LMFDB - Embedded newform 504.2.cs.a.85.14

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			85.14
Character	$\chi$	$=$	504.85
Dual form			504.2.cs.a.421.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.578023 - 1.29069i) q^{2} +(-1.26004 - 1.18840i) q^{3} +(-1.33178 + 1.49210i) q^{4} +(-3.33304 - 1.92433i) q^{5} +(-0.805523 + 2.31325i) q^{6} +(0.500000 + 0.866025i) q^{7} +(2.69564 + 0.856447i) q^{8} +(0.175418 + 2.99487i) q^{9} +O(q^{10})$	\(q+(-0.578023 - 1.29069i) q^{2} +(-1.26004 - 1.18840i) q^{3} +(-1.33178 + 1.49210i) q^{4} +(-3.33304 - 1.92433i) q^{5} +(-0.805523 + 2.31325i) q^{6} +(0.500000 + 0.866025i) q^{7} +(2.69564 + 0.856447i) q^{8} +(0.175418 + 2.99487i) q^{9} +(-0.557147 + 5.41424i) q^{10} +(-1.77389 + 1.02416i) q^{11} +(3.45131 - 0.297430i) q^{12} +(1.43524 + 0.828637i) q^{13} +(0.828761 - 1.14593i) q^{14} +(1.91290 + 6.38572i) q^{15} +(-0.452736 - 3.97430i) q^{16} -5.21444 q^{17} +(3.76406 - 1.95751i) q^{18} +1.19887i q^{19} +(7.31017 - 2.41045i) q^{20} +(0.399162 - 1.68543i) q^{21} +(2.34723 + 1.69757i) q^{22} +(1.17949 - 2.04294i) q^{23} +(-2.37883 - 4.28266i) q^{24} +(4.90611 + 8.49763i) q^{25} +(0.239913 - 2.33143i) q^{26} +(3.33806 - 3.98213i) q^{27} +(-1.95809 - 0.407303i) q^{28} +(7.19666 - 4.15499i) q^{29} +(7.13631 - 6.16007i) q^{30} +(4.75110 - 8.22914i) q^{31} +(-4.86791 + 2.88158i) q^{32} +(3.45229 + 0.817609i) q^{33} +(3.01407 + 6.73025i) q^{34} -3.84866i q^{35} +(-4.70226 - 3.72676i) q^{36} +10.0902i q^{37} +(1.54737 - 0.692973i) q^{38} +(-0.823715 - 2.74976i) q^{39} +(-7.33661 - 8.04189i) q^{40} +(-2.82225 + 4.88829i) q^{41} +(-2.40610 + 0.459022i) q^{42} +(-2.12338 + 1.22593i) q^{43} +(0.834285 - 4.01078i) q^{44} +(5.17844 - 10.3196i) q^{45} +(-3.31858 - 0.341495i) q^{46} +(4.74140 + 8.21234i) q^{47} +(-4.15258 + 5.54582i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(8.13199 - 11.2441i) q^{50} +(6.57042 + 6.19684i) q^{51} +(-3.14783 + 1.03797i) q^{52} +12.1286i q^{53} +(-7.06918 - 2.00665i) q^{54} +7.88328 q^{55} +(0.606118 + 2.76272i) q^{56} +(1.42473 - 1.51062i) q^{57} +(-9.52266 - 6.88700i) q^{58} +(-2.55889 - 1.47738i) q^{59} +(-12.0757 - 5.65012i) q^{60} +(-7.70228 + 4.44691i) q^{61} +(-13.3675 - 1.37557i) q^{62} +(-2.50592 + 1.64935i) q^{63} +(6.53300 + 4.61735i) q^{64} +(-3.18915 - 5.52376i) q^{65} +(-0.940223 - 4.92845i) q^{66} +(1.50841 + 0.870878i) q^{67} +(6.94448 - 7.78048i) q^{68} +(-3.91404 + 1.17249i) q^{69} +(-4.96745 + 2.22462i) q^{70} +10.2121 q^{71} +(-2.09208 + 8.22333i) q^{72} -4.65608 q^{73} +(13.0234 - 5.83238i) q^{74} +(3.91666 - 16.5378i) q^{75} +(-1.78883 - 1.59662i) q^{76} +(-1.77389 - 1.02416i) q^{77} +(-3.07297 + 2.65259i) q^{78} +(-1.98064 - 3.43056i) q^{79} +(-6.13888 + 14.1177i) q^{80} +(-8.93846 + 1.05071i) q^{81} +(7.94061 + 0.817119i) q^{82} +(-1.53730 + 0.887558i) q^{83} +(1.98324 + 2.84021i) q^{84} +(17.3800 + 10.0343i) q^{85} +(2.80966 + 2.03201i) q^{86} +(-14.0059 - 3.31703i) q^{87} +(-5.65893 + 1.24152i) q^{88} +1.13851 q^{89} +(-16.3127 - 0.718822i) q^{90} +1.65727i q^{91} +(1.47745 + 4.48066i) q^{92} +(-15.7661 + 4.72288i) q^{93} +(7.85897 - 10.8666i) q^{94} +(2.30702 - 3.99587i) q^{95} +(9.55824 + 2.15410i) q^{96} +(6.52591 + 11.3032i) q^{97} +(1.40678 + 0.144764i) q^{98} +(-3.37839 - 5.13292i) 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 $

$2$	−0.578023	−	1.29069i	−0.408724	−	0.912658i
$2$	−0.578023	−	1.29069i	−0.408724	−	0.912658i
$3$	−1.26004	−	1.18840i	−0.727486	−	0.686122i
$3$	−1.26004	−	1.18840i	−0.727486	−	0.686122i
$4$	−1.33178	+	1.49210i	−0.665889	+	0.746051i
$5$	−3.33304	−	1.92433i	−1.49058	−	0.860588i	−0.490640	−	0.871363i	$-0.663237\pi$
$5$	−3.33304	−	1.92433i	−1.49058	−	0.860588i	−0.999942	+	0.0107750i	$0.996570\pi$
$6$	−0.805523	+	2.31325i	−0.328853	+	0.944381i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	2.69564	+	0.856447i	0.953054	+	0.302800i
$9$	0.175418	+	2.99487i	0.0584728	+	0.998289i
$10$	−0.557147	+	5.41424i	−0.176185	+	1.71213i
$11$	−1.77389	+	1.02416i	−0.534849	+	0.308795i	−0.742989	−	0.669304i	$-0.766592\pi$
$11$	−1.77389	+	1.02416i	−0.534849	+	0.308795i	0.208140	+	0.978099i	$0.433259\pi$
$12$	3.45131	−	0.297430i	0.996307	−	0.0858607i
$13$	1.43524	+	0.828637i	0.398064	+	0.229823i	0.685648	−	0.727933i	$-0.259519\pi$
$13$	1.43524	+	0.828637i	0.398064	+	0.229823i	−0.287584	+	0.957755i	$0.592852\pi$
$14$	0.828761	−	1.14593i	0.221496	−	0.306263i
$15$	1.91290	+	6.38572i	0.493909	+	1.64879i
$16$	−0.452736	−	3.97430i	−0.113184	−	0.993574i
$17$	−5.21444			−1.26469			−0.632344	−	0.774688i	$-0.717907\pi$
$17$	−5.21444			−1.26469			−0.632344	+	0.774688i	$0.717907\pi$
$18$	3.76406	−	1.95751i	0.887197	−	0.461391i
$19$			1.19887i			0.275039i	0.990499	+	0.137519i	$0.0439129\pi$
$19$			1.19887i			0.275039i	−0.990499	+	0.137519i	$0.956087\pi$
$20$	7.31017	−	2.41045i	1.63460	−	0.538994i
$21$	0.399162	−	1.68543i	0.0871042	−	0.367791i
$22$	2.34723	+	1.69757i	0.500430	+	0.361922i
$23$	1.17949	−	2.04294i	0.245941	−	0.425982i	−0.716455	−	0.697634i	$-0.754236\pi$
$23$	1.17949	−	2.04294i	0.245941	−	0.425982i	0.962396	+	0.271651i	$0.0875697\pi$
$24$	−2.37883	−	4.28266i	−0.485576	−	0.874194i
$25$	4.90611	+	8.49763i	0.981222	+	1.69953i
$26$	0.239913	−	2.33143i	0.0470508	−	0.457231i
$27$	3.33806	−	3.98213i	0.642410	−	0.766361i
$28$	−1.95809	−	0.407303i	−0.370044	−	0.0769729i
$29$	7.19666	−	4.15499i	1.33639	−	0.771563i	0.350117	−	0.936706i	$-0.386142\pi$
$29$	7.19666	−	4.15499i	1.33639	−	0.771563i	0.986270	+	0.165143i	$0.0528086\pi$
$30$	7.13631	−	6.16007i	1.30291	−	1.12467i
$31$	4.75110	−	8.22914i	0.853322	−	1.47800i	−0.0248703	−	0.999691i	$-0.507917\pi$
$31$	4.75110	−	8.22914i	0.853322	−	1.47800i	0.878193	−	0.478307i	$-0.158749\pi$
$32$	−4.86791	+	2.88158i	−0.860532	+	0.509396i
$33$	3.45229	+	0.817609i	0.600967	+	0.142328i
$34$	3.01407	+	6.73025i	0.516909	+	1.15423i
$35$		−	3.84866i		−	0.650543i
$36$	−4.70226	−	3.72676i	−0.783711	−	0.621126i
$37$			10.0902i			1.65882i	0.558641	+	0.829410i	$0.311323\pi$
$37$			10.0902i			1.65882i	−0.558641	+	0.829410i	$0.688677\pi$
$38$	1.54737	−	0.692973i	0.251016	−	0.112415i
$39$	−0.823715	−	2.74976i	−0.131900	−	0.440314i
$40$	−7.33661	−	8.04189i	−1.16002	−	1.27153i
$41$	−2.82225	+	4.88829i	−0.440762	+	0.763422i	−0.997746	−	0.0671011i	$-0.978625\pi$
$41$	−2.82225	+	4.88829i	−0.440762	+	0.763422i	0.556984	+	0.830523i	$0.311958\pi$
$42$	−2.40610	+	0.459022i	−0.371269	+	0.0708287i
$43$	−2.12338	+	1.22593i	−0.323812	+	0.186953i	−0.653090	−	0.757280i	$-0.726528\pi$
$43$	−2.12338	+	1.22593i	−0.323812	+	0.186953i	0.329279	+	0.944233i	$0.393195\pi$
$44$	0.834285	−	4.01078i	0.125773	−	0.604648i
$45$	5.17844	−	10.3196i	0.771957	−	1.53835i
$46$	−3.31858	−	0.341495i	−0.489298	−	0.0503507i
$47$	4.74140	+	8.21234i	0.691604	+	1.19789i	0.971312	+	0.237808i	$0.0764289\pi$
$47$	4.74140	+	8.21234i	0.691604	+	1.19789i	−0.279708	+	0.960085i	$0.590238\pi$
$48$	−4.15258	+	5.54582i	−0.599373	+	0.800470i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	8.13199	−	11.2441i	1.15004	−	1.59016i
$51$	6.57042	+	6.19684i	0.920043	+	0.867730i
$52$	−3.14783	+	1.03797i	−0.436526	+	0.143940i
$53$			12.1286i			1.66600i	0.553277	+	0.832998i	$0.313377\pi$
$53$			12.1286i			1.66600i	−0.553277	+	0.832998i	$0.686623\pi$
$54$	−7.06918	−	2.00665i	−0.961994	−	0.273070i
$55$	7.88328			1.06298
$56$	0.606118	+	2.76272i	0.0809959	+	0.369184i
$57$	1.42473	−	1.51062i	0.188710	−	0.200087i
$58$	−9.52266	−	6.88700i	−1.25039	−	0.904307i
$59$	−2.55889	−	1.47738i	−0.333139	−	0.192338i	0.324095	−	0.946025i	$-0.394940\pi$
$59$	−2.55889	−	1.47738i	−0.333139	−	0.192338i	−0.657234	+	0.753687i	$0.728274\pi$
$60$	−12.0757	−	5.65012i	−1.55897	−	0.729427i
$61$	−7.70228	+	4.44691i	−0.986176	+	0.569369i	−0.904129	−	0.427259i	$-0.859479\pi$
$61$	−7.70228	+	4.44691i	−0.986176	+	0.569369i	−0.0820471	+	0.996628i	$0.526146\pi$
$62$	−13.3675	−	1.37557i	−1.69768	−	0.174698i
$63$	−2.50592	+	1.64935i	−0.315716	+	0.207799i
$64$	6.53300	+	4.61735i	0.816625	+	0.577169i
$65$	−3.18915	−	5.52376i	−0.395565	−	0.685138i
$66$	−0.940223	−	4.92845i	−0.115733	−	0.606650i
$67$	1.50841	+	0.870878i	0.184281	+	0.106395i	0.589303	−	0.807912i	$-0.299403\pi$
$67$	1.50841	+	0.870878i	0.184281	+	0.106395i	−0.405021	+	0.914307i	$0.632736\pi$
$68$	6.94448	−	7.78048i	0.842142	−	0.943522i
$69$	−3.91404	+	1.17249i	−0.471195	+	0.141151i
$70$	−4.96745	+	2.22462i	−0.593723	+	0.265893i
$71$	10.2121			1.21196			0.605978	−	0.795482i	$-0.292782\pi$
$71$	10.2121			1.21196			0.605978	+	0.795482i	$0.292782\pi$
$72$	−2.09208	+	8.22333i	−0.246554	+	0.969129i
$73$	−4.65608			−0.544952			−0.272476	−	0.962163i	$-0.587843\pi$
$73$	−4.65608			−0.544952			−0.272476	+	0.962163i	$0.587843\pi$
$74$	13.0234	−	5.83238i	1.51393	−	0.678000i
$75$	3.91666	−	16.5378i	0.452257	−	1.90962i
$76$	−1.78883	−	1.59662i	−0.205193	−	0.183145i
$77$	−1.77389	−	1.02416i	−0.202154	−	0.116714i
$78$	−3.07297	+	2.65259i	−0.347945	+	0.300346i
$79$	−1.98064	−	3.43056i	−0.222839	−	0.385969i	0.732830	−	0.680412i	$-0.238199\pi$
$79$	−1.98064	−	3.43056i	−0.222839	−	0.385969i	−0.955669	+	0.294443i	$0.904866\pi$
$80$	−6.13888	+	14.1177i	−0.686348	+	1.57841i
$81$	−8.93846	+	1.05071i	−0.993162	+	0.116746i
$82$	7.94061	+	0.817119i	0.876893	+	0.0902357i
$83$	−1.53730	+	0.887558i	−0.168740	+	0.0974222i	−0.581992	−	0.813195i	$-0.697726\pi$
$83$	−1.53730	+	0.887558i	−0.168740	+	0.0974222i	0.413251	+	0.910617i	$0.364393\pi$
$84$	1.98324	+	2.84021i	0.216389	+	0.309892i
$85$	17.3800	+	10.0343i	1.88512	+	1.08837i
$86$	2.80966	+	2.03201i	0.302974	+	0.219117i
$87$	−14.0059	−	3.31703i	−1.50159	−	0.355623i
$88$	−5.65893	+	1.24152i	−0.603243	+	0.132347i
$89$	1.13851			0.120681			0.0603407	−	0.998178i	$-0.480781\pi$
$89$	1.13851			0.120681			0.0603407	+	0.998178i	$0.480781\pi$
$90$	−16.3127	−	0.718822i	−1.71951	−	0.0757705i
$91$			1.65727i			0.173730i
$92$	1.47745	+	4.48066i	0.154035	+	0.467142i
$93$	−15.7661	+	4.72288i	−1.63487	+	0.489740i
$94$	7.85897	−	10.8666i	0.810591	−	1.12081i
$95$	2.30702	−	3.99587i	0.236695	−	0.409968i
$96$	9.55824	+	2.15410i	0.975533	+	0.219851i
$97$	6.52591	+	11.3032i	0.662606	+	1.14767i	0.979928	+	0.199350i	$0.0638830\pi$
$97$	6.52591	+	11.3032i	0.662606	+	1.14767i	−0.317322	+	0.948318i	$0.602784\pi$
$98$	1.40678	+	0.144764i	0.142107	+	0.0146233i
$99$	−3.37839	−	5.13292i	−0.339541	−	0.515878i
$100$	−19.2132	−	3.99654i	−1.92132	−	0.399654i
$101$	2.49314	−	1.43941i	0.248077	−	0.143227i	−0.370807	−	0.928710i	$-0.620919\pi$
$101$	2.49314	−	1.43941i	0.248077	−	0.143227i	0.618883	+	0.785483i	$0.287585\pi$
$102$	4.20035	−	12.0623i	0.415897	−	1.19435i
$103$	0.937780	−	1.62428i	0.0924022	−	0.160045i	−0.816119	−	0.577884i	$-0.803879\pi$
$103$	0.937780	−	1.62428i	0.0924022	−	0.160045i	0.908521	+	0.417838i	$0.137212\pi$
$104$	3.15922	+	3.46292i	0.309787	+	0.339567i
$105$	−4.57375	+	4.84948i	−0.446352	+	0.473261i
$106$	15.6543	−	7.01063i	1.52048	−	0.680933i
$107$			3.90128i			0.377151i	0.982059	+	0.188575i	$0.0603870\pi$
$107$			3.90128i			0.377151i	−0.982059	+	0.188575i	$0.939613\pi$
$108$	1.49619	+	10.2840i	0.143971	+	0.989582i
$109$		−	0.844464i		−	0.0808850i	−0.999182	−	0.0404425i	$-0.987123\pi$
$109$		−	0.844464i		−	0.0808850i	0.999182	−	0.0404425i	$-0.0128768\pi$
$110$	−4.55672	−	10.1749i	−0.434467	−	0.970139i
$111$	11.9912	−	12.7141i	1.13815	−	1.20677i
$112$	3.21547	−	2.37923i	0.303834	−	0.224816i
$113$	−9.32391	+	16.1495i	−0.877120	+	1.51922i	−0.0226327	+	0.999744i	$0.507205\pi$
$113$	−9.32391	+	16.1495i	−0.877120	+	1.51922i	−0.854487	+	0.519472i	$0.826128\pi$
$114$	−2.77328	−	0.965715i	−0.259741	−	0.0904475i
$115$	−7.86259	+	4.53947i	−0.733191	+	0.423308i
$116$	−3.38468	+	16.2717i	−0.314260	+	1.51079i
$117$	−2.22989	+	4.44372i	−0.206153	+	0.410822i
$118$	−0.427740	+	4.15670i	−0.0393767	+	0.382655i
$119$	−2.60722	−	4.51584i	−0.239004	−	0.413966i
$120$	−0.312525	+	18.8519i	−0.0285295	+	1.72094i
$121$	−3.40220	+	5.89278i	−0.309291	+	0.535707i
$122$	10.1917	+	7.37086i	0.922713	+	0.667326i
$123$	9.36539	−	2.80549i	0.844449	−	0.252963i
$124$	5.95131	+	18.0485i	0.534444	+	1.62080i
$125$		−	18.5206i		−	1.65654i
$126$	3.57729	+	2.28101i	0.318690	+	0.203209i
$127$	−14.1946			−1.25957			−0.629783	−	0.776771i	$-0.716856\pi$
$127$	−14.1946			−1.25957			−0.629783	+	0.776771i	$0.716856\pi$
$128$	2.18336	−	11.1010i	0.192983	−	0.981202i
$129$	4.13244	+	0.978690i	0.363841	+	0.0861688i
$130$	−5.28608	+	7.30907i	−0.463620	+	0.641048i
$131$	12.4309	+	7.17699i	1.08609	+	0.627056i	0.932534	−	0.361083i	$-0.117593\pi$
$131$	12.4309	+	7.17699i	1.08609	+	0.627056i	0.153560	+	0.988139i	$0.450926\pi$
$132$	−5.81764	+	4.06230i	−0.506361	+	0.353578i
$133$	−1.03825	+	0.599433i	−0.0900276	+	0.0519774i
$134$	0.252143	−	2.45028i	0.0217818	−	0.211672i
$135$	−18.7888	+	6.84906i	−1.61709	+	0.589474i
$136$	−14.0563	−	4.46589i	−1.20532	−	0.382947i
$137$	2.23009	+	3.86262i	0.190529	+	0.330006i	0.945426	−	0.325838i	$-0.105646\pi$
$137$	2.23009	+	3.86262i	0.190529	+	0.330006i	−0.754897	+	0.655844i	$0.772313\pi$
$138$	3.77573	+	4.37410i	0.321411	+	0.372348i
$139$	−4.08523	−	2.35861i	−0.346505	−	0.200055i	0.316640	−	0.948546i	$-0.397445\pi$
$139$	−4.08523	−	2.35861i	−0.346505	−	0.200055i	−0.663145	+	0.748491i	$0.730779\pi$
$140$	5.74260	+	5.12557i	0.485338	+	0.433189i
$141$	3.78517	−	15.9826i	0.318769	−	1.34598i
$142$	−5.90284	−	13.1807i	−0.495356	−	1.10610i
$143$	−3.39462			−0.283873
$144$	11.8231	−	2.05305i	0.985256	−	0.171087i
$145$	−31.9824			−2.65599
$146$	2.69132	+	6.00956i	0.222735	+	0.497355i
$147$	1.65920	−	0.497030i	0.136849	−	0.0409944i
$148$	−15.0556	−	13.4379i	−1.23756	−	1.10459i
$149$	−10.4666	−	6.04287i	−0.857454	−	0.495052i	0.00570463	−	0.999984i	$-0.498184\pi$
$149$	−10.4666	−	6.04287i	−0.857454	−	0.495052i	−0.863159	+	0.504932i	$0.831517\pi$
$150$	−23.6091	+	4.50403i	−1.92768	+	0.367752i
$151$	1.05674	+	1.83032i	0.0859960	+	0.148949i	0.905815	−	0.423673i	$-0.139259\pi$
$151$	1.05674	+	1.83032i	0.0859960	+	0.148949i	−0.819819	+	0.572622i	$0.805926\pi$
$152$	−1.02677	+	3.23172i	−0.0832816	+	0.262127i
$153$	−0.914710	−	15.6166i	−0.0739499	−	1.26252i
$154$	−0.296522	+	2.88154i	−0.0238944	+	0.232201i
$155$	−31.6712	+	18.2854i	−2.54389	+	1.46872i
$156$	5.19992	+	2.43300i	0.416327	+	0.194796i
$157$	12.3714	+	7.14261i	0.987342	+	0.570042i	0.904479	−	0.426519i	$-0.140260\pi$
$157$	12.3714	+	7.14261i	0.987342	+	0.570042i	0.0828632	+	0.996561i	$0.473594\pi$
$158$	−3.28295	+	4.53934i	−0.261178	+	0.361131i
$159$	14.4136	−	15.2826i	1.14308	−	1.21199i
$160$	21.7700	−	0.236956i	1.72107	−	0.0187330i
$161$	2.35898			0.185914
$162$	6.52278	+	10.9295i	0.512478	+	0.858700i
$163$			0.598199i			0.0468546i	0.999726	+	0.0234273i	$0.00745782\pi$
$163$			0.598199i			0.0468546i	−0.999726	+	0.0234273i	$0.992542\pi$
$164$	−3.53521	−	10.7212i	−0.276053	−	0.837185i
$165$	−9.93328	−	9.36848i	−0.773305	−	0.729335i
$166$	2.03416	+	1.47115i	0.157881	+	0.114183i
$167$	3.15942	−	5.47227i	0.244483	−	0.423457i	−0.717503	−	0.696555i	$-0.754715\pi$
$167$	3.15942	−	5.47227i	0.244483	−	0.423457i	0.961986	+	0.273098i	$0.0880484\pi$
$168$	2.51948	−	4.20146i	0.194382	−	0.324149i
$169$	−5.12672	−	8.87974i	−0.394363	−	0.683057i
$170$	2.90521	−	28.2323i	0.222819	−	2.16532i
$171$	−3.59045	+	0.210303i	−0.274568	+	0.0160823i
$172$	0.998650	−	4.80096i	0.0761464	−	0.366070i
$173$	5.43071	−	3.13542i	0.412889	−	0.238382i	−0.279141	−	0.960250i	$-0.590050\pi$
$173$	5.43071	−	3.13542i	0.412889	−	0.238382i	0.692030	+	0.721868i	$0.256716\pi$
$174$	3.81447	+	19.9946i	0.289174	+	1.51579i
$175$	−4.90611	+	8.49763i	−0.370867	+	0.642361i
$176$	4.87341	+	6.58631i	0.367347	+	0.496462i
$177$	1.46860	+	4.90254i	0.110387	+	0.368497i
$178$	−0.658084	−	1.46946i	−0.0493255	−	0.110141i
$179$			13.2058i			0.987049i	0.869732	+	0.493525i	$0.164292\pi$
$179$			13.2058i			0.987049i	−0.869732	+	0.493525i	$0.835708\pi$
$180$	8.50133	+	21.4702i	0.633652	+	1.60029i
$181$			14.8950i			1.10714i	0.832804	+	0.553568i	$0.186734\pi$
$181$			14.8950i			1.10714i	−0.832804	+	0.553568i	$0.813266\pi$
$182$	2.13903	−	0.957943i	0.158556	−	0.0710075i
$183$	14.9899	+	3.55007i	1.10809	+	0.262429i
$184$	4.92916	−	4.49687i	0.363383	−	0.331514i
$185$	19.4169	−	33.6311i	1.42756	−	2.47261i
$186$	15.2090	+	17.6192i	1.11517	+	1.29191i
$187$	9.24987	−	5.34041i	0.676417	−	0.390530i
$188$	−18.5681	−	3.86237i	−1.35422	−	0.281692i
$189$	5.11766	+	0.899780i	0.372255	+	0.0654494i
$190$	−6.49095	−	0.667944i	−0.470903	−	0.0484578i
$191$	−0.908708	−	1.57393i	−0.0657518	−	0.113886i	0.831275	−	0.555861i	$-0.187611\pi$
$191$	−0.908708	−	1.57393i	−0.0657518	−	0.113886i	−0.897027	+	0.441975i	$0.854278\pi$
$192$	−2.74461	−	13.5819i	−0.198075	−	0.980187i
$193$	11.9069	−	20.6234i	0.857078	−	1.48450i	−0.0176257	−	0.999845i	$-0.505611\pi$
$193$	11.9069	−	20.6234i	0.857078	−	1.48450i	0.874704	−	0.484658i	$-0.161056\pi$
$194$	10.8169	−	14.9565i	0.776605	−	1.07381i
$195$	−2.54597	+	10.7502i	−0.182321	+	0.769835i
$196$	−0.626309	−	1.89940i	−0.0447364	−	0.135672i
$197$		−	5.84611i		−	0.416518i	−0.978074	−	0.208259i	$-0.933220\pi$
$197$		−	5.84611i		−	0.416518i	0.978074	−	0.208259i	$-0.0667797\pi$
$198$	−4.67224	+	7.32742i	−0.332041	+	0.520737i
$199$	18.5427			1.31446			0.657230	−	0.753690i	$-0.271728\pi$
$199$	18.5427			1.31446			0.657230	+	0.753690i	$0.271728\pi$
$200$	5.94736	+	27.1084i	0.420542	+	1.91685i
$201$	−0.865706	−	2.88993i	−0.0610622	−	0.203840i
$202$	−3.29894	−	2.38586i	−0.232112	−	0.167869i
$203$	7.19666	+	4.15499i	0.505107	+	0.291623i
$204$	−17.9967	+	1.55093i	−1.26002	+	0.108587i
$205$	18.8134	−	10.8619i	1.31398	−	0.758628i
$206$	−2.63851	−	0.271513i	−0.183834	−	0.0189172i
$207$	6.32524	+	3.17405i	0.439635	+	0.220612i
$208$	2.64346	−	6.07923i	0.183291	−	0.421519i
$209$	−1.22783	−	2.12666i	−0.0849307	−	0.147104i
$210$	8.90293	+	3.10019i	0.614361	+	0.213933i
$211$	11.5780	+	6.68455i	0.797061	+	0.460183i	0.842442	−	0.538786i	$-0.181117\pi$
$211$	11.5780	+	6.68455i	0.797061	+	0.460183i	−0.0453815	+	0.998970i	$0.514450\pi$
$212$	−18.0971	−	16.1526i	−1.24292	−	1.10937i
$213$	−12.8677	−	12.1361i	−0.881681	−	0.831549i
$214$	5.03536	−	2.25503i	0.344210	−	0.154151i
$215$	9.43640			0.643557
$216$	12.4087	−	7.87553i	0.844305	−	0.535862i
$217$	9.50220			0.645051
$218$	−1.08994	+	0.488120i	−0.0738203	+	0.0330596i
$219$	5.86686	+	5.53327i	0.396445	+	0.373904i
$220$	−10.4988	+	11.7627i	−0.707828	+	0.793039i
$221$	−7.48398	−	4.32088i	−0.503427	−	0.290654i
$222$	−23.3412	−	8.12789i	−1.56656	−	0.545509i
$223$	−6.73709	−	11.6690i	−0.451149	−	0.781412i	0.547309	−	0.836931i	$-0.315652\pi$
$223$	−6.73709	−	11.6690i	−0.451149	−	0.781412i	−0.998458	+	0.0555182i	$0.982319\pi$
$224$	−4.92947	−	2.77494i	−0.329364	−	0.185408i
$225$	−24.5887	+	16.1838i	−1.63924	+	1.07892i
$226$	26.2335	+	2.69953i	1.74502	+	0.179570i
$227$	−23.3643	+	13.4894i	−1.55075	+	0.895324i	−0.552665	+	0.833403i	$0.686389\pi$
$227$	−23.3643	+	13.4894i	−1.55075	+	0.895324i	−0.998081	+	0.0619204i	$0.980277\pi$
$228$	0.356579	+	4.13766i	0.0236150	+	0.274023i
$229$	−11.1218	−	6.42118i	−0.734950	−	0.424323i	0.0852806	−	0.996357i	$-0.472821\pi$
$229$	−11.1218	−	6.42118i	−0.734950	−	0.424323i	−0.820230	+	0.572034i	$0.806155\pi$
$230$	10.4038	+	7.52427i	0.686008	+	0.496136i
$231$	1.01808	+	3.39858i	0.0669845	+	0.223610i
$232$	22.9582	−	5.03683i	1.50728	−	0.330684i
$233$	−3.15348			−0.206592			−0.103296	−	0.994651i	$-0.532939\pi$
$233$	−3.15348			−0.206592			−0.103296	+	0.994651i	$0.532939\pi$
$234$	7.02440	+	0.309532i	0.459199	+	0.0202347i
$235$		−	36.4961i		−	2.38074i
$236$	5.61227	−	1.85059i	0.365328	−	0.120463i
$237$	−1.58119	+	6.67645i	−0.102709	+	0.433682i
$238$	−4.32153	+	5.97538i	−0.280123	+	0.387327i
$239$	−9.63649	+	16.6909i	−0.623333	+	1.07964i	0.365528	+	0.930800i	$0.380888\pi$
$239$	−9.63649	+	16.6909i	−0.623333	+	1.07964i	−0.988861	+	0.148843i	$0.952445\pi$
$240$	24.5127	−	10.4935i	1.58229	−	0.677352i
$241$	1.24909	+	2.16349i	0.0804612	+	0.139363i	0.903448	−	0.428697i	$-0.141027\pi$
$241$	1.24909	+	2.16349i	0.0804612	+	0.139363i	−0.822987	+	0.568060i	$0.807694\pi$
$242$	9.57232	+	0.985029i	0.615332	+	0.0633201i
$243$	12.5115	+	9.29851i	0.802613	+	0.596500i
$244$	3.62248	−	17.4149i	0.231905	−	1.11487i
$245$	3.33304	−	1.92433i	0.212940	−	0.122941i
$246$	−9.03444	−	10.4662i	−0.576015	−	0.667301i
$247$	−0.993425	+	1.72066i	−0.0632101	+	0.109483i
$248$	19.8551	−	18.1138i	1.26080	−	1.15023i
$249$	2.99183	+	0.708558i	0.189600	+	0.0449031i
$250$	−23.9044	+	10.7054i	−1.51185	+	0.677066i
$251$		−	8.49633i		−	0.536284i	−0.963379	−	0.268142i	$-0.913590\pi$
$251$		−	8.49633i		−	0.536284i	0.963379	−	0.268142i	$-0.0864096\pi$
$252$	0.876332	−	5.93566i	0.0552037	−	0.373911i
$253$			4.83195i			0.303782i
$254$	8.20480	+	18.3209i	0.514815	+	1.14955i
$255$	−9.97472	−	33.2980i	−0.624641	−	2.08520i
$256$	−15.5901	+	3.59861i	−0.974379	+	0.224913i
$257$	−14.8930	+	25.7954i	−0.928998	+	1.60907i	−0.143995	+	0.989578i	$0.545995\pi$
$257$	−14.8930	+	25.7954i	−0.928998	+	1.60907i	−0.785002	+	0.619493i	$0.787338\pi$
$258$	−1.12546	−	5.89942i	−0.0700681	−	0.367282i
$259$	−8.73838	+	5.04510i	−0.542976	+	0.313487i
$260$	12.4893	+	2.59789i	0.774550	+	0.161115i
$261$	13.7061	+	20.8242i	0.848385	+	1.28898i
$262$	2.07793	−	20.1930i	0.128375	−	1.24753i
$263$	−15.6078	−	27.0335i	−0.962418	−	1.66696i	−0.716398	−	0.697692i	$-0.754210\pi$
$263$	−15.6078	−	27.0335i	−0.962418	−	1.66696i	−0.246020	−	0.969265i	$-0.579123\pi$
$264$	8.60591	+	5.16069i	0.529657	+	0.317618i
$265$	23.3395	−	40.4252i	1.43373	−	2.48330i
$266$	1.37382	+	0.993574i	0.0842341	+	0.0609199i
$267$	−1.43457	−	1.35300i	−0.0877941	−	0.0828022i
$268$	−3.30830	+	1.09088i	−0.202087	+	0.0666360i
$269$		−	8.58738i		−	0.523582i	−0.965125	−	0.261791i	$-0.915687\pi$
$269$		−	8.58738i		−	0.523582i	0.965125	−	0.261791i	$-0.0843131\pi$
$270$	19.7004	+	20.2917i	1.19893	+	1.23491i
$271$	−1.21679			−0.0739145			−0.0369573	−	0.999317i	$-0.511767\pi$
$271$	−1.21679			−0.0739145			−0.0369573	+	0.999317i	$0.511767\pi$
$272$	2.36076	+	20.7237i	0.143142	+	1.25656i
$273$	1.96950	−	2.08824i	0.119200	−	0.126386i
$274$	3.69642	−	5.11104i	0.223309	−	0.308769i
$275$	−17.4058	−	10.0493i	−1.04961	−	0.605994i
$276$	3.46316	−	7.40164i	0.208458	−	0.445526i
$277$	6.63440	−	3.83037i	0.398622	−	0.230145i	−0.287267	−	0.957851i	$-0.592747\pi$
$277$	6.63440	−	3.83037i	0.398622	−	0.230145i	0.685889	+	0.727706i	$0.259413\pi$
$278$	−0.682881	+	6.63611i	−0.0409565	+	0.398007i
$279$	25.4786	+	12.7854i	1.52537	+	0.765440i
$280$	3.29618	−	10.3746i	0.196984	−	0.620003i
$281$	8.84076	+	15.3126i	0.527396	+	0.913476i	0.999490	+	0.0319281i	$0.0101648\pi$
$281$	8.84076	+	15.3126i	0.527396	+	0.913476i	−0.472095	+	0.881548i	$0.656502\pi$
$282$	−22.8165	+	4.35281i	−1.35870	+	0.259206i
$283$	−15.1849	−	8.76702i	−0.902650	−	0.521145i	−0.0245907	−	0.999698i	$-0.507828\pi$
$283$	−15.1849	−	8.76702i	−0.902650	−	0.521145i	−0.878059	+	0.478553i	$0.841162\pi$
$284$	−13.6003	+	15.2375i	−0.807028	+	0.904180i
$285$	−7.65563	+	2.29332i	−0.453480	+	0.135844i
$286$	1.96217	+	4.38142i	0.116026	+	0.259079i
$287$	−5.64451			−0.333185
$288$	−9.48387	−	14.0732i	−0.558842	−	0.829274i
$289$	10.1904			0.599436
$290$	18.4866	+	41.2794i	1.08557	+	2.42401i
$291$	5.20979	−	21.9979i	0.305403	−	1.28954i
$292$	6.20086	−	6.94734i	0.362878	−	0.406562i
$293$	−10.4318	−	6.02281i	−0.609433	−	0.351856i	0.163311	−	0.986575i	$-0.447783\pi$
$293$	−10.4318	−	6.02281i	−0.609433	−	0.351856i	−0.772743	+	0.634718i	$0.781116\pi$
$294$	−1.60057	−	1.85423i	−0.0933473	−	0.108141i
$295$	5.68592	+	9.84831i	0.331047	+	0.573391i
$296$	−8.64172	+	27.1996i	−0.502290	+	1.58095i
$297$	−1.84304	+	10.4826i	−0.106944	+	0.608261i
$298$	−1.74958	+	17.0020i	−0.101350	+	0.984902i
$299$	3.38571	−	1.95474i	0.195801	−	0.113046i
$300$	19.4600	+	27.8687i	1.12352	+	1.60900i
$301$	−2.12338	−	1.22593i	−0.122389	−	0.0706615i
$302$	1.75156	−	2.42189i	0.100791	−	0.139364i
$303$	−4.85206	−	1.14912i	−0.278744	−	0.0660151i
$304$	4.76465	−	0.542770i	0.273271	−	0.0311300i
$305$	34.2294			1.95997
$306$	−19.6275	+	10.2073i	−1.12203	+	0.583515i
$307$			28.2333i			1.61136i	0.592350	+	0.805681i	$0.298200\pi$
$307$			28.2333i			1.61136i	−0.592350	+	0.805681i	$0.701800\pi$
$308$	3.89058	−	1.28288i	0.221686	−	0.0730988i
$309$	−3.11194	+	0.932210i	−0.177032	+	0.0530316i
$310$	41.9075	+	30.3084i	2.38019	+	1.72140i
$311$	−7.57153	+	13.1143i	−0.429342	+	0.743643i	−0.996815	−	0.0797496i	$-0.974588\pi$
$311$	−7.57153	+	13.1143i	−0.429342	+	0.743643i	0.567473	+	0.823392i	$0.307921\pi$
$312$	0.134576	−	8.11784i	0.00761889	−	0.459582i
$313$	−4.98989	−	8.64275i	−0.282045	−	0.488517i	0.689843	−	0.723959i	$-0.257680\pi$
$313$	−4.98989	−	8.64275i	−0.282045	−	0.488517i	−0.971888	+	0.235442i	$0.924346\pi$
$314$	2.06798	−	20.0962i	0.116703	−	1.13410i
$315$	11.5262	−	0.675127i	0.649430	−	0.0380391i
$316$	7.75652	+	1.61344i	0.436338	+	0.0907629i
$317$	−10.5261	+	6.07726i	−0.591206	+	0.341333i	−0.765574	−	0.643347i	$-0.777545\pi$
$317$	−10.5261	+	6.07726i	−0.591206	+	0.341333i	0.174368	+	0.984681i	$0.444212\pi$
$318$	−28.0566	−	9.76989i	−1.57333	−	0.547868i
$319$	−8.51074	+	14.7410i	−0.476510	+	0.825340i
$320$	−12.8894	−	27.9615i	−0.720541	−	1.56309i
$321$	4.63627	−	4.91578i	0.258772	−	0.274372i
$322$	−1.36355	−	3.04472i	−0.0759876	−	0.169676i
$323$		−	6.25142i		−	0.347838i
$324$	10.3363	−	14.7364i	0.574237	−	0.818689i
$325$			16.2615i			0.902028i
$326$	0.772091	−	0.345773i	0.0427622	−	0.0191506i
$327$	−1.00356	+	1.06406i	−0.0554970	+	0.0588427i
$328$	−11.7943	+	10.7600i	−0.651234	+	0.594120i
$329$	−4.74140	+	8.21234i	−0.261402	+	0.452761i
$330$	−6.35017	+	18.2360i	−0.349565	+	1.00386i
$331$	18.0500	−	10.4212i	0.992120	−	0.572801i	0.0862127	−	0.996277i	$-0.472524\pi$
$331$	18.0500	−	10.4212i	0.992120	−	0.572801i	0.905907	+	0.423476i	$0.139190\pi$
$332$	0.723009	−	3.47583i	0.0396803	−	0.190761i
$333$	−30.2188	+	1.77001i	−1.65598	+	0.0969959i
$334$	−8.88924	−	0.914737i	−0.486398	−	0.0500522i
$335$	−3.35172	−	5.80535i	−0.183124	−	0.317180i
$336$	−6.87911	−	0.823332i	−0.375286	−	0.0449165i
$337$	5.73844	−	9.93927i	0.312593	−	0.541426i	−0.666330	−	0.745657i	$-0.732136\pi$
$337$	5.73844	−	9.93927i	0.312593	−	0.541426i	0.978923	+	0.204230i	$0.0654692\pi$
$338$	−8.49766	+	11.7497i	−0.462212	+	0.639101i
$339$	30.9406	−	9.26854i	1.68046	−	0.503398i
$340$	−38.1185	+	12.5692i	−2.06726	+	0.681659i
$341$			19.4635i			1.05401i
$342$	2.34680	+	4.51260i	0.126900	+	0.244014i
$343$	−1.00000			−0.0539949
$344$	−6.77381	+	1.48612i	−0.365220	+	0.0801261i
$345$	15.3019	+	3.62396i	0.823827	+	0.195108i
$346$	−7.18595	−	5.19704i	−0.386319	−	0.279394i
$347$	18.5823	+	10.7285i	0.997551	+	0.575936i	0.907523	−	0.420003i	$-0.137971\pi$
$347$	18.5823	+	10.7285i	0.997551	+	0.575936i	0.0900281	+	0.995939i	$0.471304\pi$
$348$	23.6021	−	16.4807i	1.26520	−	0.883457i
$349$	16.1478	−	9.32291i	0.864369	−	0.499044i	−0.00110371	−	0.999999i	$-0.500351\pi$
$349$	16.1478	−	9.32291i	0.864369	−	0.499044i	0.865473	+	0.500956i	$0.167018\pi$
$350$	13.8037	+	1.42045i	0.737838	+	0.0759264i
$351$	8.09066	−	2.94928i	0.431848	−	0.157421i
$352$	5.68396	−	10.0971i	0.302956	−	0.538178i
$353$	−10.7552	−	18.6286i	−0.572442	−	0.991499i	−0.996314	−	0.0857768i	$-0.972663\pi$
$353$	−10.7552	−	18.6286i	−0.572442	−	0.991499i	0.423872	−	0.905722i	$-0.360671\pi$
$354$	5.47879	−	4.72930i	0.291194	−	0.251359i
$355$	−34.0374	−	19.6515i	−1.80652	−	1.04299i
$356$	−1.51624	+	1.69877i	−0.0803605	+	0.0900345i
$357$	−2.08140	+	8.78857i	−0.110160	+	0.465141i
$358$	17.0447	−	7.63327i	0.900838	−	0.403431i
$359$	−22.0752			−1.16508			−0.582542	−	0.812801i	$-0.697942\pi$
$359$	−22.0752			−1.16508			−0.582542	+	0.812801i	$0.697942\pi$
$360$	22.7974	−	23.3829i	1.20153	−	1.23238i
$361$	17.5627			0.924354
$362$	19.2249	−	8.60966i	1.01044	−	0.452514i
$363$	11.2899	−	3.38199i	0.592566	−	0.177509i
$364$	−2.47282	−	2.20712i	−0.129611	−	0.115685i
$365$	15.5189	+	8.95984i	0.812296	+	0.468979i
$366$	−4.08247	−	21.3994i	−0.213394	−	1.11856i
$367$	−1.68176	−	2.91289i	−0.0877870	−	0.152052i	0.818788	−	0.574095i	$-0.194646\pi$
$367$	−1.68176	−	2.91289i	−0.0877870	−	0.152052i	−0.906575	+	0.422044i	$0.861313\pi$
$368$	−8.65325	−	3.76274i	−0.451082	−	0.196146i
$369$	−15.1348	−	7.59478i	−0.787888	−	0.395368i
$370$	−54.6308	−	5.62172i	−2.84012	−	0.292260i
$371$	−10.5037	+	6.06431i	−0.545325	+	0.314844i
$372$	13.9499	−	29.8144i	0.723269	−	1.54581i
$373$	7.51928	+	4.34126i	0.389334	+	0.224782i	0.681871	−	0.731472i	$-0.261166\pi$
$373$	7.51928	+	4.34126i	0.389334	+	0.224782i	−0.292538	+	0.956254i	$0.594500\pi$
$374$	−12.2395	−	8.85186i	−0.632888	−	0.457719i
$375$	−22.0099	+	23.3368i	−1.13659	+	1.20511i
$376$	5.74769	+	26.1983i	0.296414	+	1.35107i
$377$	13.7719			0.709290
$378$	−1.79678	−	7.12542i	−0.0924166	−	0.366492i
$379$		−	28.2348i		−	1.45032i	−0.688578	−	0.725162i	$-0.741765\pi$
$379$		−	28.2348i		−	1.45032i	0.688578	−	0.725162i	$-0.258235\pi$
$380$	2.88981	+	8.76392i	0.148244	+	0.449579i
$381$	17.8858	+	16.8688i	0.916317	+	0.864216i
$382$	−1.50620	+	2.08263i	−0.0770641	+	0.106557i
$383$	−11.4527	+	19.8367i	−0.585207	+	1.01361i	0.409642	+	0.912246i	$0.365653\pi$
$383$	−11.4527	+	19.8367i	−0.585207	+	1.01361i	−0.994850	+	0.101362i	$0.967680\pi$
$384$	−15.9436	+	11.3931i	−0.813617	+	0.581401i
$385$	3.94164	+	6.82712i	0.200885	+	0.347942i
$386$	−33.5009	−	3.44737i	−1.70515	−	0.175467i
$387$	−4.04398	−	6.14418i	−0.205567	−	0.312326i
$388$	−25.5566	−	5.31604i	−1.29744	−	0.269881i
$389$	23.4259	−	13.5250i	1.18774	−	0.685743i	0.229948	−	0.973203i	$-0.426144\pi$
$389$	23.4259	−	13.5250i	1.18774	−	0.685743i	0.957793	+	0.287460i	$0.0928109\pi$
$390$	15.3468	−	2.92778i	0.777115	−	0.148254i
$391$	−6.15039	+	10.6528i	−0.311039	+	0.538735i
$392$	−2.08953	+	1.90627i	−0.105537	+	0.0962813i
$393$	−7.13436	−	23.8162i	−0.359881	−	1.20137i
$394$	−7.54553	+	3.37919i	−0.380139	+	0.170241i
$395$			15.2456i			0.767090i
$396$	12.1581	+	1.79501i	0.610968	+	0.0902024i
$397$			21.6189i			1.08502i	0.840048	+	0.542512i	$0.182527\pi$
$397$			21.6189i			1.08502i	−0.840048	+	0.542512i	$0.817473\pi$
$398$	−10.7181	−	23.9330i	−0.537252	−	1.19965i
$399$	2.02060	+	0.478541i	0.101157	+	0.0239570i
$400$	31.5509	−	23.3455i	1.57755	−	1.16728i
$401$	−1.97812	+	3.42620i	−0.0987826	+	0.171096i	−0.911181	−	0.412006i	$-0.864828\pi$
$401$	−1.97812	+	3.42620i	−0.0987826	+	0.171096i	0.812398	+	0.583103i	$0.198162\pi$
$402$	−3.22962	+	2.78781i	−0.161079	+	0.139043i
$403$	13.6379	−	7.87387i	0.679354	−	0.392225i
$404$	−1.17255	+	5.63700i	−0.0583368	+	0.280451i
$405$	31.8142	+	13.6985i	1.58086	+	0.680684i
$406$	1.20298	−	11.6904i	0.0597031	−	0.580183i
$407$	−10.3340	−	17.8990i	−0.512236	−	0.887219i
$408$	12.4043	+	22.3317i	0.614103	+	1.10558i
$409$	−10.2220	+	17.7050i	−0.505445	+	0.875457i	0.494535	+	0.869158i	$0.335338\pi$
$409$	−10.2220	+	17.7050i	−0.505445	+	0.875457i	−0.999980	+	0.00629932i	$0.997995\pi$
$410$	−24.8940	−	18.0039i	−1.22942	−	0.889147i
$411$	1.78033	−	7.51730i	0.0878172	−	0.370801i
$412$	1.17468	+	3.56245i	0.0578724	+	0.175509i
$413$		−	2.95475i		−	0.145394i
$414$	0.440592	−	9.99862i	0.0216539	−	0.491405i
$415$	6.83183			0.335361
$416$	−9.37440	+	0.102035i	−0.459618	+	0.00500270i
$417$	2.34460	+	7.82683i	0.114816	+	0.383281i
$418$	−2.03515	+	2.81401i	−0.0995427	+	0.137638i
$419$	−27.3061	−	15.7652i	−1.33399	−	0.770179i	−0.348081	−	0.937464i	$-0.613167\pi$
$419$	−27.3061	−	15.7652i	−1.33399	−	0.770179i	−0.985909	+	0.167285i	$0.946500\pi$
$420$	−1.14471	−	13.2829i	−0.0558561	−	0.648141i
$421$	−22.1162	+	12.7688i	−1.07788	+	0.622313i	−0.930323	−	0.366741i	$-0.880474\pi$
$421$	−22.1162	+	12.7688i	−1.07788	+	0.622313i	−0.147555	+	0.989054i	$0.547140\pi$
$422$	1.93536	−	18.8074i	0.0942118	−	0.915532i
$423$	−23.7631	+	15.6405i	−1.15540	+	0.760465i
$424$	−10.3875	+	32.6945i	−0.504463	+	1.58778i
$425$	−25.5826	−	44.3104i	−1.24094	−	2.14937i
$426$	−8.22610	+	23.6232i	−0.398556	+	1.14455i
$427$	−7.70228	−	4.44691i	−0.372740	−	0.215201i
$428$	−5.82111	−	5.19564i	−0.281374	−	0.251141i
$429$	4.27737	+	4.03416i	0.206513	+	0.194771i
$430$	−5.45446	−	12.1795i	−0.263038	−	0.587348i
$431$	17.3941			0.837845			0.418922	−	0.908022i	$-0.362408\pi$
$431$	17.3941			0.837845			0.418922	+	0.908022i	$0.362408\pi$
$432$	−17.3374	−	11.4636i	−0.834147	−	0.551542i
$433$	−26.4410			−1.27067			−0.635337	−	0.772235i	$-0.719139\pi$
$433$	−26.4410			−1.27067			−0.635337	+	0.772235i	$0.719139\pi$
$434$	−5.49249	−	12.2644i	−0.263648	−	0.588711i
$435$	40.2992	+	38.0078i	1.93220	+	1.82233i
$436$	1.26003	+	1.12464i	0.0603443	+	0.0538604i
$437$	2.44921	+	1.41405i	0.117162	+	0.0676433i
$438$	3.75058	−	10.7707i	0.179209	−	0.514643i
$439$	7.25707	+	12.5696i	0.346361	+	0.599915i	0.985600	−	0.169093i	$-0.0540839\pi$
$439$	7.25707	+	12.5696i	0.346361	+	0.599915i	−0.639239	+	0.769008i	$0.720751\pi$
$440$	21.2505	+	6.75161i	1.01308	+	0.321871i
$441$	−2.68134	−	1.34552i	−0.127683	−	0.0640722i
$442$	−1.25101	+	12.1571i	−0.0595046	+	0.578254i
$443$	30.0173	−	17.3305i	1.42616	−	0.823396i	0.429348	−	0.903139i	$-0.358743\pi$
$443$	30.0173	−	17.3305i	1.42616	−	0.823396i	0.996815	+	0.0797435i	$0.0254101\pi$
$444$	3.00113	+	34.8244i	0.142428	+	1.65269i
$445$	−3.79469	−	2.19087i	−0.179886	−	0.103857i
$446$	−11.1669	+	15.4405i	−0.528767	+	0.731127i
$447$	6.00698	+	20.0527i	0.284121	+	0.948462i
$448$	−0.732245	+	7.96642i	−0.0345953	+	0.376378i
$449$	−10.2906			−0.485642			−0.242821	−	0.970071i	$-0.578073\pi$
$449$	−10.2906			−0.485642			−0.242821	+	0.970071i	$0.578073\pi$
$450$	35.1011	+	22.3818i	1.65468	+	1.05509i
$451$		−	11.5617i		−	0.544421i
$452$	−11.6793	−	35.4198i	−0.549348	−	1.66601i
$453$	0.843617	−	3.56211i	0.0396366	−	0.167362i
$454$	30.9158	+	22.3590i	1.45095	+	1.04936i
$455$	3.18915	−	5.52376i	0.149509	−	0.258958i
$456$	5.13434	−	2.85190i	0.240437	−	0.133552i
$457$	4.79115	+	8.29851i	0.224120	+	0.388188i	0.956055	−	0.293187i	$-0.0947158\pi$
$457$	4.79115	+	8.29851i	0.224120	+	0.388188i	−0.731935	+	0.681375i	$0.761382\pi$
$458$	−1.85911	+	18.0664i	−0.0868703	+	0.844189i
$459$	−17.4061	+	20.7646i	−0.812448	+	0.969208i
$460$	3.69787	−	17.7774i	0.172414	−	0.828873i
$461$	−11.7622	+	6.79091i	−0.547820	+	0.316284i	−0.748242	−	0.663426i	$-0.769102\pi$
$461$	−11.7622	+	6.79091i	−0.547820	+	0.316284i	0.200422	+	0.979710i	$0.435769\pi$
$462$	3.79805	−	3.27848i	0.176701	−	0.152529i
$463$	−13.2044	+	22.8707i	−0.613659	+	1.06289i	0.376959	+	0.926230i	$0.376970\pi$
$463$	−13.2044	+	22.8707i	−0.613659	+	1.06289i	−0.990618	+	0.136659i	$0.956363\pi$
$464$	−19.7714	−	26.7205i	−0.917862	−	1.24047i
$465$	61.6374	+	14.5976i	2.85837	+	0.676950i
$466$	1.82279	+	4.07018i	0.0844390	+	0.188547i
$467$			9.09256i			0.420754i	0.977620	+	0.210377i	$0.0674691\pi$
$467$			9.09256i			0.420754i	−0.977620	+	0.210377i	$0.932531\pi$
$468$	−3.66076	−	9.24526i	−0.169219	−	0.427362i
$469$			1.74176i			0.0804268i
$470$	−47.1053	+	21.0956i	−2.17280	+	0.973067i
$471$	−7.10018	−	23.7021i	−0.327159	−	1.09213i
$472$	−5.63256	−	6.17403i	−0.259260	−	0.284183i
$473$	2.51110	−	4.34935i	0.115460	−	0.199983i
$474$	9.53121	−	1.81831i	0.437783	−	0.0835179i
$475$	−10.1875	+	5.88177i	−0.467436	+	0.269874i
$476$	10.2103	+	2.12386i	0.467990	+	0.0973468i
$477$	−36.3236	+	2.12759i	−1.66314	+	0.0974154i
$478$	27.1129	+	2.79003i	1.24012	+	0.127613i
$479$	19.4851	+	33.7491i	0.890296	+	1.54204i	0.839521	+	0.543327i	$0.182836\pi$
$479$	19.4851	+	33.7491i	0.890296	+	1.54204i	0.0507744	+	0.998710i	$0.483831\pi$
$480$	−27.7128	−	25.5729i	−1.26491	−	1.16724i
$481$	−8.36112	+	14.4819i	−0.381234	+	0.660317i
$482$	2.07040	−	2.86275i	0.0943042	−	0.130395i
$483$	−2.97242	−	2.80341i	−0.135250	−	0.127560i
$484$	−4.26166	−	12.9243i	−0.193712	−	0.587468i
$485$		−	50.2321i		−	2.28092i
$486$	4.76958	−	21.5233i	0.216352	−	0.976315i
$487$	−25.1294			−1.13872			−0.569362	−	0.822087i	$-0.692810\pi$
$487$	−25.1294			−1.13872			−0.569362	+	0.822087i	$0.692810\pi$
$488$	−24.5712	+	5.39071i	−1.11228	+	0.244026i
$489$	0.710899	−	0.753757i	0.0321480	−	0.0340861i
$490$	−4.41030	−	3.18962i	−0.199237	−	0.144093i
$491$	−16.8577	−	9.73281i	−0.760778	−	0.439235i	0.0687970	−	0.997631i	$-0.478084\pi$
$491$	−16.8577	−	9.73281i	−0.760778	−	0.439235i	−0.829575	+	0.558395i	$0.811417\pi$
$492$	−8.28654	+	17.7104i	−0.373586	+	0.798447i
$493$	−37.5266	+	21.6660i	−1.69011	+	0.975787i
$494$	2.79507	+	0.287624i	0.125756	+	0.0129408i
$495$	1.38287	+	23.6094i	0.0621556	+	1.06116i
$496$	−34.8560	−	15.1566i	−1.56508	−	0.680553i
$497$	5.10606	+	8.84395i	0.229038	+	0.396705i
$498$	−0.814818	−	4.27110i	−0.0365129	−	0.191393i
$499$	8.89492	+	5.13549i	0.398191	+	0.229896i	0.685703	−	0.727881i	$-0.259495\pi$
$499$	8.89492	+	5.13549i	0.398191	+	0.229896i	−0.287512	+	0.957777i	$0.592828\pi$
$500$	27.6347	+	24.6654i	1.23586	+	1.10307i
$501$	−10.4842	+	3.14065i	−0.468401	+	0.140314i
$502$	−10.9662	+	4.91108i	−0.489443	+	0.219192i
$503$	26.0834			1.16300			0.581500	−	0.813547i	$-0.302466\pi$
$503$	26.0834			1.16300			0.581500	+	0.813547i	$0.302466\pi$
$504$	−8.16765	+	2.29987i	−0.363816	+	0.102445i
$505$	−11.0797			−0.493038
$506$	6.23656	−	2.79298i	0.277249	−	0.124163i
$507$	−4.09278	+	17.2814i	−0.181767	+	0.767496i
$508$	18.9040	−	21.1798i	0.838731	−	0.939700i
$509$	6.08606	+	3.51379i	0.269760	+	0.155746i	0.628778	−	0.777584i	$-0.283555\pi$
$509$	6.08606	+	3.51379i	0.269760	+	0.155746i	−0.359019	+	0.933330i	$0.616889\pi$
$510$	−37.2119	+	32.1213i	−1.64777	+	1.42236i
$511$	−2.32804	−	4.03228i	−0.102986	−	0.178378i
$512$	13.6561	+	18.0419i	0.603521	+	0.797347i
$513$	4.77404	+	4.00189i	0.210779	+	0.176688i
$514$	41.9024	+	4.31192i	1.84824	+	0.190191i
$515$	−6.25132	+	3.60920i	−0.275466	+	0.159040i
$516$	−6.96380	+	4.86263i	−0.306564	+	0.214065i
$517$	−16.8215	−	9.71188i	−0.739808	−	0.427128i
$518$	11.5627	+	8.36237i	0.508034	+	0.367422i
$519$	−10.5691	−	2.50308i	−0.463930	−	0.109873i
$520$	−3.86600	−	17.6214i	−0.169535	−	0.772751i
$521$	22.0184			0.964643			0.482322	−	0.875994i	$-0.339794\pi$
$521$	22.0184			0.964643			0.482322	+	0.875994i	$0.339794\pi$
$522$	18.9552	−	29.7272i	0.829646	−	1.30112i
$523$			13.8466i			0.605471i	0.953075	+	0.302735i	$0.0978998\pi$
$523$			13.8466i			0.605471i	−0.953075	+	0.302735i	$0.902100\pi$
$524$	−27.2640	+	8.99003i	−1.19103	+	0.392731i
$525$	16.2805	−	4.87697i	0.710539	−	0.212848i
$526$	−25.8703	+	35.7709i	−1.12800	+	1.55968i
$527$	−24.7743	+	42.9104i	−1.07919	+	1.86921i
$528$	1.68645	−	14.0906i	0.0733931	−	0.613214i
$529$	8.71760	+	15.0993i	0.379026	+	0.656492i
$530$	−65.6673	−	6.75742i	−2.85241	−	0.293524i
$531$	3.97567	−	7.92269i	0.172529	−	0.343816i
$532$	0.488301	−	2.34748i	0.0211705	−	0.101776i
$533$	−8.10123	+	4.67725i	−0.350903	+	0.202594i
$534$	−0.917094	+	2.63365i	−0.0396865	+	0.113969i
$535$	7.50736	−	13.0031i	0.324571	−	0.562174i
$536$	3.32026	+	3.63945i	0.143414	+	0.157200i
$537$	15.6938	−	16.6399i	0.677236	−	0.718065i
$538$	−11.0837	+	4.96371i	−0.477851	+	0.214001i
$539$		−	2.04832i		−	0.0882272i
$540$	14.8031	−	37.1563i	0.637022	−	1.59895i
$541$		−	37.8518i		−	1.62738i	−0.581301	−	0.813689i	$-0.697456\pi$
$541$		−	37.8518i		−	1.62738i	0.581301	−	0.813689i	$-0.302544\pi$
$542$	0.703331	+	1.57050i	0.0302107	+	0.0674587i
$543$	17.7012	−	18.7683i	0.759631	−	0.805427i
$544$	25.3834	−	15.0258i	1.08830	−	0.644227i
$545$	−1.62503	+	2.81463i	−0.0696086	+	0.120566i
$546$	−3.83369	−	1.33497i	−0.164067	−	0.0571315i
$547$	18.7285	−	10.8129i	0.800775	−	0.462328i	−0.0429671	−	0.999076i	$-0.513681\pi$
$547$	18.7285	−	10.8129i	0.800775	−	0.462328i	0.843742	+	0.536749i	$0.180348\pi$
$548$	−8.73340	−	1.81664i	−0.373073	−	0.0776030i
$549$	−14.6690	−	22.2872i	−0.626059	−	0.951196i
$550$	−2.90954	+	28.2743i	−0.124063	+	1.20562i
$551$	4.98128	+	8.62783i	0.212210	+	0.367558i
$552$	−11.5550	−	0.191558i	−0.491815	−	0.00815324i
$553$	1.98064	−	3.43056i	0.0842253	−	0.145882i
$554$	−8.77867	−	6.34893i	−0.372970	−	0.269740i
$555$	−64.4333	+	19.3016i	−2.73504	+	0.819307i
$556$	8.95990	−	2.95444i	0.379984	−	0.125296i
$557$			22.1990i			0.940600i	0.882506	+	0.470300i	$0.155854\pi$
$557$			22.1990i			0.940600i	−0.882506	+	0.470300i	$0.844146\pi$
$558$	1.77474	−	40.2753i	0.0751308	−	1.70499i
$559$	−4.06341			−0.171864
$560$	−15.2957	+	1.74243i	−0.646363	+	0.0736310i
$561$	−18.0018	−	4.26338i	−0.760036	−	0.180000i
$562$	14.6538	−	20.2618i	0.618132	−	0.854692i
$563$	15.7834	+	9.11257i	0.665193	+	0.384049i	0.794253	−	0.607588i	$-0.207863\pi$
$563$	15.7834	+	9.11257i	0.665193	+	0.384049i	−0.129060	+	0.991637i	$0.541196\pi$
$564$	18.8066	+	26.9331i	0.791902	+	1.13409i
$565$	62.1540	−	35.8846i	2.61484	−	1.50968i
$566$	−2.53829	+	24.6666i	−0.106692	+	1.03681i
$567$	−5.37917	−	7.21558i	−0.225904	−	0.303026i
$568$	27.5282	+	8.74613i	1.15506	+	0.366980i
$569$	2.53379	+	4.38864i	0.106222	+	0.183982i	0.914237	−	0.405180i	$-0.132791\pi$
$569$	2.53379	+	4.38864i	0.106222	+	0.183982i	−0.808015	+	0.589162i	$0.799458\pi$
$570$	7.38510	+	8.55548i	0.309328	+	0.358350i
$571$	4.39296	+	2.53628i	0.183840	+	0.106140i	0.589096	−	0.808063i	$-0.299484\pi$
$571$	4.39296	+	2.53628i	0.183840	+	0.106140i	−0.405256	+	0.914203i	$0.632818\pi$
$572$	4.52088	−	5.06512i	0.189028	−	0.211783i
$573$	−0.725443	+	3.06313i	−0.0303058	+	0.127964i
$574$	3.26266	+	7.28533i	0.136181	+	0.304084i
$575$	23.1469			0.965291
$576$	−12.6823	+	20.3754i	−0.528431	+	0.848976i
$577$	−10.6402			−0.442958			−0.221479	−	0.975165i	$-0.571088\pi$
$577$	−10.6402			−0.442958			−0.221479	+	0.975165i	$0.571088\pi$
$578$	−5.89030	−	13.1527i	−0.245004	−	0.547080i
$579$	−39.5120	+	11.8362i	−1.64206	+	0.491895i
$580$	42.5934	−	47.7209i	1.76859	−	1.98150i
$581$	−1.53730	−	0.887558i	−0.0637778	−	0.0368221i
$582$	−31.4040	+	5.99108i	−1.30174	+	0.248338i
$583$	−12.4216	−	21.5149i	−0.514452	−	0.891056i
$584$	−12.5511	−	3.98768i	−0.519369	−	0.165011i
$585$	15.9835	−	10.5200i	0.660836	−	0.434950i
$586$	−1.74377	+	16.9456i	−0.0720344	+	0.700016i
$587$	14.1273	−	8.15642i	0.583097	−	0.336651i	−0.179266	−	0.983801i	$-0.557372\pi$
$587$	14.1273	−	8.15642i	0.583097	−	0.336651i	0.762363	+	0.647149i	$0.224039\pi$
$588$	−1.46807	+	3.13764i	−0.0605423	+	0.129394i
$589$	9.86564	+	5.69593i	0.406507	+	0.234697i
$590$	9.42455	−	13.0313i	0.388003	−	0.536492i
$591$	−6.94751	+	7.36635i	−0.285782	+	0.303011i
$592$	40.1015	−	4.56820i	1.64816	−	0.187752i
$593$	−1.99475			−0.0819146			−0.0409573	−	0.999161i	$-0.513041\pi$
$593$	−1.99475			−0.0819146			−0.0409573	+	0.999161i	$0.513041\pi$
$594$	14.5951	−	3.68038i	0.598845	−	0.151008i
$595$			20.0686i			0.822734i
$596$	22.9557	−	7.56941i	0.940303	−	0.310055i
$597$	−23.3647	−	22.0362i	−0.956252	−	0.901881i
$598$	−4.47999	−	3.24003i	−0.183201	−	0.132495i
$599$	4.26329	−	7.38423i	0.174193	−	0.301712i	−0.765689	−	0.643212i	$-0.777602\pi$
$599$	4.26329	−	7.38423i	0.174193	−	0.301712i	0.939882	+	0.341500i	$0.110935\pi$
$600$	24.7217	−	41.2256i	1.00926	−	1.68303i
$601$	−3.01805	−	5.22742i	−0.123109	−	0.213231i	0.797883	−	0.602812i	$-0.205953\pi$
$601$	−3.01805	−	5.22742i	−0.123109	−	0.213231i	−0.920992	+	0.389581i	$0.872620\pi$
$602$	−0.354941	+	3.44924i	−0.0144663	+	0.140581i
$603$	−2.34356	+	4.67024i	−0.0954372	+	0.190187i
$604$	−4.13836	−	0.860822i	−0.168388	−	0.0350264i
$605$	22.6793	−	13.0939i	0.922046	−	0.532344i
$606$	1.32145	+	6.92674i	0.0536801	+	0.281380i
$607$	−2.95992	+	5.12673i	−0.120139	+	0.208088i	−0.919823	−	0.392335i	$-0.871667\pi$
$607$	−2.95992	+	5.12673i	−0.120139	+	0.208088i	0.799683	+	0.600422i	$0.205001\pi$
$608$	−3.45463	−	5.83597i	−0.140104	−	0.236680i
$609$	−4.13032	−	13.7880i	−0.167369	−	0.558717i
$610$	−19.7854	−	44.1796i	−0.801086	−	1.78878i
$611$			15.7156i			0.635785i
$612$	24.5197	+	19.4330i	0.991150	+	0.785530i
$613$		−	13.3526i		−	0.539307i	−0.962957	−	0.269654i	$-0.913091\pi$
$613$		−	13.3526i		−	0.539307i	0.962957	−	0.269654i	$-0.0869092\pi$
$614$	36.4406	−	16.3195i	1.47062	−	0.658603i
$615$	−36.6139	−	8.67131i	−1.47642	−	0.349661i
$616$	−3.90465	−	4.28001i	−0.157323	−	0.172447i
$617$	−5.43146	+	9.40756i	−0.218662	+	0.378734i	−0.954399	−	0.298533i	$-0.903503\pi$
$617$	−5.43146	+	9.40756i	−0.218662	+	0.378734i	0.735737	+	0.677267i	$0.236836\pi$
$618$	3.00197	+	3.47772i	0.120757	+	0.139894i
$619$	−1.64758	+	0.951228i	−0.0662217	+	0.0382331i	−0.532745	−	0.846276i	$-0.678840\pi$
$619$	−1.64758	+	0.951228i	−0.0662217	+	0.0382331i	0.466524	+	0.884509i	$0.345506\pi$
$620$	14.8954	−	71.6087i	0.598212	−	2.87588i
$621$	−4.19804	−	11.5163i	−0.168461	−	0.462135i
$622$	21.3030	+	2.19217i	0.854174	+	0.0878978i
$623$	0.569253	+	0.985976i	0.0228067	+	0.0395023i
$624$	−10.5554	+	4.51860i	−0.422555	+	0.180889i
$625$	−11.1093	+	19.2419i	−0.444372	+	0.769674i
$626$	−8.27086	+	11.4361i	−0.330570	+	0.457080i
$627$	−0.980204	+	4.13884i	−0.0391456	+	0.165289i
$628$	−27.1334	+	8.94696i	−1.08274	+	0.357023i
$629$		−	52.6148i		−	2.09789i
$630$	−7.53382	−	14.4866i	−0.300155	−	0.577160i
$631$	21.8360			0.869276			0.434638	−	0.900605i	$-0.356876\pi$
$631$	21.8360			0.869276			0.434638	+	0.900605i	$0.356876\pi$
$632$	−2.40100	−	10.9439i	−0.0955066	−	0.435325i
$633$	−6.64485	−	22.1821i	−0.264109	−	0.881658i
$634$	13.9282	+	10.0732i	0.553161	+	0.400058i
$635$	47.3112	+	27.3151i	1.87749	+	1.08397i
$636$	3.60742	+	41.8596i	0.143044	+	1.65984i
$637$	−1.43524	+	0.828637i	−0.0568663	+	0.0328318i
$638$	23.9456	+	2.46409i	0.948014	+	0.0975543i
$639$	1.79139	+	30.5839i	0.0708664	+	1.20988i
$640$	−28.6393	+	32.7987i	−1.13207	+	1.29648i
$641$	2.69779	+	4.67271i	0.106556	+	0.184561i	0.914373	−	0.404873i	$-0.132684\pi$
$641$	2.69779	+	4.67271i	0.106556	+	0.184561i	−0.807817	+	0.589434i	$0.799351\pi$
$642$	−9.02464	−	3.14257i	−0.356174	−	0.124027i
$643$	−34.8075	−	20.0961i	−1.37267	−	0.792513i	−0.381410	−	0.924406i	$-0.624561\pi$
$643$	−34.8075	−	20.0961i	−1.37267	−	0.792513i	−0.991264	+	0.131893i	$0.957895\pi$
$644$	−3.14164	+	3.51984i	−0.123798	+	0.138701i
$645$	−11.8903	−	11.2142i	−0.468179	−	0.441559i
$646$	−8.06866	+	3.61347i	−0.317457	+	0.142170i
$647$	−2.31418			−0.0909799			−0.0454900	−	0.998965i	$-0.514485\pi$
$647$	−2.31418			−0.0909799			−0.0454900	+	0.998965i	$0.514485\pi$
$648$	−24.9948	−	4.82297i	−0.981888	−	0.189464i
$649$	6.05227			0.237572
$650$	20.9887	−	9.39955i	0.823243	−	0.368681i
$651$	−11.9732	−	11.2924i	−0.469266	−	0.442584i
$652$	−0.892574	−	0.796668i	−0.0349559	−	0.0311999i
$653$	26.2236	+	15.1402i	1.02621	+	0.592483i	0.915897	−	0.401414i	$-0.131481\pi$
$653$	26.2236	+	15.1402i	1.02621	+	0.592483i	0.110313	+	0.993897i	$0.464815\pi$
$654$	1.95346	+	0.680235i	0.0763862	+	0.0265993i
$655$	−27.6218	−	47.8424i	−1.07927	−	1.86936i
$656$	20.7052	+	9.00337i	0.808403	+	0.351522i
$657$	−0.816762	−	13.9443i	−0.0318649	−	0.544020i
$658$	13.3403	+	1.37276i	0.520057	+	0.0535159i
$659$	33.2645	−	19.2053i	1.29580	−	0.748132i	0.316126	−	0.948717i	$-0.397618\pi$
$659$	33.2645	−	19.2053i	1.29580	−	0.748132i	0.979676	+	0.200585i	$0.0642843\pi$
$660$	27.2077	−	2.34473i	1.05906	−	0.0912684i
$661$	−24.0408	−	13.8799i	−0.935077	−	0.539867i	−0.0466634	−	0.998911i	$-0.514859\pi$
$661$	−24.0408	−	13.8799i	−0.935077	−	0.539867i	−0.888414	+	0.459044i	$0.848192\pi$
$662$	−23.8839	−	17.2734i	−0.928275	−	0.671349i
$663$	4.29522	+	14.3384i	0.166812	+	0.556859i
$664$	−4.90415	+	1.07593i	−0.190318	+	0.0417542i
$665$	4.61403			0.178925
$666$	19.7517	+	37.9801i	0.765364	+	1.47170i
$667$		−	19.6031i		−	0.759036i
$668$	3.95754	+	12.0020i	0.153122	+	0.464372i
$669$	−5.37837	+	22.7098i	−0.207940	+	0.878010i
$670$	−5.55555	+	7.68167i	−0.214630	+	0.296769i
$671$	9.10869	−	15.7767i	0.351637	−	0.609053i
$672$	2.91362	+	9.35472i	0.112395	+	0.360866i
$673$	22.6946	+	39.3081i	0.874811	+	1.51522i	0.856964	+	0.515377i	$0.172348\pi$
$673$	22.6946	+	39.3081i	0.874811	+	1.51522i	0.0178477	+	0.999841i	$0.494319\pi$
$674$	−16.1455	−	1.66143i	−0.621901	−	0.0639961i
$675$	50.2156	+	8.82884i	1.93280	+	0.339822i
$676$	20.0771	+	4.17625i	0.772197	+	0.160625i
$677$	0.368450	−	0.212725i	0.0141607	−	0.00817568i	−0.492903	−	0.870084i	$-0.664064\pi$
$677$	0.368450	−	0.212725i	0.0141607	−	0.00817568i	0.507064	+	0.861909i	$0.330731\pi$
$678$	−29.8472	−	34.5773i	−1.14628	−	1.32793i
$679$	−6.52591	+	11.3032i	−0.250442	+	0.433778i
$680$	38.2563	+	41.9340i	1.46706	+	1.60809i
$681$	45.4709	+	10.7689i	1.74245	+	0.412666i
$682$	25.1214	−	11.2504i	0.961949	−	0.430799i
$683$			36.2275i			1.38621i	0.720838	+	0.693103i	$0.243757\pi$
$683$			36.2275i			1.38621i	−0.720838	+	0.693103i	$0.756243\pi$
$684$	4.46788	−	5.63739i	0.170834	−	0.215551i
$685$		−	17.1657i		−	0.655868i
$686$	0.578023	+	1.29069i	0.0220690	+	0.0492789i
$687$	6.38304	+	21.3081i	0.243528	+	0.812955i
$688$	5.83355	+	7.88390i	0.222402	+	0.300571i
$689$	−10.0502	+	17.4075i	−0.382883	+	0.663173i
$690$	−4.16744	−	21.8448i	−0.158652	−	0.831617i
$691$	−43.2632	+	24.9780i	−1.64581	+	0.950209i	−0.667098	+	0.744970i	$0.732464\pi$
$691$	−43.2632	+	24.9780i	−1.64581	+	0.950209i	−0.978712	+	0.205238i	$0.934203\pi$
$692$	−2.55413	+	12.2789i	−0.0970935	+	0.466772i
$693$	2.75604	−	5.49223i	0.104693	−	0.208633i
$694$	3.10619	−	30.1854i	0.117910	−	1.14582i
$695$	9.07749	+	15.7227i	0.344329	+	0.596395i
$696$	−34.9140	−	20.9368i	−1.32341	−	0.793608i
$697$	14.7165	−	25.4897i	0.557426	−	0.965491i
$698$	−21.3668	−	15.4529i	−0.808745	−	0.584902i
$699$	3.97353	+	3.74760i	0.150293	+	0.141747i
$700$	−6.14548	−	18.6374i	−0.232277	−	0.704427i
$701$		−	28.3097i		−	1.06924i	−0.845092	−	0.534621i	$-0.820454\pi$
$701$		−	28.3097i		−	1.06924i	0.845092	−	0.534621i	$-0.179546\pi$
$702$	−8.48320	−	8.73781i	−0.320178	−	0.329787i
$703$	−12.0968			−0.456240
$704$	−16.3177	−	1.49987i	−0.614998	−	0.0565285i
$705$	−43.3719	+	45.9867i	−1.63348	+	1.73196i
$706$	−17.8270	+	24.6494i	−0.670928	+	0.927693i
$707$	2.49314	+	1.43941i	0.0937642	+	0.0541348i
$708$	−9.27094	−	4.33779i	−0.348423	−	0.163024i
$709$	11.9128	−	6.87787i	0.447395	−	0.258304i	−0.259334	−	0.965788i	$-0.583503\pi$
$709$	11.9128	−	6.87787i	0.447395	−	0.258304i	0.706730	+	0.707484i	$0.250170\pi$
$710$	−5.68965	+	55.2909i	−0.213529	+	2.07503i
$711$	9.92664	−	6.53353i	0.372278	−	0.245026i
$712$	3.06901	+	0.975070i	0.115016	+	0.0365423i
$713$	−11.2078	−	19.4124i	−0.419734	−	0.727001i
$714$	12.5464	−	2.39355i	0.469539	−	0.0895762i
$715$	11.3144	+	6.53238i	0.423135	+	0.244297i
$716$	−19.7044	−	17.5872i	−0.736389	−	0.657265i
$717$	31.9778	−	9.57925i	1.19423	−	0.357744i
$718$	12.7600	+	28.4923i	0.476198	+	1.06332i
$719$	45.4064			1.69337			0.846687	−	0.532091i	$-0.178594\pi$
$719$	45.4064			1.69337			0.846687	+	0.532091i	$0.178594\pi$
$720$	−43.3575	−	15.9086i	−1.61584	−	0.592879i
$721$	1.87556			0.0698495
$722$	−10.1517	−	22.6681i	−0.377806	−	0.843619i
$723$	0.997180	−	4.21052i	0.0370855	−	0.156591i
$724$	−22.2249	−	19.8368i	−0.825980	−	0.737230i
$725$	70.6152	+	40.7697i	2.62258	+	1.51415i
$726$	−10.8909	−	12.6169i	−0.404201	−	0.468258i
$727$	15.4265	+	26.7196i	0.572139	+	0.990973i	0.996346	+	0.0854082i	$0.0272194\pi$
$727$	15.4265	+	26.7196i	0.572139	+	0.990973i	−0.424207	+	0.905565i	$0.639447\pi$
$728$	−1.41937	+	4.46742i	−0.0526052	+	0.165574i
$729$	−4.71471	−	26.5852i	−0.174619	−	0.984636i
$730$	2.59412	−	25.2091i	0.0960126	−	0.933032i
$731$	11.0722	−	6.39255i	0.409521	−	0.236437i
$732$	−25.2603	+	17.6386i	−0.933648	+	0.651940i
$733$	−10.0548	−	5.80516i	−0.371383	−	0.214418i	0.302679	−	0.953092i	$-0.402119\pi$
$733$	−10.0548	−	5.80516i	−0.371383	−	0.214418i	−0.674063	+	0.738674i	$0.735452\pi$
$734$	−2.78755	+	3.85435i	−0.102890	+	0.142267i
$735$	−6.48665	−	1.53624i	−0.239264	−	0.0566650i
$736$	0.145239	+	13.3436i	0.00535356	+	0.491853i
$737$	−3.56767			−0.131417
$738$	−1.05423	+	23.9244i	−0.0388069	+	0.880669i
$739$			8.15551i			0.300005i	0.988686	+	0.150003i	$0.0479282\pi$
$739$			8.15551i			0.300005i	−0.988686	+	0.150003i	$0.952072\pi$
$740$	24.3220	+	73.7611i	0.894094	+	2.71151i
$741$	3.29659	−	0.987525i	0.121103	−	0.0362776i
$742$	13.8986	+	10.0517i	0.510232	+	0.369011i
$743$	5.97669	−	10.3519i	0.219264	−	0.379776i	−0.735319	−	0.677721i	$-0.762968\pi$
$743$	5.97669	−	10.3519i	0.219264	−	0.379776i	0.954583	+	0.297945i	$0.0963012\pi$
$744$	−46.5447	−	0.771611i	−1.70641	−	0.0282886i
$745$	23.2570	+	40.2823i	0.852070	+	1.47583i
$746$	1.25691	−	12.2144i	0.0460188	−	0.447202i
$747$	−2.92779	−	4.44830i	−0.107122	−	0.162755i
$748$	−4.35033	+	20.9140i	−0.159064	+	0.764691i
$749$	−3.37861	+	1.95064i	−0.123452	+	0.0712748i
$750$	42.8429	+	14.9188i	1.56440	+	0.544757i
$751$	−6.49551	+	11.2506i	−0.237025	+	0.410539i	−0.959859	−	0.280483i	$-0.909506\pi$
$751$	−6.49551	+	11.2506i	−0.237025	+	0.410539i	0.722835	+	0.691021i	$0.242839\pi$
$752$	30.4917	−	22.5617i	1.11192	−	0.822742i
$753$	−10.0970	+	10.7057i	−0.367956	+	0.390139i
$754$	−7.96050	−	17.7753i	−0.289904	−	0.647339i
$755$		−	8.13405i		−	0.296028i
$756$	−8.15814	+	6.43776i	−0.296709	+	0.234139i
$757$			21.8618i			0.794581i	0.917693	+	0.397290i	$0.130049\pi$
$757$			21.8618i			0.794581i	−0.917693	+	0.397290i	$0.869951\pi$
$758$	−36.4425	+	16.3204i	−1.32365	+	0.592783i
$759$	5.74228	−	6.08846i	0.208431	−	0.220997i
$760$	9.64115	−	8.79561i	0.349721	−	0.319050i
$761$	8.81222	−	15.2632i	0.319443	−	0.553291i	−0.660929	−	0.750448i	$-0.729838\pi$
$761$	8.81222	−	15.2632i	0.319443	−	0.553291i	0.980372	+	0.197157i	$0.0631709\pi$
$762$	11.4341	−	32.8357i	0.414213	−	1.18951i
$763$	0.731327	−	0.422232i	0.0264758	−	0.0152858i
$764$	3.55866	+	0.740238i	0.128748	+	0.0267809i
$765$	−27.0027	+	53.8109i	−0.976284	+	1.94554i
$766$	32.2231	+	3.31588i	1.16427	+	0.119808i
$767$	−2.44842	−	4.24078i	−0.0884072	−	0.153126i
$768$	23.9207	+	13.9928i	0.863165	+	0.504922i
$769$	−4.19303	+	7.26255i	−0.151205	+	0.261894i	−0.931671	−	0.363304i	$-0.881649\pi$
$769$	−4.19303	+	7.26255i	−0.151205	+	0.261894i	0.780466	+	0.625198i	$0.214982\pi$
$770$	6.53336	−	9.03369i	0.235446	−	0.325552i
$771$	49.4210	−	14.8045i	1.77985	−	0.533171i
$772$	14.9148	+	45.2321i	0.536796	+	1.62794i
$773$			40.2234i			1.44674i	0.690462	+	0.723368i	$0.257407\pi$
$773$			40.2234i			1.44674i	−0.690462	+	0.723368i	$0.742593\pi$
$774$	−5.59273	+	8.77102i	−0.201027	+	0.315268i
$775$	93.2377			3.34920
$776$	7.91094	+	36.0585i	0.283986	+	1.29443i
$777$	17.0063	+	4.02762i	0.610098	+	0.144490i
$778$	−30.9973	−	22.4179i	−1.11131	−	0.803721i
$779$	−5.86040	−	3.38350i	−0.209971	−	0.121227i
$780$	−12.6497	−	18.1157i	−0.452931	−	0.648645i
$781$	−18.1152	+	10.4588i	−0.648213	+	0.374246i
$782$	17.3046	+	1.78071i	0.618810	+	0.0636779i
$783$	7.47716	−	42.5277i	0.267212	−	1.51981i
$784$	3.66821	+	1.59507i	0.131007	+	0.0569667i
$785$	−27.4895	−	47.6132i	−0.981142	−	1.69939i
$786$	−26.6156	+	22.9746i	−0.949346	+	0.819476i
$787$	24.4384	+	14.1095i	0.871136	+	0.502950i	0.867726	−	0.497044i	$-0.165581\pi$
$787$	24.4384	+	14.1095i	0.871136	+	0.502950i	0.00341028	+	0.999994i	$0.498914\pi$
$788$	8.72299	+	7.78572i	0.310744	+	0.277355i
$789$	−12.4601	+	52.6117i	−0.443590	+	1.87302i
$790$	19.6774	−	8.81232i	0.700091	−	0.313528i
$791$	−18.6478			−0.663040
$792$	−4.71087	−	16.7299i	−0.167393	−	0.594473i
$793$	−14.7395			−0.523415
$794$	27.9034	−	12.4963i	0.990255	−	0.443475i
$795$	−77.4501	+	23.2009i	−2.74687	+	0.822851i
$796$	−24.6948	+	27.6677i	−0.875285	+	0.980655i
$797$	15.1059	+	8.72141i	0.535079	+	0.308928i	0.743082	−	0.669200i	$-0.233363\pi$
$797$	15.1059	+	8.72141i	0.535079	+	0.308928i	−0.208003	+	0.978128i	$0.566696\pi$
$798$	−0.550306	−	2.88459i	−0.0194806	−	0.102113i
$799$	−24.7237	−	42.8228i	−0.874663	−	1.51496i
$800$	−48.3691	−	27.2283i	−1.71011	−	0.962667i
$801$	0.199715	+	3.40968i	0.00705659	+	0.120475i
$802$	5.56558	+	0.572720i	0.196527	+	0.0202234i
$803$	8.25939	−	4.76856i	0.291467	−	0.168279i
$804$	5.46500	+	2.55702i	0.192736	+	0.0901793i
$805$	−7.86259	−	4.53947i	−0.277120	−	0.159995i
$806$	−18.0458	−	13.0511i	−0.635636	−	0.459706i
$807$	−10.2052	+	10.8205i	−0.359241	+	0.380899i
$808$	7.95340	−	1.74491i	0.279800	−	0.0613857i
$809$	−23.3000			−0.819183			−0.409592	−	0.912269i	$-0.634329\pi$
$809$	−23.3000			−0.819183			−0.409592	+	0.912269i	$0.634329\pi$
$810$	−0.708768	−	48.9804i	−0.0249036	−	1.72100i
$811$		−	1.39655i		−	0.0490395i	−0.999699	−	0.0245197i	$-0.992194\pi$
$811$		−	1.39655i		−	0.0490395i	0.999699	−	0.0245197i	$-0.00780565\pi$
$812$	−15.7840	+	5.20462i	−0.553911	+	0.182646i
$813$	1.53320	+	1.44603i	0.0537718	+	0.0507144i
$814$	−17.1288	+	23.6840i	−0.600364	+	0.830124i
$815$	1.15113	−	1.99382i	0.0403225	−	0.0698405i
$816$	21.6534	−	28.9183i	0.758020	−	1.01234i
$817$	−1.46973	−	2.54564i	−0.0514193	−	0.0890608i
$818$	28.7603	+	2.95955i	1.00558	+	0.103478i
$819$	−4.96332	+	0.290716i	−0.173432	+	0.0101585i
$820$	−8.84816	+	42.5371i	−0.308991	+	1.48546i
$821$	0.0321266	−	0.0185483i	0.00112123	−	0.000647340i	−0.499439	−	0.866349i	$-0.666461\pi$
$821$	0.0321266	−	0.0185483i	0.00112123	−	0.000647340i	0.500561	+	0.865702i	$0.333127\pi$
$822$	−10.7316	+	2.04732i	−0.374308	+	0.0714084i
$823$	−9.20368	+	15.9412i	−0.320820	+	0.555677i	−0.980657	−	0.195732i	$-0.937292\pi$
$823$	−9.20368	+	15.9412i	−0.320820	+	0.555677i	0.659837	+	0.751408i	$0.270625\pi$
$824$	3.91903	−	3.57533i	0.136526	−	0.124553i
$825$	9.98958	+	33.3476i	0.347793	+	1.16101i
$826$	−3.81368	+	1.70792i	−0.132695	+	0.0594260i
$827$		−	0.177189i		−	0.00616146i	−0.999995	−	0.00308073i	$-0.999019\pi$
$827$		−	0.177189i		−	0.00616146i	0.999995	−	0.00308073i	$-0.000980628\pi$
$828$	−13.1598	+	5.21077i	−0.457335	+	0.181087i
$829$			4.67287i			0.162295i	0.996702	+	0.0811477i	$0.0258586\pi$
$829$			4.67287i			0.162295i	−0.996702	+	0.0811477i	$0.974141\pi$
$830$	−3.94896	−	8.81780i	−0.137070	−	0.306070i
$831$	−12.9116	−	3.05787i	−0.447900	−	0.106076i
$832$	5.55032	+	12.0405i	0.192423	+	0.417429i
$833$	2.60722	−	4.51584i	0.0903349	−	0.156465i
$834$	8.74680	−	7.55025i	0.302877	−	0.261444i
$835$	−21.0609	+	12.1595i	−0.728844	+	0.420798i
$836$	4.80839	+	1.00020i	0.166302	+	0.0345925i
$837$	−16.9101	−	46.3889i	−0.584497	−	1.60343i
$838$	−4.56445	+	44.3564i	−0.157676	+	1.53227i
$839$	−18.2155	−	31.5501i	−0.628868	−	1.08923i	−0.987779	−	0.155859i	$-0.950185\pi$
$839$	−18.2155	−	31.5501i	−0.628868	−	1.08923i	0.358911	−	0.933372i	$-0.383148\pi$
$840$	−16.4825	+	9.15532i	−0.568701	+	0.315888i
$841$	20.0280	−	34.6894i	0.690619	−	1.19619i
$842$	29.2643	+	21.1646i	1.00851	+	0.729379i
$843$	7.05778	−	29.8009i	0.243083	−	1.02640i
$844$	−25.3933	+	8.37319i	−0.874074	+	0.288217i
$845$			39.4621i			1.35754i
$846$	33.9227	+	21.6304i	1.16629	+	0.743668i
$847$	−6.80440			−0.233802
$848$	48.2028	−	5.49106i	1.65529	−	0.188564i
$849$	8.71495	+	29.0925i	0.299096	+	0.998454i
$850$	−42.4038	+	58.6318i	−1.45444	+	2.01105i
$851$	20.6137	+	11.9013i	0.706628	+	0.407972i
$852$	35.2452	−	3.03739i	1.20748	−	0.104059i
$853$	5.58176	−	3.22263i	0.191116	−	0.110341i	−0.401389	−	0.915908i	$-0.631472\pi$
$853$	5.58176	−	3.22263i	0.191116	−	0.110341i	0.592505	+	0.805567i	$0.298139\pi$
$854$	−1.28750	+	12.5117i	−0.0440574	+	0.428142i
$855$	12.3718	+	6.20826i	0.423107	+	0.212318i
$856$	−3.34124	+	10.5165i	−0.114201	+	0.359445i
$857$	21.7225	+	37.6244i	0.742025	+	1.28522i	0.951572	+	0.307426i	$0.0994677\pi$
$857$	21.7225	+	37.6244i	0.742025	+	1.28522i	−0.209547	+	0.977799i	$0.567199\pi$
$858$	2.73445	−	7.85261i	0.0933525	−	0.268084i
$859$	17.0155	+	9.82393i	0.580563	+	0.335188i	0.761357	−	0.648333i	$-0.224533\pi$
$859$	17.0155	+	9.82393i	0.580563	+	0.335188i	−0.180794	+	0.983521i	$0.557867\pi$
$860$	−12.5672	+	14.0801i	−0.428538	+	0.480127i
$861$	7.11232	+	6.70792i	0.242387	+	0.228605i
$862$	−10.0542	−	22.4505i	−0.342447	−	0.764665i
$863$	−12.7952			−0.435554			−0.217777	−	0.975999i	$-0.569881\pi$
$863$	−12.7952			−0.435554			−0.217777	+	0.975999i	$0.569881\pi$
$864$	−4.77454	+	29.0035i	−0.162433	+	0.986720i
$865$	−24.1344			−0.820594
$866$	15.2835	+	34.1273i	0.519356	+	1.15969i
$867$	−12.8404	−	12.1103i	−0.436081	−	0.411286i
$868$	−12.6548	+	14.1782i	−0.429532	+	0.481241i
$869$	7.02688	+	4.05697i	0.238371	+	0.137623i
$870$	25.7625	−	73.9832i	0.873432	−	2.50827i
$871$	1.44328	+	2.49984i	0.0489038	+	0.0847039i
$872$	0.723238	−	2.27637i	0.0244919	−	0.0770877i
$873$	−32.7069	+	21.5270i	−1.10696	+	0.728580i
$874$	0.409407	−	3.97854i	0.0138484	−	0.134576i
$875$	16.0393	−	9.26031i	0.542228	−	0.313056i
$876$	−16.0696	+	1.38486i	−0.542940	+	0.0467900i
$877$	25.9658	+	14.9913i	0.876802	+	0.506222i	0.869602	−	0.493752i	$-0.164375\pi$
$877$	25.9658	+	14.9913i	0.876802	+	0.506222i	0.00719906	+	0.999974i	$0.497708\pi$
$878$	12.0288	−	16.6322i	0.405951	−	0.561309i
$879$	5.98704	+	19.9861i	0.201938	+	0.674116i
$880$	−3.56904	−	31.3305i	−0.120312	−	1.05615i
$881$	−7.44995			−0.250995			−0.125498	−	0.992094i	$-0.540053\pi$
$881$	−7.44995			−0.250995			−0.125498	+	0.992094i	$0.540053\pi$
$882$	−0.186772	+	4.23853i	−0.00628893	+	0.142719i
$883$		−	57.4367i		−	1.93290i	−0.256856	−	0.966450i	$-0.582687\pi$
$883$		−	57.4367i		−	1.93290i	0.256856	−	0.966450i	$-0.417313\pi$
$884$	16.4142	−	5.41241i	0.552069	−	0.182039i
$885$	4.53920	−	19.1664i	0.152584	−	0.644273i
$886$	−39.7190	−	28.7257i	−1.33439	−	0.965057i
$887$	28.0775	−	48.6317i	0.942751	−	1.63289i	0.182557	−	0.983195i	$-0.441563\pi$
$887$	28.0775	−	48.6317i	0.942751	−	1.63289i	0.760194	−	0.649697i	$-0.225104\pi$
$888$	43.2129	−	24.0029i	1.45013	−	0.805484i
$889$	−7.09729	−	12.2929i	−0.238036	−	0.412290i
$890$	−0.634315	+	6.16415i	−0.0212623	+	0.206623i
$891$	14.7798	−	11.0182i	0.495141	−	0.369125i
$892$	26.3836	+	5.48806i	0.883388	+	0.183754i
$893$	−9.84550	+	5.68430i	−0.329467	+	0.190218i
$894$	22.4097	−	19.3441i	0.749494	−	0.646964i
$895$	25.4124	−	44.0155i	0.849442	−	1.47128i
$896$	10.7055	−	3.65967i	0.357644	−	0.122261i
$897$	−6.58916	−	1.56052i	−0.220005	−	0.0521041i
$898$	5.94819	+	13.2820i	0.198494	+	0.443225i
$899$		−	78.9631i		−	2.63357i
$900$	8.59877	−	58.2420i	0.286626	−	1.94140i
$901$		−	63.2440i		−	2.10696i
$902$	−14.9227	+	6.68295i	−0.496870	+	0.222518i
$903$	1.21865	+	4.06814i	0.0405542	+	0.135379i
$904$	−38.9651	+	35.5479i	−1.29596	+	1.18230i
$905$	28.6629	−	49.6456i	0.952788	−	1.65028i
$906$	−5.08522	+	0.970131i	−0.168945	+	0.0322304i
$907$	3.54990	−	2.04954i	0.117873	−	0.0680538i	−0.439905	−	0.898045i	$-0.644988\pi$
$907$	3.54990	−	2.04954i	0.117873	−	0.0680538i	0.557777	+	0.829991i	$0.311654\pi$
$908$	10.9885	−	52.8269i	0.364668	−	1.75312i
$909$	4.74820	+	7.21412i	0.157488	+	0.239277i
$910$	−8.97288	−	0.923345i	−0.297448	−	0.0306086i
$911$	−17.9056	−	31.0134i	−0.593238	−	1.02752i	−0.993793	−	0.111246i	$-0.964516\pi$
$911$	−17.9056	−	31.0134i	−0.593238	−	1.02752i	0.400555	−	0.916273i	$-0.368817\pi$
$912$	−6.64869	−	4.97839i	−0.220160	−	0.164851i
$913$	1.81800	−	3.14887i	0.0601670	−	0.104212i
$914$	7.94144	−	10.9806i	0.262679	−	0.363207i
$915$	−43.1305	−	40.6781i	−1.42585	−	1.34478i
$916$	24.3928	−	8.04328i	0.805962	−	0.265758i
$917$			14.3540i			0.474010i
$918$	36.8619	+	10.4635i	1.21662	+	0.345349i
$919$	−1.20205			−0.0396521			−0.0198261	−	0.999803i	$-0.506311\pi$
$919$	−1.20205			−0.0396521			−0.0198261	+	0.999803i	$0.506311\pi$
$920$	−25.0826	+	5.50291i	−0.826948	+	0.181425i
$921$	33.5525	−	35.5752i	1.10559	−	1.17224i
$922$	15.5638	+	11.2561i	0.512567	+	0.370699i
$923$	14.6569	+	8.46214i	0.482436	+	0.278535i
$924$	−6.42687	−	3.00708i	−0.211429	−	0.0989256i
$925$	−85.7429	+	49.5037i	−2.81921	+	1.62767i
$926$	37.1514	+	3.82303i	1.22087	+	0.125632i
$927$	5.02901	+	2.52360i	0.165175	+	0.0828858i
$928$	−23.0597	+	40.9639i	−0.756972	+	1.34470i
$929$	−4.94089	−	8.55788i	−0.162105	−	0.280775i	0.773518	−	0.633774i	$-0.218495\pi$
$929$	−4.94089	−	8.55788i	−0.162105	−	0.280775i	−0.935624	+	0.352999i	$0.885162\pi$
$930$	−16.7868	−	87.9928i	−0.550461	−	2.88540i
$931$	−1.03825	−	0.599433i	−0.0340272	−	0.0196456i
$932$	4.19974	−	4.70532i	0.137567	−	0.154128i
$933$	25.1255	−	7.52656i	0.822570	−	0.246409i
$934$	11.7357	−	5.25571i	0.384004	−	0.171972i
$935$	−41.1069			−1.34434
$936$	−9.81680	+	10.0689i	−0.320872	+	0.329112i
$937$	7.23607			0.236392			0.118196	−	0.992990i	$-0.462289\pi$
$937$	7.23607			0.236392			0.118196	+	0.992990i	$0.462289\pi$
$938$	2.24807	−	1.00678i	0.0734022	−	0.0328724i
$939$	−3.98355	+	16.8202i	−0.129998	+	0.548907i
$940$	54.4559	+	48.6047i	1.77616	+	1.58531i
$941$	−32.9473	−	19.0221i	−1.07405	−	0.620103i	−0.144765	−	0.989466i	$-0.546243\pi$
$941$	−32.9473	−	19.0221i	−1.07405	−	0.620103i	−0.929285	+	0.369363i	$0.879576\pi$
$942$	−26.4881	+	22.8645i	−0.863028	+	0.744967i
$943$	6.65765	+	11.5314i	0.216803	+	0.375514i
$944$	−4.71303	+	10.8386i	−0.153396	+	0.352768i
$945$	−15.3259	−	12.8471i	−0.498551	−	0.417915i
$946$	−7.06515	−	0.727031i	−0.229708	−	0.0236378i
$947$	11.9995	−	6.92792i	0.389932	−	0.225127i	−0.292199	−	0.956358i	$-0.594387\pi$
$947$	11.9995	−	6.92792i	0.389932	−	0.225127i	0.682131	+	0.731230i	$0.261054\pi$
$948$	−7.85615	−	11.2508i	−0.255156	−	0.365410i
$949$	−6.68259	−	3.85820i	−0.216926	−	0.125242i
$950$	13.4802	+	9.74917i	0.437355	+	0.316305i
$951$	20.4856	+	4.85162i	0.664291	+	0.157325i
$952$	−3.16057	−	14.4060i	−0.102435	−	0.466903i
$953$	−2.09416			−0.0678365			−0.0339183	−	0.999425i	$-0.510799\pi$
$953$	−2.09416			−0.0678365			−0.0339183	+	0.999425i	$0.510799\pi$
$954$	23.7420	+	45.6529i	0.768675	+	1.47807i
$955$			6.99463i			0.226341i
$956$	−12.0708	−	36.6072i	−0.390399	−	1.18396i
$957$	28.2421	−	8.46020i	0.912939	−	0.273479i
$958$	32.2969	−	44.6570i	1.04347	−	1.44280i
$959$	−2.23009	+	3.86262i	−0.0720132	+	0.124731i
$960$	−16.9881	+	50.5505i	−0.548290	+	1.63151i
$961$	−29.6459	−	51.3481i	−0.956318	−	1.65639i
$962$	23.5246	+	2.42077i	0.758463	+	0.0780488i
$963$	−11.6838	+	0.684357i	−0.376506	+	0.0220531i
$964$	−4.89167	−	1.01752i	−0.157550	−	0.0327721i
$965$	−79.3724	+	45.8257i	−2.55509	+	1.47518i
$966$	−1.90022	+	5.45692i	−0.0611385	+	0.175574i
$967$	−11.4741	+	19.8737i	−0.368982	+	0.639095i	−0.989407	−	0.145171i	$-0.953627\pi$
$967$	−11.4741	+	19.8737i	−0.368982	+	0.639095i	0.620425	+	0.784266i	$0.286960\pi$
$968$	−14.2180	+	12.9710i	−0.456983	+	0.416905i
$969$	−7.42918	+	7.87706i	−0.238660	+	0.253048i
$970$	−64.8342	+	29.0353i	−2.08170	+	0.932269i
$971$		−	13.1500i		−	0.422003i	−0.977486	−	0.211002i	$-0.932327\pi$
$971$		−	13.1500i		−	0.422003i	0.977486	−	0.211002i	$-0.0676725\pi$
$972$	−30.5369	+	6.28489i	−0.979470	+	0.201588i
$973$		−	4.71722i		−	0.151227i
$974$	14.5254	+	32.4344i	0.465424	+	1.03926i
$975$	19.3252	−	20.4902i	0.618901	−	0.656213i
$976$	21.1605	+	28.5979i	0.677330	+	0.915396i
$977$	−6.09983	+	10.5652i	−0.195151	+	0.338011i	−0.946950	−	0.321381i	$-0.895853\pi$
$977$	−6.09983	+	10.5652i	−0.195151	+	0.338011i	0.751799	+	0.659392i	$0.229186\pi$
$978$	−1.38378	−	0.481863i	−0.0442486	−	0.0154083i
$979$	−2.01959	+	1.16601i	−0.0645464	+	0.0372659i
$980$	−1.56757	+	7.53602i	−0.0500742	+	0.240729i
$981$	2.52906	−	0.148135i	0.0807466	−	0.00472957i
$982$	−2.81791	+	27.3839i	−0.0899232	+	0.873856i
$983$	−2.31315	−	4.00649i	−0.0737779	−	0.127787i	0.826776	−	0.562531i	$-0.190172\pi$
$983$	−2.31315	−	4.00649i	−0.0737779	−	0.127787i	−0.900554	+	0.434744i	$0.856839\pi$
$984$	27.6485	+	0.458354i	0.881403	+	0.0146118i
$985$	−11.2499	+	19.4853i	−0.358450	+	0.620854i
$986$	49.6554	+	35.9118i	1.58135	+	1.14367i
$987$	15.7339	−	4.71324i	0.500816	−	0.150024i
$988$	−1.24438	−	3.77383i	−0.0395891	−	0.120062i
$989$			5.78391i			0.183918i
$990$	29.6731	−	15.4316i	0.943074	−	0.490450i
$991$	10.5067			0.333756			0.166878	−	0.985978i	$-0.446631\pi$
$991$	10.5067			0.333756			0.166878	+	0.985978i	$0.446631\pi$
$992$	0.585034	+	53.7494i	0.0185748	+	1.70654i
$993$	−35.1284	−	8.31948i	−1.11477	−	0.264011i
$994$	8.46341	−	11.7024i	0.268443	−	0.371177i
$995$	−61.8038	−	35.6824i	−1.95931	−	1.13121i
$996$	−5.04170	+	3.52048i	−0.159752	+	0.111551i
$997$	−36.8111	+	21.2529i	−1.16582	+	0.673085i	−0.952691	−	0.303939i	$-0.901698\pi$
$997$	−36.8111	+	21.2529i	−1.16582	+	0.673085i	−0.213127	+	0.977025i	$0.568365\pi$
$998$	1.48686	−	14.4490i	0.0470658	−	0.457377i
$999$	40.1805	+	33.6817i	1.27125	+	1.06564i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cs.a.85.14	yes	72
8.5	even	2	inner	504.2.cs.a.85.12	✓	72
9.7	even	3	inner	504.2.cs.a.421.12	yes	72
72.61	even	6	inner	504.2.cs.a.421.14	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cs.a.85.12	✓	72	8.5	even	2	inner
504.2.cs.a.85.14	yes	72	1.1	even	1	trivial
504.2.cs.a.421.12	yes	72	9.7	even	3	inner
504.2.cs.a.421.14	yes	72	72.61	even	6	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)

\(f(q)\)	\(=\)	\(q+(-0.578023 - 1.29069i) q^{2} +(-1.26004 - 1.18840i) q^{3} +(-1.33178 + 1.49210i) q^{4} +(-3.33304 - 1.92433i) q^{5} +(-0.805523 + 2.31325i) q^{6} +(0.500000 + 0.866025i) q^{7} +(2.69564 + 0.856447i) q^{8} +(0.175418 + 2.99487i) q^{9} +O(q^{10})\)	\(q+(-0.578023 - 1.29069i) q^{2} +(-1.26004 - 1.18840i) q^{3} +(-1.33178 + 1.49210i) q^{4} +(-3.33304 - 1.92433i) q^{5} +(-0.805523 + 2.31325i) q^{6} +(0.500000 + 0.866025i) q^{7} +(2.69564 + 0.856447i) q^{8} +(0.175418 + 2.99487i) q^{9} +(-0.557147 + 5.41424i) q^{10} +(-1.77389 + 1.02416i) q^{11} +(3.45131 - 0.297430i) q^{12} +(1.43524 + 0.828637i) q^{13} +(0.828761 - 1.14593i) q^{14} +(1.91290 + 6.38572i) q^{15} +(-0.452736 - 3.97430i) q^{16} -5.21444 q^{17} +(3.76406 - 1.95751i) q^{18} +1.19887i q^{19} +(7.31017 - 2.41045i) q^{20} +(0.399162 - 1.68543i) q^{21} +(2.34723 + 1.69757i) q^{22} +(1.17949 - 2.04294i) q^{23} +(-2.37883 - 4.28266i) q^{24} +(4.90611 + 8.49763i) q^{25} +(0.239913 - 2.33143i) q^{26} +(3.33806 - 3.98213i) q^{27} +(-1.95809 - 0.407303i) q^{28} +(7.19666 - 4.15499i) q^{29} +(7.13631 - 6.16007i) q^{30} +(4.75110 - 8.22914i) q^{31} +(-4.86791 + 2.88158i) q^{32} +(3.45229 + 0.817609i) q^{33} +(3.01407 + 6.73025i) q^{34} -3.84866i q^{35} +(-4.70226 - 3.72676i) q^{36} +10.0902i q^{37} +(1.54737 - 0.692973i) q^{38} +(-0.823715 - 2.74976i) q^{39} +(-7.33661 - 8.04189i) q^{40} +(-2.82225 + 4.88829i) q^{41} +(-2.40610 + 0.459022i) q^{42} +(-2.12338 + 1.22593i) q^{43} +(0.834285 - 4.01078i) q^{44} +(5.17844 - 10.3196i) q^{45} +(-3.31858 - 0.341495i) q^{46} +(4.74140 + 8.21234i) q^{47} +(-4.15258 + 5.54582i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(8.13199 - 11.2441i) q^{50} +(6.57042 + 6.19684i) q^{51} +(-3.14783 + 1.03797i) q^{52} +12.1286i q^{53} +(-7.06918 - 2.00665i) q^{54} +7.88328 q^{55} +(0.606118 + 2.76272i) q^{56} +(1.42473 - 1.51062i) q^{57} +(-9.52266 - 6.88700i) q^{58} +(-2.55889 - 1.47738i) q^{59} +(-12.0757 - 5.65012i) q^{60} +(-7.70228 + 4.44691i) q^{61} +(-13.3675 - 1.37557i) q^{62} +(-2.50592 + 1.64935i) q^{63} +(6.53300 + 4.61735i) q^{64} +(-3.18915 - 5.52376i) q^{65} +(-0.940223 - 4.92845i) q^{66} +(1.50841 + 0.870878i) q^{67} +(6.94448 - 7.78048i) q^{68} +(-3.91404 + 1.17249i) q^{69} +(-4.96745 + 2.22462i) q^{70} +10.2121 q^{71} +(-2.09208 + 8.22333i) q^{72} -4.65608 q^{73} +(13.0234 - 5.83238i) q^{74} +(3.91666 - 16.5378i) q^{75} +(-1.78883 - 1.59662i) q^{76} +(-1.77389 - 1.02416i) q^{77} +(-3.07297 + 2.65259i) q^{78} +(-1.98064 - 3.43056i) q^{79} +(-6.13888 + 14.1177i) q^{80} +(-8.93846 + 1.05071i) q^{81} +(7.94061 + 0.817119i) q^{82} +(-1.53730 + 0.887558i) q^{83} +(1.98324 + 2.84021i) q^{84} +(17.3800 + 10.0343i) q^{85} +(2.80966 + 2.03201i) q^{86} +(-14.0059 - 3.31703i) q^{87} +(-5.65893 + 1.24152i) q^{88} +1.13851 q^{89} +(-16.3127 - 0.718822i) q^{90} +1.65727i q^{91} +(1.47745 + 4.48066i) q^{92} +(-15.7661 + 4.72288i) q^{93} +(7.85897 - 10.8666i) q^{94} +(2.30702 - 3.99587i) q^{95} +(9.55824 + 2.15410i) q^{96} +(6.52591 + 11.3032i) q^{97} +(1.40678 + 0.144764i) q^{98} +(-3.37839 - 5.13292i) 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

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