LMFDB - Embedded newform 1166.2.a.h.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1166,2,Mod(1,1166)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1166, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1166.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1166 = 2 \cdot 11 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1166.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,-4,0,4,2,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$9.31055687568$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.6224.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 6x^{2} - 2x + 5 $ x^4 - 6x^2 - 2x + 5
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.796815$ of defining polynomial
Character	$\chi$	$=$	1166.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +0.796815 q^{3} +1.00000 q^{4} +1.51945 q^{5} -0.796815 q^{6} -4.16190 q^{7} -1.00000 q^{8} -2.36509 q^{9} -1.51945 q^{10} +1.00000 q^{11} +0.796815 q^{12} +2.21072 q^{13} +4.16190 q^{14} +1.21072 q^{15} +1.00000 q^{16} -5.06426 q^{17} +2.36509 q^{18} +2.21072 q^{19} +1.51945 q^{20} -3.31627 q^{21} -1.00000 q^{22} +4.95872 q^{23} -0.796815 q^{24} -2.69127 q^{25} -2.21072 q^{26} -4.27498 q^{27} -4.16190 q^{28} -5.29091 q^{29} -1.21072 q^{30} -7.95872 q^{31} -1.00000 q^{32} +0.796815 q^{33} +5.06426 q^{34} -6.32380 q^{35} -2.36509 q^{36} +5.42935 q^{37} -2.21072 q^{38} +1.76154 q^{39} -1.51945 q^{40} -7.10316 q^{41} +3.31627 q^{42} -3.96864 q^{43} +1.00000 q^{44} -3.59363 q^{45} -4.95872 q^{46} -11.4833 q^{47} +0.796815 q^{48} +10.3214 q^{49} +2.69127 q^{50} -4.03528 q^{51} +2.21072 q^{52} +1.00000 q^{53} +4.27498 q^{54} +1.51945 q^{55} +4.16190 q^{56} +1.76154 q^{57} +5.29091 q^{58} -3.99008 q^{59} +1.21072 q^{60} -14.9563 q^{61} +7.95872 q^{62} +9.84325 q^{63} +1.00000 q^{64} +3.35908 q^{65} -0.796815 q^{66} +11.6865 q^{67} -5.06426 q^{68} +3.95118 q^{69} +6.32380 q^{70} +5.89998 q^{71} +2.36509 q^{72} -8.75363 q^{73} -5.42935 q^{74} -2.14445 q^{75} +2.21072 q^{76} -4.16190 q^{77} -1.76154 q^{78} +8.62224 q^{79} +1.51945 q^{80} +3.68889 q^{81} +7.10316 q^{82} +8.68926 q^{83} -3.31627 q^{84} -7.69489 q^{85} +3.96864 q^{86} -4.21587 q^{87} -1.00000 q^{88} +6.91505 q^{89} +3.59363 q^{90} -9.20080 q^{91} +4.95872 q^{92} -6.34163 q^{93} +11.4833 q^{94} +3.35908 q^{95} -0.796815 q^{96} -7.15400 q^{97} -10.3214 q^{98} -2.36509 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 4 q^{7} - 4 q^{8} - 2 q^{10} + 4 q^{11} - 6 q^{13} + 4 q^{14} - 10 q^{15} + 4 q^{16} - 12 q^{17} - 6 q^{19} + 2 q^{20} - 6 q^{21} - 4 q^{22} + 4 q^{23} + 6 q^{26} + 6 q^{27}+ \cdots + 8 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 4 * q^7 - 4 * q^8 - 2 * q^10 + 4 * q^11 - 6 * q^13 + 4 * q^14 - 10 * q^15 + 4 * q^16 - 12 * q^17 - 6 * q^19 + 2 * q^20 - 6 * q^21 - 4 * q^22 + 4 * q^23 + 6 * q^26 + 6 * q^27 - 4 * q^28 - 14 * q^29 + 10 * q^30 - 16 * q^31 - 4 * q^32 + 12 * q^34 + 4 * q^37 + 6 * q^38 - 2 * q^39 - 2 * q^40 - 12 * q^41 + 6 * q^42 - 6 * q^43 + 4 * q^44 - 8 * q^45 - 4 * q^46 + 16 * q^47 - 8 * q^49 - 22 * q^51 - 6 * q^52 + 4 * q^53 - 6 * q^54 + 2 * q^55 + 4 * q^56 - 2 * q^57 + 14 * q^58 - 10 * q^59 - 10 * q^60 - 20 * q^61 + 16 * q^62 + 10 * q^63 + 4 * q^64 - 6 * q^65 - 12 * q^67 - 12 * q^68 + 18 * q^69 + 4 * q^71 - 14 * q^73 - 4 * q^74 - 8 * q^75 - 6 * q^76 - 4 * q^77 + 2 * q^78 - 16 * q^79 + 2 * q^80 - 20 * q^81 + 12 * q^82 + 30 * q^83 - 6 * q^84 - 6 * q^85 + 6 * q^86 + 40 * q^87 - 4 * q^88 - 28 * q^89 + 8 * q^90 - 16 * q^91 + 4 * q^92 - 18 * q^93 - 16 * q^94 - 6 * q^95 - 4 * q^97 + 8 * q^98

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.796815	0.460041	0.230021	−	0.973186i	$-0.426121\pi$
$3$	0.796815	0.460041	0.230021	+	0.973186i	$0.426121\pi$
$4$	1.00000	0.500000
$5$	1.51945	0.679519	0.339759	−	0.940512i	$-0.389654\pi$
$5$	1.51945	0.679519	0.339759	+	0.940512i	$0.389654\pi$
$6$	−0.796815	−0.325298
$7$	−4.16190	−1.57305	−0.786525	−	0.617558i	$-0.788122\pi$
$7$	−4.16190	−1.57305	−0.786525	+	0.617558i	$0.788122\pi$
$8$	−1.00000	−0.353553
$9$	−2.36509	−0.788362
$10$	−1.51945	−0.480492
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.796815	0.230021
$13$	2.21072	0.613144	0.306572	−	0.951848i	$-0.400818\pi$
$13$	2.21072	0.613144	0.306572	+	0.951848i	$0.400818\pi$
$14$	4.16190	1.11231
$15$	1.21072	0.312607
$16$	1.00000	0.250000
$17$	−5.06426	−1.22826	−0.614132	−	0.789203i	$-0.710494\pi$
$17$	−5.06426	−1.22826	−0.614132	+	0.789203i	$0.710494\pi$
$18$	2.36509	0.557456
$19$	2.21072	0.507174	0.253587	−	0.967313i	$-0.418390\pi$
$19$	2.21072	0.507174	0.253587	+	0.967313i	$0.418390\pi$
$20$	1.51945	0.339759
$21$	−3.31627	−0.723668
$22$	−1.00000	−0.213201
$23$	4.95872	1.03396	0.516982	−	0.855996i	$-0.327055\pi$
$23$	4.95872	1.03396	0.516982	+	0.855996i	$0.327055\pi$
$24$	−0.796815	−0.162649
$25$	−2.69127	−0.538254
$26$	−2.21072	−0.433558
$27$	−4.27498	−0.822721
$28$	−4.16190	−0.786525
$29$	−5.29091	−0.982497	−0.491248	−	0.871020i	$-0.663459\pi$
$29$	−5.29091	−0.982497	−0.491248	+	0.871020i	$0.663459\pi$
$30$	−1.21072	−0.221046
$31$	−7.95872	−1.42943	−0.714714	−	0.699417i	$-0.753443\pi$
$31$	−7.95872	−1.42943	−0.714714	+	0.699417i	$0.753443\pi$
$32$	−1.00000	−0.176777
$33$	0.796815	0.138708
$34$	5.06426	0.868513
$35$	−6.32380	−1.06892
$36$	−2.36509	−0.394181
$37$	5.42935	0.892579	0.446289	−	0.894889i	$-0.352745\pi$
$37$	5.42935	0.892579	0.446289	+	0.894889i	$0.352745\pi$
$38$	−2.21072	−0.358626
$39$	1.76154	0.282071
$40$	−1.51945	−0.240246
$41$	−7.10316	−1.10933	−0.554664	−	0.832075i	$-0.687153\pi$
$41$	−7.10316	−1.10933	−0.554664	+	0.832075i	$0.687153\pi$
$42$	3.31627	0.511711
$43$	−3.96864	−0.605211	−0.302606	−	0.953116i	$-0.597856\pi$
$43$	−3.96864	−0.605211	−0.302606	+	0.953116i	$0.597856\pi$
$44$	1.00000	0.150756
$45$	−3.59363	−0.535707
$46$	−4.95872	−0.731123
$47$	−11.4833	−1.67501	−0.837507	−	0.546426i	$-0.815988\pi$
$47$	−11.4833	−1.67501	−0.837507	+	0.546426i	$0.815988\pi$
$48$	0.796815	0.115010
$49$	10.3214	1.47449
$50$	2.69127	0.380603
$51$	−4.03528	−0.565052
$52$	2.21072	0.306572
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	4.27498	0.581751
$55$	1.51945	0.204883
$56$	4.16190	0.556157
$57$	1.76154	0.233321
$58$	5.29091	0.694730
$59$	−3.99008	−0.519464	−0.259732	−	0.965681i	$-0.583634\pi$
$59$	−3.99008	−0.519464	−0.259732	+	0.965681i	$0.583634\pi$
$60$	1.21072	0.156303
$61$	−14.9563	−1.91496	−0.957481	−	0.288496i	$-0.906845\pi$
$61$	−14.9563	−1.91496	−0.957481	+	0.288496i	$0.906845\pi$
$62$	7.95872	1.01076
$63$	9.84325	1.24013
$64$	1.00000	0.125000
$65$	3.35908	0.416643
$66$	−0.796815	−0.0980812
$67$	11.6865	1.42773	0.713867	−	0.700281i	$-0.246942\pi$
$67$	11.6865	1.42773	0.713867	+	0.700281i	$0.246942\pi$
$68$	−5.06426	−0.614132
$69$	3.95118	0.475666
$70$	6.32380	0.755839
$71$	5.89998	0.700198	0.350099	−	0.936713i	$-0.386148\pi$
$71$	5.89998	0.700198	0.350099	+	0.936713i	$0.386148\pi$
$72$	2.36509	0.278728
$73$	−8.75363	−1.02454	−0.512268	−	0.858826i	$-0.671194\pi$
$73$	−8.75363	−1.02454	−0.512268	+	0.858826i	$0.671194\pi$
$74$	−5.42935	−0.631149
$75$	−2.14445	−0.247619
$76$	2.21072	0.253587
$77$	−4.16190	−0.474293
$78$	−1.76154	−0.199455
$79$	8.62224	0.970078	0.485039	−	0.874492i	$-0.338805\pi$
$79$	8.62224	0.970078	0.485039	+	0.874492i	$0.338805\pi$
$80$	1.51945	0.169880
$81$	3.68889	0.409876
$82$	7.10316	0.784413
$83$	8.68926	0.953770	0.476885	−	0.878966i	$-0.341766\pi$
$83$	8.68926	0.953770	0.476885	+	0.878966i	$0.341766\pi$
$84$	−3.31627	−0.361834
$85$	−7.69489	−0.834628
$86$	3.96864	0.427949
$87$	−4.21587	−0.451989
$88$	−1.00000	−0.106600
$89$	6.91505	0.732994	0.366497	−	0.930419i	$-0.380557\pi$
$89$	6.91505	0.732994	0.366497	+	0.930419i	$0.380557\pi$
$90$	3.59363	0.378802
$91$	−9.20080	−0.964506
$92$	4.95872	0.516982
$93$	−6.34163	−0.657596
$94$	11.4833	1.18441
$95$	3.35908	0.344634
$96$	−0.796815	−0.0813246
$97$	−7.15400	−0.726378	−0.363189	−	0.931715i	$-0.618312\pi$
$97$	−7.15400	−0.726378	−0.363189	+	0.931715i	$0.618312\pi$
$98$	−10.3214	−1.04262
$99$	−2.36509	−0.237700
$100$	−2.69127	−0.269127
$101$	−17.5032	−1.74163	−0.870815	−	0.491611i	$-0.836408\pi$
$101$	−17.5032	−1.74163	−0.870815	+	0.491611i	$0.836408\pi$
$102$	4.03528	0.399552
$103$	−12.3429	−1.21618	−0.608089	−	0.793869i	$-0.708064\pi$
$103$	−12.3429	−1.21618	−0.608089	+	0.793869i	$0.708064\pi$
$104$	−2.21072	−0.216779
$105$	−5.03890	−0.491746
$106$	−1.00000	−0.0971286
$107$	12.1984	1.17927	0.589633	−	0.807671i	$-0.299272\pi$
$107$	12.1984	1.17927	0.589633	+	0.807671i	$0.299272\pi$
$108$	−4.27498	−0.411360
$109$	−15.8155	−1.51485	−0.757426	−	0.652922i	$-0.773543\pi$
$109$	−15.8155	−1.51485	−0.757426	+	0.652922i	$0.773543\pi$
$110$	−1.51945	−0.144874
$111$	4.32618	0.410623
$112$	−4.16190	−0.393263
$113$	13.6278	1.28199	0.640996	−	0.767544i	$-0.278521\pi$
$113$	13.6278	1.28199	0.640996	+	0.767544i	$0.278521\pi$
$114$	−1.76154	−0.164983
$115$	7.53452	0.702598
$116$	−5.29091	−0.491248
$117$	−5.22854	−0.483379
$118$	3.99008	0.367317
$119$	21.0769	1.93212
$120$	−1.21072	−0.110523
$121$	1.00000	0.0909091
$122$	14.9563	1.35408
$123$	−5.65991	−0.510337
$124$	−7.95872	−0.714714
$125$	−11.6865	−1.04527
$126$	−9.84325	−0.876907
$127$	11.8095	1.04792	0.523962	−	0.851742i	$-0.324453\pi$
$127$	11.8095	1.04792	0.523962	+	0.851742i	$0.324453\pi$
$128$	−1.00000	−0.0883883
$129$	−3.16227	−0.278422
$130$	−3.35908	−0.294611
$131$	3.94089	0.344317	0.172159	−	0.985069i	$-0.444926\pi$
$131$	3.94089	0.344317	0.172159	+	0.985069i	$0.444926\pi$
$132$	0.796815	0.0693539
$133$	−9.20080	−0.797811
$134$	−11.6865	−1.00956
$135$	−6.49562	−0.559054
$136$	5.06426	0.434257
$137$	−10.3504	−0.884294	−0.442147	−	0.896943i	$-0.645783\pi$
$137$	−10.3504	−0.884294	−0.442147	+	0.896943i	$0.645783\pi$
$138$	−3.95118	−0.336347
$139$	−22.3651	−1.89698	−0.948491	−	0.316804i	$-0.897390\pi$
$139$	−22.3651	−1.89698	−0.948491	+	0.316804i	$0.897390\pi$
$140$	−6.32380	−0.534459
$141$	−9.15008	−0.770576
$142$	−5.89998	−0.495115
$143$	2.21072	0.184870
$144$	−2.36509	−0.197090
$145$	−8.03927	−0.667625
$146$	8.75363	0.724456
$147$	8.22426	0.678326
$148$	5.42935	0.446289
$149$	−1.72655	−0.141444	−0.0707222	−	0.997496i	$-0.522530\pi$
$149$	−1.72655	−0.141444	−0.0707222	+	0.997496i	$0.522530\pi$
$150$	2.14445	0.175093
$151$	−10.3512	−0.842367	−0.421183	−	0.906975i	$-0.638385\pi$
$151$	−10.3512	−0.842367	−0.421183	+	0.906975i	$0.638385\pi$
$152$	−2.21072	−0.179313
$153$	11.9774	0.968316
$154$	4.16190	0.335376
$155$	−12.0929	−0.971323
$156$	1.76154	0.141036
$157$	22.7687	1.81714	0.908570	−	0.417732i	$-0.137175\pi$
$157$	22.7687	1.81714	0.908570	+	0.417732i	$0.137175\pi$
$158$	−8.62224	−0.685949
$159$	0.796815	0.0631915
$160$	−1.51945	−0.120123
$161$	−20.6377	−1.62648
$162$	−3.68889	−0.289826
$163$	−13.9853	−1.09541	−0.547707	−	0.836670i	$-0.684499\pi$
$163$	−13.9853	−1.09541	−0.547707	+	0.836670i	$0.684499\pi$
$164$	−7.10316	−0.554664
$165$	1.21072	0.0942545
$166$	−8.68926	−0.674417
$167$	10.4139	0.805852	0.402926	−	0.915233i	$-0.367993\pi$
$167$	10.4139	0.805852	0.402926	+	0.915233i	$0.367993\pi$
$168$	3.31627	0.255855
$169$	−8.11271	−0.624055
$170$	7.69489	0.590171
$171$	−5.22854	−0.399837
$172$	−3.96864	−0.302606
$173$	5.13292	0.390249	0.195124	−	0.980779i	$-0.437489\pi$
$173$	5.13292	0.390249	0.195124	+	0.980779i	$0.437489\pi$
$174$	4.21587	0.319605
$175$	11.2008	0.846701
$176$	1.00000	0.0753778
$177$	−3.17936	−0.238975
$178$	−6.91505	−0.518305
$179$	15.3008	1.14364	0.571819	−	0.820380i	$-0.306238\pi$
$179$	15.3008	1.14364	0.571819	+	0.820380i	$0.306238\pi$
$180$	−3.59363	−0.267853
$181$	−1.76030	−0.130842	−0.0654210	−	0.997858i	$-0.520839\pi$
$181$	−1.76030	−0.130842	−0.0654210	+	0.997858i	$0.520839\pi$
$182$	9.20080	0.682009
$183$	−11.9174	−0.880962
$184$	−4.95872	−0.365561
$185$	8.24962	0.606524
$186$	6.34163	0.464991
$187$	−5.06426	−0.370335
$188$	−11.4833	−0.837507
$189$	17.7920	1.29418
$190$	−3.35908	−0.243693
$191$	18.9754	1.37301	0.686506	−	0.727124i	$-0.259144\pi$
$191$	18.9754	1.37301	0.686506	+	0.727124i	$0.259144\pi$
$192$	0.796815	0.0575052
$193$	9.11670	0.656235	0.328117	−	0.944637i	$-0.393586\pi$
$193$	9.11670	0.656235	0.328117	+	0.944637i	$0.393586\pi$
$194$	7.15400	0.513627
$195$	2.67657	0.191673
$196$	10.3214	0.737244
$197$	16.9658	1.20876	0.604380	−	0.796696i	$-0.293421\pi$
$197$	16.9658	1.20876	0.604380	+	0.796696i	$0.293421\pi$
$198$	2.36509	0.168079
$199$	18.9479	1.34318	0.671592	−	0.740921i	$-0.265611\pi$
$199$	18.9479	1.34318	0.671592	+	0.740921i	$0.265611\pi$
$200$	2.69127	0.190302
$201$	9.31198	0.656817
$202$	17.5032	1.23152
$203$	22.0202	1.54552
$204$	−4.03528	−0.282526
$205$	−10.7929	−0.753809
$206$	12.3429	0.859968
$207$	−11.7278	−0.815138
$208$	2.21072	0.153286
$209$	2.21072	0.152919
$210$	5.03890	0.347717
$211$	−6.70243	−0.461414	−0.230707	−	0.973023i	$-0.574104\pi$
$211$	−6.70243	−0.461414	−0.230707	+	0.973023i	$0.574104\pi$
$212$	1.00000	0.0686803
$213$	4.70119	0.322120
$214$	−12.1984	−0.833867
$215$	−6.03014	−0.411252
$216$	4.27498	0.290876
$217$	33.1234	2.24856
$218$	15.8155	1.07116
$219$	−6.97503	−0.471329
$220$	1.51945	0.102441
$221$	−11.1957	−0.753102
$222$	−4.32618	−0.290355
$223$	−8.97931	−0.601299	−0.300649	−	0.953735i	$-0.597203\pi$
$223$	−8.97931	−0.601299	−0.300649	+	0.953735i	$0.597203\pi$
$224$	4.16190	0.278079
$225$	6.36509	0.424339
$226$	−13.6278	−0.906505
$227$	2.32429	0.154268	0.0771341	−	0.997021i	$-0.475423\pi$
$227$	2.32429	0.154268	0.0771341	+	0.997021i	$0.475423\pi$
$228$	1.76154	0.116661
$229$	17.2820	1.14203	0.571014	−	0.820940i	$-0.306550\pi$
$229$	17.2820	1.14203	0.571014	+	0.820940i	$0.306550\pi$
$230$	−7.53452	−0.496812
$231$	−3.31627	−0.218194
$232$	5.29091	0.347365
$233$	13.2651	0.869023	0.434512	−	0.900666i	$-0.356921\pi$
$233$	13.2651	0.869023	0.434512	+	0.900666i	$0.356921\pi$
$234$	5.22854	0.341801
$235$	−17.4483	−1.13820
$236$	−3.99008	−0.259732
$237$	6.87033	0.446276
$238$	−21.0769	−1.36622
$239$	−4.22415	−0.273237	−0.136619	−	0.990624i	$-0.543623\pi$
$239$	−4.22415	−0.273237	−0.136619	+	0.990624i	$0.543623\pi$
$240$	1.21072	0.0781517
$241$	1.92497	0.123998	0.0619990	−	0.998076i	$-0.480252\pi$
$241$	1.92497	0.123998	0.0619990	+	0.998076i	$0.480252\pi$
$242$	−1.00000	−0.0642824
$243$	15.7643	1.01128
$244$	−14.9563	−0.957481
$245$	15.6829	1.00194
$246$	5.65991	0.360862
$247$	4.88729	0.310971
$248$	7.95872	0.505379
$249$	6.92373	0.438774
$250$	11.6865	0.739119
$251$	−23.1198	−1.45931	−0.729653	−	0.683817i	$-0.760319\pi$
$251$	−23.1198	−1.45931	−0.729653	+	0.683817i	$0.760319\pi$
$252$	9.84325	0.620067
$253$	4.95872	0.311752
$254$	−11.8095	−0.740994
$255$	−6.13141	−0.383964
$256$	1.00000	0.0625000
$257$	−22.0924	−1.37809	−0.689043	−	0.724721i	$-0.741969\pi$
$257$	−22.0924	−1.37809	−0.689043	+	0.724721i	$0.741969\pi$
$258$	3.16227	0.196874
$259$	−22.5964	−1.40407
$260$	3.35908	0.208321
$261$	12.5134	0.774563
$262$	−3.94089	−0.243469
$263$	23.2023	1.43072	0.715359	−	0.698758i	$-0.246263\pi$
$263$	23.2023	1.43072	0.715359	+	0.698758i	$0.246263\pi$
$264$	−0.796815	−0.0490406
$265$	1.51945	0.0933391
$266$	9.20080	0.564137
$267$	5.51002	0.337207
$268$	11.6865	0.713867
$269$	−4.56790	−0.278510	−0.139255	−	0.990257i	$-0.544471\pi$
$269$	−4.56790	−0.278510	−0.139255	+	0.990257i	$0.544471\pi$
$270$	6.49562	0.395311
$271$	14.5452	0.883558	0.441779	−	0.897124i	$-0.354348\pi$
$271$	14.5452	0.883558	0.441779	+	0.897124i	$0.354348\pi$
$272$	−5.06426	−0.307066
$273$	−7.33134	−0.443713
$274$	10.3504	0.625290
$275$	−2.69127	−0.162290
$276$	3.95118	0.237833
$277$	−16.4873	−0.990626	−0.495313	−	0.868714i	$-0.664947\pi$
$277$	−16.4873	−0.990626	−0.495313	+	0.868714i	$0.664947\pi$
$278$	22.3651	1.34137
$279$	18.8230	1.12691
$280$	6.32380	0.377919
$281$	−10.4270	−0.622020	−0.311010	−	0.950407i	$-0.600667\pi$
$281$	−10.4270	−0.622020	−0.311010	+	0.950407i	$0.600667\pi$
$282$	9.15008	0.544879
$283$	−13.0751	−0.777231	−0.388616	−	0.921400i	$-0.627047\pi$
$283$	−13.0751	−0.777231	−0.388616	+	0.921400i	$0.627047\pi$
$284$	5.89998	0.350099
$285$	2.67657	0.158546
$286$	−2.21072	−0.130723
$287$	29.5627	1.74503
$288$	2.36509	0.139364
$289$	8.64673	0.508631
$290$	8.03927	0.472082
$291$	−5.70041	−0.334164
$292$	−8.75363	−0.512268
$293$	−0.713493	−0.0416827	−0.0208414	−	0.999783i	$-0.506634\pi$
$293$	−0.713493	−0.0416827	−0.0208414	+	0.999783i	$0.506634\pi$
$294$	−8.22426	−0.479649
$295$	−6.06273	−0.352986
$296$	−5.42935	−0.315574
$297$	−4.27498	−0.248060
$298$	1.72655	0.100016
$299$	10.9623	0.633968
$300$	−2.14445	−0.123810
$301$	16.5171	0.952028
$302$	10.3512	0.595643
$303$	−13.9468	−0.801222
$304$	2.21072	0.126794
$305$	−22.7254	−1.30125
$306$	−11.9774	−0.684703
$307$	11.2885	0.644270	0.322135	−	0.946694i	$-0.395600\pi$
$307$	11.2885	0.644270	0.322135	+	0.946694i	$0.395600\pi$
$308$	−4.16190	−0.237146
$309$	−9.83498	−0.559492
$310$	12.0929	0.686829
$311$	33.0841	1.87603	0.938014	−	0.346597i	$-0.112663\pi$
$311$	33.0841	1.87603	0.938014	+	0.346597i	$0.112663\pi$
$312$	−1.76154	−0.0997273
$313$	−34.1816	−1.93206	−0.966030	−	0.258429i	$-0.916795\pi$
$313$	−34.1816	−1.93206	−0.966030	+	0.258429i	$0.916795\pi$
$314$	−22.7687	−1.28491
$315$	14.9563	0.842694
$316$	8.62224	0.485039
$317$	−2.22701	−0.125082	−0.0625408	−	0.998042i	$-0.519920\pi$
$317$	−2.22701	−0.125082	−0.0625408	+	0.998042i	$0.519920\pi$
$318$	−0.796815	−0.0446832
$319$	−5.29091	−0.296234
$320$	1.51945	0.0849399
$321$	9.71988	0.542511
$322$	20.6377	1.15009
$323$	−11.1957	−0.622944
$324$	3.68889	0.204938
$325$	−5.94965	−0.330027
$326$	13.9853	0.774575
$327$	−12.6020	−0.696894
$328$	7.10316	0.392206
$329$	47.7924	2.63488
$330$	−1.21072	−0.0666480
$331$	−13.9483	−0.766669	−0.383334	−	0.923610i	$-0.625224\pi$
$331$	−13.9483	−0.766669	−0.383334	+	0.923610i	$0.625224\pi$
$332$	8.68926	0.476885
$333$	−12.8409	−0.703675
$334$	−10.4139	−0.569824
$335$	17.7571	0.970172
$336$	−3.31627	−0.180917
$337$	3.87260	0.210954	0.105477	−	0.994422i	$-0.466363\pi$
$337$	3.87260	0.210954	0.105477	+	0.994422i	$0.466363\pi$
$338$	8.11271	0.441273
$339$	10.8588	0.589770
$340$	−7.69489	−0.417314
$341$	−7.95872	−0.430989
$342$	5.22854	0.282727
$343$	−13.8234	−0.746394
$344$	3.96864	0.213974
$345$	6.00362	0.323224
$346$	−5.13292	−0.275947
$347$	−3.40246	−0.182653	−0.0913267	−	0.995821i	$-0.529111\pi$
$347$	−3.40246	−0.182653	−0.0913267	+	0.995821i	$0.529111\pi$
$348$	−4.21587	−0.225995
$349$	−26.4401	−1.41531	−0.707654	−	0.706559i	$-0.750246\pi$
$349$	−26.4401	−1.41531	−0.707654	+	0.706559i	$0.750246\pi$
$350$	−11.2008	−0.598708
$351$	−9.45079	−0.504446
$352$	−1.00000	−0.0533002
$353$	29.8253	1.58744	0.793721	−	0.608282i	$-0.208141\pi$
$353$	29.8253	1.58744	0.793721	+	0.608282i	$0.208141\pi$
$354$	3.17936	0.168981
$355$	8.96472	0.475798
$356$	6.91505	0.366497
$357$	16.7944	0.888856
$358$	−15.3008	−0.808674
$359$	31.9651	1.68705	0.843527	−	0.537087i	$-0.180475\pi$
$359$	31.9651	1.68705	0.843527	+	0.537087i	$0.180475\pi$
$360$	3.59363	0.189401
$361$	−14.1127	−0.742774
$362$	1.76030	0.0925192
$363$	0.796815	0.0418219
$364$	−9.20080	−0.482253
$365$	−13.3007	−0.696191
$366$	11.9174	0.622934
$367$	−34.8492	−1.81911	−0.909556	−	0.415582i	$-0.863578\pi$
$367$	−34.8492	−1.81911	−0.909556	+	0.415582i	$0.863578\pi$
$368$	4.95872	0.258491
$369$	16.7996	0.874551
$370$	−8.24962	−0.428877
$371$	−4.16190	−0.216075
$372$	−6.34163	−0.328798
$373$	33.0418	1.71084	0.855419	−	0.517936i	$-0.173299\pi$
$373$	33.0418	1.71084	0.855419	+	0.517936i	$0.173299\pi$
$374$	5.06426	0.261867
$375$	−9.31198	−0.480869
$376$	11.4833	0.592207
$377$	−11.6967	−0.602412
$378$	−17.7920	−0.915124
$379$	22.5011	1.15581	0.577903	−	0.816105i	$-0.303871\pi$
$379$	22.5011	1.15581	0.577903	+	0.816105i	$0.303871\pi$
$380$	3.35908	0.172317
$381$	9.40999	0.482088
$382$	−18.9754	−0.970866
$383$	18.6420	0.952560	0.476280	−	0.879294i	$-0.341985\pi$
$383$	18.6420	0.952560	0.476280	+	0.879294i	$0.341985\pi$
$384$	−0.796815	−0.0406623
$385$	−6.32380	−0.322291
$386$	−9.11670	−0.464028
$387$	9.38616	0.477125
$388$	−7.15400	−0.363189
$389$	−1.92582	−0.0976430	−0.0488215	−	0.998808i	$-0.515547\pi$
$389$	−1.92582	−0.0976430	−0.0488215	+	0.998808i	$0.515547\pi$
$390$	−2.67657	−0.135533
$391$	−25.1122	−1.26998
$392$	−10.3214	−0.521310
$393$	3.14016	0.158400
$394$	−16.9658	−0.854723
$395$	13.1011	0.659186
$396$	−2.36509	−0.118850
$397$	−11.4186	−0.573082	−0.286541	−	0.958068i	$-0.592505\pi$
$397$	−11.4186	−0.573082	−0.286541	+	0.958068i	$0.592505\pi$
$398$	−18.9479	−0.949775
$399$	−7.33134	−0.367026
$400$	−2.69127	−0.134564
$401$	−9.62740	−0.480769	−0.240385	−	0.970678i	$-0.577274\pi$
$401$	−9.62740	−0.480769	−0.240385	+	0.970678i	$0.577274\pi$
$402$	−9.31198	−0.464439
$403$	−17.5945	−0.876444
$404$	−17.5032	−0.870815
$405$	5.60508	0.278519
$406$	−22.0202	−1.09285
$407$	5.42935	0.269123
$408$	4.03528	0.199776
$409$	10.0186	0.495387	0.247693	−	0.968838i	$-0.420327\pi$
$409$	10.0186	0.495387	0.247693	+	0.968838i	$0.420327\pi$
$410$	10.7929	0.533023
$411$	−8.24735	−0.406812
$412$	−12.3429	−0.608089
$413$	16.6063	0.817144
$414$	11.7278	0.576389
$415$	13.2029	0.648104
$416$	−2.21072	−0.108390
$417$	−17.8208	−0.872690
$418$	−2.21072	−0.108130
$419$	−31.6348	−1.54546	−0.772731	−	0.634734i	$-0.781110\pi$
$419$	−31.6348	−1.54546	−0.772731	+	0.634734i	$0.781110\pi$
$420$	−5.03890	−0.245873
$421$	−13.9853	−0.681602	−0.340801	−	0.940135i	$-0.610698\pi$
$421$	−13.9853	−0.681602	−0.340801	+	0.940135i	$0.610698\pi$
$422$	6.70243	0.326269
$423$	27.1590	1.32052
$424$	−1.00000	−0.0485643
$425$	13.6293	0.661118
$426$	−4.70119	−0.227773
$427$	62.2468	3.01233
$428$	12.1984	0.589633
$429$	1.76154	0.0850478
$430$	6.03014	0.290799
$431$	36.7765	1.77146	0.885731	−	0.464199i	$-0.153658\pi$
$431$	36.7765	1.77146	0.885731	+	0.464199i	$0.153658\pi$
$432$	−4.27498	−0.205680
$433$	32.7532	1.57402	0.787008	−	0.616942i	$-0.211629\pi$
$433$	32.7532	1.57402	0.787008	+	0.616942i	$0.211629\pi$
$434$	−33.1234	−1.58997
$435$	−6.40581	−0.307135
$436$	−15.8155	−0.757426
$437$	10.9623	0.524400
$438$	6.97503	0.333280
$439$	−27.5631	−1.31552	−0.657758	−	0.753229i	$-0.728495\pi$
$439$	−27.5631	−1.31552	−0.657758	+	0.753229i	$0.728495\pi$
$440$	−1.51945	−0.0724370
$441$	−24.4110	−1.16243
$442$	11.1957	0.532524
$443$	−1.09803	−0.0521688	−0.0260844	−	0.999660i	$-0.508304\pi$
$443$	−1.09803	−0.0521688	−0.0260844	+	0.999660i	$0.508304\pi$
$444$	4.32618	0.205312
$445$	10.5071	0.498083
$446$	8.97931	0.425183
$447$	−1.37574	−0.0650703
$448$	−4.16190	−0.196631
$449$	−30.4087	−1.43507	−0.717537	−	0.696521i	$-0.754730\pi$
$449$	−30.4087	−1.43507	−0.717537	+	0.696521i	$0.754730\pi$
$450$	−6.36509	−0.300053
$451$	−7.10316	−0.334475
$452$	13.6278	0.640996
$453$	−8.24797	−0.387524
$454$	−2.32429	−0.109084
$455$	−13.9802	−0.655400
$456$	−1.76154	−0.0824915
$457$	−34.7797	−1.62693	−0.813464	−	0.581615i	$-0.802421\pi$
$457$	−34.7797	−1.62693	−0.813464	+	0.581615i	$0.802421\pi$
$458$	−17.2820	−0.807536
$459$	21.6496	1.01052
$460$	7.53452	0.351299
$461$	28.3250	1.31923	0.659614	−	0.751604i	$-0.270720\pi$
$461$	28.3250	1.31923	0.659614	+	0.751604i	$0.270720\pi$
$462$	3.31627	0.154287
$463$	−17.0976	−0.794595	−0.397297	−	0.917690i	$-0.630052\pi$
$463$	−17.0976	−0.794595	−0.397297	+	0.917690i	$0.630052\pi$
$464$	−5.29091	−0.245624
$465$	−9.63578	−0.446849
$466$	−13.2651	−0.614492
$467$	−1.43688	−0.0664910	−0.0332455	−	0.999447i	$-0.510584\pi$
$467$	−1.43688	−0.0664910	−0.0332455	+	0.999447i	$0.510584\pi$
$468$	−5.22854	−0.241690
$469$	−48.6381	−2.24590
$470$	17.4483	0.804832
$471$	18.1424	0.835960
$472$	3.99008	0.183658
$473$	−3.96864	−0.182478
$474$	−6.87033	−0.315565
$475$	−5.94965	−0.272989
$476$	21.0769	0.966060
$477$	−2.36509	−0.108290
$478$	4.22415	0.193208
$479$	12.3868	0.565968	0.282984	−	0.959125i	$-0.408676\pi$
$479$	12.3868	0.565968	0.282984	+	0.959125i	$0.408676\pi$
$480$	−1.21072	−0.0552616
$481$	12.0028	0.547279
$482$	−1.92497	−0.0876799
$483$	−16.4444	−0.748247
$484$	1.00000	0.0454545
$485$	−10.8701	−0.493588
$486$	−15.7643	−0.715083
$487$	19.5142	0.884273	0.442136	−	0.896948i	$-0.354221\pi$
$487$	19.5142	0.884273	0.442136	+	0.896948i	$0.354221\pi$
$488$	14.9563	0.677041
$489$	−11.1437	−0.503936
$490$	−15.6829	−0.708480
$491$	−24.4885	−1.10515	−0.552575	−	0.833463i	$-0.686355\pi$
$491$	−24.4885	−1.10515	−0.552575	+	0.833463i	$0.686355\pi$
$492$	−5.65991	−0.255168
$493$	26.7945	1.20676
$494$	−4.88729	−0.219889
$495$	−3.59363	−0.161522
$496$	−7.95872	−0.357357
$497$	−24.5551	−1.10145
$498$	−6.92373	−0.310260
$499$	4.40246	0.197081	0.0985405	−	0.995133i	$-0.468583\pi$
$499$	4.40246	0.197081	0.0985405	+	0.995133i	$0.468583\pi$
$500$	−11.6865	−0.522636
$501$	8.29796	0.370725
$502$	23.1198	1.03189
$503$	2.88577	0.128670	0.0643352	−	0.997928i	$-0.479507\pi$
$503$	2.88577	0.128670	0.0643352	+	0.997928i	$0.479507\pi$
$504$	−9.84325	−0.438453
$505$	−26.5952	−1.18347
$506$	−4.95872	−0.220442
$507$	−6.46433	−0.287091
$508$	11.8095	0.523962
$509$	21.3877	0.947993	0.473996	−	0.880527i	$-0.342811\pi$
$509$	21.3877	0.947993	0.473996	+	0.880527i	$0.342811\pi$
$510$	6.13141	0.271503
$511$	36.4317	1.61165
$512$	−1.00000	−0.0441942
$513$	−9.45079	−0.417263
$514$	22.0924	0.974454
$515$	−18.7544	−0.826416
$516$	−3.16227	−0.139211
$517$	−11.4833	−0.505036
$518$	22.5964	0.992829
$519$	4.08999	0.179531
$520$	−3.35908	−0.147305
$521$	−13.5443	−0.593388	−0.296694	−	0.954973i	$-0.595884\pi$
$521$	−13.5443	−0.593388	−0.296694	+	0.954973i	$0.595884\pi$
$522$	−12.5134	−0.547699
$523$	−0.957478	−0.0418676	−0.0209338	−	0.999781i	$-0.506664\pi$
$523$	−0.957478	−0.0418676	−0.0209338	+	0.999781i	$0.506664\pi$
$524$	3.94089	0.172159
$525$	8.92497	0.389518
$526$	−23.2023	−1.01167
$527$	40.3050	1.75571
$528$	0.796815	0.0346769
$529$	1.58886	0.0690810
$530$	−1.51945	−0.0660007
$531$	9.43688	0.409526
$532$	−9.20080	−0.398905
$533$	−15.7031	−0.680177
$534$	−5.51002	−0.238442
$535$	18.5349	0.801333
$536$	−11.6865	−0.504780
$537$	12.1919	0.526121
$538$	4.56790	0.196936
$539$	10.3214	0.444575
$540$	−6.49562	−0.279527
$541$	1.84220	0.0792026	0.0396013	−	0.999216i	$-0.487391\pi$
$541$	1.84220	0.0792026	0.0396013	+	0.999216i	$0.487391\pi$
$542$	−14.5452	−0.624770
$543$	−1.40263	−0.0601927
$544$	5.06426	0.217128
$545$	−24.0309	−1.02937
$546$	7.33134	0.313752
$547$	19.4134	0.830058	0.415029	−	0.909808i	$-0.363771\pi$
$547$	19.4134	0.830058	0.415029	+	0.909808i	$0.363771\pi$
$548$	−10.3504	−0.442147
$549$	35.3730	1.50968
$550$	2.69127	0.114756
$551$	−11.6967	−0.498297
$552$	−3.95118	−0.168173
$553$	−35.8849	−1.52598
$554$	16.4873	0.700479
$555$	6.57342	0.279026
$556$	−22.3651	−0.948491
$557$	5.26868	0.223241	0.111621	−	0.993751i	$-0.464396\pi$
$557$	5.26868	0.223241	0.111621	+	0.993751i	$0.464396\pi$
$558$	−18.8230	−0.796843
$559$	−8.77355	−0.371081
$560$	−6.32380	−0.267229
$561$	−4.03528	−0.170370
$562$	10.4270	0.439835
$563$	−25.3972	−1.07037	−0.535183	−	0.844736i	$-0.679757\pi$
$563$	−25.3972	−1.07037	−0.535183	+	0.844736i	$0.679757\pi$
$564$	−9.15008	−0.385288
$565$	20.7067	0.871138
$566$	13.0751	0.549585
$567$	−15.3528	−0.644756
$568$	−5.89998	−0.247558
$569$	−2.28165	−0.0956516	−0.0478258	−	0.998856i	$-0.515229\pi$
$569$	−2.28165	−0.0956516	−0.0478258	+	0.998856i	$0.515229\pi$
$570$	−2.67657	−0.112109
$571$	14.8222	0.620289	0.310144	−	0.950689i	$-0.399623\pi$
$571$	14.8222	0.620289	0.310144	+	0.950689i	$0.399623\pi$
$572$	2.21072	0.0924349
$573$	15.1199	0.631642
$574$	−29.5627	−1.23392
$575$	−13.3452	−0.556535
$576$	−2.36509	−0.0985452
$577$	13.9936	0.582562	0.291281	−	0.956637i	$-0.405918\pi$
$577$	13.9936	0.582562	0.291281	+	0.956637i	$0.405918\pi$
$578$	−8.64673	−0.359657
$579$	7.26433	0.301895
$580$	−8.03927	−0.333812
$581$	−36.1638	−1.50033
$582$	5.70041	0.236290
$583$	1.00000	0.0414158
$584$	8.75363	0.362228
$585$	−7.94451	−0.328465
$586$	0.713493	0.0294741
$587$	−24.7750	−1.02257	−0.511287	−	0.859410i	$-0.670831\pi$
$587$	−24.7750	−1.02257	−0.511287	+	0.859410i	$0.670831\pi$
$588$	8.22426	0.339163
$589$	−17.5945	−0.724969
$590$	6.06273	0.249599
$591$	13.5186	0.556080
$592$	5.42935	0.223145
$593$	−4.22541	−0.173517	−0.0867583	−	0.996229i	$-0.527651\pi$
$593$	−4.22541	−0.173517	−0.0867583	+	0.996229i	$0.527651\pi$
$594$	4.27498	0.175405
$595$	32.0254	1.31291
$596$	−1.72655	−0.0707222
$597$	15.0980	0.617920
$598$	−10.9623	−0.448283
$599$	−4.34726	−0.177624	−0.0888122	−	0.996048i	$-0.528307\pi$
$599$	−4.34726	−0.177624	−0.0888122	+	0.996048i	$0.528307\pi$
$600$	2.14445	0.0875466
$601$	−34.3436	−1.40091	−0.700453	−	0.713698i	$-0.747019\pi$
$601$	−34.3436	−1.40091	−0.700453	+	0.713698i	$0.747019\pi$
$602$	−16.5171	−0.673185
$603$	−27.6396	−1.12557
$604$	−10.3512	−0.421183
$605$	1.51945	0.0617744
$606$	13.9468	0.566549
$607$	3.95670	0.160598	0.0802988	−	0.996771i	$-0.474413\pi$
$607$	3.95670	0.160598	0.0802988	+	0.996771i	$0.474413\pi$
$608$	−2.21072	−0.0896566
$609$	17.5460	0.711002
$610$	22.7254	0.920125
$611$	−25.3864	−1.02702
$612$	11.9774	0.484158
$613$	−7.33207	−0.296140	−0.148070	−	0.988977i	$-0.547306\pi$
$613$	−7.33207	−0.296140	−0.148070	+	0.988977i	$0.547306\pi$
$614$	−11.2885	−0.455568
$615$	−8.59995	−0.346783
$616$	4.16190	0.167688
$617$	−1.94163	−0.0781670	−0.0390835	−	0.999236i	$-0.512444\pi$
$617$	−1.94163	−0.0781670	−0.0390835	+	0.999236i	$0.512444\pi$
$618$	9.83498	0.395621
$619$	24.0276	0.965753	0.482876	−	0.875689i	$-0.339592\pi$
$619$	24.0276	0.965753	0.482876	+	0.875689i	$0.339592\pi$
$620$	−12.0929	−0.485661
$621$	−21.1984	−0.850663
$622$	−33.0841	−1.32655
$623$	−28.7797	−1.15304
$624$	1.76154	0.0705179
$625$	−4.30071	−0.172028
$626$	34.1816	1.36617
$627$	1.76154	0.0703490
$628$	22.7687	0.908570
$629$	−27.4956	−1.09632
$630$	−14.9563	−0.595875
$631$	−1.53966	−0.0612928	−0.0306464	−	0.999530i	$-0.509757\pi$
$631$	−1.53966	−0.0612928	−0.0306464	+	0.999530i	$0.509757\pi$
$632$	−8.62224	−0.342974
$633$	−5.34060	−0.212270
$634$	2.22701	0.0884460
$635$	17.9440	0.712084
$636$	0.796815	0.0315958
$637$	22.8178	0.904073
$638$	5.29091	0.209469
$639$	−13.9539	−0.552010
$640$	−1.51945	−0.0600615
$641$	−1.02738	−0.0405789	−0.0202894	−	0.999794i	$-0.506459\pi$
$641$	−1.02738	−0.0405789	−0.0202894	+	0.999794i	$0.506459\pi$
$642$	−9.71988	−0.383613
$643$	−47.9737	−1.89190	−0.945949	−	0.324316i	$-0.894866\pi$
$643$	−47.9737	−1.89190	−0.945949	+	0.324316i	$0.894866\pi$
$644$	−20.6377	−0.813239
$645$	−4.80491	−0.189193
$646$	11.1957	0.440488
$647$	−32.9626	−1.29589	−0.647947	−	0.761686i	$-0.724372\pi$
$647$	−32.9626	−1.29589	−0.647947	+	0.761686i	$0.724372\pi$
$648$	−3.68889	−0.144913
$649$	−3.99008	−0.156624
$650$	5.94965	0.233364
$651$	26.3932	1.03443
$652$	−13.9853	−0.547707
$653$	−31.5364	−1.23412	−0.617058	−	0.786918i	$-0.711676\pi$
$653$	−31.5364	−1.23412	−0.617058	+	0.786918i	$0.711676\pi$
$654$	12.6020	0.492779
$655$	5.98799	0.233970
$656$	−7.10316	−0.277332
$657$	20.7031	0.807704
$658$	−47.7924	−1.86314
$659$	−16.1691	−0.629858	−0.314929	−	0.949115i	$-0.601981\pi$
$659$	−16.1691	−0.629858	−0.314929	+	0.949115i	$0.601981\pi$
$660$	1.21072	0.0471273
$661$	−30.7602	−1.19643	−0.598217	−	0.801334i	$-0.704124\pi$
$661$	−30.7602	−1.19643	−0.598217	+	0.801334i	$0.704124\pi$
$662$	13.9483	0.542117
$663$	−8.92088	−0.346458
$664$	−8.68926	−0.337208
$665$	−13.9802	−0.542127
$666$	12.8409	0.497574
$667$	−26.2361	−1.01587
$668$	10.4139	0.402926
$669$	−7.15485	−0.276622
$670$	−17.7571	−0.686015
$671$	−14.9563	−0.577383
$672$	3.31627	0.127928
$673$	28.0272	1.08037	0.540184	−	0.841547i	$-0.318355\pi$
$673$	28.0272	1.08037	0.540184	+	0.841547i	$0.318355\pi$
$674$	−3.87260	−0.149167
$675$	11.5051	0.442833
$676$	−8.11271	−0.312027
$677$	−3.56943	−0.137184	−0.0685922	−	0.997645i	$-0.521851\pi$
$677$	−3.56943	−0.137184	−0.0685922	+	0.997645i	$0.521851\pi$
$678$	−10.8588	−0.417030
$679$	29.7742	1.14263
$680$	7.69489	0.295086
$681$	1.85203	0.0709698
$682$	7.95872	0.304755
$683$	−40.0662	−1.53309	−0.766545	−	0.642191i	$-0.778026\pi$
$683$	−40.0662	−1.53309	−0.766545	+	0.642191i	$0.778026\pi$
$684$	−5.22854	−0.199918
$685$	−15.7269	−0.600895
$686$	13.8234	0.527780
$687$	13.7706	0.525381
$688$	−3.96864	−0.151303
$689$	2.21072	0.0842218
$690$	−6.00362	−0.228554
$691$	9.66477	0.367665	0.183833	−	0.982958i	$-0.441150\pi$
$691$	9.66477	0.367665	0.183833	+	0.982958i	$0.441150\pi$
$692$	5.13292	0.195124
$693$	9.84325	0.373914
$694$	3.40246	0.129155
$695$	−33.9826	−1.28903
$696$	4.21587	0.159802
$697$	35.9723	1.36255
$698$	26.4401	1.00077
$699$	10.5698	0.399787
$700$	11.2008	0.423351
$701$	27.5407	1.04020	0.520099	−	0.854106i	$-0.325895\pi$
$701$	27.5407	1.04020	0.520099	+	0.854106i	$0.325895\pi$
$702$	9.45079	0.356697
$703$	12.0028	0.452693
$704$	1.00000	0.0376889
$705$	−13.9031	−0.523621
$706$	−29.8253	−1.12249
$707$	72.8464	2.73967
$708$	−3.17936	−0.119488
$709$	−11.4950	−0.431705	−0.215852	−	0.976426i	$-0.569253\pi$
$709$	−11.4950	−0.431705	−0.215852	+	0.976426i	$0.569253\pi$
$710$	−8.96472	−0.336440
$711$	−20.3923	−0.764773
$712$	−6.91505	−0.259152
$713$	−39.4650	−1.47798
$714$	−16.7944	−0.628516
$715$	3.35908	0.125622
$716$	15.3008	0.571819
$717$	−3.36586	−0.125700
$718$	−31.9651	−1.19293
$719$	−17.1674	−0.640237	−0.320118	−	0.947378i	$-0.603723\pi$
$719$	−17.1674	−0.640237	−0.320118	+	0.947378i	$0.603723\pi$
$720$	−3.59363	−0.133927
$721$	51.3698	1.91311
$722$	14.1127	0.525221
$723$	1.53384	0.0570443
$724$	−1.76030	−0.0654210
$725$	14.2393	0.528833
$726$	−0.796815	−0.0295726
$727$	−30.5576	−1.13332	−0.566660	−	0.823952i	$-0.691765\pi$
$727$	−30.5576	−1.13332	−0.566660	+	0.823952i	$0.691765\pi$
$728$	9.20080	0.341004
$729$	1.49457	0.0553546
$730$	13.3007	0.492281
$731$	20.0982	0.743359
$732$	−11.9174	−0.440481
$733$	31.0072	1.14528	0.572638	−	0.819808i	$-0.305920\pi$
$733$	31.0072	1.14528	0.572638	+	0.819808i	$0.305920\pi$
$734$	34.8492	1.28631
$735$	12.4964	0.460935
$736$	−4.95872	−0.182781
$737$	11.6865	0.430478
$738$	−16.7996	−0.618401
$739$	18.1115	0.666241	0.333121	−	0.942884i	$-0.391898\pi$
$739$	18.1115	0.666241	0.333121	+	0.942884i	$0.391898\pi$
$740$	8.24962	0.303262
$741$	3.89426	0.143059
$742$	4.16190	0.152788
$743$	34.2258	1.25562	0.627812	−	0.778365i	$-0.283951\pi$
$743$	34.2258	1.25562	0.627812	+	0.778365i	$0.283951\pi$
$744$	6.34163	0.232495
$745$	−2.62341	−0.0961142
$746$	−33.0418	−1.20975
$747$	−20.5508	−0.751916
$748$	−5.06426	−0.185168
$749$	−50.7686	−1.85504
$750$	9.31198	0.340026
$751$	−32.8106	−1.19728	−0.598638	−	0.801019i	$-0.704291\pi$
$751$	−32.8106	−1.19728	−0.598638	+	0.801019i	$0.704291\pi$
$752$	−11.4833	−0.418754
$753$	−18.4222	−0.671341
$754$	11.6967	0.425969
$755$	−15.7281	−0.572404
$756$	17.7920	0.647091
$757$	−31.0551	−1.12872	−0.564359	−	0.825529i	$-0.690877\pi$
$757$	−31.0551	−1.12872	−0.564359	+	0.825529i	$0.690877\pi$
$758$	−22.5011	−0.817278
$759$	3.95118	0.143419
$760$	−3.35908	−0.121847
$761$	−23.2666	−0.843413	−0.421707	−	0.906732i	$-0.638569\pi$
$761$	−23.2666	−0.843413	−0.421707	+	0.906732i	$0.638569\pi$
$762$	−9.40999	−0.340888
$763$	65.8226	2.38294
$764$	18.9754	0.686506
$765$	18.1991	0.657989
$766$	−18.6420	−0.673562
$767$	−8.82095	−0.318506
$768$	0.796815	0.0287526
$769$	−19.1045	−0.688926	−0.344463	−	0.938800i	$-0.611939\pi$
$769$	−19.1045	−0.688926	−0.344463	+	0.938800i	$0.611939\pi$
$770$	6.32380	0.227894
$771$	−17.6035	−0.633976
$772$	9.11670	0.328117
$773$	43.3669	1.55980	0.779899	−	0.625905i	$-0.215270\pi$
$773$	43.3669	1.55980	0.779899	+	0.625905i	$0.215270\pi$
$774$	−9.38616	−0.337379
$775$	21.4191	0.769395
$776$	7.15400	0.256814
$777$	−18.0052	−0.645931
$778$	1.92582	0.0690440
$779$	−15.7031	−0.562622
$780$	2.67657	0.0958364
$781$	5.89998	0.211118
$782$	25.1122	0.898011
$783$	22.6185	0.808320
$784$	10.3214	0.368622
$785$	34.5959	1.23478
$786$	−3.14016	−0.112006
$787$	17.2238	0.613961	0.306981	−	0.951716i	$-0.400681\pi$
$787$	17.2238	0.613961	0.306981	+	0.951716i	$0.400681\pi$
$788$	16.9658	0.604380
$789$	18.4880	0.658189
$790$	−13.1011	−0.466115
$791$	−56.7174	−2.01664
$792$	2.36509	0.0840397
$793$	−33.0643	−1.17415
$794$	11.4186	0.405230
$795$	1.21072	0.0429398
$796$	18.9479	0.671592
$797$	54.7342	1.93878	0.969392	−	0.245518i	$-0.0789580\pi$
$797$	54.7342	1.93878	0.969392	+	0.245518i	$0.0789580\pi$
$798$	7.33134	0.259527
$799$	58.1545	2.05736
$800$	2.69127	0.0951508
$801$	−16.3547	−0.577864
$802$	9.62740	0.339955
$803$	−8.75363	−0.308909
$804$	9.31198	0.328408
$805$	−31.3579	−1.10522
$806$	17.5945	0.619740
$807$	−3.63977	−0.128126
$808$	17.5032	0.615759
$809$	−23.6013	−0.829777	−0.414888	−	0.909872i	$-0.636179\pi$
$809$	−23.6013	−0.829777	−0.414888	+	0.909872i	$0.636179\pi$
$810$	−5.60508	−0.196942
$811$	−14.1245	−0.495978	−0.247989	−	0.968763i	$-0.579770\pi$
$811$	−14.1245	−0.495978	−0.247989	+	0.968763i	$0.579770\pi$
$812$	22.0202	0.772758
$813$	11.5898	0.406473
$814$	−5.42935	−0.190298
$815$	−21.2500	−0.744355
$816$	−4.03528	−0.141263
$817$	−8.77355	−0.306948
$818$	−10.0186	−0.350291
$819$	21.7607	0.760380
$820$	−10.7929	−0.376904
$821$	−22.0807	−0.770621	−0.385311	−	0.922787i	$-0.625906\pi$
$821$	−22.0807	−0.770621	−0.385311	+	0.922787i	$0.625906\pi$
$822$	8.24735	0.287660
$823$	15.0373	0.524166	0.262083	−	0.965045i	$-0.415591\pi$
$823$	15.0373	0.524166	0.262083	+	0.965045i	$0.415591\pi$
$824$	12.3429	0.429984
$825$	−2.14445	−0.0746600
$826$	−16.6063	−0.577808
$827$	6.76068	0.235092	0.117546	−	0.993067i	$-0.462497\pi$
$827$	6.76068	0.235092	0.117546	+	0.993067i	$0.462497\pi$
$828$	−11.7278	−0.407569
$829$	8.53512	0.296437	0.148219	−	0.988955i	$-0.452646\pi$
$829$	8.53512	0.296437	0.148219	+	0.988955i	$0.452646\pi$
$830$	−13.2029	−0.458279
$831$	−13.1373	−0.455729
$832$	2.21072	0.0766430
$833$	−52.2703	−1.81106
$834$	17.8208	0.617085
$835$	15.8234	0.547592
$836$	2.21072	0.0764594
$837$	34.0234	1.17602
$838$	31.6348	1.09281
$839$	54.9973	1.89872	0.949358	−	0.314196i	$-0.101735\pi$
$839$	54.9973	1.89872	0.949358	+	0.314196i	$0.101735\pi$
$840$	5.03890	0.173859
$841$	−1.00632	−0.0347006
$842$	13.9853	0.481966
$843$	−8.30836	−0.286155
$844$	−6.70243	−0.230707
$845$	−12.3269	−0.424057
$846$	−27.1590	−0.933747
$847$	−4.16190	−0.143005
$848$	1.00000	0.0343401
$849$	−10.4184	−0.357558
$850$	−13.6293	−0.467481
$851$	26.9226	0.922894
$852$	4.70119	0.161060
$853$	7.05874	0.241687	0.120843	−	0.992672i	$-0.461440\pi$
$853$	7.05874	0.241687	0.120843	+	0.992672i	$0.461440\pi$
$854$	−62.2468	−2.13004
$855$	−7.94451	−0.271697
$856$	−12.1984	−0.416933
$857$	−42.6888	−1.45822	−0.729111	−	0.684396i	$-0.760066\pi$
$857$	−42.6888	−1.45822	−0.729111	+	0.684396i	$0.760066\pi$
$858$	−1.76154	−0.0601378
$859$	45.2727	1.54468	0.772342	−	0.635207i	$-0.219085\pi$
$859$	45.2727	1.54468	0.772342	+	0.635207i	$0.219085\pi$
$860$	−6.03014	−0.205626
$861$	23.5560	0.802785
$862$	−36.7765	−1.25261
$863$	22.6287	0.770291	0.385146	−	0.922856i	$-0.374151\pi$
$863$	22.6287	0.770291	0.385146	+	0.922856i	$0.374151\pi$
$864$	4.27498	0.145438
$865$	7.79922	0.265181
$866$	−32.7532	−1.11300
$867$	6.88985	0.233991
$868$	33.1234	1.12428
$869$	8.62224	0.292490
$870$	6.40581	0.217177
$871$	25.8356	0.875406
$872$	15.8155	0.535581
$873$	16.9198	0.572649
$874$	−10.9623	−0.370807
$875$	48.6381	1.64427
$876$	−6.97503	−0.235664
$877$	25.9119	0.874984	0.437492	−	0.899222i	$-0.355867\pi$
$877$	25.9119	0.874984	0.437492	+	0.899222i	$0.355867\pi$
$878$	27.5631	0.930211
$879$	−0.568522	−0.0191758
$880$	1.51945	0.0512207
$881$	−18.3170	−0.617117	−0.308558	−	0.951205i	$-0.599847\pi$
$881$	−18.3170	−0.617117	−0.308558	+	0.951205i	$0.599847\pi$
$882$	24.4110	0.821962
$883$	−42.7723	−1.43940	−0.719702	−	0.694283i	$-0.755721\pi$
$883$	−42.7723	−1.43940	−0.719702	+	0.694283i	$0.755721\pi$
$884$	−11.1957	−0.376551
$885$	−4.83087	−0.162388
$886$	1.09803	0.0368889
$887$	−3.72790	−0.125171	−0.0625854	−	0.998040i	$-0.519935\pi$
$887$	−3.72790	−0.125171	−0.0625854	+	0.998040i	$0.519935\pi$
$888$	−4.32618	−0.145177
$889$	−49.1500	−1.64844
$890$	−10.5071	−0.352198
$891$	3.68889	0.123582
$892$	−8.97931	−0.300649
$893$	−25.3864	−0.849524
$894$	1.37574	0.0460117
$895$	23.2488	0.777123
$896$	4.16190	0.139039
$897$	8.73496	0.291652
$898$	30.4087	1.01475
$899$	42.1088	1.40441
$900$	6.36509	0.212170
$901$	−5.06426	−0.168715
$902$	7.10316	0.236509
$903$	13.1610	0.437972
$904$	−13.6278	−0.453253
$905$	−2.67469	−0.0889095
$906$	8.24797	0.274021
$907$	3.11267	0.103355	0.0516773	−	0.998664i	$-0.483543\pi$
$907$	3.11267	0.103355	0.0516773	+	0.998664i	$0.483543\pi$
$908$	2.32429	0.0771341
$909$	41.3965	1.37303
$910$	13.9802	0.463438
$911$	9.60870	0.318351	0.159175	−	0.987250i	$-0.449117\pi$
$911$	9.60870	0.318351	0.159175	+	0.987250i	$0.449117\pi$
$912$	1.76154	0.0583303
$913$	8.68926	0.287572
$914$	34.7797	1.15041
$915$	−18.1079	−0.598630
$916$	17.2820	0.571014
$917$	−16.4016	−0.541629
$918$	−21.6496	−0.714544
$919$	−28.7041	−0.946860	−0.473430	−	0.880831i	$-0.656984\pi$
$919$	−28.7041	−0.946860	−0.473430	+	0.880831i	$0.656984\pi$
$920$	−7.53452	−0.248406
$921$	8.99487	0.296391
$922$	−28.3250	−0.932836
$923$	13.0432	0.429322
$924$	−3.31627	−0.109097
$925$	−14.6118	−0.480434
$926$	17.0976	0.561863
$927$	29.1919	0.958789
$928$	5.29091	0.173682
$929$	−14.0516	−0.461018	−0.230509	−	0.973070i	$-0.574039\pi$
$929$	−14.0516	−0.461018	−0.230509	+	0.973070i	$0.574039\pi$
$930$	9.63578	0.315970
$931$	22.8178	0.747822
$932$	13.2651	0.434512
$933$	26.3619	0.863051
$934$	1.43688	0.0470162
$935$	−7.69489	−0.251650
$936$	5.22854	0.170900
$937$	−37.9689	−1.24039	−0.620195	−	0.784448i	$-0.712947\pi$
$937$	−37.9689	−1.24039	−0.620195	+	0.784448i	$0.712947\pi$
$938$	48.6381	1.58809
$939$	−27.2364	−0.888828
$940$	−17.4483	−0.569102
$941$	−3.56742	−0.116295	−0.0581473	−	0.998308i	$-0.518519\pi$
$941$	−3.56742	−0.116295	−0.0581473	+	0.998308i	$0.518519\pi$
$942$	−18.1424	−0.591113
$943$	−35.2226	−1.14700
$944$	−3.99008	−0.129866
$945$	27.0341	0.879420
$946$	3.96864	0.129031
$947$	15.0107	0.487782	0.243891	−	0.969803i	$-0.421576\pi$
$947$	15.0107	0.487782	0.243891	+	0.969803i	$0.421576\pi$
$948$	6.87033	0.223138
$949$	−19.3518	−0.628187
$950$	5.94965	0.193032
$951$	−1.77452	−0.0575427
$952$	−21.0769	−0.683108
$953$	−44.3152	−1.43551	−0.717756	−	0.696295i	$-0.754831\pi$
$953$	−44.3152	−1.43551	−0.717756	+	0.696295i	$0.754831\pi$
$954$	2.36509	0.0765725
$955$	28.8322	0.932987
$956$	−4.22415	−0.136619
$957$	−4.21587	−0.136280
$958$	−12.3868	−0.400200
$959$	43.0773	1.39104
$960$	1.21072	0.0390759
$961$	32.3412	1.04326
$962$	−12.0028	−0.386985
$963$	−28.8503	−0.929688
$964$	1.92497	0.0619990
$965$	13.8524	0.445924
$966$	16.4444	0.529090
$967$	4.14971	0.133446	0.0667229	−	0.997772i	$-0.478746\pi$
$967$	4.14971	0.133446	0.0667229	+	0.997772i	$0.478746\pi$
$968$	−1.00000	−0.0321412
$969$	−8.92088	−0.286580
$970$	10.8701	0.349019
$971$	−9.55910	−0.306766	−0.153383	−	0.988167i	$-0.549017\pi$
$971$	−9.55910	−0.306766	−0.153383	+	0.988167i	$0.549017\pi$
$972$	15.7643	0.505640
$973$	93.0813	2.98405
$974$	−19.5142	−0.625275
$975$	−4.74077	−0.151826
$976$	−14.9563	−0.478741
$977$	14.1791	0.453628	0.226814	−	0.973938i	$-0.427169\pi$
$977$	14.1791	0.453628	0.226814	+	0.973938i	$0.427169\pi$
$978$	11.1437	0.356337
$979$	6.91505	0.221006
$980$	15.6829	0.500971
$981$	37.4050	1.19425
$982$	24.4885	0.781459
$983$	22.7709	0.726278	0.363139	−	0.931735i	$-0.381705\pi$
$983$	22.7709	0.726278	0.363139	+	0.931735i	$0.381705\pi$
$984$	5.65991	0.180431
$985$	25.7786	0.821376
$986$	−26.7945	−0.853311
$987$	38.0817	1.21215
$988$	4.88729	0.155485
$989$	−19.6793	−0.625766
$990$	3.59363	0.114213
$991$	−12.4559	−0.395676	−0.197838	−	0.980235i	$-0.563392\pi$
$991$	−12.4559	−0.395676	−0.197838	+	0.980235i	$0.563392\pi$
$992$	7.95872	0.252689
$993$	−11.1142	−0.352699
$994$	24.5551	0.778841
$995$	28.7905	0.912719
$996$	6.92373	0.219387
$997$	6.38845	0.202324	0.101162	−	0.994870i	$-0.467744\pi$
$997$	6.38845	0.202324	0.101162	+	0.994870i	$0.467744\pi$
$998$	−4.40246	−0.139357
$999$	−23.2104	−0.734343

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1166.2.a.h.1.3	✓	4
4.3	odd	2		9328.2.a.z.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1166.2.a.h.1.3	✓	4	1.1	even	1	trivial
9328.2.a.z.1.2		4	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1166 = 2 \cdot 11 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1166.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.796815 q^{3} +1.00000 q^{4} +1.51945 q^{5} -0.796815 q^{6} -4.16190 q^{7} -1.00000 q^{8} -2.36509 q^{9} -1.51945 q^{10} +1.00000 q^{11} +0.796815 q^{12} +2.21072 q^{13} +4.16190 q^{14} +1.21072 q^{15} +1.00000 q^{16} -5.06426 q^{17} +2.36509 q^{18} +2.21072 q^{19} +1.51945 q^{20} -3.31627 q^{21} -1.00000 q^{22} +4.95872 q^{23} -0.796815 q^{24} -2.69127 q^{25} -2.21072 q^{26} -4.27498 q^{27} -4.16190 q^{28} -5.29091 q^{29} -1.21072 q^{30} -7.95872 q^{31} -1.00000 q^{32} +0.796815 q^{33} +5.06426 q^{34} -6.32380 q^{35} -2.36509 q^{36} +5.42935 q^{37} -2.21072 q^{38} +1.76154 q^{39} -1.51945 q^{40} -7.10316 q^{41} +3.31627 q^{42} -3.96864 q^{43} +1.00000 q^{44} -3.59363 q^{45} -4.95872 q^{46} -11.4833 q^{47} +0.796815 q^{48} +10.3214 q^{49} +2.69127 q^{50} -4.03528 q^{51} +2.21072 q^{52} +1.00000 q^{53} +4.27498 q^{54} +1.51945 q^{55} +4.16190 q^{56} +1.76154 q^{57} +5.29091 q^{58} -3.99008 q^{59} +1.21072 q^{60} -14.9563 q^{61} +7.95872 q^{62} +9.84325 q^{63} +1.00000 q^{64} +3.35908 q^{65} -0.796815 q^{66} +11.6865 q^{67} -5.06426 q^{68} +3.95118 q^{69} +6.32380 q^{70} +5.89998 q^{71} +2.36509 q^{72} -8.75363 q^{73} -5.42935 q^{74} -2.14445 q^{75} +2.21072 q^{76} -4.16190 q^{77} -1.76154 q^{78} +8.62224 q^{79} +1.51945 q^{80} +3.68889 q^{81} +7.10316 q^{82} +8.68926 q^{83} -3.31627 q^{84} -7.69489 q^{85} +3.96864 q^{86} -4.21587 q^{87} -1.00000 q^{88} +6.91505 q^{89} +3.59363 q^{90} -9.20080 q^{91} +4.95872 q^{92} -6.34163 q^{93} +11.4833 q^{94} +3.35908 q^{95} -0.796815 q^{96} -7.15400 q^{97} -10.3214 q^{98} -2.36509 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 4 q^{7} - 4 q^{8} - 2 q^{10} + 4 q^{11} - 6 q^{13} + 4 q^{14} - 10 q^{15} + 4 q^{16} - 12 q^{17} - 6 q^{19} + 2 q^{20} - 6 q^{21} - 4 q^{22} + 4 q^{23} + 6 q^{26} + 6 q^{27}+ \cdots + 8 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 4 * q^7 - 4 * q^8 - 2 * q^10 + 4 * q^11 - 6 * q^13 + 4 * q^14 - 10 * q^15 + 4 * q^16 - 12 * q^17 - 6 * q^19 + 2 * q^20 - 6 * q^21 - 4 * q^22 + 4 * q^23 + 6 * q^26 + 6 * q^27 - 4 * q^28 - 14 * q^29 + 10 * q^30 - 16 * q^31 - 4 * q^32 + 12 * q^34 + 4 * q^37 + 6 * q^38 - 2 * q^39 - 2 * q^40 - 12 * q^41 + 6 * q^42 - 6 * q^43 + 4 * q^44 - 8 * q^45 - 4 * q^46 + 16 * q^47 - 8 * q^49 - 22 * q^51 - 6 * q^52 + 4 * q^53 - 6 * q^54 + 2 * q^55 + 4 * q^56 - 2 * q^57 + 14 * q^58 - 10 * q^59 - 10 * q^60 - 20 * q^61 + 16 * q^62 + 10 * q^63 + 4 * q^64 - 6 * q^65 - 12 * q^67 - 12 * q^68 + 18 * q^69 + 4 * q^71 - 14 * q^73 - 4 * q^74 - 8 * q^75 - 6 * q^76 - 4 * q^77 + 2 * q^78 - 16 * q^79 + 2 * q^80 - 20 * q^81 + 12 * q^82 + 30 * q^83 - 6 * q^84 - 6 * q^85 + 6 * q^86 + 40 * q^87 - 4 * q^88 - 28 * q^89 + 8 * q^90 - 16 * q^91 + 4 * q^92 - 18 * q^93 - 16 * q^94 - 6 * q^95 - 4 * q^97 + 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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