LMFDB - Embedded newform 8470.2.a.da.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8470,2,Mod(1,8470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8470, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8470.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8470.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$67.6332905120$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.38498000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 12x^{4} + 5x^{3} + 38x^{2} - x - 19 $ x^6 - x^5 - 12x^4 + 5x^3 + 38*x^2 - x - 19
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 770)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$3.16330$ of defining polynomial
Character	$\chi$	$=$	8470.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.16330 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.16330 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.67988 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.16330 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.16330 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.67988 q^{9} -1.00000 q^{10} +2.16330 q^{12} -3.92049 q^{13} +1.00000 q^{14} -2.16330 q^{15} +1.00000 q^{16} -6.06013 q^{17} +1.67988 q^{18} -5.77042 q^{19} -1.00000 q^{20} +2.16330 q^{21} +1.51437 q^{23} +2.16330 q^{24} +1.00000 q^{25} -3.92049 q^{26} -2.85582 q^{27} +1.00000 q^{28} -4.12422 q^{29} -2.16330 q^{30} +5.77234 q^{31} +1.00000 q^{32} -6.06013 q^{34} -1.00000 q^{35} +1.67988 q^{36} -4.55850 q^{37} -5.77042 q^{38} -8.48120 q^{39} -1.00000 q^{40} -5.54216 q^{41} +2.16330 q^{42} +6.51122 q^{43} -1.67988 q^{45} +1.51437 q^{46} -10.9224 q^{47} +2.16330 q^{48} +1.00000 q^{49} +1.00000 q^{50} -13.1099 q^{51} -3.92049 q^{52} +3.74119 q^{53} -2.85582 q^{54} +1.00000 q^{56} -12.4832 q^{57} -4.12422 q^{58} -3.77402 q^{59} -2.16330 q^{60} -0.532894 q^{61} +5.77234 q^{62} +1.67988 q^{63} +1.00000 q^{64} +3.92049 q^{65} -1.15993 q^{67} -6.06013 q^{68} +3.27603 q^{69} -1.00000 q^{70} +0.623988 q^{71} +1.67988 q^{72} +3.10516 q^{73} -4.55850 q^{74} +2.16330 q^{75} -5.77042 q^{76} -8.48120 q^{78} +3.76727 q^{79} -1.00000 q^{80} -11.2176 q^{81} -5.54216 q^{82} -12.3739 q^{83} +2.16330 q^{84} +6.06013 q^{85} +6.51122 q^{86} -8.92194 q^{87} +3.59309 q^{89} -1.67988 q^{90} -3.92049 q^{91} +1.51437 q^{92} +12.4873 q^{93} -10.9224 q^{94} +5.77042 q^{95} +2.16330 q^{96} -15.6424 q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 5 q^{3} + 6 q^{4} - 6 q^{5} - 5 q^{6} + 6 q^{7} + 6 q^{8} + 11 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - 5 * q^3 + 6 * q^4 - 6 * q^5 - 5 * q^6 + 6 * q^7 + 6 * q^8 + 11 * q^9	$ 6 q + 6 q^{2} - 5 q^{3} + 6 q^{4} - 6 q^{5} - 5 q^{6} + 6 q^{7} + 6 q^{8} + 11 q^{9} - 6 q^{10} - 5 q^{12} + 6 q^{14} + 5 q^{15} + 6 q^{16} - 15 q^{17} + 11 q^{18} - 13 q^{19} - 6 q^{20} - 5 q^{21} - 2 q^{23} - 5 q^{24} + 6 q^{25} - 26 q^{27} + 6 q^{28} - 4 q^{29} + 5 q^{30} - 2 q^{31} + 6 q^{32} - 15 q^{34} - 6 q^{35} + 11 q^{36} - 13 q^{38} - 30 q^{39} - 6 q^{40} - 17 q^{41} - 5 q^{42} + 15 q^{43} - 11 q^{45} - 2 q^{46} - 18 q^{47} - 5 q^{48} + 6 q^{49} + 6 q^{50} + 6 q^{51} + 22 q^{53} - 26 q^{54} + 6 q^{56} - 2 q^{57} - 4 q^{58} - 7 q^{59} + 5 q^{60} - 20 q^{61} - 2 q^{62} + 11 q^{63} + 6 q^{64} - 29 q^{67} - 15 q^{68} + 12 q^{69} - 6 q^{70} - 2 q^{71} + 11 q^{72} + q^{73} - 5 q^{75} - 13 q^{76} - 30 q^{78} - 12 q^{79} - 6 q^{80} + 22 q^{81} - 17 q^{82} - 35 q^{83} - 5 q^{84} + 15 q^{85} + 15 q^{86} - 29 q^{89} - 11 q^{90} - 2 q^{92} + 8 q^{93} - 18 q^{94} + 13 q^{95} - 5 q^{96} - 19 q^{97} + 6 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 - 5 * q^3 + 6 * q^4 - 6 * q^5 - 5 * q^6 + 6 * q^7 + 6 * q^8 + 11 * q^9 - 6 * q^10 - 5 * q^12 + 6 * q^14 + 5 * q^15 + 6 * q^16 - 15 * q^17 + 11 * q^18 - 13 * q^19 - 6 * q^20 - 5 * q^21 - 2 * q^23 - 5 * q^24 + 6 * q^25 - 26 * q^27 + 6 * q^28 - 4 * q^29 + 5 * q^30 - 2 * q^31 + 6 * q^32 - 15 * q^34 - 6 * q^35 + 11 * q^36 - 13 * q^38 - 30 * q^39 - 6 * q^40 - 17 * q^41 - 5 * q^42 + 15 * q^43 - 11 * q^45 - 2 * q^46 - 18 * q^47 - 5 * q^48 + 6 * q^49 + 6 * q^50 + 6 * q^51 + 22 * q^53 - 26 * q^54 + 6 * q^56 - 2 * q^57 - 4 * q^58 - 7 * q^59 + 5 * q^60 - 20 * q^61 - 2 * q^62 + 11 * q^63 + 6 * q^64 - 29 * q^67 - 15 * q^68 + 12 * q^69 - 6 * q^70 - 2 * q^71 + 11 * q^72 + q^73 - 5 * q^75 - 13 * q^76 - 30 * q^78 - 12 * q^79 - 6 * q^80 + 22 * q^81 - 17 * q^82 - 35 * q^83 - 5 * q^84 + 15 * q^85 + 15 * q^86 - 29 * q^89 - 11 * q^90 - 2 * q^92 + 8 * q^93 - 18 * q^94 + 13 * q^95 - 5 * q^96 - 19 * q^97 + 6 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.16330	1.24898	0.624492	−	0.781031i	$-0.285306\pi$
$3$	2.16330	1.24898	0.624492	+	0.781031i	$0.285306\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.16330	0.883165
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.67988	0.559960
$10$	−1.00000	−0.316228
$11$	0	0
$11$	0	0
$12$	2.16330	0.624492
$13$	−3.92049	−1.08735	−0.543674	−	0.839297i	$-0.682967\pi$
$13$	−3.92049	−1.08735	−0.543674	+	0.839297i	$0.682967\pi$
$14$	1.00000	0.267261
$15$	−2.16330	−0.558562
$16$	1.00000	0.250000
$17$	−6.06013	−1.46980	−0.734898	−	0.678177i	$-0.762770\pi$
$17$	−6.06013	−1.46980	−0.734898	+	0.678177i	$0.762770\pi$
$18$	1.67988	0.395951
$19$	−5.77042	−1.32382	−0.661912	−	0.749581i	$-0.730255\pi$
$19$	−5.77042	−1.32382	−0.661912	+	0.749581i	$0.730255\pi$
$20$	−1.00000	−0.223607
$21$	2.16330	0.472071
$22$	0	0
$23$	1.51437	0.315767	0.157884	−	0.987458i	$-0.449533\pi$
$23$	1.51437	0.315767	0.157884	+	0.987458i	$0.449533\pi$
$24$	2.16330	0.441582
$25$	1.00000	0.200000
$26$	−3.92049	−0.768871
$27$	−2.85582	−0.549603
$28$	1.00000	0.188982
$29$	−4.12422	−0.765849	−0.382924	−	0.923780i	$-0.625083\pi$
$29$	−4.12422	−0.765849	−0.382924	+	0.923780i	$0.625083\pi$
$30$	−2.16330	−0.394963
$31$	5.77234	1.03674	0.518371	−	0.855156i	$-0.326539\pi$
$31$	5.77234	1.03674	0.518371	+	0.855156i	$0.326539\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−6.06013	−1.03930
$35$	−1.00000	−0.169031
$36$	1.67988	0.279980
$37$	−4.55850	−0.749413	−0.374707	−	0.927143i	$-0.622257\pi$
$37$	−4.55850	−0.749413	−0.374707	+	0.927143i	$0.622257\pi$
$38$	−5.77042	−0.936085
$39$	−8.48120	−1.35808
$40$	−1.00000	−0.158114
$41$	−5.54216	−0.865540	−0.432770	−	0.901504i	$-0.642464\pi$
$41$	−5.54216	−0.865540	−0.432770	+	0.901504i	$0.642464\pi$
$42$	2.16330	0.333805
$43$	6.51122	0.992951	0.496476	−	0.868051i	$-0.334627\pi$
$43$	6.51122	0.992951	0.496476	+	0.868051i	$0.334627\pi$
$44$	0	0
$45$	−1.67988	−0.250422
$46$	1.51437	0.223281
$47$	−10.9224	−1.59320	−0.796600	−	0.604506i	$-0.793370\pi$
$47$	−10.9224	−1.59320	−0.796600	+	0.604506i	$0.793370\pi$
$48$	2.16330	0.312246
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	−13.1099	−1.83575
$52$	−3.92049	−0.543674
$53$	3.74119	0.513892	0.256946	−	0.966426i	$-0.417284\pi$
$53$	3.74119	0.513892	0.256946	+	0.966426i	$0.417284\pi$
$54$	−2.85582	−0.388628
$55$	0	0
$56$	1.00000	0.133631
$57$	−12.4832	−1.65343
$58$	−4.12422	−0.541537
$59$	−3.77402	−0.491335	−0.245668	−	0.969354i	$-0.579007\pi$
$59$	−3.77402	−0.491335	−0.245668	+	0.969354i	$0.579007\pi$
$60$	−2.16330	−0.279281
$61$	−0.532894	−0.0682301	−0.0341150	−	0.999418i	$-0.510861\pi$
$61$	−0.532894	−0.0682301	−0.0341150	+	0.999418i	$0.510861\pi$
$62$	5.77234	0.733088
$63$	1.67988	0.211645
$64$	1.00000	0.125000
$65$	3.92049	0.486276
$66$	0	0
$67$	−1.15993	−0.141708	−0.0708538	−	0.997487i	$-0.522572\pi$
$67$	−1.15993	−0.141708	−0.0708538	+	0.997487i	$0.522572\pi$
$68$	−6.06013	−0.734898
$69$	3.27603	0.394388
$70$	−1.00000	−0.119523
$71$	0.623988	0.0740538	0.0370269	−	0.999314i	$-0.488211\pi$
$71$	0.623988	0.0740538	0.0370269	+	0.999314i	$0.488211\pi$
$72$	1.67988	0.197976
$73$	3.10516	0.363432	0.181716	−	0.983351i	$-0.441835\pi$
$73$	3.10516	0.363432	0.181716	+	0.983351i	$0.441835\pi$
$74$	−4.55850	−0.529915
$75$	2.16330	0.249797
$76$	−5.77042	−0.661912
$77$	0	0
$78$	−8.48120	−0.960307
$79$	3.76727	0.423851	0.211925	−	0.977286i	$-0.432027\pi$
$79$	3.76727	0.423851	0.211925	+	0.977286i	$0.432027\pi$
$80$	−1.00000	−0.111803
$81$	−11.2176	−1.24640
$82$	−5.54216	−0.612029
$83$	−12.3739	−1.35821	−0.679106	−	0.734041i	$-0.737632\pi$
$83$	−12.3739	−1.35821	−0.679106	+	0.734041i	$0.737632\pi$
$84$	2.16330	0.236036
$85$	6.06013	0.657313
$86$	6.51122	0.702123
$87$	−8.92194	−0.956532
$88$	0	0
$89$	3.59309	0.380866	0.190433	−	0.981700i	$-0.439011\pi$
$89$	3.59309	0.380866	0.190433	+	0.981700i	$0.439011\pi$
$90$	−1.67988	−0.177075
$91$	−3.92049	−0.410979
$92$	1.51437	0.157884
$93$	12.4873	1.29487
$94$	−10.9224	−1.12656
$95$	5.77042	0.592032
$96$	2.16330	0.220791
$97$	−15.6424	−1.58824	−0.794120	−	0.607761i	$-0.792068\pi$
$97$	−15.6424	−1.58824	−0.794120	+	0.607761i	$0.792068\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	−15.1917	−1.51163	−0.755815	−	0.654785i	$-0.772759\pi$
$101$	−15.1917	−1.51163	−0.755815	+	0.654785i	$0.772759\pi$
$102$	−13.1099	−1.29807
$103$	5.54781	0.546642	0.273321	−	0.961923i	$-0.411878\pi$
$103$	5.54781	0.546642	0.273321	+	0.961923i	$0.411878\pi$
$104$	−3.92049	−0.384435
$105$	−2.16330	−0.211117
$106$	3.74119	0.363377
$107$	9.25943	0.895143	0.447571	−	0.894248i	$-0.352289\pi$
$107$	9.25943	0.895143	0.447571	+	0.894248i	$0.352289\pi$
$108$	−2.85582	−0.274801
$109$	−0.167247	−0.0160193	−0.00800966	−	0.999968i	$-0.502550\pi$
$109$	−0.167247	−0.0160193	−0.00800966	+	0.999968i	$0.502550\pi$
$110$	0	0
$111$	−9.86142	−0.936005
$112$	1.00000	0.0944911
$113$	6.66364	0.626863	0.313431	−	0.949611i	$-0.398521\pi$
$113$	6.66364	0.626863	0.313431	+	0.949611i	$0.398521\pi$
$114$	−12.4832	−1.16916
$115$	−1.51437	−0.141215
$116$	−4.12422	−0.382924
$117$	−6.58594	−0.608871
$118$	−3.77402	−0.347426
$119$	−6.06013	−0.555531
$120$	−2.16330	−0.197482
$121$	0	0
$122$	−0.532894	−0.0482459
$123$	−11.9894	−1.08105
$124$	5.77234	0.518371
$125$	−1.00000	−0.0894427
$126$	1.67988	0.149656
$127$	−2.06518	−0.183255	−0.0916276	−	0.995793i	$-0.529207\pi$
$127$	−2.06518	−0.183255	−0.0916276	+	0.995793i	$0.529207\pi$
$128$	1.00000	0.0883883
$129$	14.0857	1.24018
$130$	3.92049	0.343849
$131$	22.8396	1.99550	0.997751	−	0.0670258i	$-0.0213510\pi$
$131$	22.8396	1.99550	0.997751	+	0.0670258i	$0.0213510\pi$
$132$	0	0
$133$	−5.77042	−0.500359
$134$	−1.15993	−0.100202
$135$	2.85582	0.245790
$136$	−6.06013	−0.519652
$137$	5.62769	0.480806	0.240403	−	0.970673i	$-0.422720\pi$
$137$	5.62769	0.480806	0.240403	+	0.970673i	$0.422720\pi$
$138$	3.27603	0.278874
$139$	8.55069	0.725260	0.362630	−	0.931933i	$-0.381879\pi$
$139$	8.55069	0.725260	0.362630	+	0.931933i	$0.381879\pi$
$140$	−1.00000	−0.0845154
$141$	−23.6285	−1.98988
$142$	0.623988	0.0523639
$143$	0	0
$144$	1.67988	0.139990
$145$	4.12422	0.342498
$146$	3.10516	0.256985
$147$	2.16330	0.178426
$148$	−4.55850	−0.374707
$149$	−19.4884	−1.59655	−0.798274	−	0.602294i	$-0.794253\pi$
$149$	−19.4884	−1.59655	−0.798274	+	0.602294i	$0.794253\pi$
$150$	2.16330	0.176633
$151$	−5.23785	−0.426250	−0.213125	−	0.977025i	$-0.568364\pi$
$151$	−5.23785	−0.426250	−0.213125	+	0.977025i	$0.568364\pi$
$152$	−5.77042	−0.468043
$153$	−10.1803	−0.823027
$154$	0	0
$155$	−5.77234	−0.463645
$156$	−8.48120	−0.679039
$157$	15.8121	1.26194	0.630971	−	0.775807i	$-0.282657\pi$
$157$	15.8121	1.26194	0.630971	+	0.775807i	$0.282657\pi$
$158$	3.76727	0.299708
$159$	8.09333	0.641843
$160$	−1.00000	−0.0790569
$161$	1.51437	0.119349
$162$	−11.2176	−0.881341
$163$	12.4449	0.974763	0.487381	−	0.873189i	$-0.337952\pi$
$163$	12.4449	0.974763	0.487381	+	0.873189i	$0.337952\pi$
$164$	−5.54216	−0.432770
$165$	0	0
$166$	−12.3739	−0.960400
$167$	−17.8770	−1.38336	−0.691682	−	0.722202i	$-0.743130\pi$
$167$	−17.8770	−1.38336	−0.691682	+	0.722202i	$0.743130\pi$
$168$	2.16330	0.166902
$169$	2.37021	0.182324
$170$	6.06013	0.464790
$171$	−9.69360	−0.741288
$172$	6.51122	0.496476
$173$	−19.6780	−1.49609	−0.748044	−	0.663649i	$-0.769007\pi$
$173$	−19.6780	−1.49609	−0.748044	+	0.663649i	$0.769007\pi$
$174$	−8.92194	−0.676371
$175$	1.00000	0.0755929
$176$	0	0
$177$	−8.16434	−0.613669
$178$	3.59309	0.269313
$179$	−1.69870	−0.126967	−0.0634834	−	0.997983i	$-0.520221\pi$
$179$	−1.69870	−0.126967	−0.0634834	+	0.997983i	$0.520221\pi$
$180$	−1.67988	−0.125211
$181$	−16.1203	−1.19822	−0.599108	−	0.800668i	$-0.704478\pi$
$181$	−16.1203	−1.19822	−0.599108	+	0.800668i	$0.704478\pi$
$182$	−3.92049	−0.290606
$183$	−1.15281	−0.0852182
$184$	1.51437	0.111641
$185$	4.55850	0.335148
$186$	12.4873	0.915614
$187$	0	0
$188$	−10.9224	−0.796600
$189$	−2.85582	−0.207730
$190$	5.77042	0.418630
$191$	−17.3638	−1.25640	−0.628200	−	0.778052i	$-0.716208\pi$
$191$	−17.3638	−1.25640	−0.628200	+	0.778052i	$0.716208\pi$
$192$	2.16330	0.156123
$193$	−5.33671	−0.384145	−0.192072	−	0.981381i	$-0.561521\pi$
$193$	−5.33671	−0.384145	−0.192072	+	0.981381i	$0.561521\pi$
$194$	−15.6424	−1.12306
$195$	8.48120	0.607351
$196$	1.00000	0.0714286
$197$	19.8667	1.41544	0.707722	−	0.706491i	$-0.249723\pi$
$197$	19.8667	1.41544	0.707722	+	0.706491i	$0.249723\pi$
$198$	0	0
$199$	2.93785	0.208259	0.104129	−	0.994564i	$-0.466794\pi$
$199$	2.93785	0.208259	0.104129	+	0.994564i	$0.466794\pi$
$200$	1.00000	0.0707107
$201$	−2.50927	−0.176990
$202$	−15.1917	−1.06888
$203$	−4.12422	−0.289464
$204$	−13.1099	−0.917876
$205$	5.54216	0.387081
$206$	5.54781	0.386534
$207$	2.54395	0.176817
$208$	−3.92049	−0.271837
$209$	0	0
$210$	−2.16330	−0.149282
$211$	17.9913	1.23857	0.619286	−	0.785166i	$-0.287422\pi$
$211$	17.9913	1.23857	0.619286	+	0.785166i	$0.287422\pi$
$212$	3.74119	0.256946
$213$	1.34988	0.0924919
$214$	9.25943	0.632961
$215$	−6.51122	−0.444061
$216$	−2.85582	−0.194314
$217$	5.77234	0.391852
$218$	−0.167247	−0.0113274
$219$	6.71741	0.453920
$220$	0	0
$221$	23.7586	1.59818
$222$	−9.86142	−0.661855
$223$	22.2447	1.48962	0.744808	−	0.667279i	$-0.232541\pi$
$223$	22.2447	1.48962	0.744808	+	0.667279i	$0.232541\pi$
$224$	1.00000	0.0668153
$225$	1.67988	0.111992
$226$	6.66364	0.443259
$227$	−26.2506	−1.74231	−0.871156	−	0.491006i	$-0.836629\pi$
$227$	−26.2506	−1.74231	−0.871156	+	0.491006i	$0.836629\pi$
$228$	−12.4832	−0.826717
$229$	−9.12533	−0.603019	−0.301509	−	0.953463i	$-0.597490\pi$
$229$	−9.12533	−0.603019	−0.301509	+	0.953463i	$0.597490\pi$
$230$	−1.51437	−0.0998544
$231$	0	0
$232$	−4.12422	−0.270768
$233$	−0.378654	−0.0248064	−0.0124032	−	0.999923i	$-0.503948\pi$
$233$	−0.378654	−0.0248064	−0.0124032	+	0.999923i	$0.503948\pi$
$234$	−6.58594	−0.430537
$235$	10.9224	0.712501
$236$	−3.77402	−0.245668
$237$	8.14974	0.529383
$238$	−6.06013	−0.392820
$239$	−0.173692	−0.0112352	−0.00561760	−	0.999984i	$-0.501788\pi$
$239$	−0.173692	−0.0112352	−0.00561760	+	0.999984i	$0.501788\pi$
$240$	−2.16330	−0.139641
$241$	−27.9248	−1.79880	−0.899398	−	0.437131i	$-0.855995\pi$
$241$	−27.9248	−1.79880	−0.899398	+	0.437131i	$0.855995\pi$
$242$	0	0
$243$	−15.6997	−1.00714
$244$	−0.532894	−0.0341150
$245$	−1.00000	−0.0638877
$246$	−11.9894	−0.764414
$247$	22.6228	1.43946
$248$	5.77234	0.366544
$249$	−26.7685	−1.69638
$250$	−1.00000	−0.0632456
$251$	25.6423	1.61853	0.809264	−	0.587445i	$-0.199866\pi$
$251$	25.6423	1.61853	0.809264	+	0.587445i	$0.199866\pi$
$252$	1.67988	0.105822
$253$	0	0
$254$	−2.06518	−0.129581
$255$	13.1099	0.820973
$256$	1.00000	0.0625000
$257$	31.4403	1.96119	0.980597	−	0.196036i	$-0.0628070\pi$
$257$	31.4403	1.96119	0.980597	+	0.196036i	$0.0628070\pi$
$258$	14.0857	0.876940
$259$	−4.55850	−0.283252
$260$	3.92049	0.243138
$261$	−6.92819	−0.428844
$262$	22.8396	1.41103
$263$	24.0975	1.48592	0.742958	−	0.669338i	$-0.233422\pi$
$263$	24.0975	1.48592	0.742958	+	0.669338i	$0.233422\pi$
$264$	0	0
$265$	−3.74119	−0.229820
$266$	−5.77042	−0.353807
$267$	7.77293	0.475696
$268$	−1.15993	−0.0708538
$269$	24.8472	1.51496	0.757481	−	0.652857i	$-0.226430\pi$
$269$	24.8472	1.51496	0.757481	+	0.652857i	$0.226430\pi$
$270$	2.85582	0.173800
$271$	0.300798	0.0182721	0.00913607	−	0.999958i	$-0.497092\pi$
$271$	0.300798	0.0182721	0.00913607	+	0.999958i	$0.497092\pi$
$272$	−6.06013	−0.367449
$273$	−8.48120	−0.513306
$274$	5.62769	0.339981
$275$	0	0
$276$	3.27603	0.197194
$277$	17.0103	1.02205	0.511025	−	0.859566i	$-0.329266\pi$
$277$	17.0103	1.02205	0.511025	+	0.859566i	$0.329266\pi$
$278$	8.55069	0.512836
$279$	9.69683	0.580534
$280$	−1.00000	−0.0597614
$281$	−22.0382	−1.31469	−0.657345	−	0.753590i	$-0.728321\pi$
$281$	−22.0382	−1.31469	−0.657345	+	0.753590i	$0.728321\pi$
$282$	−23.6285	−1.40706
$283$	9.47154	0.563025	0.281512	−	0.959558i	$-0.409164\pi$
$283$	9.47154	0.563025	0.281512	+	0.959558i	$0.409164\pi$
$284$	0.623988	0.0370269
$285$	12.4832	0.739439
$286$	0	0
$287$	−5.54216	−0.327143
$288$	1.67988	0.0989878
$289$	19.7251	1.16030
$290$	4.12422	0.242183
$291$	−33.8392	−1.98369
$292$	3.10516	0.181716
$293$	−16.8419	−0.983913	−0.491956	−	0.870620i	$-0.663718\pi$
$293$	−16.8419	−0.983913	−0.491956	+	0.870620i	$0.663718\pi$
$294$	2.16330	0.126166
$295$	3.77402	0.219732
$296$	−4.55850	−0.264958
$297$	0	0
$298$	−19.4884	−1.12893
$299$	−5.93705	−0.343349
$300$	2.16330	0.124898
$301$	6.51122	0.375300
$302$	−5.23785	−0.301404
$303$	−32.8642	−1.88800
$304$	−5.77042	−0.330956
$305$	0.532894	0.0305134
$306$	−10.1803	−0.581968
$307$	−1.36644	−0.0779870	−0.0389935	−	0.999239i	$-0.512415\pi$
$307$	−1.36644	−0.0779870	−0.0389935	+	0.999239i	$0.512415\pi$
$308$	0	0
$309$	12.0016	0.682747
$310$	−5.77234	−0.327847
$311$	18.5543	1.05212	0.526058	−	0.850449i	$-0.323669\pi$
$311$	18.5543	1.05212	0.526058	+	0.850449i	$0.323669\pi$
$312$	−8.48120	−0.480153
$313$	−13.8649	−0.783688	−0.391844	−	0.920032i	$-0.628163\pi$
$313$	−13.8649	−0.783688	−0.391844	+	0.920032i	$0.628163\pi$
$314$	15.8121	0.892327
$315$	−1.67988	−0.0946505
$316$	3.76727	0.211925
$317$	−23.4949	−1.31960	−0.659802	−	0.751439i	$-0.729360\pi$
$317$	−23.4949	−1.31960	−0.659802	+	0.751439i	$0.729360\pi$
$318$	8.09333	0.453852
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	20.0309	1.11802
$322$	1.51437	0.0843923
$323$	34.9695	1.94575
$324$	−11.2176	−0.623202
$325$	−3.92049	−0.217469
$326$	12.4449	0.689261
$327$	−0.361805	−0.0200079
$328$	−5.54216	−0.306015
$329$	−10.9224	−0.602173
$330$	0	0
$331$	10.6438	0.585035	0.292518	−	0.956260i	$-0.405507\pi$
$331$	10.6438	0.585035	0.292518	+	0.956260i	$0.405507\pi$
$332$	−12.3739	−0.679106
$333$	−7.65773	−0.419641
$334$	−17.8770	−0.978186
$335$	1.15993	0.0633736
$336$	2.16330	0.118018
$337$	13.3566	0.727581	0.363790	−	0.931481i	$-0.381482\pi$
$337$	13.3566	0.727581	0.363790	+	0.931481i	$0.381482\pi$
$338$	2.37021	0.128922
$339$	14.4155	0.782941
$340$	6.06013	0.328656
$341$	0	0
$342$	−9.69360	−0.524170
$343$	1.00000	0.0539949
$344$	6.51122	0.351061
$345$	−3.27603	−0.176376
$346$	−19.6780	−1.05789
$347$	14.5070	0.778778	0.389389	−	0.921073i	$-0.372686\pi$
$347$	14.5070	0.778778	0.389389	+	0.921073i	$0.372686\pi$
$348$	−8.92194	−0.478266
$349$	−26.1051	−1.39737	−0.698687	−	0.715428i	$-0.746232\pi$
$349$	−26.1051	−1.39737	−0.698687	+	0.715428i	$0.746232\pi$
$350$	1.00000	0.0534522
$351$	11.1962	0.597609
$352$	0	0
$353$	20.3692	1.08414	0.542072	−	0.840332i	$-0.317640\pi$
$353$	20.3692	1.08414	0.542072	+	0.840332i	$0.317640\pi$
$354$	−8.16434	−0.433930
$355$	−0.623988	−0.0331179
$356$	3.59309	0.190433
$357$	−13.1099	−0.693849
$358$	−1.69870	−0.0897791
$359$	18.5953	0.981422	0.490711	−	0.871322i	$-0.336737\pi$
$359$	18.5953	0.981422	0.490711	+	0.871322i	$0.336737\pi$
$360$	−1.67988	−0.0885374
$361$	14.2977	0.752511
$362$	−16.1203	−0.847266
$363$	0	0
$364$	−3.92049	−0.205489
$365$	−3.10516	−0.162532
$366$	−1.15281	−0.0602584
$367$	9.43885	0.492704	0.246352	−	0.969180i	$-0.420768\pi$
$367$	9.43885	0.492704	0.246352	+	0.969180i	$0.420768\pi$
$368$	1.51437	0.0789418
$369$	−9.31016	−0.484668
$370$	4.55850	0.236985
$371$	3.74119	0.194233
$372$	12.4873	0.647437
$373$	−17.1558	−0.888295	−0.444147	−	0.895954i	$-0.646493\pi$
$373$	−17.1558	−0.888295	−0.444147	+	0.895954i	$0.646493\pi$
$374$	0	0
$375$	−2.16330	−0.111712
$376$	−10.9224	−0.563281
$377$	16.1690	0.832743
$378$	−2.85582	−0.146888
$379$	−8.09841	−0.415988	−0.207994	−	0.978130i	$-0.566693\pi$
$379$	−8.09841	−0.415988	−0.207994	+	0.978130i	$0.566693\pi$
$380$	5.77042	0.296016
$381$	−4.46761	−0.228883
$382$	−17.3638	−0.888409
$383$	23.3157	1.19138	0.595688	−	0.803216i	$-0.296879\pi$
$383$	23.3157	1.19138	0.595688	+	0.803216i	$0.296879\pi$
$384$	2.16330	0.110396
$385$	0	0
$386$	−5.33671	−0.271631
$387$	10.9381	0.556013
$388$	−15.6424	−0.794120
$389$	18.9522	0.960915	0.480458	−	0.877018i	$-0.340471\pi$
$389$	18.9522	0.960915	0.480458	+	0.877018i	$0.340471\pi$
$390$	8.48120	0.429462
$391$	−9.17725	−0.464114
$392$	1.00000	0.0505076
$393$	49.4089	2.49235
$394$	19.8667	1.00087
$395$	−3.76727	−0.189552
$396$	0	0
$397$	6.76731	0.339641	0.169821	−	0.985475i	$-0.445681\pi$
$397$	6.76731	0.339641	0.169821	+	0.985475i	$0.445681\pi$
$398$	2.93785	0.147261
$399$	−12.4832	−0.624940
$400$	1.00000	0.0500000
$401$	−20.9845	−1.04792	−0.523958	−	0.851744i	$-0.675545\pi$
$401$	−20.9845	−1.04792	−0.523958	+	0.851744i	$0.675545\pi$
$402$	−2.50927	−0.125151
$403$	−22.6304	−1.12730
$404$	−15.1917	−0.755815
$405$	11.2176	0.557409
$406$	−4.12422	−0.204682
$407$	0	0
$408$	−13.1099	−0.649036
$409$	−31.8699	−1.57586	−0.787932	−	0.615762i	$-0.788848\pi$
$409$	−31.8699	−1.57586	−0.787932	+	0.615762i	$0.788848\pi$
$410$	5.54216	0.273708
$411$	12.1744	0.600519
$412$	5.54781	0.273321
$413$	−3.77402	−0.185707
$414$	2.54395	0.125028
$415$	12.3739	0.607410
$416$	−3.92049	−0.192218
$417$	18.4977	0.905838
$418$	0	0
$419$	−13.6261	−0.665680	−0.332840	−	0.942983i	$-0.608007\pi$
$419$	−13.6261	−0.665680	−0.332840	+	0.942983i	$0.608007\pi$
$420$	−2.16330	−0.105558
$421$	16.6683	0.812366	0.406183	−	0.913792i	$-0.366860\pi$
$421$	16.6683	0.812366	0.406183	+	0.913792i	$0.366860\pi$
$422$	17.9913	0.875802
$423$	−18.3484	−0.892128
$424$	3.74119	0.181688
$425$	−6.06013	−0.293959
$426$	1.34988	0.0654017
$427$	−0.532894	−0.0257885
$428$	9.25943	0.447571
$429$	0	0
$430$	−6.51122	−0.313999
$431$	−27.1066	−1.30568	−0.652840	−	0.757496i	$-0.726423\pi$
$431$	−27.1066	−1.30568	−0.652840	+	0.757496i	$0.726423\pi$
$432$	−2.85582	−0.137401
$433$	−19.1461	−0.920102	−0.460051	−	0.887892i	$-0.652169\pi$
$433$	−19.1461	−0.920102	−0.460051	+	0.887892i	$0.652169\pi$
$434$	5.77234	0.277081
$435$	8.92194	0.427774
$436$	−0.167247	−0.00800966
$437$	−8.73853	−0.418020
$438$	6.71741	0.320970
$439$	−17.6266	−0.841270	−0.420635	−	0.907230i	$-0.638193\pi$
$439$	−17.6266	−0.841270	−0.420635	+	0.907230i	$0.638193\pi$
$440$	0	0
$441$	1.67988	0.0799943
$442$	23.7586	1.13008
$443$	−29.6802	−1.41015	−0.705073	−	0.709134i	$-0.749086\pi$
$443$	−29.6802	−1.41015	−0.705073	+	0.709134i	$0.749086\pi$
$444$	−9.86142	−0.468002
$445$	−3.59309	−0.170329
$446$	22.2447	1.05332
$447$	−42.1592	−1.99406
$448$	1.00000	0.0472456
$449$	−22.7127	−1.07188	−0.535939	−	0.844257i	$-0.680042\pi$
$449$	−22.7127	−1.07188	−0.535939	+	0.844257i	$0.680042\pi$
$450$	1.67988	0.0791903
$451$	0	0
$452$	6.66364	0.313431
$453$	−11.3311	−0.532380
$454$	−26.2506	−1.23200
$455$	3.92049	0.183795
$456$	−12.4832	−0.584578
$457$	1.09657	0.0512952	0.0256476	−	0.999671i	$-0.491835\pi$
$457$	1.09657	0.0512952	0.0256476	+	0.999671i	$0.491835\pi$
$458$	−9.12533	−0.426399
$459$	17.3066	0.807805
$460$	−1.51437	−0.0706077
$461$	−2.22426	−0.103594	−0.0517971	−	0.998658i	$-0.516495\pi$
$461$	−2.22426	−0.103594	−0.0517971	+	0.998658i	$0.516495\pi$
$462$	0	0
$463$	−32.4265	−1.50699	−0.753495	−	0.657454i	$-0.771633\pi$
$463$	−32.4265	−1.50699	−0.753495	+	0.657454i	$0.771633\pi$
$464$	−4.12422	−0.191462
$465$	−12.4873	−0.579085
$466$	−0.378654	−0.0175408
$467$	−10.4325	−0.482757	−0.241378	−	0.970431i	$-0.577599\pi$
$467$	−10.4325	−0.482757	−0.241378	+	0.970431i	$0.577599\pi$
$468$	−6.58594	−0.304435
$469$	−1.15993	−0.0535604
$470$	10.9224	0.503814
$471$	34.2063	1.57614
$472$	−3.77402	−0.173713
$473$	0	0
$474$	8.14974	0.374330
$475$	−5.77042	−0.264765
$476$	−6.06013	−0.277765
$477$	6.28475	0.287759
$478$	−0.173692	−0.00794448
$479$	29.5228	1.34893	0.674467	−	0.738305i	$-0.264374\pi$
$479$	29.5228	1.34893	0.674467	+	0.738305i	$0.264374\pi$
$480$	−2.16330	−0.0987408
$481$	17.8715	0.814872
$482$	−27.9248	−1.27194
$483$	3.27603	0.149065
$484$	0	0
$485$	15.6424	0.710283
$486$	−15.6997	−0.712153
$487$	−30.0031	−1.35957	−0.679785	−	0.733412i	$-0.737927\pi$
$487$	−30.0031	−1.35957	−0.679785	+	0.733412i	$0.737927\pi$
$488$	−0.532894	−0.0241230
$489$	26.9222	1.21746
$490$	−1.00000	−0.0451754
$491$	−6.49265	−0.293009	−0.146505	−	0.989210i	$-0.546802\pi$
$491$	−6.49265	−0.293009	−0.146505	+	0.989210i	$0.546802\pi$
$492$	−11.9894	−0.540523
$493$	24.9933	1.12564
$494$	22.6228	1.01785
$495$	0	0
$496$	5.77234	0.259186
$497$	0.623988	0.0279897
$498$	−26.7685	−1.19952
$499$	44.2093	1.97908	0.989540	−	0.144260i	$-0.0460802\pi$
$499$	44.2093	1.97908	0.989540	+	0.144260i	$0.0460802\pi$
$500$	−1.00000	−0.0447214
$501$	−38.6734	−1.72780
$502$	25.6423	1.14447
$503$	−24.6932	−1.10101	−0.550507	−	0.834830i	$-0.685566\pi$
$503$	−24.6932	−1.10101	−0.550507	+	0.834830i	$0.685566\pi$
$504$	1.67988	0.0748278
$505$	15.1917	0.676021
$506$	0	0
$507$	5.12748	0.227720
$508$	−2.06518	−0.0916276
$509$	14.9350	0.661981	0.330990	−	0.943634i	$-0.392617\pi$
$509$	14.9350	0.661981	0.330990	+	0.943634i	$0.392617\pi$
$510$	13.1099	0.580516
$511$	3.10516	0.137364
$512$	1.00000	0.0441942
$513$	16.4793	0.727578
$514$	31.4403	1.38677
$515$	−5.54781	−0.244466
$516$	14.0857	0.620090
$517$	0	0
$518$	−4.55850	−0.200289
$519$	−42.5694	−1.86859
$520$	3.92049	0.171925
$521$	−30.4761	−1.33518	−0.667591	−	0.744528i	$-0.732675\pi$
$521$	−30.4761	−1.33518	−0.667591	+	0.744528i	$0.732675\pi$
$522$	−6.92819	−0.303239
$523$	25.2536	1.10426	0.552132	−	0.833757i	$-0.313814\pi$
$523$	25.2536	1.10426	0.552132	+	0.833757i	$0.313814\pi$
$524$	22.8396	0.997751
$525$	2.16330	0.0944143
$526$	24.0975	1.05070
$527$	−34.9811	−1.52380
$528$	0	0
$529$	−20.7067	−0.900291
$530$	−3.74119	−0.162507
$531$	−6.33989	−0.275128
$532$	−5.77042	−0.250179
$533$	21.7280	0.941143
$534$	7.77293	0.336368
$535$	−9.25943	−0.400320
$536$	−1.15993	−0.0501012
$537$	−3.67480	−0.158579
$538$	24.8472	1.07124
$539$	0	0
$540$	2.85582	0.122895
$541$	8.91666	0.383357	0.191679	−	0.981458i	$-0.438607\pi$
$541$	8.91666	0.383357	0.191679	+	0.981458i	$0.438607\pi$
$542$	0.300798	0.0129204
$543$	−34.8732	−1.49655
$544$	−6.06013	−0.259826
$545$	0.167247	0.00716405
$546$	−8.48120	−0.362962
$547$	−28.3429	−1.21186	−0.605928	−	0.795519i	$-0.707198\pi$
$547$	−28.3429	−1.21186	−0.605928	+	0.795519i	$0.707198\pi$
$548$	5.62769	0.240403
$549$	−0.895197	−0.0382061
$550$	0	0
$551$	23.7985	1.01385
$552$	3.27603	0.139437
$553$	3.76727	0.160201
$554$	17.0103	0.722698
$555$	9.86142	0.418594
$556$	8.55069	0.362630
$557$	−35.7619	−1.51528	−0.757640	−	0.652673i	$-0.773648\pi$
$557$	−35.7619	−1.51528	−0.757640	+	0.652673i	$0.773648\pi$
$558$	9.69683	0.410500
$559$	−25.5271	−1.07968
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	−22.0382	−0.929626
$563$	38.9121	1.63995	0.819974	−	0.572401i	$-0.193988\pi$
$563$	38.9121	1.63995	0.819974	+	0.572401i	$0.193988\pi$
$564$	−23.6285	−0.994941
$565$	−6.66364	−0.280341
$566$	9.47154	0.398119
$567$	−11.2176	−0.471097
$568$	0.623988	0.0261820
$569$	−38.5397	−1.61567	−0.807835	−	0.589409i	$-0.799361\pi$
$569$	−38.5397	−1.61567	−0.807835	+	0.589409i	$0.799361\pi$
$570$	12.4832	0.522862
$571$	4.21906	0.176562	0.0882811	−	0.996096i	$-0.471863\pi$
$571$	4.21906	0.176562	0.0882811	+	0.996096i	$0.471863\pi$
$572$	0	0
$573$	−37.5631	−1.56922
$574$	−5.54216	−0.231325
$575$	1.51437	0.0631534
$576$	1.67988	0.0699950
$577$	−37.8088	−1.57400	−0.786999	−	0.616954i	$-0.788367\pi$
$577$	−37.8088	−1.57400	−0.786999	+	0.616954i	$0.788367\pi$
$578$	19.7251	0.820457
$579$	−11.5449	−0.479790
$580$	4.12422	0.171249
$581$	−12.3739	−0.513356
$582$	−33.8392	−1.40268
$583$	0	0
$584$	3.10516	0.128493
$585$	6.58594	0.272295
$586$	−16.8419	−0.695731
$587$	15.0876	0.622730	0.311365	−	0.950290i	$-0.399214\pi$
$587$	15.0876	0.622730	0.311365	+	0.950290i	$0.399214\pi$
$588$	2.16330	0.0892131
$589$	−33.3088	−1.37247
$590$	3.77402	0.155374
$591$	42.9777	1.76787
$592$	−4.55850	−0.187353
$593$	38.3246	1.57380	0.786902	−	0.617079i	$-0.211684\pi$
$593$	38.3246	1.57380	0.786902	+	0.617079i	$0.211684\pi$
$594$	0	0
$595$	6.06013	0.248441
$596$	−19.4884	−0.798274
$597$	6.35546	0.260112
$598$	−5.93705	−0.242784
$599$	27.2693	1.11419	0.557097	−	0.830447i	$-0.311915\pi$
$599$	27.2693	1.11419	0.557097	+	0.830447i	$0.311915\pi$
$600$	2.16330	0.0883165
$601$	33.1915	1.35391	0.676955	−	0.736025i	$-0.263299\pi$
$601$	33.1915	1.35391	0.676955	+	0.736025i	$0.263299\pi$
$602$	6.51122	0.265377
$603$	−1.94854	−0.0793505
$604$	−5.23785	−0.213125
$605$	0	0
$606$	−32.8642	−1.33502
$607$	19.5753	0.794538	0.397269	−	0.917702i	$-0.369958\pi$
$607$	19.5753	0.794538	0.397269	+	0.917702i	$0.369958\pi$
$608$	−5.77042	−0.234021
$609$	−8.92194	−0.361535
$610$	0.532894	0.0215762
$611$	42.8212	1.73236
$612$	−10.1803	−0.411513
$613$	17.1988	0.694651	0.347326	−	0.937745i	$-0.387090\pi$
$613$	17.1988	0.694651	0.347326	+	0.937745i	$0.387090\pi$
$614$	−1.36644	−0.0551452
$615$	11.9894	0.483458
$616$	0	0
$617$	−40.4745	−1.62944	−0.814722	−	0.579852i	$-0.803110\pi$
$617$	−40.4745	−1.62944	−0.814722	+	0.579852i	$0.803110\pi$
$618$	12.0016	0.482775
$619$	24.3345	0.978088	0.489044	−	0.872259i	$-0.337346\pi$
$619$	24.3345	0.978088	0.489044	+	0.872259i	$0.337346\pi$
$620$	−5.77234	−0.231823
$621$	−4.32476	−0.173547
$622$	18.5543	0.743958
$623$	3.59309	0.143954
$624$	−8.48120	−0.339520
$625$	1.00000	0.0400000
$626$	−13.8649	−0.554151
$627$	0	0
$628$	15.8121	0.630971
$629$	27.6251	1.10148
$630$	−1.67988	−0.0669280
$631$	−40.5266	−1.61334	−0.806669	−	0.591004i	$-0.798732\pi$
$631$	−40.5266	−1.61334	−0.806669	+	0.591004i	$0.798732\pi$
$632$	3.76727	0.149854
$633$	38.9206	1.54696
$634$	−23.4949	−0.933101
$635$	2.06518	0.0819542
$636$	8.09333	0.320922
$637$	−3.92049	−0.155335
$638$	0	0
$639$	1.04822	0.0414671
$640$	−1.00000	−0.0395285
$641$	−14.8590	−0.586895	−0.293447	−	0.955975i	$-0.594803\pi$
$641$	−14.8590	−0.586895	−0.293447	+	0.955975i	$0.594803\pi$
$642$	20.0309	0.790558
$643$	−10.3430	−0.407888	−0.203944	−	0.978983i	$-0.565376\pi$
$643$	−10.3430	−0.407888	−0.203944	+	0.978983i	$0.565376\pi$
$644$	1.51437	0.0596744
$645$	−14.0857	−0.554625
$646$	34.9695	1.37585
$647$	−6.94642	−0.273092	−0.136546	−	0.990634i	$-0.543600\pi$
$647$	−6.94642	−0.273092	−0.136546	+	0.990634i	$0.543600\pi$
$648$	−11.2176	−0.440671
$649$	0	0
$650$	−3.92049	−0.153774
$651$	12.4873	0.489417
$652$	12.4449	0.487381
$653$	−25.3255	−0.991064	−0.495532	−	0.868590i	$-0.665027\pi$
$653$	−25.3255	−0.991064	−0.495532	+	0.868590i	$0.665027\pi$
$654$	−0.361805	−0.0141477
$655$	−22.8396	−0.892416
$656$	−5.54216	−0.216385
$657$	5.21630	0.203507
$658$	−10.9224	−0.425801
$659$	2.24029	0.0872694	0.0436347	−	0.999048i	$-0.486106\pi$
$659$	2.24029	0.0872694	0.0436347	+	0.999048i	$0.486106\pi$
$660$	0	0
$661$	0.565825	0.0220081	0.0110040	−	0.999939i	$-0.496497\pi$
$661$	0.565825	0.0220081	0.0110040	+	0.999939i	$0.496497\pi$
$662$	10.6438	0.413682
$663$	51.3971	1.99610
$664$	−12.3739	−0.480200
$665$	5.77042	0.223767
$666$	−7.65773	−0.296731
$667$	−6.24558	−0.241830
$668$	−17.8770	−0.691682
$669$	48.1220	1.86050
$670$	1.15993	0.0448119
$671$	0	0
$672$	2.16330	0.0834512
$673$	30.0117	1.15686	0.578432	−	0.815731i	$-0.303665\pi$
$673$	30.0117	1.15686	0.578432	+	0.815731i	$0.303665\pi$
$674$	13.3566	0.514477
$675$	−2.85582	−0.109921
$676$	2.37021	0.0911620
$677$	8.08627	0.310780	0.155390	−	0.987853i	$-0.450337\pi$
$677$	8.08627	0.310780	0.155390	+	0.987853i	$0.450337\pi$
$678$	14.4155	0.553623
$679$	−15.6424	−0.600299
$680$	6.06013	0.232395
$681$	−56.7880	−2.17612
$682$	0	0
$683$	−47.9737	−1.83566	−0.917831	−	0.396972i	$-0.870061\pi$
$683$	−47.9737	−1.83566	−0.917831	+	0.396972i	$0.870061\pi$
$684$	−9.69360	−0.370644
$685$	−5.62769	−0.215023
$686$	1.00000	0.0381802
$687$	−19.7409	−0.753161
$688$	6.51122	0.248238
$689$	−14.6673	−0.558779
$690$	−3.27603	−0.124716
$691$	−6.78793	−0.258225	−0.129113	−	0.991630i	$-0.541213\pi$
$691$	−6.78793	−0.258225	−0.129113	+	0.991630i	$0.541213\pi$
$692$	−19.6780	−0.748044
$693$	0	0
$694$	14.5070	0.550680
$695$	−8.55069	−0.324346
$696$	−8.92194	−0.338185
$697$	33.5862	1.27217
$698$	−26.1051	−0.988092
$699$	−0.819143	−0.0309828
$700$	1.00000	0.0377964
$701$	29.0743	1.09812	0.549060	−	0.835783i	$-0.314986\pi$
$701$	29.0743	1.09812	0.549060	+	0.835783i	$0.314986\pi$
$702$	11.1962	0.422574
$703$	26.3045	0.992092
$704$	0	0
$705$	23.6285	0.889902
$706$	20.3692	0.766605
$707$	−15.1917	−0.571342
$708$	−8.16434	−0.306835
$709$	8.34599	0.313440	0.156720	−	0.987643i	$-0.449908\pi$
$709$	8.34599	0.313440	0.156720	+	0.987643i	$0.449908\pi$
$710$	−0.623988	−0.0234179
$711$	6.32856	0.237339
$712$	3.59309	0.134657
$713$	8.74144	0.327369
$714$	−13.1099	−0.490625
$715$	0	0
$716$	−1.69870	−0.0634834
$717$	−0.375748	−0.0140326
$718$	18.5953	0.693970
$719$	37.1223	1.38443	0.692214	−	0.721692i	$-0.256635\pi$
$719$	37.1223	1.38443	0.692214	+	0.721692i	$0.256635\pi$
$720$	−1.67988	−0.0626054
$721$	5.54781	0.206611
$722$	14.2977	0.532106
$723$	−60.4099	−2.24667
$724$	−16.1203	−0.599108
$725$	−4.12422	−0.153170
$726$	0	0
$727$	−4.58789	−0.170155	−0.0850777	−	0.996374i	$-0.527114\pi$
$727$	−4.58789	−0.170155	−0.0850777	+	0.996374i	$0.527114\pi$
$728$	−3.92049	−0.145303
$729$	−0.310271	−0.0114915
$730$	−3.10516	−0.114927
$731$	−39.4588	−1.45944
$732$	−1.15281	−0.0426091
$733$	−28.4263	−1.04995	−0.524975	−	0.851118i	$-0.675925\pi$
$733$	−28.4263	−1.04995	−0.524975	+	0.851118i	$0.675925\pi$
$734$	9.43885	0.348394
$735$	−2.16330	−0.0797946
$736$	1.51437	0.0558203
$737$	0	0
$738$	−9.31016	−0.342712
$739$	−43.9480	−1.61665	−0.808326	−	0.588735i	$-0.799626\pi$
$739$	−43.9480	−1.61665	−0.808326	+	0.588735i	$0.799626\pi$
$740$	4.55850	0.167574
$741$	48.9401	1.79786
$742$	3.74119	0.137344
$743$	37.9450	1.39207	0.696033	−	0.718009i	$-0.254947\pi$
$743$	37.9450	1.39207	0.696033	+	0.718009i	$0.254947\pi$
$744$	12.4873	0.457807
$745$	19.4884	0.713998
$746$	−17.1558	−0.628119
$747$	−20.7866	−0.760544
$748$	0	0
$749$	9.25943	0.338332
$750$	−2.16330	−0.0789927
$751$	47.4786	1.73252	0.866259	−	0.499594i	$-0.166518\pi$
$751$	47.4786	1.73252	0.866259	+	0.499594i	$0.166518\pi$
$752$	−10.9224	−0.398300
$753$	55.4721	2.02152
$754$	16.1690	0.588839
$755$	5.23785	0.190625
$756$	−2.85582	−0.103865
$757$	−9.11510	−0.331294	−0.165647	−	0.986185i	$-0.552971\pi$
$757$	−9.11510	−0.331294	−0.165647	+	0.986185i	$0.552971\pi$
$758$	−8.09841	−0.294148
$759$	0	0
$760$	5.77042	0.209315
$761$	−47.7072	−1.72939	−0.864693	−	0.502300i	$-0.832487\pi$
$761$	−47.7072	−1.72939	−0.864693	+	0.502300i	$0.832487\pi$
$762$	−4.46761	−0.161845
$763$	−0.167247	−0.00605473
$764$	−17.3638	−0.628200
$765$	10.1803	0.368069
$766$	23.3157	0.842430
$767$	14.7960	0.534252
$768$	2.16330	0.0780615
$769$	21.7046	0.782689	0.391345	−	0.920244i	$-0.372010\pi$
$769$	21.7046	0.782689	0.391345	+	0.920244i	$0.372010\pi$
$770$	0	0
$771$	68.0149	2.44950
$772$	−5.33671	−0.192072
$773$	45.0248	1.61943	0.809715	−	0.586824i	$-0.199622\pi$
$773$	45.0248	1.61943	0.809715	+	0.586824i	$0.199622\pi$
$774$	10.9381	0.393160
$775$	5.77234	0.207349
$776$	−15.6424	−0.561528
$777$	−9.86142	−0.353777
$778$	18.9522	0.679470
$779$	31.9806	1.14582
$780$	8.48120	0.303676
$781$	0	0
$782$	−9.17725	−0.328178
$783$	11.7780	0.420913
$784$	1.00000	0.0357143
$785$	−15.8121	−0.564357
$786$	49.4089	1.76236
$787$	48.4300	1.72634	0.863172	−	0.504910i	$-0.168474\pi$
$787$	48.4300	1.72634	0.863172	+	0.504910i	$0.168474\pi$
$788$	19.8667	0.707722
$789$	52.1302	1.85589
$790$	−3.76727	−0.134033
$791$	6.66364	0.236932
$792$	0	0
$793$	2.08920	0.0741898
$794$	6.76731	0.240163
$795$	−8.09333	−0.287041
$796$	2.93785	0.104129
$797$	16.5805	0.587310	0.293655	−	0.955911i	$-0.405128\pi$
$797$	16.5805	0.587310	0.293655	+	0.955911i	$0.405128\pi$
$798$	−12.4832	−0.441899
$799$	66.1913	2.34168
$800$	1.00000	0.0353553
$801$	6.03595	0.213270
$802$	−20.9845	−0.740989
$803$	0	0
$804$	−2.50927	−0.0884952
$805$	−1.51437	−0.0533744
$806$	−22.6304	−0.797121
$807$	53.7521	1.89216
$808$	−15.1917	−0.534442
$809$	−44.2436	−1.55552	−0.777761	−	0.628560i	$-0.783645\pi$
$809$	−44.2436	−1.55552	−0.777761	+	0.628560i	$0.783645\pi$
$810$	11.2176	0.394148
$811$	30.8983	1.08498	0.542492	−	0.840061i	$-0.317481\pi$
$811$	30.8983	1.08498	0.542492	+	0.840061i	$0.317481\pi$
$812$	−4.12422	−0.144732
$813$	0.650716	0.0228216
$814$	0	0
$815$	−12.4449	−0.435927
$816$	−13.1099	−0.458938
$817$	−37.5724	−1.31449
$818$	−31.8699	−1.11430
$819$	−6.58594	−0.230131
$820$	5.54216	0.193541
$821$	4.35691	0.152057	0.0760286	−	0.997106i	$-0.475776\pi$
$821$	4.35691	0.152057	0.0760286	+	0.997106i	$0.475776\pi$
$822$	12.1744	0.424631
$823$	−38.6335	−1.34668	−0.673340	−	0.739333i	$-0.735141\pi$
$823$	−38.6335	−1.34668	−0.673340	+	0.739333i	$0.735141\pi$
$824$	5.54781	0.193267
$825$	0	0
$826$	−3.77402	−0.131315
$827$	−12.7972	−0.445002	−0.222501	−	0.974932i	$-0.571422\pi$
$827$	−12.7972	−0.445002	−0.222501	+	0.974932i	$0.571422\pi$
$828$	2.54395	0.0884085
$829$	−7.81466	−0.271414	−0.135707	−	0.990749i	$-0.543331\pi$
$829$	−7.81466	−0.271414	−0.135707	+	0.990749i	$0.543331\pi$
$830$	12.3739	0.429504
$831$	36.7984	1.27652
$832$	−3.92049	−0.135918
$833$	−6.06013	−0.209971
$834$	18.4977	0.640524
$835$	17.8770	0.618659
$836$	0	0
$837$	−16.4848	−0.569797
$838$	−13.6261	−0.470707
$839$	23.8274	0.822613	0.411307	−	0.911497i	$-0.365073\pi$
$839$	23.8274	0.822613	0.411307	+	0.911497i	$0.365073\pi$
$840$	−2.16330	−0.0746410
$841$	−11.9908	−0.413476
$842$	16.6683	0.574429
$843$	−47.6754	−1.64203
$844$	17.9913	0.619286
$845$	−2.37021	−0.0815377
$846$	−18.3484	−0.630830
$847$	0	0
$848$	3.74119	0.128473
$849$	20.4898	0.703209
$850$	−6.06013	−0.207861
$851$	−6.90324	−0.236640
$852$	1.34988	0.0462460
$853$	10.9713	0.375651	0.187826	−	0.982202i	$-0.439856\pi$
$853$	10.9713	0.375651	0.187826	+	0.982202i	$0.439856\pi$
$854$	−0.532894	−0.0182353
$855$	9.69360	0.331514
$856$	9.25943	0.316481
$857$	−46.9137	−1.60254	−0.801270	−	0.598302i	$-0.795842\pi$
$857$	−46.9137	−1.60254	−0.801270	+	0.598302i	$0.795842\pi$
$858$	0	0
$859$	−12.5547	−0.428362	−0.214181	−	0.976794i	$-0.568708\pi$
$859$	−12.5547	−0.428362	−0.214181	+	0.976794i	$0.568708\pi$
$860$	−6.51122	−0.222031
$861$	−11.9894	−0.408597
$862$	−27.1066	−0.923255
$863$	47.0563	1.60182	0.800908	−	0.598787i	$-0.204350\pi$
$863$	47.0563	1.60182	0.800908	+	0.598787i	$0.204350\pi$
$864$	−2.85582	−0.0971570
$865$	19.6780	0.669071
$866$	−19.1461	−0.650610
$867$	42.6714	1.44920
$868$	5.77234	0.195926
$869$	0	0
$870$	8.92194	0.302482
$871$	4.54748	0.154085
$872$	−0.167247	−0.00566368
$873$	−26.2773	−0.889351
$874$	−8.73853	−0.295585
$875$	−1.00000	−0.0338062
$876$	6.71741	0.226960
$877$	15.8474	0.535129	0.267564	−	0.963540i	$-0.413781\pi$
$877$	15.8474	0.535129	0.267564	+	0.963540i	$0.413781\pi$
$878$	−17.6266	−0.594868
$879$	−36.4341	−1.22889
$880$	0	0
$881$	−51.3201	−1.72902	−0.864509	−	0.502617i	$-0.832371\pi$
$881$	−51.3201	−1.72902	−0.864509	+	0.502617i	$0.832371\pi$
$882$	1.67988	0.0565645
$883$	−20.0416	−0.674452	−0.337226	−	0.941424i	$-0.609489\pi$
$883$	−20.0416	−0.674452	−0.337226	+	0.941424i	$0.609489\pi$
$884$	23.7586	0.799090
$885$	8.16434	0.274441
$886$	−29.6802	−0.997124
$887$	−20.6052	−0.691856	−0.345928	−	0.938261i	$-0.612436\pi$
$887$	−20.6052	−0.691856	−0.345928	+	0.938261i	$0.612436\pi$
$888$	−9.86142	−0.330928
$889$	−2.06518	−0.0692640
$890$	−3.59309	−0.120440
$891$	0	0
$892$	22.2447	0.744808
$893$	63.0270	2.10912
$894$	−42.1592	−1.41001
$895$	1.69870	0.0567813
$896$	1.00000	0.0334077
$897$	−12.8436	−0.428837
$898$	−22.7127	−0.757932
$899$	−23.8064	−0.793988
$900$	1.67988	0.0559960
$901$	−22.6721	−0.755317
$902$	0	0
$903$	14.0857	0.468744
$904$	6.66364	0.221629
$905$	16.1203	0.535858
$906$	−11.3311	−0.376449
$907$	−19.6445	−0.652286	−0.326143	−	0.945320i	$-0.605749\pi$
$907$	−19.6445	−0.652286	−0.326143	+	0.945320i	$0.605749\pi$
$908$	−26.2506	−0.871156
$909$	−25.5202	−0.846452
$910$	3.92049	0.129963
$911$	13.5734	0.449706	0.224853	−	0.974393i	$-0.427810\pi$
$911$	13.5734	0.449706	0.224853	+	0.974393i	$0.427810\pi$
$912$	−12.4832	−0.413359
$913$	0	0
$914$	1.09657	0.0362712
$915$	1.15281	0.0381108
$916$	−9.12533	−0.301509
$917$	22.8396	0.754229
$918$	17.3066	0.571204
$919$	41.6679	1.37450	0.687248	−	0.726423i	$-0.258818\pi$
$919$	41.6679	1.37450	0.687248	+	0.726423i	$0.258818\pi$
$920$	−1.51437	−0.0499272
$921$	−2.95603	−0.0974045
$922$	−2.22426	−0.0732521
$923$	−2.44634	−0.0805222
$924$	0	0
$925$	−4.55850	−0.149883
$926$	−32.4265	−1.06560
$927$	9.31965	0.306098
$928$	−4.12422	−0.135384
$929$	−40.8551	−1.34041	−0.670207	−	0.742175i	$-0.733794\pi$
$929$	−40.8551	−1.34041	−0.670207	+	0.742175i	$0.733794\pi$
$930$	−12.4873	−0.409475
$931$	−5.77042	−0.189118
$932$	−0.378654	−0.0124032
$933$	40.1385	1.31408
$934$	−10.4325	−0.341361
$935$	0	0
$936$	−6.58594	−0.215268
$937$	−35.0299	−1.14438	−0.572189	−	0.820122i	$-0.693905\pi$
$937$	−35.0299	−1.14438	−0.572189	+	0.820122i	$0.693905\pi$
$938$	−1.15993	−0.0378729
$939$	−29.9939	−0.978814
$940$	10.9224	0.356250
$941$	33.3630	1.08760	0.543801	−	0.839214i	$-0.316985\pi$
$941$	33.3630	1.08760	0.543801	+	0.839214i	$0.316985\pi$
$942$	34.2063	1.11450
$943$	−8.39286	−0.273309
$944$	−3.77402	−0.122834
$945$	2.85582	0.0928999
$946$	0	0
$947$	40.2802	1.30893	0.654466	−	0.756091i	$-0.272893\pi$
$947$	40.2802	1.30893	0.654466	+	0.756091i	$0.272893\pi$
$948$	8.14974	0.264691
$949$	−12.1737	−0.395176
$950$	−5.77042	−0.187217
$951$	−50.8266	−1.64816
$952$	−6.06013	−0.196410
$953$	5.29582	0.171548	0.0857742	−	0.996315i	$-0.472664\pi$
$953$	5.29582	0.171548	0.0857742	+	0.996315i	$0.472664\pi$
$954$	6.28475	0.203476
$955$	17.3638	0.561879
$956$	−0.173692	−0.00561760
$957$	0	0
$958$	29.5228	0.953840
$959$	5.62769	0.181728
$960$	−2.16330	−0.0698203
$961$	2.31989	0.0748351
$962$	17.8715	0.576202
$963$	15.5547	0.501244
$964$	−27.9248	−0.899398
$965$	5.33671	0.171795
$966$	3.27603	0.105405
$967$	36.5071	1.17399	0.586995	−	0.809590i	$-0.300311\pi$
$967$	36.5071	1.17399	0.586995	+	0.809590i	$0.300311\pi$
$968$	0	0
$969$	75.6495	2.43021
$970$	15.6424	0.502246
$971$	−17.7455	−0.569481	−0.284740	−	0.958605i	$-0.591907\pi$
$971$	−17.7455	−0.569481	−0.284740	+	0.958605i	$0.591907\pi$
$972$	−15.6997	−0.503568
$973$	8.55069	0.274123
$974$	−30.0031	−0.961361
$975$	−8.48120	−0.271616
$976$	−0.532894	−0.0170575
$977$	−16.2770	−0.520746	−0.260373	−	0.965508i	$-0.583845\pi$
$977$	−16.2770	−0.520746	−0.260373	+	0.965508i	$0.583845\pi$
$978$	26.9222	0.860876
$979$	0	0
$980$	−1.00000	−0.0319438
$981$	−0.280954	−0.00897017
$982$	−6.49265	−0.207189
$983$	17.0532	0.543911	0.271956	−	0.962310i	$-0.412330\pi$
$983$	17.0532	0.543911	0.271956	+	0.962310i	$0.412330\pi$
$984$	−11.9894	−0.382207
$985$	−19.8667	−0.633006
$986$	24.9933	0.795949
$987$	−23.6285	−0.752104
$988$	22.6228	0.719728
$989$	9.86037	0.313541
$990$	0	0
$991$	−16.9081	−0.537105	−0.268552	−	0.963265i	$-0.586545\pi$
$991$	−16.9081	−0.537105	−0.268552	+	0.963265i	$0.586545\pi$
$992$	5.77234	0.183272
$993$	23.0257	0.730700
$994$	0.623988	0.0197917
$995$	−2.93785	−0.0931361
$996$	−26.7685	−0.848192
$997$	−40.3377	−1.27751	−0.638754	−	0.769411i	$-0.720550\pi$
$997$	−40.3377	−1.27751	−0.638754	+	0.769411i	$0.720550\pi$
$998$	44.2093	1.39942
$999$	13.0183	0.411880

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.da.1.6		6
11.3	even	5		770.2.n.h.141.1	yes	12
11.4	even	5		770.2.n.h.71.1	✓	12
11.10	odd	2		8470.2.a.cu.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.h.71.1	✓	12	11.4	even	5
770.2.n.h.141.1	yes	12	11.3	even	5
8470.2.a.cu.1.6		6	11.10	odd	2
8470.2.a.da.1.6		6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8470.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.16330 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.16330 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.67988 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.16330 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.16330 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.67988 q^{9} -1.00000 q^{10} +2.16330 q^{12} -3.92049 q^{13} +1.00000 q^{14} -2.16330 q^{15} +1.00000 q^{16} -6.06013 q^{17} +1.67988 q^{18} -5.77042 q^{19} -1.00000 q^{20} +2.16330 q^{21} +1.51437 q^{23} +2.16330 q^{24} +1.00000 q^{25} -3.92049 q^{26} -2.85582 q^{27} +1.00000 q^{28} -4.12422 q^{29} -2.16330 q^{30} +5.77234 q^{31} +1.00000 q^{32} -6.06013 q^{34} -1.00000 q^{35} +1.67988 q^{36} -4.55850 q^{37} -5.77042 q^{38} -8.48120 q^{39} -1.00000 q^{40} -5.54216 q^{41} +2.16330 q^{42} +6.51122 q^{43} -1.67988 q^{45} +1.51437 q^{46} -10.9224 q^{47} +2.16330 q^{48} +1.00000 q^{49} +1.00000 q^{50} -13.1099 q^{51} -3.92049 q^{52} +3.74119 q^{53} -2.85582 q^{54} +1.00000 q^{56} -12.4832 q^{57} -4.12422 q^{58} -3.77402 q^{59} -2.16330 q^{60} -0.532894 q^{61} +5.77234 q^{62} +1.67988 q^{63} +1.00000 q^{64} +3.92049 q^{65} -1.15993 q^{67} -6.06013 q^{68} +3.27603 q^{69} -1.00000 q^{70} +0.623988 q^{71} +1.67988 q^{72} +3.10516 q^{73} -4.55850 q^{74} +2.16330 q^{75} -5.77042 q^{76} -8.48120 q^{78} +3.76727 q^{79} -1.00000 q^{80} -11.2176 q^{81} -5.54216 q^{82} -12.3739 q^{83} +2.16330 q^{84} +6.06013 q^{85} +6.51122 q^{86} -8.92194 q^{87} +3.59309 q^{89} -1.67988 q^{90} -3.92049 q^{91} +1.51437 q^{92} +12.4873 q^{93} -10.9224 q^{94} +5.77042 q^{95} +2.16330 q^{96} -15.6424 q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 5 q^{3} + 6 q^{4} - 6 q^{5} - 5 q^{6} + 6 q^{7} + 6 q^{8} + 11 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - 5 * q^3 + 6 * q^4 - 6 * q^5 - 5 * q^6 + 6 * q^7 + 6 * q^8 + 11 * q^9	\( 6 q + 6 q^{2} - 5 q^{3} + 6 q^{4} - 6 q^{5} - 5 q^{6} + 6 q^{7} + 6 q^{8} + 11 q^{9} - 6 q^{10} - 5 q^{12} + 6 q^{14} + 5 q^{15} + 6 q^{16} - 15 q^{17} + 11 q^{18} - 13 q^{19} - 6 q^{20} - 5 q^{21} - 2 q^{23} - 5 q^{24} + 6 q^{25} - 26 q^{27} + 6 q^{28} - 4 q^{29} + 5 q^{30} - 2 q^{31} + 6 q^{32} - 15 q^{34} - 6 q^{35} + 11 q^{36} - 13 q^{38} - 30 q^{39} - 6 q^{40} - 17 q^{41} - 5 q^{42} + 15 q^{43} - 11 q^{45} - 2 q^{46} - 18 q^{47} - 5 q^{48} + 6 q^{49} + 6 q^{50} + 6 q^{51} + 22 q^{53} - 26 q^{54} + 6 q^{56} - 2 q^{57} - 4 q^{58} - 7 q^{59} + 5 q^{60} - 20 q^{61} - 2 q^{62} + 11 q^{63} + 6 q^{64} - 29 q^{67} - 15 q^{68} + 12 q^{69} - 6 q^{70} - 2 q^{71} + 11 q^{72} + q^{73} - 5 q^{75} - 13 q^{76} - 30 q^{78} - 12 q^{79} - 6 q^{80} + 22 q^{81} - 17 q^{82} - 35 q^{83} - 5 q^{84} + 15 q^{85} + 15 q^{86} - 29 q^{89} - 11 q^{90} - 2 q^{92} + 8 q^{93} - 18 q^{94} + 13 q^{95} - 5 q^{96} - 19 q^{97} + 6 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 - 5 * q^3 + 6 * q^4 - 6 * q^5 - 5 * q^6 + 6 * q^7 + 6 * q^8 + 11 * q^9 - 6 * q^10 - 5 * q^12 + 6 * q^14 + 5 * q^15 + 6 * q^16 - 15 * q^17 + 11 * q^18 - 13 * q^19 - 6 * q^20 - 5 * q^21 - 2 * q^23 - 5 * q^24 + 6 * q^25 - 26 * q^27 + 6 * q^28 - 4 * q^29 + 5 * q^30 - 2 * q^31 + 6 * q^32 - 15 * q^34 - 6 * q^35 + 11 * q^36 - 13 * q^38 - 30 * q^39 - 6 * q^40 - 17 * q^41 - 5 * q^42 + 15 * q^43 - 11 * q^45 - 2 * q^46 - 18 * q^47 - 5 * q^48 + 6 * q^49 + 6 * q^50 + 6 * q^51 + 22 * q^53 - 26 * q^54 + 6 * q^56 - 2 * q^57 - 4 * q^58 - 7 * q^59 + 5 * q^60 - 20 * q^61 - 2 * q^62 + 11 * q^63 + 6 * q^64 - 29 * q^67 - 15 * q^68 + 12 * q^69 - 6 * q^70 - 2 * q^71 + 11 * q^72 + q^73 - 5 * q^75 - 13 * q^76 - 30 * q^78 - 12 * q^79 - 6 * q^80 + 22 * q^81 - 17 * q^82 - 35 * q^83 - 5 * q^84 + 15 * q^85 + 15 * q^86 - 29 * q^89 - 11 * q^90 - 2 * q^92 + 8 * q^93 - 18 * q^94 + 13 * q^95 - 5 * q^96 - 19 * q^97 + 6 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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