LMFDB - Embedded newform 240.2.bc.e.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(43,240)]

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, 1, 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("240.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bc (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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.1
Root			$0.885279 - 1.10285i$ of defining polynomial
Character	$\chi$	$=$	240.43
Dual form			240.2.bc.e.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41211 + 0.0770377i) q^{2} +1.00000i q^{3} +(1.98813 - 0.217572i) q^{4} +(-0.658594 - 2.13688i) q^{5} +(-0.0770377 - 1.41211i) q^{6} +(-3.54781 + 3.54781i) q^{7} +(-2.79070 + 0.460397i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.41211 + 0.0770377i) q^{2} +1.00000i q^{3} +(1.98813 - 0.217572i) q^{4} +(-0.658594 - 2.13688i) q^{5} +(-0.0770377 - 1.41211i) q^{6} +(-3.54781 + 3.54781i) q^{7} +(-2.79070 + 0.460397i) q^{8} -1.00000 q^{9} +(1.09463 + 2.96678i) q^{10} +(-0.707136 + 0.707136i) q^{11} +(0.217572 + 1.98813i) q^{12} +1.18824 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} +(1.41211 - 0.0770377i) q^{18} +(-5.21643 + 5.21643i) q^{19} +(-1.77430 - 4.10510i) q^{20} +(-3.54781 - 3.54781i) q^{21} +(0.944080 - 1.05303i) 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} -1.00000i q^{27} +(-6.28160 + 7.82540i) q^{28} +(-2.17456 - 2.17456i) q^{29} +(-2.96678 + 1.09463i) q^{30} -2.39439i q^{31} +(-5.44812 + 1.52251i) q^{32} +(-0.707136 - 0.707136i) q^{33} +(3.51953 - 3.92570i) q^{34} +(9.91780 + 5.24467i) q^{35} +(-1.98813 + 0.217572i) q^{36} +0.910233 q^{37} +(6.96434 - 7.76806i) q^{38} +1.18824i q^{39} +(2.82176 + 5.66019i) q^{40} +8.26953i q^{41} +(5.28322 + 4.73659i) q^{42} +10.6640 q^{43} +(-1.25202 + 1.55973i) q^{44} +(0.658594 + 2.13688i) q^{45} +(2.77745 + 2.49008i) q^{46} +(-5.06735 - 5.06735i) q^{47} +(0.865123 + 3.90532i) q^{48} -18.1738i q^{49} +(5.61874 - 4.29300i) q^{50} +(-2.63620 - 2.63620i) q^{51} +(2.36238 - 0.258529i) q^{52} +3.52470i 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} +(3.23825 + 2.90320i) q^{58} +(10.2207 + 10.2207i) q^{59} +(4.10510 - 1.77430i) q^{60} +(4.49746 - 4.49746i) q^{61} +(0.184459 + 3.38115i) 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} +1.27353 q^{67} +(-4.66755 + 5.81467i) q^{68} +(1.86512 - 1.86512i) q^{69} +(-14.4091 - 6.64203i) q^{70} -3.56257 q^{71} +(2.79070 - 0.460397i) q^{72} +(2.47003 - 2.47003i) q^{73} +(-1.28535 + 0.0701223i) q^{74} +(-2.81467 - 4.13251i) q^{75} +(-9.23600 + 11.5059i) q^{76} -5.01756i q^{77} +(-0.0915396 - 1.67794i) q^{78} -3.89252 q^{79} +(-4.42069 - 7.77544i) q^{80} +1.00000 q^{81} +(-0.637066 - 11.6775i) q^{82} +9.99092i q^{83} +(-7.82540 - 6.28160i) q^{84} +(7.36943 + 3.89706i) q^{85} +(-15.0587 + 0.821528i) q^{86} +(2.17456 - 2.17456i) q^{87} +(1.64784 - 2.29897i) q^{88} +5.16701 q^{89} +(-1.09463 - 2.96678i) q^{90} +(-4.21566 + 4.21566i) q^{91} +(-4.11391 - 3.30231i) q^{92} +2.39439 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} +(1.40007 + 25.6635i) q^{98} +(0.707136 - 0.707136i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} + 8 q^{4} - 8 q^{5} + 2 q^{6} - 4 q^{7} + 8 q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 + 8 * q^4 - 8 * q^5 + 2 * q^6 - 4 * q^7 + 8 * q^8 - 16 * q^9	$ 16 q + 2 q^{2} + 8 q^{4} - 8 q^{5} + 2 q^{6} - 4 q^{7} + 8 q^{8} - 16 q^{9} - 2 q^{10} - 4 q^{12} - 8 q^{13} + 4 q^{14} + 4 q^{15} - 8 q^{16} - 8 q^{17} - 2 q^{18} - 8 q^{19} + 4 q^{20} - 4 q^{21} + 4 q^{24} - 32 q^{25} + 20 q^{26} + 12 q^{28} - 12 q^{29} + 2 q^{30} - 28 q^{32} + 12 q^{35} - 8 q^{36} - 24 q^{37} + 16 q^{38} + 16 q^{40} + 24 q^{42} + 24 q^{43} - 52 q^{44} + 8 q^{45} - 16 q^{46} + 32 q^{47} - 16 q^{48} + 6 q^{50} - 8 q^{51} + 24 q^{52} - 2 q^{54} - 4 q^{55} + 20 q^{56} - 8 q^{57} + 12 q^{58} + 24 q^{59} + 24 q^{60} + 40 q^{61} + 28 q^{62} + 4 q^{63} + 8 q^{64} - 4 q^{65} - 8 q^{66} + 16 q^{67} - 8 q^{68} + 12 q^{70} - 8 q^{72} - 8 q^{73} - 64 q^{74} + 24 q^{75} + 16 q^{76} + 12 q^{78} + 48 q^{79} + 16 q^{81} - 32 q^{82} - 12 q^{84} - 8 q^{85} - 8 q^{86} + 12 q^{87} + 24 q^{88} + 2 q^{90} - 40 q^{91} - 16 q^{92} - 32 q^{93} + 20 q^{94} - 8 q^{95} - 28 q^{96} + 48 q^{97} + 62 q^{98}+O(q^{100}) $ 16 * q + 2 * q^2 + 8 * q^4 - 8 * q^5 + 2 * q^6 - 4 * q^7 + 8 * q^8 - 16 * q^9 - 2 * q^10 - 4 * q^12 - 8 * q^13 + 4 * q^14 + 4 * q^15 - 8 * q^16 - 8 * q^17 - 2 * q^18 - 8 * q^19 + 4 * q^20 - 4 * q^21 + 4 * q^24 - 32 * q^25 + 20 * q^26 + 12 * q^28 - 12 * q^29 + 2 * q^30 - 28 * q^32 + 12 * q^35 - 8 * q^36 - 24 * q^37 + 16 * q^38 + 16 * q^40 + 24 * q^42 + 24 * q^43 - 52 * q^44 + 8 * q^45 - 16 * q^46 + 32 * q^47 - 16 * q^48 + 6 * q^50 - 8 * q^51 + 24 * q^52 - 2 * q^54 - 4 * q^55 + 20 * q^56 - 8 * q^57 + 12 * q^58 + 24 * q^59 + 24 * q^60 + 40 * q^61 + 28 * q^62 + 4 * q^63 + 8 * q^64 - 4 * q^65 - 8 * q^66 + 16 * q^67 - 8 * q^68 + 12 * q^70 - 8 * q^72 - 8 * q^73 - 64 * q^74 + 24 * q^75 + 16 * q^76 + 12 * q^78 + 48 * q^79 + 16 * q^81 - 32 * q^82 - 12 * q^84 - 8 * q^85 - 8 * q^86 + 12 * q^87 + 24 * q^88 + 2 * q^90 - 40 * q^91 - 16 * q^92 - 32 * q^93 + 20 * q^94 - 8 * q^95 - 28 * q^96 + 48 * q^97 + 62 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.41211	+	0.0770377i	−0.998515	+	0.0544739i
$2$	−1.41211	+	0.0770377i	−0.998515	+	0.0544739i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.98813	−	0.217572i	0.994065	−	0.108786i
$5$	−0.658594	−	2.13688i	−0.294532	−	0.955642i
$5$	−0.658594	−	2.13688i	−0.294532	−	0.955642i
$6$	−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	$0.852911\pi$
$8$	−2.79070	+	0.460397i	−0.986663	+	0.162775i
$9$	−1.00000			−0.333333
$10$	1.09463	+	2.96678i	0.346152	+	0.938178i
$11$	−0.707136	+	0.707136i	−0.213209	+	0.213209i	−0.805629	−	0.592420i	$-0.798173\pi$
$11$	−0.707136	+	0.707136i	−0.213209	+	0.213209i	0.592420	+	0.805629i	$0.298173\pi$
$12$	0.217572	+	1.98813i	0.0628076	+	0.573924i
$13$	1.18824			0.329560			0.164780	−	0.986330i	$-0.447309\pi$
$13$	1.18824			0.329560			0.164780	+	0.986330i	$0.447309\pi$
$14$	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	$0.399327\pi$
$18$	1.41211	−	0.0770377i	0.332838	−	0.0181580i
$19$	−5.21643	+	5.21643i	−1.19673	+	1.19673i	−0.221593	+	0.975139i	$0.571126\pi$
$19$	−5.21643	+	5.21643i	−1.19673	+	1.19673i	−0.975139	+	0.221593i	$0.928874\pi$
$20$	−1.77430	−	4.10510i	−0.396745	−	0.917929i
$21$	−3.54781	−	3.54781i	−0.774195	−	0.774195i
$22$	0.944080	−	1.05303i	0.201279	−	0.224507i
$23$	−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
$27$		−	1.00000i		−	0.192450i
$28$	−6.28160	+	7.82540i	−1.18711	+	1.47886i
$29$	−2.17456	−	2.17456i	−0.403806	−	0.403806i	0.475766	−	0.879572i	$-0.342171\pi$
$29$	−2.17456	−	2.17456i	−0.403806	−	0.403806i	−0.879572	+	0.475766i	$0.842171\pi$
$30$	−2.96678	+	1.09463i	−0.541657	+	0.199851i
$31$		−	2.39439i		−	0.430046i	−0.976609	−	0.215023i	$-0.931017\pi$
$31$		−	2.39439i		−	0.430046i	0.976609	−	0.215023i	$-0.0689826\pi$
$32$	−5.44812	+	1.52251i	−0.963100	+	0.269144i
$33$	−0.707136	−	0.707136i	−0.123097	−	0.123097i
$34$	3.51953	−	3.92570i	0.603594	−	0.673252i
$35$	9.91780	+	5.24467i	1.67641	+	0.886511i
$36$	−1.98813	+	0.217572i	−0.331355	+	0.0362620i
$37$	0.910233			0.149641			0.0748207	−	0.997197i	$-0.476162\pi$
$37$	0.910233			0.149641			0.0748207	+	0.997197i	$0.476162\pi$
$38$	6.96434	−	7.76806i	1.12976	−	1.26015i
$39$			1.18824i			0.190271i
$40$	2.82176	+	5.66019i	0.446159	+	0.894954i
$41$			8.26953i			1.29148i	0.763556	+	0.645742i	$0.223452\pi$
$41$			8.26953i			1.29148i	−0.763556	+	0.645742i	$0.776548\pi$
$42$	5.28322	+	4.73659i	0.815219	+	0.730872i
$43$	10.6640			1.62624			0.813120	−	0.582096i	$-0.197767\pi$
$43$	10.6640			1.62624			0.813120	+	0.582096i	$0.197767\pi$
$44$	−1.25202	+	1.55973i	−0.188750	+	0.235138i
$45$	0.658594	+	2.13688i	0.0981774	+	0.318547i
$46$	2.77745	+	2.49008i	0.409513	+	0.367142i
$47$	−5.06735	−	5.06735i	−0.739150	−	0.739150i	0.233264	−	0.972413i	$-0.425059\pi$
$47$	−5.06735	−	5.06735i	−0.739150	−	0.739150i	−0.972413	+	0.233264i	$0.925059\pi$
$48$	0.865123	+	3.90532i	0.124870	+	0.563685i
$49$		−	18.1738i		−	2.59626i
$50$	5.61874	−	4.29300i	0.794609	−	0.607121i
$51$	−2.63620	−	2.63620i	−0.369142	−	0.369142i
$52$	2.36238	−	0.258529i	0.327604	−	0.0358515i
$53$			3.52470i			0.484154i	0.970257	+	0.242077i	$0.0778287\pi$
$53$			3.52470i			0.484154i	−0.970257	+	0.242077i	$0.922171\pi$
$54$	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
$58$	3.23825	+	2.90320i	0.425203	+	0.381209i
$59$	10.2207	+	10.2207i	1.33062	+	1.33062i	0.904812	+	0.425812i	$0.140011\pi$
$59$	10.2207	+	10.2207i	1.33062	+	1.33062i	0.425812	+	0.904812i	$0.359989\pi$
$60$	4.10510	−	1.77430i	0.529967	−	0.229061i
$61$	4.49746	−	4.49746i	0.575840	−	0.575840i	−0.357914	−	0.933755i	$-0.616512\pi$
$61$	4.49746	−	4.49746i	0.575840	−	0.575840i	0.933755	+	0.357914i	$0.116512\pi$
$62$	0.184459	+	3.38115i	0.0234263	+	0.429407i
$63$	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
$67$	1.27353			0.155586			0.0777931	−	0.996970i	$-0.475213\pi$
$67$	1.27353			0.155586			0.0777931	+	0.996970i	$0.475213\pi$
$68$	−4.66755	+	5.81467i	−0.566023	+	0.705133i
$69$	1.86512	−	1.86512i	0.224534	−	0.224534i
$70$	−14.4091	−	6.64203i	−1.72222	−	0.793874i
$71$	−3.56257			−0.422799			−0.211400	−	0.977400i	$-0.567802\pi$
$71$	−3.56257			−0.422799			−0.211400	+	0.977400i	$0.567802\pi$
$72$	2.79070	−	0.460397i	0.328888	−	0.0542584i
$73$	2.47003	−	2.47003i	0.289096	−	0.289096i	−0.547627	−	0.836723i	$-0.684469\pi$
$73$	2.47003	−	2.47003i	0.289096	−	0.289096i	0.836723	+	0.547627i	$0.184469\pi$
$74$	−1.28535	+	0.0701223i	−0.149419	+	0.00815155i
$75$	−2.81467	−	4.13251i	−0.325010	−	0.477181i
$76$	−9.23600	+	11.5059i	−1.05944	+	1.31982i
$77$		−	5.01756i		−	0.571804i
$78$	−0.0915396	−	1.67794i	−0.0103648	−	0.189989i
$79$	−3.89252			−0.437943			−0.218971	−	0.975731i	$-0.570270\pi$
$79$	−3.89252			−0.437943			−0.218971	+	0.975731i	$0.570270\pi$
$80$	−4.42069	−	7.77544i	−0.494248	−	0.869321i
$81$	1.00000			0.111111
$82$	−0.637066	−	11.6775i	−0.0703522	−	1.28957i
$83$			9.99092i			1.09665i	0.836267	+	0.548323i	$0.184734\pi$
$83$			9.99092i			1.09665i	−0.836267	+	0.548323i	$0.815266\pi$
$84$	−7.82540	−	6.28160i	−0.853822	−	0.685378i
$85$	7.36943	+	3.89706i	0.799327	+	0.422695i
$86$	−15.0587	+	0.821528i	−1.62383	+	0.0885876i
$87$	2.17456	−	2.17456i	0.233137	−	0.233137i
$88$	1.64784	−	2.29897i	0.175661	−	0.245071i
$89$	5.16701			0.547702			0.273851	−	0.961772i	$-0.411703\pi$
$89$	5.16701			0.547702			0.273851	+	0.961772i	$0.411703\pi$
$90$	−1.09463	−	2.96678i	−0.115384	−	0.312726i
$91$	−4.21566	+	4.21566i	−0.441921	+	0.441921i
$92$	−4.11391	−	3.30231i	−0.428904	−	0.344290i
$93$	2.39439			0.248287
$94$	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	$0.414396\pi$
$98$	1.40007	+	25.6635i	0.141429	+	2.59241i
$99$	0.707136	−	0.707136i	0.0710698	−	0.0710698i
$100$	−7.60357	+	6.49505i	−0.760357	+	0.649505i
$101$	4.17060	+	4.17060i	0.414990	+	0.414990i	0.883473	−	0.468482i	$-0.155199\pi$
$101$	4.17060	+	4.17060i	0.414990	+	0.414990i	−0.468482	+	0.883473i	$0.655199\pi$
$102$	3.92570	+	3.51953i	0.388702	+	0.348485i
$103$	−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
$107$		−	7.26820i		−	0.702644i	−0.936255	−	0.351322i	$-0.885732\pi$
$107$		−	7.26820i		−	0.702644i	0.936255	−	0.351322i	$-0.114268\pi$
$108$	−0.217572	−	1.98813i	−0.0209359	−	0.191308i
$109$	3.48141	+	3.48141i	0.333458	+	0.333458i	0.853898	−	0.520440i	$-0.174232\pi$
$109$	3.48141	+	3.48141i	0.333458	+	0.333458i	−0.520440	+	0.853898i	$0.674232\pi$
$110$	−2.87197	−	1.32386i	−0.273831	−	0.126226i
$111$			0.910233i			0.0863955i
$112$	−10.7860	+	16.9246i	−1.01919	+	1.59923i
$113$	−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
$115$	−2.75718	+	5.21390i	−0.257109	+	0.486199i
$116$	−4.79643	−	3.85019i	−0.445338	−	0.357481i
$117$	−1.18824			−0.109853
$118$	−15.2202	−	13.6454i	−1.40113	−	1.25616i
$119$		−	18.7054i		−	1.71473i
$120$	−5.66019	+	2.82176i	−0.516702	+	0.257590i
$121$			9.99992i			0.909083i
$122$	−6.00445	+	6.69739i	−0.543617	+	0.606354i
$123$	−8.26953			−0.745639
$124$	−0.520953	−	4.76036i	−0.0467829	−	0.427493i
$125$	8.73626	+	6.97695i	0.781395	+	0.624037i
$126$	−4.73659	+	5.28322i	−0.421969	+	0.470667i
$127$	2.58827	+	2.58827i	0.229671	+	0.229671i	0.812555	−	0.582884i	$-0.198076\pi$
$127$	2.58827	+	2.58827i	0.229671	+	0.229671i	−0.582884	+	0.812555i	$0.698076\pi$
$128$	−10.5003	+	4.21231i	−0.928105	+	0.372319i
$129$			10.6640i			0.938910i
$130$	1.30069	+	3.52526i	0.114078	+	0.309186i
$131$	−4.13367	−	4.13367i	−0.361160	−	0.361160i	0.503080	−	0.864240i	$-0.332200\pi$
$131$	−4.13367	−	4.13367i	−0.361160	−	0.361160i	−0.864240	+	0.503080i	$0.832200\pi$
$132$	−1.55973	−	1.25202i	−0.135757	−	0.108975i
$133$		−	37.0138i		−	3.20950i
$134$	−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	0.763669	−	0.645608i	$-0.223396\pi$
$137$	1.38187	+	1.38187i	0.118062	+	0.118062i	−0.645608	+	0.763669i	$0.723396\pi$
$138$	−2.49008	+	2.77745i	−0.211970	+	0.236432i
$139$	−12.1831	−	12.1831i	−1.03336	−	1.03336i	−0.999424	−	0.0339330i	$-0.989197\pi$
$139$	−12.1831	−	12.1831i	−1.03336	−	1.03336i	−0.0339330	−	0.999424i	$-0.510803\pi$
$140$	20.8590	+	8.26925i	1.76290	+	0.698879i
$141$	5.06735	−	5.06735i	0.426748	−	0.426748i
$142$	5.03075	−	0.274452i	0.422171	−	0.0230315i
$143$	−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
$147$	18.1738			1.49895
$148$	1.80966	−	0.198041i	0.148753	−	0.0162789i
$149$	−9.87902	+	9.87902i	−0.809321	+	0.809321i	−0.984531	−	0.175210i	$-0.943939\pi$
$149$	−9.87902	+	9.87902i	−0.809321	+	0.809321i	0.175210	+	0.984531i	$0.443939\pi$
$150$	4.29300	+	5.61874i	0.350522	+	0.458768i
$151$	−19.1820			−1.56101			−0.780505	−	0.625150i	$-0.785038\pi$
$151$	−19.1820			−1.56101			−0.780505	+	0.625150i	$0.785038\pi$
$152$	12.1559	−	16.9592i	0.985973	−	1.37557i
$153$	2.63620	−	2.63620i	0.213124	−	0.213124i
$154$	0.386541	+	7.08536i	0.0311484	+	0.570955i
$155$	−5.11653	+	1.57693i	−0.410969	+	0.126662i
$156$	0.258529	+	2.36238i	0.0206989	+	0.189142i
$157$		−	8.64456i		−	0.689911i	−0.938619	−	0.344956i	$-0.887894\pi$
$157$		−	8.64456i		−	0.689911i	0.938619	−	0.344956i	$-0.112106\pi$
$158$	5.49668	−	0.299871i	0.437292	−	0.0238564i
$159$	−3.52470			−0.279527
$160$	6.84152	+	10.6393i	0.540869	+	0.841107i
$161$	13.2342			1.04300
$162$	−1.41211	+	0.0770377i	−0.110946	+	0.00605265i
$163$		−	9.90002i		−	0.775429i	−0.921779	−	0.387715i	$-0.873265\pi$
$163$		−	9.90002i		−	0.775429i	0.921779	−	0.387715i	$-0.126735\pi$
$164$	1.79922	+	16.4409i	0.140495	+	1.28382i
$165$	−1.04535	+	1.97678i	−0.0813803	+	0.153892i
$166$	−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	$0.149953\pi$
$168$	11.5343	+	8.26748i	0.889889	+	0.637850i
$169$	−11.5881			−0.891390
$170$	−10.7067	−	4.93536i	−0.821166	−	0.378525i
$171$	5.21643	−	5.21643i	0.398911	−	0.398911i
$172$	21.2014	−	2.32018i	1.61659	−	0.176912i
$173$	−4.49197			−0.341519			−0.170759	−	0.985313i	$-0.554622\pi$
$173$	−4.49197			−0.341519			−0.170759	+	0.985313i	$0.554622\pi$
$174$	−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
$178$	−7.29640	+	0.398054i	−0.546888	+	0.0298354i
$179$	−10.5248	+	10.5248i	−0.786659	+	0.786659i	−0.980945	−	0.194286i	$-0.937761\pi$
$179$	−10.5248	+	10.5248i	−0.786659	+	0.786659i	0.194286	+	0.980945i	$0.437761\pi$
$180$	1.77430	+	4.10510i	0.132248	+	0.305976i
$181$	16.2637	+	16.2637i	1.20887	+	1.20887i	0.971394	+	0.237474i	$0.0763195\pi$
$181$	16.2637	+	16.2637i	1.20887	+	1.20887i	0.237474	+	0.971394i	$0.423681\pi$
$182$	5.62823	−	6.27776i	0.417192	−	0.465338i
$183$	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
$187$		−	3.72830i		−	0.272640i
$188$	−11.1771	−	8.97205i	−0.815172	−	0.654354i
$189$	3.54781	+	3.54781i	0.258065	+	0.258065i
$190$	−21.1861	−	9.76595i	−1.53700	−	0.708496i
$191$			18.4242i			1.33313i	0.745446	+	0.666566i	$0.232236\pi$
$191$			18.4242i			1.33313i	−0.745446	+	0.666566i	$0.767764\pi$
$192$	2.56967	+	7.57607i	0.185450	+	0.546756i
$193$	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
$195$	2.53913	−	0.782571i	0.181831	−	0.0560410i
$196$	−3.95412	−	36.1320i	−0.282437	−	2.58086i
$197$	−7.31984			−0.521517			−0.260758	−	0.965404i	$-0.583973\pi$
$197$	−7.31984			−0.521517			−0.260758	+	0.965404i	$0.583973\pi$
$198$	−0.944080	+	1.05303i	−0.0670928	+	0.0748357i
$199$			21.6050i			1.53154i	0.643115	+	0.765770i	$0.277642\pi$
$199$			21.6050i			1.53154i	−0.643115	+	0.765770i	$0.722358\pi$
$200$	10.2367	−	9.75752i	0.723847	−	0.689961i
$201$			1.27353i			0.0898278i
$202$	−6.21066	−	5.56807i	−0.436980	−	0.391768i
$203$	15.4298			1.08296
$204$	−5.81467	−	4.66755i	−0.407108	−	0.326794i
$205$	17.6710	−	5.44626i	1.23420	−	0.380384i
$206$	1.70924	+	1.53239i	0.119088	+	0.106767i
$207$	1.86512	+	1.86512i	0.129635	+	0.129635i
$208$	4.64048	−	1.02798i	0.321759	−	0.0712774i
$209$		−	7.37745i		−	0.510309i
$210$	6.64203	−	14.4091i	0.458343	−	0.994322i
$211$	−5.97567	−	5.97567i	−0.411382	−	0.411382i	0.470838	−	0.882220i	$-0.343952\pi$
$211$	−5.97567	−	5.97567i	−0.411382	−	0.411382i	−0.882220	+	0.470838i	$0.843952\pi$
$212$	0.766875	+	7.00755i	0.0526692	+	0.481281i
$213$		−	3.56257i		−	0.244103i
$214$	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
$218$	−5.18434	−	4.64794i	−0.351128	−	0.314798i
$219$	2.47003	+	2.47003i	0.166909	+	0.166909i
$220$	4.15753	+	1.64820i	0.280301	+	0.111121i
$221$	−3.13245	+	3.13245i	−0.210711	+	0.210711i
$222$	−0.0701223	−	1.28535i	−0.00470630	−	0.0862673i
$223$	−12.0372	+	12.0372i	−0.806070	+	0.806070i	−0.984037	−	0.177966i	$-0.943048\pi$
$223$	−12.0372	+	12.0372i	−0.806070	+	0.806070i	0.177966	+	0.984037i	$0.443048\pi$
$224$	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
$227$	0.181755			0.0120635			0.00603175	−	0.999982i	$-0.498080\pi$
$227$	0.181755			0.0120635			0.00603175	+	0.999982i	$0.498080\pi$
$228$	−11.5059	−	9.23600i	−0.761997	−	0.611669i
$229$	−0.556001	+	0.556001i	−0.0367416	+	0.0367416i	−0.725239	−	0.688497i	$-0.758271\pi$
$229$	−0.556001	+	0.556001i	−0.0367416	+	0.0367416i	0.688497	+	0.725239i	$0.258271\pi$
$230$	3.49179	−	7.57503i	0.230242	−	0.499483i
$231$	5.01756			0.330131
$232$	7.06972	+	5.06739i	0.464150	+	0.332691i
$233$	9.96356	−	9.96356i	0.652735	−	0.652735i	−0.300916	−	0.953651i	$-0.597292\pi$
$233$	9.96356	−	9.96356i	0.652735	−	0.652735i	0.953651	+	0.300916i	$0.0972924\pi$
$234$	1.67794	−	0.0915396i	0.109690	−	0.00598413i
$235$	−7.49100	+	14.1657i	−0.488659	+	0.924065i
$236$	22.5439	+	18.0964i	1.46748	+	1.17797i
$237$		−	3.89252i		−	0.252846i
$238$	1.44103	+	26.4142i	0.0934078	+	1.71218i
$239$	−6.80569			−0.440224			−0.220112	−	0.975475i	$-0.570642\pi$
$239$	−6.80569			−0.440224			−0.220112	+	0.975475i	$0.570642\pi$
$240$	7.77544	−	4.42069i	0.501903	−	0.285354i
$241$	18.8285			1.21285			0.606425	−	0.795141i	$-0.292603\pi$
$241$	18.8285			1.21285			0.606425	+	0.795141i	$0.292603\pi$
$242$	−0.770371	−	14.1210i	−0.0495213	−	0.907734i
$243$			1.00000i			0.0641500i
$244$	7.96301	−	9.92005i	0.509779	−	0.635066i
$245$	−38.8353	+	11.9692i	−2.48110	+	0.764683i
$246$	11.6775	−	0.637066i	0.744532	−	0.0406178i
$247$	−6.19840	+	6.19840i	−0.394395	+	0.394395i
$248$	1.10237	+	6.68204i	0.0700007	+	0.424310i
$249$	−9.99092			−0.633149
$250$	−12.8741	−	9.17922i	−0.814228	−	0.580545i
$251$	11.9160	−	11.9160i	0.752133	−	0.752133i	−0.222744	−	0.974877i	$-0.571501\pi$
$251$	11.9160	−	11.9160i	0.752133	−	0.752133i	0.974877	+	0.222744i	$0.0715013\pi$
$252$	6.28160	−	7.82540i	0.395703	−	0.492954i
$253$	2.63779			0.165836
$254$	−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	$0.464655\pi$
$258$	−0.821528	−	15.0587i	−0.0511461	−	0.937516i
$259$	−3.22933	+	3.22933i	−0.200661	+	0.200661i
$260$	−2.10830	−	4.87787i	−0.130751	−	0.302512i
$261$	2.17456	+	2.17456i	0.134602	+	0.134602i
$262$	6.15566	+	5.51876i	0.380298	+	0.340950i
$263$	−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
$267$			5.16701i			0.316216i
$268$	2.53194	−	0.277084i	0.154663	−	0.0169256i
$269$	14.0526	+	14.0526i	0.856805	+	0.856805i	0.990960	−	0.134155i	$-0.0428322\pi$
$269$	14.0526	+	14.0526i	0.856805	+	0.856805i	−0.134155	+	0.990960i	$0.542832\pi$
$270$	2.96678	−	1.09463i	0.180552	−	0.0666171i
$271$		−	0.510213i		−	0.0309933i	−0.999880	−	0.0154966i	$-0.995067\pi$
$271$		−	0.510213i		−	0.0309933i	0.999880	−	0.0154966i	$-0.00493293\pi$
$272$	−8.01458	+	12.5759i	−0.485955	+	0.762523i
$273$	−4.21566	−	4.21566i	−0.255143	−	0.255143i
$274$	−2.05782	−	1.84491i	−0.124317	−	0.111455i
$275$	0.931889	−	4.91260i	0.0561950	−	0.296241i
$276$	3.30231	−	4.11391i	0.198776	−	0.247628i
$277$	1.56728			0.0941688			0.0470844	−	0.998891i	$-0.485007\pi$
$277$	1.56728			0.0941688			0.0470844	+	0.998891i	$0.485007\pi$
$278$	18.1425	+	16.2654i	1.08811	+	0.975532i
$279$			2.39439i			0.143349i
$280$	−30.0923	−	10.0702i	−1.79836	−	0.601809i
$281$		−	26.3167i		−	1.56992i	−0.619546	−	0.784960i	$-0.712683\pi$
$281$		−	26.3167i		−	1.56992i	0.619546	−	0.784960i	$-0.287317\pi$
$282$	−6.76530	+	7.54606i	−0.402868	+	0.449361i
$283$	−16.2153			−0.963897			−0.481948	−	0.876200i	$-0.660071\pi$
$283$	−16.2153			−0.963897			−0.481948	+	0.876200i	$0.660071\pi$
$284$	−7.08285	+	0.775115i	−0.420290	+	0.0459946i
$285$	−7.71138	+	14.5824i	−0.456783	+	0.863787i
$286$	1.12180	−	1.25126i	0.0663333	−	0.0739885i
$287$	−29.3387	−	29.3387i	−1.73181	−	1.73181i
$288$	5.44812	−	1.52251i	0.321033	−	0.0897147i
$289$			3.10090i			0.182406i
$290$	4.07110	−	8.83178i	0.239063	−	0.518620i
$291$	−6.87796	−	6.87796i	−0.403193	−	0.403193i
$292$	4.37334	−	5.44816i	0.255930	−	0.318830i
$293$			21.6309i			1.26369i	0.775095	+	0.631844i	$0.217702\pi$
$293$			21.6309i			1.26369i	−0.775095	+	0.631844i	$0.782298\pi$
$294$	−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
$298$	13.1892	−	14.7114i	0.764032	−	0.852206i
$299$	−2.21622	−	2.21622i	−0.128167	−	0.128167i
$300$	−6.49505	−	7.60357i	−0.374992	−	0.438992i
$301$	−37.8337	+	37.8337i	−2.18070	+	2.18070i
$302$	27.0872	−	1.47774i	1.55869	−	0.0850342i
$303$	−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
$307$	13.9316			0.795117			0.397559	−	0.917577i	$-0.369858\pi$
$307$	13.9316			0.795117			0.397559	+	0.917577i	$0.369858\pi$
$308$	−1.09168	−	9.97556i	−0.0622043	−	0.568410i
$309$	1.14779	−	1.14779i	0.0652956	−	0.0652956i
$310$	7.10364	−	2.62097i	0.403459	−	0.148861i
$311$	1.47971			0.0839067			0.0419534	−	0.999120i	$-0.486642\pi$
$311$	1.47971			0.0839067			0.0419534	+	0.999120i	$0.486642\pi$
$312$	−0.547065	−	3.31604i	−0.0309714	−	0.187734i
$313$	−11.4062	+	11.4062i	−0.644717	+	0.644717i	−0.951711	−	0.306994i	$-0.900677\pi$
$313$	−11.4062	+	11.4062i	−0.644717	+	0.644717i	0.306994	+	0.951711i	$0.400677\pi$
$314$	0.665957	+	12.2071i	0.0375822	+	0.688887i
$315$	−9.91780	−	5.24467i	−0.558805	−	0.295504i
$316$	−7.73883	+	0.846903i	−0.435343	+	0.0476420i
$317$		−	21.2307i		−	1.19243i	−0.802824	−	0.596217i	$-0.796670\pi$
$317$		−	21.2307i		−	1.19243i	0.802824	−	0.596217i	$-0.203330\pi$
$318$	4.97727	−	0.271535i	0.279112	−	0.0152269i
$319$	3.07542			0.172190
$320$	−10.4806	−	14.4968i	−0.585885	−	0.810395i
$321$	7.26820			0.405672
$322$	−18.6882	+	1.01953i	−1.04145	+	0.0568163i
$323$		−	27.5031i		−	1.53031i
$324$	1.98813	−	0.217572i	0.110452	−	0.0120873i
$325$	−4.91043	+	3.34452i	−0.272382	+	0.185520i
$326$	0.762675	+	13.9799i	0.0422406	+	0.774278i
$327$	−3.48141	+	3.48141i	−0.192522	+	0.192522i
$328$	−3.80727	−	23.0778i	−0.210221	−	1.27426i
$329$	35.9560			1.98232
$330$	1.32386	−	2.87197i	0.0728763	−	0.158097i
$331$	2.12076	−	2.12076i	0.116567	−	0.116567i	−0.646417	−	0.762984i	$-0.723733\pi$
$331$	2.12076	−	2.12076i	0.116567	−	0.116567i	0.762984	+	0.646417i	$0.223733\pi$
$332$	2.17374	+	19.8632i	0.119300	+	1.09014i
$333$	−0.910233			−0.0498805
$334$	−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	$0.184833\pi$
$338$	16.3637	−	0.892719i	0.890067	−	0.0485575i
$339$	6.68812	−	6.68812i	0.363249	−	0.363249i
$340$	15.4993	+	6.14447i	0.840566	+	0.333231i
$341$	1.69316	+	1.69316i	0.0916898	+	0.0916898i
$342$	−6.96434	+	7.76806i	−0.376588	+	0.420049i
$343$	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
$347$			26.9264i			1.44549i	0.691116	+	0.722744i	$0.257119\pi$
$347$			26.9264i			1.44549i	−0.691116	+	0.722744i	$0.742881\pi$
$348$	3.85019	−	4.79643i	0.206392	−	0.257116i
$349$	−9.01587	−	9.01587i	−0.482609	−	0.482609i	0.423355	−	0.905964i	$-0.360852\pi$
$349$	−9.01587	−	9.01587i	−0.482609	−	0.482609i	−0.905964	+	0.423355i	$0.860852\pi$
$350$	−4.70346	+	35.1649i	−0.251411	+	1.87964i
$351$		−	1.18824i		−	0.0634238i
$352$	2.77594	−	4.92918i	0.147958	−	0.262726i
$353$	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
$355$	2.34629	+	7.61278i	0.124528	+	0.404044i
$356$	10.2727	−	1.12420i	0.544451	−	0.0595823i
$357$	18.7054			0.989997
$358$	14.0514	−	15.6730i	0.742639	−	0.828343i
$359$			22.4682i			1.18583i	0.805266	+	0.592914i	$0.202022\pi$
$359$			22.4682i			1.18583i	−0.805266	+	0.592914i	$0.797978\pi$
$360$	−2.82176	−	5.66019i	−0.148720	−	0.298318i
$361$		−	35.4224i		−	1.86433i
$362$	−24.2190	−	21.7132i	−1.27292	−	1.14122i
$363$	−9.99992			−0.524860
$364$	−7.46407	+	9.29849i	−0.391224	+	0.487373i
$365$	−6.90492	−	3.65142i	−0.361420	−	0.191124i
$366$	−6.69739	−	6.00445i	−0.350078	−	0.313857i
$367$	17.8664	+	17.8664i	0.932619	+	0.932619i	0.997869	−	0.0652495i	$-0.0207843\pi$
$367$	17.8664	+	17.8664i	0.932619	+	0.932619i	−0.0652495	+	0.997869i	$0.520784\pi$
$368$	−8.89747	−	5.67035i	−0.463813	−	0.295587i
$369$		−	8.26953i		−	0.430495i
$370$	0.996369	+	2.70046i	0.0517987	+	0.140390i
$371$	−12.5049	−	12.5049i	−0.649224	−	0.649224i
$372$	4.76036	−	0.520953i	0.246813	−	0.0270101i
$373$		−	6.19650i		−	0.320843i	−0.987049	−	0.160421i	$-0.948715\pi$
$373$		−	6.19650i		−	0.320843i	0.987049	−	0.160421i	$-0.0512853\pi$
$374$	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
$378$	−5.28322	−	4.73659i	−0.271740	−	0.243624i
$379$	−14.4005	−	14.4005i	−0.739704	−	0.739704i	0.232816	−	0.972521i	$-0.425206\pi$
$379$	−14.4005	−	14.4005i	−0.739704	−	0.739704i	−0.972521	+	0.232816i	$0.925206\pi$
$380$	30.6695	+	12.1585i	1.57331	+	0.623718i
$381$	−2.58827	+	2.58827i	−0.132601	+	0.132601i
$382$	−1.41936	−	26.0171i	−0.0726208	−	1.33115i
$383$	8.46651	−	8.46651i	0.432618	−	0.432618i	−0.456900	−	0.889518i	$-0.651040\pi$
$383$	8.46651	−	8.46651i	0.432618	−	0.432618i	0.889518	+	0.456900i	$0.151040\pi$
$384$	−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
$387$	−10.6640			−0.542080
$388$	−12.1778	+	15.1707i	−0.618236	+	0.770178i
$389$	24.2277	−	24.2277i	1.22839	−	1.22839i	0.263822	−	0.964571i	$-0.415017\pi$
$389$	24.2277	−	24.2277i	1.22839	−	1.22839i	0.964571	−	0.263822i	$-0.0849833\pi$
$390$	−3.52526	+	1.30069i	−0.178508	+	0.0658629i
$391$	9.83367			0.497310
$392$	8.36719	+	50.7179i	0.422607	+	2.56164i
$393$	4.13367	−	4.13367i	0.208516	−	0.208516i
$394$	10.3364	−	0.563903i	0.520742	−	0.0284090i
$395$	2.56359	+	8.31784i	0.128988	+	0.418516i
$396$	1.25202	−	1.55973i	0.0629166	−	0.0783794i
$397$			8.48394i			0.425797i	0.977074	+	0.212898i	$0.0682903\pi$
$397$			8.48394i			0.425797i	−0.977074	+	0.212898i	$0.931710\pi$
$398$	−1.66440	−	30.5087i	−0.0834289	−	1.52927i
$399$	37.0138			1.85301
$400$	−13.7037	+	14.5673i	−0.685187	+	0.728367i
$401$	−0.969620			−0.0484205			−0.0242103	−	0.999707i	$-0.507707\pi$
$401$	−0.969620			−0.0484205			−0.0242103	+	0.999707i	$0.507707\pi$
$402$	−0.0981097	−	1.79837i	−0.00489327	−	0.0896944i
$403$		−	2.84512i		−	0.141726i
$404$	9.19911	+	7.38429i	0.457673	+	0.367382i
$405$	−0.658594	−	2.13688i	−0.0327258	−	0.106182i
$406$	−21.7887	+	1.18868i	−1.08135	+	0.0589932i
$407$	−0.643659	+	0.643659i	−0.0319050	+	0.0319050i
$408$	8.57056	+	6.14316i	0.424306	+	0.304132i
$409$	−28.7556			−1.42187			−0.710936	−	0.703257i	$-0.751728\pi$
$409$	−28.7556			−1.42187			−0.710936	+	0.703257i	$0.751728\pi$
$410$	−24.5339	+	9.05208i	−1.21164	+	0.447050i
$411$	−1.38187	+	1.38187i	−0.0681628	+	0.0681628i
$412$	−2.53169	−	2.03223i	−0.124727	−	0.100121i
$413$	−72.5222			−3.56858
$414$	−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
$418$	0.568342	+	10.4178i	0.0277985	+	0.509551i
$419$	−16.6648	+	16.6648i	−0.814129	+	0.814129i	−0.985250	−	0.171121i	$-0.945261\pi$
$419$	−16.6648	+	16.6648i	−0.814129	+	0.814129i	0.171121	+	0.985250i	$0.445261\pi$
$420$	−8.26925	+	20.8590i	−0.403498	+	1.01781i
$421$	−3.83359	−	3.83359i	−0.186838	−	0.186838i	0.607490	−	0.794327i	$-0.292177\pi$
$421$	−3.83359	−	3.83359i	−0.186838	−	0.186838i	−0.794327	+	0.607490i	$0.792177\pi$
$422$	8.89868	+	7.97797i	0.433181	+	0.388362i
$423$	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
$427$			31.9122i			1.54434i
$428$	−1.58136	−	14.4501i	−0.0764378	−	0.698474i
$429$	−0.840250	−	0.840250i	−0.0405676	−	0.0405676i
$430$	11.6731	+	31.6376i	0.562927	+	1.52570i
$431$			6.02593i			0.290259i	0.989413	+	0.145129i	$0.0463598\pi$
$431$			6.02593i			0.290259i	−0.989413	+	0.145129i	$0.953640\pi$
$432$	−0.865123	−	3.90532i	−0.0416233	−	0.187895i
$433$	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
$435$	−6.07893	−	3.21462i	−0.291462	−	0.154129i
$436$	7.67895	+	6.16404i	0.367755	+	0.295204i
$437$	19.4586			0.930830
$438$	−3.67826	−	3.29768i	−0.175754	−	0.157569i
$439$			2.47473i			0.118112i	0.998255	+	0.0590561i	$0.0188091\pi$
$439$			2.47473i			0.118112i	−0.998255	+	0.0590561i	$0.981191\pi$
$440$	−5.99788	−	2.00715i	−0.285938	−	0.0956874i
$441$			18.1738i			0.865421i
$442$	4.18206	−	4.66469i	0.198920	−	0.221877i
$443$	3.27807			0.155746			0.0778728	−	0.996963i	$-0.475187\pi$
$443$	3.27807			0.155746			0.0778728	+	0.996963i	$0.475187\pi$
$444$	0.198041	+	1.80966i	0.00939863	+	0.0858828i
$445$	−3.40296	−	11.0413i	−0.161316	−	0.523406i
$446$	16.0706	−	17.9252i	0.760964	−	0.848783i
$447$	−9.87902	−	9.87902i	−0.467261	−	0.467261i
$448$	−17.7617	+	35.9951i	−0.839163	+	1.70061i
$449$		−	16.5248i		−	0.779852i	−0.920846	−	0.389926i	$-0.872501\pi$
$449$		−	16.5248i		−	0.779852i	0.920846	−	0.389926i	$-0.127499\pi$
$450$	−5.61874	+	4.29300i	−0.264870	+	0.202374i
$451$	−5.84768	−	5.84768i	−0.275357	−	0.275357i
$452$	−14.7520	−	11.8417i	−0.693875	−	0.556987i
$453$		−	19.1820i		−	0.901249i
$454$	−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	0.935555	−	0.353180i	$-0.114900\pi$
$457$	12.4498	+	12.4498i	0.582376	+	0.582376i	−0.353180	+	0.935555i	$0.614900\pi$
$458$	0.742304	−	0.827970i	0.0346856	−	0.0386885i
$459$	2.63620	+	2.63620i	0.123047	+	0.123047i
$460$	−4.34724	+	10.9658i	−0.202691	+	0.511283i
$461$	13.9930	−	13.9930i	0.651719	−	0.651719i	−0.301688	−	0.953407i	$-0.597550\pi$
$461$	13.9930	−	13.9930i	0.651719	−	0.651719i	0.953407	+	0.301688i	$0.0975499\pi$
$462$	−7.08536	+	0.386541i	−0.329641	+	0.0179835i
$463$	−21.7437	+	21.7437i	−1.01052	+	1.01052i	−0.0105728	+	0.999944i	$0.503365\pi$
$463$	−21.7437	+	21.7437i	−1.01052	+	1.01052i	−0.999944	+	0.0105728i	$0.996635\pi$
$464$	−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
$467$	28.3316			1.31103			0.655514	−	0.755183i	$-0.272452\pi$
$467$	28.3316			1.31103			0.655514	+	0.755183i	$0.272452\pi$
$468$	−2.36238	+	0.258529i	−0.109201	+	0.0119505i
$469$	−4.51823	+	4.51823i	−0.208633	+	0.208633i
$470$	9.48685	−	20.5806i	0.437596	−	0.949313i
$471$	8.64456			0.398320
$472$	−33.2286	−	23.8174i	−1.52947	−	1.09628i
$473$	−7.54087	+	7.54087i	−0.346730	+	0.346730i
$474$	0.299871	+	5.49668i	0.0137735	+	0.252471i
$475$	6.87440	−	36.2395i	0.315419	−	1.66278i
$476$	−4.06978	−	37.1889i	−0.186538	−	1.70455i
$477$		−	3.52470i		−	0.161385i
$478$	9.61041	−	0.524295i	0.439570	−	0.0239807i
$479$	−21.4895			−0.981879			−0.490940	−	0.871194i	$-0.663346\pi$
$479$	−21.4895			−0.981879			−0.490940	+	0.871194i	$0.663346\pi$
$480$	−10.6393	+	6.84152i	−0.485613	+	0.312271i
$481$	1.08158			0.0493158
$482$	−26.5880	+	1.45050i	−1.21105	+	0.0660687i
$483$			13.2342i			0.602176i
$484$	2.17570	+	19.8811i	0.0988956	+	0.903688i
$485$	19.2272	+	10.1676i	0.873060	+	0.461687i
$486$	−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	$0.0690816\pi$
$488$	−10.4805	+	14.6217i	−0.474428	+	0.661893i
$489$	9.90002			0.447694
$490$	53.9178	−	19.8936i	2.43576	−	0.898703i
$491$	−6.05778	+	6.05778i	−0.273384	+	0.273384i	−0.830461	−	0.557077i	$-0.811923\pi$
$491$	−6.05778	+	6.05778i	−0.273384	+	0.273384i	0.557077	+	0.830461i	$0.311923\pi$
$492$	−16.4409	+	1.79922i	−0.741213	+	0.0811151i
$493$	11.4652			0.516364
$494$	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
$498$	14.1083	−	0.769678i	0.632209	−	0.0344901i
$499$	29.7904	−	29.7904i	1.33360	−	1.33360i	0.431474	−	0.902125i	$-0.357994\pi$
$499$	29.7904	−	29.7904i	1.33360	−	1.33360i	0.902125	−	0.431474i	$-0.142006\pi$
$500$	18.8868	+	11.9703i	0.844644	+	0.535329i
$501$	5.65004	+	5.65004i	0.252425	+	0.252425i
$502$	−15.9088	+	17.7448i	−0.710045	+	0.791988i
$503$	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
$507$		−	11.5881i		−	0.514645i
$508$	5.70895	+	4.58268i	0.253293	+	0.203323i
$509$	−15.5011	−	15.5011i	−0.687074	−	0.687074i	0.274510	−	0.961584i	$-0.411484\pi$
$509$	−15.5011	−	15.5011i	−0.687074	−	0.687074i	−0.961584	+	0.274510i	$0.911484\pi$
$510$	4.93536	−	10.7067i	0.218542	−	0.474100i
$511$			17.5264i			0.775323i
$512$	−19.9595	+	10.6592i	−0.882094	+	0.471074i
$513$	5.21643	+	5.21643i	0.230311	+	0.230311i
$514$	18.8994	−	21.0805i	0.833617	−	0.929821i
$515$	−1.69677	+	3.20862i	−0.0747684	+	0.141389i
$516$	2.32018	+	21.2014i	0.102140	+	0.933338i
$517$	7.16661			0.315187
$518$	4.31140	−	4.80896i	0.189432	−	0.211294i
$519$		−	4.49197i		−	0.197176i
$520$	3.35293	+	6.72568i	0.147036	+	0.294941i
$521$		−	2.72323i		−	0.119307i	−0.998219	−	0.0596533i	$-0.981000\pi$
$521$		−	2.72323i		−	0.119307i	0.998219	−	0.0596533i	$-0.0189995\pi$
$522$	−3.23825	−	2.90320i	−0.141734	−	0.127070i
$523$	18.5563			0.811410			0.405705	−	0.914004i	$-0.367026\pi$
$523$	18.5563			0.811410			0.405705	+	0.914004i	$0.367026\pi$
$524$	−9.11764	−	7.31890i	−0.398306	−	0.319728i
$525$	24.6472	+	4.67543i	1.07569	+	0.204052i
$526$	10.7924	+	9.67578i	0.470572	+	0.421884i
$527$	6.31210	+	6.31210i	0.274959	+	0.274959i
$528$	−3.37335	−	2.14984i	−0.146806	−	0.0935596i
$529$		−	16.0426i		−	0.697506i
$530$	−10.4570	+	3.85824i	−0.454223	+	0.167591i
$531$	−10.2207	−	10.2207i	−0.443541	−	0.443541i
$532$	−8.05316	−	73.5882i	−0.349149	−	3.19045i
$533$			9.82622i			0.425621i
$534$	−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
$538$	−20.9265	−	18.7613i	−0.902206	−	0.808859i
$539$	12.8514	+	12.8514i	0.553548	+	0.553548i
$540$	−4.10510	+	1.77430i	−0.176656	+	0.0763535i
$541$	−6.87489	+	6.87489i	−0.295575	+	0.295575i	−0.839278	−	0.543703i	$-0.817022\pi$
$541$	−6.87489	+	6.87489i	−0.295575	+	0.295575i	0.543703	+	0.839278i	$0.317022\pi$
$542$	0.0393057	+	0.720479i	0.00168832	+	0.0309472i
$543$	−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
$547$	17.9983			0.769552			0.384776	−	0.923010i	$-0.374279\pi$
$547$	17.9983			0.769552			0.384776	+	0.923010i	$0.374279\pi$
$548$	3.04800	+	2.44669i	0.130204	+	0.104517i
$549$	−4.49746	+	4.49746i	−0.191947	+	0.191947i
$550$	−0.937477	+	7.00894i	−0.0399742	+	0.298862i
$551$	22.6869			0.966494
$552$	−4.34631	+	6.06371i	−0.184991	+	0.258088i
$553$	13.8099	−	13.8099i	0.587257	−	0.587257i
$554$	−2.21318	+	0.120740i	−0.0940290	+	0.00512974i
$555$	1.94506	−	0.599474i	0.0825632	−	0.0254463i
$556$	−26.8723	−	21.5709i	−1.13964	−	0.914810i
$557$		−	4.99053i		−	0.211456i	−0.994395	−	0.105728i	$-0.966283\pi$
$557$		−	4.99053i		−	0.211456i	0.994395	−	0.105728i	$-0.0337172\pi$
$558$	−0.184459	−	3.38115i	−0.00780875	−	0.143136i
$559$	12.6714			0.535943
$560$	43.2695	+	11.9020i	1.82847	+	0.502952i
$561$	3.72830			0.157409
$562$	2.02738	+	37.1621i	0.0855197	+	1.56759i
$563$			1.13365i			0.0477778i	0.999715	+	0.0238889i	$0.00760480\pi$
$563$			1.13365i			0.0477778i	−0.999715	+	0.0238889i	$0.992395\pi$
$564$	8.97205	−	11.1771i	0.377791	−	0.470640i
$565$	−9.88695	+	18.6965i	−0.415947	+	0.786566i
$566$	22.8978	−	1.24919i	0.962466	−	0.0525072i
$567$	−3.54781	+	3.54781i	−0.148994	+	0.148994i
$568$	9.94208	−	1.64020i	0.417160	−	0.0688212i
$569$	39.7427			1.66610			0.833051	−	0.553196i	$-0.186592\pi$
$569$	39.7427			1.66610			0.833051	+	0.553196i	$0.186592\pi$
$570$	9.76595	−	21.1861i	0.409051	−	0.887387i
$571$	12.9907	−	12.9907i	0.543645	−	0.543645i	−0.380950	−	0.924596i	$-0.624403\pi$
$571$	12.9907	−	12.9907i	0.543645	−	0.543645i	0.924596	+	0.380950i	$0.124403\pi$
$572$	−1.48771	+	1.85334i	−0.0622043	+	0.0774921i
$573$	−18.4242			−0.769684
$574$	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	$0.896437\pi$
$578$	−0.238886	−	4.37883i	−0.00993637	−	0.182135i
$579$	−9.23854	+	9.23854i	−0.383941	+	0.383941i
$580$	−5.06848	+	12.7851i	−0.210457	+	0.530873i
$581$	−35.4458	−	35.4458i	−1.47054	−	1.47054i
$582$	10.2423	+	9.18260i	0.424558	+	0.380631i
$583$	−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
$587$		−	10.0656i		−	0.415453i	−0.978187	−	0.207726i	$-0.933394\pi$
$587$		−	10.0656i		−	0.415453i	0.978187	−	0.207726i	$-0.0666064\pi$
$588$	36.1320	−	3.95412i	1.49006	−	0.163065i
$589$	12.4902	+	12.4902i	0.514649	+	0.514649i
$590$	−19.1347	+	41.5105i	−0.787764	+	1.70896i
$591$		−	7.31984i		−	0.301098i
$592$	3.55476	−	0.787464i	0.146100	−	0.0323646i
$593$	−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
$595$	−39.9713	+	12.3193i	−1.63866	+	0.505042i
$596$	−17.4914	+	21.7902i	−0.716475	+	0.892560i
$597$	−21.6050			−0.884235
$598$	3.30029	+	2.95882i	0.134959	+	0.120995i
$599$		−	6.47946i		−	0.264743i	−0.991200	−	0.132372i	$-0.957741\pi$
$599$		−	6.47946i		−	0.264743i	0.991200	−	0.132372i	$-0.0422593\pi$
$600$	9.75752	+	10.2367i	0.398349	+	0.417913i
$601$			9.39907i			0.383396i	0.981454	+	0.191698i	$0.0613994\pi$
$601$			9.39907i			0.383396i	−0.981454	+	0.191698i	$0.938601\pi$
$602$	50.5108	−	56.3401i	2.05867	−	2.29625i
$603$	−1.27353			−0.0518621
$604$	−38.1363	+	4.17347i	−1.55174	+	0.169816i
$605$	21.3686	−	6.58589i	0.868758	−	0.267754i
$606$	5.56807	−	6.21066i	0.226187	−	0.252291i
$607$	−19.3440	−	19.3440i	−0.785149	−	0.785149i	0.195545	−	0.980695i	$-0.437352\pi$
$607$	−19.3440	−	19.3440i	−0.785149	−	0.785149i	−0.980695	+	0.195545i	$0.937352\pi$
$608$	20.4777	−	36.3618i	0.830479	−	1.47467i
$609$			15.4298i			0.625248i
$610$	18.2660	+	8.41992i	0.739569	+	0.340912i
$611$	−6.02126	−	6.02126i	−0.243594	−	0.243594i
$612$	4.66755	−	5.81467i	0.188674	−	0.235044i
$613$			30.5351i			1.23330i	0.787238	+	0.616650i	$0.211510\pi$
$613$			30.5351i			1.23330i	−0.787238	+	0.616650i	$0.788490\pi$
$614$	−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	0.996249	−	0.0865290i	$-0.0275775\pi$
$617$	22.5970	+	22.5970i	0.909720	+	0.909720i	−0.0865290	+	0.996249i	$0.527578\pi$
$618$	−1.53239	+	1.70924i	−0.0616418	+	0.0687556i
$619$	17.0858	+	17.0858i	0.686737	+	0.686737i	0.961509	−	0.274773i	$-0.0886025\pi$
$619$	17.0858	+	17.0858i	0.686737	+	0.686737i	−0.274773	+	0.961509i	$0.588603\pi$
$620$	−9.82923	+	4.24836i	−0.394751	+	0.170618i
$621$	−1.86512	+	1.86512i	−0.0748448	+	0.0748448i
$622$	−2.08952	+	0.113994i	−0.0837822	+	0.00457073i
$623$	−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
$627$	7.37745			0.294627
$628$	−1.88082	−	17.1865i	−0.0750527	−	0.685817i
$629$	−2.39956	+	2.39956i	−0.0956766	+	0.0956766i
$630$	14.4091	+	6.64203i	0.574072	+	0.264625i
$631$	−21.9991			−0.875769			−0.437885	−	0.899031i	$-0.644272\pi$
$631$	−21.9991			−0.875769			−0.437885	+	0.899031i	$0.644272\pi$
$632$	10.8629	−	1.79211i	0.432102	−	0.0712861i
$633$	5.97567	−	5.97567i	0.237512	−	0.237512i
$634$	1.63556	+	29.9801i	0.0649565	+	1.19066i
$635$	3.82620	−	7.23543i	0.151838	−	0.287129i
$636$	−7.00755	+	0.766875i	−0.277868	+	0.0304086i
$637$		−	21.5950i		−	0.855624i
$638$	−4.34284	+	0.236923i	−0.171935	+	0.00937988i
$639$	3.56257			0.140933
$640$	15.9166	+	19.6637i	0.629160	+	0.777276i
$641$	2.69605			0.106487			0.0532437	−	0.998582i	$-0.483044\pi$
$641$	2.69605			0.106487			0.0532437	+	0.998582i	$0.483044\pi$
$642$	−10.2635	+	0.559926i	−0.405069	+	0.0220985i
$643$		−	21.5956i		−	0.851646i	−0.904807	−	0.425823i	$-0.859985\pi$
$643$		−	21.5956i		−	0.851646i	0.904807	−	0.425823i	$-0.140015\pi$
$644$	26.3113	−	2.87939i	1.03681	−	0.113464i
$645$	22.7876	−	7.02322i	0.897261	−	0.276539i
$646$	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	$0.949982\pi$
$648$	−2.79070	+	0.460397i	−0.109629	+	0.0180861i
$649$	−14.4549			−0.567403
$650$	6.67643	−	5.10113i	0.261871	−	0.200083i
$651$	−8.49484	+	8.49484i	−0.332939	+	0.332939i
$652$	−2.15397	−	19.6825i	−0.0843559	−	0.770827i
$653$	8.54847			0.334527			0.167264	−	0.985912i	$-0.446507\pi$
$653$	8.54847			0.334527			0.167264	+	0.985912i	$0.446507\pi$
$654$	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
$658$	−50.7739	+	2.76997i	−1.97937	+	0.107985i
$659$	−9.96438	+	9.96438i	−0.388157	+	0.388157i	−0.874030	−	0.485873i	$-0.838502\pi$
$659$	−9.96438	+	9.96438i	−0.388157	+	0.388157i	0.485873	+	0.874030i	$0.338502\pi$
$660$	−1.64820	+	4.15753i	−0.0641560	+	0.161832i
$661$	−20.3395	−	20.3395i	−0.791115	−	0.791115i	0.190561	−	0.981675i	$-0.438969\pi$
$661$	−20.3395	−	20.3395i	−0.791115	−	0.791115i	−0.981675	+	0.190561i	$0.938969\pi$
$662$	−2.83137	+	3.15813i	−0.110044	+	0.122744i
$663$	−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
$667$			8.11165i			0.314084i
$668$	10.0037	−	12.4623i	0.387055	−	0.482181i
$669$	−12.0372	−	12.0372i	−0.465385	−	0.465385i
$670$	1.39404	+	3.77828i	0.0538566	+	0.145968i
$671$			6.36062i			0.245549i
$672$	24.7304	+	13.9273i	0.953997	+	0.537257i
$673$	−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
$675$	2.81467	+	4.13251i	0.108337	+	0.159060i
$676$	−23.0386	+	2.52124i	−0.886100	+	0.0969708i
$677$	21.6129			0.830650			0.415325	−	0.909673i	$-0.363668\pi$
$677$	21.6129			0.830650			0.415325	+	0.909673i	$0.363668\pi$
$678$	−8.92914	+	9.95962i	−0.342922	+	0.382497i
$679$		−	48.8033i		−	1.87290i
$680$	−22.3601	−	7.48267i	−0.857470	−	0.286947i
$681$			0.181755i			0.00696486i
$682$	−2.52137	−	2.26050i	−0.0965483	−	0.0865589i
$683$	27.1548			1.03905			0.519524	−	0.854456i	$-0.326109\pi$
$683$	27.1548			1.03905			0.519524	+	0.854456i	$0.326109\pi$
$684$	9.23600	−	11.5059i	0.353147	−	0.439939i
$685$	2.04281	−	3.86299i	0.0780516	−	0.147597i
$686$	−59.0339	−	52.9259i	−2.25392	−	2.02072i
$687$	−0.556001	−	0.556001i	−0.0212128	−	0.0212128i
$688$	41.6463	−	9.22564i	1.58775	−	0.351724i
$689$			4.18820i			0.159558i
$690$	7.57503	+	3.49179i	0.288376	+	0.132930i
$691$	−8.25201	−	8.25201i	−0.313921	−	0.313921i	0.532505	−	0.846427i	$-0.321251\pi$
$691$	−8.25201	−	8.25201i	−0.313921	−	0.313921i	−0.846427	+	0.532505i	$0.821251\pi$
$692$	−8.93063	+	0.977328i	−0.339492	+	0.0371524i
$693$			5.01756i			0.190601i
$694$	−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
$698$	13.4260	+	12.0369i	0.508182	+	0.455602i
$699$	9.96356	+	9.96356i	0.376857	+	0.376857i
$700$	3.93280	−	50.0192i	0.148646	−	1.89055i
$701$	−16.4761	+	16.4761i	−0.622295	+	0.622295i	−0.946118	−	0.323823i	$-0.895032\pi$
$701$	−16.4761	+	16.4761i	−0.622295	+	0.622295i	0.323823	+	0.946118i	$0.395032\pi$
$702$	0.0915396	+	1.67794i	0.00345494	+	0.0633296i
$703$	−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
$707$	−29.5930			−1.11296
$708$	−18.0964	+	22.5439i	−0.680103	+	0.847250i
$709$	−2.56426	+	2.56426i	−0.0963029	+	0.0963029i	−0.753617	−	0.657314i	$-0.771693\pi$
$709$	−2.56426	+	2.56426i	−0.0963029	+	0.0963029i	0.657314	+	0.753617i	$0.271693\pi$
$710$	−3.89969	−	10.5694i	−0.146353	−	0.396661i
$711$	3.89252			0.145981
$712$	−14.4196	+	2.37888i	−0.540397	+	0.0891522i
$713$	−4.46584	+	4.46584i	−0.167247	+	0.167247i
$714$	−26.4142	+	1.44103i	−0.988527	+	0.0539290i
$715$	2.34890	+	1.24213i	0.0878437	+	0.0464530i
$716$	−18.6347	+	23.2145i	−0.696413	+	0.867568i
$717$		−	6.80569i		−	0.254163i
$718$	−1.73090	−	31.7277i	−0.0645966	−	1.18407i
$719$	49.6672			1.85227			0.926137	−	0.377187i	$-0.123109\pi$
$719$	49.6672			1.85227			0.926137	+	0.377187i	$0.123109\pi$
$720$	4.42069	+	7.77544i	0.164749	+	0.289774i
$721$	8.14429			0.303309
$722$	2.72886	+	50.0204i	0.101558	+	1.86157i
$723$			18.8285i			0.700239i
$724$	35.8728	+	28.7957i	1.33320	+	1.07019i
$725$	15.1071	+	2.86571i	0.561062	+	0.106430i
$726$	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	$0.265381\pi$
$728$	9.82378	−	13.7055i	0.364094	−	0.507961i
$729$	−1.00000			−0.0370370
$730$	10.0318	+	4.62428i	0.371294	+	0.171152i
$731$	−28.1123	+	28.1123i	−1.03977	+	1.03977i
$732$	9.92005	+	7.96301i	0.366656	+	0.294321i
$733$	−13.0551			−0.482202			−0.241101	−	0.970500i	$-0.577508\pi$
$733$	−13.0551			−0.482202			−0.241101	+	0.970500i	$0.577508\pi$
$734$	−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
$738$	0.637066	+	11.6775i	0.0234507	+	0.429855i
$739$	12.9439	−	12.9439i	0.476148	−	0.476148i	−0.427749	−	0.903897i	$-0.640693\pi$
$739$	12.9439	−	12.9439i	0.476148	−	0.476148i	0.903897	+	0.427749i	$0.140693\pi$
$740$	−1.61502	−	3.73660i	−0.0593694	−	0.137360i
$741$	−6.19840	−	6.19840i	−0.227704	−	0.227704i
$742$	18.6217	+	16.6950i	0.683626	+	0.612894i
$743$	−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
$747$		−	9.99092i		−	0.365549i
$748$	−0.811174	−	7.41235i	−0.0296595	−	0.271022i
$749$	25.7862	+	25.7862i	0.942206	+	0.942206i
$750$	9.17922	−	12.8741i	0.335178	−	0.470095i
$751$		−	36.5284i		−	1.33294i	−0.745532	−	0.666470i	$-0.767804\pi$
$751$		−	36.5284i		−	1.33294i	0.745532	−	0.666470i	$-0.232196\pi$
$752$	−24.1736	−	15.4058i	−0.881519	−	0.561791i
$753$	11.9160	+	11.9160i	0.434244	+	0.434244i
$754$	3.84783	+	3.44971i	0.140130	+	0.125631i
$755$	12.6332	+	40.9896i	0.459767	+	1.49177i
$756$	7.82540	+	6.28160i	0.284607	+	0.228459i
$757$	−36.7015			−1.33394			−0.666969	−	0.745086i	$-0.732409\pi$
$757$	−36.7015			−1.33394			−0.666969	+	0.745086i	$0.732409\pi$
$758$	21.4445	+	19.2258i	0.778901	+	0.698311i
$759$			2.63779i			0.0957457i
$760$	−44.2455	−	14.8065i	−1.60495	−	0.537087i
$761$			24.5206i			0.888872i	0.895811	+	0.444436i	$0.146596\pi$
$761$			24.5206i			0.888872i	−0.895811	+	0.444436i	$0.853404\pi$
$762$	3.45553	−	3.85432i	0.125181	−	0.139627i
$763$	−24.7027			−0.894298
$764$	4.00860	+	36.6298i	0.145026	+	1.32522i
$765$	−7.36943	−	3.89706i	−0.266442	−	0.140898i
$766$	−11.3034	+	12.6079i	−0.408410	+	0.455543i
$767$	12.1447	+	12.1447i	0.438520	+	0.438520i
$768$	6.75717	+	14.5031i	0.243829	+	0.523336i
$769$			42.8743i			1.54609i	0.634352	+	0.773044i	$0.281267\pi$
$769$			42.8743i			1.54609i	−0.634352	+	0.773044i	$0.718733\pi$
$770$	14.8860	−	5.49237i	0.536454	−	0.197931i
$771$	−14.1560	−	14.1560i	−0.509817	−	0.509817i
$772$	20.3775	+	16.3574i	0.733401	+	0.588715i
$773$			29.2410i			1.05172i	0.850570	+	0.525862i	$0.176257\pi$
$773$			29.2410i			1.05172i	−0.850570	+	0.525862i	$0.823743\pi$
$774$	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
$778$	−32.3458	+	36.0787i	−1.15965	+	1.29349i
$779$	−43.1375	−	43.1375i	−1.54556	−	1.54556i
$780$	4.87787	−	2.10830i	0.174656	−	0.0754891i
$781$	2.51922	−	2.51922i	0.0901448	−	0.0901448i
$782$	−13.8863	+	0.757564i	−0.496572	+	0.0270904i
$783$	−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
$787$	15.8706			0.565725			0.282863	−	0.959160i	$-0.408716\pi$
$787$	15.8706			0.565725			0.282863	+	0.959160i	$0.408716\pi$
$788$	−14.5528	+	1.59259i	−0.518422	+	0.0567337i
$789$	7.24736	−	7.24736i	0.258013	−	0.258013i
$790$	−4.26087	−	11.5482i	−0.151595	−	0.410868i
$791$	47.4563			1.68735
$792$	−1.64784	+	2.29897i	−0.0585536	+	0.0816904i
$793$	5.34408	−	5.34408i	0.189774	−	0.189774i
$794$	−0.653583	−	11.9803i	−0.0231948	−	0.425164i
$795$	2.32134	+	7.53185i	0.0823296	+	0.267127i
$796$	4.70065	+	42.9536i	0.166610	+	1.52245i
$797$			54.0422i			1.91427i	0.289637	+	0.957137i	$0.406465\pi$
$797$			54.0422i			1.91427i	−0.289637	+	0.957137i	$0.593535\pi$
$798$	−52.2677	+	2.85146i	−1.85026	+	0.100941i
$799$	26.7171			0.945184
$800$	18.2290	−	21.6264i	0.644493	−	0.764610i
$801$	−5.16701			−0.182567
$802$	1.36921	−	0.0746973i	0.0483486	−	0.00263765i
$803$			3.49330i			0.123276i
$804$	0.277084	+	2.53194i	0.00977201	+	0.0892947i
$805$	−8.71596	−	28.2799i	−0.307197	−	0.996734i
$806$	0.219182	+	4.01764i	0.00772035	+	0.141515i
$807$	−14.0526	+	14.0526i	−0.494677	+	0.494677i
$808$	−13.5591	−	9.71879i	−0.477006	−	0.341906i
$809$	−29.5553			−1.03911			−0.519555	−	0.854437i	$-0.673902\pi$
$809$	−29.5553			−1.03911			−0.519555	+	0.854437i	$0.673902\pi$
$810$	1.09463	+	2.96678i	0.0384614	+	0.104242i
$811$	0.939982	−	0.939982i	0.0330072	−	0.0330072i	−0.690411	−	0.723418i	$-0.742570\pi$
$811$	0.939982	−	0.939982i	0.0330072	−	0.0330072i	0.723418	+	0.690411i	$0.242570\pi$
$812$	30.6765	−	3.35710i	1.07653	−	0.117811i
$813$	0.510213			0.0178940
$814$	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
$818$	40.6061	−	2.21526i	1.41976	−	0.0774549i
$819$	4.21566	−	4.21566i	0.147307	−	0.147307i
$820$	33.9473	−	14.6726i	1.18549	−	0.512389i
$821$	−3.45780	−	3.45780i	−0.120678	−	0.120678i	0.644189	−	0.764867i	$-0.277195\pi$
$821$	−3.45780	−	3.45780i	−0.120678	−	0.120678i	−0.764867	+	0.644189i	$0.777195\pi$
$822$	1.84491	−	2.05782i	0.0643485	−	0.0717747i
$823$	−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
$827$		−	14.4914i		−	0.503914i	−0.967738	−	0.251957i	$-0.918926\pi$
$827$		−	14.4914i		−	0.503914i	0.967738	−	0.251957i	$-0.0810741\pi$
$828$	4.11391	+	3.30231i	0.142968	+	0.114763i
$829$	9.51029	+	9.51029i	0.330306	+	0.330306i	0.852703	−	0.522397i	$-0.174962\pi$
$829$	9.51029	+	9.51029i	0.330306	+	0.330306i	−0.522397	+	0.852703i	$0.674962\pi$
$830$	−29.6409	+	10.9364i	−1.02885	+	0.379607i
$831$			1.56728i			0.0543684i
$832$	9.00222	−	3.05339i	0.312096	−	0.105857i
$833$	47.9099	+	47.9099i	1.65998	+	1.65998i
$834$	−16.2654	+	18.1425i	−0.563224	+	0.628223i
$835$	−15.7945	−	8.35237i	−0.546592	−	0.289046i
$836$	−1.60513	−	14.6673i	−0.0555145	−	0.507280i
$837$	−2.39439			−0.0827623
$838$	22.2488	−	24.8164i	0.768571	−	0.857269i
$839$		−	22.9683i		−	0.792954i	−0.918045	−	0.396477i	$-0.870233\pi$
$839$		−	22.9683i		−	0.792954i	0.918045	−	0.396477i	$-0.129767\pi$
$840$	10.0702	−	30.0923i	0.347455	−	1.03828i
$841$		−	19.5426i		−	0.673882i
$842$	5.70879	+	5.11813i	0.196738	+	0.176383i
$843$	26.3167			0.906394
$844$	−13.1805	−	10.5803i	−0.453693	−	0.364188i
$845$	7.63184	+	24.7623i	0.262543	+	0.851850i
$846$	−7.54606	−	6.76530i	−0.259439	−	0.232596i
$847$	−35.4778	−	35.4778i	−1.21903	−	1.21903i
$848$	3.04930	+	13.7651i	0.104713	+	0.472695i
$849$		−	16.2153i		−	0.556506i
$850$	−3.49491	+	26.1293i	−0.119875	+	0.896228i
$851$	−1.69770	−	1.69770i	−0.0581963	−	0.0581963i
$852$	−0.775115	−	7.08285i	−0.0265550	−	0.242654i
$853$			19.6309i			0.672150i	0.941835	+	0.336075i	$0.109100\pi$
$853$			19.6309i			0.672150i	−0.941835	+	0.336075i	$0.890900\pi$
$854$	−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	0.867165	−	0.498021i	$-0.165940\pi$
$857$	10.8065	+	10.8065i	0.369144	+	0.369144i	−0.498021	+	0.867165i	$0.665940\pi$
$858$	1.25126	+	1.12180i	0.0427173	+	0.0382975i
$859$	−9.38485	−	9.38485i	−0.320207	−	0.320207i	0.528639	−	0.848846i	$-0.322702\pi$
$859$	−9.38485	−	9.38485i	−0.320207	−	0.320207i	−0.848846	+	0.528639i	$0.822702\pi$
$860$	−18.9210	−	43.7767i	−0.645202	−	1.49277i
$861$	29.3387	−	29.3387i	0.999860	−	0.999860i
$862$	−0.464224	−	8.50929i	−0.0158115	−	0.289828i
$863$	28.9450	−	28.9450i	0.985299	−	0.985299i	−0.0145949	−	0.999893i	$-0.504646\pi$
$863$	28.9450	−	28.9450i	0.985299	−	0.985299i	0.999893	+	0.0145949i	$0.00464587\pi$
$864$	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
$867$	−3.10090			−0.105312
$868$	18.7371	+	15.0406i	0.635978	+	0.510512i
$869$	2.75254	−	2.75254i	0.0933735	−	0.0933735i
$870$	8.83178	+	4.07110i	0.299425	+	0.138023i
$871$	1.51326			0.0512750
$872$	−11.3184	−	8.11275i	−0.383290	−	0.274732i
$873$	6.87796	−	6.87796i	0.232784	−	0.232784i
$874$	−27.4777	+	1.49904i	−0.929448	+	0.0507059i
$875$	−55.7474	+	6.24171i	−1.88461	+	0.211008i
$876$	5.44816	+	4.37334i	0.184076	+	0.147761i
$877$		−	32.0081i		−	1.08084i	−0.841396	−	0.540418i	$-0.818266\pi$
$877$		−	32.0081i		−	1.08084i	0.841396	−	0.540418i	$-0.181734\pi$
$878$	−0.190647	−	3.49459i	−0.00643403	−	0.117937i
$879$	−21.6309			−0.729591
$880$	8.62432	+	2.37227i	0.290726	+	0.0799691i
$881$	24.6429			0.830240			0.415120	−	0.909767i	$-0.363740\pi$
$881$	24.6429			0.830240			0.415120	+	0.909767i	$0.363740\pi$
$882$	−1.40007	−	25.6635i	−0.0471429	−	0.864136i
$883$			12.5160i			0.421196i	0.977573	+	0.210598i	$0.0675410\pi$
$883$			12.5160i			0.421196i	−0.977573	+	0.210598i	$0.932459\pi$
$884$	−5.54618	+	6.90925i	−0.186538	+	0.232383i
$885$	28.5717	+	15.1091i	0.960428	+	0.507888i
$886$	−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	$0.0783373\pi$
$888$	−0.419069	−	2.54019i	−0.0140630	−	0.0852433i
$889$	−18.3653			−0.615953
$890$	5.65596	+	15.3294i	0.189588	+	0.513842i
$891$	−0.707136	+	0.707136i	−0.0236899	+	0.0236899i
$892$	−21.3126	+	26.5505i	−0.713597	+	0.888975i
$893$	52.8670			1.76913
$894$	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
$898$	1.27303	+	23.3348i	0.0424815	+	0.778694i
$899$	−5.20675	+	5.20675i	−0.173655	+	0.173655i
$900$	7.60357	−	6.49505i	0.253452	−	0.216502i
$901$	−9.29180	−	9.29180i	−0.309555	−	0.309555i
$902$	8.70808	+	7.80710i	0.289947	+	0.259948i
$903$	−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
$907$		−	1.09996i		−	0.0365235i	−0.999833	−	0.0182618i	$-0.994187\pi$
$907$		−	1.09996i		−	0.0365235i	0.999833	−	0.0182618i	$-0.00581322\pi$
$908$	0.361352	−	0.0395448i	0.0119919	−	0.00131234i
$909$	−4.17060	−	4.17060i	−0.138330	−	0.138330i
$910$	−17.1215	−	7.89235i	−0.567573	−	0.261629i
$911$			10.9439i			0.362589i	0.983429	+	0.181294i	$0.0580287\pi$
$911$			10.9439i			0.362589i	−0.983429	+	0.181294i	$0.941971\pi$
$912$	−24.8847	−	15.8590i	−0.824016	−	0.525144i
$913$	−7.06493	−	7.06493i	−0.233815	−	0.233815i
$914$	−18.5396	−	16.6214i	−0.613235	−	0.549787i
$915$	6.64853	−	12.5725i	0.219793	−	0.415635i
$916$	−0.984433	+	1.22637i	−0.0325266	+	0.0405205i
$917$	29.3309			0.968592
$918$	−3.92570	−	3.51953i	−0.129567	−	0.116162i
$919$		−	4.14834i		−	0.136841i	−0.997657	−	0.0684205i	$-0.978204\pi$
$919$		−	4.14834i		−	0.136841i	0.997657	−	0.0684205i	$-0.0217960\pi$
$920$	5.29402	−	15.8199i	0.174539	−	0.521565i
$921$			13.9316i			0.459061i
$922$	−18.6817	+	20.8377i	−0.615250	+	0.686253i
$923$	−4.23320			−0.139338
$924$	9.97556	−	1.09168i	0.328172	−	0.0359137i
$925$	−3.76155	+	2.56201i	−0.123679	+	0.0842383i
$926$	29.0295	−	32.3797i	0.953970	−	1.06406i
$927$	1.14779	+	1.14779i	0.0376985	+	0.0376985i
$928$	15.1580	+	8.53647i	0.497587	+	0.280223i
$929$			5.49483i			0.180280i	0.995929	+	0.0901398i	$0.0287314\pi$
$929$			5.49483i			0.180280i	−0.995929	+	0.0901398i	$0.971269\pi$
$930$	2.62097	+	7.10364i	0.0859451	+	0.232937i
$931$	94.8027	+	94.8027i	3.10703	+	3.10703i
$932$	17.6411	−	21.9767i	0.577852	−	0.719869i
$933$			1.47971i			0.0484436i
$934$	−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	0.798406	−	0.602120i	$-0.205677\pi$
$937$	6.00841	+	6.00841i	0.196286	+	0.196286i	−0.602120	+	0.798406i	$0.705677\pi$
$938$	6.03218	−	6.72833i	0.196958	−	0.219688i
$939$	−11.4062	−	11.4062i	−0.372228	−	0.372228i
$940$	−11.8110	+	29.7930i	−0.385233	+	0.971741i
$941$	30.3741	−	30.3741i	0.990168	−	0.990168i	−0.00978427	−	0.999952i	$-0.503114\pi$
$941$	30.3741	−	30.3741i	0.990168	−	0.990168i	0.999952	+	0.00978427i	$0.00311448\pi$
$942$	−12.2071	+	0.665957i	−0.397729	+	0.0216981i
$943$	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
$947$	12.7107			0.413043			0.206521	−	0.978442i	$-0.433786\pi$
$947$	12.7107			0.413043			0.206521	+	0.978442i	$0.433786\pi$
$948$	−0.846903	−	7.73883i	−0.0275061	−	0.251346i
$949$	2.93500	−	2.93500i	0.0952743	−	0.0952743i
$950$	−6.91563	+	51.7039i	−0.224373	+	1.67750i
$951$	21.2307			0.688452
$952$	8.61194	+	52.2014i	0.279115	+	1.69186i
$953$	−21.0529	+	21.0529i	−0.681971	+	0.681971i	−0.960444	−	0.278473i	$-0.910172\pi$
$953$	−21.0529	+	21.0529i	−0.681971	+	0.681971i	0.278473	+	0.960444i	$0.410172\pi$
$954$	0.271535	+	4.97727i	0.00879125	+	0.161145i
$955$	39.3704	−	12.1341i	1.27400	−	0.392650i
$956$	−13.5306	+	1.48073i	−0.437611	+	0.0478902i
$957$			3.07542i			0.0994142i
$958$	30.3456	−	1.65550i	0.980421	−	0.0534868i
$959$	−9.80524			−0.316628
$960$	14.4968	−	10.4806i	0.467881	−	0.338261i
$961$	25.2669			0.815061
$962$	−1.52731	+	0.0833224i	−0.0492426	+	0.00268642i
$963$			7.26820i			0.234215i
$964$	37.4335	−	4.09656i	1.20565	−	0.131941i
$965$	13.6572	−	25.8261i	0.439641	−	0.831372i
$966$	−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	$0.157794\pi$
$968$	−4.60394	−	27.9068i	−0.147976	−	0.896959i
$969$	27.5031			0.883528
$970$	−27.9342	−	12.8766i	−0.896914	−	0.413442i
$971$	18.2804	−	18.2804i	0.586647	−	0.586647i	−0.350075	−	0.936722i	$-0.613844\pi$
$971$	18.2804	−	18.2804i	0.586647	−	0.586647i	0.936722	+	0.350075i	$0.113844\pi$
$972$	0.217572	+	1.98813i	0.00697863	+	0.0637693i
$973$	86.4465			2.77135
$974$	−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	$-0.0605565\pi$
$978$	−13.9799	+	0.762675i	−0.447029	+	0.0243876i
$979$	−3.65377	+	3.65377i	−0.116775	+	0.116775i
$980$	−74.6055	+	32.2458i	−2.38319	+	1.03005i
$981$	−3.48141	−	3.48141i	−0.111153	−	0.111153i
$982$	8.08760	−	9.02096i	0.258086	−	0.287870i
$983$	−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
$987$			35.9560i			1.14449i
$988$	−10.9746	+	13.6718i	−0.349149	+	0.434959i
$989$	−19.8896	−	19.8896i	−0.632453	−	0.632453i
$990$	2.87197	+	1.32386i	0.0912771	+	0.0420752i
$991$			32.0105i			1.01685i	0.861107	+	0.508424i	$0.169772\pi$
$991$			32.0105i			1.01685i	−0.861107	+	0.508424i	$0.830228\pi$
$992$	3.64549	+	13.0449i	0.115744	+	0.414177i
$993$	2.12076	+	2.12076i	0.0673001	+	0.0673001i
$994$	−16.8744	+	18.8218i	−0.535224	+	0.596992i
$995$	46.1673	−	14.2289i	1.46360	−	0.451088i
$996$	−19.8632	+	2.17374i	−0.629391	+	0.0688777i
$997$	27.1548			0.860001			0.430000	−	0.902829i	$-0.358513\pi$
$997$	27.1548			0.860001			0.430000	+	0.902829i	$0.358513\pi$
$998$	−39.7724	+	44.3624i	−1.25897	+	1.40427i
$999$		−	0.910233i		−	0.0287985i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.e.163.4	✓	16	16.3	odd	4
240.2.y.e.187.4	yes	16	5.2	odd	4
240.2.bc.e.43.1	yes	16	1.1	even	1	trivial
240.2.bc.e.67.1	yes	16	80.67	even	4	inner
720.2.z.f.163.5		16	48.35	even	4
720.2.z.f.667.5		16	15.2	even	4
720.2.bd.f.307.8		16	240.227	odd	4
720.2.bd.f.523.8		16	3.2	odd	2
960.2.y.e.847.3		16	20.7	even	4
960.2.y.e.943.3		16	16.13	even	4
960.2.bc.e.367.4		16	80.77	odd	4
960.2.bc.e.463.4		16	4.3	odd	2
1920.2.y.i.223.6		16	16.11	odd	4
1920.2.y.i.1567.6		16	40.37	odd	4
1920.2.y.j.223.6		16	16.5	even	4
1920.2.y.j.1567.6		16	40.27	even	4
1920.2.bc.i.607.5		16	80.27	even	4
1920.2.bc.i.1183.5		16	8.5	even	2
1920.2.bc.j.607.5		16	80.37	odd	4
1920.2.bc.j.1183.5		16	8.3	odd	2

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.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41211 + 0.0770377i) q^{2} +1.00000i q^{3} +(1.98813 - 0.217572i) q^{4} +(-0.658594 - 2.13688i) q^{5} +(-0.0770377 - 1.41211i) q^{6} +(-3.54781 + 3.54781i) q^{7} +(-2.79070 + 0.460397i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.41211 + 0.0770377i) q^{2} +1.00000i q^{3} +(1.98813 - 0.217572i) q^{4} +(-0.658594 - 2.13688i) q^{5} +(-0.0770377 - 1.41211i) q^{6} +(-3.54781 + 3.54781i) q^{7} +(-2.79070 + 0.460397i) q^{8} -1.00000 q^{9} +(1.09463 + 2.96678i) q^{10} +(-0.707136 + 0.707136i) q^{11} +(0.217572 + 1.98813i) q^{12} +1.18824 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} +(1.41211 - 0.0770377i) q^{18} +(-5.21643 + 5.21643i) q^{19} +(-1.77430 - 4.10510i) q^{20} +(-3.54781 - 3.54781i) q^{21} +(0.944080 - 1.05303i) 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} -1.00000i q^{27} +(-6.28160 + 7.82540i) q^{28} +(-2.17456 - 2.17456i) q^{29} +(-2.96678 + 1.09463i) q^{30} -2.39439i q^{31} +(-5.44812 + 1.52251i) q^{32} +(-0.707136 - 0.707136i) q^{33} +(3.51953 - 3.92570i) q^{34} +(9.91780 + 5.24467i) q^{35} +(-1.98813 + 0.217572i) q^{36} +0.910233 q^{37} +(6.96434 - 7.76806i) q^{38} +1.18824i q^{39} +(2.82176 + 5.66019i) q^{40} +8.26953i q^{41} +(5.28322 + 4.73659i) q^{42} +10.6640 q^{43} +(-1.25202 + 1.55973i) q^{44} +(0.658594 + 2.13688i) q^{45} +(2.77745 + 2.49008i) q^{46} +(-5.06735 - 5.06735i) q^{47} +(0.865123 + 3.90532i) q^{48} -18.1738i q^{49} +(5.61874 - 4.29300i) q^{50} +(-2.63620 - 2.63620i) q^{51} +(2.36238 - 0.258529i) q^{52} +3.52470i 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} +(3.23825 + 2.90320i) q^{58} +(10.2207 + 10.2207i) q^{59} +(4.10510 - 1.77430i) q^{60} +(4.49746 - 4.49746i) q^{61} +(0.184459 + 3.38115i) 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} +1.27353 q^{67} +(-4.66755 + 5.81467i) q^{68} +(1.86512 - 1.86512i) q^{69} +(-14.4091 - 6.64203i) q^{70} -3.56257 q^{71} +(2.79070 - 0.460397i) q^{72} +(2.47003 - 2.47003i) q^{73} +(-1.28535 + 0.0701223i) q^{74} +(-2.81467 - 4.13251i) q^{75} +(-9.23600 + 11.5059i) q^{76} -5.01756i q^{77} +(-0.0915396 - 1.67794i) q^{78} -3.89252 q^{79} +(-4.42069 - 7.77544i) q^{80} +1.00000 q^{81} +(-0.637066 - 11.6775i) q^{82} +9.99092i q^{83} +(-7.82540 - 6.28160i) q^{84} +(7.36943 + 3.89706i) q^{85} +(-15.0587 + 0.821528i) q^{86} +(2.17456 - 2.17456i) q^{87} +(1.64784 - 2.29897i) q^{88} +5.16701 q^{89} +(-1.09463 - 2.96678i) q^{90} +(-4.21566 + 4.21566i) q^{91} +(-4.11391 - 3.30231i) q^{92} +2.39439 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} +(1.40007 + 25.6635i) q^{98} +(0.707136 - 0.707136i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} + 8 q^{4} - 8 q^{5} + 2 q^{6} - 4 q^{7} + 8 q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 + 8 * q^4 - 8 * q^5 + 2 * q^6 - 4 * q^7 + 8 * q^8 - 16 * q^9	\( 16 q + 2 q^{2} + 8 q^{4} - 8 q^{5} + 2 q^{6} - 4 q^{7} + 8 q^{8} - 16 q^{9} - 2 q^{10} - 4 q^{12} - 8 q^{13} + 4 q^{14} + 4 q^{15} - 8 q^{16} - 8 q^{17} - 2 q^{18} - 8 q^{19} + 4 q^{20} - 4 q^{21} + 4 q^{24} - 32 q^{25} + 20 q^{26} + 12 q^{28} - 12 q^{29} + 2 q^{30} - 28 q^{32} + 12 q^{35} - 8 q^{36} - 24 q^{37} + 16 q^{38} + 16 q^{40} + 24 q^{42} + 24 q^{43} - 52 q^{44} + 8 q^{45} - 16 q^{46} + 32 q^{47} - 16 q^{48} + 6 q^{50} - 8 q^{51} + 24 q^{52} - 2 q^{54} - 4 q^{55} + 20 q^{56} - 8 q^{57} + 12 q^{58} + 24 q^{59} + 24 q^{60} + 40 q^{61} + 28 q^{62} + 4 q^{63} + 8 q^{64} - 4 q^{65} - 8 q^{66} + 16 q^{67} - 8 q^{68} + 12 q^{70} - 8 q^{72} - 8 q^{73} - 64 q^{74} + 24 q^{75} + 16 q^{76} + 12 q^{78} + 48 q^{79} + 16 q^{81} - 32 q^{82} - 12 q^{84} - 8 q^{85} - 8 q^{86} + 12 q^{87} + 24 q^{88} + 2 q^{90} - 40 q^{91} - 16 q^{92} - 32 q^{93} + 20 q^{94} - 8 q^{95} - 28 q^{96} + 48 q^{97} + 62 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 + 8 * q^4 - 8 * q^5 + 2 * q^6 - 4 * q^7 + 8 * q^8 - 16 * q^9 - 2 * q^10 - 4 * q^12 - 8 * q^13 + 4 * q^14 + 4 * q^15 - 8 * q^16 - 8 * q^17 - 2 * q^18 - 8 * q^19 + 4 * q^20 - 4 * q^21 + 4 * q^24 - 32 * q^25 + 20 * q^26 + 12 * q^28 - 12 * q^29 + 2 * q^30 - 28 * q^32 + 12 * q^35 - 8 * q^36 - 24 * q^37 + 16 * q^38 + 16 * q^40 + 24 * q^42 + 24 * q^43 - 52 * q^44 + 8 * q^45 - 16 * q^46 + 32 * q^47 - 16 * q^48 + 6 * q^50 - 8 * q^51 + 24 * q^52 - 2 * q^54 - 4 * q^55 + 20 * q^56 - 8 * q^57 + 12 * q^58 + 24 * q^59 + 24 * q^60 + 40 * q^61 + 28 * q^62 + 4 * q^63 + 8 * q^64 - 4 * q^65 - 8 * q^66 + 16 * q^67 - 8 * q^68 + 12 * q^70 - 8 * q^72 - 8 * q^73 - 64 * q^74 + 24 * q^75 + 16 * q^76 + 12 * q^78 + 48 * q^79 + 16 * q^81 - 32 * q^82 - 12 * q^84 - 8 * q^85 - 8 * q^86 + 12 * q^87 + 24 * q^88 + 2 * q^90 - 40 * q^91 - 16 * q^92 - 32 * q^93 + 20 * q^94 - 8 * q^95 - 28 * q^96 + 48 * q^97 + 62 * q^98

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