LMFDB - Embedded newform 483.2.i.g.277.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(277,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("483.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 16 x^{14} - 7 x^{13} + 161 x^{12} - 50 x^{11} + 929 x^{10} - 47 x^{9} + 3741 x^{8} + \cdots + 6400 $ x^16 - x^15 + 16x^14 - 7x^13 + 161x^12 - 50x^11 + 929x^10 - 47x^9 + 3741x^8 - 158x^7 + 8993x^6 + 265x^5 + 15176x^4 + 383x^3 + 12649x^2 + 2960x + 6400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.4
Root			$0.595971 - 1.03225i$ of defining polynomial
Character	$\chi$	$=$	483.277
Dual form			483.2.i.g.415.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.595971 - 1.03225i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.289637 - 0.501666i) q^{4} +(1.89410 + 3.28068i) q^{5} +1.19194 q^{6} +(2.62328 + 0.344130i) q^{7} -3.07435 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.595971 - 1.03225i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.289637 - 0.501666i) q^{4} +(1.89410 + 3.28068i) q^{5} +1.19194 q^{6} +(2.62328 + 0.344130i) q^{7} -3.07435 q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.25766 - 3.91038i) q^{10} +(0.745201 - 1.29073i) q^{11} +(0.289637 + 0.501666i) q^{12} -0.460711 q^{13} +(-1.20817 - 2.91297i) q^{14} -3.78820 q^{15} +(1.25295 + 2.17017i) q^{16} +(-3.02964 + 5.24749i) q^{17} +(-0.595971 + 1.03225i) q^{18} +(2.95317 + 5.11504i) q^{19} +2.19441 q^{20} +(-1.60966 + 2.09976i) q^{21} -1.77647 q^{22} +(0.500000 + 0.866025i) q^{23} +(1.53717 - 2.66246i) q^{24} +(-4.67524 + 8.09776i) q^{25} +(0.274571 + 0.475570i) q^{26} +1.00000 q^{27} +(0.932436 - 1.21633i) q^{28} +2.10833 q^{29} +(2.25766 + 3.91038i) q^{30} +(4.03574 - 6.99011i) q^{31} +(-1.58090 + 2.73821i) q^{32} +(0.745201 + 1.29073i) q^{33} +7.22231 q^{34} +(3.83977 + 9.25795i) q^{35} -0.579274 q^{36} +(-5.65171 - 9.78904i) q^{37} +(3.52001 - 6.09683i) q^{38} +(0.230356 - 0.398988i) q^{39} +(-5.82312 - 10.0859i) q^{40} +5.23193 q^{41} +(3.12679 + 0.410183i) q^{42} +4.64064 q^{43} +(-0.431675 - 0.747683i) q^{44} +(1.89410 - 3.28068i) q^{45} +(0.595971 - 1.03225i) q^{46} +(2.30279 + 3.98854i) q^{47} -2.50589 q^{48} +(6.76315 + 1.80550i) q^{49} +11.1452 q^{50} +(-3.02964 - 5.24749i) q^{51} +(-0.133439 + 0.231123i) q^{52} +(2.66141 - 4.60970i) q^{53} +(-0.595971 - 1.03225i) q^{54} +5.64594 q^{55} +(-8.06485 - 1.05797i) q^{56} -5.90634 q^{57} +(-1.25650 - 2.17632i) q^{58} +(-6.14546 + 10.6443i) q^{59} +(-1.09720 + 1.90041i) q^{60} +(-0.205912 - 0.356650i) q^{61} -9.62074 q^{62} +(-1.01361 - 2.44389i) q^{63} +8.78048 q^{64} +(-0.872634 - 1.51145i) q^{65} +(0.888236 - 1.53847i) q^{66} +(-7.56042 + 13.0950i) q^{67} +(1.75499 + 3.03973i) q^{68} -1.00000 q^{69} +(7.26814 - 9.48108i) q^{70} +6.85490 q^{71} +(1.53717 + 2.66246i) q^{72} +(6.07119 - 10.5156i) q^{73} +(-6.73651 + 11.6680i) q^{74} +(-4.67524 - 8.09776i) q^{75} +3.42139 q^{76} +(2.39904 - 3.12948i) q^{77} -0.549141 q^{78} +(-3.23685 - 5.60638i) q^{79} +(-4.74642 + 8.22104i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.11808 - 5.40067i) q^{82} -4.68019 q^{83} +(0.587159 + 1.41568i) q^{84} -22.9538 q^{85} +(-2.76569 - 4.79031i) q^{86} +(-1.05416 + 1.82586i) q^{87} +(-2.29100 + 3.96814i) q^{88} +(-8.14048 - 14.0997i) q^{89} -4.51532 q^{90} +(-1.20857 - 0.158545i) q^{91} +0.579274 q^{92} +(4.03574 + 6.99011i) q^{93} +(2.74479 - 4.75412i) q^{94} +(-11.1872 + 19.3768i) q^{95} +(-1.58090 - 2.73821i) q^{96} -6.78248 q^{97} +(-2.16691 - 8.05730i) q^{98} -1.49040 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} - 8 q^{3} - 15 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 8 q^{9}+O(q^{10}) $ 16 * q - q^2 - 8 * q^3 - 15 * q^4 - 5 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 - 8 * q^9	\( 16 q - q^{2} - 8 q^{3} - 15 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 8 q^{9} + 3 q^{10} - 10 q^{11} - 15 q^{12} - 12 q^{13} - 17 q^{14} + 10 q^{15} - 13 q^{16} - 21 q^{17} - q^{18} - 5 q^{19} - 2 q^{20} + 4 q^{21} + 36 q^{22} + 8 q^{23} - 9 q^{24} - 27 q^{25} - 3 q^{26} + 16 q^{27} + 6 q^{28} + 4 q^{29} + 3 q^{30} + 13 q^{31} - 29 q^{32} - 10 q^{33} - 38 q^{34} + 27 q^{35} + 30 q^{36} - 13 q^{37} + 6 q^{38} + 6 q^{39} - 7 q^{40} + 32 q^{41} + 25 q^{42} + 30 q^{43} - 24 q^{44} - 5 q^{45} + q^{46} + q^{47} + 26 q^{48} + 16 q^{49} + 32 q^{50} - 21 q^{51} + 19 q^{52} - 3 q^{53} - q^{54} - 20 q^{55} + 33 q^{56} + 10 q^{57} + 40 q^{58} - 26 q^{59} + q^{60} + 14 q^{61} - 28 q^{62} - 2 q^{63} + 98 q^{64} + 3 q^{65} - 18 q^{66} - 38 q^{67} - 43 q^{68} - 16 q^{69} + 40 q^{70} + 18 q^{71} - 9 q^{72} + 6 q^{73} - 32 q^{74} - 27 q^{75} - 28 q^{76} + 56 q^{77} + 6 q^{78} - 23 q^{79} + 17 q^{80} - 8 q^{81} - 20 q^{82} + 60 q^{83} + 3 q^{84} - 74 q^{85} + 28 q^{86} - 2 q^{87} - 86 q^{88} - 12 q^{89} - 6 q^{90} + 26 q^{91} - 30 q^{92} + 13 q^{93} + 45 q^{94} - 16 q^{95} - 29 q^{96} + 28 q^{97} + 26 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q - q^2 - 8 * q^3 - 15 * q^4 - 5 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 - 8 * q^9 + 3 * q^10 - 10 * q^11 - 15 * q^12 - 12 * q^13 - 17 * q^14 + 10 * q^15 - 13 * q^16 - 21 * q^17 - q^18 - 5 * q^19 - 2 * q^20 + 4 * q^21 + 36 * q^22 + 8 * q^23 - 9 * q^24 - 27 * q^25 - 3 * q^26 + 16 * q^27 + 6 * q^28 + 4 * q^29 + 3 * q^30 + 13 * q^31 - 29 * q^32 - 10 * q^33 - 38 * q^34 + 27 * q^35 + 30 * q^36 - 13 * q^37 + 6 * q^38 + 6 * q^39 - 7 * q^40 + 32 * q^41 + 25 * q^42 + 30 * q^43 - 24 * q^44 - 5 * q^45 + q^46 + q^47 + 26 * q^48 + 16 * q^49 + 32 * q^50 - 21 * q^51 + 19 * q^52 - 3 * q^53 - q^54 - 20 * q^55 + 33 * q^56 + 10 * q^57 + 40 * q^58 - 26 * q^59 + q^60 + 14 * q^61 - 28 * q^62 - 2 * q^63 + 98 * q^64 + 3 * q^65 - 18 * q^66 - 38 * q^67 - 43 * q^68 - 16 * q^69 + 40 * q^70 + 18 * q^71 - 9 * q^72 + 6 * q^73 - 32 * q^74 - 27 * q^75 - 28 * q^76 + 56 * q^77 + 6 * q^78 - 23 * q^79 + 17 * q^80 - 8 * q^81 - 20 * q^82 + 60 * q^83 + 3 * q^84 - 74 * q^85 + 28 * q^86 - 2 * q^87 - 86 * q^88 - 12 * q^89 - 6 * q^90 + 26 * q^91 - 30 * q^92 + 13 * q^93 + 45 * q^94 - 16 * q^95 - 29 * q^96 + 28 * q^97 + 26 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.595971	−	1.03225i	−0.421415	−	0.729913i	0.574663	−	0.818390i	$-0.305133\pi$
$2$	−0.595971	−	1.03225i	−0.421415	−	0.729913i	−0.996078	+	0.0884776i	$0.971800\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.289637	−	0.501666i	0.144818	−	0.250833i
$5$	1.89410	+	3.28068i	0.847068	+	1.46717i	0.883813	+	0.467840i	$0.154968\pi$
$5$	1.89410	+	3.28068i	0.847068	+	1.46717i	−0.0367448	+	0.999325i	$0.511699\pi$
$6$	1.19194			0.486608
$7$	2.62328	+	0.344130i	0.991505	+	0.130069i
$7$	2.62328	+	0.344130i	0.991505	+	0.130069i
$8$	−3.07435			−1.08695
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	2.25766	−	3.91038i	0.713935	−	1.23657i
$11$	0.745201	−	1.29073i	0.224686	−	0.389168i	−0.731539	−	0.681800i	$-0.761198\pi$
$11$	0.745201	−	1.29073i	0.224686	−	0.389168i	0.956225	+	0.292631i	$0.0945309\pi$
$12$	0.289637	+	0.501666i	0.0836110	+	0.144818i
$13$	−0.460711			−0.127778			−0.0638892	−	0.997957i	$-0.520350\pi$
$13$	−0.460711			−0.127778			−0.0638892	+	0.997957i	$0.520350\pi$
$14$	−1.20817	−	2.91297i	−0.322896	−	0.778525i
$15$	−3.78820			−0.978110
$16$	1.25295	+	2.17017i	0.313237	+	0.542542i
$17$	−3.02964	+	5.24749i	−0.734796	+	1.27270i	0.220017	+	0.975496i	$0.429389\pi$
$17$	−3.02964	+	5.24749i	−0.734796	+	1.27270i	−0.954813	+	0.297207i	$0.903945\pi$
$18$	−0.595971	+	1.03225i	−0.140472	+	0.243304i
$19$	2.95317	+	5.11504i	0.677504	+	1.17347i	0.975730	+	0.218976i	$0.0702715\pi$
$19$	2.95317	+	5.11504i	0.677504	+	1.17347i	−0.298227	+	0.954495i	$0.596395\pi$
$20$	2.19441			0.490684
$21$	−1.60966	+	2.09976i	−0.351257	+	0.458205i
$22$	−1.77647			−0.378745
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$24$	1.53717	−	2.66246i	0.313774	−	0.543473i
$25$	−4.67524	+	8.09776i	−0.935049	+	1.61955i
$26$	0.274571	+	0.475570i	0.0538477	+	0.0932670i
$27$	1.00000			0.192450
$28$	0.932436	−	1.21633i	0.176214	−	0.229866i
$29$	2.10833			0.391506			0.195753	−	0.980653i	$-0.437285\pi$
$29$	2.10833			0.391506			0.195753	+	0.980653i	$0.437285\pi$
$30$	2.25766	+	3.91038i	0.412190	+	0.713935i
$31$	4.03574	−	6.99011i	0.724841	−	1.25546i	−0.234199	−	0.972189i	$-0.575247\pi$
$31$	4.03574	−	6.99011i	0.724841	−	1.25546i	0.959040	−	0.283272i	$-0.0914200\pi$
$32$	−1.58090	+	2.73821i	−0.279467	+	0.484051i
$33$	0.745201	+	1.29073i	0.129723	+	0.224686i
$34$	7.22231			1.23862
$35$	3.83977	+	9.25795i	0.649040	+	1.56488i
$36$	−0.579274			−0.0965456
$37$	−5.65171	−	9.78904i	−0.929135	−	1.60931i	−0.784773	−	0.619784i	$-0.787220\pi$
$37$	−5.65171	−	9.78904i	−0.929135	−	1.60931i	−0.144362	−	0.989525i	$-0.546113\pi$
$38$	3.52001	−	6.09683i	0.571021	−	0.989037i
$39$	0.230356	−	0.398988i	0.0368864	−	0.0638892i
$40$	−5.82312	−	10.0859i	−0.920717	−	1.59473i
$41$	5.23193			0.817090			0.408545	−	0.912738i	$-0.366036\pi$
$41$	5.23193			0.817090			0.408545	+	0.912738i	$0.366036\pi$
$42$	3.12679	+	0.410183i	0.482475	+	0.0632926i
$43$	4.64064			0.707691			0.353845	−	0.935304i	$-0.384874\pi$
$43$	4.64064			0.707691			0.353845	+	0.935304i	$0.384874\pi$
$44$	−0.431675	−	0.747683i	−0.0650775	−	0.112718i
$45$	1.89410	−	3.28068i	0.282356	−	0.489055i
$46$	0.595971	−	1.03225i	0.0878711	−	0.152197i
$47$	2.30279	+	3.98854i	0.335896	+	0.581789i	0.983657	−	0.180055i	$-0.0576276\pi$
$47$	2.30279	+	3.98854i	0.335896	+	0.581789i	−0.647760	+	0.761844i	$0.724294\pi$
$48$	−2.50589			−0.361695
$49$	6.76315	+	1.80550i	0.966164	+	0.257928i
$50$	11.1452			1.57618
$51$	−3.02964	−	5.24749i	−0.424234	−	0.734796i
$52$	−0.133439	+	0.231123i	−0.0185047	+	0.0320510i
$53$	2.66141	−	4.60970i	0.365573	−	0.633191i	−0.623295	−	0.781987i	$-0.714206\pi$
$53$	2.66141	−	4.60970i	0.365573	−	0.633191i	0.988868	+	0.148796i	$0.0475397\pi$
$54$	−0.595971	−	1.03225i	−0.0811014	−	0.140472i
$55$	5.64594			0.761299
$56$	−8.06485	−	1.05797i	−1.07771	−	0.141378i
$57$	−5.90634			−0.782314
$58$	−1.25650	−	2.17632i	−0.164987	−	0.285765i
$59$	−6.14546	+	10.6443i	−0.800071	+	1.38576i	0.119498	+	0.992834i	$0.461872\pi$
$59$	−6.14546	+	10.6443i	−0.800071	+	1.38576i	−0.919569	+	0.392929i	$0.871462\pi$
$60$	−1.09720	+	1.90041i	−0.141648	+	0.245342i
$61$	−0.205912	−	0.356650i	−0.0263643	−	0.0456644i	0.852542	−	0.522658i	$-0.175060\pi$
$61$	−0.205912	−	0.356650i	−0.0263643	−	0.0456644i	−0.878907	+	0.476994i	$0.841726\pi$
$62$	−9.62074			−1.22184
$63$	−1.01361	−	2.44389i	−0.127703	−	0.307901i
$64$	8.78048			1.09756
$65$	−0.872634	−	1.51145i	−0.108237	−	0.187472i
$66$	0.888236	−	1.53847i	0.109334	−	0.189373i
$67$	−7.56042	+	13.0950i	−0.923652	+	1.59981i	−0.129937	+	0.991522i	$0.541478\pi$
$67$	−7.56042	+	13.0950i	−0.923652	+	1.59981i	−0.793715	+	0.608290i	$0.791856\pi$
$68$	1.75499	+	3.03973i	0.212824	+	0.368622i
$69$	−1.00000			−0.120386
$70$	7.26814	−	9.48108i	0.868709	−	1.13321i
$71$	6.85490			0.813527			0.406764	−	0.913533i	$-0.366657\pi$
$71$	6.85490			0.813527			0.406764	+	0.913533i	$0.366657\pi$
$72$	1.53717	+	2.66246i	0.181158	+	0.313774i
$73$	6.07119	−	10.5156i	0.710579	−	1.23076i	−0.254061	−	0.967188i	$-0.581766\pi$
$73$	6.07119	−	10.5156i	0.710579	−	1.23076i	0.964640	−	0.263571i	$-0.0849003\pi$
$74$	−6.73651	+	11.6680i	−0.783103	+	1.35637i
$75$	−4.67524	−	8.09776i	−0.539851	−	0.935049i
$76$	3.42139			0.392460
$77$	2.39904	−	3.12948i	0.273396	−	0.356638i
$78$	−0.549141			−0.0621780
$79$	−3.23685	−	5.60638i	−0.364174	−	0.630767i	0.624470	−	0.781049i	$-0.285315\pi$
$79$	−3.23685	−	5.60638i	−0.364174	−	0.630767i	−0.988643	+	0.150282i	$0.951982\pi$
$80$	−4.74642	+	8.22104i	−0.530666	+	0.919140i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.11808	−	5.40067i	−0.344334	−	0.596404i
$83$	−4.68019			−0.513717			−0.256859	−	0.966449i	$-0.582687\pi$
$83$	−4.68019			−0.513717			−0.256859	+	0.966449i	$0.582687\pi$
$84$	0.587159	+	1.41568i	0.0640643	+	0.154463i
$85$	−22.9538			−2.48969
$86$	−2.76569	−	4.79031i	−0.298232	−	0.516552i
$87$	−1.05416	+	1.82586i	−0.113018	+	0.195753i
$88$	−2.29100	+	3.96814i	−0.244222	+	0.423005i
$89$	−8.14048	−	14.0997i	−0.862889	−	1.49457i	−0.869128	−	0.494587i	$-0.835319\pi$
$89$	−8.14048	−	14.0997i	−0.862889	−	1.49457i	0.00623959	−	0.999981i	$-0.498014\pi$
$90$	−4.51532			−0.475957
$91$	−1.20857	−	0.158545i	−0.126693	−	0.0166200i
$92$	0.579274			0.0603935
$93$	4.03574	+	6.99011i	0.418487	+	0.724841i
$94$	2.74479	−	4.75412i	0.283103	−	0.490350i
$95$	−11.1872	+	19.3768i	−1.14778	+	1.98802i
$96$	−1.58090	−	2.73821i	−0.161350	−	0.279467i
$97$	−6.78248			−0.688656			−0.344328	−	0.938849i	$-0.611893\pi$
$97$	−6.78248			−0.688656			−0.344328	+	0.938849i	$0.611893\pi$
$98$	−2.16691	−	8.05730i	−0.218891	−	0.813910i
$99$	−1.49040			−0.149791
$100$	2.70825	+	4.69082i	0.270825	+	0.469082i
$101$	1.21872	−	2.11089i	0.121267	−	0.210041i	−0.799000	−	0.601330i	$-0.794638\pi$
$101$	1.21872	−	2.11089i	0.121267	−	0.210041i	0.920268	+	0.391289i	$0.127971\pi$
$102$	−3.61116	+	6.25470i	−0.357558	+	0.619308i
$103$	−2.90373	−	5.02940i	−0.286113	−	0.495562i	0.686766	−	0.726879i	$-0.259030\pi$
$103$	−2.90373	−	5.02940i	−0.286113	−	0.495562i	−0.972878	+	0.231317i	$0.925697\pi$
$104$	1.41639			0.138888
$105$	−9.93750	−	1.30364i	−0.969801	−	0.127222i
$106$	−6.34450			−0.616232
$107$	−6.12909	−	10.6159i	−0.592521	−	1.02628i	−0.993892	−	0.110361i	$-0.964799\pi$
$107$	−6.12909	−	10.6159i	−0.592521	−	1.02628i	0.401371	−	0.915916i	$-0.368534\pi$
$108$	0.289637	−	0.501666i	0.0278703	−	0.0482728i
$109$	4.49419	−	7.78417i	0.430465	−	0.745588i	−0.566448	−	0.824097i	$-0.691683\pi$
$109$	4.49419	−	7.78417i	0.430465	−	0.745588i	0.996913	+	0.0785096i	$0.0250161\pi$
$110$	−3.36482	−	5.82804i	−0.320823	−	0.555682i
$111$	11.3034			1.07287
$112$	2.54001	+	6.12413i	0.240008	+	0.578675i
$113$	6.08150			0.572099			0.286050	−	0.958215i	$-0.407658\pi$
$113$	6.08150			0.572099			0.286050	+	0.958215i	$0.407658\pi$
$114$	3.52001	+	6.09683i	0.329679	+	0.571021i
$115$	−1.89410	+	3.28068i	−0.176626	+	0.305925i
$116$	0.610649	−	1.05768i	0.0566973	−	0.0982027i
$117$	0.230356	+	0.398988i	0.0212964	+	0.0368864i
$118$	14.6501			1.34865
$119$	−9.75340	+	12.7230i	−0.894093	+	1.16632i
$120$	11.6462			1.06315
$121$	4.38935	+	7.60258i	0.399032	+	0.691144i
$122$	−0.245435	+	0.425106i	−0.0222207	+	0.0384873i
$123$	−2.61596	+	4.53098i	−0.235874	+	0.408545i
$124$	−2.33780	−	4.04919i	−0.209941	−	0.363628i
$125$	−16.4805			−1.47406
$126$	−1.91863	+	2.50279i	−0.170925	+	0.222966i
$127$	2.84429			0.252390			0.126195	−	0.992005i	$-0.459724\pi$
$127$	2.84429			0.252390			0.126195	+	0.992005i	$0.459724\pi$
$128$	−2.07110	−	3.58726i	−0.183061	−	0.317072i
$129$	−2.32032	+	4.01891i	−0.204293	+	0.353845i
$130$	−1.04013	+	1.80156i	−0.0912254	+	0.158007i
$131$	−4.96443	−	8.59865i	−0.433745	−	0.751268i	0.563448	−	0.826152i	$-0.309475\pi$
$131$	−4.96443	−	8.59865i	−0.433745	−	0.751268i	−0.997192	+	0.0748841i	$0.976141\pi$
$132$	0.863350			0.0751450
$133$	5.98674	+	14.4344i	0.519116	+	1.25162i
$134$	18.0232			1.55696
$135$	1.89410	+	3.28068i	0.163018	+	0.282356i
$136$	9.31416	−	16.1326i	0.798682	−	1.38336i
$137$	6.02046	−	10.4278i	0.514363	−	0.890903i	−0.485498	−	0.874238i	$-0.661362\pi$
$137$	6.02046	−	10.4278i	0.514363	−	0.890903i	0.999861	−	0.0166652i	$-0.00530494\pi$
$138$	0.595971	+	1.03225i	0.0507324	+	0.0878711i
$139$	−1.51537			−0.128532			−0.0642659	−	0.997933i	$-0.520471\pi$
$139$	−1.51537			−0.128532			−0.0642659	+	0.997933i	$0.520471\pi$
$140$	5.75654	+	0.755162i	0.486516	+	0.0638228i
$141$	−4.60558			−0.387859
$142$	−4.08532	−	7.07599i	−0.342833	−	0.593804i
$143$	−0.343322	+	0.594652i	−0.0287101	+	0.0497273i
$144$	1.25295	−	2.17017i	0.104412	−	0.180847i
$145$	3.99338	+	6.91674i	0.331633	+	0.574404i
$146$	−14.4730			−1.19780
$147$	−4.94518	+	4.95431i	−0.407872	+	0.408625i
$148$	−6.54777			−0.538223
$149$	−9.12604	−	15.8068i	−0.747635	−	1.29494i	−0.948954	−	0.315415i	$-0.897856\pi$
$149$	−9.12604	−	15.8068i	−0.747635	−	1.29494i	0.201319	−	0.979526i	$-0.435477\pi$
$150$	−5.57262	+	9.65206i	−0.455003	+	0.788088i
$151$	1.46583	−	2.53889i	0.119287	−	0.206612i	−0.800198	−	0.599736i	$-0.795272\pi$
$151$	1.46583	−	2.53889i	0.119287	−	0.206612i	0.919485	+	0.393124i	$0.128606\pi$
$152$	−9.07906	−	15.7254i	−0.736409	−	1.27550i
$153$	6.05928			0.489864
$154$	−4.66018	−	0.611338i	−0.375528	−	0.0492630i
$155$	30.5764			2.45596
$156$	−0.133439	−	0.231123i	−0.0106837	−	0.0185047i
$157$	−8.39877	+	14.5471i	−0.670295	+	1.16098i	0.307526	+	0.951540i	$0.400499\pi$
$157$	−8.39877	+	14.5471i	−0.670295	+	1.16098i	−0.977820	+	0.209445i	$0.932834\pi$
$158$	−3.85813	+	6.68248i	−0.306937	+	0.531630i
$159$	2.66141	+	4.60970i	0.211064	+	0.365573i
$160$	−11.9776			−0.946911
$161$	1.01361	+	2.44389i	0.0798838	+	0.192605i
$162$	1.19194			0.0936478
$163$	1.82489	+	3.16081i	0.142937	+	0.247574i	0.928601	−	0.371079i	$-0.121012\pi$
$163$	1.82489	+	3.16081i	0.142937	+	0.247574i	−0.785665	+	0.618653i	$0.787679\pi$
$164$	1.51536	−	2.62468i	0.118330	−	0.204953i
$165$	−2.82297	+	4.88953i	−0.219768	+	0.380649i
$166$	2.78926	+	4.83113i	0.216488	+	0.374969i
$167$	−15.2399			−1.17930			−0.589649	−	0.807660i	$-0.700734\pi$
$167$	−15.2399			−1.17930			−0.589649	+	0.807660i	$0.700734\pi$
$168$	4.94866	−	6.45538i	0.381797	−	0.498044i
$169$	−12.7877			−0.983673
$170$	13.6798	+	23.6941i	1.04919	+	1.81725i
$171$	2.95317	−	5.11504i	0.225835	−	0.391157i
$172$	1.34410	−	2.32805i	0.102487	−	0.177512i
$173$	−1.09316	−	1.89341i	−0.0831113	−	0.143953i	0.821474	−	0.570247i	$-0.193152\pi$
$173$	−1.09316	−	1.89341i	−0.0831113	−	0.143953i	−0.904585	+	0.426294i	$0.859819\pi$
$174$	2.51300			0.190510
$175$	−15.0511	+	19.6338i	−1.13776	+	1.48417i
$176$	3.73479			0.281520
$177$	−6.14546	−	10.6443i	−0.461921	−	0.800071i
$178$	−9.70298	+	16.8060i	−0.727269	+	1.25967i
$179$	0.930522	−	1.61171i	0.0695505	−	0.120465i	−0.829153	−	0.559022i	$-0.811177\pi$
$179$	0.930522	−	1.61171i	0.0695505	−	0.120465i	0.898704	+	0.438557i	$0.144510\pi$
$180$	−1.09720	−	1.90041i	−0.0817807	−	0.141648i
$181$	−14.4867			−1.07679			−0.538394	−	0.842693i	$-0.680969\pi$
$181$	−14.4867			−1.07679			−0.538394	+	0.842693i	$0.680969\pi$
$182$	0.556616	+	1.34204i	0.0412592	+	0.0994786i
$183$	0.411824			0.0304429
$184$	−1.53717	−	2.66246i	−0.113322	−	0.196279i
$185$	21.4098	−	37.0829i	1.57408	−	2.72639i
$186$	4.81037	−	8.33181i	0.352714	−	0.610918i
$187$	4.51538	+	7.82087i	0.330197	+	0.571918i
$188$	2.66789			0.194576
$189$	2.62328	+	0.344130i	0.190815	+	0.0250318i
$190$	26.6690			1.93477
$191$	−9.92673	−	17.1936i	−0.718273	−	1.24409i	−0.961684	−	0.274162i	$-0.911600\pi$
$191$	−9.92673	−	17.1936i	−0.718273	−	1.24409i	0.243411	−	0.969923i	$-0.421734\pi$
$192$	−4.39024	+	7.60412i	−0.316838	+	0.548780i
$193$	−0.779443	+	1.35003i	−0.0561055	+	0.0971776i	−0.892714	−	0.450624i	$-0.851202\pi$
$193$	−0.779443	+	1.35003i	−0.0561055	+	0.0971776i	0.836609	+	0.547801i	$0.184535\pi$
$194$	4.04216	+	7.00123i	0.290210	+	0.502659i
$195$	1.74527			0.124981
$196$	2.86461	−	2.86990i	0.204615	−	0.204993i
$197$	−2.48101			−0.176764			−0.0883822	−	0.996087i	$-0.528170\pi$
$197$	−2.48101			−0.176764			−0.0883822	+	0.996087i	$0.528170\pi$
$198$	0.888236	+	1.53847i	0.0631242	+	0.109334i
$199$	2.64623	−	4.58340i	0.187586	−	0.324909i	−0.756859	−	0.653578i	$-0.773267\pi$
$199$	2.64623	−	4.58340i	0.187586	−	0.324909i	0.944445	+	0.328670i	$0.106600\pi$
$200$	14.3733	−	24.8953i	1.01635	−	1.76036i
$201$	−7.56042	−	13.0950i	−0.533271	−	0.923652i
$202$	−2.90529			−0.204415
$203$	5.53072	+	0.725538i	0.388180	+	0.0509228i
$204$	−3.50998			−0.245748
$205$	9.90980	+	17.1643i	0.692131	+	1.19881i
$206$	−3.46108	+	5.99476i	−0.241145	+	0.417675i
$207$	0.500000	−	0.866025i	0.0347524	−	0.0601929i
$208$	−0.577247	−	0.999821i	−0.0400249	−	0.0693251i
$209$	8.80282			0.608904
$210$	4.57678	+	11.0349i	0.315828	+	0.761483i
$211$	27.0118			1.85957			0.929784	−	0.368105i	$-0.119993\pi$
$211$	27.0118			1.85957			0.929784	+	0.368105i	$0.119993\pi$
$212$	−1.54169	−	2.67028i	−0.105883	−	0.183395i
$213$	−3.42745	+	5.93652i	−0.234845	+	0.406764i
$214$	−7.30551	+	12.6535i	−0.499395	+	0.864977i
$215$	8.78984	+	15.2245i	0.599462	+	1.03830i
$216$	−3.07435			−0.209183
$217$	12.9924	−	16.9482i	0.881980	−	1.15052i
$218$	−10.7136			−0.725619
$219$	6.07119	+	10.5156i	0.410253	+	0.710579i
$220$	1.63527	−	2.83238i	0.110250	−	0.190959i
$221$	1.39579	−	2.41758i	0.0938909	−	0.162624i
$222$	−6.73651	−	11.6680i	−0.452125	−	0.783103i
$223$	−4.93735			−0.330630			−0.165315	−	0.986241i	$-0.552864\pi$
$223$	−4.93735			−0.330630			−0.165315	+	0.986241i	$0.552864\pi$
$224$	−5.08945	+	6.63904i	−0.340053	+	0.443589i
$225$	9.35049			0.623366
$226$	−3.62440	−	6.27764i	−0.241091	−	0.417582i
$227$	−5.72866	+	9.92233i	−0.380224	+	0.658568i	−0.991094	−	0.133163i	$-0.957487\pi$
$227$	−5.72866	+	9.92233i	−0.380224	+	0.658568i	0.610870	+	0.791731i	$0.290820\pi$
$228$	−1.71069	+	2.96301i	−0.113293	+	0.196230i
$229$	4.85646	+	8.41164i	0.320924	+	0.555857i	0.980679	−	0.195624i	$-0.0626732\pi$
$229$	4.85646	+	8.41164i	0.320924	+	0.555857i	−0.659755	+	0.751481i	$0.729340\pi$
$230$	4.51532			0.297731
$231$	1.51069	+	3.64237i	0.0993961	+	0.239651i
$232$	−6.48172			−0.425546
$233$	−4.46345	−	7.73092i	−0.292410	−	0.506470i	0.681969	−	0.731381i	$-0.261124\pi$
$233$	−4.46345	−	7.73092i	−0.292410	−	0.506470i	−0.974379	+	0.224912i	$0.927791\pi$
$234$	0.274571	−	0.475570i	0.0179492	−	0.0310890i
$235$	−8.72343	+	15.1094i	−0.569054	+	0.985630i
$236$	3.55991	+	6.16594i	0.231730	+	0.401368i
$237$	6.47369			0.420511
$238$	18.9461	+	2.48541i	1.22809	+	0.161105i
$239$	14.7250			0.952480			0.476240	−	0.879315i	$-0.341999\pi$
$239$	14.7250			0.952480			0.476240	+	0.879315i	$0.341999\pi$
$240$	−4.74642	−	8.22104i	−0.306380	−	0.530666i
$241$	12.2335	−	21.1890i	0.788027	−	1.36490i	−0.139147	−	0.990272i	$-0.544436\pi$
$241$	12.2335	−	21.1890i	0.788027	−	1.36490i	0.927174	−	0.374631i	$-0.122231\pi$
$242$	5.23185	−	9.06184i	0.336316	−	0.582517i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−0.238559			−0.0152722
$245$	6.88684	+	25.6075i	0.439984	+	1.63600i
$246$	6.23615			0.397603
$247$	−1.36056	−	2.35656i	−0.0865703	−	0.149944i
$248$	−12.4073	+	21.4900i	−0.787862	+	1.36462i
$249$	2.34009	−	4.05316i	0.148297	−	0.256859i
$250$	9.82193	+	17.0121i	0.621193	+	1.07594i
$251$	−2.61433			−0.165015			−0.0825076	−	0.996590i	$-0.526293\pi$
$251$	−2.61433			−0.165015			−0.0825076	+	0.996590i	$0.526293\pi$
$252$	−1.51959	−	0.199346i	−0.0957255	−	0.0125576i
$253$	1.49040			0.0937007
$254$	−1.69511	−	2.93602i	−0.106361	−	0.184222i
$255$	11.4769	−	19.8786i	0.718711	−	1.24484i
$256$	6.31185	−	10.9324i	0.394490	−	0.683277i
$257$	0.509978	+	0.883308i	0.0318116	+	0.0550993i	0.881493	−	0.472197i	$-0.156539\pi$
$257$	0.509978	+	0.883308i	0.0318116	+	0.0550993i	−0.849681	+	0.527297i	$0.823206\pi$
$258$	5.53137			0.344368
$259$	−11.4573	−	27.6243i	−0.711921	−	1.71649i
$260$	−1.01099			−0.0626988
$261$	−1.05416	−	1.82586i	−0.0652510	−	0.113018i
$262$	−5.91732	+	10.2491i	−0.365573	+	0.633191i
$263$	−4.46901	+	7.74054i	−0.275571	+	0.477302i	−0.970279	−	0.241989i	$-0.922200\pi$
$263$	−4.46901	+	7.74054i	−0.275571	+	0.477302i	0.694708	+	0.719292i	$0.255533\pi$
$264$	−2.29100	−	3.96814i	−0.141002	−	0.244222i
$265$	20.1639			1.23866
$266$	11.3321	−	14.7823i	0.694813	−	0.906363i
$267$	16.2810			0.996378
$268$	4.37955	+	7.58561i	0.267524	+	0.463365i
$269$	6.84056	−	11.8482i	0.417076	−	0.722397i	−0.578568	−	0.815634i	$-0.696388\pi$
$269$	6.84056	−	11.8482i	0.417076	−	0.722397i	0.995644	+	0.0932372i	$0.0297215\pi$
$270$	2.25766	−	3.91038i	0.137397	−	0.237978i
$271$	1.98691	+	3.44144i	0.120696	+	0.209052i	0.920043	−	0.391819i	$-0.128154\pi$
$271$	1.98691	+	3.44144i	0.120696	+	0.209052i	−0.799346	+	0.600871i	$0.794821\pi$
$272$	−15.1839			−0.920660
$273$	0.741590	−	0.967382i	0.0448831	−	0.0585486i
$274$	−14.3521			−0.867042
$275$	6.96799	+	12.0689i	0.420186	+	0.727783i
$276$	−0.289637	+	0.501666i	−0.0174341	+	0.0301967i
$277$	5.00728	−	8.67286i	0.300858	−	0.521101i	−0.675472	−	0.737385i	$-0.736060\pi$
$277$	5.00728	−	8.67286i	0.300858	−	0.521101i	0.976331	+	0.216284i	$0.0693936\pi$
$278$	0.903115	+	1.56424i	0.0541652	+	0.0938169i
$279$	−8.07148			−0.483227
$280$	−11.8048	−	28.4621i	−0.705471	−	1.70094i
$281$	−21.3379			−1.27291			−0.636456	−	0.771313i	$-0.719600\pi$
$281$	−21.3379			−1.27291			−0.636456	+	0.771313i	$0.719600\pi$
$282$	2.74479	+	4.75412i	0.163450	+	0.283103i
$283$	−7.24152	+	12.5427i	−0.430463	+	0.745585i	−0.996913	−	0.0785118i	$-0.974983\pi$
$283$	−7.24152	+	12.5427i	−0.430463	+	0.745585i	0.566450	+	0.824096i	$0.308317\pi$
$284$	1.98543	−	3.43887i	0.117814	−	0.204059i
$285$	−11.1872	−	19.3768i	−0.662673	−	1.14778i
$286$	0.818441			0.0483954
$287$	13.7248	+	1.80046i	0.810149	+	0.106278i
$288$	3.16181			0.186311
$289$	−9.85743	−	17.0736i	−0.579849	−	1.00433i
$290$	4.75988	−	8.24436i	0.279510	−	0.484125i
$291$	3.39124	−	5.87380i	0.198798	−	0.344328i
$292$	−3.51688	−	6.09142i	−0.205810	−	0.356473i
$293$	33.1986			1.93948			0.969741	−	0.244134i	$-0.0785038\pi$
$293$	33.1986			1.93948			0.969741	+	0.244134i	$0.0785038\pi$
$294$	8.06128	+	2.15205i	0.470144	+	0.125510i
$295$	−46.5605			−2.71086
$296$	17.3753	+	30.0949i	1.00992	+	1.74923i
$297$	0.745201	−	1.29073i	0.0432409	−	0.0748955i
$298$	−10.8777	+	18.8408i	−0.630129	+	1.09142i
$299$	−0.230356	−	0.398988i	−0.0133218	−	0.0230741i
$300$	−5.41649			−0.312721
$301$	12.1737	+	1.59698i	0.701679	+	0.0920486i
$302$	−3.49436			−0.201078
$303$	1.21872	+	2.11089i	0.0700137	+	0.121267i
$304$	−7.40033	+	12.8178i	−0.424438	+	0.735148i
$305$	0.780037	−	1.35106i	0.0446648	−	0.0773616i
$306$	−3.61116	−	6.25470i	−0.206436	−	0.357558i
$307$	31.4823			1.79679			0.898396	−	0.439187i	$-0.144733\pi$
$307$	31.4823			1.79679			0.898396	+	0.439187i	$0.144733\pi$
$308$	−0.875103	−	2.10993i	−0.0498636	−	0.120225i
$309$	5.80746			0.330375
$310$	−18.2227	−	31.5626i	−1.03498	−	1.79263i
$311$	9.10379	−	15.7682i	0.516229	−	0.894135i	−0.483594	−	0.875293i	$-0.660669\pi$
$311$	9.10379	−	15.7682i	0.516229	−	0.894135i	0.999822	−	0.0188419i	$-0.00599793\pi$
$312$	−0.708193	+	1.22663i	−0.0400935	+	0.0694440i
$313$	−10.7276	−	18.5807i	−0.606359	−	1.05025i	−0.991835	−	0.127527i	$-0.959296\pi$
$313$	−10.7276	−	18.5807i	−0.606359	−	1.05025i	0.385476	−	0.922718i	$-0.374037\pi$
$314$	20.0217			1.12989
$315$	6.09773	−	7.95431i	0.343568	−	0.448175i
$316$	−3.75004			−0.210956
$317$	1.40432	+	2.43236i	0.0788747	+	0.136615i	0.902765	−	0.430135i	$-0.141534\pi$
$317$	1.40432	+	2.43236i	0.0788747	+	0.136615i	−0.823890	+	0.566750i	$0.808201\pi$
$318$	3.17225	−	5.49450i	0.177891	−	0.308116i
$319$	1.57113	−	2.72127i	0.0879662	−	0.152362i
$320$	16.6311	+	28.8060i	0.929708	+	1.61030i
$321$	12.2582			0.684184
$322$	1.91863	−	2.50279i	0.106921	−	0.139475i
$323$	−35.7882			−1.99131
$324$	0.289637	+	0.501666i	0.0160909	+	0.0278703i
$325$	2.15394	−	3.73073i	0.119479	−	0.206944i
$326$	2.17517	−	3.76750i	0.120471	−	0.208663i
$327$	4.49419	+	7.78417i	0.248529	+	0.430465i
$328$	−16.0848			−0.888132
$329$	4.66827	+	11.2555i	0.257370	+	0.620536i
$330$	6.72964			0.370454
$331$	13.5491	+	23.4678i	0.744727	+	1.28991i	0.950322	+	0.311268i	$0.100754\pi$
$331$	13.5491	+	23.4678i	0.744727	+	1.28991i	−0.205595	+	0.978637i	$0.565913\pi$
$332$	−1.35556	+	2.34789i	−0.0743957	+	0.128857i
$333$	−5.65171	+	9.78904i	−0.309712	+	0.536436i
$334$	9.08253	+	15.7314i	0.496974	+	0.860784i
$335$	−57.2808			−3.12959
$336$	−6.57365	−	0.862354i	−0.358622	−	0.0470452i
$337$	8.21670			0.447592			0.223796	−	0.974636i	$-0.428155\pi$
$337$	8.21670			0.447592			0.223796	+	0.974636i	$0.428155\pi$
$338$	7.62113	+	13.2002i	0.414535	+	0.717995i
$339$	−3.04075	+	5.26673i	−0.165151	+	0.286050i
$340$	−6.64826	+	11.5151i	−0.360553	+	0.624496i
$341$	−6.01488	−	10.4181i	−0.325724	−	0.564170i
$342$	−7.04002			−0.380680
$343$	17.1203	+	7.06372i	0.924408	+	0.381405i
$344$	−14.2669			−0.769221
$345$	−1.89410	−	3.28068i	−0.101975	−	0.176626i
$346$	−1.30298	+	2.25683i	−0.0700487	+	0.121328i
$347$	−1.30625	+	2.26249i	−0.0701230	+	0.121457i	−0.898955	−	0.438041i	$-0.855673\pi$
$347$	−1.30625	+	2.26249i	−0.0701230	+	0.121457i	0.828832	+	0.559497i	$0.189006\pi$
$348$	0.610649	+	1.05768i	0.0327342	+	0.0566973i
$349$	−16.3975			−0.877740			−0.438870	−	0.898551i	$-0.644621\pi$
$349$	−16.3975			−0.877740			−0.438870	+	0.898551i	$0.644621\pi$
$350$	29.2370	+	3.83541i	1.56279	+	0.205011i
$351$	−0.460711			−0.0245910
$352$	2.35618	+	4.08103i	0.125585	+	0.217520i
$353$	−14.5072	+	25.1273i	−0.772142	+	1.33739i	0.164245	+	0.986420i	$0.447481\pi$
$353$	−14.5072	+	25.1273i	−0.772142	+	1.33739i	−0.936387	+	0.350969i	$0.885852\pi$
$354$	−7.32503	+	12.6873i	−0.389321	+	0.674324i
$355$	12.9839	+	22.4887i	0.689113	+	1.19358i
$356$	−9.43113			−0.499849
$357$	−6.14176	−	14.8082i	−0.325056	−	0.783733i
$358$	−2.21826			−0.117239
$359$	15.0803	+	26.1199i	0.795910	+	1.37856i	0.922259	+	0.386571i	$0.126341\pi$
$359$	15.0803	+	26.1199i	0.795910	+	1.37856i	−0.126349	+	0.991986i	$0.540326\pi$
$360$	−5.82312	+	10.0859i	−0.306906	+	0.531576i
$361$	−7.94243	+	13.7567i	−0.418022	+	0.724036i
$362$	8.63365	+	14.9539i	0.453775	+	0.785961i
$363$	−8.77870			−0.460762
$364$	−0.429584	+	0.560379i	−0.0225163	+	0.0293719i
$365$	45.9978			2.40764
$366$	−0.245435	−	0.425106i	−0.0128291	−	0.0222207i
$367$	−4.35916	+	7.55029i	−0.227546	+	0.394122i	−0.957080	−	0.289823i	$-0.906404\pi$
$367$	−4.35916	+	7.55029i	−0.227546	+	0.394122i	0.729534	+	0.683945i	$0.239737\pi$
$368$	−1.25295	+	2.17017i	−0.0653144	+	0.113128i
$369$	−2.61596	−	4.53098i	−0.136182	−	0.235874i
$370$	−51.0385			−2.65337
$371$	8.56795	−	11.1766i	0.444826	−	0.580262i
$372$	4.67560			0.242419
$373$	5.45347	+	9.44568i	0.282370	+	0.489079i	0.971968	−	0.235113i	$-0.0755461\pi$
$373$	5.45347	+	9.44568i	0.282370	+	0.489079i	−0.689598	+	0.724192i	$0.742213\pi$
$374$	5.38207	−	9.32202i	0.278300	−	0.482030i
$375$	8.24027	−	14.2726i	0.425526	−	0.737032i
$376$	−7.07956	−	12.2622i	−0.365101	−	0.632373i
$377$	−0.971330			−0.0500260
$378$	−1.20817	−	2.91297i	−0.0621414	−	0.149827i
$379$	−11.5747			−0.594551			−0.297275	−	0.954792i	$-0.596078\pi$
$379$	−11.5747			−0.594551			−0.297275	+	0.954792i	$0.596078\pi$
$380$	6.48046	+	11.2245i	0.332440	+	0.575804i
$381$	−1.42214	+	2.46322i	−0.0728586	+	0.126195i
$382$	−11.8321	+	20.4938i	−0.605382	+	1.04855i
$383$	−12.1224	−	20.9967i	−0.619428	−	1.07288i	−0.989590	−	0.143913i	$-0.954031\pi$
$383$	−12.1224	−	20.9967i	−0.619428	−	1.07288i	0.370163	−	0.928967i	$-0.379302\pi$
$384$	4.14221			0.211381
$385$	14.8109	+	1.94294i	0.754832	+	0.0990214i
$386$	1.85810			0.0945748
$387$	−2.32032	−	4.01891i	−0.117948	−	0.204293i
$388$	−1.96446	+	3.40254i	−0.0997301	+	0.172738i
$389$	−2.90240	+	5.02710i	−0.147157	+	0.254884i	−0.930176	−	0.367115i	$-0.880346\pi$
$389$	−2.90240	+	5.02710i	−0.147157	+	0.254884i	0.783018	+	0.621999i	$0.213679\pi$
$390$	−1.04013	−	1.80156i	−0.0526690	−	0.0912254i
$391$	−6.05928			−0.306431
$392$	−20.7923	−	5.55072i	−1.05017	−	0.280354i
$393$	9.92887			0.500845
$394$	1.47861	+	2.56103i	0.0744912	+	0.129023i
$395$	12.2618	−	21.2381i	0.616960	−	1.06861i
$396$	−0.431675	+	0.747683i	−0.0216925	+	0.0375725i
$397$	6.60091	+	11.4331i	0.331290	+	0.573812i	0.982765	−	0.184859i	$-0.0591827\pi$
$397$	6.60091	+	11.4331i	0.331290	+	0.573812i	−0.651475	+	0.758670i	$0.725849\pi$
$398$	−6.30830			−0.316207
$399$	−15.4940	−	2.03255i	−0.775668	−	0.101755i
$400$	−23.4313			−1.17157
$401$	−11.7994	−	20.4372i	−0.589236	−	1.02059i	−0.994333	−	0.106313i	$-0.966095\pi$
$401$	−11.7994	−	20.4372i	−0.589236	−	1.02059i	0.405097	−	0.914274i	$-0.367238\pi$
$402$	−9.01158	+	15.6085i	−0.449457	+	0.778482i
$403$	−1.85931	+	3.22042i	−0.0926189	+	0.160421i
$404$	−0.705973	−	1.22278i	−0.0351235	−	0.0608356i
$405$	−3.78820			−0.188237
$406$	−2.54721	−	6.14150i	−0.126416	−	0.304797i
$407$	−16.8466			−0.835056
$408$	9.31416	+	16.1326i	0.461120	+	0.798682i
$409$	−4.32065	+	7.48358i	−0.213642	+	0.370039i	−0.952852	−	0.303436i	$-0.901866\pi$
$409$	−4.32065	+	7.48358i	−0.213642	+	0.370039i	0.739209	+	0.673476i	$0.235199\pi$
$410$	11.8119	−	20.4588i	0.583349	−	1.01039i
$411$	6.02046	+	10.4278i	0.296968	+	0.514363i
$412$	−3.36411			−0.165738
$413$	−19.7842	+	25.8080i	−0.973519	+	1.26993i
$414$	−1.19194			−0.0585808
$415$	−8.86475	−	15.3542i	−0.435154	−	0.753708i
$416$	0.728341	−	1.26152i	0.0357098	−	0.0618513i
$417$	0.757684	−	1.31235i	0.0371039	−	0.0642659i
$418$	−5.24622	−	9.08673i	−0.256601	−	0.444446i
$419$	30.0603			1.46854			0.734270	−	0.678858i	$-0.237525\pi$
$419$	30.0603			1.46854			0.734270	+	0.678858i	$0.237525\pi$
$420$	−3.53226	+	4.60773i	−0.172356	+	0.224834i
$421$	−24.7510			−1.20629			−0.603144	−	0.797632i	$-0.706085\pi$
$421$	−24.7510			−1.20629			−0.603144	+	0.797632i	$0.706085\pi$
$422$	−16.0982	−	27.8830i	−0.783650	−	1.35732i
$423$	2.30279	−	3.98854i	0.111965	−	0.193930i
$424$	−8.18210	+	14.1718i	−0.397358	+	0.688244i
$425$	−28.3286	−	49.0666i	−1.37414	−	2.38008i
$426$	8.17065			0.395869
$427$	−0.417430	−	1.00645i	−0.0202008	−	0.0487056i
$428$	−7.10084			−0.343232
$429$	−0.343322	−	0.594652i	−0.0165758	−	0.0287101i
$430$	10.4770	−	18.1467i	0.505245	−	0.875110i
$431$	7.82692	−	13.5566i	0.377010	−	0.653000i	−0.613616	−	0.789605i	$-0.710286\pi$
$431$	7.82692	−	13.5566i	0.377010	−	0.653000i	0.990626	+	0.136605i	$0.0436191\pi$
$432$	1.25295	+	2.17017i	0.0602824	+	0.104412i
$433$	−0.941683			−0.0452544			−0.0226272	−	0.999744i	$-0.507203\pi$
$433$	−0.941683			−0.0452544			−0.0226272	+	0.999744i	$0.507203\pi$
$434$	−25.2379	−	3.31079i	−1.21146	−	0.158923i
$435$	−7.98677			−0.382936
$436$	−2.60337	−	4.50916i	−0.124679	−	0.215950i
$437$	−2.95317	+	5.11504i	−0.141269	+	0.244686i
$438$	7.23651	−	12.5340i	0.345774	−	0.598898i
$439$	9.42204	+	16.3194i	0.449689	+	0.778885i	0.998366	−	0.0571502i	$-0.0182014\pi$
$439$	9.42204	+	16.3194i	0.449689	+	0.778885i	−0.548676	+	0.836035i	$0.684868\pi$
$440$	−17.3576			−0.827490
$441$	−1.81797	−	6.75981i	−0.0865699	−	0.321896i
$442$	−3.32740			−0.158268
$443$	1.26840	+	2.19693i	0.0602634	+	0.104379i	0.894583	−	0.446902i	$-0.147473\pi$
$443$	1.26840	+	2.19693i	0.0602634	+	0.104379i	−0.834320	+	0.551281i	$0.814139\pi$
$444$	3.27389	−	5.67054i	0.155372	−	0.269112i
$445$	30.8378	−	53.4126i	1.46185	−	2.53200i
$446$	2.94252	+	5.09659i	0.139332	+	0.241331i
$447$	18.2521			0.863294
$448$	23.0336	+	3.02163i	1.08824	+	0.142759i
$449$	−34.2788			−1.61772			−0.808859	−	0.588003i	$-0.799914\pi$
$449$	−34.2788			−1.61772			−0.808859	+	0.588003i	$0.799914\pi$
$450$	−5.57262	−	9.65206i	−0.262696	−	0.455003i
$451$	3.89884	−	6.75298i	0.183589	−	0.317985i
$452$	1.76143	−	3.05088i	0.0828505	−	0.143501i
$453$	1.46583	+	2.53889i	0.0688706	+	0.119287i
$454$	13.6565			0.640929
$455$	−1.76903	−	4.26524i	−0.0829332	−	0.199958i
$456$	18.1581			0.850332
$457$	7.54327	+	13.0653i	0.352859	+	0.611170i	0.986749	−	0.162253i	$-0.0518762\pi$
$457$	7.54327	+	13.0653i	0.352859	+	0.611170i	−0.633890	+	0.773423i	$0.718543\pi$
$458$	5.78862	−	10.0262i	0.270485	−	0.468493i
$459$	−3.02964	+	5.24749i	−0.141411	+	0.244932i
$460$	1.09720	+	1.90041i	0.0511574	+	0.0886072i
$461$	15.6065			0.726865			0.363433	−	0.931621i	$-0.381605\pi$
$461$	15.6065			0.726865			0.363433	+	0.931621i	$0.381605\pi$
$462$	2.85952	−	3.73016i	0.133037	−	0.173543i
$463$	6.25815			0.290841			0.145420	−	0.989370i	$-0.453547\pi$
$463$	6.25815			0.290841			0.145420	+	0.989370i	$0.453547\pi$
$464$	2.64162	+	4.57542i	0.122634	+	0.212409i
$465$	−15.2882	+	26.4800i	−0.708974	+	1.22798i
$466$	−5.32018	+	9.21481i	−0.246452	+	0.426868i
$467$	−4.38154	−	7.58905i	−0.202753	−	0.351179i	0.746661	−	0.665205i	$-0.231656\pi$
$467$	−4.38154	−	7.58905i	−0.202753	−	0.351179i	−0.949415	+	0.314025i	$0.898322\pi$
$468$	0.266878			0.0123364
$469$	−24.3395	+	31.7501i	−1.12389	+	1.46608i
$470$	20.7956			0.959232
$471$	−8.39877	−	14.5471i	−0.386995	−	0.670295i
$472$	18.8933	−	32.7241i	0.869633	−	1.50625i
$473$	3.45821	−	5.98979i	0.159009	−	0.275411i
$474$	−3.85813	−	6.68248i	−0.177210	−	0.306937i
$475$	−55.2272			−2.53400
$476$	3.55776	+	8.57800i	0.163070	+	0.393172i
$477$	−5.32282			−0.243715
$478$	−8.77567	−	15.1999i	−0.401390	−	0.695227i
$479$	7.88811	−	13.6626i	0.360417	−	0.624260i	−0.627613	−	0.778526i	$-0.715968\pi$
$479$	7.88811	−	13.6626i	0.360417	−	0.624260i	0.988029	+	0.154266i	$0.0493012\pi$
$480$	5.98879	−	10.3729i	0.273350	−	0.473455i
$481$	2.60380	+	4.50992i	0.118723	+	0.205635i
$482$	−29.1632			−1.32835
$483$	−2.62328	−	0.344130i	−0.119363	−	0.0156585i
$484$	5.08527			0.231149
$485$	−12.8467	−	22.2511i	−0.583339	−	1.01037i
$486$	−0.595971	+	1.03225i	−0.0270338	+	0.0468239i
$487$	−20.2877	+	35.1393i	−0.919323	+	1.59231i	−0.118877	+	0.992909i	$0.537929\pi$
$487$	−20.2877	+	35.1393i	−0.919323	+	1.59231i	−0.800446	+	0.599405i	$0.795404\pi$
$488$	0.633045	+	1.09647i	0.0286566	+	0.0496347i
$489$	−3.64979			−0.165049
$490$	22.3291	−	22.3703i	1.00872	−	1.01059i
$491$	9.38984			0.423757			0.211879	−	0.977296i	$-0.432042\pi$
$491$	9.38984			0.423757			0.211879	+	0.977296i	$0.432042\pi$
$492$	1.51536	+	2.62468i	0.0683177	+	0.118330i
$493$	−6.38747	+	11.0634i	−0.287677	+	0.498271i
$494$	−1.62171	+	2.80888i	−0.0729641	+	0.126377i
$495$	−2.82297	−	4.88953i	−0.126883	−	0.219768i
$496$	20.2263			0.908187
$497$	17.9823	+	2.35898i	0.806616	+	0.105815i
$498$	−5.57851			−0.249979
$499$	−9.53902	−	16.5221i	−0.427025	−	0.739629i	0.569582	−	0.821934i	$-0.307105\pi$
$499$	−9.53902	−	16.5221i	−0.427025	−	0.739629i	−0.996607	+	0.0823054i	$0.973772\pi$
$500$	−4.77337	+	8.26773i	−0.213472	+	0.369744i
$501$	7.61994	−	13.1981i	0.340434	−	0.589649i
$502$	1.55807	+	2.69865i	0.0695399	+	0.120447i
$503$	30.4559			1.35796			0.678982	−	0.734155i	$-0.262422\pi$
$503$	30.4559			1.35796			0.678982	+	0.734155i	$0.262422\pi$
$504$	3.11619	+	7.51336i	0.138806	+	0.334671i
$505$	9.23353			0.410887
$506$	−0.888236	−	1.53847i	−0.0394869	−	0.0683933i
$507$	6.39387	−	11.0745i	0.283962	−	0.491836i
$508$	0.823810	−	1.42688i	0.0365507	−	0.0633076i
$509$	11.1695	+	19.3462i	0.495082	+	0.857506i	0.999984	−	0.00567004i	$-0.00180484\pi$
$509$	11.1695	+	19.3462i	0.495082	+	0.857506i	−0.504902	+	0.863176i	$0.668472\pi$
$510$	−27.3596			−1.21150
$511$	19.5451	−	25.4961i	0.864626	−	1.12788i
$512$	−23.3311			−1.03110
$513$	2.95317	+	5.11504i	0.130386	+	0.225835i
$514$	0.607865	−	1.05285i	0.0268118	−	0.0464393i
$515$	10.9999	−	19.0524i	0.484714	−	0.839549i
$516$	1.34410	+	2.32805i	0.0591707	+	0.102487i
$517$	6.86416			0.301885
$518$	−21.6870	+	28.2901i	−0.952873	+	1.24299i
$519$	2.18632			0.0959687
$520$	2.68278	+	4.64671i	0.117648	+	0.203772i
$521$	7.92935	−	13.7340i	0.347391	−	0.601699i	−0.638394	−	0.769710i	$-0.720401\pi$
$521$	7.92935	−	13.7340i	0.347391	−	0.601699i	0.985785	+	0.168010i	$0.0537342\pi$
$522$	−1.25650	+	2.17632i	−0.0549956	+	0.0952551i
$523$	9.36555	+	16.2216i	0.409527	+	0.709321i	0.994837	−	0.101489i	$-0.0323605\pi$
$523$	9.36555	+	16.2216i	0.409527	+	0.709321i	−0.585310	+	0.810810i	$0.699027\pi$
$524$	−5.75153			−0.251257
$525$	−9.47777	−	22.8516i	−0.413644	−	0.997324i
$526$	10.6536			0.464519
$527$	24.4537	+	42.3550i	1.06522	+	1.84501i
$528$	−1.86739	+	3.23442i	−0.0812679	+	0.140760i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	−12.0171	−	20.8143i	−0.521991	−	0.904114i
$531$	12.2909			0.533381
$532$	8.97524	+	1.17740i	0.389126	+	0.0510469i
$533$	−2.41041			−0.104406
$534$	−9.70298	−	16.8060i	−0.419889	−	0.727269i
$535$	23.2182	−	40.2151i	1.00381	−	1.73865i
$536$	23.2433	−	40.2586i	1.00396	−	1.73891i
$537$	0.930522	+	1.61171i	0.0401550	+	0.0695505i
$538$	−16.3071			−0.703049
$539$	7.37030	−	7.38391i	0.317461	−	0.318048i
$540$	2.19441			0.0944323
$541$	10.1229	+	17.5333i	0.435217	+	0.753817i	0.997313	−	0.0732543i	$-0.0233385\pi$
$541$	10.1229	+	17.5333i	0.435217	+	0.753817i	−0.562097	+	0.827071i	$0.690005\pi$
$542$	2.36829	−	4.10199i	0.101727	−	0.176196i
$543$	7.24335	−	12.5458i	0.310842	−	0.538394i
$544$	−9.57914	−	16.5916i	−0.410702	−	0.711357i
$545$	34.0498			1.45853
$546$	−1.44055	−	0.188976i	−0.0616498	−	0.00808743i
$547$	−11.9031			−0.508940			−0.254470	−	0.967081i	$-0.581901\pi$
$547$	−11.9031			−0.508940			−0.254470	+	0.967081i	$0.581901\pi$
$548$	−3.48750	−	6.04052i	−0.148979	−	0.258038i
$549$	−0.205912	+	0.356650i	−0.00878811	+	0.0152215i
$550$	8.30544	−	14.3854i	0.354145	−	0.613398i
$551$	6.22624	+	10.7842i	0.265247	+	0.459421i
$552$	3.07435			0.130853
$553$	−6.56181	−	15.8210i	−0.279037	−	0.672776i
$554$	−11.9368			−0.507145
$555$	21.4098	+	37.0829i	0.908796	+	1.57408i
$556$	−0.438906	+	0.760208i	−0.0186138	+	0.0322400i
$557$	−7.78105	+	13.4772i	−0.329694	+	0.571046i	−0.982451	−	0.186521i	$-0.940279\pi$
$557$	−7.78105	+	13.4772i	−0.329694	+	0.571046i	0.652757	+	0.757567i	$0.273612\pi$
$558$	4.81037	+	8.33181i	0.203639	+	0.352714i
$559$	−2.13799			−0.0904275
$560$	−15.2803	+	19.9327i	−0.645709	+	0.842309i
$561$	−9.03076			−0.381279
$562$	12.7168	+	22.0261i	0.536424	+	0.929114i
$563$	−10.0431	+	17.3951i	−0.423264	+	0.733115i	−0.996257	−	0.0864456i	$-0.972449\pi$
$563$	−10.0431	+	17.3951i	−0.423264	+	0.733115i	0.572992	+	0.819561i	$0.305782\pi$
$564$	−1.33394	+	2.31046i	−0.0561692	+	0.0972879i
$565$	11.5190	+	19.9514i	0.484607	+	0.839364i
$566$	17.2629			0.725615
$567$	−1.60966	+	2.09976i	−0.0675995	+	0.0881816i
$568$	−21.0743			−0.884259
$569$	−7.55265	−	13.0816i	−0.316623	−	0.548408i	0.663158	−	0.748480i	$-0.269216\pi$
$569$	−7.55265	−	13.0816i	−0.316623	−	0.548408i	−0.979781	+	0.200072i	$0.935882\pi$
$570$	−13.3345	+	23.0960i	−0.558521	+	0.967387i
$571$	−12.1016	+	20.9605i	−0.506435	+	0.877170i	0.493538	+	0.869724i	$0.335703\pi$
$571$	−12.1016	+	20.9605i	−0.506435	+	0.877170i	−0.999972	+	0.00744602i	$0.997630\pi$
$572$	0.198878	+	0.344466i	0.00831549	+	0.0144029i
$573$	19.8535			0.829390
$574$	−6.32104	−	15.2405i	−0.263835	−	0.636125i
$575$	−9.35049			−0.389942
$576$	−4.39024	−	7.60412i	−0.182927	−	0.316838i
$577$	−1.17864	+	2.04146i	−0.0490673	+	0.0849871i	−0.889516	−	0.456904i	$-0.848958\pi$
$577$	−1.17864	+	2.04146i	−0.0490673	+	0.0849871i	0.840449	+	0.541891i	$0.182292\pi$
$578$	−11.7495	+	20.3507i	−0.488714	+	0.846478i
$579$	−0.779443	−	1.35003i	−0.0323925	−	0.0561055i
$580$	4.62653			0.192106
$581$	−12.2774	−	1.61059i	−0.509353	−	0.0668187i
$582$	−8.08432			−0.335106
$583$	−3.96657	−	6.87030i	−0.164279	−	0.284539i
$584$	−18.6649	+	32.3286i	−0.772361	+	1.33777i
$585$	−0.872634	+	1.51145i	−0.0360790	+	0.0624906i
$586$	−19.7854	−	34.2693i	−0.817328	−	1.41565i
$587$	−3.74241			−0.154466			−0.0772329	−	0.997013i	$-0.524608\pi$
$587$	−3.74241			−0.154466			−0.0772329	+	0.997013i	$0.524608\pi$
$588$	1.05310	+	3.91578i	0.0434292	+	0.161484i
$589$	47.6729			1.96433
$590$	27.7487	+	48.0622i	1.14240	+	1.97869i
$591$	1.24050	−	2.14862i	0.0510275	−	0.0883822i
$592$	14.1626	−	24.5303i	0.582078	−	1.00819i
$593$	−2.26864	−	3.92941i	−0.0931621	−	0.161361i	0.815678	−	0.578506i	$-0.196364\pi$
$593$	−2.26864	−	3.92941i	−0.0931621	−	0.161361i	−0.908840	+	0.417145i	$0.863031\pi$
$594$	−1.77647			−0.0728895
$595$	−60.2141	−	7.89909i	−2.46854	−	0.323831i
$596$	−10.5730			−0.433085
$597$	2.64623	+	4.58340i	0.108303	+	0.187586i
$598$	−0.274571	+	0.475570i	−0.0112280	+	0.0194475i
$599$	−17.6106	+	30.5025i	−0.719551	+	1.24630i	0.241626	+	0.970369i	$0.422319\pi$
$599$	−17.6106	+	30.5025i	−0.719551	+	1.24630i	−0.961178	+	0.275930i	$0.911014\pi$
$600$	14.3733	+	24.8953i	0.586788	+	1.01635i
$601$	29.5802			1.20660			0.603302	−	0.797513i	$-0.293852\pi$
$601$	29.5802			1.20660			0.603302	+	0.797513i	$0.293852\pi$
$602$	−5.60667	−	13.5181i	−0.228511	−	0.550955i
$603$	15.1208			0.615768
$604$	−0.849115	−	1.47071i	−0.0345500	−	0.0598424i
$605$	−16.6278	+	28.8001i	−0.676015	+	1.17089i
$606$	1.45264	−	2.51605i	0.0590097	−	0.102208i
$607$	−10.8420	−	18.7789i	−0.440062	−	0.762210i	0.557631	−	0.830089i	$-0.311710\pi$
$607$	−10.8420	−	18.7789i	−0.440062	−	0.762210i	−0.997694	+	0.0678785i	$0.978377\pi$
$608$	−18.6747			−0.757360
$609$	−3.39369	+	4.42697i	−0.137519	+	0.179390i
$610$	−1.85952			−0.0752896
$611$	−1.06092	−	1.83757i	−0.0429202	−	0.0743400i
$612$	1.75499	−	3.03973i	0.0709413	−	0.122874i
$613$	12.4937	−	21.6398i	0.504617	−	0.874023i	−0.495368	−	0.868683i	$-0.664967\pi$
$613$	12.4937	−	21.6398i	0.504617	−	0.874023i	0.999986	−	0.00533991i	$-0.00169975\pi$
$614$	−18.7626	−	32.4977i	−0.757195	−	1.31150i
$615$	−19.8196			−0.799204
$616$	−7.37549	+	9.62111i	−0.297167	+	0.387646i
$617$	−15.3643			−0.618542			−0.309271	−	0.950974i	$-0.600085\pi$
$617$	−15.3643			−0.618542			−0.309271	+	0.950974i	$0.600085\pi$
$618$	−3.46108	−	5.99476i	−0.139225	−	0.241145i
$619$	−11.8444	+	20.5151i	−0.476067	+	0.824572i	−0.999624	−	0.0274185i	$-0.991271\pi$
$619$	−11.8444	+	20.5151i	−0.476067	+	0.824572i	0.523557	+	0.851991i	$0.324605\pi$
$620$	8.85606	−	15.3392i	0.355668	−	0.616035i
$621$	0.500000	+	0.866025i	0.0200643	+	0.0347524i
$622$	−21.7024			−0.870187
$623$	−16.5026	−	39.7888i	−0.661162	−	1.59411i
$624$	1.15449			0.0462167
$625$	−7.83961	−	13.5786i	−0.313584	−	0.543144i
$626$	−12.7867	+	22.1472i	−0.511058	+	0.885179i
$627$	−4.40141	+	7.62346i	−0.175775	+	0.304452i
$628$	4.86519	+	8.42675i	0.194142	+	0.336264i
$629$	68.4905			2.73090
$630$	−11.8449	−	1.55386i	−0.471913	−	0.0619072i
$631$	12.2965			0.489515			0.244758	−	0.969584i	$-0.421292\pi$
$631$	12.2965			0.489515			0.244758	+	0.969584i	$0.421292\pi$
$632$	9.95118	+	17.2360i	0.395837	+	0.685609i
$633$	−13.5059	+	23.3929i	−0.536811	+	0.929784i
$634$	1.67387	−	2.89923i	0.0664780	−	0.115143i
$635$	5.38737	+	9.33119i	0.213791	+	0.370297i
$636$	3.08337			0.122264
$637$	−3.11586	−	0.831813i	−0.123455	−	0.0329576i
$638$	−3.74538			−0.148281
$639$	−3.42745	−	5.93652i	−0.135588	−	0.234845i
$640$	7.84577	−	13.5893i	0.310131	−	0.537163i
$641$	−1.55282	+	2.68956i	−0.0613326	+	0.106231i	−0.895061	−	0.445943i	$-0.852868\pi$
$641$	−1.55282	+	2.68956i	−0.0613326	+	0.106231i	0.833729	+	0.552174i	$0.186202\pi$
$642$	−7.30551	−	12.6535i	−0.288326	−	0.499395i
$643$	44.2523			1.74514			0.872570	−	0.488489i	$-0.162452\pi$
$643$	44.2523			1.74514			0.872570	+	0.488489i	$0.162452\pi$
$644$	1.51959	+	0.199346i	0.0598804	+	0.00785532i
$645$	−17.5797			−0.692199
$646$	21.3287	+	36.9424i	0.839167	+	1.45348i
$647$	−14.2931	+	24.7564i	−0.561919	+	0.973273i	0.435410	+	0.900232i	$0.356604\pi$
$647$	−14.2931	+	24.7564i	−0.561919	+	0.973273i	−0.997329	+	0.0730404i	$0.976730\pi$
$648$	1.53717	−	2.66246i	0.0603858	−	0.104591i
$649$	9.15920	+	15.8642i	0.359530	+	0.622725i
$650$	−5.13474			−0.201401
$651$	8.18136	+	19.7258i	0.320653	+	0.773115i
$652$	2.11423			0.0827995
$653$	−4.85971	−	8.41727i	−0.190175	−	0.329393i	0.755133	−	0.655572i	$-0.227572\pi$
$653$	−4.85971	−	8.41727i	−0.190175	−	0.329393i	−0.945308	+	0.326179i	$0.894239\pi$
$654$	5.35681	−	9.27828i	0.209468	−	0.362809i
$655$	18.8063	−	32.5734i	0.734822	−	1.27275i
$656$	6.55533	+	11.3542i	0.255943	+	0.443306i
$657$	−12.1424			−0.473719
$658$	8.83637	−	11.5268i	0.344478	−	0.449361i
$659$	29.8923			1.16444			0.582220	−	0.813031i	$-0.302184\pi$
$659$	29.8923			1.16444			0.582220	+	0.813031i	$0.302184\pi$
$660$	1.63527	+	2.83238i	0.0636529	+	0.110250i
$661$	−21.5812	+	37.3797i	−0.839411	+	1.45390i	0.0509778	+	0.998700i	$0.483766\pi$
$661$	−21.5812	+	37.3797i	−0.839411	+	1.45390i	−0.890388	+	0.455202i	$0.849567\pi$
$662$	16.1498	−	27.9722i	0.627679	−	1.08717i
$663$	1.39579	+	2.41758i	0.0542080	+	0.0938909i
$664$	14.3885			0.558383
$665$	−36.0153	+	46.9809i	−1.39661	+	1.82184i
$666$	13.4730			0.522069
$667$	1.05416	+	1.82586i	0.0408174	+	0.0706977i
$668$	−4.41403	+	7.64533i	−0.170784	+	0.295807i
$669$	2.46868	−	4.27587i	0.0954446	−	0.165315i
$670$	34.1377	+	59.1282i	1.31885	+	2.28432i
$671$	−0.613783			−0.0236948
$672$	−3.20485	−	7.72711i	−0.123630	−	0.298080i
$673$	2.93645			0.113192			0.0565959	−	0.998397i	$-0.481975\pi$
$673$	2.93645			0.113192			0.0565959	+	0.998397i	$0.481975\pi$
$674$	−4.89692	−	8.48171i	−0.188622	−	0.326703i
$675$	−4.67524	+	8.09776i	−0.179950	+	0.311683i
$676$	−3.70380	+	6.41518i	−0.142454	+	0.246738i
$677$	−19.2810	−	33.3956i	−0.741028	−	1.28350i	−0.952028	−	0.306012i	$-0.901005\pi$
$677$	−19.2810	−	33.3956i	−0.741028	−	1.28350i	0.211000	−	0.977486i	$-0.432328\pi$
$678$	7.24879			0.278388
$679$	−17.7923	−	2.33405i	−0.682806	−	0.0895728i
$680$	70.5679			2.70615
$681$	−5.72866	−	9.92233i	−0.219523	−	0.380224i
$682$	−7.16938	+	12.4177i	−0.274530	+	0.475500i
$683$	7.12801	−	12.3461i	0.272746	−	0.472409i	−0.696818	−	0.717248i	$-0.745402\pi$
$683$	7.12801	−	12.3461i	0.272746	−	0.472409i	0.969564	+	0.244839i	$0.0787350\pi$
$684$	−1.71069	−	2.96301i	−0.0654100	−	0.113293i
$685$	45.6135			1.74280
$686$	−2.91165	−	21.8822i	−0.111167	−	0.835467i
$687$	−9.71293			−0.370571
$688$	5.81447	+	10.0710i	0.221675	+	0.383952i
$689$	−1.22614	+	2.12374i	−0.0467123	+	0.0809081i
$690$	−2.25766	+	3.91038i	−0.0859477	+	0.148866i
$691$	−0.731849	−	1.26760i	−0.0278408	−	0.0482217i	0.851769	−	0.523917i	$-0.175530\pi$
$691$	−0.731849	−	1.26760i	−0.0278408	−	0.0482217i	−0.879610	+	0.475695i	$0.842196\pi$
$692$	−1.26648			−0.0481442
$693$	−3.90973	−	0.512892i	−0.148518	−	0.0194832i
$694$	3.11394			0.118204
$695$	−2.87026	−	4.97144i	−0.108875	−	0.188577i
$696$	3.24086	−	5.61334i	0.122845	−	0.212773i
$697$	−15.8509	+	27.4545i	−0.600394	+	1.03991i
$698$	9.77246	+	16.9264i	0.369893	+	0.640674i
$699$	8.92690			0.337646
$700$	5.49023	+	13.2373i	0.207511	+	0.500323i
$701$	−26.8881			−1.01555			−0.507775	−	0.861490i	$-0.669532\pi$
$701$	−26.8881			−1.01555			−0.507775	+	0.861490i	$0.669532\pi$
$702$	0.274571	+	0.475570i	0.0103630	+	0.0179492i
$703$	33.3809	−	57.8174i	1.25898	−	2.18062i
$704$	6.54322	−	11.3332i	0.246607	−	0.427136i
$705$	−8.72343	−	15.1094i	−0.328543	−	0.569054i
$706$	34.5835			1.30157
$707$	3.92346	−	5.11804i	0.147557	−	0.192484i
$708$	−7.11981			−0.267579
$709$	−1.83576	−	3.17963i	−0.0689435	−	0.119414i	0.829493	−	0.558517i	$-0.188629\pi$
$709$	−1.83576	−	3.17963i	−0.0689435	−	0.119414i	−0.898437	+	0.439103i	$0.855296\pi$
$710$	15.4760	−	26.8053i	0.580805	−	1.00598i
$711$	−3.23685	+	5.60638i	−0.121391	+	0.210256i
$712$	25.0266	+	43.3474i	0.937913	+	1.62451i
$713$	8.07148			0.302279
$714$	−11.6255	+	15.1651i	−0.435073	+	0.567540i
$715$	−2.60115			−0.0972775
$716$	−0.539027	−	0.933622i	−0.0201444	−	0.0348911i
$717$	−7.36249	+	12.7522i	−0.274957	+	0.476240i
$718$	17.9749	−	31.1334i	0.670817	−	1.16189i
$719$	9.29585	+	16.1009i	0.346677	+	0.600462i	0.985657	−	0.168761i	$-0.0539767\pi$
$719$	9.29585	+	16.1009i	0.346677	+	0.600462i	−0.638980	+	0.769223i	$0.720643\pi$
$720$	9.49284			0.353777
$721$	−5.88651	−	14.1928i	−0.219225	−	0.528566i
$722$	18.9338			0.704644
$723$	12.2335	+	21.1890i	0.454968	+	0.788027i
$724$	−4.19588	+	7.26748i	−0.155939	+	0.270094i
$725$	−9.85694	+	17.0727i	−0.366078	+	0.634065i
$726$	5.23185	+	9.06184i	0.194172	+	0.336316i
$727$	16.8322			0.624273			0.312136	−	0.950037i	$-0.398955\pi$
$727$	16.8322			0.624273			0.312136	+	0.950037i	$0.398955\pi$
$728$	3.71557	+	0.487421i	0.137708	+	0.0180650i
$729$	1.00000			0.0370370
$730$	−27.4134	−	47.4814i	−1.01461	−	1.75736i
$731$	−14.0595	+	24.3517i	−0.520008	+	0.900680i
$732$	0.119279	−	0.206598i	0.00440869	−	0.00763608i
$733$	−9.42942	−	16.3322i	−0.348284	−	0.603245i	0.637661	−	0.770317i	$-0.279902\pi$
$733$	−9.42942	−	16.3322i	−0.348284	−	0.603245i	−0.985945	+	0.167072i	$0.946569\pi$
$734$	10.3917			0.383566
$735$	−25.6202	−	6.83959i	−0.945015	−	0.252282i
$736$	−3.16181			−0.116546
$737$	11.2681	+	19.5168i	0.415064	+	0.718912i
$738$	−3.11808	+	5.40067i	−0.114778	+	0.198801i
$739$	−22.3548	+	38.7196i	−0.822333	+	1.42432i	0.0816069	+	0.996665i	$0.473995\pi$
$739$	−22.3548	+	38.7196i	−0.822333	+	1.42432i	−0.903940	+	0.427659i	$0.859339\pi$
$740$	−12.4021	−	21.4811i	−0.455912	−	0.789663i
$741$	2.72112			0.0999628
$742$	−16.6434	−	2.18333i	−0.610997	−	0.0801527i
$743$	49.0083			1.79794			0.898970	−	0.438011i	$-0.144317\pi$
$743$	49.0083			1.79794			0.898970	+	0.438011i	$0.144317\pi$
$744$	−12.4073	−	21.4900i	−0.454872	−	0.787862i
$745$	34.5713	−	59.8793i	1.26659	−	2.19381i
$746$	6.50022	−	11.2587i	0.237990	−	0.412211i
$747$	2.34009	+	4.05316i	0.0856196	+	0.148297i
$748$	5.23128			0.191275
$749$	−12.4250	−	29.9576i	−0.454001	−	1.09463i
$750$	−19.6439			−0.717292
$751$	−5.85462	−	10.1405i	−0.213638	−	0.370032i	0.739212	−	0.673472i	$-0.235198\pi$
$751$	−5.85462	−	10.1405i	−0.213638	−	0.370032i	−0.952850	+	0.303440i	$0.901865\pi$
$752$	−5.77054	+	9.99487i	−0.210430	+	0.364475i
$753$	1.30717	−	2.26408i	0.0476358	−	0.0825076i
$754$	0.578884	+	1.00266i	0.0210817	+	0.0365146i
$755$	11.1057			0.404178
$756$	0.932436	−	1.21633i	0.0339124	−	0.0442377i
$757$	−24.2422			−0.881096			−0.440548	−	0.897729i	$-0.645216\pi$
$757$	−24.2422			−0.881096			−0.440548	+	0.897729i	$0.645216\pi$
$758$	6.89817	+	11.9480i	0.250553	+	0.433970i
$759$	−0.745201	+	1.29073i	−0.0270491	+	0.0468504i
$760$	34.3933	−	59.5710i	1.24758	−	2.16087i
$761$	−15.3628	−	26.6091i	−0.556900	−	0.964579i	−0.997753	−	0.0669997i	$-0.978657\pi$
$761$	−15.3628	−	26.6091i	−0.556900	−	0.964579i	0.440853	−	0.897579i	$-0.354676\pi$
$762$	3.39022			0.122815
$763$	14.4683	−	18.8734i	0.523786	−	0.683264i
$764$	−11.5006			−0.416077
$765$	11.4769	+	19.8786i	0.414948	+	0.718711i
$766$	−14.4492	+	25.0268i	−0.522072	+	0.904256i
$767$	2.83128	−	4.90393i	0.102232	−	0.177071i
$768$	6.31185	+	10.9324i	0.227759	+	0.394490i
$769$	−39.0901			−1.40963			−0.704813	−	0.709393i	$-0.748969\pi$
$769$	−39.0901			−1.40963			−0.704813	+	0.709393i	$0.748969\pi$
$770$	−6.82125	−	16.4465i	−0.245821	−	0.592690i
$771$	−1.01996			−0.0367328
$772$	0.451511	+	0.782039i	0.0162502	+	0.0281462i
$773$	−0.437496	+	0.757766i	−0.0157356	+	0.0272549i	−0.873786	−	0.486311i	$-0.838342\pi$
$773$	−0.437496	+	0.757766i	−0.0157356	+	0.0272549i	0.858050	+	0.513566i	$0.171676\pi$
$774$	−2.76569	+	4.79031i	−0.0994105	+	0.172184i
$775$	37.7362	+	65.3610i	1.35552	+	2.34783i
$776$	20.8517			0.748532
$777$	29.6520	+	3.88984i	1.06376	+	0.139547i
$778$	6.91898			0.248057
$779$	15.4508	+	26.7615i	0.553581	+	0.958831i
$780$	0.505494	−	0.875542i	0.0180996	−	0.0313494i
$781$	5.10828	−	8.84780i	0.182789	−	0.316599i
$782$	3.61116	+	6.25470i	0.129135	+	0.223668i
$783$	2.10833			0.0753454
$784$	4.55564	+	16.9394i	0.162701	+	0.604977i
$785$	−63.6325			−2.27114
$786$	−5.91732	−	10.2491i	−0.211064	−	0.365573i
$787$	−6.16206	+	10.6730i	−0.219654	+	0.380452i	−0.954702	−	0.297563i	$-0.903826\pi$
$787$	−6.16206	+	10.6730i	−0.219654	+	0.380452i	0.735048	+	0.678015i	$0.237159\pi$
$788$	−0.718591	+	1.24464i	−0.0255988	+	0.0443384i
$789$	−4.46901	−	7.74054i	−0.159101	−	0.275571i
$790$	−29.2308			−1.03998
$791$	15.9534	+	2.09283i	0.567239	+	0.0744123i
$792$	4.58201			0.162815
$793$	0.0948660	+	0.164313i	0.00336879	+	0.00583492i
$794$	7.86791	−	13.6276i	0.279222	−	0.483626i
$795$	−10.0820	+	17.4625i	−0.357571	+	0.619330i
$796$	−1.53289	−	2.65504i	−0.0543319	−	0.0941056i
$797$	−33.6866			−1.19324			−0.596621	−	0.802524i	$-0.703490\pi$
$797$	−33.6866			−1.19324			−0.596621	+	0.802524i	$0.703490\pi$
$798$	7.13585	+	17.2050i	0.252606	+	0.609051i
$799$	−27.9065			−0.987260
$800$	−14.7822	−	25.6036i	−0.522631	−	0.905223i
$801$	−8.14048	+	14.0997i	−0.287630	+	0.498189i
$802$	−14.0643	+	24.3600i	−0.496626	+	0.860181i
$803$	−9.04851	−	15.6725i	−0.319315	−	0.553070i
$804$	−8.75911			−0.308910
$805$	−6.09773	+	7.95431i	−0.214917	+	0.280353i
$806$	4.43238			0.156124
$807$	6.84056	+	11.8482i	0.240799	+	0.417076i
$808$	−3.74677	+	6.48959i	−0.131811	+	0.228303i
$809$	2.94113	−	5.09419i	0.103405	−	0.179102i	−0.809681	−	0.586871i	$-0.800360\pi$
$809$	2.94113	−	5.09419i	0.103405	−	0.179102i	0.913085	+	0.407769i	$0.133693\pi$
$810$	2.25766	+	3.91038i	0.0793261	+	0.137397i
$811$	13.3036			0.467152			0.233576	−	0.972339i	$-0.424957\pi$
$811$	13.3036			0.467152			0.233576	+	0.972339i	$0.424957\pi$
$812$	1.96588	−	2.56443i	0.0689888	−	0.0899939i
$813$	−3.97383			−0.139368
$814$	10.0401	+	17.3900i	0.351905	+	0.609518i
$815$	−6.91307	+	11.9738i	−0.242154	+	0.419424i
$816$	7.59196	−	13.1497i	0.265772	−	0.460330i
$817$	13.7046	+	23.7371i	0.479463	+	0.830454i
$818$	10.2999			0.360128
$819$	0.466983	+	1.12593i	0.0163177	+	0.0393431i
$820$	11.4810			0.400933
$821$	−19.5406	−	33.8454i	−0.681973	−	1.18121i	−0.974378	−	0.224917i	$-0.927789\pi$
$821$	−19.5406	−	33.8454i	−0.681973	−	1.18121i	0.292405	−	0.956295i	$-0.405545\pi$
$822$	7.17605	−	12.4293i	0.250293	−	0.433521i
$823$	9.50351	−	16.4606i	0.331272	−	0.573779i	−0.651490	−	0.758657i	$-0.725856\pi$
$823$	9.50351	−	16.4606i	0.331272	−	0.573779i	0.982761	+	0.184878i	$0.0591890\pi$
$824$	8.92706	+	15.4621i	0.310989	+	0.538649i
$825$	−13.9360			−0.485189
$826$	38.4312	+	5.04153i	1.33719	+	0.175417i
$827$	35.8180			1.24551			0.622757	−	0.782415i	$-0.286012\pi$
$827$	35.8180			1.24551			0.622757	+	0.782415i	$0.286012\pi$
$828$	−0.289637	−	0.501666i	−0.0100656	−	0.0174341i
$829$	13.5527	−	23.4740i	0.470706	−	0.815287i	−0.528733	−	0.848788i	$-0.677333\pi$
$829$	13.5527	−	23.4740i	0.470706	−	0.815287i	0.999439	+	0.0335018i	$0.0106659\pi$
$830$	−10.5663	+	18.3013i	−0.366761	+	0.635248i
$831$	5.00728	+	8.67286i	0.173700	+	0.300858i
$832$	−4.04527			−0.140244
$833$	−29.9642	+	30.0196i	−1.03820	+	1.04012i
$834$	−1.80623			−0.0625446
$835$	−28.8659	−	49.9972i	−0.998945	−	1.73022i
$836$	2.54962	−	4.41607i	0.0881805	−	0.152733i
$837$	4.03574	−	6.99011i	0.139496	−	0.241614i
$838$	−17.9150	−	31.0298i	−0.618865	−	1.07191i
$839$	25.7997			0.890704			0.445352	−	0.895356i	$-0.353079\pi$
$839$	25.7997			0.890704			0.445352	+	0.895356i	$0.353079\pi$
$840$	30.5513	+	4.00782i	1.05412	+	0.138283i
$841$	−24.5550			−0.846723
$842$	14.7509	+	25.5492i	0.508348	+	0.880484i
$843$	10.6689	−	18.4791i	0.367458	−	0.636456i
$844$	7.82361	−	13.5509i	0.269300	−	0.466441i
$845$	−24.2213	−	41.9525i	−0.833238	−	1.44321i
$846$	−5.48958			−0.188736
$847$	8.89820	+	21.4542i	0.305746	+	0.737174i
$848$	13.3384			0.458044
$849$	−7.24152	−	12.5427i	−0.248528	−	0.430463i
$850$	−33.7661	+	58.4845i	−1.15817	+	2.00600i
$851$	5.65171	−	9.78904i	0.193738	−	0.335564i
$852$	1.98543	+	3.43887i	0.0680198	+	0.117814i
$853$	−6.24250			−0.213739			−0.106870	−	0.994273i	$-0.534083\pi$
$853$	−6.24250			−0.213739			−0.106870	+	0.994273i	$0.534083\pi$
$854$	−0.790136	+	1.03071i	−0.0270379	+	0.0352701i
$855$	22.3744			0.765189
$856$	18.8429	+	32.6369i	0.644038	+	1.11551i
$857$	−10.9852	+	19.0270i	−0.375249	+	0.649950i	−0.990364	−	0.138487i	$-0.955776\pi$
$857$	−10.9852	+	19.0270i	−0.375249	+	0.649950i	0.615115	+	0.788437i	$0.289109\pi$
$858$	−0.409220	+	0.708791i	−0.0139706	+	0.0241977i
$859$	−10.1658	−	17.6078i	−0.346854	−	0.600769i	0.638835	−	0.769344i	$-0.279417\pi$
$859$	−10.1658	−	17.6078i	−0.346854	−	0.600769i	−0.985689	+	0.168575i	$0.946083\pi$
$860$	10.1835			0.347253
$861$	−8.42164	+	10.9858i	−0.287009	+	0.374394i
$862$	−18.6585			−0.635510
$863$	−13.8855	−	24.0503i	−0.472667	−	0.818683i	0.526844	−	0.849962i	$-0.323375\pi$
$863$	−13.8855	−	24.0503i	−0.472667	−	0.818683i	−0.999511	+	0.0312790i	$0.990042\pi$
$864$	−1.58090	+	2.73821i	−0.0537835	+	0.0931557i
$865$	4.14111	−	7.17261i	0.140802	−	0.243876i
$866$	0.561216	+	0.972054i	0.0190709	+	0.0330317i
$867$	19.7149			0.669552
$868$	−4.73925	−	11.4266i	−0.160860	−	0.387846i
$869$	−9.64840			−0.327300
$870$	4.75988	+	8.24436i	0.161375	+	0.279510i
$871$	3.48317	−	6.03303i	0.118023	−	0.204421i
$872$	−13.8167	+	23.9312i	−0.467892	+	0.810413i
$873$	3.39124	+	5.87380i	0.114776	+	0.198798i
$874$	7.04002			0.238132
$875$	−43.2330	−	5.67145i	−1.46154	−	0.191730i
$876$	7.03376			0.237649
$877$	−16.2656	−	28.1729i	−0.549251	−	0.951331i	−0.998326	−	0.0578367i	$-0.981580\pi$
$877$	−16.2656	−	28.1729i	−0.549251	−	0.951331i	0.449075	−	0.893494i	$-0.351754\pi$
$878$	11.2305	−	19.4518i	0.379012	−	0.656468i
$879$	−16.5993	+	28.7508i	−0.559880	+	0.969741i
$880$	7.07407	+	12.2526i	0.238467	+	0.413037i
$881$	3.88986			0.131053			0.0655263	−	0.997851i	$-0.479127\pi$
$881$	3.88986			0.131053			0.0655263	+	0.997851i	$0.479127\pi$
$882$	−5.89437	+	5.90525i	−0.198474	+	0.198840i
$883$	−35.6597			−1.20004			−0.600022	−	0.799984i	$-0.704841\pi$
$883$	−35.6597			−1.20004			−0.600022	+	0.799984i	$0.704841\pi$
$884$	−0.808544	−	1.40044i	−0.0271943	−	0.0471019i
$885$	23.2803	−	40.3226i	0.782557	−	1.35543i
$886$	1.51186	−	2.61861i	0.0507918	−	0.0879740i
$887$	23.8635	+	41.3328i	0.801259	+	1.38782i	0.918788	+	0.394752i	$0.129169\pi$
$887$	23.8635	+	41.3328i	0.801259	+	1.38782i	−0.117529	+	0.993069i	$0.537497\pi$
$888$	−34.7506			−1.16615
$889$	7.46134	+	0.978804i	0.250245	+	0.0328280i
$890$	−73.5137			−2.46419
$891$	0.745201	+	1.29073i	0.0249652	+	0.0432409i
$892$	−1.43004	+	2.47690i	−0.0478813	+	0.0829328i
$893$	−13.6010	+	23.5577i	−0.455142	+	0.788328i
$894$	−10.8777	−	18.8408i	−0.363805	−	0.630129i
$895$	7.05002			0.235656
$896$	−4.19859	−	10.1231i	−0.140265	−	0.338189i
$897$	0.460711			0.0153827
$898$	20.4292	+	35.3844i	0.681731	+	1.18079i
$899$	8.50866	−	14.7374i	0.283780	−	0.491521i
$900$	2.70825	−	4.69082i	0.0902749	−	0.156361i
$901$	16.1262	+	27.9315i	0.537243	+	0.930532i
$902$	−9.29437			−0.309469
$903$	−7.46987	+	9.74422i	−0.248582	+	0.324267i
$904$	−18.6966			−0.621840
$905$	−27.4393	−	47.5262i	−0.912113	−	1.57983i
$906$	1.74718	−	3.02621i	0.0580462	−	0.100539i
$907$	4.94034	−	8.55693i	0.164041	−	0.284128i	−0.772273	−	0.635291i	$-0.780880\pi$
$907$	4.94034	−	8.55693i	0.164041	−	0.284128i	0.936314	+	0.351163i	$0.114214\pi$
$908$	3.31846	+	5.74774i	0.110127	+	0.190746i
$909$	−2.43744			−0.0808448
$910$	−3.34852	+	4.36804i	−0.111002	+	0.144799i
$911$	−22.5568			−0.747339			−0.373669	−	0.927562i	$-0.621901\pi$
$911$	−22.5568			−0.747339			−0.373669	+	0.927562i	$0.621901\pi$
$912$	−7.40033	−	12.8178i	−0.245049	−	0.424438i
$913$	−3.48768	+	6.04084i	−0.115425	+	0.199923i
$914$	8.99114	−	15.5731i	0.297400	−	0.515113i
$915$	0.780037	+	1.35106i	0.0257872	+	0.0446648i
$916$	5.62644			0.185903
$917$	−10.0640	−	24.2650i	−0.332343	−	0.801302i
$918$	7.22231			0.238372
$919$	−17.5510	−	30.3992i	−0.578954	−	1.00278i	−0.995600	−	0.0937089i	$-0.970128\pi$
$919$	−17.5510	−	30.3992i	−0.578954	−	1.00278i	0.416646	−	0.909069i	$-0.363206\pi$
$920$	5.82312	−	10.0859i	0.191983	−	0.332524i
$921$	−15.7412	+	27.2645i	−0.518689	+	0.898396i
$922$	−9.30100	−	16.1098i	−0.306312	−	0.530548i
$923$	−3.15813			−0.103951
$924$	2.26481	+	0.297105i	0.0745067	+	0.00977403i
$925$	105.692			3.47515
$926$	−3.72968	−	6.45999i	−0.122565	−	0.212288i
$927$	−2.90373	+	5.02940i	−0.0953709	+	0.165187i
$928$	−3.33306	+	5.77303i	−0.109413	+	0.189509i
$929$	23.8750	+	41.3527i	0.783314	+	1.35674i	0.930001	+	0.367556i	$0.119805\pi$
$929$	23.8750	+	41.3527i	0.783314	+	1.35674i	−0.146688	+	0.989183i	$0.546861\pi$
$930$	36.4453			1.19509
$931$	10.7375	+	39.9257i	0.351909	+	1.30851i
$932$	−5.17112			−0.169386
$933$	9.10379	+	15.7682i	0.298045	+	0.516229i
$934$	−5.22254	+	9.04571i	−0.170887	+	0.295985i
$935$	−17.1052	+	29.6270i	−0.559399	+	0.968908i
$936$	−0.708193	−	1.22663i	−0.0231480	−	0.0400935i
$937$	16.1702			0.528258			0.264129	−	0.964487i	$-0.414916\pi$
$937$	16.1702			0.528258			0.264129	+	0.964487i	$0.414916\pi$
$938$	47.2797	+	6.20231i	1.54374	+	0.202513i
$939$	21.4552			0.700164
$940$	5.05325	+	8.75249i	0.164819	+	0.285475i
$941$	23.8793	−	41.3601i	0.778441	−	1.34830i	−0.154398	−	0.988009i	$-0.549344\pi$
$941$	23.8793	−	41.3601i	0.778441	−	1.34830i	0.932840	−	0.360291i	$-0.117323\pi$
$942$	−10.0108	+	17.3393i	−0.326171	+	0.564945i
$943$	2.61596	+	4.53098i	0.0851875	+	0.147549i
$944$	−30.7998			−1.00245
$945$	3.83977	+	9.25795i	0.124908	+	0.301161i
$946$	−8.24397			−0.268034
$947$	−2.44092	−	4.22780i	−0.0793192	−	0.137385i	0.823637	−	0.567117i	$-0.191941\pi$
$947$	−2.44092	−	4.22780i	−0.0793192	−	0.137385i	−0.902956	+	0.429732i	$0.858608\pi$
$948$	1.87502	−	3.24763i	0.0608978	−	0.105478i
$949$	−2.79707	+	4.84466i	−0.0907966	+	0.157264i
$950$	32.9138	+	57.0084i	1.06786	+	1.84960i
$951$	−2.80865			−0.0910767
$952$	29.9853	−	39.1150i	0.971830	−	1.26772i
$953$	17.0472			0.552212			0.276106	−	0.961127i	$-0.410956\pi$
$953$	17.0472			0.552212			0.276106	+	0.961127i	$0.410956\pi$
$954$	3.17225	+	5.49450i	0.102705	+	0.177891i
$955$	37.6045	−	65.1329i	1.21685	−	2.10765i
$956$	4.26490	−	7.38702i	0.137937	−	0.238913i
$957$	1.57113	+	2.72127i	0.0507873	+	0.0879662i
$958$	−18.8043			−0.607540
$959$	19.3818	−	25.2830i	0.625872	−	0.816432i
$960$	−33.2623			−1.07353
$961$	−17.0744	−	29.5738i	−0.550788	−	0.953993i
$962$	3.10358	−	5.37557i	0.100064	−	0.173315i
$963$	−6.12909	+	10.6159i	−0.197507	+	0.342092i
$964$	−7.08653	−	12.2742i	−0.228242	−	0.395326i
$965$	−5.90538			−0.190101
$966$	1.20817	+	2.91297i	0.0388721	+	0.0937234i
$967$	23.3640			0.751335			0.375667	−	0.926755i	$-0.377413\pi$
$967$	23.3640			0.751335			0.375667	+	0.926755i	$0.377413\pi$
$968$	−13.4944	−	23.3730i	−0.433726	−	0.751235i
$969$	17.8941	−	30.9935i	0.574841	−	0.995653i
$970$	−15.3125	+	26.5221i	−0.491656	+	0.851573i
$971$	−18.4523	−	31.9603i	−0.592162	−	1.02565i	−0.993941	−	0.109918i	$-0.964941\pi$
$971$	−18.4523	−	31.9603i	−0.592162	−	1.02565i	0.401779	−	0.915737i	$-0.368392\pi$
$972$	−0.579274			−0.0185802
$973$	−3.97523	−	0.521483i	−0.127440	−	0.0167180i
$974$	48.3635			1.54967
$975$	2.15394	+	3.73073i	0.0689812	+	0.119479i
$976$	0.515994	−	0.893727i	0.0165166	−	0.0286075i
$977$	−0.274426	+	0.475320i	−0.00877967	+	0.0152068i	−0.870382	−	0.492377i	$-0.836128\pi$
$977$	−0.274426	+	0.475320i	−0.00877967	+	0.0152068i	0.861602	+	0.507584i	$0.169461\pi$
$978$	2.17517	+	3.76750i	0.0695542	+	0.120471i
$979$	−24.2652			−0.775518
$980$	14.8411	+	3.96199i	0.474082	+	0.126561i
$981$	−8.98838			−0.286977
$982$	−5.59607	−	9.69268i	−0.178578	−	0.309306i
$983$	−3.48677	+	6.03926i	−0.111211	+	0.192623i	−0.916259	−	0.400587i	$-0.868806\pi$
$983$	−3.48677	+	6.03926i	−0.111211	+	0.192623i	0.805048	+	0.593210i	$0.202140\pi$
$984$	8.04238	−	13.9298i	0.256382	−	0.444066i
$985$	−4.69928	−	8.13940i	−0.149732	−	0.259343i
$986$	15.2270			0.484926
$987$	−12.0817	−	1.58492i	−0.384565	−	0.0504485i
$988$	−1.57627			−0.0501479
$989$	2.32032	+	4.01891i	0.0737819	+	0.127794i
$990$	−3.36482	+	5.82804i	−0.106941	+	0.185227i
$991$	15.6563	−	27.1174i	0.497337	−	0.861413i	−0.502658	−	0.864485i	$-0.667644\pi$
$991$	15.6563	−	27.1174i	0.497337	−	0.861413i	0.999995	+	0.00307193i	$0.000977828\pi$
$992$	12.7602	+	22.1014i	0.405138	+	0.701720i
$993$	−27.0983			−0.859937
$994$	−8.28187	−	19.9681i	−0.262685	−	0.633351i
$995$	20.0489			0.635593
$996$	−1.35556	−	2.34789i	−0.0429524	−	0.0743957i
$997$	−22.6062	+	39.1551i	−0.715947	+	1.24006i	0.246647	+	0.969105i	$0.420671\pi$
$997$	−22.6062	+	39.1551i	−0.715947	+	1.24006i	−0.962593	+	0.270950i	$0.912662\pi$
$998$	−11.3700	+	19.6933i	−0.359910	+	0.623382i
$999$	−5.65171	−	9.78904i	−0.178812	−	0.309712i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.i.g.277.4	✓	16
7.2	even	3	inner	483.2.i.g.415.4	yes	16
7.3	odd	6		3381.2.a.be.1.5		8
7.4	even	3		3381.2.a.bf.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.g.277.4	✓	16	1.1	even	1	trivial
483.2.i.g.415.4	yes	16	7.2	even	3	inner
3381.2.a.be.1.5		8	7.3	odd	6
3381.2.a.bf.1.5		8	7.4	even	3

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.595971 - 1.03225i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.289637 - 0.501666i) q^{4} +(1.89410 + 3.28068i) q^{5} +1.19194 q^{6} +(2.62328 + 0.344130i) q^{7} -3.07435 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.595971 - 1.03225i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.289637 - 0.501666i) q^{4} +(1.89410 + 3.28068i) q^{5} +1.19194 q^{6} +(2.62328 + 0.344130i) q^{7} -3.07435 q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.25766 - 3.91038i) q^{10} +(0.745201 - 1.29073i) q^{11} +(0.289637 + 0.501666i) q^{12} -0.460711 q^{13} +(-1.20817 - 2.91297i) q^{14} -3.78820 q^{15} +(1.25295 + 2.17017i) q^{16} +(-3.02964 + 5.24749i) q^{17} +(-0.595971 + 1.03225i) q^{18} +(2.95317 + 5.11504i) q^{19} +2.19441 q^{20} +(-1.60966 + 2.09976i) q^{21} -1.77647 q^{22} +(0.500000 + 0.866025i) q^{23} +(1.53717 - 2.66246i) q^{24} +(-4.67524 + 8.09776i) q^{25} +(0.274571 + 0.475570i) q^{26} +1.00000 q^{27} +(0.932436 - 1.21633i) q^{28} +2.10833 q^{29} +(2.25766 + 3.91038i) q^{30} +(4.03574 - 6.99011i) q^{31} +(-1.58090 + 2.73821i) q^{32} +(0.745201 + 1.29073i) q^{33} +7.22231 q^{34} +(3.83977 + 9.25795i) q^{35} -0.579274 q^{36} +(-5.65171 - 9.78904i) q^{37} +(3.52001 - 6.09683i) q^{38} +(0.230356 - 0.398988i) q^{39} +(-5.82312 - 10.0859i) q^{40} +5.23193 q^{41} +(3.12679 + 0.410183i) q^{42} +4.64064 q^{43} +(-0.431675 - 0.747683i) q^{44} +(1.89410 - 3.28068i) q^{45} +(0.595971 - 1.03225i) q^{46} +(2.30279 + 3.98854i) q^{47} -2.50589 q^{48} +(6.76315 + 1.80550i) q^{49} +11.1452 q^{50} +(-3.02964 - 5.24749i) q^{51} +(-0.133439 + 0.231123i) q^{52} +(2.66141 - 4.60970i) q^{53} +(-0.595971 - 1.03225i) q^{54} +5.64594 q^{55} +(-8.06485 - 1.05797i) q^{56} -5.90634 q^{57} +(-1.25650 - 2.17632i) q^{58} +(-6.14546 + 10.6443i) q^{59} +(-1.09720 + 1.90041i) q^{60} +(-0.205912 - 0.356650i) q^{61} -9.62074 q^{62} +(-1.01361 - 2.44389i) q^{63} +8.78048 q^{64} +(-0.872634 - 1.51145i) q^{65} +(0.888236 - 1.53847i) q^{66} +(-7.56042 + 13.0950i) q^{67} +(1.75499 + 3.03973i) q^{68} -1.00000 q^{69} +(7.26814 - 9.48108i) q^{70} +6.85490 q^{71} +(1.53717 + 2.66246i) q^{72} +(6.07119 - 10.5156i) q^{73} +(-6.73651 + 11.6680i) q^{74} +(-4.67524 - 8.09776i) q^{75} +3.42139 q^{76} +(2.39904 - 3.12948i) q^{77} -0.549141 q^{78} +(-3.23685 - 5.60638i) q^{79} +(-4.74642 + 8.22104i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.11808 - 5.40067i) q^{82} -4.68019 q^{83} +(0.587159 + 1.41568i) q^{84} -22.9538 q^{85} +(-2.76569 - 4.79031i) q^{86} +(-1.05416 + 1.82586i) q^{87} +(-2.29100 + 3.96814i) q^{88} +(-8.14048 - 14.0997i) q^{89} -4.51532 q^{90} +(-1.20857 - 0.158545i) q^{91} +0.579274 q^{92} +(4.03574 + 6.99011i) q^{93} +(2.74479 - 4.75412i) q^{94} +(-11.1872 + 19.3768i) q^{95} +(-1.58090 - 2.73821i) q^{96} -6.78248 q^{97} +(-2.16691 - 8.05730i) q^{98} -1.49040 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} - 8 q^{3} - 15 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 8 q^{9}+O(q^{10}) \) 16 * q - q^2 - 8 * q^3 - 15 * q^4 - 5 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 - 8 * q^9	\( 16 q - q^{2} - 8 q^{3} - 15 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 8 q^{9} + 3 q^{10} - 10 q^{11} - 15 q^{12} - 12 q^{13} - 17 q^{14} + 10 q^{15} - 13 q^{16} - 21 q^{17} - q^{18} - 5 q^{19} - 2 q^{20} + 4 q^{21} + 36 q^{22} + 8 q^{23} - 9 q^{24} - 27 q^{25} - 3 q^{26} + 16 q^{27} + 6 q^{28} + 4 q^{29} + 3 q^{30} + 13 q^{31} - 29 q^{32} - 10 q^{33} - 38 q^{34} + 27 q^{35} + 30 q^{36} - 13 q^{37} + 6 q^{38} + 6 q^{39} - 7 q^{40} + 32 q^{41} + 25 q^{42} + 30 q^{43} - 24 q^{44} - 5 q^{45} + q^{46} + q^{47} + 26 q^{48} + 16 q^{49} + 32 q^{50} - 21 q^{51} + 19 q^{52} - 3 q^{53} - q^{54} - 20 q^{55} + 33 q^{56} + 10 q^{57} + 40 q^{58} - 26 q^{59} + q^{60} + 14 q^{61} - 28 q^{62} - 2 q^{63} + 98 q^{64} + 3 q^{65} - 18 q^{66} - 38 q^{67} - 43 q^{68} - 16 q^{69} + 40 q^{70} + 18 q^{71} - 9 q^{72} + 6 q^{73} - 32 q^{74} - 27 q^{75} - 28 q^{76} + 56 q^{77} + 6 q^{78} - 23 q^{79} + 17 q^{80} - 8 q^{81} - 20 q^{82} + 60 q^{83} + 3 q^{84} - 74 q^{85} + 28 q^{86} - 2 q^{87} - 86 q^{88} - 12 q^{89} - 6 q^{90} + 26 q^{91} - 30 q^{92} + 13 q^{93} + 45 q^{94} - 16 q^{95} - 29 q^{96} + 28 q^{97} + 26 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q - q^2 - 8 * q^3 - 15 * q^4 - 5 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 - 8 * q^9 + 3 * q^10 - 10 * q^11 - 15 * q^12 - 12 * q^13 - 17 * q^14 + 10 * q^15 - 13 * q^16 - 21 * q^17 - q^18 - 5 * q^19 - 2 * q^20 + 4 * q^21 + 36 * q^22 + 8 * q^23 - 9 * q^24 - 27 * q^25 - 3 * q^26 + 16 * q^27 + 6 * q^28 + 4 * q^29 + 3 * q^30 + 13 * q^31 - 29 * q^32 - 10 * q^33 - 38 * q^34 + 27 * q^35 + 30 * q^36 - 13 * q^37 + 6 * q^38 + 6 * q^39 - 7 * q^40 + 32 * q^41 + 25 * q^42 + 30 * q^43 - 24 * q^44 - 5 * q^45 + q^46 + q^47 + 26 * q^48 + 16 * q^49 + 32 * q^50 - 21 * q^51 + 19 * q^52 - 3 * q^53 - q^54 - 20 * q^55 + 33 * q^56 + 10 * q^57 + 40 * q^58 - 26 * q^59 + q^60 + 14 * q^61 - 28 * q^62 - 2 * q^63 + 98 * q^64 + 3 * q^65 - 18 * q^66 - 38 * q^67 - 43 * q^68 - 16 * q^69 + 40 * q^70 + 18 * q^71 - 9 * q^72 + 6 * q^73 - 32 * q^74 - 27 * q^75 - 28 * q^76 + 56 * q^77 + 6 * q^78 - 23 * q^79 + 17 * q^80 - 8 * q^81 - 20 * q^82 + 60 * q^83 + 3 * q^84 - 74 * q^85 + 28 * q^86 - 2 * q^87 - 86 * q^88 - 12 * q^89 - 6 * q^90 + 26 * q^91 - 30 * q^92 + 13 * q^93 + 45 * q^94 - 16 * q^95 - 29 * q^96 + 28 * q^97 + 26 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more