LMFDB - Embedded newform 8470.2.a.cn.1.2

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:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.34292$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.14637 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.14637 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.68585 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.14637 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.14637 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.68585 q^{9} +1.00000 q^{10} +1.14637 q^{12} +1.00000 q^{14} +1.14637 q^{15} +1.00000 q^{16} -2.68585 q^{17} -1.68585 q^{18} +5.53948 q^{19} +1.00000 q^{20} +1.14637 q^{21} -1.83221 q^{23} +1.14637 q^{24} +1.00000 q^{25} -5.37169 q^{27} +1.00000 q^{28} +3.83221 q^{29} +1.14637 q^{30} +9.66442 q^{31} +1.00000 q^{32} -2.68585 q^{34} +1.00000 q^{35} -1.68585 q^{36} -1.83221 q^{37} +5.53948 q^{38} +1.00000 q^{40} -1.43910 q^{41} +1.14637 q^{42} +4.97858 q^{43} -1.68585 q^{45} -1.83221 q^{46} -0.393115 q^{47} +1.14637 q^{48} +1.00000 q^{49} +1.00000 q^{50} -3.07896 q^{51} +13.4966 q^{53} -5.37169 q^{54} +1.00000 q^{56} +6.35027 q^{57} +3.83221 q^{58} +0.685846 q^{59} +1.14637 q^{60} +2.39312 q^{61} +9.66442 q^{62} -1.68585 q^{63} +1.00000 q^{64} +3.37169 q^{67} -2.68585 q^{68} -2.10038 q^{69} +1.00000 q^{70} -0.585462 q^{71} -1.68585 q^{72} -8.97858 q^{73} -1.83221 q^{74} +1.14637 q^{75} +5.53948 q^{76} -13.2039 q^{79} +1.00000 q^{80} -1.10038 q^{81} -1.43910 q^{82} +9.37169 q^{83} +1.14637 q^{84} -2.68585 q^{85} +4.97858 q^{86} +4.39312 q^{87} +6.58546 q^{89} -1.68585 q^{90} -1.83221 q^{92} +11.0790 q^{93} -0.393115 q^{94} +5.53948 q^{95} +1.14637 q^{96} +10.1678 q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 3 q^{5} + 2 q^{6} + 3 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 3 * q^5 + 2 * q^6 + 3 * q^7 + 3 * q^8 + 7 * q^9	$ 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 3 q^{5} + 2 q^{6} + 3 q^{7} + 3 q^{8} + 7 q^{9} + 3 q^{10} + 2 q^{12} + 3 q^{14} + 2 q^{15} + 3 q^{16} + 4 q^{17} + 7 q^{18} + 6 q^{19} + 3 q^{20} + 2 q^{21} + 8 q^{23} + 2 q^{24} + 3 q^{25} + 8 q^{27} + 3 q^{28} - 2 q^{29} + 2 q^{30} + 2 q^{31} + 3 q^{32} + 4 q^{34} + 3 q^{35} + 7 q^{36} + 8 q^{37} + 6 q^{38} + 3 q^{40} + 2 q^{42} + 7 q^{45} + 8 q^{46} + 8 q^{47} + 2 q^{48} + 3 q^{49} + 3 q^{50} + 12 q^{51} + 8 q^{54} + 3 q^{56} - 20 q^{57} - 2 q^{58} - 10 q^{59} + 2 q^{60} - 2 q^{61} + 2 q^{62} + 7 q^{63} + 3 q^{64} - 14 q^{67} + 4 q^{68} + 3 q^{70} + 4 q^{71} + 7 q^{72} - 12 q^{73} + 8 q^{74} + 2 q^{75} + 6 q^{76} - 2 q^{79} + 3 q^{80} + 3 q^{81} + 4 q^{83} + 2 q^{84} + 4 q^{85} + 4 q^{87} + 14 q^{89} + 7 q^{90} + 8 q^{92} + 12 q^{93} + 8 q^{94} + 6 q^{95} + 2 q^{96} + 44 q^{97} + 3 q^{98}+O(q^{100}) $ 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 3 * q^5 + 2 * q^6 + 3 * q^7 + 3 * q^8 + 7 * q^9 + 3 * q^10 + 2 * q^12 + 3 * q^14 + 2 * q^15 + 3 * q^16 + 4 * q^17 + 7 * q^18 + 6 * q^19 + 3 * q^20 + 2 * q^21 + 8 * q^23 + 2 * q^24 + 3 * q^25 + 8 * q^27 + 3 * q^28 - 2 * q^29 + 2 * q^30 + 2 * q^31 + 3 * q^32 + 4 * q^34 + 3 * q^35 + 7 * q^36 + 8 * q^37 + 6 * q^38 + 3 * q^40 + 2 * q^42 + 7 * q^45 + 8 * q^46 + 8 * q^47 + 2 * q^48 + 3 * q^49 + 3 * q^50 + 12 * q^51 + 8 * q^54 + 3 * q^56 - 20 * q^57 - 2 * q^58 - 10 * q^59 + 2 * q^60 - 2 * q^61 + 2 * q^62 + 7 * q^63 + 3 * q^64 - 14 * q^67 + 4 * q^68 + 3 * q^70 + 4 * q^71 + 7 * q^72 - 12 * q^73 + 8 * q^74 + 2 * q^75 + 6 * q^76 - 2 * q^79 + 3 * q^80 + 3 * q^81 + 4 * q^83 + 2 * q^84 + 4 * q^85 + 4 * q^87 + 14 * q^89 + 7 * q^90 + 8 * q^92 + 12 * q^93 + 8 * q^94 + 6 * q^95 + 2 * q^96 + 44 * q^97 + 3 * 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
$3$	1.14637	0.661854	0.330927	−	0.943656i	$-0.392639\pi$
$3$	1.14637	0.661854	0.330927	+	0.943656i	$0.392639\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.14637	0.468002
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−1.68585	−0.561949
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	1.14637	0.330927
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	1.00000	0.267261
$15$	1.14637	0.295990
$16$	1.00000	0.250000
$17$	−2.68585	−0.651413	−0.325707	−	0.945471i	$-0.605602\pi$
$17$	−2.68585	−0.651413	−0.325707	+	0.945471i	$0.605602\pi$
$18$	−1.68585	−0.397358
$19$	5.53948	1.27084	0.635422	−	0.772165i	$-0.280826\pi$
$19$	5.53948	1.27084	0.635422	+	0.772165i	$0.280826\pi$
$20$	1.00000	0.223607
$21$	1.14637	0.250157
$22$	0	0
$23$	−1.83221	−0.382043	−0.191021	−	0.981586i	$-0.561180\pi$
$23$	−1.83221	−0.382043	−0.191021	+	0.981586i	$0.561180\pi$
$24$	1.14637	0.234001
$25$	1.00000	0.200000
$26$	0	0
$27$	−5.37169	−1.03378
$28$	1.00000	0.188982
$29$	3.83221	0.711624	0.355812	−	0.934558i	$-0.384204\pi$
$29$	3.83221	0.711624	0.355812	+	0.934558i	$0.384204\pi$
$30$	1.14637	0.209297
$31$	9.66442	1.73578	0.867891	−	0.496755i	$-0.165475\pi$
$31$	9.66442	1.73578	0.867891	+	0.496755i	$0.165475\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−2.68585	−0.460619
$35$	1.00000	0.169031
$36$	−1.68585	−0.280974
$37$	−1.83221	−0.301214	−0.150607	−	0.988594i	$-0.548123\pi$
$37$	−1.83221	−0.301214	−0.150607	+	0.988594i	$0.548123\pi$
$38$	5.53948	0.898622
$39$	0	0
$40$	1.00000	0.158114
$41$	−1.43910	−0.224749	−0.112375	−	0.993666i	$-0.535846\pi$
$41$	−1.43910	−0.224749	−0.112375	+	0.993666i	$0.535846\pi$
$42$	1.14637	0.176888
$43$	4.97858	0.759226	0.379613	−	0.925145i	$-0.376057\pi$
$43$	4.97858	0.759226	0.379613	+	0.925145i	$0.376057\pi$
$44$	0	0
$45$	−1.68585	−0.251311
$46$	−1.83221	−0.270145
$47$	−0.393115	−0.0573417	−0.0286709	−	0.999589i	$-0.509127\pi$
$47$	−0.393115	−0.0573417	−0.0286709	+	0.999589i	$0.509127\pi$
$48$	1.14637	0.165464
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	−3.07896	−0.431141
$52$	0	0
$53$	13.4966	1.85391	0.926953	−	0.375178i	$-0.122418\pi$
$53$	13.4966	1.85391	0.926953	+	0.375178i	$0.122418\pi$
$54$	−5.37169	−0.730995
$55$	0	0
$56$	1.00000	0.133631
$57$	6.35027	0.841114
$58$	3.83221	0.503194
$59$	0.685846	0.0892896	0.0446448	−	0.999003i	$-0.485784\pi$
$59$	0.685846	0.0892896	0.0446448	+	0.999003i	$0.485784\pi$
$60$	1.14637	0.147995
$61$	2.39312	0.306407	0.153204	−	0.988195i	$-0.451041\pi$
$61$	2.39312	0.306407	0.153204	+	0.988195i	$0.451041\pi$
$62$	9.66442	1.22738
$63$	−1.68585	−0.212397
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	3.37169	0.411918	0.205959	−	0.978561i	$-0.433969\pi$
$67$	3.37169	0.411918	0.205959	+	0.978561i	$0.433969\pi$
$68$	−2.68585	−0.325707
$69$	−2.10038	−0.252857
$70$	1.00000	0.119523
$71$	−0.585462	−0.0694816	−0.0347408	−	0.999396i	$-0.511061\pi$
$71$	−0.585462	−0.0694816	−0.0347408	+	0.999396i	$0.511061\pi$
$72$	−1.68585	−0.198679
$73$	−8.97858	−1.05086	−0.525431	−	0.850836i	$-0.676096\pi$
$73$	−8.97858	−1.05086	−0.525431	+	0.850836i	$0.676096\pi$
$74$	−1.83221	−0.212990
$75$	1.14637	0.132371
$76$	5.53948	0.635422
$77$	0	0
$78$	0	0
$79$	−13.2039	−1.48556	−0.742778	−	0.669538i	$-0.766492\pi$
$79$	−13.2039	−1.48556	−0.742778	+	0.669538i	$0.766492\pi$
$80$	1.00000	0.111803
$81$	−1.10038	−0.122265
$82$	−1.43910	−0.158922
$83$	9.37169	1.02868	0.514338	−	0.857587i	$-0.328038\pi$
$83$	9.37169	1.02868	0.514338	+	0.857587i	$0.328038\pi$
$84$	1.14637	0.125079
$85$	−2.68585	−0.291321
$86$	4.97858	0.536854
$87$	4.39312	0.470991
$88$	0	0
$89$	6.58546	0.698058	0.349029	−	0.937112i	$-0.386512\pi$
$89$	6.58546	0.698058	0.349029	+	0.937112i	$0.386512\pi$
$90$	−1.68585	−0.177704
$91$	0	0
$92$	−1.83221	−0.191021
$93$	11.0790	1.14883
$94$	−0.393115	−0.0405467
$95$	5.53948	0.568339
$96$	1.14637	0.117000
$97$	10.1678	1.03238	0.516191	−	0.856473i	$-0.327349\pi$
$97$	10.1678	1.03238	0.516191	+	0.856473i	$0.327349\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	−1.02142	−0.101635	−0.0508177	−	0.998708i	$-0.516183\pi$
$101$	−1.02142	−0.101635	−0.0508177	+	0.998708i	$0.516183\pi$
$102$	−3.07896	−0.304863
$103$	2.68585	0.264644	0.132322	−	0.991207i	$-0.457757\pi$
$103$	2.68585	0.264644	0.132322	+	0.991207i	$0.457757\pi$
$104$	0	0
$105$	1.14637	0.111874
$106$	13.4966	1.31091
$107$	0.393115	0.0380039	0.0190019	−	0.999819i	$-0.493951\pi$
$107$	0.393115	0.0380039	0.0190019	+	0.999819i	$0.493951\pi$
$108$	−5.37169	−0.516891
$109$	4.41767	0.423136	0.211568	−	0.977363i	$-0.432143\pi$
$109$	4.41767	0.423136	0.211568	+	0.977363i	$0.432143\pi$
$110$	0	0
$111$	−2.10038	−0.199360
$112$	1.00000	0.0944911
$113$	11.3717	1.06976	0.534879	−	0.844928i	$-0.320357\pi$
$113$	11.3717	1.06976	0.534879	+	0.844928i	$0.320357\pi$
$114$	6.35027	0.594757
$115$	−1.83221	−0.170855
$116$	3.83221	0.355812
$117$	0	0
$118$	0.685846	0.0631373
$119$	−2.68585	−0.246211
$120$	1.14637	0.104648
$121$	0	0
$122$	2.39312	0.216662
$123$	−1.64973	−0.148751
$124$	9.66442	0.867891
$125$	1.00000	0.0894427
$126$	−1.68585	−0.150187
$127$	16.4507	1.45976	0.729880	−	0.683576i	$-0.239576\pi$
$127$	16.4507	1.45976	0.729880	+	0.683576i	$0.239576\pi$
$128$	1.00000	0.0883883
$129$	5.70727	0.502497
$130$	0	0
$131$	−5.20390	−0.454667	−0.227334	−	0.973817i	$-0.573001\pi$
$131$	−5.20390	−0.454667	−0.227334	+	0.973817i	$0.573001\pi$
$132$	0	0
$133$	5.53948	0.480334
$134$	3.37169	0.291270
$135$	−5.37169	−0.462322
$136$	−2.68585	−0.230309
$137$	1.41454	0.120852	0.0604261	−	0.998173i	$-0.480754\pi$
$137$	1.41454	0.120852	0.0604261	+	0.998173i	$0.480754\pi$
$138$	−2.10038	−0.178797
$139$	−13.2039	−1.11994	−0.559970	−	0.828513i	$-0.689187\pi$
$139$	−13.2039	−1.11994	−0.559970	+	0.828513i	$0.689187\pi$
$140$	1.00000	0.0845154
$141$	−0.450654	−0.0379519
$142$	−0.585462	−0.0491309
$143$	0	0
$144$	−1.68585	−0.140487
$145$	3.83221	0.318248
$146$	−8.97858	−0.743072
$147$	1.14637	0.0945506
$148$	−1.83221	−0.150607
$149$	−0.417674	−0.0342172	−0.0171086	−	0.999854i	$-0.505446\pi$
$149$	−0.417674	−0.0342172	−0.0171086	+	0.999854i	$0.505446\pi$
$150$	1.14637	0.0936004
$151$	−6.91117	−0.562423	−0.281212	−	0.959646i	$-0.590736\pi$
$151$	−6.91117	−0.562423	−0.281212	+	0.959646i	$0.590736\pi$
$152$	5.53948	0.449311
$153$	4.52792	0.366061
$154$	0	0
$155$	9.66442	0.776265
$156$	0	0
$157$	14.2499	1.13726	0.568632	−	0.822592i	$-0.307473\pi$
$157$	14.2499	1.13726	0.568632	+	0.822592i	$0.307473\pi$
$158$	−13.2039	−1.05045
$159$	15.4721	1.22702
$160$	1.00000	0.0790569
$161$	−1.83221	−0.144399
$162$	−1.10038	−0.0864543
$163$	0.628308	0.0492129	0.0246064	−	0.999697i	$-0.492167\pi$
$163$	0.628308	0.0492129	0.0246064	+	0.999697i	$0.492167\pi$
$164$	−1.43910	−0.112375
$165$	0	0
$166$	9.37169	0.727384
$167$	−18.5426	−1.43487	−0.717435	−	0.696625i	$-0.754684\pi$
$167$	−18.5426	−1.43487	−0.717435	+	0.696625i	$0.754684\pi$
$168$	1.14637	0.0884440
$169$	−13.0000	−1.00000
$170$	−2.68585	−0.205995
$171$	−9.33871	−0.714149
$172$	4.97858	0.379613
$173$	10.3503	0.786916	0.393458	−	0.919343i	$-0.371279\pi$
$173$	10.3503	0.786916	0.393458	+	0.919343i	$0.371279\pi$
$174$	4.39312	0.333041
$175$	1.00000	0.0755929
$176$	0	0
$177$	0.786230	0.0590967
$178$	6.58546	0.493601
$179$	12.6430	0.944982	0.472491	−	0.881335i	$-0.343355\pi$
$179$	12.6430	0.944982	0.472491	+	0.881335i	$0.343355\pi$
$180$	−1.68585	−0.125656
$181$	−2.58546	−0.192176	−0.0960879	−	0.995373i	$-0.530633\pi$
$181$	−2.58546	−0.192176	−0.0960879	+	0.995373i	$0.530633\pi$
$182$	0	0
$183$	2.74338	0.202797
$184$	−1.83221	−0.135072
$185$	−1.83221	−0.134707
$186$	11.0790	0.812349
$187$	0	0
$188$	−0.393115	−0.0286709
$189$	−5.37169	−0.390733
$190$	5.53948	0.401876
$191$	2.87819	0.208259	0.104129	−	0.994564i	$-0.466794\pi$
$191$	2.87819	0.208259	0.104129	+	0.994564i	$0.466794\pi$
$192$	1.14637	0.0827318
$193$	−11.1793	−0.804707	−0.402353	−	0.915484i	$-0.631808\pi$
$193$	−11.1793	−0.804707	−0.402353	+	0.915484i	$0.631808\pi$
$194$	10.1678	0.730005
$195$	0	0
$196$	1.00000	0.0714286
$197$	15.6216	1.11299	0.556496	−	0.830851i	$-0.312146\pi$
$197$	15.6216	1.11299	0.556496	+	0.830851i	$0.312146\pi$
$198$	0	0
$199$	−21.7220	−1.53983	−0.769915	−	0.638147i	$-0.779701\pi$
$199$	−21.7220	−1.53983	−0.769915	+	0.638147i	$0.779701\pi$
$200$	1.00000	0.0707107
$201$	3.86519	0.272630
$202$	−1.02142	−0.0718671
$203$	3.83221	0.268969
$204$	−3.07896	−0.215570
$205$	−1.43910	−0.100511
$206$	2.68585	0.187132
$207$	3.08883	0.214688
$208$	0	0
$209$	0	0
$210$	1.14637	0.0791067
$211$	−18.5426	−1.27653	−0.638263	−	0.769818i	$-0.720347\pi$
$211$	−18.5426	−1.27653	−0.638263	+	0.769818i	$0.720347\pi$
$212$	13.4966	0.926953
$213$	−0.671153	−0.0459867
$214$	0.393115	0.0268728
$215$	4.97858	0.339536
$216$	−5.37169	−0.365497
$217$	9.66442	0.656064
$218$	4.41767	0.299203
$219$	−10.2927	−0.695518
$220$	0	0
$221$	0	0
$222$	−2.10038	−0.140969
$223$	1.31415	0.0880022	0.0440011	−	0.999031i	$-0.485989\pi$
$223$	1.31415	0.0880022	0.0440011	+	0.999031i	$0.485989\pi$
$224$	1.00000	0.0668153
$225$	−1.68585	−0.112390
$226$	11.3717	0.756434
$227$	−6.87819	−0.456522	−0.228261	−	0.973600i	$-0.573304\pi$
$227$	−6.87819	−0.456522	−0.228261	+	0.973600i	$0.573304\pi$
$228$	6.35027	0.420557
$229$	14.0575	0.928948	0.464474	−	0.885587i	$-0.346243\pi$
$229$	14.0575	0.928948	0.464474	+	0.885587i	$0.346243\pi$
$230$	−1.83221	−0.120812
$231$	0	0
$232$	3.83221	0.251597
$233$	−4.04285	−0.264856	−0.132428	−	0.991193i	$-0.542277\pi$
$233$	−4.04285	−0.264856	−0.132428	+	0.991193i	$0.542277\pi$
$234$	0	0
$235$	−0.393115	−0.0256440
$236$	0.685846	0.0446448
$237$	−15.1365	−0.983221
$238$	−2.68585	−0.174098
$239$	24.4177	1.57945	0.789724	−	0.613462i	$-0.210224\pi$
$239$	24.4177	1.57945	0.789724	+	0.613462i	$0.210224\pi$
$240$	1.14637	0.0739976
$241$	−3.73183	−0.240388	−0.120194	−	0.992750i	$-0.538352\pi$
$241$	−3.73183	−0.240388	−0.120194	+	0.992750i	$0.538352\pi$
$242$	0	0
$243$	14.8536	0.952861
$244$	2.39312	0.153204
$245$	1.00000	0.0638877
$246$	−1.64973	−0.105183
$247$	0	0
$248$	9.66442	0.613691
$249$	10.7434	0.680834
$250$	1.00000	0.0632456
$251$	23.5640	1.48735	0.743674	−	0.668542i	$-0.233081\pi$
$251$	23.5640	1.48735	0.743674	+	0.668542i	$0.233081\pi$
$252$	−1.68585	−0.106198
$253$	0	0
$254$	16.4507	1.03221
$255$	−3.07896	−0.192812
$256$	1.00000	0.0625000
$257$	−14.0821	−0.878417	−0.439209	−	0.898385i	$-0.644741\pi$
$257$	−14.0821	−0.878417	−0.439209	+	0.898385i	$0.644741\pi$
$258$	5.70727	0.355319
$259$	−1.83221	−0.113848
$260$	0	0
$261$	−6.46052	−0.399896
$262$	−5.20390	−0.321498
$263$	15.6644	0.965910	0.482955	−	0.875645i	$-0.339564\pi$
$263$	15.6644	0.965910	0.482955	+	0.875645i	$0.339564\pi$
$264$	0	0
$265$	13.4966	0.829092
$266$	5.53948	0.339647
$267$	7.54935	0.462012
$268$	3.37169	0.205959
$269$	22.0575	1.34487	0.672436	−	0.740155i	$-0.265248\pi$
$269$	22.0575	1.34487	0.672436	+	0.740155i	$0.265248\pi$
$270$	−5.37169	−0.326911
$271$	−13.0361	−0.791888	−0.395944	−	0.918275i	$-0.629583\pi$
$271$	−13.0361	−0.791888	−0.395944	+	0.918275i	$0.629583\pi$
$272$	−2.68585	−0.162853
$273$	0	0
$274$	1.41454	0.0854554
$275$	0	0
$276$	−2.10038	−0.126428
$277$	−18.2499	−1.09653	−0.548265	−	0.836305i	$-0.684711\pi$
$277$	−18.2499	−1.09653	−0.548265	+	0.836305i	$0.684711\pi$
$278$	−13.2039	−0.791918
$279$	−16.2927	−0.975420
$280$	1.00000	0.0597614
$281$	−18.4078	−1.09812	−0.549059	−	0.835784i	$-0.685014\pi$
$281$	−18.4078	−1.09812	−0.549059	+	0.835784i	$0.685014\pi$
$282$	−0.450654	−0.0268360
$283$	−9.62158	−0.571943	−0.285972	−	0.958238i	$-0.592316\pi$
$283$	−9.62158	−0.571943	−0.285972	+	0.958238i	$0.592316\pi$
$284$	−0.585462	−0.0347408
$285$	6.35027	0.376157
$286$	0	0
$287$	−1.43910	−0.0849472
$288$	−1.68585	−0.0993394
$289$	−9.78623	−0.575661
$290$	3.83221	0.225035
$291$	11.6560	0.683287
$292$	−8.97858	−0.525431
$293$	−31.9143	−1.86445	−0.932227	−	0.361874i	$-0.882137\pi$
$293$	−31.9143	−1.86445	−0.932227	+	0.361874i	$0.882137\pi$
$294$	1.14637	0.0668574
$295$	0.685846	0.0399315
$296$	−1.83221	−0.106495
$297$	0	0
$298$	−0.417674	−0.0241952
$299$	0	0
$300$	1.14637	0.0661854
$301$	4.97858	0.286960
$302$	−6.91117	−0.397693
$303$	−1.17092	−0.0672678
$304$	5.53948	0.317711
$305$	2.39312	0.137029
$306$	4.52792	0.258844
$307$	−9.03612	−0.515718	−0.257859	−	0.966183i	$-0.583017\pi$
$307$	−9.03612	−0.515718	−0.257859	+	0.966183i	$0.583017\pi$
$308$	0	0
$309$	3.07896	0.175156
$310$	9.66442	0.548902
$311$	−13.6644	−0.774838	−0.387419	−	0.921904i	$-0.626633\pi$
$311$	−13.6644	−0.774838	−0.387419	+	0.921904i	$0.626633\pi$
$312$	0	0
$313$	−4.71040	−0.266248	−0.133124	−	0.991099i	$-0.542501\pi$
$313$	−4.71040	−0.266248	−0.133124	+	0.991099i	$0.542501\pi$
$314$	14.2499	0.804168
$315$	−1.68585	−0.0949867
$316$	−13.2039	−0.742778
$317$	20.9112	1.17449	0.587244	−	0.809410i	$-0.300213\pi$
$317$	20.9112	1.17449	0.587244	+	0.809410i	$0.300213\pi$
$318$	15.4721	0.867631
$319$	0	0
$320$	1.00000	0.0559017
$321$	0.450654	0.0251530
$322$	−1.83221	−0.102105
$323$	−14.8782	−0.827845
$324$	−1.10038	−0.0611325
$325$	0	0
$326$	0.628308	0.0347987
$327$	5.06427	0.280055
$328$	−1.43910	−0.0794608
$329$	−0.393115	−0.0216731
$330$	0	0
$331$	−15.4721	−0.850422	−0.425211	−	0.905094i	$-0.639800\pi$
$331$	−15.4721	−0.850422	−0.425211	+	0.905094i	$0.639800\pi$
$332$	9.37169	0.514338
$333$	3.08883	0.169267
$334$	−18.5426	−1.01461
$335$	3.37169	0.184215
$336$	1.14637	0.0625394
$337$	−35.9572	−1.95871	−0.979356	−	0.202145i	$-0.935209\pi$
$337$	−35.9572	−1.95871	−0.979356	+	0.202145i	$0.935209\pi$
$338$	−13.0000	−0.707107
$339$	13.0361	0.708025
$340$	−2.68585	−0.145660
$341$	0	0
$342$	−9.33871	−0.504980
$343$	1.00000	0.0539949
$344$	4.97858	0.268427
$345$	−2.10038	−0.113081
$346$	10.3503	0.556434
$347$	−2.23519	−0.119991	−0.0599957	−	0.998199i	$-0.519109\pi$
$347$	−2.23519	−0.119991	−0.0599957	+	0.998199i	$0.519109\pi$
$348$	4.39312	0.235496
$349$	12.0147	0.643132	0.321566	−	0.946887i	$-0.395791\pi$
$349$	12.0147	0.643132	0.321566	+	0.946887i	$0.395791\pi$
$350$	1.00000	0.0534522
$351$	0	0
$352$	0	0
$353$	31.2039	1.66082	0.830408	−	0.557156i	$-0.188107\pi$
$353$	31.2039	1.66082	0.830408	+	0.557156i	$0.188107\pi$
$354$	0.786230	0.0417877
$355$	−0.585462	−0.0310731
$356$	6.58546	0.349029
$357$	−3.07896	−0.162956
$358$	12.6430	0.668203
$359$	20.8683	1.10139	0.550694	−	0.834707i	$-0.314363\pi$
$359$	20.8683	1.10139	0.550694	+	0.834707i	$0.314363\pi$
$360$	−1.68585	−0.0888519
$361$	11.6858	0.615045
$362$	−2.58546	−0.135889
$363$	0	0
$364$	0	0
$365$	−8.97858	−0.469960
$366$	2.74338	0.143399
$367$	−33.2285	−1.73451	−0.867256	−	0.497863i	$-0.834118\pi$
$367$	−33.2285	−1.73451	−0.867256	+	0.497863i	$0.834118\pi$
$368$	−1.83221	−0.0955106
$369$	2.42610	0.126297
$370$	−1.83221	−0.0952521
$371$	13.4966	0.700710
$372$	11.0790	0.574417
$373$	−9.66442	−0.500405	−0.250202	−	0.968194i	$-0.580497\pi$
$373$	−9.66442	−0.500405	−0.250202	+	0.968194i	$0.580497\pi$
$374$	0	0
$375$	1.14637	0.0591981
$376$	−0.393115	−0.0202734
$377$	0	0
$378$	−5.37169	−0.276290
$379$	−3.21377	−0.165080	−0.0825401	−	0.996588i	$-0.526303\pi$
$379$	−3.21377	−0.165080	−0.0825401	+	0.996588i	$0.526303\pi$
$380$	5.53948	0.284169
$381$	18.8585	0.966148
$382$	2.87819	0.147261
$383$	−24.6430	−1.25920	−0.629599	−	0.776920i	$-0.716781\pi$
$383$	−24.6430	−1.25920	−0.629599	+	0.776920i	$0.716781\pi$
$384$	1.14637	0.0585002
$385$	0	0
$386$	−11.1793	−0.569014
$387$	−8.39312	−0.426646
$388$	10.1678	0.516191
$389$	−6.92104	−0.350911	−0.175455	−	0.984487i	$-0.556140\pi$
$389$	−6.92104	−0.350911	−0.175455	+	0.984487i	$0.556140\pi$
$390$	0	0
$391$	4.92104	0.248868
$392$	1.00000	0.0505076
$393$	−5.96558	−0.300923
$394$	15.6216	0.787004
$395$	−13.2039	−0.664361
$396$	0	0
$397$	6.92104	0.347357	0.173678	−	0.984802i	$-0.444435\pi$
$397$	6.92104	0.347357	0.173678	+	0.984802i	$0.444435\pi$
$398$	−21.7220	−1.08882
$399$	6.35027	0.317911
$400$	1.00000	0.0500000
$401$	18.6430	0.930987	0.465494	−	0.885051i	$-0.345877\pi$
$401$	18.6430	0.930987	0.465494	+	0.885051i	$0.345877\pi$
$402$	3.86519	0.192778
$403$	0	0
$404$	−1.02142	−0.0508177
$405$	−1.10038	−0.0546785
$406$	3.83221	0.190189
$407$	0	0
$408$	−3.07896	−0.152431
$409$	33.6890	1.66581	0.832906	−	0.553414i	$-0.186675\pi$
$409$	33.6890	1.66581	0.832906	+	0.553414i	$0.186675\pi$
$410$	−1.43910	−0.0710719
$411$	1.62158	0.0799865
$412$	2.68585	0.132322
$413$	0.685846	0.0337483
$414$	3.08883	0.151808
$415$	9.37169	0.460038
$416$	0	0
$417$	−15.1365	−0.741238
$418$	0	0
$419$	21.0214	1.02696	0.513482	−	0.858100i	$-0.328355\pi$
$419$	21.0214	1.02696	0.513482	+	0.858100i	$0.328355\pi$
$420$	1.14637	0.0559369
$421$	−10.8353	−0.528083	−0.264041	−	0.964511i	$-0.585056\pi$
$421$	−10.8353	−0.528083	−0.264041	+	0.964511i	$0.585056\pi$
$422$	−18.5426	−0.902640
$423$	0.662732	0.0322231
$424$	13.4966	0.655455
$425$	−2.68585	−0.130283
$426$	−0.671153	−0.0325175
$427$	2.39312	0.115811
$428$	0.393115	0.0190019
$429$	0	0
$430$	4.97858	0.240088
$431$	−32.6676	−1.57354	−0.786770	−	0.617246i	$-0.788248\pi$
$431$	−32.6676	−1.57354	−0.786770	+	0.617246i	$0.788248\pi$
$432$	−5.37169	−0.258446
$433$	−16.3748	−0.786924	−0.393462	−	0.919341i	$-0.628723\pi$
$433$	−16.3748	−0.786924	−0.393462	+	0.919341i	$0.628723\pi$
$434$	9.66442	0.463907
$435$	4.39312	0.210634
$436$	4.41767	0.211568
$437$	−10.1495	−0.485516
$438$	−10.2927	−0.491806
$439$	0.450654	0.0215085	0.0107543	−	0.999942i	$-0.496577\pi$
$439$	0.450654	0.0215085	0.0107543	+	0.999942i	$0.496577\pi$
$440$	0	0
$441$	−1.68585	−0.0802784
$442$	0	0
$443$	10.7862	0.512469	0.256235	−	0.966615i	$-0.417518\pi$
$443$	10.7862	0.512469	0.256235	+	0.966615i	$0.417518\pi$
$444$	−2.10038	−0.0996798
$445$	6.58546	0.312181
$446$	1.31415	0.0622270
$447$	−0.478807	−0.0226468
$448$	1.00000	0.0472456
$449$	−19.8139	−0.935077	−0.467538	−	0.883973i	$-0.654859\pi$
$449$	−19.8139	−0.935077	−0.467538	+	0.883973i	$0.654859\pi$
$450$	−1.68585	−0.0794716
$451$	0	0
$452$	11.3717	0.534879
$453$	−7.92273	−0.372242
$454$	−6.87819	−0.322810
$455$	0	0
$456$	6.35027	0.297379
$457$	23.9572	1.12067	0.560334	−	0.828267i	$-0.310673\pi$
$457$	23.9572	1.12067	0.560334	+	0.828267i	$0.310673\pi$
$458$	14.0575	0.656866
$459$	14.4275	0.673420
$460$	−1.83221	−0.0854273
$461$	26.6430	1.24089	0.620444	−	0.784251i	$-0.286952\pi$
$461$	26.6430	1.24089	0.620444	+	0.784251i	$0.286952\pi$
$462$	0	0
$463$	2.75325	0.127954	0.0639772	−	0.997951i	$-0.479622\pi$
$463$	2.75325	0.127954	0.0639772	+	0.997951i	$0.479622\pi$
$464$	3.83221	0.177906
$465$	11.0790	0.513775
$466$	−4.04285	−0.187281
$467$	−20.1396	−0.931951	−0.465976	−	0.884798i	$-0.654297\pi$
$467$	−20.1396	−0.931951	−0.465976	+	0.884798i	$0.654297\pi$
$468$	0	0
$469$	3.37169	0.155690
$470$	−0.393115	−0.0181331
$471$	16.3356	0.752704
$472$	0.685846	0.0315686
$473$	0	0
$474$	−15.1365	−0.695242
$475$	5.53948	0.254169
$476$	−2.68585	−0.123106
$477$	−22.7533	−1.04180
$478$	24.4177	1.11684
$479$	−4.58546	−0.209515	−0.104758	−	0.994498i	$-0.533407\pi$
$479$	−4.58546	−0.209515	−0.104758	+	0.994498i	$0.533407\pi$
$480$	1.14637	0.0523242
$481$	0	0
$482$	−3.73183	−0.169980
$483$	−2.10038	−0.0955708
$484$	0	0
$485$	10.1678	0.461695
$486$	14.8536	0.673775
$487$	33.1611	1.50267	0.751335	−	0.659920i	$-0.229410\pi$
$487$	33.1611	1.50267	0.751335	+	0.659920i	$0.229410\pi$
$488$	2.39312	0.108331
$489$	0.720270	0.0325717
$490$	1.00000	0.0451754
$491$	23.9143	1.07924	0.539619	−	0.841909i	$-0.318568\pi$
$491$	23.9143	1.07924	0.539619	+	0.841909i	$0.318568\pi$
$492$	−1.64973	−0.0743756
$493$	−10.2927	−0.463561
$494$	0	0
$495$	0	0
$496$	9.66442	0.433945
$497$	−0.585462	−0.0262616
$498$	10.7434	0.481423
$499$	−39.3864	−1.76318	−0.881588	−	0.472019i	$-0.843525\pi$
$499$	−39.3864	−1.76318	−0.881588	+	0.472019i	$0.843525\pi$
$500$	1.00000	0.0447214
$501$	−21.2566	−0.949676
$502$	23.5640	1.05171
$503$	−23.5296	−1.04913	−0.524567	−	0.851369i	$-0.675773\pi$
$503$	−23.5296	−1.04913	−0.524567	+	0.851369i	$0.675773\pi$
$504$	−1.68585	−0.0750936
$505$	−1.02142	−0.0454527
$506$	0	0
$507$	−14.9028	−0.661854
$508$	16.4507	0.729880
$509$	−20.5426	−0.910535	−0.455268	−	0.890355i	$-0.650456\pi$
$509$	−20.5426	−0.910535	−0.455268	+	0.890355i	$0.650456\pi$
$510$	−3.07896	−0.136339
$511$	−8.97858	−0.397189
$512$	1.00000	0.0441942
$513$	−29.7564	−1.31378
$514$	−14.0821	−0.621135
$515$	2.68585	0.118353
$516$	5.70727	0.251249
$517$	0	0
$518$	−1.83221	−0.0805028
$519$	11.8652	0.520824
$520$	0	0
$521$	−6.53635	−0.286362	−0.143181	−	0.989696i	$-0.545733\pi$
$521$	−6.53635	−0.286362	−0.143181	+	0.989696i	$0.545733\pi$
$522$	−6.46052	−0.282769
$523$	−37.7367	−1.65011	−0.825054	−	0.565053i	$-0.808856\pi$
$523$	−37.7367	−1.65011	−0.825054	+	0.565053i	$0.808856\pi$
$524$	−5.20390	−0.227334
$525$	1.14637	0.0500315
$526$	15.6644	0.683001
$527$	−25.9572	−1.13071
$528$	0	0
$529$	−19.6430	−0.854043
$530$	13.4966	0.586256
$531$	−1.15623	−0.0501762
$532$	5.53948	0.240167
$533$	0	0
$534$	7.54935	0.326692
$535$	0.393115	0.0169959
$536$	3.37169	0.145635
$537$	14.4935	0.625441
$538$	22.0575	0.950968
$539$	0	0
$540$	−5.37169	−0.231161
$541$	−2.99686	−0.128845	−0.0644226	−	0.997923i	$-0.520521\pi$
$541$	−2.99686	−0.128845	−0.0644226	+	0.997923i	$0.520521\pi$
$542$	−13.0361	−0.559949
$543$	−2.96388	−0.127192
$544$	−2.68585	−0.115155
$545$	4.41767	0.189232
$546$	0	0
$547$	0.0856914	0.00366390	0.00183195	−	0.999998i	$-0.499417\pi$
$547$	0.0856914	0.00366390	0.00183195	+	0.999998i	$0.499417\pi$
$548$	1.41454	0.0604261
$549$	−4.03442	−0.172185
$550$	0	0
$551$	21.2285	0.904363
$552$	−2.10038	−0.0893983
$553$	−13.2039	−0.561487
$554$	−18.2499	−0.775363
$555$	−2.10038	−0.0891563
$556$	−13.2039	−0.559970
$557$	−27.2860	−1.15614	−0.578072	−	0.815985i	$-0.696195\pi$
$557$	−27.2860	−1.15614	−0.578072	+	0.815985i	$0.696195\pi$
$558$	−16.2927	−0.689726
$559$	0	0
$560$	1.00000	0.0422577
$561$	0	0
$562$	−18.4078	−0.776487
$563$	29.0852	1.22580	0.612898	−	0.790162i	$-0.290004\pi$
$563$	29.0852	1.22580	0.612898	+	0.790162i	$0.290004\pi$
$564$	−0.450654	−0.0189759
$565$	11.3717	0.478411
$566$	−9.62158	−0.404425
$567$	−1.10038	−0.0462118
$568$	−0.585462	−0.0245654
$569$	−23.9143	−1.00254	−0.501270	−	0.865291i	$-0.667134\pi$
$569$	−23.9143	−1.00254	−0.501270	+	0.865291i	$0.667134\pi$
$570$	6.35027	0.265984
$571$	−15.2797	−0.639437	−0.319718	−	0.947513i	$-0.603588\pi$
$571$	−15.2797	−0.639437	−0.319718	+	0.947513i	$0.603588\pi$
$572$	0	0
$573$	3.29946	0.137837
$574$	−1.43910	−0.0600667
$575$	−1.83221	−0.0764085
$576$	−1.68585	−0.0702436
$577$	−9.58233	−0.398917	−0.199459	−	0.979906i	$-0.563918\pi$
$577$	−9.58233	−0.398917	−0.199459	+	0.979906i	$0.563918\pi$
$578$	−9.78623	−0.407054
$579$	−12.8156	−0.532599
$580$	3.83221	0.159124
$581$	9.37169	0.388803
$582$	11.6560	0.483157
$583$	0	0
$584$	−8.97858	−0.371536
$585$	0	0
$586$	−31.9143	−1.31837
$587$	0.176210	0.00727296	0.00363648	−	0.999993i	$-0.498842\pi$
$587$	0.176210	0.00727296	0.00363648	+	0.999993i	$0.498842\pi$
$588$	1.14637	0.0472753
$589$	53.5359	2.20591
$590$	0.685846	0.0282358
$591$	17.9080	0.736638
$592$	−1.83221	−0.0753034
$593$	0.863500	0.0354597	0.0177299	−	0.999843i	$-0.494356\pi$
$593$	0.863500	0.0354597	0.0177299	+	0.999843i	$0.494356\pi$
$594$	0	0
$595$	−2.68585	−0.110109
$596$	−0.417674	−0.0171086
$597$	−24.9013	−1.01914
$598$	0	0
$599$	23.4145	0.956692	0.478346	−	0.878171i	$-0.341236\pi$
$599$	23.4145	0.956692	0.478346	+	0.878171i	$0.341236\pi$
$600$	1.14637	0.0468002
$601$	−13.1892	−0.537999	−0.269000	−	0.963140i	$-0.586693\pi$
$601$	−13.1892	−0.537999	−0.269000	+	0.963140i	$0.586693\pi$
$602$	4.97858	0.202912
$603$	−5.68415	−0.231477
$604$	−6.91117	−0.281212
$605$	0	0
$606$	−1.17092	−0.0475655
$607$	11.8077	0.479258	0.239629	−	0.970865i	$-0.422974\pi$
$607$	11.8077	0.479258	0.239629	+	0.970865i	$0.422974\pi$
$608$	5.53948	0.224656
$609$	4.39312	0.178018
$610$	2.39312	0.0968944
$611$	0	0
$612$	4.52792	0.183030
$613$	39.4868	1.59486	0.797428	−	0.603414i	$-0.206193\pi$
$613$	39.4868	1.59486	0.797428	+	0.603414i	$0.206193\pi$
$614$	−9.03612	−0.364668
$615$	−1.64973	−0.0665236
$616$	0	0
$617$	−38.3650	−1.54452	−0.772258	−	0.635310i	$-0.780873\pi$
$617$	−38.3650	−1.54452	−0.772258	+	0.635310i	$0.780873\pi$
$618$	3.07896	0.123854
$619$	−5.52119	−0.221915	−0.110958	−	0.993825i	$-0.535392\pi$
$619$	−5.52119	−0.221915	−0.110958	+	0.993825i	$0.535392\pi$
$620$	9.66442	0.388133
$621$	9.84208	0.394949
$622$	−13.6644	−0.547893
$623$	6.58546	0.263841
$624$	0	0
$625$	1.00000	0.0400000
$626$	−4.71040	−0.188266
$627$	0	0
$628$	14.2499	0.568632
$629$	4.92104	0.196215
$630$	−1.68585	−0.0671657
$631$	−46.2730	−1.84210	−0.921050	−	0.389445i	$-0.872667\pi$
$631$	−46.2730	−1.84210	−0.921050	+	0.389445i	$0.872667\pi$
$632$	−13.2039	−0.525223
$633$	−21.2566	−0.844875
$634$	20.9112	0.830489
$635$	16.4507	0.652824
$636$	15.4721	0.613508
$637$	0	0
$638$	0	0
$639$	0.986999	0.0390451
$640$	1.00000	0.0395285
$641$	−39.0852	−1.54377	−0.771887	−	0.635760i	$-0.780687\pi$
$641$	−39.0852	−1.54377	−0.771887	+	0.635760i	$0.780687\pi$
$642$	0.450654	0.0177859
$643$	40.3404	1.59087	0.795435	−	0.606039i	$-0.207242\pi$
$643$	40.3404	1.59087	0.795435	+	0.606039i	$0.207242\pi$
$644$	−1.83221	−0.0721993
$645$	5.70727	0.224723
$646$	−14.8782	−0.585375
$647$	−6.48508	−0.254955	−0.127477	−	0.991841i	$-0.540688\pi$
$647$	−6.48508	−0.254955	−0.127477	+	0.991841i	$0.540688\pi$
$648$	−1.10038	−0.0432272
$649$	0	0
$650$	0	0
$651$	11.0790	0.434219
$652$	0.628308	0.0246064
$653$	18.7533	0.733871	0.366936	−	0.930246i	$-0.380407\pi$
$653$	18.7533	0.733871	0.366936	+	0.930246i	$0.380407\pi$
$654$	5.06427	0.198029
$655$	−5.20390	−0.203333
$656$	−1.43910	−0.0561873
$657$	15.1365	0.590531
$658$	−0.393115	−0.0153252
$659$	−6.37842	−0.248468	−0.124234	−	0.992253i	$-0.539647\pi$
$659$	−6.37842	−0.248468	−0.124234	+	0.992253i	$0.539647\pi$
$660$	0	0
$661$	30.6148	1.19078	0.595390	−	0.803437i	$-0.296998\pi$
$661$	30.6148	1.19078	0.595390	+	0.803437i	$0.296998\pi$
$662$	−15.4721	−0.601339
$663$	0	0
$664$	9.37169	0.363692
$665$	5.53948	0.214812
$666$	3.08883	0.119690
$667$	−7.02142	−0.271871
$668$	−18.5426	−0.717435
$669$	1.50650	0.0582447
$670$	3.37169	0.130260
$671$	0	0
$672$	1.14637	0.0442220
$673$	−5.91431	−0.227980	−0.113990	−	0.993482i	$-0.536363\pi$
$673$	−5.91431	−0.227980	−0.113990	+	0.993482i	$0.536363\pi$
$674$	−35.9572	−1.38502
$675$	−5.37169	−0.206757
$676$	−13.0000	−0.500000
$677$	−29.9656	−1.15167	−0.575835	−	0.817566i	$-0.695323\pi$
$677$	−29.9656	−1.15167	−0.575835	+	0.817566i	$0.695323\pi$
$678$	13.0361	0.500649
$679$	10.1678	0.390204
$680$	−2.68585	−0.102997
$681$	−7.88492	−0.302151
$682$	0	0
$683$	33.0790	1.26573	0.632866	−	0.774262i	$-0.281879\pi$
$683$	33.0790	1.26573	0.632866	+	0.774262i	$0.281879\pi$
$684$	−9.33871	−0.357075
$685$	1.41454	0.0540467
$686$	1.00000	0.0381802
$687$	16.1151	0.614829
$688$	4.97858	0.189806
$689$	0	0
$690$	−2.10038	−0.0799603
$691$	35.9656	1.36819	0.684097	−	0.729391i	$-0.260196\pi$
$691$	35.9656	1.36819	0.684097	+	0.729391i	$0.260196\pi$
$692$	10.3503	0.393458
$693$	0	0
$694$	−2.23519	−0.0848467
$695$	−13.2039	−0.500853
$696$	4.39312	0.166521
$697$	3.86519	0.146405
$698$	12.0147	0.454763
$699$	−4.63458	−0.175296
$700$	1.00000	0.0377964
$701$	−4.95402	−0.187111	−0.0935554	−	0.995614i	$-0.529823\pi$
$701$	−4.95402	−0.187111	−0.0935554	+	0.995614i	$0.529823\pi$
$702$	0	0
$703$	−10.1495	−0.382796
$704$	0	0
$705$	−0.450654	−0.0169726
$706$	31.2039	1.17437
$707$	−1.02142	−0.0384146
$708$	0.786230	0.0295483
$709$	−23.5725	−0.885282	−0.442641	−	0.896699i	$-0.645958\pi$
$709$	−23.5725	−0.885282	−0.442641	+	0.896699i	$0.645958\pi$
$710$	−0.585462	−0.0219720
$711$	22.2598	0.834806
$712$	6.58546	0.246801
$713$	−17.7073	−0.663142
$714$	−3.07896	−0.115227
$715$	0	0
$716$	12.6430	0.472491
$717$	27.9916	1.04536
$718$	20.8683	0.778799
$719$	43.2944	1.61461	0.807305	−	0.590135i	$-0.200925\pi$
$719$	43.2944	1.61461	0.807305	+	0.590135i	$0.200925\pi$
$720$	−1.68585	−0.0628278
$721$	2.68585	0.100026
$722$	11.6858	0.434902
$723$	−4.27804	−0.159102
$724$	−2.58546	−0.0960879
$725$	3.83221	0.142325
$726$	0	0
$727$	39.8370	1.47747	0.738737	−	0.673994i	$-0.235423\pi$
$727$	39.8370	1.47747	0.738737	+	0.673994i	$0.235423\pi$
$728$	0	0
$729$	20.3288	0.752920
$730$	−8.97858	−0.332312
$731$	−13.3717	−0.494570
$732$	2.74338	0.101398
$733$	13.6791	0.505250	0.252625	−	0.967564i	$-0.418706\pi$
$733$	13.6791	0.505250	0.252625	+	0.967564i	$0.418706\pi$
$734$	−33.2285	−1.22648
$735$	1.14637	0.0422843
$736$	−1.83221	−0.0675362
$737$	0	0
$738$	2.42610	0.0893058
$739$	1.25662	0.0462253	0.0231127	−	0.999733i	$-0.492642\pi$
$739$	1.25662	0.0462253	0.0231127	+	0.999733i	$0.492642\pi$
$740$	−1.83221	−0.0673534
$741$	0	0
$742$	13.4966	0.495477
$743$	−1.90804	−0.0699991	−0.0349996	−	0.999387i	$-0.511143\pi$
$743$	−1.90804	−0.0699991	−0.0349996	+	0.999387i	$0.511143\pi$
$744$	11.0790	0.406174
$745$	−0.417674	−0.0153024
$746$	−9.66442	−0.353840
$747$	−15.7992	−0.578064
$748$	0	0
$749$	0.393115	0.0143641
$750$	1.14637	0.0418593
$751$	−41.0852	−1.49922	−0.749611	−	0.661879i	$-0.769759\pi$
$751$	−41.0852	−1.49922	−0.749611	+	0.661879i	$0.769759\pi$
$752$	−0.393115	−0.0143354
$753$	27.0130	0.984408
$754$	0	0
$755$	−6.91117	−0.251523
$756$	−5.37169	−0.195367
$757$	4.07583	0.148138	0.0740692	−	0.997253i	$-0.476401\pi$
$757$	4.07583	0.148138	0.0740692	+	0.997253i	$0.476401\pi$
$758$	−3.21377	−0.116729
$759$	0	0
$760$	5.53948	0.200938
$761$	5.10352	0.185002	0.0925012	−	0.995713i	$-0.470514\pi$
$761$	5.10352	0.185002	0.0925012	+	0.995713i	$0.470514\pi$
$762$	18.8585	0.683170
$763$	4.41767	0.159931
$764$	2.87819	0.104129
$765$	4.52792	0.163707
$766$	−24.6430	−0.890388
$767$	0	0
$768$	1.14637	0.0413659
$769$	−21.8406	−0.787593	−0.393797	−	0.919198i	$-0.628839\pi$
$769$	−21.8406	−0.787593	−0.393797	+	0.919198i	$0.628839\pi$
$770$	0	0
$771$	−16.1432	−0.581384
$772$	−11.1793	−0.402353
$773$	34.0294	1.22395	0.611976	−	0.790876i	$-0.290375\pi$
$773$	34.0294	1.22395	0.611976	+	0.790876i	$0.290375\pi$
$774$	−8.39312	−0.301684
$775$	9.66442	0.347156
$776$	10.1678	0.365002
$777$	−2.10038	−0.0753509
$778$	−6.92104	−0.248131
$779$	−7.97185	−0.285621
$780$	0	0
$781$	0	0
$782$	4.92104	0.175976
$783$	−20.5855	−0.735664
$784$	1.00000	0.0357143
$785$	14.2499	0.508600
$786$	−5.96558	−0.212785
$787$	−16.4998	−0.588153	−0.294077	−	0.955782i	$-0.595012\pi$
$787$	−16.4998	−0.588153	−0.294077	+	0.955782i	$0.595012\pi$
$788$	15.6216	0.556496
$789$	17.9572	0.639292
$790$	−13.2039	−0.469774
$791$	11.3717	0.404331
$792$	0	0
$793$	0	0
$794$	6.92104	0.245618
$795$	15.4721	0.548738
$796$	−21.7220	−0.769915
$797$	32.3221	1.14491	0.572454	−	0.819937i	$-0.305991\pi$
$797$	32.3221	1.14491	0.572454	+	0.819937i	$0.305991\pi$
$798$	6.35027	0.224797
$799$	1.05585	0.0373532
$800$	1.00000	0.0353553
$801$	−11.1021	−0.392273
$802$	18.6430	0.658307
$803$	0	0
$804$	3.86519	0.136315
$805$	−1.83221	−0.0645770
$806$	0	0
$807$	25.2860	0.890109
$808$	−1.02142	−0.0359335
$809$	−24.6514	−0.866698	−0.433349	−	0.901226i	$-0.642668\pi$
$809$	−24.6514	−0.866698	−0.433349	+	0.901226i	$0.642668\pi$
$810$	−1.10038	−0.0386636
$811$	−6.66129	−0.233909	−0.116955	−	0.993137i	$-0.537313\pi$
$811$	−6.66129	−0.233909	−0.116955	+	0.993137i	$0.537313\pi$
$812$	3.83221	0.134484
$813$	−14.9442	−0.524114
$814$	0	0
$815$	0.628308	0.0220087
$816$	−3.07896	−0.107785
$817$	27.5787	0.964858
$818$	33.6890	1.17791
$819$	0	0
$820$	−1.43910	−0.0502554
$821$	−42.2400	−1.47419	−0.737093	−	0.675791i	$-0.763802\pi$
$821$	−42.2400	−1.47419	−0.737093	+	0.675791i	$0.763802\pi$
$822$	1.62158	0.0565590
$823$	−26.2829	−0.916163	−0.458082	−	0.888910i	$-0.651463\pi$
$823$	−26.2829	−0.916163	−0.458082	+	0.888910i	$0.651463\pi$
$824$	2.68585	0.0935659
$825$	0	0
$826$	0.685846	0.0238636
$827$	0.986999	0.0343213	0.0171607	−	0.999853i	$-0.494537\pi$
$827$	0.986999	0.0343213	0.0171607	+	0.999853i	$0.494537\pi$
$828$	3.08883	0.107344
$829$	−1.07054	−0.0371814	−0.0185907	−	0.999827i	$-0.505918\pi$
$829$	−1.07054	−0.0371814	−0.0185907	+	0.999827i	$0.505918\pi$
$830$	9.37169	0.325296
$831$	−20.9210	−0.725743
$832$	0	0
$833$	−2.68585	−0.0930591
$834$	−15.1365	−0.524134
$835$	−18.5426	−0.641694
$836$	0	0
$837$	−51.9143	−1.79442
$838$	21.0214	0.726173
$839$	−30.4507	−1.05127	−0.525637	−	0.850709i	$-0.676173\pi$
$839$	−30.4507	−1.05127	−0.525637	+	0.850709i	$0.676173\pi$
$840$	1.14637	0.0395534
$841$	−14.3142	−0.493592
$842$	−10.8353	−0.373411
$843$	−21.1021	−0.726794
$844$	−18.5426	−0.638263
$845$	−13.0000	−0.447214
$846$	0.662732	0.0227852
$847$	0	0
$848$	13.4966	0.463476
$849$	−11.0298	−0.378543
$850$	−2.68585	−0.0921238
$851$	3.35700	0.115076
$852$	−0.671153	−0.0229933
$853$	−6.43596	−0.220363	−0.110182	−	0.993911i	$-0.535143\pi$
$853$	−6.43596	−0.220363	−0.110182	+	0.993911i	$0.535143\pi$
$854$	2.39312	0.0818907
$855$	−9.33871	−0.319377
$856$	0.393115	0.0134364
$857$	1.26504	0.0432128	0.0216064	−	0.999767i	$-0.493122\pi$
$857$	1.26504	0.0432128	0.0216064	+	0.999767i	$0.493122\pi$
$858$	0	0
$859$	1.13650	0.0387769	0.0193884	−	0.999812i	$-0.493828\pi$
$859$	1.13650	0.0387769	0.0193884	+	0.999812i	$0.493828\pi$
$860$	4.97858	0.169768
$861$	−1.64973	−0.0562227
$862$	−32.6676	−1.11266
$863$	44.7764	1.52421	0.762103	−	0.647456i	$-0.224167\pi$
$863$	44.7764	1.52421	0.762103	+	0.647456i	$0.224167\pi$
$864$	−5.37169	−0.182749
$865$	10.3503	0.351920
$866$	−16.3748	−0.556439
$867$	−11.2186	−0.381004
$868$	9.66442	0.328032
$869$	0	0
$870$	4.39312	0.148941
$871$	0	0
$872$	4.41767	0.149601
$873$	−17.1413	−0.580146
$874$	−10.1495	−0.343312
$875$	1.00000	0.0338062
$876$	−10.2927	−0.347759
$877$	−53.6644	−1.81212	−0.906059	−	0.423151i	$-0.860924\pi$
$877$	−53.6644	−1.81212	−0.906059	+	0.423151i	$0.860924\pi$
$878$	0.450654	0.0152088
$879$	−36.5855	−1.23400
$880$	0	0
$881$	4.42754	0.149168	0.0745838	−	0.997215i	$-0.476237\pi$
$881$	4.42754	0.149168	0.0745838	+	0.997215i	$0.476237\pi$
$882$	−1.68585	−0.0567654
$883$	31.7073	1.06703	0.533517	−	0.845789i	$-0.320870\pi$
$883$	31.7073	1.06703	0.533517	+	0.845789i	$0.320870\pi$
$884$	0	0
$885$	0.786230	0.0264288
$886$	10.7862	0.362370
$887$	45.9865	1.54408	0.772038	−	0.635576i	$-0.219237\pi$
$887$	45.9865	1.54408	0.772038	+	0.635576i	$0.219237\pi$
$888$	−2.10038	−0.0704843
$889$	16.4507	0.551737
$890$	6.58546	0.220745
$891$	0	0
$892$	1.31415	0.0440011
$893$	−2.17765	−0.0728724
$894$	−0.478807	−0.0160137
$895$	12.6430	0.422609
$896$	1.00000	0.0334077
$897$	0	0
$898$	−19.8139	−0.661199
$899$	37.0361	1.23522
$900$	−1.68585	−0.0561949
$901$	−36.2499	−1.20766
$902$	0	0
$903$	5.70727	0.189926
$904$	11.3717	0.378217
$905$	−2.58546	−0.0859437
$906$	−7.92273	−0.263215
$907$	−11.5065	−0.382067	−0.191034	−	0.981584i	$-0.561184\pi$
$907$	−11.5065	−0.382067	−0.191034	+	0.981584i	$0.561184\pi$
$908$	−6.87819	−0.228261
$909$	1.72196	0.0571139
$910$	0	0
$911$	16.8353	0.557780	0.278890	−	0.960323i	$-0.410034\pi$
$911$	16.8353	0.557780	0.278890	+	0.960323i	$0.410034\pi$
$912$	6.35027	0.210278
$913$	0	0
$914$	23.9572	0.792432
$915$	2.74338	0.0906935
$916$	14.0575	0.464474
$917$	−5.20390	−0.171848
$918$	14.4275	0.476180
$919$	48.6184	1.60377	0.801887	−	0.597475i	$-0.203829\pi$
$919$	48.6184	1.60377	0.801887	+	0.597475i	$0.203829\pi$
$920$	−1.83221	−0.0604062
$921$	−10.3587	−0.341330
$922$	26.6430	0.877440
$923$	0	0
$924$	0	0
$925$	−1.83221	−0.0602427
$926$	2.75325	0.0904774
$927$	−4.52792	−0.148717
$928$	3.83221	0.125799
$929$	−5.57873	−0.183032	−0.0915161	−	0.995804i	$-0.529171\pi$
$929$	−5.57873	−0.183032	−0.0915161	+	0.995804i	$0.529171\pi$
$930$	11.0790	0.363293
$931$	5.53948	0.181549
$932$	−4.04285	−0.132428
$933$	−15.6644	−0.512830
$934$	−20.1396	−0.658989
$935$	0	0
$936$	0	0
$937$	20.6430	0.674377	0.337189	−	0.941437i	$-0.390524\pi$
$937$	20.6430	0.674377	0.337189	+	0.941437i	$0.390524\pi$
$938$	3.37169	0.110090
$939$	−5.39985	−0.176217
$940$	−0.393115	−0.0128220
$941$	−45.0214	−1.46766	−0.733828	−	0.679335i	$-0.762268\pi$
$941$	−45.0214	−1.46766	−0.733828	+	0.679335i	$0.762268\pi$
$942$	16.3356	0.532242
$943$	2.63673	0.0858637
$944$	0.685846	0.0223224
$945$	−5.37169	−0.174741
$946$	0	0
$947$	−6.45065	−0.209618	−0.104809	−	0.994492i	$-0.533423\pi$
$947$	−6.45065	−0.209618	−0.104809	+	0.994492i	$0.533423\pi$
$948$	−15.1365	−0.491611
$949$	0	0
$950$	5.53948	0.179724
$951$	23.9718	0.777340
$952$	−2.68585	−0.0870488
$953$	−28.5510	−0.924859	−0.462429	−	0.886656i	$-0.653022\pi$
$953$	−28.5510	−0.924859	−0.462429	+	0.886656i	$0.653022\pi$
$954$	−22.7533	−0.736664
$955$	2.87819	0.0931361
$956$	24.4177	0.789724
$957$	0	0
$958$	−4.58546	−0.148150
$959$	1.41454	0.0456778
$960$	1.14637	0.0369988
$961$	62.4011	2.01294
$962$	0	0
$963$	−0.662732	−0.0213562
$964$	−3.73183	−0.120194
$965$	−11.1793	−0.359876
$966$	−2.10038	−0.0675788
$967$	−1.90804	−0.0613583	−0.0306792	−	0.999529i	$-0.509767\pi$
$967$	−1.90804	−0.0613583	−0.0306792	+	0.999529i	$0.509767\pi$
$968$	0	0
$969$	−17.0558	−0.547913
$970$	10.1678	0.326468
$971$	−31.8996	−1.02371	−0.511854	−	0.859073i	$-0.671041\pi$
$971$	−31.8996	−1.02371	−0.511854	+	0.859073i	$0.671041\pi$
$972$	14.8536	0.476431
$973$	−13.2039	−0.423298
$974$	33.1611	1.06255
$975$	0	0
$976$	2.39312	0.0766018
$977$	28.5426	0.913159	0.456580	−	0.889683i	$-0.349074\pi$
$977$	28.5426	0.913159	0.456580	+	0.889683i	$0.349074\pi$
$978$	0.720270	0.0230317
$979$	0	0
$980$	1.00000	0.0319438
$981$	−7.44752	−0.237781
$982$	23.9143	0.763136
$983$	−36.0869	−1.15099	−0.575497	−	0.817804i	$-0.695191\pi$
$983$	−36.0869	−1.15099	−0.575497	+	0.817804i	$0.695191\pi$
$984$	−1.64973	−0.0525915
$985$	15.6216	0.497745
$986$	−10.2927	−0.327787
$987$	−0.450654	−0.0143445
$988$	0	0
$989$	−9.12181	−0.290057
$990$	0	0
$991$	−57.2369	−1.81819	−0.909095	−	0.416589i	$-0.863225\pi$
$991$	−57.2369	−1.81819	−0.909095	+	0.416589i	$0.863225\pi$
$992$	9.66442	0.306846
$993$	−17.7367	−0.562856
$994$	−0.585462	−0.0185697
$995$	−21.7220	−0.688632
$996$	10.7434	0.340417
$997$	−34.0638	−1.07881	−0.539406	−	0.842046i	$-0.681351\pi$
$997$	−34.0638	−1.07881	−0.539406	+	0.842046i	$0.681351\pi$
$998$	−39.3864	−1.24675
$999$	9.84208	0.311390

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.cn.1.2	yes	3
11.10	odd	2		8470.2.a.ch.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8470.2.a.ch.1.2	✓	3	11.10	odd	2
8470.2.a.cn.1.2	yes	3	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.14637 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.14637 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.68585 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.14637 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.14637 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.68585 q^{9} +1.00000 q^{10} +1.14637 q^{12} +1.00000 q^{14} +1.14637 q^{15} +1.00000 q^{16} -2.68585 q^{17} -1.68585 q^{18} +5.53948 q^{19} +1.00000 q^{20} +1.14637 q^{21} -1.83221 q^{23} +1.14637 q^{24} +1.00000 q^{25} -5.37169 q^{27} +1.00000 q^{28} +3.83221 q^{29} +1.14637 q^{30} +9.66442 q^{31} +1.00000 q^{32} -2.68585 q^{34} +1.00000 q^{35} -1.68585 q^{36} -1.83221 q^{37} +5.53948 q^{38} +1.00000 q^{40} -1.43910 q^{41} +1.14637 q^{42} +4.97858 q^{43} -1.68585 q^{45} -1.83221 q^{46} -0.393115 q^{47} +1.14637 q^{48} +1.00000 q^{49} +1.00000 q^{50} -3.07896 q^{51} +13.4966 q^{53} -5.37169 q^{54} +1.00000 q^{56} +6.35027 q^{57} +3.83221 q^{58} +0.685846 q^{59} +1.14637 q^{60} +2.39312 q^{61} +9.66442 q^{62} -1.68585 q^{63} +1.00000 q^{64} +3.37169 q^{67} -2.68585 q^{68} -2.10038 q^{69} +1.00000 q^{70} -0.585462 q^{71} -1.68585 q^{72} -8.97858 q^{73} -1.83221 q^{74} +1.14637 q^{75} +5.53948 q^{76} -13.2039 q^{79} +1.00000 q^{80} -1.10038 q^{81} -1.43910 q^{82} +9.37169 q^{83} +1.14637 q^{84} -2.68585 q^{85} +4.97858 q^{86} +4.39312 q^{87} +6.58546 q^{89} -1.68585 q^{90} -1.83221 q^{92} +11.0790 q^{93} -0.393115 q^{94} +5.53948 q^{95} +1.14637 q^{96} +10.1678 q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 3 q^{5} + 2 q^{6} + 3 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 3 * q^5 + 2 * q^6 + 3 * q^7 + 3 * q^8 + 7 * q^9	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 3 q^{5} + 2 q^{6} + 3 q^{7} + 3 q^{8} + 7 q^{9} + 3 q^{10} + 2 q^{12} + 3 q^{14} + 2 q^{15} + 3 q^{16} + 4 q^{17} + 7 q^{18} + 6 q^{19} + 3 q^{20} + 2 q^{21} + 8 q^{23} + 2 q^{24} + 3 q^{25} + 8 q^{27} + 3 q^{28} - 2 q^{29} + 2 q^{30} + 2 q^{31} + 3 q^{32} + 4 q^{34} + 3 q^{35} + 7 q^{36} + 8 q^{37} + 6 q^{38} + 3 q^{40} + 2 q^{42} + 7 q^{45} + 8 q^{46} + 8 q^{47} + 2 q^{48} + 3 q^{49} + 3 q^{50} + 12 q^{51} + 8 q^{54} + 3 q^{56} - 20 q^{57} - 2 q^{58} - 10 q^{59} + 2 q^{60} - 2 q^{61} + 2 q^{62} + 7 q^{63} + 3 q^{64} - 14 q^{67} + 4 q^{68} + 3 q^{70} + 4 q^{71} + 7 q^{72} - 12 q^{73} + 8 q^{74} + 2 q^{75} + 6 q^{76} - 2 q^{79} + 3 q^{80} + 3 q^{81} + 4 q^{83} + 2 q^{84} + 4 q^{85} + 4 q^{87} + 14 q^{89} + 7 q^{90} + 8 q^{92} + 12 q^{93} + 8 q^{94} + 6 q^{95} + 2 q^{96} + 44 q^{97} + 3 q^{98}+O(q^{100}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 3 * q^5 + 2 * q^6 + 3 * q^7 + 3 * q^8 + 7 * q^9 + 3 * q^10 + 2 * q^12 + 3 * q^14 + 2 * q^15 + 3 * q^16 + 4 * q^17 + 7 * q^18 + 6 * q^19 + 3 * q^20 + 2 * q^21 + 8 * q^23 + 2 * q^24 + 3 * q^25 + 8 * q^27 + 3 * q^28 - 2 * q^29 + 2 * q^30 + 2 * q^31 + 3 * q^32 + 4 * q^34 + 3 * q^35 + 7 * q^36 + 8 * q^37 + 6 * q^38 + 3 * q^40 + 2 * q^42 + 7 * q^45 + 8 * q^46 + 8 * q^47 + 2 * q^48 + 3 * q^49 + 3 * q^50 + 12 * q^51 + 8 * q^54 + 3 * q^56 - 20 * q^57 - 2 * q^58 - 10 * q^59 + 2 * q^60 - 2 * q^61 + 2 * q^62 + 7 * q^63 + 3 * q^64 - 14 * q^67 + 4 * q^68 + 3 * q^70 + 4 * q^71 + 7 * q^72 - 12 * q^73 + 8 * q^74 + 2 * q^75 + 6 * q^76 - 2 * q^79 + 3 * q^80 + 3 * q^81 + 4 * q^83 + 2 * q^84 + 4 * q^85 + 4 * q^87 + 14 * q^89 + 7 * q^90 + 8 * q^92 + 12 * q^93 + 8 * q^94 + 6 * q^95 + 2 * q^96 + 44 * q^97 + 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more