LMFDB - Embedded newform 8470.2.a.dd.1.4

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:	$6$
Coefficient field:	6.6.745749504.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 18x^{4} - 4x^{3} + 81x^{2} + 36x - 44 $ x^6 - 18x^4 - 4x^3 + 81x^2 + 36x - 44
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.16996$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.16996 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.16996 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.63119 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.16996 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.16996 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.63119 q^{9} -1.00000 q^{10} +1.16996 q^{12} -1.43479 q^{13} -1.00000 q^{14} -1.16996 q^{15} +1.00000 q^{16} +7.28628 q^{17} -1.63119 q^{18} +4.33680 q^{19} -1.00000 q^{20} -1.16996 q^{21} +2.02643 q^{23} +1.16996 q^{24} +1.00000 q^{25} -1.43479 q^{26} -5.41832 q^{27} -1.00000 q^{28} -9.11632 q^{29} -1.16996 q^{30} +3.65509 q^{31} +1.00000 q^{32} +7.28628 q^{34} +1.00000 q^{35} -1.63119 q^{36} -3.11632 q^{37} +4.33680 q^{38} -1.67865 q^{39} -1.00000 q^{40} +2.05574 q^{41} -1.16996 q^{42} +0.705861 q^{43} +1.63119 q^{45} +2.02643 q^{46} +4.00288 q^{47} +1.16996 q^{48} +1.00000 q^{49} +1.00000 q^{50} +8.52468 q^{51} -1.43479 q^{52} -4.87480 q^{53} -5.41832 q^{54} -1.00000 q^{56} +5.07390 q^{57} -9.11632 q^{58} +12.3811 q^{59} -1.16996 q^{60} +6.62309 q^{61} +3.65509 q^{62} +1.63119 q^{63} +1.00000 q^{64} +1.43479 q^{65} -1.89373 q^{67} +7.28628 q^{68} +2.37085 q^{69} +1.00000 q^{70} +0.421681 q^{71} -1.63119 q^{72} +7.37947 q^{73} -3.11632 q^{74} +1.16996 q^{75} +4.33680 q^{76} -1.67865 q^{78} +3.98377 q^{79} -1.00000 q^{80} -1.44566 q^{81} +2.05574 q^{82} -7.15061 q^{83} -1.16996 q^{84} -7.28628 q^{85} +0.705861 q^{86} -10.6658 q^{87} +8.34280 q^{89} +1.63119 q^{90} +1.43479 q^{91} +2.02643 q^{92} +4.27632 q^{93} +4.00288 q^{94} -4.33680 q^{95} +1.16996 q^{96} +11.3050 q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 6 q^{7} + 6 q^{8} + 18 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 - 6 * q^7 + 6 * q^8 + 18 * q^9	$ 6 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 6 q^{7} + 6 q^{8} + 18 q^{9} - 6 q^{10} - 6 q^{14} + 6 q^{16} - 6 q^{17} + 18 q^{18} - 6 q^{20} + 6 q^{25} - 12 q^{27} - 6 q^{28} - 12 q^{29} + 6 q^{32} - 6 q^{34} + 6 q^{35} + 18 q^{36} + 24 q^{37} + 24 q^{39} - 6 q^{40} - 12 q^{41} + 18 q^{43} - 18 q^{45} + 24 q^{47} + 6 q^{49} + 6 q^{50} + 12 q^{51} + 36 q^{53} - 12 q^{54} - 6 q^{56} + 12 q^{57} - 12 q^{58} + 30 q^{59} - 36 q^{61} - 18 q^{63} + 6 q^{64} - 12 q^{67} - 6 q^{68} + 6 q^{70} + 6 q^{71} + 18 q^{72} + 6 q^{73} + 24 q^{74} + 24 q^{78} + 24 q^{79} - 6 q^{80} + 54 q^{81} - 12 q^{82} - 24 q^{83} + 6 q^{85} + 18 q^{86} + 24 q^{87} + 36 q^{89} - 18 q^{90} + 24 q^{94} + 6 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 - 6 * q^7 + 6 * q^8 + 18 * q^9 - 6 * q^10 - 6 * q^14 + 6 * q^16 - 6 * q^17 + 18 * q^18 - 6 * q^20 + 6 * q^25 - 12 * q^27 - 6 * q^28 - 12 * q^29 + 6 * q^32 - 6 * q^34 + 6 * q^35 + 18 * q^36 + 24 * q^37 + 24 * q^39 - 6 * q^40 - 12 * q^41 + 18 * q^43 - 18 * q^45 + 24 * q^47 + 6 * q^49 + 6 * q^50 + 12 * q^51 + 36 * q^53 - 12 * q^54 - 6 * q^56 + 12 * q^57 - 12 * q^58 + 30 * q^59 - 36 * q^61 - 18 * q^63 + 6 * q^64 - 12 * q^67 - 6 * q^68 + 6 * q^70 + 6 * q^71 + 18 * q^72 + 6 * q^73 + 24 * q^74 + 24 * q^78 + 24 * q^79 - 6 * q^80 + 54 * q^81 - 12 * q^82 - 24 * q^83 + 6 * q^85 + 18 * q^86 + 24 * q^87 + 36 * q^89 - 18 * q^90 + 24 * q^94 + 6 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.16996	0.675478	0.337739	−	0.941240i	$-0.390338\pi$
$3$	1.16996	0.675478	0.337739	+	0.941240i	$0.390338\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.16996	0.477635
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	−1.63119	−0.543729
$10$	−1.00000	−0.316228
$11$	0	0
$11$	0	0
$12$	1.16996	0.337739
$13$	−1.43479	−0.397939	−0.198970	−	0.980006i	$-0.563760\pi$
$13$	−1.43479	−0.397939	−0.198970	+	0.980006i	$0.563760\pi$
$14$	−1.00000	−0.267261
$15$	−1.16996	−0.302083
$16$	1.00000	0.250000
$17$	7.28628	1.76718	0.883591	−	0.468259i	$-0.155118\pi$
$17$	7.28628	1.76718	0.883591	+	0.468259i	$0.155118\pi$
$18$	−1.63119	−0.384475
$19$	4.33680	0.994931	0.497466	−	0.867484i	$-0.334264\pi$
$19$	4.33680	0.994931	0.497466	+	0.867484i	$0.334264\pi$
$20$	−1.00000	−0.223607
$21$	−1.16996	−0.255307
$22$	0	0
$23$	2.02643	0.422541	0.211270	−	0.977428i	$-0.432240\pi$
$23$	2.02643	0.422541	0.211270	+	0.977428i	$0.432240\pi$
$24$	1.16996	0.238818
$25$	1.00000	0.200000
$26$	−1.43479	−0.281386
$27$	−5.41832	−1.04276
$28$	−1.00000	−0.188982
$29$	−9.11632	−1.69286	−0.846429	−	0.532502i	$-0.821252\pi$
$29$	−9.11632	−1.69286	−0.846429	+	0.532502i	$0.821252\pi$
$30$	−1.16996	−0.213605
$31$	3.65509	0.656474	0.328237	−	0.944595i	$-0.393546\pi$
$31$	3.65509	0.656474	0.328237	+	0.944595i	$0.393546\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	7.28628	1.24959
$35$	1.00000	0.169031
$36$	−1.63119	−0.271865
$37$	−3.11632	−0.512320	−0.256160	−	0.966634i	$-0.582457\pi$
$37$	−3.11632	−0.512320	−0.256160	+	0.966634i	$0.582457\pi$
$38$	4.33680	0.703523
$39$	−1.67865	−0.268799
$40$	−1.00000	−0.158114
$41$	2.05574	0.321053	0.160527	−	0.987031i	$-0.448681\pi$
$41$	2.05574	0.321053	0.160527	+	0.987031i	$0.448681\pi$
$42$	−1.16996	−0.180529
$43$	0.705861	0.107643	0.0538214	−	0.998551i	$-0.482860\pi$
$43$	0.705861	0.107643	0.0538214	+	0.998551i	$0.482860\pi$
$44$	0	0
$45$	1.63119	0.243163
$46$	2.02643	0.298781
$47$	4.00288	0.583880	0.291940	−	0.956437i	$-0.405699\pi$
$47$	4.00288	0.583880	0.291940	+	0.956437i	$0.405699\pi$
$48$	1.16996	0.168870
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	8.52468	1.19369
$52$	−1.43479	−0.198970
$53$	−4.87480	−0.669606	−0.334803	−	0.942288i	$-0.608670\pi$
$53$	−4.87480	−0.669606	−0.334803	+	0.942288i	$0.608670\pi$
$54$	−5.41832	−0.737339
$55$	0	0
$56$	−1.00000	−0.133631
$57$	5.07390	0.672054
$58$	−9.11632	−1.19703
$59$	12.3811	1.61189	0.805944	−	0.591992i	$-0.201658\pi$
$59$	12.3811	1.61189	0.805944	+	0.591992i	$0.201658\pi$
$60$	−1.16996	−0.151042
$61$	6.62309	0.847999	0.424000	−	0.905662i	$-0.360626\pi$
$61$	6.62309	0.847999	0.424000	+	0.905662i	$0.360626\pi$
$62$	3.65509	0.464197
$63$	1.63119	0.205510
$64$	1.00000	0.125000
$65$	1.43479	0.177964
$66$	0	0
$67$	−1.89373	−0.231356	−0.115678	−	0.993287i	$-0.536904\pi$
$67$	−1.89373	−0.231356	−0.115678	+	0.993287i	$0.536904\pi$
$68$	7.28628	0.883591
$69$	2.37085	0.285417
$70$	1.00000	0.119523
$71$	0.421681	0.0500443	0.0250222	−	0.999687i	$-0.492034\pi$
$71$	0.421681	0.0500443	0.0250222	+	0.999687i	$0.492034\pi$
$72$	−1.63119	−0.192237
$73$	7.37947	0.863702	0.431851	−	0.901945i	$-0.357861\pi$
$73$	7.37947	0.863702	0.431851	+	0.901945i	$0.357861\pi$
$74$	−3.11632	−0.362265
$75$	1.16996	0.135096
$76$	4.33680	0.497466
$77$	0	0
$78$	−1.67865	−0.190070
$79$	3.98377	0.448209	0.224105	−	0.974565i	$-0.428054\pi$
$79$	3.98377	0.448209	0.224105	+	0.974565i	$0.428054\pi$
$80$	−1.00000	−0.111803
$81$	−1.44566	−0.160629
$82$	2.05574	0.227019
$83$	−7.15061	−0.784882	−0.392441	−	0.919777i	$-0.628369\pi$
$83$	−7.15061	−0.784882	−0.392441	+	0.919777i	$0.628369\pi$
$84$	−1.16996	−0.127653
$85$	−7.28628	−0.790308
$86$	0.705861	0.0761149
$87$	−10.6658	−1.14349
$88$	0	0
$89$	8.34280	0.884335	0.442168	−	0.896932i	$-0.354210\pi$
$89$	8.34280	0.884335	0.442168	+	0.896932i	$0.354210\pi$
$90$	1.63119	0.171942
$91$	1.43479	0.150407
$92$	2.02643	0.211270
$93$	4.27632	0.443434
$94$	4.00288	0.412865
$95$	−4.33680	−0.444947
$96$	1.16996	0.119409
$97$	11.3050	1.14785	0.573926	−	0.818907i	$-0.305420\pi$
$97$	11.3050	1.14785	0.573926	+	0.818907i	$0.305420\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	11.8936	1.18345	0.591727	−	0.806138i	$-0.298446\pi$
$101$	11.8936	1.18345	0.591727	+	0.806138i	$0.298446\pi$
$102$	8.52468	0.844069
$103$	−2.57520	−0.253742	−0.126871	−	0.991919i	$-0.540493\pi$
$103$	−2.57520	−0.253742	−0.126871	+	0.991919i	$0.540493\pi$
$104$	−1.43479	−0.140693
$105$	1.16996	0.114177
$106$	−4.87480	−0.473483
$107$	−0.0210293	−0.00203298	−0.00101649	−	0.999999i	$-0.500324\pi$
$107$	−0.0210293	−0.00203298	−0.00101649	+	0.999999i	$0.500324\pi$
$108$	−5.41832	−0.521378
$109$	−3.22024	−0.308443	−0.154222	−	0.988036i	$-0.549287\pi$
$109$	−3.22024	−0.308443	−0.154222	+	0.988036i	$0.549287\pi$
$110$	0	0
$111$	−3.64598	−0.346061
$112$	−1.00000	−0.0944911
$113$	16.8832	1.58824	0.794118	−	0.607764i	$-0.207933\pi$
$113$	16.8832	1.58824	0.794118	+	0.607764i	$0.207933\pi$
$114$	5.07390	0.475214
$115$	−2.02643	−0.188966
$116$	−9.11632	−0.846429
$117$	2.34041	0.216371
$118$	12.3811	1.13978
$119$	−7.28628	−0.667932
$120$	−1.16996	−0.106802
$121$	0	0
$122$	6.62309	0.599626
$123$	2.40514	0.216865
$124$	3.65509	0.328237
$125$	−1.00000	−0.0894427
$126$	1.63119	0.145318
$127$	−3.83782	−0.340551	−0.170276	−	0.985396i	$-0.554466\pi$
$127$	−3.83782	−0.340551	−0.170276	+	0.985396i	$0.554466\pi$
$128$	1.00000	0.0883883
$129$	0.825831	0.0727103
$130$	1.43479	0.125839
$131$	−19.4691	−1.70102	−0.850511	−	0.525958i	$-0.823707\pi$
$131$	−19.4691	−1.70102	−0.850511	+	0.525958i	$0.823707\pi$
$132$	0	0
$133$	−4.33680	−0.376049
$134$	−1.89373	−0.163594
$135$	5.41832	0.466334
$136$	7.28628	0.624793
$137$	16.1146	1.37677	0.688383	−	0.725347i	$-0.258321\pi$
$137$	16.1146	1.37677	0.688383	+	0.725347i	$0.258321\pi$
$138$	2.37085	0.201820
$139$	−16.9156	−1.43476	−0.717382	−	0.696680i	$-0.754660\pi$
$139$	−16.9156	−1.43476	−0.717382	+	0.696680i	$0.754660\pi$
$140$	1.00000	0.0845154
$141$	4.68321	0.394398
$142$	0.421681	0.0353867
$143$	0	0
$144$	−1.63119	−0.135932
$145$	9.11632	0.757069
$146$	7.37947	0.610729
$147$	1.16996	0.0964969
$148$	−3.11632	−0.256160
$149$	−5.12256	−0.419656	−0.209828	−	0.977738i	$-0.567290\pi$
$149$	−5.12256	−0.419656	−0.209828	+	0.977738i	$0.567290\pi$
$150$	1.16996	0.0955270
$151$	22.4051	1.82330	0.911652	−	0.410964i	$-0.134808\pi$
$151$	22.4051	1.82330	0.911652	+	0.410964i	$0.134808\pi$
$152$	4.33680	0.351761
$153$	−11.8853	−0.960869
$154$	0	0
$155$	−3.65509	−0.293584
$156$	−1.67865	−0.134400
$157$	14.9308	1.19161	0.595804	−	0.803130i	$-0.296834\pi$
$157$	14.9308	1.19161	0.595804	+	0.803130i	$0.296834\pi$
$158$	3.98377	0.316932
$159$	−5.70334	−0.452304
$160$	−1.00000	−0.0790569
$161$	−2.02643	−0.159705
$162$	−1.44566	−0.113582
$163$	3.69439	0.289367	0.144684	−	0.989478i	$-0.453784\pi$
$163$	3.69439	0.289367	0.144684	+	0.989478i	$0.453784\pi$
$164$	2.05574	0.160527
$165$	0	0
$166$	−7.15061	−0.554995
$167$	−9.33915	−0.722685	−0.361343	−	0.932433i	$-0.617682\pi$
$167$	−9.33915	−0.722685	−0.361343	+	0.932433i	$0.617682\pi$
$168$	−1.16996	−0.0902646
$169$	−10.9414	−0.841644
$170$	−7.28628	−0.558832
$171$	−7.07414	−0.540973
$172$	0.705861	0.0538214
$173$	1.89895	0.144375	0.0721874	−	0.997391i	$-0.477002\pi$
$173$	1.89895	0.144375	0.0721874	+	0.997391i	$0.477002\pi$
$174$	−10.6658	−0.808568
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	14.4855	1.08880
$178$	8.34280	0.625319
$179$	6.00288	0.448676	0.224338	−	0.974511i	$-0.427978\pi$
$179$	6.00288	0.448676	0.224338	+	0.974511i	$0.427978\pi$
$180$	1.63119	0.121582
$181$	−6.73019	−0.500251	−0.250126	−	0.968213i	$-0.580472\pi$
$181$	−6.73019	−0.500251	−0.250126	+	0.968213i	$0.580472\pi$
$182$	1.43479	0.106354
$183$	7.74876	0.572805
$184$	2.02643	0.149391
$185$	3.11632	0.229116
$186$	4.27632	0.313555
$187$	0	0
$188$	4.00288	0.291940
$189$	5.41832	0.394124
$190$	−4.33680	−0.314625
$191$	15.9464	1.15384	0.576919	−	0.816801i	$-0.304255\pi$
$191$	15.9464	1.15384	0.576919	+	0.816801i	$0.304255\pi$
$192$	1.16996	0.0844348
$193$	11.7470	0.845569	0.422784	−	0.906230i	$-0.361053\pi$
$193$	11.7470	0.845569	0.422784	+	0.906230i	$0.361053\pi$
$194$	11.3050	0.811655
$195$	1.67865	0.120211
$196$	1.00000	0.0714286
$197$	−2.70088	−0.192430	−0.0962148	−	0.995361i	$-0.530674\pi$
$197$	−2.70088	−0.192430	−0.0962148	+	0.995361i	$0.530674\pi$
$198$	0	0
$199$	14.5804	1.03358	0.516789	−	0.856113i	$-0.327127\pi$
$199$	14.5804	1.03358	0.516789	+	0.856113i	$0.327127\pi$
$200$	1.00000	0.0707107
$201$	−2.21560	−0.156276
$202$	11.8936	0.836828
$203$	9.11632	0.639840
$204$	8.52468	0.596847
$205$	−2.05574	−0.143579
$206$	−2.57520	−0.179423
$207$	−3.30550	−0.229748
$208$	−1.43479	−0.0994849
$209$	0	0
$210$	1.16996	0.0807351
$211$	18.2347	1.25533	0.627666	−	0.778483i	$-0.284010\pi$
$211$	18.2347	1.25533	0.627666	+	0.778483i	$0.284010\pi$
$212$	−4.87480	−0.334803
$213$	0.493351	0.0338038
$214$	−0.0210293	−0.00143754
$215$	−0.705861	−0.0481393
$216$	−5.41832	−0.368670
$217$	−3.65509	−0.248124
$218$	−3.22024	−0.218102
$219$	8.63370	0.583412
$220$	0	0
$221$	−10.4543	−0.703232
$222$	−3.64598	−0.244702
$223$	1.41856	0.0949938	0.0474969	−	0.998871i	$-0.484876\pi$
$223$	1.41856	0.0949938	0.0474969	+	0.998871i	$0.484876\pi$
$224$	−1.00000	−0.0668153
$225$	−1.63119	−0.108746
$226$	16.8832	1.12305
$227$	8.18601	0.543325	0.271662	−	0.962393i	$-0.412427\pi$
$227$	8.18601	0.543325	0.271662	+	0.962393i	$0.412427\pi$
$228$	5.07390	0.336027
$229$	−1.88578	−0.124616	−0.0623080	−	0.998057i	$-0.519846\pi$
$229$	−1.88578	−0.124616	−0.0623080	+	0.998057i	$0.519846\pi$
$230$	−2.02643	−0.133619
$231$	0	0
$232$	−9.11632	−0.598516
$233$	22.9570	1.50396	0.751982	−	0.659184i	$-0.229098\pi$
$233$	22.9570	1.50396	0.751982	+	0.659184i	$0.229098\pi$
$234$	2.34041	0.152998
$235$	−4.00288	−0.261119
$236$	12.3811	0.805944
$237$	4.66086	0.302755
$238$	−7.28628	−0.472299
$239$	0.315230	0.0203905	0.0101953	−	0.999948i	$-0.496755\pi$
$239$	0.315230	0.0203905	0.0101953	+	0.999948i	$0.496755\pi$
$240$	−1.16996	−0.0755208
$241$	−5.61640	−0.361784	−0.180892	−	0.983503i	$-0.557898\pi$
$241$	−5.61640	−0.361784	−0.180892	+	0.983503i	$0.557898\pi$
$242$	0	0
$243$	14.5636	0.934254
$244$	6.62309	0.424000
$245$	−1.00000	−0.0638877
$246$	2.40514	0.153346
$247$	−6.22241	−0.395922
$248$	3.65509	0.232099
$249$	−8.36595	−0.530170
$250$	−1.00000	−0.0632456
$251$	14.3205	0.903903	0.451951	−	0.892043i	$-0.350728\pi$
$251$	14.3205	0.903903	0.451951	+	0.892043i	$0.350728\pi$
$252$	1.63119	0.102755
$253$	0	0
$254$	−3.83782	−0.240806
$255$	−8.52468	−0.533836
$256$	1.00000	0.0625000
$257$	28.8932	1.80231	0.901153	−	0.433501i	$-0.142722\pi$
$257$	28.8932	1.80231	0.901153	+	0.433501i	$0.142722\pi$
$258$	0.825831	0.0514140
$259$	3.11632	0.193639
$260$	1.43479	0.0889820
$261$	14.8704	0.920456
$262$	−19.4691	−1.20280
$263$	21.9055	1.35075	0.675377	−	0.737473i	$-0.263981\pi$
$263$	21.9055	1.35075	0.675377	+	0.737473i	$0.263981\pi$
$264$	0	0
$265$	4.87480	0.299457
$266$	−4.33680	−0.265907
$267$	9.76076	0.597349
$268$	−1.89373	−0.115678
$269$	−2.97854	−0.181605	−0.0908025	−	0.995869i	$-0.528943\pi$
$269$	−2.97854	−0.181605	−0.0908025	+	0.995869i	$0.528943\pi$
$270$	5.41832	0.329748
$271$	0.202215	0.0122837	0.00614183	−	0.999981i	$-0.498045\pi$
$271$	0.202215	0.0122837	0.00614183	+	0.999981i	$0.498045\pi$
$272$	7.28628	0.441796
$273$	1.67865	0.101597
$274$	16.1146	0.973521
$275$	0	0
$276$	2.37085	0.142709
$277$	−4.93157	−0.296309	−0.148155	−	0.988964i	$-0.547333\pi$
$277$	−4.93157	−0.296309	−0.148155	+	0.988964i	$0.547333\pi$
$278$	−16.9156	−1.01453
$279$	−5.96214	−0.356944
$280$	1.00000	0.0597614
$281$	−17.8483	−1.06474	−0.532370	−	0.846512i	$-0.678698\pi$
$281$	−17.8483	−1.06474	−0.532370	+	0.846512i	$0.678698\pi$
$282$	4.68321	0.278881
$283$	−29.2721	−1.74005	−0.870023	−	0.493010i	$-0.835896\pi$
$283$	−29.2721	−1.74005	−0.870023	+	0.493010i	$0.835896\pi$
$284$	0.421681	0.0250222
$285$	−5.07390	−0.300552
$286$	0	0
$287$	−2.05574	−0.121347
$288$	−1.63119	−0.0961187
$289$	36.0899	2.12293
$290$	9.11632	0.535329
$291$	13.2265	0.775350
$292$	7.37947	0.431851
$293$	−29.9025	−1.74692	−0.873460	−	0.486895i	$-0.838129\pi$
$293$	−29.9025	−1.74692	−0.873460	+	0.486895i	$0.838129\pi$
$294$	1.16996	0.0682336
$295$	−12.3811	−0.720858
$296$	−3.11632	−0.181132
$297$	0	0
$298$	−5.12256	−0.296742
$299$	−2.90751	−0.168146
$300$	1.16996	0.0675478
$301$	−0.705861	−0.0406851
$302$	22.4051	1.28927
$303$	13.9150	0.799397
$304$	4.33680	0.248733
$305$	−6.62309	−0.379237
$306$	−11.8853	−0.679437
$307$	13.6023	0.776324	0.388162	−	0.921591i	$-0.373110\pi$
$307$	13.6023	0.776324	0.388162	+	0.921591i	$0.373110\pi$
$308$	0	0
$309$	−3.01289	−0.171397
$310$	−3.65509	−0.207595
$311$	29.5607	1.67623	0.838117	−	0.545490i	$-0.183656\pi$
$311$	29.5607	1.67623	0.838117	+	0.545490i	$0.183656\pi$
$312$	−1.67865	−0.0950349
$313$	9.23518	0.522003	0.261002	−	0.965338i	$-0.415947\pi$
$313$	9.23518	0.522003	0.261002	+	0.965338i	$0.415947\pi$
$314$	14.9308	0.842593
$315$	−1.63119	−0.0919070
$316$	3.98377	0.224105
$317$	−5.25554	−0.295180	−0.147590	−	0.989049i	$-0.547152\pi$
$317$	−5.25554	−0.295180	−0.147590	+	0.989049i	$0.547152\pi$
$318$	−5.70334	−0.319827
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	−0.0246035	−0.00137324
$322$	−2.02643	−0.112929
$323$	31.5992	1.75823
$324$	−1.44566	−0.0803146
$325$	−1.43479	−0.0795879
$326$	3.69439	0.204614
$327$	−3.76756	−0.208347
$328$	2.05574	0.113510
$329$	−4.00288	−0.220686
$330$	0	0
$331$	−23.4150	−1.28700	−0.643501	−	0.765445i	$-0.722519\pi$
$331$	−23.4150	−1.28700	−0.643501	+	0.765445i	$0.722519\pi$
$332$	−7.15061	−0.392441
$333$	5.08330	0.278563
$334$	−9.33915	−0.511016
$335$	1.89373	0.103466
$336$	−1.16996	−0.0638267
$337$	2.73973	0.149242	0.0746212	−	0.997212i	$-0.476225\pi$
$337$	2.73973	0.149242	0.0746212	+	0.997212i	$0.476225\pi$
$338$	−10.9414	−0.595132
$339$	19.7527	1.07282
$340$	−7.28628	−0.395154
$341$	0	0
$342$	−7.07414	−0.382526
$343$	−1.00000	−0.0539949
$344$	0.705861	0.0380575
$345$	−2.37085	−0.127642
$346$	1.89895	0.102088
$347$	5.82295	0.312592	0.156296	−	0.987710i	$-0.450045\pi$
$347$	5.82295	0.312592	0.156296	+	0.987710i	$0.450045\pi$
$348$	−10.6658	−0.571744
$349$	8.42897	0.451193	0.225596	−	0.974221i	$-0.427567\pi$
$349$	8.42897	0.451193	0.225596	+	0.974221i	$0.427567\pi$
$350$	−1.00000	−0.0534522
$351$	7.77415	0.414953
$352$	0	0
$353$	−23.9658	−1.27557	−0.637786	−	0.770214i	$-0.720149\pi$
$353$	−23.9658	−1.27557	−0.637786	+	0.770214i	$0.720149\pi$
$354$	14.4855	0.769894
$355$	−0.421681	−0.0223805
$356$	8.34280	0.442168
$357$	−8.52468	−0.451174
$358$	6.00288	0.317262
$359$	−16.0490	−0.847032	−0.423516	−	0.905889i	$-0.639204\pi$
$359$	−16.0490	−0.847032	−0.423516	+	0.905889i	$0.639204\pi$
$360$	1.63119	0.0859711
$361$	−0.192129	−0.0101120
$362$	−6.73019	−0.353731
$363$	0	0
$364$	1.43479	0.0752035
$365$	−7.37947	−0.386259
$366$	7.74876	0.405034
$367$	−2.17504	−0.113536	−0.0567680	−	0.998387i	$-0.518080\pi$
$367$	−2.17504	−0.113536	−0.0567680	+	0.998387i	$0.518080\pi$
$368$	2.02643	0.105635
$369$	−3.35331	−0.174566
$370$	3.11632	0.162010
$371$	4.87480	0.253087
$372$	4.27632	0.221717
$373$	−16.5044	−0.854566	−0.427283	−	0.904118i	$-0.640529\pi$
$373$	−16.5044	−0.854566	−0.427283	+	0.904118i	$0.640529\pi$
$374$	0	0
$375$	−1.16996	−0.0604166
$376$	4.00288	0.206433
$377$	13.0800	0.673655
$378$	5.41832	0.278688
$379$	22.3263	1.14683	0.573413	−	0.819267i	$-0.305619\pi$
$379$	22.3263	1.14683	0.573413	+	0.819267i	$0.305619\pi$
$380$	−4.33680	−0.222473
$381$	−4.49010	−0.230035
$382$	15.9464	0.815887
$383$	−21.4500	−1.09604	−0.548021	−	0.836465i	$-0.684619\pi$
$383$	−21.4500	−1.09604	−0.548021	+	0.836465i	$0.684619\pi$
$384$	1.16996	0.0597044
$385$	0	0
$386$	11.7470	0.597907
$387$	−1.15139	−0.0585285
$388$	11.3050	0.573926
$389$	−37.9771	−1.92552	−0.962759	−	0.270362i	$-0.912857\pi$
$389$	−37.9771	−1.92552	−0.962759	+	0.270362i	$0.912857\pi$
$390$	1.67865	0.0850018
$391$	14.7652	0.746707
$392$	1.00000	0.0505076
$393$	−22.7781	−1.14900
$394$	−2.70088	−0.136068
$395$	−3.98377	−0.200445
$396$	0	0
$397$	−24.9220	−1.25080	−0.625399	−	0.780305i	$-0.715064\pi$
$397$	−24.9220	−1.25080	−0.625399	+	0.780305i	$0.715064\pi$
$398$	14.5804	0.730850
$399$	−5.07390	−0.254013
$400$	1.00000	0.0500000
$401$	−23.7936	−1.18819	−0.594097	−	0.804393i	$-0.702491\pi$
$401$	−23.7936	−1.18819	−0.594097	+	0.804393i	$0.702491\pi$
$402$	−2.21560	−0.110504
$403$	−5.24430	−0.261237
$404$	11.8936	0.591727
$405$	1.44566	0.0718355
$406$	9.11632	0.452435
$407$	0	0
$408$	8.52468	0.422034
$409$	−17.4118	−0.860958	−0.430479	−	0.902601i	$-0.641655\pi$
$409$	−17.4118	−0.860958	−0.430479	+	0.902601i	$0.641655\pi$
$410$	−2.05574	−0.101526
$411$	18.8535	0.929976
$412$	−2.57520	−0.126871
$413$	−12.3811	−0.609236
$414$	−3.30550	−0.162456
$415$	7.15061	0.351010
$416$	−1.43479	−0.0703464
$417$	−19.7906	−0.969151
$418$	0	0
$419$	6.77394	0.330929	0.165464	−	0.986216i	$-0.447088\pi$
$419$	6.77394	0.330929	0.165464	+	0.986216i	$0.447088\pi$
$420$	1.16996	0.0570883
$421$	16.3820	0.798409	0.399205	−	0.916862i	$-0.369286\pi$
$421$	16.3820	0.798409	0.399205	+	0.916862i	$0.369286\pi$
$422$	18.2347	0.887653
$423$	−6.52944	−0.317472
$424$	−4.87480	−0.236741
$425$	7.28628	0.353437
$426$	0.493351	0.0239029
$427$	−6.62309	−0.320514
$428$	−0.0210293	−0.00101649
$429$	0	0
$430$	−0.705861	−0.0340396
$431$	−35.7762	−1.72328	−0.861638	−	0.507523i	$-0.830561\pi$
$431$	−35.7762	−1.72328	−0.861638	+	0.507523i	$0.830561\pi$
$432$	−5.41832	−0.260689
$433$	12.5667	0.603919	0.301959	−	0.953321i	$-0.402359\pi$
$433$	12.5667	0.603919	0.301959	+	0.953321i	$0.402359\pi$
$434$	−3.65509	−0.175450
$435$	10.6658	0.511384
$436$	−3.22024	−0.154222
$437$	8.78825	0.420399
$438$	8.63370	0.412534
$439$	−34.6171	−1.65218	−0.826092	−	0.563535i	$-0.809441\pi$
$439$	−34.6171	−1.65218	−0.826092	+	0.563535i	$0.809441\pi$
$440$	0	0
$441$	−1.63119	−0.0776756
$442$	−10.4543	−0.497260
$443$	18.9816	0.901841	0.450921	−	0.892564i	$-0.351096\pi$
$443$	18.9816	0.901841	0.450921	+	0.892564i	$0.351096\pi$
$444$	−3.64598	−0.173030
$445$	−8.34280	−0.395487
$446$	1.41856	0.0671708
$447$	−5.99320	−0.283469
$448$	−1.00000	−0.0472456
$449$	13.7748	0.650072	0.325036	−	0.945702i	$-0.394624\pi$
$449$	13.7748	0.650072	0.325036	+	0.945702i	$0.394624\pi$
$450$	−1.63119	−0.0768949
$451$	0	0
$452$	16.8832	0.794118
$453$	26.2132	1.23160
$454$	8.18601	0.384188
$455$	−1.43479	−0.0672640
$456$	5.07390	0.237607
$457$	36.0763	1.68758	0.843789	−	0.536676i	$-0.180320\pi$
$457$	36.0763	1.68758	0.843789	+	0.536676i	$0.180320\pi$
$458$	−1.88578	−0.0881168
$459$	−39.4794	−1.84274
$460$	−2.02643	−0.0944830
$461$	−23.2972	−1.08506	−0.542529	−	0.840037i	$-0.682533\pi$
$461$	−23.2972	−1.08506	−0.542529	+	0.840037i	$0.682533\pi$
$462$	0	0
$463$	−31.8729	−1.48126	−0.740629	−	0.671914i	$-0.765472\pi$
$463$	−31.8729	−1.48126	−0.740629	+	0.671914i	$0.765472\pi$
$464$	−9.11632	−0.423214
$465$	−4.27632	−0.198310
$466$	22.9570	1.06346
$467$	−11.5661	−0.535216	−0.267608	−	0.963528i	$-0.586233\pi$
$467$	−11.5661	−0.535216	−0.267608	+	0.963528i	$0.586233\pi$
$468$	2.34041	0.108186
$469$	1.89373	0.0874444
$470$	−4.00288	−0.184639
$471$	17.4685	0.804905
$472$	12.3811	0.569889
$473$	0	0
$474$	4.66086	0.214080
$475$	4.33680	0.198986
$476$	−7.28628	−0.333966
$477$	7.95172	0.364084
$478$	0.315230	0.0144183
$479$	−13.2561	−0.605689	−0.302844	−	0.953040i	$-0.597936\pi$
$479$	−13.2561	−0.605689	−0.302844	+	0.953040i	$0.597936\pi$
$480$	−1.16996	−0.0534012
$481$	4.47127	0.203872
$482$	−5.61640	−0.255820
$483$	−2.37085	−0.107878
$484$	0	0
$485$	−11.3050	−0.513335
$486$	14.5636	0.660617
$487$	5.42232	0.245709	0.122854	−	0.992425i	$-0.460795\pi$
$487$	5.42232	0.245709	0.122854	+	0.992425i	$0.460795\pi$
$488$	6.62309	0.299813
$489$	4.32230	0.195461
$490$	−1.00000	−0.0451754
$491$	−36.0238	−1.62573	−0.812866	−	0.582450i	$-0.802094\pi$
$491$	−36.0238	−1.62573	−0.812866	+	0.582450i	$0.802094\pi$
$492$	2.40514	0.108432
$493$	−66.4241	−2.99159
$494$	−6.22241	−0.279959
$495$	0	0
$496$	3.65509	0.164119
$497$	−0.421681	−0.0189150
$498$	−8.36595	−0.374887
$499$	−3.26974	−0.146374	−0.0731869	−	0.997318i	$-0.523317\pi$
$499$	−3.26974	−0.146374	−0.0731869	+	0.997318i	$0.523317\pi$
$500$	−1.00000	−0.0447214
$501$	−10.9265	−0.488158
$502$	14.3205	0.639156
$503$	−41.9101	−1.86868	−0.934339	−	0.356384i	$-0.884009\pi$
$503$	−41.9101	−1.86868	−0.934339	+	0.356384i	$0.884009\pi$
$504$	1.63119	0.0726589
$505$	−11.8936	−0.529257
$506$	0	0
$507$	−12.8010	−0.568512
$508$	−3.83782	−0.170276
$509$	19.3235	0.856500	0.428250	−	0.903660i	$-0.359130\pi$
$509$	19.3235	0.856500	0.428250	+	0.903660i	$0.359130\pi$
$510$	−8.52468	−0.377479
$511$	−7.37947	−0.326449
$512$	1.00000	0.0441942
$513$	−23.4982	−1.03747
$514$	28.8932	1.27442
$515$	2.57520	0.113477
$516$	0.825831	0.0363552
$517$	0	0
$518$	3.11632	0.136923
$519$	2.22170	0.0975220
$520$	1.43479	0.0629197
$521$	−22.0283	−0.965078	−0.482539	−	0.875874i	$-0.660285\pi$
$521$	−22.0283	−0.965078	−0.482539	+	0.875874i	$0.660285\pi$
$522$	14.8704	0.650861
$523$	−20.3706	−0.890745	−0.445373	−	0.895345i	$-0.646929\pi$
$523$	−20.3706	−0.890745	−0.445373	+	0.895345i	$0.646929\pi$
$524$	−19.4691	−0.850511
$525$	−1.16996	−0.0510613
$526$	21.9055	0.955127
$527$	26.6320	1.16011
$528$	0	0
$529$	−18.8936	−0.821459
$530$	4.87480	0.211748
$531$	−20.1960	−0.876431
$532$	−4.33680	−0.188024
$533$	−2.94956	−0.127760
$534$	9.76076	0.422390
$535$	0.0210293	0.000909178 0
$536$	−1.89373	−0.0817968
$537$	7.02314	0.303071
$538$	−2.97854	−0.128414
$539$	0	0
$540$	5.41832	0.233167
$541$	29.5866	1.27203	0.636013	−	0.771678i	$-0.280582\pi$
$541$	29.5866	1.27203	0.636013	+	0.771678i	$0.280582\pi$
$542$	0.202215	0.00868587
$543$	−7.87407	−0.337909
$544$	7.28628	0.312397
$545$	3.22024	0.137940
$546$	1.67865	0.0718397
$547$	−31.5318	−1.34820	−0.674102	−	0.738638i	$-0.735469\pi$
$547$	−31.5318	−1.34820	−0.674102	+	0.738638i	$0.735469\pi$
$548$	16.1146	0.688383
$549$	−10.8035	−0.461082
$550$	0	0
$551$	−39.5357	−1.68428
$552$	2.37085	0.100910
$553$	−3.98377	−0.169407
$554$	−4.93157	−0.209522
$555$	3.64598	0.154763
$556$	−16.9156	−0.717382
$557$	−2.97938	−0.126240	−0.0631202	−	0.998006i	$-0.520105\pi$
$557$	−2.97938	−0.126240	−0.0631202	+	0.998006i	$0.520105\pi$
$558$	−5.96214	−0.252398
$559$	−1.01276	−0.0428353
$560$	1.00000	0.0422577
$561$	0	0
$562$	−17.8483	−0.752885
$563$	15.7256	0.662754	0.331377	−	0.943498i	$-0.392487\pi$
$563$	15.7256	0.662754	0.331377	+	0.943498i	$0.392487\pi$
$564$	4.68321	0.197199
$565$	−16.8832	−0.710281
$566$	−29.2721	−1.23040
$567$	1.44566	0.0607121
$568$	0.421681	0.0176933
$569$	37.0851	1.55469	0.777345	−	0.629074i	$-0.216566\pi$
$569$	37.0851	1.55469	0.777345	+	0.629074i	$0.216566\pi$
$570$	−5.07390	−0.212522
$571$	−14.5281	−0.607982	−0.303991	−	0.952675i	$-0.598319\pi$
$571$	−14.5281	−0.607982	−0.303991	+	0.952675i	$0.598319\pi$
$572$	0	0
$573$	18.6566	0.779392
$574$	−2.05574	−0.0858051
$575$	2.02643	0.0845082
$576$	−1.63119	−0.0679662
$577$	2.22693	0.0927082	0.0463541	−	0.998925i	$-0.485240\pi$
$577$	2.22693	0.0927082	0.0463541	+	0.998925i	$0.485240\pi$
$578$	36.0899	1.50114
$579$	13.7436	0.571163
$580$	9.11632	0.378535
$581$	7.15061	0.296657
$582$	13.2265	0.548255
$583$	0	0
$584$	7.37947	0.305365
$585$	−2.34041	−0.0967642
$586$	−29.9025	−1.23526
$587$	−8.50637	−0.351095	−0.175548	−	0.984471i	$-0.556170\pi$
$587$	−8.50637	−0.351095	−0.175548	+	0.984471i	$0.556170\pi$
$588$	1.16996	0.0482484
$589$	15.8514	0.653147
$590$	−12.3811	−0.509724
$591$	−3.15993	−0.129982
$592$	−3.11632	−0.128080
$593$	24.9289	1.02371	0.511853	−	0.859073i	$-0.328959\pi$
$593$	24.9289	1.02371	0.511853	+	0.859073i	$0.328959\pi$
$594$	0	0
$595$	7.28628	0.298708
$596$	−5.12256	−0.209828
$597$	17.0585	0.698160
$598$	−2.90751	−0.118897
$599$	35.1526	1.43630	0.718149	−	0.695889i	$-0.244990\pi$
$599$	35.1526	1.43630	0.718149	+	0.695889i	$0.244990\pi$
$600$	1.16996	0.0477635
$601$	34.7898	1.41910	0.709552	−	0.704653i	$-0.248897\pi$
$601$	34.7898	1.41910	0.709552	+	0.704653i	$0.248897\pi$
$602$	−0.705861	−0.0287687
$603$	3.08903	0.125795
$604$	22.4051	0.911652
$605$	0	0
$606$	13.9150	0.565259
$607$	14.7721	0.599581	0.299791	−	0.954005i	$-0.403083\pi$
$607$	14.7721	0.599581	0.299791	+	0.954005i	$0.403083\pi$
$608$	4.33680	0.175881
$609$	10.6658	0.432198
$610$	−6.62309	−0.268161
$611$	−5.74329	−0.232349
$612$	−11.8853	−0.480435
$613$	10.3889	0.419602	0.209801	−	0.977744i	$-0.432718\pi$
$613$	10.3889	0.419602	0.209801	+	0.977744i	$0.432718\pi$
$614$	13.6023	0.548944
$615$	−2.40514	−0.0969848
$616$	0	0
$617$	35.7962	1.44110	0.720551	−	0.693402i	$-0.243889\pi$
$617$	35.7962	1.44110	0.720551	+	0.693402i	$0.243889\pi$
$618$	−3.01289	−0.121196
$619$	31.2901	1.25765	0.628827	−	0.777545i	$-0.283535\pi$
$619$	31.2901	1.25765	0.628827	+	0.777545i	$0.283535\pi$
$620$	−3.65509	−0.146792
$621$	−10.9799	−0.440607
$622$	29.5607	1.18528
$623$	−8.34280	−0.334247
$624$	−1.67865	−0.0671998
$625$	1.00000	0.0400000
$626$	9.23518	0.369112
$627$	0	0
$628$	14.9308	0.595804
$629$	−22.7064	−0.905362
$630$	−1.63119	−0.0649881
$631$	47.2969	1.88286	0.941429	−	0.337211i	$-0.109484\pi$
$631$	47.2969	1.88286	0.941429	+	0.337211i	$0.109484\pi$
$632$	3.98377	0.158466
$633$	21.3340	0.847949
$634$	−5.25554	−0.208724
$635$	3.83782	0.152299
$636$	−5.70334	−0.226152
$637$	−1.43479	−0.0568485
$638$	0	0
$639$	−0.687841	−0.0272106
$640$	−1.00000	−0.0395285
$641$	3.57172	0.141074	0.0705371	−	0.997509i	$-0.477529\pi$
$641$	3.57172	0.141074	0.0705371	+	0.997509i	$0.477529\pi$
$642$	−0.0246035	−0.000971025 0
$643$	−8.20306	−0.323497	−0.161749	−	0.986832i	$-0.551713\pi$
$643$	−8.20306	−0.323497	−0.161749	+	0.986832i	$0.551713\pi$
$644$	−2.02643	−0.0798527
$645$	−0.825831	−0.0325171
$646$	31.5992	1.24325
$647$	−33.2763	−1.30823	−0.654113	−	0.756397i	$-0.726958\pi$
$647$	−33.2763	−1.30823	−0.654113	+	0.756397i	$0.726958\pi$
$648$	−1.44566	−0.0567910
$649$	0	0
$650$	−1.43479	−0.0562771
$651$	−4.27632	−0.167602
$652$	3.69439	0.144684
$653$	−20.5390	−0.803754	−0.401877	−	0.915694i	$-0.631642\pi$
$653$	−20.5390	−0.803754	−0.401877	+	0.915694i	$0.631642\pi$
$654$	−3.76756	−0.147323
$655$	19.4691	0.760720
$656$	2.05574	0.0802634
$657$	−12.0373	−0.469620
$658$	−4.00288	−0.156048
$659$	4.70889	0.183432	0.0917161	−	0.995785i	$-0.470765\pi$
$659$	4.70889	0.183432	0.0917161	+	0.995785i	$0.470765\pi$
$660$	0	0
$661$	−8.57967	−0.333710	−0.166855	−	0.985981i	$-0.553361\pi$
$661$	−8.57967	−0.333710	−0.166855	+	0.985981i	$0.553361\pi$
$662$	−23.4150	−0.910048
$663$	−12.2311	−0.475018
$664$	−7.15061	−0.277498
$665$	4.33680	0.168174
$666$	5.08330	0.196974
$667$	−18.4736	−0.715302
$668$	−9.33915	−0.361343
$669$	1.65966	0.0641663
$670$	1.89373	0.0731613
$671$	0	0
$672$	−1.16996	−0.0451323
$673$	−37.8109	−1.45750	−0.728751	−	0.684779i	$-0.759899\pi$
$673$	−37.8109	−1.45750	−0.728751	+	0.684779i	$0.759899\pi$
$674$	2.73973	0.105530
$675$	−5.41832	−0.208551
$676$	−10.9414	−0.420822
$677$	19.9974	0.768562	0.384281	−	0.923216i	$-0.374449\pi$
$677$	19.9974	0.768562	0.384281	+	0.923216i	$0.374449\pi$
$678$	19.7527	0.758597
$679$	−11.3050	−0.433848
$680$	−7.28628	−0.279416
$681$	9.57732	0.367004
$682$	0	0
$683$	−23.1577	−0.886106	−0.443053	−	0.896495i	$-0.646105\pi$
$683$	−23.1577	−0.886106	−0.443053	+	0.896495i	$0.646105\pi$
$684$	−7.07414	−0.270487
$685$	−16.1146	−0.615709
$686$	−1.00000	−0.0381802
$687$	−2.20629	−0.0841754
$688$	0.705861	0.0269107
$689$	6.99433	0.266463
$690$	−2.37085	−0.0902568
$691$	4.71821	0.179489	0.0897446	−	0.995965i	$-0.471395\pi$
$691$	4.71821	0.179489	0.0897446	+	0.995965i	$0.471395\pi$
$692$	1.89895	0.0721874
$693$	0	0
$694$	5.82295	0.221036
$695$	16.9156	0.641646
$696$	−10.6658	−0.404284
$697$	14.9787	0.567360
$698$	8.42897	0.319041
$699$	26.8588	1.01589
$700$	−1.00000	−0.0377964
$701$	8.58415	0.324219	0.162109	−	0.986773i	$-0.448170\pi$
$701$	8.58415	0.324219	0.162109	+	0.986773i	$0.448170\pi$
$702$	7.77415	0.293416
$703$	−13.5149	−0.509723
$704$	0	0
$705$	−4.68321	−0.176380
$706$	−23.9658	−0.901965
$707$	−11.8936	−0.447303
$708$	14.4855	0.544398
$709$	−28.0704	−1.05421	−0.527103	−	0.849802i	$-0.676722\pi$
$709$	−28.0704	−1.05421	−0.527103	+	0.849802i	$0.676722\pi$
$710$	−0.421681	−0.0158254
$711$	−6.49828	−0.243704
$712$	8.34280	0.312660
$713$	7.40681	0.277387
$714$	−8.52468	−0.319028
$715$	0	0
$716$	6.00288	0.224338
$717$	0.368807	0.0137734
$718$	−16.0490	−0.598942
$719$	30.4817	1.13678	0.568388	−	0.822761i	$-0.307567\pi$
$719$	30.4817	1.13678	0.568388	+	0.822761i	$0.307567\pi$
$720$	1.63119	0.0607908
$721$	2.57520	0.0959054
$722$	−0.192129	−0.00715029
$723$	−6.57098	−0.244377
$724$	−6.73019	−0.250126
$725$	−9.11632	−0.338572
$726$	0	0
$727$	1.25367	0.0464961	0.0232480	−	0.999730i	$-0.492599\pi$
$727$	1.25367	0.0464961	0.0232480	+	0.999730i	$0.492599\pi$
$728$	1.43479	0.0531769
$729$	21.3758	0.791697
$730$	−7.37947	−0.273126
$731$	5.14310	0.190224
$732$	7.74876	0.286402
$733$	−7.95330	−0.293762	−0.146881	−	0.989154i	$-0.546923\pi$
$733$	−7.95330	−0.293762	−0.146881	+	0.989154i	$0.546923\pi$
$734$	−2.17504	−0.0802820
$735$	−1.16996	−0.0431547
$736$	2.02643	0.0746954
$737$	0	0
$738$	−3.35331	−0.123437
$739$	−11.8074	−0.434342	−0.217171	−	0.976134i	$-0.569683\pi$
$739$	−11.8074	−0.434342	−0.217171	+	0.976134i	$0.569683\pi$
$740$	3.11632	0.114558
$741$	−7.27998	−0.267437
$742$	4.87480	0.178960
$743$	41.2546	1.51348	0.756742	−	0.653714i	$-0.226790\pi$
$743$	41.2546	1.51348	0.756742	+	0.653714i	$0.226790\pi$
$744$	4.27632	0.156778
$745$	5.12256	0.187676
$746$	−16.5044	−0.604270
$747$	11.6640	0.426763
$748$	0	0
$749$	0.0210293	0.000768396 0
$750$	−1.16996	−0.0427210
$751$	−18.2805	−0.667066	−0.333533	−	0.942738i	$-0.608241\pi$
$751$	−18.2805	−0.667066	−0.333533	+	0.942738i	$0.608241\pi$
$752$	4.00288	0.145970
$753$	16.7545	0.610567
$754$	13.0800	0.476346
$755$	−22.4051	−0.815406
$756$	5.41832	0.197062
$757$	46.8864	1.70411	0.852057	−	0.523449i	$-0.175355\pi$
$757$	46.8864	1.70411	0.852057	+	0.523449i	$0.175355\pi$
$758$	22.3263	0.810928
$759$	0	0
$760$	−4.33680	−0.157312
$761$	−50.8809	−1.84443	−0.922216	−	0.386675i	$-0.873624\pi$
$761$	−50.8809	−1.84443	−0.922216	+	0.386675i	$0.873624\pi$
$762$	−4.49010	−0.162659
$763$	3.22024	0.116581
$764$	15.9464	0.576919
$765$	11.8853	0.429714
$766$	−21.4500	−0.775019
$767$	−17.7644	−0.641434
$768$	1.16996	0.0422174
$769$	−26.5666	−0.958017	−0.479008	−	0.877810i	$-0.659004\pi$
$769$	−26.5666	−0.958017	−0.479008	+	0.877810i	$0.659004\pi$
$770$	0	0
$771$	33.8039	1.21742
$772$	11.7470	0.422784
$773$	−30.5526	−1.09890	−0.549450	−	0.835527i	$-0.685163\pi$
$773$	−30.5526	−1.09890	−0.549450	+	0.835527i	$0.685163\pi$
$774$	−1.15139	−0.0413859
$775$	3.65509	0.131295
$776$	11.3050	0.405827
$777$	3.64598	0.130799
$778$	−37.9771	−1.36155
$779$	8.91536	0.319426
$780$	1.67865	0.0601054
$781$	0	0
$782$	14.7652	0.528001
$783$	49.3951	1.76524
$784$	1.00000	0.0357143
$785$	−14.9308	−0.532903
$786$	−22.7781	−0.812468
$787$	−27.0074	−0.962710	−0.481355	−	0.876526i	$-0.659855\pi$
$787$	−27.0074	−0.962710	−0.481355	+	0.876526i	$0.659855\pi$
$788$	−2.70088	−0.0962148
$789$	25.6287	0.912405
$790$	−3.98377	−0.141736
$791$	−16.8832	−0.600297
$792$	0	0
$793$	−9.50274	−0.337452
$794$	−24.9220	−0.884447
$795$	5.70334	0.202277
$796$	14.5804	0.516789
$797$	−37.5786	−1.33110	−0.665551	−	0.746352i	$-0.731803\pi$
$797$	−37.5786	−1.33110	−0.665551	+	0.746352i	$0.731803\pi$
$798$	−5.07390	−0.179614
$799$	29.1661	1.03182
$800$	1.00000	0.0353553
$801$	−13.6087	−0.480839
$802$	−23.7936	−0.840180
$803$	0	0
$804$	−2.21560	−0.0781380
$805$	2.02643	0.0714224
$806$	−5.24430	−0.184722
$807$	−3.48478	−0.122670
$808$	11.8936	0.418414
$809$	−37.3166	−1.31198	−0.655991	−	0.754769i	$-0.727749\pi$
$809$	−37.3166	−1.31198	−0.655991	+	0.754769i	$0.727749\pi$
$810$	1.44566	0.0507954
$811$	43.9822	1.54443	0.772213	−	0.635364i	$-0.219150\pi$
$811$	43.9822	1.54443	0.772213	+	0.635364i	$0.219150\pi$
$812$	9.11632	0.319920
$813$	0.236584	0.00829735
$814$	0	0
$815$	−3.69439	−0.129409
$816$	8.52468	0.298423
$817$	3.06118	0.107097
$818$	−17.4118	−0.608789
$819$	−2.34041	−0.0817807
$820$	−2.05574	−0.0717897
$821$	30.6054	1.06814	0.534068	−	0.845442i	$-0.320663\pi$
$821$	30.6054	1.06814	0.534068	+	0.845442i	$0.320663\pi$
$822$	18.8535	0.657592
$823$	−20.5472	−0.716230	−0.358115	−	0.933677i	$-0.616580\pi$
$823$	−20.5472	−0.716230	−0.358115	+	0.933677i	$0.616580\pi$
$824$	−2.57520	−0.0897113
$825$	0	0
$826$	−12.3811	−0.430795
$827$	−45.3404	−1.57664	−0.788319	−	0.615266i	$-0.789048\pi$
$827$	−45.3404	−1.57664	−0.788319	+	0.615266i	$0.789048\pi$
$828$	−3.30550	−0.114874
$829$	41.2595	1.43300	0.716500	−	0.697587i	$-0.245743\pi$
$829$	41.2595	1.43300	0.716500	+	0.697587i	$0.245743\pi$
$830$	7.15061	0.248201
$831$	−5.76975	−0.200150
$832$	−1.43479	−0.0497424
$833$	7.28628	0.252455
$834$	−19.7906	−0.685293
$835$	9.33915	0.323195
$836$	0	0
$837$	−19.8045	−0.684542
$838$	6.77394	0.234002
$839$	−27.6981	−0.956243	−0.478122	−	0.878294i	$-0.658682\pi$
$839$	−27.6981	−0.956243	−0.478122	+	0.878294i	$0.658682\pi$
$840$	1.16996	0.0403675
$841$	54.1073	1.86577
$842$	16.3820	0.564560
$843$	−20.8818	−0.719209
$844$	18.2347	0.627666
$845$	10.9414	0.376395
$846$	−6.52944	−0.224487
$847$	0	0
$848$	−4.87480	−0.167401
$849$	−34.2473	−1.17536
$850$	7.28628	0.249917
$851$	−6.31502	−0.216476
$852$	0.493351	0.0169019
$853$	−41.7746	−1.43033	−0.715167	−	0.698954i	$-0.753649\pi$
$853$	−41.7746	−1.43033	−0.715167	+	0.698954i	$0.753649\pi$
$854$	−6.62309	−0.226637
$855$	7.07414	0.241931
$856$	−0.0210293	−0.000718768 0
$857$	45.5421	1.55569	0.777845	−	0.628457i	$-0.216313\pi$
$857$	45.5421	1.55569	0.777845	+	0.628457i	$0.216313\pi$
$858$	0	0
$859$	−7.44024	−0.253858	−0.126929	−	0.991912i	$-0.540512\pi$
$859$	−7.44024	−0.253858	−0.126929	+	0.991912i	$0.540512\pi$
$860$	−0.705861	−0.0240697
$861$	−2.40514	−0.0819671
$862$	−35.7762	−1.21854
$863$	9.39601	0.319844	0.159922	−	0.987130i	$-0.448876\pi$
$863$	9.39601	0.319844	0.159922	+	0.987130i	$0.448876\pi$
$864$	−5.41832	−0.184335
$865$	−1.89895	−0.0645664
$866$	12.5667	0.427035
$867$	42.2238	1.43400
$868$	−3.65509	−0.124062
$869$	0	0
$870$	10.6658	0.361603
$871$	2.71711	0.0920658
$872$	−3.22024	−0.109051
$873$	−18.4406	−0.624121
$874$	8.78825	0.297267
$875$	1.00000	0.0338062
$876$	8.63370	0.291706
$877$	9.96978	0.336655	0.168328	−	0.985731i	$-0.446163\pi$
$877$	9.96978	0.336655	0.168328	+	0.985731i	$0.446163\pi$
$878$	−34.6171	−1.16827
$879$	−34.9848	−1.18001
$880$	0	0
$881$	−3.94025	−0.132750	−0.0663752	−	0.997795i	$-0.521143\pi$
$881$	−3.94025	−0.132750	−0.0663752	+	0.997795i	$0.521143\pi$
$882$	−1.63119	−0.0549250
$883$	−41.4577	−1.39516	−0.697582	−	0.716505i	$-0.745741\pi$
$883$	−41.4577	−1.39516	−0.697582	+	0.716505i	$0.745741\pi$
$884$	−10.4543	−0.351616
$885$	−14.4855	−0.486924
$886$	18.9816	0.637698
$887$	−31.2649	−1.04977	−0.524886	−	0.851172i	$-0.675892\pi$
$887$	−31.2649	−1.04977	−0.524886	+	0.851172i	$0.675892\pi$
$888$	−3.64598	−0.122351
$889$	3.83782	0.128716
$890$	−8.34280	−0.279651
$891$	0	0
$892$	1.41856	0.0474969
$893$	17.3597	0.580920
$894$	−5.99320	−0.200443
$895$	−6.00288	−0.200654
$896$	−1.00000	−0.0334077
$897$	−3.40168	−0.113579
$898$	13.7748	0.459670
$899$	−33.3210	−1.11132
$900$	−1.63119	−0.0543729
$901$	−35.5192	−1.18332
$902$	0	0
$903$	−0.825831	−0.0274819
$904$	16.8832	0.561526
$905$	6.73019	0.223719
$906$	26.2132	0.870874
$907$	11.8441	0.393277	0.196638	−	0.980476i	$-0.436997\pi$
$907$	11.8441	0.393277	0.196638	+	0.980476i	$0.436997\pi$
$908$	8.18601	0.271662
$909$	−19.4006	−0.643479
$910$	−1.43479	−0.0475629
$911$	52.8126	1.74976	0.874879	−	0.484341i	$-0.160941\pi$
$911$	52.8126	1.74976	0.874879	+	0.484341i	$0.160941\pi$
$912$	5.07390	0.168014
$913$	0	0
$914$	36.0763	1.19330
$915$	−7.74876	−0.256166
$916$	−1.88578	−0.0623080
$917$	19.4691	0.642926
$918$	−39.4794	−1.30301
$919$	−26.4724	−0.873243	−0.436621	−	0.899645i	$-0.643825\pi$
$919$	−26.4724	−0.873243	−0.436621	+	0.899645i	$0.643825\pi$
$920$	−2.02643	−0.0668096
$921$	15.9142	0.524390
$922$	−23.2972	−0.767252
$923$	−0.605024	−0.0199146
$924$	0	0
$925$	−3.11632	−0.102464
$926$	−31.8729	−1.04741
$927$	4.20063	0.137967
$928$	−9.11632	−0.299258
$929$	39.7722	1.30488	0.652442	−	0.757838i	$-0.273744\pi$
$929$	39.7722	1.30488	0.652442	+	0.757838i	$0.273744\pi$
$930$	−4.27632	−0.140226
$931$	4.33680	0.142133
$932$	22.9570	0.751982
$933$	34.5849	1.13226
$934$	−11.5661	−0.378455
$935$	0	0
$936$	2.34041	0.0764988
$937$	−27.1898	−0.888251	−0.444126	−	0.895965i	$-0.646486\pi$
$937$	−27.1898	−0.888251	−0.444126	+	0.895965i	$0.646486\pi$
$938$	1.89373	0.0618325
$939$	10.8048	0.352602
$940$	−4.00288	−0.130559
$941$	−39.2513	−1.27956	−0.639778	−	0.768560i	$-0.720974\pi$
$941$	−39.2513	−1.27956	−0.639778	+	0.768560i	$0.720974\pi$
$942$	17.4685	0.569153
$943$	4.16583	0.135658
$944$	12.3811	0.402972
$945$	−5.41832	−0.176258
$946$	0	0
$947$	−42.7008	−1.38759	−0.693795	−	0.720173i	$-0.744062\pi$
$947$	−42.7008	−1.38759	−0.693795	+	0.720173i	$0.744062\pi$
$948$	4.66086	0.151378
$949$	−10.5880	−0.343701
$950$	4.33680	0.140705
$951$	−6.14878	−0.199388
$952$	−7.28628	−0.236150
$953$	22.7464	0.736828	0.368414	−	0.929662i	$-0.379901\pi$
$953$	22.7464	0.736828	0.368414	+	0.929662i	$0.379901\pi$
$954$	7.95172	0.257446
$955$	−15.9464	−0.516012
$956$	0.315230	0.0101953
$957$	0	0
$958$	−13.2561	−0.428287
$959$	−16.1146	−0.520369
$960$	−1.16996	−0.0377604
$961$	−17.6403	−0.569042
$962$	4.47127	0.144159
$963$	0.0343028	0.00110539
$964$	−5.61640	−0.180892
$965$	−11.7470	−0.378150
$966$	−2.37085	−0.0762809
$967$	5.16517	0.166101	0.0830504	−	0.996545i	$-0.473534\pi$
$967$	5.16517	0.166101	0.0830504	+	0.996545i	$0.473534\pi$
$968$	0	0
$969$	36.9698	1.18764
$970$	−11.3050	−0.362983
$971$	28.1375	0.902977	0.451488	−	0.892277i	$-0.350893\pi$
$971$	28.1375	0.902977	0.451488	+	0.892277i	$0.350893\pi$
$972$	14.5636	0.467127
$973$	16.9156	0.542289
$974$	5.42232	0.173742
$975$	−1.67865	−0.0537599
$976$	6.62309	0.212000
$977$	24.0697	0.770058	0.385029	−	0.922905i	$-0.374191\pi$
$977$	24.0697	0.770058	0.385029	+	0.922905i	$0.374191\pi$
$978$	4.32230	0.138212
$979$	0	0
$980$	−1.00000	−0.0319438
$981$	5.25282	0.167710
$982$	−36.0238	−1.14957
$983$	20.4577	0.652500	0.326250	−	0.945284i	$-0.394215\pi$
$983$	20.4577	0.652500	0.326250	+	0.945284i	$0.394215\pi$
$984$	2.40514	0.0766732
$985$	2.70088	0.0860572
$986$	−66.4241	−2.11537
$987$	−4.68321	−0.149068
$988$	−6.22241	−0.197961
$989$	1.43038	0.0454835
$990$	0	0
$991$	−28.8003	−0.914870	−0.457435	−	0.889243i	$-0.651232\pi$
$991$	−28.8003	−0.914870	−0.457435	+	0.889243i	$0.651232\pi$
$992$	3.65509	0.116049
$993$	−27.3946	−0.869342
$994$	−0.421681	−0.0133749
$995$	−14.5804	−0.462230
$996$	−8.36595	−0.265085
$997$	18.0825	0.572680	0.286340	−	0.958128i	$-0.407561\pi$
$997$	18.0825	0.572680	0.286340	+	0.958128i	$0.407561\pi$
$998$	−3.26974	−0.103502
$999$	16.8852	0.534224

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.dd.1.4	yes	6
11.10	odd	2		8470.2.a.cx.1.4	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8470.2.a.cx.1.4	✓	6	11.10	odd	2
8470.2.a.dd.1.4	yes	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.16996 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.16996 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.63119 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.16996 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.16996 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.63119 q^{9} -1.00000 q^{10} +1.16996 q^{12} -1.43479 q^{13} -1.00000 q^{14} -1.16996 q^{15} +1.00000 q^{16} +7.28628 q^{17} -1.63119 q^{18} +4.33680 q^{19} -1.00000 q^{20} -1.16996 q^{21} +2.02643 q^{23} +1.16996 q^{24} +1.00000 q^{25} -1.43479 q^{26} -5.41832 q^{27} -1.00000 q^{28} -9.11632 q^{29} -1.16996 q^{30} +3.65509 q^{31} +1.00000 q^{32} +7.28628 q^{34} +1.00000 q^{35} -1.63119 q^{36} -3.11632 q^{37} +4.33680 q^{38} -1.67865 q^{39} -1.00000 q^{40} +2.05574 q^{41} -1.16996 q^{42} +0.705861 q^{43} +1.63119 q^{45} +2.02643 q^{46} +4.00288 q^{47} +1.16996 q^{48} +1.00000 q^{49} +1.00000 q^{50} +8.52468 q^{51} -1.43479 q^{52} -4.87480 q^{53} -5.41832 q^{54} -1.00000 q^{56} +5.07390 q^{57} -9.11632 q^{58} +12.3811 q^{59} -1.16996 q^{60} +6.62309 q^{61} +3.65509 q^{62} +1.63119 q^{63} +1.00000 q^{64} +1.43479 q^{65} -1.89373 q^{67} +7.28628 q^{68} +2.37085 q^{69} +1.00000 q^{70} +0.421681 q^{71} -1.63119 q^{72} +7.37947 q^{73} -3.11632 q^{74} +1.16996 q^{75} +4.33680 q^{76} -1.67865 q^{78} +3.98377 q^{79} -1.00000 q^{80} -1.44566 q^{81} +2.05574 q^{82} -7.15061 q^{83} -1.16996 q^{84} -7.28628 q^{85} +0.705861 q^{86} -10.6658 q^{87} +8.34280 q^{89} +1.63119 q^{90} +1.43479 q^{91} +2.02643 q^{92} +4.27632 q^{93} +4.00288 q^{94} -4.33680 q^{95} +1.16996 q^{96} +11.3050 q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 6 q^{7} + 6 q^{8} + 18 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 - 6 * q^7 + 6 * q^8 + 18 * q^9	\( 6 q + 6 q^{2} + 6 q^{4} - 6 q^{5} - 6 q^{7} + 6 q^{8} + 18 q^{9} - 6 q^{10} - 6 q^{14} + 6 q^{16} - 6 q^{17} + 18 q^{18} - 6 q^{20} + 6 q^{25} - 12 q^{27} - 6 q^{28} - 12 q^{29} + 6 q^{32} - 6 q^{34} + 6 q^{35} + 18 q^{36} + 24 q^{37} + 24 q^{39} - 6 q^{40} - 12 q^{41} + 18 q^{43} - 18 q^{45} + 24 q^{47} + 6 q^{49} + 6 q^{50} + 12 q^{51} + 36 q^{53} - 12 q^{54} - 6 q^{56} + 12 q^{57} - 12 q^{58} + 30 q^{59} - 36 q^{61} - 18 q^{63} + 6 q^{64} - 12 q^{67} - 6 q^{68} + 6 q^{70} + 6 q^{71} + 18 q^{72} + 6 q^{73} + 24 q^{74} + 24 q^{78} + 24 q^{79} - 6 q^{80} + 54 q^{81} - 12 q^{82} - 24 q^{83} + 6 q^{85} + 18 q^{86} + 24 q^{87} + 36 q^{89} - 18 q^{90} + 24 q^{94} + 6 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 - 6 * q^7 + 6 * q^8 + 18 * q^9 - 6 * q^10 - 6 * q^14 + 6 * q^16 - 6 * q^17 + 18 * q^18 - 6 * q^20 + 6 * q^25 - 12 * q^27 - 6 * q^28 - 12 * q^29 + 6 * q^32 - 6 * q^34 + 6 * q^35 + 18 * q^36 + 24 * q^37 + 24 * q^39 - 6 * q^40 - 12 * q^41 + 18 * q^43 - 18 * q^45 + 24 * q^47 + 6 * q^49 + 6 * q^50 + 12 * q^51 + 36 * q^53 - 12 * q^54 - 6 * q^56 + 12 * q^57 - 12 * q^58 + 30 * q^59 - 36 * q^61 - 18 * q^63 + 6 * q^64 - 12 * q^67 - 6 * q^68 + 6 * q^70 + 6 * q^71 + 18 * q^72 + 6 * q^73 + 24 * q^74 + 24 * q^78 + 24 * q^79 - 6 * q^80 + 54 * q^81 - 12 * q^82 - 24 * q^83 + 6 * q^85 + 18 * q^86 + 24 * q^87 + 36 * q^89 - 18 * q^90 + 24 * q^94 + 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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