LMFDB - Embedded newform 6069.2.a.z.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [6069,2,Mod(1,6069)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6069, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("6069.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 6069 = 3 \cdot 7 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6069.a (trivial)

Newform invariants

comment:select newform

sage:traces = [9,0,-9,6,3,0,-9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$48.4612089867$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 12x^{7} - 3x^{6} + 45x^{5} + 21x^{4} - 53x^{3} - 39x^{2} + 3 $ x^9 - 12x^7 - 3x^6 + 45x^5 + 21x^4 - 53x^3 - 39x^2 + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.445735$ of defining polynomial
Character	$\chi$	$=$	6069.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.445735 q^{2} -1.00000 q^{3} -1.80132 q^{4} +0.514255 q^{5} +0.445735 q^{6} -1.00000 q^{7} +1.69438 q^{8} +1.00000 q^{9} -0.229221 q^{10} -1.44709 q^{11} +1.80132 q^{12} -2.34882 q^{13} +0.445735 q^{14} -0.514255 q^{15} +2.84740 q^{16} -0.445735 q^{18} -3.00884 q^{19} -0.926338 q^{20} +1.00000 q^{21} +0.645017 q^{22} -3.42130 q^{23} -1.69438 q^{24} -4.73554 q^{25} +1.04695 q^{26} -1.00000 q^{27} +1.80132 q^{28} -0.288640 q^{29} +0.229221 q^{30} -0.236498 q^{31} -4.65795 q^{32} +1.44709 q^{33} -0.514255 q^{35} -1.80132 q^{36} +0.719966 q^{37} +1.34115 q^{38} +2.34882 q^{39} +0.871344 q^{40} +9.80360 q^{41} -0.445735 q^{42} +8.07825 q^{43} +2.60667 q^{44} +0.514255 q^{45} +1.52499 q^{46} -8.60291 q^{47} -2.84740 q^{48} +1.00000 q^{49} +2.11080 q^{50} +4.23098 q^{52} -10.4697 q^{53} +0.445735 q^{54} -0.744171 q^{55} -1.69438 q^{56} +3.00884 q^{57} +0.128657 q^{58} +1.16539 q^{59} +0.926338 q^{60} -8.25095 q^{61} +0.105415 q^{62} -1.00000 q^{63} -3.61858 q^{64} -1.20789 q^{65} -0.645017 q^{66} +6.38786 q^{67} +3.42130 q^{69} +0.229221 q^{70} -1.93783 q^{71} +1.69438 q^{72} -2.52808 q^{73} -0.320914 q^{74} +4.73554 q^{75} +5.41989 q^{76} +1.44709 q^{77} -1.04695 q^{78} +0.919304 q^{79} +1.46429 q^{80} +1.00000 q^{81} -4.36980 q^{82} +4.90747 q^{83} -1.80132 q^{84} -3.60076 q^{86} +0.288640 q^{87} -2.45192 q^{88} -5.33991 q^{89} -0.229221 q^{90} +2.34882 q^{91} +6.16286 q^{92} +0.236498 q^{93} +3.83462 q^{94} -1.54731 q^{95} +4.65795 q^{96} +5.97700 q^{97} -0.445735 q^{98} -1.44709 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{3} + 6 q^{4} + 3 q^{5} - 9 q^{7} + 9 q^{8} + 9 q^{9} + 12 q^{10} + 18 q^{11} - 6 q^{12} - 21 q^{13} - 3 q^{15} - 9 q^{19} + 15 q^{20} + 9 q^{21} + 6 q^{22} - 9 q^{24} + 3 q^{26} - 9 q^{27} - 6 q^{28}+ \cdots + 18 q^{99}+O(q^{100}) $ 9 * q - 9 * q^3 + 6 * q^4 + 3 * q^5 - 9 * q^7 + 9 * q^8 + 9 * q^9 + 12 * q^10 + 18 * q^11 - 6 * q^12 - 21 * q^13 - 3 * q^15 - 9 * q^19 + 15 * q^20 + 9 * q^21 + 6 * q^22 - 9 * q^24 + 3 * q^26 - 9 * q^27 - 6 * q^28 + 6 * q^29 - 12 * q^30 + 30 * q^31 + 3 * q^32 - 18 * q^33 - 3 * q^35 + 6 * q^36 + 12 * q^37 - 36 * q^38 + 21 * q^39 + 30 * q^40 + 9 * q^41 + 30 * q^44 + 3 * q^45 + 33 * q^46 - 9 * q^47 + 9 * q^49 - 12 * q^50 - 12 * q^52 + 30 * q^55 - 9 * q^56 + 9 * q^57 + 9 * q^58 - 3 * q^59 - 15 * q^60 + 33 * q^61 - 12 * q^62 - 9 * q^63 - 15 * q^64 - 15 * q^65 - 6 * q^66 - 15 * q^67 - 12 * q^70 + 9 * q^72 + 21 * q^73 + 6 * q^74 + 3 * q^76 - 18 * q^77 - 3 * q^78 + 30 * q^79 + 9 * q^81 + 9 * q^82 + 6 * q^84 + 72 * q^86 - 6 * q^87 + 48 * q^88 - 12 * q^89 + 12 * q^90 + 21 * q^91 + 48 * q^92 - 30 * q^93 + 48 * q^94 - 18 * q^95 - 3 * q^96 + 18 * q^99

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 $

$2$	−0.445735	−0.315182	−0.157591	−	0.987504i	$-0.550373\pi$
$2$	−0.445735	−0.315182	−0.157591	+	0.987504i	$0.550373\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.80132	−0.900660
$5$	0.514255	0.229982	0.114991	−	0.993367i	$-0.463316\pi$
$5$	0.514255	0.229982	0.114991	+	0.993367i	$0.463316\pi$
$6$	0.445735	0.181971
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.69438	0.599054
$9$	1.00000	0.333333
$10$	−0.229221	−0.0724862
$11$	−1.44709	−0.436313	−0.218156	−	0.975914i	$-0.570004\pi$
$11$	−1.44709	−0.436313	−0.218156	+	0.975914i	$0.570004\pi$
$12$	1.80132	0.519996
$13$	−2.34882	−0.651446	−0.325723	−	0.945465i	$-0.605608\pi$
$13$	−2.34882	−0.651446	−0.325723	+	0.945465i	$0.605608\pi$
$14$	0.445735	0.119128
$15$	−0.514255	−0.132780
$16$	2.84740	0.711849
$17$	0	0
$17$	0	0
$18$	−0.445735	−0.105061
$19$	−3.00884	−0.690276	−0.345138	−	0.938552i	$-0.612168\pi$
$19$	−3.00884	−0.690276	−0.345138	+	0.938552i	$0.612168\pi$
$20$	−0.926338	−0.207135
$21$	1.00000	0.218218
$22$	0.645017	0.137518
$23$	−3.42130	−0.713391	−0.356696	−	0.934221i	$-0.616097\pi$
$23$	−3.42130	−0.713391	−0.356696	+	0.934221i	$0.616097\pi$
$24$	−1.69438	−0.345864
$25$	−4.73554	−0.947108
$26$	1.04695	0.205324
$27$	−1.00000	−0.192450
$28$	1.80132	0.340418
$29$	−0.288640	−0.0535990	−0.0267995	−	0.999641i	$-0.508532\pi$
$29$	−0.288640	−0.0535990	−0.0267995	+	0.999641i	$0.508532\pi$
$30$	0.229221	0.0418499
$31$	−0.236498	−0.0424763	−0.0212382	−	0.999774i	$-0.506761\pi$
$31$	−0.236498	−0.0424763	−0.0212382	+	0.999774i	$0.506761\pi$
$32$	−4.65795	−0.823416
$33$	1.44709	0.251905
$34$	0	0
$35$	−0.514255	−0.0869250
$36$	−1.80132	−0.300220
$37$	0.719966	0.118362	0.0591808	−	0.998247i	$-0.481151\pi$
$37$	0.719966	0.118362	0.0591808	+	0.998247i	$0.481151\pi$
$38$	1.34115	0.217563
$39$	2.34882	0.376113
$40$	0.871344	0.137772
$41$	9.80360	1.53106	0.765532	−	0.643398i	$-0.222476\pi$
$41$	9.80360	1.53106	0.765532	+	0.643398i	$0.222476\pi$
$42$	−0.445735	−0.0687784
$43$	8.07825	1.23192	0.615961	−	0.787777i	$-0.288768\pi$
$43$	8.07825	1.23192	0.615961	+	0.787777i	$0.288768\pi$
$44$	2.60667	0.392970
$45$	0.514255	0.0766606
$46$	1.52499	0.224848
$47$	−8.60291	−1.25486	−0.627432	−	0.778672i	$-0.715894\pi$
$47$	−8.60291	−1.25486	−0.627432	+	0.778672i	$0.715894\pi$
$48$	−2.84740	−0.410986
$49$	1.00000	0.142857
$50$	2.11080	0.298512
$51$	0	0
$52$	4.23098	0.586732
$53$	−10.4697	−1.43812	−0.719062	−	0.694946i	$-0.755428\pi$
$53$	−10.4697	−1.43812	−0.719062	+	0.694946i	$0.755428\pi$
$54$	0.445735	0.0606568
$55$	−0.744171	−0.100344
$56$	−1.69438	−0.226421
$57$	3.00884	0.398531
$58$	0.128657	0.0168935
$59$	1.16539	0.151721	0.0758604	−	0.997118i	$-0.475830\pi$
$59$	1.16539	0.151721	0.0758604	+	0.997118i	$0.475830\pi$
$60$	0.926338	0.119590
$61$	−8.25095	−1.05643	−0.528213	−	0.849112i	$-0.677138\pi$
$61$	−8.25095	−1.05643	−0.528213	+	0.849112i	$0.677138\pi$
$62$	0.105415	0.0133878
$63$	−1.00000	−0.125988
$64$	−3.61858	−0.452323
$65$	−1.20789	−0.149821
$66$	−0.645017	−0.0793961
$67$	6.38786	0.780402	0.390201	−	0.920730i	$-0.372406\pi$
$67$	6.38786	0.780402	0.390201	+	0.920730i	$0.372406\pi$
$68$	0	0
$69$	3.42130	0.411877
$70$	0.229221	0.0273972
$71$	−1.93783	−0.229978	−0.114989	−	0.993367i	$-0.536683\pi$
$71$	−1.93783	−0.229978	−0.114989	+	0.993367i	$0.536683\pi$
$72$	1.69438	0.199685
$73$	−2.52808	−0.295889	−0.147945	−	0.988996i	$-0.547266\pi$
$73$	−2.52808	−0.295889	−0.147945	+	0.988996i	$0.547266\pi$
$74$	−0.320914	−0.0373055
$75$	4.73554	0.546813
$76$	5.41989	0.621704
$77$	1.44709	0.164911
$78$	−1.04695	−0.118544
$79$	0.919304	0.103430	0.0517149	−	0.998662i	$-0.483531\pi$
$79$	0.919304	0.103430	0.0517149	+	0.998662i	$0.483531\pi$
$80$	1.46429	0.163712
$81$	1.00000	0.111111
$82$	−4.36980	−0.482564
$83$	4.90747	0.538664	0.269332	−	0.963047i	$-0.413197\pi$
$83$	4.90747	0.538664	0.269332	+	0.963047i	$0.413197\pi$
$84$	−1.80132	−0.196540
$85$	0	0
$86$	−3.60076	−0.388280
$87$	0.288640	0.0309454
$88$	−2.45192	−0.261375
$89$	−5.33991	−0.566029	−0.283015	−	0.959116i	$-0.591335\pi$
$89$	−5.33991	−0.566029	−0.283015	+	0.959116i	$0.591335\pi$
$90$	−0.229221	−0.0241621
$91$	2.34882	0.246224
$92$	6.16286	0.642523
$93$	0.236498	0.0245237
$94$	3.83462	0.395510
$95$	−1.54731	−0.158751
$96$	4.65795	0.475400
$97$	5.97700	0.606872	0.303436	−	0.952852i	$-0.401866\pi$
$97$	5.97700	0.606872	0.303436	+	0.952852i	$0.401866\pi$
$98$	−0.445735	−0.0450260
$99$	−1.44709	−0.145438
$100$	8.53023	0.853023
$101$	3.17747	0.316170	0.158085	−	0.987426i	$-0.449468\pi$
$101$	3.17747	0.316170	0.158085	+	0.987426i	$0.449468\pi$
$102$	0	0
$103$	−18.6240	−1.83508	−0.917538	−	0.397648i	$-0.869827\pi$
$103$	−18.6240	−1.83508	−0.917538	+	0.397648i	$0.869827\pi$
$104$	−3.97980	−0.390252
$105$	0.514255	0.0501861
$106$	4.66671	0.453271
$107$	−4.00160	−0.386850	−0.193425	−	0.981115i	$-0.561960\pi$
$107$	−4.00160	−0.386850	−0.193425	+	0.981115i	$0.561960\pi$
$108$	1.80132	0.173332
$109$	3.56320	0.341293	0.170646	−	0.985332i	$-0.445414\pi$
$109$	3.56320	0.341293	0.170646	+	0.985332i	$0.445414\pi$
$110$	0.331703	0.0316267
$111$	−0.719966	−0.0683361
$112$	−2.84740	−0.269054
$113$	−11.2616	−1.05940	−0.529702	−	0.848184i	$-0.677696\pi$
$113$	−11.2616	−1.05940	−0.529702	+	0.848184i	$0.677696\pi$
$114$	−1.34115	−0.125610
$115$	−1.75942	−0.164067
$116$	0.519933	0.0482745
$117$	−2.34882	−0.217149
$118$	−0.519455	−0.0478197
$119$	0	0
$120$	−0.871344	−0.0795425
$121$	−8.90594	−0.809631
$122$	3.67774	0.332967
$123$	−9.80360	−0.883960
$124$	0.426009	0.0382567
$125$	−5.00655	−0.447800
$126$	0.445735	0.0397092
$127$	9.34671	0.829386	0.414693	−	0.909961i	$-0.363889\pi$
$127$	9.34671	0.829386	0.414693	+	0.909961i	$0.363889\pi$
$128$	10.9288	0.965980
$129$	−8.07825	−0.711250
$130$	0.538401	0.0472209
$131$	−1.68959	−0.147620	−0.0738100	−	0.997272i	$-0.523516\pi$
$131$	−1.68959	−0.147620	−0.0738100	+	0.997272i	$0.523516\pi$
$132$	−2.60667	−0.226881
$133$	3.00884	0.260900
$134$	−2.84729	−0.245969
$135$	−0.514255	−0.0442600
$136$	0	0
$137$	−11.5611	−0.987730	−0.493865	−	0.869539i	$-0.664416\pi$
$137$	−11.5611	−0.987730	−0.493865	+	0.869539i	$0.664416\pi$
$138$	−1.52499	−0.129816
$139$	11.2732	0.956179	0.478089	−	0.878311i	$-0.341330\pi$
$139$	11.2732	0.956179	0.478089	+	0.878311i	$0.341330\pi$
$140$	0.926338	0.0782899
$141$	8.60291	0.724496
$142$	0.863758	0.0724850
$143$	3.39895	0.284235
$144$	2.84740	0.237283
$145$	−0.148434	−0.0123268
$146$	1.12685	0.0932590
$147$	−1.00000	−0.0824786
$148$	−1.29689	−0.106604
$149$	−18.5197	−1.51719	−0.758596	−	0.651561i	$-0.774115\pi$
$149$	−18.5197	−1.51719	−0.758596	+	0.651561i	$0.774115\pi$
$150$	−2.11080	−0.172346
$151$	8.74105	0.711337	0.355668	−	0.934612i	$-0.384253\pi$
$151$	8.74105	0.711337	0.355668	+	0.934612i	$0.384253\pi$
$152$	−5.09812	−0.413513
$153$	0	0
$154$	−0.645017	−0.0519769
$155$	−0.121620	−0.00976878
$156$	−4.23098	−0.338750
$157$	−17.2693	−1.37824	−0.689121	−	0.724647i	$-0.742003\pi$
$157$	−17.2693	−1.37824	−0.689121	+	0.724647i	$0.742003\pi$
$158$	−0.409766	−0.0325992
$159$	10.4697	0.830302
$160$	−2.39537	−0.189371
$161$	3.42130	0.269636
$162$	−0.445735	−0.0350202
$163$	−7.64240	−0.598599	−0.299300	−	0.954159i	$-0.596753\pi$
$163$	−7.64240	−0.598599	−0.299300	+	0.954159i	$0.596753\pi$
$164$	−17.6594	−1.37897
$165$	0.744171	0.0579337
$166$	−2.18743	−0.169777
$167$	19.8998	1.53990	0.769948	−	0.638107i	$-0.220282\pi$
$167$	19.8998	1.53990	0.769948	+	0.638107i	$0.220282\pi$
$168$	1.69438	0.130724
$169$	−7.48303	−0.575617
$170$	0	0
$171$	−3.00884	−0.230092
$172$	−14.5515	−1.10954
$173$	−12.0975	−0.919756	−0.459878	−	0.887982i	$-0.652107\pi$
$173$	−12.0975	−0.919756	−0.459878	+	0.887982i	$0.652107\pi$
$174$	−0.128657	−0.00975345
$175$	4.73554	0.357973
$176$	−4.12043	−0.310589
$177$	−1.16539	−0.0875961
$178$	2.38018	0.178402
$179$	23.4966	1.75622	0.878108	−	0.478463i	$-0.158806\pi$
$179$	23.4966	1.75622	0.878108	+	0.478463i	$0.158806\pi$
$180$	−0.926338	−0.0690452
$181$	5.62024	0.417749	0.208874	−	0.977942i	$-0.433020\pi$
$181$	5.62024	0.417749	0.208874	+	0.977942i	$0.433020\pi$
$182$	−1.04695	−0.0776053
$183$	8.25095	0.609928
$184$	−5.79699	−0.427360
$185$	0.370246	0.0272210
$186$	−0.105415	−0.00772944
$187$	0	0
$188$	15.4966	1.13021
$189$	1.00000	0.0727393
$190$	0.689691	0.0500354
$191$	17.1383	1.24009	0.620043	−	0.784568i	$-0.287115\pi$
$191$	17.1383	1.24009	0.620043	+	0.784568i	$0.287115\pi$
$192$	3.61858	0.261149
$193$	24.3552	1.75312	0.876561	−	0.481290i	$-0.159832\pi$
$193$	24.3552	1.75312	0.876561	+	0.481290i	$0.159832\pi$
$194$	−2.66416	−0.191275
$195$	1.20789	0.0864991
$196$	−1.80132	−0.128666
$197$	−5.14873	−0.366832	−0.183416	−	0.983035i	$-0.558716\pi$
$197$	−5.14873	−0.366832	−0.183416	+	0.983035i	$0.558716\pi$
$198$	0.645017	0.0458394
$199$	−2.17553	−0.154219	−0.0771097	−	0.997023i	$-0.524569\pi$
$199$	−2.17553	−0.154219	−0.0771097	+	0.997023i	$0.524569\pi$
$200$	−8.02381	−0.567369
$201$	−6.38786	−0.450565
$202$	−1.41631	−0.0996511
$203$	0.288640	0.0202585
$204$	0	0
$205$	5.04155	0.352117
$206$	8.30136	0.578383
$207$	−3.42130	−0.237797
$208$	−6.68803	−0.463732
$209$	4.35405	0.301176
$210$	−0.229221	−0.0158178
$211$	11.5302	0.793770	0.396885	−	0.917868i	$-0.370091\pi$
$211$	11.5302	0.793770	0.396885	+	0.917868i	$0.370091\pi$
$212$	18.8593	1.29526
$213$	1.93783	0.132778
$214$	1.78365	0.121928
$215$	4.15428	0.283320
$216$	−1.69438	−0.115288
$217$	0.236498	0.0160545
$218$	−1.58824	−0.107569
$219$	2.52808	0.170832
$220$	1.34049	0.0903759
$221$	0	0
$222$	0.320914	0.0215383
$223$	−1.79652	−0.120304	−0.0601520	−	0.998189i	$-0.519159\pi$
$223$	−1.79652	−0.120304	−0.0601520	+	0.998189i	$0.519159\pi$
$224$	4.65795	0.311222
$225$	−4.73554	−0.315703
$226$	5.01969	0.333905
$227$	19.7638	1.31177	0.655883	−	0.754862i	$-0.272296\pi$
$227$	19.7638	1.31177	0.655883	+	0.754862i	$0.272296\pi$
$228$	−5.41989	−0.358941
$229$	0.479494	0.0316859	0.0158429	−	0.999874i	$-0.494957\pi$
$229$	0.479494	0.0316859	0.0158429	+	0.999874i	$0.494957\pi$
$230$	0.784236	0.0517110
$231$	−1.44709	−0.0952113
$232$	−0.489066	−0.0321087
$233$	20.3096	1.33053	0.665263	−	0.746609i	$-0.268319\pi$
$233$	20.3096	1.33053	0.665263	+	0.746609i	$0.268319\pi$
$234$	1.04695	0.0684414
$235$	−4.42409	−0.288596
$236$	−2.09924	−0.136649
$237$	−0.919304	−0.0597152
$238$	0	0
$239$	8.46865	0.547792	0.273896	−	0.961759i	$-0.411688\pi$
$239$	8.46865	0.547792	0.273896	+	0.961759i	$0.411688\pi$
$240$	−1.46429	−0.0945194
$241$	25.9117	1.66912	0.834560	−	0.550917i	$-0.185722\pi$
$241$	25.9117	1.66912	0.834560	+	0.550917i	$0.185722\pi$
$242$	3.96969	0.255181
$243$	−1.00000	−0.0641500
$244$	14.8626	0.951481
$245$	0.514255	0.0328545
$246$	4.36980	0.278609
$247$	7.06724	0.449678
$248$	−0.400718	−0.0254456
$249$	−4.90747	−0.310998
$250$	2.23159	0.141138
$251$	−15.4020	−0.972166	−0.486083	−	0.873913i	$-0.661575\pi$
$251$	−15.4020	−0.972166	−0.486083	+	0.873913i	$0.661575\pi$
$252$	1.80132	0.113473
$253$	4.95092	0.311262
$254$	−4.16616	−0.261408
$255$	0	0
$256$	2.36581	0.147863
$257$	12.3161	0.768256	0.384128	−	0.923280i	$-0.374502\pi$
$257$	12.3161	0.768256	0.384128	+	0.923280i	$0.374502\pi$
$258$	3.60076	0.224173
$259$	−0.719966	−0.0447365
$260$	2.17580	0.134938
$261$	−0.288640	−0.0178663
$262$	0.753108	0.0465272
$263$	−7.90731	−0.487585	−0.243793	−	0.969827i	$-0.578392\pi$
$263$	−7.90731	−0.487585	−0.243793	+	0.969827i	$0.578392\pi$
$264$	2.45192	0.150905
$265$	−5.38410	−0.330742
$266$	−1.34115	−0.0822309
$267$	5.33991	0.326797
$268$	−11.5066	−0.702877
$269$	15.4174	0.940014	0.470007	−	0.882663i	$-0.344251\pi$
$269$	15.4174	0.940014	0.470007	+	0.882663i	$0.344251\pi$
$270$	0.229221	0.0139500
$271$	−4.89568	−0.297391	−0.148696	−	0.988883i	$-0.547507\pi$
$271$	−4.89568	−0.297391	−0.148696	+	0.988883i	$0.547507\pi$
$272$	0	0
$273$	−2.34882	−0.142157
$274$	5.15318	0.311315
$275$	6.85274	0.413236
$276$	−6.16286	−0.370961
$277$	−0.312488	−0.0187756	−0.00938779	−	0.999956i	$-0.502988\pi$
$277$	−0.312488	−0.0187756	−0.00938779	+	0.999956i	$0.502988\pi$
$278$	−5.02485	−0.301370
$279$	−0.236498	−0.0141588
$280$	−0.871344	−0.0520728
$281$	−2.96508	−0.176882	−0.0884411	−	0.996081i	$-0.528188\pi$
$281$	−2.96508	−0.176882	−0.0884411	+	0.996081i	$0.528188\pi$
$282$	−3.83462	−0.228348
$283$	−4.89256	−0.290832	−0.145416	−	0.989371i	$-0.546452\pi$
$283$	−4.89256	−0.290832	−0.145416	+	0.989371i	$0.546452\pi$
$284$	3.49065	0.207132
$285$	1.54731	0.0916548
$286$	−1.51503	−0.0895857
$287$	−9.80360	−0.578688
$288$	−4.65795	−0.274472
$289$	0	0
$290$	0.0661624	0.00388519
$291$	−5.97700	−0.350378
$292$	4.55388	0.266496
$293$	14.1788	0.828335	0.414167	−	0.910201i	$-0.364073\pi$
$293$	14.1788	0.828335	0.414167	+	0.910201i	$0.364073\pi$
$294$	0.445735	0.0259958
$295$	0.599307	0.0348930
$296$	1.21990	0.0709050
$297$	1.44709	0.0839685
$298$	8.25488	0.478192
$299$	8.03604	0.464736
$300$	−8.53023	−0.492493
$301$	−8.07825	−0.465623
$302$	−3.89619	−0.224201
$303$	−3.17747	−0.182541
$304$	−8.56736	−0.491372
$305$	−4.24309	−0.242959
$306$	0	0
$307$	−3.39953	−0.194021	−0.0970107	−	0.995283i	$-0.530928\pi$
$307$	−3.39953	−0.194021	−0.0970107	+	0.995283i	$0.530928\pi$
$308$	−2.60667	−0.148529
$309$	18.6240	1.05948
$310$	0.0542104	0.00307894
$311$	−4.53443	−0.257124	−0.128562	−	0.991701i	$-0.541036\pi$
$311$	−4.53443	−0.257124	−0.128562	+	0.991701i	$0.541036\pi$
$312$	3.97980	0.225312
$313$	6.72503	0.380121	0.190061	−	0.981772i	$-0.439132\pi$
$313$	6.72503	0.380121	0.190061	+	0.981772i	$0.439132\pi$
$314$	7.69754	0.434397
$315$	−0.514255	−0.0289750
$316$	−1.65596	−0.0931551
$317$	−16.0885	−0.903618	−0.451809	−	0.892115i	$-0.649221\pi$
$317$	−16.0885	−0.903618	−0.451809	+	0.892115i	$0.649221\pi$
$318$	−4.66671	−0.261696
$319$	0.417687	0.0233860
$320$	−1.86087	−0.104026
$321$	4.00160	0.223348
$322$	−1.52499	−0.0849846
$323$	0	0
$324$	−1.80132	−0.100073
$325$	11.1230	0.616990
$326$	3.40648	0.188668
$327$	−3.56320	−0.197046
$328$	16.6110	0.917191
$329$	8.60291	0.474294
$330$	−0.331703	−0.0182597
$331$	12.2824	0.675100	0.337550	−	0.941308i	$-0.390402\pi$
$331$	12.2824	0.675100	0.337550	+	0.941308i	$0.390402\pi$
$332$	−8.83992	−0.485154
$333$	0.719966	0.0394539
$334$	−8.87005	−0.485348
$335$	3.28499	0.179478
$336$	2.84740	0.155338
$337$	27.9084	1.52027	0.760135	−	0.649765i	$-0.225133\pi$
$337$	27.9084	1.52027	0.760135	+	0.649765i	$0.225133\pi$
$338$	3.33545	0.181424
$339$	11.2616	0.611647
$340$	0	0
$341$	0.342233	0.0185330
$342$	1.34115	0.0725209
$343$	−1.00000	−0.0539949
$344$	13.6876	0.737988
$345$	1.75942	0.0947241
$346$	5.39228	0.289891
$347$	35.8346	1.92370	0.961851	−	0.273574i	$-0.0882059\pi$
$347$	35.8346	1.92370	0.961851	+	0.273574i	$0.0882059\pi$
$348$	−0.519933	−0.0278713
$349$	−21.4982	−1.15077	−0.575386	−	0.817882i	$-0.695148\pi$
$349$	−21.4982	−1.15077	−0.575386	+	0.817882i	$0.695148\pi$
$350$	−2.11080	−0.112827
$351$	2.34882	0.125371
$352$	6.74045	0.359267
$353$	−33.4652	−1.78117	−0.890585	−	0.454816i	$-0.849705\pi$
$353$	−33.4652	−1.78117	−0.890585	+	0.454816i	$0.849705\pi$
$354$	0.519455	0.0276087
$355$	−0.996538	−0.0528908
$356$	9.61889	0.509800
$357$	0	0
$358$	−10.4732	−0.553528
$359$	−0.184516	−0.00973838	−0.00486919	−	0.999988i	$-0.501550\pi$
$359$	−0.184516	−0.00973838	−0.00486919	+	0.999988i	$0.501550\pi$
$360$	0.871344	0.0459239
$361$	−9.94687	−0.523520
$362$	−2.50514	−0.131667
$363$	8.90594	0.467441
$364$	−4.23098	−0.221764
$365$	−1.30008	−0.0680491
$366$	−3.67774	−0.192238
$367$	−26.7096	−1.39423	−0.697115	−	0.716960i	$-0.745533\pi$
$367$	−26.7096	−1.39423	−0.697115	+	0.716960i	$0.745533\pi$
$368$	−9.74180	−0.507827
$369$	9.80360	0.510355
$370$	−0.165032	−0.00857958
$371$	10.4697	0.543560
$372$	−0.426009	−0.0220875
$373$	0.169678	0.00878559	0.00439280	−	0.999990i	$-0.498602\pi$
$373$	0.169678	0.00878559	0.00439280	+	0.999990i	$0.498602\pi$
$374$	0	0
$375$	5.00655	0.258537
$376$	−14.5766	−0.751731
$377$	0.677964	0.0349169
$378$	−0.445735	−0.0229261
$379$	15.0496	0.773048	0.386524	−	0.922279i	$-0.373676\pi$
$379$	15.0496	0.773048	0.386524	+	0.922279i	$0.373676\pi$
$380$	2.78720	0.142981
$381$	−9.34671	−0.478846
$382$	−7.63915	−0.390853
$383$	23.2469	1.18786	0.593931	−	0.804516i	$-0.297575\pi$
$383$	23.2469	1.18786	0.593931	+	0.804516i	$0.297575\pi$
$384$	−10.9288	−0.557709
$385$	0.744171	0.0379265
$386$	−10.8559	−0.552553
$387$	8.07825	0.410641
$388$	−10.7665	−0.546586
$389$	6.44486	0.326767	0.163384	−	0.986563i	$-0.447759\pi$
$389$	6.44486	0.326767	0.163384	+	0.986563i	$0.447759\pi$
$390$	−0.538401	−0.0272630
$391$	0	0
$392$	1.69438	0.0855792
$393$	1.68959	0.0852284
$394$	2.29497	0.115619
$395$	0.472757	0.0237870
$396$	2.60667	0.130990
$397$	27.8021	1.39535	0.697675	−	0.716415i	$-0.254218\pi$
$397$	27.8021	1.39535	0.697675	+	0.716415i	$0.254218\pi$
$398$	0.969711	0.0486072
$399$	−3.00884	−0.150630
$400$	−13.4840	−0.674198
$401$	25.5015	1.27348	0.636742	−	0.771077i	$-0.280282\pi$
$401$	25.5015	1.27348	0.636742	+	0.771077i	$0.280282\pi$
$402$	2.84729	0.142010
$403$	0.555492	0.0276710
$404$	−5.72363	−0.284761
$405$	0.514255	0.0255535
$406$	−0.128657	−0.00638513
$407$	−1.04185	−0.0516427
$408$	0	0
$409$	−11.5643	−0.571817	−0.285908	−	0.958257i	$-0.592295\pi$
$409$	−11.5643	−0.571817	−0.285908	+	0.958257i	$0.592295\pi$
$410$	−2.24719	−0.110981
$411$	11.5611	0.570266
$412$	33.5478	1.65278
$413$	−1.16539	−0.0573451
$414$	1.52499	0.0749494
$415$	2.52369	0.123883
$416$	10.9407	0.536412
$417$	−11.2732	−0.552050
$418$	−1.94075	−0.0949254
$419$	23.0174	1.12447	0.562237	−	0.826976i	$-0.309941\pi$
$419$	23.0174	1.12447	0.562237	+	0.826976i	$0.309941\pi$
$420$	−0.926338	−0.0452007
$421$	5.60601	0.273220	0.136610	−	0.990625i	$-0.456379\pi$
$421$	5.60601	0.273220	0.136610	+	0.990625i	$0.456379\pi$
$422$	−5.13940	−0.250182
$423$	−8.60291	−0.418288
$424$	−17.7397	−0.861515
$425$	0	0
$426$	−0.863758	−0.0418492
$427$	8.25095	0.399291
$428$	7.20817	0.348420
$429$	−3.39895	−0.164103
$430$	−1.85171	−0.0892973
$431$	3.98058	0.191738	0.0958689	−	0.995394i	$-0.469437\pi$
$431$	3.98058	0.191738	0.0958689	+	0.995394i	$0.469437\pi$
$432$	−2.84740	−0.136995
$433$	26.0067	1.24980	0.624902	−	0.780703i	$-0.285139\pi$
$433$	26.0067	1.24980	0.624902	+	0.780703i	$0.285139\pi$
$434$	−0.105415	−0.00506010
$435$	0.148434	0.00711688
$436$	−6.41847	−0.307389
$437$	10.2942	0.492436
$438$	−1.12685	−0.0538431
$439$	22.3742	1.06786	0.533931	−	0.845528i	$-0.320714\pi$
$439$	22.3742	1.06786	0.533931	+	0.845528i	$0.320714\pi$
$440$	−1.26091	−0.0601115
$441$	1.00000	0.0476190
$442$	0	0
$443$	22.2088	1.05517	0.527587	−	0.849501i	$-0.323097\pi$
$443$	22.2088	1.05517	0.527587	+	0.849501i	$0.323097\pi$
$444$	1.29689	0.0615476
$445$	−2.74608	−0.130176
$446$	0.800772	0.0379177
$447$	18.5197	0.875952
$448$	3.61858	0.170962
$449$	23.7681	1.12169	0.560844	−	0.827922i	$-0.310477\pi$
$449$	23.7681	1.12169	0.560844	+	0.827922i	$0.310477\pi$
$450$	2.11080	0.0995039
$451$	−14.1866	−0.668023
$452$	20.2858	0.954162
$453$	−8.74105	−0.410691
$454$	−8.80940	−0.413446
$455$	1.20789	0.0566270
$456$	5.09812	0.238742
$457$	26.9600	1.26113	0.630567	−	0.776135i	$-0.282822\pi$
$457$	26.9600	1.26113	0.630567	+	0.776135i	$0.282822\pi$
$458$	−0.213727	−0.00998682
$459$	0	0
$460$	3.16928	0.147769
$461$	27.1562	1.26479	0.632395	−	0.774646i	$-0.282072\pi$
$461$	27.1562	1.26479	0.632395	+	0.774646i	$0.282072\pi$
$462$	0.645017	0.0300089
$463$	−23.6835	−1.10067	−0.550333	−	0.834945i	$-0.685499\pi$
$463$	−23.6835	−1.10067	−0.550333	+	0.834945i	$0.685499\pi$
$464$	−0.821871	−0.0381544
$465$	0.121620	0.00564001
$466$	−9.05270	−0.419358
$467$	−13.6392	−0.631148	−0.315574	−	0.948901i	$-0.602197\pi$
$467$	−13.6392	−0.631148	−0.315574	+	0.948901i	$0.602197\pi$
$468$	4.23098	0.195577
$469$	−6.38786	−0.294964
$470$	1.97197	0.0909602
$471$	17.2693	0.795728
$472$	1.97461	0.0908890
$473$	−11.6899	−0.537503
$474$	0.409766	0.0188212
$475$	14.2485	0.653766
$476$	0	0
$477$	−10.4697	−0.479375
$478$	−3.77477	−0.172654
$479$	28.2855	1.29240	0.646198	−	0.763170i	$-0.276358\pi$
$479$	28.2855	1.29240	0.646198	+	0.763170i	$0.276358\pi$
$480$	2.39537	0.109333
$481$	−1.69107	−0.0771063
$482$	−11.5498	−0.526077
$483$	−3.42130	−0.155675
$484$	16.0425	0.729202
$485$	3.07370	0.139570
$486$	0.445735	0.0202189
$487$	22.4959	1.01939	0.509693	−	0.860356i	$-0.329759\pi$
$487$	22.4959	1.01939	0.509693	+	0.860356i	$0.329759\pi$
$488$	−13.9803	−0.632856
$489$	7.64240	0.345601
$490$	−0.229221	−0.0103552
$491$	17.7879	0.802755	0.401378	−	0.915913i	$-0.368532\pi$
$491$	17.7879	0.802755	0.401378	+	0.915913i	$0.368532\pi$
$492$	17.6594	0.796148
$493$	0	0
$494$	−3.15012	−0.141730
$495$	−0.744171	−0.0334480
$496$	−0.673404	−0.0302367
$497$	1.93783	0.0869235
$498$	2.18743	0.0980211
$499$	−34.3526	−1.53783	−0.768917	−	0.639348i	$-0.779204\pi$
$499$	−34.3526	−1.53783	−0.768917	+	0.639348i	$0.779204\pi$
$500$	9.01840	0.403315
$501$	−19.8998	−0.889059
$502$	6.86521	0.306409
$503$	−8.76690	−0.390897	−0.195448	−	0.980714i	$-0.562616\pi$
$503$	−8.76690	−0.390897	−0.195448	+	0.980714i	$0.562616\pi$
$504$	−1.69438	−0.0754737
$505$	1.63403	0.0727133
$506$	−2.20680	−0.0981042
$507$	7.48303	0.332333
$508$	−16.8364	−0.746995
$509$	−6.01970	−0.266819	−0.133409	−	0.991061i	$-0.542593\pi$
$509$	−6.01970	−0.266819	−0.133409	+	0.991061i	$0.542593\pi$
$510$	0	0
$511$	2.52808	0.111836
$512$	−22.9122	−1.01258
$513$	3.00884	0.132844
$514$	−5.48971	−0.242141
$515$	−9.57748	−0.422034
$516$	14.5515	0.640595
$517$	12.4492	0.547513
$518$	0.320914	0.0141001
$519$	12.0975	0.531022
$520$	−2.04663	−0.0897508
$521$	8.52210	0.373360	0.186680	−	0.982421i	$-0.440227\pi$
$521$	8.52210	0.373360	0.186680	+	0.982421i	$0.440227\pi$
$522$	0.128657	0.00563115
$523$	−34.3441	−1.50176	−0.750882	−	0.660436i	$-0.770371\pi$
$523$	−34.3441	−1.50176	−0.750882	+	0.660436i	$0.770371\pi$
$524$	3.04349	0.132955
$525$	−4.73554	−0.206676
$526$	3.52456	0.153678
$527$	0	0
$528$	4.12043	0.179319
$529$	−11.2947	−0.491073
$530$	2.39988	0.104244
$531$	1.16539	0.0505736
$532$	−5.41989	−0.234982
$533$	−23.0269	−0.997406
$534$	−2.38018	−0.103001
$535$	−2.05785	−0.0889684
$536$	10.8235	0.467503
$537$	−23.4966	−1.01395
$538$	−6.87206	−0.296276
$539$	−1.44709	−0.0623304
$540$	0.926338	0.0398632
$541$	−24.6469	−1.05965	−0.529827	−	0.848106i	$-0.677743\pi$
$541$	−24.6469	−1.05965	−0.529827	+	0.848106i	$0.677743\pi$
$542$	2.18218	0.0937325
$543$	−5.62024	−0.241187
$544$	0	0
$545$	1.83239	0.0784912
$546$	1.04695	0.0448054
$547$	27.5403	1.17754	0.588770	−	0.808301i	$-0.299612\pi$
$547$	27.5403	1.17754	0.588770	+	0.808301i	$0.299612\pi$
$548$	20.8252	0.889609
$549$	−8.25095	−0.352142
$550$	−3.05450	−0.130245
$551$	0.868471	0.0369981
$552$	5.79699	0.246736
$553$	−0.919304	−0.0390928
$554$	0.139287	0.00591773
$555$	−0.370246	−0.0157161
$556$	−20.3066	−0.861192
$557$	−26.1121	−1.10640	−0.553202	−	0.833047i	$-0.686594\pi$
$557$	−26.1121	−1.10640	−0.553202	+	0.833047i	$0.686594\pi$
$558$	0.105415	0.00446259
$559$	−18.9744	−0.802531
$560$	−1.46429	−0.0618774
$561$	0	0
$562$	1.32164	0.0557501
$563$	46.8459	1.97432	0.987160	−	0.159736i	$-0.0510643\pi$
$563$	46.8459	1.97432	0.987160	+	0.159736i	$0.0510643\pi$
$564$	−15.4966	−0.652524
$565$	−5.79134	−0.243643
$566$	2.18078	0.0916651
$567$	−1.00000	−0.0419961
$568$	−3.28342	−0.137769
$569$	34.4052	1.44234	0.721170	−	0.692758i	$-0.243605\pi$
$569$	34.4052	1.44234	0.721170	+	0.692758i	$0.243605\pi$
$570$	−0.689691	−0.0288880
$571$	29.9599	1.25378	0.626892	−	0.779106i	$-0.284327\pi$
$571$	29.9599	1.25378	0.626892	+	0.779106i	$0.284327\pi$
$572$	−6.12260	−0.255999
$573$	−17.1383	−0.715964
$574$	4.36980	0.182392
$575$	16.2017	0.675659
$576$	−3.61858	−0.150774
$577$	−16.8873	−0.703025	−0.351513	−	0.936183i	$-0.614333\pi$
$577$	−16.8873	−0.703025	−0.351513	+	0.936183i	$0.614333\pi$
$578$	0	0
$579$	−24.3552	−1.01217
$580$	0.267378	0.0111023
$581$	−4.90747	−0.203596
$582$	2.66416	0.110433
$583$	15.1506	0.627472
$584$	−4.28353	−0.177254
$585$	−1.20789	−0.0499403
$586$	−6.31999	−0.261076
$587$	24.1450	0.996570	0.498285	−	0.867013i	$-0.333963\pi$
$587$	24.1450	0.996570	0.498285	+	0.867013i	$0.333963\pi$
$588$	1.80132	0.0742852
$589$	0.711585	0.0293204
$590$	−0.267132	−0.0109977
$591$	5.14873	0.211791
$592$	2.05003	0.0842556
$593$	−2.44639	−0.100461	−0.0502307	−	0.998738i	$-0.515996\pi$
$593$	−2.44639	−0.100461	−0.0502307	+	0.998738i	$0.515996\pi$
$594$	−0.645017	−0.0264654
$595$	0	0
$596$	33.3599	1.36648
$597$	2.17553	0.0890386
$598$	−3.58194	−0.146477
$599$	4.77706	0.195185	0.0975926	−	0.995226i	$-0.468886\pi$
$599$	4.77706	0.195185	0.0975926	+	0.995226i	$0.468886\pi$
$600$	8.02381	0.327571
$601$	−0.748720	−0.0305409	−0.0152705	−	0.999883i	$-0.504861\pi$
$601$	−0.748720	−0.0305409	−0.0152705	+	0.999883i	$0.504861\pi$
$602$	3.60076	0.146756
$603$	6.38786	0.260134
$604$	−15.7454	−0.640673
$605$	−4.57992	−0.186200
$606$	1.41631	0.0575336
$607$	20.6683	0.838899	0.419449	−	0.907779i	$-0.362223\pi$
$607$	20.6683	0.838899	0.419449	+	0.907779i	$0.362223\pi$
$608$	14.0150	0.568384
$609$	−0.288640	−0.0116963
$610$	1.89129	0.0765763
$611$	20.2067	0.817476
$612$	0	0
$613$	−33.5425	−1.35477	−0.677384	−	0.735629i	$-0.736887\pi$
$613$	−33.5425	−1.35477	−0.677384	+	0.735629i	$0.736887\pi$
$614$	1.51529	0.0611521
$615$	−5.04155	−0.203295
$616$	2.45192	0.0987905
$617$	−37.2457	−1.49945	−0.749727	−	0.661747i	$-0.769815\pi$
$617$	−37.2457	−1.49945	−0.749727	+	0.661747i	$0.769815\pi$
$618$	−8.30136	−0.333930
$619$	−15.3771	−0.618059	−0.309030	−	0.951052i	$-0.600004\pi$
$619$	−15.3771	−0.618059	−0.309030	+	0.951052i	$0.600004\pi$
$620$	0.219077	0.00879835
$621$	3.42130	0.137292
$622$	2.02115	0.0810408
$623$	5.33991	0.213939
$624$	6.68803	0.267736
$625$	21.1031	0.844123
$626$	−2.99758	−0.119808
$627$	−4.35405	−0.173884
$628$	31.1076	1.24133
$629$	0	0
$630$	0.229221	0.00913240
$631$	−37.8573	−1.50707	−0.753537	−	0.657405i	$-0.771654\pi$
$631$	−37.8573	−1.50707	−0.753537	+	0.657405i	$0.771654\pi$
$632$	1.55765	0.0619600
$633$	−11.5302	−0.458283
$634$	7.17119	0.284804
$635$	4.80659	0.190744
$636$	−18.8593	−0.747820
$637$	−2.34882	−0.0930638
$638$	−0.186177	−0.00737084
$639$	−1.93783	−0.0766593
$640$	5.62020	0.222158
$641$	−9.66414	−0.381711	−0.190855	−	0.981618i	$-0.561126\pi$
$641$	−9.66414	−0.381711	−0.190855	+	0.981618i	$0.561126\pi$
$642$	−1.78365	−0.0703952
$643$	−7.15672	−0.282234	−0.141117	−	0.989993i	$-0.545069\pi$
$643$	−7.15672	−0.282234	−0.141117	+	0.989993i	$0.545069\pi$
$644$	−6.16286	−0.242851
$645$	−4.15428	−0.163575
$646$	0	0
$647$	20.4038	0.802156	0.401078	−	0.916044i	$-0.368636\pi$
$647$	20.4038	0.802156	0.401078	+	0.916044i	$0.368636\pi$
$648$	1.69438	0.0665616
$649$	−1.68642	−0.0661978
$650$	−4.95789	−0.194464
$651$	−0.236498	−0.00926909
$652$	13.7664	0.539134
$653$	6.40451	0.250628	0.125314	−	0.992117i	$-0.460006\pi$
$653$	6.40451	0.250628	0.125314	+	0.992117i	$0.460006\pi$
$654$	1.58824	0.0621052
$655$	−0.868879	−0.0339499
$656$	27.9147	1.08989
$657$	−2.52808	−0.0986297
$658$	−3.83462	−0.149489
$659$	30.0564	1.17083	0.585415	−	0.810733i	$-0.300931\pi$
$659$	30.0564	1.17083	0.585415	+	0.810733i	$0.300931\pi$
$660$	−1.34049	−0.0521785
$661$	−45.7701	−1.78025	−0.890126	−	0.455715i	$-0.849383\pi$
$661$	−45.7701	−1.78025	−0.890126	+	0.455715i	$0.849383\pi$
$662$	−5.47468	−0.212780
$663$	0	0
$664$	8.31512	0.322689
$665$	1.54731	0.0600022
$666$	−0.320914	−0.0124352
$667$	0.987524	0.0382371
$668$	−35.8460	−1.38692
$669$	1.79652	0.0694575
$670$	−1.46424	−0.0565683
$671$	11.9398	0.460932
$672$	−4.65795	−0.179684
$673$	−27.8412	−1.07320	−0.536599	−	0.843837i	$-0.680291\pi$
$673$	−27.8412	−1.07320	−0.536599	+	0.843837i	$0.680291\pi$
$674$	−12.4398	−0.479162
$675$	4.73554	0.182271
$676$	13.4793	0.518436
$677$	−2.79349	−0.107363	−0.0536813	−	0.998558i	$-0.517095\pi$
$677$	−2.79349	−0.107363	−0.0536813	+	0.998558i	$0.517095\pi$
$678$	−5.01969	−0.192780
$679$	−5.97700	−0.229376
$680$	0	0
$681$	−19.7638	−0.757349
$682$	−0.152545	−0.00584126
$683$	−8.27399	−0.316596	−0.158298	−	0.987391i	$-0.550601\pi$
$683$	−8.27399	−0.316596	−0.158298	+	0.987391i	$0.550601\pi$
$684$	5.41989	0.207235
$685$	−5.94534	−0.227160
$686$	0.445735	0.0170182
$687$	−0.479494	−0.0182938
$688$	23.0020	0.876942
$689$	24.5915	0.936861
$690$	−0.784236	−0.0298554
$691$	1.00604	0.0382714	0.0191357	−	0.999817i	$-0.493909\pi$
$691$	1.00604	0.0382714	0.0191357	+	0.999817i	$0.493909\pi$
$692$	21.7915	0.828388
$693$	1.44709	0.0549703
$694$	−15.9727	−0.606317
$695$	5.79729	0.219904
$696$	0.489066	0.0185380
$697$	0	0
$698$	9.58249	0.362703
$699$	−20.3096	−0.768180
$700$	−8.53023	−0.322412
$701$	41.0477	1.55035	0.775174	−	0.631747i	$-0.217662\pi$
$701$	41.0477	1.55035	0.775174	+	0.631747i	$0.217662\pi$
$702$	−1.04695	−0.0395147
$703$	−2.16626	−0.0817021
$704$	5.23640	0.197354
$705$	4.42409	0.166621
$706$	14.9166	0.561393
$707$	−3.17747	−0.119501
$708$	2.09924	0.0788943
$709$	26.1743	0.982995	0.491497	−	0.870879i	$-0.336450\pi$
$709$	26.1743	0.982995	0.491497	+	0.870879i	$0.336450\pi$
$710$	0.444192	0.0166702
$711$	0.919304	0.0344766
$712$	−9.04784	−0.339082
$713$	0.809132	0.0303022
$714$	0	0
$715$	1.74793	0.0653688
$716$	−42.3248	−1.58175
$717$	−8.46865	−0.316268
$718$	0.0822452	0.00306936
$719$	−46.6429	−1.73949	−0.869744	−	0.493503i	$-0.835716\pi$
$719$	−46.6429	−1.73949	−0.869744	+	0.493503i	$0.835716\pi$
$720$	1.46429	0.0545708
$721$	18.6240	0.693594
$722$	4.43367	0.165004
$723$	−25.9117	−0.963667
$724$	−10.1238	−0.376250
$725$	1.36687	0.0507641
$726$	−3.96969	−0.147329
$727$	23.4447	0.869516	0.434758	−	0.900547i	$-0.356834\pi$
$727$	23.4447	0.869516	0.434758	+	0.900547i	$0.356834\pi$
$728$	3.97980	0.147501
$729$	1.00000	0.0370370
$730$	0.579490	0.0214479
$731$	0	0
$732$	−14.8626	−0.549338
$733$	24.8488	0.917810	0.458905	−	0.888485i	$-0.348242\pi$
$733$	24.8488	0.917810	0.458905	+	0.888485i	$0.348242\pi$
$734$	11.9054	0.439436
$735$	−0.514255	−0.0189686
$736$	15.9362	0.587418
$737$	−9.24379	−0.340499
$738$	−4.36980	−0.160855
$739$	−13.2408	−0.487071	−0.243536	−	0.969892i	$-0.578307\pi$
$739$	−13.2408	−0.487071	−0.243536	+	0.969892i	$0.578307\pi$
$740$	−0.666931	−0.0245169
$741$	−7.06724	−0.259621
$742$	−4.66671	−0.171320
$743$	4.77103	0.175032	0.0875160	−	0.996163i	$-0.472107\pi$
$743$	4.77103	0.175032	0.0875160	+	0.996163i	$0.472107\pi$
$744$	0.400718	0.0146910
$745$	−9.52385	−0.348927
$746$	−0.0756314	−0.00276906
$747$	4.90747	0.179555
$748$	0	0
$749$	4.00160	0.146215
$750$	−2.23159	−0.0814863
$751$	−25.8402	−0.942921	−0.471461	−	0.881887i	$-0.656273\pi$
$751$	−25.8402	−0.942921	−0.471461	+	0.881887i	$0.656273\pi$
$752$	−24.4959	−0.893273
$753$	15.4020	0.561280
$754$	−0.302192	−0.0110052
$755$	4.49513	0.163595
$756$	−1.80132	−0.0655134
$757$	−39.3638	−1.43070	−0.715350	−	0.698766i	$-0.753733\pi$
$757$	−39.3638	−1.43070	−0.715350	+	0.698766i	$0.753733\pi$
$758$	−6.70815	−0.243651
$759$	−4.95092	−0.179707
$760$	−2.62174	−0.0951004
$761$	50.9757	1.84787	0.923934	−	0.382553i	$-0.124955\pi$
$761$	50.9757	1.84787	0.923934	+	0.382553i	$0.124955\pi$
$762$	4.16616	0.150924
$763$	−3.56320	−0.128997
$764$	−30.8716	−1.11690
$765$	0	0
$766$	−10.3620	−0.374393
$767$	−2.73730	−0.0988380
$768$	−2.36581	−0.0853687
$769$	29.1332	1.05057	0.525285	−	0.850926i	$-0.323959\pi$
$769$	29.1332	1.05057	0.525285	+	0.850926i	$0.323959\pi$
$770$	−0.331703	−0.0119538
$771$	−12.3161	−0.443553
$772$	−43.8714	−1.57897
$773$	−28.5029	−1.02518	−0.512588	−	0.858635i	$-0.671313\pi$
$773$	−28.5029	−1.02518	−0.512588	+	0.858635i	$0.671313\pi$
$774$	−3.60076	−0.129427
$775$	1.11995	0.0402297
$776$	10.1273	0.363549
$777$	0.719966	0.0258286
$778$	−2.87270	−0.102991
$779$	−29.4975	−1.05686
$780$	−2.17580	−0.0779063
$781$	2.80421	0.100342
$782$	0	0
$783$	0.288640	0.0103151
$784$	2.84740	0.101693
$785$	−8.88083	−0.316970
$786$	−0.753108	−0.0268625
$787$	−37.4755	−1.33586	−0.667929	−	0.744225i	$-0.732819\pi$
$787$	−37.4755	−1.33586	−0.667929	+	0.744225i	$0.732819\pi$
$788$	9.27451	0.330391
$789$	7.90731	0.281508
$790$	−0.210724	−0.00749723
$791$	11.2616	0.400417
$792$	−2.45192	−0.0871250
$793$	19.3800	0.688205
$794$	−12.3924	−0.439789
$795$	5.38410	0.190954
$796$	3.91883	0.138899
$797$	51.3309	1.81823	0.909116	−	0.416543i	$-0.136758\pi$
$797$	51.3309	1.81823	0.909116	+	0.416543i	$0.136758\pi$
$798$	1.34115	0.0474760
$799$	0	0
$800$	22.0579	0.779865
$801$	−5.33991	−0.188676
$802$	−11.3669	−0.401380
$803$	3.65835	0.129100
$804$	11.5066	0.405806
$805$	1.75942	0.0620115
$806$	−0.247602	−0.00872142
$807$	−15.4174	−0.542717
$808$	5.38384	0.189403
$809$	−16.9190	−0.594839	−0.297419	−	0.954747i	$-0.596126\pi$
$809$	−16.9190	−0.594839	−0.297419	+	0.954747i	$0.596126\pi$
$810$	−0.229221	−0.00805402
$811$	4.77991	0.167845	0.0839227	−	0.996472i	$-0.473255\pi$
$811$	4.77991	0.167845	0.0839227	+	0.996472i	$0.473255\pi$
$812$	−0.519933	−0.0182461
$813$	4.89568	0.171699
$814$	0.464390	0.0162769
$815$	−3.93014	−0.137667
$816$	0	0
$817$	−24.3062	−0.850366
$818$	5.15460	0.180226
$819$	2.34882	0.0820745
$820$	−9.08144	−0.317138
$821$	37.8415	1.32068	0.660339	−	0.750968i	$-0.270413\pi$
$821$	37.8415	1.32068	0.660339	+	0.750968i	$0.270413\pi$
$822$	−5.15318	−0.179738
$823$	−21.7490	−0.758122	−0.379061	−	0.925372i	$-0.623753\pi$
$823$	−21.7490	−0.758122	−0.379061	+	0.925372i	$0.623753\pi$
$824$	−31.5561	−1.09931
$825$	−6.85274	−0.238582
$826$	0.519455	0.0180741
$827$	4.06189	0.141246	0.0706230	−	0.997503i	$-0.477501\pi$
$827$	4.06189	0.141246	0.0706230	+	0.997503i	$0.477501\pi$
$828$	6.16286	0.214174
$829$	−6.31918	−0.219474	−0.109737	−	0.993961i	$-0.535001\pi$
$829$	−6.31918	−0.219474	−0.109737	+	0.993961i	$0.535001\pi$
$830$	−1.12490	−0.0390457
$831$	0.312488	0.0108401
$832$	8.49941	0.294664
$833$	0	0
$834$	5.02485	0.173996
$835$	10.2336	0.354148
$836$	−7.84305	−0.271257
$837$	0.236498	0.00817457
$838$	−10.2597	−0.354414
$839$	−56.1354	−1.93801	−0.969005	−	0.247042i	$-0.920542\pi$
$839$	−56.1354	−1.93801	−0.969005	+	0.247042i	$0.920542\pi$
$840$	0.871344	0.0300642
$841$	−28.9167	−0.997127
$842$	−2.49879	−0.0861141
$843$	2.96508	0.102123
$844$	−20.7695	−0.714917
$845$	−3.84818	−0.132382
$846$	3.83462	0.131837
$847$	8.90594	0.306012
$848$	−29.8114	−1.02373
$849$	4.89256	0.167912
$850$	0	0
$851$	−2.46322	−0.0844381
$852$	−3.49065	−0.119588
$853$	13.2070	0.452200	0.226100	−	0.974104i	$-0.427402\pi$
$853$	13.2070	0.452200	0.226100	+	0.974104i	$0.427402\pi$
$854$	−3.67774	−0.125850
$855$	−1.54731	−0.0529169
$856$	−6.78024	−0.231744
$857$	40.1590	1.37180	0.685902	−	0.727694i	$-0.259408\pi$
$857$	40.1590	1.37180	0.685902	+	0.727694i	$0.259408\pi$
$858$	1.51503	0.0517223
$859$	22.1538	0.755879	0.377940	−	0.925830i	$-0.376633\pi$
$859$	22.1538	0.755879	0.377940	+	0.925830i	$0.376633\pi$
$860$	−7.48319	−0.255175
$861$	9.80360	0.334106
$862$	−1.77428	−0.0604324
$863$	−11.6834	−0.397706	−0.198853	−	0.980029i	$-0.563722\pi$
$863$	−11.6834	−0.397706	−0.198853	+	0.980029i	$0.563722\pi$
$864$	4.65795	0.158467
$865$	−6.22120	−0.211527
$866$	−11.5921	−0.393916
$867$	0	0
$868$	−0.426009	−0.0144597
$869$	−1.33031	−0.0451277
$870$	−0.0661624	−0.00224312
$871$	−15.0040	−0.508390
$872$	6.03742	0.204453
$873$	5.97700	0.202291
$874$	−4.58847	−0.155207
$875$	5.00655	0.169252
$876$	−4.55388	−0.153861
$877$	−3.52434	−0.119008	−0.0595042	−	0.998228i	$-0.518952\pi$
$877$	−3.52434	−0.119008	−0.0595042	+	0.998228i	$0.518952\pi$
$878$	−9.97296	−0.336571
$879$	−14.1788	−0.478239
$880$	−2.11895	−0.0714298
$881$	−24.3026	−0.818776	−0.409388	−	0.912360i	$-0.634258\pi$
$881$	−24.3026	−0.818776	−0.409388	+	0.912360i	$0.634258\pi$
$882$	−0.445735	−0.0150087
$883$	18.4675	0.621482	0.310741	−	0.950495i	$-0.399423\pi$
$883$	18.4675	0.621482	0.310741	+	0.950495i	$0.399423\pi$
$884$	0	0
$885$	−0.599307	−0.0201455
$886$	−9.89925	−0.332572
$887$	−48.7259	−1.63606	−0.818028	−	0.575178i	$-0.804933\pi$
$887$	−48.7259	−1.63606	−0.818028	+	0.575178i	$0.804933\pi$
$888$	−1.21990	−0.0409370
$889$	−9.34671	−0.313479
$890$	1.22402	0.0410293
$891$	−1.44709	−0.0484792
$892$	3.23611	0.108353
$893$	25.8848	0.866201
$894$	−8.25488	−0.276084
$895$	12.0832	0.403898
$896$	−10.9288	−0.365106
$897$	−8.03604	−0.268316
$898$	−10.5943	−0.353536
$899$	0.0682627	0.00227669
$900$	8.53023	0.284341
$901$	0	0
$902$	6.32348	0.210549
$903$	8.07825	0.268827
$904$	−19.0815	−0.634640
$905$	2.89023	0.0960747
$906$	3.89619	0.129442
$907$	24.6051	0.816998	0.408499	−	0.912759i	$-0.366052\pi$
$907$	24.6051	0.816998	0.408499	+	0.912759i	$0.366052\pi$
$908$	−35.6009	−1.18146
$909$	3.17747	0.105390
$910$	−0.538401	−0.0178478
$911$	33.5850	1.11272	0.556360	−	0.830941i	$-0.312198\pi$
$911$	33.5850	1.11272	0.556360	+	0.830941i	$0.312198\pi$
$912$	8.56736	0.283694
$913$	−7.10153	−0.235026
$914$	−12.0170	−0.397487
$915$	4.24309	0.140272
$916$	−0.863722	−0.0285382
$917$	1.68959	0.0557951
$918$	0	0
$919$	−29.8477	−0.984583	−0.492292	−	0.870430i	$-0.663841\pi$
$919$	−29.8477	−0.984583	−0.492292	+	0.870430i	$0.663841\pi$
$920$	−2.98113	−0.0982850
$921$	3.39953	0.112018
$922$	−12.1045	−0.398639
$923$	4.55162	0.149818
$924$	2.60667	0.0857530
$925$	−3.40943	−0.112101
$926$	10.5566	0.346910
$927$	−18.6240	−0.611692
$928$	1.34447	0.0441343
$929$	33.5548	1.10090	0.550449	−	0.834869i	$-0.314456\pi$
$929$	33.5548	1.10090	0.550449	+	0.834869i	$0.314456\pi$
$930$	−0.0542104	−0.00177763
$931$	−3.00884	−0.0986108
$932$	−36.5841	−1.19835
$933$	4.53443	0.148450
$934$	6.07948	0.198927
$935$	0	0
$936$	−3.97980	−0.130084
$937$	−35.5864	−1.16256	−0.581278	−	0.813705i	$-0.697447\pi$
$937$	−35.5864	−1.16256	−0.581278	+	0.813705i	$0.697447\pi$
$938$	2.84729	0.0929674
$939$	−6.72503	−0.219463
$940$	7.96920	0.259927
$941$	−8.86604	−0.289025	−0.144512	−	0.989503i	$-0.546161\pi$
$941$	−8.86604	−0.289025	−0.144512	+	0.989503i	$0.546161\pi$
$942$	−7.69754	−0.250799
$943$	−33.5411	−1.09225
$944$	3.31833	0.108002
$945$	0.514255	0.0167287
$946$	5.21061	0.169412
$947$	51.6992	1.68000	0.839999	−	0.542588i	$-0.182555\pi$
$947$	51.6992	1.68000	0.839999	+	0.542588i	$0.182555\pi$
$948$	1.65596	0.0537831
$949$	5.93801	0.192756
$950$	−6.35105	−0.206055
$951$	16.0885	0.521704
$952$	0	0
$953$	27.8668	0.902695	0.451347	−	0.892348i	$-0.350944\pi$
$953$	27.8668	0.902695	0.451347	+	0.892348i	$0.350944\pi$
$954$	4.66671	0.151090
$955$	8.81347	0.285197
$956$	−15.2548	−0.493374
$957$	−0.417687	−0.0135019
$958$	−12.6078	−0.407340
$959$	11.5611	0.373327
$960$	1.86087	0.0600595
$961$	−30.9441	−0.998196
$962$	0.753770	0.0243025
$963$	−4.00160	−0.128950
$964$	−46.6753	−1.50331
$965$	12.5248	0.403186
$966$	1.52499	0.0490659
$967$	5.93299	0.190792	0.0953960	−	0.995439i	$-0.469588\pi$
$967$	5.93299	0.190792	0.0953960	+	0.995439i	$0.469588\pi$
$968$	−15.0901	−0.485013
$969$	0	0
$970$	−1.37006	−0.0439898
$971$	46.5606	1.49420	0.747100	−	0.664712i	$-0.231446\pi$
$971$	46.5606	1.49420	0.747100	+	0.664712i	$0.231446\pi$
$972$	1.80132	0.0577774
$973$	−11.2732	−0.361402
$974$	−10.0272	−0.321292
$975$	−11.1230	−0.356220
$976$	−23.4937	−0.752016
$977$	−29.0317	−0.928805	−0.464403	−	0.885624i	$-0.653731\pi$
$977$	−29.0317	−0.928805	−0.464403	+	0.885624i	$0.653731\pi$
$978$	−3.40648	−0.108927
$979$	7.72731	0.246966
$980$	−0.926338	−0.0295908
$981$	3.56320	0.113764
$982$	−7.92867	−0.253014
$983$	0.620543	0.0197923	0.00989613	−	0.999951i	$-0.496850\pi$
$983$	0.620543	0.0197923	0.00989613	+	0.999951i	$0.496850\pi$
$984$	−16.6110	−0.529540
$985$	−2.64776	−0.0843647
$986$	0	0
$987$	−8.60291	−0.273834
$988$	−12.7304	−0.405007
$989$	−27.6382	−0.878842
$990$	0.331703	0.0105422
$991$	−19.0766	−0.605989	−0.302995	−	0.952992i	$-0.597986\pi$
$991$	−19.0766	−0.605989	−0.302995	+	0.952992i	$0.597986\pi$
$992$	1.10160	0.0349757
$993$	−12.2824	−0.389769
$994$	−0.863758	−0.0273967
$995$	−1.11878	−0.0354677
$996$	8.83992	0.280104
$997$	−2.30146	−0.0728878	−0.0364439	−	0.999336i	$-0.511603\pi$
$997$	−2.30146	−0.0728878	−0.0364439	+	0.999336i	$0.511603\pi$
$998$	15.3122	0.484698
$999$	−0.719966	−0.0227787

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6069.2.a.z.1.5	✓	9
17.16	even	2		6069.2.a.bc.1.5	yes	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6069.2.a.z.1.5	✓	9	1.1	even	1	trivial
6069.2.a.bc.1.5	yes	9	17.16	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 6069 = 3 \cdot 7 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6069.a (trivial)

\(f(q)\)	\(=\)	\(q-0.445735 q^{2} -1.00000 q^{3} -1.80132 q^{4} +0.514255 q^{5} +0.445735 q^{6} -1.00000 q^{7} +1.69438 q^{8} +1.00000 q^{9} -0.229221 q^{10} -1.44709 q^{11} +1.80132 q^{12} -2.34882 q^{13} +0.445735 q^{14} -0.514255 q^{15} +2.84740 q^{16} -0.445735 q^{18} -3.00884 q^{19} -0.926338 q^{20} +1.00000 q^{21} +0.645017 q^{22} -3.42130 q^{23} -1.69438 q^{24} -4.73554 q^{25} +1.04695 q^{26} -1.00000 q^{27} +1.80132 q^{28} -0.288640 q^{29} +0.229221 q^{30} -0.236498 q^{31} -4.65795 q^{32} +1.44709 q^{33} -0.514255 q^{35} -1.80132 q^{36} +0.719966 q^{37} +1.34115 q^{38} +2.34882 q^{39} +0.871344 q^{40} +9.80360 q^{41} -0.445735 q^{42} +8.07825 q^{43} +2.60667 q^{44} +0.514255 q^{45} +1.52499 q^{46} -8.60291 q^{47} -2.84740 q^{48} +1.00000 q^{49} +2.11080 q^{50} +4.23098 q^{52} -10.4697 q^{53} +0.445735 q^{54} -0.744171 q^{55} -1.69438 q^{56} +3.00884 q^{57} +0.128657 q^{58} +1.16539 q^{59} +0.926338 q^{60} -8.25095 q^{61} +0.105415 q^{62} -1.00000 q^{63} -3.61858 q^{64} -1.20789 q^{65} -0.645017 q^{66} +6.38786 q^{67} +3.42130 q^{69} +0.229221 q^{70} -1.93783 q^{71} +1.69438 q^{72} -2.52808 q^{73} -0.320914 q^{74} +4.73554 q^{75} +5.41989 q^{76} +1.44709 q^{77} -1.04695 q^{78} +0.919304 q^{79} +1.46429 q^{80} +1.00000 q^{81} -4.36980 q^{82} +4.90747 q^{83} -1.80132 q^{84} -3.60076 q^{86} +0.288640 q^{87} -2.45192 q^{88} -5.33991 q^{89} -0.229221 q^{90} +2.34882 q^{91} +6.16286 q^{92} +0.236498 q^{93} +3.83462 q^{94} -1.54731 q^{95} +4.65795 q^{96} +5.97700 q^{97} -0.445735 q^{98} -1.44709 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{3} + 6 q^{4} + 3 q^{5} - 9 q^{7} + 9 q^{8} + 9 q^{9} + 12 q^{10} + 18 q^{11} - 6 q^{12} - 21 q^{13} - 3 q^{15} - 9 q^{19} + 15 q^{20} + 9 q^{21} + 6 q^{22} - 9 q^{24} + 3 q^{26} - 9 q^{27} - 6 q^{28}+ \cdots + 18 q^{99}+O(q^{100}) \) 9 * q - 9 * q^3 + 6 * q^4 + 3 * q^5 - 9 * q^7 + 9 * q^8 + 9 * q^9 + 12 * q^10 + 18 * q^11 - 6 * q^12 - 21 * q^13 - 3 * q^15 - 9 * q^19 + 15 * q^20 + 9 * q^21 + 6 * q^22 - 9 * q^24 + 3 * q^26 - 9 * q^27 - 6 * q^28 + 6 * q^29 - 12 * q^30 + 30 * q^31 + 3 * q^32 - 18 * q^33 - 3 * q^35 + 6 * q^36 + 12 * q^37 - 36 * q^38 + 21 * q^39 + 30 * q^40 + 9 * q^41 + 30 * q^44 + 3 * q^45 + 33 * q^46 - 9 * q^47 + 9 * q^49 - 12 * q^50 - 12 * q^52 + 30 * q^55 - 9 * q^56 + 9 * q^57 + 9 * q^58 - 3 * q^59 - 15 * q^60 + 33 * q^61 - 12 * q^62 - 9 * q^63 - 15 * q^64 - 15 * q^65 - 6 * q^66 - 15 * q^67 - 12 * q^70 + 9 * q^72 + 21 * q^73 + 6 * q^74 + 3 * q^76 - 18 * q^77 - 3 * q^78 + 30 * q^79 + 9 * q^81 + 9 * q^82 + 6 * q^84 + 72 * q^86 - 6 * q^87 + 48 * q^88 - 12 * q^89 + 12 * q^90 + 21 * q^91 + 48 * q^92 - 30 * q^93 + 48 * q^94 - 18 * q^95 - 3 * q^96 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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