LMFDB - Embedded newform 240.2.bk.b.131.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(11,240)]

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, 2, 0]))

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

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

chi := DirichletCharacter("240.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bk (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:	$60$
Relative dimension:	$30$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			131.19
Character	$\chi$	$=$	240.131
Dual form			240.2.bk.b.11.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.772787 - 1.18440i) q^{2} +(1.72837 + 0.112911i) q^{3} +(-0.805601 - 1.83058i) q^{4} +(0.707107 + 0.707107i) q^{5} +(1.46939 - 1.95982i) q^{6} -2.33502 q^{7} +(-2.79069 - 0.460493i) q^{8} +(2.97450 + 0.390304i) q^{9} +O(q^{10})$	\(q+(0.772787 - 1.18440i) q^{2} +(1.72837 + 0.112911i) q^{3} +(-0.805601 - 1.83058i) q^{4} +(0.707107 + 0.707107i) q^{5} +(1.46939 - 1.95982i) q^{6} -2.33502 q^{7} +(-2.79069 - 0.460493i) q^{8} +(2.97450 + 0.390304i) q^{9} +(1.38394 - 0.291053i) q^{10} +(4.04887 - 4.04887i) q^{11} +(-1.18568 - 3.25487i) q^{12} +(-0.834130 - 0.834130i) q^{13} +(-1.80447 + 2.76560i) q^{14} +(1.14230 + 1.30198i) q^{15} +(-2.70202 + 2.94943i) q^{16} +4.55545i q^{17} +(2.76093 - 3.22138i) q^{18} +(-3.99317 + 3.99317i) q^{19} +(0.724767 - 1.86406i) q^{20} +(-4.03577 - 0.263650i) q^{21} +(-1.66656 - 7.92440i) q^{22} +4.62939i q^{23} +(-4.77134 - 1.11100i) q^{24} +1.00000i q^{25} +(-1.63255 + 0.343338i) q^{26} +(5.09696 + 1.01044i) q^{27} +(1.88110 + 4.27443i) q^{28} +(-4.29193 + 4.29193i) q^{29} +(2.42482 - 0.346785i) q^{30} -6.62238i q^{31} +(1.40521 + 5.47954i) q^{32} +(7.45510 - 6.54077i) q^{33} +(5.39547 + 3.52040i) q^{34} +(-1.65111 - 1.65111i) q^{35} +(-1.68178 - 5.75948i) q^{36} +(-1.12654 + 1.12654i) q^{37} +(1.64364 + 7.81538i) q^{38} +(-1.34750 - 1.53586i) q^{39} +(-1.64770 - 2.29893i) q^{40} -1.26139 q^{41} +(-3.43106 + 4.57622i) q^{42} +(-5.15956 - 5.15956i) q^{43} +(-10.6735 - 4.14999i) q^{44} +(1.82730 + 2.37928i) q^{45} +(5.48304 + 3.57753i) q^{46} -3.69227 q^{47} +(-5.00310 + 4.79260i) q^{48} -1.54767 q^{49} +(1.18440 + 0.772787i) q^{50} +(-0.514362 + 7.87350i) q^{51} +(-0.854962 + 2.19891i) q^{52} +(4.30450 + 4.30450i) q^{53} +(5.13563 - 5.25598i) q^{54} +5.72597 q^{55} +(6.51632 + 1.07526i) q^{56} +(-7.35254 + 6.45079i) q^{57} +(1.76661 + 8.40011i) q^{58} +(8.10560 - 8.10560i) q^{59} +(1.46314 - 3.13994i) q^{60} +(7.50538 + 7.50538i) q^{61} +(-7.84354 - 5.11769i) q^{62} +(-6.94553 - 0.911368i) q^{63} +(7.57589 + 2.57018i) q^{64} -1.17964i q^{65} +(-1.98568 - 13.8844i) q^{66} +(2.85749 - 2.85749i) q^{67} +(8.33911 - 3.66988i) q^{68} +(-0.522709 + 8.00128i) q^{69} +(-3.23153 + 0.679616i) q^{70} -9.41730i q^{71} +(-8.12118 - 2.45895i) q^{72} +0.435077i q^{73} +(0.463696 + 2.20484i) q^{74} +(-0.112911 + 1.72837i) q^{75} +(10.5267 + 4.09290i) q^{76} +(-9.45421 + 9.45421i) q^{77} +(-2.86041 + 0.409081i) q^{78} -15.6995i q^{79} +(-3.99617 + 0.174946i) q^{80} +(8.69533 + 2.32192i) q^{81} +(-0.974783 + 1.49398i) q^{82} +(3.24036 + 3.24036i) q^{83} +(2.76859 + 7.60019i) q^{84} +(-3.22119 + 3.22119i) q^{85} +(-10.0982 + 2.12373i) q^{86} +(-7.90264 + 6.93342i) q^{87} +(-13.1636 + 9.43467i) q^{88} -2.37976 q^{89} +(4.23013 - 0.325583i) q^{90} +(1.94771 + 1.94771i) q^{91} +(8.47444 - 3.72944i) q^{92} +(0.747740 - 11.4459i) q^{93} +(-2.85333 + 4.37311i) q^{94} -5.64720 q^{95} +(1.81002 + 9.62932i) q^{96} +7.06437 q^{97} +(-1.19602 + 1.83306i) q^{98} +(13.6237 - 10.4631i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7}+O(q^{10}) $ 60 * q + 4 * q^3 + 8 * q^4 + 8 * q^6 + 16 * q^7	$ 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7} + 4 q^{12} + 16 q^{13} - 52 q^{16} - 20 q^{18} + 20 q^{19} - 16 q^{21} - 24 q^{22} - 28 q^{24} - 20 q^{27} - 56 q^{28} - 12 q^{34} + 12 q^{36} + 24 q^{37} - 80 q^{39} - 8 q^{40} + 36 q^{42} - 8 q^{45} + 36 q^{46} + 56 q^{48} + 28 q^{49} - 36 q^{51} - 24 q^{52} + 92 q^{54} - 80 q^{58} + 28 q^{60} + 20 q^{61} - 64 q^{64} + 24 q^{66} - 40 q^{67} + 12 q^{69} - 16 q^{70} - 56 q^{72} + 4 q^{75} - 20 q^{76} - 8 q^{78} - 28 q^{81} - 32 q^{82} + 16 q^{84} - 20 q^{85} - 24 q^{87} + 8 q^{88} + 32 q^{90} - 16 q^{91} - 48 q^{93} + 28 q^{94} + 72 q^{96} - 8 q^{97} + 32 q^{99}+O(q^{100}) $ 60 * q + 4 * q^3 + 8 * q^4 + 8 * q^6 + 16 * q^7 + 4 * q^12 + 16 * q^13 - 52 * q^16 - 20 * q^18 + 20 * q^19 - 16 * q^21 - 24 * q^22 - 28 * q^24 - 20 * q^27 - 56 * q^28 - 12 * q^34 + 12 * q^36 + 24 * q^37 - 80 * q^39 - 8 * q^40 + 36 * q^42 - 8 * q^45 + 36 * q^46 + 56 * q^48 + 28 * q^49 - 36 * q^51 - 24 * q^52 + 92 * q^54 - 80 * q^58 + 28 * q^60 + 20 * q^61 - 64 * q^64 + 24 * q^66 - 40 * q^67 + 12 * q^69 - 16 * q^70 - 56 * q^72 + 4 * q^75 - 20 * q^76 - 8 * q^78 - 28 * q^81 - 32 * q^82 + 16 * q^84 - 20 * q^85 - 24 * q^87 + 8 * q^88 + 32 * q^90 - 16 * q^91 - 48 * q^93 + 28 * q^94 + 72 * q^96 - 8 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.772787	−	1.18440i	0.546443	−	0.837496i
$2$	0.772787	−	1.18440i	0.546443	−	0.837496i
$3$	1.72837	+	0.112911i	0.997873	+	0.0651893i
$3$	1.72837	+	0.112911i	0.997873	+	0.0651893i
$4$	−0.805601	−	1.83058i	−0.402800	−	0.915288i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$	1.46939	−	1.95982i	0.599876	−	0.800093i
$7$	−2.33502			−0.882555			−0.441278	−	0.897371i	$-0.645475\pi$
$7$	−2.33502			−0.882555			−0.441278	+	0.897371i	$0.645475\pi$
$8$	−2.79069	−	0.460493i	−0.986658	−	0.162809i
$9$	2.97450	+	0.390304i	0.991501	+	0.130101i
$10$	1.38394	−	0.291053i	0.437640	−	0.0920392i
$11$	4.04887	−	4.04887i	1.22078	−	1.22078i	0.253426	−	0.967355i	$-0.418442\pi$
$11$	4.04887	−	4.04887i	1.22078	−	1.22078i	0.967355	−	0.253426i	$-0.0815576\pi$
$12$	−1.18568	−	3.25487i	−0.342277	−	0.939599i
$13$	−0.834130	−	0.834130i	−0.231346	−	0.231346i	0.581908	−	0.813254i	$-0.302306\pi$
$13$	−0.834130	−	0.834130i	−0.231346	−	0.231346i	−0.813254	+	0.581908i	$0.802306\pi$
$14$	−1.80447	+	2.76560i	−0.482266	+	0.739137i
$15$	1.14230	+	1.30198i	0.294940	+	0.336170i
$16$	−2.70202	+	2.94943i	−0.675504	+	0.737357i
$17$			4.55545i			1.10486i	0.833559	+	0.552430i	$0.186299\pi$
$17$			4.55545i			1.10486i	−0.833559	+	0.552430i	$0.813701\pi$
$18$	2.76093	−	3.22138i	0.650758	−	0.759285i
$19$	−3.99317	+	3.99317i	−0.916097	+	0.916097i	−0.996743	−	0.0806463i	$-0.974302\pi$
$19$	−3.99317	+	3.99317i	−0.916097	+	0.916097i	0.0806463	+	0.996743i	$0.474302\pi$
$20$	0.724767	−	1.86406i	0.162063	−	0.416816i
$21$	−4.03577	−	0.263650i	−0.880678	−	0.0575331i
$22$	−1.66656	−	7.92440i	−0.355313	−	1.68949i
$23$			4.62939i			0.965294i	0.875815	+	0.482647i	$0.160325\pi$
$23$			4.62939i			0.965294i	−0.875815	+	0.482647i	$0.839675\pi$
$24$	−4.77134	−	1.11100i	−0.973946	−	0.226782i
$25$			1.00000i			0.200000i
$26$	−1.63255	+	0.343338i	−0.320169	+	0.0673341i
$27$	5.09696	+	1.01044i	0.980911	+	0.194460i
$28$	1.88110	+	4.27443i	0.355494	+	0.807792i
$29$	−4.29193	+	4.29193i	−0.796992	+	0.796992i	−0.982620	−	0.185628i	$-0.940568\pi$
$29$	−4.29193	+	4.29193i	−0.796992	+	0.796992i	0.185628	+	0.982620i	$0.440568\pi$
$30$	2.42482	−	0.346785i	0.442709	−	0.0633140i
$31$		−	6.62238i		−	1.18941i	−0.803942	−	0.594707i	$-0.797268\pi$
$31$		−	6.62238i		−	1.18941i	0.803942	−	0.594707i	$-0.202732\pi$
$32$	1.40521	+	5.47954i	0.248409	+	0.968655i
$33$	7.45510	−	6.54077i	1.29777	−	1.13860i
$34$	5.39547	+	3.52040i	0.925316	+	0.603743i
$35$	−1.65111	−	1.65111i	−0.279089	−	0.279089i
$36$	−1.68178	−	5.75948i	−0.280297	−	0.959913i
$37$	−1.12654	+	1.12654i	−0.185202	+	0.185202i	−0.793618	−	0.608416i	$-0.791805\pi$
$37$	−1.12654	+	1.12654i	−0.185202	+	0.185202i	0.608416	+	0.793618i	$0.291805\pi$
$38$	1.64364	+	7.81538i	0.266633	+	1.26782i
$39$	−1.34750	−	1.53586i	−0.215773	−	0.245935i
$40$	−1.64770	−	2.29893i	−0.260524	−	0.363493i
$41$	−1.26139			−0.196996			−0.0984978	−	0.995137i	$-0.531404\pi$
$41$	−1.26139			−0.196996			−0.0984978	+	0.995137i	$0.531404\pi$
$42$	−3.43106	+	4.57622i	−0.529424	+	0.706126i
$43$	−5.15956	−	5.15956i	−0.786825	−	0.786825i	0.194147	−	0.980972i	$-0.437806\pi$
$43$	−5.15956	−	5.15956i	−0.786825	−	0.786825i	−0.980972	+	0.194147i	$0.937806\pi$
$44$	−10.6735	−	4.14999i	−1.60910	−	0.625635i
$45$	1.82730	+	2.37928i	0.272398	+	0.354682i
$46$	5.48304	+	3.57753i	0.808430	+	0.527478i
$47$	−3.69227			−0.538572			−0.269286	−	0.963060i	$-0.586788\pi$
$47$	−3.69227			−0.538572			−0.269286	+	0.963060i	$0.586788\pi$
$48$	−5.00310	+	4.79260i	−0.722135	+	0.691753i
$49$	−1.54767			−0.221096
$50$	1.18440	+	0.772787i	0.167499	+	0.109289i
$51$	−0.514362	+	7.87350i	−0.0720250	+	1.10251i
$52$	−0.854962	+	2.19891i	−0.118562	+	0.304934i
$53$	4.30450	+	4.30450i	0.591269	+	0.591269i	0.937974	−	0.346705i	$-0.112699\pi$
$53$	4.30450	+	4.30450i	0.591269	+	0.591269i	−0.346705	+	0.937974i	$0.612699\pi$
$54$	5.13563	−	5.25598i	0.698871	−	0.715248i
$55$	5.72597			0.772090
$56$	6.51632	+	1.07526i	0.870780	+	0.143688i
$57$	−7.35254	+	6.45079i	−0.973868	+	0.854428i
$58$	1.76661	+	8.40011i	0.231967	+	1.10299i
$59$	8.10560	−	8.10560i	1.05526	−	1.05526i	0.0568776	−	0.998381i	$-0.481886\pi$
$59$	8.10560	−	8.10560i	1.05526	−	1.05526i	0.998381	−	0.0568776i	$-0.0181145\pi$
$60$	1.46314	−	3.13994i	0.188890	−	0.405365i
$61$	7.50538	+	7.50538i	0.960966	+	0.960966i	0.999266	−	0.0383004i	$-0.0121944\pi$
$61$	7.50538	+	7.50538i	0.960966	+	0.960966i	−0.0383004	+	0.999266i	$0.512194\pi$
$62$	−7.84354	−	5.11769i	−0.996130	−	0.649947i
$63$	−6.94553	−	0.911368i	−0.875054	−	0.114822i
$64$	7.57589	+	2.57018i	0.946987	+	0.321273i
$65$		−	1.17964i		−	0.146316i
$66$	−1.98568	−	13.8844i	−0.244420	−	1.70906i
$67$	2.85749	−	2.85749i	0.349098	−	0.349098i	−0.510675	−	0.859774i	$-0.670605\pi$
$67$	2.85749	−	2.85749i	0.349098	−	0.349098i	0.859774	+	0.510675i	$0.170605\pi$
$68$	8.33911	−	3.66988i	1.01127	−	0.445038i
$69$	−0.522709	+	8.00128i	−0.0629268	+	0.963241i
$70$	−3.23153	+	0.679616i	−0.386242	+	0.0812297i
$71$		−	9.41730i		−	1.11763i	−0.829293	−	0.558814i	$-0.811257\pi$
$71$		−	9.41730i		−	1.11763i	0.829293	−	0.558814i	$-0.188743\pi$
$72$	−8.12118	−	2.45895i	−0.957090	−	0.289790i
$73$			0.435077i			0.0509219i	0.999676	+	0.0254610i	$0.00810535\pi$
$73$			0.435077i			0.0509219i	−0.999676	+	0.0254610i	$0.991895\pi$
$74$	0.463696	+	2.20484i	0.0539036	+	0.256308i
$75$	−0.112911	+	1.72837i	−0.0130379	+	0.199575i
$76$	10.5267	+	4.09290i	1.20750	+	0.469488i
$77$	−9.45421	+	9.45421i	−1.07741	+	1.07741i
$78$	−2.86041	+	0.409081i	−0.323877	+	0.0463193i
$79$		−	15.6995i		−	1.76633i	−0.469065	−	0.883164i	$-0.655409\pi$
$79$		−	15.6995i		−	1.76633i	0.469065	−	0.883164i	$-0.344591\pi$
$80$	−3.99617	+	0.174946i	−0.446786	+	0.0195596i
$81$	8.69533	+	2.32192i	0.966147	+	0.257991i
$82$	−0.974783	+	1.49398i	−0.107647	+	0.164983i
$83$	3.24036	+	3.24036i	0.355676	+	0.355676i	0.862216	−	0.506541i	$-0.169076\pi$
$83$	3.24036	+	3.24036i	0.355676	+	0.355676i	−0.506541	+	0.862216i	$0.669076\pi$
$84$	2.76859	+	7.60019i	0.302078	+	0.829248i
$85$	−3.22119	+	3.22119i	−0.349387	+	0.349387i
$86$	−10.0982	+	2.12373i	−1.08892	+	0.229008i
$87$	−7.90264	+	6.93342i	−0.847252	+	0.743341i
$88$	−13.1636	+	9.43467i	−1.40325	+	1.00574i
$89$	−2.37976			−0.252254			−0.126127	−	0.992014i	$-0.540255\pi$
$89$	−2.37976			−0.252254			−0.126127	+	0.992014i	$0.540255\pi$
$90$	4.23013	−	0.325583i	0.445895	−	0.0343194i
$91$	1.94771	+	1.94771i	0.204176	+	0.204176i
$92$	8.47444	−	3.72944i	0.883522	−	0.388821i
$93$	0.747740	−	11.4459i	0.0775370	−	1.18688i
$94$	−2.85333	+	4.37311i	−0.294299	+	0.451052i
$95$	−5.64720			−0.579390
$96$	1.81002	+	9.62932i	0.184735	+	0.982788i
$97$	7.06437			0.717278			0.358639	−	0.933476i	$-0.383241\pi$
$97$	7.06437			0.717278			0.358639	+	0.933476i	$0.383241\pi$
$98$	−1.19602	+	1.83306i	−0.120816	+	0.185167i
$99$	13.6237	−	10.4631i	1.36923	−	1.05158i
$100$	1.83058	−	0.805601i	0.183058	−	0.0805601i
$101$	1.17404	+	1.17404i	0.116822	+	0.116822i	0.763101	−	0.646279i	$-0.223676\pi$
$101$	1.17404	+	1.17404i	0.116822	+	0.116822i	−0.646279	+	0.763101i	$0.723676\pi$
$102$	8.92787	+	6.69374i	0.883991	+	0.662779i
$103$	−9.75475			−0.961164			−0.480582	−	0.876950i	$-0.659575\pi$
$103$	−9.75475			−0.961164			−0.480582	+	0.876950i	$0.659575\pi$
$104$	1.94369	+	2.71191i	0.190594	+	0.265924i
$105$	−2.66729	−	3.04015i	−0.260301	−	0.296688i
$106$	8.42472	−	1.77178i	0.818281	−	0.172091i
$107$	−8.14933	+	8.14933i	−0.787826	+	0.787826i	−0.981137	−	0.193312i	$-0.938077\pi$
$107$	−8.14933	+	8.14933i	−0.787826	+	0.787826i	0.193312	+	0.981137i	$0.438077\pi$
$108$	−2.25642	−	10.1444i	−0.217124	−	0.976144i
$109$	−11.3447	−	11.3447i	−1.08663	−	1.08663i	−0.995873	−	0.0907523i	$-0.971073\pi$
$109$	−11.3447	−	11.3447i	−1.08663	−	1.08663i	−0.0907523	−	0.995873i	$-0.528927\pi$
$110$	4.42496	−	6.78183i	0.421903	−	0.646622i
$111$	−2.07427	+	1.81987i	−0.196881	+	0.172735i
$112$	6.30926	−	6.88697i	0.596169	−	0.650758i
$113$		−	13.3697i		−	1.25771i	−0.777521	−	0.628857i	$-0.783523\pi$
$113$		−	13.3697i		−	1.25771i	0.777521	−	0.628857i	$-0.216477\pi$
$114$	1.95836	+	13.6934i	0.183418	+	1.28251i
$115$	−3.27347	+	3.27347i	−0.305253	+	0.305253i
$116$	11.3143	+	4.39912i	1.05051	+	0.408448i
$117$	−2.15556	−	2.80669i	−0.199281	−	0.259478i
$118$	−3.33636	−	15.8642i	−0.307137	−	1.46041i
$119$		−	10.6371i		−	0.975100i
$120$	−2.58825	−	4.15944i	−0.236274	−	0.379703i
$121$		−	21.7867i		−	1.98061i
$122$	14.6894	−	3.08930i	1.32992	−	0.279692i
$123$	−2.18014	−	0.142425i	−0.196576	−	0.0128420i
$124$	−12.1228	+	5.33499i	−1.08866	+	0.479096i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$	−6.44684	+	7.52198i	−0.574330	+	0.670111i
$127$		−	2.90551i		−	0.257822i	−0.991656	−	0.128911i	$-0.958852\pi$
$127$		−	2.90551i		−	0.257822i	0.991656	−	0.128911i	$-0.0411482\pi$
$128$	8.89867	−	6.98667i	0.786539	−	0.617541i
$129$	−8.33503	−	9.50018i	−0.733859	−	0.836444i
$130$	−1.39716	−	0.911609i	−0.122539	−	0.0799534i
$131$	0.767498	+	0.767498i	0.0670566	+	0.0670566i	0.739840	−	0.672783i	$-0.234901\pi$
$131$	0.767498	+	0.767498i	0.0670566	+	0.0670566i	−0.672783	+	0.739840i	$0.734901\pi$
$132$	−17.9792	−	8.37787i	−1.56489	−	0.729200i
$133$	9.32414	−	9.32414i	0.808506	−	0.808506i
$134$	−1.17618	−	5.59264i	−0.101606	−	0.483131i
$135$	2.88960	+	4.31859i	0.248698	+	0.371685i
$136$	2.09775	−	12.7129i	0.179881	−	1.09012i
$137$	3.94052			0.336661			0.168331	−	0.985731i	$-0.446162\pi$
$137$	3.94052			0.336661			0.168331	+	0.985731i	$0.446162\pi$
$138$	9.07276	+	6.80238i	0.772325	+	0.579057i
$139$	8.68502	+	8.68502i	0.736654	+	0.736654i	0.971929	−	0.235275i	$-0.0755992\pi$
$139$	8.68502	+	8.68502i	0.736654	+	0.736654i	−0.235275	+	0.971929i	$0.575599\pi$
$140$	−1.69235	+	4.35262i	−0.143029	+	0.367863i
$141$	−6.38159	−	0.416898i	−0.537427	−	0.0351091i
$142$	−11.1538	−	7.27757i	−0.936009	−	0.610720i
$143$	−6.75457			−0.564846
$144$	−9.18832	+	7.71847i	−0.765693	+	0.643206i
$145$	−6.06971			−0.504062
$146$	0.515305	+	0.336222i	0.0426469	+	0.0278259i
$147$	−2.67495	−	0.174749i	−0.220626	−	0.0144131i
$148$	2.96975	+	1.15467i	0.244112	+	0.0949135i
$149$	8.32183	+	8.32183i	0.681751	+	0.681751i	0.960395	−	0.278644i	$-0.0898849\pi$
$149$	8.32183	+	8.32183i	0.681751	+	0.681751i	−0.278644	+	0.960395i	$0.589885\pi$
$150$	1.95982	+	1.46939i	0.160019	+	0.119975i
$151$	8.10134			0.659278			0.329639	−	0.944107i	$-0.393073\pi$
$151$	8.10134			0.659278			0.329639	+	0.944107i	$0.393073\pi$
$152$	12.9825	−	9.30488i	1.05302	−	0.754725i
$153$	−1.77801	+	13.5502i	−0.143744	+	1.09547i
$154$	3.89146	+	18.5036i	0.313583	+	1.49107i
$155$	4.68273	−	4.68273i	0.376126	−	0.376126i
$156$	−1.72597	+	3.70399i	−0.138188	+	0.296557i
$157$	2.81242	+	2.81242i	0.224456	+	0.224456i	0.810372	−	0.585916i	$-0.199265\pi$
$157$	2.81242	+	2.81242i	0.224456	+	0.224456i	−0.585916	+	0.810372i	$0.699265\pi$
$158$	−18.5944	−	12.1323i	−1.47929	−	0.965197i
$159$	6.95374	+	7.92579i	0.551467	+	0.628556i
$160$	−2.88098	+	4.86826i	−0.227762	+	0.384870i
$161$		−	10.8097i		−	0.851925i
$162$	9.46971	−	8.50439i	0.744011	−	0.668168i
$163$	−13.9627	+	13.9627i	−1.09364	+	1.09364i	−0.0985042	+	0.995137i	$0.531406\pi$
$163$	−13.9627	+	13.9627i	−1.09364	+	1.09364i	−0.995137	+	0.0985042i	$0.968594\pi$
$164$	1.01617	+	2.30906i	0.0793499	+	0.180308i
$165$	9.89658	+	0.646526i	0.770447	+	0.0503320i
$166$	6.34198	−	1.33377i	0.492233	−	0.103521i
$167$		−	4.67619i		−	0.361854i	−0.983497	−	0.180927i	$-0.942090\pi$
$167$		−	4.67619i		−	0.361854i	0.983497	−	0.180927i	$-0.0579098\pi$
$168$	11.1412	+	2.59421i	0.859561	+	0.200148i
$169$		−	11.6085i		−	0.892958i
$170$	1.32588	+	6.30447i	0.101690	+	0.483531i
$171$	−13.4362	+	10.3191i	−1.02750	+	0.789125i
$172$	−5.28842	+	13.6015i	−0.403238	+	1.03710i
$173$	8.34381	−	8.34381i	0.634368	−	0.634368i	−0.314792	−	0.949161i	$-0.601935\pi$
$173$	8.34381	−	8.34381i	0.634368	−	0.634368i	0.949161	+	0.314792i	$0.101935\pi$
$174$	2.10488	+	14.7179i	0.159571	+	1.11576i
$175$		−	2.33502i		−	0.176511i
$176$	1.00174	+	22.8820i	0.0755086	+	1.72479i
$177$	14.9247	−	13.0942i	1.12181	−	0.984223i
$178$	−1.83905	+	2.81858i	−0.137842	+	0.211262i
$179$	−11.2866	−	11.2866i	−0.843598	−	0.843598i	0.145727	−	0.989325i	$-0.453448\pi$
$179$	−11.2866	−	11.2866i	−0.843598	−	0.843598i	−0.989325	+	0.145727i	$0.953448\pi$
$180$	2.88337	−	5.26177i	0.214914	−	0.392189i
$181$	−13.4827	+	13.4827i	−1.00216	+	1.00216i	−0.00216261	+	0.999998i	$0.500688\pi$
$181$	−13.4827	+	13.4827i	−1.00216	+	1.00216i	−0.999998	+	0.00216261i	$0.999312\pi$
$182$	3.81203	−	0.801701i	0.282567	−	0.0594260i
$183$	12.1246	+	13.8195i	0.896277	+	1.02157i
$184$	2.13180	−	12.9192i	0.157158	−	0.952415i
$185$	−1.59316			−0.117132
$186$	−12.9787	−	9.73086i	−0.951642	−	0.713501i
$187$	18.4445	+	18.4445i	1.34879	+	1.34879i
$188$	2.97449	+	6.75897i	0.216937	+	0.492949i
$189$	−11.9015	−	2.35940i	−0.865708	−	0.171621i
$190$	−4.36408	+	6.68853i	−0.316604	+	0.485237i
$191$	13.8582			1.00274			0.501371	−	0.865232i	$-0.332829\pi$
$191$	13.8582			1.00274			0.501371	+	0.865232i	$0.332829\pi$
$192$	12.8037	+	5.29762i	0.924029	+	0.382323i
$193$	−21.0706			−1.51669			−0.758346	−	0.651852i	$-0.773992\pi$
$193$	−21.0706			−1.51669			−0.758346	+	0.651852i	$0.773992\pi$
$194$	5.45925	−	8.36703i	0.391952	−	0.600718i
$195$	0.133194	−	2.03885i	0.00953824	−	0.146005i
$196$	1.24681	+	2.83313i	0.0890576	+	0.202367i
$197$	1.32560	+	1.32560i	0.0944450	+	0.0944450i	0.752751	−	0.658306i	$-0.228727\pi$
$197$	1.32560	+	1.32560i	0.0944450	+	0.0944450i	−0.658306	+	0.752751i	$0.728727\pi$
$198$	−1.86428	−	24.2216i	−0.132488	−	1.72135i
$199$	8.01961			0.568495			0.284248	−	0.958751i	$-0.408256\pi$
$199$	8.01961			0.568495			0.284248	+	0.958751i	$0.408256\pi$
$200$	0.460493	−	2.79069i	0.0325617	−	0.197332i
$201$	5.26144	−	4.61615i	0.371113	−	0.325598i
$202$	2.29782	−	0.483250i	0.161674	−	0.0340014i
$203$	10.0218	−	10.0218i	0.703389	−	0.703389i
$204$	14.8274	−	5.40132i	1.03813	−	0.378168i
$205$	−0.891935	−	0.891935i	−0.0622954	−	0.0622954i
$206$	−7.53834	+	11.5535i	−0.525221	+	0.804971i
$207$	−1.80687	+	13.7701i	−0.125586	+	0.957090i
$208$	4.71404	−	0.206373i	0.326860	−	0.0143094i
$209$			32.3357i			2.23671i
$210$	−5.66200	+	0.809751i	−0.390715	+	0.0558781i
$211$	−9.19540	+	9.19540i	−0.633037	+	0.633037i	−0.948829	−	0.315791i	$-0.897730\pi$
$211$	−9.19540	+	9.19540i	−0.633037	+	0.633037i	0.315791	+	0.948829i	$0.397730\pi$
$212$	4.41201	−	11.3474i	0.303018	−	0.779345i
$213$	1.06332	−	16.2765i	0.0728573	−	1.11525i
$214$	3.35436	+	15.9498i	0.229299	+	1.09030i
$215$		−	7.29672i		−	0.497632i
$216$	−13.7587	−	5.16694i	−0.936163	−	0.351566i
$217$			15.4634i			1.04972i
$218$	−22.2037	+	4.66961i	−1.50382	+	0.316266i
$219$	−0.0491251	+	0.751973i	−0.00331956	+	0.0508136i
$220$	−4.61285	−	10.4818i	−0.310998	−	0.706684i
$221$	3.79984	−	3.79984i	0.255605	−	0.255605i
$222$	0.552486	+	3.86313i	0.0370804	+	0.259277i
$223$			10.4693i			0.701077i	0.936548	+	0.350538i	$0.114001\pi$
$223$			10.4693i			0.701077i	−0.936548	+	0.350538i	$0.885999\pi$
$224$	−3.28121	−	12.7948i	−0.219235	−	0.854892i
$225$	−0.390304	+	2.97450i	−0.0260202	+	0.198300i
$226$	−15.8350	−	10.3319i	−1.05333	−	0.687268i
$227$	9.14639	+	9.14639i	0.607067	+	0.607067i	0.942178	−	0.335112i	$-0.108774\pi$
$227$	9.14639	+	9.14639i	0.607067	+	0.607067i	−0.335112	+	0.942178i	$0.608774\pi$
$228$	17.7319	+	8.26262i	1.17432	+	0.547205i
$229$	4.20638	−	4.20638i	0.277965	−	0.277965i	−0.554331	−	0.832296i	$-0.687026\pi$
$229$	4.20638	−	4.20638i	0.277965	−	0.277965i	0.832296	+	0.554331i	$0.187026\pi$
$230$	1.34740	+	6.40679i	0.0888449	+	0.422451i
$231$	−17.4078	+	15.2729i	−1.14535	+	1.00488i
$232$	13.9538	−	10.0010i	0.916115	−	0.656601i
$233$	−12.0946			−0.792341			−0.396170	−	0.918177i	$-0.629661\pi$
$233$	−12.0946			−0.792341			−0.396170	+	0.918177i	$0.629661\pi$
$234$	−4.99002	+	0.384070i	−0.326208	+	0.0251074i
$235$	−2.61083	−	2.61083i	−0.170312	−	0.170312i
$236$	−21.3678	−	8.30803i	−1.39092	−	0.540807i
$237$	1.77264	−	27.1344i	0.115146	−	1.76257i
$238$	−12.5986	−	8.22020i	−0.816643	−	0.532837i
$239$	−7.62398			−0.493154			−0.246577	−	0.969123i	$-0.579306\pi$
$239$	−7.62398			−0.493154			−0.246577	+	0.969123i	$0.579306\pi$
$240$	−6.92660	−	0.148842i	−0.447110	−	0.00960768i
$241$	6.89332			0.444038			0.222019	−	0.975042i	$-0.428735\pi$
$241$	6.89332			0.444038			0.222019	+	0.975042i	$0.428735\pi$
$242$	−25.8042	−	16.8365i	−1.65876	−	1.08229i
$243$	14.7665	+	4.99492i	0.947274	+	0.320425i
$244$	7.69283	−	19.7855i	0.492483	−	1.26664i
$245$	−1.09437	−	1.09437i	−0.0699167	−	0.0699167i
$246$	−1.85347	+	2.47209i	−0.118173	+	0.157615i
$247$	6.66165			0.423871
$248$	−3.04956	+	18.4810i	−0.193647	+	1.17354i
$249$	5.23465	+	5.96640i	0.331733	+	0.378105i
$250$	0.291053	+	1.38394i	0.0184078	+	0.0875280i
$251$	−19.4059	+	19.4059i	−1.22489	+	1.22489i	−0.259014	+	0.965874i	$0.583397\pi$
$251$	−19.4059	+	19.4059i	−1.22489	+	1.22489i	−0.965874	+	0.259014i	$0.916603\pi$
$252$	3.92699	+	13.4485i	0.247377	+	0.847177i
$253$	18.7438	+	18.7438i	1.17841	+	1.17841i
$254$	−3.44128	−	2.24534i	−0.215925	−	0.140885i
$255$	−5.93111	+	5.20369i	−0.371421	+	0.325868i
$256$	−1.39823	−	15.9388i	−0.0873893	−	0.996174i
$257$		−	0.630711i		−	0.0393427i	−0.999807	−	0.0196713i	$-0.993738\pi$
$257$		−	0.630711i		−	0.0393427i	0.999807	−	0.0196713i	$-0.00626198\pi$
$258$	−17.6932	+	2.53039i	−1.10153	+	0.157535i
$259$	2.63049	−	2.63049i	0.163451	−	0.163451i
$260$	−2.15942	+	0.950317i	−0.133921	+	0.0589362i
$261$	−14.4415	+	11.0912i	−0.893907	+	0.686528i
$262$	1.50214	−	0.315911i	0.0928023	−	0.0195171i
$263$			26.0577i			1.60679i	0.595448	+	0.803394i	$0.296974\pi$
$263$			26.0577i			1.60679i	−0.595448	+	0.803394i	$0.703026\pi$
$264$	−23.8168	+	14.8202i	−1.46583	+	0.912123i
$265$			6.08749i			0.373951i
$266$	−3.83793	−	18.2491i	−0.235318	−	1.11892i
$267$	−4.11309	−	0.268701i	−0.251717	−	0.0164442i
$268$	−7.53285	−	2.92886i	−0.460142	−	0.178908i
$269$	14.3628	−	14.3628i	0.875714	−	0.875714i	−0.117374	−	0.993088i	$-0.537448\pi$
$269$	14.3628	−	14.3628i	0.875714	−	0.875714i	0.993088	+	0.117374i	$0.0374476\pi$
$270$	7.34798	−	0.0850976i	0.447184	−	0.00517887i
$271$		−	9.19991i		−	0.558855i	−0.960167	−	0.279427i	$-0.909855\pi$
$271$		−	9.19991i		−	0.558855i	0.960167	−	0.279427i	$-0.0901446\pi$
$272$	−13.4360	−	12.3089i	−0.814676	−	0.746337i
$273$	3.14644	+	3.58628i	0.190431	+	0.217051i
$274$	3.04518	−	4.66715i	0.183966	−	0.281953i
$275$	4.04887	+	4.04887i	0.244156	+	0.244156i
$276$	15.0680	−	5.48898i	0.906989	−	0.330397i
$277$	−5.81216	+	5.81216i	−0.349219	+	0.349219i	−0.859819	−	0.510600i	$-0.829423\pi$
$277$	−5.81216	+	5.81216i	−0.349219	+	0.349219i	0.510600	+	0.859819i	$0.329423\pi$
$278$	16.9982	−	3.57486i	1.01948	−	0.214406i
$279$	2.58474	−	19.6983i	0.154744	−	1.17931i
$280$	3.84741	+	5.36806i	0.229927	+	0.320803i
$281$	17.6560			1.05327			0.526634	−	0.850092i	$-0.323454\pi$
$281$	17.6560			1.05327			0.526634	+	0.850092i	$0.323454\pi$
$282$	−5.42538	+	7.23617i	−0.323077	+	0.430908i
$283$	−11.0458	−	11.0458i	−0.656604	−	0.656604i	0.297971	−	0.954575i	$-0.403690\pi$
$283$	−11.0458	−	11.0458i	−0.656604	−	0.656604i	−0.954575	+	0.297971i	$0.903690\pi$
$284$	−17.2391	+	7.58658i	−1.02295	+	0.450181i
$285$	−9.76043	−	0.637631i	−0.578158	−	0.0377700i
$286$	−5.21985	+	8.00011i	−0.308656	+	0.473056i
$287$	2.94537			0.173859
$288$	2.04113	+	16.8474i	0.120275	+	0.992741i
$289$	−3.75217			−0.220716
$290$	−4.69059	+	7.18895i	−0.275441	+	0.422150i
$291$	12.2098	+	0.797646i	0.715752	+	0.0467588i
$292$	0.796442	−	0.350499i	0.0466082	−	0.0205114i
$293$	13.0705	+	13.0705i	0.763584	+	0.763584i	0.976968	−	0.213384i	$-0.0684486\pi$
$293$	13.0705	+	13.0705i	0.763584	+	0.763584i	−0.213384	+	0.976968i	$0.568449\pi$
$294$	−2.27414	+	3.03316i	−0.132630	+	0.176897i
$295$	11.4630			0.667404
$296$	3.66258	−	2.62505i	0.212883	−	0.152578i
$297$	24.7281	−	16.5458i	1.43487	−	0.960084i
$298$	16.2874	−	3.42536i	0.943502	−	0.198426i
$299$	3.86151	−	3.86151i	0.223317	−	0.223317i
$300$	3.25487	−	1.18568i	0.187920	−	0.0684553i
$301$	12.0477	+	12.0477i	0.694417	+	0.694417i
$302$	6.26061	−	9.59521i	0.360258	−	0.552143i
$303$	1.89662	+	2.16174i	0.108958	+	0.124189i
$304$	−0.987954	−	22.5672i	−0.0566631	−	1.29432i
$305$			10.6142i			0.607768i
$306$	14.6748	+	12.5773i	0.838904	+	0.718996i
$307$	4.54167	−	4.54167i	0.259207	−	0.259207i	−0.565525	−	0.824731i	$-0.691326\pi$
$307$	4.54167	−	4.54167i	0.259207	−	0.259207i	0.824731	+	0.565525i	$0.191326\pi$
$308$	24.9230	+	9.69033i	1.42012	+	0.552158i
$309$	−16.8598	−	1.10142i	−0.959120	−	0.0626576i
$310$	−1.92747	−	9.16497i	−0.109473	−	0.520535i
$311$		−	6.61127i		−	0.374891i	−0.982275	−	0.187445i	$-0.939979\pi$
$311$		−	6.61127i		−	0.374891i	0.982275	−	0.187445i	$-0.0600207\pi$
$312$	3.05320	+	4.90664i	0.172853	+	0.277784i
$313$			4.90590i			0.277298i	0.990342	+	0.138649i	$0.0442760\pi$
$313$			4.90590i			0.277298i	−0.990342	+	0.138649i	$0.955724\pi$
$314$	5.50443	−	1.15763i	0.310633	−	0.0653286i
$315$	−4.26680	−	5.55566i	−0.240407	−	0.313026i
$316$	−28.7390	+	12.6475i	−1.61670	+	0.711477i
$317$	−4.98437	+	4.98437i	−0.279950	+	0.279950i	−0.833089	−	0.553139i	$-0.813430\pi$
$317$	−4.98437	+	4.98437i	−0.279950	+	0.279950i	0.553139	+	0.833089i	$0.313430\pi$
$318$	14.7611	−	2.11105i	0.827759	−	0.118382i
$319$			34.7550i			1.94590i
$320$	3.53957	+	7.17436i	0.197868	+	0.401059i
$321$	−15.0052	+	13.1649i	−0.837508	+	0.734792i
$322$	−12.8030	−	8.35361i	−0.713484	−	0.465528i
$323$	−18.1907	−	18.1907i	−1.01216	−	1.01216i
$324$	−2.75451	−	17.7880i	−0.153029	−	0.988222i
$325$	0.834130	−	0.834130i	0.0462692	−	0.0462692i
$326$	5.74720	+	27.3275i	0.318308	+	1.51353i
$327$	−18.3269	−	20.8888i	−1.01348	−	1.15515i
$328$	3.52014	+	0.580859i	0.194367	+	0.0320726i
$329$	8.62152			0.475320
$330$	8.41369	−	11.2219i	0.463158	−	0.617743i
$331$	3.16037	+	3.16037i	0.173710	+	0.173710i	0.788607	−	0.614898i	$-0.210803\pi$
$331$	3.16037	+	3.16037i	0.173710	+	0.173710i	−0.614898	+	0.788607i	$0.710803\pi$
$332$	3.32129	−	8.54216i	0.182279	−	0.468812i
$333$	−3.79058	+	2.91120i	−0.207723	+	0.159533i
$334$	−5.53847	−	3.61370i	−0.303052	−	0.197733i
$335$	4.04110			0.220789
$336$	11.6823	−	11.1908i	0.637324	−	0.610510i
$337$	−27.2432			−1.48403			−0.742016	−	0.670382i	$-0.766130\pi$
$337$	−27.2432			−1.48403			−0.742016	+	0.670382i	$0.766130\pi$
$338$	−13.7490	−	8.97086i	−0.747849	−	0.487951i
$339$	1.50958	−	23.1077i	0.0819894	−	1.25504i
$340$	8.49163	+	3.30164i	0.460523	+	0.179057i
$341$	−26.8132	−	26.8132i	−1.45201	−	1.45201i
$342$	1.83863	+	23.8884i	0.0994217	+	1.29174i
$343$	19.9590			1.07768
$344$	12.0228	+	16.7747i	0.648225	+	0.904429i
$345$	−6.02737	+	5.28815i	−0.324503	+	0.284704i
$346$	−3.43441	−	16.3304i	−0.184635	−	0.877927i
$347$	−2.00841	+	2.00841i	−0.107817	+	0.107817i	−0.758957	−	0.651140i	$-0.774291\pi$
$347$	−2.00841	+	2.00841i	−0.107817	+	0.107817i	0.651140	+	0.758957i	$0.274291\pi$
$348$	19.0585	+	8.88080i	1.02164	+	0.476061i
$349$	15.7596	+	15.7596i	0.843592	+	0.843592i	0.989324	−	0.145732i	$-0.0465536\pi$
$349$	15.7596	+	15.7596i	0.843592	+	0.843592i	−0.145732	+	0.989324i	$0.546554\pi$
$350$	−2.76560	−	1.80447i	−0.147827	−	0.0964532i
$351$	−3.40869	−	5.09437i	−0.181942	−	0.271917i
$352$	27.8755	+	16.4964i	1.48577	+	0.879263i
$353$		−	13.9552i		−	0.742761i	−0.928481	−	0.371380i	$-0.878885\pi$
$353$		−	13.9552i		−	0.742761i	0.928481	−	0.371380i	$-0.121115\pi$
$354$	−3.97521	−	27.7958i	−0.211280	−	1.47733i
$355$	6.65904	−	6.65904i	0.353425	−	0.353425i
$356$	1.91713	+	4.35633i	0.101608	+	0.230885i
$357$	1.20105	−	18.3848i	0.0635661	−	0.973026i
$358$	−22.0899	+	4.64569i	−1.16749	+	0.245532i
$359$			17.2382i			0.909798i	0.890543	+	0.454899i	$0.150325\pi$
$359$			17.2382i			0.909798i	−0.890543	+	0.454899i	$0.849675\pi$
$360$	−4.00380	−	7.48128i	−0.211019	−	0.394298i
$361$		−	12.8908i		−	0.678466i
$362$	5.54963	+	26.3881i	0.291682	+	1.38693i
$363$	2.45997	−	37.6555i	0.129115	−	1.97640i
$364$	1.99636	−	5.13451i	0.104637	−	0.269122i
$365$	−0.307646	+	0.307646i	−0.0161029	+	0.0161029i
$366$	25.7375	−	3.68085i	1.34532	−	0.192401i
$367$		−	27.4809i		−	1.43449i	−0.696820	−	0.717246i	$-0.745402\pi$
$367$		−	27.4809i		−	1.43449i	0.696820	−	0.717246i	$-0.254598\pi$
$368$	−13.6540	−	12.5087i	−0.711766	−	0.652060i
$369$	−3.75200	−	0.492324i	−0.195321	−	0.0256294i
$370$	−1.23118	+	1.88694i	−0.0640058	+	0.0980975i
$371$	−10.0511	−	10.0511i	−0.521828	−	0.521828i
$372$	−21.5550	+	7.85203i	−1.11757	+	0.407109i
$373$	21.8128	−	21.8128i	1.12942	−	1.12942i	0.139152	−	0.990271i	$-0.455562\pi$
$373$	21.8128	−	21.8128i	1.12942	−	1.12942i	0.990271	−	0.139152i	$-0.0444376\pi$
$374$	36.0992	−	7.59196i	1.86665	−	0.392571i
$375$	−1.30198	+	1.14230i	−0.0672340	+	0.0589881i
$376$	10.3040	+	1.70026i	0.531387	+	0.0876843i
$377$	7.16006			0.368762
$378$	−11.9918	+	12.2728i	−0.616792	+	0.631246i
$379$	−2.07971	−	2.07971i	−0.106828	−	0.106828i	0.651673	−	0.758500i	$-0.274068\pi$
$379$	−2.07971	−	2.07971i	−0.106828	−	0.106828i	−0.758500	+	0.651673i	$0.774068\pi$
$380$	4.54939	+	10.3376i	0.233379	+	0.530309i
$381$	0.328064	−	5.02179i	0.0168073	−	0.257274i
$382$	10.7094	−	16.4136i	0.547941	−	0.839793i
$383$	22.2477			1.13681			0.568403	−	0.822750i	$-0.307561\pi$
$383$	22.2477			1.13681			0.568403	+	0.822750i	$0.307561\pi$
$384$	16.1690	−	11.0708i	0.825123	−	0.564953i
$385$	−13.3703			−0.681412
$386$	−16.2831	+	24.9559i	−0.828786	+	1.27022i
$387$	−13.3333	−	17.3609i	−0.677771	−	0.882505i
$388$	−5.69106	−	12.9319i	−0.288920	−	0.656516i
$389$	−14.3518	−	14.3518i	−0.727667	−	0.727667i	0.242488	−	0.970154i	$-0.422037\pi$
$389$	−14.3518	−	14.3518i	−0.727667	−	0.727667i	−0.970154	+	0.242488i	$0.922037\pi$
$390$	−2.31188	−	1.73335i	−0.117066	−	0.0877716i
$391$	−21.0890			−1.06651
$392$	4.31907	+	0.712692i	0.218146	+	0.0359964i
$393$	1.23986	+	1.41318i	0.0625426	+	0.0712854i
$394$	2.59444	−	0.545632i	0.130706	−	0.0274885i
$395$	11.1012	−	11.1012i	0.558562	−	0.558562i
$396$	−30.1287	−	16.5101i	−1.51403	−	0.829663i
$397$	9.21181	+	9.21181i	0.462328	+	0.462328i	0.899418	−	0.437090i	$-0.143991\pi$
$397$	9.21181	+	9.21181i	0.462328	+	0.462328i	−0.437090	+	0.899418i	$0.643991\pi$
$398$	6.19745	−	9.49841i	0.310650	−	0.476113i
$399$	17.1683	−	15.0627i	0.859492	−	0.754080i
$400$	−2.94943	−	2.70202i	−0.147471	−	0.135101i
$401$			9.32535i			0.465686i	0.972514	+	0.232843i	$0.0748028\pi$
$401$			9.32535i			0.465686i	−0.972514	+	0.232843i	$0.925197\pi$
$402$	−1.40139	−	9.79894i	−0.0698952	−	0.488727i
$403$	−5.52392	+	5.52392i	−0.275166	+	0.275166i
$404$	1.20337	−	3.09499i	0.0598697	−	0.153981i
$405$	4.50668	+	7.79037i	0.223939	+	0.387106i
$406$	−4.12507	−	19.6144i	−0.204724	−	0.973448i
$407$			9.12241i			0.452181i
$408$	5.06111	−	21.7356i	0.250562	−	1.07607i
$409$			17.7939i			0.879850i	0.898035	+	0.439925i	$0.144995\pi$
$409$			17.7939i			0.879850i	−0.898035	+	0.439925i	$0.855005\pi$
$410$	−1.74568	+	0.367131i	−0.0862131	+	0.0181313i
$411$	6.81066	+	0.444928i	0.335945	+	0.0219467i
$412$	7.85843	+	17.8568i	0.387157	+	0.879742i
$413$	−18.9267	+	18.9267i	−0.931324	+	0.931324i
$414$	14.9130	+	12.7814i	0.732933	+	0.628172i
$415$			4.58256i			0.224949i
$416$	3.39852	−	5.74278i	0.166626	−	0.281563i
$417$	14.0303	+	15.9915i	0.687065	+	0.783109i
$418$	38.2984	+	24.9886i	1.87323	+	1.22223i
$419$	24.3854	+	24.3854i	1.19130	+	1.19130i	0.976702	+	0.214601i	$0.0688452\pi$
$419$	24.3854	+	24.3854i	1.19130	+	1.19130i	0.214601	+	0.976702i	$0.431155\pi$
$420$	−3.41645	+	7.33183i	−0.166706	+	0.357757i
$421$	26.3102	−	26.3102i	1.28228	−	1.28228i	0.342917	−	0.939366i	$-0.388585\pi$
$421$	26.3102	−	26.3102i	1.28228	−	1.28228i	0.939366	−	0.342917i	$-0.111415\pi$
$422$	3.78493	+	17.9971i	0.184248	+	0.876085i
$423$	−10.9827	−	1.44110i	−0.533995	−	0.0700689i
$424$	−10.0303	−	13.9947i	−0.487117	−	0.679644i
$425$	−4.55545			−0.220972
$426$	−18.4562	−	13.8377i	−0.894206	−	0.670438i
$427$	−17.5252	−	17.5252i	−0.848106	−	0.848106i
$428$	21.4831	+	8.35286i	1.03842	+	0.403751i
$429$	−11.6744	−	0.762666i	−0.563644	−	0.0368219i
$430$	−8.64222	−	5.63881i	−0.416765	−	0.271927i
$431$	−5.13200			−0.247200			−0.123600	−	0.992332i	$-0.539444\pi$
$431$	−5.13200			−0.247200			−0.123600	+	0.992332i	$0.539444\pi$
$432$	−16.7523	+	12.3029i	−0.805995	+	0.591923i
$433$	25.8271			1.24117			0.620586	−	0.784138i	$-0.286895\pi$
$433$	25.8271			1.24117			0.620586	+	0.784138i	$0.286895\pi$
$434$	18.3148	+	11.9499i	0.879140	+	0.573614i
$435$	−10.4907	−	0.685337i	−0.502990	−	0.0328594i
$436$	−11.6280	+	29.9066i	−0.556882	+	1.43227i
$437$	−18.4859	−	18.4859i	−0.884302	−	0.884302i
$438$	0.852673	+	0.639299i	0.0407423	+	0.0305469i
$439$	−6.56874			−0.313509			−0.156755	−	0.987638i	$-0.550103\pi$
$439$	−6.56874			−0.313509			−0.156755	+	0.987638i	$0.550103\pi$
$440$	−15.9794	−	2.63677i	−0.761788	−	0.125703i
$441$	−4.60355	−	0.604062i	−0.219217	−	0.0287649i
$442$	−1.56406	−	7.43700i	−0.0743947	−	0.353742i
$443$	−22.2932	+	22.2932i	−1.05918	+	1.05918i	−0.0610464	+	0.998135i	$0.519444\pi$
$443$	−22.2932	+	22.2932i	−1.05918	+	1.05918i	−0.998135	+	0.0610464i	$0.980556\pi$
$444$	5.00244	+	2.33102i	0.237406	+	0.110625i
$445$	−1.68274	−	1.68274i	−0.0797697	−	0.0797697i
$446$	12.3998	+	8.09055i	0.587149	+	0.383098i
$447$	13.4435	+	15.3228i	0.635858	+	0.724744i
$448$	−17.6899	−	6.00144i	−0.835768	−	0.283541i
$449$			19.7304i			0.931133i	0.885013	+	0.465566i	$0.154149\pi$
$449$			19.7304i			0.931133i	−0.885013	+	0.465566i	$0.845851\pi$
$450$	3.22138	+	2.76093i	0.151857	+	0.130152i
$451$	−5.10719	+	5.10719i	−0.240488	+	0.240488i
$452$	−24.4742	+	10.7706i	−1.15117	+	0.506607i
$453$	14.0021	+	0.914731i	0.657875	+	0.0429778i
$454$	17.9012	−	3.76476i	0.840144	−	0.176689i
$455$			2.75448i			0.129132i
$456$	23.4892	−	14.6164i	1.09998	−	0.684474i
$457$		−	25.6189i		−	1.19840i	−0.800599	−	0.599201i	$-0.795485\pi$
$457$		−	25.6189i		−	1.19840i	0.800599	−	0.599201i	$-0.204515\pi$
$458$	−1.73140	−	8.23267i	−0.0809028	−	0.384687i
$459$	−4.60302	+	23.2190i	−0.214851	+	1.08377i
$460$	8.62945	+	3.35523i	0.402350	+	0.156438i
$461$	13.1368	−	13.1368i	0.611841	−	0.611841i	−0.331585	−	0.943425i	$-0.607583\pi$
$461$	13.1368	−	13.1368i	0.611841	−	0.611841i	0.943425	+	0.331585i	$0.107583\pi$
$462$	4.63661	+	32.4205i	0.215715	+	1.50834i
$463$			13.7820i			0.640502i	0.947333	+	0.320251i	$0.103767\pi$
$463$			13.7820i			0.640502i	−0.947333	+	0.320251i	$0.896233\pi$
$464$	−1.06187	−	24.2556i	−0.0492961	−	1.12604i
$465$	8.62220	−	7.56474i	0.399845	−	0.350806i
$466$	−9.34652	+	14.3248i	−0.432969	+	0.663582i
$467$	−2.88901	−	2.88901i	−0.133687	−	0.133687i	0.637097	−	0.770784i	$-0.280135\pi$
$467$	−2.88901	−	2.88901i	−0.133687	−	0.133687i	−0.770784	+	0.637097i	$0.780135\pi$
$468$	−3.40133	+	6.20698i	−0.157227	+	0.286918i
$469$	−6.67231	+	6.67231i	−0.308099	+	0.308099i
$470$	−5.10987	+	1.07465i	−0.235701	+	0.0495698i
$471$	4.54334	+	5.17845i	0.209346	+	0.238610i
$472$	−26.3528	+	18.8876i	−1.21298	+	0.869374i
$473$	−41.7808			−1.92108
$474$	−30.7681	−	23.0686i	−1.41323	−	1.05958i
$475$	−3.99317	−	3.99317i	−0.183219	−	0.183219i
$476$	−19.4720	+	8.56924i	−0.892497	+	0.392771i
$477$	11.1237	+	14.4838i	0.509319	+	0.663169i
$478$	−5.89171	+	9.02983i	−0.269481	+	0.413015i
$479$	−18.1416			−0.828912			−0.414456	−	0.910069i	$-0.636028\pi$
$479$	−18.1416			−0.828912			−0.414456	+	0.910069i	$0.636028\pi$
$480$	−5.52908	+	8.08884i	−0.252367	+	0.369203i
$481$	1.87936			0.0856913
$482$	5.32707	−	8.16444i	0.242641	−	0.371880i
$483$	1.22054	−	18.6832i	0.0555364	−	0.850113i
$484$	−39.8823	+	17.5514i	−1.81283	+	0.797792i
$485$	4.99526	+	4.99526i	0.226823	+	0.226823i
$486$	17.3274	−	13.6295i	0.785986	−	0.618245i
$487$	17.2179			0.780218			0.390109	−	0.920769i	$-0.372437\pi$
$487$	17.2179			0.780218			0.390109	+	0.920769i	$0.372437\pi$
$488$	−17.4890	−	24.4014i	−0.791691	−	1.10460i
$489$	−25.7092	+	22.5561i	−1.16261	+	1.02002i
$490$	−2.14188	+	0.450455i	−0.0967605	+	0.0203495i
$491$	−9.13362	+	9.13362i	−0.412195	+	0.412195i	−0.882502	−	0.470308i	$-0.844143\pi$
$491$	−9.13362	+	9.13362i	−0.412195	+	0.412195i	0.470308	+	0.882502i	$0.344143\pi$
$492$	1.49560	+	4.10565i	0.0674270	+	0.185097i
$493$	−19.5517	−	19.5517i	−0.880564	−	0.880564i
$494$	5.14804	−	7.89005i	0.231621	−	0.354990i
$495$	17.0319	+	2.23487i	0.765528	+	0.100450i
$496$	19.5322	+	17.8938i	0.877022	+	0.803454i
$497$			21.9896i			0.986368i
$498$	11.1119	−	1.58916i	0.497935	−	0.0712121i
$499$	−10.6968	+	10.6968i	−0.478856	+	0.478856i	−0.904766	−	0.425909i	$-0.859954\pi$
$499$	−10.6968	+	10.6968i	−0.478856	+	0.478856i	0.425909	+	0.904766i	$0.359954\pi$
$500$	1.86406	+	0.724767i	0.0833632	+	0.0324126i
$501$	0.527993	−	8.08216i	0.0235890	−	0.361084i
$502$	7.98768	+	37.9809i	0.356508	+	1.69517i
$503$		−	19.7936i		−	0.882554i	−0.897371	−	0.441277i	$-0.854526\pi$
$503$		−	19.7936i		−	0.882554i	0.897371	−	0.441277i	$-0.145474\pi$
$504$	18.9631	+	5.74171i	0.844685	+	0.255756i
$505$			1.66035i			0.0738846i
$506$	36.6851	−	7.71517i	1.63085	−	0.342981i
$507$	1.31072	−	20.0637i	0.0582113	−	0.891059i
$508$	−5.31876	+	2.34068i	−0.235982	+	0.103851i
$509$	−22.4663	+	22.4663i	−0.995800	+	0.995800i	−0.999991	−	0.00419119i	$-0.998666\pi$
$509$	−22.4663	+	22.4663i	−0.995800	+	0.995800i	0.00419119	+	0.999991i	$0.498666\pi$
$510$	1.57976	+	11.0461i	0.0699531	+	0.489132i
$511$		−	1.01591i		−	0.0449414i
$512$	−19.9584	−	10.6612i	−0.882046	−	0.471164i
$513$	−24.3879	+	16.3182i	−1.07675	+	0.720465i
$514$	−0.747013	−	0.487405i	−0.0329493	−	0.0214985i
$515$	−6.89765	−	6.89765i	−0.303947	−	0.303947i
$516$	−10.6761	+	22.9113i	−0.469988	+	1.00861i
$517$	−14.9495	+	14.9495i	−0.657479	+	0.657479i
$518$	−1.08274	−	5.14836i	−0.0475729	−	0.226206i
$519$	15.3633	−	13.4791i	0.674373	−	0.591665i
$520$	−0.543215	+	3.29200i	−0.0238215	+	0.144364i
$521$	26.0736			1.14231			0.571153	−	0.820844i	$-0.306496\pi$
$521$	26.0736			1.14231			0.571153	+	0.820844i	$0.306496\pi$
$522$	1.97619	+	25.6756i	0.0864956	+	1.12379i
$523$	−26.7306	−	26.7306i	−1.16885	−	1.16885i	−0.982480	−	0.186365i	$-0.940329\pi$
$523$	−26.7306	−	26.7306i	−1.16885	−	1.16885i	−0.186365	−	0.982480i	$-0.559671\pi$
$524$	0.786667	−	2.02326i	0.0343657	−	0.0883866i
$525$	0.263650	−	4.03577i	0.0115066	−	0.176136i
$526$	30.8627	+	20.1371i	1.34568	+	0.878017i
$527$	30.1679			1.31414
$528$	−0.852263	+	39.6615i	−0.0370900	+	1.72605i
$529$	1.56878			0.0682078
$530$	7.21001	+	4.70433i	0.313183	+	0.204343i
$531$	27.2738	−	20.9465i	1.18358	−	0.908999i
$532$	−24.5801	−	9.55702i	−1.06568	−	0.414349i
$533$	1.05216	+	1.05216i	0.0455741	+	0.0455741i
$534$	−3.49679	+	4.66389i	−0.151321	+	0.201826i
$535$	−11.5249			−0.498265
$536$	−9.29023	+	6.65852i	−0.401277	+	0.287604i
$537$	−18.2330	−	20.7817i	−0.786810	−	0.896797i
$538$	−5.91189	−	28.1106i	−0.254880	−	1.21193i
$539$	−6.26633	+	6.26633i	−0.269910	+	0.269910i
$540$	5.57763	−	8.76870i	0.240023	−	0.377345i
$541$	−5.28038	−	5.28038i	−0.227021	−	0.227021i	0.584426	−	0.811447i	$-0.301320\pi$
$541$	−5.28038	−	5.28038i	−0.227021	−	0.227021i	−0.811447	+	0.584426i	$0.801320\pi$
$542$	−10.8964	−	7.10957i	−0.468039	−	0.305382i
$543$	−24.8254	+	21.7807i	−1.06536	+	0.934699i
$544$	−24.9618	+	6.40139i	−1.07023	+	0.274457i
$545$		−	16.0438i		−	0.687242i
$546$	6.67911	−	0.955212i	0.285840	−	0.0408793i
$547$	12.7903	−	12.7903i	0.546874	−	0.546874i	−0.378661	−	0.925535i	$-0.623616\pi$
$547$	12.7903	−	12.7903i	0.546874	−	0.546874i	0.925535	+	0.378661i	$0.123616\pi$
$548$	−3.17448	−	7.21342i	−0.135607	−	0.308142i
$549$	19.3954	+	25.2542i	0.827776	+	1.07782i
$550$	7.92440	−	1.66656i	0.337897	−	0.0710625i
$551$		−	34.2768i		−	1.46024i
$552$	5.14325	−	22.0884i	0.218911	−	0.940144i
$553$			36.6586i			1.55888i
$554$	2.39235	+	11.3755i	0.101641	+	0.483298i
$555$	−2.75357	−	0.179886i	−0.116883	−	0.00763574i
$556$	8.90193	−	22.8952i	0.377526	−	0.970974i
$557$	24.2208	−	24.2208i	1.02627	−	1.02627i	0.0266206	−	0.999646i	$-0.491525\pi$
$557$	24.2208	−	24.2208i	1.02627	−	1.02627i	0.999646	−	0.0266206i	$-0.00847461\pi$
$558$	−21.3332	−	18.2839i	−0.903105	−	0.774021i
$559$			8.60748i			0.364058i
$560$	9.33115	−	0.408503i	0.394313	−	0.0172624i
$561$	29.7962	+	33.9614i	1.25800	+	1.43385i
$562$	13.6443	−	20.9117i	0.575551	−	0.882108i
$563$	8.38227	+	8.38227i	0.353270	+	0.353270i	0.861325	−	0.508055i	$-0.169635\pi$
$563$	8.38227	+	8.38227i	0.353270	+	0.353270i	−0.508055	+	0.861325i	$0.669635\pi$
$564$	4.37785	+	12.0178i	0.184341	+	0.506042i
$565$	9.45379	−	9.45379i	0.397724	−	0.397724i
$566$	−21.6187	+	4.54658i	−0.908700	+	0.191107i
$567$	−20.3038	−	5.42173i	−0.852679	−	0.227691i
$568$	−4.33660	+	26.2808i	−0.181960	+	1.10272i
$569$	−16.2033			−0.679277			−0.339639	−	0.940556i	$-0.610305\pi$
$569$	−16.2033			−0.679277			−0.339639	+	0.940556i	$0.610305\pi$
$570$	−8.29794	+	11.0675i	−0.347563	+	0.463566i
$571$	26.8812	+	26.8812i	1.12494	+	1.12494i	0.990987	+	0.133955i	$0.0427678\pi$
$571$	26.8812	+	26.8812i	1.12494	+	1.12494i	0.133955	+	0.990987i	$0.457232\pi$
$572$	5.44149	+	12.3648i	0.227520	+	0.516996i
$573$	23.9520	+	1.56474i	1.00061	+	0.0653680i
$574$	2.27614	−	3.48849i	0.0950043	−	0.145607i
$575$	−4.62939			−0.193059
$576$	21.5314	+	10.6019i	0.897140	+	0.441746i
$577$	−32.6853			−1.36071			−0.680354	−	0.732884i	$-0.738174\pi$
$577$	−32.6853			−1.36071			−0.680354	+	0.732884i	$0.738174\pi$
$578$	−2.89963	+	4.44406i	−0.120609	+	0.184849i
$579$	−36.4176	−	2.37910i	−1.51347	−	0.0988720i
$580$	4.88976	+	11.1111i	0.203036	+	0.461362i
$581$	−7.56631	−	7.56631i	−0.313903	−	0.313903i
$582$	10.3803	−	13.8449i	0.430278	−	0.573889i
$583$	34.8568			1.44362
$584$	0.200350	−	1.21417i	0.00829054	−	0.0502425i
$585$	0.460417	−	3.50884i	0.0190359	−	0.145073i
$586$	25.5813	−	5.37995i	1.05675	−	0.222244i
$587$	−17.2406	+	17.2406i	−0.711594	+	0.711594i	−0.966869	−	0.255274i	$-0.917834\pi$
$587$	−17.2406	+	17.2406i	−0.711594	+	0.711594i	0.255274	+	0.966869i	$0.417834\pi$
$588$	1.83505	+	5.03747i	0.0756760	+	0.207742i
$589$	26.4443	+	26.4443i	1.08962	+	1.08962i
$590$	8.85849	−	13.5768i	0.364698	−	0.558949i
$591$	2.14144	+	2.44079i	0.0880873	+	0.100401i
$592$	−0.278718	−	6.36656i	−0.0114552	−	0.261664i
$593$		−	24.4626i		−	1.00456i	−0.864705	−	0.502279i	$-0.832495\pi$
$593$		−	24.4626i		−	1.00456i	0.864705	−	0.502279i	$-0.167505\pi$
$594$	−0.487266	−	42.0743i	−0.0199928	−	1.72633i
$595$	7.52156	−	7.52156i	0.308354	−	0.308354i
$596$	8.52967	−	21.9378i	0.349389	−	0.898608i
$597$	13.8608	+	0.905503i	0.567286	+	0.0370598i
$598$	−1.58944	−	7.55769i	−0.0649972	−	0.309057i
$599$		−	4.30406i		−	0.175859i	−0.996127	−	0.0879296i	$-0.971975\pi$
$599$		−	4.30406i		−	0.175859i	0.996127	−	0.0879296i	$-0.0280250\pi$
$600$	1.11100	−	4.77134i	0.0453564	−	0.194789i
$601$			33.9956i			1.38671i	0.720597	+	0.693354i	$0.243868\pi$
$601$			33.9956i			1.38671i	−0.720597	+	0.693354i	$0.756132\pi$
$602$	23.5795	−	4.95897i	0.961031	−	0.202112i
$603$	9.61491	−	7.38433i	0.391549	−	0.300713i
$604$	−6.52644	−	14.8301i	−0.265557	−	0.603429i
$605$	15.4056	−	15.4056i	0.626325	−	0.626325i
$606$	4.02604	−	0.575784i	0.163547	−	0.0233896i
$607$		−	38.0508i		−	1.54443i	−0.635359	−	0.772217i	$-0.719148\pi$
$607$		−	38.0508i		−	1.54443i	0.635359	−	0.772217i	$-0.280852\pi$
$608$	−27.4920	−	16.2695i	−1.11495	−	0.659815i
$609$	18.4528	−	16.1897i	0.747746	−	0.656040i
$610$	12.5715	+	8.20253i	0.509004	+	0.332111i
$611$	3.07983	+	3.07983i	0.124597	+	0.124597i
$612$	26.2371	−	7.66128i	1.06057	−	0.309689i
$613$	2.96495	−	2.96495i	0.119753	−	0.119753i	−0.644690	−	0.764444i	$-0.723014\pi$
$613$	2.96495	−	2.96495i	0.119753	−	0.119753i	0.764444	+	0.644690i	$0.223014\pi$
$614$	−1.86940	−	8.88889i	−0.0754430	−	0.358726i
$615$	−1.44088	−	1.64230i	−0.0581019	−	0.0662239i
$616$	30.7373	−	22.0302i	1.23844	−	0.887620i
$617$	0.422670			0.0170161			0.00850803	−	0.999964i	$-0.497292\pi$
$617$	0.422670			0.0170161			0.00850803	+	0.999964i	$0.497292\pi$
$618$	−14.3335	+	19.1175i	−0.576580	+	0.769020i
$619$	0.512577	+	0.512577i	0.0206022	+	0.0206022i	0.717333	−	0.696731i	$-0.245363\pi$
$619$	0.512577	+	0.512577i	0.0206022	+	0.0206022i	−0.696731	+	0.717333i	$0.745363\pi$
$620$	−12.3445	−	4.79968i	−0.495767	−	0.192760i
$621$	−4.67773	+	23.5958i	−0.187711	+	0.946867i
$622$	−7.83038	−	5.10910i	−0.313970	−	0.204856i
$623$	5.55679			0.222628
$624$	8.17089	+	0.175579i	0.327097	+	0.00702879i
$625$	−1.00000			−0.0400000
$626$	5.81055	+	3.79122i	0.232236	+	0.151528i
$627$	−3.65106	+	55.8879i	−0.145809	+	2.23195i
$628$	2.88266	−	7.41404i	0.115031	−	0.295853i
$629$	−5.13189	−	5.13189i	−0.204622	−	0.204622i
$630$	−9.87745	+	0.760243i	−0.393527	+	0.0302888i
$631$	−41.2239			−1.64110			−0.820550	−	0.571575i	$-0.806332\pi$
$631$	−41.2239			−1.64110			−0.820550	+	0.571575i	$0.806332\pi$
$632$	−7.22949	+	43.8123i	−0.287573	+	1.74276i
$633$	−16.9313	+	14.8548i	−0.672958	+	0.590424i
$634$	2.05163	+	9.75534i	0.0814805	+	0.387434i
$635$	2.05451	−	2.05451i	0.0815306	−	0.0815306i
$636$	8.90682	−	19.1144i	0.353178	−	0.757934i
$637$	1.29096	+	1.29096i	0.0511497	+	0.0511497i
$638$	41.1637	+	26.8582i	1.62969	+	1.06333i
$639$	3.67561	−	28.0118i	0.145405	−	1.10813i
$640$	11.2326	+	1.35199i	0.444009	+	0.0534420i
$641$		−	25.6742i		−	1.01407i	−0.861926	−	0.507035i	$-0.830742\pi$
$641$		−	25.6742i		−	1.01407i	0.861926	−	0.507035i	$-0.169258\pi$
$642$	3.99666	+	27.9458i	0.157736	+	1.10293i
$643$	−10.3387	+	10.3387i	−0.407717	+	0.407717i	−0.880942	−	0.473225i	$-0.843090\pi$
$643$	−10.3387	+	10.3387i	−0.407717	+	0.407717i	0.473225	+	0.880942i	$0.343090\pi$
$644$	−19.7880	+	8.70832i	−0.779757	+	0.343156i
$645$	0.823880	−	12.6114i	0.0324403	−	0.496573i
$646$	−35.6026	+	7.48751i	−1.40077	+	0.294592i
$647$			4.44482i			0.174744i	0.996176	+	0.0873720i	$0.0278469\pi$
$647$			4.44482i			0.174744i	−0.996176	+	0.0873720i	$0.972153\pi$
$648$	−23.1967	−	10.4839i	−0.911254	−	0.411846i
$649$		−	65.6371i		−	2.57648i
$650$	−0.343338	−	1.63255i	−0.0134668	−	0.0640338i
$651$	−1.74599	+	26.7264i	−0.0684307	+	1.04749i
$652$	36.8081	+	14.3114i	1.44152	+	0.560477i
$653$	3.67007	−	3.67007i	0.143621	−	0.143621i	−0.631640	−	0.775261i	$-0.717618\pi$
$653$	3.67007	−	3.67007i	0.143621	−	0.143621i	0.775261	+	0.631640i	$0.217618\pi$
$654$	−38.9034	+	5.56376i	−1.52124	+	0.217560i
$655$			1.08541i			0.0424103i
$656$	3.40829	−	3.72037i	0.133071	−	0.145256i
$657$	−0.169812	+	1.29414i	−0.00662501	+	0.0504891i
$658$	6.66260	−	10.2113i	0.259735	−	0.398079i
$659$	0.132121	+	0.132121i	0.00514672	+	0.00514672i	0.709675	−	0.704529i	$-0.248842\pi$
$659$	0.132121	+	0.132121i	0.00514672	+	0.00514672i	−0.704529	+	0.709675i	$0.748842\pi$
$660$	−6.78917	−	18.6373i	−0.264268	−	0.725455i
$661$	−34.7392	+	34.7392i	−1.35120	+	1.35120i	−0.466874	+	0.884324i	$0.654620\pi$
$661$	−34.7392	+	34.7392i	−1.35120	+	1.35120i	−0.884324	+	0.466874i	$0.845380\pi$
$662$	6.18543	−	1.30084i	0.240403	−	0.0505588i
$663$	6.99656	−	6.13848i	0.271724	−	0.238399i
$664$	−7.55067	−	10.5350i	−0.293023	−	0.408837i
$665$	13.1863			0.511344
$666$	0.518707	+	6.73929i	0.0200995	+	0.261142i
$667$	−19.8690	−	19.8690i	−0.769331	−	0.769331i
$668$	−8.56011	+	3.76714i	−0.331201	+	0.145755i
$669$	−1.18210	+	18.0948i	−0.0457027	+	0.699586i
$670$	3.12291	−	4.78628i	0.120649	−	0.184910i
$671$	60.7767			2.34626
$672$	−4.22645	−	22.4847i	−0.163039	−	0.867365i
$673$	−17.7433			−0.683955			−0.341978	−	0.939708i	$-0.611097\pi$
$673$	−17.7433			−0.683955			−0.341978	+	0.939708i	$0.611097\pi$
$674$	−21.0532	+	32.2668i	−0.810938	+	1.24287i
$675$	−1.01044	+	5.09696i	−0.0388919	+	0.196182i
$676$	−21.2502	+	9.35178i	−0.817314	+	0.359684i
$677$	24.6454	+	24.6454i	0.947201	+	0.947201i	0.998674	−	0.0514738i	$-0.0163919\pi$
$677$	24.6454	+	24.6454i	0.947201	+	0.947201i	−0.0514738	+	0.998674i	$0.516392\pi$
$678$	−26.2021	−	19.6453i	−1.00629	−	0.754472i
$679$	−16.4955			−0.633038
$680$	10.4727	−	7.50601i	0.401609	−	0.287842i
$681$	14.7756	+	16.8410i	0.566201	+	0.645350i
$682$	−52.4783	+	11.0366i	−2.00950	+	0.422614i
$683$	13.7216	−	13.7216i	0.525042	−	0.525042i	−0.394048	−	0.919090i	$-0.628926\pi$
$683$	13.7216	−	13.7216i	0.525042	−	0.525042i	0.919090	+	0.394048i	$0.128926\pi$
$684$	29.7142	+	16.2830i	1.13615	+	0.622594i
$685$	2.78637	+	2.78637i	0.106462	+	0.106462i
$686$	15.4241	−	23.6394i	0.588893	−	0.902557i
$687$	7.74511	−	6.79522i	0.295494	−	0.259254i
$688$	29.1589	−	1.27653i	1.11167	−	0.0486673i
$689$		−	7.18103i		−	0.273576i
$690$	1.60540	+	11.2254i	0.0611166	+	0.427344i
$691$	22.7012	−	22.7012i	0.863593	−	0.863593i	−0.128160	−	0.991753i	$-0.540907\pi$
$691$	22.7012	−	22.7012i	0.863593	−	0.863593i	0.991753	+	0.128160i	$0.0409072\pi$
$692$	−21.9958	−	8.55220i	−0.836153	−	0.325106i
$693$	−31.8116	+	24.4315i	−1.20842	+	0.928078i
$694$	0.826686	+	3.93083i	0.0313806	+	0.149212i
$695$			12.2825i			0.465901i
$696$	25.2466	−	15.7099i	0.956970	−	0.595483i
$697$		−	5.74619i		−	0.217652i
$698$	30.8445	−	6.48684i	1.16748	−	0.245531i
$699$	−20.9038	−	1.36561i	−0.790655	−	0.0516521i
$700$	−4.27443	+	1.88110i	−0.161558	+	0.0710987i
$701$	−13.0196	+	13.0196i	−0.491742	+	0.491742i	−0.908855	−	0.417113i	$-0.863042\pi$
$701$	−13.0196	+	13.0196i	−0.491742	+	0.491742i	0.417113	+	0.908855i	$0.363042\pi$
$702$	−8.66795	+	0.100384i	−0.327151	+	0.00378876i
$703$		−	8.99692i		−	0.339325i
$704$	41.0802	−	20.2675i	1.54827	−	0.763859i
$705$	−4.21767	−	4.80726i	−0.158847	−	0.181052i
$706$	−16.5285	−	10.7844i	−0.622059	−	0.405876i
$707$	−2.74142	−	2.74142i	−0.103102	−	0.103102i
$708$	−35.9933	−	16.7720i	−1.35271	−	0.630330i
$709$	30.9405	−	30.9405i	1.16200	−	1.16200i	0.177958	−	0.984038i	$-0.443051\pi$
$709$	30.9405	−	30.9405i	1.16200	−	1.16200i	0.984038	−	0.177958i	$-0.0569490\pi$
$710$	−2.74094	−	13.0330i	−0.102866	−	0.489119i
$711$	6.12756	−	46.6981i	0.229801	−	1.75131i
$712$	6.64116	+	1.09586i	0.248888	+	0.0410691i
$713$	30.6575			1.14813
$714$	−20.8468	−	15.6300i	−0.780171	−	0.584940i
$715$	−4.77620	−	4.77620i	−0.178620	−	0.178620i
$716$	−11.5685	+	29.7534i	−0.432334	+	1.11194i
$717$	−13.1770	−	0.860832i	−0.492105	−	0.0321484i
$718$	20.4169	+	13.3215i	0.761953	+	0.497153i
$719$	−10.7191			−0.399755			−0.199877	−	0.979821i	$-0.564054\pi$
$719$	−10.7191			−0.399755			−0.199877	+	0.979821i	$0.564054\pi$
$720$	−11.9549	−	1.03934i	−0.445533	−	0.0387340i
$721$	22.7776			0.848280
$722$	−15.2679	−	9.96188i	−0.568213	−	0.370743i
$723$	11.9142	+	0.778333i	0.443093	+	0.0289465i
$724$	35.5427	+	13.8194i	1.32094	+	0.513595i
$725$	−4.29193	−	4.29193i	−0.159398	−	0.159398i
$726$	−42.6981	−	32.0132i	−1.58467	−	1.18812i
$727$	−11.9145			−0.441883			−0.220942	−	0.975287i	$-0.570913\pi$
$727$	−11.9145			−0.441883			−0.220942	+	0.975287i	$0.570913\pi$
$728$	−4.53855	−	6.33237i	−0.168210	−	0.234693i
$729$	24.9580	+	10.3004i	0.924371	+	0.381495i
$730$	0.126631	+	0.602120i	0.00468681	+	0.0222855i
$731$	23.5041	−	23.5041i	0.869332	−	0.869332i
$732$	15.5300	−	33.3280i	0.574007	−	1.23184i
$733$	−2.21674	−	2.21674i	−0.0818772	−	0.0818772i	0.664982	−	0.746859i	$-0.268439\pi$
$733$	−2.21674	−	2.21674i	−0.0818772	−	0.0818772i	−0.746859	+	0.664982i	$0.768439\pi$
$734$	−32.5484	−	21.2369i	−1.20138	−	0.783868i
$735$	−1.76791	−	2.01504i	−0.0652102	−	0.0743258i
$736$	−25.3669	+	6.50528i	−0.935037	+	0.239788i
$737$		−	23.1392i		−	0.852345i
$738$	−3.48260	+	4.06340i	−0.128196	+	0.149576i
$739$	−12.7235	+	12.7235i	−0.468040	+	0.468040i	−0.901279	−	0.433239i	$-0.857371\pi$
$739$	−12.7235	+	12.7235i	−0.468040	+	0.468040i	0.433239	+	0.901279i	$0.357371\pi$
$740$	1.28345	+	2.91641i	0.0471807	+	0.107209i
$741$	11.5138	+	0.752174i	0.422969	+	0.0276318i
$742$	−19.6719	+	4.13716i	−0.722178	+	0.151880i
$743$			42.5407i			1.56067i	0.625365	+	0.780333i	$0.284950\pi$
$743$			42.5407i			1.56067i	−0.625365	+	0.780333i	$0.715050\pi$
$744$	−7.35746	+	31.5976i	−0.269738	+	1.15842i
$745$			11.7688i			0.431177i
$746$	−8.97840	−	42.6917i	−0.328722	−	1.56305i
$747$	8.37373	+	10.9032i	0.306379	+	0.398926i
$748$	18.9051	−	48.6228i	0.691239	−	1.77783i
$749$	19.0289	−	19.0289i	0.695300	−	0.695300i
$750$	0.346785	+	2.42482i	0.0126628	+	0.0885418i
$751$			6.32333i			0.230742i	0.993322	+	0.115371i	$0.0368056\pi$
$751$			6.32333i			0.230742i	−0.993322	+	0.115371i	$0.963194\pi$
$752$	9.97656	−	10.8901i	0.363808	−	0.397120i
$753$	−35.7316	+	31.3493i	−1.30213	+	1.14243i
$754$	5.53320	−	8.48036i	0.201507	−	0.308837i
$755$	5.72851	+	5.72851i	0.208482	+	0.208482i
$756$	5.26880	+	23.6874i	0.191624	+	0.861501i
$757$	−31.1767	+	31.1767i	−1.13314	+	1.13314i	−0.143486	+	0.989652i	$0.545831\pi$
$757$	−31.1767	+	31.1767i	−1.13314	+	1.13314i	−0.989652	+	0.143486i	$0.954169\pi$
$758$	−4.07039	+	0.856035i	−0.147843	+	0.0310926i
$759$	30.2798	+	34.5125i	1.09909	+	1.25273i
$760$	15.7596	+	2.60049i	0.571660	+	0.0943298i
$761$	−43.3580			−1.57172			−0.785862	−	0.618401i	$-0.787781\pi$
$761$	−43.3580			−1.57172			−0.785862	+	0.618401i	$0.787781\pi$
$762$	−5.69427	−	4.26933i	−0.206282	−	0.154662i
$763$	26.4901	+	26.4901i	0.959007	+	0.959007i
$764$	−11.1642	−	25.3684i	−0.403905	−	0.917798i
$765$	−10.8387	+	8.32420i	−0.391874	+	0.300962i
$766$	17.1928	−	26.3502i	0.621200	−	0.952071i
$767$	−13.5222			−0.488260
$768$	−0.616985	−	27.7059i	−0.0222635	−	0.999752i
$769$	4.36961			0.157572			0.0787860	−	0.996892i	$-0.474896\pi$
$769$	4.36961			0.157572			0.0787860	+	0.996892i	$0.474896\pi$
$770$	−10.3324	+	15.8357i	−0.372353	+	0.570680i
$771$	0.0712143	−	1.09010i	0.00256472	−	0.0392590i
$772$	16.9745	+	38.5713i	0.610924	+	1.38821i
$773$	34.9061	+	34.9061i	1.25548	+	1.25548i	0.953226	+	0.302258i	$0.0977405\pi$
$773$	34.9061	+	34.9061i	1.25548	+	1.25548i	0.302258	+	0.953226i	$0.402259\pi$
$774$	−30.8661	+	2.37568i	−1.10946	+	0.0853922i
$775$	6.62238			0.237883
$776$	−19.7145	−	3.25309i	−0.707708	−	0.116779i
$777$	4.84346	−	4.24944i	0.173758	−	0.152448i
$778$	−28.0892	+	5.90738i	−1.00705	+	0.211790i
$779$	5.03693	−	5.03693i	0.180467	−	0.180467i
$780$	−3.83956	+	1.39867i	−0.137478	+	0.0500806i
$781$	−38.1294	−	38.1294i	−1.36438	−	1.36438i
$782$	−16.2973	+	24.9777i	−0.582789	+	0.893202i
$783$	−26.2126	+	17.5391i	−0.936760	+	0.626795i
$784$	4.18183	−	4.56475i	0.149351	−	0.163027i
$785$			3.97737i			0.141958i
$786$	2.63191	−	0.376403i	0.0938772	−	0.0134258i
$787$	1.53303	−	1.53303i	0.0546467	−	0.0546467i	−0.679255	−	0.733902i	$-0.737697\pi$
$787$	1.53303	−	1.53303i	0.0546467	−	0.0546467i	0.733902	+	0.679255i	$0.237697\pi$
$788$	1.35871	−	3.49451i	0.0484019	−	0.124487i
$789$	−2.94221	+	45.0373i	−0.104745	+	1.60337i
$790$	−4.56938	−	21.7271i	−0.162571	−	0.773015i
$791$			31.2185i			1.11000i
$792$	−42.8376	+	22.9256i	−1.52217	+	0.814627i
$793$		−	12.5209i		−	0.444631i
$794$	18.0292	−	3.79169i	0.639833	−	0.134562i
$795$	−0.687345	+	10.5214i	−0.0243776	+	0.373156i
$796$	−6.46060	−	14.6805i	−0.228990	−	0.520337i
$797$	0.378298	−	0.378298i	0.0134000	−	0.0134000i	−0.700375	−	0.713775i	$-0.746984\pi$
$797$	0.378298	−	0.378298i	0.0134000	−	0.0134000i	0.713775	+	0.700375i	$0.246984\pi$
$798$	−4.57282	−	31.9744i	−0.161876	−	1.13188i
$799$		−	16.8200i		−	0.595047i
$800$	−5.47954	+	1.40521i	−0.193731	+	0.0496818i
$801$	−7.07859	−	0.928828i	−0.250110	−	0.0328185i
$802$	11.0449	+	7.20651i	0.390010	+	0.254471i
$803$	1.76157	+	1.76157i	0.0621645	+	0.0621645i
$804$	−12.6888	−	5.91268i	−0.447501	−	0.208524i
$805$	7.64363	−	7.64363i	0.269402	−	0.269402i
$806$	2.27371	+	10.8113i	0.0800881	+	0.380813i
$807$	26.4459	−	23.2024i	0.930938	−	0.816764i
$808$	−2.73575	−	3.81703i	−0.0962435	−	0.134283i
$809$	34.6827			1.21938			0.609690	−	0.792640i	$-0.291294\pi$
$809$	34.6827			1.21938			0.609690	+	0.792640i	$0.291294\pi$
$810$	12.7096	+	0.682588i	0.446570	+	0.0239837i
$811$	8.24229	+	8.24229i	0.289426	+	0.289426i	0.836853	−	0.547427i	$-0.184393\pi$
$811$	8.24229	+	8.24229i	0.289426	+	0.289426i	−0.547427	+	0.836853i	$0.684393\pi$
$812$	−26.4191	−	10.2720i	−0.927129	−	0.360478i
$813$	1.03877	−	15.9008i	0.0364313	−	0.557666i
$814$	10.8046	+	7.04968i	0.378700	+	0.247091i
$815$	−19.7462			−0.691679
$816$	−21.8325	−	22.7914i	−0.764290	−	0.797858i
$817$	41.2060			1.44162
$818$	21.0750	+	13.7509i	0.736871	+	0.480788i
$819$	5.03327	+	6.55367i	0.175877	+	0.229004i
$820$	−0.914211	+	2.35130i	−0.0319256	+	0.0821109i
$821$	20.9859	+	20.9859i	0.732412	+	0.732412i	0.971097	−	0.238685i	$-0.0767165\pi$
$821$	20.9859	+	20.9859i	0.732412	+	0.732412i	−0.238685	+	0.971097i	$0.576716\pi$
$822$	5.79016	−	7.72270i	0.201955	−	0.269360i
$823$	−8.09445			−0.282155			−0.141077	−	0.989999i	$-0.545057\pi$
$823$	−8.09445			−0.282155			−0.141077	+	0.989999i	$0.545057\pi$
$824$	27.2225	+	4.49199i	0.948340	+	0.156486i
$825$	6.54077	+	7.45510i	0.227721	+	0.259553i
$826$	7.79047	+	37.0432i	0.271065	+	1.28890i
$827$	1.90962	−	1.90962i	0.0664038	−	0.0664038i	−0.673125	−	0.739529i	$-0.735048\pi$
$827$	1.90962	−	1.90962i	0.0664038	−	0.0664038i	0.739529	+	0.673125i	$0.235048\pi$
$828$	26.6629	−	7.78561i	0.926598	−	0.270569i
$829$	−16.7258	−	16.7258i	−0.580911	−	0.580911i	0.354242	−	0.935154i	$-0.384739\pi$
$829$	−16.7258	−	16.7258i	−0.580911	−	0.580911i	−0.935154	+	0.354242i	$0.884739\pi$
$830$	5.42758	+	3.54134i	0.188394	+	0.122922i
$831$	−10.7018	+	9.38928i	−0.371241	+	0.325711i
$832$	−4.17541	−	8.46315i	−0.144756	−	0.293407i
$833$		−	7.05035i		−	0.244280i
$834$	29.7827	−	4.25938i	1.03129	−	0.147490i
$835$	3.30656	−	3.30656i	0.114428	−	0.114428i
$836$	59.1929	−	26.0497i	2.04723	−	0.900946i
$837$	6.69153	−	33.7540i	0.231293	−	1.16671i
$838$	47.7267	−	10.0373i	1.64869	−	0.346733i
$839$			32.0878i			1.10779i	0.832586	+	0.553896i	$0.186860\pi$
$839$			32.0878i			1.10779i	−0.832586	+	0.553896i	$0.813140\pi$
$840$	6.04362	+	9.71239i	0.208525	+	0.335109i
$841$		−	7.84134i		−	0.270391i
$842$	−10.8296	−	51.4940i	−0.373213	−	1.77460i
$843$	30.5160	+	1.99356i	1.05103	+	0.0686618i
$844$	24.2407	+	9.42505i	0.834399	+	0.324424i
$845$	8.20842	−	8.20842i	0.282378	−	0.282378i
$846$	−10.1941	+	11.8942i	−0.350480	+	0.408930i
$847$			50.8725i			1.74800i
$848$	−24.3267	+	1.06498i	−0.835381	+	0.0365716i
$849$	−17.8440	−	20.3384i	−0.612404	−	0.698011i
$850$	−3.52040	+	5.39547i	−0.120749	+	0.185063i
$851$	−5.21518	−	5.21518i	−0.178774	−	0.178774i
$852$	−30.6521	+	11.1659i	−1.05012	+	0.382538i
$853$	17.1882	−	17.1882i	0.588513	−	0.588513i	−0.348716	−	0.937229i	$-0.613382\pi$
$853$	17.1882	−	17.1882i	0.588513	−	0.588513i	0.937229	+	0.348716i	$0.113382\pi$
$854$	−34.3001	+	7.21359i	−1.17373	+	0.246844i
$855$	−16.7976	−	2.20412i	−0.574466	−	0.0753794i
$856$	26.4950	−	18.9896i	0.905579	−	0.649049i
$857$	6.92877			0.236682			0.118341	−	0.992973i	$-0.462242\pi$
$857$	6.92877			0.236682			0.118341	+	0.992973i	$0.462242\pi$
$858$	−9.92511	+	13.2377i	−0.338838	+	0.451929i
$859$	−13.5608	−	13.5608i	−0.462688	−	0.462688i	0.436847	−	0.899536i	$-0.356095\pi$
$859$	−13.5608	−	13.5608i	−0.462688	−	0.462688i	−0.899536	+	0.436847i	$0.856095\pi$
$860$	−13.3572	+	5.87824i	−0.455476	+	0.200446i
$861$	5.09067	+	0.332565i	0.173490	+	0.0113338i
$862$	−3.96594	+	6.07833i	−0.135081	+	0.207029i
$863$	−51.8572			−1.76524			−0.882620	−	0.470088i	$-0.844222\pi$
$863$	−51.8572			−1.76524			−0.882620	+	0.470088i	$0.844222\pi$
$864$	1.62556	+	29.3489i	0.0553028	+	0.998470i
$865$	11.7999			0.401210
$866$	19.9589	−	30.5896i	0.678230	−	1.03948i
$867$	−6.48512	−	0.423662i	−0.220246	−	0.0143883i
$868$	28.3069	−	12.4573i	0.960800	−	0.422829i
$869$	−63.5651	−	63.5651i	−2.15630	−	2.15630i
$870$	−8.91877	+	11.8955i	−0.302375	+	0.403296i
$871$	−4.76704			−0.161525
$872$	26.4354	+	36.8837i	0.895215	+	1.24904i
$873$	21.0130	+	2.75725i	0.711182	+	0.0933187i
$874$	−36.1804	+	7.60903i	−1.22382	+	0.257379i
$875$	1.65111	−	1.65111i	0.0558177	−	0.0558177i
$876$	1.41612	−	0.515863i	0.0478462	−	0.0174294i
$877$	−33.6449	−	33.6449i	−1.13611	−	1.13611i	−0.989141	−	0.146968i	$-0.953049\pi$
$877$	−33.6449	−	33.6449i	−1.13611	−	1.13611i	−0.146968	−	0.989141i	$-0.546951\pi$
$878$	−5.07624	+	7.78001i	−0.171315	+	0.262563i
$879$	21.1147	+	24.0663i	0.712182	+	0.811737i
$880$	−15.4717	+	16.8883i	−0.521550	+	0.569305i
$881$		−	19.3279i		−	0.651174i	−0.945512	−	0.325587i	$-0.894438\pi$
$881$		−	19.3279i		−	0.651174i	0.945512	−	0.325587i	$-0.105562\pi$
$882$	−4.27302	+	4.98563i	−0.143880	+	0.167875i
$883$	10.3149	−	10.3149i	0.347125	−	0.347125i	−0.511912	−	0.859038i	$-0.671063\pi$
$883$	10.3149	−	10.3149i	0.347125	−	0.347125i	0.859038	+	0.511912i	$0.171063\pi$
$884$	−10.0171	−	3.89474i	−0.336910	−	0.130994i
$885$	19.8123	+	1.29431i	0.665985	+	0.0435076i
$886$	9.17614	+	43.6319i	0.308278	+	1.46584i
$887$		−	5.42448i		−	0.182136i	−0.995845	−	0.0910681i	$-0.970972\pi$
$887$		−	5.42448i		−	0.182136i	0.995845	−	0.0910681i	$-0.0290281\pi$
$888$	6.62668	−	4.12351i	0.222377	−	0.138376i
$889$			6.78443i			0.227543i
$890$	−3.29344	+	0.692637i	−0.110396	+	0.0232172i
$891$	44.6074	−	25.8051i	1.49440	−	0.864504i
$892$	19.1649	−	8.43408i	0.641687	−	0.282394i
$893$	14.7439	−	14.7439i	0.493384	−	0.493384i
$894$	28.5373	−	4.08126i	0.954430	−	0.136498i
$895$		−	15.9616i		−	0.533538i
$896$	−20.7786	+	16.3140i	−0.694164	+	0.545014i
$897$	7.11011	−	6.23810i	0.237400	−	0.208284i
$898$	23.3686	+	15.2474i	0.779820	+	0.508811i
$899$	28.4228	+	28.4228i	0.947953	+	0.947953i
$900$	5.75948	−	1.68178i	0.191983	−	0.0560594i
$901$	−19.6090	+	19.6090i	−0.653270	+	0.653270i
$902$	2.10218	+	9.99573i	0.0699950	+	0.332821i
$903$	19.4625	+	22.1831i	0.647671	+	0.738208i
$904$	−6.15664	+	37.3106i	−0.204767	+	1.24093i
$905$	−19.0674			−0.633822
$906$	11.9040	−	15.8772i	0.395485	−	0.527483i
$907$	29.6790	+	29.6790i	0.985477	+	0.985477i	0.999896	−	0.0144194i	$-0.00459001\pi$
$907$	29.6790	+	29.6790i	0.985477	+	0.985477i	−0.0144194	+	0.999896i	$0.504590\pi$
$908$	9.37482	−	24.1115i	0.311114	−	0.800168i
$909$	3.03396	+	3.95043i	0.100630	+	0.131027i
$910$	3.26240	+	2.12863i	0.108148	+	0.0705633i
$911$	−48.5376			−1.60812			−0.804061	−	0.594547i	$-0.797331\pi$
$911$	−48.5376			−1.60812			−0.804061	+	0.594547i	$0.797331\pi$
$912$	0.840538	−	39.1159i	0.0278330	−	1.29526i
$913$	26.2396			0.868404
$914$	−30.3430	−	19.7979i	−1.00366	−	0.654858i
$915$	−1.19846	+	18.3453i	−0.0396200	+	0.606475i
$916$	−11.0888	−	4.31143i	−0.366383	−	0.142454i
$917$	−1.79213	−	1.79213i	−0.0591812	−	0.0591812i
$918$	23.9434	+	23.3951i	0.790249	+	0.772155i
$919$	−20.9845			−0.692216			−0.346108	−	0.938195i	$-0.612497\pi$
$919$	−20.9845			−0.692216			−0.346108	+	0.938195i	$0.612497\pi$
$920$	10.6426	−	7.62783i	0.350878	−	0.251482i
$921$	8.36247	−	7.33686i	0.275553	−	0.241758i
$922$	−5.40725	−	25.7111i	−0.178078	−	0.846750i
$923$	−7.85525	+	7.85525i	−0.258559	+	0.258559i
$924$	41.9819	+	19.5625i	1.38110	+	0.643560i
$925$	−1.12654	−	1.12654i	−0.0370403	−	0.0370403i
$926$	16.3233	+	10.6505i	0.536418	+	0.349998i
$927$	−29.0155	−	3.80731i	−0.952995	−	0.125049i
$928$	−29.5489	−	17.4867i	−0.969990	−	0.574030i
$929$		−	23.9126i		−	0.784546i	−0.919849	−	0.392273i	$-0.871689\pi$
$929$		−	23.9126i		−	0.784546i	0.919849	−	0.392273i	$-0.128311\pi$
$930$	−2.29654	−	16.0581i	−0.0753066	−	0.526564i
$931$	6.18012	−	6.18012i	0.202545	−	0.202545i
$932$	9.74338	+	22.1400i	0.319155	+	0.725220i
$933$	0.746486	−	11.4267i	0.0244388	−	0.374093i
$934$	−5.65433	+	1.18915i	−0.185015	+	0.0389102i
$935$			26.0844i			0.853051i
$936$	4.72303	+	8.82521i	0.154377	+	0.288461i
$937$			2.05837i			0.0672439i	0.999435	+	0.0336219i	$0.0107042\pi$
$937$			2.05837i			0.0672439i	−0.999435	+	0.0336219i	$0.989296\pi$
$938$	2.74640	+	13.0589i	0.0896731	+	0.426390i
$939$	−0.553931	+	8.47920i	−0.0180769	+	0.276708i
$940$	−2.67603	+	6.88260i	−0.0872825	+	0.224486i
$941$	−26.4283	+	26.4283i	−0.861538	+	0.861538i	−0.991517	−	0.129979i	$-0.958509\pi$
$941$	−26.4283	+	26.4283i	−0.861538	+	0.861538i	0.129979	+	0.991517i	$0.458509\pi$
$942$	9.64439	−	1.37929i	0.314231	−	0.0449397i
$943$		−	5.83945i		−	0.190159i
$944$	2.00541	+	45.8083i	0.0652706	+	1.49093i
$945$	−6.74729	−	10.0840i	−0.219489	−	0.328032i
$946$	−32.2876	+	49.4851i	−1.04976	+	1.60890i
$947$	−12.2254	−	12.2254i	−0.397271	−	0.397271i	0.479998	−	0.877270i	$-0.340637\pi$
$947$	−12.2254	−	12.2254i	−0.397271	−	0.397271i	−0.877270	+	0.479998i	$0.840637\pi$
$948$	−51.0997	+	18.6145i	−1.65964	+	0.604572i
$949$	0.362911	−	0.362911i	0.0117806	−	0.0117806i
$950$	−7.81538	+	1.64364i	−0.253564	+	0.0533266i
$951$	−9.17761	+	8.05203i	−0.297604	+	0.261105i
$952$	−4.89830	+	29.6848i	−0.158755	+	0.962090i
$953$	−3.93546			−0.127482			−0.0637411	−	0.997966i	$-0.520303\pi$
$953$	−3.93546			−0.127482			−0.0637411	+	0.997966i	$0.520303\pi$
$954$	25.7509	−	1.98198i	0.833715	−	0.0641690i
$955$	9.79921	+	9.79921i	0.317095	+	0.317095i
$956$	6.14188	+	13.9563i	0.198643	+	0.451378i
$957$	−3.92422	+	60.0693i	−0.126852	+	1.94177i
$958$	−14.0196	+	21.4869i	−0.452953	+	0.694211i
$959$	−9.20120			−0.297122
$960$	5.30761	+	12.7996i	0.171302	+	0.413105i
$961$	−12.8559			−0.414706
$962$	1.45234	−	2.22591i	0.0468254	−	0.0717662i
$963$	−27.4209	+	21.0595i	−0.883627	+	0.678633i
$964$	−5.55326	−	12.6187i	−0.178859	−	0.406422i
$965$	−14.8991	−	14.8991i	−0.479620	−	0.479620i
$966$	−21.1851	−	15.8837i	−0.681619	−	0.511050i
$967$	18.4417			0.593046			0.296523	−	0.955026i	$-0.404173\pi$
$967$	18.4417			0.593046			0.296523	+	0.955026i	$0.404173\pi$
$968$	−10.0326	+	60.8000i	−0.322461	+	1.95419i
$969$	−29.3863	−	33.4942i	−0.944024	−	1.07599i
$970$	9.77666	−	2.05611i	0.313910	−	0.0660177i
$971$	−17.6241	+	17.6241i	−0.565585	+	0.565585i	−0.930888	−	0.365304i	$-0.880965\pi$
$971$	−17.6241	+	17.6241i	−0.565585	+	0.565585i	0.365304	+	0.930888i	$0.380965\pi$
$972$	−2.75235	−	31.0552i	−0.0882816	−	0.996096i
$973$	−20.2797	−	20.2797i	−0.650138	−	0.650138i
$974$	13.3058	−	20.3929i	0.426345	−	0.653430i
$975$	1.53586	−	1.34750i	0.0491870	−	0.0431545i
$976$	−42.4162	+	1.85691i	−1.35771	+	0.0594384i
$977$			2.74811i			0.0879199i	0.999033	+	0.0439600i	$0.0139974\pi$
$977$			2.74811i			0.0879199i	−0.999033	+	0.0439600i	$0.986003\pi$
$978$	6.84769	+	47.8809i	0.218965	+	1.53106i
$979$	−9.63534	+	9.63534i	−0.307947	+	0.307947i
$980$	−1.12170	+	2.88495i	−0.0358314	+	0.0921564i
$981$	−29.3170	−	38.1727i	−0.936019	−	1.21876i
$982$	3.75951	+	17.8762i	0.119971	+	0.570452i
$983$		−	40.7967i		−	1.30121i	−0.759415	−	0.650607i	$-0.774515\pi$
$983$		−	40.7967i		−	1.30121i	0.759415	−	0.650607i	$-0.225485\pi$
$984$	6.01850	+	1.40140i	0.191863	+	0.0446750i
$985$			1.87468i			0.0597322i
$986$	−38.2663	+	8.04771i	−1.21865	+	0.256291i
$987$	14.9012	+	0.973466i	0.474309	+	0.0309858i
$988$	−5.36663	−	12.1947i	−0.170735	−	0.387964i
$989$	23.8856	−	23.8856i	0.759517	−	0.759517i
$990$	15.8090	−	18.4455i	0.502443	−	0.586236i
$991$			6.87918i			0.218524i	0.994013	+	0.109262i	$0.0348488\pi$
$991$			6.87918i			0.218524i	−0.994013	+	0.109262i	$0.965151\pi$
$992$	36.2876	−	9.30586i	1.15213	−	0.295461i
$993$	5.10543	+	5.81912i	0.162016	+	0.184664i
$994$	26.0445	+	16.9933i	0.826080	+	0.538994i
$995$	5.67072	+	5.67072i	0.179774	+	0.179774i
$996$	6.70490	−	14.3890i	0.212453	−	0.455932i
$997$	−30.0974	+	30.0974i	−0.953196	+	0.953196i	−0.998953	−	0.0457571i	$-0.985430\pi$
$997$	−30.0974	+	30.0974i	−0.953196	+	0.953196i	0.0457571	+	0.998953i	$0.485430\pi$
$998$	4.40295	+	20.9357i	0.139373	+	0.662708i
$999$	−6.88022	+	4.60362i	−0.217680	+	0.145652i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bk.b.131.19	yes	60
3.2	odd	2	inner	240.2.bk.b.131.12	yes	60
4.3	odd	2		960.2.bk.b.431.2		60
12.11	even	2		960.2.bk.b.431.17		60
16.5	even	4		960.2.bk.b.911.17		60
16.11	odd	4	inner	240.2.bk.b.11.12	✓	60
48.5	odd	4		960.2.bk.b.911.2		60
48.11	even	4	inner	240.2.bk.b.11.19	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bk.b.11.12	✓	60	16.11	odd	4	inner
240.2.bk.b.11.19	yes	60	48.11	even	4	inner
240.2.bk.b.131.12	yes	60	3.2	odd	2	inner
240.2.bk.b.131.19	yes	60	1.1	even	1	trivial
960.2.bk.b.431.2		60	4.3	odd	2
960.2.bk.b.431.17		60	12.11	even	2
960.2.bk.b.911.2		60	48.5	odd	4
960.2.bk.b.911.17		60	16.5	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.bk (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.772787 - 1.18440i) q^{2} +(1.72837 + 0.112911i) q^{3} +(-0.805601 - 1.83058i) q^{4} +(0.707107 + 0.707107i) q^{5} +(1.46939 - 1.95982i) q^{6} -2.33502 q^{7} +(-2.79069 - 0.460493i) q^{8} +(2.97450 + 0.390304i) q^{9} +O(q^{10})\)	\(q+(0.772787 - 1.18440i) q^{2} +(1.72837 + 0.112911i) q^{3} +(-0.805601 - 1.83058i) q^{4} +(0.707107 + 0.707107i) q^{5} +(1.46939 - 1.95982i) q^{6} -2.33502 q^{7} +(-2.79069 - 0.460493i) q^{8} +(2.97450 + 0.390304i) q^{9} +(1.38394 - 0.291053i) q^{10} +(4.04887 - 4.04887i) q^{11} +(-1.18568 - 3.25487i) q^{12} +(-0.834130 - 0.834130i) q^{13} +(-1.80447 + 2.76560i) q^{14} +(1.14230 + 1.30198i) q^{15} +(-2.70202 + 2.94943i) q^{16} +4.55545i q^{17} +(2.76093 - 3.22138i) q^{18} +(-3.99317 + 3.99317i) q^{19} +(0.724767 - 1.86406i) q^{20} +(-4.03577 - 0.263650i) q^{21} +(-1.66656 - 7.92440i) q^{22} +4.62939i q^{23} +(-4.77134 - 1.11100i) q^{24} +1.00000i q^{25} +(-1.63255 + 0.343338i) q^{26} +(5.09696 + 1.01044i) q^{27} +(1.88110 + 4.27443i) q^{28} +(-4.29193 + 4.29193i) q^{29} +(2.42482 - 0.346785i) q^{30} -6.62238i q^{31} +(1.40521 + 5.47954i) q^{32} +(7.45510 - 6.54077i) q^{33} +(5.39547 + 3.52040i) q^{34} +(-1.65111 - 1.65111i) q^{35} +(-1.68178 - 5.75948i) q^{36} +(-1.12654 + 1.12654i) q^{37} +(1.64364 + 7.81538i) q^{38} +(-1.34750 - 1.53586i) q^{39} +(-1.64770 - 2.29893i) q^{40} -1.26139 q^{41} +(-3.43106 + 4.57622i) q^{42} +(-5.15956 - 5.15956i) q^{43} +(-10.6735 - 4.14999i) q^{44} +(1.82730 + 2.37928i) q^{45} +(5.48304 + 3.57753i) q^{46} -3.69227 q^{47} +(-5.00310 + 4.79260i) q^{48} -1.54767 q^{49} +(1.18440 + 0.772787i) q^{50} +(-0.514362 + 7.87350i) q^{51} +(-0.854962 + 2.19891i) q^{52} +(4.30450 + 4.30450i) q^{53} +(5.13563 - 5.25598i) q^{54} +5.72597 q^{55} +(6.51632 + 1.07526i) q^{56} +(-7.35254 + 6.45079i) q^{57} +(1.76661 + 8.40011i) q^{58} +(8.10560 - 8.10560i) q^{59} +(1.46314 - 3.13994i) q^{60} +(7.50538 + 7.50538i) q^{61} +(-7.84354 - 5.11769i) q^{62} +(-6.94553 - 0.911368i) q^{63} +(7.57589 + 2.57018i) q^{64} -1.17964i q^{65} +(-1.98568 - 13.8844i) q^{66} +(2.85749 - 2.85749i) q^{67} +(8.33911 - 3.66988i) q^{68} +(-0.522709 + 8.00128i) q^{69} +(-3.23153 + 0.679616i) q^{70} -9.41730i q^{71} +(-8.12118 - 2.45895i) q^{72} +0.435077i q^{73} +(0.463696 + 2.20484i) q^{74} +(-0.112911 + 1.72837i) q^{75} +(10.5267 + 4.09290i) q^{76} +(-9.45421 + 9.45421i) q^{77} +(-2.86041 + 0.409081i) q^{78} -15.6995i q^{79} +(-3.99617 + 0.174946i) q^{80} +(8.69533 + 2.32192i) q^{81} +(-0.974783 + 1.49398i) q^{82} +(3.24036 + 3.24036i) q^{83} +(2.76859 + 7.60019i) q^{84} +(-3.22119 + 3.22119i) q^{85} +(-10.0982 + 2.12373i) q^{86} +(-7.90264 + 6.93342i) q^{87} +(-13.1636 + 9.43467i) q^{88} -2.37976 q^{89} +(4.23013 - 0.325583i) q^{90} +(1.94771 + 1.94771i) q^{91} +(8.47444 - 3.72944i) q^{92} +(0.747740 - 11.4459i) q^{93} +(-2.85333 + 4.37311i) q^{94} -5.64720 q^{95} +(1.81002 + 9.62932i) q^{96} +7.06437 q^{97} +(-1.19602 + 1.83306i) q^{98} +(13.6237 - 10.4631i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7}+O(q^{10}) \) 60 * q + 4 * q^3 + 8 * q^4 + 8 * q^6 + 16 * q^7	\( 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7} + 4 q^{12} + 16 q^{13} - 52 q^{16} - 20 q^{18} + 20 q^{19} - 16 q^{21} - 24 q^{22} - 28 q^{24} - 20 q^{27} - 56 q^{28} - 12 q^{34} + 12 q^{36} + 24 q^{37} - 80 q^{39} - 8 q^{40} + 36 q^{42} - 8 q^{45} + 36 q^{46} + 56 q^{48} + 28 q^{49} - 36 q^{51} - 24 q^{52} + 92 q^{54} - 80 q^{58} + 28 q^{60} + 20 q^{61} - 64 q^{64} + 24 q^{66} - 40 q^{67} + 12 q^{69} - 16 q^{70} - 56 q^{72} + 4 q^{75} - 20 q^{76} - 8 q^{78} - 28 q^{81} - 32 q^{82} + 16 q^{84} - 20 q^{85} - 24 q^{87} + 8 q^{88} + 32 q^{90} - 16 q^{91} - 48 q^{93} + 28 q^{94} + 72 q^{96} - 8 q^{97} + 32 q^{99}+O(q^{100}) \) 60 * q + 4 * q^3 + 8 * q^4 + 8 * q^6 + 16 * q^7 + 4 * q^12 + 16 * q^13 - 52 * q^16 - 20 * q^18 + 20 * q^19 - 16 * q^21 - 24 * q^22 - 28 * q^24 - 20 * q^27 - 56 * q^28 - 12 * q^34 + 12 * q^36 + 24 * q^37 - 80 * q^39 - 8 * q^40 + 36 * q^42 - 8 * q^45 + 36 * q^46 + 56 * q^48 + 28 * q^49 - 36 * q^51 - 24 * q^52 + 92 * q^54 - 80 * q^58 + 28 * q^60 + 20 * q^61 - 64 * q^64 + 24 * q^66 - 40 * q^67 + 12 * q^69 - 16 * q^70 - 56 * q^72 + 4 * q^75 - 20 * q^76 - 8 * q^78 - 28 * q^81 - 32 * q^82 + 16 * q^84 - 20 * q^85 - 24 * q^87 + 8 * q^88 + 32 * q^90 - 16 * q^91 - 48 * q^93 + 28 * q^94 + 72 * q^96 - 8 * q^97 + 32 * q^99

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