LMFDB - Embedded newform 630.2.j.k.421.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(211,630)]

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([2, 0, 0]))

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

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

chi := DirichletCharacter("630.211");

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.j (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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			421.1
Root			$-1.62241 + 0.606458i$ of defining polynomial
Character	$\chi$	$=$	630.421
Dual form			630.2.j.k.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.62241 + 0.606458i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.285997 - 1.70828i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(2.26442 - 1.96784i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.62241 + 0.606458i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.285997 - 1.70828i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(2.26442 - 1.96784i) q^{9} +1.00000 q^{10} +(0.285997 - 0.495361i) q^{11} +(1.33641 + 1.10182i) q^{12} +(0.214003 + 0.370665i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(1.33641 + 1.10182i) q^{15} +(-0.500000 + 0.866025i) q^{16} +5.67282 q^{17} +(0.571993 + 2.94497i) q^{18} -4.81681 q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.285997 - 1.70828i) q^{21} +(0.285997 + 0.495361i) q^{22} +(3.88683 + 6.73218i) q^{23} +(-1.62241 + 0.606458i) q^{24} +(-0.500000 + 0.866025i) q^{25} -0.428007 q^{26} +(-2.48040 + 4.56592i) q^{27} +1.00000 q^{28} +(-4.45882 + 7.72290i) q^{29} +(-1.62241 + 0.606458i) q^{30} +(-4.24482 - 7.35224i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.163588 + 0.977122i) q^{33} +(-2.83641 + 4.91281i) q^{34} +1.00000 q^{35} +(-2.83641 - 0.977122i) q^{36} +5.95684 q^{37} +(2.40841 - 4.17148i) q^{38} +(-0.571993 - 0.471586i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(5.63164 + 9.75429i) q^{41} +(1.33641 + 1.10182i) q^{42} +(-3.07199 + 5.32085i) q^{43} -0.571993 q^{44} +(-2.83641 - 0.977122i) q^{45} -7.77365 q^{46} +(-5.67282 + 9.82562i) q^{47} +(0.285997 - 1.70828i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-9.20364 + 3.44033i) q^{51} +(0.214003 - 0.370665i) q^{52} -5.10083 q^{53} +(-2.71400 - 4.43105i) q^{54} -0.571993 q^{55} +(-0.500000 + 0.866025i) q^{56} +(7.81483 - 2.92119i) q^{57} +(-4.45882 - 7.72290i) q^{58} +(-3.16359 - 5.47950i) q^{59} +(0.285997 - 1.70828i) q^{60} +(2.12241 - 3.67612i) q^{61} +8.48963 q^{62} +(0.571993 + 2.94497i) q^{63} +1.00000 q^{64} +(0.214003 - 0.370665i) q^{65} +(-0.764419 - 0.630233i) q^{66} +(5.65322 + 9.79167i) q^{67} +(-2.83641 - 4.91281i) q^{68} +(-10.3888 - 8.56515i) q^{69} +(-0.500000 + 0.866025i) q^{70} +15.0224 q^{71} +(2.26442 - 1.96784i) q^{72} -6.34565 q^{73} +(-2.97842 + 5.15878i) q^{74} +(0.285997 - 1.70828i) q^{75} +(2.40841 + 4.17148i) q^{76} +(0.285997 + 0.495361i) q^{77} +(0.694402 - 0.259568i) q^{78} +(-3.67282 + 6.36152i) q^{79} +1.00000 q^{80} +(1.25518 - 8.91204i) q^{81} -11.2633 q^{82} +(-5.10083 + 8.83490i) q^{83} +(-1.62241 + 0.606458i) q^{84} +(-2.83641 - 4.91281i) q^{85} +(-3.07199 - 5.32085i) q^{86} +(2.55042 - 15.2338i) q^{87} +(0.285997 - 0.495361i) q^{88} +8.28797 q^{89} +(2.26442 - 1.96784i) q^{90} -0.428007 q^{91} +(3.88683 - 6.73218i) q^{92} +(11.3456 + 9.35403i) q^{93} +(-5.67282 - 9.82562i) q^{94} +(2.40841 + 4.17148i) q^{95} +(1.33641 + 1.10182i) q^{96} +(-2.74482 + 4.75416i) q^{97} +1.00000 q^{98} +(-0.327176 - 1.68450i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + q^{3} - 3 q^{4} - 3 q^{5} + q^{6} - 3 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 + q^3 - 3 * q^4 - 3 * q^5 + q^6 - 3 * q^7 + 6 * q^8 + 5 * q^9	\( 6 q - 3 q^{2} + q^{3} - 3 q^{4} - 3 q^{5} + q^{6} - 3 q^{7} + 6 q^{8} + 5 q^{9} + 6 q^{10} + q^{11} - 2 q^{12} + 2 q^{13} - 3 q^{14} - 2 q^{15} - 3 q^{16} + 14 q^{17} + 2 q^{18} - 6 q^{19} - 3 q^{20} + q^{21} + q^{22} + 4 q^{23} + q^{24} - 3 q^{25} - 4 q^{26} - 2 q^{27} + 6 q^{28} - 6 q^{29} + q^{30} - 4 q^{31} - 3 q^{32} - 11 q^{33} - 7 q^{34} + 6 q^{35} - 7 q^{36} + 20 q^{37} + 3 q^{38} - 2 q^{39} - 3 q^{40} - 7 q^{41} - 2 q^{42} - 17 q^{43} - 2 q^{44} - 7 q^{45} - 8 q^{46} - 14 q^{47} + q^{48} - 3 q^{49} - 3 q^{50} - 13 q^{51} + 2 q^{52} - 12 q^{53} - 17 q^{54} - 2 q^{55} - 3 q^{56} + 29 q^{57} - 6 q^{58} - 29 q^{59} + q^{60} + 2 q^{61} + 8 q^{62} + 2 q^{63} + 6 q^{64} + 2 q^{65} + 4 q^{66} + q^{67} - 7 q^{68} - 38 q^{69} - 3 q^{70} + 20 q^{71} + 5 q^{72} + 2 q^{73} - 10 q^{74} + q^{75} + 3 q^{76} + q^{77} - 8 q^{78} - 2 q^{79} + 6 q^{80} + 29 q^{81} + 14 q^{82} - 12 q^{83} + q^{84} - 7 q^{85} - 17 q^{86} + 6 q^{87} + q^{88} + 44 q^{89} + 5 q^{90} - 4 q^{91} + 4 q^{92} + 28 q^{93} - 14 q^{94} + 3 q^{95} - 2 q^{96} + 5 q^{97} + 6 q^{98} - 22 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + q^3 - 3 * q^4 - 3 * q^5 + q^6 - 3 * q^7 + 6 * q^8 + 5 * q^9 + 6 * q^10 + q^11 - 2 * q^12 + 2 * q^13 - 3 * q^14 - 2 * q^15 - 3 * q^16 + 14 * q^17 + 2 * q^18 - 6 * q^19 - 3 * q^20 + q^21 + q^22 + 4 * q^23 + q^24 - 3 * q^25 - 4 * q^26 - 2 * q^27 + 6 * q^28 - 6 * q^29 + q^30 - 4 * q^31 - 3 * q^32 - 11 * q^33 - 7 * q^34 + 6 * q^35 - 7 * q^36 + 20 * q^37 + 3 * q^38 - 2 * q^39 - 3 * q^40 - 7 * q^41 - 2 * q^42 - 17 * q^43 - 2 * q^44 - 7 * q^45 - 8 * q^46 - 14 * q^47 + q^48 - 3 * q^49 - 3 * q^50 - 13 * q^51 + 2 * q^52 - 12 * q^53 - 17 * q^54 - 2 * q^55 - 3 * q^56 + 29 * q^57 - 6 * q^58 - 29 * q^59 + q^60 + 2 * q^61 + 8 * q^62 + 2 * q^63 + 6 * q^64 + 2 * q^65 + 4 * q^66 + q^67 - 7 * q^68 - 38 * q^69 - 3 * q^70 + 20 * q^71 + 5 * q^72 + 2 * q^73 - 10 * q^74 + q^75 + 3 * q^76 + q^77 - 8 * q^78 - 2 * q^79 + 6 * q^80 + 29 * q^81 + 14 * q^82 - 12 * q^83 + q^84 - 7 * q^85 - 17 * q^86 + 6 * q^87 + q^88 + 44 * q^89 + 5 * q^90 - 4 * q^91 + 4 * q^92 + 28 * q^93 - 14 * q^94 + 3 * q^95 - 2 * q^96 + 5 * q^97 + 6 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−1.62241	+	0.606458i	−0.936698	+	0.350138i
$3$	−1.62241	+	0.606458i	−0.936698	+	0.350138i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	0.285997	−	1.70828i	0.116758	−	0.697401i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	1.00000			0.353553
$9$	2.26442	−	1.96784i	0.754806	−	0.655948i
$10$	1.00000			0.316228
$11$	0.285997	−	0.495361i	0.0862312	−	0.149357i	−0.819684	−	0.572816i	$-0.805851\pi$
$11$	0.285997	−	0.495361i	0.0862312	−	0.149357i	0.905915	+	0.423459i	$0.139184\pi$
$12$	1.33641	+	1.10182i	0.385789	+	0.318068i
$13$	0.214003	+	0.370665i	0.0593539	+	0.102804i	0.894176	−	0.447717i	$-0.147763\pi$
$13$	0.214003	+	0.370665i	0.0593539	+	0.102804i	−0.834822	+	0.550520i	$0.814429\pi$
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$	1.33641	+	1.10182i	0.345060	+	0.284488i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	5.67282			1.37586			0.687931	−	0.725776i	$-0.258519\pi$
$17$	5.67282			1.37586			0.687931	+	0.725776i	$0.258519\pi$
$18$	0.571993	+	2.94497i	0.134820	+	0.694135i
$19$	−4.81681			−1.10505			−0.552526	−	0.833496i	$-0.686336\pi$
$19$	−4.81681			−1.10505			−0.552526	+	0.833496i	$0.686336\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	0.285997	−	1.70828i	0.0624096	−	0.372776i
$22$	0.285997	+	0.495361i	0.0609747	+	0.105611i
$23$	3.88683	+	6.73218i	0.810459	+	1.40376i	0.912543	+	0.408981i	$0.134116\pi$
$23$	3.88683	+	6.73218i	0.810459	+	1.40376i	−0.102083	+	0.994776i	$0.532551\pi$
$24$	−1.62241	+	0.606458i	−0.331173	+	0.123793i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.428007			−0.0839390
$27$	−2.48040	+	4.56592i	−0.477353	+	0.878712i
$28$	1.00000			0.188982
$29$	−4.45882	+	7.72290i	−0.827982	+	1.43411i	0.0716365	+	0.997431i	$0.477178\pi$
$29$	−4.45882	+	7.72290i	−0.827982	+	1.43411i	−0.899619	+	0.436676i	$0.856155\pi$
$30$	−1.62241	+	0.606458i	−0.296210	+	0.110723i
$31$	−4.24482	−	7.35224i	−0.762392	−	1.32050i	−0.941615	−	0.336693i	$-0.890692\pi$
$31$	−4.24482	−	7.35224i	−0.762392	−	1.32050i	0.179223	−	0.983808i	$-0.442642\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.163588	+	0.977122i	−0.0284770	+	0.170095i
$34$	−2.83641	+	4.91281i	−0.486441	+	0.842540i
$35$	1.00000			0.169031
$36$	−2.83641	−	0.977122i	−0.472735	−	0.162854i
$37$	5.95684			0.979299			0.489650	−	0.871919i	$-0.337125\pi$
$37$	5.95684			0.979299			0.489650	+	0.871919i	$0.337125\pi$
$38$	2.40841	−	4.17148i	0.390695	−	0.676703i
$39$	−0.571993	−	0.471586i	−0.0915922	−	0.0755141i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	5.63164	+	9.75429i	0.879515	+	1.52336i	0.851874	+	0.523747i	$0.175466\pi$
$41$	5.63164	+	9.75429i	0.879515	+	1.52336i	0.0276411	+	0.999618i	$0.491200\pi$
$42$	1.33641	+	1.10182i	0.206213	+	0.170014i
$43$	−3.07199	+	5.32085i	−0.468475	+	0.811422i	−0.999351	−	0.0360276i	$-0.988530\pi$
$43$	−3.07199	+	5.32085i	−0.468475	+	0.811422i	0.530876	+	0.847449i	$0.321863\pi$
$44$	−0.571993			−0.0862312
$45$	−2.83641	−	0.977122i	−0.422827	−	0.145661i
$46$	−7.77365			−1.14616
$47$	−5.67282	+	9.82562i	−0.827466	+	1.43321i	0.0725533	+	0.997365i	$0.476885\pi$
$47$	−5.67282	+	9.82562i	−0.827466	+	1.43321i	−0.900020	+	0.435849i	$0.856448\pi$
$48$	0.285997	−	1.70828i	0.0412801	−	0.246568i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−9.20364	+	3.44033i	−1.28877	+	0.481742i
$52$	0.214003	−	0.370665i	0.0296769	−	0.0514019i
$53$	−5.10083			−0.700653			−0.350326	−	0.936628i	$-0.613929\pi$
$53$	−5.10083			−0.700653			−0.350326	+	0.936628i	$0.613929\pi$
$54$	−2.71400	−	4.43105i	−0.369329	−	0.602989i
$55$	−0.571993			−0.0771276
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$	7.81483	−	2.92119i	1.03510	−	0.386921i
$58$	−4.45882	−	7.72290i	−0.585472	−	1.01407i
$59$	−3.16359	−	5.47950i	−0.411864	−	0.713370i	0.583230	−	0.812307i	$-0.301789\pi$
$59$	−3.16359	−	5.47950i	−0.411864	−	0.713370i	−0.995094	+	0.0989379i	$0.968455\pi$
$60$	0.285997	−	1.70828i	0.0369220	−	0.220537i
$61$	2.12241	−	3.67612i	0.271747	−	0.470679i	−0.697563	−	0.716524i	$-0.745732\pi$
$61$	2.12241	−	3.67612i	0.271747	−	0.470679i	0.969309	+	0.245845i	$0.0790654\pi$
$62$	8.48963			1.07818
$63$	0.571993	+	2.94497i	0.0720644	+	0.371031i
$64$	1.00000			0.125000
$65$	0.214003	−	0.370665i	0.0265439	−	0.0459753i
$66$	−0.764419	−	0.630233i	−0.0940934	−	0.0775763i
$67$	5.65322	+	9.79167i	0.690651	+	1.19624i	0.971625	+	0.236527i	$0.0760092\pi$
$67$	5.65322	+	9.79167i	0.690651	+	1.19624i	−0.280974	+	0.959715i	$0.590657\pi$
$68$	−2.83641	−	4.91281i	−0.343965	−	0.595766i
$69$	−10.3888	−	8.56515i	−1.25066	−	1.03112i
$70$	−0.500000	+	0.866025i	−0.0597614	+	0.103510i
$71$	15.0224			1.78283			0.891417	−	0.453184i	$-0.149712\pi$
$71$	15.0224			1.78283			0.891417	+	0.453184i	$0.149712\pi$
$72$	2.26442	−	1.96784i	0.266864	−	0.231913i
$73$	−6.34565			−0.742702			−0.371351	−	0.928493i	$-0.621105\pi$
$73$	−6.34565			−0.742702			−0.371351	+	0.928493i	$0.621105\pi$
$74$	−2.97842	+	5.15878i	−0.346235	+	0.599696i
$75$	0.285997	−	1.70828i	0.0330240	−	0.197255i
$76$	2.40841	+	4.17148i	0.276263	+	0.478502i
$77$	0.285997	+	0.495361i	0.0325923	+	0.0564516i
$78$	0.694402	−	0.259568i	0.0786255	−	0.0293903i
$79$	−3.67282	+	6.36152i	−0.413225	+	0.715727i	−0.995240	−	0.0974512i	$-0.968931\pi$
$79$	−3.67282	+	6.36152i	−0.413225	+	0.715727i	0.582015	+	0.813178i	$0.302264\pi$
$80$	1.00000			0.111803
$81$	1.25518	−	8.91204i	0.139465	−	0.990227i
$82$	−11.2633			−1.24382
$83$	−5.10083	+	8.83490i	−0.559889	+	0.969756i	0.437616	+	0.899162i	$0.355823\pi$
$83$	−5.10083	+	8.83490i	−0.559889	+	0.969756i	−0.997505	+	0.0705941i	$0.977510\pi$
$84$	−1.62241	+	0.606458i	−0.177019	+	0.0661699i
$85$	−2.83641	−	4.91281i	−0.307652	−	0.532869i
$86$	−3.07199	−	5.32085i	−0.331262	−	0.573762i
$87$	2.55042	−	15.2338i	0.273433	−	1.63323i
$88$	0.285997	−	0.495361i	0.0304873	−	0.0528056i
$89$	8.28797			0.878523			0.439262	−	0.898359i	$-0.355240\pi$
$89$	8.28797			0.878523			0.439262	+	0.898359i	$0.355240\pi$
$90$	2.26442	−	1.96784i	0.238691	−	0.207429i
$91$	−0.428007			−0.0448673
$92$	3.88683	−	6.73218i	0.405230	−	0.701878i
$93$	11.3456	+	9.35403i	1.17649	+	0.969968i
$94$	−5.67282	−	9.82562i	−0.585107	−	1.01344i
$95$	2.40841	+	4.17148i	0.247097	+	0.427985i
$96$	1.33641	+	1.10182i	0.136397	+	0.112454i
$97$	−2.74482	+	4.75416i	−0.278694	+	0.482712i	−0.971060	−	0.238834i	$-0.923235\pi$
$97$	−2.74482	+	4.75416i	−0.278694	+	0.482712i	0.692366	+	0.721546i	$0.256568\pi$
$98$	1.00000			0.101015
$99$	−0.327176	−	1.68450i	−0.0328825	−	0.169299i
$100$	1.00000			0.100000
$101$	1.71598	−	2.97216i	0.170746	−	0.295741i	−0.767935	−	0.640528i	$-0.778715\pi$
$101$	1.71598	−	2.97216i	0.170746	−	0.295741i	0.938681	+	0.344787i	$0.112049\pi$
$102$	1.62241	−	9.69075i	0.160642	−	0.959527i
$103$	−4.36723	−	7.56426i	−0.430316	−	0.745328i	0.566585	−	0.824003i	$-0.308264\pi$
$103$	−4.36723	−	7.56426i	−0.430316	−	0.745328i	−0.996900	+	0.0786751i	$0.974931\pi$
$104$	0.214003	+	0.370665i	0.0209848	+	0.0363467i
$105$	−1.62241	+	0.606458i	−0.158331	+	0.0591842i
$106$	2.55042	−	4.41745i	0.247718	−	0.429061i
$107$	14.7305			1.42405			0.712025	−	0.702154i	$-0.247778\pi$
$107$	14.7305			1.42405			0.712025	+	0.702154i	$0.247778\pi$
$108$	5.19440	−	0.134872i	0.499832	−	0.0129781i
$109$	3.00395			0.287727			0.143863	−	0.989598i	$-0.454047\pi$
$109$	3.00395			0.287727			0.143863	+	0.989598i	$0.454047\pi$
$110$	0.285997	−	0.495361i	0.0272687	−	0.0472308i
$111$	−9.66443	+	3.61257i	−0.917307	+	0.342890i
$112$	−0.500000	−	0.866025i	−0.0472456	−	0.0818317i
$113$	3.05239	+	5.28690i	0.287145	+	0.497349i	0.973127	−	0.230269i	$-0.0739606\pi$
$113$	3.05239	+	5.28690i	0.287145	+	0.497349i	−0.685982	+	0.727618i	$0.740627\pi$
$114$	−1.37759	+	8.22844i	−0.129023	+	0.770664i
$115$	3.88683	−	6.73218i	0.362448	−	0.627779i
$116$	8.91764			0.827982
$117$	1.21400	+	0.418215i	0.112235	+	0.0386640i
$118$	6.32718			0.582464
$119$	−2.83641	+	4.91281i	−0.260013	+	0.450357i
$120$	1.33641	+	1.10182i	0.121997	+	0.100582i
$121$	5.33641	+	9.24294i	0.485128	+	0.840267i
$122$	2.12241	+	3.67612i	0.192154	+	0.332820i
$123$	−15.0524	−	12.4101i	−1.35723	−	1.11898i
$124$	−4.24482	+	7.35224i	−0.381196	+	0.660251i
$125$	1.00000			0.0894427
$126$	−2.83641	−	0.977122i	−0.252688	−	0.0870490i
$127$	12.0616			1.07030			0.535148	−	0.844758i	$-0.320256\pi$
$127$	12.0616			1.07030			0.535148	+	0.844758i	$0.320256\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	1.75716	−	10.4956i	0.154709	−	0.924088i
$130$	0.214003	+	0.370665i	0.0187693	+	0.0325094i
$131$	1.00924	+	1.74805i	0.0881773	+	0.152728i	0.906741	−	0.421689i	$-0.138562\pi$
$131$	1.00924	+	1.74805i	0.0881773	+	0.152728i	−0.818563	+	0.574416i	$0.805229\pi$
$132$	0.928007	−	0.346890i	0.0807726	−	0.0301929i
$133$	2.40841	−	4.17148i	0.208835	−	0.361713i
$134$	−11.3064			−0.976728
$135$	5.19440	−	0.134872i	0.447063	−	0.0116079i
$136$	5.67282			0.486441
$137$	10.6801	−	18.4984i	0.912461	−	1.58043i	0.101884	−	0.994796i	$-0.467513\pi$
$137$	10.6801	−	18.4984i	0.912461	−	1.58043i	0.810577	−	0.585633i	$-0.199154\pi$
$138$	12.6120	−	4.71439i	1.07361	−	0.401316i
$139$	6.41764	+	11.1157i	0.544337	+	0.942820i	0.998648	+	0.0519766i	$0.0165521\pi$
$139$	6.41764	+	11.1157i	0.544337	+	0.942820i	−0.454311	+	0.890843i	$0.650115\pi$
$140$	−0.500000	−	0.866025i	−0.0422577	−	0.0731925i
$141$	3.24482	−	19.3815i	0.273263	−	1.63222i
$142$	−7.51121	+	13.0098i	−0.630327	+	1.09176i
$143$	0.244817			0.0204726
$144$	0.571993	+	2.94497i	0.0476661	+	0.245414i
$145$	8.91764			0.740570
$146$	3.17282	−	5.49549i	0.262585	−	0.454810i
$147$	1.33641	+	1.10182i	0.110225	+	0.0908764i
$148$	−2.97842	−	5.15878i	−0.244825	−	0.424049i
$149$	−2.10083	−	3.63875i	−0.172107	−	0.298098i	0.767049	−	0.641588i	$-0.221724\pi$
$149$	−2.10083	−	3.63875i	−0.172107	−	0.298098i	−0.939156	+	0.343490i	$0.888391\pi$
$150$	1.33641	+	1.10182i	0.109118	+	0.0899631i
$151$	−1.81681	+	3.14681i	−0.147850	+	0.256084i	−0.930433	−	0.366463i	$-0.880569\pi$
$151$	−1.81681	+	3.14681i	−0.147850	+	0.256084i	0.782583	+	0.622547i	$0.213902\pi$
$152$	−4.81681			−0.390695
$153$	12.8456	−	11.1632i	1.03851	−	0.902494i
$154$	−0.571993			−0.0460925
$155$	−4.24482	+	7.35224i	−0.340952	+	0.590546i
$156$	−0.122408	+	0.731154i	−0.00980052	+	0.0585391i
$157$	2.17480	+	3.76686i	0.173568	+	0.300629i	0.939665	−	0.342097i	$-0.111137\pi$
$157$	2.17480	+	3.76686i	0.173568	+	0.300629i	−0.766097	+	0.642725i	$0.777804\pi$
$158$	−3.67282	−	6.36152i	−0.292194	−	0.506095i
$159$	8.27563	−	3.09344i	0.656300	−	0.245326i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−7.77365			−0.612650
$162$	7.09046	+	5.54304i	0.557079	+	0.435503i
$163$	−10.1048			−0.791468			−0.395734	−	0.918365i	$-0.629510\pi$
$163$	−10.1048			−0.791468			−0.395734	+	0.918365i	$0.629510\pi$
$164$	5.63164	−	9.75429i	0.439758	−	0.761682i
$165$	0.928007	−	0.346890i	0.0722452	−	0.0270053i
$166$	−5.10083	−	8.83490i	−0.395901	−	0.685721i
$167$	−3.69440	−	6.39889i	−0.285881	−	0.495161i	0.686941	−	0.726713i	$-0.258953\pi$
$167$	−3.69440	−	6.39889i	−0.285881	−	0.495161i	−0.972823	+	0.231552i	$0.925620\pi$
$168$	0.285997	−	1.70828i	0.0220651	−	0.131796i
$169$	6.40841	−	11.0997i	0.492954	−	0.853822i
$170$	5.67282			0.435086
$171$	−10.9073	+	9.47873i	−0.834100	+	0.724857i
$172$	6.14399			0.468475
$173$	−0.244817	+	0.424035i	−0.0186131	+	0.0322388i	−0.875182	−	0.483794i	$-0.839258\pi$
$173$	−0.244817	+	0.424035i	−0.0186131	+	0.0322388i	0.856569	+	0.516033i	$0.172592\pi$
$174$	11.9176	+	9.82562i	0.903474	+	0.744878i
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$	0.285997	+	0.495361i	0.0215578	+	0.0373392i
$177$	8.45571	+	6.97140i	0.635570	+	0.524002i
$178$	−4.14399	+	7.17760i	−0.310605	+	0.537984i
$179$	−2.67282			−0.199776			−0.0998881	−	0.994999i	$-0.531848\pi$
$179$	−2.67282			−0.199776			−0.0998881	+	0.994999i	$0.531848\pi$
$180$	0.571993	+	2.94497i	0.0426339	+	0.219505i
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	0.214003	−	0.370665i	0.0158630	−	0.0274755i
$183$	−1.21400	+	7.25132i	−0.0897417	+	0.536033i
$184$	3.88683	+	6.73218i	0.286541	+	0.496303i
$185$	−2.97842	−	5.15878i	−0.218978	−	0.379281i
$186$	−13.7737	+	5.14860i	−1.00993	+	0.377514i
$187$	1.62241	−	2.81009i	0.118642	−	0.205494i
$188$	11.3456			0.827466
$189$	−2.71400	−	4.43105i	−0.197415	−	0.322311i
$190$	−4.81681			−0.349448
$191$	−5.42801	+	9.40158i	−0.392757	+	0.680275i	−0.992812	−	0.119684i	$-0.961812\pi$
$191$	−5.42801	+	9.40158i	−0.392757	+	0.680275i	0.600055	+	0.799959i	$0.295145\pi$
$192$	−1.62241	+	0.606458i	−0.117087	+	0.0437673i
$193$	1.43922	+	2.49280i	0.103597	+	0.179436i	0.913164	−	0.407592i	$-0.133631\pi$
$193$	1.43922	+	2.49280i	0.103597	+	0.179436i	−0.809567	+	0.587027i	$0.800298\pi$
$194$	−2.74482	−	4.75416i	−0.197066	−	0.341329i
$195$	−0.122408	+	0.731154i	−0.00876585	+	0.0523590i
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	−18.5697			−1.32304			−0.661519	−	0.749928i	$-0.730088\pi$
$197$	−18.5697			−1.32304			−0.661519	+	0.749928i	$0.730088\pi$
$198$	1.62241	+	0.558907i	0.115300	+	0.0397198i
$199$	−15.3210			−1.08607			−0.543037	−	0.839709i	$-0.682726\pi$
$199$	−15.3210			−1.08607			−0.543037	+	0.839709i	$0.682726\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	−15.1101	−	12.4576i	−1.06578	−	0.878695i
$202$	1.71598	+	2.97216i	0.120736	+	0.209121i
$203$	−4.45882	−	7.72290i	−0.312948	−	0.542042i
$204$	7.58123	+	6.25042i	0.530792	+	0.437617i
$205$	5.63164	−	9.75429i	0.393331	−	0.681269i
$206$	8.73445			0.608558
$207$	22.0493	+	7.59581i	1.53253	+	0.527945i
$208$	−0.428007			−0.0296769
$209$	−1.37759	+	2.38606i	−0.0952900	+	0.165047i
$210$	0.285997	−	1.70828i	0.0197356	−	0.117882i
$211$	−5.63362	−	9.75772i	−0.387834	−	0.671749i	0.604324	−	0.796739i	$-0.293443\pi$
$211$	−5.63362	−	9.75772i	−0.387834	−	0.671749i	−0.992158	+	0.124990i	$0.960110\pi$
$212$	2.55042	+	4.41745i	0.175163	+	0.303392i
$213$	−24.3725	+	9.11046i	−1.66998	+	0.624239i
$214$	−7.36525	+	12.7570i	−0.503478	+	0.872050i
$215$	6.14399			0.419016
$216$	−2.48040	+	4.56592i	−0.168770	+	0.310671i
$217$	8.48963			0.576314
$218$	−1.50198	+	2.60150i	−0.101727	+	0.176196i
$219$	10.2952	−	3.84837i	0.695687	−	0.260048i
$220$	0.285997	+	0.495361i	0.0192819	+	0.0333972i
$221$	1.21400	+	2.10272i	0.0816627	+	0.141444i
$222$	1.70364	−	10.1759i	0.114341	−	0.682964i
$223$	−3.22324	+	5.58281i	−0.215844	+	0.373853i	−0.953533	−	0.301288i	$-0.902584\pi$
$223$	−3.22324	+	5.58281i	−0.215844	+	0.373853i	0.737689	+	0.675140i	$0.235917\pi$
$224$	1.00000			0.0668153
$225$	0.571993	+	2.94497i	0.0381329	+	0.196331i
$226$	−6.10478			−0.406084
$227$	1.86723	−	3.23413i	0.123932	−	0.214657i	−0.797383	−	0.603474i	$-0.793783\pi$
$227$	1.86723	−	3.23413i	0.123932	−	0.214657i	0.921315	+	0.388817i	$0.127116\pi$
$228$	−6.43724	−	5.30725i	−0.426317	−	0.351481i
$229$	−2.07925	−	3.60137i	−0.137401	−	0.237985i	0.789111	−	0.614250i	$-0.210542\pi$
$229$	−2.07925	−	3.60137i	−0.137401	−	0.237985i	−0.926512	+	0.376265i	$0.877208\pi$
$230$	3.88683	+	6.73218i	0.256290	+	0.443907i
$231$	−0.764419	−	0.630233i	−0.0502951	−	0.0414663i
$232$	−4.45882	+	7.72290i	−0.292736	+	0.507033i
$233$	−20.0409			−1.31292			−0.656461	−	0.754360i	$-0.727947\pi$
$233$	−20.0409			−1.31292			−0.656461	+	0.754360i	$0.727947\pi$
$234$	−0.969186	+	0.842250i	−0.0633577	+	0.0550596i
$235$	11.3456			0.740108
$236$	−3.16359	+	5.47950i	−0.205932	+	0.356685i
$237$	2.10083	−	12.5484i	0.136464	−	0.815106i
$238$	−2.83641	−	4.91281i	−0.183857	−	0.318450i
$239$	−6.24482	−	10.8163i	−0.403944	−	0.699651i	0.590254	−	0.807217i	$-0.299027\pi$
$239$	−6.24482	−	10.8163i	−0.403944	−	0.699651i	−0.994198	+	0.107566i	$0.965694\pi$
$240$	−1.62241	+	0.606458i	−0.104726	+	0.0391467i
$241$	1.19440	−	2.06876i	0.0769382	−	0.133261i	−0.824989	−	0.565148i	$-0.808819\pi$
$241$	1.19440	−	2.06876i	0.0769382	−	0.133261i	0.901927	+	0.431888i	$0.142152\pi$
$242$	−10.6728			−0.686075
$243$	3.36836	+	15.2202i	0.216080	+	0.976376i
$244$	−4.24482			−0.271747
$245$	−0.500000	+	0.866025i	−0.0319438	+	0.0553283i
$246$	18.2737	−	6.83071i	1.16509	−	0.435510i
$247$	−1.03081	−	1.78542i	−0.0655891	−	0.113604i
$248$	−4.24482	−	7.35224i	−0.269546	−	0.466868i
$249$	2.91764	−	17.4272i	0.184898	−	1.10441i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	30.3826			1.91773			0.958866	−	0.283859i	$-0.0916148\pi$
$251$	30.3826			1.91773			0.958866	+	0.283859i	$0.0916148\pi$
$252$	2.26442	−	1.96784i	0.142645	−	0.123962i
$253$	4.44648			0.279548
$254$	−6.03081	+	10.4457i	−0.378407	+	0.655420i
$255$	7.58123	+	6.25042i	0.474755	+	0.391417i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−8.12967	−	14.0810i	−0.507115	−	0.878348i	−0.999966	−	0.00823496i	$-0.997379\pi$
$257$	−8.12967	−	14.0810i	−0.507115	−	0.878348i	0.492851	−	0.870114i	$-0.335955\pi$
$258$	8.21090	+	6.76956i	0.511188	+	0.421454i
$259$	−2.97842	+	5.15878i	−0.185070	+	0.320551i
$260$	−0.428007			−0.0265439
$261$	5.10083	+	26.2621i	0.315733	+	1.62559i
$262$	−2.01847			−0.124702
$263$	−1.45882	+	2.52675i	−0.0899547	+	0.155806i	−0.907492	−	0.420070i	$-0.862006\pi$
$263$	−1.45882	+	2.52675i	−0.0899547	+	0.155806i	0.817537	+	0.575876i	$0.195339\pi$
$264$	−0.163588	+	0.977122i	−0.0100682	+	0.0601377i
$265$	2.55042	+	4.41745i	0.156671	+	0.271362i
$266$	2.40841	+	4.17148i	0.147669	+	0.255770i
$267$	−13.4465	+	5.02630i	−0.822911	+	0.307605i
$268$	5.65322	−	9.79167i	0.345326	−	0.598121i
$269$	16.1664			0.985683			0.492842	−	0.870119i	$-0.335958\pi$
$269$	16.1664			0.985683			0.492842	+	0.870119i	$0.335958\pi$
$270$	−2.48040	+	4.56592i	−0.150952	+	0.277873i
$271$	−3.37033			−0.204733			−0.102367	−	0.994747i	$-0.532641\pi$
$271$	−3.37033			−0.204733			−0.102367	+	0.994747i	$0.532641\pi$
$272$	−2.83641	+	4.91281i	−0.171983	+	0.297883i
$273$	0.694402	−	0.259568i	0.0420271	−	0.0157098i
$274$	10.6801	+	18.4984i	0.645207	+	1.11753i
$275$	0.285997	+	0.495361i	0.0172462	+	0.0298714i
$276$	−2.22324	+	13.2795i	−0.133823	+	0.799335i
$277$	−3.01847	+	5.22815i	−0.181362	+	0.314129i	−0.942345	−	0.334644i	$-0.891384\pi$
$277$	−3.01847	+	5.22815i	−0.181362	+	0.314129i	0.760982	+	0.648773i	$0.224717\pi$
$278$	−12.8353			−0.769809
$279$	−24.0801	−	8.29541i	−1.44164	−	0.496633i
$280$	1.00000			0.0597614
$281$	−9.59970	+	16.6272i	−0.572670	+	0.991894i	0.423620	+	0.905840i	$0.360759\pi$
$281$	−9.59970	+	16.6272i	−0.572670	+	0.991894i	−0.996290	+	0.0860539i	$0.972574\pi$
$282$	15.1625	+	12.5008i	0.902911	+	0.744414i
$283$	−6.53279	−	11.3151i	−0.388334	−	0.672614i	0.603892	−	0.797066i	$-0.293616\pi$
$283$	−6.53279	−	11.3151i	−0.388334	−	0.672614i	−0.992226	+	0.124452i	$0.960283\pi$
$284$	−7.51121	−	13.0098i	−0.445708	−	0.771990i
$285$	−6.43724	−	5.30725i	−0.381309	−	0.314374i
$286$	−0.122408	+	0.212018i	−0.00723817	+	0.0125369i
$287$	−11.2633			−0.664851
$288$	−2.83641	−	0.977122i	−0.167137	−	0.0575775i
$289$	15.1809			0.892996
$290$	−4.45882	+	7.72290i	−0.261831	+	0.453505i
$291$	1.57002	−	9.37781i	0.0920360	−	0.549737i
$292$	3.17282	+	5.49549i	0.185675	+	0.321599i
$293$	−11.2756	−	19.5300i	−0.658729	−	1.14095i	−0.980945	−	0.194286i	$-0.937761\pi$
$293$	−11.2756	−	19.5300i	−0.658729	−	1.14095i	0.322215	−	0.946666i	$-0.395572\pi$
$294$	−1.62241	+	0.606458i	−0.0946208	+	0.0353693i
$295$	−3.16359	+	5.47950i	−0.184191	+	0.319029i
$296$	5.95684			0.346235
$297$	1.55239	+	2.53453i	0.0900789	+	0.147068i
$298$	4.20166			0.243396
$299$	−1.66359	+	2.88142i	−0.0962078	+	0.166637i
$300$	−1.62241	+	0.606458i	−0.0936698	+	0.0350138i
$301$	−3.07199	−	5.32085i	−0.177067	−	0.306689i
$302$	−1.81681	−	3.14681i	−0.104546	−	0.181078i
$303$	−0.981529	+	5.86273i	−0.0563874	+	0.336805i
$304$	2.40841	−	4.17148i	0.138132	−	0.239251i
$305$	−4.24482			−0.243058
$306$	3.24482	+	16.7063i	0.185494	+	0.955034i
$307$	−12.4857			−0.712595			−0.356298	−	0.934372i	$-0.615961\pi$
$307$	−12.4857			−0.712595			−0.356298	+	0.934372i	$0.615961\pi$
$308$	0.285997	−	0.495361i	0.0162962	−	0.0282258i
$309$	11.6728	+	9.62378i	0.664044	+	0.547478i
$310$	−4.24482	−	7.35224i	−0.241089	−	0.417579i
$311$	3.05767	+	5.29605i	0.173385	+	0.300311i	0.939601	−	0.342271i	$-0.111196\pi$
$311$	3.05767	+	5.29605i	0.173385	+	0.300311i	−0.766216	+	0.642583i	$0.777863\pi$
$312$	−0.571993	−	0.471586i	−0.0323827	−	0.0266983i
$313$	14.8157	−	25.6615i	0.837432	−	1.45047i	−0.0546033	−	0.998508i	$-0.517389\pi$
$313$	14.8157	−	25.6615i	0.837432	−	1.45047i	0.892035	−	0.451966i	$-0.149277\pi$
$314$	−4.34960			−0.245462
$315$	2.26442	−	1.96784i	0.127586	−	0.110875i
$316$	7.34565			0.413225
$317$	−8.41038	+	14.5672i	−0.472374	+	0.818176i	−0.999500	−	0.0316111i	$-0.989936\pi$
$317$	−8.41038	+	14.5672i	−0.472374	+	0.818176i	0.527126	+	0.849787i	$0.323270\pi$
$318$	−1.45882	+	8.71362i	−0.0818066	+	0.488636i
$319$	2.55042	+	4.41745i	0.142796	+	0.247330i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−23.8989	+	8.93342i	−1.33391	+	0.498615i
$322$	3.88683	−	6.73218i	0.216604	−	0.375170i
$323$	−27.3249			−1.52040
$324$	−8.34565	+	3.36900i	−0.463647	+	0.187167i
$325$	−0.428007			−0.0237415
$326$	5.05239	−	8.75100i	0.279826	−	0.484673i
$327$	−4.87364	+	1.82177i	−0.269513	+	0.100744i
$328$	5.63164	+	9.75429i	0.310956	+	0.538591i
$329$	−5.67282	−	9.82562i	−0.312753	−	0.541704i
$330$	−0.163588	+	0.977122i	−0.00900523	+	0.0537888i
$331$	13.5905	−	23.5394i	0.746999	−	1.29384i	−0.202255	−	0.979333i	$-0.564827\pi$
$331$	13.5905	−	23.5394i	0.746999	−	1.29384i	0.949255	−	0.314508i	$-0.101840\pi$
$332$	10.2017			0.559889
$333$	13.4888	−	11.7221i	0.739181	−	0.642369i
$334$	7.38880			0.404297
$335$	5.65322	−	9.79167i	0.308869	−	0.534976i
$336$	1.33641	+	1.10182i	0.0729072	+	0.0601091i
$337$	7.25208	+	12.5610i	0.395046	+	0.684239i	0.993107	−	0.117211i	$-0.0373954\pi$
$337$	7.25208	+	12.5610i	0.395046	+	0.684239i	−0.598061	+	0.801450i	$0.704062\pi$
$338$	6.40841	+	11.0997i	0.348571	+	0.603743i
$339$	−8.15850	−	6.72636i	−0.443109	−	0.365326i
$340$	−2.83641	+	4.91281i	−0.153826	+	0.266435i
$341$	−4.85601			−0.262968
$342$	−2.75518	−	14.1853i	−0.148983	−	0.767055i
$343$	1.00000			0.0539949
$344$	−3.07199	+	5.32085i	−0.165631	+	0.286881i
$345$	−2.22324	+	13.2795i	−0.119695	+	0.714947i
$346$	−0.244817	−	0.424035i	−0.0131614	−	0.0227963i
$347$	−3.32605	−	5.76088i	−0.178551	−	0.309260i	0.762833	−	0.646595i	$-0.223808\pi$
$347$	−3.32605	−	5.76088i	−0.178551	−	0.309260i	−0.941385	+	0.337335i	$0.890474\pi$
$348$	−14.4681	+	5.40817i	−0.775569	+	0.289908i
$349$	−5.56889	+	9.64559i	−0.298096	+	0.516317i	−0.975700	−	0.219110i	$-0.929685\pi$
$349$	−5.56889	+	9.64559i	−0.298096	+	0.516317i	0.677605	+	0.735426i	$0.263018\pi$
$350$	1.00000			0.0534522
$351$	−2.22324	+	0.0577261i	−0.118668	+	0.00308119i
$352$	−0.571993			−0.0304873
$353$	−12.6008	+	21.8253i	−0.670675	+	1.16164i	0.307039	+	0.951697i	$0.400662\pi$
$353$	−12.6008	+	21.8253i	−0.670675	+	1.16164i	−0.977713	+	0.209945i	$0.932671\pi$
$354$	−10.2653	+	3.83716i	−0.545593	+	0.203943i
$355$	−7.51121	−	13.0098i	−0.398654	−	0.690489i
$356$	−4.14399	−	7.17760i	−0.219631	−	0.380412i
$357$	1.62241	−	9.69075i	0.0858670	−	0.512889i
$358$	1.33641	−	2.31473i	0.0706316	−	0.122337i
$359$	−11.4257			−0.603028			−0.301514	−	0.953462i	$-0.597492\pi$
$359$	−11.4257			−0.603028			−0.301514	+	0.953462i	$0.597492\pi$
$360$	−2.83641	−	0.977122i	−0.149492	−	0.0514989i
$361$	4.20166			0.221140
$362$	5.00000	−	8.66025i	0.262794	−	0.455173i
$363$	−14.2633	−	11.7595i	−0.748628	−	0.617214i
$364$	0.214003	+	0.370665i	0.0112168	+	0.0194281i
$365$	3.17282	+	5.49549i	0.166073	+	0.287647i
$366$	−5.67282	−	4.67702i	−0.296523	−	0.244472i
$367$	−13.1801	+	22.8286i	−0.687995	+	1.19164i	0.284491	+	0.958679i	$0.408175\pi$
$367$	−13.1801	+	22.8286i	−0.687995	+	1.19164i	−0.972486	+	0.232963i	$0.925158\pi$
$368$	−7.77365			−0.405230
$369$	31.9473	+	11.0056i	1.66311	+	0.572929i
$370$	5.95684			0.309682
$371$	2.55042	−	4.41745i	0.132411	−	0.229343i
$372$	2.42801	−	14.5026i	0.125886	−	0.751927i
$373$	17.3025	+	29.9688i	0.895889	+	1.55173i	0.832700	+	0.553724i	$0.186794\pi$
$373$	17.3025	+	29.9688i	0.895889	+	1.55173i	0.0631886	+	0.998002i	$0.479873\pi$
$374$	1.62241	+	2.81009i	0.0838927	+	0.145306i
$375$	−1.62241	+	0.606458i	−0.0837808	+	0.0313173i
$376$	−5.67282	+	9.82562i	−0.292554	+	0.506718i
$377$	−3.81681			−0.196576
$378$	5.19440	−	0.134872i	0.267171	−	0.00693706i
$379$	−15.0432			−0.772715			−0.386358	−	0.922349i	$-0.626267\pi$
$379$	−15.0432			−0.772715			−0.386358	+	0.922349i	$0.626267\pi$
$380$	2.40841	−	4.17148i	0.123549	−	0.213992i
$381$	−19.5689	+	7.31486i	−1.00254	+	0.374752i
$382$	−5.42801	−	9.40158i	−0.277721	−	0.481027i
$383$	11.9176	+	20.6420i	0.608963	+	1.05475i	0.991412	+	0.130778i	$0.0417475\pi$
$383$	11.9176	+	20.6420i	0.608963	+	1.05475i	−0.382449	+	0.923977i	$0.624919\pi$
$384$	0.285997	−	1.70828i	0.0145947	−	0.0871751i
$385$	0.285997	−	0.495361i	0.0145757	−	0.0252459i
$386$	−2.87844			−0.146509
$387$	3.51432	+	18.0938i	0.178643	+	0.919761i
$388$	5.48963			0.278694
$389$	3.81681	−	6.61091i	0.193520	−	0.335186i	−0.752894	−	0.658141i	$-0.771343\pi$
$389$	3.81681	−	6.61091i	0.193520	−	0.335186i	0.946414	+	0.322955i	$0.104676\pi$
$390$	−0.571993	−	0.471586i	−0.0289640	−	0.0238797i
$391$	22.0493	+	38.1905i	1.11508	+	1.93138i
$392$	−0.500000	−	0.866025i	−0.0252538	−	0.0437409i
$393$	−2.69751	−	2.22399i	−0.136071	−	0.112185i
$394$	9.28487	−	16.0819i	0.467765	−	0.810192i
$395$	7.34565			0.369600
$396$	−1.29523	+	1.12559i	−0.0650879	+	0.0565632i
$397$	−10.7944			−0.541755			−0.270877	−	0.962614i	$-0.587314\pi$
$397$	−10.7944			−0.541755			−0.270877	+	0.962614i	$0.587314\pi$
$398$	7.66048	−	13.2683i	0.383985	−	0.665082i
$399$	−1.37759	+	8.22844i	−0.0689658	+	0.411937i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	9.13362	+	15.8199i	0.456111	+	0.790008i	0.998751	−	0.0499575i	$-0.0159086\pi$
$401$	9.13362	+	15.8199i	0.456111	+	0.790008i	−0.542640	+	0.839965i	$0.682575\pi$
$402$	18.3437	−	6.85688i	0.914899	−	0.341990i
$403$	1.81681	−	3.14681i	0.0905018	−	0.156754i
$404$	−3.43196			−0.170746
$405$	−8.34565	+	3.36900i	−0.414699	+	0.167407i
$406$	8.91764			0.442575
$407$	1.70364	−	2.95079i	0.0844462	−	0.146265i
$408$	−9.20364	+	3.44033i	−0.455648	+	0.170322i
$409$	−2.95487	−	5.11798i	−0.146109	−	0.253068i	0.783677	−	0.621168i	$-0.213342\pi$
$409$	−2.95487	−	5.11798i	−0.146109	−	0.253068i	−0.929786	+	0.368100i	$0.880008\pi$
$410$	5.63164	+	9.75429i	0.278127	+	0.481730i
$411$	−6.10894	+	36.4891i	−0.301332	+	1.79987i
$412$	−4.36723	+	7.56426i	−0.215158	+	0.372664i
$413$	6.32718			0.311340
$414$	−17.6028	+	15.2973i	−0.865131	+	0.751823i
$415$	10.2017			0.500780
$416$	0.214003	−	0.370665i	0.0104924	−	0.0181733i
$417$	−17.1532	−	14.1421i	−0.839997	−	0.692544i
$418$	−1.37759	−	2.38606i	−0.0673802	−	0.116706i
$419$	−4.99076	−	8.64426i	−0.243815	−	0.422300i	0.717983	−	0.696061i	$-0.245066\pi$
$419$	−4.99076	−	8.64426i	−0.243815	−	0.422300i	−0.961798	+	0.273761i	$0.911732\pi$
$420$	1.33641	+	1.10182i	0.0652102	+	0.0537632i
$421$	18.8661	−	32.6770i	0.919477	−	1.59258i	0.119267	−	0.992862i	$-0.461946\pi$
$421$	18.8661	−	32.6770i	0.919477	−	1.59258i	0.800211	−	0.599719i	$-0.204721\pi$
$422$	11.2672			0.548481
$423$	6.48963	+	33.4125i	0.315537	+	1.62457i
$424$	−5.10083			−0.247718
$425$	−2.83641	+	4.91281i	−0.137586	+	0.238306i
$426$	4.29636	−	25.6624i	0.208159	−	1.24335i
$427$	2.12241	+	3.67612i	0.102711	+	0.177900i
$428$	−7.36525	−	12.7570i	−0.356013	−	0.616632i
$429$	−0.397193	+	0.148471i	−0.0191767	+	0.00716825i
$430$	−3.07199	+	5.32085i	−0.148145	+	0.256594i
$431$	14.2386			0.685849			0.342925	−	0.939363i	$-0.388582\pi$
$431$	14.2386			0.685849			0.342925	+	0.939363i	$0.388582\pi$
$432$	−2.71400	−	4.43105i	−0.130578	−	0.213189i
$433$	17.2096			0.827039			0.413519	−	0.910495i	$-0.364299\pi$
$433$	17.2096			0.827039			0.413519	+	0.910495i	$0.364299\pi$
$434$	−4.24482	+	7.35224i	−0.203758	+	0.352919i
$435$	−14.4681	+	5.40817i	−0.693690	+	0.259302i
$436$	−1.50198	−	2.60150i	−0.0719316	−	0.124589i
$437$	−18.7221	−	32.4276i	−0.895600	−	1.55122i
$438$	−1.81483	+	10.8401i	−0.0867161	+	0.517961i
$439$	20.0453	−	34.7195i	0.956711	−	1.65707i	0.226309	−	0.974055i	$-0.427334\pi$
$439$	20.0453	−	34.7195i	0.956711	−	1.65707i	0.730402	−	0.683017i	$-0.239333\pi$
$440$	−0.571993			−0.0272687
$441$	−2.83641	−	0.977122i	−0.135067	−	0.0465296i
$442$	−2.42801			−0.115489
$443$	4.25518	−	7.37019i	0.202170	−	0.350168i	−0.747057	−	0.664759i	$-0.768534\pi$
$443$	4.25518	−	7.37019i	0.202170	−	0.350168i	0.949227	+	0.314591i	$0.101867\pi$
$444$	7.96080	+	6.56336i	0.377803	+	0.311483i
$445$	−4.14399	−	7.17760i	−0.196444	−	0.340251i
$446$	−3.22324	−	5.58281i	−0.152625	−	0.264354i
$447$	5.61515	+	4.62947i	0.265587	+	0.218966i
$448$	−0.500000	+	0.866025i	−0.0236228	+	0.0409159i
$449$	13.0969			0.618080			0.309040	−	0.951049i	$-0.399992\pi$
$449$	13.0969			0.618080			0.309040	+	0.951049i	$0.399992\pi$
$450$	−2.83641	−	0.977122i	−0.133710	−	0.0460620i
$451$	6.44252			0.303367
$452$	3.05239	−	5.28690i	0.143572	−	0.248675i
$453$	1.03920	−	6.20723i	0.0488260	−	0.291641i
$454$	1.86723	+	3.23413i	0.0876332	+	0.151785i
$455$	0.214003	+	0.370665i	0.0100326	+	0.0173770i
$456$	7.81483	−	2.92119i	0.365963	−	0.136797i
$457$	14.0165	−	24.2773i	0.655664	−	1.13564i	−0.326063	−	0.945348i	$-0.605722\pi$
$457$	14.0165	−	24.2773i	0.655664	−	1.13564i	0.981727	−	0.190295i	$-0.0609445\pi$
$458$	4.15850			0.194314
$459$	−14.0709	+	25.9017i	−0.656772	+	1.20899i
$460$	−7.77365			−0.362448
$461$	−10.9784	+	19.0152i	−0.511316	+	0.885625i	0.488598	+	0.872509i	$0.337509\pi$
$461$	−10.9784	+	19.0152i	−0.511316	+	0.885625i	−0.999914	+	0.0131164i	$0.995825\pi$
$462$	0.928007	−	0.346890i	0.0431748	−	0.0161388i
$463$	−6.10083	−	10.5669i	−0.283530	−	0.491088i	0.688722	−	0.725026i	$-0.258172\pi$
$463$	−6.10083	−	10.5669i	−0.283530	−	0.491088i	−0.972252	+	0.233938i	$0.924839\pi$
$464$	−4.45882	−	7.72290i	−0.206996	−	0.358527i
$465$	2.42801	−	14.5026i	0.112596	−	0.672544i
$466$	10.0204	−	17.3559i	0.464188	−	0.803998i
$467$	−26.4257			−1.22284			−0.611419	−	0.791307i	$-0.709401\pi$
$467$	−26.4257			−1.22284			−0.611419	+	0.791307i	$0.709401\pi$
$468$	−0.244817	−	1.26047i	−0.0113167	−	0.0582650i
$469$	−11.3064			−0.522083
$470$	−5.67282	+	9.82562i	−0.261668	+	0.453222i
$471$	−5.81286	−	4.79247i	−0.267842	−	0.220825i
$472$	−3.16359	−	5.47950i	−0.145616	−	0.252214i
$473$	1.75716	+	3.04349i	0.0807943	+	0.139940i
$474$	9.81681	+	8.09357i	0.450901	+	0.371750i
$475$	2.40841	−	4.17148i	0.110505	−	0.191401i
$476$	5.67282			0.260013
$477$	−11.5504	+	10.0376i	−0.528857	+	0.459592i
$478$	12.4896			0.571263
$479$	18.3949	−	31.8610i	0.840486	−	1.45576i	−0.0489986	−	0.998799i	$-0.515603\pi$
$479$	18.3949	−	31.8610i	0.840486	−	1.45576i	0.889484	−	0.456965i	$-0.151064\pi$
$480$	0.285997	−	1.70828i	0.0130539	−	0.0779718i
$481$	1.27478	+	2.20799i	0.0581252	+	0.100676i
$482$	1.19440	+	2.06876i	0.0544035	+	0.0942296i
$483$	12.6120	−	4.71439i	0.573868	−	0.214512i
$484$	5.33641	−	9.24294i	0.242564	−	0.420133i
$485$	5.48963			0.249271
$486$	−14.8652	−	4.69301i	−0.674301	−	0.212879i
$487$	16.7776			0.760266			0.380133	−	0.924932i	$-0.375878\pi$
$487$	16.7776			0.760266			0.380133	+	0.924932i	$0.375878\pi$
$488$	2.12241	−	3.67612i	0.0960769	−	0.166410i
$489$	16.3941	−	6.12812i	0.741366	−	0.277123i
$490$	−0.500000	−	0.866025i	−0.0225877	−	0.0391230i
$491$	11.6840	+	20.2373i	0.527293	+	0.913299i	0.999494	+	0.0318075i	$0.0101264\pi$
$491$	11.6840	+	20.2373i	0.527293	+	0.913299i	−0.472201	+	0.881491i	$0.656540\pi$
$492$	−3.22126	+	19.2408i	−0.145226	+	0.867442i
$493$	−25.2941	+	43.8107i	−1.13919	+	1.97313i
$494$	2.06163			0.0927570
$495$	−1.29523	+	1.12559i	−0.0582164	+	0.0505917i
$496$	8.48963			0.381196
$497$	−7.51121	+	13.0098i	−0.336924	+	0.583569i
$498$	13.6336	+	11.2404i	0.610937	+	0.503693i
$499$	−11.4053	−	19.7546i	−0.510571	−	0.884335i	−0.999925	−	0.0122500i	$-0.996101\pi$
$499$	−11.4053	−	19.7546i	−0.510571	−	0.884335i	0.489354	−	0.872085i	$-0.337233\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	9.87448	+	8.14112i	0.441159	+	0.363718i
$502$	−15.1913	+	26.3121i	−0.678021	+	1.17437i
$503$	32.6129			1.45414			0.727068	−	0.686565i	$-0.240882\pi$
$503$	32.6129			1.45414			0.727068	+	0.686565i	$0.240882\pi$
$504$	0.571993	+	2.94497i	0.0254786	+	0.131179i
$505$	−3.43196			−0.152720
$506$	−2.22324	+	3.85076i	−0.0988350	+	0.171187i
$507$	−3.66556	+	21.8946i	−0.162793	+	0.972375i
$508$	−6.03081	−	10.4457i	−0.267574	−	0.463452i
$509$	2.65520	+	4.59894i	0.117690	+	0.203844i	0.918852	−	0.394603i	$-0.129118\pi$
$509$	2.65520	+	4.59894i	0.117690	+	0.203844i	−0.801162	+	0.598447i	$0.795785\pi$
$510$	−9.20364	+	3.44033i	−0.407544	+	0.152340i
$511$	3.17282	−	5.49549i	0.140357	−	0.243106i
$512$	1.00000			0.0441942
$513$	11.9476	−	21.9932i	0.527500	−	0.971022i
$514$	16.2593			0.717169
$515$	−4.36723	+	7.56426i	−0.192443	+	0.333321i
$516$	−9.96806	+	3.72607i	−0.438819	+	0.164031i
$517$	3.24482	+	5.62019i	0.142707	+	0.247176i
$518$	−2.97842	−	5.15878i	−0.130864	−	0.226664i
$519$	0.140034	−	0.836430i	0.00614680	−	0.0367152i
$520$	0.214003	−	0.370665i	0.00938467	−	0.0162547i
$521$	11.5328			0.505261			0.252630	−	0.967563i	$-0.418704\pi$
$521$	11.5328			0.505261			0.252630	+	0.967563i	$0.418704\pi$
$522$	−25.2941	−	8.71362i	−1.10709	−	0.381385i
$523$	21.1546			0.925024			0.462512	−	0.886613i	$-0.346948\pi$
$523$	21.1546			0.925024			0.462512	+	0.886613i	$0.346948\pi$
$524$	1.00924	−	1.74805i	0.0440887	−	0.0763638i
$525$	1.33641	+	1.10182i	0.0583258	+	0.0480873i
$526$	−1.45882	−	2.52675i	−0.0636076	−	0.110172i
$527$	−24.0801	−	41.7080i	−1.04895	−	1.81683i
$528$	−0.764419	−	0.630233i	−0.0332670	−	0.0274274i
$529$	−18.7148	+	32.4151i	−0.813689	+	1.40935i
$530$	−5.10083			−0.221566
$531$	−17.9465	−	6.18242i	−0.778811	−	0.268294i
$532$	−4.81681			−0.208835
$533$	−2.41038	+	4.17490i	−0.104405	+	0.180835i
$534$	2.37033	−	14.1581i	0.102574	−	0.612683i
$535$	−7.36525	−	12.7570i	−0.318427	−	0.551533i
$536$	5.65322	+	9.79167i	0.244182	+	0.422936i
$537$	4.33641	−	1.62095i	0.187130	−	0.0699493i
$538$	−8.08321	+	14.0005i	−0.348492	+	0.603605i
$539$	−0.571993			−0.0246375
$540$	−2.71400	−	4.43105i	−0.116792	−	0.190682i
$541$	−34.0000			−1.46177			−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000			−1.46177			−0.730887	+	0.682498i	$0.760893\pi$
$542$	1.68517	−	2.91879i	0.0723841	−	0.125373i
$543$	16.2241	−	6.06458i	0.696242	−	0.260256i
$544$	−2.83641	−	4.91281i	−0.121610	−	0.210635i
$545$	−1.50198	−	2.60150i	−0.0643376	−	0.111436i
$546$	−0.122408	+	0.731154i	−0.00523860	+	0.0312905i
$547$	16.4216	−	28.4430i	0.702137	−	1.21614i	−0.265578	−	0.964089i	$-0.585563\pi$
$547$	16.4216	−	28.4430i	0.702137	−	1.21614i	0.967715	−	0.252047i	$-0.0811038\pi$
$548$	−21.3602			−0.912461
$549$	−2.42801	−	12.5008i	−0.103625	−	0.533523i
$550$	−0.571993			−0.0243899
$551$	21.4773	−	37.1998i	0.914963	−	1.58476i
$552$	−10.3888	−	8.56515i	−0.442177	−	0.364557i
$553$	−3.67282	−	6.36152i	−0.156184	−	0.270519i
$554$	−3.01847	−	5.22815i	−0.128243	−	0.222123i
$555$	7.96080	+	6.56336i	0.337917	+	0.278599i
$556$	6.41764	−	11.1157i	0.272169	−	0.471410i
$557$	−15.9216			−0.674620			−0.337310	−	0.941394i	$-0.609517\pi$
$557$	−15.9216			−0.674620			−0.337310	+	0.941394i	$0.609517\pi$
$558$	19.2241	−	16.7063i	0.813820	−	0.707233i
$559$	−2.62967			−0.111223
$560$	−0.500000	+	0.866025i	−0.0211289	+	0.0365963i
$561$	−0.928007	+	5.54304i	−0.0391805	+	0.234027i
$562$	−9.59970	−	16.6272i	−0.404939	−	0.701375i
$563$	0.810881	+	1.40449i	0.0341746	+	0.0591921i	0.882607	−	0.470112i	$-0.155786\pi$
$563$	0.810881	+	1.40449i	0.0341746	+	0.0591921i	−0.848432	+	0.529304i	$0.822453\pi$
$564$	−18.4073	+	6.88065i	−0.775086	+	0.289728i
$565$	3.05239	−	5.28690i	0.128415	−	0.222421i
$566$	13.0656			0.549187
$567$	7.09046	+	5.54304i	0.297772	+	0.232786i
$568$	15.0224			0.630327
$569$	−7.65717	+	13.2626i	−0.321005	+	0.555998i	−0.980696	−	0.195540i	$-0.937354\pi$
$569$	−7.65717	+	13.2626i	−0.321005	+	0.555998i	0.659690	+	0.751538i	$0.270687\pi$
$570$	7.81483	−	2.92119i	0.327327	−	0.122355i
$571$	2.42075	+	4.19286i	0.101305	+	0.175466i	0.912223	−	0.409695i	$-0.134365\pi$
$571$	2.42075	+	4.19286i	0.101305	+	0.175466i	−0.810917	+	0.585161i	$0.801031\pi$
$572$	−0.122408	−	0.212018i	−0.00511816	−	0.00886491i
$573$	3.10478	−	18.5451i	0.129704	−	0.774731i
$574$	5.63164	−	9.75429i	0.235060	−	0.407136i
$575$	−7.77365			−0.324184
$576$	2.26442	−	1.96784i	0.0943508	−	0.0819935i
$577$	28.2857			1.17755			0.588775	−	0.808297i	$-0.299610\pi$
$577$	28.2857			1.17755			0.588775	+	0.808297i	$0.299610\pi$
$578$	−7.59046	+	13.1471i	−0.315722	+	0.546846i
$579$	−3.84678	−	3.17151i	−0.159867	−	0.131804i
$580$	−4.45882	−	7.72290i	−0.185142	−	0.320676i
$581$	−5.10083	−	8.83490i	−0.211618	−	0.366533i
$582$	7.33641	+	6.04858i	0.304104	+	0.250722i
$583$	−1.45882	+	2.52675i	−0.0604182	+	0.104647i
$584$	−6.34565			−0.262585
$585$	−0.244817	−	1.26047i	−0.0101219	−	0.0521138i
$586$	22.5513			0.931584
$587$	11.4093	−	19.7614i	0.470910	−	0.815640i	−0.528536	−	0.848911i	$-0.677259\pi$
$587$	11.4093	−	19.7614i	0.470910	−	0.815640i	0.999446	+	0.0332704i	$0.0105923\pi$
$588$	0.285997	−	1.70828i	0.0117943	−	0.0704481i
$589$	20.4465	+	35.4143i	0.842482	+	1.45922i
$590$	−3.16359	−	5.47950i	−0.130243	−	0.225587i
$591$	30.1277	−	11.2618i	1.23929	−	0.463247i
$592$	−2.97842	+	5.15878i	−0.122412	+	0.212024i
$593$	25.8538			1.06169			0.530843	−	0.847470i	$-0.321875\pi$
$593$	25.8538			1.06169			0.530843	+	0.847470i	$0.321875\pi$
$594$	−2.97116	+	0.0771458i	−0.121908	+	0.00316533i
$595$	5.67282			0.232563
$596$	−2.10083	+	3.63875i	−0.0860534	+	0.149049i
$597$	24.8569	−	9.29151i	1.01732	−	0.380276i
$598$	−1.66359	−	2.88142i	−0.0680292	−	0.117830i
$599$	12.8745	+	22.2993i	0.526037	+	0.911123i	0.999540	+	0.0303308i	$0.00965607\pi$
$599$	12.8745	+	22.2993i	0.526037	+	0.911123i	−0.473503	+	0.880792i	$0.657011\pi$
$600$	0.285997	−	1.70828i	0.0116758	−	0.0697401i
$601$	5.94035	−	10.2890i	0.242312	−	0.419697i	−0.719061	−	0.694947i	$-0.755428\pi$
$601$	5.94035	−	10.2890i	0.242312	−	0.419697i	0.961372	+	0.275251i	$0.0887609\pi$
$602$	6.14399			0.250410
$603$	32.0697	+	11.0478i	1.30598	+	0.449900i
$604$	3.63362			0.147850
$605$	5.33641	−	9.24294i	0.216956	−	0.375779i
$606$	−4.58651	−	3.78140i	−0.186314	−	0.153609i
$607$	−0.287973	−	0.498784i	−0.0116885	−	0.0202450i	0.860122	−	0.510088i	$-0.170387\pi$
$607$	−0.287973	−	0.498784i	−0.0116885	−	0.0202450i	−0.871810	+	0.489843i	$0.837054\pi$
$608$	2.40841	+	4.17148i	0.0976737	+	0.169176i
$609$	11.9176	+	9.82562i	0.482927	+	0.398154i
$610$	2.12241	−	3.67612i	0.0859338	−	0.148842i
$611$	−4.85601			−0.196453
$612$	−16.0905	−	5.54304i	−0.650418	−	0.224064i
$613$	14.8639			0.600348			0.300174	−	0.953884i	$-0.402955\pi$
$613$	14.8639			0.600348			0.300174	+	0.953884i	$0.402955\pi$
$614$	6.24284	−	10.8129i	0.251941	−	0.436374i
$615$	−3.22126	+	19.2408i	−0.129894	+	0.775864i
$616$	0.285997	+	0.495361i	0.0115231	+	0.0199587i
$617$	−14.3569	−	24.8668i	−0.577985	−	1.00110i	−0.995710	−	0.0925265i	$-0.970506\pi$
$617$	−14.3569	−	24.8668i	−0.577985	−	1.00110i	0.417725	−	0.908574i	$-0.362828\pi$
$618$	−14.1708	+	5.29707i	−0.570035	+	0.213080i
$619$	10.8417	−	18.7784i	0.435764	−	0.754766i	−0.561593	−	0.827413i	$-0.689811\pi$
$619$	10.8417	−	18.7784i	0.435764	−	0.754766i	0.997358	+	0.0726472i	$0.0231447\pi$
$620$	8.48963			0.340952
$621$	−40.3795	+	1.04845i	−1.62037	+	0.0420727i
$622$	−6.11535			−0.245203
$623$	−4.14399	+	7.17760i	−0.166025	+	0.287564i
$624$	0.694402	−	0.259568i	0.0277983	−	0.0103910i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	14.8157	+	25.6615i	0.592154	+	1.02564i
$627$	0.787973	−	4.70661i	0.0314686	−	0.187964i
$628$	2.17480	−	3.76686i	0.0867840	−	0.150314i
$629$	33.7921			1.34738
$630$	0.571993	+	2.94497i	0.0227888	+	0.117330i
$631$	−13.0224			−0.518415			−0.259207	−	0.965822i	$-0.583461\pi$
$631$	−13.0224			−0.518415			−0.259207	+	0.965822i	$0.583461\pi$
$632$	−3.67282	+	6.36152i	−0.146097	+	0.253048i
$633$	15.0577	+	12.4145i	0.598489	+	0.493430i
$634$	−8.41038	−	14.5672i	−0.334019	−	0.578538i
$635$	−6.03081	−	10.4457i	−0.239326	−	0.414524i
$636$	−6.81681	−	5.62019i	−0.270304	−	0.222855i
$637$	0.214003	−	0.370665i	0.00847912	−	0.0146863i
$638$	−5.10083			−0.201944
$639$	34.0171	−	29.5618i	1.34569	−	1.16945i
$640$	1.00000			0.0395285
$641$	19.2252	−	33.2990i	0.759350	−	1.31523i	−0.183832	−	0.982958i	$-0.558850\pi$
$641$	19.2252	−	33.2990i	0.759350	−	1.31523i	0.943182	−	0.332276i	$-0.107816\pi$
$642$	4.21287	−	25.1638i	0.166269	−	0.993134i
$643$	−15.0649	−	26.0932i	−0.594103	−	1.02902i	−0.993673	−	0.112314i	$-0.964174\pi$
$643$	−15.0649	−	26.0932i	−0.594103	−	1.02902i	0.399570	−	0.916703i	$-0.369160\pi$
$644$	3.88683	+	6.73218i	0.153162	+	0.265285i
$645$	−9.96806	+	3.72607i	−0.392492	+	0.146714i
$646$	13.6625	−	23.6641i	0.537542	−	0.931050i
$647$	−22.4913			−0.884225			−0.442113	−	0.896960i	$-0.645771\pi$
$647$	−22.4913			−0.884225			−0.442113	+	0.896960i	$0.645771\pi$
$648$	1.25518	−	8.91204i	0.0493082	−	0.350098i
$649$	−3.61910			−0.142062
$650$	0.214003	−	0.370665i	0.00839390	−	0.0145387i
$651$	−13.7737	+	5.14860i	−0.539832	+	0.201790i
$652$	5.05239	+	8.75100i	0.197867	+	0.342716i
$653$	7.85601	+	13.6070i	0.307430	+	0.532484i	0.977799	−	0.209544i	$-0.0671978\pi$
$653$	7.85601	+	13.6070i	0.307430	+	0.532484i	−0.670370	+	0.742027i	$0.733864\pi$
$654$	0.859120	−	5.13158i	0.0335943	−	0.200661i
$655$	1.00924	−	1.74805i	0.0394341	−	0.0683019i
$656$	−11.2633			−0.439758
$657$	−14.3692	+	12.4872i	−0.560596	+	0.487174i
$658$	11.3456			0.442299
$659$	−8.67282	+	15.0218i	−0.337845	+	0.585165i	−0.984027	−	0.178018i	$-0.943031\pi$
$659$	−8.67282	+	15.0218i	−0.337845	+	0.585165i	0.646182	+	0.763183i	$0.276365\pi$
$660$	−0.764419	−	0.630233i	−0.0297550	−	0.0245318i
$661$	−4.34960	−	7.53373i	−0.169180	−	0.293028i	0.768952	−	0.639307i	$-0.220779\pi$
$661$	−4.34960	−	7.53373i	−0.169180	−	0.293028i	−0.938132	+	0.346279i	$0.887445\pi$
$662$	13.5905	+	23.5394i	0.528208	+	0.914884i
$663$	−3.24482	−	2.67522i	−0.126018	−	0.103897i
$664$	−5.10083	+	8.83490i	−0.197951	+	0.342861i
$665$	−4.81681			−0.186788
$666$	3.40727	+	17.5427i	0.132029	+	0.679766i
$667$	−69.3227			−2.68418
$668$	−3.69440	+	6.39889i	−0.142941	+	0.247581i
$669$	1.84367	−	11.0124i	0.0712804	−	0.425762i
$670$	5.65322	+	9.79167i	0.218403	+	0.378285i
$671$	−1.21400	−	2.10272i	−0.0468661	−	0.0811744i
$672$	−1.62241	+	0.606458i	−0.0625858	+	0.0233946i
$673$	0.284020	−	0.491937i	0.0109482	−	0.0189628i	−0.860499	−	0.509451i	$-0.829848\pi$
$673$	0.284020	−	0.491937i	0.0109482	−	0.0189628i	0.871448	+	0.490489i	$0.163182\pi$
$674$	−14.5042			−0.558679
$675$	−2.71400	−	4.43105i	−0.104462	−	0.170551i
$676$	−12.8168			−0.492954
$677$	−18.4773	+	32.0036i	−0.710140	+	1.23000i	0.254664	+	0.967030i	$0.418035\pi$
$677$	−18.4773	+	32.0036i	−0.710140	+	1.23000i	−0.964804	+	0.262969i	$0.915298\pi$
$678$	9.90445	−	3.70229i	0.380378	−	0.142186i
$679$	−2.74482	−	4.75416i	−0.105336	−	0.182448i
$680$	−2.83641	−	4.91281i	−0.108771	−	0.188398i
$681$	−1.06804	+	6.37947i	−0.0409274	+	0.244462i
$682$	2.42801	−	4.20543i	0.0929732	−	0.161034i
$683$	32.7753			1.25411			0.627057	−	0.778973i	$-0.284259\pi$
$683$	32.7753			1.25411			0.627057	+	0.778973i	$0.284259\pi$
$684$	13.6625	+	4.70661i	0.522397	+	0.179962i
$685$	−21.3602			−0.816130
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$	5.55748	+	4.58192i	0.212031	+	0.174811i
$688$	−3.07199	−	5.32085i	−0.117119	−	0.202855i
$689$	−1.09159	−	1.89070i	−0.0415865	−	0.0720298i
$690$	−10.3888	−	8.56515i	−0.395495	−	0.326070i
$691$	12.6913	−	21.9820i	0.482800	−	0.836233i	−0.517005	−	0.855982i	$-0.672953\pi$
$691$	12.6913	−	21.9820i	0.482800	−	0.836233i	0.999805	+	0.0197487i	$0.00628662\pi$
$692$	0.489634			0.0186131
$693$	1.62241	+	0.558907i	0.0616302	+	0.0212311i
$694$	6.65209			0.252510
$695$	6.41764	−	11.1157i	0.243435	−	0.421642i
$696$	2.55042	−	15.2338i	0.0966732	−	0.577435i
$697$	31.9473	+	55.3344i	1.21009	+	2.09594i
$698$	−5.56889	−	9.64559i	−0.210785	−	0.365091i
$699$	32.5145	−	12.1540i	1.22981	−	0.459705i
$700$	−0.500000	+	0.866025i	−0.0188982	+	0.0327327i
$701$	−47.9259			−1.81014			−0.905069	−	0.425265i	$-0.860181\pi$
$701$	−47.9259			−1.81014			−0.905069	+	0.425265i	$0.860181\pi$
$702$	1.06163	−	1.95424i	0.0400685	−	0.0737582i
$703$	−28.6930			−1.08218
$704$	0.285997	−	0.495361i	0.0107789	−	0.0186696i
$705$	−18.4073	+	6.88065i	−0.693258	+	0.259140i
$706$	−12.6008	−	21.8253i	−0.474239	−	0.821405i
$707$	1.71598	+	2.97216i	0.0645361	+	0.111780i
$708$	1.80955	−	10.8086i	0.0680071	−	0.406211i
$709$	16.1132	−	27.9088i	0.605143	−	1.04814i	−0.386886	−	0.922128i	$-0.626449\pi$
$709$	16.1132	−	27.9088i	0.605143	−	1.04814i	0.992029	−	0.126011i	$-0.0402174\pi$
$710$	15.0224			0.563782
$711$	4.20166	+	21.6327i	0.157575	+	0.811289i
$712$	8.28797			0.310605
$713$	32.9977	−	57.1538i	1.23578	−	2.14043i
$714$	7.58123	+	6.25042i	0.283720	+	0.233916i
$715$	−0.122408	−	0.212018i	−0.00457782	−	0.00792901i
$716$	1.33641	+	2.31473i	0.0499441	+	0.0865056i
$717$	16.6913	+	13.7613i	0.623348	+	0.513925i
$718$	5.71287	−	9.89499i	0.213203	−	0.369278i
$719$	41.1562			1.53487			0.767434	−	0.641127i	$-0.221533\pi$
$719$	41.1562			1.53487			0.767434	+	0.641127i	$0.221533\pi$
$720$	2.26442	−	1.96784i	0.0843899	−	0.0733372i
$721$	8.73445			0.325288
$722$	−2.10083	+	3.63875i	−0.0781848	+	0.135420i
$723$	−0.683190	+	4.08074i	−0.0254081	+	0.151764i
$724$	5.00000	+	8.66025i	0.185824	+	0.321856i
$725$	−4.45882	−	7.72290i	−0.165596	−	0.286821i
$726$	17.3157	−	6.47261i	0.642645	−	0.240221i
$727$	−12.1409	+	21.0286i	−0.450280	+	0.779908i	−0.998403	−	0.0564894i	$-0.982009\pi$
$727$	−12.1409	+	21.0286i	−0.450280	+	0.779908i	0.548123	+	0.836398i	$0.315343\pi$
$728$	−0.428007			−0.0158630
$729$	−14.6952	−	22.6506i	−0.544268	−	0.838911i
$730$	−6.34565			−0.234863
$731$	−17.4269	+	30.1842i	−0.644556	+	1.11640i
$732$	6.88683	−	2.57430i	0.254544	−	0.0951489i
$733$	7.90530	+	13.6924i	0.291989	+	0.505740i	0.974280	−	0.225341i	$-0.0723496\pi$
$733$	7.90530	+	13.6924i	0.291989	+	0.505740i	−0.682291	+	0.731081i	$0.739016\pi$
$734$	−13.1801	−	22.8286i	−0.486486	−	0.842618i
$735$	0.285997	−	1.70828i	0.0105491	−	0.0630107i
$736$	3.88683	−	6.73218i	0.143270	−	0.248152i
$737$	6.46721			0.238223
$738$	−25.5048	+	22.1644i	−0.938845	+	0.815882i
$739$	−39.3081			−1.44597			−0.722987	−	0.690862i	$-0.757231\pi$
$739$	−39.3081			−1.44597			−0.722987	+	0.690862i	$0.757231\pi$
$740$	−2.97842	+	5.15878i	−0.109489	+	0.189640i
$741$	2.75518	+	2.27154i	0.101214	+	0.0834470i
$742$	2.55042	+	4.41745i	0.0936287	+	0.162170i
$743$	−1.20166	−	2.08134i	−0.0440847	−	0.0763569i	0.843141	−	0.537692i	$-0.180704\pi$
$743$	−1.20166	−	2.08134i	−0.0440847	−	0.0763569i	−0.887226	+	0.461335i	$0.847370\pi$
$744$	11.3456	+	9.35403i	0.415952	+	0.342935i
$745$	−2.10083	+	3.63875i	−0.0769685	+	0.133313i
$746$	−34.6050			−1.26698
$747$	5.83528	+	30.0435i	0.213502	+	1.09924i
$748$	−3.24482			−0.118642
$749$	−7.36525	+	12.7570i	−0.269120	+	0.466130i
$750$	0.285997	−	1.70828i	0.0104431	−	0.0623774i
$751$	−4.18008	−	7.24012i	−0.152533	−	0.264196i	0.779625	−	0.626247i	$-0.215410\pi$
$751$	−4.18008	−	7.24012i	−0.152533	−	0.264196i	−0.932158	+	0.362051i	$0.882076\pi$
$752$	−5.67282	−	9.82562i	−0.206867	−	0.358303i
$753$	−49.2930	+	18.4257i	−1.79634	+	0.671472i
$754$	1.90841	−	3.30545i	0.0695000	−	0.120378i
$755$	3.63362			0.132241
$756$	−2.48040	+	4.56592i	−0.0902112	+	0.166061i
$757$	−28.8992			−1.05036			−0.525179	−	0.850992i	$-0.676002\pi$
$757$	−28.8992			−1.05036			−0.525179	+	0.850992i	$0.676002\pi$
$758$	7.52158	−	13.0278i	0.273196	−	0.473189i
$759$	−7.21400	+	2.69660i	−0.261852	+	0.0978804i
$760$	2.40841	+	4.17148i	0.0873620	+	0.151315i
$761$	14.2409	+	24.6659i	0.516231	+	0.894138i	0.999822	+	0.0188444i	$0.00599871\pi$
$761$	14.2409	+	24.6659i	0.516231	+	0.894138i	−0.483592	+	0.875294i	$0.660668\pi$
$762$	3.44958	−	20.6046i	0.124965	−	0.746425i
$763$	−1.50198	+	2.60150i	−0.0543752	+	0.0941806i
$764$	10.8560			0.392757
$765$	−16.0905	−	5.54304i	−0.581752	−	0.200409i
$766$	−23.8353			−0.861204
$767$	1.35404	−	2.34526i	0.0488914	−	0.0846825i
$768$	1.33641	+	1.10182i	0.0482236	+	0.0397584i
$769$	26.2148	+	45.4055i	0.945332	+	1.63736i	0.755086	+	0.655626i	$0.227595\pi$
$769$	26.2148	+	45.4055i	0.945332	+	1.63736i	0.190246	+	0.981736i	$0.439072\pi$
$770$	0.285997	+	0.495361i	0.0103066	+	0.0178516i
$771$	21.7292	+	17.9148i	0.782557	+	0.645187i
$772$	1.43922	−	2.49280i	0.0517986	−	0.0897178i
$773$	−32.6376			−1.17389			−0.586946	−	0.809626i	$-0.699670\pi$
$773$	−32.6376			−1.17389			−0.586946	+	0.809626i	$0.699670\pi$
$774$	−17.4269	−	6.00343i	−0.626396	−	0.215789i
$775$	8.48963			0.304957
$776$	−2.74482	+	4.75416i	−0.0985332	+	0.170664i
$777$	1.70364	−	10.1759i	0.0611176	−	0.365060i
$778$	3.81681	+	6.61091i	0.136839	+	0.237013i
$779$	−27.1266	−	46.9846i	−0.971910	−	1.68340i
$780$	0.694402	−	0.259568i	0.0248636	−	0.00929402i
$781$	4.29636	−	7.44152i	0.153736	−	0.266278i
$782$	−44.0986			−1.57696
$783$	−24.2025	−	39.5145i	−0.864927	−	1.41213i
$784$	1.00000			0.0357143
$785$	2.17480	−	3.76686i	0.0776219	−	0.134445i
$786$	3.27478	−	1.22412i	0.116808	−	0.0436628i
$787$	23.1378	+	40.0758i	0.824773	+	1.42855i	0.902093	+	0.431542i	$0.142030\pi$
$787$	23.1378	+	40.0758i	0.824773	+	1.42855i	−0.0773205	+	0.997006i	$0.524636\pi$
$788$	9.28487	+	16.0819i	0.330760	+	0.572893i
$789$	0.834435	−	4.98413i	0.0297067	−	0.177440i
$790$	−3.67282	+	6.36152i	−0.130673	+	0.226333i
$791$	−6.10478			−0.217061
$792$	−0.327176	−	1.68450i	−0.0116257	−	0.0598561i
$793$	1.81681			0.0645168
$794$	5.39719	−	9.34821i	0.191539	−	0.331756i
$795$	−6.81681	−	5.62019i	−0.241767	−	0.199328i
$796$	7.66048	+	13.2683i	0.271519	+	0.470284i
$797$	6.30249	+	10.9162i	0.223246	+	0.386673i	0.955792	−	0.294045i	$-0.0950014\pi$
$797$	6.30249	+	10.9162i	0.223246	+	0.386673i	−0.732546	+	0.680718i	$0.761668\pi$
$798$	−6.43724	−	5.30725i	−0.227876	−	0.187875i
$799$	−32.1809	+	55.7390i	−1.13848	+	1.97190i
$800$	1.00000			0.0353553
$801$	18.7674	−	16.3094i	0.663115	−	0.576266i
$802$	−18.2672			−0.645039
$803$	−1.81483	+	3.14338i	−0.0640441	+	0.110928i
$804$	−3.23360	+	19.3145i	−0.114040	+	0.681171i
$805$	3.88683	+	6.73218i	0.136993	+	0.237278i
$806$	1.81681	+	3.14681i	0.0639944	+	0.110842i
$807$	−26.2285	+	9.80424i	−0.923288	+	0.345126i
$808$	1.71598	−	2.97216i	0.0603680	−	0.104560i
$809$	−12.7015			−0.446560			−0.223280	−	0.974754i	$-0.571676\pi$
$809$	−12.7015			−0.446560			−0.223280	+	0.974754i	$0.571676\pi$
$810$	1.25518	−	8.91204i	0.0441026	−	0.313137i
$811$	3.63136			0.127514			0.0637571	−	0.997965i	$-0.479692\pi$
$811$	3.63136			0.127514			0.0637571	+	0.997965i	$0.479692\pi$
$812$	−4.45882	+	7.72290i	−0.156474	+	0.271021i
$813$	5.46806	−	2.04396i	0.191773	−	0.0716849i
$814$	1.70364	+	2.95079i	0.0597125	+	0.103425i
$815$	5.05239	+	8.75100i	0.176978	+	0.306534i
$816$	1.62241	−	9.69075i	0.0567957	−	0.339244i
$817$	14.7972	−	25.6295i	0.517689	−	0.896663i
$818$	5.90973			0.206629
$819$	−0.969186	+	0.842250i	−0.0338661	+	0.0294306i
$820$	−11.2633			−0.393331
$821$	0.584336	−	1.01210i	0.0203935	−	0.0353225i	−0.855649	−	0.517557i	$-0.826841\pi$
$821$	0.584336	−	1.01210i	0.0203935	−	0.0353225i	0.876042	+	0.482235i	$0.160175\pi$
$822$	−28.5460	−	23.5350i	−0.995655	−	0.820878i
$823$	5.27958	+	9.14451i	0.184035	+	0.318757i	0.943251	−	0.332081i	$-0.107751\pi$
$823$	5.27958	+	9.14451i	0.184035	+	0.318757i	−0.759216	+	0.650839i	$0.774417\pi$
$824$	−4.36723	−	7.56426i	−0.152140	−	0.263513i
$825$	−0.764419	−	0.630233i	−0.0266136	−	0.0219419i
$826$	−3.16359	+	5.47950i	−0.110075	+	0.190656i
$827$	0.220132			0.00765474			0.00382737	−	0.999993i	$-0.498782\pi$
$827$	0.220132			0.00765474			0.00382737	+	0.999993i	$0.498782\pi$
$828$	−4.44648	−	22.8931i	−0.154526	−	0.795592i
$829$	9.02864			0.313578			0.156789	−	0.987632i	$-0.449886\pi$
$829$	9.02864			0.313578			0.156789	+	0.987632i	$0.449886\pi$
$830$	−5.10083	+	8.83490i	−0.177052	+	0.306664i
$831$	1.72655	−	10.3128i	0.0598932	−	0.357746i
$832$	0.214003	+	0.370665i	0.00741923	+	0.0128505i
$833$	−2.83641	−	4.91281i	−0.0982758	−	0.170219i
$834$	20.8241	−	7.78405i	0.721079	−	0.269540i
$835$	−3.69440	+	6.39889i	−0.127850	+	0.221443i
$836$	2.75518			0.0952900
$837$	44.0986	−	1.14501i	1.52427	−	0.0395774i
$838$	9.98153			0.344806
$839$	−27.9445	+	48.4013i	−0.964751	+	1.67100i	−0.254470	+	0.967081i	$0.581901\pi$
$839$	−27.9445	+	48.4013i	−0.964751	+	1.67100i	−0.710282	+	0.703918i	$0.751432\pi$
$840$	−1.62241	+	0.606458i	−0.0559784	+	0.0209248i
$841$	−25.2622	−	43.7553i	−0.871109	−	1.50880i
$842$	18.8661	+	32.6770i	0.650169	+	1.12612i
$843$	5.49096	−	32.7979i	0.189119	−	1.12962i
$844$	−5.63362	+	9.75772i	−0.193917	+	0.335874i
$845$	−12.8168			−0.440912
$846$	−32.1809	−	11.0861i	−1.10640	−	0.381147i
$847$	−10.6728			−0.366723
$848$	2.55042	−	4.41745i	0.0875816	−	0.151696i
$849$	17.4610	+	14.3959i	0.599260	+	0.494066i
$850$	−2.83641	−	4.91281i	−0.0972881	−	0.168508i
$851$	23.1532	+	40.1026i	0.793682	+	1.37470i
$852$	20.0761	+	16.5520i	0.687797	+	0.567062i
$853$	−19.8969	+	34.4625i	−0.681257	+	1.17997i	0.293340	+	0.956008i	$0.405233\pi$
$853$	−19.8969	+	34.4625i	−0.681257	+	1.17997i	−0.974597	+	0.223964i	$0.928100\pi$
$854$	−4.24482			−0.145255
$855$	13.6625	+	4.70661i	0.467246	+	0.160963i
$856$	14.7305			0.503478
$857$	−23.5028	+	40.7081i	−0.802841	+	1.39056i	0.114898	+	0.993377i	$0.463346\pi$
$857$	−23.5028	+	40.7081i	−0.802841	+	1.39056i	−0.917739	+	0.397184i	$0.869987\pi$
$858$	0.0700168	−	0.418215i	0.00239034	−	0.0142776i
$859$	−10.1613	−	17.5999i	−0.346700	−	0.600502i	0.638961	−	0.769239i	$-0.279364\pi$
$859$	−10.1613	−	17.5999i	−0.346700	−	0.600502i	−0.985661	+	0.168737i	$0.946031\pi$
$860$	−3.07199	−	5.32085i	−0.104754	−	0.181439i
$861$	18.2737	−	6.83071i	0.622764	−	0.232790i
$862$	−7.11930	+	12.3310i	−0.242484	+	0.419995i
$863$	−44.4033			−1.51151			−0.755753	−	0.654856i	$-0.772729\pi$
$863$	−44.4033			−1.51151			−0.755753	+	0.654856i	$0.772729\pi$
$864$	5.19440	−	0.134872i	0.176717	−	0.00458844i
$865$	0.489634			0.0166481
$866$	−8.60478	+	14.9039i	−0.292402	+	0.506456i
$867$	−24.6297	+	9.20659i	−0.836467	+	0.312672i
$868$	−4.24482	−	7.35224i	−0.144078	−	0.249551i
$869$	2.10083	+	3.63875i	0.0712658	+	0.123436i
$870$	2.55042	−	15.2338i	0.0864672	−	0.516474i
$871$	−2.41962	+	4.19090i	−0.0819856	+	0.142003i
$872$	3.00395			0.101727
$873$	3.14003	+	16.1668i	0.106274	+	0.547163i
$874$	37.4442			1.26657
$875$	−0.500000	+	0.866025i	−0.0169031	+	0.0292770i
$876$	−8.48040	−	6.99175i	−0.286526	−	0.236229i
$877$	−9.30334	−	16.1139i	−0.314151	−	0.544126i	0.665105	−	0.746750i	$-0.268387\pi$
$877$	−9.30334	−	16.1139i	−0.314151	−	0.544126i	−0.979257	+	0.202623i	$0.935053\pi$
$878$	20.0453	+	34.7195i	0.676497	+	1.17173i
$879$	30.1378	+	24.8474i	1.01652	+	0.838082i
$880$	0.285997	−	0.495361i	0.00964094	−	0.0166986i
$881$	−0.549569			−0.0185155			−0.00925773	−	0.999957i	$-0.502947\pi$
$881$	−0.549569			−0.0185155			−0.00925773	+	0.999957i	$0.502947\pi$
$882$	2.26442	−	1.96784i	0.0762469	−	0.0662607i
$883$	21.6359			0.728105			0.364053	−	0.931378i	$-0.381393\pi$
$883$	21.6359			0.728105			0.364053	+	0.931378i	$0.381393\pi$
$884$	1.21400	−	2.10272i	0.0408314	−	0.0707220i
$885$	1.80955	−	10.8086i	0.0608274	−	0.363326i
$886$	4.25518	+	7.37019i	0.142956	+	0.247606i
$887$	4.52884	+	7.84418i	0.152063	+	0.263382i	0.931986	−	0.362495i	$-0.118075\pi$
$887$	4.52884	+	7.84418i	0.152063	+	0.263382i	−0.779922	+	0.625876i	$0.784742\pi$
$888$	−9.66443	+	3.61257i	−0.324317	+	0.121230i
$889$	−6.03081	+	10.4457i	−0.202267	+	0.350337i
$890$	8.28797			0.277813
$891$	−4.05570	−	3.17058i	−0.135871	−	0.106219i
$892$	6.44648			0.215844
$893$	27.3249	−	47.3281i	0.914393	−	1.58378i
$894$	−6.81681	+	2.54813i	−0.227988	+	0.0852222i
$895$	1.33641	+	2.31473i	0.0446713	+	0.0773730i
$896$	−0.500000	−	0.866025i	−0.0167038	−	0.0289319i
$897$	0.951561	−	5.68373i	0.0317717	−	0.189774i
$898$	−6.54844	+	11.3422i	−0.218524	+	0.378495i
$899$	75.7075			2.52499
$900$	2.26442	−	1.96784i	0.0754806	−	0.0655948i
$901$	−28.9361			−0.964002
$902$	−3.22126	+	5.57939i	−0.107256	+	0.185773i
$903$	8.21090	+	6.76956i	0.273242	+	0.225277i
$904$	3.05239	+	5.28690i	0.101521	+	0.175840i
$905$	5.00000	+	8.66025i	0.166206	+	0.287877i
$906$	4.85601	+	4.00359i	0.161330	+	0.133010i
$907$	−17.7972	+	30.8257i	−0.590947	+	1.02355i	0.403159	+	0.915130i	$0.367912\pi$
$907$	−17.7972	+	30.8257i	−0.590947	+	1.02355i	−0.994105	+	0.108419i	$0.965421\pi$
$908$	−3.73445			−0.123932
$909$	−1.96306	−	10.1070i	−0.0651105	−	0.335228i
$910$	−0.428007			−0.0141883
$911$	12.8344	−	22.2299i	0.425224	−	0.736509i	−0.571217	−	0.820799i	$-0.693529\pi$
$911$	12.8344	−	22.2299i	0.425224	−	0.736509i	0.996441	+	0.0842895i	$0.0268620\pi$
$912$	−1.37759	+	8.22844i	−0.0456166	+	0.272471i
$913$	2.91764	+	5.05350i	0.0965598	+	0.167247i
$914$	14.0165	+	24.2773i	0.463624	+	0.803021i
$915$	6.88683	−	2.57430i	0.227671	−	0.0851038i
$916$	−2.07925	+	3.60137i	−0.0687004	+	0.118993i
$917$	−2.01847			−0.0666558
$918$	−15.3961	−	25.1366i	−0.508146	−	0.829630i
$919$	−11.7842			−0.388726			−0.194363	−	0.980930i	$-0.562264\pi$
$919$	−11.7842			−0.388726			−0.194363	+	0.980930i	$0.562264\pi$
$920$	3.88683	−	6.73218i	0.128145	−	0.221953i
$921$	20.2569	−	7.57204i	0.667487	−	0.249507i
$922$	−10.9784	−	19.0152i	−0.361555	−	0.626232i
$923$	3.21485	+	5.56828i	0.105818	+	0.183282i
$924$	−0.163588	+	0.977122i	−0.00538166	+	0.0321450i
$925$	−2.97842	+	5.15878i	−0.0979299	+	0.169620i
$926$	12.2017			0.400971
$927$	−24.7745	−	8.53463i	−0.813701	−	0.280314i
$928$	8.91764			0.292736
$929$	11.4280	−	19.7939i	0.374941	−	0.649416i	−0.615377	−	0.788233i	$-0.710996\pi$
$929$	11.4280	−	19.7939i	0.374941	−	0.649416i	0.990318	+	0.138816i	$0.0443297\pi$
$930$	11.3456	+	9.35403i	0.372038	+	0.306731i
$931$	2.40841	+	4.17148i	0.0789323	+	0.136715i
$932$	10.0204	+	17.3559i	0.328231	+	0.568512i
$933$	−8.17262	−	6.73800i	−0.267560	−	0.220592i
$934$	13.2129	−	22.8854i	0.432338	−	0.748832i
$935$	−3.24482			−0.106117
$936$	1.21400	+	0.418215i	0.0396809	+	0.0136698i
$937$	−25.2073			−0.823487			−0.411743	−	0.911300i	$-0.635080\pi$
$937$	−25.2073			−0.823487			−0.411743	+	0.911300i	$0.635080\pi$
$938$	5.65322	−	9.79167i	0.184584	−	0.319709i
$939$	−8.47447	+	50.6185i	−0.276554	+	1.65187i
$940$	−5.67282	−	9.82562i	−0.185027	−	0.320476i
$941$	6.73445	+	11.6644i	0.219537	+	0.380249i	0.954666	−	0.297678i	$-0.0962121\pi$
$941$	6.73445	+	11.6644i	0.219537	+	0.380249i	−0.735130	+	0.677927i	$0.762879\pi$
$942$	7.05683	−	2.63785i	0.229924	−	0.0859457i
$943$	−43.7785	+	75.8265i	−1.42562	+	2.46925i
$944$	6.32718			0.205932
$945$	−2.48040	+	4.56592i	−0.0806874	+	0.148529i
$946$	−3.51432			−0.114260
$947$	24.4832	−	42.4062i	0.795598	−	1.37802i	−0.126861	−	0.991920i	$-0.540490\pi$
$947$	24.4832	−	42.4062i	0.795598	−	1.37802i	0.922459	−	0.386095i	$-0.126176\pi$
$948$	−11.9176	+	4.45482i	−0.387067	+	0.144686i
$949$	−1.35799	−	2.35211i	−0.0440822	−	0.0763526i
$950$	2.40841	+	4.17148i	0.0781390	+	0.135341i
$951$	4.81068	−	28.7345i	0.155997	−	0.931780i
$952$	−2.83641	+	4.91281i	−0.0919286	+	0.159225i
$953$	27.9546			0.905538			0.452769	−	0.891628i	$-0.350436\pi$
$953$	27.9546			0.905538			0.452769	+	0.891628i	$0.350436\pi$
$954$	−2.91764	−	15.0218i	−0.0944621	−	0.486348i
$955$	10.8560			0.351292
$956$	−6.24482	+	10.8163i	−0.201972	+	0.349825i
$957$	−6.81681	−	5.62019i	−0.220356	−	0.181675i
$958$	18.3949	+	31.8610i	0.594313	+	1.02938i
$959$	10.6801	+	18.4984i	0.344878	+	0.597346i
$960$	1.33641	+	1.10182i	0.0431325	+	0.0355610i
$961$	−20.5369	+	35.5710i	−0.662482	+	1.14745i
$962$	−2.54957			−0.0822014
$963$	33.3560	−	28.9873i	1.07488	−	0.934103i
$964$	−2.38880			−0.0769382
$965$	1.43922	−	2.49280i	0.0463301	−	0.0802461i
$966$	−2.22324	+	13.2795i	−0.0715315	+	0.427262i
$967$	−18.6481	−	32.2995i	−0.599684	−	1.03868i	−0.992868	−	0.119223i	$-0.961960\pi$
$967$	−18.6481	−	32.2995i	−0.599684	−	1.03868i	0.393184	−	0.919460i	$-0.371374\pi$
$968$	5.33641	+	9.24294i	0.171519	+	0.297079i
$969$	44.3322	−	16.5714i	1.42415	−	0.532350i
$970$	−2.74482	+	4.75416i	−0.0881308	+	0.152647i
$971$	20.0739			0.644202			0.322101	−	0.946705i	$-0.395611\pi$
$971$	20.0739			0.644202			0.322101	+	0.946705i	$0.395611\pi$
$972$	11.4969	−	10.5272i	0.368763	−	0.337659i
$973$	−12.8353			−0.411480
$974$	−8.38880	+	14.5298i	−0.268795	+	0.465566i
$975$	0.694402	−	0.259568i	0.0222387	−	0.00831283i
$976$	2.12241	+	3.67612i	0.0679366	+	0.117670i
$977$	4.21513	+	7.30083i	0.134854	+	0.233574i	0.925542	−	0.378646i	$-0.123610\pi$
$977$	4.21513	+	7.30083i	0.134854	+	0.233574i	−0.790688	+	0.612220i	$0.790277\pi$
$978$	−2.88993	+	17.2618i	−0.0924099	+	0.551970i
$979$	2.37033	−	4.10554i	0.0757562	−	0.131214i
$980$	1.00000			0.0319438
$981$	6.80221	−	5.91131i	0.217178	−	0.188734i
$982$	−23.3681			−0.745705
$983$	18.4896	−	32.0250i	0.589728	−	1.02144i	−0.404540	−	0.914520i	$-0.632568\pi$
$983$	18.4896	−	32.0250i	0.589728	−	1.02144i	0.994268	−	0.106918i	$-0.0340983\pi$
$984$	−15.0524	−	12.4101i	−0.479853	−	0.395619i
$985$	9.28487	+	16.0819i	0.295840	+	0.512411i
$986$	−25.2941	−	43.8107i	−0.805528	−	1.39522i
$987$	15.1625	+	12.5008i	0.482626	+	0.397906i
$988$	−1.03081	+	1.78542i	−0.0327945	+	0.0568018i
$989$	−47.7612			−1.51872
$990$	−0.327176	−	1.68450i	−0.0103983	−	0.0535369i
$991$	−12.4482			−0.395429			−0.197715	−	0.980260i	$-0.563352\pi$
$991$	−12.4482			−0.395429			−0.197715	+	0.980260i	$0.563352\pi$
$992$	−4.24482	+	7.35224i	−0.134773	+	0.233434i
$993$	−7.77365	+	46.4325i	−0.246689	+	1.47349i
$994$	−7.51121	−	13.0098i	−0.238241	−	0.412646i
$995$	7.66048	+	13.2683i	0.242854	+	0.420635i
$996$	−16.5513	+	6.18687i	−0.524447	+	0.196039i
$997$	−1.30249	+	2.25598i	−0.0412503	+	0.0714476i	−0.885913	−	0.463851i	$-0.846467\pi$
$997$	−1.30249	+	2.25598i	−0.0412503	+	0.0714476i	0.844663	+	0.535298i	$0.179801\pi$
$998$	22.8106			0.722057
$999$	−14.7753	+	27.1985i	−0.467471	+	0.860522i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.j.k.421.1	yes	6
3.2	odd	2		1890.2.j.j.1261.2		6
9.2	odd	6		5670.2.a.bp.1.2		3
9.4	even	3	inner	630.2.j.k.211.1	✓	6
9.5	odd	6		1890.2.j.j.631.2		6
9.7	even	3		5670.2.a.bt.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.j.k.211.1	✓	6	9.4	even	3	inner
630.2.j.k.421.1	yes	6	1.1	even	1	trivial
1890.2.j.j.631.2		6	9.5	odd	6
1890.2.j.j.1261.2		6	3.2	odd	2
5670.2.a.bp.1.2		3	9.2	odd	6
5670.2.a.bt.1.2		3	9.7	even	3

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.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.62241 + 0.606458i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.285997 - 1.70828i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(2.26442 - 1.96784i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.62241 + 0.606458i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.285997 - 1.70828i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(2.26442 - 1.96784i) q^{9} +1.00000 q^{10} +(0.285997 - 0.495361i) q^{11} +(1.33641 + 1.10182i) q^{12} +(0.214003 + 0.370665i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(1.33641 + 1.10182i) q^{15} +(-0.500000 + 0.866025i) q^{16} +5.67282 q^{17} +(0.571993 + 2.94497i) q^{18} -4.81681 q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.285997 - 1.70828i) q^{21} +(0.285997 + 0.495361i) q^{22} +(3.88683 + 6.73218i) q^{23} +(-1.62241 + 0.606458i) q^{24} +(-0.500000 + 0.866025i) q^{25} -0.428007 q^{26} +(-2.48040 + 4.56592i) q^{27} +1.00000 q^{28} +(-4.45882 + 7.72290i) q^{29} +(-1.62241 + 0.606458i) q^{30} +(-4.24482 - 7.35224i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.163588 + 0.977122i) q^{33} +(-2.83641 + 4.91281i) q^{34} +1.00000 q^{35} +(-2.83641 - 0.977122i) q^{36} +5.95684 q^{37} +(2.40841 - 4.17148i) q^{38} +(-0.571993 - 0.471586i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(5.63164 + 9.75429i) q^{41} +(1.33641 + 1.10182i) q^{42} +(-3.07199 + 5.32085i) q^{43} -0.571993 q^{44} +(-2.83641 - 0.977122i) q^{45} -7.77365 q^{46} +(-5.67282 + 9.82562i) q^{47} +(0.285997 - 1.70828i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-9.20364 + 3.44033i) q^{51} +(0.214003 - 0.370665i) q^{52} -5.10083 q^{53} +(-2.71400 - 4.43105i) q^{54} -0.571993 q^{55} +(-0.500000 + 0.866025i) q^{56} +(7.81483 - 2.92119i) q^{57} +(-4.45882 - 7.72290i) q^{58} +(-3.16359 - 5.47950i) q^{59} +(0.285997 - 1.70828i) q^{60} +(2.12241 - 3.67612i) q^{61} +8.48963 q^{62} +(0.571993 + 2.94497i) q^{63} +1.00000 q^{64} +(0.214003 - 0.370665i) q^{65} +(-0.764419 - 0.630233i) q^{66} +(5.65322 + 9.79167i) q^{67} +(-2.83641 - 4.91281i) q^{68} +(-10.3888 - 8.56515i) q^{69} +(-0.500000 + 0.866025i) q^{70} +15.0224 q^{71} +(2.26442 - 1.96784i) q^{72} -6.34565 q^{73} +(-2.97842 + 5.15878i) q^{74} +(0.285997 - 1.70828i) q^{75} +(2.40841 + 4.17148i) q^{76} +(0.285997 + 0.495361i) q^{77} +(0.694402 - 0.259568i) q^{78} +(-3.67282 + 6.36152i) q^{79} +1.00000 q^{80} +(1.25518 - 8.91204i) q^{81} -11.2633 q^{82} +(-5.10083 + 8.83490i) q^{83} +(-1.62241 + 0.606458i) q^{84} +(-2.83641 - 4.91281i) q^{85} +(-3.07199 - 5.32085i) q^{86} +(2.55042 - 15.2338i) q^{87} +(0.285997 - 0.495361i) q^{88} +8.28797 q^{89} +(2.26442 - 1.96784i) q^{90} -0.428007 q^{91} +(3.88683 - 6.73218i) q^{92} +(11.3456 + 9.35403i) q^{93} +(-5.67282 - 9.82562i) q^{94} +(2.40841 + 4.17148i) q^{95} +(1.33641 + 1.10182i) q^{96} +(-2.74482 + 4.75416i) q^{97} +1.00000 q^{98} +(-0.327176 - 1.68450i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + q^{3} - 3 q^{4} - 3 q^{5} + q^{6} - 3 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 + q^3 - 3 * q^4 - 3 * q^5 + q^6 - 3 * q^7 + 6 * q^8 + 5 * q^9	\( 6 q - 3 q^{2} + q^{3} - 3 q^{4} - 3 q^{5} + q^{6} - 3 q^{7} + 6 q^{8} + 5 q^{9} + 6 q^{10} + q^{11} - 2 q^{12} + 2 q^{13} - 3 q^{14} - 2 q^{15} - 3 q^{16} + 14 q^{17} + 2 q^{18} - 6 q^{19} - 3 q^{20} + q^{21} + q^{22} + 4 q^{23} + q^{24} - 3 q^{25} - 4 q^{26} - 2 q^{27} + 6 q^{28} - 6 q^{29} + q^{30} - 4 q^{31} - 3 q^{32} - 11 q^{33} - 7 q^{34} + 6 q^{35} - 7 q^{36} + 20 q^{37} + 3 q^{38} - 2 q^{39} - 3 q^{40} - 7 q^{41} - 2 q^{42} - 17 q^{43} - 2 q^{44} - 7 q^{45} - 8 q^{46} - 14 q^{47} + q^{48} - 3 q^{49} - 3 q^{50} - 13 q^{51} + 2 q^{52} - 12 q^{53} - 17 q^{54} - 2 q^{55} - 3 q^{56} + 29 q^{57} - 6 q^{58} - 29 q^{59} + q^{60} + 2 q^{61} + 8 q^{62} + 2 q^{63} + 6 q^{64} + 2 q^{65} + 4 q^{66} + q^{67} - 7 q^{68} - 38 q^{69} - 3 q^{70} + 20 q^{71} + 5 q^{72} + 2 q^{73} - 10 q^{74} + q^{75} + 3 q^{76} + q^{77} - 8 q^{78} - 2 q^{79} + 6 q^{80} + 29 q^{81} + 14 q^{82} - 12 q^{83} + q^{84} - 7 q^{85} - 17 q^{86} + 6 q^{87} + q^{88} + 44 q^{89} + 5 q^{90} - 4 q^{91} + 4 q^{92} + 28 q^{93} - 14 q^{94} + 3 q^{95} - 2 q^{96} + 5 q^{97} + 6 q^{98} - 22 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + q^3 - 3 * q^4 - 3 * q^5 + q^6 - 3 * q^7 + 6 * q^8 + 5 * q^9 + 6 * q^10 + q^11 - 2 * q^12 + 2 * q^13 - 3 * q^14 - 2 * q^15 - 3 * q^16 + 14 * q^17 + 2 * q^18 - 6 * q^19 - 3 * q^20 + q^21 + q^22 + 4 * q^23 + q^24 - 3 * q^25 - 4 * q^26 - 2 * q^27 + 6 * q^28 - 6 * q^29 + q^30 - 4 * q^31 - 3 * q^32 - 11 * q^33 - 7 * q^34 + 6 * q^35 - 7 * q^36 + 20 * q^37 + 3 * q^38 - 2 * q^39 - 3 * q^40 - 7 * q^41 - 2 * q^42 - 17 * q^43 - 2 * q^44 - 7 * q^45 - 8 * q^46 - 14 * q^47 + q^48 - 3 * q^49 - 3 * q^50 - 13 * q^51 + 2 * q^52 - 12 * q^53 - 17 * q^54 - 2 * q^55 - 3 * q^56 + 29 * q^57 - 6 * q^58 - 29 * q^59 + q^60 + 2 * q^61 + 8 * q^62 + 2 * q^63 + 6 * q^64 + 2 * q^65 + 4 * q^66 + q^67 - 7 * q^68 - 38 * q^69 - 3 * q^70 + 20 * q^71 + 5 * q^72 + 2 * q^73 - 10 * q^74 + q^75 + 3 * q^76 + q^77 - 8 * q^78 - 2 * q^79 + 6 * q^80 + 29 * q^81 + 14 * q^82 - 12 * q^83 + q^84 - 7 * q^85 - 17 * q^86 + 6 * q^87 + q^88 + 44 * q^89 + 5 * q^90 - 4 * q^91 + 4 * q^92 + 28 * q^93 - 14 * q^94 + 3 * q^95 - 2 * q^96 + 5 * q^97 + 6 * q^98 - 22 * q^99

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