LMFDB - Embedded newform 630.2.r.a.299.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(59,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("630.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.r (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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			299.16
Character	$\chi$	$=$	630.299
Dual form			630.2.r.a.59.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.960509 + 1.44133i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.19316 - 0.435950i) q^{5} +(0.767971 - 1.55249i) q^{6} +(-2.64572 + 0.0128895i) q^{7} +1.00000 q^{8} +(-1.15485 + 2.76881i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.960509 + 1.44133i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.19316 - 0.435950i) q^{5} +(0.767971 - 1.55249i) q^{6} +(-2.64572 + 0.0128895i) q^{7} +1.00000 q^{8} +(-1.15485 + 2.76881i) q^{9} +(-1.47412 - 1.68136i) q^{10} +4.12106i q^{11} +(-1.72848 + 0.111161i) q^{12} +(1.18566 + 2.05363i) q^{13} +(1.33402 + 2.28482i) q^{14} +(2.73489 + 2.74233i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.28111 + 1.31700i) q^{17} +(2.97529 - 0.384280i) q^{18} +(0.956982 + 0.552514i) q^{19} +(-0.719036 + 2.11731i) q^{20} +(-2.55981 - 3.80097i) q^{21} +(3.56894 - 2.06053i) q^{22} +0.592478 q^{23} +(0.960509 + 1.44133i) q^{24} +(4.61990 - 1.91221i) q^{25} +(1.18566 - 2.05363i) q^{26} +(-5.10001 + 0.994957i) q^{27} +(1.31170 - 2.29771i) q^{28} +(2.36953 + 1.36805i) q^{29} +(1.00748 - 3.73965i) q^{30} +(2.33615 + 1.34878i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-5.93979 + 3.95831i) q^{33} +(2.28111 + 1.31700i) q^{34} +(-5.79687 + 1.18167i) q^{35} +(-1.82044 - 2.38453i) q^{36} +(-6.05512 - 3.49593i) q^{37} -1.10503i q^{38} +(-1.82111 + 3.68146i) q^{39} +(2.19316 - 0.435950i) q^{40} +(-0.257087 - 0.445287i) q^{41} +(-2.01183 + 4.11735i) q^{42} +(10.4023 + 6.00577i) q^{43} +(-3.56894 - 2.06053i) q^{44} +(-1.32570 + 6.57590i) q^{45} +(-0.296239 - 0.513101i) q^{46} +(-3.57645 + 2.06487i) q^{47} +(0.767971 - 1.55249i) q^{48} +(6.99967 - 0.0682042i) q^{49} +(-3.96597 - 3.04484i) q^{50} +(-4.08925 - 2.02283i) q^{51} -2.37133 q^{52} +(-4.54406 - 7.87055i) q^{53} +(3.41166 + 3.91926i) q^{54} +(1.79657 + 9.03814i) q^{55} +(-2.64572 + 0.0128895i) q^{56} +(0.122836 + 1.91002i) q^{57} -2.73609i q^{58} +(-3.46974 + 6.00977i) q^{59} +(-3.74237 + 0.997325i) q^{60} +(3.71806 - 2.14662i) q^{61} -2.69755i q^{62} +(3.01971 - 7.34039i) q^{63} +1.00000 q^{64} +(3.49563 + 3.98705i) q^{65} +(6.39790 + 3.16486i) q^{66} +(11.7043 + 6.75750i) q^{67} -2.63400i q^{68} +(0.569081 + 0.853955i) q^{69} +(3.92179 + 4.42940i) q^{70} +1.60164i q^{71} +(-1.15485 + 2.76881i) q^{72} +(3.29147 + 5.70100i) q^{73} +6.99185i q^{74} +(7.19357 + 4.82208i) q^{75} +(-0.956982 + 0.552514i) q^{76} +(-0.0531186 - 10.9032i) q^{77} +(4.09879 - 0.263600i) q^{78} +(-6.72172 - 11.6424i) q^{79} +(-1.47412 - 1.68136i) q^{80} +(-6.33266 - 6.39511i) q^{81} +(-0.257087 + 0.445287i) q^{82} +(-3.80374 - 2.19609i) q^{83} +(4.57164 - 0.316381i) q^{84} +(-4.42869 + 3.88283i) q^{85} -12.0115i q^{86} +(0.304148 + 4.72928i) q^{87} +4.12106i q^{88} +(7.82648 - 13.5559i) q^{89} +(6.35775 - 2.13986i) q^{90} +(-3.16341 - 5.41805i) q^{91} +(-0.296239 + 0.513101i) q^{92} +(0.299863 + 4.66266i) q^{93} +(3.57645 + 2.06487i) q^{94} +(2.33968 + 0.794555i) q^{95} +(-1.72848 + 0.111161i) q^{96} +(6.92406 - 11.9928i) q^{97} +(-3.55890 - 6.02779i) q^{98} +(-11.4104 - 4.75919i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{2} + 3 q^{3} - 24 q^{4} + 48 q^{8} + 3 q^{9}+O(q^{10}) $ 48 * q - 24 * q^2 + 3 * q^3 - 24 * q^4 + 48 * q^8 + 3 * q^9	$ 48 q - 24 q^{2} + 3 q^{3} - 24 q^{4} + 48 q^{8} + 3 q^{9} - 3 q^{12} + 3 q^{14} - 4 q^{15} - 24 q^{16} - 3 q^{18} + 5 q^{21} + 6 q^{22} - 6 q^{23} + 3 q^{24} - 3 q^{28} - 3 q^{29} + 5 q^{30} - 24 q^{32} + 24 q^{33} + 18 q^{35} + 3 q^{41} + 8 q^{42} - 6 q^{44} + 9 q^{45} + 3 q^{46} - 6 q^{49} - 18 q^{50} - 8 q^{51} + 42 q^{55} - 22 q^{57} - q^{60} - 9 q^{61} - 10 q^{63} + 48 q^{64} - 33 q^{65} - 24 q^{66} - 33 q^{67} + 42 q^{69} - 6 q^{70} + 3 q^{72} + 18 q^{73} + 9 q^{75} + 6 q^{77} - 18 q^{78} - 37 q^{81} + 3 q^{82} - 9 q^{83} - 13 q^{84} - 33 q^{85} - 18 q^{87} + 33 q^{89} + 39 q^{90} + 3 q^{92} - 32 q^{93} + 33 q^{95} - 3 q^{96} + 24 q^{97} + 3 q^{98} - 26 q^{99}+O(q^{100}) $ 48 * q - 24 * q^2 + 3 * q^3 - 24 * q^4 + 48 * q^8 + 3 * q^9 - 3 * q^12 + 3 * q^14 - 4 * q^15 - 24 * q^16 - 3 * q^18 + 5 * q^21 + 6 * q^22 - 6 * q^23 + 3 * q^24 - 3 * q^28 - 3 * q^29 + 5 * q^30 - 24 * q^32 + 24 * q^33 + 18 * q^35 + 3 * q^41 + 8 * q^42 - 6 * q^44 + 9 * q^45 + 3 * q^46 - 6 * q^49 - 18 * q^50 - 8 * q^51 + 42 * q^55 - 22 * q^57 - q^60 - 9 * q^61 - 10 * q^63 + 48 * q^64 - 33 * q^65 - 24 * q^66 - 33 * q^67 + 42 * q^69 - 6 * q^70 + 3 * q^72 + 18 * q^73 + 9 * q^75 + 6 * q^77 - 18 * q^78 - 37 * q^81 + 3 * q^82 - 9 * q^83 - 13 * q^84 - 33 * q^85 - 18 * q^87 + 33 * q^89 + 39 * q^90 + 3 * q^92 - 32 * q^93 + 33 * q^95 - 3 * q^96 + 24 * q^97 + 3 * q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.960509	+	1.44133i	0.554550	+	0.832151i
$3$	0.960509	+	1.44133i	0.554550	+	0.832151i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	2.19316	−	0.435950i	0.980811	−	0.194963i
$5$	2.19316	−	0.435950i	0.980811	−	0.194963i
$6$	0.767971	−	1.55249i	0.313523	−	0.633801i
$7$	−2.64572	+	0.0128895i	−0.999988	+	0.00487179i
$7$	−2.64572	+	0.0128895i	−0.999988	+	0.00487179i
$8$	1.00000			0.353553
$9$	−1.15485	+	2.76881i	−0.384949	+	0.922938i
$10$	−1.47412	−	1.68136i	−0.466159	−	0.531692i
$11$			4.12106i			1.24255i	0.783594	+	0.621273i	$0.213384\pi$
$11$			4.12106i			1.24255i	−0.783594	+	0.621273i	$0.786616\pi$
$12$	−1.72848	+	0.111161i	−0.498969	+	0.0320895i
$13$	1.18566	+	2.05363i	0.328844	+	0.569575i	0.982283	−	0.187405i	$-0.0600076\pi$
$13$	1.18566	+	2.05363i	0.328844	+	0.569575i	−0.653439	+	0.756979i	$0.726674\pi$
$14$	1.33402	+	2.28482i	0.356533	+	0.610643i
$15$	2.73489	+	2.74233i	0.706147	+	0.708066i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.28111	+	1.31700i	−0.553250	+	0.319419i	−0.750432	−	0.660948i	$-0.770154\pi$
$17$	−2.28111	+	1.31700i	−0.553250	+	0.319419i	0.197182	+	0.980367i	$0.436821\pi$
$18$	2.97529	−	0.384280i	0.701282	−	0.0905757i
$19$	0.956982	+	0.552514i	0.219547	+	0.126755i	0.605740	−	0.795662i	$-0.292877\pi$
$19$	0.956982	+	0.552514i	0.219547	+	0.126755i	−0.386194	+	0.922418i	$0.626210\pi$
$20$	−0.719036	+	2.11731i	−0.160781	+	0.473444i
$21$	−2.55981	−	3.80097i	−0.558597	−	0.829439i
$22$	3.56894	−	2.06053i	0.760901	−	0.439306i
$23$	0.592478			0.123540			0.0617701	−	0.998090i	$-0.480325\pi$
$23$	0.592478			0.123540			0.0617701	+	0.998090i	$0.480325\pi$
$24$	0.960509	+	1.44133i	0.196063	+	0.294210i
$25$	4.61990	−	1.91221i	0.923979	−	0.382443i
$26$	1.18566	−	2.05363i	0.232528	−	0.402750i
$27$	−5.10001	+	0.994957i	−0.981497	+	0.191480i
$28$	1.31170	−	2.29771i	0.247887	−	0.434226i
$29$	2.36953	+	1.36805i	0.440010	+	0.254040i	0.703602	−	0.710594i	$-0.251574\pi$
$29$	2.36953	+	1.36805i	0.440010	+	0.254040i	−0.263592	+	0.964634i	$0.584907\pi$
$30$	1.00748	−	3.73965i	0.183939	−	0.682764i
$31$	2.33615	+	1.34878i	0.419585	+	0.242247i	0.694900	−	0.719107i	$-0.255449\pi$
$31$	2.33615	+	1.34878i	0.419585	+	0.242247i	−0.275315	+	0.961354i	$0.588782\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−5.93979	+	3.95831i	−1.03399	+	0.689054i
$34$	2.28111	+	1.31700i	0.391207	+	0.225863i
$35$	−5.79687	+	1.18167i	−0.979849	+	0.199739i
$36$	−1.82044	−	2.38453i	−0.303407	−	0.397422i
$37$	−6.05512	−	3.49593i	−0.995456	−	0.574727i	−0.0885553	−	0.996071i	$-0.528225\pi$
$37$	−6.05512	−	3.49593i	−0.995456	−	0.574727i	−0.906901	+	0.421345i	$0.861558\pi$
$38$		−	1.10503i		−	0.179259i
$39$	−1.82111	+	3.68146i	−0.291611	+	0.589505i
$40$	2.19316	−	0.435950i	0.346769	−	0.0689297i
$41$	−0.257087	−	0.445287i	−0.0401502	−	0.0695422i	0.845252	−	0.534368i	$-0.179450\pi$
$41$	−0.257087	−	0.445287i	−0.0401502	−	0.0695422i	−0.885402	+	0.464826i	$0.846117\pi$
$42$	−2.01183	+	4.11735i	−0.310432	+	0.635321i
$43$	10.4023	+	6.00577i	1.58634	+	0.915872i	0.993904	+	0.110251i	$0.0351655\pi$
$43$	10.4023	+	6.00577i	1.58634	+	0.915872i	0.592432	+	0.805620i	$0.298168\pi$
$44$	−3.56894	−	2.06053i	−0.538038	−	0.310636i
$45$	−1.32570	+	6.57590i	−0.197624	+	0.980278i
$46$	−0.296239	−	0.513101i	−0.0436781	−	0.0756527i
$47$	−3.57645	+	2.06487i	−0.521679	+	0.301192i	−0.737622	−	0.675214i	$-0.764051\pi$
$47$	−3.57645	+	2.06487i	−0.521679	+	0.301192i	0.215942	+	0.976406i	$0.430718\pi$
$48$	0.767971	−	1.55249i	0.110847	−	0.224082i
$49$	6.99967	−	0.0682042i	0.999953	−	0.00974346i
$50$	−3.96597	−	3.04484i	−0.560873	−	0.430605i
$51$	−4.08925	−	2.02283i	−0.572609	−	0.283253i
$52$	−2.37133			−0.328844
$53$	−4.54406	−	7.87055i	−0.624175	−	1.08110i	−0.988700	−	0.149909i	$-0.952102\pi$
$53$	−4.54406	−	7.87055i	−0.624175	−	1.08110i	0.364525	−	0.931194i	$-0.381232\pi$
$54$	3.41166	+	3.91926i	0.464268	+	0.533343i
$55$	1.79657	+	9.03814i	0.242250	+	1.21870i
$56$	−2.64572	+	0.0128895i	−0.353549	+	0.00172244i
$57$	0.122836	+	1.91002i	0.0162701	+	0.252988i
$58$		−	2.73609i		−	0.359266i
$59$	−3.46974	+	6.00977i	−0.451722	+	0.782405i	−0.998493	−	0.0548770i	$-0.982523\pi$
$59$	−3.46974	+	6.00977i	−0.451722	+	0.782405i	0.546771	+	0.837282i	$0.315857\pi$
$60$	−3.74237	+	0.997325i	−0.483138	+	0.128754i
$61$	3.71806	−	2.14662i	0.476048	−	0.274847i	−0.242720	−	0.970096i	$-0.578040\pi$
$61$	3.71806	−	2.14662i	0.476048	−	0.274847i	0.718768	+	0.695250i	$0.244706\pi$
$62$		−	2.69755i		−	0.342589i
$63$	3.01971	−	7.34039i	0.380448	−	0.924802i
$64$	1.00000			0.125000
$65$	3.49563	+	3.98705i	0.433579	+	0.494533i
$66$	6.39790	+	3.16486i	0.787526	+	0.389567i
$67$	11.7043	+	6.75750i	1.42991	+	0.825560i	0.997113	−	0.0759308i	$-0.0241928\pi$
$67$	11.7043	+	6.75750i	1.42991	+	0.825560i	0.432799	+	0.901491i	$0.357526\pi$
$68$		−	2.63400i		−	0.319419i
$69$	0.569081	+	0.853955i	0.0685092	+	0.102804i
$70$	3.92179	+	4.42940i	0.468743	+	0.529414i
$71$			1.60164i			0.190079i	0.995473	+	0.0950396i	$0.0302978\pi$
$71$			1.60164i			0.190079i	−0.995473	+	0.0950396i	$0.969702\pi$
$72$	−1.15485	+	2.76881i	−0.136100	+	0.326308i
$73$	3.29147	+	5.70100i	0.385238	+	0.667252i	0.991802	−	0.127783i	$-0.0407860\pi$
$73$	3.29147	+	5.70100i	0.385238	+	0.667252i	−0.606564	+	0.795035i	$0.707453\pi$
$74$			6.99185i			0.812786i
$75$	7.19357	+	4.82208i	0.830642	+	0.556806i
$76$	−0.956982	+	0.552514i	−0.109773	+	0.0633777i
$77$	−0.0531186	−	10.9032i	−0.00605342	−	1.24253i
$78$	4.09879	−	0.263600i	0.464097	−	0.0298468i
$79$	−6.72172	−	11.6424i	−0.756253	−	1.30987i	−0.944749	−	0.327794i	$-0.893695\pi$
$79$	−6.72172	−	11.6424i	−0.756253	−	1.30987i	0.188497	−	0.982074i	$-0.439639\pi$
$80$	−1.47412	−	1.68136i	−0.164812	−	0.187981i
$81$	−6.33266	−	6.39511i	−0.703629	−	0.710568i
$82$	−0.257087	+	0.445287i	−0.0283905	+	0.0491738i
$83$	−3.80374	−	2.19609i	−0.417515	−	0.241052i	0.276499	−	0.961014i	$-0.410826\pi$
$83$	−3.80374	−	2.19609i	−0.417515	−	0.241052i	−0.694013	+	0.719962i	$0.744159\pi$
$84$	4.57164	−	0.316381i	0.498807	−	0.0345200i
$85$	−4.42869	+	3.88283i	−0.480359	+	0.421152i
$86$		−	12.0115i		−	1.29524i
$87$	0.304148	+	4.72928i	0.0326080	+	0.507032i
$88$			4.12106i			0.439306i
$89$	7.82648	−	13.5559i	0.829605	−	1.43692i	−0.0687438	−	0.997634i	$-0.521899\pi$
$89$	7.82648	−	13.5559i	0.829605	−	1.43692i	0.898349	−	0.439283i	$-0.144768\pi$
$90$	6.35775	−	2.13986i	0.670166	−	0.225561i
$91$	−3.16341	−	5.41805i	−0.331615	−	0.567966i
$92$	−0.296239	+	0.513101i	−0.0308851	+	0.0534945i
$93$	0.299863	+	4.66266i	0.0310944	+	0.483496i
$94$	3.57645	+	2.06487i	0.368883	+	0.212975i
$95$	2.33968	+	0.794555i	0.240046	+	0.0815196i
$96$	−1.72848	+	0.111161i	−0.176412	+	0.0113454i
$97$	6.92406	−	11.9928i	0.703032	−	1.21769i	−0.264365	−	0.964423i	$-0.585162\pi$
$97$	6.92406	−	11.9928i	0.703032	−	1.21769i	0.967397	−	0.253265i	$-0.0815044\pi$
$98$	−3.55890	−	6.02779i	−0.359503	−	0.608899i
$99$	−11.4104	−	4.75919i	−1.14679	−	0.478317i
$100$	−0.653922	+	4.95705i	−0.0653922	+	0.495705i
$101$	2.70907			0.269562			0.134781	−	0.990875i	$-0.456967\pi$
$101$	2.70907			0.269562			0.134781	+	0.990875i	$0.456967\pi$
$102$	0.292798	+	4.55281i	0.0289914	+	0.450795i
$103$	18.1448			1.78786			0.893929	−	0.448209i	$-0.147938\pi$
$103$	18.1448			1.78786			0.893929	+	0.448209i	$0.147938\pi$
$104$	1.18566	+	2.05363i	0.116264	+	0.201375i
$105$	−7.27111	−	7.22018i	−0.709588	−	0.704617i
$106$	−4.54406	+	7.87055i	−0.441358	+	0.764455i
$107$	−4.33862	+	7.51471i	−0.419430	+	0.726475i	−0.995882	−	0.0906565i	$-0.971103\pi$
$107$	−4.33862	+	7.51471i	−0.419430	+	0.726475i	0.576452	+	0.817131i	$0.304437\pi$
$108$	1.68834	−	4.91421i	0.162461	−	0.472870i
$109$	−7.55567	−	13.0868i	−0.723702	−	1.25349i	−0.959506	−	0.281688i	$-0.909106\pi$
$109$	−7.55567	−	13.0868i	−0.723702	−	1.25349i	0.235804	−	0.971801i	$-0.424228\pi$
$110$	6.92897	−	6.07495i	0.660651	−	0.579224i
$111$	−0.777223	−	12.0853i	−0.0737708	−	1.14708i
$112$	1.33402	+	2.28482i	0.126053	+	0.215895i
$113$	0.503287	+	0.871718i	0.0473452	+	0.0820044i	0.888727	−	0.458437i	$-0.151591\pi$
$113$	0.503287	+	0.871718i	0.0473452	+	0.0820044i	−0.841382	+	0.540441i	$0.818257\pi$
$114$	1.59271	−	1.06139i	0.149171	−	0.0994081i
$115$	1.29940	−	0.258291i	0.121170	−	0.0240857i
$116$	−2.36953	+	1.36805i	−0.220005	+	0.127020i
$117$	−7.05538	+	0.911254i	−0.652270	+	0.0842455i
$118$	6.93948			0.638831
$119$	6.01820	−	3.51381i	0.551687	−	0.322110i
$120$	2.73489	+	2.74233i	0.249661	+	0.250339i
$121$	−5.98313			−0.543921
$122$	−3.71806	−	2.14662i	−0.336617	−	0.194346i
$123$	0.394871	−	0.798248i	0.0356043	−	0.0719756i
$124$	−2.33615	+	1.34878i	−0.209792	+	0.121124i
$125$	9.29854	−	6.20783i	0.831687	−	0.555245i
$126$	−7.86682	+	1.05505i	−0.700832	+	0.0939911i
$127$		−	3.12538i		−	0.277333i	−0.990339	−	0.138666i	$-0.955718\pi$
$127$		−	3.12538i		−	0.277333i	0.990339	−	0.138666i	$-0.0442816\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	1.33522	+	20.7617i	0.117559	+	1.82797i
$130$	1.70507	−	5.02083i	0.149545	−	0.440356i
$131$	−21.5741			−1.88494			−0.942469	−	0.334294i	$-0.891502\pi$
$131$	−21.5741			−1.88494			−0.942469	+	0.334294i	$0.891502\pi$
$132$	−0.458102	−	7.12317i	−0.0398727	−	0.619992i
$133$	−2.53903	−	1.44946i	−0.220162	−	0.125684i
$134$		−	13.5150i		−	1.16752i
$135$	−10.7514	+	4.40545i	−0.925331	+	0.379160i
$136$	−2.28111	+	1.31700i	−0.195603	+	0.112932i
$137$	3.76795			0.321917			0.160959	−	0.986961i	$-0.448541\pi$
$137$	3.76795			0.321917			0.160959	+	0.986961i	$0.448541\pi$
$138$	0.455007	−	0.919816i	0.0387327	−	0.0782999i
$139$	−5.20651	+	3.00598i	−0.441610	+	0.254964i	−0.704280	−	0.709922i	$-0.748730\pi$
$139$	−5.20651	+	3.00598i	−0.441610	+	0.254964i	0.262670	+	0.964886i	$0.415397\pi$
$140$	1.87508	−	5.61107i	0.158473	−	0.474222i
$141$	−6.41136	−	3.17152i	−0.539934	−	0.267090i
$142$	1.38706	−	0.800818i	0.116399	−	0.0672032i
$143$	−8.46313	+	4.88619i	−0.707723	+	0.408604i
$144$	2.97529	−	0.384280i	0.247941	−	0.0320233i
$145$	5.79315	+	1.96735i	0.481095	+	0.163379i
$146$	3.29147	−	5.70100i	0.272404	−	0.471818i
$147$	6.82155	+	10.0233i	0.562632	+	0.826708i
$148$	6.05512	−	3.49593i	0.497728	−	0.287363i
$149$			11.1918i			0.916866i	0.888729	+	0.458433i	$0.151589\pi$
$149$			11.1918i			0.916866i	−0.888729	+	0.458433i	$0.848411\pi$
$150$	0.579259	−	8.64086i	0.0472963	−	0.705523i
$151$	−18.5494			−1.50953			−0.754763	−	0.655997i	$-0.772248\pi$
$151$	−18.5494			−1.50953			−0.754763	+	0.655997i	$0.772248\pi$
$152$	0.956982	+	0.552514i	0.0776215	+	0.0448148i
$153$	−1.01219	−	7.83689i	−0.0818309	−	0.633575i
$154$	−9.41586	+	5.49759i	−0.758752	+	0.443008i
$155$	5.71154	+	1.93964i	0.458762	+	0.155795i
$156$	−2.27768	−	3.41786i	−0.182360	−	0.273648i
$157$	5.83514	−	10.1068i	0.465695	−	0.806607i	−0.533538	−	0.845776i	$-0.679138\pi$
$157$	5.83514	−	10.1068i	0.465695	−	0.806607i	0.999233	+	0.0391693i	$0.0124712\pi$
$158$	−6.72172	+	11.6424i	−0.534751	+	0.926217i
$159$	6.97942	−	14.1092i	0.553504	−	1.11893i
$160$	−0.719036	+	2.11731i	−0.0568448	+	0.167388i
$161$	−1.56753	+	0.00763677i	−0.123539	+	0.000601862i
$162$	−2.37200	+	8.68180i	−0.186362	+	0.682106i
$163$	−10.7728	−	6.21967i	−0.843789	−	0.487162i	0.0147613	−	0.999891i	$-0.495301\pi$
$163$	−10.7728	−	6.21967i	−0.843789	−	0.487162i	−0.858550	+	0.512729i	$0.828634\pi$
$164$	0.514173			0.0401502
$165$	−11.3013	+	11.2707i	−0.879804	+	0.877420i
$166$			4.39218i			0.340899i
$167$	11.4205	−	6.59363i	0.883745	−	0.510230i	0.0118537	−	0.999930i	$-0.496227\pi$
$167$	11.4205	−	6.59363i	0.883745	−	0.510230i	0.871891	+	0.489699i	$0.162893\pi$
$168$	−2.55981	−	3.80097i	−0.197494	−	0.293251i
$169$	3.68840	−	6.38850i	0.283723	−	0.491423i
$170$	5.57698	+	1.89394i	0.427735	+	0.145258i
$171$	−2.63497	+	2.01164i	−0.201502	+	0.153834i
$172$	−10.4023	+	6.00577i	−0.793168	+	0.457936i
$173$	−12.8284	+	7.40645i	−0.975321	+	0.563102i	−0.900854	−	0.434121i	$-0.857059\pi$
$173$	−12.8284	+	7.40645i	−0.975321	+	0.563102i	−0.0744670	+	0.997223i	$0.523726\pi$
$174$	3.94360	−	2.62804i	0.298964	−	0.199231i
$175$	−12.1983	+	5.11873i	−0.922105	+	0.386940i
$176$	3.56894	−	2.06053i	0.269019	−	0.155318i
$177$	−11.9948	+	0.771402i	−0.901581	+	0.0579821i
$178$	−15.6530			−1.17324
$179$	−20.6373	+	11.9149i	−1.54250	+	0.890564i	−0.543823	+	0.839200i	$0.683024\pi$
$179$	−20.6373	+	11.9149i	−1.54250	+	0.890564i	−0.998680	+	0.0513644i	$0.983643\pi$
$180$	−5.03205	−	4.43604i	−0.375067	−	0.330643i
$181$		−	11.6911i		−	0.868992i	−0.900674	−	0.434496i	$-0.856926\pi$
$181$		−	11.6911i		−	0.868992i	0.900674	−	0.434496i	$-0.143074\pi$
$182$	−3.11046	+	5.44861i	−0.230563	+	0.403878i
$183$	6.66521	+	3.29709i	0.492706	+	0.243728i
$184$	0.592478			0.0436781
$185$	−14.8039	−	5.02740i	−1.08840	−	0.369621i
$186$	3.88805	−	2.59102i	0.285086	−	0.189983i
$187$	−5.42743	−	9.40058i	−0.396893	−	0.687438i
$188$		−	4.12973i		−	0.301192i
$189$	13.4804	−	2.69812i	0.980552	−	0.196259i
$190$	−0.481736	−	2.42350i	−0.0349488	−	0.175819i
$191$	22.5387	−	13.0127i	1.63084	−	0.941567i	0.647009	−	0.762482i	$-0.276020\pi$
$191$	22.5387	−	13.0127i	1.63084	−	0.941567i	0.983834	−	0.179085i	$-0.0573137\pi$
$192$	0.960509	+	1.44133i	0.0693187	+	0.104019i
$193$	15.6522	+	9.03678i	1.12667	+	0.650482i	0.943095	−	0.332524i	$-0.107900\pi$
$193$	15.6522	+	9.03678i	1.12667	+	0.650482i	0.183573	+	0.983006i	$0.441234\pi$
$194$	−13.8481			−0.994238
$195$	−2.38906	+	8.86794i	−0.171084	+	0.635046i
$196$	−3.44077	+	6.09599i	−0.245769	+	0.435428i
$197$	19.0964			1.36056			0.680281	−	0.732951i	$-0.261858\pi$
$197$	19.0964			1.36056			0.680281	+	0.732951i	$0.261858\pi$
$198$	1.58364	+	12.2613i	0.112544	+	0.871375i
$199$	21.6198	−	12.4822i	1.53259	−	0.884840i	0.533346	−	0.845897i	$-0.320934\pi$
$199$	21.6198	−	12.4822i	1.53259	−	0.884840i	0.999241	−	0.0389429i	$-0.0123991\pi$
$200$	4.61990	−	1.91221i	0.326676	−	0.135214i
$201$	1.50234	+	23.3604i	0.105967	+	1.64772i
$202$	−1.35453	−	2.34612i	−0.0953046	−	0.165072i
$203$	−6.28673	−	3.58892i	−0.441242	−	0.251893i
$204$	3.79645	−	2.52998i	0.265805	−	0.177134i
$205$	−0.757955	−	0.864509i	−0.0529379	−	0.0603799i
$206$	−9.07239	−	15.7138i	−0.632103	−	1.09483i
$207$	−0.684222	+	1.64046i	−0.0475567	+	0.114020i
$208$	1.18566	−	2.05363i	0.0822110	−	0.142394i
$209$	−2.27694	+	3.94378i	−0.157499	+	0.272797i
$210$	−2.61730	+	9.90706i	−0.180611	+	0.683652i
$211$	−6.61689	−	11.4608i	−0.455525	−	0.788993i	0.543193	−	0.839608i	$-0.317215\pi$
$211$	−6.61689	−	11.4608i	−0.455525	−	0.788993i	−0.998718	+	0.0506149i	$0.983882\pi$
$212$	9.08813			0.624175
$213$	−2.30848	+	1.53839i	−0.158175	+	0.105408i
$214$	8.67724			0.593164
$215$	25.4321	+	8.63673i	1.73446	+	0.589020i
$216$	−5.10001	+	0.994957i	−0.347011	+	0.0676983i
$217$	−6.19818	−	3.53837i	−0.420760	−	0.240200i
$218$	−7.55567	+	13.0868i	−0.511735	+	0.886351i
$219$	−5.05552	+	10.2200i	−0.341620	+	0.690600i
$220$	−8.72554	−	2.96319i	−0.588276	−	0.199778i
$221$	−5.40925	−	3.12303i	−0.363866	−	0.210078i
$222$	−10.0775	+	6.71573i	−0.676361	+	0.450731i
$223$	−2.44383	+	4.23284i	−0.163651	+	0.283452i	−0.936175	−	0.351533i	$-0.885660\pi$
$223$	−2.44383	+	4.23284i	−0.163651	+	0.283452i	0.772524	+	0.634985i	$0.218994\pi$
$224$	1.31170	−	2.29771i	0.0876415	−	0.153522i
$225$	−0.0407079	+	14.9999i	−0.00271386	+	0.999996i
$226$	0.503287	−	0.871718i	0.0334781	−	0.0579858i
$227$		−	11.9942i		−	0.796084i	−0.917367	−	0.398042i	$-0.869690\pi$
$227$		−	11.9942i		−	0.796084i	0.917367	−	0.398042i	$-0.130310\pi$
$228$	−1.71554	−	0.848629i	−0.113615	−	0.0562018i
$229$			10.5849i			0.699467i	0.936849	+	0.349734i	$0.113728\pi$
$229$			10.5849i			0.699467i	−0.936849	+	0.349734i	$0.886272\pi$
$230$	−0.873386	−	0.996168i	−0.0575894	−	0.0656853i
$231$	15.6640	−	10.5491i	1.03062	−	0.694083i
$232$	2.36953	+	1.36805i	0.155567	+	0.0898166i
$233$	0.259858	−	0.450088i	0.0170239	−	0.0294862i	−0.857388	−	0.514671i	$-0.827914\pi$
$233$	0.259858	−	0.450088i	0.0170239	−	0.0294862i	0.874412	+	0.485184i	$0.161248\pi$
$234$	4.31686	+	5.65451i	0.282202	+	0.369647i
$235$	−6.94356	+	6.08774i	−0.452948	+	0.397120i
$236$	−3.46974	−	6.00977i	−0.225861	−	0.391202i
$237$	10.3242	−	20.8708i	0.670628	−	1.35570i
$238$	−6.05215	−	3.45501i	−0.392302	−	0.223955i
$239$	−2.39886	+	1.38498i	−0.155169	+	0.0895869i	−0.575574	−	0.817750i	$-0.695221\pi$
$239$	−2.39886	+	1.38498i	−0.155169	+	0.0895869i	0.420405	+	0.907337i	$0.361888\pi$
$240$	1.00748	−	3.73965i	0.0650324	−	0.241393i
$241$		−	20.2007i		−	1.30124i	−0.759403	−	0.650621i	$-0.774509\pi$
$241$		−	20.2007i		−	1.30124i	0.759403	−	0.650621i	$-0.225491\pi$
$242$	2.99156	+	5.18154i	0.192305	+	0.333082i
$243$	3.13487	−	15.2700i	0.201102	−	0.979570i
$244$			4.29324i			0.274847i
$245$	15.3217	−	3.20109i	0.978865	−	0.204510i
$246$	−0.888739	+	0.0571562i	−0.0566639	+	0.00364415i
$247$			2.62038i			0.166731i
$248$	2.33615	+	1.34878i	0.148346	+	0.0856474i
$249$	−0.488240	−	7.59179i	−0.0309410	−	0.481110i
$250$	−10.0254	−	4.94886i	−0.634063	−	0.312993i
$251$	20.9869			1.32468			0.662340	−	0.749203i	$-0.269563\pi$
$251$	20.9869			1.32468			0.662340	+	0.749203i	$0.269563\pi$
$252$	4.84711	+	6.28534i	0.305339	+	0.395939i
$253$			2.44164i			0.153504i
$254$	−2.70666	+	1.56269i	−0.169831	+	0.0980519i
$255$	−9.85023	−	2.65369i	−0.616845	−	0.166181i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$		−	9.48293i		−	0.591529i	−0.955261	−	0.295764i	$-0.904426\pi$
$257$		−	9.48293i		−	0.591529i	0.955261	−	0.295764i	$-0.0955743\pi$
$258$	17.3126	−	11.5372i	1.07783	−	0.718274i
$259$	16.0652	+	9.17119i	0.998244	+	0.569870i
$260$	−5.20070	+	1.03378i	−0.322534	+	0.0641123i
$261$	−6.52430	+	4.98089i	−0.403844	+	0.308309i
$262$	10.7870	+	18.6837i	0.666426	+	1.15428i
$263$	−11.6732			−0.719800			−0.359900	−	0.932991i	$-0.617189\pi$
$263$	−11.6732			−0.719800			−0.359900	+	0.932991i	$0.617189\pi$
$264$	−5.93979	+	3.95831i	−0.365569	+	0.243617i
$265$	−13.3970	−	15.2804i	−0.822972	−	0.938667i
$266$	0.0142433	+	2.92359i	0.000873312	+	0.179257i
$267$	27.0558	−	1.74000i	1.65579	−	0.106486i
$268$	−11.7043	+	6.75750i	−0.714956	+	0.412780i
$269$	−8.14330	−	14.1046i	−0.496506	−	0.859973i	0.503486	−	0.864003i	$-0.332050\pi$
$269$	−8.14330	−	14.1046i	−0.496506	−	0.859973i	−0.999992	+	0.00403039i	$0.998717\pi$
$270$	9.19091	+	7.10824i	0.559341	+	0.432594i
$271$	21.8041	+	12.5886i	1.32450	+	0.764703i	0.984444	−	0.175701i	$-0.0562192\pi$
$271$	21.8041	+	12.5886i	1.32450	+	0.764703i	0.340060	+	0.940404i	$0.389553\pi$
$272$	2.28111	+	1.31700i	0.138312	+	0.0798547i
$273$	4.77070	−	9.76358i	0.288736	−	0.590919i
$274$	−1.88397	−	3.26314i	−0.113815	−	0.197133i
$275$	7.88035	+	19.0389i	0.475203	+	1.14809i
$276$	−1.02409	+	0.0658607i	−0.0616428	+	0.00396435i
$277$		−	20.7421i		−	1.24627i	−0.782114	−	0.623136i	$-0.785858\pi$
$277$		−	20.7421i		−	1.24627i	0.782114	−	0.623136i	$-0.214142\pi$
$278$	5.20651	+	3.00598i	0.312265	+	0.180287i
$279$	−6.43240	+	4.91073i	−0.385098	+	0.293998i
$280$	−5.79687	+	1.18167i	−0.346429	+	0.0706183i
$281$	1.17815	+	0.680206i	0.0702827	+	0.0405777i	0.534730	−	0.845023i	$-0.320413\pi$
$281$	1.17815	+	0.680206i	0.0702827	+	0.0405777i	−0.464447	+	0.885601i	$0.653747\pi$
$282$	0.459067	+	7.13816i	0.0273370	+	0.425071i
$283$	−7.46757	+	12.9342i	−0.443901	+	0.768859i	−0.997975	−	0.0636082i	$-0.979739\pi$
$283$	−7.46757	+	12.9342i	−0.443901	+	0.768859i	0.554074	+	0.832468i	$0.313073\pi$
$284$	−1.38706	−	0.800818i	−0.0823067	−	0.0475198i
$285$	1.10207	+	4.13542i	0.0652810	+	0.244961i
$286$	8.46313	+	4.88619i	0.500435	+	0.288927i
$287$	0.685919	+	1.17479i	0.0404885	+	0.0693458i
$288$	−1.82044	−	2.38453i	−0.107270	−	0.140510i
$289$	−5.03103	+	8.71400i	−0.295943	+	0.512589i
$290$	−1.19280	−	6.00069i	−0.0700435	−	0.352372i
$291$	23.9362	−	1.53938i	1.40317	−	0.0902398i
$292$	−6.58295			−0.385238
$293$	−9.63607	+	5.56339i	−0.562945	+	0.325016i	−0.754327	−	0.656499i	$-0.772037\pi$
$293$	−9.63607	+	5.56339i	−0.562945	+	0.325016i	0.191382	+	0.981516i	$0.438703\pi$
$294$	5.26966	−	10.9193i	0.307333	−	0.636825i
$295$	−4.98974	+	14.6930i	−0.290514	+	0.855460i
$296$	−6.05512	−	3.49593i	−0.351947	−	0.203197i
$297$	−4.10028	−	21.0174i	−0.237922	−	1.21955i
$298$	9.69236	−	5.59589i	0.561464	−	0.324161i
$299$	0.702480	+	1.21673i	0.0406255	+	0.0703654i
$300$	−7.77283	+	3.81878i	−0.448765	+	0.220477i
$301$	−27.5990	−	15.7555i	−1.59078	−	0.908132i
$302$	9.27469	+	16.0642i	0.533698	+	0.924392i
$303$	2.60208	+	3.90465i	0.149486	+	0.224316i
$304$		−	1.10503i		−	0.0633777i
$305$	7.21847	−	6.32877i	0.413329	−	0.362384i
$306$	−6.28085	+	4.79503i	−0.359052	+	0.274114i
$307$	14.1337			0.806651			0.403325	−	0.915057i	$-0.367854\pi$
$307$	14.1337			0.806651			0.403325	+	0.915057i	$0.367854\pi$
$308$	9.46898	+	5.40558i	0.539545	+	0.308012i
$309$	17.4282	+	26.1526i	0.991456	+	1.48777i
$310$	−1.17600	−	5.91616i	−0.0667921	−	0.336015i
$311$	−2.93752	+	5.08794i	−0.166572	+	0.288510i	−0.937212	−	0.348760i	$-0.886603\pi$
$311$	−2.93752	+	5.08794i	−0.166572	+	0.288510i	0.770641	+	0.637270i	$0.219936\pi$
$312$	−1.82111	+	3.68146i	−0.103100	+	0.208422i
$313$	9.51843	+	16.4864i	0.538014	+	0.931867i	0.999011	+	0.0444656i	$0.0141585\pi$
$313$	9.51843	+	16.4864i	0.538014	+	0.931867i	−0.460997	+	0.887402i	$0.652508\pi$
$314$	−11.6703			−0.658592
$315$	3.42267	−	17.4151i	0.192846	−	0.981229i
$316$	13.4434			0.756253
$317$	7.70830	+	13.3512i	0.432941	+	0.749876i	0.997125	−	0.0757731i	$-0.0241425\pi$
$317$	7.70830	+	13.3512i	0.432941	+	0.749876i	−0.564184	+	0.825649i	$0.690809\pi$
$318$	−15.7086	+	1.01025i	−0.880897	+	0.0566519i
$319$	−5.63780	+	9.76495i	−0.315656	+	0.546732i
$320$	2.19316	−	0.435950i	0.122601	−	0.0243703i
$321$	−14.9984	+	0.964573i	−0.837131	+	0.0538372i
$322$	0.790380	+	1.35370i	0.0440461	+	0.0754390i
$323$	−2.91064			−0.161952
$324$	8.70466	−	2.28669i	0.483592	−	0.127038i
$325$	9.40463	+	7.22032i	0.521675	+	0.400511i
$326$			12.4393i			0.688951i
$327$	11.6051	−	23.4602i	0.641763	−	1.29735i
$328$	−0.257087	−	0.445287i	−0.0141952	−	0.0245869i
$329$	9.43568	−	5.50916i	0.520206	−	0.303730i
$330$	15.4113	+	4.15187i	0.848365	+	0.228553i
$331$	15.4650	+	26.7862i	0.850033	+	1.47230i	0.881178	+	0.472785i	$0.156751\pi$
$331$	15.4650	+	26.7862i	0.850033	+	1.47230i	−0.0311447	+	0.999515i	$0.509915\pi$
$332$	3.80374	−	2.19609i	0.208757	−	0.120526i
$333$	16.6723	−	12.7282i	0.913637	−	0.697504i
$334$	−11.4205	−	6.59363i	−0.624902	−	0.360787i
$335$	28.6154	+	9.71777i	1.56343	+	0.530939i
$336$	−2.01183	+	4.11735i	−0.109754	+	0.224620i
$337$	−21.3417	+	12.3216i	−1.16256	+	0.671202i	−0.951915	−	0.306362i	$-0.900888\pi$
$337$	−21.3417	+	12.3216i	−1.16256	+	0.671202i	−0.210640	+	0.977564i	$0.567555\pi$
$338$	−7.37680			−0.401245
$339$	−0.773020	+	1.56269i	−0.0419847	+	0.0848739i
$340$	−1.14829	−	5.77677i	−0.0622747	−	0.313289i
$341$	−5.55839	+	9.62741i	−0.301003	+	0.521353i
$342$	3.05961	+	1.27614i	0.165445	+	0.0690056i
$343$	−18.5183	+	0.270672i	−0.999893	+	0.0146149i
$344$	10.4023	+	6.00577i	0.560854	+	0.323809i
$345$	1.62037	+	1.62477i	0.0872376	+	0.0874746i
$346$	12.8284	+	7.40645i	0.689656	+	0.398173i
$347$	−0.273072	+	0.472975i	−0.0146593	+	0.0253906i	−0.873262	−	0.487251i	$-0.838000\pi$
$347$	−0.273072	+	0.472975i	−0.0146593	+	0.0253906i	0.858603	+	0.512642i	$0.171333\pi$
$348$	−4.24775	−	2.10124i	−0.227703	−	0.112638i
$349$	5.63017	+	3.25058i	0.301376	+	0.174000i	0.643061	−	0.765815i	$-0.277664\pi$
$349$	5.63017	+	3.25058i	0.301376	+	0.174000i	−0.341685	+	0.939815i	$0.610997\pi$
$350$	10.5321	+	8.00467i	0.562965	+	0.427868i
$351$	−8.09017	−	9.29384i	−0.431821	−	0.496069i
$352$	−3.56894	−	2.06053i	−0.190225	−	0.109827i
$353$			6.55439i			0.348855i	0.984670	+	0.174427i	$0.0558074\pi$
$353$			6.55439i			0.348855i	−0.984670	+	0.174427i	$0.944193\pi$
$354$	6.66543	+	10.0021i	0.354264	+	0.531604i
$355$	0.698233	+	3.51264i	0.0370583	+	0.186432i
$356$	7.82648	+	13.5559i	0.414802	+	0.718459i
$357$	10.8451	+	5.29914i	0.573982	+	0.280460i
$358$	20.6373	+	11.9149i	1.09071	+	0.629724i
$359$	3.55244	+	2.05100i	0.187490	+	0.108248i	0.590807	−	0.806813i	$-0.298809\pi$
$359$	3.55244	+	2.05100i	0.187490	+	0.108248i	−0.403317	+	0.915060i	$0.632143\pi$
$360$	−1.32570	+	6.57590i	−0.0698705	+	0.346581i
$361$	−8.88946	−	15.3970i	−0.467866	−	0.810368i
$362$	−10.1248	+	5.84555i	−0.532147	+	0.307235i
$363$	−5.74684	−	8.62364i	−0.301631	−	0.452624i
$364$	6.27387	−	0.0305653i	0.328840	−	0.00160206i
$365$	9.70408	+	11.0683i	0.507935	+	0.579341i
$366$	−0.477242	−	7.42078i	−0.0249459	−	0.387891i
$367$	20.1571			1.05219			0.526096	−	0.850425i	$-0.323655\pi$
$367$	20.1571			1.05219			0.526096	+	0.850425i	$0.323655\pi$
$368$	−0.296239	−	0.513101i	−0.0154425	−	0.0267473i
$369$	1.52981	−	0.197587i	0.0796389	−	0.0102860i
$370$	3.04810	+	15.3342i	0.158463	+	0.797190i
$371$	12.1238	+	20.7647i	0.629435	+	1.07805i
$372$	−4.18792	−	2.07164i	−0.217133	−	0.107410i
$373$			5.71061i			0.295684i	0.989011	+	0.147842i	$0.0472327\pi$
$373$			5.71061i			0.295684i	−0.989011	+	0.147842i	$0.952767\pi$
$374$	−5.42743	+	9.40058i	−0.280646	+	0.486092i
$375$	17.8788	+	7.43956i	0.923259	+	0.384177i
$376$	−3.57645	+	2.06487i	−0.184442	+	0.106487i
$377$			6.48817i			0.334158i
$378$	−9.07682	−	10.3253i	−0.466861	−	0.531075i
$379$	5.42424			0.278624			0.139312	−	0.990249i	$-0.455511\pi$
$379$	5.42424			0.278624			0.139312	+	0.990249i	$0.455511\pi$
$380$	−1.85794	+	1.62895i	−0.0953106	+	0.0835632i
$381$	4.50470	−	3.00195i	0.230783	−	0.153795i
$382$	−22.5387	−	13.0127i	−1.15318	−	0.665789i
$383$			33.3230i			1.70273i	0.524578	+	0.851363i	$0.324223\pi$
$383$			33.3230i			1.70273i	−0.524578	+	0.851363i	$0.675777\pi$
$384$	0.767971	−	1.55249i	0.0391904	−	0.0792251i
$385$	−4.86973	−	23.8892i	−0.248184	−	1.21751i
$386$		−	18.0736i		−	0.919920i
$387$	−28.6419	+	21.8663i	−1.45595	+	1.11153i
$388$	6.92406	+	11.9928i	0.351516	+	0.608844i
$389$			29.2794i			1.48453i	0.670109	+	0.742263i	$0.266247\pi$
$389$			29.2794i			1.48453i	−0.670109	+	0.742263i	$0.733753\pi$
$390$	8.87439	−	2.36498i	0.449372	−	0.119756i
$391$	−1.35151	+	0.780293i	−0.0683486	+	0.0394611i
$392$	6.99967	−	0.0682042i	0.353537	−	0.00344483i
$393$	−20.7221	−	31.0953i	−1.04529	−	1.56855i
$394$	−9.54821	−	16.5380i	−0.481032	−	0.833171i
$395$	−19.8173	−	22.6032i	−0.997116	−	1.13729i
$396$	9.82680	−	7.50214i	0.493815	−	0.376997i
$397$	−5.42713	+	9.40006i	−0.272380	+	0.471775i	−0.969471	−	0.245207i	$-0.921144\pi$
$397$	−5.42713	+	9.40006i	−0.272380	+	0.471775i	0.697091	+	0.716983i	$0.254477\pi$
$398$	−21.6198	−	12.4822i	−1.08370	−	0.625676i
$399$	−0.349610	−	5.05179i	−0.0175024	−	0.252906i
$400$	−3.96597	−	3.04484i	−0.198299	−	0.152242i
$401$			18.2813i			0.912925i	0.889743	+	0.456463i	$0.150884\pi$
$401$			18.2813i			0.912925i	−0.889743	+	0.456463i	$0.849116\pi$
$402$	19.4795	−	12.9813i	0.971551	−	0.647447i
$403$			6.39678i			0.318646i
$404$	−1.35453	+	2.34612i	−0.0673905	+	0.116724i
$405$	−16.6765	−	11.2648i	−0.828661	−	0.559751i
$406$	0.0352670	+	7.23893i	0.00175027	+	0.359262i
$407$	14.4069	−	24.9535i	0.714124	−	1.23690i
$408$	−4.08925	−	2.02283i	−0.202448	−	0.100145i
$409$	8.38163	+	4.83914i	0.414445	+	0.239280i	0.692698	−	0.721228i	$-0.256422\pi$
$409$	8.38163	+	4.83914i	0.414445	+	0.239280i	−0.278253	+	0.960508i	$0.589755\pi$
$410$	−0.369709	+	1.08866i	−0.0182586	+	0.0537652i
$411$	3.61914	+	5.43084i	0.178519	+	0.267884i
$412$	−9.07239	+	15.7138i	−0.446964	+	0.774165i
$413$	9.10250	−	15.9449i	0.447905	−	0.784596i
$414$	1.76279	−	0.227678i	0.0866365	−	0.0111897i
$415$	−9.29959	−	3.15814i	−0.456499	−	0.155027i
$416$	−2.37133			−0.116264
$417$	−9.33349	−	4.61701i	−0.457063	−	0.226096i
$418$	4.55388			0.222738
$419$	−5.02659	−	8.70630i	−0.245565	−	0.425331i	0.716725	−	0.697355i	$-0.245640\pi$
$419$	−5.02659	−	8.70630i	−0.245565	−	0.425331i	−0.962290	+	0.272025i	$0.912307\pi$
$420$	9.88841	−	2.68688i	0.482505	−	0.131106i
$421$	−6.61761	+	11.4620i	−0.322522	+	0.558625i	−0.981008	−	0.193968i	$-0.937864\pi$
$421$	−6.61761	+	11.4620i	−0.322522	+	0.558625i	0.658485	+	0.752594i	$0.271197\pi$
$422$	−6.61689	+	11.4608i	−0.322105	+	0.557902i
$423$	−1.58697	−	12.2871i	−0.0771614	−	0.597421i
$424$	−4.54406	−	7.87055i	−0.220679	−	0.382228i
$425$	−8.02010	+	10.4464i	−0.389032	+	0.506723i
$426$	2.48652	+	1.23001i	0.120472	+	0.0595942i
$427$	−9.80927	+	5.72728i	−0.474704	+	0.277163i
$428$	−4.33862	−	7.51471i	−0.209715	−	0.363237i
$429$	−15.1715	−	7.50491i	−0.732487	−	0.362341i
$430$	−5.23643	−	26.3432i	−0.252523	−	1.27038i
$431$	−4.44716	+	2.56757i	−0.214212	+	0.123675i	−0.603267	−	0.797539i	$-0.706135\pi$
$431$	−4.44716	+	2.56757i	−0.214212	+	0.123675i	0.389055	+	0.921214i	$0.372801\pi$
$432$	3.41166	+	3.91926i	0.164144	+	0.188565i
$433$	−7.97362			−0.383188			−0.191594	−	0.981474i	$-0.561366\pi$
$433$	−7.97362			−0.383188			−0.191594	+	0.981474i	$0.561366\pi$
$434$	0.0347702	+	7.13697i	0.00166902	+	0.342585i
$435$	2.72877	+	10.2395i	0.130835	+	0.490945i
$436$	15.1113			0.723702
$437$	0.566991	+	0.327352i	0.0271229	+	0.0156594i
$438$	11.3785	−	0.731769i	0.543686	−	0.0349653i
$439$	22.3502	−	12.9039i	1.06672	−	0.615869i	0.139434	−	0.990231i	$-0.455472\pi$
$439$	22.3502	−	12.9039i	1.06672	−	0.615869i	0.927282	+	0.374362i	$0.122138\pi$
$440$	1.79657	+	9.03814i	0.0856483	+	0.430876i
$441$	−7.89470	+	19.4595i	−0.375938	+	0.926645i
$442$			6.24607i			0.297095i
$443$	−15.6440	−	27.0962i	−0.743269	−	1.28738i	−0.950999	−	0.309194i	$-0.899941\pi$
$443$	−15.6440	−	27.0962i	−0.743269	−	1.28738i	0.207729	−	0.978186i	$-0.433393\pi$
$444$	10.8548	+	5.36954i	0.515145	+	0.254827i
$445$	11.2550	−	33.1421i	0.533540	−	1.57109i
$446$	4.88766			0.231437
$447$	−16.1310	+	10.7498i	−0.762971	+	0.508448i
$448$	−2.64572	+	0.0128895i	−0.124999	+	0.000608974i
$449$		−	6.93666i		−	0.327361i	−0.986513	−	0.163681i	$-0.947663\pi$
$449$		−	6.93666i		−	0.327361i	0.986513	−	0.163681i	$-0.0523366\pi$
$450$	13.0107	−	7.46472i	0.613330	−	0.351890i
$451$	1.83506	−	1.05947i	0.0864094	−	0.0498885i
$452$	−1.00657			−0.0473452
$453$	−17.8168	−	26.7357i	−0.837108	−	1.25615i
$454$	−10.3873	+	5.99711i	−0.487500	+	0.281458i
$455$	−9.29985	−	10.5036i	−0.435984	−	0.492414i
$456$	0.122836	+	1.91002i	0.00575233	+	0.0894448i
$457$	−23.7421	+	13.7075i	−1.11061	+	0.641209i	−0.938986	−	0.343954i	$-0.888233\pi$
$457$	−23.7421	+	13.7075i	−1.11061	+	0.641209i	−0.171620	+	0.985163i	$0.554900\pi$
$458$	9.16676	−	5.29243i	0.428335	−	0.247299i
$459$	10.3233	−	8.98630i	0.481851	−	0.419445i
$460$	−0.426013	+	1.25446i	−0.0198630	+	0.0584894i
$461$	9.16139	−	15.8680i	0.426689	−	0.739046i	−0.569888	−	0.821722i	$-0.693013\pi$
$461$	9.16139	−	15.8680i	0.426689	−	0.739046i	0.996576	+	0.0826762i	$0.0263467\pi$
$462$	−16.9678	−	8.29086i	−0.789415	−	0.385726i
$463$	−16.6964	+	9.63966i	−0.775947	+	0.447993i	−0.834992	−	0.550262i	$-0.814528\pi$
$463$	−16.6964	+	9.63966i	−0.775947	+	0.447993i	0.0590450	+	0.998255i	$0.481194\pi$
$464$		−	2.73609i		−	0.127020i
$465$	2.69034	+	10.0952i	0.124761	+	0.468156i
$466$	−0.519717			−0.0240754
$467$	11.2146	+	6.47476i	0.518951	+	0.299616i	0.736505	−	0.676432i	$-0.236475\pi$
$467$	11.2146	+	6.47476i	0.518951	+	0.299616i	−0.217555	+	0.976048i	$0.569808\pi$
$468$	2.73852	−	6.56577i	0.126588	−	0.303503i
$469$	−31.0535	−	17.7276i	−1.43392	−	0.818584i
$470$	8.74391	+	2.96943i	0.403327	+	0.136970i
$471$	20.1718	−	1.29728i	0.929469	−	0.0597757i
$472$	−3.46974	+	6.00977i	−0.159708	+	0.276622i
$473$	−24.7501	+	42.8685i	−1.13801	+	1.97110i
$474$	−23.2367	+	1.49439i	−1.06730	+	0.0686396i
$475$	5.47768	+	0.722602i	0.251333	+	0.0331552i
$476$	0.0339510	+	6.96882i	0.00155614	+	0.319415i
$477$	27.0398	−	3.49239i	1.23807	−	0.159905i
$478$	2.39886	+	1.38498i	0.109721	+	0.0633475i
$479$	−27.0757			−1.23712			−0.618560	−	0.785738i	$-0.712284\pi$
$479$	−27.0757			−1.23712			−0.618560	+	0.785738i	$0.712284\pi$
$480$	−3.74237	+	0.997325i	−0.170815	+	0.0455214i
$481$		−	16.5800i		−	0.755982i
$482$	−17.4943	+	10.1004i	−0.796845	+	0.460059i
$483$	−1.51663	−	2.25199i	−0.0690093	−	0.102469i
$484$	2.99156	−	5.18154i	0.135980	−	0.235524i
$485$	9.95731	−	29.3207i	0.452138	−	1.33139i
$486$	−14.7916	+	4.92011i	−0.670962	+	0.223181i
$487$	−2.98800	+	1.72512i	−0.135399	+	0.0781727i	−0.566169	−	0.824289i	$-0.691575\pi$
$487$	−2.98800	+	1.72512i	−0.135399	+	0.0781727i	0.430770	+	0.902462i	$0.358242\pi$
$488$	3.71806	−	2.14662i	0.168309	−	0.0971730i
$489$	−1.38277	−	21.5011i	−0.0625311	−	0.972315i
$490$	−10.4330	−	11.6684i	−0.471317	−	0.527125i
$491$	−36.9916	+	21.3571i	−1.66941	+	0.963833i	−0.701449	+	0.712719i	$0.747463\pi$
$491$	−36.9916	+	21.3571i	−1.66941	+	0.963833i	−0.967958	+	0.251113i	$0.919203\pi$
$492$	0.493868	+	0.741092i	0.0222653	+	0.0334110i
$493$	−7.20685			−0.324580
$494$	2.26932	−	1.31019i	0.102101	−	0.0589483i
$495$	−27.0997	−	5.46329i	−1.21804	−	0.245556i
$496$		−	2.69755i		−	0.121124i
$497$	−0.0206444	−	4.23748i	−0.000926026	−	0.190077i
$498$	−6.33057	+	4.21872i	−0.283679	+	0.189046i
$499$	36.0386			1.61331			0.806654	−	0.591024i	$-0.201276\pi$
$499$	36.0386			1.61331			0.806654	+	0.591024i	$0.201276\pi$
$500$	0.726870	+	11.1567i	0.0325066	+	0.498942i
$501$	20.4731	+	10.1274i	0.914669	+	0.452461i
$502$	−10.4934	−	18.1752i	−0.468345	−	0.811198i
$503$			4.41774i			0.196977i	0.995138	+	0.0984887i	$0.0314008\pi$
$503$			4.41774i			0.196977i	−0.995138	+	0.0984887i	$0.968599\pi$
$504$	3.01971	−	7.34039i	0.134509	−	0.326967i
$505$	5.94141	−	1.18102i	0.264389	−	0.0525545i
$506$	2.11452	−	1.22082i	0.0940019	−	0.0542720i
$507$	12.7507	−	0.820015i	0.566277	−	0.0364181i
$508$	2.70666	+	1.56269i	0.120089	+	0.0693332i
$509$	24.2045			1.07284			0.536422	−	0.843950i	$-0.319775\pi$
$509$	24.2045			1.07284			0.536422	+	0.843950i	$0.319775\pi$
$510$	2.62695	+	9.85739i	0.116323	+	0.436493i
$511$	−8.78180	−	15.0408i	−0.388484	−	0.665367i
$512$	1.00000			0.0441942
$513$	−5.43034	−	1.86567i	−0.239755	−	0.0823712i
$514$	−8.21246	+	4.74146i	−0.362236	+	0.209137i
$515$	39.7944	−	7.91021i	1.75355	−	0.348565i
$516$	−18.6478	−	9.22452i	−0.820923	−	0.406087i
$517$	−8.50944	−	14.7388i	−0.374245	−	0.648211i
$518$	−0.0901218	−	18.4985i	−0.00395972	−	0.812777i
$519$	−22.9969	−	11.3759i	−1.00945	−	0.499346i
$520$	3.49563	+	3.98705i	0.153293	+	0.174844i
$521$	−7.58138	−	13.1313i	−0.332146	−	0.575294i	0.650786	−	0.759261i	$-0.274439\pi$
$521$	−7.58138	−	13.1313i	−0.332146	−	0.575294i	−0.982932	+	0.183967i	$0.941106\pi$
$522$	7.57573	+	3.15977i	0.331581	+	0.138299i
$523$	−0.294517	+	0.510118i	−0.0128783	+	0.0223059i	−0.872393	−	0.488806i	$-0.837433\pi$
$523$	−0.294517	+	0.510118i	−0.0128783	+	0.0223059i	0.859514	+	0.511111i	$0.170766\pi$
$524$	10.7870	−	18.6837i	0.471234	−	0.816202i
$525$	−19.0943	−	12.6652i	−0.833345	−	0.552753i
$526$	5.83660	+	10.1093i	0.254488	+	0.440786i
$527$	−7.10534			−0.309514
$528$	6.39790	+	3.16486i	0.278433	+	0.137733i
$529$	−22.6490			−0.984738
$530$	−6.53469	+	19.2424i	−0.283849	+	0.835834i
$531$	−12.6329	−	16.5474i	−0.548221	−	0.718097i
$532$	2.52478	−	1.47413i	0.109463	−	0.0639117i
$533$	0.609637	−	1.05592i	0.0264063	−	0.0457371i
$534$	−15.0348	−	22.5610i	−0.650619	−	0.976311i
$535$	−6.23925	+	18.3724i	−0.269746	+	0.794307i
$536$	11.7043	+	6.75750i	0.505550	+	0.291879i
$537$	−36.9956	−	18.3007i	−1.59648	−	0.789732i
$538$	−8.14330	+	14.1046i	−0.351082	+	0.608093i
$539$	0.281074	+	28.8460i	0.0121067	+	1.24249i
$540$	1.56046	−	11.5137i	0.0671515	−	0.495470i
$541$	−21.2555	+	36.8156i	−0.913846	+	1.58283i	−0.105264	+	0.994444i	$0.533569\pi$
$541$	−21.2555	+	36.8156i	−0.913846	+	1.58283i	−0.808582	+	0.588384i	$0.799764\pi$
$542$		−	25.1772i		−	1.08145i
$543$	16.8507	−	11.2294i	0.723132	−	0.481899i
$544$		−	2.63400i		−	0.112932i
$545$	−22.2760	−	25.4076i	−0.954198	−	1.08834i
$546$	−10.8409	+	0.750243i	−0.463946	+	0.0321074i
$547$	−7.46589	−	4.31044i	−0.319219	−	0.184301i	0.331826	−	0.943341i	$-0.392335\pi$
$547$	−7.46589	−	4.31044i	−0.319219	−	0.184301i	−0.651044	+	0.759040i	$0.725669\pi$
$548$	−1.88397	+	3.26314i	−0.0804793	+	0.139394i
$549$	1.64981	+	12.7736i	0.0704121	+	0.545165i
$550$	12.5480	−	16.3440i	0.535047	−	0.696911i
$551$	1.51173	+	2.61839i	0.0644018	+	0.111547i
$552$	0.569081	+	0.853955i	0.0242217	+	0.0363467i
$553$	17.9339	+	30.7158i	0.762625	+	1.30617i
$554$	−17.9632	+	10.3710i	−0.763182	+	0.440623i
$555$	−6.97315	−	26.1661i	−0.295994	−	1.11069i
$556$		−	6.01195i		−	0.254964i
$557$	−3.09319	−	5.35757i	−0.131063	−	0.227007i	0.793024	−	0.609191i	$-0.208506\pi$
$557$	−3.09319	−	5.35757i	−0.131063	−	0.227007i	−0.924087	+	0.382183i	$0.875172\pi$
$558$	7.46902	+	3.11526i	0.316189	+	0.131879i
$559$			28.4833i			1.20472i
$560$	3.92179	+	4.42940i	0.165726	+	0.187176i
$561$	8.33622	−	16.8520i	0.351955	−	0.711493i
$562$		−	1.36041i		−	0.0573856i
$563$	28.2325	+	16.3001i	1.18986	+	0.686966i	0.958275	−	0.285849i	$-0.0922755\pi$
$563$	28.2325	+	16.3001i	1.18986	+	0.686966i	0.231585	+	0.972815i	$0.425609\pi$
$564$	5.95230	−	3.96664i	0.250637	−	0.167026i
$565$	1.48381	+	1.69241i	0.0624245	+	0.0712002i
$566$	14.9351			0.627771
$567$	16.8369	+	16.8380i	0.707082	+	0.707132i
$568$			1.60164i			0.0672032i
$569$	5.68792	−	3.28392i	0.238450	−	0.137669i	−0.376014	−	0.926614i	$-0.622706\pi$
$569$	5.68792	−	3.28392i	0.238450	−	0.137669i	0.614464	+	0.788945i	$0.289372\pi$
$570$	3.03034	−	3.02213i	0.126927	−	0.126583i
$571$	8.99355	−	15.5773i	0.376369	−	0.651889i	−0.614162	−	0.789180i	$-0.710506\pi$
$571$	8.99355	−	15.5773i	0.376369	−	0.651889i	0.990531	+	0.137290i	$0.0438393\pi$
$572$		−	9.77238i		−	0.408604i
$573$	40.4042	+	19.9868i	1.68791	+	0.834960i
$574$	0.674440	−	1.18142i	0.0281506	−	0.0493115i
$575$	2.73719	−	1.13295i	0.114149	−	0.0472471i
$576$	−1.15485	+	2.76881i	−0.0481186	+	0.115367i
$577$	−11.8915	−	20.5968i	−0.495051	−	0.857454i	0.504932	−	0.863159i	$-0.331517\pi$
$577$	−11.8915	−	20.5968i	−0.495051	−	0.857454i	−0.999984	+	0.00570479i	$0.998184\pi$
$578$	10.0621			0.418527
$579$	2.00908	+	31.2398i	0.0834946	+	1.29828i
$580$	−4.60035	+	4.03334i	−0.191019	+	0.167475i
$581$	10.0919	+	5.76121i	0.418684	+	0.239015i
$582$	−13.3012	−	19.9597i	−0.551354	−	0.827355i
$583$	32.4350	−	18.7264i	1.34332	−	0.775566i
$584$	3.29147	+	5.70100i	0.136202	+	0.235909i
$585$	−15.0763	+	5.07432i	−0.623329	+	0.209797i
$586$	9.63607	+	5.56339i	0.398062	+	0.229821i
$587$	14.2796	+	8.24435i	0.589384	+	0.340281i	0.764854	−	0.644204i	$-0.222811\pi$
$587$	14.2796	+	8.24435i	0.589384	+	0.340281i	−0.175470	+	0.984485i	$0.556145\pi$
$588$	−12.0912	+	0.895982i	−0.498633	+	0.0369497i
$589$	1.49043	+	2.58151i	0.0614123	+	0.106369i
$590$	15.2194	−	3.02526i	0.626572	−	0.124548i
$591$	18.3423	+	27.5242i	0.754500	+	1.13219i
$592$			6.99185i			0.287363i
$593$	8.69178	+	5.01820i	0.356928	+	0.206073i	0.667733	−	0.744401i	$-0.267265\pi$
$593$	8.69178	+	5.01820i	0.356928	+	0.206073i	−0.310804	+	0.950474i	$0.600598\pi$
$594$	−16.1515	+	14.0597i	−0.662703	+	0.576875i
$595$	11.6670	−	10.3300i	0.478301	−	0.423488i
$596$	−9.69236	−	5.59589i	−0.397015	−	0.229217i
$597$	38.7569	+	19.1720i	1.58622	+	0.784656i
$598$	0.702480	−	1.21673i	0.0287266	−	0.0497559i
$599$	−30.4424	−	17.5759i	−1.24384	−	0.718134i	−0.273970	−	0.961738i	$-0.588337\pi$
$599$	−30.4424	−	17.5759i	−1.24384	−	0.718134i	−0.969875	+	0.243605i	$0.921670\pi$
$600$	7.19357	+	4.82208i	0.293676	+	0.196861i
$601$	32.5093	+	18.7692i	1.32608	+	0.765613i	0.984691	−	0.174309i	$-0.0557691\pi$
$601$	32.5093	+	18.7692i	1.32608	+	0.765613i	0.341390	+	0.939922i	$0.389102\pi$
$602$	0.154823	+	31.7792i	0.00631013	+	1.29522i
$603$	−32.2270	+	24.6032i	−1.31238	+	1.00192i
$604$	9.27469	−	16.0642i	0.377382	−	0.653644i
$605$	−13.1219	+	2.60834i	−0.533483	+	0.106044i
$606$	2.08049	−	4.20579i	0.0845140	−	0.170849i
$607$	−24.1853			−0.981653			−0.490827	−	0.871257i	$-0.663305\pi$
$607$	−24.1853			−0.981653			−0.490827	+	0.871257i	$0.663305\pi$
$608$	−0.956982	+	0.552514i	−0.0388107	+	0.0224074i
$609$	−0.865648	−	12.5084i	−0.0350778	−	0.506867i
$610$	−9.09011	−	3.08700i	−0.368048	−	0.124989i
$611$	−8.48095	−	4.89648i	−0.343102	−	0.198090i
$612$	7.29304	+	3.04186i	0.294804	+	0.122960i
$613$	23.6618	−	13.6611i	0.955690	−	0.551768i	0.0608460	−	0.998147i	$-0.480620\pi$
$613$	23.6618	−	13.6611i	0.955690	−	0.551768i	0.894844	+	0.446379i	$0.147287\pi$
$614$	−7.06683	−	12.2401i	−0.285194	−	0.493971i
$615$	0.518018	−	1.92283i	0.0208885	−	0.0775360i
$616$	−0.0531186	−	10.9032i	−0.00214021	−	0.439301i
$617$	−7.76658	−	13.4521i	−0.312671	−	0.541562i	0.666269	−	0.745712i	$-0.267890\pi$
$617$	−7.76658	−	13.4521i	−0.312671	−	0.541562i	−0.978940	+	0.204150i	$0.934557\pi$
$618$	13.9347	−	28.1695i	0.560535	−	1.13315i
$619$		−	21.2581i		−	0.854435i	−0.904149	−	0.427218i	$-0.859494\pi$
$619$		−	21.2581i		−	0.854435i	0.904149	−	0.427218i	$-0.140506\pi$
$620$	−4.53555	+	3.97652i	−0.182152	+	0.159701i
$621$	−3.02164	+	0.589491i	−0.121254	+	0.0236554i
$622$	5.87504			0.235568
$623$	−20.5319	+	35.9659i	−0.822595	+	1.44094i
$624$	4.09879	−	0.263600i	0.164083	−	0.0105524i
$625$	17.6869	−	17.6685i	0.707475	−	0.706738i
$626$	9.51843	−	16.4864i	0.380433	−	0.658930i
$627$	−7.87129	+	0.506215i	−0.314349	+	0.0202163i
$628$	5.83514	+	10.1068i	0.232847	+	0.403303i
$629$	18.4165			0.734314
$630$	−16.7932	+	5.74343i	−0.669059	+	0.228824i
$631$	22.0357			0.877226			0.438613	−	0.898676i	$-0.355470\pi$
$631$	22.0357			0.877226			0.438613	+	0.898676i	$0.355470\pi$
$632$	−6.72172	−	11.6424i	−0.267376	−	0.463108i
$633$	10.1632	−	20.5453i	0.403949	−	0.816602i
$634$	7.70830	−	13.3512i	0.306136	−	0.530242i
$635$	−1.36251	−	6.85446i	−0.0540695	−	0.272011i
$636$	8.72922	+	13.0990i	0.346136	+	0.519408i
$637$	8.43932	+	14.2939i	0.334378	+	0.566343i
$638$	11.2756			0.446405
$639$	−4.43463	−	1.84964i	−0.175431	−	0.0731708i
$640$	−1.47412	−	1.68136i	−0.0582698	−	0.0664615i
$641$			25.6700i			1.01390i	0.861975	+	0.506951i	$0.169228\pi$
$641$			25.6700i			1.01390i	−0.861975	+	0.506951i	$0.830772\pi$
$642$	8.33456	+	12.5067i	0.328939	+	0.493602i
$643$	−0.505064	−	0.874797i	−0.0199178	−	0.0344986i	0.855895	−	0.517150i	$-0.173007\pi$
$643$	−0.505064	−	0.874797i	−0.0199178	−	0.0344986i	−0.875813	+	0.482651i	$0.839674\pi$
$644$	0.777152	−	1.36134i	0.0306241	−	0.0536443i
$645$	11.9794	+	44.9517i	0.471689	+	1.76997i
$646$	1.45532	+	2.52069i	0.0572587	+	0.0991750i
$647$	12.5056	−	7.22013i	0.491647	−	0.283852i	−0.233611	−	0.972330i	$-0.575054\pi$
$647$	12.5056	−	7.22013i	0.491647	−	0.283852i	0.725257	+	0.688478i	$0.241721\pi$
$648$	−6.33266	−	6.39511i	−0.248770	−	0.251224i
$649$	−24.7666	−	14.2990i	−0.972174	−	0.561285i
$650$	1.55066	−	11.7548i	0.0608220	−	0.461061i
$651$	−0.853454	−	12.3322i	−0.0334495	−	0.483339i
$652$	10.7728	−	6.21967i	0.421895	−	0.243581i
$653$	44.2235			1.73060			0.865299	−	0.501256i	$-0.167129\pi$
$653$	44.2235			1.73060			0.865299	+	0.501256i	$0.167129\pi$
$654$	−26.1197	+	1.67980i	−1.02136	+	0.0656853i
$655$	−47.3154	+	9.40522i	−1.84877	+	0.367492i
$656$	−0.257087	+	0.445287i	−0.0100376	+	0.0173855i
$657$	−19.5862	+	2.52970i	−0.764129	+	0.0986929i
$658$	−9.48891	−	5.41696i	−0.369916	−	0.211175i
$659$	−24.1702	−	13.9547i	−0.941539	−	0.543598i	−0.0510965	−	0.998694i	$-0.516272\pi$
$659$	−24.1702	−	13.9547i	−0.941539	−	0.543598i	−0.890442	+	0.455096i	$0.849605\pi$
$660$	−4.11003	−	15.4225i	−0.159983	−	0.600321i
$661$	−0.0371085	−	0.0214246i	−0.00144335	−	0.000833320i	0.499278	−	0.866442i	$-0.333599\pi$
$661$	−0.0371085	−	0.0214246i	−0.00144335	−	0.000833320i	−0.500722	+	0.865608i	$0.666932\pi$
$662$	15.4650	−	26.7862i	0.601064	−	1.04107i
$663$	−0.694321	−	10.7962i	−0.0269652	−	0.419290i
$664$	−3.80374	−	2.19609i	−0.147614	−	0.0852248i
$665$	−6.20038	−	2.07201i	−0.240441	−	0.0803492i
$666$	−19.3591	−	8.07452i	−0.750151	−	0.312881i
$667$	1.40389	+	0.810538i	0.0543589	+	0.0313841i
$668$			13.1873i			0.510230i
$669$	−8.44822	+	0.543319i	−0.326627	+	0.0210059i
$670$	−5.89186	−	29.6405i	−0.227622	−	1.14511i
$671$	8.84635	+	15.3223i	0.341510	+	0.591512i
$672$	4.57164	−	0.316381i	0.176355	−	0.0122047i
$673$	−17.4536	−	10.0769i	−0.672788	−	0.388434i	0.124344	−	0.992239i	$-0.460317\pi$
$673$	−17.4536	−	10.0769i	−0.672788	−	0.388434i	−0.797132	+	0.603805i	$0.793651\pi$
$674$	21.3417	+	12.3216i	0.822051	+	0.474611i
$675$	−21.6589	+	14.3489i	−0.833652	+	0.552289i
$676$	3.68840	+	6.38850i	0.141862	+	0.245711i
$677$	−24.3021	+	14.0308i	−0.934004	+	0.539248i	−0.888076	−	0.459697i	$-0.847958\pi$
$677$	−24.3021	+	14.0308i	−0.934004	+	0.539248i	−0.0459284	+	0.998945i	$0.514625\pi$
$678$	1.73984	−	0.111892i	0.0668182	−	0.00429719i
$679$	−18.1646	+	31.8189i	−0.697092	+	1.22110i
$680$	−4.42869	+	3.88283i	−0.169832	+	0.148900i
$681$	17.2876	−	11.5205i	0.662462	−	0.441468i
$682$	11.1168			0.425683
$683$	−14.7248	−	25.5040i	−0.563428	−	0.975885i	−0.997194	−	0.0748598i	$-0.976149\pi$
$683$	−14.7248	−	25.5040i	−0.563428	−	0.975885i	0.433767	−	0.901025i	$-0.357184\pi$
$684$	−0.424640	−	3.28777i	−0.0162365	−	0.125711i
$685$	8.26371	−	1.64263i	0.315740	−	0.0627618i
$686$	9.49355	+	15.9020i	0.362465	+	0.607140i
$687$	−15.2562	+	10.1669i	−0.582062	+	0.387890i
$688$		−	12.0115i		−	0.457936i
$689$	10.7755	−	18.6637i	0.410513	−	0.711029i
$690$	0.596908	−	2.21566i	0.0227239	−	0.0843488i
$691$	6.03382	−	3.48363i	0.229537	−	0.132523i	−0.380821	−	0.924649i	$-0.624359\pi$
$691$	6.03382	−	3.48363i	0.229537	−	0.132523i	0.610359	+	0.792125i	$0.291025\pi$
$692$		−	14.8129i		−	0.563102i
$693$	30.2502	+	12.4444i	1.14911	+	0.472724i
$694$	0.546144			0.0207313
$695$	−10.1082	+	8.86236i	−0.383427	+	0.336169i
$696$	0.304148	+	4.72928i	0.0115287	+	0.179263i
$697$	1.17288	+	0.677165i	0.0444262	+	0.0256495i
$698$		−	6.50116i		−	0.246073i
$699$	0.898320	−	0.0577724i	0.0339776	−	0.00218515i
$700$	1.66620	−	13.1234i	0.0629765	−	0.496018i
$701$			17.0338i			0.643357i	0.946849	+	0.321678i	$0.104247\pi$
$701$			17.0338i			0.643357i	−0.946849	+	0.321678i	$0.895753\pi$
$702$	−4.00362	+	11.6532i	−0.151107	+	0.439822i
$703$	−3.86309	−	6.69107i	−0.145699	−	0.252359i
$704$			4.12106i			0.155318i
$705$	−15.4438	−	4.16061i	−0.581646	−	0.156698i
$706$	5.67627	−	3.27719i	0.213629	−	0.123339i
$707$	−7.16743	+	0.0349186i	−0.269559	+	0.00131325i
$708$	5.32932	−	10.7735i	0.200288	−	0.404892i
$709$	0.510534	+	0.884271i	0.0191735	+	0.0332095i	0.875453	−	0.483303i	$-0.160563\pi$
$709$	0.510534	+	0.884271i	0.0191735	+	0.0332095i	−0.856279	+	0.516513i	$0.827230\pi$
$710$	2.69292	−	2.36101i	0.101064	−	0.0886071i
$711$	39.9981	−	5.16605i	1.50005	−	0.193742i
$712$	7.82648	−	13.5559i	0.293310	−	0.508027i
$713$	1.38412	+	0.799121i	0.0518356	+	0.0299273i
$714$	−0.833346	−	12.0417i	−0.0311872	−	0.450649i
$715$	−16.4309	+	14.4057i	−0.614479	+	0.538742i
$716$		−	23.8299i		−	0.890564i
$717$	−4.30033	−	2.12725i	−0.160599	−	0.0794436i
$718$		−	4.10200i		−	0.153085i
$719$	20.6417	−	35.7524i	0.769804	−	1.33334i	−0.167865	−	0.985810i	$-0.553687\pi$
$719$	20.6417	−	35.7524i	0.769804	−	1.33334i	0.937669	−	0.347530i	$-0.112980\pi$
$720$	6.35775	−	2.13986i	0.236939	−	0.0797480i
$721$	−48.0060	+	0.233878i	−1.78784	+	0.00871006i
$722$	−8.88946	+	15.3970i	−0.330831	+	0.573017i
$723$	29.1158	−	19.4030i	1.08283	−	0.721604i
$724$	10.1248	+	5.84555i	0.376285	+	0.217248i
$725$	13.5630	+	1.78919i	0.503716	+	0.0664489i
$726$	−4.59487	+	9.28873i	−0.170532	+	0.344737i
$727$	7.79834	−	13.5071i	0.289224	−	0.500951i	−0.684400	−	0.729106i	$-0.739936\pi$
$727$	7.79834	−	13.5071i	0.289224	−	0.500951i	0.973625	+	0.228155i	$0.0732693\pi$
$728$	−3.16341	−	5.41805i	−0.117244	−	0.200806i
$729$	25.0201	−	10.1486i	0.926671	−	0.375873i
$730$	4.73338	−	13.9381i	0.175190	−	0.515873i
$731$	−31.6384			−1.17019
$732$	−6.18797	+	4.12370i	−0.228714	+	0.152416i
$733$	44.6299			1.64844			0.824222	−	0.566267i	$-0.191613\pi$
$733$	44.6299			1.64844			0.824222	+	0.566267i	$0.191613\pi$
$734$	−10.0785	−	17.4565i	−0.372006	−	0.644333i
$735$	19.3304	+	19.0088i	0.713012	+	0.701152i
$736$	−0.296239	+	0.513101i	−0.0109195	+	0.0189132i
$737$	−27.8480	+	48.2342i	−1.02580	+	1.77673i
$738$	−0.936022	−	1.22606i	−0.0344554	−	0.0451320i
$739$	−14.6785	−	25.4239i	−0.539957	−	0.935233i	−0.998906	−	0.0467704i	$-0.985107\pi$
$739$	−14.6785	−	25.4239i	−0.539957	−	0.935233i	0.458949	−	0.888463i	$-0.348226\pi$
$740$	11.7558	−	10.3069i	0.432152	−	0.378887i
$741$	−3.77683	+	2.51690i	−0.138745	+	0.0924606i
$742$	11.9209	−	20.8818i	0.437629	−	0.766596i
$743$	−20.1964	−	34.9813i	−0.740936	−	1.28334i	−0.952070	−	0.305881i	$-0.901049\pi$
$743$	−20.1964	−	34.9813i	−0.740936	−	1.28334i	0.211134	−	0.977457i	$-0.432284\pi$
$744$	0.299863	+	4.66266i	0.0109935	+	0.170942i
$745$	4.87905	+	24.5454i	0.178755	+	0.899272i
$746$	4.94553	−	2.85530i	0.181069	−	0.104540i
$747$	10.4733	−	7.99570i	0.383198	−	0.292547i
$748$	10.8549			0.396893
$749$	11.3819	−	19.9377i	0.415886	−	0.728509i
$750$	−2.49657	−	19.2033i	−0.0911619	−	0.701206i
$751$	−21.8635			−0.797811			−0.398905	−	0.916992i	$-0.630610\pi$
$751$	−21.8635			−0.797811			−0.398905	+	0.916992i	$0.630610\pi$
$752$	3.57645	+	2.06487i	0.130420	+	0.0752979i
$753$	20.1581	+	30.2490i	0.734601	+	1.10233i
$754$	5.61892	−	3.24409i	0.204629	−	0.118143i
$755$	−40.6817	+	8.08659i	−1.48056	+	0.294301i
$756$	−4.40355	+	13.0234i	−0.160155	+	0.473656i
$757$			14.0506i			0.510679i	0.966851	+	0.255339i	$0.0821872\pi$
$757$			14.0506i			0.510679i	−0.966851	+	0.255339i	$0.917813\pi$
$758$	−2.71212	−	4.69753i	−0.0985086	−	0.170622i
$759$	−3.51920	+	2.34521i	−0.127739	+	0.0851259i
$760$	2.33968	+	0.794555i	0.0848692	+	0.0288215i
$761$	39.1837			1.42041			0.710204	−	0.703996i	$-0.248603\pi$
$761$	39.1837			1.42041			0.710204	+	0.703996i	$0.248603\pi$
$762$	−4.85212	−	2.40020i	−0.175774	−	0.0869502i
$763$	20.1589	+	34.5266i	0.729800	+	1.24995i
$764$			26.0254i			0.941567i
$765$	−5.63639	−	16.7463i	−0.203784	−	0.605463i
$766$	28.8586	−	16.6615i	1.04270	−	0.602004i
$767$	−16.4558			−0.594184
$768$	−1.72848	+	0.111161i	−0.0623712	+	0.00401119i
$769$	−16.4424	+	9.49301i	−0.592927	+	0.342327i	−0.766254	−	0.642538i	$-0.777882\pi$
$769$	−16.4424	+	9.49301i	−0.592927	+	0.342327i	0.173327	+	0.984864i	$0.444548\pi$
$770$	−18.2538	+	16.1619i	−0.657822	+	0.582435i
$771$	13.6680	−	9.10843i	0.492241	−	0.328032i
$772$	−15.6522	+	9.03678i	−0.563334	+	0.325241i
$773$	−28.9315	+	16.7036i	−1.04060	+	0.600788i	−0.920002	−	0.391914i	$-0.871813\pi$
$773$	−28.9315	+	16.7036i	−1.04060	+	0.600788i	−0.120593	+	0.992702i	$0.538480\pi$
$774$	33.2577	+	13.8715i	1.19542	+	0.498600i
$775$	13.3719	+	1.76399i	0.480333	+	0.0633644i
$776$	6.92406	−	11.9928i	0.248559	−	0.430518i
$777$	2.21209	+	31.9642i	0.0793583	+	1.14671i
$778$	25.3567	−	14.6397i	0.909082	−	0.524859i
$779$		−	0.568176i		−	0.0203570i
$780$	−6.48533	−	6.50296i	−0.232212	−	0.232843i
$781$	−6.60044			−0.236182
$782$	1.35151	+	0.780293i	0.0483298	+	0.0279032i
$783$	−13.4457	−	4.61947i	−0.480512	−	0.165086i
$784$	−3.55890	−	6.02779i	−0.127104	−	0.215278i
$785$	8.39135	−	24.7096i	0.299500	−	0.881922i
$786$	−16.5683	+	33.4935i	−0.590971	+	1.19467i
$787$	0.436343	−	0.755767i	0.0155539	−	0.0269402i	−0.858144	−	0.513410i	$-0.828382\pi$
$787$	0.436343	−	0.755767i	0.0155539	−	0.0269402i	0.873698	+	0.486469i	$0.161715\pi$
$788$	−9.54821	+	16.5380i	−0.340141	+	0.589141i
$789$	−11.2122	−	16.8249i	−0.399165	−	0.598982i
$790$	−9.66632	+	28.4639i	−0.343912	+	1.01270i
$791$	−1.34279	−	2.29984i	−0.0477442	−	0.0817727i
$792$	−11.4104	−	4.75919i	−0.405452	−	0.169111i
$793$	8.81673	+	5.09034i	0.313091	+	0.180763i
$794$	10.8543			0.385203
$795$	9.15608	−	33.9864i	0.324733	−	1.20537i
$796$			24.9644i			0.884840i
$797$	24.9244	−	14.3901i	0.882867	−	0.509724i	0.0112647	−	0.999937i	$-0.496414\pi$
$797$	24.9244	−	14.3901i	0.882867	−	0.509724i	0.871603	+	0.490213i	$0.163081\pi$
$798$	−4.20017	+	2.82866i	−0.148684	+	0.100134i
$799$	5.43885	−	9.42037i	0.192413	−	0.333269i
$800$	−0.653922	+	4.95705i	−0.0231196	+	0.175258i
$801$	28.4953	+	37.3250i	1.00683	+	1.31881i
$802$	15.8321	−	9.14066i	0.559050	−	0.322768i
$803$	−23.4942	+	13.5644i	−0.829091	+	0.478676i
$804$	−20.9819	−	10.3791i	−0.739974	−	0.366044i
$805$	−3.43452	+	0.700114i	−0.121051	+	0.0246758i
$806$	5.53978	−	3.19839i	0.195130	−	0.112659i
$807$	12.5076	−	25.2847i	0.440290	−	0.890065i
$808$	2.70907			0.0953046
$809$	−3.58630	+	2.07055i	−0.126088	+	0.0727967i	−0.561717	−	0.827329i	$-0.689859\pi$
$809$	−3.58630	+	2.07055i	−0.126088	+	0.0727967i	0.435630	+	0.900126i	$0.356526\pi$
$810$	−1.41735	+	20.0746i	−0.0498005	+	0.705351i
$811$			17.4383i			0.612342i	0.951977	+	0.306171i	$0.0990479\pi$
$811$			17.4383i			0.612342i	−0.951977	+	0.306171i	$0.900952\pi$
$812$	6.25147	−	3.65001i	0.219383	−	0.128090i
$813$	2.79873	+	43.5183i	0.0981557	+	1.52625i
$814$	−28.8138			−1.00992
$815$	−26.3379	−	8.94433i	−0.922576	−	0.313306i
$816$	0.292798	+	4.55281i	0.0102500	+	0.159380i
$817$	6.63654	+	11.4948i	0.232183	+	0.402153i
$818$		−	9.67827i		−	0.338393i
$819$	18.6548	−	2.50186i	0.651852	−	0.0874222i
$820$	1.12766	−	0.224154i	0.0393797	−	0.00782779i
$821$	−26.6695	+	15.3976i	−0.930771	+	0.537381i	−0.887055	−	0.461663i	$-0.847253\pi$
$821$	−26.6695	+	15.3976i	−0.930771	+	0.537381i	−0.0437160	+	0.999044i	$0.513920\pi$
$822$	2.89368	−	5.84969i	0.100929	−	0.204031i
$823$	−30.3149	−	17.5023i	−1.05671	−	0.610092i	−0.132190	−	0.991224i	$-0.542201\pi$
$823$	−30.3149	−	17.5023i	−1.05671	−	0.610092i	−0.924520	+	0.381133i	$0.875534\pi$
$824$	18.1448			0.632103
$825$	−19.8721	+	29.6451i	−0.691857	+	1.03211i
$826$	−18.3599	+	0.0894467i	−0.638823	+	0.00311225i
$827$	−34.7736			−1.20919			−0.604597	−	0.796531i	$-0.706666\pi$
$827$	−34.7736			−1.20919			−0.604597	+	0.796531i	$0.706666\pi$
$828$	−1.07857	−	1.41278i	−0.0374829	−	0.0490977i
$829$	−7.21777	+	4.16718i	−0.250683	+	0.144732i	−0.620077	−	0.784541i	$-0.712899\pi$
$829$	−7.21777	+	4.16718i	−0.250683	+	0.144732i	0.369394	+	0.929273i	$0.379565\pi$
$830$	1.91477	+	9.63275i	0.0664626	+	0.334358i
$831$	29.8961	−	19.9230i	1.03709	−	0.691120i
$832$	1.18566	+	2.05363i	0.0411055	+	0.0711968i
$833$	−15.8772	+	9.37413i	−0.550111	+	0.324794i
$834$	0.668297	+	10.3915i	0.0231412	+	0.359830i
$835$	22.1725	−	19.4396i	0.767311	−	0.672737i
$836$	−2.27694	−	3.94378i	−0.0787496	−	0.136398i
$837$	−13.2563	−	4.55440i	−0.458206	−	0.157423i
$838$	−5.02659	+	8.70630i	−0.173641	+	0.300754i
$839$	15.4855	−	26.8216i	0.534618	−	0.925985i	−0.464564	−	0.885540i	$-0.653789\pi$
$839$	15.4855	−	26.8216i	0.534618	−	0.925985i	0.999182	−	0.0404455i	$-0.0128777\pi$
$840$	−7.27111	−	7.22018i	−0.250877	−	0.249120i
$841$	−10.7569	−	18.6315i	−0.370928	−	0.642465i
$842$	13.2352			0.456116
$843$	0.151225	+	2.35145i	0.00520848	+	0.0809881i
$844$	13.2338			0.455525
$845$	5.30419	−	15.6190i	0.182470	−	0.537308i
$846$	−9.84749	+	7.51793i	−0.338564	+	0.258472i
$847$	15.8297	−	0.0771197i	0.543914	−	0.00264987i
$848$	−4.54406	+	7.87055i	−0.156044	+	0.270276i
$849$	−25.8151	+	1.66021i	−0.885972	+	0.0569783i
$850$	13.0569	+	1.72243i	0.447847	+	0.0590788i
$851$	−3.58753	−	2.07126i	−0.122979	−	0.0710019i
$852$	−0.178040	−	2.76840i	−0.00609955	−	0.0948437i
$853$	−12.6526	+	21.9150i	−0.433217	+	0.750355i	−0.997148	−	0.0754673i	$-0.975955\pi$
$853$	−12.6526	+	21.9150i	−0.433217	+	0.750355i	0.563931	+	0.825822i	$0.309288\pi$
$854$	9.86461	+	5.63143i	0.337560	+	0.192704i
$855$	−4.90195	+	5.56055i	−0.167643	+	0.190167i
$856$	−4.33862	+	7.51471i	−0.148291	+	0.256848i
$857$		−	15.0001i		−	0.512393i	−0.966625	−	0.256196i	$-0.917531\pi$
$857$		−	15.0001i		−	0.512393i	0.966625	−	0.256196i	$-0.0824693\pi$
$858$	1.08631	+	16.8914i	0.0370860	+	0.576662i
$859$			35.2896i			1.20406i	0.798472	+	0.602032i	$0.205642\pi$
$859$			35.2896i			1.20406i	−0.798472	+	0.602032i	$0.794358\pi$
$860$	−20.1957	+	17.7065i	−0.688667	+	0.603786i
$861$	−1.03443	+	2.11703i	−0.0352532	+	0.0721482i
$862$	4.44716	+	2.56757i	0.151471	+	0.0874517i
$863$	8.04268	−	13.9303i	0.273776	−	0.474194i	−0.696050	−	0.717994i	$-0.745061\pi$
$863$	8.04268	−	13.9303i	0.273776	−	0.474194i	0.969826	+	0.243800i	$0.0783940\pi$
$864$	1.68834	−	4.91421i	0.0574387	−	0.167185i
$865$	−24.9058	+	21.8360i	−0.846822	+	0.742448i
$866$	3.98681	+	6.90536i	0.135477	+	0.234654i
$867$	−17.3921	+	1.11851i	−0.590666	+	0.0379867i
$868$	6.16341	−	3.59860i	0.209200	−	0.122144i
$869$	47.9789	−	27.7006i	1.62757	−	0.939679i
$870$	7.50326	−	7.48292i	0.254384	−	0.253695i
$871$			32.0485i			1.08592i
$872$	−7.55567	−	13.0868i	−0.255867	−	0.443175i
$873$	25.2097	+	33.0213i	0.853218	+	1.11760i
$874$		−	0.654705i		−	0.0221457i
$875$	−24.5213	+	16.5440i	−0.828972	+	0.559291i
$876$	−6.32298	−	9.48818i	−0.213634	−	0.320576i
$877$			27.8272i			0.939657i	0.882758	+	0.469829i	$0.155684\pi$
$877$			27.8272i			0.939657i	−0.882758	+	0.469829i	$0.844316\pi$
$878$	−22.3502	−	12.9039i	−0.754282	−	0.435485i
$879$	−17.2742	−	8.54504i	−0.582644	−	0.288217i
$880$	6.92897	−	6.07495i	0.233576	−	0.204786i
$881$	36.4477			1.22795			0.613977	−	0.789324i	$-0.289569\pi$
$881$	36.4477			1.22795			0.613977	+	0.789324i	$0.289569\pi$
$882$	20.7998	−	2.89276i	0.700366	−	0.0974043i
$883$		−	27.9433i		−	0.940367i	−0.882569	−	0.470184i	$-0.844188\pi$
$883$		−	27.9433i		−	0.940367i	0.882569	−	0.470184i	$-0.155812\pi$
$884$	5.40925	−	3.12303i	0.181933	−	0.105039i
$885$	−25.9701	+	6.92092i	−0.872976	+	0.232644i
$886$	−15.6440	+	27.0962i	−0.525571	+	0.910316i
$887$		−	53.1573i		−	1.78485i	−0.451198	−	0.892424i	$-0.649003\pi$
$887$		−	53.1573i		−	1.78485i	0.451198	−	0.892424i	$-0.350997\pi$
$888$	−0.777223	−	12.0853i	−0.0260819	−	0.405555i
$889$	0.0402847	+	8.26888i	0.00135111	+	0.277329i
$890$	−34.3294	+	6.82390i	−1.15072	+	0.228738i
$891$	26.3546	−	26.0973i	0.882913	−	0.874291i
$892$	−2.44383	−	4.23284i	−0.0818255	−	0.141726i
$893$	−4.56347			−0.152711
$894$	17.3751	+	8.59497i	0.581110	+	0.287459i
$895$	−40.0665	+	35.1282i	−1.33928	+	1.17421i
$896$	1.33402	+	2.28482i	0.0445666	+	0.0763303i
$897$	−1.07897	+	2.18118i	−0.0360258	+	0.0728276i
$898$	−6.00732	+	3.46833i	−0.200467	+	0.115740i
$899$	3.69038	+	6.39192i	0.123081	+	0.213182i
$900$	−12.9700	−	7.53523i	−0.432333	−	0.251174i
$901$	20.7310	+	11.9690i	0.690650	+	0.398747i
$902$	−1.83506	−	1.05947i	−0.0611006	−	0.0352765i
$903$	−3.80022	−	54.9125i	−0.126464	−	1.82737i
$904$	0.503287	+	0.871718i	0.0167391	+	0.0289929i
$905$	−5.09673	−	25.6404i	−0.169421	−	0.852317i
$906$	−14.2454	+	28.7977i	−0.473271	+	0.956739i
$907$			16.0566i			0.533149i	0.963814	+	0.266575i	$0.0858919\pi$
$907$			16.0566i			0.533149i	−0.963814	+	0.266575i	$0.914108\pi$
$908$	10.3873	+	5.99711i	0.344714	+	0.199021i
$909$	−3.12856	+	7.50090i	−0.103768	+	0.248789i
$910$	−4.44642	+	13.3057i	−0.147398	+	0.441079i
$911$	−36.7577	−	21.2220i	−1.21784	−	0.703118i	−0.253381	−	0.967367i	$-0.581543\pi$
$911$	−36.7577	−	21.2220i	−1.21784	−	0.703118i	−0.964455	+	0.264249i	$0.914876\pi$
$912$	1.59271	−	1.06139i	0.0527397	−	0.0351461i
$913$	9.05021	−	15.6754i	0.299518	−	0.518781i
$914$	23.7421	+	13.7075i	0.785317	+	0.453403i
$915$	16.0552	+	4.32534i	0.530769	+	0.142991i
$916$	−9.16676	−	5.29243i	−0.302878	−	0.174867i
$917$	57.0790	−	0.278080i	1.88492	−	0.00918302i
$918$	−12.9440	−	4.44709i	−0.427216	−	0.146776i
$919$	−11.3435	+	19.6475i	−0.374188	+	0.648112i	−0.990205	−	0.139621i	$-0.955412\pi$
$919$	−11.3435	+	19.6475i	−0.374188	+	0.648112i	0.616017	+	0.787732i	$0.288745\pi$
$920$	1.29940	−	0.258291i	0.0428399	−	0.00851559i
$921$	13.5755	+	20.3712i	0.447328	+	0.671255i
$922$	−18.3228			−0.603429
$923$	−3.28917	+	1.89900i	−0.108264	+	0.0625064i
$924$	1.30382	+	18.8400i	0.0428927	+	0.619791i
$925$	−34.6590	−	4.57213i	−1.13958	−	0.150331i
$926$	16.6964	+	9.63966i	0.548677	+	0.316779i
$927$	−20.9544	+	50.2395i	−0.688234	+	1.65008i
$928$	−2.36953	+	1.36805i	−0.0777835	+	0.0449083i
$929$	−2.82041	−	4.88508i	−0.0925345	−	0.160274i	0.816042	−	0.577992i	$-0.196164\pi$
$929$	−2.82041	−	4.88508i	−0.0925345	−	0.160274i	−0.908577	+	0.417718i	$0.862830\pi$
$930$	7.39757	−	7.37752i	0.242576	−	0.241918i
$931$	6.73624	+	3.80214i	0.220771	+	0.124610i
$932$	0.259858	+	0.450088i	0.00851194	+	0.0147431i
$933$	−10.1549	+	0.653077i	−0.332456	+	0.0213808i
$934$		−	12.9495i		−	0.423721i
$935$	−16.0014	−	18.2509i	−0.523301	−	0.596868i
$936$	−7.05538	+	0.911254i	−0.230612	+	0.0297853i
$937$	−33.6125			−1.09807			−0.549036	−	0.835799i	$-0.685005\pi$
$937$	−33.6125			−1.09807			−0.549036	+	0.835799i	$0.685005\pi$
$938$	0.174202	+	35.7569i	0.00568790	+	1.16750i
$939$	−14.6198	+	29.5545i	−0.477098	+	0.964475i
$940$	−1.80036	−	9.05716i	−0.0587211	−	0.295412i
$941$	0.116632	−	0.202012i	0.00380208	−	0.00658540i	−0.864118	−	0.503289i	$-0.832123\pi$
$941$	0.116632	−	0.202012i	0.00380208	−	0.00658540i	0.867920	+	0.496704i	$0.165456\pi$
$942$	−11.2094	−	16.8207i	−0.365222	−	0.548047i
$943$	−0.152318	−	0.263823i	−0.00496017	−	0.00859126i
$944$	6.93948			0.225861
$945$	28.3883	−	11.7942i	0.923473	−	0.383664i
$946$	49.5003			1.60939
$947$	1.31252	+	2.27335i	0.0426512	+	0.0738740i	0.886563	−	0.462608i	$-0.153086\pi$
$947$	1.31252	+	2.27335i	0.0426512	+	0.0738740i	−0.843912	+	0.536482i	$0.819753\pi$
$948$	12.9125	+	19.3764i	0.419380	+	0.629316i
$949$	−7.80517	+	13.5189i	−0.253366	+	0.438844i
$950$	−2.11305	−	5.10511i	−0.0685563	−	0.165632i
$951$	−11.8395	+	23.9341i	−0.383922	+	0.776116i
$952$	6.01820	−	3.51381i	0.195051	−	0.113883i
$953$	−15.1772			−0.491637			−0.245818	−	0.969316i	$-0.579057\pi$
$953$	−15.1772			−0.491637			−0.245818	+	0.969316i	$0.579057\pi$
$954$	−16.5444	−	21.6709i	−0.535644	−	0.701623i
$955$	43.7581	−	38.3647i	1.41598	−	1.24145i
$956$		−	2.76996i		−	0.0895869i
$957$	−19.4896	+	1.25341i	−0.630011	+	0.0405170i
$958$	13.5378	+	23.4482i	0.437388	+	0.757578i
$959$	−9.96893	+	0.0485671i	−0.321914	+	0.00156831i
$960$	2.73489	+	2.74233i	0.0882683	+	0.0885082i
$961$	−11.8616	−	20.5449i	−0.382632	−	0.662739i
$962$	−14.3587	+	8.28999i	−0.462942	+	0.267280i
$963$	−15.7964	−	20.6912i	−0.509032	−	0.666764i
$964$	17.4943	+	10.1004i	0.563454	+	0.325310i
$965$	38.2673	+	12.9956i	1.23187	+	0.418342i
$966$	−1.19196	+	2.43944i	−0.0383508	+	0.0784877i
$967$	11.1551	−	6.44040i	0.358724	−	0.207109i	−0.309797	−	0.950803i	$-0.600261\pi$
$967$	11.1551	−	6.44040i	0.358724	−	0.207109i	0.668521	+	0.743693i	$0.266928\pi$
$968$	−5.98313			−0.192305
$969$	−2.79569	−	4.19518i	−0.0898105	−	0.134769i
$970$	−30.3712	+	6.03709i	−0.975159	+	0.193839i
$971$	−14.3294	+	24.8192i	−0.459851	+	0.796486i	−0.998953	−	0.0457549i	$-0.985431\pi$
$971$	−14.3294	+	24.8192i	−0.459851	+	0.796486i	0.539101	+	0.842241i	$0.318764\pi$
$972$	11.6568	+	10.3499i	0.373891	+	0.331972i
$973$	13.7362	−	8.02008i	0.440363	−	0.257112i
$974$	2.98800	+	1.72512i	0.0957416	+	0.0552765i
$975$	−1.37361	+	20.4903i	−0.0439908	+	0.656215i
$976$	−3.71806	−	2.14662i	−0.119012	−	0.0687117i
$977$	−7.08037	+	12.2636i	−0.226521	+	0.392346i	−0.956775	−	0.290830i	$-0.906069\pi$
$977$	−7.08037	+	12.2636i	−0.226521	+	0.392346i	0.730254	+	0.683176i	$0.239402\pi$
$978$	−17.9291	+	11.9481i	−0.573311	+	0.382058i
$979$	55.8645	+	32.2534i	1.78544	+	1.03082i
$980$	−4.88861	+	14.8695i	−0.156161	+	0.474988i
$981$	44.9606	−	5.80699i	1.43548	−	0.185403i
$982$	36.9916	+	21.3571i	1.18045	+	0.681533i
$983$		−	39.5519i		−	1.26151i	−0.775982	−	0.630755i	$-0.782745\pi$
$983$		−	39.5519i		−	1.26151i	0.775982	−	0.630755i	$-0.217255\pi$
$984$	0.394871	−	0.798248i	0.0125880	−	0.0254472i
$985$	41.8815	−	8.32507i	1.33445	−	0.265259i
$986$	3.60343	+	6.24132i	0.114757	+	0.198764i
$987$	17.0035	+	8.30831i	0.541229	+	0.264456i
$988$	−2.26932	−	1.31019i	−0.0721966	−	0.0416827i
$989$	6.16314	+	3.55829i	0.195976	+	0.113147i
$990$	8.81850	+	26.2007i	0.280270	+	0.832712i
$991$	10.3535	+	17.9329i	0.328891	+	0.569656i	0.982292	−	0.187356i	$-0.0599917\pi$
$991$	10.3535	+	17.9329i	0.328891	+	0.569656i	−0.653401	+	0.757012i	$0.726658\pi$
$992$	−2.33615	+	1.34878i	−0.0741728	+	0.0428237i
$993$	−23.7533	+	48.0184i	−0.753790	+	1.52382i
$994$	−3.65944	+	2.13662i	−0.116070	+	0.0677694i
$995$	41.9741	−	36.8006i	1.33067	−	1.16666i
$996$	6.81881	+	3.37307i	0.216062	+	0.106880i
$997$	49.7520			1.57566			0.787831	−	0.615892i	$-0.211204\pi$
$997$	49.7520			1.57566			0.787831	+	0.615892i	$0.211204\pi$
$998$	−18.0193	−	31.2103i	−0.570391	−	0.987946i
$999$	34.3595	+	11.8047i	1.08709	+	0.373483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.r.a.299.16	yes	48
3.2	odd	2		1890.2.r.b.89.3		48
5.4	even	2		630.2.r.b.299.9	yes	48
7.3	odd	6		630.2.bi.b.479.9	yes	48
9.4	even	3		1890.2.bi.b.719.8		48
9.5	odd	6		630.2.bi.a.509.16	yes	48
15.14	odd	2		1890.2.r.a.89.3		48
21.17	even	6		1890.2.bi.a.899.9		48
35.24	odd	6		630.2.bi.a.479.16	yes	48
45.4	even	6		1890.2.bi.a.719.9		48
45.14	odd	6		630.2.bi.b.509.9	yes	48
63.31	odd	6		1890.2.r.a.1529.3		48
63.59	even	6		630.2.r.b.59.9	yes	48
105.59	even	6		1890.2.bi.b.899.8		48
315.59	even	6	inner	630.2.r.a.59.16	✓	48
315.94	odd	6		1890.2.r.b.1529.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.16	✓	48	315.59	even	6	inner
630.2.r.a.299.16	yes	48	1.1	even	1	trivial
630.2.r.b.59.9	yes	48	63.59	even	6
630.2.r.b.299.9	yes	48	5.4	even	2
630.2.bi.a.479.16	yes	48	35.24	odd	6
630.2.bi.a.509.16	yes	48	9.5	odd	6
630.2.bi.b.479.9	yes	48	7.3	odd	6
630.2.bi.b.509.9	yes	48	45.14	odd	6
1890.2.r.a.89.3		48	15.14	odd	2
1890.2.r.a.1529.3		48	63.31	odd	6
1890.2.r.b.89.3		48	3.2	odd	2
1890.2.r.b.1529.3		48	315.94	odd	6
1890.2.bi.a.719.9		48	45.4	even	6
1890.2.bi.a.899.9		48	21.17	even	6
1890.2.bi.b.719.8		48	9.4	even	3
1890.2.bi.b.899.8		48	105.59	even	6

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.960509 + 1.44133i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.19316 - 0.435950i) q^{5} +(0.767971 - 1.55249i) q^{6} +(-2.64572 + 0.0128895i) q^{7} +1.00000 q^{8} +(-1.15485 + 2.76881i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.960509 + 1.44133i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.19316 - 0.435950i) q^{5} +(0.767971 - 1.55249i) q^{6} +(-2.64572 + 0.0128895i) q^{7} +1.00000 q^{8} +(-1.15485 + 2.76881i) q^{9} +(-1.47412 - 1.68136i) q^{10} +4.12106i q^{11} +(-1.72848 + 0.111161i) q^{12} +(1.18566 + 2.05363i) q^{13} +(1.33402 + 2.28482i) q^{14} +(2.73489 + 2.74233i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.28111 + 1.31700i) q^{17} +(2.97529 - 0.384280i) q^{18} +(0.956982 + 0.552514i) q^{19} +(-0.719036 + 2.11731i) q^{20} +(-2.55981 - 3.80097i) q^{21} +(3.56894 - 2.06053i) q^{22} +0.592478 q^{23} +(0.960509 + 1.44133i) q^{24} +(4.61990 - 1.91221i) q^{25} +(1.18566 - 2.05363i) q^{26} +(-5.10001 + 0.994957i) q^{27} +(1.31170 - 2.29771i) q^{28} +(2.36953 + 1.36805i) q^{29} +(1.00748 - 3.73965i) q^{30} +(2.33615 + 1.34878i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-5.93979 + 3.95831i) q^{33} +(2.28111 + 1.31700i) q^{34} +(-5.79687 + 1.18167i) q^{35} +(-1.82044 - 2.38453i) q^{36} +(-6.05512 - 3.49593i) q^{37} -1.10503i q^{38} +(-1.82111 + 3.68146i) q^{39} +(2.19316 - 0.435950i) q^{40} +(-0.257087 - 0.445287i) q^{41} +(-2.01183 + 4.11735i) q^{42} +(10.4023 + 6.00577i) q^{43} +(-3.56894 - 2.06053i) q^{44} +(-1.32570 + 6.57590i) q^{45} +(-0.296239 - 0.513101i) q^{46} +(-3.57645 + 2.06487i) q^{47} +(0.767971 - 1.55249i) q^{48} +(6.99967 - 0.0682042i) q^{49} +(-3.96597 - 3.04484i) q^{50} +(-4.08925 - 2.02283i) q^{51} -2.37133 q^{52} +(-4.54406 - 7.87055i) q^{53} +(3.41166 + 3.91926i) q^{54} +(1.79657 + 9.03814i) q^{55} +(-2.64572 + 0.0128895i) q^{56} +(0.122836 + 1.91002i) q^{57} -2.73609i q^{58} +(-3.46974 + 6.00977i) q^{59} +(-3.74237 + 0.997325i) q^{60} +(3.71806 - 2.14662i) q^{61} -2.69755i q^{62} +(3.01971 - 7.34039i) q^{63} +1.00000 q^{64} +(3.49563 + 3.98705i) q^{65} +(6.39790 + 3.16486i) q^{66} +(11.7043 + 6.75750i) q^{67} -2.63400i q^{68} +(0.569081 + 0.853955i) q^{69} +(3.92179 + 4.42940i) q^{70} +1.60164i q^{71} +(-1.15485 + 2.76881i) q^{72} +(3.29147 + 5.70100i) q^{73} +6.99185i q^{74} +(7.19357 + 4.82208i) q^{75} +(-0.956982 + 0.552514i) q^{76} +(-0.0531186 - 10.9032i) q^{77} +(4.09879 - 0.263600i) q^{78} +(-6.72172 - 11.6424i) q^{79} +(-1.47412 - 1.68136i) q^{80} +(-6.33266 - 6.39511i) q^{81} +(-0.257087 + 0.445287i) q^{82} +(-3.80374 - 2.19609i) q^{83} +(4.57164 - 0.316381i) q^{84} +(-4.42869 + 3.88283i) q^{85} -12.0115i q^{86} +(0.304148 + 4.72928i) q^{87} +4.12106i q^{88} +(7.82648 - 13.5559i) q^{89} +(6.35775 - 2.13986i) q^{90} +(-3.16341 - 5.41805i) q^{91} +(-0.296239 + 0.513101i) q^{92} +(0.299863 + 4.66266i) q^{93} +(3.57645 + 2.06487i) q^{94} +(2.33968 + 0.794555i) q^{95} +(-1.72848 + 0.111161i) q^{96} +(6.92406 - 11.9928i) q^{97} +(-3.55890 - 6.02779i) q^{98} +(-11.4104 - 4.75919i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{2} + 3 q^{3} - 24 q^{4} + 48 q^{8} + 3 q^{9}+O(q^{10}) \) 48 * q - 24 * q^2 + 3 * q^3 - 24 * q^4 + 48 * q^8 + 3 * q^9	\( 48 q - 24 q^{2} + 3 q^{3} - 24 q^{4} + 48 q^{8} + 3 q^{9} - 3 q^{12} + 3 q^{14} - 4 q^{15} - 24 q^{16} - 3 q^{18} + 5 q^{21} + 6 q^{22} - 6 q^{23} + 3 q^{24} - 3 q^{28} - 3 q^{29} + 5 q^{30} - 24 q^{32} + 24 q^{33} + 18 q^{35} + 3 q^{41} + 8 q^{42} - 6 q^{44} + 9 q^{45} + 3 q^{46} - 6 q^{49} - 18 q^{50} - 8 q^{51} + 42 q^{55} - 22 q^{57} - q^{60} - 9 q^{61} - 10 q^{63} + 48 q^{64} - 33 q^{65} - 24 q^{66} - 33 q^{67} + 42 q^{69} - 6 q^{70} + 3 q^{72} + 18 q^{73} + 9 q^{75} + 6 q^{77} - 18 q^{78} - 37 q^{81} + 3 q^{82} - 9 q^{83} - 13 q^{84} - 33 q^{85} - 18 q^{87} + 33 q^{89} + 39 q^{90} + 3 q^{92} - 32 q^{93} + 33 q^{95} - 3 q^{96} + 24 q^{97} + 3 q^{98} - 26 q^{99}+O(q^{100}) \) 48 * q - 24 * q^2 + 3 * q^3 - 24 * q^4 + 48 * q^8 + 3 * q^9 - 3 * q^12 + 3 * q^14 - 4 * q^15 - 24 * q^16 - 3 * q^18 + 5 * q^21 + 6 * q^22 - 6 * q^23 + 3 * q^24 - 3 * q^28 - 3 * q^29 + 5 * q^30 - 24 * q^32 + 24 * q^33 + 18 * q^35 + 3 * q^41 + 8 * q^42 - 6 * q^44 + 9 * q^45 + 3 * q^46 - 6 * q^49 - 18 * q^50 - 8 * q^51 + 42 * q^55 - 22 * q^57 - q^60 - 9 * q^61 - 10 * q^63 + 48 * q^64 - 33 * q^65 - 24 * q^66 - 33 * q^67 + 42 * q^69 - 6 * q^70 + 3 * q^72 + 18 * q^73 + 9 * q^75 + 6 * q^77 - 18 * q^78 - 37 * q^81 + 3 * q^82 - 9 * q^83 - 13 * q^84 - 33 * q^85 - 18 * q^87 + 33 * q^89 + 39 * q^90 + 3 * q^92 - 32 * q^93 + 33 * q^95 - 3 * q^96 + 24 * q^97 + 3 * q^98 - 26 * q^99

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