LMFDB - Embedded newform 770.2.a.j.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [770,2,Mod(1,770)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("770.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(770, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,2,2,2,-2,2,2] 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
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			1.1
Root			$-1.73205$ of defining polynomial
Character	$\chi$	$=$	770.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} -0.732051 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.732051 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.46410 q^{9} -1.00000 q^{10} +1.00000 q^{11} -0.732051 q^{12} +5.46410 q^{13} +1.00000 q^{14} +0.732051 q^{15} +1.00000 q^{16} +3.46410 q^{17} -2.46410 q^{18} +3.26795 q^{19} -1.00000 q^{20} -0.732051 q^{21} +1.00000 q^{22} +2.19615 q^{23} -0.732051 q^{24} +1.00000 q^{25} +5.46410 q^{26} +4.00000 q^{27} +1.00000 q^{28} -1.26795 q^{29} +0.732051 q^{30} +2.00000 q^{31} +1.00000 q^{32} -0.732051 q^{33} +3.46410 q^{34} -1.00000 q^{35} -2.46410 q^{36} -2.73205 q^{37} +3.26795 q^{38} -4.00000 q^{39} -1.00000 q^{40} +8.19615 q^{41} -0.732051 q^{42} +2.00000 q^{43} +1.00000 q^{44} +2.46410 q^{45} +2.19615 q^{46} -6.92820 q^{47} -0.732051 q^{48} +1.00000 q^{49} +1.00000 q^{50} -2.53590 q^{51} +5.46410 q^{52} -10.7321 q^{53} +4.00000 q^{54} -1.00000 q^{55} +1.00000 q^{56} -2.39230 q^{57} -1.26795 q^{58} -6.92820 q^{59} +0.732051 q^{60} +8.92820 q^{61} +2.00000 q^{62} -2.46410 q^{63} +1.00000 q^{64} -5.46410 q^{65} -0.732051 q^{66} -4.00000 q^{67} +3.46410 q^{68} -1.60770 q^{69} -1.00000 q^{70} +2.53590 q^{71} -2.46410 q^{72} +6.39230 q^{73} -2.73205 q^{74} -0.732051 q^{75} +3.26795 q^{76} +1.00000 q^{77} -4.00000 q^{78} -1.80385 q^{79} -1.00000 q^{80} +4.46410 q^{81} +8.19615 q^{82} +4.39230 q^{83} -0.732051 q^{84} -3.46410 q^{85} +2.00000 q^{86} +0.928203 q^{87} +1.00000 q^{88} -3.46410 q^{89} +2.46410 q^{90} +5.46410 q^{91} +2.19615 q^{92} -1.46410 q^{93} -6.92820 q^{94} -3.26795 q^{95} -0.732051 q^{96} -16.5885 q^{97} +1.00000 q^{98} -2.46410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 4 q^{13} + 2 q^{14} - 2 q^{15} + 2 q^{16} + 2 q^{18} + 10 q^{19} - 2 q^{20} + 2 q^{21}+ \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 + 4 * q^13 + 2 * q^14 - 2 * q^15 + 2 * q^16 + 2 * q^18 + 10 * q^19 - 2 * q^20 + 2 * q^21 + 2 * q^22 - 6 * q^23 + 2 * q^24 + 2 * q^25 + 4 * q^26 + 8 * q^27 + 2 * q^28 - 6 * q^29 - 2 * q^30 + 4 * q^31 + 2 * q^32 + 2 * q^33 - 2 * q^35 + 2 * q^36 - 2 * q^37 + 10 * q^38 - 8 * q^39 - 2 * q^40 + 6 * q^41 + 2 * q^42 + 4 * q^43 + 2 * q^44 - 2 * q^45 - 6 * q^46 + 2 * q^48 + 2 * q^49 + 2 * q^50 - 12 * q^51 + 4 * q^52 - 18 * q^53 + 8 * q^54 - 2 * q^55 + 2 * q^56 + 16 * q^57 - 6 * q^58 - 2 * q^60 + 4 * q^61 + 4 * q^62 + 2 * q^63 + 2 * q^64 - 4 * q^65 + 2 * q^66 - 8 * q^67 - 24 * q^69 - 2 * q^70 + 12 * q^71 + 2 * q^72 - 8 * q^73 - 2 * q^74 + 2 * q^75 + 10 * q^76 + 2 * q^77 - 8 * q^78 - 14 * q^79 - 2 * q^80 + 2 * q^81 + 6 * q^82 - 12 * q^83 + 2 * q^84 + 4 * q^86 - 12 * q^87 + 2 * q^88 - 2 * q^90 + 4 * q^91 - 6 * q^92 + 4 * q^93 - 10 * q^95 + 2 * q^96 - 2 * q^97 + 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
$3$	−0.732051	−0.422650	−0.211325	−	0.977416i	$-0.567778\pi$
$3$	−0.732051	−0.422650	−0.211325	+	0.977416i	$0.567778\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.732051	−0.298858
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−2.46410	−0.821367
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.732051	−0.211325
$13$	5.46410	1.51547	0.757735	−	0.652563i	$-0.226306\pi$
$13$	5.46410	1.51547	0.757735	+	0.652563i	$0.226306\pi$
$14$	1.00000	0.267261
$15$	0.732051	0.189015
$16$	1.00000	0.250000
$17$	3.46410	0.840168	0.420084	−	0.907485i	$-0.362001\pi$
$17$	3.46410	0.840168	0.420084	+	0.907485i	$0.362001\pi$
$18$	−2.46410	−0.580794
$19$	3.26795	0.749719	0.374859	−	0.927082i	$-0.377691\pi$
$19$	3.26795	0.749719	0.374859	+	0.927082i	$0.377691\pi$
$20$	−1.00000	−0.223607
$21$	−0.732051	−0.159747
$22$	1.00000	0.213201
$23$	2.19615	0.457929	0.228965	−	0.973435i	$-0.426466\pi$
$23$	2.19615	0.457929	0.228965	+	0.973435i	$0.426466\pi$
$24$	−0.732051	−0.149429
$25$	1.00000	0.200000
$26$	5.46410	1.07160
$27$	4.00000	0.769800
$28$	1.00000	0.188982
$29$	−1.26795	−0.235452	−0.117726	−	0.993046i	$-0.537560\pi$
$29$	−1.26795	−0.235452	−0.117726	+	0.993046i	$0.537560\pi$
$30$	0.732051	0.133654
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	1.00000	0.176777
$33$	−0.732051	−0.127434
$34$	3.46410	0.594089
$35$	−1.00000	−0.169031
$36$	−2.46410	−0.410684
$37$	−2.73205	−0.449146	−0.224573	−	0.974457i	$-0.572099\pi$
$37$	−2.73205	−0.449146	−0.224573	+	0.974457i	$0.572099\pi$
$38$	3.26795	0.530131
$39$	−4.00000	−0.640513
$40$	−1.00000	−0.158114
$41$	8.19615	1.28002	0.640012	−	0.768365i	$-0.278929\pi$
$41$	8.19615	1.28002	0.640012	+	0.768365i	$0.278929\pi$
$42$	−0.732051	−0.112958
$43$	2.00000	0.304997	0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000	0.304997	0.152499	+	0.988304i	$0.451268\pi$
$44$	1.00000	0.150756
$45$	2.46410	0.367327
$46$	2.19615	0.323805
$47$	−6.92820	−1.01058	−0.505291	−	0.862949i	$-0.668615\pi$
$47$	−6.92820	−1.01058	−0.505291	+	0.862949i	$0.668615\pi$
$48$	−0.732051	−0.105662
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	−2.53590	−0.355097
$52$	5.46410	0.757735
$53$	−10.7321	−1.47416	−0.737080	−	0.675805i	$-0.763796\pi$
$53$	−10.7321	−1.47416	−0.737080	+	0.675805i	$0.763796\pi$
$54$	4.00000	0.544331
$55$	−1.00000	−0.134840
$56$	1.00000	0.133631
$57$	−2.39230	−0.316869
$58$	−1.26795	−0.166490
$59$	−6.92820	−0.901975	−0.450988	−	0.892530i	$-0.648928\pi$
$59$	−6.92820	−0.901975	−0.450988	+	0.892530i	$0.648928\pi$
$60$	0.732051	0.0945074
$61$	8.92820	1.14314	0.571570	−	0.820554i	$-0.306335\pi$
$61$	8.92820	1.14314	0.571570	+	0.820554i	$0.306335\pi$
$62$	2.00000	0.254000
$63$	−2.46410	−0.310448
$64$	1.00000	0.125000
$65$	−5.46410	−0.677738
$66$	−0.732051	−0.0901092
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	3.46410	0.420084
$69$	−1.60770	−0.193544
$70$	−1.00000	−0.119523
$71$	2.53590	0.300956	0.150478	−	0.988613i	$-0.451919\pi$
$71$	2.53590	0.300956	0.150478	+	0.988613i	$0.451919\pi$
$72$	−2.46410	−0.290397
$73$	6.39230	0.748163	0.374081	−	0.927396i	$-0.377958\pi$
$73$	6.39230	0.748163	0.374081	+	0.927396i	$0.377958\pi$
$74$	−2.73205	−0.317594
$75$	−0.732051	−0.0845299
$76$	3.26795	0.374859
$77$	1.00000	0.113961
$78$	−4.00000	−0.452911
$79$	−1.80385	−0.202949	−0.101474	−	0.994838i	$-0.532356\pi$
$79$	−1.80385	−0.202949	−0.101474	+	0.994838i	$0.532356\pi$
$80$	−1.00000	−0.111803
$81$	4.46410	0.496011
$82$	8.19615	0.905114
$83$	4.39230	0.482118	0.241059	−	0.970510i	$-0.422505\pi$
$83$	4.39230	0.482118	0.241059	+	0.970510i	$0.422505\pi$
$84$	−0.732051	−0.0798733
$85$	−3.46410	−0.375735
$86$	2.00000	0.215666
$87$	0.928203	0.0995138
$88$	1.00000	0.106600
$89$	−3.46410	−0.367194	−0.183597	−	0.983002i	$-0.558774\pi$
$89$	−3.46410	−0.367194	−0.183597	+	0.983002i	$0.558774\pi$
$90$	2.46410	0.259739
$91$	5.46410	0.572793
$92$	2.19615	0.228965
$93$	−1.46410	−0.151820
$94$	−6.92820	−0.714590
$95$	−3.26795	−0.335285
$96$	−0.732051	−0.0747146
$97$	−16.5885	−1.68430	−0.842151	−	0.539241i	$-0.818711\pi$
$97$	−16.5885	−1.68430	−0.842151	+	0.539241i	$0.818711\pi$
$98$	1.00000	0.101015
$99$	−2.46410	−0.247652
$100$	1.00000	0.100000
$101$	19.8564	1.97579	0.987893	−	0.155136i	$-0.0495815\pi$
$101$	19.8564	1.97579	0.987893	+	0.155136i	$0.0495815\pi$
$102$	−2.53590	−0.251091
$103$	−8.39230	−0.826918	−0.413459	−	0.910523i	$-0.635680\pi$
$103$	−8.39230	−0.826918	−0.413459	+	0.910523i	$0.635680\pi$
$104$	5.46410	0.535799
$105$	0.732051	0.0714408
$106$	−10.7321	−1.04239
$107$	−19.8564	−1.91959	−0.959796	−	0.280700i	$-0.909433\pi$
$107$	−19.8564	−1.91959	−0.959796	+	0.280700i	$0.909433\pi$
$108$	4.00000	0.384900
$109$	1.66025	0.159023	0.0795117	−	0.996834i	$-0.474664\pi$
$109$	1.66025	0.159023	0.0795117	+	0.996834i	$0.474664\pi$
$110$	−1.00000	−0.0953463
$111$	2.00000	0.189832
$112$	1.00000	0.0944911
$113$	−19.8564	−1.86793	−0.933967	−	0.357360i	$-0.883677\pi$
$113$	−19.8564	−1.86793	−0.933967	+	0.357360i	$0.883677\pi$
$114$	−2.39230	−0.224060
$115$	−2.19615	−0.204792
$116$	−1.26795	−0.117726
$117$	−13.4641	−1.24476
$118$	−6.92820	−0.637793
$119$	3.46410	0.317554
$120$	0.732051	0.0668268
$121$	1.00000	0.0909091
$122$	8.92820	0.808322
$123$	−6.00000	−0.541002
$124$	2.00000	0.179605
$125$	−1.00000	−0.0894427
$126$	−2.46410	−0.219520
$127$	14.9282	1.32466	0.662332	−	0.749211i	$-0.269567\pi$
$127$	14.9282	1.32466	0.662332	+	0.749211i	$0.269567\pi$
$128$	1.00000	0.0883883
$129$	−1.46410	−0.128907
$130$	−5.46410	−0.479233
$131$	−11.6603	−1.01876	−0.509381	−	0.860541i	$-0.670125\pi$
$131$	−11.6603	−1.01876	−0.509381	+	0.860541i	$0.670125\pi$
$132$	−0.732051	−0.0637168
$133$	3.26795	0.283367
$134$	−4.00000	−0.345547
$135$	−4.00000	−0.344265
$136$	3.46410	0.297044
$137$	12.9282	1.10453	0.552265	−	0.833668i	$-0.313763\pi$
$137$	12.9282	1.10453	0.552265	+	0.833668i	$0.313763\pi$
$138$	−1.60770	−0.136856
$139$	−3.66025	−0.310459	−0.155229	−	0.987878i	$-0.549612\pi$
$139$	−3.66025	−0.310459	−0.155229	+	0.987878i	$0.549612\pi$
$140$	−1.00000	−0.0845154
$141$	5.07180	0.427122
$142$	2.53590	0.212808
$143$	5.46410	0.456931
$144$	−2.46410	−0.205342
$145$	1.26795	0.105297
$146$	6.39230	0.529031
$147$	−0.732051	−0.0603785
$148$	−2.73205	−0.224573
$149$	−10.7321	−0.879204	−0.439602	−	0.898193i	$-0.644880\pi$
$149$	−10.7321	−0.879204	−0.439602	+	0.898193i	$0.644880\pi$
$150$	−0.732051	−0.0597717
$151$	−13.1244	−1.06804	−0.534022	−	0.845470i	$-0.679320\pi$
$151$	−13.1244	−1.06804	−0.534022	+	0.845470i	$0.679320\pi$
$152$	3.26795	0.265066
$153$	−8.53590	−0.690086
$154$	1.00000	0.0805823
$155$	−2.00000	−0.160644
$156$	−4.00000	−0.320256
$157$	11.4641	0.914935	0.457467	−	0.889226i	$-0.348757\pi$
$157$	11.4641	0.914935	0.457467	+	0.889226i	$0.348757\pi$
$158$	−1.80385	−0.143506
$159$	7.85641	0.623054
$160$	−1.00000	−0.0790569
$161$	2.19615	0.173081
$162$	4.46410	0.350733
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	8.19615	0.640012
$165$	0.732051	0.0569901
$166$	4.39230	0.340909
$167$	−13.8564	−1.07224	−0.536120	−	0.844141i	$-0.680111\pi$
$167$	−13.8564	−1.07224	−0.536120	+	0.844141i	$0.680111\pi$
$168$	−0.732051	−0.0564789
$169$	16.8564	1.29665
$170$	−3.46410	−0.265684
$171$	−8.05256	−0.615795
$172$	2.00000	0.152499
$173$	−12.9282	−0.982913	−0.491457	−	0.870902i	$-0.663535\pi$
$173$	−12.9282	−0.982913	−0.491457	+	0.870902i	$0.663535\pi$
$174$	0.928203	0.0703669
$175$	1.00000	0.0755929
$176$	1.00000	0.0753778
$177$	5.07180	0.381220
$178$	−3.46410	−0.259645
$179$	−6.00000	−0.448461	−0.224231	−	0.974536i	$-0.571987\pi$
$179$	−6.00000	−0.448461	−0.224231	+	0.974536i	$0.571987\pi$
$180$	2.46410	0.183663
$181$	14.0000	1.04061	0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000	1.04061	0.520306	+	0.853980i	$0.325818\pi$
$182$	5.46410	0.405026
$183$	−6.53590	−0.483148
$184$	2.19615	0.161903
$185$	2.73205	0.200864
$186$	−1.46410	−0.107353
$187$	3.46410	0.253320
$188$	−6.92820	−0.505291
$189$	4.00000	0.290957
$190$	−3.26795	−0.237082
$191$	−12.0000	−0.868290	−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000	−0.868290	−0.434145	+	0.900843i	$0.642949\pi$
$192$	−0.732051	−0.0528312
$193$	−8.39230	−0.604091	−0.302046	−	0.953293i	$-0.597670\pi$
$193$	−8.39230	−0.604091	−0.302046	+	0.953293i	$0.597670\pi$
$194$	−16.5885	−1.19098
$195$	4.00000	0.286446
$196$	1.00000	0.0714286
$197$	24.2487	1.72765	0.863825	−	0.503793i	$-0.168062\pi$
$197$	24.2487	1.72765	0.863825	+	0.503793i	$0.168062\pi$
$198$	−2.46410	−0.175116
$199$	−10.9282	−0.774680	−0.387340	−	0.921937i	$-0.626606\pi$
$199$	−10.9282	−0.774680	−0.387340	+	0.921937i	$0.626606\pi$
$200$	1.00000	0.0707107
$201$	2.92820	0.206540
$202$	19.8564	1.39709
$203$	−1.26795	−0.0889926
$204$	−2.53590	−0.177548
$205$	−8.19615	−0.572444
$206$	−8.39230	−0.584720
$207$	−5.41154	−0.376128
$208$	5.46410	0.378867
$209$	3.26795	0.226049
$210$	0.732051	0.0505163
$211$	13.0718	0.899900	0.449950	−	0.893054i	$-0.351442\pi$
$211$	13.0718	0.899900	0.449950	+	0.893054i	$0.351442\pi$
$212$	−10.7321	−0.737080
$213$	−1.85641	−0.127199
$214$	−19.8564	−1.35736
$215$	−2.00000	−0.136399
$216$	4.00000	0.272166
$217$	2.00000	0.135769
$218$	1.66025	0.112447
$219$	−4.67949	−0.316211
$220$	−1.00000	−0.0674200
$221$	18.9282	1.27325
$222$	2.00000	0.134231
$223$	−18.5359	−1.24126	−0.620628	−	0.784105i	$-0.713122\pi$
$223$	−18.5359	−1.24126	−0.620628	+	0.784105i	$0.713122\pi$
$224$	1.00000	0.0668153
$225$	−2.46410	−0.164273
$226$	−19.8564	−1.32083
$227$	−6.92820	−0.459841	−0.229920	−	0.973209i	$-0.573847\pi$
$227$	−6.92820	−0.459841	−0.229920	+	0.973209i	$0.573847\pi$
$228$	−2.39230	−0.158434
$229$	3.60770	0.238403	0.119202	−	0.992870i	$-0.461967\pi$
$229$	3.60770	0.238403	0.119202	+	0.992870i	$0.461967\pi$
$230$	−2.19615	−0.144810
$231$	−0.732051	−0.0481654
$232$	−1.26795	−0.0832449
$233$	19.8564	1.30084	0.650418	−	0.759576i	$-0.274594\pi$
$233$	19.8564	1.30084	0.650418	+	0.759576i	$0.274594\pi$
$234$	−13.4641	−0.880176
$235$	6.92820	0.451946
$236$	−6.92820	−0.450988
$237$	1.32051	0.0857762
$238$	3.46410	0.224544
$239$	4.73205	0.306091	0.153045	−	0.988219i	$-0.451092\pi$
$239$	4.73205	0.306091	0.153045	+	0.988219i	$0.451092\pi$
$240$	0.732051	0.0472537
$241$	6.73205	0.433650	0.216825	−	0.976211i	$-0.430430\pi$
$241$	6.73205	0.433650	0.216825	+	0.976211i	$0.430430\pi$
$242$	1.00000	0.0642824
$243$	−15.2679	−0.979439
$244$	8.92820	0.571570
$245$	−1.00000	−0.0638877
$246$	−6.00000	−0.382546
$247$	17.8564	1.13618
$248$	2.00000	0.127000
$249$	−3.21539	−0.203767
$250$	−1.00000	−0.0632456
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	−2.46410	−0.155224
$253$	2.19615	0.138071
$254$	14.9282	0.936679
$255$	2.53590	0.158804
$256$	1.00000	0.0625000
$257$	−6.33975	−0.395462	−0.197731	−	0.980256i	$-0.563357\pi$
$257$	−6.33975	−0.395462	−0.197731	+	0.980256i	$0.563357\pi$
$258$	−1.46410	−0.0911510
$259$	−2.73205	−0.169761
$260$	−5.46410	−0.338869
$261$	3.12436	0.193393
$262$	−11.6603	−0.720373
$263$	−24.0000	−1.47990	−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000	−1.47990	−0.739952	+	0.672660i	$0.765152\pi$
$264$	−0.732051	−0.0450546
$265$	10.7321	0.659265
$266$	3.26795	0.200371
$267$	2.53590	0.155194
$268$	−4.00000	−0.244339
$269$	7.60770	0.463849	0.231925	−	0.972734i	$-0.425498\pi$
$269$	7.60770	0.463849	0.231925	+	0.972734i	$0.425498\pi$
$270$	−4.00000	−0.243432
$271$	−20.3923	−1.23874	−0.619372	−	0.785098i	$-0.712613\pi$
$271$	−20.3923	−1.23874	−0.619372	+	0.785098i	$0.712613\pi$
$272$	3.46410	0.210042
$273$	−4.00000	−0.242091
$274$	12.9282	0.781021
$275$	1.00000	0.0603023
$276$	−1.60770	−0.0967719
$277$	20.9282	1.25745	0.628727	−	0.777626i	$-0.283576\pi$
$277$	20.9282	1.25745	0.628727	+	0.777626i	$0.283576\pi$
$278$	−3.66025	−0.219527
$279$	−4.92820	−0.295044
$280$	−1.00000	−0.0597614
$281$	1.60770	0.0959071	0.0479535	−	0.998850i	$-0.484730\pi$
$281$	1.60770	0.0959071	0.0479535	+	0.998850i	$0.484730\pi$
$282$	5.07180	0.302021
$283$	23.7128	1.40958	0.704790	−	0.709416i	$-0.251041\pi$
$283$	23.7128	1.40958	0.704790	+	0.709416i	$0.251041\pi$
$284$	2.53590	0.150478
$285$	2.39230	0.141708
$286$	5.46410	0.323099
$287$	8.19615	0.483804
$288$	−2.46410	−0.145199
$289$	−5.00000	−0.294118
$290$	1.26795	0.0744565
$291$	12.1436	0.711870
$292$	6.39230	0.374081
$293$	14.5359	0.849196	0.424598	−	0.905382i	$-0.360415\pi$
$293$	14.5359	0.849196	0.424598	+	0.905382i	$0.360415\pi$
$294$	−0.732051	−0.0426941
$295$	6.92820	0.403376
$296$	−2.73205	−0.158797
$297$	4.00000	0.232104
$298$	−10.7321	−0.621691
$299$	12.0000	0.693978
$300$	−0.732051	−0.0422650
$301$	2.00000	0.115278
$302$	−13.1244	−0.755222
$303$	−14.5359	−0.835066
$304$	3.26795	0.187430
$305$	−8.92820	−0.511227
$306$	−8.53590	−0.487965
$307$	3.60770	0.205902	0.102951	−	0.994686i	$-0.467172\pi$
$307$	3.60770	0.205902	0.102951	+	0.994686i	$0.467172\pi$
$308$	1.00000	0.0569803
$309$	6.14359	0.349497
$310$	−2.00000	−0.113592
$311$	11.0718	0.627824	0.313912	−	0.949452i	$-0.398360\pi$
$311$	11.0718	0.627824	0.313912	+	0.949452i	$0.398360\pi$
$312$	−4.00000	−0.226455
$313$	11.8038	0.667193	0.333596	−	0.942716i	$-0.391738\pi$
$313$	11.8038	0.667193	0.333596	+	0.942716i	$0.391738\pi$
$314$	11.4641	0.646957
$315$	2.46410	0.138836
$316$	−1.80385	−0.101474
$317$	−0.588457	−0.0330511	−0.0165255	−	0.999863i	$-0.505260\pi$
$317$	−0.588457	−0.0330511	−0.0165255	+	0.999863i	$0.505260\pi$
$318$	7.85641	0.440565
$319$	−1.26795	−0.0709915
$320$	−1.00000	−0.0559017
$321$	14.5359	0.811315
$322$	2.19615	0.122387
$323$	11.3205	0.629890
$324$	4.46410	0.248006
$325$	5.46410	0.303094
$326$	−4.00000	−0.221540
$327$	−1.21539	−0.0672112
$328$	8.19615	0.452557
$329$	−6.92820	−0.381964
$330$	0.732051	0.0402981
$331$	22.7846	1.25236	0.626178	−	0.779680i	$-0.284618\pi$
$331$	22.7846	1.25236	0.626178	+	0.779680i	$0.284618\pi$
$332$	4.39230	0.241059
$333$	6.73205	0.368914
$334$	−13.8564	−0.758189
$335$	4.00000	0.218543
$336$	−0.732051	−0.0399366
$337$	−18.7846	−1.02326	−0.511631	−	0.859205i	$-0.670959\pi$
$337$	−18.7846	−1.02326	−0.511631	+	0.859205i	$0.670959\pi$
$338$	16.8564	0.916868
$339$	14.5359	0.789482
$340$	−3.46410	−0.187867
$341$	2.00000	0.108306
$342$	−8.05256	−0.435433
$343$	1.00000	0.0539949
$344$	2.00000	0.107833
$345$	1.60770	0.0865554
$346$	−12.9282	−0.695025
$347$	−36.9282	−1.98241	−0.991205	−	0.132336i	$-0.957752\pi$
$347$	−36.9282	−1.98241	−0.991205	+	0.132336i	$0.957752\pi$
$348$	0.928203	0.0497569
$349$	−26.3923	−1.41275	−0.706374	−	0.707839i	$-0.749670\pi$
$349$	−26.3923	−1.41275	−0.706374	+	0.707839i	$0.749670\pi$
$350$	1.00000	0.0534522
$351$	21.8564	1.16661
$352$	1.00000	0.0533002
$353$	3.80385	0.202458	0.101229	−	0.994863i	$-0.467722\pi$
$353$	3.80385	0.202458	0.101229	+	0.994863i	$0.467722\pi$
$354$	5.07180	0.269563
$355$	−2.53590	−0.134592
$356$	−3.46410	−0.183597
$357$	−2.53590	−0.134214
$358$	−6.00000	−0.317110
$359$	4.05256	0.213886	0.106943	−	0.994265i	$-0.465894\pi$
$359$	4.05256	0.213886	0.106943	+	0.994265i	$0.465894\pi$
$360$	2.46410	0.129870
$361$	−8.32051	−0.437921
$362$	14.0000	0.735824
$363$	−0.732051	−0.0384227
$364$	5.46410	0.286397
$365$	−6.39230	−0.334589
$366$	−6.53590	−0.341637
$367$	−8.39230	−0.438075	−0.219037	−	0.975716i	$-0.570292\pi$
$367$	−8.39230	−0.438075	−0.219037	+	0.975716i	$0.570292\pi$
$368$	2.19615	0.114482
$369$	−20.1962	−1.05137
$370$	2.73205	0.142033
$371$	−10.7321	−0.557180
$372$	−1.46410	−0.0759101
$373$	−2.39230	−0.123869	−0.0619344	−	0.998080i	$-0.519727\pi$
$373$	−2.39230	−0.123869	−0.0619344	+	0.998080i	$0.519727\pi$
$374$	3.46410	0.179124
$375$	0.732051	0.0378029
$376$	−6.92820	−0.357295
$377$	−6.92820	−0.356821
$378$	4.00000	0.205738
$379$	33.8564	1.73909	0.869543	−	0.493857i	$-0.164413\pi$
$379$	33.8564	1.73909	0.869543	+	0.493857i	$0.164413\pi$
$380$	−3.26795	−0.167642
$381$	−10.9282	−0.559869
$382$	−12.0000	−0.613973
$383$	−26.5359	−1.35592	−0.677961	−	0.735098i	$-0.737136\pi$
$383$	−26.5359	−1.35592	−0.677961	+	0.735098i	$0.737136\pi$
$384$	−0.732051	−0.0373573
$385$	−1.00000	−0.0509647
$386$	−8.39230	−0.427157
$387$	−4.92820	−0.250515
$388$	−16.5885	−0.842151
$389$	−22.3923	−1.13533	−0.567667	−	0.823258i	$-0.692154\pi$
$389$	−22.3923	−1.13533	−0.567667	+	0.823258i	$0.692154\pi$
$390$	4.00000	0.202548
$391$	7.60770	0.384738
$392$	1.00000	0.0505076
$393$	8.53590	0.430579
$394$	24.2487	1.22163
$395$	1.80385	0.0907614
$396$	−2.46410	−0.123826
$397$	9.60770	0.482196	0.241098	−	0.970501i	$-0.422492\pi$
$397$	9.60770	0.482196	0.241098	+	0.970501i	$0.422492\pi$
$398$	−10.9282	−0.547781
$399$	−2.39230	−0.119765
$400$	1.00000	0.0500000
$401$	9.46410	0.472615	0.236307	−	0.971678i	$-0.424063\pi$
$401$	9.46410	0.472615	0.236307	+	0.971678i	$0.424063\pi$
$402$	2.92820	0.146046
$403$	10.9282	0.544373
$404$	19.8564	0.987893
$405$	−4.46410	−0.221823
$406$	−1.26795	−0.0629273
$407$	−2.73205	−0.135423
$408$	−2.53590	−0.125546
$409$	35.1244	1.73679	0.868394	−	0.495875i	$-0.165153\pi$
$409$	35.1244	1.73679	0.868394	+	0.495875i	$0.165153\pi$
$410$	−8.19615	−0.404779
$411$	−9.46410	−0.466830
$412$	−8.39230	−0.413459
$413$	−6.92820	−0.340915
$414$	−5.41154	−0.265963
$415$	−4.39230	−0.215610
$416$	5.46410	0.267900
$417$	2.67949	0.131215
$418$	3.26795	0.159841
$419$	17.0718	0.834012	0.417006	−	0.908904i	$-0.363079\pi$
$419$	17.0718	0.834012	0.417006	+	0.908904i	$0.363079\pi$
$420$	0.732051	0.0357204
$421$	−8.14359	−0.396894	−0.198447	−	0.980112i	$-0.563590\pi$
$421$	−8.14359	−0.396894	−0.198447	+	0.980112i	$0.563590\pi$
$422$	13.0718	0.636325
$423$	17.0718	0.830059
$424$	−10.7321	−0.521194
$425$	3.46410	0.168034
$426$	−1.85641	−0.0899432
$427$	8.92820	0.432066
$428$	−19.8564	−0.959796
$429$	−4.00000	−0.193122
$430$	−2.00000	−0.0964486
$431$	−21.1244	−1.01752	−0.508762	−	0.860907i	$-0.669897\pi$
$431$	−21.1244	−1.01752	−0.508762	+	0.860907i	$0.669897\pi$
$432$	4.00000	0.192450
$433$	−7.80385	−0.375029	−0.187514	−	0.982262i	$-0.560043\pi$
$433$	−7.80385	−0.375029	−0.187514	+	0.982262i	$0.560043\pi$
$434$	2.00000	0.0960031
$435$	−0.928203	−0.0445039
$436$	1.66025	0.0795117
$437$	7.17691	0.343318
$438$	−4.67949	−0.223595
$439$	−22.2487	−1.06187	−0.530937	−	0.847412i	$-0.678160\pi$
$439$	−22.2487	−1.06187	−0.530937	+	0.847412i	$0.678160\pi$
$440$	−1.00000	−0.0476731
$441$	−2.46410	−0.117338
$442$	18.9282	0.900323
$443$	0	0		−	1.00000i	$-0.5\pi$
$443$	0	0			1.00000i	$0.5\pi$
$444$	2.00000	0.0949158
$445$	3.46410	0.164214
$446$	−18.5359	−0.877700
$447$	7.85641	0.371595
$448$	1.00000	0.0472456
$449$	19.6077	0.925344	0.462672	−	0.886529i	$-0.346891\pi$
$449$	19.6077	0.925344	0.462672	+	0.886529i	$0.346891\pi$
$450$	−2.46410	−0.116159
$451$	8.19615	0.385942
$452$	−19.8564	−0.933967
$453$	9.60770	0.451409
$454$	−6.92820	−0.325157
$455$	−5.46410	−0.256161
$456$	−2.39230	−0.112030
$457$	2.00000	0.0935561	0.0467780	−	0.998905i	$-0.485105\pi$
$457$	2.00000	0.0935561	0.0467780	+	0.998905i	$0.485105\pi$
$458$	3.60770	0.168577
$459$	13.8564	0.646762
$460$	−2.19615	−0.102396
$461$	1.60770	0.0748778	0.0374389	−	0.999299i	$-0.488080\pi$
$461$	1.60770	0.0748778	0.0374389	+	0.999299i	$0.488080\pi$
$462$	−0.732051	−0.0340581
$463$	−17.5167	−0.814068	−0.407034	−	0.913413i	$-0.633437\pi$
$463$	−17.5167	−0.814068	−0.407034	+	0.913413i	$0.633437\pi$
$464$	−1.26795	−0.0588631
$465$	1.46410	0.0678961
$466$	19.8564	0.919830
$467$	4.05256	0.187530	0.0937650	−	0.995594i	$-0.470110\pi$
$467$	4.05256	0.187530	0.0937650	+	0.995594i	$0.470110\pi$
$468$	−13.4641	−0.622378
$469$	−4.00000	−0.184703
$470$	6.92820	0.319574
$471$	−8.39230	−0.386697
$472$	−6.92820	−0.318896
$473$	2.00000	0.0919601
$474$	1.32051	0.0606529
$475$	3.26795	0.149944
$476$	3.46410	0.158777
$477$	26.4449	1.21083
$478$	4.73205	0.216439
$479$	8.78461	0.401379	0.200690	−	0.979655i	$-0.435682\pi$
$479$	8.78461	0.401379	0.200690	+	0.979655i	$0.435682\pi$
$480$	0.732051	0.0334134
$481$	−14.9282	−0.680667
$482$	6.73205	0.306637
$483$	−1.60770	−0.0731527
$484$	1.00000	0.0454545
$485$	16.5885	0.753243
$486$	−15.2679	−0.692568
$487$	−6.19615	−0.280774	−0.140387	−	0.990097i	$-0.544835\pi$
$487$	−6.19615	−0.280774	−0.140387	+	0.990097i	$0.544835\pi$
$488$	8.92820	0.404161
$489$	2.92820	0.132418
$490$	−1.00000	−0.0451754
$491$	27.7128	1.25066	0.625331	−	0.780360i	$-0.284964\pi$
$491$	27.7128	1.25066	0.625331	+	0.780360i	$0.284964\pi$
$492$	−6.00000	−0.270501
$493$	−4.39230	−0.197819
$494$	17.8564	0.803398
$495$	2.46410	0.110753
$496$	2.00000	0.0898027
$497$	2.53590	0.113751
$498$	−3.21539	−0.144085
$499$	39.8564	1.78422	0.892109	−	0.451820i	$-0.149225\pi$
$499$	39.8564	1.78422	0.892109	+	0.451820i	$0.149225\pi$
$500$	−1.00000	−0.0447214
$501$	10.1436	0.453182
$502$	12.0000	0.535586
$503$	−32.7846	−1.46179	−0.730897	−	0.682488i	$-0.760898\pi$
$503$	−32.7846	−1.46179	−0.730897	+	0.682488i	$0.760898\pi$
$504$	−2.46410	−0.109760
$505$	−19.8564	−0.883598
$506$	2.19615	0.0976309
$507$	−12.3397	−0.548027
$508$	14.9282	0.662332
$509$	24.9282	1.10492	0.552462	−	0.833538i	$-0.313689\pi$
$509$	24.9282	1.10492	0.552462	+	0.833538i	$0.313689\pi$
$510$	2.53590	0.112291
$511$	6.39230	0.282779
$512$	1.00000	0.0441942
$513$	13.0718	0.577134
$514$	−6.33975	−0.279634
$515$	8.39230	0.369809
$516$	−1.46410	−0.0644535
$517$	−6.92820	−0.304702
$518$	−2.73205	−0.120039
$519$	9.46410	0.415428
$520$	−5.46410	−0.239617
$521$	−10.3923	−0.455295	−0.227648	−	0.973744i	$-0.573103\pi$
$521$	−10.3923	−0.455295	−0.227648	+	0.973744i	$0.573103\pi$
$522$	3.12436	0.136749
$523$	33.1769	1.45073	0.725363	−	0.688367i	$-0.241672\pi$
$523$	33.1769	1.45073	0.725363	+	0.688367i	$0.241672\pi$
$524$	−11.6603	−0.509381
$525$	−0.732051	−0.0319493
$526$	−24.0000	−1.04645
$527$	6.92820	0.301797
$528$	−0.732051	−0.0318584
$529$	−18.1769	−0.790301
$530$	10.7321	0.466170
$531$	17.0718	0.740853
$532$	3.26795	0.141684
$533$	44.7846	1.93984
$534$	2.53590	0.109739
$535$	19.8564	0.858467
$536$	−4.00000	−0.172774
$537$	4.39230	0.189542
$538$	7.60770	0.327991
$539$	1.00000	0.0430730
$540$	−4.00000	−0.172133
$541$	−17.2679	−0.742407	−0.371204	−	0.928552i	$-0.621055\pi$
$541$	−17.2679	−0.742407	−0.371204	+	0.928552i	$0.621055\pi$
$542$	−20.3923	−0.875924
$543$	−10.2487	−0.439814
$544$	3.46410	0.148522
$545$	−1.66025	−0.0711175
$546$	−4.00000	−0.171184
$547$	−12.7846	−0.546630	−0.273315	−	0.961925i	$-0.588120\pi$
$547$	−12.7846	−0.546630	−0.273315	+	0.961925i	$0.588120\pi$
$548$	12.9282	0.552265
$549$	−22.0000	−0.938937
$550$	1.00000	0.0426401
$551$	−4.14359	−0.176523
$552$	−1.60770	−0.0684280
$553$	−1.80385	−0.0767074
$554$	20.9282	0.889154
$555$	−2.00000	−0.0848953
$556$	−3.66025	−0.155229
$557$	−46.3923	−1.96571	−0.982853	−	0.184393i	$-0.940968\pi$
$557$	−46.3923	−1.96571	−0.982853	+	0.184393i	$0.940968\pi$
$558$	−4.92820	−0.208627
$559$	10.9282	0.462214
$560$	−1.00000	−0.0422577
$561$	−2.53590	−0.107066
$562$	1.60770	0.0678165
$563$	18.9282	0.797729	0.398864	−	0.917010i	$-0.369404\pi$
$563$	18.9282	0.797729	0.398864	+	0.917010i	$0.369404\pi$
$564$	5.07180	0.213561
$565$	19.8564	0.835365
$566$	23.7128	0.996724
$567$	4.46410	0.187475
$568$	2.53590	0.106404
$569$	−6.00000	−0.251533	−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000	−0.251533	−0.125767	+	0.992060i	$0.540139\pi$
$570$	2.39230	0.100203
$571$	24.3923	1.02079	0.510393	−	0.859941i	$-0.329500\pi$
$571$	24.3923	1.02079	0.510393	+	0.859941i	$0.329500\pi$
$572$	5.46410	0.228466
$573$	8.78461	0.366982
$574$	8.19615	0.342101
$575$	2.19615	0.0915859
$576$	−2.46410	−0.102671
$577$	−3.41154	−0.142024	−0.0710122	−	0.997475i	$-0.522623\pi$
$577$	−3.41154	−0.142024	−0.0710122	+	0.997475i	$0.522623\pi$
$578$	−5.00000	−0.207973
$579$	6.14359	0.255319
$580$	1.26795	0.0526487
$581$	4.39230	0.182224
$582$	12.1436	0.503368
$583$	−10.7321	−0.444476
$584$	6.39230	0.264515
$585$	13.4641	0.556672
$586$	14.5359	0.600472
$587$	−42.5885	−1.75781	−0.878907	−	0.476993i	$-0.841727\pi$
$587$	−42.5885	−1.75781	−0.878907	+	0.476993i	$0.841727\pi$
$588$	−0.732051	−0.0301893
$589$	6.53590	0.269307
$590$	6.92820	0.285230
$591$	−17.7513	−0.730190
$592$	−2.73205	−0.112287
$593$	−48.2487	−1.98134	−0.990669	−	0.136293i	$-0.956481\pi$
$593$	−48.2487	−1.98134	−0.990669	+	0.136293i	$0.956481\pi$
$594$	4.00000	0.164122
$595$	−3.46410	−0.142014
$596$	−10.7321	−0.439602
$597$	8.00000	0.327418
$598$	12.0000	0.490716
$599$	−25.1769	−1.02870	−0.514350	−	0.857580i	$-0.671967\pi$
$599$	−25.1769	−1.02870	−0.514350	+	0.857580i	$0.671967\pi$
$600$	−0.732051	−0.0298858
$601$	39.5167	1.61192	0.805959	−	0.591971i	$-0.201650\pi$
$601$	39.5167	1.61192	0.805959	+	0.591971i	$0.201650\pi$
$602$	2.00000	0.0815139
$603$	9.85641	0.401384
$604$	−13.1244	−0.534022
$605$	−1.00000	−0.0406558
$606$	−14.5359	−0.590481
$607$	7.07180	0.287035	0.143518	−	0.989648i	$-0.454159\pi$
$607$	7.07180	0.287035	0.143518	+	0.989648i	$0.454159\pi$
$608$	3.26795	0.132533
$609$	0.928203	0.0376127
$610$	−8.92820	−0.361492
$611$	−37.8564	−1.53151
$612$	−8.53590	−0.345043
$613$	27.1769	1.09767	0.548833	−	0.835932i	$-0.315072\pi$
$613$	27.1769	1.09767	0.548833	+	0.835932i	$0.315072\pi$
$614$	3.60770	0.145595
$615$	6.00000	0.241943
$616$	1.00000	0.0402911
$617$	−17.3205	−0.697297	−0.348649	−	0.937253i	$-0.613359\pi$
$617$	−17.3205	−0.697297	−0.348649	+	0.937253i	$0.613359\pi$
$618$	6.14359	0.247132
$619$	−12.7846	−0.513857	−0.256928	−	0.966430i	$-0.582710\pi$
$619$	−12.7846	−0.513857	−0.256928	+	0.966430i	$0.582710\pi$
$620$	−2.00000	−0.0803219
$621$	8.78461	0.352514
$622$	11.0718	0.443939
$623$	−3.46410	−0.138786
$624$	−4.00000	−0.160128
$625$	1.00000	0.0400000
$626$	11.8038	0.471777
$627$	−2.39230	−0.0955395
$628$	11.4641	0.457467
$629$	−9.46410	−0.377358
$630$	2.46410	0.0981722
$631$	−33.0718	−1.31657	−0.658284	−	0.752770i	$-0.728717\pi$
$631$	−33.0718	−1.31657	−0.658284	+	0.752770i	$0.728717\pi$
$632$	−1.80385	−0.0717532
$633$	−9.56922	−0.380342
$634$	−0.588457	−0.0233706
$635$	−14.9282	−0.592408
$636$	7.85641	0.311527
$637$	5.46410	0.216496
$638$	−1.26795	−0.0501986
$639$	−6.24871	−0.247195
$640$	−1.00000	−0.0395285
$641$	47.5692	1.87887	0.939436	−	0.342725i	$-0.111350\pi$
$641$	47.5692	1.87887	0.939436	+	0.342725i	$0.111350\pi$
$642$	14.5359	0.573686
$643$	36.7321	1.44857	0.724285	−	0.689500i	$-0.242170\pi$
$643$	36.7321	1.44857	0.724285	+	0.689500i	$0.242170\pi$
$644$	2.19615	0.0865405
$645$	1.46410	0.0576489
$646$	11.3205	0.445399
$647$	−33.4641	−1.31561	−0.657805	−	0.753188i	$-0.728515\pi$
$647$	−33.4641	−1.31561	−0.657805	+	0.753188i	$0.728515\pi$
$648$	4.46410	0.175366
$649$	−6.92820	−0.271956
$650$	5.46410	0.214320
$651$	−1.46410	−0.0573827
$652$	−4.00000	−0.156652
$653$	−5.66025	−0.221503	−0.110751	−	0.993848i	$-0.535326\pi$
$653$	−5.66025	−0.221503	−0.110751	+	0.993848i	$0.535326\pi$
$654$	−1.21539	−0.0475255
$655$	11.6603	0.455604
$656$	8.19615	0.320006
$657$	−15.7513	−0.614516
$658$	−6.92820	−0.270089
$659$	−18.2487	−0.710869	−0.355434	−	0.934701i	$-0.615667\pi$
$659$	−18.2487	−0.710869	−0.355434	+	0.934701i	$0.615667\pi$
$660$	0.732051	0.0284950
$661$	−46.0000	−1.78919	−0.894596	−	0.446875i	$-0.852537\pi$
$661$	−46.0000	−1.78919	−0.894596	+	0.446875i	$0.852537\pi$
$662$	22.7846	0.885549
$663$	−13.8564	−0.538138
$664$	4.39230	0.170454
$665$	−3.26795	−0.126726
$666$	6.73205	0.260862
$667$	−2.78461	−0.107821
$668$	−13.8564	−0.536120
$669$	13.5692	0.524616
$670$	4.00000	0.154533
$671$	8.92820	0.344669
$672$	−0.732051	−0.0282395
$673$	2.00000	0.0770943	0.0385472	−	0.999257i	$-0.487727\pi$
$673$	2.00000	0.0770943	0.0385472	+	0.999257i	$0.487727\pi$
$674$	−18.7846	−0.723556
$675$	4.00000	0.153960
$676$	16.8564	0.648323
$677$	−31.8564	−1.22434	−0.612171	−	0.790726i	$-0.709703\pi$
$677$	−31.8564	−1.22434	−0.612171	+	0.790726i	$0.709703\pi$
$678$	14.5359	0.558248
$679$	−16.5885	−0.636607
$680$	−3.46410	−0.132842
$681$	5.07180	0.194352
$682$	2.00000	0.0765840
$683$	−42.2487	−1.61660	−0.808301	−	0.588769i	$-0.799613\pi$
$683$	−42.2487	−1.61660	−0.808301	+	0.588769i	$0.799613\pi$
$684$	−8.05256	−0.307897
$685$	−12.9282	−0.493961
$686$	1.00000	0.0381802
$687$	−2.64102	−0.100761
$688$	2.00000	0.0762493
$689$	−58.6410	−2.23404
$690$	1.60770	0.0612039
$691$	−6.53590	−0.248637	−0.124319	−	0.992242i	$-0.539675\pi$
$691$	−6.53590	−0.248637	−0.124319	+	0.992242i	$0.539675\pi$
$692$	−12.9282	−0.491457
$693$	−2.46410	−0.0936035
$694$	−36.9282	−1.40178
$695$	3.66025	0.138841
$696$	0.928203	0.0351835
$697$	28.3923	1.07544
$698$	−26.3923	−0.998963
$699$	−14.5359	−0.549798
$700$	1.00000	0.0377964
$701$	−23.9090	−0.903029	−0.451515	−	0.892264i	$-0.649116\pi$
$701$	−23.9090	−0.903029	−0.451515	+	0.892264i	$0.649116\pi$
$702$	21.8564	0.824917
$703$	−8.92820	−0.336734
$704$	1.00000	0.0376889
$705$	−5.07180	−0.191015
$706$	3.80385	0.143160
$707$	19.8564	0.746777
$708$	5.07180	0.190610
$709$	−9.32051	−0.350039	−0.175020	−	0.984565i	$-0.555999\pi$
$709$	−9.32051	−0.350039	−0.175020	+	0.984565i	$0.555999\pi$
$710$	−2.53590	−0.0951706
$711$	4.44486	0.166695
$712$	−3.46410	−0.129823
$713$	4.39230	0.164493
$714$	−2.53590	−0.0949036
$715$	−5.46410	−0.204346
$716$	−6.00000	−0.224231
$717$	−3.46410	−0.129369
$718$	4.05256	0.151240
$719$	27.7128	1.03351	0.516757	−	0.856132i	$-0.327139\pi$
$719$	27.7128	1.03351	0.516757	+	0.856132i	$0.327139\pi$
$720$	2.46410	0.0918316
$721$	−8.39230	−0.312546
$722$	−8.32051	−0.309657
$723$	−4.92820	−0.183282
$724$	14.0000	0.520306
$725$	−1.26795	−0.0470905
$726$	−0.732051	−0.0271690
$727$	−4.00000	−0.148352	−0.0741759	−	0.997245i	$-0.523633\pi$
$727$	−4.00000	−0.148352	−0.0741759	+	0.997245i	$0.523633\pi$
$728$	5.46410	0.202513
$729$	−2.21539	−0.0820515
$730$	−6.39230	−0.236590
$731$	6.92820	0.256249
$732$	−6.53590	−0.241574
$733$	26.0000	0.960332	0.480166	−	0.877178i	$-0.340576\pi$
$733$	26.0000	0.960332	0.480166	+	0.877178i	$0.340576\pi$
$734$	−8.39230	−0.309766
$735$	0.732051	0.0270021
$736$	2.19615	0.0809513
$737$	−4.00000	−0.147342
$738$	−20.1962	−0.743431
$739$	−43.7128	−1.60800	−0.804001	−	0.594628i	$-0.797299\pi$
$739$	−43.7128	−1.60800	−0.804001	+	0.594628i	$0.797299\pi$
$740$	2.73205	0.100432
$741$	−13.0718	−0.480204
$742$	−10.7321	−0.393986
$743$	8.78461	0.322276	0.161138	−	0.986932i	$-0.448484\pi$
$743$	8.78461	0.322276	0.161138	+	0.986932i	$0.448484\pi$
$744$	−1.46410	−0.0536766
$745$	10.7321	0.393192
$746$	−2.39230	−0.0875885
$747$	−10.8231	−0.395996
$748$	3.46410	0.126660
$749$	−19.8564	−0.725537
$750$	0.732051	0.0267307
$751$	−32.3923	−1.18201	−0.591006	−	0.806667i	$-0.701269\pi$
$751$	−32.3923	−1.18201	−0.591006	+	0.806667i	$0.701269\pi$
$752$	−6.92820	−0.252646
$753$	−8.78461	−0.320129
$754$	−6.92820	−0.252310
$755$	13.1244	0.477644
$756$	4.00000	0.145479
$757$	29.3731	1.06758	0.533791	−	0.845616i	$-0.320767\pi$
$757$	29.3731	1.06758	0.533791	+	0.845616i	$0.320767\pi$
$758$	33.8564	1.22972
$759$	−1.60770	−0.0583556
$760$	−3.26795	−0.118541
$761$	−29.6603	−1.07518	−0.537592	−	0.843205i	$-0.680666\pi$
$761$	−29.6603	−1.07518	−0.537592	+	0.843205i	$0.680666\pi$
$762$	−10.9282	−0.395887
$763$	1.66025	0.0601052
$764$	−12.0000	−0.434145
$765$	8.53590	0.308616
$766$	−26.5359	−0.958781
$767$	−37.8564	−1.36692
$768$	−0.732051	−0.0264156
$769$	−7.80385	−0.281414	−0.140707	−	0.990051i	$-0.544938\pi$
$769$	−7.80385	−0.281414	−0.140707	+	0.990051i	$0.544938\pi$
$770$	−1.00000	−0.0360375
$771$	4.64102	0.167142
$772$	−8.39230	−0.302046
$773$	12.9282	0.464995	0.232498	−	0.972597i	$-0.425310\pi$
$773$	12.9282	0.464995	0.232498	+	0.972597i	$0.425310\pi$
$774$	−4.92820	−0.177141
$775$	2.00000	0.0718421
$776$	−16.5885	−0.595491
$777$	2.00000	0.0717496
$778$	−22.3923	−0.802803
$779$	26.7846	0.959658
$780$	4.00000	0.143223
$781$	2.53590	0.0907416
$782$	7.60770	0.272051
$783$	−5.07180	−0.181251
$784$	1.00000	0.0357143
$785$	−11.4641	−0.409171
$786$	8.53590	0.304465
$787$	45.8564	1.63460	0.817302	−	0.576209i	$-0.195469\pi$
$787$	45.8564	1.63460	0.817302	+	0.576209i	$0.195469\pi$
$788$	24.2487	0.863825
$789$	17.5692	0.625481
$790$	1.80385	0.0641780
$791$	−19.8564	−0.706013
$792$	−2.46410	−0.0875580
$793$	48.7846	1.73239
$794$	9.60770	0.340964
$795$	−7.85641	−0.278638
$796$	−10.9282	−0.387340
$797$	−46.3923	−1.64330	−0.821650	−	0.569993i	$-0.806946\pi$
$797$	−46.3923	−1.64330	−0.821650	+	0.569993i	$0.806946\pi$
$798$	−2.39230	−0.0846867
$799$	−24.0000	−0.849059
$800$	1.00000	0.0353553
$801$	8.53590	0.301601
$802$	9.46410	0.334189
$803$	6.39230	0.225580
$804$	2.92820	0.103270
$805$	−2.19615	−0.0774042
$806$	10.9282	0.384930
$807$	−5.56922	−0.196046
$808$	19.8564	0.698546
$809$	31.1769	1.09612	0.548061	−	0.836438i	$-0.315366\pi$
$809$	31.1769	1.09612	0.548061	+	0.836438i	$0.315366\pi$
$810$	−4.46410	−0.156853
$811$	−18.8756	−0.662814	−0.331407	−	0.943488i	$-0.607523\pi$
$811$	−18.8756	−0.662814	−0.331407	+	0.943488i	$0.607523\pi$
$812$	−1.26795	−0.0444963
$813$	14.9282	0.523555
$814$	−2.73205	−0.0957583
$815$	4.00000	0.140114
$816$	−2.53590	−0.0887742
$817$	6.53590	0.228662
$818$	35.1244	1.22809
$819$	−13.4641	−0.470474
$820$	−8.19615	−0.286222
$821$	−47.9090	−1.67203	−0.836017	−	0.548703i	$-0.815122\pi$
$821$	−47.9090	−1.67203	−0.836017	+	0.548703i	$0.815122\pi$
$822$	−9.46410	−0.330098
$823$	−25.1244	−0.875780	−0.437890	−	0.899029i	$-0.644274\pi$
$823$	−25.1244	−0.875780	−0.437890	+	0.899029i	$0.644274\pi$
$824$	−8.39230	−0.292360
$825$	−0.732051	−0.0254867
$826$	−6.92820	−0.241063
$827$	1.85641	0.0645536	0.0322768	−	0.999479i	$-0.489724\pi$
$827$	1.85641	0.0645536	0.0322768	+	0.999479i	$0.489724\pi$
$828$	−5.41154	−0.188064
$829$	−46.2487	−1.60628	−0.803142	−	0.595788i	$-0.796840\pi$
$829$	−46.2487	−1.60628	−0.803142	+	0.595788i	$0.796840\pi$
$830$	−4.39230	−0.152459
$831$	−15.3205	−0.531463
$832$	5.46410	0.189434
$833$	3.46410	0.120024
$834$	2.67949	0.0927832
$835$	13.8564	0.479521
$836$	3.26795	0.113024
$837$	8.00000	0.276520
$838$	17.0718	0.589735
$839$	−4.14359	−0.143053	−0.0715264	−	0.997439i	$-0.522787\pi$
$839$	−4.14359	−0.143053	−0.0715264	+	0.997439i	$0.522787\pi$
$840$	0.732051	0.0252582
$841$	−27.3923	−0.944562
$842$	−8.14359	−0.280647
$843$	−1.17691	−0.0405351
$844$	13.0718	0.449950
$845$	−16.8564	−0.579878
$846$	17.0718	0.586940
$847$	1.00000	0.0343604
$848$	−10.7321	−0.368540
$849$	−17.3590	−0.595759
$850$	3.46410	0.118818
$851$	−6.00000	−0.205677
$852$	−1.85641	−0.0635994
$853$	−13.2154	−0.452486	−0.226243	−	0.974071i	$-0.572644\pi$
$853$	−13.2154	−0.452486	−0.226243	+	0.974071i	$0.572644\pi$
$854$	8.92820	0.305517
$855$	8.05256	0.275392
$856$	−19.8564	−0.678678
$857$	−20.5359	−0.701493	−0.350746	−	0.936470i	$-0.614072\pi$
$857$	−20.5359	−0.701493	−0.350746	+	0.936470i	$0.614072\pi$
$858$	−4.00000	−0.136558
$859$	28.7846	0.982118	0.491059	−	0.871126i	$-0.336610\pi$
$859$	28.7846	0.982118	0.491059	+	0.871126i	$0.336610\pi$
$860$	−2.00000	−0.0681994
$861$	−6.00000	−0.204479
$862$	−21.1244	−0.719498
$863$	37.5167	1.27708	0.638541	−	0.769588i	$-0.279538\pi$
$863$	37.5167	1.27708	0.638541	+	0.769588i	$0.279538\pi$
$864$	4.00000	0.136083
$865$	12.9282	0.439572
$866$	−7.80385	−0.265186
$867$	3.66025	0.124309
$868$	2.00000	0.0678844
$869$	−1.80385	−0.0611913
$870$	−0.928203	−0.0314690
$871$	−21.8564	−0.740576
$872$	1.66025	0.0562233
$873$	40.8756	1.38343
$874$	7.17691	0.242763
$875$	−1.00000	−0.0338062
$876$	−4.67949	−0.158105
$877$	13.3205	0.449802	0.224901	−	0.974382i	$-0.427794\pi$
$877$	13.3205	0.449802	0.224901	+	0.974382i	$0.427794\pi$
$878$	−22.2487	−0.750858
$879$	−10.6410	−0.358913
$880$	−1.00000	−0.0337100
$881$	24.9282	0.839853	0.419926	−	0.907558i	$-0.362056\pi$
$881$	24.9282	0.839853	0.419926	+	0.907558i	$0.362056\pi$
$882$	−2.46410	−0.0829706
$883$	−56.3923	−1.89775	−0.948876	−	0.315649i	$-0.897778\pi$
$883$	−56.3923	−1.89775	−0.948876	+	0.315649i	$0.897778\pi$
$884$	18.9282	0.636624
$885$	−5.07180	−0.170487
$886$	0	0
$887$	−13.8564	−0.465253	−0.232626	−	0.972566i	$-0.574732\pi$
$887$	−13.8564	−0.465253	−0.232626	+	0.972566i	$0.574732\pi$
$888$	2.00000	0.0671156
$889$	14.9282	0.500676
$890$	3.46410	0.116117
$891$	4.46410	0.149553
$892$	−18.5359	−0.620628
$893$	−22.6410	−0.757653
$894$	7.85641	0.262758
$895$	6.00000	0.200558
$896$	1.00000	0.0334077
$897$	−8.78461	−0.293310
$898$	19.6077	0.654317
$899$	−2.53590	−0.0845769
$900$	−2.46410	−0.0821367
$901$	−37.1769	−1.23854
$902$	8.19615	0.272902
$903$	−1.46410	−0.0487223
$904$	−19.8564	−0.660414
$905$	−14.0000	−0.465376
$906$	9.60770	0.319194
$907$	59.0333	1.96017	0.980085	−	0.198580i	$-0.0636331\pi$
$907$	59.0333	1.96017	0.980085	+	0.198580i	$0.0636331\pi$
$908$	−6.92820	−0.229920
$909$	−48.9282	−1.62285
$910$	−5.46410	−0.181133
$911$	2.53590	0.0840181	0.0420090	−	0.999117i	$-0.486624\pi$
$911$	2.53590	0.0840181	0.0420090	+	0.999117i	$0.486624\pi$
$912$	−2.39230	−0.0792171
$913$	4.39230	0.145364
$914$	2.00000	0.0661541
$915$	6.53590	0.216070
$916$	3.60770	0.119202
$917$	−11.6603	−0.385056
$918$	13.8564	0.457330
$919$	47.3731	1.56269	0.781347	−	0.624097i	$-0.214533\pi$
$919$	47.3731	1.56269	0.781347	+	0.624097i	$0.214533\pi$
$920$	−2.19615	−0.0724050
$921$	−2.64102	−0.0870244
$922$	1.60770	0.0529466
$923$	13.8564	0.456089
$924$	−0.732051	−0.0240827
$925$	−2.73205	−0.0898293
$926$	−17.5167	−0.575633
$927$	20.6795	0.679204
$928$	−1.26795	−0.0416225
$929$	−46.3923	−1.52208	−0.761041	−	0.648704i	$-0.775311\pi$
$929$	−46.3923	−1.52208	−0.761041	+	0.648704i	$0.775311\pi$
$930$	1.46410	0.0480098
$931$	3.26795	0.107103
$932$	19.8564	0.650418
$933$	−8.10512	−0.265350
$934$	4.05256	0.132604
$935$	−3.46410	−0.113288
$936$	−13.4641	−0.440088
$937$	−42.7846	−1.39771	−0.698856	−	0.715262i	$-0.746307\pi$
$937$	−42.7846	−1.39771	−0.698856	+	0.715262i	$0.746307\pi$
$938$	−4.00000	−0.130605
$939$	−8.64102	−0.281989
$940$	6.92820	0.225973
$941$	26.7846	0.873153	0.436577	−	0.899667i	$-0.356191\pi$
$941$	26.7846	0.873153	0.436577	+	0.899667i	$0.356191\pi$
$942$	−8.39230	−0.273436
$943$	18.0000	0.586161
$944$	−6.92820	−0.225494
$945$	−4.00000	−0.130120
$946$	2.00000	0.0650256
$947$	12.6795	0.412028	0.206014	−	0.978549i	$-0.433951\pi$
$947$	12.6795	0.412028	0.206014	+	0.978549i	$0.433951\pi$
$948$	1.32051	0.0428881
$949$	34.9282	1.13382
$950$	3.26795	0.106026
$951$	0.430781	0.0139690
$952$	3.46410	0.112272
$953$	33.4641	1.08401	0.542004	−	0.840376i	$-0.317666\pi$
$953$	33.4641	1.08401	0.542004	+	0.840376i	$0.317666\pi$
$954$	26.4449	0.856184
$955$	12.0000	0.388311
$956$	4.73205	0.153045
$957$	0.928203	0.0300045
$958$	8.78461	0.283818
$959$	12.9282	0.417473
$960$	0.732051	0.0236268
$961$	−27.0000	−0.870968
$962$	−14.9282	−0.481305
$963$	48.9282	1.57669
$964$	6.73205	0.216825
$965$	8.39230	0.270158
$966$	−1.60770	−0.0517267
$967$	13.0718	0.420361	0.210180	−	0.977663i	$-0.432595\pi$
$967$	13.0718	0.420361	0.210180	+	0.977663i	$0.432595\pi$
$968$	1.00000	0.0321412
$969$	−8.28719	−0.266223
$970$	16.5885	0.532623
$971$	29.0718	0.932958	0.466479	−	0.884532i	$-0.345522\pi$
$971$	29.0718	0.932958	0.466479	+	0.884532i	$0.345522\pi$
$972$	−15.2679	−0.489720
$973$	−3.66025	−0.117342
$974$	−6.19615	−0.198538
$975$	−4.00000	−0.128103
$976$	8.92820	0.285785
$977$	21.7128	0.694654	0.347327	−	0.937744i	$-0.387089\pi$
$977$	21.7128	0.694654	0.347327	+	0.937744i	$0.387089\pi$
$978$	2.92820	0.0936336
$979$	−3.46410	−0.110713
$980$	−1.00000	−0.0319438
$981$	−4.09103	−0.130617
$982$	27.7128	0.884351
$983$	25.1769	0.803019	0.401509	−	0.915855i	$-0.368486\pi$
$983$	25.1769	0.803019	0.401509	+	0.915855i	$0.368486\pi$
$984$	−6.00000	−0.191273
$985$	−24.2487	−0.772628
$986$	−4.39230	−0.139879
$987$	5.07180	0.161437
$988$	17.8564	0.568088
$989$	4.39230	0.139667
$990$	2.46410	0.0783143
$991$	−4.00000	−0.127064	−0.0635321	−	0.997980i	$-0.520237\pi$
$991$	−4.00000	−0.127064	−0.0635321	+	0.997980i	$0.520237\pi$
$992$	2.00000	0.0635001
$993$	−16.6795	−0.529308
$994$	2.53590	0.0804338
$995$	10.9282	0.346447
$996$	−3.21539	−0.101884
$997$	−37.7128	−1.19438	−0.597188	−	0.802101i	$-0.703716\pi$
$997$	−37.7128	−1.19438	−0.597188	+	0.802101i	$0.703716\pi$
$998$	39.8564	1.26163
$999$	−10.9282	−0.345753

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.a.j.1.1	✓	2
3.2	odd	2		6930.2.a.bv.1.2		2
4.3	odd	2		6160.2.a.t.1.2		2
5.2	odd	4		3850.2.c.x.1849.4		4
5.3	odd	4		3850.2.c.x.1849.1		4
5.4	even	2		3850.2.a.bd.1.2		2
7.6	odd	2		5390.2.a.bs.1.2		2
11.10	odd	2		8470.2.a.br.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.a.j.1.1	✓	2	1.1	even	1	trivial
3850.2.a.bd.1.2		2	5.4	even	2
3850.2.c.x.1849.1		4	5.3	odd	4
3850.2.c.x.1849.4		4	5.2	odd	4
5390.2.a.bs.1.2		2	7.6	odd	2
6160.2.a.t.1.2		2	4.3	odd	2
6930.2.a.bv.1.2		2	3.2	odd	2
8470.2.a.br.1.1		2	11.10	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.732051 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.732051 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.46410 q^{9} -1.00000 q^{10} +1.00000 q^{11} -0.732051 q^{12} +5.46410 q^{13} +1.00000 q^{14} +0.732051 q^{15} +1.00000 q^{16} +3.46410 q^{17} -2.46410 q^{18} +3.26795 q^{19} -1.00000 q^{20} -0.732051 q^{21} +1.00000 q^{22} +2.19615 q^{23} -0.732051 q^{24} +1.00000 q^{25} +5.46410 q^{26} +4.00000 q^{27} +1.00000 q^{28} -1.26795 q^{29} +0.732051 q^{30} +2.00000 q^{31} +1.00000 q^{32} -0.732051 q^{33} +3.46410 q^{34} -1.00000 q^{35} -2.46410 q^{36} -2.73205 q^{37} +3.26795 q^{38} -4.00000 q^{39} -1.00000 q^{40} +8.19615 q^{41} -0.732051 q^{42} +2.00000 q^{43} +1.00000 q^{44} +2.46410 q^{45} +2.19615 q^{46} -6.92820 q^{47} -0.732051 q^{48} +1.00000 q^{49} +1.00000 q^{50} -2.53590 q^{51} +5.46410 q^{52} -10.7321 q^{53} +4.00000 q^{54} -1.00000 q^{55} +1.00000 q^{56} -2.39230 q^{57} -1.26795 q^{58} -6.92820 q^{59} +0.732051 q^{60} +8.92820 q^{61} +2.00000 q^{62} -2.46410 q^{63} +1.00000 q^{64} -5.46410 q^{65} -0.732051 q^{66} -4.00000 q^{67} +3.46410 q^{68} -1.60770 q^{69} -1.00000 q^{70} +2.53590 q^{71} -2.46410 q^{72} +6.39230 q^{73} -2.73205 q^{74} -0.732051 q^{75} +3.26795 q^{76} +1.00000 q^{77} -4.00000 q^{78} -1.80385 q^{79} -1.00000 q^{80} +4.46410 q^{81} +8.19615 q^{82} +4.39230 q^{83} -0.732051 q^{84} -3.46410 q^{85} +2.00000 q^{86} +0.928203 q^{87} +1.00000 q^{88} -3.46410 q^{89} +2.46410 q^{90} +5.46410 q^{91} +2.19615 q^{92} -1.46410 q^{93} -6.92820 q^{94} -3.26795 q^{95} -0.732051 q^{96} -16.5885 q^{97} +1.00000 q^{98} -2.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{11} + 2 q^{12} + 4 q^{13} + 2 q^{14} - 2 q^{15} + 2 q^{16} + 2 q^{18} + 10 q^{19} - 2 q^{20} + 2 q^{21}+ \cdots + 2 q^{99}+O(q^{100}) \) 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 + 4 * q^13 + 2 * q^14 - 2 * q^15 + 2 * q^16 + 2 * q^18 + 10 * q^19 - 2 * q^20 + 2 * q^21 + 2 * q^22 - 6 * q^23 + 2 * q^24 + 2 * q^25 + 4 * q^26 + 8 * q^27 + 2 * q^28 - 6 * q^29 - 2 * q^30 + 4 * q^31 + 2 * q^32 + 2 * q^33 - 2 * q^35 + 2 * q^36 - 2 * q^37 + 10 * q^38 - 8 * q^39 - 2 * q^40 + 6 * q^41 + 2 * q^42 + 4 * q^43 + 2 * q^44 - 2 * q^45 - 6 * q^46 + 2 * q^48 + 2 * q^49 + 2 * q^50 - 12 * q^51 + 4 * q^52 - 18 * q^53 + 8 * q^54 - 2 * q^55 + 2 * q^56 + 16 * q^57 - 6 * q^58 - 2 * q^60 + 4 * q^61 + 4 * q^62 + 2 * q^63 + 2 * q^64 - 4 * q^65 + 2 * q^66 - 8 * q^67 - 24 * q^69 - 2 * q^70 + 12 * q^71 + 2 * q^72 - 8 * q^73 - 2 * q^74 + 2 * q^75 + 10 * q^76 + 2 * q^77 - 8 * q^78 - 14 * q^79 - 2 * q^80 + 2 * q^81 + 6 * q^82 - 12 * q^83 + 2 * q^84 + 4 * q^86 - 12 * q^87 + 2 * q^88 - 2 * q^90 + 4 * q^91 - 6 * q^92 + 4 * q^93 - 10 * q^95 + 2 * q^96 - 2 * q^97 + 2 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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