LMFDB - Embedded newform 630.2.bf.e.419.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(209,630)]

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([1, 3, 3]))

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

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

chi := DirichletCharacter("630.209");

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.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			419.6
Character	$\chi$	$=$	630.419
Dual form			630.2.bf.e.209.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.777586 - 1.54770i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.55878 + 1.60318i) q^{5} +(-0.951551 + 1.44726i) q^{6} +(2.64557 + 0.0312377i) q^{7} +1.00000 q^{8} +(-1.79072 + 2.40693i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.777586 - 1.54770i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.55878 + 1.60318i) q^{5} +(-0.951551 + 1.44726i) q^{6} +(2.64557 + 0.0312377i) q^{7} +1.00000 q^{8} +(-1.79072 + 2.40693i) q^{9} +(0.609005 - 2.15154i) q^{10} +(-2.30587 + 1.33130i) q^{11} +(1.72914 + 0.100439i) q^{12} +(-1.15988 + 2.00897i) q^{13} +(-1.29573 - 2.30675i) q^{14} +(1.26915 - 3.65913i) q^{15} +(-0.500000 - 0.866025i) q^{16} +7.23248i q^{17} +(2.97982 + 0.347345i) q^{18} +5.58729i q^{19} +(-2.16779 + 0.548354i) q^{20} +(-2.00881 - 4.11882i) q^{21} +(2.30587 + 1.33130i) q^{22} +(-0.354226 + 0.613538i) q^{23} +(-0.777586 - 1.54770i) q^{24} +(-0.140390 + 4.99803i) q^{25} +2.31976 q^{26} +(5.11763 + 0.899897i) q^{27} +(-1.34984 + 2.27551i) q^{28} +(-2.68539 + 1.55041i) q^{29} +(-3.80348 + 0.730449i) q^{30} +(-5.32011 - 3.07156i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.85345 + 2.53359i) q^{33} +(6.26351 - 3.61624i) q^{34} +(4.07379 + 4.29002i) q^{35} +(-1.18910 - 2.75428i) q^{36} -8.09944i q^{37} +(4.83874 - 2.79365i) q^{38} +(4.01118 + 0.232994i) q^{39} +(1.55878 + 1.60318i) q^{40} +(-3.67973 + 6.37348i) q^{41} +(-2.56260 + 3.79909i) q^{42} +(11.3383 - 6.54616i) q^{43} -2.66259i q^{44} +(-6.65010 + 0.881030i) q^{45} +0.708453 q^{46} +(4.91158 - 2.83570i) q^{47} +(-0.951551 + 1.44726i) q^{48} +(6.99805 + 0.165283i) q^{49} +(4.39861 - 2.37743i) q^{50} +(11.1937 - 5.62387i) q^{51} +(-1.15988 - 2.00897i) q^{52} -3.40917 q^{53} +(-1.77948 - 4.88195i) q^{54} +(-5.72866 - 1.62153i) q^{55} +(2.64557 + 0.0312377i) q^{56} +(8.64743 - 4.34460i) q^{57} +(2.68539 + 1.55041i) q^{58} +(-1.98592 + 3.43972i) q^{59} +(2.53433 + 2.92868i) q^{60} +(8.66705 - 5.00392i) q^{61} +6.14313i q^{62} +(-4.81266 + 6.31176i) q^{63} +1.00000 q^{64} +(-5.02875 + 1.27205i) q^{65} +(0.267428 - 4.60398i) q^{66} +(-4.96469 - 2.86637i) q^{67} +(-6.26351 - 3.61624i) q^{68} +(1.22501 + 0.0711562i) q^{69} +(1.67837 - 5.67301i) q^{70} -9.75935i q^{71} +(-1.79072 + 2.40693i) q^{72} +4.33252 q^{73} +(-7.01432 + 4.04972i) q^{74} +(7.84459 - 3.66911i) q^{75} +(-4.83874 - 2.79365i) q^{76} +(-6.14192 + 3.45000i) q^{77} +(-1.80381 - 3.59028i) q^{78} +(7.29204 + 12.6302i) q^{79} +(0.609005 - 2.15154i) q^{80} +(-2.58663 - 8.62029i) q^{81} +7.35946 q^{82} +(2.25905 - 1.30426i) q^{83} +(4.57141 + 0.319732i) q^{84} +(-11.5950 + 11.2739i) q^{85} +(-11.3383 - 6.54616i) q^{86} +(4.48768 + 2.95058i) q^{87} +(-2.30587 + 1.33130i) q^{88} -5.66299 q^{89} +(4.08804 + 5.31864i) q^{90} +(-3.13130 + 5.27864i) q^{91} +(-0.354226 - 0.613538i) q^{92} +(-0.617009 + 10.6223i) q^{93} +(-4.91158 - 2.83570i) q^{94} +(-8.95745 + 8.70938i) q^{95} +(1.72914 + 0.100439i) q^{96} +(-6.43250 - 11.1414i) q^{97} +(-3.35589 - 6.14313i) q^{98} +(0.924837 - 7.93405i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} - 6 q^{9}+O(q^{10}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 - 6 * q^9	$ 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} - 6 q^{9} - 24 q^{11} - 16 q^{15} - 16 q^{16} + 6 q^{18} + 2 q^{21} + 24 q^{22} - 24 q^{23} - 58 q^{25} - 36 q^{29} - 10 q^{30} - 16 q^{32} - 48 q^{35} - 66 q^{39} + 2 q^{42} - 54 q^{43} + 48 q^{46} + 32 q^{49} + 50 q^{50} - 26 q^{51} - 24 q^{53} + 110 q^{57} + 36 q^{58} + 26 q^{60} + 20 q^{63} + 32 q^{64} - 90 q^{65} - 66 q^{67} + 36 q^{70} - 6 q^{72} + 12 q^{74} + 18 q^{77} + 60 q^{78} + 34 q^{79} + 2 q^{81} - 4 q^{84} + 4 q^{85} + 54 q^{86} - 24 q^{88} + 16 q^{91} - 24 q^{92} + 28 q^{93} + 12 q^{95} - 64 q^{98} + 58 q^{99}+O(q^{100}) $ 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 - 6 * q^9 - 24 * q^11 - 16 * q^15 - 16 * q^16 + 6 * q^18 + 2 * q^21 + 24 * q^22 - 24 * q^23 - 58 * q^25 - 36 * q^29 - 10 * q^30 - 16 * q^32 - 48 * q^35 - 66 * q^39 + 2 * q^42 - 54 * q^43 + 48 * q^46 + 32 * q^49 + 50 * q^50 - 26 * q^51 - 24 * q^53 + 110 * q^57 + 36 * q^58 + 26 * q^60 + 20 * q^63 + 32 * q^64 - 90 * q^65 - 66 * q^67 + 36 * q^70 - 6 * q^72 + 12 * q^74 + 18 * q^77 + 60 * q^78 + 34 * q^79 + 2 * q^81 - 4 * q^84 + 4 * q^85 + 54 * q^86 - 24 * q^88 + 16 * q^91 - 24 * q^92 + 28 * q^93 + 12 * q^95 - 64 * q^98 + 58 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.777586	−	1.54770i	−0.448939	−	0.893562i
$3$	−0.777586	−	1.54770i	−0.448939	−	0.893562i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.55878	+	1.60318i	0.697109	+	0.716965i
$5$	1.55878	+	1.60318i	0.697109	+	0.716965i
$6$	−0.951551	+	1.44726i	−0.388469	+	0.590840i
$7$	2.64557	+	0.0312377i	0.999930	+	0.0118067i
$7$	2.64557	+	0.0312377i	0.999930	+	0.0118067i
$8$	1.00000			0.353553
$9$	−1.79072	+	2.40693i	−0.596907	+	0.802310i
$10$	0.609005	−	2.15154i	0.192584	−	0.680376i
$11$	−2.30587	+	1.33130i	−0.695246	+	0.401401i	−0.805574	−	0.592495i	$-0.798143\pi$
$11$	−2.30587	+	1.33130i	−0.695246	+	0.401401i	0.110328	+	0.993895i	$0.464810\pi$
$12$	1.72914	+	0.100439i	0.499159	+	0.0289942i
$13$	−1.15988	+	2.00897i	−0.321693	+	0.557189i	−0.980837	−	0.194828i	$-0.937585\pi$
$13$	−1.15988	+	2.00897i	−0.321693	+	0.557189i	0.659144	+	0.752016i	$0.270919\pi$
$14$	−1.29573	−	2.30675i	−0.346299	−	0.616504i
$15$	1.26915	−	3.65913i	0.327693	−	0.944784i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$			7.23248i			1.75413i	0.480369	+	0.877067i	$0.340503\pi$
$17$			7.23248i			1.75413i	−0.480369	+	0.877067i	$0.659497\pi$
$18$	2.97982	+	0.347345i	0.702351	+	0.0818700i
$19$			5.58729i			1.28181i	0.767619	+	0.640906i	$0.221441\pi$
$19$			5.58729i			1.28181i	−0.767619	+	0.640906i	$0.778559\pi$
$20$	−2.16779	+	0.548354i	−0.484732	+	0.122616i
$21$	−2.00881	−	4.11882i	−0.438358	−	0.898801i
$22$	2.30587	+	1.33130i	0.491613	+	0.283833i
$23$	−0.354226	+	0.613538i	−0.0738613	+	0.127932i	−0.900591	−	0.434668i	$-0.856866\pi$
$23$	−0.354226	+	0.613538i	−0.0738613	+	0.127932i	0.826729	+	0.562600i	$0.190199\pi$
$24$	−0.777586	−	1.54770i	−0.158724	−	0.315922i
$25$	−0.140390	+	4.99803i	−0.0280780	+	0.999606i
$26$	2.31976			0.454943
$27$	5.11763	+	0.899897i	0.984889	+	0.173185i
$28$	−1.34984	+	2.27551i	−0.255095	+	0.430031i
$29$	−2.68539	+	1.55041i	−0.498664	+	0.287904i	−0.728162	−	0.685406i	$-0.759625\pi$
$29$	−2.68539	+	1.55041i	−0.498664	+	0.287904i	0.229498	+	0.973309i	$0.426292\pi$
$30$	−3.80348	+	0.730449i	−0.694417	+	0.133361i
$31$	−5.32011	−	3.07156i	−0.955519	−	0.551669i	−0.0607281	−	0.998154i	$-0.519342\pi$
$31$	−5.32011	−	3.07156i	−0.955519	−	0.551669i	−0.894791	+	0.446485i	$0.852676\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	3.85345	+	2.53359i	0.670800	+	0.441041i
$34$	6.26351	−	3.61624i	1.07418	−	0.620180i
$35$	4.07379	+	4.29002i	0.688595	+	0.725146i
$36$	−1.18910	−	2.75428i	−0.198184	−	0.459046i
$37$		−	8.09944i		−	1.33154i	−0.746157	−	0.665770i	$-0.768103\pi$
$37$		−	8.09944i		−	1.33154i	0.746157	−	0.665770i	$-0.231897\pi$
$38$	4.83874	−	2.79365i	0.784947	−	0.453189i
$39$	4.01118	+	0.232994i	0.642303	+	0.0373089i
$40$	1.55878	+	1.60318i	0.246465	+	0.253485i
$41$	−3.67973	+	6.37348i	−0.574677	+	0.995370i	0.421400	+	0.906875i	$0.361539\pi$
$41$	−3.67973	+	6.37348i	−0.574677	+	0.995370i	−0.996077	+	0.0884948i	$0.971794\pi$
$42$	−2.56260	+	3.79909i	−0.395418	+	0.586212i
$43$	11.3383	−	6.54616i	1.72907	−	0.998280i	0.835224	−	0.549909i	$-0.185338\pi$
$43$	11.3383	−	6.54616i	1.72907	−	0.998280i	0.893848	−	0.448371i	$-0.147996\pi$
$44$		−	2.66259i		−	0.401401i
$45$	−6.65010	+	0.881030i	−0.991338	+	0.131336i
$46$	0.708453			0.104456
$47$	4.91158	−	2.83570i	0.716428	−	0.413630i	−0.0970085	−	0.995284i	$-0.530927\pi$
$47$	4.91158	−	2.83570i	0.716428	−	0.413630i	0.813437	+	0.581654i	$0.197594\pi$
$48$	−0.951551	+	1.44726i	−0.137345	+	0.208893i
$49$	6.99805	+	0.165283i	0.999721	+	0.0236118i
$50$	4.39861	−	2.37743i	0.622058	−	0.336220i
$51$	11.1937	−	5.62387i	1.56743	−	0.787499i
$52$	−1.15988	−	2.00897i	−0.160847	−	0.278594i
$53$	−3.40917			−0.468286			−0.234143	−	0.972202i	$-0.575228\pi$
$53$	−3.40917			−0.468286			−0.234143	+	0.972202i	$0.575228\pi$
$54$	−1.77948	−	4.88195i	−0.242157	−	0.664349i
$55$	−5.72866	−	1.62153i	−0.772453	−	0.218647i
$56$	2.64557	+	0.0312377i	0.353529	+	0.00417431i
$57$	8.64743	−	4.34460i	1.14538	−	0.575456i
$58$	2.68539	+	1.55041i	0.352608	+	0.203579i
$59$	−1.98592	+	3.43972i	−0.258545	+	0.447814i	−0.965852	−	0.259093i	$-0.916576\pi$
$59$	−1.98592	+	3.43972i	−0.258545	+	0.447814i	0.707307	+	0.706906i	$0.249910\pi$
$60$	2.53433	+	2.92868i	0.327180	+	0.378091i
$61$	8.66705	−	5.00392i	1.10970	−	0.640687i	0.170950	−	0.985280i	$-0.445316\pi$
$61$	8.66705	−	5.00392i	1.10970	−	0.640687i	0.938752	+	0.344593i	$0.111983\pi$
$62$			6.14313i			0.780178i
$63$	−4.81266	+	6.31176i	−0.606338	+	0.795207i
$64$	1.00000			0.125000
$65$	−5.02875	+	1.27205i	−0.623740	+	0.157779i
$66$	0.267428	−	4.60398i	0.0329181	−	0.566711i
$67$	−4.96469	−	2.86637i	−0.606534	−	0.350183i	0.165074	−	0.986281i	$-0.447214\pi$
$67$	−4.96469	−	2.86637i	−0.606534	−	0.350183i	−0.771608	+	0.636099i	$0.780547\pi$
$68$	−6.26351	−	3.61624i	−0.759562	−	0.438533i
$69$	1.22501	+	0.0711562i	0.147474	+	0.00856620i
$70$	1.67837	−	5.67301i	0.200604	−	0.678055i
$71$		−	9.75935i		−	1.15822i	−0.815249	−	0.579111i	$-0.803400\pi$
$71$		−	9.75935i		−	1.15822i	0.815249	−	0.579111i	$-0.196600\pi$
$72$	−1.79072	+	2.40693i	−0.211039	+	0.283660i
$73$	4.33252			0.507083			0.253541	−	0.967325i	$-0.418405\pi$
$73$	4.33252			0.507083			0.253541	+	0.967325i	$0.418405\pi$
$74$	−7.01432	+	4.04972i	−0.815398	+	0.470770i
$75$	7.84459	−	3.66911i	0.905815	−	0.423673i
$76$	−4.83874	−	2.79365i	−0.555041	−	0.320453i
$77$	−6.14192	+	3.45000i	−0.699937	+	0.393164i
$78$	−1.80381	−	3.59028i	−0.204242	−	0.406520i
$79$	7.29204	+	12.6302i	0.820419	+	1.42101i	0.905371	+	0.424622i	$0.139593\pi$
$79$	7.29204	+	12.6302i	0.820419	+	1.42101i	−0.0849523	+	0.996385i	$0.527074\pi$
$80$	0.609005	−	2.15154i	0.0680889	−	0.240549i
$81$	−2.58663	−	8.62029i	−0.287404	−	0.957810i
$82$	7.35946			0.812716
$83$	2.25905	−	1.30426i	0.247963	−	0.143162i	−0.370868	−	0.928686i	$-0.620940\pi$
$83$	2.25905	−	1.30426i	0.247963	−	0.143162i	0.618831	+	0.785524i	$0.287606\pi$
$84$	4.57141	+	0.319732i	0.498782	+	0.0348856i
$85$	−11.5950	+	11.2739i	−1.25765	+	1.22282i
$86$	−11.3383	−	6.54616i	−1.22264	−	0.705891i
$87$	4.48768	+	2.95058i	0.481129	+	0.316336i
$88$	−2.30587	+	1.33130i	−0.245807	+	0.141917i
$89$	−5.66299			−0.600276			−0.300138	−	0.953896i	$-0.597033\pi$
$89$	−5.66299			−0.600276			−0.300138	+	0.953896i	$0.597033\pi$
$90$	4.08804	+	5.31864i	0.430918	+	0.560634i
$91$	−3.13130	+	5.27864i	−0.328249	+	0.553352i
$92$	−0.354226	−	0.613538i	−0.0369307	−	0.0639658i
$93$	−0.617009	+	10.6223i	−0.0639808	+	1.10148i
$94$	−4.91158	−	2.83570i	−0.506591	−	0.292481i
$95$	−8.95745	+	8.70938i	−0.919015	+	0.893563i
$96$	1.72914	+	0.100439i	0.176479	+	0.0102510i
$97$	−6.43250	−	11.1414i	−0.653122	−	1.13124i	−0.982361	−	0.186993i	$-0.940126\pi$
$97$	−6.43250	−	11.1414i	−0.653122	−	1.13124i	0.329239	−	0.944246i	$-0.393208\pi$
$98$	−3.35589	−	6.14313i	−0.338996	−	0.620550i
$99$	0.924837	−	7.93405i	0.0929496	−	0.797402i
$100$	−4.25822	−	2.62060i	−0.425822	−	0.262060i
$101$	−2.06435	−	3.57555i	−0.205410	−	0.355781i	0.744853	−	0.667228i	$-0.232519\pi$
$101$	−2.06435	−	3.57555i	−0.205410	−	0.355781i	−0.950263	+	0.311448i	$0.899186\pi$
$102$	−10.4672	−	6.88207i	−1.03641	−	0.681426i
$103$	4.09983	−	7.10111i	0.403968	−	0.699694i	−0.590233	−	0.807233i	$-0.700964\pi$
$103$	4.09983	−	7.10111i	0.403968	−	0.699694i	0.994201	+	0.107540i	$0.0342973\pi$
$104$	−1.15988	+	2.00897i	−0.113736	+	0.196996i
$105$	3.47193	−	9.64084i	0.338825	−	0.940849i
$106$	1.70459	+	2.95243i	0.165564	+	0.286765i
$107$	10.5158			1.01660			0.508299	−	0.861180i	$-0.330274\pi$
$107$	10.5158			1.01660			0.508299	+	0.861180i	$0.330274\pi$
$108$	−3.33815	+	3.98205i	−0.321214	+	0.383173i
$109$	7.38448			0.707305			0.353653	−	0.935377i	$-0.384940\pi$
$109$	7.38448			0.707305			0.353653	+	0.935377i	$0.384940\pi$
$110$	1.46004	+	5.77193i	0.139210	+	0.550332i
$111$	−12.5355	+	6.29801i	−1.18981	+	0.597780i
$112$	−1.29573	−	2.30675i	−0.122435	−	0.217967i
$113$	−8.92367	+	15.4563i	−0.839468	+	1.45400i	0.0508712	+	0.998705i	$0.483800\pi$
$113$	−8.92367	+	15.4563i	−0.839468	+	1.45400i	−0.890340	+	0.455297i	$0.849533\pi$
$114$	−8.08625	−	5.31659i	−0.757346	−	0.497944i
$115$	−1.53578	+	0.388483i	−0.143212	+	0.0362262i
$116$		−	3.10082i		−	0.287904i
$117$	−2.75843	−	6.38926i	−0.255017	−	0.590688i
$118$	3.97185			0.365638
$119$	−0.225926	+	19.1340i	−0.0207106	+	1.75401i
$120$	1.26915	−	3.65913i	0.115857	−	0.334032i
$121$	−1.95531	+	3.38669i	−0.177755	+	0.307881i
$122$	−8.66705	−	5.00392i	−0.784678	−	0.453034i
$123$	12.7255	+	0.739175i	1.14742	+	0.0666492i
$124$	5.32011	−	3.07156i	0.477760	−	0.275835i
$125$	−8.23159	+	7.56577i	−0.736256	+	0.676703i
$126$	7.87247	+	1.01201i	0.701336	+	0.0901567i
$127$			16.2541i			1.44232i	0.692770	+	0.721159i	$0.256390\pi$
$127$			16.2541i			1.44232i	−0.692770	+	0.721159i	$0.743610\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−18.9479	−	12.4580i	−1.66827	−	1.09687i
$130$	3.61601	+	3.71900i	0.317145	+	0.326178i
$131$	−1.95598	+	3.38785i	−0.170895	+	0.295998i	−0.938733	−	0.344646i	$-0.887999\pi$
$131$	−1.95598	+	3.38785i	−0.170895	+	0.295998i	0.767838	+	0.640644i	$0.221332\pi$
$132$	−4.12088	+	2.07039i	−0.358676	+	0.180204i
$133$	−0.174534	+	14.7816i	−0.0151340	+	1.28172i
$134$			5.73274i			0.495233i
$135$	6.53458	+	9.60725i	0.562407	+	0.826860i
$136$			7.23248i			0.620180i
$137$	−0.467496	−	0.809727i	−0.0399409	−	0.0691796i	0.845364	−	0.534191i	$-0.179384\pi$
$137$	−0.467496	−	0.809727i	−0.0399409	−	0.0691796i	−0.885305	+	0.465011i	$0.846050\pi$
$138$	−0.550883	−	1.09647i	−0.0468942	−	0.0933376i
$139$	10.8220	+	6.24810i	0.917912	+	0.529957i	0.882968	−	0.469432i	$-0.155541\pi$
$139$	10.8220	+	6.24810i	0.917912	+	0.529957i	0.0349439	+	0.999389i	$0.488875\pi$
$140$	−5.75216	+	1.38299i	−0.486146	+	0.116884i
$141$	−8.20798	−	5.39663i	−0.691237	−	0.454478i
$142$	−8.45184	+	4.87967i	−0.709263	+	0.409493i
$143$		−	6.17657i		−	0.516511i
$144$	2.97982	+	0.347345i	0.248319	+	0.0289454i
$145$	−6.67152	−	1.88841i	−0.554040	−	0.156824i
$146$	−2.16626	−	3.75207i	−0.179281	−	0.310524i
$147$	−5.18577	−	10.9594i	−0.427715	−	0.903913i
$148$	7.01432	+	4.04972i	0.576574	+	0.332885i
$149$	2.62453	+	1.51527i	0.215010	+	0.124136i	0.603638	−	0.797259i	$-0.293717\pi$
$149$	2.62453	+	1.51527i	0.215010	+	0.124136i	−0.388628	+	0.921395i	$0.627051\pi$
$150$	−7.09984	−	4.95906i	−0.579700	−	0.404905i
$151$	−4.75076	−	8.22856i	−0.386612	−	0.669631i	0.605380	−	0.795937i	$-0.293021\pi$
$151$	−4.75076	−	8.22856i	−0.386612	−	0.669631i	−0.991991	+	0.126306i	$0.959688\pi$
$152$			5.58729i			0.453189i
$153$	−17.4081	−	12.9514i	−1.40736	−	1.04705i
$154$	6.05875	+	3.59406i	0.488228	+	0.289618i
$155$	−3.36861	−	13.3170i	−0.270573	−	1.06965i
$156$	−2.20737	+	3.35729i	−0.176731	+	0.268798i
$157$	−3.53933	+	6.13030i	−0.282470	+	0.489252i	−0.971992	−	0.235012i	$-0.924487\pi$
$157$	−3.53933	+	6.13030i	−0.282470	+	0.489252i	0.689523	+	0.724264i	$0.257820\pi$
$158$	7.29204	−	12.6302i	0.580124	−	1.00480i
$159$	2.65092	+	5.27636i	0.210232	+	0.418443i
$160$	−2.16779	+	0.548354i	−0.171379	+	0.0433512i
$161$	−0.956295	+	1.61209i	−0.0753666	+	0.127051i
$162$	−6.17207	+	6.55023i	−0.484924	+	0.514635i
$163$		−	18.8251i		−	1.47449i	−0.675624	−	0.737246i	$-0.736126\pi$
$163$		−	18.8251i		−	1.47449i	0.675624	−	0.737246i	$-0.263874\pi$
$164$	−3.67973	−	6.37348i	−0.287339	−	0.497685i
$165$	1.94489	+	10.1271i	0.151409	+	0.788394i
$166$	−2.25905	−	1.30426i	−0.175336	−	0.101231i
$167$	−8.32228	−	4.80487i	−0.643997	−	0.371812i	0.142155	−	0.989844i	$-0.454597\pi$
$167$	−8.32228	−	4.80487i	−0.643997	−	0.371812i	−0.786153	+	0.618032i	$0.787930\pi$
$168$	−2.00881	−	4.11882i	−0.154983	−	0.317774i
$169$	3.80935	+	6.59799i	0.293027	+	0.507538i
$170$	15.5609	+	4.40462i	1.19347	+	0.337819i
$171$	−13.4482	−	10.0053i	−1.02841	−	0.765123i
$172$			13.0923i			0.998280i
$173$	18.9914	−	10.9647i	1.44389	−	0.833629i	0.445782	−	0.895142i	$-0.352926\pi$
$173$	18.9914	−	10.9647i	1.44389	−	0.833629i	0.998106	+	0.0615122i	$0.0195923\pi$
$174$	0.311442	−	5.36173i	0.0236104	−	0.406472i
$175$	−0.527537	+	13.2182i	−0.0398781	+	0.999205i
$176$	2.30587	+	1.33130i	0.173812	+	0.100350i
$177$	6.86787	+	0.398928i	0.516221	+	0.0299853i
$178$	2.83150	+	4.90430i	0.212230	+	0.367593i
$179$			2.33029i			0.174174i	0.996201	+	0.0870870i	$0.0277558\pi$
$179$			2.33029i			0.174174i	−0.996201	+	0.0870870i	$0.972244\pi$
$180$	2.56205	−	6.19967i	0.190964	−	0.462096i
$181$		−	19.7070i		−	1.46481i	−0.680868	−	0.732406i	$-0.738397\pi$
$181$		−	19.7070i		−	1.46481i	0.680868	−	0.732406i	$-0.261603\pi$
$182$	6.13708	+	0.0724640i	0.454911	+	0.00537139i
$183$	−14.4839	−	9.52297i	−1.07068	−	0.703959i
$184$	−0.354226	+	0.613538i	−0.0261139	+	0.0452306i
$185$	12.9849	−	12.6253i	0.954668	−	0.928229i
$186$	9.50769	−	4.77681i	0.697138	−	0.350253i
$187$	−9.62856	−	16.6772i	−0.704110	−	1.21955i
$188$			5.67141i			0.413630i
$189$	13.5109	+	2.54060i	0.982776	+	0.184801i
$190$	12.0213	+	3.40269i	0.872114	+	0.246857i
$191$	11.7316	−	6.77323i	0.848867	−	0.490094i	−0.0114013	−	0.999935i	$-0.503629\pi$
$191$	11.7316	−	6.77323i	0.848867	−	0.490094i	0.860268	+	0.509841i	$0.170296\pi$
$192$	−0.777586	−	1.54770i	−0.0561174	−	0.111695i
$193$	−6.99314	−	4.03749i	−0.503378	−	0.290625i	0.226730	−	0.973958i	$-0.427197\pi$
$193$	−6.99314	−	4.03749i	−0.503378	−	0.290625i	−0.730107	+	0.683333i	$0.760530\pi$
$194$	−6.43250	+	11.1414i	−0.461827	+	0.799907i
$195$	5.87903	+	6.79385i	0.421006	+	0.486518i
$196$	−3.64216	+	5.97785i	−0.260155	+	0.426989i
$197$	−1.76372			−0.125660			−0.0628299	−	0.998024i	$-0.520013\pi$
$197$	−1.76372			−0.125660			−0.0628299	+	0.998024i	$0.520013\pi$
$198$	−7.33351	+	3.16609i	−0.521170	+	0.225004i
$199$		−	3.39022i		−	0.240327i	−0.992754	−	0.120163i	$-0.961658\pi$
$199$		−	3.39022i		−	0.240327i	0.992754	−	0.120163i	$-0.0383418\pi$
$200$	−0.140390	+	4.99803i	−0.00992706	+	0.353414i
$201$	−0.575789	+	9.91268i	−0.0406130	+	0.699187i
$202$	−2.06435	+	3.57555i	−0.145247	+	0.251575i
$203$	−7.15280	+	4.01782i	−0.502028	+	0.281996i
$204$	−0.726422	+	12.5059i	−0.0508597	+	0.875591i
$205$	−15.9537	+	4.03559i	−1.11426	+	0.281858i
$206$	−8.19966			−0.571297
$207$	−0.842423	−	1.95127i	−0.0585524	−	0.135623i
$208$	2.31976			0.160847
$209$	−7.43834	−	12.8836i	−0.514520	−	0.891176i
$210$	−10.0852	+	1.81364i	−0.695943	+	0.125153i
$211$	1.09815	−	1.90206i	0.0756000	−	0.130943i	−0.825747	−	0.564041i	$-0.809246\pi$
$211$	1.09815	−	1.90206i	0.0756000	−	0.130943i	0.901347	+	0.433098i	$0.142579\pi$
$212$	1.70459	−	2.95243i	0.117072	−	0.202774i
$213$	−15.1045	+	7.58873i	−1.03494	+	0.519971i
$214$	−5.25789	−	9.10693i	−0.359422	−	0.622537i
$215$	28.1686	+	7.97329i	1.92108	+	0.543774i
$216$	5.11763	+	0.899897i	0.348211	+	0.0612302i
$217$	−13.9787	−	8.29222i	−0.948939	−	0.562912i
$218$	−3.69224	−	6.39515i	−0.250070	−	0.433134i
$219$	−3.36890	−	6.70542i	−0.227649	−	0.453110i
$220$	4.26862	−	4.15040i	0.287790	−	0.279820i
$221$	−14.5298	−	8.38881i	−0.977383	−	0.564292i
$222$	11.7220	+	7.70703i	0.786727	+	0.517262i
$223$	4.69564	+	8.13309i	0.314444	+	0.544632i	0.979319	−	0.202322i	$-0.0648487\pi$
$223$	4.69564	+	8.13309i	0.314444	+	0.544632i	−0.664875	+	0.746954i	$0.731515\pi$
$224$	−1.34984	+	2.27551i	−0.0901897	+	0.152039i
$225$	−11.7785	−	9.28799i	−0.785234	−	0.619199i
$226$	17.8473			1.18719
$227$	−2.25992	+	1.30477i	−0.149996	+	0.0866003i	−0.573120	−	0.819472i	$-0.694267\pi$
$227$	−2.25992	+	1.30477i	−0.149996	+	0.0866003i	0.423123	+	0.906072i	$0.360934\pi$
$228$	−0.561181	+	9.66119i	−0.0371651	+	0.639828i
$229$	−2.92097	−	1.68642i	−0.193023	−	0.111442i	0.400374	−	0.916352i	$-0.368880\pi$
$229$	−2.92097	−	1.68642i	−0.193023	−	0.111442i	−0.593397	+	0.804910i	$0.702214\pi$
$230$	1.10432	+	1.13578i	0.0728170	+	0.0748911i
$231$	10.1154	+	6.82315i	0.665546	+	0.448931i
$232$	−2.68539	+	1.55041i	−0.176304	+	0.101789i
$233$	24.4650			1.60275			0.801377	−	0.598159i	$-0.204101\pi$
$233$	24.4650			1.60275			0.801377	+	0.598159i	$0.204101\pi$
$234$	−4.15405	+	5.58351i	−0.271559	+	0.365005i
$235$	12.2022	+	3.45392i	0.795987	+	0.225309i
$236$	−1.98592	−	3.43972i	−0.129273	−	0.223907i
$237$	13.8775	−	21.1069i	0.901440	−	1.37104i
$238$	16.6835	−	9.37134i	1.08143	−	0.607454i
$239$	14.3027	+	8.25768i	0.925166	+	0.534145i	0.885279	−	0.465060i	$-0.153967\pi$
$239$	14.3027	+	8.25768i	0.925166	+	0.534145i	0.0398863	+	0.999204i	$0.487300\pi$
$240$	−3.80348	+	0.730449i	−0.245513	+	0.0471503i
$241$	−15.4951	+	8.94612i	−0.998129	+	0.576270i	−0.907694	−	0.419632i	$-0.862159\pi$
$241$	−15.4951	+	8.94612i	−0.998129	+	0.576270i	−0.0904351	+	0.995902i	$0.528826\pi$
$242$	3.91061			0.251384
$243$	−11.3302	+	10.7063i	−0.726836	+	0.686811i
$244$			10.0078i			0.640687i
$245$	10.6435	+	11.4768i	0.679986	+	0.733225i
$246$	−5.72261	−	11.3902i	−0.364860	−	0.726212i
$247$	−11.2247	−	6.48059i	−0.714212	−	0.412350i
$248$	−5.32011	−	3.07156i	−0.337827	−	0.195045i
$249$	−3.77521	−	2.48215i	−0.239244	−	0.157300i
$250$	10.6679	+	3.34588i	0.674700	+	0.211612i
$251$	4.13340			0.260898			0.130449	−	0.991455i	$-0.458358\pi$
$251$	4.13340			0.260898			0.130449	+	0.991455i	$0.458358\pi$
$252$	−3.05981	−	7.32377i	−0.192750	−	0.461354i
$253$		−	1.88632i		−	0.118592i
$254$	14.0765	−	8.12704i	0.883235	−	0.509936i
$255$	26.4646	+	9.17911i	1.65728	+	0.574818i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.85275	+	1.06969i	0.115571	+	0.0667252i	0.556671	−	0.830733i	$-0.312078\pi$
$257$	1.85275	+	1.06969i	0.115571	+	0.0667252i	−0.441100	+	0.897458i	$0.645412\pi$
$258$	−1.31498	+	22.6384i	−0.0818669	+	1.40941i
$259$	0.253008	−	21.4276i	0.0157211	−	1.33145i
$260$	1.41275	−	4.99105i	0.0876149	−	0.309532i
$261$	1.07705	−	9.23989i	0.0666679	−	0.571935i
$262$	3.91196			0.241681
$263$	−7.24259	−	12.5445i	−0.446597	−	0.773530i	0.551564	−	0.834132i	$-0.314031\pi$
$263$	−7.24259	−	12.5445i	−0.446597	−	0.773530i	−0.998162	+	0.0606027i	$0.980698\pi$
$264$	3.85345	+	2.53359i	0.237164	+	0.155932i
$265$	−5.31416	−	5.46553i	−0.326446	−	0.335745i
$266$	12.8885	−	7.23963i	0.790243	−	0.443890i
$267$	4.40346	+	8.76459i	0.269488	+	0.536384i
$268$	4.96469	−	2.86637i	0.303267	−	0.175091i
$269$	−12.8786			−0.785219			−0.392610	−	0.919705i	$-0.628428\pi$
$269$	−12.8786			−0.785219			−0.392610	+	0.919705i	$0.628428\pi$
$270$	5.05283	−	10.4627i	0.307505	−	0.636742i
$271$			8.07664i			0.490621i	0.969445	+	0.245310i	$0.0788899\pi$
$271$			8.07664i			0.490621i	−0.969445	+	0.245310i	$0.921110\pi$
$272$	6.26351	−	3.61624i	0.379781	−	0.219267i
$273$	10.6046	+	0.741702i	0.641818	+	0.0448898i
$274$	−0.467496	+	0.809727i	−0.0282425	+	0.0489174i
$275$	−6.33013	−	11.7117i	−0.381721	−	0.706243i
$276$	−0.674129	+	1.02531i	−0.0405778	+	0.0617166i
$277$	9.07801	−	5.24119i	0.545445	−	0.314913i	−0.201838	−	0.979419i	$-0.564691\pi$
$277$	9.07801	−	5.24119i	0.545445	−	0.314913i	0.747283	+	0.664506i	$0.231358\pi$
$278$		−	12.4962i		−	0.749472i
$279$	16.9199	−	7.30481i	1.01297	−	0.437328i
$280$	4.07379	+	4.29002i	0.243455	+	0.256378i
$281$	8.62857	−	4.98171i	0.514737	−	0.297184i	−0.220041	−	0.975491i	$-0.570619\pi$
$281$	8.62857	−	4.98171i	0.514737	−	0.297184i	0.734779	+	0.678307i	$0.237286\pi$
$282$	−0.569630	+	9.80664i	−0.0339210	+	0.583977i
$283$	−10.6894	+	18.5146i	−0.635418	+	1.10058i	0.351008	+	0.936373i	$0.385839\pi$
$283$	−10.6894	+	18.5146i	−0.635418	+	1.10058i	−0.986426	+	0.164205i	$0.947494\pi$
$284$	8.45184	+	4.87967i	0.501525	+	0.289555i
$285$	20.4446	+	7.09112i	1.21104	+	0.420042i
$286$	−5.34907	+	3.08829i	−0.316297	+	0.182614i
$287$	−9.93406	+	16.7465i	−0.586389	+	0.988515i
$288$	−1.18910	−	2.75428i	−0.0700685	−	0.162297i
$289$	−35.3087			−2.07698
$290$	1.70035	+	6.72191i	0.0998478	+	0.394724i
$291$	−12.2417	+	18.6190i	−0.717621	+	1.09146i
$292$	−2.16626	+	3.75207i	−0.126771	+	0.219573i
$293$	−9.94849	−	5.74376i	−0.581197	−	0.335554i	0.180412	−	0.983591i	$-0.442257\pi$
$293$	−9.94849	−	5.74376i	−0.581197	−	0.335554i	−0.761609	+	0.648037i	$0.775590\pi$
$294$	−6.89820	+	9.97070i	−0.402311	+	0.581503i
$295$	−8.61013	+	2.17798i	−0.501301	+	0.126807i
$296$		−	8.09944i		−	0.470770i
$297$	−12.9986	+	4.73804i	−0.754257	+	0.274929i
$298$		−	3.03055i		−	0.175555i
$299$	−0.821721	−	1.42326i	−0.0475213	−	0.0823094i
$300$	−0.744749	+	8.62817i	−0.0429981	+	0.498148i
$301$	30.2007	−	16.9641i	1.74074	−	0.977796i
$302$	−4.75076	+	8.22856i	−0.273376	+	0.473500i
$303$	−3.92866	+	5.97527i	−0.225696	+	0.343271i
$304$	4.83874	−	2.79365i	0.277521	−	0.160227i
$305$	21.5323	+	6.09483i	1.23293	+	0.348989i
$306$	−2.51216	+	21.5515i	−0.143611	+	1.23202i
$307$	5.44565			0.310800			0.155400	−	0.987852i	$-0.450333\pi$
$307$	5.44565			0.310800			0.155400	+	0.987852i	$0.450333\pi$
$308$	0.0831731	−	7.04406i	0.00473923	−	0.401373i
$309$	−14.1783	−	0.823564i	−0.806577	−	0.0468509i
$310$	−9.84856	+	9.57581i	−0.559361	+	0.543869i
$311$	−1.67706	+	2.90474i	−0.0950971	+	0.164713i	−0.909649	−	0.415378i	$-0.863649\pi$
$311$	−1.67706	+	2.90474i	−0.0950971	+	0.164713i	0.814552	+	0.580090i	$0.196983\pi$
$312$	4.01118	+	0.232994i	0.227089	+	0.0131907i
$313$	15.6710	+	27.1430i	0.885779	+	1.53421i	0.844819	+	0.535053i	$0.179708\pi$
$313$	15.6710	+	27.1430i	0.885779	+	1.53421i	0.0409598	+	0.999161i	$0.486958\pi$
$314$	7.07867			0.399472
$315$	−17.6208	+	2.12309i	−0.992819	+	0.119623i
$316$	−14.5841			−0.820419
$317$	11.8243	+	20.4803i	0.664120	+	1.15029i	0.979523	+	0.201332i	$0.0645270\pi$
$317$	11.8243	+	20.4803i	0.664120	+	1.15029i	−0.315403	+	0.948958i	$0.602140\pi$
$318$	3.24400	−	4.93395i	0.181915	−	0.276682i
$319$	4.12810	−	7.15008i	0.231129	−	0.400328i
$320$	1.55878	+	1.60318i	0.0871386	+	0.0896206i
$321$	−8.17692	−	16.2752i	−0.456391	−	0.908394i
$322$	1.87426	+	0.0221304i	0.104448	+	0.00123328i
$323$	−40.4100			−2.24847
$324$	8.75870	+	2.07005i	0.486595	+	0.115003i
$325$	−9.87807	−	6.07916i	−0.547936	−	0.337211i
$326$	−16.3030	+	9.41253i	−0.902938	+	0.521312i
$327$	−5.74207	−	11.4289i	−0.317537	−	0.632021i
$328$	−3.67973	+	6.37348i	−0.203179	+	0.351916i
$329$	13.0825	−	7.34862i	0.721262	−	0.405142i
$330$	7.79789	−	6.74787i	0.429259	−	0.371458i
$331$	−4.96127	−	8.59317i	−0.272696	−	0.472323i	0.696855	−	0.717212i	$-0.254582\pi$
$331$	−4.96127	−	8.59317i	−0.272696	−	0.472323i	−0.969551	+	0.244889i	$0.921249\pi$
$332$			2.60853i			0.143162i
$333$	19.4948	+	14.5038i	1.06831	+	0.794806i
$334$			9.60974i			0.525822i
$335$	−3.14357	−	12.4274i	−0.171752	−	0.678979i
$336$	−2.56260	+	3.79909i	−0.139801	+	0.207257i
$337$	22.7611	+	13.1411i	1.23987	+	0.715842i	0.969069	−	0.246792i	$-0.0793764\pi$
$337$	22.7611	+	13.1411i	1.23987	+	0.715842i	0.270806	+	0.962634i	$0.412710\pi$
$338$	3.80935	−	6.59799i	0.207202	−	0.358884i
$339$	30.8605	+	1.79257i	1.67611	+	0.0973589i
$340$	−3.96596	−	15.6785i	−0.215084	−	0.850285i
$341$	16.3566			0.885762
$342$	−1.94072	+	16.6491i	−0.104942	+	0.900283i
$343$	18.5086	+	0.655869i	0.999373	+	0.0354136i
$344$	11.3383	−	6.54616i	0.611319	−	0.352945i
$345$	1.79545	+	2.07483i	0.0966638	+	0.111705i
$346$	−18.9914	−	10.9647i	−1.02098	−	0.589465i
$347$	14.0818	−	24.3904i	0.755950	−	1.30934i	−0.188951	−	0.981987i	$-0.560509\pi$
$347$	14.0818	−	24.3904i	0.755950	−	1.30934i	0.944901	−	0.327357i	$-0.106158\pi$
$348$	−4.79912	+	2.41115i	−0.257260	+	0.129251i
$349$	−1.18630	+	0.684908i	−0.0635010	+	0.0366623i	−0.531414	−	0.847112i	$-0.678339\pi$
$349$	−1.18630	+	0.684908i	−0.0635010	+	0.0366623i	0.467913	+	0.883774i	$0.345006\pi$
$350$	11.7111	−	6.15226i	0.625984	−	0.328852i
$351$	−7.74371	+	9.23741i	−0.413329	+	0.493057i
$352$		−	2.66259i		−	0.141917i
$353$	9.38447	−	5.41813i	0.499485	−	0.288378i	−0.229016	−	0.973423i	$-0.573551\pi$
$353$	9.38447	−	5.41813i	0.499485	−	0.288378i	0.728501	+	0.685045i	$0.240217\pi$
$354$	−3.08845	−	6.14721i	−0.164149	−	0.326721i
$355$	15.6460	−	15.2127i	0.830405	−	0.807407i
$356$	2.83150	−	4.90430i	0.150069	−	0.259927i
$357$	29.7893	−	14.5287i	1.57662	−	0.768938i
$358$	2.01809	−	1.16514i	0.106659	−	0.0615798i
$359$			5.43488i			0.286842i	0.989662	+	0.143421i	$0.0458103\pi$
$359$			5.43488i			0.286842i	−0.989662	+	0.143421i	$0.954190\pi$
$360$	−6.65010	+	0.881030i	−0.350491	+	0.0464343i
$361$	−12.2178			−0.643044
$362$	−17.0668	+	9.85352i	−0.897011	+	0.517890i
$363$	6.76198	+	0.392777i	0.354912	+	0.0206155i
$364$	−3.00579	−	5.35110i	−0.157546	−	0.280474i
$365$	6.75345	+	6.94582i	0.353492	+	0.363561i
$366$	−1.00518	+	17.3049i	−0.0525414	+	0.904543i
$367$	7.28483	+	12.6177i	0.380265	+	0.658639i	0.991100	−	0.133119i	$-0.0424994\pi$
$367$	7.28483	+	12.6177i	0.380265	+	0.658639i	−0.610835	+	0.791758i	$0.709166\pi$
$368$	0.708453			0.0369307
$369$	−8.75115	−	20.2700i	−0.455567	−	1.05521i
$370$	−17.4262	−	4.93260i	−0.905948	−	0.256434i
$371$	−9.01920	−	0.106495i	−0.468253	−	0.00552893i
$372$	−8.89068	−	5.84550i	−0.460960	−	0.303075i
$373$	−31.1363	−	17.9766i	−1.61218	−	0.930792i	−0.988864	−	0.148820i	$-0.952452\pi$
$373$	−31.1363	−	17.9766i	−1.61218	−	0.930792i	−0.623314	−	0.781971i	$-0.714214\pi$
$374$	−9.62856	+	16.6772i	−0.497881	+	0.862355i
$375$	18.1103	+	6.85696i	0.935211	+	0.354092i
$376$	4.91158	−	2.83570i	0.253296	−	0.146240i
$377$		−	7.19315i		−	0.370466i
$378$	−4.55524	−	12.9711i	−0.234296	−	0.667162i
$379$	2.04160			0.104870			0.0524348	−	0.998624i	$-0.483302\pi$
$379$	2.04160			0.104870			0.0524348	+	0.998624i	$0.483302\pi$
$380$	−3.06382	−	12.1121i	−0.157171	−	0.621336i
$381$	25.1564	−	12.6389i	1.28880	−	0.647513i
$382$	−11.7316	−	6.77323i	−0.600240	−	0.346549i
$383$	−7.15091	−	4.12858i	−0.365395	−	0.210961i	0.306050	−	0.952015i	$-0.400993\pi$
$383$	−7.15091	−	4.12858i	−0.365395	−	0.210961i	−0.671445	+	0.741055i	$0.734326\pi$
$384$	−0.951551	+	1.44726i	−0.0485586	+	0.0738550i
$385$	−15.1049	−	4.46882i	−0.769817	−	0.227752i
$386$			8.07499i			0.411006i
$387$	−4.54755	+	39.0128i	−0.231165	+	1.98313i
$388$	12.8650			0.653122
$389$	15.6859	−	9.05627i	0.795308	−	0.459171i	−0.0465201	−	0.998917i	$-0.514813\pi$
$389$	15.6859	−	9.05627i	0.795308	−	0.459171i	0.841828	+	0.539746i	$0.181480\pi$
$390$	2.94413	−	8.48832i	0.149082	−	0.429823i
$391$	−4.43740	−	2.56193i	−0.224409	−	0.129563i
$392$	6.99805	+	0.165283i	0.353455	+	0.00834804i
$393$	6.76430	+	0.392912i	0.341214	+	0.0198198i
$394$	0.881859	+	1.52743i	0.0444274	+	0.0769506i
$395$	−8.88178	+	31.3782i	−0.446891	+	1.57881i
$396$	6.40867	+	4.76796i	0.322048	+	0.239599i
$397$	−2.48825			−0.124882			−0.0624409	−	0.998049i	$-0.519889\pi$
$397$	−2.48825			−0.124882			−0.0624409	+	0.998049i	$0.519889\pi$
$398$	−2.93602	+	1.69511i	−0.147169	+	0.0849683i
$399$	23.0131	−	11.2238i	1.15209	−	0.561893i
$400$	4.39861	−	2.37743i	0.219931	−	0.118872i
$401$	30.2082	+	17.4407i	1.50853	+	0.870948i	0.999951	+	0.00993115i	$0.00316124\pi$
$401$	30.2082	+	17.4407i	1.50853	+	0.870948i	0.508576	+	0.861017i	$0.330172\pi$
$402$	8.87253	−	4.45769i	0.442521	−	0.222329i
$403$	12.3414	−	7.12530i	0.614768	−	0.354936i
$404$	4.12869			0.205410
$405$	9.78789	−	17.5840i	0.486364	−	0.873756i
$406$	7.05594	+	4.18559i	0.350180	+	0.207728i
$407$	10.7827	+	18.6763i	0.534481	+	0.925748i
$408$	11.1937	−	5.62387i	0.554169	−	0.278423i
$409$	−7.61870	−	4.39866i	−0.376721	−	0.217500i	0.299670	−	0.954043i	$-0.403123\pi$
$409$	−7.61870	−	4.39866i	−0.376721	−	0.217500i	−0.676391	+	0.736543i	$0.736457\pi$
$410$	11.4718	+	11.7986i	0.566552	+	0.582689i
$411$	−0.889692	+	1.35317i	−0.0438853	+	0.0667471i
$412$	4.09983	+	7.10111i	0.201984	+	0.349847i
$413$	−5.36135	+	9.03798i	−0.263815	+	0.444730i
$414$	−1.26864	+	1.70520i	−0.0623503	+	0.0838058i
$415$	5.61234	+	1.58861i	0.275499	+	0.0779817i
$416$	−1.15988	−	2.00897i	−0.0568678	−	0.0984980i
$417$	1.25510	−	21.6076i	0.0614627	−	1.05813i
$418$	−7.43834	+	12.8836i	−0.363821	+	0.630156i
$419$	0.0360658	−	0.0624677i	0.00176193	−	0.00305175i	−0.865143	−	0.501525i	$-0.832772\pi$
$419$	0.0360658	−	0.0624677i	0.00176193	−	0.00305175i	0.866905	+	0.498473i	$0.166106\pi$
$420$	6.61325	+	7.82720i	0.322693	+	0.381928i
$421$	3.42682	+	5.93543i	0.167013	+	0.289275i	0.937368	−	0.348340i	$-0.113254\pi$
$421$	3.42682	+	5.93543i	0.167013	+	0.289275i	−0.770355	+	0.637615i	$0.779921\pi$
$422$	−2.19631			−0.106914
$423$	−1.96993	+	16.8998i	−0.0957815	+	0.821696i
$424$	−3.40917			−0.165564
$425$	−36.1481	−	1.01537i	−1.75344	−	0.0492525i
$426$	14.1243	+	9.28652i	0.684324	+	0.449933i
$427$	23.0856	−	12.9675i	1.11719	−	0.627540i
$428$	−5.25789	+	9.10693i	−0.254150	+	0.440200i
$429$	−9.55946	+	4.80281i	−0.461535	+	0.231882i
$430$	−7.17923	−	28.3814i	−0.346213	−	1.36867i
$431$		−	4.36097i		−	0.210060i	−0.994469	−	0.105030i	$-0.966506\pi$
$431$		−	4.36097i		−	0.210060i	0.994469	−	0.105030i	$-0.0334939\pi$
$432$	−1.77948	−	4.88195i	−0.0856155	−	0.234883i
$433$	32.5668			1.56506			0.782530	−	0.622613i	$-0.213929\pi$
$433$	32.5668			1.56506			0.782530	+	0.622613i	$0.213929\pi$
$434$	−0.191897	+	16.2521i	−0.00921135	+	0.780124i
$435$	2.26499	+	11.7939i	0.108598	+	0.565474i
$436$	−3.69224	+	6.39515i	−0.176826	+	0.306272i
$437$	−3.42802	−	1.97917i	−0.163984	−	0.0946764i
$438$	−4.12261	+	6.27026i	−0.196986	+	0.299605i
$439$	−26.2998	+	15.1842i	−1.25522	+	0.724703i	−0.972142	−	0.234393i	$-0.924690\pi$
$439$	−26.2998	+	15.1842i	−1.25522	+	0.724703i	−0.283081	+	0.959096i	$0.591357\pi$
$440$	−5.72866	−	1.62153i	−0.273103	−	0.0773035i
$441$	−12.9294	+	16.5478i	−0.615685	+	0.787993i
$442$			16.7776i			0.798030i
$443$	−18.8007	−	32.5637i	−0.893246	−	1.54715i	−0.835960	−	0.548790i	$-0.815089\pi$
$443$	−18.8007	−	32.5637i	−0.893246	−	1.54715i	−0.0572857	−	0.998358i	$-0.518245\pi$
$444$	0.813499	−	14.0050i	0.0386069	−	0.664650i
$445$	−8.82738	−	9.07882i	−0.418458	−	0.430377i
$446$	4.69564	−	8.13309i	0.222345	−	0.385113i
$447$	0.304385	−	5.24023i	0.0143969	−	0.247854i
$448$	2.64557	+	0.0312377i	0.124991	+	0.00147584i
$449$		−	4.32560i		−	0.204138i	−0.994777	−	0.102069i	$-0.967454\pi$
$449$		−	4.32560i		−	0.204138i	0.994777	−	0.102069i	$-0.0325462\pi$
$450$	−2.15438	+	14.8445i	−0.101558	+	0.699776i
$451$		−	19.5952i		−	0.922703i
$452$	−8.92367	−	15.4563i	−0.419734	−	0.727001i
$453$	−9.04118	+	13.7511i	−0.424792	+	0.646085i
$454$	2.25992	+	1.30477i	0.106063	+	0.0612357i
$455$	−13.3436	+	3.20821i	−0.625559	+	0.150403i
$456$	8.64743	−	4.34460i	0.404953	−	0.203454i
$457$	−18.5026	+	10.6825i	−0.865513	+	0.499704i	−0.865855	−	0.500296i	$-0.833225\pi$
$457$	−18.5026	+	10.6825i	−0.865513	+	0.499704i	0.000341340		1.00000i	$0.499891\pi$
$458$			3.37284i			0.157603i
$459$	−6.50848	+	37.0132i	−0.303790	+	1.72763i
$460$	0.431452	−	1.52426i	0.0201165	−	0.0710691i
$461$	9.79603	+	16.9672i	0.456246	+	0.790242i	0.998759	−	0.0498057i	$-0.0158602\pi$
$461$	9.79603	+	16.9672i	0.456246	+	0.790242i	−0.542512	+	0.840048i	$0.682527\pi$
$462$	0.851315	−	12.1718i	0.0396068	−	0.566283i
$463$	17.7591	+	10.2532i	0.825335	+	0.476507i	0.852253	−	0.523130i	$-0.175236\pi$
$463$	17.7591	+	10.2532i	0.825335	+	0.476507i	−0.0269180	+	0.999638i	$0.508569\pi$
$464$	2.68539	+	1.55041i	0.124666	+	0.0719759i
$465$	−17.9913	+	15.5687i	−0.834326	+	0.721981i
$466$	−12.2325	−	21.1873i	−0.566659	−	0.981483i
$467$			14.3203i			0.662663i	0.943514	+	0.331331i	$0.107498\pi$
$467$			14.3203i			0.662663i	−0.943514	+	0.331331i	$0.892502\pi$
$468$	6.91248	+	0.805757i	0.319530	+	0.0372461i
$469$	−13.0449	−	7.73825i	−0.602357	−	0.357319i
$470$	−3.10994	−	12.2944i	−0.143451	−	0.567099i
$471$	12.2400	+	0.710973i	0.563988	+	0.0327599i
$472$	−1.98592	+	3.43972i	−0.0914096	+	0.158326i
$473$	−17.4297	+	30.1892i	−0.801421	+	1.38810i
$474$	−25.2179	−	1.46481i	−1.15829	−	0.0672809i
$475$	−27.9254	−	0.784399i	−1.28131	−	0.0359907i
$476$	−16.4576	−	9.76266i	−0.754331	−	0.447471i
$477$	6.10488	−	8.20565i	0.279523	−	0.375711i
$478$		−	16.5154i		−	0.755395i
$479$	−12.6756	−	21.9548i	−0.579164	−	1.00314i	−0.995575	−	0.0939651i	$-0.970046\pi$
$479$	−12.6756	−	21.9548i	−0.579164	−	1.00314i	0.416412	−	0.909176i	$-0.363288\pi$
$480$	2.53433	+	2.92868i	0.115676	+	0.133676i
$481$	16.2716	+	9.39439i	0.741919	+	0.428347i
$482$	15.4951	+	8.94612i	0.705784	+	0.407485i
$483$	3.23863	+	0.226515i	0.147363	+	0.0103068i
$484$	−1.95531	−	3.38669i	−0.0888776	−	0.153940i
$485$	7.83486	−	27.6795i	0.355763	−	1.25686i
$486$	14.9371	+	4.45912i	0.677560	+	0.202270i
$487$		−	11.5027i		−	0.521235i	−0.965442	−	0.260618i	$-0.916074\pi$
$487$		−	11.5027i		−	0.521235i	0.965442	−	0.260618i	$-0.0839262\pi$
$488$	8.66705	−	5.00392i	0.392339	−	0.226517i
$489$	−29.1355	+	14.6381i	−1.31755	+	0.661957i
$490$	4.61746	−	14.9559i	0.208596	−	0.675639i
$491$	22.6834	+	13.0963i	1.02369	+	0.591027i	0.915170	−	0.403068i	$-0.132056\pi$
$491$	22.6834	+	13.0963i	1.02369	+	0.591027i	0.108518	+	0.994094i	$0.465389\pi$
$492$	−7.00290	+	10.6510i	−0.315715	+	0.480185i
$493$	−11.2133	−	19.4220i	−0.505021	−	0.874722i
$494$			12.9612i			0.583151i
$495$	14.1614	−	10.8848i	0.636506	−	0.489235i
$496$			6.14313i			0.275835i
$497$	0.304859	−	25.8190i	0.0136748	−	1.15814i
$498$	−0.261998	+	4.51050i	−0.0117404	+	0.202120i
$499$	9.95558	−	17.2436i	0.445673	−	0.771928i	−0.552426	−	0.833562i	$-0.686298\pi$
$499$	9.95558	−	17.2436i	0.445673	−	0.771928i	0.998099	+	0.0616337i	$0.0196311\pi$
$500$	−2.43636	−	10.9117i	−0.108957	−	0.487984i
$501$	−0.965191	+	16.6165i	−0.0431216	+	0.742373i
$502$	−2.06670	−	3.57963i	−0.0922413	−	0.159767i
$503$		−	29.7206i		−	1.32518i	−0.748983	−	0.662589i	$-0.769458\pi$
$503$		−	29.7206i		−	1.32518i	0.748983	−	0.662589i	$-0.230542\pi$
$504$	−4.81266	+	6.31176i	−0.214373	+	0.281148i
$505$	2.51440	−	8.88303i	0.111889	−	0.395290i
$506$	−1.63360	+	0.943160i	−0.0726224	+	0.0419286i
$507$	7.24959	−	11.0262i	0.321965	−	0.489692i
$508$	−14.0765	−	8.12704i	−0.624542	−	0.360579i
$509$	2.08928	−	3.61874i	0.0926057	−	0.160398i	−0.816001	−	0.578050i	$-0.803814\pi$
$509$	2.08928	−	3.61874i	0.0926057	−	0.160398i	0.908607	+	0.417653i	$0.137147\pi$
$510$	−5.28296	−	27.5086i	−0.233933	−	1.21810i
$511$	11.4620	+	0.135338i	0.507047	+	0.00598699i
$512$	1.00000			0.0441942
$513$	−5.02799	+	28.5937i	−0.221991	+	1.26244i
$514$		−	2.13937i		−	0.0943637i
$515$	17.7751	−	4.49632i	0.783266	−	0.198132i
$516$	20.2629	−	10.1804i	0.892026	−	0.448167i
$517$	−7.55032	+	13.0775i	−0.332063	+	0.575149i
$518$	−18.6834	+	10.4947i	−0.820900	+	0.461110i
$519$	−31.7374	−	20.8669i	−1.39312	−	0.915955i
$520$	−5.02875	+	1.27205i	−0.220525	+	0.0557832i
$521$	−2.01258			−0.0881725			−0.0440863	−	0.999028i	$-0.514038\pi$
$521$	−2.01258			−0.0881725			−0.0440863	+	0.999028i	$0.514038\pi$
$522$	−8.54050	+	3.68719i	−0.373808	+	0.161384i
$523$	−40.1926			−1.75750			−0.878750	−	0.477283i	$-0.841622\pi$
$523$	−40.1926			−1.75750			−0.878750	+	0.477283i	$0.841622\pi$
$524$	−1.95598	−	3.38785i	−0.0854473	−	0.147999i
$525$	20.8680	−	9.46184i	0.910754	−	0.412949i
$526$	−7.24259	+	12.5445i	−0.315792	+	0.546968i
$527$	22.2150	−	38.4775i	0.967701	−	1.67611i
$528$	0.267428	−	4.60398i	0.0116383	−	0.200363i
$529$	11.2490	+	19.4839i	0.489089	+	0.847127i
$530$	−2.07621	+	7.33496i	−0.0901846	+	0.318610i
$531$	−4.72294	−	10.9396i	−0.204958	−	0.474737i
$532$	−12.7139	−	7.54193i	−0.551219	−	0.326984i
$533$	−8.53609	−	14.7849i	−0.369739	−	0.640407i
$534$	5.38863	−	8.19581i	0.233189	−	0.354667i
$535$	16.3918	+	16.8587i	0.708680	+	0.728866i
$536$	−4.96469	−	2.86637i	−0.214442	−	0.123808i
$537$	3.60658	−	1.81200i	0.155635	−	0.0781936i
$538$	6.43928	+	11.1532i	0.277617	+	0.480847i
$539$	−16.3566	+	8.93535i	−0.704530	+	0.384873i
$540$	−11.5874	+	0.855492i	−0.498643	+	0.0368145i
$541$	−26.0853			−1.12149			−0.560746	−	0.827988i	$-0.689486\pi$
$541$	−26.0853			−1.12149			−0.560746	+	0.827988i	$0.689486\pi$
$542$	6.99458	−	4.03832i	0.300443	−	0.173461i
$543$	−30.5005	+	15.3239i	−1.30890	+	0.657612i
$544$	−6.26351	−	3.61624i	−0.268546	−	0.155045i
$545$	11.5108	+	11.8387i	0.493069	+	0.507113i
$546$	−4.65996	−	9.55468i	−0.199428	−	0.408903i
$547$	26.3226	−	15.1974i	1.12547	−	0.649792i	0.182680	−	0.983172i	$-0.441523\pi$
$547$	26.3226	−	15.1974i	1.12547	−	0.649792i	0.942792	+	0.333381i	$0.108189\pi$
$548$	0.934992			0.0399409
$549$	−3.47617	+	29.8216i	−0.148360	+	1.27276i
$550$	−6.97757	+	11.3379i	−0.297525	+	0.483450i
$551$	−8.66258	−	15.0040i	−0.369038	−	0.639193i
$552$	1.22501	+	0.0711562i	0.0521399	+	0.00302861i
$553$	18.8970	+	33.6418i	0.803584	+	1.43059i
$554$	−9.07801	−	5.24119i	−0.385688	−	0.222677i
$555$	−29.6369	−	10.2794i	−1.25802	−	0.436337i
$556$	−10.8220	+	6.24810i	−0.458956	+	0.264978i
$557$	3.05968			0.129643			0.0648214	−	0.997897i	$-0.479352\pi$
$557$	3.05968			0.129643			0.0648214	+	0.997897i	$0.479352\pi$
$558$	−14.7861	−	11.0006i	−0.625945	−	0.465694i
$559$			30.3711i			1.28456i
$560$	1.67837	−	5.67301i	0.0709242	−	0.239729i
$561$	−18.3241	+	27.8700i	−0.773645	+	1.17667i
$562$	−8.62857	−	4.98171i	−0.363974	−	0.210141i
$563$	−13.2448	−	7.64689i	−0.558202	−	0.322278i	0.194222	−	0.980958i	$-0.437782\pi$
$563$	−13.2448	−	7.64689i	−0.558202	−	0.322278i	−0.752423	+	0.658680i	$0.771115\pi$
$564$	8.77761	−	4.41000i	0.369604	−	0.185695i
$565$	−38.6893	+	9.78667i	−1.62767	+	0.411728i
$566$	21.3788			0.898617
$567$	−6.57383	−	22.8863i	−0.276075	−	0.961136i
$568$		−	9.75935i		−	0.409493i
$569$	−36.2482	+	20.9279i	−1.51960	+	0.877342i	−0.519868	+	0.854246i	$0.674019\pi$
$569$	−36.2482	+	20.9279i	−1.51960	+	0.877342i	−0.999733	+	0.0230961i	$0.992648\pi$
$570$	−4.08123	−	21.2511i	−0.170944	−	0.890112i
$571$	−3.71411	+	6.43303i	−0.155431	+	0.269214i	−0.933216	−	0.359317i	$-0.883010\pi$
$571$	−3.71411	+	6.43303i	−0.155431	+	0.269214i	0.777785	+	0.628530i	$0.216343\pi$
$572$	5.34907	+	3.08829i	0.223656	+	0.129128i
$573$	−19.6052	−	12.8901i	−0.819019	−	0.538493i
$574$	19.4699	+	0.229892i	0.812659	+	0.00959552i
$575$	−3.01675	−	1.85657i	−0.125807	−	0.0774242i
$576$	−1.79072	+	2.40693i	−0.0746134	+	0.100289i
$577$	−16.4756			−0.685890			−0.342945	−	0.939356i	$-0.611424\pi$
$577$	−16.4756			−0.685890			−0.342945	+	0.939356i	$0.611424\pi$
$578$	17.6544	+	30.5782i	0.734325	+	1.27189i
$579$	−0.811042	+	13.9628i	−0.0337058	+	0.580272i
$580$	4.97118	−	4.83350i	0.206417	−	0.200700i
$581$	6.01721	−	3.37995i	0.249636	−	0.140224i
$582$	22.2453	+	1.29215i	0.922099	+	0.0535612i
$583$	7.86111	−	4.53862i	0.325574	−	0.187970i
$584$	4.33252			0.179281
$585$	5.94335	−	14.3817i	0.245727	−	0.594612i
$586$			11.4875i			0.474545i
$587$	9.52825	−	5.50114i	0.393273	−	0.227056i	−0.290304	−	0.956934i	$-0.593757\pi$
$587$	9.52825	−	5.50114i	0.393273	−	0.227056i	0.683577	+	0.729878i	$0.260423\pi$
$588$	12.0840	+	0.988672i	0.498335	+	0.0407722i
$589$	17.1617	−	29.7250i	0.707137	−	1.22480i
$590$	6.19125	+	6.36760i	0.254890	+	0.262150i
$591$	1.37144	+	2.72970i	0.0564136	+	0.112285i
$592$	−7.01432	+	4.04972i	−0.288287	+	0.166442i
$593$		−	33.4327i		−	1.37292i	−0.727170	−	0.686458i	$-0.759165\pi$
$593$		−	33.4327i		−	1.37292i	0.727170	−	0.686458i	$-0.240835\pi$
$594$	10.6026	+	8.88813i	0.435029	+	0.364684i
$595$	−31.0275	+	29.4636i	−1.27200	+	1.20789i
$596$	−2.62453	+	1.51527i	−0.107505	+	0.0620681i
$597$	−5.24704	+	2.63619i	−0.214747	+	0.107892i
$598$	−0.821721	+	1.42326i	−0.0336027	+	0.0582015i
$599$	−18.1385	−	10.4723i	−0.741120	−	0.427886i	0.0813566	−	0.996685i	$-0.474075\pi$
$599$	−18.1385	−	10.4723i	−0.741120	−	0.427886i	−0.822476	+	0.568799i	$0.807408\pi$
$600$	7.84459	−	3.66911i	0.320254	−	0.149791i
$601$	−16.4433	+	9.49353i	−0.670735	+	0.387249i	−0.796355	−	0.604829i	$-0.793241\pi$
$601$	−16.4433	+	9.49353i	−0.670735	+	0.387249i	0.125620	+	0.992078i	$0.459908\pi$
$602$	−29.7917	−	17.6725i	−1.21422	−	0.720277i
$603$	15.7895	−	6.81681i	0.643000	−	0.277602i
$604$	9.50152			0.386612
$605$	−8.47738	+	2.14440i	−0.344655	+	0.0871823i
$606$	7.13907	+	0.414681i	0.290005	+	0.0168453i
$607$	0.824585	−	1.42822i	0.0334689	−	0.0579698i	−0.848806	−	0.528705i	$-0.822678\pi$
$607$	0.824585	−	1.42822i	0.0334689	−	0.0579698i	0.882275	+	0.470735i	$0.156011\pi$
$608$	−4.83874	−	2.79365i	−0.196237	−	0.113297i
$609$	11.7803	+	7.94615i	0.477361	+	0.321994i
$610$	−5.48785	−	21.6949i	−0.222196	−	0.878401i
$611$			13.1563i			0.532247i
$612$	19.9202	−	8.60016i	0.805228	−	0.347641i
$613$			9.15196i			0.369644i	0.982772	+	0.184822i	$0.0591709\pi$
$613$			9.15196i			0.369644i	−0.982772	+	0.184822i	$0.940829\pi$
$614$	−2.72283	−	4.71607i	−0.109884	−	0.190325i
$615$	18.6513	+	21.5535i	0.752092	+	0.869122i
$616$	−6.14192	+	3.45000i	−0.247465	+	0.139004i
$617$	−9.03988	+	15.6575i	−0.363932	+	0.630349i	−0.988604	−	0.150538i	$-0.951899\pi$
$617$	−9.03988	+	15.6575i	−0.363932	+	0.630349i	0.624672	+	0.780887i	$0.285233\pi$
$618$	6.37594	+	12.6906i	0.256478	+	0.510490i
$619$	1.46056	−	0.843257i	0.0587050	−	0.0338934i	−0.470360	−	0.882475i	$-0.655876\pi$
$619$	1.46056	−	0.843257i	0.0587050	−	0.0338934i	0.529065	+	0.848581i	$0.322543\pi$
$620$	13.2172	+	3.74120i	0.530814	+	0.150250i
$621$	−2.36492	+	2.82110i	−0.0949011	+	0.113207i
$622$	3.35411			0.134488
$623$	−14.9818	−	0.176899i	−0.600234	−	0.00708730i
$624$	−1.80381	−	3.59028i	−0.0722103	−	0.143726i
$625$	−24.9606	−	1.40334i	−0.998423	−	0.0561338i
$626$	15.6710	−	27.1430i	0.626340	−	1.08485i
$627$	−14.1559	+	21.5304i	−0.565332	+	0.859840i
$628$	−3.53933	−	6.13030i	−0.141235	−	0.244626i
$629$	58.5790			2.33570
$630$	10.6490	+	14.1985i	0.424268	+	0.565682i
$631$	7.16980			0.285425			0.142713	−	0.989764i	$-0.454418\pi$
$631$	7.16980			0.285425			0.142713	+	0.989764i	$0.454418\pi$
$632$	7.29204	+	12.6302i	0.290062	+	0.502402i
$633$	−3.79771	−	0.220594i	−0.150945	−	0.00876784i
$634$	11.8243	−	20.4803i	0.469604	−	0.813378i
$635$	−26.0583	+	25.3366i	−1.03409	+	1.00545i
$636$	−5.89493	−	0.342413i	−0.233749	−	0.0135776i
$637$	−8.44895	+	13.8672i	−0.334760	+	0.549438i
$638$	−8.25620			−0.326866
$639$	23.4901	+	17.4763i	0.929253	+	0.691351i
$640$	0.609005	−	2.15154i	0.0240731	−	0.0850470i
$641$	6.85692	−	3.95884i	0.270832	−	0.156365i	−0.358434	−	0.933555i	$-0.616689\pi$
$641$	6.85692	−	3.95884i	0.270832	−	0.156365i	0.629266	+	0.777190i	$0.283356\pi$
$642$	−10.0063	+	15.2190i	−0.394917	+	0.600647i
$643$	18.5820	−	32.1850i	0.732802	−	1.26925i	−0.222879	−	0.974846i	$-0.571545\pi$
$643$	18.5820	−	32.1850i	0.732802	−	1.26925i	0.955681	−	0.294404i	$-0.0951213\pi$
$644$	−0.917964	−	1.63422i	−0.0361728	−	0.0643973i
$645$	−9.56328	−	49.7964i	−0.376554	−	1.96073i
$646$	20.2050	+	34.9961i	0.794954	+	1.37690i
$647$			32.8858i			1.29287i	0.762967	+	0.646437i	$0.223742\pi$
$647$			32.8858i			1.29287i	−0.762967	+	0.646437i	$0.776258\pi$
$648$	−2.58663	−	8.62029i	−0.101613	−	0.338637i
$649$		−	10.5754i		−	0.415121i
$650$	−0.325671	+	11.5942i	−0.0127739	+	0.454763i
$651$	−1.96415	+	28.0827i	−0.0769813	+	1.10065i
$652$	16.3030	+	9.41253i	0.638474	+	0.368623i
$653$	8.87167	−	15.3662i	0.347175	−	0.601325i	−0.638571	−	0.769563i	$-0.720474\pi$
$653$	8.87167	−	15.3662i	0.347175	−	0.601325i	0.985746	+	0.168238i	$0.0538076\pi$
$654$	−7.02671	+	10.6872i	−0.274766	+	0.417904i
$655$	−8.48029	+	2.14514i	−0.331352	+	0.0838175i
$656$	7.35946			0.287339
$657$	−7.75833	+	10.4281i	−0.302681	+	0.406838i
$658$	−12.9053	−	7.65547i	−0.503103	−	0.298441i
$659$	31.1902	−	18.0077i	1.21500	−	0.701479i	0.251154	−	0.967947i	$-0.419190\pi$
$659$	31.1902	−	18.0077i	1.21500	−	0.701479i	0.963844	+	0.266468i	$0.0858567\pi$
$660$	−9.74277	−	3.37923i	−0.379237	−	0.131536i
$661$	32.5566	+	18.7966i	1.26630	+	0.731101i	0.974287	−	0.225312i	$-0.0723401\pi$
$661$	32.5566	+	18.7966i	1.26630	+	0.731101i	0.292018	+	0.956413i	$0.405673\pi$
$662$	−4.96127	+	8.59317i	−0.192825	+	0.333983i
$663$	−1.68512	+	29.0108i	−0.0654448	+	1.12669i
$664$	2.25905	−	1.30426i	0.0876682	−	0.0506153i
$665$	−23.9696	+	22.7614i	−0.929501	+	0.882651i
$666$	2.81330	−	24.1349i	0.109013	−	0.935209i
$667$		−	2.19678i		−	0.0850597i
$668$	8.32228	−	4.80487i	0.321999	−	0.185906i
$669$	8.93629	−	13.5916i	0.345497	−	0.525482i
$670$	−9.19062	+	8.93609i	−0.355065	+	0.345231i
$671$	−13.3234	+	23.0768i	−0.514344	+	0.890870i
$672$	4.57141	+	0.319732i	0.176346	+	0.0123339i
$673$	−10.9840	+	6.34162i	−0.423402	+	0.244451i	−0.696532	−	0.717526i	$-0.745275\pi$
$673$	−10.9840	+	6.34162i	−0.423402	+	0.244451i	0.273130	+	0.961977i	$0.411941\pi$
$674$		−	26.2822i		−	1.01235i
$675$	−5.21617	+	25.4517i	−0.200771	+	0.979638i
$676$	−7.61871			−0.293027
$677$	16.5374	−	9.54785i	0.635583	−	0.366954i	−0.147328	−	0.989088i	$-0.547067\pi$
$677$	16.5374	−	9.54785i	0.635583	−	0.366954i	0.782911	+	0.622134i	$0.213734\pi$
$678$	−13.8778	−	27.6223i	−0.532975	−	1.06083i
$679$	−16.6696	−	29.6763i	−0.639720	−	1.13887i
$680$	−11.5950	+	11.2739i	−0.444647	+	0.432333i
$681$	3.77666	+	2.48310i	0.144722	+	0.0951527i
$682$	−8.17832	−	14.1653i	−0.313164	−	0.542416i
$683$	6.31366			0.241585			0.120793	−	0.992678i	$-0.461456\pi$
$683$	6.31366			0.241585			0.120793	+	0.992678i	$0.461456\pi$
$684$	15.3889	−	6.64386i	0.588411	−	0.254034i
$685$	0.569415	−	2.01167i	0.0217562	−	0.0768620i
$686$	−8.68632	−	16.3569i	−0.331645	−	0.624509i
$687$	−0.338765	+	5.83211i	−0.0129247	+	0.222509i
$688$	−11.3383	−	6.54616i	−0.432268	−	0.249570i
$689$	3.95423	−	6.84894i	0.150644	−	0.260924i
$690$	0.899134	−	2.59232i	0.0342294	−	0.0986880i
$691$	34.5932	−	19.9724i	1.31599	−	0.759786i	0.332908	−	0.942959i	$-0.391970\pi$
$691$	34.5932	−	19.9724i	1.31599	−	0.759786i	0.983081	+	0.183173i	$0.0586370\pi$
$692$			21.9294i			0.833629i
$693$	2.69456	−	20.9612i	0.102358	−	0.796249i
$694$	−28.1636			−1.06907
$695$	6.85235	+	27.0891i	0.259924	+	1.02755i
$696$	4.48768	+	2.95058i	0.170105	+	0.111842i
$697$	−46.0960	−	26.6136i	−1.74601	−	1.00806i
$698$	1.18630	+	0.684908i	0.0449020	+	0.0259242i
$699$	−19.0236	−	37.8643i	−0.719539	−	1.43216i
$700$	−11.1836	−	7.06598i	−0.422699	−	0.267069i
$701$			8.43098i			0.318434i	0.987244	+	0.159217i	$0.0508969\pi$
$701$			8.43098i			0.318434i	−0.987244	+	0.159217i	$0.949103\pi$
$702$	11.8717	+	2.08755i	0.448068	+	0.0787893i
$703$	45.2540			1.70679
$704$	−2.30587	+	1.33130i	−0.0869058	+	0.0501751i
$705$	−4.14268	−	21.5711i	−0.156022	−	0.812414i
$706$	−9.38447	−	5.41813i	−0.353189	−	0.203914i
$707$	−5.34967	−	9.52385i	−0.201195	−	0.358181i
$708$	−3.77942	+	5.74828i	−0.142039	+	0.216034i
$709$	3.49123	+	6.04699i	0.131116	+	0.227100i	0.924107	−	0.382134i	$-0.124811\pi$
$709$	3.49123	+	6.04699i	0.131116	+	0.227100i	−0.792991	+	0.609233i	$0.791477\pi$
$710$	−20.9976	−	5.94350i	−0.788026	−	0.223055i
$711$	−43.4580	−	5.06571i	−1.62980	−	0.189979i
$712$	−5.66299			−0.212230
$713$	3.76904	−	2.17606i	0.141152	−	0.0814940i
$714$	−27.4768	−	18.5339i	−1.02829	−	0.693615i
$715$	9.90218	−	9.62794i	0.370320	−	0.360065i
$716$	−2.01809	−	1.16514i	−0.0754196	−	0.0435435i
$717$	1.65878	−	28.5573i	0.0619484	−	1.06649i
$718$	4.70674	−	2.71744i	0.175654	−	0.101414i
$719$	−29.3256			−1.09366			−0.546830	−	0.837243i	$-0.684166\pi$
$719$	−29.3256			−1.09366			−0.546830	+	0.837243i	$0.684166\pi$
$720$	4.08804	+	5.31864i	0.152352	+	0.198214i
$721$	11.0682	−	18.6584i	0.412201	−	0.694875i
$722$	6.10892	+	10.5810i	0.227350	+	0.393783i
$723$	25.8947	+	17.0254i	0.963033	+	0.633181i
$724$	17.0668	+	9.85352i	0.634283	+	0.366203i
$725$	−7.37198	−	13.6393i	−0.273789	−	0.506551i
$726$	−3.04084	−	6.05244i	−0.112856	−	0.224627i
$727$	−14.8721	−	25.7593i	−0.551576	−	0.955358i	−0.998161	−	0.0606167i	$-0.980693\pi$
$727$	−14.8721	−	25.7593i	−0.551576	−	0.955358i	0.446585	−	0.894741i	$-0.352640\pi$
$728$	−3.13130	+	5.27864i	−0.116054	+	0.195639i
$729$	25.3804	+	9.21069i	0.940014	+	0.341137i
$730$	2.63853	−	9.32157i	0.0976562	−	0.345007i
$731$	47.3450	+	82.0039i	1.75112	+	3.03302i
$732$	15.4891	−	7.78196i	0.572494	−	0.287629i
$733$	8.26100	−	14.3085i	0.305127	−	0.528496i	−0.672163	−	0.740404i	$-0.734634\pi$
$733$	8.26100	−	14.3085i	0.305127	−	0.528496i	0.977290	+	0.211908i	$0.0679677\pi$
$734$	7.28483	−	12.6177i	0.268888	−	0.465728i
$735$	9.48637	−	25.3970i	0.349910	−	0.936783i
$736$	−0.354226	−	0.613538i	−0.0130570	−	0.0226153i
$737$	15.2639			0.562254
$738$	−13.1787	+	17.7137i	−0.485116	+	0.652051i
$739$	−6.19918			−0.228041			−0.114020	−	0.993478i	$-0.536373\pi$
$739$	−6.19918			−0.228041			−0.114020	+	0.993478i	$0.536373\pi$
$740$	4.44137	+	17.5579i	0.163268	+	0.645440i
$741$	−1.30181	+	22.4117i	−0.0478231	+	0.823313i
$742$	4.41737	+	7.86410i	0.162167	+	0.288700i
$743$	18.3211	−	31.7331i	0.672137	−	1.16418i	−0.305160	−	0.952301i	$-0.598710\pi$
$743$	18.3211	−	31.7331i	0.672137	−	1.16418i	0.977297	−	0.211874i	$-0.0679568\pi$
$744$	−0.617009	+	10.6223i	−0.0226206	+	0.389433i
$745$	1.66181	+	6.56959i	0.0608842	+	0.240691i
$746$			35.9531i			1.31634i
$747$	−0.906059	+	7.77295i	−0.0331510	+	0.284397i
$748$	19.2571			0.704110
$749$	27.8202	+	0.328489i	1.01653	+	0.0120027i
$750$	−3.11684	−	19.1124i	−0.113811	−	0.697888i
$751$	0.432438	−	0.749005i	0.0157799	−	0.0273316i	−0.858028	−	0.513604i	$-0.828310\pi$
$751$	0.432438	−	0.749005i	0.0157799	−	0.0273316i	0.873808	+	0.486272i	$0.161644\pi$
$752$	−4.91158	−	2.83570i	−0.179107	−	0.103407i
$753$	−3.21407	−	6.39724i	−0.117127	−	0.233129i
$754$	−6.22945	+	3.59658i	−0.226863	+	0.130980i
$755$	5.78648	−	20.4429i	0.210592	−	0.743993i
$756$	−8.95569	+	10.4305i	−0.325715	+	0.379354i
$757$			43.1842i			1.56956i	0.619777	+	0.784778i	$0.287223\pi$
$757$			43.1842i			1.56956i	−0.619777	+	0.784778i	$0.712777\pi$
$758$	−1.02080	−	1.76807i	−0.0370770	−	0.0642193i
$759$	−2.91945	+	1.46677i	−0.105969	+	0.0532405i
$760$	−8.95745	+	8.70938i	−0.324921	+	0.315922i
$761$	−7.49231	+	12.9771i	−0.271596	+	0.470418i	−0.969271	−	0.245996i	$-0.920885\pi$
$761$	−7.49231	+	12.9771i	−0.271596	+	0.470418i	0.697675	+	0.716415i	$0.254218\pi$
$762$	−23.5238	−	15.4666i	−0.852179	−	0.560295i
$763$	19.5361	+	0.230674i	0.707256	+	0.00835096i
$764$			13.5465i			0.490094i
$765$	−6.37203	−	48.0967i	−0.230381	−	1.73894i
$766$			8.25716i			0.298343i
$767$	−4.60687	−	7.97934i	−0.166344	−	0.288117i
$768$	1.72914	+	0.100439i	0.0623948	+	0.00362427i
$769$	0.786782	+	0.454249i	0.0283721	+	0.0163806i	0.514119	−	0.857719i	$-0.328119\pi$
$769$	0.786782	+	0.454249i	0.0283721	+	0.0163806i	−0.485747	+	0.874100i	$0.661452\pi$
$770$	3.68234	+	15.3156i	0.132702	+	0.551937i
$771$	0.214876	−	3.69927i	0.00773857	−	0.133226i
$772$	6.99314	−	4.03749i	0.251689	−	0.145313i
$773$		−	44.2918i		−	1.59307i	−0.604595	−	0.796533i	$-0.706665\pi$
$773$		−	44.2918i		−	1.59307i	0.604595	−	0.796533i	$-0.293335\pi$
$774$	36.0599	−	15.5681i	1.29615	−	0.559584i
$775$	16.0987	−	26.1588i	0.578281	−	0.939653i
$776$	−6.43250	−	11.1414i	−0.230913	−	0.399954i
$777$	−33.3602	+	16.2702i	−1.19679	+	0.583691i
$778$	−15.6859	−	9.05627i	−0.562367	−	0.324683i
$779$	−35.6105	−	20.5597i	−1.27588	−	0.736628i
$780$	−8.82316	+	1.69447i	−0.315920	+	0.0606717i
$781$	12.9926	+	22.5038i	0.464911	+	0.805249i
$782$			5.12387i			0.183229i
$783$	−15.1380	+	5.51785i	−0.540989	+	0.197192i
$784$	−3.35589	−	6.14313i	−0.119853	−	0.219397i
$785$	−15.3451	+	3.88162i	−0.547688	+	0.138541i
$786$	−3.04188	−	6.05451i	−0.108500	−	0.215957i
$787$	15.5156	−	26.8737i	0.553070	−	0.957945i	−0.444981	−	0.895540i	$-0.646790\pi$
$787$	15.5156	−	26.8737i	0.553070	−	0.957945i	0.998051	−	0.0624052i	$-0.0198771\pi$
$788$	0.881859	−	1.52743i	0.0314149	−	0.0544123i
$789$	−13.7834	+	20.9638i	−0.490702	+	0.746330i
$790$	31.6152	−	7.99725i	1.12482	−	0.284529i
$791$	−24.0910	+	40.6118i	−0.856577	+	1.44399i
$792$	0.924837	−	7.93405i	0.0328627	−	0.281924i
$793$			23.2158i			0.824418i
$794$	1.24413	+	2.15489i	0.0441524	+	0.0764742i
$795$	−4.32676	+	12.4746i	−0.153454	+	0.442429i
$796$	2.93602	+	1.69511i	0.104064	+	0.0600817i
$797$	−15.7354	−	9.08484i	−0.557377	−	0.321802i	0.194715	−	0.980860i	$-0.437622\pi$
$797$	−15.7354	−	9.08484i	−0.557377	−	0.321802i	−0.752092	+	0.659058i	$0.770955\pi$
$798$	−21.2266	−	14.3180i	−0.751414	−	0.506852i
$799$	20.5092	+	35.5229i	0.725562	+	1.25671i
$800$	−4.25822	−	2.62060i	−0.150551	−	0.0926520i
$801$	10.1408	−	13.6304i	0.358309	−	0.481608i
$802$		−	34.8815i		−	1.23171i
$803$	−9.99022	+	5.76786i	−0.352547	+	0.203543i
$804$	−8.29674	−	5.45499i	−0.292603	−	0.192383i
$805$	−4.07513	+	0.979784i	−0.143630	+	0.0345329i
$806$	−12.3414	−	7.12530i	−0.434706	−	0.250978i
$807$	10.0142	+	19.9321i	0.352516	+	0.701642i
$808$	−2.06435	−	3.57555i	−0.0726234	−	0.125787i
$809$		−	52.2729i		−	1.83782i	−0.394471	−	0.918908i	$-0.629072\pi$
$809$		−	52.2729i		−	1.83782i	0.394471	−	0.918908i	$-0.370928\pi$
$810$	−20.1221	+	0.315436i	−0.707020	+	0.0110833i
$811$		−	10.4441i		−	0.366741i	−0.983044	−	0.183370i	$-0.941299\pi$
$811$		−	10.4441i		−	0.366741i	0.983044	−	0.183370i	$-0.0587008\pi$
$812$	0.0968623	−	8.20342i	0.00339920	−	0.287883i
$813$	12.5002	−	6.28028i	0.438400	−	0.220259i
$814$	10.7827	−	18.6763i	0.377935	−	0.654603i
$815$	30.1800	−	29.3442i	1.05716	−	1.02788i
$816$	−10.4672	−	6.88207i	−0.366427	−	0.240921i
$817$	36.5753	+	63.3503i	1.27961	+	2.21635i
$818$			8.79732i			0.307591i
$819$	−7.09804	−	16.9894i	−0.248025	−	0.593657i
$820$	4.48195	−	15.8341i	0.156516	−	0.552952i
$821$	11.0056	−	6.35410i	0.384099	−	0.221760i	−0.295501	−	0.955342i	$-0.595487\pi$
$821$	11.0056	−	6.35410i	0.384099	−	0.221760i	0.679600	+	0.733583i	$0.262153\pi$
$822$	1.61673	+	0.0939095i	0.0563899	+	0.00327547i
$823$	22.4253	+	12.9473i	0.781697	+	0.451313i	0.837031	−	0.547155i	$-0.184289\pi$
$823$	22.4253	+	12.9473i	0.781697	+	0.451313i	−0.0553342	+	0.998468i	$0.517622\pi$
$824$	4.09983	−	7.10111i	0.142824	−	0.247379i
$825$	−13.2039	+	18.9040i	−0.459702	+	0.658152i
$826$	10.5078	+	0.124071i	0.365613	+	0.00431699i
$827$	−14.3307			−0.498329			−0.249164	−	0.968461i	$-0.580156\pi$
$827$	−14.3307			−0.498329			−0.249164	+	0.968461i	$0.580156\pi$
$828$	2.11106	+	0.246077i	0.0733646	+	0.00855178i
$829$		−	5.00694i		−	0.173898i	−0.996213	−	0.0869490i	$-0.972288\pi$
$829$		−	5.00694i		−	0.173898i	0.996213	−	0.0869490i	$-0.0277117\pi$
$830$	−1.43040	−	5.65474i	−0.0496498	−	0.196279i
$831$	−15.1707	−	9.97452i	−0.526266	−	0.346012i
$832$	−1.15988	+	2.00897i	−0.0402116	+	0.0696486i
$833$	−1.19540	+	50.6132i	−0.0414183	+	1.75364i
$834$	−19.3403	+	9.71687i	−0.669700	+	0.336468i
$835$	−5.26954	−	20.8319i	−0.182360	−	0.720917i
$836$	14.8767			0.514520
$837$	−24.4623	−	20.5067i	−0.845540	−	0.708815i
$838$	−0.0721315			−0.00249174
$839$	−17.1066	−	29.6295i	−0.590586	−	1.02292i	−0.994154	−	0.107975i	$-0.965564\pi$
$839$	−17.1066	−	29.6295i	−0.590586	−	1.02292i	0.403568	−	0.914950i	$-0.367770\pi$
$840$	3.47193	−	9.64084i	0.119793	−	0.332640i
$841$	−9.69247	+	16.7878i	−0.334223	+	0.578891i
$842$	3.42682	−	5.93543i	0.118096	−	0.204549i
$843$	−14.4196	−	9.48070i	−0.496638	−	0.326532i
$844$	1.09815	+	1.90206i	0.0378000	+	0.0654715i
$845$	−4.63983	+	16.3919i	−0.159615	+	0.563900i
$846$	15.6206	−	6.74389i	0.537048	−	0.231860i
$847$	−5.27869	+	8.89864i	−0.181378	+	0.305761i
$848$	1.70459	+	2.95243i	0.0585358	+	0.101387i
$849$	36.9668	+	2.14726i	1.26870	+	0.0736938i
$850$	17.1947	+	31.8129i	0.589774	+	1.09117i
$851$	4.96932	+	2.86904i	0.170346	+	0.0983493i
$852$	0.980218	−	16.8752i	0.0335817	−	0.578136i
$853$	17.5564	+	30.4086i	0.601119	+	1.04117i	0.992652	+	0.121005i	$0.0386117\pi$
$853$	17.5564	+	30.4086i	0.601119	+	1.04117i	−0.391532	+	0.920164i	$0.628055\pi$
$854$	−22.7730	−	13.5090i	−0.779274	−	0.462267i
$855$	−4.92257	−	37.1560i	−0.168348	−	1.27071i
$856$	10.5158			0.359422
$857$	−5.45905	+	3.15178i	−0.186477	+	0.107663i	−0.590332	−	0.807160i	$-0.701003\pi$
$857$	−5.45905	+	3.15178i	−0.186477	+	0.107663i	0.403855	+	0.914823i	$0.367670\pi$
$858$	8.93909	+	5.87732i	0.305175	+	0.200649i
$859$	−28.2571	−	16.3143i	−0.964121	−	0.556636i	−0.0666823	−	0.997774i	$-0.521241\pi$
$859$	−28.2571	−	16.3143i	−0.964121	−	0.556636i	−0.897439	+	0.441139i	$0.854575\pi$
$860$	−20.9894	+	20.4081i	−0.715732	+	0.695910i
$861$	33.6431	+	2.35305i	1.14655	+	0.0801918i
$862$	−3.77671	+	2.18048i	−0.128635	+	0.0742676i
$863$	43.4092			1.47767			0.738834	−	0.673888i	$-0.235377\pi$
$863$	43.4092			1.47767			0.738834	+	0.673888i	$0.235377\pi$
$864$	−3.33815	+	3.98205i	−0.113566	+	0.135472i
$865$	47.1818	+	13.3551i	1.60423	+	0.454087i
$866$	−16.2834	−	28.2037i	−0.553332	−	0.958399i
$867$	27.4555	+	54.6471i	0.932439	+	1.85591i
$868$	14.1706	−	7.95984i	0.480983	−	0.270175i
$869$	−33.6290	−	19.4157i	−1.14079	−	0.658633i
$870$	9.08131	−	7.85848i	0.307885	−	0.266427i
$871$	11.5169	−	6.64929i	0.390236	−	0.225303i
$872$	7.38448			0.250070
$873$	38.3355	+	4.46859i	1.29746	+	0.151239i
$874$			3.95833i			0.133893i
$875$	−22.0136	+	19.7586i	−0.744194	+	0.667963i
$876$	7.49151	+	0.435153i	0.253115	+	0.0147025i
$877$	22.5421	+	13.0147i	0.761193	+	0.439475i	0.829724	−	0.558174i	$-0.188498\pi$
$877$	22.5421	+	13.0147i	0.761193	+	0.439475i	−0.0685308	+	0.997649i	$0.521831\pi$
$878$	26.2998	+	15.1842i	0.887577	+	0.512443i
$879$	−1.15379	+	19.8635i	−0.0389165	+	0.669979i
$880$	1.46004	+	5.77193i	0.0492181	+	0.194572i
$881$	−3.51648			−0.118473			−0.0592366	−	0.998244i	$-0.518867\pi$
$881$	−3.51648			−0.118473			−0.0592366	+	0.998244i	$0.518867\pi$
$882$	20.7955	+	2.92325i	0.700222	+	0.0984309i
$883$		−	5.38947i		−	0.181370i	−0.995880	−	0.0906851i	$-0.971094\pi$
$883$		−	5.38947i		−	0.181370i	0.995880	−	0.0906851i	$-0.0289057\pi$
$884$	14.5298	−	8.38881i	0.488692	−	0.282146i
$885$	10.0660	+	11.6323i	0.338364	+	0.391015i
$886$	−18.8007	+	32.5637i	−0.631620	+	1.09400i
$887$	−33.1558	−	19.1425i	−1.11326	−	0.642742i	−0.173589	−	0.984818i	$-0.555536\pi$
$887$	−33.1558	−	19.1425i	−1.11326	−	0.642742i	−0.939672	+	0.342076i	$0.888870\pi$
$888$	−12.5355	+	6.29801i	−0.420663	+	0.211347i
$889$	−0.507740	+	43.0013i	−0.0170291	+	1.44222i
$890$	−3.44879	+	12.1841i	−0.115604	+	0.408413i
$891$	17.4406	+	16.4337i	0.584282	+	0.550549i
$892$	−9.39129			−0.314444
$893$	15.8439	+	27.4425i	0.530196	+	0.918327i
$894$	−4.69037	+	2.35651i	−0.156869	+	0.0788135i
$895$	−3.73588	+	3.63242i	−0.124877	+	0.121418i
$896$	−1.29573	−	2.30675i	−0.0432873	−	0.0770630i
$897$	−1.56382	+	2.37848i	−0.0522144	+	0.0794152i
$898$	−3.74608	+	2.16280i	−0.125008	+	0.0721736i
$899$	19.0487			0.635310
$900$	13.9329	−	5.55650i	0.464430	−	0.185217i
$901$		−	24.6568i		−	0.821436i
$902$	−16.9700	+	9.79761i	−0.565038	+	0.326225i
$903$	−49.7389	−	33.5504i	−1.65521	−	1.11649i
$904$	−8.92367	+	15.4563i	−0.296797	+	0.514067i
$905$	31.5940	−	30.7190i	1.05022	−	1.02113i
$906$	16.4294	+	0.954322i	0.545831	+	0.0317052i
$907$	3.01367	−	1.73994i	0.100067	−	0.0577738i	−0.449131	−	0.893466i	$-0.648266\pi$
$907$	3.01367	−	1.73994i	0.100067	−	0.0577738i	0.549198	+	0.835692i	$0.314933\pi$
$908$		−	2.60953i		−	0.0866003i
$909$	12.3028	+	1.43408i	0.408057	+	0.0475654i
$910$	9.45021	+	9.95182i	0.313271	+	0.329900i
$911$	−46.3590	+	26.7654i	−1.53594	+	0.886777i	−0.536872	+	0.843664i	$0.680394\pi$
$911$	−46.3590	+	26.7654i	−1.53594	+	0.886777i	−0.999070	+	0.0431128i	$0.986273\pi$
$912$	−8.08625	−	5.31659i	−0.267762	−	0.176050i
$913$	−3.47272	+	6.01493i	−0.114930	+	0.199065i
$914$	18.5026	+	10.6825i	0.612010	+	0.353344i
$915$	−7.31023	−	38.0646i	−0.241669	−	1.25838i
$916$	2.92097	−	1.68642i	0.0965115	−	0.0557210i
$917$	−5.28050	+	8.90169i	−0.174377	+	0.293960i
$918$	35.3086	−	12.8701i	1.16536	−	0.424776i
$919$	−15.2442			−0.502861			−0.251430	−	0.967875i	$-0.580901\pi$
$919$	−15.2442			−0.502861			−0.251430	+	0.967875i	$0.580901\pi$
$920$	−1.53578	+	0.388483i	−0.0506330	+	0.0128079i
$921$	−4.23446	−	8.42821i	−0.139530	−	0.277719i
$922$	9.79603	−	16.9672i	0.322615	−	0.558786i
$923$	19.6063	+	11.3197i	0.645348	+	0.372592i
$924$	−10.9667	+	5.34863i	−0.360779	+	0.175957i
$925$	40.4812	+	1.13708i	1.33101	+	0.0373869i
$926$		−	20.5064i		−	0.673883i
$927$	9.75024	+	22.5841i	0.320240	+	0.741760i
$928$		−	3.10082i		−	0.101789i
$929$	15.7876	+	27.3450i	0.517975	+	0.897159i	0.999782	+	0.0208818i	$0.00664736\pi$
$929$	15.7876	+	27.3450i	0.517975	+	0.897159i	−0.481807	+	0.876277i	$0.660019\pi$
$930$	22.4785	+	7.79656i	0.737100	+	0.255659i
$931$	−0.923483	+	39.1001i	−0.0302659	+	1.28146i
$932$	−12.2325	+	21.1873i	−0.400689	+	0.694013i
$933$	5.79971	+	0.336883i	0.189874	+	0.0110291i
$934$	12.4017	−	7.16013i	0.405796	−	0.234287i
$935$	11.7277	−	41.4324i	0.383537	−	1.35498i
$936$	−2.75843	−	6.38926i	−0.0901622	−	0.208840i
$937$	−3.67779			−0.120148			−0.0600741	−	0.998194i	$-0.519134\pi$
$937$	−3.67779			−0.120148			−0.0600741	+	0.998194i	$0.519134\pi$
$938$	−0.179077	+	15.1663i	−0.00584708	+	0.495198i
$939$	29.8235	−	45.3600i	0.973255	−	1.48027i
$940$	−9.09230	+	8.84050i	−0.296558	+	0.288345i
$941$	−16.5040	+	28.5858i	−0.538016	+	0.931870i	0.460995	+	0.887403i	$0.347493\pi$
$941$	−16.5040	+	28.5858i	−0.538016	+	0.931870i	−0.999011	+	0.0444678i	$0.985841\pi$
$942$	−5.50427	−	10.9556i	−0.179339	−	0.356953i
$943$	−2.60691	−	4.51531i	−0.0848928	−	0.147039i
$944$	3.97185			0.129273
$945$	16.9876	+	25.6207i	0.552606	+	0.833443i
$946$	34.8595			1.13338
$947$	3.23974	+	5.61139i	0.105277	+	0.182346i	0.913851	−	0.406049i	$-0.133094\pi$
$947$	3.23974	+	5.61139i	0.105277	+	0.182346i	−0.808574	+	0.588394i	$0.799760\pi$
$948$	11.3404	+	22.5717i	0.368318	+	0.733095i
$949$	−5.02520	+	8.70391i	−0.163125	+	0.282541i
$950$	13.2834	+	24.5763i	0.430971	+	0.797362i
$951$	22.5029	−	34.2257i	0.729706	−	1.10984i
$952$	−0.225926	+	19.1340i	−0.00732230	+	0.620137i
$953$	16.0190			0.518908			0.259454	−	0.965756i	$-0.416457\pi$
$953$	16.0190			0.518908			0.259454	+	0.965756i	$0.416457\pi$
$954$	−10.1587	−	1.18416i	−0.328901	−	0.0383386i
$955$	29.1457	+	8.24987i	0.943133	+	0.266959i
$956$	−14.3027	+	8.25768i	−0.462583	+	0.267072i
$957$	−14.2761	−	0.829244i	−0.461481	−	0.0268056i
$958$	−12.6756	+	21.9548i	−0.409531	+	0.709328i
$959$	−1.21150	−	2.15679i	−0.0391213	−	0.0696464i
$960$	1.26915	−	3.65913i	0.0409617	−	0.118098i
$961$	3.36902	+	5.83531i	0.108678	+	0.188236i
$962$		−	18.7888i		−	0.605774i
$963$	−18.8308	+	25.3108i	−0.606815	+	0.815628i
$964$		−	17.8922i		−	0.576270i
$965$	−4.42796	−	17.5049i	−0.142541	−	0.563502i
$966$	−1.42315	−	2.91799i	−0.0457890	−	0.0938848i
$967$	44.9097	+	25.9286i	1.44420	+	0.833808i	0.998126	−	0.0611892i	$-0.0194893\pi$
$967$	44.9097	+	25.9286i	1.44420	+	0.833808i	0.446072	+	0.894997i	$0.352823\pi$
$968$	−1.95531	+	3.38669i	−0.0628459	+	0.108852i
$969$	31.4222	+	62.5423i	1.00943	+	2.00915i
$970$	−27.8886	+	7.05458i	−0.895449	+	0.226509i
$971$	−12.7024			−0.407638			−0.203819	−	0.979009i	$-0.565335\pi$
$971$	−12.7024			−0.407638			−0.203819	+	0.979009i	$0.565335\pi$
$972$	−3.60683	−	15.1654i	−0.115689	−	0.486432i
$973$	28.4352	+	16.8678i	0.911591	+	0.540758i
$974$	−9.96159	+	5.75133i	−0.319190	+	0.184284i
$975$	−1.72764	+	20.0153i	−0.0553288	+	0.641003i
$976$	−8.66705	−	5.00392i	−0.277426	−	0.160172i
$977$	6.82737	−	11.8253i	0.218427	−	0.378326i	−0.735900	−	0.677090i	$-0.763241\pi$
$977$	6.82737	−	11.8253i	0.218427	−	0.378326i	0.954327	+	0.298763i	$0.0965742\pi$
$978$	27.2447	+	17.9130i	0.871189	+	0.572794i
$979$	13.0581	−	7.53912i	0.417340	−	0.240951i
$980$	−15.2609	+	3.47911i	−0.487492	+	0.111136i
$981$	−13.2236	+	17.7739i	−0.422196	+	0.567478i
$982$		−	26.1926i		−	0.835838i
$983$	−9.69185	+	5.59559i	−0.309122	+	0.178472i	−0.646534	−	0.762886i	$-0.723782\pi$
$983$	−9.69185	+	5.59559i	−0.309122	+	0.178472i	0.337411	+	0.941357i	$0.390449\pi$
$984$	12.7255	+	0.739175i	0.405674	+	0.0235641i
$985$	−2.74926	−	2.82756i	−0.0875986	−	0.0900937i
$986$	−11.2133	+	19.4220i	−0.357104	+	0.618522i
$987$	−21.5462	−	14.5335i	−0.685823	−	0.462608i
$988$	11.2247	−	6.48059i	0.357106	−	0.206175i
$989$			9.27529i			0.294937i
$990$	−16.5072	−	6.82170i	−0.524632	−	0.216808i
$991$	25.9249			0.823530			0.411765	−	0.911290i	$-0.364912\pi$
$991$	25.9249			0.823530			0.411765	+	0.911290i	$0.364912\pi$
$992$	5.32011	−	3.07156i	0.168914	−	0.0975223i
$993$	−9.44179	+	14.3604i	−0.299626	+	0.455715i
$994$	−22.5123	+	12.6455i	−0.714048	+	0.401091i
$995$	5.43515	−	5.28463i	0.172306	−	0.167534i
$996$	4.03721	−	2.02835i	0.127924	−	0.0642708i
$997$	−9.94358	−	17.2228i	−0.314916	−	0.545451i	0.664503	−	0.747285i	$-0.268643\pi$
$997$	−9.94358	−	17.2228i	−0.314916	−	0.545451i	−0.979420	+	0.201834i	$0.935310\pi$
$998$	−19.9112			−0.630277
$999$	7.28866	−	41.4500i	0.230603	−	1.31142i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bf.e.419.6	yes	32
3.2	odd	2		1890.2.bf.f.1259.2		32
5.4	even	2		630.2.bf.f.419.11	yes	32
7.6	odd	2	inner	630.2.bf.e.419.11	yes	32
9.2	odd	6		630.2.bf.f.209.6	yes	32
9.7	even	3		1890.2.bf.e.629.3		32
15.14	odd	2		1890.2.bf.e.1259.14		32
21.20	even	2		1890.2.bf.f.1259.15		32
35.34	odd	2		630.2.bf.f.419.6	yes	32
45.29	odd	6	inner	630.2.bf.e.209.11	yes	32
45.34	even	6		1890.2.bf.f.629.15		32
63.20	even	6		630.2.bf.f.209.11	yes	32
63.34	odd	6		1890.2.bf.e.629.14		32
105.104	even	2		1890.2.bf.e.1259.3		32
315.34	odd	6		1890.2.bf.f.629.2		32
315.209	even	6	inner	630.2.bf.e.209.6	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bf.e.209.6	✓	32	315.209	even	6	inner
630.2.bf.e.209.11	yes	32	45.29	odd	6	inner
630.2.bf.e.419.6	yes	32	1.1	even	1	trivial
630.2.bf.e.419.11	yes	32	7.6	odd	2	inner
630.2.bf.f.209.6	yes	32	9.2	odd	6
630.2.bf.f.209.11	yes	32	63.20	even	6
630.2.bf.f.419.6	yes	32	35.34	odd	2
630.2.bf.f.419.11	yes	32	5.4	even	2
1890.2.bf.e.629.3		32	9.7	even	3
1890.2.bf.e.629.14		32	63.34	odd	6
1890.2.bf.e.1259.3		32	105.104	even	2
1890.2.bf.e.1259.14		32	15.14	odd	2
1890.2.bf.f.629.2		32	315.34	odd	6
1890.2.bf.f.629.15		32	45.34	even	6
1890.2.bf.f.1259.2		32	3.2	odd	2
1890.2.bf.f.1259.15		32	21.20	even	2

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.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.777586 - 1.54770i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.55878 + 1.60318i) q^{5} +(-0.951551 + 1.44726i) q^{6} +(2.64557 + 0.0312377i) q^{7} +1.00000 q^{8} +(-1.79072 + 2.40693i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.777586 - 1.54770i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.55878 + 1.60318i) q^{5} +(-0.951551 + 1.44726i) q^{6} +(2.64557 + 0.0312377i) q^{7} +1.00000 q^{8} +(-1.79072 + 2.40693i) q^{9} +(0.609005 - 2.15154i) q^{10} +(-2.30587 + 1.33130i) q^{11} +(1.72914 + 0.100439i) q^{12} +(-1.15988 + 2.00897i) q^{13} +(-1.29573 - 2.30675i) q^{14} +(1.26915 - 3.65913i) q^{15} +(-0.500000 - 0.866025i) q^{16} +7.23248i q^{17} +(2.97982 + 0.347345i) q^{18} +5.58729i q^{19} +(-2.16779 + 0.548354i) q^{20} +(-2.00881 - 4.11882i) q^{21} +(2.30587 + 1.33130i) q^{22} +(-0.354226 + 0.613538i) q^{23} +(-0.777586 - 1.54770i) q^{24} +(-0.140390 + 4.99803i) q^{25} +2.31976 q^{26} +(5.11763 + 0.899897i) q^{27} +(-1.34984 + 2.27551i) q^{28} +(-2.68539 + 1.55041i) q^{29} +(-3.80348 + 0.730449i) q^{30} +(-5.32011 - 3.07156i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.85345 + 2.53359i) q^{33} +(6.26351 - 3.61624i) q^{34} +(4.07379 + 4.29002i) q^{35} +(-1.18910 - 2.75428i) q^{36} -8.09944i q^{37} +(4.83874 - 2.79365i) q^{38} +(4.01118 + 0.232994i) q^{39} +(1.55878 + 1.60318i) q^{40} +(-3.67973 + 6.37348i) q^{41} +(-2.56260 + 3.79909i) q^{42} +(11.3383 - 6.54616i) q^{43} -2.66259i q^{44} +(-6.65010 + 0.881030i) q^{45} +0.708453 q^{46} +(4.91158 - 2.83570i) q^{47} +(-0.951551 + 1.44726i) q^{48} +(6.99805 + 0.165283i) q^{49} +(4.39861 - 2.37743i) q^{50} +(11.1937 - 5.62387i) q^{51} +(-1.15988 - 2.00897i) q^{52} -3.40917 q^{53} +(-1.77948 - 4.88195i) q^{54} +(-5.72866 - 1.62153i) q^{55} +(2.64557 + 0.0312377i) q^{56} +(8.64743 - 4.34460i) q^{57} +(2.68539 + 1.55041i) q^{58} +(-1.98592 + 3.43972i) q^{59} +(2.53433 + 2.92868i) q^{60} +(8.66705 - 5.00392i) q^{61} +6.14313i q^{62} +(-4.81266 + 6.31176i) q^{63} +1.00000 q^{64} +(-5.02875 + 1.27205i) q^{65} +(0.267428 - 4.60398i) q^{66} +(-4.96469 - 2.86637i) q^{67} +(-6.26351 - 3.61624i) q^{68} +(1.22501 + 0.0711562i) q^{69} +(1.67837 - 5.67301i) q^{70} -9.75935i q^{71} +(-1.79072 + 2.40693i) q^{72} +4.33252 q^{73} +(-7.01432 + 4.04972i) q^{74} +(7.84459 - 3.66911i) q^{75} +(-4.83874 - 2.79365i) q^{76} +(-6.14192 + 3.45000i) q^{77} +(-1.80381 - 3.59028i) q^{78} +(7.29204 + 12.6302i) q^{79} +(0.609005 - 2.15154i) q^{80} +(-2.58663 - 8.62029i) q^{81} +7.35946 q^{82} +(2.25905 - 1.30426i) q^{83} +(4.57141 + 0.319732i) q^{84} +(-11.5950 + 11.2739i) q^{85} +(-11.3383 - 6.54616i) q^{86} +(4.48768 + 2.95058i) q^{87} +(-2.30587 + 1.33130i) q^{88} -5.66299 q^{89} +(4.08804 + 5.31864i) q^{90} +(-3.13130 + 5.27864i) q^{91} +(-0.354226 - 0.613538i) q^{92} +(-0.617009 + 10.6223i) q^{93} +(-4.91158 - 2.83570i) q^{94} +(-8.95745 + 8.70938i) q^{95} +(1.72914 + 0.100439i) q^{96} +(-6.43250 - 11.1414i) q^{97} +(-3.35589 - 6.14313i) q^{98} +(0.924837 - 7.93405i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} - 6 q^{9}+O(q^{10}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 - 6 * q^9	\( 32 q - 16 q^{2} - 16 q^{4} + 32 q^{8} - 6 q^{9} - 24 q^{11} - 16 q^{15} - 16 q^{16} + 6 q^{18} + 2 q^{21} + 24 q^{22} - 24 q^{23} - 58 q^{25} - 36 q^{29} - 10 q^{30} - 16 q^{32} - 48 q^{35} - 66 q^{39} + 2 q^{42} - 54 q^{43} + 48 q^{46} + 32 q^{49} + 50 q^{50} - 26 q^{51} - 24 q^{53} + 110 q^{57} + 36 q^{58} + 26 q^{60} + 20 q^{63} + 32 q^{64} - 90 q^{65} - 66 q^{67} + 36 q^{70} - 6 q^{72} + 12 q^{74} + 18 q^{77} + 60 q^{78} + 34 q^{79} + 2 q^{81} - 4 q^{84} + 4 q^{85} + 54 q^{86} - 24 q^{88} + 16 q^{91} - 24 q^{92} + 28 q^{93} + 12 q^{95} - 64 q^{98} + 58 q^{99}+O(q^{100}) \) 32 * q - 16 * q^2 - 16 * q^4 + 32 * q^8 - 6 * q^9 - 24 * q^11 - 16 * q^15 - 16 * q^16 + 6 * q^18 + 2 * q^21 + 24 * q^22 - 24 * q^23 - 58 * q^25 - 36 * q^29 - 10 * q^30 - 16 * q^32 - 48 * q^35 - 66 * q^39 + 2 * q^42 - 54 * q^43 + 48 * q^46 + 32 * q^49 + 50 * q^50 - 26 * q^51 - 24 * q^53 + 110 * q^57 + 36 * q^58 + 26 * q^60 + 20 * q^63 + 32 * q^64 - 90 * q^65 - 66 * q^67 + 36 * q^70 - 6 * q^72 + 12 * q^74 + 18 * q^77 + 60 * q^78 + 34 * q^79 + 2 * q^81 - 4 * q^84 + 4 * q^85 + 54 * q^86 - 24 * q^88 + 16 * q^91 - 24 * q^92 + 28 * q^93 + 12 * q^95 - 64 * q^98 + 58 * q^99

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