LMFDB - Embedded newform 8381.2.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8381,2,Mod(1,8381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8381, 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("8381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8381 = 17^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8381.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:	$66.9226219340$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	8381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.414214 q^{2} +0.414214 q^{3} -1.82843 q^{4} +1.00000 q^{5} +0.171573 q^{6} -2.82843 q^{7} -1.58579 q^{8} -2.82843 q^{9} +O(q^{10})$	\(q+0.414214 q^{2} +0.414214 q^{3} -1.82843 q^{4} +1.00000 q^{5} +0.171573 q^{6} -2.82843 q^{7} -1.58579 q^{8} -2.82843 q^{9} +0.414214 q^{10} -2.41421 q^{11} -0.757359 q^{12} +1.82843 q^{13} -1.17157 q^{14} +0.414214 q^{15} +3.00000 q^{16} -1.17157 q^{18} +6.00000 q^{19} -1.82843 q^{20} -1.17157 q^{21} -1.00000 q^{22} +7.65685 q^{23} -0.656854 q^{24} -4.00000 q^{25} +0.757359 q^{26} -2.41421 q^{27} +5.17157 q^{28} -1.00000 q^{29} +0.171573 q^{30} +4.07107 q^{31} +4.41421 q^{32} -1.00000 q^{33} -2.82843 q^{35} +5.17157 q^{36} +4.00000 q^{37} +2.48528 q^{38} +0.757359 q^{39} -1.58579 q^{40} -12.4853 q^{41} -0.485281 q^{42} +6.41421 q^{43} +4.41421 q^{44} -2.82843 q^{45} +3.17157 q^{46} +5.24264 q^{47} +1.24264 q^{48} +1.00000 q^{49} -1.65685 q^{50} -3.34315 q^{52} -7.48528 q^{53} -1.00000 q^{54} -2.41421 q^{55} +4.48528 q^{56} +2.48528 q^{57} -0.414214 q^{58} +7.65685 q^{59} -0.757359 q^{60} -0.828427 q^{61} +1.68629 q^{62} +8.00000 q^{63} -4.17157 q^{64} +1.82843 q^{65} -0.414214 q^{66} -5.65685 q^{67} +3.17157 q^{69} -1.17157 q^{70} +3.17157 q^{71} +4.48528 q^{72} -4.00000 q^{73} +1.65685 q^{74} -1.65685 q^{75} -10.9706 q^{76} +6.82843 q^{77} +0.313708 q^{78} -0.414214 q^{79} +3.00000 q^{80} +7.48528 q^{81} -5.17157 q^{82} -3.65685 q^{83} +2.14214 q^{84} +2.65685 q^{86} -0.414214 q^{87} +3.82843 q^{88} +4.48528 q^{89} -1.17157 q^{90} -5.17157 q^{91} -14.0000 q^{92} +1.68629 q^{93} +2.17157 q^{94} +6.00000 q^{95} +1.82843 q^{96} +12.4853 q^{97} +0.414214 q^{98} +6.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 6 q^{6} - 6 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 6 * q^6 - 6 * q^8	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 6 q^{6} - 6 q^{8} - 2 q^{10} - 2 q^{11} - 10 q^{12} - 2 q^{13} - 8 q^{14} - 2 q^{15} + 6 q^{16} - 8 q^{18} + 12 q^{19} + 2 q^{20} - 8 q^{21} - 2 q^{22} + 4 q^{23} + 10 q^{24} - 8 q^{25} + 10 q^{26} - 2 q^{27} + 16 q^{28} - 2 q^{29} + 6 q^{30} - 6 q^{31} + 6 q^{32} - 2 q^{33} + 16 q^{36} + 8 q^{37} - 12 q^{38} + 10 q^{39} - 6 q^{40} - 8 q^{41} + 16 q^{42} + 10 q^{43} + 6 q^{44} + 12 q^{46} + 2 q^{47} - 6 q^{48} + 2 q^{49} + 8 q^{50} - 18 q^{52} + 2 q^{53} - 2 q^{54} - 2 q^{55} - 8 q^{56} - 12 q^{57} + 2 q^{58} + 4 q^{59} - 10 q^{60} + 4 q^{61} + 26 q^{62} + 16 q^{63} - 14 q^{64} - 2 q^{65} + 2 q^{66} + 12 q^{69} - 8 q^{70} + 12 q^{71} - 8 q^{72} - 8 q^{73} - 8 q^{74} + 8 q^{75} + 12 q^{76} + 8 q^{77} - 22 q^{78} + 2 q^{79} + 6 q^{80} - 2 q^{81} - 16 q^{82} + 4 q^{83} - 24 q^{84} - 6 q^{86} + 2 q^{87} + 2 q^{88} - 8 q^{89} - 8 q^{90} - 16 q^{91} - 28 q^{92} + 26 q^{93} + 10 q^{94} + 12 q^{95} - 2 q^{96} + 8 q^{97} - 2 q^{98} + 8 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 6 * q^6 - 6 * q^8 - 2 * q^10 - 2 * q^11 - 10 * q^12 - 2 * q^13 - 8 * q^14 - 2 * q^15 + 6 * q^16 - 8 * q^18 + 12 * q^19 + 2 * q^20 - 8 * q^21 - 2 * q^22 + 4 * q^23 + 10 * q^24 - 8 * q^25 + 10 * q^26 - 2 * q^27 + 16 * q^28 - 2 * q^29 + 6 * q^30 - 6 * q^31 + 6 * q^32 - 2 * q^33 + 16 * q^36 + 8 * q^37 - 12 * q^38 + 10 * q^39 - 6 * q^40 - 8 * q^41 + 16 * q^42 + 10 * q^43 + 6 * q^44 + 12 * q^46 + 2 * q^47 - 6 * q^48 + 2 * q^49 + 8 * q^50 - 18 * q^52 + 2 * q^53 - 2 * q^54 - 2 * q^55 - 8 * q^56 - 12 * q^57 + 2 * q^58 + 4 * q^59 - 10 * q^60 + 4 * q^61 + 26 * q^62 + 16 * q^63 - 14 * q^64 - 2 * q^65 + 2 * q^66 + 12 * q^69 - 8 * q^70 + 12 * q^71 - 8 * q^72 - 8 * q^73 - 8 * q^74 + 8 * q^75 + 12 * q^76 + 8 * q^77 - 22 * q^78 + 2 * q^79 + 6 * q^80 - 2 * q^81 - 16 * q^82 + 4 * q^83 - 24 * q^84 - 6 * q^86 + 2 * q^87 + 2 * q^88 - 8 * q^89 - 8 * q^90 - 16 * q^91 - 28 * q^92 + 26 * q^93 + 10 * q^94 + 12 * q^95 - 2 * q^96 + 8 * q^97 - 2 * q^98 + 8 * 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 $

$2$	0.414214	0.292893	0.146447	−	0.989219i	$-0.453216\pi$
$2$	0.414214	0.292893	0.146447	+	0.989219i	$0.453216\pi$
$3$	0.414214	0.239146	0.119573	−	0.992825i	$-0.461847\pi$
$3$	0.414214	0.239146	0.119573	+	0.992825i	$0.461847\pi$
$4$	−1.82843	−0.914214
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	0.171573	0.0700443
$7$	−2.82843	−1.06904	−0.534522	−	0.845154i	$-0.679509\pi$
$7$	−2.82843	−1.06904	−0.534522	+	0.845154i	$0.679509\pi$
$8$	−1.58579	−0.560660
$9$	−2.82843	−0.942809
$10$	0.414214	0.130986
$11$	−2.41421	−0.727913	−0.363956	−	0.931416i	$-0.618574\pi$
$11$	−2.41421	−0.727913	−0.363956	+	0.931416i	$0.618574\pi$
$12$	−0.757359	−0.218631
$13$	1.82843	0.507114	0.253557	−	0.967320i	$-0.418399\pi$
$13$	1.82843	0.507114	0.253557	+	0.967320i	$0.418399\pi$
$14$	−1.17157	−0.313116
$15$	0.414214	0.106949
$16$	3.00000	0.750000
$17$	0	0
$17$	0	0
$18$	−1.17157	−0.276142
$19$	6.00000	1.37649	0.688247	−	0.725476i	$-0.258380\pi$
$19$	6.00000	1.37649	0.688247	+	0.725476i	$0.258380\pi$
$20$	−1.82843	−0.408849
$21$	−1.17157	−0.255658
$22$	−1.00000	−0.213201
$23$	7.65685	1.59656	0.798282	−	0.602284i	$-0.205742\pi$
$23$	7.65685	1.59656	0.798282	+	0.602284i	$0.205742\pi$
$24$	−0.656854	−0.134080
$25$	−4.00000	−0.800000
$26$	0.757359	0.148530
$27$	−2.41421	−0.464616
$28$	5.17157	0.977335
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0.171573	0.0313248
$31$	4.07107	0.731185	0.365593	−	0.930775i	$-0.380866\pi$
$31$	4.07107	0.731185	0.365593	+	0.930775i	$0.380866\pi$
$32$	4.41421	0.780330
$33$	−1.00000	−0.174078
$34$	0	0
$35$	−2.82843	−0.478091
$36$	5.17157	0.861929
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	2.48528	0.403166
$39$	0.757359	0.121275
$40$	−1.58579	−0.250735
$41$	−12.4853	−1.94987	−0.974937	−	0.222483i	$-0.928584\pi$
$41$	−12.4853	−1.94987	−0.974937	+	0.222483i	$0.928584\pi$
$42$	−0.485281	−0.0748805
$43$	6.41421	0.978158	0.489079	−	0.872239i	$-0.337333\pi$
$43$	6.41421	0.978158	0.489079	+	0.872239i	$0.337333\pi$
$44$	4.41421	0.665468
$45$	−2.82843	−0.421637
$46$	3.17157	0.467623
$47$	5.24264	0.764718	0.382359	−	0.924014i	$-0.375112\pi$
$47$	5.24264	0.764718	0.382359	+	0.924014i	$0.375112\pi$
$48$	1.24264	0.179360
$49$	1.00000	0.142857
$50$	−1.65685	−0.234315
$51$	0	0
$52$	−3.34315	−0.463611
$53$	−7.48528	−1.02818	−0.514091	−	0.857736i	$-0.671871\pi$
$53$	−7.48528	−1.02818	−0.514091	+	0.857736i	$0.671871\pi$
$54$	−1.00000	−0.136083
$55$	−2.41421	−0.325532
$56$	4.48528	0.599371
$57$	2.48528	0.329184
$58$	−0.414214	−0.0543889
$59$	7.65685	0.996838	0.498419	−	0.866936i	$-0.333914\pi$
$59$	7.65685	0.996838	0.498419	+	0.866936i	$0.333914\pi$
$60$	−0.757359	−0.0977747
$61$	−0.828427	−0.106069	−0.0530346	−	0.998593i	$-0.516889\pi$
$61$	−0.828427	−0.106069	−0.0530346	+	0.998593i	$0.516889\pi$
$62$	1.68629	0.214159
$63$	8.00000	1.00791
$64$	−4.17157	−0.521447
$65$	1.82843	0.226788
$66$	−0.414214	−0.0509862
$67$	−5.65685	−0.691095	−0.345547	−	0.938401i	$-0.612307\pi$
$67$	−5.65685	−0.691095	−0.345547	+	0.938401i	$0.612307\pi$
$68$	0	0
$69$	3.17157	0.381813
$70$	−1.17157	−0.140030
$71$	3.17157	0.376396	0.188198	−	0.982131i	$-0.439735\pi$
$71$	3.17157	0.376396	0.188198	+	0.982131i	$0.439735\pi$
$72$	4.48528	0.528595
$73$	−4.00000	−0.468165	−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000	−0.468165	−0.234082	+	0.972217i	$0.575209\pi$
$74$	1.65685	0.192605
$75$	−1.65685	−0.191317
$76$	−10.9706	−1.25841
$77$	6.82843	0.778171
$78$	0.313708	0.0355205
$79$	−0.414214	−0.0466027	−0.0233013	−	0.999728i	$-0.507418\pi$
$79$	−0.414214	−0.0466027	−0.0233013	+	0.999728i	$0.507418\pi$
$80$	3.00000	0.335410
$81$	7.48528	0.831698
$82$	−5.17157	−0.571105
$83$	−3.65685	−0.401392	−0.200696	−	0.979654i	$-0.564320\pi$
$83$	−3.65685	−0.401392	−0.200696	+	0.979654i	$0.564320\pi$
$84$	2.14214	0.233726
$85$	0	0
$86$	2.65685	0.286496
$87$	−0.414214	−0.0444084
$88$	3.82843	0.408112
$89$	4.48528	0.475439	0.237719	−	0.971334i	$-0.423600\pi$
$89$	4.48528	0.475439	0.237719	+	0.971334i	$0.423600\pi$
$90$	−1.17157	−0.123495
$91$	−5.17157	−0.542128
$92$	−14.0000	−1.45960
$93$	1.68629	0.174860
$94$	2.17157	0.223981
$95$	6.00000	0.615587
$96$	1.82843	0.186613
$97$	12.4853	1.26769	0.633844	−	0.773461i	$-0.281476\pi$
$97$	12.4853	1.26769	0.633844	+	0.773461i	$0.281476\pi$
$98$	0.414214	0.0418419
$99$	6.82843	0.686283
$100$	7.31371	0.731371
$101$	−13.6569	−1.35891	−0.679454	−	0.733718i	$-0.737783\pi$
$101$	−13.6569	−1.35891	−0.679454	+	0.733718i	$0.737783\pi$
$102$	0	0
$103$	0.828427	0.0816274	0.0408137	−	0.999167i	$-0.487005\pi$
$103$	0.828427	0.0816274	0.0408137	+	0.999167i	$0.487005\pi$
$104$	−2.89949	−0.284319
$105$	−1.17157	−0.114334
$106$	−3.10051	−0.301148
$107$	9.17157	0.886649	0.443325	−	0.896361i	$-0.353799\pi$
$107$	9.17157	0.886649	0.443325	+	0.896361i	$0.353799\pi$
$108$	4.41421	0.424758
$109$	−1.34315	−0.128650	−0.0643250	−	0.997929i	$-0.520489\pi$
$109$	−1.34315	−0.128650	−0.0643250	+	0.997929i	$0.520489\pi$
$110$	−1.00000	−0.0953463
$111$	1.65685	0.157262
$112$	−8.48528	−0.801784
$113$	−9.31371	−0.876160	−0.438080	−	0.898936i	$-0.644341\pi$
$113$	−9.31371	−0.876160	−0.438080	+	0.898936i	$0.644341\pi$
$114$	1.02944	0.0964156
$115$	7.65685	0.714005
$116$	1.82843	0.169765
$117$	−5.17157	−0.478112
$118$	3.17157	0.291967
$119$	0	0
$120$	−0.656854	−0.0599623
$121$	−5.17157	−0.470143
$122$	−0.343146	−0.0310670
$123$	−5.17157	−0.466305
$124$	−7.44365	−0.668460
$125$	−9.00000	−0.804984
$126$	3.31371	0.295209
$127$	−15.6569	−1.38932	−0.694661	−	0.719338i	$-0.744445\pi$
$127$	−15.6569	−1.38932	−0.694661	+	0.719338i	$0.744445\pi$
$128$	−10.5563	−0.933058
$129$	2.65685	0.233923
$130$	0.757359	0.0664248
$131$	1.31371	0.114779	0.0573896	−	0.998352i	$-0.481722\pi$
$131$	1.31371	0.114779	0.0573896	+	0.998352i	$0.481722\pi$
$132$	1.82843	0.159144
$133$	−16.9706	−1.47153
$134$	−2.34315	−0.202417
$135$	−2.41421	−0.207782
$136$	0	0
$137$	12.0000	1.02523	0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000	1.02523	0.512615	+	0.858619i	$0.328677\pi$
$138$	1.31371	0.111830
$139$	−14.0000	−1.18746	−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000	−1.18746	−0.593732	+	0.804663i	$0.702346\pi$
$140$	5.17157	0.437078
$141$	2.17157	0.182879
$142$	1.31371	0.110244
$143$	−4.41421	−0.369135
$144$	−8.48528	−0.707107
$145$	−1.00000	−0.0830455
$146$	−1.65685	−0.137122
$147$	0.414214	0.0341638
$148$	−7.31371	−0.601183
$149$	−2.17157	−0.177902	−0.0889511	−	0.996036i	$-0.528351\pi$
$149$	−2.17157	−0.177902	−0.0889511	+	0.996036i	$0.528351\pi$
$150$	−0.686292	−0.0560355
$151$	14.1421	1.15087	0.575435	−	0.817847i	$-0.304833\pi$
$151$	14.1421	1.15087	0.575435	+	0.817847i	$0.304833\pi$
$152$	−9.51472	−0.771746
$153$	0	0
$154$	2.82843	0.227921
$155$	4.07107	0.326996
$156$	−1.38478	−0.110871
$157$	−8.48528	−0.677199	−0.338600	−	0.940931i	$-0.609953\pi$
$157$	−8.48528	−0.677199	−0.338600	+	0.940931i	$0.609953\pi$
$158$	−0.171573	−0.0136496
$159$	−3.10051	−0.245886
$160$	4.41421	0.348974
$161$	−21.6569	−1.70680
$162$	3.10051	0.243599
$163$	−18.0711	−1.41544	−0.707718	−	0.706495i	$-0.750275\pi$
$163$	−18.0711	−1.41544	−0.707718	+	0.706495i	$0.750275\pi$
$164$	22.8284	1.78260
$165$	−1.00000	−0.0778499
$166$	−1.51472	−0.117565
$167$	8.82843	0.683164	0.341582	−	0.939852i	$-0.389037\pi$
$167$	8.82843	0.683164	0.341582	+	0.939852i	$0.389037\pi$
$168$	1.85786	0.143337
$169$	−9.65685	−0.742835
$170$	0	0
$171$	−16.9706	−1.29777
$172$	−11.7279	−0.894246
$173$	−23.6569	−1.79860	−0.899299	−	0.437335i	$-0.855922\pi$
$173$	−23.6569	−1.79860	−0.899299	+	0.437335i	$0.855922\pi$
$174$	−0.171573	−0.0130069
$175$	11.3137	0.855236
$176$	−7.24264	−0.545935
$177$	3.17157	0.238390
$178$	1.85786	0.139253
$179$	10.4853	0.783707	0.391853	−	0.920028i	$-0.371834\pi$
$179$	10.4853	0.783707	0.391853	+	0.920028i	$0.371834\pi$
$180$	5.17157	0.385466
$181$	14.3137	1.06393	0.531965	−	0.846766i	$-0.321454\pi$
$181$	14.3137	1.06393	0.531965	+	0.846766i	$0.321454\pi$
$182$	−2.14214	−0.158786
$183$	−0.343146	−0.0253661
$184$	−12.1421	−0.895130
$185$	4.00000	0.294086
$186$	0.698485	0.0512154
$187$	0	0
$188$	−9.58579	−0.699115
$189$	6.82843	0.496695
$190$	2.48528	0.180301
$191$	2.68629	0.194373	0.0971866	−	0.995266i	$-0.469016\pi$
$191$	2.68629	0.194373	0.0971866	+	0.995266i	$0.469016\pi$
$192$	−1.72792	−0.124702
$193$	10.8284	0.779447	0.389724	−	0.920932i	$-0.372571\pi$
$193$	10.8284	0.779447	0.389724	+	0.920932i	$0.372571\pi$
$194$	5.17157	0.371297
$195$	0.757359	0.0542356
$196$	−1.82843	−0.130602
$197$	−2.00000	−0.142494	−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000	−0.142494	−0.0712470	+	0.997459i	$0.522698\pi$
$198$	2.82843	0.201008
$199$	−16.4853	−1.16861	−0.584305	−	0.811534i	$-0.698633\pi$
$199$	−16.4853	−1.16861	−0.584305	+	0.811534i	$0.698633\pi$
$200$	6.34315	0.448528
$201$	−2.34315	−0.165273
$202$	−5.65685	−0.398015
$203$	2.82843	0.198517
$204$	0	0
$205$	−12.4853	−0.872010
$206$	0.343146	0.0239081
$207$	−21.6569	−1.50526
$208$	5.48528	0.380336
$209$	−14.4853	−1.00197
$210$	−0.485281	−0.0334876
$211$	−17.3848	−1.19682	−0.598409	−	0.801191i	$-0.704200\pi$
$211$	−17.3848	−1.19682	−0.598409	+	0.801191i	$0.704200\pi$
$212$	13.6863	0.939978
$213$	1.31371	0.0900138
$214$	3.79899	0.259694
$215$	6.41421	0.437446
$216$	3.82843	0.260491
$217$	−11.5147	−0.781670
$218$	−0.556349	−0.0376807
$219$	−1.65685	−0.111960
$220$	4.41421	0.297606
$221$	0	0
$222$	0.686292	0.0460609
$223$	−8.82843	−0.591195	−0.295598	−	0.955313i	$-0.595519\pi$
$223$	−8.82843	−0.591195	−0.295598	+	0.955313i	$0.595519\pi$
$224$	−12.4853	−0.834208
$225$	11.3137	0.754247
$226$	−3.85786	−0.256621
$227$	−20.1421	−1.33688	−0.668440	−	0.743766i	$-0.733038\pi$
$227$	−20.1421	−1.33688	−0.668440	+	0.743766i	$0.733038\pi$
$228$	−4.54416	−0.300944
$229$	−20.4853	−1.35371	−0.676853	−	0.736118i	$-0.736657\pi$
$229$	−20.4853	−1.35371	−0.676853	+	0.736118i	$0.736657\pi$
$230$	3.17157	0.209127
$231$	2.82843	0.186097
$232$	1.58579	0.104112
$233$	4.31371	0.282600	0.141300	−	0.989967i	$-0.454872\pi$
$233$	4.31371	0.282600	0.141300	+	0.989967i	$0.454872\pi$
$234$	−2.14214	−0.140036
$235$	5.24264	0.341992
$236$	−14.0000	−0.911322
$237$	−0.171573	−0.0111449
$238$	0	0
$239$	−8.34315	−0.539673	−0.269837	−	0.962906i	$-0.586970\pi$
$239$	−8.34315	−0.539673	−0.269837	+	0.962906i	$0.586970\pi$
$240$	1.24264	0.0802121
$241$	−4.31371	−0.277870	−0.138935	−	0.990301i	$-0.544368\pi$
$241$	−4.31371	−0.277870	−0.138935	+	0.990301i	$0.544368\pi$
$242$	−2.14214	−0.137702
$243$	10.3431	0.663513
$244$	1.51472	0.0969699
$245$	1.00000	0.0638877
$246$	−2.14214	−0.136578
$247$	10.9706	0.698040
$248$	−6.45584	−0.409947
$249$	−1.51472	−0.0959914
$250$	−3.72792	−0.235774
$251$	5.92893	0.374231	0.187115	−	0.982338i	$-0.440086\pi$
$251$	5.92893	0.374231	0.187115	+	0.982338i	$0.440086\pi$
$252$	−14.6274	−0.921441
$253$	−18.4853	−1.16216
$254$	−6.48528	−0.406923
$255$	0	0
$256$	3.97056	0.248160
$257$	−23.8284	−1.48638	−0.743188	−	0.669082i	$-0.766687\pi$
$257$	−23.8284	−1.48638	−0.743188	+	0.669082i	$0.766687\pi$
$258$	1.10051	0.0685145
$259$	−11.3137	−0.703000
$260$	−3.34315	−0.207333
$261$	2.82843	0.175075
$262$	0.544156	0.0336181
$263$	11.2426	0.693251	0.346625	−	0.938004i	$-0.387327\pi$
$263$	11.2426	0.693251	0.346625	+	0.938004i	$0.387327\pi$
$264$	1.58579	0.0975984
$265$	−7.48528	−0.459817
$266$	−7.02944	−0.431002
$267$	1.85786	0.113699
$268$	10.3431	0.631808
$269$	19.4558	1.18624	0.593122	−	0.805113i	$-0.297895\pi$
$269$	19.4558	1.18624	0.593122	+	0.805113i	$0.297895\pi$
$270$	−1.00000	−0.0608581
$271$	−14.5563	−0.884235	−0.442118	−	0.896957i	$-0.645773\pi$
$271$	−14.5563	−0.884235	−0.442118	+	0.896957i	$0.645773\pi$
$272$	0	0
$273$	−2.14214	−0.129648
$274$	4.97056	0.300283
$275$	9.65685	0.582330
$276$	−5.79899	−0.349058
$277$	−5.31371	−0.319270	−0.159635	−	0.987176i	$-0.551032\pi$
$277$	−5.31371	−0.319270	−0.159635	+	0.987176i	$0.551032\pi$
$278$	−5.79899	−0.347800
$279$	−11.5147	−0.689368
$280$	4.48528	0.268047
$281$	−1.97056	−0.117554	−0.0587770	−	0.998271i	$-0.518720\pi$
$281$	−1.97056	−0.117554	−0.0587770	+	0.998271i	$0.518720\pi$
$282$	0.899495	0.0535641
$283$	−0.343146	−0.0203979	−0.0101989	−	0.999948i	$-0.503246\pi$
$283$	−0.343146	−0.0203979	−0.0101989	+	0.999948i	$0.503246\pi$
$284$	−5.79899	−0.344107
$285$	2.48528	0.147215
$286$	−1.82843	−0.108117
$287$	35.3137	2.08450
$288$	−12.4853	−0.735702
$289$	0	0
$290$	−0.414214	−0.0243235
$291$	5.17157	0.303163
$292$	7.31371	0.428002
$293$	−3.65685	−0.213636	−0.106818	−	0.994279i	$-0.534066\pi$
$293$	−3.65685	−0.213636	−0.106818	+	0.994279i	$0.534066\pi$
$294$	0.171573	0.0100063
$295$	7.65685	0.445799
$296$	−6.34315	−0.368688
$297$	5.82843	0.338200
$298$	−0.899495	−0.0521063
$299$	14.0000	0.809641
$300$	3.02944	0.174905
$301$	−18.1421	−1.04570
$302$	5.85786	0.337082
$303$	−5.65685	−0.324978
$304$	18.0000	1.03237
$305$	−0.828427	−0.0474356
$306$	0	0
$307$	−16.8995	−0.964505	−0.482253	−	0.876032i	$-0.660181\pi$
$307$	−16.8995	−0.964505	−0.482253	+	0.876032i	$0.660181\pi$
$308$	−12.4853	−0.711415
$309$	0.343146	0.0195209
$310$	1.68629	0.0957749
$311$	−25.3137	−1.43541	−0.717704	−	0.696348i	$-0.754807\pi$
$311$	−25.3137	−1.43541	−0.717704	+	0.696348i	$0.754807\pi$
$312$	−1.20101	−0.0679938
$313$	−4.17157	−0.235791	−0.117896	−	0.993026i	$-0.537615\pi$
$313$	−4.17157	−0.235791	−0.117896	+	0.993026i	$0.537615\pi$
$314$	−3.51472	−0.198347
$315$	8.00000	0.450749
$316$	0.757359	0.0426048
$317$	−19.4558	−1.09275	−0.546375	−	0.837541i	$-0.683992\pi$
$317$	−19.4558	−1.09275	−0.546375	+	0.837541i	$0.683992\pi$
$318$	−1.28427	−0.0720184
$319$	2.41421	0.135170
$320$	−4.17157	−0.233198
$321$	3.79899	0.212039
$322$	−8.97056	−0.499910
$323$	0	0
$324$	−13.6863	−0.760350
$325$	−7.31371	−0.405692
$326$	−7.48528	−0.414571
$327$	−0.556349	−0.0307662
$328$	19.7990	1.09322
$329$	−14.8284	−0.817518
$330$	−0.414214	−0.0228017
$331$	0.414214	0.0227672	0.0113836	−	0.999935i	$-0.496376\pi$
$331$	0.414214	0.0227672	0.0113836	+	0.999935i	$0.496376\pi$
$332$	6.68629	0.366958
$333$	−11.3137	−0.619987
$334$	3.65685	0.200094
$335$	−5.65685	−0.309067
$336$	−3.51472	−0.191744
$337$	17.7990	0.969573	0.484786	−	0.874633i	$-0.338897\pi$
$337$	17.7990	0.969573	0.484786	+	0.874633i	$0.338897\pi$
$338$	−4.00000	−0.217571
$339$	−3.85786	−0.209530
$340$	0	0
$341$	−9.82843	−0.532239
$342$	−7.02944	−0.380108
$343$	16.9706	0.916324
$344$	−10.1716	−0.548414
$345$	3.17157	0.170752
$346$	−9.79899	−0.526797
$347$	14.4853	0.777611	0.388805	−	0.921320i	$-0.372888\pi$
$347$	14.4853	0.777611	0.388805	+	0.921320i	$0.372888\pi$
$348$	0.757359	0.0405987
$349$	23.1421	1.23877	0.619385	−	0.785087i	$-0.287382\pi$
$349$	23.1421	1.23877	0.619385	+	0.785087i	$0.287382\pi$
$350$	4.68629	0.250493
$351$	−4.41421	−0.235613
$352$	−10.6569	−0.568012
$353$	−6.97056	−0.371006	−0.185503	−	0.982644i	$-0.559391\pi$
$353$	−6.97056	−0.371006	−0.185503	+	0.982644i	$0.559391\pi$
$354$	1.31371	0.0698228
$355$	3.17157	0.168330
$356$	−8.20101	−0.434653
$357$	0	0
$358$	4.34315	0.229542
$359$	18.0711	0.953754	0.476877	−	0.878970i	$-0.341769\pi$
$359$	18.0711	0.953754	0.476877	+	0.878970i	$0.341769\pi$
$360$	4.48528	0.236395
$361$	17.0000	0.894737
$362$	5.92893	0.311618
$363$	−2.14214	−0.112433
$364$	9.45584	0.495621
$365$	−4.00000	−0.209370
$366$	−0.142136	−0.00742955
$367$	−18.0000	−0.939592	−0.469796	−	0.882775i	$-0.655673\pi$
$367$	−18.0000	−0.939592	−0.469796	+	0.882775i	$0.655673\pi$
$368$	22.9706	1.19742
$369$	35.3137	1.83836
$370$	1.65685	0.0861358
$371$	21.1716	1.09917
$372$	−3.08326	−0.159860
$373$	−3.68629	−0.190869	−0.0954345	−	0.995436i	$-0.530424\pi$
$373$	−3.68629	−0.190869	−0.0954345	+	0.995436i	$0.530424\pi$
$374$	0	0
$375$	−3.72792	−0.192509
$376$	−8.31371	−0.428747
$377$	−1.82843	−0.0941688
$378$	2.82843	0.145479
$379$	−26.9706	−1.38538	−0.692692	−	0.721233i	$-0.743576\pi$
$379$	−26.9706	−1.38538	−0.692692	+	0.721233i	$0.743576\pi$
$380$	−10.9706	−0.562778
$381$	−6.48528	−0.332251
$382$	1.11270	0.0569306
$383$	−20.4853	−1.04675	−0.523374	−	0.852103i	$-0.675327\pi$
$383$	−20.4853	−1.04675	−0.523374	+	0.852103i	$0.675327\pi$
$384$	−4.37258	−0.223137
$385$	6.82843	0.348009
$386$	4.48528	0.228295
$387$	−18.1421	−0.922217
$388$	−22.8284	−1.15894
$389$	36.9706	1.87448	0.937241	−	0.348682i	$-0.113371\pi$
$389$	36.9706	1.87448	0.937241	+	0.348682i	$0.113371\pi$
$390$	0.313708	0.0158852
$391$	0	0
$392$	−1.58579	−0.0800943
$393$	0.544156	0.0274490
$394$	−0.828427	−0.0417356
$395$	−0.414214	−0.0208413
$396$	−12.4853	−0.627409
$397$	−30.6569	−1.53862	−0.769312	−	0.638874i	$-0.779401\pi$
$397$	−30.6569	−1.53862	−0.769312	+	0.638874i	$0.779401\pi$
$398$	−6.82843	−0.342278
$399$	−7.02944	−0.351912
$400$	−12.0000	−0.600000
$401$	7.34315	0.366699	0.183350	−	0.983048i	$-0.441306\pi$
$401$	7.34315	0.366699	0.183350	+	0.983048i	$0.441306\pi$
$402$	−0.970563	−0.0484073
$403$	7.44365	0.370795
$404$	24.9706	1.24233
$405$	7.48528	0.371947
$406$	1.17157	0.0581442
$407$	−9.65685	−0.478672
$408$	0	0
$409$	14.9706	0.740247	0.370123	−	0.928983i	$-0.379315\pi$
$409$	14.9706	0.740247	0.370123	+	0.928983i	$0.379315\pi$
$410$	−5.17157	−0.255406
$411$	4.97056	0.245180
$412$	−1.51472	−0.0746248
$413$	−21.6569	−1.06566
$414$	−8.97056	−0.440879
$415$	−3.65685	−0.179508
$416$	8.07107	0.395717
$417$	−5.79899	−0.283978
$418$	−6.00000	−0.293470
$419$	26.4853	1.29389	0.646945	−	0.762536i	$-0.276046\pi$
$419$	26.4853	1.29389	0.646945	+	0.762536i	$0.276046\pi$
$420$	2.14214	0.104526
$421$	−25.1127	−1.22392	−0.611959	−	0.790889i	$-0.709618\pi$
$421$	−25.1127	−1.22392	−0.611959	+	0.790889i	$0.709618\pi$
$422$	−7.20101	−0.350540
$423$	−14.8284	−0.720983
$424$	11.8701	0.576461
$425$	0	0
$426$	0.544156	0.0263644
$427$	2.34315	0.113393
$428$	−16.7696	−0.810587
$429$	−1.82843	−0.0882773
$430$	2.65685	0.128125
$431$	−8.34315	−0.401875	−0.200938	−	0.979604i	$-0.564399\pi$
$431$	−8.34315	−0.401875	−0.200938	+	0.979604i	$0.564399\pi$
$432$	−7.24264	−0.348462
$433$	−14.6274	−0.702949	−0.351474	−	0.936197i	$-0.614320\pi$
$433$	−14.6274	−0.702949	−0.351474	+	0.936197i	$0.614320\pi$
$434$	−4.76955	−0.228946
$435$	−0.414214	−0.0198600
$436$	2.45584	0.117614
$437$	45.9411	2.19766
$438$	−0.686292	−0.0327923
$439$	11.6569	0.556351	0.278176	−	0.960530i	$-0.410270\pi$
$439$	11.6569	0.556351	0.278176	+	0.960530i	$0.410270\pi$
$440$	3.82843	0.182513
$441$	−2.82843	−0.134687
$442$	0	0
$443$	−35.6569	−1.69411	−0.847054	−	0.531507i	$-0.821626\pi$
$443$	−35.6569	−1.69411	−0.847054	+	0.531507i	$0.821626\pi$
$444$	−3.02944	−0.143771
$445$	4.48528	0.212623
$446$	−3.65685	−0.173157
$447$	−0.899495	−0.0425447
$448$	11.7990	0.557450
$449$	1.02944	0.0485821	0.0242911	−	0.999705i	$-0.492267\pi$
$449$	1.02944	0.0485821	0.0242911	+	0.999705i	$0.492267\pi$
$450$	4.68629	0.220914
$451$	30.1421	1.41934
$452$	17.0294	0.800997
$453$	5.85786	0.275226
$454$	−8.34315	−0.391563
$455$	−5.17157	−0.242447
$456$	−3.94113	−0.184560
$457$	34.9706	1.63585	0.817927	−	0.575322i	$-0.195123\pi$
$457$	34.9706	1.63585	0.817927	+	0.575322i	$0.195123\pi$
$458$	−8.48528	−0.396491
$459$	0	0
$460$	−14.0000	−0.652753
$461$	14.0000	0.652045	0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000	0.652045	0.326023	+	0.945362i	$0.394291\pi$
$462$	1.17157	0.0545065
$463$	−26.0000	−1.20832	−0.604161	−	0.796862i	$-0.706492\pi$
$463$	−26.0000	−1.20832	−0.604161	+	0.796862i	$0.706492\pi$
$464$	−3.00000	−0.139272
$465$	1.68629	0.0781999
$466$	1.78680	0.0827718
$467$	32.3553	1.49723	0.748613	−	0.663007i	$-0.230720\pi$
$467$	32.3553	1.49723	0.748613	+	0.663007i	$0.230720\pi$
$468$	9.45584	0.437097
$469$	16.0000	0.738811
$470$	2.17157	0.100167
$471$	−3.51472	−0.161950
$472$	−12.1421	−0.558887
$473$	−15.4853	−0.712014
$474$	−0.0710678	−0.00326425
$475$	−24.0000	−1.10120
$476$	0	0
$477$	21.1716	0.969380
$478$	−3.45584	−0.158067
$479$	12.8995	0.589393	0.294696	−	0.955591i	$-0.404781\pi$
$479$	12.8995	0.589393	0.294696	+	0.955591i	$0.404781\pi$
$480$	1.82843	0.0834559
$481$	7.31371	0.333476
$482$	−1.78680	−0.0813864
$483$	−8.97056	−0.408175
$484$	9.45584	0.429811
$485$	12.4853	0.566927
$486$	4.28427	0.194338
$487$	28.4853	1.29079	0.645396	−	0.763848i	$-0.276693\pi$
$487$	28.4853	1.29079	0.645396	+	0.763848i	$0.276693\pi$
$488$	1.31371	0.0594688
$489$	−7.48528	−0.338496
$490$	0.414214	0.0187123
$491$	−12.7574	−0.575732	−0.287866	−	0.957671i	$-0.592946\pi$
$491$	−12.7574	−0.575732	−0.287866	+	0.957671i	$0.592946\pi$
$492$	9.45584	0.426302
$493$	0	0
$494$	4.54416	0.204451
$495$	6.82843	0.306915
$496$	12.2132	0.548389
$497$	−8.97056	−0.402385
$498$	−0.627417	−0.0281152
$499$	14.9706	0.670174	0.335087	−	0.942187i	$-0.391234\pi$
$499$	14.9706	0.670174	0.335087	+	0.942187i	$0.391234\pi$
$500$	16.4558	0.735928
$501$	3.65685	0.163376
$502$	2.45584	0.109610
$503$	−25.7279	−1.14715	−0.573576	−	0.819153i	$-0.694444\pi$
$503$	−25.7279	−1.14715	−0.573576	+	0.819153i	$0.694444\pi$
$504$	−12.6863	−0.565092
$505$	−13.6569	−0.607722
$506$	−7.65685	−0.340389
$507$	−4.00000	−0.177646
$508$	28.6274	1.27014
$509$	−27.4853	−1.21826	−0.609132	−	0.793069i	$-0.708482\pi$
$509$	−27.4853	−1.21826	−0.609132	+	0.793069i	$0.708482\pi$
$510$	0	0
$511$	11.3137	0.500489
$512$	22.7574	1.00574
$513$	−14.4853	−0.639541
$514$	−9.87006	−0.435350
$515$	0.828427	0.0365049
$516$	−4.85786	−0.213856
$517$	−12.6569	−0.556648
$518$	−4.68629	−0.205904
$519$	−9.79899	−0.430128
$520$	−2.89949	−0.127151
$521$	0.857864	0.0375837	0.0187919	−	0.999823i	$-0.494018\pi$
$521$	0.857864	0.0375837	0.0187919	+	0.999823i	$0.494018\pi$
$522$	1.17157	0.0512784
$523$	27.3137	1.19435	0.597173	−	0.802113i	$-0.296291\pi$
$523$	27.3137	1.19435	0.597173	+	0.802113i	$0.296291\pi$
$524$	−2.40202	−0.104933
$525$	4.68629	0.204527
$526$	4.65685	0.203048
$527$	0	0
$528$	−3.00000	−0.130558
$529$	35.6274	1.54902
$530$	−3.10051	−0.134677
$531$	−21.6569	−0.939827
$532$	31.0294	1.34530
$533$	−22.8284	−0.988809
$534$	0.769553	0.0333018
$535$	9.17157	0.396522
$536$	8.97056	0.387469
$537$	4.34315	0.187421
$538$	8.05887	0.347443
$539$	−2.41421	−0.103988
$540$	4.41421	0.189958
$541$	21.6569	0.931101	0.465550	−	0.885021i	$-0.345856\pi$
$541$	21.6569	0.931101	0.465550	+	0.885021i	$0.345856\pi$
$542$	−6.02944	−0.258987
$543$	5.92893	0.254435
$544$	0	0
$545$	−1.34315	−0.0575340
$546$	−0.887302	−0.0379730
$547$	3.79899	0.162433	0.0812165	−	0.996696i	$-0.474119\pi$
$547$	3.79899	0.162433	0.0812165	+	0.996696i	$0.474119\pi$
$548$	−21.9411	−0.937278
$549$	2.34315	0.100003
$550$	4.00000	0.170561
$551$	−6.00000	−0.255609
$552$	−5.02944	−0.214067
$553$	1.17157	0.0498203
$554$	−2.20101	−0.0935120
$555$	1.65685	0.0703295
$556$	25.5980	1.08560
$557$	5.31371	0.225149	0.112575	−	0.993643i	$-0.464090\pi$
$557$	5.31371	0.225149	0.112575	+	0.993643i	$0.464090\pi$
$558$	−4.76955	−0.201911
$559$	11.7279	0.496038
$560$	−8.48528	−0.358569
$561$	0	0
$562$	−0.816234	−0.0344307
$563$	−9.24264	−0.389531	−0.194765	−	0.980850i	$-0.562395\pi$
$563$	−9.24264	−0.389531	−0.194765	+	0.980850i	$0.562395\pi$
$564$	−3.97056	−0.167191
$565$	−9.31371	−0.391831
$566$	−0.142136	−0.00597441
$567$	−21.1716	−0.889122
$568$	−5.02944	−0.211030
$569$	−28.3431	−1.18821	−0.594103	−	0.804389i	$-0.702493\pi$
$569$	−28.3431	−1.18821	−0.594103	+	0.804389i	$0.702493\pi$
$570$	1.02944	0.0431184
$571$	30.6274	1.28172	0.640859	−	0.767659i	$-0.278578\pi$
$571$	30.6274	1.28172	0.640859	+	0.767659i	$0.278578\pi$
$572$	8.07107	0.337468
$573$	1.11270	0.0464836
$574$	14.6274	0.610537
$575$	−30.6274	−1.27725
$576$	11.7990	0.491625
$577$	9.79899	0.407937	0.203969	−	0.978977i	$-0.434616\pi$
$577$	9.79899	0.407937	0.203969	+	0.978977i	$0.434616\pi$
$578$	0	0
$579$	4.48528	0.186402
$580$	1.82843	0.0759213
$581$	10.3431	0.429106
$582$	2.14214	0.0887944
$583$	18.0711	0.748427
$584$	6.34315	0.262481
$585$	−5.17157	−0.213818
$586$	−1.51472	−0.0625724
$587$	−3.65685	−0.150935	−0.0754673	−	0.997148i	$-0.524045\pi$
$587$	−3.65685	−0.150935	−0.0754673	+	0.997148i	$0.524045\pi$
$588$	−0.757359	−0.0312330
$589$	24.4264	1.00647
$590$	3.17157	0.130572
$591$	−0.828427	−0.0340769
$592$	12.0000	0.493197
$593$	−2.51472	−0.103267	−0.0516336	−	0.998666i	$-0.516443\pi$
$593$	−2.51472	−0.103267	−0.0516336	+	0.998666i	$0.516443\pi$
$594$	2.41421	0.0990564
$595$	0	0
$596$	3.97056	0.162641
$597$	−6.82843	−0.279469
$598$	5.79899	0.237138
$599$	−43.8701	−1.79248	−0.896241	−	0.443567i	$-0.853713\pi$
$599$	−43.8701	−1.79248	−0.896241	+	0.443567i	$0.853713\pi$
$600$	2.62742	0.107264
$601$	22.8284	0.931191	0.465595	−	0.884998i	$-0.345840\pi$
$601$	22.8284	0.931191	0.465595	+	0.884998i	$0.345840\pi$
$602$	−7.51472	−0.306277
$603$	16.0000	0.651570
$604$	−25.8579	−1.05214
$605$	−5.17157	−0.210254
$606$	−2.34315	−0.0951838
$607$	−17.7279	−0.719554	−0.359777	−	0.933038i	$-0.617147\pi$
$607$	−17.7279	−0.719554	−0.359777	+	0.933038i	$0.617147\pi$
$608$	26.4853	1.07412
$609$	1.17157	0.0474745
$610$	−0.343146	−0.0138936
$611$	9.58579	0.387799
$612$	0	0
$613$	−9.00000	−0.363507	−0.181753	−	0.983344i	$-0.558177\pi$
$613$	−9.00000	−0.363507	−0.181753	+	0.983344i	$0.558177\pi$
$614$	−7.00000	−0.282497
$615$	−5.17157	−0.208538
$616$	−10.8284	−0.436290
$617$	−23.3137	−0.938575	−0.469287	−	0.883046i	$-0.655489\pi$
$617$	−23.3137	−0.938575	−0.469287	+	0.883046i	$0.655489\pi$
$618$	0.142136	0.00571753
$619$	−36.4142	−1.46361	−0.731805	−	0.681514i	$-0.761322\pi$
$619$	−36.4142	−1.46361	−0.731805	+	0.681514i	$0.761322\pi$
$620$	−7.44365	−0.298944
$621$	−18.4853	−0.741789
$622$	−10.4853	−0.420421
$623$	−12.6863	−0.508266
$624$	2.27208	0.0909559
$625$	11.0000	0.440000
$626$	−1.72792	−0.0690617
$627$	−6.00000	−0.239617
$628$	15.5147	0.619105
$629$	0	0
$630$	3.31371	0.132021
$631$	−31.1716	−1.24092	−0.620460	−	0.784238i	$-0.713054\pi$
$631$	−31.1716	−1.24092	−0.620460	+	0.784238i	$0.713054\pi$
$632$	0.656854	0.0261283
$633$	−7.20101	−0.286214
$634$	−8.05887	−0.320059
$635$	−15.6569	−0.621323
$636$	5.66905	0.224792
$637$	1.82843	0.0724449
$638$	1.00000	0.0395904
$639$	−8.97056	−0.354870
$640$	−10.5563	−0.417276
$641$	21.7990	0.861008	0.430504	−	0.902589i	$-0.358336\pi$
$641$	21.7990	0.861008	0.430504	+	0.902589i	$0.358336\pi$
$642$	1.57359	0.0621048
$643$	−15.5147	−0.611841	−0.305920	−	0.952057i	$-0.598964\pi$
$643$	−15.5147	−0.611841	−0.305920	+	0.952057i	$0.598964\pi$
$644$	39.5980	1.56038
$645$	2.65685	0.104614
$646$	0	0
$647$	28.3431	1.11428	0.557142	−	0.830417i	$-0.311898\pi$
$647$	28.3431	1.11428	0.557142	+	0.830417i	$0.311898\pi$
$648$	−11.8701	−0.466300
$649$	−18.4853	−0.725611
$650$	−3.02944	−0.118824
$651$	−4.76955	−0.186934
$652$	33.0416	1.29401
$653$	1.85786	0.0727039	0.0363519	−	0.999339i	$-0.488426\pi$
$653$	1.85786	0.0727039	0.0363519	+	0.999339i	$0.488426\pi$
$654$	−0.230447	−0.00901121
$655$	1.31371	0.0513308
$656$	−37.4558	−1.46241
$657$	11.3137	0.441390
$658$	−6.14214	−0.239445
$659$	11.5858	0.451318	0.225659	−	0.974206i	$-0.427546\pi$
$659$	11.5858	0.451318	0.225659	+	0.974206i	$0.427546\pi$
$660$	1.82843	0.0711714
$661$	10.6863	0.415649	0.207824	−	0.978166i	$-0.433362\pi$
$661$	10.6863	0.415649	0.207824	+	0.978166i	$0.433362\pi$
$662$	0.171573	0.00666837
$663$	0	0
$664$	5.79899	0.225044
$665$	−16.9706	−0.658090
$666$	−4.68629	−0.181590
$667$	−7.65685	−0.296475
$668$	−16.1421	−0.624558
$669$	−3.65685	−0.141382
$670$	−2.34315	−0.0905236
$671$	2.00000	0.0772091
$672$	−5.17157	−0.199498
$673$	−23.6274	−0.910770	−0.455385	−	0.890295i	$-0.650498\pi$
$673$	−23.6274	−0.910770	−0.455385	+	0.890295i	$0.650498\pi$
$674$	7.37258	0.283981
$675$	9.65685	0.371692
$676$	17.6569	0.679110
$677$	22.0000	0.845529	0.422764	−	0.906240i	$-0.361060\pi$
$677$	22.0000	0.845529	0.422764	+	0.906240i	$0.361060\pi$
$678$	−1.59798	−0.0613700
$679$	−35.3137	−1.35522
$680$	0	0
$681$	−8.34315	−0.319710
$682$	−4.07107	−0.155889
$683$	12.9706	0.496305	0.248152	−	0.968721i	$-0.420177\pi$
$683$	12.9706	0.496305	0.248152	+	0.968721i	$0.420177\pi$
$684$	31.0294	1.18644
$685$	12.0000	0.458496
$686$	7.02944	0.268385
$687$	−8.48528	−0.323734
$688$	19.2426	0.733619
$689$	−13.6863	−0.521406
$690$	1.31371	0.0500120
$691$	−48.0000	−1.82601	−0.913003	−	0.407953i	$-0.866243\pi$
$691$	−48.0000	−1.82601	−0.913003	+	0.407953i	$0.866243\pi$
$692$	43.2548	1.64430
$693$	−19.3137	−0.733667
$694$	6.00000	0.227757
$695$	−14.0000	−0.531050
$696$	0.656854	0.0248980
$697$	0	0
$698$	9.58579	0.362827
$699$	1.78680	0.0675829
$700$	−20.6863	−0.781868
$701$	22.1127	0.835185	0.417593	−	0.908634i	$-0.362874\pi$
$701$	22.1127	0.835185	0.417593	+	0.908634i	$0.362874\pi$
$702$	−1.82843	−0.0690095
$703$	24.0000	0.905177
$704$	10.0711	0.379568
$705$	2.17157	0.0817862
$706$	−2.88730	−0.108665
$707$	38.6274	1.45273
$708$	−5.79899	−0.217939
$709$	−0.857864	−0.0322178	−0.0161089	−	0.999870i	$-0.505128\pi$
$709$	−0.857864	−0.0322178	−0.0161089	+	0.999870i	$0.505128\pi$
$710$	1.31371	0.0493026
$711$	1.17157	0.0439374
$712$	−7.11270	−0.266560
$713$	31.1716	1.16738
$714$	0	0
$715$	−4.41421	−0.165082
$716$	−19.1716	−0.716475
$717$	−3.45584	−0.129061
$718$	7.48528	0.279348
$719$	−8.14214	−0.303650	−0.151825	−	0.988407i	$-0.548515\pi$
$719$	−8.14214	−0.303650	−0.151825	+	0.988407i	$0.548515\pi$
$720$	−8.48528	−0.316228
$721$	−2.34315	−0.0872633
$722$	7.04163	0.262062
$723$	−1.78680	−0.0664517
$724$	−26.1716	−0.972659
$725$	4.00000	0.148556
$726$	−0.887302	−0.0329309
$727$	−21.3137	−0.790482	−0.395241	−	0.918578i	$-0.629339\pi$
$727$	−21.3137	−0.790482	−0.395241	+	0.918578i	$0.629339\pi$
$728$	8.20101	0.303950
$729$	−18.1716	−0.673021
$730$	−1.65685	−0.0613229
$731$	0	0
$732$	0.627417	0.0231900
$733$	49.2548	1.81927	0.909634	−	0.415410i	$-0.136362\pi$
$733$	49.2548	1.81927	0.909634	+	0.415410i	$0.136362\pi$
$734$	−7.45584	−0.275200
$735$	0.414214	0.0152785
$736$	33.7990	1.24585
$737$	13.6569	0.503057
$738$	14.6274	0.538443
$739$	−10.0711	−0.370470	−0.185235	−	0.982694i	$-0.559305\pi$
$739$	−10.0711	−0.370470	−0.185235	+	0.982694i	$0.559305\pi$
$740$	−7.31371	−0.268857
$741$	4.54416	0.166934
$742$	8.76955	0.321940
$743$	−12.3431	−0.452826	−0.226413	−	0.974031i	$-0.572700\pi$
$743$	−12.3431	−0.452826	−0.226413	+	0.974031i	$0.572700\pi$
$744$	−2.67410	−0.0980372
$745$	−2.17157	−0.0795603
$746$	−1.52691	−0.0559042
$747$	10.3431	0.378436
$748$	0	0
$749$	−25.9411	−0.947868
$750$	−1.54416	−0.0563846
$751$	−2.68629	−0.0980242	−0.0490121	−	0.998798i	$-0.515607\pi$
$751$	−2.68629	−0.0980242	−0.0490121	+	0.998798i	$0.515607\pi$
$752$	15.7279	0.573538
$753$	2.45584	0.0894959
$754$	−0.757359	−0.0275814
$755$	14.1421	0.514685
$756$	−12.4853	−0.454085
$757$	42.4853	1.54415	0.772077	−	0.635529i	$-0.219218\pi$
$757$	42.4853	1.54415	0.772077	+	0.635529i	$0.219218\pi$
$758$	−11.1716	−0.405770
$759$	−7.65685	−0.277926
$760$	−9.51472	−0.345135
$761$	−33.5980	−1.21793	−0.608963	−	0.793199i	$-0.708414\pi$
$761$	−33.5980	−1.21793	−0.608963	+	0.793199i	$0.708414\pi$
$762$	−2.68629	−0.0973141
$763$	3.79899	0.137533
$764$	−4.91169	−0.177699
$765$	0	0
$766$	−8.48528	−0.306586
$767$	14.0000	0.505511
$768$	1.64466	0.0593466
$769$	13.1127	0.472856	0.236428	−	0.971649i	$-0.424023\pi$
$769$	13.1127	0.472856	0.236428	+	0.971649i	$0.424023\pi$
$770$	2.82843	0.101929
$771$	−9.87006	−0.355461
$772$	−19.7990	−0.712581
$773$	−36.4853	−1.31228	−0.656142	−	0.754637i	$-0.727813\pi$
$773$	−36.4853	−1.31228	−0.656142	+	0.754637i	$0.727813\pi$
$774$	−7.51472	−0.270111
$775$	−16.2843	−0.584948
$776$	−19.7990	−0.710742
$777$	−4.68629	−0.168120
$778$	15.3137	0.549023
$779$	−74.9117	−2.68399
$780$	−1.38478	−0.0495829
$781$	−7.65685	−0.273984
$782$	0	0
$783$	2.41421	0.0862770
$784$	3.00000	0.107143
$785$	−8.48528	−0.302853
$786$	0.225397	0.00803964
$787$	−42.0833	−1.50011	−0.750053	−	0.661378i	$-0.769972\pi$
$787$	−42.0833	−1.50011	−0.750053	+	0.661378i	$0.769972\pi$
$788$	3.65685	0.130270
$789$	4.65685	0.165788
$790$	−0.171573	−0.00610429
$791$	26.3431	0.936654
$792$	−10.8284	−0.384771
$793$	−1.51472	−0.0537892
$794$	−12.6985	−0.450652
$795$	−3.10051	−0.109964
$796$	30.1421	1.06836
$797$	−55.7401	−1.97442	−0.987208	−	0.159437i	$-0.949032\pi$
$797$	−55.7401	−1.97442	−0.987208	+	0.159437i	$0.949032\pi$
$798$	−2.91169	−0.103073
$799$	0	0
$800$	−17.6569	−0.624264
$801$	−12.6863	−0.448248
$802$	3.04163	0.107404
$803$	9.65685	0.340783
$804$	4.28427	0.151095
$805$	−21.6569	−0.763304
$806$	3.08326	0.108603
$807$	8.05887	0.283686
$808$	21.6569	0.761885
$809$	20.2843	0.713157	0.356578	−	0.934265i	$-0.383943\pi$
$809$	20.2843	0.713157	0.356578	+	0.934265i	$0.383943\pi$
$810$	3.10051	0.108941
$811$	−5.17157	−0.181598	−0.0907992	−	0.995869i	$-0.528942\pi$
$811$	−5.17157	−0.181598	−0.0907992	+	0.995869i	$0.528942\pi$
$812$	−5.17157	−0.181487
$813$	−6.02944	−0.211462
$814$	−4.00000	−0.140200
$815$	−18.0711	−0.633002
$816$	0	0
$817$	38.4853	1.34643
$818$	6.20101	0.216813
$819$	14.6274	0.511123
$820$	22.8284	0.797203
$821$	−15.4853	−0.540440	−0.270220	−	0.962799i	$-0.587096\pi$
$821$	−15.4853	−0.540440	−0.270220	+	0.962799i	$0.587096\pi$
$822$	2.05887	0.0718115
$823$	−2.28427	−0.0796247	−0.0398123	−	0.999207i	$-0.512676\pi$
$823$	−2.28427	−0.0796247	−0.0398123	+	0.999207i	$0.512676\pi$
$824$	−1.31371	−0.0457652
$825$	4.00000	0.139262
$826$	−8.97056	−0.312126
$827$	−13.1005	−0.455549	−0.227775	−	0.973714i	$-0.573145\pi$
$827$	−13.1005	−0.455549	−0.227775	+	0.973714i	$0.573145\pi$
$828$	39.5980	1.37612
$829$	9.79899	0.340333	0.170166	−	0.985415i	$-0.445569\pi$
$829$	9.79899	0.340333	0.170166	+	0.985415i	$0.445569\pi$
$830$	−1.51472	−0.0525767
$831$	−2.20101	−0.0763522
$832$	−7.62742	−0.264433
$833$	0	0
$834$	−2.40202	−0.0831752
$835$	8.82843	0.305520
$836$	26.4853	0.916013
$837$	−9.82843	−0.339720
$838$	10.9706	0.378972
$839$	22.0711	0.761978	0.380989	−	0.924580i	$-0.375584\pi$
$839$	22.0711	0.761978	0.380989	+	0.924580i	$0.375584\pi$
$840$	1.85786	0.0641024
$841$	1.00000	0.0344828
$842$	−10.4020	−0.358477
$843$	−0.816234	−0.0281126
$844$	31.7868	1.09415
$845$	−9.65685	−0.332206
$846$	−6.14214	−0.211171
$847$	14.6274	0.502604
$848$	−22.4558	−0.771137
$849$	−0.142136	−0.00487808
$850$	0	0
$851$	30.6274	1.04989
$852$	−2.40202	−0.0822919
$853$	−10.9706	−0.375625	−0.187812	−	0.982205i	$-0.560140\pi$
$853$	−10.9706	−0.375625	−0.187812	+	0.982205i	$0.560140\pi$
$854$	0.970563	0.0332120
$855$	−16.9706	−0.580381
$856$	−14.5442	−0.497109
$857$	11.8284	0.404051	0.202026	−	0.979380i	$-0.435248\pi$
$857$	11.8284	0.404051	0.202026	+	0.979380i	$0.435248\pi$
$858$	−0.757359	−0.0258558
$859$	−5.72792	−0.195434	−0.0977171	−	0.995214i	$-0.531154\pi$
$859$	−5.72792	−0.195434	−0.0977171	+	0.995214i	$0.531154\pi$
$860$	−11.7279	−0.399919
$861$	14.6274	0.498501
$862$	−3.45584	−0.117707
$863$	−45.1127	−1.53565	−0.767827	−	0.640657i	$-0.778662\pi$
$863$	−45.1127	−1.53565	−0.767827	+	0.640657i	$0.778662\pi$
$864$	−10.6569	−0.362554
$865$	−23.6569	−0.804357
$866$	−6.05887	−0.205889
$867$	0	0
$868$	21.0538	0.714613
$869$	1.00000	0.0339227
$870$	−0.171573	−0.00581687
$871$	−10.3431	−0.350464
$872$	2.12994	0.0721289
$873$	−35.3137	−1.19519
$874$	19.0294	0.643680
$875$	25.4558	0.860565
$876$	3.02944	0.102355
$877$	8.85786	0.299109	0.149554	−	0.988753i	$-0.452216\pi$
$877$	8.85786	0.299109	0.149554	+	0.988753i	$0.452216\pi$
$878$	4.82843	0.162952
$879$	−1.51472	−0.0510902
$880$	−7.24264	−0.244149
$881$	−14.0000	−0.471672	−0.235836	−	0.971793i	$-0.575783\pi$
$881$	−14.0000	−0.471672	−0.235836	+	0.971793i	$0.575783\pi$
$882$	−1.17157	−0.0394489
$883$	−46.4264	−1.56237	−0.781186	−	0.624298i	$-0.785385\pi$
$883$	−46.4264	−1.56237	−0.781186	+	0.624298i	$0.785385\pi$
$884$	0	0
$885$	3.17157	0.106611
$886$	−14.7696	−0.496193
$887$	−36.8995	−1.23896	−0.619482	−	0.785011i	$-0.712657\pi$
$887$	−36.8995	−1.23896	−0.619482	+	0.785011i	$0.712657\pi$
$888$	−2.62742	−0.0881703
$889$	44.2843	1.48525
$890$	1.85786	0.0622758
$891$	−18.0711	−0.605404
$892$	16.1421	0.540479
$893$	31.4558	1.05263
$894$	−0.372583	−0.0124610
$895$	10.4853	0.350484
$896$	29.8579	0.997481
$897$	5.79899	0.193623
$898$	0.426407	0.0142294
$899$	−4.07107	−0.135778
$900$	−20.6863	−0.689543
$901$	0	0
$902$	12.4853	0.415714
$903$	−7.51472	−0.250074
$904$	14.7696	0.491228
$905$	14.3137	0.475804
$906$	2.42641	0.0806120
$907$	34.2843	1.13839	0.569195	−	0.822202i	$-0.307255\pi$
$907$	34.2843	1.13839	0.569195	+	0.822202i	$0.307255\pi$
$908$	36.8284	1.22219
$909$	38.6274	1.28119
$910$	−2.14214	−0.0710111
$911$	46.5563	1.54248	0.771240	−	0.636544i	$-0.219637\pi$
$911$	46.5563	1.54248	0.771240	+	0.636544i	$0.219637\pi$
$912$	7.45584	0.246888
$913$	8.82843	0.292178
$914$	14.4853	0.479131
$915$	−0.343146	−0.0113440
$916$	37.4558	1.23758
$917$	−3.71573	−0.122704
$918$	0	0
$919$	−20.1421	−0.664428	−0.332214	−	0.943204i	$-0.607796\pi$
$919$	−20.1421	−0.664428	−0.332214	+	0.943204i	$0.607796\pi$
$920$	−12.1421	−0.400314
$921$	−7.00000	−0.230658
$922$	5.79899	0.190980
$923$	5.79899	0.190876
$924$	−5.17157	−0.170132
$925$	−16.0000	−0.526077
$926$	−10.7696	−0.353909
$927$	−2.34315	−0.0769590
$928$	−4.41421	−0.144904
$929$	−41.3137	−1.35546	−0.677729	−	0.735311i	$-0.737036\pi$
$929$	−41.3137	−1.35546	−0.677729	+	0.735311i	$0.737036\pi$
$930$	0.698485	0.0229042
$931$	6.00000	0.196642
$932$	−7.88730	−0.258357
$933$	−10.4853	−0.343273
$934$	13.4020	0.438527
$935$	0	0
$936$	8.20101	0.268058
$937$	28.6274	0.935217	0.467608	−	0.883936i	$-0.345116\pi$
$937$	28.6274	0.935217	0.467608	+	0.883936i	$0.345116\pi$
$938$	6.62742	0.216393
$939$	−1.72792	−0.0563886
$940$	−9.58579	−0.312654
$941$	−22.5980	−0.736673	−0.368337	−	0.929693i	$-0.620073\pi$
$941$	−22.5980	−0.736673	−0.368337	+	0.929693i	$0.620073\pi$
$942$	−1.45584	−0.0474340
$943$	−95.5980	−3.11310
$944$	22.9706	0.747628
$945$	6.82843	0.222129
$946$	−6.41421	−0.208544
$947$	−39.3848	−1.27983	−0.639917	−	0.768444i	$-0.721031\pi$
$947$	−39.3848	−1.27983	−0.639917	+	0.768444i	$0.721031\pi$
$948$	0.313708	0.0101888
$949$	−7.31371	−0.237413
$950$	−9.94113	−0.322533
$951$	−8.05887	−0.261327
$952$	0	0
$953$	9.62742	0.311863	0.155931	−	0.987768i	$-0.450162\pi$
$953$	9.62742	0.311863	0.155931	+	0.987768i	$0.450162\pi$
$954$	8.76955	0.283925
$955$	2.68629	0.0869264
$956$	15.2548	0.493377
$957$	1.00000	0.0323254
$958$	5.34315	0.172629
$959$	−33.9411	−1.09602
$960$	−1.72792	−0.0557684
$961$	−14.4264	−0.465368
$962$	3.02944	0.0976730
$963$	−25.9411	−0.835941
$964$	7.88730	0.254033
$965$	10.8284	0.348579
$966$	−3.71573	−0.119552
$967$	−26.7574	−0.860459	−0.430229	−	0.902720i	$-0.641567\pi$
$967$	−26.7574	−0.860459	−0.430229	+	0.902720i	$0.641567\pi$
$968$	8.20101	0.263590
$969$	0	0
$970$	5.17157	0.166049
$971$	−4.34315	−0.139378	−0.0696891	−	0.997569i	$-0.522201\pi$
$971$	−4.34315	−0.139378	−0.0696891	+	0.997569i	$0.522201\pi$
$972$	−18.9117	−0.606593
$973$	39.5980	1.26945
$974$	11.7990	0.378064
$975$	−3.02944	−0.0970196
$976$	−2.48528	−0.0795519
$977$	41.8284	1.33821	0.669105	−	0.743168i	$-0.266678\pi$
$977$	41.8284	1.33821	0.669105	+	0.743168i	$0.266678\pi$
$978$	−3.10051	−0.0991432
$979$	−10.8284	−0.346078
$980$	−1.82843	−0.0584070
$981$	3.79899	0.121292
$982$	−5.28427	−0.168628
$983$	−31.8701	−1.01650	−0.508248	−	0.861210i	$-0.669707\pi$
$983$	−31.8701	−1.01650	−0.508248	+	0.861210i	$0.669707\pi$
$984$	8.20101	0.261439
$985$	−2.00000	−0.0637253
$986$	0	0
$987$	−6.14214	−0.195506
$988$	−20.0589	−0.638158
$989$	49.1127	1.56169
$990$	2.82843	0.0898933
$991$	7.17157	0.227813	0.113906	−	0.993492i	$-0.463664\pi$
$991$	7.17157	0.227813	0.113906	+	0.993492i	$0.463664\pi$
$992$	17.9706	0.570566
$993$	0.171573	0.00544470
$994$	−3.71573	−0.117856
$995$	−16.4853	−0.522619
$996$	2.76955	0.0877566
$997$	28.2843	0.895772	0.447886	−	0.894091i	$-0.352177\pi$
$997$	28.2843	0.895772	0.447886	+	0.894091i	$0.352177\pi$
$998$	6.20101	0.196290
$999$	−9.65685	−0.305529

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8381.2.a.e.1.2		2
17.16	even	2		29.2.a.a.1.2	✓	2
51.50	odd	2		261.2.a.d.1.1		2
68.67	odd	2		464.2.a.h.1.2		2
85.33	odd	4		725.2.b.b.349.2		4
85.67	odd	4		725.2.b.b.349.3		4
85.84	even	2		725.2.a.b.1.1		2
119.118	odd	2		1421.2.a.j.1.2		2
136.67	odd	2		1856.2.a.w.1.1		2
136.101	even	2		1856.2.a.r.1.2		2
187.186	odd	2		3509.2.a.j.1.1		2
204.203	even	2		4176.2.a.bq.1.1		2
221.220	even	2		4901.2.a.g.1.1		2
255.254	odd	2		6525.2.a.o.1.2		2
493.16	even	14		841.2.d.j.778.2		12
493.33	even	14		841.2.d.f.190.2		12
493.50	odd	28		841.2.e.k.267.2		24
493.67	even	14		841.2.d.f.574.1		12
493.84	odd	28		841.2.e.k.270.2		24
493.101	odd	28		841.2.e.k.196.2		24
493.118	odd	28		841.2.e.k.236.3		24
493.135	odd	28		841.2.e.k.651.2		24
493.152	even	14		841.2.d.j.571.1		12
493.169	even	14		841.2.d.j.605.1		12
493.186	odd	4		841.2.b.a.840.3		4
493.220	odd	4		841.2.b.a.840.2		4
493.237	even	14		841.2.d.f.605.2		12
493.254	even	14		841.2.d.f.571.2		12
493.271	odd	28		841.2.e.k.651.3		24
493.288	odd	28		841.2.e.k.236.2		24
493.305	odd	28		841.2.e.k.196.3		24
493.322	odd	28		841.2.e.k.270.3		24
493.339	even	14		841.2.d.j.574.2		12
493.356	odd	28		841.2.e.k.267.3		24
493.373	even	14		841.2.d.j.190.1		12
493.390	even	14		841.2.d.f.778.1		12
493.424	odd	28		841.2.e.k.63.2		24
493.441	even	14		841.2.d.f.645.2		12
493.458	even	14		841.2.d.j.645.1		12
493.475	odd	28		841.2.e.k.63.3		24
493.492	even	2		841.2.a.d.1.1		2
1479.1478	odd	2		7569.2.a.c.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.a.a.1.2	✓	2	17.16	even	2
261.2.a.d.1.1		2	51.50	odd	2
464.2.a.h.1.2		2	68.67	odd	2
725.2.a.b.1.1		2	85.84	even	2
725.2.b.b.349.2		4	85.33	odd	4
725.2.b.b.349.3		4	85.67	odd	4
841.2.a.d.1.1		2	493.492	even	2
841.2.b.a.840.2		4	493.220	odd	4
841.2.b.a.840.3		4	493.186	odd	4
841.2.d.f.190.2		12	493.33	even	14
841.2.d.f.571.2		12	493.254	even	14
841.2.d.f.574.1		12	493.67	even	14
841.2.d.f.605.2		12	493.237	even	14
841.2.d.f.645.2		12	493.441	even	14
841.2.d.f.778.1		12	493.390	even	14
841.2.d.j.190.1		12	493.373	even	14
841.2.d.j.571.1		12	493.152	even	14
841.2.d.j.574.2		12	493.339	even	14
841.2.d.j.605.1		12	493.169	even	14
841.2.d.j.645.1		12	493.458	even	14
841.2.d.j.778.2		12	493.16	even	14
841.2.e.k.63.2		24	493.424	odd	28
841.2.e.k.63.3		24	493.475	odd	28
841.2.e.k.196.2		24	493.101	odd	28
841.2.e.k.196.3		24	493.305	odd	28
841.2.e.k.236.2		24	493.288	odd	28
841.2.e.k.236.3		24	493.118	odd	28
841.2.e.k.267.2		24	493.50	odd	28
841.2.e.k.267.3		24	493.356	odd	28
841.2.e.k.270.2		24	493.84	odd	28
841.2.e.k.270.3		24	493.322	odd	28
841.2.e.k.651.2		24	493.135	odd	28
841.2.e.k.651.3		24	493.271	odd	28
1421.2.a.j.1.2		2	119.118	odd	2
1856.2.a.r.1.2		2	136.101	even	2
1856.2.a.w.1.1		2	136.67	odd	2
3509.2.a.j.1.1		2	187.186	odd	2
4176.2.a.bq.1.1		2	204.203	even	2
4901.2.a.g.1.1		2	221.220	even	2
6525.2.a.o.1.2		2	255.254	odd	2
7569.2.a.c.1.2		2	1479.1478	odd	2
8381.2.a.e.1.2		2	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:	\( N \)	\(=\)	\( 8381 = 17^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8381.a (trivial)

\(f(q)\)	\(=\)	\(q+0.414214 q^{2} +0.414214 q^{3} -1.82843 q^{4} +1.00000 q^{5} +0.171573 q^{6} -2.82843 q^{7} -1.58579 q^{8} -2.82843 q^{9} +O(q^{10})\)	\(q+0.414214 q^{2} +0.414214 q^{3} -1.82843 q^{4} +1.00000 q^{5} +0.171573 q^{6} -2.82843 q^{7} -1.58579 q^{8} -2.82843 q^{9} +0.414214 q^{10} -2.41421 q^{11} -0.757359 q^{12} +1.82843 q^{13} -1.17157 q^{14} +0.414214 q^{15} +3.00000 q^{16} -1.17157 q^{18} +6.00000 q^{19} -1.82843 q^{20} -1.17157 q^{21} -1.00000 q^{22} +7.65685 q^{23} -0.656854 q^{24} -4.00000 q^{25} +0.757359 q^{26} -2.41421 q^{27} +5.17157 q^{28} -1.00000 q^{29} +0.171573 q^{30} +4.07107 q^{31} +4.41421 q^{32} -1.00000 q^{33} -2.82843 q^{35} +5.17157 q^{36} +4.00000 q^{37} +2.48528 q^{38} +0.757359 q^{39} -1.58579 q^{40} -12.4853 q^{41} -0.485281 q^{42} +6.41421 q^{43} +4.41421 q^{44} -2.82843 q^{45} +3.17157 q^{46} +5.24264 q^{47} +1.24264 q^{48} +1.00000 q^{49} -1.65685 q^{50} -3.34315 q^{52} -7.48528 q^{53} -1.00000 q^{54} -2.41421 q^{55} +4.48528 q^{56} +2.48528 q^{57} -0.414214 q^{58} +7.65685 q^{59} -0.757359 q^{60} -0.828427 q^{61} +1.68629 q^{62} +8.00000 q^{63} -4.17157 q^{64} +1.82843 q^{65} -0.414214 q^{66} -5.65685 q^{67} +3.17157 q^{69} -1.17157 q^{70} +3.17157 q^{71} +4.48528 q^{72} -4.00000 q^{73} +1.65685 q^{74} -1.65685 q^{75} -10.9706 q^{76} +6.82843 q^{77} +0.313708 q^{78} -0.414214 q^{79} +3.00000 q^{80} +7.48528 q^{81} -5.17157 q^{82} -3.65685 q^{83} +2.14214 q^{84} +2.65685 q^{86} -0.414214 q^{87} +3.82843 q^{88} +4.48528 q^{89} -1.17157 q^{90} -5.17157 q^{91} -14.0000 q^{92} +1.68629 q^{93} +2.17157 q^{94} +6.00000 q^{95} +1.82843 q^{96} +12.4853 q^{97} +0.414214 q^{98} +6.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 6 q^{6} - 6 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 6 * q^6 - 6 * q^8	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 6 q^{6} - 6 q^{8} - 2 q^{10} - 2 q^{11} - 10 q^{12} - 2 q^{13} - 8 q^{14} - 2 q^{15} + 6 q^{16} - 8 q^{18} + 12 q^{19} + 2 q^{20} - 8 q^{21} - 2 q^{22} + 4 q^{23} + 10 q^{24} - 8 q^{25} + 10 q^{26} - 2 q^{27} + 16 q^{28} - 2 q^{29} + 6 q^{30} - 6 q^{31} + 6 q^{32} - 2 q^{33} + 16 q^{36} + 8 q^{37} - 12 q^{38} + 10 q^{39} - 6 q^{40} - 8 q^{41} + 16 q^{42} + 10 q^{43} + 6 q^{44} + 12 q^{46} + 2 q^{47} - 6 q^{48} + 2 q^{49} + 8 q^{50} - 18 q^{52} + 2 q^{53} - 2 q^{54} - 2 q^{55} - 8 q^{56} - 12 q^{57} + 2 q^{58} + 4 q^{59} - 10 q^{60} + 4 q^{61} + 26 q^{62} + 16 q^{63} - 14 q^{64} - 2 q^{65} + 2 q^{66} + 12 q^{69} - 8 q^{70} + 12 q^{71} - 8 q^{72} - 8 q^{73} - 8 q^{74} + 8 q^{75} + 12 q^{76} + 8 q^{77} - 22 q^{78} + 2 q^{79} + 6 q^{80} - 2 q^{81} - 16 q^{82} + 4 q^{83} - 24 q^{84} - 6 q^{86} + 2 q^{87} + 2 q^{88} - 8 q^{89} - 8 q^{90} - 16 q^{91} - 28 q^{92} + 26 q^{93} + 10 q^{94} + 12 q^{95} - 2 q^{96} + 8 q^{97} - 2 q^{98} + 8 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 6 * q^6 - 6 * q^8 - 2 * q^10 - 2 * q^11 - 10 * q^12 - 2 * q^13 - 8 * q^14 - 2 * q^15 + 6 * q^16 - 8 * q^18 + 12 * q^19 + 2 * q^20 - 8 * q^21 - 2 * q^22 + 4 * q^23 + 10 * q^24 - 8 * q^25 + 10 * q^26 - 2 * q^27 + 16 * q^28 - 2 * q^29 + 6 * q^30 - 6 * q^31 + 6 * q^32 - 2 * q^33 + 16 * q^36 + 8 * q^37 - 12 * q^38 + 10 * q^39 - 6 * q^40 - 8 * q^41 + 16 * q^42 + 10 * q^43 + 6 * q^44 + 12 * q^46 + 2 * q^47 - 6 * q^48 + 2 * q^49 + 8 * q^50 - 18 * q^52 + 2 * q^53 - 2 * q^54 - 2 * q^55 - 8 * q^56 - 12 * q^57 + 2 * q^58 + 4 * q^59 - 10 * q^60 + 4 * q^61 + 26 * q^62 + 16 * q^63 - 14 * q^64 - 2 * q^65 + 2 * q^66 + 12 * q^69 - 8 * q^70 + 12 * q^71 - 8 * q^72 - 8 * q^73 - 8 * q^74 + 8 * q^75 + 12 * q^76 + 8 * q^77 - 22 * q^78 + 2 * q^79 + 6 * q^80 - 2 * q^81 - 16 * q^82 + 4 * q^83 - 24 * q^84 - 6 * q^86 + 2 * q^87 + 2 * q^88 - 8 * q^89 - 8 * q^90 - 16 * q^91 - 28 * q^92 + 26 * q^93 + 10 * q^94 + 12 * q^95 - 2 * q^96 + 8 * q^97 - 2 * q^98 + 8 * q^99

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