LMFDB - Embedded newform 8470.2.a.cu.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8470.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$67.6332905120$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.38498000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 12x^{4} + 5x^{3} + 38x^{2} - x - 19 $ x^6 - x^5 - 12x^4 + 5x^3 + 38*x^2 - x - 19
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 770)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.824369$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.82437 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.82437 q^{6} -1.00000 q^{7} -1.00000 q^{8} +0.328323 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.82437 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.82437 q^{6} -1.00000 q^{7} -1.00000 q^{8} +0.328323 q^{9} +1.00000 q^{10} -1.82437 q^{12} +2.21432 q^{13} +1.00000 q^{14} +1.82437 q^{15} +1.00000 q^{16} +7.96638 q^{17} -0.328323 q^{18} +0.915653 q^{19} -1.00000 q^{20} +1.82437 q^{21} +6.07737 q^{23} +1.82437 q^{24} +1.00000 q^{25} -2.21432 q^{26} +4.87412 q^{27} -1.00000 q^{28} -5.06597 q^{29} -1.82437 q^{30} +9.33892 q^{31} -1.00000 q^{32} -7.96638 q^{34} +1.00000 q^{35} +0.328323 q^{36} +4.32937 q^{37} -0.915653 q^{38} -4.03973 q^{39} +1.00000 q^{40} +8.99953 q^{41} -1.82437 q^{42} -2.76947 q^{43} -0.328323 q^{45} -6.07737 q^{46} +4.22816 q^{47} -1.82437 q^{48} +1.00000 q^{49} -1.00000 q^{50} -14.5336 q^{51} +2.21432 q^{52} -9.33444 q^{53} -4.87412 q^{54} +1.00000 q^{56} -1.67049 q^{57} +5.06597 q^{58} +7.19487 q^{59} +1.82437 q^{60} +12.6895 q^{61} -9.33892 q^{62} -0.328323 q^{63} +1.00000 q^{64} -2.21432 q^{65} -1.29018 q^{67} +7.96638 q^{68} -11.0874 q^{69} -1.00000 q^{70} +0.0202370 q^{71} -0.328323 q^{72} -11.8463 q^{73} -4.32937 q^{74} -1.82437 q^{75} +0.915653 q^{76} +4.03973 q^{78} +9.39226 q^{79} -1.00000 q^{80} -9.87717 q^{81} -8.99953 q^{82} -0.747575 q^{83} +1.82437 q^{84} -7.96638 q^{85} +2.76947 q^{86} +9.24220 q^{87} -14.2639 q^{89} +0.328323 q^{90} -2.21432 q^{91} +6.07737 q^{92} -17.0376 q^{93} -4.22816 q^{94} -0.915653 q^{95} +1.82437 q^{96} -7.27431 q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 5 q^{3} + 6 q^{4} - 6 q^{5} + 5 q^{6} - 6 q^{7} - 6 q^{8} + 11 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 5 * q^3 + 6 * q^4 - 6 * q^5 + 5 * q^6 - 6 * q^7 - 6 * q^8 + 11 * q^9	$ 6 q - 6 q^{2} - 5 q^{3} + 6 q^{4} - 6 q^{5} + 5 q^{6} - 6 q^{7} - 6 q^{8} + 11 q^{9} + 6 q^{10} - 5 q^{12} + 6 q^{14} + 5 q^{15} + 6 q^{16} + 15 q^{17} - 11 q^{18} + 13 q^{19} - 6 q^{20} + 5 q^{21} - 2 q^{23} + 5 q^{24} + 6 q^{25} - 26 q^{27} - 6 q^{28} + 4 q^{29} - 5 q^{30} - 2 q^{31} - 6 q^{32} - 15 q^{34} + 6 q^{35} + 11 q^{36} - 13 q^{38} + 30 q^{39} + 6 q^{40} + 17 q^{41} - 5 q^{42} - 15 q^{43} - 11 q^{45} + 2 q^{46} - 18 q^{47} - 5 q^{48} + 6 q^{49} - 6 q^{50} - 6 q^{51} + 22 q^{53} + 26 q^{54} + 6 q^{56} + 2 q^{57} - 4 q^{58} - 7 q^{59} + 5 q^{60} + 20 q^{61} + 2 q^{62} - 11 q^{63} + 6 q^{64} - 29 q^{67} + 15 q^{68} + 12 q^{69} - 6 q^{70} - 2 q^{71} - 11 q^{72} - q^{73} - 5 q^{75} + 13 q^{76} - 30 q^{78} + 12 q^{79} - 6 q^{80} + 22 q^{81} - 17 q^{82} + 35 q^{83} + 5 q^{84} - 15 q^{85} + 15 q^{86} - 29 q^{89} + 11 q^{90} - 2 q^{92} + 8 q^{93} + 18 q^{94} - 13 q^{95} + 5 q^{96} - 19 q^{97} - 6 q^{98}+O(q^{100}) $ 6 * q - 6 * q^2 - 5 * q^3 + 6 * q^4 - 6 * q^5 + 5 * q^6 - 6 * q^7 - 6 * q^8 + 11 * q^9 + 6 * q^10 - 5 * q^12 + 6 * q^14 + 5 * q^15 + 6 * q^16 + 15 * q^17 - 11 * q^18 + 13 * q^19 - 6 * q^20 + 5 * q^21 - 2 * q^23 + 5 * q^24 + 6 * q^25 - 26 * q^27 - 6 * q^28 + 4 * q^29 - 5 * q^30 - 2 * q^31 - 6 * q^32 - 15 * q^34 + 6 * q^35 + 11 * q^36 - 13 * q^38 + 30 * q^39 + 6 * q^40 + 17 * q^41 - 5 * q^42 - 15 * q^43 - 11 * q^45 + 2 * q^46 - 18 * q^47 - 5 * q^48 + 6 * q^49 - 6 * q^50 - 6 * q^51 + 22 * q^53 + 26 * q^54 + 6 * q^56 + 2 * q^57 - 4 * q^58 - 7 * q^59 + 5 * q^60 + 20 * q^61 + 2 * q^62 - 11 * q^63 + 6 * q^64 - 29 * q^67 + 15 * q^68 + 12 * q^69 - 6 * q^70 - 2 * q^71 - 11 * q^72 - q^73 - 5 * q^75 + 13 * q^76 - 30 * q^78 + 12 * q^79 - 6 * q^80 + 22 * q^81 - 17 * q^82 + 35 * q^83 + 5 * q^84 - 15 * q^85 + 15 * q^86 - 29 * q^89 + 11 * q^90 - 2 * q^92 + 8 * q^93 + 18 * q^94 - 13 * q^95 + 5 * q^96 - 19 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.82437	−1.05330	−0.526650	−	0.850082i	$-0.676552\pi$
$3$	−1.82437	−1.05330	−0.526650	+	0.850082i	$0.676552\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.82437	0.744796
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	0.328323	0.109441
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	−1.82437	−0.526650
$13$	2.21432	0.614141	0.307071	−	0.951687i	$-0.400651\pi$
$13$	2.21432	0.614141	0.307071	+	0.951687i	$0.400651\pi$
$14$	1.00000	0.267261
$15$	1.82437	0.471050
$16$	1.00000	0.250000
$17$	7.96638	1.93213	0.966066	−	0.258297i	$-0.0831614\pi$
$17$	7.96638	1.93213	0.966066	+	0.258297i	$0.0831614\pi$
$18$	−0.328323	−0.0773866
$19$	0.915653	0.210065	0.105033	−	0.994469i	$-0.466505\pi$
$19$	0.915653	0.210065	0.105033	+	0.994469i	$0.466505\pi$
$20$	−1.00000	−0.223607
$21$	1.82437	0.398110
$22$	0	0
$23$	6.07737	1.26722	0.633610	−	0.773653i	$-0.281572\pi$
$23$	6.07737	1.26722	0.633610	+	0.773653i	$0.281572\pi$
$24$	1.82437	0.372398
$25$	1.00000	0.200000
$26$	−2.21432	−0.434263
$27$	4.87412	0.938026
$28$	−1.00000	−0.188982
$29$	−5.06597	−0.940727	−0.470364	−	0.882473i	$-0.655877\pi$
$29$	−5.06597	−0.940727	−0.470364	+	0.882473i	$0.655877\pi$
$30$	−1.82437	−0.333083
$31$	9.33892	1.67732	0.838660	−	0.544655i	$-0.183339\pi$
$31$	9.33892	1.67732	0.838660	+	0.544655i	$0.183339\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−7.96638	−1.36622
$35$	1.00000	0.169031
$36$	0.328323	0.0547206
$37$	4.32937	0.711744	0.355872	−	0.934535i	$-0.384184\pi$
$37$	4.32937	0.711744	0.355872	+	0.934535i	$0.384184\pi$
$38$	−0.915653	−0.148538
$39$	−4.03973	−0.646875
$40$	1.00000	0.158114
$41$	8.99953	1.40549	0.702745	−	0.711441i	$-0.251957\pi$
$41$	8.99953	1.40549	0.702745	+	0.711441i	$0.251957\pi$
$42$	−1.82437	−0.281506
$43$	−2.76947	−0.422340	−0.211170	−	0.977449i	$-0.567727\pi$
$43$	−2.76947	−0.422340	−0.211170	+	0.977449i	$0.567727\pi$
$44$	0	0
$45$	−0.328323	−0.0489436
$46$	−6.07737	−0.896060
$47$	4.22816	0.616740	0.308370	−	0.951266i	$-0.400216\pi$
$47$	4.22816	0.616740	0.308370	+	0.951266i	$0.400216\pi$
$48$	−1.82437	−0.263325
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	−14.5336	−2.03511
$52$	2.21432	0.307071
$53$	−9.33444	−1.28218	−0.641092	−	0.767464i	$-0.721518\pi$
$53$	−9.33444	−1.28218	−0.641092	+	0.767464i	$0.721518\pi$
$54$	−4.87412	−0.663284
$55$	0	0
$56$	1.00000	0.133631
$57$	−1.67049	−0.221262
$58$	5.06597	0.665195
$59$	7.19487	0.936693	0.468346	−	0.883545i	$-0.344850\pi$
$59$	7.19487	0.936693	0.468346	+	0.883545i	$0.344850\pi$
$60$	1.82437	0.235525
$61$	12.6895	1.62473	0.812365	−	0.583150i	$-0.198180\pi$
$61$	12.6895	1.62473	0.812365	+	0.583150i	$0.198180\pi$
$62$	−9.33892	−1.18604
$63$	−0.328323	−0.0413649
$64$	1.00000	0.125000
$65$	−2.21432	−0.274652
$66$	0	0
$67$	−1.29018	−0.157620	−0.0788101	−	0.996890i	$-0.525112\pi$
$67$	−1.29018	−0.157620	−0.0788101	+	0.996890i	$0.525112\pi$
$68$	7.96638	0.966066
$69$	−11.0874	−1.33476
$70$	−1.00000	−0.119523
$71$	0.0202370	0.00240169	0.00120084	−	0.999999i	$-0.499618\pi$
$71$	0.0202370	0.00240169	0.00120084	+	0.999999i	$0.499618\pi$
$72$	−0.328323	−0.0386933
$73$	−11.8463	−1.38650	−0.693250	−	0.720698i	$-0.743822\pi$
$73$	−11.8463	−1.38650	−0.693250	+	0.720698i	$0.743822\pi$
$74$	−4.32937	−0.503279
$75$	−1.82437	−0.210660
$76$	0.915653	0.105033
$77$	0	0
$78$	4.03973	0.457410
$79$	9.39226	1.05671	0.528356	−	0.849023i	$-0.322809\pi$
$79$	9.39226	1.05671	0.528356	+	0.849023i	$0.322809\pi$
$80$	−1.00000	−0.111803
$81$	−9.87717	−1.09746
$82$	−8.99953	−0.993832
$83$	−0.747575	−0.0820570	−0.0410285	−	0.999158i	$-0.513063\pi$
$83$	−0.747575	−0.0820570	−0.0410285	+	0.999158i	$0.513063\pi$
$84$	1.82437	0.199055
$85$	−7.96638	−0.864075
$86$	2.76947	0.298639
$87$	9.24220	0.990868
$88$	0	0
$89$	−14.2639	−1.51197	−0.755983	−	0.654591i	$-0.772841\pi$
$89$	−14.2639	−1.51197	−0.755983	+	0.654591i	$0.772841\pi$
$90$	0.328323	0.0346083
$91$	−2.21432	−0.232124
$92$	6.07737	0.633610
$93$	−17.0376	−1.76672
$94$	−4.22816	−0.436101
$95$	−0.915653	−0.0939440
$96$	1.82437	0.186199
$97$	−7.27431	−0.738594	−0.369297	−	0.929311i	$-0.620402\pi$
$97$	−7.27431	−0.738594	−0.369297	+	0.929311i	$0.620402\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	5.35283	0.532627	0.266313	−	0.963886i	$-0.414194\pi$
$101$	5.35283	0.532627	0.266313	+	0.963886i	$0.414194\pi$
$102$	14.5336	1.43904
$103$	−14.3938	−1.41826	−0.709130	−	0.705078i	$-0.750912\pi$
$103$	−14.3938	−1.41826	−0.709130	+	0.705078i	$0.750912\pi$
$104$	−2.21432	−0.217132
$105$	−1.82437	−0.178040
$106$	9.33444	0.906641
$107$	4.27627	0.413402	0.206701	−	0.978404i	$-0.433727\pi$
$107$	4.27627	0.413402	0.206701	+	0.978404i	$0.433727\pi$
$108$	4.87412	0.469013
$109$	5.04265	0.482998	0.241499	−	0.970401i	$-0.422361\pi$
$109$	5.04265	0.482998	0.241499	+	0.970401i	$0.422361\pi$
$110$	0	0
$111$	−7.89837	−0.749680
$112$	−1.00000	−0.0944911
$113$	13.8169	1.29979	0.649894	−	0.760025i	$-0.274813\pi$
$113$	13.8169	1.29979	0.649894	+	0.760025i	$0.274813\pi$
$114$	1.67049	0.156456
$115$	−6.07737	−0.566718
$116$	−5.06597	−0.470364
$117$	0.727012	0.0672123
$118$	−7.19487	−0.662342
$119$	−7.96638	−0.730277
$120$	−1.82437	−0.166541
$121$	0	0
$122$	−12.6895	−1.14886
$123$	−16.4185	−1.48040
$124$	9.33892	0.838660
$125$	−1.00000	−0.0894427
$126$	0.328323	0.0292494
$127$	−14.6820	−1.30281	−0.651407	−	0.758729i	$-0.725821\pi$
$127$	−14.6820	−1.30281	−0.651407	+	0.758729i	$0.725821\pi$
$128$	−1.00000	−0.0883883
$129$	5.05253	0.444850
$130$	2.21432	0.194209
$131$	7.62582	0.666271	0.333135	−	0.942879i	$-0.391893\pi$
$131$	7.62582	0.666271	0.333135	+	0.942879i	$0.391893\pi$
$132$	0	0
$133$	−0.915653	−0.0793972
$134$	1.29018	0.111454
$135$	−4.87412	−0.419498
$136$	−7.96638	−0.683111
$137$	−4.93059	−0.421248	−0.210624	−	0.977567i	$-0.567550\pi$
$137$	−4.93059	−0.421248	−0.210624	+	0.977567i	$0.567550\pi$
$138$	11.0874	0.943820
$139$	4.17718	0.354304	0.177152	−	0.984184i	$-0.443312\pi$
$139$	4.17718	0.354304	0.177152	+	0.984184i	$0.443312\pi$
$140$	1.00000	0.0845154
$141$	−7.71373	−0.649613
$142$	−0.0202370	−0.00169825
$143$	0	0
$144$	0.328323	0.0273603
$145$	5.06597	0.420706
$146$	11.8463	0.980403
$147$	−1.82437	−0.150471
$148$	4.32937	0.355872
$149$	13.4785	1.10420	0.552102	−	0.833776i	$-0.313826\pi$
$149$	13.4785	1.10420	0.552102	+	0.833776i	$0.313826\pi$
$150$	1.82437	0.148959
$151$	−17.6102	−1.43309	−0.716547	−	0.697538i	$-0.754279\pi$
$151$	−17.6102	−1.43309	−0.716547	+	0.697538i	$0.754279\pi$
$152$	−0.915653	−0.0742692
$153$	2.61555	0.211455
$154$	0	0
$155$	−9.33892	−0.750121
$156$	−4.03973	−0.323438
$157$	11.4836	0.916491	0.458245	−	0.888826i	$-0.348478\pi$
$157$	11.4836	0.916491	0.458245	+	0.888826i	$0.348478\pi$
$158$	−9.39226	−0.747208
$159$	17.0295	1.35052
$160$	1.00000	0.0790569
$161$	−6.07737	−0.478964
$162$	9.87717	0.776024
$163$	−0.139250	−0.0109069	−0.00545347	−	0.999985i	$-0.501736\pi$
$163$	−0.139250	−0.0109069	−0.00545347	+	0.999985i	$0.501736\pi$
$164$	8.99953	0.702745
$165$	0	0
$166$	0.747575	0.0580230
$167$	−7.04367	−0.545056	−0.272528	−	0.962148i	$-0.587860\pi$
$167$	−7.04367	−0.545056	−0.272528	+	0.962148i	$0.587860\pi$
$168$	−1.82437	−0.140753
$169$	−8.09680	−0.622830
$170$	7.96638	0.610993
$171$	0.300630	0.0229898
$172$	−2.76947	−0.211170
$173$	14.0443	1.06777	0.533883	−	0.845558i	$-0.320732\pi$
$173$	14.0443	1.06777	0.533883	+	0.845558i	$0.320732\pi$
$174$	−9.24220	−0.700650
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	−13.1261	−0.986619
$178$	14.2639	1.06912
$179$	12.8339	0.959254	0.479627	−	0.877473i	$-0.340772\pi$
$179$	12.8339	0.959254	0.479627	+	0.877473i	$0.340772\pi$
$180$	−0.328323	−0.0244718
$181$	19.2871	1.43360	0.716798	−	0.697281i	$-0.245607\pi$
$181$	19.2871	1.43360	0.716798	+	0.697281i	$0.245607\pi$
$182$	2.21432	0.164136
$183$	−23.1504	−1.71133
$184$	−6.07737	−0.448030
$185$	−4.32937	−0.318302
$186$	17.0376	1.24926
$187$	0	0
$188$	4.22816	0.308370
$189$	−4.87412	−0.354540
$190$	0.915653	0.0664284
$191$	−12.0109	−0.869076	−0.434538	−	0.900653i	$-0.643088\pi$
$191$	−12.0109	−0.869076	−0.434538	+	0.900653i	$0.643088\pi$
$192$	−1.82437	−0.131663
$193$	17.2998	1.24527	0.622635	−	0.782512i	$-0.286062\pi$
$193$	17.2998	1.24527	0.622635	+	0.782512i	$0.286062\pi$
$194$	7.27431	0.522265
$195$	4.03973	0.289291
$196$	1.00000	0.0714286
$197$	13.1724	0.938497	0.469248	−	0.883066i	$-0.344525\pi$
$197$	13.1724	0.938497	0.469248	+	0.883066i	$0.344525\pi$
$198$	0	0
$199$	−22.9779	−1.62886	−0.814431	−	0.580260i	$-0.802951\pi$
$199$	−22.9779	−1.62886	−0.814431	+	0.580260i	$0.802951\pi$
$200$	−1.00000	−0.0707107
$201$	2.35376	0.166021
$202$	−5.35283	−0.376624
$203$	5.06597	0.355561
$204$	−14.5336	−1.01756
$205$	−8.99953	−0.628555
$206$	14.3938	1.00286
$207$	1.99534	0.138686
$208$	2.21432	0.153535
$209$	0	0
$210$	1.82437	0.125893
$211$	16.5609	1.14010	0.570050	−	0.821610i	$-0.306924\pi$
$211$	16.5609	1.14010	0.570050	+	0.821610i	$0.306924\pi$
$212$	−9.33444	−0.641092
$213$	−0.0369197	−0.00252970
$214$	−4.27627	−0.292320
$215$	2.76947	0.188876
$216$	−4.87412	−0.331642
$217$	−9.33892	−0.633968
$218$	−5.04265	−0.341531
$219$	21.6119	1.46040
$220$	0	0
$221$	17.6401	1.18660
$222$	7.89837	0.530104
$223$	−19.1235	−1.28060	−0.640301	−	0.768124i	$-0.721190\pi$
$223$	−19.1235	−1.28060	−0.640301	+	0.768124i	$0.721190\pi$
$224$	1.00000	0.0668153
$225$	0.328323	0.0218882
$226$	−13.8169	−0.919088
$227$	−19.6989	−1.30746	−0.653732	−	0.756726i	$-0.726798\pi$
$227$	−19.6989	−1.30746	−0.653732	+	0.756726i	$0.726798\pi$
$228$	−1.67049	−0.110631
$229$	27.5813	1.82263	0.911313	−	0.411714i	$-0.135070\pi$
$229$	27.5813	1.82263	0.911313	+	0.411714i	$0.135070\pi$
$230$	6.07737	0.400730
$231$	0	0
$232$	5.06597	0.332597
$233$	12.9463	0.848141	0.424071	−	0.905629i	$-0.360601\pi$
$233$	12.9463	0.848141	0.424071	+	0.905629i	$0.360601\pi$
$234$	−0.727012	−0.0475263
$235$	−4.22816	−0.275815
$236$	7.19487	0.468346
$237$	−17.1349	−1.11303
$238$	7.96638	0.516384
$239$	5.77626	0.373635	0.186818	−	0.982395i	$-0.440183\pi$
$239$	5.77626	0.373635	0.186818	+	0.982395i	$0.440183\pi$
$240$	1.82437	0.117763
$241$	25.0323	1.61247	0.806237	−	0.591593i	$-0.201501\pi$
$241$	25.0323	1.61247	0.806237	+	0.591593i	$0.201501\pi$
$242$	0	0
$243$	3.39724	0.217933
$244$	12.6895	0.812365
$245$	−1.00000	−0.0638877
$246$	16.4185	1.04680
$247$	2.02755	0.129010
$248$	−9.33892	−0.593022
$249$	1.36385	0.0864306
$250$	1.00000	0.0632456
$251$	−6.66594	−0.420750	−0.210375	−	0.977621i	$-0.567469\pi$
$251$	−6.66594	−0.420750	−0.210375	+	0.977621i	$0.567469\pi$
$252$	−0.328323	−0.0206824
$253$	0	0
$254$	14.6820	0.921228
$255$	14.5336	0.910131
$256$	1.00000	0.0625000
$257$	−22.7153	−1.41694	−0.708472	−	0.705739i	$-0.750615\pi$
$257$	−22.7153	−1.41694	−0.708472	+	0.705739i	$0.750615\pi$
$258$	−5.05253	−0.314557
$259$	−4.32937	−0.269014
$260$	−2.21432	−0.137326
$261$	−1.66328	−0.102954
$262$	−7.62582	−0.471124
$263$	−14.5015	−0.894200	−0.447100	−	0.894484i	$-0.647543\pi$
$263$	−14.5015	−0.894200	−0.447100	+	0.894484i	$0.647543\pi$
$264$	0	0
$265$	9.33444	0.573410
$266$	0.915653	0.0561423
$267$	26.0225	1.59255
$268$	−1.29018	−0.0788101
$269$	−21.2753	−1.29718	−0.648590	−	0.761138i	$-0.724641\pi$
$269$	−21.2753	−1.29718	−0.648590	+	0.761138i	$0.724641\pi$
$270$	4.87412	0.296630
$271$	−8.06611	−0.489981	−0.244991	−	0.969525i	$-0.578785\pi$
$271$	−8.06611	−0.489981	−0.244991	+	0.969525i	$0.578785\pi$
$272$	7.96638	0.483033
$273$	4.03973	0.244496
$274$	4.93059	0.297868
$275$	0	0
$276$	−11.0874	−0.667382
$277$	−17.4563	−1.04885	−0.524423	−	0.851458i	$-0.675719\pi$
$277$	−17.4563	−1.04885	−0.524423	+	0.851458i	$0.675719\pi$
$278$	−4.17718	−0.250531
$279$	3.06619	0.183568
$280$	−1.00000	−0.0597614
$281$	20.4688	1.22106	0.610532	−	0.791992i	$-0.290956\pi$
$281$	20.4688	1.22106	0.610532	+	0.791992i	$0.290956\pi$
$282$	7.71373	0.459346
$283$	−5.27282	−0.313437	−0.156718	−	0.987643i	$-0.550091\pi$
$283$	−5.27282	−0.313437	−0.156718	+	0.987643i	$0.550091\pi$
$284$	0.0202370	0.00120084
$285$	1.67049	0.0989512
$286$	0	0
$287$	−8.99953	−0.531226
$288$	−0.328323	−0.0193466
$289$	46.4632	2.73313
$290$	−5.06597	−0.297484
$291$	13.2710	0.777961
$292$	−11.8463	−0.693250
$293$	−6.40613	−0.374250	−0.187125	−	0.982336i	$-0.559917\pi$
$293$	−6.40613	−0.374250	−0.187125	+	0.982336i	$0.559917\pi$
$294$	1.82437	0.106399
$295$	−7.19487	−0.418902
$296$	−4.32937	−0.251640
$297$	0	0
$298$	−13.4785	−0.780790
$299$	13.4572	0.778252
$300$	−1.82437	−0.105330
$301$	2.76947	0.159629
$302$	17.6102	1.01335
$303$	−9.76555	−0.561016
$304$	0.915653	0.0525163
$305$	−12.6895	−0.726601
$306$	−2.61555	−0.149521
$307$	−5.35970	−0.305894	−0.152947	−	0.988234i	$-0.548876\pi$
$307$	−5.35970	−0.305894	−0.152947	+	0.988234i	$0.548876\pi$
$308$	0	0
$309$	26.2595	1.49385
$310$	9.33892	0.530415
$311$	−26.9819	−1.53001	−0.765003	−	0.644027i	$-0.777262\pi$
$311$	−26.9819	−1.53001	−0.765003	+	0.644027i	$0.777262\pi$
$312$	4.03973	0.228705
$313$	−28.5633	−1.61449	−0.807245	−	0.590216i	$-0.799043\pi$
$313$	−28.5633	−1.61449	−0.807245	+	0.590216i	$0.799043\pi$
$314$	−11.4836	−0.648057
$315$	0.328323	0.0184989
$316$	9.39226	0.528356
$317$	21.0077	1.17991	0.589954	−	0.807437i	$-0.299146\pi$
$317$	21.0077	1.17991	0.589954	+	0.807437i	$0.299146\pi$
$318$	−17.0295	−0.954965
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	−7.80149	−0.435437
$322$	6.07737	0.338679
$323$	7.29444	0.405873
$324$	−9.87717	−0.548732
$325$	2.21432	0.122828
$326$	0.139250	0.00771236
$327$	−9.19965	−0.508742
$328$	−8.99953	−0.496916
$329$	−4.22816	−0.233106
$330$	0	0
$331$	11.6022	0.637717	0.318858	−	0.947802i	$-0.396701\pi$
$331$	11.6022	0.637717	0.318858	+	0.947802i	$0.396701\pi$
$332$	−0.747575	−0.0410285
$333$	1.42143	0.0778941
$334$	7.04367	0.385413
$335$	1.29018	0.0704899
$336$	1.82437	0.0995275
$337$	−2.34874	−0.127944	−0.0639720	−	0.997952i	$-0.520377\pi$
$337$	−2.34874	−0.127944	−0.0639720	+	0.997952i	$0.520377\pi$
$338$	8.09680	0.440408
$339$	−25.2072	−1.36907
$340$	−7.96638	−0.432038
$341$	0	0
$342$	−0.300630	−0.0162562
$343$	−1.00000	−0.0539949
$344$	2.76947	0.149320
$345$	11.0874	0.596924
$346$	−14.0443	−0.755025
$347$	31.4811	1.68999	0.844997	−	0.534771i	$-0.179602\pi$
$347$	31.4811	1.68999	0.844997	+	0.534771i	$0.179602\pi$
$348$	9.24220	0.495434
$349$	−2.60777	−0.139591	−0.0697955	−	0.997561i	$-0.522235\pi$
$349$	−2.60777	−0.139591	−0.0697955	+	0.997561i	$0.522235\pi$
$350$	1.00000	0.0534522
$351$	10.7929	0.576080
$352$	0	0
$353$	−0.416007	−0.0221418	−0.0110709	−	0.999939i	$-0.503524\pi$
$353$	−0.416007	−0.0221418	−0.0110709	+	0.999939i	$0.503524\pi$
$354$	13.1261	0.697645
$355$	−0.0202370	−0.00107407
$356$	−14.2639	−0.755983
$357$	14.5336	0.769201
$358$	−12.8339	−0.678295
$359$	11.6150	0.613017	0.306508	−	0.951868i	$-0.400839\pi$
$359$	11.6150	0.613017	0.306508	+	0.951868i	$0.400839\pi$
$360$	0.328323	0.0173042
$361$	−18.1616	−0.955873
$362$	−19.2871	−1.01371
$363$	0	0
$364$	−2.21432	−0.116062
$365$	11.8463	0.620061
$366$	23.1504	1.21009
$367$	−8.00709	−0.417966	−0.208983	−	0.977919i	$-0.567015\pi$
$367$	−8.00709	−0.417966	−0.208983	+	0.977919i	$0.567015\pi$
$368$	6.07737	0.316805
$369$	2.95476	0.153819
$370$	4.32937	0.225073
$371$	9.33444	0.484620
$372$	−17.0376	−0.883361
$373$	16.6329	0.861217	0.430609	−	0.902539i	$-0.358299\pi$
$373$	16.6329	0.861217	0.430609	+	0.902539i	$0.358299\pi$
$374$	0	0
$375$	1.82437	0.0942100
$376$	−4.22816	−0.218051
$377$	−11.2177	−0.577739
$378$	4.87412	0.250698
$379$	−0.0831686	−0.00427208	−0.00213604	−	0.999998i	$-0.500680\pi$
$379$	−0.0831686	−0.00427208	−0.00213604	+	0.999998i	$0.500680\pi$
$380$	−0.915653	−0.0469720
$381$	26.7853	1.37225
$382$	12.0109	0.614530
$383$	6.28284	0.321038	0.160519	−	0.987033i	$-0.448683\pi$
$383$	6.28284	0.321038	0.160519	+	0.987033i	$0.448683\pi$
$384$	1.82437	0.0930995
$385$	0	0
$386$	−17.2998	−0.880539
$387$	−0.909280	−0.0462213
$388$	−7.27431	−0.369297
$389$	−3.67862	−0.186513	−0.0932567	−	0.995642i	$-0.529728\pi$
$389$	−3.67862	−0.186513	−0.0932567	+	0.995642i	$0.529728\pi$
$390$	−4.03973	−0.204560
$391$	48.4147	2.44844
$392$	−1.00000	−0.0505076
$393$	−13.9123	−0.701783
$394$	−13.1724	−0.663618
$395$	−9.39226	−0.472576
$396$	0	0
$397$	7.12152	0.357419	0.178709	−	0.983902i	$-0.442808\pi$
$397$	7.12152	0.357419	0.178709	+	0.983902i	$0.442808\pi$
$398$	22.9779	1.15178
$399$	1.67049	0.0836290
$400$	1.00000	0.0500000
$401$	5.70426	0.284857	0.142429	−	0.989805i	$-0.454509\pi$
$401$	5.70426	0.284857	0.142429	+	0.989805i	$0.454509\pi$
$402$	−2.35376	−0.117395
$403$	20.6793	1.03011
$404$	5.35283	0.266313
$405$	9.87717	0.490801
$406$	−5.06597	−0.251420
$407$	0	0
$408$	14.5336	0.719521
$409$	−23.7324	−1.17349	−0.586745	−	0.809772i	$-0.699591\pi$
$409$	−23.7324	−1.17349	−0.586745	+	0.809772i	$0.699591\pi$
$410$	8.99953	0.444455
$411$	8.99521	0.443701
$412$	−14.3938	−0.709130
$413$	−7.19487	−0.354037
$414$	−1.99534	−0.0980658
$415$	0.747575	0.0366970
$416$	−2.21432	−0.108566
$417$	−7.62072	−0.373188
$418$	0	0
$419$	26.3585	1.28770	0.643848	−	0.765154i	$-0.277337\pi$
$419$	26.3585	1.28770	0.643848	+	0.765154i	$0.277337\pi$
$420$	−1.82437	−0.0890201
$421$	−37.5160	−1.82842	−0.914209	−	0.405243i	$-0.867187\pi$
$421$	−37.5160	−1.82842	−0.914209	+	0.405243i	$0.867187\pi$
$422$	−16.5609	−0.806172
$423$	1.38820	0.0674968
$424$	9.33444	0.453320
$425$	7.96638	0.386426
$426$	0.0369197	0.00178877
$427$	−12.6895	−0.614090
$428$	4.27627	0.206701
$429$	0	0
$430$	−2.76947	−0.133556
$431$	6.43804	0.310110	0.155055	−	0.987906i	$-0.450445\pi$
$431$	6.43804	0.310110	0.155055	+	0.987906i	$0.450445\pi$
$432$	4.87412	0.234506
$433$	14.6478	0.703930	0.351965	−	0.936013i	$-0.385514\pi$
$433$	14.6478	0.703930	0.351965	+	0.936013i	$0.385514\pi$
$434$	9.33892	0.448283
$435$	−9.24220	−0.443130
$436$	5.04265	0.241499
$437$	5.56476	0.266199
$438$	−21.6119	−1.03266
$439$	31.4583	1.50143	0.750713	−	0.660629i	$-0.229710\pi$
$439$	31.4583	1.50143	0.750713	+	0.660629i	$0.229710\pi$
$440$	0	0
$441$	0.328323	0.0156344
$442$	−17.6401	−0.839054
$443$	−31.0007	−1.47289	−0.736444	−	0.676499i	$-0.763496\pi$
$443$	−31.0007	−1.47289	−0.736444	+	0.676499i	$0.763496\pi$
$444$	−7.89837	−0.374840
$445$	14.2639	0.676172
$446$	19.1235	0.905523
$447$	−24.5898	−1.16306
$448$	−1.00000	−0.0472456
$449$	17.5963	0.830419	0.415209	−	0.909726i	$-0.363708\pi$
$449$	17.5963	0.830419	0.415209	+	0.909726i	$0.363708\pi$
$450$	−0.328323	−0.0154773
$451$	0	0
$452$	13.8169	0.649894
$453$	32.1274	1.50948
$454$	19.6989	0.924517
$455$	2.21432	0.103809
$456$	1.67049	0.0782278
$457$	−34.3749	−1.60799	−0.803996	−	0.594635i	$-0.797297\pi$
$457$	−34.3749	−1.60799	−0.803996	+	0.594635i	$0.797297\pi$
$458$	−27.5813	−1.28879
$459$	38.8291	1.81239
$460$	−6.07737	−0.283359
$461$	10.0757	0.469271	0.234635	−	0.972083i	$-0.424610\pi$
$461$	10.0757	0.469271	0.234635	+	0.972083i	$0.424610\pi$
$462$	0	0
$463$	−30.0439	−1.39626	−0.698128	−	0.715973i	$-0.745983\pi$
$463$	−30.0439	−1.39626	−0.698128	+	0.715973i	$0.745983\pi$
$464$	−5.06597	−0.235182
$465$	17.0376	0.790102
$466$	−12.9463	−0.599726
$467$	−19.7362	−0.913280	−0.456640	−	0.889652i	$-0.650947\pi$
$467$	−19.7362	−0.913280	−0.456640	+	0.889652i	$0.650947\pi$
$468$	0.727012	0.0336062
$469$	1.29018	0.0595749
$470$	4.22816	0.195030
$471$	−20.9503	−0.965340
$472$	−7.19487	−0.331171
$473$	0	0
$474$	17.1349	0.787034
$475$	0.915653	0.0420130
$476$	−7.96638	−0.365138
$477$	−3.06471	−0.140324
$478$	−5.77626	−0.264200
$479$	−5.39968	−0.246718	−0.123359	−	0.992362i	$-0.539367\pi$
$479$	−5.39968	−0.246718	−0.123359	+	0.992362i	$0.539367\pi$
$480$	−1.82437	−0.0832707
$481$	9.58660	0.437111
$482$	−25.0323	−1.14019
$483$	11.0874	0.504493
$484$	0	0
$485$	7.27431	0.330309
$486$	−3.39724	−0.154102
$487$	−12.6656	−0.573933	−0.286967	−	0.957941i	$-0.592647\pi$
$487$	−12.6656	−0.573933	−0.286967	+	0.957941i	$0.592647\pi$
$488$	−12.6895	−0.574428
$489$	0.254044	0.0114883
$490$	1.00000	0.0451754
$491$	28.7791	1.29878	0.649392	−	0.760454i	$-0.275023\pi$
$491$	28.7791	1.29878	0.649392	+	0.760454i	$0.275023\pi$
$492$	−16.4185	−0.740202
$493$	−40.3575	−1.81761
$494$	−2.02755	−0.0912236
$495$	0	0
$496$	9.33892	0.419330
$497$	−0.0202370	−0.000907752 0
$498$	−1.36385	−0.0611157
$499$	−19.3858	−0.867826	−0.433913	−	0.900955i	$-0.642867\pi$
$499$	−19.3858	−0.867826	−0.433913	+	0.900955i	$0.642867\pi$
$500$	−1.00000	−0.0447214
$501$	12.8503	0.574107
$502$	6.66594	0.297516
$503$	−1.14878	−0.0512218	−0.0256109	−	0.999672i	$-0.508153\pi$
$503$	−1.14878	−0.0512218	−0.0256109	+	0.999672i	$0.508153\pi$
$504$	0.328323	0.0146247
$505$	−5.35283	−0.238198
$506$	0	0
$507$	14.7715	0.656027
$508$	−14.6820	−0.651407
$509$	−1.32413	−0.0586909	−0.0293454	−	0.999569i	$-0.509342\pi$
$509$	−1.32413	−0.0586909	−0.0293454	+	0.999569i	$0.509342\pi$
$510$	−14.5336	−0.643559
$511$	11.8463	0.524047
$512$	−1.00000	−0.0441942
$513$	4.46301	0.197047
$514$	22.7153	1.00193
$515$	14.3938	0.634265
$516$	5.05253	0.222425
$517$	0	0
$518$	4.32937	0.190222
$519$	−25.6220	−1.12468
$520$	2.21432	0.0971043
$521$	−27.2341	−1.19315	−0.596573	−	0.802559i	$-0.703471\pi$
$521$	−27.2341	−1.19315	−0.596573	+	0.802559i	$0.703471\pi$
$522$	1.66328	0.0727997
$523$	−23.8982	−1.04499	−0.522497	−	0.852641i	$-0.674999\pi$
$523$	−23.8982	−1.04499	−0.522497	+	0.852641i	$0.674999\pi$
$524$	7.62582	0.333135
$525$	1.82437	0.0796220
$526$	14.5015	0.632295
$527$	74.3974	3.24080
$528$	0	0
$529$	13.9345	0.605847
$530$	−9.33444	−0.405462
$531$	2.36225	0.102513
$532$	−0.915653	−0.0396986
$533$	19.9278	0.863170
$534$	−26.0225	−1.12611
$535$	−4.27627	−0.184879
$536$	1.29018	0.0557272
$537$	−23.4138	−1.01038
$538$	21.2753	0.917244
$539$	0	0
$540$	−4.87412	−0.209749
$541$	33.8027	1.45329	0.726645	−	0.687013i	$-0.241079\pi$
$541$	33.8027	1.45329	0.726645	+	0.687013i	$0.241079\pi$
$542$	8.06611	0.346469
$543$	−35.1867	−1.51001
$544$	−7.96638	−0.341556
$545$	−5.04265	−0.216003
$546$	−4.03973	−0.172885
$547$	23.6009	1.00910	0.504550	−	0.863382i	$-0.331658\pi$
$547$	23.6009	1.00910	0.504550	+	0.863382i	$0.331658\pi$
$548$	−4.93059	−0.210624
$549$	4.16627	0.177812
$550$	0	0
$551$	−4.63867	−0.197614
$552$	11.0874	0.471910
$553$	−9.39226	−0.399399
$554$	17.4563	0.741646
$555$	7.89837	0.335267
$556$	4.17718	0.177152
$557$	−6.01368	−0.254808	−0.127404	−	0.991851i	$-0.540664\pi$
$557$	−6.01368	−0.254808	−0.127404	+	0.991851i	$0.540664\pi$
$558$	−3.06619	−0.129802
$559$	−6.13248	−0.259376
$560$	1.00000	0.0422577
$561$	0	0
$562$	−20.4688	−0.863423
$563$	−6.87116	−0.289585	−0.144793	−	0.989462i	$-0.546251\pi$
$563$	−6.87116	−0.289585	−0.144793	+	0.989462i	$0.546251\pi$
$564$	−7.71373	−0.324806
$565$	−13.8169	−0.581283
$566$	5.27282	0.221633
$567$	9.87717	0.414802
$568$	−0.0202370	−0.000849124 0
$569$	−18.9976	−0.796420	−0.398210	−	0.917294i	$-0.630368\pi$
$569$	−18.9976	−0.796420	−0.398210	+	0.917294i	$0.630368\pi$
$570$	−1.67049	−0.0699691
$571$	−0.393382	−0.0164625	−0.00823127	−	0.999966i	$-0.502620\pi$
$571$	−0.393382	−0.0164625	−0.00823127	+	0.999966i	$0.502620\pi$
$572$	0	0
$573$	21.9123	0.915398
$574$	8.99953	0.375633
$575$	6.07737	0.253444
$576$	0.328323	0.0136801
$577$	8.43804	0.351280	0.175640	−	0.984454i	$-0.443800\pi$
$577$	8.43804	0.351280	0.175640	+	0.984454i	$0.443800\pi$
$578$	−46.4632	−1.93261
$579$	−31.5613	−1.31164
$580$	5.06597	0.210353
$581$	0.747575	0.0310146
$582$	−13.2710	−0.550102
$583$	0	0
$584$	11.8463	0.490201
$585$	−0.727012	−0.0300583
$586$	6.40613	0.264635
$587$	46.3445	1.91284	0.956422	−	0.291988i	$-0.0943166\pi$
$587$	46.3445	1.91284	0.956422	+	0.291988i	$0.0943166\pi$
$588$	−1.82437	−0.0752357
$589$	8.55121	0.352347
$590$	7.19487	0.296208
$591$	−24.0314	−0.988519
$592$	4.32937	0.177936
$593$	25.9525	1.06574	0.532871	−	0.846197i	$-0.321113\pi$
$593$	25.9525	1.06574	0.532871	+	0.846197i	$0.321113\pi$
$594$	0	0
$595$	7.96638	0.326590
$596$	13.4785	0.552102
$597$	41.9202	1.71568
$598$	−13.4572	−0.550307
$599$	4.80045	0.196141	0.0980705	−	0.995179i	$-0.468733\pi$
$599$	4.80045	0.196141	0.0980705	+	0.995179i	$0.468733\pi$
$600$	1.82437	0.0744796
$601$	30.5112	1.24458	0.622289	−	0.782787i	$-0.286203\pi$
$601$	30.5112	1.24458	0.622289	+	0.782787i	$0.286203\pi$
$602$	−2.76947	−0.112875
$603$	−0.423595	−0.0172501
$604$	−17.6102	−0.716547
$605$	0	0
$606$	9.76555	0.396698
$607$	−16.5488	−0.671697	−0.335848	−	0.941916i	$-0.609023\pi$
$607$	−16.5488	−0.671697	−0.335848	+	0.941916i	$0.609023\pi$
$608$	−0.915653	−0.0371346
$609$	−9.24220	−0.374513
$610$	12.6895	0.513784
$611$	9.36249	0.378766
$612$	2.61555	0.105727
$613$	42.0921	1.70008	0.850041	−	0.526716i	$-0.176577\pi$
$613$	42.0921	1.70008	0.850041	+	0.526716i	$0.176577\pi$
$614$	5.35970	0.216300
$615$	16.4185	0.662057
$616$	0	0
$617$	7.32983	0.295088	0.147544	−	0.989056i	$-0.452863\pi$
$617$	7.32983	0.295088	0.147544	+	0.989056i	$0.452863\pi$
$618$	−26.2595	−1.05631
$619$	−11.9509	−0.480347	−0.240173	−	0.970730i	$-0.577204\pi$
$619$	−11.9509	−0.480347	−0.240173	+	0.970730i	$0.577204\pi$
$620$	−9.33892	−0.375060
$621$	29.6219	1.18869
$622$	26.9819	1.08188
$623$	14.2639	0.571469
$624$	−4.03973	−0.161719
$625$	1.00000	0.0400000
$626$	28.5633	1.14162
$627$	0	0
$628$	11.4836	0.458245
$629$	34.4894	1.37518
$630$	−0.328323	−0.0130807
$631$	43.7266	1.74073	0.870363	−	0.492410i	$-0.163884\pi$
$631$	43.7266	1.74073	0.870363	+	0.492410i	$0.163884\pi$
$632$	−9.39226	−0.373604
$633$	−30.2132	−1.20087
$634$	−21.0077	−0.834321
$635$	14.6820	0.582636
$636$	17.0295	0.675262
$637$	2.21432	0.0877345
$638$	0	0
$639$	0.00664427	0.000262843 0
$640$	1.00000	0.0395285
$641$	37.6723	1.48796	0.743982	−	0.668199i	$-0.232935\pi$
$641$	37.6723	1.48796	0.743982	+	0.668199i	$0.232935\pi$
$642$	7.80149	0.307900
$643$	24.7735	0.976973	0.488486	−	0.872572i	$-0.337549\pi$
$643$	24.7735	0.976973	0.488486	+	0.872572i	$0.337549\pi$
$644$	−6.07737	−0.239482
$645$	−5.05253	−0.198943
$646$	−7.29444	−0.286996
$647$	36.2066	1.42343	0.711714	−	0.702470i	$-0.247919\pi$
$647$	36.2066	1.42343	0.711714	+	0.702470i	$0.247919\pi$
$648$	9.87717	0.388012
$649$	0	0
$650$	−2.21432	−0.0868527
$651$	17.0376	0.667758
$652$	−0.139250	−0.00545347
$653$	−16.7136	−0.654055	−0.327027	−	0.945015i	$-0.606047\pi$
$653$	−16.7136	−0.654055	−0.327027	+	0.945015i	$0.606047\pi$
$654$	9.19965	0.359735
$655$	−7.62582	−0.297965
$656$	8.99953	0.351373
$657$	−3.88940	−0.151740
$658$	4.22816	0.164831
$659$	−34.0997	−1.32834	−0.664168	−	0.747584i	$-0.731214\pi$
$659$	−34.0997	−1.32834	−0.664168	+	0.747584i	$0.731214\pi$
$660$	0	0
$661$	−29.1326	−1.13313	−0.566563	−	0.824018i	$-0.691727\pi$
$661$	−29.1326	−1.13313	−0.566563	+	0.824018i	$0.691727\pi$
$662$	−11.6022	−0.450934
$663$	−32.1821	−1.24985
$664$	0.747575	0.0290115
$665$	0.915653	0.0355075
$666$	−1.42143	−0.0550794
$667$	−30.7878	−1.19211
$668$	−7.04367	−0.272528
$669$	34.8883	1.34886
$670$	−1.29018	−0.0498439
$671$	0	0
$672$	−1.82437	−0.0703766
$673$	−27.1266	−1.04565	−0.522826	−	0.852439i	$-0.675122\pi$
$673$	−27.1266	−1.04565	−0.522826	+	0.852439i	$0.675122\pi$
$674$	2.34874	0.0904700
$675$	4.87412	0.187605
$676$	−8.09680	−0.311415
$677$	45.5790	1.75174	0.875872	−	0.482543i	$-0.160287\pi$
$677$	45.5790	1.75174	0.875872	+	0.482543i	$0.160287\pi$
$678$	25.2072	0.968076
$679$	7.27431	0.279162
$680$	7.96638	0.305497
$681$	35.9381	1.37715
$682$	0	0
$683$	−6.68497	−0.255793	−0.127897	−	0.991787i	$-0.540823\pi$
$683$	−6.68497	−0.255793	−0.127897	+	0.991787i	$0.540823\pi$
$684$	0.300630	0.0114949
$685$	4.93059	0.188388
$686$	1.00000	0.0381802
$687$	−50.3185	−1.91977
$688$	−2.76947	−0.105585
$689$	−20.6694	−0.787442
$690$	−11.0874	−0.422089
$691$	2.37244	0.0902518	0.0451259	−	0.998981i	$-0.485631\pi$
$691$	2.37244	0.0902518	0.0451259	+	0.998981i	$0.485631\pi$
$692$	14.0443	0.533883
$693$	0	0
$694$	−31.4811	−1.19501
$695$	−4.17718	−0.158450
$696$	−9.24220	−0.350325
$697$	71.6937	2.71559
$698$	2.60777	0.0987057
$699$	−23.6189	−0.893347
$700$	−1.00000	−0.0377964
$701$	30.5560	1.15408	0.577042	−	0.816714i	$-0.304207\pi$
$701$	30.5560	1.15408	0.577042	+	0.816714i	$0.304207\pi$
$702$	−10.7929	−0.407350
$703$	3.96420	0.149513
$704$	0	0
$705$	7.71373	0.290516
$706$	0.416007	0.0156566
$707$	−5.35283	−0.201314
$708$	−13.1261	−0.493309
$709$	10.5970	0.397980	0.198990	−	0.980002i	$-0.436234\pi$
$709$	10.5970	0.397980	0.198990	+	0.980002i	$0.436234\pi$
$710$	0.0202370	0.000759480 0
$711$	3.08370	0.115648
$712$	14.2639	0.534561
$713$	56.7561	2.12553
$714$	−14.5336	−0.543907
$715$	0	0
$716$	12.8339	0.479627
$717$	−10.5380	−0.393550
$718$	−11.6150	−0.433468
$719$	11.8939	0.443568	0.221784	−	0.975096i	$-0.428812\pi$
$719$	11.8939	0.443568	0.221784	+	0.975096i	$0.428812\pi$
$720$	−0.328323	−0.0122359
$721$	14.3938	0.536052
$722$	18.1616	0.675904
$723$	−45.6682	−1.69842
$724$	19.2871	0.716798
$725$	−5.06597	−0.188145
$726$	0	0
$727$	−23.4180	−0.868527	−0.434264	−	0.900786i	$-0.642991\pi$
$727$	−23.4180	−0.868527	−0.434264	+	0.900786i	$0.642991\pi$
$728$	2.21432	0.0820681
$729$	23.4337	0.867915
$730$	−11.8463	−0.438450
$731$	−22.0626	−0.816016
$732$	−23.1504	−0.855664
$733$	−12.0816	−0.446242	−0.223121	−	0.974791i	$-0.571625\pi$
$733$	−12.0816	−0.446242	−0.223121	+	0.974791i	$0.571625\pi$
$734$	8.00709	0.295547
$735$	1.82437	0.0672929
$736$	−6.07737	−0.224015
$737$	0	0
$738$	−2.95476	−0.108766
$739$	−35.0133	−1.28798	−0.643992	−	0.765032i	$-0.722723\pi$
$739$	−35.0133	−1.28798	−0.643992	+	0.765032i	$0.722723\pi$
$740$	−4.32937	−0.159151
$741$	−3.69899	−0.135886
$742$	−9.33444	−0.342678
$743$	48.5288	1.78035	0.890174	−	0.455620i	$-0.150583\pi$
$743$	48.5288	1.78035	0.890174	+	0.455620i	$0.150583\pi$
$744$	17.0376	0.624630
$745$	−13.4785	−0.493815
$746$	−16.6329	−0.608973
$747$	−0.245446	−0.00898041
$748$	0	0
$749$	−4.27627	−0.156251
$750$	−1.82437	−0.0666165
$751$	−0.0449682	−0.00164091	−0.000820457	−	1.00000i	$-0.500261\pi$
$751$	−0.0449682	−0.00164091	−0.000820457		1.00000i	$0.500261\pi$
$752$	4.22816	0.154185
$753$	12.1611	0.443177
$754$	11.2177	0.408523
$755$	17.6102	0.640899
$756$	−4.87412	−0.177270
$757$	28.8381	1.04814	0.524069	−	0.851676i	$-0.324413\pi$
$757$	28.8381	1.04814	0.524069	+	0.851676i	$0.324413\pi$
$758$	0.0831686	0.00302082
$759$	0	0
$760$	0.915653	0.0332142
$761$	18.3746	0.666078	0.333039	−	0.942913i	$-0.391926\pi$
$761$	18.3746	0.666078	0.333039	+	0.942913i	$0.391926\pi$
$762$	−26.7853	−0.970330
$763$	−5.04265	−0.182556
$764$	−12.0109	−0.434538
$765$	−2.61555	−0.0945654
$766$	−6.28284	−0.227008
$767$	15.9317	0.575262
$768$	−1.82437	−0.0658313
$769$	−20.2436	−0.730003	−0.365002	−	0.931007i	$-0.618932\pi$
$769$	−20.2436	−0.730003	−0.365002	+	0.931007i	$0.618932\pi$
$770$	0	0
$771$	41.4412	1.49247
$772$	17.2998	0.622635
$773$	−27.2469	−0.980003	−0.490001	−	0.871722i	$-0.663004\pi$
$773$	−27.2469	−0.980003	−0.490001	+	0.871722i	$0.663004\pi$
$774$	0.909280	0.0326834
$775$	9.33892	0.335464
$776$	7.27431	0.261132
$777$	7.89837	0.283352
$778$	3.67862	0.131885
$779$	8.24045	0.295245
$780$	4.03973	0.144646
$781$	0	0
$782$	−48.4147	−1.73131
$783$	−24.6922	−0.882426
$784$	1.00000	0.0357143
$785$	−11.4836	−0.409867
$786$	13.9123	0.496235
$787$	26.8288	0.956342	0.478171	−	0.878267i	$-0.341300\pi$
$787$	26.8288	0.956342	0.478171	+	0.878267i	$0.341300\pi$
$788$	13.1724	0.469248
$789$	26.4561	0.941861
$790$	9.39226	0.334161
$791$	−13.8169	−0.491273
$792$	0	0
$793$	28.0987	0.997813
$794$	−7.12152	−0.252733
$795$	−17.0295	−0.603973
$796$	−22.9779	−0.814431
$797$	36.4937	1.29267	0.646337	−	0.763052i	$-0.276300\pi$
$797$	36.4937	1.29267	0.646337	+	0.763052i	$0.276300\pi$
$798$	−1.67049	−0.0591347
$799$	33.6831	1.19162
$800$	−1.00000	−0.0353553
$801$	−4.68316	−0.165471
$802$	−5.70426	−0.201424
$803$	0	0
$804$	2.35376	0.0830107
$805$	6.07737	0.214199
$806$	−20.6793	−0.728399
$807$	38.8141	1.36632
$808$	−5.35283	−0.188312
$809$	8.52614	0.299763	0.149882	−	0.988704i	$-0.452111\pi$
$809$	8.52614	0.299763	0.149882	+	0.988704i	$0.452111\pi$
$810$	−9.87717	−0.347049
$811$	−43.5605	−1.52962	−0.764808	−	0.644258i	$-0.777166\pi$
$811$	−43.5605	−1.52962	−0.764808	+	0.644258i	$0.777166\pi$
$812$	5.06597	0.177781
$813$	14.7156	0.516097
$814$	0	0
$815$	0.139250	0.00487773
$816$	−14.5336	−0.508778
$817$	−2.53587	−0.0887188
$818$	23.7324	0.829783
$819$	−0.727012	−0.0254039
$820$	−8.99953	−0.314277
$821$	22.0579	0.769825	0.384913	−	0.922953i	$-0.374232\pi$
$821$	22.0579	0.769825	0.384913	+	0.922953i	$0.374232\pi$
$822$	−8.99521	−0.313744
$823$	3.37693	0.117712	0.0588562	−	0.998266i	$-0.481255\pi$
$823$	3.37693	0.117712	0.0588562	+	0.998266i	$0.481255\pi$
$824$	14.3938	0.501431
$825$	0	0
$826$	7.19487	0.250342
$827$	−17.2810	−0.600919	−0.300460	−	0.953795i	$-0.597140\pi$
$827$	−17.2810	−0.600919	−0.300460	+	0.953795i	$0.597140\pi$
$828$	1.99534	0.0693430
$829$	−23.8021	−0.826682	−0.413341	−	0.910576i	$-0.635638\pi$
$829$	−23.8021	−0.826682	−0.413341	+	0.910576i	$0.635638\pi$
$830$	−0.747575	−0.0259487
$831$	31.8467	1.10475
$832$	2.21432	0.0767677
$833$	7.96638	0.276019
$834$	7.62072	0.263884
$835$	7.04367	0.243756
$836$	0	0
$837$	45.5191	1.57337
$838$	−26.3585	−0.910538
$839$	2.14765	0.0741451	0.0370726	−	0.999313i	$-0.488197\pi$
$839$	2.14765	0.0741451	0.0370726	+	0.999313i	$0.488197\pi$
$840$	1.82437	0.0629467
$841$	−3.33593	−0.115032
$842$	37.5160	1.29289
$843$	−37.3426	−1.28615
$844$	16.5609	0.570050
$845$	8.09680	0.278538
$846$	−1.38820	−0.0477274
$847$	0	0
$848$	−9.33444	−0.320546
$849$	9.61957	0.330143
$850$	−7.96638	−0.273245
$851$	26.3112	0.901936
$852$	−0.0369197	−0.00126485
$853$	−10.0469	−0.343998	−0.171999	−	0.985097i	$-0.555023\pi$
$853$	−10.0469	−0.343998	−0.171999	+	0.985097i	$0.555023\pi$
$854$	12.6895	0.434227
$855$	−0.300630	−0.0102813
$856$	−4.27627	−0.146160
$857$	27.9578	0.955019	0.477510	−	0.878626i	$-0.341540\pi$
$857$	27.9578	0.955019	0.477510	+	0.878626i	$0.341540\pi$
$858$	0	0
$859$	−20.7449	−0.707805	−0.353903	−	0.935282i	$-0.615146\pi$
$859$	−20.7449	−0.707805	−0.353903	+	0.935282i	$0.615146\pi$
$860$	2.76947	0.0944380
$861$	16.4185	0.559540
$862$	−6.43804	−0.219281
$863$	2.03460	0.0692587	0.0346293	−	0.999400i	$-0.488975\pi$
$863$	2.03460	0.0692587	0.0346293	+	0.999400i	$0.488975\pi$
$864$	−4.87412	−0.165821
$865$	−14.0443	−0.477520
$866$	−14.6478	−0.497754
$867$	−84.7661	−2.87881
$868$	−9.33892	−0.316984
$869$	0	0
$870$	9.24220	0.313340
$871$	−2.85686	−0.0968011
$872$	−5.04265	−0.170766
$873$	−2.38833	−0.0808326
$874$	−5.56476	−0.188231
$875$	1.00000	0.0338062
$876$	21.6119	0.730200
$877$	−32.2740	−1.08982	−0.544908	−	0.838496i	$-0.683435\pi$
$877$	−32.2740	−1.08982	−0.544908	+	0.838496i	$0.683435\pi$
$878$	−31.4583	−1.06167
$879$	11.6872	0.394198
$880$	0	0
$881$	−3.99069	−0.134450	−0.0672248	−	0.997738i	$-0.521414\pi$
$881$	−3.99069	−0.134450	−0.0672248	+	0.997738i	$0.521414\pi$
$882$	−0.328323	−0.0110552
$883$	16.2835	0.547982	0.273991	−	0.961732i	$-0.411656\pi$
$883$	16.2835	0.547982	0.273991	+	0.961732i	$0.411656\pi$
$884$	17.6401	0.593301
$885$	13.1261	0.441229
$886$	31.0007	1.04149
$887$	37.4984	1.25907	0.629536	−	0.776971i	$-0.283245\pi$
$887$	37.4984	1.25907	0.629536	+	0.776971i	$0.283245\pi$
$888$	7.89837	0.265052
$889$	14.6820	0.492417
$890$	−14.2639	−0.478126
$891$	0	0
$892$	−19.1235	−0.640301
$893$	3.87153	0.129556
$894$	24.5898	0.822407
$895$	−12.8339	−0.428991
$896$	1.00000	0.0334077
$897$	−24.5510	−0.819733
$898$	−17.5963	−0.587195
$899$	−47.3107	−1.57790
$900$	0.328323	0.0109441
$901$	−74.3617	−2.47735
$902$	0	0
$903$	−5.05253	−0.168138
$904$	−13.8169	−0.459544
$905$	−19.2871	−0.641124
$906$	−32.1274	−1.06736
$907$	4.16415	0.138268	0.0691341	−	0.997607i	$-0.477976\pi$
$907$	4.16415	0.138268	0.0691341	+	0.997607i	$0.477976\pi$
$908$	−19.6989	−0.653732
$909$	1.75746	0.0582913
$910$	−2.21432	−0.0734039
$911$	−45.0657	−1.49309	−0.746546	−	0.665333i	$-0.768289\pi$
$911$	−45.0657	−1.49309	−0.746546	+	0.665333i	$0.768289\pi$
$912$	−1.67049	−0.0553154
$913$	0	0
$914$	34.3749	1.13702
$915$	23.1504	0.765329
$916$	27.5813	0.911313
$917$	−7.62582	−0.251827
$918$	−38.8291	−1.28155
$919$	−32.0466	−1.05712	−0.528561	−	0.848896i	$-0.677268\pi$
$919$	−32.0466	−1.05712	−0.528561	+	0.848896i	$0.677268\pi$
$920$	6.07737	0.200365
$921$	9.77808	0.322199
$922$	−10.0757	−0.331824
$923$	0.0448111	0.00147497
$924$	0	0
$925$	4.32937	0.142349
$926$	30.0439	0.987302
$927$	−4.72581	−0.155216
$928$	5.06597	0.166299
$929$	51.0738	1.67568	0.837839	−	0.545918i	$-0.183819\pi$
$929$	51.0738	1.67568	0.837839	+	0.545918i	$0.183819\pi$
$930$	−17.0376	−0.558686
$931$	0.915653	0.0300093
$932$	12.9463	0.424071
$933$	49.2250	1.61156
$934$	19.7362	0.645787
$935$	0	0
$936$	−0.727012	−0.0237631
$937$	5.41242	0.176816	0.0884080	−	0.996084i	$-0.471822\pi$
$937$	5.41242	0.176816	0.0884080	+	0.996084i	$0.471822\pi$
$938$	−1.29018	−0.0421258
$939$	52.1099	1.70054
$940$	−4.22816	−0.137907
$941$	−4.74009	−0.154523	−0.0772613	−	0.997011i	$-0.524618\pi$
$941$	−4.74009	−0.154523	−0.0772613	+	0.997011i	$0.524618\pi$
$942$	20.9503	0.682598
$943$	54.6935	1.78107
$944$	7.19487	0.234173
$945$	4.87412	0.158555
$946$	0	0
$947$	16.4424	0.534306	0.267153	−	0.963654i	$-0.413917\pi$
$947$	16.4424	0.534306	0.267153	+	0.963654i	$0.413917\pi$
$948$	−17.1349	−0.556517
$949$	−26.2314	−0.851506
$950$	−0.915653	−0.0297077
$951$	−38.3258	−1.24280
$952$	7.96638	0.258192
$953$	−45.6007	−1.47715	−0.738575	−	0.674171i	$-0.764501\pi$
$953$	−45.6007	−1.47715	−0.738575	+	0.674171i	$0.764501\pi$
$954$	3.06471	0.0992238
$955$	12.0109	0.388663
$956$	5.77626	0.186818
$957$	0	0
$958$	5.39968	0.174456
$959$	4.93059	0.159217
$960$	1.82437	0.0588813
$961$	56.2155	1.81340
$962$	−9.58660	−0.309084
$963$	1.40400	0.0452432
$964$	25.0323	0.806237
$965$	−17.2998	−0.556902
$966$	−11.0874	−0.356730
$967$	−28.9513	−0.931012	−0.465506	−	0.885045i	$-0.654128\pi$
$967$	−28.9513	−0.931012	−0.465506	+	0.885045i	$0.654128\pi$
$968$	0	0
$969$	−13.3077	−0.427506
$970$	−7.27431	−0.233564
$971$	7.09959	0.227837	0.113918	−	0.993490i	$-0.463660\pi$
$971$	7.09959	0.227837	0.113918	+	0.993490i	$0.463660\pi$
$972$	3.39724	0.108966
$973$	−4.17718	−0.133914
$974$	12.6656	0.405832
$975$	−4.03973	−0.129375
$976$	12.6895	0.406182
$977$	−0.0166861	−0.000533837 0	−0.000266918	−	1.00000i	$-0.500085\pi$
$977$	−0.0166861	−0.000533837 0	−0.000266918		1.00000i	$0.500085\pi$
$978$	−0.254044	−0.00812343
$979$	0	0
$980$	−1.00000	−0.0319438
$981$	1.65562	0.0528599
$982$	−28.7791	−0.918379
$983$	−30.3585	−0.968286	−0.484143	−	0.874989i	$-0.660869\pi$
$983$	−30.3585	−0.968286	−0.484143	+	0.874989i	$0.660869\pi$
$984$	16.4185	0.523402
$985$	−13.1724	−0.419709
$986$	40.3575	1.28524
$987$	7.71373	0.245531
$988$	2.02755	0.0645048
$989$	−16.8311	−0.535197
$990$	0	0
$991$	−55.9611	−1.77766	−0.888831	−	0.458234i	$-0.848482\pi$
$991$	−55.9611	−1.77766	−0.888831	+	0.458234i	$0.848482\pi$
$992$	−9.33892	−0.296511
$993$	−21.1668	−0.671707
$994$	0.0202370	0.000641878 0
$995$	22.9779	0.728449
$996$	1.36385	0.0432153
$997$	−46.4336	−1.47057	−0.735284	−	0.677759i	$-0.762951\pi$
$997$	−46.4336	−1.47057	−0.735284	+	0.677759i	$0.762951\pi$
$998$	19.3858	0.613645
$999$	21.1019	0.667634

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.cu.1.3		6
11.2	odd	10		770.2.n.h.631.2	yes	12
11.6	odd	10		770.2.n.h.421.2	✓	12
11.10	odd	2		8470.2.a.da.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.h.421.2	✓	12	11.6	odd	10
770.2.n.h.631.2	yes	12	11.2	odd	10
8470.2.a.cu.1.3		6	1.1	even	1	trivial
8470.2.a.da.1.3		6	11.10	odd	2

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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.82437 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.82437 q^{6} -1.00000 q^{7} -1.00000 q^{8} +0.328323 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.82437 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.82437 q^{6} -1.00000 q^{7} -1.00000 q^{8} +0.328323 q^{9} +1.00000 q^{10} -1.82437 q^{12} +2.21432 q^{13} +1.00000 q^{14} +1.82437 q^{15} +1.00000 q^{16} +7.96638 q^{17} -0.328323 q^{18} +0.915653 q^{19} -1.00000 q^{20} +1.82437 q^{21} +6.07737 q^{23} +1.82437 q^{24} +1.00000 q^{25} -2.21432 q^{26} +4.87412 q^{27} -1.00000 q^{28} -5.06597 q^{29} -1.82437 q^{30} +9.33892 q^{31} -1.00000 q^{32} -7.96638 q^{34} +1.00000 q^{35} +0.328323 q^{36} +4.32937 q^{37} -0.915653 q^{38} -4.03973 q^{39} +1.00000 q^{40} +8.99953 q^{41} -1.82437 q^{42} -2.76947 q^{43} -0.328323 q^{45} -6.07737 q^{46} +4.22816 q^{47} -1.82437 q^{48} +1.00000 q^{49} -1.00000 q^{50} -14.5336 q^{51} +2.21432 q^{52} -9.33444 q^{53} -4.87412 q^{54} +1.00000 q^{56} -1.67049 q^{57} +5.06597 q^{58} +7.19487 q^{59} +1.82437 q^{60} +12.6895 q^{61} -9.33892 q^{62} -0.328323 q^{63} +1.00000 q^{64} -2.21432 q^{65} -1.29018 q^{67} +7.96638 q^{68} -11.0874 q^{69} -1.00000 q^{70} +0.0202370 q^{71} -0.328323 q^{72} -11.8463 q^{73} -4.32937 q^{74} -1.82437 q^{75} +0.915653 q^{76} +4.03973 q^{78} +9.39226 q^{79} -1.00000 q^{80} -9.87717 q^{81} -8.99953 q^{82} -0.747575 q^{83} +1.82437 q^{84} -7.96638 q^{85} +2.76947 q^{86} +9.24220 q^{87} -14.2639 q^{89} +0.328323 q^{90} -2.21432 q^{91} +6.07737 q^{92} -17.0376 q^{93} -4.22816 q^{94} -0.915653 q^{95} +1.82437 q^{96} -7.27431 q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 5 q^{3} + 6 q^{4} - 6 q^{5} + 5 q^{6} - 6 q^{7} - 6 q^{8} + 11 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 5 * q^3 + 6 * q^4 - 6 * q^5 + 5 * q^6 - 6 * q^7 - 6 * q^8 + 11 * q^9	\( 6 q - 6 q^{2} - 5 q^{3} + 6 q^{4} - 6 q^{5} + 5 q^{6} - 6 q^{7} - 6 q^{8} + 11 q^{9} + 6 q^{10} - 5 q^{12} + 6 q^{14} + 5 q^{15} + 6 q^{16} + 15 q^{17} - 11 q^{18} + 13 q^{19} - 6 q^{20} + 5 q^{21} - 2 q^{23} + 5 q^{24} + 6 q^{25} - 26 q^{27} - 6 q^{28} + 4 q^{29} - 5 q^{30} - 2 q^{31} - 6 q^{32} - 15 q^{34} + 6 q^{35} + 11 q^{36} - 13 q^{38} + 30 q^{39} + 6 q^{40} + 17 q^{41} - 5 q^{42} - 15 q^{43} - 11 q^{45} + 2 q^{46} - 18 q^{47} - 5 q^{48} + 6 q^{49} - 6 q^{50} - 6 q^{51} + 22 q^{53} + 26 q^{54} + 6 q^{56} + 2 q^{57} - 4 q^{58} - 7 q^{59} + 5 q^{60} + 20 q^{61} + 2 q^{62} - 11 q^{63} + 6 q^{64} - 29 q^{67} + 15 q^{68} + 12 q^{69} - 6 q^{70} - 2 q^{71} - 11 q^{72} - q^{73} - 5 q^{75} + 13 q^{76} - 30 q^{78} + 12 q^{79} - 6 q^{80} + 22 q^{81} - 17 q^{82} + 35 q^{83} + 5 q^{84} - 15 q^{85} + 15 q^{86} - 29 q^{89} + 11 q^{90} - 2 q^{92} + 8 q^{93} + 18 q^{94} - 13 q^{95} + 5 q^{96} - 19 q^{97} - 6 q^{98}+O(q^{100}) \) 6 * q - 6 * q^2 - 5 * q^3 + 6 * q^4 - 6 * q^5 + 5 * q^6 - 6 * q^7 - 6 * q^8 + 11 * q^9 + 6 * q^10 - 5 * q^12 + 6 * q^14 + 5 * q^15 + 6 * q^16 + 15 * q^17 - 11 * q^18 + 13 * q^19 - 6 * q^20 + 5 * q^21 - 2 * q^23 + 5 * q^24 + 6 * q^25 - 26 * q^27 - 6 * q^28 + 4 * q^29 - 5 * q^30 - 2 * q^31 - 6 * q^32 - 15 * q^34 + 6 * q^35 + 11 * q^36 - 13 * q^38 + 30 * q^39 + 6 * q^40 + 17 * q^41 - 5 * q^42 - 15 * q^43 - 11 * q^45 + 2 * q^46 - 18 * q^47 - 5 * q^48 + 6 * q^49 - 6 * q^50 - 6 * q^51 + 22 * q^53 + 26 * q^54 + 6 * q^56 + 2 * q^57 - 4 * q^58 - 7 * q^59 + 5 * q^60 + 20 * q^61 + 2 * q^62 - 11 * q^63 + 6 * q^64 - 29 * q^67 + 15 * q^68 + 12 * q^69 - 6 * q^70 - 2 * q^71 - 11 * q^72 - q^73 - 5 * q^75 + 13 * q^76 - 30 * q^78 + 12 * q^79 - 6 * q^80 + 22 * q^81 - 17 * q^82 + 35 * q^83 + 5 * q^84 - 15 * q^85 + 15 * q^86 - 29 * q^89 + 11 * q^90 - 2 * q^92 + 8 * q^93 + 18 * q^94 - 13 * q^95 + 5 * q^96 - 19 * q^97 - 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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