LMFDB - Embedded newform 8470.2.a.db.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:	6.6.4642000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 8x^{4} + 5x^{3} + 14x^{2} - 9x - 1 $ x^6 - x^5 - 8x^4 + 5x^3 + 14x^2 - 9x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
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			$-1.92474$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.92474 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.92474 q^{6} -1.00000 q^{7} +1.00000 q^{8} +0.704605 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.92474 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.92474 q^{6} -1.00000 q^{7} +1.00000 q^{8} +0.704605 q^{9} +1.00000 q^{10} +1.92474 q^{12} -5.24489 q^{13} -1.00000 q^{14} +1.92474 q^{15} +1.00000 q^{16} -4.30919 q^{17} +0.704605 q^{18} -0.740633 q^{19} +1.00000 q^{20} -1.92474 q^{21} -0.856965 q^{23} +1.92474 q^{24} +1.00000 q^{25} -5.24489 q^{26} -4.41803 q^{27} -1.00000 q^{28} -8.37564 q^{29} +1.92474 q^{30} +1.10298 q^{31} +1.00000 q^{32} -4.30919 q^{34} -1.00000 q^{35} +0.704605 q^{36} -1.77921 q^{37} -0.740633 q^{38} -10.0950 q^{39} +1.00000 q^{40} -10.7200 q^{41} -1.92474 q^{42} +1.13472 q^{43} +0.704605 q^{45} -0.856965 q^{46} +8.40172 q^{47} +1.92474 q^{48} +1.00000 q^{49} +1.00000 q^{50} -8.29405 q^{51} -5.24489 q^{52} -8.80661 q^{53} -4.41803 q^{54} -1.00000 q^{56} -1.42552 q^{57} -8.37564 q^{58} -12.9838 q^{59} +1.92474 q^{60} +13.0887 q^{61} +1.10298 q^{62} -0.704605 q^{63} +1.00000 q^{64} -5.24489 q^{65} +8.93617 q^{67} -4.30919 q^{68} -1.64943 q^{69} -1.00000 q^{70} -4.50750 q^{71} +0.704605 q^{72} -3.33413 q^{73} -1.77921 q^{74} +1.92474 q^{75} -0.740633 q^{76} -10.0950 q^{78} -1.56183 q^{79} +1.00000 q^{80} -10.6173 q^{81} -10.7200 q^{82} +0.609215 q^{83} -1.92474 q^{84} -4.30919 q^{85} +1.13472 q^{86} -16.1209 q^{87} +1.46836 q^{89} +0.704605 q^{90} +5.24489 q^{91} -0.856965 q^{92} +2.12295 q^{93} +8.40172 q^{94} -0.740633 q^{95} +1.92474 q^{96} +8.41705 q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - q^{3} + 6 q^{4} + 6 q^{5} - q^{6} - 6 q^{7} + 6 q^{8} - q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - q^3 + 6 * q^4 + 6 * q^5 - q^6 - 6 * q^7 + 6 * q^8 - q^9	$ 6 q + 6 q^{2} - q^{3} + 6 q^{4} + 6 q^{5} - q^{6} - 6 q^{7} + 6 q^{8} - q^{9} + 6 q^{10} - q^{12} - 6 q^{13} - 6 q^{14} - q^{15} + 6 q^{16} - 21 q^{17} - q^{18} + 3 q^{19} + 6 q^{20} + q^{21} - 10 q^{23} - q^{24} + 6 q^{25} - 6 q^{26} - 4 q^{27} - 6 q^{28} - 10 q^{29} - q^{30} - 4 q^{31} + 6 q^{32} - 21 q^{34} - 6 q^{35} - q^{36} - 2 q^{37} + 3 q^{38} - 26 q^{39} + 6 q^{40} - 7 q^{41} + q^{42} - 19 q^{43} - q^{45} - 10 q^{46} + 10 q^{47} - q^{48} + 6 q^{49} + 6 q^{50} + 4 q^{51} - 6 q^{52} - 16 q^{53} - 4 q^{54} - 6 q^{56} - 16 q^{57} - 10 q^{58} - 3 q^{59} - q^{60} + 8 q^{61} - 4 q^{62} + q^{63} + 6 q^{64} - 6 q^{65} - 27 q^{67} - 21 q^{68} + 4 q^{69} - 6 q^{70} + 4 q^{71} - q^{72} - 13 q^{73} - 2 q^{74} - q^{75} + 3 q^{76} - 26 q^{78} - 14 q^{79} + 6 q^{80} - 14 q^{81} - 7 q^{82} - 51 q^{83} + q^{84} - 21 q^{85} - 19 q^{86} - 8 q^{87} + q^{89} - q^{90} + 6 q^{91} - 10 q^{92} + 4 q^{93} + 10 q^{94} + 3 q^{95} - q^{96} + 7 q^{97} + 6 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 - q^3 + 6 * q^4 + 6 * q^5 - q^6 - 6 * q^7 + 6 * q^8 - q^9 + 6 * q^10 - q^12 - 6 * q^13 - 6 * q^14 - q^15 + 6 * q^16 - 21 * q^17 - q^18 + 3 * q^19 + 6 * q^20 + q^21 - 10 * q^23 - q^24 + 6 * q^25 - 6 * q^26 - 4 * q^27 - 6 * q^28 - 10 * q^29 - q^30 - 4 * q^31 + 6 * q^32 - 21 * q^34 - 6 * q^35 - q^36 - 2 * q^37 + 3 * q^38 - 26 * q^39 + 6 * q^40 - 7 * q^41 + q^42 - 19 * q^43 - q^45 - 10 * q^46 + 10 * q^47 - q^48 + 6 * q^49 + 6 * q^50 + 4 * q^51 - 6 * q^52 - 16 * q^53 - 4 * q^54 - 6 * q^56 - 16 * q^57 - 10 * q^58 - 3 * q^59 - q^60 + 8 * q^61 - 4 * q^62 + q^63 + 6 * q^64 - 6 * q^65 - 27 * q^67 - 21 * q^68 + 4 * q^69 - 6 * q^70 + 4 * q^71 - q^72 - 13 * q^73 - 2 * q^74 - q^75 + 3 * q^76 - 26 * q^78 - 14 * q^79 + 6 * q^80 - 14 * q^81 - 7 * q^82 - 51 * q^83 + q^84 - 21 * q^85 - 19 * q^86 - 8 * q^87 + q^89 - q^90 + 6 * q^91 - 10 * q^92 + 4 * q^93 + 10 * q^94 + 3 * q^95 - q^96 + 7 * 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
$3$	1.92474	1.11125	0.555623	−	0.831434i	$-0.312480\pi$
$3$	1.92474	1.11125	0.555623	+	0.831434i	$0.312480\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.92474	0.785770
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	0.704605	0.234868
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	1.92474	0.555623
$13$	−5.24489	−1.45467	−0.727335	−	0.686283i	$-0.759241\pi$
$13$	−5.24489	−1.45467	−0.727335	+	0.686283i	$0.759241\pi$
$14$	−1.00000	−0.267261
$15$	1.92474	0.496964
$16$	1.00000	0.250000
$17$	−4.30919	−1.04513	−0.522566	−	0.852599i	$-0.675025\pi$
$17$	−4.30919	−1.04513	−0.522566	+	0.852599i	$0.675025\pi$
$18$	0.704605	0.166077
$19$	−0.740633	−0.169913	−0.0849564	−	0.996385i	$-0.527075\pi$
$19$	−0.740633	−0.169913	−0.0849564	+	0.996385i	$0.527075\pi$
$20$	1.00000	0.223607
$21$	−1.92474	−0.420012
$22$	0	0
$23$	−0.856965	−0.178689	−0.0893447	−	0.996001i	$-0.528477\pi$
$23$	−0.856965	−0.178689	−0.0893447	+	0.996001i	$0.528477\pi$
$24$	1.92474	0.392885
$25$	1.00000	0.200000
$26$	−5.24489	−1.02861
$27$	−4.41803	−0.850250
$28$	−1.00000	−0.188982
$29$	−8.37564	−1.55532	−0.777658	−	0.628687i	$-0.783593\pi$
$29$	−8.37564	−1.55532	−0.777658	+	0.628687i	$0.783593\pi$
$30$	1.92474	0.351407
$31$	1.10298	0.198101	0.0990506	−	0.995082i	$-0.468419\pi$
$31$	1.10298	0.198101	0.0990506	+	0.995082i	$0.468419\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−4.30919	−0.739020
$35$	−1.00000	−0.169031
$36$	0.704605	0.117434
$37$	−1.77921	−0.292500	−0.146250	−	0.989248i	$-0.546720\pi$
$37$	−1.77921	−0.292500	−0.146250	+	0.989248i	$0.546720\pi$
$38$	−0.740633	−0.120146
$39$	−10.0950	−1.61650
$40$	1.00000	0.158114
$41$	−10.7200	−1.67418	−0.837090	−	0.547065i	$-0.815745\pi$
$41$	−10.7200	−1.67418	−0.837090	+	0.547065i	$0.815745\pi$
$42$	−1.92474	−0.296993
$43$	1.13472	0.173044	0.0865218	−	0.996250i	$-0.472425\pi$
$43$	1.13472	0.173044	0.0865218	+	0.996250i	$0.472425\pi$
$44$	0	0
$45$	0.704605	0.105036
$46$	−0.856965	−0.126353
$47$	8.40172	1.22552	0.612758	−	0.790271i	$-0.290060\pi$
$47$	8.40172	1.22552	0.612758	+	0.790271i	$0.290060\pi$
$48$	1.92474	0.277812
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	−8.29405	−1.16140
$52$	−5.24489	−0.727335
$53$	−8.80661	−1.20968	−0.604840	−	0.796347i	$-0.706763\pi$
$53$	−8.80661	−1.20968	−0.604840	+	0.796347i	$0.706763\pi$
$54$	−4.41803	−0.601217
$55$	0	0
$56$	−1.00000	−0.133631
$57$	−1.42552	−0.188815
$58$	−8.37564	−1.09977
$59$	−12.9838	−1.69035	−0.845175	−	0.534490i	$-0.820504\pi$
$59$	−12.9838	−1.69035	−0.845175	+	0.534490i	$0.820504\pi$
$60$	1.92474	0.248482
$61$	13.0887	1.67584	0.837920	−	0.545793i	$-0.183772\pi$
$61$	13.0887	1.67584	0.837920	+	0.545793i	$0.183772\pi$
$62$	1.10298	0.140079
$63$	−0.704605	−0.0887719
$64$	1.00000	0.125000
$65$	−5.24489	−0.650548
$66$	0	0
$67$	8.93617	1.09173	0.545864	−	0.837874i	$-0.316202\pi$
$67$	8.93617	1.09173	0.545864	+	0.837874i	$0.316202\pi$
$68$	−4.30919	−0.522566
$69$	−1.64943	−0.198568
$70$	−1.00000	−0.119523
$71$	−4.50750	−0.534942	−0.267471	−	0.963566i	$-0.586188\pi$
$71$	−4.50750	−0.534942	−0.267471	+	0.963566i	$0.586188\pi$
$72$	0.704605	0.0830385
$73$	−3.33413	−0.390230	−0.195115	−	0.980780i	$-0.562508\pi$
$73$	−3.33413	−0.390230	−0.195115	+	0.980780i	$0.562508\pi$
$74$	−1.77921	−0.206829
$75$	1.92474	0.222249
$76$	−0.740633	−0.0849564
$77$	0	0
$78$	−10.0950	−1.14304
$79$	−1.56183	−0.175719	−0.0878597	−	0.996133i	$-0.528003\pi$
$79$	−1.56183	−0.175719	−0.0878597	+	0.996133i	$0.528003\pi$
$80$	1.00000	0.111803
$81$	−10.6173	−1.17971
$82$	−10.7200	−1.18382
$83$	0.609215	0.0668700	0.0334350	−	0.999441i	$-0.489355\pi$
$83$	0.609215	0.0668700	0.0334350	+	0.999441i	$0.489355\pi$
$84$	−1.92474	−0.210006
$85$	−4.30919	−0.467397
$86$	1.13472	0.122360
$87$	−16.1209	−1.72834
$88$	0	0
$89$	1.46836	0.155646	0.0778228	−	0.996967i	$-0.475203\pi$
$89$	1.46836	0.155646	0.0778228	+	0.996967i	$0.475203\pi$
$90$	0.704605	0.0742719
$91$	5.24489	0.549813
$92$	−0.856965	−0.0893447
$93$	2.12295	0.220139
$94$	8.40172	0.866571
$95$	−0.740633	−0.0759873
$96$	1.92474	0.196442
$97$	8.41705	0.854622	0.427311	−	0.904105i	$-0.359461\pi$
$97$	8.41705	0.854622	0.427311	+	0.904105i	$0.359461\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	−11.0295	−1.09748	−0.548740	−	0.835993i	$-0.684892\pi$
$101$	−11.0295	−1.09748	−0.548740	+	0.835993i	$0.684892\pi$
$102$	−8.29405	−0.821233
$103$	5.86953	0.578342	0.289171	−	0.957277i	$-0.406620\pi$
$103$	5.86953	0.578342	0.289171	+	0.957277i	$0.406620\pi$
$104$	−5.24489	−0.514303
$105$	−1.92474	−0.187835
$106$	−8.80661	−0.855373
$107$	6.83162	0.660438	0.330219	−	0.943904i	$-0.392877\pi$
$107$	6.83162	0.660438	0.330219	+	0.943904i	$0.392877\pi$
$108$	−4.41803	−0.425125
$109$	−7.76784	−0.744025	−0.372012	−	0.928228i	$-0.621332\pi$
$109$	−7.76784	−0.744025	−0.372012	+	0.928228i	$0.621332\pi$
$110$	0	0
$111$	−3.42451	−0.325040
$112$	−1.00000	−0.0944911
$113$	4.63948	0.436446	0.218223	−	0.975899i	$-0.429974\pi$
$113$	4.63948	0.436446	0.218223	+	0.975899i	$0.429974\pi$
$114$	−1.42552	−0.133512
$115$	−0.856965	−0.0799124
$116$	−8.37564	−0.777658
$117$	−3.69557	−0.341656
$118$	−12.9838	−1.19526
$119$	4.30919	0.395023
$120$	1.92474	0.175703
$121$	0	0
$122$	13.0887	1.18500
$123$	−20.6331	−1.86043
$124$	1.10298	0.0990506
$125$	1.00000	0.0894427
$126$	−0.704605	−0.0627712
$127$	9.42065	0.835947	0.417974	−	0.908459i	$-0.362740\pi$
$127$	9.42065	0.835947	0.417974	+	0.908459i	$0.362740\pi$
$128$	1.00000	0.0883883
$129$	2.18404	0.192294
$130$	−5.24489	−0.460007
$131$	−0.862825	−0.0753854	−0.0376927	−	0.999289i	$-0.512001\pi$
$131$	−0.862825	−0.0753854	−0.0376927	+	0.999289i	$0.512001\pi$
$132$	0	0
$133$	0.740633	0.0642210
$134$	8.93617	0.771968
$135$	−4.41803	−0.380243
$136$	−4.30919	−0.369510
$137$	−17.2469	−1.47350	−0.736751	−	0.676164i	$-0.763641\pi$
$137$	−17.2469	−1.47350	−0.736751	+	0.676164i	$0.763641\pi$
$138$	−1.64943	−0.140409
$139$	20.4448	1.73411	0.867054	−	0.498213i	$-0.166010\pi$
$139$	20.4448	1.73411	0.867054	+	0.498213i	$0.166010\pi$
$140$	−1.00000	−0.0845154
$141$	16.1711	1.36185
$142$	−4.50750	−0.378261
$143$	0	0
$144$	0.704605	0.0587171
$145$	−8.37564	−0.695559
$146$	−3.33413	−0.275934
$147$	1.92474	0.158749
$148$	−1.77921	−0.146250
$149$	1.88298	0.154260	0.0771299	−	0.997021i	$-0.475424\pi$
$149$	1.88298	0.154260	0.0771299	+	0.997021i	$0.475424\pi$
$150$	1.92474	0.157154
$151$	5.45095	0.443592	0.221796	−	0.975093i	$-0.428808\pi$
$151$	5.45095	0.443592	0.221796	+	0.975093i	$0.428808\pi$
$152$	−0.740633	−0.0600732
$153$	−3.03628	−0.245468
$154$	0	0
$155$	1.10298	0.0885935
$156$	−10.0950	−0.808248
$157$	−11.9779	−0.955944	−0.477972	−	0.878375i	$-0.658628\pi$
$157$	−11.9779	−0.955944	−0.477972	+	0.878375i	$0.658628\pi$
$158$	−1.56183	−0.124252
$159$	−16.9504	−1.34425
$160$	1.00000	0.0790569
$161$	0.856965	0.0675383
$162$	−10.6173	−0.834178
$163$	−15.5543	−1.21830	−0.609152	−	0.793053i	$-0.708490\pi$
$163$	−15.5543	−1.21830	−0.609152	+	0.793053i	$0.708490\pi$
$164$	−10.7200	−0.837090
$165$	0	0
$166$	0.609215	0.0472843
$167$	18.0474	1.39655	0.698274	−	0.715830i	$-0.253952\pi$
$167$	18.0474	1.39655	0.698274	+	0.715830i	$0.253952\pi$
$168$	−1.92474	−0.148497
$169$	14.5088	1.11606
$170$	−4.30919	−0.330500
$171$	−0.521854	−0.0399071
$172$	1.13472	0.0865218
$173$	−9.60665	−0.730380	−0.365190	−	0.930933i	$-0.618996\pi$
$173$	−9.60665	−0.730380	−0.365190	+	0.930933i	$0.618996\pi$
$174$	−16.1209	−1.22212
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	−24.9904	−1.87839
$178$	1.46836	0.110058
$179$	13.2673	0.991643	0.495822	−	0.868424i	$-0.334867\pi$
$179$	13.2673	0.991643	0.495822	+	0.868424i	$0.334867\pi$
$180$	0.704605	0.0525182
$181$	19.5835	1.45563	0.727815	−	0.685774i	$-0.240536\pi$
$181$	19.5835	1.45563	0.727815	+	0.685774i	$0.240536\pi$
$182$	5.24489	0.388777
$183$	25.1923	1.86227
$184$	−0.856965	−0.0631763
$185$	−1.77921	−0.130810
$186$	2.12295	0.155662
$187$	0	0
$188$	8.40172	0.612758
$189$	4.41803	0.321364
$190$	−0.740633	−0.0537311
$191$	−12.7555	−0.922954	−0.461477	−	0.887152i	$-0.652680\pi$
$191$	−12.7555	−0.922954	−0.461477	+	0.887152i	$0.652680\pi$
$192$	1.92474	0.138906
$193$	11.8288	0.851459	0.425729	−	0.904851i	$-0.360018\pi$
$193$	11.8288	0.851459	0.425729	+	0.904851i	$0.360018\pi$
$194$	8.41705	0.604309
$195$	−10.0950	−0.722919
$196$	1.00000	0.0714286
$197$	−21.9105	−1.56106	−0.780528	−	0.625121i	$-0.785050\pi$
$197$	−21.9105	−1.56106	−0.780528	+	0.625121i	$0.785050\pi$
$198$	0	0
$199$	10.3121	0.731006	0.365503	−	0.930810i	$-0.380897\pi$
$199$	10.3121	0.731006	0.365503	+	0.930810i	$0.380897\pi$
$200$	1.00000	0.0707107
$201$	17.1998	1.21318
$202$	−11.0295	−0.776036
$203$	8.37564	0.587854
$204$	−8.29405	−0.580700
$205$	−10.7200	−0.748716
$206$	5.86953	0.408950
$207$	−0.603822	−0.0419685
$208$	−5.24489	−0.363667
$209$	0	0
$210$	−1.92474	−0.132819
$211$	−24.8455	−1.71043	−0.855217	−	0.518270i	$-0.826576\pi$
$211$	−24.8455	−1.71043	−0.855217	+	0.518270i	$0.826576\pi$
$212$	−8.80661	−0.604840
$213$	−8.67574	−0.594452
$214$	6.83162	0.467000
$215$	1.13472	0.0773875
$216$	−4.41803	−0.300609
$217$	−1.10298	−0.0748752
$218$	−7.76784	−0.526105
$219$	−6.41731	−0.433641
$220$	0	0
$221$	22.6012	1.52032
$222$	−3.42451	−0.229838
$223$	−20.2394	−1.35533	−0.677667	−	0.735369i	$-0.737009\pi$
$223$	−20.2394	−1.35533	−0.677667	+	0.735369i	$0.737009\pi$
$224$	−1.00000	−0.0668153
$225$	0.704605	0.0469737
$226$	4.63948	0.308614
$227$	11.8090	0.783792	0.391896	−	0.920009i	$-0.371819\pi$
$227$	11.8090	0.783792	0.391896	+	0.920009i	$0.371819\pi$
$228$	−1.42552	−0.0944075
$229$	1.67906	0.110955	0.0554776	−	0.998460i	$-0.482332\pi$
$229$	1.67906	0.110955	0.0554776	+	0.998460i	$0.482332\pi$
$230$	−0.856965	−0.0565066
$231$	0	0
$232$	−8.37564	−0.549887
$233$	−15.5220	−1.01688	−0.508440	−	0.861097i	$-0.669778\pi$
$233$	−15.5220	−1.01688	−0.508440	+	0.861097i	$0.669778\pi$
$234$	−3.69557	−0.241587
$235$	8.40172	0.548067
$236$	−12.9838	−0.845175
$237$	−3.00610	−0.195267
$238$	4.30919	0.279323
$239$	−22.0037	−1.42330	−0.711652	−	0.702532i	$-0.752053\pi$
$239$	−22.0037	−1.42330	−0.711652	+	0.702532i	$0.752053\pi$
$240$	1.92474	0.124241
$241$	−23.8155	−1.53409	−0.767047	−	0.641591i	$-0.778274\pi$
$241$	−23.8155	−1.53409	−0.767047	+	0.641591i	$0.778274\pi$
$242$	0	0
$243$	−7.18150	−0.460693
$244$	13.0887	0.837920
$245$	1.00000	0.0638877
$246$	−20.6331	−1.31552
$247$	3.88453	0.247167
$248$	1.10298	0.0700393
$249$	1.17258	0.0743091
$250$	1.00000	0.0632456
$251$	28.5083	1.79943	0.899715	−	0.436477i	$-0.143774\pi$
$251$	28.5083	1.79943	0.899715	+	0.436477i	$0.143774\pi$
$252$	−0.704605	−0.0443859
$253$	0	0
$254$	9.42065	0.591104
$255$	−8.29405	−0.519393
$256$	1.00000	0.0625000
$257$	29.6194	1.84760	0.923802	−	0.382870i	$-0.125064\pi$
$257$	29.6194	1.84760	0.923802	+	0.382870i	$0.125064\pi$
$258$	2.18404	0.135973
$259$	1.77921	0.110555
$260$	−5.24489	−0.325274
$261$	−5.90151	−0.365295
$262$	−0.862825	−0.0533055
$263$	4.09184	0.252314	0.126157	−	0.992010i	$-0.459736\pi$
$263$	4.09184	0.252314	0.126157	+	0.992010i	$0.459736\pi$
$264$	0	0
$265$	−8.80661	−0.540986
$266$	0.740633	0.0454111
$267$	2.82620	0.172960
$268$	8.93617	0.545864
$269$	2.99735	0.182752	0.0913759	−	0.995816i	$-0.470874\pi$
$269$	2.99735	0.182752	0.0913759	+	0.995816i	$0.470874\pi$
$270$	−4.41803	−0.268873
$271$	24.7015	1.50051	0.750255	−	0.661148i	$-0.229930\pi$
$271$	24.7015	1.50051	0.750255	+	0.661148i	$0.229930\pi$
$272$	−4.30919	−0.261283
$273$	10.0950	0.610978
$274$	−17.2469	−1.04192
$275$	0	0
$276$	−1.64943	−0.0992840
$277$	2.67858	0.160941	0.0804703	−	0.996757i	$-0.474358\pi$
$277$	2.67858	0.160941	0.0804703	+	0.996757i	$0.474358\pi$
$278$	20.4448	1.22620
$279$	0.777166	0.0465277
$280$	−1.00000	−0.0597614
$281$	−11.6213	−0.693271	−0.346636	−	0.938000i	$-0.612676\pi$
$281$	−11.6213	−0.693271	−0.346636	+	0.938000i	$0.612676\pi$
$282$	16.1711	0.962974
$283$	18.1362	1.07808	0.539042	−	0.842279i	$-0.318786\pi$
$283$	18.1362	1.07808	0.539042	+	0.842279i	$0.318786\pi$
$284$	−4.50750	−0.267471
$285$	−1.42552	−0.0844406
$286$	0	0
$287$	10.7200	0.632781
$288$	0.704605	0.0415192
$289$	1.56912	0.0923010
$290$	−8.37564	−0.491834
$291$	16.2006	0.949695
$292$	−3.33413	−0.195115
$293$	−22.8700	−1.33608	−0.668041	−	0.744125i	$-0.732867\pi$
$293$	−22.8700	−1.33608	−0.668041	+	0.744125i	$0.732867\pi$
$294$	1.92474	0.112253
$295$	−12.9838	−0.755947
$296$	−1.77921	−0.103415
$297$	0	0
$298$	1.88298	0.109078
$299$	4.49468	0.259934
$300$	1.92474	0.111125
$301$	−1.13472	−0.0654044
$302$	5.45095	0.313667
$303$	−21.2290	−1.21957
$304$	−0.740633	−0.0424782
$305$	13.0887	0.749458
$306$	−3.03628	−0.173572
$307$	−19.9326	−1.13761	−0.568806	−	0.822472i	$-0.692594\pi$
$307$	−19.9326	−1.13761	−0.568806	+	0.822472i	$0.692594\pi$
$308$	0	0
$309$	11.2973	0.642681
$310$	1.10298	0.0626451
$311$	−1.28437	−0.0728299	−0.0364149	−	0.999337i	$-0.511594\pi$
$311$	−1.28437	−0.0728299	−0.0364149	+	0.999337i	$0.511594\pi$
$312$	−10.0950	−0.571518
$313$	−13.3964	−0.757210	−0.378605	−	0.925558i	$-0.623596\pi$
$313$	−13.3964	−0.757210	−0.378605	+	0.925558i	$0.623596\pi$
$314$	−11.9779	−0.675954
$315$	−0.704605	−0.0397000
$316$	−1.56183	−0.0878597
$317$	16.6640	0.935941	0.467971	−	0.883744i	$-0.344985\pi$
$317$	16.6640	0.935941	0.467971	+	0.883744i	$0.344985\pi$
$318$	−16.9504	−0.950530
$319$	0	0
$320$	1.00000	0.0559017
$321$	13.1491	0.733909
$322$	0.856965	0.0477568
$323$	3.19153	0.177581
$324$	−10.6173	−0.589853
$325$	−5.24489	−0.290934
$326$	−15.5543	−0.861471
$327$	−14.9510	−0.826795
$328$	−10.7200	−0.591912
$329$	−8.40172	−0.463202
$330$	0	0
$331$	11.1340	0.611979	0.305989	−	0.952035i	$-0.401013\pi$
$331$	11.1340	0.611979	0.305989	+	0.952035i	$0.401013\pi$
$332$	0.609215	0.0334350
$333$	−1.25364	−0.0686991
$334$	18.0474	0.987509
$335$	8.93617	0.488235
$336$	−1.92474	−0.105003
$337$	−6.71838	−0.365974	−0.182987	−	0.983115i	$-0.558577\pi$
$337$	−6.71838	−0.365974	−0.182987	+	0.983115i	$0.558577\pi$
$338$	14.5088	0.789176
$339$	8.92978	0.484999
$340$	−4.30919	−0.233699
$341$	0	0
$342$	−0.521854	−0.0282186
$343$	−1.00000	−0.0539949
$344$	1.13472	0.0611802
$345$	−1.64943	−0.0888023
$346$	−9.60665	−0.516456
$347$	−19.4103	−1.04200	−0.520999	−	0.853557i	$-0.674441\pi$
$347$	−19.4103	−1.04200	−0.520999	+	0.853557i	$0.674441\pi$
$348$	−16.1209	−0.864170
$349$	26.7685	1.43289	0.716444	−	0.697645i	$-0.245769\pi$
$349$	26.7685	1.43289	0.716444	+	0.697645i	$0.245769\pi$
$350$	−1.00000	−0.0534522
$351$	23.1720	1.23683
$352$	0	0
$353$	−32.9268	−1.75252	−0.876259	−	0.481841i	$-0.839968\pi$
$353$	−32.9268	−1.75252	−0.876259	+	0.481841i	$0.839968\pi$
$354$	−24.9904	−1.32823
$355$	−4.50750	−0.239233
$356$	1.46836	0.0778228
$357$	8.29405	0.438968
$358$	13.2673	0.701198
$359$	36.1167	1.90617	0.953083	−	0.302709i	$-0.0978912\pi$
$359$	36.1167	1.90617	0.953083	+	0.302709i	$0.0978912\pi$
$360$	0.704605	0.0371359
$361$	−18.4515	−0.971130
$362$	19.5835	1.02929
$363$	0	0
$364$	5.24489	0.274907
$365$	−3.33413	−0.174516
$366$	25.1923	1.31682
$367$	−8.35672	−0.436217	−0.218109	−	0.975925i	$-0.569989\pi$
$367$	−8.35672	−0.436217	−0.218109	+	0.975925i	$0.569989\pi$
$368$	−0.856965	−0.0446724
$369$	−7.55335	−0.393212
$370$	−1.77921	−0.0924968
$371$	8.80661	0.457216
$372$	2.12295	0.110070
$373$	−16.0205	−0.829509	−0.414755	−	0.909933i	$-0.636133\pi$
$373$	−16.0205	−0.829509	−0.414755	+	0.909933i	$0.636133\pi$
$374$	0	0
$375$	1.92474	0.0993929
$376$	8.40172	0.433285
$377$	43.9292	2.26247
$378$	4.41803	0.227239
$379$	25.3872	1.30405	0.652027	−	0.758196i	$-0.273919\pi$
$379$	25.3872	1.30405	0.652027	+	0.758196i	$0.273919\pi$
$380$	−0.740633	−0.0379937
$381$	18.1323	0.928943
$382$	−12.7555	−0.652627
$383$	−0.303318	−0.0154988	−0.00774942	−	0.999970i	$-0.502467\pi$
$383$	−0.303318	−0.0154988	−0.00774942	+	0.999970i	$0.502467\pi$
$384$	1.92474	0.0982212
$385$	0	0
$386$	11.8288	0.602072
$387$	0.799532	0.0406425
$388$	8.41705	0.427311
$389$	−6.74058	−0.341761	−0.170880	−	0.985292i	$-0.554661\pi$
$389$	−6.74058	−0.341761	−0.170880	+	0.985292i	$0.554661\pi$
$390$	−10.0950	−0.511181
$391$	3.69282	0.186754
$392$	1.00000	0.0505076
$393$	−1.66071	−0.0837717
$394$	−21.9105	−1.10383
$395$	−1.56183	−0.0785841
$396$	0	0
$397$	−19.9230	−0.999904	−0.499952	−	0.866053i	$-0.666649\pi$
$397$	−19.9230	−0.999904	−0.499952	+	0.866053i	$0.666649\pi$
$398$	10.3121	0.516899
$399$	1.42552	0.0713654
$400$	1.00000	0.0500000
$401$	34.0886	1.70230	0.851151	−	0.524920i	$-0.175905\pi$
$401$	34.0886	1.70230	0.851151	+	0.524920i	$0.175905\pi$
$402$	17.1998	0.857846
$403$	−5.78501	−0.288172
$404$	−11.0295	−0.548740
$405$	−10.6173	−0.527580
$406$	8.37564	0.415676
$407$	0	0
$408$	−8.29405	−0.410617
$409$	8.09670	0.400356	0.200178	−	0.979760i	$-0.435848\pi$
$409$	8.09670	0.400356	0.200178	+	0.979760i	$0.435848\pi$
$410$	−10.7200	−0.529422
$411$	−33.1957	−1.63742
$412$	5.86953	0.289171
$413$	12.9838	0.638892
$414$	−0.603822	−0.0296762
$415$	0.609215	0.0299052
$416$	−5.24489	−0.257152
$417$	39.3509	1.92702
$418$	0	0
$419$	−24.0686	−1.17583	−0.587915	−	0.808923i	$-0.700051\pi$
$419$	−24.0686	−1.17583	−0.587915	+	0.808923i	$0.700051\pi$
$420$	−1.92474	−0.0939175
$421$	13.7871	0.671942	0.335971	−	0.941872i	$-0.390936\pi$
$421$	13.7871	0.671942	0.335971	+	0.941872i	$0.390936\pi$
$422$	−24.8455	−1.20946
$423$	5.91989	0.287835
$424$	−8.80661	−0.427687
$425$	−4.30919	−0.209026
$426$	−8.67574	−0.420341
$427$	−13.0887	−0.633408
$428$	6.83162	0.330219
$429$	0	0
$430$	1.13472	0.0547212
$431$	−8.72005	−0.420030	−0.210015	−	0.977698i	$-0.567351\pi$
$431$	−8.72005	−0.420030	−0.210015	+	0.977698i	$0.567351\pi$
$432$	−4.41803	−0.212562
$433$	−8.51892	−0.409393	−0.204697	−	0.978825i	$-0.565621\pi$
$433$	−8.51892	−0.409393	−0.204697	+	0.978825i	$0.565621\pi$
$434$	−1.10298	−0.0529448
$435$	−16.1209	−0.772937
$436$	−7.76784	−0.372012
$437$	0.634696	0.0303616
$438$	−6.41731	−0.306631
$439$	−22.5402	−1.07579	−0.537894	−	0.843013i	$-0.680780\pi$
$439$	−22.5402	−1.07579	−0.537894	+	0.843013i	$0.680780\pi$
$440$	0	0
$441$	0.704605	0.0335526
$442$	22.6012	1.07503
$443$	37.9089	1.80110	0.900552	−	0.434748i	$-0.143163\pi$
$443$	37.9089	1.80110	0.900552	+	0.434748i	$0.143163\pi$
$444$	−3.42451	−0.162520
$445$	1.46836	0.0696068
$446$	−20.2394	−0.958365
$447$	3.62424	0.171421
$448$	−1.00000	−0.0472456
$449$	−32.0551	−1.51277	−0.756387	−	0.654125i	$-0.773037\pi$
$449$	−32.0551	−1.51277	−0.756387	+	0.654125i	$0.773037\pi$
$450$	0.704605	0.0332154
$451$	0	0
$452$	4.63948	0.218223
$453$	10.4916	0.492940
$454$	11.8090	0.554225
$455$	5.24489	0.245884
$456$	−1.42552	−0.0667562
$457$	24.5243	1.14720	0.573600	−	0.819136i	$-0.305547\pi$
$457$	24.5243	1.14720	0.573600	+	0.819136i	$0.305547\pi$
$458$	1.67906	0.0784572
$459$	19.0381	0.888623
$460$	−0.856965	−0.0399562
$461$	−0.188328	−0.00877132	−0.00438566	−	0.999990i	$-0.501396\pi$
$461$	−0.188328	−0.00877132	−0.00438566	+	0.999990i	$0.501396\pi$
$462$	0	0
$463$	−9.40956	−0.437299	−0.218650	−	0.975803i	$-0.570165\pi$
$463$	−9.40956	−0.437299	−0.218650	+	0.975803i	$0.570165\pi$
$464$	−8.37564	−0.388829
$465$	2.12295	0.0984492
$466$	−15.5220	−0.719043
$467$	1.84720	0.0854781	0.0427390	−	0.999086i	$-0.486392\pi$
$467$	1.84720	0.0854781	0.0427390	+	0.999086i	$0.486392\pi$
$468$	−3.69557	−0.170828
$469$	−8.93617	−0.412634
$470$	8.40172	0.387542
$471$	−23.0544	−1.06229
$472$	−12.9838	−0.597629
$473$	0	0
$474$	−3.00610	−0.138075
$475$	−0.740633	−0.0339826
$476$	4.30919	0.197511
$477$	−6.20518	−0.284116
$478$	−22.0037	−1.00643
$479$	33.3506	1.52383	0.761913	−	0.647679i	$-0.224260\pi$
$479$	33.3506	1.52383	0.761913	+	0.647679i	$0.224260\pi$
$480$	1.92474	0.0878517
$481$	9.33176	0.425491
$482$	−23.8155	−1.08477
$483$	1.64943	0.0750517
$484$	0	0
$485$	8.41705	0.382198
$486$	−7.18150	−0.325759
$487$	14.1136	0.639550	0.319775	−	0.947493i	$-0.396393\pi$
$487$	14.1136	0.639550	0.319775	+	0.947493i	$0.396393\pi$
$488$	13.0887	0.592499
$489$	−29.9378	−1.35384
$490$	1.00000	0.0451754
$491$	−8.40881	−0.379484	−0.189742	−	0.981834i	$-0.560765\pi$
$491$	−8.40881	−0.379484	−0.189742	+	0.981834i	$0.560765\pi$
$492$	−20.6331	−0.930213
$493$	36.0922	1.62551
$494$	3.88453	0.174773
$495$	0	0
$496$	1.10298	0.0495253
$497$	4.50750	0.202189
$498$	1.17258	0.0525444
$499$	−22.8087	−1.02106	−0.510529	−	0.859860i	$-0.670550\pi$
$499$	−22.8087	−1.02106	−0.510529	+	0.859860i	$0.670550\pi$
$500$	1.00000	0.0447214
$501$	34.7364	1.55191
$502$	28.5083	1.27239
$503$	−22.6508	−1.00995	−0.504975	−	0.863134i	$-0.668498\pi$
$503$	−22.6508	−1.00995	−0.504975	+	0.863134i	$0.668498\pi$
$504$	−0.704605	−0.0313856
$505$	−11.0295	−0.490808
$506$	0	0
$507$	27.9256	1.24022
$508$	9.42065	0.417974
$509$	−15.0533	−0.667224	−0.333612	−	0.942710i	$-0.608268\pi$
$509$	−15.0533	−0.667224	−0.333612	+	0.942710i	$0.608268\pi$
$510$	−8.29405	−0.367267
$511$	3.33413	0.147493
$512$	1.00000	0.0441942
$513$	3.27214	0.144468
$514$	29.6194	1.30645
$515$	5.86953	0.258643
$516$	2.18404	0.0961471
$517$	0	0
$518$	1.77921	0.0781740
$519$	−18.4902	−0.811632
$520$	−5.24489	−0.230003
$521$	−7.47977	−0.327695	−0.163847	−	0.986486i	$-0.552390\pi$
$521$	−7.47977	−0.327695	−0.163847	+	0.986486i	$0.552390\pi$
$522$	−5.90151	−0.258302
$523$	−5.14535	−0.224990	−0.112495	−	0.993652i	$-0.535884\pi$
$523$	−5.14535	−0.224990	−0.112495	+	0.993652i	$0.535884\pi$
$524$	−0.862825	−0.0376927
$525$	−1.92474	−0.0840023
$526$	4.09184	0.178413
$527$	−4.75295	−0.207042
$528$	0	0
$529$	−22.2656	−0.968070
$530$	−8.80661	−0.382535
$531$	−9.14846	−0.397010
$532$	0.740633	0.0321105
$533$	56.2251	2.43538
$534$	2.82620	0.122302
$535$	6.83162	0.295357
$536$	8.93617	0.385984
$537$	25.5360	1.10196
$538$	2.99735	0.129225
$539$	0	0
$540$	−4.41803	−0.190122
$541$	−1.92055	−0.0825709	−0.0412855	−	0.999147i	$-0.513145\pi$
$541$	−1.92055	−0.0825709	−0.0412855	+	0.999147i	$0.513145\pi$
$542$	24.7015	1.06102
$543$	37.6930	1.61756
$544$	−4.30919	−0.184755
$545$	−7.76784	−0.332738
$546$	10.0950	0.432027
$547$	0.260956	0.0111577	0.00557884	−	0.999984i	$-0.498224\pi$
$547$	0.260956	0.0111577	0.00557884	+	0.999984i	$0.498224\pi$
$548$	−17.2469	−0.736751
$549$	9.22238	0.393602
$550$	0	0
$551$	6.20327	0.264268
$552$	−1.64943	−0.0702044
$553$	1.56183	0.0664157
$554$	2.67858	0.113802
$555$	−3.42451	−0.145362
$556$	20.4448	0.867054
$557$	−6.31867	−0.267731	−0.133865	−	0.991000i	$-0.542739\pi$
$557$	−6.31867	−0.267731	−0.133865	+	0.991000i	$0.542739\pi$
$558$	0.777166	0.0329000
$559$	−5.95149	−0.251721
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	−11.6213	−0.490217
$563$	0.958697	0.0404043	0.0202021	−	0.999796i	$-0.493569\pi$
$563$	0.958697	0.0404043	0.0202021	+	0.999796i	$0.493569\pi$
$564$	16.1711	0.680925
$565$	4.63948	0.195185
$566$	18.1362	0.762321
$567$	10.6173	0.445887
$568$	−4.50750	−0.189130
$569$	−7.11799	−0.298402	−0.149201	−	0.988807i	$-0.547670\pi$
$569$	−7.11799	−0.298402	−0.149201	+	0.988807i	$0.547670\pi$
$570$	−1.42552	−0.0597085
$571$	−27.1751	−1.13724	−0.568621	−	0.822599i	$-0.692523\pi$
$571$	−27.1751	−1.13724	−0.568621	+	0.822599i	$0.692523\pi$
$572$	0	0
$573$	−24.5509	−1.02563
$574$	10.7200	0.447443
$575$	−0.856965	−0.0357379
$576$	0.704605	0.0293585
$577$	−32.3702	−1.34759	−0.673795	−	0.738918i	$-0.735337\pi$
$577$	−32.3702	−1.34759	−0.673795	+	0.738918i	$0.735337\pi$
$578$	1.56912	0.0652667
$579$	22.7674	0.946181
$580$	−8.37564	−0.347779
$581$	−0.609215	−0.0252745
$582$	16.2006	0.671536
$583$	0	0
$584$	−3.33413	−0.137967
$585$	−3.69557	−0.152793
$586$	−22.8700	−0.944753
$587$	−8.04888	−0.332213	−0.166106	−	0.986108i	$-0.553120\pi$
$587$	−8.04888	−0.332213	−0.166106	+	0.986108i	$0.553120\pi$
$588$	1.92474	0.0793747
$589$	−0.816904	−0.0336599
$590$	−12.9838	−0.534535
$591$	−42.1718	−1.73472
$592$	−1.77921	−0.0731251
$593$	−39.8151	−1.63501	−0.817506	−	0.575920i	$-0.804644\pi$
$593$	−39.8151	−1.63501	−0.817506	+	0.575920i	$0.804644\pi$
$594$	0	0
$595$	4.30919	0.176660
$596$	1.88298	0.0771299
$597$	19.8481	0.812327
$598$	4.49468	0.183801
$599$	30.7925	1.25815	0.629074	−	0.777346i	$-0.283434\pi$
$599$	30.7925	1.25815	0.629074	+	0.777346i	$0.283434\pi$
$600$	1.92474	0.0785770
$601$	33.3140	1.35891	0.679454	−	0.733718i	$-0.262217\pi$
$601$	33.3140	1.35891	0.679454	+	0.733718i	$0.262217\pi$
$602$	−1.13472	−0.0462479
$603$	6.29647	0.256412
$604$	5.45095	0.221796
$605$	0	0
$606$	−21.2290	−0.862367
$607$	−16.8748	−0.684927	−0.342463	−	0.939531i	$-0.611261\pi$
$607$	−16.8748	−0.684927	−0.342463	+	0.939531i	$0.611261\pi$
$608$	−0.740633	−0.0300366
$609$	16.1209	0.653251
$610$	13.0887	0.529947
$611$	−44.0660	−1.78272
$612$	−3.03628	−0.122734
$613$	26.7574	1.08072	0.540360	−	0.841434i	$-0.318288\pi$
$613$	26.7574	1.08072	0.540360	+	0.841434i	$0.318288\pi$
$614$	−19.9326	−0.804413
$615$	−20.6331	−0.832008
$616$	0	0
$617$	32.5387	1.30996	0.654979	−	0.755647i	$-0.272677\pi$
$617$	32.5387	1.30996	0.654979	+	0.755647i	$0.272677\pi$
$618$	11.2973	0.454444
$619$	−13.9252	−0.559701	−0.279850	−	0.960044i	$-0.590285\pi$
$619$	−13.9252	−0.559701	−0.279850	+	0.960044i	$0.590285\pi$
$620$	1.10298	0.0442968
$621$	3.78609	0.151931
$622$	−1.28437	−0.0514985
$623$	−1.46836	−0.0588285
$624$	−10.0950	−0.404124
$625$	1.00000	0.0400000
$626$	−13.3964	−0.535429
$627$	0	0
$628$	−11.9779	−0.477972
$629$	7.66696	0.305702
$630$	−0.704605	−0.0280721
$631$	−12.8350	−0.510954	−0.255477	−	0.966815i	$-0.582232\pi$
$631$	−12.8350	−0.510954	−0.255477	+	0.966815i	$0.582232\pi$
$632$	−1.56183	−0.0621262
$633$	−47.8210	−1.90071
$634$	16.6640	0.661810
$635$	9.42065	0.373847
$636$	−16.9504	−0.672126
$637$	−5.24489	−0.207810
$638$	0	0
$639$	−3.17601	−0.125641
$640$	1.00000	0.0395285
$641$	−48.5629	−1.91812	−0.959059	−	0.283207i	$-0.908602\pi$
$641$	−48.5629	−1.91812	−0.959059	+	0.283207i	$0.908602\pi$
$642$	13.1491	0.518952
$643$	−14.1751	−0.559009	−0.279505	−	0.960144i	$-0.590170\pi$
$643$	−14.1751	−0.559009	−0.279505	+	0.960144i	$0.590170\pi$
$644$	0.856965	0.0337691
$645$	2.18404	0.0859966
$646$	3.19153	0.125569
$647$	−24.7982	−0.974917	−0.487459	−	0.873146i	$-0.662076\pi$
$647$	−24.7982	−0.974917	−0.487459	+	0.873146i	$0.662076\pi$
$648$	−10.6173	−0.417089
$649$	0	0
$650$	−5.24489	−0.205721
$651$	−2.12295	−0.0832048
$652$	−15.5543	−0.609152
$653$	−29.0557	−1.13704	−0.568519	−	0.822670i	$-0.692483\pi$
$653$	−29.0557	−1.13704	−0.568519	+	0.822670i	$0.692483\pi$
$654$	−14.9510	−0.584632
$655$	−0.862825	−0.0337134
$656$	−10.7200	−0.418545
$657$	−2.34924	−0.0916526
$658$	−8.40172	−0.327533
$659$	44.0463	1.71580	0.857899	−	0.513818i	$-0.171769\pi$
$659$	44.0463	1.71580	0.857899	+	0.513818i	$0.171769\pi$
$660$	0	0
$661$	−0.575059	−0.0223672	−0.0111836	−	0.999937i	$-0.503560\pi$
$661$	−0.575059	−0.0223672	−0.0111836	+	0.999937i	$0.503560\pi$
$662$	11.1340	0.432734
$663$	43.5013	1.68945
$664$	0.609215	0.0236421
$665$	0.740633	0.0287205
$666$	−1.25364	−0.0485776
$667$	7.17762	0.277919
$668$	18.0474	0.698274
$669$	−38.9556	−1.50611
$670$	8.93617	0.345234
$671$	0	0
$672$	−1.92474	−0.0742483
$673$	−27.7568	−1.06995	−0.534974	−	0.844869i	$-0.679679\pi$
$673$	−27.7568	−1.06995	−0.534974	+	0.844869i	$0.679679\pi$
$674$	−6.71838	−0.258782
$675$	−4.41803	−0.170050
$676$	14.5088	0.558032
$677$	51.1859	1.96723	0.983617	−	0.180272i	$-0.0576979\pi$
$677$	51.1859	1.96723	0.983617	+	0.180272i	$0.0576979\pi$
$678$	8.92978	0.342946
$679$	−8.41705	−0.323017
$680$	−4.30919	−0.165250
$681$	22.7292	0.870986
$682$	0	0
$683$	−1.55522	−0.0595090	−0.0297545	−	0.999557i	$-0.509473\pi$
$683$	−1.55522	−0.0595090	−0.0297545	+	0.999557i	$0.509473\pi$
$684$	−0.521854	−0.0199536
$685$	−17.2469	−0.658970
$686$	−1.00000	−0.0381802
$687$	3.23174	0.123299
$688$	1.13472	0.0432609
$689$	46.1896	1.75969
$690$	−1.64943	−0.0627927
$691$	4.60492	0.175179	0.0875896	−	0.996157i	$-0.472084\pi$
$691$	4.60492	0.175179	0.0875896	+	0.996157i	$0.472084\pi$
$692$	−9.60665	−0.365190
$693$	0	0
$694$	−19.4103	−0.736804
$695$	20.4448	0.775517
$696$	−16.1209	−0.611060
$697$	46.1944	1.74974
$698$	26.7685	1.01320
$699$	−29.8757	−1.13000
$700$	−1.00000	−0.0377964
$701$	−2.91484	−0.110092	−0.0550460	−	0.998484i	$-0.517531\pi$
$701$	−2.91484	−0.110092	−0.0550460	+	0.998484i	$0.517531\pi$
$702$	23.1720	0.874573
$703$	1.31774	0.0496996
$704$	0	0
$705$	16.1711	0.609038
$706$	−32.9268	−1.23922
$707$	11.0295	0.414809
$708$	−24.9904	−0.939197
$709$	3.62357	0.136086	0.0680430	−	0.997682i	$-0.478324\pi$
$709$	3.62357	0.136086	0.0680430	+	0.997682i	$0.478324\pi$
$710$	−4.50750	−0.169163
$711$	−1.10047	−0.0412709
$712$	1.46836	0.0550290
$713$	−0.945215	−0.0353986
$714$	8.29405	0.310397
$715$	0	0
$716$	13.2673	0.495822
$717$	−42.3514	−1.58164
$718$	36.1167	1.34786
$719$	−8.72290	−0.325309	−0.162655	−	0.986683i	$-0.552006\pi$
$719$	−8.72290	−0.325309	−0.162655	+	0.986683i	$0.552006\pi$
$720$	0.704605	0.0262591
$721$	−5.86953	−0.218593
$722$	−18.4515	−0.686692
$723$	−45.8386	−1.70476
$724$	19.5835	0.727815
$725$	−8.37564	−0.311063
$726$	0	0
$727$	37.3206	1.38415	0.692073	−	0.721828i	$-0.256698\pi$
$727$	37.3206	1.38415	0.692073	+	0.721828i	$0.256698\pi$
$728$	5.24489	0.194388
$729$	18.0296	0.667761
$730$	−3.33413	−0.123402
$731$	−4.88974	−0.180854
$732$	25.1923	0.931136
$733$	8.80262	0.325132	0.162566	−	0.986698i	$-0.448023\pi$
$733$	8.80262	0.325132	0.162566	+	0.986698i	$0.448023\pi$
$734$	−8.35672	−0.308452
$735$	1.92474	0.0709949
$736$	−0.856965	−0.0315881
$737$	0	0
$738$	−7.55335	−0.278043
$739$	50.6335	1.86258	0.931292	−	0.364274i	$-0.118683\pi$
$739$	50.6335	1.86258	0.931292	+	0.364274i	$0.118683\pi$
$740$	−1.77921	−0.0654051
$741$	7.47670	0.274663
$742$	8.80661	0.323301
$743$	−50.4494	−1.85081	−0.925404	−	0.378983i	$-0.876274\pi$
$743$	−50.4494	−1.85081	−0.925404	+	0.378983i	$0.876274\pi$
$744$	2.12295	0.0778310
$745$	1.88298	0.0689871
$746$	−16.0205	−0.586552
$747$	0.429256	0.0157057
$748$	0	0
$749$	−6.83162	−0.249622
$750$	1.92474	0.0702814
$751$	−23.9655	−0.874512	−0.437256	−	0.899337i	$-0.644050\pi$
$751$	−23.9655	−0.874512	−0.437256	+	0.899337i	$0.644050\pi$
$752$	8.40172	0.306379
$753$	54.8710	1.99961
$754$	43.9292	1.59981
$755$	5.45095	0.198380
$756$	4.41803	0.160682
$757$	−4.87670	−0.177247	−0.0886233	−	0.996065i	$-0.528247\pi$
$757$	−4.87670	−0.177247	−0.0886233	+	0.996065i	$0.528247\pi$
$758$	25.3872	0.922105
$759$	0	0
$760$	−0.740633	−0.0268656
$761$	−44.6872	−1.61991	−0.809955	−	0.586492i	$-0.800509\pi$
$761$	−44.6872	−1.61991	−0.809955	+	0.586492i	$0.800509\pi$
$762$	18.1323	0.656862
$763$	7.76784	0.281215
$764$	−12.7555	−0.461477
$765$	−3.03628	−0.109777
$766$	−0.303318	−0.0109593
$767$	68.0986	2.45890
$768$	1.92474	0.0694529
$769$	52.9611	1.90983	0.954914	−	0.296884i	$-0.0959474\pi$
$769$	52.9611	1.90983	0.954914	+	0.296884i	$0.0959474\pi$
$770$	0	0
$771$	57.0094	2.05314
$772$	11.8288	0.425729
$773$	38.4372	1.38249	0.691246	−	0.722620i	$-0.257062\pi$
$773$	38.4372	1.38249	0.691246	+	0.722620i	$0.257062\pi$
$774$	0.799532	0.0287386
$775$	1.10298	0.0396202
$776$	8.41705	0.302154
$777$	3.42451	0.122854
$778$	−6.74058	−0.241661
$779$	7.93957	0.284465
$780$	−10.0950	−0.361459
$781$	0	0
$782$	3.69282	0.132055
$783$	37.0038	1.32241
$784$	1.00000	0.0357143
$785$	−11.9779	−0.427511
$786$	−1.66071	−0.0592356
$787$	−11.9075	−0.424458	−0.212229	−	0.977220i	$-0.568072\pi$
$787$	−11.9075	−0.424458	−0.212229	+	0.977220i	$0.568072\pi$
$788$	−21.9105	−0.780528
$789$	7.87570	0.280383
$790$	−1.56183	−0.0555673
$791$	−4.63948	−0.164961
$792$	0	0
$793$	−68.6489	−2.43779
$794$	−19.9230	−0.707039
$795$	−16.9504	−0.601168
$796$	10.3121	0.365503
$797$	−2.09798	−0.0743142	−0.0371571	−	0.999309i	$-0.511830\pi$
$797$	−2.09798	−0.0743142	−0.0371571	+	0.999309i	$0.511830\pi$
$798$	1.42552	0.0504629
$799$	−36.2046	−1.28083
$800$	1.00000	0.0353553
$801$	1.03461	0.0365562
$802$	34.0886	1.20371
$803$	0	0
$804$	17.1998	0.606589
$805$	0.856965	0.0302040
$806$	−5.78501	−0.203768
$807$	5.76911	0.203082
$808$	−11.0295	−0.388018
$809$	−12.0315	−0.423005	−0.211503	−	0.977377i	$-0.567836\pi$
$809$	−12.0315	−0.423005	−0.211503	+	0.977377i	$0.567836\pi$
$810$	−10.6173	−0.373056
$811$	−8.52991	−0.299526	−0.149763	−	0.988722i	$-0.547851\pi$
$811$	−8.52991	−0.299526	−0.149763	+	0.988722i	$0.547851\pi$
$812$	8.37564	0.293927
$813$	47.5439	1.66744
$814$	0	0
$815$	−15.5543	−0.544842
$816$	−8.29405	−0.290350
$817$	−0.840413	−0.0294023
$818$	8.09670	0.283094
$819$	3.69557	0.129134
$820$	−10.7200	−0.374358
$821$	49.8308	1.73911	0.869554	−	0.493839i	$-0.164407\pi$
$821$	49.8308	1.73911	0.869554	+	0.493839i	$0.164407\pi$
$822$	−33.1957	−1.15783
$823$	−14.8465	−0.517516	−0.258758	−	0.965942i	$-0.583313\pi$
$823$	−14.8465	−0.517516	−0.258758	+	0.965942i	$0.583313\pi$
$824$	5.86953	0.204475
$825$	0	0
$826$	12.9838	0.451765
$827$	−1.52007	−0.0528580	−0.0264290	−	0.999651i	$-0.508414\pi$
$827$	−1.52007	−0.0528580	−0.0264290	+	0.999651i	$0.508414\pi$
$828$	−0.603822	−0.0209842
$829$	−10.4514	−0.362993	−0.181497	−	0.983392i	$-0.558094\pi$
$829$	−10.4514	−0.362993	−0.181497	+	0.983392i	$0.558094\pi$
$830$	0.609215	0.0211462
$831$	5.15556	0.178845
$832$	−5.24489	−0.181834
$833$	−4.30919	−0.149305
$834$	39.3509	1.36261
$835$	18.0474	0.624555
$836$	0	0
$837$	−4.87300	−0.168435
$838$	−24.0686	−0.831437
$839$	−39.9761	−1.38013	−0.690064	−	0.723748i	$-0.742418\pi$
$839$	−39.9761	−1.38013	−0.690064	+	0.723748i	$0.742418\pi$
$840$	−1.92474	−0.0664097
$841$	41.1513	1.41901
$842$	13.7871	0.475135
$843$	−22.3680	−0.770395
$844$	−24.8455	−0.855217
$845$	14.5088	0.499119
$846$	5.91989	0.203530
$847$	0	0
$848$	−8.80661	−0.302420
$849$	34.9074	1.19802
$850$	−4.30919	−0.147804
$851$	1.52472	0.0522668
$852$	−8.67574	−0.297226
$853$	−22.2228	−0.760893	−0.380446	−	0.924803i	$-0.624230\pi$
$853$	−22.2228	−0.760893	−0.380446	+	0.924803i	$0.624230\pi$
$854$	−13.0887	−0.447887
$855$	−0.521854	−0.0178470
$856$	6.83162	0.233500
$857$	−15.8282	−0.540681	−0.270340	−	0.962765i	$-0.587136\pi$
$857$	−15.8282	−0.540681	−0.270340	+	0.962765i	$0.587136\pi$
$858$	0	0
$859$	−20.7983	−0.709628	−0.354814	−	0.934937i	$-0.615456\pi$
$859$	−20.7983	−0.709628	−0.354814	+	0.934937i	$0.615456\pi$
$860$	1.13472	0.0386937
$861$	20.6331	0.703175
$862$	−8.72005	−0.297006
$863$	−18.8317	−0.641040	−0.320520	−	0.947242i	$-0.603858\pi$
$863$	−18.8317	−0.641040	−0.320520	+	0.947242i	$0.603858\pi$
$864$	−4.41803	−0.150304
$865$	−9.60665	−0.326636
$866$	−8.51892	−0.289485
$867$	3.02013	0.102569
$868$	−1.10298	−0.0374376
$869$	0	0
$870$	−16.1209	−0.546549
$871$	−46.8692	−1.58810
$872$	−7.76784	−0.263052
$873$	5.93069	0.200724
$874$	0.634696	0.0214689
$875$	−1.00000	−0.0338062
$876$	−6.41731	−0.216821
$877$	−16.6176	−0.561138	−0.280569	−	0.959834i	$-0.590523\pi$
$877$	−16.6176	−0.561138	−0.280569	+	0.959834i	$0.590523\pi$
$878$	−22.5402	−0.760697
$879$	−44.0188	−1.48472
$880$	0	0
$881$	21.6943	0.730901	0.365450	−	0.930831i	$-0.380915\pi$
$881$	21.6943	0.730901	0.365450	+	0.930831i	$0.380915\pi$
$882$	0.704605	0.0237253
$883$	32.8896	1.10682	0.553412	−	0.832907i	$-0.313325\pi$
$883$	32.8896	1.10682	0.553412	+	0.832907i	$0.313325\pi$
$884$	22.6012	0.760161
$885$	−24.9904	−0.840044
$886$	37.9089	1.27357
$887$	4.02388	0.135109	0.0675544	−	0.997716i	$-0.478480\pi$
$887$	4.02388	0.135109	0.0675544	+	0.997716i	$0.478480\pi$
$888$	−3.42451	−0.114919
$889$	−9.42065	−0.315958
$890$	1.46836	0.0492194
$891$	0	0
$892$	−20.2394	−0.677667
$893$	−6.22259	−0.208231
$894$	3.62424	0.121213
$895$	13.2673	0.443476
$896$	−1.00000	−0.0334077
$897$	8.65107	0.288851
$898$	−32.0551	−1.06969
$899$	−9.23816	−0.308110
$900$	0.704605	0.0234868
$901$	37.9493	1.26428
$902$	0	0
$903$	−2.18404	−0.0726804
$904$	4.63948	0.154307
$905$	19.5835	0.650977
$906$	10.4916	0.348561
$907$	20.4539	0.679162	0.339581	−	0.940577i	$-0.389715\pi$
$907$	20.4539	0.679162	0.339581	+	0.940577i	$0.389715\pi$
$908$	11.8090	0.391896
$909$	−7.77147	−0.257763
$910$	5.24489	0.173866
$911$	27.9283	0.925305	0.462653	−	0.886540i	$-0.346898\pi$
$911$	27.9283	0.925305	0.462653	+	0.886540i	$0.346898\pi$
$912$	−1.42552	−0.0472037
$913$	0	0
$914$	24.5243	0.811192
$915$	25.1923	0.832833
$916$	1.67906	0.0554776
$917$	0.862825	0.0284930
$918$	19.0381	0.628352
$919$	−13.3202	−0.439394	−0.219697	−	0.975568i	$-0.570507\pi$
$919$	−13.3202	−0.439394	−0.219697	+	0.975568i	$0.570507\pi$
$920$	−0.856965	−0.0282533
$921$	−38.3649	−1.26417
$922$	−0.188328	−0.00620226
$923$	23.6413	0.778163
$924$	0	0
$925$	−1.77921	−0.0585001
$926$	−9.40956	−0.309217
$927$	4.13570	0.135834
$928$	−8.37564	−0.274944
$929$	39.2113	1.28648	0.643240	−	0.765664i	$-0.277590\pi$
$929$	39.2113	1.28648	0.643240	+	0.765664i	$0.277590\pi$
$930$	2.12295	0.0696141
$931$	−0.740633	−0.0242733
$932$	−15.5220	−0.508440
$933$	−2.47207	−0.0809319
$934$	1.84720	0.0604421
$935$	0	0
$936$	−3.69557	−0.120794
$937$	−21.7403	−0.710225	−0.355112	−	0.934824i	$-0.615557\pi$
$937$	−21.7403	−0.710225	−0.355112	+	0.934824i	$0.615557\pi$
$938$	−8.93617	−0.291776
$939$	−25.7846	−0.841447
$940$	8.40172	0.274034
$941$	16.4125	0.535033	0.267516	−	0.963553i	$-0.413797\pi$
$941$	16.4125	0.535033	0.267516	+	0.963553i	$0.413797\pi$
$942$	−23.0544	−0.751152
$943$	9.18665	0.299158
$944$	−12.9838	−0.422587
$945$	4.41803	0.143718
$946$	0	0
$947$	−45.1297	−1.46652	−0.733259	−	0.679949i	$-0.762002\pi$
$947$	−45.1297	−1.46652	−0.733259	+	0.679949i	$0.762002\pi$
$948$	−3.00610	−0.0976337
$949$	17.4871	0.567655
$950$	−0.740633	−0.0240293
$951$	32.0737	1.04006
$952$	4.30919	0.139662
$953$	−46.8181	−1.51659	−0.758294	−	0.651913i	$-0.773967\pi$
$953$	−46.8181	−1.51659	−0.758294	+	0.651913i	$0.773967\pi$
$954$	−6.20518	−0.200900
$955$	−12.7555	−0.412758
$956$	−22.0037	−0.711652
$957$	0	0
$958$	33.3506	1.07751
$959$	17.2469	0.556931
$960$	1.92474	0.0621206
$961$	−29.7834	−0.960756
$962$	9.33176	0.300868
$963$	4.81359	0.155116
$964$	−23.8155	−0.767047
$965$	11.8288	0.380784
$966$	1.64943	0.0530695
$967$	−57.9645	−1.86401	−0.932007	−	0.362441i	$-0.881943\pi$
$967$	−57.9645	−1.86401	−0.932007	+	0.362441i	$0.881943\pi$
$968$	0	0
$969$	6.14284	0.197337
$970$	8.41705	0.270255
$971$	−10.6264	−0.341019	−0.170509	−	0.985356i	$-0.554541\pi$
$971$	−10.6264	−0.341019	−0.170509	+	0.985356i	$0.554541\pi$
$972$	−7.18150	−0.230347
$973$	−20.4448	−0.655432
$974$	14.1136	0.452230
$975$	−10.0950	−0.323299
$976$	13.0887	0.418960
$977$	−33.6202	−1.07561	−0.537803	−	0.843071i	$-0.680745\pi$
$977$	−33.6202	−1.07561	−0.537803	+	0.843071i	$0.680745\pi$
$978$	−29.9378	−0.957307
$979$	0	0
$980$	1.00000	0.0319438
$981$	−5.47326	−0.174748
$982$	−8.40881	−0.268336
$983$	38.3652	1.22366	0.611830	−	0.790989i	$-0.290434\pi$
$983$	38.3652	1.22366	0.611830	+	0.790989i	$0.290434\pi$
$984$	−20.6331	−0.657760
$985$	−21.9105	−0.698125
$986$	36.0922	1.14941
$987$	−16.1711	−0.514731
$988$	3.88453	0.123583
$989$	−0.972418	−0.0309211
$990$	0	0
$991$	55.5999	1.76619	0.883094	−	0.469196i	$-0.155456\pi$
$991$	55.5999	1.76619	0.883094	+	0.469196i	$0.155456\pi$
$992$	1.10298	0.0350197
$993$	21.4300	0.680059
$994$	4.50750	0.142969
$995$	10.3121	0.326916
$996$	1.17258	0.0371545
$997$	22.9698	0.727462	0.363731	−	0.931504i	$-0.381503\pi$
$997$	22.9698	0.727462	0.363731	+	0.931504i	$0.381503\pi$
$998$	−22.8087	−0.721997
$999$	7.86060	0.248698

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.db.1.6		6
11.5	even	5		770.2.n.g.421.3	✓	12
11.9	even	5		770.2.n.g.631.3	yes	12
11.10	odd	2		8470.2.a.cv.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.g.421.3	✓	12	11.5	even	5
770.2.n.g.631.3	yes	12	11.9	even	5
8470.2.a.cv.1.6		6	11.10	odd	2
8470.2.a.db.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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.92474 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.92474 q^{6} -1.00000 q^{7} +1.00000 q^{8} +0.704605 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.92474 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.92474 q^{6} -1.00000 q^{7} +1.00000 q^{8} +0.704605 q^{9} +1.00000 q^{10} +1.92474 q^{12} -5.24489 q^{13} -1.00000 q^{14} +1.92474 q^{15} +1.00000 q^{16} -4.30919 q^{17} +0.704605 q^{18} -0.740633 q^{19} +1.00000 q^{20} -1.92474 q^{21} -0.856965 q^{23} +1.92474 q^{24} +1.00000 q^{25} -5.24489 q^{26} -4.41803 q^{27} -1.00000 q^{28} -8.37564 q^{29} +1.92474 q^{30} +1.10298 q^{31} +1.00000 q^{32} -4.30919 q^{34} -1.00000 q^{35} +0.704605 q^{36} -1.77921 q^{37} -0.740633 q^{38} -10.0950 q^{39} +1.00000 q^{40} -10.7200 q^{41} -1.92474 q^{42} +1.13472 q^{43} +0.704605 q^{45} -0.856965 q^{46} +8.40172 q^{47} +1.92474 q^{48} +1.00000 q^{49} +1.00000 q^{50} -8.29405 q^{51} -5.24489 q^{52} -8.80661 q^{53} -4.41803 q^{54} -1.00000 q^{56} -1.42552 q^{57} -8.37564 q^{58} -12.9838 q^{59} +1.92474 q^{60} +13.0887 q^{61} +1.10298 q^{62} -0.704605 q^{63} +1.00000 q^{64} -5.24489 q^{65} +8.93617 q^{67} -4.30919 q^{68} -1.64943 q^{69} -1.00000 q^{70} -4.50750 q^{71} +0.704605 q^{72} -3.33413 q^{73} -1.77921 q^{74} +1.92474 q^{75} -0.740633 q^{76} -10.0950 q^{78} -1.56183 q^{79} +1.00000 q^{80} -10.6173 q^{81} -10.7200 q^{82} +0.609215 q^{83} -1.92474 q^{84} -4.30919 q^{85} +1.13472 q^{86} -16.1209 q^{87} +1.46836 q^{89} +0.704605 q^{90} +5.24489 q^{91} -0.856965 q^{92} +2.12295 q^{93} +8.40172 q^{94} -0.740633 q^{95} +1.92474 q^{96} +8.41705 q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - q^{3} + 6 q^{4} + 6 q^{5} - q^{6} - 6 q^{7} + 6 q^{8} - q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - q^3 + 6 * q^4 + 6 * q^5 - q^6 - 6 * q^7 + 6 * q^8 - q^9	\( 6 q + 6 q^{2} - q^{3} + 6 q^{4} + 6 q^{5} - q^{6} - 6 q^{7} + 6 q^{8} - q^{9} + 6 q^{10} - q^{12} - 6 q^{13} - 6 q^{14} - q^{15} + 6 q^{16} - 21 q^{17} - q^{18} + 3 q^{19} + 6 q^{20} + q^{21} - 10 q^{23} - q^{24} + 6 q^{25} - 6 q^{26} - 4 q^{27} - 6 q^{28} - 10 q^{29} - q^{30} - 4 q^{31} + 6 q^{32} - 21 q^{34} - 6 q^{35} - q^{36} - 2 q^{37} + 3 q^{38} - 26 q^{39} + 6 q^{40} - 7 q^{41} + q^{42} - 19 q^{43} - q^{45} - 10 q^{46} + 10 q^{47} - q^{48} + 6 q^{49} + 6 q^{50} + 4 q^{51} - 6 q^{52} - 16 q^{53} - 4 q^{54} - 6 q^{56} - 16 q^{57} - 10 q^{58} - 3 q^{59} - q^{60} + 8 q^{61} - 4 q^{62} + q^{63} + 6 q^{64} - 6 q^{65} - 27 q^{67} - 21 q^{68} + 4 q^{69} - 6 q^{70} + 4 q^{71} - q^{72} - 13 q^{73} - 2 q^{74} - q^{75} + 3 q^{76} - 26 q^{78} - 14 q^{79} + 6 q^{80} - 14 q^{81} - 7 q^{82} - 51 q^{83} + q^{84} - 21 q^{85} - 19 q^{86} - 8 q^{87} + q^{89} - q^{90} + 6 q^{91} - 10 q^{92} + 4 q^{93} + 10 q^{94} + 3 q^{95} - q^{96} + 7 q^{97} + 6 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 - q^3 + 6 * q^4 + 6 * q^5 - q^6 - 6 * q^7 + 6 * q^8 - q^9 + 6 * q^10 - q^12 - 6 * q^13 - 6 * q^14 - q^15 + 6 * q^16 - 21 * q^17 - q^18 + 3 * q^19 + 6 * q^20 + q^21 - 10 * q^23 - q^24 + 6 * q^25 - 6 * q^26 - 4 * q^27 - 6 * q^28 - 10 * q^29 - q^30 - 4 * q^31 + 6 * q^32 - 21 * q^34 - 6 * q^35 - q^36 - 2 * q^37 + 3 * q^38 - 26 * q^39 + 6 * q^40 - 7 * q^41 + q^42 - 19 * q^43 - q^45 - 10 * q^46 + 10 * q^47 - q^48 + 6 * q^49 + 6 * q^50 + 4 * q^51 - 6 * q^52 - 16 * q^53 - 4 * q^54 - 6 * q^56 - 16 * q^57 - 10 * q^58 - 3 * q^59 - q^60 + 8 * q^61 - 4 * q^62 + q^63 + 6 * q^64 - 6 * q^65 - 27 * q^67 - 21 * q^68 + 4 * q^69 - 6 * q^70 + 4 * q^71 - q^72 - 13 * q^73 - 2 * q^74 - q^75 + 3 * q^76 - 26 * q^78 - 14 * q^79 + 6 * q^80 - 14 * q^81 - 7 * q^82 - 51 * q^83 + q^84 - 21 * q^85 - 19 * q^86 - 8 * q^87 + q^89 - q^90 + 6 * q^91 - 10 * q^92 + 4 * q^93 + 10 * q^94 + 3 * q^95 - q^96 + 7 * q^97 + 6 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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