LMFDB - Embedded newform 6027.2.a.y.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, 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("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 6x^{5} + 16x^{4} + 14x^{3} - 20x^{2} - 10x + 4 $ x^7 - 3x^6 - 6x^5 + 16x^4 + 14x^3 - 20x^2 - 10x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.281557$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.718443 q^{2} -1.00000 q^{3} -1.48384 q^{4} +3.61951 q^{5} -0.718443 q^{6} -2.50294 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.718443 q^{2} -1.00000 q^{3} -1.48384 q^{4} +3.61951 q^{5} -0.718443 q^{6} -2.50294 q^{8} +1.00000 q^{9} +2.60041 q^{10} +4.77078 q^{11} +1.48384 q^{12} +1.67717 q^{13} -3.61951 q^{15} +1.16946 q^{16} -4.10812 q^{17} +0.718443 q^{18} -7.21202 q^{19} -5.37077 q^{20} +3.42753 q^{22} +6.09173 q^{23} +2.50294 q^{24} +8.10083 q^{25} +1.20495 q^{26} -1.00000 q^{27} +4.27679 q^{29} -2.60041 q^{30} +9.68962 q^{31} +5.84607 q^{32} -4.77078 q^{33} -2.95145 q^{34} -1.48384 q^{36} -9.29150 q^{37} -5.18143 q^{38} -1.67717 q^{39} -9.05941 q^{40} -1.00000 q^{41} +0.493197 q^{43} -7.07907 q^{44} +3.61951 q^{45} +4.37656 q^{46} +0.929521 q^{47} -1.16946 q^{48} +5.81998 q^{50} +4.10812 q^{51} -2.48865 q^{52} +11.2593 q^{53} -0.718443 q^{54} +17.2679 q^{55} +7.21202 q^{57} +3.07263 q^{58} -0.276180 q^{59} +5.37077 q^{60} -8.28534 q^{61} +6.96144 q^{62} +1.86114 q^{64} +6.07053 q^{65} -3.42753 q^{66} -6.10165 q^{67} +6.09579 q^{68} -6.09173 q^{69} -4.71258 q^{71} -2.50294 q^{72} +9.42904 q^{73} -6.67541 q^{74} -8.10083 q^{75} +10.7015 q^{76} -1.20495 q^{78} +12.3654 q^{79} +4.23288 q^{80} +1.00000 q^{81} -0.718443 q^{82} +8.22541 q^{83} -14.8694 q^{85} +0.354334 q^{86} -4.27679 q^{87} -11.9410 q^{88} -5.51271 q^{89} +2.60041 q^{90} -9.03915 q^{92} -9.68962 q^{93} +0.667807 q^{94} -26.1040 q^{95} -5.84607 q^{96} -4.56102 q^{97} +4.77078 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 4 q^{2} - 7 q^{3} + 8 q^{4} - q^{5} - 4 q^{6} + 12 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + 4 * q^2 - 7 * q^3 + 8 * q^4 - q^5 - 4 * q^6 + 12 * q^8 + 7 * q^9	$ 7 q + 4 q^{2} - 7 q^{3} + 8 q^{4} - q^{5} - 4 q^{6} + 12 q^{8} + 7 q^{9} + 3 q^{10} + 11 q^{11} - 8 q^{12} + 7 q^{13} + q^{15} + 6 q^{16} - 11 q^{17} + 4 q^{18} - 4 q^{19} + 7 q^{20} + 6 q^{22} + 7 q^{23} - 12 q^{24} + 2 q^{25} + 13 q^{26} - 7 q^{27} + 4 q^{29} - 3 q^{30} + 7 q^{31} + 18 q^{32} - 11 q^{33} + 20 q^{34} + 8 q^{36} - 4 q^{38} - 7 q^{39} + 9 q^{40} - 7 q^{41} + q^{43} + 18 q^{44} - q^{45} - 17 q^{46} - 14 q^{47} - 6 q^{48} + 19 q^{50} + 11 q^{51} + 27 q^{52} + 23 q^{53} - 4 q^{54} + 30 q^{55} + 4 q^{57} - 3 q^{58} - 8 q^{59} - 7 q^{60} + 3 q^{61} + 16 q^{62} + 6 q^{64} + 15 q^{65} - 6 q^{66} + 3 q^{67} - 7 q^{69} + 7 q^{71} + 12 q^{72} + 11 q^{73} - 13 q^{74} - 2 q^{75} + 40 q^{76} - 13 q^{78} - q^{79} + 43 q^{80} + 7 q^{81} - 4 q^{82} - 10 q^{85} - 12 q^{86} - 4 q^{87} + 10 q^{88} - 32 q^{89} + 3 q^{90} - 19 q^{92} - 7 q^{93} - 21 q^{94} - 8 q^{95} - 18 q^{96} + 25 q^{97} + 11 q^{99}+O(q^{100}) $ 7 * q + 4 * q^2 - 7 * q^3 + 8 * q^4 - q^5 - 4 * q^6 + 12 * q^8 + 7 * q^9 + 3 * q^10 + 11 * q^11 - 8 * q^12 + 7 * q^13 + q^15 + 6 * q^16 - 11 * q^17 + 4 * q^18 - 4 * q^19 + 7 * q^20 + 6 * q^22 + 7 * q^23 - 12 * q^24 + 2 * q^25 + 13 * q^26 - 7 * q^27 + 4 * q^29 - 3 * q^30 + 7 * q^31 + 18 * q^32 - 11 * q^33 + 20 * q^34 + 8 * q^36 - 4 * q^38 - 7 * q^39 + 9 * q^40 - 7 * q^41 + q^43 + 18 * q^44 - q^45 - 17 * q^46 - 14 * q^47 - 6 * q^48 + 19 * q^50 + 11 * q^51 + 27 * q^52 + 23 * q^53 - 4 * q^54 + 30 * q^55 + 4 * q^57 - 3 * q^58 - 8 * q^59 - 7 * q^60 + 3 * q^61 + 16 * q^62 + 6 * q^64 + 15 * q^65 - 6 * q^66 + 3 * q^67 - 7 * q^69 + 7 * q^71 + 12 * q^72 + 11 * q^73 - 13 * q^74 - 2 * q^75 + 40 * q^76 - 13 * q^78 - q^79 + 43 * q^80 + 7 * q^81 - 4 * q^82 - 10 * q^85 - 12 * q^86 - 4 * q^87 + 10 * q^88 - 32 * q^89 + 3 * q^90 - 19 * q^92 - 7 * q^93 - 21 * q^94 - 8 * q^95 - 18 * q^96 + 25 * q^97 + 11 * q^99

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 $

$2$	0.718443	0.508016	0.254008	−	0.967202i	$-0.418251\pi$
$2$	0.718443	0.508016	0.254008	+	0.967202i	$0.418251\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.48384	−0.741920
$5$	3.61951	1.61869	0.809346	−	0.587332i	$-0.199822\pi$
$5$	3.61951	1.61869	0.809346	+	0.587332i	$0.199822\pi$
$6$	−0.718443	−0.293303
$7$	0	0
$7$	0	0
$8$	−2.50294	−0.884923
$9$	1.00000	0.333333
$10$	2.60041	0.822321
$11$	4.77078	1.43844	0.719221	−	0.694781i	$-0.244499\pi$
$11$	4.77078	1.43844	0.719221	+	0.694781i	$0.244499\pi$
$12$	1.48384	0.428348
$13$	1.67717	0.465163	0.232582	−	0.972577i	$-0.425283\pi$
$13$	1.67717	0.465163	0.232582	+	0.972577i	$0.425283\pi$
$14$	0	0
$15$	−3.61951	−0.934553
$16$	1.16946	0.292366
$17$	−4.10812	−0.996364	−0.498182	−	0.867072i	$-0.665999\pi$
$17$	−4.10812	−0.996364	−0.498182	+	0.867072i	$0.665999\pi$
$18$	0.718443	0.169339
$19$	−7.21202	−1.65455	−0.827276	−	0.561796i	$-0.810111\pi$
$19$	−7.21202	−1.65455	−0.827276	+	0.561796i	$0.810111\pi$
$20$	−5.37077	−1.20094
$21$	0	0
$22$	3.42753	0.730751
$23$	6.09173	1.27021	0.635106	−	0.772425i	$-0.280956\pi$
$23$	6.09173	1.27021	0.635106	+	0.772425i	$0.280956\pi$
$24$	2.50294	0.510910
$25$	8.10083	1.62017
$26$	1.20495	0.236310
$27$	−1.00000	−0.192450
$28$	0	0
$29$	4.27679	0.794180	0.397090	−	0.917780i	$-0.370020\pi$
$29$	4.27679	0.794180	0.397090	+	0.917780i	$0.370020\pi$
$30$	−2.60041	−0.474767
$31$	9.68962	1.74031	0.870154	−	0.492780i	$-0.164019\pi$
$31$	9.68962	1.74031	0.870154	+	0.492780i	$0.164019\pi$
$32$	5.84607	1.03345
$33$	−4.77078	−0.830485
$34$	−2.95145	−0.506169
$35$	0	0
$36$	−1.48384	−0.247307
$37$	−9.29150	−1.52751	−0.763756	−	0.645505i	$-0.776647\pi$
$37$	−9.29150	−1.52751	−0.763756	+	0.645505i	$0.776647\pi$
$38$	−5.18143	−0.840538
$39$	−1.67717	−0.268562
$40$	−9.05941	−1.43242
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	0.493197	0.0752119	0.0376059	−	0.999293i	$-0.488027\pi$
$43$	0.493197	0.0752119	0.0376059	+	0.999293i	$0.488027\pi$
$44$	−7.07907	−1.06721
$45$	3.61951	0.539564
$46$	4.37656	0.645288
$47$	0.929521	0.135585	0.0677923	−	0.997699i	$-0.478404\pi$
$47$	0.929521	0.135585	0.0677923	+	0.997699i	$0.478404\pi$
$48$	−1.16946	−0.168797
$49$	0	0
$50$	5.81998	0.823070
$51$	4.10812	0.575251
$52$	−2.48865	−0.345114
$53$	11.2593	1.54659	0.773293	−	0.634049i	$-0.218608\pi$
$53$	11.2593	1.54659	0.773293	+	0.634049i	$0.218608\pi$
$54$	−0.718443	−0.0977677
$55$	17.2679	2.32840
$56$	0	0
$57$	7.21202	0.955256
$58$	3.07263	0.403456
$59$	−0.276180	−0.0359556	−0.0179778	−	0.999838i	$-0.505723\pi$
$59$	−0.276180	−0.0359556	−0.0179778	+	0.999838i	$0.505723\pi$
$60$	5.37077	0.693364
$61$	−8.28534	−1.06083	−0.530414	−	0.847739i	$-0.677964\pi$
$61$	−8.28534	−1.06083	−0.530414	+	0.847739i	$0.677964\pi$
$62$	6.96144	0.884103
$63$	0	0
$64$	1.86114	0.232643
$65$	6.07053	0.752956
$66$	−3.42753	−0.421900
$67$	−6.10165	−0.745436	−0.372718	−	0.927945i	$-0.621574\pi$
$67$	−6.10165	−0.745436	−0.372718	+	0.927945i	$0.621574\pi$
$68$	6.09579	0.739223
$69$	−6.09173	−0.733358
$70$	0	0
$71$	−4.71258	−0.559281	−0.279640	−	0.960105i	$-0.590215\pi$
$71$	−4.71258	−0.559281	−0.279640	+	0.960105i	$0.590215\pi$
$72$	−2.50294	−0.294974
$73$	9.42904	1.10359	0.551793	−	0.833981i	$-0.313944\pi$
$73$	9.42904	1.10359	0.551793	+	0.833981i	$0.313944\pi$
$74$	−6.67541	−0.776000
$75$	−8.10083	−0.935404
$76$	10.7015	1.22755
$77$	0	0
$78$	−1.20495	−0.136434
$79$	12.3654	1.39122	0.695610	−	0.718419i	$-0.255134\pi$
$79$	12.3654	1.39122	0.695610	+	0.718419i	$0.255134\pi$
$80$	4.23288	0.473250
$81$	1.00000	0.111111
$82$	−0.718443	−0.0793387
$83$	8.22541	0.902856	0.451428	−	0.892308i	$-0.350915\pi$
$83$	8.22541	0.902856	0.451428	+	0.892308i	$0.350915\pi$
$84$	0	0
$85$	−14.8694	−1.61281
$86$	0.354334	0.0382088
$87$	−4.27679	−0.458520
$88$	−11.9410	−1.27291
$89$	−5.51271	−0.584346	−0.292173	−	0.956365i	$-0.594378\pi$
$89$	−5.51271	−0.584346	−0.292173	+	0.956365i	$0.594378\pi$
$90$	2.60041	0.274107
$91$	0	0
$92$	−9.03915	−0.942396
$93$	−9.68962	−1.00477
$94$	0.667807	0.0688791
$95$	−26.1040	−2.67821
$96$	−5.84607	−0.596662
$97$	−4.56102	−0.463102	−0.231551	−	0.972823i	$-0.574380\pi$
$97$	−4.56102	−0.463102	−0.231551	+	0.972823i	$0.574380\pi$
$98$	0	0
$99$	4.77078	0.479481
$100$	−12.0203	−1.20203
$101$	6.54576	0.651327	0.325664	−	0.945486i	$-0.394412\pi$
$101$	6.54576	0.651327	0.325664	+	0.945486i	$0.394412\pi$
$102$	2.95145	0.292237
$103$	−10.3795	−1.02272	−0.511359	−	0.859367i	$-0.670858\pi$
$103$	−10.3795	−1.02272	−0.511359	+	0.859367i	$0.670858\pi$
$104$	−4.19785	−0.411633
$105$	0	0
$106$	8.08917	0.785689
$107$	0.428154	0.0413912	0.0206956	−	0.999786i	$-0.493412\pi$
$107$	0.428154	0.0413912	0.0206956	+	0.999786i	$0.493412\pi$
$108$	1.48384	0.142783
$109$	9.21699	0.882827	0.441414	−	0.897304i	$-0.354477\pi$
$109$	9.21699	0.882827	0.441414	+	0.897304i	$0.354477\pi$
$110$	12.4060	1.18286
$111$	9.29150	0.881910
$112$	0	0
$113$	15.1405	1.42430	0.712150	−	0.702028i	$-0.247722\pi$
$113$	15.1405	1.42430	0.712150	+	0.702028i	$0.247722\pi$
$114$	5.18143	0.485285
$115$	22.0491	2.05608
$116$	−6.34607	−0.589218
$117$	1.67717	0.155054
$118$	−0.198419	−0.0182660
$119$	0	0
$120$	9.05941	0.827007
$121$	11.7603	1.06912
$122$	−5.95254	−0.538917
$123$	1.00000	0.0901670
$124$	−14.3779	−1.29117
$125$	11.2235	1.00386
$126$	0	0
$127$	−12.3127	−1.09257	−0.546286	−	0.837599i	$-0.683959\pi$
$127$	−12.3127	−1.09257	−0.546286	+	0.837599i	$0.683959\pi$
$128$	−10.3550	−0.915263
$129$	−0.493197	−0.0434236
$130$	4.36133	0.382514
$131$	−7.55733	−0.660287	−0.330143	−	0.943931i	$-0.607097\pi$
$131$	−7.55733	−0.660287	−0.330143	+	0.943931i	$0.607097\pi$
$132$	7.07907	0.616154
$133$	0	0
$134$	−4.38369	−0.378693
$135$	−3.61951	−0.311518
$136$	10.2824	0.881705
$137$	3.85038	0.328960	0.164480	−	0.986380i	$-0.447405\pi$
$137$	3.85038	0.328960	0.164480	+	0.986380i	$0.447405\pi$
$138$	−4.37656	−0.372557
$139$	−18.3824	−1.55917	−0.779586	−	0.626295i	$-0.784570\pi$
$139$	−18.3824	−1.55917	−0.779586	+	0.626295i	$0.784570\pi$
$140$	0	0
$141$	−0.929521	−0.0782798
$142$	−3.38572	−0.284123
$143$	8.00140	0.669111
$144$	1.16946	0.0974552
$145$	15.4799	1.28553
$146$	6.77423	0.560639
$147$	0	0
$148$	13.7871	1.13329
$149$	10.1266	0.829606	0.414803	−	0.909911i	$-0.363851\pi$
$149$	10.1266	0.829606	0.414803	+	0.909911i	$0.363851\pi$
$150$	−5.81998	−0.475200
$151$	−13.7468	−1.11870	−0.559351	−	0.828931i	$-0.688950\pi$
$151$	−13.7468	−1.11870	−0.559351	+	0.828931i	$0.688950\pi$
$152$	18.0513	1.46415
$153$	−4.10812	−0.332121
$154$	0	0
$155$	35.0717	2.81702
$156$	2.48865	0.199252
$157$	7.62988	0.608931	0.304466	−	0.952523i	$-0.401522\pi$
$157$	7.62988	0.608931	0.304466	+	0.952523i	$0.401522\pi$
$158$	8.88386	0.706762
$159$	−11.2593	−0.892921
$160$	21.1599	1.67284
$161$	0	0
$162$	0.718443	0.0564462
$163$	−6.42437	−0.503196	−0.251598	−	0.967832i	$-0.580956\pi$
$163$	−6.42437	−0.503196	−0.251598	+	0.967832i	$0.580956\pi$
$164$	1.48384	0.115868
$165$	−17.2679	−1.34430
$166$	5.90948	0.458665
$167$	22.3236	1.72745	0.863725	−	0.503963i	$-0.168125\pi$
$167$	22.3236	1.72745	0.863725	+	0.503963i	$0.168125\pi$
$168$	0	0
$169$	−10.1871	−0.783623
$170$	−10.6828	−0.819332
$171$	−7.21202	−0.551517
$172$	−0.731826	−0.0558012
$173$	−2.33229	−0.177321	−0.0886605	−	0.996062i	$-0.528259\pi$
$173$	−2.33229	−0.177321	−0.0886605	+	0.996062i	$0.528259\pi$
$174$	−3.07263	−0.232935
$175$	0	0
$176$	5.57924	0.420551
$177$	0.276180	0.0207590
$178$	−3.96057	−0.296857
$179$	18.0617	1.35000	0.674998	−	0.737820i	$-0.264144\pi$
$179$	18.0617	1.35000	0.674998	+	0.737820i	$0.264144\pi$
$180$	−5.37077	−0.400314
$181$	16.9055	1.25658	0.628289	−	0.777980i	$-0.283756\pi$
$181$	16.9055	1.25658	0.628289	+	0.777980i	$0.283756\pi$
$182$	0	0
$183$	8.28534	0.612470
$184$	−15.2472	−1.12404
$185$	−33.6306	−2.47257
$186$	−6.96144	−0.510437
$187$	−19.5989	−1.43321
$188$	−1.37926	−0.100593
$189$	0	0
$190$	−18.7542	−1.36057
$191$	11.9555	0.865071	0.432535	−	0.901617i	$-0.357619\pi$
$191$	11.9555	0.865071	0.432535	+	0.901617i	$0.357619\pi$
$192$	−1.86114	−0.134316
$193$	−11.2986	−0.813290	−0.406645	−	0.913586i	$-0.633301\pi$
$193$	−11.2986	−0.813290	−0.406645	+	0.913586i	$0.633301\pi$
$194$	−3.27683	−0.235263
$195$	−6.07053	−0.434719
$196$	0	0
$197$	15.2853	1.08903	0.544517	−	0.838750i	$-0.316713\pi$
$197$	15.2853	1.08903	0.544517	+	0.838750i	$0.316713\pi$
$198$	3.42753	0.243584
$199$	19.9661	1.41536	0.707681	−	0.706532i	$-0.249741\pi$
$199$	19.9661	1.41536	0.707681	+	0.706532i	$0.249741\pi$
$200$	−20.2759	−1.43372
$201$	6.10165	0.430378
$202$	4.70275	0.330884
$203$	0	0
$204$	−6.09579	−0.426790
$205$	−3.61951	−0.252797
$206$	−7.45704	−0.519557
$207$	6.09173	0.423404
$208$	1.96139	0.135998
$209$	−34.4069	−2.37998
$210$	0	0
$211$	−6.26636	−0.431394	−0.215697	−	0.976460i	$-0.569202\pi$
$211$	−6.26636	−0.431394	−0.215697	+	0.976460i	$0.569202\pi$
$212$	−16.7070	−1.14744
$213$	4.71258	0.322901
$214$	0.307604	0.0210274
$215$	1.78513	0.121745
$216$	2.50294	0.170303
$217$	0	0
$218$	6.62188	0.448490
$219$	−9.42904	−0.637156
$220$	−25.6227	−1.72748
$221$	−6.89001	−0.463472
$222$	6.67541	0.448024
$223$	−24.0197	−1.60848	−0.804239	−	0.594306i	$-0.797427\pi$
$223$	−24.0197	−1.60848	−0.804239	+	0.594306i	$0.797427\pi$
$224$	0	0
$225$	8.10083	0.540056
$226$	10.8776	0.723566
$227$	17.2170	1.14273	0.571365	−	0.820696i	$-0.306414\pi$
$227$	17.2170	1.14273	0.571365	+	0.820696i	$0.306414\pi$
$228$	−10.7015	−0.708724
$229$	0.410688	0.0271390	0.0135695	−	0.999908i	$-0.495681\pi$
$229$	0.410688	0.0271390	0.0135695	+	0.999908i	$0.495681\pi$
$230$	15.8410	1.04452
$231$	0	0
$232$	−10.7045	−0.702788
$233$	20.4805	1.34172	0.670861	−	0.741583i	$-0.265925\pi$
$233$	20.4805	1.34172	0.670861	+	0.741583i	$0.265925\pi$
$234$	1.20495	0.0787700
$235$	3.36441	0.219470
$236$	0.409807	0.0266762
$237$	−12.3654	−0.803222
$238$	0	0
$239$	−14.3115	−0.925736	−0.462868	−	0.886427i	$-0.653180\pi$
$239$	−14.3115	−0.925736	−0.462868	+	0.886427i	$0.653180\pi$
$240$	−4.23288	−0.273231
$241$	−27.0366	−1.74158	−0.870789	−	0.491658i	$-0.836391\pi$
$241$	−27.0366	−1.74158	−0.870789	+	0.491658i	$0.836391\pi$
$242$	8.44910	0.543129
$243$	−1.00000	−0.0641500
$244$	12.2941	0.787050
$245$	0	0
$246$	0.718443	0.0458062
$247$	−12.0958	−0.769637
$248$	−24.2525	−1.54004
$249$	−8.22541	−0.521264
$250$	8.06343	0.509976
$251$	−2.15039	−0.135732	−0.0678658	−	0.997694i	$-0.521619\pi$
$251$	−2.15039	−0.135732	−0.0678658	+	0.997694i	$0.521619\pi$
$252$	0	0
$253$	29.0623	1.82713
$254$	−8.84594	−0.555044
$255$	14.8694	0.931155
$256$	−11.1618	−0.697611
$257$	29.1832	1.82040	0.910200	−	0.414170i	$-0.135928\pi$
$257$	29.1832	1.82040	0.910200	+	0.414170i	$0.135928\pi$
$258$	−0.354334	−0.0220599
$259$	0	0
$260$	−9.00769	−0.558633
$261$	4.27679	0.264727
$262$	−5.42951	−0.335436
$263$	1.29066	0.0795858	0.0397929	−	0.999208i	$-0.487330\pi$
$263$	1.29066	0.0795858	0.0397929	+	0.999208i	$0.487330\pi$
$264$	11.9410	0.734915
$265$	40.7532	2.50345
$266$	0	0
$267$	5.51271	0.337372
$268$	9.05388	0.553054
$269$	23.0819	1.40733	0.703665	−	0.710531i	$-0.251545\pi$
$269$	23.0819	1.40733	0.703665	+	0.710531i	$0.251545\pi$
$270$	−2.60041	−0.158256
$271$	18.2013	1.10565	0.552826	−	0.833297i	$-0.313549\pi$
$271$	18.2013	1.10565	0.552826	+	0.833297i	$0.313549\pi$
$272$	−4.80429	−0.291303
$273$	0	0
$274$	2.76628	0.167117
$275$	38.6473	2.33052
$276$	9.03915	0.544093
$277$	−19.3138	−1.16045	−0.580227	−	0.814455i	$-0.697036\pi$
$277$	−19.3138	−1.16045	−0.580227	+	0.814455i	$0.697036\pi$
$278$	−13.2067	−0.792084
$279$	9.68962	0.580102
$280$	0	0
$281$	−10.6700	−0.636517	−0.318258	−	0.948004i	$-0.603098\pi$
$281$	−10.6700	−0.636517	−0.318258	+	0.948004i	$0.603098\pi$
$282$	−0.667807	−0.0397674
$283$	19.6343	1.16714	0.583570	−	0.812063i	$-0.301655\pi$
$283$	19.6343	1.16714	0.583570	+	0.812063i	$0.301655\pi$
$284$	6.99272	0.414942
$285$	26.1040	1.54627
$286$	5.74855	0.339919
$287$	0	0
$288$	5.84607	0.344483
$289$	−0.123387	−0.00725803
$290$	11.1214	0.653071
$291$	4.56102	0.267372
$292$	−13.9912	−0.818773
$293$	6.13638	0.358491	0.179246	−	0.983804i	$-0.442634\pi$
$293$	6.13638	0.358491	0.179246	+	0.983804i	$0.442634\pi$
$294$	0	0
$295$	−0.999635	−0.0582010
$296$	23.2561	1.35173
$297$	−4.77078	−0.276828
$298$	7.27540	0.421453
$299$	10.2169	0.590856
$300$	12.0203	0.693995
$301$	0	0
$302$	−9.87632	−0.568318
$303$	−6.54576	−0.376044
$304$	−8.43419	−0.483734
$305$	−29.9888	−1.71716
$306$	−2.95145	−0.168723
$307$	9.85765	0.562606	0.281303	−	0.959619i	$-0.409233\pi$
$307$	9.85765	0.562606	0.281303	+	0.959619i	$0.409233\pi$
$308$	0	0
$309$	10.3795	0.590467
$310$	25.1970	1.43109
$311$	20.2723	1.14954	0.574768	−	0.818316i	$-0.305092\pi$
$311$	20.2723	1.14954	0.574768	+	0.818316i	$0.305092\pi$
$312$	4.19785	0.237657
$313$	17.9597	1.01514	0.507571	−	0.861610i	$-0.330544\pi$
$313$	17.9597	1.01514	0.507571	+	0.861610i	$0.330544\pi$
$314$	5.48163	0.309346
$315$	0	0
$316$	−18.3483	−1.03217
$317$	26.1554	1.46903	0.734516	−	0.678592i	$-0.237409\pi$
$317$	26.1554	1.46903	0.734516	+	0.678592i	$0.237409\pi$
$318$	−8.08917	−0.453618
$319$	20.4036	1.14238
$320$	6.73642	0.376577
$321$	−0.428154	−0.0238972
$322$	0	0
$323$	29.6278	1.64854
$324$	−1.48384	−0.0824356
$325$	13.5865	0.753642
$326$	−4.61554	−0.255631
$327$	−9.21699	−0.509701
$328$	2.50294	0.138202
$329$	0	0
$330$	−12.4060	−0.682926
$331$	−4.78518	−0.263017	−0.131509	−	0.991315i	$-0.541982\pi$
$331$	−4.78518	−0.263017	−0.131509	+	0.991315i	$0.541982\pi$
$332$	−12.2052	−0.669847
$333$	−9.29150	−0.509171
$334$	16.0382	0.877572
$335$	−22.0850	−1.20663
$336$	0	0
$337$	3.08688	0.168153	0.0840767	−	0.996459i	$-0.473206\pi$
$337$	3.08688	0.168153	0.0840767	+	0.996459i	$0.473206\pi$
$338$	−7.31885	−0.398093
$339$	−15.1405	−0.822319
$340$	22.0637	1.19657
$341$	46.2270	2.50333
$342$	−5.18143	−0.280179
$343$	0	0
$344$	−1.23444	−0.0665567
$345$	−22.0491	−1.18708
$346$	−1.67562	−0.0900818
$347$	5.57233	0.299138	0.149569	−	0.988751i	$-0.452211\pi$
$347$	5.57233	0.299138	0.149569	+	0.988751i	$0.452211\pi$
$348$	6.34607	0.340185
$349$	7.19830	0.385316	0.192658	−	0.981266i	$-0.438289\pi$
$349$	7.19830	0.385316	0.192658	+	0.981266i	$0.438289\pi$
$350$	0	0
$351$	−1.67717	−0.0895207
$352$	27.8903	1.48656
$353$	31.8045	1.69278	0.846392	−	0.532560i	$-0.178770\pi$
$353$	31.8045	1.69278	0.846392	+	0.532560i	$0.178770\pi$
$354$	0.198419	0.0105459
$355$	−17.0572	−0.905304
$356$	8.17998	0.433538
$357$	0	0
$358$	12.9763	0.685819
$359$	−11.4920	−0.606523	−0.303261	−	0.952907i	$-0.598076\pi$
$359$	−11.4920	−0.606523	−0.303261	+	0.952907i	$0.598076\pi$
$360$	−9.05941	−0.477473
$361$	33.0133	1.73754
$362$	12.1456	0.638361
$363$	−11.7603	−0.617255
$364$	0	0
$365$	34.1285	1.78637
$366$	5.95254	0.311144
$367$	−36.6507	−1.91315	−0.956574	−	0.291489i	$-0.905849\pi$
$367$	−36.6507	−1.91315	−0.956574	+	0.291489i	$0.905849\pi$
$368$	7.12404	0.371366
$369$	−1.00000	−0.0520579
$370$	−24.1617	−1.25611
$371$	0	0
$372$	14.3779	0.745457
$373$	23.9922	1.24227	0.621134	−	0.783704i	$-0.286672\pi$
$373$	23.9922	1.24227	0.621134	+	0.783704i	$0.286672\pi$
$374$	−14.0807	−0.728095
$375$	−11.2235	−0.579579
$376$	−2.32653	−0.119982
$377$	7.17290	0.369423
$378$	0	0
$379$	12.8095	0.657978	0.328989	−	0.944334i	$-0.393292\pi$
$379$	12.8095	0.657978	0.328989	+	0.944334i	$0.393292\pi$
$380$	38.7341	1.98702
$381$	12.3127	0.630797
$382$	8.58935	0.439469
$383$	−9.99249	−0.510592	−0.255296	−	0.966863i	$-0.582173\pi$
$383$	−9.99249	−0.510592	−0.255296	+	0.966863i	$0.582173\pi$
$384$	10.3550	0.528427
$385$	0	0
$386$	−8.11739	−0.413164
$387$	0.493197	0.0250706
$388$	6.76783	0.343585
$389$	−4.36094	−0.221108	−0.110554	−	0.993870i	$-0.535263\pi$
$389$	−4.36094	−0.221108	−0.110554	+	0.993870i	$0.535263\pi$
$390$	−4.36133	−0.220844
$391$	−25.0255	−1.26559
$392$	0	0
$393$	7.55733	0.381217
$394$	10.9816	0.553247
$395$	44.7568	2.25196
$396$	−7.07907	−0.355737
$397$	−1.04587	−0.0524907	−0.0262454	−	0.999656i	$-0.508355\pi$
$397$	−1.04587	−0.0524907	−0.0262454	+	0.999656i	$0.508355\pi$
$398$	14.3445	0.719026
$399$	0	0
$400$	9.47362	0.473681
$401$	34.4257	1.71914	0.859569	−	0.511020i	$-0.170732\pi$
$401$	34.4257	1.71914	0.859569	+	0.511020i	$0.170732\pi$
$402$	4.38369	0.218639
$403$	16.2511	0.809527
$404$	−9.71286	−0.483233
$405$	3.61951	0.179855
$406$	0	0
$407$	−44.3276	−2.19724
$408$	−10.2824	−0.509053
$409$	31.0567	1.53566	0.767828	−	0.640656i	$-0.221338\pi$
$409$	31.0567	1.53566	0.767828	+	0.640656i	$0.221338\pi$
$410$	−2.60041	−0.128425
$411$	−3.85038	−0.189925
$412$	15.4015	0.758775
$413$	0	0
$414$	4.37656	0.215096
$415$	29.7719	1.46145
$416$	9.80485	0.480722
$417$	18.3824	0.900188
$418$	−24.7194	−1.20907
$419$	−9.64209	−0.471047	−0.235523	−	0.971869i	$-0.575680\pi$
$419$	−9.64209	−0.471047	−0.235523	+	0.971869i	$0.575680\pi$
$420$	0	0
$421$	17.1549	0.836077	0.418039	−	0.908429i	$-0.362718\pi$
$421$	17.1549	0.836077	0.418039	+	0.908429i	$0.362718\pi$
$422$	−4.50202	−0.219155
$423$	0.929521	0.0451949
$424$	−28.1814	−1.36861
$425$	−33.2792	−1.61428
$426$	3.38572	0.164039
$427$	0	0
$428$	−0.635311	−0.0307089
$429$	−8.00140	−0.386311
$430$	1.28251	0.0618483
$431$	−30.7376	−1.48058	−0.740290	−	0.672287i	$-0.765312\pi$
$431$	−30.7376	−1.48058	−0.740290	+	0.672287i	$0.765312\pi$
$432$	−1.16946	−0.0562658
$433$	6.14874	0.295490	0.147745	−	0.989026i	$-0.452799\pi$
$433$	6.14874	0.295490	0.147745	+	0.989026i	$0.452799\pi$
$434$	0	0
$435$	−15.4799	−0.742203
$436$	−13.6765	−0.654987
$437$	−43.9337	−2.10163
$438$	−6.77423	−0.323685
$439$	−12.8538	−0.613477	−0.306739	−	0.951794i	$-0.599238\pi$
$439$	−12.8538	−0.613477	−0.306739	+	0.951794i	$0.599238\pi$
$440$	−43.2204	−2.06045
$441$	0	0
$442$	−4.95007	−0.235451
$443$	−14.4939	−0.688625	−0.344312	−	0.938855i	$-0.611888\pi$
$443$	−14.4939	−0.688625	−0.344312	+	0.938855i	$0.611888\pi$
$444$	−13.7871	−0.654307
$445$	−19.9533	−0.945877
$446$	−17.2568	−0.817132
$447$	−10.1266	−0.478973
$448$	0	0
$449$	−24.5899	−1.16047	−0.580236	−	0.814449i	$-0.697040\pi$
$449$	−24.5899	−1.16047	−0.580236	+	0.814449i	$0.697040\pi$
$450$	5.81998	0.274357
$451$	−4.77078	−0.224647
$452$	−22.4661	−1.05672
$453$	13.7468	0.645883
$454$	12.3694	0.580524
$455$	0	0
$456$	−18.0513	−0.845328
$457$	−30.5890	−1.43089	−0.715447	−	0.698667i	$-0.753777\pi$
$457$	−30.5890	−1.43089	−0.715447	+	0.698667i	$0.753777\pi$
$458$	0.295056	0.0137871
$459$	4.10812	0.191750
$460$	−32.7173	−1.52545
$461$	−2.50315	−0.116583	−0.0582917	−	0.998300i	$-0.518565\pi$
$461$	−2.50315	−0.116583	−0.0582917	+	0.998300i	$0.518565\pi$
$462$	0	0
$463$	3.38170	0.157161	0.0785806	−	0.996908i	$-0.474961\pi$
$463$	3.38170	0.157161	0.0785806	+	0.996908i	$0.474961\pi$
$464$	5.00154	0.232191
$465$	−35.0717	−1.62641
$466$	14.7141	0.681616
$467$	−20.3032	−0.939522	−0.469761	−	0.882794i	$-0.655660\pi$
$467$	−20.3032	−0.939522	−0.469761	+	0.882794i	$0.655660\pi$
$468$	−2.48865	−0.115038
$469$	0	0
$470$	2.41713	0.111494
$471$	−7.62988	−0.351566
$472$	0.691262	0.0318179
$473$	2.35293	0.108188
$474$	−8.88386	−0.408049
$475$	−58.4234	−2.68065
$476$	0	0
$477$	11.2593	0.515528
$478$	−10.2820	−0.470289
$479$	−29.0637	−1.32796	−0.663978	−	0.747752i	$-0.731133\pi$
$479$	−29.0637	−1.32796	−0.663978	+	0.747752i	$0.731133\pi$
$480$	−21.1599	−0.965813
$481$	−15.5834	−0.710542
$482$	−19.4242	−0.884749
$483$	0	0
$484$	−17.4504	−0.793200
$485$	−16.5087	−0.749620
$486$	−0.718443	−0.0325892
$487$	3.58717	0.162550	0.0812752	−	0.996692i	$-0.474101\pi$
$487$	3.58717	0.162550	0.0812752	+	0.996692i	$0.474101\pi$
$488$	20.7377	0.938751
$489$	6.42437	0.290520
$490$	0	0
$491$	−12.8947	−0.581929	−0.290964	−	0.956734i	$-0.593976\pi$
$491$	−12.8947	−0.581929	−0.290964	+	0.956734i	$0.593976\pi$
$492$	−1.48384	−0.0668967
$493$	−17.5695	−0.791293
$494$	−8.69013	−0.390987
$495$	17.2679	0.776132
$496$	11.3316	0.508806
$497$	0	0
$498$	−5.90948	−0.264810
$499$	−29.8308	−1.33541	−0.667705	−	0.744426i	$-0.732723\pi$
$499$	−29.8308	−1.33541	−0.667705	+	0.744426i	$0.732723\pi$
$500$	−16.6539	−0.744784
$501$	−22.3236	−0.997344
$502$	−1.54493	−0.0689538
$503$	20.0091	0.892163	0.446082	−	0.894992i	$-0.352819\pi$
$503$	20.0091	0.892163	0.446082	+	0.894992i	$0.352819\pi$
$504$	0	0
$505$	23.6924	1.05430
$506$	20.8796	0.928210
$507$	10.1871	0.452425
$508$	18.2700	0.810601
$509$	−16.2303	−0.719394	−0.359697	−	0.933069i	$-0.617120\pi$
$509$	−16.2303	−0.719394	−0.359697	+	0.933069i	$0.617120\pi$
$510$	10.6828	0.473041
$511$	0	0
$512$	12.6909	0.560866
$513$	7.21202	0.318419
$514$	20.9665	0.924791
$515$	−37.5685	−1.65547
$516$	0.731826	0.0322168
$517$	4.43454	0.195031
$518$	0	0
$519$	2.33229	0.102376
$520$	−15.1942	−0.666308
$521$	15.7030	0.687963	0.343981	−	0.938976i	$-0.388224\pi$
$521$	15.7030	0.687963	0.343981	+	0.938976i	$0.388224\pi$
$522$	3.07263	0.134485
$523$	−2.08067	−0.0909812	−0.0454906	−	0.998965i	$-0.514485\pi$
$523$	−2.08067	−0.0909812	−0.0454906	+	0.998965i	$0.514485\pi$
$524$	11.2139	0.489880
$525$	0	0
$526$	0.927268	0.0404308
$527$	−39.8061	−1.73398
$528$	−5.57924	−0.242805
$529$	14.1091	0.613441
$530$	29.2788	1.27179
$531$	−0.276180	−0.0119852
$532$	0	0
$533$	−1.67717	−0.0726463
$534$	3.96057	0.171390
$535$	1.54970	0.0669996
$536$	15.2721	0.659653
$537$	−18.0617	−0.779421
$538$	16.5831	0.714946
$539$	0	0
$540$	5.37077	0.231121
$541$	−18.2552	−0.784854	−0.392427	−	0.919783i	$-0.628364\pi$
$541$	−18.2552	−0.784854	−0.392427	+	0.919783i	$0.628364\pi$
$542$	13.0766	0.561689
$543$	−16.9055	−0.725485
$544$	−24.0163	−1.02969
$545$	33.3610	1.42903
$546$	0	0
$547$	5.89322	0.251976	0.125988	−	0.992032i	$-0.459790\pi$
$547$	5.89322	0.251976	0.125988	+	0.992032i	$0.459790\pi$
$548$	−5.71335	−0.244062
$549$	−8.28534	−0.353609
$550$	27.7658	1.18394
$551$	−30.8443	−1.31401
$552$	15.2472	0.648965
$553$	0	0
$554$	−13.8759	−0.589529
$555$	33.6306	1.42754
$556$	27.2765	1.15678
$557$	21.6502	0.917350	0.458675	−	0.888604i	$-0.348324\pi$
$557$	21.6502	0.917350	0.458675	+	0.888604i	$0.348324\pi$
$558$	6.96144	0.294701
$559$	0.827175	0.0349858
$560$	0	0
$561$	19.5989	0.827466
$562$	−7.66576	−0.323361
$563$	−3.85381	−0.162419	−0.0812093	−	0.996697i	$-0.525878\pi$
$563$	−3.85381	−0.162419	−0.0812093	+	0.996697i	$0.525878\pi$
$564$	1.37926	0.0580773
$565$	54.8012	2.30550
$566$	14.1061	0.592926
$567$	0	0
$568$	11.7953	0.494920
$569$	41.0410	1.72053	0.860264	−	0.509849i	$-0.170299\pi$
$569$	41.0410	1.72053	0.860264	+	0.509849i	$0.170299\pi$
$570$	18.7542	0.785527
$571$	26.1479	1.09426	0.547128	−	0.837049i	$-0.315721\pi$
$571$	26.1479	1.09426	0.547128	+	0.837049i	$0.315721\pi$
$572$	−11.8728	−0.496427
$573$	−11.9555	−0.499449
$574$	0	0
$575$	49.3481	2.05796
$576$	1.86114	0.0775476
$577$	−8.41211	−0.350201	−0.175100	−	0.984551i	$-0.556025\pi$
$577$	−8.41211	−0.350201	−0.175100	+	0.984551i	$0.556025\pi$
$578$	−0.0886462	−0.00368719
$579$	11.2986	0.469553
$580$	−22.9697	−0.953763
$581$	0	0
$582$	3.27683	0.135829
$583$	53.7156	2.22467
$584$	−23.6003	−0.976588
$585$	6.07053	0.250985
$586$	4.40864	0.182119
$587$	15.9572	0.658624	0.329312	−	0.944221i	$-0.393183\pi$
$587$	15.9572	0.658624	0.329312	+	0.944221i	$0.393183\pi$
$588$	0	0
$589$	−69.8818	−2.87943
$590$	−0.718181	−0.0295670
$591$	−15.2853	−0.628755
$592$	−10.8661	−0.446592
$593$	−24.8072	−1.01871	−0.509354	−	0.860557i	$-0.670116\pi$
$593$	−24.8072	−1.01871	−0.509354	+	0.860557i	$0.670116\pi$
$594$	−3.42753	−0.140633
$595$	0	0
$596$	−15.0263	−0.615501
$597$	−19.9661	−0.817160
$598$	7.34023	0.300164
$599$	28.4289	1.16157	0.580786	−	0.814056i	$-0.302745\pi$
$599$	28.4289	1.16157	0.580786	+	0.814056i	$0.302745\pi$
$600$	20.2759	0.827760
$601$	20.8714	0.851362	0.425681	−	0.904873i	$-0.360035\pi$
$601$	20.8714	0.851362	0.425681	+	0.904873i	$0.360035\pi$
$602$	0	0
$603$	−6.10165	−0.248479
$604$	20.3981	0.829988
$605$	42.5665	1.73057
$606$	−4.70275	−0.191036
$607$	−24.7136	−1.00309	−0.501547	−	0.865131i	$-0.667235\pi$
$607$	−24.7136	−1.00309	−0.501547	+	0.865131i	$0.667235\pi$
$608$	−42.1620	−1.70989
$609$	0	0
$610$	−21.5453	−0.872342
$611$	1.55896	0.0630689
$612$	6.09579	0.246408
$613$	33.3329	1.34630	0.673151	−	0.739505i	$-0.264941\pi$
$613$	33.3329	1.34630	0.673151	+	0.739505i	$0.264941\pi$
$614$	7.08215	0.285813
$615$	3.61951	0.145953
$616$	0	0
$617$	−34.5080	−1.38924	−0.694619	−	0.719378i	$-0.744427\pi$
$617$	−34.5080	−1.38924	−0.694619	+	0.719378i	$0.744427\pi$
$618$	7.45704	0.299966
$619$	−12.5191	−0.503184	−0.251592	−	0.967833i	$-0.580954\pi$
$619$	−12.5191	−0.503184	−0.251592	+	0.967833i	$0.580954\pi$
$620$	−52.0407	−2.09001
$621$	−6.09173	−0.244453
$622$	14.5645	0.583983
$623$	0	0
$624$	−1.96139	−0.0785183
$625$	0.119342	0.00477369
$626$	12.9030	0.515708
$627$	34.4069	1.37408
$628$	−11.3215	−0.451778
$629$	38.1705	1.52196
$630$	0	0
$631$	18.1805	0.723756	0.361878	−	0.932225i	$-0.382136\pi$
$631$	18.1805	0.723756	0.361878	+	0.932225i	$0.382136\pi$
$632$	−30.9499	−1.23112
$633$	6.26636	0.249066
$634$	18.7911	0.746291
$635$	−44.5658	−1.76854
$636$	16.7070	0.662476
$637$	0	0
$638$	14.6588	0.580348
$639$	−4.71258	−0.186427
$640$	−37.4801	−1.48153
$641$	−35.2943	−1.39404	−0.697020	−	0.717051i	$-0.745491\pi$
$641$	−35.2943	−1.39404	−0.697020	+	0.717051i	$0.745491\pi$
$642$	−0.307604	−0.0121402
$643$	6.80232	0.268257	0.134129	−	0.990964i	$-0.457176\pi$
$643$	6.80232	0.268257	0.134129	+	0.990964i	$0.457176\pi$
$644$	0	0
$645$	−1.78513	−0.0702895
$646$	21.2859	0.837482
$647$	17.8299	0.700965	0.350483	−	0.936569i	$-0.386018\pi$
$647$	17.8299	0.700965	0.350483	+	0.936569i	$0.386018\pi$
$648$	−2.50294	−0.0983247
$649$	−1.31759	−0.0517200
$650$	9.76110	0.382862
$651$	0	0
$652$	9.53274	0.373331
$653$	−2.93708	−0.114937	−0.0574684	−	0.998347i	$-0.518303\pi$
$653$	−2.93708	−0.114937	−0.0574684	+	0.998347i	$0.518303\pi$
$654$	−6.62188	−0.258936
$655$	−27.3538	−1.06880
$656$	−1.16946	−0.0456598
$657$	9.42904	0.367862
$658$	0	0
$659$	−40.1383	−1.56357	−0.781783	−	0.623551i	$-0.785689\pi$
$659$	−40.1383	−1.56357	−0.781783	+	0.623551i	$0.785689\pi$
$660$	25.6227	0.997364
$661$	−30.1636	−1.17323	−0.586615	−	0.809866i	$-0.699540\pi$
$661$	−30.1636	−1.17323	−0.586615	+	0.809866i	$0.699540\pi$
$662$	−3.43788	−0.133617
$663$	6.89001	0.267586
$664$	−20.5877	−0.798958
$665$	0	0
$666$	−6.67541	−0.258667
$667$	26.0530	1.00878
$668$	−33.1246	−1.28163
$669$	24.0197	0.928655
$670$	−15.8668	−0.612988
$671$	−39.5275	−1.52594
$672$	0	0
$673$	−36.7315	−1.41589	−0.707947	−	0.706266i	$-0.750378\pi$
$673$	−36.7315	−1.41589	−0.707947	+	0.706266i	$0.750378\pi$
$674$	2.21775	0.0854245
$675$	−8.10083	−0.311801
$676$	15.1160	0.581386
$677$	−1.25934	−0.0484003	−0.0242002	−	0.999707i	$-0.507704\pi$
$677$	−1.25934	−0.0484003	−0.0242002	+	0.999707i	$0.507704\pi$
$678$	−10.8776	−0.417751
$679$	0	0
$680$	37.2171	1.42721
$681$	−17.2170	−0.659755
$682$	33.2115	1.27173
$683$	35.0039	1.33939	0.669694	−	0.742637i	$-0.266425\pi$
$683$	35.0039	1.33939	0.669694	+	0.742637i	$0.266425\pi$
$684$	10.7015	0.409182
$685$	13.9365	0.532486
$686$	0	0
$687$	−0.410688	−0.0156687
$688$	0.576776	0.0219894
$689$	18.8838	0.719414
$690$	−15.8410	−0.603056
$691$	−46.5992	−1.77272	−0.886359	−	0.462999i	$-0.846773\pi$
$691$	−46.5992	−1.77272	−0.886359	+	0.462999i	$0.846773\pi$
$692$	3.46075	0.131558
$693$	0	0
$694$	4.00340	0.151967
$695$	−66.5351	−2.52382
$696$	10.7045	0.405755
$697$	4.10812	0.155606
$698$	5.17156	0.195747
$699$	−20.4805	−0.774644
$700$	0	0
$701$	3.08338	0.116457	0.0582287	−	0.998303i	$-0.481455\pi$
$701$	3.08338	0.116457	0.0582287	+	0.998303i	$0.481455\pi$
$702$	−1.20495	−0.0454779
$703$	67.0105	2.52735
$704$	8.87909	0.334643
$705$	−3.36441	−0.126711
$706$	22.8497	0.859961
$707$	0	0
$708$	−0.409807	−0.0154015
$709$	11.0616	0.415425	0.207713	−	0.978190i	$-0.433398\pi$
$709$	11.0616	0.415425	0.207713	+	0.978190i	$0.433398\pi$
$710$	−12.2546	−0.459909
$711$	12.3654	0.463740
$712$	13.7980	0.517101
$713$	59.0265	2.21056
$714$	0	0
$715$	28.9611	1.08308
$716$	−26.8007	−1.00159
$717$	14.3115	0.534474
$718$	−8.25632	−0.308123
$719$	−29.0002	−1.08152	−0.540762	−	0.841176i	$-0.681864\pi$
$719$	−29.0002	−1.08152	−0.540762	+	0.841176i	$0.681864\pi$
$720$	4.23288	0.157750
$721$	0	0
$722$	23.7182	0.882699
$723$	27.0366	1.00550
$724$	−25.0851	−0.932280
$725$	34.6456	1.28670
$726$	−8.44910	−0.313575
$727$	29.4341	1.09165	0.545826	−	0.837899i	$-0.316216\pi$
$727$	29.4341	1.09165	0.545826	+	0.837899i	$0.316216\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	24.5194	0.907502
$731$	−2.02611	−0.0749384
$732$	−12.2941	−0.454404
$733$	−22.9658	−0.848261	−0.424130	−	0.905601i	$-0.639420\pi$
$733$	−22.9658	−0.848261	−0.424130	+	0.905601i	$0.639420\pi$
$734$	−26.3314	−0.971909
$735$	0	0
$736$	35.6127	1.31270
$737$	−29.1096	−1.07227
$738$	−0.718443	−0.0264462
$739$	−8.80545	−0.323914	−0.161957	−	0.986798i	$-0.551781\pi$
$739$	−8.80545	−0.323914	−0.161957	+	0.986798i	$0.551781\pi$
$740$	49.9025	1.83445
$741$	12.0958	0.444350
$742$	0	0
$743$	−7.42487	−0.272392	−0.136196	−	0.990682i	$-0.543488\pi$
$743$	−7.42487	−0.272392	−0.136196	+	0.990682i	$0.543488\pi$
$744$	24.2525	0.889141
$745$	36.6534	1.34288
$746$	17.2370	0.631092
$747$	8.22541	0.300952
$748$	29.0816	1.06333
$749$	0	0
$750$	−8.06343	−0.294435
$751$	−19.7969	−0.722398	−0.361199	−	0.932489i	$-0.617633\pi$
$751$	−19.7969	−0.722398	−0.361199	+	0.932489i	$0.617633\pi$
$752$	1.08704	0.0396403
$753$	2.15039	0.0783647
$754$	5.15332	0.187673
$755$	−49.7568	−1.81084
$756$	0	0
$757$	−46.0253	−1.67282	−0.836410	−	0.548104i	$-0.815350\pi$
$757$	−46.0253	−1.67282	−0.836410	+	0.548104i	$0.815350\pi$
$758$	9.20286	0.334263
$759$	−29.0623	−1.05489
$760$	65.3367	2.37001
$761$	15.3347	0.555882	0.277941	−	0.960598i	$-0.410348\pi$
$761$	15.3347	0.555882	0.277941	+	0.960598i	$0.410348\pi$
$762$	8.84594	0.320455
$763$	0	0
$764$	−17.7401	−0.641813
$765$	−14.8694	−0.537603
$766$	−7.17903	−0.259389
$767$	−0.463200	−0.0167252
$768$	11.1618	0.402766
$769$	51.0290	1.84015	0.920076	−	0.391740i	$-0.128127\pi$
$769$	51.0290	1.84015	0.920076	+	0.391740i	$0.128127\pi$
$770$	0	0
$771$	−29.1832	−1.05101
$772$	16.7653	0.603397
$773$	−19.1501	−0.688782	−0.344391	−	0.938826i	$-0.611915\pi$
$773$	−19.1501	−0.688782	−0.344391	+	0.938826i	$0.611915\pi$
$774$	0.354334	0.0127363
$775$	78.4940	2.81959
$776$	11.4160	0.409809
$777$	0	0
$778$	−3.13308	−0.112326
$779$	7.21202	0.258398
$780$	9.00769	0.322527
$781$	−22.4827	−0.804494
$782$	−17.9794	−0.642942
$783$	−4.27679	−0.152840
$784$	0	0
$785$	27.6164	0.985672
$786$	5.42951	0.193664
$787$	3.43549	0.122462	0.0612310	−	0.998124i	$-0.480497\pi$
$787$	3.43549	0.122462	0.0612310	+	0.998124i	$0.480497\pi$
$788$	−22.6810	−0.807977
$789$	−1.29066	−0.0459489
$790$	32.1552	1.14403
$791$	0	0
$792$	−11.9410	−0.424304
$793$	−13.8959	−0.493458
$794$	−0.751397	−0.0266661
$795$	−40.7532	−1.44537
$796$	−29.6266	−1.05009
$797$	11.2344	0.397943	0.198971	−	0.980005i	$-0.436240\pi$
$797$	11.2344	0.397943	0.198971	+	0.980005i	$0.436240\pi$
$798$	0	0
$799$	−3.81858	−0.135092
$800$	47.3580	1.67436
$801$	−5.51271	−0.194782
$802$	24.7329	0.873349
$803$	44.9838	1.58745
$804$	−9.05388	−0.319306
$805$	0	0
$806$	11.6755	0.411252
$807$	−23.0819	−0.812523
$808$	−16.3836	−0.576374
$809$	−1.39828	−0.0491610	−0.0245805	−	0.999698i	$-0.507825\pi$
$809$	−1.39828	−0.0491610	−0.0245805	+	0.999698i	$0.507825\pi$
$810$	2.60041	0.0913690
$811$	−43.1209	−1.51418	−0.757089	−	0.653311i	$-0.773379\pi$
$811$	−43.1209	−1.51418	−0.757089	+	0.653311i	$0.773379\pi$
$812$	0	0
$813$	−18.2013	−0.638349
$814$	−31.8469	−1.11623
$815$	−23.2531	−0.814519
$816$	4.80429	0.168184
$817$	−3.55695	−0.124442
$818$	22.3125	0.780137
$819$	0	0
$820$	5.37077	0.187555
$821$	−40.0686	−1.39840	−0.699202	−	0.714924i	$-0.746461\pi$
$821$	−40.0686	−1.39840	−0.699202	+	0.714924i	$0.746461\pi$
$822$	−2.76628	−0.0964850
$823$	−29.2972	−1.02124	−0.510619	−	0.859807i	$-0.670584\pi$
$823$	−29.2972	−1.02124	−0.510619	+	0.859807i	$0.670584\pi$
$824$	25.9791	0.905026
$825$	−38.6473	−1.34552
$826$	0	0
$827$	19.6538	0.683429	0.341714	−	0.939804i	$-0.388992\pi$
$827$	19.6538	0.683429	0.341714	+	0.939804i	$0.388992\pi$
$828$	−9.03915	−0.314132
$829$	−45.6356	−1.58499	−0.792495	−	0.609878i	$-0.791218\pi$
$829$	−45.6356	−1.58499	−0.792495	+	0.609878i	$0.791218\pi$
$830$	21.3894	0.742438
$831$	19.3138	0.669988
$832$	3.12145	0.108217
$833$	0	0
$834$	13.2067	0.457310
$835$	80.8004	2.79621
$836$	51.0544	1.76575
$837$	−9.68962	−0.334922
$838$	−6.92729	−0.239299
$839$	−46.1805	−1.59433	−0.797164	−	0.603763i	$-0.793667\pi$
$839$	−46.1805	−1.59433	−0.797164	+	0.603763i	$0.793667\pi$
$840$	0	0
$841$	−10.7091	−0.369278
$842$	12.3248	0.424740
$843$	10.6700	0.367493
$844$	9.29828	0.320060
$845$	−36.8723	−1.26845
$846$	0.667807	0.0229597
$847$	0	0
$848$	13.1673	0.452168
$849$	−19.6343	−0.673849
$850$	−23.9092	−0.820078
$851$	−56.6013	−1.94027
$852$	−6.99272	−0.239567
$853$	9.33699	0.319693	0.159846	−	0.987142i	$-0.448900\pi$
$853$	9.33699	0.319693	0.159846	+	0.987142i	$0.448900\pi$
$854$	0	0
$855$	−26.1040	−0.892737
$856$	−1.07164	−0.0366280
$857$	44.6137	1.52397	0.761987	−	0.647593i	$-0.224224\pi$
$857$	44.6137	1.52397	0.761987	+	0.647593i	$0.224224\pi$
$858$	−5.74855	−0.196252
$859$	14.9917	0.511512	0.255756	−	0.966741i	$-0.417676\pi$
$859$	14.9917	0.511512	0.255756	+	0.966741i	$0.417676\pi$
$860$	−2.64885	−0.0903250
$861$	0	0
$862$	−22.0832	−0.752158
$863$	−55.6314	−1.89371	−0.946857	−	0.321655i	$-0.895761\pi$
$863$	−55.6314	−1.89371	−0.946857	+	0.321655i	$0.895761\pi$
$864$	−5.84607	−0.198887
$865$	−8.44175	−0.287028
$866$	4.41752	0.150113
$867$	0.123387	0.00419043
$868$	0	0
$869$	58.9927	2.00119
$870$	−11.1214	−0.377051
$871$	−10.2335	−0.346749
$872$	−23.0696	−0.781234
$873$	−4.56102	−0.154367
$874$	−31.5638	−1.06766
$875$	0	0
$876$	13.9912	0.472719
$877$	−21.7454	−0.734291	−0.367145	−	0.930164i	$-0.619665\pi$
$877$	−21.7454	−0.734291	−0.367145	+	0.930164i	$0.619665\pi$
$878$	−9.23470	−0.311656
$879$	−6.13638	−0.206975
$880$	20.1941	0.680743
$881$	12.9402	0.435967	0.217984	−	0.975952i	$-0.430052\pi$
$881$	12.9402	0.435967	0.217984	+	0.975952i	$0.430052\pi$
$882$	0	0
$883$	32.5785	1.09636	0.548178	−	0.836362i	$-0.315322\pi$
$883$	32.5785	1.09636	0.548178	+	0.836362i	$0.315322\pi$
$884$	10.2237	0.343859
$885$	0.999635	0.0336024
$886$	−10.4130	−0.349832
$887$	11.2722	0.378484	0.189242	−	0.981931i	$-0.439397\pi$
$887$	11.2722	0.378484	0.189242	+	0.981931i	$0.439397\pi$
$888$	−23.2561	−0.780422
$889$	0	0
$890$	−14.3353	−0.480520
$891$	4.77078	0.159827
$892$	35.6414	1.19336
$893$	−6.70373	−0.224332
$894$	−7.27540	−0.243326
$895$	65.3745	2.18523
$896$	0	0
$897$	−10.2169	−0.341131
$898$	−17.6665	−0.589538
$899$	41.4405	1.38212
$900$	−12.0203	−0.400678
$901$	−46.2545	−1.54096
$902$	−3.42753	−0.114124
$903$	0	0
$904$	−37.8958	−1.26039
$905$	61.1897	2.03401
$906$	9.87632	0.328119
$907$	32.1498	1.06752	0.533758	−	0.845638i	$-0.320780\pi$
$907$	32.1498	1.06752	0.533758	+	0.845638i	$0.320780\pi$
$908$	−25.5472	−0.847814
$909$	6.54576	0.217109
$910$	0	0
$911$	−29.0538	−0.962596	−0.481298	−	0.876557i	$-0.659835\pi$
$911$	−29.0538	−0.962596	−0.481298	+	0.876557i	$0.659835\pi$
$912$	8.43419	0.279284
$913$	39.2416	1.29871
$914$	−21.9765	−0.726917
$915$	29.9888	0.991400
$916$	−0.609396	−0.0201350
$917$	0	0
$918$	2.95145	0.0974122
$919$	−32.7485	−1.08027	−0.540136	−	0.841578i	$-0.681627\pi$
$919$	−32.7485	−1.08027	−0.540136	+	0.841578i	$0.681627\pi$
$920$	−55.1874	−1.81948
$921$	−9.85765	−0.324821
$922$	−1.79837	−0.0592262
$923$	−7.90380	−0.260157
$924$	0	0
$925$	−75.2689	−2.47483
$926$	2.42956	0.0798403
$927$	−10.3795	−0.340906
$928$	25.0024	0.820744
$929$	2.69655	0.0884709	0.0442354	−	0.999021i	$-0.485915\pi$
$929$	2.69655	0.0884709	0.0442354	+	0.999021i	$0.485915\pi$
$930$	−25.1970	−0.826241
$931$	0	0
$932$	−30.3898	−0.995451
$933$	−20.2723	−0.663685
$934$	−14.5867	−0.477292
$935$	−70.9383	−2.31993
$936$	−4.19785	−0.137211
$937$	4.00234	0.130751	0.0653753	−	0.997861i	$-0.479176\pi$
$937$	4.00234	0.130751	0.0653753	+	0.997861i	$0.479176\pi$
$938$	0	0
$939$	−17.9597	−0.586092
$940$	−4.99224	−0.162829
$941$	−20.5073	−0.668518	−0.334259	−	0.942481i	$-0.608486\pi$
$941$	−20.5073	−0.668518	−0.334259	+	0.942481i	$0.608486\pi$
$942$	−5.48163	−0.178601
$943$	−6.09173	−0.198374
$944$	−0.322982	−0.0105122
$945$	0	0
$946$	1.69045	0.0549612
$947$	−37.4551	−1.21713	−0.608564	−	0.793505i	$-0.708254\pi$
$947$	−37.4551	−1.21713	−0.608564	+	0.793505i	$0.708254\pi$
$948$	18.3483	0.595926
$949$	15.8141	0.513347
$950$	−41.9739	−1.36181
$951$	−26.1554	−0.848146
$952$	0	0
$953$	−18.1604	−0.588273	−0.294137	−	0.955763i	$-0.595032\pi$
$953$	−18.1604	−0.588273	−0.294137	+	0.955763i	$0.595032\pi$
$954$	8.08917	0.261896
$955$	43.2731	1.40028
$956$	21.2360	0.686823
$957$	−20.4036	−0.659555
$958$	−20.8806	−0.674622
$959$	0	0
$960$	−6.73642	−0.217417
$961$	62.8888	2.02867
$962$	−11.1958	−0.360967
$963$	0.428154	0.0137971
$964$	40.1179	1.29211
$965$	−40.8953	−1.31647
$966$	0	0
$967$	−11.7555	−0.378032	−0.189016	−	0.981974i	$-0.560530\pi$
$967$	−11.7555	−0.378032	−0.189016	+	0.981974i	$0.560530\pi$
$968$	−29.4353	−0.946086
$969$	−29.6278	−0.951783
$970$	−11.8605	−0.380819
$971$	−40.4149	−1.29698	−0.648489	−	0.761224i	$-0.724599\pi$
$971$	−40.4149	−1.29698	−0.648489	+	0.761224i	$0.724599\pi$
$972$	1.48384	0.0475942
$973$	0	0
$974$	2.57718	0.0825781
$975$	−13.5865	−0.435115
$976$	−9.68939	−0.310150
$977$	−5.19469	−0.166193	−0.0830965	−	0.996542i	$-0.526481\pi$
$977$	−5.19469	−0.166193	−0.0830965	+	0.996542i	$0.526481\pi$
$978$	4.61554	0.147589
$979$	−26.2999	−0.840548
$980$	0	0
$981$	9.21699	0.294276
$982$	−9.26409	−0.295629
$983$	−4.47416	−0.142704	−0.0713518	−	0.997451i	$-0.522731\pi$
$983$	−4.47416	−0.142704	−0.0713518	+	0.997451i	$0.522731\pi$
$984$	−2.50294	−0.0797908
$985$	55.3254	1.76281
$986$	−12.6227	−0.401989
$987$	0	0
$988$	17.9482	0.571009
$989$	3.00442	0.0955351
$990$	12.4060	0.394287
$991$	40.0982	1.27376	0.636881	−	0.770963i	$-0.280224\pi$
$991$	40.0982	1.27376	0.636881	+	0.770963i	$0.280224\pi$
$992$	56.6462	1.79852
$993$	4.78518	0.151853
$994$	0	0
$995$	72.2676	2.29104
$996$	12.2052	0.386736
$997$	−18.2843	−0.579069	−0.289534	−	0.957168i	$-0.593500\pi$
$997$	−18.2843	−0.579069	−0.289534	+	0.957168i	$0.593500\pi$
$998$	−21.4317	−0.678409
$999$	9.29150	0.293970

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.y.1.4		7
7.6	odd	2		861.2.a.m.1.4	✓	7
21.20	even	2		2583.2.a.u.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.a.m.1.4	✓	7	7.6	odd	2
2583.2.a.u.1.4		7	21.20	even	2
6027.2.a.y.1.4		7	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q+0.718443 q^{2} -1.00000 q^{3} -1.48384 q^{4} +3.61951 q^{5} -0.718443 q^{6} -2.50294 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.718443 q^{2} -1.00000 q^{3} -1.48384 q^{4} +3.61951 q^{5} -0.718443 q^{6} -2.50294 q^{8} +1.00000 q^{9} +2.60041 q^{10} +4.77078 q^{11} +1.48384 q^{12} +1.67717 q^{13} -3.61951 q^{15} +1.16946 q^{16} -4.10812 q^{17} +0.718443 q^{18} -7.21202 q^{19} -5.37077 q^{20} +3.42753 q^{22} +6.09173 q^{23} +2.50294 q^{24} +8.10083 q^{25} +1.20495 q^{26} -1.00000 q^{27} +4.27679 q^{29} -2.60041 q^{30} +9.68962 q^{31} +5.84607 q^{32} -4.77078 q^{33} -2.95145 q^{34} -1.48384 q^{36} -9.29150 q^{37} -5.18143 q^{38} -1.67717 q^{39} -9.05941 q^{40} -1.00000 q^{41} +0.493197 q^{43} -7.07907 q^{44} +3.61951 q^{45} +4.37656 q^{46} +0.929521 q^{47} -1.16946 q^{48} +5.81998 q^{50} +4.10812 q^{51} -2.48865 q^{52} +11.2593 q^{53} -0.718443 q^{54} +17.2679 q^{55} +7.21202 q^{57} +3.07263 q^{58} -0.276180 q^{59} +5.37077 q^{60} -8.28534 q^{61} +6.96144 q^{62} +1.86114 q^{64} +6.07053 q^{65} -3.42753 q^{66} -6.10165 q^{67} +6.09579 q^{68} -6.09173 q^{69} -4.71258 q^{71} -2.50294 q^{72} +9.42904 q^{73} -6.67541 q^{74} -8.10083 q^{75} +10.7015 q^{76} -1.20495 q^{78} +12.3654 q^{79} +4.23288 q^{80} +1.00000 q^{81} -0.718443 q^{82} +8.22541 q^{83} -14.8694 q^{85} +0.354334 q^{86} -4.27679 q^{87} -11.9410 q^{88} -5.51271 q^{89} +2.60041 q^{90} -9.03915 q^{92} -9.68962 q^{93} +0.667807 q^{94} -26.1040 q^{95} -5.84607 q^{96} -4.56102 q^{97} +4.77078 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 4 q^{2} - 7 q^{3} + 8 q^{4} - q^{5} - 4 q^{6} + 12 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + 4 * q^2 - 7 * q^3 + 8 * q^4 - q^5 - 4 * q^6 + 12 * q^8 + 7 * q^9	\( 7 q + 4 q^{2} - 7 q^{3} + 8 q^{4} - q^{5} - 4 q^{6} + 12 q^{8} + 7 q^{9} + 3 q^{10} + 11 q^{11} - 8 q^{12} + 7 q^{13} + q^{15} + 6 q^{16} - 11 q^{17} + 4 q^{18} - 4 q^{19} + 7 q^{20} + 6 q^{22} + 7 q^{23} - 12 q^{24} + 2 q^{25} + 13 q^{26} - 7 q^{27} + 4 q^{29} - 3 q^{30} + 7 q^{31} + 18 q^{32} - 11 q^{33} + 20 q^{34} + 8 q^{36} - 4 q^{38} - 7 q^{39} + 9 q^{40} - 7 q^{41} + q^{43} + 18 q^{44} - q^{45} - 17 q^{46} - 14 q^{47} - 6 q^{48} + 19 q^{50} + 11 q^{51} + 27 q^{52} + 23 q^{53} - 4 q^{54} + 30 q^{55} + 4 q^{57} - 3 q^{58} - 8 q^{59} - 7 q^{60} + 3 q^{61} + 16 q^{62} + 6 q^{64} + 15 q^{65} - 6 q^{66} + 3 q^{67} - 7 q^{69} + 7 q^{71} + 12 q^{72} + 11 q^{73} - 13 q^{74} - 2 q^{75} + 40 q^{76} - 13 q^{78} - q^{79} + 43 q^{80} + 7 q^{81} - 4 q^{82} - 10 q^{85} - 12 q^{86} - 4 q^{87} + 10 q^{88} - 32 q^{89} + 3 q^{90} - 19 q^{92} - 7 q^{93} - 21 q^{94} - 8 q^{95} - 18 q^{96} + 25 q^{97} + 11 q^{99}+O(q^{100}) \) 7 * q + 4 * q^2 - 7 * q^3 + 8 * q^4 - q^5 - 4 * q^6 + 12 * q^8 + 7 * q^9 + 3 * q^10 + 11 * q^11 - 8 * q^12 + 7 * q^13 + q^15 + 6 * q^16 - 11 * q^17 + 4 * q^18 - 4 * q^19 + 7 * q^20 + 6 * q^22 + 7 * q^23 - 12 * q^24 + 2 * q^25 + 13 * q^26 - 7 * q^27 + 4 * q^29 - 3 * q^30 + 7 * q^31 + 18 * q^32 - 11 * q^33 + 20 * q^34 + 8 * q^36 - 4 * q^38 - 7 * q^39 + 9 * q^40 - 7 * q^41 + q^43 + 18 * q^44 - q^45 - 17 * q^46 - 14 * q^47 - 6 * q^48 + 19 * q^50 + 11 * q^51 + 27 * q^52 + 23 * q^53 - 4 * q^54 + 30 * q^55 + 4 * q^57 - 3 * q^58 - 8 * q^59 - 7 * q^60 + 3 * q^61 + 16 * q^62 + 6 * q^64 + 15 * q^65 - 6 * q^66 + 3 * q^67 - 7 * q^69 + 7 * q^71 + 12 * q^72 + 11 * q^73 - 13 * q^74 - 2 * q^75 + 40 * q^76 - 13 * q^78 - q^79 + 43 * q^80 + 7 * q^81 - 4 * q^82 - 10 * q^85 - 12 * q^86 - 4 * q^87 + 10 * q^88 - 32 * q^89 + 3 * q^90 - 19 * q^92 - 7 * q^93 - 21 * q^94 - 8 * q^95 - 18 * q^96 + 25 * q^97 + 11 * q^99

Introduction

L-functions

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Database

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