819
$147$	5.47214	0.451334
$148$	−6.00000	−0.493197
$149$	−18.4721	−1.51330	−0.756648	−	0.653822i	$-0.773164\pi$
$149$	−18.4721	−1.51330	−0.756648	+	0.653822i	$0.773164\pi$
$150$	−1.00000	−0.0816497
$151$	−5.52786	−0.449851	−0.224926	−	0.974376i	$-0.572214\pi$
$151$	−5.52786	−0.449851	−0.224926	+	0.974376i	$0.572214\pi$
$152$	5.70820	0.462996
$153$	−1.00000	−0.0808452
$154$	−1.23607	−0.0996052
$155$	4.00000	0.321288
$156$	3.23607	0.259093
$157$	−7.41641	−0.591894	−0.295947	−	0.955204i	$-0.595635\pi$
$157$	−7.41641	−0.591894	−0.295947	+	0.955204i	$0.595635\pi$
$158$	−9.70820	−0.772343
$159$	1.23607	0.0980266
$160$	−1.00000	−0.0790569
$161$	0.944272	0.0744191
$162$	1.00000	0.0785674
$163$	2.47214	0.193633	0.0968163	−	0.995302i	$-0.469134\pi$
$163$	2.47214	0.193633	0.0968163	+	0.995302i	$0.469134\pi$
$164$	8.94427	0.698430
$165$	1.00000	0.0778499
$166$	−12.9443	−1.00467
$167$	−12.0000	−0.928588	−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000	−0.928588	−0.464294	+	0.885681i	$0.653692\pi$
$168$	1.23607	0.0953647
$169$	−2.52786	−0.194451
$170$	1.00000	0.0766965
$171$	5.70820	0.436517
$172$	1.23607	0.0942493
$173$	−13.4164	−1.02003	−0.510015	−	0.860165i	$-0.670360\pi$
$173$	−13.4164	−1.02003	−0.510015	+	0.860165i	$0.670360\pi$
$174$	−0.472136	−0.0357925
$175$	−1.23607	−0.0934380
$176$	1.00000	0.0753778
$177$	−1.23607	−0.0929086
$178$	10.9443	0.820308
$179$	−17.2361	−1.28828	−0.644142	−	0.764906i	$-0.722785\pi$
$179$	−17.2361	−1.28828	−0.644142	+	0.764906i	$0.722785\pi$
$180$	−1.00000	−0.0745356
$181$	−0.472136	−0.0350936	−0.0175468	−	0.999846i	$-0.505586\pi$
$181$	−0.472136	−0.0350936	−0.0175468	+	0.999846i	$0.505586\pi$
$182$	4.00000	0.296500
$183$	−6.00000	−0.443533
$184$	−0.763932	−0.0563178
$185$	6.00000	0.441129
$186$	4.00000	0.293294
$187$	−1.00000	−0.0731272
$188$	−6.47214	−0.472029
$189$	1.23607	0.0899107
$190$	−5.70820	−0.414117
$191$	10.4721	0.757737	0.378869	−	0.925450i	$-0.376313\pi$
$191$	10.4721	0.757737	0.378869	+	0.925450i	$0.376313\pi$
$192$	−1.00000	−0.0721688
$193$	−5.70820	−0.410886	−0.205443	−	0.978669i	$-0.565863\pi$
$193$	−5.70820	−0.410886	−0.205443	+	0.978669i	$0.565863\pi$
$194$	0	0
$195$	−3.23607	−0.231740
$196$	−5.47214	−0.390867
$197$	−2.94427	−0.209771	−0.104885	−	0.994484i	$-0.533448\pi$
$197$	−2.94427	−0.209771	−0.104885	+	0.994484i	$0.533448\pi$
$198$	1.00000	0.0710669
$199$	−12.0000	−0.850657	−0.425329	−	0.905039i	$-0.639842\pi$
$199$	−12.0000	−0.850657	−0.425329	+	0.905039i	$0.639842\pi$
$200$	1.00000	0.0707107
$201$	−6.00000	−0.423207
$202$	−8.94427	−0.629317
$203$	−0.583592	−0.0409601
$204$	1.00000	0.0700140
$205$	−8.94427	−0.624695
$206$	4.00000	0.278693
$207$	−0.763932	−0.0530969
$208$	−3.23607	−0.224381
$209$	5.70820	0.394845
$210$	−1.23607	−0.0852968
$211$	−24.3607	−1.67706	−0.838529	−	0.544857i	$-0.816584\pi$
$211$	−24.3607	−1.67706	−0.838529	+	0.544857i	$0.816584\pi$
$212$	−1.23607	−0.0848935
$213$	5.23607	0.358769
$214$	−16.9443	−1.15829
$215$	−1.23607	−0.0842991
$216$	−1.00000	−0.0680414
$217$	4.94427	0.335639
$218$	−6.00000	−0.406371
$219$	3.23607	0.218673
$220$	−1.00000	−0.0674200
$221$	3.23607	0.217681
$222$	6.00000	0.402694
$223$	3.41641	0.228780	0.114390	−	0.993436i	$-0.463509\pi$
$223$	3.41641	0.228780	0.114390	+	0.993436i	$0.463509\pi$
$224$	−1.23607	−0.0825883
$225$	1.00000	0.0666667
$226$	−10.7639	−0.716006
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	−5.70820	−0.378035
$229$	2.58359	0.170729	0.0853643	−	0.996350i	$-0.472795\pi$
$229$	2.58359	0.170729	0.0853643	+	0.996350i	$0.472795\pi$
$230$	0.763932	0.0503722
$231$	1.23607	0.0813273
$232$	0.472136	0.0309972
$233$	−16.4721	−1.07913	−0.539563	−	0.841945i	$-0.681410\pi$
$233$	−16.4721	−1.07913	−0.539563	+	0.841945i	$0.681410\pi$
$234$	−3.23607	−0.211548
$235$	6.47214	0.422196
$236$	1.23607	0.0804612
$237$	9.70820	0.630616
$238$	1.23607	0.0801224
$239$	28.3607	1.83450	0.917250	−	0.398312i	$-0.130404\pi$
$239$	28.3607	1.83450	0.917250	+	0.398312i	$0.130404\pi$
$240$	1.00000	0.0645497
$241$	−18.1803	−1.17110	−0.585549	−	0.810637i	$-0.699121\pi$
$241$	−18.1803	−1.17110	−0.585549	+	0.810637i	$0.699121\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	6.00000	0.384111
$245$	5.47214	0.349602
$246$	−8.94427	−0.570266
$247$	−18.4721	−1.17535
$248$	−4.00000	−0.254000
$249$	12.9443	0.820310
$250$	−1.00000	−0.0632456
$251$	18.7639	1.18437	0.592184	−	0.805802i	$-0.298266\pi$
$251$	18.7639	1.18437	0.592184	+	0.805802i	$0.298266\pi$
$252$	−1.23607	−0.0778650
$253$	−0.763932	−0.0480280
$254$	−12.0000	−0.752947
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	4.47214	0.278964	0.139482	−	0.990225i	$-0.455456\pi$
$257$	4.47214	0.278964	0.139482	+	0.990225i	$0.455456\pi$
$258$	−1.23607	−0.0769542
$259$	7.41641	0.460833
$260$	3.23607	0.200692
$261$	0.472136	0.0292245
$262$	0	0
$263$	−12.0000	−0.739952	−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000	−0.739952	−0.369976	+	0.929041i	$0.620634\pi$
$264$	−1.00000	−0.0615457
$265$	1.23607	0.0759311
$266$	−7.05573	−0.432614
$267$	−10.9443	−0.669779
$268$	6.00000	0.366508
$269$	−15.5279	−0.946751	−0.473375	−	0.880861i	$-0.656965\pi$
$269$	−15.5279	−0.946751	−0.473375	+	0.880861i	$0.656965\pi$
$270$	1.00000	0.0608581
$271$	20.0000	1.21491	0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000	1.21491	0.607457	+	0.794353i	$0.292190\pi$
$272$	−1.00000	−0.0606339
$273$	−4.00000	−0.242091
$274$	19.8885	1.20151
$275$	1.00000	0.0603023
$276$	0.763932	0.0459833
$277$	14.0000	0.841178	0.420589	−	0.907251i	$-0.361823\pi$
$277$	14.0000	0.841178	0.420589	+	0.907251i	$0.361823\pi$
$278$	8.00000	0.479808
$279$	−4.00000	−0.239474
$280$	1.23607	0.0738692
$281$	−7.52786	−0.449075	−0.224537	−	0.974465i	$-0.572087\pi$
$281$	−7.52786	−0.449075	−0.224537	+	0.974465i	$0.572087\pi$
$282$	6.47214	0.385410
$283$	23.4164	1.39196	0.695980	−	0.718061i	$-0.254970\pi$
$283$	23.4164	1.39196	0.695980	+	0.718061i	$0.254970\pi$
$284$	−5.23607	−0.310703
$285$	5.70820	0.338125
$286$	−3.23607	−0.191353
$287$	−11.0557	−0.652599
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−0.472136	−0.0277248
$291$	0	0
$292$	−3.23607	−0.189377
$293$	−18.0000	−1.05157	−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000	−1.05157	−0.525786	+	0.850617i	$0.676229\pi$
$294$	5.47214	0.319141
$295$	−1.23607	−0.0719667
$296$	−6.00000	−0.348743
$297$	−1.00000	−0.0580259
$298$	−18.4721	−1.07006
$299$	2.47214	0.142967
$300$	−1.00000	−0.0577350
$301$	−1.52786	−0.0880646
$302$	−5.52786	−0.318093
$303$	8.94427	0.513835
$304$	5.70820	0.327388
$305$	−6.00000	−0.343559
$306$	−1.00000	−0.0571662
$307$	23.7082	1.35310	0.676549	−	0.736397i	$-0.263475\pi$
$307$	23.7082	1.35310	0.676549	+	0.736397i	$0.263475\pi$
$308$	−1.23607	−0.0704315
$309$	−4.00000	−0.227552
$310$	4.00000	0.227185
$311$	6.76393	0.383547	0.191774	−	0.981439i	$-0.438576\pi$
$311$	6.76393	0.383547	0.191774	+	0.981439i	$0.438576\pi$
$312$	3.23607	0.183206
$313$	0	0		−	1.00000i	$-0.5\pi$
$313$	0	0			1.00000i	$0.5\pi$
$314$	−7.41641	−0.418532
$315$	1.23607	0.0696445
$316$	−9.70820	−0.546129
$317$	−30.9443	−1.73800	−0.869002	−	0.494809i	$-0.835238\pi$
$317$	−30.9443	−1.73800	−0.869002	+	0.494809i	$0.835238\pi$
$318$	1.23607	0.0693153
$319$	0.472136	0.0264345
$320$	−1.00000	−0.0559017
$321$	16.9443	0.945737
$322$	0.944272	0.0526222
$323$	−5.70820	−0.317613
$324$	1.00000	0.0555556
$325$	−3.23607	−0.179505
$326$	2.47214	0.136919
$327$	6.00000	0.331801
$328$	8.94427	0.493865
$329$	8.00000	0.441054
$330$	1.00000	0.0550482
$331$	−1.88854	−0.103804	−0.0519019	−	0.998652i	$-0.516528\pi$
$331$	−1.88854	−0.103804	−0.0519019	+	0.998652i	$0.516528\pi$
$332$	−12.9443	−0.710409
$333$	−6.00000	−0.328798
$334$	−12.0000	−0.656611
$335$	−6.00000	−0.327815
$336$	1.23607	0.0674330
$337$	9.70820	0.528840	0.264420	−	0.964408i	$-0.414820\pi$
$337$	9.70820	0.528840	0.264420	+	0.964408i	$0.414820\pi$
$338$	−2.52786	−0.137498
$339$	10.7639	0.584617
$340$	1.00000	0.0542326
$341$	−4.00000	−0.216612
$342$	5.70820	0.308664
$343$	15.4164	0.832408
$344$	1.23607	0.0666443
$345$	−0.763932	−0.0411287
$346$	−13.4164	−0.721271
$347$	−4.94427	−0.265422	−0.132711	−	0.991155i	$-0.542368\pi$
$347$	−4.94427	−0.265422	−0.132711	+	0.991155i	$0.542368\pi$
$348$	−0.472136	−0.0253091
$349$	−11.7082	−0.626726	−0.313363	−	0.949633i	$-0.601456\pi$
$349$	−11.7082	−0.626726	−0.313363	+	0.949633i	$0.601456\pi$
$350$	−1.23607	−0.0660706
$351$	3.23607	0.172729
$352$	1.00000	0.0533002
$353$	4.47214	0.238028	0.119014	−	0.992893i	$-0.462027\pi$
$353$	4.47214	0.238028	0.119014	+	0.992893i	$0.462027\pi$
$354$	−1.23607	−0.0656963
$355$	5.23607	0.277902
$356$	10.9443	0.580045
$357$	−1.23607	−0.0654197
$358$	−17.2361	−0.910954
$359$	19.4164	1.02476	0.512379	−	0.858759i	$-0.328764\pi$
$359$	19.4164	1.02476	0.512379	+	0.858759i	$0.328764\pi$
$360$	−1.00000	−0.0527046
$361$	13.5836	0.714926
$362$	−0.472136	−0.0248149
$363$	−1.00000	−0.0524864
$364$	4.00000	0.209657
$365$	3.23607	0.169384
$366$	−6.00000	−0.313625
$367$	−24.8328	−1.29626	−0.648131	−	0.761529i	$-0.724449\pi$
$367$	−24.8328	−1.29626	−0.648131	+	0.761529i	$0.724449\pi$
$368$	−0.763932	−0.0398227
$369$	8.94427	0.465620
$370$	6.00000	0.311925
$371$	1.52786	0.0793227
$372$	4.00000	0.207390
$373$	−2.29180	−0.118665	−0.0593324	−	0.998238i	$-0.518897\pi$
$373$	−2.29180	−0.118665	−0.0593324	+	0.998238i	$0.518897\pi$
$374$	−1.00000	−0.0517088
$375$	1.00000	0.0516398
$376$	−6.47214	−0.333775
$377$	−1.52786	−0.0786890
$378$	1.23607	0.0635765
$379$	−7.05573	−0.362428	−0.181214	−	0.983444i	$-0.558003\pi$
$379$	−7.05573	−0.362428	−0.181214	+	0.983444i	$0.558003\pi$
$380$	−5.70820	−0.292825
$381$	12.0000	0.614779
$382$	10.4721	0.535801
$383$	1.52786	0.0780702	0.0390351	−	0.999238i	$-0.487572\pi$
$383$	1.52786	0.0780702	0.0390351	+	0.999238i	$0.487572\pi$
$384$	−1.00000	−0.0510310
$385$	1.23607	0.0629959
$386$	−5.70820	−0.290540
$387$	1.23607	0.0628329
$388$	0	0
$389$	−23.5967	−1.19640	−0.598201	−	0.801346i	$-0.704118\pi$
$389$	−23.5967	−1.19640	−0.598201	+	0.801346i	$0.704118\pi$
$390$	−3.23607	−0.163865
$391$	0.763932	0.0386337
$392$	−5.47214	−0.276385
$393$	0	0
$394$	−2.94427	−0.148330
$395$	9.70820	0.488473
$396$	1.00000	0.0502519
$397$	15.8885	0.797423	0.398712	−	0.917076i	$-0.369457\pi$
$397$	15.8885	0.797423	0.398712	+	0.917076i	$0.369457\pi$
$398$	−12.0000	−0.601506
$399$	7.05573	0.353228
$400$	1.00000	0.0500000
$401$	−33.7082	−1.68331	−0.841654	−	0.540018i	$-0.818418\pi$
$401$	−33.7082	−1.68331	−0.841654	+	0.540018i	$0.818418\pi$
$402$	−6.00000	−0.299253
$403$	12.9443	0.644800
$404$	−8.94427	−0.444994
$405$	−1.00000	−0.0496904
$406$	−0.583592	−0.0289632
$407$	−6.00000	−0.297409
$408$	1.00000	0.0495074
$409$	−6.94427	−0.343372	−0.171686	−	0.985152i	$-0.554921\pi$
$409$	−6.94427	−0.343372	−0.171686	+	0.985152i	$0.554921\pi$
$410$	−8.94427	−0.441726
$411$	−19.8885	−0.981030
$412$	4.00000	0.197066
$413$	−1.52786	−0.0751813
$414$	−0.763932	−0.0375452
$415$	12.9443	0.635409
$416$	−3.23607	−0.158661
$417$	−8.00000	−0.391762
$418$	5.70820	0.279197
$419$	1.52786	0.0746410	0.0373205	−	0.999303i	$-0.488118\pi$
$419$	1.52786	0.0746410	0.0373205	+	0.999303i	$0.488118\pi$
$420$	−1.23607	−0.0603139
$421$	10.9443	0.533391	0.266696	−	0.963781i	$-0.414068\pi$
$421$	10.9443	0.533391	0.266696	+	0.963781i	$0.414068\pi$
$422$	−24.3607	−1.18586
$423$	−6.47214	−0.314686
$424$	−1.23607	−0.0600288
$425$	−1.00000	−0.0485071
$426$	5.23607	0.253688
$427$	−7.41641	−0.358905
$428$	−16.9443	−0.819032
$429$	3.23607	0.156239
$430$	−1.23607	−0.0596085
$431$	−22.9443	−1.10519	−0.552593	−	0.833451i	$-0.686362\pi$
$431$	−22.9443	−1.10519	−0.552593	+	0.833451i	$0.686362\pi$
$432$	−1.00000	−0.0481125
$433$	−6.00000	−0.288342	−0.144171	−	0.989553i	$-0.546051\pi$
$433$	−6.00000	−0.288342	−0.144171	+	0.989553i	$0.546051\pi$
$434$	4.94427	0.237333
$435$	0.472136	0.0226372
$436$	−6.00000	−0.287348
$437$	−4.36068	−0.208600
$438$	3.23607	0.154625
$439$	−17.7082	−0.845166	−0.422583	−	0.906324i	$-0.638877\pi$
$439$	−17.7082	−0.845166	−0.422583	+	0.906324i	$0.638877\pi$
$440$	−1.00000	−0.0476731
$441$	−5.47214	−0.260578
$442$	3.23607	0.153924
$443$	−34.6525	−1.64639	−0.823194	−	0.567760i	$-0.807810\pi$
$443$	−34.6525	−1.64639	−0.823194	+	0.567760i	$0.807810\pi$
$444$	6.00000	0.284747
$445$	−10.9443	−0.518808
$446$	3.41641	0.161772
$447$	18.4721	0.873702
$448$	−1.23607	−0.0583987
$449$	−16.1803	−0.763597	−0.381799	−	0.924245i	$-0.624695\pi$
$449$	−16.1803	−0.763597	−0.381799	+	0.924245i	$0.624695\pi$
$450$	1.00000	0.0471405
$451$	8.94427	0.421169
$452$	−10.7639	−0.506293
$453$	5.52786	0.259722
$454$	0	0
$455$	−4.00000	−0.187523
$456$	−5.70820	−0.267311
$457$	18.0000	0.842004	0.421002	−	0.907060i	$-0.361678\pi$
$457$	18.0000	0.842004	0.421002	+	0.907060i	$0.361678\pi$
$458$	2.58359	0.120723
$459$	1.00000	0.0466760
$460$	0.763932	0.0356185
$461$	−19.4164	−0.904312	−0.452156	−	0.891939i	$-0.649345\pi$
$461$	−19.4164	−0.904312	−0.452156	+	0.891939i	$0.649345\pi$
$462$	1.23607	0.0575071
$463$	−24.3607	−1.13214	−0.566068	−	0.824358i	$-0.691536\pi$
$463$	−24.3607	−1.13214	−0.566068	+	0.824358i	$0.691536\pi$
$464$	0.472136	0.0219184
$465$	−4.00000	−0.185496
$466$	−16.4721	−0.763057
$467$	19.2361	0.890139	0.445070	−	0.895496i	$-0.353179\pi$
$467$	19.2361	0.890139	0.445070	+	0.895496i	$0.353179\pi$
$468$	−3.23607	−0.149587
$469$	−7.41641	−0.342458
$470$	6.47214	0.298537
$471$	7.41641	0.341730
$472$	1.23607	0.0568946
$473$	1.23607	0.0568345
$474$	9.70820	0.445913
$475$	5.70820	0.261910
$476$	1.23607	0.0566551
$477$	−1.23607	−0.0565957
$478$	28.3607	1.29719
$479$	−36.4721	−1.66645	−0.833227	−	0.552931i	$-0.813509\pi$
$479$	−36.4721	−1.66645	−0.833227	+	0.552931i	$0.813509\pi$
$480$	1.00000	0.0456435
$481$	19.4164	0.885312
$482$	−18.1803	−0.828092
$483$	−0.944272	−0.0429659
$484$	1.00000	0.0454545
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	32.8328	1.48780	0.743898	−	0.668293i	$-0.232975\pi$
$487$	32.8328	1.48780	0.743898	+	0.668293i	$0.232975\pi$
$488$	6.00000	0.271607
$489$	−2.47214	−0.111794
$490$	5.47214	0.247206
$491$	18.9443	0.854943	0.427472	−	0.904029i	$-0.359404\pi$
$491$	18.9443	0.854943	0.427472	+	0.904029i	$0.359404\pi$
$492$	−8.94427	−0.403239
$493$	−0.472136	−0.0212639
$494$	−18.4721	−0.831101
$495$	−1.00000	−0.0449467
$496$	−4.00000	−0.179605
$497$	6.47214	0.290315
$498$	12.9443	0.580047
$499$	30.8328	1.38027	0.690133	−	0.723682i	$-0.257552\pi$
$499$	30.8328	1.38027	0.690133	+	0.723682i	$0.257552\pi$
$500$	−1.00000	−0.0447214
$501$	12.0000	0.536120
$502$	18.7639	0.837475
$503$	9.52786	0.424826	0.212413	−	0.977180i	$-0.431868\pi$
$503$	9.52786	0.424826	0.212413	+	0.977180i	$0.431868\pi$
$504$	−1.23607	−0.0550588
$505$	8.94427	0.398015
$506$	−0.763932	−0.0339609
$507$	2.52786	0.112266
$508$	−12.0000	−0.532414
$509$	39.2361	1.73911	0.869554	−	0.493838i	$-0.164406\pi$
$509$	39.2361	1.73911	0.869554	+	0.493838i	$0.164406\pi$
$510$	−1.00000	−0.0442807
$511$	4.00000	0.176950
$512$	1.00000	0.0441942
$513$	−5.70820	−0.252023
$514$	4.47214	0.197257
$515$	−4.00000	−0.176261
$516$	−1.23607	−0.0544149
$517$	−6.47214	−0.284644
$518$	7.41641	0.325858
$519$	13.4164	0.588915
$520$	3.23607	0.141911
$521$	5.12461	0.224513	0.112257	−	0.993679i	$-0.464192\pi$
$521$	5.12461	0.224513	0.112257	+	0.993679i	$0.464192\pi$
$522$	0.472136	0.0206648
$523$	−19.1246	−0.836261	−0.418130	−	0.908387i	$-0.637315\pi$
$523$	−19.1246	−0.836261	−0.418130	+	0.908387i	$0.637315\pi$
$524$	0	0
$525$	1.23607	0.0539464
$526$	−12.0000	−0.523225
$527$	4.00000	0.174243
$528$	−1.00000	−0.0435194
$529$	−22.4164	−0.974626
$530$	1.23607	0.0536914
$531$	1.23607	0.0536408
$532$	−7.05573	−0.305905
$533$	−28.9443	−1.25372
$534$	−10.9443	−0.473605
$535$	16.9443	0.732565
$536$	6.00000	0.259161
$537$	17.2361	0.743791
$538$	−15.5279	−0.669454
$539$	−5.47214	−0.235702
$540$	1.00000	0.0430331
$541$	25.7771	1.10824	0.554122	−	0.832436i	$-0.313054\pi$
$541$	25.7771	1.10824	0.554122	+	0.832436i	$0.313054\pi$
$542$	20.0000	0.859074
$543$	0.472136	0.0202613
$544$	−1.00000	−0.0428746
$545$	6.00000	0.257012
$546$	−4.00000	−0.171184
$547$	31.4164	1.34327	0.671634	−	0.740883i	$-0.265593\pi$
$547$	31.4164	1.34327	0.671634	+	0.740883i	$0.265593\pi$
$548$	19.8885	0.849596
$549$	6.00000	0.256074
$550$	1.00000	0.0426401
$551$	2.69505	0.114813
$552$	0.763932	0.0325151
$553$	12.0000	0.510292
$554$	14.0000	0.594803
$555$	−6.00000	−0.254686
$556$	8.00000	0.339276
$557$	32.8328	1.39117	0.695586	−	0.718443i	$-0.255145\pi$
$557$	32.8328	1.39117	0.695586	+	0.718443i	$0.255145\pi$
$558$	−4.00000	−0.169334
$559$	−4.00000	−0.169182
$560$	1.23607	0.0522334
$561$	1.00000	0.0422200
$562$	−7.52786	−0.317544
$563$	35.7771	1.50782	0.753912	−	0.656975i	$-0.228164\pi$
$563$	35.7771	1.50782	0.753912	+	0.656975i	$0.228164\pi$
$564$	6.47214	0.272526
$565$	10.7639	0.452842
$566$	23.4164	0.984265
$567$	−1.23607	−0.0519100
$568$	−5.23607	−0.219701
$569$	−43.3050	−1.81544	−0.907719	−	0.419579i	$-0.862178\pi$
$569$	−43.3050	−1.81544	−0.907719	+	0.419579i	$0.862178\pi$
$570$	5.70820	0.239090
$571$	9.88854	0.413823	0.206911	−	0.978360i	$-0.433659\pi$
$571$	9.88854	0.413823	0.206911	+	0.978360i	$0.433659\pi$
$572$	−3.23607	−0.135307
$573$	−10.4721	−0.437480
$574$	−11.0557	−0.461457
$575$	−0.763932	−0.0318582
$576$	1.00000	0.0416667
$577$	19.8885	0.827971	0.413985	−	0.910283i	$-0.364136\pi$
$577$	19.8885	0.827971	0.413985	+	0.910283i	$0.364136\pi$
$578$	1.00000	0.0415945
$579$	5.70820	0.237225
$580$	−0.472136	−0.0196044
$581$	16.0000	0.663792
$582$	0	0
$583$	−1.23607	−0.0511927
$584$	−3.23607	−0.133909
$585$	3.23607	0.133795
$586$	−18.0000	−0.743573
$587$	20.1803	0.832932	0.416466	−	0.909151i	$-0.363269\pi$
$587$	20.1803	0.832932	0.416466	+	0.909151i	$0.363269\pi$
$588$	5.47214	0.225667
$589$	−22.8328	−0.940810
$590$	−1.23607	−0.0508881
$591$	2.94427	0.121111
$592$	−6.00000	−0.246598
$593$	−13.4164	−0.550946	−0.275473	−	0.961309i	$-0.588834\pi$
$593$	−13.4164	−0.550946	−0.275473	+	0.961309i	$0.588834\pi$
$594$	−1.00000	−0.0410305
$595$	−1.23607	−0.0506738
$596$	−18.4721	−0.756648
$597$	12.0000	0.491127
$598$	2.47214	0.101093
$599$	31.4164	1.28364	0.641820	−	0.766855i	$-0.278180\pi$
$599$	31.4164	1.28364	0.641820	+	0.766855i	$0.278180\pi$
$600$	−1.00000	−0.0408248
$601$	39.1246	1.59593	0.797963	−	0.602706i	$-0.205911\pi$
$601$	39.1246	1.59593	0.797963	+	0.602706i	$0.205911\pi$
$602$	−1.52786	−0.0622711
$603$	6.00000	0.244339
$604$	−5.52786	−0.224926
$605$	−1.00000	−0.0406558
$606$	8.94427	0.363336
$607$	−11.1246	−0.451534	−0.225767	−	0.974181i	$-0.572489\pi$
$607$	−11.1246	−0.451534	−0.225767	+	0.974181i	$0.572489\pi$
$608$	5.70820	0.231498
$609$	0.583592	0.0236483
$610$	−6.00000	−0.242933
$611$	20.9443	0.847315
$612$	−1.00000	−0.0404226
$613$	−33.1246	−1.33789	−0.668945	−	0.743312i	$-0.733254\pi$
$613$	−33.1246	−1.33789	−0.668945	+	0.743312i	$0.733254\pi$
$614$	23.7082	0.956785
$615$	8.94427	0.360668
$616$	−1.23607	−0.0498026
$617$	−5.23607	−0.210796	−0.105398	−	0.994430i	$-0.533612\pi$
$617$	−5.23607	−0.210796	−0.105398	+	0.994430i	$0.533612\pi$
$618$	−4.00000	−0.160904
$619$	25.8885	1.04055	0.520274	−	0.853999i	$-0.325830\pi$
$619$	25.8885	1.04055	0.520274	+	0.853999i	$0.325830\pi$
$620$	4.00000	0.160644
$621$	0.763932	0.0306555
$622$	6.76393	0.271209
$623$	−13.5279	−0.541982
$624$	3.23607	0.129546
$625$	1.00000	0.0400000
$626$	0	0
$627$	−5.70820	−0.227964
$628$	−7.41641	−0.295947
$629$	6.00000	0.239236
$630$	1.23607	0.0492461
$631$	20.0000	0.796187	0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000	0.796187	0.398094	+	0.917345i	$0.369672\pi$
$632$	−9.70820	−0.386172
$633$	24.3607	0.968250
$634$	−30.9443	−1.22895
$635$	12.0000	0.476205
$636$	1.23607	0.0490133
$637$	17.7082	0.701625
$638$	0.472136	0.0186920
$639$	−5.23607	−0.207136
$640$	−1.00000	−0.0395285
$641$	−22.6525	−0.894719	−0.447360	−	0.894354i	$-0.647636\pi$
$641$	−22.6525	−0.894719	−0.447360	+	0.894354i	$0.647636\pi$
$642$	16.9443	0.668737
$643$	−19.0557	−0.751485	−0.375742	−	0.926724i	$-0.622612\pi$
$643$	−19.0557	−0.751485	−0.375742	+	0.926724i	$0.622612\pi$
$644$	0.944272	0.0372095
$645$	1.23607	0.0486701
$646$	−5.70820	−0.224586
$647$	38.8328	1.52668	0.763338	−	0.646000i	$-0.223559\pi$
$647$	38.8328	1.52668	0.763338	+	0.646000i	$0.223559\pi$
$648$	1.00000	0.0392837
$649$	1.23607	0.0485199
$650$	−3.23607	−0.126929
$651$	−4.94427	−0.193781
$652$	2.47214	0.0968163
$653$	−23.8885	−0.934831	−0.467415	−	0.884038i	$-0.654815\pi$
$653$	−23.8885	−0.934831	−0.467415	+	0.884038i	$0.654815\pi$
$654$	6.00000	0.234619
$655$	0	0
$656$	8.94427	0.349215
$657$	−3.23607	−0.126251
$658$	8.00000	0.311872
$659$	−8.83282	−0.344078	−0.172039	−	0.985090i	$-0.555035\pi$
$659$	−8.83282	−0.344078	−0.172039	+	0.985090i	$0.555035\pi$
$660$	1.00000	0.0389249
$661$	−25.4164	−0.988584	−0.494292	−	0.869296i	$-0.664573\pi$
$661$	−25.4164	−0.988584	−0.494292	+	0.869296i	$0.664573\pi$
$662$	−1.88854	−0.0734003
$663$	−3.23607	−0.125678
$664$	−12.9443	−0.502335
$665$	7.05573	0.273609
$666$	−6.00000	−0.232495
$667$	−0.360680	−0.0139656
$668$	−12.0000	−0.464294
$669$	−3.41641	−0.132086
$670$	−6.00000	−0.231800
$671$	6.00000	0.231627
$672$	1.23607	0.0476824
$673$	−40.7639	−1.57133	−0.785667	−	0.618650i	$-0.787680\pi$
$673$	−40.7639	−1.57133	−0.785667	+	0.618650i	$0.787680\pi$
$674$	9.70820	0.373946
$675$	−1.00000	−0.0384900
$676$	−2.52786	−0.0972255
$677$	−4.11146	−0.158016	−0.0790080	−	0.996874i	$-0.525175\pi$
$677$	−4.11146	−0.158016	−0.0790080	+	0.996874i	$0.525175\pi$
$678$	10.7639	0.413386
$679$	0	0
$680$	1.00000	0.0383482
$681$	0	0
$682$	−4.00000	−0.153168
$683$	47.7771	1.82814	0.914070	−	0.405557i	$-0.132922\pi$
$683$	47.7771	1.82814	0.914070	+	0.405557i	$0.132922\pi$
$684$	5.70820	0.218259
$685$	−19.8885	−0.759902
$686$	15.4164	0.588601
$687$	−2.58359	−0.0985702
$688$	1.23607	0.0471246
$689$	4.00000	0.152388
$690$	−0.763932	−0.0290824
$691$	−10.8328	−0.412100	−0.206050	−	0.978541i	$-0.566061\pi$
$691$	−10.8328	−0.412100	−0.206050	+	0.978541i	$0.566061\pi$
$692$	−13.4164	−0.510015
$693$	−1.23607	−0.0469543
$694$	−4.94427	−0.187682
$695$	−8.00000	−0.303457
$696$	−0.472136	−0.0178963
$697$	−8.94427	−0.338788
$698$	−11.7082	−0.443162
$699$	16.4721	0.623033
$700$	−1.23607	−0.0467190
$701$	17.5279	0.662018	0.331009	−	0.943628i	$-0.392611\pi$
$701$	17.5279	0.662018	0.331009	+	0.943628i	$0.392611\pi$
$702$	3.23607	0.122138
$703$	−34.2492	−1.29173
$704$	1.00000	0.0376889
$705$	−6.47214	−0.243755
$706$	4.47214	0.168311
$707$	11.0557	0.415793
$708$	−1.23607	−0.0464543
$709$	28.8328	1.08284	0.541420	−	0.840753i	$-0.317887\pi$
$709$	28.8328	1.08284	0.541420	+	0.840753i	$0.317887\pi$
$710$	5.23607	0.196506
$711$	−9.70820	−0.364086
$712$	10.9443	0.410154
$713$	3.05573	0.114438
$714$	−1.23607	−0.0462587
$715$	3.23607	0.121022
$716$	−17.2361	−0.644142
$717$	−28.3607	−1.05915
$718$	19.4164	0.724614
$719$	−18.5410	−0.691463	−0.345732	−	0.938333i	$-0.612369\pi$
$719$	−18.5410	−0.691463	−0.345732	+	0.938333i	$0.612369\pi$
$720$	−1.00000	−0.0372678
$721$	−4.94427	−0.184134
$722$	13.5836	0.505529
$723$	18.1803	0.676134
$724$	−0.472136	−0.0175468
$725$	0.472136	0.0175347
$726$	−1.00000	−0.0371135
$727$	34.8328	1.29188	0.645939	−	0.763389i	$-0.276466\pi$
$727$	34.8328	1.29188	0.645939	+	0.763389i	$0.276466\pi$
$728$	4.00000	0.148250
$729$	1.00000	0.0370370
$730$	3.23607	0.119772
$731$	−1.23607	−0.0457176
$732$	−6.00000	−0.221766
$733$	34.6525	1.27992	0.639959	−	0.768409i	$-0.278951\pi$
$733$	34.6525	1.27992	0.639959	+	0.768409i	$0.278951\pi$
$734$	−24.8328	−0.916596
$735$	−5.47214	−0.201843
$736$	−0.763932	−0.0281589
$737$	6.00000	0.221013
$738$	8.94427	0.329243
$739$	41.7082	1.53426	0.767131	−	0.641491i	$-0.221684\pi$
$739$	41.7082	1.53426	0.767131	+	0.641491i	$0.221684\pi$
$740$	6.00000	0.220564
$741$	18.4721	0.678591
$742$	1.52786	0.0560897
$743$	−13.5279	−0.496289	−0.248145	−	0.968723i	$-0.579821\pi$
$743$	−13.5279	−0.496289	−0.248145	+	0.968723i	$0.579821\pi$
$744$	4.00000	0.146647
$745$	18.4721	0.676767
$746$	−2.29180	−0.0839086
$747$	−12.9443	−0.473606
$748$	−1.00000	−0.0365636
$749$	20.9443	0.765287
$750$	1.00000	0.0365148
$751$	−19.4164	−0.708515	−0.354257	−	0.935148i	$-0.615266\pi$
$751$	−19.4164	−0.708515	−0.354257	+	0.935148i	$0.615266\pi$
$752$	−6.47214	−0.236015
$753$	−18.7639	−0.683796
$754$	−1.52786	−0.0556415
$755$	5.52786	0.201180
$756$	1.23607	0.0449554
$757$	−13.8885	−0.504788	−0.252394	−	0.967625i	$-0.581218\pi$
$757$	−13.8885	−0.504788	−0.252394	+	0.967625i	$0.581218\pi$
$758$	−7.05573	−0.256276
$759$	0.763932	0.0277290
$760$	−5.70820	−0.207058
$761$	−27.5279	−0.997884	−0.498942	−	0.866635i	$-0.666278\pi$
$761$	−27.5279	−0.997884	−0.498942	+	0.866635i	$0.666278\pi$
$762$	12.0000	0.434714
$763$	7.41641	0.268492
$764$	10.4721	0.378869
$765$	1.00000	0.0361551
$766$	1.52786	0.0552040
$767$	−4.00000	−0.144432
$768$	−1.00000	−0.0360844
$769$	15.5279	0.559949	0.279975	−	0.960007i	$-0.409674\pi$
$769$	15.5279	0.559949	0.279975	+	0.960007i	$0.409674\pi$
$770$	1.23607	0.0445448
$771$	−4.47214	−0.161060
$772$	−5.70820	−0.205443
$773$	−26.7639	−0.962632	−0.481316	−	0.876547i	$-0.659841\pi$
$773$	−26.7639	−0.962632	−0.481316	+	0.876547i	$0.659841\pi$
$774$	1.23607	0.0444295
$775$	−4.00000	−0.143684
$776$	0	0
$777$	−7.41641	−0.266062
$778$	−23.5967	−0.845984
$779$	51.0557	1.82926
$780$	−3.23607	−0.115870
$781$	−5.23607	−0.187361
$782$	0.763932	0.0273182
$783$	−0.472136	−0.0168728
$784$	−5.47214	−0.195433
$785$	7.41641	0.264703
$786$	0	0
$787$	36.9443	1.31692	0.658461	−	0.752615i	$-0.271208\pi$
$787$	36.9443	1.31692	0.658461	+	0.752615i	$0.271208\pi$
$788$	−2.94427	−0.104885
$789$	12.0000	0.427211
$790$	9.70820	0.345402
$791$	13.3050	0.473070
$792$	1.00000	0.0355335
$793$	−19.4164	−0.689497
$794$	15.8885	0.563863
$795$	−1.23607	−0.0438388
$796$	−12.0000	−0.425329
$797$	−41.0132	−1.45276	−0.726380	−	0.687293i	$-0.758799\pi$
$797$	−41.0132	−1.45276	−0.726380	+	0.687293i	$0.758799\pi$
$798$	7.05573	0.249770
$799$	6.47214	0.228968
$800$	1.00000	0.0353553
$801$	10.9443	0.386697
$802$	−33.7082	−1.19028
$803$	−3.23607	−0.114198
$804$	−6.00000	−0.211604
$805$	−0.944272	−0.0332812
$806$	12.9443	0.455943
$807$	15.5279	0.546607
$808$	−8.94427	−0.314658
$809$	28.3607	0.997108	0.498554	−	0.866859i	$-0.333864\pi$
$809$	28.3607	0.997108	0.498554	+	0.866859i	$0.333864\pi$
$810$	−1.00000	−0.0351364
$811$	50.2492	1.76449	0.882244	−	0.470792i	$-0.156032\pi$
$811$	50.2492	1.76449	0.882244	+	0.470792i	$0.156032\pi$
$812$	−0.583592	−0.0204801
$813$	−20.0000	−0.701431
$814$	−6.00000	−0.210300
$815$	−2.47214	−0.0865951
$816$	1.00000	0.0350070
$817$	7.05573	0.246849
$818$	−6.94427	−0.242801
$819$	4.00000	0.139771
$820$	−8.94427	−0.312348
$821$	34.3607	1.19920	0.599598	−	0.800301i	$-0.295327\pi$
$821$	34.3607	1.19920	0.599598	+	0.800301i	$0.295327\pi$
$822$	−19.8885	−0.693693
$823$	10.5836	0.368921	0.184460	−	0.982840i	$-0.440946\pi$
$823$	10.5836	0.368921	0.184460	+	0.982840i	$0.440946\pi$
$824$	4.00000	0.139347
$825$	−1.00000	−0.0348155
$826$	−1.52786	−0.0531612
$827$	−15.0557	−0.523539	−0.261769	−	0.965130i	$-0.584306\pi$
$827$	−15.0557	−0.523539	−0.261769	+	0.965130i	$0.584306\pi$
$828$	−0.763932	−0.0265485
$829$	21.7771	0.756350	0.378175	−	0.925734i	$-0.376552\pi$
$829$	21.7771	0.756350	0.378175	+	0.925734i	$0.376552\pi$
$830$	12.9443	0.449302
$831$	−14.0000	−0.485655
$832$	−3.23607	−0.112190
$833$	5.47214	0.189598
$834$	−8.00000	−0.277017
$835$	12.0000	0.415277
$836$	5.70820	0.197422
$837$	4.00000	0.138260
$838$	1.52786	0.0527792
$839$	27.7082	0.956593	0.478297	−	0.878198i	$-0.341254\pi$
$839$	27.7082	0.956593	0.478297	+	0.878198i	$0.341254\pi$
$840$	−1.23607	−0.0426484
$841$	−28.7771	−0.992313
$842$	10.9443	0.377165
$843$	7.52786	0.259273
$844$	−24.3607	−0.838529
$845$	2.52786	0.0869612
$846$	−6.47214	−0.222517
$847$	−1.23607	−0.0424718
$848$	−1.23607	−0.0424467
$849$	−23.4164	−0.803649
$850$	−1.00000	−0.0342997
$851$	4.58359	0.157124
$852$	5.23607	0.179385
$853$	30.3607	1.03953	0.519765	−	0.854309i	$-0.326020\pi$
$853$	30.3607	1.03953	0.519765	+	0.854309i	$0.326020\pi$
$854$	−7.41641	−0.253784
$855$	−5.70820	−0.195216
$856$	−16.9443	−0.579143
$857$	15.8885	0.542742	0.271371	−	0.962475i	$-0.412523\pi$
$857$	15.8885	0.542742	0.271371	+	0.962475i	$0.412523\pi$
$858$	3.23607	0.110478
$859$	−4.94427	−0.168696	−0.0843482	−	0.996436i	$-0.526881\pi$
$859$	−4.94427	−0.168696	−0.0843482	+	0.996436i	$0.526881\pi$
$860$	−1.23607	−0.0421496
$861$	11.0557	0.376778
$862$	−22.9443	−0.781485
$863$	−35.0557	−1.19331	−0.596655	−	0.802498i	$-0.703504\pi$
$863$	−35.0557	−1.19331	−0.596655	+	0.802498i	$0.703504\pi$
$864$	−1.00000	−0.0340207
$865$	13.4164	0.456172
$866$	−6.00000	−0.203888
$867$	−1.00000	−0.0339618
$868$	4.94427	0.167820
$869$	−9.70820	−0.329328
$870$	0.472136	0.0160069
$871$	−19.4164	−0.657900
$872$	−6.00000	−0.203186
$873$	0	0
$874$	−4.36068	−0.147502
$875$	1.23607	0.0417867
$876$	3.23607	0.109337
$877$	−2.36068	−0.0797145	−0.0398572	−	0.999205i	$-0.512690\pi$
$877$	−2.36068	−0.0797145	−0.0398572	+	0.999205i	$0.512690\pi$
$878$	−17.7082	−0.597623
$879$	18.0000	0.607125
$880$	−1.00000	−0.0337100
$881$	−8.18034	−0.275603	−0.137801	−	0.990460i	$-0.544004\pi$
$881$	−8.18034	−0.275603	−0.137801	+	0.990460i	$0.544004\pi$
$882$	−5.47214	−0.184256
$883$	6.58359	0.221556	0.110778	−	0.993845i	$-0.464666\pi$
$883$	6.58359	0.221556	0.110778	+	0.993845i	$0.464666\pi$
$884$	3.23607	0.108841
$885$	1.23607	0.0415500
$886$	−34.6525	−1.16417
$887$	32.7214	1.09868	0.549338	−	0.835600i	$-0.314880\pi$
$887$	32.7214	1.09868	0.549338	+	0.835600i	$0.314880\pi$
$888$	6.00000	0.201347
$889$	14.8328	0.497477
$890$	−10.9443	−0.366853
$891$	1.00000	0.0335013
$892$	3.41641	0.114390
$893$	−36.9443	−1.23629
$894$	18.4721	0.617801
$895$	17.2361	0.576138
$896$	−1.23607	−0.0412941
$897$	−2.47214	−0.0825422
$898$	−16.1803	−0.539945
$899$	−1.88854	−0.0629865
$900$	1.00000	0.0333333
$901$	1.23607	0.0411794
$902$	8.94427	0.297812
$903$	1.52786	0.0508441
$904$	−10.7639	−0.358003
$905$	0.472136	0.0156943
$906$	5.52786	0.183651
$907$	14.8328	0.492516	0.246258	−	0.969204i	$-0.420799\pi$
$907$	14.8328	0.492516	0.246258	+	0.969204i	$0.420799\pi$
$908$	0	0
$909$	−8.94427	−0.296663
$910$	−4.00000	−0.132599
$911$	26.7639	0.886729	0.443364	−	0.896342i	$-0.353785\pi$
$911$	26.7639	0.886729	0.443364	+	0.896342i	$0.353785\pi$
$912$	−5.70820	−0.189018
$913$	−12.9443	−0.428393
$914$	18.0000	0.595387
$915$	6.00000	0.198354
$916$	2.58359	0.0853643
$917$	0	0
$918$	1.00000	0.0330049
$919$	2.47214	0.0815482	0.0407741	−	0.999168i	$-0.487018\pi$
$919$	2.47214	0.0815482	0.0407741	+	0.999168i	$0.487018\pi$
$920$	0.763932	0.0251861
$921$	−23.7082	−0.781212
$922$	−19.4164	−0.639445
$923$	16.9443	0.557728
$924$	1.23607	0.0406637
$925$	−6.00000	−0.197279
$926$	−24.3607	−0.800542
$927$	4.00000	0.131377
$928$	0.472136	0.0154986
$929$	−43.0132	−1.41122	−0.705608	−	0.708602i	$-0.749326\pi$
$929$	−43.0132	−1.41122	−0.705608	+	0.708602i	$0.749326\pi$
$930$	−4.00000	−0.131165
$931$	−31.2361	−1.02372
$932$	−16.4721	−0.539563
$933$	−6.76393	−0.221441
$934$	19.2361	0.629423
$935$	1.00000	0.0327035
$936$	−3.23607	−0.105774
$937$	20.2492	0.661513	0.330757	−	0.943716i	$-0.392696\pi$
$937$	20.2492	0.661513	0.330757	+	0.943716i	$0.392696\pi$
$938$	−7.41641	−0.242154
$939$	0	0
$940$	6.47214	0.211098
$941$	3.52786	0.115005	0.0575025	−	0.998345i	$-0.481686\pi$
$941$	3.52786	0.115005	0.0575025	+	0.998345i	$0.481686\pi$
$942$	7.41641	0.241640
$943$	−6.83282	−0.222507
$944$	1.23607	0.0402306
$945$	−1.23607	−0.0402093
$946$	1.23607	0.0401880
$947$	−44.7214	−1.45325	−0.726624	−	0.687035i	$-0.758912\pi$
$947$	−44.7214	−1.45325	−0.726624	+	0.687035i	$0.758912\pi$
$948$	9.70820	0.315308
$949$	10.4721	0.339940
$950$	5.70820	0.185199
$951$	30.9443	1.00344
$952$	1.23607	0.0400612
$953$	−19.3050	−0.625349	−0.312674	−	0.949860i	$-0.601225\pi$
$953$	−19.3050	−0.625349	−0.312674	+	0.949860i	$0.601225\pi$
$954$	−1.23607	−0.0400192
$955$	−10.4721	−0.338870
$956$	28.3607	0.917250
$957$	−0.472136	−0.0152620
$958$	−36.4721	−1.17836
$959$	−24.5836	−0.793846
$960$	1.00000	0.0322749
$961$	−15.0000	−0.483871
$962$	19.4164	0.626010
$963$	−16.9443	−0.546022
$964$	−18.1803	−0.585549
$965$	5.70820	0.183754
$966$	−0.944272	−0.0303815
$967$	19.4164	0.624390	0.312195	−	0.950018i	$-0.398936\pi$
$967$	19.4164	0.624390	0.312195	+	0.950018i	$0.398936\pi$
$968$	1.00000	0.0321412
$969$	5.70820	0.183374
$970$	0	0
$971$	53.2361	1.70843	0.854213	−	0.519923i	$-0.174039\pi$
$971$	53.2361	1.70843	0.854213	+	0.519923i	$0.174039\pi$
$972$	−1.00000	−0.0320750
$973$	−9.88854	−0.317012
$974$	32.8328	1.05203
$975$	3.23607	0.103637
$976$	6.00000	0.192055
$977$	−16.4721	−0.526990	−0.263495	−	0.964661i	$-0.584875\pi$
$977$	−16.4721	−0.526990	−0.263495	+	0.964661i	$0.584875\pi$
$978$	−2.47214	−0.0790502
$979$	10.9443	0.349780
$980$	5.47214	0.174801
$981$	−6.00000	−0.191565
$982$	18.9443	0.604536
$983$	−30.6525	−0.977662	−0.488831	−	0.872378i	$-0.662577\pi$
$983$	−30.6525	−0.977662	−0.488831	+	0.872378i	$0.662577\pi$
$984$	−8.94427	−0.285133
$985$	2.94427	0.0938123
$986$	−0.472136	−0.0150359
$987$	−8.00000	−0.254643
$988$	−18.4721	−0.587677
$989$	−0.944272	−0.0300261
$990$	−1.00000	−0.0317821
$991$	−46.2492	−1.46916	−0.734578	−	0.678525i	$-0.762620\pi$
$991$	−46.2492	−1.46916	−0.734578	+	0.678525i	$0.762620\pi$
$992$	−4.00000	−0.127000
$993$	1.88854	0.0599311
$994$	6.47214	0.205284
$995$	12.0000	0.380426
$996$	12.9443	0.410155
$997$	50.3607	1.59494	0.797469	−	0.603359i	$-0.206172\pi$
$997$	50.3607	1.59494	0.797469	+	0.603359i	$0.206172\pi$
$998$	30.8328	0.975996
$999$	6.00000	0.189832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.bu.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.bu.1.1	✓	2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5610.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.23607 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} -3.23607 q^{13} -1.23607 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +5.70820 q^{19} -1.00000 q^{20} +1.23607 q^{21} +1.00000 q^{22} -0.763932 q^{23} -1.00000 q^{24} +1.00000 q^{25} -3.23607 q^{26} -1.00000 q^{27} -1.23607 q^{28} +0.472136 q^{29} +1.00000 q^{30} -4.00000 q^{31} +1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +1.23607 q^{35} +1.00000 q^{36} -6.00000 q^{37} +5.70820 q^{38} +3.23607 q^{39} -1.00000 q^{40} +8.94427 q^{41} +1.23607 q^{42} +1.23607 q^{43} +1.00000 q^{44} -1.00000 q^{45} -0.763932 q^{46} -6.47214 q^{47} -1.00000 q^{48} -5.47214 q^{49} +1.00000 q^{50} +1.00000 q^{51} -3.23607 q^{52} -1.23607 q^{53} -1.00000 q^{54} -1.00000 q^{55} -1.23607 q^{56} -5.70820 q^{57} +0.472136 q^{58} +1.23607 q^{59} +1.00000 q^{60} +6.00000 q^{61} -4.00000 q^{62} -1.23607 q^{63} +1.00000 q^{64} +3.23607 q^{65} -1.00000 q^{66} +6.00000 q^{67} -1.00000 q^{68} +0.763932 q^{69} +1.23607 q^{70} -5.23607 q^{71} +1.00000 q^{72} -3.23607 q^{73} -6.00000 q^{74} -1.00000 q^{75} +5.70820 q^{76} -1.23607 q^{77} +3.23607 q^{78} -9.70820 q^{79} -1.00000 q^{80} +1.00000 q^{81} +8.94427 q^{82} -12.9443 q^{83} +1.23607 q^{84} +1.00000 q^{85} +1.23607 q^{86} -0.472136 q^{87} +1.00000 q^{88} +10.9443 q^{89} -1.00000 q^{90} +4.00000 q^{91} -0.763932 q^{92} +4.00000 q^{93} -6.47214 q^{94} -5.70820 q^{95} -1.00000 q^{96} -5.47214 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} - 2 q^{13} + 2 q^{14} + 2 q^{15} + 2 q^{16} - 2 q^{17} + 2 q^{18} - 2 q^{19} - 2 q^{20}+ \cdots + 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^12 - 2 * q^13 + 2 * q^14 + 2 * q^15 + 2 * q^16 - 2 * q^17 + 2 * q^18 - 2 * q^19 - 2 * q^20 - 2 * q^21 + 2 * q^22 - 6 * q^23 - 2 * q^24 + 2 * q^25 - 2 * q^26 - 2 * q^27 + 2 * q^28 - 8 * q^29 + 2 * q^30 - 8 * q^31 + 2 * q^32 - 2 * q^33 - 2 * q^34 - 2 * q^35 + 2 * q^36 - 12 * q^37 - 2 * q^38 + 2 * q^39 - 2 * q^40 - 2 * q^42 - 2 * q^43 + 2 * q^44 - 2 * q^45 - 6 * q^46 - 4 * q^47 - 2 * q^48 - 2 * q^49 + 2 * q^50 + 2 * q^51 - 2 * q^52 + 2 * q^53 - 2 * q^54 - 2 * q^55 + 2 * q^56 + 2 * q^57 - 8 * q^58 - 2 * q^59 + 2 * q^60 + 12 * q^61 - 8 * q^62 + 2 * q^63 + 2 * q^64 + 2 * q^65 - 2 * q^66 + 12 * q^67 - 2 * q^68 + 6 * q^69 - 2 * q^70 - 6 * q^71 + 2 * q^72 - 2 * q^73 - 12 * q^74 - 2 * q^75 - 2 * q^76 + 2 * q^77 + 2 * q^78 - 6 * q^79 - 2 * q^80 + 2 * q^81 - 8 * q^83 - 2 * q^84 + 2 * q^85 - 2 * q^86 + 8 * q^87 + 2 * q^88 + 4 * q^89 - 2 * q^90 + 8 * q^91 - 6 * q^92 + 8 * q^93 - 4 * q^94 + 2 * q^95 - 2 * q^96 - 2 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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