LMFDB - Embedded newform 8470.2.a.db.1.3

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			1.3
Root			$0.803425$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.803425 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.803425 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.35451 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.803425 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.803425 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.35451 q^{9} +1.00000 q^{10} -0.803425 q^{12} -2.64314 q^{13} -1.00000 q^{14} -0.803425 q^{15} +1.00000 q^{16} +1.60450 q^{17} -2.35451 q^{18} +1.90940 q^{19} +1.00000 q^{20} +0.803425 q^{21} -4.22916 q^{23} -0.803425 q^{24} +1.00000 q^{25} -2.64314 q^{26} +4.30195 q^{27} -1.00000 q^{28} +8.97936 q^{29} -0.803425 q^{30} +2.47600 q^{31} +1.00000 q^{32} +1.60450 q^{34} -1.00000 q^{35} -2.35451 q^{36} -5.60877 q^{37} +1.90940 q^{38} +2.12356 q^{39} +1.00000 q^{40} -9.69579 q^{41} +0.803425 q^{42} -4.00169 q^{43} -2.35451 q^{45} -4.22916 q^{46} -6.54502 q^{47} -0.803425 q^{48} +1.00000 q^{49} +1.00000 q^{50} -1.28909 q^{51} -2.64314 q^{52} +10.0478 q^{53} +4.30195 q^{54} -1.00000 q^{56} -1.53406 q^{57} +8.97936 q^{58} +4.16663 q^{59} -0.803425 q^{60} +13.2629 q^{61} +2.47600 q^{62} +2.35451 q^{63} +1.00000 q^{64} -2.64314 q^{65} -10.5029 q^{67} +1.60450 q^{68} +3.39781 q^{69} -1.00000 q^{70} +4.58489 q^{71} -2.35451 q^{72} +3.69293 q^{73} -5.60877 q^{74} -0.803425 q^{75} +1.90940 q^{76} +2.12356 q^{78} -13.9477 q^{79} +1.00000 q^{80} +3.60723 q^{81} -9.69579 q^{82} -13.5603 q^{83} +0.803425 q^{84} +1.60450 q^{85} -4.00169 q^{86} -7.21424 q^{87} -3.41009 q^{89} -2.35451 q^{90} +2.64314 q^{91} -4.22916 q^{92} -1.98928 q^{93} -6.54502 q^{94} +1.90940 q^{95} -0.803425 q^{96} -17.4713 q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.803425	−0.463858	−0.231929	−	0.972733i	$-0.574504\pi$
$3$	−0.803425	−0.463858	−0.231929	+	0.972733i	$0.574504\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.803425	−0.327997
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	−2.35451	−0.784836
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	−0.803425	−0.231929
$13$	−2.64314	−0.733075	−0.366537	−	0.930403i	$-0.619457\pi$
$13$	−2.64314	−0.733075	−0.366537	+	0.930403i	$0.619457\pi$
$14$	−1.00000	−0.267261
$15$	−0.803425	−0.207443
$16$	1.00000	0.250000
$17$	1.60450	0.389147	0.194574	−	0.980888i	$-0.437668\pi$
$17$	1.60450	0.389147	0.194574	+	0.980888i	$0.437668\pi$
$18$	−2.35451	−0.554963
$19$	1.90940	0.438046	0.219023	−	0.975720i	$-0.429713\pi$
$19$	1.90940	0.438046	0.219023	+	0.975720i	$0.429713\pi$
$20$	1.00000	0.223607
$21$	0.803425	0.175322
$22$	0	0
$23$	−4.22916	−0.881840	−0.440920	−	0.897546i	$-0.645348\pi$
$23$	−4.22916	−0.881840	−0.440920	+	0.897546i	$0.645348\pi$
$24$	−0.803425	−0.163998
$25$	1.00000	0.200000
$26$	−2.64314	−0.518362
$27$	4.30195	0.827910
$28$	−1.00000	−0.188982
$29$	8.97936	1.66742	0.833712	−	0.552199i	$-0.186211\pi$
$29$	8.97936	1.66742	0.833712	+	0.552199i	$0.186211\pi$
$30$	−0.803425	−0.146685
$31$	2.47600	0.444702	0.222351	−	0.974967i	$-0.428627\pi$
$31$	2.47600	0.444702	0.222351	+	0.974967i	$0.428627\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	1.60450	0.275169
$35$	−1.00000	−0.169031
$36$	−2.35451	−0.392418
$37$	−5.60877	−0.922076	−0.461038	−	0.887380i	$-0.652523\pi$
$37$	−5.60877	−0.922076	−0.461038	+	0.887380i	$0.652523\pi$
$38$	1.90940	0.309746
$39$	2.12356	0.340042
$40$	1.00000	0.158114
$41$	−9.69579	−1.51423	−0.757114	−	0.653283i	$-0.773391\pi$
$41$	−9.69579	−1.51423	−0.757114	+	0.653283i	$0.773391\pi$
$42$	0.803425	0.123971
$43$	−4.00169	−0.610252	−0.305126	−	0.952312i	$-0.598699\pi$
$43$	−4.00169	−0.610252	−0.305126	+	0.952312i	$0.598699\pi$
$44$	0	0
$45$	−2.35451	−0.350989
$46$	−4.22916	−0.623555
$47$	−6.54502	−0.954690	−0.477345	−	0.878716i	$-0.658401\pi$
$47$	−6.54502	−0.954690	−0.477345	+	0.878716i	$0.658401\pi$
$48$	−0.803425	−0.115964
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	−1.28909	−0.180509
$52$	−2.64314	−0.366537
$53$	10.0478	1.38017	0.690087	−	0.723727i	$-0.257572\pi$
$53$	10.0478	1.38017	0.690087	+	0.723727i	$0.257572\pi$
$54$	4.30195	0.585421
$55$	0	0
$56$	−1.00000	−0.133631
$57$	−1.53406	−0.203191
$58$	8.97936	1.17905
$59$	4.16663	0.542449	0.271225	−	0.962516i	$-0.412571\pi$
$59$	4.16663	0.542449	0.271225	+	0.962516i	$0.412571\pi$
$60$	−0.803425	−0.103722
$61$	13.2629	1.69814	0.849068	−	0.528284i	$-0.177164\pi$
$61$	13.2629	1.69814	0.849068	+	0.528284i	$0.177164\pi$
$62$	2.47600	0.314452
$63$	2.35451	0.296640
$64$	1.00000	0.125000
$65$	−2.64314	−0.327841
$66$	0	0
$67$	−10.5029	−1.28314	−0.641570	−	0.767065i	$-0.721716\pi$
$67$	−10.5029	−1.28314	−0.641570	+	0.767065i	$0.721716\pi$
$68$	1.60450	0.194574
$69$	3.39781	0.409048
$70$	−1.00000	−0.119523
$71$	4.58489	0.544126	0.272063	−	0.962279i	$-0.412294\pi$
$71$	4.58489	0.544126	0.272063	+	0.962279i	$0.412294\pi$
$72$	−2.35451	−0.277481
$73$	3.69293	0.432224	0.216112	−	0.976369i	$-0.430662\pi$
$73$	3.69293	0.432224	0.216112	+	0.976369i	$0.430662\pi$
$74$	−5.60877	−0.652006
$75$	−0.803425	−0.0927715
$76$	1.90940	0.219023
$77$	0	0
$78$	2.12356	0.240446
$79$	−13.9477	−1.56924	−0.784620	−	0.619977i	$-0.787142\pi$
$79$	−13.9477	−1.56924	−0.784620	+	0.619977i	$0.787142\pi$
$80$	1.00000	0.111803
$81$	3.60723	0.400804
$82$	−9.69579	−1.07072
$83$	−13.5603	−1.48843	−0.744215	−	0.667940i	$-0.767176\pi$
$83$	−13.5603	−1.48843	−0.744215	+	0.667940i	$0.767176\pi$
$84$	0.803425	0.0876609
$85$	1.60450	0.174032
$86$	−4.00169	−0.431513
$87$	−7.21424	−0.773448
$88$	0	0
$89$	−3.41009	−0.361469	−0.180735	−	0.983532i	$-0.557847\pi$
$89$	−3.41009	−0.361469	−0.180735	+	0.983532i	$0.557847\pi$
$90$	−2.35451	−0.248187
$91$	2.64314	0.277076
$92$	−4.22916	−0.440920
$93$	−1.98928	−0.206279
$94$	−6.54502	−0.675068
$95$	1.90940	0.195900
$96$	−0.803425	−0.0819992
$97$	−17.4713	−1.77394	−0.886968	−	0.461830i	$-0.847193\pi$
$97$	−17.4713	−1.77394	−0.886968	+	0.461830i	$0.847193\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	−10.6494	−1.05965	−0.529827	−	0.848106i	$-0.677743\pi$
$101$	−10.6494	−1.05965	−0.529827	+	0.848106i	$0.677743\pi$
$102$	−1.28909	−0.127639
$103$	−6.86666	−0.676592	−0.338296	−	0.941040i	$-0.609851\pi$
$103$	−6.86666	−0.676592	−0.338296	+	0.941040i	$0.609851\pi$
$104$	−2.64314	−0.259181
$105$	0.803425	0.0784063
$106$	10.0478	0.975930
$107$	−2.88270	−0.278681	−0.139341	−	0.990245i	$-0.544498\pi$
$107$	−2.88270	−0.278681	−0.139341	+	0.990245i	$0.544498\pi$
$108$	4.30195	0.413955
$109$	−18.4938	−1.77139	−0.885693	−	0.464271i	$-0.846316\pi$
$109$	−18.4938	−1.77139	−0.885693	+	0.464271i	$0.846316\pi$
$110$	0	0
$111$	4.50623	0.427712
$112$	−1.00000	−0.0944911
$113$	11.9566	1.12478	0.562391	−	0.826871i	$-0.309882\pi$
$113$	11.9566	1.12478	0.562391	+	0.826871i	$0.309882\pi$
$114$	−1.53406	−0.143678
$115$	−4.22916	−0.394371
$116$	8.97936	0.833712
$117$	6.22329	0.575343
$118$	4.16663	0.383570
$119$	−1.60450	−0.147084
$120$	−0.803425	−0.0733423
$121$	0	0
$122$	13.2629	1.20076
$123$	7.78984	0.702386
$124$	2.47600	0.222351
$125$	1.00000	0.0894427
$126$	2.35451	0.209756
$127$	−13.4085	−1.18982	−0.594908	−	0.803794i	$-0.702811\pi$
$127$	−13.4085	−1.18982	−0.594908	+	0.803794i	$0.702811\pi$
$128$	1.00000	0.0883883
$129$	3.21506	0.283070
$130$	−2.64314	−0.231819
$131$	−8.49928	−0.742585	−0.371293	−	0.928516i	$-0.621085\pi$
$131$	−8.49928	−0.742585	−0.371293	+	0.928516i	$0.621085\pi$
$132$	0	0
$133$	−1.90940	−0.165566
$134$	−10.5029	−0.907317
$135$	4.30195	0.370253
$136$	1.60450	0.137584
$137$	10.0747	0.860737	0.430369	−	0.902653i	$-0.358384\pi$
$137$	10.0747	0.860737	0.430369	+	0.902653i	$0.358384\pi$
$138$	3.39781	0.289241
$139$	13.8200	1.17220	0.586100	−	0.810238i	$-0.300662\pi$
$139$	13.8200	1.17220	0.586100	+	0.810238i	$0.300662\pi$
$140$	−1.00000	−0.0845154
$141$	5.25844	0.442840
$142$	4.58489	0.384755
$143$	0	0
$144$	−2.35451	−0.196209
$145$	8.97936	0.745695
$146$	3.69293	0.305629
$147$	−0.803425	−0.0662654
$148$	−5.60877	−0.461038
$149$	−18.3638	−1.50442	−0.752211	−	0.658922i	$-0.771013\pi$
$149$	−18.3638	−1.50442	−0.752211	+	0.658922i	$0.771013\pi$
$150$	−0.803425	−0.0655994
$151$	20.5718	1.67411	0.837055	−	0.547118i	$-0.184275\pi$
$151$	20.5718	1.67411	0.837055	+	0.547118i	$0.184275\pi$
$152$	1.90940	0.154873
$153$	−3.77780	−0.305417
$154$	0	0
$155$	2.47600	0.198877
$156$	2.12356	0.170021
$157$	−4.64886	−0.371019	−0.185510	−	0.982642i	$-0.559394\pi$
$157$	−4.64886	−0.371019	−0.185510	+	0.982642i	$0.559394\pi$
$158$	−13.9477	−1.10962
$159$	−8.07267	−0.640204
$160$	1.00000	0.0790569
$161$	4.22916	0.333304
$162$	3.60723	0.283411
$163$	4.99400	0.391160	0.195580	−	0.980688i	$-0.437341\pi$
$163$	4.99400	0.391160	0.195580	+	0.980688i	$0.437341\pi$
$164$	−9.69579	−0.757114
$165$	0	0
$166$	−13.5603	−1.05248
$167$	−1.86847	−0.144586	−0.0722932	−	0.997383i	$-0.523032\pi$
$167$	−1.86847	−0.144586	−0.0722932	+	0.997383i	$0.523032\pi$
$168$	0.803425	0.0619856
$169$	−6.01382	−0.462602
$170$	1.60450	0.123059
$171$	−4.49570	−0.343795
$172$	−4.00169	−0.305126
$173$	−11.7799	−0.895613	−0.447806	−	0.894131i	$-0.647795\pi$
$173$	−11.7799	−0.895613	−0.447806	+	0.894131i	$0.647795\pi$
$174$	−7.21424	−0.546910
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	−3.34758	−0.251619
$178$	−3.41009	−0.255597
$179$	−10.3705	−0.775128	−0.387564	−	0.921843i	$-0.626683\pi$
$179$	−10.3705	−0.775128	−0.387564	+	0.921843i	$0.626683\pi$
$180$	−2.35451	−0.175495
$181$	−22.6738	−1.68533	−0.842664	−	0.538440i	$-0.819014\pi$
$181$	−22.6738	−1.68533	−0.842664	+	0.538440i	$0.819014\pi$
$182$	2.64314	0.195922
$183$	−10.6557	−0.787693
$184$	−4.22916	−0.311778
$185$	−5.60877	−0.412365
$186$	−1.98928	−0.145861
$187$	0	0
$188$	−6.54502	−0.477345
$189$	−4.30195	−0.312921
$190$	1.90940	0.138522
$191$	−8.48643	−0.614056	−0.307028	−	0.951700i	$-0.599335\pi$
$191$	−8.48643	−0.614056	−0.307028	+	0.951700i	$0.599335\pi$
$192$	−0.803425	−0.0579822
$193$	−25.1578	−1.81090	−0.905451	−	0.424452i	$-0.860467\pi$
$193$	−25.1578	−1.81090	−0.905451	+	0.424452i	$0.860467\pi$
$194$	−17.4713	−1.25436
$195$	2.12356	0.152072
$196$	1.00000	0.0714286
$197$	−13.2603	−0.944757	−0.472379	−	0.881396i	$-0.656604\pi$
$197$	−13.2603	−0.944757	−0.472379	+	0.881396i	$0.656604\pi$
$198$	0	0
$199$	3.59813	0.255065	0.127532	−	0.991834i	$-0.459294\pi$
$199$	3.59813	0.255065	0.127532	+	0.991834i	$0.459294\pi$
$200$	1.00000	0.0707107
$201$	8.43833	0.595194
$202$	−10.6494	−0.749288
$203$	−8.97936	−0.630227
$204$	−1.28909	−0.0902545
$205$	−9.69579	−0.677183
$206$	−6.86666	−0.478423
$207$	9.95758	0.692100
$208$	−2.64314	−0.183269
$209$	0	0
$210$	0.803425	0.0554416
$211$	−10.0058	−0.688828	−0.344414	−	0.938818i	$-0.611922\pi$
$211$	−10.0058	−0.688828	−0.344414	+	0.938818i	$0.611922\pi$
$212$	10.0478	0.690087
$213$	−3.68361	−0.252397
$214$	−2.88270	−0.197057
$215$	−4.00169	−0.272913
$216$	4.30195	0.292710
$217$	−2.47600	−0.168082
$218$	−18.4938	−1.25256
$219$	−2.96699	−0.200491
$220$	0	0
$221$	−4.24090	−0.285274
$222$	4.50623	0.302438
$223$	25.0397	1.67678	0.838391	−	0.545069i	$-0.183497\pi$
$223$	25.0397	1.67678	0.838391	+	0.545069i	$0.183497\pi$
$224$	−1.00000	−0.0668153
$225$	−2.35451	−0.156967
$226$	11.9566	0.795341
$227$	−0.182924	−0.0121411	−0.00607054	−	0.999982i	$-0.501932\pi$
$227$	−0.182924	−0.0121411	−0.00607054	+	0.999982i	$0.501932\pi$
$228$	−1.53406	−0.101596
$229$	−0.134371	−0.00887950	−0.00443975	−	0.999990i	$-0.501413\pi$
$229$	−0.134371	−0.00887950	−0.00443975	+	0.999990i	$0.501413\pi$
$230$	−4.22916	−0.278862
$231$	0	0
$232$	8.97936	0.589524
$233$	−2.93010	−0.191957	−0.0959785	−	0.995383i	$-0.530598\pi$
$233$	−2.93010	−0.191957	−0.0959785	+	0.995383i	$0.530598\pi$
$234$	6.22329	0.406829
$235$	−6.54502	−0.426950
$236$	4.16663	0.271225
$237$	11.2059	0.727904
$238$	−1.60450	−0.104004
$239$	8.27410	0.535207	0.267604	−	0.963529i	$-0.413768\pi$
$239$	8.27410	0.535207	0.267604	+	0.963529i	$0.413768\pi$
$240$	−0.803425	−0.0518609
$241$	16.5842	1.06828	0.534142	−	0.845395i	$-0.320635\pi$
$241$	16.5842	1.06828	0.534142	+	0.845395i	$0.320635\pi$
$242$	0	0
$243$	−15.8040	−1.01383
$244$	13.2629	0.849068
$245$	1.00000	0.0638877
$246$	7.78984	0.496662
$247$	−5.04681	−0.321121
$248$	2.47600	0.157226
$249$	10.8946	0.690420
$250$	1.00000	0.0632456
$251$	−13.5486	−0.855180	−0.427590	−	0.903973i	$-0.640637\pi$
$251$	−13.5486	−0.855180	−0.427590	+	0.903973i	$0.640637\pi$
$252$	2.35451	0.148320
$253$	0	0
$254$	−13.4085	−0.841327
$255$	−1.28909	−0.0807261
$256$	1.00000	0.0625000
$257$	18.4226	1.14917	0.574584	−	0.818446i	$-0.305164\pi$
$257$	18.4226	1.14917	0.574584	+	0.818446i	$0.305164\pi$
$258$	3.21506	0.200161
$259$	5.60877	0.348512
$260$	−2.64314	−0.163920
$261$	−21.1420	−1.30865
$262$	−8.49928	−0.525087
$263$	−19.1658	−1.18181	−0.590907	−	0.806740i	$-0.701230\pi$
$263$	−19.1658	−1.18181	−0.590907	+	0.806740i	$0.701230\pi$
$264$	0	0
$265$	10.0478	0.617232
$266$	−1.90940	−0.117073
$267$	2.73975	0.167670
$268$	−10.5029	−0.641570
$269$	9.08666	0.554023	0.277012	−	0.960867i	$-0.410656\pi$
$269$	9.08666	0.554023	0.277012	+	0.960867i	$0.410656\pi$
$270$	4.30195	0.261808
$271$	19.1739	1.16473	0.582366	−	0.812927i	$-0.302127\pi$
$271$	19.1739	1.16473	0.582366	+	0.812927i	$0.302127\pi$
$272$	1.60450	0.0972869
$273$	−2.12356	−0.128524
$274$	10.0747	0.608633
$275$	0	0
$276$	3.39781	0.204524
$277$	−20.6691	−1.24189	−0.620944	−	0.783855i	$-0.713251\pi$
$277$	−20.6691	−1.24189	−0.620944	+	0.783855i	$0.713251\pi$
$278$	13.8200	0.828871
$279$	−5.82976	−0.349018
$280$	−1.00000	−0.0597614
$281$	−1.37153	−0.0818184	−0.0409092	−	0.999163i	$-0.513025\pi$
$281$	−1.37153	−0.0818184	−0.0409092	+	0.999163i	$0.513025\pi$
$282$	5.25844	0.313135
$283$	−6.43513	−0.382528	−0.191264	−	0.981539i	$-0.561259\pi$
$283$	−6.43513	−0.382528	−0.191264	+	0.981539i	$0.561259\pi$
$284$	4.58489	0.272063
$285$	−1.53406	−0.0908699
$286$	0	0
$287$	9.69579	0.572324
$288$	−2.35451	−0.138741
$289$	−14.4256	−0.848564
$290$	8.97936	0.527286
$291$	14.0368	0.822854
$292$	3.69293	0.216112
$293$	4.59731	0.268578	0.134289	−	0.990942i	$-0.457125\pi$
$293$	4.59731	0.268578	0.134289	+	0.990942i	$0.457125\pi$
$294$	−0.803425	−0.0468567
$295$	4.16663	0.242591
$296$	−5.60877	−0.326003
$297$	0	0
$298$	−18.3638	−1.06379
$299$	11.1782	0.646454
$300$	−0.803425	−0.0463858
$301$	4.00169	0.230654
$302$	20.5718	1.18377
$303$	8.55598	0.491528
$304$	1.90940	0.109512
$305$	13.2629	0.759429
$306$	−3.77780	−0.215962
$307$	−24.8042	−1.41565	−0.707825	−	0.706388i	$-0.750323\pi$
$307$	−24.8042	−1.41565	−0.707825	+	0.706388i	$0.750323\pi$
$308$	0	0
$309$	5.51685	0.313843
$310$	2.47600	0.140627
$311$	25.8023	1.46311	0.731556	−	0.681782i	$-0.238795\pi$
$311$	25.8023	1.46311	0.731556	+	0.681782i	$0.238795\pi$
$312$	2.12356	0.120223
$313$	16.5081	0.933093	0.466547	−	0.884497i	$-0.345498\pi$
$313$	16.5081	0.933093	0.466547	+	0.884497i	$0.345498\pi$
$314$	−4.64886	−0.262350
$315$	2.35451	0.132662
$316$	−13.9477	−0.784620
$317$	2.33084	0.130913	0.0654566	−	0.997855i	$-0.479150\pi$
$317$	2.33084	0.130913	0.0654566	+	0.997855i	$0.479150\pi$
$318$	−8.07267	−0.452693
$319$	0	0
$320$	1.00000	0.0559017
$321$	2.31603	0.129268
$322$	4.22916	0.235682
$323$	3.06363	0.170465
$324$	3.60723	0.200402
$325$	−2.64314	−0.146615
$326$	4.99400	0.276592
$327$	14.8584	0.821671
$328$	−9.69579	−0.535361
$329$	6.54502	0.360839
$330$	0	0
$331$	6.54411	0.359697	0.179848	−	0.983694i	$-0.442439\pi$
$331$	6.54411	0.359697	0.179848	+	0.983694i	$0.442439\pi$
$332$	−13.5603	−0.744215
$333$	13.2059	0.723678
$334$	−1.86847	−0.102238
$335$	−10.5029	−0.573837
$336$	0.803425	0.0438304
$337$	16.6761	0.908407	0.454204	−	0.890898i	$-0.349924\pi$
$337$	16.6761	0.908407	0.454204	+	0.890898i	$0.349924\pi$
$338$	−6.01382	−0.327109
$339$	−9.60623	−0.521739
$340$	1.60450	0.0870160
$341$	0	0
$342$	−4.49570	−0.243099
$343$	−1.00000	−0.0539949
$344$	−4.00169	−0.215757
$345$	3.39781	0.182932
$346$	−11.7799	−0.633294
$347$	29.2816	1.57192	0.785959	−	0.618279i	$-0.212170\pi$
$347$	29.2816	1.57192	0.785959	+	0.618279i	$0.212170\pi$
$348$	−7.21424	−0.386724
$349$	−16.7836	−0.898406	−0.449203	−	0.893430i	$-0.648292\pi$
$349$	−16.7836	−0.898406	−0.449203	+	0.893430i	$0.648292\pi$
$350$	−1.00000	−0.0534522
$351$	−11.3706	−0.606920
$352$	0	0
$353$	22.9110	1.21943	0.609715	−	0.792621i	$-0.291284\pi$
$353$	22.9110	1.21943	0.609715	+	0.792621i	$0.291284\pi$
$354$	−3.34758	−0.177922
$355$	4.58489	0.243340
$356$	−3.41009	−0.180735
$357$	1.28909	0.0682260
$358$	−10.3705	−0.548098
$359$	8.36518	0.441497	0.220749	−	0.975331i	$-0.429150\pi$
$359$	8.36518	0.441497	0.220749	+	0.975331i	$0.429150\pi$
$360$	−2.35451	−0.124093
$361$	−15.3542	−0.808115
$362$	−22.6738	−1.19171
$363$	0	0
$364$	2.64314	0.138538
$365$	3.69293	0.193297
$366$	−10.6557	−0.556983
$367$	−1.80322	−0.0941273	−0.0470637	−	0.998892i	$-0.514986\pi$
$367$	−1.80322	−0.0941273	−0.0470637	+	0.998892i	$0.514986\pi$
$368$	−4.22916	−0.220460
$369$	22.8288	1.18842
$370$	−5.60877	−0.291586
$371$	−10.0478	−0.521657
$372$	−1.98928	−0.103139
$373$	9.60451	0.497303	0.248651	−	0.968593i	$-0.420013\pi$
$373$	9.60451	0.497303	0.248651	+	0.968593i	$0.420013\pi$
$374$	0	0
$375$	−0.803425	−0.0414887
$376$	−6.54502	−0.337534
$377$	−23.7337	−1.22235
$378$	−4.30195	−0.221268
$379$	−5.94046	−0.305141	−0.152570	−	0.988293i	$-0.548755\pi$
$379$	−5.94046	−0.305141	−0.152570	+	0.988293i	$0.548755\pi$
$380$	1.90940	0.0979502
$381$	10.7728	0.551905
$382$	−8.48643	−0.434203
$383$	−29.4258	−1.50359	−0.751794	−	0.659399i	$-0.770811\pi$
$383$	−29.4258	−1.50359	−0.751794	+	0.659399i	$0.770811\pi$
$384$	−0.803425	−0.0409996
$385$	0	0
$386$	−25.1578	−1.28050
$387$	9.42201	0.478948
$388$	−17.4713	−0.886968
$389$	−18.8617	−0.956324	−0.478162	−	0.878272i	$-0.658697\pi$
$389$	−18.8617	−0.956324	−0.478162	+	0.878272i	$0.658697\pi$
$390$	2.12356	0.107531
$391$	−6.78566	−0.343166
$392$	1.00000	0.0505076
$393$	6.82853	0.344454
$394$	−13.2603	−0.668044
$395$	−13.9477	−0.701785
$396$	0	0
$397$	25.4542	1.27751	0.638756	−	0.769409i	$-0.279449\pi$
$397$	25.4542	1.27751	0.638756	+	0.769409i	$0.279449\pi$
$398$	3.59813	0.180358
$399$	1.53406	0.0767991
$400$	1.00000	0.0500000
$401$	14.9867	0.748399	0.374199	−	0.927348i	$-0.377918\pi$
$401$	14.9867	0.748399	0.374199	+	0.927348i	$0.377918\pi$
$402$	8.43833	0.420866
$403$	−6.54440	−0.326000
$404$	−10.6494	−0.529827
$405$	3.60723	0.179245
$406$	−8.97936	−0.445638
$407$	0	0
$408$	−1.28909	−0.0638196
$409$	4.85775	0.240200	0.120100	−	0.992762i	$-0.461678\pi$
$409$	4.85775	0.240200	0.120100	+	0.992762i	$0.461678\pi$
$410$	−9.69579	−0.478841
$411$	−8.09424	−0.399260
$412$	−6.86666	−0.338296
$413$	−4.16663	−0.205027
$414$	9.95758	0.489388
$415$	−13.5603	−0.665647
$416$	−2.64314	−0.129590
$417$	−11.1034	−0.543734
$418$	0	0
$419$	−1.77493	−0.0867109	−0.0433554	−	0.999060i	$-0.513805\pi$
$419$	−1.77493	−0.0867109	−0.0433554	+	0.999060i	$0.513805\pi$
$420$	0.803425	0.0392031
$421$	−16.9245	−0.824851	−0.412426	−	0.910991i	$-0.635318\pi$
$421$	−16.9245	−0.824851	−0.412426	+	0.910991i	$0.635318\pi$
$422$	−10.0058	−0.487075
$423$	15.4103	0.749275
$424$	10.0478	0.487965
$425$	1.60450	0.0778295
$426$	−3.68361	−0.178472
$427$	−13.2629	−0.641835
$428$	−2.88270	−0.139341
$429$	0	0
$430$	−4.00169	−0.192979
$431$	4.15621	0.200198	0.100099	−	0.994977i	$-0.468084\pi$
$431$	4.15621	0.200198	0.100099	+	0.994977i	$0.468084\pi$
$432$	4.30195	0.206977
$433$	22.2410	1.06883	0.534417	−	0.845221i	$-0.320531\pi$
$433$	22.2410	1.06883	0.534417	+	0.845221i	$0.320531\pi$
$434$	−2.47600	−0.118852
$435$	−7.21424	−0.345896
$436$	−18.4938	−0.885693
$437$	−8.07515	−0.386287
$438$	−2.96699	−0.141768
$439$	−21.6172	−1.03173	−0.515866	−	0.856669i	$-0.672530\pi$
$439$	−21.6172	−1.03173	−0.515866	+	0.856669i	$0.672530\pi$
$440$	0	0
$441$	−2.35451	−0.112119
$442$	−4.24090	−0.201719
$443$	−12.9462	−0.615092	−0.307546	−	0.951533i	$-0.599508\pi$
$443$	−12.9462	−0.615092	−0.307546	+	0.951533i	$0.599508\pi$
$444$	4.50623	0.213856
$445$	−3.41009	−0.161654
$446$	25.0397	1.18566
$447$	14.7540	0.697838
$448$	−1.00000	−0.0472456
$449$	13.8561	0.653910	0.326955	−	0.945040i	$-0.393977\pi$
$449$	13.8561	0.653910	0.326955	+	0.945040i	$0.393977\pi$
$450$	−2.35451	−0.110993
$451$	0	0
$452$	11.9566	0.562391
$453$	−16.5279	−0.776549
$454$	−0.182924	−0.00858503
$455$	2.64314	0.123912
$456$	−1.53406	−0.0718389
$457$	−9.98796	−0.467217	−0.233608	−	0.972331i	$-0.575053\pi$
$457$	−9.98796	−0.467217	−0.233608	+	0.972331i	$0.575053\pi$
$458$	−0.134371	−0.00627876
$459$	6.90246	0.322179
$460$	−4.22916	−0.197185
$461$	27.8198	1.29570	0.647850	−	0.761768i	$-0.275668\pi$
$461$	27.8198	1.29570	0.647850	+	0.761768i	$0.275668\pi$
$462$	0	0
$463$	−10.2727	−0.477413	−0.238707	−	0.971092i	$-0.576723\pi$
$463$	−10.2727	−0.477413	−0.238707	+	0.971092i	$0.576723\pi$
$464$	8.97936	0.416856
$465$	−1.98928	−0.0922506
$466$	−2.93010	−0.135734
$467$	9.03790	0.418224	0.209112	−	0.977892i	$-0.432943\pi$
$467$	9.03790	0.418224	0.209112	+	0.977892i	$0.432943\pi$
$468$	6.22329	0.287672
$469$	10.5029	0.484981
$470$	−6.54502	−0.301899
$471$	3.73501	0.172100
$472$	4.16663	0.191785
$473$	0	0
$474$	11.2059	0.514706
$475$	1.90940	0.0876093
$476$	−1.60450	−0.0735420
$477$	−23.6577	−1.08321
$478$	8.27410	0.378449
$479$	−39.4300	−1.80160	−0.900801	−	0.434233i	$-0.857020\pi$
$479$	−39.4300	−1.80160	−0.900801	+	0.434233i	$0.857020\pi$
$480$	−0.803425	−0.0366712
$481$	14.8247	0.675950
$482$	16.5842	0.755391
$483$	−3.39781	−0.154606
$484$	0	0
$485$	−17.4713	−0.793329
$486$	−15.8040	−0.716883
$487$	−18.9186	−0.857282	−0.428641	−	0.903475i	$-0.641007\pi$
$487$	−18.9186	−0.857282	−0.428641	+	0.903475i	$0.641007\pi$
$488$	13.2629	0.600381
$489$	−4.01230	−0.181443
$490$	1.00000	0.0451754
$491$	−1.51922	−0.0685615	−0.0342808	−	0.999412i	$-0.510914\pi$
$491$	−1.51922	−0.0685615	−0.0342808	+	0.999412i	$0.510914\pi$
$492$	7.78984	0.351193
$493$	14.4073	0.648874
$494$	−5.04681	−0.227067
$495$	0	0
$496$	2.47600	0.111176
$497$	−4.58489	−0.205660
$498$	10.8946	0.488201
$499$	11.8172	0.529012	0.264506	−	0.964384i	$-0.414791\pi$
$499$	11.8172	0.529012	0.264506	+	0.964384i	$0.414791\pi$
$500$	1.00000	0.0447214
$501$	1.50117	0.0670675
$502$	−13.5486	−0.604703
$503$	−16.0491	−0.715592	−0.357796	−	0.933800i	$-0.616472\pi$
$503$	−16.0491	−0.715592	−0.357796	+	0.933800i	$0.616472\pi$
$504$	2.35451	0.104878
$505$	−10.6494	−0.473891
$506$	0	0
$507$	4.83166	0.214581
$508$	−13.4085	−0.594908
$509$	40.2765	1.78522	0.892612	−	0.450826i	$-0.148870\pi$
$509$	40.2765	1.78522	0.892612	+	0.450826i	$0.148870\pi$
$510$	−1.28909	−0.0570820
$511$	−3.69293	−0.163365
$512$	1.00000	0.0441942
$513$	8.21414	0.362663
$514$	18.4226	0.812584
$515$	−6.86666	−0.302581
$516$	3.21506	0.141535
$517$	0	0
$518$	5.60877	0.246435
$519$	9.46431	0.415437
$520$	−2.64314	−0.115909
$521$	−27.4901	−1.20436	−0.602182	−	0.798359i	$-0.705702\pi$
$521$	−27.4901	−1.20436	−0.602182	+	0.798359i	$0.705702\pi$
$522$	−21.1420	−0.925359
$523$	20.2364	0.884875	0.442438	−	0.896799i	$-0.354114\pi$
$523$	20.2364	0.884875	0.442438	+	0.896799i	$0.354114\pi$
$524$	−8.49928	−0.371293
$525$	0.803425	0.0350643
$526$	−19.1658	−0.835668
$527$	3.97273	0.173055
$528$	0	0
$529$	−5.11424	−0.222358
$530$	10.0478	0.436449
$531$	−9.81037	−0.425734
$532$	−1.90940	−0.0827830
$533$	25.6273	1.11004
$534$	2.73975	0.118561
$535$	−2.88270	−0.124630
$536$	−10.5029	−0.453658
$537$	8.33193	0.359549
$538$	9.08666	0.391754
$539$	0	0
$540$	4.30195	0.185126
$541$	26.5254	1.14042	0.570209	−	0.821500i	$-0.306862\pi$
$541$	26.5254	1.14042	0.570209	+	0.821500i	$0.306862\pi$
$542$	19.1739	0.823590
$543$	18.2167	0.781752
$544$	1.60450	0.0687922
$545$	−18.4938	−0.792188
$546$	−2.12356	−0.0908801
$547$	3.17578	0.135787	0.0678933	−	0.997693i	$-0.478372\pi$
$547$	3.17578	0.135787	0.0678933	+	0.997693i	$0.478372\pi$
$548$	10.0747	0.430369
$549$	−31.2275	−1.33276
$550$	0	0
$551$	17.1452	0.730409
$552$	3.39781	0.144620
$553$	13.9477	0.593117
$554$	−20.6691	−0.878148
$555$	4.50623	0.191279
$556$	13.8200	0.586100
$557$	−29.2227	−1.23821	−0.619103	−	0.785310i	$-0.712503\pi$
$557$	−29.2227	−1.23821	−0.619103	+	0.785310i	$0.712503\pi$
$558$	−5.82976	−0.246793
$559$	10.5770	0.447360
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	−1.37153	−0.0578543
$563$	−6.15480	−0.259394	−0.129697	−	0.991554i	$-0.541400\pi$
$563$	−6.15480	−0.259394	−0.129697	+	0.991554i	$0.541400\pi$
$564$	5.25844	0.221420
$565$	11.9566	0.503018
$566$	−6.43513	−0.270488
$567$	−3.60723	−0.151490
$568$	4.58489	0.192378
$569$	−3.59047	−0.150520	−0.0752601	−	0.997164i	$-0.523979\pi$
$569$	−3.59047	−0.150520	−0.0752601	+	0.997164i	$0.523979\pi$
$570$	−1.53406	−0.0642547
$571$	−28.1128	−1.17649	−0.588243	−	0.808684i	$-0.700180\pi$
$571$	−28.1128	−1.17649	−0.588243	+	0.808684i	$0.700180\pi$
$572$	0	0
$573$	6.81821	0.284835
$574$	9.69579	0.404695
$575$	−4.22916	−0.176368
$576$	−2.35451	−0.0981045
$577$	28.5378	1.18804	0.594022	−	0.804448i	$-0.297539\pi$
$577$	28.5378	1.18804	0.594022	+	0.804448i	$0.297539\pi$
$578$	−14.4256	−0.600026
$579$	20.2124	0.840000
$580$	8.97936	0.372847
$581$	13.5603	0.562574
$582$	14.0368	0.581846
$583$	0	0
$584$	3.69293	0.152814
$585$	6.22329	0.257301
$586$	4.59731	0.189913
$587$	−19.5107	−0.805291	−0.402646	−	0.915356i	$-0.631909\pi$
$587$	−19.5107	−0.805291	−0.402646	+	0.915356i	$0.631909\pi$
$588$	−0.803425	−0.0331327
$589$	4.72767	0.194800
$590$	4.16663	0.171538
$591$	10.6537	0.438233
$592$	−5.60877	−0.230519
$593$	4.84298	0.198877	0.0994386	−	0.995044i	$-0.468295\pi$
$593$	4.84298	0.198877	0.0994386	+	0.995044i	$0.468295\pi$
$594$	0	0
$595$	−1.60450	−0.0657779
$596$	−18.3638	−0.752211
$597$	−2.89083	−0.118314
$598$	11.1782	0.457112
$599$	−3.67149	−0.150013	−0.0750064	−	0.997183i	$-0.523898\pi$
$599$	−3.67149	−0.150013	−0.0750064	+	0.997183i	$0.523898\pi$
$600$	−0.803425	−0.0327997
$601$	−1.73373	−0.0707203	−0.0353601	−	0.999375i	$-0.511258\pi$
$601$	−1.73373	−0.0707203	−0.0353601	+	0.999375i	$0.511258\pi$
$602$	4.00169	0.163097
$603$	24.7293	1.00705
$604$	20.5718	0.837055
$605$	0	0
$606$	8.55598	0.347563
$607$	−28.4589	−1.15511	−0.577555	−	0.816351i	$-0.695993\pi$
$607$	−28.4589	−1.15511	−0.577555	+	0.816351i	$0.695993\pi$
$608$	1.90940	0.0774364
$609$	7.21424	0.292336
$610$	13.2629	0.536997
$611$	17.2994	0.699859
$612$	−3.77780	−0.152708
$613$	−8.07904	−0.326309	−0.163155	−	0.986601i	$-0.552167\pi$
$613$	−8.07904	−0.326309	−0.163155	+	0.986601i	$0.552167\pi$
$614$	−24.8042	−1.00102
$615$	7.78984	0.314117
$616$	0	0
$617$	2.53152	0.101915	0.0509577	−	0.998701i	$-0.483773\pi$
$617$	2.53152	0.101915	0.0509577	+	0.998701i	$0.483773\pi$
$618$	5.51685	0.221920
$619$	−27.6305	−1.11056	−0.555281	−	0.831663i	$-0.687389\pi$
$619$	−27.6305	−1.11056	−0.555281	+	0.831663i	$0.687389\pi$
$620$	2.47600	0.0994385
$621$	−18.1936	−0.730084
$622$	25.8023	1.03458
$623$	3.41009	0.136622
$624$	2.12356	0.0850106
$625$	1.00000	0.0400000
$626$	16.5081	0.659797
$627$	0	0
$628$	−4.64886	−0.185510
$629$	−8.99925	−0.358823
$630$	2.35451	0.0938058
$631$	−32.2983	−1.28577	−0.642887	−	0.765961i	$-0.722263\pi$
$631$	−32.2983	−1.28577	−0.642887	+	0.765961i	$0.722263\pi$
$632$	−13.9477	−0.554810
$633$	8.03891	0.319518
$634$	2.33084	0.0925696
$635$	−13.4085	−0.532102
$636$	−8.07267	−0.320102
$637$	−2.64314	−0.104725
$638$	0	0
$639$	−10.7952	−0.427050
$640$	1.00000	0.0395285
$641$	31.3973	1.24012	0.620060	−	0.784554i	$-0.287108\pi$
$641$	31.3973	1.24012	0.620060	+	0.784554i	$0.287108\pi$
$642$	2.31603	0.0914066
$643$	4.12543	0.162691	0.0813456	−	0.996686i	$-0.474078\pi$
$643$	4.12543	0.162691	0.0813456	+	0.996686i	$0.474078\pi$
$644$	4.22916	0.166652
$645$	3.21506	0.126593
$646$	3.06363	0.120537
$647$	20.9288	0.822794	0.411397	−	0.911456i	$-0.365041\pi$
$647$	20.9288	0.822794	0.411397	+	0.911456i	$0.365041\pi$
$648$	3.60723	0.141705
$649$	0	0
$650$	−2.64314	−0.103672
$651$	1.98928	0.0779660
$652$	4.99400	0.195580
$653$	−2.00850	−0.0785988	−0.0392994	−	0.999227i	$-0.512513\pi$
$653$	−2.00850	−0.0785988	−0.0392994	+	0.999227i	$0.512513\pi$
$654$	14.8584	0.581009
$655$	−8.49928	−0.332094
$656$	−9.69579	−0.378557
$657$	−8.69502	−0.339225
$658$	6.54502	0.255152
$659$	11.7132	0.456282	0.228141	−	0.973628i	$-0.426735\pi$
$659$	11.7132	0.456282	0.228141	+	0.973628i	$0.426735\pi$
$660$	0	0
$661$	35.8654	1.39500	0.697502	−	0.716583i	$-0.254295\pi$
$661$	35.8654	1.39500	0.697502	+	0.716583i	$0.254295\pi$
$662$	6.54411	0.254344
$663$	3.40725	0.132327
$664$	−13.5603	−0.526240
$665$	−1.90940	−0.0740434
$666$	13.2059	0.511718
$667$	−37.9751	−1.47040
$668$	−1.86847	−0.0722932
$669$	−20.1175	−0.777788
$670$	−10.5029	−0.405764
$671$	0	0
$672$	0.803425	0.0309928
$673$	−33.3617	−1.28600	−0.642999	−	0.765867i	$-0.722310\pi$
$673$	−33.3617	−1.28600	−0.642999	+	0.765867i	$0.722310\pi$
$674$	16.6761	0.642341
$675$	4.30195	0.165582
$676$	−6.01382	−0.231301
$677$	−13.2733	−0.510134	−0.255067	−	0.966923i	$-0.582097\pi$
$677$	−13.2733	−0.510134	−0.255067	+	0.966923i	$0.582097\pi$
$678$	−9.60623	−0.368925
$679$	17.4713	0.670485
$680$	1.60450	0.0615296
$681$	0.146965	0.00563173
$682$	0	0
$683$	−15.3702	−0.588123	−0.294061	−	0.955787i	$-0.595007\pi$
$683$	−15.3702	−0.588123	−0.294061	+	0.955787i	$0.595007\pi$
$684$	−4.49570	−0.171897
$685$	10.0747	0.384933
$686$	−1.00000	−0.0381802
$687$	0.107957	0.00411883
$688$	−4.00169	−0.152563
$689$	−26.5578	−1.01177
$690$	3.39781	0.129352
$691$	20.7798	0.790501	0.395251	−	0.918573i	$-0.370658\pi$
$691$	20.7798	0.790501	0.395251	+	0.918573i	$0.370658\pi$
$692$	−11.7799	−0.447806
$693$	0	0
$694$	29.2816	1.11151
$695$	13.8200	0.524224
$696$	−7.21424	−0.273455
$697$	−15.5569	−0.589258
$698$	−16.7836	−0.635269
$699$	2.35411	0.0890407
$700$	−1.00000	−0.0377964
$701$	−4.18595	−0.158101	−0.0790506	−	0.996871i	$-0.525189\pi$
$701$	−4.18595	−0.158101	−0.0790506	+	0.996871i	$0.525189\pi$
$702$	−11.3706	−0.429157
$703$	−10.7094	−0.403912
$704$	0	0
$705$	5.25844	0.198044
$706$	22.9110	0.862267
$707$	10.6494	0.400511
$708$	−3.34758	−0.125810
$709$	5.48528	0.206004	0.103002	−	0.994681i	$-0.467155\pi$
$709$	5.48528	0.206004	0.103002	+	0.994681i	$0.467155\pi$
$710$	4.58489	0.172068
$711$	32.8400	1.23160
$712$	−3.41009	−0.127799
$713$	−10.4714	−0.392156
$714$	1.28909	0.0482431
$715$	0	0
$716$	−10.3705	−0.387564
$717$	−6.64762	−0.248260
$718$	8.36518	0.312186
$719$	−16.6013	−0.619122	−0.309561	−	0.950880i	$-0.600182\pi$
$719$	−16.6013	−0.619122	−0.309561	+	0.950880i	$0.600182\pi$
$720$	−2.35451	−0.0877473
$721$	6.86666	0.255728
$722$	−15.3542	−0.571424
$723$	−13.3242	−0.495532
$724$	−22.6738	−0.842664
$725$	8.97936	0.333485
$726$	0	0
$727$	−22.9499	−0.851164	−0.425582	−	0.904920i	$-0.639931\pi$
$727$	−22.9499	−0.851164	−0.425582	+	0.904920i	$0.639931\pi$
$728$	2.64314	0.0979612
$729$	1.87562	0.0694673
$730$	3.69293	0.136681
$731$	−6.42070	−0.237478
$732$	−10.6557	−0.393847
$733$	−15.9482	−0.589060	−0.294530	−	0.955642i	$-0.595163\pi$
$733$	−15.9482	−0.589060	−0.294530	+	0.955642i	$0.595163\pi$
$734$	−1.80322	−0.0665581
$735$	−0.803425	−0.0296348
$736$	−4.22916	−0.155889
$737$	0	0
$738$	22.8288	0.840340
$739$	−41.6561	−1.53234	−0.766171	−	0.642636i	$-0.777841\pi$
$739$	−41.6561	−1.53234	−0.766171	+	0.642636i	$0.777841\pi$
$740$	−5.60877	−0.206182
$741$	4.05473	0.148954
$742$	−10.0478	−0.368867
$743$	−41.9839	−1.54024	−0.770120	−	0.637899i	$-0.779804\pi$
$743$	−41.9839	−1.54024	−0.770120	+	0.637899i	$0.779804\pi$
$744$	−1.98928	−0.0729305
$745$	−18.3638	−0.672798
$746$	9.60451	0.351646
$747$	31.9277	1.16817
$748$	0	0
$749$	2.88270	0.105332
$750$	−0.803425	−0.0293369
$751$	30.9563	1.12961	0.564806	−	0.825223i	$-0.308951\pi$
$751$	30.9563	1.12961	0.564806	+	0.825223i	$0.308951\pi$
$752$	−6.54502	−0.238672
$753$	10.8853	0.396682
$754$	−23.7337	−0.864330
$755$	20.5718	0.748685
$756$	−4.30195	−0.156460
$757$	19.9821	0.726261	0.363130	−	0.931738i	$-0.381708\pi$
$757$	19.9821	0.726261	0.363130	+	0.931738i	$0.381708\pi$
$758$	−5.94046	−0.215767
$759$	0	0
$760$	1.90940	0.0692612
$761$	8.32474	0.301771	0.150886	−	0.988551i	$-0.451787\pi$
$761$	8.32474	0.301771	0.150886	+	0.988551i	$0.451787\pi$
$762$	10.7728	0.390256
$763$	18.4938	0.669521
$764$	−8.48643	−0.307028
$765$	−3.77780	−0.136587
$766$	−29.4258	−1.06320
$767$	−11.0130	−0.397656
$768$	−0.803425	−0.0289911
$769$	−38.3934	−1.38450	−0.692251	−	0.721657i	$-0.743381\pi$
$769$	−38.3934	−1.38450	−0.692251	+	0.721657i	$0.743381\pi$
$770$	0	0
$771$	−14.8011	−0.533050
$772$	−25.1578	−0.905451
$773$	28.1213	1.01145	0.505726	−	0.862694i	$-0.331225\pi$
$773$	28.1213	1.01145	0.505726	+	0.862694i	$0.331225\pi$
$774$	9.42201	0.338667
$775$	2.47600	0.0889405
$776$	−17.4713	−0.627181
$777$	−4.50623	−0.161660
$778$	−18.8617	−0.676223
$779$	−18.5131	−0.663302
$780$	2.12356	0.0760358
$781$	0	0
$782$	−6.78566	−0.242655
$783$	38.6287	1.38048
$784$	1.00000	0.0357143
$785$	−4.64886	−0.165925
$786$	6.82853	0.243566
$787$	−30.1966	−1.07639	−0.538197	−	0.842819i	$-0.680894\pi$
$787$	−30.1966	−1.07639	−0.538197	+	0.842819i	$0.680894\pi$
$788$	−13.2603	−0.472379
$789$	15.3983	0.548193
$790$	−13.9477	−0.496237
$791$	−11.9566	−0.425128
$792$	0	0
$793$	−35.0556	−1.24486
$794$	25.4542	0.903337
$795$	−8.07267	−0.286308
$796$	3.59813	0.127532
$797$	46.4224	1.64436	0.822182	−	0.569224i	$-0.192756\pi$
$797$	46.4224	1.64436	0.822182	+	0.569224i	$0.192756\pi$
$798$	1.53406	0.0543051
$799$	−10.5015	−0.371515
$800$	1.00000	0.0353553
$801$	8.02909	0.283694
$802$	14.9867	0.529198
$803$	0	0
$804$	8.43833	0.297597
$805$	4.22916	0.149058
$806$	−6.54440	−0.230517
$807$	−7.30045	−0.256988
$808$	−10.6494	−0.374644
$809$	−12.0678	−0.424282	−0.212141	−	0.977239i	$-0.568044\pi$
$809$	−12.0678	−0.424282	−0.212141	+	0.977239i	$0.568044\pi$
$810$	3.60723	0.126745
$811$	14.9538	0.525098	0.262549	−	0.964919i	$-0.415437\pi$
$811$	14.9538	0.525098	0.262549	+	0.964919i	$0.415437\pi$
$812$	−8.97936	−0.315114
$813$	−15.4048	−0.540270
$814$	0	0
$815$	4.99400	0.174932
$816$	−1.28909	−0.0451273
$817$	−7.64083	−0.267319
$818$	4.85775	0.169847
$819$	−6.22329	−0.217459
$820$	−9.69579	−0.338592
$821$	23.8592	0.832693	0.416347	−	0.909206i	$-0.363310\pi$
$821$	23.8592	0.832693	0.416347	+	0.909206i	$0.363310\pi$
$822$	−8.09424	−0.282319
$823$	−42.3899	−1.47762	−0.738809	−	0.673914i	$-0.764612\pi$
$823$	−42.3899	−1.47762	−0.738809	+	0.673914i	$0.764612\pi$
$824$	−6.86666	−0.239212
$825$	0	0
$826$	−4.16663	−0.144976
$827$	−52.9595	−1.84158	−0.920790	−	0.390058i	$-0.872455\pi$
$827$	−52.9595	−1.84158	−0.920790	+	0.390058i	$0.872455\pi$
$828$	9.95758	0.346050
$829$	44.8068	1.55620	0.778102	−	0.628137i	$-0.216182\pi$
$829$	44.8068	1.55620	0.778102	+	0.628137i	$0.216182\pi$
$830$	−13.5603	−0.470683
$831$	16.6061	0.576060
$832$	−2.64314	−0.0916343
$833$	1.60450	0.0555925
$834$	−11.1034	−0.384478
$835$	−1.86847	−0.0646610
$836$	0	0
$837$	10.6516	0.368174
$838$	−1.77493	−0.0613138
$839$	−40.6109	−1.40204	−0.701022	−	0.713140i	$-0.747272\pi$
$839$	−40.6109	−1.40204	−0.701022	+	0.713140i	$0.747272\pi$
$840$	0.803425	0.0277208
$841$	51.6288	1.78030
$842$	−16.9245	−0.583258
$843$	1.10192	0.0379521
$844$	−10.0058	−0.344414
$845$	−6.01382	−0.206882
$846$	15.4103	0.529817
$847$	0	0
$848$	10.0478	0.345043
$849$	5.17014	0.177439
$850$	1.60450	0.0550338
$851$	23.7204	0.813123
$852$	−3.68361	−0.126198
$853$	−0.116843	−0.00400061	−0.00200031	−	0.999998i	$-0.500637\pi$
$853$	−0.116843	−0.00400061	−0.00200031	+	0.999998i	$0.500637\pi$
$854$	−13.2629	−0.453846
$855$	−4.49570	−0.153750
$856$	−2.88270	−0.0985287
$857$	22.2623	0.760465	0.380233	−	0.924891i	$-0.375844\pi$
$857$	22.2623	0.760465	0.380233	+	0.924891i	$0.375844\pi$
$858$	0	0
$859$	37.0142	1.26291	0.631454	−	0.775413i	$-0.282458\pi$
$859$	37.0142	1.26291	0.631454	+	0.775413i	$0.282458\pi$
$860$	−4.00169	−0.136457
$861$	−7.78984	−0.265477
$862$	4.15621	0.141561
$863$	44.0257	1.49865	0.749326	−	0.662201i	$-0.230377\pi$
$863$	44.0257	1.49865	0.749326	+	0.662201i	$0.230377\pi$
$864$	4.30195	0.146355
$865$	−11.7799	−0.400530
$866$	22.2410	0.755780
$867$	11.5899	0.393613
$868$	−2.47600	−0.0840408
$869$	0	0
$870$	−7.21424	−0.244586
$871$	27.7607	0.940637
$872$	−18.4938	−0.626280
$873$	41.1362	1.39225
$874$	−8.07515	−0.273146
$875$	−1.00000	−0.0338062
$876$	−2.96699	−0.100245
$877$	−29.4099	−0.993100	−0.496550	−	0.868008i	$-0.665400\pi$
$877$	−29.4099	−0.993100	−0.496550	+	0.868008i	$0.665400\pi$
$878$	−21.6172	−0.729545
$879$	−3.69359	−0.124582
$880$	0	0
$881$	34.0756	1.14804	0.574019	−	0.818842i	$-0.305384\pi$
$881$	34.0756	1.14804	0.574019	+	0.818842i	$0.305384\pi$
$882$	−2.35451	−0.0792804
$883$	−18.4353	−0.620397	−0.310199	−	0.950672i	$-0.600396\pi$
$883$	−18.4353	−0.620397	−0.310199	+	0.950672i	$0.600396\pi$
$884$	−4.24090	−0.142637
$885$	−3.34758	−0.112528
$886$	−12.9462	−0.434936
$887$	2.19623	0.0737421	0.0368711	−	0.999320i	$-0.488261\pi$
$887$	2.19623	0.0737421	0.0368711	+	0.999320i	$0.488261\pi$
$888$	4.50623	0.151219
$889$	13.4085	0.449708
$890$	−3.41009	−0.114307
$891$	0	0
$892$	25.0397	0.838391
$893$	−12.4971	−0.418198
$894$	14.7540	0.493446
$895$	−10.3705	−0.346648
$896$	−1.00000	−0.0334077
$897$	−8.98088	−0.299863
$898$	13.8561	0.462384
$899$	22.2329	0.741508
$900$	−2.35451	−0.0784836
$901$	16.1217	0.537091
$902$	0	0
$903$	−3.21506	−0.106990
$904$	11.9566	0.397671
$905$	−22.6738	−0.753702
$906$	−16.5279	−0.549103
$907$	4.84606	0.160911	0.0804554	−	0.996758i	$-0.474363\pi$
$907$	4.84606	0.160911	0.0804554	+	0.996758i	$0.474363\pi$
$908$	−0.182924	−0.00607054
$909$	25.0741	0.831654
$910$	2.64314	0.0876192
$911$	59.6573	1.97653	0.988267	−	0.152736i	$-0.0488085\pi$
$911$	59.6573	1.97653	0.988267	+	0.152736i	$0.0488085\pi$
$912$	−1.53406	−0.0507978
$913$	0	0
$914$	−9.98796	−0.330372
$915$	−10.6557	−0.352267
$916$	−0.134371	−0.00443975
$917$	8.49928	0.280671
$918$	6.90246	0.227815
$919$	−16.9163	−0.558018	−0.279009	−	0.960288i	$-0.590006\pi$
$919$	−16.9163	−0.558018	−0.279009	+	0.960288i	$0.590006\pi$
$920$	−4.22916	−0.139431
$921$	19.9283	0.656660
$922$	27.8198	0.916198
$923$	−12.1185	−0.398885
$924$	0	0
$925$	−5.60877	−0.184415
$926$	−10.2727	−0.337582
$927$	16.1676	0.531014
$928$	8.97936	0.294762
$929$	23.9924	0.787164	0.393582	−	0.919290i	$-0.371236\pi$
$929$	23.9924	0.787164	0.393582	+	0.919290i	$0.371236\pi$
$930$	−1.98928	−0.0652310
$931$	1.90940	0.0625781
$932$	−2.93010	−0.0959785
$933$	−20.7302	−0.678676
$934$	9.03790	0.295729
$935$	0	0
$936$	6.22329	0.203415
$937$	30.5167	0.996937	0.498468	−	0.866908i	$-0.333896\pi$
$937$	30.5167	0.996937	0.498468	+	0.866908i	$0.333896\pi$
$938$	10.5029	0.342933
$939$	−13.2630	−0.432822
$940$	−6.54502	−0.213475
$941$	17.6656	0.575882	0.287941	−	0.957648i	$-0.407029\pi$
$941$	17.6656	0.575882	0.287941	+	0.957648i	$0.407029\pi$
$942$	3.73501	0.121693
$943$	41.0050	1.33531
$944$	4.16663	0.135612
$945$	−4.30195	−0.139942
$946$	0	0
$947$	4.02455	0.130780	0.0653902	−	0.997860i	$-0.479171\pi$
$947$	4.02455	0.130780	0.0653902	+	0.997860i	$0.479171\pi$
$948$	11.2059	0.363952
$949$	−9.76091	−0.316853
$950$	1.90940	0.0619491
$951$	−1.87266	−0.0607251
$952$	−1.60450	−0.0520020
$953$	−51.5532	−1.66997	−0.834985	−	0.550272i	$-0.814524\pi$
$953$	−51.5532	−1.66997	−0.834985	+	0.550272i	$0.814524\pi$
$954$	−23.6577	−0.765945
$955$	−8.48643	−0.274614
$956$	8.27410	0.267604
$957$	0	0
$958$	−39.4300	−1.27392
$959$	−10.0747	−0.325328
$960$	−0.803425	−0.0259304
$961$	−24.8694	−0.802240
$962$	14.8247	0.477969
$963$	6.78734	0.218719
$964$	16.5842	0.534142
$965$	−25.1578	−0.809860
$966$	−3.39781	−0.109323
$967$	25.3238	0.814359	0.407179	−	0.913348i	$-0.366512\pi$
$967$	25.3238	0.814359	0.407179	+	0.913348i	$0.366512\pi$
$968$	0	0
$969$	−2.46139	−0.0790713
$970$	−17.4713	−0.560968
$971$	−41.2627	−1.32418	−0.662091	−	0.749423i	$-0.730331\pi$
$971$	−41.2627	−1.32418	−0.662091	+	0.749423i	$0.730331\pi$
$972$	−15.8040	−0.506913
$973$	−13.8200	−0.443050
$974$	−18.9186	−0.606190
$975$	2.12356	0.0680085
$976$	13.2629	0.424534
$977$	14.0714	0.450184	0.225092	−	0.974337i	$-0.427732\pi$
$977$	14.0714	0.450184	0.225092	+	0.974337i	$0.427732\pi$
$978$	−4.01230	−0.128299
$979$	0	0
$980$	1.00000	0.0319438
$981$	43.5438	1.39025
$982$	−1.51922	−0.0484803
$983$	51.4025	1.63949	0.819743	−	0.572732i	$-0.194117\pi$
$983$	51.4025	1.63949	0.819743	+	0.572732i	$0.194117\pi$
$984$	7.78984	0.248331
$985$	−13.2603	−0.422508
$986$	14.4073	0.458823
$987$	−5.25844	−0.167378
$988$	−5.04681	−0.160560
$989$	16.9238	0.538145
$990$	0	0
$991$	45.9460	1.45952	0.729761	−	0.683702i	$-0.239631\pi$
$991$	45.9460	1.45952	0.729761	+	0.683702i	$0.239631\pi$
$992$	2.47600	0.0786130
$993$	−5.25770	−0.166848
$994$	−4.58489	−0.145424
$995$	3.59813	0.114068
$996$	10.8946	0.345210
$997$	12.2089	0.386659	0.193329	−	0.981134i	$-0.438071\pi$
$997$	12.2089	0.386659	0.193329	+	0.981134i	$0.438071\pi$
$998$	11.8172	0.374068
$999$	−24.1286	−0.763396

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.db.1.3		6
11.5	even	5		770.2.n.g.421.2	✓	12
11.9	even	5		770.2.n.g.631.2	yes	12
11.10	odd	2		8470.2.a.cv.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.g.421.2	✓	12	11.5	even	5
770.2.n.g.631.2	yes	12	11.9	even	5
8470.2.a.cv.1.3		6	11.10	odd	2
8470.2.a.db.1.3		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.803425 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.803425 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.35451 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.803425 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.803425 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.35451 q^{9} +1.00000 q^{10} -0.803425 q^{12} -2.64314 q^{13} -1.00000 q^{14} -0.803425 q^{15} +1.00000 q^{16} +1.60450 q^{17} -2.35451 q^{18} +1.90940 q^{19} +1.00000 q^{20} +0.803425 q^{21} -4.22916 q^{23} -0.803425 q^{24} +1.00000 q^{25} -2.64314 q^{26} +4.30195 q^{27} -1.00000 q^{28} +8.97936 q^{29} -0.803425 q^{30} +2.47600 q^{31} +1.00000 q^{32} +1.60450 q^{34} -1.00000 q^{35} -2.35451 q^{36} -5.60877 q^{37} +1.90940 q^{38} +2.12356 q^{39} +1.00000 q^{40} -9.69579 q^{41} +0.803425 q^{42} -4.00169 q^{43} -2.35451 q^{45} -4.22916 q^{46} -6.54502 q^{47} -0.803425 q^{48} +1.00000 q^{49} +1.00000 q^{50} -1.28909 q^{51} -2.64314 q^{52} +10.0478 q^{53} +4.30195 q^{54} -1.00000 q^{56} -1.53406 q^{57} +8.97936 q^{58} +4.16663 q^{59} -0.803425 q^{60} +13.2629 q^{61} +2.47600 q^{62} +2.35451 q^{63} +1.00000 q^{64} -2.64314 q^{65} -10.5029 q^{67} +1.60450 q^{68} +3.39781 q^{69} -1.00000 q^{70} +4.58489 q^{71} -2.35451 q^{72} +3.69293 q^{73} -5.60877 q^{74} -0.803425 q^{75} +1.90940 q^{76} +2.12356 q^{78} -13.9477 q^{79} +1.00000 q^{80} +3.60723 q^{81} -9.69579 q^{82} -13.5603 q^{83} +0.803425 q^{84} +1.60450 q^{85} -4.00169 q^{86} -7.21424 q^{87} -3.41009 q^{89} -2.35451 q^{90} +2.64314 q^{91} -4.22916 q^{92} -1.98928 q^{93} -6.54502 q^{94} +1.90940 q^{95} -0.803425 q^{96} -17.4713 q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - q^{3} + 6 q^{4} + 6 q^{5} - q^{6} - 6 q^{7} + 6 q^{8} - q^{9}+O(q^{10}) \) 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

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Database

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