LMFDB - Embedded newform 57.2.i.a.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [57,2,Mod(4,57)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(57, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("57.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 57 = 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	57.i (of order $9$, degree $6$, minimal)

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:	no
Analytic conductor:	$0.455147291521$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			43.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	57.43
Dual form			57.2.i.a.4.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.43969 - 0.524005i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(0.266044 - 0.223238i) q^{4} +(-1.93969 - 1.62760i) q^{5} +(0.266044 + 1.50881i) q^{6} +(-0.266044 - 0.460802i) q^{7} +(-1.26604 + 2.19285i) q^{8} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})$	\(q+(1.43969 - 0.524005i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(0.266044 - 0.223238i) q^{4} +(-1.93969 - 1.62760i) q^{5} +(0.266044 + 1.50881i) q^{6} +(-0.266044 - 0.460802i) q^{7} +(-1.26604 + 2.19285i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(-3.64543 - 1.32683i) q^{10} +(2.55303 - 4.42198i) q^{11} +(0.173648 + 0.300767i) q^{12} +(0.705737 + 4.00243i) q^{13} +(-0.624485 - 0.524005i) q^{14} +(1.93969 - 1.62760i) q^{15} +(-0.794263 + 4.50449i) q^{16} +(-1.82635 + 0.664738i) q^{17} -1.53209 q^{18} +(2.23396 + 3.74292i) q^{19} -0.879385 q^{20} +(0.500000 - 0.181985i) q^{21} +(1.35844 - 7.70410i) q^{22} +(2.33022 - 1.95529i) q^{23} +(-1.93969 - 1.62760i) q^{24} +(0.245100 + 1.39003i) q^{25} +(3.11334 + 5.39246i) q^{26} +(0.500000 - 0.866025i) q^{27} +(-0.173648 - 0.0632028i) q^{28} +(-1.51367 - 0.550931i) q^{29} +(1.93969 - 3.35965i) q^{30} +(-4.93969 - 8.55580i) q^{31} +(0.337496 + 1.91404i) q^{32} +(3.91147 + 3.28212i) q^{33} +(-2.28106 + 1.91404i) q^{34} +(-0.233956 + 1.32683i) q^{35} +(-0.326352 + 0.118782i) q^{36} +6.10607 q^{37} +(5.17752 + 4.21805i) q^{38} -4.06418 q^{39} +(6.02481 - 2.19285i) q^{40} +(-1.47178 + 8.34689i) q^{41} +(0.624485 - 0.524005i) q^{42} +(-0.135630 - 0.113807i) q^{43} +(-0.307934 - 1.74638i) q^{44} +(1.26604 + 2.19285i) q^{45} +(2.33022 - 4.03606i) q^{46} +(-7.10354 - 2.58548i) q^{47} +(-4.29813 - 1.56439i) q^{48} +(3.35844 - 5.81699i) q^{49} +(1.08125 + 1.87278i) q^{50} +(-0.337496 - 1.91404i) q^{51} +(1.08125 + 0.907278i) q^{52} +(-7.58512 + 6.36467i) q^{53} +(0.266044 - 1.50881i) q^{54} +(-12.1493 + 4.42198i) q^{55} +1.34730 q^{56} +(-4.07398 + 1.55007i) q^{57} -2.46791 q^{58} +(3.58512 - 1.30488i) q^{59} +(0.152704 - 0.866025i) q^{60} +(-10.6702 + 8.95340i) q^{61} +(-11.5949 - 9.72930i) q^{62} +(0.0923963 + 0.524005i) q^{63} +(-3.08512 - 5.34359i) q^{64} +(5.14543 - 8.91215i) q^{65} +(7.35117 + 2.67561i) q^{66} +(9.59627 + 3.49276i) q^{67} +(-0.337496 + 0.584561i) q^{68} +(1.52094 + 2.63435i) q^{69} +(0.358441 + 2.03282i) q^{70} +(2.92855 + 2.45734i) q^{71} +(1.93969 - 1.62760i) q^{72} +(-0.322481 + 1.82888i) q^{73} +(8.79086 - 3.19961i) q^{74} -1.41147 q^{75} +(1.42989 + 0.497079i) q^{76} -2.71688 q^{77} +(-5.85117 + 2.12965i) q^{78} +(1.82635 - 10.3578i) q^{79} +(8.87211 - 7.44459i) q^{80} +(0.766044 + 0.642788i) q^{81} +(2.25490 + 12.7882i) q^{82} +(5.73783 + 9.93821i) q^{83} +(0.0923963 - 0.160035i) q^{84} +(4.62449 + 1.68317i) q^{85} +(-0.254900 - 0.0927760i) q^{86} +(0.805407 - 1.39501i) q^{87} +(6.46451 + 11.1969i) q^{88} +(-1.02869 - 5.83396i) q^{89} +(2.97178 + 2.49362i) q^{90} +(1.65657 - 1.39003i) q^{91} +(0.183448 - 1.04039i) q^{92} +(9.28359 - 3.37895i) q^{93} -11.5817 q^{94} +(1.75877 - 10.8961i) q^{95} -1.94356 q^{96} +(6.39053 - 2.32596i) q^{97} +(1.78699 - 10.1345i) q^{98} +(-3.91147 + 3.28212i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8	$ 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} - 6 q^{10} + 3 q^{11} - 6 q^{13} + 9 q^{14} + 6 q^{15} - 15 q^{16} - 12 q^{17} + 18 q^{19} + 6 q^{20} + 3 q^{21} - 9 q^{23} - 6 q^{24} + 12 q^{26} + 3 q^{27} + 12 q^{29} + 6 q^{30} - 24 q^{31} - 3 q^{32} + 3 q^{33} + 21 q^{34} - 6 q^{35} - 3 q^{36} + 12 q^{37} + 6 q^{38} - 6 q^{39} + 9 q^{40} + 6 q^{41} - 9 q^{42} + 18 q^{43} + 9 q^{44} + 3 q^{45} - 9 q^{46} - 33 q^{47} - 12 q^{48} + 12 q^{49} + 9 q^{50} + 3 q^{51} + 9 q^{52} - 24 q^{53} - 3 q^{54} - 33 q^{55} + 6 q^{56} - 9 q^{57} - 24 q^{58} + 3 q^{60} - 21 q^{61} - 51 q^{62} - 3 q^{63} + 3 q^{64} + 15 q^{65} + 18 q^{66} + 30 q^{67} + 3 q^{68} + 6 q^{69} - 6 q^{70} + 18 q^{71} + 6 q^{72} - 27 q^{73} + 21 q^{74} + 12 q^{75} - 9 q^{78} + 12 q^{79} + 24 q^{80} + 15 q^{82} + 15 q^{83} - 3 q^{84} + 15 q^{85} - 3 q^{86} + 9 q^{87} + 6 q^{88} + 45 q^{89} + 3 q^{90} - 12 q^{91} + 3 q^{92} + 6 q^{93} - 6 q^{94} - 12 q^{95} + 18 q^{96} + 21 q^{97} + 3 q^{98} - 3 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 - 6 * q^10 + 3 * q^11 - 6 * q^13 + 9 * q^14 + 6 * q^15 - 15 * q^16 - 12 * q^17 + 18 * q^19 + 6 * q^20 + 3 * q^21 - 9 * q^23 - 6 * q^24 + 12 * q^26 + 3 * q^27 + 12 * q^29 + 6 * q^30 - 24 * q^31 - 3 * q^32 + 3 * q^33 + 21 * q^34 - 6 * q^35 - 3 * q^36 + 12 * q^37 + 6 * q^38 - 6 * q^39 + 9 * q^40 + 6 * q^41 - 9 * q^42 + 18 * q^43 + 9 * q^44 + 3 * q^45 - 9 * q^46 - 33 * q^47 - 12 * q^48 + 12 * q^49 + 9 * q^50 + 3 * q^51 + 9 * q^52 - 24 * q^53 - 3 * q^54 - 33 * q^55 + 6 * q^56 - 9 * q^57 - 24 * q^58 + 3 * q^60 - 21 * q^61 - 51 * q^62 - 3 * q^63 + 3 * q^64 + 15 * q^65 + 18 * q^66 + 30 * q^67 + 3 * q^68 + 6 * q^69 - 6 * q^70 + 18 * q^71 + 6 * q^72 - 27 * q^73 + 21 * q^74 + 12 * q^75 - 9 * q^78 + 12 * q^79 + 24 * q^80 + 15 * q^82 + 15 * q^83 - 3 * q^84 + 15 * q^85 - 3 * q^86 + 9 * q^87 + 6 * q^88 + 45 * q^89 + 3 * q^90 - 12 * q^91 + 3 * q^92 + 6 * q^93 - 6 * q^94 - 12 * q^95 + 18 * q^96 + 21 * q^97 + 3 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	1.43969	−	0.524005i	1.01802	−	0.370528i	0.221510	−	0.975158i	$-0.428901\pi$
$2$	1.43969	−	0.524005i	1.01802	−	0.370528i	0.796506	+	0.604630i	$0.206679\pi$
$3$	−0.173648	+	0.984808i	−0.100256	+	0.568579i
$3$	−0.173648	+	0.984808i	−0.100256	+	0.568579i
$4$	0.266044	−	0.223238i	0.133022	−	0.111619i
$5$	−1.93969	−	1.62760i	−0.867457	−	0.727883i	0.0961041	−	0.995371i	$-0.469362\pi$
$5$	−1.93969	−	1.62760i	−0.867457	−	0.727883i	−0.963561	+	0.267489i	$0.913806\pi$
$6$	0.266044	+	1.50881i	0.108612	+	0.615970i
$7$	−0.266044	−	0.460802i	−0.100555	−	0.174167i	0.811358	−	0.584549i	$-0.198729\pi$
$7$	−0.266044	−	0.460802i	−0.100555	−	0.174167i	−0.911914	+	0.410382i	$0.865395\pi$
$8$	−1.26604	+	2.19285i	−0.447614	+	0.775291i
$9$	−0.939693	−	0.342020i	−0.313231	−	0.114007i
$10$	−3.64543	−	1.32683i	−1.15279	−	0.419580i
$11$	2.55303	−	4.42198i	0.769769	−	1.33328i	−0.167920	−	0.985801i	$-0.553705\pi$
$11$	2.55303	−	4.42198i	0.769769	−	1.33328i	0.937688	−	0.347478i	$-0.112962\pi$
$12$	0.173648	+	0.300767i	0.0501279	+	0.0868241i
$13$	0.705737	+	4.00243i	0.195736	+	1.11008i	0.911366	+	0.411596i	$0.135029\pi$
$13$	0.705737	+	4.00243i	0.195736	+	1.11008i	−0.715630	+	0.698479i	$0.753860\pi$
$14$	−0.624485	−	0.524005i	−0.166901	−	0.140046i
$15$	1.93969	−	1.62760i	0.500826	−	0.420243i
$16$	−0.794263	+	4.50449i	−0.198566	+	1.12612i
$17$	−1.82635	+	0.664738i	−0.442955	+	0.161223i	−0.553862	−	0.832608i	$-0.686847\pi$
$17$	−1.82635	+	0.664738i	−0.442955	+	0.161223i	0.110907	+	0.993831i	$0.464624\pi$
$18$	−1.53209			−0.361117
$19$	2.23396	+	3.74292i	0.512505	+	0.858685i
$19$	2.23396	+	3.74292i	0.512505	+	0.858685i
$20$	−0.879385			−0.196637
$21$	0.500000	−	0.181985i	0.109109	−	0.0397124i
$22$	1.35844	−	7.70410i	0.289621	−	1.64252i
$23$	2.33022	−	1.95529i	0.485885	−	0.407706i	−0.366664	−	0.930353i	$-0.619500\pi$
$23$	2.33022	−	1.95529i	0.485885	−	0.407706i	0.852549	+	0.522648i	$0.175056\pi$
$24$	−1.93969	−	1.62760i	−0.395938	−	0.332232i
$25$	0.245100	+	1.39003i	0.0490200	+	0.278006i
$26$	3.11334	+	5.39246i	0.610576	+	1.05755i
$27$	0.500000	−	0.866025i	0.0962250	−	0.166667i
$28$	−0.173648	−	0.0632028i	−0.0328164	−	0.0119442i
$29$	−1.51367	−	0.550931i	−0.281082	−	0.102305i	0.197633	−	0.980276i	$-0.436675\pi$
$29$	−1.51367	−	0.550931i	−0.281082	−	0.102305i	−0.478714	+	0.877971i	$0.658897\pi$
$30$	1.93969	−	3.35965i	0.354138	−	0.613385i
$31$	−4.93969	−	8.55580i	−0.887195	−	1.53667i	−0.843177	−	0.537636i	$-0.819317\pi$
$31$	−4.93969	−	8.55580i	−0.887195	−	1.53667i	−0.0440180	−	0.999031i	$-0.514016\pi$
$32$	0.337496	+	1.91404i	0.0596615	+	0.338357i
$33$	3.91147	+	3.28212i	0.680900	+	0.571343i
$34$	−2.28106	+	1.91404i	−0.391198	+	0.328254i
$35$	−0.233956	+	1.32683i	−0.0395457	+	0.224275i
$36$	−0.326352	+	0.118782i	−0.0543920	+	0.0197971i
$37$	6.10607			1.00383			0.501916	−	0.864917i	$-0.332629\pi$
$37$	6.10607			1.00383			0.501916	+	0.864917i	$0.332629\pi$
$38$	5.17752	+	4.21805i	0.839904	+	0.684258i
$39$	−4.06418			−0.650789
$40$	6.02481	−	2.19285i	0.952607	−	0.346721i
$41$	−1.47178	+	8.34689i	−0.229854	+	1.30356i	0.623332	+	0.781957i	$0.285779\pi$
$41$	−1.47178	+	8.34689i	−0.229854	+	1.30356i	−0.853186	+	0.521607i	$0.825333\pi$
$42$	0.624485	−	0.524005i	0.0963602	−	0.0808558i
$43$	−0.135630	−	0.113807i	−0.0206833	−	0.0173554i	0.632387	−	0.774652i	$-0.282075\pi$
$43$	−0.135630	−	0.113807i	−0.0206833	−	0.0173554i	−0.653071	+	0.757297i	$0.726520\pi$
$44$	−0.307934	−	1.74638i	−0.0464227	−	0.263276i
$45$	1.26604	+	2.19285i	0.188731	+	0.326891i
$46$	2.33022	−	4.03606i	0.343573	−	0.595085i
$47$	−7.10354	−	2.58548i	−1.03616	−	0.377131i	−0.232735	−	0.972540i	$-0.574768\pi$
$47$	−7.10354	−	2.58548i	−1.03616	−	0.377131i	−0.803422	+	0.595409i	$0.796990\pi$
$48$	−4.29813	−	1.56439i	−0.620382	−	0.225801i
$49$	3.35844	−	5.81699i	0.479777	−	0.830999i
$50$	1.08125	+	1.87278i	0.152912	+	0.264852i
$51$	−0.337496	−	1.91404i	−0.0472589	−	0.268019i
$52$	1.08125	+	0.907278i	0.149943	+	0.125817i
$53$	−7.58512	+	6.36467i	−1.04190	+	0.874255i	−0.992218	−	0.124510i	$-0.960264\pi$
$53$	−7.58512	+	6.36467i	−1.04190	+	0.874255i	−0.0496783	+	0.998765i	$0.515820\pi$
$54$	0.266044	−	1.50881i	0.0362041	−	0.205323i
$55$	−12.1493	+	4.42198i	−1.63821	+	0.596260i
$56$	1.34730			0.180040
$57$	−4.07398	+	1.55007i	−0.539612	+	0.205311i
$58$	−2.46791			−0.324053
$59$	3.58512	−	1.30488i	0.466743	−	0.169881i	−0.0979333	−	0.995193i	$-0.531223\pi$
$59$	3.58512	−	1.30488i	0.466743	−	0.169881i	0.564676	+	0.825312i	$0.309001\pi$
$60$	0.152704	−	0.866025i	0.0197140	−	0.111803i
$61$	−10.6702	+	8.95340i	−1.36618	+	1.14637i	−0.392167	+	0.919894i	$0.628274\pi$
$61$	−10.6702	+	8.95340i	−1.36618	+	1.14637i	−0.974018	+	0.226471i	$0.927281\pi$
$62$	−11.5949	−	9.72930i	−1.47256	−	1.23562i
$63$	0.0923963	+	0.524005i	0.0116408	+	0.0660185i
$64$	−3.08512	−	5.34359i	−0.385640	−	0.667949i
$65$	5.14543	−	8.91215i	0.638212	−	1.10542i
$66$	7.35117	+	2.67561i	0.904866	+	0.329344i
$67$	9.59627	+	3.49276i	1.17237	+	0.426708i	0.853501	−	0.521091i	$-0.174475\pi$
$67$	9.59627	+	3.49276i	1.17237	+	0.426708i	0.318869	+	0.947799i	$0.396697\pi$
$68$	−0.337496	+	0.584561i	−0.0409274	+	0.0708884i
$69$	1.52094	+	2.63435i	0.183100	+	0.317139i
$70$	0.358441	+	2.03282i	0.0428419	+	0.242968i
$71$	2.92855	+	2.45734i	0.347555	+	0.291633i	0.799807	−	0.600257i	$-0.204935\pi$
$71$	2.92855	+	2.45734i	0.347555	+	0.291633i	−0.452253	+	0.891890i	$0.649379\pi$
$72$	1.93969	−	1.62760i	0.228595	−	0.191814i
$73$	−0.322481	+	1.82888i	−0.0377436	+	0.214055i	−0.997847	−	0.0655924i	$-0.979106\pi$
$73$	−0.322481	+	1.82888i	−0.0377436	+	0.214055i	0.960103	+	0.279647i	$0.0902174\pi$
$74$	8.79086	−	3.19961i	1.02192	−	0.371947i
$75$	−1.41147			−0.162983
$76$	1.42989	+	0.497079i	0.164020	+	0.0570189i
$77$	−2.71688			−0.309617
$78$	−5.85117	+	2.12965i	−0.662514	+	0.241135i
$79$	1.82635	−	10.3578i	0.205481	−	1.16534i	−0.691201	−	0.722663i	$-0.742918\pi$
$79$	1.82635	−	10.3578i	0.205481	−	1.16534i	0.896682	−	0.442676i	$-0.145971\pi$
$80$	8.87211	−	7.44459i	0.991932	−	0.832330i
$81$	0.766044	+	0.642788i	0.0851160	+	0.0714208i
$82$	2.25490	+	12.7882i	0.249012	+	1.41222i
$83$	5.73783	+	9.93821i	0.629808	+	1.09086i	0.987590	+	0.157055i	$0.0501999\pi$
$83$	5.73783	+	9.93821i	0.629808	+	1.09086i	−0.357782	+	0.933805i	$0.616467\pi$
$84$	0.0923963	−	0.160035i	0.0100813	−	0.0174613i
$85$	4.62449	+	1.68317i	0.501596	+	0.182566i
$86$	−0.254900	−	0.0927760i	−0.0274866	−	0.0100043i
$87$	0.805407	−	1.39501i	0.0863487	−	0.149560i
$88$	6.46451	+	11.1969i	0.689119	+	1.19359i
$89$	−1.02869	−	5.83396i	−0.109040	−	0.618399i	−0.989529	−	0.144332i	$-0.953897\pi$
$89$	−1.02869	−	5.83396i	−0.109040	−	0.618399i	0.880489	−	0.474067i	$-0.157214\pi$
$90$	2.97178	+	2.49362i	0.313253	+	0.262851i
$91$	1.65657	−	1.39003i	0.173656	−	0.145715i
$92$	0.183448	−	1.04039i	0.0191258	−	0.108468i
$93$	9.28359	−	3.37895i	0.962663	−	0.350381i
$94$	−11.5817			−1.19456
$95$	1.75877	−	10.8961i	0.180446	−	1.11792i
$96$	−1.94356			−0.198364
$97$	6.39053	−	2.32596i	0.648860	−	0.236166i	0.00344055	−	0.999994i	$-0.498905\pi$
$97$	6.39053	−	2.32596i	0.648860	−	0.236166i	0.645419	+	0.763828i	$0.276683\pi$
$98$	1.78699	−	10.1345i	0.180513	−	1.02374i
$99$	−3.91147	+	3.28212i	−0.393118	+	0.329865i
$100$	0.375515	+	0.315094i	0.0375515	+	0.0315094i
$101$	−1.52094	−	8.62571i	−0.151340	−	0.858290i	−0.962056	−	0.272851i	$-0.912033\pi$
$101$	−1.52094	−	8.62571i	−0.151340	−	0.858290i	0.810717	−	0.585439i	$-0.199078\pi$
$102$	−1.48886	−	2.57877i	−0.147419	−	0.255337i
$103$	1.92262	−	3.33007i	0.189441	−	0.328122i	−0.755623	−	0.655007i	$-0.772666\pi$
$103$	1.92262	−	3.33007i	0.189441	−	0.328122i	0.945064	+	0.326885i	$0.105999\pi$
$104$	−9.67024	−	3.51968i	−0.948245	−	0.345133i
$105$	−1.26604	−	0.460802i	−0.123553	−	0.0449697i
$106$	−7.58512	+	13.1378i	−0.736732	+	1.27606i
$107$	2.83750	+	4.91469i	0.274311	+	0.475121i	0.969961	−	0.243260i	$-0.0782169\pi$
$107$	2.83750	+	4.91469i	0.274311	+	0.475121i	−0.695650	+	0.718381i	$0.744884\pi$
$108$	−0.0603074	−	0.342020i	−0.00580308	−	0.0329109i
$109$	−1.59833	−	1.34115i	−0.153092	−	0.128459i	0.563025	−	0.826440i	$-0.309638\pi$
$109$	−1.59833	−	1.34115i	−0.153092	−	0.128459i	−0.716116	+	0.697981i	$0.754082\pi$
$110$	−15.1741	+	12.7326i	−1.44680	+	1.21401i
$111$	−1.06031	+	6.01330i	−0.100640	+	0.570757i
$112$	2.28699	−	0.832396i	0.216100	−	0.0786540i
$113$	7.27631			0.684498			0.342249	−	0.939609i	$-0.388811\pi$
$113$	7.27631			0.684498			0.342249	+	0.939609i	$0.388811\pi$
$114$	−5.05303	+	4.36640i	−0.473260	+	0.408951i
$115$	−7.70233			−0.718246
$116$	−0.525692	+	0.191336i	−0.0488093	+	0.0177651i
$117$	0.705737	−	4.00243i	0.0652454	−	0.370025i
$118$	4.47771	−	3.75725i	0.412207	−	0.345883i
$119$	0.792204	+	0.664738i	0.0726212	+	0.0609364i
$120$	1.11334	+	6.31407i	0.101634	+	0.576393i
$121$	−7.53596	−	13.0527i	−0.685087	−	1.18661i
$122$	−10.6702	+	18.4814i	−0.966039	+	1.67323i
$123$	−7.96451	−	2.89884i	−0.718135	−	0.261380i
$124$	−3.22416	−	1.17350i	−0.289538	−	0.105383i
$125$	−4.54323	+	7.86911i	−0.406359	+	0.703835i
$126$	0.407604	+	0.705990i	0.0363122	+	0.0628946i
$127$	0.317734	+	1.80196i	0.0281943	+	0.159898i	0.995654	−	0.0931261i	$-0.0296860\pi$
$127$	0.317734	+	1.80196i	0.0281943	+	0.159898i	−0.967460	+	0.253024i	$0.918575\pi$
$128$	−10.2194	−	8.57510i	−0.903277	−	0.757939i
$129$	0.135630	−	0.113807i	0.0119415	−	0.0100201i
$130$	2.73783	−	15.5270i	0.240123	−	1.36181i
$131$	8.25624	−	3.00503i	0.721351	−	0.262550i	0.0448520	−	0.998994i	$-0.485718\pi$
$131$	8.25624	−	3.00503i	0.721351	−	0.262550i	0.676499	+	0.736443i	$0.263496\pi$
$132$	1.77332			0.154348
$133$	1.13041	−	2.02520i	0.0980194	−	0.175607i
$134$	15.6459			1.35160
$135$	−2.37939	+	0.866025i	−0.204785	+	0.0745356i
$136$	0.854570	−	4.84651i	0.0732788	−	0.415585i
$137$	−9.67546	+	8.11867i	−0.826630	+	0.693625i	−0.954515	−	0.298164i	$-0.903626\pi$
$137$	−9.67546	+	8.11867i	−0.826630	+	0.693625i	0.127884	+	0.991789i	$0.459181\pi$
$138$	3.57011	+	2.99568i	0.303908	+	0.255009i
$139$	−0.703211	−	3.98811i	−0.0596456	−	0.338267i	0.940353	−	0.340201i	$-0.110495\pi$
$139$	−0.703211	−	3.98811i	−0.0596456	−	0.338267i	−0.999998	+	0.00193468i	$0.999384\pi$
$140$	0.233956	+	0.405223i	0.0197729	+	0.0342476i
$141$	3.77972	−	6.54666i	0.318309	−	0.551328i
$142$	5.50387	+	2.00324i	0.461875	+	0.168109i
$143$	19.5005	+	7.09759i	1.63071	+	0.593530i
$144$	2.28699	−	3.96118i	0.190582	−	0.330098i
$145$	2.03936	+	3.53228i	0.169360	+	0.293340i
$146$	0.494070	+	2.80201i	0.0408895	+	0.231896i
$147$	5.14543	+	4.31753i	0.424388	+	0.356104i
$148$	1.62449	−	1.36310i	0.133532	−	0.112047i
$149$	1.05391	−	5.97702i	0.0863397	−	0.489657i	−0.910720	−	0.413025i	$-0.864472\pi$
$149$	1.05391	−	5.97702i	0.0863397	−	0.489657i	0.997059	−	0.0766320i	$-0.0244167\pi$
$150$	−2.03209	+	0.739620i	−0.165919	+	0.0603897i
$151$	−0.162504			−0.0132244			−0.00661219	−	0.999978i	$-0.502105\pi$
$151$	−0.162504			−0.0132244			−0.00661219	+	0.999978i	$0.502105\pi$
$152$	−11.0360	+	0.160035i	−0.895134	+	0.0129806i
$153$	1.94356			0.157128
$154$	−3.91147	+	1.42366i	−0.315196	+	0.114722i
$155$	−4.34389	+	24.6354i	−0.348910	+	1.97877i
$156$	−1.08125	+	0.907278i	−0.0865694	+	0.0726404i
$157$	5.10220	+	4.28125i	0.407200	+	0.341681i	0.823269	−	0.567652i	$-0.192148\pi$
$157$	5.10220	+	4.28125i	0.407200	+	0.341681i	−0.416069	+	0.909333i	$0.636593\pi$
$158$	−2.79813	−	15.8690i	−0.222608	−	1.26247i
$159$	−4.95084	−	8.57510i	−0.392627	−	0.680050i
$160$	2.46064	−	4.26195i	0.194530	−	0.336937i
$161$	−1.52094	−	0.553579i	−0.119867	−	0.0436281i
$162$	1.43969	+	0.524005i	0.113113	+	0.0411697i
$163$	0.224155	−	0.388249i	0.0175572	−	0.0304100i	−0.857113	−	0.515128i	$-0.827744\pi$
$163$	0.224155	−	0.388249i	0.0175572	−	0.0304100i	0.874671	+	0.484718i	$0.161078\pi$
$164$	1.47178	+	2.54920i	0.114927	+	0.199059i
$165$	−2.24510	−	12.7326i	−0.174781	−	0.991231i
$166$	13.4684	+	11.3013i	1.04535	+	0.877152i
$167$	2.59627	−	2.17853i	0.200905	−	0.168579i	−0.536785	−	0.843719i	$-0.680361\pi$
$167$	2.59627	−	2.17853i	0.200905	−	0.168579i	0.737690	+	0.675140i	$0.235917\pi$
$168$	−0.233956	+	1.32683i	−0.0180501	+	0.102367i
$169$	−3.30541	+	1.20307i	−0.254262	+	0.0925438i
$170$	7.53983			0.578279
$171$	−0.819078	−	4.28125i	−0.0626364	−	0.327395i
$172$	−0.0614894			−0.00468852
$173$	1.51842	−	0.552659i	0.115443	−	0.0420179i	−0.283653	−	0.958927i	$-0.591546\pi$
$173$	1.51842	−	0.552659i	0.115443	−	0.0420179i	0.399096	+	0.916909i	$0.369324\pi$
$174$	0.428548	−	2.43042i	0.0324882	−	0.184250i
$175$	0.575322	−	0.482753i	0.0434903	−	0.0364927i
$176$	17.8910	+	15.0123i	1.34858	+	1.13160i
$177$	0.662504	+	3.75725i	0.0497968	+	0.282412i
$178$	−4.53802	−	7.86008i	−0.340139	−	0.589138i
$179$	−1.05690	+	1.83061i	−0.0789967	+	0.136826i	−0.902817	−	0.430024i	$-0.858505\pi$
$179$	−1.05690	+	1.83061i	−0.0789967	+	0.136826i	0.823821	+	0.566851i	$0.191838\pi$
$180$	0.826352	+	0.300767i	0.0615926	+	0.0224179i
$181$	−8.22416	−	2.99335i	−0.611297	−	0.222494i	0.0177739	−	0.999842i	$-0.494342\pi$
$181$	−8.22416	−	2.99335i	−0.611297	−	0.222494i	−0.629071	+	0.777348i	$0.716564\pi$
$182$	1.65657	−	2.86927i	0.122793	−	0.212684i
$183$	−6.96451	−	12.0629i	−0.514831	−	0.891714i
$184$	1.33750	+	7.58532i	0.0986015	+	0.559197i
$185$	−11.8439	−	9.93821i	−0.870780	−	0.730671i
$186$	11.5949	−	9.72930i	0.850181	−	0.713387i
$187$	−1.72328	+	9.77320i	−0.126019	+	0.714687i
$188$	−2.46703	+	0.897927i	−0.179927	+	0.0654880i
$189$	−0.532089			−0.0387038
$190$	−3.17752	−	16.6086i	−0.230521	−	1.20492i
$191$	−19.0719			−1.38000			−0.689998	−	0.723811i	$-0.742389\pi$
$191$	−19.0719			−1.38000			−0.689998	+	0.723811i	$0.742389\pi$
$192$	5.79813	−	2.11035i	0.418444	−	0.152301i
$193$	−4.13903	+	23.4736i	−0.297934	+	1.68967i	0.357098	+	0.934067i	$0.383766\pi$
$193$	−4.13903	+	23.4736i	−0.297934	+	1.68967i	−0.655032	+	0.755601i	$0.727345\pi$
$194$	7.98158	−	6.69734i	0.573044	−	0.480841i
$195$	7.88326	+	6.61484i	0.564532	+	0.473698i
$196$	−0.405078	−	2.29731i	−0.0289341	−	0.164093i
$197$	2.19459	+	3.80115i	0.156358	+	0.270820i	0.933553	−	0.358440i	$-0.116691\pi$
$197$	2.19459	+	3.80115i	0.156358	+	0.270820i	−0.777195	+	0.629260i	$0.783358\pi$
$198$	−3.91147	+	6.77487i	−0.277976	+	0.481469i
$199$	18.8293	+	6.85332i	1.33478	+	0.485819i	0.908164	−	0.418615i	$-0.137484\pi$
$199$	18.8293	+	6.85332i	1.33478	+	0.485819i	0.426613	+	0.904434i	$0.359707\pi$
$200$	−3.35844	−	1.22237i	−0.237478	−	0.0864348i
$201$	−5.10607	+	8.84397i	−0.360154	+	0.623805i
$202$	−6.70961	−	11.6214i	−0.472086	−	0.817678i
$203$	0.148833	+	0.844075i	0.0104460	+	0.0592425i
$204$	−0.517074	−	0.433877i	−0.0362024	−	0.0303774i
$205$	16.4402	−	13.7949i	1.14823	−	0.963480i
$206$	1.02300	−	5.80174i	0.0712761	−	0.404227i
$207$	−2.85844	+	1.04039i	−0.198675	+	0.0723119i
$208$	−18.5895			−1.28895
$209$	22.2545	−	0.322718i	1.53938	−	0.0223228i
$210$	−2.06418			−0.142442
$211$	−25.5526	+	9.30039i	−1.75912	+	0.640266i	−0.999944	−	0.0106250i	$-0.996618\pi$
$211$	−25.5526	+	9.30039i	−1.75912	+	0.640266i	−0.759172	+	0.650891i	$0.774396\pi$
$212$	−0.597144	+	3.38657i	−0.0410120	+	0.232591i
$213$	−2.92855	+	2.45734i	−0.200661	+	0.168374i
$214$	6.66044	+	5.58878i	0.455299	+	0.382041i
$215$	0.0778483	+	0.441500i	0.00530921	+	0.0301100i
$216$	1.26604	+	2.19285i	0.0861434	+	0.149205i
$217$	−2.62836	+	4.55245i	−0.178424	+	0.309040i
$218$	−3.00387	−	1.09332i	−0.203448	−	0.0740489i
$219$	−1.74510	−	0.635164i	−0.117923	−	0.0429204i
$220$	−2.24510	+	3.88863i	−0.151365	+	0.262171i
$221$	−3.94949	−	6.84072i	−0.265672	−	0.460157i
$222$	1.62449	+	9.21291i	0.109028	+	0.618330i
$223$	−9.20233	−	7.72167i	−0.616234	−	0.517082i	0.280383	−	0.959888i	$-0.409538\pi$
$223$	−9.20233	−	7.72167i	−0.616234	−	0.517082i	−0.896617	+	0.442807i	$0.853983\pi$
$224$	0.792204	−	0.664738i	0.0529313	−	0.0444147i
$225$	0.245100	−	1.39003i	0.0163400	−	0.0926687i
$226$	10.4757	−	3.81283i	0.696830	−	0.253625i
$227$	4.34049			0.288088			0.144044	−	0.989571i	$-0.453989\pi$
$227$	4.34049			0.288088			0.144044	+	0.989571i	$0.453989\pi$
$228$	−0.737826	+	1.32185i	−0.0488637	+	0.0875418i
$229$	3.29591			0.217800			0.108900	−	0.994053i	$-0.465267\pi$
$229$	3.29591			0.217800			0.108900	+	0.994053i	$0.465267\pi$
$230$	−11.0890	+	4.03606i	−0.731187	+	0.266130i
$231$	0.471782	−	2.67561i	0.0310409	−	0.176042i
$232$	3.12449	−	2.62175i	0.205132	−	0.172127i
$233$	−11.8209	−	9.91890i	−0.774412	−	0.649809i	0.167423	−	0.985885i	$-0.446456\pi$
$233$	−11.8209	−	9.91890i	−0.774412	−	0.649809i	−0.941835	+	0.336076i	$0.890900\pi$
$234$	−1.08125	−	6.13208i	−0.0706836	−	0.400867i
$235$	9.57057	+	16.5767i	0.624315	+	1.08135i
$236$	0.662504	−	1.14749i	0.0431253	−	0.0746953i
$237$	9.88326	+	3.59721i	0.641986	+	0.233664i
$238$	1.48886	+	0.541899i	0.0965082	+	0.0351261i
$239$	−7.91147	+	13.7031i	−0.511751	+	0.886378i	0.488156	+	0.872756i	$0.337670\pi$
$239$	−7.91147	+	13.7031i	−0.511751	+	0.886378i	−0.999907	+	0.0136221i	$0.995664\pi$
$240$	5.79086	+	10.0301i	0.373798	+	0.647438i
$241$	−4.10607	−	23.2867i	−0.264495	−	1.50003i	−0.770469	−	0.637477i	$-0.779978\pi$
$241$	−4.10607	−	23.2867i	−0.264495	−	1.50003i	0.505974	−	0.862549i	$-0.331133\pi$
$242$	−17.6891	−	14.8429i	−1.13710	−	0.954140i
$243$	−0.766044	+	0.642788i	−0.0491418	+	0.0412348i
$244$	−0.840022	+	4.76400i	−0.0537769	+	0.304984i
$245$	−15.9820	+	5.81699i	−1.02106	+	0.371634i
$246$	−12.9855			−0.827922
$247$	−13.4042	+	11.5828i	−0.852889	+	0.736994i
$248$	25.0155			1.58848
$249$	−10.7836	+	3.92490i	−0.683382	+	0.248731i
$250$	−2.41740	+	13.7098i	−0.152890	+	0.867083i
$251$	14.8701	−	12.4775i	0.938589	−	0.787570i	−0.0387499	−	0.999249i	$-0.512338\pi$
$251$	14.8701	−	12.4775i	0.938589	−	0.787570i	0.977339	+	0.211679i	$0.0678931\pi$
$252$	0.141559	+	0.118782i	0.00891740	+	0.00748258i
$253$	−2.69712	−	15.2961i	−0.169566	−	0.961659i
$254$	1.40167	+	2.42777i	0.0879488	+	0.152332i
$255$	−2.46064	+	4.26195i	−0.154091	+	0.266894i
$256$	−7.60994	−	2.76979i	−0.475621	−	0.173112i
$257$	−11.5544	−	4.20545i	−0.720742	−	0.262329i	−0.0445014	−	0.999009i	$-0.514170\pi$
$257$	−11.5544	−	4.20545i	−0.720742	−	0.262329i	−0.676241	+	0.736681i	$0.736392\pi$
$258$	0.135630	−	0.234917i	0.00844392	−	0.0146253i
$259$	−1.62449	−	2.81369i	−0.100941	−	0.174834i
$260$	−0.620615	−	3.51968i	−0.0384889	−	0.218281i
$261$	1.23396	+	1.03541i	0.0763799	+	0.0640904i
$262$	10.3118	−	8.65263i	0.637065	−	0.534561i
$263$	1.10101	−	6.24416i	0.0678915	−	0.385032i	−0.931862	−	0.362814i	$-0.881816\pi$
$263$	1.10101	−	6.24416i	0.0678915	−	0.385032i	0.999753	−	0.0222179i	$-0.00707275\pi$
$264$	−12.1493	+	4.42198i	−0.747738	+	0.272154i
$265$	25.0719			1.54016
$266$	0.566237	−	3.50800i	0.0347182	−	0.215089i
$267$	5.92396			0.362541
$268$	3.33275	−	1.21302i	0.203580	−	0.0740971i
$269$	−0.403733	+	2.28969i	−0.0246161	+	0.139605i	−0.994639	−	0.103409i	$-0.967025\pi$
$269$	−0.403733	+	2.28969i	−0.0246161	+	0.139605i	0.970023	+	0.243014i	$0.0781360\pi$
$270$	−2.97178	+	2.49362i	−0.180857	+	0.151757i
$271$	11.4474	+	9.60554i	0.695382	+	0.583495i	0.920456	−	0.390847i	$-0.127818\pi$
$271$	11.4474	+	9.60554i	0.695382	+	0.583495i	−0.225074	+	0.974342i	$0.572262\pi$
$272$	−1.54370	−	8.75476i	−0.0936006	−	0.530835i
$273$	1.08125	+	1.87278i	0.0654403	+	0.113346i
$274$	−9.67546	+	16.7584i	−0.584516	+	1.01241i
$275$	6.77244	+	2.46497i	0.408394	+	0.148643i
$276$	0.992726	+	0.361323i	0.0597551	+	0.0217491i
$277$	11.9829	−	20.7550i	0.719984	−	1.24705i	−0.241021	−	0.970520i	$-0.577482\pi$
$277$	11.9829	−	20.7550i	0.719984	−	1.24705i	0.961005	−	0.276529i	$-0.0891843\pi$
$278$	−3.10220	−	5.37316i	−0.186057	−	0.322261i
$279$	1.71554	+	9.72930i	0.102707	+	0.582478i
$280$	−2.61334	−	2.19285i	−0.156177	−	0.131048i
$281$	19.5804	−	16.4299i	1.16807	−	0.980125i	0.168083	−	0.985773i	$-0.446242\pi$
$281$	19.5804	−	16.4299i	1.16807	−	0.980125i	0.999984	+	0.00564805i	$0.00179784\pi$
$282$	2.01114	−	11.4058i	0.119762	−	0.679204i
$283$	7.05778	−	2.56882i	0.419542	−	0.152701i	−0.123619	−	0.992330i	$-0.539450\pi$
$283$	7.05778	−	2.56882i	0.419542	−	0.152701i	0.543160	+	0.839629i	$0.317228\pi$
$284$	1.32770			0.0787843
$285$	10.4251	+	3.62414i	0.617532	+	0.214675i
$286$	31.7939			1.88001
$287$	4.23783	−	1.54244i	0.250151	−	0.0910475i
$288$	0.337496	−	1.91404i	0.0198872	−	0.112786i
$289$	−10.1291	+	8.49930i	−0.595828	+	0.499959i
$290$	4.78699	+	4.01676i	0.281102	+	0.235872i
$291$	1.18092	+	6.69734i	0.0692269	+	0.392605i
$292$	0.322481	+	0.558554i	0.0188718	+	0.0326869i
$293$	−7.38326	+	12.7882i	−0.431334	+	0.747093i	−0.996989	−	0.0775495i	$-0.975290\pi$
$293$	−7.38326	+	12.7882i	−0.431334	+	0.747093i	0.565654	+	0.824643i	$0.308624\pi$
$294$	9.67024	+	3.51968i	0.563980	+	0.205272i
$295$	−9.07785	−	3.30407i	−0.528533	−	0.192370i
$296$	−7.73055	+	13.3897i	−0.449329	+	0.778261i
$297$	−2.55303	−	4.42198i	−0.148142	−	0.256590i
$298$	−1.61468	−	9.15733i	−0.0935362	−	0.530470i
$299$	9.47044	+	7.94664i	0.547690	+	0.459566i
$300$	−0.375515	+	0.315094i	−0.0216804	+	0.0181920i
$301$	−0.0163589	+	0.0927760i	−0.000942912	+	0.00534752i
$302$	−0.233956	+	0.0851529i	−0.0134626	+	0.00490000i
$303$	8.75877			0.503178
$304$	−18.6343	+	7.08997i	−1.06875	+	0.406637i
$305$	35.2695			2.01953
$306$	2.79813	−	1.01844i	0.159959	−	0.0582202i
$307$	0.957234	−	5.42874i	0.0546322	−	0.309835i	−0.945231	−	0.326404i	$-0.894163\pi$
$307$	0.957234	−	5.42874i	0.0546322	−	0.309835i	0.999863	+	0.0165689i	$0.00527428\pi$
$308$	−0.722811	+	0.606511i	−0.0411860	+	0.0345591i
$309$	2.94562	+	2.47167i	0.167571	+	0.140608i
$310$	6.65523	+	37.7437i	0.377992	+	2.14370i
$311$	−8.69981	−	15.0685i	−0.493321	−	0.854457i	0.506650	−	0.862152i	$-0.330884\pi$
$311$	−8.69981	−	15.0685i	−0.493321	−	0.854457i	−0.999970	+	0.00769537i	$0.997550\pi$
$312$	5.14543	−	8.91215i	0.291303	−	0.504551i
$313$	−14.9820	−	5.45302i	−0.846835	−	0.308223i	−0.118086	−	0.993003i	$-0.537676\pi$
$313$	−14.9820	−	5.45302i	−0.846835	−	0.308223i	−0.728749	+	0.684780i	$0.759898\pi$
$314$	9.58899	+	3.49011i	0.541138	+	0.196958i
$315$	0.673648	−	1.16679i	0.0379558	−	0.0657413i
$316$	−1.82635	−	3.16333i	−0.102740	−	0.177951i
$317$	0.342711	+	1.94361i	0.0192486	+	0.109164i	0.992918	−	0.118799i	$-0.0379045\pi$
$317$	0.342711	+	1.94361i	0.0192486	+	0.109164i	−0.973670	+	0.227963i	$0.926793\pi$
$318$	−11.6211	−	9.75125i	−0.651678	−	0.546823i
$319$	−6.30066	+	5.28688i	−0.352769	+	0.296009i
$320$	−2.71301	+	15.3863i	−0.151662	+	0.860118i
$321$	−5.33275	+	1.94096i	−0.297645	+	0.108334i
$322$	−2.47977			−0.138192
$323$	−6.56805	−	5.35089i	−0.365456	−	0.297732i
$324$	0.347296			0.0192942
$325$	−5.39053	+	1.96199i	−0.299013	+	0.108832i
$326$	0.119271	−	0.676417i	0.00660579	−	0.0374633i
$327$	1.59833	−	1.34115i	0.0883876	−	0.0741660i
$328$	−16.4402	−	13.7949i	−0.907756	−	0.761698i
$329$	0.698463	+	3.96118i	0.0385075	+	0.218387i
$330$	−9.90420	−	17.1546i	−0.545208	−	0.944328i
$331$	0.418748	−	0.725293i	0.0230165	−	0.0398657i	−0.854288	−	0.519800i	$-0.826006\pi$
$331$	0.418748	−	0.725293i	0.0230165	−	0.0398657i	0.877304	+	0.479935i	$0.159340\pi$
$332$	3.74510	+	1.36310i	0.205539	+	0.0748101i
$333$	−5.73783	−	2.08840i	−0.314431	−	0.114443i
$334$	2.59627	−	4.49687i	0.142061	−	0.246058i
$335$	−12.9290	−	22.3937i	−0.706388	−	1.22350i
$336$	0.422618	+	2.39679i	0.0230557	+	0.130756i
$337$	−2.54916	−	2.13900i	−0.138862	−	0.116519i	0.570711	−	0.821151i	$-0.306668\pi$
$337$	−2.54916	−	2.13900i	−0.138862	−	0.116519i	−0.709573	+	0.704632i	$0.751112\pi$
$338$	−4.12836	+	3.46410i	−0.224553	+	0.188422i
$339$	−1.26352	+	7.16577i	−0.0686249	+	0.389191i
$340$	1.60607	−	0.584561i	0.0871012	−	0.0317022i
$341$	−50.4448			−2.73174
$342$	−3.42262	−	5.73448i	−0.185074	−	0.310085i
$343$	−7.29860			−0.394087
$344$	0.421274	−	0.153331i	0.0227136	−	0.00826707i
$345$	1.33750	−	7.58532i	0.0720084	−	0.408380i
$346$	1.89646	−	1.59132i	0.101954	−	0.0855498i
$347$	3.07011	+	2.57613i	0.164812	+	0.138294i	0.721464	−	0.692452i	$-0.243470\pi$
$347$	3.07011	+	2.57613i	0.164812	+	0.138294i	−0.556652	+	0.830746i	$0.687914\pi$
$348$	−0.0971440	−	0.550931i	−0.00520747	−	0.0295330i
$349$	13.9513	+	24.1644i	0.746796	+	1.29349i	0.949351	+	0.314218i	$0.101742\pi$
$349$	13.9513	+	24.1644i	0.746796	+	1.29349i	−0.202555	+	0.979271i	$0.564924\pi$
$350$	0.575322	−	0.996487i	0.0307523	−	0.0532645i
$351$	3.81908	+	1.39003i	0.203847	+	0.0741943i
$352$	9.32547	+	3.39420i	0.497049	+	0.180911i
$353$	−6.47178	+	11.2095i	−0.344458	+	0.596619i	−0.985255	−	0.171091i	$-0.945271\pi$
$353$	−6.47178	+	11.2095i	−0.344458	+	0.596619i	0.640797	+	0.767710i	$0.278604\pi$
$354$	2.92262	+	5.06212i	0.155335	+	0.269049i
$355$	−1.68092	−	9.53298i	−0.0892141	−	0.505958i
$356$	−1.57604	−	1.32245i	−0.0835298	−	0.0700898i
$357$	−0.792204	+	0.664738i	−0.0419279	+	0.0351816i
$358$	−0.562367	+	3.18934i	−0.0297220	+	0.168562i
$359$	−10.7562	+	3.91495i	−0.567693	+	0.206623i	−0.609890	−	0.792486i	$-0.708786\pi$
$359$	−10.7562	+	3.91495i	−0.567693	+	0.206623i	0.0421972	+	0.999109i	$0.486564\pi$
$360$	−6.41147			−0.337914
$361$	−9.01889	+	16.7230i	−0.474678	+	0.880159i
$362$	−13.4088			−0.704750
$363$	14.1630	−	5.15490i	0.743363	−	0.270562i
$364$	0.130415	−	0.739620i	0.00683560	−	0.0387666i
$365$	3.60220	−	3.02260i	0.188548	−	0.158210i
$366$	−16.3478	−	13.7174i	−0.854511	−	0.717020i
$367$	−4.96657	−	28.1668i	−0.259253	−	1.47030i	−0.784916	−	0.619602i	$-0.787294\pi$
$367$	−4.96657	−	28.1668i	−0.259253	−	1.47030i	0.525663	−	0.850693i	$-0.323817\pi$
$368$	6.95677	+	12.0495i	0.362647	+	0.628122i
$369$	4.23783	−	7.34013i	0.220612	−	0.382112i
$370$	−22.2592	−	8.10170i	−1.15720	−	0.421187i
$371$	4.95084	+	1.80196i	0.257035	+	0.0935530i
$372$	1.71554	−	2.97140i	0.0889465	−	0.154060i
$373$	6.28312	+	10.8827i	0.325328	+	0.563484i	0.981579	−	0.191059i	$-0.0611921\pi$
$373$	6.28312	+	10.8827i	0.325328	+	0.563484i	−0.656251	+	0.754543i	$0.727859\pi$
$374$	2.64022	+	14.9734i	0.136522	+	0.774256i
$375$	−6.96064	−	5.84067i	−0.359446	−	0.301611i
$376$	14.6630	−	12.3037i	0.756185	−	0.634515i
$377$	1.13681	−	6.44718i	0.0585488	−	0.332047i
$378$	−0.766044	+	0.278817i	−0.0394011	+	0.0143408i
$379$	−2.19934			−0.112973			−0.0564863	−	0.998403i	$-0.517990\pi$
$379$	−2.19934			−0.112973			−0.0564863	+	0.998403i	$0.517990\pi$
$380$	−1.96451	−	3.29147i	−0.100777	−	0.168849i
$381$	−1.82976			−0.0937412
$382$	−27.4577	+	9.99379i	−1.40486	+	0.511327i
$383$	−1.02940	+	5.83802i	−0.0525999	+	0.298309i	−0.999747	−	0.0224905i	$-0.992840\pi$
$383$	−1.02940	+	5.83802i	−0.0525999	+	0.298309i	0.947147	+	0.320799i	$0.103952\pi$
$384$	10.2194	−	8.57510i	0.521507	−	0.437596i
$385$	5.26991	+	4.42198i	0.268580	+	0.225365i
$386$	6.34137	+	35.9637i	0.322767	+	1.83050i
$387$	0.0885259	+	0.153331i	0.00450002	+	0.00779427i
$388$	1.18092	−	2.04542i	0.0599522	−	0.103840i
$389$	31.1215	+	11.3273i	1.57793	+	0.574318i	0.974752	−	0.223292i	$-0.0716804\pi$
$389$	31.1215	+	11.3273i	1.57793	+	0.574318i	0.603174	+	0.797610i	$0.293903\pi$
$390$	14.8157	+	5.39246i	0.750221	+	0.273058i
$391$	−2.95605	+	5.12003i	−0.149494	+	0.258931i
$392$	8.50387	+	14.7291i	0.429510	+	0.743934i
$393$	1.52569	+	8.65263i	0.0769610	+	0.436467i
$394$	5.15136	+	4.32250i	0.259522	+	0.217765i
$395$	−20.4008	+	17.1183i	−1.02648	+	0.861315i
$396$	−0.307934	+	1.74638i	−0.0154742	+	0.0877588i
$397$	24.4786	−	8.90950i	1.22855	−	0.447155i	0.355448	−	0.934696i	$-0.384328\pi$
$397$	24.4786	−	8.90950i	1.22855	−	0.447155i	0.873100	+	0.487541i	$0.162106\pi$
$398$	30.6996			1.53883
$399$	1.79813	+	1.46491i	0.0900193	+	0.0733374i
$400$	−6.45605			−0.322803
$401$	15.0052	−	5.46145i	0.749325	−	0.272732i	0.0610031	−	0.998138i	$-0.480570\pi$
$401$	15.0052	−	5.46145i	0.749325	−	0.272732i	0.688322	+	0.725406i	$0.258348\pi$
$402$	−2.71688	+	15.4082i	−0.135506	+	0.768491i
$403$	30.7579	−	25.8089i	1.53216	−	1.28563i
$404$	−2.33022	−	1.95529i	−0.115933	−	0.0972792i
$405$	−0.439693	−	2.49362i	−0.0218485	−	0.123909i
$406$	0.656574	+	1.13722i	0.0325852	+	0.0564393i
$407$	15.5890	−	27.0009i	0.772718	−	1.33839i
$408$	4.62449	+	1.68317i	0.228946	+	0.0833296i
$409$	2.77079	+	1.00849i	0.137007	+	0.0498664i	0.409614	−	0.912259i	$-0.365664\pi$
$409$	2.77079	+	1.00849i	0.137007	+	0.0498664i	−0.272607	+	0.962126i	$0.587886\pi$
$410$	16.4402	−	28.4752i	0.811922	−	1.40629i
$411$	−6.31521	−	10.9383i	−0.311506	−	0.539545i
$412$	−0.231896	−	1.31515i	−0.0114247	−	0.0647927i
$413$	−1.55509	−	1.30488i	−0.0765211	−	0.0642088i
$414$	−3.57011	+	2.99568i	−0.175461	+	0.147229i
$415$	5.04576	−	28.6159i	0.247687	−	1.40470i
$416$	−7.42262	+	2.70161i	−0.363924	+	0.132457i
$417$	4.04963			0.198311
$418$	31.8705	−	12.1261i	1.55884	−	0.593106i
$419$	−33.4962			−1.63640			−0.818198	−	0.574937i	$-0.805027\pi$
$419$	−33.4962			−1.63640			−0.818198	+	0.574937i	$0.805027\pi$
$420$	−0.439693	+	0.160035i	−0.0214548	+	0.00780891i
$421$	3.12877	−	17.7441i	0.152487	−	0.864795i	−0.808561	−	0.588412i	$-0.799753\pi$
$421$	3.12877	−	17.7441i	0.152487	−	0.864795i	0.961048	−	0.276383i	$-0.0891357\pi$
$422$	−31.9145	+	26.7794i	−1.55357	+	1.30360i
$423$	5.79086	+	4.85911i	0.281561	+	0.236258i
$424$	−4.35369	−	24.6910i	−0.211434	−	1.19910i
$425$	−1.37164	−	2.37576i	−0.0665345	−	0.115241i
$426$	−2.92855	+	5.07239i	−0.141889	+	0.245758i
$427$	6.96451	+	2.53487i	0.337036	+	0.122671i
$428$	1.85204	+	0.674089i	0.0895219	+	0.0325833i
$429$	−10.3760	+	17.9717i	−0.500957	+	0.867683i
$430$	0.343426	+	0.594831i	0.0165615	+	0.0286853i
$431$	3.70233	+	20.9970i	0.178335	+	1.01139i	0.934223	+	0.356688i	$0.116094\pi$
$431$	3.70233	+	20.9970i	0.178335	+	1.01139i	−0.755888	+	0.654701i	$0.772795\pi$
$432$	3.50387	+	2.94010i	0.168580	+	0.141455i
$433$	−16.8931	+	14.1750i	−0.811828	+	0.681205i	−0.951043	−	0.309057i	$-0.899987\pi$
$433$	−16.8931	+	14.1750i	−0.811828	+	0.681205i	0.139215	+	0.990262i	$0.455542\pi$
$434$	−1.39852	+	7.93139i	−0.0671310	+	0.380719i
$435$	−3.83275	+	1.39501i	−0.183766	+	0.0668854i
$436$	−0.724622			−0.0347031
$437$	12.5241	+	4.35381i	0.599109	+	0.208271i
$438$	−2.84524			−0.135951
$439$	3.18257	−	1.15836i	0.151896	−	0.0552856i	−0.264953	−	0.964261i	$-0.585357\pi$
$439$	3.18257	−	1.15836i	0.151896	−	0.0552856i	0.416849	+	0.908976i	$0.363134\pi$
$440$	5.68479	−	32.2401i	0.271012	−	1.53698i
$441$	−5.14543	+	4.31753i	−0.245020	+	0.205597i
$442$	−9.27063	−	7.77898i	−0.440959	−	0.370008i
$443$	−5.23799	−	29.7061i	−0.248864	−	1.41138i	−0.811344	−	0.584569i	$-0.801264\pi$
$443$	−5.23799	−	29.7061i	−0.248864	−	1.41138i	0.562480	−	0.826811i	$-0.309847\pi$
$444$	1.06031	+	1.83651i	0.0503200	+	0.0871567i
$445$	−7.50000	+	12.9904i	−0.355534	+	0.615803i
$446$	−17.2947	−	6.29477i	−0.818929	−	0.298066i
$447$	5.70321	+	2.07580i	0.269753	+	0.0981819i
$448$	−1.64156	+	2.84326i	−0.0775564	+	0.134332i
$449$	15.4559	+	26.7704i	0.729409	+	1.26337i	0.957134	+	0.289647i	$0.0935380\pi$
$449$	15.4559	+	26.7704i	0.729409	+	1.26337i	−0.227725	+	0.973725i	$0.573129\pi$
$450$	−0.375515	−	2.12965i	−0.0177019	−	0.100393i
$451$	33.1523	+	27.8181i	1.56108	+	1.30990i
$452$	1.93582	−	1.62435i	0.0910534	−	0.0764029i
$453$	0.0282185	−	0.160035i	0.00132582	−	0.00751910i
$454$	6.24897	−	2.27444i	0.293279	−	0.106745i
$455$	−5.47565			−0.256703
$456$	1.75877	−	10.8961i	0.0823620	−	0.510256i
$457$	−39.0479			−1.82658			−0.913291	−	0.407307i	$-0.866468\pi$
$457$	−39.0479			−1.82658			−0.913291	+	0.407307i	$0.866468\pi$
$458$	4.74510	−	1.72708i	0.221724	−	0.0807009i
$459$	−0.337496	+	1.91404i	−0.0157530	+	0.0893395i
$460$	−2.04916	+	1.71945i	−0.0955427	+	0.0801699i
$461$	−1.15476	−	0.968961i	−0.0537827	−	0.0451290i	0.615500	−	0.788137i	$-0.288954\pi$
$461$	−1.15476	−	0.968961i	−0.0537827	−	0.0451290i	−0.669283	+	0.743008i	$0.733399\pi$
$462$	−0.722811	−	4.09927i	−0.0336282	−	0.190715i
$463$	1.64156	+	2.84326i	0.0762897	+	0.132138i	0.901646	−	0.432474i	$-0.142359\pi$
$463$	1.64156	+	2.84326i	0.0762897	+	0.132138i	−0.825357	+	0.564612i	$0.809026\pi$
$464$	3.68392	−	6.38073i	0.171021	−	0.296218i
$465$	−23.5069	−	8.55580i	−1.09010	−	0.396766i
$466$	−22.2160	−	8.08596i	−1.02914	−	0.374575i
$467$	11.4436	−	19.8208i	0.529545	−	0.917199i	−0.469861	−	0.882740i	$-0.655696\pi$
$467$	11.4436	−	19.8208i	0.529545	−	0.917199i	0.999406	−	0.0344584i	$-0.0109706\pi$
$468$	−0.705737	−	1.22237i	−0.0326227	−	0.0565042i
$469$	−0.943563	−	5.35121i	−0.0435697	−	0.247096i
$470$	22.4650	+	18.8504i	1.03623	+	0.869502i
$471$	−5.10220	+	4.28125i	−0.235097	+	0.197270i
$472$	−1.67752	+	9.51368i	−0.0772141	+	0.437903i
$473$	−0.849518	+	0.309199i	−0.0390609	+	0.0142170i
$474$	16.1138			0.740132
$475$	−4.65523	+	4.02266i	−0.213597	+	0.184572i
$476$	0.359156			0.0164619
$477$	9.30453	−	3.38657i	0.426025	−	0.155060i
$478$	−4.20961	+	23.8739i	−0.192543	+	1.09197i
$479$	−7.39827	+	6.20789i	−0.338036	+	0.283646i	−0.795965	−	0.605343i	$-0.793036\pi$
$479$	−7.39827	+	6.20789i	−0.338036	+	0.283646i	0.457929	+	0.888989i	$0.348591\pi$
$480$	3.76991	+	3.16333i	0.172072	+	0.144386i
$481$	4.30928	+	24.4391i	0.196486	+	1.11433i
$482$	−18.1138	−	31.3740i	−0.825061	−	1.42905i
$483$	0.809278	−	1.40171i	0.0368234	−	0.0637800i
$484$	−4.91875	−	1.79028i	−0.223579	−	0.0813763i
$485$	−16.1814	−	5.88954i	−0.734759	−	0.267430i
$486$	−0.766044	+	1.32683i	−0.0347485	+	0.0601861i
$487$	11.2554	+	19.4949i	0.510029	+	0.883397i	0.999932	+	0.0116199i	$0.00369881\pi$
$487$	11.2554	+	19.4949i	0.510029	+	0.883397i	−0.489903	+	0.871777i	$0.662968\pi$
$488$	−6.12449	−	34.7337i	−0.277242	−	1.57232i
$489$	0.343426	+	0.288169i	0.0155303	+	0.0130314i
$490$	−19.9611	+	16.7494i	−0.901751	+	0.756659i
$491$	1.26264	−	7.16079i	0.0569822	−	0.323162i	−0.942971	−	0.332876i	$-0.891981\pi$
$491$	1.26264	−	7.16079i	0.0569822	−	0.323162i	0.999953	+	0.00971390i	$0.00309208\pi$
$492$	−2.76604	+	1.00676i	−0.124703	+	0.0453881i
$493$	3.13072			0.141001
$494$	−13.2285	+	23.6995i	−0.595178	+	1.06629i
$495$	12.9290			0.581116
$496$	42.4629	−	15.4552i	1.90664	−	0.693961i
$497$	0.353226	−	2.00324i	0.0158444	−	0.0898578i
$498$	−13.4684	+	11.3013i	−0.603532	+	0.506424i
$499$	−9.81386	−	8.23481i	−0.439329	−	0.368641i	0.396129	−	0.918195i	$-0.370353\pi$
$499$	−9.81386	−	8.23481i	−0.439329	−	0.368641i	−0.835458	+	0.549554i	$0.814798\pi$
$500$	0.547981	+	3.10775i	0.0245065	+	0.138983i
$501$	1.69459	+	2.93512i	0.0757088	+	0.131132i
$502$	14.8701	−	25.7557i	0.663683	−	1.14953i
$503$	−7.86571	−	2.86289i	−0.350715	−	0.127650i	0.160655	−	0.987011i	$-0.448639\pi$
$503$	−7.86571	−	2.86289i	−0.350715	−	0.127650i	−0.511370	+	0.859361i	$0.670862\pi$
$504$	−1.26604	−	0.460802i	−0.0563941	−	0.0205258i
$505$	−11.0890	+	19.2067i	−0.493454	+	0.854687i
$506$	−11.8983	−	20.6084i	−0.528943	−	0.916156i
$507$	−0.610815	−	3.46410i	−0.0271272	−	0.153846i
$508$	0.486796	+	0.408471i	0.0215981	+	0.0181230i
$509$	10.4816	−	8.79509i	0.464588	−	0.389836i	−0.380228	−	0.924893i	$-0.624154\pi$
$509$	10.4816	−	8.79509i	0.464588	−	0.389836i	0.844816	+	0.535057i	$0.179710\pi$
$510$	−1.30928	+	7.42528i	−0.0579758	+	0.328797i
$511$	0.928548	−	0.337964i	0.0410766	−	0.0149506i
$512$	14.2736			0.630811
$513$	4.35844	−	0.0632028i	0.192430	−	0.00279047i
$514$	−18.8384			−0.830928
$515$	−9.14930	+	3.33007i	−0.403166	+	0.146741i
$516$	0.0106775	−	0.0605553i	0.000470052	−	0.00266580i
$517$	−29.5685	+	24.8109i	−1.30042	+	1.09118i
$518$	−3.81315	−	3.19961i	−0.167540	−	0.140583i
$519$	0.280592	+	1.59132i	0.0123166	+	0.0698511i
$520$	13.0287	+	22.5663i	0.571346	+	0.989600i
$521$	8.48205	−	14.6913i	0.371605	−	0.643639i	−0.618207	−	0.786015i	$-0.712141\pi$
$521$	8.48205	−	14.6913i	0.371605	−	0.643639i	0.989813	+	0.142376i	$0.0454741\pi$
$522$	2.31908	+	0.844075i	0.101503	+	0.0369442i
$523$	3.67112	+	1.33618i	0.160527	+	0.0584270i	0.421034	−	0.907045i	$-0.361667\pi$
$523$	3.67112	+	1.33618i	0.160527	+	0.0584270i	−0.260507	+	0.965472i	$0.583890\pi$
$524$	1.52569	−	2.64258i	0.0666502	−	0.115441i
$525$	0.375515	+	0.650411i	0.0163888	+	0.0283863i
$526$	−1.68685	−	9.56661i	−0.0735502	−	0.417124i
$527$	14.7090	+	12.3423i	0.640733	+	0.537639i
$528$	−17.8910	+	15.0123i	−0.778606	+	0.653328i
$529$	−2.38713	+	13.5381i	−0.103788	+	0.588611i
$530$	36.0959	−	13.1378i	1.56790	−	0.570670i
$531$	−3.81521			−0.165566
$532$	−0.151359	−	0.791143i	−0.00656227	−	0.0343004i
$533$	−34.4466			−1.49205
$534$	8.52869	−	3.10419i	0.369072	−	0.134331i
$535$	2.49525	−	14.1513i	0.107879	−	0.611813i
$536$	−19.8084	+	16.6212i	−0.855593	+	0.717927i
$537$	−1.61927	−	1.35873i	−0.0698767	−	0.0586335i
$538$	0.618555	+	3.50800i	0.0266678	+	0.151241i
$539$	−17.1484	−	29.7019i	−0.738635	−	1.27935i
$540$	−0.439693	+	0.761570i	−0.0189214	+	0.0327728i
$541$	−12.4017	−	4.51384i	−0.533190	−	0.194065i	0.0613724	−	0.998115i	$-0.480452\pi$
$541$	−12.4017	−	4.51384i	−0.533190	−	0.194065i	−0.594562	+	0.804050i	$0.702675\pi$
$542$	21.5141	+	7.83051i	0.924111	+	0.336349i
$543$	4.37598	−	7.57942i	0.187791	−	0.325264i
$544$	−1.88872	−	3.27136i	−0.0809781	−	0.140258i
$545$	0.917404	+	5.20286i	0.0392973	+	0.222866i
$546$	2.53802	+	2.12965i	0.108617	+	0.0911406i
$547$	−24.1878	+	20.2960i	−1.03420	+	0.867793i	−0.991344	−	0.131289i	$-0.958088\pi$
$547$	−24.1878	+	20.2960i	−1.03420	+	0.867793i	−0.0428509	+	0.999081i	$0.513644\pi$
$548$	−0.761707	+	4.31986i	−0.0325385	+	0.184535i
$549$	13.0890	−	4.76400i	0.558625	−	0.203323i
$550$	11.0419			0.470828
$551$	−1.31938	−	6.89630i	−0.0562076	−	0.293792i
$552$	−7.70233			−0.327833
$553$	−5.25877	+	1.91404i	−0.223626	+	0.0813931i
$554$	6.37598	−	36.1600i	0.270890	−	1.53629i
$555$	11.8439	−	9.93821i	0.502745	−	0.421853i
$556$	−1.07738	−	0.904030i	−0.0456912	−	0.0383394i
$557$	6.18748	+	35.0909i	0.262172	+	1.48685i	0.776969	+	0.629539i	$0.216756\pi$
$557$	6.18748	+	35.0909i	0.262172	+	1.48685i	−0.514797	+	0.857312i	$0.672133\pi$
$558$	7.56805	+	13.1082i	0.320381	+	0.554916i
$559$	0.359785	−	0.623166i	0.0152173	−	0.0263571i
$560$	−5.79086	−	2.10770i	−0.244708	−	0.0890666i
$561$	−9.32547	−	3.39420i	−0.393722	−	0.143303i
$562$	19.5804	−	33.9142i	0.825948	−	1.43058i
$563$	10.9957	+	19.0451i	0.463414	+	0.802657i	0.999128	−	0.0417423i	$-0.0132909\pi$
$563$	10.9957	+	19.0451i	0.463414	+	0.802657i	−0.535714	+	0.844399i	$0.679958\pi$
$564$	−0.455889	−	2.58548i	−0.0191964	−	0.108868i
$565$	−14.1138	−	11.8429i	−0.593772	−	0.498234i
$566$	8.81496	−	7.39663i	0.370520	−	0.310904i
$567$	0.0923963	−	0.524005i	0.00388028	−	0.0220062i
$568$	−9.09627	+	3.31077i	−0.381671	+	0.138917i
$569$	28.7588			1.20563			0.602815	−	0.797881i	$-0.294046\pi$
$569$	28.7588			1.20563			0.602815	+	0.797881i	$0.294046\pi$
$570$	16.9081	−	0.245188i	0.708201	−	0.0102698i
$571$	7.30365			0.305648			0.152824	−	0.988253i	$-0.451163\pi$
$571$	7.30365			0.305648			0.152824	+	0.988253i	$0.451163\pi$
$572$	6.77244	−	2.46497i	0.283170	−	0.103065i
$573$	3.31180	−	18.7822i	0.138353	−	0.784637i
$574$	5.29292	−	4.44129i	0.220922	−	0.185376i
$575$	3.28905	+	2.75984i	0.137163	+	0.115093i
$576$	1.07145	+	6.07650i	0.0446438	+	0.253188i
$577$	−15.7545	−	27.2876i	−0.655868	−	1.13600i	−0.981675	−	0.190561i	$-0.938969\pi$
$577$	−15.7545	−	27.2876i	−0.655868	−	1.13600i	0.325807	−	0.945436i	$-0.394364\pi$
$578$	−10.1291	+	17.5441i	−0.421314	+	0.729737i
$579$	−22.3983	−	8.15230i	−0.930840	−	0.338798i
$580$	1.33110	+	0.484481i	0.0552709	+	0.0201170i
$581$	3.05303	−	5.28801i	0.126661	−	0.219384i
$582$	5.20961	+	9.02330i	0.215945	+	0.374028i
$583$	8.77941	+	49.7905i	0.363606	+	2.06211i
$584$	−3.60220	−	3.02260i	−0.149060	−	0.125076i
$585$	−7.88326	+	6.61484i	−0.325933	+	0.273490i
$586$	−3.92855	+	22.2799i	−0.162287	+	0.920374i
$587$	−25.6434	+	9.33342i	−1.05842	+	0.385232i	−0.811833	−	0.583890i	$-0.801530\pi$
$587$	−25.6434	+	9.33342i	−1.05842	+	0.385232i	−0.246583	+	0.969122i	$0.579308\pi$
$588$	2.33275			0.0962009
$589$	20.9886	−	37.6021i	0.864820	−	1.54937i
$590$	−14.8007			−0.609334
$591$	−4.12449	+	1.50119i	−0.169659	+	0.0617507i
$592$	−4.84982	+	27.5047i	−0.199326	+	1.13044i
$593$	26.6366	−	22.3507i	1.09383	−	0.917834i	0.0968375	−	0.995300i	$-0.469127\pi$
$593$	26.6366	−	22.3507i	1.09383	−	0.917834i	0.996995	+	0.0774657i	$0.0246828\pi$
$594$	−5.99273	−	5.02849i	−0.245885	−	0.206322i
$595$	−0.454707	−	2.57877i	−0.0186412	−	0.105719i
$596$	−1.05391	−	1.82543i	−0.0431699	−	0.0747724i
$597$	−10.0189	+	17.3532i	−0.410046	+	0.710220i
$598$	17.7986	+	6.47816i	0.727839	+	0.264912i
$599$	−14.9402	−	5.43777i	−0.610438	−	0.222181i	0.0182567	−	0.999833i	$-0.494188\pi$
$599$	−14.9402	−	5.43777i	−0.610438	−	0.222181i	−0.628695	+	0.777652i	$0.716411\pi$
$600$	1.78699	−	3.09516i	0.0729535	−	0.126359i
$601$	12.3464	+	21.3846i	0.503621	+	0.872297i	0.999991	+	0.00418616i	$0.00133250\pi$
$601$	12.3464	+	21.3846i	0.503621	+	0.872297i	−0.496370	+	0.868111i	$0.665334\pi$
$602$	0.0250633	+	0.142141i	0.00102150	+	0.00579324i
$603$	−7.82295	−	6.56423i	−0.318575	−	0.267316i
$604$	−0.0432332	+	0.0362770i	−0.00175914	+	0.00147609i
$605$	−6.62701	+	37.5836i	−0.269426	+	1.52799i
$606$	12.6099	−	4.58964i	0.512244	−	0.186441i
$607$	4.01455			0.162945			0.0814727	−	0.996676i	$-0.474038\pi$
$607$	4.01455			0.162945			0.0814727	+	0.996676i	$0.474038\pi$
$608$	−6.41013	+	5.53909i	−0.259965	+	0.224640i
$609$	−0.857097			−0.0347313
$610$	50.7772	−	18.4814i	2.05591	−	0.748290i
$611$	5.33497	−	30.2561i	0.215830	−	1.22403i
$612$	0.517074	−	0.433877i	0.0209015	−	0.0175384i
$613$	−30.8082	−	25.8511i	−1.24433	−	1.04412i	−0.997173	−	0.0751409i	$-0.976059\pi$
$613$	−30.8082	−	25.8511i	−1.24433	−	1.04412i	−0.247157	−	0.968976i	$-0.579496\pi$
$614$	−1.46657	−	8.31731i	−0.0591858	−	0.335659i
$615$	10.7306	+	18.5859i	0.432698	+	0.749454i
$616$	3.43969	−	5.95772i	0.138589	−	0.240043i
$617$	20.8427	+	7.58613i	0.839096	+	0.305406i	0.725586	−	0.688131i	$-0.241569\pi$
$617$	20.8427	+	7.58613i	0.839096	+	0.305406i	0.113509	+	0.993537i	$0.463791\pi$
$618$	5.53596	+	2.01492i	0.222689	+	0.0810521i
$619$	11.6177	−	20.1224i	0.466954	−	0.808788i	−0.532333	−	0.846535i	$-0.678685\pi$
$619$	11.6177	−	20.1224i	0.466954	−	0.808788i	0.999287	+	0.0377469i	$0.0120181\pi$
$620$	4.34389	+	7.52384i	0.174455	+	0.302165i
$621$	−0.528218	−	2.99568i	−0.0211967	−	0.120212i
$622$	−20.4210	−	17.1353i	−0.818809	−	0.687062i
$623$	−2.41463	+	2.02611i	−0.0967401	+	0.0811746i
$624$	3.22803	−	18.3070i	0.129224	−	0.732868i
$625$	28.2520	−	10.2829i	1.13008	−	0.411315i
$626$	−24.4270			−0.976298
$627$	−3.54664	+	21.9724i	−0.141639	+	0.877494i
$628$	2.31315			0.0923047
$629$	−11.1518	+	4.05893i	−0.444652	+	0.161840i
$630$	0.358441	−	2.03282i	0.0142806	−	0.0809894i
$631$	21.4893	−	18.0317i	0.855476	−	0.717830i	−0.105512	−	0.994418i	$-0.533648\pi$
$631$	21.4893	−	18.0317i	0.855476	−	0.717830i	0.960989	+	0.276588i	$0.0892037\pi$
$632$	20.4008	+	17.1183i	0.811500	+	0.680929i
$633$	−4.72193	−	26.7794i	−0.187680	−	1.06439i
$634$	1.51186	+	2.61862i	0.0600436	+	0.103999i
$635$	2.31655	−	4.01239i	0.0919295	−	0.159227i
$636$	−3.23143	−	1.17614i	−0.128135	−	0.0466371i
$637$	25.6523	+	9.33667i	1.01638	+	0.369932i
$638$	−6.30066	+	10.9131i	−0.249446	+	0.432052i
$639$	−1.91147	−	3.31077i	−0.0756167	−	0.130972i
$640$	5.86571	+	33.2661i	0.231863	+	1.31496i
$641$	33.3068	+	27.9477i	1.31554	+	1.10387i	0.987230	+	0.159299i	$0.0509233\pi$
$641$	33.3068	+	27.9477i	1.31554	+	1.10387i	0.328309	+	0.944570i	$0.393521\pi$
$642$	−6.66044	+	5.58878i	−0.262867	+	0.220571i
$643$	6.83322	−	38.7531i	0.269476	−	1.52827i	−0.486504	−	0.873678i	$-0.661728\pi$
$643$	6.83322	−	38.7531i	0.269476	−	1.52827i	0.755980	−	0.654595i	$-0.227161\pi$
$644$	−0.528218	+	0.192256i	−0.0208147	+	0.00757594i
$645$	−0.448311			−0.0176522
$646$	−12.2599	−	4.26195i	−0.482358	−	0.167684i
$647$	18.8862			0.742493			0.371246	−	0.928534i	$-0.378931\pi$
$647$	18.8862			0.742493			0.371246	+	0.928534i	$0.378931\pi$
$648$	−2.37939	+	0.866025i	−0.0934711	+	0.0340207i
$649$	3.38279	−	19.1847i	0.132786	−	0.753067i
$650$	−6.73261	+	5.64933i	−0.264075	+	0.221585i
$651$	−4.02687	−	3.37895i	−0.157826	−	0.132431i
$652$	−0.0270364	−	0.153331i	−0.00105883	−	0.00600492i
$653$	23.3714	+	40.4804i	0.914593	+	1.58412i	0.807495	+	0.589874i	$0.200823\pi$
$653$	23.3714	+	40.4804i	0.914593	+	1.58412i	0.107098	+	0.994248i	$0.465844\pi$
$654$	1.59833	−	2.76838i	0.0624995	−	0.108252i
$655$	−20.9055	−	7.60900i	−0.816847	−	0.297308i
$656$	−36.4295	−	13.2592i	−1.42233	−	0.517687i
$657$	0.928548	−	1.60829i	0.0362261	−	0.0627455i
$658$	3.08125	+	5.33688i	0.120120	+	0.208053i
$659$	0.362778	+	2.05742i	0.0141318	+	0.0801455i	0.991058	−	0.133432i	$-0.0425996\pi$
$659$	0.362778	+	2.05742i	0.0141318	+	0.0801455i	−0.976926	+	0.213577i	$0.931489\pi$
$660$	−3.43969	−	2.88624i	−0.133890	−	0.112347i
$661$	−9.53596	+	8.00162i	−0.370906	+	0.311227i	−0.809120	−	0.587644i	$-0.800056\pi$
$661$	−9.53596	+	8.00162i	−0.370906	+	0.311227i	0.438214	+	0.898871i	$0.355611\pi$
$662$	0.222811	−	1.26363i	0.00865980	−	0.0491122i
$663$	7.42262	−	2.70161i	0.288271	−	0.104922i
$664$	−29.0574			−1.12764
$665$	−5.48886	+	2.08840i	−0.212849	+	0.0809846i
$666$	−9.35504			−0.362500
$667$	−4.60442	+	1.67587i	−0.178284	+	0.0648900i
$668$	0.204393	−	1.15917i	0.00790820	−	0.0448496i
$669$	9.20233	−	7.72167i	0.355783	−	0.298537i
$670$	−30.3482	−	25.4652i	−1.17245	−	0.983806i
$671$	12.3503	+	70.0420i	0.476778	+	2.70394i
$672$	0.517074	+	0.895599i	0.0199466	+	0.0345485i
$673$	5.41060	−	9.37143i	0.208563	−	0.361242i	−0.742699	−	0.669625i	$-0.766455\pi$
$673$	5.41060	−	9.37143i	0.208563	−	0.361242i	0.951262	+	0.308383i	$0.0997880\pi$
$674$	−4.79086	−	1.74373i	−0.184537	−	0.0671660i
$675$	1.32635	+	0.482753i	0.0510513	+	0.0185812i
$676$	−0.610815	+	1.05796i	−0.0234929	+	0.0406908i
$677$	−2.18092	−	3.77747i	−0.0838196	−	0.145180i	0.821068	−	0.570830i	$-0.193379\pi$
$677$	−2.18092	−	3.77747i	−0.0838196	−	0.145180i	−0.904888	+	0.425651i	$0.860045\pi$
$678$	1.93582	+	10.9786i	0.0743448	+	0.421630i
$679$	−2.77197	−	2.32596i	−0.106379	−	0.0892623i
$680$	−9.54576	+	8.00984i	−0.366063	+	0.307163i
$681$	−0.753718	+	4.27455i	−0.0288825	+	0.163801i
$682$	−72.6250	+	26.4333i	−2.78096	+	1.01218i
$683$	−44.6441			−1.70826			−0.854130	−	0.520059i	$-0.825910\pi$
$683$	−44.6441			−1.70826			−0.854130	+	0.520059i	$0.825910\pi$
$684$	−1.17365	−	0.956154i	−0.0448756	−	0.0365595i
$685$	31.9813			1.22194
$686$	−10.5077	+	3.82450i	−0.401187	+	0.146020i
$687$	−0.572329	+	3.24584i	−0.0218357	+	0.123837i
$688$	0.620366	−	0.520549i	0.0236512	−	0.0198458i
$689$	−30.8273	−	25.8672i	−1.17443	−	0.985460i
$690$	−2.04916	−	11.6214i	−0.0780103	−	0.442418i
$691$	−12.1604	−	21.0625i	−0.462605	−	0.801256i	0.536485	−	0.843910i	$-0.319752\pi$
$691$	−12.1604	−	21.0625i	−0.462605	−	0.801256i	−0.999090	+	0.0426544i	$0.986419\pi$
$692$	0.280592	−	0.486000i	0.0106665	−	0.0184750i
$693$	2.55303	+	0.929228i	0.0969817	+	0.0352985i
$694$	5.76991	+	2.10008i	0.219023	+	0.0797178i
$695$	−5.12701	+	8.88024i	−0.194479	+	0.336847i
$696$	2.03936	+	3.53228i	0.0773018	+	0.133891i
$697$	−2.86050	−	16.2227i	−0.108349	−	0.614479i
$698$	32.7478	+	27.4787i	1.23952	+	1.04008i
$699$	11.8209	−	9.91890i	0.447107	−	0.375167i
$700$	0.0452926	−	0.256867i	0.00171190	−	0.00970867i
$701$	22.1386	−	8.05780i	0.836164	−	0.304339i	0.111778	−	0.993733i	$-0.464345\pi$
$701$	22.1386	−	8.05780i	0.836164	−	0.304339i	0.724386	+	0.689394i	$0.242123\pi$
$702$	6.22668			0.235011
$703$	13.6407	+	22.8545i	0.514468	+	0.861974i
$704$	−31.5057			−1.18742
$705$	−17.9868	+	6.54666i	−0.677422	+	0.246561i
$706$	−3.44356	+	19.5294i	−0.129600	+	0.734999i
$707$	−3.57011	+	2.99568i	−0.134268	+	0.112664i
$708$	1.01501	+	0.851698i	0.0381466	+	0.0320088i
$709$	−1.06851	−	6.05985i	−0.0401289	−	0.227582i	0.958147	−	0.286276i	$-0.0924175\pi$
$709$	−1.06851	−	6.05985i	−0.0401289	−	0.227582i	−0.998276	+	0.0586939i	$0.981306\pi$
$710$	−7.41534	−	12.8438i	−0.278293	−	0.482017i
$711$	−5.25877	+	9.10846i	−0.197219	+	0.341594i
$712$	14.0954	+	5.13030i	0.528247	+	0.192266i
$713$	−28.2396	−	10.2784i	−1.05758	−	0.384929i
$714$	−0.792204	+	1.37214i	−0.0296475	+	0.0513509i
$715$	−26.2729	−	45.5060i	−0.982551	−	1.70183i
$716$	0.127478	+	0.722965i	0.00476408	+	0.0270185i
$717$	−12.1211	−	10.1708i	−0.452670	−	0.379835i
$718$	−13.4342	+	11.2727i	−0.501361	+	0.420692i
$719$	5.65657	−	32.0800i	0.210955	−	1.19638i	−0.676835	−	0.736134i	$-0.736649\pi$
$719$	5.65657	−	32.0800i	0.210955	−	1.19638i	0.887790	−	0.460249i	$-0.152240\pi$
$720$	−10.8833	+	3.96118i	−0.405595	+	0.147625i
$721$	−2.04601			−0.0761973
$722$	−4.22147	+	28.8020i	−0.157107	+	1.07190i
$723$	23.6459			0.879400
$724$	−2.85622	+	1.03958i	−0.106151	+	0.0386356i
$725$	0.394811	−	2.23908i	0.0146629	−	0.0831574i
$726$	17.6891	−	14.8429i	0.656505	−	0.550873i
$727$	24.6896	+	20.7170i	0.915686	+	0.768352i	0.973192	−	0.229993i	$-0.0738703\pi$
$727$	24.6896	+	20.7170i	0.915686	+	0.768352i	−0.0575058	+	0.998345i	$0.518315\pi$
$728$	0.950837	+	5.39246i	0.0352404	+	0.199858i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	3.60220	−	6.23919i	0.133323	−	0.230923i
$731$	0.323359	+	0.117693i	0.0119599	+	0.00435303i
$732$	−4.54576	−	1.65452i	−0.168016	−	0.0611529i
$733$	−4.89053	+	8.47065i	−0.180636	+	0.312870i	−0.942097	−	0.335340i	$-0.891149\pi$
$733$	−4.89053	+	8.47065i	−0.180636	+	0.312870i	0.761461	+	0.648210i	$0.224482\pi$
$734$	−21.9099	−	37.9490i	−0.808708	−	1.40072i
$735$	−2.95336	−	16.7494i	−0.108936	−	0.617809i
$736$	4.52893	+	3.80023i	0.166939	+	0.140078i
$737$	39.9445	−	33.5174i	1.47137	−	1.23463i
$738$	2.25490	−	12.7882i	0.0830040	−	0.470739i
$739$	−26.0993	+	9.49935i	−0.960077	+	0.349439i	−0.774064	−	0.633108i	$-0.781779\pi$
$739$	−26.0993	+	9.49935i	−0.960077	+	0.349439i	−0.186013	+	0.982547i	$0.559557\pi$
$740$	−5.36959			−0.197390
$741$	−9.07919	−	15.2119i	−0.333532	−	0.558823i
$742$	8.07192			0.296329
$743$	30.3542	−	11.0480i	1.11359	−	0.405312i	0.281278	−	0.959626i	$-0.409242\pi$
$743$	30.3542	−	11.0480i	1.11359	−	0.405312i	0.832308	+	0.554314i	$0.187019\pi$
$744$	−4.34389	+	24.6354i	−0.159255	+	0.903179i
$745$	−11.7724	+	9.87825i	−0.431309	+	0.361911i
$746$	14.7483	+	12.3753i	0.539975	+	0.453093i
$747$	−1.99273	−	11.3013i	−0.0729100	−	0.413493i
$748$	1.72328	+	2.98481i	0.0630093	+	0.109135i
$749$	1.50980	−	2.61505i	0.0551669	−	0.0955519i
$750$	−13.0817	−	4.76136i	−0.477677	−	0.173860i
$751$	−3.27497	−	1.19199i	−0.119505	−	0.0434964i	0.281575	−	0.959539i	$-0.409143\pi$
$751$	−3.27497	−	1.19199i	−0.119505	−	0.0434964i	−0.401081	+	0.916043i	$0.631365\pi$
$752$	17.2883	−	29.9443i	0.630441	−	1.09196i
$753$	9.70574	+	16.8108i	0.353697	+	0.612621i
$754$	−1.74170	−	9.87765i	−0.0634288	−	0.359723i
$755$	0.315207	+	0.264490i	0.0114716	+	0.00962579i
$756$	−0.141559	+	0.118782i	−0.00514846	+	0.00432007i
$757$	−6.41353	+	36.3730i	−0.233104	+	1.32200i	0.613467	+	0.789721i	$0.289775\pi$
$757$	−6.41353	+	36.3730i	−0.233104	+	1.32200i	−0.846570	+	0.532277i	$0.821337\pi$
$758$	−3.16637	+	1.15247i	−0.115008	+	0.0418594i
$759$	15.5321			0.563779
$760$	21.6668	+	17.6517i	0.785939	+	0.640293i
$761$	31.3429			1.13618			0.568089	−	0.822967i	$-0.307683\pi$
$761$	31.3429			1.13618			0.568089	+	0.822967i	$0.307683\pi$
$762$	−2.63429	+	0.958801i	−0.0954301	+	0.0347337i
$763$	−0.192782	+	1.09332i	−0.00697917	+	0.0395808i
$764$	−5.07398	+	4.25757i	−0.183570	+	0.154034i
$765$	−3.76991	−	3.16333i	−0.136302	−	0.114371i
$766$	1.57713	+	8.94437i	0.0569841	+	0.323173i
$767$	7.75284	+	13.4283i	0.279939	+	0.484868i
$768$	4.04916	−	7.01336i	0.146112	−	0.253073i
$769$	29.8282	+	10.8566i	1.07563	+	0.391498i	0.818280	−	0.574820i	$-0.194928\pi$
$769$	29.8282	+	10.8566i	1.07563	+	0.391498i	0.257351	+	0.966318i	$0.417150\pi$
$770$	9.90420	+	3.60483i	0.356923	+	0.129909i
$771$	6.14796	−	10.6486i	0.221413	−	0.383499i
$772$	4.13903	+	7.16902i	0.148967	+	0.258019i
$773$	1.90269	+	10.7907i	0.0684351	+	0.388115i	0.999716	+	0.0238140i	$0.00758095\pi$
$773$	1.90269	+	10.7907i	0.0684351	+	0.388115i	−0.931281	+	0.364301i	$0.881308\pi$
$774$	0.207796	+	0.174362i	0.00746909	+	0.00626731i
$775$	10.6821	−	8.96335i	0.383713	−	0.321973i
$776$	−2.99020	+	16.9583i	−0.107342	+	0.608766i
$777$	3.05303	−	1.11121i	0.109527	−	0.0398646i
$778$	50.7410			1.81915
$779$	−34.5296	+	13.1378i	−1.23715	+	0.470711i
$780$	3.57398			0.127969
$781$	18.3430	−	6.67631i	0.656365	−	0.238897i
$782$	−1.57288	+	8.92026i	−0.0562462	+	0.318988i
$783$	−1.23396	+	1.03541i	−0.0440980	+	0.0370026i
$784$	23.5351	+	19.7483i	0.840539	+	0.705296i
$785$	−2.92855	−	16.6086i	−0.104524	−	0.592787i
$786$	6.73055	+	11.6577i	0.240071	+	0.415815i
$787$	−23.1771	+	40.1439i	−0.826175	+	1.43098i	0.0748436	+	0.997195i	$0.476154\pi$
$787$	−23.1771	+	40.1439i	−0.826175	+	1.43098i	−0.901018	+	0.433781i	$0.857179\pi$
$788$	1.43242	+	0.521358i	0.0510278	+	0.0185726i
$789$	5.95811	+	2.16858i	0.212114	+	0.0772033i
$790$	−20.4008	+	35.3352i	−0.725828	+	1.25717i
$791$	−1.93582	−	3.35294i	−0.0688299	−	0.119217i
$792$	−2.24510	−	12.7326i	−0.0797762	−	0.452433i
$793$	−43.3658	−	36.3882i	−1.53996	−	1.29218i
$794$	30.5731	−	25.6539i	1.08500	−	0.910422i
$795$	−4.35369	+	24.6910i	−0.154410	+	0.875700i
$796$	6.53936	−	2.38013i	0.231782	−	0.0843616i
$797$	−3.47296			−0.123019			−0.0615093	−	0.998107i	$-0.519591\pi$
$797$	−3.47296			−0.123019			−0.0615093	+	0.998107i	$0.519591\pi$
$798$	3.35638	+	1.16679i	0.118815	+	0.0413040i
$799$	14.6922			0.519774
$800$	−2.57785	+	0.938260i	−0.0911407	+	0.0331725i
$801$	−1.02869	+	5.83396i	−0.0363468	+	0.206133i
$802$	18.7411	−	15.7256i	0.661770	−	0.555291i
$803$	7.26399	+	6.09521i	0.256340	+	0.215095i
$804$	0.615867	+	3.49276i	0.0217200	+	0.123180i
$805$	2.04916	+	3.54925i	0.0722235	+	0.125095i
$806$	30.7579	−	53.2742i	1.08340	−	1.87650i
$807$	−2.18479	−	0.795199i	−0.0769083	−	0.0279923i
$808$	20.8405	+	7.58532i	0.733166	+	0.266851i
$809$	25.9748	−	44.9896i	0.913224	−	1.58175i	0.103744	−	0.994604i	$-0.466918\pi$
$809$	25.9748	−	44.9896i	0.913224	−	1.58175i	0.809480	−	0.587147i	$-0.199749\pi$
$810$	−1.93969	−	3.35965i	−0.0681539	−	0.118046i
$811$	2.91329	+	16.5221i	0.102299	+	0.580168i	0.992265	+	0.124140i	$0.0396172\pi$
$811$	2.91329	+	16.5221i	0.102299	+	0.580168i	−0.889965	+	0.456028i	$0.849272\pi$
$812$	0.228026	+	0.191336i	0.00800214	+	0.00671459i
$813$	−11.4474	+	9.60554i	−0.401479	+	0.336881i
$814$	8.29473	−	47.0418i	0.290730	−	1.64881i
$815$	−1.06670	+	0.388249i	−0.0373650	+	0.0135998i
$816$	8.88981			0.311206
$817$	0.122979	−	0.761889i	0.00430249	−	0.0266551i
$818$	4.51754			0.157952
$819$	−2.03209	+	0.739620i	−0.0710069	+	0.0258444i
$820$	1.29426	−	7.34013i	0.0451976	−	0.256328i
$821$	−28.5330	+	23.9420i	−0.995809	+	0.835583i	−0.986398	−	0.164372i	$-0.947440\pi$
$821$	−28.5330	+	23.9420i	−0.995809	+	0.835583i	−0.00941101	+	0.999956i	$0.502996\pi$
$822$	−14.8237	−	12.4385i	−0.517035	−	0.433844i
$823$	−0.763985	−	4.33277i	−0.0266308	−	0.151031i	0.968593	−	0.248652i	$-0.0799877\pi$
$823$	−0.763985	−	4.33277i	−0.0266308	−	0.151031i	−0.995224	+	0.0976214i	$0.968877\pi$
$824$	4.86824	+	8.43204i	0.169593	+	0.293744i
$825$	−3.60354	+	6.24152i	−0.125459	+	0.217302i
$826$	−2.92262	−	1.06375i	−0.101691	−	0.0370125i
$827$	13.0265	+	4.74125i	0.452975	+	0.164869i	0.558424	−	0.829555i	$-0.311406\pi$
$827$	13.0265	+	4.74125i	0.452975	+	0.164869i	−0.105450	+	0.994425i	$0.533628\pi$
$828$	−0.528218	+	0.914901i	−0.0183569	+	0.0317950i
$829$	−8.18850	−	14.1829i	−0.284398	−	0.492592i	0.688065	−	0.725649i	$-0.258461\pi$
$829$	−8.18850	−	14.1829i	−0.284398	−	0.492592i	−0.972463	+	0.233057i	$0.925127\pi$
$830$	−7.73055	−	43.8421i	−0.268331	−	1.52178i
$831$	18.3589	+	15.4050i	0.636863	+	0.534392i
$832$	19.2101	−	16.1192i	0.665989	−	0.558832i
$833$	−2.26692	+	12.8564i	−0.0785442	+	0.445446i
$834$	5.83022	−	2.12203i	0.201884	−	0.0734798i
$835$	−8.58172			−0.296983
$836$	5.84864	−	5.05390i	0.202279	−	0.174793i
$837$	−9.87939			−0.341482
$838$	−48.2242	+	17.5522i	−1.66588	+	0.606330i
$839$	−6.64883	+	37.7074i	−0.229543	+	1.30180i	0.624263	+	0.781214i	$0.285399\pi$
$839$	−6.64883	+	37.7074i	−0.229543	+	1.30180i	−0.853807	+	0.520590i	$0.825712\pi$
$840$	2.61334	−	2.19285i	0.0901688	−	0.0756606i
$841$	−20.2276	−	16.9730i	−0.697504	−	0.585275i
$842$	−4.79355	−	27.1856i	−0.165197	−	0.936876i
$843$	12.7802	+	22.1359i	0.440173	+	0.762402i
$844$	−4.72193	+	8.17863i	−0.162536	+	0.281520i
$845$	8.36959	+	3.04628i	0.287922	+	0.104795i
$846$	10.8833	+	3.96118i	0.374174	+	0.136188i
$847$	−4.00980	+	6.94518i	−0.137778	+	0.238639i
$848$	−22.6450	−	39.2223i	−0.777633	−	1.34690i
$849$	1.30423	+	7.39663i	0.0447609	+	0.253852i
$850$	−3.21966	−	2.70161i	−0.110433	−	0.0926645i
$851$	14.2285	−	11.9391i	0.487746	−	0.409268i
$852$	−0.230552	+	1.30753i	−0.00789858	+	0.0447951i
$853$	−20.7579	+	7.55526i	−0.710737	+	0.258687i	−0.671988	−	0.740562i	$-0.734559\pi$
$853$	−20.7579	+	7.55526i	−0.710737	+	0.258687i	−0.0387487	+	0.999249i	$0.512337\pi$
$854$	11.3550			0.388561
$855$	−5.37939	+	9.63744i	−0.183971	+	0.329593i
$856$	−14.3696			−0.491142
$857$	−42.2934	+	15.3936i	−1.44472	+	0.525834i	−0.941110	−	0.338100i	$-0.890216\pi$
$857$	−42.2934	+	15.3936i	−1.44472	+	0.525834i	−0.503606	+	0.863933i	$0.667994\pi$
$858$	−5.52094	+	31.3108i	−0.188482	+	1.06893i
$859$	−12.2358	+	10.2670i	−0.417479	+	0.350306i	−0.827203	−	0.561903i	$-0.810069\pi$
$859$	−12.2358	+	10.2670i	−0.417479	+	0.350306i	0.409724	+	0.912209i	$0.365625\pi$
$860$	0.119271	+	0.100080i	0.00406709	+	0.00341270i
$861$	0.783119	+	4.44129i	0.0266886	+	0.151359i
$862$	16.3327	+	28.2892i	0.556296	+	0.963532i
$863$	−20.6288	+	35.7302i	−0.702213	+	1.21627i	0.265475	+	0.964118i	$0.414471\pi$
$863$	−20.6288	+	35.7302i	−0.702213	+	1.21627i	−0.967688	+	0.252151i	$0.918862\pi$
$864$	1.82635	+	0.664738i	0.0621338	+	0.0226148i
$865$	−3.84477	−	1.39938i	−0.130726	−	0.0475804i
$866$	−16.8931	+	29.2596i	−0.574049	+	0.994283i
$867$	−6.61128	−	11.4511i	−0.224531	−	0.388899i
$868$	0.317018	+	1.79790i	0.0107603	+	0.0610247i
$869$	−41.1391	−	34.5198i	−1.39555	−	1.17100i
$870$	−4.78699	+	4.01676i	−0.162294	+	0.136181i
$871$	−7.20708	+	40.8734i	−0.244203	+	1.38494i
$872$	4.96451	−	1.80693i	0.168119	−	0.0611905i
$873$	−6.80066			−0.230167
$874$	20.3123	−	0.294553i	0.687073	−	0.00996340i
$875$	4.83481			0.163446
$876$	−0.606067	+	0.220590i	−0.0204771	+	0.00745306i
$877$	8.01650	−	45.4638i	0.270698	−	1.53520i	−0.481606	−	0.876388i	$-0.659946\pi$
$877$	8.01650	−	45.4638i	0.270698	−	1.53520i	0.752304	−	0.658817i	$-0.228943\pi$
$878$	3.97494	−	3.33537i	0.134148	−	0.112563i
$879$	−11.3118	−	9.49173i	−0.381538	−	0.320148i
$880$	−10.2690	−	58.2386i	−0.346169	−	1.96322i
$881$	−9.47906	−	16.4182i	−0.319357	−	0.553143i	0.660997	−	0.750389i	$-0.270134\pi$
$881$	−9.47906	−	16.4182i	−0.319357	−	0.553143i	−0.980354	+	0.197245i	$0.936800\pi$
$882$	−5.14543	+	8.91215i	−0.173256	+	0.300088i
$883$	−32.9359	−	11.9877i	−1.10838	−	0.403418i	−0.277981	−	0.960586i	$-0.589665\pi$
$883$	−32.9359	−	11.9877i	−1.10838	−	0.403418i	−0.830399	+	0.557169i	$0.811888\pi$
$884$	−2.57785	−	0.938260i	−0.0867024	−	0.0315571i
$885$	4.83022	−	8.36619i	0.162366	−	0.281226i
$886$	−23.1072	−	40.0229i	−0.776303	−	1.34460i
$887$	−3.09745	−	17.5665i	−0.104002	−	0.589825i	−0.991614	−	0.129234i	$-0.958748\pi$
$887$	−3.09745	−	17.5665i	−0.104002	−	0.589825i	0.887612	−	0.460592i	$-0.152363\pi$
$888$	−11.8439	−	9.93821i	−0.397455	−	0.333504i
$889$	0.745815	−	0.625813i	0.0250138	−	0.0209891i
$890$	−3.99067	+	22.6322i	−0.133767	+	0.758633i
$891$	4.79813	−	1.74638i	0.160744	−	0.0585059i
$892$	−4.17200			−0.139689
$893$	−6.19176	−	32.3638i	−0.207199	−	1.08301i
$894$	9.29860			0.310992
$895$	5.02956	−	1.83061i	0.168120	−	0.0611906i
$896$	−1.23261	+	6.99049i	−0.0411787	+	0.233536i
$897$	−9.47044	+	7.94664i	−0.316209	+	0.265331i
$898$	36.2796	+	30.4422i	1.21066	+	1.01587i
$899$	2.76341	+	15.6721i	0.0921650	+	0.522693i
$900$	−0.245100	−	0.424525i	−0.00817000	−	0.0141508i
$901$	9.62226	−	16.6662i	0.320564	−	0.555233i
$902$	62.3059	+	22.6775i	2.07456	+	0.755078i
$903$	−0.0885259	−	0.0322208i	−0.00294596	−	0.00107224i
$904$	−9.21213	+	15.9559i	−0.306391	+	0.530685i
$905$	11.0804	+	19.1918i	0.368324	+	0.637956i
$906$	−0.0432332	−	0.245188i	−0.00143633	−	0.00814582i
$907$	−10.9172	−	9.16058i	−0.362498	−	0.304172i	0.443287	−	0.896380i	$-0.353812\pi$
$907$	−10.9172	−	9.16058i	−0.362498	−	0.304172i	−0.805786	+	0.592207i	$0.798257\pi$
$908$	1.15476	−	0.968961i	0.0383222	−	0.0321561i
$909$	−1.52094	+	8.62571i	−0.0504465	+	0.286097i
$910$	−7.88326	+	2.86927i	−0.261327	+	0.0951154i
$911$	−16.4466			−0.544899			−0.272449	−	0.962170i	$-0.587834\pi$
$911$	−16.4466			−0.544899			−0.272449	+	0.962170i	$0.587834\pi$
$912$	−3.74644	−	19.5823i	−0.124057	−	0.648436i
$913$	58.5954			1.93923
$914$	−56.2169	+	20.4613i	−1.85949	+	0.676799i
$915$	−6.12449	+	34.7337i	−0.202469	+	1.14826i
$916$	0.876859	−	0.735772i	0.0289722	−	0.0243106i
$917$	−3.58125	−	3.00503i	−0.118263	−	0.0992347i
$918$	0.517074	+	2.93247i	0.0170660	+	0.0967860i
$919$	16.9500	+	29.3582i	0.559128	+	0.968437i	0.997570	+	0.0696779i	$0.0221971\pi$
$919$	16.9500	+	29.3582i	0.559128	+	0.968437i	−0.438442	+	0.898760i	$0.644470\pi$
$920$	9.75150	−	16.8901i	0.321497	−	0.556850i
$921$	5.18004	+	1.88538i	0.170688	+	0.0621255i
$922$	−2.17024	−	0.789904i	−0.0714732	−	0.0260141i
$923$	−7.76857	+	13.4556i	−0.255706	+	0.442895i
$924$	−0.471782	−	0.817150i	−0.0155205	−	0.0268822i
$925$	1.49660	+	8.48762i	0.0492078	+	0.279071i
$926$	3.85323	+	3.23324i	0.126625	+	0.106251i
$927$	−2.94562	+	2.47167i	−0.0967469	+	0.0811803i
$928$	0.543644	−	3.08316i	0.0178460	−	0.101210i
$929$	−20.2358	+	7.36522i	−0.663914	+	0.241645i	−0.651925	−	0.758283i	$-0.726038\pi$
$929$	−20.2358	+	7.36522i	−0.663914	+	0.241645i	−0.0119887	+	0.999928i	$0.503816\pi$
$930$	−38.3259			−1.25676
$931$	29.2751	−	0.424525i	0.959454	−	0.0139133i
$932$	−5.35916			−0.175545
$933$	16.3503	−	5.95102i	0.535284	−	0.194828i
$934$	6.08899	−	34.5324i	0.199238	−	1.12993i
$935$	19.2494	−	16.1522i	0.629524	−	0.528233i
$936$	7.88326	+	6.61484i	0.257672	+	0.216213i
$937$	1.31386	+	7.45129i	0.0429220	+	0.243423i	0.998719	−	0.0506054i	$-0.0161151\pi$
$937$	1.31386	+	7.45129i	0.0429220	+	0.243423i	−0.955797	+	0.294028i	$0.905004\pi$
$938$	−4.16250	−	7.20967i	−0.135911	−	0.235404i
$939$	7.97178	−	13.8075i	0.260149	−	0.450592i
$940$	6.24675	+	2.27363i	0.203746	+	0.0741577i
$941$	−17.9740	−	6.54200i	−0.585936	−	0.213263i	0.0320052	−	0.999488i	$-0.489811\pi$
$941$	−17.9740	−	6.54200i	−0.585936	−	0.213263i	−0.617941	+	0.786225i	$0.712033\pi$
$942$	−5.10220	+	8.83726i	−0.166239	+	0.287934i
$943$	12.8910	+	22.3279i	0.419789	+	0.727095i
$944$	3.03028	+	17.1856i	0.0986271	+	0.559342i
$945$	1.03209	+	0.866025i	0.0335739	+	0.0281718i
$946$	−1.06102	+	0.890304i	−0.0344968	+	0.0289463i
$947$	10.4549	−	59.2925i	0.339738	−	1.92675i	−0.0344768	−	0.999405i	$-0.510976\pi$
$947$	10.4549	−	59.2925i	0.339738	−	1.92675i	0.374214	−	0.927342i	$-0.377912\pi$
$948$	3.43242	−	1.24930i	0.111480	−	0.0405753i
$949$	−7.54757			−0.245005
$950$	−4.59421	+	8.23075i	−0.149056	+	0.267041i
$951$	−1.97359			−0.0639981
$952$	−2.46064	+	0.895599i	−0.0797497	+	0.0290265i
$953$	−3.42918	+	19.4478i	−0.111082	+	0.629977i	0.877534	+	0.479515i	$0.159187\pi$
$953$	−3.42918	+	19.4478i	−0.111082	+	0.629977i	−0.988616	+	0.150462i	$0.951924\pi$
$954$	11.6211	−	9.75125i	0.376246	−	0.315708i
$955$	36.9937	+	31.0414i	1.19709	+	1.00448i
$956$	0.954241	+	5.41177i	0.0308623	+	0.175029i
$957$	−4.11246	−	7.12300i	−0.132937	−	0.230254i
$958$	−7.39827	+	12.8142i	−0.239027	+	0.414007i
$959$	6.31521	+	2.29855i	0.203929	+	0.0742240i
$960$	−14.6814	−	5.34359i	−0.473840	−	0.172464i
$961$	−33.3011	+	57.6792i	−1.07423	+	1.86062i
$962$	19.0103	+	32.9267i	0.612916	+	1.06160i
$963$	−0.985452	−	5.58878i	−0.0317557	−	0.180096i
$964$	−6.29086	−	5.27866i	−0.202615	−	0.170014i
$965$	46.2340	−	38.7949i	1.48833	−	1.24885i
$966$	0.430608	−	2.44210i	0.0138546	−	0.0785732i
$967$	4.85679	−	1.76773i	0.156184	−	0.0568463i	−0.262745	−	0.964865i	$-0.584628\pi$
$967$	4.85679	−	1.76773i	0.156184	−	0.0568463i	0.418929	+	0.908019i	$0.362406\pi$
$968$	38.1634			1.22662
$969$	6.41013	−	5.53909i	0.205923	−	0.177941i
$970$	−26.3824			−0.847087
$971$	8.22967	−	2.99536i	0.264103	−	0.0961256i	−0.206575	−	0.978431i	$-0.566232\pi$
$971$	8.22967	−	2.99536i	0.264103	−	0.0961256i	0.470678	+	0.882305i	$0.344009\pi$
$972$	−0.0603074	+	0.342020i	−0.00193436	+	0.0109703i
$973$	−1.65064	+	1.38505i	−0.0529172	+	0.0444028i
$974$	26.4197	+	22.1687i	0.846541	+	0.710332i
$975$	−0.996130	−	5.64933i	−0.0319017	−	0.180923i
$976$	−31.8555	−	55.1754i	−1.01967	−	1.76612i
$977$	−20.3640	+	35.2714i	−0.651501	+	1.12843i	0.331258	+	0.943540i	$0.392527\pi$
$977$	−20.3640	+	35.2714i	−0.651501	+	1.12843i	−0.982759	+	0.184892i	$0.940806\pi$
$978$	0.645430	+	0.234917i	0.0206386	+	0.00751182i
$979$	−28.4240	−	10.3455i	−0.908434	−	0.330643i
$980$	−2.95336	+	5.11538i	−0.0943417	+	0.163405i
$981$	1.04323	+	1.80693i	0.0333079	+	0.0576909i
$982$	−1.93448	−	10.9710i	−0.0617317	−	0.350098i
$983$	3.02616	+	2.53925i	0.0965195	+	0.0809895i	0.689771	−	0.724028i	$-0.257711\pi$
$983$	3.02616	+	2.53925i	0.0965195	+	0.0809895i	−0.593251	+	0.805018i	$0.702156\pi$
$984$	16.4402	−	13.7949i	0.524093	−	0.439766i
$985$	1.92989	−	10.9450i	0.0614915	−	0.348736i
$986$	4.50727	−	1.64051i	0.143541	−	0.0522446i
$987$	−4.02229			−0.128031
$988$	−0.980400	+	6.07386i	−0.0311907	+	0.193235i
$989$	−0.538572			−0.0171256
$990$	18.6138	−	6.77487i	0.591586	−	0.215320i
$991$	−3.22328	+	18.2801i	−0.102391	+	0.580687i	0.889840	+	0.456273i	$0.150816\pi$
$991$	−3.22328	+	18.2801i	−0.102391	+	0.580687i	−0.992230	+	0.124414i	$0.960295\pi$
$992$	14.7090	−	12.3423i	0.467011	−	0.391868i
$993$	0.641559	+	0.538332i	0.0203593	+	0.0170835i
$994$	−0.541174	−	3.06915i	−0.0171650	−	0.0973475i
$995$	−25.3687	−	43.9399i	−0.804242	−	1.39299i
$996$	−1.99273	+	3.45150i	−0.0631419	+	0.109365i
$997$	−2.57398	−	0.936851i	−0.0815187	−	0.0296704i	0.300939	−	0.953643i	$-0.402700\pi$
$997$	−2.57398	−	0.936851i	−0.0815187	−	0.0296704i	−0.382458	+	0.923973i	$0.624922\pi$
$998$	−18.4440	−	6.71308i	−0.583836	−	0.212499i
$999$	3.05303	−	5.28801i	0.0965937	−	0.167305i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.2.i.a.43.1	yes	6
3.2	odd	2		171.2.u.a.100.1		6
4.3	odd	2		912.2.bo.b.385.1		6
19.2	odd	18		1083.2.a.n.1.3		3
19.4	even	9	inner	57.2.i.a.4.1	✓	6
19.17	even	9		1083.2.a.m.1.1		3
57.2	even	18		3249.2.a.x.1.1		3
57.17	odd	18		3249.2.a.w.1.3		3
57.23	odd	18		171.2.u.a.118.1		6
76.23	odd	18		912.2.bo.b.289.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.i.a.4.1	✓	6	19.4	even	9	inner
57.2.i.a.43.1	yes	6	1.1	even	1	trivial
171.2.u.a.100.1		6	3.2	odd	2
171.2.u.a.118.1		6	57.23	odd	18
912.2.bo.b.289.1		6	76.23	odd	18
912.2.bo.b.385.1		6	4.3	odd	2
1083.2.a.m.1.1		3	19.17	even	9
1083.2.a.n.1.3		3	19.2	odd	18
3249.2.a.w.1.3		3	57.17	odd	18
3249.2.a.x.1.1		3	57.2	even	18

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:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	57.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.43969 - 0.524005i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(0.266044 - 0.223238i) q^{4} +(-1.93969 - 1.62760i) q^{5} +(0.266044 + 1.50881i) q^{6} +(-0.266044 - 0.460802i) q^{7} +(-1.26604 + 2.19285i) q^{8} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})\)	\(q+(1.43969 - 0.524005i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(0.266044 - 0.223238i) q^{4} +(-1.93969 - 1.62760i) q^{5} +(0.266044 + 1.50881i) q^{6} +(-0.266044 - 0.460802i) q^{7} +(-1.26604 + 2.19285i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(-3.64543 - 1.32683i) q^{10} +(2.55303 - 4.42198i) q^{11} +(0.173648 + 0.300767i) q^{12} +(0.705737 + 4.00243i) q^{13} +(-0.624485 - 0.524005i) q^{14} +(1.93969 - 1.62760i) q^{15} +(-0.794263 + 4.50449i) q^{16} +(-1.82635 + 0.664738i) q^{17} -1.53209 q^{18} +(2.23396 + 3.74292i) q^{19} -0.879385 q^{20} +(0.500000 - 0.181985i) q^{21} +(1.35844 - 7.70410i) q^{22} +(2.33022 - 1.95529i) q^{23} +(-1.93969 - 1.62760i) q^{24} +(0.245100 + 1.39003i) q^{25} +(3.11334 + 5.39246i) q^{26} +(0.500000 - 0.866025i) q^{27} +(-0.173648 - 0.0632028i) q^{28} +(-1.51367 - 0.550931i) q^{29} +(1.93969 - 3.35965i) q^{30} +(-4.93969 - 8.55580i) q^{31} +(0.337496 + 1.91404i) q^{32} +(3.91147 + 3.28212i) q^{33} +(-2.28106 + 1.91404i) q^{34} +(-0.233956 + 1.32683i) q^{35} +(-0.326352 + 0.118782i) q^{36} +6.10607 q^{37} +(5.17752 + 4.21805i) q^{38} -4.06418 q^{39} +(6.02481 - 2.19285i) q^{40} +(-1.47178 + 8.34689i) q^{41} +(0.624485 - 0.524005i) q^{42} +(-0.135630 - 0.113807i) q^{43} +(-0.307934 - 1.74638i) q^{44} +(1.26604 + 2.19285i) q^{45} +(2.33022 - 4.03606i) q^{46} +(-7.10354 - 2.58548i) q^{47} +(-4.29813 - 1.56439i) q^{48} +(3.35844 - 5.81699i) q^{49} +(1.08125 + 1.87278i) q^{50} +(-0.337496 - 1.91404i) q^{51} +(1.08125 + 0.907278i) q^{52} +(-7.58512 + 6.36467i) q^{53} +(0.266044 - 1.50881i) q^{54} +(-12.1493 + 4.42198i) q^{55} +1.34730 q^{56} +(-4.07398 + 1.55007i) q^{57} -2.46791 q^{58} +(3.58512 - 1.30488i) q^{59} +(0.152704 - 0.866025i) q^{60} +(-10.6702 + 8.95340i) q^{61} +(-11.5949 - 9.72930i) q^{62} +(0.0923963 + 0.524005i) q^{63} +(-3.08512 - 5.34359i) q^{64} +(5.14543 - 8.91215i) q^{65} +(7.35117 + 2.67561i) q^{66} +(9.59627 + 3.49276i) q^{67} +(-0.337496 + 0.584561i) q^{68} +(1.52094 + 2.63435i) q^{69} +(0.358441 + 2.03282i) q^{70} +(2.92855 + 2.45734i) q^{71} +(1.93969 - 1.62760i) q^{72} +(-0.322481 + 1.82888i) q^{73} +(8.79086 - 3.19961i) q^{74} -1.41147 q^{75} +(1.42989 + 0.497079i) q^{76} -2.71688 q^{77} +(-5.85117 + 2.12965i) q^{78} +(1.82635 - 10.3578i) q^{79} +(8.87211 - 7.44459i) q^{80} +(0.766044 + 0.642788i) q^{81} +(2.25490 + 12.7882i) q^{82} +(5.73783 + 9.93821i) q^{83} +(0.0923963 - 0.160035i) q^{84} +(4.62449 + 1.68317i) q^{85} +(-0.254900 - 0.0927760i) q^{86} +(0.805407 - 1.39501i) q^{87} +(6.46451 + 11.1969i) q^{88} +(-1.02869 - 5.83396i) q^{89} +(2.97178 + 2.49362i) q^{90} +(1.65657 - 1.39003i) q^{91} +(0.183448 - 1.04039i) q^{92} +(9.28359 - 3.37895i) q^{93} -11.5817 q^{94} +(1.75877 - 10.8961i) q^{95} -1.94356 q^{96} +(6.39053 - 2.32596i) q^{97} +(1.78699 - 10.1345i) q^{98} +(-3.91147 + 3.28212i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8	\( 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} - 6 q^{10} + 3 q^{11} - 6 q^{13} + 9 q^{14} + 6 q^{15} - 15 q^{16} - 12 q^{17} + 18 q^{19} + 6 q^{20} + 3 q^{21} - 9 q^{23} - 6 q^{24} + 12 q^{26} + 3 q^{27} + 12 q^{29} + 6 q^{30} - 24 q^{31} - 3 q^{32} + 3 q^{33} + 21 q^{34} - 6 q^{35} - 3 q^{36} + 12 q^{37} + 6 q^{38} - 6 q^{39} + 9 q^{40} + 6 q^{41} - 9 q^{42} + 18 q^{43} + 9 q^{44} + 3 q^{45} - 9 q^{46} - 33 q^{47} - 12 q^{48} + 12 q^{49} + 9 q^{50} + 3 q^{51} + 9 q^{52} - 24 q^{53} - 3 q^{54} - 33 q^{55} + 6 q^{56} - 9 q^{57} - 24 q^{58} + 3 q^{60} - 21 q^{61} - 51 q^{62} - 3 q^{63} + 3 q^{64} + 15 q^{65} + 18 q^{66} + 30 q^{67} + 3 q^{68} + 6 q^{69} - 6 q^{70} + 18 q^{71} + 6 q^{72} - 27 q^{73} + 21 q^{74} + 12 q^{75} - 9 q^{78} + 12 q^{79} + 24 q^{80} + 15 q^{82} + 15 q^{83} - 3 q^{84} + 15 q^{85} - 3 q^{86} + 9 q^{87} + 6 q^{88} + 45 q^{89} + 3 q^{90} - 12 q^{91} + 3 q^{92} + 6 q^{93} - 6 q^{94} - 12 q^{95} + 18 q^{96} + 21 q^{97} + 3 q^{98} - 3 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 - 6 * q^10 + 3 * q^11 - 6 * q^13 + 9 * q^14 + 6 * q^15 - 15 * q^16 - 12 * q^17 + 18 * q^19 + 6 * q^20 + 3 * q^21 - 9 * q^23 - 6 * q^24 + 12 * q^26 + 3 * q^27 + 12 * q^29 + 6 * q^30 - 24 * q^31 - 3 * q^32 + 3 * q^33 + 21 * q^34 - 6 * q^35 - 3 * q^36 + 12 * q^37 + 6 * q^38 - 6 * q^39 + 9 * q^40 + 6 * q^41 - 9 * q^42 + 18 * q^43 + 9 * q^44 + 3 * q^45 - 9 * q^46 - 33 * q^47 - 12 * q^48 + 12 * q^49 + 9 * q^50 + 3 * q^51 + 9 * q^52 - 24 * q^53 - 3 * q^54 - 33 * q^55 + 6 * q^56 - 9 * q^57 - 24 * q^58 + 3 * q^60 - 21 * q^61 - 51 * q^62 - 3 * q^63 + 3 * q^64 + 15 * q^65 + 18 * q^66 + 30 * q^67 + 3 * q^68 + 6 * q^69 - 6 * q^70 + 18 * q^71 + 6 * q^72 - 27 * q^73 + 21 * q^74 + 12 * q^75 - 9 * q^78 + 12 * q^79 + 24 * q^80 + 15 * q^82 + 15 * q^83 - 3 * q^84 + 15 * q^85 - 3 * q^86 + 9 * q^87 + 6 * q^88 + 45 * q^89 + 3 * q^90 - 12 * q^91 + 3 * q^92 + 6 * q^93 - 6 * q^94 - 12 * q^95 + 18 * q^96 + 21 * q^97 + 3 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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