LMFDB - Embedded newform 63.2.f.b.22.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,2,Mod(22,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("63.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	63.f (of order $3$, 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:	$0.503057532734$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.2
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	63.22
Dual form			63.2.f.b.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.119562 + 0.207087i) q^{2} +(-0.619562 - 1.61745i) q^{3} +(0.971410 - 1.68253i) q^{4} +(-0.590972 + 1.02359i) q^{5} +(0.260877 - 0.321688i) q^{6} +(0.500000 + 0.866025i) q^{7} +0.942820 q^{8} +(-2.23229 + 2.00422i) q^{9} -0.282630 q^{10} +(1.85185 + 3.20750i) q^{11} +(-3.32326 - 0.528775i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-0.119562 + 0.207087i) q^{14} +(2.02175 + 0.321688i) q^{15} +(-1.83009 - 3.16982i) q^{16} -6.94282 q^{17} +(-0.681943 - 0.222649i) q^{18} +1.94282 q^{19} +(1.14815 + 1.98866i) q^{20} +(1.09097 - 1.34528i) q^{21} +(-0.442820 + 0.766987i) q^{22} +(2.80150 - 4.85235i) q^{23} +(-0.584135 - 1.52496i) q^{24} +(1.80150 + 3.12030i) q^{25} -0.239123 q^{26} +(4.62476 + 2.36887i) q^{27} +1.94282 q^{28} +(-0.119562 - 0.207087i) q^{29} +(0.175107 + 0.457140i) q^{30} +(-0.830095 + 1.43777i) q^{31} +(1.38044 - 2.39099i) q^{32} +(4.04063 - 4.98251i) q^{33} +(-0.830095 - 1.43777i) q^{34} -1.18194 q^{35} +(1.20370 + 5.70281i) q^{36} -9.54583 q^{37} +(0.232287 + 0.402332i) q^{38} +(1.71053 + 0.272169i) q^{39} +(-0.557180 + 0.965064i) q^{40} +(5.09097 - 8.81782i) q^{41} +(0.409028 + 0.0650819i) q^{42} +(-1.11273 - 1.92730i) q^{43} +7.19562 q^{44} +(-0.732287 - 3.46939i) q^{45} +1.33981 q^{46} +(-2.91423 - 5.04759i) q^{47} +(-3.99316 + 4.92398i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.430782 + 0.746136i) q^{50} +(4.30150 + 11.2297i) q^{51} +(0.971410 + 1.68253i) q^{52} -11.6030 q^{53} +(0.0623817 + 1.24095i) q^{54} -4.37756 q^{55} +(0.471410 + 0.816506i) q^{56} +(-1.20370 - 3.14241i) q^{57} +(0.0285900 - 0.0495193i) q^{58} +(-1.30150 + 2.25427i) q^{59} +(2.50520 - 3.08917i) q^{60} +(3.80150 + 6.58440i) q^{61} -0.396990 q^{62} +(-2.85185 - 0.931107i) q^{63} -6.66019 q^{64} +(-0.590972 - 1.02359i) q^{65} +(1.51492 + 0.241044i) q^{66} +(-1.75404 + 3.03809i) q^{67} +(-6.74433 + 11.6815i) q^{68} +(-9.58414 - 1.52496i) q^{69} +(-0.141315 - 0.244765i) q^{70} +8.60301 q^{71} +(-2.10464 + 1.88962i) q^{72} +15.1488 q^{73} +(-1.14132 - 1.97682i) q^{74} +(3.93078 - 4.84706i) q^{75} +(1.88727 - 3.26886i) q^{76} +(-1.85185 + 3.20750i) q^{77} +(0.148152 + 0.386770i) q^{78} +(-3.68878 - 6.38915i) q^{79} +4.32614 q^{80} +(0.966208 - 8.94799i) q^{81} +2.43474 q^{82} +(3.47141 + 6.01266i) q^{83} +(-1.20370 - 3.14241i) q^{84} +(4.10301 - 7.10662i) q^{85} +(0.266078 - 0.460861i) q^{86} +(-0.260877 + 0.321688i) q^{87} +(1.74596 + 3.02409i) q^{88} +2.74720 q^{89} +(0.630912 - 0.566453i) q^{90} -1.00000 q^{91} +(-5.44282 - 9.42724i) q^{92} +(2.83981 + 0.451852i) q^{93} +(0.696860 - 1.20700i) q^{94} +(-1.14815 + 1.98866i) q^{95} +(-4.72257 - 0.751424i) q^{96} +(-3.58414 - 6.20790i) q^{97} -0.239123 q^{98} +(-10.5624 - 3.44854i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 4 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} + 3 q^{7} - 12 q^{8} - 4 q^{9} + 2 q^{11} - 2 q^{12} - 3 q^{13} - q^{14} + 11 q^{15} - 3 q^{16} - 24 q^{17} + 13 q^{18} - 6 q^{19} + 16 q^{20} - 2 q^{21}+ \cdots - 46 q^{99}+O(q^{100}) $ 6 * q + q^2 - 4 * q^3 - 3 * q^4 + 5 * q^5 + q^6 + 3 * q^7 - 12 * q^8 - 4 * q^9 + 2 * q^11 - 2 * q^12 - 3 * q^13 - q^14 + 11 * q^15 - 3 * q^16 - 24 * q^17 + 13 * q^18 - 6 * q^19 + 16 * q^20 - 2 * q^21 + 15 * q^22 + 15 * q^24 - 6 * q^25 - 2 * q^26 - 7 * q^27 - 6 * q^28 - q^29 - 26 * q^30 + 3 * q^31 + 8 * q^32 + 8 * q^33 + 3 * q^34 + 10 * q^35 - 11 * q^36 - 6 * q^37 - 8 * q^38 + 2 * q^39 - 21 * q^40 + 22 * q^41 + 11 * q^42 + 3 * q^43 + 46 * q^44 + 5 * q^45 + 24 * q^46 + 9 * q^47 - 14 * q^48 - 3 * q^49 - 10 * q^50 + 9 * q^51 - 3 * q^52 - 36 * q^53 - 17 * q^54 - 12 * q^55 - 6 * q^56 + 11 * q^57 + 9 * q^58 + 9 * q^59 - 20 * q^60 + 6 * q^61 - 36 * q^62 - 8 * q^63 - 24 * q^64 + 5 * q^65 - 2 * q^66 - 6 * q^68 - 39 * q^69 + 18 * q^71 - 24 * q^72 + 6 * q^73 - 6 * q^74 + 31 * q^75 + 21 * q^76 - 2 * q^77 + 10 * q^78 - 15 * q^79 + 22 * q^80 + 32 * q^81 + 18 * q^82 + 12 * q^83 + 11 * q^84 - 9 * q^85 - 34 * q^86 - q^87 + 21 * q^88 - 4 * q^89 + 73 * q^90 - 6 * q^91 - 15 * q^92 + 33 * q^93 - 24 * q^94 - 16 * q^95 + 5 * q^96 - 3 * q^97 - 2 * q^98 - 46 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.119562	+	0.207087i	0.0845428	+	0.146433i	0.905196	−	0.424994i	$-0.139724\pi$
$2$	0.119562	+	0.207087i	0.0845428	+	0.146433i	−0.820653	+	0.571426i	$0.806390\pi$
$3$	−0.619562	−	1.61745i	−0.357704	−	0.933835i
$3$	−0.619562	−	1.61745i	−0.357704	−	0.933835i
$4$	0.971410	−	1.68253i	0.485705	−	0.841266i
$5$	−0.590972	+	1.02359i	−0.264291	+	0.457765i	−0.967378	−	0.253339i	$-0.918471\pi$
$5$	−0.590972	+	1.02359i	−0.264291	+	0.457765i	0.703087	+	0.711104i	$0.251804\pi$
$6$	0.260877	−	0.321688i	0.106502	−	0.131329i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	0.942820			0.333337
$9$	−2.23229	+	2.00422i	−0.744096	+	0.668073i
$10$	−0.282630			−0.0893755
$11$	1.85185	+	3.20750i	0.558353	+	0.967096i	0.997634	+	0.0687465i	$0.0219000\pi$
$11$	1.85185	+	3.20750i	0.558353	+	0.967096i	−0.439281	+	0.898350i	$0.644767\pi$
$12$	−3.32326	−	0.528775i	−0.959342	−	0.152644i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	−0.926995	−	0.375073i	$-0.877618\pi$
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	0.788320	+	0.615265i	$0.210951\pi$
$14$	−0.119562	+	0.207087i	−0.0319542	+	0.0553463i
$15$	2.02175	+	0.321688i	0.522014	+	0.0830595i
$16$	−1.83009	−	3.16982i	−0.457524	−	0.792454i
$17$	−6.94282			−1.68388			−0.841941	−	0.539570i	$-0.818587\pi$
$17$	−6.94282			−1.68388			−0.841941	+	0.539570i	$0.818587\pi$
$18$	−0.681943	−	0.222649i	−0.160736	−	0.0524790i
$19$	1.94282			0.445713			0.222857	−	0.974851i	$-0.428462\pi$
$19$	1.94282			0.445713			0.222857	+	0.974851i	$0.428462\pi$
$20$	1.14815	+	1.98866i	0.256735	+	0.444677i
$21$	1.09097	−	1.34528i	0.238070	−	0.293564i
$22$	−0.442820	+	0.766987i	−0.0944096	+	0.163522i
$23$	2.80150	−	4.85235i	0.584154	−	1.01178i	−0.410826	−	0.911714i	$-0.634760\pi$
$23$	2.80150	−	4.85235i	0.584154	−	1.01178i	0.994980	−	0.100071i	$-0.0319070\pi$
$24$	−0.584135	−	1.52496i	−0.119236	−	0.311282i
$25$	1.80150	+	3.12030i	0.360301	+	0.624060i
$26$	−0.239123			−0.0468959
$27$	4.62476	+	2.36887i	0.890036	+	0.455890i
$28$	1.94282			0.367158
$29$	−0.119562	−	0.207087i	−0.0222020	−	0.0384551i	0.854711	−	0.519104i	$-0.173734\pi$
$29$	−0.119562	−	0.207087i	−0.0222020	−	0.0384551i	−0.876913	+	0.480649i	$0.840401\pi$
$30$	0.175107	+	0.457140i	0.0319700	+	0.0834620i
$31$	−0.830095	+	1.43777i	−0.149089	+	0.258231i	−0.930891	−	0.365297i	$-0.880968\pi$
$31$	−0.830095	+	1.43777i	−0.149089	+	0.258231i	0.781802	+	0.623527i	$0.214301\pi$
$32$	1.38044	−	2.39099i	0.244029	−	0.422671i
$33$	4.04063	−	4.98251i	0.703383	−	0.867344i
$34$	−0.830095	−	1.43777i	−0.142360	−	0.246575i
$35$	−1.18194			−0.199785
$36$	1.20370	+	5.70281i	0.200616	+	0.950469i
$37$	−9.54583			−1.56932			−0.784662	−	0.619923i	$-0.787164\pi$
$37$	−9.54583			−1.56932			−0.784662	+	0.619923i	$0.787164\pi$
$38$	0.232287	+	0.402332i	0.0376819	+	0.0652669i
$39$	1.71053	+	0.272169i	0.273905	+	0.0435819i
$40$	−0.557180	+	0.965064i	−0.0880979	+	0.152590i
$41$	5.09097	−	8.81782i	0.795076	−	1.37711i	−0.127715	−	0.991811i	$-0.540764\pi$
$41$	5.09097	−	8.81782i	0.795076	−	1.37711i	0.922791	−	0.385301i	$-0.125903\pi$
$42$	0.409028	+	0.0650819i	0.0631144	+	0.0100424i
$43$	−1.11273	−	1.92730i	−0.169689	−	0.293910i	0.768622	−	0.639704i	$-0.220943\pi$
$43$	−1.11273	−	1.92730i	−0.169689	−	0.293910i	−0.938311	+	0.345794i	$0.887610\pi$
$44$	7.19562			1.08478
$45$	−0.732287	−	3.46939i	−0.109163	−	0.517186i
$46$	1.33981			0.197544
$47$	−2.91423	−	5.04759i	−0.425084	−	0.736267i	0.571344	−	0.820711i	$-0.306422\pi$
$47$	−2.91423	−	5.04759i	−0.425084	−	0.736267i	−0.996428	+	0.0844432i	$0.973089\pi$
$48$	−3.99316	+	4.92398i	−0.576364	+	0.710716i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−0.430782	+	0.746136i	−0.0609217	+	0.105520i
$51$	4.30150	+	11.2297i	0.602331	+	1.57247i
$52$	0.971410	+	1.68253i	0.134710	+	0.233325i
$53$	−11.6030			−1.59380			−0.796898	−	0.604114i	$-0.793527\pi$
$53$	−11.6030			−1.59380			−0.796898	+	0.604114i	$0.793527\pi$
$54$	0.0623817	+	1.24095i	0.00848907	+	0.168872i
$55$	−4.37756			−0.590270
$56$	0.471410	+	0.816506i	0.0629948	+	0.109110i
$57$	−1.20370	−	3.14241i	−0.159434	−	0.416223i
$58$	0.0285900	−	0.0495193i	0.00375405	−	0.00650220i
$59$	−1.30150	+	2.25427i	−0.169442	+	0.293481i	−0.938224	−	0.346029i	$-0.887530\pi$
$59$	−1.30150	+	2.25427i	−0.169442	+	0.293481i	0.768782	+	0.639511i	$0.220863\pi$
$60$	2.50520	−	3.08917i	0.323420	−	0.398811i
$61$	3.80150	+	6.58440i	0.486733	+	0.843046i	0.999884	−	0.0152524i	$-0.00485519\pi$
$61$	3.80150	+	6.58440i	0.486733	+	0.843046i	−0.513151	+	0.858298i	$0.671522\pi$
$62$	−0.396990			−0.0504178
$63$	−2.85185	−	0.931107i	−0.359299	−	0.117308i
$64$	−6.66019			−0.832524
$65$	−0.590972	−	1.02359i	−0.0733010	−	0.126961i
$66$	1.51492	+	0.241044i	0.186473	+	0.0296704i
$67$	−1.75404	+	3.03809i	−0.214290	+	0.371161i	−0.953053	−	0.302804i	$-0.902077\pi$
$67$	−1.75404	+	3.03809i	−0.214290	+	0.371161i	0.738763	+	0.673966i	$0.235410\pi$
$68$	−6.74433	+	11.6815i	−0.817870	+	1.41659i
$69$	−9.58414	−	1.52496i	−1.15379	−	0.183584i
$70$	−0.141315	−	0.244765i	−0.0168904	−	0.0292550i
$71$	8.60301			1.02099			0.510495	−	0.859881i	$-0.329462\pi$
$71$	8.60301			1.02099			0.510495	+	0.859881i	$0.329462\pi$
$72$	−2.10464	+	1.88962i	−0.248035	+	0.222694i
$73$	15.1488			1.77304			0.886519	−	0.462693i	$-0.153117\pi$
$73$	15.1488			1.77304			0.886519	+	0.462693i	$0.153117\pi$
$74$	−1.14132	−	1.97682i	−0.132675	−	0.229800i
$75$	3.93078	−	4.84706i	0.453888	−	0.559690i
$76$	1.88727	−	3.26886i	0.216485	−	0.374963i
$77$	−1.85185	+	3.20750i	−0.211038	+	0.365528i
$78$	0.148152	+	0.386770i	0.0167749	+	0.0437931i
$79$	−3.68878	−	6.38915i	−0.415020	−	0.718836i	0.580410	−	0.814324i	$-0.302892\pi$
$79$	−3.68878	−	6.38915i	−0.415020	−	0.718836i	−0.995431	+	0.0954881i	$0.969559\pi$
$80$	4.32614			0.483677
$81$	0.966208	−	8.94799i	0.107356	−	0.994221i
$82$	2.43474			0.268872
$83$	3.47141	+	6.01266i	0.381037	+	0.659975i	0.991211	−	0.132292i	$-0.0422338\pi$
$83$	3.47141	+	6.01266i	0.381037	+	0.659975i	−0.610174	+	0.792267i	$0.708900\pi$
$84$	−1.20370	−	3.14241i	−0.131334	−	0.342865i
$85$	4.10301	−	7.10662i	0.445034	−	0.770821i
$86$	0.266078	−	0.460861i	0.0286920	−	0.0496960i
$87$	−0.260877	+	0.321688i	−0.0279689	+	0.0344886i
$88$	1.74596	+	3.02409i	0.186120	+	0.322369i
$89$	2.74720			0.291203			0.145602	−	0.989343i	$-0.453488\pi$
$89$	2.74720			0.291203			0.145602	+	0.989343i	$0.453488\pi$
$90$	0.630912	−	0.566453i	0.0665039	−	0.0597094i
$91$	−1.00000			−0.104828
$92$	−5.44282	−	9.42724i	−0.567453	−	0.982858i
$93$	2.83981	+	0.451852i	0.294475	+	0.0468548i
$94$	0.696860	−	1.20700i	0.0718756	−	0.124492i
$95$	−1.14815	+	1.98866i	−0.117798	+	0.204032i
$96$	−4.72257	−	0.751424i	−0.481995	−	0.0766919i
$97$	−3.58414	−	6.20790i	−0.363914	−	0.630317i	0.624687	−	0.780875i	$-0.285226\pi$
$97$	−3.58414	−	6.20790i	−0.363914	−	0.630317i	−0.988601	+	0.150558i	$0.951893\pi$
$98$	−0.239123			−0.0241551
$99$	−10.5624	−	3.44854i	−1.06156	−	0.346591i
$100$	7.00000			0.700000
$101$	6.39248	+	11.0721i	0.636075	+	1.10171i	0.986286	+	0.165044i	$0.0527765\pi$
$101$	6.39248	+	11.0721i	0.636075	+	1.10171i	−0.350211	+	0.936671i	$0.613890\pi$
$102$	−1.81122	+	2.23342i	−0.179338	+	0.221142i
$103$	2.19850	−	3.80791i	0.216624	−	0.375204i	−0.737150	−	0.675730i	$-0.763829\pi$
$103$	2.19850	−	3.80791i	0.216624	−	0.375204i	0.953774	+	0.300526i	$0.0971621\pi$
$104$	−0.471410	+	0.816506i	−0.0462256	+	0.0800650i
$105$	0.732287	+	1.91173i	0.0714639	+	0.186566i
$106$	−1.38727	−	2.40283i	−0.134744	−	0.233384i
$107$	13.7278			1.32711			0.663557	−	0.748126i	$-0.269046\pi$
$107$	13.7278			1.32711			0.663557	+	0.748126i	$0.269046\pi$
$108$	8.47825	−	5.48016i	0.815820	−	0.527329i
$109$	1.26320			0.120993			0.0604963	−	0.998168i	$-0.480732\pi$
$109$	1.26320			0.120993			0.0604963	+	0.998168i	$0.480732\pi$
$110$	−0.523388	−	0.906535i	−0.0499031	−	0.0864347i
$111$	5.91423	+	15.4399i	0.561354	+	1.46549i
$112$	1.83009	−	3.16982i	0.172928	−	0.299520i
$113$	−6.08126	+	10.5330i	−0.572076	+	0.990866i	0.424276	+	0.905533i	$0.360529\pi$
$113$	−6.08126	+	10.5330i	−0.572076	+	0.990866i	−0.996353	+	0.0853326i	$0.972805\pi$
$114$	0.506837	−	0.624982i	0.0474696	−	0.0585349i
$115$	3.31122	+	5.73520i	0.308773	+	0.534810i
$116$	−0.464574			−0.0431346
$117$	−0.619562	−	2.93533i	−0.0572785	−	0.271371i
$118$	−0.622440			−0.0573003
$119$	−3.47141	−	6.01266i	−0.318224	−	0.551180i
$120$	1.90615	+	0.303294i	0.174007	+	0.0276868i
$121$	−1.35868	+	2.35331i	−0.123517	+	0.213937i
$122$	−0.909028	+	1.57448i	−0.0822996	+	0.142547i
$123$	−17.4166	−	2.77121i	−1.57040	−	0.249871i
$124$	1.61273	+	2.79332i	0.144827	+	0.250848i
$125$	−10.1683			−0.909478
$126$	−0.148152	−	0.701905i	−0.0131984	−	0.0625307i
$127$	1.33981			0.118889			0.0594445	−	0.998232i	$-0.481067\pi$
$127$	1.33981			0.118889			0.0594445	+	0.998232i	$0.481067\pi$
$128$	−3.55718	−	6.16122i	−0.314413	−	0.544580i
$129$	−2.42790	+	2.99386i	−0.213765	+	0.263594i
$130$	0.141315	−	0.244765i	0.0123942	−	0.0214673i
$131$	2.48345	−	4.30146i	0.216980	−	0.375820i	−0.736903	−	0.675998i	$-0.763713\pi$
$131$	2.48345	−	4.30146i	0.216980	−	0.375820i	0.953883	+	0.300178i	$0.0970461\pi$
$132$	−4.45813	−	11.6385i	−0.388030	−	1.01301i
$133$	0.971410	+	1.68253i	0.0842319	+	0.145894i
$134$	−0.838864			−0.0724668
$135$	−5.15787	+	3.33394i	−0.443918	+	0.286940i
$136$	−6.54583			−0.561300
$137$	2.16991	+	3.75839i	0.185387	+	0.321101i	0.943707	−	0.330782i	$-0.107313\pi$
$137$	2.16991	+	3.75839i	0.185387	+	0.321101i	−0.758320	+	0.651883i	$0.773979\pi$
$138$	−0.830095	−	2.16708i	−0.0706624	−	0.184474i
$139$	−1.97141	+	3.41458i	−0.167213	+	0.289621i	−0.937439	−	0.348150i	$-0.886810\pi$
$139$	−1.97141	+	3.41458i	−0.167213	+	0.289621i	0.770226	+	0.637771i	$0.220143\pi$
$140$	−1.14815	+	1.98866i	−0.0970365	+	0.168072i
$141$	−6.35868	+	7.84092i	−0.535498	+	0.660324i
$142$	1.02859	+	1.78157i	0.0863174	+	0.149506i
$143$	−3.70370			−0.309719
$144$	10.4383	+	3.40803i	0.869859	+	0.284002i
$145$	0.282630			0.0234712
$146$	1.81122	+	3.13713i	0.149898	+	0.259630i
$147$	1.71053	+	0.272169i	0.141082	+	0.0224481i
$148$	−9.27292	+	16.0612i	−0.762229	+	1.32022i
$149$	−5.55555	+	9.62249i	−0.455128	+	0.788305i	−0.998696	−	0.0510606i	$-0.983740\pi$
$149$	−5.55555	+	9.62249i	−0.455128	+	0.788305i	0.543568	+	0.839365i	$0.317073\pi$
$150$	1.47373	+	0.234491i	0.120330	+	0.0191461i
$151$	−6.96169	−	12.0580i	−0.566535	−	0.981267i	−0.996905	−	0.0786145i	$-0.974950\pi$
$151$	−6.96169	−	12.0580i	−0.566535	−	0.981267i	0.430370	−	0.902652i	$-0.358383\pi$
$152$	1.83173			0.148573
$153$	15.4984	−	13.9149i	1.25297	−	1.12496i
$154$	−0.885640			−0.0713669
$155$	−0.981125	−	1.69936i	−0.0788059	−	0.136496i
$156$	2.11956	−	2.61364i	0.169701	−	0.209259i
$157$	−0.0285900	+	0.0495193i	−0.00228173	+	0.00395207i	−0.867164	−	0.498023i	$-0.834060\pi$
$157$	−0.0285900	+	0.0495193i	−0.00228173	+	0.00395207i	0.864882	+	0.501975i	$0.167393\pi$
$158$	0.882073	−	1.52780i	0.0701740	−	0.121545i
$159$	7.18878	+	18.7673i	0.570107	+	1.48834i
$160$	1.63160	+	2.82601i	0.128989	+	0.223416i
$161$	5.60301			0.441579
$162$	1.96853	−	0.869747i	0.154662	−	0.0683338i
$163$	−1.50808			−0.118122			−0.0590610	−	0.998254i	$-0.518811\pi$
$163$	−1.50808			−0.118122			−0.0590610	+	0.998254i	$0.518811\pi$
$164$	−9.89084	−	17.1314i	−0.772345	−	1.33774i
$165$	2.71217	+	7.08048i	0.211142	+	0.551215i
$166$	−0.830095	+	1.43777i	−0.0644279	+	0.111592i
$167$	7.34213	−	12.7169i	0.568151	−	0.984067i	−0.428598	−	0.903496i	$-0.640992\pi$
$167$	7.34213	−	12.7169i	0.568151	−	0.984067i	0.996749	−	0.0805714i	$-0.0256745\pi$
$168$	1.02859	−	1.26836i	0.0793574	−	0.0978559i
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$	1.96225			0.150498
$171$	−4.33693	+	3.89384i	−0.331653	+	0.297769i
$172$	−4.32365			−0.329675
$173$	−0.126398	−	0.218928i	−0.00960987	−	0.0166448i	0.861180	−	0.508299i	$-0.169726\pi$
$173$	−0.126398	−	0.218928i	−0.00960987	−	0.0166448i	−0.870790	+	0.491655i	$0.836392\pi$
$174$	−0.0978082	−	0.0155626i	−0.00741482	−	0.00117980i
$175$	−1.80150	+	3.12030i	−0.136181	+	0.235872i
$176$	6.77812	−	11.7400i	0.510920	−	0.884939i
$177$	4.45254	+	0.708458i	0.334673	+	0.0532510i
$178$	0.328460	+	0.568910i	0.0246191	+	0.0426416i
$179$	14.1923			1.06079			0.530393	−	0.847752i	$-0.322044\pi$
$179$	14.1923			1.06079			0.530393	+	0.847752i	$0.322044\pi$
$180$	−6.54871	−	2.13810i	−0.488112	−	0.159365i
$181$	−1.43147			−0.106400			−0.0532002	−	0.998584i	$-0.516942\pi$
$181$	−1.43147			−0.106400			−0.0532002	+	0.998584i	$0.516942\pi$
$182$	−0.119562	−	0.207087i	−0.00886250	−	0.0153503i
$183$	8.29467	−	10.2282i	0.613160	−	0.756089i
$184$	2.64132	−	4.57489i	0.194720	−	0.337266i
$185$	5.64132	−	9.77104i	0.414758	−	0.718381i
$186$	0.245960	+	0.642111i	0.0180346	+	0.0470819i
$187$	−12.8571	−	22.2691i	−0.940201	−	1.62848i
$188$	−11.3236			−0.825862
$189$	0.260877	+	5.18960i	0.0189760	+	0.377488i
$190$	−0.549100			−0.0398359
$191$	−7.53379	−	13.0489i	−0.545126	−	0.944186i	−0.998599	−	0.0529159i	$-0.983148\pi$
$191$	−7.53379	−	13.0489i	−0.545126	−	0.944186i	0.453473	−	0.891270i	$-0.350185\pi$
$192$	4.12640	+	10.7725i	0.297797	+	0.777440i
$193$	3.92395	−	6.79647i	0.282452	−	0.489221i	−0.689536	−	0.724251i	$-0.742186\pi$
$193$	3.92395	−	6.79647i	0.282452	−	0.489221i	0.971988	+	0.235030i	$0.0755190\pi$
$194$	0.857050	−	1.48445i	0.0615326	−	0.106578i
$195$	−1.28947	+	1.59005i	−0.0923406	+	0.113866i
$196$	0.971410	+	1.68253i	0.0693864	+	0.120181i
$197$	6.69002			0.476644			0.238322	−	0.971186i	$-0.423403\pi$
$197$	6.69002			0.476644			0.238322	+	0.971186i	$0.423403\pi$
$198$	−0.548709	−	2.59964i	−0.0389950	−	0.184749i
$199$	−19.9396			−1.41348			−0.706739	−	0.707475i	$-0.749834\pi$
$199$	−19.9396			−1.41348			−0.706739	+	0.707475i	$0.749834\pi$
$200$	1.69850	+	2.94188i	0.120102	+	0.208022i
$201$	6.00069	+	0.954790i	0.423256	+	0.0673457i
$202$	−1.52859	+	2.64760i	−0.107551	+	0.186284i
$203$	0.119562	−	0.207087i	0.00839158	−	0.0145346i
$204$	23.0728	+	3.67119i	1.61542	+	0.257035i
$205$	6.01724	+	10.4222i	0.420262	+	0.727916i
$206$	1.05142			0.0732561
$207$	3.47141	+	16.4467i	0.241280	+	1.14312i
$208$	3.66019			0.253789
$209$	3.59781	+	6.23159i	0.248866	+	0.431048i
$210$	−0.308342	+	0.380217i	−0.0212776	+	0.0262375i
$211$	9.04583	−	15.6678i	0.622741	−	1.07862i	−0.366233	−	0.930523i	$-0.619353\pi$
$211$	9.04583	−	15.6678i	0.622741	−	1.07862i	0.988973	−	0.148095i	$-0.0473141\pi$
$212$	−11.2713	+	19.5224i	−0.774115	+	1.34081i
$213$	−5.33009	−	13.9149i	−0.365212	−	0.953436i
$214$	1.64132	+	2.84284i	0.112198	+	0.194333i
$215$	2.63036			0.179389
$216$	4.36032	+	2.23342i	0.296682	+	0.151965i
$217$	−1.66019			−0.112701
$218$	0.151030	+	0.261592i	0.0102291	+	0.0177172i
$219$	−9.38564	−	24.5025i	−0.634223	−	1.65572i
$220$	−4.25241	+	7.36538i	−0.286697	+	0.496574i
$221$	3.47141	−	6.01266i	0.233512	−	0.404455i
$222$	−2.49028	+	3.07078i	−0.167137	+	0.206097i
$223$	11.3285	+	19.6215i	0.758610	+	1.31395i	0.943560	+	0.331203i	$0.107454\pi$
$223$	11.3285	+	19.6215i	0.758610	+	1.31395i	−0.184950	+	0.982748i	$0.559212\pi$
$224$	2.76088			0.184469
$225$	−10.2752	−	3.35479i	−0.685016	−	0.223653i
$226$	−2.90834			−0.193460
$227$	2.64132	+	4.57489i	0.175310	+	0.303646i	0.940269	−	0.340433i	$-0.110574\pi$
$227$	2.64132	+	4.57489i	0.175310	+	0.303646i	−0.764958	+	0.644080i	$0.777240\pi$
$228$	−6.45649	−	1.02731i	−0.427592	−	0.0680356i
$229$	−9.66827	+	16.7459i	−0.638897	+	1.10660i	0.346778	+	0.937947i	$0.387276\pi$
$229$	−9.66827	+	16.7459i	−0.638897	+	1.10660i	−0.985675	+	0.168655i	$0.946058\pi$
$230$	−0.791790	+	1.37142i	−0.0522091	+	0.0904288i
$231$	6.33530	+	1.00803i	0.416832	+	0.0663235i
$232$	−0.112725	−	0.195246i	−0.00740077	−	0.0128185i
$233$	−16.9806			−1.11243			−0.556217	−	0.831037i	$-0.687748\pi$
$233$	−16.9806			−1.11243			−0.556217	+	0.831037i	$0.687748\pi$
$234$	0.533792	−	0.479256i	0.0348951	−	0.0313299i
$235$	6.88891			0.449383
$236$	2.52859	+	4.37965i	0.164597	+	0.285091i
$237$	−8.04871	+	9.92489i	−0.522820	+	0.644691i
$238$	0.830095	−	1.43777i	0.0538071	−	0.0931966i
$239$	−8.44282	+	14.6234i	−0.546121	+	0.945909i	0.452415	+	0.891808i	$0.350563\pi$
$239$	−8.44282	+	14.6234i	−0.546121	+	0.945909i	−0.998535	+	0.0541011i	$0.982771\pi$
$240$	−2.68031	−	6.99731i	−0.173013	−	0.451674i
$241$	−13.5728	−	23.5088i	−0.874300	−	1.51433i	−0.857507	−	0.514473i	$-0.827988\pi$
$241$	−13.5728	−	23.5088i	−0.874300	−	1.51433i	−0.0167933	−	0.999859i	$-0.505346\pi$
$242$	−0.649786			−0.0417699
$243$	−15.0715	+	3.98104i	−0.966840	+	0.255384i
$244$	14.7713			0.945634
$245$	−0.590972	−	1.02359i	−0.0377558	−	0.0653950i
$246$	−1.50847	−	3.93807i	−0.0961766	−	0.251082i
$247$	−0.971410	+	1.68253i	−0.0618093	+	0.107057i
$248$	−0.782630	+	1.35556i	−0.0496971	+	0.0860778i
$249$	7.57442	−	9.34004i	0.480009	−	0.591901i
$250$	−1.21574	−	2.10571i	−0.0768898	−	0.133177i
$251$	−19.0780			−1.20419			−0.602096	−	0.798424i	$-0.705668\pi$
$251$	−19.0780			−1.20419			−0.602096	+	0.798424i	$0.705668\pi$
$252$	−4.33693	+	3.89384i	−0.273201	+	0.245289i
$253$	20.7518			1.30466
$254$	0.160190	+	0.277457i	0.0100512	+	0.0174092i
$255$	−14.0367	−	2.23342i	−0.879010	−	0.139862i
$256$	−5.80959	+	10.0625i	−0.363099	+	0.628906i
$257$	7.42107	−	12.8537i	0.462913	−	0.801790i	−0.536191	−	0.844097i	$-0.680137\pi$
$257$	7.42107	−	12.8537i	0.462913	−	0.801790i	0.999105	+	0.0423070i	$0.0134707\pi$
$258$	−0.910272	−	0.144836i	−0.0566711	−	0.00901712i
$259$	−4.77292	−	8.26693i	−0.296575	−	0.513682i
$260$	−2.29630			−0.142411
$261$	0.681943	+	0.222649i	0.0422112	+	0.0137817i
$262$	1.18770			0.0733764
$263$	3.87072	+	6.70429i	0.238679	+	0.413404i	0.960335	−	0.278847i	$-0.0899523\pi$
$263$	3.87072	+	6.70429i	0.238679	+	0.413404i	−0.721656	+	0.692251i	$0.756619\pi$
$264$	3.80959	−	4.69761i	0.234464	−	0.289118i
$265$	6.85705	−	11.8768i	0.421225	−	0.729584i
$266$	−0.232287	+	0.402332i	−0.0142424	+	0.0246686i
$267$	−1.70206	−	4.44346i	−0.104165	−	0.271936i
$268$	3.40778	+	5.90246i	0.208164	+	0.360550i
$269$	−1.51135			−0.0921486			−0.0460743	−	0.998938i	$-0.514671\pi$
$269$	−1.51135			−0.0921486			−0.0460743	+	0.998938i	$0.514671\pi$
$270$	−1.30710	−	0.669515i	−0.0795474	−	0.0407454i
$271$	−21.9806			−1.33522			−0.667612	−	0.744509i	$-0.732684\pi$
$271$	−21.9806			−1.33522			−0.667612	+	0.744509i	$0.732684\pi$
$272$	12.7060	+	22.0075i	0.770416	+	1.33440i
$273$	0.619562	+	1.61745i	0.0374976	+	0.0978925i
$274$	−0.518875	+	0.898718i	−0.0313464	+	0.0542935i
$275$	−6.67223	+	11.5566i	−0.402350	+	0.696892i
$276$	−11.8759	+	14.6442i	−0.714847	+	0.881480i
$277$	5.41423	+	9.37772i	0.325310	+	0.563453i	0.981575	−	0.191077i	$-0.0611982\pi$
$277$	5.41423	+	9.37772i	0.325310	+	0.563453i	−0.656265	+	0.754530i	$0.727865\pi$
$278$	−0.942820			−0.0565466
$279$	−1.02859	−	4.87320i	−0.0615801	−	0.291751i
$280$	−1.11436			−0.0665957
$281$	8.43831	+	14.6156i	0.503387	+	0.871892i	0.999992	+	0.00391559i	$0.00124638\pi$
$281$	8.43831	+	14.6156i	0.503387	+	0.871892i	−0.496605	+	0.867977i	$0.665420\pi$
$282$	−2.38401	−	0.379327i	−0.141965	−	0.0225886i
$283$	7.65856	−	13.2650i	0.455254	−	0.788523i	−0.543449	−	0.839442i	$-0.682882\pi$
$283$	7.65856	−	13.2650i	0.455254	−	0.788523i	0.998703	+	0.0509194i	$0.0162152\pi$
$284$	8.35705	−	14.4748i	0.495900	−	0.858923i
$285$	3.92790	+	0.624982i	0.232669	+	0.0370207i
$286$	−0.442820	−	0.766987i	−0.0261845	−	0.0453529i
$287$	10.1819			0.601021
$288$	1.71053	+	8.10408i	0.100794	+	0.477537i
$289$	31.2028			1.83546
$290$	0.0337917	+	0.0585290i	0.00198432	+	0.00343694i
$291$	−7.82038	+	9.64334i	−0.458439	+	0.565302i
$292$	14.7157	−	25.4884i	0.861173	−	1.49160i
$293$	4.68482	−	8.11435i	0.273690	−	0.474045i	−0.696114	−	0.717932i	$-0.745089\pi$
$293$	4.68482	−	8.11435i	0.273690	−	0.474045i	0.969804	+	0.243886i	$0.0784224\pi$
$294$	0.148152	+	0.386770i	0.00864038	+	0.0225569i
$295$	−1.53831	−	2.66442i	−0.0895636	−	0.155129i
$296$	−9.00000			−0.523114
$297$	0.966208	+	19.2207i	0.0560651	+	1.11530i
$298$	−2.65692			−0.153911
$299$	2.80150	+	4.85235i	0.162015	+	0.280619i
$300$	−4.33693	−	11.3221i	−0.250393	−	0.653684i
$301$	1.11273	−	1.92730i	0.0641364	−	0.111088i
$302$	1.66470	−	2.88335i	0.0957929	−	0.165918i
$303$	13.9480	−	17.1994i	0.801293	−	0.988077i
$304$	−3.55555	−	6.15838i	−0.203925	−	0.353208i
$305$	−8.98633			−0.514556
$306$	4.73461	+	1.54581i	0.270660	+	0.0883684i
$307$	2.71410			0.154902			0.0774509	−	0.996996i	$-0.475322\pi$
$307$	2.71410			0.154902			0.0774509	+	0.996996i	$0.475322\pi$
$308$	3.59781	+	6.23159i	0.205004	+	0.355078i
$309$	−7.52120	−	1.19672i	−0.427866	−	0.0680792i
$310$	0.234610	−	0.406356i	0.0133249	−	0.0230795i
$311$	6.99028	−	12.1075i	0.396383	−	0.686555i	−0.596894	−	0.802320i	$-0.703599\pi$
$311$	6.99028	−	12.1075i	0.396383	−	0.686555i	0.993277	+	0.115765i	$0.0369320\pi$
$312$	1.61273	+	0.256606i	0.0913026	+	0.0145275i
$313$	9.52696	+	16.5012i	0.538495	+	0.932701i	0.998985	+	0.0450364i	$0.0143404\pi$
$313$	9.52696	+	16.5012i	0.538495	+	0.932701i	−0.460490	+	0.887665i	$0.652326\pi$
$314$	−0.0136731			−0.000771615
$315$	2.63844	−	2.36887i	0.148659	−	0.133471i
$316$	−14.3333			−0.806309
$317$	2.00972	+	3.48093i	0.112877	+	0.195508i	0.916929	−	0.399050i	$-0.130660\pi$
$317$	2.00972	+	3.48093i	0.112877	+	0.195508i	−0.804052	+	0.594559i	$0.797327\pi$
$318$	−3.02696	+	3.73255i	−0.169743	+	0.209311i
$319$	0.442820	−	0.766987i	0.0247932	−	0.0429430i
$320$	3.93598	−	6.81732i	0.220028	−	0.381100i
$321$	−8.50520	−	22.2040i	−0.474714	−	1.23931i
$322$	0.669905	+	1.16031i	0.0373323	+	0.0646615i
$323$	−13.4887			−0.750529
$324$	−14.1167	−	10.3178i	−0.784260	−	0.573213i
$325$	−3.60301			−0.199859
$326$	−0.180309	−	0.312304i	−0.00998637	−	0.0172969i
$327$	−0.782630	−	2.04316i	−0.0432795	−	0.112987i
$328$	4.79987	−	8.31362i	0.265028	−	0.459043i
$329$	2.91423	−	5.04759i	0.160667	−	0.278283i
$330$	−1.14200	+	1.40821i	−0.0628652	+	0.0775193i
$331$	6.18878	+	10.7193i	0.340166	+	0.589185i	0.984463	−	0.175590i	$-0.0561834\pi$
$331$	6.18878	+	10.7193i	0.340166	+	0.589185i	−0.644297	+	0.764775i	$0.722850\pi$
$332$	13.4887			0.740286
$333$	21.3090	−	19.1319i	1.16773	−	1.04842i
$334$	3.51135			0.192133
$335$	−2.07318	−	3.59085i	−0.113270	−	0.196189i
$336$	−6.26088	−	0.996189i	−0.341559	−	0.0543466i
$337$	−6.12997	+	10.6174i	−0.333920	+	0.578367i	−0.983277	−	0.182117i	$-0.941705\pi$
$337$	−6.12997	+	10.6174i	−0.333920	+	0.578367i	0.649356	+	0.760484i	$0.275038\pi$
$338$	−1.43474	+	2.48504i	−0.0780395	+	0.135168i
$339$	20.8044	+	3.31026i	1.12994	+	0.179788i
$340$	−7.97141	−	13.8069i	−0.432310	−	0.748784i
$341$	−6.14884			−0.332978
$342$	−1.32489	−	0.432568i	−0.0716420	−	0.0233906i
$343$	−1.00000			−0.0539949
$344$	−1.04910	−	1.81709i	−0.0565637	−	0.0979711i
$345$	7.22489	−	8.90904i	0.388975	−	0.479647i
$346$	0.0302247	−	0.0523508i	0.00162489	−	0.00281440i
$347$	−3.32489	+	5.75888i	−0.178490	+	0.309153i	−0.941363	−	0.337394i	$-0.890454\pi$
$347$	−3.32489	+	5.75888i	−0.178490	+	0.309153i	0.762874	+	0.646547i	$0.223788\pi$
$348$	0.287832	+	0.751424i	0.0154294	+	0.0402806i
$349$	−5.71737	−	9.90278i	−0.306044	−	0.530083i	0.671449	−	0.741050i	$-0.265672\pi$
$349$	−5.71737	−	9.90278i	−0.306044	−	0.530083i	−0.977493	+	0.210967i	$0.932339\pi$
$350$	−0.861564			−0.0460525
$351$	−4.36389	+	2.82073i	−0.232927	+	0.150559i
$352$	10.2255			0.545018
$353$	11.0978	+	19.2220i	0.590677	+	1.02308i	0.994141	+	0.108087i	$0.0344725\pi$
$353$	11.0978	+	19.2220i	0.590677	+	1.02308i	−0.403465	+	0.914995i	$0.632194\pi$
$354$	0.385640	+	1.00677i	0.0204965	+	0.0535090i
$355$	−5.08414	+	8.80598i	−0.269838	+	0.467373i
$356$	2.66866	−	4.62226i	0.141439	−	0.244979i
$357$	−7.57442	+	9.34004i	−0.400881	+	0.494328i
$358$	1.69686	+	2.93905i	0.0896819	+	0.155334i
$359$	−7.55623			−0.398803			−0.199401	−	0.979918i	$-0.563900\pi$
$359$	−7.55623			−0.398803			−0.199401	+	0.979918i	$0.563900\pi$
$360$	−0.690415	−	3.27101i	−0.0363880	−	0.172397i
$361$	−15.2255			−0.801339
$362$	−0.171149	−	0.296439i	−0.00899539	−	0.0155805i
$363$	4.64815	+	0.739583i	0.243965	+	0.0388180i
$364$	−0.971410	+	1.68253i	−0.0509157	+	0.0881886i
$365$	−8.95254	+	15.5062i	−0.468597	+	0.811634i
$366$	3.10985	+	0.494818i	0.162554	+	0.0258646i
$367$	9.26157	+	16.0415i	0.483450	+	0.837360i	0.999819	−	0.0190063i	$-0.00605025\pi$
$367$	9.26157	+	16.0415i	0.483450	+	0.837360i	−0.516370	+	0.856366i	$0.672717\pi$
$368$	−20.5081			−1.06906
$369$	6.30834	+	29.8873i	0.328399	+	1.55587i
$370$	2.69794			0.140259
$371$	−5.80150	−	10.0485i	−0.301199	−	0.521692i
$372$	3.51887	−	4.33914i	0.182445	−	0.224974i
$373$	−7.83009	+	13.5621i	−0.405427	+	0.702220i	−0.994371	−	0.105954i	$-0.966210\pi$
$373$	−7.83009	+	13.5621i	−0.405427	+	0.702220i	0.588944	+	0.808174i	$0.299544\pi$
$374$	3.07442	−	5.32505i	0.158974	−	0.275352i
$375$	6.29987	+	16.4467i	0.325324	+	0.849302i
$376$	−2.74759	−	4.75897i	−0.141696	−	0.245425i
$377$	0.239123			0.0123155
$378$	−1.04351	+	0.674501i	−0.0536722	+	0.0346926i
$379$	4.03775			0.207405			0.103703	−	0.994608i	$-0.466931\pi$
$379$	4.03775			0.207405			0.103703	+	0.994608i	$0.466931\pi$
$380$	2.23065	+	3.86360i	0.114430	+	0.198199i
$381$	−0.830095	−	2.16708i	−0.0425271	−	0.111023i
$382$	1.80150	−	3.12030i	0.0921730	−	0.159648i
$383$	−0.112725	+	0.195246i	−0.00575998	+	0.00997659i	−0.868891	−	0.495003i	$-0.835167\pi$
$383$	−0.112725	+	0.195246i	−0.00575998	+	0.00997659i	0.863131	+	0.504980i	$0.168500\pi$
$384$	−7.76157	+	9.57081i	−0.396081	+	0.488408i
$385$	−2.18878	−	3.79108i	−0.111551	−	0.193211i
$386$	1.87661			0.0955171
$387$	6.34665	+	2.07213i	0.322618	+	0.105332i
$388$	−13.9267			−0.707019
$389$	−12.6316	−	21.8786i	−0.640448	−	1.10929i	−0.985333	−	0.170643i	$-0.945416\pi$
$389$	−12.6316	−	21.8786i	−0.640448	−	1.10929i	0.344885	−	0.938645i	$-0.387918\pi$
$390$	−0.483448	−	0.0769231i	−0.0244804	−	0.00389515i
$391$	−19.4503	+	33.6890i	−0.983646	+	1.70373i
$392$	−0.471410	+	0.816506i	−0.0238098	+	0.0412398i
$393$	−8.49604	−	1.35183i	−0.428569	−	0.0681910i
$394$	0.799870	+	1.38542i	0.0402969	+	0.0697962i
$395$	8.71986			0.438744
$396$	−16.0627	+	14.4216i	−0.807180	+	0.724712i
$397$	−20.3009			−1.01888			−0.509438	−	0.860508i	$-0.670147\pi$
$397$	−20.3009			−1.01888			−0.509438	+	0.860508i	$0.670147\pi$
$398$	−2.38401	−	4.12922i	−0.119499	−	0.206979i
$399$	2.11956	−	2.61364i	0.106111	−	0.130846i
$400$	6.59385	−	11.4209i	0.329693	−	0.571044i
$401$	7.61273	−	13.1856i	0.380161	−	0.658459i	−0.610924	−	0.791689i	$-0.709202\pi$
$401$	7.61273	−	13.1856i	0.380161	−	0.658459i	0.991085	+	0.133231i	$0.0425351\pi$
$402$	0.519728	+	1.35682i	0.0259217	+	0.0676720i
$403$	−0.830095	−	1.43777i	−0.0413500	−	0.0716203i
$404$	24.8389			1.23578
$405$	8.58809	+	6.27701i	0.426746	+	0.311907i
$406$	0.0571799			0.00283779
$407$	−17.6774	−	30.6182i	−0.876238	−	1.51769i
$408$	4.05555	+	10.5876i	0.200779	+	0.524162i
$409$	−0.828460	+	1.43494i	−0.0409647	+	0.0709530i	−0.885781	−	0.464104i	$-0.846376\pi$
$409$	−0.828460	+	1.43494i	−0.0409647	+	0.0709530i	0.844816	+	0.535057i	$0.179710\pi$
$410$	−1.43886	+	2.49218i	−0.0710603	+	0.123080i
$411$	4.73461	−	5.83826i	0.233541	−	0.287980i
$412$	−4.27128	−	7.39807i	−0.210431	−	0.364477i
$413$	−2.60301			−0.128086
$414$	−2.99084	+	2.68527i	−0.146992	+	0.131974i
$415$	−8.20602			−0.402818
$416$	1.38044	+	2.39099i	0.0676816	+	0.117228i
$417$	6.74433	+	1.07311i	0.330271	+	0.0525505i
$418$	−0.860320	+	1.49012i	−0.0420796	+	0.0728840i
$419$	−16.6871	+	28.9030i	−0.815220	+	1.41200i	0.0939492	+	0.995577i	$0.470051\pi$
$419$	−16.6871	+	28.9030i	−0.815220	+	1.41200i	−0.909170	+	0.416426i	$0.863282\pi$
$420$	3.92790	+	0.624982i	0.191662	+	0.0304960i
$421$	−9.12025	−	15.7967i	−0.444494	−	0.769886i	0.553523	−	0.832834i	$-0.313283\pi$
$421$	−9.12025	−	15.7967i	−0.444494	−	0.769886i	−0.998017	+	0.0629481i	$0.979950\pi$
$422$	4.32614			0.210593
$423$	16.6219	+	5.42692i	0.808184	+	0.263866i
$424$	−10.9396			−0.531272
$425$	−12.5075	−	21.6637i	−0.606704	−	1.05084i
$426$	2.24433	−	2.76748i	0.108738	−	0.134085i
$427$	−3.80150	+	6.58440i	−0.183968	+	0.318641i
$428$	13.3353	−	23.0974i	0.644586	−	1.11646i
$429$	2.29467	+	5.99054i	0.110788	+	0.289226i
$430$	0.314490	+	0.544712i	0.0151660	+	0.0262684i
$431$	29.2826			1.41049			0.705247	−	0.708961i	$-0.250836\pi$
$431$	29.2826			1.41049			0.705247	+	0.708961i	$0.250836\pi$
$432$	−0.954858	−	18.9949i	−0.0459406	−	0.913894i
$433$	−12.2449			−0.588451			−0.294226	−	0.955736i	$-0.595062\pi$
$433$	−12.2449			−0.588451			−0.294226	+	0.955736i	$0.595062\pi$
$434$	−0.198495	−	0.343803i	−0.00952807	−	0.0165031i
$435$	−0.175107	−	0.457140i	−0.00839573	−	0.0219182i
$436$	1.22708	−	2.12537i	0.0587667	−	0.101787i
$437$	5.44282	−	9.42724i	0.260365	−	0.450966i
$438$	3.95198	−	4.87320i	0.188833	−	0.232850i
$439$	2.41586	+	4.18440i	0.115303	+	0.199711i	0.917901	−	0.396810i	$-0.129883\pi$
$439$	2.41586	+	4.18440i	0.115303	+	0.199711i	−0.802598	+	0.596520i	$0.796549\pi$
$440$	−4.12725			−0.196759
$441$	−0.619562	−	2.93533i	−0.0295029	−	0.139777i
$442$	1.66019			0.0789672
$443$	−0.622440	−	1.07810i	−0.0295730	−	0.0512220i	0.850860	−	0.525392i	$-0.176081\pi$
$443$	−0.622440	−	1.07810i	−0.0295730	−	0.0512220i	−0.880433	+	0.474170i	$0.842748\pi$
$444$	31.7233	+	5.04759i	1.50552	+	0.239548i
$445$	−1.62352	+	2.81202i	−0.0769622	+	0.133302i
$446$	−2.70890	+	4.69195i	−0.128270	+	0.222170i
$447$	19.0059	+	3.02409i	0.898948	+	0.143035i
$448$	−3.33009	−	5.76789i	−0.157332	−	0.272507i
$449$	8.82846			0.416641			0.208320	−	0.978061i	$-0.433200\pi$
$449$	8.82846			0.416641			0.208320	+	0.978061i	$0.433200\pi$
$450$	−0.533792	−	2.52897i	−0.0251632	−	0.119217i
$451$	37.7108			1.77573
$452$	11.8148	+	20.4638i	0.555721	+	0.962537i
$453$	−15.1900	+	18.7309i	−0.713690	+	0.880053i
$454$	−0.631600	+	1.09396i	−0.0296425	+	0.0513422i
$455$	0.590972	−	1.02359i	0.0277052	−	0.0479868i
$456$	−1.13487	−	2.96273i	−0.0531451	−	0.138743i
$457$	5.25404	+	9.10026i	0.245774	+	0.425692i	0.962349	−	0.271817i	$-0.0876247\pi$
$457$	5.25404	+	9.10026i	0.245774	+	0.425692i	−0.716575	+	0.697510i	$0.754291\pi$
$458$	−4.62382			−0.216057
$459$	−32.1089	−	16.4467i	−1.49872	−	0.767665i
$460$	12.8662			0.599890
$461$	−11.2758	−	19.5302i	−0.525166	−	0.909614i	−0.999570	−	0.0293073i	$-0.990670\pi$
$461$	−11.2758	−	19.5302i	−0.525166	−	0.909614i	0.474404	−	0.880307i	$-0.342663\pi$
$462$	0.548709	+	1.43248i	0.0255282	+	0.0666449i
$463$	−5.19850	+	9.00406i	−0.241595	+	0.418454i	−0.961169	−	0.275962i	$-0.911004\pi$
$463$	−5.19850	+	9.00406i	−0.241595	+	0.418454i	0.719574	+	0.694416i	$0.244337\pi$
$464$	−0.437618	+	0.757977i	−0.0203159	+	0.0351882i
$465$	−2.14076	+	2.63978i	−0.0992753	+	0.122417i
$466$	−2.03022	−	3.51645i	−0.0940483	−	0.162897i
$467$	13.3171			0.616242			0.308121	−	0.951347i	$-0.400300\pi$
$467$	13.3171			0.616242			0.308121	+	0.951347i	$0.400300\pi$
$468$	−5.54063	−	1.80897i	−0.256116	−	0.0836198i
$469$	−3.50808			−0.161988
$470$	0.823649	+	1.42660i	0.0379921	+	0.0658043i
$471$	0.0978082	+	0.0155626i	0.00450676	+	0.000717086i
$472$	−1.22708	+	2.12537i	−0.0564812	+	0.0978282i
$473$	4.12120	−	7.13812i	0.189493	−	0.328211i
$474$	−3.01763	−	0.480145i	−0.138604	−	0.0220538i
$475$	3.50000	+	6.06218i	0.160591	+	0.278152i
$476$	−13.4887			−0.618251
$477$	25.9012	−	23.2550i	1.18594	−	1.06477i
$478$	−4.03775			−0.184682
$479$	−7.26771	−	12.5880i	−0.332070	−	0.575163i	0.650847	−	0.759209i	$-0.274414\pi$
$479$	−7.26771	−	12.5880i	−0.332070	−	0.575163i	−0.982918	+	0.184046i	$0.941080\pi$
$480$	3.56006	−	4.38992i	0.162494	−	0.200372i
$481$	4.77292	−	8.26693i	0.217626	−	0.376940i
$482$	3.24557	−	5.62149i	0.147832	−	0.256052i
$483$	−3.47141	−	9.06259i	−0.157955	−	0.412362i
$484$	2.63968	+	4.57206i	0.119985	+	0.207821i
$485$	8.47249			0.384716
$486$	−2.62640	−	2.64514i	−0.119136	−	0.119986i
$487$	13.0539			0.591529			0.295765	−	0.955261i	$-0.404426\pi$
$487$	13.0539			0.591529			0.295765	+	0.955261i	$0.404426\pi$
$488$	3.58414	+	6.20790i	0.162246	+	0.281019i
$489$	0.934349	+	2.43924i	0.0422527	+	0.110306i
$490$	0.141315	−	0.244765i	0.00638396	−	0.0110574i
$491$	−9.67223	+	16.7528i	−0.436502	+	0.756043i	−0.997417	−	0.0718303i	$-0.977116\pi$
$491$	−9.67223	+	16.7528i	−0.436502	+	0.756043i	0.560915	+	0.827873i	$0.310449\pi$
$492$	−21.5813	+	26.6119i	−0.972958	+	1.19976i
$493$	0.830095	+	1.43777i	0.0373856	+	0.0647538i
$494$	−0.464574			−0.0209022
$495$	9.77197	−	8.77359i	0.439217	−	0.394344i
$496$	6.07661			0.272848
$497$	4.30150	+	7.45043i	0.192949	+	0.334197i
$498$	2.83981	+	0.451852i	0.127255	+	0.0202480i
$499$	18.1111	−	31.3693i	0.810764	−	1.40428i	−0.101566	−	0.994829i	$-0.532385\pi$
$499$	18.1111	−	31.3693i	0.810764	−	1.40428i	0.912330	−	0.409455i	$-0.134281\pi$
$500$	−9.87756	+	17.1084i	−0.441738	+	0.765112i
$501$	−25.1179	−	3.99660i	−1.12219	−	0.178555i
$502$	−2.28100	−	3.95080i	−0.101806	−	0.176333i
$503$	15.6764			0.698974			0.349487	−	0.936941i	$-0.386356\pi$
$503$	15.6764			0.698974			0.349487	+	0.936941i	$0.386356\pi$
$504$	−2.68878	−	0.877867i	−0.119768	−	0.0391033i
$505$	−15.1111			−0.672435
$506$	2.48113	+	4.29743i	0.110299	+	0.191044i
$507$	13.0917	−	16.1434i	0.581421	−	0.716952i
$508$	1.30150	−	2.25427i	0.0577449	−	0.100017i
$509$	−17.1517	+	29.7076i	−0.760237	+	1.31677i	0.182492	+	0.983207i	$0.441584\pi$
$509$	−17.1517	+	29.7076i	−0.760237	+	1.31677i	−0.942729	+	0.333561i	$0.891750\pi$
$510$	−1.21574	−	3.17384i	−0.0538337	−	0.140540i
$511$	7.57442	+	13.1193i	0.335073	+	0.580363i
$512$	−17.0071			−0.751616
$513$	8.98508	+	4.60230i	0.396701	+	0.203196i
$514$	3.54910			0.156544
$515$	2.59850	+	4.50073i	0.114503	+	0.198326i
$516$	2.67877	+	6.99329i	0.117926	+	0.307862i
$517$	10.7934	−	18.6948i	0.474694	−	0.822195i
$518$	1.14132	−	1.97682i	0.0501465	−	0.0868563i
$519$	−0.275794	+	0.340082i	−0.0121060	+	0.0149279i
$520$	−0.557180	−	0.965064i	−0.0244340	−	0.0423209i
$521$	−10.2449			−0.448836			−0.224418	−	0.974493i	$-0.572048\pi$
$521$	−10.2449			−0.448836			−0.224418	+	0.974493i	$0.572048\pi$
$522$	0.0354265	+	0.167842i	0.00155058	+	0.00734624i
$523$	30.6030			1.33818			0.669088	−	0.743183i	$-0.266685\pi$
$523$	30.6030			1.33818			0.669088	+	0.743183i	$0.266685\pi$
$524$	−4.82489	−	8.35696i	−0.210776	−	0.365075i
$525$	6.16307	+	0.980627i	0.268978	+	0.0427981i
$526$	−0.925580	+	1.60315i	−0.0403572	+	0.0699007i
$527$	5.76320	−	9.98215i	0.251049	−	0.434829i
$528$	−23.1884	−	3.68958i	−1.00915	−	0.160568i
$529$	−4.19686	−	7.26918i	−0.182472	−	0.316051i
$530$	3.27936			0.142446
$531$	−1.61273	−	7.64068i	−0.0699863	−	0.331577i
$532$	3.77455			0.163647
$533$	5.09097	+	8.81782i	0.220514	+	0.381942i
$534$	0.716681	−	0.883742i	0.0310138	−	0.0382433i
$535$	−8.11273	+	14.0517i	−0.350744	+	0.607506i
$536$	−1.65374	+	2.86437i	−0.0714309	+	0.123722i
$537$	−8.79303	−	22.9554i	−0.379447	−	0.990599i
$538$	−0.180699	−	0.312981i	−0.00779051	−	0.0134936i
$539$	−3.70370			−0.159530
$540$	0.599052	+	11.9169i	0.0257791	+	0.512821i
$541$	−26.0917			−1.12177			−0.560884	−	0.827894i	$-0.689539\pi$
$541$	−26.0917			−1.12177			−0.560884	+	0.827894i	$0.689539\pi$
$542$	−2.62803	−	4.55189i	−0.112884	−	0.195520i
$543$	0.886884	+	2.31533i	0.0380598	+	0.0993604i
$544$	−9.58414	+	16.6002i	−0.410916	+	0.711728i
$545$	−0.746515	+	1.29300i	−0.0319772	+	0.0553861i
$546$	−0.260877	+	0.321688i	−0.0111645	+	0.0137670i
$547$	5.46169	+	9.45993i	0.233525	+	0.404478i	0.958843	−	0.283937i	$-0.0916405\pi$
$547$	5.46169	+	9.45993i	0.233525	+	0.404478i	−0.725318	+	0.688414i	$0.758307\pi$
$548$	8.43147			0.360175
$549$	−21.6826	−	7.07922i	−0.925392	−	0.302134i
$550$	−3.19097			−0.136063
$551$	−0.232287	−	0.402332i	−0.00989575	−	0.0171399i
$552$	−9.03611	−	1.43777i	−0.384603	−	0.0611954i
$553$	3.68878	−	6.38915i	0.156863	−	0.271694i
$554$	−1.29467	+	2.24243i	−0.0550052	+	0.0952718i
$555$	−19.2993	−	3.07078i	−0.819210	−	0.130347i
$556$	3.83009	+	6.63392i	0.162432	+	0.281341i
$557$	−13.9442			−0.590835			−0.295417	−	0.955368i	$-0.595459\pi$
$557$	−13.9442			−0.590835			−0.295417	+	0.955368i	$0.595459\pi$
$558$	0.886196	−	0.795655i	0.0375157	−	0.0336828i
$559$	2.22545			0.0941265
$560$	2.16307	+	3.74654i	0.0914063	+	0.158320i
$561$	−28.0534	+	34.5927i	−1.18441	+	1.46050i
$562$	−2.01780	+	3.49492i	−0.0851156	+	0.147424i
$563$	−15.1287	+	26.2037i	−0.637600	+	1.10435i	0.348358	+	0.937361i	$0.386739\pi$
$563$	−15.1287	+	26.2037i	−0.637600	+	1.10435i	−0.985958	+	0.166993i	$0.946594\pi$
$564$	7.01570	+	18.3154i	0.295414	+	0.771219i
$565$	−7.18770	−	12.4495i	−0.302389	−	0.523753i
$566$	3.66268			0.153954
$567$	8.23229	−	3.63723i	0.345724	−	0.152749i
$568$	8.11109			0.340334
$569$	10.5676	+	18.3036i	0.443016	+	0.767326i	0.997912	−	0.0645936i	$-0.0205751\pi$
$569$	10.5676	+	18.3036i	0.443016	+	0.767326i	−0.554896	+	0.831920i	$0.687242\pi$
$570$	0.340201	+	0.888141i	0.0142495	+	0.0372001i
$571$	16.3932	−	28.3938i	0.686033	−	1.18824i	−0.287078	−	0.957907i	$-0.592684\pi$
$571$	16.3932	−	28.3938i	0.686033	−	1.18824i	0.973111	−	0.230336i	$-0.0739826\pi$
$572$	−3.59781	+	6.23159i	−0.150432	+	0.260556i
$573$	−16.4383	+	20.2701i	−0.686720	+	0.846797i
$574$	1.21737	+	2.10855i	0.0508120	+	0.0880090i
$575$	20.1877			0.841885
$576$	14.8675	−	13.3485i	0.619477	−	0.556187i
$577$	−17.3743			−0.723301			−0.361651	−	0.932314i	$-0.617787\pi$
$577$	−17.3743			−0.723301			−0.361651	+	0.932314i	$0.617787\pi$
$578$	3.73065	+	6.46168i	0.155175	+	0.268770i
$579$	−13.4241	−	2.13595i	−0.557886	−	0.0887671i
$580$	0.274550	−	0.475534i	0.0114001	−	0.0197455i
$581$	−3.47141	+	6.01266i	−0.144018	+	0.249447i
$582$	−2.93203	−	0.466524i	−0.121536	−	0.0193381i
$583$	−21.4870	−	37.2166i	−0.889901	−	1.54135i
$584$	14.2826			0.591019
$585$	3.37072	+	1.10052i	0.139362	+	0.0455007i
$586$	2.24050			0.0925542
$587$	−8.48796	−	14.7016i	−0.350336	−	0.606799i	0.635973	−	0.771712i	$-0.280599\pi$
$587$	−8.48796	−	14.7016i	−0.350336	−	0.606799i	−0.986308	+	0.164913i	$0.947266\pi$
$588$	2.11956	−	2.61364i	0.0874092	−	0.107785i
$589$	−1.61273	+	2.79332i	−0.0664512	+	0.115097i
$590$	0.367845	−	0.637125i	0.0151439	−	0.0262300i
$591$	−4.14488	−	10.8208i	−0.170498	−	0.445107i
$592$	17.4698	+	30.2585i	0.718003	+	1.24362i
$593$	−13.0733			−0.536858			−0.268429	−	0.963300i	$-0.586504\pi$
$593$	−13.0733			−0.536858			−0.268429	+	0.963300i	$0.586504\pi$
$594$	−3.86483	+	2.49815i	−0.158576	+	0.102500i
$595$	8.20602			0.336414
$596$	10.7934	+	18.6948i	0.442116	+	0.765767i
$597$	12.3538	+	32.2512i	0.505607	+	1.31995i
$598$	−0.669905	+	1.16031i	−0.0273945	+	0.0474486i
$599$	−14.6030	+	25.2932i	−0.596663	+	1.03345i	0.396647	+	0.917971i	$0.370174\pi$
$599$	−14.6030	+	25.2932i	−0.596663	+	1.03345i	−0.993310	+	0.115479i	$0.963160\pi$
$600$	3.70602	−	4.56991i	0.151298	−	0.186566i
$601$	−3.89536	−	6.74695i	−0.158895	−	0.275214i	0.775576	−	0.631255i	$-0.217460\pi$
$601$	−3.89536	−	6.74695i	−0.158895	−	0.275214i	−0.934470	+	0.356041i	$0.884126\pi$
$602$	0.532157			0.0216891
$603$	−2.17347	−	10.2974i	−0.0885106	−	0.419341i
$604$	−27.0506			−1.10067
$605$	−1.60589	−	2.78148i	−0.0652887	−	0.113083i
$606$	5.22941	+	0.832069i	0.212430	+	0.0338005i
$607$	9.82038	−	17.0094i	0.398597	−	0.690390i	−0.594956	−	0.803758i	$-0.702831\pi$
$607$	9.82038	−	17.0094i	0.398597	−	0.690390i	0.993553	+	0.113368i	$0.0361639\pi$
$608$	2.68194	−	4.64526i	0.108767	−	0.188390i
$609$	−0.409028	−	0.0650819i	−0.0165747	−	0.00263725i
$610$	−1.07442	−	1.86095i	−0.0435020	−	0.0753477i
$611$	5.82846			0.235794
$612$	−8.35705	−	39.5936i	−0.337814	−	1.60048i
$613$	23.5653			0.951792			0.475896	−	0.879502i	$-0.342124\pi$
$613$	23.5653			0.951792			0.475896	+	0.879502i	$0.342124\pi$
$614$	0.324502	+	0.562054i	0.0130958	+	0.0226827i
$615$	13.1293	−	16.1898i	0.529424	−	0.652834i
$616$	−1.74596	+	3.02409i	−0.0703467	+	0.121844i
$617$	5.33009	−	9.23200i	0.214582	−	0.371666i	−0.738562	−	0.674186i	$-0.764495\pi$
$617$	5.33009	−	9.23200i	0.214582	−	0.371666i	0.953143	+	0.302520i	$0.0978279\pi$
$618$	−0.651421	−	1.70062i	−0.0262040	−	0.0684091i
$619$	9.00752	+	15.6015i	0.362043	+	0.627077i	0.988297	−	0.152542i	$-0.0487460\pi$
$619$	9.00752	+	15.6015i	0.362043	+	0.627077i	−0.626254	+	0.779619i	$0.715413\pi$
$620$	−3.81230			−0.153106
$621$	24.4509	−	15.8046i	0.981181	−	0.634215i
$622$	3.34308			0.134045
$623$	1.37360	+	2.37915i	0.0550322	+	0.0953186i
$624$	−2.26771	−	5.92017i	−0.0907812	−	0.236997i
$625$	−2.99837	+	5.19332i	−0.119935	+	0.207733i
$626$	−2.27812	+	3.94581i	−0.0910519	+	0.157706i
$627$	7.85021	−	9.68013i	0.313507	−	0.386587i
$628$	0.0555452	+	0.0962071i	0.00221649	+	0.00383908i
$629$	66.2750			2.64256
$630$	0.806018	+	0.263159i	0.0321125	+	0.0104845i
$631$	12.4703			0.496436			0.248218	−	0.968704i	$-0.420155\pi$
$631$	12.4703			0.496436			0.248218	+	0.968704i	$0.420155\pi$
$632$	−3.47786	−	6.02382i	−0.138342	−	0.239615i
$633$	−30.9464	−	4.92398i	−1.23001	−	0.195711i
$634$	−0.480570	+	0.832371i	−0.0190859	+	0.0330577i
$635$	−0.791790	+	1.37142i	−0.0314212	+	0.0544232i
$636$	38.5598	+	6.13538i	1.52900	+	0.243284i
$637$	−0.500000	−	0.866025i	−0.0198107	−	0.0343132i
$638$	0.211777			0.00838434
$639$	−19.2044	+	17.2423i	−0.759714	+	0.682096i
$640$	8.40877			0.332386
$641$	−9.57279	−	16.5806i	−0.378102	−	0.654892i	0.612684	−	0.790328i	$-0.290090\pi$
$641$	−9.57279	−	16.5806i	−0.378102	−	0.654892i	−0.990786	+	0.135436i	$0.956757\pi$
$642$	3.58126	−	4.41606i	0.141341	−	0.174288i
$643$	−3.24433	+	5.61934i	−0.127944	+	0.221605i	−0.922880	−	0.385088i	$-0.874171\pi$
$643$	−3.24433	+	5.61934i	−0.127944	+	0.221605i	0.794936	+	0.606693i	$0.207504\pi$
$644$	5.44282	−	9.42724i	0.214477	−	0.371485i
$645$	−1.62967	−	4.25447i	−0.0641681	−	0.167520i
$646$	−1.61273	−	2.79332i	−0.0634518	−	0.109902i
$647$	−48.0988			−1.89096			−0.945479	−	0.325682i	$-0.894406\pi$
$647$	−48.0988			−1.89096			−0.945479	+	0.325682i	$0.894406\pi$
$648$	0.910961	−	8.43634i	0.0357859	−	0.331411i
$649$	−9.64076			−0.378433
$650$	−0.430782	−	0.746136i	−0.0168967	−	0.0292659i
$651$	1.02859	+	2.68527i	0.0403136	+	0.105244i
$652$	−1.46496	+	2.53739i	−0.0573724	+	0.0993720i
$653$	21.6202	−	37.4474i	0.846066	−	1.46543i	−0.0386267	−	0.999254i	$-0.512298\pi$
$653$	21.6202	−	37.4474i	0.846066	−	1.46543i	0.884692	−	0.466175i	$-0.154368\pi$
$654$	0.329539	−	0.406356i	0.0128860	−	0.0158898i
$655$	2.93530	+	5.08408i	0.114691	+	0.198651i
$656$	−37.2678			−1.45506
$657$	−33.8166	+	30.3616i	−1.31931	+	1.18452i
$658$	1.39372			0.0543329
$659$	1.25404	+	2.17206i	0.0488505	+	0.0846115i	0.889417	−	0.457097i	$-0.151111\pi$
$659$	1.25404	+	2.17206i	0.0488505	+	0.0846115i	−0.840566	+	0.541709i	$0.817778\pi$
$660$	14.5478	+	2.31474i	0.566271	+	0.0901013i
$661$	21.1677	−	36.6636i	0.823329	−	1.42605i	−0.0798613	−	0.996806i	$-0.525448\pi$
$661$	21.1677	−	36.6636i	0.823329	−	1.42605i	0.903190	−	0.429241i	$-0.141219\pi$
$662$	−1.47988	+	2.56323i	−0.0575172	+	0.0996227i
$663$	−11.8759	−	1.88962i	−0.461223	−	0.0733867i
$664$	3.27292	+	5.66886i	0.127014	+	0.219994i
$665$	−2.29630			−0.0890468
$666$	6.50972	+	2.12537i	0.252246	+	0.0823566i
$667$	−1.33981			−0.0518777
$668$	−14.2644	−	24.7067i	−0.551908	−	0.955933i
$669$	24.7181	−	30.4799i	0.955655	−	1.17842i
$670$	0.495745	−	0.858655i	0.0191523	−	0.0331727i
$671$	−14.0796	+	24.3866i	−0.543538	+	0.941435i
$672$	−1.71053	−	4.46558i	−0.0659853	−	0.172263i
$673$	−6.70765	−	11.6180i	−0.258561	−	0.447841i	0.707296	−	0.706918i	$-0.249915\pi$
$673$	−6.70765	−	11.6180i	−0.258561	−	0.447841i	−0.965857	+	0.259077i	$0.916582\pi$
$674$	−2.93163			−0.112922
$675$	0.939941	+	18.6982i	0.0361784	+	0.719693i
$676$	23.3138			0.896686
$677$	−0.981125	−	1.69936i	−0.0377077	−	0.0653117i	0.846556	−	0.532300i	$-0.178672\pi$
$677$	−0.981125	−	1.69936i	−0.0377077	−	0.0653117i	−0.884263	+	0.466989i	$0.845339\pi$
$678$	1.80190	+	4.70409i	0.0692014	+	0.180660i
$679$	3.58414	−	6.20790i	0.137546	−	0.238237i
$680$	3.86840	−	6.70027i	0.148346	−	0.256943i
$681$	5.76320	−	7.10662i	0.220846	−	0.272326i
$682$	−0.735165	−	1.27334i	−0.0281509	−	0.0487589i
$683$	27.1672			1.03952			0.519761	−	0.854312i	$-0.326021\pi$
$683$	27.1672			1.03952			0.519761	+	0.854312i	$0.326021\pi$
$684$	2.33857	+	11.0795i	0.0894173	+	0.423637i
$685$	−5.12941			−0.195985
$686$	−0.119562	−	0.207087i	−0.00456488	−	0.00790661i
$687$	33.0758	+	5.26280i	1.26192	+	0.200788i
$688$	−4.07279	+	7.05427i	−0.155273	+	0.268942i
$689$	5.80150	−	10.0485i	0.221020	−	0.382817i
$690$	2.70877	+	0.431001i	0.103121	+	0.0164079i
$691$	25.1586	+	43.5759i	0.957077	+	1.65771i	0.729543	+	0.683935i	$0.239733\pi$
$691$	25.1586	+	43.5759i	0.957077	+	1.65771i	0.227534	+	0.973770i	$0.426934\pi$
$692$	−0.491138			−0.0186703
$693$	−2.29467	−	10.8716i	−0.0871672	−	0.412976i
$694$	−1.59012			−0.0603601
$695$	−2.33009	−	4.03584i	−0.0883855	−	0.153088i
$696$	−0.245960	+	0.303294i	−0.00932308	+	0.0114963i
$697$	−35.3457	+	61.2205i	−1.33881	+	2.31889i
$698$	1.36716	−	2.36798i	0.0517476	−	0.0896295i
$699$	10.5205	+	27.4652i	0.397922	+	1.03883i
$700$	3.50000	+	6.06218i	0.132288	+	0.229129i
$701$	45.1672			1.70594			0.852970	−	0.521960i	$-0.174799\pi$
$701$	45.1672			1.70594			0.852970	+	0.521960i	$0.174799\pi$
$702$	−1.10589	−	0.566453i	−0.0417391	−	0.0213794i
$703$	−18.5458			−0.699469
$704$	−12.3337	−	21.3625i	−0.464842	−	0.805131i
$705$	−4.26810	−	11.1425i	−0.160746	−	0.419649i
$706$	−2.65374	+	4.59642i	−0.0998750	+	0.172989i
$707$	−6.39248	+	11.0721i	−0.240414	+	0.416409i
$708$	5.51724	−	6.80333i	0.207351	−	0.255685i
$709$	−19.8090	−	34.3102i	−0.743944	−	1.28855i	−0.950687	−	0.310153i	$-0.899620\pi$
$709$	−19.8090	−	34.3102i	−0.743944	−	1.28855i	0.206743	−	0.978395i	$-0.433714\pi$
$710$	−2.43147			−0.0912514
$711$	21.0397	+	6.86930i	0.789050	+	0.257619i
$712$	2.59012			0.0970688
$713$	4.65103	+	8.05582i	0.174182	+	0.301693i
$714$	−2.83981	−	0.451852i	−0.106277	−	0.0169101i
$715$	2.18878	−	3.79108i	0.0818557	−	0.141778i
$716$	13.7866	−	23.8791i	0.515229	−	0.892403i
$717$	28.8834	+	4.59574i	1.07867	+	0.171631i
$718$	−0.903436	−	1.56480i	−0.0337159	−	0.0583977i
$719$	−22.0377			−0.821869			−0.410935	−	0.911665i	$-0.634798\pi$
$719$	−22.0377			−0.821869			−0.410935	+	0.911665i	$0.634798\pi$
$720$	−9.65718	+	8.67053i	−0.359902	+	0.323132i
$721$	4.39699			0.163752
$722$	−1.82038	−	3.15299i	−0.0677475	−	0.117342i
$723$	−29.6150	+	36.5184i	−1.10140	+	1.35813i
$724$	−1.39054	+	2.40849i	−0.0516792	+	0.0895110i
$725$	0.430782	−	0.746136i	0.0159988	−	0.0277108i
$726$	0.402583	+	1.05100i	0.0149412	+	0.0390061i
$727$	−14.0555	−	24.3449i	−0.521291	−	0.902903i	−0.999693	−	0.0247621i	$-0.992117\pi$
$727$	−14.0555	−	24.3449i	−0.521291	−	0.902903i	0.478402	−	0.878141i	$-0.341216\pi$
$728$	−0.942820			−0.0349432
$729$	15.7769	+	21.9110i	0.584329	+	0.811517i
$730$	−4.28152			−0.158466
$731$	7.72545	+	13.3809i	0.285736	+	0.494909i
$732$	−9.15172	−	23.8918i	−0.338257	−	0.883066i
$733$	−5.93474	+	10.2793i	−0.219205	+	0.379674i	−0.954565	−	0.298003i	$-0.903680\pi$
$733$	−5.93474	+	10.2793i	−0.219205	+	0.379674i	0.735360	+	0.677676i	$0.237013\pi$
$734$	−2.21466	+	3.83590i	−0.0817444	+	0.141586i
$735$	−1.28947	+	1.59005i	−0.0475627	+	0.0586497i
$736$	−7.73461	−	13.3967i	−0.285102	−	0.493810i
$737$	−12.9929			−0.478598
$738$	−5.43504	+	4.87975i	−0.200066	+	0.179626i
$739$	−12.1844			−0.448212			−0.224106	−	0.974565i	$-0.571946\pi$
$739$	−12.1844			−0.448212			−0.224106	+	0.974565i	$0.571946\pi$
$740$	−10.9601	−	18.9834i	−0.402900	−	0.697843i
$741$	3.32326	+	0.528775i	0.122083	+	0.0194250i
$742$	1.38727	−	2.40283i	0.0509285	−	0.0882107i
$743$	22.2427	−	38.5255i	0.816005	−	1.41336i	−0.0925987	−	0.995704i	$-0.529517\pi$
$743$	22.2427	−	38.5255i	0.816005	−	1.41336i	0.908604	−	0.417659i	$-0.137149\pi$
$744$	2.67743	+	0.426015i	0.0981593	+	0.0156185i
$745$	−6.56634	−	11.3732i	−0.240572	−	0.416683i
$746$	−3.74472			−0.137104
$747$	−19.7999	−	6.46451i	−0.724439	−	0.236524i
$748$	−49.9579			−1.82664
$749$	6.86389	+	11.8886i	0.250801	+	0.434400i
$750$	−2.65267	+	3.27101i	−0.0968616	+	0.119440i
$751$	−21.4029	+	37.0709i	−0.781002	+	1.35274i	0.150356	+	0.988632i	$0.451958\pi$
$751$	−21.4029	+	37.0709i	−0.781002	+	1.35274i	−0.931358	+	0.364104i	$0.881375\pi$
$752$	−10.6666	+	18.4752i	−0.388972	+	0.673720i
$753$	11.8200	+	30.8577i	0.430744	+	1.12452i
$754$	0.0285900	+	0.0495193i	0.00104119	+	0.00180339i
$755$	16.4567			0.598919
$756$	8.98508	+	4.60230i	0.326784	+	0.167384i
$757$	−22.4919			−0.817483			−0.408741	−	0.912650i	$-0.634032\pi$
$757$	−22.4919			−0.817483			−0.408741	+	0.912650i	$0.634032\pi$
$758$	0.482760	+	0.836165i	0.0175346	+	0.0303709i
$759$	−12.8571	−	33.5651i	−0.466681	−	1.21833i
$760$	−1.08250	+	1.87495i	−0.0392664	+	0.0680114i
$761$	7.16827	−	12.4158i	0.259850	−	0.450073i	−0.706352	−	0.707861i	$-0.749660\pi$
$761$	7.16827	−	12.4158i	0.259850	−	0.450073i	0.966201	+	0.257788i	$0.0829937\pi$
$762$	0.349525	−	0.431001i	0.0126620	−	0.0156135i
$763$	0.631600	+	1.09396i	0.0228655	+	0.0396041i
$764$	−29.2736			−1.05908
$765$	5.08414	+	24.0874i	0.183817	+	0.870880i
$766$	−0.0539104			−0.00194786
$767$	−1.30150	−	2.25427i	−0.0469946	−	0.0813971i
$768$	19.8750	+	3.16237i	0.717177	+	0.114112i
$769$	15.6105	−	27.0382i	0.562930	−	0.975024i	−0.434309	−	0.900764i	$-0.643007\pi$
$769$	15.6105	−	27.0382i	0.562930	−	0.975024i	0.997239	−	0.0742597i	$-0.0236594\pi$
$770$	0.523388	−	0.906535i	0.0188616	−	0.0326693i
$771$	−25.3880	−	4.03956i	−0.914325	−	0.145481i
$772$	−7.62352	−	13.2043i	−0.274376	−	0.475234i
$773$	4.38005			0.157539			0.0787697	−	0.996893i	$-0.474901\pi$
$773$	4.38005			0.157539			0.0787697	+	0.996893i	$0.474901\pi$
$774$	0.329704	+	1.56205i	0.0118510	+	0.0561469i
$775$	−5.98168			−0.214868
$776$	−3.37919	−	5.85294i	−0.121306	−	0.210108i
$777$	−10.4142	+	12.8418i	−0.373608	+	0.460698i
$778$	3.02051	−	5.23168i	0.108291	−	0.187565i
$779$	9.89084	−	17.1314i	0.354376	−	0.613798i
$780$	1.42270	+	3.71415i	0.0509409	+	0.132988i
$781$	15.9315	+	27.5941i	0.570073	+	0.987395i
$782$	−9.30206			−0.332641
$783$	−0.0623817	−	1.24095i	−0.00222934	−	0.0443481i
$784$	3.66019			0.130721
$785$	−0.0337917	−	0.0585290i	−0.00120608	−	0.00208899i
$786$	−0.735854	−	1.92105i	−0.0262470	−	0.0685214i
$787$	−13.8107	+	23.9208i	−0.492297	+	0.852683i	−0.999961	−	0.00887191i	$-0.997176\pi$
$787$	−13.8107	+	23.9208i	−0.492297	+	0.852683i	0.507664	+	0.861555i	$0.330509\pi$
$788$	6.49876	−	11.2562i	0.231509	−	0.400985i
$789$	8.44570	−	10.4144i	0.300675	−	0.370763i
$790$	1.04256	+	1.80577i	0.0370926	+	0.0642463i
$791$	−12.1625			−0.432449
$792$	−9.95843	−	3.25135i	−0.353857	−	0.115532i
$793$	−7.60301			−0.269991
$794$	−2.42721	−	4.20406i	−0.0861386	−	0.149196i
$795$	−23.4584	−	3.73255i	−0.831985	−	0.132380i
$796$	−19.3695	+	33.5489i	−0.686533	+	1.18911i
$797$	1.48181	−	2.56658i	0.0524885	−	0.0909128i	−0.838587	−	0.544767i	$-0.816618\pi$
$797$	1.48181	−	2.56658i	0.0524885	−	0.0909128i	0.891076	+	0.453854i	$0.149951\pi$
$798$	0.794668	+	0.126442i	0.0281310	+	0.00447601i
$799$	20.2330	+	35.0445i	0.715791	+	1.23979i
$800$	9.94747			0.351696
$801$	−6.13255	+	5.50600i	−0.216683	+	0.194545i
$802$	3.64076			0.128560
$803$	28.0534	+	48.5898i	0.989981	+	1.71470i
$804$	7.43559	−	9.16886i	0.262233	−	0.323361i
$805$	−3.31122	+	5.73520i	−0.116705	+	0.202139i
$806$	0.198495	−	0.343803i	0.00699169	−	0.0121100i
$807$	0.936374	+	2.44453i	0.0329619	+	0.0860516i
$808$	6.02696	+	10.4390i	0.212028	+	0.367242i
$809$	−24.7896			−0.871556			−0.435778	−	0.900054i	$-0.643527\pi$
$809$	−24.7896			−0.871556			−0.435778	+	0.900054i	$0.643527\pi$
$810$	−0.273080	+	2.52897i	−0.00959504	+	0.0888590i
$811$	8.24377			0.289478			0.144739	−	0.989470i	$-0.453766\pi$
$811$	8.24377			0.289478			0.144739	+	0.989470i	$0.453766\pi$
$812$	−0.232287	−	0.402332i	−0.00815167	−	0.0141191i
$813$	13.6183	+	35.5525i	0.477615	+	1.24688i
$814$	4.22708	−	7.32153i	0.148159	−	0.256619i
$815$	0.891233	−	1.54366i	0.0312185	−	0.0540721i
$816$	27.7238	−	34.1863i	0.970528	−	1.19676i
$817$	−2.16182	−	3.74439i	−0.0756327	−	0.131000i
$818$	−0.396208			−0.0138531
$819$	2.23229	−	2.00422i	0.0780024	−	0.0700331i
$820$	23.3808			0.816494
$821$	14.4497	+	25.0275i	0.504296	+	0.873467i	0.999988	+	0.00496829i	$0.00158146\pi$
$821$	14.4497	+	25.0275i	0.504296	+	0.873467i	−0.495691	+	0.868499i	$0.665085\pi$
$822$	1.77511	+	0.282443i	0.0619139	+	0.00985133i
$823$	18.0000	−	31.1769i	0.627441	−	1.08676i	−0.360623	−	0.932712i	$-0.617436\pi$
$823$	18.0000	−	31.1769i	0.627441	−	1.08676i	0.988063	−	0.154047i	$-0.0492308\pi$
$824$	2.07279	−	3.59017i	0.0722089	−	0.125069i
$825$	22.8261	+	3.63194i	0.794704	+	0.126448i
$826$	−0.311220	−	0.539049i	−0.0108287	−	0.0187559i
$827$	−50.7108			−1.76339			−0.881694	−	0.471821i	$-0.843597\pi$
$827$	−50.7108			−1.76339			−0.881694	+	0.471821i	$0.843597\pi$
$828$	31.0442	+	10.1357i	1.07886	+	0.352240i
$829$	14.8123			0.514452			0.257226	−	0.966351i	$-0.417191\pi$
$829$	14.8123			0.514452			0.257226	+	0.966351i	$0.417191\pi$
$830$	−0.981125	−	1.69936i	−0.0340554	−	0.0589856i
$831$	11.8135	−	14.5673i	0.409807	−	0.505335i
$832$	3.33009	−	5.76789i	0.115450	−	0.199966i
$833$	3.47141	−	6.01266i	0.120277	−	0.208326i
$834$	0.584135	+	1.52496i	0.0202269	+	0.0528052i
$835$	8.67799	+	15.0307i	0.300314	+	0.520159i
$836$	13.9798			0.483501
$837$	−7.24488	+	4.68294i	−0.250420	+	0.161866i
$838$	−7.98057			−0.275684
$839$	−16.8606	−	29.2034i	−0.582093	−	1.00821i	−0.995231	−	0.0975464i	$-0.968901\pi$
$839$	−16.8606	−	29.2034i	−0.582093	−	1.00821i	0.413138	−	0.910669i	$-0.364433\pi$
$840$	0.690415	+	1.80242i	0.0238216	+	0.0621894i
$841$	14.4714	−	25.0652i	0.499014	−	0.864318i
$842$	2.18086	−	3.77737i	0.0751575	−	0.130177i
$843$	18.4119	−	22.7038i	0.634140	−	0.781960i
$844$	−17.5744	−	30.4398i	−0.604936	−	1.04778i
$845$	−14.1833			−0.487921
$846$	0.863496	+	4.09103i	0.0296876	+	0.140652i
$847$	−2.71737			−0.0933699
$848$	21.2346	+	36.7794i	0.729199	+	1.26301i
$849$	−26.2004	−	4.16884i	−0.899196	−	0.143074i
$850$	2.99084	−	5.18029i	0.102585	−	0.177682i
$851$	−26.7427	+	46.3197i	−0.916728	+	1.58782i
$852$	−28.5900	−	4.54906i	−0.979478	−	0.155848i
$853$	−5.89480	−	10.2101i	−0.201834	−	0.349587i	0.747285	−	0.664503i	$-0.231357\pi$
$853$	−5.89480	−	10.2101i	−0.201834	−	0.349587i	−0.949119	+	0.314916i	$0.898024\pi$
$854$	−1.81806			−0.0622126
$855$	−1.42270	−	6.74040i	−0.0486554	−	0.230517i
$856$	12.9428			0.442376
$857$	15.6631	+	27.1292i	0.535040	+	0.926717i	0.999161	+	0.0409451i	$0.0130369\pi$
$857$	15.6631	+	27.1292i	0.535040	+	0.926717i	−0.464121	+	0.885772i	$0.653630\pi$
$858$	−0.966208	+	1.19143i	−0.0329858	+	0.0406749i
$859$	25.1947	−	43.6384i	0.859631	−	1.48892i	−0.0126501	−	0.999920i	$-0.504027\pi$
$859$	25.1947	−	43.6384i	0.859631	−	1.48892i	0.872281	−	0.489005i	$-0.162640\pi$
$860$	2.55515	−	4.42566i	0.0871300	−	0.150914i
$861$	−6.30834	−	16.4688i	−0.214988	−	0.561255i
$862$	3.50108	+	6.06405i	0.119247	+	0.206542i
$863$	1.13268			0.0385568			0.0192784	−	0.999814i	$-0.493863\pi$
$863$	1.13268			0.0385568			0.0192784	+	0.999814i	$0.493863\pi$
$864$	12.0482	−	7.78768i	0.409886	−	0.264942i
$865$	0.298791			0.0101592
$866$	−1.46402	−	2.53575i	−0.0497494	−	0.0861684i
$867$	−19.3320	−	50.4689i	−0.656550	−	1.71401i
$868$	−1.61273	+	2.79332i	−0.0547395	+	0.0948115i
$869$	13.6621	−	23.6635i	0.463456	−	0.802729i
$870$	0.0737316	−	0.0909187i	0.00249974	−	0.00308243i
$871$	−1.75404	−	3.03809i	−0.0594334	−	0.102942i
$872$	1.19097			0.0403313
$873$	20.4428	+	6.67443i	0.691885	+	0.225895i
$874$	2.60301			0.0880481
$875$	−5.08414	−	8.80598i	−0.171875	−	0.297696i
$876$	−50.3435	−	8.01033i	−1.70095	−	0.270644i
$877$	13.6969	−	23.7237i	0.462510	−	0.801091i	−0.536575	−	0.843853i	$-0.680282\pi$
$877$	13.6969	−	23.7237i	0.462510	−	0.801091i	0.999085	+	0.0427615i	$0.0136156\pi$
$878$	−0.577690	+	1.00059i	−0.0194961	+	0.0337682i
$879$	−16.0271	−	2.55012i	−0.540580	−	0.0860135i
$880$	8.01135	+	13.8761i	0.270063	+	0.467762i
$881$	1.20929			0.0407420			0.0203710	−	0.999792i	$-0.493515\pi$
$881$	1.20929			0.0407420			0.0203710	+	0.999792i	$0.493515\pi$
$882$	0.533792	−	0.479256i	0.0179737	−	0.0161374i
$883$	−51.0884			−1.71926			−0.859631	−	0.510916i	$-0.829306\pi$
$883$	−51.0884			−1.71926			−0.859631	+	0.510916i	$0.829306\pi$
$884$	−6.74433	−	11.6815i	−0.226836	−	0.392892i
$885$	−3.35649	+	4.13891i	−0.112827	+	0.139128i
$886$	0.148840	−	0.257798i	0.00500038	−	0.00866091i
$887$	20.7878	−	36.0056i	0.697987	−	1.20895i	−0.271176	−	0.962530i	$-0.587413\pi$
$887$	20.7878	−	36.0056i	0.697987	−	1.20895i	0.969163	−	0.246419i	$-0.0792541\pi$
$888$	5.57605	+	14.5570i	0.187120	+	0.488503i
$889$	0.669905	+	1.16031i	0.0224679	+	0.0389155i
$890$	−0.776443			−0.0260264
$891$	30.4899	−	13.4712i	1.02145	−	0.451302i
$892$	44.0183			1.47384
$893$	−5.66182	−	9.80657i	−0.189466	−	0.328164i
$894$	1.64613	+	4.29743i	0.0550547	+	0.143728i
$895$	−8.38727	+	14.5272i	−0.280356	+	0.485590i
$896$	3.55718	−	6.16122i	0.118837	−	0.205832i
$897$	6.11273	−	7.53762i	0.204098	−	0.251674i
$898$	1.05555	+	1.82826i	0.0352240	+	0.0610098i
$899$	0.396990			0.0132404
$900$	−15.6260	+	14.0295i	−0.520867	+	0.467651i
$901$	80.5576			2.68376
$902$	4.50877	+	7.80942i	0.150126	+	0.260025i
$903$	−3.80671	−	0.605698i	−0.126679	−	0.0201564i
$904$	−5.73353	+	9.93077i	−0.190694	+	0.330292i
$905$	0.845958	−	1.46524i	0.0281206	−	0.0487063i
$906$	−5.69506	−	0.906160i	−0.189206	−	0.0301052i
$907$	−17.7255	−	30.7014i	−0.588564	−	1.01942i	−0.994421	−	0.105486i	$-0.966360\pi$
$907$	−17.7255	−	30.7014i	−0.588564	−	1.01942i	0.405857	−	0.913937i	$-0.366973\pi$
$908$	10.2632			0.340596
$909$	−36.4607	−	11.9042i	−1.20933	−	0.394836i
$910$	0.282630			0.00936910
$911$	10.3554	+	17.9361i	0.343090	+	0.594250i	0.985005	−	0.172526i	$-0.0551930\pi$
$911$	10.3554	+	17.9361i	0.343090	+	0.594250i	−0.641915	+	0.766776i	$0.721860\pi$
$912$	−7.75800	+	9.56641i	−0.256893	+	0.316776i
$913$	−12.8571	+	22.2691i	−0.425506	+	0.736998i
$914$	−1.25636	+	2.17609i	−0.0415568	+	0.0719785i
$915$	5.56758	+	14.5349i	0.184059	+	0.480510i
$916$	18.7837	+	32.5343i	0.620631	+	1.07496i
$917$	4.96690			0.164021
$918$	−0.433105	−	8.61572i	−0.0142946	−	0.284361i
$919$	14.3926			0.474768			0.237384	−	0.971416i	$-0.423710\pi$
$919$	14.3926			0.474768			0.237384	+	0.971416i	$0.423710\pi$
$920$	3.12188	+	5.40726i	0.102925	+	0.178272i
$921$	−1.68155	−	4.38992i	−0.0554090	−	0.144653i
$922$	2.69630	−	4.67014i	0.0887981	−	0.153803i
$923$	−4.30150	+	7.45043i	−0.141586	+	0.245234i
$924$	7.85021	−	9.68013i	0.258253	−	0.318453i
$925$	−17.1969	−	29.7858i	−0.565429	−	0.979352i
$926$	−2.48616			−0.0817004
$927$	2.72421	+	12.9066i	0.0894747	+	0.423908i
$928$	−0.660190			−0.0216718
$929$	20.8714	+	36.1503i	0.684769	+	1.18605i	0.973509	+	0.228647i	$0.0734302\pi$
$929$	20.8714	+	36.1503i	0.684769	+	1.18605i	−0.288741	+	0.957407i	$0.593237\pi$
$930$	−0.802616	−	0.127707i	−0.0263188	−	0.00418768i
$931$	−0.971410	+	1.68253i	−0.0318367	+	0.0551427i
$932$	−16.4951	+	28.5703i	−0.540315	+	0.935853i
$933$	−23.9142	−	3.80507i	−0.782917	−	0.124573i
$934$	1.59222	+	2.75780i	0.0520989	+	0.0902379i
$935$	30.3926			0.993945
$936$	−0.584135	−	2.76748i	−0.0190931	−	0.0904581i
$937$	3.17154			0.103610			0.0518048	−	0.998657i	$-0.483503\pi$
$937$	3.17154			0.103610			0.0518048	+	0.998657i	$0.483503\pi$
$938$	−0.419432	−	0.726477i	−0.0136949	−	0.0237203i
$939$	20.7873	−	25.6329i	0.678367	−	0.836497i
$940$	6.69196	−	11.5908i	0.218268	−	0.378050i
$941$	1.61040	−	2.78930i	0.0524976	−	0.0909285i	−0.838582	−	0.544775i	$-0.816615\pi$
$941$	1.61040	−	2.78930i	0.0524976	−	0.0909285i	0.891080	+	0.453846i	$0.149948\pi$
$942$	0.00847130	+	0.0221155i	0.000276010	+	0.000720561i
$943$	−28.5248	−	49.4063i	−0.928894	−	1.60889i
$944$	9.52751			0.310094
$945$	−5.46621	−	2.79987i	−0.177816	−	0.0910799i
$946$	1.97095			0.0640810
$947$	22.6735	+	39.2716i	0.736789	+	1.27616i	0.953934	+	0.300016i	$0.0969922\pi$
$947$	22.6735	+	39.2716i	0.736789	+	1.27616i	−0.217145	+	0.976139i	$0.569675\pi$
$948$	8.88034	+	23.1833i	0.288420	+	0.752960i
$949$	−7.57442	+	13.1193i	−0.245876	+	0.425870i
$950$	−0.836931	+	1.44961i	−0.0271536	+	0.0470315i
$951$	4.38508	−	5.40726i	0.142196	−	0.175343i
$952$	−3.27292	−	5.66886i	−0.106076	−	0.183729i
$953$	−54.2703			−1.75799			−0.878994	−	0.476832i	$-0.841785\pi$
$953$	−54.2703			−1.75799			−0.878994	+	0.476832i	$0.841785\pi$
$954$	7.91260	+	2.58340i	0.256180	+	0.0836408i
$955$	17.8090			0.576287
$956$	16.4029	+	28.4106i	0.530507	+	0.918865i
$957$	−1.51492	−	0.241044i	−0.0489703	−	0.00779183i
$958$	1.73788	−	3.01010i	0.0561483	−	0.0972518i
$959$	−2.16991	+	3.75839i	−0.0700699	+	0.121365i
$960$	−13.4653	−	2.14250i	−0.434589	−	0.0691490i
$961$	14.1219	+	24.4598i	0.455545	+	0.789027i
$962$	2.28263			0.0735950
$963$	−30.6443	+	27.5135i	−0.987500	+	0.886609i
$964$	−52.7390			−1.69861
$965$	4.63788	+	8.03305i	0.149299	+	0.258593i
$966$	1.46169	−	1.80242i	0.0470293	−	0.0579919i
$967$	−12.8295	+	22.2214i	−0.412570	+	0.714593i	−0.995170	−	0.0981667i	$-0.968702\pi$
$967$	−12.8295	+	22.2214i	−0.412570	+	0.714593i	0.582600	+	0.812759i	$0.302036\pi$
$968$	−1.28100	+	2.21875i	−0.0411728	+	0.0713133i
$969$	8.35705	+	21.8172i	0.268467	+	0.700870i
$970$	1.01298	+	1.75454i	0.0325250	+	0.0563349i
$971$	−21.0183			−0.674510			−0.337255	−	0.941413i	$-0.609498\pi$
$971$	−21.0183			−0.674510			−0.337255	+	0.941413i	$0.609498\pi$
$972$	−7.94243	+	29.2256i	−0.254754	+	0.937410i
$973$	−3.94282			−0.126401
$974$	1.56075	+	2.70329i	0.0500096	+	0.0866191i
$975$	2.23229	+	5.82769i	0.0714904	+	0.186635i
$976$	13.9142	−	24.1002i	0.445384	−	0.771427i
$977$	1.04910	−	1.81709i	0.0335637	−	0.0581340i	−0.848756	−	0.528785i	$-0.822648\pi$
$977$	1.04910	−	1.81709i	0.0335637	−	0.0581340i	0.882319	+	0.470651i	$0.155981\pi$
$978$	−0.393423	+	0.485131i	−0.0125803	+	0.0155128i
$979$	5.08740	+	8.81164i	0.162594	+	0.281621i
$980$	−2.29630			−0.0733527
$981$	−2.81982	+	2.53173i	−0.0900301	+	0.0808319i
$982$	−4.62571			−0.147612
$983$	−21.4962	−	37.2325i	−0.685622	−	1.18753i	−0.973241	−	0.229787i	$-0.926197\pi$
$983$	−21.4962	−	37.2325i	−0.685622	−	1.18753i	0.287620	−	0.957745i	$-0.407136\pi$
$984$	−16.4207	−	2.61275i	−0.523472	−	0.0832914i
$985$	−3.95361	+	6.84786i	−0.125973	+	0.218191i
$986$	−0.198495	+	0.343803i	−0.00632137	+	0.0109489i
$987$	−9.96978	−	1.58632i	−0.317341	−	0.0504933i
$988$	1.88727	+	3.26886i	0.0600422	+	0.103996i
$989$	−12.4692			−0.396498
$990$	2.98525	+	0.974661i	0.0948774	+	0.0309768i
$991$	−17.2632			−0.548384			−0.274192	−	0.961675i	$-0.588410\pi$
$991$	−17.2632			−0.548384			−0.274192	+	0.961675i	$0.588410\pi$
$992$	2.29179	+	3.96950i	0.0727644	+	0.126032i
$993$	13.5036	−	16.6513i	0.428523	−	0.528413i
$994$	−1.02859	+	1.78157i	−0.0326249	+	0.0565080i
$995$	11.7837	−	20.4100i	0.373569	−	0.647040i
$996$	−8.35705	−	21.8172i	−0.264803	−	0.691305i
$997$	19.4509	+	33.6899i	0.616016	+	1.06697i	0.990205	+	0.139619i	$0.0445878\pi$
$997$	19.4509	+	33.6899i	0.616016	+	1.06697i	−0.374189	+	0.927352i	$0.622079\pi$
$998$	8.66157			0.274177
$999$	−44.1472	−	22.6129i	−1.39676	−	0.715439i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.2.f.b.22.2	✓	6
3.2	odd	2		189.2.f.a.64.2		6
4.3	odd	2		1008.2.r.k.337.2		6
7.2	even	3		441.2.g.e.67.2		6
7.3	odd	6		441.2.h.b.373.2		6
7.4	even	3		441.2.h.c.373.2		6
7.5	odd	6		441.2.g.d.67.2		6
7.6	odd	2		441.2.f.d.148.2		6
9.2	odd	6		189.2.f.a.127.2		6
9.4	even	3		567.2.a.d.1.2		3
9.5	odd	6		567.2.a.g.1.2		3
9.7	even	3	inner	63.2.f.b.43.2	yes	6
12.11	even	2		3024.2.r.g.1009.3		6
21.2	odd	6		1323.2.g.c.361.2		6
21.5	even	6		1323.2.g.b.361.2		6
21.11	odd	6		1323.2.h.d.226.2		6
21.17	even	6		1323.2.h.e.226.2		6
21.20	even	2		1323.2.f.c.442.2		6
36.7	odd	6		1008.2.r.k.673.2		6
36.11	even	6		3024.2.r.g.2017.3		6
36.23	even	6		9072.2.a.cd.1.1		3
36.31	odd	6		9072.2.a.bq.1.3		3
63.2	odd	6		1323.2.h.d.802.2		6
63.11	odd	6		1323.2.g.c.667.2		6
63.13	odd	6		3969.2.a.m.1.2		3
63.16	even	3		441.2.h.c.214.2		6
63.20	even	6		1323.2.f.c.883.2		6
63.25	even	3		441.2.g.e.79.2		6
63.34	odd	6		441.2.f.d.295.2		6
63.38	even	6		1323.2.g.b.667.2		6
63.41	even	6		3969.2.a.p.1.2		3
63.47	even	6		1323.2.h.e.802.2		6
63.52	odd	6		441.2.g.d.79.2		6
63.61	odd	6		441.2.h.b.214.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.b.22.2	✓	6	1.1	even	1	trivial
63.2.f.b.43.2	yes	6	9.7	even	3	inner
189.2.f.a.64.2		6	3.2	odd	2
189.2.f.a.127.2		6	9.2	odd	6
441.2.f.d.148.2		6	7.6	odd	2
441.2.f.d.295.2		6	63.34	odd	6
441.2.g.d.67.2		6	7.5	odd	6
441.2.g.d.79.2		6	63.52	odd	6
441.2.g.e.67.2		6	7.2	even	3
441.2.g.e.79.2		6	63.25	even	3
441.2.h.b.214.2		6	63.61	odd	6
441.2.h.b.373.2		6	7.3	odd	6
441.2.h.c.214.2		6	63.16	even	3
441.2.h.c.373.2		6	7.4	even	3
567.2.a.d.1.2		3	9.4	even	3
567.2.a.g.1.2		3	9.5	odd	6
1008.2.r.k.337.2		6	4.3	odd	2
1008.2.r.k.673.2		6	36.7	odd	6
1323.2.f.c.442.2		6	21.20	even	2
1323.2.f.c.883.2		6	63.20	even	6
1323.2.g.b.361.2		6	21.5	even	6
1323.2.g.b.667.2		6	63.38	even	6
1323.2.g.c.361.2		6	21.2	odd	6
1323.2.g.c.667.2		6	63.11	odd	6
1323.2.h.d.226.2		6	21.11	odd	6
1323.2.h.d.802.2		6	63.2	odd	6
1323.2.h.e.226.2		6	21.17	even	6
1323.2.h.e.802.2		6	63.47	even	6
3024.2.r.g.1009.3		6	12.11	even	2
3024.2.r.g.2017.3		6	36.11	even	6
3969.2.a.m.1.2		3	63.13	odd	6
3969.2.a.p.1.2		3	63.41	even	6
9072.2.a.bq.1.3		3	36.31	odd	6
9072.2.a.cd.1.1		3	36.23	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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	63.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.119562 + 0.207087i) q^{2} +(-0.619562 - 1.61745i) q^{3} +(0.971410 - 1.68253i) q^{4} +(-0.590972 + 1.02359i) q^{5} +(0.260877 - 0.321688i) q^{6} +(0.500000 + 0.866025i) q^{7} +0.942820 q^{8} +(-2.23229 + 2.00422i) q^{9} -0.282630 q^{10} +(1.85185 + 3.20750i) q^{11} +(-3.32326 - 0.528775i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-0.119562 + 0.207087i) q^{14} +(2.02175 + 0.321688i) q^{15} +(-1.83009 - 3.16982i) q^{16} -6.94282 q^{17} +(-0.681943 - 0.222649i) q^{18} +1.94282 q^{19} +(1.14815 + 1.98866i) q^{20} +(1.09097 - 1.34528i) q^{21} +(-0.442820 + 0.766987i) q^{22} +(2.80150 - 4.85235i) q^{23} +(-0.584135 - 1.52496i) q^{24} +(1.80150 + 3.12030i) q^{25} -0.239123 q^{26} +(4.62476 + 2.36887i) q^{27} +1.94282 q^{28} +(-0.119562 - 0.207087i) q^{29} +(0.175107 + 0.457140i) q^{30} +(-0.830095 + 1.43777i) q^{31} +(1.38044 - 2.39099i) q^{32} +(4.04063 - 4.98251i) q^{33} +(-0.830095 - 1.43777i) q^{34} -1.18194 q^{35} +(1.20370 + 5.70281i) q^{36} -9.54583 q^{37} +(0.232287 + 0.402332i) q^{38} +(1.71053 + 0.272169i) q^{39} +(-0.557180 + 0.965064i) q^{40} +(5.09097 - 8.81782i) q^{41} +(0.409028 + 0.0650819i) q^{42} +(-1.11273 - 1.92730i) q^{43} +7.19562 q^{44} +(-0.732287 - 3.46939i) q^{45} +1.33981 q^{46} +(-2.91423 - 5.04759i) q^{47} +(-3.99316 + 4.92398i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.430782 + 0.746136i) q^{50} +(4.30150 + 11.2297i) q^{51} +(0.971410 + 1.68253i) q^{52} -11.6030 q^{53} +(0.0623817 + 1.24095i) q^{54} -4.37756 q^{55} +(0.471410 + 0.816506i) q^{56} +(-1.20370 - 3.14241i) q^{57} +(0.0285900 - 0.0495193i) q^{58} +(-1.30150 + 2.25427i) q^{59} +(2.50520 - 3.08917i) q^{60} +(3.80150 + 6.58440i) q^{61} -0.396990 q^{62} +(-2.85185 - 0.931107i) q^{63} -6.66019 q^{64} +(-0.590972 - 1.02359i) q^{65} +(1.51492 + 0.241044i) q^{66} +(-1.75404 + 3.03809i) q^{67} +(-6.74433 + 11.6815i) q^{68} +(-9.58414 - 1.52496i) q^{69} +(-0.141315 - 0.244765i) q^{70} +8.60301 q^{71} +(-2.10464 + 1.88962i) q^{72} +15.1488 q^{73} +(-1.14132 - 1.97682i) q^{74} +(3.93078 - 4.84706i) q^{75} +(1.88727 - 3.26886i) q^{76} +(-1.85185 + 3.20750i) q^{77} +(0.148152 + 0.386770i) q^{78} +(-3.68878 - 6.38915i) q^{79} +4.32614 q^{80} +(0.966208 - 8.94799i) q^{81} +2.43474 q^{82} +(3.47141 + 6.01266i) q^{83} +(-1.20370 - 3.14241i) q^{84} +(4.10301 - 7.10662i) q^{85} +(0.266078 - 0.460861i) q^{86} +(-0.260877 + 0.321688i) q^{87} +(1.74596 + 3.02409i) q^{88} +2.74720 q^{89} +(0.630912 - 0.566453i) q^{90} -1.00000 q^{91} +(-5.44282 - 9.42724i) q^{92} +(2.83981 + 0.451852i) q^{93} +(0.696860 - 1.20700i) q^{94} +(-1.14815 + 1.98866i) q^{95} +(-4.72257 - 0.751424i) q^{96} +(-3.58414 - 6.20790i) q^{97} -0.239123 q^{98} +(-10.5624 - 3.44854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 4 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} + 3 q^{7} - 12 q^{8} - 4 q^{9} + 2 q^{11} - 2 q^{12} - 3 q^{13} - q^{14} + 11 q^{15} - 3 q^{16} - 24 q^{17} + 13 q^{18} - 6 q^{19} + 16 q^{20} - 2 q^{21}+ \cdots - 46 q^{99}+O(q^{100}) \) 6 * q + q^2 - 4 * q^3 - 3 * q^4 + 5 * q^5 + q^6 + 3 * q^7 - 12 * q^8 - 4 * q^9 + 2 * q^11 - 2 * q^12 - 3 * q^13 - q^14 + 11 * q^15 - 3 * q^16 - 24 * q^17 + 13 * q^18 - 6 * q^19 + 16 * q^20 - 2 * q^21 + 15 * q^22 + 15 * q^24 - 6 * q^25 - 2 * q^26 - 7 * q^27 - 6 * q^28 - q^29 - 26 * q^30 + 3 * q^31 + 8 * q^32 + 8 * q^33 + 3 * q^34 + 10 * q^35 - 11 * q^36 - 6 * q^37 - 8 * q^38 + 2 * q^39 - 21 * q^40 + 22 * q^41 + 11 * q^42 + 3 * q^43 + 46 * q^44 + 5 * q^45 + 24 * q^46 + 9 * q^47 - 14 * q^48 - 3 * q^49 - 10 * q^50 + 9 * q^51 - 3 * q^52 - 36 * q^53 - 17 * q^54 - 12 * q^55 - 6 * q^56 + 11 * q^57 + 9 * q^58 + 9 * q^59 - 20 * q^60 + 6 * q^61 - 36 * q^62 - 8 * q^63 - 24 * q^64 + 5 * q^65 - 2 * q^66 - 6 * q^68 - 39 * q^69 + 18 * q^71 - 24 * q^72 + 6 * q^73 - 6 * q^74 + 31 * q^75 + 21 * q^76 - 2 * q^77 + 10 * q^78 - 15 * q^79 + 22 * q^80 + 32 * q^81 + 18 * q^82 + 12 * q^83 + 11 * q^84 - 9 * q^85 - 34 * q^86 - q^87 + 21 * q^88 - 4 * q^89 + 73 * q^90 - 6 * q^91 - 15 * q^92 + 33 * q^93 - 24 * q^94 - 16 * q^95 + 5 * q^96 - 3 * q^97 - 2 * q^98 - 46 * q^99

Introduction

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