LMFDB - Embedded newform 630.2.i.f.121.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(121,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 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("630.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.i (of order $3$, degree $2$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	12.0.91830304992969.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + x^{10} + 4x^{9} - 7x^{8} + x^{7} + 7x^{6} + 2x^{5} - 28x^{4} + 32x^{3} + 16x^{2} - 64x + 64 $ x^12 - 2x^11 + x^10 + 4x^9 - 7x^8 + x^7 + 7x^6 + 2x^5 - 28x^4 + 32x^3 + 16x^2 - 64*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.6
Root			$0.309529 + 1.37992i$ of defining polynomial
Character	$\chi$	$=$	630.121
Dual form			630.2.i.f.151.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(1.72817 + 0.115916i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.72817 - 0.115916i) q^{6} +(1.23855 - 2.33795i) q^{7} -1.00000 q^{8} +(2.97313 + 0.400645i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(1.72817 + 0.115916i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.72817 - 0.115916i) q^{6} +(1.23855 - 2.33795i) q^{7} -1.00000 q^{8} +(2.97313 + 0.400645i) q^{9} +(0.500000 + 0.866025i) q^{10} +(1.85703 - 3.21646i) q^{11} +(1.72817 + 0.115916i) q^{12} +(-1.26810 + 2.19641i) q^{13} +(-1.23855 + 2.33795i) q^{14} +(-0.763698 - 1.55460i) q^{15} +1.00000 q^{16} +(-1.48113 - 2.56539i) q^{17} +(-2.97313 - 0.400645i) q^{18} +(-1.26810 + 2.19641i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(2.41143 - 3.89680i) q^{21} +(-1.85703 + 3.21646i) q^{22} +(-1.21303 - 2.10103i) q^{23} +(-1.72817 - 0.115916i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.26810 - 2.19641i) q^{26} +(5.09162 + 1.03701i) q^{27} +(1.23855 - 2.33795i) q^{28} +(-5.04131 - 8.73180i) q^{29} +(0.763698 + 1.55460i) q^{30} +9.87519 q^{31} -1.00000 q^{32} +(3.58209 - 5.34333i) q^{33} +(1.48113 + 2.56539i) q^{34} +(-2.64400 + 0.0963576i) q^{35} +(2.97313 + 0.400645i) q^{36} +(1.36906 - 2.37128i) q^{37} +(1.26810 - 2.19641i) q^{38} +(-2.44609 + 3.64877i) q^{39} +(0.500000 + 0.866025i) q^{40} +(-5.50745 + 9.53918i) q^{41} +(-2.41143 + 3.89680i) q^{42} +(1.65213 + 2.86157i) q^{43} +(1.85703 - 3.21646i) q^{44} +(-1.13960 - 2.77513i) q^{45} +(1.21303 + 2.10103i) q^{46} -0.695738 q^{47} +(1.72817 + 0.115916i) q^{48} +(-3.93199 - 5.79133i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-2.26227 - 4.60511i) q^{51} +(-1.26810 + 2.19641i) q^{52} +(4.25802 + 7.37510i) q^{53} +(-5.09162 - 1.03701i) q^{54} -3.71405 q^{55} +(-1.23855 + 2.33795i) q^{56} +(-2.44609 + 3.64877i) q^{57} +(5.04131 + 8.73180i) q^{58} +12.2301 q^{59} +(-0.763698 - 1.55460i) q^{60} +12.5327 q^{61} -9.87519 q^{62} +(4.61905 - 6.45479i) q^{63} +1.00000 q^{64} +2.53620 q^{65} +(-3.58209 + 5.34333i) q^{66} -10.3227 q^{67} +(-1.48113 - 2.56539i) q^{68} +(-1.85278 - 3.77154i) q^{69} +(2.64400 - 0.0963576i) q^{70} +2.43471 q^{71} +(-2.97313 - 0.400645i) q^{72} +(0.729393 + 1.26335i) q^{73} +(-1.36906 + 2.37128i) q^{74} +(-0.964470 + 1.43868i) q^{75} +(-1.26810 + 2.19641i) q^{76} +(-5.21990 - 8.32538i) q^{77} +(2.44609 - 3.64877i) q^{78} +2.27946 q^{79} +(-0.500000 - 0.866025i) q^{80} +(8.67897 + 2.38233i) q^{81} +(5.50745 - 9.53918i) q^{82} +(-5.39560 - 9.34546i) q^{83} +(2.41143 - 3.89680i) q^{84} +(-1.48113 + 2.56539i) q^{85} +(-1.65213 - 2.86157i) q^{86} +(-7.70007 - 15.6744i) q^{87} +(-1.85703 + 3.21646i) q^{88} +(-7.50572 + 13.0003i) q^{89} +(1.13960 + 2.77513i) q^{90} +(3.56449 + 5.68511i) q^{91} +(-1.21303 - 2.10103i) q^{92} +(17.0660 + 1.14469i) q^{93} +0.695738 q^{94} +2.53620 q^{95} +(-1.72817 - 0.115916i) q^{96} +(0.0494422 + 0.0856364i) q^{97} +(3.93199 + 5.79133i) q^{98} +(6.80983 - 8.81895i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 2 q^{3} + 12 q^{4} - 6 q^{5} - 2 q^{6} + 4 q^{7} - 12 q^{8} - 4 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 + 2 * q^3 + 12 * q^4 - 6 * q^5 - 2 * q^6 + 4 * q^7 - 12 * q^8 - 4 * q^9	\( 12 q - 12 q^{2} + 2 q^{3} + 12 q^{4} - 6 q^{5} - 2 q^{6} + 4 q^{7} - 12 q^{8} - 4 q^{9} + 6 q^{10} - 7 q^{11} + 2 q^{12} - 2 q^{13} - 4 q^{14} - q^{15} + 12 q^{16} + q^{17} + 4 q^{18} - 2 q^{19} - 6 q^{20} + 29 q^{21} + 7 q^{22} - 9 q^{23} - 2 q^{24} - 6 q^{25} + 2 q^{26} + 11 q^{27} + 4 q^{28} + 3 q^{29} + q^{30} + 18 q^{31} - 12 q^{32} + 27 q^{33} - q^{34} - 8 q^{35} - 4 q^{36} + 6 q^{37} + 2 q^{38} + 10 q^{39} + 6 q^{40} - 11 q^{41} - 29 q^{42} + 23 q^{43} - 7 q^{44} + 5 q^{45} + 9 q^{46} - 2 q^{47} + 2 q^{48} + 24 q^{49} + 6 q^{50} - 15 q^{51} - 2 q^{52} - 4 q^{53} - 11 q^{54} + 14 q^{55} - 4 q^{56} + 10 q^{57} - 3 q^{58} - 22 q^{59} - q^{60} + 50 q^{61} - 18 q^{62} - q^{63} + 12 q^{64} + 4 q^{65} - 27 q^{66} + 4 q^{67} + q^{68} - 12 q^{69} + 8 q^{70} + 22 q^{71} + 4 q^{72} + 24 q^{73} - 6 q^{74} - q^{75} - 2 q^{76} - 11 q^{77} - 10 q^{78} + 2 q^{79} - 6 q^{80} + 20 q^{81} + 11 q^{82} + 4 q^{83} + 29 q^{84} + q^{85} - 23 q^{86} + 7 q^{88} + 2 q^{89} - 5 q^{90} - 8 q^{91} - 9 q^{92} + 40 q^{93} + 2 q^{94} + 4 q^{95} - 2 q^{96} - 36 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 2 * q^3 + 12 * q^4 - 6 * q^5 - 2 * q^6 + 4 * q^7 - 12 * q^8 - 4 * q^9 + 6 * q^10 - 7 * q^11 + 2 * q^12 - 2 * q^13 - 4 * q^14 - q^15 + 12 * q^16 + q^17 + 4 * q^18 - 2 * q^19 - 6 * q^20 + 29 * q^21 + 7 * q^22 - 9 * q^23 - 2 * q^24 - 6 * q^25 + 2 * q^26 + 11 * q^27 + 4 * q^28 + 3 * q^29 + q^30 + 18 * q^31 - 12 * q^32 + 27 * q^33 - q^34 - 8 * q^35 - 4 * q^36 + 6 * q^37 + 2 * q^38 + 10 * q^39 + 6 * q^40 - 11 * q^41 - 29 * q^42 + 23 * q^43 - 7 * q^44 + 5 * q^45 + 9 * q^46 - 2 * q^47 + 2 * q^48 + 24 * q^49 + 6 * q^50 - 15 * q^51 - 2 * q^52 - 4 * q^53 - 11 * q^54 + 14 * q^55 - 4 * q^56 + 10 * q^57 - 3 * q^58 - 22 * q^59 - q^60 + 50 * q^61 - 18 * q^62 - q^63 + 12 * q^64 + 4 * q^65 - 27 * q^66 + 4 * q^67 + q^68 - 12 * q^69 + 8 * q^70 + 22 * q^71 + 4 * q^72 + 24 * q^73 - 6 * q^74 - q^75 - 2 * q^76 - 11 * q^77 - 10 * q^78 + 2 * q^79 - 6 * q^80 + 20 * q^81 + 11 * q^82 + 4 * q^83 + 29 * q^84 + q^85 - 23 * q^86 + 7 * q^88 + 2 * q^89 - 5 * q^90 - 8 * q^91 - 9 * q^92 + 40 * q^93 + 2 * q^94 + 4 * q^95 - 2 * q^96 - 36 * q^97 - 24 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	1.72817	+	0.115916i	0.997758	+	0.0669241i
$3$	1.72817	+	0.115916i	0.997758	+	0.0669241i
$4$	1.00000			0.500000
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−1.72817	−	0.115916i	−0.705521	−	0.0473225i
$7$	1.23855	−	2.33795i	0.468128	−	0.883661i
$7$	1.23855	−	2.33795i	0.468128	−	0.883661i
$8$	−1.00000			−0.353553
$9$	2.97313	+	0.400645i	0.991042	+	0.133548i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	1.85703	−	3.21646i	0.559914	−	0.969800i	−0.437589	−	0.899175i	$-0.644167\pi$
$11$	1.85703	−	3.21646i	0.559914	−	0.969800i	0.997503	−	0.0706248i	$-0.0224993\pi$
$12$	1.72817	+	0.115916i	0.498879	+	0.0334621i
$13$	−1.26810	+	2.19641i	−0.351707	+	0.609175i	−0.986549	−	0.163468i	$-0.947732\pi$
$13$	−1.26810	+	2.19641i	−0.351707	+	0.609175i	0.634841	+	0.772642i	$0.281065\pi$
$14$	−1.23855	+	2.33795i	−0.331016	+	0.624843i
$15$	−0.763698	−	1.55460i	−0.197186	−	0.401395i
$16$	1.00000			0.250000
$17$	−1.48113	−	2.56539i	−0.359226	−	0.622198i	0.628605	−	0.777724i	$-0.283626\pi$
$17$	−1.48113	−	2.56539i	−0.359226	−	0.622198i	−0.987832	+	0.155526i	$0.950293\pi$
$18$	−2.97313	−	0.400645i	−0.700773	−	0.0944328i
$19$	−1.26810	+	2.19641i	−0.290922	+	0.503891i	−0.974028	−	0.226428i	$-0.927295\pi$
$19$	−1.26810	+	2.19641i	−0.290922	+	0.503891i	0.683106	+	0.730319i	$0.260629\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	2.41143	−	3.89680i	0.526217	−	0.850351i
$22$	−1.85703	+	3.21646i	−0.395919	+	0.685752i
$23$	−1.21303	−	2.10103i	−0.252934	−	0.438095i	0.711398	−	0.702789i	$-0.248062\pi$
$23$	−1.21303	−	2.10103i	−0.252934	−	0.438095i	−0.964332	+	0.264694i	$0.914729\pi$
$24$	−1.72817	−	0.115916i	−0.352761	−	0.0236613i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.26810	−	2.19641i	0.248695	−	0.430752i
$27$	5.09162	+	1.03701i	0.979883	+	0.199573i
$28$	1.23855	−	2.33795i	0.234064	−	0.441830i
$29$	−5.04131	−	8.73180i	−0.936147	−	1.62145i	−0.772575	−	0.634923i	$-0.781032\pi$
$29$	−5.04131	−	8.73180i	−0.936147	−	1.62145i	−0.163572	−	0.986531i	$-0.552302\pi$
$30$	0.763698	+	1.55460i	0.139431	+	0.283829i
$31$	9.87519			1.77364			0.886819	−	0.462118i	$-0.152910\pi$
$31$	9.87519			1.77364			0.886819	+	0.462118i	$0.152910\pi$
$32$	−1.00000			−0.176777
$33$	3.58209	−	5.34333i	0.623562	−	0.930154i
$34$	1.48113	+	2.56539i	0.254011	+	0.439961i
$35$	−2.64400	+	0.0963576i	−0.446917	+	0.0162874i
$36$	2.97313	+	0.400645i	0.495521	+	0.0667741i
$37$	1.36906	−	2.37128i	0.225072	−	0.389837i	−0.731269	−	0.682089i	$-0.761071\pi$
$37$	1.36906	−	2.37128i	0.225072	−	0.389837i	0.956341	+	0.292253i	$0.0944048\pi$
$38$	1.26810	−	2.19641i	0.205713	−	0.356305i
$39$	−2.44609	+	3.64877i	−0.391687	+	0.584271i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−5.50745	+	9.53918i	−0.860119	+	1.48977i	0.0116943	+	0.999932i	$0.496278\pi$
$41$	−5.50745	+	9.53918i	−0.860119	+	1.48977i	−0.871813	+	0.489838i	$0.837056\pi$
$42$	−2.41143	+	3.89680i	−0.372091	+	0.601289i
$43$	1.65213	+	2.86157i	0.251948	+	0.436386i	0.964062	−	0.265677i	$-0.0855956\pi$
$43$	1.65213	+	2.86157i	0.251948	+	0.436386i	−0.712114	+	0.702063i	$0.752262\pi$
$44$	1.85703	−	3.21646i	0.279957	−	0.484900i
$45$	−1.13960	−	2.77513i	−0.169881	−	0.413691i
$46$	1.21303	+	2.10103i	0.178851	+	0.309780i
$47$	−0.695738			−0.101484			−0.0507419	−	0.998712i	$-0.516159\pi$
$47$	−0.695738			−0.101484			−0.0507419	+	0.998712i	$0.516159\pi$
$48$	1.72817	+	0.115916i	0.249440	+	0.0167310i
$49$	−3.93199	−	5.79133i	−0.561713	−	0.827332i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−2.26227	−	4.60511i	−0.316781	−	0.644844i
$52$	−1.26810	+	2.19641i	−0.175854	+	0.304587i
$53$	4.25802	+	7.37510i	0.584884	+	1.01305i	0.994890	+	0.100965i	$0.0321932\pi$
$53$	4.25802	+	7.37510i	0.584884	+	1.01305i	−0.410006	+	0.912083i	$0.634473\pi$
$54$	−5.09162	−	1.03701i	−0.692882	−	0.141120i
$55$	−3.71405			−0.500803
$56$	−1.23855	+	2.33795i	−0.165508	+	0.312421i
$57$	−2.44609	+	3.64877i	−0.323992	+	0.483292i
$58$	5.04131	+	8.73180i	0.661956	+	1.14654i
$59$	12.2301			1.59222			0.796111	−	0.605151i	$-0.206887\pi$
$59$	12.2301			1.59222			0.796111	+	0.605151i	$0.206887\pi$
$60$	−0.763698	−	1.55460i	−0.0985929	−	0.200697i
$61$	12.5327			1.60465			0.802327	−	0.596885i	$-0.203595\pi$
$61$	12.5327			1.60465			0.802327	+	0.596885i	$0.203595\pi$
$62$	−9.87519			−1.25415
$63$	4.61905	−	6.45479i	0.581946	−	0.813228i
$64$	1.00000			0.125000
$65$	2.53620			0.314577
$66$	−3.58209	+	5.34333i	−0.440925	+	0.657718i
$67$	−10.3227			−1.26112			−0.630561	−	0.776140i	$-0.717175\pi$
$67$	−10.3227			−1.26112			−0.630561	+	0.776140i	$0.717175\pi$
$68$	−1.48113	−	2.56539i	−0.179613	−	0.311099i
$69$	−1.85278	−	3.77154i	−0.223048	−	0.454040i
$70$	2.64400	−	0.0963576i	0.316018	−	0.0115169i
$71$	2.43471			0.288947			0.144474	−	0.989509i	$-0.453851\pi$
$71$	2.43471			0.288947			0.144474	+	0.989509i	$0.453851\pi$
$72$	−2.97313	−	0.400645i	−0.350386	−	0.0472164i
$73$	0.729393	+	1.26335i	0.0853690	+	0.147863i	0.905548	−	0.424243i	$-0.139460\pi$
$73$	0.729393	+	1.26335i	0.0853690	+	0.147863i	−0.820179	+	0.572106i	$0.806126\pi$
$74$	−1.36906	+	2.37128i	−0.159150	+	0.275656i
$75$	−0.964470	+	1.43868i	−0.111367	+	0.166124i
$76$	−1.26810	+	2.19641i	−0.145461	+	0.251946i
$77$	−5.21990	−	8.32538i	−0.594863	−	0.948765i
$78$	2.44609	−	3.64877i	0.276965	−	0.413142i
$79$	2.27946			0.256459			0.128229	−	0.991745i	$-0.459071\pi$
$79$	2.27946			0.256459			0.128229	+	0.991745i	$0.459071\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	8.67897	+	2.38233i	0.964330	+	0.264704i
$82$	5.50745	−	9.53918i	0.608196	−	1.05343i
$83$	−5.39560	−	9.34546i	−0.592244	−	1.02580i	−0.993929	−	0.110020i	$-0.964909\pi$
$83$	−5.39560	−	9.34546i	−0.592244	−	1.02580i	0.401685	−	0.915778i	$-0.368425\pi$
$84$	2.41143	−	3.89680i	0.263108	−	0.425175i
$85$	−1.48113	+	2.56539i	−0.160651	+	0.278256i
$86$	−1.65213	−	2.86157i	−0.178154	−	0.308572i
$87$	−7.70007	−	15.6744i	−0.825534	−	1.68047i
$88$	−1.85703	+	3.21646i	−0.197960	+	0.342876i
$89$	−7.50572	+	13.0003i	−0.795605	+	1.37803i	0.126849	+	0.991922i	$0.459514\pi$
$89$	−7.50572	+	13.0003i	−0.795605	+	1.37803i	−0.922454	+	0.386106i	$0.873820\pi$
$90$	1.13960	+	2.77513i	0.120124	+	0.292524i
$91$	3.56449	+	5.68511i	0.373660	+	0.595962i
$92$	−1.21303	−	2.10103i	−0.126467	−	0.219047i
$93$	17.0660	+	1.14469i	1.76966	+	0.118699i
$94$	0.695738			0.0717599
$95$	2.53620			0.260208
$96$	−1.72817	−	0.115916i	−0.176380	−	0.0118306i
$97$	0.0494422	+	0.0856364i	0.00502010	+	0.00869506i	0.868525	−	0.495646i	$-0.165069\pi$
$97$	0.0494422	+	0.0856364i	0.00502010	+	0.00869506i	−0.863504	+	0.504341i	$0.831735\pi$
$98$	3.93199	+	5.79133i	0.397191	+	0.585012i
$99$	6.80983	−	8.81895i	0.684414	−	0.886337i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	5.29440	−	9.17017i	0.526813	−	0.912466i	−0.472699	−	0.881224i	$-0.656720\pi$
$101$	5.29440	−	9.17017i	0.526813	−	0.912466i	0.999512	−	0.0312424i	$-0.00994639\pi$
$102$	2.26227	+	4.60511i	0.223998	+	0.455974i
$103$	−2.80875	−	4.86490i	−0.276754	−	0.479353i	0.693822	−	0.720147i	$-0.255926\pi$
$103$	−2.80875	−	4.86490i	−0.276754	−	0.479353i	−0.970576	+	0.240794i	$0.922592\pi$
$104$	1.26810	−	2.19641i	0.124347	−	0.215376i
$105$	−4.58044	−	0.139959i	−0.447005	−	0.0136586i
$106$	−4.25802	−	7.37510i	−0.413575	−	0.716333i
$107$	−7.95511	+	13.7787i	−0.769049	+	1.33203i	0.169029	+	0.985611i	$0.445937\pi$
$107$	−7.95511	+	13.7787i	−0.769049	+	1.33203i	−0.938079	+	0.346422i	$0.887397\pi$
$108$	5.09162	+	1.03701i	0.489941	+	0.0997867i
$109$	5.34068	+	9.25033i	0.511544	+	0.886021i	0.999910	+	0.0133820i	$0.00425975\pi$
$109$	5.34068	+	9.25033i	0.511544	+	0.886021i	−0.488366	+	0.872639i	$0.662407\pi$
$110$	3.71405			0.354121
$111$	2.64084	−	3.93928i	0.250657	−	0.373900i
$112$	1.23855	−	2.33795i	0.117032	−	0.220915i
$113$	3.45901	−	5.99118i	0.325396	−	0.563603i	−0.656196	−	0.754590i	$-0.727836\pi$
$113$	3.45901	−	5.99118i	0.325396	−	0.563603i	0.981593	+	0.190987i	$0.0611689\pi$
$114$	2.44609	−	3.64877i	0.229097	−	0.341739i
$115$	−1.21303	+	2.10103i	−0.113116	+	0.195922i
$116$	−5.04131	−	8.73180i	−0.468074	−	0.810727i
$117$	−4.65020	+	6.02215i	−0.429911	+	0.556748i
$118$	−12.2301			−1.12587
$119$	−7.83220	+	0.285436i	−0.717976	+	0.0261659i
$120$	0.763698	+	1.55460i	0.0697157	+	0.141914i
$121$	−1.39709	−	2.41983i	−0.127008	−	0.219985i
$122$	−12.5327			−1.13466
$123$	−10.6235	+	15.8469i	−0.957892	+	1.42887i
$124$	9.87519			0.886819
$125$	1.00000			0.0894427
$126$	−4.61905	+	6.45479i	−0.411498	+	0.575039i
$127$	−16.7729			−1.48835			−0.744175	−	0.667984i	$-0.767157\pi$
$127$	−16.7729			−1.48835			−0.744175	+	0.667984i	$0.767157\pi$
$128$	−1.00000			−0.0883883
$129$	2.52346	+	5.13679i	0.222178	+	0.452269i
$130$	−2.53620			−0.222439
$131$	8.02229	+	13.8950i	0.700911	+	1.21401i	0.968147	+	0.250382i	$0.0805562\pi$
$131$	8.02229	+	13.8950i	0.700911	+	1.21401i	−0.267236	+	0.963631i	$0.586110\pi$
$132$	3.58209	−	5.34333i	0.311781	−	0.465077i
$133$	3.56449	+	5.68511i	0.309080	+	0.492962i
$134$	10.3227			0.891748
$135$	−1.64773	−	4.92798i	−0.141814	−	0.424133i
$136$	1.48113	+	2.56539i	0.127006	+	0.219980i
$137$	−4.24243	+	7.34811i	−0.362456	+	0.627791i	−0.988364	−	0.152105i	$-0.951395\pi$
$137$	−4.24243	+	7.34811i	−0.362456	+	0.627791i	0.625909	+	0.779896i	$0.284728\pi$
$138$	1.85278	+	3.77154i	0.157719	+	0.321055i
$139$	−1.67921	+	2.90848i	−0.142429	+	0.246694i	−0.928411	−	0.371555i	$-0.878825\pi$
$139$	−1.67921	+	2.90848i	−0.142429	+	0.246694i	0.785982	+	0.618250i	$0.212158\pi$
$140$	−2.64400	+	0.0963576i	−0.223458	+	0.00814370i
$141$	−1.20235	−	0.0806472i	−0.101256	−	0.00679172i
$142$	−2.43471			−0.204317
$143$	4.70978	+	8.15759i	0.393852	+	0.682172i
$144$	2.97313	+	0.400645i	0.247761	+	0.0333871i
$145$	−5.04131	+	8.73180i	−0.418658	+	0.725137i
$146$	−0.729393	−	1.26335i	−0.0603650	−	0.104555i
$147$	−6.12383	−	10.4642i	−0.505085	−	0.863070i
$148$	1.36906	−	2.37128i	0.112536	−	0.194918i
$149$	−5.84456	−	10.1231i	−0.478805	−	0.829315i	0.520899	−	0.853618i	$-0.325597\pi$
$149$	−5.84456	−	10.1231i	−0.478805	−	0.829315i	−0.999705	+	0.0243030i	$0.992263\pi$
$150$	0.964470	−	1.43868i	0.0787486	−	0.117468i
$151$	−8.69754	+	15.0646i	−0.707796	+	1.22594i	0.257877	+	0.966178i	$0.416977\pi$
$151$	−8.69754	+	15.0646i	−0.707796	+	1.22594i	−0.965673	+	0.259761i	$0.916356\pi$
$152$	1.26810	−	2.19641i	0.102856	−	0.178152i
$153$	−3.37577	−	8.22064i	−0.272915	−	0.664599i
$154$	5.21990	+	8.32538i	0.420632	+	0.670878i
$155$	−4.93760	−	8.55217i	−0.396597	−	0.686927i
$156$	−2.44609	+	3.64877i	−0.195844	+	0.292136i
$157$	−5.10624			−0.407523			−0.203761	−	0.979021i	$-0.565317\pi$
$157$	−5.10624			−0.407523			−0.203761	+	0.979021i	$0.565317\pi$
$158$	−2.27946			−0.181344
$159$	6.50368	+	13.2390i	0.515775	+	1.04992i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−6.41449	+	0.233769i	−0.505533	+	0.0184236i
$162$	−8.67897	−	2.38233i	−0.681884	−	0.187174i
$163$	−4.57141	+	7.91792i	−0.358061	+	0.620180i	−0.987637	−	0.156759i	$-0.949895\pi$
$163$	−4.57141	+	7.91792i	−0.358061	+	0.620180i	0.629576	+	0.776939i	$0.283229\pi$
$164$	−5.50745	+	9.53918i	−0.430060	+	0.744885i
$165$	−6.41850	−	0.430518i	−0.499680	−	0.0335158i
$166$	5.39560	+	9.34546i	0.418780	+	0.725348i
$167$	−10.9734	+	19.0065i	−0.849150	+	1.47077i	0.0328178	+	0.999461i	$0.489552\pi$
$167$	−10.9734	+	19.0065i	−0.849150	+	1.47077i	−0.881968	+	0.471310i	$0.843781\pi$
$168$	−2.41143	+	3.89680i	−0.186046	+	0.300644i
$169$	3.28385	+	5.68780i	0.252604	+	0.437523i
$170$	1.48113	−	2.56539i	0.113597	−	0.196756i
$171$	−4.65020	+	6.02215i	−0.355610	+	0.460526i
$172$	1.65213	+	2.86157i	0.125974	+	0.218193i
$173$	1.26648			0.0962889			0.0481445	−	0.998840i	$-0.484669\pi$
$173$	1.26648			0.0962889			0.0481445	+	0.998840i	$0.484669\pi$
$174$	7.70007	+	15.6744i	0.583741	+	1.18827i
$175$	1.40545	+	2.24159i	0.106242	+	0.169448i
$176$	1.85703	−	3.21646i	0.139979	−	0.242450i
$177$	21.1356	+	1.41766i	1.58865	+	0.106558i
$178$	7.50572	−	13.0003i	0.562578	−	0.974413i
$179$	2.20490	+	3.81899i	0.164802	+	0.285445i	0.936585	−	0.350441i	$-0.113968\pi$
$179$	2.20490	+	3.81899i	0.164802	+	0.285445i	−0.771783	+	0.635886i	$0.780635\pi$
$180$	−1.13960	−	2.77513i	−0.0849404	−	0.206846i
$181$	−5.47131			−0.406679			−0.203339	−	0.979108i	$-0.565180\pi$
$181$	−5.47131			−0.406679			−0.203339	+	0.979108i	$0.565180\pi$
$182$	−3.56449	−	5.68511i	−0.264217	−	0.421409i
$183$	21.6587	+	1.45275i	1.60106	+	0.107390i
$184$	1.21303	+	2.10103i	0.0894257	+	0.154890i
$185$	−2.73812			−0.201311
$186$	−17.0660	−	1.14469i	−1.25134	−	0.0839330i
$187$	−11.0020			−0.804544
$188$	−0.695738			−0.0507419
$189$	8.73071	−	10.6195i	0.635066	−	0.772458i
$190$	−2.53620			−0.183995
$191$	8.34357			0.603720			0.301860	−	0.953352i	$-0.402393\pi$
$191$	8.34357			0.603720			0.301860	+	0.953352i	$0.402393\pi$
$192$	1.72817	+	0.115916i	0.124720	+	0.00836552i
$193$	−20.5384			−1.47839			−0.739194	−	0.673492i	$-0.764793\pi$
$193$	−20.5384			−1.47839			−0.739194	+	0.673492i	$0.764793\pi$
$194$	−0.0494422	−	0.0856364i	−0.00354974	−	0.00614834i
$195$	4.38297	+	0.293986i	0.313871	+	0.0210528i
$196$	−3.93199	−	5.79133i	−0.280856	−	0.413666i
$197$	7.91528			0.563940			0.281970	−	0.959423i	$-0.409012\pi$
$197$	7.91528			0.563940			0.281970	+	0.959423i	$0.409012\pi$
$198$	−6.80983	+	8.81895i	−0.483954	+	0.626735i
$199$	1.32856	+	2.30113i	0.0941790	+	0.163123i	0.909266	−	0.416216i	$-0.136644\pi$
$199$	1.32856	+	2.30113i	0.0941790	+	0.163123i	−0.815087	+	0.579339i	$0.803311\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	−17.8394	−	1.19657i	−1.25829	−	0.0843995i
$202$	−5.29440	+	9.17017i	−0.372513	+	0.645211i
$203$	−26.6584	+	0.971536i	−1.87105	+	0.0681885i
$204$	−2.26227	−	4.60511i	−0.158390	−	0.322422i
$205$	11.0149			0.769314
$206$	2.80875	+	4.86490i	0.195695	+	0.338954i
$207$	−2.76473	−	6.73262i	−0.192162	−	0.467949i
$208$	−1.26810	+	2.19641i	−0.0879268	+	0.152294i
$209$	4.70978	+	8.15759i	0.325783	+	0.564272i
$210$	4.58044	+	0.139959i	0.316080	+	0.00965812i
$211$	−2.51110	+	4.34936i	−0.172871	+	0.299422i	−0.939423	−	0.342761i	$-0.888638\pi$
$211$	−2.51110	+	4.34936i	−0.172871	+	0.299422i	0.766551	+	0.642183i	$0.221971\pi$
$212$	4.25802	+	7.37510i	0.292442	+	0.506524i
$213$	4.20759	+	0.282222i	0.288300	+	0.0193376i
$214$	7.95511	−	13.7787i	0.543800	−	0.941889i
$215$	1.65213	−	2.86157i	0.112674	−	0.195158i
$216$	−5.09162	−	1.03701i	−0.346441	−	0.0705599i
$217$	12.2309	−	23.0877i	0.830289	−	1.56729i
$218$	−5.34068	−	9.25033i	−0.361717	−	0.626511i
$219$	1.11407	+	2.26782i	0.0752820	+	0.153245i
$220$	−3.71405			−0.250401
$221$	7.51287			0.505370
$222$	−2.64084	+	3.93928i	−0.177241	+	0.264387i
$223$	−3.74932	−	6.49401i	−0.251073	−	0.434871i	0.712748	−	0.701420i	$-0.247450\pi$
$223$	−3.74932	−	6.49401i	−0.251073	−	0.434871i	−0.963822	+	0.266548i	$0.914117\pi$
$224$	−1.23855	+	2.33795i	−0.0827541	+	0.156211i
$225$	−1.83353	+	2.37448i	−0.122235	+	0.158299i
$226$	−3.45901	+	5.99118i	−0.230090	+	0.398528i
$227$	−4.63500	+	8.02806i	−0.307636	+	0.532841i	−0.977845	−	0.209332i	$-0.932871\pi$
$227$	−4.63500	+	8.02806i	−0.307636	+	0.532841i	0.670209	+	0.742173i	$0.266205\pi$
$228$	−2.44609	+	3.64877i	−0.161996	+	0.241646i
$229$	−9.57481	−	16.5841i	−0.632721	−	1.09591i	−0.986993	−	0.160763i	$-0.948604\pi$
$229$	−9.57481	−	16.5841i	−0.632721	−	1.09591i	0.354272	−	0.935143i	$-0.384729\pi$
$230$	1.21303	−	2.10103i	0.0799848	−	0.138538i
$231$	−8.05582	−	14.9927i	−0.530034	−	0.986448i
$232$	5.04131	+	8.73180i	0.330978	+	0.573271i
$233$	−2.23261	+	3.86699i	−0.146263	+	0.253335i	−0.929843	−	0.367955i	$-0.880058\pi$
$233$	−2.23261	+	3.86699i	−0.146263	+	0.253335i	0.783580	+	0.621290i	$0.213391\pi$
$234$	4.65020	−	6.02215i	0.303993	−	0.393680i
$235$	0.347869	+	0.602527i	0.0226925	+	0.0393045i
$236$	12.2301			0.796111
$237$	3.93928	+	0.264226i	0.255884	+	0.0171633i
$238$	7.83220	−	0.285436i	0.507686	−	0.0185021i
$239$	−1.17657	+	2.03788i	−0.0761059	+	0.131819i	−0.901567	−	0.432640i	$-0.857582\pi$
$239$	−1.17657	+	2.03788i	−0.0761059	+	0.131819i	0.825461	+	0.564460i	$0.190915\pi$
$240$	−0.763698	−	1.55460i	−0.0492965	−	0.100349i
$241$	1.41479	−	2.45049i	0.0911346	−	0.157850i	−0.816854	−	0.576844i	$-0.804284\pi$
$241$	1.41479	−	2.45049i	0.0911346	−	0.157850i	0.907989	+	0.418994i	$0.137617\pi$
$242$	1.39709	+	2.41983i	0.0898084	+	0.155553i
$243$	14.7226	+	5.12311i	0.944453	+	0.328647i
$244$	12.5327			0.802327
$245$	−3.04944	+	6.30087i	−0.194822	+	0.402548i
$246$	10.6235	−	15.8469i	0.677332	−	1.01036i
$247$	−3.21615	−	5.57053i	−0.204639	−	0.354444i
$248$	−9.87519			−0.627075
$249$	−8.24122	−	16.7760i	−0.522266	−	1.06313i
$250$	−1.00000			−0.0632456
$251$	25.2659			1.59477			0.797384	−	0.603472i	$-0.206217\pi$
$251$	25.2659			1.59477			0.797384	+	0.603472i	$0.206217\pi$
$252$	4.61905	−	6.45479i	0.290973	−	0.406614i
$253$	−9.01051			−0.566486
$254$	16.7729			1.05242
$255$	−2.85701	+	4.26174i	−0.178913	+	0.266880i
$256$	1.00000			0.0625000
$257$	9.27094	+	16.0577i	0.578305	+	1.00165i	0.995674	+	0.0929169i	$0.0296191\pi$
$257$	9.27094	+	16.0577i	0.578305	+	1.00165i	−0.417369	+	0.908737i	$0.637048\pi$
$258$	−2.52346	−	5.13679i	−0.157104	−	0.319803i
$259$	−3.84829	−	6.13775i	−0.239121	−	0.381381i
$260$	2.53620			0.157288
$261$	−11.4901	−	27.9805i	−0.711219	−	1.73195i
$262$	−8.02229	−	13.8950i	−0.495619	−	0.858437i
$263$	0.380539	−	0.659113i	0.0234651	−	0.0406427i	−0.854054	−	0.520184i	$-0.825863\pi$
$263$	0.380539	−	0.659113i	0.0234651	−	0.0406427i	0.877519	+	0.479541i	$0.159197\pi$
$264$	−3.58209	+	5.34333i	−0.220463	+	0.328859i
$265$	4.25802	−	7.37510i	0.261568	−	0.453049i
$266$	−3.56449	−	5.68511i	−0.218553	−	0.348577i
$267$	−14.4781	+	21.5967i	−0.886045	+	1.32169i
$268$	−10.3227			−0.630561
$269$	4.08137	+	7.06914i	0.248846	+	0.431013i	0.963206	−	0.268765i	$-0.0866155\pi$
$269$	4.08137	+	7.06914i	0.248846	+	0.431013i	−0.714360	+	0.699778i	$0.753282\pi$
$270$	1.64773	+	4.92798i	0.100278	+	0.299907i
$271$	4.35725	−	7.54697i	0.264684	−	0.458446i	−0.702797	−	0.711391i	$-0.748066\pi$
$271$	4.35725	−	7.54697i	0.264684	−	0.458446i	0.967481	+	0.252945i	$0.0813990\pi$
$272$	−1.48113	−	2.56539i	−0.0898066	−	0.155550i
$273$	5.50104	+	10.2380i	0.332938	+	0.619632i
$274$	4.24243	−	7.34811i	0.256295	−	0.443916i
$275$	1.85703	+	3.21646i	0.111983	+	0.193960i
$276$	−1.85278	−	3.77154i	−0.111524	−	0.227020i
$277$	7.60976	−	13.1805i	0.457226	−	0.791939i	−0.541587	−	0.840645i	$-0.682176\pi$
$277$	7.60976	−	13.1805i	0.457226	−	0.791939i	0.998813	+	0.0487056i	$0.0155096\pi$
$278$	1.67921	−	2.90848i	0.100713	−	0.174439i
$279$	29.3602	+	3.95644i	1.75775	+	0.236866i
$280$	2.64400	−	0.0963576i	0.158009	−	0.00575847i
$281$	−3.84654	−	6.66240i	−0.229465	−	0.397445i	0.728185	−	0.685381i	$-0.240364\pi$
$281$	−3.84654	−	6.66240i	−0.229465	−	0.397445i	−0.957650	+	0.287936i	$0.907031\pi$
$282$	1.20235	+	0.0806472i	0.0715991	+	0.00480247i
$283$	22.5464			1.34025			0.670123	−	0.742250i	$-0.266241\pi$
$283$	22.5464			1.34025			0.670123	+	0.742250i	$0.266241\pi$
$284$	2.43471			0.144474
$285$	4.38297	+	0.293986i	0.259625	+	0.0174142i
$286$	−4.70978	−	8.15759i	−0.278495	−	0.482368i
$287$	15.4808	+	24.6909i	0.913805	+	1.45746i
$288$	−2.97313	−	0.400645i	−0.175193	−	0.0236082i
$289$	4.11252	−	7.12309i	0.241913	−	0.419005i
$290$	5.04131	−	8.73180i	0.296036	−	0.512749i
$291$	0.0755178	+	0.153725i	0.00442693	+	0.00901154i
$292$	0.729393	+	1.26335i	0.0426845	+	0.0739317i
$293$	6.30276	−	10.9167i	0.368211	−	0.637760i	−0.621075	−	0.783751i	$-0.713304\pi$
$293$	6.30276	−	10.9167i	0.368211	−	0.637760i	0.989286	+	0.145991i	$0.0466371\pi$
$294$	6.12383	+	10.4642i	0.357149	+	0.610282i
$295$	−6.11504	−	10.5916i	−0.356032	−	0.616665i
$296$	−1.36906	+	2.37128i	−0.0795751	+	0.137828i
$297$	12.7908	−	14.4512i	0.742197	−	0.838546i
$298$	5.84456	+	10.1231i	0.338566	+	0.586414i
$299$	6.15297			0.355835
$300$	−0.964470	+	1.43868i	−0.0556837	+	0.0830622i
$301$	8.73645	−	0.318391i	0.503561	−	0.0183517i
$302$	8.69754	−	15.0646i	0.500487	−	0.866870i
$303$	10.2126	−	15.2339i	0.586698	−	0.875164i
$304$	−1.26810	+	2.19641i	−0.0727304	+	0.125973i
$305$	−6.26637	−	10.8537i	−0.358811	−	0.621480i
$306$	3.37577	+	8.22064i	0.192980	+	0.469942i
$307$	11.1144			0.634331			0.317165	−	0.948370i	$-0.397269\pi$
$307$	11.1144			0.634331			0.317165	+	0.948370i	$0.397269\pi$
$308$	−5.21990	−	8.32538i	−0.297431	−	0.474382i
$309$	−4.29007	−	8.73294i	−0.244054	−	0.496800i
$310$	4.93760	+	8.55217i	0.280437	+	0.485731i
$311$	−24.3681			−1.38179			−0.690893	−	0.722957i	$-0.742782\pi$
$311$	−24.3681			−1.38179			−0.690893	+	0.722957i	$0.742782\pi$
$312$	2.44609	−	3.64877i	0.138482	−	0.206571i
$313$	29.2538			1.65352			0.826761	−	0.562553i	$-0.190181\pi$
$313$	29.2538			1.65352			0.826761	+	0.562553i	$0.190181\pi$
$314$	5.10624			0.288162
$315$	−7.89954	−	0.772820i	−0.445089	−	0.0435434i
$316$	2.27946			0.128229
$317$	−9.16527			−0.514773			−0.257386	−	0.966309i	$-0.582861\pi$
$317$	−9.16527			−0.514773			−0.257386	+	0.966309i	$0.582861\pi$
$318$	−6.50368	−	13.2390i	−0.364708	−	0.742405i
$319$	−37.4474			−2.09665
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−15.3449	+	22.8897i	−0.856470	+	1.27758i
$322$	6.41449	−	0.233769i	0.357466	−	0.0130275i
$323$	7.51287			0.418027
$324$	8.67897	+	2.38233i	0.482165	+	0.132352i
$325$	−1.26810	−	2.19641i	−0.0703415	−	0.121835i
$326$	4.57141	−	7.91792i	0.253187	−	0.438533i
$327$	8.15733	+	16.6052i	0.451101	+	0.918269i
$328$	5.50745	−	9.53918i	0.304098	−	0.526713i
$329$	−0.861707	+	1.62660i	−0.0475074	+	0.0896773i
$330$	6.41850	+	0.430518i	0.353327	+	0.0236992i
$331$	−31.8638			−1.75139			−0.875696	−	0.482862i	$-0.839597\pi$
$331$	−31.8638			−1.75139			−0.875696	+	0.482862i	$0.839597\pi$
$332$	−5.39560	−	9.34546i	−0.296122	−	0.512899i
$333$	5.02044	−	6.50162i	0.275118	−	0.356287i
$334$	10.9734	−	19.0065i	0.600440	−	1.03999i
$335$	5.16136	+	8.93974i	0.281995	+	0.488430i
$336$	2.41143	−	3.89680i	0.131554	−	0.212588i
$337$	6.25621	−	10.8361i	0.340797	−	0.590278i	−0.643784	−	0.765208i	$-0.722636\pi$
$337$	6.25621	−	10.8361i	0.340797	−	0.590278i	0.984581	+	0.174929i	$0.0559697\pi$
$338$	−3.28385	−	5.68780i	−0.178618	−	0.309375i
$339$	6.67223	−	9.95281i	0.362386	−	0.540563i
$340$	−1.48113	+	2.56539i	−0.0803255	+	0.139128i
$341$	18.3385	−	31.7632i	0.993085	−	1.72007i
$342$	4.65020	−	6.02215i	0.251454	−	0.325641i
$343$	−18.4098	+	2.01993i	−0.994035	+	0.109066i
$344$	−1.65213	−	2.86157i	−0.0890769	−	0.154286i
$345$	−2.33986	+	3.49032i	−0.125974	+	0.187913i
$346$	−1.26648			−0.0680865
$347$	−16.7011			−0.896560			−0.448280	−	0.893893i	$-0.647963\pi$
$347$	−16.7011			−0.896560			−0.448280	+	0.893893i	$0.647963\pi$
$348$	−7.70007	−	15.6744i	−0.412767	−	0.840235i
$349$	0.378874	+	0.656229i	0.0202807	+	0.0351271i	0.875988	−	0.482334i	$-0.160211\pi$
$349$	0.378874	+	0.656229i	0.0202807	+	0.0351271i	−0.855707	+	0.517461i	$0.826877\pi$
$350$	−1.40545	−	2.24159i	−0.0751243	−	0.119818i
$351$	−8.73439	+	9.86826i	−0.466207	+	0.526729i
$352$	−1.85703	+	3.21646i	−0.0989798	+	0.171438i
$353$	4.66708	−	8.08361i	0.248403	−	0.430247i	−0.714680	−	0.699452i	$-0.753427\pi$
$353$	4.66708	−	8.08361i	0.248403	−	0.430247i	0.963083	+	0.269205i	$0.0867608\pi$
$354$	−21.1356	−	1.41766i	−1.12335	−	0.0753479i
$355$	−1.21736	−	2.10852i	−0.0646106	−	0.111909i
$356$	−7.50572	+	13.0003i	−0.397803	+	0.689014i
$357$	−13.5684	−	0.414596i	−0.718118	−	0.0219427i
$358$	−2.20490	−	3.81899i	−0.116532	−	0.201840i
$359$	5.81797	−	10.0770i	0.307061	−	0.531845i	−0.670657	−	0.741768i	$-0.733988\pi$
$359$	5.81797	−	10.0770i	0.307061	−	0.531845i	0.977718	+	0.209922i	$0.0673211\pi$
$360$	1.13960	+	2.77513i	0.0600619	+	0.146262i
$361$	6.28385	+	10.8840i	0.330729	+	0.572839i
$362$	5.47131			0.287565
$363$	−2.13391	−	4.34382i	−0.112001	−	0.227991i
$364$	3.56449	+	5.68511i	0.186830	+	0.297981i
$365$	0.729393	−	1.26335i	0.0381782	−	0.0661266i
$366$	−21.6587	−	1.45275i	−1.13212	−	0.0759363i
$367$	−0.297341	+	0.515009i	−0.0155211	+	0.0268832i	−0.873682	−	0.486498i	$-0.838274\pi$
$367$	−0.297341	+	0.515009i	−0.0155211	+	0.0268832i	0.858161	+	0.513381i	$0.171607\pi$
$368$	−1.21303	−	2.10103i	−0.0632335	−	0.109524i
$369$	−20.1962	+	26.1547i	−1.05137	+	1.36156i
$370$	2.73812			0.142348
$371$	22.5164	−	0.820585i	1.16899	−	0.0426026i
$372$	17.0660	+	1.14469i	0.884830	+	0.0593496i
$373$	−2.11272	−	3.65934i	−0.109393	−	0.189474i	0.806132	−	0.591736i	$-0.201557\pi$
$373$	−2.11272	−	3.65934i	−0.109393	−	0.189474i	−0.915524	+	0.402263i	$0.868224\pi$
$374$	11.0020			0.568899
$375$	1.72817	+	0.115916i	0.0892422	+	0.00598588i
$376$	0.695738			0.0358800
$377$	25.5715			1.31700
$378$	−8.73071	+	10.6195i	−0.449059	+	0.546210i
$379$	−27.7458			−1.42521			−0.712603	−	0.701567i	$-0.752484\pi$
$379$	−27.7458			−1.42521			−0.712603	+	0.701567i	$0.752484\pi$
$380$	2.53620			0.130104
$381$	−28.9863	−	1.94424i	−1.48501	−	0.0996066i
$382$	−8.34357			−0.426894
$383$	14.8026	+	25.6388i	0.756376	+	1.31008i	0.944687	+	0.327973i	$0.106365\pi$
$383$	14.8026	+	25.6388i	0.756376	+	1.31008i	−0.188311	+	0.982109i	$0.560301\pi$
$384$	−1.72817	−	0.115916i	−0.0881902	−	0.00591531i
$385$	−4.60004	+	8.68325i	−0.234440	+	0.442540i
$386$	20.5384			1.04538
$387$	3.76552	+	9.16974i	0.191412	+	0.466124i
$388$	0.0494422	+	0.0856364i	0.00251005	+	0.00434753i
$389$	14.3708	−	24.8910i	0.728629	−	1.26202i	−0.228834	−	0.973466i	$-0.573491\pi$
$389$	14.3708	−	24.8910i	0.728629	−	1.26202i	0.957463	−	0.288557i	$-0.0931755\pi$
$390$	−4.38297	−	0.293986i	−0.221941	−	0.0148866i
$391$	−3.59331	+	6.22379i	−0.181721	+	0.314751i
$392$	3.93199	+	5.79133i	0.198595	+	0.292506i
$393$	12.2532	+	24.9428i	0.618093	+	1.25820i
$394$	−7.91528			−0.398766
$395$	−1.13973	−	1.97407i	−0.0573460	−	0.0993261i
$396$	6.80983	−	8.81895i	0.342207	−	0.443169i
$397$	17.1373	−	29.6827i	0.860097	−	1.48973i	−0.0117378	−	0.999931i	$-0.503736\pi$
$397$	17.1373	−	29.6827i	0.860097	−	1.48973i	0.871835	−	0.489800i	$-0.162930\pi$
$398$	−1.32856	−	2.30113i	−0.0665946	−	0.115345i
$399$	5.50104	+	10.2380i	0.275396	+	0.512541i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	5.35942	+	9.28278i	0.267637	+	0.463560i	0.968251	−	0.249980i	$-0.0804240\pi$
$401$	5.35942	+	9.28278i	0.267637	+	0.463560i	−0.700614	+	0.713540i	$0.747091\pi$
$402$	17.8394	+	1.19657i	0.889749	+	0.0596795i
$403$	−12.5227	+	21.6900i	−0.623801	+	1.08046i
$404$	5.29440	−	9.17017i	0.263406	−	0.456233i
$405$	−2.27632	−	8.70737i	−0.113111	−	0.432673i
$406$	26.6584	−	0.971536i	1.32303	−	0.0482165i
$407$	−5.08477	−	8.80707i	−0.252043	−	0.436550i
$408$	2.26227	+	4.60511i	0.111999	+	0.227987i
$409$	27.2083			1.34537			0.672683	−	0.739931i	$-0.265142\pi$
$409$	27.2083			1.34537			0.672683	+	0.739931i	$0.265142\pi$
$410$	−11.0149			−0.543987
$411$	−8.18340	+	12.2070i	−0.403657	+	0.602127i
$412$	−2.80875	−	4.86490i	−0.138377	−	0.239676i
$413$	15.1476	−	28.5933i	0.745363	−	1.40698i
$414$	2.76473	+	6.73262i	0.135879	+	0.330890i
$415$	−5.39560	+	9.34546i	−0.264860	+	0.458751i
$416$	1.26810	−	2.19641i	0.0621737	−	0.107688i
$417$	−3.23910	+	4.83170i	−0.158619	+	0.236609i
$418$	−4.70978	−	8.15759i	−0.230363	−	0.399001i
$419$	−10.5111	+	18.2058i	−0.513502	+	0.889411i	0.486376	+	0.873750i	$0.338319\pi$
$419$	−10.5111	+	18.2058i	−0.513502	+	0.889411i	−0.999877	+	0.0156611i	$0.995015\pi$
$420$	−4.58044	−	0.139959i	−0.223502	−	0.00682932i
$421$	6.73036	+	11.6573i	0.328017	+	0.568143i	0.982118	−	0.188264i	$-0.0602862\pi$
$421$	6.73036	+	11.6573i	0.328017	+	0.568143i	−0.654101	+	0.756407i	$0.726953\pi$
$422$	2.51110	−	4.34936i	0.122239	−	0.211723i
$423$	−2.06852	−	0.278744i	−0.100575	−	0.0135530i
$424$	−4.25802	−	7.37510i	−0.206788	−	0.358167i
$425$	2.96226			0.143691
$426$	−4.20759	−	0.282222i	−0.203859	−	0.0136737i
$427$	15.5224	−	29.3009i	0.751183	−	1.41797i
$428$	−7.95511	+	13.7787i	−0.384525	+	0.666016i
$429$	7.19370	+	14.6436i	0.347315	+	0.707000i
$430$	−1.65213	+	2.86157i	−0.0796728	+	0.137997i
$431$	−2.84972	−	4.93585i	−0.137266	−	0.237752i	0.789195	−	0.614143i	$-0.210498\pi$
$431$	−2.84972	−	4.93585i	−0.137266	−	0.237752i	−0.926461	+	0.376391i	$0.877165\pi$
$432$	5.09162	+	1.03701i	0.244971	+	0.0498934i
$433$	−17.7157			−0.851363			−0.425682	−	0.904873i	$-0.639966\pi$
$433$	−17.7157			−0.851363			−0.425682	+	0.904873i	$0.639966\pi$
$434$	−12.2309	+	23.0877i	−0.587103	+	1.10824i
$435$	−9.72438	+	14.5056i	−0.466248	+	0.695493i
$436$	5.34068	+	9.25033i	0.255772	+	0.443010i
$437$	6.15297			0.294336
$438$	−1.11407	−	2.26782i	−0.0532324	−	0.108361i
$439$	−5.39022			−0.257261			−0.128631	−	0.991693i	$-0.541058\pi$
$439$	−5.39022			−0.257261			−0.128631	+	0.991693i	$0.541058\pi$
$440$	3.71405			0.177060
$441$	−9.37004	−	18.7937i	−0.446192	−	0.894937i
$442$	−7.51287			−0.357351
$443$	11.6840			0.555122			0.277561	−	0.960708i	$-0.410474\pi$
$443$	11.6840			0.555122			0.277561	+	0.960708i	$0.410474\pi$
$444$	2.64084	−	3.93928i	0.125329	−	0.186950i
$445$	15.0114			0.711611
$446$	3.74932	+	6.49401i	0.177535	+	0.307501i
$447$	−8.92696	−	18.1719i	−0.422231	−	0.859499i
$448$	1.23855	−	2.33795i	0.0585160	−	0.110458i
$449$	−23.4124			−1.10490			−0.552450	−	0.833546i	$-0.686307\pi$
$449$	−23.4124			−1.10490			−0.552450	+	0.833546i	$0.686307\pi$
$450$	1.83353	−	2.37448i	0.0864335	−	0.111934i
$451$	20.4550	+	35.4290i	0.963186	+	1.66829i
$452$	3.45901	−	5.99118i	0.162698	−	0.281802i
$453$	−16.7770	+	25.0259i	−0.788254	+	1.17582i
$454$	4.63500	−	8.02806i	0.217531	−	0.376775i
$455$	3.14121	−	5.92949i	0.147262	−	0.277979i
$456$	2.44609	−	3.64877i	0.114548	−	0.170869i
$457$	−8.99567			−0.420800			−0.210400	−	0.977615i	$-0.567477\pi$
$457$	−8.99567			−0.420800			−0.210400	+	0.977615i	$0.567477\pi$
$458$	9.57481	+	16.5841i	0.447402	+	0.774922i
$459$	−4.88100	−	14.5979i	−0.227826	−	0.681374i
$460$	−1.21303	+	2.10103i	−0.0565578	+	0.0979610i
$461$	2.25201	+	3.90059i	0.104887	+	0.181669i	0.913692	−	0.406408i	$-0.133219\pi$
$461$	2.25201	+	3.90059i	0.104887	+	0.181669i	−0.808805	+	0.588076i	$0.799885\pi$
$462$	8.05582	+	14.9927i	0.374791	+	0.697524i
$463$	15.6097	−	27.0367i	0.725442	−	1.25650i	−0.233350	−	0.972393i	$-0.574969\pi$
$463$	15.6097	−	27.0367i	0.725442	−	1.25650i	0.958792	−	0.284110i	$-0.0916980\pi$
$464$	−5.04131	−	8.73180i	−0.234037	−	0.405364i
$465$	−7.54166	−	15.3519i	−0.349736	−	0.711929i
$466$	2.23261	−	3.86699i	0.103424	−	0.179135i
$467$	−9.65889	+	16.7297i	−0.446960	+	0.774158i	−0.998186	−	0.0601981i	$-0.980827\pi$
$467$	−9.65889	+	16.7297i	−0.446960	+	0.774158i	0.551226	+	0.834356i	$0.314160\pi$
$468$	−4.65020	+	6.02215i	−0.214956	+	0.278374i
$469$	−12.7852	+	24.1340i	−0.590366	+	1.11440i
$470$	−0.347869	−	0.602527i	−0.0160460	−	0.0277925i
$471$	−8.82445	−	0.591896i	−0.406609	−	0.0272731i
$472$	−12.2301			−0.562935
$473$	12.2722			0.564276
$474$	−3.93928	−	0.264226i	−0.180937	−	0.0121363i
$475$	−1.26810	−	2.19641i	−0.0581844	−	0.100778i
$476$	−7.83220	+	0.285436i	−0.358988	+	0.0130829i
$477$	9.70483	+	23.6331i	0.444354	+	1.08208i
$478$	1.17657	−	2.03788i	0.0538150	−	0.0932104i
$479$	−10.6993	+	18.5318i	−0.488865	+	0.846738i	−0.999918	−	0.0128107i	$-0.995922\pi$
$479$	−10.6993	+	18.5318i	−0.488865	+	0.846738i	0.511053	+	0.859549i	$0.329255\pi$
$480$	0.763698	+	1.55460i	0.0348579	+	0.0709572i
$481$	3.47221	+	6.01405i	0.158319	+	0.274217i
$482$	−1.41479	+	2.45049i	−0.0644419	+	0.111617i
$483$	−11.1124	−	0.339550i	−0.505632	−	0.0154501i
$484$	−1.39709	−	2.41983i	−0.0635041	−	0.109992i
$485$	0.0494422	−	0.0856364i	0.00224506	−	0.00388855i
$486$	−14.7226	−	5.12311i	−0.667829	−	0.232389i
$487$	−18.9039	−	32.7426i	−0.856618	−	1.48371i	−0.875135	−	0.483878i	$-0.839228\pi$
$487$	−18.9039	−	32.7426i	−0.856618	−	1.48371i	0.0185169	−	0.999829i	$-0.494106\pi$
$488$	−12.5327			−0.567331
$489$	−8.81798	+	13.1536i	−0.398763	+	0.594826i
$490$	3.04944	−	6.30087i	0.137760	−	0.284644i
$491$	−0.607232	+	1.05176i	−0.0274040	+	0.0474651i	−0.879402	−	0.476080i	$-0.842057\pi$
$491$	−0.607232	+	1.05176i	−0.0274040	+	0.0474651i	0.851998	+	0.523545i	$0.175391\pi$
$492$	−10.6235	+	15.8469i	−0.478946	+	0.714434i
$493$	−14.9336	+	25.8658i	−0.672578	+	1.16494i
$494$	3.21615	+	5.57053i	0.144701	+	0.250630i
$495$	−11.0423	−	1.48801i	−0.496317	−	0.0668813i
$496$	9.87519			0.443409
$497$	3.01552	−	5.69223i	0.135264	−	0.255332i
$498$	8.24122	+	16.7760i	0.369298	+	0.751749i
$499$	−13.7499	−	23.8155i	−0.615529	−	1.06613i	−0.990291	−	0.139007i	$-0.955609\pi$
$499$	−13.7499	−	23.8155i	−0.615529	−	1.06613i	0.374762	−	0.927121i	$-0.377724\pi$
$500$	1.00000			0.0447214
$501$	−21.1671	+	31.5745i	−0.945676	+	1.41064i
$502$	−25.2659			−1.12767
$503$	−10.9548			−0.488450			−0.244225	−	0.969719i	$-0.578534\pi$
$503$	−10.9548			−0.488450			−0.244225	+	0.969719i	$0.578534\pi$
$504$	−4.61905	+	6.45479i	−0.205749	+	0.287519i
$505$	−10.5888			−0.471196
$506$	9.01051			0.400566
$507$	5.01574	+	10.2101i	0.222757	+	0.453447i
$508$	−16.7729			−0.744175
$509$	−6.67082	−	11.5542i	−0.295679	−	0.512131i	0.679464	−	0.733709i	$-0.262212\pi$
$509$	−6.67082	−	11.5542i	−0.295679	−	0.512131i	−0.975143	+	0.221578i	$0.928879\pi$
$510$	2.85701	−	4.26174i	0.126510	−	0.188713i
$511$	3.85703	−	0.140565i	0.170625	−	0.00621824i
$512$	−1.00000			−0.0441942
$513$	−8.73439	+	9.86826i	−0.385633	+	0.435694i
$514$	−9.27094	−	16.0577i	−0.408924	−	0.708277i
$515$	−2.80875	+	4.86490i	−0.123768	+	0.214373i
$516$	2.52346	+	5.13679i	0.111089	+	0.226135i
$517$	−1.29200	+	2.23782i	−0.0568223	+	0.0984191i
$518$	3.84829	+	6.13775i	0.169084	+	0.269677i
$519$	2.18869	+	0.146806i	0.0960730	+	0.00644405i
$520$	−2.53620			−0.111220
$521$	−3.49625	−	6.05568i	−0.153173	−	0.265304i	0.779219	−	0.626752i	$-0.215616\pi$
$521$	−3.49625	−	6.05568i	−0.153173	−	0.265304i	−0.932392	+	0.361448i	$0.882283\pi$
$522$	11.4901	+	27.9805i	0.502908	+	1.22467i
$523$	18.4547	−	31.9645i	0.806968	−	1.39771i	−0.107987	−	0.994152i	$-0.534440\pi$
$523$	18.4547	−	31.9645i	0.806968	−	1.39771i	0.914955	−	0.403557i	$-0.132226\pi$
$524$	8.02229	+	13.8950i	0.350455	+	0.607007i
$525$	2.16901	+	4.03676i	0.0946634	+	0.176178i
$526$	−0.380539	+	0.659113i	−0.0165923	+	0.0287387i
$527$	−14.6264	−	25.3337i	−0.637137	−	1.10355i
$528$	3.58209	−	5.34333i	0.155891	−	0.232539i
$529$	8.55712	−	14.8214i	0.372049	−	0.644407i
$530$	−4.25802	+	7.37510i	−0.184956	+	0.320354i
$531$	36.3616	+	4.89992i	1.57796	+	0.212638i
$532$	3.56449	+	5.68511i	0.154540	+	0.246481i
$533$	−13.9680	−	24.1932i	−0.605020	−	1.04793i
$534$	14.4781	−	21.5967i	0.626528	−	0.934579i
$535$	15.9102			0.687859
$536$	10.3227			0.445874
$537$	3.36775	+	6.85544i	0.145329	+	0.295834i
$538$	−4.08137	−	7.06914i	−0.175960	−	0.304772i
$539$	−25.9294	+	1.89245i	−1.11686	+	0.0815136i
$540$	−1.64773	−	4.92798i	−0.0709070	−	0.212066i
$541$	3.52168	−	6.09973i	0.151409	−	0.262248i	−0.780337	−	0.625359i	$-0.784952\pi$
$541$	3.52168	−	6.09973i	0.151409	−	0.262248i	0.931746	+	0.363112i	$0.118286\pi$
$542$	−4.35725	+	7.54697i	−0.187160	+	0.324170i
$543$	−9.45533	−	0.634212i	−0.405767	−	0.0272166i
$544$	1.48113	+	2.56539i	0.0635029	+	0.109990i
$545$	5.34068	−	9.25033i	0.228770	−	0.396241i
$546$	−5.50104	−	10.2380i	−0.235423	−	0.438146i
$547$	1.72161	+	2.98191i	0.0736106	+	0.127497i	0.900481	−	0.434895i	$-0.143214\pi$
$547$	1.72161	+	2.98191i	0.0736106	+	0.127497i	−0.826871	+	0.562392i	$0.809881\pi$
$548$	−4.24243	+	7.34811i	−0.181228	+	0.313896i
$549$	37.2614	+	5.02118i	1.59028	+	0.214299i
$550$	−1.85703	−	3.21646i	−0.0791838	−	0.137150i
$551$	25.5715			1.08938
$552$	1.85278	+	3.77154i	0.0788594	+	0.160527i
$553$	2.82322	−	5.32925i	0.120056	−	0.226623i
$554$	−7.60976	+	13.1805i	−0.323308	+	0.559986i
$555$	−4.73194	−	0.317392i	−0.200860	−	0.0134726i
$556$	−1.67921	+	2.90848i	−0.0712145	+	0.123347i
$557$	22.2943	+	38.6148i	0.944638	+	1.63616i	0.756475	+	0.654023i	$0.226920\pi$
$557$	22.2943	+	38.6148i	0.944638	+	1.63616i	0.188163	+	0.982138i	$0.439747\pi$
$558$	−29.3602	−	3.95644i	−1.24292	−	0.167490i
$559$	−8.38026			−0.354447
$560$	−2.64400	+	0.0963576i	−0.111729	+	0.00407185i
$561$	−19.0133	−	1.27531i	−0.802740	−	0.0538434i
$562$	3.84654	+	6.66240i	0.162256	+	0.281036i
$563$	11.4941			0.484419			0.242210	−	0.970224i	$-0.422128\pi$
$563$	11.4941			0.484419			0.242210	+	0.970224i	$0.422128\pi$
$564$	−1.20235	−	0.0806472i	−0.0506282	−	0.00339586i
$565$	−6.91802			−0.291043
$566$	−22.5464			−0.947697
$567$	16.3191	−	17.3403i	0.685338	−	0.728225i
$568$	−2.43471			−0.102158
$569$	−26.5591			−1.11341			−0.556707	−	0.830709i	$-0.687936\pi$
$569$	−26.5591			−1.11341			−0.556707	+	0.830709i	$0.687936\pi$
$570$	−4.38297	−	0.293986i	−0.183583	−	0.0123137i
$571$	30.1135			1.26021			0.630106	−	0.776509i	$-0.283011\pi$
$571$	30.1135			1.26021			0.630106	+	0.776509i	$0.283011\pi$
$572$	4.70978	+	8.15759i	0.196926	+	0.341086i
$573$	14.4191	+	0.967153i	0.602366	+	0.0404034i
$574$	−15.4808	−	24.6909i	−0.646158	−	1.03058i
$575$	2.42606			0.101174
$576$	2.97313	+	0.400645i	0.123880	+	0.0166935i
$577$	23.3251	+	40.4003i	0.971037	+	1.68189i	0.692437	+	0.721479i	$0.256537\pi$
$577$	23.3251	+	40.4003i	0.971037	+	1.68189i	0.278600	+	0.960407i	$0.410130\pi$
$578$	−4.11252	+	7.12309i	−0.171058	+	0.296281i
$579$	−35.4938	−	2.38073i	−1.47507	−	0.0989399i
$580$	−5.04131	+	8.73180i	−0.209329	+	0.362568i
$581$	−28.5319	+	1.03981i	−1.18370	+	0.0431388i
$582$	−0.0755178	−	0.153725i	−0.00313031	−	0.00637212i
$583$	31.6290			1.30994
$584$	−0.729393	−	1.26335i	−0.0301825	−	0.0522776i
$585$	7.54044	+	1.01611i	0.311759	+	0.0420111i
$586$	−6.30276	+	10.9167i	−0.260365	+	0.450965i
$587$	7.68787	+	13.3158i	0.317312	+	0.549601i	0.979926	−	0.199360i	$-0.0638863\pi$
$587$	7.68787	+	13.3158i	0.317312	+	0.549601i	−0.662614	+	0.748961i	$0.730553\pi$
$588$	−6.12383	−	10.4642i	−0.252542	−	0.431535i
$589$	−12.5227	+	21.6900i	−0.515990	+	0.893720i
$590$	6.11504	+	10.5916i	0.251752	+	0.436048i
$591$	13.6789	+	0.917508i	0.562676	+	0.0377412i
$592$	1.36906	−	2.37128i	0.0562681	−	0.0974592i
$593$	5.21537	−	9.03328i	0.214170	−	0.370952i	−0.738846	−	0.673875i	$-0.764629\pi$
$593$	5.21537	−	9.03328i	0.214170	−	0.370952i	0.953015	+	0.302922i	$0.0979622\pi$
$594$	−12.7908	+	14.4512i	−0.524812	+	0.592942i
$595$	4.16329	+	6.64016i	0.170678	+	0.272220i
$596$	−5.84456	−	10.1231i	−0.239403	−	0.414658i
$597$	2.02923	+	4.13074i	0.0830510	+	0.169060i
$598$	−6.15297			−0.251613
$599$	28.0067			1.14432			0.572161	−	0.820142i	$-0.306105\pi$
$599$	28.0067			1.14432			0.572161	+	0.820142i	$0.306105\pi$
$600$	0.964470	−	1.43868i	0.0393743	−	0.0587338i
$601$	−21.4358	−	37.1280i	−0.874386	−	1.51448i	−0.857415	−	0.514625i	$-0.827931\pi$
$601$	−21.4358	−	37.1280i	−0.874386	−	1.51448i	−0.0169711	−	0.999856i	$-0.505402\pi$
$602$	−8.73645	+	0.318391i	−0.356071	+	0.0129766i
$603$	−30.6908	−	4.13575i	−1.24983	−	0.168421i
$604$	−8.69754	+	15.0646i	−0.353898	+	0.612969i
$605$	−1.39709	+	2.41983i	−0.0567998	+	0.0983801i
$606$	−10.2126	+	15.2339i	−0.414858	+	0.618834i
$607$	3.76587	+	6.52268i	0.152852	+	0.264747i	0.932275	−	0.361751i	$-0.117821\pi$
$607$	3.76587	+	6.52268i	0.152852	+	0.264747i	−0.779423	+	0.626498i	$0.784488\pi$
$608$	1.26810	−	2.19641i	0.0514282	−	0.0890762i
$609$	−46.1828	−	1.41116i	−1.87142	−	0.0571830i
$610$	6.26637	+	10.8537i	0.253718	+	0.439453i
$611$	0.882265	−	1.52813i	0.0356926	−	0.0618214i
$612$	−3.37577	−	8.22064i	−0.136458	−	0.332299i
$613$	7.96337	+	13.7930i	0.321638	+	0.557093i	0.980826	−	0.194885i	$-0.0624334\pi$
$613$	7.96337	+	13.7930i	0.321638	+	0.557093i	−0.659188	+	0.751978i	$0.729100\pi$
$614$	−11.1144			−0.448539
$615$	19.0356	+	1.27680i	0.767589	+	0.0514857i
$616$	5.21990	+	8.32538i	0.210316	+	0.335439i
$617$	4.50891	−	7.80967i	0.181522	−	0.314405i	−0.760877	−	0.648896i	$-0.775231\pi$
$617$	4.50891	−	7.80967i	0.181522	−	0.314405i	0.942399	+	0.334491i	$0.108564\pi$
$618$	4.29007	+	8.73294i	0.172572	+	0.351290i
$619$	−6.24427	+	10.8154i	−0.250978	+	0.434707i	−0.963795	−	0.266643i	$-0.914086\pi$
$619$	−6.24427	+	10.8154i	−0.250978	+	0.434707i	0.712817	+	0.701350i	$0.247419\pi$
$620$	−4.93760	−	8.55217i	−0.198299	−	0.343463i
$621$	−3.99749	−	11.9556i	−0.160414	−	0.479761i
$622$	24.3681			0.977070
$623$	21.0978	+	33.6495i	0.845265	+	1.34814i
$624$	−2.44609	+	3.64877i	−0.0979218	+	0.146068i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−29.2538			−1.16922
$627$	7.19370	+	14.6436i	0.287289	+	0.584810i
$628$	−5.10624			−0.203761
$629$	−8.11103			−0.323408
$630$	7.89954	+	0.772820i	0.314725	+	0.0307899i
$631$	−4.67653			−0.186170			−0.0930849	−	0.995658i	$-0.529673\pi$
$631$	−4.67653			−0.186170			−0.0930849	+	0.995658i	$0.529673\pi$
$632$	−2.27946			−0.0906719
$633$	−4.84377	+	7.22534i	−0.192522	+	0.287182i
$634$	9.16527			0.363999
$635$	8.38643	+	14.5257i	0.332805	+	0.576436i
$636$	6.50368	+	13.2390i	0.257887	+	0.524960i
$637$	17.7063	−	1.29229i	0.701549	−	0.0512024i
$638$	37.4474			1.48255
$639$	7.23872	+	0.975455i	0.286359	+	0.0385884i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	17.2546	−	29.8859i	0.681518	−	1.18042i	−0.293000	−	0.956112i	$-0.594654\pi$
$641$	17.2546	−	29.8859i	0.681518	−	1.18042i	0.974518	−	0.224311i	$-0.0720131\pi$
$642$	15.3449	−	22.8897i	0.605616	−	0.903384i
$643$	−6.13601	+	10.6279i	−0.241980	+	0.419122i	−0.961278	−	0.275579i	$-0.911130\pi$
$643$	−6.13601	+	10.6279i	−0.241980	+	0.419122i	0.719298	+	0.694702i	$0.244464\pi$
$644$	−6.41449	+	0.233769i	−0.252766	+	0.00921180i
$645$	3.18686	−	4.75377i	0.125483	−	0.187180i
$646$	−7.51287			−0.295590
$647$	−10.0097	−	17.3372i	−0.393520	−	0.681597i	0.599391	−	0.800457i	$-0.295410\pi$
$647$	−10.0097	−	17.3372i	−0.393520	−	0.681597i	−0.992911	+	0.118859i	$0.962076\pi$
$648$	−8.67897	−	2.38233i	−0.340942	−	0.0935869i
$649$	22.7116	−	39.3376i	0.891508	−	1.54414i
$650$	1.26810	+	2.19641i	0.0497389	+	0.0861503i
$651$	23.8133	−	38.4816i	0.933317	−	1.50821i
$652$	−4.57141	+	7.91792i	−0.179030	+	0.310090i
$653$	−16.0036	−	27.7191i	−0.626271	−	1.08473i	−0.988294	−	0.152564i	$-0.951247\pi$
$653$	−16.0036	−	27.7191i	−0.626271	−	1.08473i	0.362023	−	0.932169i	$-0.382086\pi$
$654$	−8.15733	−	16.6052i	−0.318977	−	0.649314i
$655$	8.02229	−	13.8950i	0.313457	−	0.542923i
$656$	−5.50745	+	9.53918i	−0.215030	+	0.372442i
$657$	1.66243	+	4.04832i	0.0648574	+	0.157940i
$658$	0.861707	−	1.62660i	0.0335928	−	0.0634114i
$659$	−16.5079	−	28.5925i	−0.643055	−	1.11380i	−0.984747	−	0.173993i	$-0.944333\pi$
$659$	−16.5079	−	28.5925i	−0.643055	−	1.11380i	0.341691	−	0.939812i	$-0.389000\pi$
$660$	−6.41850	−	0.430518i	−0.249840	−	0.0167579i
$661$	12.1087			0.470973			0.235487	−	0.971878i	$-0.424332\pi$
$661$	12.1087			0.470973			0.235487	+	0.971878i	$0.424332\pi$
$662$	31.8638			1.23842
$663$	12.9835	+	0.870862i	0.504237	+	0.0338215i
$664$	5.39560	+	9.34546i	0.209390	+	0.362674i
$665$	3.14121	−	5.92949i	0.121811	−	0.229936i
$666$	−5.02044	+	6.50162i	−0.194538	+	0.251933i
$667$	−12.2305	+	21.1839i	−0.473567	+	0.820243i
$668$	−10.9734	+	19.0065i	−0.424575	+	0.735385i
$669$	−5.72670	−	11.6574i	−0.221407	−	0.450699i
$670$	−5.16136	−	8.93974i	−0.199401	−	0.345372i
$671$	23.2736	−	40.3111i	0.898469	−	1.55619i
$672$	−2.41143	+	3.89680i	−0.0930228	+	0.150322i
$673$	8.01111	+	13.8757i	0.308806	+	0.534867i	0.978101	−	0.208129i	$-0.0667374\pi$
$673$	8.01111	+	13.8757i	0.308806	+	0.534867i	−0.669296	+	0.742996i	$0.733404\pi$
$674$	−6.25621	+	10.8361i	−0.240980	+	0.417390i
$675$	−3.44389	+	3.89097i	−0.132555	+	0.149763i
$676$	3.28385	+	5.68780i	0.126302	+	0.218761i
$677$	0.179898			0.00691403			0.00345701	−	0.999994i	$-0.498900\pi$
$677$	0.179898			0.00691403			0.00345701	+	0.999994i	$0.498900\pi$
$678$	−6.67223	+	9.95281i	−0.256245	+	0.382236i
$679$	0.261450	−	0.00952827i	0.0100335	−	0.000365661i
$680$	1.48113	−	2.56539i	0.0567987	−	0.0983782i
$681$	−8.94064	+	13.3366i	−0.342606	+	0.511058i
$682$	−18.3385	+	31.7632i	−0.702217	+	1.21628i
$683$	0.947905	+	1.64182i	0.0362706	+	0.0628225i	0.883591	−	0.468260i	$-0.155119\pi$
$683$	0.947905	+	1.64182i	0.0362706	+	0.0628225i	−0.847320	+	0.531082i	$0.821786\pi$
$684$	−4.65020	+	6.02215i	−0.177805	+	0.230263i
$685$	8.48487			0.324190
$686$	18.4098	−	2.01993i	0.702889	−	0.0771213i
$687$	−14.6245	−	29.7699i	−0.557960	−	1.13579i
$688$	1.65213	+	2.86157i	0.0629869	+	0.109097i
$689$	−21.5983			−0.822831
$690$	2.33986	−	3.49032i	0.0890770	−	0.132874i
$691$	−30.1079			−1.14536			−0.572679	−	0.819780i	$-0.694096\pi$
$691$	−30.1079			−1.14536			−0.572679	+	0.819780i	$0.694096\pi$
$692$	1.26648			0.0481445
$693$	−12.1839	−	26.8437i	−0.462828	−	1.01971i
$694$	16.7011			0.633963
$695$	3.35843			0.127392
$696$	7.70007	+	15.6744i	0.291870	+	0.594136i
$697$	32.6290			1.23591
$698$	−0.378874	−	0.656229i	−0.0143406	−	0.0248386i
$699$	−4.30657	+	6.42401i	−0.162889	+	0.242978i
$700$	1.40545	+	2.24159i	0.0531209	+	0.0847241i
$701$	6.91381			0.261131			0.130566	−	0.991440i	$-0.458321\pi$
$701$	6.91381			0.261131			0.130566	+	0.991440i	$0.458321\pi$
$702$	8.73439	−	9.86826i	0.329658	−	0.372453i
$703$	3.47221	+	6.01405i	0.130957	+	0.226824i
$704$	1.85703	−	3.21646i	0.0699893	−	0.121225i
$705$	0.531334	+	1.08159i	0.0200112	+	0.0407351i
$706$	−4.66708	+	8.08361i	−0.175648	+	0.304231i
$707$	−14.8820	−	23.7357i	−0.559695	−	0.892675i
$708$	21.1356	+	1.41766i	0.794326	+	0.0532790i
$709$	15.0601			0.565595			0.282797	−	0.959180i	$-0.408738\pi$
$709$	15.0601			0.565595			0.282797	+	0.959180i	$0.408738\pi$
$710$	1.21736	+	2.10852i	0.0456866	+	0.0791315i
$711$	6.77711	+	0.913252i	0.254162	+	0.0342496i
$712$	7.50572	−	13.0003i	0.281289	−	0.487207i
$713$	−11.9789	−	20.7481i	−0.448613	−	0.777021i
$714$	13.5684	+	0.414596i	0.507786	+	0.0155159i
$715$	4.70978	−	8.15759i	0.176136	−	0.305076i
$716$	2.20490	+	3.81899i	0.0824008	+	0.142722i
$717$	−2.26953	+	3.38541i	−0.0847572	+	0.126431i
$718$	−5.81797	+	10.0770i	−0.217125	+	0.376071i
$719$	−9.07755	+	15.7228i	−0.338535	+	0.586360i	−0.984157	−	0.177297i	$-0.943265\pi$
$719$	−9.07755	+	15.7228i	−0.338535	+	0.586360i	0.645622	+	0.763657i	$0.276598\pi$
$720$	−1.13960	−	2.77513i	−0.0424702	−	0.103423i
$721$	−14.8527	+	0.541289i	−0.553142	+	0.0201587i
$722$	−6.28385	−	10.8840i	−0.233861	−	0.405059i
$723$	2.72904	−	4.07086i	0.101494	−	0.151397i
$724$	−5.47131			−0.203339
$725$	10.0826			0.374459
$726$	2.13391	+	4.34382i	0.0791968	+	0.161214i
$727$	−13.7267	−	23.7753i	−0.509095	−	0.881778i	−0.999945	−	0.0105335i	$-0.996647\pi$
$727$	−13.7267	−	23.7753i	−0.509095	−	0.881778i	0.490850	−	0.871244i	$-0.336686\pi$
$728$	−3.56449	−	5.68511i	−0.132109	−	0.210704i
$729$	24.8492	+	10.5602i	0.920341	+	0.391117i
$730$	−0.729393	+	1.26335i	−0.0269961	+	0.0467585i
$731$	4.89404	−	8.47672i	0.181012	−	0.313523i
$732$	21.6587	+	1.45275i	0.800528	+	0.0536950i
$733$	−16.9658	−	29.3857i	−0.626647	−	1.08538i	−0.988220	−	0.153041i	$-0.951093\pi$
$733$	−16.9658	−	29.3857i	−0.626647	−	1.08538i	0.361573	−	0.932344i	$-0.382240\pi$
$734$	0.297341	−	0.515009i	0.0109750	−	0.0190093i
$735$	−6.00032	+	10.5355i	−0.221325	+	0.388607i
$736$	1.21303	+	2.10103i	0.0447129	+	0.0774450i
$737$	−19.1696	+	33.2027i	−0.706120	+	1.22304i
$738$	20.1962	−	26.1547i	0.743431	−	0.962767i
$739$	−22.7074	−	39.3304i	−0.835307	−	1.44679i	−0.893780	−	0.448505i	$-0.851957\pi$
$739$	−22.7074	−	39.3304i	−0.835307	−	1.44679i	0.0584735	−	0.998289i	$-0.481377\pi$
$740$	−2.73812			−0.100655
$741$	−4.91233	−	9.99962i	−0.180459	−	0.367345i
$742$	−22.5164	+	0.820585i	−0.826602	+	0.0301246i
$743$	−16.0822	+	27.8552i	−0.589999	+	1.02191i	0.404233	+	0.914656i	$0.367539\pi$
$743$	−16.0822	+	27.8552i	−0.589999	+	1.02191i	−0.994232	+	0.107252i	$0.965795\pi$
$744$	−17.0660	−	1.14469i	−0.625670	−	0.0419665i
$745$	−5.84456	+	10.1231i	−0.214128	+	0.370881i
$746$	2.11272	+	3.65934i	0.0773522	+	0.133978i
$747$	−12.2976	−	29.9470i	−0.449946	−	1.09570i
$748$	−11.0020			−0.402272
$749$	22.3610	+	35.6642i	0.817052	+	1.30314i
$750$	−1.72817	−	0.115916i	−0.0631038	−	0.00423265i
$751$	22.4049	+	38.8064i	0.817566	+	1.41607i	0.907471	+	0.420115i	$0.138010\pi$
$751$	22.4049	+	38.8064i	0.817566	+	1.41607i	−0.0899052	+	0.995950i	$0.528656\pi$
$752$	−0.695738			−0.0253710
$753$	43.6637	+	2.92872i	1.59119	+	0.106729i
$754$	−25.5715			−0.931259
$755$	17.3951			0.633072
$756$	8.73071	−	10.6195i	0.317533	−	0.386229i
$757$	54.0481			1.96441			0.982206	−	0.187808i	$-0.0601383\pi$
$757$	54.0481			1.96441			0.982206	+	0.187808i	$0.0601383\pi$
$758$	27.7458			1.00777
$759$	−15.5717	−	1.04446i	−0.565216	−	0.0379116i
$760$	−2.53620			−0.0919975
$761$	−7.63810	−	13.2296i	−0.276881	−	0.479572i	0.693727	−	0.720238i	$-0.255967\pi$
$761$	−7.63810	−	13.2296i	−0.276881	−	0.479572i	−0.970608	+	0.240666i	$0.922634\pi$
$762$	28.9863	+	1.94424i	1.05006	+	0.0704325i
$763$	28.2415	−	1.02923i	1.02241	−	0.0372606i
$764$	8.34357			0.301860
$765$	−5.43139	+	7.03382i	−0.196372	+	0.254308i
$766$	−14.8026	−	25.6388i	−0.534839	−	0.926368i
$767$	−15.5090	+	26.8623i	−0.559996	+	0.969941i
$768$	1.72817	+	0.115916i	0.0623599	+	0.00418276i
$769$	−13.7320	+	23.7844i	−0.495187	+	0.857689i	−0.999985	−	0.00554869i	$-0.998234\pi$
$769$	−13.7320	+	23.7844i	−0.495187	+	0.857689i	0.504798	+	0.863238i	$0.331567\pi$
$770$	4.60004	−	8.68325i	0.165774	−	0.312923i
$771$	14.1604	+	28.8251i	0.509974	+	1.03811i
$772$	−20.5384			−0.739194
$773$	0.348202	+	0.603103i	0.0125239	+	0.0216921i	0.872219	−	0.489115i	$-0.162680\pi$
$773$	0.348202	+	0.603103i	0.0125239	+	0.0216921i	−0.859696	+	0.510807i	$0.829347\pi$
$774$	−3.76552	−	9.16974i	−0.135349	−	0.329600i
$775$	−4.93760	+	8.55217i	−0.177364	+	0.307203i
$776$	−0.0494422	−	0.0856364i	−0.00177487	−	0.00307417i
$777$	−5.93902	−	11.0531i	−0.213061	−	0.396529i
$778$	−14.3708	+	24.8910i	−0.515219	+	0.892385i
$779$	−13.9680	−	24.1932i	−0.500455	−	0.866813i
$780$	4.38297	+	0.293986i	0.156936	+	0.0105264i
$781$	4.52133	−	7.83117i	0.161786	−	0.280221i
$782$	3.59331	−	6.22379i	0.128496	−	0.222562i
$783$	−16.6134	−	49.6869i	−0.593715	−	1.77567i
$784$	−3.93199	−	5.79133i	−0.140428	−	0.206833i
$785$	2.55312	+	4.42214i	0.0911248	+	0.157833i
$786$	−12.2532	−	24.9428i	−0.437057	−	0.889681i
$787$	24.6287			0.877918			0.438959	−	0.898507i	$-0.355347\pi$
$787$	24.6287			0.877918			0.438959	+	0.898507i	$0.355347\pi$
$788$	7.91528			0.281970
$789$	0.734037	−	1.09495i	0.0261324	−	0.0389812i
$790$	1.13973	+	1.97407i	0.0405497	+	0.0702342i
$791$	−9.72291	−	15.5074i	−0.345707	−	0.551378i
$792$	−6.80983	+	8.81895i	−0.241977	+	0.313368i
$793$	−15.8928	+	27.5271i	−0.564368	+	0.977515i
$794$	−17.1373	+	29.6827i	−0.608180	+	1.05340i
$795$	8.21346	−	12.2518i	0.291301	−	0.434528i
$796$	1.32856	+	2.30113i	0.0470895	+	0.0815614i
$797$	2.29266	−	3.97100i	0.0812101	−	0.140660i	−0.822560	−	0.568679i	$-0.807455\pi$
$797$	2.29266	−	3.97100i	0.0812101	−	0.140660i	0.903770	+	0.428018i	$0.140788\pi$
$798$	−5.50104	−	10.2380i	−0.194735	−	0.362422i
$799$	1.03048	+	1.78484i	0.0364557	+	0.0631431i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−27.5240	+	35.6444i	−0.972512	+	1.25943i
$802$	−5.35942	−	9.28278i	−0.189248	−	0.327787i
$803$	5.41801			0.191197
$804$	−17.8394	−	1.19657i	−0.629147	−	0.0421998i
$805$	3.40970	+	5.43823i	0.120176	+	0.191672i
$806$	12.5227	−	21.6900i	0.441094	−	0.763997i
$807$	6.23387	+	12.6898i	0.219443	+	0.446701i
$808$	−5.29440	+	9.17017i	−0.186256	+	0.322606i
$809$	−19.9200	−	34.5024i	−0.700349	−	1.21304i	−0.968344	−	0.249619i	$-0.919694\pi$
$809$	−19.9200	−	34.5024i	−0.700349	−	1.21304i	0.267995	−	0.963420i	$-0.413639\pi$
$810$	2.27632	+	8.70737i	0.0799818	+	0.305946i
$811$	−29.9620			−1.05211			−0.526054	−	0.850451i	$-0.676329\pi$
$811$	−29.9620			−1.05211			−0.526054	+	0.850451i	$0.676329\pi$
$812$	−26.6584	+	0.971536i	−0.935526	+	0.0340942i
$813$	8.40487	−	12.5374i	0.294772	−	0.439704i
$814$	5.08477	+	8.80707i	0.178221	+	0.308688i
$815$	9.14283			0.320259
$816$	−2.26227	−	4.60511i	−0.0791952	−	0.161211i
$817$	−8.38026			−0.293188
$818$	−27.2083			−0.951318
$819$	8.31997	+	18.3307i	0.290723	+	0.640525i
$820$	11.0149			0.384657
$821$	−51.1031			−1.78351			−0.891755	−	0.452519i	$-0.850525\pi$
$821$	−51.1031			−1.78351			−0.891755	+	0.452519i	$0.850525\pi$
$822$	8.18340	−	12.2070i	0.285429	−	0.425768i
$823$	−6.21872			−0.216771			−0.108385	−	0.994109i	$-0.534568\pi$
$823$	−6.21872			−0.216771			−0.108385	+	0.994109i	$0.534568\pi$
$824$	2.80875	+	4.86490i	0.0978475	+	0.169477i
$825$	2.83641	+	5.77385i	0.0987512	+	0.201020i
$826$	−15.1476	+	28.5933i	−0.527051	+	0.994888i
$827$	9.24524			0.321489			0.160744	−	0.986996i	$-0.448611\pi$
$827$	9.24524			0.321489			0.160744	+	0.986996i	$0.448611\pi$
$828$	−2.76473	−	6.73262i	−0.0960809	−	0.233975i
$829$	−4.07784	−	7.06303i	−0.141629	−	0.245309i	0.786481	−	0.617615i	$-0.211901\pi$
$829$	−4.07784	−	7.06303i	−0.141629	−	0.245309i	−0.928110	+	0.372305i	$0.878567\pi$
$830$	5.39560	−	9.34546i	0.187284	−	0.324386i
$831$	14.6788	−	21.8960i	0.509201	−	0.759564i
$832$	−1.26810	+	2.19641i	−0.0439634	+	0.0761469i
$833$	−9.03323	+	18.6648i	−0.312983	+	0.646696i
$834$	3.23910	−	4.83170i	0.112161	−	0.167308i
$835$	21.9469			0.759503
$836$	4.70978	+	8.15759i	0.162891	+	0.282136i
$837$	50.2807	+	10.2407i	1.73796	+	0.353971i
$838$	10.5111	−	18.2058i	0.363100	−	0.628908i
$839$	10.1336	+	17.5518i	0.349849	+	0.605957i	0.986222	−	0.165425i	$-0.0528995\pi$
$839$	10.1336	+	17.5518i	0.349849	+	0.605957i	−0.636373	+	0.771381i	$0.719566\pi$
$840$	4.58044	+	0.139959i	0.158040	+	0.00482906i
$841$	−36.3296	+	62.9246i	−1.25274	+	2.16982i
$842$	−6.73036	−	11.6573i	−0.231943	−	0.401738i
$843$	−5.87518	−	11.9596i	−0.202352	−	0.411911i
$844$	−2.51110	+	4.34936i	−0.0864357	+	0.149711i
$845$	3.28385	−	5.68780i	0.112968	−	0.195666i
$846$	2.06852	+	0.278744i	0.0711171	+	0.00958341i
$847$	−7.38780	+	0.269240i	−0.253848	+	0.00925121i
$848$	4.25802	+	7.37510i	0.146221	+	0.253262i
$849$	38.9640	+	2.61349i	1.33724	+	0.0896948i
$850$	−2.96226			−0.101605
$851$	−6.64285			−0.227714
$852$	4.20759	+	0.282222i	0.144150	+	0.00966878i
$853$	16.0421	+	27.7857i	0.549270	+	0.951364i	0.998325	+	0.0578597i	$0.0184276\pi$
$853$	16.0421	+	27.7857i	0.549270	+	0.951364i	−0.449054	+	0.893504i	$0.648239\pi$
$854$	−15.5224	+	29.3009i	−0.531167	+	1.00266i
$855$	7.54044	+	1.01611i	0.257877	+	0.0347504i
$856$	7.95511	−	13.7787i	0.271900	−	0.470945i
$857$	−26.5519	+	45.9893i	−0.906996	+	1.57096i	−0.0887817	+	0.996051i	$0.528297\pi$
$857$	−26.5519	+	45.9893i	−0.906996	+	1.57096i	−0.818215	+	0.574913i	$0.805036\pi$
$858$	−7.19370	−	14.6436i	−0.245589	−	0.499925i
$859$	15.9337	+	27.5980i	0.543652	+	0.941633i	0.998690	+	0.0511613i	$0.0162923\pi$
$859$	15.9337	+	27.5980i	0.543652	+	0.941633i	−0.455038	+	0.890472i	$0.650374\pi$
$860$	1.65213	−	2.86157i	0.0563372	−	0.0975789i
$861$	23.8914	+	44.4644i	0.814218	+	1.51534i
$862$	2.84972	+	4.93585i	0.0970617	+	0.168116i
$863$	−13.9010	+	24.0772i	−0.473195	+	0.819598i	−0.999529	−	0.0306799i	$-0.990233\pi$
$863$	−13.9010	+	24.0772i	−0.473195	+	0.819598i	0.526334	+	0.850278i	$0.323566\pi$
$864$	−5.09162	−	1.03701i	−0.173220	−	0.0352799i
$865$	−0.633241	−	1.09681i	−0.0215309	−	0.0372925i
$866$	17.7157			0.602005
$867$	7.93280	−	11.8332i	0.269412	−	0.401876i
$868$	12.2309	−	23.0877i	0.415144	−	0.783647i
$869$	4.23301	−	7.33179i	0.143595	−	0.248714i
$870$	9.72438	−	14.5056i	0.329687	−	0.491788i
$871$	13.0902	−	22.6730i	0.443546	−	0.768244i
$872$	−5.34068	−	9.25033i	−0.180858	−	0.313256i
$873$	0.112688	+	0.274417i	0.00381392	+	0.00928760i
$874$	−6.15297			−0.208127
$875$	1.23855	−	2.33795i	0.0418706	−	0.0790370i
$876$	1.11407	+	2.26782i	0.0376410	+	0.0766226i
$877$	−13.5194	−	23.4163i	−0.456519	−	0.790714i	0.542255	−	0.840214i	$-0.317571\pi$
$877$	−13.5194	−	23.4163i	−0.456519	−	0.790714i	−0.998774	+	0.0495001i	$0.984237\pi$
$878$	5.39022			0.181911
$879$	12.1576	−	18.1353i	0.410067	−	0.611688i
$880$	−3.71405			−0.125201
$881$	−29.1581			−0.982361			−0.491181	−	0.871058i	$-0.663434\pi$
$881$	−29.1581			−0.982361			−0.491181	+	0.871058i	$0.663434\pi$
$882$	9.37004	+	18.7937i	0.315506	+	0.632816i
$883$	−46.0062			−1.54823			−0.774116	−	0.633044i	$-0.781805\pi$
$883$	−46.0062			−1.54823			−0.774116	+	0.633044i	$0.781805\pi$
$884$	7.51287			0.252685
$885$	−9.34009	−	19.0128i	−0.313964	−	0.639109i
$886$	−11.6840			−0.392530
$887$	10.7773	+	18.6668i	0.361867	+	0.626771i	0.988268	−	0.152729i	$-0.0488063\pi$
$887$	10.7773	+	18.6668i	0.361867	+	0.626771i	−0.626402	+	0.779501i	$0.715473\pi$
$888$	−2.64084	+	3.93928i	−0.0886207	+	0.132194i
$889$	−20.7740	+	39.2140i	−0.696738	+	1.31520i
$890$	−15.0114			−0.503185
$891$	23.7798	−	23.4915i	0.796652	−	0.786996i
$892$	−3.74932	−	6.49401i	−0.125537	−	0.217436i
$893$	0.882265	−	1.52813i	0.0295239	−	0.0511368i
$894$	8.92696	+	18.1719i	0.298562	+	0.607758i
$895$	2.20490	−	3.81899i	0.0737015	−	0.127655i
$896$	−1.23855	+	2.33795i	−0.0413770	+	0.0781053i
$897$	10.6334	+	0.713227i	0.355037	+	0.0238140i
$898$	23.4124			0.781282
$899$	−49.7839	−	86.2282i	−1.66039	−	2.87587i
$900$	−1.83353	+	2.37448i	−0.0611177	+	0.0791494i
$901$	12.6133	−	21.8469i	0.420211	−	0.727827i
$902$	−20.4550	−	35.4290i	−0.681075	−	1.17966i
$903$	15.1350	+	0.462463i	0.503660	+	0.0153898i
$904$	−3.45901	+	5.99118i	−0.115045	+	0.199264i
$905$	2.73565	+	4.73829i	0.0909362	+	0.157506i
$906$	16.7770	−	25.0259i	0.557380	−	0.831431i
$907$	13.8267	−	23.9486i	0.459109	−	0.795200i	−0.539805	−	0.841790i	$-0.681502\pi$
$907$	13.8267	−	23.9486i	0.459109	−	0.795200i	0.998914	+	0.0465902i	$0.0148355\pi$
$908$	−4.63500	+	8.02806i	−0.153818	+	0.266420i
$909$	19.4149	−	25.1429i	0.643952	−	0.833938i
$910$	−3.14121	+	5.92949i	−0.104130	+	0.196561i
$911$	−1.00730	−	1.74469i	−0.0333732	−	0.0578040i	0.848856	−	0.528623i	$-0.177292\pi$
$911$	−1.00730	−	1.74469i	−0.0333732	−	0.0578040i	−0.882230	+	0.470819i	$0.843958\pi$
$912$	−2.44609	+	3.64877i	−0.0809980	+	0.120823i
$913$	−40.0791			−1.32642
$914$	8.99567			0.297550
$915$	−9.57123	−	19.4833i	−0.316415	−	0.644100i
$916$	−9.57481	−	16.5841i	−0.316361	−	0.547953i
$917$	42.4218	−	1.54602i	1.40089	−	0.0510540i
$918$	4.88100	+	14.5979i	0.161097	+	0.481804i
$919$	16.6669	−	28.8680i	0.549791	−	0.952266i	−0.448497	−	0.893784i	$-0.648041\pi$
$919$	16.6669	−	28.8680i	0.549791	−	0.952266i	0.998288	−	0.0584819i	$-0.0186260\pi$
$920$	1.21303	−	2.10103i	0.0399924	−	0.0692689i
$921$	19.2075	+	1.28833i	0.632908	+	0.0424520i
$922$	−2.25201	−	3.90059i	−0.0741660	−	0.128459i
$923$	−3.08746	+	5.34763i	−0.101625	+	0.176020i
$924$	−8.05582	−	14.9927i	−0.265017	−	0.493224i
$925$	1.36906	+	2.37128i	0.0450145	+	0.0779674i
$926$	−15.6097	+	27.0367i	−0.512965	+	0.888482i
$927$	−6.40168	−	15.5893i	−0.210259	−	0.512019i
$928$	5.04131	+	8.73180i	0.165489	+	0.286635i
$929$	−46.6067			−1.52912			−0.764558	−	0.644555i	$-0.777043\pi$
$929$	−46.6067			−1.52912			−0.764558	+	0.644555i	$0.777043\pi$
$930$	7.54166	+	15.3519i	0.247301	+	0.503410i
$931$	17.7063	−	1.29229i	0.580300	−	0.0423531i
$932$	−2.23261	+	3.86699i	−0.0731315	+	0.126667i
$933$	−42.1121	−	2.82465i	−1.37869	−	0.0924748i
$934$	9.65889	−	16.7297i	0.316049	−	0.547412i
$935$	5.50099	+	9.52799i	0.179902	+	0.311599i
$936$	4.65020	−	6.02215i	0.151996	−	0.196840i
$937$	−28.6255			−0.935154			−0.467577	−	0.883952i	$-0.654873\pi$
$937$	−28.6255			−0.935154			−0.467577	+	0.883952i	$0.654873\pi$
$938$	12.7852	−	24.1340i	0.417452	−	0.788003i
$939$	50.5555	+	3.39098i	1.64981	+	0.110661i
$940$	0.347869	+	0.602527i	0.0113462	+	0.0196523i
$941$	54.4118			1.77377			0.886887	−	0.461987i	$-0.152863\pi$
$941$	54.4118			1.77377			0.886887	+	0.461987i	$0.152863\pi$
$942$	8.82445	+	0.591896i	0.287516	+	0.0192850i
$943$	26.7228			0.870214
$944$	12.2301			0.398055
$945$	−13.5621	−	2.25125i	−0.441177	−	0.0732330i
$946$	−12.2722			−0.399004
$947$	49.8788			1.62084			0.810422	−	0.585847i	$-0.199238\pi$
$947$	49.8788			1.62084			0.810422	+	0.585847i	$0.199238\pi$
$948$	3.93928	+	0.264226i	0.127942	+	0.00858165i
$949$	−3.69977			−0.120100
$950$	1.26810	+	2.19641i	0.0411426	+	0.0712610i
$951$	−15.8391	−	1.06240i	−0.513619	−	0.0344507i
$952$	7.83220	−	0.285436i	0.253843	−	0.00925103i
$953$	−23.1721			−0.750618			−0.375309	−	0.926900i	$-0.622463\pi$
$953$	−23.1721			−0.750618			−0.375309	+	0.926900i	$0.622463\pi$
$954$	−9.70483	−	23.6331i	−0.314205	−	0.765149i
$955$	−4.17179	−	7.22574i	−0.134996	−	0.233820i
$956$	−1.17657	+	2.03788i	−0.0380530	+	0.0659097i
$957$	−64.7153	−	4.34075i	−2.09195	−	0.140316i
$958$	10.6993	−	18.5318i	0.345679	−	0.598734i
$959$	11.9250	+	19.0196i	0.385079	+	0.614174i
$960$	−0.763698	−	1.55460i	−0.0246482	−	0.0501743i
$961$	66.5195			2.14579
$962$	−3.47221	−	6.01405i	−0.111949	−	0.193901i
$963$	−29.1719	+	37.7785i	−0.940051	+	1.21740i
$964$	1.41479	−	2.45049i	0.0455673	−	0.0789249i
$965$	10.2692	+	17.7868i	0.330578	+	0.572577i
$966$	11.1124	+	0.339550i	0.357536	+	0.0109248i
$967$	−24.5921	+	42.5948i	−0.790829	+	1.36976i	0.134625	+	0.990897i	$0.457017\pi$
$967$	−24.5921	+	42.5948i	−0.790829	+	1.36976i	−0.925454	+	0.378859i	$0.876316\pi$
$968$	1.39709	+	2.41983i	0.0449042	+	0.0777763i
$969$	12.9835	+	0.870862i	0.417090	+	0.0279761i
$970$	−0.0494422	+	0.0856364i	−0.00158749	+	0.00274962i
$971$	5.09309	−	8.82149i	0.163445	−	0.283095i	−0.772657	−	0.634824i	$-0.781073\pi$
$971$	5.09309	−	8.82149i	0.163445	−	0.283095i	0.936102	+	0.351729i	$0.114406\pi$
$972$	14.7226	+	5.12311i	0.472226	+	0.164324i
$973$	4.72009	+	7.52821i	0.151319	+	0.241343i
$974$	18.9039	+	32.7426i	0.605721	+	1.04914i
$975$	−1.93689	−	3.94276i	−0.0620301	−	0.126269i
$976$	12.5327			0.401163
$977$	9.67495			0.309529			0.154765	−	0.987951i	$-0.450538\pi$
$977$	9.67495			0.309529			0.154765	+	0.987951i	$0.450538\pi$
$978$	8.81798	−	13.1536i	0.281968	−	0.420606i
$979$	27.8766	+	48.2838i	0.890941	+	1.54316i
$980$	−3.04944	+	6.30087i	−0.0974109	+	0.201274i
$981$	12.1724	+	29.6421i	0.388636	+	0.946400i
$982$	0.607232	−	1.05176i	0.0193775	−	0.0335629i
$983$	−8.71874	+	15.1013i	−0.278085	+	0.481657i	−0.970909	−	0.239450i	$-0.923033\pi$
$983$	−8.71874	+	15.1013i	−0.278085	+	0.481657i	0.692824	+	0.721107i	$0.256366\pi$
$984$	10.6235	−	15.8469i	0.338666	−	0.505181i
$985$	−3.95764	−	6.85483i	−0.126101	−	0.218413i
$986$	14.9336	−	25.8658i	0.475584	−	0.823736i
$987$	−1.67772	+	2.71115i	−0.0534025	+	0.0862969i
$988$	−3.21615	−	5.57053i	−0.102319	−	0.177222i
$989$	4.00817	−	6.94235i	0.127452	−	0.220754i
$990$	11.0423	+	1.48801i	0.350949	+	0.0472922i
$991$	24.1017	+	41.7453i	0.765615	+	1.32608i	0.939921	+	0.341392i	$0.110898\pi$
$991$	24.1017	+	41.7453i	0.765615	+	1.32608i	−0.174306	+	0.984692i	$0.555768\pi$
$992$	−9.87519			−0.313538
$993$	−55.0660	−	3.69352i	−1.74747	−	0.117210i
$994$	−3.01552	+	5.69223i	−0.0956463	+	0.180547i
$995$	1.32856	−	2.30113i	0.0421181	−	0.0729508i
$996$	−8.24122	−	16.7760i	−0.261133	−	0.531567i
$997$	18.3316	−	31.7513i	0.580569	−	1.00558i	−0.414843	−	0.909893i	$-0.636163\pi$
$997$	18.3316	−	31.7513i	0.580569	−	1.00558i	0.995412	−	0.0956822i	$-0.0305032\pi$
$998$	13.7499	+	23.8155i	0.435245	+	0.753866i
$999$	9.42980	−	10.6539i	0.298346	−	0.337076i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.i.f.121.6	✓	12
3.2	odd	2		1890.2.i.h.1171.3		12
7.4	even	3		630.2.l.h.571.3	yes	12
9.2	odd	6		1890.2.l.f.1801.2		12
9.7	even	3		630.2.l.h.331.3	yes	12
21.11	odd	6		1890.2.l.f.361.2		12
63.11	odd	6		1890.2.i.h.991.3		12
63.25	even	3	inner	630.2.i.f.151.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.f.121.6	✓	12	1.1	even	1	trivial
630.2.i.f.151.6	yes	12	63.25	even	3	inner
630.2.l.h.331.3	yes	12	9.7	even	3
630.2.l.h.571.3	yes	12	7.4	even	3
1890.2.i.h.991.3		12	63.11	odd	6
1890.2.i.h.1171.3		12	3.2	odd	2
1890.2.l.f.361.2		12	21.11	odd	6
1890.2.l.f.1801.2		12	9.2	odd	6

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(1.72817 + 0.115916i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.72817 - 0.115916i) q^{6} +(1.23855 - 2.33795i) q^{7} -1.00000 q^{8} +(2.97313 + 0.400645i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(1.72817 + 0.115916i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.72817 - 0.115916i) q^{6} +(1.23855 - 2.33795i) q^{7} -1.00000 q^{8} +(2.97313 + 0.400645i) q^{9} +(0.500000 + 0.866025i) q^{10} +(1.85703 - 3.21646i) q^{11} +(1.72817 + 0.115916i) q^{12} +(-1.26810 + 2.19641i) q^{13} +(-1.23855 + 2.33795i) q^{14} +(-0.763698 - 1.55460i) q^{15} +1.00000 q^{16} +(-1.48113 - 2.56539i) q^{17} +(-2.97313 - 0.400645i) q^{18} +(-1.26810 + 2.19641i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(2.41143 - 3.89680i) q^{21} +(-1.85703 + 3.21646i) q^{22} +(-1.21303 - 2.10103i) q^{23} +(-1.72817 - 0.115916i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.26810 - 2.19641i) q^{26} +(5.09162 + 1.03701i) q^{27} +(1.23855 - 2.33795i) q^{28} +(-5.04131 - 8.73180i) q^{29} +(0.763698 + 1.55460i) q^{30} +9.87519 q^{31} -1.00000 q^{32} +(3.58209 - 5.34333i) q^{33} +(1.48113 + 2.56539i) q^{34} +(-2.64400 + 0.0963576i) q^{35} +(2.97313 + 0.400645i) q^{36} +(1.36906 - 2.37128i) q^{37} +(1.26810 - 2.19641i) q^{38} +(-2.44609 + 3.64877i) q^{39} +(0.500000 + 0.866025i) q^{40} +(-5.50745 + 9.53918i) q^{41} +(-2.41143 + 3.89680i) q^{42} +(1.65213 + 2.86157i) q^{43} +(1.85703 - 3.21646i) q^{44} +(-1.13960 - 2.77513i) q^{45} +(1.21303 + 2.10103i) q^{46} -0.695738 q^{47} +(1.72817 + 0.115916i) q^{48} +(-3.93199 - 5.79133i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-2.26227 - 4.60511i) q^{51} +(-1.26810 + 2.19641i) q^{52} +(4.25802 + 7.37510i) q^{53} +(-5.09162 - 1.03701i) q^{54} -3.71405 q^{55} +(-1.23855 + 2.33795i) q^{56} +(-2.44609 + 3.64877i) q^{57} +(5.04131 + 8.73180i) q^{58} +12.2301 q^{59} +(-0.763698 - 1.55460i) q^{60} +12.5327 q^{61} -9.87519 q^{62} +(4.61905 - 6.45479i) q^{63} +1.00000 q^{64} +2.53620 q^{65} +(-3.58209 + 5.34333i) q^{66} -10.3227 q^{67} +(-1.48113 - 2.56539i) q^{68} +(-1.85278 - 3.77154i) q^{69} +(2.64400 - 0.0963576i) q^{70} +2.43471 q^{71} +(-2.97313 - 0.400645i) q^{72} +(0.729393 + 1.26335i) q^{73} +(-1.36906 + 2.37128i) q^{74} +(-0.964470 + 1.43868i) q^{75} +(-1.26810 + 2.19641i) q^{76} +(-5.21990 - 8.32538i) q^{77} +(2.44609 - 3.64877i) q^{78} +2.27946 q^{79} +(-0.500000 - 0.866025i) q^{80} +(8.67897 + 2.38233i) q^{81} +(5.50745 - 9.53918i) q^{82} +(-5.39560 - 9.34546i) q^{83} +(2.41143 - 3.89680i) q^{84} +(-1.48113 + 2.56539i) q^{85} +(-1.65213 - 2.86157i) q^{86} +(-7.70007 - 15.6744i) q^{87} +(-1.85703 + 3.21646i) q^{88} +(-7.50572 + 13.0003i) q^{89} +(1.13960 + 2.77513i) q^{90} +(3.56449 + 5.68511i) q^{91} +(-1.21303 - 2.10103i) q^{92} +(17.0660 + 1.14469i) q^{93} +0.695738 q^{94} +2.53620 q^{95} +(-1.72817 - 0.115916i) q^{96} +(0.0494422 + 0.0856364i) q^{97} +(3.93199 + 5.79133i) q^{98} +(6.80983 - 8.81895i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 2 q^{3} + 12 q^{4} - 6 q^{5} - 2 q^{6} + 4 q^{7} - 12 q^{8} - 4 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 + 2 * q^3 + 12 * q^4 - 6 * q^5 - 2 * q^6 + 4 * q^7 - 12 * q^8 - 4 * q^9	\( 12 q - 12 q^{2} + 2 q^{3} + 12 q^{4} - 6 q^{5} - 2 q^{6} + 4 q^{7} - 12 q^{8} - 4 q^{9} + 6 q^{10} - 7 q^{11} + 2 q^{12} - 2 q^{13} - 4 q^{14} - q^{15} + 12 q^{16} + q^{17} + 4 q^{18} - 2 q^{19} - 6 q^{20} + 29 q^{21} + 7 q^{22} - 9 q^{23} - 2 q^{24} - 6 q^{25} + 2 q^{26} + 11 q^{27} + 4 q^{28} + 3 q^{29} + q^{30} + 18 q^{31} - 12 q^{32} + 27 q^{33} - q^{34} - 8 q^{35} - 4 q^{36} + 6 q^{37} + 2 q^{38} + 10 q^{39} + 6 q^{40} - 11 q^{41} - 29 q^{42} + 23 q^{43} - 7 q^{44} + 5 q^{45} + 9 q^{46} - 2 q^{47} + 2 q^{48} + 24 q^{49} + 6 q^{50} - 15 q^{51} - 2 q^{52} - 4 q^{53} - 11 q^{54} + 14 q^{55} - 4 q^{56} + 10 q^{57} - 3 q^{58} - 22 q^{59} - q^{60} + 50 q^{61} - 18 q^{62} - q^{63} + 12 q^{64} + 4 q^{65} - 27 q^{66} + 4 q^{67} + q^{68} - 12 q^{69} + 8 q^{70} + 22 q^{71} + 4 q^{72} + 24 q^{73} - 6 q^{74} - q^{75} - 2 q^{76} - 11 q^{77} - 10 q^{78} + 2 q^{79} - 6 q^{80} + 20 q^{81} + 11 q^{82} + 4 q^{83} + 29 q^{84} + q^{85} - 23 q^{86} + 7 q^{88} + 2 q^{89} - 5 q^{90} - 8 q^{91} - 9 q^{92} + 40 q^{93} + 2 q^{94} + 4 q^{95} - 2 q^{96} - 36 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 2 * q^3 + 12 * q^4 - 6 * q^5 - 2 * q^6 + 4 * q^7 - 12 * q^8 - 4 * q^9 + 6 * q^10 - 7 * q^11 + 2 * q^12 - 2 * q^13 - 4 * q^14 - q^15 + 12 * q^16 + q^17 + 4 * q^18 - 2 * q^19 - 6 * q^20 + 29 * q^21 + 7 * q^22 - 9 * q^23 - 2 * q^24 - 6 * q^25 + 2 * q^26 + 11 * q^27 + 4 * q^28 + 3 * q^29 + q^30 + 18 * q^31 - 12 * q^32 + 27 * q^33 - q^34 - 8 * q^35 - 4 * q^36 + 6 * q^37 + 2 * q^38 + 10 * q^39 + 6 * q^40 - 11 * q^41 - 29 * q^42 + 23 * q^43 - 7 * q^44 + 5 * q^45 + 9 * q^46 - 2 * q^47 + 2 * q^48 + 24 * q^49 + 6 * q^50 - 15 * q^51 - 2 * q^52 - 4 * q^53 - 11 * q^54 + 14 * q^55 - 4 * q^56 + 10 * q^57 - 3 * q^58 - 22 * q^59 - q^60 + 50 * q^61 - 18 * q^62 - q^63 + 12 * q^64 + 4 * q^65 - 27 * q^66 + 4 * q^67 + q^68 - 12 * q^69 + 8 * q^70 + 22 * q^71 + 4 * q^72 + 24 * q^73 - 6 * q^74 - q^75 - 2 * q^76 - 11 * q^77 - 10 * q^78 + 2 * q^79 - 6 * q^80 + 20 * q^81 + 11 * q^82 + 4 * q^83 + 29 * q^84 + q^85 - 23 * q^86 + 7 * q^88 + 2 * q^89 - 5 * q^90 - 8 * q^91 - 9 * q^92 + 40 * q^93 + 2 * q^94 + 4 * q^95 - 2 * q^96 - 36 * q^97 - 24 * q^98 + 15 * q^99

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