LMFDB - Embedded newform 630.2.r.b.59.9

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			59.9
Character	$\chi$	$=$	630.59
Dual form			630.2.r.b.299.9

$q$-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} +(0.719036 - 2.11731i) q^{10} -4.12106i q^{11} +(1.72848 + 0.111161i) q^{12} +(-1.18566 + 2.05363i) q^{13} +(1.33402 - 2.28482i) q^{14} +(-1.47820 + 3.57979i) 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} +(-1.47412 - 1.68136i) 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} +(2.36109 + 3.07006i) 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} +(5.80810 - 1.12513i) 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} +(-3.73983 - 5.56899i) 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} +(0.653922 - 4.95705i) 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} +(3.83929 - 0.509736i) q^{60} +(3.71806 + 2.14662i) q^{61} -2.69755i q^{62} +(-3.01971 - 7.34039i) q^{63} +1.00000 q^{64} +(-1.70507 + 5.02083i) q^{65} +(6.39790 - 3.16486i) q^{66} +(-11.7043 + 6.75750i) q^{67} -2.63400i q^{68} +(0.569081 - 0.853955i) q^{69} +(1.92966 - 5.59253i) q^{70} -1.60164i q^{71} +(1.15485 + 2.76881i) q^{72} +(-3.29147 + 5.70100i) q^{73} -6.99185i q^{74} +(-1.68132 + 8.49548i) 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} +(-0.719036 + 2.11731i) 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} +(5.57698 + 1.89394i) q^{85} +12.0115i q^{86} +(-0.304148 + 4.72928i) q^{87} +4.12106i q^{88} +(7.82648 + 13.5559i) q^{89} +(-6.69280 + 0.454287i) 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} +(1.85794 - 1.62895i) 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} + 6 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} - 3 q^{30} + 24 q^{32} - 24 q^{33} + 12 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} - 9 q^{60} - 9 q^{61} + 10 q^{63} + 48 q^{64} - 21 q^{65} - 24 q^{66} + 33 q^{67} + 42 q^{69} + 12 q^{70} - 3 q^{72} - 18 q^{73} - 39 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} + 15 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 + 6 * 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 - 3 * q^30 + 24 * q^32 - 24 * q^33 + 12 * 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 - 9 * q^60 - 9 * q^61 + 10 * q^63 + 48 * q^64 - 21 * q^65 - 24 * q^66 + 33 * q^67 + 42 * q^69 + 12 * q^70 - 3 * q^72 - 18 * q^73 - 39 * 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 + 15 * 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

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

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
$10$	0.719036	−	2.11731i	0.227379	−	0.669551i
$11$		−	4.12106i		−	1.24255i	−0.783594	−	0.621273i	$-0.786616\pi$
$11$		−	4.12106i		−	1.24255i	0.783594	−	0.621273i	$-0.213384\pi$
$12$	1.72848	+	0.111161i	0.498969	+	0.0320895i
$13$	−1.18566	+	2.05363i	−0.328844	+	0.569575i	−0.982283	−	0.187405i	$-0.939992\pi$
$13$	−1.18566	+	2.05363i	−0.328844	+	0.569575i	0.653439	+	0.756979i	$0.273326\pi$
$14$	1.33402	−	2.28482i	0.356533	−	0.610643i
$15$	−1.47820	+	3.57979i	−0.381670	+	0.924299i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.28111	+	1.31700i	0.553250	+	0.319419i	0.750432	−	0.660948i	$-0.229846\pi$
$17$	2.28111	+	1.31700i	0.553250	+	0.319419i	−0.197182	+	0.980367i	$0.563179\pi$
$18$	−2.97529	−	0.384280i	−0.701282	−	0.0905757i
$19$	0.956982	−	0.552514i	0.219547	−	0.126755i	−0.386194	−	0.922418i	$-0.626210\pi$
$19$	0.956982	−	0.552514i	0.219547	−	0.126755i	0.605740	+	0.795662i	$0.292877\pi$
$20$	−1.47412	−	1.68136i	−0.329624	−	0.375963i
$21$	−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	$-0.519675\pi$
$23$	−0.592478			−0.123540			−0.0617701	+	0.998090i	$0.519675\pi$
$24$	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	−0.263592	−	0.964634i	$-0.584907\pi$
$29$	2.36953	−	1.36805i	0.440010	−	0.254040i	0.703602	+	0.710594i	$0.251574\pi$
$30$	2.36109	+	3.07006i	0.431074	+	0.560513i
$31$	2.33615	−	1.34878i	0.419585	−	0.242247i	−0.275315	−	0.961354i	$-0.588782\pi$
$31$	2.33615	−	1.34878i	0.419585	−	0.242247i	0.694900	+	0.719107i	$0.255449\pi$
$32$	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
$35$	5.80810	−	1.12513i	0.981749	−	0.190182i
$36$	−1.82044	+	2.38453i	−0.303407	+	0.397422i
$37$	6.05512	−	3.49593i	0.995456	−	0.574727i	0.0885553	−	0.996071i	$-0.471775\pi$
$37$	6.05512	−	3.49593i	0.995456	−	0.574727i	0.906901	+	0.421345i	$0.138442\pi$
$38$		−	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	−0.885402	−	0.464826i	$-0.846117\pi$
$41$	−0.257087	+	0.445287i	−0.0401502	+	0.0695422i	0.845252	+	0.534368i	$0.179450\pi$
$42$	2.01183	+	4.11735i	0.310432	+	0.635321i
$43$	−10.4023	+	6.00577i	−1.58634	+	0.915872i	−0.592432	+	0.805620i	$0.701832\pi$
$43$	−10.4023	+	6.00577i	−1.58634	+	0.915872i	−0.993904	+	0.110251i	$0.964834\pi$
$44$	−3.56894	+	2.06053i	−0.538038	+	0.310636i
$45$	−3.73983	−	5.56899i	−0.557500	−	0.830177i
$46$	−0.296239	+	0.513101i	−0.0436781	+	0.0756527i
$47$	3.57645	+	2.06487i	0.521679	+	0.301192i	0.737622	−	0.675214i	$-0.235949\pi$
$47$	3.57645	+	2.06487i	0.521679	+	0.301192i	−0.215942	+	0.976406i	$0.569282\pi$
$48$	−0.767971	−	1.55249i	−0.110847	−	0.224082i
$49$	6.99967	+	0.0682042i	0.999953	+	0.00974346i
$50$	0.653922	−	4.95705i	0.0924786	−	0.701033i
$51$	−4.08925	+	2.02283i	−0.572609	+	0.283253i
$52$	2.37133			0.328844
$53$	4.54406	−	7.87055i	0.624175	−	1.08110i	−0.364525	−	0.931194i	$-0.618768\pi$
$53$	4.54406	−	7.87055i	0.624175	−	1.08110i	0.988700	−	0.149909i	$-0.0478982\pi$
$54$	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	0.546771	−	0.837282i	$-0.315857\pi$
$59$	−3.46974	−	6.00977i	−0.451722	−	0.782405i	−0.998493	+	0.0548770i	$0.982523\pi$
$60$	3.83929	−	0.509736i	0.495651	−	0.0658066i
$61$	3.71806	+	2.14662i	0.476048	+	0.274847i	0.718768	−	0.695250i	$-0.244706\pi$
$61$	3.71806	+	2.14662i	0.476048	+	0.274847i	−0.242720	+	0.970096i	$0.578040\pi$
$62$		−	2.69755i		−	0.342589i
$63$	−3.01971	−	7.34039i	−0.380448	−	0.924802i
$64$	1.00000			0.125000
$65$	−1.70507	+	5.02083i	−0.211488	+	0.622757i
$66$	6.39790	−	3.16486i	0.787526	−	0.389567i
$67$	−11.7043	+	6.75750i	−1.42991	+	0.825560i	−0.997113	−	0.0759308i	$-0.975807\pi$
$67$	−11.7043	+	6.75750i	−1.42991	+	0.825560i	−0.432799	+	0.901491i	$0.642474\pi$
$68$		−	2.63400i		−	0.319419i
$69$	0.569081	−	0.853955i	0.0685092	−	0.102804i
$70$	1.92966	−	5.59253i	0.230638	−	0.668435i
$71$		−	1.60164i		−	0.190079i	−0.995473	−	0.0950396i	$-0.969702\pi$
$71$		−	1.60164i		−	0.190079i	0.995473	−	0.0950396i	$-0.0302978\pi$
$72$	1.15485	+	2.76881i	0.136100	+	0.326308i
$73$	−3.29147	+	5.70100i	−0.385238	+	0.667252i	−0.991802	−	0.127783i	$-0.959214\pi$
$73$	−3.29147	+	5.70100i	−0.385238	+	0.667252i	0.606564	+	0.795035i	$0.292547\pi$
$74$		−	6.99185i		−	0.812786i
$75$	−1.68132	+	8.49548i	−0.194143	+	0.980973i
$76$	−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	0.188497	+	0.982074i	$0.439639\pi$
$79$	−6.72172	+	11.6424i	−0.756253	+	1.30987i	−0.944749	+	0.327794i	$0.893695\pi$
$80$	−0.719036	+	2.11731i	−0.0803907	+	0.236722i
$81$	−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	$-0.589174\pi$
$83$	3.80374	−	2.19609i	0.417515	−	0.241052i	0.694013	+	0.719962i	$0.255841\pi$
$84$	4.57164	+	0.316381i	0.498807	+	0.0345200i
$85$	5.57698	+	1.89394i	0.604908	+	0.205426i
$86$			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	0.898349	+	0.439283i	$0.144768\pi$
$89$	7.82648	+	13.5559i	0.829605	+	1.43692i	−0.0687438	+	0.997634i	$0.521899\pi$
$90$	−6.69280	+	0.454287i	−0.705483	+	0.0478861i
$91$	−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
$95$	1.85794	−	1.62895i	0.190621	−	0.167126i
$96$	−1.72848	−	0.111161i	−0.176412	−	0.0113454i
$97$	−6.92406	−	11.9928i	−0.703032	−	1.21769i	−0.967397	−	0.253265i	$-0.918496\pi$
$97$	−6.92406	−	11.9928i	−0.703032	−	1.21769i	0.264365	−	0.964423i	$-0.414838\pi$
$98$	3.55890	−	6.02779i	0.359503	−	0.608899i
$99$	−11.4104	+	4.75919i	−1.14679	+	0.478317i
$100$	−3.96597	−	3.04484i	−0.396597	−	0.304484i
$101$	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	$-0.852062\pi$
$103$	−18.1448			−1.78786			−0.893929	+	0.448209i	$0.852062\pi$
$104$	1.18566	−	2.05363i	0.116264	−	0.201375i
$105$	−3.95705	+	9.45208i	−0.386169	+	0.922428i
$106$	−4.54406	−	7.87055i	−0.441358	−	0.764455i
$107$	4.33862	+	7.51471i	0.419430	+	0.726475i	0.995882	−	0.0906565i	$-0.0288965\pi$
$107$	4.33862	+	7.51471i	0.419430	+	0.726475i	−0.576452	+	0.817131i	$0.695563\pi$
$108$	−1.68834	−	4.91421i	−0.162461	−	0.472870i
$109$	−7.55567	+	13.0868i	−0.723702	+	1.25349i	0.235804	+	0.971801i	$0.424228\pi$
$109$	−7.55567	+	13.0868i	−0.723702	+	1.25349i	−0.959506	+	0.281688i	$0.909106\pi$
$110$	−8.72554	−	2.96319i	−0.831948	−	0.282529i
$111$	−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	$-0.848409\pi$
$113$	−0.503287	+	0.871718i	−0.0473452	+	0.0820044i	0.841382	+	0.540441i	$0.181743\pi$
$114$	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
$120$	1.47820	−	3.57979i	0.134941	−	0.326789i
$121$	−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
$130$	3.49563	+	3.98705i	0.306587	+	0.349687i
$131$	−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
$135$	11.6189	−	0.0412456i	0.999994	−	0.00354985i
$136$	−2.28111	−	1.31700i	−0.195603	−	0.112932i
$137$	−3.76795			−0.321917			−0.160959	−	0.986961i	$-0.551459\pi$
$137$	−3.76795			−0.321917			−0.160959	+	0.986961i	$0.551459\pi$
$138$	−0.455007	−	0.919816i	−0.0387327	−	0.0782999i
$139$	−5.20651	−	3.00598i	−0.441610	−	0.254964i	0.262670	−	0.964886i	$-0.415397\pi$
$139$	−5.20651	−	3.00598i	−0.441610	−	0.254964i	−0.704280	+	0.709922i	$0.748730\pi$
$140$	−3.87844	−	4.46740i	−0.327788	−	0.377564i
$141$	−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
$145$	4.60035	−	4.03334i	0.382038	−	0.334950i
$146$	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	$-0.848411\pi$
$149$		−	11.1918i		−	0.916866i	0.888729	−	0.458433i	$-0.151589\pi$
$150$	6.51664	+	5.70381i	0.532081	+	0.465714i
$151$	−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
$155$	4.53555	−	3.97652i	0.364304	−	0.319402i
$156$	−2.27768	+	3.41786i	−0.182360	+	0.273648i
$157$	−5.83514	−	10.1068i	−0.465695	−	0.806607i	0.533538	−	0.845776i	$-0.320862\pi$
$157$	−5.83514	−	10.1068i	−0.465695	−	0.806607i	−0.999233	+	0.0391693i	$0.987529\pi$
$158$	6.72172	+	11.6424i	0.534751	+	0.926217i
$159$	6.97942	+	14.1092i	0.553504	+	1.11893i
$160$	1.47412	+	1.68136i	0.116540	+	0.132923i
$161$	−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	$-0.504699\pi$
$163$	10.7728	−	6.21967i	0.843789	−	0.487162i	0.858550	+	0.512729i	$0.171366\pi$
$164$	0.514173			0.0401502
$165$	14.7525	+	6.09176i	1.14848	+	0.474243i
$166$		−	4.39218i		−	0.340899i
$167$	−11.4205	−	6.59363i	−0.883745	−	0.510230i	−0.0118537	−	0.999930i	$-0.503773\pi$
$167$	−11.4205	−	6.59363i	−0.883745	−	0.510230i	−0.871891	+	0.489699i	$0.837107\pi$
$168$	2.55981	−	3.80097i	0.197494	−	0.293251i
$169$	3.68840	+	6.38850i	0.283723	+	0.491423i
$170$	4.42869	−	3.88283i	0.339665	−	0.297800i
$171$	−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	$-0.142941\pi$
$173$	12.8284	+	7.40645i	0.975321	+	0.563102i	0.0744670	+	0.997223i	$0.476274\pi$
$174$	3.94360	+	2.62804i	0.298964	+	0.199231i
$175$	12.2476	−	4.99963i	0.925831	−	0.377937i
$176$	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	−0.998680	−	0.0513644i	$-0.983643\pi$
$179$	−20.6373	−	11.9149i	−1.54250	−	0.890564i	−0.543823	−	0.839200i	$-0.683024\pi$
$180$	−2.95298	+	6.02328i	−0.220102	+	0.448949i
$181$			11.6911i			0.868992i	0.900674	+	0.434496i	$0.143074\pi$
$181$			11.6911i			0.868992i	−0.900674	+	0.434496i	$0.856926\pi$
$182$	3.11046	+	5.44861i	0.230563	+	0.403878i
$183$	−6.66521	+	3.29709i	−0.492706	+	0.243728i
$184$	0.592478			0.0436781
$185$	11.7558	−	10.3069i	0.864304	−	0.757775i
$186$	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	0.983834	+	0.179085i	$0.0573137\pi$
$191$	22.5387	+	13.0127i	1.63084	+	0.941567i	0.647009	+	0.762482i	$0.276020\pi$
$192$	−0.960509	+	1.44133i	−0.0693187	+	0.104019i
$193$	−15.6522	+	9.03678i	−1.12667	+	0.650482i	−0.943095	−	0.332524i	$-0.892100\pi$
$193$	−15.6522	+	9.03678i	−1.12667	+	0.650482i	−0.183573	+	0.983006i	$0.558766\pi$
$194$	−13.8481			−0.994238
$195$	−5.59892	−	7.28011i	−0.400947	−	0.521340i
$196$	−3.44077	−	6.09599i	−0.245769	−	0.435428i
$197$	−19.0964			−1.36056			−0.680281	−	0.732951i	$-0.738142\pi$
$197$	−19.0964			−1.36056			−0.680281	+	0.732951i	$0.738142\pi$
$198$	−1.58364	+	12.2613i	−0.112544	+	0.871375i
$199$	21.6198	+	12.4822i	1.53259	+	0.884840i	0.999241	+	0.0389429i	$0.0123991\pi$
$199$	21.6198	+	12.4822i	1.53259	+	0.884840i	0.533346	+	0.845897i	$0.320934\pi$
$200$	−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
$205$	−0.369709	+	1.08866i	−0.0258216	+	0.0760355i
$206$	−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
$210$	6.20721	+	8.15295i	0.428338	+	0.562607i
$211$	−6.61689	+	11.4608i	−0.455525	+	0.788993i	−0.998718	−	0.0506149i	$-0.983882\pi$
$211$	−6.61689	+	11.4608i	−0.455525	+	0.788993i	0.543193	+	0.839608i	$0.317215\pi$
$212$	−9.08813			−0.624175
$213$	2.30848	+	1.53839i	0.158175	+	0.105408i
$214$	8.67724			0.593164
$215$	−20.1957	+	17.7065i	−1.37733	+	1.20757i
$216$	−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
$220$	−6.92897	+	6.07495i	−0.467151	+	0.409573i
$221$	−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	$-0.114340\pi$
$223$	2.44383	+	4.23284i	0.163651	+	0.283452i	−0.772524	+	0.634985i	$0.781006\pi$
$224$	1.31170	+	2.29771i	0.0876415	+	0.153522i
$225$	−10.6298	−	10.5833i	−0.708656	−	0.705554i
$226$	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	$-0.886272\pi$
$229$		−	10.5849i		−	0.699467i	0.936849	−	0.349734i	$-0.113728\pi$
$230$	−0.426013	+	1.25446i	−0.0280905	+	0.0827165i
$231$	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	$-0.172086\pi$
$233$	−0.259858	−	0.450088i	−0.0170239	−	0.0294862i	−0.874412	+	0.485184i	$0.838752\pi$
$234$	4.31686	−	5.65451i	0.282202	−	0.369647i
$235$	8.74391	+	2.96943i	0.570390	+	0.193704i
$236$	−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	0.420405	−	0.907337i	$-0.361888\pi$
$239$	−2.39886	−	1.38498i	−0.155169	−	0.0895869i	−0.575574	+	0.817750i	$0.695221\pi$
$240$	−2.36109	−	3.07006i	−0.152408	−	0.198171i
$241$			20.2007i			1.30124i	0.759403	+	0.650621i	$0.225491\pi$
$241$			20.2007i			1.30124i	−0.759403	+	0.650621i	$0.774509\pi$
$242$	−2.99156	+	5.18154i	−0.192305	+	0.333082i
$243$	−3.13487	−	15.2700i	−0.201102	−	0.979570i
$244$		−	4.29324i		−	0.274847i
$245$	15.3811	−	2.90192i	0.982664	−	0.185397i
$246$	−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
$250$	−0.726870	−	11.1567i	−0.0459713	−	0.705611i
$251$	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
$255$	−8.08652	+	6.21910i	−0.506397	+	0.389455i
$256$	−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	$-0.382811\pi$
$263$	11.6732			0.719800			0.359900	+	0.932991i	$0.382811\pi$
$264$	−5.93979	−	3.95831i	−0.365569	−	0.243617i
$265$	6.53469	−	19.2424i	0.401423	−	1.18205i
$266$	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	−0.999992	−	0.00403039i	$-0.998717\pi$
$269$	−8.14330	+	14.1046i	−0.496506	+	0.859973i	0.503486	+	0.864003i	$0.332050\pi$
$270$	5.77372	−	10.0829i	0.351377	−	0.613624i
$271$	21.8041	−	12.5886i	1.32450	−	0.764703i	0.340060	−	0.940404i	$-0.389553\pi$
$271$	21.8041	−	12.5886i	1.32450	−	0.764703i	0.984444	+	0.175701i	$0.0562192\pi$
$272$	−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
$280$	−5.80810	+	1.12513i	−0.347101	+	0.0672395i
$281$	1.17815	−	0.680206i	0.0702827	−	0.0405777i	−0.464447	−	0.885601i	$-0.653747\pi$
$281$	1.17815	−	0.680206i	0.0702827	−	0.0405777i	0.534730	+	0.845023i	$0.320413\pi$
$282$	−0.459067	+	7.13816i	−0.0273370	+	0.425071i
$283$	7.46757	+	12.9342i	0.443901	+	0.768859i	0.997975	−	0.0636082i	$-0.0202608\pi$
$283$	7.46757	+	12.9342i	0.443901	+	0.768859i	−0.554074	+	0.832468i	$0.686927\pi$
$284$	−1.38706	+	0.800818i	−0.0823067	+	0.0475198i
$285$	0.563272	+	4.24252i	0.0333653	+	0.251305i
$286$	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	$-0.227963\pi$
$293$	9.63607	+	5.56339i	0.562945	+	0.325016i	−0.191382	+	0.981516i	$0.561297\pi$
$294$	5.26966	+	10.9193i	0.307333	+	0.636825i
$295$	−10.2296	−	11.6677i	−0.595593	−	0.679322i
$296$	−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
$300$	8.19796	−	2.79167i	0.473310	−	0.161177i
$301$	−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
$305$	9.09011	+	3.08700i	0.520498	+	0.176761i
$306$	−6.28085	−	4.79503i	−0.359052	−	0.274114i
$307$	−14.1337			−0.806651			−0.403325	−	0.915057i	$-0.632146\pi$
$307$	−14.1337			−0.806651			−0.403325	+	0.915057i	$0.632146\pi$
$308$	−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	0.770641	−	0.637270i	$-0.219936\pi$
$311$	−2.93752	−	5.08794i	−0.166572	−	0.288510i	−0.937212	+	0.348760i	$0.886603\pi$
$312$	1.82111	+	3.68146i	0.103100	+	0.208422i
$313$	−9.51843	+	16.4864i	−0.538014	+	0.931867i	0.460997	+	0.887402i	$0.347492\pi$
$313$	−9.51843	+	16.4864i	−0.538014	+	0.931867i	−0.999011	+	0.0444656i	$0.985842\pi$
$314$	−11.6703			−0.658592
$315$	−9.82275	−	14.7822i	−0.553449	−	0.832883i
$316$	13.4434			0.756253
$317$	−7.70830	+	13.3512i	−0.432941	+	0.749876i	−0.997125	−	0.0757731i	$-0.975858\pi$
$317$	−7.70830	+	13.3512i	−0.432941	+	0.749876i	0.564184	+	0.825649i	$0.309191\pi$
$318$	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
$325$	−1.55066	+	11.7548i	−0.0860154	+	0.652039i
$326$		−	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
$330$	12.6519	−	9.73019i	0.696463	−	0.535629i
$331$	15.4650	−	26.7862i	0.850033	−	1.47230i	−0.0311447	−	0.999515i	$-0.509915\pi$
$331$	15.4650	−	26.7862i	0.850033	−	1.47230i	0.881178	−	0.472785i	$-0.156751\pi$
$332$	−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
$335$	−22.7235	+	19.9228i	−1.24152	+	1.08850i
$336$	−2.01183	−	4.11735i	−0.109754	−	0.224620i
$337$	21.3417	+	12.3216i	1.16256	+	0.671202i	0.951915	−	0.306362i	$-0.0991119\pi$
$337$	21.3417	+	12.3216i	1.16256	+	0.671202i	0.210640	+	0.977564i	$0.432445\pi$
$338$	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
$345$	0.875803	−	2.12095i	0.0471516	−	0.114188i
$346$	12.8284	−	7.40645i	0.689656	−	0.398173i
$347$	0.273072	+	0.472975i	0.0146593	+	0.0253906i	0.873262	−	0.487251i	$-0.162000\pi$
$347$	0.273072	+	0.472975i	0.0146593	+	0.0253906i	−0.858603	+	0.512642i	$0.828667\pi$
$348$	4.24775	−	2.10124i	0.227703	−	0.112638i
$349$	5.63017	−	3.25058i	0.301376	−	0.174000i	−0.341685	−	0.939815i	$-0.610997\pi$
$349$	5.63017	−	3.25058i	0.301376	−	0.174000i	0.643061	+	0.765815i	$0.277664\pi$
$350$	1.79399	−	13.1065i	0.0958927	−	0.700574i
$351$	−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	−0.403317	−	0.915060i	$-0.632143\pi$
$359$	3.55244	−	2.05100i	0.187490	−	0.108248i	0.590807	+	0.806813i	$0.298809\pi$
$360$	3.73983	+	5.56899i	0.197106	+	0.293512i
$361$	−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
$365$	−4.73338	+	13.9381i	−0.247756	+	0.729555i
$366$	−0.477242	+	7.42078i	−0.0249459	+	0.387891i
$367$	−20.1571			−1.05219			−0.526096	−	0.850425i	$-0.676345\pi$
$367$	−20.1571			−1.05219			−0.526096	+	0.850425i	$0.676345\pi$
$368$	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
$375$	0.0161890	+	19.3649i	0.000835997	+	1.00000i
$376$	−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	$0.455511\pi$
$380$	−2.33968	−	0.794555i	−0.120023	−	0.0407598i
$381$	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
$385$	−4.63673	−	23.9355i	−0.236310	−	1.21987i
$386$			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	$-0.733753\pi$
$389$		−	29.2794i		−	1.48453i	0.670109	−	0.742263i	$-0.266247\pi$
$390$	−9.10422	+	1.20875i	−0.461010	+	0.0612075i
$391$	−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
$395$	−9.66632	+	28.4639i	−0.486365	+	1.43217i
$396$	9.82680	+	7.50214i	0.493815	+	0.376997i
$397$	5.42713	+	9.40006i	0.272380	+	0.471775i	0.969471	−	0.245207i	$-0.0788560\pi$
$397$	5.42713	+	9.40006i	0.272380	+	0.471775i	−0.697091	+	0.716983i	$0.745523\pi$
$398$	21.6198	−	12.4822i	1.08370	−	0.625676i
$399$	−0.349610	+	5.05179i	−0.0175024	+	0.252906i
$400$	−0.653922	+	4.95705i	−0.0326961	+	0.247853i
$401$		−	18.2813i		−	0.912925i	−0.889743	−	0.456463i	$-0.849116\pi$
$401$		−	18.2813i		−	0.912925i	0.889743	−	0.456463i	$-0.150884\pi$
$402$	−19.4795	−	12.9813i	−0.971551	−	0.647447i
$403$			6.39678i			0.318646i
$404$	−1.35453	−	2.34612i	−0.0673905	−	0.116724i
$405$	−11.1006	+	16.7862i	−0.551592	+	0.834114i
$406$	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	−0.278253	−	0.960508i	$-0.589755\pi$
$409$	8.38163	−	4.83914i	0.414445	−	0.239280i	0.692698	+	0.721228i	$0.256422\pi$
$410$	0.757955	+	0.864509i	0.0374327	+	0.0426951i
$411$	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
$415$	7.38482	−	6.47461i	0.362507	−	0.317826i
$416$	−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	−0.962290	−	0.272025i	$-0.912307\pi$
$419$	−5.02659	+	8.70630i	−0.245565	+	0.425331i	0.716725	+	0.697355i	$0.245640\pi$
$420$	10.1643	−	1.29913i	0.495965	−	0.0633911i
$421$	−6.61761	−	11.4620i	−0.322522	−	0.558625i	0.658485	−	0.752594i	$-0.271197\pi$
$421$	−6.61761	−	11.4620i	−0.322522	−	0.558625i	−0.981008	+	0.193968i	$0.937864\pi$
$422$	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
$425$	13.0569	+	1.72243i	0.633351	+	0.0835500i
$426$	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	0.389055	−	0.921214i	$-0.372801\pi$
$431$	−4.44716	−	2.56757i	−0.214212	−	0.123675i	−0.603267	+	0.797539i	$0.706135\pi$
$432$	−3.41166	+	3.91926i	−0.164144	+	0.188565i
$433$	7.97362			0.383188			0.191594	−	0.981474i	$-0.438634\pi$
$433$	7.97362			0.383188			0.191594	+	0.981474i	$0.438634\pi$
$434$	0.0347702	−	7.13697i	0.00166902	−	0.342585i
$435$	1.39468	+	10.5047i	0.0668700	+	0.503660i
$436$	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	0.927282	−	0.374362i	$-0.122138\pi$
$439$	22.3502	+	12.9039i	1.06672	+	0.615869i	0.139434	+	0.990231i	$0.455472\pi$
$440$	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	−0.207729	−	0.978186i	$-0.566607\pi$
$443$	15.6440	−	27.0962i	0.743269	−	1.28738i	0.950999	−	0.309194i	$-0.100059\pi$
$444$	10.8548	−	5.36954i	0.515145	−	0.254827i
$445$	23.0744	+	26.3182i	1.09383	+	1.24760i
$446$	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	$0.0523366\pi$
$449$			6.93666i			0.327361i	−0.986513	+	0.163681i	$0.947663\pi$
$450$	−14.4803	+	3.91405i	−0.682610	+	0.184510i
$451$	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
$455$	−4.57586	+	13.2617i	−0.214519	+	0.621719i
$456$	0.122836	−	1.91002i	0.00575233	−	0.0894448i
$457$	23.7421	+	13.7075i	1.11061	+	0.641209i	0.938986	−	0.343954i	$-0.111767\pi$
$457$	23.7421	+	13.7075i	1.11061	+	0.641209i	0.171620	+	0.985163i	$0.445100\pi$
$458$	−9.16676	−	5.29243i	−0.428335	−	0.247299i
$459$	10.3233	+	8.98630i	0.481851	+	0.419445i
$460$	0.873386	+	0.996168i	0.0407218	+	0.0464466i
$461$	9.16139	+	15.8680i	0.426689	+	0.739046i	0.996576	−	0.0826762i	$-0.0263467\pi$
$461$	9.16139	+	15.8680i	0.426689	+	0.739046i	−0.569888	+	0.821722i	$0.693013\pi$
$462$	16.9678	−	8.29086i	0.789415	−	0.385726i
$463$	16.6964	+	9.63966i	0.775947	+	0.447993i	0.834992	−	0.550262i	$-0.185472\pi$
$463$	16.6964	+	9.63966i	0.775947	+	0.447993i	−0.0590450	+	0.998255i	$0.518806\pi$
$464$			2.73609i			0.127020i
$465$	1.37504	+	10.3567i	0.0637659	+	0.480280i
$466$	−0.519717			−0.0240754
$467$	−11.2146	+	6.47476i	−0.518951	+	0.299616i	−0.736505	−	0.676432i	$-0.763525\pi$
$467$	−11.2146	+	6.47476i	−0.518951	+	0.299616i	0.217555	+	0.976048i	$0.430192\pi$
$468$	−2.73852	−	6.56577i	−0.126588	−	0.303503i
$469$	−31.0535	+	17.7276i	−1.43392	+	0.818584i
$470$	6.94356	−	6.08774i	0.320282	−	0.280806i
$471$	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
$475$	3.36463	−	4.38251i	0.154380	−	0.201083i
$476$	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	$0.712284\pi$
$480$	−3.83929	+	0.509736i	−0.175239	+	0.0232661i
$481$			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
$485$	−20.4138	−	23.2836i	−0.926945	−	1.05726i
$486$	−14.7916	−	4.92011i	−0.670962	−	0.223181i
$487$	2.98800	+	1.72512i	0.135399	+	0.0781727i	0.566169	−	0.824289i	$-0.308425\pi$
$487$	2.98800	+	1.72512i	0.135399	+	0.0781727i	−0.430770	+	0.902462i	$0.641758\pi$
$488$	−3.71806	−	2.14662i	−0.168309	−	0.0971730i
$489$	−1.38277	+	21.5011i	−0.0625311	+	0.972315i
$490$	5.17742	−	14.7714i	0.233892	−	0.667304i
$491$	−36.9916	−	21.3571i	−1.66941	−	0.963833i	−0.967958	−	0.251113i	$-0.919203\pi$
$491$	−36.9916	−	21.3571i	−1.66941	−	0.963833i	−0.701449	−	0.712719i	$-0.747463\pi$
$492$	−0.493868	+	0.741092i	−0.0222653	+	0.0334110i
$493$	7.20685			0.324580
$494$	2.26932	+	1.31019i	0.102101	+	0.0589483i
$495$	−22.9502	+	15.4120i	−1.03153	+	0.692720i
$496$			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	$0.201276\pi$
$500$	−10.0254	−	4.94886i	−0.448350	−	0.221320i
$501$	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	$0.319775\pi$
$510$	1.34264	+	10.1127i	0.0594532	+	0.447797i
$511$	−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
$520$	1.70507	−	5.02083i	0.0747723	−	0.220178i
$521$	−7.58138	+	13.1313i	−0.332146	+	0.575294i	−0.982932	−	0.183967i	$-0.941106\pi$
$521$	−7.58138	+	13.1313i	−0.332146	+	0.575294i	0.650786	+	0.759261i	$0.274439\pi$
$522$	−7.57573	+	3.15977i	−0.331581	+	0.138299i
$523$	0.294517	+	0.510118i	0.0128783	+	0.0223059i	0.872393	−	0.488806i	$-0.162567\pi$
$523$	0.294517	+	0.510118i	0.0128783	+	0.0223059i	−0.859514	+	0.511111i	$0.829234\pi$
$524$	10.7870	+	18.6837i	0.471234	+	0.816202i
$525$	−4.55782	+	22.4550i	−0.198919	+	0.980016i
$526$	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
$530$	−13.3970	−	15.2804i	−0.581929	−	0.663738i
$531$	−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
$535$	12.7913	+	14.5895i	0.553017	+	0.630761i
$536$	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
$540$	−5.84516	−	10.0416i	−0.251536	−	0.432123i
$541$	−21.2555	−	36.8156i	−0.913846	−	1.58283i	−0.808582	−	0.588384i	$-0.799764\pi$
$541$	−21.2555	−	36.8156i	−0.913846	−	1.58283i	−0.105264	−	0.994444i	$-0.533569\pi$
$542$		−	25.1772i		−	1.08145i
$543$	−16.8507	−	11.2294i	−0.723132	−	0.481899i
$544$			2.63400i			0.112932i
$545$	−10.8656	+	31.9954i	−0.465431	+	1.37053i
$546$	−10.8409	−	0.750243i	−0.463946	−	0.0321074i
$547$	7.46589	−	4.31044i	0.319219	−	0.184301i	−0.331826	−	0.943341i	$-0.607665\pi$
$547$	7.46589	−	4.31044i	0.319219	−	0.184301i	0.651044	+	0.759040i	$0.274331\pi$
$548$	1.88397	+	3.26314i	0.0804793	+	0.139394i
$549$	1.64981	−	12.7736i	0.0704121	−	0.545165i
$550$	−20.4283	−	2.69485i	−0.871066	−	0.114909i
$551$	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
$555$	3.56400	+	26.8438i	0.151283	+	1.13945i
$556$			6.01195i			0.254964i
$557$	3.09319	−	5.35757i	0.131063	−	0.227007i	−0.793024	−	0.609191i	$-0.791494\pi$
$557$	3.09319	−	5.35757i	0.131063	−	0.227007i	0.924087	+	0.382183i	$0.124828\pi$
$558$	−7.46902	+	3.11526i	−0.316189	+	0.131879i
$559$		−	28.4833i		−	1.20472i
$560$	−1.92966	+	5.59253i	−0.0815430	+	0.236328i
$561$	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	$-0.907725\pi$
$563$	−28.2325	+	16.3001i	−1.18986	+	0.686966i	−0.231585	+	0.972815i	$0.574391\pi$
$564$	5.95230	+	3.96664i	0.250637	+	0.167026i
$565$	−0.723763	+	2.13122i	−0.0304489	+	0.0896613i
$566$	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	0.614464	−	0.788945i	$-0.289372\pi$
$569$	5.68792	+	3.28392i	0.238450	+	0.137669i	−0.376014	+	0.926614i	$0.622706\pi$
$570$	3.95577	+	1.63345i	0.165689	+	0.0684178i
$571$	8.99355	+	15.5773i	0.376369	+	0.651889i	0.990531	−	0.137290i	$-0.0438393\pi$
$571$	8.99355	+	15.5773i	0.376369	+	0.651889i	−0.614162	+	0.789180i	$0.710506\pi$
$572$		−	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	$-0.668483\pi$
$577$	11.8915	−	20.5968i	0.495051	−	0.857454i	0.999984	+	0.00570479i	$0.00181590\pi$
$578$	−10.0621			−0.418527
$579$	2.00908	−	31.2398i	0.0834946	−	1.29828i
$580$	−5.79315	−	1.96735i	−0.240547	−	0.0816897i
$581$	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
$585$	15.8708	−	1.07726i	0.656178	−	0.0445394i
$586$	9.63607	−	5.56339i	0.398062	−	0.229821i
$587$	−14.2796	+	8.24435i	−0.589384	+	0.340281i	−0.764854	−	0.644204i	$-0.777189\pi$
$587$	−14.2796	+	8.24435i	−0.589384	+	0.340281i	0.175470	+	0.984485i	$0.443855\pi$
$588$	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	$-0.732735\pi$
$593$	−8.69178	+	5.01820i	−0.356928	+	0.206073i	0.310804	+	0.950474i	$0.399402\pi$
$594$	−16.1515	−	14.0597i	−0.662703	−	0.576875i
$595$	14.7307	+	5.08272i	0.603900	+	0.208371i
$596$	−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	−0.969875	−	0.243605i	$-0.921670\pi$
$599$	−30.4424	+	17.5759i	−1.24384	+	0.718134i	−0.273970	+	0.961738i	$0.588337\pi$
$600$	1.68132	−	8.49548i	0.0686398	−	0.346826i
$601$	32.5093	−	18.7692i	1.32608	−	0.765613i	0.341390	−	0.939922i	$-0.389102\pi$
$601$	32.5093	−	18.7692i	1.32608	−	0.765613i	0.984691	+	0.174309i	$0.0557691\pi$
$602$	−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	$-0.336695\pi$
$607$	24.1853			0.981653			0.490827	+	0.871257i	$0.336695\pi$
$608$	0.956982	+	0.552514i	0.0388107	+	0.0224074i
$609$	−0.865648	+	12.5084i	−0.0350778	+	0.506867i
$610$	7.21847	−	6.32877i	0.292267	−	0.256244i
$611$	−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	$-0.519380\pi$
$613$	−23.6618	−	13.6611i	−0.955690	−	0.551768i	−0.894844	+	0.446379i	$0.852713\pi$
$614$	−7.06683	+	12.2401i	−0.285194	+	0.493971i
$615$	−1.21401	−	1.57854i	−0.0489536	−	0.0636530i
$616$	−0.0531186	+	10.9032i	−0.00214021	+	0.439301i
$617$	7.76658	−	13.4521i	0.312671	−	0.541562i	−0.666269	−	0.745712i	$-0.732110\pi$
$617$	7.76658	−	13.4521i	0.312671	−	0.541562i	0.978940	+	0.204150i	$0.0654430\pi$
$618$	−13.9347	−	28.1695i	−0.560535	−	1.13315i
$619$			21.2581i			0.854435i	0.904149	+	0.427218i	$0.140506\pi$
$619$			21.2581i			0.854435i	−0.904149	+	0.427218i	$0.859494\pi$
$620$	−5.71154	−	1.93964i	−0.229381	−	0.0778977i
$621$	−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
$630$	−17.7131	+	1.11565i	−0.705708	+	0.0444485i
$631$	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
$640$	0.719036	−	2.11731i	0.0284224	−	0.0836939i
$641$		−	25.6700i		−	1.01390i	−0.861975	−	0.506951i	$-0.830772\pi$
$641$		−	25.6700i		−	1.01390i	0.861975	−	0.506951i	$-0.169228\pi$
$642$	−8.33456	+	12.5067i	−0.328939	+	0.493602i
$643$	0.505064	−	0.874797i	0.0199178	−	0.0344986i	−0.855895	−	0.517150i	$-0.826993\pi$
$643$	0.505064	−	0.874797i	0.0199178	−	0.0344986i	0.875813	+	0.482651i	$0.160326\pi$
$644$	0.777152	+	1.36134i	0.0306241	+	0.0536443i
$645$	−6.12271	−	46.1158i	−0.241082	−	1.81581i
$646$	1.45532	−	2.52069i	0.0572587	−	0.0991750i
$647$	−12.5056	−	7.22013i	−0.491647	−	0.283852i	0.233611	−	0.972330i	$-0.424946\pi$
$647$	−12.5056	−	7.22013i	−0.491647	−	0.283852i	−0.725257	+	0.688478i	$0.758279\pi$
$648$	6.33266	−	6.39511i	0.248770	−	0.251224i
$649$	−24.7666	+	14.2990i	−0.972174	+	0.561285i
$650$	9.40463	+	7.22032i	0.368880	+	0.283204i
$651$	−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	$-0.832871\pi$
$653$	−44.2235			−1.73060			−0.865299	+	0.501256i	$0.832871\pi$
$654$	−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	−0.890442	−	0.455096i	$-0.849605\pi$
$659$	−24.1702	+	13.9547i	−0.941539	+	0.543598i	−0.0510965	+	0.998694i	$0.516272\pi$
$660$	−2.10065	−	15.8220i	−0.0817677	−	0.615869i
$661$	−0.0371085	+	0.0214246i	−0.00144335	+	0.000833320i	−0.500722	−	0.865608i	$-0.666932\pi$
$661$	−0.0371085	+	0.0214246i	−0.00144335	+	0.000833320i	0.499278	+	0.866442i	$0.333599\pi$
$662$	−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
$665$	4.93660	−	4.28579i	0.191433	−	0.166196i
$666$	−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	$-0.539683\pi$
$673$	17.4536	−	10.0769i	0.672788	−	0.388434i	0.797132	+	0.603805i	$0.206349\pi$
$674$	21.3417	−	12.3216i	0.822051	−	0.474611i
$675$	25.4641	−	5.15570i	0.980112	−	0.198443i
$676$	3.68840	−	6.38850i	0.141862	−	0.245711i
$677$	24.3021	+	14.0308i	0.934004	+	0.539248i	0.888076	−	0.459697i	$-0.152042\pi$
$677$	24.3021	+	14.0308i	0.934004	+	0.539248i	0.0459284	+	0.998945i	$0.485375\pi$
$678$	−1.73984	−	0.111892i	−0.0668182	−	0.00429719i
$679$	−18.1646	−	31.8189i	−0.697092	−	1.22110i
$680$	−5.57698	−	1.89394i	−0.213867	−	0.0726292i
$681$	17.2876	+	11.5205i	0.662462	+	0.441468i
$682$	−11.1168			−0.425683
$683$	14.7248	−	25.5040i	0.563428	−	0.975885i	−0.433767	−	0.901025i	$-0.642816\pi$
$683$	14.7248	−	25.5040i	0.563428	−	0.975885i	0.997194	−	0.0748598i	$-0.0238509\pi$
$684$	−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
$690$	−1.39890	−	1.81894i	−0.0532550	−	0.0692460i
$691$	6.03382	+	3.48363i	0.229537	+	0.132523i	0.610359	−	0.792125i	$-0.291025\pi$
$691$	6.03382	+	3.48363i	0.229537	+	0.132523i	−0.380821	+	0.924649i	$0.624359\pi$
$692$		−	14.8129i		−	0.563102i
$693$	−30.2502	+	12.4444i	−1.14911	+	0.472724i
$694$	0.546144			0.0207313
$695$	−12.7292	−	4.32281i	−0.482844	−	0.163974i
$696$	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
$700$	−10.4536	−	8.10691i	−0.395109	−	0.306413i
$701$		−	17.0338i		−	0.643357i	−0.946849	−	0.321678i	$-0.895753\pi$
$701$		−	17.0338i		−	0.643357i	0.946849	−	0.321678i	$-0.104247\pi$
$702$	4.00362	+	11.6532i	0.151107	+	0.439822i
$703$	3.86309	−	6.69107i	0.145699	−	0.252359i
$704$		−	4.12106i		−	0.155318i
$705$	−12.6785	+	9.75067i	−0.477501	+	0.367232i
$706$	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	−0.856279	−	0.516513i	$-0.827230\pi$
$709$	0.510534	−	0.884271i	0.0191735	−	0.0332095i	0.875453	+	0.483303i	$0.160563\pi$
$710$	−3.39115	−	1.15163i	−0.127268	−	0.0432201i
$711$	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
$715$	20.6911	+	7.02670i	0.773804	+	0.262784i
$716$			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	0.937669	+	0.347530i	$0.112980\pi$
$719$	20.6417	+	35.7524i	0.769804	+	1.33334i	−0.167865	+	0.985810i	$0.553687\pi$
$720$	6.69280	−	0.454287i	0.249426	−	0.0169303i
$721$	−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
$725$	8.33096	−	10.8513i	0.309404	−	0.403006i
$726$	−4.59487	−	9.28873i	−0.170532	−	0.344737i
$727$	−7.79834	−	13.5071i	−0.289224	−	0.500951i	0.684400	−	0.729106i	$-0.260064\pi$
$727$	−7.79834	−	13.5071i	−0.289224	−	0.500951i	−0.973625	+	0.228155i	$0.926731\pi$
$728$	3.16341	−	5.41805i	0.117244	−	0.200806i
$729$	25.0201	+	10.1486i	0.926671	+	0.375873i
$730$	9.70408	+	11.0683i	0.359164	+	0.409656i
$731$	−31.6384			−1.17019
$732$	6.18797	+	4.12370i	0.228714	+	0.152416i
$733$	−44.6299			−1.64844			−0.824222	−	0.566267i	$-0.808387\pi$
$733$	−44.6299			−1.64844			−0.824222	+	0.566267i	$0.808387\pi$
$734$	−10.0785	+	17.4565i	−0.372006	+	0.644333i
$735$	−10.5911	+	24.9565i	−0.390658	+	0.920536i
$736$	−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	0.458949	+	0.888463i	$0.348226\pi$
$739$	−14.6785	+	25.4239i	−0.539957	+	0.935233i	−0.998906	+	0.0467704i	$0.985107\pi$
$740$	−14.8039	−	5.02740i	−0.544202	−	0.184811i
$741$	−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	−0.211134	−	0.977457i	$-0.567716\pi$
$743$	20.1964	−	34.9813i	0.740936	−	1.28334i	0.952070	−	0.305881i	$-0.0989510\pi$
$744$	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
$750$	16.7786	+	9.66843i	0.612668	+	0.353041i
$751$	−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
$760$	−1.85794	+	1.62895i	−0.0673947	+	0.0590881i
$761$	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
$765$	−1.19659	−	17.6288i	−0.0432628	−	0.637371i
$766$	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	0.173327	−	0.984864i	$-0.444548\pi$
$769$	−16.4424	−	9.49301i	−0.592927	−	0.342327i	−0.766254	+	0.642538i	$0.777882\pi$
$770$	−23.0472	−	7.95224i	−0.830562	−	0.286579i
$771$	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	$-0.128187\pi$
$773$	28.9315	+	16.7036i	1.04060	+	0.600788i	0.120593	+	0.992702i	$0.461520\pi$
$774$	33.2577	−	13.8715i	1.19542	−	0.498600i
$775$	8.21362	−	10.6984i	0.295042	−	0.384299i
$776$	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
$780$	−3.50530	+	8.48886i	−0.125510	+	0.303950i
$781$	−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
$785$	−17.2034	−	19.6219i	−0.614017	−	0.700336i
$786$	−16.5683	−	33.4935i	−0.590971	−	1.19467i
$787$	−0.436343	−	0.755767i	−0.0155539	−	0.0269402i	0.858144	−	0.513410i	$-0.171618\pi$
$787$	−0.436343	−	0.755767i	−0.0155539	−	0.0269402i	−0.873698	+	0.486469i	$0.838285\pi$
$788$	9.54821	+	16.5380i	0.340141	+	0.589141i
$789$	−11.2122	+	16.8249i	−0.399165	+	0.598982i
$790$	19.8173	+	22.6032i	0.705067	+	0.804187i
$791$	−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
$795$	21.4579	+	27.9011i	0.761033	+	0.989549i
$796$		−	24.9644i		−	0.884840i
$797$	−24.9244	−	14.3901i	−0.882867	−	0.509724i	−0.0112647	−	0.999937i	$-0.503586\pi$
$797$	−24.9244	−	14.3901i	−0.882867	−	0.509724i	−0.871603	+	0.490213i	$0.836919\pi$
$798$	4.20017	+	2.82866i	0.148684	+	0.100134i
$799$	5.43885	+	9.42037i	0.192413	+	0.333269i
$800$	3.96597	+	3.04484i	0.140218	+	0.107651i
$801$	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
$805$	−3.44118	+	0.666616i	−0.121286	+	0.0234951i
$806$	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	0.435630	−	0.900126i	$-0.356526\pi$
$809$	−3.58630	−	2.07055i	−0.126088	−	0.0727967i	−0.561717	+	0.827329i	$0.689859\pi$
$810$	8.98700	+	18.0065i	0.315771	+	0.632684i
$811$		−	17.4383i		−	0.612342i	−0.951977	−	0.306171i	$-0.900952\pi$
$811$		−	17.4383i		−	0.612342i	0.951977	−	0.306171i	$-0.0990479\pi$
$812$	−6.25147	−	3.65001i	−0.219383	−	0.128090i
$813$	−2.79873	+	43.5183i	−0.0981557	+	1.52625i
$814$	−28.8138			−1.00992
$815$	20.9150	−	18.3371i	0.732619	−	0.642321i
$816$	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	−0.0437160	−	0.999044i	$-0.513920\pi$
$821$	−26.6695	−	15.3976i	−0.930771	−	0.537381i	−0.887055	+	0.461663i	$0.847253\pi$
$822$	−2.89368	−	5.84969i	−0.100929	−	0.204031i
$823$	30.3149	−	17.5023i	1.05671	−	0.610092i	0.132190	−	0.991224i	$-0.457799\pi$
$823$	30.3149	−	17.5023i	1.05671	−	0.610092i	0.924520	+	0.381133i	$0.124466\pi$
$824$	18.1448			0.632103
$825$	35.0104	+	6.92883i	1.21890	+	0.241231i
$826$	−18.3599	−	0.0894467i	−0.638823	−	0.00311225i
$827$	34.7736			1.20919			0.604597	−	0.796531i	$-0.293334\pi$
$827$	34.7736			1.20919			0.604597	+	0.796531i	$0.293334\pi$
$828$	1.07857	−	1.41278i	0.0374829	−	0.0490977i
$829$	−7.21777	−	4.16718i	−0.250683	−	0.144732i	0.369394	−	0.929273i	$-0.379565\pi$
$829$	−7.21777	−	4.16718i	−0.250683	−	0.144732i	−0.620077	+	0.784541i	$0.712899\pi$
$830$	−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
$835$	−27.9215	−	9.48212i	−0.966262	−	0.328142i
$836$	−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	0.999182	+	0.0404455i	$0.0128777\pi$
$839$	15.4855	+	26.8216i	0.534618	+	0.925985i	−0.464564	+	0.885540i	$0.653789\pi$
$840$	3.95705	−	9.45208i	0.136531	−	0.326128i
$841$	−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
$845$	10.8743	+	12.4030i	0.374088	+	0.426677i
$846$	−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
$850$	8.02010	−	10.4464i	0.275087	−	0.358307i
$851$	−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	$-0.0240449\pi$
$853$	12.6526	+	21.9150i	0.433217	+	0.750355i	−0.563931	+	0.825822i	$0.690712\pi$
$854$	9.86461	−	5.63143i	0.337560	−	0.192704i
$855$	−6.65589	−	3.26312i	−0.227627	−	0.111596i
$856$	−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	$-0.794358\pi$
$859$		−	35.2896i		−	1.20406i	0.798472	−	0.602032i	$-0.205642\pi$
$860$	25.4321	+	8.63673i	0.867228	+	0.294510i
$861$	−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	$-0.254939\pi$
$863$	−8.04268	−	13.9303i	−0.273776	−	0.474194i	−0.969826	+	0.243800i	$0.921606\pi$
$864$	1.68834	+	4.91421i	0.0574387	+	0.167185i
$865$	31.3635	+	10.6510i	1.06639	+	0.362145i
$866$	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
$870$	9.79464	+	4.04450i	0.332069	+	0.137121i
$871$		−	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
$875$	24.6813	−	16.3043i	0.834382	−	0.551187i
$876$	−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
$880$	8.72554	+	2.96319i	0.294138	+	0.0998891i
$881$	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
$885$	26.6427	−	3.53730i	0.895585	−	0.118905i
$886$	−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
$895$	−50.4552	−	17.1345i	−1.68653	−	0.572745i
$896$	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
$900$	−3.85050	+	14.4974i	−0.128350	+	0.483246i
$901$	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
$910$	9.19707	+	10.5937i	0.304880	+	0.351177i
$911$	−36.7577	+	21.2220i	−1.21784	+	0.703118i	−0.964455	−	0.264249i	$-0.914876\pi$
$911$	−36.7577	+	21.2220i	−1.21784	+	0.703118i	−0.253381	+	0.967367i	$0.581543\pi$
$912$	−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
$915$	−13.1805	+	10.1367i	−0.435734	+	0.335110i
$916$	−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	0.616017	−	0.787732i	$-0.288745\pi$
$919$	−11.3435	−	19.6475i	−0.374188	−	0.648112i	−0.990205	+	0.139621i	$0.955412\pi$
$920$	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
$925$	21.2891	−	27.7295i	0.699980	−	0.911740i
$926$	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	−0.908577	−	0.417718i	$-0.862830\pi$
$929$	−2.82041	+	4.88508i	−0.0925345	+	0.160274i	0.816042	+	0.577992i	$0.196164\pi$
$930$	9.65668	+	3.98753i	0.316655	+	0.130756i
$931$	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
$935$	7.80503	−	22.9830i	0.255252	−	0.751626i
$936$	−7.05538	−	0.911254i	−0.230612	−	0.0297853i
$937$	33.6125			1.09807			0.549036	−	0.835799i	$-0.314995\pi$
$937$	33.6125			1.09807			0.549036	+	0.835799i	$0.314995\pi$
$938$	−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	0.867920	−	0.496704i	$-0.165456\pi$
$941$	0.116632	+	0.202012i	0.00380208	+	0.00658540i	−0.864118	+	0.503289i	$0.832123\pi$
$942$	11.2094	−	16.8207i	0.365222	−	0.548047i
$943$	0.152318	−	0.263823i	0.00496017	−	0.00859126i
$944$	6.93948			0.225861
$945$	30.7408	+	0.0406378i	0.999999	+	0.00132195i
$946$	49.5003			1.60939
$947$	−1.31252	+	2.27335i	−0.0426512	+	0.0738740i	−0.886563	−	0.462608i	$-0.846914\pi$
$947$	−1.31252	+	2.27335i	−0.0426512	+	0.0738740i	0.843912	+	0.536482i	$0.180247\pi$
$948$	−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	$-0.420943\pi$
$953$	15.1772			0.491637			0.245818	+	0.969316i	$0.420943\pi$
$954$	−16.5444	+	21.6709i	−0.535644	+	0.701623i
$955$	55.1038	+	18.7132i	1.78312	+	0.605546i
$956$			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
$960$	−1.47820	+	3.57979i	−0.0477088	+	0.115537i
$961$	−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
$965$	−30.3881	+	26.6427i	−0.978228	+	0.857658i
$966$	−1.19196	−	2.43944i	−0.0383508	−	0.0784877i
$967$	−11.1551	−	6.44040i	−0.358724	−	0.207109i	0.309797	−	0.950803i	$-0.399739\pi$
$967$	−11.1551	−	6.44040i	−0.358724	−	0.207109i	−0.668521	+	0.743693i	$0.733072\pi$
$968$	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	0.539101	−	0.842241i	$-0.318764\pi$
$971$	−14.3294	−	24.8192i	−0.459851	−	0.796486i	−0.998953	+	0.0457549i	$0.985431\pi$
$972$	−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
$975$	−15.4531	−	13.5256i	−0.494895	−	0.433166i
$976$	−3.71806	+	2.14662i	−0.119012	+	0.0687117i
$977$	7.08037	+	12.2636i	0.226521	+	0.392346i	0.956775	−	0.290830i	$-0.0939315\pi$
$977$	7.08037	+	12.2636i	0.226521	+	0.392346i	−0.730254	+	0.683176i	$0.760598\pi$
$978$	17.9291	+	11.9481i	0.573311	+	0.382058i
$979$	55.8645	−	32.2534i	1.78544	−	1.03082i
$980$	−10.2037	−	11.8695i	−0.325945	−	0.379157i
$981$	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
$990$	1.87214	+	27.5814i	0.0595007	+	0.876596i
$991$	10.3535	−	17.9329i	0.328891	−	0.569656i	−0.653401	−	0.757012i	$-0.726658\pi$
$991$	10.3535	−	17.9329i	0.328891	−	0.569656i	0.982292	+	0.187356i	$0.0599917\pi$
$992$	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
$995$	52.8573	+	17.9503i	1.67569	+	0.569063i
$996$	6.81881	−	3.37307i	0.216062	−	0.106880i
$997$	−49.7520			−1.57566			−0.787831	−	0.615892i	$-0.788796\pi$
$997$	−49.7520			−1.57566			−0.787831	+	0.615892i	$0.788796\pi$
$998$	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.b.59.9	yes	48
3.2	odd	2		1890.2.r.a.1529.3		48
5.4	even	2		630.2.r.a.59.16	✓	48
7.5	odd	6		630.2.bi.a.509.16	yes	48
9.2	odd	6		630.2.bi.b.479.9	yes	48
9.7	even	3		1890.2.bi.a.899.9		48
15.14	odd	2		1890.2.r.b.1529.3		48
21.5	even	6		1890.2.bi.b.719.8		48
35.19	odd	6		630.2.bi.b.509.9	yes	48
45.29	odd	6		630.2.bi.a.479.16	yes	48
45.34	even	6		1890.2.bi.b.899.8		48
63.47	even	6		630.2.r.a.299.16	yes	48
63.61	odd	6		1890.2.r.b.89.3		48
105.89	even	6		1890.2.bi.a.719.9		48
315.124	odd	6		1890.2.r.a.89.3		48
315.299	even	6	inner	630.2.r.b.299.9	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.16	✓	48	5.4	even	2
630.2.r.a.299.16	yes	48	63.47	even	6
630.2.r.b.59.9	yes	48	1.1	even	1	trivial
630.2.r.b.299.9	yes	48	315.299	even	6	inner
630.2.bi.a.479.16	yes	48	45.29	odd	6
630.2.bi.a.509.16	yes	48	7.5	odd	6
630.2.bi.b.479.9	yes	48	9.2	odd	6
630.2.bi.b.509.9	yes	48	35.19	odd	6
1890.2.r.a.89.3		48	315.124	odd	6
1890.2.r.a.1529.3		48	3.2	odd	2
1890.2.r.b.89.3		48	63.61	odd	6
1890.2.r.b.1529.3		48	15.14	odd	2
1890.2.bi.a.719.9		48	105.89	even	6
1890.2.bi.a.899.9		48	9.7	even	3
1890.2.bi.b.719.8		48	21.5	even	6
1890.2.bi.b.899.8		48	45.34	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} +(0.719036 - 2.11731i) q^{10} -4.12106i q^{11} +(1.72848 + 0.111161i) q^{12} +(-1.18566 + 2.05363i) q^{13} +(1.33402 - 2.28482i) q^{14} +(-1.47820 + 3.57979i) 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} +(-1.47412 - 1.68136i) 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} +(2.36109 + 3.07006i) 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} +(5.80810 - 1.12513i) 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} +(-3.73983 - 5.56899i) 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} +(0.653922 - 4.95705i) 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} +(3.83929 - 0.509736i) q^{60} +(3.71806 + 2.14662i) q^{61} -2.69755i q^{62} +(-3.01971 - 7.34039i) q^{63} +1.00000 q^{64} +(-1.70507 + 5.02083i) q^{65} +(6.39790 - 3.16486i) q^{66} +(-11.7043 + 6.75750i) q^{67} -2.63400i q^{68} +(0.569081 - 0.853955i) q^{69} +(1.92966 - 5.59253i) q^{70} -1.60164i q^{71} +(1.15485 + 2.76881i) q^{72} +(-3.29147 + 5.70100i) q^{73} -6.99185i q^{74} +(-1.68132 + 8.49548i) 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} +(-0.719036 + 2.11731i) 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} +(5.57698 + 1.89394i) q^{85} +12.0115i q^{86} +(-0.304148 + 4.72928i) q^{87} +4.12106i q^{88} +(7.82648 + 13.5559i) q^{89} +(-6.69280 + 0.454287i) 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} +(1.85794 - 1.62895i) 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	\( 48 q + 24 q^{2} - 3 q^{3} - 24 q^{4} - 48 q^{8} + 3 q^{9} + 3 q^{12} + 3 q^{14} + 6 q^{15} - 24 q^{16} + 3 q^{18} + 5 q^{21} - 6 q^{22} + 6 q^{23} + 3 q^{24} + 3 q^{28} - 3 q^{29} - 3 q^{30} + 24 q^{32} - 24 q^{33} + 12 q^{35} + 3 q^{41} - 8 q^{42} - 6 q^{44} + 9 q^{45} + 3 q^{46} - 6 q^{49} - 18 q^{50} - 8 q^{51} - 42 q^{55} + 22 q^{57} - 9 q^{60} - 9 q^{61} + 10 q^{63} + 48 q^{64} - 21 q^{65} - 24 q^{66} + 33 q^{67} + 42 q^{69} + 12 q^{70} - 3 q^{72} - 18 q^{73} - 39 q^{75} - 6 q^{77} + 18 q^{78} - 37 q^{81} - 3 q^{82} + 9 q^{83} - 13 q^{84} + 33 q^{85} + 18 q^{87} + 33 q^{89} + 15 q^{90} - 3 q^{92} + 32 q^{93} + 33 q^{95} - 3 q^{96} - 24 q^{97} - 3 q^{98} - 26 q^{99}+O(q^{100}) \) 48 * q + 24 * q^2 - 3 * q^3 - 24 * q^4 - 48 * q^8 + 3 * q^9 + 3 * q^12 + 3 * q^14 + 6 * 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 - 3 * q^30 + 24 * q^32 - 24 * q^33 + 12 * 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 - 9 * q^60 - 9 * q^61 + 10 * q^63 + 48 * q^64 - 21 * q^65 - 24 * q^66 + 33 * q^67 + 42 * q^69 + 12 * q^70 - 3 * q^72 - 18 * q^73 - 39 * 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 + 15 * 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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