LMFDB - Embedded newform 8410.2.a.bx.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [8410,2,Mod(1,8410)] 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("8410.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8410, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 8410 = 2 \cdot 5 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8410.a (trivial)

Newform invariants

comment:select newform

sage:traces = [12,12,-4,12,-12,-4,-8] 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:	$67.1541880999$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 13 x^{10} + 56 x^{9} + 41 x^{8} - 234 x^{7} - 8 x^{6} + 298 x^{5} + 41 x^{4} + \cdots + 1 $ x^12 - 4x^11 - 13x^10 + 56x^9 + 41x^8 - 234x^7 - 8x^6 + 298x^5 + 41x^4 - 140x^3 - 62x^2 - 4*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 290)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.28705$ of defining polynomial
Character	$\chi$	$=$	8410.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} -0.959933 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.959933 q^{6} +4.10940 q^{7} +1.00000 q^{8} -2.07853 q^{9} -1.00000 q^{10} -4.21069 q^{11} -0.959933 q^{12} +3.81231 q^{13} +4.10940 q^{14} +0.959933 q^{15} +1.00000 q^{16} -7.44933 q^{17} -2.07853 q^{18} +4.70595 q^{19} -1.00000 q^{20} -3.94475 q^{21} -4.21069 q^{22} -1.16549 q^{23} -0.959933 q^{24} +1.00000 q^{25} +3.81231 q^{26} +4.87505 q^{27} +4.10940 q^{28} +0.959933 q^{30} -3.85350 q^{31} +1.00000 q^{32} +4.04198 q^{33} -7.44933 q^{34} -4.10940 q^{35} -2.07853 q^{36} +1.60320 q^{37} +4.70595 q^{38} -3.65956 q^{39} -1.00000 q^{40} -0.116852 q^{41} -3.94475 q^{42} +0.648590 q^{43} -4.21069 q^{44} +2.07853 q^{45} -1.16549 q^{46} -9.31488 q^{47} -0.959933 q^{48} +9.88715 q^{49} +1.00000 q^{50} +7.15086 q^{51} +3.81231 q^{52} -5.39773 q^{53} +4.87505 q^{54} +4.21069 q^{55} +4.10940 q^{56} -4.51739 q^{57} -0.531452 q^{59} +0.959933 q^{60} -10.9858 q^{61} -3.85350 q^{62} -8.54150 q^{63} +1.00000 q^{64} -3.81231 q^{65} +4.04198 q^{66} -3.75707 q^{67} -7.44933 q^{68} +1.11879 q^{69} -4.10940 q^{70} +12.6402 q^{71} -2.07853 q^{72} +5.31428 q^{73} +1.60320 q^{74} -0.959933 q^{75} +4.70595 q^{76} -17.3034 q^{77} -3.65956 q^{78} -17.4174 q^{79} -1.00000 q^{80} +1.55587 q^{81} -0.116852 q^{82} +3.65039 q^{83} -3.94475 q^{84} +7.44933 q^{85} +0.648590 q^{86} -4.21069 q^{88} +7.35968 q^{89} +2.07853 q^{90} +15.6663 q^{91} -1.16549 q^{92} +3.69910 q^{93} -9.31488 q^{94} -4.70595 q^{95} -0.959933 q^{96} +15.3893 q^{97} +9.88715 q^{98} +8.75204 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} - 4 q^{3} + 12 q^{4} - 12 q^{5} - 4 q^{6} - 8 q^{7} + 12 q^{8} + 6 q^{9} - 12 q^{10} - 14 q^{11} - 4 q^{12} - 4 q^{13} - 8 q^{14} + 4 q^{15} + 12 q^{16} - 8 q^{17} + 6 q^{18} + 16 q^{19}+ \cdots + 2 q^{99}+O(q^{100}) $ 12 * q + 12 * q^2 - 4 * q^3 + 12 * q^4 - 12 * q^5 - 4 * q^6 - 8 * q^7 + 12 * q^8 + 6 * q^9 - 12 * q^10 - 14 * q^11 - 4 * q^12 - 4 * q^13 - 8 * q^14 + 4 * q^15 + 12 * q^16 - 8 * q^17 + 6 * q^18 + 16 * q^19 - 12 * q^20 + 4 * q^21 - 14 * q^22 + 4 * q^23 - 4 * q^24 + 12 * q^25 - 4 * q^26 - 28 * q^27 - 8 * q^28 + 4 * q^30 + 2 * q^31 + 12 * q^32 + 4 * q^33 - 8 * q^34 + 8 * q^35 + 6 * q^36 - 18 * q^37 + 16 * q^38 + 24 * q^39 - 12 * q^40 - 4 * q^41 + 4 * q^42 - 28 * q^43 - 14 * q^44 - 6 * q^45 + 4 * q^46 - 36 * q^47 - 4 * q^48 + 18 * q^49 + 12 * q^50 - 24 * q^51 - 4 * q^52 - 28 * q^54 + 14 * q^55 - 8 * q^56 - 50 * q^57 - 12 * q^59 + 4 * q^60 + 12 * q^61 + 2 * q^62 - 22 * q^63 + 12 * q^64 + 4 * q^65 + 4 * q^66 - 14 * q^67 - 8 * q^68 + 42 * q^69 + 8 * q^70 - 18 * q^71 + 6 * q^72 - 48 * q^73 - 18 * q^74 - 4 * q^75 + 16 * q^76 - 46 * q^77 + 24 * q^78 - 12 * q^80 + 12 * q^81 - 4 * q^82 + 20 * q^83 + 4 * q^84 + 8 * q^85 - 28 * q^86 - 14 * q^88 - 32 * q^89 - 6 * q^90 + 50 * q^91 + 4 * q^92 - 42 * q^93 - 36 * q^94 - 16 * q^95 - 4 * q^96 - 16 * q^97 + 18 * 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
$3$	−0.959933	−0.554217	−0.277109	−	0.960839i	$-0.589376\pi$
$3$	−0.959933	−0.554217	−0.277109	+	0.960839i	$0.589376\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.959933	−0.391891
$7$	4.10940	1.55321	0.776603	−	0.629990i	$-0.216941\pi$
$7$	4.10940	1.55321	0.776603	+	0.629990i	$0.216941\pi$
$8$	1.00000	0.353553
$9$	−2.07853	−0.692843
$10$	−1.00000	−0.316228
$11$	−4.21069	−1.26957	−0.634785	−	0.772688i	$-0.718912\pi$
$11$	−4.21069	−1.26957	−0.634785	+	0.772688i	$0.718912\pi$
$12$	−0.959933	−0.277109
$13$	3.81231	1.05734	0.528672	−	0.848826i	$-0.322690\pi$
$13$	3.81231	1.05734	0.528672	+	0.848826i	$0.322690\pi$
$14$	4.10940	1.09828
$15$	0.959933	0.247854
$16$	1.00000	0.250000
$17$	−7.44933	−1.80673	−0.903364	−	0.428875i	$-0.858910\pi$
$17$	−7.44933	−1.80673	−0.903364	+	0.428875i	$0.858910\pi$
$18$	−2.07853	−0.489914
$19$	4.70595	1.07962	0.539809	−	0.841787i	$-0.318496\pi$
$19$	4.70595	1.07962	0.539809	+	0.841787i	$0.318496\pi$
$20$	−1.00000	−0.223607
$21$	−3.94475	−0.860814
$22$	−4.21069	−0.897722
$23$	−1.16549	−0.243022	−0.121511	−	0.992590i	$-0.538774\pi$
$23$	−1.16549	−0.243022	−0.121511	+	0.992590i	$0.538774\pi$
$24$	−0.959933	−0.195945
$25$	1.00000	0.200000
$26$	3.81231	0.747655
$27$	4.87505	0.938203
$28$	4.10940	0.776603
$29$	0	0
$29$	0	0
$30$	0.959933	0.175259
$31$	−3.85350	−0.692109	−0.346055	−	0.938214i	$-0.612479\pi$
$31$	−3.85350	−0.692109	−0.346055	+	0.938214i	$0.612479\pi$
$32$	1.00000	0.176777
$33$	4.04198	0.703618
$34$	−7.44933	−1.27755
$35$	−4.10940	−0.694615
$36$	−2.07853	−0.346421
$37$	1.60320	0.263565	0.131783	−	0.991279i	$-0.457930\pi$
$37$	1.60320	0.263565	0.131783	+	0.991279i	$0.457930\pi$
$38$	4.70595	0.763405
$39$	−3.65956	−0.585999
$40$	−1.00000	−0.158114
$41$	−0.116852	−0.0182492	−0.00912462	−	0.999958i	$-0.502904\pi$
$41$	−0.116852	−0.0182492	−0.00912462	+	0.999958i	$0.502904\pi$
$42$	−3.94475	−0.608688
$43$	0.648590	0.0989090	0.0494545	−	0.998776i	$-0.484252\pi$
$43$	0.648590	0.0989090	0.0494545	+	0.998776i	$0.484252\pi$
$44$	−4.21069	−0.634785
$45$	2.07853	0.309849
$46$	−1.16549	−0.171842
$47$	−9.31488	−1.35872	−0.679358	−	0.733807i	$-0.737741\pi$
$47$	−9.31488	−1.35872	−0.679358	+	0.733807i	$0.737741\pi$
$48$	−0.959933	−0.138554
$49$	9.88715	1.41245
$50$	1.00000	0.141421
$51$	7.15086	1.00132
$52$	3.81231	0.528672
$53$	−5.39773	−0.741436	−0.370718	−	0.928746i	$-0.620888\pi$
$53$	−5.39773	−0.741436	−0.370718	+	0.928746i	$0.620888\pi$
$54$	4.87505	0.663410
$55$	4.21069	0.567769
$56$	4.10940	0.549141
$57$	−4.51739	−0.598343
$58$	0	0
$59$	−0.531452	−0.0691892	−0.0345946	−	0.999401i	$-0.511014\pi$
$59$	−0.531452	−0.0691892	−0.0345946	+	0.999401i	$0.511014\pi$
$60$	0.959933	0.123927
$61$	−10.9858	−1.40659	−0.703293	−	0.710900i	$-0.748288\pi$
$61$	−10.9858	−1.40659	−0.703293	+	0.710900i	$0.748288\pi$
$62$	−3.85350	−0.489395
$63$	−8.54150	−1.07613
$64$	1.00000	0.125000
$65$	−3.81231	−0.472859
$66$	4.04198	0.497533
$67$	−3.75707	−0.458999	−0.229500	−	0.973309i	$-0.573709\pi$
$67$	−3.75707	−0.458999	−0.229500	+	0.973309i	$0.573709\pi$
$68$	−7.44933	−0.903364
$69$	1.11879	0.134687
$70$	−4.10940	−0.491167
$71$	12.6402	1.50011	0.750056	−	0.661374i	$-0.230026\pi$
$71$	12.6402	1.50011	0.750056	+	0.661374i	$0.230026\pi$
$72$	−2.07853	−0.244957
$73$	5.31428	0.621989	0.310995	−	0.950412i	$-0.399338\pi$
$73$	5.31428	0.621989	0.310995	+	0.950412i	$0.399338\pi$
$74$	1.60320	0.186369
$75$	−0.959933	−0.110843
$76$	4.70595	0.539809
$77$	−17.3034	−1.97191
$78$	−3.65956	−0.414364
$79$	−17.4174	−1.95961	−0.979805	−	0.199956i	$-0.935920\pi$
$79$	−17.4174	−1.95961	−0.979805	+	0.199956i	$0.935920\pi$
$80$	−1.00000	−0.111803
$81$	1.55587	0.172874
$82$	−0.116852	−0.0129042
$83$	3.65039	0.400682	0.200341	−	0.979726i	$-0.435795\pi$
$83$	3.65039	0.400682	0.200341	+	0.979726i	$0.435795\pi$
$84$	−3.94475	−0.430407
$85$	7.44933	0.807993
$86$	0.648590	0.0699393
$87$	0	0
$88$	−4.21069	−0.448861
$89$	7.35968	0.780124	0.390062	−	0.920789i	$-0.372454\pi$
$89$	7.35968	0.780124	0.390062	+	0.920789i	$0.372454\pi$
$90$	2.07853	0.219096
$91$	15.6663	1.64227
$92$	−1.16549	−0.121511
$93$	3.69910	0.383579
$94$	−9.31488	−0.960757
$95$	−4.70595	−0.482820
$96$	−0.959933	−0.0979727
$97$	15.3893	1.56254	0.781272	−	0.624191i	$-0.214571\pi$
$97$	15.3893	1.56254	0.781272	+	0.624191i	$0.214571\pi$
$98$	9.88715	0.998753
$99$	8.75204	0.879613
$100$	1.00000	0.100000
$101$	−18.1348	−1.80448	−0.902242	−	0.431231i	$-0.858079\pi$
$101$	−18.1348	−1.80448	−0.902242	+	0.431231i	$0.858079\pi$
$102$	7.15086	0.708040
$103$	2.03192	0.200211	0.100105	−	0.994977i	$-0.468082\pi$
$103$	2.03192	0.200211	0.100105	+	0.994977i	$0.468082\pi$
$104$	3.81231	0.373828
$105$	3.94475	0.384968
$106$	−5.39773	−0.524274
$107$	−7.83283	−0.757228	−0.378614	−	0.925555i	$-0.623599\pi$
$107$	−7.83283	−0.757228	−0.378614	+	0.925555i	$0.623599\pi$
$108$	4.87505	0.469102
$109$	−13.8320	−1.32487	−0.662433	−	0.749121i	$-0.730476\pi$
$109$	−13.8320	−1.32487	−0.662433	+	0.749121i	$0.730476\pi$
$110$	4.21069	0.401474
$111$	−1.53897	−0.146072
$112$	4.10940	0.388302
$113$	−7.89404	−0.742609	−0.371304	−	0.928511i	$-0.621089\pi$
$113$	−7.89404	−0.742609	−0.371304	+	0.928511i	$0.621089\pi$
$114$	−4.51739	−0.423093
$115$	1.16549	0.108683
$116$	0	0
$117$	−7.92400	−0.732574
$118$	−0.531452	−0.0489241
$119$	−30.6123	−2.80622
$120$	0.959933	0.0876295
$121$	6.72991	0.611810
$122$	−10.9858	−0.994606
$123$	0.112170	0.0101140
$124$	−3.85350	−0.346055
$125$	−1.00000	−0.0894427
$126$	−8.54150	−0.760938
$127$	3.28402	0.291410	0.145705	−	0.989328i	$-0.453455\pi$
$127$	3.28402	0.291410	0.145705	+	0.989328i	$0.453455\pi$
$128$	1.00000	0.0883883
$129$	−0.622603	−0.0548171
$130$	−3.81231	−0.334362
$131$	−11.9835	−1.04701	−0.523503	−	0.852024i	$-0.675375\pi$
$131$	−11.9835	−1.04701	−0.523503	+	0.852024i	$0.675375\pi$
$132$	4.04198	0.351809
$133$	19.3386	1.67687
$134$	−3.75707	−0.324561
$135$	−4.87505	−0.419577
$136$	−7.44933	−0.638775
$137$	22.9142	1.95769	0.978846	−	0.204597i	$-0.0655884\pi$
$137$	22.9142	1.95769	0.978846	+	0.204597i	$0.0655884\pi$
$138$	1.11879	0.0952379
$139$	−14.6593	−1.24339	−0.621694	−	0.783260i	$-0.713555\pi$
$139$	−14.6593	−1.24339	−0.621694	+	0.783260i	$0.713555\pi$
$140$	−4.10940	−0.347308
$141$	8.94166	0.753024
$142$	12.6402	1.06074
$143$	−16.0525	−1.34237
$144$	−2.07853	−0.173211
$145$	0	0
$146$	5.31428	0.439813
$147$	−9.49100	−0.782805
$148$	1.60320	0.131783
$149$	2.44324	0.200158	0.100079	−	0.994979i	$-0.468090\pi$
$149$	2.44324	0.200158	0.100079	+	0.994979i	$0.468090\pi$
$150$	−0.959933	−0.0783782
$151$	−15.2563	−1.24154	−0.620769	−	0.783993i	$-0.713180\pi$
$151$	−15.2563	−1.24154	−0.620769	+	0.783993i	$0.713180\pi$
$152$	4.70595	0.381703
$153$	15.4836	1.25178
$154$	−17.3034	−1.39435
$155$	3.85350	0.309521
$156$	−3.65956	−0.292999
$157$	−17.9046	−1.42894	−0.714472	−	0.699664i	$-0.753333\pi$
$157$	−17.9046	−1.42894	−0.714472	+	0.699664i	$0.753333\pi$
$158$	−17.4174	−1.38565
$159$	5.18146	0.410917
$160$	−1.00000	−0.0790569
$161$	−4.78946	−0.377463
$162$	1.55587	0.122241
$163$	8.12882	0.636698	0.318349	−	0.947974i	$-0.396872\pi$
$163$	8.12882	0.636698	0.318349	+	0.947974i	$0.396872\pi$
$164$	−0.116852	−0.00912462
$165$	−4.04198	−0.314668
$166$	3.65039	0.283325
$167$	−18.9947	−1.46985	−0.734927	−	0.678146i	$-0.762784\pi$
$167$	−18.9947	−1.46985	−0.734927	+	0.678146i	$0.762784\pi$
$168$	−3.94475	−0.304344
$169$	1.53371	0.117977
$170$	7.44933	0.571337
$171$	−9.78145	−0.748006
$172$	0.648590	0.0494545
$173$	18.8696	1.43463	0.717314	−	0.696750i	$-0.245371\pi$
$173$	18.8696	1.43463	0.717314	+	0.696750i	$0.245371\pi$
$174$	0	0
$175$	4.10940	0.310641
$176$	−4.21069	−0.317393
$177$	0.510158	0.0383458
$178$	7.35968	0.551631
$179$	−3.73175	−0.278924	−0.139462	−	0.990227i	$-0.544537\pi$
$179$	−3.73175	−0.278924	−0.139462	+	0.990227i	$0.544537\pi$
$180$	2.07853	0.154924
$181$	−3.28579	−0.244231	−0.122116	−	0.992516i	$-0.538968\pi$
$181$	−3.28579	−0.244231	−0.122116	+	0.992516i	$0.538968\pi$
$182$	15.6663	1.16126
$183$	10.5456	0.779554
$184$	−1.16549	−0.0859211
$185$	−1.60320	−0.117870
$186$	3.69910	0.271231
$187$	31.3668	2.29377
$188$	−9.31488	−0.679358
$189$	20.0335	1.45722
$190$	−4.70595	−0.341405
$191$	14.0579	1.01719	0.508596	−	0.861005i	$-0.330165\pi$
$191$	14.0579	1.01719	0.508596	+	0.861005i	$0.330165\pi$
$192$	−0.959933	−0.0692772
$193$	−2.97324	−0.214018	−0.107009	−	0.994258i	$-0.534127\pi$
$193$	−2.97324	−0.214018	−0.107009	+	0.994258i	$0.534127\pi$
$194$	15.3893	1.10489
$195$	3.65956	0.262067
$196$	9.88715	0.706225
$197$	−4.21263	−0.300138	−0.150069	−	0.988676i	$-0.547950\pi$
$197$	−4.21263	−0.300138	−0.150069	+	0.988676i	$0.547950\pi$
$198$	8.75204	0.621980
$199$	−23.4542	−1.66262	−0.831310	−	0.555808i	$-0.812409\pi$
$199$	−23.4542	−1.66262	−0.831310	+	0.555808i	$0.812409\pi$
$200$	1.00000	0.0707107
$201$	3.60653	0.254385
$202$	−18.1348	−1.27596
$203$	0	0
$204$	7.15086	0.500660
$205$	0.116852	0.00816131
$206$	2.03192	0.141570
$207$	2.42251	0.168376
$208$	3.81231	0.264336
$209$	−19.8153	−1.37065
$210$	3.94475	0.272213
$211$	−1.63033	−0.112237	−0.0561184	−	0.998424i	$-0.517872\pi$
$211$	−1.63033	−0.112237	−0.0561184	+	0.998424i	$0.517872\pi$
$212$	−5.39773	−0.370718
$213$	−12.1337	−0.831388
$214$	−7.83283	−0.535441
$215$	−0.648590	−0.0442335
$216$	4.87505	0.331705
$217$	−15.8356	−1.07499
$218$	−13.8320	−0.936822
$219$	−5.10135	−0.344717
$220$	4.21069	0.283885
$221$	−28.3991	−1.91033
$222$	−1.53897	−0.103289
$223$	12.2060	0.817378	0.408689	−	0.912674i	$-0.365986\pi$
$223$	12.2060	0.817378	0.408689	+	0.912674i	$0.365986\pi$
$224$	4.10940	0.274571
$225$	−2.07853	−0.138569
$226$	−7.89404	−0.525104
$227$	14.7048	0.975991	0.487995	−	0.872846i	$-0.337728\pi$
$227$	14.7048	0.975991	0.487995	+	0.872846i	$0.337728\pi$
$228$	−4.51739	−0.299172
$229$	−9.73181	−0.643096	−0.321548	−	0.946893i	$-0.604203\pi$
$229$	−9.73181	−0.643096	−0.321548	+	0.946893i	$0.604203\pi$
$230$	1.16549	0.0768502
$231$	16.6101	1.09286
$232$	0	0
$233$	−19.2700	−1.26242	−0.631209	−	0.775613i	$-0.717441\pi$
$233$	−19.2700	−1.26242	−0.631209	+	0.775613i	$0.717441\pi$
$234$	−7.92400	−0.518008
$235$	9.31488	0.607636
$236$	−0.531452	−0.0345946
$237$	16.7195	1.08605
$238$	−30.6123	−1.98430
$239$	−12.5692	−0.813032	−0.406516	−	0.913644i	$-0.633256\pi$
$239$	−12.5692	−0.813032	−0.406516	+	0.913644i	$0.633256\pi$
$240$	0.959933	0.0619634
$241$	−13.9791	−0.900472	−0.450236	−	0.892910i	$-0.648660\pi$
$241$	−13.9791	−0.900472	−0.450236	+	0.892910i	$0.648660\pi$
$242$	6.72991	0.432615
$243$	−16.1187	−1.03401
$244$	−10.9858	−0.703293
$245$	−9.88715	−0.631667
$246$	0.112170	0.00715171
$247$	17.9405	1.14153
$248$	−3.85350	−0.244698
$249$	−3.50413	−0.222065
$250$	−1.00000	−0.0632456
$251$	11.3099	0.713877	0.356938	−	0.934128i	$-0.383821\pi$
$251$	11.3099	0.713877	0.356938	+	0.934128i	$0.383821\pi$
$252$	−8.54150	−0.538064
$253$	4.90752	0.308533
$254$	3.28402	0.206058
$255$	−7.15086	−0.447804
$256$	1.00000	0.0625000
$257$	20.6322	1.28700	0.643502	−	0.765445i	$-0.277481\pi$
$257$	20.6322	1.28700	0.643502	+	0.765445i	$0.277481\pi$
$258$	−0.622603	−0.0387616
$259$	6.58820	0.409371
$260$	−3.81231	−0.236429
$261$	0	0
$262$	−11.9835	−0.740345
$263$	−18.2705	−1.12661	−0.563304	−	0.826250i	$-0.690470\pi$
$263$	−18.2705	−1.12661	−0.563304	+	0.826250i	$0.690470\pi$
$264$	4.04198	0.248767
$265$	5.39773	0.331580
$266$	19.3386	1.18573
$267$	−7.06480	−0.432359
$268$	−3.75707	−0.229500
$269$	1.75159	0.106797	0.0533983	−	0.998573i	$-0.482995\pi$
$269$	1.75159	0.106797	0.0533983	+	0.998573i	$0.482995\pi$
$270$	−4.87505	−0.296686
$271$	14.4741	0.879238	0.439619	−	0.898184i	$-0.355113\pi$
$271$	14.4741	0.879238	0.439619	+	0.898184i	$0.355113\pi$
$272$	−7.44933	−0.451682
$273$	−15.0386	−0.910177
$274$	22.9142	1.38430
$275$	−4.21069	−0.253914
$276$	1.11879	0.0673434
$277$	−15.3192	−0.920439	−0.460220	−	0.887805i	$-0.652229\pi$
$277$	−15.3192	−0.920439	−0.460220	+	0.887805i	$0.652229\pi$
$278$	−14.6593	−0.879208
$279$	8.00961	0.479523
$280$	−4.10940	−0.245584
$281$	19.3776	1.15597	0.577986	−	0.816047i	$-0.303839\pi$
$281$	19.3776	1.15597	0.577986	+	0.816047i	$0.303839\pi$
$282$	8.94166	0.532468
$283$	25.7297	1.52947	0.764735	−	0.644345i	$-0.222870\pi$
$283$	25.7297	1.52947	0.764735	+	0.644345i	$0.222870\pi$
$284$	12.6402	0.750056
$285$	4.51739	0.267587
$286$	−16.0525	−0.949202
$287$	−0.480192	−0.0283448
$288$	−2.07853	−0.122478
$289$	38.4925	2.26426
$290$	0	0
$291$	−14.7727	−0.865989
$292$	5.31428	0.310995
$293$	−12.1860	−0.711912	−0.355956	−	0.934503i	$-0.615845\pi$
$293$	−12.1860	−0.711912	−0.355956	+	0.934503i	$0.615845\pi$
$294$	−9.49100	−0.553526
$295$	0.531452	0.0309423
$296$	1.60320	0.0931843
$297$	−20.5273	−1.19112
$298$	2.44324	0.141533
$299$	−4.44321	−0.256958
$300$	−0.959933	−0.0554217
$301$	2.66531	0.153626
$302$	−15.2563	−0.877901
$303$	17.4082	1.00008
$304$	4.70595	0.269905
$305$	10.9858	0.629044
$306$	15.4836	0.885141
$307$	−1.19779	−0.0683613	−0.0341807	−	0.999416i	$-0.510882\pi$
$307$	−1.19779	−0.0683613	−0.0341807	+	0.999416i	$0.510882\pi$
$308$	−17.3034	−0.985953
$309$	−1.95050	−0.110960
$310$	3.85350	0.218864
$311$	−16.2878	−0.923596	−0.461798	−	0.886985i	$-0.652796\pi$
$311$	−16.2878	−0.923596	−0.461798	+	0.886985i	$0.652796\pi$
$312$	−3.65956	−0.207182
$313$	−1.02513	−0.0579438	−0.0289719	−	0.999580i	$-0.509223\pi$
$313$	−1.02513	−0.0579438	−0.0289719	+	0.999580i	$0.509223\pi$
$314$	−17.9046	−1.01042
$315$	8.54150	0.481259
$316$	−17.4174	−0.979805
$317$	−21.6671	−1.21695	−0.608473	−	0.793575i	$-0.708218\pi$
$317$	−21.6671	−1.21695	−0.608473	+	0.793575i	$0.708218\pi$
$318$	5.18146	0.290562
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	7.51899	0.419669
$322$	−4.78946	−0.266906
$323$	−35.0561	−1.95058
$324$	1.55587	0.0864372
$325$	3.81231	0.211469
$326$	8.12882	0.450214
$327$	13.2778	0.734264
$328$	−0.116852	−0.00645208
$329$	−38.2786	−2.11037
$330$	−4.04198	−0.222504
$331$	−16.8469	−0.925991	−0.462996	−	0.886361i	$-0.653225\pi$
$331$	−16.8469	−0.925991	−0.462996	+	0.886361i	$0.653225\pi$
$332$	3.65039	0.200341
$333$	−3.33231	−0.182609
$334$	−18.9947	−1.03934
$335$	3.75707	0.205271
$336$	−3.94475	−0.215204
$337$	27.4529	1.49545	0.747726	−	0.664007i	$-0.231145\pi$
$337$	27.4529	1.49545	0.747726	+	0.664007i	$0.231145\pi$
$338$	1.53371	0.0834227
$339$	7.57775	0.411567
$340$	7.44933	0.403997
$341$	16.2259	0.878682
$342$	−9.78145	−0.528920
$343$	11.8645	0.640620
$344$	0.648590	0.0349696
$345$	−1.11879	−0.0602338
$346$	18.8696	1.01444
$347$	19.9237	1.06956	0.534781	−	0.844991i	$-0.320394\pi$
$347$	19.9237	1.06956	0.534781	+	0.844991i	$0.320394\pi$
$348$	0	0
$349$	27.1775	1.45478	0.727388	−	0.686226i	$-0.240734\pi$
$349$	27.1775	1.45478	0.727388	+	0.686226i	$0.240734\pi$
$350$	4.10940	0.219657
$351$	18.5852	0.992004
$352$	−4.21069	−0.224431
$353$	−13.5278	−0.720013	−0.360006	−	0.932950i	$-0.617225\pi$
$353$	−13.5278	−0.720013	−0.360006	+	0.932950i	$0.617225\pi$
$354$	0.510158	0.0271146
$355$	−12.6402	−0.670871
$356$	7.35968	0.390062
$357$	29.3857	1.55526
$358$	−3.73175	−0.197229
$359$	−10.3500	−0.546250	−0.273125	−	0.961979i	$-0.588057\pi$
$359$	−10.3500	−0.546250	−0.273125	+	0.961979i	$0.588057\pi$
$360$	2.07853	0.109548
$361$	3.14593	0.165575
$362$	−3.28579	−0.172698
$363$	−6.46026	−0.339076
$364$	15.6663	0.821137
$365$	−5.31428	−0.278162
$366$	10.5456	0.551228
$367$	−13.2019	−0.689132	−0.344566	−	0.938762i	$-0.611974\pi$
$367$	−13.2019	−0.689132	−0.344566	+	0.938762i	$0.611974\pi$
$368$	−1.16549	−0.0607554
$369$	0.242881	0.0126439
$370$	−1.60320	−0.0833466
$371$	−22.1814	−1.15160
$372$	3.69910	0.191789
$373$	9.10105	0.471234	0.235617	−	0.971846i	$-0.424289\pi$
$373$	9.10105	0.471234	0.235617	+	0.971846i	$0.424289\pi$
$374$	31.3668	1.62194
$375$	0.959933	0.0495707
$376$	−9.31488	−0.480378
$377$	0	0
$378$	20.0335	1.03041
$379$	0.168819	0.00867166	0.00433583	−	0.999991i	$-0.498620\pi$
$379$	0.168819	0.00867166	0.00433583	+	0.999991i	$0.498620\pi$
$380$	−4.70595	−0.241410
$381$	−3.15244	−0.161504
$382$	14.0579	0.719264
$383$	−37.6079	−1.92167	−0.960836	−	0.277118i	$-0.910621\pi$
$383$	−37.6079	−1.92167	−0.960836	+	0.277118i	$0.910621\pi$
$384$	−0.959933	−0.0489864
$385$	17.3034	0.881863
$386$	−2.97324	−0.151334
$387$	−1.34811	−0.0685284
$388$	15.3893	0.781272
$389$	1.45750	0.0738980	0.0369490	−	0.999317i	$-0.488236\pi$
$389$	1.45750	0.0738980	0.0369490	+	0.999317i	$0.488236\pi$
$390$	3.65956	0.185309
$391$	8.68212	0.439074
$392$	9.88715	0.499377
$393$	11.5034	0.580269
$394$	−4.21263	−0.212229
$395$	17.4174	0.876364
$396$	8.75204	0.439807
$397$	−8.51165	−0.427188	−0.213594	−	0.976923i	$-0.568517\pi$
$397$	−8.51165	−0.427188	−0.213594	+	0.976923i	$0.568517\pi$
$398$	−23.4542	−1.17565
$399$	−18.5638	−0.929351
$400$	1.00000	0.0500000
$401$	−18.4975	−0.923722	−0.461861	−	0.886952i	$-0.652818\pi$
$401$	−18.4975	−0.923722	−0.461861	+	0.886952i	$0.652818\pi$
$402$	3.60653	0.179878
$403$	−14.6907	−0.731798
$404$	−18.1348	−0.902242
$405$	−1.55587	−0.0773118
$406$	0	0
$407$	−6.75059	−0.334615
$408$	7.15086	0.354020
$409$	−13.3082	−0.658047	−0.329023	−	0.944322i	$-0.606719\pi$
$409$	−13.3082	−0.658047	−0.329023	+	0.944322i	$0.606719\pi$
$410$	0.116852	0.00577092
$411$	−21.9961	−1.08499
$412$	2.03192	0.100105
$413$	−2.18395	−0.107465
$414$	2.42251	0.119060
$415$	−3.65039	−0.179190
$416$	3.81231	0.186914
$417$	14.0720	0.689107
$418$	−19.8153	−0.969197
$419$	−16.7277	−0.817203	−0.408602	−	0.912713i	$-0.633983\pi$
$419$	−16.7277	−0.817203	−0.408602	+	0.912713i	$0.633983\pi$
$420$	3.94475	0.192484
$421$	34.7977	1.69593	0.847967	−	0.530048i	$-0.177826\pi$
$421$	34.7977	1.69593	0.847967	+	0.530048i	$0.177826\pi$
$422$	−1.63033	−0.0793634
$423$	19.3613	0.941376
$424$	−5.39773	−0.262137
$425$	−7.44933	−0.361346
$426$	−12.1337	−0.587880
$427$	−45.1449	−2.18472
$428$	−7.83283	−0.378614
$429$	15.4093	0.743967
$430$	−0.648590	−0.0312778
$431$	17.0050	0.819104	0.409552	−	0.912287i	$-0.365685\pi$
$431$	17.0050	0.819104	0.409552	+	0.912287i	$0.365685\pi$
$432$	4.87505	0.234551
$433$	−33.5266	−1.61118	−0.805592	−	0.592471i	$-0.798152\pi$
$433$	−33.5266	−1.61118	−0.805592	+	0.592471i	$0.798152\pi$
$434$	−15.8356	−0.760132
$435$	0	0
$436$	−13.8320	−0.662433
$437$	−5.48474	−0.262370
$438$	−5.10135	−0.243752
$439$	−13.0712	−0.623856	−0.311928	−	0.950106i	$-0.600975\pi$
$439$	−13.0712	−0.623856	−0.311928	+	0.950106i	$0.600975\pi$
$440$	4.21069	0.200737
$441$	−20.5507	−0.978606
$442$	−28.3991	−1.35081
$443$	6.64141	0.315543	0.157772	−	0.987476i	$-0.449569\pi$
$443$	6.64141	0.315543	0.157772	+	0.987476i	$0.449569\pi$
$444$	−1.53897	−0.0730362
$445$	−7.35968	−0.348882
$446$	12.2060	0.577973
$447$	−2.34535	−0.110931
$448$	4.10940	0.194151
$449$	−19.7479	−0.931962	−0.465981	−	0.884795i	$-0.654298\pi$
$449$	−19.7479	−0.931962	−0.465981	+	0.884795i	$0.654298\pi$
$450$	−2.07853	−0.0979828
$451$	0.492028	0.0231687
$452$	−7.89404	−0.371304
$453$	14.6450	0.688083
$454$	14.7048	0.690130
$455$	−15.6663	−0.734447
$456$	−4.51739	−0.211546
$457$	6.12161	0.286357	0.143179	−	0.989697i	$-0.454268\pi$
$457$	6.12161	0.286357	0.143179	+	0.989697i	$0.454268\pi$
$458$	−9.73181	−0.454738
$459$	−36.3158	−1.69508
$460$	1.16549	0.0543413
$461$	−24.4356	−1.13808	−0.569040	−	0.822310i	$-0.692685\pi$
$461$	−24.4356	−1.13808	−0.569040	+	0.822310i	$0.692685\pi$
$462$	16.6101	0.772772
$463$	−31.5188	−1.46480	−0.732402	−	0.680873i	$-0.761601\pi$
$463$	−31.5188	−1.46480	−0.732402	+	0.680873i	$0.761601\pi$
$464$	0	0
$465$	−3.69910	−0.171542
$466$	−19.2700	−0.892664
$467$	−19.5284	−0.903665	−0.451833	−	0.892103i	$-0.649230\pi$
$467$	−19.5284	−0.903665	−0.451833	+	0.892103i	$0.649230\pi$
$468$	−7.92400	−0.366287
$469$	−15.4393	−0.712920
$470$	9.31488	0.429663
$471$	17.1872	0.791946
$472$	−0.531452	−0.0244621
$473$	−2.73101	−0.125572
$474$	16.7195	0.767953
$475$	4.70595	0.215924
$476$	−30.6123	−1.40311
$477$	11.2193	0.513698
$478$	−12.5692	−0.574901
$479$	1.48149	0.0676911	0.0338456	−	0.999427i	$-0.489225\pi$
$479$	1.48149	0.0676911	0.0338456	+	0.999427i	$0.489225\pi$
$480$	0.959933	0.0438147
$481$	6.11191	0.278679
$482$	−13.9791	−0.636730
$483$	4.59756	0.209196
$484$	6.72991	0.305905
$485$	−15.3893	−0.698791
$486$	−16.1187	−0.731158
$487$	3.80566	0.172451	0.0862255	−	0.996276i	$-0.472519\pi$
$487$	3.80566	0.172451	0.0862255	+	0.996276i	$0.472519\pi$
$488$	−10.9858	−0.497303
$489$	−7.80312	−0.352869
$490$	−9.88715	−0.446656
$491$	−10.0979	−0.455713	−0.227856	−	0.973695i	$-0.573172\pi$
$491$	−10.0979	−0.455713	−0.227856	+	0.973695i	$0.573172\pi$
$492$	0.112170	0.00505702
$493$	0	0
$494$	17.9405	0.807182
$495$	−8.75204	−0.393375
$496$	−3.85350	−0.173027
$497$	51.9435	2.32998
$498$	−3.50413	−0.157024
$499$	4.30988	0.192937	0.0964685	−	0.995336i	$-0.469245\pi$
$499$	4.30988	0.192937	0.0964685	+	0.995336i	$0.469245\pi$
$500$	−1.00000	−0.0447214
$501$	18.2336	0.814619
$502$	11.3099	0.504787
$503$	−29.3703	−1.30956	−0.654779	−	0.755820i	$-0.727238\pi$
$503$	−29.3703	−1.30956	−0.654779	+	0.755820i	$0.727238\pi$
$504$	−8.54150	−0.380469
$505$	18.1348	0.806989
$506$	4.90752	0.218166
$507$	−1.47226	−0.0653852
$508$	3.28402	0.145705
$509$	29.3308	1.30007	0.650033	−	0.759906i	$-0.274755\pi$
$509$	29.3308	1.30007	0.650033	+	0.759906i	$0.274755\pi$
$510$	−7.15086	−0.316645
$511$	21.8385	0.966077
$512$	1.00000	0.0441942
$513$	22.9417	1.01290
$514$	20.6322	0.910049
$515$	−2.03192	−0.0895370
$516$	−0.622603	−0.0274086
$517$	39.2221	1.72499
$518$	6.58820	0.289469
$519$	−18.1135	−0.795096
$520$	−3.81231	−0.167181
$521$	−17.1811	−0.752716	−0.376358	−	0.926474i	$-0.622824\pi$
$521$	−17.1811	−0.752716	−0.376358	+	0.926474i	$0.622824\pi$
$522$	0	0
$523$	−7.90704	−0.345751	−0.172875	−	0.984944i	$-0.555306\pi$
$523$	−7.90704	−0.345751	−0.172875	+	0.984944i	$0.555306\pi$
$524$	−11.9835	−0.523503
$525$	−3.94475	−0.172163
$526$	−18.2705	−0.796632
$527$	28.7060	1.25045
$528$	4.04198	0.175905
$529$	−21.6416	−0.940941
$530$	5.39773	0.234463
$531$	1.10464	0.0479372
$532$	19.3386	0.838435
$533$	−0.445477	−0.0192957
$534$	−7.06480	−0.305724
$535$	7.83283	0.338643
$536$	−3.75707	−0.162281
$537$	3.58223	0.154585
$538$	1.75159	0.0755166
$539$	−41.6317	−1.79321
$540$	−4.87505	−0.209789
$541$	−9.62411	−0.413773	−0.206886	−	0.978365i	$-0.566333\pi$
$541$	−9.62411	−0.413773	−0.206886	+	0.978365i	$0.566333\pi$
$542$	14.4741	0.621715
$543$	3.15414	0.135357
$544$	−7.44933	−0.319387
$545$	13.8320	0.592498
$546$	−15.0386	−0.643592
$547$	37.5682	1.60630	0.803150	−	0.595776i	$-0.203155\pi$
$547$	37.5682	1.60630	0.803150	+	0.595776i	$0.203155\pi$
$548$	22.9142	0.978846
$549$	22.8343	0.974543
$550$	−4.21069	−0.179544
$551$	0	0
$552$	1.11879	0.0476190
$553$	−71.5750	−3.04368
$554$	−15.3192	−0.650849
$555$	1.53897	0.0653256
$556$	−14.6593	−0.621694
$557$	43.1083	1.82656	0.913278	−	0.407336i	$-0.133542\pi$
$557$	43.1083	1.82656	0.913278	+	0.407336i	$0.133542\pi$
$558$	8.00961	0.339074
$559$	2.47263	0.104581
$560$	−4.10940	−0.173654
$561$	−30.1100	−1.27125
$562$	19.3776	0.817395
$563$	15.5705	0.656219	0.328109	−	0.944640i	$-0.393589\pi$
$563$	15.5705	0.656219	0.328109	+	0.944640i	$0.393589\pi$
$564$	8.94166	0.376512
$565$	7.89404	0.332105
$566$	25.7297	1.08150
$567$	6.39369	0.268510
$568$	12.6402	0.530370
$569$	12.0100	0.503484	0.251742	−	0.967794i	$-0.418997\pi$
$569$	12.0100	0.503484	0.251742	+	0.967794i	$0.418997\pi$
$570$	4.51739	0.189213
$571$	14.5166	0.607499	0.303750	−	0.952752i	$-0.401761\pi$
$571$	14.5166	0.607499	0.303750	+	0.952752i	$0.401761\pi$
$572$	−16.0525	−0.671187
$573$	−13.4946	−0.563746
$574$	−0.480192	−0.0200428
$575$	−1.16549	−0.0486043
$576$	−2.07853	−0.0866054
$577$	36.0660	1.50145	0.750724	−	0.660617i	$-0.229705\pi$
$577$	36.0660	1.50145	0.750724	+	0.660617i	$0.229705\pi$
$578$	38.4925	1.60108
$579$	2.85411	0.118613
$580$	0	0
$581$	15.0009	0.622342
$582$	−14.7727	−0.612347
$583$	22.7282	0.941305
$584$	5.31428	0.219906
$585$	7.92400	0.327617
$586$	−12.1860	−0.503397
$587$	1.27023	0.0524279	0.0262140	−	0.999656i	$-0.491655\pi$
$587$	1.27023	0.0524279	0.0262140	+	0.999656i	$0.491655\pi$
$588$	−9.49100	−0.391402
$589$	−18.1344	−0.747214
$590$	0.531452	0.0218795
$591$	4.04385	0.166342
$592$	1.60320	0.0658913
$593$	−10.0385	−0.412233	−0.206117	−	0.978527i	$-0.566083\pi$
$593$	−10.0385	−0.412233	−0.206117	+	0.978527i	$0.566083\pi$
$594$	−20.5273	−0.842246
$595$	30.6123	1.25498
$596$	2.44324	0.100079
$597$	22.5144	0.921454
$598$	−4.44321	−0.181696
$599$	25.7627	1.05264	0.526318	−	0.850288i	$-0.323572\pi$
$599$	25.7627	1.05264	0.526318	+	0.850288i	$0.323572\pi$
$600$	−0.959933	−0.0391891
$601$	1.38969	0.0566867	0.0283434	−	0.999598i	$-0.490977\pi$
$601$	1.38969	0.0566867	0.0283434	+	0.999598i	$0.490977\pi$
$602$	2.66531	0.108630
$603$	7.80918	0.318014
$604$	−15.2563	−0.620769
$605$	−6.72991	−0.273610
$606$	17.4082	0.707161
$607$	−0.403309	−0.0163698	−0.00818491	−	0.999967i	$-0.502605\pi$
$607$	−0.403309	−0.0163698	−0.00818491	+	0.999967i	$0.502605\pi$
$608$	4.70595	0.190851
$609$	0	0
$610$	10.9858	0.444801
$611$	−35.5112	−1.43663
$612$	15.4836	0.625889
$613$	−39.0402	−1.57682	−0.788409	−	0.615152i	$-0.789095\pi$
$613$	−39.0402	−1.57682	−0.788409	+	0.615152i	$0.789095\pi$
$614$	−1.19779	−0.0483387
$615$	−0.112170	−0.00452314
$616$	−17.3034	−0.697174
$617$	−30.4047	−1.22405	−0.612023	−	0.790840i	$-0.709644\pi$
$617$	−30.4047	−1.22405	−0.612023	+	0.790840i	$0.709644\pi$
$618$	−1.95050	−0.0784608
$619$	36.0224	1.44786	0.723932	−	0.689872i	$-0.242333\pi$
$619$	36.0224	1.44786	0.723932	+	0.689872i	$0.242333\pi$
$620$	3.85350	0.154760
$621$	−5.68182	−0.228004
$622$	−16.2878	−0.653081
$623$	30.2438	1.21169
$624$	−3.65956	−0.146500
$625$	1.00000	0.0400000
$626$	−1.02513	−0.0409725
$627$	19.0213	0.759639
$628$	−17.9046	−0.714472
$629$	−11.9428	−0.476190
$630$	8.54150	0.340302
$631$	−39.2534	−1.56265	−0.781327	−	0.624122i	$-0.785457\pi$
$631$	−39.2534	−1.56265	−0.781327	+	0.624122i	$0.785457\pi$
$632$	−17.4174	−0.692827
$633$	1.56501	0.0622036
$634$	−21.6671	−0.860511
$635$	−3.28402	−0.130322
$636$	5.18146	0.205458
$637$	37.6929	1.49345
$638$	0	0
$639$	−26.2730	−1.03934
$640$	−1.00000	−0.0395285
$641$	−44.8695	−1.77224	−0.886119	−	0.463457i	$-0.846609\pi$
$641$	−44.8695	−1.77224	−0.886119	+	0.463457i	$0.846609\pi$
$642$	7.51899	0.296751
$643$	20.3336	0.801879	0.400939	−	0.916105i	$-0.368684\pi$
$643$	20.3336	0.801879	0.400939	+	0.916105i	$0.368684\pi$
$644$	−4.78946	−0.188731
$645$	0.622603	0.0245150
$646$	−35.0561	−1.37927
$647$	−15.0425	−0.591381	−0.295690	−	0.955284i	$-0.595550\pi$
$647$	−15.0425	−0.591381	−0.295690	+	0.955284i	$0.595550\pi$
$648$	1.55587	0.0611203
$649$	2.23778	0.0878406
$650$	3.81231	0.149531
$651$	15.2011	0.595777
$652$	8.12882	0.318349
$653$	−37.3149	−1.46024	−0.730122	−	0.683316i	$-0.760537\pi$
$653$	−37.3149	−1.46024	−0.730122	+	0.683316i	$0.760537\pi$
$654$	13.2778	0.519203
$655$	11.9835	0.468236
$656$	−0.116852	−0.00456231
$657$	−11.0459	−0.430941
$658$	−38.2786	−1.49225
$659$	−0.0979351	−0.00381501	−0.00190751	−	0.999998i	$-0.500607\pi$
$659$	−0.0979351	−0.00381501	−0.00190751	+	0.999998i	$0.500607\pi$
$660$	−4.04198	−0.157334
$661$	−21.2498	−0.826521	−0.413260	−	0.910613i	$-0.635610\pi$
$661$	−21.2498	−0.826521	−0.413260	+	0.910613i	$0.635610\pi$
$662$	−16.8469	−0.654775
$663$	27.2613	1.05874
$664$	3.65039	0.141663
$665$	−19.3386	−0.749919
$666$	−3.33231	−0.129124
$667$	0	0
$668$	−18.9947	−0.734927
$669$	−11.7170	−0.453005
$670$	3.75707	0.145148
$671$	46.2577	1.78576
$672$	−3.94475	−0.152172
$673$	7.19665	0.277410	0.138705	−	0.990334i	$-0.455706\pi$
$673$	7.19665	0.277410	0.138705	+	0.990334i	$0.455706\pi$
$674$	27.4529	1.05744
$675$	4.87505	0.187641
$676$	1.53371	0.0589887
$677$	−28.0561	−1.07828	−0.539141	−	0.842215i	$-0.681251\pi$
$677$	−28.0561	−1.07828	−0.539141	+	0.842215i	$0.681251\pi$
$678$	7.57775	0.291022
$679$	63.2407	2.42695
$680$	7.44933	0.285669
$681$	−14.1156	−0.540911
$682$	16.2259	0.621322
$683$	−31.0220	−1.18702	−0.593511	−	0.804826i	$-0.702259\pi$
$683$	−31.0220	−1.18702	−0.593511	+	0.804826i	$0.702259\pi$
$684$	−9.78145	−0.374003
$685$	−22.9142	−0.875507
$686$	11.8645	0.452987
$687$	9.34189	0.356415
$688$	0.648590	0.0247273
$689$	−20.5778	−0.783953
$690$	−1.11879	−0.0425917
$691$	28.9514	1.10136	0.550682	−	0.834715i	$-0.314368\pi$
$691$	28.9514	1.10136	0.550682	+	0.834715i	$0.314368\pi$
$692$	18.8696	0.717314
$693$	35.9656	1.36622
$694$	19.9237	0.756295
$695$	14.6593	0.556060
$696$	0	0
$697$	0.870470	0.0329714
$698$	27.1775	1.02868
$699$	18.4979	0.699654
$700$	4.10940	0.155321
$701$	−0.653120	−0.0246680	−0.0123340	−	0.999924i	$-0.503926\pi$
$701$	−0.653120	−0.0246680	−0.0123340	+	0.999924i	$0.503926\pi$
$702$	18.5852	0.701453
$703$	7.54459	0.284550
$704$	−4.21069	−0.158696
$705$	−8.94166	−0.336762
$706$	−13.5278	−0.509126
$707$	−74.5232	−2.80274
$708$	0.510158	0.0191729
$709$	2.36896	0.0889683	0.0444842	−	0.999010i	$-0.485836\pi$
$709$	2.36896	0.0889683	0.0444842	+	0.999010i	$0.485836\pi$
$710$	−12.6402	−0.474377
$711$	36.2026	1.35770
$712$	7.35968	0.275816
$713$	4.49122	0.168197
$714$	29.3857	1.09973
$715$	16.0525	0.600328
$716$	−3.73175	−0.139462
$717$	12.0656	0.450597
$718$	−10.3500	−0.386257
$719$	33.4174	1.24626	0.623130	−	0.782118i	$-0.285861\pi$
$719$	33.4174	1.24626	0.623130	+	0.782118i	$0.285861\pi$
$720$	2.07853	0.0774622
$721$	8.34996	0.310969
$722$	3.14593	0.117079
$723$	13.4190	0.499057
$724$	−3.28579	−0.122116
$725$	0	0
$726$	−6.46026	−0.239763
$727$	−2.91504	−0.108113	−0.0540565	−	0.998538i	$-0.517215\pi$
$727$	−2.91504	−0.108113	−0.0540565	+	0.998538i	$0.517215\pi$
$728$	15.6663	0.580632
$729$	10.8052	0.400194
$730$	−5.31428	−0.196690
$731$	−4.83156	−0.178702
$732$	10.5456	0.389777
$733$	11.7142	0.432673	0.216336	−	0.976319i	$-0.430589\pi$
$733$	11.7142	0.432673	0.216336	+	0.976319i	$0.430589\pi$
$734$	−13.2019	−0.487290
$735$	9.49100	0.350081
$736$	−1.16549	−0.0429605
$737$	15.8199	0.582732
$738$	0.242881	0.00894056
$739$	−32.2147	−1.18504	−0.592519	−	0.805556i	$-0.701867\pi$
$739$	−32.2147	−1.18504	−0.592519	+	0.805556i	$0.701867\pi$
$740$	−1.60320	−0.0589349
$741$	−17.2217	−0.632655
$742$	−22.1814	−0.814306
$743$	−12.2621	−0.449853	−0.224927	−	0.974376i	$-0.572214\pi$
$743$	−12.2621	−0.449853	−0.224927	+	0.974376i	$0.572214\pi$
$744$	3.69910	0.135616
$745$	−2.44324	−0.0895135
$746$	9.10105	0.333213
$747$	−7.58744	−0.277610
$748$	31.3668	1.14688
$749$	−32.1882	−1.17613
$750$	0.959933	0.0350518
$751$	53.3230	1.94578	0.972891	−	0.231264i	$-0.0742860\pi$
$751$	53.3230	1.94578	0.972891	+	0.231264i	$0.0742860\pi$
$752$	−9.31488	−0.339679
$753$	−10.8568	−0.395643
$754$	0	0
$755$	15.2563	0.555233
$756$	20.0335	0.728612
$757$	1.74254	0.0633338	0.0316669	−	0.999498i	$-0.489918\pi$
$757$	1.74254	0.0633338	0.0316669	+	0.999498i	$0.489918\pi$
$758$	0.168819	0.00613179
$759$	−4.71089	−0.170994
$760$	−4.70595	−0.170703
$761$	28.2498	1.02406	0.512028	−	0.858969i	$-0.328894\pi$
$761$	28.2498	1.02406	0.512028	+	0.858969i	$0.328894\pi$
$762$	−3.15244	−0.114201
$763$	−56.8412	−2.05779
$764$	14.0579	0.508596
$765$	−15.4836	−0.559812
$766$	−37.6079	−1.35883
$767$	−2.02606	−0.0731568
$768$	−0.959933	−0.0346386
$769$	−9.81324	−0.353874	−0.176937	−	0.984222i	$-0.556619\pi$
$769$	−9.81324	−0.353874	−0.176937	+	0.984222i	$0.556619\pi$
$770$	17.3034	0.623571
$771$	−19.8056	−0.713280
$772$	−2.97324	−0.107009
$773$	−13.4221	−0.482761	−0.241381	−	0.970431i	$-0.577600\pi$
$773$	−13.4221	−0.482761	−0.241381	+	0.970431i	$0.577600\pi$
$774$	−1.34811	−0.0484569
$775$	−3.85350	−0.138422
$776$	15.3893	0.552443
$777$	−6.32423	−0.226881
$778$	1.45750	0.0522538
$779$	−0.549900	−0.0197022
$780$	3.65956	0.131033
$781$	−53.2238	−1.90450
$782$	8.68212	0.310472
$783$	0	0
$784$	9.88715	0.353113
$785$	17.9046	0.639043
$786$	11.5034	0.410312
$787$	−39.7206	−1.41589	−0.707944	−	0.706269i	$-0.750377\pi$
$787$	−39.7206	−1.41589	−0.707944	+	0.706269i	$0.750377\pi$
$788$	−4.21263	−0.150069
$789$	17.5385	0.624386
$790$	17.4174	0.619683
$791$	−32.4398	−1.15342
$792$	8.75204	0.310990
$793$	−41.8812	−1.48725
$794$	−8.51165	−0.302067
$795$	−5.18146	−0.183767
$796$	−23.4542	−0.831310
$797$	27.0561	0.958378	0.479189	−	0.877712i	$-0.340931\pi$
$797$	27.0561	0.958378	0.479189	+	0.877712i	$0.340931\pi$
$798$	−18.5638	−0.657150
$799$	69.3896	2.45483
$800$	1.00000	0.0353553
$801$	−15.2973	−0.540504
$802$	−18.4975	−0.653170
$803$	−22.3768	−0.789659
$804$	3.60653	0.127193
$805$	4.78946	0.168806
$806$	−14.6907	−0.517459
$807$	−1.68141	−0.0591885
$808$	−18.1348	−0.637981
$809$	7.59995	0.267200	0.133600	−	0.991035i	$-0.457346\pi$
$809$	7.59995	0.267200	0.133600	+	0.991035i	$0.457346\pi$
$810$	−1.55587	−0.0546677
$811$	11.8236	0.415182	0.207591	−	0.978216i	$-0.433438\pi$
$811$	11.8236	0.415182	0.207591	+	0.978216i	$0.433438\pi$
$812$	0	0
$813$	−13.8942	−0.487289
$814$	−6.75059	−0.236608
$815$	−8.12882	−0.284740
$816$	7.15086	0.250330
$817$	3.05223	0.106784
$818$	−13.3082	−0.465309
$819$	−32.5629	−1.13784
$820$	0.116852	0.00408065
$821$	−26.3202	−0.918581	−0.459290	−	0.888286i	$-0.651896\pi$
$821$	−26.3202	−0.918581	−0.459290	+	0.888286i	$0.651896\pi$
$822$	−21.9961	−0.767202
$823$	26.8289	0.935197	0.467599	−	0.883941i	$-0.345119\pi$
$823$	26.8289	0.935197	0.467599	+	0.883941i	$0.345119\pi$
$824$	2.03192	0.0707852
$825$	4.04198	0.140724
$826$	−2.18395	−0.0759893
$827$	19.1316	0.665272	0.332636	−	0.943055i	$-0.392062\pi$
$827$	19.1316	0.665272	0.332636	+	0.943055i	$0.392062\pi$
$828$	2.42251	0.0841879
$829$	−13.7458	−0.477410	−0.238705	−	0.971092i	$-0.576723\pi$
$829$	−13.7458	−0.477410	−0.238705	+	0.971092i	$0.576723\pi$
$830$	−3.65039	−0.126707
$831$	14.7054	0.510123
$832$	3.81231	0.132168
$833$	−73.6526	−2.55191
$834$	14.0720	0.487272
$835$	18.9947	0.657339
$836$	−19.8153	−0.685326
$837$	−18.7860	−0.649339
$838$	−16.7277	−0.577850
$839$	−39.0427	−1.34790	−0.673952	−	0.738775i	$-0.735404\pi$
$839$	−39.0427	−1.34790	−0.673952	+	0.738775i	$0.735404\pi$
$840$	3.94475	0.136107
$841$	0	0
$842$	34.7977	1.19921
$843$	−18.6012	−0.640660
$844$	−1.63033	−0.0561184
$845$	−1.53371	−0.0527611
$846$	19.3613	0.665654
$847$	27.6559	0.950267
$848$	−5.39773	−0.185359
$849$	−24.6987	−0.847659
$850$	−7.44933	−0.255510
$851$	−1.86852	−0.0640520
$852$	−12.1337	−0.415694
$853$	−24.5689	−0.841223	−0.420612	−	0.907241i	$-0.638184\pi$
$853$	−24.5689	−0.841223	−0.420612	+	0.907241i	$0.638184\pi$
$854$	−45.1449	−1.54483
$855$	9.78145	0.334518
$856$	−7.83283	−0.267721
$857$	−2.33010	−0.0795948	−0.0397974	−	0.999208i	$-0.512671\pi$
$857$	−2.33010	−0.0795948	−0.0397974	+	0.999208i	$0.512671\pi$
$858$	15.4093	0.526064
$859$	23.5168	0.802382	0.401191	−	0.915994i	$-0.368596\pi$
$859$	23.5168	0.802382	0.401191	+	0.915994i	$0.368596\pi$
$860$	−0.648590	−0.0221167
$861$	0.460952	0.0157092
$862$	17.0050	0.579194
$863$	−6.26920	−0.213406	−0.106703	−	0.994291i	$-0.534029\pi$
$863$	−6.26920	−0.213406	−0.106703	+	0.994291i	$0.534029\pi$
$864$	4.87505	0.165852
$865$	−18.8696	−0.641585
$866$	−33.5266	−1.13928
$867$	−36.9502	−1.25489
$868$	−15.8356	−0.537494
$869$	73.3392	2.48786
$870$	0	0
$871$	−14.3231	−0.485320
$872$	−13.8320	−0.468411
$873$	−31.9871	−1.08260
$874$	−5.48474	−0.185524
$875$	−4.10940	−0.138923
$876$	−5.10135	−0.172359
$877$	35.5522	1.20051	0.600257	−	0.799807i	$-0.295065\pi$
$877$	35.5522	1.20051	0.600257	+	0.799807i	$0.295065\pi$
$878$	−13.0712	−0.441133
$879$	11.6977	0.394554
$880$	4.21069	0.141942
$881$	57.0453	1.92190	0.960952	−	0.276715i	$-0.0892459\pi$
$881$	57.0453	1.92190	0.960952	+	0.276715i	$0.0892459\pi$
$882$	−20.5507	−0.691979
$883$	16.6921	0.561734	0.280867	−	0.959747i	$-0.409378\pi$
$883$	16.6921	0.561734	0.280867	+	0.959747i	$0.409378\pi$
$884$	−28.3991	−0.955167
$885$	−0.510158	−0.0171488
$886$	6.64141	0.223123
$887$	−1.04928	−0.0352313	−0.0176157	−	0.999845i	$-0.505608\pi$
$887$	−1.04928	−0.0352313	−0.0176157	+	0.999845i	$0.505608\pi$
$888$	−1.53897	−0.0516444
$889$	13.4953	0.452619
$890$	−7.35968	−0.246697
$891$	−6.55129	−0.219476
$892$	12.2060	0.408689
$893$	−43.8353	−1.46689
$894$	−2.34535	−0.0784402
$895$	3.73175	0.124739
$896$	4.10940	0.137285
$897$	4.26518	0.142410
$898$	−19.7479	−0.658996
$899$	0	0
$900$	−2.07853	−0.0692843
$901$	40.2095	1.33957
$902$	0.492028	0.0163827
$903$	−2.55852	−0.0851423
$904$	−7.89404	−0.262552
$905$	3.28579	0.109224
$906$	14.6450	0.486548
$907$	49.1378	1.63159	0.815797	−	0.578338i	$-0.196298\pi$
$907$	49.1378	1.63159	0.815797	+	0.578338i	$0.196298\pi$
$908$	14.7048	0.487995
$909$	37.6938	1.25022
$910$	−15.6663	−0.519333
$911$	13.6376	0.451833	0.225917	−	0.974147i	$-0.427462\pi$
$911$	13.6376	0.451833	0.225917	+	0.974147i	$0.427462\pi$
$912$	−4.51739	−0.149586
$913$	−15.3707	−0.508694
$914$	6.12161	0.202485
$915$	−10.5456	−0.348627
$916$	−9.73181	−0.321548
$917$	−49.2451	−1.62622
$918$	−36.3158	−1.19860
$919$	−37.2201	−1.22778	−0.613889	−	0.789392i	$-0.710396\pi$
$919$	−37.2201	−1.22778	−0.613889	+	0.789392i	$0.710396\pi$
$920$	1.16549	0.0384251
$921$	1.14980	0.0378870
$922$	−24.4356	−0.804744
$923$	48.1882	1.58614
$924$	16.6101	0.546432
$925$	1.60320	0.0527130
$926$	−31.5188	−1.03577
$927$	−4.22340	−0.138715
$928$	0	0
$929$	−25.0203	−0.820891	−0.410445	−	0.911885i	$-0.634627\pi$
$929$	−25.0203	−0.820891	−0.410445	+	0.911885i	$0.634627\pi$
$930$	−3.69910	−0.121298
$931$	46.5284	1.52491
$932$	−19.2700	−0.631209
$933$	15.6352	0.511873
$934$	−19.5284	−0.638988
$935$	−31.3668	−1.02580
$936$	−7.92400	−0.259004
$937$	13.5433	0.442440	0.221220	−	0.975224i	$-0.428996\pi$
$937$	13.5433	0.442440	0.221220	+	0.975224i	$0.428996\pi$
$938$	−15.4393	−0.504111
$939$	0.984057	0.0321135
$940$	9.31488	0.303818
$941$	42.5667	1.38764	0.693818	−	0.720150i	$-0.255927\pi$
$941$	42.5667	1.38764	0.693818	+	0.720150i	$0.255927\pi$
$942$	17.1872	0.559990
$943$	0.136190	0.00443496
$944$	−0.531452	−0.0172973
$945$	−20.0335	−0.651690
$946$	−2.73101	−0.0887928
$947$	24.0731	0.782270	0.391135	−	0.920333i	$-0.372082\pi$
$947$	24.0731	0.782270	0.391135	+	0.920333i	$0.372082\pi$
$948$	16.7195	0.543025
$949$	20.2597	0.657657
$950$	4.70595	0.152681
$951$	20.7990	0.674453
$952$	−30.6123	−0.992149
$953$	−1.80965	−0.0586204	−0.0293102	−	0.999570i	$-0.509331\pi$
$953$	−1.80965	−0.0586204	−0.0293102	+	0.999570i	$0.509331\pi$
$954$	11.2193	0.363240
$955$	−14.0579	−0.454902
$956$	−12.5692	−0.406516
$957$	0	0
$958$	1.48149	0.0478648
$959$	94.1636	3.04070
$960$	0.959933	0.0309817
$961$	−16.1505	−0.520985
$962$	6.11191	0.197056
$963$	16.2808	0.524640
$964$	−13.9791	−0.450236
$965$	2.97324	0.0957119
$966$	4.59756	0.147924
$967$	11.5895	0.372692	0.186346	−	0.982484i	$-0.440335\pi$
$967$	11.5895	0.372692	0.186346	+	0.982484i	$0.440335\pi$
$968$	6.72991	0.216308
$969$	33.6515	1.08104
$970$	−15.3893	−0.494120
$971$	11.3734	0.364991	0.182495	−	0.983207i	$-0.441583\pi$
$971$	11.3734	0.364991	0.182495	+	0.983207i	$0.441583\pi$
$972$	−16.1187	−0.517007
$973$	−60.2410	−1.93124
$974$	3.80566	0.121941
$975$	−3.65956	−0.117200
$976$	−10.9858	−0.351646
$977$	29.4365	0.941755	0.470878	−	0.882198i	$-0.343937\pi$
$977$	29.4365	0.941755	0.470878	+	0.882198i	$0.343937\pi$
$978$	−7.80312	−0.249516
$979$	−30.9893	−0.990423
$980$	−9.88715	−0.315833
$981$	28.7502	0.917924
$982$	−10.0979	−0.322238
$983$	−45.8337	−1.46187	−0.730934	−	0.682448i	$-0.760915\pi$
$983$	−45.8337	−1.46187	−0.730934	+	0.682448i	$0.760915\pi$
$984$	0.112170	0.00357586
$985$	4.21263	0.134226
$986$	0	0
$987$	36.7448	1.16960
$988$	17.9405	0.570764
$989$	−0.755925	−0.0240370
$990$	−8.75204	−0.278158
$991$	−7.12814	−0.226433	−0.113216	−	0.993570i	$-0.536115\pi$
$991$	−7.12814	−0.226433	−0.113216	+	0.993570i	$0.536115\pi$
$992$	−3.85350	−0.122349
$993$	16.1719	0.513200
$994$	51.9435	1.64755
$995$	23.4542	0.743547
$996$	−3.50413	−0.111033
$997$	−19.4496	−0.615973	−0.307987	−	0.951391i	$-0.599655\pi$
$997$	−19.4496	−0.615973	−0.307987	+	0.951391i	$0.599655\pi$
$998$	4.30988	0.136427
$999$	7.81569	0.247278

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8410.2.a.bx.1.5		12
29.8	odd	28		290.2.m.a.151.3	yes	24
29.11	odd	28		290.2.m.a.121.3	✓	24
29.28	even	2		8410.2.a.bw.1.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.m.a.121.3	✓	24	29.11	odd	28
290.2.m.a.151.3	yes	24	29.8	odd	28
8410.2.a.bw.1.8		12	29.28	even	2
8410.2.a.bx.1.5		12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8410 = 2 \cdot 5 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8410.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.959933 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.959933 q^{6} +4.10940 q^{7} +1.00000 q^{8} -2.07853 q^{9} -1.00000 q^{10} -4.21069 q^{11} -0.959933 q^{12} +3.81231 q^{13} +4.10940 q^{14} +0.959933 q^{15} +1.00000 q^{16} -7.44933 q^{17} -2.07853 q^{18} +4.70595 q^{19} -1.00000 q^{20} -3.94475 q^{21} -4.21069 q^{22} -1.16549 q^{23} -0.959933 q^{24} +1.00000 q^{25} +3.81231 q^{26} +4.87505 q^{27} +4.10940 q^{28} +0.959933 q^{30} -3.85350 q^{31} +1.00000 q^{32} +4.04198 q^{33} -7.44933 q^{34} -4.10940 q^{35} -2.07853 q^{36} +1.60320 q^{37} +4.70595 q^{38} -3.65956 q^{39} -1.00000 q^{40} -0.116852 q^{41} -3.94475 q^{42} +0.648590 q^{43} -4.21069 q^{44} +2.07853 q^{45} -1.16549 q^{46} -9.31488 q^{47} -0.959933 q^{48} +9.88715 q^{49} +1.00000 q^{50} +7.15086 q^{51} +3.81231 q^{52} -5.39773 q^{53} +4.87505 q^{54} +4.21069 q^{55} +4.10940 q^{56} -4.51739 q^{57} -0.531452 q^{59} +0.959933 q^{60} -10.9858 q^{61} -3.85350 q^{62} -8.54150 q^{63} +1.00000 q^{64} -3.81231 q^{65} +4.04198 q^{66} -3.75707 q^{67} -7.44933 q^{68} +1.11879 q^{69} -4.10940 q^{70} +12.6402 q^{71} -2.07853 q^{72} +5.31428 q^{73} +1.60320 q^{74} -0.959933 q^{75} +4.70595 q^{76} -17.3034 q^{77} -3.65956 q^{78} -17.4174 q^{79} -1.00000 q^{80} +1.55587 q^{81} -0.116852 q^{82} +3.65039 q^{83} -3.94475 q^{84} +7.44933 q^{85} +0.648590 q^{86} -4.21069 q^{88} +7.35968 q^{89} +2.07853 q^{90} +15.6663 q^{91} -1.16549 q^{92} +3.69910 q^{93} -9.31488 q^{94} -4.70595 q^{95} -0.959933 q^{96} +15.3893 q^{97} +9.88715 q^{98} +8.75204 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} - 4 q^{3} + 12 q^{4} - 12 q^{5} - 4 q^{6} - 8 q^{7} + 12 q^{8} + 6 q^{9} - 12 q^{10} - 14 q^{11} - 4 q^{12} - 4 q^{13} - 8 q^{14} + 4 q^{15} + 12 q^{16} - 8 q^{17} + 6 q^{18} + 16 q^{19}+ \cdots + 2 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 - 4 * q^3 + 12 * q^4 - 12 * q^5 - 4 * q^6 - 8 * q^7 + 12 * q^8 + 6 * q^9 - 12 * q^10 - 14 * q^11 - 4 * q^12 - 4 * q^13 - 8 * q^14 + 4 * q^15 + 12 * q^16 - 8 * q^17 + 6 * q^18 + 16 * q^19 - 12 * q^20 + 4 * q^21 - 14 * q^22 + 4 * q^23 - 4 * q^24 + 12 * q^25 - 4 * q^26 - 28 * q^27 - 8 * q^28 + 4 * q^30 + 2 * q^31 + 12 * q^32 + 4 * q^33 - 8 * q^34 + 8 * q^35 + 6 * q^36 - 18 * q^37 + 16 * q^38 + 24 * q^39 - 12 * q^40 - 4 * q^41 + 4 * q^42 - 28 * q^43 - 14 * q^44 - 6 * q^45 + 4 * q^46 - 36 * q^47 - 4 * q^48 + 18 * q^49 + 12 * q^50 - 24 * q^51 - 4 * q^52 - 28 * q^54 + 14 * q^55 - 8 * q^56 - 50 * q^57 - 12 * q^59 + 4 * q^60 + 12 * q^61 + 2 * q^62 - 22 * q^63 + 12 * q^64 + 4 * q^65 + 4 * q^66 - 14 * q^67 - 8 * q^68 + 42 * q^69 + 8 * q^70 - 18 * q^71 + 6 * q^72 - 48 * q^73 - 18 * q^74 - 4 * q^75 + 16 * q^76 - 46 * q^77 + 24 * q^78 - 12 * q^80 + 12 * q^81 - 4 * q^82 + 20 * q^83 + 4 * q^84 + 8 * q^85 - 28 * q^86 - 14 * q^88 - 32 * q^89 - 6 * q^90 + 50 * q^91 + 4 * q^92 - 42 * q^93 - 36 * q^94 - 16 * q^95 - 4 * q^96 - 16 * q^97 + 18 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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