LMFDB - Embedded newform 57.2.i.a.4.1

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			4.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	57.4
Dual form			57.2.i.a.43.1

$q$-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} +(-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} - 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}+ \cdots - 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

Character values

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

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

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	0.796506	−	0.604630i	$-0.206679\pi$
$2$	1.43969	+	0.524005i	1.01802	+	0.370528i	0.221510	+	0.975158i	$0.428901\pi$
$3$	−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	−0.963561	−	0.267489i	$-0.913806\pi$
$5$	−1.93969	+	1.62760i	−0.867457	+	0.727883i	0.0961041	+	0.995371i	$0.469362\pi$
$6$	0.266044	−	1.50881i	0.108612	−	0.615970i
$7$	−0.266044	+	0.460802i	−0.100555	+	0.174167i	−0.911914	−	0.410382i	$-0.865395\pi$
$7$	−0.266044	+	0.460802i	−0.100555	+	0.174167i	0.811358	+	0.584549i	$0.198729\pi$
$8$	−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	0.937688	+	0.347478i	$0.112962\pi$
$11$	2.55303	+	4.42198i	0.769769	+	1.33328i	−0.167920	+	0.985801i	$0.553705\pi$
$12$	0.173648	−	0.300767i	0.0501279	−	0.0868241i
$13$	0.705737	−	4.00243i	0.195736	−	1.11008i	−0.715630	−	0.698479i	$-0.753860\pi$
$13$	0.705737	−	4.00243i	0.195736	−	1.11008i	0.911366	−	0.411596i	$-0.135029\pi$
$14$	−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	0.110907	−	0.993831i	$-0.464624\pi$
$17$	−1.82635	−	0.664738i	−0.442955	−	0.161223i	−0.553862	+	0.832608i	$0.686847\pi$
$18$	−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	0.852549	−	0.522648i	$-0.175056\pi$
$23$	2.33022	+	1.95529i	0.485885	+	0.407706i	−0.366664	+	0.930353i	$0.619500\pi$
$24$	−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	−0.478714	−	0.877971i	$-0.658897\pi$
$29$	−1.51367	+	0.550931i	−0.281082	+	0.102305i	0.197633	+	0.980276i	$0.436675\pi$
$30$	1.93969	+	3.35965i	0.354138	+	0.613385i
$31$	−4.93969	+	8.55580i	−0.887195	+	1.53667i	−0.0440180	+	0.999031i	$0.514016\pi$
$31$	−4.93969	+	8.55580i	−0.887195	+	1.53667i	−0.843177	+	0.537636i	$0.819317\pi$
$32$	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	−0.853186	−	0.521607i	$-0.825333\pi$
$41$	−1.47178	−	8.34689i	−0.229854	−	1.30356i	0.623332	−	0.781957i	$-0.285779\pi$
$42$	0.624485	+	0.524005i	0.0963602	+	0.0808558i
$43$	−0.135630	+	0.113807i	−0.0206833	+	0.0173554i	−0.653071	−	0.757297i	$-0.726520\pi$
$43$	−0.135630	+	0.113807i	−0.0206833	+	0.0173554i	0.632387	+	0.774652i	$0.282075\pi$
$44$	−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	−0.803422	−	0.595409i	$-0.796990\pi$
$47$	−7.10354	+	2.58548i	−1.03616	+	0.377131i	−0.232735	+	0.972540i	$0.574768\pi$
$48$	−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	−0.0496783	−	0.998765i	$-0.515820\pi$
$53$	−7.58512	−	6.36467i	−1.04190	−	0.874255i	−0.992218	+	0.124510i	$0.960264\pi$
$54$	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	0.564676	−	0.825312i	$-0.309001\pi$
$59$	3.58512	+	1.30488i	0.466743	+	0.169881i	−0.0979333	+	0.995193i	$0.531223\pi$
$60$	0.152704	+	0.866025i	0.0197140	+	0.111803i
$61$	−10.6702	−	8.95340i	−1.36618	−	1.14637i	−0.974018	−	0.226471i	$-0.927281\pi$
$61$	−10.6702	−	8.95340i	−1.36618	−	1.14637i	−0.392167	−	0.919894i	$-0.628274\pi$
$62$	−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	0.318869	−	0.947799i	$-0.396697\pi$
$67$	9.59627	−	3.49276i	1.17237	−	0.426708i	0.853501	+	0.521091i	$0.174475\pi$
$68$	−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	−0.452253	−	0.891890i	$-0.649379\pi$
$71$	2.92855	−	2.45734i	0.347555	−	0.291633i	0.799807	+	0.600257i	$0.204935\pi$
$72$	1.93969	+	1.62760i	0.228595	+	0.191814i
$73$	−0.322481	−	1.82888i	−0.0377436	−	0.214055i	0.960103	−	0.279647i	$-0.0902174\pi$
$73$	−0.322481	−	1.82888i	−0.0377436	−	0.214055i	−0.997847	+	0.0655924i	$0.979106\pi$
$74$	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	0.896682	+	0.442676i	$0.145971\pi$
$79$	1.82635	+	10.3578i	0.205481	+	1.16534i	−0.691201	+	0.722663i	$0.742918\pi$
$80$	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	−0.357782	−	0.933805i	$-0.616467\pi$
$83$	5.73783	−	9.93821i	0.629808	−	1.09086i	0.987590	−	0.157055i	$-0.0501999\pi$
$84$	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	0.880489	+	0.474067i	$0.157214\pi$
$89$	−1.02869	+	5.83396i	−0.109040	+	0.618399i	−0.989529	+	0.144332i	$0.953897\pi$
$90$	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	0.645419	−	0.763828i	$-0.276683\pi$
$97$	6.39053	+	2.32596i	0.648860	+	0.236166i	0.00344055	+	0.999994i	$0.498905\pi$
$98$	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	0.810717	+	0.585439i	$0.199078\pi$
$101$	−1.52094	+	8.62571i	−0.151340	+	0.858290i	−0.962056	+	0.272851i	$0.912033\pi$
$102$	−1.48886	+	2.57877i	−0.147419	+	0.255337i
$103$	1.92262	+	3.33007i	0.189441	+	0.328122i	0.945064	−	0.326885i	$-0.105999\pi$
$103$	1.92262	+	3.33007i	0.189441	+	0.328122i	−0.755623	+	0.655007i	$0.772666\pi$
$104$	−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	−0.695650	−	0.718381i	$-0.744884\pi$
$107$	2.83750	−	4.91469i	0.274311	−	0.475121i	0.969961	+	0.243260i	$0.0782169\pi$
$108$	−0.0603074	+	0.342020i	−0.00580308	+	0.0329109i
$109$	−1.59833	+	1.34115i	−0.153092	+	0.128459i	−0.716116	−	0.697981i	$-0.754082\pi$
$109$	−1.59833	+	1.34115i	−0.153092	+	0.128459i	0.563025	+	0.826440i	$0.309638\pi$
$110$	−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	−0.967460	−	0.253024i	$-0.918575\pi$
$127$	0.317734	−	1.80196i	0.0281943	−	0.159898i	0.995654	+	0.0931261i	$0.0296860\pi$
$128$	−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	0.676499	−	0.736443i	$-0.263496\pi$
$131$	8.25624	+	3.00503i	0.721351	+	0.262550i	0.0448520	+	0.998994i	$0.485718\pi$
$132$	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	0.127884	−	0.991789i	$-0.459181\pi$
$137$	−9.67546	−	8.11867i	−0.826630	−	0.693625i	−0.954515	+	0.298164i	$0.903626\pi$
$138$	3.57011	−	2.99568i	0.303908	−	0.255009i
$139$	−0.703211	+	3.98811i	−0.0596456	+	0.338267i	−0.999998	−	0.00193468i	$-0.999384\pi$
$139$	−0.703211	+	3.98811i	−0.0596456	+	0.338267i	0.940353	+	0.340201i	$0.110495\pi$
$140$	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	0.997059	+	0.0766320i	$0.0244167\pi$
$149$	1.05391	+	5.97702i	0.0863397	+	0.489657i	−0.910720	+	0.413025i	$0.864472\pi$
$150$	−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	−0.416069	−	0.909333i	$-0.636593\pi$
$157$	5.10220	−	4.28125i	0.407200	−	0.341681i	0.823269	+	0.567652i	$0.192148\pi$
$158$	−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	0.874671	−	0.484718i	$-0.161078\pi$
$163$	0.224155	+	0.388249i	0.0175572	+	0.0304100i	−0.857113	+	0.515128i	$0.827744\pi$
$164$	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	0.737690	−	0.675140i	$-0.235917\pi$
$167$	2.59627	+	2.17853i	0.200905	+	0.168579i	−0.536785	+	0.843719i	$0.680361\pi$
$168$	−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	0.399096	−	0.916909i	$-0.369324\pi$
$173$	1.51842	+	0.552659i	0.115443	+	0.0420179i	−0.283653	+	0.958927i	$0.591546\pi$
$174$	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	0.823821	−	0.566851i	$-0.191838\pi$
$179$	−1.05690	−	1.83061i	−0.0789967	−	0.136826i	−0.902817	+	0.430024i	$0.858505\pi$
$180$	0.826352	−	0.300767i	0.0615926	−	0.0224179i
$181$	−8.22416	+	2.99335i	−0.611297	+	0.222494i	−0.629071	−	0.777348i	$-0.716564\pi$
$181$	−8.22416	+	2.99335i	−0.611297	+	0.222494i	0.0177739	+	0.999842i	$0.494342\pi$
$182$	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	−0.655032	−	0.755601i	$-0.727345\pi$
$193$	−4.13903	−	23.4736i	−0.297934	−	1.68967i	0.357098	−	0.934067i	$-0.383766\pi$
$194$	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	−0.777195	−	0.629260i	$-0.783358\pi$
$197$	2.19459	−	3.80115i	0.156358	−	0.270820i	0.933553	+	0.358440i	$0.116691\pi$
$198$	−3.91147	−	6.77487i	−0.277976	−	0.481469i
$199$	18.8293	−	6.85332i	1.33478	−	0.485819i	0.426613	−	0.904434i	$-0.359707\pi$
$199$	18.8293	−	6.85332i	1.33478	−	0.485819i	0.908164	+	0.418615i	$0.137484\pi$
$200$	−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	−0.759172	−	0.650891i	$-0.774396\pi$
$211$	−25.5526	−	9.30039i	−1.75912	−	0.640266i	−0.999944	+	0.0106250i	$0.996618\pi$
$212$	−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	−0.896617	−	0.442807i	$-0.853983\pi$
$223$	−9.20233	+	7.72167i	−0.616234	+	0.517082i	0.280383	+	0.959888i	$0.409538\pi$
$224$	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	−0.941835	−	0.336076i	$-0.890900\pi$
$233$	−11.8209	+	9.91890i	−0.774412	+	0.649809i	0.167423	+	0.985885i	$0.446456\pi$
$234$	−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	−0.999907	−	0.0136221i	$-0.995664\pi$
$239$	−7.91147	−	13.7031i	−0.511751	−	0.886378i	0.488156	−	0.872756i	$-0.337670\pi$
$240$	5.79086	−	10.0301i	0.373798	−	0.647438i
$241$	−4.10607	+	23.2867i	−0.264495	+	1.50003i	0.505974	+	0.862549i	$0.331133\pi$
$241$	−4.10607	+	23.2867i	−0.264495	+	1.50003i	−0.770469	+	0.637477i	$0.779978\pi$
$242$	−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	0.977339	−	0.211679i	$-0.0678931\pi$
$251$	14.8701	+	12.4775i	0.938589	+	0.787570i	−0.0387499	+	0.999249i	$0.512338\pi$
$252$	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	−0.676241	−	0.736681i	$-0.736392\pi$
$257$	−11.5544	+	4.20545i	−0.720742	+	0.262329i	−0.0445014	+	0.999009i	$0.514170\pi$
$258$	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	0.999753	+	0.0222179i	$0.00707275\pi$
$263$	1.10101	+	6.24416i	0.0678915	+	0.385032i	−0.931862	+	0.362814i	$0.881816\pi$
$264$	−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	0.970023	−	0.243014i	$-0.0781360\pi$
$269$	−0.403733	−	2.28969i	−0.0246161	−	0.139605i	−0.994639	+	0.103409i	$0.967025\pi$
$270$	−2.97178	−	2.49362i	−0.180857	−	0.151757i
$271$	11.4474	−	9.60554i	0.695382	−	0.583495i	−0.225074	−	0.974342i	$-0.572262\pi$
$271$	11.4474	−	9.60554i	0.695382	−	0.583495i	0.920456	+	0.390847i	$0.127818\pi$
$272$	−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	0.961005	+	0.276529i	$0.0891843\pi$
$277$	11.9829	+	20.7550i	0.719984	+	1.24705i	−0.241021	+	0.970520i	$0.577482\pi$
$278$	−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	0.999984	−	0.00564805i	$-0.00179784\pi$
$281$	19.5804	+	16.4299i	1.16807	+	0.980125i	0.168083	+	0.985773i	$0.446242\pi$
$282$	2.01114	+	11.4058i	0.119762	+	0.679204i
$283$	7.05778	+	2.56882i	0.419542	+	0.152701i	0.543160	−	0.839629i	$-0.317228\pi$
$283$	7.05778	+	2.56882i	0.419542	+	0.152701i	−0.123619	+	0.992330i	$0.539450\pi$
$284$	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	0.565654	−	0.824643i	$-0.308624\pi$
$293$	−7.38326	−	12.7882i	−0.431334	−	0.747093i	−0.996989	+	0.0775495i	$0.975290\pi$
$294$	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	0.999863	−	0.0165689i	$-0.00527428\pi$
$307$	0.957234	+	5.42874i	0.0546322	+	0.309835i	−0.945231	+	0.326404i	$0.894163\pi$
$308$	−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	−0.999970	−	0.00769537i	$-0.997550\pi$
$311$	−8.69981	+	15.0685i	−0.493321	+	0.854457i	0.506650	+	0.862152i	$0.330884\pi$
$312$	5.14543	+	8.91215i	0.291303	+	0.504551i
$313$	−14.9820	+	5.45302i	−0.846835	+	0.308223i	−0.728749	−	0.684780i	$-0.759898\pi$
$313$	−14.9820	+	5.45302i	−0.846835	+	0.308223i	−0.118086	+	0.993003i	$0.537676\pi$
$314$	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	−0.973670	−	0.227963i	$-0.926793\pi$
$317$	0.342711	−	1.94361i	0.0192486	−	0.109164i	0.992918	+	0.118799i	$0.0379045\pi$
$318$	−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	0.877304	−	0.479935i	$-0.159340\pi$
$331$	0.418748	+	0.725293i	0.0230165	+	0.0398657i	−0.854288	+	0.519800i	$0.826006\pi$
$332$	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	−0.709573	−	0.704632i	$-0.751112\pi$
$337$	−2.54916	+	2.13900i	−0.138862	+	0.116519i	0.570711	+	0.821151i	$0.306668\pi$
$338$	−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	−0.556652	−	0.830746i	$-0.687914\pi$
$347$	3.07011	−	2.57613i	0.164812	−	0.138294i	0.721464	+	0.692452i	$0.243470\pi$
$348$	−0.0971440	+	0.550931i	−0.00520747	+	0.0295330i
$349$	13.9513	−	24.1644i	0.746796	−	1.29349i	−0.202555	−	0.979271i	$-0.564924\pi$
$349$	13.9513	−	24.1644i	0.746796	−	1.29349i	0.949351	−	0.314218i	$-0.101742\pi$
$350$	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	0.640797	−	0.767710i	$-0.278604\pi$
$353$	−6.47178	−	11.2095i	−0.344458	−	0.596619i	−0.985255	+	0.171091i	$0.945271\pi$
$354$	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	0.0421972	−	0.999109i	$-0.486564\pi$
$359$	−10.7562	−	3.91495i	−0.567693	−	0.206623i	−0.609890	+	0.792486i	$0.708786\pi$
$360$	−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	0.525663	+	0.850693i	$0.323817\pi$
$367$	−4.96657	+	28.1668i	−0.259253	+	1.47030i	−0.784916	+	0.619602i	$0.787294\pi$
$368$	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	−0.656251	−	0.754543i	$-0.727859\pi$
$373$	6.28312	−	10.8827i	0.325328	−	0.563484i	0.981579	+	0.191059i	$0.0611921\pi$
$374$	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	0.947147	−	0.320799i	$-0.103952\pi$
$383$	−1.02940	−	5.83802i	−0.0525999	−	0.298309i	−0.999747	+	0.0224905i	$0.992840\pi$
$384$	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	0.603174	−	0.797610i	$-0.293903\pi$
$389$	31.1215	−	11.3273i	1.57793	−	0.574318i	0.974752	+	0.223292i	$0.0716804\pi$
$390$	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	0.873100	−	0.487541i	$-0.162106\pi$
$397$	24.4786	+	8.90950i	1.22855	+	0.447155i	0.355448	+	0.934696i	$0.384328\pi$
$398$	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	0.688322	−	0.725406i	$-0.258348\pi$
$401$	15.0052	+	5.46145i	0.749325	+	0.272732i	0.0610031	+	0.998138i	$0.480570\pi$
$402$	−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	−0.272607	−	0.962126i	$-0.587886\pi$
$409$	2.77079	−	1.00849i	0.137007	−	0.0498664i	0.409614	+	0.912259i	$0.365664\pi$
$410$	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	0.961048	+	0.276383i	$0.0891357\pi$
$421$	3.12877	+	17.7441i	0.152487	+	0.864795i	−0.808561	+	0.588412i	$0.799753\pi$
$422$	−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	−0.755888	−	0.654701i	$-0.772795\pi$
$431$	3.70233	−	20.9970i	0.178335	−	1.01139i	0.934223	−	0.356688i	$-0.116094\pi$
$432$	3.50387	−	2.94010i	0.168580	−	0.141455i
$433$	−16.8931	−	14.1750i	−0.811828	−	0.681205i	0.139215	−	0.990262i	$-0.455542\pi$
$433$	−16.8931	−	14.1750i	−0.811828	−	0.681205i	−0.951043	+	0.309057i	$0.899987\pi$
$434$	−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	0.416849	−	0.908976i	$-0.363134\pi$
$439$	3.18257	+	1.15836i	0.151896	+	0.0552856i	−0.264953	+	0.964261i	$0.585357\pi$
$440$	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	0.562480	+	0.826811i	$0.309847\pi$
$443$	−5.23799	+	29.7061i	−0.248864	+	1.41138i	−0.811344	+	0.584569i	$0.801264\pi$
$444$	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	−0.227725	−	0.973725i	$-0.573129\pi$
$449$	15.4559	−	26.7704i	0.729409	−	1.26337i	0.957134	−	0.289647i	$-0.0935380\pi$
$450$	−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	−0.669283	−	0.743008i	$-0.733399\pi$
$461$	−1.15476	+	0.968961i	−0.0537827	+	0.0451290i	0.615500	+	0.788137i	$0.288954\pi$
$462$	−0.722811	+	4.09927i	−0.0336282	+	0.190715i
$463$	1.64156	−	2.84326i	0.0762897	−	0.132138i	−0.825357	−	0.564612i	$-0.809026\pi$
$463$	1.64156	−	2.84326i	0.0762897	−	0.132138i	0.901646	+	0.432474i	$0.142359\pi$
$464$	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	0.999406	+	0.0344584i	$0.0109706\pi$
$467$	11.4436	+	19.8208i	0.529545	+	0.917199i	−0.469861	+	0.882740i	$0.655696\pi$
$468$	−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	0.457929	−	0.888989i	$-0.348591\pi$
$479$	−7.39827	−	6.20789i	−0.338036	−	0.283646i	−0.795965	+	0.605343i	$0.793036\pi$
$480$	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	−0.489903	−	0.871777i	$-0.662968\pi$
$487$	11.2554	−	19.4949i	0.510029	−	0.883397i	0.999932	−	0.0116199i	$-0.00369881\pi$
$488$	−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	0.999953	−	0.00971390i	$-0.00309208\pi$
$491$	1.26264	+	7.16079i	0.0569822	+	0.323162i	−0.942971	+	0.332876i	$0.891981\pi$
$492$	−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	−0.835458	−	0.549554i	$-0.814798\pi$
$499$	−9.81386	+	8.23481i	−0.439329	+	0.368641i	0.396129	+	0.918195i	$0.370353\pi$
$500$	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	−0.511370	−	0.859361i	$-0.670862\pi$
$503$	−7.86571	+	2.86289i	−0.350715	+	0.127650i	0.160655	+	0.987011i	$0.448639\pi$
$504$	−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	0.844816	−	0.535057i	$-0.179710\pi$
$509$	10.4816	+	8.79509i	0.464588	+	0.389836i	−0.380228	+	0.924893i	$0.624154\pi$
$510$	−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	0.989813	−	0.142376i	$-0.0454741\pi$
$521$	8.48205	+	14.6913i	0.371605	+	0.643639i	−0.618207	+	0.786015i	$0.712141\pi$
$522$	2.31908	−	0.844075i	0.101503	−	0.0369442i
$523$	3.67112	−	1.33618i	0.160527	−	0.0584270i	−0.260507	−	0.965472i	$-0.583890\pi$
$523$	3.67112	−	1.33618i	0.160527	−	0.0584270i	0.421034	+	0.907045i	$0.361667\pi$
$524$	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	−0.594562	−	0.804050i	$-0.702675\pi$
$541$	−12.4017	+	4.51384i	−0.533190	+	0.194065i	0.0613724	+	0.998115i	$0.480452\pi$
$542$	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	−0.0428509	−	0.999081i	$-0.513644\pi$
$547$	−24.1878	−	20.2960i	−1.03420	−	0.867793i	−0.991344	+	0.131289i	$0.958088\pi$
$548$	−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	−0.514797	−	0.857312i	$-0.672133\pi$
$557$	6.18748	−	35.0909i	0.262172	−	1.48685i	0.776969	−	0.629539i	$-0.216756\pi$
$558$	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	−0.535714	−	0.844399i	$-0.679958\pi$
$563$	10.9957	−	19.0451i	0.463414	−	0.802657i	0.999128	+	0.0417423i	$0.0132909\pi$
$564$	−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	0.325807	+	0.945436i	$0.394364\pi$
$577$	−15.7545	+	27.2876i	−0.655868	+	1.13600i	−0.981675	+	0.190561i	$0.938969\pi$
$578$	−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	−0.246583	−	0.969122i	$-0.579308\pi$
$587$	−25.6434	−	9.33342i	−1.05842	−	0.385232i	−0.811833	+	0.583890i	$0.801530\pi$
$588$	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	0.996995	−	0.0774657i	$-0.0246828\pi$
$593$	26.6366	+	22.3507i	1.09383	+	0.917834i	0.0968375	+	0.995300i	$0.469127\pi$
$594$	−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	−0.628695	−	0.777652i	$-0.716411\pi$
$599$	−14.9402	+	5.43777i	−0.610438	+	0.222181i	0.0182567	+	0.999833i	$0.494188\pi$
$600$	1.78699	+	3.09516i	0.0729535	+	0.126359i
$601$	12.3464	−	21.3846i	0.503621	−	0.872297i	−0.496370	−	0.868111i	$-0.665334\pi$
$601$	12.3464	−	21.3846i	0.503621	−	0.872297i	0.999991	−	0.00418616i	$-0.00133250\pi$
$602$	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	−0.247157	+	0.968976i	$0.579496\pi$
$613$	−30.8082	+	25.8511i	−1.24433	+	1.04412i	−0.997173	+	0.0751409i	$0.976059\pi$
$614$	−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	0.113509	−	0.993537i	$-0.463791\pi$
$617$	20.8427	−	7.58613i	0.839096	−	0.305406i	0.725586	+	0.688131i	$0.241569\pi$
$618$	5.53596	−	2.01492i	0.222689	−	0.0810521i
$619$	11.6177	+	20.1224i	0.466954	+	0.808788i	0.999287	−	0.0377469i	$-0.0120181\pi$
$619$	11.6177	+	20.1224i	0.466954	+	0.808788i	−0.532333	+	0.846535i	$0.678685\pi$
$620$	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	0.960989	−	0.276588i	$-0.0892037\pi$
$631$	21.4893	+	18.0317i	0.855476	+	0.717830i	−0.105512	+	0.994418i	$0.533648\pi$
$632$	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	0.328309	−	0.944570i	$-0.393521\pi$
$641$	33.3068	−	27.9477i	1.31554	−	1.10387i	0.987230	−	0.159299i	$-0.0509233\pi$
$642$	−6.66044	−	5.58878i	−0.262867	−	0.220571i
$643$	6.83322	+	38.7531i	0.269476	+	1.52827i	0.755980	+	0.654595i	$0.227161\pi$
$643$	6.83322	+	38.7531i	0.269476	+	1.52827i	−0.486504	+	0.873678i	$0.661728\pi$
$644$	−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	0.107098	−	0.994248i	$-0.465844\pi$
$653$	23.3714	−	40.4804i	0.914593	−	1.58412i	0.807495	−	0.589874i	$-0.200823\pi$
$654$	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	−0.976926	−	0.213577i	$-0.931489\pi$
$659$	0.362778	−	2.05742i	0.0141318	−	0.0801455i	0.991058	+	0.133432i	$0.0425996\pi$
$660$	−3.43969	+	2.88624i	−0.133890	+	0.112347i
$661$	−9.53596	−	8.00162i	−0.370906	−	0.311227i	0.438214	−	0.898871i	$-0.355611\pi$
$661$	−9.53596	−	8.00162i	−0.370906	−	0.311227i	−0.809120	+	0.587644i	$0.800056\pi$
$662$	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	0.951262	−	0.308383i	$-0.0997880\pi$
$673$	5.41060	+	9.37143i	0.208563	+	0.361242i	−0.742699	+	0.669625i	$0.766455\pi$
$674$	−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	−0.904888	−	0.425651i	$-0.860045\pi$
$677$	−2.18092	+	3.77747i	−0.0838196	+	0.145180i	0.821068	+	0.570830i	$0.193379\pi$
$678$	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	−0.999090	−	0.0426544i	$-0.986419\pi$
$691$	−12.1604	+	21.0625i	−0.462605	+	0.801256i	0.536485	+	0.843910i	$0.319752\pi$
$692$	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	0.724386	−	0.689394i	$-0.242123\pi$
$701$	22.1386	+	8.05780i	0.836164	+	0.304339i	0.111778	+	0.993733i	$0.464345\pi$
$702$	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	−0.998276	−	0.0586939i	$-0.981306\pi$
$709$	−1.06851	+	6.05985i	−0.0401289	+	0.227582i	0.958147	+	0.286276i	$0.0924175\pi$
$710$	−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	0.887790	+	0.460249i	$0.152240\pi$
$719$	5.65657	+	32.0800i	0.210955	+	1.19638i	−0.676835	+	0.736134i	$0.736649\pi$
$720$	−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	−0.0575058	−	0.998345i	$-0.518315\pi$
$727$	24.6896	−	20.7170i	0.915686	−	0.768352i	0.973192	+	0.229993i	$0.0738703\pi$
$728$	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	0.761461	−	0.648210i	$-0.224482\pi$
$733$	−4.89053	−	8.47065i	−0.180636	−	0.312870i	−0.942097	+	0.335340i	$0.891149\pi$
$734$	−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	−0.186013	−	0.982547i	$-0.559557\pi$
$739$	−26.0993	−	9.49935i	−0.960077	−	0.349439i	−0.774064	+	0.633108i	$0.781779\pi$
$740$	−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	0.832308	−	0.554314i	$-0.187019\pi$
$743$	30.3542	+	11.0480i	1.11359	+	0.405312i	0.281278	+	0.959626i	$0.409242\pi$
$744$	−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	−0.401081	−	0.916043i	$-0.631365\pi$
$751$	−3.27497	+	1.19199i	−0.119505	+	0.0434964i	0.281575	+	0.959539i	$0.409143\pi$
$752$	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	−0.846570	−	0.532277i	$-0.821337\pi$
$757$	−6.41353	−	36.3730i	−0.233104	−	1.32200i	0.613467	−	0.789721i	$-0.289775\pi$
$758$	−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	0.257351	−	0.966318i	$-0.417150\pi$
$769$	29.8282	−	10.8566i	1.07563	−	0.391498i	0.818280	+	0.574820i	$0.194928\pi$
$770$	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	−0.931281	−	0.364301i	$-0.881308\pi$
$773$	1.90269	−	10.7907i	0.0684351	−	0.388115i	0.999716	−	0.0238140i	$-0.00758095\pi$
$774$	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	−0.901018	−	0.433781i	$-0.857179\pi$
$787$	−23.1771	−	40.1439i	−0.826175	−	1.43098i	0.0748436	−	0.997195i	$-0.476154\pi$
$788$	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	0.809480	+	0.587147i	$0.199749\pi$
$809$	25.9748	+	44.9896i	0.913224	+	1.58175i	0.103744	+	0.994604i	$0.466918\pi$
$810$	−1.93969	+	3.35965i	−0.0681539	+	0.118046i
$811$	2.91329	−	16.5221i	0.102299	−	0.580168i	−0.889965	−	0.456028i	$-0.849272\pi$
$811$	2.91329	−	16.5221i	0.102299	−	0.580168i	0.992265	−	0.124140i	$-0.0396172\pi$
$812$	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	−0.00941101	−	0.999956i	$-0.502996\pi$
$821$	−28.5330	−	23.9420i	−0.995809	−	0.835583i	−0.986398	+	0.164372i	$0.947440\pi$
$822$	−14.8237	+	12.4385i	−0.517035	+	0.433844i
$823$	−0.763985	+	4.33277i	−0.0266308	+	0.151031i	−0.995224	−	0.0976214i	$-0.968877\pi$
$823$	−0.763985	+	4.33277i	−0.0266308	+	0.151031i	0.968593	+	0.248652i	$0.0799877\pi$
$824$	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	−0.105450	−	0.994425i	$-0.533628\pi$
$827$	13.0265	−	4.74125i	0.452975	−	0.164869i	0.558424	+	0.829555i	$0.311406\pi$
$828$	−0.528218	−	0.914901i	−0.0183569	−	0.0317950i
$829$	−8.18850	+	14.1829i	−0.284398	+	0.492592i	−0.972463	−	0.233057i	$-0.925127\pi$
$829$	−8.18850	+	14.1829i	−0.284398	+	0.492592i	0.688065	+	0.725649i	$0.258461\pi$
$830$	−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	−0.853807	−	0.520590i	$-0.825712\pi$
$839$	−6.64883	−	37.7074i	−0.229543	−	1.30180i	0.624263	−	0.781214i	$-0.285399\pi$
$840$	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	−0.0387487	−	0.999249i	$-0.512337\pi$
$853$	−20.7579	−	7.55526i	−0.710737	−	0.258687i	−0.671988	+	0.740562i	$0.734559\pi$
$854$	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	−0.503606	−	0.863933i	$-0.667994\pi$
$857$	−42.2934	−	15.3936i	−1.44472	−	0.525834i	−0.941110	+	0.338100i	$0.890216\pi$
$858$	−5.52094	−	31.3108i	−0.188482	−	1.06893i
$859$	−12.2358	−	10.2670i	−0.417479	−	0.350306i	0.409724	−	0.912209i	$-0.365625\pi$
$859$	−12.2358	−	10.2670i	−0.417479	−	0.350306i	−0.827203	+	0.561903i	$0.810069\pi$
$860$	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	−0.967688	−	0.252151i	$-0.918862\pi$
$863$	−20.6288	−	35.7302i	−0.702213	−	1.21627i	0.265475	−	0.964118i	$-0.414471\pi$
$864$	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	0.752304	+	0.658817i	$0.228943\pi$
$877$	8.01650	+	45.4638i	0.270698	+	1.53520i	−0.481606	+	0.876388i	$0.659946\pi$
$878$	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	−0.980354	−	0.197245i	$-0.936800\pi$
$881$	−9.47906	+	16.4182i	−0.319357	+	0.553143i	0.660997	+	0.750389i	$0.270134\pi$
$882$	−5.14543	−	8.91215i	−0.173256	−	0.300088i
$883$	−32.9359	+	11.9877i	−1.10838	+	0.403418i	−0.830399	−	0.557169i	$-0.811888\pi$
$883$	−32.9359	+	11.9877i	−1.10838	+	0.403418i	−0.277981	+	0.960586i	$0.589665\pi$
$884$	−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	0.887612	+	0.460592i	$0.152363\pi$
$887$	−3.09745	+	17.5665i	−0.104002	+	0.589825i	−0.991614	+	0.129234i	$0.958748\pi$
$888$	−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	−0.805786	−	0.592207i	$-0.798257\pi$
$907$	−10.9172	+	9.16058i	−0.362498	+	0.304172i	0.443287	+	0.896380i	$0.353812\pi$
$908$	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	−0.438442	−	0.898760i	$-0.644470\pi$
$919$	16.9500	−	29.3582i	0.559128	−	0.968437i	0.997570	−	0.0696779i	$-0.0221971\pi$
$920$	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	−0.0119887	−	0.999928i	$-0.503816\pi$
$929$	−20.2358	−	7.36522i	−0.663914	−	0.241645i	−0.651925	+	0.758283i	$0.726038\pi$
$930$	−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	−0.955797	−	0.294028i	$-0.905004\pi$
$937$	1.31386	−	7.45129i	0.0429220	−	0.243423i	0.998719	+	0.0506054i	$0.0161151\pi$
$938$	−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	−0.617941	−	0.786225i	$-0.712033\pi$
$941$	−17.9740	+	6.54200i	−0.585936	+	0.213263i	0.0320052	+	0.999488i	$0.489811\pi$
$942$	−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	0.374214	+	0.927342i	$0.377912\pi$
$947$	10.4549	+	59.2925i	0.339738	+	1.92675i	−0.0344768	+	0.999405i	$0.510976\pi$
$948$	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	−0.988616	−	0.150462i	$-0.951924\pi$
$953$	−3.42918	−	19.4478i	−0.111082	−	0.629977i	0.877534	−	0.479515i	$-0.159187\pi$
$954$	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	0.418929	−	0.908019i	$-0.362406\pi$
$967$	4.85679	+	1.76773i	0.156184	+	0.0568463i	−0.262745	+	0.964865i	$0.584628\pi$
$968$	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	0.470678	−	0.882305i	$-0.344009\pi$
$971$	8.22967	+	2.99536i	0.264103	+	0.0961256i	−0.206575	+	0.978431i	$0.566232\pi$
$972$	−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	−0.982759	−	0.184892i	$-0.940806\pi$
$977$	−20.3640	−	35.2714i	−0.651501	−	1.12843i	0.331258	−	0.943540i	$-0.392527\pi$
$978$	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	−0.593251	−	0.805018i	$-0.702156\pi$
$983$	3.02616	−	2.53925i	0.0965195	−	0.0809895i	0.689771	+	0.724028i	$0.257711\pi$
$984$	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	−0.992230	−	0.124414i	$-0.960295\pi$
$991$	−3.22328	−	18.2801i	−0.102391	−	0.580687i	0.889840	−	0.456273i	$-0.150816\pi$
$992$	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	−0.382458	−	0.923973i	$-0.624922\pi$
$997$	−2.57398	+	0.936851i	−0.0815187	+	0.0296704i	0.300939	+	0.953643i	$0.402700\pi$
$998$	−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.4.1	✓	6
3.2	odd	2		171.2.u.a.118.1		6
4.3	odd	2		912.2.bo.b.289.1		6
19.5	even	9	inner	57.2.i.a.43.1	yes	6
19.9	even	9		1083.2.a.m.1.1		3
19.10	odd	18		1083.2.a.n.1.3		3
57.5	odd	18		171.2.u.a.100.1		6
57.29	even	18		3249.2.a.x.1.1		3
57.47	odd	18		3249.2.a.w.1.3		3
76.43	odd	18		912.2.bo.b.385.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.i.a.4.1	✓	6	1.1	even	1	trivial
57.2.i.a.43.1	yes	6	19.5	even	9	inner
171.2.u.a.100.1		6	57.5	odd	18
171.2.u.a.118.1		6	3.2	odd	2
912.2.bo.b.289.1		6	4.3	odd	2
912.2.bo.b.385.1		6	76.43	odd	18
1083.2.a.m.1.1		3	19.9	even	9
1083.2.a.n.1.3		3	19.10	odd	18
3249.2.a.w.1.3		3	57.47	odd	18
3249.2.a.x.1.1		3	57.29	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} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} - 6 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} - 6 q^{10} + 3 q^{11} - 6 q^{13} + 9 q^{14} + 6 q^{15} - 15 q^{16} - 12 q^{17} + 18 q^{19} + 6 q^{20} + 3 q^{21} - 9 q^{23} - 6 q^{24} + 12 q^{26}+ \cdots - 3 q^{99}+O(q^{100}) \) 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

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Database

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