LMFDB - Embedded newform 504.2.cs.a.85.10

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			85.10
Character	$\chi$	$=$	504.85
Dual form			504.2.cs.a.421.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.930716 + 1.06479i) q^{2} +(-1.06868 - 1.36306i) q^{3} +(-0.267536 - 1.98203i) q^{4} +(0.220108 + 0.127079i) q^{5} +(2.44600 + 0.130709i) q^{6} +(0.500000 + 0.866025i) q^{7} +(2.35943 + 1.55983i) q^{8} +(-0.715859 + 2.91334i) q^{9} +O(q^{10})$	\(q+(-0.930716 + 1.06479i) q^{2} +(-1.06868 - 1.36306i) q^{3} +(-0.267536 - 1.98203i) q^{4} +(0.220108 + 0.127079i) q^{5} +(2.44600 + 0.130709i) q^{6} +(0.500000 + 0.866025i) q^{7} +(2.35943 + 1.55983i) q^{8} +(-0.715859 + 2.91334i) q^{9} +(-0.340170 + 0.116093i) q^{10} +(4.34297 - 2.50742i) q^{11} +(-2.41571 + 2.48281i) q^{12} +(-3.45679 - 1.99578i) q^{13} +(-1.38749 - 0.273631i) q^{14} +(-0.0620075 - 0.435826i) q^{15} +(-3.85685 + 1.06053i) q^{16} +0.203198 q^{17} +(-2.43582 - 3.47373i) q^{18} +6.81839i q^{19} +(0.192987 - 0.470257i) q^{20} +(0.646105 - 1.60703i) q^{21} +(-1.37221 + 6.95803i) q^{22} +(3.06189 - 5.30336i) q^{23} +(-0.395325 - 4.88300i) q^{24} +(-2.46770 - 4.27418i) q^{25} +(5.34236 - 1.82324i) q^{26} +(4.73607 - 2.13766i) q^{27} +(1.58272 - 1.22271i) q^{28} +(4.59056 - 2.65036i) q^{29} +(0.521773 + 0.339606i) q^{30} +(2.99023 - 5.17922i) q^{31} +(2.46040 - 5.09377i) q^{32} +(-8.05899 - 3.24011i) q^{33} +(-0.189119 + 0.216362i) q^{34} +0.254158i q^{35} +(5.96583 + 0.639427i) q^{36} -6.79121i q^{37} +(-7.26012 - 6.34598i) q^{38} +(0.973828 + 6.84465i) q^{39} +(0.321106 + 0.643166i) q^{40} +(1.43059 - 2.47786i) q^{41} +(1.10980 + 2.18365i) q^{42} +(4.99065 - 2.88135i) q^{43} +(-6.13166 - 7.93706i) q^{44} +(-0.527791 + 0.550277i) q^{45} +(2.79718 + 8.19618i) q^{46} +(0.740876 + 1.28323i) q^{47} +(5.56729 + 4.12375i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(6.84782 + 1.35048i) q^{50} +(-0.217153 - 0.276971i) q^{51} +(-3.03087 + 7.38538i) q^{52} -7.46607i q^{53} +(-2.13179 + 7.03246i) q^{54} +1.27456 q^{55} +(-0.171140 + 2.82324i) q^{56} +(9.29387 - 7.28666i) q^{57} +(-1.45044 + 7.35470i) q^{58} +(11.0846 + 6.39971i) q^{59} +(-0.847229 + 0.239500i) q^{60} +(-5.50067 + 3.17581i) q^{61} +(2.73171 + 8.00433i) q^{62} +(-2.88096 + 0.836718i) q^{63} +(3.13384 + 7.36064i) q^{64} +(-0.507244 - 0.878572i) q^{65} +(10.9507 - 5.56548i) q^{66} +(-0.664133 - 0.383438i) q^{67} +(-0.0543627 - 0.402743i) q^{68} +(-10.5010 + 1.49403i) q^{69} +(-0.270624 - 0.236549i) q^{70} -11.7312 q^{71} +(-6.23335 + 5.75720i) q^{72} -6.45194 q^{73} +(7.23118 + 6.32069i) q^{74} +(-3.18879 + 7.93135i) q^{75} +(13.5142 - 1.82416i) q^{76} +(4.34297 + 2.50742i) q^{77} +(-8.19444 - 5.33350i) q^{78} +(-3.02270 - 5.23547i) q^{79} +(-0.983693 - 0.256695i) q^{80} +(-7.97509 - 4.17108i) q^{81} +(1.30691 + 3.82945i) q^{82} +(1.77677 - 1.02582i) q^{83} +(-3.35803 - 0.850658i) q^{84} +(0.0447254 + 0.0258222i) q^{85} +(-1.57685 + 7.99569i) q^{86} +(-8.51843 - 3.42483i) q^{87} +(14.1581 + 0.858238i) q^{88} +9.87904 q^{89} +(-0.0947041 - 1.07414i) q^{90} -3.99156i q^{91} +(-11.3306 - 4.64991i) q^{92} +(-10.2552 + 1.45906i) q^{93} +(-2.05591 - 0.405453i) q^{94} +(-0.866475 + 1.50078i) q^{95} +(-9.57247 + 2.08992i) q^{96} +(5.72262 + 9.91187i) q^{97} +(-0.456773 - 1.33842i) q^{98} +(4.19600 + 14.4475i) 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 $

$2$	−0.930716	+	1.06479i	−0.658115	+	0.752917i
$2$	−0.930716	+	1.06479i	−0.658115	+	0.752917i
$3$	−1.06868	−	1.36306i	−0.617001	−	0.786962i
$3$	−1.06868	−	1.36306i	−0.617001	−	0.786962i
$4$	−0.267536	−	1.98203i	−0.133768	−	0.991013i
$5$	0.220108	+	0.127079i	0.0984351	+	0.0568315i	0.548409	−	0.836210i	$-0.315234\pi$
$5$	0.220108	+	0.127079i	0.0984351	+	0.0568315i	−0.449974	+	0.893041i	$0.648567\pi$
$6$	2.44600	+	0.130709i	0.998575	+	0.0533616i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	2.35943	+	1.55983i	0.834185	+	0.551485i
$9$	−0.715859	+	2.91334i	−0.238620	+	0.971113i
$10$	−0.340170	+	0.116093i	−0.107571	+	0.0367117i
$11$	4.34297	−	2.50742i	1.30946	−	0.756014i	0.327450	−	0.944868i	$-0.393811\pi$
$11$	4.34297	−	2.50742i	1.30946	−	0.756014i	0.982005	+	0.188854i	$0.0604773\pi$
$12$	−2.41571	+	2.48281i	−0.697355	+	0.716726i
$13$	−3.45679	−	1.99578i	−0.958741	−	0.553529i	−0.0629553	−	0.998016i	$-0.520053\pi$
$13$	−3.45679	−	1.99578i	−0.958741	−	0.553529i	−0.895785	+	0.444487i	$0.853386\pi$
$14$	−1.38749	−	0.273631i	−0.370822	−	0.0731309i
$15$	−0.0620075	−	0.435826i	−0.0160103	−	0.112530i
$16$	−3.85685	+	1.06053i	−0.964212	+	0.265132i
$17$	0.203198			0.0492827			0.0246413	−	0.999696i	$-0.492156\pi$
$17$	0.203198			0.0492827			0.0246413	+	0.999696i	$0.492156\pi$
$18$	−2.43582	−	3.47373i	−0.574128	−	0.818765i
$19$			6.81839i			1.56425i	0.623124	+	0.782123i	$0.285863\pi$
$19$			6.81839i			1.56425i	−0.623124	+	0.782123i	$0.714137\pi$
$20$	0.192987	−	0.470257i	0.0431533	−	0.105153i
$21$	0.646105	−	1.60703i	0.140992	−	0.350683i
$22$	−1.37221	+	6.95803i	−0.292557	+	1.48346i
$23$	3.06189	−	5.30336i	0.638449	−	1.10583i	−0.347324	−	0.937745i	$-0.612910\pi$
$23$	3.06189	−	5.30336i	0.638449	−	1.10583i	0.985773	−	0.168081i	$-0.0537570\pi$
$24$	−0.395325	−	4.88300i	−0.0806954	−	0.996739i
$25$	−2.46770	−	4.27418i	−0.493540	−	0.854837i
$26$	5.34236	−	1.82324i	1.04772	−	0.357566i
$27$	4.73607	−	2.13766i	0.911458	−	0.411393i
$28$	1.58272	−	1.22271i	0.299105	−	0.231070i
$29$	4.59056	−	2.65036i	0.852446	−	0.492160i	−0.00902939	−	0.999959i	$-0.502874\pi$
$29$	4.59056	−	2.65036i	0.852446	−	0.492160i	0.861475	+	0.507799i	$0.169541\pi$
$30$	0.521773	+	0.339606i	0.0952622	+	0.0620032i
$31$	2.99023	−	5.17922i	0.537060	−	0.930216i	−0.462000	−	0.886880i	$-0.652868\pi$
$31$	2.99023	−	5.17922i	0.537060	−	0.930216i	0.999061	−	0.0433360i	$-0.0137986\pi$
$32$	2.46040	−	5.09377i	0.434941	−	0.900459i
$33$	−8.05899	−	3.24011i	−1.40289	−	0.564031i
$34$	−0.189119	+	0.216362i	−0.0324337	+	0.0371058i
$35$			0.254158i			0.0429606i
$36$	5.96583	+	0.639427i	0.994305	+	0.106571i
$37$		−	6.79121i		−	1.11647i	−0.829684	−	0.558234i	$-0.811479\pi$
$37$		−	6.79121i		−	1.11647i	0.829684	−	0.558234i	$-0.188521\pi$
$38$	−7.26012	−	6.34598i	−1.17775	−	1.02945i
$39$	0.973828	+	6.84465i	0.155937	+	1.09602i
$40$	0.321106	+	0.643166i	0.0507714	+	0.101693i
$41$	1.43059	−	2.47786i	0.223421	−	0.386976i	−0.732424	−	0.680849i	$-0.761611\pi$
$41$	1.43059	−	2.47786i	0.223421	−	0.386976i	0.955844	+	0.293873i	$0.0949443\pi$
$42$	1.10980	+	2.18365i	0.171246	+	0.336945i
$43$	4.99065	−	2.88135i	0.761067	−	0.439402i	−0.0686118	−	0.997643i	$-0.521857\pi$
$43$	4.99065	−	2.88135i	0.761067	−	0.439402i	0.829679	+	0.558241i	$0.188524\pi$
$44$	−6.13166	−	7.93706i	−0.924383	−	1.19656i
$45$	−0.527791	+	0.550277i	−0.0786784	+	0.0820305i
$46$	2.79718	+	8.19618i	0.412422	+	1.20846i
$47$	0.740876	+	1.28323i	0.108068	+	0.187179i	0.914987	−	0.403482i	$-0.132200\pi$
$47$	0.740876	+	1.28323i	0.108068	+	0.187179i	−0.806920	+	0.590661i	$0.798867\pi$
$48$	5.56729	+	4.12375i	0.803568	+	0.595212i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	6.84782	+	1.35048i	0.968428	+	0.190987i
$51$	−0.217153	−	0.276971i	−0.0304075	−	0.0387836i
$52$	−3.03087	+	7.38538i	−0.420306	+	1.02417i
$53$		−	7.46607i		−	1.02554i	−0.858525	−	0.512772i	$-0.828619\pi$
$53$		−	7.46607i		−	1.02554i	0.858525	−	0.512772i	$-0.171381\pi$
$54$	−2.13179	+	7.03246i	−0.290100	+	0.956996i
$55$	1.27456			0.171862
$56$	−0.171140	+	2.82324i	−0.0228695	+	0.377272i
$57$	9.29387	−	7.28666i	1.23100	−	0.965141i
$58$	−1.45044	+	7.35470i	−0.190452	+	0.965719i
$59$	11.0846	+	6.39971i	1.44309	+	0.833171i	0.998055	−	0.0623401i	$-0.0198563\pi$
$59$	11.0846	+	6.39971i	1.44309	+	0.833171i	0.445039	+	0.895511i	$0.353190\pi$
$60$	−0.847229	+	0.239500i	−0.109377	+	0.0309193i
$61$	−5.50067	+	3.17581i	−0.704289	+	0.406621i	−0.808943	−	0.587888i	$-0.799960\pi$
$61$	−5.50067	+	3.17581i	−0.704289	+	0.406621i	0.104654	+	0.994509i	$0.466626\pi$
$62$	2.73171	+	8.00433i	0.346928	+	1.01655i
$63$	−2.88096	+	0.836718i	−0.362966	+	0.105417i
$64$	3.13384	+	7.36064i	0.391730	+	0.920080i
$65$	−0.507244	−	0.878572i	−0.0629158	−	0.108973i
$66$	10.9507	−	5.56548i	1.34793	−	0.685063i
$67$	−0.664133	−	0.383438i	−0.0811368	−	0.0468444i	0.458883	−	0.888497i	$-0.348250\pi$
$67$	−0.664133	−	0.383438i	−0.0811368	−	0.0468444i	−0.540020	+	0.841653i	$0.681583\pi$
$68$	−0.0543627	−	0.402743i	−0.00659245	−	0.0488398i
$69$	−10.5010	+	1.49403i	−1.26417	+	0.179860i
$70$	−0.270624	−	0.236549i	−0.0323458	−	0.0282730i
$71$	−11.7312			−1.39224			−0.696121	−	0.717924i	$-0.745093\pi$
$71$	−11.7312			−1.39224			−0.696121	+	0.717924i	$0.745093\pi$
$72$	−6.23335	+	5.75720i	−0.734607	+	0.678493i
$73$	−6.45194			−0.755143			−0.377571	−	0.925981i	$-0.623241\pi$
$73$	−6.45194			−0.755143			−0.377571	+	0.925981i	$0.623241\pi$
$74$	7.23118	+	6.32069i	0.840608	+	0.734765i
$75$	−3.18879	+	7.93135i	−0.368210	+	0.915833i
$76$	13.5142	−	1.82416i	1.55019	−	0.209246i
$77$	4.34297	+	2.50742i	0.494928	+	0.285747i
$78$	−8.19444	−	5.33350i	−0.927837	−	0.603900i
$79$	−3.02270	−	5.23547i	−0.340080	−	0.589036i	0.644367	−	0.764716i	$-0.277121\pi$
$79$	−3.02270	−	5.23547i	−0.340080	−	0.589036i	−0.984447	+	0.175680i	$0.943788\pi$
$80$	−0.983693	−	0.256695i	−0.109980	−	0.0286994i
$81$	−7.97509	−	4.17108i	−0.886121	−	0.463453i
$82$	1.30691	+	3.82945i	0.144324	+	0.422892i
$83$	1.77677	−	1.02582i	0.195026	−	0.112598i	−0.399307	−	0.916817i	$-0.630749\pi$
$83$	1.77677	−	1.02582i	0.195026	−	0.112598i	0.594333	+	0.804219i	$0.297416\pi$
$84$	−3.35803	−	0.850658i	−0.366391	−	0.0928144i
$85$	0.0447254	+	0.0258222i	0.00485115	+	0.00280081i
$86$	−1.57685	+	7.99569i	−0.170037	+	0.862198i
$87$	−8.51843	−	3.42483i	−0.913271	−	0.367180i
$88$	14.1581	+	0.858238i	1.50926	+	0.0914885i
$89$	9.87904			1.04718			0.523588	−	0.851971i	$-0.324593\pi$
$89$	9.87904			1.04718			0.523588	+	0.851971i	$0.324593\pi$
$90$	−0.0947041	−	1.07414i	−0.00998268	−	0.113224i
$91$		−	3.99156i		−	0.418429i
$92$	−11.3306	−	4.64991i	−1.18129	−	0.484787i
$93$	−10.2552	+	1.45906i	−1.06341	+	0.151298i
$94$	−2.05591	−	0.405453i	−0.212051	−	0.0418193i
$95$	−0.866475	+	1.50078i	−0.0888985	+	0.153977i
$96$	−9.57247	+	2.08992i	−0.976986	+	0.213302i
$97$	5.72262	+	9.91187i	0.581044	+	1.00640i	0.995356	+	0.0962627i	$0.0306889\pi$
$97$	5.72262	+	9.91187i	0.581044	+	1.00640i	−0.414312	+	0.910135i	$0.635978\pi$
$98$	−0.456773	−	1.33842i	−0.0461411	−	0.135200i
$99$	4.19600	+	14.4475i	0.421714	+	1.45203i
$100$	−7.81134	+	6.03455i	−0.781134	+	0.603455i
$101$	−11.5173	+	6.64949i	−1.14601	+	0.661649i	−0.947912	−	0.318533i	$-0.896810\pi$
$101$	−11.5173	+	6.64949i	−1.14601	+	0.661649i	−0.198098	+	0.980182i	$0.563477\pi$
$102$	0.497022	+	0.0265597i	0.0492125	+	0.00262981i
$103$	3.44538	−	5.96757i	0.339483	−	0.588002i	−0.644853	−	0.764307i	$-0.723081\pi$
$103$	3.44538	−	5.96757i	0.339483	−	0.588002i	0.984336	+	0.176305i	$0.0564146\pi$
$104$	−5.04297	−	10.1009i	−0.494504	−	0.990476i
$105$	0.346433	−	0.271613i	0.0338084	−	0.0265067i
$106$	7.94976	+	6.94879i	0.772149	+	0.674926i
$107$		−	17.8300i		−	1.72369i	−0.507172	−	0.861845i	$-0.669309\pi$
$107$		−	17.8300i		−	1.72369i	0.507172	−	0.861845i	$-0.330691\pi$
$108$	−5.50397	−	8.81512i	−0.529620	−	0.848235i
$109$			8.64399i			0.827944i	0.910290	+	0.413972i	$0.135859\pi$
$109$			8.64399i			0.827944i	−0.910290	+	0.413972i	$0.864141\pi$
$110$	−1.18625	+	1.35713i	−0.113105	+	0.129398i
$111$	−9.25682	+	7.25761i	−0.878618	+	0.688862i
$112$	−2.84687	−	2.80987i	−0.269004	−	0.265507i
$113$	−2.75767	+	4.77642i	−0.259420	+	0.449328i	−0.966087	−	0.258218i	$-0.916865\pi$
$113$	−2.75767	+	4.77642i	−0.259420	+	0.449328i	0.706667	+	0.707546i	$0.250198\pi$
$114$	−0.891223	+	16.6778i	−0.0834707	+	1.56202i
$115$	1.34789	−	0.778206i	0.125692	−	0.0725681i
$116$	−6.48123	−	8.38954i	−0.601767	−	0.778950i
$117$	8.28895	−	8.64210i	0.766314	−	0.798963i
$118$	−17.1309	+	5.84643i	−1.57703	+	0.538208i
$119$	0.101599	+	0.175974i	0.00931355	+	0.0161315i
$120$	0.533514	−	1.12502i	0.0487029	−	0.102700i
$121$	7.07427	−	12.2530i	0.643116	−	1.11391i
$122$	1.73800	−	8.81281i	0.157351	−	0.797874i
$123$	−4.90630	+	0.698048i	−0.442386	+	0.0629409i
$124$	−11.0653	−	4.54107i	−0.993697	−	0.407801i
$125$		−	2.52517i		−	0.225858i
$126$	1.79043	−	3.84635i	0.159504	−	0.342660i
$127$	15.2413			1.35245			0.676225	−	0.736695i	$-0.263615\pi$
$127$	15.2413			1.35245			0.676225	+	0.736695i	$0.263615\pi$
$128$	−10.7542	−	3.51380i	−0.950547	−	0.310579i
$129$	−9.26085	−	3.72331i	−0.815372	−	0.327819i
$130$	1.40759	+	0.277595i	0.123454	+	0.0243467i
$131$	17.1003	+	9.87288i	1.49406	+	0.862597i	0.999977	−	0.00681604i	$-0.00216963\pi$
$131$	17.1003	+	9.87288i	1.49406	+	0.862597i	0.494086	+	0.869413i	$0.335503\pi$
$132$	−4.26591	+	16.8400i	−0.371300	+	1.46573i
$133$	−5.90490	+	3.40919i	−0.512020	+	0.295615i
$134$	1.02640	−	0.350288i	0.0886673	−	0.0302603i
$135$	1.31410	+	0.131341i	0.113100	+	0.0113040i
$136$	0.479431	+	0.316955i	0.0411109	+	0.0271786i
$137$	2.40610	+	4.16748i	0.205567	+	0.356052i	0.950313	−	0.311295i	$-0.100763\pi$
$137$	2.40610	+	4.16748i	0.205567	+	0.356052i	−0.744746	+	0.667348i	$0.767430\pi$
$138$	8.18259	−	12.5718i	0.696548	−	1.07018i
$139$	−10.0762	−	5.81749i	−0.854651	−	0.493433i	0.00756638	−	0.999971i	$-0.497592\pi$
$139$	−10.0762	−	5.81749i	−0.854651	−	0.493433i	−0.862217	+	0.506538i	$0.830925\pi$
$140$	0.503748	−	0.0679965i	0.0425745	−	0.00574675i
$141$	0.957368	−	2.38122i	0.0806249	−	0.200535i
$142$	10.9185	−	12.4913i	0.916257	−	1.04824i
$143$	−20.0170			−1.67390
$144$	−0.328713	−	11.9955i	−0.0273928	−	0.999625i
$145$	1.34722			0.111881
$146$	6.00492	−	6.86993i	0.496971	−	0.568560i
$147$	1.71478	−	0.243972i	0.141433	−	0.0201225i
$148$	−13.4603	+	1.81689i	−1.10643	+	0.149348i
$149$	8.63944	+	4.98798i	0.707771	+	0.408632i	0.810235	−	0.586105i	$-0.199339\pi$
$149$	8.63944	+	4.98798i	0.707771	+	0.408632i	−0.102464	+	0.994737i	$0.532673\pi$
$150$	−5.47732	−	10.7772i	−0.447222	−	0.879955i
$151$	10.4812	+	18.1540i	0.852948	+	1.47735i	0.878536	+	0.477676i	$0.158521\pi$
$151$	10.4812	+	18.1540i	0.852948	+	1.47735i	−0.0255883	+	0.999673i	$0.508146\pi$
$152$	−10.6356	+	16.0875i	−0.862657	+	1.30487i
$153$	−0.145461	+	0.591984i	−0.0117598	+	0.0478591i
$154$	−6.71193	+	2.29064i	−0.540863	+	0.184585i
$155$	1.31634	−	0.759991i	0.105731	−	0.0610439i
$156$	13.3057	−	3.76134i	1.06531	−	0.301148i
$157$	−12.1413	−	7.00978i	−0.968980	−	0.559441i	−0.0700552	−	0.997543i	$-0.522318\pi$
$157$	−12.1413	−	7.00978i	−0.968980	−	0.559441i	−0.898925	+	0.438102i	$0.855651\pi$
$158$	8.38792	+	1.65421i	0.667307	+	0.131602i
$159$	−10.1767	+	7.97881i	−0.807064	+	0.632761i
$160$	1.18886	−	0.808511i	0.0939879	−	0.0639184i
$161$	6.12379			0.482622
$162$	11.8638	−	4.60967i	0.932112	−	0.362170i
$163$			11.7579i			0.920950i	0.887673	+	0.460475i	$0.152321\pi$
$163$			11.7579i			0.920950i	−0.887673	+	0.460475i	$0.847679\pi$
$164$	−5.29391	−	2.17255i	−0.413385	−	0.169648i
$165$	−1.36209	−	1.73730i	−0.106039	−	0.135249i
$166$	−0.561391	+	2.84662i	−0.0435724	+	0.220941i
$167$	−10.6907	+	18.5168i	−0.827268	+	1.43287i	0.0729063	+	0.997339i	$0.476773\pi$
$167$	−10.6907	+	18.5168i	−0.827268	+	1.43287i	−0.900174	+	0.435531i	$0.856561\pi$
$168$	4.03114	−	2.78386i	0.311009	−	0.214780i
$169$	1.46626	+	2.53963i	0.112789	+	0.195356i
$170$	−0.0691217	+	0.0235898i	−0.00530139	+	0.00180925i
$171$	−19.8643	−	4.88100i	−1.51906	−	0.373260i
$172$	−7.04609	−	9.12073i	−0.537260	−	0.695449i
$173$	3.69099	−	2.13099i	0.280621	−	0.162017i	−0.353084	−	0.935592i	$-0.614867\pi$
$173$	3.69099	−	2.13099i	0.280621	−	0.162017i	0.633704	+	0.773575i	$0.281534\pi$
$174$	11.5749	−	5.88276i	0.877494	−	0.445971i
$175$	2.46770	−	4.27418i	0.186541	−	0.323098i
$176$	−14.0910	+	14.2766i	−1.06215	+	1.07614i
$177$	−3.12270	−	21.9482i	−0.234716	−	1.64973i
$178$	−9.19458	+	10.5191i	−0.689163	+	0.788437i
$179$		−	2.22486i		−	0.166294i	−0.996537	−	0.0831468i	$-0.973503\pi$
$179$		−	2.22486i		−	0.166294i	0.996537	−	0.0831468i	$-0.0264970\pi$
$180$	1.23187	+	0.898876i	0.0918179	+	0.0669982i
$181$		−	17.8576i		−	1.32734i	−0.748024	−	0.663672i	$-0.768997\pi$
$181$		−	17.8576i		−	1.32734i	0.748024	−	0.663672i	$-0.231003\pi$
$182$	4.25015	+	3.71500i	0.315042	+	0.275374i
$183$	10.2073	+	4.10382i	0.754542	+	0.303363i
$184$	15.4967	−	7.73686i	1.14243	−	0.570369i
$185$	0.863021	−	1.49480i	0.0634506	−	0.109900i
$186$	7.99106	−	12.2775i	0.585933	−	0.900232i
$187$	0.882482	−	0.509501i	0.0645335	−	0.0372584i
$188$	2.34519	−	1.81175i	0.171041	−	0.132135i
$189$	4.21931	+	3.03273i	0.306909	+	0.220599i
$190$	−0.791565	−	2.31941i	−0.0574262	−	0.168268i
$191$	5.87177	+	10.1702i	0.424867	+	0.735890i	0.996408	−	0.0846827i	$-0.0269877\pi$
$191$	5.87177	+	10.1702i	0.424867	+	0.735890i	−0.571541	+	0.820573i	$0.693654\pi$
$192$	6.68393	−	12.1378i	0.482371	−	0.875967i
$193$	−11.0097	+	19.0694i	−0.792499	+	1.37265i	0.131916	+	0.991261i	$0.457887\pi$
$193$	−11.0097	+	19.0694i	−0.792499	+	1.37265i	−0.924415	+	0.381388i	$0.875446\pi$
$194$	−15.8801	−	3.13177i	−1.14013	−	0.224848i
$195$	−0.655465	+	1.63031i	−0.0469388	+	0.116749i
$196$	1.85025	+	0.759320i	0.132161	+	0.0542371i
$197$			12.2074i			0.869741i	0.900493	+	0.434870i	$0.143206\pi$
$197$			12.2074i			0.869741i	−0.900493	+	0.434870i	$0.856794\pi$
$198$	−19.2888	−	8.97869i	−1.37079	−	0.638087i
$199$	−1.01905			−0.0722386			−0.0361193	−	0.999347i	$-0.511500\pi$
$199$	−1.01905			−0.0722386			−0.0361193	+	0.999347i	$0.511500\pi$
$200$	0.844645	−	13.9339i	0.0597254	−	0.985272i
$201$	0.187096	+	1.31502i	0.0131967	+	0.0927546i
$202$	3.63901	−	18.4522i	0.256040	−	1.29829i
$203$	4.59056	+	2.65036i	0.322194	+	0.186019i
$204$	−0.490866	+	0.504502i	−0.0343675	+	0.0353222i
$205$	0.629768	−	0.363596i	0.0439849	−	0.0253947i
$206$	3.14751	+	9.22269i	0.219298	+	0.642576i
$207$	13.2586	+	12.7168i	0.921536	+	0.883878i
$208$	15.4489	+	4.03140i	1.07119	+	0.279527i
$209$	17.0965	+	29.6121i	1.18259	+	2.04831i
$210$	−0.0332207	+	0.621671i	−0.00229245	+	0.0428994i
$211$	8.99194	+	5.19150i	0.619031	+	0.357398i	0.776492	−	0.630128i	$-0.216997\pi$
$211$	8.99194	+	5.19150i	0.619031	+	0.357398i	−0.157461	+	0.987525i	$0.550331\pi$
$212$	−14.7979	+	1.99744i	−1.01633	+	0.137185i
$213$	12.5369	+	15.9904i	0.859015	+	1.09564i
$214$	18.9851	+	16.5946i	1.29780	+	1.13439i
$215$	1.46464			0.0998876
$216$	14.5088	+	2.34383i	0.987202	+	0.159477i
$217$	5.98045			0.405979
$218$	−9.20399	−	8.04510i	−0.623373	−	0.544883i
$219$	6.89504	+	8.79438i	0.465924	+	0.594269i
$220$	−0.340991	−	2.52621i	−0.0229896	−	0.170317i
$221$	−0.702412	−	0.405538i	−0.0472493	−	0.0272794i
$222$	0.887671	−	16.6113i	0.0595766	−	1.11488i
$223$	−7.95688	−	13.7817i	−0.532832	−	0.922892i	−0.999265	−	0.0383358i	$-0.987794\pi$
$223$	−7.95688	−	13.7817i	−0.532832	−	0.922892i	0.466433	−	0.884557i	$-0.345539\pi$
$224$	5.64153	−	0.416116i	0.376941	−	0.0278029i
$225$	14.2187	−	4.12954i	0.947912	−	0.275303i
$226$	−2.51926	−	7.38182i	−0.167579	−	0.491031i
$227$	0.450884	−	0.260318i	0.0299262	−	0.0172779i	−0.484962	−	0.874535i	$-0.661167\pi$
$227$	0.450884	−	0.260318i	0.0299262	−	0.0172779i	0.514888	+	0.857257i	$0.327833\pi$
$228$	−16.9288	−	16.4712i	−1.12114	−	1.09083i
$229$	−6.94664	−	4.01064i	−0.459047	−	0.265031i	0.252597	−	0.967572i	$-0.418715\pi$
$229$	−6.94664	−	4.01064i	−0.459047	−	0.265031i	−0.711643	+	0.702541i	$0.752049\pi$
$230$	−0.425882	+	2.15950i	−0.0280818	+	0.142394i
$231$	−1.22348	−	8.59935i	−0.0804990	−	0.565795i
$232$	14.9652	+	0.907166i	0.982516	+	0.0595584i
$233$	4.00958			0.262676			0.131338	−	0.991338i	$-0.458073\pi$
$233$	4.00958			0.262676			0.131338	+	0.991338i	$0.458073\pi$
$234$	1.48733	+	16.8693i	0.0972296	+	1.10278i
$235$			0.376600i			0.0245667i
$236$	9.71885	−	23.6821i	0.632643	−	1.54158i
$237$	−3.90596	+	9.71514i	−0.253719	+	0.631066i
$238$	−0.281935	−	0.0556012i	−0.0182751	−	0.00360409i
$239$	5.16222	−	8.94122i	0.333916	−	0.578360i	−0.649360	−	0.760481i	$-0.724963\pi$
$239$	5.16222	−	8.94122i	0.333916	−	0.578360i	0.983276	+	0.182122i	$0.0582965\pi$
$240$	0.701359	+	1.61516i	0.0452725	+	0.104258i
$241$	8.81271	+	15.2641i	0.567677	+	0.983245i	0.996795	+	0.0799965i	$0.0254909\pi$
$241$	8.81271	+	15.2641i	0.567677	+	0.983245i	−0.429119	+	0.903248i	$0.641176\pi$
$242$	6.46268	+	18.9366i	0.415437	+	1.21729i
$243$	2.83737	+	15.3281i	0.182017	+	0.983295i
$244$	7.76617	+	10.0528i	0.497178	+	0.643566i
$245$	−0.220108	+	0.127079i	−0.0140622	+	0.00811879i
$246$	3.82310	−	5.87384i	0.243752	−	0.374503i
$247$	13.6080	−	23.5697i	0.865855	−	1.49971i
$248$	15.1340	−	7.55577i	0.961007	−	0.479792i
$249$	−3.29704	−	1.32557i	−0.208942	−	0.0840048i
$250$	2.68876	+	2.35021i	0.170052	+	0.148640i
$251$			2.66959i			0.168503i	0.996445	+	0.0842515i	$0.0268499\pi$
$251$			2.66959i			0.168503i	−0.996445	+	0.0842515i	$0.973150\pi$
$252$	2.42915	+	5.48627i	0.153022	+	0.345603i
$253$		−	30.7098i		−	1.93071i
$254$	−14.1854	+	16.2288i	−0.890068	+	1.01828i
$255$	−0.0125998	−	0.0885589i	−0.000789029	−	0.00554577i
$256$	13.7506	−	8.18058i	0.859410	−	0.511286i
$257$	10.3673	−	17.9568i	0.646697	−	1.12011i	−0.337210	−	0.941429i	$-0.609483\pi$
$257$	10.3673	−	17.9568i	0.646697	−	1.12011i	0.983907	−	0.178682i	$-0.0571835\pi$
$258$	12.5837	−	6.39547i	0.783430	−	0.398164i
$259$	5.88136	−	3.39560i	0.365450	−	0.210993i
$260$	−1.60565	+	1.24042i	−0.0995779	+	0.0769275i
$261$	4.43521	+	15.2712i	0.274533	+	0.945261i
$262$	−26.4280	+	9.01933i	−1.63273	+	0.557216i
$263$	0.407649	+	0.706069i	0.0251367	+	0.0435381i	0.878320	−	0.478073i	$-0.158665\pi$
$263$	0.407649	+	0.706069i	0.0251367	+	0.0435381i	−0.853183	+	0.521611i	$0.825331\pi$
$264$	−13.9606	−	20.2155i	−0.859216	−	1.24418i
$265$	0.948782	−	1.64334i	0.0582832	−	0.100949i
$266$	1.86572	−	9.46044i	0.114395	−	0.580057i
$267$	−10.5575	−	13.4657i	−0.646109	−	0.824089i
$268$	−0.582303	+	1.41891i	−0.0355698	+	0.0866739i
$269$			5.86347i			0.357502i	0.983894	+	0.178751i	$0.0572057\pi$
$269$			5.86347i			0.357502i	−0.983894	+	0.178751i	$0.942794\pi$
$270$	−1.36290	+	1.27699i	−0.0829436	+	0.0777152i
$271$	−8.84763			−0.537455			−0.268728	−	0.963216i	$-0.586603\pi$
$271$	−8.84763			−0.537455			−0.268728	+	0.963216i	$0.586603\pi$
$272$	−0.783703	+	0.215497i	−0.0475190	+	0.0130664i
$273$	−5.44072	+	4.26568i	−0.329288	+	0.258171i
$274$	−6.67687	−	1.31677i	−0.403364	−	0.0795487i
$275$	−21.4343	−	12.3751i	−1.29254	−	0.746247i
$276$	5.77060	+	20.4135i	0.347349	+	1.22875i
$277$	−11.7513	+	6.78461i	−0.706067	+	0.407648i	−0.809603	−	0.586978i	$-0.800318\pi$
$277$	−11.7513	+	6.78461i	−0.706067	+	0.407648i	0.103536	+	0.994626i	$0.466984\pi$
$278$	15.5724	−	5.31455i	0.933973	−	0.318745i
$279$	12.9483	+	12.4191i	0.775192	+	0.743514i
$280$	−0.396445	+	0.599669i	−0.0236921	+	0.0358371i
$281$	10.7746	+	18.6621i	0.642758	+	1.11329i	0.984814	+	0.173611i	$0.0555434\pi$
$281$	10.7746	+	18.6621i	0.642758	+	1.11329i	−0.342056	+	0.939680i	$0.611123\pi$
$282$	1.64445	+	3.23563i	0.0979257	+	0.192679i
$283$	−22.9395	−	13.2441i	−1.36361	−	0.787281i	−0.373508	−	0.927627i	$-0.621845\pi$
$283$	−22.9395	−	13.2441i	−1.36361	−	0.787281i	−0.990103	+	0.140346i	$0.955179\pi$
$284$	3.13853	+	23.2516i	0.186238	+	1.37973i
$285$	2.97163	−	0.422791i	0.176024	−	0.0250440i
$286$	18.6301	−	21.3138i	1.10162	−	1.26031i
$287$	2.86118			0.168890
$288$	13.0786	+	10.8144i	0.770662	+	0.637244i
$289$	−16.9587			−0.997571
$290$	−1.25388	+	1.43450i	−0.0736305	+	0.0842370i
$291$	7.39483	−	18.3929i	0.433492	−	1.07821i
$292$	1.72613	+	12.7879i	0.101014	+	0.748356i
$293$	−6.82284	−	3.93917i	−0.398594	−	0.230129i	0.287283	−	0.957846i	$-0.407248\pi$
$293$	−6.82284	−	3.93917i	−0.398594	−	0.230129i	−0.685877	+	0.727717i	$0.740581\pi$
$294$	−1.33620	+	2.05294i	−0.0779286	+	0.119730i
$295$	1.62654	+	2.81725i	0.0947008	+	0.164027i
$296$	10.5932	−	16.0234i	0.615715	−	0.931341i
$297$	15.2086	−	21.1591i	0.882495	−	1.22778i
$298$	−13.3520	+	4.55676i	−0.773461	+	0.263966i
$299$	−21.1686	+	12.2217i	−1.22421	+	0.706800i
$300$	16.5732	+	4.19834i	0.956857	+	0.242391i
$301$	4.99065	+	2.88135i	0.287656	+	0.166078i
$302$	−29.0851	−	5.73596i	−1.67366	−	0.330067i
$303$	21.3719	+	8.59254i	1.22778	+	0.493629i
$304$	−7.23108	−	26.2975i	−0.414731	−	1.50826i
$305$	−1.61432			−0.0924356
$306$	−0.494953	−	0.705854i	−0.0282946	−	0.0403510i
$307$			3.95485i			0.225715i	0.993611	+	0.112858i	$0.0360004\pi$
$307$			3.95485i			0.225715i	−0.993611	+	0.112858i	$0.964000\pi$
$308$	3.80786	−	9.27871i	0.216973	−	0.528703i
$309$	−11.8161	+	1.68115i	−0.672197	+	0.0956373i
$310$	−0.415914	+	2.10896i	−0.0236223	+	0.119781i
$311$	3.40298	−	5.89414i	0.192965	−	0.334226i	−0.753266	−	0.657716i	$-0.771523\pi$
$311$	3.40298	−	5.89414i	0.192965	−	0.334226i	0.946232	+	0.323490i	$0.104856\pi$
$312$	−8.37883	+	17.6685i	−0.474358	+	1.00028i
$313$	−11.4898	−	19.9009i	−0.649441	−	1.12486i	−0.983257	−	0.182226i	$-0.941670\pi$
$313$	−11.4898	−	19.9009i	−0.649441	−	1.12486i	0.333816	−	0.942638i	$-0.391664\pi$
$314$	18.7640	−	6.40376i	1.05891	−	0.361385i
$315$	−0.740449	−	0.181942i	−0.0417196	−	0.0102512i
$316$	−9.56815	+	7.39174i	−0.538250	+	0.415818i
$317$	−8.73416	+	5.04267i	−0.490559	+	0.283225i	−0.724807	−	0.688952i	$-0.758071\pi$
$317$	−8.73416	+	5.04267i	−0.490559	+	0.283225i	0.234247	+	0.972177i	$0.424738\pi$
$318$	0.975881	−	18.2620i	0.0547247	−	1.02408i
$319$	13.2911	−	23.0209i	0.744160	−	1.28892i
$320$	−0.245603	+	2.01838i	−0.0137296	+	0.112831i
$321$	−24.3033	+	19.0545i	−1.35648	+	1.06352i
$322$	−5.69951	+	6.52052i	−0.317621	+	0.363374i
$323$			1.38548i			0.0770902i
$324$	−6.13356	+	16.9227i	−0.340753	+	0.940153i
$325$			19.6999i			1.09276i
$326$	−12.5196	−	10.9433i	−0.693399	−	0.606091i
$327$	11.7823	−	9.23763i	0.651561	−	0.510842i
$328$	7.24042	−	3.61485i	0.399785	−	0.199597i
$329$	−0.740876	+	1.28323i	−0.0408458	+	0.0707470i
$330$	3.11758	+	0.166596i	0.171617	+	0.00917083i
$331$	25.1203	−	14.5032i	1.38074	−	0.797168i	0.388489	−	0.921454i	$-0.372997\pi$
$331$	25.1203	−	14.5032i	1.38074	−	0.797168i	0.992246	+	0.124286i	$0.0396640\pi$
$332$	−2.50855	−	3.24716i	−0.137674	−	0.178211i
$333$	19.7851	+	4.86155i	1.08422	+	0.266411i
$334$	−9.76641	−	28.6171i	−0.534394	−	1.56586i
$335$	−0.0974539	−	0.168795i	−0.00532447	−	0.00922226i
$336$	−0.787631	+	6.88329i	−0.0429688	+	0.375514i
$337$	−7.38374	+	12.7890i	−0.402218	+	0.696662i	−0.993993	−	0.109441i	$-0.965094\pi$
$337$	−7.38374	+	12.7890i	−0.402218	+	0.696662i	0.591775	+	0.806103i	$0.298427\pi$
$338$	−4.06883	−	0.802426i	−0.221315	−	0.0436462i
$339$	9.45761	−	1.34559i	0.513667	−	0.0730823i
$340$	0.0392146	−	0.0955552i	0.00212671	−	0.00518221i
$341$		−	29.9910i		−	1.62410i
$342$	23.6852	−	16.6084i	1.28075	−	0.898078i
$343$	−1.00000			−0.0539949
$344$	16.2695	+	0.986229i	0.877194	+	0.0531739i
$345$	−2.50120	−	1.00561i	−0.134660	−	0.0541400i
$346$	−1.16621	+	5.91346i	−0.0626959	+	0.317910i
$347$	−22.2915	−	12.8700i	−1.19667	−	0.690899i	−0.236860	−	0.971544i	$-0.576118\pi$
$347$	−22.2915	−	12.8700i	−1.19667	−	0.690899i	−0.959812	+	0.280645i	$0.909452\pi$
$348$	−4.50910	+	17.8000i	−0.241713	+	0.954180i
$349$	11.9730	−	6.91262i	0.640901	−	0.370024i	−0.144061	−	0.989569i	$-0.546016\pi$
$349$	11.9730	−	6.91262i	0.640901	−	0.370024i	0.784962	+	0.619545i	$0.212683\pi$
$350$	2.25436	+	6.60562i	0.120501	+	0.353085i
$351$	−20.6379	−	2.06271i	−1.10157	−	0.110099i
$352$	−2.08675	−	28.2913i	−0.111224	−	1.50793i
$353$	6.79240	+	11.7648i	0.361523	+	0.626176i	0.988212	−	0.153094i	$-0.0489236\pi$
$353$	6.79240	+	11.7648i	0.361523	+	0.626176i	−0.626689	+	0.779270i	$0.715590\pi$
$354$	26.2765	+	17.1025i	1.39658	+	0.908990i
$355$	−2.58214	−	1.49080i	−0.137046	−	0.0791233i
$356$	−2.64300	−	19.5805i	−0.140079	−	1.03777i
$357$	0.131287	−	0.326545i	0.00694845	−	0.0172826i
$358$	2.36900	+	2.07071i	0.125205	+	0.109440i
$359$	−20.3192			−1.07241			−0.536204	−	0.844088i	$-0.680142\pi$
$359$	−20.3192			−1.07241			−0.536204	+	0.844088i	$0.680142\pi$
$360$	−2.10363	+	0.475076i	−0.110871	+	0.0250387i
$361$	−27.4904			−1.44686
$362$	19.0145	+	16.6203i	0.999380	+	0.873546i
$363$	−24.2617	+	3.45185i	−1.27341	+	0.181175i
$364$	−7.91136	+	1.06788i	−0.414668	+	0.0559724i
$365$	−1.42012	−	0.819907i	−0.0743325	−	0.0429159i
$366$	−13.8697	+	7.04905i	−0.724983	+	0.368460i
$367$	17.2172	+	29.8210i	0.898730	+	1.55665i	0.829120	+	0.559071i	$0.188842\pi$
$367$	17.2172	+	29.8210i	0.898730	+	1.55665i	0.0696100	+	0.997574i	$0.477825\pi$
$368$	−6.18491	+	23.7015i	−0.322411	+	1.23552i
$369$	6.19473	+	5.94159i	0.322485	+	0.309307i
$370$	0.788410	+	2.31016i	0.0409875	+	0.120100i
$371$	6.46580	−	3.73303i	0.335688	−	0.193809i
$372$	5.63553	+	19.9357i	0.292188	+	1.03362i
$373$	26.1665	+	15.1072i	1.35485	+	0.782223i	0.988924	−	0.148421i	$-0.0474190\pi$
$373$	26.1665	+	15.1072i	1.35485	+	0.782223i	0.365926	+	0.930644i	$0.380752\pi$
$374$	−0.278831	+	1.41386i	−0.0144180	+	0.0731087i
$375$	−3.44195	+	2.69859i	−0.177742	+	0.139354i
$376$	−0.253587	+	4.18335i	−0.0130778	+	0.215740i
$377$	−21.1581			−1.08970
$378$	−7.15618	+	1.67004i	−0.368074	+	0.0858978i
$379$			15.9096i			0.817220i	0.912709	+	0.408610i	$0.133986\pi$
$379$			15.9096i			0.817220i	−0.912709	+	0.408610i	$0.866014\pi$
$380$	3.20640	+	1.31586i	0.164485	+	0.0675024i
$381$	−16.2881	−	20.7748i	−0.834463	−	1.06433i
$382$	−16.2940	−	3.21340i	−0.833676	−	0.164412i
$383$	6.49915	−	11.2569i	0.332091	−	0.575199i	−0.650831	−	0.759223i	$-0.725579\pi$
$383$	6.49915	−	11.2569i	0.332091	−	0.575199i	0.982922	+	0.184024i	$0.0589125\pi$
$384$	6.70326	+	18.4138i	0.342074	+	0.939673i
$385$	0.637281	+	1.10380i	0.0324788	+	0.0562550i
$386$	−10.0579	−	29.4713i	−0.511935	−	1.50005i
$387$	4.82176	+	16.6021i	0.245104	+	0.843932i
$388$	18.1146	−	13.9942i	0.919628	−	0.710446i
$389$	−11.6358	+	6.71792i	−0.589957	+	0.340612i	−0.765081	−	0.643935i	$-0.777301\pi$
$389$	−11.6358	+	6.71792i	−0.589957	+	0.340612i	0.175123	+	0.984546i	$0.443968\pi$
$390$	−1.12588	−	2.21529i	−0.0570112	−	0.112175i
$391$	0.622170	−	1.07763i	0.0314645	−	0.0544981i
$392$	−2.53057	+	1.26341i	−0.127813	+	0.0638119i
$393$	−4.81741	−	33.8597i	−0.243006	−	1.70799i
$394$	−12.9983	−	11.3616i	−0.654842	−	0.572390i
$395$		−	1.53649i		−	0.0773091i
$396$	27.5127	−	12.1818i	1.38257	−	0.612159i
$397$		−	12.4433i		−	0.624512i	−0.949998	−	0.312256i	$-0.898915\pi$
$397$		−	12.4433i		−	0.624512i	0.949998	−	0.312256i	$-0.101085\pi$
$398$	0.948447	−	1.08507i	0.0475413	−	0.0543897i
$399$	10.9574	+	4.40540i	0.548554	+	0.220546i
$400$	14.0504	+	13.8678i	0.702522	+	0.693391i
$401$	−2.05108	+	3.55257i	−0.102426	+	0.177407i	−0.912684	−	0.408667i	$-0.865994\pi$
$401$	−2.05108	+	3.55257i	−0.102426	+	0.177407i	0.810258	+	0.586074i	$0.199327\pi$
$402$	−1.57435	−	1.02470i	−0.0785215	−	0.0511072i
$403$	−20.6732	+	11.9357i	−1.02980	+	0.594557i
$404$	16.2607	+	21.0485i	0.809002	+	1.04720i
$405$	−1.22532	−	1.93155i	−0.0608867	−	0.0959797i
$406$	−7.09458	+	2.42123i	−0.352098	+	0.120164i
$407$	−17.0284	−	29.4940i	−0.844066	−	1.46197i
$408$	−0.0803291	−	0.992215i	−0.00397688	−	0.0491220i
$409$	−6.01472	+	10.4178i	−0.297409	+	0.515127i	−0.975542	−	0.219811i	$-0.929456\pi$
$409$	−6.01472	+	10.4178i	−0.297409	+	0.515127i	0.678133	+	0.734939i	$0.262789\pi$
$410$	−0.198982	+	1.00897i	−0.00982704	+	0.0498296i
$411$	3.10918	−	7.73335i	0.153365	−	0.381458i
$412$	−12.7496	−	5.23228i	−0.628129	−	0.257776i
$413$			12.7994i			0.629818i
$414$	−25.8806	+	2.28184i	−1.27196	+	0.112146i
$415$	0.521441			0.0255965
$416$	−18.6711	+	12.6977i	−0.915426	+	0.622554i
$417$	2.83861	+	19.9515i	0.139007	+	0.977027i
$418$	−47.4425	−	9.35628i	−2.32049	−	0.457631i
$419$	−20.8015	−	12.0097i	−1.01622	−	0.586714i	−0.103212	−	0.994659i	$-0.532912\pi$
$419$	−20.8015	−	12.0097i	−1.01622	−	0.586714i	−0.913006	+	0.407946i	$0.866245\pi$
$420$	−0.631027	−	0.613972i	−0.0307910	−	0.0299588i
$421$	6.99309	−	4.03746i	0.340822	−	0.196774i	−0.319813	−	0.947481i	$-0.603620\pi$
$421$	6.99309	−	4.03746i	0.340822	−	0.196774i	0.660636	+	0.750707i	$0.270287\pi$
$422$	−13.8968	+	4.74268i	−0.676484	+	0.230870i
$423$	−4.26886	+	1.23981i	−0.207559	+	0.0602815i
$424$	11.6458	−	17.6157i	0.565571	−	0.855493i
$425$	−0.501431	−	0.868505i	−0.0243230	−	0.0421287i
$426$	−28.6946	−	1.53338i	−1.39026	−	0.0742924i
$427$	−5.50067	−	3.17581i	−0.266196	−	0.153688i
$428$	−35.3395	+	4.77016i	−1.70820	+	0.230575i
$429$	21.3917	+	27.2843i	1.03280	+	1.31730i
$430$	−1.36316	+	1.55953i	−0.0657376	+	0.0752071i
$431$	25.3324			1.22022			0.610108	−	0.792318i	$-0.291126\pi$
$431$	25.3324			1.22022			0.610108	+	0.792318i	$0.291126\pi$
$432$	−15.9993	+	13.2674i	−0.769766	+	0.638326i
$433$	−6.10314			−0.293298			−0.146649	−	0.989189i	$-0.546849\pi$
$433$	−6.10314			−0.293298			−0.146649	+	0.989189i	$0.546849\pi$
$434$	−5.56610	+	6.36790i	−0.267181	+	0.305669i
$435$	−1.43975	−	1.83634i	−0.0690306	−	0.0880460i
$436$	17.1326	−	2.31258i	0.820503	−	0.110752i
$437$	36.1603	+	20.8772i	1.72978	+	0.998691i
$438$	−15.7814	−	0.843325i	−0.754067	−	0.0402956i
$439$	−9.02755	−	15.6362i	−0.430862	−	0.746274i	0.566086	−	0.824346i	$-0.308457\pi$
$439$	−9.02755	−	15.6362i	−0.430862	−	0.746274i	−0.996948	+	0.0780719i	$0.975124\pi$
$440$	3.00724	+	1.98810i	0.143365	+	0.0947792i
$441$	−2.16510	−	2.07662i	−0.103100	−	0.0988867i
$442$	1.08556	−	0.370477i	0.0516346	−	0.0176218i
$443$	−1.58951	+	0.917704i	−0.0755199	+	0.0436014i	−0.537284	−	0.843401i	$-0.680550\pi$
$443$	−1.58951	+	0.917704i	−0.0755199	+	0.0436014i	0.461765	+	0.887003i	$0.347217\pi$
$444$	16.8613	+	16.4056i	0.800202	+	0.778574i
$445$	2.17445	+	1.25542i	0.103079	+	0.0595126i
$446$	22.0802	+	4.35450i	1.04553	+	0.206191i
$447$	−2.43386	−	17.1066i	−0.115117	−	0.809115i
$448$	−4.80759	+	6.39430i	−0.227137	+	0.302102i
$449$	2.38153			0.112391			0.0561956	−	0.998420i	$-0.482103\pi$
$449$	2.38153			0.112391			0.0561956	+	0.998420i	$0.482103\pi$
$450$	−8.83648	+	18.9833i	−0.416555	+	0.894880i
$451$		−	14.3483i		−	0.675637i
$452$	10.2048	+	4.18791i	0.479992	+	0.196983i
$453$	13.5439	−	33.6872i	0.636348	−	1.58276i
$454$	−0.142462	+	0.722376i	−0.00668607	+	0.0339028i
$455$	0.507244	−	0.878572i	0.0237799	−	0.0411881i
$456$	33.2942	−	2.69548i	1.55914	−	0.126227i
$457$	−6.35724	−	11.0111i	−0.297379	−	0.515075i	0.678157	−	0.734918i	$-0.262779\pi$
$457$	−6.35724	−	11.0111i	−0.297379	−	0.515075i	−0.975535	+	0.219842i	$0.929446\pi$
$458$	10.7358	−	3.66391i	0.501652	−	0.171203i
$459$	0.962360	−	0.434368i	0.0449191	−	0.0202746i
$460$	−1.90303	−	2.46336i	−0.0887294	−	0.114855i
$461$	−0.284429	+	0.164215i	−0.0132472	+	0.00764827i	−0.506609	−	0.862176i	$-0.669101\pi$
$461$	−0.284429	+	0.164215i	−0.0132472	+	0.00764827i	0.493362	+	0.869824i	$0.335768\pi$
$462$	10.2952	+	6.70080i	0.478975	+	0.311750i
$463$	−3.38565	+	5.86413i	−0.157345	+	0.272529i	−0.933910	−	0.357507i	$-0.883627\pi$
$463$	−3.38565	+	5.86413i	−0.157345	+	0.272529i	0.776566	+	0.630036i	$0.216960\pi$
$464$	−14.8943	+	15.0905i	−0.691452	+	0.700557i
$465$	−2.44266	−	0.982068i	−0.113276	−	0.0455423i
$466$	−3.73178	+	4.26934i	−0.172871	+	0.197773i
$467$		−	8.58775i		−	0.397394i	−0.980061	−	0.198697i	$-0.936329\pi$
$467$		−	8.58775i		−	0.397394i	0.980061	−	0.198697i	$-0.0636709\pi$
$468$	−19.3465	−	14.1168i	−0.894290	−	0.652551i
$469$		−	0.766875i		−	0.0354110i
$470$	−0.400998	−	0.350507i	−0.0184966	−	0.0161677i
$471$	3.42038	+	24.0405i	0.157603	+	1.10773i
$472$	16.1709	+	32.3898i	0.744327	+	1.49086i
$473$	14.4495	−	25.0273i	0.664389	−	1.15076i
$474$	−6.70920	−	13.2010i	−0.308164	−	0.606344i
$475$	29.1431	−	16.8257i	1.33718	−	0.772018i
$476$	0.321604	−	0.248451i	0.0147407	−	0.0113877i
$477$	21.7512	+	5.34465i	0.995918	+	0.244715i
$478$	4.71593	+	13.8184i	0.215701	+	0.632038i
$479$	−14.8774	−	25.7685i	−0.679768	−	1.17739i	−0.975051	−	0.221982i	$-0.928747\pi$
$479$	−14.8774	−	25.7685i	−0.679768	−	1.17739i	0.295283	−	0.955410i	$-0.404586\pi$
$480$	−2.37256	−	0.756454i	−0.108292	−	0.0345272i
$481$	−13.5537	+	23.4758i	−0.617998	+	1.07040i
$482$	−24.4551	−	4.82286i	−1.11390	−	0.219675i
$483$	−6.54435	−	8.34708i	−0.297778	−	0.379805i
$484$	−26.1784	−	10.7433i	−1.18993	−	0.488330i
$485$			2.90890i			0.132086i
$486$	−18.9619	−	11.2449i	−0.860128	−	0.510078i
$487$	−26.6355			−1.20697			−0.603485	−	0.797374i	$-0.706222\pi$
$487$	−26.6355			−1.20697			−0.603485	+	0.797374i	$0.706222\pi$
$488$	−17.9322	−	1.08702i	−0.811752	−	0.0492069i
$489$	16.0267	−	12.5654i	0.724753	−	0.568227i
$490$	0.0695456	−	0.352642i	0.00314175	−	0.0159307i
$491$	27.1446	+	15.6719i	1.22502	+	0.707265i	0.965984	−	0.258603i	$-0.0832622\pi$
$491$	27.1446	+	15.6719i	1.22502	+	0.707265i	0.259035	+	0.965868i	$0.416595\pi$
$492$	2.69616	+	9.53766i	0.121552	+	0.429991i
$493$	0.932792	−	0.538548i	0.0420108	−	0.0242550i
$494$	12.4315	+	36.4263i	0.559321	+	1.63890i
$495$	−0.912406	+	3.71323i	−0.0410096	+	0.166897i
$496$	−6.04015	+	23.1467i	−0.271211	+	1.03932i
$497$	−5.86562	−	10.1596i	−0.263109	−	0.455718i
$498$	4.48006	−	2.27691i	0.200756	−	0.102031i
$499$	5.37094	+	3.10091i	0.240436	+	0.138816i	0.615377	−	0.788233i	$-0.289004\pi$
$499$	5.37094	+	3.10091i	0.240436	+	0.138816i	−0.374941	+	0.927049i	$0.622337\pi$
$500$	−5.00494	+	0.675573i	−0.223828	+	0.0302125i
$501$	36.6643	−	5.21644i	1.63804	−	0.233053i
$502$	−2.84254	−	2.48463i	−0.126869	−	0.110894i
$503$	−24.4990			−1.09236			−0.546178	−	0.837669i	$-0.683918\pi$
$503$	−24.4990			−1.09236			−0.546178	+	0.837669i	$0.683918\pi$
$504$	−8.10256	−	2.51963i	−0.360917	−	0.112233i
$505$	−3.38005			−0.150410
$506$	32.6993	+	28.5821i	1.45366	+	1.27063i
$507$	1.89471	−	4.71264i	0.0841471	−	0.209296i
$508$	−4.07761	−	30.2087i	−0.180915	−	1.34029i
$509$	−4.38137	−	2.52958i	−0.194201	−	0.112122i	0.399747	−	0.916626i	$-0.369098\pi$
$509$	−4.38137	−	2.52958i	−0.194201	−	0.112122i	−0.593948	+	0.804504i	$0.702431\pi$
$510$	0.106023	+	0.0690071i	0.00469478	+	0.00305569i
$511$	−3.22597	−	5.58754i	−0.142709	−	0.247178i
$512$	−4.08731	+	22.2552i	−0.180635	+	0.983550i
$513$	14.5754	+	32.2924i	0.643520	+	1.42574i
$514$	9.47105	+	27.7516i	0.417750	+	1.22407i
$515$	1.51671	−	0.875671i	0.0668341	−	0.0385867i
$516$	−4.90209	+	19.3514i	−0.215803	+	0.851896i
$517$	6.43521	+	3.71537i	0.283020	+	0.163402i
$518$	−1.85828	+	9.42273i	−0.0816483	+	0.414011i
$519$	−6.84915	−	2.75369i	−0.300644	−	0.120874i
$520$	0.173619	−	2.86415i	0.00761371	−	0.125601i
$521$	−0.123334			−0.00540337			−0.00270168	−	0.999996i	$-0.500860\pi$
$521$	−0.123334			−0.00540337			−0.00270168	+	0.999996i	$0.500860\pi$
$522$	−20.3884	−	9.49056i	−0.892377	−	0.415390i
$523$			31.9796i			1.39837i	0.714941	+	0.699185i	$0.246454\pi$
$523$			31.9796i			1.39837i	−0.714941	+	0.699185i	$0.753546\pi$
$524$	14.9933	−	36.5346i	0.654987	−	1.59602i
$525$	−8.46314	+	1.20410i	−0.369362	+	0.0525512i
$526$	−1.13122	−	0.223091i	−0.0493234	−	0.00972722i
$527$	0.607607	−	1.05241i	0.0264678	−	0.0458435i
$528$	34.5185	+	3.94984i	1.50223	+	0.171895i
$529$	−7.25039	−	12.5580i	−0.315234	−	0.546002i
$530$	0.866756	+	2.53973i	0.0376495	+	0.110319i
$531$	−26.5795	+	27.7120i	−1.15345	+	1.20260i
$532$	8.33688	+	10.7916i	0.361450	+	0.467874i
$533$	−9.89050	+	5.71028i	−0.428405	+	0.247340i
$534$	24.1641	+	1.29128i	1.04568	+	0.0558791i
$535$	2.26582	−	3.92451i	0.0979599	−	0.169672i
$536$	−0.968879	−	1.94063i	−0.0418492	−	0.0838226i
$537$	−3.03261	+	2.37765i	−0.130867	+	0.102603i
$538$	−6.24334	−	5.45723i	−0.269170	−	0.235278i
$539$			5.01483i			0.216004i
$540$	−0.0912471	−	2.63971i	−0.00392665	−	0.113595i
$541$			31.9134i			1.37206i	0.727571	+	0.686032i	$0.240649\pi$
$541$			31.9134i			1.37206i	−0.727571	+	0.686032i	$0.759351\pi$
$542$	8.23463	−	9.42083i	0.353708	−	0.404659i
$543$	−24.3409	+	19.0840i	−1.04457	+	0.818973i
$544$	0.499947	−	1.03504i	0.0214351	−	0.0443770i
$545$	−1.09847	+	1.90261i	−0.0470533	+	0.0814988i
$546$	0.521731	−	9.76334i	0.0223280	−	0.417833i
$547$	−2.58266	+	1.49110i	−0.110426	+	0.0637548i	−0.554196	−	0.832386i	$-0.686974\pi$
$547$	−2.58266	+	1.49110i	−0.110426	+	0.0637548i	0.443770	+	0.896141i	$0.353641\pi$
$548$	7.61634	−	5.88390i	0.325354	−	0.251348i
$549$	−5.31452	−	18.2987i	−0.226818	−	0.780972i
$550$	33.1261	−	11.3052i	1.41250	−	0.482057i
$551$	18.0712	+	31.3002i	0.769859	+	1.33343i
$552$	−27.1067	−	12.8547i	−1.15374	−	0.547132i
$553$	3.02270	−	5.23547i	0.128538	−	0.222635i
$554$	3.71296	−	18.8271i	0.157748	−	0.799889i
$555$	−2.95979	+	0.421106i	−0.125636	+	0.0178750i
$556$	−8.83467	+	21.5276i	−0.374673	+	0.912976i
$557$			32.1814i			1.36357i	0.731553	+	0.681785i	$0.238796\pi$
$557$			32.1814i			1.36357i	−0.731553	+	0.681785i	$0.761204\pi$
$558$	−25.2749	+	2.22843i	−1.06997	+	0.0943368i
$559$	−23.0022			−0.972888
$560$	−0.269542	−	0.980250i	−0.0113902	−	0.0414231i
$561$	−1.63757	−	0.658383i	−0.0691382	−	0.0277969i
$562$	−29.8993	−	5.89652i	−1.26122	−	0.248730i
$563$	−0.122910	−	0.0709620i	−0.00518003	−	0.00299069i	0.497408	−	0.867517i	$-0.334285\pi$
$563$	−0.122910	−	0.0709620i	−0.00518003	−	0.00299069i	−0.502588	+	0.864526i	$0.667619\pi$
$564$	−4.97577	−	1.26046i	−0.209518	−	0.0530751i
$565$	−1.21397	+	0.700885i	−0.0510720	+	0.0294864i
$566$	35.4523	−	12.0991i	1.49017	−	0.508564i
$567$	−0.375285	−	8.99217i	−0.0157605	−	0.377636i
$568$	−27.6791	−	18.2988i	−1.16139	−	0.767801i
$569$	−7.36740	−	12.7607i	−0.308858	−	0.534957i	0.669255	−	0.743033i	$-0.266613\pi$
$569$	−7.36740	−	12.7607i	−0.308858	−	0.534957i	−0.978113	+	0.208076i	$0.933280\pi$
$570$	−2.31556	+	3.55765i	−0.0969883	+	0.149014i
$571$	−18.1155	−	10.4590i	−0.758109	−	0.437694i	0.0705077	−	0.997511i	$-0.477538\pi$
$571$	−18.1155	−	10.4590i	−0.758109	−	0.437694i	−0.828616	+	0.559817i	$0.810871\pi$
$572$	5.35526	+	39.6742i	0.223915	+	1.65886i
$573$	7.58756	−	18.8722i	0.316975	−	0.788399i
$574$	−2.66295	+	3.04654i	−0.111149	+	0.127160i
$575$	−30.2234			−1.26040
$576$	−23.6874	+	3.86075i	−0.986977	+	0.160864i
$577$	−14.2403			−0.592829			−0.296415	−	0.955059i	$-0.595791\pi$
$577$	−14.2403			−0.592829			−0.296415	+	0.955059i	$0.595791\pi$
$578$	15.7837	−	18.0574i	0.656517	−	0.751088i
$579$	37.7586	−	5.37214i	1.56920	−	0.223259i
$580$	−0.360431	−	2.67023i	−0.0149661	−	0.110875i
$581$	1.77677	+	1.02582i	0.0737128	+	0.0425581i
$582$	12.7020	+	24.9924i	0.526513	+	1.03597i
$583$	−18.7205	−	32.4249i	−0.775325	−	1.34290i
$584$	−15.2229	−	10.0640i	−0.629929	−	0.416449i
$585$	2.92269	−	0.848839i	0.120838	−	0.0350952i
$586$	10.5445	−	3.59861i	0.435589	−	0.148657i
$587$	−5.36965	+	3.10017i	−0.221629	+	0.127958i	−0.606704	−	0.794927i	$-0.707509\pi$
$587$	−5.36965	+	3.10017i	−0.221629	+	0.127958i	0.385075	+	0.922885i	$0.374176\pi$
$588$	−0.942325	−	3.33347i	−0.0388608	−	0.137470i
$589$	35.3140	+	20.3885i	1.45509	+	0.840094i
$590$	−4.51361	−	0.890143i	−0.185822	−	0.0366466i
$591$	16.6394	−	13.0458i	0.684453	−	0.536631i
$592$	7.20226	+	26.1927i	0.296011	+	1.07651i
$593$	3.61151			0.148307			0.0741534	−	0.997247i	$-0.476375\pi$
$593$	3.61151			0.148307			0.0741534	+	0.997247i	$0.476375\pi$
$594$	8.37500	+	35.8871i	0.343630	+	1.47246i
$595$			0.0516444i			0.00211721i
$596$	7.57495	−	18.4581i	0.310282	−	0.756072i
$597$	1.08904	+	1.38903i	0.0445713	+	0.0568490i
$598$	6.68848	−	33.9150i	0.273512	−	1.38689i
$599$	11.6063	−	20.1027i	0.474221	−	0.821374i	−0.525344	−	0.850890i	$-0.676063\pi$
$599$	11.6063	−	20.1027i	0.474221	−	0.821374i	0.999564	+	0.0295157i	$0.00939652\pi$
$600$	−19.8953	+	13.7395i	−0.812223	+	0.560912i
$601$	15.3514	+	26.5894i	0.626196	+	1.08460i	0.988308	+	0.152469i	$0.0487225\pi$
$601$	15.3514	+	26.5894i	0.626196	+	1.08460i	−0.362112	+	0.932135i	$0.617944\pi$
$602$	−7.71290	+	2.63225i	−0.314354	+	0.107283i
$603$	1.59251	−	1.66036i	0.0648520	−	0.0676150i
$604$	33.1775	−	25.6308i	1.34997	−	1.04290i
$605$	3.11420	−	1.79799i	0.126610	−	0.0730985i
$606$	−29.0404	+	14.7593i	−1.17968	+	0.599554i
$607$	−4.06047	+	7.03295i	−0.164810	+	0.285459i	−0.936588	−	0.350433i	$-0.886034\pi$
$607$	−4.06047	+	7.03295i	−0.164810	+	0.285459i	0.771778	+	0.635892i	$0.219368\pi$
$608$	34.7313	+	16.7759i	1.40854	+	0.680354i
$609$	−1.29323	−	9.08959i	−0.0524043	−	0.368329i
$610$	1.50247	−	1.71890i	0.0608333	−	0.0695963i
$611$		−	5.91450i		−	0.239275i
$612$	1.21224	+	0.129930i	0.0490020	+	0.00525212i
$613$			6.48972i			0.262118i	0.991375	+	0.131059i	$0.0418377\pi$
$613$			6.48972i			0.262118i	−0.991375	+	0.131059i	$0.958162\pi$
$614$	−4.21107	−	3.68085i	−0.169945	−	0.148547i
$615$	−1.16862	−	0.469843i	−0.0471234	−	0.0189459i
$616$	6.33579	+	12.6904i	0.255276	+	0.511311i
$617$	−0.670868	+	1.16198i	−0.0270081	+	0.0467795i	−0.879214	−	0.476428i	$-0.841931\pi$
$617$	−0.670868	+	1.16198i	−0.0270081	+	0.0467795i	0.852205	+	0.523207i	$0.175265\pi$
$618$	9.20740	−	14.1463i	0.370376	−	0.569049i
$619$	14.2755	−	8.24198i	0.573782	−	0.331273i	−0.184876	−	0.982762i	$-0.559188\pi$
$619$	14.2755	−	8.24198i	0.573782	−	0.331273i	0.758659	+	0.651488i	$0.225855\pi$
$620$	−1.85849	−	2.40570i	−0.0746388	−	0.0966152i
$621$	3.16458	−	31.6624i	0.126990	−	1.27057i
$622$	3.10878	+	9.10921i	0.124651	+	0.365246i
$623$	4.93952	+	8.55550i	0.197898	+	0.342769i
$624$	−11.0148	−	25.3660i	−0.440946	−	1.01545i
$625$	−12.0176	+	20.8151i	−0.480705	+	0.832605i
$626$	31.8839	+	6.28792i	1.27434	+	0.251316i
$627$	22.0923	−	54.9493i	0.882282	−	2.19446i
$628$	−10.6453	+	25.9397i	−0.424795	+	1.03511i
$629$		−	1.37996i		−	0.0550226i
$630$	0.882877	−	0.619084i	0.0351747	−	0.0246649i
$631$	38.3904			1.52830			0.764149	−	0.645039i	$-0.223159\pi$
$631$	38.3904			1.52830			0.764149	+	0.645039i	$0.223159\pi$
$632$	1.03461	−	17.0676i	0.0411545	−	0.678914i
$633$	−2.53316	−	17.8046i	−0.100684	−	0.707668i
$634$	2.75966	−	13.9933i	0.109600	−	0.555745i
$635$	3.35473	+	1.93686i	0.133129	+	0.0768618i
$636$	18.5368	+	18.0358i	0.735034	+	0.715167i
$637$	3.45679	−	1.99578i	0.136963	−	0.0790756i
$638$	12.1421	+	35.5781i	0.480709	+	1.40855i
$639$	8.39792	−	34.1771i	0.332217	−	1.35203i
$640$	−1.92055	−	2.14005i	−0.0759165	−	0.0845930i
$641$	−2.22309	−	3.85050i	−0.0878068	−	0.152086i	0.818777	−	0.574112i	$-0.194652\pi$
$641$	−2.22309	−	3.85050i	−0.0878068	−	0.152086i	−0.906584	+	0.422026i	$0.861319\pi$
$642$	2.33054	−	43.6121i	0.0919789	−	1.72123i
$643$	5.36316	+	3.09642i	0.211502	+	0.122111i	0.602009	−	0.798489i	$-0.294367\pi$
$643$	5.36316	+	3.09642i	0.211502	+	0.122111i	−0.390507	+	0.920600i	$0.627700\pi$
$644$	−1.63833	−	12.1375i	−0.0645594	−	0.478285i
$645$	−1.56523	−	1.99639i	−0.0616307	−	0.0786078i
$646$	−1.47524	−	1.28949i	−0.0580426	−	0.0507343i
$647$	39.6498			1.55879			0.779397	−	0.626531i	$-0.215526\pi$
$647$	39.6498			1.55879			0.779397	+	0.626531i	$0.215526\pi$
$648$	−12.3105	−	22.2812i	−0.483602	−	0.875288i
$649$	64.1869			2.51956
$650$	−20.9762	−	18.3350i	−0.822754	−	0.719160i
$651$	−6.39117	−	8.15171i	−0.250490	−	0.319491i
$652$	23.3045	−	3.14566i	0.912673	−	0.123194i
$653$	−28.4168	−	16.4064i	−1.11204	−	0.642034i	−0.172680	−	0.984978i	$-0.555243\pi$
$653$	−28.4168	−	16.4064i	−1.11204	−	0.642034i	−0.939356	+	0.342944i	$0.888576\pi$
$654$	−1.12985	+	21.1432i	−0.0441805	+	0.826764i
$655$	2.50927	+	4.34619i	0.0980455	+	0.169820i
$656$	−2.88974	+	11.0739i	−0.112825	+	0.432363i
$657$	4.61868	−	18.7967i	0.180192	−	0.733329i
$658$	−0.676825	−	1.98320i	−0.0263854	−	0.0773132i
$659$	0.854992	−	0.493630i	0.0333058	−	0.0192291i	−0.483255	−	0.875480i	$-0.660545\pi$
$659$	0.854992	−	0.493630i	0.0333058	−	0.0192291i	0.516560	+	0.856251i	$0.327212\pi$
$660$	−3.07897	+	3.16450i	−0.119849	+	0.123178i
$661$	12.1319	+	7.00436i	0.471876	+	0.272438i	0.717025	−	0.697048i	$-0.245503\pi$
$661$	12.1319	+	7.00436i	0.471876	+	0.272438i	−0.245148	+	0.969486i	$0.578837\pi$
$662$	−7.93704	+	40.2461i	−0.308482	+	1.56421i
$663$	0.197880	+	1.39082i	0.00768501	+	0.0540149i
$664$	5.79227	+	0.351117i	0.224784	+	0.0136260i
$665$	−1.73295			−0.0672009
$666$	−23.5908	+	16.5422i	−0.914125	+	0.640996i
$667$		−	32.4605i		−	1.25688i
$668$	39.5608	+	16.2352i	1.53065	+	0.628161i
$669$	−10.2820	+	25.5739i	−0.397524	+	0.988744i
$670$	0.270432	+	0.0533328i	0.0104477	+	0.00206042i
$671$	−15.9262	+	27.5849i	−0.614823	+	1.06490i
$672$	−6.59616	−	7.24504i	−0.254452	−	0.279484i
$673$	−19.3905	−	33.5854i	−0.747450	−	1.29462i	−0.949041	−	0.315152i	$-0.897945\pi$
$673$	−19.3905	−	33.5854i	−0.747450	−	1.29462i	0.201591	−	0.979470i	$-0.435389\pi$
$674$	−6.74539	−	19.7650i	−0.259823	−	0.761321i
$675$	−20.8240	−	14.9678i	−0.801515	−	0.576109i
$676$	4.64133	−	3.58560i	0.178513	−	0.137908i
$677$	2.62861	−	1.51763i	0.101026	−	0.0583271i	−0.448636	−	0.893715i	$-0.648090\pi$
$677$	2.62861	−	1.51763i	0.101026	−	0.0583271i	0.549662	+	0.835387i	$0.314757\pi$
$678$	−7.36958	+	11.3227i	−0.283027	+	0.434845i
$679$	−5.72262	+	9.91187i	−0.219614	+	0.380383i
$680$	0.0652481	+	0.130690i	0.00250215	+	0.00501173i
$681$	−0.836677	−	0.336385i	−0.0320615	−	0.0128903i
$682$	31.9339	+	27.9131i	1.22281	+	1.06885i
$683$		−	23.6025i		−	0.903124i	−0.892240	−	0.451562i	$-0.850867\pi$
$683$		−	23.6025i		−	0.903124i	0.892240	−	0.451562i	$-0.149133\pi$
$684$	−4.35986	+	40.6774i	−0.166704	+	1.55534i
$685$			1.22306i			0.0467307i
$686$	0.930716	−	1.06479i	0.0355349	−	0.0406537i
$687$	1.95697	+	13.7548i	0.0746630	+	0.524777i
$688$	−16.1924	+	16.4057i	−0.617331	+	0.625460i
$689$	−14.9006	+	25.8086i	−0.567668	+	0.983230i
$690$	3.39866	−	1.72731i	0.129385	−	0.0657576i
$691$	−37.1841	+	21.4682i	−1.41455	+	0.816690i	−0.995813	−	0.0914186i	$-0.970860\pi$
$691$	−37.1841	+	21.4682i	−1.41455	+	0.816690i	−0.418735	+	0.908108i	$0.637527\pi$
$692$	−5.21116	−	6.74552i	−0.198099	−	0.256426i
$693$	−10.4139	+	10.8576i	−0.395592	+	0.412446i
$694$	34.4509	−	11.7574i	1.30774	−	0.446303i
$695$	−1.47856	−	2.56095i	−0.0560851	−	0.0971423i
$696$	−14.7565	−	21.3680i	−0.559343	−	0.809951i
$697$	0.290693	−	0.503495i	0.0110108	−	0.0190712i
$698$	−3.78301	+	19.1824i	−0.143189	+	0.726064i
$699$	−4.28494	−	5.46529i	−0.162071	−	0.206716i
$700$	−9.13174	−	3.74755i	−0.345147	−	0.141644i
$701$		−	31.0482i		−	1.17267i	−0.810067	−	0.586337i	$-0.800569\pi$
$701$		−	31.0482i		−	1.17267i	0.810067	−	0.586337i	$-0.199431\pi$
$702$	21.4044	−	20.0551i	0.807856	−	0.756932i
$703$	46.3051			1.74643
$704$	32.0664	+	24.1092i	1.20855	+	0.908651i
$705$	0.513327	−	0.402463i	0.0193330	−	0.0151576i
$706$	−18.8488	−	3.71722i	−0.709382	−	0.139899i
$707$	−11.5173	−	6.64949i	−0.433151	−	0.250080i
$708$	−42.6665	+	12.0612i	−1.60350	+	0.453288i
$709$	2.01845	−	1.16536i	0.0758047	−	0.0437658i	−0.461619	−	0.887079i	$-0.652731\pi$
$709$	2.01845	−	1.16536i	0.0758047	−	0.0437658i	0.537423	+	0.843313i	$0.319398\pi$
$710$	3.99061	−	1.36191i	0.149765	−	0.0511117i
$711$	17.4165	−	5.05829i	0.653170	−	0.189701i
$712$	23.3089	+	15.4097i	0.873539	+	0.577502i
$713$	−18.3115	−	31.7165i	−0.685771	−	1.18779i
$714$	0.225509	+	0.443713i	0.00843948	+	0.0166056i
$715$	−4.40589	−	2.54374i	−0.164771	−	0.0951305i
$716$	−4.40972	+	0.595229i	−0.164799	+	0.0222448i
$717$	−17.7042	+	2.51887i	−0.661174	+	0.0940690i
$718$	18.9114	−	21.6356i	0.705769	−	0.807435i
$719$	−48.8553			−1.82199			−0.910997	−	0.412412i	$-0.864686\pi$
$719$	−48.8553			−1.82199			−0.910997	+	0.412412i	$0.864686\pi$
$720$	1.45203	−	2.68207i	0.0541138	−	0.0999549i
$721$	6.89075			0.256625
$722$	25.5858	−	29.2714i	0.952204	−	1.08937i
$723$	11.3879	−	28.3246i	0.423520	−	1.05340i
$724$	−35.3942	+	4.77755i	−1.31542	+	0.177556i
$725$	−22.6563	−	13.0806i	−0.841433	−	0.485802i
$726$	18.9052	−	29.0462i	0.701639	−	1.07800i
$727$	18.8536	+	32.6554i	0.699242	+	1.21112i	0.968729	+	0.248119i	$0.0798125\pi$
$727$	18.8536	+	32.6554i	0.699242	+	1.21112i	−0.269487	+	0.963004i	$0.586854\pi$
$728$	6.22616	−	9.41780i	0.230757	−	0.349047i
$729$	17.8608	−	20.2482i	0.661512	−	0.749935i
$730$	2.19475	−	0.749024i	0.0812315	−	0.0277226i
$731$	1.01409	−	0.585484i	0.0375074	−	0.0216549i
$732$	5.40306	−	21.3290i	0.199703	−	0.788341i
$733$	−4.64280	−	2.68052i	−0.171486	−	0.0990072i	0.411801	−	0.911274i	$-0.364900\pi$
$733$	−4.64280	−	2.68052i	−0.171486	−	0.0990072i	−0.583286	+	0.812267i	$0.698233\pi$
$734$	−47.7773	−	9.42231i	−1.76349	−	0.347784i
$735$	0.408440	+	0.164213i	0.0150655	+	0.00605709i
$736$	−19.4806	−	28.6449i	−0.718063	−	1.05587i
$737$	−3.84575			−0.141660
$738$	−12.0921	+	1.06613i	−0.445115	+	0.0392447i
$739$			46.4352i			1.70815i	0.520153	+	0.854073i	$0.325875\pi$
$739$			46.4352i			1.70815i	−0.520153	+	0.854073i	$0.674125\pi$
$740$	−3.19361	−	1.31062i	−0.117400	−	0.0481793i
$741$	−46.6695	+	6.63994i	−1.71445	+	0.243924i
$742$	−2.04295	+	10.3591i	−0.0749989	+	0.380294i
$743$	13.5550	−	23.4780i	0.497286	−	0.861324i	−0.502709	−	0.864455i	$-0.667663\pi$
$743$	13.5550	−	23.4780i	0.497286	−	0.861324i	0.999995	+	0.00313137i	$0.000996749\pi$
$744$	−26.4723	−	12.5538i	−0.970521	−	0.460245i
$745$	1.26774	+	2.19579i	0.0464463	+	0.0804474i
$746$	−40.4396	+	13.8012i	−1.48060	+	0.505297i
$747$	1.71664	+	5.91068i	0.0628086	+	0.216260i
$748$	−1.24594	−	1.61279i	−0.0455561	−	0.0589695i
$749$	15.4412	−	8.91499i	0.564210	−	0.325747i
$750$	0.330061	−	6.17655i	0.0120521	−	0.225536i
$751$	−23.8276	+	41.2707i	−0.869483	+	1.50599i	−0.00695740	+	0.999976i	$0.502215\pi$
$751$	−23.8276	+	41.2707i	−0.869483	+	1.50599i	−0.862526	+	0.506013i	$0.831119\pi$
$752$	−4.21835	−	4.16352i	−0.153827	−	0.151828i
$753$	3.63881	−	2.85293i	0.132606	−	0.103967i
$754$	19.6922	−	22.5289i	0.717148	−	0.820453i
$755$			5.32777i			0.193897i
$756$	4.88213	−	9.17414i	0.177561	−	0.333660i
$757$		−	31.2514i		−	1.13585i	−0.823079	−	0.567927i	$-0.807746\pi$
$757$		−	31.2514i		−	1.13585i	0.823079	−	0.567927i	$-0.192254\pi$
$758$	−16.9403	−	14.8073i	−0.615299	−	0.537825i
$759$	−41.8592	+	32.8188i	−1.51939	+	1.19125i
$760$	−4.38536	+	2.18943i	−0.159074	+	0.0794189i
$761$	26.1310	−	45.2602i	0.947248	−	1.64068i	0.196060	−	0.980592i	$-0.437185\pi$
$761$	26.1310	−	45.2602i	0.947248	−	1.64068i	0.751187	−	0.660089i	$-0.229481\pi$
$762$	37.2803	+	1.99218i	1.35052	+	0.0721689i
$763$	−7.48591	+	4.32199i	−0.271008	+	0.156467i
$764$	18.5867	−	14.3589i	0.672443	−	0.519487i
$765$	−0.107246	+	0.111815i	−0.00387748	+	0.00404268i
$766$	5.93728	+	17.3971i	0.214522	+	0.628584i
$767$	−25.5448	−	44.2449i	−0.922369	−	1.59759i
$768$	−25.8455	−	10.0004i	−0.932620	−	0.360860i
$769$	16.2155	−	28.0861i	0.584747	−	1.01281i	−0.410160	−	0.912013i	$-0.634527\pi$
$769$	16.2155	−	28.0861i	0.584747	−	1.01281i	0.994907	−	0.100797i	$-0.0321394\pi$
$770$	−1.76844	−	0.348759i	−0.0637302	−	0.0125684i
$771$	−35.5555	+	5.05868i	−1.28050	+	0.182184i
$772$	40.7416	+	16.7198i	1.46632	+	0.601760i
$773$			8.34619i			0.300192i	0.988671	+	0.150096i	$0.0479582\pi$
$773$			8.34619i			0.300192i	−0.988671	+	0.150096i	$0.952042\pi$
$774$	−22.1654	−	10.3177i	−0.796717	−	0.370862i
$775$	−29.5159			−1.06024
$776$	−1.95874	+	32.3127i	−0.0703146	+	1.15996i
$777$	−10.9137	−	4.38784i	−0.391526	−	0.157413i
$778$	3.67646	−	18.6421i	0.131807	−	0.668351i
$779$	16.8950	+	9.75432i	0.605325	+	0.349485i
$780$	3.40668	+	0.862982i	0.121979	+	0.0308997i
$781$	−50.9485	+	29.4151i	−1.82308	+	1.05256i
$782$	0.568381	+	1.66544i	0.0203253	+	0.0595562i
$783$	16.0757	−	22.3654i	0.574498	−	0.799273i
$784$	1.00998	−	3.87039i	0.0360708	−	0.138228i
$785$	−1.78159	−	3.08581i	−0.0635878	−	0.110137i
$786$	40.5369	+	26.3842i	1.44590	+	0.941094i
$787$	29.6456	+	17.1159i	1.05675	+	0.610116i	0.924532	−	0.381105i	$-0.124456\pi$
$787$	29.6456	+	17.1159i	1.05675	+	0.610116i	0.132220	+	0.991220i	$0.457790\pi$
$788$	24.1954	−	3.26592i	0.861924	−	0.116343i
$789$	0.526769	−	1.31021i	0.0187535	−	0.0466447i
$790$	1.63603	+	1.43003i	0.0582073	+	0.0508783i
$791$	−5.51534			−0.196103
$792$	−12.6355	+	40.6330i	−0.448984	+	1.44383i
$793$	25.3529			0.900307
$794$	13.2495	+	11.5812i	0.470206	+	0.411001i
$795$	−3.25391	+	0.462952i	−0.115404	+	0.0164192i
$796$	0.272633	+	2.01978i	0.00966321	+	0.0715893i
$797$	28.3556	+	16.3711i	1.00441	+	0.579894i	0.909549	−	0.415597i	$-0.136427\pi$
$797$	28.3556	+	16.3711i	1.00441	+	0.579894i	0.0948565	+	0.995491i	$0.469761\pi$
$798$	−14.8890	+	7.56707i	−0.527065	+	0.267871i
$799$	0.150544	+	0.260750i	0.00532588	+	0.00922469i
$800$	−27.8432	+	2.05370i	−0.984407	+	0.0726093i
$801$	−7.07200	+	28.7810i	−0.249877	+	1.01693i
$802$	−1.87376	−	5.49040i	−0.0661647	−	0.193873i
$803$	−28.0206	+	16.1777i	−0.988826	+	0.570899i
$804$	2.55636	−	0.722645i	0.0901557	−	0.0254857i
$805$	1.34789	+	0.778206i	0.0475070	+	0.0274282i
$806$	6.53192	−	33.1212i	0.230077	−	1.16664i
$807$	7.99226	−	6.26616i	0.281341	−	0.220579i
$808$	−37.5463	−	2.27599i	−1.32087	−	0.0800690i
$809$	23.0950			0.811976			0.405988	−	0.913878i	$-0.366928\pi$
$809$	23.0950			0.811976			0.405988	+	0.913878i	$0.366928\pi$
$810$	3.19712	+	0.493025i	0.112335	+	0.0173231i
$811$			9.57698i			0.336293i	0.985762	+	0.168147i	$0.0537782\pi$
$811$			9.57698i			0.336293i	−0.985762	+	0.168147i	$0.946222\pi$
$812$	4.02494	−	9.80768i	0.141248	−	0.344182i
$813$	9.45526	+	12.0598i	0.331611	+	0.422957i
$814$	47.2534	+	9.31899i	1.65623	+	0.326630i
$815$	−1.49418	+	2.58800i	−0.0523390	+	0.0906538i
$816$	1.13126	+	0.837937i	0.0396020	+	0.0293337i
$817$	19.6462	+	34.0282i	0.687333	+	1.19050i
$818$	−5.49473	−	16.1004i	−0.192119	−	0.562938i
$819$	11.6288	+	2.85739i	0.406342	+	0.0998453i
$820$	−0.889143	−	1.15094i	−0.0310502	−	0.0401926i
$821$	10.4161	−	6.01371i	0.363523	−	0.209880i	−0.307102	−	0.951677i	$-0.599359\pi$
$821$	10.4161	−	6.01371i	0.363523	−	0.209880i	0.670625	+	0.741797i	$0.266026\pi$
$822$	5.34059	+	10.5082i	0.186274	+	0.366514i
$823$	−13.0732	+	22.6435i	−0.455704	+	0.789303i	−0.998728	−	0.0504144i	$-0.983946\pi$
$823$	−13.0732	+	22.6435i	−0.455704	+	0.789303i	0.543024	+	0.839717i	$0.317279\pi$
$824$	17.4375	−	8.70585i	0.607466	−	0.303283i
$825$	6.03836	+	42.4412i	0.210229	+	1.47761i
$826$	−13.6286	−	11.9126i	−0.474201	−	0.414493i
$827$			28.0582i			0.975678i	0.872934	+	0.487839i	$0.162215\pi$
$827$			28.0582i			0.975678i	−0.872934	+	0.487839i	$0.837785\pi$
$828$	21.6579	−	29.6811i	0.752662	−	1.03149i
$829$		−	50.5440i		−	1.75547i	−0.479150	−	0.877733i	$-0.659055\pi$
$829$		−	50.5440i		−	1.75547i	0.479150	−	0.877733i	$-0.340945\pi$
$830$	−0.485313	+	0.555222i	−0.0168455	+	0.0192721i
$831$	21.8062	+	8.76714i	0.756447	+	0.304129i
$832$	3.85720	−	31.6986i	0.133724	−	1.09895i
$833$	−0.101599	+	0.175974i	−0.00352019	+	0.00609715i
$834$	−23.8860	−	15.5466i	−0.827103	−	0.538336i
$835$	−4.70619	+	2.71712i	−0.162864	+	0.0940298i
$836$	54.1179	−	41.8081i	1.87171	−	1.44596i
$837$	3.09051	−	30.9213i	0.106824	−	1.06880i
$838$	32.1480	−	10.9714i	1.11054	−	0.379002i
$839$	11.6436	+	20.1674i	0.401983	+	0.696255i	0.993965	−	0.109696i	$-0.0349878\pi$
$839$	11.6436	+	20.1674i	0.401983	+	0.696255i	−0.591982	+	0.805951i	$0.701655\pi$
$840$	1.24106	−	0.100475i	0.0428205	−	0.00346672i
$841$	−0.451159	+	0.781430i	−0.0155572	+	0.0269459i
$842$	−2.20955	+	11.2039i	−0.0761461	+	0.386111i
$843$	13.9230	−	34.6302i	0.479535	−	1.19273i
$844$	7.88401	−	19.2112i	0.271379	−	0.661276i
$845$			0.745322i			0.0256399i
$846$	2.65297	−	5.69933i	0.0912109	−	0.195947i
$847$	14.1485			0.486150
$848$	7.91796	+	28.7955i	0.271904	+	0.988841i
$849$	6.46239	+	45.4215i	0.221789	+	1.55886i
$850$	1.39146	+	0.274414i	0.0477267	+	0.00941233i
$851$	−36.0162	−	20.7940i	−1.23462	−	0.712808i
$852$	28.3393	−	29.1265i	0.970887	−	0.997857i
$853$	−38.1842	+	22.0457i	−1.30740	+	0.754830i	−0.981662	−	0.190629i	$-0.938947\pi$
$853$	−38.1842	+	22.0457i	−1.30740	+	0.754830i	−0.325741	+	0.945459i	$0.605614\pi$
$854$	8.50112	−	2.90125i	0.290902	−	0.0992788i
$855$	−3.75200	−	3.59868i	−0.128316	−	0.123072i
$856$	27.8118	−	42.0686i	0.950588	−	1.43788i
$857$	11.5254	+	19.9626i	0.393700	+	0.681908i	0.992934	−	0.118666i	$-0.0378616\pi$
$857$	11.5254	+	19.9626i	0.393700	+	0.681908i	−0.599235	+	0.800574i	$0.704528\pi$
$858$	−48.9615	−	2.61640i	−1.67152	−	0.0893223i
$859$	25.8222	+	14.9084i	0.881042	+	0.508670i	0.871002	−	0.491280i	$-0.163471\pi$
$859$	25.8222	+	14.9084i	0.881042	+	0.508670i	0.0100400	+	0.999950i	$0.496804\pi$
$860$	−0.391844	−	2.90295i	−0.0133618	−	0.0989899i
$861$	−3.05768	−	3.89996i	−0.104205	−	0.132910i
$862$	−23.5772	+	26.9735i	−0.803043	+	0.918722i
$863$	34.6683			1.18012			0.590061	−	0.807359i	$-0.299104\pi$
$863$	34.6683			1.18012			0.590061	+	0.807359i	$0.299104\pi$
$864$	0.763885	−	29.3839i	0.0259879	−	0.999662i
$865$	1.08322			0.0368306
$866$	5.68029	−	6.49853i	0.193024	−	0.220829i
$867$	18.1234	+	23.1157i	0.615502	+	0.785051i
$868$	−1.59999	−	11.8534i	−0.0543071	−	0.402331i
$869$	−26.2550	−	15.1583i	−0.890639	−	0.514211i
$870$	3.29531	+	0.176094i	0.111721	+	0.00597014i
$871$	1.53051	+	2.65093i	0.0518594	+	0.0898232i
$872$	−13.4832	+	20.3949i	−0.456598	+	0.690659i
$873$	−32.9732	+	9.57643i	−1.11597	+	0.324113i
$874$	−55.8847	+	19.0723i	−1.89033	+	0.645129i
$875$	2.18686	−	1.26258i	0.0739293	−	0.0426831i
$876$	15.5860	−	16.0190i	0.526602	−	0.541230i
$877$	28.3523	+	16.3692i	0.957390	+	0.552749i	0.895369	−	0.445325i	$-0.146912\pi$
$877$	28.3523	+	16.3692i	0.957390	+	0.552749i	0.0620212	+	0.998075i	$0.480245\pi$
$878$	25.0513	+	4.94043i	0.845439	+	0.166732i
$879$	1.92209	+	13.5096i	0.0648306	+	0.455668i
$880$	−4.91579	+	1.35171i	−0.165711	+	0.0455660i
$881$	−43.3544			−1.46065			−0.730324	−	0.683101i	$-0.760631\pi$
$881$	−43.3544			−1.46065			−0.730324	+	0.683101i	$0.760631\pi$
$882$	4.22625	−	0.372618i	0.142305	−	0.0125467i
$883$			43.6468i			1.46883i	0.678700	+	0.734415i	$0.262544\pi$
$883$			43.6468i			1.46883i	−0.678700	+	0.734415i	$0.737456\pi$
$884$	−0.615865	+	1.50069i	−0.0207138	+	0.0504738i
$885$	2.10183	−	5.22780i	0.0706523	−	0.175730i
$886$	0.502224	−	2.54661i	0.0168726	−	0.0855550i
$887$	21.8498	−	37.8450i	0.733646	−	1.27071i	−0.221669	−	0.975122i	$-0.571150\pi$
$887$	21.8498	−	37.8450i	0.733646	−	1.27071i	0.955315	−	0.295590i	$-0.0955163\pi$
$888$	−33.1615	+	2.68473i	−1.11283	+	0.0900938i
$889$	7.62067	+	13.1994i	0.255589	+	0.442693i
$890$	−3.36055	+	1.14689i	−0.112646	+	0.0384437i
$891$	−45.0942	+	1.88199i	−1.51071	+	0.0630490i
$892$	−25.1870	+	19.4578i	−0.843322	+	0.651497i
$893$	−8.74959	+	5.05158i	−0.292794	+	0.169045i
$894$	20.4801	+	13.3299i	0.684957	+	0.445817i
$895$	0.282733	−	0.489708i	0.00945072	−	0.0163691i
$896$	−2.33406	−	11.0703i	−0.0779756	−	0.369834i
$897$	39.2814	+	15.7930i	1.31157	+	0.527314i
$898$	−2.21652	+	2.53581i	−0.0739664	+	0.0846212i
$899$		−	31.7007i		−	1.05728i
$900$	−11.9889	−	27.0770i	−0.399629	−	0.902566i
$901$		−	1.51709i		−	0.0505415i
$902$	15.2779	+	13.3542i	0.508699	+	0.444647i
$903$	−1.40594	−	9.88178i	−0.0467867	−	0.328845i
$904$	−13.9570	+	6.96814i	−0.464202	+	0.231757i
$905$	2.26933	−	3.93059i	0.0754350	−	0.130657i
$906$	23.2641	+	45.7746i	0.772899	+	1.52076i
$907$	38.5674	−	22.2669i	1.28061	−	0.739361i	0.303650	−	0.952784i	$-0.401795\pi$
$907$	38.5674	−	22.2669i	1.28061	−	0.739361i	0.976960	+	0.213423i	$0.0684612\pi$
$908$	−0.636584	−	0.824018i	−0.0211258	−	0.0273460i
$909$	−11.1275	−	38.3138i	−0.369076	−	1.27079i
$910$	0.463391	+	1.35781i	0.0153612	+	0.0450108i
$911$	14.9392	+	25.8754i	0.494957	+	0.857291i	0.999983	−	0.00581324i	$-0.00185042\pi$
$911$	14.9392	+	25.8754i	0.494957	+	0.857291i	−0.505026	+	0.863104i	$0.668517\pi$
$912$	−28.1173	+	37.9599i	−0.931058	+	1.25698i
$913$	5.14431	−	8.91020i	0.170252	−	0.294885i
$914$	17.6412	+	3.47907i	0.583519	+	0.115077i
$915$	1.72519	+	2.20041i	0.0570329	+	0.0727434i
$916$	−6.09072	+	14.8414i	−0.201243	+	0.490374i
$917$			19.7458i			0.652062i
$918$	−0.433175	+	1.42898i	−0.0142969	+	0.0471634i
$919$	1.35788			0.0447923			0.0223962	−	0.999749i	$-0.492870\pi$
$919$	1.35788			0.0447923			0.0223962	+	0.999749i	$0.492870\pi$
$920$	4.39413	+	0.266364i	0.144870	+	0.00878177i
$921$	5.39070	−	4.22646i	0.177630	−	0.139267i
$922$	0.0898688	−	0.455694i	0.00295967	−	0.0150075i
$923$	40.5524	+	23.4130i	1.33480	+	0.770647i
$924$	−16.7168	+	4.72560i	−0.549942	+	0.155461i
$925$	−29.0269	+	16.7587i	−0.954398	+	0.551022i
$926$	−3.09295	−	9.06283i	−0.101641	−	0.297823i
$927$	14.9191	+	14.3095i	0.490009	+	0.469985i
$928$	−2.20572	−	29.9042i	−0.0724062	−	0.981653i
$929$	0.525684	+	0.910512i	0.0172471	+	0.0298729i	0.874520	−	0.484989i	$-0.161176\pi$
$929$	0.525684	+	0.910512i	0.0172471	+	0.0298729i	−0.857273	+	0.514862i	$0.827843\pi$
$930$	3.31911	−	1.68688i	0.108838	−	0.0553150i
$931$	−5.90490	−	3.40919i	−0.193525	−	0.111732i
$932$	−1.07271	−	7.94708i	−0.0351377	−	0.260315i
$933$	−11.6707	+	1.66046i	−0.382083	+	0.0543612i
$934$	9.14411	+	7.99276i	0.299205	+	0.261531i
$935$	0.258988			0.00846982
$936$	33.0375	−	7.46106i	1.07986	−	0.243872i
$937$	9.68691			0.316458			0.158229	−	0.987402i	$-0.449422\pi$
$937$	9.68691			0.316458			0.158229	+	0.987402i	$0.449422\pi$
$938$	0.816558	+	0.713743i	0.0266616	+	0.0233045i
$939$	−14.8472	+	36.9289i	−0.484521	+	1.20513i
$940$	0.746430	−	0.100754i	0.0243459	−	0.00328623i
$941$	5.40488	+	3.12051i	0.176194	+	0.101726i	0.585503	−	0.810670i	$-0.300897\pi$
$941$	5.40488	+	3.12051i	0.176194	+	0.101726i	−0.409309	+	0.912396i	$0.634230\pi$
$942$	−28.7814	−	18.7329i	−0.937747	−	0.610350i
$943$	−8.76063	−	15.1739i	−0.285285	−	0.494129i
$944$	−49.5388	−	12.9272i	−1.61235	−	0.420744i
$945$	0.543304	+	1.20371i	0.0176737	+	0.0391568i
$946$	13.2003	+	38.6789i	0.429179	+	1.25756i
$947$	−4.38864	+	2.53378i	−0.142612	+	0.0823369i	−0.569608	−	0.821916i	$-0.692905\pi$
$947$	−4.38864	+	2.53378i	−0.142612	+	0.0823369i	0.426996	+	0.904253i	$0.359572\pi$
$948$	20.3006	+	5.14256i	0.659334	+	0.167023i
$949$	22.3030	+	12.8766i	0.723986	+	0.417993i
$950$	−9.20809	+	46.6911i	−0.298750	+	1.51486i
$951$	16.2075	+	6.51619i	0.525563	+	0.211302i
$952$	−0.0347753	+	0.573677i	−0.00112707	+	0.0185930i
$953$	10.7465			0.348115			0.174057	−	0.984736i	$-0.444312\pi$
$953$	10.7465			0.348115			0.174057	+	0.984736i	$0.444312\pi$
$954$	−25.9351	+	18.1860i	−0.839679	+	0.588793i
$955$			2.98472i			0.0965833i
$956$	−19.1028	−	7.83955i	−0.617829	−	0.253549i
$957$	−45.5828	+	6.48532i	−1.47348	+	0.209641i
$958$	41.2846	+	8.14185i	1.33384	+	0.263051i
$959$	−2.40610	+	4.16748i	−0.0776970	+	0.134575i
$960$	3.01364	−	1.82222i	0.0972648	−	0.0588120i
$961$	−2.38290	−	4.12730i	−0.0768677	−	0.133139i
$962$	−12.3820	−	36.2811i	−0.399211	−	1.16975i
$963$	51.9448	+	12.7638i	1.67390	+	0.411306i
$964$	27.8960	−	21.5507i	0.898471	−	0.694101i
$965$	−4.84666	+	2.79822i	−0.156019	+	0.0900779i
$966$	14.9788	+	0.800433i	0.481934	+	0.0257535i
$967$	11.5170	−	19.9480i	0.370362	−	0.641486i	−0.619259	−	0.785187i	$-0.712567\pi$
$967$	11.5170	−	19.9480i	0.370362	−	0.641486i	0.989621	+	0.143701i	$0.0459003\pi$
$968$	35.8039	−	17.8754i	1.15078	−	0.574538i
$969$	1.88849	−	1.48063i	0.0606671	−	0.0475648i
$970$	−3.09736	−	2.70736i	−0.0994502	−	0.0869282i
$971$			50.6797i			1.62639i	0.581991	+	0.813195i	$0.302274\pi$
$971$			50.6797i			1.62639i	−0.581991	+	0.813195i	$0.697726\pi$
$972$	29.6215	−	9.72455i	0.950110	−	0.311915i
$973$		−	11.6350i		−	0.373000i
$974$	24.7901	−	28.3611i	0.794326	−	0.908749i
$975$	26.8522	−	21.0529i	0.859958	−	0.674231i
$976$	17.8472	−	18.0822i	0.571275	−	0.578798i
$977$	−25.2476	+	43.7301i	−0.807743	+	1.39905i	0.106681	+	0.994293i	$0.465978\pi$
$977$	−25.2476	+	43.7301i	−0.807743	+	1.39905i	−0.914424	+	0.404758i	$0.867356\pi$
$978$	−1.53686	+	28.7598i	−0.0491434	+	0.919638i
$979$	42.9044	−	24.7709i	1.37123	−	0.791681i
$980$	0.310761	+	0.402261i	0.00992689	+	0.0128497i
$981$	−25.1829	−	6.18788i	−0.804027	−	0.197564i
$982$	−41.9512	+	14.3171i	−1.33872	+	0.456875i
$983$	24.1172	+	41.7721i	0.769218	+	1.33232i	0.937988	+	0.346669i	$0.112687\pi$
$983$	24.1172	+	41.7721i	0.769218	+	1.33232i	−0.168770	+	0.985655i	$0.553979\pi$
$984$	−12.6649	−	6.00602i	−0.403743	−	0.191465i
$985$	−1.55131	+	2.68694i	−0.0494287	+	0.0856130i
$986$	−0.294727	+	1.49446i	−0.00938601	+	0.0475932i
$987$	2.54088	−	0.361506i	0.0808772	−	0.0115069i
$988$	−50.3564	−	20.6656i	−1.60205	−	0.657461i
$989$		−	35.2896i		−	1.12214i
$990$	−3.10460	−	4.42748i	−0.0986707	−	0.140715i
$991$	−31.2525			−0.992767			−0.496384	−	0.868103i	$-0.665339\pi$
$991$	−31.2525			−0.992767			−0.496384	+	0.868103i	$0.665339\pi$
$992$	−19.0246	−	27.9745i	−0.604032	−	0.888190i
$993$	−46.6142	−	18.7412i	−1.47926	−	0.594733i
$994$	16.2770	+	3.21003i	0.516274	+	0.101816i
$995$	−0.224301	−	0.129500i	−0.00711081	−	0.00410543i
$996$	−1.74524	+	6.88946i	−0.0553001	+	0.218301i
$997$	9.79992	−	5.65799i	0.310367	−	0.179190i	−0.336724	−	0.941603i	$-0.609319\pi$
$997$	9.79992	−	5.65799i	0.310367	−	0.179190i	0.647091	+	0.762413i	$0.275986\pi$
$998$	−8.30062	+	2.83283i	−0.262752	+	0.0896716i
$999$	−14.5173	−	32.1637i	−0.459307	−	1.01761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cs.a.85.10	✓	72
8.5	even	2	inner	504.2.cs.a.85.34	yes	72
9.7	even	3	inner	504.2.cs.a.421.34	yes	72
72.61	even	6	inner	504.2.cs.a.421.10	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cs.a.85.10	✓	72	1.1	even	1	trivial
504.2.cs.a.85.34	yes	72	8.5	even	2	inner
504.2.cs.a.421.10	yes	72	72.61	even	6	inner
504.2.cs.a.421.34	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)

\(f(q)\)	\(=\)	\(q+(-0.930716 + 1.06479i) q^{2} +(-1.06868 - 1.36306i) q^{3} +(-0.267536 - 1.98203i) q^{4} +(0.220108 + 0.127079i) q^{5} +(2.44600 + 0.130709i) q^{6} +(0.500000 + 0.866025i) q^{7} +(2.35943 + 1.55983i) q^{8} +(-0.715859 + 2.91334i) q^{9} +O(q^{10})\)	\(q+(-0.930716 + 1.06479i) q^{2} +(-1.06868 - 1.36306i) q^{3} +(-0.267536 - 1.98203i) q^{4} +(0.220108 + 0.127079i) q^{5} +(2.44600 + 0.130709i) q^{6} +(0.500000 + 0.866025i) q^{7} +(2.35943 + 1.55983i) q^{8} +(-0.715859 + 2.91334i) q^{9} +(-0.340170 + 0.116093i) q^{10} +(4.34297 - 2.50742i) q^{11} +(-2.41571 + 2.48281i) q^{12} +(-3.45679 - 1.99578i) q^{13} +(-1.38749 - 0.273631i) q^{14} +(-0.0620075 - 0.435826i) q^{15} +(-3.85685 + 1.06053i) q^{16} +0.203198 q^{17} +(-2.43582 - 3.47373i) q^{18} +6.81839i q^{19} +(0.192987 - 0.470257i) q^{20} +(0.646105 - 1.60703i) q^{21} +(-1.37221 + 6.95803i) q^{22} +(3.06189 - 5.30336i) q^{23} +(-0.395325 - 4.88300i) q^{24} +(-2.46770 - 4.27418i) q^{25} +(5.34236 - 1.82324i) q^{26} +(4.73607 - 2.13766i) q^{27} +(1.58272 - 1.22271i) q^{28} +(4.59056 - 2.65036i) q^{29} +(0.521773 + 0.339606i) q^{30} +(2.99023 - 5.17922i) q^{31} +(2.46040 - 5.09377i) q^{32} +(-8.05899 - 3.24011i) q^{33} +(-0.189119 + 0.216362i) q^{34} +0.254158i q^{35} +(5.96583 + 0.639427i) q^{36} -6.79121i q^{37} +(-7.26012 - 6.34598i) q^{38} +(0.973828 + 6.84465i) q^{39} +(0.321106 + 0.643166i) q^{40} +(1.43059 - 2.47786i) q^{41} +(1.10980 + 2.18365i) q^{42} +(4.99065 - 2.88135i) q^{43} +(-6.13166 - 7.93706i) q^{44} +(-0.527791 + 0.550277i) q^{45} +(2.79718 + 8.19618i) q^{46} +(0.740876 + 1.28323i) q^{47} +(5.56729 + 4.12375i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(6.84782 + 1.35048i) q^{50} +(-0.217153 - 0.276971i) q^{51} +(-3.03087 + 7.38538i) q^{52} -7.46607i q^{53} +(-2.13179 + 7.03246i) q^{54} +1.27456 q^{55} +(-0.171140 + 2.82324i) q^{56} +(9.29387 - 7.28666i) q^{57} +(-1.45044 + 7.35470i) q^{58} +(11.0846 + 6.39971i) q^{59} +(-0.847229 + 0.239500i) q^{60} +(-5.50067 + 3.17581i) q^{61} +(2.73171 + 8.00433i) q^{62} +(-2.88096 + 0.836718i) q^{63} +(3.13384 + 7.36064i) q^{64} +(-0.507244 - 0.878572i) q^{65} +(10.9507 - 5.56548i) q^{66} +(-0.664133 - 0.383438i) q^{67} +(-0.0543627 - 0.402743i) q^{68} +(-10.5010 + 1.49403i) q^{69} +(-0.270624 - 0.236549i) q^{70} -11.7312 q^{71} +(-6.23335 + 5.75720i) q^{72} -6.45194 q^{73} +(7.23118 + 6.32069i) q^{74} +(-3.18879 + 7.93135i) q^{75} +(13.5142 - 1.82416i) q^{76} +(4.34297 + 2.50742i) q^{77} +(-8.19444 - 5.33350i) q^{78} +(-3.02270 - 5.23547i) q^{79} +(-0.983693 - 0.256695i) q^{80} +(-7.97509 - 4.17108i) q^{81} +(1.30691 + 3.82945i) q^{82} +(1.77677 - 1.02582i) q^{83} +(-3.35803 - 0.850658i) q^{84} +(0.0447254 + 0.0258222i) q^{85} +(-1.57685 + 7.99569i) q^{86} +(-8.51843 - 3.42483i) q^{87} +(14.1581 + 0.858238i) q^{88} +9.87904 q^{89} +(-0.0947041 - 1.07414i) q^{90} -3.99156i q^{91} +(-11.3306 - 4.64991i) q^{92} +(-10.2552 + 1.45906i) q^{93} +(-2.05591 - 0.405453i) q^{94} +(-0.866475 + 1.50078i) q^{95} +(-9.57247 + 2.08992i) q^{96} +(5.72262 + 9.91187i) q^{97} +(-0.456773 - 1.33842i) q^{98} +(4.19600 + 14.4475i) 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

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