LMFDB - Embedded newform 240.2.y.e.163.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(163,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0, 3]))

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

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

chi := DirichletCharacter("240.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.y (of order $4$, 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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
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} - 6 x^{15} + 14 x^{14} - 10 x^{13} - 26 x^{12} + 78 x^{11} - 66 x^{10} - 74 x^{9} + 233 x^{8} + \cdots + 256 $ x^16 - 6x^15 + 14x^14 - 10x^13 - 26x^12 + 78x^11 - 66x^10 - 74x^9 + 233x^8 - 148x^7 - 264x^6 + 624x^5 - 416x^4 - 320x^3 + 896x^2 - 768*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			163.4
Root			$0.885279 - 1.10285i$ of defining polynomial
Character	$\chi$	$=$	240.163
Dual form			240.2.y.e.187.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0770377 + 1.41211i) q^{2} +1.00000 q^{3} +(-1.98813 - 0.217572i) q^{4} +(-2.13688 + 0.658594i) q^{5} +(-0.0770377 + 1.41211i) q^{6} +(-3.54781 + 3.54781i) q^{7} +(0.460397 - 2.79070i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.0770377 + 1.41211i) q^{2} +1.00000 q^{3} +(-1.98813 - 0.217572i) q^{4} +(-2.13688 + 0.658594i) q^{5} +(-0.0770377 + 1.41211i) q^{6} +(-3.54781 + 3.54781i) q^{7} +(0.460397 - 2.79070i) q^{8} +1.00000 q^{9} +(-0.765389 - 3.06825i) q^{10} +(-0.707136 - 0.707136i) q^{11} +(-1.98813 - 0.217572i) q^{12} +1.18824i q^{13} +(-4.73659 - 5.28322i) q^{14} +(-2.13688 + 0.658594i) q^{15} +(3.90532 + 0.865123i) q^{16} +(-2.63620 + 2.63620i) q^{17} +(-0.0770377 + 1.41211i) q^{18} +(5.21643 + 5.21643i) q^{19} +(4.39169 - 0.844446i) q^{20} +(-3.54781 + 3.54781i) q^{21} +(1.05303 - 0.944080i) q^{22} +(-1.86512 - 1.86512i) q^{23} +(0.460397 - 2.79070i) q^{24} +(4.13251 - 2.81467i) q^{25} +(-1.67794 - 0.0915396i) q^{26} +1.00000 q^{27} +(7.82540 - 6.28160i) q^{28} +(2.17456 - 2.17456i) q^{29} +(-0.765389 - 3.06825i) q^{30} +2.39439i q^{31} +(-1.52251 + 5.44812i) q^{32} +(-0.707136 - 0.707136i) q^{33} +(-3.51953 - 3.92570i) q^{34} +(5.24467 - 9.91780i) q^{35} +(-1.98813 - 0.217572i) q^{36} -0.910233i q^{37} +(-7.76806 + 6.96434i) q^{38} +1.18824i q^{39} +(0.854128 + 6.26662i) q^{40} -8.26953i q^{41} +(-4.73659 - 5.28322i) q^{42} +10.6640i q^{43} +(1.25202 + 1.55973i) q^{44} +(-2.13688 + 0.658594i) q^{45} +(2.77745 - 2.49008i) q^{46} +(5.06735 + 5.06735i) q^{47} +(3.90532 + 0.865123i) q^{48} -18.1738i q^{49} +(3.65628 + 6.05241i) q^{50} +(-2.63620 + 2.63620i) q^{51} +(0.258529 - 2.36238i) q^{52} +3.52470 q^{53} +(-0.0770377 + 1.41211i) q^{54} +(1.97678 + 1.04535i) q^{55} +(8.26748 + 11.5343i) q^{56} +(5.21643 + 5.21643i) q^{57} +(2.90320 + 3.23825i) q^{58} +(-10.2207 + 10.2207i) q^{59} +(4.39169 - 0.844446i) q^{60} +(4.49746 + 4.49746i) q^{61} +(-3.38115 - 0.184459i) q^{62} +(-3.54781 + 3.54781i) q^{63} +(-7.57607 - 2.56967i) q^{64} +(-0.782571 - 2.53913i) q^{65} +(1.05303 - 0.944080i) q^{66} -1.27353i q^{67} +(5.81467 - 4.66755i) q^{68} +(-1.86512 - 1.86512i) q^{69} +(13.6010 + 8.17011i) q^{70} -3.56257 q^{71} +(0.460397 - 2.79070i) q^{72} +(-2.47003 + 2.47003i) q^{73} +(1.28535 + 0.0701223i) q^{74} +(4.13251 - 2.81467i) q^{75} +(-9.23600 - 11.5059i) q^{76} +5.01756 q^{77} +(-1.67794 - 0.0915396i) q^{78} +3.89252 q^{79} +(-8.91497 + 0.723360i) q^{80} +1.00000 q^{81} +(11.6775 + 0.637066i) q^{82} +9.99092 q^{83} +(7.82540 - 6.28160i) q^{84} +(3.89706 - 7.36943i) q^{85} +(-15.0587 - 0.821528i) q^{86} +(2.17456 - 2.17456i) q^{87} +(-2.29897 + 1.64784i) q^{88} -5.16701 q^{89} +(-0.765389 - 3.06825i) q^{90} +(-4.21566 - 4.21566i) q^{91} +(3.30231 + 4.11391i) q^{92} +2.39439i q^{93} +(-7.54606 + 6.76530i) q^{94} +(-14.5824 - 7.71138i) q^{95} +(-1.52251 + 5.44812i) q^{96} +(-6.87796 + 6.87796i) q^{97} +(25.6635 + 1.40007i) q^{98} +(-0.707136 - 0.707136i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} + 16 q^{3} - 8 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 + 16 * q^3 - 8 * q^4 - 4 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 + 16 * q^9	$ 16 q + 2 q^{2} + 16 q^{3} - 8 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} + 16 q^{9} - 14 q^{10} - 8 q^{12} - 4 q^{14} - 4 q^{15} - 8 q^{16} - 8 q^{17} + 2 q^{18} + 8 q^{19} - 12 q^{20} - 4 q^{21} - 8 q^{22} - 4 q^{24} + 32 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{28} + 12 q^{29} - 14 q^{30} - 28 q^{32} - 20 q^{35} - 8 q^{36} - 16 q^{38} - 44 q^{40} - 4 q^{42} + 52 q^{44} - 4 q^{45} - 16 q^{46} - 32 q^{47} - 8 q^{48} + 22 q^{50} - 8 q^{51} + 8 q^{52} + 16 q^{53} + 2 q^{54} - 4 q^{55} + 20 q^{56} + 8 q^{57} - 44 q^{58} - 24 q^{59} - 12 q^{60} + 40 q^{61} + 40 q^{62} - 4 q^{63} - 8 q^{64} - 4 q^{65} - 8 q^{66} + 24 q^{68} + 56 q^{70} - 4 q^{72} + 8 q^{73} + 64 q^{74} + 32 q^{75} + 16 q^{76} - 72 q^{77} + 20 q^{78} - 48 q^{79} + 16 q^{80} + 16 q^{81} + 8 q^{82} - 8 q^{83} + 12 q^{84} - 8 q^{85} - 8 q^{86} + 12 q^{87} - 16 q^{88} - 14 q^{90} - 40 q^{91} - 20 q^{94} + 8 q^{95} - 28 q^{96} + 48 q^{97} + 30 q^{98}+O(q^{100}) $ 16 * q + 2 * q^2 + 16 * q^3 - 8 * q^4 - 4 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 + 16 * q^9 - 14 * q^10 - 8 * q^12 - 4 * q^14 - 4 * q^15 - 8 * q^16 - 8 * q^17 + 2 * q^18 + 8 * q^19 - 12 * q^20 - 4 * q^21 - 8 * q^22 - 4 * q^24 + 32 * q^25 + 20 * q^26 + 16 * q^27 + 12 * q^28 + 12 * q^29 - 14 * q^30 - 28 * q^32 - 20 * q^35 - 8 * q^36 - 16 * q^38 - 44 * q^40 - 4 * q^42 + 52 * q^44 - 4 * q^45 - 16 * q^46 - 32 * q^47 - 8 * q^48 + 22 * q^50 - 8 * q^51 + 8 * q^52 + 16 * q^53 + 2 * q^54 - 4 * q^55 + 20 * q^56 + 8 * q^57 - 44 * q^58 - 24 * q^59 - 12 * q^60 + 40 * q^61 + 40 * q^62 - 4 * q^63 - 8 * q^64 - 4 * q^65 - 8 * q^66 + 24 * q^68 + 56 * q^70 - 4 * q^72 + 8 * q^73 + 64 * q^74 + 32 * q^75 + 16 * q^76 - 72 * q^77 + 20 * q^78 - 48 * q^79 + 16 * q^80 + 16 * q^81 + 8 * q^82 - 8 * q^83 + 12 * q^84 - 8 * q^85 - 8 * q^86 + 12 * q^87 - 16 * q^88 - 14 * q^90 - 40 * q^91 - 20 * q^94 + 8 * q^95 - 28 * q^96 + 48 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.0770377	+	1.41211i	−0.0544739	+	0.998515i
$2$	−0.0770377	+	1.41211i	−0.0544739	+	0.998515i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−1.98813	−	0.217572i	−0.994065	−	0.108786i
$5$	−2.13688	+	0.658594i	−0.955642	+	0.294532i
$5$	−2.13688	+	0.658594i	−0.955642	+	0.294532i
$6$	−0.0770377	+	1.41211i	−0.0314505	+	0.576493i
$7$	−3.54781	+	3.54781i	−1.34094	+	1.34094i	−0.445824	+	0.895121i	$0.647089\pi$
$7$	−3.54781	+	3.54781i	−1.34094	+	1.34094i	−0.895121	+	0.445824i	$0.852911\pi$
$8$	0.460397	−	2.79070i	0.162775	−	0.986663i
$9$	1.00000			0.333333
$10$	−0.765389	−	3.06825i	−0.242037	−	0.970267i
$11$	−0.707136	−	0.707136i	−0.213209	−	0.213209i	0.592420	−	0.805629i	$-0.298173\pi$
$11$	−0.707136	−	0.707136i	−0.213209	−	0.213209i	−0.805629	+	0.592420i	$0.798173\pi$
$12$	−1.98813	−	0.217572i	−0.573924	−	0.0628076i
$13$			1.18824i			0.329560i	0.986330	+	0.164780i	$0.0526914\pi$
$13$			1.18824i			0.329560i	−0.986330	+	0.164780i	$0.947309\pi$
$14$	−4.73659	−	5.28322i	−1.26591	−	1.41200i
$15$	−2.13688	+	0.658594i	−0.551740	+	0.170048i
$16$	3.90532	+	0.865123i	0.976331	+	0.216281i
$17$	−2.63620	+	2.63620i	−0.639372	+	0.639372i	−0.950401	−	0.311028i	$-0.899327\pi$
$17$	−2.63620	+	2.63620i	−0.639372	+	0.639372i	0.311028	+	0.950401i	$0.399327\pi$
$18$	−0.0770377	+	1.41211i	−0.0181580	+	0.332838i
$19$	5.21643	+	5.21643i	1.19673	+	1.19673i	0.975139	+	0.221593i	$0.0711255\pi$
$19$	5.21643	+	5.21643i	1.19673	+	1.19673i	0.221593	+	0.975139i	$0.428874\pi$
$20$	4.39169	−	0.844446i	0.982011	−	0.188824i
$21$	−3.54781	+	3.54781i	−0.774195	+	0.774195i
$22$	1.05303	−	0.944080i	0.224507	−	0.201279i
$23$	−1.86512	−	1.86512i	−0.388905	−	0.388905i	0.485392	−	0.874297i	$-0.338677\pi$
$23$	−1.86512	−	1.86512i	−0.388905	−	0.388905i	−0.874297	+	0.485392i	$0.838677\pi$
$24$	0.460397	−	2.79070i	0.0939782	−	0.569650i
$25$	4.13251	−	2.81467i	0.826502	−	0.562934i
$26$	−1.67794	−	0.0915396i	−0.329070	−	0.0179524i
$27$	1.00000			0.192450
$28$	7.82540	−	6.28160i	1.47886	−	1.18711i
$29$	2.17456	−	2.17456i	0.403806	−	0.403806i	−0.475766	−	0.879572i	$-0.657829\pi$
$29$	2.17456	−	2.17456i	0.403806	−	0.403806i	0.879572	+	0.475766i	$0.157829\pi$
$30$	−0.765389	−	3.06825i	−0.139740	−	0.560184i
$31$			2.39439i			0.430046i	0.976609	+	0.215023i	$0.0689826\pi$
$31$			2.39439i			0.430046i	−0.976609	+	0.215023i	$0.931017\pi$
$32$	−1.52251	+	5.44812i	−0.269144	+	0.963100i
$33$	−0.707136	−	0.707136i	−0.123097	−	0.123097i
$34$	−3.51953	−	3.92570i	−0.603594	−	0.673252i
$35$	5.24467	−	9.91780i	0.886511	−	1.67641i
$36$	−1.98813	−	0.217572i	−0.331355	−	0.0362620i
$37$		−	0.910233i		−	0.149641i	−0.997197	−	0.0748207i	$-0.976162\pi$
$37$		−	0.910233i		−	0.149641i	0.997197	−	0.0748207i	$-0.0238385\pi$
$38$	−7.76806	+	6.96434i	−1.26015	+	1.12976i
$39$			1.18824i			0.190271i
$40$	0.854128	+	6.26662i	0.135049	+	0.990839i
$41$		−	8.26953i		−	1.29148i	−0.763556	−	0.645742i	$-0.776548\pi$
$41$		−	8.26953i		−	1.29148i	0.763556	−	0.645742i	$-0.223452\pi$
$42$	−4.73659	−	5.28322i	−0.730872	−	0.815219i
$43$			10.6640i			1.62624i	0.582096	+	0.813120i	$0.302233\pi$
$43$			10.6640i			1.62624i	−0.582096	+	0.813120i	$0.697767\pi$
$44$	1.25202	+	1.55973i	0.188750	+	0.235138i
$45$	−2.13688	+	0.658594i	−0.318547	+	0.0981774i
$46$	2.77745	−	2.49008i	0.409513	−	0.367142i
$47$	5.06735	+	5.06735i	0.739150	+	0.739150i	0.972413	−	0.233264i	$-0.0749406\pi$
$47$	5.06735	+	5.06735i	0.739150	+	0.739150i	−0.233264	+	0.972413i	$0.574941\pi$
$48$	3.90532	+	0.865123i	0.563685	+	0.124870i
$49$		−	18.1738i		−	2.59626i
$50$	3.65628	+	6.05241i	0.517076	+	0.855940i
$51$	−2.63620	+	2.63620i	−0.369142	+	0.369142i
$52$	0.258529	−	2.36238i	0.0358515	−	0.327604i
$53$	3.52470			0.484154			0.242077	−	0.970257i	$-0.422171\pi$
$53$	3.52470			0.484154			0.242077	+	0.970257i	$0.422171\pi$
$54$	−0.0770377	+	1.41211i	−0.0104835	+	0.192164i
$55$	1.97678	+	1.04535i	0.266549	+	0.140955i
$56$	8.26748	+	11.5343i	1.10479	+	1.54133i
$57$	5.21643	+	5.21643i	0.690934	+	0.690934i
$58$	2.90320	+	3.23825i	0.381209	+	0.425203i
$59$	−10.2207	+	10.2207i	−1.33062	+	1.33062i	−0.425812	+	0.904812i	$0.640011\pi$
$59$	−10.2207	+	10.2207i	−1.33062	+	1.33062i	−0.904812	+	0.425812i	$0.859989\pi$
$60$	4.39169	−	0.844446i	0.566964	−	0.109017i
$61$	4.49746	+	4.49746i	0.575840	+	0.575840i	0.933755	−	0.357914i	$-0.116512\pi$
$61$	4.49746	+	4.49746i	0.575840	+	0.575840i	−0.357914	+	0.933755i	$0.616512\pi$
$62$	−3.38115	−	0.184459i	−0.429407	−	0.0234263i
$63$	−3.54781	+	3.54781i	−0.446981	+	0.446981i
$64$	−7.57607	−	2.56967i	−0.947009	−	0.321208i
$65$	−0.782571	−	2.53913i	−0.0970659	−	0.314941i
$66$	1.05303	−	0.944080i	0.129619	−	0.116208i
$67$		−	1.27353i		−	0.155586i	−0.996970	−	0.0777931i	$-0.975213\pi$
$67$		−	1.27353i		−	0.155586i	0.996970	−	0.0777931i	$-0.0247874\pi$
$68$	5.81467	−	4.66755i	0.705133	−	0.566023i
$69$	−1.86512	−	1.86512i	−0.224534	−	0.224534i
$70$	13.6010	+	8.17011i	1.62563	+	0.976515i
$71$	−3.56257			−0.422799			−0.211400	−	0.977400i	$-0.567802\pi$
$71$	−3.56257			−0.422799			−0.211400	+	0.977400i	$0.567802\pi$
$72$	0.460397	−	2.79070i	0.0542584	−	0.328888i
$73$	−2.47003	+	2.47003i	−0.289096	+	0.289096i	−0.836723	−	0.547627i	$-0.815531\pi$
$73$	−2.47003	+	2.47003i	−0.289096	+	0.289096i	0.547627	+	0.836723i	$0.315531\pi$
$74$	1.28535	+	0.0701223i	0.149419	+	0.00815155i
$75$	4.13251	−	2.81467i	0.477181	−	0.325010i
$76$	−9.23600	−	11.5059i	−1.05944	−	1.31982i
$77$	5.01756			0.571804
$78$	−1.67794	−	0.0915396i	−0.189989	−	0.0103648i
$79$	3.89252			0.437943			0.218971	−	0.975731i	$-0.429730\pi$
$79$	3.89252			0.437943			0.218971	+	0.975731i	$0.429730\pi$
$80$	−8.91497	+	0.723360i	−0.996724	+	0.0808741i
$81$	1.00000			0.111111
$82$	11.6775	+	0.637066i	1.28957	+	0.0703522i
$83$	9.99092			1.09665			0.548323	−	0.836267i	$-0.315266\pi$
$83$	9.99092			1.09665			0.548323	+	0.836267i	$0.315266\pi$
$84$	7.82540	−	6.28160i	0.853822	−	0.685378i
$85$	3.89706	−	7.36943i	0.422695	−	0.799327i
$86$	−15.0587	−	0.821528i	−1.62383	−	0.0885876i
$87$	2.17456	−	2.17456i	0.233137	−	0.233137i
$88$	−2.29897	+	1.64784i	−0.245071	+	0.175661i
$89$	−5.16701			−0.547702			−0.273851	−	0.961772i	$-0.588297\pi$
$89$	−5.16701			−0.547702			−0.273851	+	0.961772i	$0.588297\pi$
$90$	−0.765389	−	3.06825i	−0.0806791	−	0.323422i
$91$	−4.21566	−	4.21566i	−0.441921	−	0.441921i
$92$	3.30231	+	4.11391i	0.344290	+	0.428904i
$93$			2.39439i			0.248287i
$94$	−7.54606	+	6.76530i	−0.778317	+	0.697788i
$95$	−14.5824	−	7.71138i	−1.49612	−	0.791171i
$96$	−1.52251	+	5.44812i	−0.155390	+	0.556046i
$97$	−6.87796	+	6.87796i	−0.698351	+	0.698351i	−0.964055	−	0.265703i	$-0.914396\pi$
$97$	−6.87796	+	6.87796i	−0.698351	+	0.698351i	0.265703	+	0.964055i	$0.414396\pi$
$98$	25.6635	+	1.40007i	2.59241	+	0.141429i
$99$	−0.707136	−	0.707136i	−0.0710698	−	0.0710698i
$100$	−8.82836	+	4.69682i	−0.882836	+	0.469682i
$101$	4.17060	−	4.17060i	0.414990	−	0.414990i	−0.468482	−	0.883473i	$-0.655199\pi$
$101$	4.17060	−	4.17060i	0.414990	−	0.414990i	0.883473	+	0.468482i	$0.155199\pi$
$102$	−3.51953	−	3.92570i	−0.348485	−	0.388702i
$103$	−1.14779	−	1.14779i	−0.113095	−	0.113095i	0.648294	−	0.761390i	$-0.275483\pi$
$103$	−1.14779	−	1.14779i	−0.113095	−	0.113095i	−0.761390	+	0.648294i	$0.775483\pi$
$104$	3.31604	+	0.547065i	0.325164	+	0.0536441i
$105$	5.24467	−	9.91780i	0.511827	−	0.967878i
$106$	−0.271535	+	4.97727i	−0.0263738	+	0.483435i
$107$	7.26820			0.702644			0.351322	−	0.936255i	$-0.385732\pi$
$107$	7.26820			0.702644			0.351322	+	0.936255i	$0.385732\pi$
$108$	−1.98813	−	0.217572i	−0.191308	−	0.0209359i
$109$	−3.48141	+	3.48141i	−0.333458	+	0.333458i	−0.853898	−	0.520440i	$-0.825768\pi$
$109$	−3.48141	+	3.48141i	−0.333458	+	0.333458i	0.520440	+	0.853898i	$0.325768\pi$
$110$	−1.62844	+	2.71091i	−0.155265	+	0.258475i
$111$		−	0.910233i		−	0.0863955i
$112$	−16.9246	+	10.7860i	−1.59923	+	1.01919i
$113$	−6.68812	−	6.68812i	−0.629165	−	0.629165i	0.318693	−	0.947858i	$-0.396756\pi$
$113$	−6.68812	−	6.68812i	−0.629165	−	0.629165i	−0.947858	+	0.318693i	$0.896756\pi$
$114$	−7.76806	+	6.96434i	−0.727545	+	0.652270i
$115$	5.21390	+	2.75718i	0.486199	+	0.257109i
$116$	−4.79643	+	3.85019i	−0.445338	+	0.357481i
$117$			1.18824i			0.109853i
$118$	−13.6454	−	15.2202i	−1.25616	−	1.40113i
$119$		−	18.7054i		−	1.71473i
$120$	0.854128	+	6.26662i	0.0779708	+	0.572061i
$121$		−	9.99992i		−	0.909083i
$122$	−6.69739	+	6.00445i	−0.606354	+	0.543617i
$123$		−	8.26953i		−	0.745639i
$124$	0.520953	−	4.76036i	0.0467829	−	0.427493i
$125$	−6.97695	+	8.73626i	−0.624037	+	0.781395i
$126$	−4.73659	−	5.28322i	−0.421969	−	0.470667i
$127$	−2.58827	−	2.58827i	−0.229671	−	0.229671i	0.582884	−	0.812555i	$-0.301924\pi$
$127$	−2.58827	−	2.58827i	−0.229671	−	0.229671i	−0.812555	+	0.582884i	$0.801924\pi$
$128$	4.21231	−	10.5003i	0.372319	−	0.928105i
$129$			10.6640i			0.938910i
$130$	3.64583	−	0.909469i	0.319761	−	0.0797657i
$131$	−4.13367	+	4.13367i	−0.361160	+	0.361160i	−0.864240	−	0.503080i	$-0.832200\pi$
$131$	−4.13367	+	4.13367i	−0.361160	+	0.361160i	0.503080	+	0.864240i	$0.332200\pi$
$132$	1.25202	+	1.55973i	0.108975	+	0.135757i
$133$	−37.0138			−3.20950
$134$	1.79837	+	0.0981097i	0.155355	+	0.00847539i
$135$	−2.13688	+	0.658594i	−0.183913	+	0.0566827i
$136$	6.14316	+	8.57056i	0.526771	+	0.734919i
$137$	−1.38187	−	1.38187i	−0.118062	−	0.118062i	0.645608	−	0.763669i	$-0.276604\pi$
$137$	−1.38187	−	1.38187i	−0.118062	−	0.118062i	−0.763669	+	0.645608i	$0.776604\pi$
$138$	2.77745	−	2.49008i	0.236432	−	0.211970i
$139$	12.1831	−	12.1831i	1.03336	−	1.03336i	0.0339330	−	0.999424i	$-0.489197\pi$
$139$	12.1831	−	12.1831i	1.03336	−	1.03336i	0.999424	−	0.0339330i	$-0.0108033\pi$
$140$	−12.5849	+	18.5768i	−1.06362	+	1.57002i
$141$	5.06735	+	5.06735i	0.426748	+	0.426748i
$142$	0.274452	−	5.03075i	0.0230315	−	0.422171i
$143$	0.840250	−	0.840250i	0.0702652	−	0.0702652i
$144$	3.90532	+	0.865123i	0.325444	+	0.0720936i
$145$	−3.21462	+	6.07893i	−0.266960	+	0.504827i
$146$	−3.29768	−	3.67826i	−0.272918	−	0.304415i
$147$		−	18.1738i		−	1.49895i
$148$	−0.198041	+	1.80966i	−0.0162789	+	0.148753i
$149$	9.87902	+	9.87902i	0.809321	+	0.809321i	0.984531	−	0.175210i	$-0.0560606\pi$
$149$	9.87902	+	9.87902i	0.809321	+	0.809321i	−0.175210	+	0.984531i	$0.556061\pi$
$150$	3.65628	+	6.05241i	0.298534	+	0.494177i
$151$	−19.1820			−1.56101			−0.780505	−	0.625150i	$-0.785038\pi$
$151$	−19.1820			−1.56101			−0.780505	+	0.625150i	$0.785038\pi$
$152$	16.9592	−	12.1559i	1.37557	−	0.985973i
$153$	−2.63620	+	2.63620i	−0.213124	+	0.213124i
$154$	−0.386541	+	7.08536i	−0.0311484	+	0.570955i
$155$	−1.57693	−	5.11653i	−0.126662	−	0.410969i
$156$	0.258529	−	2.36238i	0.0206989	−	0.189142i
$157$	8.64456			0.689911			0.344956	−	0.938619i	$-0.387894\pi$
$157$	8.64456			0.689911			0.344956	+	0.938619i	$0.387894\pi$
$158$	−0.299871	+	5.49668i	−0.0238564	+	0.437292i
$159$	3.52470			0.279527
$160$	−0.334677	−	12.6447i	−0.0264585	−	0.999650i
$161$	13.2342			1.04300
$162$	−0.0770377	+	1.41211i	−0.00605265	+	0.110946i
$163$	−9.90002			−0.775429			−0.387715	−	0.921779i	$-0.626735\pi$
$163$	−9.90002			−0.775429			−0.387715	+	0.921779i	$0.626735\pi$
$164$	−1.79922	+	16.4409i	−0.140495	+	1.28382i
$165$	1.97678	+	1.04535i	0.153892	+	0.0813803i
$166$	−0.769678	+	14.1083i	−0.0597386	+	1.09502i
$167$	5.65004	−	5.65004i	0.437213	−	0.437213i	−0.453860	−	0.891073i	$-0.649953\pi$
$167$	5.65004	−	5.65004i	0.437213	−	0.437213i	0.891073	+	0.453860i	$0.149953\pi$
$168$	8.26748	+	11.5343i	0.637850	+	0.889889i
$169$	11.5881			0.891390
$170$	10.1062	+	6.07081i	0.775114	+	0.465610i
$171$	5.21643	+	5.21643i	0.398911	+	0.398911i
$172$	2.32018	−	21.2014i	0.176912	−	1.61659i
$173$		−	4.49197i		−	0.341519i	−0.985313	−	0.170759i	$-0.945378\pi$
$173$		−	4.49197i		−	0.341519i	0.985313	−	0.170759i	$-0.0546220\pi$
$174$	2.90320	+	3.23825i	0.220091	+	0.245491i
$175$	−4.67543	+	24.6472i	−0.353429	+	1.86316i
$176$	−2.14984	−	3.37335i	−0.162050	−	0.254276i
$177$	−10.2207	+	10.2207i	−0.768236	+	0.768236i
$178$	0.398054	−	7.29640i	0.0298354	−	0.546888i
$179$	10.5248	+	10.5248i	0.786659	+	0.786659i	0.980945	−	0.194286i	$-0.0622390\pi$
$179$	10.5248	+	10.5248i	0.786659	+	0.786659i	−0.194286	+	0.980945i	$0.562239\pi$
$180$	4.39169	−	0.844446i	0.327337	−	0.0629413i
$181$	16.2637	−	16.2637i	1.20887	−	1.20887i	0.237474	−	0.971394i	$-0.423681\pi$
$181$	16.2637	−	16.2637i	1.20887	−	1.20887i	0.971394	−	0.237474i	$-0.0763195\pi$
$182$	6.27776	−	5.62823i	0.465338	−	0.417192i
$183$	4.49746	+	4.49746i	0.332462	+	0.332462i
$184$	−6.06371	+	4.34631i	−0.447022	+	0.320414i
$185$	0.599474	+	1.94506i	0.0440742	+	0.143004i
$186$	−3.38115	−	0.184459i	−0.247918	−	0.0135252i
$187$	3.72830			0.272640
$188$	−8.97205	−	11.1771i	−0.654354	−	0.815172i
$189$	−3.54781	+	3.54781i	−0.258065	+	0.258065i
$190$	12.0127	−	19.9979i	0.871496	−	1.45080i
$191$		−	18.4242i		−	1.33313i	−0.745446	−	0.666566i	$-0.767764\pi$
$191$		−	18.4242i		−	1.33313i	0.745446	−	0.666566i	$-0.232236\pi$
$192$	−7.57607	−	2.56967i	−0.546756	−	0.185450i
$193$	9.23854	+	9.23854i	0.665005	+	0.665005i	0.956555	−	0.291551i	$-0.0941712\pi$
$193$	9.23854	+	9.23854i	0.665005	+	0.665005i	−0.291551	+	0.956555i	$0.594171\pi$
$194$	−9.18260	−	10.2423i	−0.659272	−	0.735356i
$195$	−0.782571	−	2.53913i	−0.0560410	−	0.181831i
$196$	−3.95412	+	36.1320i	−0.282437	+	2.58086i
$197$			7.31984i			0.521517i	0.965404	+	0.260758i	$0.0839726\pi$
$197$			7.31984i			0.521517i	−0.965404	+	0.260758i	$0.916027\pi$
$198$	1.05303	−	0.944080i	0.0748357	−	0.0670928i
$199$			21.6050i			1.53154i	0.643115	+	0.765770i	$0.277642\pi$
$199$			21.6050i			1.53154i	−0.643115	+	0.765770i	$0.722358\pi$
$200$	−5.95232	−	12.8285i	−0.420893	−	0.907110i
$201$		−	1.27353i		−	0.0898278i
$202$	5.56807	+	6.21066i	0.391768	+	0.436980i
$203$			15.4298i			1.08296i
$204$	5.81467	−	4.66755i	0.407108	−	0.326794i
$205$	5.44626	+	17.6710i	0.380384	+	1.23420i
$206$	1.70924	−	1.53239i	0.119088	−	0.106767i
$207$	−1.86512	−	1.86512i	−0.129635	−	0.129635i
$208$	−1.02798	+	4.64048i	−0.0712774	+	0.321759i
$209$		−	7.37745i		−	0.510309i
$210$	13.6010	+	8.17011i	0.938559	+	0.563791i
$211$	−5.97567	+	5.97567i	−0.411382	+	0.411382i	−0.882220	−	0.470838i	$-0.843952\pi$
$211$	−5.97567	+	5.97567i	−0.411382	+	0.411382i	0.470838	+	0.882220i	$0.343952\pi$
$212$	−7.00755	−	0.766875i	−0.481281	−	0.0526692i
$213$	−3.56257			−0.244103
$214$	−0.559926	+	10.2635i	−0.0382757	+	0.701600i
$215$	−7.02322	−	22.7876i	−0.478980	−	1.55410i
$216$	0.460397	−	2.79070i	0.0313261	−	0.189883i
$217$	−8.49484	−	8.49484i	−0.576667	−	0.576667i
$218$	−4.64794	−	5.18434i	−0.314798	−	0.351128i
$219$	−2.47003	+	2.47003i	−0.166909	+	0.166909i
$220$	−3.70266	−	2.50838i	−0.249633	−	0.169115i
$221$	−3.13245	−	3.13245i	−0.210711	−	0.210711i
$222$	1.28535	+	0.0701223i	0.0862673	+	0.00470630i
$223$	12.0372	−	12.0372i	0.806070	−	0.806070i	−0.177966	−	0.984037i	$-0.556952\pi$
$223$	12.0372	−	12.0372i	0.806070	−	0.806070i	0.984037	+	0.177966i	$0.0569518\pi$
$224$	−13.9273	−	24.7304i	−0.930556	−	1.65237i
$225$	4.13251	−	2.81467i	0.275501	−	0.187645i
$226$	9.95962	−	8.92914i	0.662504	−	0.593958i
$227$		−	0.181755i		−	0.0120635i	−0.999982	−	0.00603175i	$-0.998080\pi$
$227$		−	0.181755i		−	0.0120635i	0.999982	−	0.00603175i	$-0.00191998\pi$
$228$	−9.23600	−	11.5059i	−0.611669	−	0.761997i
$229$	0.556001	+	0.556001i	0.0367416	+	0.0367416i	0.725239	−	0.688497i	$-0.241729\pi$
$229$	0.556001	+	0.556001i	0.0367416	+	0.0367416i	−0.688497	+	0.725239i	$0.741729\pi$
$230$	−4.29513	+	7.15022i	−0.283212	+	0.471471i
$231$	5.01756			0.330131
$232$	−5.06739	−	7.06972i	−0.332691	−	0.464150i
$233$	−9.96356	+	9.96356i	−0.652735	+	0.652735i	−0.953651	−	0.300916i	$-0.902708\pi$
$233$	−9.96356	+	9.96356i	−0.652735	+	0.652735i	0.300916	+	0.953651i	$0.402708\pi$
$234$	−1.67794	−	0.0915396i	−0.109690	−	0.00598413i
$235$	−14.1657	−	7.49100i	−0.924065	−	0.488659i
$236$	22.5439	−	18.0964i	1.46748	−	1.17797i
$237$	3.89252			0.252846
$238$	26.4142	+	1.44103i	1.71218	+	0.0934078i
$239$	6.80569			0.440224			0.220112	−	0.975475i	$-0.429358\pi$
$239$	6.80569			0.440224			0.220112	+	0.975475i	$0.429358\pi$
$240$	−8.91497	+	0.723360i	−0.575459	+	0.0466927i
$241$	18.8285			1.21285			0.606425	−	0.795141i	$-0.292603\pi$
$241$	18.8285			1.21285			0.606425	+	0.795141i	$0.292603\pi$
$242$	14.1210	+	0.770371i	0.907734	+	0.0495213i
$243$	1.00000			0.0641500
$244$	−7.96301	−	9.92005i	−0.509779	−	0.635066i
$245$	11.9692	+	38.8353i	0.764683	+	2.48110i
$246$	11.6775	+	0.637066i	0.744532	+	0.0406178i
$247$	−6.19840	+	6.19840i	−0.394395	+	0.394395i
$248$	6.68204	+	1.10237i	0.424310	+	0.0700007i
$249$	9.99092			0.633149
$250$	−11.7991	−	10.5253i	−0.746241	−	0.665676i
$251$	11.9160	+	11.9160i	0.752133	+	0.752133i	0.974877	−	0.222744i	$-0.0715013\pi$
$251$	11.9160	+	11.9160i	0.752133	+	0.752133i	−0.222744	+	0.974877i	$0.571501\pi$
$252$	7.82540	−	6.28160i	0.492954	−	0.395703i
$253$			2.63779i			0.165836i
$254$	3.85432	−	3.45553i	0.241842	−	0.216819i
$255$	3.89706	−	7.36943i	0.244043	−	0.461491i
$256$	14.5031	+	6.75717i	0.906445	+	0.422323i
$257$	−14.1560	+	14.1560i	−0.883030	+	0.883030i	−0.993841	−	0.110812i	$-0.964655\pi$
$257$	−14.1560	+	14.1560i	−0.883030	+	0.883030i	0.110812	+	0.993841i	$0.464655\pi$
$258$	−15.0587	−	0.821528i	−0.937516	−	0.0511461i
$259$	3.22933	+	3.22933i	0.200661	+	0.200661i
$260$	1.00341	+	5.21840i	0.0622287	+	0.323631i
$261$	2.17456	−	2.17456i	0.134602	−	0.134602i
$262$	−5.51876	−	6.15566i	−0.340950	−	0.380298i
$263$	−7.24736	−	7.24736i	−0.446892	−	0.446892i	0.447428	−	0.894320i	$-0.352340\pi$
$263$	−7.24736	−	7.24736i	−0.446892	−	0.446892i	−0.894320	+	0.447428i	$0.852340\pi$
$264$	−2.29897	+	1.64784i	−0.141492	+	0.101418i
$265$	−7.53185	+	2.32134i	−0.462678	+	0.142599i
$266$	2.85146	−	52.2677i	0.174834	−	3.20474i
$267$	−5.16701			−0.316216
$268$	−0.277084	+	2.53194i	−0.0169256	+	0.154663i
$269$	−14.0526	+	14.0526i	−0.856805	+	0.856805i	−0.990960	−	0.134155i	$-0.957168\pi$
$269$	−14.0526	+	14.0526i	−0.856805	+	0.856805i	0.134155	+	0.990960i	$0.457168\pi$
$270$	−0.765389	−	3.06825i	−0.0465801	−	0.186728i
$271$			0.510213i			0.0309933i	0.999880	+	0.0154966i	$0.00493293\pi$
$271$			0.510213i			0.0309933i	−0.999880	+	0.0154966i	$0.995067\pi$
$272$	−12.5759	+	8.01458i	−0.762523	+	0.485955i
$273$	−4.21566	−	4.21566i	−0.255143	−	0.255143i
$274$	2.05782	−	1.84491i	0.124317	−	0.111455i
$275$	−4.91260	−	0.931889i	−0.296241	−	0.0561950i
$276$	3.30231	+	4.11391i	0.198776	+	0.247628i
$277$		−	1.56728i		−	0.0941688i	−0.998891	−	0.0470844i	$-0.985007\pi$
$277$		−	1.56728i		−	0.0941688i	0.998891	−	0.0470844i	$-0.0149930\pi$
$278$	16.2654	+	18.1425i	0.975532	+	1.08811i
$279$			2.39439i			0.143349i
$280$	−25.2630	−	19.2025i	−1.50975	−	1.14757i
$281$			26.3167i			1.56992i	0.619546	+	0.784960i	$0.287317\pi$
$281$			26.3167i			1.56992i	−0.619546	+	0.784960i	$0.712683\pi$
$282$	−7.54606	+	6.76530i	−0.449361	+	0.402868i
$283$		−	16.2153i		−	0.963897i	−0.876200	−	0.481948i	$-0.839929\pi$
$283$		−	16.2153i		−	0.963897i	0.876200	−	0.481948i	$-0.160071\pi$
$284$	7.08285	+	0.775115i	0.420290	+	0.0459946i
$285$	−14.5824	−	7.71138i	−0.863787	−	0.456783i
$286$	1.12180	+	1.25126i	0.0663333	+	0.0739885i
$287$	29.3387	+	29.3387i	1.73181	+	1.73181i
$288$	−1.52251	+	5.44812i	−0.0897147	+	0.321033i
$289$			3.10090i			0.182406i
$290$	−8.33649	−	5.00772i	−0.489535	−	0.294063i
$291$	−6.87796	+	6.87796i	−0.403193	+	0.403193i
$292$	5.44816	−	4.37334i	0.318830	−	0.255930i
$293$	21.6309			1.26369			0.631844	−	0.775095i	$-0.282298\pi$
$293$	21.6309			1.26369			0.631844	+	0.775095i	$0.282298\pi$
$294$	25.6635	+	1.40007i	1.49673	+	0.0816538i
$295$	15.1091	−	28.5717i	0.879688	−	1.66351i
$296$	−2.54019	−	0.419069i	−0.147646	−	0.0243579i
$297$	−0.707136	−	0.707136i	−0.0410322	−	0.0410322i
$298$	−14.7114	+	13.1892i	−0.852206	+	0.764032i
$299$	2.21622	−	2.21622i	0.128167	−	0.128167i
$300$	−8.82836	+	4.69682i	−0.509706	+	0.271171i
$301$	−37.8337	−	37.8337i	−2.18070	−	2.18070i
$302$	1.47774	−	27.0872i	0.0850342	−	1.55869i
$303$	4.17060	−	4.17060i	0.239595	−	0.239595i
$304$	15.8590	+	24.8847i	0.909577	+	1.42724i
$305$	−12.5725	−	6.64853i	−0.719901	−	0.380693i
$306$	−3.51953	−	3.92570i	−0.201198	−	0.224417i
$307$		−	13.9316i		−	0.795117i	−0.917577	−	0.397559i	$-0.869858\pi$
$307$		−	13.9316i		−	0.795117i	0.917577	−	0.397559i	$-0.130142\pi$
$308$	−9.97556	−	1.09168i	−0.568410	−	0.0622043i
$309$	−1.14779	−	1.14779i	−0.0652956	−	0.0652956i
$310$	7.34660	−	1.83264i	0.417259	−	0.104087i
$311$	1.47971			0.0839067			0.0419534	−	0.999120i	$-0.486642\pi$
$311$	1.47971			0.0839067			0.0419534	+	0.999120i	$0.486642\pi$
$312$	3.31604	+	0.547065i	0.187734	+	0.0309714i
$313$	11.4062	−	11.4062i	0.644717	−	0.644717i	−0.306994	−	0.951711i	$-0.599323\pi$
$313$	11.4062	−	11.4062i	0.644717	−	0.644717i	0.951711	+	0.306994i	$0.0993232\pi$
$314$	−0.665957	+	12.2071i	−0.0375822	+	0.688887i
$315$	5.24467	−	9.91780i	0.295504	−	0.558805i
$316$	−7.73883	−	0.846903i	−0.435343	−	0.0476420i
$317$	21.2307			1.19243			0.596217	−	0.802824i	$-0.296670\pi$
$317$	21.2307			1.19243			0.596217	+	0.802824i	$0.296670\pi$
$318$	−0.271535	+	4.97727i	−0.0152269	+	0.279112i
$319$	−3.07542			−0.172190
$320$	17.8815	+	0.501516i	0.999607	+	0.0280356i
$321$	7.26820			0.405672
$322$	−1.01953	+	18.6882i	−0.0568163	+	1.04145i
$323$	−27.5031			−1.53031
$324$	−1.98813	−	0.217572i	−0.110452	−	0.0120873i
$325$	3.34452	+	4.91043i	0.185520	+	0.272382i
$326$	0.762675	−	13.9799i	0.0422406	−	0.774278i
$327$	−3.48141	+	3.48141i	−0.192522	+	0.192522i
$328$	−23.0778	−	3.80727i	−1.27426	−	0.210221i
$329$	−35.9560			−1.98232
$330$	−1.62844	+	2.71091i	−0.0896425	+	0.149230i
$331$	2.12076	+	2.12076i	0.116567	+	0.116567i	0.762984	−	0.646417i	$-0.223733\pi$
$331$	2.12076	+	2.12076i	0.116567	+	0.116567i	−0.646417	+	0.762984i	$0.723733\pi$
$332$	−19.8632	−	2.17374i	−1.09014	−	0.119300i
$333$		−	0.910233i		−	0.0498805i
$334$	7.54323	+	8.41376i	0.412747	+	0.460380i
$335$	0.838738	+	2.72138i	0.0458252	+	0.148685i
$336$	−16.9246	+	10.7860i	−0.923314	+	0.588427i
$337$	5.27802	−	5.27802i	0.287512	−	0.287512i	−0.548584	−	0.836096i	$-0.684833\pi$
$337$	5.27802	−	5.27802i	0.287512	−	0.287512i	0.836096	+	0.548584i	$0.184833\pi$
$338$	−0.892719	+	16.3637i	−0.0485575	+	0.890067i
$339$	−6.68812	−	6.68812i	−0.363249	−	0.363249i
$340$	−9.35124	+	13.8035i	−0.507142	+	0.748599i
$341$	1.69316	−	1.69316i	0.0916898	−	0.0916898i
$342$	−7.76806	+	6.96434i	−0.420049	+	0.376588i
$343$	39.6426	+	39.6426i	2.14050	+	2.14050i
$344$	29.7600	+	4.90966i	1.60455	+	0.264711i
$345$	5.21390	+	2.75718i	0.280707	+	0.148442i
$346$	6.34318	+	0.346051i	0.341011	+	0.0186038i
$347$	−26.9264			−1.44549			−0.722744	−	0.691116i	$-0.757119\pi$
$347$	−26.9264			−1.44549			−0.722744	+	0.691116i	$0.757119\pi$
$348$	−4.79643	+	3.85019i	−0.257116	+	0.206392i
$349$	9.01587	−	9.01587i	0.482609	−	0.482609i	−0.423355	−	0.905964i	$-0.639148\pi$
$349$	9.01587	−	9.01587i	0.482609	−	0.482609i	0.905964	+	0.423355i	$0.139148\pi$
$350$	−34.4445	−	8.50100i	−1.84114	−	0.454398i
$351$			1.18824i			0.0634238i
$352$	4.92918	−	2.77594i	0.262726	−	0.147958i
$353$	18.7513	+	18.7513i	0.998030	+	0.998030i	0.999998	−	0.00196788i	$-0.000626397\pi$
$353$	18.7513	+	18.7513i	0.998030	+	0.998030i	−0.00196788	+	0.999998i	$0.500626\pi$
$354$	−13.6454	−	15.2202i	−0.725246	−	0.808944i
$355$	7.61278	−	2.34629i	0.404044	−	0.124528i
$356$	10.2727	+	1.12420i	0.544451	+	0.0595823i
$357$		−	18.7054i		−	0.989997i
$358$	−15.6730	+	14.0514i	−0.828343	+	0.742639i
$359$			22.4682i			1.18583i	0.805266	+	0.592914i	$0.202022\pi$
$359$			22.4682i			1.18583i	−0.805266	+	0.592914i	$0.797978\pi$
$360$	0.854128	+	6.26662i	0.0450165	+	0.330280i
$361$			35.4224i			1.86433i
$362$	21.7132	+	24.2190i	1.14122	+	1.27292i
$363$		−	9.99992i		−	0.524860i
$364$	7.46407	+	9.29849i	0.391224	+	0.487373i
$365$	3.65142	−	6.90492i	0.191124	−	0.361420i
$366$	−6.69739	+	6.00445i	−0.350078	+	0.313857i
$367$	−17.8664	−	17.8664i	−0.932619	−	0.932619i	0.0652495	−	0.997869i	$-0.479216\pi$
$367$	−17.8664	−	17.8664i	−0.932619	−	0.932619i	−0.997869	+	0.0652495i	$0.979216\pi$
$368$	−5.67035	−	8.89747i	−0.295587	−	0.463813i
$369$		−	8.26953i		−	0.430495i
$370$	−2.79283	+	0.696683i	−0.145192	+	0.0362188i
$371$	−12.5049	+	12.5049i	−0.649224	+	0.649224i
$372$	0.520953	−	4.76036i	0.0270101	−	0.246813i
$373$	−6.19650			−0.320843			−0.160421	−	0.987049i	$-0.551285\pi$
$373$	−6.19650			−0.320843			−0.160421	+	0.987049i	$0.551285\pi$
$374$	−0.287220	+	5.26479i	−0.0148518	+	0.272236i
$375$	−6.97695	+	8.73626i	−0.360288	+	0.451139i
$376$	16.4745	−	11.8085i	0.849607	−	0.608977i
$377$	2.58391	+	2.58391i	0.133078	+	0.133078i
$378$	−4.73659	−	5.28322i	−0.243624	−	0.271740i
$379$	14.4005	−	14.4005i	0.739704	−	0.739704i	−0.232816	−	0.972521i	$-0.574794\pi$
$379$	14.4005	−	14.4005i	0.739704	−	0.739704i	0.972521	+	0.232816i	$0.0747941\pi$
$380$	27.3139	+	18.5039i	1.40118	+	0.949233i
$381$	−2.58827	−	2.58827i	−0.132601	−	0.132601i
$382$	26.0171	+	1.41936i	1.33115	+	0.0726208i
$383$	−8.46651	+	8.46651i	−0.432618	+	0.432618i	−0.889518	−	0.456900i	$-0.848960\pi$
$383$	−8.46651	+	8.46651i	−0.432618	+	0.432618i	0.456900	+	0.889518i	$0.348960\pi$
$384$	4.21231	−	10.5003i	0.214958	−	0.535842i
$385$	−10.7219	+	3.30453i	−0.546440	+	0.168415i
$386$	−13.7576	+	12.3342i	−0.700243	+	0.627792i
$387$			10.6640i			0.542080i
$388$	15.1707	−	12.1778i	0.770178	−	0.618236i
$389$	−24.2277	−	24.2277i	−1.22839	−	1.22839i	−0.964571	−	0.263822i	$-0.915017\pi$
$389$	−24.2277	−	24.2277i	−1.22839	−	1.22839i	−0.263822	−	0.964571i	$-0.584983\pi$
$390$	3.64583	−	0.909469i	0.184614	−	0.0460528i
$391$	9.83367			0.497310
$392$	−50.7179	−	8.36719i	−2.56164	−	0.422607i
$393$	−4.13367	+	4.13367i	−0.208516	+	0.208516i
$394$	−10.3364	−	0.563903i	−0.520742	−	0.0284090i
$395$	−8.31784	+	2.56359i	−0.418516	+	0.128988i
$396$	1.25202	+	1.55973i	0.0629166	+	0.0783794i
$397$	−8.48394			−0.425797			−0.212898	−	0.977074i	$-0.568290\pi$
$397$	−8.48394			−0.425797			−0.212898	+	0.977074i	$0.568290\pi$
$398$	−30.5087	−	1.66440i	−1.52927	−	0.0834289i
$399$	−37.0138			−1.85301
$400$	18.5738	−	7.41708i	0.928691	−	0.370854i
$401$	−0.969620			−0.0484205			−0.0242103	−	0.999707i	$-0.507707\pi$
$401$	−0.969620			−0.0484205			−0.0242103	+	0.999707i	$0.507707\pi$
$402$	1.79837	+	0.0981097i	0.0896944	+	0.00489327i
$403$	−2.84512			−0.141726
$404$	−9.19911	+	7.38429i	−0.457673	+	0.367382i
$405$	−2.13688	+	0.658594i	−0.106182	+	0.0327258i
$406$	−21.7887	−	1.18868i	−1.08135	−	0.0589932i
$407$	−0.643659	+	0.643659i	−0.0319050	+	0.0319050i
$408$	6.14316	+	8.57056i	0.304132	+	0.424306i
$409$	28.7556			1.42187			0.710936	−	0.703257i	$-0.248272\pi$
$409$	28.7556			1.42187			0.710936	+	0.703257i	$0.248272\pi$
$410$	−25.3730	+	6.32941i	−1.25308	+	0.312587i
$411$	−1.38187	−	1.38187i	−0.0681628	−	0.0681628i
$412$	2.03223	+	2.53169i	0.100121	+	0.124727i
$413$		−	72.5222i		−	3.56858i
$414$	2.77745	−	2.49008i	0.136504	−	0.122381i
$415$	−21.3494	+	6.57996i	−1.04800	+	0.322997i
$416$	−6.47369	−	1.80911i	−0.317399	−	0.0886991i
$417$	12.1831	−	12.1831i	0.596609	−	0.596609i
$418$	10.4178	+	0.568342i	0.509551	+	0.0277985i
$419$	16.6648	+	16.6648i	0.814129	+	0.814129i	0.985250	−	0.171121i	$-0.0547390\pi$
$419$	16.6648	+	16.6648i	0.814129	+	0.814129i	−0.171121	+	0.985250i	$0.554739\pi$
$420$	−12.5849	+	18.5768i	−0.614081	+	0.906454i
$421$	−3.83359	+	3.83359i	−0.186838	+	0.186838i	−0.794327	−	0.607490i	$-0.792177\pi$
$421$	−3.83359	+	3.83359i	−0.186838	+	0.186838i	0.607490	+	0.794327i	$0.292177\pi$
$422$	−7.97797	−	8.89868i	−0.388362	−	0.433181i
$423$	5.06735	+	5.06735i	0.246383	+	0.246383i
$424$	1.62276	−	9.83639i	0.0788082	−	0.477697i
$425$	−3.47408	+	18.3142i	−0.168518	+	0.888367i
$426$	0.274452	−	5.03075i	0.0132972	−	0.243741i
$427$	−31.9122			−1.54434
$428$	−14.4501	−	1.58136i	−0.698474	−	0.0764378i
$429$	0.840250	−	0.840250i	0.0405676	−	0.0405676i
$430$	32.7198	−	8.16209i	1.57789	−	0.393611i
$431$		−	6.02593i		−	0.290259i	−0.989413	−	0.145129i	$-0.953640\pi$
$431$		−	6.02593i		−	0.290259i	0.989413	−	0.145129i	$-0.0463598\pi$
$432$	3.90532	+	0.865123i	0.187895	+	0.0416233i
$433$	7.34342	+	7.34342i	0.352902	+	0.352902i	0.861188	−	0.508286i	$-0.169721\pi$
$433$	7.34342	+	7.34342i	0.352902	+	0.352902i	−0.508286	+	0.861188i	$0.669721\pi$
$434$	12.6501	−	11.3413i	0.607224	−	0.544398i
$435$	−3.21462	+	6.07893i	−0.154129	+	0.291462i
$436$	7.67895	−	6.16404i	0.367755	−	0.295204i
$437$		−	19.4586i		−	0.930830i
$438$	−3.29768	−	3.67826i	−0.157569	−	0.175754i
$439$			2.47473i			0.118112i	0.998255	+	0.0590561i	$0.0188091\pi$
$439$			2.47473i			0.118112i	−0.998255	+	0.0590561i	$0.981191\pi$
$440$	3.82736	−	5.03533i	0.182462	−	0.240050i
$441$		−	18.1738i		−	0.865421i
$442$	4.66469	−	4.18206i	0.221877	−	0.198920i
$443$			3.27807i			0.155746i	0.996963	+	0.0778728i	$0.0248128\pi$
$443$			3.27807i			0.155746i	−0.996963	+	0.0778728i	$0.975187\pi$
$444$	−0.198041	+	1.80966i	−0.00939863	+	0.0858828i
$445$	11.0413	−	3.40296i	0.523406	−	0.161316i
$446$	16.0706	+	17.9252i	0.760964	+	0.848783i
$447$	9.87902	+	9.87902i	0.467261	+	0.467261i
$448$	35.9951	−	17.7617i	1.70061	−	0.839163i
$449$		−	16.5248i		−	0.779852i	−0.920846	−	0.389926i	$-0.872501\pi$
$449$		−	16.5248i		−	0.779852i	0.920846	−	0.389926i	$-0.127499\pi$
$450$	3.65628	+	6.05241i	0.172359	+	0.285313i
$451$	−5.84768	+	5.84768i	−0.275357	+	0.275357i
$452$	11.8417	+	14.7520i	0.556987	+	0.693875i
$453$	−19.1820			−0.901249
$454$	0.256659	+	0.0140020i	0.0120456	+	0.000657146i
$455$	11.7848	+	6.23195i	0.552478	+	0.292158i
$456$	16.9592	−	12.1559i	0.794185	−	0.569252i
$457$	−12.4498	−	12.4498i	−0.582376	−	0.582376i	0.353180	−	0.935555i	$-0.385100\pi$
$457$	−12.4498	−	12.4498i	−0.582376	−	0.582376i	−0.935555	+	0.353180i	$0.885100\pi$
$458$	−0.827970	+	0.742304i	−0.0386885	+	0.0346856i
$459$	−2.63620	+	2.63620i	−0.123047	+	0.123047i
$460$	−9.76603	−	6.61604i	−0.455344	−	0.308475i
$461$	13.9930	+	13.9930i	0.651719	+	0.651719i	0.953407	−	0.301688i	$-0.0975499\pi$
$461$	13.9930	+	13.9930i	0.651719	+	0.651719i	−0.301688	+	0.953407i	$0.597550\pi$
$462$	−0.386541	+	7.08536i	−0.0179835	+	0.329641i
$463$	21.7437	−	21.7437i	1.01052	−	1.01052i	0.0105728	−	0.999944i	$-0.496635\pi$
$463$	21.7437	−	21.7437i	1.01052	−	1.01052i	0.999944	−	0.0105728i	$-0.00336549\pi$
$464$	10.3736	−	6.61110i	0.481584	−	0.306913i
$465$	−1.57693	−	5.11653i	−0.0731285	−	0.237273i
$466$	−13.3021	−	14.8373i	−0.616209	−	0.687323i
$467$		−	28.3316i		−	1.31103i	−0.755183	−	0.655514i	$-0.772452\pi$
$467$		−	28.3316i		−	1.31103i	0.755183	−	0.655514i	$-0.227548\pi$
$468$	0.258529	−	2.36238i	0.0119505	−	0.109201i
$469$	4.51823	+	4.51823i	0.208633	+	0.208633i
$470$	11.6694	−	19.4264i	0.538271	−	0.896074i
$471$	8.64456			0.398320
$472$	23.8174	+	33.2286i	1.09628	+	1.52947i
$473$	7.54087	−	7.54087i	0.346730	−	0.346730i
$474$	−0.299871	+	5.49668i	−0.0137735	+	0.252471i
$475$	36.2395	+	6.87440i	1.66278	+	0.315419i
$476$	−4.06978	+	37.1889i	−0.186538	+	1.70455i
$477$	3.52470			0.161385
$478$	−0.524295	+	9.61041i	−0.0239807	+	0.439570i
$479$	21.4895			0.981879			0.490940	−	0.871194i	$-0.336654\pi$
$479$	21.4895			0.981879			0.490940	+	0.871194i	$0.336654\pi$
$480$	−0.334677	−	12.6447i	−0.0152758	−	0.577148i
$481$	1.08158			0.0493158
$482$	−1.45050	+	26.5880i	−0.0660687	+	1.21105i
$483$	13.2342			0.602176
$484$	−2.17570	+	19.8811i	−0.0988956	+	0.903688i
$485$	10.1676	−	19.2272i	0.461687	−	0.873060i
$486$	−0.0770377	+	1.41211i	−0.00349450	+	0.0640548i
$487$	16.7986	−	16.7986i	0.761216	−	0.761216i	−0.215327	−	0.976542i	$-0.569082\pi$
$487$	16.7986	−	16.7986i	0.761216	−	0.761216i	0.976542	+	0.215327i	$0.0690816\pi$
$488$	14.6217	−	10.4805i	0.661893	−	0.474428i
$489$	−9.90002			−0.447694
$490$	−55.7620	+	13.9101i	−2.51907	+	0.628393i
$491$	−6.05778	−	6.05778i	−0.273384	−	0.273384i	0.557077	−	0.830461i	$-0.311923\pi$
$491$	−6.05778	−	6.05778i	−0.273384	−	0.273384i	−0.830461	+	0.557077i	$0.811923\pi$
$492$	−1.79922	+	16.4409i	−0.0811151	+	0.741213i
$493$			11.4652i			0.516364i
$494$	−8.27533	−	9.23035i	−0.372325	−	0.415293i
$495$	1.97678	+	1.04535i	0.0888496	+	0.0469849i
$496$	−2.07144	+	9.35088i	−0.0930106	+	0.419867i
$497$	12.6393	−	12.6393i	0.566950	−	0.566950i
$498$	−0.769678	+	14.1083i	−0.0344901	+	0.632209i
$499$	−29.7904	−	29.7904i	−1.33360	−	1.33360i	−0.902125	−	0.431474i	$-0.857994\pi$
$499$	−29.7904	−	29.7904i	−1.33360	−	1.33360i	−0.431474	−	0.902125i	$-0.642006\pi$
$500$	15.7718	−	15.8508i	0.705338	−	0.708871i
$501$	5.65004	−	5.65004i	0.252425	−	0.252425i
$502$	−17.7448	+	15.9088i	−0.791988	+	0.710045i
$503$	5.71063	+	5.71063i	0.254624	+	0.254624i	0.822863	−	0.568239i	$-0.192375\pi$
$503$	5.71063	+	5.71063i	0.254624	+	0.254624i	−0.568239	+	0.822863i	$0.692375\pi$
$504$	8.26748	+	11.5343i	0.368263	+	0.513778i
$505$	−6.16534	+	11.6588i	−0.274354	+	0.518810i
$506$	−3.72486	−	0.203209i	−0.165590	−	0.00903376i
$507$	11.5881			0.514645
$508$	4.58268	+	5.70895i	0.203323	+	0.253293i
$509$	15.5011	−	15.5011i	0.687074	−	0.687074i	−0.274510	−	0.961584i	$-0.588516\pi$
$509$	15.5011	−	15.5011i	0.687074	−	0.687074i	0.961584	+	0.274510i	$0.0885156\pi$
$510$	10.1062	+	6.07081i	0.447512	+	0.268820i
$511$		−	17.5264i		−	0.775323i
$512$	−10.6592	+	19.9595i	−0.471074	+	0.882094i
$513$	5.21643	+	5.21643i	0.230311	+	0.230311i
$514$	−18.8994	−	21.0805i	−0.833617	−	0.929821i
$515$	3.20862	+	1.69677i	0.141389	+	0.0747684i
$516$	2.32018	−	21.2014i	0.102140	−	0.933338i
$517$		−	7.16661i		−	0.315187i
$518$	−4.80896	+	4.31140i	−0.211294	+	0.189432i
$519$		−	4.49197i		−	0.197176i
$520$	−7.44627	+	1.01491i	−0.326541	+	0.0445068i
$521$			2.72323i			0.119307i	0.998219	+	0.0596533i	$0.0189995\pi$
$521$			2.72323i			0.119307i	−0.998219	+	0.0596533i	$0.981000\pi$
$522$	2.90320	+	3.23825i	0.127070	+	0.141734i
$523$			18.5563i			0.811410i	0.914004	+	0.405705i	$0.132974\pi$
$523$			18.5563i			0.811410i	−0.914004	+	0.405705i	$0.867026\pi$
$524$	9.11764	−	7.31890i	0.398306	−	0.319728i
$525$	−4.67543	+	24.6472i	−0.204052	+	1.07569i
$526$	10.7924	−	9.67578i	0.470572	−	0.421884i
$527$	−6.31210	−	6.31210i	−0.274959	−	0.274959i
$528$	−2.14984	−	3.37335i	−0.0935596	−	0.146806i
$529$		−	16.0426i		−	0.697506i
$530$	−2.69776	−	10.8147i	−0.117183	−	0.469759i
$531$	−10.2207	+	10.2207i	−0.443541	+	0.443541i
$532$	73.5882	+	8.05316i	3.19045	+	0.349149i
$533$	9.82622			0.425621
$534$	0.398054	−	7.29640i	0.0172255	−	0.315746i
$535$	−15.5313	+	4.78679i	−0.671475	+	0.206951i
$536$	−3.55404	−	0.586329i	−0.153511	−	0.0253256i
$537$	10.5248	+	10.5248i	0.454178	+	0.454178i
$538$	−18.7613	−	20.9265i	−0.808859	−	0.902206i
$539$	−12.8514	+	12.8514i	−0.553548	+	0.553548i
$540$	4.39169	−	0.844446i	0.188988	−	0.0363392i
$541$	−6.87489	−	6.87489i	−0.295575	−	0.295575i	0.543703	−	0.839278i	$-0.317022\pi$
$541$	−6.87489	−	6.87489i	−0.295575	−	0.295575i	−0.839278	+	0.543703i	$0.817022\pi$
$542$	−0.720479	−	0.0393057i	−0.0309472	−	0.00168832i
$543$	16.2637	−	16.2637i	0.697940	−	0.697940i
$544$	−10.3487	−	18.3760i	−0.443696	−	0.787863i
$545$	5.14651	−	9.73218i	0.220452	−	0.416881i
$546$	6.27776	−	5.62823i	0.268663	−	0.240866i
$547$		−	17.9983i		−	0.769552i	−0.923010	−	0.384776i	$-0.874279\pi$
$547$		−	17.9983i		−	0.769552i	0.923010	−	0.384776i	$-0.125721\pi$
$548$	2.44669	+	3.04800i	0.104517	+	0.130204i
$549$	4.49746	+	4.49746i	0.191947	+	0.191947i
$550$	1.69439	−	6.86536i	0.0722490	−	0.292740i
$551$	22.6869			0.966494
$552$	−6.06371	+	4.34631i	−0.258088	+	0.184991i
$553$	−13.8099	+	13.8099i	−0.587257	+	0.587257i
$554$	2.21318	+	0.120740i	0.0940290	+	0.00512974i
$555$	0.599474	+	1.94506i	0.0254463	+	0.0825632i
$556$	−26.8723	+	21.5709i	−1.13964	+	0.914810i
$557$	4.99053			0.211456			0.105728	−	0.994395i	$-0.466283\pi$
$557$	4.99053			0.211456			0.105728	+	0.994395i	$0.466283\pi$
$558$	−3.38115	−	0.184459i	−0.143136	−	0.00780875i
$559$	−12.6714			−0.535943
$560$	29.0623	−	34.1949i	1.22810	−	1.44500i
$561$	3.72830			0.157409
$562$	−37.1621	−	2.02738i	−1.56759	−	0.0855197i
$563$	1.13365			0.0477778			0.0238889	−	0.999715i	$-0.492395\pi$
$563$	1.13365			0.0477778			0.0238889	+	0.999715i	$0.492395\pi$
$564$	−8.97205	−	11.1771i	−0.377791	−	0.470640i
$565$	18.6965	+	9.88695i	0.786566	+	0.415947i
$566$	22.8978	+	1.24919i	0.962466	+	0.0525072i
$567$	−3.54781	+	3.54781i	−0.148994	+	0.148994i
$568$	−1.64020	+	9.94208i	−0.0688212	+	0.417160i
$569$	−39.7427			−1.66610			−0.833051	−	0.553196i	$-0.813408\pi$
$569$	−39.7427			−1.66610			−0.833051	+	0.553196i	$0.813408\pi$
$570$	12.0127	−	19.9979i	0.503158	−	0.837622i
$571$	12.9907	+	12.9907i	0.543645	+	0.543645i	0.924596	−	0.380950i	$-0.124403\pi$
$571$	12.9907	+	12.9907i	0.543645	+	0.543645i	−0.380950	+	0.924596i	$0.624403\pi$
$572$	−1.85334	+	1.48771i	−0.0774921	+	0.0622043i
$573$		−	18.4242i		−	0.769684i
$574$	−43.6898	+	39.1694i	−1.82358	+	1.63490i
$575$	−12.9573	−	2.45793i	−0.540359	−	0.102503i
$576$	−7.57607	−	2.56967i	−0.315670	−	0.107069i
$577$	−30.4387	+	30.4387i	−1.26718	+	1.26718i	−0.319643	+	0.947538i	$0.603563\pi$
$577$	−30.4387	+	30.4387i	−1.26718	+	1.26718i	−0.947538	+	0.319643i	$0.896437\pi$
$578$	−4.37883	−	0.238886i	−0.182135	−	0.00993637i
$579$	9.23854	+	9.23854i	0.383941	+	0.383941i
$580$	7.71369	−	11.3863i	0.320294	−	0.472790i
$581$	−35.4458	+	35.4458i	−1.47054	+	1.47054i
$582$	−9.18260	−	10.2423i	−0.380631	−	0.424558i
$583$	−2.49244	−	2.49244i	−0.103226	−	0.103226i
$584$	5.75594	+	8.03034i	0.238183	+	0.332298i
$585$	−0.782571	−	2.53913i	−0.0323553	−	0.104980i
$586$	−1.66639	+	30.5452i	−0.0688380	+	1.26181i
$587$	10.0656			0.415453			0.207726	−	0.978187i	$-0.433394\pi$
$587$	10.0656			0.415453			0.207726	+	0.978187i	$0.433394\pi$
$588$	−3.95412	+	36.1320i	−0.163065	+	1.49006i
$589$	−12.4902	+	12.4902i	−0.514649	+	0.514649i
$590$	39.1826	+	23.5369i	1.61312	+	0.968999i
$591$			7.31984i			0.301098i
$592$	0.787464	−	3.55476i	0.0323646	−	0.146100i
$593$	−14.4752	−	14.4752i	−0.594425	−	0.594425i	0.344399	−	0.938823i	$-0.388083\pi$
$593$	−14.4752	−	14.4752i	−0.594425	−	0.594425i	−0.938823	+	0.344399i	$0.888083\pi$
$594$	1.05303	−	0.944080i	0.0432064	−	0.0387361i
$595$	12.3193	+	39.9713i	0.505042	+	1.63866i
$596$	−17.4914	−	21.7902i	−0.716475	−	0.892560i
$597$			21.6050i			0.884235i
$598$	2.95882	+	3.30029i	0.120995	+	0.134959i
$599$		−	6.47946i		−	0.264743i	−0.991200	−	0.132372i	$-0.957741\pi$
$599$		−	6.47946i		−	0.264743i	0.991200	−	0.132372i	$-0.0422593\pi$
$600$	−5.95232	−	12.8285i	−0.243003	−	0.523720i
$601$		−	9.39907i		−	0.383396i	−0.981454	−	0.191698i	$-0.938601\pi$
$601$		−	9.39907i		−	0.383396i	0.981454	−	0.191698i	$-0.0613994\pi$
$602$	56.3401	−	50.5108i	2.29625	−	2.05867i
$603$		−	1.27353i		−	0.0518621i
$604$	38.1363	+	4.17347i	1.55174	+	0.169816i
$605$	6.58589	+	21.3686i	0.267754	+	0.868758i
$606$	5.56807	+	6.21066i	0.226187	+	0.252291i
$607$	19.3440	+	19.3440i	0.785149	+	0.785149i	0.980695	−	0.195545i	$-0.0626477\pi$
$607$	19.3440	+	19.3440i	0.785149	+	0.785149i	−0.195545	+	0.980695i	$0.562648\pi$
$608$	−36.3618	+	20.4777i	−1.47467	+	0.830479i
$609$			15.4298i			0.625248i
$610$	10.3570	−	17.2416i	0.419344	−	0.698094i
$611$	−6.02126	+	6.02126i	−0.243594	+	0.243594i
$612$	5.81467	−	4.66755i	0.235044	−	0.188674i
$613$	30.5351			1.23330			0.616650	−	0.787238i	$-0.288490\pi$
$613$	30.5351			1.23330			0.616650	+	0.787238i	$0.288490\pi$
$614$	19.6730	+	1.07326i	0.793937	+	0.0433131i
$615$	5.44626	+	17.6710i	0.219615	+	0.712563i
$616$	2.31007	−	14.0025i	0.0930754	−	0.564178i
$617$	−22.5970	−	22.5970i	−0.909720	−	0.909720i	0.0865290	−	0.996249i	$-0.472422\pi$
$617$	−22.5970	−	22.5970i	−0.909720	−	0.909720i	−0.996249	+	0.0865290i	$0.972422\pi$
$618$	1.70924	−	1.53239i	0.0687556	−	0.0616418i
$619$	−17.0858	+	17.0858i	−0.686737	+	0.686737i	−0.961509	−	0.274773i	$-0.911397\pi$
$619$	−17.0858	+	17.0858i	−0.686737	+	0.686737i	0.274773	+	0.961509i	$0.411397\pi$
$620$	2.02193	+	10.5154i	0.0812028	+	0.422309i
$621$	−1.86512	−	1.86512i	−0.0748448	−	0.0748448i
$622$	−0.113994	+	2.08952i	−0.00457073	+	0.0837822i
$623$	18.3315	−	18.3315i	0.734437	−	0.734437i
$624$	−1.02798	+	4.64048i	−0.0411520	+	0.185768i
$625$	9.15524	−	23.2633i	0.366210	−	0.930532i
$626$	15.2282	+	16.9856i	0.608640	+	0.678880i
$627$		−	7.37745i		−	0.294627i
$628$	−17.1865	−	1.88082i	−0.685817	−	0.0750527i
$629$	2.39956	+	2.39956i	0.0956766	+	0.0956766i
$630$	13.6010	+	8.17011i	0.541878	+	0.325505i
$631$	−21.9991			−0.875769			−0.437885	−	0.899031i	$-0.644272\pi$
$631$	−21.9991			−0.875769			−0.437885	+	0.899031i	$0.644272\pi$
$632$	1.79211	−	10.8629i	0.0712861	−	0.432102i
$633$	−5.97567	+	5.97567i	−0.237512	+	0.237512i
$634$	−1.63556	+	29.9801i	−0.0649565	+	1.19066i
$635$	7.23543	+	3.82620i	0.287129	+	0.151838i
$636$	−7.00755	−	0.766875i	−0.277868	−	0.0304086i
$637$	21.5950			0.855624
$638$	0.236923	−	4.34284i	0.00937988	−	0.171935i
$639$	−3.56257			−0.140933
$640$	−2.08575	+	25.2121i	−0.0824464	+	0.996595i
$641$	2.69605			0.106487			0.0532437	−	0.998582i	$-0.483044\pi$
$641$	2.69605			0.106487			0.0532437	+	0.998582i	$0.483044\pi$
$642$	−0.559926	+	10.2635i	−0.0220985	+	0.405069i
$643$	−21.5956			−0.851646			−0.425823	−	0.904807i	$-0.640015\pi$
$643$	−21.5956			−0.851646			−0.425823	+	0.904807i	$0.640015\pi$
$644$	−26.3113	−	2.87939i	−1.03681	−	0.113464i
$645$	−7.02322	−	22.7876i	−0.276539	−	0.897261i
$646$	2.11878	−	38.8375i	0.0833622	−	1.52804i
$647$	−29.1033	+	29.1033i	−1.14417	+	1.14417i	−0.156491	+	0.987679i	$0.550018\pi$
$647$	−29.1033	+	29.1033i	−1.14417	+	1.14417i	−0.987679	+	0.156491i	$0.949982\pi$
$648$	0.460397	−	2.79070i	0.0180861	−	0.109629i
$649$	14.4549			0.567403
$650$	−7.19174	+	4.34455i	−0.282083	+	0.170407i
$651$	−8.49484	−	8.49484i	−0.332939	−	0.332939i
$652$	19.6825	+	2.15397i	0.770827	+	0.0843559i
$653$			8.54847i			0.334527i	0.985912	+	0.167264i	$0.0534931\pi$
$653$			8.54847i			0.334527i	−0.985912	+	0.167264i	$0.946507\pi$
$654$	−4.64794	−	5.18434i	−0.181749	−	0.202724i
$655$	6.11074	−	11.5556i	0.238766	−	0.451513i
$656$	7.15416	−	32.2952i	0.279323	−	1.26092i
$657$	−2.47003	+	2.47003i	−0.0963652	+	0.0963652i
$658$	2.76997	−	50.7739i	0.107985	−	1.97937i
$659$	9.96438	+	9.96438i	0.388157	+	0.388157i	0.874030	−	0.485873i	$-0.161498\pi$
$659$	9.96438	+	9.96438i	0.388157	+	0.388157i	−0.485873	+	0.874030i	$0.661498\pi$
$660$	−3.70266	−	2.50838i	−0.144126	−	0.0976386i
$661$	−20.3395	+	20.3395i	−0.791115	+	0.791115i	−0.981675	−	0.190561i	$-0.938969\pi$
$661$	−20.3395	+	20.3395i	−0.791115	+	0.791115i	0.190561	+	0.981675i	$0.438969\pi$
$662$	−3.15813	+	2.83137i	−0.122744	+	0.110044i
$663$	−3.13245	−	3.13245i	−0.121654	−	0.121654i
$664$	4.59979	−	27.8817i	0.178507	−	1.08202i
$665$	79.0940	−	24.3771i	3.06713	−	0.945302i
$666$	1.28535	+	0.0701223i	0.0498064	+	0.00271718i
$667$	−8.11165			−0.314084
$668$	−12.4623	+	10.0037i	−0.482181	+	0.387055i
$669$	12.0372	−	12.0372i	0.465385	−	0.465385i
$670$	−3.90751	+	0.974745i	−0.150960	+	0.0376577i
$671$		−	6.36062i		−	0.245549i
$672$	−13.9273	−	24.7304i	−0.537257	−	0.953997i
$673$	−26.6025	−	26.6025i	−1.02545	−	1.02545i	−0.999668	−	0.0257841i	$-0.991792\pi$
$673$	−26.6025	−	26.6025i	−1.02545	−	1.02545i	−0.0257841	−	0.999668i	$-0.508208\pi$
$674$	7.04656	+	7.85978i	0.271423	+	0.302747i
$675$	4.13251	−	2.81467i	0.159060	−	0.108337i
$676$	−23.0386	−	2.52124i	−0.886100	−	0.0969708i
$677$		−	21.6129i		−	0.830650i	−0.909673	−	0.415325i	$-0.863668\pi$
$677$		−	21.6129i		−	0.830650i	0.909673	−	0.415325i	$-0.136332\pi$
$678$	9.95962	−	8.92914i	0.382497	−	0.342922i
$679$		−	48.8033i		−	1.87290i
$680$	−18.7717	−	14.2684i	−0.719862	−	0.547168i
$681$		−	0.181755i		−	0.00696486i
$682$	2.26050	+	2.52137i	0.0865589	+	0.0965483i
$683$			27.1548i			1.03905i	0.854456	+	0.519524i	$0.173891\pi$
$683$			27.1548i			1.03905i	−0.854456	+	0.519524i	$0.826109\pi$
$684$	−9.23600	−	11.5059i	−0.353147	−	0.439939i
$685$	3.86299	+	2.04281i	0.147597	+	0.0780516i
$686$	−59.0339	+	52.9259i	−2.25392	+	2.02072i
$687$	0.556001	+	0.556001i	0.0212128	+	0.0212128i
$688$	−9.22564	+	41.6463i	−0.351724	+	1.58775i
$689$			4.18820i			0.159558i
$690$	−4.29513	+	7.15022i	−0.163513	+	0.272204i
$691$	−8.25201	+	8.25201i	−0.313921	+	0.313921i	−0.846427	−	0.532505i	$-0.821251\pi$
$691$	−8.25201	+	8.25201i	−0.313921	+	0.313921i	0.532505	+	0.846427i	$0.321251\pi$
$692$	−0.977328	+	8.93063i	−0.0371524	+	0.339492i
$693$	5.01756			0.190601
$694$	2.07435	−	38.0232i	0.0787413	−	1.44334i
$695$	−18.0101	+	34.0575i	−0.683162	+	1.29188i
$696$	−5.06739	−	7.06972i	−0.192079	−	0.267977i
$697$	21.8001	+	21.8001i	0.825739	+	0.825739i
$698$	12.0369	+	13.4260i	0.455602	+	0.508182i
$699$	−9.96356	+	9.96356i	−0.376857	+	0.376857i
$700$	14.6579	−	47.9847i	0.554017	−	1.81365i
$701$	−16.4761	−	16.4761i	−0.622295	−	0.622295i	0.323823	−	0.946118i	$-0.395032\pi$
$701$	−16.4761	−	16.4761i	−0.622295	−	0.622295i	−0.946118	+	0.323823i	$0.895032\pi$
$702$	−1.67794	−	0.0915396i	−0.0633296	−	0.00345494i
$703$	4.74817	−	4.74817i	0.179081	−	0.179081i
$704$	3.54020	+	7.17441i	0.133426	+	0.270396i
$705$	−14.1657	−	7.49100i	−0.533509	−	0.282127i
$706$	−27.9235	+	25.0344i	−1.05091	+	0.942182i
$707$			29.5930i			1.11296i
$708$	22.5439	−	18.0964i	0.847250	−	0.680103i
$709$	2.56426	+	2.56426i	0.0963029	+	0.0963029i	0.753617	−	0.657314i	$-0.228307\pi$
$709$	2.56426	+	2.56426i	0.0963029	+	0.0963029i	−0.657314	+	0.753617i	$0.728307\pi$
$710$	2.72675	+	10.9309i	0.102333	+	0.410228i
$711$	3.89252			0.145981
$712$	−2.37888	+	14.4196i	−0.0891522	+	0.540397i
$713$	4.46584	−	4.46584i	0.167247	−	0.167247i
$714$	26.4142	+	1.44103i	0.988527	+	0.0539290i
$715$	−1.24213	+	2.34890i	−0.0464530	+	0.0878437i
$716$	−18.6347	−	23.2145i	−0.696413	−	0.867568i
$717$	6.80569			0.254163
$718$	−31.7277	−	1.73090i	−1.18407	−	0.0645966i
$719$	−49.6672			−1.85227			−0.926137	−	0.377187i	$-0.876891\pi$
$719$	−49.6672			−1.85227			−0.926137	+	0.377187i	$0.876891\pi$
$720$	−8.91497	+	0.723360i	−0.332241	+	0.0269580i
$721$	8.14429			0.303309
$722$	−50.0204	−	2.72886i	−1.86157	−	0.101558i
$723$	18.8285			0.700239
$724$	−35.8728	+	28.7957i	−1.33320	+	1.07019i
$725$	2.86571	−	15.1071i	0.106430	−	0.561062i
$726$	14.1210	+	0.770371i	0.524080	+	0.0285911i
$727$	−1.84178	+	1.84178i	−0.0683077	+	0.0683077i	−0.740435	−	0.672128i	$-0.765381\pi$
$727$	−1.84178	+	1.84178i	−0.0683077	+	0.0683077i	0.672128	+	0.740435i	$0.265381\pi$
$728$	−13.7055	+	9.82378i	−0.507961	+	0.364094i
$729$	1.00000			0.0370370
$730$	9.46923	+	5.68815i	0.350472	+	0.210528i
$731$	−28.1123	−	28.1123i	−1.03977	−	1.03977i
$732$	−7.96301	−	9.92005i	−0.294321	−	0.366656i
$733$		−	13.0551i		−	0.482202i	−0.970500	−	0.241101i	$-0.922492\pi$
$733$		−	13.0551i		−	0.482202i	0.970500	−	0.241101i	$-0.0775085\pi$
$734$	26.6058	−	23.8530i	0.982038	−	0.880431i
$735$	11.9692	+	38.8353i	0.441490	+	1.43246i
$736$	13.0011	−	7.32174i	0.479226	−	0.269883i
$737$	−0.900557	+	0.900557i	−0.0331725	+	0.0331725i
$738$	11.6775	+	0.637066i	0.429855	+	0.0234507i
$739$	−12.9439	−	12.9439i	−0.476148	−	0.476148i	0.427749	−	0.903897i	$-0.359307\pi$
$739$	−12.9439	−	12.9439i	−0.476148	−	0.476148i	−0.903897	+	0.427749i	$0.859307\pi$
$740$	−0.768643	−	3.99746i	−0.0282559	−	0.146950i
$741$	−6.19840	+	6.19840i	−0.227704	+	0.227704i
$742$	−16.6950	−	18.6217i	−0.612894	−	0.683626i
$743$	−11.3763	−	11.3763i	−0.417355	−	0.417355i	0.466936	−	0.884291i	$-0.345358\pi$
$743$	−11.3763	−	11.3763i	−0.417355	−	0.417355i	−0.884291	+	0.466936i	$0.845358\pi$
$744$	6.68204	+	1.10237i	0.244976	+	0.0404149i
$745$	−27.6165	−	14.6040i	−1.01179	−	0.535049i
$746$	0.477364	−	8.75017i	0.0174776	−	0.320366i
$747$	9.99092			0.365549
$748$	−7.41235	−	0.811174i	−0.271022	−	0.0296595i
$749$	−25.7862	+	25.7862i	−0.942206	+	0.942206i
$750$	−11.7991	−	10.5253i	−0.430842	−	0.384328i
$751$			36.5284i			1.33294i	0.745532	+	0.666470i	$0.232196\pi$
$751$			36.5284i			1.33294i	−0.745532	+	0.666470i	$0.767804\pi$
$752$	15.4058	+	24.1736i	0.561791	+	0.881519i
$753$	11.9160	+	11.9160i	0.434244	+	0.434244i
$754$	−3.84783	+	3.44971i	−0.140130	+	0.125631i
$755$	40.9896	−	12.6332i	1.49177	−	0.459767i
$756$	7.82540	−	6.28160i	0.284607	−	0.228459i
$757$			36.7015i			1.33394i	0.745086	+	0.666969i	$0.232409\pi$
$757$			36.7015i			1.33394i	−0.745086	+	0.666969i	$0.767591\pi$
$758$	19.2258	+	21.4445i	0.698311	+	0.778901i
$759$			2.63779i			0.0957457i
$760$	−28.2339	+	37.1449i	−1.02415	+	1.34739i
$761$		−	24.5206i		−	0.888872i	−0.895811	−	0.444436i	$-0.853404\pi$
$761$		−	24.5206i		−	0.888872i	0.895811	−	0.444436i	$-0.146596\pi$
$762$	3.85432	−	3.45553i	0.139627	−	0.125181i
$763$		−	24.7027i		−	0.894298i
$764$	−4.00860	+	36.6298i	−0.145026	+	1.32522i
$765$	3.89706	−	7.36943i	0.140898	−	0.266442i
$766$	−11.3034	−	12.6079i	−0.408410	−	0.455543i
$767$	−12.1447	−	12.1447i	−0.438520	−	0.438520i
$768$	14.5031	+	6.75717i	0.523336	+	0.243829i
$769$			42.8743i			1.54609i	0.634352	+	0.773044i	$0.281267\pi$
$769$			42.8743i			1.54609i	−0.634352	+	0.773044i	$0.718733\pi$
$770$	−3.84039	−	15.3951i	−0.138398	−	0.554803i
$771$	−14.1560	+	14.1560i	−0.509817	+	0.509817i
$772$	−16.3574	−	20.3775i	−0.588715	−	0.733401i
$773$	29.2410			1.05172			0.525862	−	0.850570i	$-0.323743\pi$
$773$	29.2410			1.05172			0.525862	+	0.850570i	$0.323743\pi$
$774$	−15.0587	−	0.821528i	−0.541275	−	0.0295292i
$775$	6.73943	+	9.89485i	0.242087	+	0.355433i
$776$	16.0278	+	22.3610i	0.575363	+	0.802712i
$777$	3.22933	+	3.22933i	0.115852	+	0.115852i
$778$	36.0787	−	32.3458i	1.29349	−	1.15965i
$779$	43.1375	−	43.1375i	1.54556	−	1.54556i
$780$	1.00341	+	5.21840i	0.0359278	+	0.186849i
$781$	2.51922	+	2.51922i	0.0901448	+	0.0901448i
$782$	−0.757564	+	13.8863i	−0.0270904	+	0.496572i
$783$	2.17456	−	2.17456i	0.0777124	−	0.0777124i
$784$	15.7226	−	70.9748i	0.561522	−	2.53481i
$785$	−18.4724	+	5.69326i	−0.659308	+	0.203201i
$786$	−5.51876	−	6.15566i	−0.196848	−	0.219565i
$787$		−	15.8706i		−	0.565725i	−0.959160	−	0.282863i	$-0.908716\pi$
$787$		−	15.8706i		−	0.565725i	0.959160	−	0.282863i	$-0.0912841\pi$
$788$	1.59259	−	14.5528i	0.0567337	−	0.518422i
$789$	−7.24736	−	7.24736i	−0.258013	−	0.258013i
$790$	−2.97929	−	11.9432i	−0.105998	−	0.424921i
$791$	47.4563			1.68735
$792$	−2.29897	+	1.64784i	−0.0816904	+	0.0585536i
$793$	−5.34408	+	5.34408i	−0.189774	+	0.189774i
$794$	0.653583	−	11.9803i	0.0231948	−	0.425164i
$795$	−7.53185	+	2.32134i	−0.267127	+	0.0823296i
$796$	4.70065	−	42.9536i	0.166610	−	1.52245i
$797$	−54.0422			−1.91427			−0.957137	−	0.289637i	$-0.906465\pi$
$797$	−54.0422			−1.91427			−0.957137	+	0.289637i	$0.906465\pi$
$798$	2.85146	−	52.2677i	0.100941	−	1.85026i
$799$	−26.7171			−0.945184
$800$	9.04288	+	26.7997i	0.319714	+	0.947514i
$801$	−5.16701			−0.182567
$802$	0.0746973	−	1.36921i	0.00263765	−	0.0483486i
$803$	3.49330			0.123276
$804$	−0.277084	+	2.53194i	−0.00977201	+	0.0892947i
$805$	−28.2799	+	8.71596i	−0.996734	+	0.307197i
$806$	0.219182	−	4.01764i	0.00772035	−	0.141515i
$807$	−14.0526	+	14.0526i	−0.494677	+	0.494677i
$808$	−9.71879	−	13.5591i	−0.341906	−	0.477006i
$809$	29.5553			1.03911			0.519555	−	0.854437i	$-0.326098\pi$
$809$	29.5553			1.03911			0.519555	+	0.854437i	$0.326098\pi$
$810$	−0.765389	−	3.06825i	−0.0268930	−	0.107807i
$811$	0.939982	+	0.939982i	0.0330072	+	0.0330072i	0.723418	−	0.690411i	$-0.242570\pi$
$811$	0.939982	+	0.939982i	0.0330072	+	0.0330072i	−0.690411	+	0.723418i	$0.742570\pi$
$812$	3.35710	−	30.6765i	0.117811	−	1.07653i
$813$			0.510213i			0.0178940i
$814$	−0.859333	−	0.958505i	−0.0301196	−	0.0335956i
$815$	21.1551	−	6.52009i	0.741032	−	0.228389i
$816$	−12.5759	+	8.01458i	−0.440243	+	0.280566i
$817$	−55.6279	+	55.6279i	−1.94617	+	1.94617i
$818$	−2.21526	+	40.6061i	−0.0774549	+	1.41976i
$819$	−4.21566	−	4.21566i	−0.147307	−	0.147307i
$820$	−6.98317	−	36.3172i	−0.243863	−	1.26825i
$821$	−3.45780	+	3.45780i	−0.120678	+	0.120678i	−0.764867	−	0.644189i	$-0.777195\pi$
$821$	−3.45780	+	3.45780i	−0.120678	+	0.120678i	0.644189	+	0.764867i	$0.277195\pi$
$822$	2.05782	−	1.84491i	0.0717747	−	0.0643485i
$823$	−15.7908	−	15.7908i	−0.550432	−	0.550432i	0.376133	−	0.926566i	$-0.377254\pi$
$823$	−15.7908	−	15.7908i	−0.550432	−	0.550432i	−0.926566	+	0.376133i	$0.877254\pi$
$824$	−3.73159	+	2.67471i	−0.129996	+	0.0931779i
$825$	−4.91260	−	0.931889i	−0.171035	−	0.0324442i
$826$	102.410	+	5.58695i	3.56329	+	0.194395i
$827$	14.4914			0.503914			0.251957	−	0.967738i	$-0.418926\pi$
$827$	14.4914			0.503914			0.251957	+	0.967738i	$0.418926\pi$
$828$	3.30231	+	4.11391i	0.114763	+	0.142968i
$829$	−9.51029	+	9.51029i	−0.330306	+	0.330306i	−0.852703	−	0.522397i	$-0.825038\pi$
$829$	−9.51029	+	9.51029i	−0.330306	+	0.330306i	0.522397	+	0.852703i	$0.325038\pi$
$830$	−7.64694	−	30.6547i	−0.265429	−	1.06404i
$831$		−	1.56728i		−	0.0543684i
$832$	3.05339	−	9.00222i	0.105857	−	0.312096i
$833$	47.9099	+	47.9099i	1.65998	+	1.65998i
$834$	16.2654	+	18.1425i	0.563224	+	0.628223i
$835$	−8.35237	+	15.7945i	−0.289046	+	0.546592i
$836$	−1.60513	+	14.6673i	−0.0555145	+	0.507280i
$837$			2.39439i			0.0827623i
$838$	−24.8164	+	22.2488i	−0.857269	+	0.768571i
$839$		−	22.9683i		−	0.792954i	−0.918045	−	0.396477i	$-0.870233\pi$
$839$		−	22.9683i		−	0.792954i	0.918045	−	0.396477i	$-0.129767\pi$
$840$	−25.2630	−	19.2025i	−0.871657	−	0.662548i
$841$			19.5426i			0.673882i
$842$	−5.11813	−	5.70879i	−0.176383	−	0.196738i
$843$			26.3167i			0.906394i
$844$	13.1805	−	10.5803i	0.453693	−	0.364188i
$845$	−24.7623	+	7.63184i	−0.851850	+	0.262543i
$846$	−7.54606	+	6.76530i	−0.259439	+	0.232596i
$847$	35.4778	+	35.4778i	1.21903	+	1.21903i
$848$	13.7651	+	3.04930i	0.472695	+	0.104713i
$849$		−	16.2153i		−	0.556506i
$850$	−25.5940	−	6.31667i	−0.877868	−	0.216660i
$851$	−1.69770	+	1.69770i	−0.0581963	+	0.0581963i
$852$	7.08285	+	0.775115i	0.242654	+	0.0265550i
$853$	19.6309			0.672150			0.336075	−	0.941835i	$-0.390900\pi$
$853$	19.6309			0.672150			0.336075	+	0.941835i	$0.390900\pi$
$854$	2.45844	−	45.0637i	0.0841262	−	1.54205i
$855$	−14.5824	−	7.71138i	−0.498708	−	0.263724i
$856$	3.34626	−	20.2834i	0.114373	−	0.693273i
$857$	−10.8065	−	10.8065i	−0.369144	−	0.369144i	0.498021	−	0.867165i	$-0.334060\pi$
$857$	−10.8065	−	10.8065i	−0.369144	−	0.369144i	−0.867165	+	0.498021i	$0.834060\pi$
$858$	1.12180	+	1.25126i	0.0382975	+	0.0427173i
$859$	9.38485	−	9.38485i	0.320207	−	0.320207i	−0.528639	−	0.848846i	$-0.677298\pi$
$859$	9.38485	−	9.38485i	0.320207	−	0.320207i	0.848846	+	0.528639i	$0.177298\pi$
$860$	9.00514	+	46.8328i	0.307073	+	1.59699i
$861$	29.3387	+	29.3387i	0.999860	+	0.999860i
$862$	8.50929	+	0.464224i	0.289828	+	0.0158115i
$863$	−28.9450	+	28.9450i	−0.985299	+	0.985299i	−0.999893	−	0.0145949i	$-0.995354\pi$
$863$	−28.9450	+	28.9450i	−0.985299	+	0.985299i	0.0145949	+	0.999893i	$0.495354\pi$
$864$	−1.52251	+	5.44812i	−0.0517968	+	0.185349i
$865$	2.95839	+	9.59881i	0.100588	+	0.326369i
$866$	−10.9355	+	9.80402i	−0.371602	+	0.333154i
$867$			3.10090i			0.105312i
$868$	15.0406	+	18.7371i	0.510512	+	0.635978i
$869$	−2.75254	−	2.75254i	−0.0933735	−	0.0933735i
$870$	−8.33649	−	5.00772i	−0.282633	−	0.169778i
$871$	1.51326			0.0512750
$872$	8.11275	+	11.3184i	0.274732	+	0.383290i
$873$	−6.87796	+	6.87796i	−0.232784	+	0.232784i
$874$	27.4777	+	1.49904i	0.929448	+	0.0507059i
$875$	−6.24171	−	55.7474i	−0.211008	−	1.88461i
$876$	5.44816	−	4.37334i	0.184076	−	0.147761i
$877$	32.0081			1.08084			0.540418	−	0.841396i	$-0.318266\pi$
$877$	32.0081			1.08084			0.540418	+	0.841396i	$0.318266\pi$
$878$	−3.49459	−	0.190647i	−0.117937	−	0.00643403i
$879$	21.6309			0.729591
$880$	6.81561	+	5.79258i	0.229754	+	0.195268i
$881$	24.6429			0.830240			0.415120	−	0.909767i	$-0.363740\pi$
$881$	24.6429			0.830240			0.415120	+	0.909767i	$0.363740\pi$
$882$	25.6635	+	1.40007i	0.864136	+	0.0471429i
$883$	12.5160			0.421196			0.210598	−	0.977573i	$-0.432459\pi$
$883$	12.5160			0.421196			0.210598	+	0.977573i	$0.432459\pi$
$884$	5.54618	+	6.90925i	0.186538	+	0.232383i
$885$	15.1091	−	28.5717i	0.507888	−	0.960428i
$886$	−4.62900	−	0.252535i	−0.155514	−	0.00848407i
$887$	21.6293	−	21.6293i	0.726242	−	0.726242i	−0.243627	−	0.969869i	$-0.578337\pi$
$887$	21.6293	−	21.6293i	0.726242	−	0.726242i	0.969869	+	0.243627i	$0.0783373\pi$
$888$	−2.54019	−	0.419069i	−0.0852433	−	0.0140630i
$889$	18.3653			0.615953
$890$	3.95477	+	15.8537i	0.132564	+	0.531417i
$891$	−0.707136	−	0.707136i	−0.0236899	−	0.0236899i
$892$	−26.5505	+	21.3126i	−0.888975	+	0.713597i
$893$			52.8670i			1.76913i
$894$	−14.7114	+	13.1892i	−0.492021	+	0.441114i
$895$	−29.4217	−	15.5586i	−0.983460	−	0.520068i
$896$	22.3086	+	52.1975i	0.745279	+	1.74380i
$897$	2.21622	−	2.21622i	0.0739975	−	0.0739975i
$898$	23.3348	+	1.27303i	0.778694	+	0.0424815i
$899$	5.20675	+	5.20675i	0.173655	+	0.173655i
$900$	−8.82836	+	4.69682i	−0.294279	+	0.156561i
$901$	−9.29180	+	9.29180i	−0.309555	+	0.309555i
$902$	−7.80710	−	8.70808i	−0.259948	−	0.289947i
$903$	−37.8337	−	37.8337i	−1.25903	−	1.25903i
$904$	−21.7438	+	15.5854i	−0.723186	+	0.518362i
$905$	−24.0423	+	45.4646i	−0.799194	+	1.51129i
$906$	1.47774	−	27.0872i	0.0490945	−	0.899911i
$907$	1.09996			0.0365235			0.0182618	−	0.999833i	$-0.494187\pi$
$907$	1.09996			0.0365235			0.0182618	+	0.999833i	$0.494187\pi$
$908$	−0.0395448	+	0.361352i	−0.00131234	+	0.0119919i
$909$	4.17060	−	4.17060i	0.138330	−	0.138330i
$910$	−9.70809	+	16.1613i	−0.321820	+	0.535743i
$911$		−	10.9439i		−	0.362589i	−0.983429	−	0.181294i	$-0.941971\pi$
$911$		−	10.9439i		−	0.362589i	0.983429	−	0.181294i	$-0.0580287\pi$
$912$	15.8590	+	24.8847i	0.525144	+	0.824016i
$913$	−7.06493	−	7.06493i	−0.233815	−	0.233815i
$914$	18.5396	−	16.6214i	0.613235	−	0.549787i
$915$	−12.5725	−	6.64853i	−0.415635	−	0.219793i
$916$	−0.984433	−	1.22637i	−0.0325266	−	0.0405205i
$917$		−	29.3309i		−	0.968592i
$918$	−3.51953	−	3.92570i	−0.116162	−	0.129567i
$919$		−	4.14834i		−	0.136841i	−0.997657	−	0.0684205i	$-0.978204\pi$
$919$		−	4.14834i		−	0.136841i	0.997657	−	0.0684205i	$-0.0217960\pi$
$920$	10.0950	−	13.2811i	0.332821	−	0.437864i
$921$		−	13.9316i		−	0.459061i
$922$	−20.8377	+	18.6817i	−0.686253	+	0.615250i
$923$		−	4.23320i		−	0.139338i
$924$	−9.97556	−	1.09168i	−0.328172	−	0.0359137i
$925$	−2.56201	−	3.76155i	−0.0842383	−	0.123679i
$926$	29.0295	+	32.3797i	0.953970	+	1.06406i
$927$	−1.14779	−	1.14779i	−0.0376985	−	0.0376985i
$928$	8.53647	+	15.1580i	0.280223	+	0.497587i
$929$			5.49483i			0.180280i	0.995929	+	0.0901398i	$0.0287314\pi$
$929$			5.49483i			0.180280i	−0.995929	+	0.0901398i	$0.971269\pi$
$930$	7.34660	−	1.83264i	0.240905	−	0.0600947i
$931$	94.8027	−	94.8027i	3.10703	−	3.10703i
$932$	21.9767	−	17.6411i	0.719869	−	0.577852i
$933$	1.47971			0.0484436
$934$	40.0074	+	2.18260i	1.30908	+	0.0714168i
$935$	−7.96693	+	2.45544i	−0.260547	+	0.0803014i
$936$	3.31604	+	0.547065i	0.108388	+	0.0178814i
$937$	−6.00841	−	6.00841i	−0.196286	−	0.196286i	0.602120	−	0.798406i	$-0.294323\pi$
$937$	−6.00841	−	6.00841i	−0.196286	−	0.196286i	−0.798406	+	0.602120i	$0.794323\pi$
$938$	−6.72833	+	6.03218i	−0.219688	+	0.196958i
$939$	11.4062	−	11.4062i	0.372228	−	0.372228i
$940$	26.5333	+	17.9751i	0.865422	+	0.586284i
$941$	30.3741	+	30.3741i	0.990168	+	0.990168i	0.999952	−	0.00978427i	$-0.00311448\pi$
$941$	30.3741	+	30.3741i	0.990168	+	0.990168i	−0.00978427	+	0.999952i	$0.503114\pi$
$942$	−0.665957	+	12.2071i	−0.0216981	+	0.397729i
$943$	−15.4237	+	15.4237i	−0.502265	+	0.502265i
$944$	−48.7574	+	31.0730i	−1.58692	+	1.01134i
$945$	5.24467	−	9.91780i	0.170609	−	0.322626i
$946$	10.0676	+	11.2295i	0.327327	+	0.365103i
$947$		−	12.7107i		−	0.413043i	−0.978442	−	0.206521i	$-0.933786\pi$
$947$		−	12.7107i		−	0.413043i	0.978442	−	0.206521i	$-0.0662143\pi$
$948$	−7.73883	−	0.846903i	−0.251346	−	0.0275061i
$949$	−2.93500	−	2.93500i	−0.0952743	−	0.0952743i
$950$	−12.4992	+	50.6447i	−0.405529	+	1.64313i
$951$	21.2307			0.688452
$952$	−52.2014	−	8.61194i	−1.69186	−	0.279115i
$953$	21.0529	−	21.0529i	0.681971	−	0.681971i	−0.278473	−	0.960444i	$-0.589828\pi$
$953$	21.0529	−	21.0529i	0.681971	−	0.681971i	0.960444	+	0.278473i	$0.0898283\pi$
$954$	−0.271535	+	4.97727i	−0.00879125	+	0.161145i
$955$	12.1341	+	39.3704i	0.392650	+	1.27400i
$956$	−13.5306	−	1.48073i	−0.437611	−	0.0478902i
$957$	−3.07542			−0.0994142
$958$	−1.65550	+	30.3456i	−0.0534868	+	0.980421i
$959$	9.80524			0.316628
$960$	17.8815	+	0.501516i	0.577123	+	0.0161863i
$961$	25.2669			0.815061
$962$	−0.0833224	+	1.52731i	−0.00268642	+	0.0492426i
$963$	7.26820			0.234215
$964$	−37.4335	−	4.09656i	−1.20565	−	0.131941i
$965$	−25.8261	−	13.6572i	−0.831372	−	0.439641i
$966$	−1.01953	+	18.6882i	−0.0328029	+	0.601282i
$967$	12.5616	−	12.5616i	0.403955	−	0.403955i	−0.475669	−	0.879624i	$-0.657794\pi$
$967$	12.5616	−	12.5616i	0.403955	−	0.403955i	0.879624	+	0.475669i	$0.157794\pi$
$968$	−27.9068	−	4.60394i	−0.896959	−	0.147976i
$969$	−27.5031			−0.883528
$970$	26.3677	+	15.8390i	0.846614	+	0.508560i
$971$	18.2804	+	18.2804i	0.586647	+	0.586647i	0.936722	−	0.350075i	$-0.113844\pi$
$971$	18.2804	+	18.2804i	0.586647	+	0.586647i	−0.350075	+	0.936722i	$0.613844\pi$
$972$	−1.98813	−	0.217572i	−0.0637693	−	0.00697863i
$973$			86.4465i			2.77135i
$974$	22.4274	+	25.0156i	0.718619	+	0.801552i
$975$	3.34452	+	4.91043i	0.107110	+	0.157260i
$976$	13.6732	+	21.4549i	0.437668	+	0.686754i
$977$	36.6037	−	36.6037i	1.17106	−	1.17106i	0.189098	−	0.981958i	$-0.439444\pi$
$977$	36.6037	−	36.6037i	1.17106	−	1.17106i	0.981958	−	0.189098i	$-0.0605565\pi$
$978$	0.762675	−	13.9799i	0.0243876	−	0.447029i
$979$	3.65377	+	3.65377i	0.116775	+	0.116775i
$980$	−15.3468	−	79.8139i	−0.490236	−	2.54956i
$981$	−3.48141	+	3.48141i	−0.111153	+	0.111153i
$982$	9.02096	−	8.08760i	0.287870	−	0.258086i
$983$	−40.2722	−	40.2722i	−1.28448	−	1.28448i	−0.938089	−	0.346393i	$-0.887406\pi$
$983$	−40.2722	−	40.2722i	−1.28448	−	1.28448i	−0.346393	−	0.938089i	$-0.612594\pi$
$984$	−23.0778	−	3.80727i	−0.735694	−	0.121371i
$985$	−4.82080	−	15.6416i	−0.153603	−	0.498383i
$986$	−16.1901	−	0.883249i	−0.515598	−	0.0281284i
$987$	−35.9560			−1.14449
$988$	13.6718	−	10.9746i	0.434959	−	0.349149i
$989$	19.8896	−	19.8896i	0.632453	−	0.632453i
$990$	−1.62844	+	2.71091i	−0.0517551	+	0.0861582i
$991$		−	32.0105i		−	1.01685i	−0.861107	−	0.508424i	$-0.830228\pi$
$991$		−	32.0105i		−	1.01685i	0.861107	−	0.508424i	$-0.169772\pi$
$992$	−13.0449	−	3.64549i	−0.414177	−	0.115744i
$993$	2.12076	+	2.12076i	0.0673001	+	0.0673001i
$994$	16.8744	+	18.8218i	0.535224	+	0.596992i
$995$	−14.2289	−	46.1673i	−0.451088	−	1.46360i
$996$	−19.8632	−	2.17374i	−0.629391	−	0.0688777i
$997$		−	27.1548i		−	0.860001i	−0.902829	−	0.430000i	$-0.858513\pi$
$997$		−	27.1548i		−	0.860001i	0.902829	−	0.430000i	$-0.141487\pi$
$998$	44.3624	−	39.7724i	1.40427	−	1.25897i
$999$		−	0.910233i		−	0.0287985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.y.e.163.4	✓	16
3.2	odd	2		720.2.z.f.163.5		16
4.3	odd	2		960.2.y.e.943.3		16
5.2	odd	4		240.2.bc.e.67.1	yes	16
8.3	odd	2		1920.2.y.j.223.6		16
8.5	even	2		1920.2.y.i.223.6		16
15.2	even	4		720.2.bd.f.307.8		16
16.3	odd	4		1920.2.bc.i.1183.5		16
16.5	even	4		960.2.bc.e.463.4		16
16.11	odd	4		240.2.bc.e.43.1	yes	16
16.13	even	4		1920.2.bc.j.1183.5		16
20.7	even	4		960.2.bc.e.367.4		16
40.27	even	4		1920.2.bc.j.607.5		16
40.37	odd	4		1920.2.bc.i.607.5		16
48.11	even	4		720.2.bd.f.523.8		16
80.27	even	4	inner	240.2.y.e.187.4	yes	16
80.37	odd	4		960.2.y.e.847.3		16
80.67	even	4		1920.2.y.i.1567.6		16
80.77	odd	4		1920.2.y.j.1567.6		16
240.107	odd	4		720.2.z.f.667.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.e.163.4	✓	16	1.1	even	1	trivial
240.2.y.e.187.4	yes	16	80.27	even	4	inner
240.2.bc.e.43.1	yes	16	16.11	odd	4
240.2.bc.e.67.1	yes	16	5.2	odd	4
720.2.z.f.163.5		16	3.2	odd	2
720.2.z.f.667.5		16	240.107	odd	4
720.2.bd.f.307.8		16	15.2	even	4
720.2.bd.f.523.8		16	48.11	even	4
960.2.y.e.847.3		16	80.37	odd	4
960.2.y.e.943.3		16	4.3	odd	2
960.2.bc.e.367.4		16	20.7	even	4
960.2.bc.e.463.4		16	16.5	even	4
1920.2.y.i.223.6		16	8.5	even	2
1920.2.y.i.1567.6		16	80.67	even	4
1920.2.y.j.223.6		16	8.3	odd	2
1920.2.y.j.1567.6		16	80.77	odd	4
1920.2.bc.i.607.5		16	40.37	odd	4
1920.2.bc.i.1183.5		16	16.3	odd	4
1920.2.bc.j.607.5		16	40.27	even	4
1920.2.bc.j.1183.5		16	16.13	even	4

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.y (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0770377 + 1.41211i) q^{2} +1.00000 q^{3} +(-1.98813 - 0.217572i) q^{4} +(-2.13688 + 0.658594i) q^{5} +(-0.0770377 + 1.41211i) q^{6} +(-3.54781 + 3.54781i) q^{7} +(0.460397 - 2.79070i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.0770377 + 1.41211i) q^{2} +1.00000 q^{3} +(-1.98813 - 0.217572i) q^{4} +(-2.13688 + 0.658594i) q^{5} +(-0.0770377 + 1.41211i) q^{6} +(-3.54781 + 3.54781i) q^{7} +(0.460397 - 2.79070i) q^{8} +1.00000 q^{9} +(-0.765389 - 3.06825i) q^{10} +(-0.707136 - 0.707136i) q^{11} +(-1.98813 - 0.217572i) q^{12} +1.18824i q^{13} +(-4.73659 - 5.28322i) q^{14} +(-2.13688 + 0.658594i) q^{15} +(3.90532 + 0.865123i) q^{16} +(-2.63620 + 2.63620i) q^{17} +(-0.0770377 + 1.41211i) q^{18} +(5.21643 + 5.21643i) q^{19} +(4.39169 - 0.844446i) q^{20} +(-3.54781 + 3.54781i) q^{21} +(1.05303 - 0.944080i) q^{22} +(-1.86512 - 1.86512i) q^{23} +(0.460397 - 2.79070i) q^{24} +(4.13251 - 2.81467i) q^{25} +(-1.67794 - 0.0915396i) q^{26} +1.00000 q^{27} +(7.82540 - 6.28160i) q^{28} +(2.17456 - 2.17456i) q^{29} +(-0.765389 - 3.06825i) q^{30} +2.39439i q^{31} +(-1.52251 + 5.44812i) q^{32} +(-0.707136 - 0.707136i) q^{33} +(-3.51953 - 3.92570i) q^{34} +(5.24467 - 9.91780i) q^{35} +(-1.98813 - 0.217572i) q^{36} -0.910233i q^{37} +(-7.76806 + 6.96434i) q^{38} +1.18824i q^{39} +(0.854128 + 6.26662i) q^{40} -8.26953i q^{41} +(-4.73659 - 5.28322i) q^{42} +10.6640i q^{43} +(1.25202 + 1.55973i) q^{44} +(-2.13688 + 0.658594i) q^{45} +(2.77745 - 2.49008i) q^{46} +(5.06735 + 5.06735i) q^{47} +(3.90532 + 0.865123i) q^{48} -18.1738i q^{49} +(3.65628 + 6.05241i) q^{50} +(-2.63620 + 2.63620i) q^{51} +(0.258529 - 2.36238i) q^{52} +3.52470 q^{53} +(-0.0770377 + 1.41211i) q^{54} +(1.97678 + 1.04535i) q^{55} +(8.26748 + 11.5343i) q^{56} +(5.21643 + 5.21643i) q^{57} +(2.90320 + 3.23825i) q^{58} +(-10.2207 + 10.2207i) q^{59} +(4.39169 - 0.844446i) q^{60} +(4.49746 + 4.49746i) q^{61} +(-3.38115 - 0.184459i) q^{62} +(-3.54781 + 3.54781i) q^{63} +(-7.57607 - 2.56967i) q^{64} +(-0.782571 - 2.53913i) q^{65} +(1.05303 - 0.944080i) q^{66} -1.27353i q^{67} +(5.81467 - 4.66755i) q^{68} +(-1.86512 - 1.86512i) q^{69} +(13.6010 + 8.17011i) q^{70} -3.56257 q^{71} +(0.460397 - 2.79070i) q^{72} +(-2.47003 + 2.47003i) q^{73} +(1.28535 + 0.0701223i) q^{74} +(4.13251 - 2.81467i) q^{75} +(-9.23600 - 11.5059i) q^{76} +5.01756 q^{77} +(-1.67794 - 0.0915396i) q^{78} +3.89252 q^{79} +(-8.91497 + 0.723360i) q^{80} +1.00000 q^{81} +(11.6775 + 0.637066i) q^{82} +9.99092 q^{83} +(7.82540 - 6.28160i) q^{84} +(3.89706 - 7.36943i) q^{85} +(-15.0587 - 0.821528i) q^{86} +(2.17456 - 2.17456i) q^{87} +(-2.29897 + 1.64784i) q^{88} -5.16701 q^{89} +(-0.765389 - 3.06825i) q^{90} +(-4.21566 - 4.21566i) q^{91} +(3.30231 + 4.11391i) q^{92} +2.39439i q^{93} +(-7.54606 + 6.76530i) q^{94} +(-14.5824 - 7.71138i) q^{95} +(-1.52251 + 5.44812i) q^{96} +(-6.87796 + 6.87796i) q^{97} +(25.6635 + 1.40007i) q^{98} +(-0.707136 - 0.707136i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} + 16 q^{3} - 8 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 + 16 * q^3 - 8 * q^4 - 4 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 + 16 * q^9	\( 16 q + 2 q^{2} + 16 q^{3} - 8 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{7} - 4 q^{8} + 16 q^{9} - 14 q^{10} - 8 q^{12} - 4 q^{14} - 4 q^{15} - 8 q^{16} - 8 q^{17} + 2 q^{18} + 8 q^{19} - 12 q^{20} - 4 q^{21} - 8 q^{22} - 4 q^{24} + 32 q^{25} + 20 q^{26} + 16 q^{27} + 12 q^{28} + 12 q^{29} - 14 q^{30} - 28 q^{32} - 20 q^{35} - 8 q^{36} - 16 q^{38} - 44 q^{40} - 4 q^{42} + 52 q^{44} - 4 q^{45} - 16 q^{46} - 32 q^{47} - 8 q^{48} + 22 q^{50} - 8 q^{51} + 8 q^{52} + 16 q^{53} + 2 q^{54} - 4 q^{55} + 20 q^{56} + 8 q^{57} - 44 q^{58} - 24 q^{59} - 12 q^{60} + 40 q^{61} + 40 q^{62} - 4 q^{63} - 8 q^{64} - 4 q^{65} - 8 q^{66} + 24 q^{68} + 56 q^{70} - 4 q^{72} + 8 q^{73} + 64 q^{74} + 32 q^{75} + 16 q^{76} - 72 q^{77} + 20 q^{78} - 48 q^{79} + 16 q^{80} + 16 q^{81} + 8 q^{82} - 8 q^{83} + 12 q^{84} - 8 q^{85} - 8 q^{86} + 12 q^{87} - 16 q^{88} - 14 q^{90} - 40 q^{91} - 20 q^{94} + 8 q^{95} - 28 q^{96} + 48 q^{97} + 30 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 + 16 * q^3 - 8 * q^4 - 4 * q^5 + 2 * q^6 - 4 * q^7 - 4 * q^8 + 16 * q^9 - 14 * q^10 - 8 * q^12 - 4 * q^14 - 4 * q^15 - 8 * q^16 - 8 * q^17 + 2 * q^18 + 8 * q^19 - 12 * q^20 - 4 * q^21 - 8 * q^22 - 4 * q^24 + 32 * q^25 + 20 * q^26 + 16 * q^27 + 12 * q^28 + 12 * q^29 - 14 * q^30 - 28 * q^32 - 20 * q^35 - 8 * q^36 - 16 * q^38 - 44 * q^40 - 4 * q^42 + 52 * q^44 - 4 * q^45 - 16 * q^46 - 32 * q^47 - 8 * q^48 + 22 * q^50 - 8 * q^51 + 8 * q^52 + 16 * q^53 + 2 * q^54 - 4 * q^55 + 20 * q^56 + 8 * q^57 - 44 * q^58 - 24 * q^59 - 12 * q^60 + 40 * q^61 + 40 * q^62 - 4 * q^63 - 8 * q^64 - 4 * q^65 - 8 * q^66 + 24 * q^68 + 56 * q^70 - 4 * q^72 + 8 * q^73 + 64 * q^74 + 32 * q^75 + 16 * q^76 - 72 * q^77 + 20 * q^78 - 48 * q^79 + 16 * q^80 + 16 * q^81 + 8 * q^82 - 8 * q^83 + 12 * q^84 - 8 * q^85 - 8 * q^86 + 12 * q^87 - 16 * q^88 - 14 * q^90 - 40 * q^91 - 20 * q^94 + 8 * q^95 - 28 * q^96 + 48 * q^97 + 30 * q^98

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