LMFDB - Embedded newform 504.2.cs.a.85.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(85,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("504.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cs (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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			85.16
Character	$\chi$	$=$	504.85
Dual form			504.2.cs.a.421.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.305084 + 1.38091i) q^{2} +(1.64418 + 0.544667i) q^{3} +(-1.81385 - 0.842588i) q^{4} +(2.23227 + 1.28880i) q^{5} +(-1.25375 + 2.10431i) q^{6} +(0.500000 + 0.866025i) q^{7} +(1.71692 - 2.24771i) q^{8} +(2.40668 + 1.79106i) q^{9} +O(q^{10})$	\(q+(-0.305084 + 1.38091i) q^{2} +(1.64418 + 0.544667i) q^{3} +(-1.81385 - 0.842588i) q^{4} +(2.23227 + 1.28880i) q^{5} +(-1.25375 + 2.10431i) q^{6} +(0.500000 + 0.866025i) q^{7} +(1.71692 - 2.24771i) q^{8} +(2.40668 + 1.79106i) q^{9} +(-2.46075 + 2.68938i) q^{10} +(-3.42515 + 1.97751i) q^{11} +(-2.52337 - 2.37331i) q^{12} +(-2.82212 - 1.62935i) q^{13} +(-1.34845 + 0.426247i) q^{14} +(2.96829 + 3.33487i) q^{15} +(2.58009 + 3.05665i) q^{16} +5.82223 q^{17} +(-3.20754 + 2.77699i) q^{18} +1.87998i q^{19} +(-2.96307 - 4.21857i) q^{20} +(0.350396 + 1.69624i) q^{21} +(-1.68582 - 5.33315i) q^{22} +(2.74976 - 4.76272i) q^{23} +(4.04718 - 2.76050i) q^{24} +(0.822012 + 1.42377i) q^{25} +(3.11098 - 3.40002i) q^{26} +(2.98148 + 4.25567i) q^{27} +(-0.177221 - 1.99213i) q^{28} +(-0.765874 + 0.442178i) q^{29} +(-5.51074 + 3.08154i) q^{30} +(-4.30921 + 7.46376i) q^{31} +(-5.00812 + 2.63035i) q^{32} +(-6.70867 + 1.38583i) q^{33} +(-1.77627 + 8.04000i) q^{34} +2.57760i q^{35} +(-2.85622 - 5.27655i) q^{36} -2.75070i q^{37} +(-2.59610 - 0.573552i) q^{38} +(-3.75263 - 4.21607i) q^{39} +(6.72947 - 2.80472i) q^{40} +(-0.516793 + 0.895111i) q^{41} +(-2.44926 - 0.0336269i) q^{42} +(2.92914 - 1.69114i) q^{43} +(7.87894 - 0.700914i) q^{44} +(3.06402 + 7.09986i) q^{45} +(5.73800 + 5.25021i) q^{46} +(-5.13956 - 8.90198i) q^{47} +(2.57728 + 6.43099i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-2.21688 + 0.700761i) q^{50} +(9.57282 + 3.17118i) q^{51} +(3.74603 + 5.33329i) q^{52} -10.7309i q^{53} +(-6.78632 + 2.81884i) q^{54} -10.1945 q^{55} +(2.80503 + 0.363040i) q^{56} +(-1.02396 + 3.09104i) q^{57} +(-0.376954 - 1.19251i) q^{58} +(-5.40695 - 3.12171i) q^{59} +(-2.57411 - 8.54999i) q^{60} +(-3.18487 + 1.83878i) q^{61} +(-8.99215 - 8.22771i) q^{62} +(-0.347768 + 2.97977i) q^{63} +(-2.10439 - 7.71826i) q^{64} +(-4.19982 - 7.27431i) q^{65} +(0.132995 - 9.68689i) q^{66} +(9.75587 + 5.63255i) q^{67} +(-10.5606 - 4.90575i) q^{68} +(7.11520 - 6.33308i) q^{69} +(-3.55945 - 0.786384i) q^{70} -2.59931 q^{71} +(8.15785 - 2.33440i) q^{72} +8.72862 q^{73} +(3.79849 + 0.839195i) q^{74} +(0.576060 + 2.78866i) q^{75} +(1.58405 - 3.41000i) q^{76} +(-3.42515 - 1.97751i) q^{77} +(6.96690 - 3.89581i) q^{78} +(-5.32542 - 9.22390i) q^{79} +(1.82003 + 10.1485i) q^{80} +(2.58418 + 8.62102i) q^{81} +(-1.07841 - 0.986730i) q^{82} +(0.700961 - 0.404700i) q^{83} +(0.793664 - 3.37196i) q^{84} +(12.9968 + 7.50370i) q^{85} +(1.44168 + 4.56082i) q^{86} +(-1.50008 + 0.309875i) q^{87} +(-1.43583 + 11.0940i) q^{88} +7.98844 q^{89} +(-10.7391 + 2.06510i) q^{90} -3.25871i q^{91} +(-9.00066 + 6.32194i) q^{92} +(-11.1504 + 9.92471i) q^{93} +(13.8609 - 4.38145i) q^{94} +(-2.42292 + 4.19663i) q^{95} +(-9.66693 + 1.59702i) q^{96} +(0.259517 + 0.449497i) q^{97} +(-1.04337 - 0.954667i) q^{98} +(-11.7851 - 1.37543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8}+O(q^{10}) $ 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8	$ 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8} + 20 q^{12} + 40 q^{17} - q^{18} + 2 q^{20} - 12 q^{22} + 12 q^{23} + 10 q^{24} + 36 q^{25} - 42 q^{26} + 4 q^{30} + 5 q^{32} + 8 q^{33} + 6 q^{34} - 18 q^{36} - 25 q^{38} - 4 q^{39} - 9 q^{40} + 24 q^{41} - 7 q^{42} + 12 q^{46} - 53 q^{48} - 36 q^{49} + 41 q^{50} - 9 q^{52} + 12 q^{54} + 3 q^{56} + 4 q^{57} + 9 q^{58} - 50 q^{60} + 60 q^{62} - 6 q^{64} - 40 q^{65} - 2 q^{66} + 23 q^{68} - 56 q^{71} + 19 q^{72} + 22 q^{74} - 24 q^{76} - 54 q^{78} - 6 q^{80} - 4 q^{81} - 48 q^{82} + 10 q^{84} - 39 q^{86} - 76 q^{87} - 12 q^{88} - 88 q^{89} - 77 q^{90} + 11 q^{92} + 24 q^{94} - 24 q^{95} + 59 q^{96}+O(q^{100}) $ 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8 + 20 * q^12 + 40 * q^17 - q^18 + 2 * q^20 - 12 * q^22 + 12 * q^23 + 10 * q^24 + 36 * q^25 - 42 * q^26 + 4 * q^30 + 5 * q^32 + 8 * q^33 + 6 * q^34 - 18 * q^36 - 25 * q^38 - 4 * q^39 - 9 * q^40 + 24 * q^41 - 7 * q^42 + 12 * q^46 - 53 * q^48 - 36 * q^49 + 41 * q^50 - 9 * q^52 + 12 * q^54 + 3 * q^56 + 4 * q^57 + 9 * q^58 - 50 * q^60 + 60 * q^62 - 6 * q^64 - 40 * q^65 - 2 * q^66 + 23 * q^68 - 56 * q^71 + 19 * q^72 + 22 * q^74 - 24 * q^76 - 54 * q^78 - 6 * q^80 - 4 * q^81 - 48 * q^82 + 10 * q^84 - 39 * q^86 - 76 * q^87 - 12 * q^88 - 88 * q^89 - 77 * q^90 + 11 * q^92 + 24 * q^94 - 24 * q^95 + 59 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.305084	+	1.38091i	−0.215727	+	0.976454i
$2$	−0.305084	+	1.38091i	−0.215727	+	0.976454i
$3$	1.64418	+	0.544667i	0.949270	+	0.314463i
$3$	1.64418	+	0.544667i	0.949270	+	0.314463i
$4$	−1.81385	−	0.842588i	−0.906924	−	0.421294i
$5$	2.23227	+	1.28880i	0.998300	+	0.576369i	0.907745	−	0.419522i	$-0.137802\pi$
$5$	2.23227	+	1.28880i	0.998300	+	0.576369i	0.0905554	+	0.995891i	$0.471136\pi$
$6$	−1.25375	+	2.10431i	−0.511842	+	0.859080i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	1.71692	−	2.24771i	0.607022	−	0.794685i
$9$	2.40668	+	1.79106i	0.802225	+	0.597021i
$10$	−2.46075	+	2.68938i	−0.778158	+	0.850456i
$11$	−3.42515	+	1.97751i	−1.03272	+	0.596243i	−0.917764	−	0.397127i	$-0.870007\pi$
$11$	−3.42515	+	1.97751i	−1.03272	+	0.596243i	−0.114959	+	0.993370i	$0.536674\pi$
$12$	−2.52337	−	2.37331i	−0.728434	−	0.685116i
$13$	−2.82212	−	1.62935i	−0.782716	−	0.451901i	0.0546758	−	0.998504i	$-0.482587\pi$
$13$	−2.82212	−	1.62935i	−0.782716	−	0.451901i	−0.837392	+	0.546603i	$0.815921\pi$
$14$	−1.34845	+	0.426247i	−0.360388	+	0.113919i
$15$	2.96829	+	3.33487i	0.766409	+	0.861059i
$16$	2.58009	+	3.05665i	0.645022	+	0.764164i
$17$	5.82223			1.41210			0.706049	−	0.708163i	$-0.250476\pi$
$17$	5.82223			1.41210			0.706049	+	0.708163i	$0.250476\pi$
$18$	−3.20754	+	2.77699i	−0.756025	+	0.654543i
$19$			1.87998i			0.431298i	0.976471	+	0.215649i	$0.0691866\pi$
$19$			1.87998i			0.431298i	−0.976471	+	0.215649i	$0.930813\pi$
$20$	−2.96307	−	4.21857i	−0.662562	−	0.943301i
$21$	0.350396	+	1.69624i	0.0764628	+	0.370149i
$22$	−1.68582	−	5.33315i	−0.359418	−	1.13703i
$23$	2.74976	−	4.76272i	0.573364	−	0.993096i	−0.422853	−	0.906198i	$-0.638971\pi$
$23$	2.74976	−	4.76272i	0.573364	−	0.993096i	0.996217	−	0.0868976i	$-0.0276953\pi$
$24$	4.04718	−	2.76050i	0.826127	−	0.563484i
$25$	0.822012	+	1.42377i	0.164402	+	0.284753i
$26$	3.11098	−	3.40002i	0.610114	−	0.666799i
$27$	2.98148	+	4.25567i	0.573787	+	0.819005i
$28$	−0.177221	−	1.99213i	−0.0334916	−	0.376478i
$29$	−0.765874	+	0.442178i	−0.142219	+	0.0821104i	−0.569421	−	0.822046i	$-0.692833\pi$
$29$	−0.765874	+	0.442178i	−0.142219	+	0.0821104i	0.427202	+	0.904156i	$0.359499\pi$
$30$	−5.51074	+	3.08154i	−1.00612	+	0.562610i
$31$	−4.30921	+	7.46376i	−0.773956	+	1.34053i	0.161423	+	0.986885i	$0.448392\pi$
$31$	−4.30921	+	7.46376i	−0.773956	+	1.34053i	−0.935379	+	0.353646i	$0.884942\pi$
$32$	−5.00812	+	2.63035i	−0.885319	+	0.464984i
$33$	−6.70867	+	1.38583i	−1.16783	+	0.241242i
$34$	−1.77627	+	8.04000i	−0.304627	+	1.37885i
$35$			2.57760i			0.435694i
$36$	−2.85622	−	5.27655i	−0.476036	−	0.879426i
$37$		−	2.75070i		−	0.452213i	−0.974103	−	0.226106i	$-0.927400\pi$
$37$		−	2.75070i		−	0.452213i	0.974103	−	0.226106i	$-0.0725997\pi$
$38$	−2.59610	−	0.573552i	−0.421142	−	0.0930424i
$39$	−3.75263	−	4.21607i	−0.600902	−	0.675112i
$40$	6.72947	−	2.80472i	1.06402	−	0.443466i
$41$	−0.516793	+	0.895111i	−0.0807095	+	0.139793i	−0.903555	−	0.428472i	$-0.859052\pi$
$41$	−0.516793	+	0.895111i	−0.0807095	+	0.139793i	0.822845	+	0.568265i	$0.192385\pi$
$42$	−2.44926	−	0.0336269i	−0.377929	−	0.00518874i
$43$	2.92914	−	1.69114i	0.446689	−	0.257896i	−0.259742	−	0.965678i	$-0.583637\pi$
$43$	2.92914	−	1.69114i	0.446689	−	0.257896i	0.706431	+	0.707782i	$0.250304\pi$
$44$	7.87894	−	0.700914i	1.18779	−	0.105667i
$45$	3.06402	+	7.09986i	0.456757	+	1.05838i
$46$	5.73800	+	5.25021i	0.846022	+	0.774101i
$47$	−5.13956	−	8.90198i	−0.749682	−	1.29849i	−0.947975	−	0.318345i	$-0.896873\pi$
$47$	−5.13956	−	8.90198i	−0.749682	−	1.29849i	0.198293	−	0.980143i	$-0.436460\pi$
$48$	2.57728	+	6.43099i	0.371999	+	0.928233i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−2.21688	+	0.700761i	−0.313515	+	0.0991025i
$51$	9.57282	+	3.17118i	1.34046	+	0.444053i
$52$	3.74603	+	5.33329i	0.519481	+	0.739594i
$53$		−	10.7309i		−	1.47400i	−0.675893	−	0.736999i	$-0.736242\pi$
$53$		−	10.7309i		−	1.47400i	0.675893	−	0.736999i	$-0.263758\pi$
$54$	−6.78632	+	2.81884i	−0.923501	+	0.383595i
$55$	−10.1945			−1.37462
$56$	2.80503	+	0.363040i	0.374838	+	0.0485132i
$57$	−1.02396	+	3.09104i	−0.135627	+	0.409418i
$58$	−0.376954	−	1.19251i	−0.0494965	−	0.156584i
$59$	−5.40695	−	3.12171i	−0.703925	−	0.406411i	0.104883	−	0.994485i	$-0.466553\pi$
$59$	−5.40695	−	3.12171i	−0.703925	−	0.406411i	−0.808808	+	0.588073i	$0.799887\pi$
$60$	−2.57411	−	8.54999i	−0.332316	−	1.10380i
$61$	−3.18487	+	1.83878i	−0.407781	+	0.235432i	−0.689836	−	0.723966i	$-0.742317\pi$
$61$	−3.18487	+	1.83878i	−0.407781	+	0.235432i	0.282055	+	0.959398i	$0.408984\pi$
$62$	−8.99215	−	8.22771i	−1.14200	−	1.04492i
$63$	−0.347768	+	2.97977i	−0.0438147	+	0.375416i
$64$	−2.10439	−	7.71826i	−0.263049	−	0.964783i
$65$	−4.19982	−	7.27431i	−0.520924	−	0.902267i
$66$	0.132995	−	9.68689i	0.0163706	−	1.19237i
$67$	9.75587	+	5.63255i	1.19187	+	0.688126i	0.958730	−	0.284318i	$-0.0917671\pi$
$67$	9.75587	+	5.63255i	1.19187	+	0.688126i	0.233139	+	0.972444i	$0.425100\pi$
$68$	−10.5606	−	4.90575i	−1.28067	−	0.594909i
$69$	7.11520	−	6.33308i	0.856569	−	0.762414i
$70$	−3.55945	−	0.786384i	−0.425435	−	0.0939908i
$71$	−2.59931			−0.308481			−0.154241	−	0.988033i	$-0.549293\pi$
$71$	−2.59931			−0.308481			−0.154241	+	0.988033i	$0.549293\pi$
$72$	8.15785	−	2.33440i	0.961412	−	0.275112i
$73$	8.72862			1.02161			0.510804	−	0.859697i	$-0.329348\pi$
$73$	8.72862			1.02161			0.510804	+	0.859697i	$0.329348\pi$
$74$	3.79849	+	0.839195i	0.441565	+	0.0975544i
$75$	0.576060	+	2.78866i	0.0665177	+	0.322006i
$76$	1.58405	−	3.41000i	0.181703	−	0.391154i
$77$	−3.42515	−	1.97751i	−0.390333	−	0.225359i
$78$	6.96690	−	3.89581i	0.788846	−	0.441114i
$79$	−5.32542	−	9.22390i	−0.599157	−	1.03777i	−0.992946	−	0.118569i	$-0.962169\pi$
$79$	−5.32542	−	9.22390i	−0.599157	−	1.03777i	0.393789	−	0.919201i	$-0.371164\pi$
$80$	1.82003	+	10.1485i	0.203486	+	1.13464i
$81$	2.58418	+	8.62102i	0.287131	+	0.957891i
$82$	−1.07841	−	0.986730i	−0.119090	−	0.108966i
$83$	0.700961	−	0.404700i	0.0769405	−	0.0444216i	−0.461036	−	0.887381i	$-0.652522\pi$
$83$	0.700961	−	0.404700i	0.0769405	−	0.0444216i	0.537977	+	0.842960i	$0.319189\pi$
$84$	0.793664	−	3.37196i	0.0865959	−	0.367911i
$85$	12.9968	+	7.50370i	1.40970	+	0.813890i
$86$	1.44168	+	4.56082i	0.155461	+	0.491806i
$87$	−1.50008	+	0.309875i	−0.160825	+	0.0332221i
$88$	−1.43583	+	11.0940i	−0.153060	+	1.18262i
$89$	7.98844			0.846773			0.423386	−	0.905949i	$-0.360841\pi$
$89$	7.98844			0.846773			0.423386	+	0.905949i	$0.360841\pi$
$90$	−10.7391	+	2.06510i	−1.13200	+	0.217681i
$91$		−	3.25871i		−	0.341605i
$92$	−9.00066	+	6.32194i	−0.938383	+	0.659107i
$93$	−11.1504	+	9.92471i	−1.15624	+	1.02914i
$94$	13.8609	−	4.38145i	1.42964	−	0.451912i
$95$	−2.42292	+	4.19663i	−0.248587	+	0.430565i
$96$	−9.66693	+	1.59702i	−0.986627	+	0.162995i
$97$	0.259517	+	0.449497i	0.0263500	+	0.0456395i	0.878900	−	0.477007i	$-0.158278\pi$
$97$	0.259517	+	0.449497i	0.0263500	+	0.0456395i	−0.852550	+	0.522646i	$0.824945\pi$
$98$	−1.04337	−	0.954667i	−0.105396	−	0.0964360i
$99$	−11.7851	−	1.37543i	−1.18445	−	0.138236i
$100$	−0.291356	−	3.27512i	−0.0291356	−	0.327512i
$101$	9.07180	−	5.23761i	0.902678	−	0.521162i	0.0246101	−	0.999697i	$-0.492166\pi$
$101$	9.07180	−	5.23761i	0.902678	−	0.521162i	0.878068	+	0.478536i	$0.158832\pi$
$102$	−7.29963	+	12.2518i	−0.722771	+	1.21311i
$103$	−0.143263	+	0.248139i	−0.0141161	+	0.0244499i	−0.872997	−	0.487725i	$-0.837827\pi$
$103$	−0.143263	+	0.248139i	−0.0141161	+	0.0244499i	0.858881	+	0.512175i	$0.171160\pi$
$104$	−8.50767	+	3.54585i	−0.834245	+	0.347699i
$105$	−1.40393	+	4.23805i	−0.137010	+	0.413591i
$106$	14.8184	+	3.27381i	1.43929	+	0.317981i
$107$			11.4768i			1.10950i	0.832017	+	0.554751i	$0.187186\pi$
$107$			11.4768i			1.10950i	−0.832017	+	0.554751i	$0.812814\pi$
$108$	−1.82218	−	10.2313i	−0.175339	−	0.984508i
$109$		−	3.42342i		−	0.327904i	−0.986468	−	0.163952i	$-0.947576\pi$
$109$		−	3.42342i		−	0.327904i	0.986468	−	0.163952i	$-0.0524242\pi$
$110$	3.11017	−	14.0777i	0.296543	−	1.34226i
$111$	1.49822	−	4.52266i	0.142204	−	0.429272i
$112$	−1.35710	+	3.76275i	−0.128234	+	0.355546i
$113$	9.23986	−	16.0039i	0.869213	−	1.50552i	0.00641118	−	0.999979i	$-0.497959\pi$
$113$	9.23986	−	16.0039i	0.869213	−	1.50552i	0.862802	−	0.505542i	$-0.168707\pi$
$114$	−3.95606	−	2.35703i	−0.370519	−	0.220756i
$115$	12.2764	−	7.08778i	1.14478	−	0.660939i
$116$	1.76175	−	0.156726i	0.163575	−	0.0145517i
$117$	−3.87366	−	8.97593i	−0.358120	−	0.829825i
$118$	5.96038	−	6.51416i	0.548697	−	0.599677i
$119$	2.91112	+	5.04220i	0.266862	+	0.462218i
$120$	12.5921	−	0.946163i	1.14950	−	0.0863724i
$121$	2.32112	−	4.02030i	0.211011	−	0.365482i
$122$	−1.56755	−	4.95901i	−0.141920	−	0.448968i
$123$	−1.33724	+	1.19025i	−0.120575	+	0.107321i
$124$	14.1051	−	9.90725i	1.26668	−	0.889697i
$125$		−	8.65036i		−	0.773712i
$126$	−4.00871	−	1.38932i	−0.357125	−	0.123770i
$127$	−16.4153			−1.45662			−0.728312	−	0.685246i	$-0.759695\pi$
$127$	−16.4153			−1.45662			−0.728312	+	0.685246i	$0.759695\pi$
$128$	11.3003	−	0.551266i	0.998812	−	0.0487255i
$129$	5.73714	−	1.18514i	0.505127	−	0.104345i
$130$	11.3265	−	3.58032i	0.993399	−	0.314015i
$131$	18.0219	+	10.4050i	1.57458	+	0.909086i	0.995596	+	0.0937495i	$0.0298853\pi$
$131$	18.0219	+	10.4050i	1.57458	+	0.909086i	0.578987	+	0.815336i	$0.303448\pi$
$132$	13.3362	+	3.13896i	1.16077	+	0.273212i
$133$	−1.62811	+	0.939992i	−0.141175	+	0.0815076i
$134$	−10.7544	+	11.7536i	−0.929041	+	1.01536i
$135$	1.17076	+	13.3423i	0.100763	+	1.14833i
$136$	9.99629	−	13.0867i	0.857175	−	1.12217i
$137$	−8.88768	−	15.3939i	−0.759326	−	1.31519i	−0.943195	−	0.332240i	$-0.892196\pi$
$137$	−8.88768	−	15.3939i	−0.759326	−	1.31519i	0.183869	−	0.982951i	$-0.441138\pi$
$138$	6.57471	+	11.7576i	0.559677	+	1.00087i
$139$	−18.0333	−	10.4115i	−1.52956	−	0.883094i	−0.999380	−	0.0352117i	$-0.988789\pi$
$139$	−18.0333	−	10.4115i	−1.52956	−	0.883094i	−0.530184	−	0.847883i	$-0.677877\pi$
$140$	2.17186	−	4.67538i	0.183555	−	0.395141i
$141$	−3.60177	−	17.4358i	−0.303324	−	1.46836i
$142$	0.793007	−	3.58942i	0.0665476	−	0.301218i
$143$	12.8883			1.07777
$144$	0.734778	+	11.9775i	0.0612315	+	0.998124i
$145$	−2.27952			−0.189303
$146$	−2.66296	+	12.0535i	−0.220388	+	0.997553i
$147$	−1.29379	+	1.15157i	−0.106710	+	0.0949800i
$148$	−2.31771	+	4.98936i	−0.190515	+	0.410123i
$149$	11.8383	+	6.83487i	0.969835	+	0.559935i	0.899186	−	0.437567i	$-0.144160\pi$
$149$	11.8383	+	6.83487i	0.969835	+	0.559935i	0.0706493	+	0.997501i	$0.477493\pi$
$150$	−4.02664	−	0.0552834i	−0.328774	−	0.00451387i
$151$	10.3618	+	17.9472i	0.843231	+	1.46052i	0.887149	+	0.461483i	$0.152683\pi$
$151$	10.3618	+	17.9472i	0.843231	+	1.46052i	−0.0439182	+	0.999035i	$0.513984\pi$
$152$	4.22565	+	3.22778i	0.342746	+	0.261807i
$153$	14.0122	+	10.4280i	1.13282	+	0.843053i
$154$	3.77574	−	4.12654i	0.304257	−	0.332526i
$155$	−19.2386	+	11.1074i	−1.54528	+	0.892169i
$156$	3.25429	+	10.8092i	0.260552	+	0.865432i
$157$	9.41985	+	5.43855i	0.751786	+	0.434044i	0.826339	−	0.563173i	$-0.190420\pi$
$157$	9.41985	+	5.43855i	0.751786	+	0.434044i	−0.0745529	+	0.997217i	$0.523753\pi$
$158$	14.3621	−	4.53989i	1.14259	−	0.361174i
$159$	5.84475	−	17.6435i	0.463519	−	1.39922i
$160$	−14.5695	−	0.582829i	−1.15182	−	0.0460766i
$161$	5.49952			0.433423
$162$	−12.6933	+	0.938403i	−0.997278	+	0.0737279i
$163$			3.45719i			0.270788i	0.990792	+	0.135394i	$0.0432300\pi$
$163$			3.45719i			0.270788i	−0.990792	+	0.135394i	$0.956770\pi$
$164$	1.69159	−	1.18815i	0.132091	−	0.0927791i
$165$	−16.7616	−	5.55259i	−1.30489	−	0.432269i
$166$	0.345004	+	1.09143i	0.0267775	+	0.0847117i
$167$	5.38746	−	9.33135i	0.416894	−	0.722081i	−0.578731	−	0.815518i	$-0.696452\pi$
$167$	5.38746	−	9.33135i	0.416894	−	0.722081i	0.995625	+	0.0934369i	$0.0297853\pi$
$168$	4.41425	+	2.12471i	0.340567	+	0.163925i
$169$	−1.19041	−	2.06185i	−0.0915701	−	0.158604i
$170$	−14.3271	+	15.6582i	−1.09884	+	1.20093i
$171$	−3.36717	+	4.52451i	−0.257494	+	0.345998i
$172$	−6.73794	+	0.599410i	−0.513763	+	0.0457046i
$173$	12.5484	−	7.24480i	0.954035	−	0.550812i	0.0597028	−	0.998216i	$-0.480985\pi$
$173$	12.5484	−	7.24480i	0.954035	−	0.550812i	0.894332	+	0.447404i	$0.147651\pi$
$174$	0.0297381	−	2.16602i	0.00225444	−	0.164205i
$175$	−0.822012	+	1.42377i	−0.0621383	+	0.107627i
$176$	−14.8818	−	5.36735i	−1.12176	−	0.404579i
$177$	−7.18973	−	8.07764i	−0.540413	−	0.607153i
$178$	−2.43714	+	11.0313i	−0.182671	+	0.826835i
$179$		−	13.7806i		−	1.03001i	−0.857186	−	0.515007i	$-0.827789\pi$
$179$		−	13.7806i		−	1.03001i	0.857186	−	0.515007i	$-0.172211\pi$
$180$	0.424587	−	15.4598i	0.0316469	−	1.15230i
$181$		−	13.1688i		−	0.978832i	−0.872051	−	0.489416i	$-0.837210\pi$
$181$		−	13.1688i		−	0.978832i	0.872051	−	0.489416i	$-0.162790\pi$
$182$	4.50000	+	0.994178i	0.333562	+	0.0736934i
$183$	−6.23803	+	1.28861i	−0.461129	+	0.0952566i
$184$	−5.98410	−	14.3579i	−0.441154	−	1.05847i
$185$	3.54511	−	6.14031i	0.260642	−	0.451444i
$186$	−10.3034	−	18.4256i	−0.755480	−	1.35103i
$187$	−19.9420	+	11.5135i	−1.45831	+	0.841954i
$188$	1.82168	+	20.4774i	0.132859	+	1.49347i
$189$	−2.19478	+	4.70988i	−0.159647	+	0.342593i
$190$	−5.05599	−	4.62617i	−0.366800	−	0.335618i
$191$	0.668053	+	1.15710i	0.0483386	+	0.0837249i	0.889182	−	0.457553i	$-0.151274\pi$
$191$	0.668053	+	1.15710i	0.0483386	+	0.0837249i	−0.840844	+	0.541278i	$0.817941\pi$
$192$	0.743879	−	13.8364i	0.0536849	−	0.998558i
$193$	−9.94432	+	17.2241i	−0.715808	+	1.23982i	0.246839	+	0.969056i	$0.420608\pi$
$193$	−9.94432	+	17.2241i	−0.715808	+	1.23982i	−0.962647	+	0.270759i	$0.912725\pi$
$194$	−0.699891	+	0.221237i	−0.0502492	+	0.0158839i
$195$	−2.94321	−	14.2478i	−0.210767	−	1.02031i
$196$	1.63663	−	1.14954i	0.116902	−	0.0821103i
$197$			12.8540i			0.915807i	0.889002	+	0.457903i	$0.151399\pi$
$197$			12.8540i			0.915807i	−0.889002	+	0.457903i	$0.848601\pi$
$198$	5.49479	−	15.8546i	0.390498	−	1.12674i
$199$	−15.3390			−1.08735			−0.543676	−	0.839295i	$-0.682968\pi$
$199$	−15.3390			−1.08735			−0.543676	+	0.839295i	$0.682968\pi$
$200$	4.61154	+	0.596846i	0.326085	+	0.0422034i
$201$	12.9726	+	14.5746i	0.915014	+	1.02802i
$202$	4.46503	+	14.1253i	0.314158	+	0.993852i
$203$	−0.765874	−	0.442178i	−0.0537538	−	0.0310348i
$204$	−14.6916	−	13.8180i	−1.02862	−	0.967452i
$205$	−2.30724	+	1.33209i	−0.161145	+	0.0930369i
$206$	−0.298952	−	0.273537i	−0.0208289	−	0.0190582i
$207$	15.1481	−	6.53734i	1.05287	−	0.454376i
$208$	−2.30096	−	12.8301i	−0.159543	−	0.889610i
$209$	−3.71769	−	6.43923i	−0.257158	−	0.445411i
$210$	−5.42406	−	3.23167i	−0.374296	−	0.223006i
$211$	−18.5634	−	10.7176i	−1.27795	−	0.737827i	−0.301483	−	0.953472i	$-0.597482\pi$
$211$	−18.5634	−	10.7176i	−1.27795	−	0.737827i	−0.976472	+	0.215644i	$0.930815\pi$
$212$	−9.04171	+	19.4642i	−0.620987	+	1.33680i
$213$	−4.27374	−	1.41576i	−0.292832	−	0.0970061i
$214$	−15.8484	−	3.50137i	−1.08338	−	0.239349i
$215$	8.71815			0.594573
$216$	14.6845	+	0.605132i	0.999152	+	0.0411740i
$217$	−8.61841			−0.585056
$218$	4.72744	+	1.04443i	0.320183	+	0.0707376i
$219$	14.3515	+	4.75419i	0.969781	+	0.321258i
$220$	18.4912	+	8.58975i	1.24668	+	0.579121i
$221$	−16.4311	−	9.48648i	−1.10527	−	0.638130i
$222$	5.78833	+	3.44870i	0.388487	+	0.231462i
$223$	0.855459	+	1.48170i	0.0572858	+	0.0992219i	0.893246	−	0.449568i	$-0.148422\pi$
$223$	0.855459	+	1.48170i	0.0572858	+	0.0992219i	−0.835960	+	0.548790i	$0.815089\pi$
$224$	−4.78201	−	3.02199i	−0.319511	−	0.201915i
$225$	−0.571740	+	4.89882i	−0.0381160	+	0.326588i
$226$	19.2811	+	17.6420i	1.28256	+	1.17353i
$227$	−19.0976	+	11.0260i	−1.26755	+	0.731822i	−0.974524	−	0.224282i	$-0.927996\pi$
$227$	−19.0976	+	11.0260i	−1.26755	+	0.731822i	−0.293029	+	0.956104i	$0.594663\pi$
$228$	4.46179	−	4.74389i	0.295489	−	0.314172i
$229$	3.57811	+	2.06582i	0.236448	+	0.136513i	0.613543	−	0.789661i	$-0.289744\pi$
$229$	3.57811	+	2.06582i	0.236448	+	0.136513i	−0.377095	+	0.926175i	$0.623077\pi$
$230$	6.04229	+	19.1150i	0.398417	+	1.26041i
$231$	−4.55450	−	5.11696i	−0.299664	−	0.336671i
$232$	−0.321056	+	2.48065i	−0.0210784	+	0.162862i
$233$	−24.1806			−1.58412			−0.792061	−	0.610442i	$-0.790992\pi$
$233$	−24.1806			−1.58412			−0.792061	+	0.610442i	$0.790992\pi$
$234$	13.5768	−	2.61079i	0.887542	−	0.170672i
$235$		−	26.4955i		−	1.72837i
$236$	7.17708	+	10.2181i	0.467188	+	0.665144i
$237$	−3.73202	−	18.0664i	−0.242421	−	1.17354i
$238$	−7.85098	+	2.48171i	−0.508904	+	0.160865i
$239$	−9.46159	+	16.3880i	−0.612019	+	1.06005i	0.378880	+	0.925446i	$0.376309\pi$
$239$	−9.46159	+	16.3880i	−0.612019	+	1.06005i	−0.990900	+	0.134603i	$0.957024\pi$
$240$	−2.53508	+	17.6773i	−0.163639	+	1.14106i
$241$	−8.09801	−	14.0262i	−0.521639	−	0.903505i	−0.999683	−	0.0251694i	$-0.991987\pi$
$241$	−8.09801	−	14.0262i	−0.521639	−	0.903505i	0.478044	−	0.878336i	$-0.341346\pi$
$242$	4.84355	+	4.43180i	0.311355	+	0.284887i
$243$	−0.446714	+	15.5821i	−0.0286567	+	0.999589i
$244$	7.32621	−	0.651743i	0.469012	−	0.0417236i
$245$	−2.23227	+	1.28880i	−0.142614	+	0.0823384i
$246$	−1.23566	−	2.20974i	−0.0787828	−	0.140888i
$247$	3.06316	−	5.30554i	0.194904	−	0.337584i
$248$	9.37781	+	22.5005i	0.595492	+	1.42878i
$249$	1.37293	−	0.283611i	0.0870062	−	0.0179731i
$250$	11.9454	+	2.63908i	0.755494	+	0.166910i
$251$		−	22.6766i		−	1.43133i	−0.698443	−	0.715666i	$-0.746123\pi$
$251$		−	22.6766i		−	1.43133i	0.698443	−	0.715666i	$-0.253877\pi$
$252$	3.14152	−	5.11183i	0.197897	−	0.322015i
$253$			21.7507i			1.36746i
$254$	5.00804	−	22.6681i	0.314232	−	1.42233i
$255$	17.2821	+	19.4164i	1.08225	+	1.21590i
$256$	−2.68628	+	15.7729i	−0.167892	+	0.985805i
$257$	−11.6725	+	20.2173i	−0.728108	+	1.26112i	0.229573	+	0.973291i	$0.426267\pi$
$257$	−11.6725	+	20.2173i	−0.728108	+	1.26112i	−0.957682	+	0.287829i	$0.907066\pi$
$258$	−0.113735	+	8.28407i	−0.00708085	+	0.515743i
$259$	2.38218	−	1.37535i	0.148021	−	0.0854602i
$260$	1.48859	+	16.7332i	0.0923187	+	1.03775i
$261$	−2.63518	−	0.307551i	−0.163114	−	0.0190369i
$262$	−19.8666	+	21.7124i	−1.22736	+	1.34139i
$263$	6.94518	+	12.0294i	0.428258	+	0.741765i	0.996718	−	0.0809459i	$-0.0257941\pi$
$263$	6.94518	+	12.0294i	0.428258	+	0.741765i	−0.568460	+	0.822711i	$0.692461\pi$
$264$	−8.40329	+	17.4585i	−0.517187	+	1.07450i
$265$	13.8300	−	23.9542i	0.849567	−	1.47149i
$266$	−0.801337	−	2.53506i	−0.0491331	−	0.155435i
$267$	13.1345	+	4.35104i	0.803816	+	0.266279i
$268$	−12.9497	−	18.4368i	−0.791031	−	1.12621i
$269$			10.7365i			0.654614i	0.944918	+	0.327307i	$0.106141\pi$
$269$			10.7365i			0.654614i	−0.944918	+	0.327307i	$0.893859\pi$
$270$	−18.7818	−	2.45381i	−1.14302	−	0.149334i
$271$	−17.2715			−1.04917			−0.524585	−	0.851358i	$-0.675779\pi$
$271$	−17.2715			−1.04917			−0.524585	+	0.851358i	$0.675779\pi$
$272$	15.0219	+	17.7966i	0.910835	+	1.07907i
$273$	1.77491	−	5.35791i	0.107422	−	0.324276i
$274$	23.9692	−	7.57669i	1.44803	−	0.457725i
$275$	−5.63104	−	3.25108i	−0.339564	−	0.196048i
$276$	−18.2421	+	5.49206i	−1.09804	+	0.330583i
$277$	−19.1452	+	11.0535i	−1.15032	+	0.664139i	−0.948966	−	0.315379i	$-0.897868\pi$
$277$	−19.1452	+	11.0535i	−1.15032	+	0.664139i	−0.201356	+	0.979518i	$0.564535\pi$
$278$	19.8791	−	21.7260i	1.19227	−	1.30304i
$279$	−23.7389	+	10.2448i	−1.42121	+	0.613340i
$280$	5.79370	+	4.42553i	0.346240	+	0.264476i
$281$	2.98556	+	5.17115i	0.178104	+	0.308485i	0.941231	−	0.337763i	$-0.109670\pi$
$281$	2.98556	+	5.17115i	0.178104	+	0.308485i	−0.763127	+	0.646248i	$0.776337\pi$
$282$	25.1762	+	0.345655i	1.49922	+	0.0205835i
$283$	16.0793	+	9.28340i	0.955817	+	0.551841i	0.894883	−	0.446301i	$-0.147259\pi$
$283$	16.0793	+	9.28340i	0.955817	+	0.551841i	0.0609337	+	0.998142i	$0.480592\pi$
$284$	4.71475	+	2.19015i	0.279769	+	0.129961i
$285$	−6.26949	+	5.58034i	−0.371373	+	0.330551i
$286$	−3.93200	+	17.7976i	−0.232504	+	1.05239i
$287$	−1.03359			−0.0610106
$288$	−16.7640	−	2.63947i	−0.987831	−	0.155532i
$289$	16.8984			0.994023
$290$	0.695443	−	3.14782i	0.0408378	−	0.184846i
$291$	0.181868	+	0.880405i	0.0106613	+	0.0516103i
$292$	−15.8324	−	7.35464i	−0.926521	−	0.430398i
$293$	6.66076	+	3.84559i	0.389126	+	0.224662i	0.681781	−	0.731556i	$-0.261206\pi$
$293$	6.66076	+	3.84559i	0.389126	+	0.224662i	−0.292656	+	0.956218i	$0.594539\pi$
$294$	−1.19551	−	2.13793i	−0.0697234	−	0.124687i
$295$	−8.04651	−	13.9370i	−0.468486	−	0.811441i
$296$	−6.18278	−	4.72273i	−0.359367	−	0.274503i
$297$	−18.6277	−	8.68041i	−1.08089	−	0.503689i
$298$	−13.0501	+	14.2625i	−0.755970	+	0.826207i
$299$	−15.5203	+	8.96066i	−0.897563	+	0.518208i
$300$	1.30480	−	5.54358i	0.0753329	−	0.320059i
$301$	2.92914	+	1.69114i	0.168833	+	0.0974755i
$302$	−27.9447	+	8.83337i	−1.60804	+	0.508303i
$303$	17.7685	−	3.67048i	1.02077	−	0.210863i
$304$	−5.74646	+	4.85052i	−0.329582	+	0.278197i
$305$	−9.47931			−0.542783
$306$	−18.6751	+	16.1683i	−1.06758	+	0.924279i
$307$		−	22.7276i		−	1.29713i	−0.761158	−	0.648566i	$-0.775369\pi$
$307$		−	22.7276i		−	1.29713i	0.761158	−	0.648566i	$-0.224631\pi$
$308$	4.54648	+	6.47290i	0.259060	+	0.368828i
$309$	−0.370704	+	0.329955i	−0.0210886	+	0.0187705i
$310$	−9.46900	−	29.9555i	−0.537803	−	1.70136i
$311$	6.19130	−	10.7236i	0.351076	−	0.608082i	−0.635362	−	0.772214i	$-0.719149\pi$
$311$	6.19130	−	10.7236i	0.351076	−	0.608082i	0.986438	+	0.164133i	$0.0524825\pi$
$312$	−15.9195	+	1.19618i	−0.901262	+	0.0677202i
$313$	14.2671	+	24.7113i	0.806421	+	1.39676i	0.915327	+	0.402711i	$0.131932\pi$
$313$	14.2671	+	24.7113i	0.806421	+	1.39676i	−0.108906	+	0.994052i	$0.534735\pi$
$314$	−10.3840	+	11.3488i	−0.586004	+	0.640449i
$315$	−4.61665	+	6.20345i	−0.260119	+	0.349525i
$316$	1.88755	+	21.2179i	0.106183	+	1.19360i
$317$	−20.8041	+	12.0113i	−1.16848	+	0.674620i	−0.953321	−	0.301960i	$-0.902359\pi$
$317$	−20.8041	+	12.0113i	−1.16848	+	0.674620i	−0.215155	+	0.976580i	$0.569026\pi$
$318$	22.5811	+	13.4538i	1.26628	+	0.754454i
$319$	1.74883	−	3.02905i	0.0979154	−	0.169594i
$320$	5.24974	−	19.9414i	0.293469	−	1.11476i
$321$	−6.25102	+	18.8699i	−0.348898	+	1.05322i
$322$	−1.67781	+	7.59436i	−0.0935008	+	0.423217i
$323$			10.9457i			0.609035i
$324$	2.57666	−	17.8146i	0.143148	−	0.989701i
$325$		−	5.35740i		−	0.297175i
$326$	−4.77408	−	1.05473i	−0.264412	−	0.0584161i
$327$	1.86462	−	5.62872i	0.103114	−	0.311269i
$328$	1.12466	+	2.69843i	0.0620989	+	0.148996i
$329$	5.13956	−	8.90198i	0.283353	−	0.490782i
$330$	12.7813	−	21.4523i	0.703590	−	1.18091i
$331$	−11.5141	+	6.64765i	−0.632870	+	0.365388i	−0.781863	−	0.623451i	$-0.785730\pi$
$331$	−11.5141	+	6.64765i	−0.632870	+	0.365388i	0.148993	+	0.988838i	$0.452397\pi$
$332$	−1.61243	+	0.143443i	−0.0884937	+	0.00787244i
$333$	4.92669	−	6.62005i	0.269981	−	0.362777i
$334$	11.2422	+	10.2865i	0.615144	+	0.562850i
$335$	14.5185	+	25.1467i	0.793229	+	1.37391i
$336$	−4.28076	+	5.44749i	−0.233535	+	0.297185i
$337$	−9.46325	+	16.3908i	−0.515496	+	0.892865i	0.484342	+	0.874879i	$0.339059\pi$
$337$	−9.46325	+	16.3908i	−0.515496	+	0.892865i	−0.999838	+	0.0179867i	$0.994274\pi$
$338$	3.21042	−	1.01482i	0.174624	−	0.0551988i
$339$	23.9088	−	21.2807i	1.29855	−	1.15581i
$340$	−17.2517	−	24.5615i	−0.935603	−	1.33203i
$341$		−	34.0861i		−	1.84586i
$342$	−5.22069	−	6.03013i	−0.282303	−	0.326072i
$343$	−1.00000			−0.0539949
$344$	1.22790	−	9.48739i	0.0662040	−	0.511526i
$345$	24.0451	−	4.96706i	1.29455	−	0.267418i
$346$	6.17615	+	19.5385i	0.332032	+	1.05040i
$347$	15.6108	+	9.01292i	0.838033	+	0.483839i	0.856595	−	0.515989i	$-0.172575\pi$
$347$	15.6108	+	9.01292i	0.838033	+	0.483839i	−0.0185619	+	0.999828i	$0.505909\pi$
$348$	2.98201	+	0.701882i	0.159852	+	0.0376248i
$349$	−8.52220	+	4.92029i	−0.456183	+	0.263377i	−0.710438	−	0.703760i	$-0.751503\pi$
$349$	−8.52220	+	4.92029i	−0.456183	+	0.263377i	0.254255	+	0.967137i	$0.418170\pi$
$350$	−1.71532	−	1.56950i	−0.0916876	−	0.0838931i
$351$	−1.48012	−	16.8679i	−0.0790029	−	0.900343i
$352$	11.9520	−	18.9130i	0.637046	−	1.00806i
$353$	−10.0132	−	17.3433i	−0.532947	−	0.923091i	−0.999260	−	0.0384714i	$-0.987751\pi$
$353$	−10.0132	−	17.3433i	−0.532947	−	0.923091i	0.466313	−	0.884620i	$-0.345582\pi$
$354$	13.3480	−	7.46405i	0.709438	−	0.396710i
$355$	−5.80236	−	3.34999i	−0.307957	−	0.177799i
$356$	−14.4898	−	6.73097i	−0.767959	−	0.356740i
$357$	2.04009	+	9.87589i	0.107973	+	0.522688i
$358$	19.0299	+	4.20425i	1.00576	+	0.222201i
$359$	1.90227			0.100398			0.0501991	−	0.998739i	$-0.484014\pi$
$359$	1.90227			0.100398			0.0501991	+	0.998739i	$0.484014\pi$
$360$	21.2191	+	5.30284i	1.11834	+	0.279484i
$361$	15.4657			0.813982
$362$	18.1850	+	4.01759i	0.955784	+	0.211160i
$363$	6.00607	−	5.34587i	0.315237	−	0.280586i
$364$	−2.74575	+	5.91080i	−0.143916	+	0.309810i
$365$	19.4846	+	11.2495i	1.01987	+	0.588823i
$366$	0.123665	−	9.00732i	0.00646408	−	0.470820i
$367$	−10.1851	−	17.6412i	−0.531659	−	0.920861i	−0.999317	−	0.0369514i	$-0.988235\pi$
$367$	−10.1851	−	17.6412i	−0.531659	−	0.920861i	0.467658	−	0.883910i	$-0.345098\pi$
$368$	21.6526	−	3.88318i	1.12872	−	0.202425i
$369$	−2.84695	+	1.22863i	−0.148207	+	0.0639602i
$370$	7.39768	+	6.76880i	0.384587	+	0.351893i
$371$	9.29321	−	5.36544i	0.482479	−	0.278560i
$372$	28.5876	−	8.60673i	1.48220	−	0.446238i
$373$	−6.69189	−	3.86356i	−0.346493	−	0.200048i	0.316647	−	0.948544i	$-0.397443\pi$
$373$	−6.69189	−	3.86356i	−0.346493	−	0.200048i	−0.663139	+	0.748496i	$0.730776\pi$
$374$	−9.81523	−	31.0508i	−0.507533	−	1.60560i
$375$	4.71156	−	14.2228i	0.243304	−	0.734461i
$376$	−28.8333	−	3.73173i	−1.48696	−	0.192449i
$377$	2.88186			0.148423
$378$	−5.83435	−	4.46771i	−0.300086	−	0.229794i
$379$			11.7762i			0.604905i	0.953165	+	0.302452i	$0.0978053\pi$
$379$			11.7762i			0.604905i	−0.953165	+	0.302452i	$0.902195\pi$
$380$	7.93084	−	5.57051i	0.406844	−	0.285761i
$381$	−26.9898	−	8.94087i	−1.38273	−	0.458055i
$382$	−1.80167	+	0.569511i	−0.0921814	+	0.0291387i
$383$	6.42548	−	11.1293i	0.328327	−	0.568679i	−0.653853	−	0.756621i	$-0.726849\pi$
$383$	6.42548	−	11.1293i	0.328327	−	0.568679i	0.982180	+	0.187943i	$0.0601820\pi$
$384$	18.8800	+	5.24850i	0.963464	+	0.267836i
$385$	−5.09724	−	8.82868i	−0.259779	−	0.449951i
$386$	−20.7511	−	18.9870i	−1.05620	−	0.966415i
$387$	10.0784	+	1.17625i	0.512315	+	0.0597921i
$388$	−0.0919837	−	1.03398i	−0.00466977	−	0.0524926i
$389$	−6.27426	+	3.62245i	−0.318118	+	0.183665i	−0.650553	−	0.759461i	$-0.725463\pi$
$389$	−6.27426	+	3.62245i	−0.318118	+	0.183665i	0.332436	+	0.943126i	$0.392130\pi$
$390$	20.5729	+	0.282454i	1.04175	+	0.0143026i
$391$	16.0097	−	27.7297i	0.809647	−	1.40235i
$392$	1.08811	+	2.61075i	0.0549581	+	0.131863i
$393$	23.9641	+	26.9236i	1.20883	+	1.35812i
$394$	−17.7502	−	3.92153i	−0.894243	−	0.197564i
$395$		−	27.4536i		−	1.38134i
$396$	20.2174	+	12.4248i	1.01596	+	0.624370i
$397$			15.0241i			0.754038i	0.926206	+	0.377019i	$0.123051\pi$
$397$			15.0241i			0.754038i	−0.926206	+	0.377019i	$0.876949\pi$
$398$	4.67967	−	21.1818i	0.234571	−	1.06175i
$399$	−3.18890	+	0.658739i	−0.159645	+	0.0329782i
$400$	−2.23110	+	6.18606i	−0.111555	+	0.309303i
$401$	−11.7680	+	20.3827i	−0.587663	+	1.01786i	0.406874	+	0.913484i	$0.366619\pi$
$401$	−11.7680	+	20.3827i	−0.587663	+	1.01786i	−0.994538	+	0.104379i	$0.966715\pi$
$402$	−24.0840	+	13.4675i	−1.20120	+	0.671699i
$403$	24.3222	−	14.0424i	1.21158	−	0.699504i
$404$	−20.8680	+	1.85643i	−1.03822	+	0.0923608i
$405$	−5.34219	+	22.5749i	−0.265455	+	1.12176i
$406$	0.844265	−	0.922706i	0.0419002	−	0.0457931i
$407$	5.43956	+	9.42159i	0.269629	+	0.467011i
$408$	23.5636	−	16.0723i	1.16657	−	0.795695i
$409$	0.955642	−	1.65522i	0.0472535	−	0.0818454i	−0.841431	−	0.540364i	$-0.818286\pi$
$409$	0.955642	−	1.65522i	0.0472535	−	0.0818454i	0.888685	+	0.458519i	$0.151620\pi$
$410$	−1.13559	−	3.59250i	−0.0560830	−	0.177421i
$411$	−6.22842	−	30.1512i	−0.307225	−	1.48725i
$412$	0.468937	−	0.329375i	0.0231029	−	0.0162271i
$413$		−	6.24341i		−	0.307218i
$414$	4.40606	+	22.9127i	0.216546	+	1.12610i
$415$	2.08631			0.102413
$416$	18.4193	+	0.736836i	0.903081	+	0.0361263i
$417$	−23.9792	−	26.9406i	−1.17427	−	1.31929i
$418$	10.0262	−	3.16931i	0.490399	−	0.155016i
$419$	17.2962	+	9.98596i	0.844974	+	0.487846i	0.858952	−	0.512056i	$-0.171116\pi$
$419$	17.2962	+	9.98596i	0.844974	+	0.487846i	−0.0139777	+	0.999902i	$0.504449\pi$
$420$	6.11745	−	6.50424i	0.298501	−	0.317374i
$421$	−25.4493	+	14.6932i	−1.24032	+	0.716101i	−0.969160	−	0.246432i	$-0.920742\pi$
$421$	−25.4493	+	14.6932i	−1.24032	+	0.716101i	−0.271164	+	0.962533i	$0.587409\pi$
$422$	20.4634	−	22.3647i	0.996143	−	1.08869i
$423$	3.57475	−	30.6295i	0.173811	−	1.48926i
$424$	−24.1199	−	18.4240i	−1.17136	−	0.894750i
$425$	4.78595	+	8.28950i	0.232153	+	0.402100i
$426$	3.25889	−	5.46975i	0.157894	−	0.265010i
$427$	−3.18487	−	1.83878i	−0.154127	−	0.0889850i
$428$	9.67020	−	20.8171i	0.467427	−	1.00623i
$429$	21.1907	+	7.01982i	1.02310	+	0.338920i
$430$	−2.65977	+	12.0390i	−0.128265	+	0.580573i
$431$	−16.8252			−0.810442			−0.405221	−	0.914219i	$-0.632805\pi$
$431$	−16.8252			−0.810442			−0.405221	+	0.914219i	$0.632805\pi$
$432$	−5.31563	+	20.0934i	−0.255748	+	0.966743i
$433$	−35.1470			−1.68906			−0.844530	−	0.535509i	$-0.820120\pi$
$433$	−35.1470			−1.68906			−0.844530	+	0.535509i	$0.820120\pi$
$434$	2.62934	−	11.9013i	0.126212	−	0.571280i
$435$	−3.74794	−	1.24158i	−0.179700	−	0.0595290i
$436$	−2.88453	+	6.20956i	−0.138144	+	0.297384i
$437$	8.95383	+	5.16950i	0.428320	+	0.247291i
$438$	−10.9435	+	18.3677i	−0.522902	+	0.877643i
$439$	14.3255	+	24.8125i	0.683719	+	1.18424i	0.973838	+	0.227245i	$0.0729719\pi$
$439$	14.3255	+	24.8125i	0.683719	+	1.18424i	−0.290119	+	0.956991i	$0.593695\pi$
$440$	−17.5031	+	22.9142i	−0.834427	+	1.09239i
$441$	−2.75444	+	1.18871i	−0.131164	+	0.0566053i
$442$	18.1129	−	19.7957i	0.861541	−	0.941586i
$443$	16.3702	−	9.45136i	0.777773	−	0.449048i	−0.0578673	−	0.998324i	$-0.518430\pi$
$443$	16.3702	−	9.45136i	0.777773	−	0.449048i	0.835641	+	0.549277i	$0.185097\pi$
$444$	−6.52828	+	6.94104i	−0.309818	+	0.329407i
$445$	17.8323	+	10.2955i	0.845334	+	0.488054i
$446$	−2.30709	+	0.729274i	−0.109244	+	0.0345321i
$447$	15.7417	+	17.6857i	0.744556	+	0.836507i
$448$	5.63202	−	5.68158i	0.266088	−	0.268430i
$449$	−23.9257			−1.12913			−0.564563	−	0.825390i	$-0.690955\pi$
$449$	−23.9257			−1.12913			−0.564563	+	0.825390i	$0.690955\pi$
$450$	−6.59043	−	2.28407i	−0.310676	−	0.107672i
$451$		−	4.08786i		−	0.192490i
$452$	−30.2444	+	21.2433i	−1.42258	+	0.999199i
$453$	7.26147	+	35.1521i	0.341174	+	1.65159i
$454$	−9.39961	−	29.7360i	−0.441145	−	1.39558i
$455$	4.19982	−	7.27431i	0.196891	−	0.341025i
$456$	5.18969	+	7.60863i	0.243029	+	0.356307i
$457$	−9.42160	−	16.3187i	−0.440724	−	0.763356i	0.557020	−	0.830499i	$-0.311945\pi$
$457$	−9.42160	−	16.3187i	−0.440724	−	0.763356i	−0.997743	+	0.0671435i	$0.978611\pi$
$458$	−3.94435	+	4.31081i	−0.184307	+	0.201431i
$459$	17.3589	+	24.7775i	0.810244	+	1.15652i
$460$	−28.2396	+	2.51221i	−1.31668	+	0.117132i
$461$	13.5737	−	7.83680i	0.632192	−	0.364996i	−0.149408	−	0.988776i	$-0.547737\pi$
$461$	13.5737	−	7.83680i	0.632192	−	0.364996i	0.781601	+	0.623779i	$0.214404\pi$
$462$	8.45559	−	4.72827i	0.393390	−	0.219979i
$463$	12.2404	−	21.2009i	0.568858	−	0.985291i	−0.427821	−	0.903863i	$-0.640719\pi$
$463$	12.2404	−	21.2009i	0.568858	−	0.985291i	0.996679	−	0.0814278i	$-0.0259480\pi$
$464$	−3.32761	−	1.20016i	−0.154480	−	0.0557158i
$465$	−37.6816	+	7.78399i	−1.74744	+	0.360974i
$466$	7.37710	−	33.3913i	0.341737	−	1.54682i
$467$		−	2.83373i		−	0.131129i	−0.997848	−	0.0655646i	$-0.979115\pi$
$467$		−	2.83373i		−	0.131129i	0.997848	−	0.0655646i	$-0.0208848\pi$
$468$	−0.536781	+	19.5449i	−0.0248127	+	0.903462i
$469$			11.2651i			0.520174i
$470$	36.5880	+	8.08333i	1.68768	+	0.372856i
$471$	12.5258	+	14.0727i	0.577157	+	0.648434i
$472$	−16.3000	+	6.79354i	−0.750267	+	0.312698i
$473$	−6.68850	+	11.5848i	−0.307537	+	0.532670i
$474$	26.0867	+	0.358155i	1.19820	+	0.0164506i
$475$	−2.67666	+	1.54537i	−0.122814	+	0.0709064i
$476$	−1.03182	−	11.5987i	−0.0472935	−	0.531624i
$477$	19.2197	−	25.8257i	0.880008	−	1.18248i
$478$	−19.7438	−	18.0653i	−0.903060	−	0.826289i
$479$	6.05042	+	10.4796i	0.276451	+	0.478827i	0.970500	−	0.241101i	$-0.0775084\pi$
$479$	6.05042	+	10.4796i	0.276451	+	0.478827i	−0.694049	+	0.719927i	$0.744175\pi$
$480$	−23.6374	−	8.89378i	−1.07890	−	0.405943i
$481$	−4.48187	+	7.76283i	−0.204356	+	0.353954i
$482$	21.8395	−	6.90351i	0.994762	−	0.314446i
$483$	9.04221	+	2.99540i	0.411435	+	0.136296i
$484$	−7.59762	+	5.33646i	−0.345346	+	0.242567i
$485$			1.33786i			0.0607492i
$486$	−21.3812	−	5.37070i	−0.969871	−	0.243620i
$487$	1.28298			0.0581375			0.0290688	−	0.999577i	$-0.490746\pi$
$487$	1.28298			0.0581375			0.0290688	+	0.999577i	$0.490746\pi$
$488$	−1.33510	+	10.3157i	−0.0604373	+	0.466970i
$489$	−1.88301	+	5.68425i	−0.0851529	+	0.257051i
$490$	−1.09869	−	3.47576i	−0.0496340	−	0.157019i
$491$	4.55899	+	2.63213i	0.205744	+	0.118786i	0.599332	−	0.800501i	$-0.295433\pi$
$491$	4.55899	+	2.63213i	0.205744	+	0.118786i	−0.393588	+	0.919287i	$0.628766\pi$
$492$	3.42844	−	1.03219i	0.154566	−	0.0465345i
$493$	−4.45910	+	2.57446i	−0.200828	+	0.115948i
$494$	6.39198	+	5.84859i	0.287589	+	0.263141i
$495$	−24.5348	−	18.2590i	−1.10276	−	0.820679i
$496$	−33.9323	+	6.08542i	−1.52360	+	0.273244i
$497$	−1.29965	−	2.25107i	−0.0582975	−	0.100974i
$498$	−0.0272176	+	1.98243i	−0.00121965	+	0.0888348i
$499$	−11.8375	−	6.83436i	−0.529918	−	0.305948i	0.211065	−	0.977472i	$-0.432307\pi$
$499$	−11.8375	−	6.83436i	−0.529918	−	0.305948i	−0.740983	+	0.671524i	$0.765640\pi$
$500$	−7.28870	+	15.6904i	−0.325960	+	0.701698i
$501$	13.9404	−	12.4081i	0.622813	−	0.554352i
$502$	31.3144	+	6.91825i	1.39763	+	0.308776i
$503$	−9.89978			−0.441409			−0.220705	−	0.975341i	$-0.570836\pi$
$503$	−9.89978			−0.441409			−0.220705	+	0.975341i	$0.570836\pi$
$504$	6.10058	+	5.89771i	0.271741	+	0.262705i
$505$	27.0009			1.20153
$506$	−30.0359	−	6.63579i	−1.33526	−	0.294997i
$507$	−0.834232	−	4.03844i	−0.0370495	−	0.179353i
$508$	29.7749	+	13.8313i	1.32105	+	0.613667i
$509$	28.7915	+	16.6228i	1.27616	+	0.736793i	0.976141	−	0.217139i	$-0.0696726\pi$
$509$	28.7915	+	16.6228i	1.27616	+	0.736793i	0.300022	+	0.953932i	$0.403006\pi$
$510$	−32.0848	+	17.9415i	−1.42074	+	0.794461i
$511$	4.36431	+	7.55921i	0.193066	+	0.334400i
$512$	−20.9615	−	8.52156i	−0.926375	−	0.376603i
$513$	−8.00059	+	5.60514i	−0.353235	+	0.247473i
$514$	−24.3573	−	22.2866i	−1.07435	−	0.983022i
$515$	−0.639604	+	0.369275i	−0.0281843	+	0.0162722i
$516$	−11.4049	−	2.68439i	−0.502072	−	0.118174i
$517$	35.2076	+	20.3271i	1.54843	+	0.893985i
$518$	1.17248	+	3.70918i	0.0515158	+	0.162972i
$519$	24.5778	−	5.07711i	1.07885	−	0.222860i
$520$	−23.5613	−	3.04941i	−1.03323	−	0.133725i
$521$	36.7131			1.60843			0.804215	−	0.594338i	$-0.202586\pi$
$521$	36.7131			1.60843			0.804215	+	0.594338i	$0.202586\pi$
$522$	1.22865	−	3.54513i	0.0537766	−	0.155166i
$523$			30.9026i			1.35128i	0.737233	+	0.675639i	$0.236132\pi$
$523$			30.9026i			1.35128i	−0.737233	+	0.675639i	$0.763868\pi$
$524$	−23.9219	−	34.0581i	−1.04503	−	1.48783i
$525$	−2.12702	+	1.89321i	−0.0928307	+	0.0826265i
$526$	−18.7304	+	5.92072i	−0.816686	+	0.258156i
$527$	−25.0892	+	43.4558i	−1.09290	+	1.89296i
$528$	−21.5450	−	16.9305i	−0.937624	−	0.736806i
$529$	−3.62234	−	6.27407i	−0.157493	−	0.272786i
$530$	28.8594	+	26.4060i	1.25357	+	1.14700i
$531$	−7.42161	−	17.1971i	−0.322070	−	0.746292i
$532$	3.74518	−	0.333173i	0.162374	−	0.0144449i
$533$	2.91691	−	1.68408i	0.126345	−	0.0729455i
$534$	−10.0155	+	16.8101i	−0.433414	+	0.727445i
$535$	−14.7913	+	25.6192i	−0.639482	+	1.10762i
$536$	29.4104	−	12.2577i	1.27033	−	0.529453i
$537$	7.50586	−	22.6579i	0.323902	−	0.977761i
$538$	−14.8261	−	3.27552i	−0.639200	−	0.141218i
$539$		−	3.95503i		−	0.170355i
$540$	9.11852	−	25.1874i	0.392399	−	1.08389i
$541$			11.5917i			0.498367i	0.968456	+	0.249184i	$0.0801623\pi$
$541$			11.5917i			0.498367i	−0.968456	+	0.249184i	$0.919838\pi$
$542$	5.26925	−	23.8505i	0.226334	−	1.02447i
$543$	7.17263	−	21.6520i	0.307807	−	0.929175i
$544$	−29.1584	+	15.3145i	−1.25016	+	0.656604i
$545$	4.41210	−	7.64198i	0.188994	−	0.327347i
$546$	6.85732	+	4.08561i	0.293466	+	0.174848i
$547$	33.0717	−	19.0940i	1.41405	−	0.816400i	0.418279	−	0.908318i	$-0.362633\pi$
$547$	33.0717	−	19.0940i	1.41405	−	0.816400i	0.995767	+	0.0919186i	$0.0293000\pi$
$548$	3.15017	+	35.4109i	0.134569	+	1.51268i
$549$	−10.9583	−	1.27894i	−0.467690	−	0.0545839i
$550$	6.20740	−	6.78413i	0.264685	−	0.289276i
$551$	−0.831287	−	1.43983i	−0.0354140	−	0.0613389i
$552$	−2.01871	−	26.8663i	−0.0859221	−	1.14350i
$553$	5.32542	−	9.22390i	0.226460	−	0.392240i
$554$	−9.42302	−	29.8101i	−0.400346	−	1.26651i
$555$	9.17323	−	8.16489i	0.389382	−	0.346580i
$556$	23.9370	+	34.0796i	1.01516	+	1.44530i
$557$			11.1188i			0.471119i	0.971860	+	0.235559i	$0.0756922\pi$
$557$			11.1188i			0.471119i	−0.971860	+	0.235559i	$0.924308\pi$
$558$	−6.90483	−	35.9070i	−0.292305	−	1.52006i
$559$	−11.0218			−0.466174
$560$	−7.87883	+	6.65044i	−0.332942	+	0.281032i
$561$	−39.0594	+	8.06861i	−1.64909	+	0.340657i
$562$	−8.05176	+	2.54518i	−0.339643	+	0.107362i
$563$	−9.36603	−	5.40748i	−0.394731	−	0.227898i	0.289477	−	0.957185i	$-0.406519\pi$
$563$	−9.36603	−	5.40748i	−0.394731	−	0.227898i	−0.684208	+	0.729287i	$0.739852\pi$
$564$	−8.15818	+	34.6608i	−0.343521	+	1.45948i
$565$	41.2517	−	23.8167i	1.73547	−	1.00198i
$566$	−17.7251	+	19.3720i	−0.745042	+	0.814264i
$567$	−6.17393	+	6.54848i	−0.259281	+	0.275010i
$568$	−4.46280	+	5.84249i	−0.187255	+	0.245145i
$569$	7.63106	+	13.2174i	0.319911	+	0.554102i	0.980469	−	0.196673i	$-0.0630137\pi$
$569$	7.63106	+	13.2174i	0.319911	+	0.554102i	−0.660558	+	0.750775i	$0.729680\pi$
$570$	−5.79325	−	10.3601i	−0.242652	−	0.433937i
$571$	−14.2512	−	8.22791i	−0.596392	−	0.344327i	0.171229	−	0.985231i	$-0.445226\pi$
$571$	−14.2512	−	8.22791i	−0.596392	−	0.344327i	−0.767621	+	0.640904i	$0.778560\pi$
$572$	−23.3774	−	10.8595i	−0.977457	−	0.454059i
$573$	0.468166	+	2.26635i	0.0195579	+	0.0946782i
$574$	0.315330	−	1.42729i	0.0131616	−	0.0595741i
$575$	9.04134			0.377050
$576$	8.75931	−	22.3444i	0.364971	−	0.931019i
$577$	15.6574			0.651827			0.325914	−	0.945400i	$-0.394328\pi$
$577$	15.6574			0.651827			0.325914	+	0.945400i	$0.394328\pi$
$578$	−5.15542	+	23.3352i	−0.214437	+	0.970618i
$579$	−25.7317	+	22.9032i	−1.06937	+	0.951824i
$580$	4.13469	+	1.92069i	0.171684	+	0.0797524i
$581$	0.700961	+	0.404700i	0.0290808	+	0.0167898i
$582$	−1.27125	−	0.0174535i	−0.0526949	−	0.000723471i
$583$	21.2204	+	36.7549i	0.878861	+	1.52223i
$584$	14.9863	−	19.6194i	0.620138	−	0.811857i
$585$	2.92113	−	25.0291i	0.120774	−	1.03482i
$586$	−7.34252	+	8.02471i	−0.303317	+	0.331498i
$587$	−9.14704	+	5.28104i	−0.377539	+	0.217972i	−0.676747	−	0.736216i	$-0.736611\pi$
$587$	−9.14704	+	5.28104i	−0.377539	+	0.217972i	0.299208	+	0.954188i	$0.403277\pi$
$588$	3.31703	−	0.998645i	0.136792	−	0.0411834i
$589$	−14.0317	−	8.10123i	−0.578168	−	0.333806i
$590$	21.7006	−	6.85960i	0.893400	−	0.282405i
$591$	−7.00112	+	21.1343i	−0.287988	+	0.869347i
$592$	8.40795	−	7.09706i	0.345565	−	0.291688i
$593$	−15.7740			−0.647759			−0.323880	−	0.946098i	$-0.604987\pi$
$593$	−15.7740			−0.647759			−0.323880	+	0.946098i	$0.604987\pi$
$594$	17.6699	−	23.0750i	0.725005	−	0.946779i
$595$			15.0074i			0.615243i
$596$	−15.7140	−	22.3723i	−0.643670	−	0.916404i
$597$	−25.2201	−	8.35463i	−1.03219	−	0.341932i
$598$	−7.63891	−	24.1660i	−0.312378	−	0.988220i
$599$	−6.46962	+	11.2057i	−0.264341	+	0.457853i	−0.967391	−	0.253288i	$-0.918488\pi$
$599$	−6.46962	+	11.2057i	−0.264341	+	0.457853i	0.703050	+	0.711141i	$0.251821\pi$
$600$	7.25714	+	3.49308i	0.296271	+	0.142604i
$601$	−5.40596	−	9.36339i	−0.220514	−	0.381941i	0.734450	−	0.678662i	$-0.237440\pi$
$601$	−5.40596	−	9.36339i	−0.220514	−	0.381941i	−0.954964	+	0.296722i	$0.904107\pi$
$602$	−3.22895	+	3.52895i	−0.131602	+	0.143829i
$603$	13.3910	+	31.0291i	0.545322	+	1.26360i
$604$	−3.67266	−	41.2841i	−0.149438	−	1.67983i
$605$	10.3627	−	5.98292i	0.421305	−	0.243240i
$606$	−0.352249	+	25.6565i	−0.0143091	+	1.04222i
$607$	13.7520	−	23.8192i	0.558176	−	0.966790i	−0.439472	−	0.898256i	$-0.644835\pi$
$607$	13.7520	−	23.8192i	0.558176	−	0.966790i	0.997649	−	0.0685339i	$-0.0218321\pi$
$608$	−4.94501	−	9.41518i	−0.200547	−	0.381836i
$609$	−1.01840	−	1.14417i	−0.0412676	−	0.0463640i
$610$	2.89198	−	13.0901i	0.117093	−	0.530003i
$611$			33.4967i			1.35513i
$612$	−16.6296	−	30.7213i	−0.672210	−	1.24184i
$613$			8.66387i			0.349930i	0.984575	+	0.174965i	$0.0559813\pi$
$613$			8.66387i			0.349930i	−0.984575	+	0.174965i	$0.944019\pi$
$614$	31.3849	+	6.93382i	1.26659	+	0.279826i
$615$	−4.51907	+	0.933516i	−0.182226	+	0.0376430i
$616$	−10.3256	+	4.30352i	−0.416030	+	0.173394i
$617$	19.3068	−	33.4403i	0.777262	−	1.34626i	−0.156253	−	0.987717i	$-0.549941\pi$
$617$	19.3068	−	33.4403i	0.777262	−	1.34626i	0.933514	−	0.358540i	$-0.116725\pi$
$618$	−0.342544	−	0.612574i	−0.0137792	−	0.0246414i
$619$	−3.68667	+	2.12850i	−0.148180	+	0.0855516i	−0.572257	−	0.820075i	$-0.693932\pi$
$619$	−3.68667	+	2.12850i	−0.148180	+	0.0855516i	0.424077	+	0.905626i	$0.360599\pi$
$620$	44.2549	−	3.93693i	1.77732	−	0.158111i
$621$	28.4669	−	2.49790i	1.14234	−	0.100237i
$622$	12.9196	+	11.8213i	0.518027	+	0.473989i
$623$	3.99422	+	6.91819i	0.160025	+	0.277171i
$624$	3.20495	−	22.3484i	0.128301	−	0.894650i
$625$	15.2587	−	26.4288i	0.610346	−	1.05715i
$626$	−38.4768	+	12.1626i	−1.53784	+	0.486114i
$627$	−2.60533	−	12.6122i	−0.104047	−	0.503682i
$628$	−12.5037	−	17.8018i	−0.498953	−	0.710368i
$629$		−	16.0152i		−	0.638569i
$630$	−7.15797	−	8.26776i	−0.285180	−	0.329396i
$631$	38.1422			1.51842			0.759209	−	0.650847i	$-0.225586\pi$
$631$	38.1422			1.51842			0.759209	+	0.650847i	$0.225586\pi$
$632$	−29.8760	−	3.86668i	−1.18840	−	0.153808i
$633$	−24.6841	−	27.7325i	−0.981104	−	1.10227i
$634$	−10.2395	−	32.3931i	−0.406664	−	1.28650i
$635$	−36.6434	−	21.1561i	−1.45415	−	0.839552i
$636$	−25.4677	+	27.0779i	−1.00986	+	1.07371i
$637$	2.82212	−	1.62935i	0.111817	−	0.0645574i
$638$	3.64933	+	3.33909i	0.144478	+	0.132196i
$639$	−6.25570	−	4.65553i	−0.247472	−	0.184170i
$640$	25.9357	+	13.3332i	1.02520	+	0.527042i
$641$	−9.28061	−	16.0745i	−0.366562	−	0.634904i	0.622463	−	0.782649i	$-0.286132\pi$
$641$	−9.28061	−	16.0745i	−0.366562	−	0.634904i	−0.989026	+	0.147745i	$0.952799\pi$
$642$	−24.1507	−	14.3890i	−0.953150	−	0.567889i
$643$	2.08975	+	1.20652i	0.0824116	+	0.0475803i	0.540639	−	0.841254i	$-0.318182\pi$
$643$	2.08975	+	1.20652i	0.0824116	+	0.0475803i	−0.458228	+	0.888835i	$0.651516\pi$
$644$	−9.97529	−	4.63383i	−0.393081	−	0.182598i
$645$	14.3342	+	4.74849i	0.564410	+	0.186972i
$646$	−15.1151	−	3.33935i	−0.594695	−	0.131385i
$647$	29.8309			1.17277			0.586386	−	0.810032i	$-0.300550\pi$
$647$	29.8309			1.17277			0.586386	+	0.810032i	$0.300550\pi$
$648$	23.8144	+	8.99309i	0.935517	+	0.353282i
$649$	24.6929			0.969280
$650$	7.39811	+	1.63445i	0.290178	+	0.0641085i
$651$	−14.1702	−	4.69416i	−0.555376	−	0.183979i
$652$	2.91299	−	6.27081i	0.114081	−	0.245584i
$653$	14.6977	+	8.48570i	0.575164	+	0.332071i	0.759209	−	0.650847i	$-0.225586\pi$
$653$	14.6977	+	8.48570i	0.575164	+	0.332071i	−0.184045	+	0.982918i	$0.558919\pi$
$654$	7.20392	+	4.29211i	0.281696	+	0.167835i
$655$	26.8198	+	46.4533i	1.04794	+	1.81508i
$656$	−4.06942	+	0.729810i	−0.158884	+	0.0284943i
$657$	21.0070	+	15.6335i	0.819560	+	0.609922i
$658$	10.7249	+	9.81314i	0.418099	+	0.382556i
$659$	−21.3058	+	12.3009i	−0.829956	+	0.479175i	−0.853837	−	0.520540i	$-0.825731\pi$
$659$	−21.3058	+	12.3009i	−0.829956	+	0.479175i	0.0238819	+	0.999715i	$0.492397\pi$
$660$	25.7244	+	24.1947i	1.00132	+	0.941777i
$661$	−9.47528	−	5.47055i	−0.368546	−	0.212780i	0.304277	−	0.952584i	$-0.401585\pi$
$661$	−9.47528	−	5.47055i	−0.368546	−	0.212780i	−0.672823	+	0.739804i	$0.734918\pi$
$662$	−5.66708	−	17.9280i	−0.220257	−	0.696792i
$663$	−21.8487	−	24.5470i	−0.848533	−	0.953325i
$664$	0.293844	−	2.27039i	0.0114034	−	0.0881083i
$665$	−4.84585			−0.187914
$666$	7.63868	+	8.82300i	0.295993	+	0.341884i
$667$			4.86353i			0.188317i
$668$	−17.6345	+	12.3862i	−0.682300	+	0.479238i
$669$	0.599500	+	2.90213i	0.0231780	+	0.112203i
$670$	−39.1548	+	12.3769i	−1.51268	+	0.478162i
$671$	7.27244	−	12.5962i	0.280750	−	0.486273i
$672$	−6.21652	−	7.57330i	−0.239808	−	0.292146i
$673$	−0.455510	−	0.788967i	−0.0175586	−	0.0304124i	0.857113	−	0.515129i	$-0.172256\pi$
$673$	−0.455510	−	0.788967i	−0.0175586	−	0.0304124i	−0.874671	+	0.484717i	$0.838923\pi$
$674$	−19.7472	−	18.0685i	−0.760635	−	0.695973i
$675$	−3.60827	+	7.74316i	−0.138882	+	0.298034i
$676$	0.421932	+	4.74291i	0.0162282	+	0.182420i
$677$	−27.9620	+	16.1438i	−1.07467	+	0.620458i	−0.929452	−	0.368942i	$-0.879720\pi$
$677$	−27.9620	+	16.1438i	−1.07467	+	0.620458i	−0.145213	+	0.989400i	$0.546387\pi$
$678$	22.0927	+	39.5084i	0.848463	+	1.51731i
$679$	−0.259517	+	0.449497i	−0.00995935	+	0.0172501i
$680$	39.1805	−	16.3298i	1.50250	−	0.626217i
$681$	−37.4055	+	7.72695i	−1.43338	+	0.296097i
$682$	47.0699	+	10.3991i	1.80240	+	0.398202i
$683$		−	7.62095i		−	0.291608i	−0.989314	−	0.145804i	$-0.953423\pi$
$683$		−	7.62095i		−	0.291608i	0.989314	−	0.145804i	$-0.0465768\pi$
$684$	9.91983	−	5.36964i	0.379294	−	0.205313i
$685$		−	45.8178i		−	1.75061i
$686$	0.305084	−	1.38091i	0.0116481	−	0.0527235i
$687$	4.75788	+	5.34547i	0.181525	+	0.203942i
$688$	12.7267	+	4.59007i	0.485199	+	0.174995i
$689$	−17.4844	+	30.2839i	−0.666102	+	1.15372i
$690$	−0.476680	+	34.7196i	−0.0181469	+	1.32175i
$691$	24.4741	−	14.1301i	0.931039	−	0.537535i	0.0438988	−	0.999036i	$-0.486022\pi$
$691$	24.4741	−	14.1301i	0.931039	−	0.537535i	0.887140	+	0.461501i	$0.152689\pi$
$692$	−28.8652	+	2.56786i	−1.09729	+	0.0976155i
$693$	−4.70139	−	10.8939i	−0.178591	−	0.413825i
$694$	−17.2087	+	18.8075i	−0.653232	+	0.713924i
$695$	−26.8368	−	46.4826i	−1.01798	−	1.76319i
$696$	−1.87900	+	3.90377i	−0.0712233	+	0.147972i
$697$	−3.00889	+	5.21155i	−0.113970	+	0.197401i
$698$	−4.19452	−	13.2695i	−0.158765	−	0.502259i
$699$	−39.7573	−	13.1704i	−1.50376	−	0.498149i
$700$	2.69066	−	1.88988i	0.101697	−	0.0714307i
$701$		−	31.4502i		−	1.18786i	−0.804517	−	0.593929i	$-0.797576\pi$
$701$		−	31.4502i		−	1.18786i	0.804517	−	0.593929i	$-0.202424\pi$
$702$	23.7447	+	3.10221i	0.896187	+	0.117085i
$703$	5.17128			0.195038
$704$	22.4708	+	22.2748i	0.846901	+	0.839512i
$705$	14.4312	−	43.5634i	0.543511	−	1.64069i
$706$	27.0045	−	8.53616i	1.01633	−	0.321263i
$707$	9.07180	+	5.23761i	0.341180	+	0.196981i
$708$	6.23495	+	20.7096i	0.234324	+	0.778314i
$709$	−27.4529	+	15.8500i	−1.03102	+	0.595258i	−0.917276	−	0.398253i	$-0.869617\pi$
$709$	−27.4529	+	15.8500i	−1.03102	+	0.595258i	−0.113741	+	0.993510i	$0.536283\pi$
$710$	6.39625	−	6.99053i	0.240047	−	0.262350i
$711$	3.70403	−	31.7371i	0.138912	−	1.19023i
$712$	13.7155	−	17.9557i	0.514010	−	0.672918i
$713$	23.6985	+	41.0471i	0.887517	+	1.53723i
$714$	−14.2602	−	0.195784i	−0.533673	−	0.00732702i
$715$	28.7701	+	16.6104i	1.07594	+	0.621194i
$716$	−11.6114	+	24.9960i	−0.433939	+	0.934145i
$717$	−24.4826	+	21.7914i	−0.914318	+	0.813814i
$718$	−0.580352	+	2.62688i	−0.0216586	+	0.0980342i
$719$	−31.8775			−1.18883			−0.594414	−	0.804159i	$-0.702616\pi$
$719$	−31.8775			−1.18883			−0.594414	+	0.804159i	$0.702616\pi$
$720$	−13.7964	+	27.6839i	−0.514160	+	1.03172i
$721$	−0.286526			−0.0106708
$722$	−4.71832	+	21.3568i	−0.175598	+	0.794816i
$723$	−5.67503	−	27.4723i	−0.211057	−	1.02171i
$724$	−11.0959	+	23.8863i	−0.412376	+	0.887726i
$725$	−1.25912	−	0.726951i	−0.0467624	−	0.0269983i
$726$	5.54984	+	9.92481i	0.205974	+	0.368344i
$727$	8.26362	+	14.3130i	0.306481	+	0.530840i	0.977590	−	0.210518i	$-0.0675151\pi$
$727$	8.26362	+	14.3130i	0.306481	+	0.530840i	−0.671109	+	0.741359i	$0.734182\pi$
$728$	−7.32463	−	5.59493i	−0.271469	−	0.207362i
$729$	−9.22151	+	25.3764i	−0.341537	+	0.939868i
$730$	−21.4790	+	23.4746i	−0.794972	+	0.868833i
$731$	17.0541	−	9.84620i	0.630769	−	0.364175i
$732$	12.4006	+	2.91876i	0.458340	+	0.107880i
$733$	0.945601	+	0.545943i	0.0349266	+	0.0201649i	0.517362	−	0.855767i	$-0.326914\pi$
$733$	0.945601	+	0.545943i	0.0349266	+	0.0201649i	−0.482435	+	0.875932i	$0.660248\pi$
$734$	27.4682	−	8.68276i	1.01387	−	0.320487i
$735$	−4.37222	+	0.903182i	−0.161272	+	0.0333144i
$736$	−1.24351	+	31.0851i	−0.0458364	+	1.14581i
$737$	−44.5538			−1.64116
$738$	−0.828080	−	4.30624i	−0.0304820	−	0.158515i
$739$			8.78457i			0.323146i	0.986861	+	0.161573i	$0.0516567\pi$
$739$			8.78457i			0.323146i	−0.986861	+	0.161573i	$0.948343\pi$
$740$	−11.6040	+	8.15052i	−0.426573	+	0.299619i
$741$	7.92615	−	7.05489i	0.291174	−	0.259168i
$742$	4.57400	+	14.4700i	0.167917	+	0.531212i
$743$	−3.03569	+	5.25797i	−0.111369	+	0.192896i	−0.916322	−	0.400442i	$-0.868857\pi$
$743$	−3.03569	+	5.25797i	−0.111369	+	0.192896i	0.804954	+	0.593338i	$0.202190\pi$
$744$	3.16357	+	42.1027i	0.115982	+	1.54356i
$745$	17.6176	+	30.5145i	0.645458	+	1.11797i
$746$	7.37683	−	8.06221i	0.270085	−	0.295178i
$747$	2.41183	+	0.281484i	0.0882442	+	0.0102990i
$748$	45.8730	−	4.08089i	1.67728	−	0.149212i
$749$	−9.93918	+	5.73839i	−0.363170	+	0.209676i
$750$	18.2030	+	10.8454i	0.664680	+	0.396018i
$751$	−18.8787	+	32.6989i	−0.688894	+	1.19320i	0.283302	+	0.959031i	$0.408570\pi$
$751$	−18.8787	+	32.6989i	−0.688894	+	1.19320i	−0.972196	+	0.234169i	$0.924763\pi$
$752$	13.9498	−	38.6778i	0.508695	−	1.41043i
$753$	12.3512	−	37.2844i	0.450102	−	1.35872i
$754$	−0.879207	+	3.97960i	−0.0320188	+	0.144928i
$755$			53.4171i			1.94405i
$756$	7.94948	−	6.69371i	0.289120	−	0.243448i
$757$		−	8.91618i		−	0.324064i	−0.986786	−	0.162032i	$-0.948195\pi$
$757$		−	8.91618i		−	0.324064i	0.986786	−	0.162032i	$-0.0518048\pi$
$758$	−16.2620	−	3.59274i	−0.590661	−	0.130494i
$759$	−11.8469	+	35.7622i	−0.430015	+	1.29809i
$760$	5.27283	+	12.6513i	0.191266	+	0.458910i
$761$	−8.72625	+	15.1143i	−0.316326	+	0.547893i	−0.979719	−	0.200379i	$-0.935783\pi$
$761$	−8.72625	+	15.1143i	−0.316326	+	0.547893i	0.663392	+	0.748272i	$0.269116\pi$
$762$	20.5807	−	34.5429i	0.745561	−	1.25136i
$763$	2.96477	−	1.71171i	0.107332	−	0.0619680i
$764$	−0.236786	−	2.66170i	−0.00856662	−	0.0962969i
$765$	17.8395	+	41.3370i	0.644987	+	1.49454i
$766$	13.4082	+	12.2684i	0.484460	+	0.443275i
$767$	10.1727	+	17.6197i	0.367316	+	0.636210i
$768$	−13.0077	+	24.4704i	−0.469375	+	0.882999i
$769$	−1.13250	+	1.96155i	−0.0408390	+	0.0707352i	−0.885722	−	0.464215i	$-0.846336\pi$
$769$	−1.13250	+	1.96155i	−0.0408390	+	0.0707352i	0.844883	+	0.534950i	$0.179670\pi$
$770$	13.7467	−	4.34537i	0.495398	−	0.156596i
$771$	−30.2034	+	26.8833i	−1.08775	+	0.968180i
$772$	32.5503	−	22.8629i	1.17151	−	0.822853i
$773$		−	4.05732i		−	0.145932i	−0.997334	−	0.0729658i	$-0.976754\pi$
$773$		−	4.05732i		−	0.145932i	0.997334	−	0.0729658i	$-0.0232464\pi$
$774$	−4.69906	+	13.5586i	−0.168904	+	0.487353i
$775$	−14.1689			−0.508961
$776$	1.45591	+	0.188430i	0.0522640	+	0.00676424i
$777$	4.66585	−	0.963837i	0.167386	−	0.0345775i
$778$	−3.08811	−	9.76937i	−0.110714	−	0.350249i
$779$	−1.68279	−	0.971562i	−0.0602924	−	0.0348098i
$780$	−6.66650	+	28.3233i	−0.238699	+	1.01414i
$781$	8.90304	−	5.14017i	0.318576	−	0.183930i
$782$	33.4080	+	30.5679i	1.19467	+	1.09311i
$783$	−4.16521	−	1.94096i	−0.148852	−	0.0693644i
$784$	−3.93719	+	0.706096i	−0.140614	+	0.0252177i
$785$	14.0184	+	24.2806i	0.500339	+	0.866612i
$786$	−44.4903	+	24.8784i	−1.58691	+	0.887384i
$787$	−2.44385	−	1.41096i	−0.0871138	−	0.0502952i	0.455810	−	0.890077i	$-0.349350\pi$
$787$	−2.44385	−	1.41096i	−0.0871138	−	0.0502952i	−0.542924	+	0.839782i	$0.682683\pi$
$788$	10.8306	−	23.3151i	0.385824	−	0.830567i
$789$	4.86713	+	23.5613i	0.173274	+	0.838806i
$790$	37.9111	+	8.37565i	1.34882	+	0.297992i
$791$	18.4797			0.657063
$792$	−23.3256	+	24.1279i	−0.828839	+	0.857349i
$793$	11.9841			0.425569
$794$	−20.7470	−	4.58360i	−0.736283	−	0.162666i
$795$	35.7860	−	31.8523i	1.26920	−	1.12969i
$796$	27.8226	+	12.9245i	0.986145	+	0.458095i
$797$	−27.9523	−	16.1382i	−0.990120	−	0.571646i	−0.0848099	−	0.996397i	$-0.527028\pi$
$797$	−27.9523	−	16.1382i	−0.990120	−	0.571646i	−0.905310	+	0.424751i	$0.860362\pi$
$798$	0.0632180	−	4.60457i	0.00223789	−	0.163000i
$799$	−29.9237	−	51.8294i	−1.05863	−	1.83359i
$800$	−7.86174	−	4.96822i	−0.277954	−	0.175653i
$801$	19.2256	+	14.3078i	0.679303	+	0.505541i
$802$	−24.5565	−	22.4690i	−0.867121	−	0.793406i
$803$	−29.8969	+	17.2610i	−1.05504	+	0.609126i
$804$	−11.2498	−	37.3667i	−0.396751	−	1.31782i
$805$	12.2764	+	7.08778i	0.432686	+	0.249811i
$806$	11.9711	+	37.8710i	0.421664	+	1.33395i
$807$	−5.84779	+	17.6527i	−0.205852	+	0.621405i
$808$	3.80292	−	29.3833i	0.133786	−	1.03370i
$809$	−22.3690			−0.786451			−0.393226	−	0.919442i	$-0.628641\pi$
$809$	−22.3690			−0.786451			−0.393226	+	0.919442i	$0.628641\pi$
$810$	−29.5442	−	14.2643i	−1.03808	−	0.501198i
$811$			23.1499i			0.812903i	0.913672	+	0.406451i	$0.133234\pi$
$811$			23.1499i			0.812903i	−0.913672	+	0.406451i	$0.866766\pi$
$812$	1.01661	+	1.44736i	0.0356759	+	0.0507924i
$813$	−28.3975	−	9.40721i	−0.995945	−	0.329925i
$814$	−14.6699	+	4.63719i	−0.514180	+	0.162533i
$815$	−4.45562	+	7.71737i	−0.156074	+	0.270328i
$816$	15.0055	+	37.4427i	0.525299	+	1.31076i
$817$	3.17931	+	5.50673i	0.111230	+	0.192656i
$818$	1.99417	+	1.82464i	0.0697244	+	0.0637971i
$819$	5.83655	−	7.84266i	0.203946	−	0.274045i
$820$	5.30738	−	0.472147i	0.185342	−	0.0164881i
$821$	−27.1027	+	15.6477i	−0.945891	+	0.546110i	−0.891802	−	0.452426i	$-0.850559\pi$
$821$	−27.1027	+	15.6477i	−0.945891	+	0.546110i	−0.0540886	+	0.998536i	$0.517225\pi$
$822$	43.5365	+	0.597730i	1.51851	+	0.0208482i
$823$	−3.80070	+	6.58301i	−0.132484	+	0.229469i	−0.924634	−	0.380858i	$-0.875629\pi$
$823$	−3.80070	+	6.58301i	−0.132484	+	0.229469i	0.792149	+	0.610327i	$0.208962\pi$
$824$	0.311773	+	0.748048i	0.0108611	+	0.0260595i
$825$	−7.48770	−	8.41241i	−0.260688	−	0.292883i
$826$	8.62161	+	1.90476i	0.299984	+	0.0662751i
$827$		−	21.7961i		−	0.757924i	−0.925412	−	0.378962i	$-0.876281\pi$
$827$		−	21.7961i		−	0.757924i	0.925412	−	0.378962i	$-0.123719\pi$
$828$	−32.9847	−	0.905891i	−1.14630	−	0.0314819i
$829$		−	3.29111i		−	0.114305i	−0.998365	−	0.0571524i	$-0.981798\pi$
$829$		−	3.29111i		−	0.114305i	0.998365	−	0.0571524i	$-0.0182021\pi$
$830$	−0.636499	+	2.88102i	−0.0220932	+	0.100001i
$831$	−37.4986	+	7.74619i	−1.30081	+	0.268712i
$832$	−6.63693	+	25.2107i	−0.230094	+	0.874023i
$833$	−2.91112	+	5.04220i	−0.100864	+	0.174702i
$834$	44.5183	−	24.8941i	1.54154	−	0.862013i
$835$	24.0525	−	13.8867i	0.832371	−	0.480569i
$836$	1.31771	+	14.8123i	0.0455738	+	0.512293i
$837$	−44.6112	+	3.91452i	−1.54199	+	0.135306i
$838$	−19.0665	+	20.8380i	−0.658643	+	0.719837i
$839$	−18.8790	−	32.6994i	−0.651775	−	1.12891i	−0.982692	−	0.185247i	$-0.940691\pi$
$839$	−18.8790	−	32.6994i	−0.651775	−	1.12891i	0.330917	−	0.943660i	$-0.392642\pi$
$840$	7.11546	+	10.4320i	0.245507	+	0.359939i
$841$	−14.1090	+	24.4374i	−0.486516	+	0.842670i
$842$	−12.5258	−	39.6260i	−0.431669	−	1.36560i
$843$	2.09226	+	10.1285i	0.0720613	+	0.348843i
$844$	24.6406	+	35.0813i	0.848165	+	1.20755i
$845$		−	6.13681i		−	0.211113i
$846$	41.2061	+	14.2810i	1.41669	+	0.490990i
$847$	4.64224			0.159509
$848$	32.8006	−	27.6866i	1.12638	−	0.950762i
$849$	21.3810	+	24.0215i	0.733794	+	0.824415i
$850$	−12.9072	+	4.07999i	−0.442714	+	0.139943i
$851$	−13.1008	−	7.56377i	−0.449091	−	0.259283i
$852$	6.55902	+	6.16897i	0.224708	+	0.211346i
$853$	1.99083	−	1.14941i	0.0681648	−	0.0393550i	−0.465530	−	0.885032i	$-0.654136\pi$
$853$	1.99083	−	1.14941i	0.0681648	−	0.0393550i	0.533695	+	0.845677i	$0.320803\pi$
$854$	3.51086	−	3.83705i	0.120139	−	0.131301i
$855$	−13.3476	+	5.76031i	−0.456479	+	0.196998i
$856$	25.7964	+	19.7047i	0.881704	+	0.673492i
$857$	8.49388	+	14.7118i	0.290146	+	0.502547i	0.973844	−	0.227218i	$-0.0729630\pi$
$857$	8.49388	+	14.7118i	0.290146	+	0.502547i	−0.683698	+	0.729765i	$0.739630\pi$
$858$	−16.1587	+	27.1209i	−0.551649	+	0.925892i
$859$	−31.5462	−	18.2132i	−1.07634	−	0.621426i	−0.146435	−	0.989220i	$-0.546780\pi$
$859$	−31.5462	−	18.2132i	−1.07634	−	0.621426i	−0.929907	+	0.367794i	$0.880113\pi$
$860$	−15.8134	−	7.34582i	−0.539233	−	0.250490i
$861$	−1.69940	−	0.562960i	−0.0579155	−	0.0191856i
$862$	5.13309	−	23.2342i	0.174834	−	0.791359i
$863$	25.0704			0.853405			0.426703	−	0.904392i	$-0.359675\pi$
$863$	25.0704			0.853405			0.426703	+	0.904392i	$0.359675\pi$
$864$	−26.1255	−	13.4706i	−0.888809	−	0.458279i
$865$	37.3484			1.26988
$866$	10.7228	−	48.5350i	0.364375	−	1.64929i
$867$	27.7841	+	9.20399i	0.943596	+	0.312584i
$868$	15.6325	+	7.26177i	0.530601	+	0.246481i
$869$	36.4808	+	21.0622i	1.23753	+	0.714486i
$870$	2.85795	−	4.79680i	0.0968934	−	0.162627i
$871$	−18.3548	−	31.7915i	−0.621930	−	1.07721i
$872$	−7.69484	−	5.87772i	−0.260580	−	0.199045i
$873$	−0.180504	+	1.54660i	−0.00610912	+	0.0523446i
$874$	−9.87030	+	10.7873i	−0.333868	+	0.364887i
$875$	7.49143	−	4.32518i	0.253257	−	0.146218i
$876$	−22.0255	−	20.7157i	−0.744174	−	0.699920i
$877$	−26.3470	−	15.2114i	−0.889675	−	0.513654i	−0.0158386	−	0.999875i	$-0.505042\pi$
$877$	−26.3470	−	15.2114i	−0.889675	−	0.513654i	−0.873836	+	0.486221i	$0.838375\pi$
$878$	−38.6344	+	12.2124i	−1.30385	+	0.412149i
$879$	8.85694	+	9.95075i	0.298737	+	0.335630i
$880$	−26.3027	−	31.1610i	−0.886663	−	1.05044i
$881$	33.6774			1.13462			0.567310	−	0.823505i	$-0.307984\pi$
$881$	33.6774			1.13462			0.567310	+	0.823505i	$0.307984\pi$
$882$	−0.801172	−	4.16631i	−0.0269769	−	0.140287i
$883$		−	14.7021i		−	0.494766i	−0.968918	−	0.247383i	$-0.920429\pi$
$883$		−	14.7021i		−	0.494766i	0.968918	−	0.247383i	$-0.0795706\pi$
$884$	21.8103	+	31.0517i	0.733558	+	1.04438i
$885$	−5.63894	−	27.2976i	−0.189551	−	0.917598i
$886$	8.05723	+	25.4893i	0.270688	+	0.856331i
$887$	7.08276	−	12.2677i	0.237816	−	0.411909i	−0.722272	−	0.691610i	$-0.756902\pi$
$887$	7.08276	−	12.2677i	0.237816	−	0.411909i	0.960087	+	0.279701i	$0.0902352\pi$
$888$	−7.59331	−	11.1326i	−0.254815	−	0.373585i
$889$	−8.20766	−	14.2161i	−0.275276	−	0.476792i
$890$	−19.6576	+	21.4839i	−0.658923	+	0.720143i
$891$	−25.8994	−	24.4181i	−0.867663	−	0.818036i
$892$	−0.303211	−	3.40838i	−0.0101523	−	0.114121i
$893$	16.7356	−	9.66229i	0.560035	−	0.323336i
$894$	−29.2250	+	16.3423i	−0.977431	+	0.546568i
$895$	17.7605	−	30.7621i	0.593668	−	1.02826i
$896$	6.12755	+	9.51069i	0.204707	+	0.317730i
$897$	−30.3988	+	6.27956i	−1.01499	+	0.209669i
$898$	7.29935	−	33.0394i	0.243582	−	1.10254i
$899$		−	7.62174i		−	0.254199i
$900$	5.16474	−	8.40398i	0.172158	−	0.280133i
$901$		−	62.4776i		−	2.08143i
$902$	5.64498	+	1.24714i	0.187957	+	0.0415252i
$903$	3.89493	+	4.37594i	0.129615	+	0.145622i
$904$	−20.1080	−	48.2459i	−0.668784	−	1.60464i
$905$	16.9720	−	29.3964i	0.564168	−	0.977168i
$906$	−50.7574	−	0.696870i	−1.68630	−	0.0231519i
$907$	−17.5951	+	10.1585i	−0.584234	+	0.337308i	−0.762814	−	0.646618i	$-0.776183\pi$
$907$	−17.5951	+	10.1585i	−0.584234	+	0.337308i	0.178580	+	0.983925i	$0.442850\pi$
$908$	43.9306	−	3.90808i	1.45789	−	0.129694i
$909$	31.2138	+	3.64295i	1.03530	+	0.120829i
$910$	8.76390	+	8.01887i	0.290520	+	0.265823i
$911$	−8.95962	−	15.5185i	−0.296845	−	0.514151i	0.678567	−	0.734538i	$-0.262601\pi$
$911$	−8.95962	−	15.5185i	−0.296845	−	0.514151i	−0.975412	+	0.220387i	$0.929268\pi$
$912$	−12.0902	+	4.84525i	−0.400345	+	0.160442i
$913$	−1.60060	+	2.77232i	−0.0529721	+	0.0917504i
$914$	25.4091	−	8.03185i	0.840457	−	0.265670i
$915$	−15.5857	−	5.16306i	−0.515248	−	0.170686i
$916$	−4.74951	−	6.76196i	−0.156928	−	0.223422i
$917$			20.8099i			0.687204i
$918$	−39.5115	+	16.4119i	−1.30408	+	0.541674i
$919$	42.4133			1.39909			0.699543	−	0.714591i	$-0.253387\pi$
$919$	42.4133			1.39909			0.699543	+	0.714591i	$0.253387\pi$
$920$	5.14629	−	39.7629i	0.169668	−	1.31094i
$921$	12.3790	−	37.3683i	0.407901	−	1.23133i
$922$	6.68083	+	21.1351i	0.220021	+	0.696046i
$923$	7.33557	+	4.23520i	0.241453	+	0.139403i
$924$	3.94967	+	13.1190i	0.129935	+	0.431582i
$925$	3.91636	−	2.26111i	0.128769	−	0.0743449i
$926$	25.5423	+	23.3710i	0.839374	+	0.768017i
$927$	−0.789221	+	0.340597i	−0.0259214	+	0.0111867i
$928$	2.67251	−	4.22900i	0.0877294	−	0.138824i
$929$	4.39465	+	7.61175i	0.144184	+	0.249733i	0.929068	−	0.369909i	$-0.120611\pi$
$929$	4.39465	+	7.61175i	0.144184	+	0.249733i	−0.784884	+	0.619642i	$0.787278\pi$
$930$	0.747015	−	54.4099i	0.0244956	−	1.78417i
$931$	−1.62811	−	0.939992i	−0.0533593	−	0.0308070i
$932$	43.8599	+	20.3743i	1.43668	+	0.667381i
$933$	16.0204	−	14.2594i	0.524485	−	0.466833i
$934$	3.91313	+	0.864523i	0.128042	+	0.0282881i
$935$	−59.3546			−1.94110
$936$	−26.8260	−	6.70407i	−0.876836	−	0.219129i
$937$	34.1901			1.11694			0.558471	−	0.829524i	$-0.311388\pi$
$937$	34.1901			1.11694			0.558471	+	0.829524i	$0.311388\pi$
$938$	−15.5561	−	3.43680i	−0.507926	−	0.112215i
$939$	9.99825	+	48.4006i	0.326280	+	1.57949i
$940$	−22.3248	+	48.0588i	−0.728154	+	1.56750i
$941$	−41.0622	−	23.7072i	−1.33859	−	0.772834i	−0.351990	−	0.936004i	$-0.614495\pi$
$941$	−41.0622	−	23.7072i	−1.33859	−	0.772834i	−0.986598	+	0.163169i	$0.947828\pi$
$942$	−23.2545	+	13.0037i	−0.757674	+	0.423682i
$943$	2.84211	+	4.92268i	0.0925518	+	0.160304i
$944$	−4.40845	−	24.5815i	−0.143483	−	0.800059i
$945$	−10.9694	+	7.68508i	−0.356835	+	0.249996i
$946$	−13.9571	−	12.7706i	−0.453784	−	0.415207i
$947$	20.0835	−	11.5952i	0.652626	−	0.376794i	−0.136836	−	0.990594i	$-0.543693\pi$
$947$	20.0835	−	11.5952i	0.652626	−	0.376794i	0.789462	+	0.613800i	$0.210360\pi$
$948$	−8.45320	+	35.9142i	−0.274547	+	1.16644i
$949$	−24.6333	−	14.2220i	−0.799629	−	0.461666i
$950$	−1.31742	−	4.16770i	−0.0427427	−	0.135218i
$951$	−40.7479	+	8.41741i	−1.32134	+	0.272953i
$952$	16.3315	+	2.11370i	0.529308	+	0.0685055i
$953$	36.1497			1.17100			0.585501	−	0.810672i	$-0.300898\pi$
$953$	36.1497			1.17100			0.585501	+	0.810672i	$0.300898\pi$
$954$	29.7995	+	34.4197i	0.964795	+	1.11438i
$955$			3.44395i			0.111443i
$956$	30.9702	−	21.7530i	1.00165	−	0.703543i
$957$	4.52521	−	4.02779i	0.146279	−	0.130200i
$958$	−16.3174	+	5.15795i	−0.527190	+	0.166646i
$959$	8.88768	−	15.3939i	0.286998	−	0.497095i
$960$	19.4929	−	29.9279i	0.629131	−	0.965919i
$961$	−21.6385	−	37.4790i	−0.698016	−	1.20900i
$962$	−9.35245	−	8.55739i	−0.301535	−	0.275901i
$963$	−20.5556	+	27.6209i	−0.662396	+	0.890070i
$964$	2.87028	+	32.2646i	0.0924454	+	1.03917i
$965$	−44.3968	+	25.6325i	−1.42918	+	0.825139i
$966$	−6.89502	+	11.5727i	−0.221844	+	0.372345i
$967$	−4.95874	+	8.58880i	−0.159462	+	0.276197i	−0.934675	−	0.355503i	$-0.884309\pi$
$967$	−4.95874	+	8.58880i	−0.159462	+	0.276197i	0.775213	+	0.631701i	$0.217643\pi$
$968$	−5.05129	−	12.1197i	−0.162355	−	0.389543i
$969$	−5.96176	+	17.9967i	−0.191519	+	0.578138i
$970$	−1.84747	−	0.408160i	−0.0593188	−	0.0131052i
$971$		−	38.8391i		−	1.24641i	−0.782060	−	0.623203i	$-0.785831\pi$
$971$		−	38.8391i		−	1.24641i	0.782060	−	0.623203i	$-0.214169\pi$
$972$	13.9395	−	27.8871i	0.447111	−	0.894479i
$973$		−	20.8231i		−	0.667556i
$974$	−0.391417	+	1.77169i	−0.0125418	+	0.0567686i
$975$	2.91800	−	8.80854i	0.0934507	−	0.282099i
$976$	−13.8378	−	4.99081i	−0.442936	−	0.159752i
$977$	17.7926	−	30.8176i	0.569235	−	0.985943i	−0.427407	−	0.904059i	$-0.640573\pi$
$977$	17.7926	−	30.8176i	0.569235	−	0.985943i	0.996642	−	0.0818840i	$-0.0260937\pi$
$978$	−7.27498	−	4.33445i	−0.232628	−	0.138600i
$979$	−27.3616	+	15.7972i	−0.874482	+	0.504882i
$980$	5.13492	−	0.456805i	0.164029	−	0.0145921i
$981$	6.13156	−	8.23905i	0.195766	−	0.263053i
$982$	−5.02562	+	5.49255i	−0.160374	+	0.175274i
$983$	3.42018	+	5.92392i	0.109087	+	0.188944i	0.915401	−	0.402544i	$-0.131874\pi$
$983$	3.42018	+	5.92392i	0.109087	+	0.188944i	−0.806314	+	0.591488i	$0.798541\pi$
$984$	0.379399	+	5.04928i	0.0120948	+	0.160965i
$985$	−16.5662	+	28.6935i	−0.527843	+	0.914250i
$986$	−2.19471	−	6.94306i	−0.0698939	−	0.221112i
$987$	13.2990	−	11.8371i	0.423312	−	0.376780i
$988$	−10.0265	+	7.04247i	−0.318985	+	0.224051i
$989$		−	18.6009i		−	0.591473i
$990$	32.6992	−	28.3100i	1.03925	−	0.899750i
$991$	33.3550			1.05956			0.529778	−	0.848136i	$-0.322275\pi$
$991$	33.3550			1.05956			0.529778	+	0.848136i	$0.322275\pi$
$992$	1.94873	−	48.7141i	0.0618723	−	1.54668i
$993$	−22.5520	+	4.65862i	−0.715665	+	0.147837i
$994$	3.50504	−	1.10795i	0.111173	−	0.0351420i
$995$	−34.2407	−	19.7689i	−1.08550	−	0.626716i
$996$	−2.72926	−	0.642392i	−0.0864800	−	0.0203550i
$997$	−25.5735	+	14.7649i	−0.809920	+	0.467608i	−0.846928	−	0.531707i	$-0.821551\pi$
$997$	−25.5735	+	14.7649i	−0.809920	+	0.467608i	0.0370080	+	0.999315i	$0.488217\pi$
$998$	13.0491	−	14.2615i	0.413062	−	0.451439i
$999$	11.7061	−	8.20118i	0.370365	−	0.259474i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cs.a.85.16	✓	72
8.5	even	2	inner	504.2.cs.a.85.33	yes	72
9.7	even	3	inner	504.2.cs.a.421.33	yes	72
72.61	even	6	inner	504.2.cs.a.421.16	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cs.a.85.16	✓	72	1.1	even	1	trivial
504.2.cs.a.85.33	yes	72	8.5	even	2	inner
504.2.cs.a.421.16	yes	72	72.61	even	6	inner
504.2.cs.a.421.33	yes	72	9.7	even	3	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.305084 + 1.38091i) q^{2} +(1.64418 + 0.544667i) q^{3} +(-1.81385 - 0.842588i) q^{4} +(2.23227 + 1.28880i) q^{5} +(-1.25375 + 2.10431i) q^{6} +(0.500000 + 0.866025i) q^{7} +(1.71692 - 2.24771i) q^{8} +(2.40668 + 1.79106i) q^{9} +O(q^{10})\)	\(q+(-0.305084 + 1.38091i) q^{2} +(1.64418 + 0.544667i) q^{3} +(-1.81385 - 0.842588i) q^{4} +(2.23227 + 1.28880i) q^{5} +(-1.25375 + 2.10431i) q^{6} +(0.500000 + 0.866025i) q^{7} +(1.71692 - 2.24771i) q^{8} +(2.40668 + 1.79106i) q^{9} +(-2.46075 + 2.68938i) q^{10} +(-3.42515 + 1.97751i) q^{11} +(-2.52337 - 2.37331i) q^{12} +(-2.82212 - 1.62935i) q^{13} +(-1.34845 + 0.426247i) q^{14} +(2.96829 + 3.33487i) q^{15} +(2.58009 + 3.05665i) q^{16} +5.82223 q^{17} +(-3.20754 + 2.77699i) q^{18} +1.87998i q^{19} +(-2.96307 - 4.21857i) q^{20} +(0.350396 + 1.69624i) q^{21} +(-1.68582 - 5.33315i) q^{22} +(2.74976 - 4.76272i) q^{23} +(4.04718 - 2.76050i) q^{24} +(0.822012 + 1.42377i) q^{25} +(3.11098 - 3.40002i) q^{26} +(2.98148 + 4.25567i) q^{27} +(-0.177221 - 1.99213i) q^{28} +(-0.765874 + 0.442178i) q^{29} +(-5.51074 + 3.08154i) q^{30} +(-4.30921 + 7.46376i) q^{31} +(-5.00812 + 2.63035i) q^{32} +(-6.70867 + 1.38583i) q^{33} +(-1.77627 + 8.04000i) q^{34} +2.57760i q^{35} +(-2.85622 - 5.27655i) q^{36} -2.75070i q^{37} +(-2.59610 - 0.573552i) q^{38} +(-3.75263 - 4.21607i) q^{39} +(6.72947 - 2.80472i) q^{40} +(-0.516793 + 0.895111i) q^{41} +(-2.44926 - 0.0336269i) q^{42} +(2.92914 - 1.69114i) q^{43} +(7.87894 - 0.700914i) q^{44} +(3.06402 + 7.09986i) q^{45} +(5.73800 + 5.25021i) q^{46} +(-5.13956 - 8.90198i) q^{47} +(2.57728 + 6.43099i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-2.21688 + 0.700761i) q^{50} +(9.57282 + 3.17118i) q^{51} +(3.74603 + 5.33329i) q^{52} -10.7309i q^{53} +(-6.78632 + 2.81884i) q^{54} -10.1945 q^{55} +(2.80503 + 0.363040i) q^{56} +(-1.02396 + 3.09104i) q^{57} +(-0.376954 - 1.19251i) q^{58} +(-5.40695 - 3.12171i) q^{59} +(-2.57411 - 8.54999i) q^{60} +(-3.18487 + 1.83878i) q^{61} +(-8.99215 - 8.22771i) q^{62} +(-0.347768 + 2.97977i) q^{63} +(-2.10439 - 7.71826i) q^{64} +(-4.19982 - 7.27431i) q^{65} +(0.132995 - 9.68689i) q^{66} +(9.75587 + 5.63255i) q^{67} +(-10.5606 - 4.90575i) q^{68} +(7.11520 - 6.33308i) q^{69} +(-3.55945 - 0.786384i) q^{70} -2.59931 q^{71} +(8.15785 - 2.33440i) q^{72} +8.72862 q^{73} +(3.79849 + 0.839195i) q^{74} +(0.576060 + 2.78866i) q^{75} +(1.58405 - 3.41000i) q^{76} +(-3.42515 - 1.97751i) q^{77} +(6.96690 - 3.89581i) q^{78} +(-5.32542 - 9.22390i) q^{79} +(1.82003 + 10.1485i) q^{80} +(2.58418 + 8.62102i) q^{81} +(-1.07841 - 0.986730i) q^{82} +(0.700961 - 0.404700i) q^{83} +(0.793664 - 3.37196i) q^{84} +(12.9968 + 7.50370i) q^{85} +(1.44168 + 4.56082i) q^{86} +(-1.50008 + 0.309875i) q^{87} +(-1.43583 + 11.0940i) q^{88} +7.98844 q^{89} +(-10.7391 + 2.06510i) q^{90} -3.25871i q^{91} +(-9.00066 + 6.32194i) q^{92} +(-11.1504 + 9.92471i) q^{93} +(13.8609 - 4.38145i) q^{94} +(-2.42292 + 4.19663i) q^{95} +(-9.66693 + 1.59702i) q^{96} +(0.259517 + 0.449497i) q^{97} +(-1.04337 - 0.954667i) q^{98} +(-11.7851 - 1.37543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8}+O(q^{10}) \) 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8	\( 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8} + 20 q^{12} + 40 q^{17} - q^{18} + 2 q^{20} - 12 q^{22} + 12 q^{23} + 10 q^{24} + 36 q^{25} - 42 q^{26} + 4 q^{30} + 5 q^{32} + 8 q^{33} + 6 q^{34} - 18 q^{36} - 25 q^{38} - 4 q^{39} - 9 q^{40} + 24 q^{41} - 7 q^{42} + 12 q^{46} - 53 q^{48} - 36 q^{49} + 41 q^{50} - 9 q^{52} + 12 q^{54} + 3 q^{56} + 4 q^{57} + 9 q^{58} - 50 q^{60} + 60 q^{62} - 6 q^{64} - 40 q^{65} - 2 q^{66} + 23 q^{68} - 56 q^{71} + 19 q^{72} + 22 q^{74} - 24 q^{76} - 54 q^{78} - 6 q^{80} - 4 q^{81} - 48 q^{82} + 10 q^{84} - 39 q^{86} - 76 q^{87} - 12 q^{88} - 88 q^{89} - 77 q^{90} + 11 q^{92} + 24 q^{94} - 24 q^{95} + 59 q^{96}+O(q^{100}) \) 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8 + 20 * q^12 + 40 * q^17 - q^18 + 2 * q^20 - 12 * q^22 + 12 * q^23 + 10 * q^24 + 36 * q^25 - 42 * q^26 + 4 * q^30 + 5 * q^32 + 8 * q^33 + 6 * q^34 - 18 * q^36 - 25 * q^38 - 4 * q^39 - 9 * q^40 + 24 * q^41 - 7 * q^42 + 12 * q^46 - 53 * q^48 - 36 * q^49 + 41 * q^50 - 9 * q^52 + 12 * q^54 + 3 * q^56 + 4 * q^57 + 9 * q^58 - 50 * q^60 + 60 * q^62 - 6 * q^64 - 40 * q^65 - 2 * q^66 + 23 * q^68 - 56 * q^71 + 19 * q^72 + 22 * q^74 - 24 * q^76 - 54 * q^78 - 6 * q^80 - 4 * q^81 - 48 * q^82 + 10 * q^84 - 39 * q^86 - 76 * q^87 - 12 * q^88 - 88 * q^89 - 77 * q^90 + 11 * q^92 + 24 * q^94 - 24 * q^95 + 59 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more