LMFDB - Embedded newform 360.2.bk.a.349.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(229,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("360.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bk (of order $6$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.32
Character	$\chi$	$=$	360.349
Dual form			360.2.bk.a.229.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.256155 + 1.39082i) q^{2} +(1.70505 + 0.304648i) q^{3} +(-1.86877 - 0.712532i) q^{4} +(-1.56778 - 1.59439i) q^{5} +(-0.860468 + 2.29338i) q^{6} +(4.00243 + 2.31080i) q^{7} +(1.46970 - 2.41661i) q^{8} +(2.81438 + 1.03888i) q^{9} +O(q^{10})$	\(q+(-0.256155 + 1.39082i) q^{2} +(1.70505 + 0.304648i) q^{3} +(-1.86877 - 0.712532i) q^{4} +(-1.56778 - 1.59439i) q^{5} +(-0.860468 + 2.29338i) q^{6} +(4.00243 + 2.31080i) q^{7} +(1.46970 - 2.41661i) q^{8} +(2.81438 + 1.03888i) q^{9} +(2.61910 - 1.77209i) q^{10} +(1.89283 + 1.09283i) q^{11} +(-2.96927 - 1.78422i) q^{12} +(-1.56540 - 2.71134i) q^{13} +(-4.23916 + 4.97474i) q^{14} +(-2.18741 - 3.19613i) q^{15} +(2.98460 + 2.66312i) q^{16} -2.09803i q^{17} +(-2.16581 + 3.64819i) q^{18} +7.51339i q^{19} +(1.79377 + 4.09663i) q^{20} +(6.12035 + 5.15936i) q^{21} +(-2.00479 + 2.35266i) q^{22} +(0.173434 - 0.100132i) q^{23} +(3.24212 - 3.67269i) q^{24} +(-0.0841378 + 4.99929i) q^{25} +(4.17198 - 1.48266i) q^{26} +(4.48216 + 2.62873i) q^{27} +(-5.83309 - 7.17021i) q^{28} +(-4.48703 - 2.59059i) q^{29} +(5.00556 - 2.22360i) q^{30} +(0.115444 + 0.199954i) q^{31} +(-4.46844 + 3.46887i) q^{32} +(2.89445 + 2.43997i) q^{33} +(2.91798 + 0.537420i) q^{34} +(-2.59061 - 10.0042i) q^{35} +(-4.51919 - 3.94676i) q^{36} -0.0984028 q^{37} +(-10.4498 - 1.92459i) q^{38} +(-1.84307 - 5.09987i) q^{39} +(-6.15717 + 1.44544i) q^{40} +(-2.10507 - 3.64609i) q^{41} +(-8.74351 + 7.19072i) q^{42} +(4.69577 - 8.13332i) q^{43} +(-2.75860 - 3.39095i) q^{44} +(-2.75595 - 6.11594i) q^{45} +(0.0948400 + 0.266865i) q^{46} +(-6.70474 - 3.87099i) q^{47} +(4.27757 + 5.44999i) q^{48} +(7.17962 + 12.4355i) q^{49} +(-6.93157 - 1.39761i) q^{50} +(0.639160 - 3.57724i) q^{51} +(0.993443 + 6.18227i) q^{52} +7.81882 q^{53} +(-4.80423 + 5.56052i) q^{54} +(-1.22516 - 4.73122i) q^{55} +(11.4667 - 6.27610i) q^{56} +(-2.28894 + 12.8107i) q^{57} +(4.75242 - 5.57706i) q^{58} +(0.434562 - 0.250894i) q^{59} +(1.81043 + 7.53142i) q^{60} +(-8.80696 - 5.08470i) q^{61} +(-0.307673 + 0.109342i) q^{62} +(8.86370 + 10.6615i) q^{63} +(-3.67997 - 7.10337i) q^{64} +(-1.86874 + 6.74663i) q^{65} +(-4.13499 + 3.40065i) q^{66} +(-2.36402 - 4.09460i) q^{67} +(-1.49491 + 3.92073i) q^{68} +(0.326218 - 0.117894i) q^{69} +(14.5777 - 1.04044i) q^{70} -12.8654 q^{71} +(6.64685 - 5.27441i) q^{72} -4.83099i q^{73} +(0.0252064 - 0.136861i) q^{74} +(-1.66648 + 8.49840i) q^{75} +(5.35353 - 14.0408i) q^{76} +(5.05062 + 8.74793i) q^{77} +(7.56512 - 1.25702i) q^{78} +(2.14223 - 3.71045i) q^{79} +(-0.433153 - 8.93378i) q^{80} +(6.84146 + 5.84760i) q^{81} +(5.61028 - 1.99381i) q^{82} +(-0.320637 + 0.555359i) q^{83} +(-7.76131 - 14.0026i) q^{84} +(-3.34507 + 3.28924i) q^{85} +(10.1091 + 8.61437i) q^{86} +(-6.86138 - 5.78404i) q^{87} +(5.42283 - 2.96811i) q^{88} -0.894402 q^{89} +(9.21213 - 2.26641i) q^{90} -14.4693i q^{91} +(-0.395455 + 0.0635467i) q^{92} +(0.135921 + 0.376102i) q^{93} +(7.10130 - 8.33353i) q^{94} +(11.9792 - 11.7793i) q^{95} +(-8.67569 + 4.55329i) q^{96} +(-12.2234 - 7.05717i) q^{97} +(-19.1346 + 6.80016i) q^{98} +(4.19184 + 5.04206i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 2 q^{4} - 8 q^{9}+O(q^{10}) $ 136 * q - 2 * q^4 - 8 * q^9	$ 136 q - 2 q^{4} - 8 q^{9} - 10 q^{14} + 2 q^{15} - 2 q^{16} - 2 q^{20} - 38 q^{24} - 2 q^{25} + 16 q^{26} - 12 q^{30} - 4 q^{31} + 8 q^{34} - 24 q^{36} + 4 q^{39} - 6 q^{40} - 4 q^{41} - 56 q^{44} - 28 q^{46} + 40 q^{49} - 12 q^{50} + 10 q^{54} - 28 q^{55} + 26 q^{56} - 58 q^{60} - 20 q^{64} + 18 q^{65} + 16 q^{66} - 6 q^{70} - 128 q^{71} + 36 q^{74} + 12 q^{76} - 4 q^{79} - 36 q^{80} - 16 q^{81} - 110 q^{84} + 44 q^{86} - 32 q^{89} + 32 q^{90} - 34 q^{94} + 8 q^{95} - 2 q^{96}+O(q^{100}) $ 136 * q - 2 * q^4 - 8 * q^9 - 10 * q^14 + 2 * q^15 - 2 * q^16 - 2 * q^20 - 38 * q^24 - 2 * q^25 + 16 * q^26 - 12 * q^30 - 4 * q^31 + 8 * q^34 - 24 * q^36 + 4 * q^39 - 6 * q^40 - 4 * q^41 - 56 * q^44 - 28 * q^46 + 40 * q^49 - 12 * q^50 + 10 * q^54 - 28 * q^55 + 26 * q^56 - 58 * q^60 - 20 * q^64 + 18 * q^65 + 16 * q^66 - 6 * q^70 - 128 * q^71 + 36 * q^74 + 12 * q^76 - 4 * q^79 - 36 * q^80 - 16 * q^81 - 110 * q^84 + 44 * q^86 - 32 * q^89 + 32 * q^90 - 34 * q^94 + 8 * q^95 - 2 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.256155	+	1.39082i	−0.181129	+	0.983459i
$2$	−0.256155	+	1.39082i	−0.181129	+	0.983459i
$3$	1.70505	+	0.304648i	0.984410	+	0.175889i
$3$	1.70505	+	0.304648i	0.984410	+	0.175889i
$4$	−1.86877	−	0.712532i	−0.934385	−	0.356266i
$5$	−1.56778	−	1.59439i	−0.701132	−	0.713031i
$5$	−1.56778	−	1.59439i	−0.701132	−	0.713031i
$6$	−0.860468	+	2.29338i	−0.351284	+	0.936269i
$7$	4.00243	+	2.31080i	1.51278	+	0.873401i	0.999888	+	0.0149451i	$0.00475734\pi$
$7$	4.00243	+	2.31080i	1.51278	+	0.873401i	0.512887	+	0.858456i	$0.328576\pi$
$8$	1.46970	−	2.41661i	0.519617	−	0.854399i
$9$	2.81438	+	1.03888i	0.938126	+	0.346293i
$10$	2.61910	−	1.77209i	0.828233	−	0.560384i
$11$	1.89283	+	1.09283i	0.570711	+	0.329500i	0.757433	−	0.652913i	$-0.226453\pi$
$11$	1.89283	+	1.09283i	0.570711	+	0.329500i	−0.186722	+	0.982413i	$0.559786\pi$
$12$	−2.96927	−	1.78422i	−0.857155	−	0.515059i
$13$	−1.56540	−	2.71134i	−0.434162	−	0.751991i	0.563064	−	0.826413i	$-0.309622\pi$
$13$	−1.56540	−	2.71134i	−0.434162	−	0.751991i	−0.997227	+	0.0744216i	$0.976289\pi$
$14$	−4.23916	+	4.97474i	−1.13296	+	1.32955i
$15$	−2.18741	−	3.19613i	−0.564787	−	0.825236i
$16$	2.98460	+	2.66312i	0.746149	+	0.665779i
$17$		−	2.09803i		−	0.508846i	−0.967093	−	0.254423i	$-0.918114\pi$
$17$		−	2.09803i		−	0.508846i	0.967093	−	0.254423i	$-0.0818856\pi$
$18$	−2.16581	+	3.64819i	−0.510487	+	0.859886i
$19$			7.51339i			1.72369i	0.507172	+	0.861845i	$0.330691\pi$
$19$			7.51339i			1.72369i	−0.507172	+	0.861845i	$0.669309\pi$
$20$	1.79377	+	4.09663i	0.401098	+	0.916035i
$21$	6.12035	+	5.15936i	1.33557	+	1.12586i
$22$	−2.00479	+	2.35266i	−0.427422	+	0.501589i
$23$	0.173434	−	0.100132i	0.0361635	−	0.0208790i	−0.481809	−	0.876276i	$-0.660020\pi$
$23$	0.173434	−	0.100132i	0.0361635	−	0.0208790i	0.517973	+	0.855397i	$0.326687\pi$
$24$	3.24212	−	3.67269i	0.661795	−	0.749685i
$25$	−0.0841378	+	4.99929i	−0.0168276	+	0.999858i
$26$	4.17198	−	1.48266i	0.818192	−	0.290774i
$27$	4.48216	+	2.62873i	0.862592	+	0.505900i
$28$	−5.83309	−	7.17021i	−1.10235	−	1.35504i
$29$	−4.48703	−	2.59059i	−0.833220	−	0.481060i	0.0217339	−	0.999764i	$-0.493081\pi$
$29$	−4.48703	−	2.59059i	−0.833220	−	0.481060i	−0.854954	+	0.518704i	$0.826415\pi$
$30$	5.00556	−	2.22360i	0.913886	−	0.405971i
$31$	0.115444	+	0.199954i	0.0207343	+	0.0359129i	0.876206	−	0.481936i	$-0.160066\pi$
$31$	0.115444	+	0.199954i	0.0207343	+	0.0359129i	−0.855472	+	0.517849i	$0.826733\pi$
$32$	−4.46844	+	3.46887i	−0.789916	+	0.613216i
$33$	2.89445	+	2.43997i	0.503858	+	0.424745i
$34$	2.91798	+	0.537420i	0.500430	+	0.0921668i
$35$	−2.59061	−	10.0042i	−0.437893	−	1.69103i
$36$	−4.51919	−	3.94676i	−0.753199	−	0.657793i
$37$	−0.0984028			−0.0161773			−0.00808866	−	0.999967i	$-0.502575\pi$
$37$	−0.0984028			−0.0161773			−0.00808866	+	0.999967i	$0.502575\pi$
$38$	−10.4498	−	1.92459i	−1.69518	−	0.312210i
$39$	−1.84307	−	5.09987i	−0.295127	−	0.816632i
$40$	−6.15717	+	1.44544i	−0.973534	+	0.228543i
$41$	−2.10507	−	3.64609i	−0.328757	−	0.569423i	0.653509	−	0.756919i	$-0.273296\pi$
$41$	−2.10507	−	3.64609i	−0.328757	−	0.569423i	−0.982265	+	0.187496i	$0.939963\pi$
$42$	−8.74351	+	7.19072i	−1.34915	+	1.10955i
$43$	4.69577	−	8.13332i	0.716099	−	1.24032i	−0.246436	−	0.969159i	$-0.579259\pi$
$43$	4.69577	−	8.13332i	0.716099	−	1.24032i	0.962534	−	0.271160i	$-0.0874073\pi$
$44$	−2.75860	−	3.39095i	−0.415874	−	0.511205i
$45$	−2.75595	−	6.11594i	−0.410833	−	0.911711i
$46$	0.0948400	+	0.266865i	0.0139834	+	0.0393471i
$47$	−6.70474	−	3.87099i	−0.977987	−	0.564641i	−0.0763255	−	0.997083i	$-0.524319\pi$
$47$	−6.70474	−	3.87099i	−0.977987	−	0.564641i	−0.901662	+	0.432442i	$0.857652\pi$
$48$	4.27757	+	5.44999i	0.617414	+	0.786638i
$49$	7.17962	+	12.4355i	1.02566	+	1.77649i
$50$	−6.93157	−	1.39761i	−0.980272	−	0.197653i
$51$	0.639160	−	3.57724i	0.0895003	−	0.500914i
$52$	0.993443	+	6.18227i	0.137766	+	0.857327i
$53$	7.81882			1.07400			0.536999	−	0.843583i	$-0.319558\pi$
$53$	7.81882			1.07400			0.536999	+	0.843583i	$0.319558\pi$
$54$	−4.80423	+	5.56052i	−0.653772	+	0.756691i
$55$	−1.22516	−	4.73122i	−0.165200	−	0.637958i
$56$	11.4667	−	6.27610i	1.53230	−	0.838680i
$57$	−2.28894	+	12.8107i	−0.303177	+	1.69682i
$58$	4.75242	−	5.57706i	0.624023	−	0.732304i
$59$	0.434562	−	0.250894i	0.0565751	−	0.0326637i	−0.471446	−	0.881895i	$-0.656268\pi$
$59$	0.434562	−	0.250894i	0.0565751	−	0.0326637i	0.528021	+	0.849231i	$0.322934\pi$
$60$	1.81043	+	7.53142i	0.233725	+	0.972303i
$61$	−8.80696	−	5.08470i	−1.12762	−	0.651030i	−0.184282	−	0.982873i	$-0.558996\pi$
$61$	−8.80696	−	5.08470i	−1.12762	−	0.651030i	−0.943334	+	0.331844i	$0.892329\pi$
$62$	−0.307673	+	0.109342i	−0.0390744	+	0.0138865i
$63$	8.86370	+	10.6615i	1.11672	+	1.34322i
$64$	−3.67997	−	7.10337i	−0.459996	−	0.887921i
$65$	−1.86874	+	6.74663i	−0.231788	+	0.836817i
$66$	−4.13499	+	3.40065i	−0.508983	+	0.418591i
$67$	−2.36402	−	4.09460i	−0.288811	−	0.500235i	0.684715	−	0.728811i	$-0.259926\pi$
$67$	−2.36402	−	4.09460i	−0.288811	−	0.500235i	−0.973526	+	0.228576i	$0.926593\pi$
$68$	−1.49491	+	3.92073i	−0.181285	+	0.475458i
$69$	0.326218	−	0.117894i	0.0392721	−	0.0141928i
$70$	14.5777	−	1.04044i	1.74237	−	0.124356i
$71$	−12.8654			−1.52684			−0.763421	−	0.645902i	$-0.776482\pi$
$71$	−12.8654			−1.52684			−0.763421	+	0.645902i	$0.776482\pi$
$72$	6.64685	−	5.27441i	0.783339	−	0.621595i
$73$		−	4.83099i		−	0.565425i	−0.959205	−	0.282712i	$-0.908766\pi$
$73$		−	4.83099i		−	0.565425i	0.959205	−	0.282712i	$-0.0912342\pi$
$74$	0.0252064	−	0.136861i	0.00293018	−	0.0159097i
$75$	−1.66648	+	8.49840i	−0.192429	+	0.981311i
$76$	5.35353	−	14.0408i	0.614092	−	1.61059i
$77$	5.05062	+	8.74793i	0.575572	+	0.996920i
$78$	7.56512	−	1.25702i	0.856581	−	0.142330i
$79$	2.14223	−	3.71045i	0.241020	−	0.417458i	−0.719985	−	0.693989i	$-0.755852\pi$
$79$	2.14223	−	3.71045i	0.241020	−	0.417458i	0.961005	+	0.276531i	$0.0891849\pi$
$80$	−0.433153	−	8.93378i	−0.0484280	−	0.998827i
$81$	6.84146	+	5.84760i	0.760162	+	0.649733i
$82$	5.61028	−	1.99381i	0.619552	−	0.220180i
$83$	−0.320637	+	0.555359i	−0.0351944	+	0.0609586i	−0.883086	−	0.469211i	$-0.844538\pi$
$83$	−0.320637	+	0.555359i	−0.0351944	+	0.0609586i	0.847892	+	0.530170i	$0.177872\pi$
$84$	−7.76131	−	14.0026i	−0.846829	−	1.52781i
$85$	−3.34507	+	3.28924i	−0.362823	+	0.356769i
$86$	10.1091	+	8.61437i	1.09010	+	0.928912i
$87$	−6.86138	−	5.78404i	−0.735617	−	0.620114i
$88$	5.42283	−	2.96811i	0.578076	−	0.316401i
$89$	−0.894402			−0.0948064			−0.0474032	−	0.998876i	$-0.515095\pi$
$89$	−0.894402			−0.0948064			−0.0474032	+	0.998876i	$0.515095\pi$
$90$	9.21213	−	2.26641i	0.971044	−	0.238900i
$91$		−	14.4693i		−	1.51679i
$92$	−0.395455	+	0.0635467i	−0.0412291	+	0.00662520i
$93$	0.135921	+	0.376102i	0.0140944	+	0.0389999i
$94$	7.10130	−	8.33353i	0.732444	−	0.859538i
$95$	11.9792	−	11.7793i	1.22904	−	1.20853i
$96$	−8.67569	+	4.55329i	−0.885458	+	0.464719i
$97$	−12.2234	−	7.05717i	−1.24110	−	0.716547i	−0.271779	−	0.962360i	$-0.587612\pi$
$97$	−12.2234	−	7.05717i	−1.24110	−	0.716547i	−0.969317	+	0.245813i	$0.920945\pi$
$98$	−19.1346	+	6.80016i	−1.93289	+	0.686920i
$99$	4.19184	+	5.04206i	0.421296	+	0.506746i
$100$	3.71939	−	9.28257i	0.371939	−	0.928257i
$101$	10.6281	+	6.13613i	1.05754	+	0.610568i	0.924749	−	0.380577i	$-0.124274\pi$
$101$	10.6281	+	6.13613i	1.05754	+	0.610568i	0.132786	+	0.991145i	$0.457608\pi$
$102$	4.81158	+	1.80528i	0.476417	+	0.178750i
$103$	7.06779	−	4.08059i	0.696410	−	0.402073i	−0.109599	−	0.993976i	$-0.534957\pi$
$103$	7.06779	−	4.08059i	0.696410	−	0.402073i	0.806009	+	0.591903i	$0.201623\pi$
$104$	−8.85291	−	0.201917i	−0.868099	−	0.0197996i
$105$	−1.36934	−	17.8469i	−0.133634	−	1.74168i
$106$	−2.00283	+	10.8746i	−0.194532	+	1.05623i
$107$	−13.8413			−1.33809			−0.669044	−	0.743223i	$-0.733296\pi$
$107$	−13.8413			−1.33809			−0.669044	+	0.743223i	$0.733296\pi$
$108$	−6.50307	−	8.10618i	−0.625758	−	0.780017i
$109$			7.69725i			0.737263i	0.929576	+	0.368631i	$0.120174\pi$
$109$			7.69725i			0.737263i	−0.929576	+	0.368631i	$0.879826\pi$
$110$	6.89412	−	0.492045i	0.657328	−	0.0469147i
$111$	−0.167782	−	0.0299782i	−0.0159251	−	0.00284541i
$112$	5.79170	+	17.5557i	0.547264	+	1.65886i
$113$	−13.1424	+	7.58775i	−1.23633	+	0.713795i	−0.968342	−	0.249627i	$-0.919692\pi$
$113$	−13.1424	+	7.58775i	−1.23633	+	0.713795i	−0.267988	+	0.963422i	$0.586359\pi$
$114$	−17.2311	−	6.46503i	−1.61384	−	0.605505i
$115$	−0.431555	−	0.119536i	−0.0402428	−	0.0111468i
$116$	6.53934	+	8.03836i	0.607163	+	0.746343i
$117$	−1.58886	−	9.25701i	−0.146890	−	0.855810i
$118$	0.237634	+	0.668666i	0.0218760	+	0.0615557i
$119$	4.84813	−	8.39720i	0.444427	−	0.769770i
$120$	−10.9386	+	0.588769i	−0.998555	+	0.0537470i
$121$	−3.11145	−	5.38919i	−0.282859	−	0.489927i
$122$	9.32786	−	10.9464i	0.844505	−	0.991044i
$123$	−2.47847	−	6.85806i	−0.223476	−	0.618370i
$124$	−0.0732638	−	0.455926i	−0.00657929	−	0.0409434i
$125$	8.10271	−	7.70364i	0.724729	−	0.689034i
$126$	−17.0987	+	9.59683i	−1.52328	+	0.854954i
$127$			12.4252i			1.10256i	0.834320	+	0.551280i	$0.185860\pi$
$127$			12.4252i			1.10256i	−0.834320	+	0.551280i	$0.814140\pi$
$128$	10.8222	−	3.29862i	0.956553	−	0.291559i
$129$	10.4843	−	12.4371i	0.923093	−	1.09503i
$130$	−8.90468	−	4.32726i	−0.780992	−	0.379526i
$131$	0.00857433	−	0.00495039i	0.000749143	−	0.000432518i	−0.499625	−	0.866242i	$-0.666529\pi$
$131$	0.00857433	−	0.00495039i	0.000749143	−	0.000432518i	0.500375	+	0.865809i	$0.333196\pi$
$132$	−3.67049	−	6.62213i	−0.319475	−	0.576383i
$133$	−17.3620	+	30.0718i	−1.50547	+	2.60755i
$134$	6.30041	−	2.23907i	0.544273	−	0.193427i
$135$	−2.83582	−	11.2676i	−0.244068	−	0.969758i
$136$	−5.07011	−	3.08347i	−0.434758	−	0.264405i
$137$	2.21400	+	1.27825i	0.189155	+	0.109208i	0.591587	−	0.806241i	$-0.298502\pi$
$137$	2.21400	+	1.27825i	0.189155	+	0.109208i	−0.402432	+	0.915450i	$0.631835\pi$
$138$	0.0804068	+	0.483911i	0.00684469	+	0.0411932i
$139$	1.74603	−	1.00807i	0.148096	−	0.0855033i	−0.424121	−	0.905606i	$-0.639417\pi$
$139$	1.74603	−	1.00807i	0.148096	−	0.0855033i	0.572217	+	0.820102i	$0.306084\pi$
$140$	−2.28709	+	20.5415i	−0.193295	+	1.73607i
$141$	−10.2526	−	8.64280i	−0.863427	−	0.727855i
$142$	3.29554	−	17.8935i	0.276555	−	1.50159i
$143$		−	6.84283i		−	0.572226i
$144$	5.63313	+	10.5957i	0.469428	+	0.882971i
$145$	2.90427	+	11.2155i	0.241187	+	0.931398i
$146$	6.71905	+	1.23748i	0.556072	+	0.102415i
$147$	8.45315	+	23.3903i	0.697204	+	1.92920i
$148$	0.183892	+	0.0701151i	0.0151158	+	0.00576343i
$149$	2.10492	−	1.21527i	0.172441	−	0.0995591i	−0.411295	−	0.911502i	$-0.634923\pi$
$149$	2.10492	−	1.21527i	0.172441	−	0.0995591i	0.583737	+	0.811943i	$0.301590\pi$
$150$	−11.3929	−	4.49469i	−0.930225	−	0.366990i
$151$	−7.97044	+	13.8052i	−0.648625	+	1.12345i	0.334826	+	0.942280i	$0.391322\pi$
$151$	−7.97044	+	13.8052i	−0.648625	+	1.12345i	−0.983451	+	0.181172i	$0.942011\pi$
$152$	18.1569	+	11.0424i	1.47272	+	0.895659i
$153$	2.17960	−	5.90464i	0.176210	−	0.477362i
$154$	−13.4606	+	4.78369i	−1.08468	+	0.385480i
$155$	0.137814	−	0.497546i	0.0110695	−	0.0399639i
$156$	−0.189546	+	10.8437i	−0.0151759	+	0.868192i
$157$	−4.41535	−	7.64760i	−0.352383	−	0.610345i	0.634283	−	0.773101i	$-0.281295\pi$
$157$	−4.41535	−	7.64760i	−0.352383	−	0.610345i	−0.986666	+	0.162755i	$0.947962\pi$
$158$	4.61183	+	3.92991i	0.366898	+	0.312647i
$159$	13.3315	+	2.38199i	1.05725	+	0.188904i
$160$	12.5362	+	1.68599i	0.991077	+	0.133289i
$161$	0.925542			0.0729430
$162$	−9.88544	+	8.01736i	−0.776674	+	0.629903i
$163$	16.5538			1.29660			0.648298	−	0.761386i	$-0.275481\pi$
$163$	16.5538			1.29660			0.648298	+	0.761386i	$0.275481\pi$
$164$	1.33594	+	8.31362i	0.104319	+	0.649185i
$165$	−0.647591	−	8.44021i	−0.0504149	−	0.657069i
$166$	−0.690272	−	0.588206i	−0.0535755	−	0.0456537i
$167$	−11.3110	+	6.53039i	−0.875268	+	0.505336i	−0.869095	−	0.494645i	$-0.835298\pi$
$167$	−11.3110	+	6.53039i	−0.875268	+	0.505336i	−0.00617297	+	0.999981i	$0.501965\pi$
$168$	21.4632	−	7.20777i	1.65592	−	0.556091i
$169$	1.59908	−	2.76968i	0.123006	−	0.213052i
$170$	−3.71789	−	5.49495i	−0.285150	−	0.421443i
$171$	−7.80550	+	21.1455i	−0.596901	+	1.61704i
$172$	−14.5706	+	11.8534i	−1.11100	+	0.903814i
$173$	−4.62414	+	8.00925i	−0.351567	+	0.608932i	−0.986524	−	0.163615i	$-0.947684\pi$
$173$	−4.62414	+	8.00925i	−0.351567	+	0.608932i	0.634957	+	0.772547i	$0.281018\pi$
$174$	9.80214	−	8.06135i	0.743098	−	0.611129i
$175$	−11.8891	+	19.8149i	−0.898734	+	1.49786i
$176$	2.73902	+	8.30249i	0.206461	+	0.625824i
$177$	0.817384	−	0.295399i	0.0614383	−	0.0222035i
$178$	0.229106	−	1.24395i	0.0171722	−	0.0932383i
$179$			1.48075i			0.110676i	0.998468	+	0.0553382i	$0.0176237\pi$
$179$			1.48075i			0.110676i	−0.998468	+	0.0553382i	$0.982376\pi$
$180$	0.792432	+	13.3930i	0.0590644	+	0.998254i
$181$		−	3.16795i		−	0.235472i	−0.993045	−	0.117736i	$-0.962436\pi$
$181$		−	3.16795i		−	0.235472i	0.993045	−	0.117736i	$-0.0375636\pi$
$182$	20.1242	+	3.70638i	1.49170	+	0.274735i
$183$	−13.4673	−	11.3527i	−0.995528	−	0.839215i
$184$	0.0129158	−	0.566286i	0.000952167	−	0.0417471i
$185$	0.154274	+	0.156892i	0.0113424	+	0.0115349i
$186$	−0.557907	+	0.0927022i	−0.0409078	+	0.00679726i
$187$	2.29278	−	3.97122i	0.167665	−	0.290404i
$188$	9.77142	+	12.0113i	0.712654	+	0.876016i
$189$	11.8650	+	20.8787i	0.863054	+	1.51870i
$190$	13.3144	+	19.6783i	0.965928	+	1.42762i
$191$	7.42363	−	12.8581i	0.537155	−	0.930380i	−0.461900	−	0.886932i	$-0.652832\pi$
$191$	7.42363	−	12.8581i	0.537155	−	0.930380i	0.999056	−	0.0434484i	$-0.0138344\pi$
$192$	−4.11050	−	13.2327i	−0.296650	−	0.954986i
$193$	−0.514796	+	0.297218i	−0.0370559	+	0.0213942i	−0.518413	−	0.855130i	$-0.673477\pi$
$193$	−0.514796	+	0.297218i	−0.0370559	+	0.0213942i	0.481358	+	0.876524i	$0.340144\pi$
$194$	12.9463	−	15.1928i	0.929493	−	1.09078i
$195$	−5.24163	+	10.9340i	−0.375361	+	0.783002i
$196$	−4.55638	−	28.3547i	−0.325456	−	2.02534i
$197$	7.77837			0.554186			0.277093	−	0.960843i	$-0.410629\pi$
$197$	7.77837			0.554186			0.277093	+	0.960843i	$0.410629\pi$
$198$	−8.08637	+	4.53855i	−0.574673	+	0.322541i
$199$	7.20235			0.510561			0.255280	−	0.966867i	$-0.417832\pi$
$199$	7.20235			0.510561			0.255280	+	0.966867i	$0.417832\pi$
$200$	11.9577	+	7.55078i	0.845534	+	0.533921i
$201$	−2.78335	−	7.70168i	−0.196323	−	0.543235i
$202$	−11.2567	+	13.2100i	−0.792019	+	0.929451i
$203$	−11.9727	−	20.7373i	−0.840316	−	1.45547i
$204$	−3.74334	+	6.22961i	−0.262086	+	0.436160i
$205$	−2.51299	+	9.07255i	−0.175515	+	0.633655i
$206$	3.86492	+	10.8753i	0.269282	+	0.757718i
$207$	0.592134	−	0.101633i	0.0411562	−	0.00706398i
$208$	2.54855	−	12.2611i	0.176710	−	0.850154i
$209$	−8.21084	+	14.2216i	−0.567956	+	0.983729i
$210$	25.1727	+	2.66707i	1.73708	+	0.184046i
$211$	−13.5190	+	7.80519i	−0.930686	+	0.537332i	−0.887028	−	0.461715i	$-0.847234\pi$
$211$	−13.5190	+	7.80519i	−0.930686	+	0.537332i	−0.0436573	+	0.999047i	$0.513901\pi$
$212$	−14.6116	−	5.57116i	−1.00353	−	0.382629i
$213$	−21.9361	−	3.91942i	−1.50304	−	0.268554i
$214$	3.54551	−	19.2508i	0.242366	−	1.31595i
$215$	−20.3296	+	5.26437i	−1.38647	+	0.359027i
$216$	12.9400	−	6.96817i	0.880458	−	0.474124i
$217$			1.06707i			0.0724375i
$218$	−10.7055	−	1.97169i	−0.725068	−	0.133540i
$219$	1.47175	−	8.23707i	0.0994517	−	0.556610i
$220$	−1.08162	+	9.71453i	−0.0729225	+	0.654953i
$221$	−5.68847	+	3.28424i	−0.382648	+	0.220922i
$222$	0.0846724	−	0.225675i	0.00568284	−	0.0151463i
$223$	−15.7400	−	9.08748i	−1.05403	−	0.608542i	−0.130253	−	0.991481i	$-0.541579\pi$
$223$	−15.7400	−	9.08748i	−1.05403	−	0.608542i	−0.923774	+	0.382938i	$0.874912\pi$
$224$	−25.9005	+	3.55823i	−1.73055	+	0.237744i
$225$	−5.43045	+	13.9825i	−0.362030	+	0.932166i
$226$	−7.18672	−	20.2223i	−0.478054	−	1.34517i
$227$	−9.87001	+	17.0954i	−0.655096	+	1.13466i	0.326774	+	0.945102i	$0.394038\pi$
$227$	−9.87001	+	17.0954i	−0.655096	+	1.13466i	−0.981870	+	0.189557i	$0.939295\pi$
$228$	13.4055	−	22.3093i	0.887802	−	1.47747i
$229$	−15.5917	+	9.00188i	−1.03033	+	0.594861i	−0.917079	−	0.398705i	$-0.869460\pi$
$229$	−15.5917	+	9.00188i	−1.03033	+	0.594861i	−0.113251	+	0.993566i	$0.536126\pi$
$230$	0.276798	−	0.569597i	0.0182515	−	0.0375581i
$231$	5.94651	+	16.4543i	0.391252	+	1.08261i
$232$	−12.8550	+	7.03599i	−0.843972	+	0.461936i
$233$		−	0.450632i		−	0.0295219i	−0.999891	−	0.0147609i	$-0.995301\pi$
$233$		−	0.450632i		−	0.0295219i	0.999891	−	0.0147609i	$-0.00469872\pi$
$234$	13.2818	+	0.161410i	0.868261	+	0.0105517i
$235$	4.33971	+	16.7588i	0.283091	+	1.09322i
$236$	−0.990866	+	0.159225i	−0.0644999	+	0.0103646i
$237$	4.78298	−	5.67387i	0.310688	−	0.368557i
$238$	10.4371	+	8.89386i	0.676539	+	0.576504i
$239$	12.7762	+	22.1290i	0.826422	+	1.43140i	0.900828	+	0.434176i	$0.142960\pi$
$239$	12.7762	+	22.1290i	0.826422	+	1.43140i	−0.0744065	+	0.997228i	$0.523706\pi$
$240$	1.98311	−	15.3645i	0.128009	−	0.991773i
$241$	3.39288	−	5.87664i	0.218555	−	0.378548i	−0.735812	−	0.677186i	$-0.763199\pi$
$241$	3.39288	−	5.87664i	0.218555	−	0.378548i	0.954366	+	0.298639i	$0.0965325\pi$
$242$	8.29242	−	2.94701i	0.533057	−	0.189441i
$243$	9.88356	+	12.0547i	0.634031	+	0.773308i
$244$	12.8352	+	15.7774i	0.821688	+	1.01004i
$245$	8.57088	−	30.9431i	0.547573	−	1.97688i
$246$	10.1732	−	1.69039i	0.648620	−	0.107775i
$247$	20.3714	−	11.7614i	1.29620	−	0.748361i
$248$	0.652879	+	0.0148908i	0.0414578	+	0.000945569i
$249$	−0.715890	+	0.849232i	−0.0453677	+	0.0538179i
$250$	8.63883	+	13.2428i	0.546368	+	0.837545i
$251$		−	21.1794i		−	1.33683i	−0.743787	−	0.668417i	$-0.766972\pi$
$251$		−	21.1794i		−	1.33683i	0.743787	−	0.668417i	$-0.233028\pi$
$252$	−8.96755	−	26.2396i	−0.564903	−	1.65294i
$253$	0.437709			0.0275185
$254$	−17.2813	−	3.18278i	−1.08432	−	0.199705i
$255$	−6.70556	+	4.58925i	−0.419919	+	0.287390i
$256$	1.81564	+	15.8966i	0.113477	+	0.993541i
$257$	18.5004	−	10.6812i	1.15403	−	0.666277i	0.204160	−	0.978937i	$-0.434554\pi$
$257$	18.5004	−	10.6812i	1.15403	−	0.666277i	0.949865	+	0.312661i	$0.101220\pi$
$258$	14.6122	+	17.7677i	0.909718	+	1.10617i
$259$	−0.393850	−	0.227389i	−0.0244727	−	0.0141293i
$260$	8.29943	−	11.2764i	0.514709	−	0.699330i
$261$	−9.93689	−	11.9524i	−0.615078	−	0.739833i
$262$	0.00468875	+	0.0131934i	0.000289672	+	0.000815093i
$263$	20.5261	+	11.8507i	1.26569	+	0.730748i	0.974170	−	0.225816i	$-0.0725047\pi$
$263$	20.5261	+	11.8507i	1.26569	+	0.730748i	0.291523	+	0.956564i	$0.405838\pi$
$264$	10.1504	−	3.40871i	0.624715	−	0.209792i
$265$	−12.2582	−	12.4662i	−0.753015	−	0.765794i
$266$	−37.3771	−	31.8504i	−2.29174	−	1.95287i
$267$	−1.52500	−	0.272478i	−0.0933284	−	0.0166754i
$268$	1.50027	+	9.33630i	0.0916437	+	0.570305i
$269$			12.2928i			0.749504i	0.927125	+	0.374752i	$0.122272\pi$
$269$			12.2928i			0.749504i	−0.927125	+	0.374752i	$0.877728\pi$
$270$	16.3976	−	1.05787i	0.997925	−	0.0643802i
$271$	−7.73588			−0.469921			−0.234961	−	0.972005i	$-0.575496\pi$
$271$	−7.73588			−0.469921			−0.234961	+	0.972005i	$0.575496\pi$
$272$	5.58729	−	6.26177i	0.338779	−	0.379675i
$273$	4.40803	−	24.6708i	0.266786	−	1.49315i
$274$	−2.34495	+	2.75184i	−0.141663	+	0.166245i
$275$	−5.62263	+	9.37088i	−0.339057	+	0.565086i
$276$	−0.693630	−	0.0121245i	−0.0417516	−	0.000729812i
$277$	2.39019	−	4.13992i	0.143612	−	0.248744i	−0.785242	−	0.619189i	$-0.787461\pi$
$277$	2.39019	−	4.13992i	0.143612	−	0.248744i	0.928854	+	0.370445i	$0.120795\pi$
$278$	0.954790	+	2.68663i	0.0572645	+	0.161134i
$279$	0.117174	+	0.682680i	0.00701503	+	0.0408710i
$280$	−27.9837	−	8.44275i	−1.67235	−	0.504551i
$281$	7.28700	−	12.6215i	0.434706	−	0.752933i	−0.562565	−	0.826753i	$-0.690186\pi$
$281$	7.28700	−	12.6215i	0.434706	−	0.752933i	0.997272	+	0.0738196i	$0.0235189\pi$
$282$	14.6469	−	12.0457i	0.872208	−	0.717309i
$283$	−11.9769	−	20.7446i	−0.711953	−	1.23314i	−0.964123	−	0.265456i	$-0.914477\pi$
$283$	−11.9769	−	20.7446i	−0.711953	−	1.23314i	0.252170	−	0.967683i	$-0.418856\pi$
$284$	24.0425	+	9.16700i	1.42666	+	0.543962i
$285$	24.0137	−	16.4349i	1.42245	−	0.973518i
$286$	9.51716	+	1.75283i	0.562761	+	0.103647i
$287$		−	19.4576i		−	1.14855i
$288$	−16.1796	+	5.12056i	−0.953393	+	0.301732i
$289$	12.5983			0.741075
$290$	−16.3427	+	1.16641i	−0.959678	+	0.0684939i
$291$	−18.6915	−	15.7566i	−1.09571	−	0.923671i
$292$	−3.44224	+	9.02801i	−0.201442	+	0.528324i
$293$	4.74433	+	8.21741i	0.277166	+	0.480066i	0.970679	−	0.240378i	$-0.0772713\pi$
$293$	4.74433	+	8.21741i	0.277166	+	0.480066i	−0.693513	+	0.720444i	$0.743938\pi$
$294$	−34.6971	+	5.76528i	−2.02357	+	0.336238i
$295$	−1.08132	−	0.299513i	−0.0629569	−	0.0174383i
$296$	−0.144623	+	0.237801i	−0.00840601	+	0.0138219i
$297$	5.61123	+	9.87399i	0.325597	+	0.572947i
$298$	1.15104	+	3.23886i	0.0666782	+	0.187622i
$299$	−0.542985	−	0.313493i	−0.0314017	−	0.0181298i
$300$	9.16965	−	14.6941i	0.529410	−	0.848366i
$301$	37.5890	−	21.7020i	2.16659	−	1.25088i
$302$	−17.1589	−	14.6217i	−0.987385	−	0.841386i
$303$	16.2521	+	13.7002i	0.933656	+	0.787058i
$304$	−20.0090	+	22.4244i	−1.14760	+	1.28613i
$305$	5.70039	+	22.0134i	0.326403	+	1.26048i
$306$	7.65399	+	4.54393i	0.437550	+	0.259759i
$307$	12.5350			0.715408			0.357704	−	0.933835i	$-0.383560\pi$
$307$	12.5350			0.715408			0.357704	+	0.933835i	$0.383560\pi$
$308$	−3.20527	−	19.9466i	−0.182637	−	1.13656i
$309$	13.2941	−	4.80442i	0.756273	−	0.273314i
$310$	0.656697	+	0.319124i	0.0372979	+	0.0181250i
$311$	13.4009	+	23.2110i	0.759896	+	1.31618i	0.942903	+	0.333066i	$0.108083\pi$
$311$	13.4009	+	23.2110i	0.759896	+	1.31618i	−0.183008	+	0.983111i	$0.558583\pi$
$312$	−15.0331	−	3.04130i	−0.851083	−	0.172180i
$313$	−24.5893	−	14.1966i	−1.38987	−	0.802441i	−0.396569	−	0.918005i	$-0.629799\pi$
$313$	−24.5893	−	14.1966i	−1.38987	−	0.802441i	−0.993300	+	0.115564i	$0.963132\pi$
$314$	11.7675	−	4.18199i	0.664076	−	0.236003i
$315$	3.10224	−	30.8471i	0.174792	−	1.73804i
$316$	−6.64715	+	5.40757i	−0.373931	+	0.304199i
$317$	−0.294763	+	0.510545i	−0.0165555	+	0.0286750i	−0.874184	−	0.485594i	$-0.838603\pi$
$317$	−0.294763	+	0.510545i	−0.0165555	+	0.0286750i	0.857629	+	0.514269i	$0.171937\pi$
$318$	−6.72784	+	17.9315i	−0.377279	+	1.00555i
$319$	−5.66213	−	9.80710i	−0.317019	−	0.549092i
$320$	−5.55614	+	17.0038i	−0.310598	+	0.950542i
$321$	−23.6001	−	4.21672i	−1.31723	−	0.235354i
$322$	−0.237082	+	1.28726i	−0.0132121	+	0.0717364i
$323$	15.7633			0.877093
$324$	−8.61851	−	15.8026i	−0.478806	−	0.877921i
$325$	13.6865	−	7.59774i	0.759191	−	0.421447i
$326$	−4.24035	+	23.0234i	−0.234851	+	1.27515i
$327$	−2.34495	+	13.1242i	−0.129676	+	0.725769i
$328$	−11.9050	−	0.271528i	−0.657342	−	0.0149926i
$329$	−17.8902	−	30.9867i	−0.986317	−	1.70835i
$330$	11.9047	+	1.26132i	0.655332	+	0.0694332i
$331$	20.5118	+	11.8425i	1.12743	+	0.650923i	0.943288	−	0.331977i	$-0.107715\pi$
$331$	20.5118	+	11.8425i	1.12743	+	0.650923i	0.184144	+	0.982899i	$0.441049\pi$
$332$	0.994907	−	0.809374i	0.0546026	−	0.0444202i
$333$	−0.276943	−	0.102229i	−0.0151764	−	0.00560209i
$334$	−6.18524	−	17.4043i	−0.338441	−	0.952322i
$335$	−2.82212	+	10.1886i	−0.154189	+	0.556662i
$336$	4.52681	+	31.6978i	0.246958	+	1.72926i
$337$	24.5827	−	14.1928i	1.33910	−	0.773132i	0.352430	−	0.935838i	$-0.385355\pi$
$337$	24.5827	−	14.1928i	1.33910	−	0.773132i	0.986675	+	0.162706i	$0.0520221\pi$
$338$	3.44252	+	2.93350i	0.187249	+	0.159561i
$339$	−24.7200	+	8.93368i	−1.34260	+	0.485211i
$340$	8.59485	−	3.76337i	0.466121	−	0.204097i
$341$			0.504641i			0.0273278i
$342$	−27.4102	−	16.2726i	−1.48218	−	0.879921i
$343$			34.0115i			1.83645i
$344$	−12.7537	−	23.3014i	−0.687631	−	1.25633i
$345$	−0.699407	−	0.335287i	−0.0376548	−	0.0180512i
$346$	−9.95494	−	8.48297i	−0.535181	−	0.456047i
$347$	−5.66681	−	9.81520i	−0.304210	−	0.526907i	0.672875	−	0.739756i	$-0.265059\pi$
$347$	−5.66681	−	9.81520i	−0.304210	−	0.526907i	−0.977085	+	0.212849i	$0.931726\pi$
$348$	8.70103	+	15.6980i	0.466424	+	0.841500i
$349$	−4.06099	−	2.34461i	−0.217380	−	0.125504i	0.387357	−	0.921930i	$-0.373388\pi$
$349$	−4.06099	−	2.34461i	−0.217380	−	0.125504i	−0.604736	+	0.796426i	$0.706722\pi$
$350$	−24.5135	−	21.6113i	−1.31030	−	1.15517i
$351$	0.111048	−	16.2677i	0.00592730	−	0.868305i
$352$	−12.2489	+	1.68276i	−0.652868	+	0.0896916i
$353$	4.10521	+	2.37014i	0.218498	+	0.126150i	0.605255	−	0.796032i	$-0.293071\pi$
$353$	4.10521	+	2.37014i	0.218498	+	0.126150i	−0.386756	+	0.922182i	$0.626405\pi$
$354$	0.201470	+	1.21250i	0.0107080	+	0.0644438i
$355$	20.1701	+	20.5124i	1.07052	+	1.08869i
$356$	1.67143	+	0.637290i	0.0885857	+	0.0337763i
$357$	10.8245	−	12.8407i	0.572892	−	0.679600i
$358$	−2.05946	−	0.379301i	−0.108846	−	0.0200467i
$359$	26.0996			1.37748			0.688742	−	0.725007i	$-0.258163\pi$
$359$	26.0996			1.37748			0.688742	+	0.725007i	$0.258163\pi$
$360$	−18.8302	−	2.32855i	−0.992441	−	0.122725i
$361$	−37.4510			−1.97110
$362$	4.40605	+	0.811486i	0.231577	+	0.0426507i
$363$	−3.66337	−	10.1367i	−0.192277	−	0.532040i
$364$	−10.3098	+	27.0397i	−0.540381	+	1.41727i
$365$	−7.70247	+	7.57393i	−0.403166	+	0.396437i
$366$	19.2393	−	15.8225i	1.00565	−	0.827055i
$367$	5.82958	+	3.36571i	0.304302	+	0.175689i	0.644374	−	0.764711i	$-0.277118\pi$
$367$	5.82958	+	3.36571i	0.304302	+	0.175689i	−0.340072	+	0.940399i	$0.610451\pi$
$368$	0.784294	+	0.163021i	0.0408841	+	0.00849803i
$369$	−2.13662	−	12.4484i	−0.111228	−	0.648037i
$370$	−0.257727	+	0.174379i	−0.0133986	+	0.00906552i
$371$	31.2943	+	18.0678i	1.62472	+	0.938031i
$372$	0.0139786	−	0.799696i	0.000724754	−	0.0414623i
$373$	7.68104	+	13.3040i	0.397709	+	0.688852i	0.993443	−	0.114330i	$-0.0364720\pi$
$373$	7.68104	+	13.3040i	0.397709	+	0.688852i	−0.595734	+	0.803182i	$0.703139\pi$
$374$	4.93595	+	4.20610i	0.255232	+	0.217492i
$375$	16.1624	−	10.6666i	0.834624	−	0.550821i
$376$	−19.2086	+	10.5135i	−0.990608	+	0.542194i
$377$			16.2212i			0.835432i
$378$	−32.0778	+	11.1540i	−1.64991	+	0.573698i
$379$			7.88904i			0.405233i	0.979258	+	0.202616i	$0.0649445\pi$
$379$			7.88904i			0.405233i	−0.979258	+	0.202616i	$0.935056\pi$
$380$	−30.7796	+	13.4773i	−1.57896	+	0.691369i
$381$	−3.78532	+	21.1856i	−0.193928	+	1.08537i
$382$	15.9817	+	13.6186i	0.817697	+	0.696789i
$383$	−7.33495	+	4.23484i	−0.374799	+	0.216390i	−0.675553	−	0.737312i	$-0.736095\pi$
$383$	−7.33495	+	4.23484i	−0.374799	+	0.216390i	0.300754	+	0.953702i	$0.402762\pi$
$384$	19.4572	−	2.32735i	0.992922	−	0.118767i
$385$	6.02933	−	21.7675i	0.307283	−	1.10937i
$386$	−0.281509	−	0.792124i	−0.0143284	−	0.0403180i
$387$	21.6652	−	18.0119i	1.10130	−	0.915596i
$388$	17.8142	+	21.8978i	0.904380	+	1.11169i
$389$	−4.38581	−	2.53215i	−0.222369	−	0.128385i	0.384678	−	0.923051i	$-0.374313\pi$
$389$	−4.38581	−	2.53215i	−0.222369	−	0.128385i	−0.607047	+	0.794666i	$0.707646\pi$
$390$	−13.8646	−	10.0910i	−0.702062	−	0.510977i
$391$	−0.210080	−	0.363869i	−0.0106242	−	0.0184017i
$392$	40.6035	+	0.926082i	2.05079	+	0.0467742i
$393$	0.0161278	−	0.00582851i	0.000813539	−	0.000294009i
$394$	−1.99247	+	10.8183i	−0.100379	+	0.545019i
$395$	−9.27443	+	2.40162i	−0.466647	+	0.120839i
$396$	−4.24095	−	12.4093i	−0.213116	−	0.623589i
$397$	−16.5579			−0.831016			−0.415508	−	0.909589i	$-0.636396\pi$
$397$	−16.5579			−0.831016			−0.415508	+	0.909589i	$0.636396\pi$
$398$	−1.84492	+	10.0172i	−0.0924773	+	0.502116i
$399$	−38.7643	+	45.9846i	−1.94064	+	2.30211i
$400$	−13.5648	+	14.6968i	−0.678240	+	0.734840i
$401$	4.23386	+	7.33326i	0.211429	+	0.366205i	0.952162	−	0.305594i	$-0.0988550\pi$
$401$	4.23386	+	7.33326i	0.211429	+	0.366205i	−0.740733	+	0.671799i	$0.765522\pi$
$402$	11.4246	−	1.89832i	0.569809	−	0.0946798i
$403$	0.361430	−	0.626016i	0.0180041	−	0.0311841i
$404$	−15.4893	−	19.0399i	−0.770620	−	0.947269i
$405$	−1.40257	−	20.0757i	−0.0696942	−	0.997568i
$406$	31.9087	−	11.3399i	1.58360	−	0.562789i
$407$	−0.186260	−	0.107537i	−0.00923258	−	0.00533043i
$408$	−7.70540	−	6.80206i	−0.381474	−	0.336752i
$409$	0.571613	+	0.990063i	0.0282645	+	0.0489555i	0.879812	−	0.475323i	$-0.157669\pi$
$409$	0.571613	+	0.990063i	0.0282645	+	0.0489555i	−0.851547	+	0.524278i	$0.824335\pi$
$410$	−11.9746	−	5.81910i	−0.591383	−	0.287385i
$411$	3.38555	+	2.85397i	0.166997	+	0.140776i
$412$	−16.1156	+	2.58966i	−0.793960	+	0.127583i
$413$	2.31907			0.114114
$414$	−0.0103248	+	0.849587i	−0.000507436	+	0.0417549i
$415$	1.38814	−	0.359461i	0.0681413	−	0.0176453i
$416$	16.4002	+	6.68532i	0.804085	+	0.327775i
$417$	3.28416	−	1.18688i	0.160826	−	0.0581219i
$418$	−17.6765	−	15.0628i	−0.864584	−	0.736743i
$419$	−10.0894	+	5.82511i	−0.492899	+	0.284575i	−0.725776	−	0.687931i	$-0.758519\pi$
$419$	−10.0894	+	5.82511i	−0.492899	+	0.284575i	0.232877	+	0.972506i	$0.425186\pi$
$420$	−10.1575	+	34.3275i	−0.495637	+	1.67501i
$421$	−7.47128	−	4.31355i	−0.364128	−	0.210229i	0.306762	−	0.951786i	$-0.400754\pi$
$421$	−7.47128	−	4.31355i	−0.364128	−	0.210229i	−0.670890	+	0.741557i	$0.734088\pi$
$422$	−7.39267	−	20.8018i	−0.359870	−	1.01262i
$423$	−14.8482	−	17.8598i	−0.721945	−	0.868375i
$424$	11.4913	−	18.8950i	0.558068	−	0.917623i
$425$	10.4887	+	0.176524i	0.508774	+	0.00856265i
$426$	11.0703	−	29.5052i	0.536356	−	1.42953i
$427$	−23.4995	−	40.7023i	−1.13722	−	1.96972i
$428$	25.8662	+	9.86236i	1.25029	+	0.476715i
$429$	2.08465	−	11.6674i	0.100648	−	0.563306i
$430$	−2.11427	−	29.6233i	−0.101959	−	1.42856i
$431$	−2.84066			−0.136830			−0.0684150	−	0.997657i	$-0.521794\pi$
$431$	−2.84066			−0.136830			−0.0684150	+	0.997657i	$0.521794\pi$
$432$	6.37682	+	19.7822i	0.306805	+	0.951772i
$433$			31.7616i			1.52637i	0.646183	+	0.763183i	$0.276364\pi$
$433$			31.7616i			1.52637i	−0.646183	+	0.763183i	$0.723636\pi$
$434$	−1.48411	−	0.273336i	−0.0712393	−	0.0131205i
$435$	1.53514	+	20.0078i	0.0736041	+	0.959300i
$436$	5.48453	−	14.3844i	0.262662	−	0.688887i
$437$	0.752332	+	1.30308i	0.0359889	+	0.0623346i
$438$	11.0793	+	4.15691i	0.529390	+	0.198625i
$439$	11.5938	−	20.0811i	0.553342	−	0.958417i	−0.444688	−	0.895685i	$-0.646686\pi$
$439$	11.5938	−	20.0811i	0.553342	−	0.958417i	0.998030	−	0.0627313i	$-0.0199811\pi$
$440$	−13.2341	−	3.99276i	−0.630912	−	0.190347i
$441$	7.28723	+	42.4568i	0.347011	+	2.02175i
$442$	−3.11066	−	8.75293i	−0.147959	−	0.416334i
$443$	14.1723	−	24.5472i	0.673347	−	1.16627i	−0.303602	−	0.952799i	$-0.598189\pi$
$443$	14.1723	−	24.5472i	0.673347	−	1.16627i	0.976949	−	0.213473i	$-0.0684774\pi$
$444$	0.292185	+	0.175572i	0.0138665	+	0.00833228i
$445$	1.40222	+	1.42602i	0.0664718	+	0.0676000i
$446$	16.6709	−	19.5637i	0.789391	−	0.926367i
$447$	3.95921	−	1.43084i	0.187264	−	0.0676765i
$448$	1.68567	−	36.9344i	0.0796406	−	1.74499i
$449$	−2.98484			−0.140863			−0.0704317	−	0.997517i	$-0.522438\pi$
$449$	−2.98484			−0.140863			−0.0704317	+	0.997517i	$0.522438\pi$
$450$	−18.0561	−	11.1345i	−0.851174	−	0.524884i
$451$		−	9.20192i		−	0.433301i
$452$	29.9666	−	4.81540i	1.40951	−	0.226497i
$453$	−17.7957	+	21.1104i	−0.836116	+	0.991852i
$454$	−21.2483	−	18.1065i	−0.997234	−	0.849780i
$455$	−23.0696	+	22.6846i	−1.08152	+	1.06347i
$456$	27.5943	+	24.3593i	1.29222	+	1.14073i
$457$	30.7880	+	17.7755i	1.44020	+	0.831502i	0.997863	−	0.0653453i	$-0.0208149\pi$
$457$	30.7880	+	17.7755i	1.44020	+	0.831502i	0.442341	+	0.896847i	$0.354148\pi$
$458$	−8.52612	−	23.9912i	−0.398399	−	1.12103i
$459$	5.51515	−	9.40370i	0.257425	−	0.438927i
$460$	0.721305	+	0.530882i	0.0336310	+	0.0247525i
$461$	10.9739	+	6.33580i	0.511107	+	0.295088i	0.733288	−	0.679918i	$-0.237985\pi$
$461$	10.9739	+	6.33580i	0.511107	+	0.295088i	−0.222182	+	0.975005i	$0.571318\pi$
$462$	−24.4082	+	4.05569i	−1.13557	+	0.188688i
$463$	15.8157	−	9.13117i	0.735016	−	0.424362i	−0.0852384	−	0.996361i	$-0.527165\pi$
$463$	15.8157	−	9.13117i	0.735016	−	0.424362i	0.820254	+	0.571999i	$0.193832\pi$
$464$	−6.49294	−	19.6813i	−0.301427	−	0.913683i
$465$	0.386557	−	0.806356i	0.0179261	−	0.0373939i
$466$	0.626749	+	0.115432i	0.0290336	+	0.00534727i
$467$	−15.3569			−0.710632			−0.355316	−	0.934746i	$-0.615627\pi$
$467$	−15.3569			−0.710632			−0.355316	+	0.934746i	$0.615627\pi$
$468$	−3.62670	+	18.4313i	−0.167644	+	0.851988i
$469$		−	21.8511i		−	1.00899i
$470$	−24.4201	+	1.74291i	−1.12642	+	0.0803944i
$471$	−5.19855	−	14.3847i	−0.239537	−	0.662810i
$472$	0.0323623	−	1.41890i	0.00148960	−	0.0653104i
$473$	17.7766	−	10.2634i	0.817371	−	0.471909i
$474$	6.66616	+	8.10567i	0.306187	+	0.372306i
$475$	−37.5616	−	0.632160i	−1.72345	−	0.0290055i
$476$	−15.0433	+	12.2380i	−0.689509	+	0.560927i
$477$	22.0051	+	8.12281i	1.00755	+	0.371918i
$478$	−34.0501	+	12.1009i	−1.55742	+	0.553483i
$479$	0.968888	−	1.67816i	0.0442696	−	0.0766772i	−0.843042	−	0.537848i	$-0.819237\pi$
$479$	0.968888	−	1.67816i	0.0442696	−	0.0766772i	0.887311	+	0.461171i	$0.152571\pi$
$480$	20.8613	+	6.69384i	0.952182	+	0.305531i
$481$	0.154039	+	0.266804i	0.00702359	+	0.0121652i
$482$	7.30425	+	6.22422i	0.332700	+	0.283505i
$483$	1.57809	+	0.281965i	0.0718058	+	0.0128298i
$484$	1.97461	+	12.2882i	0.0897552	+	0.558553i
$485$	7.91170	+	30.5529i	0.359252	+	1.38733i
$486$	−19.2976	+	10.6584i	−0.875358	+	0.483475i
$487$		−	22.0666i		−	0.999932i	−0.866045	−	0.499966i	$-0.833346\pi$
$487$		−	22.0666i		−	0.999932i	0.866045	−	0.499966i	$-0.166654\pi$
$488$	−25.2313	+	13.8100i	−1.14217	+	0.625148i
$489$	28.2251	+	5.04309i	1.27638	+	0.228056i
$490$	40.8409	+	19.8468i	1.84500	+	0.896587i
$491$	−18.1933	+	10.5039i	−0.821051	+	0.474034i	−0.850779	−	0.525524i	$-0.823869\pi$
$491$	−18.1933	+	10.5039i	−0.821051	+	0.474034i	0.0297277	+	0.999558i	$0.490536\pi$
$492$	−0.254893	+	14.5821i	−0.0114915	+	0.657413i
$493$	−5.43512	+	9.41391i	−0.244786	+	0.423981i
$494$	11.1398	+	31.3457i	0.501204	+	1.41031i
$495$	1.46712	−	14.5882i	0.0659420	−	0.655693i
$496$	−0.187949	+	0.904224i	−0.00843914	+	0.0406008i
$497$	−51.4928	−	29.7294i	−2.30977	−	1.33355i
$498$	−0.997752	−	1.21321i	−0.0447103	−	0.0543652i
$499$	29.9923	−	17.3160i	1.34264	−	0.775173i	0.355444	−	0.934697i	$-0.384330\pi$
$499$	29.9923	−	17.3160i	1.34264	−	0.775173i	0.987194	+	0.159525i	$0.0509962\pi$
$500$	−20.6312	+	8.62288i	−0.922655	+	0.385627i
$501$	−21.2752	+	7.68876i	−0.950506	+	0.343509i
$502$	29.4568	+	5.42522i	1.31472	+	0.242139i
$503$			0.624483i			0.0278443i	0.999903	+	0.0139222i	$0.00443170\pi$
$503$			0.624483i			0.0278443i	−0.999903	+	0.0139222i	$0.995568\pi$
$504$	38.7917	−	5.75087i	1.72792	−	0.256164i
$505$	−6.87914	−	26.5654i	−0.306117	−	1.18214i
$506$	−0.112121	+	0.608775i	−0.00498440	+	0.0270634i
$507$	3.57028	−	4.23529i	0.158562	−	0.188096i
$508$	8.85336	−	23.2199i	0.392804	−	1.03021i
$509$	30.1814	−	17.4252i	1.33777	−	0.772360i	0.351291	−	0.936267i	$-0.385743\pi$
$509$	30.1814	−	17.4252i	1.33777	−	0.772360i	0.986476	+	0.163907i	$0.0524096\pi$
$510$	−4.66517	−	10.5018i	−0.206577	−	0.465027i
$511$	11.1635	−	19.3357i	0.493843	−	0.855361i
$512$	−22.5745	−	1.54678i	−0.997661	−	0.0683587i
$513$	−19.7507	+	33.6762i	−0.872014	+	1.48684i
$514$	10.1167	+	28.4668i	0.446229	+	1.25562i
$515$	−17.5868	−	4.87133i	−0.774966	−	0.214656i
$516$	−28.4546	+	15.7717i	−1.25265	+	0.694312i
$517$	−8.46065	−	14.6543i	−0.372099	−	0.644494i
$518$	0.417145	−	0.489528i	0.0183283	−	0.0215086i
$519$	−10.3244	+	12.2474i	−0.453190	+	0.537602i
$520$	13.5575	+	14.4315i	0.594534	+	0.632864i
$521$	43.4812			1.90494			0.952472	−	0.304625i	$-0.0985312\pi$
$521$	43.4812			1.90494			0.952472	+	0.304625i	$0.0985312\pi$
$522$	19.1690	−	10.7588i	0.839004	−	0.470899i
$523$	20.2848			0.886992			0.443496	−	0.896276i	$-0.353738\pi$
$523$	20.2848			0.886992			0.443496	+	0.896276i	$0.353738\pi$
$524$	−0.0195508	+	0.00314166i	−0.000854079	+	0.000137244i
$525$	−26.3081	+	30.1633i	−1.14818	+	1.31644i
$526$	−21.7401	+	25.5125i	−0.947915	+	1.11240i
$527$	0.419510	−	0.242204i	0.0182741	−	0.0105506i
$528$	2.14083	+	14.9906i	0.0931675	+	0.652381i
$529$	−11.4799	+	19.8839i	−0.499128	+	0.864515i
$530$	20.4783	−	13.8557i	0.889520	−	0.601852i
$531$	1.48367	−	0.254655i	0.0643858	−	0.0110511i
$532$	53.8726	−	43.8263i	2.33567	−	1.90011i
$533$	−6.59053	+	11.4151i	−0.285468	+	0.494444i
$534$	0.769604	−	2.05120i	0.0333040	−	0.0887643i
$535$	21.7001	+	22.0684i	0.938176	+	0.954098i
$536$	−13.3694	−	0.304929i	−0.577471	−	0.0131709i
$537$	−0.451107	+	2.52475i	−0.0194667	+	0.108951i
$538$	−17.0971	−	3.14886i	−0.737106	−	0.135757i
$539$			31.3844i			1.35182i
$540$	−2.72901	+	23.0771i	−0.117438	+	0.993080i
$541$			31.5322i			1.35568i	0.735211	+	0.677839i	$0.237083\pi$
$541$			31.5322i			1.35568i	−0.735211	+	0.677839i	$0.762917\pi$
$542$	1.98159	−	10.7592i	0.0851164	−	0.462149i
$543$	0.965109	−	5.40150i	0.0414168	−	0.231801i
$544$	7.27779	+	9.37490i	0.312033	+	0.401946i
$545$	12.2724	−	12.0676i	0.525691	−	0.516919i
$546$	33.1836	+	12.4503i	1.42013	+	0.532825i
$547$	−7.90235	+	13.6873i	−0.337880	+	0.585226i	−0.984034	−	0.177982i	$-0.943043\pi$
$547$	−7.90235	+	13.6873i	−0.337880	+	0.585226i	0.646154	+	0.763207i	$0.276377\pi$
$548$	−3.22665	−	3.96630i	−0.137836	−	0.169432i
$549$	−19.5037	−	23.4597i	−0.832400	−	1.00123i
$550$	−11.5930	−	10.2205i	−0.494326	−	0.435802i
$551$	19.4641	−	33.7128i	0.829198	−	1.43621i
$552$	0.194540	−	0.961610i	0.00828017	−	0.0409288i
$553$	17.1482	−	9.90054i	0.729217	−	0.421014i
$554$	5.14564	+	4.38478i	0.218617	+	0.186292i
$555$	0.215248	+	0.314508i	0.00913675	+	0.0133501i
$556$	−3.98120	+	0.639748i	−0.168841	+	0.0271314i
$557$	−40.2293			−1.70457			−0.852284	−	0.523079i	$-0.824783\pi$
$557$	−40.2293			−1.70457			−0.852284	+	0.523079i	$0.824783\pi$
$558$	−0.979501	−	0.0119036i	−0.0414656	−	0.000503920i
$559$	−29.4030			−1.24361
$560$	18.9105	−	36.7577i	0.799116	−	1.55330i
$561$	5.11913	−	6.07263i	0.216130	−	0.256387i
$562$	15.6876	+	13.3680i	0.661741	+	0.563894i
$563$	2.65347	+	4.59595i	0.111830	+	0.193696i	0.916508	−	0.400016i	$-0.130995\pi$
$563$	2.65347	+	4.59595i	0.111830	+	0.193696i	−0.804678	+	0.593712i	$0.797662\pi$
$564$	13.0015	+	23.4567i	0.547463	+	0.987706i
$565$	32.7021	+	9.05810i	1.37579	+	0.381077i
$566$	31.9200	−	11.3439i	1.34170	−	0.476820i
$567$	13.8698	+	39.2139i	0.582477	+	1.64683i
$568$	−18.9083	+	31.0906i	−0.793373	+	1.30453i
$569$	−11.7181	+	20.2964i	−0.491250	+	0.850870i	−0.999949	−	0.0100746i	$-0.996793\pi$
$569$	−11.7181	+	20.2964i	−0.491250	+	0.850870i	0.508699	+	0.860944i	$0.330126\pi$
$570$	16.7067	+	37.6087i	0.699768	+	1.57526i
$571$	30.2311	−	17.4540i	1.26513	−	0.730425i	0.291070	−	0.956702i	$-0.405989\pi$
$571$	30.2311	−	17.4540i	1.26513	−	0.730425i	0.974063	+	0.226277i	$0.0726553\pi$
$572$	−4.87574	+	12.7877i	−0.203865	+	0.534680i
$573$	16.5749	−	19.6621i	0.692424	−	0.821396i
$574$	27.0620	+	4.98416i	1.12955	+	0.208035i
$575$	0.485997	+	0.875472i	0.0202675	+	0.0365097i
$576$	−2.97729	−	23.8146i	−0.124054	−	0.992276i
$577$		−	19.4970i		−	0.811673i	−0.913946	−	0.405836i	$-0.866980\pi$
$577$		−	19.4970i		−	0.811673i	0.913946	−	0.405836i	$-0.133020\pi$
$578$	−3.22711	+	17.5220i	−0.134230	+	0.728817i
$579$	−0.968299	+	0.349939i	−0.0402412	+	0.0145430i
$580$	2.56401	−	23.0286i	0.106465	−	0.956211i
$581$	−2.56665	+	1.48186i	−0.106483	+	0.0614777i
$582$	26.7026	−	21.9604i	1.10686	−	0.910288i
$583$	14.7997	+	8.54463i	0.612943	+	0.353883i
$584$	−11.6746	−	7.10010i	−0.483099	−	0.293804i
$585$	−12.2683	+	17.0462i	−0.507230	+	0.704773i
$586$	−12.6442	+	4.49358i	−0.522329	+	0.185628i
$587$	−15.8184	+	27.3982i	−0.652893	+	1.13084i	0.329524	+	0.944147i	$0.393112\pi$
$587$	−15.8184	+	27.3982i	−0.652893	+	1.13084i	−0.982417	+	0.186697i	$0.940222\pi$
$588$	0.869347	−	49.7342i	0.0358513	−	2.05101i
$589$	−1.50234	+	0.867374i	−0.0619027	+	0.0357395i
$590$	0.693554	−	1.42720i	0.0285532	−	0.0587570i
$591$	13.2625	+	2.36966i	0.545546	+	0.0974750i
$592$	−0.293693	−	0.262058i	−0.0120707	−	0.0107705i
$593$		−	0.602279i		−	0.0247326i	−0.999924	−	0.0123663i	$-0.996064\pi$
$593$		−	0.602279i		−	0.0247326i	0.999924	−	0.0123663i	$-0.00393642\pi$
$594$	−15.1703	+	5.27495i	−0.622445	+	0.216434i
$595$	−20.9892	+	5.43517i	−0.860472	+	0.222820i
$596$	−4.79952	+	0.771247i	−0.196596	+	0.0315915i
$597$	12.2803	+	2.19418i	0.502601	+	0.0898018i
$598$	0.575101	−	0.674893i	0.0235176	−	0.0275984i
$599$	4.08597	+	7.07711i	0.166948	+	0.289163i	0.937345	−	0.348401i	$-0.113275\pi$
$599$	4.08597	+	7.07711i	0.166948	+	0.289163i	−0.770397	+	0.637564i	$0.779942\pi$
$600$	18.0881	+	16.5173i	0.738442	+	0.674317i
$601$	3.85232	−	6.67241i	0.157139	−	0.272173i	−0.776697	−	0.629875i	$-0.783106\pi$
$601$	3.85232	−	6.67241i	0.157139	−	0.272173i	0.933836	+	0.357702i	$0.116440\pi$
$602$	20.5550	+	57.8386i	0.837760	+	2.35733i
$603$	−2.39945	−	13.9797i	−0.0977132	−	0.569297i
$604$	24.7316	−	20.1196i	1.00631	−	0.818653i
$605$	−3.71439	+	13.4099i	−0.151011	+	0.545191i
$606$	−23.2176	+	19.0943i	−0.943151	+	0.775654i
$607$	9.35464	−	5.40090i	0.379693	−	0.219216i	−0.297992	−	0.954568i	$-0.596317\pi$
$607$	9.35464	−	5.40090i	0.379693	−	0.219216i	0.677685	+	0.735353i	$0.262983\pi$
$608$	−26.0630	−	33.5731i	−1.05699	−	1.36157i
$609$	−14.0964	−	39.0055i	−0.571215	−	1.58058i
$610$	−32.0769	+	2.28938i	−1.29876	+	0.0926945i
$611$			24.2385i			0.980584i
$612$	−8.28041	+	9.48139i	−0.334716	+	0.383262i
$613$	25.9976			1.05003			0.525016	−	0.851092i	$-0.324059\pi$
$613$	25.9976			1.05003			0.525016	+	0.851092i	$0.324059\pi$
$614$	−3.21089	+	17.4339i	−0.129581	+	0.703575i
$615$	−7.04870	+	14.7036i	−0.284231	+	0.592905i
$616$	28.5632	+	0.651468i	1.15084	+	0.0262484i
$617$	−31.8716	+	18.4011i	−1.28310	+	0.740800i	−0.977414	−	0.211332i	$-0.932220\pi$
$617$	−31.8716	+	18.4011i	−1.28310	+	0.740800i	−0.305688	+	0.952132i	$0.598887\pi$
$618$	3.27674	+	19.7204i	0.131810	+	0.793269i
$619$	3.84060	+	2.21737i	0.154367	+	0.0891236i	0.575194	−	0.818017i	$-0.304927\pi$
$619$	3.84060	+	2.21737i	0.154367	+	0.0891236i	−0.420827	+	0.907141i	$0.638260\pi$
$620$	−0.612061	+	0.831602i	−0.0245810	+	0.0333980i
$621$	1.04058	+	0.00710330i	0.0417570	+	0.000285046i
$622$	−35.7151	+	12.6926i	−1.43205	+	0.508929i
$623$	−3.57978	−	2.06679i	−0.143421	−	0.0828041i
$624$	8.08071	−	20.1293i	0.323487	−	0.805819i
$625$	−24.9858	−	0.841259i	−0.999434	−	0.0336504i
$626$	26.0436	−	30.5628i	1.04091	−	1.22153i
$627$	−18.3325	+	21.7471i	−0.732128	+	0.868495i
$628$	2.80210	+	17.4377i	0.111816	+	0.695839i
$629$			0.206452i			0.00823177i
$630$	42.1081	+	12.2163i	1.67763	+	0.486709i
$631$	16.2943			0.648666			0.324333	−	0.945943i	$-0.394860\pi$
$631$	16.2943			0.648666			0.324333	+	0.945943i	$0.394860\pi$
$632$	−5.81826	−	10.6302i	−0.231438	−	0.422845i
$633$	−25.4284	+	9.18970i	−1.01069	+	0.365258i
$634$	−0.634572	−	0.540742i	−0.0252021	−	0.0214756i
$635$	19.8106	−	19.4800i	0.786160	−	0.773040i
$636$	−23.2162	−	13.9505i	−0.920582	−	0.553173i
$637$	22.4779	−	38.9328i	0.890606	−	1.54257i
$638$	15.0903	−	5.36288i	0.597431	−	0.212318i
$639$	−36.2081	−	13.3656i	−1.43237	−	0.528734i
$640$	−22.2260	−	12.0832i	−0.878561	−	0.477631i
$641$	−17.5690	+	30.4303i	−0.693932	+	1.20193i	0.276607	+	0.960983i	$0.410790\pi$
$641$	−17.5690	+	30.4303i	−0.693932	+	1.20193i	−0.970539	+	0.240943i	$0.922543\pi$
$642$	11.9100	−	31.7433i	0.470049	−	1.25281i
$643$	13.5973	+	23.5512i	0.536225	+	0.928768i	0.999103	+	0.0423464i	$0.0134833\pi$
$643$	13.5973	+	23.5512i	0.536225	+	0.928768i	−0.462878	+	0.886422i	$0.653183\pi$
$644$	−1.72963	−	0.659478i	−0.0681568	−	0.0259871i
$645$	−36.2667	+	2.78263i	−1.42800	+	0.109566i
$646$	−4.03785	+	21.9239i	−0.158867	+	0.862585i
$647$		−	21.8547i		−	0.859197i	−0.903020	−	0.429598i	$-0.858655\pi$
$647$		−	21.8547i		−	0.859197i	0.903020	−	0.429598i	$-0.141345\pi$
$648$	24.1862	−	7.93891i	0.950125	−	0.311870i
$649$	1.09674			0.0430508
$650$	7.06123	+	20.9817i	0.276964	+	0.822970i
$651$	−0.325081	+	1.81941i	−0.0127409	+	0.0713082i
$652$	−30.9353	−	11.7951i	−1.21152	−	0.461933i
$653$	−1.48294	−	2.56853i	−0.0580321	−	0.100515i	0.835550	−	0.549415i	$-0.185149\pi$
$653$	−1.48294	−	2.56853i	−0.0580321	−	0.100515i	−0.893582	+	0.448900i	$0.851816\pi$
$654$	−17.6527	−	6.62323i	−0.690276	−	0.258989i
$655$	−0.0213355	−	0.00590968i	−0.000833647	−	0.000230910i
$656$	3.42717	−	16.4881i	0.133808	−	0.643754i
$657$	5.01881	−	13.5962i	0.195803	−	0.530440i
$658$	47.6796	−	16.9446i	1.85874	−	0.660571i
$659$	−28.3724	−	16.3808i	−1.10523	−	0.638107i	−0.167643	−	0.985848i	$-0.553616\pi$
$659$	−28.3724	−	16.3808i	−1.10523	−	0.638107i	−0.937591	+	0.347741i	$0.886949\pi$
$660$	−4.80372	+	16.2342i	−0.186984	+	0.631916i
$661$	−19.5382	+	11.2804i	−0.759950	+	0.438757i	−0.829278	−	0.558837i	$-0.811248\pi$
$661$	−19.5382	+	11.2804i	−0.759950	+	0.438757i	0.0693281	+	0.997594i	$0.477914\pi$
$662$	−21.7250	+	25.4948i	−0.844367	+	0.990882i
$663$	−10.6997	+	3.86681i	−0.415540	+	0.150174i
$664$	0.870844	+	1.59106i	0.0337953	+	0.0617452i
$665$	75.1658	−	19.4642i	2.91480	−	0.754791i
$666$	0.213122	−	0.358992i	0.00825831	−	0.0139106i
$667$	−1.03760			−0.0401762
$668$	25.7907	−	4.14437i	0.997871	−	0.160350i
$669$	−24.0689	−	20.2897i	−0.930559	−	0.784446i
$670$	−13.4476	−	6.53492i	−0.519526	−	0.252466i
$671$	−11.1134	−	19.2490i	−0.429029	−	0.743100i
$672$	−45.2456	−	1.82357i	−1.74539	−	0.0703458i
$673$	−16.9745	−	9.80026i	−0.654321	−	0.377772i	0.135789	−	0.990738i	$-0.456643\pi$
$673$	−16.9745	−	9.80026i	−0.654321	−	0.377772i	−0.790110	+	0.612966i	$0.789976\pi$
$674$	13.4427	+	37.8257i	0.517794	+	1.45699i
$675$	−13.5189	+	22.1865i	−0.520344	+	0.853957i
$676$	−4.96179	+	4.03650i	−0.190838	+	0.155250i
$677$	−8.73705	+	15.1330i	−0.335792	+	0.581609i	−0.983637	−	0.180164i	$-0.942337\pi$
$677$	−8.73705	+	15.1330i	−0.335792	+	0.581609i	0.647845	+	0.761773i	$0.275671\pi$
$678$	−6.09302	−	36.6695i	−0.234001	−	1.40828i
$679$	−32.6155	−	56.4916i	−1.25167	−	2.16795i
$680$	3.03256	+	12.9179i	0.116293	+	0.495379i
$681$	−22.0369	+	26.1415i	−0.844456	+	1.00175i
$682$	−0.701866	−	0.129266i	−0.0268758	−	0.00494986i
$683$	−6.62592			−0.253534			−0.126767	−	0.991933i	$-0.540460\pi$
$683$	−6.62592			−0.253534			−0.126767	+	0.991933i	$0.540460\pi$
$684$	29.6535	−	33.9544i	1.13383	−	1.29828i
$685$	−1.43303	−	5.53398i	−0.0547533	−	0.211443i
$686$	−47.3039	−	8.71221i	−1.80607	−	0.332634i
$687$	−29.3270	+	10.5987i	−1.11890	+	0.404364i
$688$	35.6750	−	11.7693i	1.36009	−	0.448700i
$689$	−12.2395	−	21.1995i	−0.466290	−	0.807637i
$690$	0.645480	−	0.886864i	0.0245730	−	0.0337624i
$691$	−18.4808	−	10.6699i	−0.703042	−	0.405901i	0.105438	−	0.994426i	$-0.466376\pi$
$691$	−18.4808	−	10.6699i	−0.703042	−	0.405901i	−0.808479	+	0.588525i	$0.799709\pi$
$692$	14.3483	−	11.6726i	0.545441	−	0.443725i
$693$	5.12632	+	29.8670i	0.194733	+	1.13455i
$694$	15.1028	−	5.36730i	0.573293	−	0.203740i
$695$	−4.34463	−	1.20341i	−0.164801	−	0.0456480i
$696$	−24.0619	+	8.08046i	−0.912064	+	0.306289i
$697$	−7.64959	+	4.41649i	−0.289749	+	0.167287i
$698$	4.30118	−	5.04753i	0.162802	−	0.191052i
$699$	0.137284	−	0.768349i	0.00519256	−	0.0290616i
$700$	36.3368	−	28.5580i	1.37340	−	1.07939i
$701$			7.84565i			0.296326i	0.988963	+	0.148163i	$0.0473360\pi$
$701$			7.84565i			0.296326i	−0.988963	+	0.148163i	$0.952664\pi$
$702$	22.5970	+	4.32150i	0.852869	+	0.163104i
$703$		−	0.739339i		−	0.0278847i
$704$	0.797191	−	17.4671i	0.0300453	−	0.658315i
$705$	2.29388	+	29.8967i	0.0863924	+	1.12597i
$706$	−4.34802	+	5.10249i	−0.163640	+	0.192035i
$707$	28.3588	+	49.1189i	1.06654	+	1.84730i
$708$	−1.73798	−	0.0303797i	−0.0653174	−	0.00114174i
$709$	27.1860	+	15.6959i	1.02099	+	0.589471i	0.914392	−	0.404831i	$-0.132670\pi$
$709$	27.1860	+	15.6959i	1.02099	+	0.589471i	0.106602	+	0.994302i	$0.466003\pi$
$710$	−33.6958	+	22.7986i	−1.26458	+	0.855618i
$711$	9.88375	−	8.21710i	0.370670	−	0.308165i
$712$	−1.31450	+	2.16142i	−0.0492630	+	0.0810025i
$713$	0.0400437	+	0.0231193i	0.00149965	+	0.000865823i
$714$	15.0863	+	18.3441i	0.564592	+	0.686511i
$715$	−10.9101	+	10.7281i	−0.408015	+	0.401206i
$716$	1.05508	−	2.76718i	0.0394302	−	0.103414i
$717$	15.0424	+	41.6232i	0.561770	+	1.55445i
$718$	−6.68554	+	36.2999i	−0.249502	+	1.35470i
$719$	6.09017			0.227125			0.113562	−	0.993531i	$-0.463774\pi$
$719$	6.09017			0.227125			0.113562	+	0.993531i	$0.463774\pi$
$720$	8.06205	−	25.5930i	0.300455	−	0.953796i
$721$	37.7178			1.40468
$722$	9.59326	−	52.0877i	0.357024	−	1.93850i
$723$	7.57533	−	8.98632i	0.281729	−	0.334205i
$724$	−2.25726	+	5.92016i	−0.0838905	+	0.220021i
$725$	13.3286	−	22.2140i	0.495013	−	0.825007i
$726$	15.0368	−	2.49852i	0.558067	−	0.0927287i
$727$	−39.1849	−	22.6234i	−1.45329	−	0.839056i	−0.454620	−	0.890685i	$-0.650225\pi$
$727$	−39.1849	−	22.6234i	−1.45329	−	0.839056i	−0.998666	+	0.0516297i	$0.983558\pi$
$728$	−34.9665	−	21.2655i	−1.29595	−	0.788151i
$729$	13.1795	+	23.5648i	0.488130	+	0.872771i
$730$	−8.56096	−	12.6529i	−0.316855	−	0.468303i
$731$	−17.0639	−	9.85186i	−0.631132	−	0.364384i
$732$	17.0780	+	30.8114i	0.631223	+	1.13882i
$733$	−12.3105	−	21.3224i	−0.454699	−	0.787562i	0.543971	−	0.839104i	$-0.316920\pi$
$733$	−12.3105	−	21.3224i	−0.454699	−	0.787562i	−0.998671	+	0.0515413i	$0.983587\pi$
$734$	−6.17438	+	7.24576i	−0.227901	+	0.267446i
$735$	24.0405	−	50.1484i	0.886748	−	1.84975i
$736$	−0.427633	+	1.04905i	−0.0157628	+	0.0386687i
$737$		−	10.3339i		−	0.380653i
$738$	17.8608	+	0.217057i	0.657465	+	0.00798999i
$739$		−	18.4734i		−	0.679557i	−0.940506	−	0.339778i	$-0.889648\pi$
$739$		−	18.4734i		−	0.679557i	0.940506	−	0.339778i	$-0.110352\pi$
$740$	−0.176512	−	0.403120i	−0.00648870	−	0.0148190i
$741$	38.3173	−	13.8477i	1.40762	−	0.508708i
$742$	−33.1452	+	38.8966i	−1.21680	+	1.42794i
$743$	18.9414	−	10.9358i	0.694893	−	0.401197i	−0.110549	−	0.993871i	$-0.535261\pi$
$743$	18.9414	−	10.9358i	0.694893	−	0.401197i	0.805442	+	0.592674i	$0.201928\pi$
$744$	1.10865	+	0.224288i	0.0406452	+	0.00822279i
$745$	−5.23766	−	1.45077i	−0.191893	−	0.0531521i
$746$	−20.4710	+	7.27508i	−0.749495	+	0.266360i
$747$	−1.47934	+	1.22989i	−0.0541264	+	0.0449992i
$748$	−7.11430	+	5.78761i	−0.260125	+	0.211616i
$749$	−55.3987	−	31.9845i	−2.02423	−	1.16869i
$750$	10.6953	+	25.2113i	0.390535	+	0.920588i
$751$	2.23341	+	3.86839i	0.0814984	+	0.141159i	0.903894	−	0.427757i	$-0.140696\pi$
$751$	2.23341	+	3.86839i	0.0814984	+	0.141159i	−0.822395	+	0.568916i	$0.807363\pi$
$752$	−9.70208	−	29.4088i	−0.353798	−	1.07243i
$753$	6.45227	−	36.1120i	0.235134	−	1.31599i
$754$	−22.5607	−	4.15513i	−0.821614	−	0.151321i
$755$	34.5067	−	8.93555i	1.25583	−	0.325198i
$756$	−7.29628	−	47.4717i	−0.265363	−	1.72653i
$757$	−28.1070			−1.02157			−0.510784	−	0.859709i	$-0.670645\pi$
$757$	−28.1070			−1.02157			−0.510784	+	0.859709i	$0.670645\pi$
$758$	−10.9722	−	2.02082i	−0.398530	−	0.0733994i
$759$	0.746315	+	0.133347i	0.0270895	+	0.00484020i
$760$	−10.8601	−	46.2612i	−0.393938	−	1.67807i
$761$	7.55724	+	13.0895i	0.273950	+	0.474495i	0.969870	−	0.243624i	$-0.0783364\pi$
$761$	7.55724	+	13.0895i	0.273950	+	0.474495i	−0.695920	+	0.718119i	$0.745003\pi$
$762$	−28.4958	−	10.6915i	−1.03229	−	0.387312i
$763$	−17.7868	+	30.8077i	−0.643926	+	1.11531i
$764$	−23.0349	+	18.7393i	−0.833372	+	0.677963i
$765$	−12.8314	+	5.78206i	−0.463921	+	0.209051i
$766$	−4.01102	−	11.2864i	−0.144924	−	0.407794i
$767$	−1.36052	−	0.785498i	−0.0491256	−	0.0283627i
$768$	−1.74713	+	27.6577i	−0.0630442	+	0.998011i
$769$	18.2248	+	31.5663i	0.657203	+	1.13831i	0.981337	+	0.192298i	$0.0615939\pi$
$769$	18.2248	+	31.5663i	0.657203	+	1.13831i	−0.324134	+	0.946011i	$0.605073\pi$
$770$	28.7302	+	13.9616i	1.03537	+	0.503140i
$771$	34.7981	−	12.5759i	1.25322	−	0.452910i
$772$	1.17381	−	0.188623i	0.0422464	−	0.00678868i
$773$	−45.0468			−1.62022			−0.810110	−	0.586278i	$-0.800593\pi$
$773$	−45.0468			−1.62022			−0.810110	+	0.586278i	$0.800593\pi$
$774$	19.5017	+	34.7463i	0.700974	+	1.24893i
$775$	−1.00934	+	0.560313i	−0.0362567	+	0.0201271i
$776$	−35.0191	+	19.1672i	−1.25711	+	0.688061i
$777$	−0.602260	−	0.507696i	−0.0216059	−	0.0182135i
$778$	4.64521	−	5.45126i	0.166539	−	0.195437i
$779$	27.3945	−	15.8162i	0.981509	−	0.566674i
$780$	17.5862	−	16.6983i	0.629689	−	0.597897i
$781$	−24.3521	−	14.0597i	−0.871385	−	0.503095i
$782$	0.559890	−	0.198977i	0.0200216	−	0.00711540i
$783$	−13.3016	−	23.4066i	−0.475361	−	0.836484i
$784$	−11.6888	+	56.2350i	−0.417457	+	2.00839i
$785$	−5.27095	+	19.0295i	−0.188128	+	0.679193i
$786$	0.00397520	+	0.0239239i	0.000141791	+	0.000853336i
$787$	3.98574	+	6.90350i	0.142076	+	0.246083i	0.928278	−	0.371886i	$-0.121289\pi$
$787$	3.98574	+	6.90350i	0.142076	+	0.246083i	−0.786202	+	0.617969i	$0.787956\pi$
$788$	−14.5360	−	5.54234i	−0.517823	−	0.197438i
$789$	31.3877	+	26.4593i	1.11743	+	0.941977i
$790$	−0.964537	−	13.5143i	−0.0343167	−	0.480816i
$791$	−70.1352			−2.49372
$792$	18.3454	−	2.71971i	0.651876	−	0.0966407i
$793$			31.8383i			1.13061i
$794$	4.24139	−	23.0291i	0.150521	−	0.817271i
$795$	−17.1030	−	24.9900i	−0.606581	−	0.886302i
$796$	−13.4595	−	5.13190i	−0.477060	−	0.181895i
$797$	−11.4728	−	19.8714i	−0.406386	−	0.703881i	0.588096	−	0.808791i	$-0.299878\pi$
$797$	−11.4728	−	19.8714i	−0.406386	−	0.703881i	−0.994482	+	0.104910i	$0.966545\pi$
$798$	−54.0267	−	65.6934i	−1.91252	−	2.32552i
$799$	−8.12143	+	14.0667i	−0.287316	+	0.497645i
$800$	−16.9659	−	22.6309i	−0.599836	−	0.800123i
$801$	−2.51719	−	0.929175i	−0.0889404	−	0.0328308i
$802$	−11.2838	+	4.01009i	−0.398444	+	0.141601i
$803$	5.27945	−	9.14427i	0.186308	−	0.322694i
$804$	−0.286248	+	16.3759i	−0.0100952	+	0.577533i
$805$	−1.45105	−	1.47567i	−0.0511427	−	0.0520106i
$806$	0.778094	+	0.663042i	0.0274072	+	0.0233547i
$807$	−3.74497	+	20.9598i	−0.131829	+	0.737819i
$808$	30.4487	−	16.6656i	1.07118	−	0.586295i
$809$	−7.09601			−0.249482			−0.124741	−	0.992189i	$-0.539810\pi$
$809$	−7.09601			−0.249482			−0.124741	+	0.992189i	$0.539810\pi$
$810$	28.2810	+	3.19176i	0.993692	+	0.112147i
$811$			3.76265i			0.132125i	0.997816	+	0.0660623i	$0.0210436\pi$
$811$			3.76265i			0.132125i	−0.997816	+	0.0660623i	$0.978956\pi$
$812$	7.59819	+	47.2841i	0.266644	+	1.65935i
$813$	−13.1901	−	2.35672i	−0.462595	−	0.0826538i
$814$	0.197277	−	0.231509i	0.00691455	−	0.00811437i
$815$	−25.9528	−	26.3932i	−0.909085	−	0.924514i
$816$	11.4342	−	8.97446i	0.400278	−	0.314169i
$817$	61.1088	+	35.2812i	2.13793	+	1.23433i
$818$	−1.52342	+	0.541402i	−0.0532652	+	0.0189297i
$819$	15.0318	−	40.7220i	0.525254	−	1.42294i
$820$	11.1607	−	15.1639i	0.389748	−	0.529547i
$821$	−28.6223	−	16.5251i	−0.998925	−	0.576730i	−0.0909949	−	0.995851i	$-0.529005\pi$
$821$	−28.6223	−	16.5251i	−0.998925	−	0.576730i	−0.907930	+	0.419122i	$0.862338\pi$
$822$	−4.83659	+	3.97764i	−0.168695	+	0.138736i
$823$	−37.3901	+	21.5872i	−1.30334	+	0.752482i	−0.980975	−	0.194134i	$-0.937810\pi$
$823$	−37.3901	+	21.5872i	−1.30334	+	0.752482i	−0.322362	+	0.946616i	$0.604477\pi$
$824$	0.526346	−	23.0773i	0.0183361	−	0.803936i
$825$	−12.4417	+	14.2649i	−0.433163	+	0.496640i
$826$	−0.594041	+	3.22541i	−0.0206693	+	0.112226i
$827$	39.5272			1.37450			0.687249	−	0.726422i	$-0.258818\pi$
$827$	39.5272			1.37450			0.687249	+	0.726422i	$0.258818\pi$
$828$	−1.17898	−	0.231986i	−0.0409723	−	0.00806206i
$829$			4.39738i			0.152727i	0.997080	+	0.0763636i	$0.0243310\pi$
$829$			4.39738i			0.152727i	−0.997080	+	0.0763636i	$0.975669\pi$
$830$	0.144366	+	2.02274i	0.00501103	+	0.0702103i
$831$	5.33660	−	6.33060i	0.185125	−	0.219606i
$832$	−13.4991	+	21.0972i	−0.467996	+	0.731415i
$833$	26.0899	−	15.0630i	0.903963	−	0.521903i
$834$	0.809486	+	4.87171i	0.0280302	+	0.168694i
$835$	28.1450	+	7.79584i	0.973999	+	0.269786i
$836$	25.4775	−	20.7264i	0.881158	−	0.716838i
$837$	−0.00818950	+	1.19970i	−0.000283070	+	0.0414677i
$838$	−5.51724	−	15.5247i	−0.190590	−	0.536291i
$839$	15.1864	−	26.3036i	0.524292	−	0.908101i	−0.475308	−	0.879820i	$-0.657663\pi$
$839$	15.1864	−	26.3036i	0.524292	−	0.908101i	0.999600	−	0.0282811i	$-0.00900335\pi$
$840$	−45.1415	−	22.9205i	−1.55753	−	0.790832i
$841$	−1.07773	−	1.86668i	−0.0371630	−	0.0643682i
$842$	7.91318	−	9.28628i	0.272706	−	0.320027i
$843$	16.2698	−	19.3002i	0.560361	−	0.664735i
$844$	30.8253	−	4.95339i	1.06105	−	0.170503i
$845$	−6.92294	+	1.79270i	−0.238157	+	0.0616709i
$846$	28.6433	−	16.0763i	0.984777	−	0.552715i
$847$		−	28.7598i		−	0.988198i
$848$	23.3360	+	20.8224i	0.801363	+	0.715045i
$849$	−14.1014	−	39.0193i	−0.483959	−	1.33914i
$850$	−2.93223	+	14.5426i	−0.100575	+	0.498808i
$851$	−0.0170664	+	0.00985329i	−0.000585028	+	0.000337766i
$852$	38.2008	+	22.9547i	1.30874	+	0.786414i
$853$	8.09875	−	14.0274i	0.277296	−	0.480290i	−0.693416	−	0.720537i	$-0.743895\pi$
$853$	8.09875	−	14.0274i	0.277296	−	0.480290i	0.970712	+	0.240247i	$0.0772285\pi$
$854$	62.6292	−	22.2575i	2.14313	−	0.761636i
$855$	45.9514	−	20.7065i	1.57151	−	0.708148i
$856$	−20.3425	+	33.4489i	−0.695293	+	1.14326i
$857$	10.6451	+	6.14596i	0.363630	+	0.209942i	0.670672	−	0.741754i	$-0.266006\pi$
$857$	10.6451	+	6.14596i	0.363630	+	0.209942i	−0.307042	+	0.951696i	$0.599339\pi$
$858$	15.6932	+	5.88804i	0.535758	+	0.201014i
$859$	−6.43114	+	3.71302i	−0.219428	+	0.126687i	−0.605685	−	0.795704i	$-0.707101\pi$
$859$	−6.43114	+	3.71302i	−0.219428	+	0.126687i	0.386258	+	0.922391i	$0.373768\pi$
$860$	41.7423	+	4.64759i	1.42340	+	0.158482i
$861$	5.92772	−	33.1761i	0.202016	−	1.13064i
$862$	0.727651	−	3.95086i	0.0247839	−	0.134567i
$863$			47.7746i			1.62626i	0.582079	+	0.813132i	$0.302240\pi$
$863$			47.7746i			1.62626i	−0.582079	+	0.813132i	$0.697760\pi$
$864$	−29.1470	+	3.80171i	−0.991601	+	0.129337i
$865$	20.0195	−	5.18406i	0.680683	−	0.176263i
$866$	−44.1747	−	8.13589i	−1.50112	−	0.276469i
$867$	21.4807	+	3.83804i	0.729522	+	0.130347i
$868$	0.760322	−	1.99411i	0.0258070	−	0.0676845i
$869$	8.10977	−	4.68218i	0.275105	−	0.158832i
$870$	−28.2205	−	2.98999i	−0.956764	−	0.101370i
$871$	−7.40124	+	12.8193i	−0.250782	+	0.434366i
$872$	18.6012	+	11.3126i	0.629917	+	0.383094i
$873$	−27.0697	−	32.5602i	−0.916170	−	1.10199i
$874$	−2.00506	+	0.712569i	−0.0678222	+	0.0241030i
$875$	50.2321	−	12.1095i	1.69816	−	0.409375i
$876$	−8.61954	+	14.3445i	−0.291227	+	0.484656i
$877$	25.6334	+	44.3984i	0.865580	+	1.49923i	0.866471	+	0.499228i	$0.166383\pi$
$877$	25.6334	+	44.3984i	0.865580	+	1.49923i	−0.000891102		1.00000i	$0.500284\pi$
$878$	24.9594	+	21.2688i	0.842338	+	0.717787i
$879$	5.58589	+	15.4564i	0.188407	+	0.521333i
$880$	8.94320	−	17.3835i	0.301475	−	0.585999i
$881$	−29.4991			−0.993851			−0.496925	−	0.867793i	$-0.665538\pi$
$881$	−29.4991			−0.993851			−0.496925	+	0.867793i	$0.665538\pi$
$882$	−60.9166	−	0.740302i	−2.05117	−	0.0249273i
$883$	−29.1137			−0.979753			−0.489876	−	0.871792i	$-0.662958\pi$
$883$	−29.1137			−0.979753			−0.489876	+	0.871792i	$0.662958\pi$
$884$	12.9706	−	2.08427i	0.436247	−	0.0701016i
$885$	−1.75246	−	0.840106i	−0.0589082	−	0.0282398i
$886$	30.5104	+	25.9991i	1.02502	+	0.873455i
$887$	27.8025	−	16.0518i	0.933517	−	0.538966i	0.0455948	−	0.998960i	$-0.485482\pi$
$887$	27.8025	−	16.0518i	0.933517	−	0.538966i	0.887922	+	0.459994i	$0.152148\pi$
$888$	−0.319034	+	0.361403i	−0.0107061	+	0.0121279i
$889$	−28.7122	+	49.7310i	−0.962977	+	1.66793i
$890$	−2.34253	+	1.58496i	−0.0785218	+	0.0531280i
$891$	6.55933	+	18.5451i	0.219746	+	0.621284i
$892$	22.9393	+	28.1976i	0.768063	+	0.944126i
$893$	29.0842	−	50.3753i	0.973266	−	1.68575i
$894$	0.975874	+	5.87308i	0.0326381	+	0.196425i
$895$	2.36089	−	2.32149i	0.0789157	−	0.0775987i
$896$	50.9374	+	11.8054i	1.70170	+	0.394391i
$897$	−0.830311	−	0.699940i	−0.0277233	−	0.0233703i
$898$	0.764582	−	4.15138i	0.0255144	−	0.138533i
$899$		−	1.19627i		−	0.0398978i
$900$	20.1112	−	22.2607i	0.670375	−	0.742023i
$901$		−	16.4041i		−	0.546500i
$902$	12.7982	+	2.35712i	0.426134	+	0.0784834i
$903$	70.7025	−	25.5516i	2.35283	−	0.850303i
$904$	−0.978727	+	42.9116i	−0.0325520	+	1.42722i
$905$	−5.05093	+	4.96664i	−0.167899	+	0.165097i
$906$	−24.8023	−	30.1582i	−0.824001	−	1.00194i
$907$	−10.3985	+	18.0107i	−0.345276	+	0.598035i	−0.985404	−	0.170233i	$-0.945548\pi$
$907$	−10.3985	+	18.0107i	−0.345276	+	0.598035i	0.640128	+	0.768268i	$0.278881\pi$
$908$	30.6258	−	24.9146i	1.01635	−	0.826820i
$909$	23.5368	+	28.3107i	0.780666	+	0.939007i
$910$	−25.6409	−	37.8965i	−0.849986	−	1.25626i
$911$	−11.0811	+	19.1930i	−0.367132	+	0.635891i	−0.989116	−	0.147139i	$-0.952994\pi$
$911$	−11.0811	+	19.1930i	−0.367132	+	0.635891i	0.621984	+	0.783030i	$0.286327\pi$
$912$	−40.9479	+	32.1390i	−1.35592	+	1.06423i
$913$	−1.21382	+	0.700802i	−0.0401717	+	0.0231932i
$914$	−32.6090	+	38.2674i	−1.07861	+	1.26577i
$915$	3.01311	+	39.2705i	0.0996102	+	1.29824i
$916$	35.5515	−	5.71285i	1.17465	−	0.188758i
$917$	0.0457575			0.00151105
$918$	11.6661	+	10.0794i	0.385040	+	0.332670i
$919$	−25.2546			−0.833071			−0.416536	−	0.909119i	$-0.636756\pi$
$919$	−25.2546			−0.833071			−0.416536	+	0.909119i	$0.636756\pi$
$920$	−0.923127	+	0.867218i	−0.0304346	+	0.0285913i
$921$	21.3727	+	3.81875i	0.704255	+	0.125832i
$922$	−11.6230	+	13.6398i	−0.382783	+	0.449204i
$923$	20.1394	+	34.8825i	0.662897	+	1.14817i
$924$	0.611557	−	34.9864i	0.0201187	−	1.15097i
$925$	0.00827940	−	0.491944i	0.000272225	−	0.0161750i
$926$	8.64857	+	24.3358i	0.284210	+	0.799723i
$927$	24.1307	−	4.14175i	0.792556	−	0.136033i
$928$	29.0364	−	3.98905i	0.953167	−	0.130947i
$929$	−29.9716	+	51.9124i	−0.983337	+	1.70319i	−0.334233	+	0.942490i	$0.608477\pi$
$929$	−29.9716	+	51.9124i	−0.983337	+	1.70319i	−0.649104	+	0.760700i	$0.724856\pi$
$930$	1.02248	+	0.744184i	0.0335284	+	0.0244027i
$931$	−93.4324	+	53.9432i	−3.06212	+	1.76792i
$932$	−0.321090	+	0.842127i	−0.0105176	+	0.0275848i
$933$	15.7780	+	43.6585i	0.516548	+	1.42932i
$934$	3.93375	−	21.3587i	0.128716	−	0.698878i
$935$	−9.92624	+	2.57041i	−0.324623	+	0.0840614i
$936$	−24.7057	−	9.76537i	−0.807530	−	0.319191i
$937$		−	12.5525i		−	0.410071i	−0.978755	−	0.205035i	$-0.934269\pi$
$937$		−	12.5525i		−	0.410071i	0.978755	−	0.205035i	$-0.0657309\pi$
$938$	30.3910	+	5.59727i	0.992301	+	0.182757i
$939$	−37.6009	−	31.6970i	−1.22706	−	1.03439i
$940$	3.83127	−	34.4105i	0.124962	−	1.12235i
$941$	−17.5803	+	10.1500i	−0.573101	+	0.330880i	−0.758387	−	0.651805i	$-0.774012\pi$
$941$	−17.5803	+	10.1500i	−0.573101	+	0.330880i	0.185286	+	0.982685i	$0.440679\pi$
$942$	21.3381	−	3.54556i	0.695234	−	0.115520i
$943$	−0.730181	−	0.421570i	−0.0237780	−	0.0137282i
$944$	1.96515	+	0.408470i	0.0639603	+	0.0132946i
$945$	14.6870	−	51.6506i	0.477767	−	1.68020i
$946$	9.72091	+	27.3531i	0.316054	+	0.889328i
$947$	12.5564	−	21.7483i	0.408029	−	0.706726i	−0.586640	−	0.809848i	$-0.699550\pi$
$947$	12.5564	−	21.7483i	0.408029	−	0.706726i	0.994669	+	0.103121i	$0.0328830\pi$
$948$	−12.9811	+	7.19513i	−0.421607	+	0.233687i
$949$	−13.0985	+	7.56241i	−0.425195	+	0.245486i
$950$	10.5008	−	52.0796i	0.340692	−	1.68968i
$951$	−0.658122	+	0.780704i	−0.0213411	+	0.0253161i
$952$	−13.1674	−	24.0574i	−0.426759	−	0.779704i
$953$			25.4825i			0.825459i	0.910854	+	0.412729i	$0.135424\pi$
$953$			25.4825i			0.825459i	−0.910854	+	0.412729i	$0.864576\pi$
$954$	−16.9341	+	28.5245i	−0.548262	+	0.923515i
$955$	−32.1394	+	8.32253i	−1.04001	+	0.269311i
$956$	−8.10811	−	50.4574i	−0.262235	−	1.63191i
$957$	−6.66650	−	18.4465i	−0.215497	−	0.596292i
$958$	2.08584	+	1.77742i	0.0673904	+	0.0574258i
$959$	5.90757	+	10.2322i	0.190766	+	0.330416i
$960$	−14.6537	+	27.2996i	−0.472945	+	0.881092i
$961$	15.4733	−	26.8006i	0.499140	−	0.864536i
$962$	−0.410535	+	0.145898i	−0.0132362	+	0.00470394i
$963$	−38.9546	−	14.3794i	−1.25530	−	0.463370i
$964$	−10.5278	+	8.56455i	−0.339078	+	0.275846i
$965$	1.28097	+	0.354813i	0.0412358	+	0.0114218i
$966$	−0.796399	+	2.12262i	−0.0256237	+	0.0682942i
$967$	−39.8470	+	23.0056i	−1.28139	+	0.739812i	−0.977103	−	0.212768i	$-0.931752\pi$
$967$	−39.8470	+	23.0056i	−1.28139	+	0.739812i	−0.304289	+	0.952580i	$0.598419\pi$
$968$	−17.5965	−	0.401339i	−0.565571	−	0.0128995i
$969$	26.8772	+	4.80225i	0.863419	+	0.154271i
$970$	−44.5202	+	3.17749i	−1.42946	+	0.102023i
$971$		−	60.4962i		−	1.94142i	−0.240264	−	0.970708i	$-0.577234\pi$
$971$		−	60.4962i		−	1.94142i	0.240264	−	0.970708i	$-0.422766\pi$
$972$	−9.88076	−	29.5698i	−0.316926	−	0.948450i
$973$	9.31779			0.298715
$974$	30.6907	+	5.65247i	0.983393	+	0.181117i
$975$	25.6508	−	8.78495i	0.821483	−	0.281343i
$976$	−12.7441	−	38.6297i	−0.407928	−	1.23651i
$977$	−35.2401	+	20.3459i	−1.12743	+	0.650923i	−0.943288	−	0.331976i	$-0.892285\pi$
$977$	−35.2401	+	20.3459i	−1.12743	+	0.650923i	−0.184144	+	0.982899i	$0.558951\pi$
$978$	−14.2440	+	37.9643i	−0.455474	+	1.21396i
$979$	−1.69296	−	0.977428i	−0.0541071	−	0.0312387i
$980$	−38.0650	+	51.7186i	−1.21594	+	1.65209i
$981$	−7.99651	+	21.6630i	−0.255309	+	0.691646i
$982$	−9.94874	−	27.9942i	−0.317477	−	0.893332i
$983$	−19.7592	−	11.4080i	−0.630221	−	0.363858i	0.150617	−	0.988592i	$-0.451874\pi$
$983$	−19.7592	−	11.4080i	−0.630221	−	0.363858i	−0.780838	+	0.624734i	$0.785207\pi$
$984$	−20.2158	−	4.08979i	−0.644457	−	0.130378i
$985$	−12.1948	−	12.4017i	−0.388558	−	0.395152i
$986$	−11.7008	−	9.97070i	−0.372630	−	0.317532i
$987$	−21.0636	−	58.2840i	−0.670461	−	1.85520i
$988$	−46.4498	+	7.46413i	−1.47776	+	0.237465i
$989$		−	1.88079i		−	0.0598057i
$990$	19.9138	+	5.77735i	0.632903	+	0.183616i
$991$	35.6989			1.13401			0.567006	−	0.823713i	$-0.308101\pi$
$991$	35.6989			1.13401			0.567006	+	0.823713i	$0.308101\pi$
$992$	−1.20947	−	0.493024i	−0.0384007	−	0.0156535i
$993$	31.3658	+	26.4409i	0.995365	+	0.839077i
$994$	54.5384	−	64.0020i	1.72985	−	2.03002i
$995$	−11.2917	−	11.4833i	−0.357971	−	0.364046i
$996$	1.94294	−	1.07693i	0.0615643	−	0.0341237i
$997$	18.2978	−	31.6926i	0.579496	−	1.00372i	−0.416041	−	0.909346i	$-0.636583\pi$
$997$	18.2978	−	31.6926i	0.579496	−	1.00372i	0.995537	−	0.0943704i	$-0.0300838\pi$
$998$	16.4009	+	46.1495i	0.519160	+	1.46084i
$999$	−0.441057	−	0.258675i	−0.0139544	−	0.00818411i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bk.a.349.32	yes	136
5.4	even	2	inner	360.2.bk.a.349.37	yes	136
8.5	even	2	inner	360.2.bk.a.349.54	yes	136
9.4	even	3	inner	360.2.bk.a.229.15	✓	136
40.29	even	2	inner	360.2.bk.a.349.15	yes	136
45.4	even	6	inner	360.2.bk.a.229.54	yes	136
72.13	even	6	inner	360.2.bk.a.229.37	yes	136
360.229	even	6	inner	360.2.bk.a.229.32	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bk.a.229.15	✓	136	9.4	even	3	inner
360.2.bk.a.229.32	yes	136	360.229	even	6	inner
360.2.bk.a.229.37	yes	136	72.13	even	6	inner
360.2.bk.a.229.54	yes	136	45.4	even	6	inner
360.2.bk.a.349.15	yes	136	40.29	even	2	inner
360.2.bk.a.349.32	yes	136	1.1	even	1	trivial
360.2.bk.a.349.37	yes	136	5.4	even	2	inner
360.2.bk.a.349.54	yes	136	8.5	even	2	inner

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.256155 + 1.39082i) q^{2} +(1.70505 + 0.304648i) q^{3} +(-1.86877 - 0.712532i) q^{4} +(-1.56778 - 1.59439i) q^{5} +(-0.860468 + 2.29338i) q^{6} +(4.00243 + 2.31080i) q^{7} +(1.46970 - 2.41661i) q^{8} +(2.81438 + 1.03888i) q^{9} +O(q^{10})\)	\(q+(-0.256155 + 1.39082i) q^{2} +(1.70505 + 0.304648i) q^{3} +(-1.86877 - 0.712532i) q^{4} +(-1.56778 - 1.59439i) q^{5} +(-0.860468 + 2.29338i) q^{6} +(4.00243 + 2.31080i) q^{7} +(1.46970 - 2.41661i) q^{8} +(2.81438 + 1.03888i) q^{9} +(2.61910 - 1.77209i) q^{10} +(1.89283 + 1.09283i) q^{11} +(-2.96927 - 1.78422i) q^{12} +(-1.56540 - 2.71134i) q^{13} +(-4.23916 + 4.97474i) q^{14} +(-2.18741 - 3.19613i) q^{15} +(2.98460 + 2.66312i) q^{16} -2.09803i q^{17} +(-2.16581 + 3.64819i) q^{18} +7.51339i q^{19} +(1.79377 + 4.09663i) q^{20} +(6.12035 + 5.15936i) q^{21} +(-2.00479 + 2.35266i) q^{22} +(0.173434 - 0.100132i) q^{23} +(3.24212 - 3.67269i) q^{24} +(-0.0841378 + 4.99929i) q^{25} +(4.17198 - 1.48266i) q^{26} +(4.48216 + 2.62873i) q^{27} +(-5.83309 - 7.17021i) q^{28} +(-4.48703 - 2.59059i) q^{29} +(5.00556 - 2.22360i) q^{30} +(0.115444 + 0.199954i) q^{31} +(-4.46844 + 3.46887i) q^{32} +(2.89445 + 2.43997i) q^{33} +(2.91798 + 0.537420i) q^{34} +(-2.59061 - 10.0042i) q^{35} +(-4.51919 - 3.94676i) q^{36} -0.0984028 q^{37} +(-10.4498 - 1.92459i) q^{38} +(-1.84307 - 5.09987i) q^{39} +(-6.15717 + 1.44544i) q^{40} +(-2.10507 - 3.64609i) q^{41} +(-8.74351 + 7.19072i) q^{42} +(4.69577 - 8.13332i) q^{43} +(-2.75860 - 3.39095i) q^{44} +(-2.75595 - 6.11594i) q^{45} +(0.0948400 + 0.266865i) q^{46} +(-6.70474 - 3.87099i) q^{47} +(4.27757 + 5.44999i) q^{48} +(7.17962 + 12.4355i) q^{49} +(-6.93157 - 1.39761i) q^{50} +(0.639160 - 3.57724i) q^{51} +(0.993443 + 6.18227i) q^{52} +7.81882 q^{53} +(-4.80423 + 5.56052i) q^{54} +(-1.22516 - 4.73122i) q^{55} +(11.4667 - 6.27610i) q^{56} +(-2.28894 + 12.8107i) q^{57} +(4.75242 - 5.57706i) q^{58} +(0.434562 - 0.250894i) q^{59} +(1.81043 + 7.53142i) q^{60} +(-8.80696 - 5.08470i) q^{61} +(-0.307673 + 0.109342i) q^{62} +(8.86370 + 10.6615i) q^{63} +(-3.67997 - 7.10337i) q^{64} +(-1.86874 + 6.74663i) q^{65} +(-4.13499 + 3.40065i) q^{66} +(-2.36402 - 4.09460i) q^{67} +(-1.49491 + 3.92073i) q^{68} +(0.326218 - 0.117894i) q^{69} +(14.5777 - 1.04044i) q^{70} -12.8654 q^{71} +(6.64685 - 5.27441i) q^{72} -4.83099i q^{73} +(0.0252064 - 0.136861i) q^{74} +(-1.66648 + 8.49840i) q^{75} +(5.35353 - 14.0408i) q^{76} +(5.05062 + 8.74793i) q^{77} +(7.56512 - 1.25702i) q^{78} +(2.14223 - 3.71045i) q^{79} +(-0.433153 - 8.93378i) q^{80} +(6.84146 + 5.84760i) q^{81} +(5.61028 - 1.99381i) q^{82} +(-0.320637 + 0.555359i) q^{83} +(-7.76131 - 14.0026i) q^{84} +(-3.34507 + 3.28924i) q^{85} +(10.1091 + 8.61437i) q^{86} +(-6.86138 - 5.78404i) q^{87} +(5.42283 - 2.96811i) q^{88} -0.894402 q^{89} +(9.21213 - 2.26641i) q^{90} -14.4693i q^{91} +(-0.395455 + 0.0635467i) q^{92} +(0.135921 + 0.376102i) q^{93} +(7.10130 - 8.33353i) q^{94} +(11.9792 - 11.7793i) q^{95} +(-8.67569 + 4.55329i) q^{96} +(-12.2234 - 7.05717i) q^{97} +(-19.1346 + 6.80016i) q^{98} +(4.19184 + 5.04206i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 2 q^{4} - 8 q^{9}+O(q^{10}) \) 136 * q - 2 * q^4 - 8 * q^9	\( 136 q - 2 q^{4} - 8 q^{9} - 10 q^{14} + 2 q^{15} - 2 q^{16} - 2 q^{20} - 38 q^{24} - 2 q^{25} + 16 q^{26} - 12 q^{30} - 4 q^{31} + 8 q^{34} - 24 q^{36} + 4 q^{39} - 6 q^{40} - 4 q^{41} - 56 q^{44} - 28 q^{46} + 40 q^{49} - 12 q^{50} + 10 q^{54} - 28 q^{55} + 26 q^{56} - 58 q^{60} - 20 q^{64} + 18 q^{65} + 16 q^{66} - 6 q^{70} - 128 q^{71} + 36 q^{74} + 12 q^{76} - 4 q^{79} - 36 q^{80} - 16 q^{81} - 110 q^{84} + 44 q^{86} - 32 q^{89} + 32 q^{90} - 34 q^{94} + 8 q^{95} - 2 q^{96}+O(q^{100}) \) 136 * q - 2 * q^4 - 8 * q^9 - 10 * q^14 + 2 * q^15 - 2 * q^16 - 2 * q^20 - 38 * q^24 - 2 * q^25 + 16 * q^26 - 12 * q^30 - 4 * q^31 + 8 * q^34 - 24 * q^36 + 4 * q^39 - 6 * q^40 - 4 * q^41 - 56 * q^44 - 28 * q^46 + 40 * q^49 - 12 * q^50 + 10 * q^54 - 28 * q^55 + 26 * q^56 - 58 * q^60 - 20 * q^64 + 18 * q^65 + 16 * q^66 - 6 * q^70 - 128 * q^71 + 36 * q^74 + 12 * q^76 - 4 * q^79 - 36 * q^80 - 16 * q^81 - 110 * q^84 + 44 * q^86 - 32 * q^89 + 32 * q^90 - 34 * q^94 + 8 * q^95 - 2 * q^96

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