LMFDB - Embedded newform 504.2.cs.a.85.12

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			85.12
Character	$\chi$	$=$	504.85
Dual form			504.2.cs.a.421.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.828761 - 1.14593i) q^{2} +(1.26004 + 1.18840i) q^{3} +(-0.626309 + 1.89940i) q^{4} +(3.33304 + 1.92433i) q^{5} +(0.317546 - 2.42882i) q^{6} +(0.500000 + 0.866025i) q^{7} +(2.69564 - 0.856447i) q^{8} +(0.175418 + 2.99487i) q^{9} +O(q^{10})$	\(q+(-0.828761 - 1.14593i) q^{2} +(1.26004 + 1.18840i) q^{3} +(-0.626309 + 1.89940i) q^{4} +(3.33304 + 1.92433i) q^{5} +(0.317546 - 2.42882i) 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} +(-3.04643 + 1.64903i) q^{12} +(-1.43524 - 0.828637i) q^{13} +(0.578023 - 1.29069i) q^{14} +(1.91290 + 6.38572i) q^{15} +(-3.21547 - 2.37923i) q^{16} -5.21444 q^{17} +(3.28653 - 2.68305i) q^{18} -1.19887i q^{19} +(-5.74260 + 5.12557i) q^{20} +(-0.399162 + 1.68543i) q^{21} +(-2.64375 - 1.18398i) q^{22} +(1.17949 - 2.04294i) q^{23} +(4.41443 + 2.12434i) 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} +(5.73225 - 7.48429i) q^{30} +(4.75110 - 8.22914i) q^{31} +(-0.0615683 + 5.65652i) q^{32} +(3.45229 + 0.817609i) q^{33} +(4.32153 + 5.97538i) q^{34} +3.84866i q^{35} +(-5.79833 - 1.54252i) q^{36} -10.0902i q^{37} +(-1.37382 + 0.993574i) q^{38} +(-0.823715 - 2.74976i) q^{39} +(10.6328 + 2.33274i) q^{40} +(-2.82225 + 4.88829i) q^{41} +(2.26219 - 0.939407i) 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} +(-1.22416 - 6.81920i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(5.67169 - 12.6646i) q^{50} +(-6.57042 - 6.19684i) q^{51} +(2.47282 - 2.20712i) q^{52} -12.1286i q^{53} +(7.32970 + 0.524947i) q^{54} +7.88328 q^{55} +(2.08953 + 1.90627i) q^{56} +(1.42473 - 1.51062i) q^{57} +(10.7256 + 4.80337i) q^{58} +(2.55889 + 1.47738i) q^{59} +(-13.3271 - 0.366061i) 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} +(-1.92420 - 4.63369i) q^{66} +(-1.50841 - 0.870878i) q^{67} +(3.26585 - 9.90433i) q^{68} +(3.91404 - 1.17249i) q^{69} +(4.41030 - 3.18962i) q^{70} +10.2121 q^{71} +(3.03781 + 7.92286i) q^{72} -4.65608 q^{73} +(-11.5627 + 8.36237i) q^{74} +(-3.91666 + 16.5378i) q^{75} +(2.27713 + 0.750861i) q^{76} +(1.77389 + 1.02416i) q^{77} +(-2.46836 + 3.22281i) 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} +(-2.95131 - 1.81377i) q^{84} +(-17.3800 - 10.0343i) q^{85} +(-3.16460 - 1.41723i) q^{86} +(-14.0059 - 3.31703i) q^{87} +(3.90465 - 4.28001i) q^{88} +1.13851 q^{89} +(16.1172 - 2.61834i) q^{90} -1.65727i q^{91} +(3.14164 + 3.51984i) q^{92} +(15.7661 - 4.72288i) q^{93} +(5.48128 - 12.2394i) q^{94} +(2.30702 - 3.99587i) q^{95} +(-6.79978 + 7.05429i) 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 $

$2$	−0.828761	−	1.14593i	−0.586023	−	0.810295i
$2$	−0.828761	−	1.14593i	−0.586023	−	0.810295i
$3$	1.26004	+	1.18840i	0.727486	+	0.686122i
$3$	1.26004	+	1.18840i	0.727486	+	0.686122i
$4$	−0.626309	+	1.89940i	−0.313155	+	0.949702i
$5$	3.33304	+	1.92433i	1.49058	+	0.860588i	0.999942	−	0.0107750i	$-0.00342986\pi$
$5$	3.33304	+	1.92433i	1.49058	+	0.860588i	0.490640	+	0.871363i	$0.336763\pi$
$6$	0.317546	−	2.42882i	0.129637	−	0.991561i
$7$	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	−0.208140	−	0.978099i	$-0.566741\pi$
$11$	1.77389	−	1.02416i	0.534849	−	0.308795i	0.742989	+	0.669304i	$0.233408\pi$
$12$	−3.04643	+	1.64903i	−0.879427	+	0.476033i
$13$	−1.43524	−	0.828637i	−0.398064	−	0.229823i	0.287584	−	0.957755i	$-0.407148\pi$
$13$	−1.43524	−	0.828637i	−0.398064	−	0.229823i	−0.685648	+	0.727933i	$0.740481\pi$
$14$	0.578023	−	1.29069i	0.154483	−	0.344952i
$15$	1.91290	+	6.38572i	0.493909	+	1.64879i
$16$	−3.21547	−	2.37923i	−0.803868	−	0.594807i
$17$	−5.21444			−1.26469			−0.632344	−	0.774688i	$-0.717907\pi$
$17$	−5.21444			−1.26469			−0.632344	+	0.774688i	$0.717907\pi$
$18$	3.28653	−	2.68305i	0.774642	−	0.632400i
$19$		−	1.19887i		−	0.275039i	−0.990499	−	0.137519i	$-0.956087\pi$
$19$		−	1.19887i		−	0.275039i	0.990499	−	0.137519i	$-0.0439129\pi$
$20$	−5.74260	+	5.12557i	−1.28408	+	1.14611i
$21$	−0.399162	+	1.68543i	−0.0871042	+	0.367791i
$22$	−2.64375	−	1.18398i	−0.563649	−	0.252424i
$23$	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	$0.0875697\pi$
$24$	4.41443	+	2.12434i	0.901091	+	0.433629i
$25$	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	−0.986270	−	0.165143i	$-0.947191\pi$
$29$	−7.19666	+	4.15499i	−1.33639	+	0.771563i	−0.350117	+	0.936706i	$0.613858\pi$
$30$	5.73225	−	7.48429i	1.04656	−	1.36644i
$31$	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	$-0.158749\pi$
$32$	−0.0615683	+	5.65652i	−0.0108838	+	0.999941i
$33$	3.45229	+	0.817609i	0.600967	+	0.142328i
$34$	4.32153	+	5.97538i	0.741136	+	1.02477i
$35$			3.84866i			0.650543i
$36$	−5.79833	−	1.54252i	−0.966388	−	0.257087i
$37$		−	10.0902i		−	1.65882i	−0.558641	−	0.829410i	$-0.688677\pi$
$37$		−	10.0902i		−	1.65882i	0.558641	−	0.829410i	$-0.311323\pi$
$38$	−1.37382	+	0.993574i	−0.222862	+	0.161179i
$39$	−0.823715	−	2.74976i	−0.131900	−	0.440314i
$40$	10.6328	+	2.33274i	1.68119	+	0.368839i
$41$	−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	$0.311958\pi$
$42$	2.26219	−	0.939407i	0.349064	−	0.144954i
$43$	2.12338	−	1.22593i	0.323812	−	0.186953i	−0.329279	−	0.944233i	$-0.606805\pi$
$43$	2.12338	−	1.22593i	0.323812	−	0.186953i	0.653090	+	0.757280i	$0.273472\pi$
$44$	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	$0.590238\pi$
$48$	−1.22416	−	6.81920i	−0.176693	−	0.984266i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	5.67169	−	12.6646i	0.802099	−	1.79104i
$51$	−6.57042	−	6.19684i	−0.920043	−	0.867730i
$52$	2.47282	−	2.20712i	0.342919	−	0.306073i
$53$		−	12.1286i		−	1.66600i	−0.553277	−	0.832998i	$-0.686623\pi$
$53$		−	12.1286i		−	1.66600i	0.553277	−	0.832998i	$-0.313377\pi$
$54$	7.32970	+	0.524947i	0.997445	+	0.0714363i
$55$	7.88328			1.06298
$56$	2.08953	+	1.90627i	0.279225	+	0.254736i
$57$	1.42473	−	1.51062i	0.188710	−	0.200087i
$58$	10.7256	+	4.80337i	1.40835	+	0.630713i
$59$	2.55889	+	1.47738i	0.333139	+	0.192338i	0.657234	−	0.753687i	$-0.271726\pi$
$59$	2.55889	+	1.47738i	0.333139	+	0.192338i	−0.324095	+	0.946025i	$0.605060\pi$
$60$	−13.3271	−	0.366061i	−1.72053	−	0.0472582i
$61$	7.70228	−	4.44691i	0.986176	−	0.569369i	0.0820471	−	0.996628i	$-0.473854\pi$
$61$	7.70228	−	4.44691i	0.986176	−	0.569369i	0.904129	+	0.427259i	$0.140521\pi$
$62$	−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
$66$	−1.92420	−	4.63369i	−0.236853	−	0.570367i
$67$	−1.50841	−	0.870878i	−0.184281	−	0.106395i	0.405021	−	0.914307i	$-0.367264\pi$
$67$	−1.50841	−	0.870878i	−0.184281	−	0.106395i	−0.589303	+	0.807912i	$0.700597\pi$
$68$	3.26585	−	9.90433i	0.396043	−	1.20108i
$69$	3.91404	−	1.17249i	0.471195	−	0.141151i
$70$	4.41030	−	3.18962i	0.527132	−	0.381233i
$71$	10.2121			1.21196			0.605978	−	0.795482i	$-0.292782\pi$
$71$	10.2121			1.21196			0.605978	+	0.795482i	$0.292782\pi$
$72$	3.03781	+	7.92286i	0.358009	+	0.933718i
$73$	−4.65608			−0.544952			−0.272476	−	0.962163i	$-0.587843\pi$
$73$	−4.65608			−0.544952			−0.272476	+	0.962163i	$0.587843\pi$
$74$	−11.5627	+	8.36237i	−1.34413	+	0.972106i
$75$	−3.91666	+	16.5378i	−0.452257	+	1.90962i
$76$	2.27713	+	0.750861i	0.261205	+	0.0861297i
$77$	1.77389	+	1.02416i	0.202154	+	0.116714i
$78$	−2.46836	+	3.22281i	−0.279487	+	0.364912i
$79$	−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	−0.413251	−	0.910617i	$-0.635607\pi$
$83$	1.53730	−	0.887558i	0.168740	−	0.0974222i	0.581992	+	0.813195i	$0.302274\pi$
$84$	−2.95131	−	1.81377i	−0.322015	−	0.197898i
$85$	−17.3800	−	10.0343i	−1.88512	−	1.08837i
$86$	−3.16460	−	1.41723i	−0.341248	−	0.152824i
$87$	−14.0059	−	3.31703i	−1.50159	−	0.355623i
$88$	3.90465	−	4.28001i	0.416237	−	0.456251i
$89$	1.13851			0.120681			0.0603407	−	0.998178i	$-0.480781\pi$
$89$	1.13851			0.120681			0.0603407	+	0.998178i	$0.480781\pi$
$90$	16.1172	−	2.61834i	1.69890	−	0.275997i
$91$		−	1.65727i		−	0.173730i
$92$	3.14164	+	3.51984i	0.327539	+	0.366969i
$93$	15.7661	−	4.72288i	1.63487	−	0.489740i
$94$	5.48128	−	12.2394i	0.565351	−	1.26240i
$95$	2.30702	−	3.99587i	0.236695	−	0.409968i
$96$	−6.79978	+	7.05429i	−0.693999	+	0.719976i
$97$	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	−0.618883	−	0.785483i	$-0.712415\pi$
$101$	−2.49314	+	1.43941i	−0.248077	+	0.143227i	0.370807	+	0.928710i	$0.379081\pi$
$102$	−1.65582	+	12.6649i	−0.163951	+	1.25402i
$103$	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	$0.137212\pi$
$104$	−4.57858	−	1.00450i	−0.448967	−	0.0984996i
$105$	−4.57375	+	4.84948i	−0.446352	+	0.473261i
$106$	−13.8986	+	10.0517i	−1.34995	+	0.976311i
$107$		−	3.90128i		−	0.377151i	−0.982059	−	0.188575i	$-0.939613\pi$
$107$		−	3.90128i		−	0.377151i	0.982059	−	0.188575i	$-0.0603870\pi$
$108$	−5.47302	−	8.83437i	−0.526641	−	0.850088i
$109$			0.844464i			0.0808850i	0.999182	+	0.0404425i	$0.0128768\pi$
$109$			0.844464i			0.0808850i	−0.999182	+	0.0404425i	$0.987123\pi$
$110$	−6.53336	−	9.03369i	−0.622932	−	0.861328i
$111$	11.9912	−	12.7141i	1.13815	−	1.20677i
$112$	0.452736	−	3.97430i	0.0427795	−	0.375536i
$113$	−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	$0.826128\pi$
$114$	−2.91183	−	0.380695i	−0.272718	−	0.0356553i
$115$	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
$120$	10.6255	+	15.5753i	0.969975	+	1.42183i
$121$	−3.40220	+	5.89278i	−0.309291	+	0.535707i
$122$	−11.4792	−	5.14084i	−1.03928	−	0.465430i
$123$	−9.36539	+	2.80549i	−0.844449	+	0.252963i
$124$	12.6548	+	14.1782i	1.13644	+	1.27324i
$125$			18.5206i			1.65654i
$126$	3.96685	+	1.50469i	0.353395	+	0.134049i
$127$	−14.1946			−1.25957			−0.629783	−	0.776771i	$-0.716856\pi$
$127$	−14.1946			−1.25957			−0.629783	+	0.776771i	$0.716856\pi$
$128$	−10.7055	−	3.65967i	−0.946238	−	0.323472i
$129$	4.13244	+	0.978690i	0.363841	+	0.0861688i
$130$	−3.68680	+	8.23242i	−0.323354	+	0.722031i
$131$	−12.4309	−	7.17699i	−1.08609	−	0.627056i	−0.153560	−	0.988139i	$-0.549074\pi$
$131$	−12.4309	−	7.17699i	−1.08609	−	0.627056i	−0.932534	+	0.361083i	$0.882407\pi$
$132$	−3.71517	+	6.04522i	−0.323364	+	0.526169i
$133$	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	$0.772313\pi$
$138$	−4.58739	−	3.51350i	−0.390505	−	0.299089i
$139$	4.08523	+	2.35861i	0.346505	+	0.200055i	0.663145	−	0.748491i	$-0.269221\pi$
$139$	4.08523	+	2.35861i	0.346505	+	0.200055i	−0.316640	+	0.948546i	$0.602555\pi$
$140$	−7.31017	−	2.41045i	−0.617822	−	0.203721i
$141$	−3.78517	+	15.9826i	−0.318769	+	1.34598i
$142$	−8.46341	−	11.7024i	−0.710233	−	0.982041i
$143$	−3.39462			−0.283873
$144$	6.56142	−	10.0473i	0.546785	−	0.837273i
$145$	−31.9824			−2.65599
$146$	3.85878	+	5.33553i	0.319355	+	0.441572i
$147$	−1.65920	+	0.497030i	−0.136849	+	0.0409944i
$148$	19.1654	+	6.31959i	1.57538	+	0.519467i
$149$	10.4666	+	6.04287i	0.857454	+	0.495052i	0.863159	−	0.504932i	$-0.168483\pi$
$149$	10.4666	+	6.04287i	0.857454	+	0.495052i	−0.00570463	+	0.999984i	$0.501816\pi$
$150$	22.1971	−	9.21767i	1.81239	−	0.752620i
$151$	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
$156$	5.73880	+	0.157629i	0.459472	+	0.0126205i
$157$	−12.3714	−	7.14261i	−0.987342	−	0.570042i	−0.0828632	−	0.996561i	$-0.526406\pi$
$157$	−12.3714	−	7.14261i	−0.987342	−	0.570042i	−0.904479	+	0.426519i	$0.859740\pi$
$158$	−2.28971	+	5.11279i	−0.182160	+	0.406752i
$159$	14.4136	−	15.2826i	1.14308	−	1.21199i
$160$	−11.0902	+	18.7349i	−0.876760	+	1.48113i
$161$	2.35898			0.185914
$162$	8.61189	+	9.37205i	0.676614	+	0.736338i
$163$		−	0.598199i		−	0.0468546i	−0.999726	−	0.0234273i	$-0.992542\pi$
$163$		−	0.598199i		−	0.0468546i	0.999726	−	0.0234273i	$-0.00745782\pi$
$164$	−7.51723	−	8.42218i	−0.586997	−	0.657662i
$165$	9.93328	+	9.36848i	0.773305	+	0.729335i
$166$	−2.29113	−	1.02606i	−0.177826	−	0.0796376i
$167$	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	$0.0880484\pi$
$168$	0.367482	+	4.88518i	0.0283519	+	0.376900i
$169$	−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	−0.692030	−	0.721868i	$-0.743284\pi$
$173$	−5.43071	+	3.13542i	−0.412889	+	0.238382i	0.279141	+	0.960250i	$0.409950\pi$
$174$	7.80646	+	18.7988i	0.591806	+	1.42513i
$175$	−4.90611	+	8.49763i	−0.370867	+	0.642361i
$176$	−8.14062	−	0.927346i	−0.613622	−	0.0699013i
$177$	1.46860	+	4.90254i	0.110387	+	0.368497i
$178$	−0.943550	−	1.30465i	−0.0707221	−	0.0977876i
$179$		−	13.2058i		−	0.987049i	−0.869732	−	0.493525i	$-0.835708\pi$
$179$		−	13.2058i		−	0.987049i	0.869732	−	0.493525i	$-0.164292\pi$
$180$	−16.3577	−	16.2992i	−1.21923	−	1.21487i
$181$		−	14.8950i		−	1.10714i	−0.832804	−	0.553568i	$-0.813266\pi$
$181$		−	14.8950i		−	1.10714i	0.832804	−	0.553568i	$-0.186734\pi$
$182$	−1.89912	+	1.37348i	−0.140772	+	0.101809i
$183$	14.9899	+	3.55007i	1.10809	+	0.262429i
$184$	1.42982	−	6.51721i	0.105408	−	0.480455i
$185$	19.4169	−	33.6311i	1.42756	−	2.47261i
$186$	−18.4784	−	14.1527i	−1.35490	−	1.03773i
$187$	−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	$0.854278\pi$
$192$	13.7191	+	1.94574i	0.990092	+	0.140422i
$193$	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	$-0.161056\pi$
$194$	7.54426	−	16.8459i	0.541646	−	1.20947i
$195$	2.54597	−	10.7502i	0.182321	−	0.769835i
$196$	−1.33178	−	1.49210i	−0.0951270	−	0.106579i
$197$			5.84611i			0.416518i	0.978074	+	0.208259i	$0.0667797\pi$
$197$			5.84611i			0.416518i	−0.978074	+	0.208259i	$0.933220\pi$
$198$	3.08209	−	8.12537i	0.219034	−	0.577445i
$199$	18.5427			1.31446			0.657230	−	0.753690i	$-0.271728\pi$
$199$	18.5427			1.31446			0.657230	+	0.753690i	$0.271728\pi$
$200$	20.5029	+	18.7048i	1.44977	+	1.32263i
$201$	−0.865706	−	2.88993i	−0.0610622	−	0.203840i
$202$	3.71569	+	1.66403i	0.261435	+	0.117081i
$203$	−7.19666	−	4.15499i	−0.505107	−	0.291623i
$204$	15.8854	−	8.59876i	1.11220	−	0.602033i
$205$	−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
$210$	9.34771	+	1.22213i	0.645053	+	0.0843348i
$211$	−11.5780	−	6.68455i	−0.797061	−	0.460183i	0.0453815	−	0.998970i	$-0.485550\pi$
$211$	−11.5780	−	6.68455i	−0.797061	−	0.460183i	−0.842442	+	0.538786i	$0.818883\pi$
$212$	23.0372	+	7.59627i	1.58220	+	0.521714i
$213$	12.8677	+	12.1361i	0.881681	+	0.831549i
$214$	−4.47059	+	3.23323i	−0.305603	+	0.221019i
$215$	9.43640			0.643557
$216$	−5.58774	+	13.5933i	−0.380198	+	0.924905i
$217$	9.50220			0.645051
$218$	0.967696	−	0.699859i	0.0655406	−	0.0474004i
$219$	−5.86686	−	5.53327i	−0.396445	−	0.373904i
$220$	−4.93737	+	14.9735i	−0.332878	+	1.00952i
$221$	7.48398	+	4.32088i	0.503427	+	0.290654i
$222$	−24.5073	−	3.20410i	−1.64482	−	0.215045i
$223$	−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	$-0.313611\pi$
$227$	23.3643	−	13.4894i	1.55075	−	0.895324i	0.998081	−	0.0619204i	$-0.0197225\pi$
$228$	1.97696	+	3.65226i	0.130928	+	0.241877i
$229$	11.1218	+	6.42118i	0.734950	+	0.424323i	0.820230	−	0.572034i	$-0.193845\pi$
$229$	11.1218	+	6.42118i	0.734950	+	0.424323i	−0.0852806	+	0.996357i	$0.527179\pi$
$230$	−11.7181	−	5.24784i	−0.772670	−	0.346032i
$231$	1.01808	+	3.39858i	0.0669845	+	0.223610i
$232$	−15.8411	+	17.3639i	−1.04002	+	1.14000i
$233$	−3.15348			−0.206592			−0.103296	−	0.994651i	$-0.532939\pi$
$233$	−3.15348			−0.206592			−0.103296	+	0.994651i	$0.532939\pi$
$234$	−6.94023	+	1.12748i	−0.453697	+	0.0737059i
$235$			36.4961i			2.38074i
$236$	−4.40879	+	3.93507i	−0.286988	+	0.256151i
$237$	1.58119	−	6.67645i	0.102709	−	0.433682i
$238$	−3.01407	+	6.73025i	−0.195373	+	0.436257i
$239$	−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	$0.952445\pi$
$240$	9.04221	−	25.0844i	0.583672	−	1.61919i
$241$	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
$246$	10.9766	+	8.40700i	0.699841	+	0.536011i
$247$	−0.993425	+	1.72066i	−0.0632101	+	0.109483i
$248$	5.75945	−	26.2519i	0.365725	−	1.66700i
$249$	2.99183	+	0.708558i	0.189600	+	0.0449031i
$250$	21.2233	−	15.3492i	1.34228	−	0.970767i
$251$			8.49633i			0.536284i	0.963379	+	0.268142i	$0.0864096\pi$
$251$			8.49633i			0.536284i	−0.963379	+	0.268142i	$0.913590\pi$
$252$	−1.56330	−	5.79276i	−0.0984787	−	0.364910i
$253$		−	4.83195i		−	0.303782i
$254$	11.7639	+	16.2660i	0.738134	+	1.02062i
$255$	−9.97472	−	33.2980i	−0.624641	−	2.08520i
$256$	4.67854	+	15.3007i	0.292409	+	0.956293i
$257$	−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	$0.787338\pi$
$258$	−2.30330	−	5.54659i	−0.143397	−	0.345315i
$259$	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	$-0.579123\pi$
$264$	10.0064	−	0.752720i	0.615851	−	0.0463267i
$265$	23.3395	−	40.4252i	1.43373	−	2.48330i
$266$	−1.54737	−	0.692973i	−0.0948753	−	0.0424889i
$267$	1.43457	+	1.35300i	0.0877941	+	0.0828022i
$268$	2.59888	−	2.31963i	0.158752	−	0.141694i
$269$			8.58738i			0.523582i	0.965125	+	0.261791i	$0.0843131\pi$
$269$			8.58738i			0.523582i	−0.965125	+	0.261791i	$0.915687\pi$
$270$	23.4200	+	15.8544i	1.42530	+	0.964871i
$271$	−1.21679			−0.0739145			−0.0369573	−	0.999317i	$-0.511767\pi$
$271$	−1.21679			−0.0739145			−0.0369573	+	0.999317i	$0.511767\pi$
$272$	16.7669	+	12.4064i	1.01664	+	0.752246i
$273$	1.96950	−	2.08824i	0.119200	−	0.126386i
$274$	2.57808	−	5.75671i	0.155748	−	0.347776i
$275$	17.4058	+	10.0493i	1.04961	+	0.605994i
$276$	−0.224372	+	8.16868i	−0.0135056	+	0.491697i
$277$	−6.63440	+	3.83037i	−0.398622	+	0.230145i	−0.685889	−	0.727706i	$-0.740587\pi$
$277$	−6.63440	+	3.83037i	−0.398622	+	0.230145i	0.287267	+	0.957851i	$0.407253\pi$
$278$	−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	$0.656502\pi$
$282$	21.4519	−	8.90821i	1.27744	−	0.530476i
$283$	15.1849	+	8.76702i	0.902650	+	0.521145i	0.878059	−	0.478553i	$-0.158838\pi$
$283$	15.1849	+	8.76702i	0.902650	+	0.521145i	0.0245907	+	0.999698i	$0.492172\pi$
$284$	−6.39594	+	19.3969i	−0.379529	+	1.15100i
$285$	7.65563	−	2.29332i	0.453480	−	0.135844i
$286$	2.81333	+	3.89000i	0.166356	+	0.230020i
$287$	−5.64451			−0.333185
$288$	−16.9513	+	0.807869i	−0.998866	+	0.0476041i
$289$	10.1904			0.599436
$290$	26.5057	+	36.6495i	1.55647	+	2.15213i
$291$	−5.20979	+	21.9979i	−0.305403	+	1.28954i
$292$	2.91614	−	8.84377i	0.170654	−	0.517542i
$293$	10.4318	+	6.02281i	0.609433	+	0.351856i	0.772743	−	0.634718i	$-0.218884\pi$
$293$	10.4318	+	6.02281i	0.609433	+	0.351856i	−0.163311	+	0.986575i	$0.552217\pi$
$294$	1.94465	+	1.48941i	0.113414	+	0.0868643i
$295$	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
$300$	−28.9589	−	17.7971i	−1.67194	−	1.02752i
$301$	2.12338	+	1.22593i	0.122389	+	0.0706615i
$302$	1.22164	−	2.72784i	0.0702973	−	0.156970i
$303$	−4.85206	−	1.14912i	−0.278744	−	0.0660151i
$304$	−2.85238	+	3.85492i	−0.163595	+	0.221095i
$305$	34.2294			1.95997
$306$	−17.1374	+	13.9906i	−0.979680	+	0.799789i
$307$		−	28.2333i		−	1.61136i	−0.592350	−	0.805681i	$-0.701800\pi$
$307$		−	28.2333i		−	1.61136i	0.592350	−	0.805681i	$-0.298200\pi$
$308$	−3.05630	+	2.72790i	−0.174149	+	0.155437i
$309$	3.11194	−	0.932210i	0.177032	−	0.0530316i
$310$	−47.2016	−	21.1388i	−2.68087	−	1.20060i
$311$	−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	$0.307921\pi$
$312$	−4.57546	−	6.70690i	−0.259035	−	0.379703i
$313$	−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	−0.174368	−	0.984681i	$-0.555788\pi$
$317$	10.5261	−	6.07726i	0.591206	−	0.341333i	0.765574	+	0.643347i	$0.222455\pi$
$318$	−29.4583	−	3.85139i	−1.65194	−	0.215975i
$319$	−8.51074	+	14.7410i	−0.476510	+	0.825340i
$320$	30.6601	−	2.81817i	1.71395	−	0.157540i
$321$	4.63627	−	4.91578i	0.258772	−	0.274372i
$322$	−1.95503	−	2.70323i	−0.108950	−	0.150645i
$323$			6.25142i			0.347838i
$324$	3.60251	−	17.6358i	0.200140	−	0.979767i
$325$		−	16.2615i		−	0.902028i
$326$	−0.685494	+	0.495764i	−0.0379660	+	0.0274578i
$327$	−1.00356	+	1.06406i	−0.0554970	+	0.0588427i
$328$	−3.42123	+	15.5942i	−0.188906	+	0.861045i
$329$	−4.74140	+	8.21234i	−0.261402	+	0.452761i
$330$	2.50330	−	19.1471i	0.137802	−	1.05401i
$331$	−18.0500	+	10.4212i	−0.992120	+	0.572801i	−0.905907	−	0.423476i	$-0.860810\pi$
$331$	−18.0500	+	10.4212i	−0.992120	+	0.572801i	−0.0862127	+	0.996277i	$0.527476\pi$
$332$	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
$336$	5.29351	−	4.46976i	0.288785	−	0.243845i
$337$	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	$0.0654692\pi$
$338$	−5.92673	+	13.2340i	−0.322372	+	0.719837i
$339$	−30.9406	+	9.26854i	−1.68046	+	0.503398i
$340$	29.9445	−	26.7270i	1.62397	−	1.44947i
$341$		−	19.4635i		−	1.05401i
$342$	−3.21662	−	3.94011i	−0.173935	−	0.213057i
$343$	−1.00000			−0.0539949
$344$	4.67392	−	5.12324i	0.252001	−	0.276226i
$345$	15.3019	+	3.62396i	0.823827	+	0.195108i
$346$	8.09374	+	3.62470i	0.435122	+	0.194865i
$347$	−18.5823	−	10.7285i	−0.997551	−	0.575936i	−0.0900281	−	0.995939i	$-0.528696\pi$
$347$	−18.5823	−	10.7285i	−0.997551	−	0.575936i	−0.907523	+	0.420003i	$0.862029\pi$
$348$	15.0724	−	24.5254i	0.807965	−	1.31470i
$349$	−16.1478	+	9.32291i	−0.864369	+	0.499044i	−0.865473	−	0.500956i	$-0.832982\pi$
$349$	−16.1478	+	9.32291i	−0.864369	+	0.499044i	0.00110371	+	0.999999i	$0.499649\pi$
$350$	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	$-0.360671\pi$
$354$	4.40084	−	5.74595i	0.233902	−	0.305394i
$355$	34.0374	+	19.6515i	1.80652	+	1.04299i
$356$	−0.713057	+	2.16248i	−0.0377920	+	0.114611i
$357$	2.08140	−	8.78857i	0.110160	−	0.465141i
$358$	−15.1329	+	10.9445i	−0.799801	+	0.578433i
$359$	−22.0752			−1.16508			−0.582542	−	0.812801i	$-0.697942\pi$
$359$	−22.0752			−1.16508			−0.582542	+	0.812801i	$0.697942\pi$
$360$	−5.12107	+	32.2530i	−0.269904	+	1.69988i
$361$	17.5627			0.924354
$362$	−17.0686	+	12.3444i	−0.897107	+	0.648807i
$363$	−11.2899	+	3.38199i	−0.592566	+	0.177509i
$364$	3.14783	+	1.03797i	0.164991	+	0.0544042i
$365$	−15.5189	−	8.95984i	−0.812296	−	0.468979i
$366$	−8.35493	−	20.1196i	−0.436719	−	1.05167i
$367$	−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
$372$	−0.903789	+	32.9042i	−0.0468593	+	1.70600i
$373$	−7.51928	−	4.34126i	−0.389334	−	0.224782i	0.292538	−	0.956254i	$-0.405500\pi$
$373$	−7.51928	−	4.34126i	−0.389334	−	0.224782i	−0.681871	+	0.731472i	$0.738834\pi$
$374$	13.7857	+	6.17377i	0.712840	+	0.319238i
$375$	−22.0099	+	23.3368i	−1.13659	+	1.20511i
$376$	19.8146	+	18.0768i	1.02186	+	0.932240i
$377$	13.7719			0.709290
$378$	3.21023	+	6.61018i	0.165116	+	0.339991i
$379$			28.2348i			1.45032i	0.688578	+	0.725162i	$0.258235\pi$
$379$			28.2348i			1.45032i	−0.688578	+	0.725162i	$0.741765\pi$
$380$	6.14487	+	6.88461i	0.315225	+	0.353173i
$381$	−17.8858	−	16.8688i	−0.916317	−	0.864216i
$382$	−1.05051	+	2.34573i	−0.0537487	+	0.120018i
$383$	−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	$0.967680\pi$
$384$	−9.14019	−	17.3337i	−0.466433	−	0.884556i
$385$	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	−0.957793	−	0.287460i	$-0.907189\pi$
$389$	−23.4259	+	13.5250i	−1.18774	+	0.685743i	−0.229948	+	0.973203i	$0.573856\pi$
$390$	−14.4289	+	5.99181i	−0.730637	+	0.303407i
$391$	−6.15039	+	10.6528i	−0.311039	+	0.538735i
$392$	−0.606118	+	2.76272i	−0.0306136	+	0.139538i
$393$	−7.13436	−	23.8162i	−0.359881	−	1.20137i
$394$	6.69923	−	4.84503i	0.337502	−	0.244089i
$395$		−	15.2456i		−	0.767090i
$396$	−11.8654	+	3.20214i	−0.596259	+	0.160913i
$397$		−	21.6189i		−	1.08502i	−0.840048	−	0.542512i	$-0.817473\pi$
$397$		−	21.6189i		−	1.08502i	0.840048	−	0.542512i	$-0.182527\pi$
$398$	−15.3675	−	21.2487i	−0.770304	−	1.06510i
$399$	2.02060	+	0.478541i	0.101157	+	0.0239570i
$400$	4.44234	−	38.9967i	0.222117	−	1.94983i
$401$	−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	$0.198162\pi$
$402$	−2.59419	+	3.38710i	−0.129387	+	0.168933i
$403$	−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
$408$	−23.0188	−	11.0772i	−1.13960	−	0.548405i
$409$	−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	$0.997995\pi$
$410$	28.0388	+	12.5569i	1.38474	+	0.620140i
$411$	−1.78033	+	7.51730i	−0.0878172	+	0.370801i
$412$	2.49783	+	2.79853i	0.123059	+	0.137874i
$413$			2.95475i			0.145394i
$414$	−1.60487	−	9.87881i	−0.0788752	−	0.485517i
$415$	6.83183			0.335361
$416$	4.77557	−	8.06745i	0.234141	−	0.395539i
$417$	2.34460	+	7.82683i	0.114816	+	0.383281i
$418$	−1.41943	+	3.16950i	−0.0694265	+	0.155025i
$419$	27.3061	+	15.7652i	1.33399	+	0.770179i	0.985909	−	0.167285i	$-0.0535000\pi$
$419$	27.3061	+	15.7652i	1.33399	+	0.770179i	0.348081	+	0.937464i	$0.386833\pi$
$420$	−6.34655	−	11.7247i	−0.309680	−	0.572105i
$421$	22.1162	−	12.7688i	1.07788	−	0.622313i	0.147555	−	0.989054i	$-0.452860\pi$
$421$	22.1162	−	12.7688i	1.07788	−	0.622313i	0.930323	+	0.366741i	$0.119526\pi$
$422$	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
$426$	3.24281	−	24.8034i	0.157115	−	1.20173i
$427$	7.70228	+	4.44691i	0.372740	+	0.215201i
$428$	7.41011	+	2.44341i	0.358181	+	0.118107i
$429$	−4.27737	−	4.03416i	−0.206513	−	0.194771i
$430$	−7.82053	−	10.8135i	−0.377139	−	0.521471i
$431$	17.3941			0.837845			0.418922	−	0.908022i	$-0.362408\pi$
$431$	17.3941			0.837845			0.418922	+	0.908022i	$0.362408\pi$
$432$	20.2078	−	4.86242i	0.972250	−	0.233943i
$433$	−26.4410			−1.27067			−0.635337	−	0.772235i	$-0.719139\pi$
$433$	−26.4410			−1.27067			−0.635337	+	0.772235i	$0.719139\pi$
$434$	−7.87505	−	10.8888i	−0.378015	−	0.522681i
$435$	−40.2992	−	38.0078i	−1.93220	−	1.82233i
$436$	−1.60398	−	0.528895i	−0.0768166	−	0.0253295i
$437$	−2.44921	−	1.41405i	−0.117162	−	0.0676433i
$438$	−1.47852	+	11.3088i	−0.0706462	+	0.540354i
$439$	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	−0.996815	−	0.0797435i	$-0.974590\pi$
$443$	−30.0173	+	17.3305i	−1.42616	+	0.823396i	−0.429348	+	0.903139i	$0.641257\pi$
$444$	16.6390	+	30.7391i	0.789653	+	1.45881i
$445$	3.79469	+	2.19087i	0.179886	+	0.103857i
$446$	−7.78839	+	17.3910i	−0.368791	+	0.823489i
$447$	6.00698	+	20.0527i	0.284121	+	0.948462i
$448$	7.26524	+	3.34907i	0.343250	+	0.158229i
$449$	−10.2906			−0.485642			−0.242821	−	0.970071i	$-0.578073\pi$
$449$	−10.2906			−0.485642			−0.242821	+	0.970071i	$0.578073\pi$
$450$	38.9236	+	14.7644i	1.83488	+	0.695999i
$451$			11.5617i			0.544421i
$452$	−24.8348	−	27.8245i	−1.16813	−	1.30875i
$453$	−0.843617	+	3.56211i	−0.0396366	+	0.167362i
$454$	−34.8214	−	15.5944i	−1.63425	−	0.731881i
$455$	3.18915	−	5.52376i	0.149509	−	0.258958i
$456$	2.54680	−	5.29231i	0.119265	−	0.247835i
$457$	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	−0.200422	−	0.979710i	$-0.564231\pi$
$461$	11.7622	−	6.79091i	0.547820	−	0.316284i	0.748242	+	0.663426i	$0.230898\pi$
$462$	3.05079	−	3.98325i	0.141936	−	0.185318i
$463$	−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	$0.956363\pi$
$464$	33.0264	+	3.76223i	1.53321	+	0.174657i
$465$	61.6374	+	14.5976i	2.85837	+	0.676950i
$466$	2.61349	+	3.61367i	0.121067	+	0.167400i
$467$		−	9.09256i		−	0.420754i	−0.977620	−	0.210377i	$-0.932531\pi$
$467$		−	9.09256i		−	0.420754i	0.977620	−	0.210377i	$-0.0674691\pi$
$468$	7.04381	+	7.01860i	0.325600	+	0.324435i
$469$		−	1.74176i		−	0.0804268i
$470$	41.8220	−	30.2466i	1.92910	−	1.39517i
$471$	−7.10018	−	23.7021i	−0.327159	−	1.09213i
$472$	8.16315	+	1.79093i	0.375739	+	0.0824341i
$473$	2.51110	−	4.34935i	0.115460	−	0.199983i
$474$	−8.96116	+	3.72125i	−0.411600	+	0.170923i
$475$	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	$0.483831\pi$
$480$	−36.2387	+	10.4272i	−1.65406	+	0.475935i
$481$	−8.36112	+	14.4819i	−0.381234	+	0.660317i
$482$	1.44401	−	3.22439i	0.0657729	−	0.146867i
$483$	2.97242	+	2.80341i	0.135250	+	0.127560i
$484$	−9.06195	−	10.1529i	−0.411907	−	0.461493i
$485$			50.2321i			2.28092i
$486$	−0.286383	+	22.0435i	−0.0129906	+	0.999916i
$487$	−25.1294			−1.13872			−0.569362	−	0.822087i	$-0.692810\pi$
$487$	−25.1294			−1.13872			−0.569362	+	0.822087i	$0.692810\pi$
$488$	16.9541	−	18.5839i	0.767475	−	0.841253i
$489$	0.710899	−	0.753757i	0.0321480	−	0.0340861i
$490$	4.96745	+	2.22462i	0.224406	+	0.100498i
$491$	16.8577	+	9.73281i	0.760778	+	0.439235i	0.829575	−	0.558395i	$-0.188583\pi$
$491$	16.8577	+	9.73281i	0.760778	+	0.439235i	−0.0687970	+	0.997631i	$0.521916\pi$
$492$	0.536870	−	19.5458i	0.0242040	−	0.881191i
$493$	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
$498$	−1.66756	−	4.01566i	−0.0747250	−	0.179946i
$499$	−8.89492	−	5.13549i	−0.398191	−	0.229896i	0.287512	−	0.957777i	$-0.407172\pi$
$499$	−8.89492	−	5.13549i	−0.398191	−	0.229896i	−0.685703	+	0.727881i	$0.740505\pi$
$500$	−35.1782	−	11.5996i	−1.57322	−	0.518752i
$501$	10.4842	−	3.14065i	0.468401	−	0.140314i
$502$	9.73620	−	7.04143i	0.434548	−	0.314274i
$503$	26.0834			1.16300			0.581500	−	0.813547i	$-0.302466\pi$
$503$	26.0834			1.16300			0.581500	+	0.813547i	$0.302466\pi$
$504$	−5.34249	+	6.59225i	−0.237974	+	0.293642i
$505$	−11.0797			−0.493038
$506$	−5.53707	+	4.00453i	−0.246153	+	0.178023i
$507$	4.09278	−	17.2814i	0.181767	−	0.767496i
$508$	8.89020	−	26.9613i	0.394439	−	1.19621i
$509$	−6.08606	−	3.51379i	−0.269760	−	0.155746i	0.359019	−	0.933330i	$-0.383111\pi$
$509$	−6.08606	−	3.51379i	−0.269760	−	0.155746i	−0.628778	+	0.777584i	$0.716445\pi$
$510$	−29.8905	+	39.0264i	−1.32357	+	1.72812i
$511$	−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
$516$	−4.44711	+	7.23622i	−0.195773	+	0.318557i
$517$	16.8215	+	9.71188i	0.739808	+	0.427128i
$518$	−13.0234	−	5.83238i	−0.572214	−	0.256260i
$519$	−10.5691	−	2.50308i	−0.463930	−	0.109873i
$520$	−13.3276	−	12.1588i	−0.584454	−	0.533197i
$521$	22.0184			0.964643			0.482322	−	0.875994i	$-0.339794\pi$
$521$	22.0184			0.964643			0.482322	+	0.875994i	$0.339794\pi$
$522$	−12.5040	+	32.9645i	−0.547284	+	1.44282i
$523$		−	13.8466i		−	0.605471i	−0.953075	−	0.302735i	$-0.902100\pi$
$523$		−	13.8466i		−	0.605471i	0.953075	−	0.302735i	$-0.0978998\pi$
$524$	21.4176	−	19.1163i	0.935632	−	0.835100i
$525$	−16.2805	+	4.87697i	−0.710539	+	0.212848i
$526$	−18.0433	+	40.2898i	−0.786727	+	1.75672i
$527$	−24.7743	+	42.9104i	−1.07919	+	1.86921i
$528$	−9.15547	−	10.8428i	−0.398441	−	0.471872i
$529$	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
$534$	0.361528	−	2.76523i	0.0156448	−	0.119663i
$535$	7.50736	−	13.0031i	0.324571	−	0.562174i
$536$	−4.81198	−	1.05571i	−0.207846	−	0.0455997i
$537$	15.6938	−	16.6399i	0.677236	−	0.718065i
$538$	9.84053	−	7.11689i	0.424255	−	0.306831i
$539$			2.04832i			0.0882272i
$540$	−1.24152	−	39.9772i	−0.0534267	−	1.72035i
$541$			37.8518i			1.62738i	0.581301	+	0.813689i	$0.302544\pi$
$541$			37.8518i			1.62738i	−0.581301	+	0.813689i	$0.697456\pi$
$542$	1.00843	+	1.39435i	0.0433156	+	0.0598925i
$543$	17.7012	−	18.7683i	0.759631	−	0.805427i
$544$	0.321044	−	29.4956i	0.0137647	−	1.26461i
$545$	−1.62503	+	2.81463i	−0.0696086	+	0.120566i
$546$	−4.02522	−	0.526260i	−0.172263	−	0.0225219i
$547$	−18.7285	+	10.8129i	−0.800775	+	0.462328i	−0.843742	−	0.536749i	$-0.819652\pi$
$547$	−18.7285	+	10.8129i	−0.800775	+	0.462328i	0.0429671	+	0.999076i	$0.486319\pi$
$548$	−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
$552$	9.54668	−	6.51277i	0.406334	−	0.277202i
$553$	1.98064	−	3.43056i	0.0842253	−	0.145882i
$554$	9.88767	+	4.42809i	0.420087	+	0.188132i
$555$	64.4333	−	19.3016i	2.73504	−	0.819307i
$556$	−7.03857	+	6.28228i	−0.298502	+	0.266428i
$557$		−	22.1990i		−	0.940600i	−0.882506	−	0.470300i	$-0.844146\pi$
$557$		−	22.1990i		−	0.940600i	0.882506	−	0.470300i	$-0.155854\pi$
$558$	−6.46457	−	39.7927i	−0.273667	−	1.68456i
$559$	−4.06341			−0.171864
$560$	9.15685	−	12.3753i	0.386948	−	0.522951i
$561$	−18.0018	−	4.26338i	−0.760036	−	0.180000i
$562$	10.2203	−	22.8214i	0.431119	−	0.962664i
$563$	−15.7834	−	9.11257i	−0.665193	−	0.384049i	0.129060	−	0.991637i	$-0.458804\pi$
$563$	−15.7834	−	9.11257i	−0.665193	−	0.384049i	−0.794253	+	0.607588i	$0.792137\pi$
$564$	−27.9867	−	17.1996i	−1.17845	−	0.724234i
$565$	−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	$0.799458\pi$
$570$	−8.97267	−	6.87220i	−0.375824	−	0.287845i
$571$	−4.39296	−	2.53628i	−0.183840	−	0.106140i	0.405256	−	0.914203i	$-0.367182\pi$
$571$	−4.39296	−	2.53628i	−0.183840	−	0.106140i	−0.589096	+	0.808063i	$0.700516\pi$
$572$	2.12608	−	6.44776i	0.0888960	−	0.269594i
$573$	0.725443	−	3.06313i	0.0303058	−	0.127964i
$574$	4.67795	+	6.46821i	0.195254	+	0.269978i
$575$	23.1469			0.965291
$576$	14.9744	+	18.7555i	0.623932	+	0.781479i
$577$	−10.6402			−0.442958			−0.221479	−	0.975165i	$-0.571088\pi$
$577$	−10.6402			−0.442958			−0.221479	+	0.975165i	$0.571088\pi$
$578$	−8.44542	−	11.6775i	−0.351283	−	0.485720i
$579$	39.5120	−	11.8362i	1.64206	−	0.491895i
$580$	20.0308	−	60.7474i	0.831736	−	2.52240i
$581$	1.53730	+	0.887558i	0.0637778	+	0.0368221i
$582$	29.5257	−	12.2610i	1.22388	−	0.508234i
$583$	−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	−0.762363	−	0.647149i	$-0.775961\pi$
$587$	−14.1273	+	8.15642i	−0.583097	+	0.336651i	0.179266	+	0.983801i	$0.442628\pi$
$588$	0.0951137	−	3.46280i	0.00392242	−	0.142803i
$589$	−9.86564	−	5.69593i	−0.406507	−	0.234697i
$590$	6.57319	−	14.6776i	0.270614	−	0.604266i
$591$	−6.94751	+	7.36635i	−0.285782	+	0.303011i
$592$	−24.0069	+	32.4448i	−0.986678	+	1.33347i
$593$	−1.99475			−0.0819146			−0.0409573	−	0.999161i	$-0.513041\pi$
$593$	−1.99475			−0.0819146			−0.0409573	+	0.999161i	$0.513041\pi$
$594$	13.5397	−	6.57557i	0.555542	−	0.269799i
$595$		−	20.0686i		−	0.822734i
$596$	−18.0332	+	16.0955i	−0.738667	+	0.659299i
$597$	23.3647	+	22.0362i	0.956252	+	0.901881i
$598$	5.04594	+	2.25977i	0.206344	+	0.0924090i
$599$	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	$0.110935\pi$
$600$	3.60582	+	47.9344i	0.147207	+	1.95692i
$601$	−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
$606$	2.70439	+	6.51247i	0.109858	+	0.264551i
$607$	−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	$0.205001\pi$
$608$	6.78141	+	0.0738121i	0.275023	+	0.00299348i
$609$	−4.13032	−	13.7880i	−0.167369	−	0.558717i
$610$	−28.3680	−	39.2244i	−1.14859	−	1.58815i
$611$		−	15.7156i		−	0.635785i
$612$	30.2351	+	8.04339i	1.22218	+	0.325135i
$613$			13.3526i			0.539307i	0.962957	+	0.269654i	$0.0869092\pi$
$613$			13.3526i			0.539307i	−0.962957	+	0.269654i	$0.913091\pi$
$614$	−32.3534	+	23.3987i	−1.30568	+	0.944295i
$615$	−36.6139	−	8.67131i	−1.47642	−	0.349661i
$616$	5.65893	+	1.24152i	0.228005	+	0.0500223i
$617$	−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	$0.236836\pi$
$618$	−3.64730	−	2.79348i	−0.146716	−	0.112370i
$619$	1.64758	−	0.951228i	0.0662217	−	0.0382331i	−0.466524	−	0.884509i	$-0.654494\pi$
$619$	1.64758	−	0.951228i	0.0662217	−	0.0382331i	0.532745	+	0.846276i	$0.321160\pi$
$620$	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
$624$	−3.89367	+	10.8016i	−0.155871	+	0.432409i
$625$	−11.1093	+	19.2419i	−0.444372	+	0.769674i
$626$	−5.76855	+	12.8808i	−0.230558	+	0.514822i
$627$	0.980204	−	4.13884i	0.0391456	−	0.165289i
$628$	21.3150	−	19.0247i	0.850561	−	0.759169i
$629$			52.6148i			2.09789i
$630$	10.3261	+	12.6487i	0.411404	+	0.503938i
$631$	21.8360			0.869276			0.434638	−	0.900605i	$-0.356876\pi$
$631$	21.8360			0.869276			0.434638	+	0.900605i	$0.356876\pi$
$632$	−8.27719	−	7.55127i	−0.329249	−	0.300373i
$633$	−6.64485	−	22.1821i	−0.264109	−	0.881658i
$634$	−15.6878	−	7.02560i	−0.623041	−	0.279022i
$635$	−47.3112	−	27.3151i	−1.87749	−	1.08397i
$636$	20.0004	+	36.9490i	0.793069	+	1.46512i
$637$	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	$0.799351\pi$
$642$	−9.47550	−	1.23883i	−0.373968	−	0.0488929i
$643$	34.8075	+	20.0961i	1.37267	+	0.792513i	0.991264	−	0.131893i	$-0.0421054\pi$
$643$	34.8075	+	20.0961i	1.37267	+	0.792513i	0.381410	+	0.924406i	$0.375439\pi$
$644$	−1.47745	+	4.48066i	−0.0582198	+	0.176563i
$645$	11.8903	+	11.2142i	0.468179	+	0.441559i
$646$	7.16369	−	5.18093i	0.281851	−	0.203841i
$647$	−2.31418			−0.0909799			−0.0454900	−	0.998965i	$-0.514485\pi$
$647$	−2.31418			−0.0909799			−0.0454900	+	0.998965i	$0.514485\pi$
$648$	−23.1950	+	10.4877i	−0.911187	+	0.411994i
$649$	6.05227			0.237572
$650$	−18.6346	+	13.4769i	−0.730908	+	0.528609i
$651$	11.9732	+	11.2924i	0.469266	+	0.442584i
$652$	1.13622	+	0.374658i	0.0444979	+	0.0146727i
$653$	−26.2236	−	15.1402i	−1.02621	−	0.592483i	−0.110313	−	0.993897i	$-0.535185\pi$
$653$	−26.2236	−	15.1402i	−1.02621	−	0.592483i	−0.915897	+	0.401414i	$0.868519\pi$
$654$	2.05105	+	0.268156i	0.0802024	+	0.0104857i
$655$	−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	−0.979676	−	0.200585i	$-0.935716\pi$
$659$	−33.2645	+	19.2053i	−1.29580	+	0.748132i	−0.316126	+	0.948717i	$0.602382\pi$
$660$	−24.0158	+	12.9997i	−0.934815	+	0.506015i
$661$	24.0408	+	13.8799i	0.935077	+	0.539867i	0.888414	−	0.459044i	$-0.151808\pi$
$661$	24.0408	+	13.8799i	0.935077	+	0.539867i	0.0466634	+	0.998911i	$0.485141\pi$
$662$	26.9011	+	12.0474i	1.04554	+	0.468235i
$663$	4.29522	+	14.3384i	0.166812	+	0.556859i
$664$	3.38386	−	3.70915i	0.131319	−	0.143943i
$665$	4.61403			0.178925
$666$	−27.0725	−	33.1617i	−1.04904	−	1.28499i
$667$			19.6031i			0.759036i
$668$	8.41528	+	9.42835i	0.325597	+	0.364794i
$669$	5.37837	−	22.7098i	0.207940	−	0.878010i
$670$	−3.87474	+	8.65208i	−0.149694	+	0.334259i
$671$	9.10869	−	15.7767i	0.351637	−	0.609053i
$672$	−9.50908	−	2.36163i	−0.366821	−	0.0911020i
$673$	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	−0.507064	−	0.861909i	$-0.669269\pi$
$677$	−0.368450	+	0.212725i	−0.0141607	+	0.00817568i	0.492903	+	0.870084i	$0.335936\pi$
$678$	36.2634	+	27.7743i	1.39269	+	1.06667i
$679$	−6.52591	+	11.3032i	−0.250442	+	0.433778i
$680$	−55.4440	−	12.1640i	−2.12618	−	0.466466i
$681$	45.4709	+	10.7689i	1.74245	+	0.412666i
$682$	−22.3038	+	16.1306i	−0.854057	+	0.617673i
$683$		−	36.2275i		−	1.38621i	−0.720838	−	0.693103i	$-0.756243\pi$
$683$		−	36.2275i		−	1.38621i	0.720838	−	0.693103i	$-0.243757\pi$
$684$	−1.84928	+	6.95142i	−0.0707089	+	0.265794i
$685$			17.1657i			0.655868i
$686$	0.828761	+	1.14593i	0.0316423	+	0.0437518i
$687$	6.38304	+	21.3081i	0.243528	+	0.812955i
$688$	−9.74443	−	1.11005i	−0.371503	−	0.0423201i
$689$	−10.0502	+	17.4075i	−0.382883	+	0.663173i
$690$	−8.52882	−	20.5383i	−0.324687	−	0.781880i
$691$	43.2632	−	24.9780i	1.64581	−	0.950209i	0.667098	−	0.744970i	$-0.267536\pi$
$691$	43.2632	−	24.9780i	1.64581	−	0.950209i	0.978712	−	0.205238i	$-0.0657969\pi$
$692$	−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
$696$	−40.5958	+	3.05377i	−1.53878	+	0.115753i
$697$	14.7165	−	25.4897i	0.557426	−	0.965491i
$698$	24.0660	+	10.7777i	0.910913	+	0.407943i
$699$	−3.97353	−	3.74760i	−0.150293	−	0.141747i
$700$	−13.0677	−	14.6408i	−0.493913	−	0.553371i
$701$			28.3097i			1.06924i	0.845092	+	0.534621i	$0.179546\pi$
$701$			28.3097i			1.06924i	−0.845092	+	0.534621i	$0.820454\pi$
$702$	−10.0849	−	6.82708i	−0.380630	−	0.257672i
$703$	−12.0968			−0.456240
$704$	6.85995	−	14.8815i	0.258544	−	0.560868i
$705$	−43.3719	+	45.9867i	−1.63348	+	1.73196i
$706$	−12.4335	+	27.7634i	−0.467942	+	1.04489i
$707$	−2.49314	−	1.43941i	−0.0937642	−	0.0541348i
$708$	−10.2317	−	0.281037i	−0.384531	−	0.0105620i
$709$	−11.9128	+	6.87787i	−0.447395	+	0.258304i	−0.706730	−	0.707484i	$-0.749830\pi$
$709$	−11.9128	+	6.87787i	−0.447395	+	0.258304i	0.259334	+	0.965788i	$0.416497\pi$
$710$	−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
$714$	−11.7961	+	4.89848i	−0.441457	+	0.183321i
$715$	−11.3144	−	6.53238i	−0.423135	−	0.244297i
$716$	25.0832	+	8.27092i	0.937403	+	0.309099i
$717$	−31.9778	+	9.57925i	−1.19423	+	0.357744i
$718$	18.2951	+	25.2966i	0.682765	+	0.944061i
$719$	45.4064			1.69337			0.846687	−	0.532091i	$-0.178594\pi$
$719$	45.4064			1.69337			0.846687	+	0.532091i	$0.178594\pi$
$720$	41.2038	−	20.8616i	1.53557	−	0.777467i
$721$	1.87556			0.0698495
$722$	−14.5553	−	20.1256i	−0.541692	−	0.748999i
$723$	−0.997180	+	4.21052i	−0.0370855	+	0.156591i
$724$	28.2916	+	9.32887i	1.05145	+	0.346705i
$725$	−70.6152	−	40.7697i	−2.62258	−	1.51415i
$726$	13.2322	+	10.1346i	0.491091	+	0.376129i
$727$	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
$732$	−16.1313	+	26.2485i	−0.596232	+	0.970171i
$733$	10.0548	+	5.80516i	0.371383	+	0.214418i	0.674063	−	0.738674i	$-0.264548\pi$
$733$	10.0548	+	5.80516i	0.371383	+	0.214418i	−0.302679	+	0.953092i	$0.597881\pi$
$734$	−1.94419	+	4.34126i	−0.0717613	+	0.160239i
$735$	−6.48665	−	1.53624i	−0.239264	−	0.0566650i
$736$	11.4833	+	6.79760i	0.423280	+	0.250563i
$737$	−3.56767			−0.131417
$738$	3.84009	+	23.6377i	0.141356	+	0.870116i
$739$		−	8.15551i		−	0.300005i	−0.988686	−	0.150003i	$-0.952072\pi$
$739$		−	8.15551i		−	0.300005i	0.988686	−	0.150003i	$-0.0479282\pi$
$740$	51.7180	+	57.9440i	1.90119	+	2.13006i
$741$	−3.29659	+	0.987525i	−0.121103	+	0.0362776i
$742$	−15.6543	−	7.01063i	−0.574689	−	0.257368i
$743$	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	$0.0963012\pi$
$744$	38.4549	−	26.2340i	1.40982	−	0.961786i
$745$	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
$750$	44.9833	+	5.88114i	1.64256	+	0.214749i
$751$	−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	$0.242839\pi$
$752$	4.29320	−	37.6874i	0.156557	−	1.37432i
$753$	−10.0970	+	10.7057i	−0.367956	+	0.390139i
$754$	−11.4136	−	15.7817i	−0.415660	−	0.574734i
$755$			8.13405i			0.296028i
$756$	4.91428	−	9.15696i	0.178731	−	0.333035i
$757$		−	21.8618i		−	0.794581i	−0.917693	−	0.397290i	$-0.869951\pi$
$757$		−	21.8618i		−	0.794581i	0.917693	−	0.397290i	$-0.130049\pi$
$758$	32.3551	−	23.3999i	1.17519	−	0.849923i
$759$	5.74228	−	6.08846i	0.208431	−	0.220997i
$760$	2.79665	−	12.7473i	0.101445	−	0.462393i
$761$	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	$0.0631709\pi$
$762$	−4.50743	+	34.4761i	−0.163287	+	1.24894i
$763$	−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
$768$	−12.2882	+	24.8395i	−0.443411	+	0.896319i
$769$	−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	$0.214982\pi$
$770$	4.55672	−	10.1749i	0.164213	−	0.366678i
$771$	−49.4210	+	14.8045i	−1.77985	+	0.533171i
$772$	31.7147	+	35.5326i	1.14144	+	1.27885i
$773$		−	40.2234i		−	1.44674i	−0.690462	−	0.723368i	$-0.742593\pi$
$773$		−	40.2234i		−	1.44674i	0.690462	−	0.723368i	$-0.257407\pi$
$774$	3.68930	−	9.72618i	0.132609	−	0.349600i
$775$	93.2377			3.34920
$776$	27.2721	+	24.8803i	0.979013	+	0.893153i
$777$	17.0063	+	4.02762i	0.610098	+	0.144490i
$778$	34.9131	+	15.6355i	1.25170	+	0.560559i
$779$	5.86040	+	3.38350i	0.209971	+	0.121227i
$780$	18.8243	+	11.5687i	0.674019	+	0.414228i
$781$	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
$786$	−21.3790	+	27.9134i	−0.762563	+	0.995639i
$787$	−24.4384	−	14.1095i	−0.871136	−	0.502950i	−0.00341028	−	0.999994i	$-0.501086\pi$
$787$	−24.4384	−	14.1095i	−0.871136	−	0.502950i	−0.867726	+	0.497044i	$0.834419\pi$
$788$	−11.1041	−	3.66147i	−0.395568	−	0.130435i
$789$	12.4601	−	52.6117i	0.443590	−	1.87302i
$790$	−17.4704	+	12.6350i	−0.621569	+	0.449532i
$791$	−18.6478			−0.663040
$792$	13.5030	+	10.9431i	0.479809	+	0.388847i
$793$	−14.7395			−0.523415
$794$	−24.7738	+	17.9169i	−0.879188	+	0.635848i
$795$	77.4501	−	23.2009i	2.74687	−	0.822851i
$796$	−11.6135	+	35.2202i	−0.411629	+	1.24835i
$797$	−15.1059	−	8.72141i	−0.535079	−	0.308928i	0.208003	−	0.978128i	$-0.433304\pi$
$797$	−15.1059	−	8.72141i	−0.535079	−	0.308928i	−0.743082	+	0.669200i	$0.766637\pi$
$798$	−1.12622	−	2.71207i	−0.0398679	−	0.0960061i
$799$	−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
$804$	6.03135	+	0.165665i	0.212709	+	0.00584255i
$805$	7.86259	+	4.53947i	0.277120	+	0.159995i
$806$	20.3255	+	9.10256i	0.715935	+	0.320624i
$807$	−10.2052	+	10.8205i	−0.359241	+	0.380899i
$808$	−5.48784	+	6.01539i	−0.193061	+	0.211621i
$809$	−23.3000			−0.819183			−0.409592	−	0.912269i	$-0.634329\pi$
$809$	−23.3000			−0.819183			−0.409592	+	0.912269i	$0.634329\pi$
$810$	10.6688	+	47.8096i	0.374864	+	1.67986i
$811$			1.39655i			0.0490395i	0.999699	+	0.0245197i	$0.00780565\pi$
$811$			1.39655i			0.0490395i	−0.999699	+	0.0245197i	$0.992194\pi$
$812$	12.3993	−	11.0671i	0.435132	−	0.388378i
$813$	−1.53320	−	1.44603i	−0.0537718	−	0.0507144i
$814$	−11.9466	+	26.6760i	−0.418726	+	0.934992i
$815$	1.15113	−	1.99382i	0.0403225	−	0.0698405i
$816$	6.38334	+	35.5583i	0.223461	+	1.24479i
$817$	−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	−0.500561	−	0.865702i	$-0.666873\pi$
$821$	−0.0321266	+	0.0185483i	−0.00112123	+	0.000647340i	0.499439	+	0.866349i	$0.333539\pi$
$822$	10.0898	−	4.18992i	0.351921	−	0.146140i
$823$	−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	$0.270625\pi$
$824$	1.13681	−	5.18165i	0.0396027	−	0.180511i
$825$	9.98958	+	33.3476i	0.347793	+	1.16101i
$826$	3.38594	−	2.44878i	0.117812	−	0.0852041i
$827$			0.177189i			0.00616146i	0.999995	+	0.00308073i	$0.000980628\pi$
$827$			0.177189i			0.00616146i	−0.999995	+	0.00308073i	$0.999019\pi$
$828$	−9.99036	+	10.0262i	−0.347189	+	0.348436i
$829$		−	4.67287i		−	0.162295i	−0.996702	−	0.0811477i	$-0.974141\pi$
$829$		−	4.67287i		−	0.162295i	0.996702	−	0.0811477i	$-0.0258586\pi$
$830$	−5.66196	−	7.82880i	−0.196529	−	0.271741i
$831$	−12.9116	−	3.05787i	−0.447900	−	0.106076i
$832$	−13.2025	+	1.21353i	−0.457716	+	0.0420716i
$833$	2.60722	−	4.51584i	0.0903349	−	0.156465i
$834$	7.02588	−	9.17332i	0.243286	−	0.317646i
$835$	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	$-0.383148\pi$
$840$	−8.17587	+	16.9897i	−0.282094	+	0.586199i
$841$	20.0280	−	34.6894i	0.690619	−	1.19619i
$842$	−32.9612	−	14.7613i	−1.13592	−	0.508709i
$843$	−7.05778	+	29.8009i	−0.243083	+	1.02640i
$844$	19.9481	−	17.8047i	0.686640	−	0.612862i
$845$		−	39.4621i		−	1.35754i
$846$	37.6168	+	14.2687i	1.29329	+	0.490567i
$847$	−6.80440			−0.233802
$848$	−28.8568	+	38.9993i	−0.990946	+	1.33924i
$849$	8.71495	+	29.0925i	0.299096	+	0.998454i
$850$	−29.5747	+	66.0387i	−1.01440	+	2.26511i
$851$	−20.6137	−	11.9013i	−0.706628	−	0.407972i
$852$	−31.1105	+	16.8401i	−1.06583	+	0.576931i
$853$	−5.58176	+	3.22263i	−0.191116	+	0.110341i	−0.592505	−	0.805567i	$-0.701861\pi$
$853$	−5.58176	+	3.22263i	−0.191116	+	0.110341i	0.401389	+	0.915908i	$0.368528\pi$
$854$	−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	$0.567199\pi$
$858$	−1.07795	+	8.24492i	−0.0368005	+	0.281477i
$859$	−17.0155	−	9.82393i	−0.580563	−	0.335188i	0.180794	−	0.983521i	$-0.442133\pi$
$859$	−17.0155	−	9.82393i	−0.580563	−	0.335188i	−0.761357	+	0.648333i	$0.775467\pi$
$860$	−5.91011	+	17.9235i	−0.201533	+	0.611188i
$861$	−7.11232	−	6.70792i	−0.242387	−	0.228605i
$862$	−14.4156	−	19.9324i	−0.490996	−	0.678901i
$863$	−12.7952			−0.435554			−0.217777	−	0.975999i	$-0.569881\pi$
$863$	−12.7952			−0.435554			−0.217777	+	0.975999i	$0.569881\pi$
$864$	−22.3195	−	19.1270i	−0.759324	−	0.650713i
$865$	−24.1344			−0.820594
$866$	21.9133	+	30.2996i	0.744644	+	1.02962i
$867$	12.8404	+	12.1103i	0.436081	+	0.411286i
$868$	−5.95131	+	18.0485i	−0.202001	+	0.612606i
$869$	−7.02688	−	4.05697i	−0.238371	−	0.137623i
$870$	−10.1559	+	77.6794i	−0.344316	+	2.63358i
$871$	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
$876$	14.1844	−	7.67799i	0.479246	−	0.259415i
$877$	−25.9658	−	14.9913i	−0.876802	−	0.506222i	−0.00719906	−	0.999974i	$-0.502292\pi$
$877$	−25.9658	−	14.9913i	−0.876802	−	0.506222i	−0.869602	+	0.493752i	$0.835625\pi$
$878$	8.38951	−	18.7333i	0.283132	−	0.632218i
$879$	5.98704	+	19.9861i	0.201938	+	0.674116i
$880$	−25.3485	−	18.7561i	−0.854498	−	0.632269i
$881$	−7.44995			−0.250995			−0.125498	−	0.992094i	$-0.540053\pi$
$881$	−7.44995			−0.250995			−0.125498	+	0.992094i	$0.540053\pi$
$882$	0.680324	+	4.18774i	0.0229077	+	0.141009i
$883$			57.4367i			1.93290i	0.256856	+	0.966450i	$0.417313\pi$
$883$			57.4367i			1.93290i	−0.256856	+	0.966450i	$0.582687\pi$
$884$	−12.8944	+	11.5089i	−0.433685	+	0.387086i
$885$	−4.53920	+	19.1664i	−0.152584	+	0.644273i
$886$	44.7367	+	20.0348i	1.50296	+	0.673084i
$887$	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	$-0.225104\pi$
$888$	21.4350	−	44.5425i	0.719312	−	1.49475i
$889$	−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
$894$	18.0007	−	23.5025i	0.602032	−	0.786041i
$895$	25.4124	−	44.0155i	0.849442	−	1.47128i
$896$	−2.18336	−	11.1010i	−0.0729409	−	0.370860i
$897$	−6.58916	−	1.56052i	−0.220005	−	0.0521041i
$898$	8.52842	+	11.7923i	0.284597	+	0.393513i
$899$			78.9631i			2.63357i
$900$	−15.3395	−	56.8399i	−0.511315	−	1.89466i
$901$			63.2440i			2.10696i
$902$	13.2489	−	9.58192i	0.441141	−	0.319043i
$903$	1.21865	+	4.06814i	0.0405542	+	0.135379i
$904$	−11.3028	+	51.5187i	−0.375925	+	1.71349i
$905$	28.6629	−	49.6456i	0.952788	−	1.65028i
$906$	4.78108	−	1.98541i	0.158841	−	0.0659609i
$907$	−3.54990	+	2.04954i	−0.117873	+	0.0680538i	−0.557777	−	0.829991i	$-0.688346\pi$
$907$	−3.54990	+	2.04954i	−0.117873	+	0.0680538i	0.439905	+	0.898045i	$0.355012\pi$
$908$	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	$-0.368817\pi$
$912$	−8.17530	+	1.46761i	−0.270711	+	0.0485974i
$913$	1.81800	−	3.14887i	0.0601670	−	0.104212i
$914$	5.53879	−	12.3678i	0.183207	−	0.409091i
$915$	43.1305	+	40.6781i	1.42585	+	1.34478i
$916$	−19.1621	+	17.1032i	−0.633134	+	0.565104i
$917$		−	14.3540i		−	0.474010i
$918$	−38.2203	−	2.73731i	−1.26146	−	0.0903446i
$919$	−1.20205			−0.0396521			−0.0198261	−	0.999803i	$-0.506311\pi$
$919$	−1.20205			−0.0396521			−0.0198261	+	0.999803i	$0.506311\pi$
$920$	17.3069	−	18.9707i	0.570593	−	0.625445i
$921$	33.5525	−	35.5752i	1.10559	−	1.17224i
$922$	−17.5300	−	7.85061i	−0.577318	−	0.258546i
$923$	−14.6569	−	8.46214i	−0.482436	−	0.278535i
$924$	−7.09290	−	0.194823i	−0.233339	−	0.00640920i
$925$	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	$0.885162\pi$
$930$	−34.3548	−	82.7301i	−1.12654	−	2.71283i
$931$	1.03825	+	0.599433i	0.0340272	+	0.0196456i
$932$	1.97506	−	5.98974i	0.0646951	−	0.196201i
$933$	−25.1255	+	7.52656i	−0.822570	+	0.246409i
$934$	−10.4194	+	7.53557i	−0.340934	+	0.246571i
$935$	−41.1069			−1.34434
$936$	2.20518	−	13.8885i	0.0720787	−	0.453958i
$937$	7.23607			0.236392			0.118196	−	0.992990i	$-0.462289\pi$
$937$	7.23607			0.236392			0.118196	+	0.992990i	$0.462289\pi$
$938$	−1.99593	+	1.44350i	−0.0651694	+	0.0471320i
$939$	3.98355	−	16.8202i	0.129998	−	0.548907i
$940$	−69.3208	−	22.8578i	−2.26100	−	0.745541i
$941$	32.9473	+	19.0221i	1.07405	+	0.620103i	0.929285	−	0.369363i	$-0.120424\pi$
$941$	32.9473	+	19.0221i	1.07405	+	0.620103i	0.144765	+	0.989466i	$0.453757\pi$
$942$	−21.2766	+	27.7797i	−0.693228	+	0.905111i
$943$	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	−0.682131	−	0.731230i	$-0.738946\pi$
$947$	−11.9995	+	6.92792i	−0.389932	+	0.225127i	0.292199	+	0.956358i	$0.405613\pi$
$948$	11.6910	+	7.18484i	0.379705	+	0.233353i
$949$	6.68259	+	3.85820i	0.216926	+	0.125242i
$950$	−15.1831	−	6.79960i	−0.492606	−	0.220608i
$951$	20.4856	+	4.85162i	0.664291	+	0.157325i
$952$	−10.8957	−	9.94015i	−0.353132	−	0.322162i
$953$	−2.09416			−0.0678365			−0.0339183	−	0.999425i	$-0.510799\pi$
$953$	−2.09416			−0.0678365			−0.0339183	+	0.999425i	$0.510799\pi$
$954$	−32.5417	−	39.8611i	−1.05358	−	1.29055i
$955$		−	6.99463i		−	0.226341i
$956$	−25.6673	−	28.7572i	−0.830140	−	0.930076i
$957$	−28.2421	+	8.46020i	−0.912939	+	0.273479i
$958$	22.5257	−	50.2985i	0.727771	−	1.62507i
$959$	−2.23009	+	3.86262i	−0.0720132	+	0.124731i
$960$	41.9821	+	32.8854i	1.35497	+	1.06137i
$961$	−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
$966$	0.749085	−	5.72955i	0.0241014	−	0.184345i
$967$	−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	$0.286960\pi$
$968$	−4.12427	+	18.7986i	−0.132559	+	0.604211i
$969$	−7.42918	+	7.87706i	−0.238660	+	0.253048i
$970$	57.5625	−	41.6304i	1.84822	−	1.33667i
$971$			13.1500i			0.422003i	0.977486	+	0.211002i	$0.0676725\pi$
$971$			13.1500i			0.422003i	−0.977486	+	0.211002i	$0.932327\pi$
$972$	25.4977	−	17.9407i	0.817839	−	0.575447i
$973$			4.71722i			0.151227i
$974$	20.8263	+	28.7966i	0.667318	+	0.922701i
$975$	19.3252	−	20.4902i	0.618901	−	0.656213i
$976$	−35.3467	−	4.02655i	−1.13142	−	0.128887i
$977$	−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	$0.229186\pi$
$978$	−1.45292	−	0.189955i	−0.0464592	−	0.00607411i
$979$	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	$0.856839\pi$
$984$	−22.8430	+	15.5836i	−0.728209	+	0.496786i
$985$	−11.2499	+	19.4853i	−0.358450	+	0.620854i
$986$	−55.9283	−	25.0469i	−1.78112	−	0.797655i
$987$	−15.7339	+	4.71324i	−0.500816	+	0.150024i
$988$	−2.64604	−	2.96458i	−0.0841818	−	0.0943159i
$989$		−	5.78391i		−	0.183918i
$990$	25.9086	−	21.1512i	0.823430	−	0.672230i
$991$	10.5067			0.333756			0.166878	−	0.985978i	$-0.446631\pi$
$991$	10.5067			0.333756			0.166878	+	0.985978i	$0.446631\pi$
$992$	46.2558	+	27.3813i	1.46862	+	0.869358i
$993$	−35.1284	−	8.31948i	−1.11477	−	0.264011i
$994$	5.90284	−	13.1807i	0.187227	−	0.418067i
$995$	61.8038	+	35.6824i	1.95931	+	1.13121i
$996$	−3.21965	+	5.23892i	−0.102019	+	0.166002i
$997$	36.8111	−	21.2529i	1.16582	−	0.673085i	0.213127	−	0.977025i	$-0.431635\pi$
$997$	36.8111	−	21.2529i	1.16582	−	0.673085i	0.952691	+	0.303939i	$0.0983020\pi$
$998$	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.85.12	✓	72
8.5	even	2	inner	504.2.cs.a.85.14	yes	72
9.7	even	3	inner	504.2.cs.a.421.14	yes	72
72.61	even	6	inner	504.2.cs.a.421.12	yes	72

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

\(f(q)\)	\(=\)	\(q+(-0.828761 - 1.14593i) q^{2} +(1.26004 + 1.18840i) q^{3} +(-0.626309 + 1.89940i) q^{4} +(3.33304 + 1.92433i) q^{5} +(0.317546 - 2.42882i) q^{6} +(0.500000 + 0.866025i) q^{7} +(2.69564 - 0.856447i) q^{8} +(0.175418 + 2.99487i) q^{9} +O(q^{10})\)	\(q+(-0.828761 - 1.14593i) q^{2} +(1.26004 + 1.18840i) q^{3} +(-0.626309 + 1.89940i) q^{4} +(3.33304 + 1.92433i) q^{5} +(0.317546 - 2.42882i) 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} +(-3.04643 + 1.64903i) q^{12} +(-1.43524 - 0.828637i) q^{13} +(0.578023 - 1.29069i) q^{14} +(1.91290 + 6.38572i) q^{15} +(-3.21547 - 2.37923i) q^{16} -5.21444 q^{17} +(3.28653 - 2.68305i) q^{18} -1.19887i q^{19} +(-5.74260 + 5.12557i) q^{20} +(-0.399162 + 1.68543i) q^{21} +(-2.64375 - 1.18398i) q^{22} +(1.17949 - 2.04294i) q^{23} +(4.41443 + 2.12434i) 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} +(5.73225 - 7.48429i) q^{30} +(4.75110 - 8.22914i) q^{31} +(-0.0615683 + 5.65652i) q^{32} +(3.45229 + 0.817609i) q^{33} +(4.32153 + 5.97538i) q^{34} +3.84866i q^{35} +(-5.79833 - 1.54252i) q^{36} -10.0902i q^{37} +(-1.37382 + 0.993574i) q^{38} +(-0.823715 - 2.74976i) q^{39} +(10.6328 + 2.33274i) q^{40} +(-2.82225 + 4.88829i) q^{41} +(2.26219 - 0.939407i) 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} +(-1.22416 - 6.81920i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(5.67169 - 12.6646i) q^{50} +(-6.57042 - 6.19684i) q^{51} +(2.47282 - 2.20712i) q^{52} -12.1286i q^{53} +(7.32970 + 0.524947i) q^{54} +7.88328 q^{55} +(2.08953 + 1.90627i) q^{56} +(1.42473 - 1.51062i) q^{57} +(10.7256 + 4.80337i) q^{58} +(2.55889 + 1.47738i) q^{59} +(-13.3271 - 0.366061i) 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} +(-1.92420 - 4.63369i) q^{66} +(-1.50841 - 0.870878i) q^{67} +(3.26585 - 9.90433i) q^{68} +(3.91404 - 1.17249i) q^{69} +(4.41030 - 3.18962i) q^{70} +10.2121 q^{71} +(3.03781 + 7.92286i) q^{72} -4.65608 q^{73} +(-11.5627 + 8.36237i) q^{74} +(-3.91666 + 16.5378i) q^{75} +(2.27713 + 0.750861i) q^{76} +(1.77389 + 1.02416i) q^{77} +(-2.46836 + 3.22281i) 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} +(-2.95131 - 1.81377i) q^{84} +(-17.3800 - 10.0343i) q^{85} +(-3.16460 - 1.41723i) q^{86} +(-14.0059 - 3.31703i) q^{87} +(3.90465 - 4.28001i) q^{88} +1.13851 q^{89} +(16.1172 - 2.61834i) q^{90} -1.65727i q^{91} +(3.14164 + 3.51984i) q^{92} +(15.7661 - 4.72288i) q^{93} +(5.48128 - 12.2394i) q^{94} +(2.30702 - 3.99587i) q^{95} +(-6.79978 + 7.05429i) 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

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