LMFDB - Embedded newform 720.2.cf.a.131.72

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(11,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 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("720.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.cf (of order $12$, degree $4$, 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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$96$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			131.72
Character	$\chi$	$=$	720.131
Dual form			720.2.cf.a.11.72

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.948954 + 1.04856i) q^{2} +(-1.03510 - 1.38873i) q^{3} +(-0.198972 + 1.99008i) q^{4} +(-0.965926 + 0.258819i) q^{5} +(0.473908 - 2.40321i) q^{6} +(-0.374804 - 0.649179i) q^{7} +(-2.27554 + 1.67986i) q^{8} +(-0.857136 + 2.87495i) q^{9} +O(q^{10})$	\(q+(0.948954 + 1.04856i) q^{2} +(-1.03510 - 1.38873i) q^{3} +(-0.198972 + 1.99008i) q^{4} +(-0.965926 + 0.258819i) q^{5} +(0.473908 - 2.40321i) q^{6} +(-0.374804 - 0.649179i) q^{7} +(-2.27554 + 1.67986i) q^{8} +(-0.857136 + 2.87495i) q^{9} +(-1.18801 - 0.767227i) q^{10} +(-3.66632 - 0.982388i) q^{11} +(2.96963 - 1.78361i) q^{12} +(3.15228 - 0.844650i) q^{13} +(0.325034 - 1.00905i) q^{14} +(1.35926 + 1.07351i) q^{15} +(-3.92082 - 0.791941i) q^{16} -6.29856i q^{17} +(-3.82795 + 1.82943i) q^{18} +(-3.26849 + 3.26849i) q^{19} +(-0.322878 - 1.97377i) q^{20} +(-0.513575 + 1.19247i) q^{21} +(-2.44907 - 4.77661i) q^{22} +(-6.11539 - 3.53072i) q^{23} +(4.68828 + 1.42129i) q^{24} +(0.866025 - 0.500000i) q^{25} +(3.87704 + 2.50383i) q^{26} +(4.87974 - 1.78553i) q^{27} +(1.36649 - 0.616720i) q^{28} +(-4.82086 - 1.29174i) q^{29} +(0.164236 + 2.44398i) q^{30} +(-7.57963 - 4.37610i) q^{31} +(-2.89028 - 4.86275i) q^{32} +(2.43074 + 6.10840i) q^{33} +(6.60445 - 5.97705i) q^{34} +(0.530053 + 0.530053i) q^{35} +(-5.55082 - 2.27780i) q^{36} +(-4.87924 + 4.87924i) q^{37} +(-6.52887 - 0.325574i) q^{38} +(-4.43591 - 3.50336i) q^{39} +(1.76322 - 2.21157i) q^{40} +(2.10347 - 3.64332i) q^{41} +(-1.73774 + 0.593080i) q^{42} +(-3.23761 + 12.0829i) q^{43} +(2.68452 - 7.10080i) q^{44} +(0.0838385 - 2.99883i) q^{45} +(-2.10104 - 9.76288i) q^{46} +(2.64304 + 4.57788i) q^{47} +(2.95865 + 6.26469i) q^{48} +(3.21904 - 5.57555i) q^{49} +(1.34610 + 0.433606i) q^{50} +(-8.74700 + 6.51964i) q^{51} +(1.05370 + 6.44134i) q^{52} +(4.61391 + 4.61391i) q^{53} +(6.50289 + 3.42234i) q^{54} +3.79566 q^{55} +(1.94341 + 0.847616i) q^{56} +(7.92227 + 1.15583i) q^{57} +(-3.22029 - 6.28078i) q^{58} +(0.589470 + 2.19993i) q^{59} +(-2.40681 + 2.49143i) q^{60} +(-0.523104 + 1.95225i) q^{61} +(-2.60410 - 12.1004i) q^{62} +(2.18761 - 0.521106i) q^{63} +(2.35616 - 7.64516i) q^{64} +(-2.82625 + 1.63174i) q^{65} +(-4.09838 + 8.34537i) q^{66} +(-2.45594 - 9.16570i) q^{67} +(12.5346 + 1.25324i) q^{68} +(1.42683 + 12.1473i) q^{69} +(-0.0527984 + 1.05879i) q^{70} -2.14152i q^{71} +(-2.87905 - 7.98192i) q^{72} +4.18607i q^{73} +(-9.74637 - 0.486020i) q^{74} +(-1.59079 - 0.685124i) q^{75} +(-5.85422 - 7.15489i) q^{76} +(0.736406 + 2.74830i) q^{77} +(-0.535980 - 7.97587i) q^{78} +(10.8642 - 6.27244i) q^{79} +(3.99219 - 0.249827i) q^{80} +(-7.53064 - 4.92844i) q^{81} +(5.81635 - 1.25172i) q^{82} +(3.47930 - 12.9849i) q^{83} +(-2.27091 - 1.25932i) q^{84} +(1.63019 + 6.08395i) q^{85} +(-15.7420 + 8.07129i) q^{86} +(3.19619 + 8.03195i) q^{87} +(9.99313 - 3.92344i) q^{88} -3.54371 q^{89} +(3.22402 - 2.75784i) q^{90} +(-1.72981 - 1.72981i) q^{91} +(8.24321 - 11.4676i) q^{92} +(1.76846 + 15.0558i) q^{93} +(-2.29208 + 7.11560i) q^{94} +(2.31117 - 4.00307i) q^{95} +(-3.76131 + 9.04724i) q^{96} +(5.79039 + 10.0293i) q^{97} +(8.90104 - 1.91557i) q^{98} +(5.96685 - 9.69844i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 12 q^{6}+O(q^{10}) $ 384 * q - 12 * q^6	$ 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64} - 72 q^{66} - 156 q^{68} - 112 q^{72} - 168 q^{74} + 12 q^{76} - 116 q^{78} + 72 q^{82} - 120 q^{83} - 116 q^{84} - 36 q^{90} + 48 q^{93} + 20 q^{96} - 32 q^{99}+O(q^{100}) $ 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.948954	+	1.04856i	0.671012	+	0.741447i
$2$	0.948954	+	1.04856i	0.671012	+	0.741447i
$3$	−1.03510	−	1.38873i	−0.597615	−	0.801783i
$3$	−1.03510	−	1.38873i	−0.597615	−	0.801783i
$4$	−0.198972	+	1.99008i	−0.0994861	+	0.995039i
$5$	−0.965926	+	0.258819i	−0.431975	+	0.115747i
$5$	−0.965926	+	0.258819i	−0.431975	+	0.115747i
$6$	0.473908	−	2.40321i	0.193472	−	0.981106i
$7$	−0.374804	−	0.649179i	−0.141663	−	0.245367i	0.786460	−	0.617641i	$-0.211911\pi$
$7$	−0.374804	−	0.649179i	−0.141663	−	0.245367i	−0.928123	+	0.372274i	$0.878578\pi$
$8$	−2.27554	+	1.67986i	−0.804525	+	0.593919i
$9$	−0.857136	+	2.87495i	−0.285712	+	0.958316i
$10$	−1.18801	−	0.767227i	−0.375681	−	0.242619i
$11$	−3.66632	−	0.982388i	−1.10544	−	0.296201i	−0.340461	−	0.940259i	$-0.610583\pi$
$11$	−3.66632	−	0.982388i	−1.10544	−	0.296201i	−0.764977	+	0.644058i	$0.777250\pi$
$12$	2.96963	−	1.78361i	0.857260	−	0.514884i
$13$	3.15228	−	0.844650i	0.874284	−	0.234264i	0.206345	−	0.978479i	$-0.433843\pi$
$13$	3.15228	−	0.844650i	0.874284	−	0.234264i	0.667940	+	0.744216i	$0.267176\pi$
$14$	0.325034	−	1.00905i	0.0868691	−	0.269679i
$15$	1.35926	+	1.07351i	0.350959	+	0.277178i
$16$	−3.92082	−	0.791941i	−0.980205	−	0.197985i
$17$		−	6.29856i		−	1.52763i	−0.645438	−	0.763813i	$-0.723325\pi$
$17$		−	6.29856i		−	1.52763i	0.645438	−	0.763813i	$-0.276675\pi$
$18$	−3.82795	+	1.82943i	−0.902256	+	0.431201i
$19$	−3.26849	+	3.26849i	−0.749844	+	0.749844i	−0.974450	−	0.224606i	$-0.927890\pi$
$19$	−3.26849	+	3.26849i	−0.749844	+	0.749844i	0.224606	+	0.974450i	$0.427890\pi$
$20$	−0.322878	−	1.97377i	−0.0721976	−	0.441347i
$21$	−0.513575	+	1.19247i	−0.112071	+	0.260218i
$22$	−2.44907	−	4.77661i	−0.522144	−	1.01838i
$23$	−6.11539	−	3.53072i	−1.27515	−	0.736207i	−0.299196	−	0.954192i	$-0.596718\pi$
$23$	−6.11539	−	3.53072i	−1.27515	−	0.736207i	−0.975952	+	0.217985i	$0.930052\pi$
$24$	4.68828	+	1.42129i	0.956991	+	0.290119i
$25$	0.866025	−	0.500000i	0.173205	−	0.100000i
$26$	3.87704	+	2.50383i	0.760349	+	0.491041i
$27$	4.87974	−	1.78553i	0.939107	−	0.343625i
$28$	1.36649	−	0.616720i	0.258243	−	0.116549i
$29$	−4.82086	−	1.29174i	−0.895210	−	0.239871i	−0.218252	−	0.975892i	$-0.570036\pi$
$29$	−4.82086	−	1.29174i	−0.895210	−	0.239871i	−0.676958	+	0.736021i	$0.736702\pi$
$30$	0.164236	+	2.44398i	0.0299852	+	0.446207i
$31$	−7.57963	−	4.37610i	−1.36134	−	0.785971i	−0.371539	−	0.928417i	$-0.621170\pi$
$31$	−7.57963	−	4.37610i	−1.36134	−	0.785971i	−0.989802	+	0.142447i	$0.954503\pi$
$32$	−2.89028	−	4.86275i	−0.510934	−	0.859620i
$33$	2.43074	+	6.10840i	0.423137	+	1.06334i
$34$	6.60445	−	5.97705i	1.13265	−	1.02506i
$35$	0.530053	+	0.530053i	0.0895953	+	0.0895953i
$36$	−5.55082	−	2.27780i	−0.925137	−	0.379634i
$37$	−4.87924	+	4.87924i	−0.802142	+	0.802142i	−0.983430	−	0.181288i	$-0.941973\pi$
$37$	−4.87924	+	4.87924i	−0.802142	+	0.802142i	0.181288	+	0.983430i	$0.441973\pi$
$38$	−6.52887	−	0.325574i	−1.05912	−	0.0528150i
$39$	−4.43591	−	3.50336i	−0.710314	−	0.560987i
$40$	1.76322	−	2.21157i	0.278790	−	0.349680i
$41$	2.10347	−	3.64332i	0.328507	−	0.568991i	−0.653709	−	0.756746i	$-0.726788\pi$
$41$	2.10347	−	3.64332i	0.328507	−	0.568991i	0.982216	+	0.187755i	$0.0601213\pi$
$42$	−1.73774	+	0.593080i	−0.268138	+	0.0915143i
$43$	−3.23761	+	12.0829i	−0.493730	+	1.84263i	0.0432979	+	0.999062i	$0.486214\pi$
$43$	−3.23761	+	12.0829i	−0.493730	+	1.84263i	−0.537028	+	0.843564i	$0.680453\pi$
$44$	2.68452	−	7.10080i	0.404707	−	1.07049i
$45$	0.0838385	−	2.99883i	0.0124979	−	0.447039i
$46$	−2.10104	−	9.76288i	−0.309781	−	1.43946i
$47$	2.64304	+	4.57788i	0.385527	+	0.667753i	0.991842	−	0.127472i	$-0.0406862\pi$
$47$	2.64304	+	4.57788i	0.385527	+	0.667753i	−0.606315	+	0.795225i	$0.707353\pi$
$48$	2.95865	+	6.26469i	0.427044	+	0.904231i
$49$	3.21904	−	5.57555i	0.459863	−	0.796507i
$50$	1.34610	+	0.433606i	0.190367	+	0.0613211i
$51$	−8.74700	+	6.51964i	−1.22482	+	0.912933i
$52$	1.05370	+	6.44134i	0.146122	+	0.893253i
$53$	4.61391	+	4.61391i	0.633769	+	0.633769i	0.949011	−	0.315242i	$-0.102086\pi$
$53$	4.61391	+	4.61391i	0.633769	+	0.633769i	−0.315242	+	0.949011i	$0.602086\pi$
$54$	6.50289	+	3.42234i	0.884932	+	0.465721i
$55$	3.79566			0.511806
$56$	1.94341	+	0.847616i	0.259699	+	0.113267i
$57$	7.92227	+	1.15583i	1.04933	+	0.153094i
$58$	−3.22029	−	6.28078i	−0.422845	−	0.824707i
$59$	0.589470	+	2.19993i	0.0767425	+	0.286407i	0.993623	−	0.112755i	$-0.0359677\pi$
$59$	0.589470	+	2.19993i	0.0767425	+	0.286407i	−0.916880	+	0.399162i	$0.869301\pi$
$60$	−2.40681	+	2.49143i	−0.310718	+	0.321643i
$61$	−0.523104	+	1.95225i	−0.0669766	+	0.249960i	−0.991294	−	0.131663i	$-0.957968\pi$
$61$	−0.523104	+	1.95225i	−0.0669766	+	0.249960i	0.924318	+	0.381623i	$0.124635\pi$
$62$	−2.60410	−	12.1004i	−0.330721	−	1.53676i
$63$	2.18761	−	0.521106i	0.275613	−	0.0656532i
$64$	2.35616	−	7.64516i	0.294520	−	0.955645i
$65$	−2.82625	+	1.63174i	−0.350554	+	0.202392i
$66$	−4.09838	+	8.34537i	−0.504476	+	1.02724i
$67$	−2.45594	−	9.16570i	−0.300041	−	1.11977i	−0.937131	−	0.348978i	$-0.886529\pi$
$67$	−2.45594	−	9.16570i	−0.300041	−	1.11977i	0.637090	−	0.770790i	$-0.280138\pi$
$68$	12.5346	+	1.25324i	1.52005	+	0.151978i
$69$	1.42683	+	12.1473i	0.171770	+	1.46236i
$70$	−0.0527984	+	1.05879i	−0.00631062	+	0.126550i
$71$		−	2.14152i		−	0.254151i	−0.991893	−	0.127076i	$-0.959441\pi$
$71$		−	2.14152i		−	0.254151i	0.991893	−	0.127076i	$-0.0405591\pi$
$72$	−2.87905	−	7.98192i	−0.339300	−	0.940678i
$73$			4.18607i			0.489942i	0.969530	+	0.244971i	$0.0787785\pi$
$73$			4.18607i			0.489942i	−0.969530	+	0.244971i	$0.921222\pi$
$74$	−9.74637	−	0.486020i	−1.13299	−	0.0564987i
$75$	−1.59079	−	0.685124i	−0.183688	−	0.0791114i
$76$	−5.85422	−	7.15489i	−0.671525	−	0.820723i
$77$	0.736406	+	2.74830i	0.0839212	+	0.313198i
$78$	−0.535980	−	7.97587i	−0.0606877	−	0.903089i
$79$	10.8642	−	6.27244i	1.22232	−	0.705704i	0.256905	−	0.966437i	$-0.417297\pi$
$79$	10.8642	−	6.27244i	1.22232	−	0.705704i	0.965411	+	0.260733i	$0.0839641\pi$
$80$	3.99219	−	0.249827i	0.446340	−	0.0279315i
$81$	−7.53064	−	4.92844i	−0.836737	−	0.547604i
$82$	5.81635	−	1.25172i	0.642308	−	0.138229i
$83$	3.47930	−	12.9849i	0.381902	−	1.42528i	−0.461090	−	0.887353i	$-0.652541\pi$
$83$	3.47930	−	12.9849i	0.381902	−	1.42528i	0.842992	−	0.537926i	$-0.180792\pi$
$84$	−2.27091	−	1.25932i	−0.247777	−	0.137403i
$85$	1.63019	+	6.08395i	0.176819	+	0.659897i
$86$	−15.7420	+	8.07129i	−1.69751	+	0.870350i
$87$	3.19619	+	8.03195i	0.342667	+	0.861115i
$88$	9.99313	−	3.92344i	1.06527	−	0.418240i
$89$	−3.54371			−0.375633			−0.187816	−	0.982204i	$-0.560141\pi$
$89$	−3.54371			−0.375633			−0.187816	+	0.982204i	$0.560141\pi$
$90$	3.22402	−	2.75784i	0.339842	−	0.290702i
$91$	−1.72981	−	1.72981i	−0.181334	−	0.181334i
$92$	8.24321	−	11.4676i	0.859414	−	1.19558i
$93$	1.76846	+	15.0558i	0.183380	+	1.56121i
$94$	−2.29208	+	7.11560i	−0.236410	+	0.733918i
$95$	2.31117	−	4.00307i	0.237121	−	0.410706i
$96$	−3.76131	+	9.04724i	−0.383887	+	0.923380i
$97$	5.79039	+	10.0293i	0.587926	+	1.01832i	0.994504	+	0.104701i	$0.0333885\pi$
$97$	5.79039	+	10.0293i	0.587926	+	1.01832i	−0.406578	+	0.913616i	$0.633278\pi$
$98$	8.90104	−	1.91557i	0.899141	−	0.193501i
$99$	5.96685	−	9.69844i	0.599691	−	0.974730i
$100$	0.822724	+	1.82294i	0.0822724	+	0.182294i
$101$	−0.353395	+	1.31889i	−0.0351641	+	0.131234i	−0.981277	−	0.192604i	$-0.938307\pi$
$101$	−0.353395	+	1.31889i	−0.0351641	+	0.131234i	0.946112	+	0.323838i	$0.104973\pi$
$102$	−15.1368	−	2.98494i	−1.49876	−	0.295553i
$103$	−2.10483	+	3.64567i	−0.207395	+	0.359219i	−0.950893	−	0.309519i	$-0.899832\pi$
$103$	−2.10483	+	3.64567i	−0.207395	+	0.359219i	0.743498	+	0.668738i	$0.233165\pi$
$104$	−5.75424	+	7.21741i	−0.564249	+	0.707725i
$105$	0.187442	−	1.28476i	0.0182925	−	0.125379i
$106$	−0.459590	+	9.21636i	−0.0446393	+	0.895172i
$107$	−1.89744	+	1.89744i	−0.183433	+	0.183433i	−0.792850	−	0.609417i	$-0.791403\pi$
$107$	−1.89744	+	1.89744i	−0.183433	+	0.183433i	0.609417	+	0.792850i	$0.291403\pi$
$108$	2.58241	+	10.0663i	0.248492	+	0.968634i
$109$	14.5672	+	14.5672i	1.39529	+	1.39529i	0.812940	+	0.582348i	$0.197866\pi$
$109$	14.5672	+	14.5672i	1.39529	+	1.39529i	0.582348	+	0.812940i	$0.302134\pi$
$110$	3.60190	+	3.97999i	0.343428	+	0.379477i
$111$	11.8264	+	1.72544i	1.12252	+	0.163771i
$112$	0.955427	+	2.84214i	0.0902794	+	0.268557i
$113$	−7.20655	−	4.16070i	−0.677935	−	0.391406i	0.121142	−	0.992635i	$-0.461344\pi$
$113$	−7.20655	−	4.16070i	−0.677935	−	0.391406i	−0.799076	+	0.601229i	$0.794678\pi$
$114$	6.30590	+	9.40383i	0.590602	+	0.880750i
$115$	6.82083	+	1.82764i	0.636046	+	0.170428i
$116$	3.52989	−	9.33686i	0.327742	−	0.866905i
$117$	−0.273605	+	9.78661i	−0.0252948	+	0.904772i
$118$	−1.74739	+	2.70573i	−0.160860	+	0.249083i
$119$	−4.08890	+	2.36073i	−0.374829	+	0.216407i
$120$	−4.89638	−	0.159442i	−0.446977	−	0.0145550i
$121$	2.95055	+	1.70350i	0.268232	+	0.154864i
$122$	−2.54346	+	1.30409i	−0.230274	+	0.118067i
$123$	−7.23688	+	0.850048i	−0.652528	+	0.0766463i
$124$	10.2169	−	14.2133i	0.917506	−	1.27639i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$	2.62236	+	1.79935i	0.233618	+	0.160299i
$127$			20.3017i			1.80148i	0.434354	+	0.900742i	$0.356977\pi$
$127$			20.3017i			1.80148i	−0.434354	+	0.900742i	$0.643023\pi$
$128$	10.2523	−	4.78433i	0.906186	−	0.422879i
$129$	20.1311	−	8.01086i	1.77245	−	0.705317i
$130$	−4.39297	−	1.41506i	−0.385289	−	0.124109i
$131$	−3.56149	+	0.954300i	−0.311169	+	0.0833775i	−0.411024	−	0.911624i	$-0.634829\pi$
$131$	−3.56149	+	0.954300i	−0.311169	+	0.0833775i	0.0998549	+	0.995002i	$0.468162\pi$
$132$	−12.6398	+	3.62196i	−1.10016	+	0.315251i
$133$	3.34688	+	0.896794i	0.290211	+	0.0777619i
$134$	7.28024	−	11.2730i	0.628917	−	0.973842i
$135$	−4.25134	+	2.98766i	−0.365897	+	0.257137i
$136$	10.5807	+	14.3326i	0.907287	+	1.22901i
$137$	0.372051	+	0.644410i	0.0317864	+	0.0550557i	0.881481	−	0.472219i	$-0.156547\pi$
$137$	0.372051	+	0.644410i	0.0317864	+	0.0550557i	−0.849695	+	0.527275i	$0.823214\pi$
$138$	−11.3832	+	13.0233i	−0.969002	+	1.10862i
$139$	−15.4225	+	4.13245i	−1.30812	+	0.350510i	−0.844515	−	0.535531i	$-0.820111\pi$
$139$	−15.4225	+	4.13245i	−1.30812	+	0.350510i	−0.463606	+	0.886041i	$0.653445\pi$
$140$	−1.16031	+	0.949380i	−0.0980643	+	0.0802373i
$141$	3.62162	−	8.40903i	0.304996	−	0.708168i
$142$	2.24552	−	2.03220i	0.188440	−	0.170538i
$143$	−12.3870			−1.03586
$144$	5.63746	−	10.5933i	0.469788	−	0.882779i
$145$	4.99092			0.414473
$146$	−4.38936	+	3.97239i	−0.363266	+	0.328757i
$147$	−11.0750	+	1.30087i	−0.913447	+	0.107294i
$148$	−8.73924	−	10.6809i	−0.718361	−	0.877965i
$149$	−19.5423	+	5.23633i	−1.60096	+	0.428977i	−0.945334	−	0.326105i	$-0.894264\pi$
$149$	−19.5423	+	5.23633i	−1.60096	+	0.428977i	−0.655630	+	0.755082i	$0.727597\pi$
$150$	−0.791188	−	2.31819i	−0.0646002	−	0.189280i
$151$	−5.03706	−	8.72445i	−0.409910	−	0.709986i	0.584969	−	0.811056i	$-0.301107\pi$
$151$	−5.03706	−	8.72445i	−0.409910	−	0.709986i	−0.994879	+	0.101070i	$0.967773\pi$
$152$	1.94698	−	12.9282i	0.157921	−	1.04861i
$153$	18.1080	+	5.39872i	1.46395	+	0.436461i
$154$	−2.18296	+	3.38018i	−0.175908	+	0.272383i
$155$	8.45398	+	2.26524i	0.679040	+	0.181948i
$156$	7.85458	−	8.13074i	0.628870	−	0.650980i
$157$	4.99974	−	1.33968i	0.399023	−	0.106918i	−0.0537264	−	0.998556i	$-0.517110\pi$
$157$	4.99974	−	1.33968i	0.399023	−	0.106918i	0.452749	+	0.891638i	$0.350443\pi$
$158$	16.8867	+	5.43953i	1.34343	+	0.432746i
$159$	1.63161	−	11.1833i	0.129395	−	0.886895i
$160$	4.05037	+	3.94899i	0.320210	+	0.312195i
$161$			5.29332i			0.417172i
$162$	−1.97845	−	12.5732i	−0.155441	−	0.987845i
$163$	15.8613	−	15.8613i	1.24235	−	1.24235i	0.283331	−	0.959022i	$-0.408560\pi$
$163$	15.8613	−	15.8613i	1.24235	−	1.24235i	0.959022	−	0.283331i	$-0.0914397\pi$
$164$	6.83195	+	4.91099i	0.533486	+	0.383484i
$165$	−3.92888	−	5.27114i	−0.305863	−	0.410357i
$166$	16.9172	−	8.67382i	1.31303	−	0.673219i
$167$	12.0672	+	6.96699i	0.933787	+	0.539122i	0.888007	−	0.459830i	$-0.152089\pi$
$167$	12.0672	+	6.96699i	0.933787	+	0.539122i	0.0457795	+	0.998952i	$0.485423\pi$
$168$	−0.834515	−	3.57624i	−0.0643842	−	0.275913i
$169$	−2.03491	+	1.17486i	−0.156532	+	0.0903737i
$170$	−4.83243	+	7.48274i	−0.370631	+	0.573900i
$171$	−6.59520	−	12.1983i	−0.504348	−	0.932826i
$172$	−23.4017	−	8.84725i	−1.78437	−	0.674597i
$173$	−14.5442	−	3.89710i	−1.10577	−	0.296291i	−0.340659	−	0.940187i	$-0.610650\pi$
$173$	−14.5442	−	3.89710i	−1.10577	−	0.296291i	−0.765113	+	0.643896i	$0.777317\pi$
$174$	−5.38898	+	10.9734i	−0.408537	+	0.831888i
$175$	−0.649179	−	0.374804i	−0.0490733	−	0.0283325i
$176$	13.5970	+	6.75527i	1.02491	+	0.509198i
$177$	2.44495	−	3.09576i	0.183774	−	0.232692i
$178$	−3.36282	−	3.71581i	−0.252054	−	0.278511i
$179$	−2.98913	−	2.98913i	−0.223418	−	0.223418i	0.586518	−	0.809936i	$-0.300498\pi$
$179$	−2.98913	−	2.98913i	−0.223418	−	0.223418i	−0.809936	+	0.586518i	$0.800498\pi$
$180$	5.95122	+	0.763529i	0.443578	+	0.0569101i
$181$	−1.94677	+	1.94677i	−0.144702	+	0.144702i	−0.775747	−	0.631044i	$-0.782627\pi$
$181$	−1.94677	+	1.94677i	−0.144702	+	0.144702i	0.631044	+	0.775747i	$0.282627\pi$
$182$	0.172306	−	3.45534i	0.0127722	−	0.256127i
$183$	3.25261	−	1.29433i	0.240440	−	0.0956793i
$184$	19.8469	−	2.23869i	1.46314	−	0.165038i
$185$	3.45014	−	5.97582i	0.253660	−	0.439351i
$186$	−14.1087	+	16.1416i	−1.03450	+	1.18356i
$187$	−6.18763	+	23.0926i	−0.452485	+	1.68870i
$188$	−9.63623	+	4.34899i	−0.702795	+	0.317182i
$189$	−2.98807	−	2.49861i	−0.217350	−	0.181747i
$190$	6.39067	−	1.37532i	0.463628	−	0.0997759i
$191$	−4.74697	−	8.22199i	−0.343478	−	0.594922i	0.641598	−	0.767041i	$-0.278272\pi$
$191$	−4.74697	−	8.22199i	−0.343478	−	0.594922i	−0.985076	+	0.172119i	$0.944939\pi$
$192$	−13.0559	+	4.64144i	−0.942230	+	0.334967i
$193$	7.65045	−	13.2510i	0.550691	−	0.953825i	−0.447533	−	0.894267i	$-0.647697\pi$
$193$	7.65045	−	13.2510i	0.550691	−	0.953825i	0.998225	−	0.0595583i	$-0.0189692\pi$
$194$	−5.02150	+	15.5889i	−0.360523	+	1.11922i
$195$	5.19150	+	2.23589i	0.371771	+	0.160115i
$196$	10.4553	+	7.51553i	0.746805	+	0.536823i
$197$	−1.10780	−	1.10780i	−0.0789278	−	0.0789278i	0.666541	−	0.745469i	$-0.267774\pi$
$197$	−1.10780	−	1.10780i	−0.0789278	−	0.0789278i	−0.745469	+	0.666541i	$0.767774\pi$
$198$	15.8317	−	2.94675i	1.12511	−	0.209417i
$199$	4.25273			0.301468			0.150734	−	0.988574i	$-0.451836\pi$
$199$	4.25273			0.301468			0.150734	+	0.988574i	$0.451836\pi$
$200$	−1.13075	+	2.59257i	−0.0799558	+	0.183322i
$201$	−10.1865	+	12.8980i	−0.718502	+	0.909758i
$202$	−1.71829	+	0.881007i	−0.120899	+	0.0619875i
$203$	0.968302	+	3.61375i	0.0679615	+	0.253636i
$204$	−11.2342	−	18.7044i	−0.786551	−	1.30957i
$205$	−1.08884	+	4.06359i	−0.0760476	+	0.283814i
$206$	−5.82010	+	1.25253i	−0.405506	+	0.0872677i
$207$	15.3924	−	14.5551i	1.06984	−	1.01165i
$208$	−13.0284	+	0.815305i	−0.903359	+	0.0565312i
$209$	15.1943	−	8.77242i	1.05101	−	0.606801i
$210$	1.52502	−	1.02263i	0.105237	−	0.0705682i
$211$	−4.93974	−	18.4354i	−0.340066	−	1.26914i	−0.898271	−	0.439441i	$-0.855177\pi$
$211$	−4.93974	−	18.4354i	−0.340066	−	1.26914i	0.558205	−	0.829703i	$-0.311490\pi$
$212$	−10.1001	+	8.26399i	−0.693676	+	0.567573i
$213$	−2.97399	+	2.21668i	−0.203774	+	0.151885i
$214$	−3.79017	−	0.189004i	−0.259091	−	0.0129200i
$215$		−	12.5091i		−	0.853117i
$216$	−8.10461	+	12.2603i	−0.551449	+	0.834209i
$217$			6.56072i			0.445371i
$218$	−1.45104	+	29.0983i	−0.0982767	+	1.97079i
$219$	5.81331	−	4.33300i	0.392827	−	0.292797i
$220$	−0.755230	+	7.55365i	−0.0509176	+	0.509267i
$221$	−5.32008	−	19.8548i	−0.357867	−	1.33558i
$222$	9.41352	+	14.0381i	0.631794	+	0.942179i
$223$	−9.16884	+	5.29363i	−0.613991	+	0.354488i	−0.774526	−	0.632542i	$-0.782011\pi$
$223$	−9.16884	+	5.29363i	−0.613991	+	0.354488i	0.160535	+	0.987030i	$0.448678\pi$
$224$	−2.07351	+	3.69888i	−0.138542	+	0.247142i
$225$	0.695172	+	2.91834i	0.0463448	+	0.194556i
$226$	−2.47592	−	11.5048i	−0.164696	−	0.765290i
$227$	−0.230578	+	0.860529i	−0.0153040	+	0.0571153i	−0.973156	−	0.230148i	$-0.926079\pi$
$227$	−0.230578	+	0.860529i	−0.0153040	+	0.0571153i	0.957852	+	0.287264i	$0.0927456\pi$
$228$	−3.87651	+	15.5359i	−0.256728	+	1.02889i
$229$	1.62981	+	6.08252i	0.107701	+	0.401944i	0.998638	−	0.0521828i	$-0.0166179\pi$
$229$	1.62981	+	6.08252i	0.107701	+	0.401944i	−0.890937	+	0.454127i	$0.849951\pi$
$230$	4.55626	+	8.88642i	0.300431	+	0.585953i
$231$	3.05439	−	3.86744i	0.200964	−	0.254459i
$232$	13.1400	−	5.15894i	0.862683	−	0.338701i
$233$	4.57522			0.299732			0.149866	−	0.988706i	$-0.452116\pi$
$233$	4.57522			0.299732			0.149866	+	0.988706i	$0.452116\pi$
$234$	−10.5215	+	9.00015i	−0.687813	+	0.588358i
$235$	−3.73783	−	3.73783i	−0.243829	−	0.243829i
$236$	−4.49533	+	0.735366i	−0.292621	+	0.0478682i
$237$	−19.9562	−	8.59480i	−1.29630	−	0.558292i
$238$	−6.35555	−	2.04725i	−0.411969	−	0.132703i
$239$	−4.94611	+	8.56691i	−0.319937	+	0.554147i	−0.980475	−	0.196646i	$-0.936995\pi$
$239$	−4.94611	+	8.56691i	−0.319937	+	0.554147i	0.660538	+	0.750793i	$0.270328\pi$
$240$	−4.47926	−	5.28547i	−0.289135	−	0.341176i
$241$	−10.5418	−	18.2589i	−0.679055	−	1.17616i	−0.975266	−	0.221035i	$-0.929057\pi$
$241$	−10.5418	−	18.2589i	−0.679055	−	1.17616i	0.296211	−	0.955123i	$-0.404277\pi$
$242$	1.01371	+	4.71038i	0.0651635	+	0.302795i
$243$	0.950698	+	15.5594i	0.0609873	+	0.998139i
$244$	−3.78105	−	1.42946i	−0.242057	−	0.0915119i
$245$	−1.66630	+	6.21872i	−0.106456	+	0.397299i
$246$	−7.75880	−	6.78168i	−0.494683	−	0.432384i
$247$	−7.54246	+	13.0639i	−0.479915	+	0.831238i
$248$	24.5990	−	2.77471i	1.56204	−	0.176194i
$249$	−21.6339	+	8.60888i	−1.37099	+	0.545566i
$250$	−1.41246	−	0.0704347i	−0.0893317	−	0.00445468i
$251$	−4.44052	+	4.44052i	−0.280283	+	0.280283i	−0.833222	−	0.552939i	$-0.813506\pi$
$251$	−4.44052	+	4.44052i	−0.280283	+	0.280283i	0.552939	+	0.833222i	$0.313506\pi$
$252$	0.601768	+	4.45721i	0.0379078	+	0.280778i
$253$	18.9525	+	18.9525i	1.19153	+	1.19153i
$254$	−21.2876	+	19.2654i	−1.33570	+	1.20882i
$255$	6.76154	−	8.56138i	0.423424	−	0.536135i
$256$	14.7457	+	6.21011i	0.921604	+	0.388132i
$257$	−22.1557	−	12.7916i	−1.38203	−	0.797918i	−0.389634	−	0.920970i	$-0.627398\pi$
$257$	−22.1557	−	12.7916i	−1.38203	−	0.797918i	−0.992400	+	0.123052i	$0.960732\pi$
$258$	27.5034	+	13.5068i	1.71229	+	0.840899i
$259$	4.99626	+	1.33874i	0.310453	+	0.0831855i
$260$	−2.68494	−	5.94914i	−0.166513	−	0.368950i
$261$	7.84582	−	12.7525i	0.485644	−	0.789360i
$262$	−4.38034	−	2.82887i	−0.270618	−	0.174768i
$263$	−4.22062	+	2.43677i	−0.260254	+	0.150258i	−0.624451	−	0.781064i	$-0.714677\pi$
$263$	−4.22062	+	2.43677i	−0.260254	+	0.150258i	0.364196	+	0.931322i	$0.381344\pi$
$264$	−15.7925	−	9.81660i	−0.971960	−	0.604170i
$265$	−5.65086	−	3.26252i	−0.347129	−	0.200415i
$266$	2.23569	+	4.36044i	0.137079	+	0.267355i
$267$	3.66810	+	4.92125i	0.224484	+	0.301176i
$268$	18.7291	−	3.06379i	1.14406	−	0.187151i
$269$	−21.9133	+	21.9133i	−1.33608	+	1.33608i	−0.436257	+	0.899822i	$0.643696\pi$
$269$	−21.9133	+	21.9133i	−1.33608	+	1.33608i	−0.899822	+	0.436257i	$0.856304\pi$
$270$	−7.16708	−	1.62265i	−0.436174	−	0.0987514i
$271$		−	6.24125i		−	0.379129i	−0.981868	−	0.189564i	$-0.939292\pi$
$271$		−	6.24125i		−	0.379129i	0.981868	−	0.189564i	$-0.0607076\pi$
$272$	−4.98809	+	24.6955i	−0.302447	+	1.49739i
$273$	−0.611712	+	4.19278i	−0.0370225	+	0.253758i
$274$	−0.322647	+	1.00163i	−0.0194918	+	0.0605110i
$275$	−3.66632	+	0.982388i	−0.221088	+	0.0592402i
$276$	−24.4579	+	0.422524i	−1.47219	+	0.0254330i
$277$	7.81716	+	2.09460i	0.469688	+	0.125852i	0.485897	−	0.874016i	$-0.338493\pi$
$277$	7.81716	+	2.09460i	0.469688	+	0.125852i	−0.0162090	+	0.999869i	$0.505160\pi$
$278$	−18.9684	−	12.2500i	−1.13765	−	0.734706i
$279$	19.0778	−	18.0401i	1.14216	−	1.08003i
$280$	−2.09657	−	0.315743i	−0.125294	−	0.0188692i
$281$	−8.55881	−	14.8243i	−0.510576	−	0.884343i	−0.999925	−	0.0122551i	$-0.996099\pi$
$281$	−8.55881	−	14.8243i	−0.510576	−	0.884343i	0.489349	−	0.872088i	$-0.337234\pi$
$282$	12.2542	−	4.18228i	0.729725	−	0.249051i
$283$	−11.0735	+	2.96714i	−0.658252	+	0.176378i	−0.572457	−	0.819935i	$-0.694010\pi$
$283$	−11.0735	+	2.96714i	−0.658252	+	0.176378i	−0.0857950	+	0.996313i	$0.527343\pi$
$284$	4.26178	+	0.426102i	0.252890	+	0.0252845i
$285$	−7.95147	+	0.933985i	−0.471005	+	0.0553245i
$286$	−11.7547	−	12.9886i	−0.695072	−	0.768032i
$287$	−3.15356			−0.186148
$288$	16.4575	−	4.14136i	0.969767	−	0.244032i
$289$	−22.6719			−1.33364
$290$	4.73615	+	5.23330i	0.278116	+	0.307310i
$291$	7.93428	−	18.4226i	0.465116	−	1.07995i
$292$	−8.33060	−	0.832912i	−0.487512	−	0.0487425i
$293$	13.2780	−	3.55784i	0.775711	−	0.207851i	0.150818	−	0.988562i	$-0.451809\pi$
$293$	13.2780	−	3.55784i	0.775711	−	0.207851i	0.624893	+	0.780711i	$0.285143\pi$
$294$	−11.8737	−	10.3783i	−0.692487	−	0.605277i
$295$	−1.13877	−	1.97241i	−0.0663017	−	0.114838i
$296$	2.90647	−	19.2993i	0.168935	−	1.12175i
$297$	−19.6448	+	1.75252i	−1.13991	+	0.101692i
$298$	−24.0353	−	15.5223i	−1.39233	−	0.899181i
$299$	−22.2596	−	5.96445i	−1.28731	−	0.344933i
$300$	1.67997	−	3.02947i	0.0969933	−	0.174907i
$301$	9.05744	−	2.42693i	0.522062	−	0.139886i
$302$	4.36820	−	13.5608i	0.251362	−	0.780335i
$303$	2.19738	−	0.874412i	0.126236	−	0.0502336i
$304$	15.4036	−	10.2267i	0.883458	−	0.586543i
$305$		−	2.02112i		−	0.115729i
$306$	11.5228	+	24.1106i	0.658714	+	1.37831i
$307$	4.26075	−	4.26075i	0.243174	−	0.243174i	−0.574988	−	0.818162i	$-0.694993\pi$
$307$	4.26075	−	4.26075i	0.243174	−	0.243174i	0.818162	+	0.574988i	$0.194993\pi$
$308$	−5.61586	+	0.918668i	−0.319993	+	0.0523460i
$309$	7.24156	−	0.850597i	0.411958	−	0.0483888i
$310$	5.64719	+	11.0141i	0.320739	+	0.625561i
$311$	15.8847	+	9.17106i	0.900742	+	0.520043i	0.877441	−	0.479685i	$-0.159249\pi$
$311$	15.8847	+	9.17106i	0.900742	+	0.520043i	0.0233008	+	0.999728i	$0.492582\pi$
$312$	15.9792	+	0.520334i	0.904646	+	0.0294581i
$313$	17.4722	−	10.0876i	0.987587	−	0.570184i	0.0830348	−	0.996547i	$-0.473539\pi$
$313$	17.4722	−	10.0876i	0.987587	−	0.570184i	0.904552	+	0.426363i	$0.140205\pi$
$314$	6.14926	+	3.97126i	0.347023	+	0.224111i
$315$	−1.97820	+	1.06955i	−0.111459	+	0.0602621i
$316$	10.3210	+	22.8686i	0.580600	+	1.28646i
$317$	1.62976	+	0.436692i	0.0915363	+	0.0245271i	0.304296	−	0.952577i	$-0.401579\pi$
$317$	1.62976	+	0.436692i	0.0915363	+	0.0245271i	−0.212760	+	0.977104i	$0.568245\pi$
$318$	13.2747	−	8.90161i	0.744411	−	0.499177i
$319$	16.4058	+	9.47190i	0.918549	+	0.530325i
$320$	−0.297160	+	7.99448i	−0.0166117	+	0.446905i
$321$	4.59907	+	0.670990i	0.256695	+	0.0374510i
$322$	−5.55038	+	5.02311i	−0.309311	+	0.279927i
$323$	20.5868	+	20.5868i	1.14548	+	1.14548i
$324$	11.3064	−	14.0059i	0.628131	−	0.778107i
$325$	2.30763	−	2.30763i	0.128004	−	0.128004i
$326$	31.6832	+	1.57994i	1.75477	+	0.0875048i
$327$	5.15139	−	35.3085i	0.284873	−	1.95256i
$328$	1.33372	+	11.8240i	0.0736426	+	0.652874i
$329$	1.98124	−	3.43162i	0.109230	−	0.189191i
$330$	1.79879	−	9.12175i	0.0990203	−	0.502136i
$331$	7.60475	−	28.3813i	0.417995	−	1.55998i	−0.360766	−	0.932656i	$-0.617485\pi$
$331$	7.60475	−	28.3813i	0.417995	−	1.55998i	0.778761	−	0.627321i	$-0.215849\pi$
$332$	25.1487	+	9.50771i	1.38021	+	0.521803i
$333$	−9.84539	−	18.2097i	−0.539524	−	0.997887i
$334$	4.14587	+	19.2646i	0.226852	+	1.05411i
$335$	4.74451	+	8.21774i	0.259220	+	0.448983i
$336$	2.95800	−	4.26873i	0.161372	−	0.232878i
$337$	5.63491	−	9.75996i	0.306953	−	0.531659i	−0.670741	−	0.741692i	$-0.734024\pi$
$337$	5.63491	−	9.75996i	0.306953	−	0.531659i	0.977694	+	0.210033i	$0.0673571\pi$
$338$	−3.16295	−	1.01885i	−0.172042	−	0.0554182i
$339$	1.68141	+	14.3147i	0.0913217	+	0.777467i
$340$	−12.4319	+	2.03367i	−0.674214	+	0.110291i
$341$	23.4903	+	23.4903i	1.27207	+	1.27207i
$342$	6.53214	−	18.4911i	0.353217	−	0.999884i
$343$	−10.0733			−0.543907
$344$	−12.9303	−	32.9339i	−0.697153	−	1.77567i
$345$	−4.52215	−	11.3641i	−0.243465	−	0.611821i
$346$	−9.71539	−	18.9486i	−0.522302	−	1.01869i
$347$	−0.253913	−	0.947616i	−0.0136308	−	0.0508707i	0.958775	−	0.284165i	$-0.0917162\pi$
$347$	−0.253913	−	0.947616i	−0.0136308	−	0.0508707i	−0.972406	+	0.233294i	$0.925050\pi$
$348$	−16.6202	+	4.76252i	−0.890934	+	0.255298i
$349$	3.04308	−	11.3569i	0.162892	−	0.607923i	−0.835407	−	0.549631i	$-0.814768\pi$
$349$	3.04308	−	11.3569i	0.162892	−	0.607923i	0.998300	−	0.0582912i	$-0.0185652\pi$
$350$	−0.223036	−	1.03638i	−0.0119218	−	0.0553967i
$351$	13.8742	−	9.75016i	0.740547	−	0.520425i
$352$	5.81959	+	20.6678i	0.310185	+	1.10160i
$353$	10.2705	−	5.92966i	0.546642	−	0.315604i	−0.201125	−	0.979566i	$-0.564460\pi$
$353$	10.2705	−	5.92966i	0.546642	−	0.315604i	0.747766	+	0.663962i	$0.231126\pi$
$354$	5.56625	−	0.374053i	0.295843	−	0.0198807i
$355$	0.554265	+	2.06855i	0.0294173	+	0.109787i
$356$	0.705100	−	7.05226i	0.0373702	−	0.373769i
$357$	7.51083	+	3.23478i	0.397515	+	0.171203i
$358$	0.297747	−	5.97084i	0.0157364	−	0.315569i
$359$			0.300923i			0.0158821i	0.999968	+	0.00794104i	$0.00252774\pi$
$359$			0.300923i			0.0158821i	−0.999968	+	0.00794104i	$0.997472\pi$
$360$	4.84683	+	6.96479i	0.255450	+	0.367077i
$361$		−	2.36609i		−	0.124531i
$362$	−3.88871	−	0.193917i	−0.204386	−	0.0101921i
$363$	−0.688413	−	5.86080i	−0.0361323	−	0.307612i
$364$	3.78665	−	3.09828i	0.198474	−	0.162394i
$365$	−1.08343	−	4.04343i	−0.0567095	−	0.211643i
$366$	4.44376	+	2.18232i	0.232279	+	0.114072i
$367$	−8.32868	+	4.80856i	−0.434753	+	0.251005i	−0.701370	−	0.712798i	$-0.747428\pi$
$367$	−8.32868	+	4.80856i	−0.434753	+	0.251005i	0.266616	+	0.963803i	$0.414094\pi$
$368$	21.1812	+	18.6864i	1.10415	+	0.974094i
$369$	8.67138	+	9.17018i	0.451414	+	0.477381i
$370$	9.54006	−	2.05309i	0.495964	−	0.106735i
$371$	1.26594	−	4.72456i	0.0657245	−	0.245287i
$372$	−30.3140	+	0.523691i	−1.57171	+	0.0271521i
$373$	−6.64911	−	24.8148i	−0.344278	−	1.28486i	−0.893453	−	0.449156i	$-0.851725\pi$
$373$	−6.64911	−	24.8148i	−0.344278	−	1.28486i	0.549175	−	0.835707i	$-0.314942\pi$
$374$	−30.0858	+	15.4257i	−1.55570	+	0.797641i
$375$	1.71391	+	0.250053i	0.0885057	+	0.0129127i
$376$	−13.7045	−	5.97722i	−0.706757	−	0.308251i
$377$	−16.2877			−0.838862
$378$	−0.215599	−	5.50425i	−0.0110892	−	0.283108i
$379$	−24.0984	−	24.0984i	−1.23785	−	1.23785i	−0.960878	−	0.276972i	$-0.910669\pi$
$379$	−24.0984	−	24.0984i	−1.23785	−	1.23785i	−0.276972	−	0.960878i	$-0.589331\pi$
$380$	7.50656	+	5.39591i	0.385078	+	0.276805i
$381$	28.1936	−	21.0143i	1.44440	−	1.07659i
$382$	4.11663	−	12.7798i	0.210625	−	0.653871i
$383$	9.50962	−	16.4711i	0.485919	−	0.841636i	−0.513950	−	0.857820i	$-0.671818\pi$
$383$	9.50962	−	16.4711i	0.485919	−	0.841636i	0.999869	+	0.0161837i	$0.00515166\pi$
$384$	−17.2563	−	9.28544i	−0.880608	−	0.473846i
$385$	−1.42263	−	2.46406i	−0.0725038	−	0.125580i
$386$	21.1544	−	4.55257i	1.07673	−	0.231720i
$387$	−31.9627	−	19.6646i	−1.62475	−	0.999610i
$388$	−21.1111	+	9.52779i	−1.07176	+	0.483700i
$389$	−0.214502	+	0.800532i	−0.0108757	+	0.0405886i	−0.971150	−	0.238468i	$-0.923355\pi$
$389$	−0.214502	+	0.800532i	−0.0108757	+	0.0405886i	0.960275	+	0.279056i	$0.0900216\pi$
$390$	2.58202	+	7.56537i	0.130746	+	0.383088i
$391$	−22.2385	+	38.5182i	−1.12465	+	1.94795i
$392$	2.04106	+	18.0949i	0.103089	+	0.913931i
$393$	5.01177	+	3.95815i	0.252810	+	0.199662i
$394$	0.110348	−	2.21286i	0.00555926	−	0.111482i
$395$	−8.87056	+	8.87056i	−0.446327	+	0.446327i
$396$	18.1134	+	13.8042i	0.910233	+	0.693688i
$397$	−18.9188	−	18.9188i	−0.949508	−	0.949508i	0.0492769	−	0.998785i	$-0.484308\pi$
$397$	−18.9188	−	18.9188i	−0.949508	−	0.949508i	−0.998785	+	0.0492769i	$0.984308\pi$
$398$	4.03564	+	4.45926i	0.202288	+	0.223522i
$399$	−2.21895	−	5.57618i	−0.111087	−	0.279158i
$400$	−3.79150	+	1.27457i	−0.189575	+	0.0637285i
$401$	−2.97214	−	1.71597i	−0.148422	−	0.0856914i	0.423950	−	0.905686i	$-0.360643\pi$
$401$	−2.97214	−	1.71597i	−0.148422	−	0.0856914i	−0.572372	+	0.819994i	$0.693977\pi$
$402$	−23.1910	+	1.55844i	−1.15666	+	0.0777278i
$403$	−27.5894	−	7.39255i	−1.37432	−	0.368249i
$404$	−2.55438	−	0.965706i	−0.127085	−	0.0480457i
$405$	8.54961	+	2.81143i	0.424834	+	0.139701i
$406$	−2.87037	+	4.44461i	−0.142454	+	0.220582i
$407$	22.6822	−	13.0956i	1.12431	−	0.649123i
$408$	8.95206	−	29.5294i	0.443193	−	1.46192i
$409$	9.08128	+	5.24308i	0.449040	+	0.259253i	0.707425	−	0.706789i	$-0.249857\pi$
$409$	9.08128	+	5.24308i	0.449040	+	0.259253i	−0.258385	+	0.966042i	$0.583190\pi$
$410$	−5.29419	+	2.71445i	−0.261462	+	0.134057i
$411$	0.509802	−	1.18371i	0.0251467	−	0.0583879i
$412$	−6.83637	−	4.91416i	−0.336804	−	0.242103i
$413$	1.20722	−	1.20722i	0.0594032	−	0.0594032i
$414$	29.8686	+	2.32774i	1.46796	+	0.114402i
$415$			13.4430i			0.659889i
$416$	−13.2183	−	12.8874i	−0.648079	−	0.631859i
$417$	21.7027	+	17.1402i	1.06279	+	0.839359i
$418$	23.6171	+	7.60754i	1.15515	+	0.372097i
$419$	2.27027	−	0.608318i	0.110910	−	0.0297183i	−0.202937	−	0.979192i	$-0.565049\pi$
$419$	2.27027	−	0.608318i	0.110910	−	0.0297183i	0.313847	+	0.949474i	$0.398382\pi$
$420$	2.51947	+	0.628655i	0.122938	+	0.0306752i
$421$	12.9168	+	3.46105i	0.629528	+	0.168681i	0.559455	−	0.828860i	$-0.311010\pi$
$421$	12.9168	+	3.46105i	0.629528	+	0.168681i	0.0700723	+	0.997542i	$0.477677\pi$
$422$	14.6431	−	22.6740i	0.712814	−	1.10375i
$423$	−15.4266	+	3.67474i	−0.750068	+	0.178672i
$424$	−18.2498	−	2.74842i	−0.886290	−	0.133475i
$425$	−3.14928	−	5.45472i	−0.152763	−	0.264593i
$426$	−5.14651	−	1.01488i	−0.249349	−	0.0491712i
$427$	1.46342	−	0.392123i	0.0708200	−	0.0189762i
$428$	−3.39852	−	4.15359i	−0.164274	−	0.200771i
$429$	12.8218	+	17.2022i	0.619043	+	0.830532i
$430$	13.1166	−	11.8706i	0.632541	−	0.572452i
$431$	−1.60575			−0.0773464			−0.0386732	−	0.999252i	$-0.512313\pi$
$431$	−1.60575			−0.0773464			−0.0386732	+	0.999252i	$0.512313\pi$
$432$	−20.5466	+	3.13627i	−0.988550	+	0.150894i
$433$	2.84034			0.136498			0.0682491	−	0.997668i	$-0.478259\pi$
$433$	2.84034			0.136498			0.0682491	+	0.997668i	$0.478259\pi$
$434$	−6.87933	+	6.22582i	−0.330218	+	0.298849i
$435$	−5.16610	−	6.93103i	−0.247695	−	0.332317i
$436$	−31.8884	+	26.0914i	−1.52718	+	1.24955i
$437$	31.5283	−	8.44797i	1.50820	−	0.404121i
$438$	10.0600	+	1.98381i	0.480685	+	0.0947903i
$439$	9.28780	+	16.0869i	0.443283	+	0.767788i	0.997931	−	0.0642970i	$-0.0204805\pi$
$439$	9.28780	+	16.0869i	0.443283	+	0.767788i	−0.554648	+	0.832085i	$0.687147\pi$
$440$	−8.63716	+	6.37616i	−0.411761	+	0.303972i
$441$	13.2702	+	14.0336i	0.631916	+	0.668266i
$442$	15.7705	−	24.4198i	0.750128	−	1.16153i
$443$	7.06885	+	1.89409i	0.335851	+	0.0899911i	0.422803	−	0.906221i	$-0.361046\pi$
$443$	7.06885	+	1.89409i	0.335851	+	0.0899911i	−0.0869521	+	0.996212i	$0.527713\pi$
$444$	−5.78689	+	23.1922i	−0.274634	+	1.10065i
$445$	3.42296	−	0.917180i	0.162264	−	0.0434785i
$446$	−14.2515	−	4.59070i	−0.674829	−	0.217376i
$447$	27.5000	+	21.7188i	1.30071	+	1.02726i
$448$	−5.84618	+	1.33587i	−0.276206	+	0.0631138i
$449$		−	24.2909i		−	1.14636i	−0.819429	−	0.573180i	$-0.805709\pi$
$449$		−	24.2909i		−	1.14636i	0.819429	−	0.573180i	$-0.194291\pi$
$450$	−2.40038	+	3.49831i	−0.113155	+	0.164912i
$451$	−11.2911	+	11.2911i	−0.531679	+	0.531679i
$452$	9.71402	−	13.5137i	0.456909	−	0.635632i
$453$	−6.90203	+	16.0258i	−0.324286	+	0.752957i
$454$	−1.12113	+	0.574826i	−0.0526171	+	0.0269779i
$455$	2.11858	+	1.22316i	0.0993207	+	0.0573428i
$456$	−19.9691	+	10.6781i	−0.935137	+	0.500050i
$457$	−15.2835	+	8.82392i	−0.714931	+	0.412765i	−0.812884	−	0.582426i	$-0.802104\pi$
$457$	−15.2835	+	8.82392i	−0.714931	+	0.412765i	0.0979533	+	0.995191i	$0.468770\pi$
$458$	−4.83130	+	7.48099i	−0.225752	+	0.349564i
$459$	−11.2463	−	30.7354i	−0.524931	−	1.43460i
$460$	−4.99430	+	13.2103i	−0.232860	+	0.615935i
$461$	−34.9169	−	9.35595i	−1.62624	−	0.435750i	−0.673414	−	0.739265i	$-0.735173\pi$
$461$	−34.9169	−	9.35595i	−1.62624	−	0.435750i	−0.952827	+	0.303515i	$0.901840\pi$
$462$	6.95373	−	0.467292i	0.323517	−	0.0217404i
$463$	11.5554	+	6.67150i	0.537024	+	0.310051i	0.743872	−	0.668322i	$-0.232987\pi$
$463$	11.5554	+	6.67150i	0.537024	+	0.310051i	−0.206848	+	0.978373i	$0.566321\pi$
$464$	17.8787	+	8.88253i	0.829999	+	0.412361i
$465$	−5.60491	−	14.0850i	−0.259922	−	0.653178i
$466$	4.34167	+	4.79741i	0.201124	+	0.222236i
$467$	19.0131	+	19.0131i	0.879820	+	0.879820i	0.993516	−	0.113696i	$-0.0362689\pi$
$467$	19.0131	+	19.0131i	0.879820	+	0.879820i	−0.113696	+	0.993516i	$0.536269\pi$
$468$	−19.4217	−	2.49176i	−0.897767	−	0.115182i
$469$	−5.02968	+	5.02968i	−0.232249	+	0.232249i
$470$	0.372324	−	7.46637i	0.0171740	−	0.344398i
$471$	−7.03568	−	5.55659i	−0.324187	−	0.256034i
$472$	−5.03694	−	4.01581i	−0.231844	−	0.184842i
$473$	23.7402	−	41.1192i	1.09158	−	1.89067i
$474$	−9.92535	−	29.0814i	−0.455886	−	1.33576i
$475$	−1.19635	+	4.46484i	−0.0548924	+	0.204861i
$476$	−3.88445	−	8.60694i	−0.178044	−	0.394499i
$477$	−17.2195	+	9.30999i	−0.788426	+	0.426275i
$478$	−13.6766	+	2.94329i	−0.625552	+	0.134623i
$479$	7.00155	+	12.1270i	0.319909	+	0.554098i	0.980469	−	0.196675i	$-0.0630144\pi$
$479$	7.00155	+	12.1270i	0.319909	+	0.554098i	−0.660560	+	0.750773i	$0.729681\pi$
$480$	1.29155	−	9.71246i	0.0589507	−	0.443311i
$481$	−11.2595	+	19.5020i	−0.513387	+	0.889213i
$482$	9.14194	−	28.3805i	0.416404	−	1.29270i
$483$	7.35098	−	5.47911i	0.334481	−	0.249308i
$484$	−3.97717	+	5.53287i	−0.180781	+	0.251494i
$485$	−8.18886	−	8.18886i	−0.371837	−	0.371837i
$486$	−15.4129	+	15.7621i	−0.699143	+	0.714982i
$487$	16.5416			0.749571			0.374786	−	0.927111i	$-0.377716\pi$
$487$	16.5416			0.749571			0.374786	+	0.927111i	$0.377716\pi$
$488$	−2.08916	−	5.32117i	−0.0945718	−	0.240878i
$489$	−38.4451	−	5.60901i	−1.73855	−	0.253648i
$490$	−8.10196	+	4.15405i	−0.366009	+	0.187661i
$491$	−0.573851	−	2.14164i	−0.0258976	−	0.0966510i	0.951767	−	0.306820i	$-0.0992651\pi$
$491$	−0.573851	−	2.14164i	−0.0258976	−	0.0966510i	−0.977665	+	0.210169i	$0.932598\pi$
$492$	−0.251724	−	14.5711i	−0.0113486	−	0.656916i
$493$	−8.13613	+	30.3645i	−0.366433	+	1.36755i
$494$	−20.8558	+	4.48831i	−0.938347	+	0.201939i
$495$	−3.25339	+	10.9123i	−0.146229	+	0.490472i
$496$	26.2527	+	23.1605i	1.17878	+	1.03994i
$497$	−1.39023	+	0.802649i	−0.0623602	+	0.0360037i
$498$	−29.5566	−	14.5151i	−1.32446	−	0.650439i
$499$	−2.38590	−	8.90429i	−0.106807	−	0.398611i	0.891736	−	0.452555i	$-0.149487\pi$
$499$	−2.38590	−	8.90429i	−0.106807	−	0.398611i	−0.998544	+	0.0539441i	$0.982821\pi$
$500$	−1.26650	−	1.54789i	−0.0566397	−	0.0692238i
$501$	−2.81548	−	23.9696i	−0.125786	−	1.07088i
$502$	−8.87002	−	0.442319i	−0.395889	−	0.0197417i
$503$		−	13.6796i		−	0.609944i	−0.952361	−	0.304972i	$-0.901353\pi$
$503$		−	13.6796i		−	0.609944i	0.952361	−	0.304972i	$-0.0986471\pi$
$504$	−4.10262	+	4.86068i	−0.182745	+	0.216512i
$505$		−	1.36541i		−	0.0607601i
$506$	−1.88785	+	37.8579i	−0.0839251	+	1.68299i
$507$	3.73790	+	1.60985i	0.166006	+	0.0714959i
$508$	−40.4020	−	4.03947i	−1.79255	−	0.179223i
$509$	3.17276	+	11.8409i	0.140630	+	0.524839i	0.999911	+	0.0133350i	$0.00424479\pi$
$509$	3.17276	+	11.8409i	0.140630	+	0.524839i	−0.859281	+	0.511504i	$0.829089\pi$
$510$	15.3935	−	1.03445i	0.681638	−	0.0458062i
$511$	2.71751	−	1.56895i	0.120216	−	0.0694065i
$512$	7.48126	+	21.3549i	0.330628	+	0.943761i
$513$	−10.1134	+	21.7854i	−0.446518	+	0.961848i
$514$	−7.61193	−	35.3703i	−0.335748	−	1.56012i
$515$	1.08954	−	4.06622i	0.0480109	−	0.179179i
$516$	11.9367	+	41.6565i	0.525484	+	1.83382i
$517$	−5.19298	−	19.3805i	−0.228387	−	0.852353i
$518$	3.33746	+	6.50930i	0.146640	+	0.286002i
$519$	9.64265	+	24.2318i	0.423265	+	1.06366i
$520$	3.69016	−	8.46079i	0.161824	−	0.371030i
$521$	19.8939			0.871568			0.435784	−	0.900051i	$-0.356471\pi$
$521$	19.8939			0.871568			0.435784	+	0.900051i	$0.356471\pi$
$522$	20.8171	−	3.87469i	0.911141	−	0.169591i
$523$	20.9438	+	20.9438i	0.915808	+	0.915808i	0.996721	−	0.0809134i	$-0.0257837\pi$
$523$	20.9438	+	20.9438i	0.915808	+	0.915808i	−0.0809134	+	0.996721i	$0.525784\pi$
$524$	−1.19049	−	7.27753i	−0.0520069	−	0.317920i
$525$	0.151465	+	1.28949i	0.00661046	+	0.0562781i
$526$	−6.56029	−	2.11320i	−0.286042	−	0.0921399i
$527$	−27.5631	+	47.7408i	−1.20067	+	2.07962i
$528$	−4.69301	−	25.8749i	−0.204237	−	1.12606i
$529$	13.4320	+	23.2649i	0.584001	+	1.01152i
$530$	−1.94144	−	9.02127i	−0.0843308	−	0.391859i
$531$	−6.82994	−	0.190945i	−0.296394	−	0.00828632i
$532$	−2.45063	+	6.48212i	−0.106248	+	0.281035i
$533$	3.55339	−	13.2614i	0.153915	−	0.574417i
$534$	−1.67939	+	8.51628i	−0.0726745	+	0.368535i
$535$	1.34169	−	2.32388i	0.0580065	−	0.100470i
$536$	20.9857	+	16.7313i	0.906442	+	0.722681i
$537$	−1.05704	+	7.24514i	−0.0456148	+	0.312651i
$538$	−43.7723	−	2.18278i	−1.88716	−	0.0941064i
$539$	−17.2794	+	17.2794i	−0.744277	+	0.744277i
$540$	−5.09977	−	9.05496i	−0.219459	−	0.389663i
$541$	−9.95450	−	9.95450i	−0.427977	−	0.427977i	0.459962	−	0.887939i	$-0.347863\pi$
$541$	−9.95450	−	9.95450i	−0.427977	−	0.427977i	−0.887939	+	0.459962i	$0.847863\pi$
$542$	6.54435	−	5.92266i	0.281104	−	0.254400i
$543$	4.71864	+	0.688434i	0.202496	+	0.0295435i
$544$	−30.6283	+	18.2046i	−1.31318	+	0.780516i
$545$	−17.8411	−	10.3006i	−0.764231	−	0.441229i
$546$	−4.97688	+	3.33733i	−0.212991	+	0.142825i
$547$	17.6538	+	4.73032i	0.754821	+	0.202254i	0.615655	−	0.788015i	$-0.288891\pi$
$547$	17.6538	+	4.73032i	0.754821	+	0.202254i	0.139166	+	0.990269i	$0.455558\pi$
$548$	−1.35645	+	0.612190i	−0.0579449	+	0.0261515i
$549$	−5.16425	−	3.17724i	−0.220405	−	0.135601i
$550$	−4.50927	−	2.91213i	−0.192276	−	0.124174i
$551$	19.9790	−	11.5349i	0.851133	−	0.491402i
$552$	−23.6525	−	25.2447i	−1.00672	−	1.07449i
$553$	−8.14387	−	4.70187i	−0.346313	−	0.199944i
$554$	5.22181	+	10.1845i	0.221853	+	0.432697i
$555$	−11.8700	+	1.39426i	−0.503855	+	0.0591831i
$556$	−5.15525	−	31.5143i	−0.218631	−	1.33650i
$557$	−14.4981	+	14.4981i	−0.614306	+	0.614306i	−0.944065	−	0.329759i	$-0.893032\pi$
$557$	−14.4981	+	14.4981i	−0.614306	+	0.614306i	0.329759	+	0.944065i	$0.393032\pi$
$558$	37.0202	+	2.88508i	1.56719	+	0.122135i
$559$			40.8233i			1.72664i
$560$	−1.65847	−	2.49801i	−0.0700832	−	0.105560i
$561$	38.4741	−	15.3102i	1.62438	−	0.646396i
$562$	7.42230	−	23.0420i	0.313091	−	0.971969i
$563$	−14.4060	+	3.86008i	−0.607141	+	0.162683i	−0.549275	−	0.835641i	$-0.685096\pi$
$563$	−14.4060	+	3.86008i	−0.607141	+	0.162683i	−0.0578657	+	0.998324i	$0.518430\pi$
$564$	16.0140	+	8.88048i	0.674312	+	0.373936i
$565$	8.03786	+	2.15374i	0.338155	+	0.0906084i
$566$	−13.6195	−	8.79561i	−0.572470	−	0.369707i
$567$	−0.376929	+	6.73593i	−0.0158295	+	0.282883i
$568$	3.59744	+	4.87310i	0.150945	+	0.204471i
$569$	12.5320	+	21.7060i	0.525368	+	0.909963i	0.999563	+	0.0295441i	$0.00940554\pi$
$569$	12.5320	+	21.7060i	0.525368	+	0.909963i	−0.474196	+	0.880419i	$0.657261\pi$
$570$	−8.52493	−	7.45132i	−0.357070	−	0.312101i
$571$	−35.0827	+	9.40039i	−1.46817	+	0.393394i	−0.902302	−	0.431104i	$-0.858124\pi$
$571$	−35.0827	+	9.40039i	−1.46817	+	0.393394i	−0.565865	+	0.824498i	$0.691458\pi$
$572$	2.46468	−	24.6512i	0.103053	−	1.03072i
$573$	−6.50453	+	15.1028i	−0.271730	+	0.630930i
$574$	−2.99258	−	3.30670i	−0.124908	−	0.138019i
$575$	−7.06145			−0.294483
$576$	19.9599	+	13.3268i	0.831662	+	0.555282i
$577$	−39.2204			−1.63277			−0.816383	−	0.577511i	$-0.804024\pi$
$577$	−39.2204			−1.63277			−0.816383	+	0.577511i	$0.804024\pi$
$578$	−21.5146	−	23.7729i	−0.894889	−	0.988824i
$579$	−26.3210	+	3.09168i	−1.09386	+	0.128486i
$580$	−0.993054	+	9.93231i	−0.0412343	+	0.412417i
$581$	−9.73359	+	2.60811i	−0.403817	+	0.108203i
$582$	26.8465	−	9.16258i	1.11282	−	0.379801i
$583$	−12.3834	−	21.4487i	−0.512869	−	0.888315i
$584$	−7.03200	−	9.52556i	−0.290986	−	0.394171i
$585$	−2.26868	−	9.52395i	−0.0937983	−	0.393767i
$586$	16.3309	+	10.5466i	0.674621	+	0.435677i
$587$	42.7497	+	11.4548i	1.76447	+	0.472788i	0.987616	−	0.156892i	$-0.0501475\pi$
$587$	42.7497	+	11.4548i	1.76447	+	0.472788i	0.776854	+	0.629680i	$0.216814\pi$
$588$	−0.385225	−	22.2989i	−0.0158864	−	0.919590i
$589$	39.0772	−	10.4707i	1.61015	−	0.431438i
$590$	0.987554	−	3.06579i	0.0406569	−	0.126217i
$591$	−0.391751	+	2.68513i	−0.0161145	+	0.110451i
$592$	22.9947	−	15.2666i	0.945076	−	0.627452i
$593$		−	22.7247i		−	0.933190i	−0.884471	−	0.466595i	$-0.845481\pi$
$593$		−	22.7247i		−	0.933190i	0.884471	−	0.466595i	$-0.154519\pi$
$594$	−20.4796	−	18.9358i	−0.840289	−	0.776943i
$595$	3.33857	−	3.33857i	0.136868	−	0.136868i
$596$	−6.53234	−	39.9325i	−0.267575	−	1.63570i
$597$	−4.40200	−	5.90588i	−0.180162	−	0.241712i
$598$	−14.8693	−	29.0006i	−0.608050	−	1.18592i
$599$	−22.6053	−	13.0512i	−0.923627	−	0.533256i	−0.0388368	−	0.999246i	$-0.512365\pi$
$599$	−22.6053	−	13.0512i	−0.923627	−	0.533256i	−0.884790	+	0.465989i	$0.845699\pi$
$600$	4.77081	−	1.11327i	0.194768	−	0.0454490i
$601$	−4.18271	+	2.41489i	−0.170616	+	0.0985053i	−0.582876	−	0.812561i	$-0.698073\pi$
$601$	−4.18271	+	2.41489i	−0.170616	+	0.0985053i	0.412260	+	0.911066i	$0.364739\pi$
$602$	11.1399	+	7.19426i	0.454028	+	0.293216i
$603$	28.4560	+	0.795546i	1.15882	+	0.0323971i
$604$	18.3646	−	8.28822i	0.747244	−	0.337243i
$605$	−3.29091	−	0.881796i	−0.133794	−	0.0358501i
$606$	3.00209	+	1.47431i	0.121951	+	0.0598899i
$607$	−19.2796	−	11.1311i	−0.782534	−	0.451796i	0.0547938	−	0.998498i	$-0.482550\pi$
$607$	−19.2796	−	11.1311i	−0.782534	−	0.451796i	−0.837327	+	0.546702i	$0.815883\pi$
$608$	25.3407	+	6.44699i	1.02770	+	0.261460i
$609$	4.01623	−	5.08530i	0.162746	−	0.206067i
$610$	2.11927	−	1.91795i	0.0858068	−	0.0776555i
$611$	12.1983	+	12.1983i	0.493491	+	0.493491i
$612$	−14.3469	+	34.9622i	−0.579938	+	1.41326i
$613$	−6.22905	+	6.22905i	−0.251589	+	0.251589i	−0.821622	−	0.570033i	$-0.806930\pi$
$613$	−6.22905	+	6.22905i	−0.251589	+	0.251589i	0.570033	+	0.821622i	$0.306930\pi$
$614$	8.51092	+	0.424412i	0.343473	+	0.0171279i
$615$	6.77028	−	2.69413i	0.273004	−	0.108638i
$616$	−6.29248	−	5.01682i	−0.253531	−	0.202133i
$617$	19.3109	−	33.4475i	0.777429	−	1.34655i	−0.155990	−	0.987759i	$-0.549857\pi$
$617$	19.3109	−	33.4475i	0.777429	−	1.34655i	0.933419	−	0.358788i	$-0.116810\pi$
$618$	7.76381	+	6.78606i	0.312306	+	0.272975i
$619$	−1.26446	+	4.71902i	−0.0508228	+	0.189673i	−0.986670	−	0.162732i	$-0.947969\pi$
$619$	−1.26446	+	4.71902i	−0.0508228	+	0.189673i	0.935847	+	0.352405i	$0.114636\pi$
$620$	−6.19010	+	16.3734i	−0.248601	+	0.657570i
$621$	−36.1458	−	6.30981i	−1.45048	−	0.253204i
$622$	5.45745	+	25.3591i	0.218824	+	1.01681i
$623$	1.32820	+	2.30050i	0.0532131	+	0.0921677i
$624$	14.6180	+	17.2490i	0.585187	+	0.690514i
$625$	0.500000	−	0.866025i	0.0200000	−	0.0346410i
$626$	27.1578	+	8.74806i	1.08544	+	0.349643i
$627$	−27.9101	−	12.0204i	−1.11462	−	0.480048i
$628$	1.67125	+	10.2164i	0.0666902	+	0.407680i
$629$	30.7322	+	30.7322i	1.22537	+	1.22537i
$630$	−2.99871	−	1.05932i	−0.119471	−	0.0422043i
$631$	−29.3873			−1.16989			−0.584946	−	0.811072i	$-0.698884\pi$
$631$	−29.3873			−1.16989			−0.584946	+	0.811072i	$0.698884\pi$
$632$	−14.1851	+	32.5234i	−0.564252	+	1.29371i
$633$	−20.4886	+	25.9424i	−0.814349	+	1.03112i
$634$	1.08867	+	2.12331i	0.0432364	+	0.0843272i
$635$	−5.25447	−	19.6099i	−0.208517	−	0.778196i
$636$	21.9310	+	5.47220i	0.869622	+	0.216987i
$637$	5.43793	−	20.2946i	0.215459	−	0.804103i
$638$	5.63647	+	26.1909i	0.223150	+	1.03691i
$639$	6.15674	+	1.83557i	0.243557	+	0.0726140i
$640$	−8.66471	+	7.27480i	−0.342503	+	0.287562i
$641$	−8.00573	+	4.62211i	−0.316207	+	0.182562i	−0.649701	−	0.760190i	$-0.725106\pi$
$641$	−8.00573	+	4.62211i	−0.316207	+	0.182562i	0.333493	+	0.942752i	$0.391772\pi$
$642$	3.66073	+	5.45916i	0.144478	+	0.215456i
$643$	−3.23963	−	12.0905i	−0.127759	−	0.476802i	0.872164	−	0.489213i	$-0.162716\pi$
$643$	−3.23963	−	12.0905i	−0.127759	−	0.476802i	−0.999923	+	0.0124112i	$0.996049\pi$
$644$	−10.5341	−	1.05322i	−0.415102	−	0.0415028i
$645$	−17.3718	+	12.9482i	−0.684015	+	0.509836i
$646$	−2.05065	+	41.1225i	−0.0806816	+	1.61794i
$647$			27.3583i			1.07556i	0.843084	+	0.537782i	$0.180738\pi$
$647$			27.3583i			1.07556i	−0.843084	+	0.537782i	$0.819262\pi$
$648$	25.4153	−	1.43554i	0.998409	−	0.0563934i
$649$		−	8.64475i		−	0.339336i
$650$	4.60953	+	0.229862i	0.180800	+	0.00901593i
$651$	9.11106	−	6.79100i	0.357091	−	0.266160i
$652$	28.4093	+	34.7212i	1.11259	+	1.35979i
$653$	2.16384	+	8.07557i	0.0846777	+	0.316021i	0.995253	−	0.0973219i	$-0.0310276\pi$
$653$	2.16384	+	8.07557i	0.0846777	+	0.316021i	−0.910575	+	0.413343i	$0.864361\pi$
$654$	41.9116	−	28.1046i	1.63887	−	1.09898i
$655$	3.19315	−	1.84357i	0.124767	−	0.0720341i
$656$	−11.1326	+	12.6190i	−0.434656	+	0.492688i
$657$	−12.0347	−	3.58803i	−0.469519	−	0.139982i
$658$	5.47838	−	1.17898i	0.213569	−	0.0459616i
$659$	−8.00608	+	29.8791i	−0.311872	+	1.16392i	0.614994	+	0.788532i	$0.289159\pi$
$659$	−8.00608	+	29.8791i	−0.311872	+	1.16392i	−0.926866	+	0.375392i	$0.877508\pi$
$660$	11.2717	−	6.76997i	0.438751	−	0.263521i
$661$	−1.48966	−	5.55947i	−0.0579409	−	0.216238i	0.930885	−	0.365312i	$-0.119038\pi$
$661$	−1.48966	−	5.55947i	−0.0579409	−	0.216238i	−0.988826	+	0.149073i	$0.952371\pi$
$662$	36.9762	−	18.9585i	1.43712	−	0.736843i
$663$	−22.0661	+	27.9399i	−0.856978	+	1.08509i
$664$	13.8955	+	35.3924i	0.539251	+	1.37349i
$665$	−3.46495			−0.134365
$666$	9.75124	−	27.6037i	0.377853	−	1.06962i
$667$	24.9206	+	24.9206i	0.964931	+	0.964931i
$668$	−16.2659	+	22.6284i	−0.629346	+	0.875519i
$669$	16.8421	+	7.25359i	0.651152	+	0.280440i
$670$	−4.11450	+	12.7732i	−0.158957	+	0.493471i
$671$	3.83574	−	6.64369i	0.148077	−	0.256477i
$672$	7.28303	−	0.949178i	0.280949	−	0.0366153i
$673$	5.57963	+	9.66421i	0.215079	+	0.372528i	0.953297	−	0.302034i	$-0.0976657\pi$
$673$	5.57963	+	9.66421i	0.215079	+	0.372528i	−0.738218	+	0.674562i	$0.764332\pi$
$674$	15.5812	−	3.35318i	0.600166	−	0.129160i
$675$	3.33322	−	3.98618i	0.128296	−	0.153428i
$676$	−1.93317	−	4.28340i	−0.0743526	−	0.164746i
$677$	6.96730	−	26.0023i	0.267775	−	0.999350i	−0.692755	−	0.721173i	$-0.743603\pi$
$677$	6.96730	−	26.0023i	0.267775	−	0.999350i	0.960530	−	0.278177i	$-0.0897302\pi$
$678$	−13.4143	+	15.3470i	−0.515172	+	0.589400i
$679$	4.34052	−	7.51801i	0.166574	−	0.288515i
$680$	−13.9297	−	11.1058i	−0.534180	−	0.425887i
$681$	1.43371	−	0.570523i	0.0549400	−	0.0218625i
$682$	−2.33987	+	46.9223i	−0.0895981	+	1.79675i
$683$	28.2112	−	28.2112i	1.07947	−	1.07947i	0.0829146	−	0.996557i	$-0.473577\pi$
$683$	28.2112	−	28.2112i	1.07947	−	1.07947i	0.996557	−	0.0829146i	$-0.0264229\pi$
$684$	25.5878	−	10.6978i	0.978374	−	0.409042i
$685$	−0.526159	−	0.526159i	−0.0201035	−	0.0201035i
$686$	−9.55909	−	10.5625i	−0.364968	−	0.403278i
$687$	6.75996	−	8.55938i	0.257909	−	0.326561i
$688$	22.2630	−	44.8109i	0.848770	−	1.70840i
$689$	18.4414	+	10.6472i	0.702563	+	0.405625i
$690$	7.62464	−	15.5258i	0.290265	−	0.591055i
$691$	−40.0581	−	10.7335i	−1.52388	−	0.408323i	−0.602864	−	0.797844i	$-0.705974\pi$
$691$	−40.0581	−	10.7335i	−1.52388	−	0.408323i	−0.921017	+	0.389522i	$0.872640\pi$
$692$	10.6494	−	28.1686i	0.404830	−	1.07081i
$693$	−8.53242	−	0.238542i	−0.324120	−	0.00906145i
$694$	0.752684	−	1.16549i	0.0285715	−	0.0442413i
$695$	13.8275	−	7.98329i	0.524505	−	0.302823i
$696$	−20.7656	−	12.9079i	−0.787117	−	0.489272i
$697$	−22.9477	−	13.2488i	−0.869205	−	0.501836i
$698$	14.7962	−	7.58634i	0.560045	−	0.287147i
$699$	−4.73581	−	6.35374i	−0.179125	−	0.240320i
$700$	0.875058	−	1.21734i	0.0330741	−	0.0460112i
$701$	−36.1265	+	36.1265i	−1.36448	+	1.36448i	−0.496362	+	0.868116i	$0.665331\pi$
$701$	−36.1265	+	36.1265i	−1.36448	+	1.36448i	−0.868116	+	0.496362i	$0.834669\pi$
$702$	23.3896	+	5.29549i	0.882783	+	0.199865i
$703$		−	31.8955i		−	1.20296i
$704$	−16.1489	+	25.7150i	−0.608636	+	0.969169i
$705$	−1.32180	+	9.05985i	−0.0497820	+	0.341214i
$706$	15.9638	+	5.14227i	0.600807	+	0.193532i
$707$	0.988649	−	0.264908i	0.0371820	−	0.00996288i
$708$	5.67434	+	5.48161i	0.213255	+	0.206012i
$709$	20.2788	+	5.43368i	0.761585	+	0.204066i	0.618651	−	0.785666i	$-0.287680\pi$
$709$	20.2788	+	5.43368i	0.761585	+	0.204066i	0.142934	+	0.989732i	$0.454346\pi$
$710$	−1.64303	+	2.54414i	−0.0616618	+	0.0954798i
$711$	8.72085	+	36.6103i	0.327057	+	1.37299i
$712$	8.06385	−	5.95293i	0.302206	−	0.223095i
$713$	30.9016	+	53.5231i	1.15727	+	2.00446i
$714$	3.73555	+	10.9452i	0.139800	+	0.409615i
$715$	11.9650	−	3.20600i	0.447464	−	0.119898i
$716$	6.54336	−	5.35385i	0.244537	−	0.200083i
$717$	17.0168	−	1.99881i	0.635505	−	0.0746468i
$718$	−0.315536	+	0.285562i	−0.0117757	+	0.0106571i
$719$	4.78505			0.178452			0.0892260	−	0.996011i	$-0.471561\pi$
$719$	4.78505			0.178452			0.0892260	+	0.996011i	$0.471561\pi$
$720$	−2.70361	+	11.6915i	−0.100758	+	0.435715i
$721$	3.15559			0.117520
$722$	2.48099	−	2.24531i	0.0923329	−	0.0835617i
$723$	−14.4448	+	33.5394i	−0.537209	+	1.24734i
$724$	−3.48687	−	4.26158i	−0.129588	−	0.158380i
$725$	−4.82086	+	1.29174i	−0.179042	+	0.0479742i
$726$	5.49216	−	6.28348i	0.203833	−	0.233202i
$727$	9.91478	+	17.1729i	0.367719	+	0.636908i	0.989209	−	0.146514i	$-0.0468055\pi$
$727$	9.91478	+	17.1729i	0.367719	+	0.636908i	−0.621490	+	0.783422i	$0.713472\pi$
$728$	6.84210	+	1.03042i	0.253585	+	0.0381899i
$729$	20.6238	−	17.4258i	0.763844	−	0.645401i
$730$	3.21167	−	4.97308i	0.118869	−	0.184062i
$731$	76.1050	+	20.3923i	2.81484	+	0.754235i
$732$	1.92863	+	6.73049i	0.0712842	+	0.248766i
$733$	48.6717	−	13.0415i	1.79773	−	0.481700i	0.804110	−	0.594481i	$-0.202642\pi$
$733$	48.6717	−	13.0415i	1.79773	−	0.481700i	0.993620	+	0.112781i	$0.0359757\pi$
$734$	−12.9456	−	4.17004i	−0.477832	−	0.153919i
$735$	10.3609	−	4.12295i	0.382167	−	0.152077i
$736$	0.506176	+	39.9424i	0.0186579	+	1.47230i
$737$			36.0171i			1.32671i
$738$	−1.38678	+	17.7946i	−0.0510479	+	0.655028i
$739$	16.5849	−	16.5849i	0.610087	−	0.610087i	−0.332882	−	0.942969i	$-0.608021\pi$
$739$	16.5849	−	16.5849i	0.610087	−	0.610087i	0.942969	+	0.332882i	$0.108021\pi$
$740$	11.2059	+	8.05508i	0.411936	+	0.296111i
$741$	25.9495	−	3.04804i	0.953277	−	0.111972i
$742$	6.15533	−	3.15597i	0.225969	−	0.115859i
$743$	−23.5046	−	13.5704i	−0.862299	−	0.497848i	0.00248278	−	0.999997i	$-0.499210\pi$
$743$	−23.5046	−	13.5704i	−0.862299	−	0.497848i	−0.864781	+	0.502149i	$0.832543\pi$
$744$	−29.3157	−	31.2892i	−1.07477	−	1.14712i
$745$	17.5211	−	10.1158i	0.641924	−	0.370615i
$746$	19.7102	−	30.5202i	0.721643	−	1.11742i
$747$	34.3487	+	21.1326i	1.25675	+	0.773202i
$748$	−44.7248	−	16.9087i	−1.63530	−	0.618241i
$749$	1.94295	+	0.520611i	0.0709938	+	0.0190227i
$750$	1.36422	+	2.03443i	0.0498143	+	0.0742868i
$751$	25.4365	+	14.6858i	0.928191	+	0.535892i	0.886239	−	0.463228i	$-0.153309\pi$
$751$	25.4365	+	14.6858i	0.928191	+	0.535892i	0.0419523	+	0.999120i	$0.486642\pi$
$752$	−6.73748	−	20.0422i	−0.245691	−	0.730863i
$753$	10.7631	+	1.57030i	0.392228	+	0.0572248i
$754$	−15.4563	−	17.0787i	−0.562886	−	0.621971i
$755$	7.12348	+	7.12348i	0.259250	+	0.259250i
$756$	5.56696	−	5.44935i	0.202468	−	0.198191i
$757$	−27.5195	+	27.5195i	−1.00021	+	1.00021i	−0.000211580		1.00000i	$0.500067\pi$
$757$	−27.5195	+	27.5195i	−1.00021	+	1.00021i	−1.00000		0.000211580i	$0.999933\pi$
$758$	2.40043	−	48.1369i	0.0871876	−	1.74841i
$759$	6.70213	−	45.9375i	0.243272	−	1.66743i
$760$	1.46542	+	12.9916i	0.0531564	+	0.471254i
$761$	−23.4387	+	40.5971i	−0.849653	+	1.47164i	0.0318648	+	0.999492i	$0.489855\pi$
$761$	−23.4387	+	40.5971i	−0.849653	+	1.47164i	−0.881518	+	0.472150i	$0.843478\pi$
$762$	48.7892	+	9.62114i	1.76745	+	0.348537i
$763$	3.99689	−	14.9166i	0.144697	−	0.540017i
$764$	17.3069	−	7.81089i	0.626142	−	0.282588i
$765$	−18.8883	−	0.528062i	−0.682908	−	0.0190921i
$766$	26.2952	−	5.65892i	0.950086	−	0.204465i
$767$	3.71635	+	6.43690i	0.134189	+	0.232423i
$768$	−6.63907	−	26.9058i	−0.239567	−	0.970880i
$769$	16.0434	−	27.7880i	0.578540	−	1.00206i	−0.417107	−	0.908858i	$-0.636956\pi$
$769$	16.0434	−	27.7880i	0.578540	−	1.00206i	0.995647	−	0.0932039i	$-0.0297108\pi$
$770$	1.23372	−	3.83000i	0.0444601	−	0.138023i
$771$	5.16930	+	44.0088i	0.186168	+	1.58494i
$772$	24.8482	+	17.8616i	0.894307	+	0.642852i
$773$	−31.7817	−	31.7817i	−1.14311	−	1.14311i	−0.987878	−	0.155230i	$-0.950388\pi$
$773$	−31.7817	−	31.7817i	−1.14311	−	1.14311i	−0.155230	−	0.987878i	$-0.549612\pi$
$774$	−9.71146	−	52.1757i	−0.349071	−	1.87542i
$775$	−8.75220			−0.314388
$776$	−30.0240	−	13.0949i	−1.07780	−	0.470081i
$777$	−3.31248	−	8.32418i	−0.118834	−	0.298628i
$778$	−1.04296	+	0.534749i	−0.0373920	+	0.0191717i
$779$	5.03298	+	18.7833i	0.180325	+	0.672983i
$780$	−5.48256	+	9.88661i	−0.196307	+	0.353997i
$781$	−2.10380	+	7.85149i	−0.0752799	+	0.280948i
$782$	−61.4921	+	13.2335i	−2.19895	+	0.473230i
$783$	−25.8310	+	2.30440i	−0.923124	+	0.0823524i
$784$	−17.0368	+	19.3114i	−0.608457	+	0.689694i
$785$	−4.48265	+	2.58806i	−0.159993	+	0.0923717i
$786$	0.605559	+	9.01126i	0.0215996	+	0.321421i
$787$	7.64235	+	28.5216i	0.272420	+	1.01669i	0.957551	+	0.288266i	$0.0930786\pi$
$787$	7.64235	+	28.5216i	0.272420	+	1.01669i	−0.685130	+	0.728421i	$0.740255\pi$
$788$	2.42504	−	1.98419i	0.0863884	−	0.0706840i
$789$	7.75278	+	3.33899i	0.276006	+	0.118871i
$790$	−17.7191	−	0.883595i	−0.630418	−	0.0314369i
$791$			6.23779i			0.221790i
$792$	2.71420	+	32.0926i	0.0964449	+	1.14036i
$793$			6.59588i			0.234226i
$794$	1.88450	−	37.7907i	0.0668784	−	1.34114i
$795$	1.31844	+	11.2245i	0.0467603	+	0.398094i
$796$	−0.846175	+	8.46326i	−0.0299919	+	0.299972i
$797$	−0.446496	−	1.66635i	−0.0158157	−	0.0590250i	0.957567	−	0.288211i	$-0.0930604\pi$
$797$	−0.446496	−	1.66635i	−0.0158157	−	0.0590250i	−0.973383	+	0.229186i	$0.926394\pi$
$798$	3.74130	−	7.61826i	0.132441	−	0.269683i
$799$	28.8341	−	16.6474i	1.02008	−	0.588942i
$800$	−4.93443	−	2.76612i	−0.174458	−	0.0977972i
$801$	3.03744	−	10.1880i	0.107323	−	0.359975i
$802$	−1.02113	−	4.74486i	−0.0360572	−	0.167547i
$803$	4.11234	−	15.3475i	0.145121	−	0.541601i
$804$	−23.6413	−	22.8383i	−0.833764	−	0.805446i
$805$	−1.37001	−	5.11295i	−0.0482865	−	0.180208i
$806$	−18.4295	−	35.9444i	−0.649151	−	1.26609i
$807$	53.1142	+	7.74918i	1.86971	+	0.272784i
$808$	−1.41138	−	3.59484i	−0.0496522	−	0.126466i
$809$	−30.7298			−1.08040			−0.540201	−	0.841536i	$-0.681652\pi$
$809$	−30.7298			−1.08040			−0.540201	+	0.841536i	$0.681652\pi$
$810$	5.16522	+	11.6327i	0.181487	+	0.408733i
$811$	−22.2097	−	22.2097i	−0.779887	−	0.779887i	0.199924	−	0.979811i	$-0.435930\pi$
$811$	−22.2097	−	22.2097i	−0.779887	−	0.779887i	−0.979811	+	0.199924i	$0.935930\pi$
$812$	−7.38431	+	1.20796i	−0.259139	+	0.0423911i
$813$	−8.66740	+	6.46032i	−0.303979	+	0.226573i
$814$	35.2559	+	11.3566i	1.23572	+	0.398049i
$815$	−11.2156	+	19.4261i	−0.392867	+	0.680465i
$816$	39.4586	−	18.6352i	1.38133	−	0.652364i
$817$	−28.9108	−	50.0750i	−1.01146	−	1.75190i
$818$	3.12001	+	14.4977i	0.109089	+	0.506901i
$819$	6.45581	−	3.49044i	0.225584	−	0.121966i
$820$	−7.87022	−	2.97541i	−0.274840	−	0.103906i
$821$	8.06115	−	30.0846i	0.281336	−	1.04996i	−0.670139	−	0.742235i	$-0.733766\pi$
$821$	8.06115	−	30.0846i	0.281336	−	1.04996i	0.951475	−	0.307725i	$-0.0995677\pi$
$822$	1.72497	−	0.588724i	0.0601653	−	0.0205341i
$823$	−15.3976	+	26.6693i	−0.536725	+	0.929635i	0.462353	+	0.886696i	$0.347005\pi$
$823$	−15.3976	+	26.6693i	−0.536725	+	0.929635i	−0.999078	+	0.0429388i	$0.986328\pi$
$824$	−1.33459	−	11.8317i	−0.0464925	−	0.412176i
$825$	5.15928	+	4.07466i	0.179623	+	0.141861i
$826$	2.41143	+	0.120250i	0.0839045	+	0.00418405i
$827$	−23.7498	+	23.7498i	−0.825863	+	0.825863i	−0.986942	−	0.161079i	$-0.948503\pi$
$827$	−23.7498	+	23.7498i	−0.825863	+	0.825863i	0.161079	+	0.986942i	$0.448503\pi$
$828$	25.9032	+	33.5281i	0.900197	+	1.16518i
$829$	9.08631	+	9.08631i	0.315581	+	0.315581i	0.847067	−	0.531486i	$-0.178366\pi$
$829$	9.08631	+	9.08631i	0.315581	+	0.315581i	−0.531486	+	0.847067i	$0.678366\pi$
$830$	−14.0958	+	12.7568i	−0.489273	+	0.442794i
$831$	−5.18271	−	13.0240i	−0.179786	−	0.451799i
$832$	0.969774	−	26.0898i	0.0336209	−	0.904501i
$833$	−35.1179	−	20.2754i	−1.21676	−	0.702499i
$834$	2.62228	+	39.0219i	0.0908022	+	1.35122i
$835$	−13.4592	−	3.60638i	−0.465775	−	0.124804i
$836$	14.4346	+	31.9833i	0.499230	+	1.10616i
$837$	−44.8003	−	7.82060i	−1.54852	−	0.270320i
$838$	2.79224	+	1.80326i	0.0964565	+	0.0622926i
$839$	25.6902	−	14.8322i	0.886923	−	0.512065i	0.0139882	−	0.999902i	$-0.495547\pi$
$839$	25.6902	−	14.8322i	0.886923	−	0.512065i	0.872935	+	0.487837i	$0.162214\pi$
$840$	1.73168	+	3.23839i	0.0597485	+	0.111735i
$841$	−3.54269	−	2.04537i	−0.122162	−	0.0705301i
$842$	8.62834	+	16.8285i	0.297352	+	0.579948i
$843$	−11.7277	+	27.2305i	−0.403923	+	0.937868i
$844$	37.6707	−	6.16235i	1.29668	−	0.212117i
$845$	1.66150	−	1.66150i	0.0571574	−	0.0571574i
$846$	−18.4923	−	12.6886i	−0.635780	−	0.436244i
$847$		−	2.55391i		−	0.0877535i
$848$	−14.4364	−	21.7442i	−0.495747	−	0.746700i
$849$	15.5827	+	12.3068i	0.534798	+	0.422369i
$850$	2.73109	−	8.47850i	0.0936758	−	0.290810i
$851$	47.0657	−	12.6112i	1.61339	−	0.432307i
$852$	−3.81963	−	6.35952i	−0.130858	−	0.217874i
$853$	−22.0876	−	5.91835i	−0.756264	−	0.202640i	−0.139969	−	0.990156i	$-0.544700\pi$
$853$	−22.0876	−	5.91835i	−0.756264	−	0.202640i	−0.616295	+	0.787515i	$0.711367\pi$
$854$	1.79989	+	1.16239i	0.0615909	+	0.0397760i
$855$	9.52762	+	10.0757i	0.325838	+	0.344581i
$856$	1.13027	−	7.50513i	0.0386319	−	0.256520i
$857$	9.74076	+	16.8715i	0.332738	+	0.576319i	0.983048	−	0.183350i	$-0.0586942\pi$
$857$	9.74076	+	16.8715i	0.332738	+	0.576319i	−0.650310	+	0.759669i	$0.725361\pi$
$858$	−5.87032	+	29.7686i	−0.200409	+	1.01628i
$859$	−40.9096	+	10.9617i	−1.39582	+	0.374009i	−0.876842	−	0.480779i	$-0.840354\pi$
$859$	−40.9096	+	10.9617i	−1.39582	+	0.374009i	−0.518977	+	0.854788i	$0.673687\pi$
$860$	24.8942	+	2.48897i	0.848885	+	0.0848733i
$861$	3.26425	+	4.37943i	0.111245	+	0.149251i
$862$	−1.52379	−	1.68374i	−0.0519004	−	0.0573482i
$863$	−3.70414			−0.126091			−0.0630453	−	0.998011i	$-0.520081\pi$
$863$	−3.70414			−0.126091			−0.0630453	+	0.998011i	$0.520081\pi$
$864$	−22.7864	−	18.5683i	−0.775209	−	0.631705i
$865$	15.0572			0.511961
$866$	2.69536	+	2.97828i	0.0915919	+	0.101206i
$867$	23.4677	+	31.4851i	0.797005	+	1.06929i
$868$	−13.0563	−	1.30540i	−0.443161	−	0.0443082i
$869$	−45.9935	+	12.3239i	−1.56022	+	0.418061i
$870$	2.36524	−	11.9942i	0.0801891	−	0.406642i
$871$	−15.4836	−	26.8184i	−0.524642	−	0.908707i
$872$	−57.6192	−	8.67743i	−1.95123	−	0.293855i
$873$	−33.7967	+	8.05064i	−1.14385	+	0.272473i
$874$	38.7771	+	25.0427i	1.31166	+	0.847081i
$875$	0.724065	+	0.194013i	0.0244779	+	0.00655883i
$876$	7.46632	+	12.4311i	0.252264	+	0.420008i
$877$	3.16896	−	0.849119i	0.107008	−	0.0286727i	−0.204918	−	0.978779i	$-0.565693\pi$
$877$	3.16896	−	0.849119i	0.107008	−	0.0286727i	0.311926	+	0.950106i	$0.399026\pi$
$878$	−8.05449	+	25.0046i	−0.271826	+	0.843865i
$879$	−18.6850	−	14.7569i	−0.630228	−	0.497737i
$880$	−14.8821	−	3.00593i	−0.501675	−	0.101330i
$881$			4.36165i			0.146948i	0.997297	+	0.0734738i	$0.0234085\pi$
$881$			4.36165i			0.146948i	−0.997297	+	0.0734738i	$0.976591\pi$
$882$	−2.12225	+	27.2319i	−0.0714599	+	0.916947i
$883$	22.9338	−	22.9338i	0.771785	−	0.771785i	−0.206634	−	0.978418i	$-0.566251\pi$
$883$	22.9338	−	22.9338i	0.771785	−	0.771785i	0.978418	+	0.206634i	$0.0662509\pi$
$884$	40.5712	−	6.63682i	1.36456	−	0.223220i
$885$	−1.56040	+	3.62308i	−0.0524522	+	0.121788i
$886$	4.72194	+	9.20955i	0.158637	+	0.309401i
$887$	−28.2233	−	16.2947i	−0.947645	−	0.547123i	−0.0552964	−	0.998470i	$-0.517610\pi$
$887$	−28.2233	−	16.2947i	−0.947645	−	0.547123i	−0.892349	+	0.451347i	$0.850944\pi$
$888$	−29.8100	+	15.9404i	−1.00036	+	0.534926i
$889$	13.1794	−	7.60915i	0.442024	−	0.255203i
$890$	4.20995	+	2.71883i	0.141118	+	0.0911355i
$891$	22.7681	+	25.4672i	0.762760	+	0.853185i
$892$	−8.71039	−	19.3000i	−0.291646	−	0.646211i
$893$	−23.6015	−	6.32401i	−0.789795	−	0.211625i
$894$	3.32276	+	49.4457i	0.111130	+	1.65371i
$895$	3.66092	+	2.11363i	0.122371	+	0.0706510i
$896$	−6.94850	−	4.86241i	−0.232133	−	0.162442i
$897$	14.7579	+	37.0864i	0.492754	+	1.23828i
$898$	25.4706	−	23.0510i	0.849965	−	0.769222i
$899$	30.8875	+	30.8875i	1.03016	+	1.03016i
$900$	−5.94605	+	0.802777i	−0.198202	+	0.0267592i
$901$	29.0610	−	29.0610i	0.968162	−	0.968162i
$902$	−22.5543	−	1.12471i	−0.750975	−	0.0374487i
$903$	−12.7457	−	10.0662i	−0.424151	−	0.334983i
$904$	23.3882	−	2.63813i	0.777879	−	0.0877429i
$905$	1.37657	−	2.38430i	0.0457589	−	0.0792567i
$906$	−23.3538	+	7.97052i	−0.775877	+	0.264803i
$907$	10.5867	−	39.5101i	0.351526	−	1.31191i	−0.533275	−	0.845942i	$-0.679039\pi$
$907$	10.5867	−	39.5101i	0.351526	−	1.31191i	0.884801	−	0.465970i	$-0.154294\pi$
$908$	−1.66664	−	0.630089i	−0.0553094	−	0.0209103i
$909$	−3.48883	−	2.14646i	−0.115717	−	0.0711935i
$910$	0.727872	+	3.38219i	0.0241287	+	0.112119i
$911$	4.77056	+	8.26286i	0.158056	+	0.273761i	0.934168	−	0.356835i	$-0.116144\pi$
$911$	4.77056	+	8.26286i	0.158056	+	0.273761i	−0.776112	+	0.630595i	$0.782811\pi$
$912$	−30.1464	−	10.8058i	−0.998248	−	0.357815i
$913$	−25.5124	+	44.1888i	−0.844338	+	1.46244i
$914$	−23.7558	−	7.65220i	−0.785771	−	0.253112i
$915$	−2.80679	+	2.09206i	−0.0927895	+	0.0691614i
$916$	−12.4290	+	2.03319i	−0.410665	+	0.0671785i
$917$	1.95437	+	1.95437i	0.0645391	+	0.0645391i
$918$	21.5558	−	40.9589i	0.711448	−	1.35184i
$919$	−23.7798			−0.784424			−0.392212	−	0.919875i	$-0.628290\pi$
$919$	−23.7798			−0.784424			−0.392212	+	0.919875i	$0.628290\pi$
$920$	−18.5912	+	7.29917i	−0.612935	+	0.240647i
$921$	−10.3273	−	1.50672i	−0.340297	−	0.0496482i
$922$	−23.3242	−	45.4909i	−0.768142	−	1.49816i
$923$	−1.80883	−	6.75065i	−0.0595384	−	0.222200i
$924$	7.08876	+	6.84800i	0.233203	+	0.225282i
$925$	−1.78593	+	6.66517i	−0.0587209	+	0.219149i
$926$	3.97003	+	18.4475i	0.130463	+	0.606223i
$927$	−8.67699	−	9.17611i	−0.284990	−	0.301383i
$928$	7.65219	+	27.1761i	0.251195	+	0.892099i
$929$	30.4693	−	17.5914i	0.999664	−	0.577156i	0.0915150	−	0.995804i	$-0.470829\pi$
$929$	30.4693	−	17.5914i	0.999664	−	0.577156i	0.908149	+	0.418648i	$0.137496\pi$
$930$	9.45025	−	19.2432i	0.309886	−	0.631008i
$931$	7.70221	+	28.7451i	0.252430	+	0.942081i
$932$	−0.910341	+	9.10504i	−0.0298192	+	0.298245i
$933$	−3.70618	−	31.5526i	−0.121335	−	1.03299i
$934$	−1.89389	+	37.9789i	−0.0619699	+	1.24271i
$935$		−	23.9072i		−	0.781848i
$936$	−15.8175	−	22.7294i	−0.517011	−	0.742935i
$937$		−	58.0985i		−	1.89799i	−0.315284	−	0.948997i	$-0.602100\pi$
$937$		−	58.0985i		−	1.89799i	0.315284	−	0.948997i	$-0.397900\pi$
$938$	−10.0469	−	0.501006i	−0.328042	−	0.0163584i
$939$	−32.0944	−	13.8225i	−1.04736	−	0.451080i
$940$	8.18229	−	6.69484i	0.266877	−	0.218362i
$941$	5.19333	+	19.3818i	0.169298	+	0.631828i	0.997453	+	0.0713289i	$0.0227240\pi$
$941$	5.19333	+	19.3818i	0.169298	+	0.631828i	−0.828155	+	0.560499i	$0.810609\pi$
$942$	−0.850103	−	12.6503i	−0.0276979	−	0.412169i
$943$	−25.7271	+	14.8535i	−0.837790	+	0.483698i
$944$	−0.568991	−	9.09236i	−0.0185191	−	0.295931i
$945$	3.53295	+	1.64010i	0.114927	+	0.0533523i
$946$	65.6445	−	14.1272i	2.13429	−	0.459313i
$947$	−12.9537	+	48.3439i	−0.420939	+	1.57097i	0.351695	+	0.936115i	$0.385606\pi$
$947$	−12.9537	+	48.3439i	−0.420939	+	1.57097i	−0.772634	+	0.634852i	$0.781061\pi$
$948$	21.0751	−	38.0043i	0.684486	−	1.23432i
$949$	3.53576	+	13.1956i	0.114776	+	0.428349i
$950$	−5.81696	+	2.98248i	−0.188727	+	0.0967645i
$951$	−1.08051	−	2.71531i	−0.0350381	−	0.0880500i
$952$	5.33876	−	12.2407i	0.173030	−	0.396723i
$953$	−3.66221			−0.118631			−0.0593154	−	0.998239i	$-0.518892\pi$
$953$	−3.66221			−0.118631			−0.0593154	+	0.998239i	$0.518892\pi$
$954$	−26.1026	−	9.22097i	−0.845103	−	0.298540i
$955$	6.71323	+	6.71323i	0.217235	+	0.217235i
$956$	−16.0647	−	11.5477i	−0.519569	−	0.373480i
$957$	−3.82776	−	32.5876i	−0.123734	−	1.05341i
$958$	−6.07182	+	18.8496i	−0.196172	+	0.609002i
$959$	0.278892	−	0.483055i	0.00900589	−	0.0155987i
$960$	11.4098	−	7.86241i	0.368248	−	0.253758i
$961$	22.8005	+	39.4916i	0.735500	+	1.27392i
$962$	−31.1338	+	6.70020i	−1.00379	+	0.216023i
$963$	−3.82868	−	7.08140i	−0.123377	−	0.228195i
$964$	38.4341	−	17.3459i	1.23788	−	0.558675i
$965$	−3.96016	+	14.7795i	−0.127482	+	0.475770i
$966$	12.7209	+	2.50855i	0.409290	+	0.0807112i
$967$	2.27084	−	3.93321i	0.0730254	−	0.126484i	−0.827201	−	0.561907i	$-0.810068\pi$
$967$	2.27084	−	3.93321i	0.0730254	−	0.126484i	0.900226	+	0.435423i	$0.143401\pi$
$968$	−9.57573	+	1.08012i	−0.307775	+	0.0347164i
$969$	7.28009	−	49.8989i	0.233870	−	1.60298i
$970$	0.815690	−	16.3574i	0.0261902	−	0.525204i
$971$	−8.13524	+	8.13524i	−0.261072	+	0.261072i	−0.825490	−	0.564417i	$-0.809101\pi$
$971$	−8.13524	+	8.13524i	−0.261072	+	0.261072i	0.564417	+	0.825490i	$0.309101\pi$
$972$	−31.1537	−	1.20393i	−0.999254	−	0.0386162i
$973$	8.46313	+	8.46313i	0.271315	+	0.271315i
$974$	15.6972	+	17.3449i	0.502971	+	0.555767i
$975$	−5.59329	−	0.816043i	−0.179129	−	0.0261343i
$976$	3.59706	−	7.24016i	0.115139	−	0.231752i
$977$	11.8563	+	6.84523i	0.379316	+	0.218998i	0.677521	−	0.735504i	$-0.263054\pi$
$977$	11.8563	+	6.84523i	0.379316	+	0.218998i	−0.298204	+	0.954502i	$0.596388\pi$
$978$	−30.6012	−	45.6348i	−0.978519	−	1.45924i
$979$	12.9924	+	3.48130i	0.415238	+	0.111263i
$980$	−12.0442	−	4.55342i	−0.384737	−	0.145454i
$981$	−54.3661	+	29.3939i	−1.73578	+	0.938476i
$982$	1.70109	−	2.63404i	0.0542840	−	0.0840556i
$983$	−18.3033	+	10.5674i	−0.583783	+	0.337048i	−0.762636	−	0.646828i	$-0.776095\pi$
$983$	−18.3033	+	10.5674i	−0.583783	+	0.337048i	0.178852	+	0.983876i	$0.442762\pi$
$984$	15.0398	−	14.0912i	0.479453	−	0.449213i
$985$	1.35678	+	0.783336i	0.0432305	+	0.0249592i
$986$	−39.5599	+	20.2832i	−1.25984	+	0.645950i
$987$	−6.81637	+	0.800655i	−0.216967	+	0.0254851i
$988$	−24.4975	−	17.6094i	−0.779369	−	0.560231i
$989$	62.4607	−	62.4607i	1.98613	−	1.98613i
$990$	−14.5296	+	6.94389i	−0.461780	+	0.220691i
$991$			10.5693i			0.335744i	0.985809	+	0.167872i	$0.0536895\pi$
$991$			10.5693i			0.335744i	−0.985809	+	0.167872i	$0.946311\pi$
$992$	0.627372	+	49.5059i	0.0199191	+	1.57182i
$993$	−47.2856	+	18.8166i	−1.50056	+	0.597125i
$994$	−2.16089	−	0.696066i	−0.0685393	−	0.0220779i
$995$	−4.10782	+	1.10069i	−0.130227	+	0.0348941i
$996$	−12.8278	−	44.7661i	−0.406464	−	1.41847i
$997$	13.3566	+	3.57890i	0.423009	+	0.113345i	0.464043	−	0.885813i	$-0.346398\pi$
$997$	13.3566	+	3.57890i	0.423009	+	0.113345i	−0.0410338	+	0.999158i	$0.513065\pi$
$998$	7.07261	−	10.9515i	0.223880	−	0.346665i
$999$	−15.0974	+	32.5215i	−0.477661	+	1.02893i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.cf.a.131.72	yes	384
9.2	odd	6	inner	720.2.cf.a.371.38	yes	384
16.11	odd	4	inner	720.2.cf.a.491.38	yes	384
144.11	even	12	inner	720.2.cf.a.11.72	✓	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.cf.a.11.72	✓	384	144.11	even	12	inner
720.2.cf.a.131.72	yes	384	1.1	even	1	trivial
720.2.cf.a.371.38	yes	384	9.2	odd	6	inner
720.2.cf.a.491.38	yes	384	16.11	odd	4	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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.cf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.948954 + 1.04856i) q^{2} +(-1.03510 - 1.38873i) q^{3} +(-0.198972 + 1.99008i) q^{4} +(-0.965926 + 0.258819i) q^{5} +(0.473908 - 2.40321i) q^{6} +(-0.374804 - 0.649179i) q^{7} +(-2.27554 + 1.67986i) q^{8} +(-0.857136 + 2.87495i) q^{9} +O(q^{10})\)	\(q+(0.948954 + 1.04856i) q^{2} +(-1.03510 - 1.38873i) q^{3} +(-0.198972 + 1.99008i) q^{4} +(-0.965926 + 0.258819i) q^{5} +(0.473908 - 2.40321i) q^{6} +(-0.374804 - 0.649179i) q^{7} +(-2.27554 + 1.67986i) q^{8} +(-0.857136 + 2.87495i) q^{9} +(-1.18801 - 0.767227i) q^{10} +(-3.66632 - 0.982388i) q^{11} +(2.96963 - 1.78361i) q^{12} +(3.15228 - 0.844650i) q^{13} +(0.325034 - 1.00905i) q^{14} +(1.35926 + 1.07351i) q^{15} +(-3.92082 - 0.791941i) q^{16} -6.29856i q^{17} +(-3.82795 + 1.82943i) q^{18} +(-3.26849 + 3.26849i) q^{19} +(-0.322878 - 1.97377i) q^{20} +(-0.513575 + 1.19247i) q^{21} +(-2.44907 - 4.77661i) q^{22} +(-6.11539 - 3.53072i) q^{23} +(4.68828 + 1.42129i) q^{24} +(0.866025 - 0.500000i) q^{25} +(3.87704 + 2.50383i) q^{26} +(4.87974 - 1.78553i) q^{27} +(1.36649 - 0.616720i) q^{28} +(-4.82086 - 1.29174i) q^{29} +(0.164236 + 2.44398i) q^{30} +(-7.57963 - 4.37610i) q^{31} +(-2.89028 - 4.86275i) q^{32} +(2.43074 + 6.10840i) q^{33} +(6.60445 - 5.97705i) q^{34} +(0.530053 + 0.530053i) q^{35} +(-5.55082 - 2.27780i) q^{36} +(-4.87924 + 4.87924i) q^{37} +(-6.52887 - 0.325574i) q^{38} +(-4.43591 - 3.50336i) q^{39} +(1.76322 - 2.21157i) q^{40} +(2.10347 - 3.64332i) q^{41} +(-1.73774 + 0.593080i) q^{42} +(-3.23761 + 12.0829i) q^{43} +(2.68452 - 7.10080i) q^{44} +(0.0838385 - 2.99883i) q^{45} +(-2.10104 - 9.76288i) q^{46} +(2.64304 + 4.57788i) q^{47} +(2.95865 + 6.26469i) q^{48} +(3.21904 - 5.57555i) q^{49} +(1.34610 + 0.433606i) q^{50} +(-8.74700 + 6.51964i) q^{51} +(1.05370 + 6.44134i) q^{52} +(4.61391 + 4.61391i) q^{53} +(6.50289 + 3.42234i) q^{54} +3.79566 q^{55} +(1.94341 + 0.847616i) q^{56} +(7.92227 + 1.15583i) q^{57} +(-3.22029 - 6.28078i) q^{58} +(0.589470 + 2.19993i) q^{59} +(-2.40681 + 2.49143i) q^{60} +(-0.523104 + 1.95225i) q^{61} +(-2.60410 - 12.1004i) q^{62} +(2.18761 - 0.521106i) q^{63} +(2.35616 - 7.64516i) q^{64} +(-2.82625 + 1.63174i) q^{65} +(-4.09838 + 8.34537i) q^{66} +(-2.45594 - 9.16570i) q^{67} +(12.5346 + 1.25324i) q^{68} +(1.42683 + 12.1473i) q^{69} +(-0.0527984 + 1.05879i) q^{70} -2.14152i q^{71} +(-2.87905 - 7.98192i) q^{72} +4.18607i q^{73} +(-9.74637 - 0.486020i) q^{74} +(-1.59079 - 0.685124i) q^{75} +(-5.85422 - 7.15489i) q^{76} +(0.736406 + 2.74830i) q^{77} +(-0.535980 - 7.97587i) q^{78} +(10.8642 - 6.27244i) q^{79} +(3.99219 - 0.249827i) q^{80} +(-7.53064 - 4.92844i) q^{81} +(5.81635 - 1.25172i) q^{82} +(3.47930 - 12.9849i) q^{83} +(-2.27091 - 1.25932i) q^{84} +(1.63019 + 6.08395i) q^{85} +(-15.7420 + 8.07129i) q^{86} +(3.19619 + 8.03195i) q^{87} +(9.99313 - 3.92344i) q^{88} -3.54371 q^{89} +(3.22402 - 2.75784i) q^{90} +(-1.72981 - 1.72981i) q^{91} +(8.24321 - 11.4676i) q^{92} +(1.76846 + 15.0558i) q^{93} +(-2.29208 + 7.11560i) q^{94} +(2.31117 - 4.00307i) q^{95} +(-3.76131 + 9.04724i) q^{96} +(5.79039 + 10.0293i) q^{97} +(8.90104 - 1.91557i) q^{98} +(5.96685 - 9.69844i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 12 q^{6}+O(q^{10}) \) 384 * q - 12 * q^6	\( 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64} - 72 q^{66} - 156 q^{68} - 112 q^{72} - 168 q^{74} + 12 q^{76} - 116 q^{78} + 72 q^{82} - 120 q^{83} - 116 q^{84} - 36 q^{90} + 48 q^{93} + 20 q^{96} - 32 q^{99}+O(q^{100}) \) 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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