LMFDB - Embedded newform 770.2.n.h.631.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(71,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("770.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.n (of order $5$, degree $4$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 7 x^{10} - 9 x^{9} + 55 x^{8} - 32 x^{7} + 287 x^{6} - 302 x^{5} + 1175 x^{4} + \cdots + 361 $ x^12 - 3x^11 + 7x^10 - 9x^9 + 55x^8 - 32x^7 + 287x^6 - 302x^5 + 1175x^4 - 1639x^3 + 1692x^2 - 988*x + 361
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			631.2
Root			$0.254744 + 0.784022i$ of defining polynomial
Character	$\chi$	$=$	770.631
Dual form			770.2.n.h.421.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-0.563761 + 1.73508i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(1.47595 - 1.07234i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.265619 - 0.192984i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.563761 + 1.73508i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(1.47595 - 1.07234i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.265619 - 0.192984i) q^{9} -1.00000 q^{10} +(-0.645341 - 3.25323i) q^{11} -1.82437 q^{12} +(1.79142 + 1.30154i) q^{13} +(0.309017 - 0.951057i) q^{14} +(0.563761 + 1.73508i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(6.44494 - 4.68252i) q^{17} +(0.101458 + 0.312254i) q^{18} +(-0.282952 + 0.870838i) q^{19} +(0.809017 + 0.587785i) q^{20} -1.82437 q^{21} +(-1.39011 + 3.01124i) q^{22} +6.07737 q^{23} +(1.47595 + 1.07234i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-0.684262 - 2.10594i) q^{26} +(-3.94325 + 2.86494i) q^{27} +(-0.809017 + 0.587785i) q^{28} +(1.56547 + 4.81803i) q^{29} +(0.563761 - 1.73508i) q^{30} +(-7.55535 - 5.48928i) q^{31} +1.00000 q^{32} +(6.00843 + 0.714329i) q^{33} -7.96638 q^{34} +(0.809017 + 0.587785i) q^{35} +(0.101458 - 0.312254i) q^{36} +(1.33785 + 4.11748i) q^{37} +(0.740779 - 0.538207i) q^{38} +(-3.26821 + 2.37450i) q^{39} +(-0.309017 - 0.951057i) q^{40} +(-2.78101 + 8.55906i) q^{41} +(1.47595 + 1.07234i) q^{42} +2.76947 q^{43} +(2.89459 - 1.61906i) q^{44} -0.328323 q^{45} +(-4.91670 - 3.57219i) q^{46} +(1.30657 - 4.02122i) q^{47} +(-0.563761 - 1.73508i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(4.49114 + 13.8223i) q^{51} +(-0.684262 + 2.10594i) q^{52} +(7.55172 + 5.48664i) q^{53} +4.87412 q^{54} +(-2.43430 - 2.25260i) q^{55} +1.00000 q^{56} +(-1.35145 - 0.981889i) q^{57} +(1.56547 - 4.81803i) q^{58} +(2.22334 + 6.84273i) q^{59} +(-1.47595 + 1.07234i) q^{60} +(10.2661 - 7.45872i) q^{61} +(2.88589 + 8.88185i) q^{62} +(0.101458 - 0.312254i) q^{63} +(-0.809017 - 0.587785i) q^{64} +2.21432 q^{65} +(-4.44105 - 4.10957i) q^{66} -1.29018 q^{67} +(6.44494 + 4.68252i) q^{68} +(-3.42619 + 10.5447i) q^{69} +(-0.309017 - 0.951057i) q^{70} +(-0.0163721 + 0.0118950i) q^{71} +(-0.265619 + 0.192984i) q^{72} +(3.66069 + 11.2665i) q^{73} +(1.33785 - 4.11748i) q^{74} +(1.47595 + 1.07234i) q^{75} -0.915653 q^{76} +(2.89459 - 1.61906i) q^{77} +4.03973 q^{78} +(7.59849 + 5.52063i) q^{79} +(-0.309017 + 0.951057i) q^{80} +(-3.05221 - 9.39375i) q^{81} +(7.28078 - 5.28979i) q^{82} +(-0.604801 + 0.439413i) q^{83} +(-0.563761 - 1.73508i) q^{84} +(2.46175 - 7.57648i) q^{85} +(-2.24055 - 1.62785i) q^{86} -9.24220 q^{87} +(-3.29343 - 0.391549i) q^{88} -14.2639 q^{89} +(0.265619 + 0.192984i) q^{90} +(-0.684262 + 2.10594i) q^{91} +(1.87801 + 5.77993i) q^{92} +(13.7837 - 10.0145i) q^{93} +(-3.42065 + 2.48525i) q^{94} +(0.282952 + 0.870838i) q^{95} +(-0.563761 + 1.73508i) q^{96} +(5.88504 + 4.27573i) q^{97} +1.00000 q^{98} +(-0.456406 + 0.988662i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 5 q^{6} - 3 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 5 * q^6 - 3 * q^7 - 3 * q^8 - 3 * q^9	$ 12 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 5 q^{6} - 3 q^{7} - 3 q^{8} - 3 q^{9} - 12 q^{10} - q^{11} - 10 q^{12} - 3 q^{14} - 3 q^{16} - 8 q^{18} - q^{19} + 3 q^{20} - 10 q^{21} - q^{22} - 4 q^{23} + 5 q^{24} - 3 q^{25} + 3 q^{27} - 3 q^{28} + 22 q^{29} + 6 q^{31} + 12 q^{32} - 29 q^{33} - 30 q^{34} + 3 q^{35} - 8 q^{36} - 10 q^{37} + 14 q^{38} + 20 q^{39} + 3 q^{40} + 16 q^{41} + 5 q^{42} + 30 q^{43} + 14 q^{44} - 22 q^{45} - 4 q^{46} + 34 q^{47} - 3 q^{49} - 3 q^{50} + 37 q^{51} - 26 q^{53} - 52 q^{54} + 11 q^{55} + 12 q^{56} - 19 q^{57} + 22 q^{58} + q^{59} - 5 q^{60} + 40 q^{61} - 4 q^{62} - 8 q^{63} - 3 q^{64} + 16 q^{66} - 58 q^{67} + 14 q^{69} + 3 q^{70} - 14 q^{71} - 3 q^{72} + 32 q^{73} - 10 q^{74} + 5 q^{75} - 26 q^{76} + 14 q^{77} - 60 q^{78} + 16 q^{79} + 3 q^{80} - 46 q^{81} + q^{82} + 35 q^{83} - 15 q^{85} + 5 q^{86} - q^{88} - 58 q^{89} + 3 q^{90} + 6 q^{92} + 46 q^{93} - 16 q^{94} + q^{95} + 57 q^{97} + 12 q^{98} + 69 q^{99}+O(q^{100}) $ 12 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 5 * q^6 - 3 * q^7 - 3 * q^8 - 3 * q^9 - 12 * q^10 - q^11 - 10 * q^12 - 3 * q^14 - 3 * q^16 - 8 * q^18 - q^19 + 3 * q^20 - 10 * q^21 - q^22 - 4 * q^23 + 5 * q^24 - 3 * q^25 + 3 * q^27 - 3 * q^28 + 22 * q^29 + 6 * q^31 + 12 * q^32 - 29 * q^33 - 30 * q^34 + 3 * q^35 - 8 * q^36 - 10 * q^37 + 14 * q^38 + 20 * q^39 + 3 * q^40 + 16 * q^41 + 5 * q^42 + 30 * q^43 + 14 * q^44 - 22 * q^45 - 4 * q^46 + 34 * q^47 - 3 * q^49 - 3 * q^50 + 37 * q^51 - 26 * q^53 - 52 * q^54 + 11 * q^55 + 12 * q^56 - 19 * q^57 + 22 * q^58 + q^59 - 5 * q^60 + 40 * q^61 - 4 * q^62 - 8 * q^63 - 3 * q^64 + 16 * q^66 - 58 * q^67 + 14 * q^69 + 3 * q^70 - 14 * q^71 - 3 * q^72 + 32 * q^73 - 10 * q^74 + 5 * q^75 - 26 * q^76 + 14 * q^77 - 60 * q^78 + 16 * q^79 + 3 * q^80 - 46 * q^81 + q^82 + 35 * q^83 - 15 * q^85 + 5 * q^86 - q^88 - 58 * q^89 + 3 * q^90 + 6 * q^92 + 46 * q^93 - 16 * q^94 + q^95 + 57 * q^97 + 12 * q^98 + 69 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−0.563761	+	1.73508i	−0.325488	+	1.00175i	0.645732	+	0.763564i	$0.276552\pi$
$3$	−0.563761	+	1.73508i	−0.325488	+	1.00175i	−0.971220	+	0.238184i	$0.923448\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$	1.47595	−	1.07234i	0.602552	−	0.437780i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−0.265619	−	0.192984i	−0.0885397	−	0.0643279i
$10$	−1.00000			−0.316228
$11$	−0.645341	−	3.25323i	−0.194578	−	0.980887i
$11$	−0.645341	−	3.25323i	−0.194578	−	0.980887i
$12$	−1.82437			−0.526650
$13$	1.79142	+	1.30154i	0.496851	+	0.360983i	0.807813	−	0.589439i	$-0.200651\pi$
$13$	1.79142	+	1.30154i	0.496851	+	0.360983i	−0.310962	+	0.950422i	$0.600651\pi$
$14$	0.309017	−	0.951057i	0.0825883	−	0.254181i
$15$	0.563761	+	1.73508i	0.145562	+	0.447995i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	6.44494	−	4.68252i	1.56313	−	1.13568i	0.629740	−	0.776806i	$-0.283161\pi$
$17$	6.44494	−	4.68252i	1.56313	−	1.13568i	0.933387	−	0.358872i	$-0.116839\pi$
$18$	0.101458	+	0.312254i	0.0239138	+	0.0735990i
$19$	−0.282952	+	0.870838i	−0.0649137	+	0.199784i	−0.978253	−	0.207416i	$-0.933495\pi$
$19$	−0.282952	+	0.870838i	−0.0649137	+	0.199784i	0.913339	+	0.407200i	$0.133495\pi$
$20$	0.809017	+	0.587785i	0.180902	+	0.131433i
$21$	−1.82437			−0.398110
$22$	−1.39011	+	3.01124i	−0.296373	+	0.641999i
$23$	6.07737			1.26722			0.633610	−	0.773653i	$-0.281572\pi$
$23$	6.07737			1.26722			0.633610	+	0.773653i	$0.281572\pi$
$24$	1.47595	+	1.07234i	0.301276	+	0.218890i
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	−0.684262	−	2.10594i	−0.134195	−	0.413009i
$27$	−3.94325	+	2.86494i	−0.758879	+	0.551358i
$28$	−0.809017	+	0.587785i	−0.152890	+	0.111081i
$29$	1.56547	+	4.81803i	0.290701	+	0.894685i	0.984632	+	0.174643i	$0.0558772\pi$
$29$	1.56547	+	4.81803i	0.290701	+	0.894685i	−0.693931	+	0.720041i	$0.744123\pi$
$30$	0.563761	−	1.73508i	0.102928	−	0.316781i
$31$	−7.55535	−	5.48928i	−1.35698	−	0.985904i	−0.998631	−	0.0523170i	$-0.983339\pi$
$31$	−7.55535	−	5.48928i	−1.35698	−	0.985904i	−0.358350	−	0.933587i	$-0.616661\pi$
$32$	1.00000			0.176777
$33$	6.00843	+	0.714329i	1.04593	+	0.124349i
$34$	−7.96638			−1.36622
$35$	0.809017	+	0.587785i	0.136749	+	0.0993538i
$36$	0.101458	−	0.312254i	0.0169096	−	0.0520423i
$37$	1.33785	+	4.11748i	0.219941	+	0.676909i	0.998766	+	0.0496673i	$0.0158161\pi$
$37$	1.33785	+	4.11748i	0.219941	+	0.676909i	−0.778825	+	0.627241i	$0.784184\pi$
$38$	0.740779	−	0.538207i	0.120170	−	0.0873087i
$39$	−3.26821	+	2.37450i	−0.523333	+	0.380224i
$40$	−0.309017	−	0.951057i	−0.0488599	−	0.150375i
$41$	−2.78101	+	8.55906i	−0.434321	+	1.33670i	0.459461	+	0.888198i	$0.348043\pi$
$41$	−2.78101	+	8.55906i	−0.434321	+	1.33670i	−0.893781	+	0.448503i	$0.851957\pi$
$42$	1.47595	+	1.07234i	0.227743	+	0.165465i
$43$	2.76947			0.422340			0.211170	−	0.977449i	$-0.432273\pi$
$43$	2.76947			0.422340			0.211170	+	0.977449i	$0.432273\pi$
$44$	2.89459	−	1.61906i	0.436376	−	0.244083i
$45$	−0.328323			−0.0489436
$46$	−4.91670	−	3.57219i	−0.724928	−	0.526691i
$47$	1.30657	−	4.02122i	0.190583	−	0.586555i	−0.809416	−	0.587235i	$-0.800216\pi$
$47$	1.30657	−	4.02122i	0.190583	−	0.586555i	1.00000		0.000679952i	$0.000216436\pi$
$48$	−0.563761	−	1.73508i	−0.0813719	−	0.250437i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	−0.809017	+	0.587785i	−0.114412	+	0.0831254i
$51$	4.49114	+	13.8223i	0.628885	+	1.93551i
$52$	−0.684262	+	2.10594i	−0.0948900	+	0.292042i
$53$	7.55172	+	5.48664i	1.03731	+	0.753649i	0.969758	−	0.244067i	$-0.0784818\pi$
$53$	7.55172	+	5.48664i	1.03731	+	0.753649i	0.0675500	+	0.997716i	$0.478482\pi$
$54$	4.87412			0.663284
$55$	−2.43430	−	2.25260i	−0.328240	−	0.303741i
$56$	1.00000			0.133631
$57$	−1.35145	−	0.981889i	−0.179004	−	0.130054i
$58$	1.56547	−	4.81803i	0.205556	−	0.632638i
$59$	2.22334	+	6.84273i	0.289454	+	0.890848i	0.985028	+	0.172394i	$0.0551501\pi$
$59$	2.22334	+	6.84273i	0.289454	+	0.890848i	−0.695574	+	0.718454i	$0.744850\pi$
$60$	−1.47595	+	1.07234i	−0.190544	+	0.138438i
$61$	10.2661	−	7.45872i	1.31443	−	0.954992i	0.314450	−	0.949274i	$-0.398180\pi$
$61$	10.2661	−	7.45872i	1.31443	−	0.954992i	0.999984	−	0.00571767i	$-0.00182000\pi$
$62$	2.88589	+	8.88185i	0.366508	+	1.12800i
$63$	0.101458	−	0.312254i	0.0127824	−	0.0393403i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	2.21432			0.274652
$66$	−4.44105	−	4.10957i	−0.546656	−	0.505854i
$67$	−1.29018			−0.157620			−0.0788101	−	0.996890i	$-0.525112\pi$
$67$	−1.29018			−0.157620			−0.0788101	+	0.996890i	$0.525112\pi$
$68$	6.44494	+	4.68252i	0.781563	+	0.567839i
$69$	−3.42619	+	10.5447i	−0.412464	+	1.26944i
$70$	−0.309017	−	0.951057i	−0.0369346	−	0.113673i
$71$	−0.0163721	+	0.0118950i	−0.00194301	+	0.00141168i	−0.588756	−	0.808311i	$-0.700382\pi$
$71$	−0.0163721	+	0.0118950i	−0.00194301	+	0.00141168i	0.586813	+	0.809722i	$0.300382\pi$
$72$	−0.265619	+	0.192984i	−0.0313035	+	0.0227433i
$73$	3.66069	+	11.2665i	0.428452	+	1.31864i	0.899650	+	0.436612i	$0.143822\pi$
$73$	3.66069	+	11.2665i	0.428452	+	1.31864i	−0.471198	+	0.882027i	$0.656178\pi$
$74$	1.33785	−	4.11748i	0.155522	−	0.478647i
$75$	1.47595	+	1.07234i	0.170428	+	0.123823i
$76$	−0.915653			−0.105033
$77$	2.89459	−	1.61906i	0.329869	−	0.184509i
$78$	4.03973			0.457410
$79$	7.59849	+	5.52063i	0.854897	+	0.621119i	0.926492	−	0.376315i	$-0.122809\pi$
$79$	7.59849	+	5.52063i	0.854897	+	0.621119i	−0.0715946	+	0.997434i	$0.522809\pi$
$80$	−0.309017	+	0.951057i	−0.0345492	+	0.106331i
$81$	−3.05221	−	9.39375i	−0.339135	−	1.04375i
$82$	7.28078	−	5.28979i	0.804027	−	0.584160i
$83$	−0.604801	+	0.439413i	−0.0663855	+	0.0482319i	−0.620483	−	0.784220i	$-0.713063\pi$
$83$	−0.604801	+	0.439413i	−0.0663855	+	0.0482319i	0.554098	+	0.832452i	$0.313063\pi$
$84$	−0.563761	−	1.73508i	−0.0615114	−	0.189313i
$85$	2.46175	−	7.57648i	0.267014	−	0.821784i
$86$	−2.24055	−	1.62785i	−0.241604	−	0.175536i
$87$	−9.24220			−0.990868
$88$	−3.29343	−	0.391549i	−0.351081	−	0.0417392i
$89$	−14.2639			−1.51197			−0.755983	−	0.654591i	$-0.772841\pi$
$89$	−14.2639			−1.51197			−0.755983	+	0.654591i	$0.772841\pi$
$90$	0.265619	+	0.192984i	0.0279987	+	0.0203423i
$91$	−0.684262	+	2.10594i	−0.0717301	+	0.220763i
$92$	1.87801	+	5.77993i	0.195796	+	0.602599i
$93$	13.7837	−	10.0145i	1.42931	−	1.03845i
$94$	−3.42065	+	2.48525i	−0.352813	+	0.256334i
$95$	0.282952	+	0.870838i	0.0290303	+	0.0893460i
$96$	−0.563761	+	1.73508i	−0.0575386	+	0.177086i
$97$	5.88504	+	4.27573i	0.597535	+	0.434135i	0.845003	−	0.534761i	$-0.179598\pi$
$97$	5.88504	+	4.27573i	0.597535	+	0.434135i	−0.247468	+	0.968896i	$0.579598\pi$
$98$	1.00000			0.101015
$99$	−0.456406	+	0.988662i	−0.0458705	+	0.0993643i
$100$	1.00000			0.100000
$101$	4.33053	+	3.14632i	0.430904	+	0.313070i	0.782010	−	0.623265i	$-0.214194\pi$
$101$	4.33053	+	3.14632i	0.430904	+	0.313070i	−0.351106	+	0.936336i	$0.614194\pi$
$102$	4.49114	−	13.8223i	0.444689	−	1.36861i
$103$	−4.44792	−	13.6893i	−0.438266	−	1.34885i	−0.889702	−	0.456542i	$-0.849088\pi$
$103$	−4.44792	−	13.6893i	−0.438266	−	1.34885i	0.451435	−	0.892304i	$-0.350912\pi$
$104$	1.79142	−	1.30154i	0.175663	−	0.127627i
$105$	−1.47595	+	1.07234i	−0.144038	+	0.104649i
$106$	−2.88450	−	8.87758i	−0.280167	−	0.862267i
$107$	−1.32144	+	4.06697i	−0.127748	+	0.393169i	−0.994392	−	0.105759i	$-0.966273\pi$
$107$	−1.32144	+	4.06697i	−0.127748	+	0.393169i	0.866643	+	0.498928i	$0.166273\pi$
$108$	−3.94325	−	2.86494i	−0.379439	−	0.275679i
$109$	−5.04265			−0.482998			−0.241499	−	0.970401i	$-0.577639\pi$
$109$	−5.04265			−0.482998			−0.241499	+	0.970401i	$0.577639\pi$
$110$	0.645341	+	3.25323i	0.0615309	+	0.310184i
$111$	−7.89837			−0.749680
$112$	−0.809017	−	0.587785i	−0.0764449	−	0.0555405i
$113$	4.26967	−	13.1407i	0.401656	−	1.23617i	−0.521999	−	0.852946i	$-0.674813\pi$
$113$	4.26967	−	13.1407i	0.401656	−	1.23617i	0.923655	−	0.383225i	$-0.125187\pi$
$114$	0.516209	+	1.58873i	0.0483474	+	0.148798i
$115$	4.91670	−	3.57219i	0.458485	−	0.333109i
$116$	−4.09846	+	2.97770i	−0.380532	+	0.276473i
$117$	−0.224659	−	0.691430i	−0.0207697	−	0.0639227i
$118$	2.22334	−	6.84273i	0.204675	−	0.629925i
$119$	6.44494	+	4.68252i	0.590806	+	0.429246i
$120$	1.82437			0.166541
$121$	−10.1671	+	4.19889i	−0.924279	+	0.381718i
$122$	−12.6895			−1.14886
$123$	−13.2828	−	9.65054i	−1.19767	−	0.870160i
$124$	2.88589	−	8.88185i	0.259160	−	0.797613i
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$	−0.265619	+	0.192984i	−0.0236632	+	0.0171923i
$127$	−11.8780	+	8.62984i	−1.05400	+	0.765775i	−0.972969	−	0.230937i	$-0.925821\pi$
$127$	−11.8780	+	8.62984i	−1.05400	+	0.765775i	−0.0810298	+	0.996712i	$0.525821\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−1.56132	+	4.80524i	−0.137466	+	0.423078i
$130$	−1.79142	−	1.30154i	−0.157118	−	0.114153i
$131$	−7.62582			−0.666271			−0.333135	−	0.942879i	$-0.608107\pi$
$131$	−7.62582			−0.666271			−0.333135	+	0.942879i	$0.608107\pi$
$132$	1.17734	+	5.93510i	0.102474	+	0.516584i
$133$	−0.915653			−0.0793972
$134$	1.04378	+	0.758347i	0.0901685	+	0.0655112i
$135$	−1.50619	+	4.63557i	−0.129632	+	0.398966i
$136$	−2.46175	−	7.57648i	−0.211093	−	0.649678i
$137$	3.98893	−	2.89813i	0.340797	−	0.247604i	−0.404201	−	0.914670i	$-0.632450\pi$
$137$	3.98893	−	2.89813i	0.340797	−	0.247604i	0.744998	+	0.667067i	$0.232450\pi$
$138$	8.96987	−	6.51700i	0.763566	−	0.554764i
$139$	−1.29082	−	3.97274i	−0.109486	−	0.336963i	0.881271	−	0.472611i	$-0.156688\pi$
$139$	−1.29082	−	3.97274i	−0.109486	−	0.336963i	−0.990757	+	0.135648i	$0.956688\pi$
$140$	−0.309017	+	0.951057i	−0.0261167	+	0.0803789i
$141$	6.24053	+	4.53401i	0.525548	+	0.381833i
$142$	0.0202370			0.00169825
$143$	3.07815	−	6.66785i	0.257408	−	0.557594i
$144$	0.328323			0.0273603
$145$	4.09846	+	2.97770i	0.340358	+	0.247285i
$146$	3.66069	−	11.2665i	0.302961	−	0.932419i
$147$	−0.563761	−	1.73508i	−0.0464982	−	0.143107i
$148$	−3.50253	+	2.54474i	−0.287906	+	0.209176i
$149$	10.9044	−	7.92248i	0.893320	−	0.649035i	−0.0434214	−	0.999057i	$-0.513826\pi$
$149$	10.9044	−	7.92248i	0.893320	−	0.649035i	0.936742	+	0.350022i	$0.113826\pi$
$150$	−0.563761	−	1.73508i	−0.0460309	−	0.141669i
$151$	5.44184	−	16.7483i	0.442851	−	1.36295i	−0.441973	−	0.897028i	$-0.645721\pi$
$151$	5.44184	−	16.7483i	0.442851	−	1.36295i	0.884824	−	0.465926i	$-0.154279\pi$
$152$	0.740779	+	0.538207i	0.0600851	+	0.0436544i
$153$	−2.61555			−0.211455
$154$	−3.29343	−	0.391549i	−0.265392	−	0.0315519i
$155$	−9.33892			−0.750121
$156$	−3.26821	−	2.37450i	−0.261666	−	0.190112i
$157$	3.54863	−	10.9216i	0.283211	−	0.871635i	−0.703718	−	0.710480i	$-0.748478\pi$
$157$	3.54863	−	10.9216i	0.283211	−	0.871635i	0.986929	−	0.161155i	$-0.0515219\pi$
$158$	−2.90237	−	8.93257i	−0.230900	−	0.710637i
$159$	−13.7771	+	10.0097i	−1.09260	+	0.793818i
$160$	0.809017	−	0.587785i	0.0639584	−	0.0464685i
$161$	1.87801	+	5.77993i	0.148008	+	0.455522i
$162$	−3.05221	+	9.39375i	−0.239805	+	0.738043i
$163$	0.112656	+	0.0818493i	0.00882389	+	0.00641093i	0.592188	−	0.805799i	$-0.298264\pi$
$163$	0.112656	+	0.0818493i	0.00882389	+	0.00641093i	−0.583365	+	0.812210i	$0.698264\pi$
$164$	−8.99953			−0.702745
$165$	5.28080	−	2.95376i	0.411110	−	0.229950i
$166$	0.747575			0.0580230
$167$	−5.69845	−	4.14017i	−0.440959	−	0.320376i	0.345057	−	0.938582i	$-0.387860\pi$
$167$	−5.69845	−	4.14017i	−0.440959	−	0.320376i	−0.786016	+	0.618206i	$0.787860\pi$
$168$	−0.563761	+	1.73508i	−0.0434951	+	0.133864i
$169$	−2.50205	−	7.70051i	−0.192465	−	0.592347i
$170$	−6.44494	+	4.68252i	−0.494304	+	0.359133i
$171$	0.243215	−	0.176706i	0.0185991	−	0.0135130i
$172$	0.855812	+	2.63392i	0.0652551	+	0.200834i
$173$	−4.33992	+	13.3569i	−0.329958	+	1.01551i	0.639194	+	0.769045i	$0.279268\pi$
$173$	−4.33992	+	13.3569i	−0.329958	+	1.01551i	−0.969153	+	0.246462i	$0.920732\pi$
$174$	7.47710	+	5.43243i	0.566837	+	0.411831i
$175$	1.00000			0.0755929
$176$	2.43430	+	2.25260i	0.183492	+	0.169796i
$177$	−13.1261			−0.986619
$178$	11.5397	+	8.38409i	0.864937	+	0.628414i
$179$	3.96591	−	12.2058i	0.296426	−	0.912304i	−0.686313	−	0.727306i	$-0.740772\pi$
$179$	3.96591	−	12.2058i	0.296426	−	0.912304i	0.982739	−	0.184998i	$-0.0592280\pi$
$180$	−0.101458	−	0.312254i	−0.00756220	−	0.0232740i
$181$	−15.6036	+	11.3367i	−1.15980	+	0.842647i	−0.989753	−	0.142789i	$-0.954393\pi$
$181$	−15.6036	+	11.3367i	−1.15980	+	0.842647i	−0.170050	+	0.985435i	$0.554393\pi$
$182$	1.79142	−	1.30154i	0.132789	−	0.0964768i
$183$	7.15387	+	22.0173i	0.528829	+	1.62757i
$184$	1.87801	−	5.77993i	0.138449	−	0.426102i
$185$	3.50253	+	2.54474i	0.257511	+	0.187093i
$186$	−17.0376			−1.24926
$187$	−19.3925	−	17.9451i	−1.41812	−	1.31227i
$188$	4.22816			0.308370
$189$	−3.94325	−	2.86494i	−0.286829	−	0.208394i
$190$	0.282952	−	0.870838i	0.0205275	−	0.0631772i
$191$	−3.71156	−	11.4230i	−0.268559	−	0.826541i	−0.990852	−	0.134953i	$-0.956912\pi$
$191$	−3.71156	−	11.4230i	−0.268559	−	0.826541i	0.722293	−	0.691588i	$-0.243088\pi$
$192$	1.47595	−	1.07234i	0.106517	−	0.0773893i
$193$	13.9959	−	10.1686i	1.00744	−	0.731951i	0.0437731	−	0.999041i	$-0.486062\pi$
$193$	13.9959	−	10.1686i	1.00744	−	0.731951i	0.963672	+	0.267090i	$0.0860621\pi$
$194$	−2.24789	−	6.91828i	−0.161389	−	0.496704i
$195$	−1.24835	+	3.84201i	−0.0893959	+	0.275132i
$196$	−0.809017	−	0.587785i	−0.0577869	−	0.0419847i
$197$	−13.1724			−0.938497			−0.469248	−	0.883066i	$-0.655475\pi$
$197$	−13.1724			−0.938497			−0.469248	+	0.883066i	$0.655475\pi$
$198$	0.950361	−	0.531576i	0.0675392	−	0.0377774i
$199$	−22.9779			−1.62886			−0.814431	−	0.580260i	$-0.802951\pi$
$199$	−22.9779			−1.62886			−0.814431	+	0.580260i	$0.802951\pi$
$200$	−0.809017	−	0.587785i	−0.0572061	−	0.0415627i
$201$	0.727352	−	2.23856i	0.0513034	−	0.157896i
$202$	−1.65412	−	5.09085i	−0.116383	−	0.358191i
$203$	−4.09846	+	2.97770i	−0.287655	+	0.208994i
$204$	−11.7579	+	8.54265i	−0.823221	+	0.598105i
$205$	2.78101	+	8.55906i	0.194234	+	0.597791i
$206$	−4.44792	+	13.6893i	−0.309901	+	0.953778i
$207$	−1.61427	−	1.17283i	−0.112199	−	0.0815176i
$208$	−2.21432			−0.153535
$209$	3.01564	+	0.358523i	0.208596	+	0.0247995i
$210$	1.82437			0.125893
$211$	13.3981	+	9.73426i	0.922360	+	0.670134i	0.944110	−	0.329630i	$-0.106924\pi$
$211$	13.3981	+	9.73426i	0.922360	+	0.670134i	−0.0217503	+	0.999763i	$0.506924\pi$
$212$	−2.88450	+	8.87758i	−0.198108	+	0.609715i
$213$	−0.0114088	−	0.0351127i	−0.000781719	−	0.00240588i
$214$	3.45957	−	2.51353i	0.236492	−	0.171821i
$215$	2.24055	−	1.62785i	0.152804	−	0.111019i
$216$	1.50619	+	4.63557i	0.102483	+	0.315410i
$217$	2.88589	−	8.88185i	0.195907	−	0.602939i
$218$	4.07959	+	2.96399i	0.276305	+	0.200747i
$219$	−21.6119			−1.46040
$220$	1.39011	−	3.01124i	0.0937213	−	0.203018i
$221$	17.6401			1.18660
$222$	6.38991	+	4.64254i	0.428863	+	0.311587i
$223$	−5.90948	+	18.1875i	−0.395728	+	1.21793i	0.532665	+	0.846326i	$0.321190\pi$
$223$	−5.90948	+	18.1875i	−0.395728	+	1.21793i	−0.928393	+	0.371599i	$0.878810\pi$
$224$	0.309017	+	0.951057i	0.0206471	+	0.0635451i
$225$	−0.265619	+	0.192984i	−0.0177079	+	0.0128656i
$226$	−11.1781	+	8.12139i	−0.743558	+	0.540227i
$227$	6.08730	+	18.7348i	0.404029	+	1.24347i	0.921704	+	0.387895i	$0.126798\pi$
$227$	6.08730	+	18.7348i	0.404029	+	1.24347i	−0.517675	+	0.855577i	$0.673202\pi$
$228$	0.516209	−	1.58873i	0.0341868	−	0.105216i
$229$	−22.3138	−	16.2119i	−1.47454	−	1.07131i	−0.979267	−	0.202572i	$-0.935070\pi$
$229$	−22.3138	−	16.2119i	−1.47454	−	1.07131i	−0.495268	−	0.868740i	$-0.664930\pi$
$230$	−6.07737			−0.400730
$231$	1.17734	+	5.93510i	0.0774633	+	0.390501i
$232$	5.06597			0.332597
$233$	10.4738	+	7.60965i	0.686161	+	0.498525i	0.875396	−	0.483407i	$-0.160601\pi$
$233$	10.4738	+	7.60965i	0.686161	+	0.498525i	−0.189235	+	0.981932i	$0.560601\pi$
$234$	−0.224659	+	0.691430i	−0.0146864	+	0.0452002i
$235$	−1.30657	−	4.02122i	−0.0852314	−	0.262315i
$236$	−5.82078	+	4.22904i	−0.378900	+	0.275287i
$237$	−13.8625	+	10.0717i	−0.900464	+	0.654225i
$238$	−2.46175	−	7.57648i	−0.159571	−	0.491110i
$239$	−1.78496	+	5.49355i	−0.115460	+	0.355348i	−0.992043	−	0.125903i	$-0.959817\pi$
$239$	−1.78496	+	5.49355i	−0.115460	+	0.355348i	0.876583	+	0.481251i	$0.159817\pi$
$240$	−1.47595	−	1.07234i	−0.0952719	−	0.0692191i
$241$	−25.0323			−1.61247			−0.806237	−	0.591593i	$-0.798499\pi$
$241$	−25.0323			−1.61247			−0.806237	+	0.591593i	$0.798499\pi$
$242$	10.6934	+	2.57908i	0.687396	+	0.165789i
$243$	3.39724			0.217933
$244$	10.2661	+	7.45872i	0.657217	+	0.477496i
$245$	−0.309017	+	0.951057i	−0.0197424	+	0.0607608i
$246$	5.07359	+	15.6149i	0.323480	+	0.995569i
$247$	−1.64032	+	1.19176i	−0.104371	+	0.0758300i
$248$	−7.55535	+	5.48928i	−0.479765	+	0.348570i
$249$	−0.421453	−	1.29710i	−0.0267085	−	0.0822004i
$250$	−0.309017	+	0.951057i	−0.0195440	+	0.0601501i
$251$	5.39286	+	3.91814i	0.340394	+	0.247311i	0.744828	−	0.667256i	$-0.232531\pi$
$251$	5.39286	+	3.91814i	0.340394	+	0.247311i	−0.404434	+	0.914567i	$0.632531\pi$
$252$	0.328323			0.0206824
$253$	−3.92198	−	19.7711i	−0.246573	−	1.24300i
$254$	14.6820			0.921228
$255$	11.7579	+	8.54265i	0.736311	+	0.534961i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−7.01943	−	21.6036i	−0.437860	−	1.34759i	−0.890127	−	0.455712i	$-0.849385\pi$
$257$	−7.01943	−	21.6036i	−0.437860	−	1.34759i	0.452268	−	0.891882i	$-0.350615\pi$
$258$	4.08758	−	2.96980i	0.254482	−	0.184892i
$259$	−3.50253	+	2.54474i	−0.217637	+	0.158122i
$260$	0.684262	+	2.10594i	0.0424361	+	0.130605i
$261$	0.513981	−	1.58187i	0.0318146	−	0.0979153i
$262$	6.16941	+	4.48234i	0.381148	+	0.276920i
$263$	14.5015			0.894200			0.447100	−	0.894484i	$-0.352457\pi$
$263$	14.5015			0.894200			0.447100	+	0.894484i	$0.352457\pi$
$264$	2.53608	−	5.49362i	0.156085	−	0.338109i
$265$	9.33444			0.573410
$266$	0.740779	+	0.538207i	0.0454201	+	0.0329996i
$267$	8.04141	−	24.7489i	0.492126	−	1.51461i
$268$	−0.398687	−	1.22703i	−0.0243537	−	0.0749529i
$269$	17.2121	−	12.5053i	1.04944	−	0.762463i	0.0773343	−	0.997005i	$-0.475359\pi$
$269$	17.2121	−	12.5053i	1.04944	−	0.762463i	0.972106	+	0.234542i	$0.0753591\pi$
$270$	3.94325	−	2.86494i	0.239979	−	0.174355i
$271$	2.49256	+	7.67132i	0.151412	+	0.466000i	0.997780	−	0.0666000i	$-0.0212152\pi$
$271$	2.49256	+	7.67132i	0.151412	+	0.466000i	−0.846367	+	0.532600i	$0.821215\pi$
$272$	−2.46175	+	7.57648i	−0.149265	+	0.459391i
$273$	−3.26821	−	2.37450i	−0.197801	−	0.143711i
$274$	−4.93059			−0.297868
$275$	−3.29343	−	0.391549i	−0.198601	−	0.0236113i
$276$	−11.0874			−0.667382
$277$	−14.1224	−	10.2605i	−0.848534	−	0.616496i	0.0762076	−	0.997092i	$-0.475719\pi$
$277$	−14.1224	−	10.2605i	−0.848534	−	0.616496i	−0.924741	+	0.380596i	$0.875719\pi$
$278$	−1.29082	+	3.97274i	−0.0774183	+	0.238269i
$279$	0.947504	+	2.91612i	0.0567256	+	0.174583i
$280$	0.809017	−	0.587785i	0.0483480	−	0.0351269i
$281$	16.5596	−	12.0312i	0.987861	−	0.717723i	0.0284098	−	0.999596i	$-0.490956\pi$
$281$	16.5596	−	12.0312i	0.987861	−	0.717723i	0.959452	+	0.281873i	$0.0909557\pi$
$282$	−2.38367	−	7.33619i	−0.141946	−	0.436864i
$283$	1.62939	−	5.01475i	0.0968572	−	0.298096i	−0.890876	−	0.454247i	$-0.849909\pi$
$283$	1.62939	−	5.01475i	0.0968572	−	0.298096i	0.987733	+	0.156151i	$0.0499085\pi$
$284$	−0.0163721	−	0.0118950i	−0.000971503	−	0.000705838i
$285$	−1.67049			−0.0989512
$286$	−6.40954	+	3.58512i	−0.379004	+	0.211992i
$287$	−8.99953			−0.531226
$288$	−0.265619	−	0.192984i	−0.0156518	−	0.0113717i
$289$	14.3579	−	44.1891i	0.844584	−	2.59936i
$290$	−1.56547	−	4.81803i	−0.0919276	−	0.282924i
$291$	−10.7365	+	7.80051i	−0.629384	+	0.457274i
$292$	−9.58382	+	6.96305i	−0.560851	+	0.407482i
$293$	1.97960	+	6.09260i	0.115650	+	0.355933i	0.992082	−	0.125592i	$-0.0400830\pi$
$293$	1.97960	+	6.09260i	0.115650	+	0.355933i	−0.876432	+	0.481525i	$0.840083\pi$
$294$	−0.563761	+	1.73508i	−0.0328792	+	0.101192i
$295$	5.82078	+	4.22904i	0.338899	+	0.246224i
$296$	4.32937			0.251640
$297$	11.8651	+	10.9795i	0.688481	+	0.637092i
$298$	−13.4785			−0.780790
$299$	10.8871	+	7.90997i	0.629619	+	0.457445i
$300$	−0.563761	+	1.73508i	−0.0325488	+	0.100175i
$301$	0.855812	+	2.63392i	0.0493282	+	0.151817i
$302$	−14.2469	+	10.3510i	−0.819818	+	0.595633i
$303$	−7.90049	+	5.74004i	−0.453871	+	0.329757i
$304$	−0.282952	−	0.870838i	−0.0162284	−	0.0499460i
$305$	3.92128	−	12.0685i	0.224532	−	0.691039i
$306$	2.11602	+	1.53738i	0.120965	+	0.0878862i
$307$	5.35970			0.305894			0.152947	−	0.988234i	$-0.451124\pi$
$307$	5.35970			0.305894			0.152947	+	0.988234i	$0.451124\pi$
$308$	2.43430	+	2.25260i	0.138707	+	0.128354i
$309$	26.2595			1.49385
$310$	7.55535	+	5.48928i	0.429115	+	0.311770i
$311$	−8.33788	+	25.6614i	−0.472798	+	1.45512i	0.376107	+	0.926576i	$0.377262\pi$
$311$	−8.33788	+	25.6614i	−0.472798	+	1.45512i	−0.848905	+	0.528546i	$0.822738\pi$
$312$	1.24835	+	3.84201i	0.0706737	+	0.217511i
$313$	23.1082	−	16.7891i	1.30615	−	0.948974i	0.306155	−	0.951982i	$-0.400957\pi$
$313$	23.1082	−	16.7891i	1.30615	−	0.948974i	0.999995	+	0.00300783i	$0.000957423\pi$
$314$	−9.29043	+	6.74989i	−0.524289	+	0.380918i
$315$	−0.101458	−	0.312254i	−0.00571648	−	0.0175935i
$316$	−2.90237	+	8.93257i	−0.163271	+	0.502496i
$317$	−16.9956	−	12.3480i	−0.954566	−	0.693533i	−0.00268378	−	0.999996i	$-0.500854\pi$
$317$	−16.9956	−	12.3480i	−0.954566	−	0.693533i	−0.951882	+	0.306463i	$0.900854\pi$
$318$	17.0295			0.954965
$319$	14.6639	−	8.20212i	0.821021	−	0.459230i
$320$	−1.00000			−0.0559017
$321$	−6.31154	−	4.58560i	−0.352276	−	0.255943i
$322$	1.87801	−	5.77993i	0.104658	−	0.322103i
$323$	2.25411	+	6.93742i	0.125422	+	0.386009i
$324$	7.99080	−	5.80566i	0.443933	−	0.322537i
$325$	1.79142	−	1.30154i	0.0993701	−	0.0721966i
$326$	−0.0430307	−	0.132435i	−0.00238325	−	0.00733489i
$327$	2.84285	−	8.74939i	0.157210	−	0.483842i
$328$	7.28078	+	5.28979i	0.402014	+	0.292080i
$329$	4.22816			0.233106
$330$	−6.00843	−	0.714329i	−0.330753	−	0.0393225i
$331$	11.6022			0.637717			0.318858	−	0.947802i	$-0.396701\pi$
$331$	11.6022			0.637717			0.318858	+	0.947802i	$0.396701\pi$
$332$	−0.604801	−	0.439413i	−0.0331927	−	0.0241159i
$333$	0.439247	−	1.35186i	0.0240706	−	0.0740817i
$334$	2.17661	+	6.69893i	0.119099	+	0.366549i
$335$	−1.04378	+	0.758347i	−0.0570275	+	0.0414329i
$336$	1.47595	−	1.07234i	0.0805194	−	0.0585008i
$337$	0.725800	+	2.23378i	0.0395369	+	0.121682i	0.968877	−	0.247543i	$-0.0796232\pi$
$337$	0.725800	+	2.23378i	0.0395369	+	0.121682i	−0.929340	+	0.369225i	$0.879623\pi$
$338$	−2.50205	+	7.70051i	−0.136093	+	0.418853i
$339$	20.3930	+	14.8164i	1.10760	+	0.804717i
$340$	7.96638			0.432038
$341$	−12.9821	+	28.1218i	−0.703023	+	1.52288i
$342$	−0.300630			−0.0162562
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$	0.855812	−	2.63392i	0.0461423	−	0.142011i
$345$	3.42619	+	10.5447i	0.184460	+	0.567709i
$346$	11.3621	−	8.25502i	0.610828	−	0.443793i
$347$	25.4687	−	18.5041i	1.36723	−	0.993353i	0.369286	−	0.929316i	$-0.379602\pi$
$347$	25.4687	−	18.5041i	1.36723	−	0.993353i	0.997947	−	0.0640378i	$-0.0203978\pi$
$348$	−2.85600	−	8.78986i	−0.153098	−	0.471186i
$349$	0.805847	−	2.48014i	0.0431360	−	0.132759i	−0.927169	−	0.374643i	$-0.877765\pi$
$349$	0.805847	−	2.48014i	0.0431360	−	0.132759i	0.970305	+	0.241884i	$0.0777653\pi$
$350$	−0.809017	−	0.587785i	−0.0432438	−	0.0314184i
$351$	−10.7929			−0.576080
$352$	−0.645341	−	3.25323i	−0.0343968	−	0.173398i
$353$	−0.416007			−0.0221418			−0.0110709	−	0.999939i	$-0.503524\pi$
$353$	−0.416007			−0.0221418			−0.0110709	+	0.999939i	$0.503524\pi$
$354$	10.6192	+	7.71533i	0.564406	+	0.410065i
$355$	−0.00625357	+	0.0192465i	−0.000331905	+	0.00102150i
$356$	−4.40777	−	13.5657i	−0.233612	−	0.718982i
$357$	−11.7579	+	8.54265i	−0.622296	+	0.452125i
$358$	−10.3829	+	7.54360i	−0.548752	+	0.398692i
$359$	−3.58924	−	11.0465i	−0.189433	−	0.583014i	0.810564	−	0.585650i	$-0.199161\pi$
$359$	−3.58924	−	11.0465i	−0.189433	−	0.583014i	−0.999997	+	0.00263648i	$0.999161\pi$
$360$	−0.101458	+	0.312254i	−0.00534728	+	0.0164572i
$361$	14.6930	+	10.6751i	0.773317	+	0.561848i
$362$	19.2871			1.01371
$363$	−1.55361	−	20.0078i	−0.0815434	−	1.05014i
$364$	−2.21432			−0.116062
$365$	9.58382	+	6.96305i	0.501640	+	0.364463i
$366$	7.15387	−	22.0173i	0.373939	−	1.15087i
$367$	−2.47433	−	7.61519i	−0.129159	−	0.397510i	0.865477	−	0.500949i	$-0.167015\pi$
$367$	−2.47433	−	7.61519i	−0.129159	−	0.397510i	−0.994636	+	0.103439i	$0.967015\pi$
$368$	−4.91670	+	3.57219i	−0.256301	+	0.186213i
$369$	2.39045	−	1.73676i	0.124442	−	0.0904123i
$370$	−1.33785	−	4.11748i	−0.0695514	−	0.214057i
$371$	−2.88450	+	8.87758i	−0.149756	+	0.460901i
$372$	13.7837	+	10.0145i	0.714654	+	0.519227i
$373$	−16.6329			−0.861217			−0.430609	−	0.902539i	$-0.641701\pi$
$373$	−16.6329			−0.861217			−0.430609	+	0.902539i	$0.641701\pi$
$374$	5.14103	+	25.9165i	0.265837	+	1.34011i
$375$	1.82437			0.0942100
$376$	−3.42065	−	2.48525i	−0.176407	−	0.128167i
$377$	−3.46645	+	10.6686i	−0.178531	+	0.549463i
$378$	1.50619	+	4.63557i	0.0774699	+	0.238428i
$379$	0.0672848	−	0.0488853i	0.00345619	−	0.00251107i	−0.586056	−	0.810271i	$-0.699320\pi$
$379$	0.0672848	−	0.0488853i	0.00345619	−	0.00251107i	0.589512	+	0.807760i	$0.299320\pi$
$380$	−0.740779	+	0.538207i	−0.0380011	+	0.0276094i
$381$	−8.27712	−	25.4744i	−0.424050	−	1.30509i
$382$	−3.71156	+	11.4230i	−0.189900	+	0.584453i
$383$	−5.08293	−	3.69296i	−0.259725	−	0.188702i	0.450301	−	0.892877i	$-0.351317\pi$
$383$	−5.08293	−	3.69296i	−0.259725	−	0.188702i	−0.710026	+	0.704175i	$0.751317\pi$
$384$	−1.82437			−0.0930995
$385$	1.39011	−	3.01124i	0.0708466	−	0.153467i
$386$	−17.2998			−0.880539
$387$	−0.735623	−	0.534462i	−0.0373938	−	0.0271682i
$388$	−2.24789	+	6.91828i	−0.114119	+	0.351222i
$389$	−1.13676	−	3.49857i	−0.0576358	−	0.177385i	0.918094	−	0.396363i	$-0.129728\pi$
$389$	−1.13676	−	3.49857i	−0.0576358	−	0.177385i	−0.975730	+	0.218978i	$0.929728\pi$
$390$	3.26821	−	2.37450i	0.165492	−	0.120237i
$391$	39.1683	−	28.4574i	1.98083	−	1.43915i
$392$	0.309017	+	0.951057i	0.0156077	+	0.0480356i
$393$	4.29914	−	13.2314i	0.216863	−	0.667435i
$394$	10.6567	+	7.74256i	0.536878	+	0.390065i
$395$	9.39226			0.472576
$396$	−1.08131	−	0.128555i	−0.0543379	−	0.00646011i
$397$	7.12152			0.357419			0.178709	−	0.983902i	$-0.442808\pi$
$397$	7.12152			0.357419			0.178709	+	0.983902i	$0.442808\pi$
$398$	18.5895	+	13.5061i	0.931809	+	0.676999i
$399$	0.516209	−	1.58873i	0.0258428	−	0.0795359i
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	−4.61484	+	3.35288i	−0.230454	+	0.167435i	−0.697020	−	0.717052i	$-0.745491\pi$
$401$	−4.61484	+	3.35288i	−0.230454	+	0.167435i	0.466566	+	0.884487i	$0.345491\pi$
$402$	−1.90423	+	1.38351i	−0.0949745	+	0.0690030i
$403$	−6.39027	−	19.6672i	−0.318322	−	0.979694i
$404$	−1.65412	+	5.09085i	−0.0822954	+	0.253279i
$405$	−7.99080	−	5.80566i	−0.397066	−	0.288485i
$406$	5.06597			0.251420
$407$	12.5317	−	7.00951i	0.621175	−	0.347449i
$408$	14.5336			0.719521
$409$	−19.1999	−	13.9495i	−0.949374	−	0.689760i	0.00128500	−	0.999999i	$-0.499591\pi$
$409$	−19.1999	−	13.9495i	−0.949374	−	0.689760i	−0.950659	+	0.310239i	$0.899591\pi$
$410$	2.78101	−	8.55906i	0.137344	−	0.422702i
$411$	2.77967	+	8.55495i	0.137111	+	0.421985i
$412$	11.6448	−	8.46044i	0.573698	−	0.416816i
$413$	−5.82078	+	4.22904i	−0.286422	+	0.208098i
$414$	0.616595	+	1.89768i	0.0303040	+	0.0932661i
$415$	−0.231013	+	0.710986i	−0.0113400	+	0.0349009i
$416$	1.79142	+	1.30154i	0.0878316	+	0.0638134i
$417$	7.62072			0.373188
$418$	−2.22897	−	2.06260i	−0.109022	−	0.100885i
$419$	26.3585			1.28770			0.643848	−	0.765154i	$-0.277337\pi$
$419$	26.3585			1.28770			0.643848	+	0.765154i	$0.277337\pi$
$420$	−1.47595	−	1.07234i	−0.0720188	−	0.0523247i
$421$	−11.5931	+	35.6798i	−0.565012	+	1.73893i	0.102903	+	0.994691i	$0.467187\pi$
$421$	−11.5931	+	35.6798i	−0.565012	+	1.73893i	−0.667915	+	0.744237i	$0.732813\pi$
$422$	−5.11760	−	15.7504i	−0.249121	−	0.766715i
$423$	−1.12308	+	0.815966i	−0.0546060	+	0.0396736i
$424$	7.55172	−	5.48664i	0.366744	−	0.266455i
$425$	−2.46175	−	7.57648i	−0.119412	−	0.367513i
$426$	−0.0114088	+	0.0351127i	−0.000552759	+	0.00170122i
$427$	10.2661	+	7.45872i	0.496809	+	0.360953i
$428$	−4.27627			−0.206701
$429$	9.83390	+	9.09990i	0.474785	+	0.439347i
$430$	−2.76947			−0.133556
$431$	5.20849	+	3.78419i	0.250884	+	0.182278i	0.706119	−	0.708094i	$-0.250445\pi$
$431$	5.20849	+	3.78419i	0.250884	+	0.182278i	−0.455234	+	0.890372i	$0.650445\pi$
$432$	1.50619	−	4.63557i	0.0724665	−	0.223029i
$433$	4.52643	+	13.9309i	0.217526	+	0.669477i	0.998965	+	0.0454946i	$0.0144864\pi$
$433$	4.52643	+	13.9309i	0.217526	+	0.669477i	−0.781438	+	0.623983i	$0.785514\pi$
$434$	−7.55535	+	5.48928i	−0.362668	+	0.263494i
$435$	−7.47710	+	5.43243i	−0.358499	+	0.260465i
$436$	−1.55826	−	4.79584i	−0.0746273	−	0.229679i
$437$	−1.71961	+	5.29241i	−0.0822599	+	0.253170i
$438$	17.4844	+	12.7032i	0.835438	+	0.606981i
$439$	−31.4583			−1.50143			−0.750713	−	0.660629i	$-0.770290\pi$
$439$	−31.4583			−1.50143			−0.750713	+	0.660629i	$0.770290\pi$
$440$	−2.89459	+	1.61906i	−0.137994	+	0.0771857i
$441$	0.328323			0.0156344
$442$	−14.2711	−	10.3686i	−0.678809	−	0.493184i
$443$	−9.57974	+	29.4834i	−0.455147	+	1.40080i	0.415815	+	0.909449i	$0.363496\pi$
$443$	−9.57974	+	29.4834i	−0.455147	+	1.40080i	−0.870962	+	0.491350i	$0.836504\pi$
$444$	−2.44073	−	7.51180i	−0.115832	−	0.356494i
$445$	−11.5397	+	8.38409i	−0.547034	+	0.397444i
$446$	15.4712	−	11.2405i	0.732583	−	0.532253i
$447$	7.59867	+	23.3863i	0.359405	+	1.10613i
$448$	0.309017	−	0.951057i	0.0145997	−	0.0449332i
$449$	−14.2357	−	10.3428i	−0.671823	−	0.488108i	0.198812	−	0.980038i	$-0.436292\pi$
$449$	−14.2357	−	10.3428i	−0.671823	−	0.488108i	−0.870635	+	0.491930i	$0.836292\pi$
$450$	0.328323			0.0154773
$451$	29.6393	+	3.52376i	1.39566	+	0.165927i
$452$	13.8169			0.649894
$453$	25.9916	+	18.8840i	1.22119	+	0.887249i
$454$	6.08730	−	18.7348i	0.285691	−	0.879268i
$455$	0.684262	+	2.10594i	0.0320787	+	0.0987281i
$456$	−1.35145	+	0.981889i	−0.0632876	+	0.0459811i
$457$	−27.8099	+	20.2051i	−1.30089	+	0.945154i	−0.999964	−	0.00849262i	$-0.997297\pi$
$457$	−27.8099	+	20.2051i	−1.30089	+	0.945154i	−0.300929	+	0.953647i	$0.597297\pi$
$458$	8.52310	+	26.2314i	0.398258	+	1.22571i
$459$	−11.9989	+	36.9287i	−0.560059	+	1.72368i
$460$	4.91670	+	3.57219i	0.229242	+	0.166554i
$461$	−10.0757			−0.469271			−0.234635	−	0.972083i	$-0.575390\pi$
$461$	−10.0757			−0.469271			−0.234635	+	0.972083i	$0.575390\pi$
$462$	2.53608	−	5.49362i	0.117989	−	0.255586i
$463$	−30.0439			−1.39626			−0.698128	−	0.715973i	$-0.745983\pi$
$463$	−30.0439			−1.39626			−0.698128	+	0.715973i	$0.745983\pi$
$464$	−4.09846	−	2.97770i	−0.190266	−	0.138236i
$465$	5.26492	−	16.2038i	0.244155	−	0.751432i
$466$	−4.00063	−	12.3127i	−0.185326	−	0.570374i
$467$	15.9669	−	11.6006i	0.738859	−	0.536813i	−0.153494	−	0.988150i	$-0.549053\pi$
$467$	15.9669	−	11.6006i	0.738859	−	0.536813i	0.892354	+	0.451337i	$0.149053\pi$
$468$	0.588165	−	0.427327i	0.0271880	−	0.0197532i
$469$	−0.398687	−	1.22703i	−0.0184096	−	0.0566591i
$470$	−1.30657	+	4.02122i	−0.0602677	+	0.185485i
$471$	16.9492	+	12.3143i	0.780976	+	0.567413i
$472$	7.19487			0.331171
$473$	−1.78725	−	9.00972i	−0.0821779	−	0.414268i
$474$	17.1349			0.787034
$475$	0.740779	+	0.538207i	0.0339893	+	0.0246946i
$476$	−2.46175	+	7.57648i	−0.112834	+	0.347267i
$477$	−0.947049	−	2.91472i	−0.0433624	−	0.133456i
$478$	4.67309	−	3.39520i	0.213742	−	0.155293i
$479$	−4.36844	+	3.17385i	−0.199599	+	0.145017i	−0.683095	−	0.730329i	$-0.739367\pi$
$479$	−4.36844	+	3.17385i	−0.199599	+	0.145017i	0.483496	+	0.875346i	$0.339367\pi$
$480$	0.563761	+	1.73508i	0.0257321	+	0.0791951i
$481$	−2.96242	+	9.11740i	−0.135075	+	0.415718i
$482$	20.2516	+	14.7136i	0.922434	+	0.670187i
$483$	−11.0874			−0.504493
$484$	−7.13518	−	8.37193i	−0.324326	−	0.380542i
$485$	7.27431			0.330309
$486$	−2.74842	−	1.99685i	−0.124671	−	0.0905788i
$487$	−3.91389	+	12.0457i	−0.177355	+	0.545843i	−0.999733	−	0.0230984i	$-0.992647\pi$
$487$	−3.91389	+	12.0457i	−0.177355	+	0.545843i	0.822378	+	0.568941i	$0.192647\pi$
$488$	−3.92128	−	12.0685i	−0.177508	−	0.546314i
$489$	−0.205526	+	0.149323i	−0.00929421	+	0.00675264i
$490$	0.809017	−	0.587785i	0.0365477	−	0.0265534i
$491$	−8.89324	−	27.3706i	−0.401346	−	1.23522i	−0.923908	−	0.382615i	$-0.875023\pi$
$491$	−8.89324	−	27.3706i	−0.401346	−	1.23522i	0.522561	−	0.852602i	$-0.324977\pi$
$492$	5.07359	−	15.6149i	0.228735	−	0.703974i
$493$	32.6499	+	23.7215i	1.47048	+	1.06836i
$494$	2.02755			0.0912236
$495$	0.211881	+	1.06811i	0.00952333	+	0.0480081i
$496$	9.33892			0.419330
$497$	−0.0163721	−	0.0118950i	−0.000734387	−	0.000533563i
$498$	−0.421453	+	1.29710i	−0.0188858	+	0.0581245i
$499$	−5.99053	−	18.4370i	−0.268173	−	0.825351i	−0.990945	−	0.134265i	$-0.957133\pi$
$499$	−5.99053	−	18.4370i	−0.268173	−	0.825351i	0.722773	−	0.691086i	$-0.242867\pi$
$500$	0.809017	−	0.587785i	0.0361803	−	0.0262866i
$501$	10.3961	−	7.55319i	0.464462	−	0.337452i
$502$	−2.05989	−	6.33969i	−0.0919374	−	0.282954i
$503$	0.354994	−	1.09256i	0.0158284	−	0.0487148i	−0.942830	−	0.333273i	$-0.891847\pi$
$503$	0.354994	−	1.09256i	0.0158284	−	0.0487148i	0.958659	+	0.284558i	$0.0918469\pi$
$504$	−0.265619	−	0.192984i	−0.0118316	−	0.00859617i
$505$	5.35283			0.238198
$506$	−8.44823	+	18.3005i	−0.375569	+	0.813555i
$507$	14.7715			0.656027
$508$	−11.8780	−	8.62984i	−0.526999	−	0.382887i
$509$	−0.409178	+	1.25932i	−0.0181365	+	0.0558183i	−0.959715	−	0.280975i	$-0.909342\pi$
$509$	−0.409178	+	1.25932i	−0.0181365	+	0.0558183i	0.941579	+	0.336793i	$0.109342\pi$
$510$	−4.49114	−	13.8223i	−0.198871	−	0.612061i
$511$	−9.58382	+	6.96305i	−0.423963	+	0.308027i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−1.37914	−	4.24457i	−0.0608907	−	0.187402i
$514$	−7.01943	+	21.6036i	−0.309614	+	0.952893i
$515$	−11.6448	−	8.46044i	−0.513131	−	0.372812i
$516$	−5.05253			−0.222425
$517$	−13.9252	−	1.65553i	−0.612428	−	0.0728101i
$518$	4.32937			0.190222
$519$	−20.7286	−	15.0602i	−0.909884	−	0.661070i
$520$	0.684262	−	2.10594i	0.0300069	−	0.0923516i
$521$	−8.41579	−	25.9011i	−0.368702	−	1.13475i	−0.947630	−	0.319370i	$-0.896529\pi$
$521$	−8.41579	−	25.9011i	−0.368702	−	1.13475i	0.578928	−	0.815379i	$-0.303471\pi$
$522$	−1.34562	+	0.977650i	−0.0588962	+	0.0427906i
$523$	−19.3340	+	14.0470i	−0.845418	+	0.614232i	−0.923879	−	0.382685i	$-0.874999\pi$
$523$	−19.3340	+	14.0470i	−0.845418	+	0.614232i	0.0784609	+	0.996917i	$0.474999\pi$
$524$	−2.35651	−	7.25258i	−0.102944	−	0.316830i
$525$	−0.563761	+	1.73508i	−0.0246046	+	0.0757250i
$526$	−11.7319	−	8.52376i	−0.511537	−	0.371654i
$527$	−74.3974			−3.24080
$528$	−5.28080	+	2.95376i	−0.229817	+	0.128546i
$529$	13.9345			0.605847
$530$	−7.55172	−	5.48664i	−0.328026	−	0.238325i
$531$	0.729974	−	2.24663i	0.0316782	−	0.0974954i
$532$	−0.282952	−	0.870838i	−0.0122675	−	0.0377556i
$533$	−16.1220	+	11.7133i	−0.698319	+	0.507359i
$534$	−21.0527	+	15.2957i	−0.911039	+	0.661908i
$535$	1.32144	+	4.06697i	0.0571308	+	0.175831i
$536$	−0.398687	+	1.22703i	−0.0172206	+	0.0529997i
$537$	18.9422	+	13.7623i	0.817416	+	0.593888i
$538$	−21.2753			−0.917244
$539$	2.43430	+	2.25260i	0.104853	+	0.0970263i
$540$	−4.87412			−0.209749
$541$	27.3469	+	19.8687i	1.17574	+	0.854222i	0.991684	−	0.128694i	$-0.0410785\pi$
$541$	27.3469	+	19.8687i	1.17574	+	0.854222i	0.184052	+	0.982917i	$0.441079\pi$
$542$	2.49256	−	7.67132i	0.107065	−	0.329511i
$543$	−10.8733	−	33.4646i	−0.466618	−	1.43610i
$544$	6.44494	−	4.68252i	0.276324	−	0.200761i
$545$	−4.07959	+	2.96399i	−0.174750	+	0.126964i
$546$	1.24835	+	3.84201i	0.0534243	+	0.164423i
$547$	−7.29307	+	22.4458i	−0.311829	+	0.959711i	0.665211	+	0.746655i	$0.268342\pi$
$547$	−7.29307	+	22.4458i	−0.311829	+	0.959711i	−0.977040	+	0.213056i	$0.931658\pi$
$548$	3.98893	+	2.89813i	0.170399	+	0.123802i
$549$	−4.16627			−0.177812
$550$	2.43430	+	2.25260i	0.103799	+	0.0960512i
$551$	−4.63867			−0.197614
$552$	8.96987	+	6.51700i	0.381783	+	0.277382i
$553$	−2.90237	+	8.93257i	−0.123421	+	0.379851i
$554$	5.39428	+	16.6019i	0.229181	+	0.705347i
$555$	−6.38991	+	4.64254i	−0.271237	+	0.197065i
$556$	3.37941	−	2.45529i	0.143319	−	0.104127i
$557$	1.85833	+	5.71935i	0.0787399	+	0.242337i	0.982676	−	0.185331i	$-0.0593356\pi$
$557$	1.85833	+	5.71935i	0.0787399	+	0.242337i	−0.903936	+	0.427667i	$0.859336\pi$
$558$	0.947504	−	2.91612i	0.0401110	−	0.123449i
$559$	4.96128	+	3.60458i	0.209840	+	0.152458i
$560$	−1.00000			−0.0422577
$561$	42.0688	−	23.5308i	1.77615	−	0.993472i
$562$	−20.4688			−0.863423
$563$	−5.55889	−	4.03877i	−0.234279	−	0.170214i	0.464452	−	0.885599i	$-0.346251\pi$
$563$	−5.55889	−	4.03877i	−0.234279	−	0.170214i	−0.698731	+	0.715385i	$0.746251\pi$
$564$	−2.38367	+	7.33619i	−0.100371	+	0.308909i
$565$	−4.26967	−	13.1407i	−0.179626	−	0.552833i
$566$	−4.26580	+	3.09929i	−0.179305	+	0.130273i
$567$	7.99080	−	5.80566i	0.335582	−	0.243815i
$568$	0.00625357	+	0.0192465i	0.000262394	+	0.000807565i
$569$	5.87057	−	18.0678i	0.246107	−	0.757440i	−0.749345	−	0.662180i	$-0.769632\pi$
$569$	5.87057	−	18.0678i	0.246107	−	0.757440i	0.995452	−	0.0952605i	$-0.0303684\pi$
$570$	1.35145	+	0.981889i	0.0566062	+	0.0411268i
$571$	0.393382			0.0164625			0.00823127	−	0.999966i	$-0.497380\pi$
$571$	0.393382			0.0164625			0.00823127	+	0.999966i	$0.497380\pi$
$572$	7.29270	+	0.867013i	0.304923	+	0.0362516i
$573$	21.9123			0.915398
$574$	7.28078	+	5.28979i	0.303894	+	0.220792i
$575$	1.87801	−	5.77993i	0.0783185	−	0.241040i
$576$	0.101458	+	0.312254i	0.00422740	+	0.0130106i
$577$	−6.82652	+	4.95976i	−0.284192	+	0.206477i	−0.720744	−	0.693202i	$-0.756200\pi$
$577$	−6.82652	+	4.95976i	−0.284192	+	0.206477i	0.436552	+	0.899679i	$0.356200\pi$
$578$	−37.5895	+	27.3104i	−1.56352	+	1.13596i
$579$	9.75298	+	30.0166i	0.405320	+	1.24745i
$580$	−1.56547	+	4.81803i	−0.0650027	+	0.200058i
$581$	−0.604801	−	0.439413i	−0.0250914	−	0.0182299i
$582$	13.2710			0.550102
$583$	12.9759	−	28.1083i	0.537407	−	1.16413i
$584$	11.8463			0.490201
$585$	−0.588165	−	0.427327i	−0.0243176	−	0.0176678i
$586$	1.97960	−	6.09260i	0.0817767	−	0.251683i
$587$	14.3213	+	44.0763i	0.591101	+	1.81922i	0.573247	+	0.819382i	$0.305683\pi$
$587$	14.3213	+	44.0763i	0.591101	+	1.81922i	0.0178540	+	0.999841i	$0.494317\pi$
$588$	1.47595	−	1.07234i	0.0608670	−	0.0442224i
$589$	6.91808	−	5.02628i	0.285054	−	0.207104i
$590$	−2.22334	−	6.84273i	−0.0915334	−	0.281711i
$591$	7.42610	−	22.8552i	0.305469	−	0.940137i
$592$	−3.50253	−	2.54474i	−0.143953	−	0.104588i
$593$	−25.9525			−1.06574			−0.532871	−	0.846197i	$-0.678887\pi$
$593$	−25.9525			−1.06574			−0.532871	+	0.846197i	$0.678887\pi$
$594$	−3.14547	−	15.8567i	−0.129060	−	0.650607i
$595$	7.96638			0.326590
$596$	10.9044	+	7.92248i	0.446660	+	0.324518i
$597$	12.9541	−	39.8685i	0.530175	−	1.63171i
$598$	−4.15852	−	12.7986i	−0.170054	−	0.523373i
$599$	−3.88364	+	2.82163i	−0.158681	+	0.115289i	−0.664292	−	0.747473i	$-0.731267\pi$
$599$	−3.88364	+	2.82163i	−0.158681	+	0.115289i	0.505611	+	0.862761i	$0.331267\pi$
$600$	1.47595	−	1.07234i	0.0602552	−	0.0437780i
$601$	−9.42848	−	29.0179i	−0.384596	−	1.18366i	−0.936773	−	0.349938i	$-0.886203\pi$
$601$	−9.42848	−	29.0179i	−0.384596	−	1.18366i	0.552177	−	0.833727i	$-0.313797\pi$
$602$	0.855812	−	2.63392i	0.0348803	−	0.107351i
$603$	0.342696	+	0.248983i	0.0139557	+	0.0101394i
$604$	17.6102			0.716547
$605$	−5.75728	+	9.37303i	−0.234067	+	0.381068i
$606$	9.76555			0.396698
$607$	−13.3883	−	9.72716i	−0.543414	−	0.394813i	0.281937	−	0.959433i	$-0.409023\pi$
$607$	−13.3883	−	9.72716i	−0.543414	−	0.394813i	−0.825351	+	0.564619i	$0.809023\pi$
$608$	−0.282952	+	0.870838i	−0.0114752	+	0.0353171i
$609$	−2.85600	−	8.78986i	−0.115731	−	0.356183i
$610$	−10.2661	+	7.45872i	−0.415660	+	0.301995i
$611$	7.57441	−	5.50313i	0.306428	−	0.222633i
$612$	−0.808249	−	2.48753i	−0.0326715	−	0.100553i
$613$	−13.0072	+	40.0319i	−0.525354	+	1.61687i	0.238260	+	0.971201i	$0.423423\pi$
$613$	−13.0072	+	40.0319i	−0.525354	+	1.61687i	−0.763614	+	0.645673i	$0.776577\pi$
$614$	−4.33609	−	3.15035i	−0.174990	−	0.127138i
$615$	−16.4185			−0.662057
$616$	−0.645341	−	3.25323i	−0.0260015	−	0.131077i
$617$	7.32983			0.295088			0.147544	−	0.989056i	$-0.452863\pi$
$617$	7.32983			0.295088			0.147544	+	0.989056i	$0.452863\pi$
$618$	−21.2444	−	15.4350i	−0.854576	−	0.620886i
$619$	−3.69303	+	11.3660i	−0.148435	+	0.456837i	−0.997437	−	0.0715536i	$-0.977204\pi$
$619$	−3.69303	+	11.3660i	−0.148435	+	0.456837i	0.849001	+	0.528391i	$0.177204\pi$
$620$	−2.88589	−	8.88185i	−0.115900	−	0.356703i
$621$	−23.9646	+	17.4113i	−0.961666	+	0.698692i
$622$	21.8288	−	15.8596i	0.875257	−	0.635912i
$623$	−4.40777	−	13.5657i	−0.176594	−	0.543500i
$624$	1.24835	−	3.84201i	0.0499738	−	0.153804i
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	−28.5633			−1.14162
$627$	−2.32217	+	5.03025i	−0.0927383	+	0.200889i
$628$	11.4836			0.458245
$629$	27.9025	+	20.2724i	1.11255	+	0.808312i
$630$	−0.101458	+	0.312254i	−0.00404216	+	0.0124405i
$631$	13.5122	+	41.5864i	0.537914	+	1.65553i	0.737267	+	0.675602i	$0.236116\pi$
$631$	13.5122	+	41.5864i	0.537914	+	1.65553i	−0.199353	+	0.979928i	$0.563884\pi$
$632$	7.59849	−	5.52063i	0.302252	−	0.219599i
$633$	−24.4430	+	17.7589i	−0.971522	+	0.705852i
$634$	6.49173	+	19.9795i	0.257820	+	0.793487i
$635$	−4.53698	+	13.9634i	−0.180044	+	0.554120i
$636$	−13.7771	−	10.0097i	−0.546298	−	0.396909i
$637$	−2.21432			−0.0877345
$638$	−16.6844	−	1.98357i	−0.660543	−	0.0785305i
$639$	0.00664427			0.000262843
$640$	0.809017	+	0.587785i	0.0319792	+	0.0232343i
$641$	11.6414	−	35.8285i	0.459806	−	1.41514i	−0.405592	−	0.914054i	$-0.632935\pi$
$641$	11.6414	−	35.8285i	0.459806	−	1.41514i	0.865398	−	0.501084i	$-0.167065\pi$
$642$	2.41079	+	7.41966i	0.0951464	+	0.292831i
$643$	−20.0422	+	14.5615i	−0.790387	+	0.574250i	−0.908078	−	0.418800i	$-0.862451\pi$
$643$	−20.0422	+	14.5615i	−0.790387	+	0.574250i	0.117691	+	0.993050i	$0.462451\pi$
$644$	−4.91670	+	3.57219i	−0.193745	+	0.140764i
$645$	1.56132	+	4.80524i	0.0614768	+	0.189206i
$646$	2.25411	−	6.93742i	0.0886866	−	0.272949i
$647$	−29.2917	−	21.2817i	−1.15158	−	0.836670i	−0.162887	−	0.986645i	$-0.552081\pi$
$647$	−29.2917	−	21.2817i	−1.15158	−	0.836670i	−0.988690	+	0.149975i	$0.952081\pi$
$648$	−9.87717			−0.388012
$649$	20.8262	−	11.6489i	0.817500	−	0.457261i
$650$	−2.21432			−0.0868527
$651$	13.7837	+	10.0145i	0.540228	+	0.392498i
$652$	−0.0430307	+	0.132435i	−0.00168521	+	0.00518655i
$653$	−5.16480	−	15.8956i	−0.202114	−	0.622043i	−0.999820	−	0.0189960i	$-0.993953\pi$
$653$	−5.16480	−	15.8956i	−0.202114	−	0.622043i	0.797705	−	0.603047i	$-0.206047\pi$
$654$	−7.44268	+	5.40742i	−0.291032	+	0.211447i
$655$	−6.16941	+	4.48234i	−0.241059	+	0.175140i
$656$	−2.78101	−	8.55906i	−0.108580	−	0.334175i
$657$	1.20189	−	3.69904i	0.0468902	−	0.144313i
$658$	−3.42065	−	2.48525i	−0.133351	−	0.0968851i
$659$	34.0997			1.32834			0.664168	−	0.747584i	$-0.268786\pi$
$659$	34.0997			1.32834			0.664168	+	0.747584i	$0.268786\pi$
$660$	4.44105	+	4.10957i	0.172868	+	0.159965i
$661$	−29.1326			−1.13313			−0.566563	−	0.824018i	$-0.691727\pi$
$661$	−29.1326			−1.13313			−0.566563	+	0.824018i	$0.691727\pi$
$662$	−9.38641	−	6.81963i	−0.364813	−	0.265052i
$663$	−9.94480	+	30.6070i	−0.386224	+	1.18868i
$664$	0.231013	+	0.710986i	0.00896505	+	0.0275916i
$665$	−0.740779	+	0.538207i	−0.0287262	+	0.0208708i
$666$	−1.14996	+	0.835498i	−0.0445602	+	0.0323749i
$667$	9.51395	+	29.2809i	0.368382	+	1.13376i
$668$	2.17661	−	6.69893i	0.0842157	−	0.259189i
$669$	−28.2252	−	20.5068i	−1.09125	−	0.792839i
$670$	1.29018			0.0498439
$671$	−30.8901	−	28.5845i	−1.19250	−	1.10349i
$672$	−1.82437			−0.0703766
$673$	−21.9458	−	15.9446i	−0.845950	−	0.614619i	0.0780763	−	0.996947i	$-0.475122\pi$
$673$	−21.9458	−	15.9446i	−0.845950	−	0.614619i	−0.924026	+	0.382329i	$0.875122\pi$
$674$	0.725800	−	2.23378i	0.0279568	−	0.0860421i
$675$	1.50619	+	4.63557i	0.0579732	+	0.178423i
$676$	6.55045	−	4.75918i	0.251940	−	0.183045i
$677$	36.8742	−	26.7907i	1.41719	−	1.02965i	0.424963	−	0.905211i	$-0.360287\pi$
$677$	36.8742	−	26.7907i	1.41719	−	1.02965i	0.992227	−	0.124439i	$-0.0397130\pi$
$678$	−7.78945	−	23.9735i	−0.299152	−	0.920695i
$679$	−2.24789	+	6.91828i	−0.0862659	+	0.265499i
$680$	−6.44494	−	4.68252i	−0.247152	−	0.179566i
$681$	−35.9381			−1.37715
$682$	27.0323	−	15.1203i	1.03512	−	0.578986i
$683$	−6.68497			−0.255793			−0.127897	−	0.991787i	$-0.540823\pi$
$683$	−6.68497			−0.255793			−0.127897	+	0.991787i	$0.540823\pi$
$684$	0.243215	+	0.176706i	0.00929956	+	0.00675652i
$685$	1.52364	−	4.68927i	0.0582151	−	0.179168i
$686$	0.309017	+	0.951057i	0.0117983	+	0.0363115i
$687$	40.7086	−	29.5765i	1.55313	−	1.12841i
$688$	−2.24055	+	1.62785i	−0.0854200	+	0.0620613i
$689$	6.38720	+	19.6578i	0.243333	+	0.748902i
$690$	3.42619	−	10.5447i	0.130433	−	0.401431i
$691$	−1.91934	−	1.39448i	−0.0730152	−	0.0530487i	0.550679	−	0.834717i	$-0.314369\pi$
$691$	−1.91934	−	1.39448i	−0.0730152	−	0.0530487i	−0.623694	+	0.781669i	$0.714369\pi$
$692$	−14.0443			−0.533883
$693$	−1.08131	−	0.128555i	−0.0410756	−	0.00488339i
$694$	−31.4811			−1.19501
$695$	−3.37941	−	2.45529i	−0.128188	−	0.0931343i
$696$	−2.85600	+	8.78986i	−0.108256	+	0.333179i
$697$	22.1546	+	68.1848i	0.839164	+	2.58268i
$698$	−2.10973	+	1.53281i	−0.0798546	+	0.0580178i
$699$	−19.1081	+	13.8828i	−0.722733	+	0.525096i
$700$	0.309017	+	0.951057i	0.0116797	+	0.0359466i
$701$	−9.44233	+	29.0605i	−0.356632	+	1.09760i	0.598426	+	0.801178i	$0.295793\pi$
$701$	−9.44233	+	29.0605i	−0.356632	+	1.09760i	−0.955057	+	0.296421i	$0.904207\pi$
$702$	8.73161	+	6.34388i	0.329553	+	0.239435i
$703$	−3.96420			−0.149513
$704$	−1.39011	+	3.01124i	−0.0523918	+	0.113491i
$705$	7.71373			0.290516
$706$	0.336557	+	0.244523i	0.0126665	+	0.00920274i
$707$	−1.65412	+	5.09085i	−0.0622095	+	0.191461i
$708$	−4.05619	−	12.4837i	−0.152441	−	0.469165i
$709$	−8.57318	+	6.22878i	−0.321973	+	0.233927i	−0.737017	−	0.675874i	$-0.763766\pi$
$709$	−8.57318	+	6.22878i	−0.321973	+	0.233927i	0.415044	+	0.909801i	$0.363766\pi$
$710$	0.0163721	−	0.0118950i	0.000614432	−	0.000446411i
$711$	−0.952915	−	2.93277i	−0.0357371	−	0.109987i
$712$	−4.40777	+	13.5657i	−0.165188	+	0.508397i
$713$	−45.9167	−	33.3604i	−1.71959	−	1.24936i
$714$	14.5336			0.543907
$715$	−1.42899	−	7.20370i	−0.0534412	−	0.269403i
$716$	12.8339			0.479627
$717$	−8.52545	−	6.19410i	−0.318389	−	0.231323i
$718$	−3.58924	+	11.0465i	−0.133949	+	0.412253i
$719$	3.67542	+	11.3118i	0.137070	+	0.421858i	0.995906	−	0.0903922i	$-0.0288120\pi$
$719$	3.67542	+	11.3118i	0.137070	+	0.421858i	−0.858836	+	0.512250i	$0.828812\pi$
$720$	0.265619	−	0.192984i	0.00989904	−	0.00719208i
$721$	11.6448	−	8.46044i	0.433675	−	0.315083i
$722$	−5.61224	−	17.2727i	−0.208866	−	0.642823i
$723$	14.1122	−	43.4330i	0.524840	−	1.61529i
$724$	−15.6036	−	11.3367i	−0.579902	−	0.421323i
$725$	5.06597			0.188145
$726$	−10.5034	+	17.0999i	−0.389818	+	0.634636i
$727$	−23.4180			−0.868527			−0.434264	−	0.900786i	$-0.642991\pi$
$727$	−23.4180			−0.868527			−0.434264	+	0.900786i	$0.642991\pi$
$728$	1.79142	+	1.30154i	0.0663945	+	0.0482384i
$729$	7.24141	−	22.2868i	0.268200	−	0.825436i
$730$	−3.66069	−	11.2665i	−0.135488	−	0.416990i
$731$	17.8490	−	12.9681i	0.660170	−	0.479642i
$732$	−18.7291	+	13.6075i	−0.692246	+	0.502946i
$733$	3.73341	+	11.4902i	0.137896	+	0.424402i	0.996029	−	0.0890260i	$-0.0283754\pi$
$733$	3.73341	+	11.4902i	0.137896	+	0.424402i	−0.858133	+	0.513428i	$0.828375\pi$
$734$	−2.47433	+	7.61519i	−0.0913290	+	0.281082i
$735$	−1.47595	−	1.07234i	−0.0544411	−	0.0395538i
$736$	6.07737			0.224015
$737$	0.832605	+	4.19725i	0.0306694	+	0.154608i
$738$	−2.95476			−0.108766
$739$	−28.3263	−	20.5803i	−1.04200	−	0.757058i	−0.0713256	−	0.997453i	$-0.522723\pi$
$739$	−28.3263	−	20.5803i	−1.04200	−	0.757058i	−0.970675	+	0.240395i	$0.922723\pi$
$740$	−1.33785	+	4.11748i	−0.0491803	+	0.151361i
$741$	−1.14305	−	3.51795i	−0.0419911	−	0.129235i
$742$	7.55172	−	5.48664i	0.277232	−	0.201421i
$743$	39.2606	−	28.5245i	1.44033	−	1.04646i	0.452359	−	0.891836i	$-0.350583\pi$
$743$	39.2606	−	28.5245i	1.44033	−	1.04646i	0.987973	−	0.154627i	$-0.0494175\pi$
$744$	−5.26492	−	16.2038i	−0.193021	−	0.594059i
$745$	4.16510	−	12.8188i	0.152597	−	0.469646i
$746$	13.4563	+	9.77656i	0.492669	+	0.357945i
$747$	0.245446			0.00898041
$748$	11.0742	−	23.9887i	0.404911	−	0.877114i
$749$	−4.27627			−0.156251
$750$	−1.47595	−	1.07234i	−0.0538939	−	0.0391562i
$751$	−0.0138959	+	0.0427673i	−0.000507070	+	0.00156060i	−0.951310	−	0.308237i	$-0.900261\pi$
$751$	−0.0138959	+	0.0427673i	−0.000507070	+	0.00156060i	0.950803	+	0.309797i	$0.100261\pi$
$752$	1.30657	+	4.02122i	0.0476458	+	0.146639i
$753$	−9.83857	+	7.14814i	−0.358537	+	0.260493i
$754$	9.07529	−	6.59358i	0.330502	−	0.240124i
$755$	−5.44184	−	16.7483i	−0.198049	−	0.609532i
$756$	1.50619	−	4.63557i	0.0547795	−	0.168594i
$757$	−23.3305	−	16.9506i	−0.847962	−	0.616080i	0.0766216	−	0.997060i	$-0.475587\pi$
$757$	−23.3305	−	16.9506i	−0.847962	−	0.616080i	−0.924583	+	0.380980i	$0.875587\pi$
$758$	−0.0831686			−0.00302082
$759$	36.5155	+	4.34125i	1.32543	+	0.157577i
$760$	0.915653			0.0332142
$761$	14.8654	+	10.8003i	0.538869	+	0.391511i	0.823665	−	0.567077i	$-0.191926\pi$
$761$	14.8654	+	10.8003i	0.538869	+	0.391511i	−0.284796	+	0.958588i	$0.591926\pi$
$762$	−8.27712	+	25.4744i	−0.299848	+	0.922839i
$763$	−1.55826	−	4.79584i	−0.0564129	−	0.173621i
$764$	9.71700	−	7.05982i	0.351549	−	0.255415i
$765$	−2.11602	+	1.53738i	−0.0765050	+	0.0555841i
$766$	1.94151	+	5.97534i	0.0701494	+	0.215898i
$767$	−4.92318	+	15.1520i	−0.177766	+	0.547106i
$768$	1.47595	+	1.07234i	0.0532586	+	0.0386946i
$769$	20.2436			0.730003			0.365002	−	0.931007i	$-0.381068\pi$
$769$	20.2436			0.730003			0.365002	+	0.931007i	$0.381068\pi$
$770$	−2.89459	+	1.61906i	−0.104314	+	0.0583469i
$771$	41.4412			1.49247
$772$	13.9959	+	10.1686i	0.503722	+	0.365976i
$773$	−8.41975	+	25.9133i	−0.302837	+	0.932038i	0.677638	+	0.735396i	$0.263004\pi$
$773$	−8.41975	+	25.9133i	−0.302837	+	0.932038i	−0.980475	+	0.196642i	$0.936996\pi$
$774$	0.280983	+	0.864777i	0.0100997	+	0.0310838i
$775$	−7.55535	+	5.48928i	−0.271396	+	0.197181i
$776$	5.88504	−	4.27573i	0.211261	−	0.153490i
$777$	−2.44073	−	7.51180i	−0.0875607	−	0.269484i
$778$	−1.13676	+	3.49857i	−0.0407547	+	0.125430i
$779$	−6.66666	−	4.84361i	−0.238858	−	0.173540i
$780$	−4.03973			−0.144646
$781$	0.0492628	+	0.0455858i	0.00176276	+	0.00163119i
$782$	−48.4147			−1.73131
$783$	−19.9764	−	14.5137i	−0.713898	−	0.518677i
$784$	0.309017	−	0.951057i	0.0110363	−	0.0339663i
$785$	−3.54863	−	10.9216i	−0.126656	−	0.389807i
$786$	−11.2553	+	8.17745i	−0.401463	+	0.291680i
$787$	21.7049	−	15.7695i	0.773697	−	0.562124i	−0.129384	−	0.991595i	$-0.541300\pi$
$787$	21.7049	−	15.7695i	0.773697	−	0.562124i	0.903081	+	0.429471i	$0.141300\pi$
$788$	−4.07051	−	12.5277i	−0.145006	−	0.446282i
$789$	−8.17537	+	25.1612i	−0.291051	+	0.895763i
$790$	−7.59849	−	5.52063i	−0.270342	−	0.196415i
$791$	13.8169			0.491273
$792$	0.799236	+	0.739581i	0.0283996	+	0.0262799i
$793$	28.0987			0.997813
$794$	−5.76143	−	4.18593i	−0.204466	−	0.148553i
$795$	−5.26239	+	16.1960i	−0.186638	+	0.574412i
$796$	−7.10057	−	21.8533i	−0.251673	−	0.774570i
$797$	−29.5241	+	21.4505i	−1.04580	+	0.759815i	−0.971409	−	0.237414i	$-0.923700\pi$
$797$	−29.5241	+	21.4505i	−1.04580	+	0.759815i	−0.0743874	+	0.997229i	$0.523700\pi$
$798$	−1.35145	+	0.981889i	−0.0478409	+	0.0347585i
$799$	−10.4087	−	32.0346i	−0.368232	−	1.13330i
$800$	0.309017	−	0.951057i	0.0109254	−	0.0336249i
$801$	3.78875	+	2.75269i	0.133869	+	0.0972616i
$802$	5.70426			0.201424
$803$	34.2900	−	19.1798i	1.21007	−	0.676841i
$804$	2.35376			0.0830107
$805$	4.91670	+	3.57219i	0.173291	+	0.125903i
$806$	−6.39027	+	19.6672i	−0.225088	+	0.692749i
$807$	11.9942	+	36.9144i	0.422216	+	1.29945i
$808$	4.33053	−	3.14632i	0.152348	−	0.110687i
$809$	6.89780	−	5.01154i	0.242514	−	0.176196i	−0.459889	−	0.887977i	$-0.652111\pi$
$809$	6.89780	−	5.01154i	0.242514	−	0.176196i	0.702402	+	0.711780i	$0.252111\pi$
$810$	3.05221	+	9.39375i	0.107244	+	0.330063i
$811$	13.4609	−	41.4285i	0.472677	−	1.45475i	−0.376387	−	0.926462i	$-0.622834\pi$
$811$	13.4609	−	41.4285i	0.472677	−	1.45475i	0.849065	−	0.528289i	$-0.177166\pi$
$812$	−4.09846	−	2.97770i	−0.143828	−	0.104497i
$813$	−14.7156			−0.516097
$814$	−14.2585	−	1.69516i	−0.499760	−	0.0594153i
$815$	0.139250			0.00487773
$816$	−11.7579	−	8.54265i	−0.411610	−	0.299052i
$817$	−0.783627	+	2.41176i	−0.0274156	+	0.0843766i
$818$	7.33371	+	22.5708i	0.256417	+	0.789171i
$819$	0.588165	−	0.427327i	0.0205522	−	0.0149320i
$820$	−7.28078	+	5.28979i	−0.254256	+	0.184728i
$821$	−6.81626	−	20.9783i	−0.237889	−	0.732147i	−0.996725	−	0.0808656i	$-0.974232\pi$
$821$	−6.81626	−	20.9783i	−0.237889	−	0.732147i	0.758836	−	0.651282i	$-0.225768\pi$
$822$	2.77967	−	8.55495i	0.0969522	−	0.298388i
$823$	−2.73199	−	1.98491i	−0.0952313	−	0.0691896i	0.539151	−	0.842209i	$-0.318745\pi$
$823$	−2.73199	−	1.98491i	−0.0952313	−	0.0691896i	−0.634382	+	0.773020i	$0.718745\pi$
$824$	−14.3938			−0.501431
$825$	2.53608	−	5.49362i	0.0882948	−	0.191263i
$826$	7.19487			0.250342
$827$	−13.9806	−	10.1575i	−0.486154	−	0.353212i	0.317549	−	0.948242i	$-0.397140\pi$
$827$	−13.9806	−	10.1575i	−0.486154	−	0.353212i	−0.803703	+	0.595030i	$0.797140\pi$
$828$	0.616595	−	1.89768i	0.0214282	−	0.0659491i
$829$	−7.35526	−	22.6372i	−0.255459	−	0.786221i	−0.993739	−	0.111727i	$-0.964362\pi$
$829$	−7.35526	−	22.6372i	−0.255459	−	0.786221i	0.738280	−	0.674494i	$-0.235638\pi$
$830$	0.604801	−	0.439413i	0.0209929	−	0.0152523i
$831$	25.7645	−	18.7190i	0.893761	−	0.649355i
$832$	−0.684262	−	2.10594i	−0.0237225	−	0.0730104i
$833$	−2.46175	+	7.57648i	−0.0852945	+	0.262509i
$834$	−6.16529	−	4.47935i	−0.213487	−	0.155107i
$835$	−7.04367			−0.243756
$836$	0.590909	+	2.97883i	0.0204370	+	0.103025i
$837$	45.5191			1.57337
$838$	−21.3245	−	15.4931i	−0.736641	−	0.535201i
$839$	0.663661	−	2.04254i	0.0229121	−	0.0705162i	−0.938947	−	0.344063i	$-0.888197\pi$
$839$	0.663661	−	2.04254i	0.0229121	−	0.0705162i	0.961859	+	0.273546i	$0.0881967\pi$
$840$	0.563761	+	1.73508i	0.0194516	+	0.0598659i
$841$	2.69883	−	1.96081i	0.0930630	−	0.0676142i
$842$	30.3511	−	22.0513i	1.04597	−	0.759940i
$843$	11.5395	+	35.5149i	0.397441	+	1.22320i
$844$	−5.11760	+	15.7504i	−0.176155	+	0.542150i
$845$	−6.55045	−	4.75918i	−0.225342	−	0.163721i
$846$	1.38820			0.0477274
$847$	−7.13518	−	8.37193i	−0.245168	−	0.287663i
$848$	−9.33444			−0.320546
$849$	7.78240	+	5.65424i	0.267091	+	0.194053i
$850$	−2.46175	+	7.57648i	−0.0844372	+	0.259871i
$851$	8.13061	+	25.0234i	0.278714	+	0.857792i
$852$	0.0298687	−	0.0217009i	0.00102328	−	0.000743459i
$853$	−8.12808	+	5.90540i	−0.278300	+	0.202197i	−0.718176	−	0.695862i	$-0.755023\pi$
$853$	−8.12808	+	5.90540i	−0.278300	+	0.202197i	0.439875	+	0.898059i	$0.355023\pi$
$854$	−3.92128	−	12.0685i	−0.134184	−	0.412975i
$855$	0.0928998	−	0.285916i	0.00317711	−	0.00977813i
$856$	3.45957	+	2.51353i	0.118246	+	0.0859106i
$857$	−27.9578			−0.955019			−0.477510	−	0.878626i	$-0.658460\pi$
$857$	−27.9578			−0.955019			−0.477510	+	0.878626i	$0.658460\pi$
$858$	−2.60701	−	13.1422i	−0.0890017	−	0.448667i
$859$	−20.7449			−0.707805			−0.353903	−	0.935282i	$-0.615146\pi$
$859$	−20.7449			−0.707805			−0.353903	+	0.935282i	$0.615146\pi$
$860$	2.24055	+	1.62785i	0.0764020	+	0.0555093i
$861$	5.07359	−	15.6149i	0.172907	−	0.532154i
$862$	−1.98947	−	6.12294i	−0.0677615	−	0.208548i
$863$	−1.64603	+	1.19591i	−0.0560314	+	0.0407092i	−0.615448	−	0.788177i	$-0.711025\pi$
$863$	−1.64603	+	1.19591i	−0.0560314	+	0.0407092i	0.559417	+	0.828886i	$0.311025\pi$
$864$	−3.94325	+	2.86494i	−0.134152	+	0.0974672i
$865$	4.33992	+	13.3569i	0.147562	+	0.454148i
$866$	4.52643	−	13.9309i	0.153814	−	0.473392i
$867$	68.5772	+	49.8242i	2.32900	+	1.69212i
$868$	9.33892			0.316984
$869$	13.0563	−	28.2824i	0.442904	−	0.959414i
$870$	9.24220			0.313340
$871$	−2.31125	−	1.67922i	−0.0783137	−	0.0568983i
$872$	−1.55826	+	4.79584i	−0.0527695	+	0.162408i
$873$	−0.738033	−	2.27143i	−0.0249786	−	0.0768764i
$874$	4.50199	−	3.27089i	0.152282	−	0.110639i
$875$	0.809017	−	0.587785i	0.0273498	−	0.0198708i
$876$	−6.67846	−	20.5542i	−0.225644	−	0.694461i
$877$	9.97322	−	30.6944i	0.336772	−	1.03648i	−0.629071	−	0.777348i	$-0.716565\pi$
$877$	9.97322	−	30.6944i	0.336772	−	1.03648i	0.965843	−	0.259129i	$-0.0834354\pi$
$878$	25.4503	+	18.4908i	0.858907	+	0.624033i
$879$	−11.6872			−0.394198
$880$	3.29343	+	0.391549i	0.111022	+	0.0131991i
$881$	−3.99069			−0.134450			−0.0672248	−	0.997738i	$-0.521414\pi$
$881$	−3.99069			−0.134450			−0.0672248	+	0.997738i	$0.521414\pi$
$882$	−0.265619	−	0.192984i	−0.00894386	−	0.00649810i
$883$	5.03186	−	15.4865i	0.169336	−	0.521162i	−0.829994	−	0.557772i	$-0.811656\pi$
$883$	5.03186	−	15.4865i	0.169336	−	0.521162i	0.999330	+	0.0366108i	$0.0116562\pi$
$884$	5.45109	+	16.7767i	0.183340	+	0.564262i
$885$	−10.6192	+	7.71533i	−0.356962	+	0.259348i
$886$	25.0801	−	18.2217i	0.842582	−	0.612172i
$887$	−11.5876	−	35.6631i	−0.389075	−	1.19745i	−0.933481	−	0.358627i	$-0.883245\pi$
$887$	−11.5876	−	35.6631i	−0.389075	−	1.19745i	0.544406	−	0.838822i	$-0.316755\pi$
$888$	−2.44073	+	7.51180i	−0.0819055	+	0.252079i
$889$	−11.8780	−	8.62984i	−0.398374	−	0.289436i
$890$	14.2639			0.478126
$891$	−28.5904	+	15.9917i	−0.957813	+	0.535744i
$892$	−19.1235			−0.640301
$893$	3.13213	+	2.27563i	0.104813	+	0.0761509i
$894$	7.59867	−	23.3863i	0.254138	−	0.782155i
$895$	−3.96591	−	12.2058i	−0.132566	−	0.407995i
$896$	−0.809017	+	0.587785i	−0.0270274	+	0.0196365i
$897$	−19.8622	+	14.4307i	−0.663178	+	0.481827i
$898$	5.43754	+	16.7350i	0.181453	+	0.558455i
$899$	14.6198	−	44.9952i	0.487598	−	1.50067i
$900$	−0.265619	−	0.192984i	−0.00885397	−	0.00643279i
$901$	74.3617			2.47735
$902$	−21.9075	−	20.2723i	−0.729441	−	0.674995i
$903$	−5.05253			−0.168138
$904$	−11.1781	−	8.12139i	−0.371779	−	0.270113i
$905$	−5.96003	+	18.3431i	−0.198118	+	0.609745i
$906$	−9.92793	−	30.5550i	−0.329833	−	1.01512i
$907$	−3.36887	+	2.44763i	−0.111861	+	0.0812721i	−0.642310	−	0.766445i	$-0.722024\pi$
$907$	−3.36887	+	2.44763i	−0.111861	+	0.0812721i	0.530448	+	0.847717i	$0.322024\pi$
$908$	−15.9368	+	11.5787i	−0.528880	+	0.384254i
$909$	−0.543085	−	1.67144i	−0.0180130	−	0.0554383i
$910$	0.684262	−	2.10594i	0.0226831	−	0.0698113i
$911$	36.4589	+	26.4889i	1.20794	+	0.877618i	0.995042	−	0.0994571i	$-0.0317106\pi$
$911$	36.4589	+	26.4889i	1.20794	+	0.877618i	0.212896	+	0.977075i	$0.431711\pi$
$912$	1.67049			0.0553154
$913$	1.81982	+	1.68399i	0.0602272	+	0.0557318i
$914$	34.3749			1.13702
$915$	18.7291	+	13.6075i	0.619164	+	0.449849i
$916$	8.52310	−	26.2314i	0.281611	−	0.866710i
$917$	−2.35651	−	7.25258i	−0.0778187	−	0.239501i
$918$	31.4134	−	22.8232i	1.03680	−	0.753278i
$919$	−25.9263	+	18.8365i	−0.855229	+	0.621360i	−0.926583	−	0.376091i	$-0.877268\pi$
$919$	−25.9263	+	18.8365i	−0.855229	+	0.621360i	0.0713537	+	0.997451i	$0.477268\pi$
$920$	−1.87801	−	5.77993i	−0.0619162	−	0.190559i
$921$	−3.02159	+	9.29950i	−0.0995648	+	0.306429i
$922$	8.15139	+	5.92233i	0.268452	+	0.195042i
$923$	−0.0448111			−0.00147497
$924$	−5.28080	+	2.95376i	−0.173726	+	0.0971717i
$925$	4.32937			0.142349
$926$	24.3060	+	17.6593i	0.798744	+	0.580322i
$927$	−1.46036	+	4.49451i	−0.0479644	+	0.147619i
$928$	1.56547	+	4.81803i	0.0513891	+	0.158159i
$929$	−41.3196	+	30.0204i	−1.35565	+	0.984938i	−0.356943	+	0.934126i	$0.616181\pi$
$929$	−41.3196	+	30.0204i	−1.35565	+	0.984938i	−0.998708	+	0.0508124i	$0.983819\pi$
$930$	−13.7837	+	10.0145i	−0.451987	+	0.328388i
$931$	−0.282952	−	0.870838i	−0.00927339	−	0.0285405i
$932$	−4.00063	+	12.3127i	−0.131045	+	0.403315i
$933$	−39.8239	−	28.9337i	−1.30378	−	0.947248i
$934$	−19.7362			−0.645787
$935$	−26.2367	−	3.11923i	−0.858033	−	0.102010i
$936$	−0.727012			−0.0237631
$937$	4.37874	+	3.18134i	0.143047	+	0.103930i	0.657007	−	0.753884i	$-0.271822\pi$
$937$	4.37874	+	3.18134i	0.143047	+	0.103930i	−0.513960	+	0.857814i	$0.671822\pi$
$938$	−0.398687	+	1.22703i	−0.0130176	+	0.0400640i
$939$	16.1029	+	49.5595i	0.525497	+	1.61731i
$940$	3.42065	−	2.48525i	0.111569	−	0.0810599i
$941$	−3.83481	+	2.78616i	−0.125011	+	0.0908261i	−0.648534	−	0.761186i	$-0.724618\pi$
$941$	−3.83481	+	2.78616i	−0.125011	+	0.0908261i	0.523523	+	0.852012i	$0.324618\pi$
$942$	−6.47401	−	19.9249i	−0.210935	−	0.649190i
$943$	−16.9012	+	52.0166i	−0.550380	+	1.69389i
$944$	−5.82078	−	4.22904i	−0.189450	−	0.137644i
$945$	−4.87412			−0.158555
$946$	−3.84987	+	8.33954i	−0.125170	+	0.271142i
$947$	16.4424			0.534306			0.267153	−	0.963654i	$-0.413917\pi$
$947$	16.4424			0.534306			0.267153	+	0.963654i	$0.413917\pi$
$948$	−13.8625	−	10.0717i	−0.450232	−	0.327113i
$949$	−8.10594	+	24.9475i	−0.263130	+	0.809831i
$950$	−0.282952	−	0.870838i	−0.00918018	−	0.0282537i
$951$	31.0062	−	22.5273i	1.00544	−	0.730498i
$952$	6.44494	−	4.68252i	0.208882	−	0.151761i
$953$	14.0914	+	43.3688i	0.456465	+	1.40485i	0.869407	+	0.494097i	$0.164501\pi$
$953$	14.0914	+	43.3688i	0.456465	+	1.40485i	−0.412942	+	0.910757i	$0.635499\pi$
$954$	−0.947049	+	2.91472i	−0.0306618	+	0.0943674i
$955$	−9.71700	−	7.05982i	−0.314435	−	0.228450i
$956$	−5.77626			−0.186818
$957$	5.96438	+	30.0671i	0.192801	+	0.971930i
$958$	5.39968			0.174456
$959$	3.98893	+	2.89813i	0.128809	+	0.0935854i
$960$	0.563761	−	1.73508i	0.0181953	−	0.0559994i
$961$	17.3716	+	53.4641i	0.560373	+	1.72465i
$962$	7.75572	−	5.63486i	0.250055	−	0.181675i
$963$	1.13586	−	0.825250i	0.0366025	−	0.0265933i
$964$	−7.73541	−	23.8071i	−0.249141	−	0.766777i
$965$	5.34595	−	16.4531i	0.172092	−	0.529645i
$966$	8.96987	+	6.51700i	0.288601	+	0.209681i
$967$	28.9513			0.931012			0.465506	−	0.885045i	$-0.345872\pi$
$967$	28.9513			0.931012			0.465506	+	0.885045i	$0.345872\pi$
$968$	0.851587	+	10.9670i	0.0273711	+	0.352492i
$969$	−13.3077			−0.427506
$970$	−5.88504	−	4.27573i	−0.188957	−	0.137285i
$971$	2.19389	−	6.75211i	0.0704054	−	0.216685i	−0.909663	−	0.415348i	$-0.863660\pi$
$971$	2.19389	−	6.75211i	0.0704054	−	0.216685i	0.980068	+	0.198663i	$0.0636598\pi$
$972$	1.04980	+	3.23097i	0.0336725	+	0.103633i
$973$	3.37941	−	2.45529i	0.108339	−	0.0787129i
$974$	10.2467	−	7.44465i	0.328325	−	0.238542i
$975$	1.24835	+	3.84201i	0.0399791	+	0.123043i
$976$	−3.92128	+	12.0685i	−0.125517	+	0.386302i
$977$	0.0134994	+	0.00980786i	0.000431883	+	0.000313781i	0.588001	−	0.808860i	$-0.299915\pi$
$977$	0.0134994	+	0.00980786i	0.000431883	+	0.000313781i	−0.587569	+	0.809174i	$0.699915\pi$
$978$	0.254044			0.00812343
$979$	9.20506	+	46.4037i	0.294195	+	1.48307i
$980$	−1.00000			−0.0319438
$981$	1.33942	+	0.973149i	0.0427645	+	0.0310702i
$982$	−8.89324	+	27.3706i	−0.283795	+	0.873430i
$983$	−9.38129	−	28.8727i	−0.299217	−	0.920895i	−0.981772	−	0.190061i	$-0.939131\pi$
$983$	−9.38129	−	28.8727i	−0.299217	−	0.920895i	0.682555	−	0.730834i	$-0.260869\pi$
$984$	−13.2828	+	9.65054i	−0.423441	+	0.307648i
$985$	−10.6567	+	7.74256i	−0.339551	+	0.246699i
$986$	−12.4711	−	38.3822i	−0.397162	−	1.22234i
$987$	−2.38367	+	7.33619i	−0.0758731	+	0.233513i
$988$	−1.64032	−	1.19176i	−0.0521855	−	0.0379150i
$989$	16.8311			0.535197
$990$	0.456406	−	0.988662i	0.0145055	−	0.0314217i
$991$	−55.9611			−1.77766			−0.888831	−	0.458234i	$-0.848482\pi$
$991$	−55.9611			−1.77766			−0.888831	+	0.458234i	$0.848482\pi$
$992$	−7.55535	−	5.48928i	−0.239883	−	0.174285i
$993$	−6.54089	+	20.1308i	−0.207569	+	0.638831i
$994$	0.00625357	+	0.0192465i	0.000198351	+	0.000610462i
$995$	−18.5895	+	13.5061i	−0.589328	+	0.428172i
$996$	1.10338	−	0.801652i	0.0349619	−	0.0254013i
$997$	14.3488	+	44.1610i	0.454431	+	1.39859i	0.871802	+	0.489858i	$0.162951\pi$
$997$	14.3488	+	44.1610i	0.454431	+	1.39859i	−0.417372	+	0.908736i	$0.637049\pi$
$998$	−5.99053	+	18.4370i	−0.189627	+	0.583611i
$999$	−17.0718	−	12.4034i	−0.540127	−	0.392426i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.h.631.2	yes	12
11.3	even	5	inner	770.2.n.h.421.2	✓	12
11.5	even	5		8470.2.a.da.1.3		6
11.6	odd	10		8470.2.a.cu.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.h.421.2	✓	12	11.3	even	5	inner
770.2.n.h.631.2	yes	12	1.1	even	1	trivial
8470.2.a.cu.1.3		6	11.6	odd	10
8470.2.a.da.1.3		6	11.5	even	5

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.563761 + 1.73508i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(1.47595 - 1.07234i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.265619 - 0.192984i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.563761 + 1.73508i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(1.47595 - 1.07234i) q^{6} +(0.309017 + 0.951057i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.265619 - 0.192984i) q^{9} -1.00000 q^{10} +(-0.645341 - 3.25323i) q^{11} -1.82437 q^{12} +(1.79142 + 1.30154i) q^{13} +(0.309017 - 0.951057i) q^{14} +(0.563761 + 1.73508i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(6.44494 - 4.68252i) q^{17} +(0.101458 + 0.312254i) q^{18} +(-0.282952 + 0.870838i) q^{19} +(0.809017 + 0.587785i) q^{20} -1.82437 q^{21} +(-1.39011 + 3.01124i) q^{22} +6.07737 q^{23} +(1.47595 + 1.07234i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-0.684262 - 2.10594i) q^{26} +(-3.94325 + 2.86494i) q^{27} +(-0.809017 + 0.587785i) q^{28} +(1.56547 + 4.81803i) q^{29} +(0.563761 - 1.73508i) q^{30} +(-7.55535 - 5.48928i) q^{31} +1.00000 q^{32} +(6.00843 + 0.714329i) q^{33} -7.96638 q^{34} +(0.809017 + 0.587785i) q^{35} +(0.101458 - 0.312254i) q^{36} +(1.33785 + 4.11748i) q^{37} +(0.740779 - 0.538207i) q^{38} +(-3.26821 + 2.37450i) q^{39} +(-0.309017 - 0.951057i) q^{40} +(-2.78101 + 8.55906i) q^{41} +(1.47595 + 1.07234i) q^{42} +2.76947 q^{43} +(2.89459 - 1.61906i) q^{44} -0.328323 q^{45} +(-4.91670 - 3.57219i) q^{46} +(1.30657 - 4.02122i) q^{47} +(-0.563761 - 1.73508i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(4.49114 + 13.8223i) q^{51} +(-0.684262 + 2.10594i) q^{52} +(7.55172 + 5.48664i) q^{53} +4.87412 q^{54} +(-2.43430 - 2.25260i) q^{55} +1.00000 q^{56} +(-1.35145 - 0.981889i) q^{57} +(1.56547 - 4.81803i) q^{58} +(2.22334 + 6.84273i) q^{59} +(-1.47595 + 1.07234i) q^{60} +(10.2661 - 7.45872i) q^{61} +(2.88589 + 8.88185i) q^{62} +(0.101458 - 0.312254i) q^{63} +(-0.809017 - 0.587785i) q^{64} +2.21432 q^{65} +(-4.44105 - 4.10957i) q^{66} -1.29018 q^{67} +(6.44494 + 4.68252i) q^{68} +(-3.42619 + 10.5447i) q^{69} +(-0.309017 - 0.951057i) q^{70} +(-0.0163721 + 0.0118950i) q^{71} +(-0.265619 + 0.192984i) q^{72} +(3.66069 + 11.2665i) q^{73} +(1.33785 - 4.11748i) q^{74} +(1.47595 + 1.07234i) q^{75} -0.915653 q^{76} +(2.89459 - 1.61906i) q^{77} +4.03973 q^{78} +(7.59849 + 5.52063i) q^{79} +(-0.309017 + 0.951057i) q^{80} +(-3.05221 - 9.39375i) q^{81} +(7.28078 - 5.28979i) q^{82} +(-0.604801 + 0.439413i) q^{83} +(-0.563761 - 1.73508i) q^{84} +(2.46175 - 7.57648i) q^{85} +(-2.24055 - 1.62785i) q^{86} -9.24220 q^{87} +(-3.29343 - 0.391549i) q^{88} -14.2639 q^{89} +(0.265619 + 0.192984i) q^{90} +(-0.684262 + 2.10594i) q^{91} +(1.87801 + 5.77993i) q^{92} +(13.7837 - 10.0145i) q^{93} +(-3.42065 + 2.48525i) q^{94} +(0.282952 + 0.870838i) q^{95} +(-0.563761 + 1.73508i) q^{96} +(5.88504 + 4.27573i) q^{97} +1.00000 q^{98} +(-0.456406 + 0.988662i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 5 q^{6} - 3 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 5 * q^6 - 3 * q^7 - 3 * q^8 - 3 * q^9	\( 12 q - 3 q^{2} - 3 q^{4} + 3 q^{5} + 5 q^{6} - 3 q^{7} - 3 q^{8} - 3 q^{9} - 12 q^{10} - q^{11} - 10 q^{12} - 3 q^{14} - 3 q^{16} - 8 q^{18} - q^{19} + 3 q^{20} - 10 q^{21} - q^{22} - 4 q^{23} + 5 q^{24} - 3 q^{25} + 3 q^{27} - 3 q^{28} + 22 q^{29} + 6 q^{31} + 12 q^{32} - 29 q^{33} - 30 q^{34} + 3 q^{35} - 8 q^{36} - 10 q^{37} + 14 q^{38} + 20 q^{39} + 3 q^{40} + 16 q^{41} + 5 q^{42} + 30 q^{43} + 14 q^{44} - 22 q^{45} - 4 q^{46} + 34 q^{47} - 3 q^{49} - 3 q^{50} + 37 q^{51} - 26 q^{53} - 52 q^{54} + 11 q^{55} + 12 q^{56} - 19 q^{57} + 22 q^{58} + q^{59} - 5 q^{60} + 40 q^{61} - 4 q^{62} - 8 q^{63} - 3 q^{64} + 16 q^{66} - 58 q^{67} + 14 q^{69} + 3 q^{70} - 14 q^{71} - 3 q^{72} + 32 q^{73} - 10 q^{74} + 5 q^{75} - 26 q^{76} + 14 q^{77} - 60 q^{78} + 16 q^{79} + 3 q^{80} - 46 q^{81} + q^{82} + 35 q^{83} - 15 q^{85} + 5 q^{86} - q^{88} - 58 q^{89} + 3 q^{90} + 6 q^{92} + 46 q^{93} - 16 q^{94} + q^{95} + 57 q^{97} + 12 q^{98} + 69 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^4 + 3 * q^5 + 5 * q^6 - 3 * q^7 - 3 * q^8 - 3 * q^9 - 12 * q^10 - q^11 - 10 * q^12 - 3 * q^14 - 3 * q^16 - 8 * q^18 - q^19 + 3 * q^20 - 10 * q^21 - q^22 - 4 * q^23 + 5 * q^24 - 3 * q^25 + 3 * q^27 - 3 * q^28 + 22 * q^29 + 6 * q^31 + 12 * q^32 - 29 * q^33 - 30 * q^34 + 3 * q^35 - 8 * q^36 - 10 * q^37 + 14 * q^38 + 20 * q^39 + 3 * q^40 + 16 * q^41 + 5 * q^42 + 30 * q^43 + 14 * q^44 - 22 * q^45 - 4 * q^46 + 34 * q^47 - 3 * q^49 - 3 * q^50 + 37 * q^51 - 26 * q^53 - 52 * q^54 + 11 * q^55 + 12 * q^56 - 19 * q^57 + 22 * q^58 + q^59 - 5 * q^60 + 40 * q^61 - 4 * q^62 - 8 * q^63 - 3 * q^64 + 16 * q^66 - 58 * q^67 + 14 * q^69 + 3 * q^70 - 14 * q^71 - 3 * q^72 + 32 * q^73 - 10 * q^74 + 5 * q^75 - 26 * q^76 + 14 * q^77 - 60 * q^78 + 16 * q^79 + 3 * q^80 - 46 * q^81 + q^82 + 35 * q^83 - 15 * q^85 + 5 * q^86 - q^88 - 58 * q^89 + 3 * q^90 + 6 * q^92 + 46 * q^93 - 16 * q^94 + q^95 + 57 * q^97 + 12 * q^98 + 69 * q^99

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