LMFDB - Embedded newform 8018.2.a.i.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$43$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.98111 q^{3} +1.00000 q^{4} -2.70035 q^{5} +1.98111 q^{6} +2.97081 q^{7} -1.00000 q^{8} +0.924794 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.98111 q^{3} +1.00000 q^{4} -2.70035 q^{5} +1.98111 q^{6} +2.97081 q^{7} -1.00000 q^{8} +0.924794 q^{9} +2.70035 q^{10} -1.51806 q^{11} -1.98111 q^{12} +5.78666 q^{13} -2.97081 q^{14} +5.34969 q^{15} +1.00000 q^{16} -3.10974 q^{17} -0.924794 q^{18} +1.00000 q^{19} -2.70035 q^{20} -5.88549 q^{21} +1.51806 q^{22} -4.86069 q^{23} +1.98111 q^{24} +2.29190 q^{25} -5.78666 q^{26} +4.11121 q^{27} +2.97081 q^{28} -1.87188 q^{29} -5.34969 q^{30} +0.914430 q^{31} -1.00000 q^{32} +3.00745 q^{33} +3.10974 q^{34} -8.02222 q^{35} +0.924794 q^{36} +8.04419 q^{37} -1.00000 q^{38} -11.4640 q^{39} +2.70035 q^{40} +7.68665 q^{41} +5.88549 q^{42} +5.81248 q^{43} -1.51806 q^{44} -2.49727 q^{45} +4.86069 q^{46} -5.88087 q^{47} -1.98111 q^{48} +1.82569 q^{49} -2.29190 q^{50} +6.16073 q^{51} +5.78666 q^{52} -4.81750 q^{53} -4.11121 q^{54} +4.09931 q^{55} -2.97081 q^{56} -1.98111 q^{57} +1.87188 q^{58} +11.4183 q^{59} +5.34969 q^{60} -5.49154 q^{61} -0.914430 q^{62} +2.74738 q^{63} +1.00000 q^{64} -15.6260 q^{65} -3.00745 q^{66} -10.8661 q^{67} -3.10974 q^{68} +9.62956 q^{69} +8.02222 q^{70} +15.8022 q^{71} -0.924794 q^{72} +6.76947 q^{73} -8.04419 q^{74} -4.54050 q^{75} +1.00000 q^{76} -4.50987 q^{77} +11.4640 q^{78} -3.16386 q^{79} -2.70035 q^{80} -10.9191 q^{81} -7.68665 q^{82} +1.66996 q^{83} -5.88549 q^{84} +8.39738 q^{85} -5.81248 q^{86} +3.70839 q^{87} +1.51806 q^{88} -5.68530 q^{89} +2.49727 q^{90} +17.1910 q^{91} -4.86069 q^{92} -1.81159 q^{93} +5.88087 q^{94} -2.70035 q^{95} +1.98111 q^{96} -5.64199 q^{97} -1.82569 q^{98} -1.40390 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9}+O(q^{10}) $ 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9	$ 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9} + 14 q^{11} + 3 q^{13} - 19 q^{14} + q^{15} + 43 q^{16} + 8 q^{17} - 53 q^{18} + 43 q^{19} - 14 q^{22} + 43 q^{23} + 97 q^{25} - 3 q^{26} + 15 q^{27} + 19 q^{28} - 25 q^{29} - q^{30} + 22 q^{31} - 43 q^{32} + 22 q^{33} - 8 q^{34} - 6 q^{35} + 53 q^{36} + 42 q^{37} - 43 q^{38} + 9 q^{39} - 40 q^{41} + 72 q^{43} + 14 q^{44} - q^{45} - 43 q^{46} + 27 q^{47} + 86 q^{49} - 97 q^{50} - 3 q^{51} + 3 q^{52} - 5 q^{53} - 15 q^{54} + 86 q^{55} - 19 q^{56} + 25 q^{58} - 43 q^{59} + q^{60} + 31 q^{61} - 22 q^{62} + 38 q^{63} + 43 q^{64} - 32 q^{65} - 22 q^{66} + 15 q^{67} + 8 q^{68} - 7 q^{69} + 6 q^{70} + 14 q^{71} - 53 q^{72} + 93 q^{73} - 42 q^{74} - 13 q^{75} + 43 q^{76} + 38 q^{77} - 9 q^{78} + 15 q^{79} + 43 q^{81} + 40 q^{82} + 34 q^{83} + 16 q^{85} - 72 q^{86} + 60 q^{87} - 14 q^{88} - 37 q^{89} + q^{90} - 3 q^{91} + 43 q^{92} + 19 q^{93} - 27 q^{94} + 27 q^{97} - 86 q^{98} - 24 q^{99}+O(q^{100}) $ 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9 + 14 * q^11 + 3 * q^13 - 19 * q^14 + q^15 + 43 * q^16 + 8 * q^17 - 53 * q^18 + 43 * q^19 - 14 * q^22 + 43 * q^23 + 97 * q^25 - 3 * q^26 + 15 * q^27 + 19 * q^28 - 25 * q^29 - q^30 + 22 * q^31 - 43 * q^32 + 22 * q^33 - 8 * q^34 - 6 * q^35 + 53 * q^36 + 42 * q^37 - 43 * q^38 + 9 * q^39 - 40 * q^41 + 72 * q^43 + 14 * q^44 - q^45 - 43 * q^46 + 27 * q^47 + 86 * q^49 - 97 * q^50 - 3 * q^51 + 3 * q^52 - 5 * q^53 - 15 * q^54 + 86 * q^55 - 19 * q^56 + 25 * q^58 - 43 * q^59 + q^60 + 31 * q^61 - 22 * q^62 + 38 * q^63 + 43 * q^64 - 32 * q^65 - 22 * q^66 + 15 * q^67 + 8 * q^68 - 7 * q^69 + 6 * q^70 + 14 * q^71 - 53 * q^72 + 93 * q^73 - 42 * q^74 - 13 * q^75 + 43 * q^76 + 38 * q^77 - 9 * q^78 + 15 * q^79 + 43 * q^81 + 40 * q^82 + 34 * q^83 + 16 * q^85 - 72 * q^86 + 60 * q^87 - 14 * q^88 - 37 * q^89 + q^90 - 3 * q^91 + 43 * q^92 + 19 * q^93 - 27 * q^94 + 27 * q^97 - 86 * q^98 - 24 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.98111	−1.14379	−0.571897	−	0.820325i	$-0.693792\pi$
$3$	−1.98111	−1.14379	−0.571897	+	0.820325i	$0.693792\pi$
$4$	1.00000	0.500000
$5$	−2.70035	−1.20763	−0.603817	−	0.797123i	$-0.706354\pi$
$5$	−2.70035	−1.20763	−0.603817	+	0.797123i	$0.706354\pi$
$6$	1.98111	0.808784
$7$	2.97081	1.12286	0.561430	−	0.827525i	$-0.310252\pi$
$7$	2.97081	1.12286	0.561430	+	0.827525i	$0.310252\pi$
$8$	−1.00000	−0.353553
$9$	0.924794	0.308265
$10$	2.70035	0.853926
$11$	−1.51806	−0.457714	−0.228857	−	0.973460i	$-0.573499\pi$
$11$	−1.51806	−0.457714	−0.228857	+	0.973460i	$0.573499\pi$
$12$	−1.98111	−0.571897
$13$	5.78666	1.60493	0.802465	−	0.596699i	$-0.203522\pi$
$13$	5.78666	1.60493	0.802465	+	0.596699i	$0.203522\pi$
$14$	−2.97081	−0.793981
$15$	5.34969	1.38128
$16$	1.00000	0.250000
$17$	−3.10974	−0.754222	−0.377111	−	0.926168i	$-0.623082\pi$
$17$	−3.10974	−0.754222	−0.377111	+	0.926168i	$0.623082\pi$
$18$	−0.924794	−0.217976
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−2.70035	−0.603817
$21$	−5.88549	−1.28432
$22$	1.51806	0.323652
$23$	−4.86069	−1.01352	−0.506762	−	0.862086i	$-0.669158\pi$
$23$	−4.86069	−1.01352	−0.506762	+	0.862086i	$0.669158\pi$
$24$	1.98111	0.404392
$25$	2.29190	0.458380
$26$	−5.78666	−1.13486
$27$	4.11121	0.791203
$28$	2.97081	0.561430
$29$	−1.87188	−0.347599	−0.173799	−	0.984781i	$-0.555604\pi$
$29$	−1.87188	−0.347599	−0.173799	+	0.984781i	$0.555604\pi$
$30$	−5.34969	−0.976716
$31$	0.914430	0.164237	0.0821183	−	0.996623i	$-0.473831\pi$
$31$	0.914430	0.164237	0.0821183	+	0.996623i	$0.473831\pi$
$32$	−1.00000	−0.176777
$33$	3.00745	0.523530
$34$	3.10974	0.533315
$35$	−8.02222	−1.35600
$36$	0.924794	0.154132
$37$	8.04419	1.32246	0.661229	−	0.750184i	$-0.270035\pi$
$37$	8.04419	1.32246	0.661229	+	0.750184i	$0.270035\pi$
$38$	−1.00000	−0.162221
$39$	−11.4640	−1.83571
$40$	2.70035	0.426963
$41$	7.68665	1.20045	0.600226	−	0.799830i	$-0.295077\pi$
$41$	7.68665	1.20045	0.600226	+	0.799830i	$0.295077\pi$
$42$	5.88549	0.908151
$43$	5.81248	0.886395	0.443198	−	0.896424i	$-0.353844\pi$
$43$	5.81248	0.886395	0.443198	+	0.896424i	$0.353844\pi$
$44$	−1.51806	−0.228857
$45$	−2.49727	−0.372271
$46$	4.86069	0.716670
$47$	−5.88087	−0.857813	−0.428906	−	0.903349i	$-0.641101\pi$
$47$	−5.88087	−0.857813	−0.428906	+	0.903349i	$0.641101\pi$
$48$	−1.98111	−0.285948
$49$	1.82569	0.260812
$50$	−2.29190	−0.324124
$51$	6.16073	0.862674
$52$	5.78666	0.802465
$53$	−4.81750	−0.661734	−0.330867	−	0.943677i	$-0.607341\pi$
$53$	−4.81750	−0.661734	−0.330867	+	0.943677i	$0.607341\pi$
$54$	−4.11121	−0.559465
$55$	4.09931	0.552750
$56$	−2.97081	−0.396991
$57$	−1.98111	−0.262404
$58$	1.87188	0.245789
$59$	11.4183	1.48654	0.743271	−	0.668991i	$-0.233273\pi$
$59$	11.4183	1.48654	0.743271	+	0.668991i	$0.233273\pi$
$60$	5.34969	0.690642
$61$	−5.49154	−0.703120	−0.351560	−	0.936165i	$-0.614349\pi$
$61$	−5.49154	−0.703120	−0.351560	+	0.936165i	$0.614349\pi$
$62$	−0.914430	−0.116133
$63$	2.74738	0.346138
$64$	1.00000	0.125000
$65$	−15.6260	−1.93817
$66$	−3.00745	−0.370192
$67$	−10.8661	−1.32751	−0.663753	−	0.747952i	$-0.731037\pi$
$67$	−10.8661	−1.32751	−0.663753	+	0.747952i	$0.731037\pi$
$68$	−3.10974	−0.377111
$69$	9.62956	1.15926
$70$	8.02222	0.958839
$71$	15.8022	1.87538	0.937689	−	0.347475i	$-0.112961\pi$
$71$	15.8022	1.87538	0.937689	+	0.347475i	$0.112961\pi$
$72$	−0.924794	−0.108988
$73$	6.76947	0.792306	0.396153	−	0.918185i	$-0.370345\pi$
$73$	6.76947	0.792306	0.396153	+	0.918185i	$0.370345\pi$
$74$	−8.04419	−0.935119
$75$	−4.54050	−0.524292
$76$	1.00000	0.114708
$77$	−4.50987	−0.513948
$78$	11.4640	1.29804
$79$	−3.16386	−0.355962	−0.177981	−	0.984034i	$-0.556957\pi$
$79$	−3.16386	−0.355962	−0.177981	+	0.984034i	$0.556957\pi$
$80$	−2.70035	−0.301909
$81$	−10.9191	−1.21324
$82$	−7.68665	−0.848848
$83$	1.66996	0.183302	0.0916509	−	0.995791i	$-0.470786\pi$
$83$	1.66996	0.183302	0.0916509	+	0.995791i	$0.470786\pi$
$84$	−5.88549	−0.642160
$85$	8.39738	0.910824
$86$	−5.81248	−0.626776
$87$	3.70839	0.397581
$88$	1.51806	0.161826
$89$	−5.68530	−0.602641	−0.301320	−	0.953523i	$-0.597427\pi$
$89$	−5.68530	−0.602641	−0.301320	+	0.953523i	$0.597427\pi$
$90$	2.49727	0.263235
$91$	17.1910	1.80211
$92$	−4.86069	−0.506762
$93$	−1.81159	−0.187853
$94$	5.88087	0.606565
$95$	−2.70035	−0.277050
$96$	1.98111	0.202196
$97$	−5.64199	−0.572857	−0.286428	−	0.958102i	$-0.592468\pi$
$97$	−5.64199	−0.572857	−0.286428	+	0.958102i	$0.592468\pi$
$98$	−1.82569	−0.184422
$99$	−1.40390	−0.141097
$100$	2.29190	0.229190
$101$	8.08322	0.804311	0.402155	−	0.915571i	$-0.368261\pi$
$101$	8.08322	0.804311	0.402155	+	0.915571i	$0.368261\pi$
$102$	−6.16073	−0.610003
$103$	19.3372	1.90535	0.952677	−	0.303984i	$-0.0983168\pi$
$103$	19.3372	1.90535	0.952677	+	0.303984i	$0.0983168\pi$
$104$	−5.78666	−0.567428
$105$	15.8929	1.55099
$106$	4.81750	0.467917
$107$	−15.4030	−1.48906	−0.744531	−	0.667588i	$-0.767327\pi$
$107$	−15.4030	−1.48906	−0.744531	+	0.667588i	$0.767327\pi$
$108$	4.11121	0.395601
$109$	−7.10497	−0.680533	−0.340267	−	0.940329i	$-0.610517\pi$
$109$	−7.10497	−0.680533	−0.340267	+	0.940329i	$0.610517\pi$
$110$	−4.09931	−0.390854
$111$	−15.9364	−1.51262
$112$	2.97081	0.280715
$113$	10.5458	0.992065	0.496032	−	0.868304i	$-0.334790\pi$
$113$	10.5458	0.992065	0.496032	+	0.868304i	$0.334790\pi$
$114$	1.98111	0.185548
$115$	13.1256	1.22397
$116$	−1.87188	−0.173799
$117$	5.35146	0.494743
$118$	−11.4183	−1.05114
$119$	−9.23842	−0.846885
$120$	−5.34969	−0.488358
$121$	−8.69548	−0.790498
$122$	5.49154	0.497181
$123$	−15.2281	−1.37307
$124$	0.914430	0.0821183
$125$	7.31282	0.654079
$126$	−2.74738	−0.244756
$127$	−1.75017	−0.155303	−0.0776514	−	0.996981i	$-0.524742\pi$
$127$	−1.75017	−0.155303	−0.0776514	+	0.996981i	$0.524742\pi$
$128$	−1.00000	−0.0883883
$129$	−11.5152	−1.01385
$130$	15.6260	1.37049
$131$	−3.78656	−0.330833	−0.165417	−	0.986224i	$-0.552897\pi$
$131$	−3.78656	−0.330833	−0.165417	+	0.986224i	$0.552897\pi$
$132$	3.00745	0.261765
$133$	2.97081	0.257602
$134$	10.8661	0.938688
$135$	−11.1017	−0.955483
$136$	3.10974	0.266658
$137$	−9.79871	−0.837160	−0.418580	−	0.908180i	$-0.637472\pi$
$137$	−9.79871	−0.837160	−0.418580	+	0.908180i	$0.637472\pi$
$138$	−9.62956	−0.819723
$139$	−6.42904	−0.545304	−0.272652	−	0.962113i	$-0.587901\pi$
$139$	−6.42904	−0.545304	−0.272652	+	0.962113i	$0.587901\pi$
$140$	−8.02222	−0.678001
$141$	11.6506	0.981161
$142$	−15.8022	−1.32609
$143$	−8.78451	−0.734598
$144$	0.924794	0.0770662
$145$	5.05472	0.419772
$146$	−6.76947	−0.560245
$147$	−3.61689	−0.298316
$148$	8.04419	0.661229
$149$	15.2783	1.25165	0.625824	−	0.779964i	$-0.284763\pi$
$149$	15.2783	1.25165	0.625824	+	0.779964i	$0.284763\pi$
$150$	4.54050	0.370731
$151$	−17.1387	−1.39473	−0.697364	−	0.716717i	$-0.745644\pi$
$151$	−17.1387	−1.39473	−0.697364	+	0.716717i	$0.745644\pi$
$152$	−1.00000	−0.0811107
$153$	−2.87586	−0.232500
$154$	4.50987	0.363416
$155$	−2.46928	−0.198338
$156$	−11.4640	−0.917854
$157$	13.4674	1.07482	0.537409	−	0.843321i	$-0.319403\pi$
$157$	13.4674	1.07482	0.537409	+	0.843321i	$0.319403\pi$
$158$	3.16386	0.251703
$159$	9.54399	0.756887
$160$	2.70035	0.213482
$161$	−14.4402	−1.13804
$162$	10.9191	0.857888
$163$	−20.3110	−1.59088	−0.795440	−	0.606033i	$-0.792760\pi$
$163$	−20.3110	−1.59088	−0.795440	+	0.606033i	$0.792760\pi$
$164$	7.68665	0.600226
$165$	−8.12117	−0.632233
$166$	−1.66996	−0.129614
$167$	−17.5482	−1.35792	−0.678958	−	0.734177i	$-0.737568\pi$
$167$	−17.5482	−1.35792	−0.678958	+	0.734177i	$0.737568\pi$
$168$	5.88549	0.454075
$169$	20.4854	1.57580
$170$	−8.39738	−0.644050
$171$	0.924794	0.0707208
$172$	5.81248	0.443198
$173$	−19.7852	−1.50424	−0.752122	−	0.659024i	$-0.770970\pi$
$173$	−19.7852	−1.50424	−0.752122	+	0.659024i	$0.770970\pi$
$174$	−3.70839	−0.281132
$175$	6.80879	0.514696
$176$	−1.51806	−0.114428
$177$	−22.6210	−1.70030
$178$	5.68530	0.426131
$179$	0.413013	0.0308700	0.0154350	−	0.999881i	$-0.495087\pi$
$179$	0.413013	0.0308700	0.0154350	+	0.999881i	$0.495087\pi$
$180$	−2.49727	−0.186135
$181$	−25.7154	−1.91141	−0.955706	−	0.294322i	$-0.904906\pi$
$181$	−25.7154	−1.91141	−0.955706	+	0.294322i	$0.904906\pi$
$182$	−17.1910	−1.27428
$183$	10.8793	0.804224
$184$	4.86069	0.358335
$185$	−21.7222	−1.59704
$186$	1.81159	0.132832
$187$	4.72078	0.345217
$188$	−5.88087	−0.428906
$189$	12.2136	0.888409
$190$	2.70035	0.195904
$191$	−18.5631	−1.34318	−0.671588	−	0.740925i	$-0.734388\pi$
$191$	−18.5631	−1.34318	−0.671588	+	0.740925i	$0.734388\pi$
$192$	−1.98111	−0.142974
$193$	22.2164	1.59917	0.799584	−	0.600554i	$-0.205053\pi$
$193$	22.2164	1.59917	0.799584	+	0.600554i	$0.205053\pi$
$194$	5.64199	0.405071
$195$	30.9568	2.21686
$196$	1.82569	0.130406
$197$	−19.5952	−1.39610	−0.698050	−	0.716049i	$-0.745949\pi$
$197$	−19.5952	−1.39610	−0.698050	+	0.716049i	$0.745949\pi$
$198$	1.40390	0.0997706
$199$	19.1677	1.35876	0.679380	−	0.733786i	$-0.262249\pi$
$199$	19.1677	1.35876	0.679380	+	0.733786i	$0.262249\pi$
$200$	−2.29190	−0.162062
$201$	21.5269	1.51839
$202$	−8.08322	−0.568734
$203$	−5.56098	−0.390304
$204$	6.16073	0.431337
$205$	−20.7567	−1.44971
$206$	−19.3372	−1.34729
$207$	−4.49514	−0.312434
$208$	5.78666	0.401232
$209$	−1.51806	−0.105007
$210$	−15.8929	−1.09671
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−4.81750	−0.330867
$213$	−31.3059	−2.14505
$214$	15.4030	1.05293
$215$	−15.6958	−1.07044
$216$	−4.11121	−0.279732
$217$	2.71660	0.184415
$218$	7.10497	0.481210
$219$	−13.4110	−0.906235
$220$	4.09931	0.276375
$221$	−17.9950	−1.21047
$222$	15.9364	1.06958
$223$	19.8589	1.32985	0.664925	−	0.746910i	$-0.268463\pi$
$223$	19.8589	1.32985	0.664925	+	0.746910i	$0.268463\pi$
$224$	−2.97081	−0.198495
$225$	2.11953	0.141302
$226$	−10.5458	−0.701496
$227$	23.9873	1.59209	0.796047	−	0.605234i	$-0.206921\pi$
$227$	23.9873	1.59209	0.796047	+	0.605234i	$0.206921\pi$
$228$	−1.98111	−0.131202
$229$	−1.81717	−0.120082	−0.0600409	−	0.998196i	$-0.519123\pi$
$229$	−1.81717	−0.120082	−0.0600409	+	0.998196i	$0.519123\pi$
$230$	−13.1256	−0.865475
$231$	8.93455	0.587850
$232$	1.87188	0.122895
$233$	−15.2008	−0.995838	−0.497919	−	0.867223i	$-0.665902\pi$
$233$	−15.2008	−0.995838	−0.497919	+	0.867223i	$0.665902\pi$
$234$	−5.35146	−0.349836
$235$	15.8804	1.03592
$236$	11.4183	0.743271
$237$	6.26795	0.407147
$238$	9.23842	0.598838
$239$	21.7802	1.40884	0.704422	−	0.709781i	$-0.251206\pi$
$239$	21.7802	1.40884	0.704422	+	0.709781i	$0.251206\pi$
$240$	5.34969	0.345321
$241$	12.2800	0.791023	0.395512	−	0.918461i	$-0.370567\pi$
$241$	12.2800	0.791023	0.395512	+	0.918461i	$0.370567\pi$
$242$	8.69548	0.558967
$243$	9.29837	0.596491
$244$	−5.49154	−0.351560
$245$	−4.93000	−0.314966
$246$	15.2281	0.970907
$247$	5.78666	0.368196
$248$	−0.914430	−0.0580664
$249$	−3.30837	−0.209659
$250$	−7.31282	−0.462504
$251$	−17.9933	−1.13572	−0.567862	−	0.823124i	$-0.692229\pi$
$251$	−17.9933	−1.13572	−0.567862	+	0.823124i	$0.692229\pi$
$252$	2.74738	0.173069
$253$	7.37884	0.463904
$254$	1.75017	0.109816
$255$	−16.6361	−1.04179
$256$	1.00000	0.0625000
$257$	2.91014	0.181530	0.0907648	−	0.995872i	$-0.471069\pi$
$257$	2.91014	0.181530	0.0907648	+	0.995872i	$0.471069\pi$
$258$	11.5152	0.716903
$259$	23.8977	1.48493
$260$	−15.6260	−0.969084
$261$	−1.73110	−0.107152
$262$	3.78656	0.233934
$263$	3.38762	0.208890	0.104445	−	0.994531i	$-0.466693\pi$
$263$	3.38762	0.208890	0.104445	+	0.994531i	$0.466693\pi$
$264$	−3.00745	−0.185096
$265$	13.0089	0.799132
$266$	−2.97081	−0.182152
$267$	11.2632	0.689297
$268$	−10.8661	−0.663753
$269$	14.8434	0.905016	0.452508	−	0.891760i	$-0.350529\pi$
$269$	14.8434	0.905016	0.452508	+	0.891760i	$0.350529\pi$
$270$	11.1017	0.675629
$271$	−24.9234	−1.51399	−0.756995	−	0.653421i	$-0.773333\pi$
$271$	−24.9234	−1.51399	−0.756995	+	0.653421i	$0.773333\pi$
$272$	−3.10974	−0.188555
$273$	−34.0573	−2.06124
$274$	9.79871	0.591962
$275$	−3.47925	−0.209807
$276$	9.62956	0.579631
$277$	0.297572	0.0178794	0.00893970	−	0.999960i	$-0.497154\pi$
$277$	0.297572	0.0178794	0.00893970	+	0.999960i	$0.497154\pi$
$278$	6.42904	0.385588
$279$	0.845660	0.0506283
$280$	8.02222	0.479419
$281$	17.3768	1.03661	0.518306	−	0.855195i	$-0.326563\pi$
$281$	17.3768	1.03661	0.518306	+	0.855195i	$0.326563\pi$
$282$	−11.6506	−0.693785
$283$	−13.7593	−0.817904	−0.408952	−	0.912556i	$-0.634106\pi$
$283$	−13.7593	−0.817904	−0.408952	+	0.912556i	$0.634106\pi$
$284$	15.8022	0.937689
$285$	5.34969	0.316888
$286$	8.78451	0.519439
$287$	22.8355	1.34794
$288$	−0.924794	−0.0544940
$289$	−7.32954	−0.431150
$290$	−5.05472	−0.296824
$291$	11.1774	0.655230
$292$	6.76947	0.396153
$293$	−11.6747	−0.682044	−0.341022	−	0.940055i	$-0.610773\pi$
$293$	−11.6747	−0.682044	−0.341022	+	0.940055i	$0.610773\pi$
$294$	3.61689	0.210941
$295$	−30.8335	−1.79520
$296$	−8.04419	−0.467559
$297$	−6.24108	−0.362144
$298$	−15.2783	−0.885049
$299$	−28.1272	−1.62664
$300$	−4.54050	−0.262146
$301$	17.2678	0.995297
$302$	17.1387	0.986222
$303$	−16.0137	−0.919966
$304$	1.00000	0.0573539
$305$	14.8291	0.849111
$306$	2.87586	0.164402
$307$	8.85820	0.505564	0.252782	−	0.967523i	$-0.418654\pi$
$307$	8.85820	0.505564	0.252782	+	0.967523i	$0.418654\pi$
$308$	−4.50987	−0.256974
$309$	−38.3092	−2.17933
$310$	2.46928	0.140246
$311$	30.1748	1.71106	0.855529	−	0.517755i	$-0.173232\pi$
$311$	30.1748	1.71106	0.855529	+	0.517755i	$0.173232\pi$
$312$	11.4640	0.649021
$313$	−12.6629	−0.715750	−0.357875	−	0.933769i	$-0.616499\pi$
$313$	−12.6629	−0.715750	−0.357875	+	0.933769i	$0.616499\pi$
$314$	−13.4674	−0.760012
$315$	−7.41890	−0.418008
$316$	−3.16386	−0.177981
$317$	25.8417	1.45141	0.725707	−	0.688003i	$-0.241513\pi$
$317$	25.8417	1.45141	0.725707	+	0.688003i	$0.241513\pi$
$318$	−9.54399	−0.535200
$319$	2.84163	0.159101
$320$	−2.70035	−0.150954
$321$	30.5150	1.70318
$322$	14.4402	0.804719
$323$	−3.10974	−0.173030
$324$	−10.9191	−0.606619
$325$	13.2624	0.735667
$326$	20.3110	1.12492
$327$	14.0757	0.778390
$328$	−7.68665	−0.424424
$329$	−17.4709	−0.963203
$330$	8.12117	0.447056
$331$	19.0149	1.04515	0.522577	−	0.852592i	$-0.324971\pi$
$331$	19.0149	1.04515	0.522577	+	0.852592i	$0.324971\pi$
$332$	1.66996	0.0916509
$333$	7.43922	0.407667
$334$	17.5482	0.960192
$335$	29.3423	1.60314
$336$	−5.88549	−0.321080
$337$	8.37442	0.456184	0.228092	−	0.973640i	$-0.426751\pi$
$337$	8.37442	0.456184	0.228092	+	0.973640i	$0.426751\pi$
$338$	−20.4854	−1.11426
$339$	−20.8924	−1.13472
$340$	8.39738	0.455412
$341$	−1.38816	−0.0751733
$342$	−0.924794	−0.0500071
$343$	−15.3719	−0.830003
$344$	−5.81248	−0.313388
$345$	−26.0032	−1.39997
$346$	19.7852	1.06366
$347$	9.53373	0.511798	0.255899	−	0.966704i	$-0.417629\pi$
$347$	9.53373	0.511798	0.255899	+	0.966704i	$0.417629\pi$
$348$	3.70839	0.198791
$349$	24.1249	1.29138	0.645688	−	0.763601i	$-0.276571\pi$
$349$	24.1249	1.29138	0.645688	+	0.763601i	$0.276571\pi$
$350$	−6.80879	−0.363945
$351$	23.7902	1.26982
$352$	1.51806	0.0809131
$353$	28.6589	1.52536	0.762681	−	0.646775i	$-0.223883\pi$
$353$	28.6589	1.52536	0.762681	+	0.646775i	$0.223883\pi$
$354$	22.6210	1.20229
$355$	−42.6715	−2.26477
$356$	−5.68530	−0.301320
$357$	18.3023	0.968662
$358$	−0.413013	−0.0218284
$359$	9.19223	0.485147	0.242574	−	0.970133i	$-0.422008\pi$
$359$	9.19223	0.485147	0.242574	+	0.970133i	$0.422008\pi$
$360$	2.49727	0.131618
$361$	1.00000	0.0526316
$362$	25.7154	1.35157
$363$	17.2267	0.904167
$364$	17.1910	0.901055
$365$	−18.2799	−0.956816
$366$	−10.8793	−0.568672
$367$	−5.67002	−0.295972	−0.147986	−	0.988989i	$-0.547279\pi$
$367$	−5.67002	−0.295972	−0.147986	+	0.988989i	$0.547279\pi$
$368$	−4.86069	−0.253381
$369$	7.10856	0.370057
$370$	21.7222	1.12928
$371$	−14.3118	−0.743034
$372$	−1.81159	−0.0939264
$373$	−24.5262	−1.26992	−0.634959	−	0.772546i	$-0.718983\pi$
$373$	−24.5262	−1.26992	−0.634959	+	0.772546i	$0.718983\pi$
$374$	−4.72078	−0.244106
$375$	−14.4875	−0.748131
$376$	5.88087	0.303283
$377$	−10.8319	−0.557871
$378$	−12.2136	−0.628200
$379$	−32.6356	−1.67638	−0.838190	−	0.545379i	$-0.816386\pi$
$379$	−32.6356	−1.67638	−0.838190	+	0.545379i	$0.816386\pi$
$380$	−2.70035	−0.138525
$381$	3.46728	0.177634
$382$	18.5631	0.949769
$383$	12.8683	0.657540	0.328770	−	0.944410i	$-0.393366\pi$
$383$	12.8683	0.657540	0.328770	+	0.944410i	$0.393366\pi$
$384$	1.98111	0.101098
$385$	12.1782	0.620661
$386$	−22.2164	−1.13078
$387$	5.37535	0.273244
$388$	−5.64199	−0.286428
$389$	8.97385	0.454992	0.227496	−	0.973779i	$-0.426946\pi$
$389$	8.97385	0.454992	0.227496	+	0.973779i	$0.426946\pi$
$390$	−30.9568	−1.56756
$391$	15.1155	0.764422
$392$	−1.82569	−0.0922111
$393$	7.50159	0.378405
$394$	19.5952	0.987192
$395$	8.54354	0.429872
$396$	−1.40390	−0.0705484
$397$	18.1322	0.910027	0.455013	−	0.890485i	$-0.349634\pi$
$397$	18.1322	0.910027	0.455013	+	0.890485i	$0.349634\pi$
$398$	−19.1677	−0.960789
$399$	−5.88549	−0.294643
$400$	2.29190	0.114595
$401$	14.0458	0.701414	0.350707	−	0.936485i	$-0.385941\pi$
$401$	14.0458	0.701414	0.350707	+	0.936485i	$0.385941\pi$
$402$	−21.5269	−1.07367
$403$	5.29149	0.263588
$404$	8.08322	0.402155
$405$	29.4855	1.46515
$406$	5.56098	0.275987
$407$	−12.2116	−0.605307
$408$	−6.16073	−0.305001
$409$	−22.6422	−1.11959	−0.559793	−	0.828633i	$-0.689119\pi$
$409$	−22.6422	−1.11959	−0.559793	+	0.828633i	$0.689119\pi$
$410$	20.7567	1.02510
$411$	19.4123	0.957539
$412$	19.3372	0.952677
$413$	33.9217	1.66918
$414$	4.49514	0.220924
$415$	−4.50948	−0.221361
$416$	−5.78666	−0.283714
$417$	12.7366	0.623715
$418$	1.51806	0.0742509
$419$	4.10907	0.200741	0.100371	−	0.994950i	$-0.467997\pi$
$419$	4.10907	0.200741	0.100371	+	0.994950i	$0.467997\pi$
$420$	15.8929	0.775494
$421$	−17.8849	−0.871658	−0.435829	−	0.900030i	$-0.643545\pi$
$421$	−17.8849	−0.871658	−0.435829	+	0.900030i	$0.643545\pi$
$422$	1.00000	0.0486792
$423$	−5.43859	−0.264433
$424$	4.81750	0.233958
$425$	−7.12720	−0.345720
$426$	31.3059	1.51678
$427$	−16.3143	−0.789504
$428$	−15.4030	−0.744531
$429$	17.4031	0.840229
$430$	15.6958	0.756916
$431$	19.8837	0.957766	0.478883	−	0.877879i	$-0.341042\pi$
$431$	19.8837	0.957766	0.478883	+	0.877879i	$0.341042\pi$
$432$	4.11121	0.197801
$433$	−10.7142	−0.514890	−0.257445	−	0.966293i	$-0.582881\pi$
$433$	−10.7142	−0.514890	−0.257445	+	0.966293i	$0.582881\pi$
$434$	−2.71660	−0.130401
$435$	−10.0140	−0.480133
$436$	−7.10497	−0.340267
$437$	−4.86069	−0.232518
$438$	13.4110	0.640805
$439$	14.7793	0.705378	0.352689	−	0.935741i	$-0.385267\pi$
$439$	14.7793	0.705378	0.352689	+	0.935741i	$0.385267\pi$
$440$	−4.09931	−0.195427
$441$	1.68838	0.0803993
$442$	17.9950	0.855934
$443$	35.9311	1.70714	0.853569	−	0.520980i	$-0.174433\pi$
$443$	35.9311	1.70714	0.853569	+	0.520980i	$0.174433\pi$
$444$	−15.9364	−0.756309
$445$	15.3523	0.727769
$446$	−19.8589	−0.940346
$447$	−30.2680	−1.43163
$448$	2.97081	0.140357
$449$	37.0040	1.74633	0.873163	−	0.487428i	$-0.162065\pi$
$449$	37.0040	1.74633	0.873163	+	0.487428i	$0.162065\pi$
$450$	−2.11953	−0.0999158
$451$	−11.6688	−0.549463
$452$	10.5458	0.496032
$453$	33.9537	1.59528
$454$	−23.9873	−1.12578
$455$	−46.4218	−2.17629
$456$	1.98111	0.0927739
$457$	30.5269	1.42799	0.713994	−	0.700152i	$-0.246884\pi$
$457$	30.5269	1.42799	0.713994	+	0.700152i	$0.246884\pi$
$458$	1.81717	0.0849106
$459$	−12.7848	−0.596742
$460$	13.1256	0.611983
$461$	−21.5693	−1.00458	−0.502292	−	0.864698i	$-0.667510\pi$
$461$	−21.5693	−1.00458	−0.502292	+	0.864698i	$0.667510\pi$
$462$	−8.93455	−0.415673
$463$	18.6129	0.865015	0.432507	−	0.901630i	$-0.357629\pi$
$463$	18.6129	0.865015	0.432507	+	0.901630i	$0.357629\pi$
$464$	−1.87188	−0.0868997
$465$	4.89192	0.226857
$466$	15.2008	0.704164
$467$	−3.98437	−0.184375	−0.0921873	−	0.995742i	$-0.529386\pi$
$467$	−3.98437	−0.184375	−0.0921873	+	0.995742i	$0.529386\pi$
$468$	5.35146	0.247371
$469$	−32.2811	−1.49060
$470$	−15.8804	−0.732509
$471$	−26.6805	−1.22937
$472$	−11.4183	−0.525572
$473$	−8.82372	−0.405715
$474$	−6.26795	−0.287897
$475$	2.29190	0.105160
$476$	−9.23842	−0.423442
$477$	−4.45519	−0.203989
$478$	−21.7802	−0.996203
$479$	−23.3867	−1.06856	−0.534282	−	0.845306i	$-0.679418\pi$
$479$	−23.3867	−1.06856	−0.534282	+	0.845306i	$0.679418\pi$
$480$	−5.34969	−0.244179
$481$	46.5490	2.12245
$482$	−12.2800	−0.559338
$483$	28.6076	1.30169
$484$	−8.69548	−0.395249
$485$	15.2353	0.691801
$486$	−9.29837	−0.421783
$487$	−17.2521	−0.781769	−0.390884	−	0.920440i	$-0.627831\pi$
$487$	−17.2521	−0.781769	−0.390884	+	0.920440i	$0.627831\pi$
$488$	5.49154	0.248590
$489$	40.2383	1.81964
$490$	4.93000	0.222715
$491$	−36.5647	−1.65014	−0.825070	−	0.565030i	$-0.808865\pi$
$491$	−36.5647	−1.65014	−0.825070	+	0.565030i	$0.808865\pi$
$492$	−15.2281	−0.686535
$493$	5.82104	0.262167
$494$	−5.78666	−0.260354
$495$	3.79101	0.170393
$496$	0.914430	0.0410591
$497$	46.9453	2.10579
$498$	3.30837	0.148252
$499$	31.1919	1.39634	0.698170	−	0.715932i	$-0.253998\pi$
$499$	31.1919	1.39634	0.698170	+	0.715932i	$0.253998\pi$
$500$	7.31282	0.327039
$501$	34.7648	1.55318
$502$	17.9933	0.803078
$503$	1.90323	0.0848610	0.0424305	−	0.999099i	$-0.486490\pi$
$503$	1.90323	0.0848610	0.0424305	+	0.999099i	$0.486490\pi$
$504$	−2.74738	−0.122378
$505$	−21.8275	−0.971313
$506$	−7.37884	−0.328029
$507$	−40.5838	−1.80239
$508$	−1.75017	−0.0776514
$509$	−3.48271	−0.154368	−0.0771842	−	0.997017i	$-0.524593\pi$
$509$	−3.48271	−0.154368	−0.0771842	+	0.997017i	$0.524593\pi$
$510$	16.6361	0.736660
$511$	20.1108	0.889648
$512$	−1.00000	−0.0441942
$513$	4.11121	0.181514
$514$	−2.91014	−0.128361
$515$	−52.2173	−2.30097
$516$	−11.5152	−0.506927
$517$	8.92753	0.392632
$518$	−23.8977	−1.05001
$519$	39.1967	1.72055
$520$	15.6260	0.685246
$521$	−15.2993	−0.670275	−0.335138	−	0.942169i	$-0.608783\pi$
$521$	−15.2993	−0.670275	−0.335138	+	0.942169i	$0.608783\pi$
$522$	1.73110	0.0757682
$523$	−11.9436	−0.522259	−0.261130	−	0.965304i	$-0.584095\pi$
$523$	−11.9436	−0.522259	−0.261130	+	0.965304i	$0.584095\pi$
$524$	−3.78656	−0.165417
$525$	−13.4890	−0.588706
$526$	−3.38762	−0.147707
$527$	−2.84364	−0.123871
$528$	3.00745	0.130882
$529$	0.626325	0.0272315
$530$	−13.0089	−0.565072
$531$	10.5596	0.458248
$532$	2.97081	0.128801
$533$	44.4800	1.92664
$534$	−11.2632	−0.487406
$535$	41.5935	1.79824
$536$	10.8661	0.469344
$537$	−0.818223	−0.0353089
$538$	−14.8434	−0.639943
$539$	−2.77151	−0.119377
$540$	−11.1017	−0.477742
$541$	−7.72805	−0.332255	−0.166127	−	0.986104i	$-0.553126\pi$
$541$	−7.72805	−0.332255	−0.166127	+	0.986104i	$0.553126\pi$
$542$	24.9234	1.07055
$543$	50.9451	2.18626
$544$	3.10974	0.133329
$545$	19.1859	0.821835
$546$	34.0573	1.45752
$547$	12.5821	0.537971	0.268985	−	0.963144i	$-0.413312\pi$
$547$	12.5821	0.537971	0.268985	+	0.963144i	$0.413312\pi$
$548$	−9.79871	−0.418580
$549$	−5.07854	−0.216747
$550$	3.47925	0.148356
$551$	−1.87188	−0.0797446
$552$	−9.62956	−0.409861
$553$	−9.39922	−0.399695
$554$	−0.297572	−0.0126426
$555$	43.0340	1.82669
$556$	−6.42904	−0.272652
$557$	−20.4985	−0.868550	−0.434275	−	0.900780i	$-0.642995\pi$
$557$	−20.4985	−0.868550	−0.434275	+	0.900780i	$0.642995\pi$
$558$	−0.845660	−0.0357996
$559$	33.6348	1.42260
$560$	−8.02222	−0.339001
$561$	−9.35238	−0.394858
$562$	−17.3768	−0.732995
$563$	−29.1540	−1.22869	−0.614347	−	0.789036i	$-0.710580\pi$
$563$	−29.1540	−1.22869	−0.614347	+	0.789036i	$0.710580\pi$
$564$	11.6506	0.490580
$565$	−28.4774	−1.19805
$566$	13.7593	0.578345
$567$	−32.4386	−1.36229
$568$	−15.8022	−0.663046
$569$	−42.9518	−1.80063	−0.900316	−	0.435236i	$-0.856665\pi$
$569$	−42.9518	−1.80063	−0.900316	+	0.435236i	$0.856665\pi$
$570$	−5.34969	−0.224074
$571$	40.8045	1.70762	0.853808	−	0.520588i	$-0.174287\pi$
$571$	40.8045	1.70762	0.853808	+	0.520588i	$0.174287\pi$
$572$	−8.78451	−0.367299
$573$	36.7755	1.53632
$574$	−22.8355	−0.953137
$575$	−11.1402	−0.464579
$576$	0.924794	0.0385331
$577$	37.7086	1.56983	0.784914	−	0.619604i	$-0.212707\pi$
$577$	37.7086	1.56983	0.784914	+	0.619604i	$0.212707\pi$
$578$	7.32954	0.304869
$579$	−44.0130	−1.82912
$580$	5.05472	0.209886
$581$	4.96112	0.205822
$582$	−11.1774	−0.463318
$583$	7.31327	0.302885
$584$	−6.76947	−0.280122
$585$	−14.4508	−0.597468
$586$	11.6747	0.482278
$587$	35.5751	1.46834	0.734171	−	0.678965i	$-0.237571\pi$
$587$	35.5751	1.46834	0.734171	+	0.678965i	$0.237571\pi$
$588$	−3.61689	−0.149158
$589$	0.914430	0.0376784
$590$	30.8335	1.26940
$591$	38.8202	1.59685
$592$	8.04419	0.330614
$593$	12.9536	0.531939	0.265969	−	0.963981i	$-0.414308\pi$
$593$	12.9536	0.531939	0.265969	+	0.963981i	$0.414308\pi$
$594$	6.24108	0.256075
$595$	24.9470	1.02273
$596$	15.2783	0.625824
$597$	−37.9733	−1.55414
$598$	28.1272	1.15020
$599$	31.6855	1.29464	0.647318	−	0.762220i	$-0.275891\pi$
$599$	31.6855	1.29464	0.647318	+	0.762220i	$0.275891\pi$
$600$	4.54050	0.185365
$601$	42.1573	1.71963	0.859817	−	0.510603i	$-0.170578\pi$
$601$	42.1573	1.71963	0.859817	+	0.510603i	$0.170578\pi$
$602$	−17.2678	−0.703781
$603$	−10.0489	−0.409223
$604$	−17.1387	−0.697364
$605$	23.4809	0.954633
$606$	16.0137	0.650514
$607$	−31.7746	−1.28969	−0.644846	−	0.764312i	$-0.723079\pi$
$607$	−31.7746	−1.28969	−0.644846	+	0.764312i	$0.723079\pi$
$608$	−1.00000	−0.0405554
$609$	11.0169	0.446428
$610$	−14.8291	−0.600412
$611$	−34.0306	−1.37673
$612$	−2.87586	−0.116250
$613$	−37.6503	−1.52068	−0.760340	−	0.649525i	$-0.774968\pi$
$613$	−37.6503	−1.52068	−0.760340	+	0.649525i	$0.774968\pi$
$614$	−8.85820	−0.357488
$615$	41.1212	1.65817
$616$	4.50987	0.181708
$617$	26.3311	1.06005	0.530025	−	0.847982i	$-0.322182\pi$
$617$	26.3311	1.06005	0.530025	+	0.847982i	$0.322182\pi$
$618$	38.3092	1.54102
$619$	−13.0221	−0.523403	−0.261701	−	0.965149i	$-0.584284\pi$
$619$	−13.0221	−0.523403	−0.261701	+	0.965149i	$0.584284\pi$
$620$	−2.46928	−0.0991688
$621$	−19.9833	−0.801903
$622$	−30.1748	−1.20990
$623$	−16.8899	−0.676681
$624$	−11.4640	−0.458927
$625$	−31.2067	−1.24827
$626$	12.6629	0.506112
$627$	3.00745	0.120106
$628$	13.4674	0.537409
$629$	−25.0153	−0.997426
$630$	7.41890	0.295576
$631$	6.18022	0.246031	0.123015	−	0.992405i	$-0.460744\pi$
$631$	6.18022	0.246031	0.123015	+	0.992405i	$0.460744\pi$
$632$	3.16386	0.125852
$633$	1.98111	0.0787420
$634$	−25.8417	−1.02631
$635$	4.72608	0.187549
$636$	9.54399	0.378444
$637$	10.5646	0.418586
$638$	−2.84163	−0.112501
$639$	14.6138	0.578113
$640$	2.70035	0.106741
$641$	35.7160	1.41070	0.705349	−	0.708861i	$-0.250790\pi$
$641$	35.7160	1.41070	0.705349	+	0.708861i	$0.250790\pi$
$642$	−30.5150	−1.20433
$643$	7.20350	0.284078	0.142039	−	0.989861i	$-0.454634\pi$
$643$	7.20350	0.284078	0.142039	+	0.989861i	$0.454634\pi$
$644$	−14.4402	−0.569022
$645$	31.0950	1.22436
$646$	3.10974	0.122351
$647$	48.4876	1.90624	0.953121	−	0.302589i	$-0.0978509\pi$
$647$	48.4876	1.90624	0.953121	+	0.302589i	$0.0978509\pi$
$648$	10.9191	0.428944
$649$	−17.3338	−0.680410
$650$	−13.2624	−0.520195
$651$	−5.38187	−0.210932
$652$	−20.3110	−0.795440
$653$	20.2593	0.792808	0.396404	−	0.918076i	$-0.370258\pi$
$653$	20.2593	0.792808	0.396404	+	0.918076i	$0.370258\pi$
$654$	−14.0757	−0.550405
$655$	10.2250	0.399526
$656$	7.68665	0.300113
$657$	6.26036	0.244240
$658$	17.4709	0.681087
$659$	−29.5198	−1.14993	−0.574964	−	0.818178i	$-0.694984\pi$
$659$	−29.5198	−1.14993	−0.574964	+	0.818178i	$0.694984\pi$
$660$	−8.12117	−0.316116
$661$	−11.1728	−0.434572	−0.217286	−	0.976108i	$-0.569720\pi$
$661$	−11.1728	−0.434572	−0.217286	+	0.976108i	$0.569720\pi$
$662$	−19.0149	−0.739035
$663$	35.6500	1.38453
$664$	−1.66996	−0.0648070
$665$	−8.02222	−0.311088
$666$	−7.43922	−0.288264
$667$	9.09861	0.352300
$668$	−17.5482	−0.678958
$669$	−39.3427	−1.52107
$670$	−29.3423	−1.13359
$671$	8.33651	0.321827
$672$	5.88549	0.227038
$673$	−17.4444	−0.672432	−0.336216	−	0.941785i	$-0.609147\pi$
$673$	−17.4444	−0.672432	−0.336216	+	0.941785i	$0.609147\pi$
$674$	−8.37442	−0.322570
$675$	9.42248	0.362671
$676$	20.4854	0.787900
$677$	−11.0078	−0.423064	−0.211532	−	0.977371i	$-0.567845\pi$
$677$	−11.0078	−0.423064	−0.211532	+	0.977371i	$0.567845\pi$
$678$	20.8924	0.802367
$679$	−16.7612	−0.643238
$680$	−8.39738	−0.322025
$681$	−47.5215	−1.82103
$682$	1.38816	0.0531555
$683$	26.5356	1.01536	0.507679	−	0.861546i	$-0.330504\pi$
$683$	26.5356	1.01536	0.507679	+	0.861546i	$0.330504\pi$
$684$	0.924794	0.0353604
$685$	26.4600	1.01098
$686$	15.3719	0.586901
$687$	3.60001	0.137349
$688$	5.81248	0.221599
$689$	−27.8772	−1.06204
$690$	26.0032	0.989925
$691$	21.8455	0.831043	0.415522	−	0.909583i	$-0.363599\pi$
$691$	21.8455	0.831043	0.415522	+	0.909583i	$0.363599\pi$
$692$	−19.7852	−0.752122
$693$	−4.17070	−0.158432
$694$	−9.53373	−0.361896
$695$	17.3607	0.658527
$696$	−3.70839	−0.140566
$697$	−23.9034	−0.905407
$698$	−24.1249	−0.913141
$699$	30.1145	1.13903
$700$	6.80879	0.257348
$701$	3.36410	0.127060	0.0635301	−	0.997980i	$-0.479764\pi$
$701$	3.36410	0.127060	0.0635301	+	0.997980i	$0.479764\pi$
$702$	−23.7902	−0.897902
$703$	8.04419	0.303393
$704$	−1.51806	−0.0572142
$705$	−31.4608	−1.18488
$706$	−28.6589	−1.07859
$707$	24.0137	0.903128
$708$	−22.6210	−0.850149
$709$	48.8176	1.83338	0.916692	−	0.399595i	$-0.130849\pi$
$709$	48.8176	1.83338	0.916692	+	0.399595i	$0.130849\pi$
$710$	42.6715	1.60143
$711$	−2.92592	−0.109731
$712$	5.68530	0.213066
$713$	−4.44476	−0.166458
$714$	−18.3023	−0.684947
$715$	23.7213	0.887125
$716$	0.413013	0.0154350
$717$	−43.1490	−1.61143
$718$	−9.19223	−0.343051
$719$	47.1606	1.75879	0.879396	−	0.476091i	$-0.157947\pi$
$719$	47.1606	1.75879	0.879396	+	0.476091i	$0.157947\pi$
$720$	−2.49727	−0.0930677
$721$	57.4472	2.13944
$722$	−1.00000	−0.0372161
$723$	−24.3280	−0.904767
$724$	−25.7154	−0.955706
$725$	−4.29015	−0.159332
$726$	−17.2267	−0.639343
$727$	−3.14750	−0.116734	−0.0583672	−	0.998295i	$-0.518589\pi$
$727$	−3.14750	−0.116734	−0.0583672	+	0.998295i	$0.518589\pi$
$728$	−17.1910	−0.637142
$729$	14.3363	0.530975
$730$	18.2799	0.676571
$731$	−18.0753	−0.668539
$732$	10.8793	0.402112
$733$	12.5536	0.463679	0.231840	−	0.972754i	$-0.425526\pi$
$733$	12.5536	0.463679	0.231840	+	0.972754i	$0.425526\pi$
$734$	5.67002	0.209284
$735$	9.76687	0.360256
$736$	4.86069	0.179167
$737$	16.4954	0.607617
$738$	−7.10856	−0.261670
$739$	30.5467	1.12368	0.561839	−	0.827246i	$-0.310094\pi$
$739$	30.5467	1.12368	0.561839	+	0.827246i	$0.310094\pi$
$740$	−21.7222	−0.798522
$741$	−11.4640	−0.421140
$742$	14.3118	0.525404
$743$	18.1305	0.665142	0.332571	−	0.943078i	$-0.392084\pi$
$743$	18.1305	0.665142	0.332571	+	0.943078i	$0.392084\pi$
$744$	1.81159	0.0664160
$745$	−41.2568	−1.51153
$746$	24.5262	0.897968
$747$	1.54437	0.0565055
$748$	4.72078	0.172609
$749$	−45.7593	−1.67201
$750$	14.4875	0.529009
$751$	45.6982	1.66755	0.833776	−	0.552103i	$-0.186174\pi$
$751$	45.6982	1.66755	0.833776	+	0.552103i	$0.186174\pi$
$752$	−5.88087	−0.214453
$753$	35.6466	1.29903
$754$	10.8319	0.394475
$755$	46.2805	1.68432
$756$	12.2136	0.444205
$757$	13.9401	0.506660	0.253330	−	0.967380i	$-0.418474\pi$
$757$	13.9401	0.506660	0.253330	+	0.967380i	$0.418474\pi$
$758$	32.6356	1.18538
$759$	−14.6183	−0.530610
$760$	2.70035	0.0979521
$761$	19.0449	0.690379	0.345189	−	0.938533i	$-0.387815\pi$
$761$	19.0449	0.690379	0.345189	+	0.938533i	$0.387815\pi$
$762$	−3.46728	−0.125606
$763$	−21.1075	−0.764143
$764$	−18.5631	−0.671588
$765$	7.76585	0.280775
$766$	−12.8683	−0.464951
$767$	66.0740	2.38579
$768$	−1.98111	−0.0714871
$769$	−14.4103	−0.519649	−0.259825	−	0.965656i	$-0.583665\pi$
$769$	−14.4103	−0.519649	−0.259825	+	0.965656i	$0.583665\pi$
$770$	−12.1782	−0.438873
$771$	−5.76531	−0.207632
$772$	22.2164	0.799584
$773$	3.37379	0.121347	0.0606735	−	0.998158i	$-0.480675\pi$
$773$	3.37379	0.121347	0.0606735	+	0.998158i	$0.480675\pi$
$774$	−5.37535	−0.193213
$775$	2.09578	0.0752827
$776$	5.64199	0.202535
$777$	−47.3440	−1.69846
$778$	−8.97385	−0.321728
$779$	7.68665	0.275403
$780$	30.9568	1.10843
$781$	−23.9888	−0.858386
$782$	−15.1155	−0.540528
$783$	−7.69568	−0.275021
$784$	1.82569	0.0652031
$785$	−36.3668	−1.29799
$786$	−7.50159	−0.267573
$787$	0.515944	0.0183914	0.00919571	−	0.999958i	$-0.497073\pi$
$787$	0.515944	0.0183914	0.00919571	+	0.999958i	$0.497073\pi$
$788$	−19.5952	−0.698050
$789$	−6.71125	−0.238927
$790$	−8.54354	−0.303965
$791$	31.3295	1.11395
$792$	1.40390	0.0498853
$793$	−31.7777	−1.12846
$794$	−18.1322	−0.643486
$795$	−25.7721	−0.914043
$796$	19.1677	0.679380
$797$	−3.42194	−0.121211	−0.0606056	−	0.998162i	$-0.519303\pi$
$797$	−3.42194	−0.121211	−0.0606056	+	0.998162i	$0.519303\pi$
$798$	5.88549	0.208344
$799$	18.2879	0.646981
$800$	−2.29190	−0.0810309
$801$	−5.25773	−0.185773
$802$	−14.0458	−0.495974
$803$	−10.2765	−0.362649
$804$	21.5269	0.759196
$805$	38.9935	1.37434
$806$	−5.29149	−0.186385
$807$	−29.4063	−1.03515
$808$	−8.08322	−0.284367
$809$	53.8766	1.89420	0.947100	−	0.320938i	$-0.103998\pi$
$809$	53.8766	1.89420	0.947100	+	0.320938i	$0.103998\pi$
$810$	−29.4855	−1.03602
$811$	−43.2751	−1.51960	−0.759798	−	0.650160i	$-0.774702\pi$
$811$	−43.2751	−1.51960	−0.759798	+	0.650160i	$0.774702\pi$
$812$	−5.56098	−0.195152
$813$	49.3760	1.73169
$814$	12.2116	0.428016
$815$	54.8468	1.92120
$816$	6.16073	0.215669
$817$	5.81248	0.203353
$818$	22.6422	0.791666
$819$	15.8982	0.555527
$820$	−20.7567	−0.724854
$821$	−7.12338	−0.248608	−0.124304	−	0.992244i	$-0.539670\pi$
$821$	−7.12338	−0.248608	−0.124304	+	0.992244i	$0.539670\pi$
$822$	−19.4123	−0.677082
$823$	23.8149	0.830134	0.415067	−	0.909791i	$-0.363758\pi$
$823$	23.8149	0.830134	0.415067	+	0.909791i	$0.363758\pi$
$824$	−19.3372	−0.673645
$825$	6.89277	0.239976
$826$	−33.9217	−1.18029
$827$	50.0690	1.74107	0.870534	−	0.492108i	$-0.163773\pi$
$827$	50.0690	1.74107	0.870534	+	0.492108i	$0.163773\pi$
$828$	−4.49514	−0.156217
$829$	26.8993	0.934253	0.467126	−	0.884191i	$-0.345289\pi$
$829$	26.8993	0.934253	0.467126	+	0.884191i	$0.345289\pi$
$830$	4.50948	0.156526
$831$	−0.589524	−0.0204503
$832$	5.78666	0.200616
$833$	−5.67741	−0.196710
$834$	−12.7366	−0.441033
$835$	47.3862	1.63987
$836$	−1.51806	−0.0525033
$837$	3.75942	0.129944
$838$	−4.10907	−0.141945
$839$	9.48976	0.327623	0.163811	−	0.986492i	$-0.447621\pi$
$839$	9.48976	0.327623	0.163811	+	0.986492i	$0.447621\pi$
$840$	−15.8929	−0.548357
$841$	−25.4961	−0.879175
$842$	17.8849	0.616355
$843$	−34.4253	−1.18567
$844$	−1.00000	−0.0344214
$845$	−55.3178	−1.90299
$846$	5.43859	0.186983
$847$	−25.8326	−0.887618
$848$	−4.81750	−0.165434
$849$	27.2586	0.935513
$850$	7.12720	0.244461
$851$	−39.1003	−1.34034
$852$	−31.3059	−1.07252
$853$	−10.6291	−0.363933	−0.181967	−	0.983305i	$-0.558246\pi$
$853$	−10.6291	−0.363933	−0.181967	+	0.983305i	$0.558246\pi$
$854$	16.3143	0.558264
$855$	−2.49727	−0.0854048
$856$	15.4030	0.526463
$857$	1.26377	0.0431696	0.0215848	−	0.999767i	$-0.493129\pi$
$857$	1.26377	0.0431696	0.0215848	+	0.999767i	$0.493129\pi$
$858$	−17.4031	−0.594131
$859$	−10.2035	−0.348139	−0.174070	−	0.984733i	$-0.555692\pi$
$859$	−10.2035	−0.348139	−0.174070	+	0.984733i	$0.555692\pi$
$860$	−15.6958	−0.535221
$861$	−45.2397	−1.54176
$862$	−19.8837	−0.677243
$863$	45.8913	1.56216	0.781078	−	0.624433i	$-0.214670\pi$
$863$	45.8913	1.56216	0.781078	+	0.624433i	$0.214670\pi$
$864$	−4.11121	−0.139866
$865$	53.4271	1.81658
$866$	10.7142	0.364082
$867$	14.5206	0.493146
$868$	2.71660	0.0922073
$869$	4.80294	0.162929
$870$	10.0140	0.339505
$871$	−62.8784	−2.13055
$872$	7.10497	0.240605
$873$	−5.21767	−0.176592
$874$	4.86069	0.164415
$875$	21.7250	0.734438
$876$	−13.4110	−0.453117
$877$	10.7449	0.362828	0.181414	−	0.983407i	$-0.441933\pi$
$877$	10.7449	0.362828	0.181414	+	0.983407i	$0.441933\pi$
$878$	−14.7793	−0.498777
$879$	23.1289	0.780118
$880$	4.09931	0.138188
$881$	47.7663	1.60929	0.804644	−	0.593758i	$-0.202356\pi$
$881$	47.7663	1.60929	0.804644	+	0.593758i	$0.202356\pi$
$882$	−1.68838	−0.0568509
$883$	−13.1088	−0.441147	−0.220574	−	0.975370i	$-0.570793\pi$
$883$	−13.1088	−0.441147	−0.220574	+	0.975370i	$0.570793\pi$
$884$	−17.9950	−0.605236
$885$	61.0846	2.05334
$886$	−35.9311	−1.20713
$887$	27.3257	0.917508	0.458754	−	0.888563i	$-0.348296\pi$
$887$	27.3257	0.917508	0.458754	+	0.888563i	$0.348296\pi$
$888$	15.9364	0.534791
$889$	−5.19942	−0.174383
$890$	−15.3523	−0.514611
$891$	16.5759	0.555315
$892$	19.8589	0.664925
$893$	−5.88087	−0.196796
$894$	30.2680	1.01231
$895$	−1.11528	−0.0372797
$896$	−2.97081	−0.0992477
$897$	55.7230	1.86054
$898$	−37.0040	−1.23484
$899$	−1.71170	−0.0570884
$900$	2.11953	0.0706512
$901$	14.9811	0.499094
$902$	11.6688	0.388529
$903$	−34.2093	−1.13841
$904$	−10.5458	−0.350748
$905$	69.4407	2.30829
$906$	−33.9537	−1.12803
$907$	29.6135	0.983301	0.491651	−	0.870793i	$-0.336394\pi$
$907$	29.6135	0.983301	0.491651	+	0.870793i	$0.336394\pi$
$908$	23.9873	0.796047
$909$	7.47531	0.247941
$910$	46.4218	1.53887
$911$	−20.8982	−0.692389	−0.346195	−	0.938163i	$-0.612526\pi$
$911$	−20.8982	−0.692389	−0.346195	+	0.938163i	$0.612526\pi$
$912$	−1.98111	−0.0656011
$913$	−2.53510	−0.0838997
$914$	−30.5269	−1.00974
$915$	−29.3781	−0.971209
$916$	−1.81717	−0.0600409
$917$	−11.2491	−0.371479
$918$	12.7848	0.421961
$919$	−25.6445	−0.845932	−0.422966	−	0.906145i	$-0.639011\pi$
$919$	−25.6445	−0.845932	−0.422966	+	0.906145i	$0.639011\pi$
$920$	−13.1256	−0.432737
$921$	−17.5491	−0.578261
$922$	21.5693	0.710347
$923$	91.4420	3.00985
$924$	8.93455	0.293925
$925$	18.4365	0.606188
$926$	−18.6129	−0.611658
$927$	17.8830	0.587353
$928$	1.87188	0.0614474
$929$	−53.7023	−1.76191	−0.880957	−	0.473196i	$-0.843100\pi$
$929$	−53.7023	−1.76191	−0.880957	+	0.473196i	$0.843100\pi$
$930$	−4.89192	−0.160412
$931$	1.82569	0.0598345
$932$	−15.2008	−0.497919
$933$	−59.7797	−1.95710
$934$	3.98437	0.130372
$935$	−12.7478	−0.416896
$936$	−5.35146	−0.174918
$937$	23.0814	0.754037	0.377018	−	0.926206i	$-0.376949\pi$
$937$	23.0814	0.754037	0.377018	+	0.926206i	$0.376949\pi$
$938$	32.2811	1.05401
$939$	25.0866	0.818671
$940$	15.8804	0.517962
$941$	−10.5620	−0.344311	−0.172156	−	0.985070i	$-0.555073\pi$
$941$	−10.5620	−0.344311	−0.172156	+	0.985070i	$0.555073\pi$
$942$	26.6805	0.869297
$943$	−37.3624	−1.21669
$944$	11.4183	0.371635
$945$	−32.9810	−1.07287
$946$	8.82372	0.286884
$947$	44.9707	1.46135	0.730675	−	0.682725i	$-0.239205\pi$
$947$	44.9707	1.46135	0.730675	+	0.682725i	$0.239205\pi$
$948$	6.26795	0.203574
$949$	39.1726	1.27160
$950$	−2.29190	−0.0743590
$951$	−51.1952	−1.66012
$952$	9.23842	0.299419
$953$	−27.3190	−0.884949	−0.442475	−	0.896781i	$-0.645899\pi$
$953$	−27.3190	−0.884949	−0.442475	+	0.896781i	$0.645899\pi$
$954$	4.45519	0.144242
$955$	50.1268	1.62207
$956$	21.7802	0.704422
$957$	−5.62958	−0.181978
$958$	23.3867	0.755589
$959$	−29.1101	−0.940013
$960$	5.34969	0.172661
$961$	−30.1638	−0.973026
$962$	−46.5490	−1.50080
$963$	−14.2446	−0.459025
$964$	12.2800	0.395512
$965$	−59.9920	−1.93121
$966$	−28.6076	−0.920433
$967$	49.9349	1.60580	0.802899	−	0.596115i	$-0.203290\pi$
$967$	49.9349	1.60580	0.802899	+	0.596115i	$0.203290\pi$
$968$	8.69548	0.279483
$969$	6.16073	0.197911
$970$	−15.2353	−0.489178
$971$	8.73528	0.280329	0.140164	−	0.990128i	$-0.455237\pi$
$971$	8.73528	0.280329	0.140164	+	0.990128i	$0.455237\pi$
$972$	9.29837	0.298246
$973$	−19.0994	−0.612299
$974$	17.2521	0.552794
$975$	−26.2743	−0.841452
$976$	−5.49154	−0.175780
$977$	−16.1986	−0.518238	−0.259119	−	0.965845i	$-0.583432\pi$
$977$	−16.1986	−0.518238	−0.259119	+	0.965845i	$0.583432\pi$
$978$	−40.2383	−1.28668
$979$	8.63065	0.275837
$980$	−4.93000	−0.157483
$981$	−6.57064	−0.209784
$982$	36.5647	1.16683
$983$	−9.47939	−0.302346	−0.151173	−	0.988507i	$-0.548305\pi$
$983$	−9.47939	−0.302346	−0.151173	+	0.988507i	$0.548305\pi$
$984$	15.2281	0.485454
$985$	52.9140	1.68598
$986$	−5.82104	−0.185380
$987$	34.6118	1.10171
$988$	5.78666	0.184098
$989$	−28.2527	−0.898383
$990$	−3.79101	−0.120486
$991$	3.45503	0.109753	0.0548764	−	0.998493i	$-0.482524\pi$
$991$	3.45503	0.109753	0.0548764	+	0.998493i	$0.482524\pi$
$992$	−0.914430	−0.0290332
$993$	−37.6706	−1.19544
$994$	−46.9453	−1.48902
$995$	−51.7595	−1.64089
$996$	−3.30837	−0.104830
$997$	2.56284	0.0811661	0.0405830	−	0.999176i	$-0.487078\pi$
$997$	2.56284	0.0811661	0.0405830	+	0.999176i	$0.487078\pi$
$998$	−31.1919	−0.987362
$999$	33.0714	1.04633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.i.1.11	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.i.1.11	✓	43	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.98111 q^{3} +1.00000 q^{4} -2.70035 q^{5} +1.98111 q^{6} +2.97081 q^{7} -1.00000 q^{8} +0.924794 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.98111 q^{3} +1.00000 q^{4} -2.70035 q^{5} +1.98111 q^{6} +2.97081 q^{7} -1.00000 q^{8} +0.924794 q^{9} +2.70035 q^{10} -1.51806 q^{11} -1.98111 q^{12} +5.78666 q^{13} -2.97081 q^{14} +5.34969 q^{15} +1.00000 q^{16} -3.10974 q^{17} -0.924794 q^{18} +1.00000 q^{19} -2.70035 q^{20} -5.88549 q^{21} +1.51806 q^{22} -4.86069 q^{23} +1.98111 q^{24} +2.29190 q^{25} -5.78666 q^{26} +4.11121 q^{27} +2.97081 q^{28} -1.87188 q^{29} -5.34969 q^{30} +0.914430 q^{31} -1.00000 q^{32} +3.00745 q^{33} +3.10974 q^{34} -8.02222 q^{35} +0.924794 q^{36} +8.04419 q^{37} -1.00000 q^{38} -11.4640 q^{39} +2.70035 q^{40} +7.68665 q^{41} +5.88549 q^{42} +5.81248 q^{43} -1.51806 q^{44} -2.49727 q^{45} +4.86069 q^{46} -5.88087 q^{47} -1.98111 q^{48} +1.82569 q^{49} -2.29190 q^{50} +6.16073 q^{51} +5.78666 q^{52} -4.81750 q^{53} -4.11121 q^{54} +4.09931 q^{55} -2.97081 q^{56} -1.98111 q^{57} +1.87188 q^{58} +11.4183 q^{59} +5.34969 q^{60} -5.49154 q^{61} -0.914430 q^{62} +2.74738 q^{63} +1.00000 q^{64} -15.6260 q^{65} -3.00745 q^{66} -10.8661 q^{67} -3.10974 q^{68} +9.62956 q^{69} +8.02222 q^{70} +15.8022 q^{71} -0.924794 q^{72} +6.76947 q^{73} -8.04419 q^{74} -4.54050 q^{75} +1.00000 q^{76} -4.50987 q^{77} +11.4640 q^{78} -3.16386 q^{79} -2.70035 q^{80} -10.9191 q^{81} -7.68665 q^{82} +1.66996 q^{83} -5.88549 q^{84} +8.39738 q^{85} -5.81248 q^{86} +3.70839 q^{87} +1.51806 q^{88} -5.68530 q^{89} +2.49727 q^{90} +17.1910 q^{91} -4.86069 q^{92} -1.81159 q^{93} +5.88087 q^{94} -2.70035 q^{95} +1.98111 q^{96} -5.64199 q^{97} -1.82569 q^{98} -1.40390 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9}+O(q^{10}) \) 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9	\( 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9} + 14 q^{11} + 3 q^{13} - 19 q^{14} + q^{15} + 43 q^{16} + 8 q^{17} - 53 q^{18} + 43 q^{19} - 14 q^{22} + 43 q^{23} + 97 q^{25} - 3 q^{26} + 15 q^{27} + 19 q^{28} - 25 q^{29} - q^{30} + 22 q^{31} - 43 q^{32} + 22 q^{33} - 8 q^{34} - 6 q^{35} + 53 q^{36} + 42 q^{37} - 43 q^{38} + 9 q^{39} - 40 q^{41} + 72 q^{43} + 14 q^{44} - q^{45} - 43 q^{46} + 27 q^{47} + 86 q^{49} - 97 q^{50} - 3 q^{51} + 3 q^{52} - 5 q^{53} - 15 q^{54} + 86 q^{55} - 19 q^{56} + 25 q^{58} - 43 q^{59} + q^{60} + 31 q^{61} - 22 q^{62} + 38 q^{63} + 43 q^{64} - 32 q^{65} - 22 q^{66} + 15 q^{67} + 8 q^{68} - 7 q^{69} + 6 q^{70} + 14 q^{71} - 53 q^{72} + 93 q^{73} - 42 q^{74} - 13 q^{75} + 43 q^{76} + 38 q^{77} - 9 q^{78} + 15 q^{79} + 43 q^{81} + 40 q^{82} + 34 q^{83} + 16 q^{85} - 72 q^{86} + 60 q^{87} - 14 q^{88} - 37 q^{89} + q^{90} - 3 q^{91} + 43 q^{92} + 19 q^{93} - 27 q^{94} + 27 q^{97} - 86 q^{98} - 24 q^{99}+O(q^{100}) \) 43 * q - 43 * q^2 + 43 * q^4 + 19 * q^7 - 43 * q^8 + 53 * q^9 + 14 * q^11 + 3 * q^13 - 19 * q^14 + q^15 + 43 * q^16 + 8 * q^17 - 53 * q^18 + 43 * q^19 - 14 * q^22 + 43 * q^23 + 97 * q^25 - 3 * q^26 + 15 * q^27 + 19 * q^28 - 25 * q^29 - q^30 + 22 * q^31 - 43 * q^32 + 22 * q^33 - 8 * q^34 - 6 * q^35 + 53 * q^36 + 42 * q^37 - 43 * q^38 + 9 * q^39 - 40 * q^41 + 72 * q^43 + 14 * q^44 - q^45 - 43 * q^46 + 27 * q^47 + 86 * q^49 - 97 * q^50 - 3 * q^51 + 3 * q^52 - 5 * q^53 - 15 * q^54 + 86 * q^55 - 19 * q^56 + 25 * q^58 - 43 * q^59 + q^60 + 31 * q^61 - 22 * q^62 + 38 * q^63 + 43 * q^64 - 32 * q^65 - 22 * q^66 + 15 * q^67 + 8 * q^68 - 7 * q^69 + 6 * q^70 + 14 * q^71 - 53 * q^72 + 93 * q^73 - 42 * q^74 - 13 * q^75 + 43 * q^76 + 38 * q^77 - 9 * q^78 + 15 * q^79 + 43 * q^81 + 40 * q^82 + 34 * q^83 + 16 * q^85 - 72 * q^86 + 60 * q^87 - 14 * q^88 - 37 * q^89 + q^90 - 3 * q^91 + 43 * q^92 + 19 * q^93 - 27 * q^94 + 27 * q^97 - 86 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

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Database

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