LMFDB - Embedded newform 211.2.a.d.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [211,2,Mod(1,211)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(211, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("211.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	211.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:	$1.68484348265$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 14x^{7} + 11x^{6} + 66x^{5} - 36x^{4} - 123x^{3} + 38x^{2} + 72x - 8 $ x^9 - x^8 - 14x^7 + 11x^6 + 66x^5 - 36x^4 - 123x^3 + 38x^2 + 72*x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-1.79023$ of defining polynomial
Character	$\chi$	$=$	211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.79023 q^{2} +0.155219 q^{3} +1.20493 q^{4} +0.0597430 q^{5} +0.277877 q^{6} +4.81622 q^{7} -1.42336 q^{8} -2.97591 q^{9} +O(q^{10})$	\(q+1.79023 q^{2} +0.155219 q^{3} +1.20493 q^{4} +0.0597430 q^{5} +0.277877 q^{6} +4.81622 q^{7} -1.42336 q^{8} -2.97591 q^{9} +0.106954 q^{10} +2.06576 q^{11} +0.187028 q^{12} -4.00072 q^{13} +8.62216 q^{14} +0.00927322 q^{15} -4.95800 q^{16} -0.192873 q^{17} -5.32757 q^{18} +2.59531 q^{19} +0.0719863 q^{20} +0.747568 q^{21} +3.69819 q^{22} +0.395442 q^{23} -0.220931 q^{24} -4.99643 q^{25} -7.16221 q^{26} -0.927572 q^{27} +5.80323 q^{28} +4.46491 q^{29} +0.0166012 q^{30} -10.2119 q^{31} -6.02927 q^{32} +0.320645 q^{33} -0.345287 q^{34} +0.287736 q^{35} -3.58577 q^{36} -6.30175 q^{37} +4.64622 q^{38} -0.620986 q^{39} -0.0850355 q^{40} +0.0191523 q^{41} +1.33832 q^{42} -4.41220 q^{43} +2.48910 q^{44} -0.177790 q^{45} +0.707933 q^{46} +11.3138 q^{47} -0.769574 q^{48} +16.1960 q^{49} -8.94477 q^{50} -0.0299374 q^{51} -4.82059 q^{52} +7.19074 q^{53} -1.66057 q^{54} +0.123415 q^{55} -6.85520 q^{56} +0.402841 q^{57} +7.99322 q^{58} -2.60805 q^{59} +0.0111736 q^{60} +6.47741 q^{61} -18.2817 q^{62} -14.3326 q^{63} -0.877783 q^{64} -0.239015 q^{65} +0.574028 q^{66} +7.28209 q^{67} -0.232398 q^{68} +0.0613800 q^{69} +0.515114 q^{70} -5.05253 q^{71} +4.23577 q^{72} +15.0934 q^{73} -11.2816 q^{74} -0.775539 q^{75} +3.12718 q^{76} +9.94917 q^{77} -1.11171 q^{78} -2.76825 q^{79} -0.296206 q^{80} +8.78375 q^{81} +0.0342871 q^{82} +11.6996 q^{83} +0.900769 q^{84} -0.0115228 q^{85} -7.89886 q^{86} +0.693037 q^{87} -2.94031 q^{88} -14.4184 q^{89} -0.318285 q^{90} -19.2683 q^{91} +0.476481 q^{92} -1.58508 q^{93} +20.2544 q^{94} +0.155052 q^{95} -0.935854 q^{96} +4.92089 q^{97} +28.9946 q^{98} -6.14751 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - q^{2} - q^{3} + 11 q^{4} + 15 q^{5} - 5 q^{6} - 2 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) $ 9 * q - q^2 - q^3 + 11 * q^4 + 15 * q^5 - 5 * q^6 - 2 * q^7 - 6 * q^8 + 14 * q^9	\( 9 q - q^{2} - q^{3} + 11 q^{4} + 15 q^{5} - 5 q^{6} - 2 q^{7} - 6 q^{8} + 14 q^{9} - 2 q^{10} + 13 q^{11} - 5 q^{12} - 4 q^{13} + 13 q^{14} + 2 q^{15} + 3 q^{16} + 4 q^{17} - 21 q^{18} - 2 q^{19} + 32 q^{20} + 9 q^{21} - 8 q^{22} - 3 q^{23} + 4 q^{24} + 14 q^{25} + 13 q^{26} - 4 q^{27} - 20 q^{28} + 26 q^{29} - 17 q^{30} + 5 q^{31} - 8 q^{32} - 10 q^{33} - 21 q^{34} - 21 q^{35} - 10 q^{36} + 5 q^{37} + 13 q^{38} - 40 q^{39} - 52 q^{40} + 20 q^{41} - 46 q^{42} - 37 q^{43} - 10 q^{44} + 36 q^{45} - 38 q^{46} + 4 q^{47} - 32 q^{48} + 11 q^{49} - 16 q^{50} - 42 q^{51} - 20 q^{52} + 13 q^{53} - 30 q^{54} + 6 q^{55} + 23 q^{56} + 4 q^{57} - 17 q^{58} + 14 q^{59} - 4 q^{60} + 23 q^{61} - 19 q^{62} + q^{63} + 14 q^{64} - 13 q^{65} + 31 q^{66} - 3 q^{67} + 53 q^{68} + 16 q^{69} + 9 q^{70} + 19 q^{71} - 21 q^{72} + 17 q^{73} + 7 q^{74} + 4 q^{75} - 34 q^{76} + 13 q^{77} + 44 q^{78} + 7 q^{79} + 27 q^{80} + 13 q^{81} - 14 q^{82} + 6 q^{83} + 48 q^{84} - 4 q^{85} - 24 q^{86} - 5 q^{87} - 38 q^{88} + 33 q^{89} - 44 q^{90} - 27 q^{91} + 37 q^{92} - 27 q^{93} - 10 q^{94} - 23 q^{95} + 43 q^{96} - 11 q^{97} + 26 q^{98} + 2 q^{99}+O(q^{100}) \) 9 * q - q^2 - q^3 + 11 * q^4 + 15 * q^5 - 5 * q^6 - 2 * q^7 - 6 * q^8 + 14 * q^9 - 2 * q^10 + 13 * q^11 - 5 * q^12 - 4 * q^13 + 13 * q^14 + 2 * q^15 + 3 * q^16 + 4 * q^17 - 21 * q^18 - 2 * q^19 + 32 * q^20 + 9 * q^21 - 8 * q^22 - 3 * q^23 + 4 * q^24 + 14 * q^25 + 13 * q^26 - 4 * q^27 - 20 * q^28 + 26 * q^29 - 17 * q^30 + 5 * q^31 - 8 * q^32 - 10 * q^33 - 21 * q^34 - 21 * q^35 - 10 * q^36 + 5 * q^37 + 13 * q^38 - 40 * q^39 - 52 * q^40 + 20 * q^41 - 46 * q^42 - 37 * q^43 - 10 * q^44 + 36 * q^45 - 38 * q^46 + 4 * q^47 - 32 * q^48 + 11 * q^49 - 16 * q^50 - 42 * q^51 - 20 * q^52 + 13 * q^53 - 30 * q^54 + 6 * q^55 + 23 * q^56 + 4 * q^57 - 17 * q^58 + 14 * q^59 - 4 * q^60 + 23 * q^61 - 19 * q^62 + q^63 + 14 * q^64 - 13 * q^65 + 31 * q^66 - 3 * q^67 + 53 * q^68 + 16 * q^69 + 9 * q^70 + 19 * q^71 - 21 * q^72 + 17 * q^73 + 7 * q^74 + 4 * q^75 - 34 * q^76 + 13 * q^77 + 44 * q^78 + 7 * q^79 + 27 * q^80 + 13 * q^81 - 14 * q^82 + 6 * q^83 + 48 * q^84 - 4 * q^85 - 24 * q^86 - 5 * q^87 - 38 * q^88 + 33 * q^89 - 44 * q^90 - 27 * q^91 + 37 * q^92 - 27 * q^93 - 10 * q^94 - 23 * q^95 + 43 * q^96 - 11 * q^97 + 26 * q^98 + 2 * 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 $

$2$	1.79023	1.26589	0.632943	−	0.774199i	$-0.281847\pi$
$2$	1.79023	1.26589	0.632943	+	0.774199i	$0.281847\pi$
$3$	0.155219	0.0896155	0.0448078	−	0.998996i	$-0.485732\pi$
$3$	0.155219	0.0896155	0.0448078	+	0.998996i	$0.485732\pi$
$4$	1.20493	0.602466
$5$	0.0597430	0.0267179	0.0133589	−	0.999911i	$-0.495748\pi$
$5$	0.0597430	0.0267179	0.0133589	+	0.999911i	$0.495748\pi$
$6$	0.277877	0.113443
$7$	4.81622	1.82036	0.910181	−	0.414211i	$-0.135942\pi$
$7$	4.81622	1.82036	0.910181	+	0.414211i	$0.135942\pi$
$8$	−1.42336	−0.503232
$9$	−2.97591	−0.991969
$10$	0.106954	0.0338218
$11$	2.06576	0.622850	0.311425	−	0.950271i	$-0.399194\pi$
$11$	2.06576	0.622850	0.311425	+	0.950271i	$0.399194\pi$
$12$	0.187028	0.0539903
$13$	−4.00072	−1.10960	−0.554800	−	0.831984i	$-0.687205\pi$
$13$	−4.00072	−1.10960	−0.554800	+	0.831984i	$0.687205\pi$
$14$	8.62216	2.30437
$15$	0.00927322	0.00239434
$16$	−4.95800	−1.23950
$17$	−0.192873	−0.0467785	−0.0233892	−	0.999726i	$-0.507446\pi$
$17$	−0.192873	−0.0467785	−0.0233892	+	0.999726i	$0.507446\pi$
$18$	−5.32757	−1.25572
$19$	2.59531	0.595406	0.297703	−	0.954659i	$-0.403779\pi$
$19$	2.59531	0.595406	0.297703	+	0.954659i	$0.403779\pi$
$20$	0.0719863	0.0160966
$21$	0.747568	0.163133
$22$	3.69819	0.788457
$23$	0.395442	0.0824554	0.0412277	−	0.999150i	$-0.486873\pi$
$23$	0.395442	0.0824554	0.0412277	+	0.999150i	$0.486873\pi$
$24$	−0.220931	−0.0450974
$25$	−4.99643	−0.999286
$26$	−7.16221	−1.40463
$27$	−0.927572	−0.178511
$28$	5.80323	1.09671
$29$	4.46491	0.829112	0.414556	−	0.910024i	$-0.363937\pi$
$29$	4.46491	0.829112	0.414556	+	0.910024i	$0.363937\pi$
$30$	0.0166012	0.00303096
$31$	−10.2119	−1.83411	−0.917056	−	0.398759i	$-0.869441\pi$
$31$	−10.2119	−1.83411	−0.917056	+	0.398759i	$0.869441\pi$
$32$	−6.02927	−1.06583
$33$	0.320645	0.0558171
$34$	−0.345287	−0.0592162
$35$	0.287736	0.0486362
$36$	−3.58577	−0.597628
$37$	−6.30175	−1.03600	−0.518001	−	0.855380i	$-0.673324\pi$
$37$	−6.30175	−1.03600	−0.518001	+	0.855380i	$0.673324\pi$
$38$	4.64622	0.753716
$39$	−0.620986	−0.0994373
$40$	−0.0850355	−0.0134453
$41$	0.0191523	0.00299109	0.00149554	−	0.999999i	$-0.499524\pi$
$41$	0.0191523	0.00299109	0.00149554	+	0.999999i	$0.499524\pi$
$42$	1.33832	0.206507
$43$	−4.41220	−0.672854	−0.336427	−	0.941710i	$-0.609218\pi$
$43$	−4.41220	−0.672854	−0.336427	+	0.941710i	$0.609218\pi$
$44$	2.48910	0.375246
$45$	−0.177790	−0.0265033
$46$	0.707933	0.104379
$47$	11.3138	1.65029	0.825145	−	0.564921i	$-0.191093\pi$
$47$	11.3138	1.65029	0.825145	+	0.564921i	$0.191093\pi$
$48$	−0.769574	−0.111078
$49$	16.1960	2.31372
$50$	−8.94477	−1.26498
$51$	−0.0299374	−0.00419208
$52$	−4.82059	−0.668496
$53$	7.19074	0.987725	0.493862	−	0.869540i	$-0.335585\pi$
$53$	7.19074	0.987725	0.493862	+	0.869540i	$0.335585\pi$
$54$	−1.66057	−0.225975
$55$	0.123415	0.0166412
$56$	−6.85520	−0.916065
$57$	0.402841	0.0533576
$58$	7.99322	1.04956
$59$	−2.60805	−0.339539	−0.169769	−	0.985484i	$-0.554302\pi$
$59$	−2.60805	−0.339539	−0.169769	+	0.985484i	$0.554302\pi$
$60$	0.0111736	0.00144251
$61$	6.47741	0.829347	0.414673	−	0.909970i	$-0.363896\pi$
$61$	6.47741	0.829347	0.414673	+	0.909970i	$0.363896\pi$
$62$	−18.2817	−2.32178
$63$	−14.3326	−1.80574
$64$	−0.877783	−0.109723
$65$	−0.239015	−0.0296461
$66$	0.574028	0.0706580
$67$	7.28209	0.889649	0.444824	−	0.895618i	$-0.353266\pi$
$67$	7.28209	0.889649	0.444824	+	0.895618i	$0.353266\pi$
$68$	−0.232398	−0.0281824
$69$	0.0613800	0.00738928
$70$	0.515114	0.0615679
$71$	−5.05253	−0.599625	−0.299813	−	0.953998i	$-0.596924\pi$
$71$	−5.05253	−0.599625	−0.299813	+	0.953998i	$0.596924\pi$
$72$	4.23577	0.499191
$73$	15.0934	1.76655	0.883274	−	0.468857i	$-0.155334\pi$
$73$	15.0934	1.76655	0.883274	+	0.468857i	$0.155334\pi$
$74$	−11.2816	−1.31146
$75$	−0.775539	−0.0895515
$76$	3.12718	0.358712
$77$	9.94917	1.13381
$78$	−1.11171	−0.125876
$79$	−2.76825	−0.311453	−0.155726	−	0.987800i	$-0.549772\pi$
$79$	−2.76825	−0.311453	−0.155726	+	0.987800i	$0.549772\pi$
$80$	−0.296206	−0.0331168
$81$	8.78375	0.975972
$82$	0.0342871	0.00378638
$83$	11.6996	1.28419	0.642096	−	0.766624i	$-0.278065\pi$
$83$	11.6996	1.28419	0.642096	+	0.766624i	$0.278065\pi$
$84$	0.900769	0.0982819
$85$	−0.0115228	−0.00124982
$86$	−7.89886	−0.851756
$87$	0.693037	0.0743013
$88$	−2.94031	−0.313438
$89$	−14.4184	−1.52834	−0.764171	−	0.645013i	$-0.776852\pi$
$89$	−14.4184	−1.52834	−0.764171	+	0.645013i	$0.776852\pi$
$90$	−0.318285	−0.0335502
$91$	−19.2683	−2.01987
$92$	0.476481	0.0496766
$93$	−1.58508	−0.164365
$94$	20.2544	2.08908
$95$	0.155052	0.0159080
$96$	−0.935854	−0.0955152
$97$	4.92089	0.499641	0.249820	−	0.968292i	$-0.419628\pi$
$97$	4.92089	0.499641	0.249820	+	0.968292i	$0.419628\pi$
$98$	28.9946	2.92890
$99$	−6.14751	−0.617848
$100$	−6.02036	−0.602036
$101$	13.8029	1.37344	0.686722	−	0.726920i	$-0.259049\pi$
$101$	13.8029	1.37344	0.686722	+	0.726920i	$0.259049\pi$
$102$	−0.0535949	−0.00530669
$103$	−9.85426	−0.970969	−0.485484	−	0.874245i	$-0.661357\pi$
$103$	−9.85426	−0.970969	−0.485484	+	0.874245i	$0.661357\pi$
$104$	5.69444	0.558386
$105$	0.0446619	0.00435856
$106$	12.8731	1.25035
$107$	3.30868	0.319862	0.159931	−	0.987128i	$-0.448873\pi$
$107$	3.30868	0.319862	0.159931	+	0.987128i	$0.448873\pi$
$108$	−1.11766	−0.107547
$109$	−9.72923	−0.931891	−0.465946	−	0.884813i	$-0.654286\pi$
$109$	−9.72923	−0.931891	−0.465946	+	0.884813i	$0.654286\pi$
$110$	0.220941	0.0210659
$111$	−0.978150	−0.0928419
$112$	−23.8789	−2.25634
$113$	−17.4471	−1.64128	−0.820642	−	0.571442i	$-0.806384\pi$
$113$	−17.4471	−1.64128	−0.820642	+	0.571442i	$0.806384\pi$
$114$	0.721179	0.0675446
$115$	0.0236249	0.00220303
$116$	5.37991	0.499512
$117$	11.9058	1.10069
$118$	−4.66901	−0.429818
$119$	−0.928918	−0.0851537
$120$	−0.0131991	−0.00120491
$121$	−6.73263	−0.612057
$122$	11.5961	1.04986
$123$	0.00297280	0.000268048 0
$124$	−12.3047	−1.10499
$125$	−0.597217	−0.0534167
$126$	−25.6588	−2.28586
$127$	−10.1961	−0.904758	−0.452379	−	0.891826i	$-0.649424\pi$
$127$	−10.1961	−0.904758	−0.452379	+	0.891826i	$0.649424\pi$
$128$	10.4871	0.926937
$129$	−0.684855	−0.0602981
$130$	−0.427892	−0.0375286
$131$	13.8657	1.21145	0.605726	−	0.795674i	$-0.292883\pi$
$131$	13.8657	1.21145	0.605726	+	0.795674i	$0.292883\pi$
$132$	0.386355	0.0336279
$133$	12.4996	1.08385
$134$	13.0366	1.12619
$135$	−0.0554159	−0.00476944
$136$	0.274526	0.0235404
$137$	8.73716	0.746466	0.373233	−	0.927738i	$-0.378249\pi$
$137$	8.73716	0.746466	0.373233	+	0.927738i	$0.378249\pi$
$138$	0.109884	0.00935399
$139$	10.2989	0.873542	0.436771	−	0.899573i	$-0.356122\pi$
$139$	10.2989	0.873542	0.436771	+	0.899573i	$0.356122\pi$
$140$	0.346702	0.0293017
$141$	1.75612	0.147892
$142$	−9.04521	−0.759057
$143$	−8.26452	−0.691114
$144$	14.7546	1.22955
$145$	0.266747	0.0221521
$146$	27.0207	2.23625
$147$	2.51392	0.207345
$148$	−7.59319	−0.624156
$149$	20.3672	1.66855	0.834275	−	0.551349i	$-0.185887\pi$
$149$	20.3672	1.66855	0.834275	+	0.551349i	$0.185887\pi$
$150$	−1.38840	−0.113362
$151$	−1.26511	−0.102953	−0.0514767	−	0.998674i	$-0.516393\pi$
$151$	−1.26511	−0.102953	−0.0514767	+	0.998674i	$0.516393\pi$
$152$	−3.69406	−0.299628
$153$	0.573971	0.0464028
$154$	17.8113	1.43528
$155$	−0.610089	−0.0490036
$156$	−0.748246	−0.0599076
$157$	−13.9354	−1.11216	−0.556082	−	0.831127i	$-0.687696\pi$
$157$	−13.9354	−1.11216	−0.556082	+	0.831127i	$0.687696\pi$
$158$	−4.95582	−0.394264
$159$	1.11614	0.0885154
$160$	−0.360206	−0.0284768
$161$	1.90454	0.150099
$162$	15.7249	1.23547
$163$	−6.37301	−0.499173	−0.249586	−	0.968353i	$-0.580295\pi$
$163$	−6.37301	−0.499173	−0.249586	+	0.968353i	$0.580295\pi$
$164$	0.0230772	0.00180203
$165$	0.0191563	0.00149131
$166$	20.9449	1.62564
$167$	18.1332	1.40319	0.701593	−	0.712578i	$-0.252473\pi$
$167$	18.1332	1.40319	0.701593	+	0.712578i	$0.252473\pi$
$168$	−1.06405	−0.0820936
$169$	3.00573	0.231210
$170$	−0.0206285	−0.00158213
$171$	−7.72342	−0.590624
$172$	−5.31640	−0.405372
$173$	−10.4755	−0.796438	−0.398219	−	0.917290i	$-0.630372\pi$
$173$	−10.4755	−0.796438	−0.398219	+	0.917290i	$0.630372\pi$
$174$	1.24070	0.0940570
$175$	−24.0639	−1.81906
$176$	−10.2421	−0.772024
$177$	−0.404818	−0.0304280
$178$	−25.8122	−1.93471
$179$	−18.2362	−1.36304	−0.681519	−	0.731801i	$-0.738680\pi$
$179$	−18.2362	−1.36304	−0.681519	+	0.731801i	$0.738680\pi$
$180$	−0.214224	−0.0159673
$181$	0.711772	0.0529056	0.0264528	−	0.999650i	$-0.491579\pi$
$181$	0.711772	0.0529056	0.0264528	+	0.999650i	$0.491579\pi$
$182$	−34.4948	−2.55693
$183$	1.00541	0.0743224
$184$	−0.562855	−0.0414942
$185$	−0.376486	−0.0276798
$186$	−2.83766	−0.208067
$187$	−0.398429	−0.0291360
$188$	13.6324	0.994244
$189$	−4.46740	−0.324955
$190$	0.277579	0.0201377
$191$	−21.6049	−1.56328	−0.781638	−	0.623732i	$-0.785616\pi$
$191$	−21.6049	−1.56328	−0.781638	+	0.623732i	$0.785616\pi$
$192$	−0.136248	−0.00983287
$193$	−14.5991	−1.05086	−0.525432	−	0.850836i	$-0.676096\pi$
$193$	−14.5991	−1.05086	−0.525432	+	0.850836i	$0.676096\pi$
$194$	8.80954	0.632488
$195$	−0.0370995	−0.00265675
$196$	19.5151	1.39394
$197$	−10.5420	−0.751086	−0.375543	−	0.926805i	$-0.622544\pi$
$197$	−10.5420	−0.751086	−0.375543	+	0.926805i	$0.622544\pi$
$198$	−11.0055	−0.782125
$199$	−4.24119	−0.300650	−0.150325	−	0.988637i	$-0.548032\pi$
$199$	−4.24119	−0.300650	−0.150325	+	0.988637i	$0.548032\pi$
$200$	7.11170	0.502873
$201$	1.13032	0.0797263
$202$	24.7105	1.73862
$203$	21.5040	1.50928
$204$	−0.0360726	−0.00252558
$205$	0.00114422	7.99155e−5 0
$206$	−17.6414	−1.22914
$207$	−1.17680	−0.0817932
$208$	19.8356	1.37535
$209$	5.36130	0.370849
$210$	0.0799552	0.00551744
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	8.66436	0.595071
$213$	−0.784247	−0.0537357
$214$	5.92331	0.404909
$215$	−0.263598	−0.0179772
$216$	1.32027	0.0898327
$217$	−49.1828	−3.33875
$218$	−17.4176	−1.17967
$219$	2.34278	0.158310
$220$	0.148706	0.0100258
$221$	0.771628	0.0519053
$222$	−1.75112	−0.117527
$223$	7.96135	0.533132	0.266566	−	0.963817i	$-0.414111\pi$
$223$	7.96135	0.533132	0.266566	+	0.963817i	$0.414111\pi$
$224$	−29.0383	−1.94020
$225$	14.8689	0.991261
$226$	−31.2344	−2.07768
$227$	−18.9906	−1.26045	−0.630226	−	0.776412i	$-0.717038\pi$
$227$	−18.9906	−1.26045	−0.630226	+	0.776412i	$0.717038\pi$
$228$	0.485396	0.0321462
$229$	2.76154	0.182488	0.0912440	−	0.995829i	$-0.470916\pi$
$229$	2.76154	0.182488	0.0912440	+	0.995829i	$0.470916\pi$
$230$	0.0422941	0.00278879
$231$	1.54430	0.101607
$232$	−6.35515	−0.417236
$233$	−13.0678	−0.856097	−0.428049	−	0.903756i	$-0.640799\pi$
$233$	−13.0678	−0.856097	−0.428049	+	0.903756i	$0.640799\pi$
$234$	21.3141	1.39334
$235$	0.675922	0.0440923
$236$	−3.14252	−0.204561
$237$	−0.429685	−0.0279110
$238$	−1.66298	−0.107795
$239$	11.8287	0.765136	0.382568	−	0.923927i	$-0.375040\pi$
$239$	11.8287	0.765136	0.382568	+	0.923927i	$0.375040\pi$
$240$	−0.0459767	−0.00296778
$241$	13.1180	0.845007	0.422503	−	0.906361i	$-0.361151\pi$
$241$	13.1180	0.845007	0.422503	+	0.906361i	$0.361151\pi$
$242$	−12.0530	−0.774794
$243$	4.14612	0.265974
$244$	7.80484	0.499654
$245$	0.967599	0.0618176
$246$	0.00532200	0.000339318 0
$247$	−10.3831	−0.660662
$248$	14.5352	0.922984
$249$	1.81599	0.115084
$250$	−1.06916	−0.0676194
$251$	11.2787	0.711907	0.355953	−	0.934504i	$-0.384156\pi$
$251$	11.2787	0.711907	0.355953	+	0.934504i	$0.384156\pi$
$252$	−17.2699	−1.08790
$253$	0.816889	0.0513574
$254$	−18.2534	−1.14532
$255$	−0.00178855	−0.000112003 0
$256$	20.5299	1.28312
$257$	−6.94577	−0.433265	−0.216633	−	0.976253i	$-0.569507\pi$
$257$	−6.94577	−0.433265	−0.216633	+	0.976253i	$0.569507\pi$
$258$	−1.22605	−0.0763305
$259$	−30.3507	−1.88590
$260$	−0.287997	−0.0178608
$261$	−13.2871	−0.822454
$262$	24.8228	1.53356
$263$	3.57750	0.220598	0.110299	−	0.993898i	$-0.464819\pi$
$263$	3.57750	0.220598	0.110299	+	0.993898i	$0.464819\pi$
$264$	−0.456391	−0.0280889
$265$	0.429596	0.0263899
$266$	22.3772	1.37204
$267$	−2.23800	−0.136963
$268$	8.77443	0.535983
$269$	1.61864	0.0986905	0.0493453	−	0.998782i	$-0.484287\pi$
$269$	1.61864	0.0986905	0.0493453	+	0.998782i	$0.484287\pi$
$270$	−0.0992074	−0.00603757
$271$	4.92583	0.299223	0.149612	−	0.988745i	$-0.452198\pi$
$271$	4.92583	0.299223	0.149612	+	0.988745i	$0.452198\pi$
$272$	0.956263	0.0579819
$273$	−2.99081	−0.181012
$274$	15.6415	0.944940
$275$	−10.3214	−0.622406
$276$	0.0739587	0.00445179
$277$	−1.28488	−0.0772010	−0.0386005	−	0.999255i	$-0.512290\pi$
$277$	−1.28488	−0.0772010	−0.0386005	+	0.999255i	$0.512290\pi$
$278$	18.4374	1.10580
$279$	30.3897	1.81938
$280$	−0.409550	−0.0244753
$281$	6.38440	0.380861	0.190431	−	0.981701i	$-0.439012\pi$
$281$	6.38440	0.380861	0.190431	+	0.981701i	$0.439012\pi$
$282$	3.14386	0.187214
$283$	−23.6087	−1.40339	−0.701696	−	0.712476i	$-0.747574\pi$
$283$	−23.6087	−1.40339	−0.701696	+	0.712476i	$0.747574\pi$
$284$	−6.08796	−0.361254
$285$	0.0240669	0.00142560
$286$	−14.7954	−0.874872
$287$	0.0922418	0.00544486
$288$	17.9425	1.05727
$289$	−16.9628	−0.997812
$290$	0.477539	0.0280420
$291$	0.763814	0.0447756
$292$	18.1865	1.06429
$293$	22.0893	1.29047	0.645235	−	0.763984i	$-0.276759\pi$
$293$	22.0893	1.29047	0.645235	+	0.763984i	$0.276759\pi$
$294$	4.50051	0.262475
$295$	−0.155813	−0.00907176
$296$	8.96964	0.521350
$297$	−1.91614	−0.111186
$298$	36.4621	2.11219
$299$	−1.58205	−0.0914924
$300$	−0.934472	−0.0539518
$301$	−21.2501	−1.22484
$302$	−2.26485	−0.130327
$303$	2.14247	0.123082
$304$	−12.8676	−0.738006
$305$	0.386980	0.0221584
$306$	1.02754	0.0587406
$307$	9.61393	0.548696	0.274348	−	0.961630i	$-0.411538\pi$
$307$	9.61393	0.548696	0.274348	+	0.961630i	$0.411538\pi$
$308$	11.9881	0.683084
$309$	−1.52956	−0.0870139
$310$	−1.09220	−0.0620329
$311$	3.38745	0.192084	0.0960422	−	0.995377i	$-0.469382\pi$
$311$	3.38745	0.192084	0.0960422	+	0.995377i	$0.469382\pi$
$312$	0.883884	0.0500401
$313$	7.55901	0.427260	0.213630	−	0.976915i	$-0.431471\pi$
$313$	7.55901	0.427260	0.213630	+	0.976915i	$0.431471\pi$
$314$	−24.9476	−1.40787
$315$	−0.856275	−0.0482456
$316$	−3.33556	−0.187640
$317$	21.5740	1.21172	0.605859	−	0.795572i	$-0.292830\pi$
$317$	21.5740	1.21172	0.605859	+	0.795572i	$0.292830\pi$
$318$	1.99815	0.112050
$319$	9.22343	0.516413
$320$	−0.0524414	−0.00293156
$321$	0.513569	0.0286646
$322$	3.40957	0.190008
$323$	−0.500565	−0.0278522
$324$	10.5838	0.587990
$325$	19.9893	1.10881
$326$	−11.4092	−0.631895
$327$	−1.51016	−0.0835119
$328$	−0.0272606	−0.00150521
$329$	54.4899	3.00413
$330$	0.0342942	0.00188783
$331$	−22.6955	−1.24746	−0.623730	−	0.781640i	$-0.714383\pi$
$331$	−22.6955	−1.24746	−0.623730	+	0.781640i	$0.714383\pi$
$332$	14.0972	0.773683
$333$	18.7534	1.02768
$334$	32.4626	1.77627
$335$	0.435054	0.0237695
$336$	−3.70644	−0.202203
$337$	20.8621	1.13643	0.568217	−	0.822879i	$-0.307634\pi$
$337$	20.8621	1.13643	0.568217	+	0.822879i	$0.307634\pi$
$338$	5.38096	0.292685
$339$	−2.70811	−0.147085
$340$	−0.0138842	−0.000752975 0
$341$	−21.0953	−1.14238
$342$	−13.8267	−0.747663
$343$	44.2901	2.39144
$344$	6.28013	0.338602
$345$	0.00366702	0.000197426 0
$346$	−18.7536	−1.00820
$347$	−31.0238	−1.66545	−0.832723	−	0.553690i	$-0.813219\pi$
$347$	−31.0238	−1.66545	−0.832723	+	0.553690i	$0.813219\pi$
$348$	0.835062	0.0447640
$349$	25.3335	1.35607	0.678036	−	0.735029i	$-0.262831\pi$
$349$	25.3335	1.35607	0.678036	+	0.735029i	$0.262831\pi$
$350$	−43.0800	−2.30272
$351$	3.71095	0.198076
$352$	−12.4550	−0.663855
$353$	0.193283	0.0102874	0.00514371	−	0.999987i	$-0.498363\pi$
$353$	0.193283	0.0102874	0.00514371	+	0.999987i	$0.498363\pi$
$354$	−0.724718	−0.0385183
$355$	−0.301853	−0.0160207
$356$	−17.3731	−0.920775
$357$	−0.144185	−0.00763110
$358$	−32.6470	−1.72545
$359$	7.63993	0.403220	0.201610	−	0.979466i	$-0.435383\pi$
$359$	7.63993	0.403220	0.201610	+	0.979466i	$0.435383\pi$
$360$	0.253058	0.0133373
$361$	−12.2643	−0.645492
$362$	1.27424	0.0669724
$363$	−1.04503	−0.0548498
$364$	−23.2171	−1.21690
$365$	0.901725	0.0471984
$366$	1.79993	0.0940836
$367$	−8.17824	−0.426901	−0.213450	−	0.976954i	$-0.568470\pi$
$367$	−8.17824	−0.426901	−0.213450	+	0.976954i	$0.568470\pi$
$368$	−1.96060	−0.102204
$369$	−0.0569955	−0.00296707
$370$	−0.673997	−0.0350394
$371$	34.6322	1.79802
$372$	−1.90991	−0.0990243
$373$	25.9230	1.34224	0.671121	−	0.741347i	$-0.265813\pi$
$373$	25.9230	1.34224	0.671121	+	0.741347i	$0.265813\pi$
$374$	−0.713280	−0.0368828
$375$	−0.0926991	−0.00478696
$376$	−16.1036	−0.830479
$377$	−17.8628	−0.919982
$378$	−7.99768	−0.411356
$379$	29.1825	1.49900	0.749501	−	0.662003i	$-0.230293\pi$
$379$	29.1825	1.49900	0.749501	+	0.662003i	$0.230293\pi$
$380$	0.186827	0.00958402
$381$	−1.58262	−0.0810803
$382$	−38.6778	−1.97893
$383$	−28.9330	−1.47841	−0.739204	−	0.673481i	$-0.764798\pi$
$383$	−28.9330	−1.47841	−0.739204	+	0.673481i	$0.764798\pi$
$384$	1.62779	0.0830680
$385$	0.594393	0.0302931
$386$	−26.1357	−1.33027
$387$	13.1303	0.667450
$388$	5.92934	0.301017
$389$	26.5660	1.34695	0.673474	−	0.739211i	$-0.264801\pi$
$389$	26.5660	1.34695	0.673474	+	0.739211i	$0.264801\pi$
$390$	−0.0664168	−0.00336315
$391$	−0.0762699	−0.00385714
$392$	−23.0527	−1.16434
$393$	2.15221	0.108565
$394$	−18.8726	−0.950789
$395$	−0.165384	−0.00832136
$396$	−7.40734	−0.372233
$397$	6.06292	0.304289	0.152145	−	0.988358i	$-0.451382\pi$
$397$	6.06292	0.304289	0.152145	+	0.988358i	$0.451382\pi$
$398$	−7.59272	−0.380588
$399$	1.94017	0.0971302
$400$	24.7723	1.23862
$401$	−28.3752	−1.41699	−0.708494	−	0.705717i	$-0.750625\pi$
$401$	−28.3752	−1.41699	−0.708494	+	0.705717i	$0.750625\pi$
$402$	2.02353	0.100924
$403$	40.8549	2.03513
$404$	16.6316	0.827454
$405$	0.524767	0.0260759
$406$	38.4971	1.91058
$407$	−13.0179	−0.645274
$408$	0.0426116	0.00210959
$409$	−23.9059	−1.18207	−0.591034	−	0.806646i	$-0.701280\pi$
$409$	−23.9059	−1.18207	−0.591034	+	0.806646i	$0.701280\pi$
$410$	0.00204841	0.000101164 0
$411$	1.35617	0.0668949
$412$	−11.8737	−0.584976
$413$	−12.5609	−0.618084
$414$	−2.10674	−0.103541
$415$	0.698966	0.0343109
$416$	24.1214	1.18265
$417$	1.59858	0.0782829
$418$	9.59798	0.469452
$419$	−5.34096	−0.260923	−0.130462	−	0.991453i	$-0.541646\pi$
$419$	−5.34096	−0.260923	−0.130462	+	0.991453i	$0.541646\pi$
$420$	0.0538146	0.00262588
$421$	9.08557	0.442804	0.221402	−	0.975183i	$-0.428937\pi$
$421$	9.08557	0.442804	0.221402	+	0.975183i	$0.428937\pi$
$422$	1.79023	0.0871472
$423$	−33.6689	−1.63704
$424$	−10.2350	−0.497055
$425$	0.963674	0.0467451
$426$	−1.40398	−0.0680233
$427$	31.1966	1.50971
$428$	3.98674	0.192706
$429$	−1.28281	−0.0619346
$430$	−0.471901	−0.0227571
$431$	11.7221	0.564633	0.282316	−	0.959321i	$-0.408897\pi$
$431$	11.7221	0.564633	0.282316	+	0.959321i	$0.408897\pi$
$432$	4.59891	0.221265
$433$	−11.3028	−0.543180	−0.271590	−	0.962413i	$-0.587549\pi$
$433$	−11.3028	−0.543180	−0.271590	+	0.962413i	$0.587549\pi$
$434$	−88.0487	−4.22647
$435$	0.0414041	0.00198517
$436$	−11.7231	−0.561433
$437$	1.02630	0.0490944
$438$	4.19411	0.200403
$439$	19.9451	0.951928	0.475964	−	0.879465i	$-0.342099\pi$
$439$	19.9451	0.951928	0.475964	+	0.879465i	$0.342099\pi$
$440$	−0.175663	−0.00837441
$441$	−48.1979	−2.29514
$442$	1.38139	0.0657062
$443$	−40.9953	−1.94774	−0.973872	−	0.227098i	$-0.927076\pi$
$443$	−40.9953	−1.94774	−0.973872	+	0.227098i	$0.927076\pi$
$444$	−1.17860	−0.0559341
$445$	−0.861395	−0.0408341
$446$	14.2527	0.674884
$447$	3.16137	0.149528
$448$	−4.22760	−0.199735
$449$	14.4969	0.684151	0.342076	−	0.939672i	$-0.388870\pi$
$449$	14.4969	0.684151	0.342076	+	0.939672i	$0.388870\pi$
$450$	26.6188	1.25482
$451$	0.0395641	0.00186300
$452$	−21.0226	−0.988819
$453$	−0.196369	−0.00922623
$454$	−33.9976	−1.59559
$455$	−1.15115	−0.0539667
$456$	−0.573386	−0.0268513
$457$	−33.4629	−1.56533	−0.782665	−	0.622443i	$-0.786140\pi$
$457$	−33.4629	−1.56533	−0.782665	+	0.622443i	$0.786140\pi$
$458$	4.94380	0.231009
$459$	0.178903	0.00835049
$460$	0.0284664	0.00132725
$461$	10.0699	0.469003	0.234501	−	0.972116i	$-0.424654\pi$
$461$	10.0699	0.469003	0.234501	+	0.972116i	$0.424654\pi$
$462$	2.76465	0.128623
$463$	−33.7501	−1.56850	−0.784251	−	0.620443i	$-0.786953\pi$
$463$	−33.7501	−1.56850	−0.784251	+	0.620443i	$0.786953\pi$
$464$	−22.1370	−1.02769
$465$	−0.0946972	−0.00439148
$466$	−23.3943	−1.08372
$467$	−21.6743	−1.00297	−0.501485	−	0.865167i	$-0.667213\pi$
$467$	−21.6743	−1.00297	−0.501485	+	0.865167i	$0.667213\pi$
$468$	14.3456	0.663127
$469$	35.0722	1.61948
$470$	1.21006	0.0558158
$471$	−2.16303	−0.0996672
$472$	3.71218	0.170867
$473$	−9.11455	−0.419087
$474$	−0.769236	−0.0353322
$475$	−12.9673	−0.594981
$476$	−1.11928	−0.0513023
$477$	−21.3990	−0.979792
$478$	21.1761	0.968574
$479$	12.2291	0.558763	0.279381	−	0.960180i	$-0.409871\pi$
$479$	12.2291	0.558763	0.279381	+	0.960180i	$0.409871\pi$
$480$	−0.0559107	−0.00255196
$481$	25.2115	1.14955
$482$	23.4843	1.06968
$483$	0.295620	0.0134512
$484$	−8.11236	−0.368744
$485$	0.293989	0.0133493
$486$	7.42251	0.336692
$487$	27.6141	1.25131	0.625656	−	0.780099i	$-0.284831\pi$
$487$	27.6141	1.25131	0.625656	+	0.780099i	$0.284831\pi$
$488$	−9.21965	−0.417354
$489$	−0.989210	−0.0447336
$490$	1.73223	0.0782540
$491$	15.8590	0.715706	0.357853	−	0.933778i	$-0.383509\pi$
$491$	15.8590	0.715706	0.357853	+	0.933778i	$0.383509\pi$
$492$	0.00358202	0.000161490 0
$493$	−0.861158	−0.0387846
$494$	−18.5882	−0.836323
$495$	−0.367271	−0.0165076
$496$	50.6306	2.27338
$497$	−24.3341	−1.09154
$498$	3.25104	0.145683
$499$	−36.8106	−1.64787	−0.823933	−	0.566687i	$-0.808225\pi$
$499$	−36.8106	−1.64787	−0.823933	+	0.566687i	$0.808225\pi$
$500$	−0.719606	−0.0321817
$501$	2.81460	0.125747
$502$	20.1915	0.901193
$503$	−26.7747	−1.19382	−0.596911	−	0.802307i	$-0.703606\pi$
$503$	−26.7747	−1.19382	−0.596911	+	0.802307i	$0.703606\pi$
$504$	20.4004	0.908708
$505$	0.824629	0.0366955
$506$	1.46242	0.0650126
$507$	0.466545	0.0207200
$508$	−12.2856	−0.545086
$509$	30.1014	1.33422	0.667110	−	0.744959i	$-0.267531\pi$
$509$	30.1014	1.33422	0.667110	+	0.744959i	$0.267531\pi$
$510$	−0.00320192	−0.000141783 0
$511$	72.6932	3.21576
$512$	15.7791	0.697345
$513$	−2.40734	−0.106287
$514$	−12.4345	−0.548464
$515$	−0.588723	−0.0259422
$516$	−0.825204	−0.0363276
$517$	23.3717	1.02788
$518$	−54.3348	−2.38733
$519$	−1.62599	−0.0713732
$520$	0.340203	0.0149189
$521$	10.1031	0.442623	0.221312	−	0.975203i	$-0.428966\pi$
$521$	10.1031	0.442623	0.221312	+	0.975203i	$0.428966\pi$
$522$	−23.7871	−1.04113
$523$	−12.9295	−0.565369	−0.282684	−	0.959213i	$-0.591225\pi$
$523$	−12.9295	−0.565369	−0.282684	+	0.959213i	$0.591225\pi$
$524$	16.7072	0.729859
$525$	−3.73517	−0.163016
$526$	6.40456	0.279252
$527$	1.96960	0.0857969
$528$	−1.58976	−0.0691853
$529$	−22.8436	−0.993201
$530$	0.769078	0.0334066
$531$	7.76131	0.336812
$532$	15.0612	0.652986
$533$	−0.0766230	−0.00331891
$534$	−4.00654	−0.173380
$535$	0.197670	0.00854604
$536$	−10.3650	−0.447700
$537$	−2.83060	−0.122149
$538$	2.89775	0.124931
$539$	33.4571	1.44110
$540$	−0.0667725	−0.00287343
$541$	25.0393	1.07652	0.538261	−	0.842778i	$-0.319081\pi$
$541$	25.0393	1.07652	0.538261	+	0.842778i	$0.319081\pi$
$542$	8.81839	0.378782
$543$	0.110480	0.00474116
$544$	1.16288	0.0498581
$545$	−0.581253	−0.0248982
$546$	−5.35424	−0.229140
$547$	−7.32438	−0.313168	−0.156584	−	0.987665i	$-0.550048\pi$
$547$	−7.32438	−0.313168	−0.156584	+	0.987665i	$0.550048\pi$
$548$	10.5277	0.449720
$549$	−19.2762	−0.822687
$550$	−18.4778	−0.787895
$551$	11.5878	0.493658
$552$	−0.0873656	−0.00371853
$553$	−13.3325	−0.566957
$554$	−2.30023	−0.0977276
$555$	−0.0584376	−0.00248054
$556$	12.4095	0.526280
$557$	41.8472	1.77312	0.886562	−	0.462609i	$-0.153087\pi$
$557$	41.8472	1.77312	0.886562	+	0.462609i	$0.153087\pi$
$558$	54.4046	2.30313
$559$	17.6519	0.746598
$560$	−1.42659	−0.0602846
$561$	−0.0618436	−0.00261104
$562$	11.4296	0.482127
$563$	22.3841	0.943376	0.471688	−	0.881765i	$-0.343645\pi$
$563$	22.3841	0.943376	0.471688	+	0.881765i	$0.343645\pi$
$564$	2.11600	0.0890997
$565$	−1.04234	−0.0438516
$566$	−42.2651	−1.77653
$567$	42.3045	1.77662
$568$	7.19155	0.301751
$569$	7.07779	0.296716	0.148358	−	0.988934i	$-0.452601\pi$
$569$	7.07779	0.296716	0.148358	+	0.988934i	$0.452601\pi$
$570$	0.0430854	0.00180465
$571$	−21.5096	−0.900147	−0.450073	−	0.892992i	$-0.648602\pi$
$571$	−21.5096	−0.900147	−0.450073	+	0.892992i	$0.648602\pi$
$572$	−9.95819	−0.416373
$573$	−3.35349	−0.140094
$574$	0.165134	0.00689257
$575$	−1.97580	−0.0823965
$576$	2.61220	0.108842
$577$	−4.17397	−0.173765	−0.0868824	−	0.996219i	$-0.527690\pi$
$577$	−4.17397	−0.173765	−0.0868824	+	0.996219i	$0.527690\pi$
$578$	−30.3674	−1.26312
$579$	−2.26605	−0.0941736
$580$	0.321412	0.0133459
$581$	56.3477	2.33770
$582$	1.36740	0.0566807
$583$	14.8544	0.615205
$584$	−21.4833	−0.888984
$585$	0.711286	0.0294080
$586$	39.5450	1.63359
$587$	17.0326	0.703012	0.351506	−	0.936186i	$-0.385670\pi$
$587$	17.0326	0.703012	0.351506	+	0.936186i	$0.385670\pi$
$588$	3.02911	0.124918
$589$	−26.5031	−1.09204
$590$	−0.278941	−0.0114838
$591$	−1.63631	−0.0673090
$592$	31.2441	1.28413
$593$	−43.5062	−1.78658	−0.893292	−	0.449476i	$-0.851611\pi$
$593$	−43.5062	−1.78658	−0.893292	+	0.449476i	$0.851611\pi$
$594$	−3.43034	−0.140749
$595$	−0.0554963	−0.00227513
$596$	24.5411	1.00524
$597$	−0.658312	−0.0269429
$598$	−2.83224	−0.115819
$599$	−8.13173	−0.332254	−0.166127	−	0.986104i	$-0.553126\pi$
$599$	−8.13173	−0.332254	−0.166127	+	0.986104i	$0.553126\pi$
$600$	1.10387	0.0450652
$601$	28.1556	1.14849	0.574245	−	0.818683i	$-0.305296\pi$
$601$	28.1556	1.14849	0.574245	+	0.818683i	$0.305296\pi$
$602$	−38.0427	−1.55050
$603$	−21.6708	−0.882504
$604$	−1.52438	−0.0620260
$605$	−0.402227	−0.0163529
$606$	3.83553	0.155808
$607$	−1.08765	−0.0441465	−0.0220732	−	0.999756i	$-0.507027\pi$
$607$	−1.08765	−0.0441465	−0.0220732	+	0.999756i	$0.507027\pi$
$608$	−15.6478	−0.634604
$609$	3.33782	0.135255
$610$	0.692784	0.0280500
$611$	−45.2634	−1.83116
$612$	0.691596	0.0279561
$613$	−37.3835	−1.50990	−0.754952	−	0.655780i	$-0.772340\pi$
$613$	−37.3835	−1.50990	−0.754952	+	0.655780i	$0.772340\pi$
$614$	17.2112	0.694586
$615$	0.000177604 0	7.16167e−6 0
$616$	−14.1612	−0.570571
$617$	−30.0208	−1.20859	−0.604297	−	0.796760i	$-0.706546\pi$
$617$	−30.0208	−1.20859	−0.604297	+	0.796760i	$0.706546\pi$
$618$	−2.73828	−0.110150
$619$	−44.3798	−1.78377	−0.891887	−	0.452258i	$-0.850619\pi$
$619$	−44.3798	−1.78377	−0.891887	+	0.452258i	$0.850619\pi$
$620$	−0.735117	−0.0295230
$621$	−0.366801	−0.0147192
$622$	6.06431	0.243157
$623$	−69.4420	−2.78214
$624$	3.07885	0.123253
$625$	24.9465	0.997859
$626$	13.5324	0.540863
$627$	0.832174	0.0332338
$628$	−16.7912	−0.670041
$629$	1.21544	0.0484626
$630$	−1.53293	−0.0610734
$631$	44.3779	1.76666	0.883328	−	0.468756i	$-0.155297\pi$
$631$	44.3779	1.76666	0.883328	+	0.468756i	$0.155297\pi$
$632$	3.94021	0.156733
$633$	0.155219	0.00616939
$634$	38.6225	1.53390
$635$	−0.609146	−0.0241732
$636$	1.34487	0.0533276
$637$	−64.7957	−2.56730
$638$	16.5121	0.653720
$639$	15.0359	0.594810
$640$	0.626530	0.0247658
$641$	−10.2781	−0.405962	−0.202981	−	0.979183i	$-0.565063\pi$
$641$	−10.2781	−0.405962	−0.202981	+	0.979183i	$0.565063\pi$
$642$	0.919408	0.0362861
$643$	22.4742	0.886296	0.443148	−	0.896449i	$-0.353862\pi$
$643$	22.4742	0.886296	0.443148	+	0.896449i	$0.353862\pi$
$644$	2.29484	0.0904294
$645$	−0.0409153	−0.00161104
$646$	−0.896128	−0.0352577
$647$	13.9695	0.549199	0.274600	−	0.961559i	$-0.411455\pi$
$647$	13.9695	0.549199	0.274600	+	0.961559i	$0.411455\pi$
$648$	−12.5024	−0.491140
$649$	−5.38761	−0.211482
$650$	35.7855	1.40362
$651$	−7.63409	−0.299204
$652$	−7.67905	−0.300735
$653$	−29.5765	−1.15742	−0.578708	−	0.815534i	$-0.696443\pi$
$653$	−29.5765	−1.15742	−0.578708	+	0.815534i	$0.696443\pi$
$654$	−2.70353	−0.105717
$655$	0.828378	0.0323674
$656$	−0.0949572	−0.00370746
$657$	−44.9165	−1.75236
$658$	97.5496	3.80288
$659$	29.6697	1.15577	0.577884	−	0.816119i	$-0.303879\pi$
$659$	29.6697	1.15577	0.577884	+	0.816119i	$0.303879\pi$
$660$	0.0230820	0.000898466 0
$661$	−4.58952	−0.178512	−0.0892559	−	0.996009i	$-0.528449\pi$
$661$	−4.58952	−0.178512	−0.0892559	+	0.996009i	$0.528449\pi$
$662$	−40.6303	−1.57914
$663$	0.119771	0.00465152
$664$	−16.6526	−0.646247
$665$	0.746765	0.0289583
$666$	33.5730	1.30093
$667$	1.76561	0.0683648
$668$	21.8492	0.845372
$669$	1.23575	0.0477769
$670$	0.778847	0.0300895
$671$	13.3808	0.516559
$672$	−4.50729	−0.173872
$673$	26.5692	1.02417	0.512084	−	0.858936i	$-0.328874\pi$
$673$	26.5692	1.02417	0.512084	+	0.858936i	$0.328874\pi$
$674$	37.3481	1.43859
$675$	4.63455	0.178384
$676$	3.62170	0.139296
$677$	−45.0672	−1.73207	−0.866036	−	0.499981i	$-0.833340\pi$
$677$	−45.0672	−1.73207	−0.866036	+	0.499981i	$0.833340\pi$
$678$	−4.84815	−0.186192
$679$	23.7001	0.909527
$680$	0.0164010	0.000628950 0
$681$	−2.94770	−0.112956
$682$	−37.7656	−1.44612
$683$	39.8374	1.52434	0.762168	−	0.647379i	$-0.224135\pi$
$683$	39.8374	1.52434	0.762168	+	0.647379i	$0.224135\pi$
$684$	−9.30620	−0.355831
$685$	0.521984	0.0199440
$686$	79.2896	3.02729
$687$	0.428643	0.0163537
$688$	21.8757	0.834003
$689$	−28.7681	−1.09598
$690$	0.00656483	0.000249919 0
$691$	−29.9736	−1.14025	−0.570125	−	0.821558i	$-0.693105\pi$
$691$	−29.9736	−1.14025	−0.570125	+	0.821558i	$0.693105\pi$
$692$	−12.6223	−0.479827
$693$	−29.6078	−1.12471
$694$	−55.5399	−2.10826
$695$	0.615288	0.0233392
$696$	−0.986438	−0.0373908
$697$	−0.00369396	−0.000139919 0
$698$	45.3529	1.71663
$699$	−2.02836	−0.0767196
$700$	−28.9954	−1.09592
$701$	20.2587	0.765160	0.382580	−	0.923922i	$-0.375036\pi$
$701$	20.2587	0.765160	0.382580	+	0.923922i	$0.375036\pi$
$702$	6.64347	0.250742
$703$	−16.3550	−0.616842
$704$	−1.81329	−0.0683409
$705$	0.104916	0.00395135
$706$	0.346022	0.0130227
$707$	66.4781	2.50017
$708$	−0.487778	−0.0183318
$709$	−18.5172	−0.695428	−0.347714	−	0.937601i	$-0.613042\pi$
$709$	−18.5172	−0.695428	−0.347714	+	0.937601i	$0.613042\pi$
$710$	−0.540388	−0.0202804
$711$	8.23807	0.308952
$712$	20.5224	0.769111
$713$	−4.03822	−0.151232
$714$	−0.258125	−0.00966009
$715$	−0.493747	−0.0184651
$716$	−21.9734	−0.821184
$717$	1.83604	0.0685681
$718$	13.6773	0.510431
$719$	11.0209	0.411011	0.205505	−	0.978656i	$-0.434116\pi$
$719$	11.0209	0.411011	0.205505	+	0.978656i	$0.434116\pi$
$720$	0.881481	0.0328509
$721$	−47.4603	−1.76751
$722$	−21.9560	−0.817118
$723$	2.03616	0.0757257
$724$	0.857637	0.0318738
$725$	−22.3086	−0.828520
$726$	−1.87085	−0.0694336
$727$	−50.8618	−1.88636	−0.943181	−	0.332280i	$-0.892182\pi$
$727$	−50.8618	−1.88636	−0.943181	+	0.332280i	$0.892182\pi$
$728$	27.4257	1.01646
$729$	−25.7077	−0.952136
$730$	1.61430	0.0597478
$731$	0.850992	0.0314751
$732$	1.21146	0.0447767
$733$	−17.0377	−0.629303	−0.314652	−	0.949207i	$-0.601888\pi$
$733$	−17.0377	−0.629303	−0.314652	+	0.949207i	$0.601888\pi$
$734$	−14.6410	−0.540408
$735$	0.150189	0.00553982
$736$	−2.38423	−0.0878837
$737$	15.0431	0.554118
$738$	−0.102035	−0.00375597
$739$	5.29491	0.194776	0.0973882	−	0.995246i	$-0.468951\pi$
$739$	5.29491	0.194776	0.0973882	+	0.995246i	$0.468951\pi$
$740$	−0.453640	−0.0166761
$741$	−1.61165	−0.0592056
$742$	61.9998	2.27608
$743$	7.95190	0.291727	0.145863	−	0.989305i	$-0.453404\pi$
$743$	7.95190	0.291727	0.145863	+	0.989305i	$0.453404\pi$
$744$	2.25613	0.0827137
$745$	1.21680	0.0445801
$746$	46.4082	1.69913
$747$	−34.8168	−1.27388
$748$	−0.480080	−0.0175534
$749$	15.9353	0.582265
$750$	−0.165953	−0.00605975
$751$	8.09390	0.295351	0.147675	−	0.989036i	$-0.452821\pi$
$751$	8.09390	0.295351	0.147675	+	0.989036i	$0.452821\pi$
$752$	−56.0940	−2.04554
$753$	1.75067	0.0637979
$754$	−31.9786	−1.16459
$755$	−0.0755817	−0.00275070
$756$	−5.38291	−0.195775
$757$	43.9391	1.59699	0.798497	−	0.601999i	$-0.205629\pi$
$757$	43.9391	1.59699	0.798497	+	0.601999i	$0.205629\pi$
$758$	52.2434	1.89757
$759$	0.126796	0.00460242
$760$	−0.220694	−0.00800541
$761$	53.3296	1.93320	0.966598	−	0.256296i	$-0.0825023\pi$
$761$	53.3296	1.93320	0.966598	+	0.256296i	$0.0825023\pi$
$762$	−2.83327	−0.102638
$763$	−46.8582	−1.69638
$764$	−26.0325	−0.941821
$765$	0.0342907	0.00123978
$766$	−51.7968	−1.87150
$767$	10.4341	0.376752
$768$	3.18662	0.114987
$769$	4.58397	0.165302	0.0826510	−	0.996579i	$-0.473661\pi$
$769$	4.58397	0.165302	0.0826510	+	0.996579i	$0.473661\pi$
$770$	1.06410	0.0383476
$771$	−1.07811	−0.0388273
$772$	−17.5909	−0.633110
$773$	−29.2984	−1.05379	−0.526895	−	0.849930i	$-0.676644\pi$
$773$	−29.2984	−1.05379	−0.526895	+	0.849930i	$0.676644\pi$
$774$	23.5063	0.844915
$775$	51.0231	1.83280
$776$	−7.00418	−0.251435
$777$	−4.71099	−0.169006
$778$	47.5592	1.70508
$779$	0.0497063	0.00178091
$780$	−0.0447024	−0.00160060
$781$	−10.4373	−0.373477
$782$	−0.136541	−0.00488269
$783$	−4.14152	−0.148006
$784$	−80.2999	−2.86785
$785$	−0.832541	−0.0297147
$786$	3.85296	0.137431
$787$	46.7670	1.66706	0.833532	−	0.552471i	$-0.186315\pi$
$787$	46.7670	1.66706	0.833532	+	0.552471i	$0.186315\pi$
$788$	−12.7024	−0.452504
$789$	0.555295	0.0197690
$790$	−0.296075	−0.0105339
$791$	−84.0291	−2.98773
$792$	8.75010	0.310921
$793$	−25.9143	−0.920243
$794$	10.8540	0.385196
$795$	0.0666814	0.00236494
$796$	−5.11035	−0.181131
$797$	20.6170	0.730291	0.365146	−	0.930950i	$-0.381019\pi$
$797$	20.6170	0.730291	0.365146	+	0.930950i	$0.381019\pi$
$798$	3.47336	0.122956
$799$	−2.18213	−0.0771981
$800$	30.1248	1.06507
$801$	42.9077	1.51607
$802$	−50.7982	−1.79375
$803$	31.1794	1.10030
$804$	1.36195	0.0480324
$805$	0.113783	0.00401032
$806$	73.1398	2.57624
$807$	0.251244	0.00884420
$808$	−19.6465	−0.691162
$809$	20.7872	0.730838	0.365419	−	0.930843i	$-0.380926\pi$
$809$	20.7872	0.730838	0.365419	+	0.930843i	$0.380926\pi$
$810$	0.939455	0.0330091
$811$	12.4296	0.436464	0.218232	−	0.975897i	$-0.429971\pi$
$811$	12.4296	0.436464	0.218232	+	0.975897i	$0.429971\pi$
$812$	25.9109	0.909293
$813$	0.764581	0.0268150
$814$	−23.3051	−0.816844
$815$	−0.380743	−0.0133368
$816$	0.148430	0.00519608
$817$	−11.4510	−0.400621
$818$	−42.7971	−1.49636
$819$	57.3408	2.00365
$820$	0.00137870	4.81464e−5 0
$821$	7.00427	0.244451	0.122225	−	0.992502i	$-0.460997\pi$
$821$	7.00427	0.244451	0.122225	+	0.992502i	$0.460997\pi$
$822$	2.42786	0.0846813
$823$	−12.4748	−0.434844	−0.217422	−	0.976078i	$-0.569765\pi$
$823$	−12.4748	−0.434844	−0.217422	+	0.976078i	$0.569765\pi$
$824$	14.0261	0.488623
$825$	−1.60208	−0.0557772
$826$	−22.4870	−0.782423
$827$	8.00731	0.278441	0.139221	−	0.990261i	$-0.455540\pi$
$827$	8.00731	0.278441	0.139221	+	0.990261i	$0.455540\pi$
$828$	−1.41796	−0.0492776
$829$	−38.5029	−1.33726	−0.668630	−	0.743595i	$-0.733119\pi$
$829$	−38.5029	−1.33726	−0.668630	+	0.743595i	$0.733119\pi$
$830$	1.25131	0.0434337
$831$	−0.199437	−0.00691841
$832$	3.51176	0.121748
$833$	−3.12377	−0.108232
$834$	2.86183	0.0990972
$835$	1.08333	0.0374901
$836$	6.46001	0.223424
$837$	9.47227	0.327410
$838$	−9.56156	−0.330299
$839$	−7.90582	−0.272939	−0.136470	−	0.990644i	$-0.543576\pi$
$839$	−7.90582	−0.272939	−0.136470	+	0.990644i	$0.543576\pi$
$840$	−0.0635698	−0.00219337
$841$	−9.06462	−0.312573
$842$	16.2653	0.560539
$843$	0.990978	0.0341311
$844$	1.20493	0.0414755
$845$	0.179571	0.00617744
$846$	−60.2751	−2.07230
$847$	−32.4259	−1.11417
$848$	−35.6517	−1.22429
$849$	−3.66451	−0.125766
$850$	1.72520	0.0591739
$851$	−2.49198	−0.0854240
$852$	−0.944965	−0.0323740
$853$	−7.66212	−0.262346	−0.131173	−	0.991359i	$-0.541874\pi$
$853$	−7.66212	−0.262346	−0.131173	+	0.991359i	$0.541874\pi$
$854$	55.8493	1.91112
$855$	−0.461420	−0.0157802
$856$	−4.70943	−0.160965
$857$	−1.66912	−0.0570162	−0.0285081	−	0.999594i	$-0.509076\pi$
$857$	−1.66912	−0.0570162	−0.0285081	+	0.999594i	$0.509076\pi$
$858$	−2.29653	−0.0784021
$859$	42.3374	1.44453	0.722267	−	0.691615i	$-0.243100\pi$
$859$	42.3374	1.44453	0.722267	+	0.691615i	$0.243100\pi$
$860$	−0.317618	−0.0108307
$861$	0.0143177	0.000487944 0
$862$	20.9852	0.714760
$863$	−39.3345	−1.33896	−0.669481	−	0.742829i	$-0.733483\pi$
$863$	−39.3345	−1.33896	−0.669481	+	0.742829i	$0.733483\pi$
$864$	5.59258	0.190263
$865$	−0.625838	−0.0212791
$866$	−20.2347	−0.687603
$867$	−2.63294	−0.0894194
$868$	−59.2620	−2.01148
$869$	−5.71855	−0.193989
$870$	0.0741229	0.00251300
$871$	−29.1336	−0.987154
$872$	13.8482	0.468958
$873$	−14.6441	−0.495628
$874$	1.83731	0.0621479
$875$	−2.87633	−0.0972377
$876$	2.82289	0.0953765
$877$	−16.0959	−0.543521	−0.271761	−	0.962365i	$-0.587606\pi$
$877$	−16.0959	−0.543521	−0.271761	+	0.962365i	$0.587606\pi$
$878$	35.7064	1.20503
$879$	3.42867	0.115646
$880$	−0.611891	−0.0206268
$881$	15.0695	0.507703	0.253851	−	0.967243i	$-0.418303\pi$
$881$	15.0695	0.507703	0.253851	+	0.967243i	$0.418303\pi$
$882$	−86.2854	−2.90538
$883$	26.8930	0.905020	0.452510	−	0.891759i	$-0.350529\pi$
$883$	26.8930	0.905020	0.452510	+	0.891759i	$0.350529\pi$
$884$	0.929760	0.0312712
$885$	−0.0241850	−0.000812971 0
$886$	−73.3911	−2.46562
$887$	−20.0836	−0.674343	−0.337171	−	0.941443i	$-0.609470\pi$
$887$	−20.0836	−0.674343	−0.337171	+	0.941443i	$0.609470\pi$
$888$	1.39226	0.0467210
$889$	−49.1067	−1.64699
$890$	−1.54210	−0.0516912
$891$	18.1451	0.607884
$892$	9.59289	0.321194
$893$	29.3629	0.982593
$894$	5.65960	0.189285
$895$	−1.08949	−0.0364175
$896$	50.5082	1.68736
$897$	−0.245564	−0.00819914
$898$	25.9528	0.866057
$899$	−45.5952	−1.52068
$900$	17.9160	0.597201
$901$	−1.38690	−0.0462042
$902$	0.0708290	0.00235835
$903$	−3.29842	−0.109764
$904$	24.8334	0.825947
$905$	0.0425234	0.00141352
$906$	−0.351547	−0.0116794
$907$	1.70574	0.0566383	0.0283192	−	0.999599i	$-0.490985\pi$
$907$	1.70574	0.0566383	0.0283192	+	0.999599i	$0.490985\pi$
$908$	−22.8824	−0.759379
$909$	−41.0763	−1.36241
$910$	−2.06082	−0.0683156
$911$	−44.8448	−1.48577	−0.742887	−	0.669417i	$-0.766544\pi$
$911$	−44.8448	−1.48577	−0.742887	+	0.669417i	$0.766544\pi$
$912$	−1.99729	−0.0661368
$913$	24.1685	0.799860
$914$	−59.9064	−1.98153
$915$	0.0600664	0.00198574
$916$	3.32747	0.109943
$917$	66.7803	2.20528
$918$	0.320278	0.0105708
$919$	22.5677	0.744441	0.372221	−	0.928144i	$-0.378597\pi$
$919$	22.5677	0.744441	0.372221	+	0.928144i	$0.378597\pi$
$920$	−0.0336266	−0.00110864
$921$	1.49226	0.0491717
$922$	18.0275	0.593704
$923$	20.2137	0.665344
$924$	1.86077	0.0612149
$925$	31.4863	1.03526
$926$	−60.4206	−1.98554
$927$	29.3254	0.963171
$928$	−26.9201	−0.883696
$929$	−29.3669	−0.963498	−0.481749	−	0.876309i	$-0.659998\pi$
$929$	−29.3669	−0.963498	−0.481749	+	0.876309i	$0.659998\pi$
$930$	−0.169530	−0.00555911
$931$	42.0338	1.37760
$932$	−15.7458	−0.515770
$933$	0.525795	0.0172137
$934$	−38.8021	−1.26964
$935$	−0.0238033	−0.000778452 0
$936$	−16.9461	−0.553902
$937$	−35.0311	−1.14442	−0.572208	−	0.820108i	$-0.693913\pi$
$937$	−35.0311	−1.14442	−0.572208	+	0.820108i	$0.693913\pi$
$938$	62.7874	2.05008
$939$	1.17330	0.0382892
$940$	0.814440	0.0265641
$941$	−1.64825	−0.0537315	−0.0268658	−	0.999639i	$-0.508553\pi$
$941$	−1.64825	−0.0537315	−0.0268658	+	0.999639i	$0.508553\pi$
$942$	−3.87233	−0.126167
$943$	0.00757363	0.000246631 0
$944$	12.9307	0.420859
$945$	−0.266896	−0.00868211
$946$	−16.3172	−0.530517
$947$	−1.07176	−0.0348276	−0.0174138	−	0.999848i	$-0.505543\pi$
$947$	−1.07176	−0.0348276	−0.0174138	+	0.999848i	$0.505543\pi$
$948$	−0.517741	−0.0168154
$949$	−60.3844	−1.96016
$950$	−23.2145	−0.753178
$951$	3.34869	0.108589
$952$	1.32218	0.0428521
$953$	−3.74089	−0.121179	−0.0605897	−	0.998163i	$-0.519298\pi$
$953$	−3.74089	−0.121179	−0.0605897	+	0.998163i	$0.519298\pi$
$954$	−38.3092	−1.24030
$955$	−1.29074	−0.0417674
$956$	14.2528	0.460969
$957$	1.43165	0.0462786
$958$	21.8930	0.707330
$959$	42.0801	1.35884
$960$	−0.00813988	−0.000262713 0
$961$	73.2829	2.36396
$962$	45.1345	1.45519
$963$	−9.84633	−0.317293
$964$	15.8063	0.509088
$965$	−0.872191	−0.0280768
$966$	0.529228	0.0170276
$967$	36.7355	1.18133	0.590666	−	0.806916i	$-0.298865\pi$
$967$	36.7355	1.18133	0.590666	+	0.806916i	$0.298865\pi$
$968$	9.58293	0.308007
$969$	−0.0776970	−0.00249599
$970$	0.526308	0.0168987
$971$	−47.1084	−1.51178	−0.755890	−	0.654698i	$-0.772796\pi$
$971$	−47.1084	−1.51178	−0.755890	+	0.654698i	$0.772796\pi$
$972$	4.99579	0.160240
$973$	49.6019	1.59016
$974$	49.4356	1.58402
$975$	3.10271	0.0993663
$976$	−32.1150	−1.02798
$977$	7.19266	0.230114	0.115057	−	0.993359i	$-0.463295\pi$
$977$	7.19266	0.230114	0.115057	+	0.993359i	$0.463295\pi$
$978$	−1.77092	−0.0566276
$979$	−29.7849	−0.951929
$980$	1.16589	0.0372430
$981$	28.9533	0.924407
$982$	28.3913	0.906001
$983$	−47.3159	−1.50914	−0.754572	−	0.656217i	$-0.772155\pi$
$983$	−47.3159	−1.50914	−0.754572	+	0.656217i	$0.772155\pi$
$984$	−0.00423135	−0.000134890 0
$985$	−0.629810	−0.0200674
$986$	−1.54167	−0.0490969
$987$	8.45785	0.269216
$988$	−12.5110	−0.398027
$989$	−1.74477	−0.0554804
$990$	−0.657500	−0.0208967
$991$	36.8359	1.17013	0.585066	−	0.810986i	$-0.301069\pi$
$991$	36.8359	1.17013	0.585066	+	0.810986i	$0.301069\pi$
$992$	61.5703	1.95486
$993$	−3.52277	−0.111792
$994$	−43.5638	−1.38176
$995$	−0.253381	−0.00803273
$996$	2.18814	0.0693340
$997$	−15.1915	−0.481118	−0.240559	−	0.970634i	$-0.577331\pi$
$997$	−15.1915	−0.481118	−0.240559	+	0.970634i	$0.577331\pi$
$998$	−65.8994	−2.08601
$999$	5.84533	0.184938

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	211.2.a.d.1.8	✓	9
3.2	odd	2		1899.2.a.j.1.2		9
4.3	odd	2		3376.2.a.s.1.5		9
5.4	even	2		5275.2.a.o.1.2		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
211.2.a.d.1.8	✓	9	1.1	even	1	trivial
1899.2.a.j.1.2		9	3.2	odd	2
3376.2.a.s.1.5		9	4.3	odd	2
5275.2.a.o.1.2		9	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	211.a (trivial)

\(f(q)\)	\(=\)	\(q+1.79023 q^{2} +0.155219 q^{3} +1.20493 q^{4} +0.0597430 q^{5} +0.277877 q^{6} +4.81622 q^{7} -1.42336 q^{8} -2.97591 q^{9} +O(q^{10})\)	\(q+1.79023 q^{2} +0.155219 q^{3} +1.20493 q^{4} +0.0597430 q^{5} +0.277877 q^{6} +4.81622 q^{7} -1.42336 q^{8} -2.97591 q^{9} +0.106954 q^{10} +2.06576 q^{11} +0.187028 q^{12} -4.00072 q^{13} +8.62216 q^{14} +0.00927322 q^{15} -4.95800 q^{16} -0.192873 q^{17} -5.32757 q^{18} +2.59531 q^{19} +0.0719863 q^{20} +0.747568 q^{21} +3.69819 q^{22} +0.395442 q^{23} -0.220931 q^{24} -4.99643 q^{25} -7.16221 q^{26} -0.927572 q^{27} +5.80323 q^{28} +4.46491 q^{29} +0.0166012 q^{30} -10.2119 q^{31} -6.02927 q^{32} +0.320645 q^{33} -0.345287 q^{34} +0.287736 q^{35} -3.58577 q^{36} -6.30175 q^{37} +4.64622 q^{38} -0.620986 q^{39} -0.0850355 q^{40} +0.0191523 q^{41} +1.33832 q^{42} -4.41220 q^{43} +2.48910 q^{44} -0.177790 q^{45} +0.707933 q^{46} +11.3138 q^{47} -0.769574 q^{48} +16.1960 q^{49} -8.94477 q^{50} -0.0299374 q^{51} -4.82059 q^{52} +7.19074 q^{53} -1.66057 q^{54} +0.123415 q^{55} -6.85520 q^{56} +0.402841 q^{57} +7.99322 q^{58} -2.60805 q^{59} +0.0111736 q^{60} +6.47741 q^{61} -18.2817 q^{62} -14.3326 q^{63} -0.877783 q^{64} -0.239015 q^{65} +0.574028 q^{66} +7.28209 q^{67} -0.232398 q^{68} +0.0613800 q^{69} +0.515114 q^{70} -5.05253 q^{71} +4.23577 q^{72} +15.0934 q^{73} -11.2816 q^{74} -0.775539 q^{75} +3.12718 q^{76} +9.94917 q^{77} -1.11171 q^{78} -2.76825 q^{79} -0.296206 q^{80} +8.78375 q^{81} +0.0342871 q^{82} +11.6996 q^{83} +0.900769 q^{84} -0.0115228 q^{85} -7.89886 q^{86} +0.693037 q^{87} -2.94031 q^{88} -14.4184 q^{89} -0.318285 q^{90} -19.2683 q^{91} +0.476481 q^{92} -1.58508 q^{93} +20.2544 q^{94} +0.155052 q^{95} -0.935854 q^{96} +4.92089 q^{97} +28.9946 q^{98} -6.14751 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - q^{2} - q^{3} + 11 q^{4} + 15 q^{5} - 5 q^{6} - 2 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) \) 9 * q - q^2 - q^3 + 11 * q^4 + 15 * q^5 - 5 * q^6 - 2 * q^7 - 6 * q^8 + 14 * q^9	\( 9 q - q^{2} - q^{3} + 11 q^{4} + 15 q^{5} - 5 q^{6} - 2 q^{7} - 6 q^{8} + 14 q^{9} - 2 q^{10} + 13 q^{11} - 5 q^{12} - 4 q^{13} + 13 q^{14} + 2 q^{15} + 3 q^{16} + 4 q^{17} - 21 q^{18} - 2 q^{19} + 32 q^{20} + 9 q^{21} - 8 q^{22} - 3 q^{23} + 4 q^{24} + 14 q^{25} + 13 q^{26} - 4 q^{27} - 20 q^{28} + 26 q^{29} - 17 q^{30} + 5 q^{31} - 8 q^{32} - 10 q^{33} - 21 q^{34} - 21 q^{35} - 10 q^{36} + 5 q^{37} + 13 q^{38} - 40 q^{39} - 52 q^{40} + 20 q^{41} - 46 q^{42} - 37 q^{43} - 10 q^{44} + 36 q^{45} - 38 q^{46} + 4 q^{47} - 32 q^{48} + 11 q^{49} - 16 q^{50} - 42 q^{51} - 20 q^{52} + 13 q^{53} - 30 q^{54} + 6 q^{55} + 23 q^{56} + 4 q^{57} - 17 q^{58} + 14 q^{59} - 4 q^{60} + 23 q^{61} - 19 q^{62} + q^{63} + 14 q^{64} - 13 q^{65} + 31 q^{66} - 3 q^{67} + 53 q^{68} + 16 q^{69} + 9 q^{70} + 19 q^{71} - 21 q^{72} + 17 q^{73} + 7 q^{74} + 4 q^{75} - 34 q^{76} + 13 q^{77} + 44 q^{78} + 7 q^{79} + 27 q^{80} + 13 q^{81} - 14 q^{82} + 6 q^{83} + 48 q^{84} - 4 q^{85} - 24 q^{86} - 5 q^{87} - 38 q^{88} + 33 q^{89} - 44 q^{90} - 27 q^{91} + 37 q^{92} - 27 q^{93} - 10 q^{94} - 23 q^{95} + 43 q^{96} - 11 q^{97} + 26 q^{98} + 2 q^{99}+O(q^{100}) \) 9 * q - q^2 - q^3 + 11 * q^4 + 15 * q^5 - 5 * q^6 - 2 * q^7 - 6 * q^8 + 14 * q^9 - 2 * q^10 + 13 * q^11 - 5 * q^12 - 4 * q^13 + 13 * q^14 + 2 * q^15 + 3 * q^16 + 4 * q^17 - 21 * q^18 - 2 * q^19 + 32 * q^20 + 9 * q^21 - 8 * q^22 - 3 * q^23 + 4 * q^24 + 14 * q^25 + 13 * q^26 - 4 * q^27 - 20 * q^28 + 26 * q^29 - 17 * q^30 + 5 * q^31 - 8 * q^32 - 10 * q^33 - 21 * q^34 - 21 * q^35 - 10 * q^36 + 5 * q^37 + 13 * q^38 - 40 * q^39 - 52 * q^40 + 20 * q^41 - 46 * q^42 - 37 * q^43 - 10 * q^44 + 36 * q^45 - 38 * q^46 + 4 * q^47 - 32 * q^48 + 11 * q^49 - 16 * q^50 - 42 * q^51 - 20 * q^52 + 13 * q^53 - 30 * q^54 + 6 * q^55 + 23 * q^56 + 4 * q^57 - 17 * q^58 + 14 * q^59 - 4 * q^60 + 23 * q^61 - 19 * q^62 + q^63 + 14 * q^64 - 13 * q^65 + 31 * q^66 - 3 * q^67 + 53 * q^68 + 16 * q^69 + 9 * q^70 + 19 * q^71 - 21 * q^72 + 17 * q^73 + 7 * q^74 + 4 * q^75 - 34 * q^76 + 13 * q^77 + 44 * q^78 + 7 * q^79 + 27 * q^80 + 13 * q^81 - 14 * q^82 + 6 * q^83 + 48 * q^84 - 4 * q^85 - 24 * q^86 - 5 * q^87 - 38 * q^88 + 33 * q^89 - 44 * q^90 - 27 * q^91 + 37 * q^92 - 27 * q^93 - 10 * q^94 - 23 * q^95 + 43 * q^96 - 11 * q^97 + 26 * q^98 + 2 * q^99

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