LMFDB - Embedded newform 350.2.m.b.29.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(29,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("350.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.m (of order $10$, degree $4$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.8
Character	$\chi$	$=$	350.29
Dual form			350.2.m.b.169.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 + 0.309017i) q^{2} +(0.454807 - 0.625988i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.27366 + 1.83787i) q^{5} +(0.625988 - 0.454807i) q^{6} +1.00000i q^{7} +(0.587785 + 0.809017i) q^{8} +(0.742040 + 2.28376i) q^{9} +O(q^{10})$	\(q+(0.951057 + 0.309017i) q^{2} +(0.454807 - 0.625988i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.27366 + 1.83787i) q^{5} +(0.625988 - 0.454807i) q^{6} +1.00000i q^{7} +(0.587785 + 0.809017i) q^{8} +(0.742040 + 2.28376i) q^{9} +(-1.77926 + 1.35434i) q^{10} +(-1.04713 + 3.22273i) q^{11} +(0.735893 - 0.239106i) q^{12} +(5.05447 - 1.64230i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(0.571215 + 1.63318i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-2.43606 - 3.35295i) q^{17} +2.40129i q^{18} +(5.39266 - 3.91800i) q^{19} +(-2.11069 + 0.738230i) q^{20} +(0.625988 + 0.454807i) q^{21} +(-1.99176 + 2.74142i) q^{22} +(-0.249307 - 0.0810046i) q^{23} +0.773763 q^{24} +(-1.75556 - 4.68167i) q^{25} +5.31458 q^{26} +(3.97477 + 1.29148i) q^{27} +(-0.587785 + 0.809017i) q^{28} +(-7.94519 - 5.77252i) q^{29} +(0.0385788 + 1.72976i) q^{30} +(-3.74752 + 2.72273i) q^{31} +1.00000i q^{32} +(1.54115 + 2.12121i) q^{33} +(-1.28071 - 3.94163i) q^{34} +(-1.83787 - 1.27366i) q^{35} +(-0.742040 + 2.28376i) q^{36} +(-0.340253 + 0.110555i) q^{37} +(6.33946 - 2.05981i) q^{38} +(1.27075 - 3.91096i) q^{39} +(-2.23551 + 0.0498587i) q^{40} +(0.254376 + 0.782888i) q^{41} +(0.454807 + 0.625988i) q^{42} +2.32743i q^{43} +(-2.74142 + 1.99176i) q^{44} +(-5.14238 - 1.54497i) q^{45} +(-0.212073 - 0.154080i) q^{46} +(2.75381 - 3.79030i) q^{47} +(0.735893 + 0.239106i) q^{48} -1.00000 q^{49} +(-0.222920 - 4.99503i) q^{50} -3.20684 q^{51} +(5.05447 + 1.64230i) q^{52} +(0.624792 - 0.859953i) q^{53} +(3.38114 + 2.45654i) q^{54} +(-4.58928 - 6.02916i) q^{55} +(-0.809017 + 0.587785i) q^{56} -5.15767i q^{57} +(-5.77252 - 7.94519i) q^{58} +(-0.489148 - 1.50544i) q^{59} +(-0.497834 + 1.65702i) q^{60} +(0.462805 - 1.42437i) q^{61} +(-4.40547 + 1.43142i) q^{62} +(-2.28376 + 0.742040i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-3.41936 + 11.3812i) q^{65} +(0.810229 + 2.49363i) q^{66} +(4.68745 + 6.45172i) q^{67} -4.14447i q^{68} +(-0.164094 + 0.119221i) q^{69} +(-1.35434 - 1.77926i) q^{70} +(6.82418 + 4.95806i) q^{71} +(-1.41144 + 1.94268i) q^{72} +(-1.37982 - 0.448330i) q^{73} -0.357763 q^{74} +(-3.72911 - 1.03030i) q^{75} +6.66570 q^{76} +(-3.22273 - 1.04713i) q^{77} +(2.41711 - 3.32686i) q^{78} +(-5.16613 - 3.75342i) q^{79} +(-2.14151 - 0.643393i) q^{80} +(-3.21185 + 2.33355i) q^{81} +0.823177i q^{82} +(-3.26654 - 4.49600i) q^{83} +(0.239106 + 0.735893i) q^{84} +(9.26502 - 0.206638i) q^{85} +(-0.719216 + 2.21352i) q^{86} +(-7.22705 + 2.34821i) q^{87} +(-3.22273 + 1.04713i) q^{88} +(4.39198 - 13.5171i) q^{89} +(-4.41327 - 3.05844i) q^{90} +(1.64230 + 5.05447i) q^{91} +(-0.154080 - 0.212073i) q^{92} +3.58422i q^{93} +(3.79030 - 2.75381i) q^{94} +(0.332343 + 14.9013i) q^{95} +(0.625988 + 0.454807i) q^{96} +(11.3670 - 15.6454i) q^{97} +(-0.951057 - 0.309017i) q^{98} -8.13696 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9}+O(q^{10}) $ 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9	$ 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9} - 4 q^{10} - 6 q^{11} + 10 q^{12} + 10 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{19} + 4 q^{20} - 2 q^{21} - 10 q^{22} - 10 q^{23} - 8 q^{24} - 10 q^{25} + 12 q^{26} - 30 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{31} - 60 q^{33} - 4 q^{35} - 20 q^{36} + 10 q^{37} + 10 q^{38} + 36 q^{39} - 6 q^{40} - 34 q^{41} + 6 q^{44} + 112 q^{45} - 6 q^{46} + 30 q^{47} + 10 q^{48} - 40 q^{49} - 16 q^{50} + 44 q^{51} + 10 q^{53} + 20 q^{54} + 34 q^{55} - 10 q^{56} + 20 q^{58} + 12 q^{59} + 2 q^{60} + 2 q^{61} + 10 q^{64} - 106 q^{65} + 10 q^{66} - 30 q^{67} + 84 q^{69} + 4 q^{70} + 16 q^{71} - 110 q^{73} - 60 q^{74} + 10 q^{75} + 32 q^{76} + 20 q^{77} - 20 q^{78} + 4 q^{79} - 4 q^{80} - 20 q^{81} + 10 q^{83} + 2 q^{84} - 42 q^{85} - 14 q^{86} - 20 q^{87} + 20 q^{88} - 38 q^{90} + 2 q^{91} - 30 q^{92} + 6 q^{94} + 64 q^{95} - 2 q^{96} + 30 q^{97} - 72 q^{99}+O(q^{100}) $ 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9 - 4 * q^10 - 6 * q^11 + 10 * q^12 + 10 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^19 + 4 * q^20 - 2 * q^21 - 10 * q^22 - 10 * q^23 - 8 * q^24 - 10 * q^25 + 12 * q^26 - 30 * q^27 + 4 * q^29 - 22 * q^30 - 24 * q^31 - 60 * q^33 - 4 * q^35 - 20 * q^36 + 10 * q^37 + 10 * q^38 + 36 * q^39 - 6 * q^40 - 34 * q^41 + 6 * q^44 + 112 * q^45 - 6 * q^46 + 30 * q^47 + 10 * q^48 - 40 * q^49 - 16 * q^50 + 44 * q^51 + 10 * q^53 + 20 * q^54 + 34 * q^55 - 10 * q^56 + 20 * q^58 + 12 * q^59 + 2 * q^60 + 2 * q^61 + 10 * q^64 - 106 * q^65 + 10 * q^66 - 30 * q^67 + 84 * q^69 + 4 * q^70 + 16 * q^71 - 110 * q^73 - 60 * q^74 + 10 * q^75 + 32 * q^76 + 20 * q^77 - 20 * q^78 + 4 * q^79 - 4 * q^80 - 20 * q^81 + 10 * q^83 + 2 * q^84 - 42 * q^85 - 14 * q^86 - 20 * q^87 + 20 * q^88 - 38 * q^90 + 2 * q^91 - 30 * q^92 + 6 * q^94 + 64 * q^95 - 2 * q^96 + 30 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$3$	0.454807	−	0.625988i	0.262583	−	0.361414i	−0.657286	−	0.753642i	$-0.728295\pi$
$3$	0.454807	−	0.625988i	0.262583	−	0.361414i	0.919868	+	0.392228i	$0.128295\pi$
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	−1.27366	+	1.83787i	−0.569600	+	0.821922i
$5$	−1.27366	+	1.83787i	−0.569600	+	0.821922i
$6$	0.625988	−	0.454807i	0.255558	−	0.185674i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	0.587785	+	0.809017i	0.207813	+	0.286031i
$9$	0.742040	+	2.28376i	0.247347	+	0.761254i
$10$	−1.77926	+	1.35434i	−0.562652	+	0.428279i
$11$	−1.04713	+	3.22273i	−0.315721	+	0.971689i	0.659736	+	0.751498i	$0.270668\pi$
$11$	−1.04713	+	3.22273i	−0.315721	+	0.971689i	−0.975457	+	0.220191i	$0.929332\pi$
$12$	0.735893	−	0.239106i	0.212434	−	0.0690240i
$13$	5.05447	−	1.64230i	1.40186	−	0.455491i	0.492066	−	0.870558i	$-0.336242\pi$
$13$	5.05447	−	1.64230i	1.40186	−	0.455491i	0.909791	+	0.415067i	$0.136242\pi$
$14$	−0.309017	+	0.951057i	−0.0825883	+	0.254181i
$15$	0.571215	+	1.63318i	0.147487	+	0.421684i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−2.43606	−	3.35295i	−0.590831	−	0.813210i	0.403999	−	0.914759i	$-0.367620\pi$
$17$	−2.43606	−	3.35295i	−0.590831	−	0.813210i	−0.994830	+	0.101550i	$0.967620\pi$
$18$			2.40129i			0.565990i
$19$	5.39266	−	3.91800i	1.23716	−	0.898851i	0.239756	−	0.970833i	$-0.422933\pi$
$19$	5.39266	−	3.91800i	1.23716	−	0.898851i	0.997406	+	0.0719823i	$0.0229325\pi$
$20$	−2.11069	+	0.738230i	−0.471965	+	0.165073i
$21$	0.625988	+	0.454807i	0.136602	+	0.0992469i
$22$	−1.99176	+	2.74142i	−0.424644	+	0.584472i
$23$	−0.249307	−	0.0810046i	−0.0519840	−	0.0168906i	0.282910	−	0.959147i	$-0.408700\pi$
$23$	−0.249307	−	0.0810046i	−0.0519840	−	0.0168906i	−0.334894	+	0.942256i	$0.608700\pi$
$24$	0.773763			0.157944
$25$	−1.75556	−	4.68167i	−0.351112	−	0.936334i
$26$	5.31458			1.04227
$27$	3.97477	+	1.29148i	0.764945	+	0.248546i
$28$	−0.587785	+	0.809017i	−0.111081	+	0.152890i
$29$	−7.94519	−	5.77252i	−1.47539	−	1.07193i	−0.979008	−	0.203824i	$-0.934663\pi$
$29$	−7.94519	−	5.77252i	−1.47539	−	1.07193i	−0.496378	−	0.868107i	$-0.665337\pi$
$30$	0.0385788	+	1.72976i	0.00704350	+	0.315809i
$31$	−3.74752	+	2.72273i	−0.673074	+	0.489017i	−0.871053	−	0.491189i	$-0.836562\pi$
$31$	−3.74752	+	2.72273i	−0.673074	+	0.489017i	0.197979	+	0.980206i	$0.436562\pi$
$32$			1.00000i			0.176777i
$33$	1.54115	+	2.12121i	0.268279	+	0.369255i
$34$	−1.28071	−	3.94163i	−0.219640	−	0.675984i
$35$	−1.83787	−	1.27366i	−0.310657	−	0.215289i
$36$	−0.742040	+	2.28376i	−0.123673	+	0.380627i
$37$	−0.340253	+	0.110555i	−0.0559372	+	0.0181751i	−0.336852	−	0.941558i	$-0.609362\pi$
$37$	−0.340253	+	0.110555i	−0.0559372	+	0.0181751i	0.280915	+	0.959733i	$0.409362\pi$
$38$	6.33946	−	2.05981i	1.02840	−	0.334146i
$39$	1.27075	−	3.91096i	0.203483	−	0.626255i
$40$	−2.23551	+	0.0498587i	−0.353465	+	0.00788336i
$41$	0.254376	+	0.782888i	0.0397268	+	0.122267i	0.968953	−	0.247245i	$-0.0795251\pi$
$41$	0.254376	+	0.782888i	0.0397268	+	0.122267i	−0.929226	+	0.369511i	$0.879525\pi$
$42$	0.454807	+	0.625988i	0.0701782	+	0.0965920i
$43$			2.32743i			0.354930i	0.984127	+	0.177465i	$0.0567897\pi$
$43$			2.32743i			0.354930i	−0.984127	+	0.177465i	$0.943210\pi$
$44$	−2.74142	+	1.99176i	−0.413284	+	0.300268i
$45$	−5.14238	−	1.54497i	−0.766580	−	0.230311i
$46$	−0.212073	−	0.154080i	−0.0312684	−	0.0227178i
$47$	2.75381	−	3.79030i	0.401685	−	0.552872i	−0.559481	−	0.828843i	$-0.688999\pi$
$47$	2.75381	−	3.79030i	0.401685	−	0.552872i	0.961166	+	0.275971i	$0.0889994\pi$
$48$	0.735893	+	0.239106i	0.106217	+	0.0345120i
$49$	−1.00000			−0.142857
$50$	−0.222920	−	4.99503i	−0.0315256	−	0.706404i
$51$	−3.20684			−0.449047
$52$	5.05447	+	1.64230i	0.700928	+	0.227745i
$53$	0.624792	−	0.859953i	0.0858218	−	0.118124i	−0.763947	−	0.645279i	$-0.776741\pi$
$53$	0.624792	−	0.859953i	0.0858218	−	0.118124i	0.849769	+	0.527155i	$0.176741\pi$
$54$	3.38114	+	2.45654i	0.460115	+	0.334293i
$55$	−4.58928	−	6.02916i	−0.618818	−	0.812972i
$56$	−0.809017	+	0.587785i	−0.108109	+	0.0785461i
$57$		−	5.15767i		−	0.683150i
$58$	−5.77252	−	7.94519i	−0.757969	−	1.04326i
$59$	−0.489148	−	1.50544i	−0.0636817	−	0.195992i	0.914153	−	0.405368i	$-0.132857\pi$
$59$	−0.489148	−	1.50544i	−0.0636817	−	0.195992i	−0.977835	+	0.209376i	$0.932857\pi$
$60$	−0.497834	+	1.65702i	−0.0642700	+	0.213920i
$61$	0.462805	−	1.42437i	0.0592562	−	0.182372i	−0.917047	−	0.398779i	$-0.869434\pi$
$61$	0.462805	−	1.42437i	0.0592562	−	0.182372i	0.976303	+	0.216408i	$0.0694340\pi$
$62$	−4.40547	+	1.43142i	−0.559495	+	0.181791i
$63$	−2.28376	+	0.742040i	−0.287727	+	0.0934882i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	−3.41936	+	11.3812i	−0.424120	+	1.41166i
$66$	0.810229	+	2.49363i	0.0997323	+	0.306944i
$67$	4.68745	+	6.45172i	0.572663	+	0.788202i	0.992867	−	0.119227i	$-0.0380416\pi$
$67$	4.68745	+	6.45172i	0.572663	+	0.788202i	−0.420204	+	0.907429i	$0.638042\pi$
$68$		−	4.14447i		−	0.502591i
$69$	−0.164094	+	0.119221i	−0.0197546	+	0.0143526i
$70$	−1.35434	−	1.77926i	−0.161874	−	0.212662i
$71$	6.82418	+	4.95806i	0.809882	+	0.588413i	0.913796	−	0.406173i	$-0.133137\pi$
$71$	6.82418	+	4.95806i	0.809882	+	0.588413i	−0.103915	+	0.994586i	$0.533137\pi$
$72$	−1.41144	+	1.94268i	−0.166340	+	0.228948i
$73$	−1.37982	−	0.448330i	−0.161495	−	0.0524731i	0.227153	−	0.973859i	$-0.427058\pi$
$73$	−1.37982	−	0.448330i	−0.161495	−	0.0524731i	−0.388649	+	0.921386i	$0.627058\pi$
$74$	−0.357763			−0.0415891
$75$	−3.72911	−	1.03030i	−0.430600	−	0.118968i
$76$	6.66570			0.764608
$77$	−3.22273	−	1.04713i	−0.367264	−	0.119331i
$78$	2.41711	−	3.32686i	0.273683	−	0.376693i
$79$	−5.16613	−	3.75342i	−0.581235	−	0.422292i	0.257934	−	0.966163i	$-0.416958\pi$
$79$	−5.16613	−	3.75342i	−0.581235	−	0.422292i	−0.839169	+	0.543870i	$0.816958\pi$
$80$	−2.14151	−	0.643393i	−0.239428	−	0.0719335i
$81$	−3.21185	+	2.33355i	−0.356872	+	0.259283i
$82$			0.823177i			0.0909047i
$83$	−3.26654	−	4.49600i	−0.358549	−	0.493500i	0.591195	−	0.806529i	$-0.298656\pi$
$83$	−3.26654	−	4.49600i	−0.358549	−	0.493500i	−0.949744	+	0.313029i	$0.898656\pi$
$84$	0.239106	+	0.735893i	0.0260886	+	0.0802925i
$85$	9.26502	−	0.206638i	1.00493	−	0.0224130i
$86$	−0.719216	+	2.21352i	−0.0775551	+	0.238690i
$87$	−7.22705	+	2.34821i	−0.774821	+	0.251755i
$88$	−3.22273	+	1.04713i	−0.343544	+	0.111624i
$89$	4.39198	−	13.5171i	0.465549	−	1.43281i	−0.392741	−	0.919649i	$-0.628473\pi$
$89$	4.39198	−	13.5171i	0.465549	−	1.43281i	0.858290	−	0.513164i	$-0.171527\pi$
$90$	−4.41327	−	3.05844i	−0.465199	−	0.322388i
$91$	1.64230	+	5.05447i	0.172159	+	0.529852i
$92$	−0.154080	−	0.212073i	−0.0160639	−	0.0221101i
$93$			3.58422i			0.371666i
$94$	3.79030	−	2.75381i	0.390940	−	0.284034i
$95$	0.332343	+	14.9013i	0.0340977	+	1.52884i
$96$	0.625988	+	0.454807i	0.0638896	+	0.0464185i
$97$	11.3670	−	15.6454i	1.15415	−	1.58855i	0.423324	−	0.905978i	$-0.360863\pi$
$97$	11.3670	−	15.6454i	1.15415	−	1.58855i	0.730822	−	0.682568i	$-0.239137\pi$
$98$	−0.951057	−	0.309017i	−0.0960712	−	0.0312154i
$99$	−8.13696			−0.817795
$100$	1.33154	−	4.81944i	0.133154	−	0.481944i
$101$	−9.99672			−0.994711			−0.497355	−	0.867547i	$-0.665695\pi$
$101$	−9.99672			−0.994711			−0.497355	+	0.867547i	$0.665695\pi$
$102$	−3.04989	−	0.990968i	−0.301984	−	0.0981205i
$103$	4.16284	−	5.72966i	0.410177	−	0.564560i	−0.553085	−	0.833125i	$-0.686549\pi$
$103$	4.16284	−	5.72966i	0.410177	−	0.564560i	0.963262	+	0.268565i	$0.0865494\pi$
$104$	4.29959	+	3.12383i	0.421609	+	0.306317i
$105$	−1.63318	+	0.571215i	−0.159382	+	0.0557449i
$106$	0.859953	−	0.624792i	0.0835260	−	0.0606852i
$107$			3.41714i			0.330347i	0.986265	+	0.165174i	$0.0528184\pi$
$107$			3.41714i			0.330347i	−0.986265	+	0.165174i	$0.947182\pi$
$108$	2.45654	+	3.38114i	0.236381	+	0.325350i
$109$	−6.36105	−	19.5773i	−0.609278	−	1.87517i	−0.464161	−	0.885751i	$-0.653644\pi$
$109$	−6.36105	−	19.5773i	−0.609278	−	1.87517i	−0.145118	−	0.989414i	$-0.546356\pi$
$110$	−2.50155	−	7.15224i	−0.238513	−	0.681939i
$111$	−0.0855433	+	0.263275i	−0.00811941	+	0.0249890i
$112$	−0.951057	+	0.309017i	−0.0898664	+	0.0291994i
$113$	16.0558	−	5.21685i	1.51040	−	0.490760i	0.567372	−	0.823462i	$-0.307960\pi$
$113$	16.0558	−	5.21685i	1.51040	−	0.490760i	0.943032	+	0.332701i	$0.107960\pi$
$114$	1.59381	−	4.90524i	0.149274	−	0.459418i
$115$	0.466409	−	0.355021i	0.0434929	−	0.0331059i
$116$	−3.03479	−	9.34014i	−0.281774	−	0.867210i
$117$	7.50123	+	10.3246i	0.693489	+	0.954505i
$118$		−	1.58292i		−	0.145719i
$119$	3.35295	−	2.43606i	0.307364	−	0.223313i
$120$	−0.985515	+	1.42208i	−0.0899648	+	0.129817i
$121$	−0.390309	−	0.283576i	−0.0354826	−	0.0257796i
$122$	0.880308	−	1.21164i	0.0796993	−	0.109697i
$123$	0.605770	+	0.196827i	0.0546205	+	0.0177473i
$124$	−4.63219			−0.415983
$125$	10.8403	+	2.73638i	0.969586	+	0.244749i
$126$	−2.40129			−0.213924
$127$	14.1713	+	4.60452i	1.25750	+	0.408585i	0.860602	−	0.509279i	$-0.170088\pi$
$127$	14.1713	+	4.60452i	1.25750	+	0.408585i	0.396895	+	0.917864i	$0.370088\pi$
$128$	−0.587785	+	0.809017i	−0.0519534	+	0.0715077i
$129$	1.45694	+	1.05853i	0.128277	+	0.0931985i
$130$	−6.76899	+	9.76753i	−0.593680	+	0.856669i
$131$	−14.2324	+	10.3404i	−1.24349	+	0.903448i	−0.997826	−	0.0659069i	$-0.979006\pi$
$131$	−14.2324	+	10.3404i	−1.24349	+	0.903448i	−0.245664	+	0.969355i	$0.579006\pi$
$132$			2.62196i			0.228212i
$133$	3.91800	+	5.39266i	0.339734	+	0.467603i
$134$	2.46434	+	7.58445i	0.212886	+	0.655196i
$135$	−7.43610	+	5.66021i	−0.639998	+	0.487153i
$136$	1.28071	−	3.94163i	0.109820	−	0.337992i
$137$	6.46570	−	2.10083i	0.552402	−	0.179486i	−0.0194978	−	0.999810i	$-0.506207\pi$
$137$	6.46570	−	2.10083i	0.552402	−	0.179486i	0.571899	+	0.820324i	$0.306207\pi$
$138$	−0.192904	+	0.0626784i	−0.0164211	+	0.00533554i
$139$	−4.72732	+	14.5492i	−0.400966	+	1.23405i	0.523251	+	0.852179i	$0.324719\pi$
$139$	−4.72732	+	14.5492i	−0.400966	+	1.23405i	−0.924217	+	0.381868i	$0.875281\pi$
$140$	−0.738230	−	2.11069i	−0.0623918	−	0.178386i
$141$	−1.12023	−	3.44771i	−0.0943402	−	0.290349i
$142$	4.95806	+	6.82418i	0.416071	+	0.572673i
$143$			18.0089i			1.50598i
$144$	−1.94268	+	1.41144i	−0.161890	+	0.117620i
$145$	20.7287	−	7.25001i	1.72142	−	0.602080i
$146$	−1.17374	−	0.852774i	−0.0971397	−	0.0705761i
$147$	−0.454807	+	0.625988i	−0.0375118	+	0.0516306i
$148$	−0.340253	−	0.110555i	−0.0279686	−	0.00908755i
$149$	−12.2852			−1.00644			−0.503221	−	0.864158i	$-0.667852\pi$
$149$	−12.2852			−1.00644			−0.503221	+	0.864158i	$0.667852\pi$
$150$	−3.22821	−	2.13223i	−0.263582	−	0.174096i
$151$	−11.8568			−0.964896			−0.482448	−	0.875925i	$-0.660252\pi$
$151$	−11.8568			−0.964896			−0.482448	+	0.875925i	$0.660252\pi$
$152$	6.33946	+	2.05981i	0.514198	+	0.167073i
$153$	5.84969	−	8.05140i	0.472919	−	0.650917i
$154$	−2.74142	−	1.99176i	−0.220910	−	0.160500i
$155$	−0.230955	−	10.3553i	−0.0185507	−	0.831758i
$156$	3.32686	−	2.41711i	0.266362	−	0.193523i
$157$			18.4980i			1.47630i	0.674636	+	0.738150i	$0.264300\pi$
$157$			18.4980i			1.47630i	−0.674636	+	0.738150i	$0.735700\pi$
$158$	−3.75342	−	5.16613i	−0.298606	−	0.410996i
$159$	−0.254160	−	0.782224i	−0.0201562	−	0.0620344i
$160$	−1.83787	−	1.27366i	−0.145297	−	0.100692i
$161$	0.0810046	−	0.249307i	0.00638406	−	0.0196481i
$162$	−3.77576	+	1.22682i	−0.296652	+	0.0963880i
$163$	−14.2234	+	4.62146i	−1.11406	+	0.361981i	−0.807499	−	0.589869i	$-0.799179\pi$
$163$	−14.2234	+	4.62146i	−1.11406	+	0.361981i	−0.306564	+	0.951850i	$0.599179\pi$
$164$	−0.254376	+	0.782888i	−0.0198634	+	0.0611333i
$165$	−5.86141	+	0.130727i	−0.456310	+	0.0101771i
$166$	−1.71732	−	5.28537i	−0.133290	−	0.410224i
$167$	−7.68012	−	10.5708i	−0.594305	−	0.817991i	0.400867	−	0.916136i	$-0.368709\pi$
$167$	−7.68012	−	10.5708i	−0.594305	−	0.817991i	−0.995172	+	0.0981454i	$0.968709\pi$
$168$			0.773763i			0.0596971i
$169$	12.3333	−	8.96065i	0.948713	−	0.689281i
$170$	8.87541	+	2.66652i	0.680713	+	0.204513i
$171$	12.9494	+	9.40826i	0.990262	+	0.719467i
$172$	−1.36803	+	1.88293i	−0.104311	+	0.143572i
$173$	−11.6076	−	3.77155i	−0.882512	−	0.286746i	−0.167512	−	0.985870i	$-0.553573\pi$
$173$	−11.6076	−	3.77155i	−0.882512	−	0.286746i	−0.715000	+	0.699124i	$0.753573\pi$
$174$	−7.59897			−0.576077
$175$	4.68167	−	1.75556i	0.353901	−	0.132708i
$176$	−3.38858			−0.255424
$177$	−1.16486	−	0.378485i	−0.0875560	−	0.0284487i
$178$	8.35405	−	11.4984i	0.626162	−	0.861839i
$179$	17.6411	+	12.8170i	1.31856	+	0.957991i	0.999949	+	0.0101054i	$0.00321670\pi$
$179$	17.6411	+	12.8170i	1.31856	+	0.957991i	0.318612	+	0.947885i	$0.396783\pi$
$180$	−3.25216	−	4.27252i	−0.242402	−	0.318455i
$181$	−10.0424	+	7.29621i	−0.746443	+	0.542323i	−0.894722	−	0.446623i	$-0.852627\pi$
$181$	−10.0424	+	7.29621i	−0.746443	+	0.542323i	0.148279	+	0.988946i	$0.452627\pi$
$182$			5.31458i			0.393943i
$183$	−0.681150	−	0.937523i	−0.0503521	−	0.0693037i
$184$	−0.0810046	−	0.249307i	−0.00597174	−	0.0183791i
$185$	0.230182	−	0.766151i	0.0169233	−	0.0563286i
$186$	−1.10758	+	3.40879i	−0.0812120	+	0.249945i
$187$	13.3565	−	4.33979i	0.976724	−	0.317357i
$188$	4.45577	−	1.44777i	0.324970	−	0.105589i
$189$	−1.29148	+	3.97477i	−0.0939414	+	0.289122i
$190$	−4.28866	+	14.2746i	−0.311132	+	1.03559i
$191$	6.51528	+	20.0520i	0.471429	+	1.45091i	0.850714	+	0.525629i	$0.176170\pi$
$191$	6.51528	+	20.0520i	0.471429	+	1.45091i	−0.379285	+	0.925280i	$0.623830\pi$
$192$	0.454807	+	0.625988i	0.0328228	+	0.0451768i
$193$			17.5299i			1.26183i	0.775851	+	0.630916i	$0.217321\pi$
$193$			17.5299i			1.26183i	−0.775851	+	0.630916i	$0.782679\pi$
$194$	15.6454	−	11.3670i	1.12327	−	0.816105i
$195$	5.56934	+	7.31672i	0.398829	+	0.523962i
$196$	−0.809017	−	0.587785i	−0.0577869	−	0.0419847i
$197$	−10.7449	+	14.7891i	−0.765544	+	1.05368i	0.231188	+	0.972909i	$0.425739\pi$
$197$	−10.7449	+	14.7891i	−0.765544	+	1.05368i	−0.996733	+	0.0807725i	$0.974261\pi$
$198$	−7.73870	−	2.51446i	−0.549966	−	0.178695i
$199$	−23.5300			−1.66800			−0.833999	−	0.551766i	$-0.813954\pi$
$199$	−23.5300			−1.66800			−0.833999	+	0.551766i	$0.813954\pi$
$200$	2.75566	−	4.17209i	0.194854	−	0.295011i
$201$	6.17057			0.435239
$202$	−9.50745	−	3.08916i	−0.668942	−	0.217352i
$203$	5.77252	−	7.94519i	0.405152	−	0.557643i
$204$	−2.59439	−	1.88493i	−0.181644	−	0.131972i
$205$	−1.76284	−	0.529626i	−0.123122	−	0.0369907i
$206$	5.72966	−	4.16284i	0.399204	−	0.290039i
$207$		−	0.629466i		−	0.0437509i
$208$	3.12383	+	4.29959i	0.216599	+	0.298123i
$209$	6.97984	+	21.4817i	0.482806	+	1.48592i
$210$	−1.72976	+	0.0385788i	−0.119365	+	0.00266219i
$211$	3.93725	−	12.1176i	0.271052	−	0.834211i	−0.719186	−	0.694818i	$-0.755485\pi$
$211$	3.93725	−	12.1176i	0.271052	−	0.834211i	0.990237	−	0.139393i	$-0.0445151\pi$
$212$	1.01094	−	0.328473i	0.0694313	−	0.0225596i
$213$	6.20737	−	2.01690i	0.425322	−	0.138195i
$214$	−1.05595	+	3.24989i	−0.0721835	+	0.222158i
$215$	−4.27753	−	2.96437i	−0.291725	−	0.202168i
$216$	1.29148	+	3.97477i	0.0878741	+	0.270449i
$217$	−2.72273	−	3.74752i	−0.184831	−	0.254398i
$218$		−	20.5848i		−	1.39418i
$219$	−0.908199	+	0.659845i	−0.0613704	+	0.0445882i
$220$	−0.168950	−	7.57520i	−0.0113906	−	0.510720i
$221$	−17.8195	−	12.9466i	−1.19867	−	0.870885i
$222$	−0.162713	+	0.223955i	−0.0109206	+	0.0150309i
$223$	12.1579	+	3.95033i	0.814151	+	0.264534i	0.686355	−	0.727267i	$-0.259210\pi$
$223$	12.1579	+	3.95033i	0.814151	+	0.264534i	0.127796	+	0.991800i	$0.459210\pi$
$224$	−1.00000			−0.0668153
$225$	9.38913	−	7.48326i	0.625942	−	0.498884i
$226$	16.8821			1.12298
$227$	1.11666	+	0.362824i	0.0741151	+	0.0240815i	0.345840	−	0.938294i	$-0.387594\pi$
$227$	1.11666	+	0.362824i	0.0741151	+	0.0240815i	−0.271725	+	0.962375i	$0.587594\pi$
$228$	3.03160	−	4.17265i	0.200773	−	0.276340i
$229$	5.01980	+	3.64710i	0.331718	+	0.241007i	0.741159	−	0.671329i	$-0.234276\pi$
$229$	5.01980	+	3.64710i	0.331718	+	0.241007i	−0.409441	+	0.912336i	$0.634276\pi$
$230$	0.553289	−	0.193517i	0.0364828	−	0.0127601i
$231$	−2.12121	+	1.54115i	−0.139565	+	0.101400i
$232$		−	9.82080i		−	0.644767i
$233$	−6.44561	−	8.87162i	−0.422266	−	0.581199i	0.543891	−	0.839156i	$-0.316951\pi$
$233$	−6.44561	−	8.87162i	−0.422266	−	0.581199i	−0.966156	+	0.257957i	$0.916951\pi$
$234$	3.94363	+	12.1372i	0.257803	+	0.793436i
$235$	3.45866	+	9.88873i	0.225618	+	0.645070i
$236$	0.489148	−	1.50544i	0.0318408	−	0.0979961i
$237$	−4.69918	+	1.52686i	−0.305245	+	0.0991800i
$238$	3.94163	−	1.28071i	0.255498	−	0.0830163i
$239$	−6.03835	+	18.5841i	−0.390588	+	1.20211i	0.541756	+	0.840536i	$0.317760\pi$
$239$	−6.03835	+	18.5841i	−0.390588	+	1.20211i	−0.932344	+	0.361572i	$0.882240\pi$
$240$	−1.37673	+	1.04794i	−0.0888673	+	0.0676440i
$241$	−3.51895	−	10.8302i	−0.226676	−	0.697635i	−0.998117	−	0.0613355i	$-0.980464\pi$
$241$	−3.51895	−	10.8302i	−0.226676	−	0.697635i	0.771442	−	0.636300i	$-0.219536\pi$
$242$	−0.283576	−	0.390309i	−0.0182289	−	0.0250900i
$243$			15.6099i			1.00137i
$244$	1.21164	−	0.880308i	0.0775673	−	0.0563560i
$245$	1.27366	−	1.83787i	0.0813714	−	0.117417i
$246$	0.515299	+	0.374387i	0.0328543	+	0.0238700i
$247$	20.8225	−	28.6597i	1.32491	−	1.82358i
$248$	−4.40547	−	1.43142i	−0.279748	−	0.0908955i
$249$	−4.30008			−0.272507
$250$	9.46415	+	5.95229i	0.598566	+	0.376456i
$251$	16.2938			1.02846			0.514229	−	0.857653i	$-0.328078\pi$
$251$	16.2938			1.02846			0.514229	+	0.857653i	$0.328078\pi$
$252$	−2.28376	−	0.742040i	−0.143864	−	0.0467441i
$253$	0.522112	−	0.718625i	0.0328249	−	0.0451796i
$254$	12.0548	+	8.75832i	0.756385	+	0.549546i
$255$	4.08444	−	5.89377i	0.255777	−	0.369082i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$			3.82946i			0.238875i	0.992842	+	0.119438i	$0.0381091\pi$
$257$			3.82946i			0.238875i	−0.992842	+	0.119438i	$0.961891\pi$
$258$	1.05853	+	1.45694i	0.0659013	+	0.0907053i
$259$	−0.110555	−	0.340253i	−0.00686954	−	0.0211423i
$260$	−9.45603	+	7.19774i	−0.586438	+	0.446385i
$261$	7.28742	−	22.4284i	0.451080	−	1.38828i
$262$	−16.7312	+	5.43629i	−1.03366	+	0.335855i
$263$	−15.8282	+	5.14289i	−0.976008	+	0.317124i	−0.753239	−	0.657747i	$-0.771510\pi$
$263$	−15.8282	+	5.14289i	−0.976008	+	0.317124i	−0.222769	+	0.974871i	$0.571510\pi$
$264$	−0.810229	+	2.49363i	−0.0498661	+	0.153472i
$265$	0.784709	+	2.24358i	0.0482043	+	0.137822i
$266$	2.05981	+	6.33946i	0.126295	+	0.388697i
$267$	−6.46406	−	8.89701i	−0.395594	−	0.544488i
$268$			7.97476i			0.487136i
$269$	−11.0513	+	8.02920i	−0.673807	+	0.489549i	−0.871297	−	0.490756i	$-0.836721\pi$
$269$	−11.0513	+	8.02920i	−0.673807	+	0.489549i	0.197491	+	0.980305i	$0.436721\pi$
$270$	−8.82125	+	3.08530i	−0.536844	+	0.187765i
$271$	−21.4041	−	15.5510i	−1.30021	−	0.944656i	−0.300250	−	0.953860i	$-0.597070\pi$
$271$	−21.4041	−	15.5510i	−1.30021	−	0.944656i	−0.999958	+	0.00920417i	$0.997070\pi$
$272$	2.43606	−	3.35295i	0.147708	−	0.203302i
$273$	3.91096	+	1.27075i	0.236702	+	0.0769092i
$274$	6.79843			0.410708
$275$	16.9260	−	0.755380i	1.02068	−	0.0455511i
$276$	−0.202832			−0.0122090
$277$	21.5964	+	7.01710i	1.29760	+	0.421616i	0.874746	−	0.484581i	$-0.161028\pi$
$277$	21.5964	+	7.01710i	1.29760	+	0.421616i	0.422855	+	0.906197i	$0.361028\pi$
$278$	−8.99190	+	12.3763i	−0.539298	+	0.742280i
$279$	−8.99888	−	6.53807i	−0.538749	−	0.391424i
$280$	−0.0498587	−	2.23551i	−0.00297963	−	0.133597i
$281$	2.12022	−	1.54043i	0.126482	−	0.0918943i	−0.522746	−	0.852489i	$-0.675092\pi$
$281$	2.12022	−	1.54043i	0.126482	−	0.0918943i	0.649228	+	0.760594i	$0.275092\pi$
$282$		−	3.62513i		−	0.215874i
$283$	−6.25053	−	8.60312i	−0.371556	−	0.511403i	0.581767	−	0.813355i	$-0.302361\pi$
$283$	−6.25053	−	8.60312i	−0.371556	−	0.511403i	−0.953323	+	0.301953i	$0.902361\pi$
$284$	2.60661	+	8.02231i	0.154674	+	0.476036i
$285$	9.47915	+	6.56915i	0.561496	+	0.389123i
$286$	−5.56504	+	17.1274i	−0.329068	+	1.01277i
$287$	−0.782888	+	0.254376i	−0.0462124	+	0.0150153i
$288$	−2.28376	+	0.742040i	−0.134572	+	0.0437251i
$289$	−0.0545892	+	0.168008i	−0.00321113	+	0.00988283i
$290$	21.9545	−	0.489652i	1.28921	−	0.0287534i
$291$	−4.62401	−	14.2312i	−0.271064	−	0.834250i
$292$	−0.852774	−	1.17374i	−0.0499048	−	0.0686881i
$293$			14.3113i			0.836077i	0.908429	+	0.418038i	$0.137282\pi$
$293$			14.3113i			0.836077i	−0.908429	+	0.418038i	$0.862718\pi$
$294$	−0.625988	+	0.454807i	−0.0365083	+	0.0265249i
$295$	3.38983	+	1.01844i	0.197363	+	0.0592957i
$296$	−0.289436	−	0.210288i	−0.0168231	−	0.0122227i
$297$	−8.32418	+	11.4573i	−0.483018	+	0.664817i
$298$	−11.6839	−	3.79633i	−0.676831	−	0.219916i
$299$	−1.39315			−0.0805677
$300$	−2.41132	−	3.02544i	−0.139217	−	0.174674i
$301$	−2.32743			−0.134151
$302$	−11.2765	−	3.66396i	−0.648891	−	0.210837i
$303$	−4.54657	+	6.25782i	−0.261194	+	0.359502i
$304$	5.39266	+	3.91800i	0.309291	+	0.224713i
$305$	2.02835	+	2.66475i	0.116143	+	0.152583i
$306$	8.05140	−	5.84969i	0.460268	−	0.334404i
$307$		−	12.1292i		−	0.692250i	−0.938188	−	0.346125i	$-0.887497\pi$
$307$		−	12.1292i		−	0.692250i	0.938188	−	0.346125i	$-0.112503\pi$
$308$	−1.99176	−	2.74142i	−0.113491	−	0.156207i
$309$	−1.69341	−	5.21177i	−0.0963346	−	0.296487i
$310$	2.98032	−	9.91985i	0.169271	−	0.563410i
$311$	−6.76704	+	20.8268i	−0.383724	+	1.18098i	0.553678	+	0.832731i	$0.313224\pi$
$311$	−6.76704	+	20.8268i	−0.383724	+	1.18098i	−0.937402	+	0.348249i	$0.886776\pi$
$312$	3.91096	−	1.27075i	0.221415	−	0.0719419i
$313$	14.9522	−	4.85825i	0.845146	−	0.274605i	0.145735	−	0.989324i	$-0.453445\pi$
$313$	14.9522	−	4.85825i	0.845146	−	0.274605i	0.699412	+	0.714719i	$0.253445\pi$
$314$	−5.71619	+	17.5926i	−0.322583	+	0.992810i
$315$	1.54497	−	5.14238i	0.0870494	−	0.289740i
$316$	−1.97329	−	6.07315i	−0.111006	−	0.341642i
$317$	−11.7506	−	16.1733i	−0.659977	−	0.908381i	0.339503	−	0.940605i	$-0.389741\pi$
$317$	−11.7506	−	16.1733i	−0.659977	−	0.908381i	−0.999481	+	0.0322238i	$0.989741\pi$
$318$		−	0.822479i		−	0.0461223i
$319$	26.9229	−	19.5606i	1.50739	−	1.09518i
$320$	−1.35434	−	1.77926i	−0.0757098	−	0.0994637i
$321$	2.13908	+	1.55414i	0.119392	+	0.0867434i
$322$	0.154080	−	0.212073i	0.00858654	−	0.0118184i
$323$	−26.2737	−	8.53685i	−1.46191	−	0.475003i
$324$	−3.97007			−0.220559
$325$	−16.5621	−	20.7802i	−0.918699	−	1.15268i
$326$	−14.9554			−0.828301
$327$	−15.1482	−	4.92195i	−0.837697	−	0.272184i
$328$	−0.483852	+	0.665965i	−0.0267162	+	0.0367717i
$329$	3.79030	+	2.75381i	0.208966	+	0.151823i
$330$	−5.61493	−	1.68695i	−0.309092	−	0.0928634i
$331$	1.81842	−	1.32116i	0.0999491	−	0.0726173i	−0.536688	−	0.843781i	$-0.680325\pi$
$331$	1.81842	−	1.32116i	0.0999491	−	0.0726173i	0.636637	+	0.771163i	$0.280325\pi$
$332$		−	5.55736i		−	0.305000i
$333$	−0.504962	−	0.695021i	−0.0276718	−	0.0380869i
$334$	−4.03768	−	12.4267i	−0.220932	−	0.679958i
$335$	−17.8277	+	0.397611i	−0.974030	+	0.0217238i
$336$	−0.239106	+	0.735893i	−0.0130443	+	0.0401462i
$337$	−7.93218	+	2.57732i	−0.432093	+	0.140396i	−0.516985	−	0.855995i	$-0.672946\pi$
$337$	−7.93218	+	2.57732i	−0.432093	+	0.140396i	0.0848915	+	0.996390i	$0.472946\pi$
$338$	14.4986	−	4.71089i	0.788622	−	0.256239i
$339$	4.03661	−	12.4234i	0.219238	−	0.674747i
$340$	7.61702	+	5.27867i	0.413091	+	0.286276i
$341$	−4.85049	−	14.9283i	−0.262669	−	0.808411i
$342$	9.40826	+	12.9494i	0.508740	+	0.700221i
$343$		−	1.00000i		−	0.0539949i
$344$	−1.88293	+	1.36803i	−0.101521	+	0.0737592i
$345$	−0.0101129	−	0.453432i	−0.000544461	−	0.0244120i
$346$	−9.87404	−	7.17391i	−0.530832	−	0.385672i
$347$	−3.84294	+	5.28936i	−0.206300	+	0.283948i	−0.899612	−	0.436690i	$-0.856151\pi$
$347$	−3.84294	+	5.28936i	−0.206300	+	0.283948i	0.693312	+	0.720637i	$0.256151\pi$
$348$	−7.22705	−	2.34821i	−0.387411	−	0.125877i
$349$	−7.39272			−0.395723			−0.197862	−	0.980230i	$-0.563400\pi$
$349$	−7.39272			−0.395723			−0.197862	+	0.980230i	$0.563400\pi$
$350$	4.99503	−	0.222920i	0.266995	−	0.0119156i
$351$	22.2113			1.18555
$352$	−3.22273	−	1.04713i	−0.171772	−	0.0558121i
$353$	9.57677	−	13.1813i	0.509720	−	0.701569i	−0.474152	−	0.880443i	$-0.657245\pi$
$353$	9.57677	−	13.1813i	0.509720	−	0.701569i	0.983872	+	0.178874i	$0.0572453\pi$
$354$	−0.990887	−	0.719921i	−0.0526650	−	0.0382634i
$355$	−17.8040	+	6.22708i	−0.944939	+	0.330499i
$356$	11.4984	−	8.35405i	0.609412	−	0.442764i
$357$		−	3.20684i		−	0.169724i
$358$	12.8170	+	17.6411i	0.677402	+	0.932363i
$359$	−1.19944	−	3.69149i	−0.0633040	−	0.194830i	0.914402	−	0.404807i	$-0.132661\pi$
$359$	−1.19944	−	3.69149i	−0.0633040	−	0.194830i	−0.977706	+	0.209977i	$0.932661\pi$
$360$	−1.77270	−	5.06838i	−0.0934297	−	0.267127i
$361$	7.85878	−	24.1868i	0.413620	−	1.27299i
$362$	−11.8055	+	3.83584i	−0.620484	+	0.201607i
$363$	−0.355030	+	0.115356i	−0.0186342	+	0.00605463i
$364$	−1.64230	+	5.05447i	−0.0860797	+	0.264926i
$365$	2.58140	−	1.96491i	0.135117	−	0.102848i
$366$	−0.358102	−	1.10212i	−0.0187183	−	0.0576089i
$367$	−17.6232	−	24.2563i	−0.919924	−	1.26617i	−0.963662	−	0.267124i	$-0.913927\pi$
$367$	−17.6232	−	24.2563i	−0.919924	−	1.26617i	0.0437377	−	0.999043i	$-0.486073\pi$
$368$		−	0.262136i		−	0.0136648i
$369$	−1.59917	+	1.16187i	−0.0832497	+	0.0604844i
$370$	0.455670	−	0.657523i	0.0236892	−	0.0341830i
$371$	0.859953	+	0.624792i	0.0446465	+	0.0324376i
$372$	−2.10675	+	2.89969i	−0.109230	+	0.150342i
$373$	−34.8391	−	11.3199i	−1.80390	−	0.586123i	−0.803938	−	0.594713i	$-0.797266\pi$
$373$	−34.8391	−	11.3199i	−1.80390	−	0.586123i	−0.999963	+	0.00858938i	$0.997266\pi$
$374$	14.0439			0.726191
$375$	6.64318	−	5.54137i	0.343053	−	0.286155i
$376$	4.68507			0.241614
$377$	−49.6389	−	16.1287i	−2.55653	−	0.830668i
$378$	−2.45654	+	3.38114i	−0.126351	+	0.173907i
$379$	11.6247	+	8.44587i	0.597123	+	0.433835i	0.844857	−	0.534993i	$-0.179686\pi$
$379$	11.6247	+	8.44587i	0.597123	+	0.433835i	−0.247733	+	0.968828i	$0.579686\pi$
$380$	−8.48986	+	12.2507i	−0.435521	+	0.628448i
$381$	9.32756	−	6.77687i	0.477865	−	0.347189i
$382$			21.0839i			1.07875i
$383$	1.69154	+	2.32821i	0.0864338	+	0.118966i	0.850044	−	0.526711i	$-0.176575\pi$
$383$	1.69154	+	2.32821i	0.0864338	+	0.118966i	−0.763610	+	0.645677i	$0.776575\pi$
$384$	0.239106	+	0.735893i	0.0122018	+	0.0375534i
$385$	6.02916	−	4.58928i	0.307275	−	0.233891i
$386$	−5.41705	+	16.6720i	−0.275720	+	0.848580i
$387$	−5.31530	+	1.72705i	−0.270192	+	0.0877907i
$388$	18.3922	−	5.97600i	0.933724	−	0.303385i
$389$	3.42674	−	10.5464i	0.173743	−	0.534725i	−0.825831	−	0.563917i	$-0.809294\pi$
$389$	3.42674	−	10.5464i	0.173743	−	0.534725i	0.999574	+	0.0291927i	$0.00929365\pi$
$390$	3.03577	+	8.67964i	0.153722	+	0.439511i
$391$	0.335721	+	1.03324i	0.0169782	+	0.0522534i
$392$	−0.587785	−	0.809017i	−0.0296876	−	0.0408615i
$393$			13.6122i			0.686645i
$394$	−14.7891	+	10.7449i	−0.745065	+	0.541322i
$395$	13.4782	−	4.71411i	0.678163	−	0.237192i
$396$	−6.58294	−	4.78278i	−0.330805	−	0.240344i
$397$	−10.3580	+	14.2565i	−0.519852	+	0.715515i	−0.985542	−	0.169433i	$-0.945806\pi$
$397$	−10.3580	+	14.2565i	−0.519852	+	0.715515i	0.465690	+	0.884948i	$0.345806\pi$
$398$	−22.3784	−	7.27117i	−1.12173	−	0.364471i
$399$	5.15767			0.258207
$400$	3.91003	−	3.11635i	0.195502	−	0.155817i
$401$	−10.4960			−0.524145			−0.262073	−	0.965048i	$-0.584406\pi$
$401$	−10.4960			−0.524145			−0.262073	+	0.965048i	$0.584406\pi$
$402$	5.86857	+	1.90681i	0.292697	+	0.0951032i
$403$	−14.4702	+	19.9165i	−0.720811	+	0.992111i
$404$	−8.08752	−	5.87592i	−0.402369	−	0.292338i
$405$	−0.197942	−	8.87513i	−0.00983584	−	0.441009i
$406$	7.94519	−	5.77252i	0.394313	−	0.286485i
$407$		−	1.21231i		−	0.0600918i
$408$	−1.88493	−	2.59439i	−0.0933181	−	0.128441i
$409$	1.07117	+	3.29673i	0.0529661	+	0.163013i	0.974041	−	0.226374i	$-0.0726870\pi$
$409$	1.07117	+	3.29673i	0.0529661	+	0.163013i	−0.921074	+	0.389387i	$0.872687\pi$
$410$	−1.51290	−	1.04845i	−0.0747166	−	0.0517793i
$411$	1.62555	−	5.00292i	0.0801823	−	0.246776i
$412$	6.73562	−	2.18854i	0.331840	−	0.107821i
$413$	1.50544	−	0.489148i	0.0740781	−	0.0240694i
$414$	0.194516	−	0.598658i	0.00955992	−	0.0294224i
$415$	12.4236	−	0.277083i	0.609848	−	0.0136015i
$416$	1.64230	+	5.05447i	0.0805202	+	0.247816i
$417$	6.95760	+	9.57632i	0.340715	+	0.468954i
$418$			22.5872i			1.10478i
$419$	11.0126	−	8.00113i	0.538001	−	0.390881i	−0.285341	−	0.958426i	$-0.592107\pi$
$419$	11.0126	−	8.00113i	0.538001	−	0.390881i	0.823342	+	0.567545i	$0.192107\pi$
$420$	−1.65702	−	0.497834i	−0.0808542	−	0.0242918i
$421$	29.3151	+	21.2987i	1.42873	+	1.03803i	0.990251	+	0.139294i	$0.0444832\pi$
$421$	29.3151	+	21.2987i	1.42873	+	1.03803i	0.438481	+	0.898741i	$0.355517\pi$
$422$	7.48910	−	10.3079i	0.364564	−	0.501779i
$423$	10.6996	+	3.47651i	0.520232	+	0.169034i
$424$	1.06296			0.0516219
$425$	−11.4208	+	17.2911i	−0.553988	+	0.838743i
$426$	6.52681			0.316225
$427$	1.42437	+	0.462805i	0.0689300	+	0.0223967i
$428$	−2.00854	+	2.76452i	−0.0970866	+	0.133628i
$429$	11.2733	+	8.19055i	0.544281	+	0.395443i
$430$	−3.15213	−	4.14111i	−0.152009	−	0.199702i
$431$	29.7440	−	21.6103i	1.43272	−	1.04093i	0.443218	−	0.896414i	$-0.353837\pi$
$431$	29.7440	−	21.6103i	1.43272	−	1.04093i	0.989502	−	0.144518i	$-0.0461631\pi$
$432$			4.17932i			0.201078i
$433$	−1.98130	−	2.72702i	−0.0952151	−	0.131052i	0.758751	−	0.651380i	$-0.225810\pi$
$433$	−1.98130	−	2.72702i	−0.0952151	−	0.131052i	−0.853967	+	0.520328i	$0.825810\pi$
$434$	−1.43142	−	4.40547i	−0.0687106	−	0.211469i
$435$	4.88912	−	16.2732i	0.234416	−	0.780242i
$436$	6.36105	−	19.5773i	0.304639	−	0.937583i
$437$	−1.66180	+	0.539952i	−0.0794948	+	0.0258294i
$438$	−1.06765	+	0.346901i	−0.0510144	+	0.0165756i
$439$	−4.00480	+	12.3255i	−0.191139	+	0.588264i	0.808861	+	0.587999i	$0.200084\pi$
$439$	−4.00480	+	12.3255i	−0.191139	+	0.588264i	−1.00000		0.000264761i	$0.999916\pi$
$440$	2.18019	−	7.25665i	0.103936	−	0.345947i
$441$	−0.742040	−	2.28376i	−0.0353352	−	0.108751i
$442$	−12.9466	−	17.8195i	−0.615809	−	0.847588i
$443$			12.9549i			0.615508i	0.951466	+	0.307754i	$0.0995774\pi$
$443$			12.9549i			0.615508i	−0.951466	+	0.307754i	$0.900423\pi$
$444$	−0.223955	+	0.162713i	−0.0106284	+	0.00772202i
$445$	19.2489	+	25.2882i	0.912484	+	1.19878i
$446$	10.3421	+	7.51398i	0.489713	+	0.355797i
$447$	−5.58739	+	7.69038i	−0.264274	+	0.363742i
$448$	−0.951057	−	0.309017i	−0.0449332	−	0.0145997i
$449$	−32.9951			−1.55714			−0.778568	−	0.627560i	$-0.784054\pi$
$449$	−32.9951			−1.55714			−0.778568	+	0.627560i	$0.784054\pi$
$450$	11.2420	−	4.21560i	0.529955	−	0.198725i
$451$	−2.78940			−0.131348
$452$	16.0558	+	5.21685i	0.755202	+	0.245380i
$453$	−5.39257	+	7.42223i	−0.253365	+	0.348727i
$454$	0.949885	+	0.690132i	0.0445803	+	0.0323895i
$455$	−11.3812	−	3.41936i	−0.533559	−	0.160302i
$456$	4.17265	−	3.03160i	0.195402	−	0.141968i
$457$		−	3.75483i		−	0.175643i	−0.996136	−	0.0878217i	$-0.972009\pi$
$457$		−	3.75483i		−	0.175643i	0.996136	−	0.0878217i	$-0.0279906\pi$
$458$	3.64710	+	5.01980i	0.170418	+	0.234560i
$459$	−5.35251	−	16.4733i	−0.249834	−	0.768909i
$460$	0.586009	−	0.0130698i	0.0273228	−	0.000609382i
$461$	−3.97110	+	12.2218i	−0.184952	+	0.569225i	−0.999948	−	0.0102428i	$-0.996740\pi$
$461$	−3.97110	+	12.2218i	−0.184952	+	0.569225i	0.814995	+	0.579468i	$0.196740\pi$
$462$	−2.49363	+	0.810229i	−0.116014	+	0.0376953i
$463$	−18.6803	+	6.06960i	−0.868147	+	0.282078i	−0.709027	−	0.705181i	$-0.750866\pi$
$463$	−18.6803	+	6.06960i	−0.868147	+	0.282078i	−0.159120	+	0.987259i	$0.550866\pi$
$464$	3.03479	−	9.34014i	0.140887	−	0.433605i
$465$	−6.58733	−	4.56509i	−0.305480	−	0.211701i
$466$	−3.38866	−	10.4292i	−0.156977	−	0.483124i
$467$	−6.98705	−	9.61685i	−0.323322	−	0.445015i	0.616156	−	0.787624i	$-0.288689\pi$
$467$	−6.98705	−	9.61685i	−0.323322	−	0.445015i	−0.939478	+	0.342610i	$0.888689\pi$
$468$			12.7619i			0.589917i
$469$	−6.45172	+	4.68745i	−0.297913	+	0.216446i
$470$	0.233592	+	10.4735i	0.0107748	+	0.483108i
$471$	11.5795	+	8.41301i	0.533556	+	0.387651i
$472$	0.930416	−	1.28061i	0.0428258	−	0.0589447i
$473$	−7.50068	−	2.43712i	−0.344882	−	0.112059i
$474$	−4.94101			−0.226948
$475$	−27.8099	−	18.3684i	−1.27601	−	0.842800i
$476$	4.14447			0.189962
$477$	2.42755	+	0.788758i	0.111150	+	0.0361148i
$478$	−11.4856	+	15.8086i	−0.525340	+	0.723069i
$479$	28.5035	+	20.7090i	1.30236	+	0.946218i	0.999976	−	0.00696886i	$-0.00221827\pi$
$479$	28.5035	+	20.7090i	1.30236	+	0.946218i	0.302382	+	0.953187i	$0.402218\pi$
$480$	−1.63318	+	0.571215i	−0.0745439	+	0.0260723i
$481$	−1.53823	+	1.11759i	−0.0701374	+	0.0509578i
$482$		−	11.3876i		−	0.518689i
$483$	−0.119221	−	0.164094i	−0.00542476	−	0.00746654i
$484$	−0.149085	−	0.458835i	−0.00677658	−	0.0208562i
$485$	14.2764	+	40.8181i	0.648259	+	1.85345i
$486$	−4.82371	+	14.8459i	−0.218808	+	0.673421i
$487$	28.5882	−	9.28886i	1.29545	−	0.420919i	0.421457	−	0.906849i	$-0.361519\pi$
$487$	28.5882	−	9.28886i	1.29545	−	0.420919i	0.873998	+	0.485930i	$0.161519\pi$
$488$	1.42437	−	0.462805i	0.0644781	−	0.0209502i
$489$	−3.57592	+	11.0055i	−0.161709	+	0.497688i
$490$	1.77926	−	1.35434i	0.0803788	−	0.0611827i
$491$	4.61997	+	14.2188i	0.208496	+	0.641686i	0.999552	+	0.0299410i	$0.00953194\pi$
$491$	4.61997	+	14.2188i	0.208496	+	0.641686i	−0.791055	+	0.611745i	$0.790468\pi$
$492$	0.374387	+	0.515299i	0.0168786	+	0.0232315i
$493$			40.7020i			1.83313i
$494$	28.6597	−	20.8225i	1.28946	−	0.936850i
$495$	10.3638	−	14.9547i	0.465816	−	0.672164i
$496$	−3.74752	−	2.72273i	−0.168269	−	0.122254i
$497$	−4.95806	+	6.82418i	−0.222399	+	0.306106i
$498$	−4.08962	−	1.32880i	−0.183260	−	0.0595449i
$499$	23.6177			1.05727			0.528636	−	0.848848i	$-0.322704\pi$
$499$	23.6177			1.05727			0.528636	+	0.848848i	$0.322704\pi$
$500$	7.16159	+	8.58555i	0.320276	+	0.383957i
$501$	−10.1101			−0.451688
$502$	15.4964	+	5.03507i	0.691636	+	0.224726i
$503$	23.0369	−	31.7075i	1.02716	−	1.41377i	0.120106	−	0.992761i	$-0.461676\pi$
$503$	23.0369	−	31.7075i	1.02716	−	1.41377i	0.907057	−	0.421008i	$-0.138324\pi$
$504$	−1.94268	−	1.41144i	−0.0865341	−	0.0628707i
$505$	12.7325	−	18.3727i	0.566587	−	0.817575i
$506$	0.718625	−	0.522112i	0.0319468	−	0.0232107i
$507$		−	11.7958i		−	0.523871i
$508$	8.75832	+	12.0548i	0.388588	+	0.534845i
$509$	5.53952	+	17.0489i	0.245535	+	0.755679i	0.995548	+	0.0942560i	$0.0300472\pi$
$509$	5.53952	+	17.0489i	0.245535	+	0.755679i	−0.750013	+	0.661423i	$0.769953\pi$
$510$	5.70581	−	4.34314i	0.252657	−	0.192318i
$511$	0.448330	−	1.37982i	0.0198330	−	0.0610396i
$512$	−0.951057	+	0.309017i	−0.0420312	+	0.0136568i
$513$	26.4946	−	8.60862i	1.16977	−	0.380080i
$514$	−1.18337	+	3.64203i	−0.0521961	+	0.160643i
$515$	5.22833	+	14.9484i	0.230388	+	0.658707i
$516$	0.556503	+	1.71274i	0.0244987	+	0.0753992i
$517$	9.33151	+	12.8437i	0.410399	+	0.564866i
$518$		−	0.357763i		−	0.0157192i
$519$	−7.64017	+	5.55091i	−0.335366	+	0.243658i
$520$	−11.2174	+	3.92338i	−0.491917	+	0.172052i
$521$	12.6738	+	9.20806i	0.555249	+	0.403412i	0.829717	−	0.558184i	$-0.188502\pi$
$521$	12.6738	+	9.20806i	0.555249	+	0.403412i	−0.274468	+	0.961596i	$0.588502\pi$
$522$	13.8615	−	19.0787i	0.606701	−	0.835053i
$523$	−33.1029	−	10.7558i	−1.44749	−	0.470318i	−0.523267	−	0.852169i	$-0.675287\pi$
$523$	−33.1029	−	10.7558i	−1.44749	−	0.470318i	−0.924224	+	0.381851i	$0.875287\pi$
$524$	−17.5922			−0.768519
$525$	1.03030	−	3.72911i	0.0449658	−	0.162752i
$526$	−16.6427			−0.725658
$527$	18.2584	+	5.93250i	0.795346	+	0.258424i
$528$	−1.54115	+	2.12121i	−0.0670698	+	0.0923137i
$529$	−18.5518	−	13.4787i	−0.806600	−	0.586029i
$530$	0.0529978	+	2.37626i	0.00230208	+	0.103218i
$531$	3.07511	−	2.23420i	0.133448	−	0.0969559i
$532$			6.66570i			0.288995i
$533$	2.57147	+	3.53932i	0.111383	+	0.153305i
$534$	−3.39836	−	10.4591i	−0.147061	−	0.452608i
$535$	−6.28026	−	4.35228i	−0.271519	−	0.188166i
$536$	−2.46434	+	7.58445i	−0.106443	+	0.327598i
$537$	16.0466	−	5.21386i	0.692463	−	0.224995i
$538$	−12.9915	+	4.22120i	−0.560104	+	0.181989i
$539$	1.04713	−	3.22273i	0.0451030	−	0.138813i
$540$	−9.34292	+	0.208376i	−0.402055	+	0.00896706i
$541$	−0.934700	−	2.87671i	−0.0401859	−	0.123680i	0.928951	−	0.370203i	$-0.120712\pi$
$541$	−0.934700	−	2.87671i	−0.0401859	−	0.123680i	−0.969137	+	0.246523i	$0.920712\pi$
$542$	−15.5510	−	21.4041i	−0.667973	−	0.919386i
$543$			9.60476i			0.412180i
$544$	3.35295	−	2.43606i	0.143756	−	0.104445i
$545$	44.0824	+	13.2441i	1.88828	+	0.567315i
$546$	3.32686	+	2.41711i	0.142377	+	0.103443i
$547$	2.49185	−	3.42974i	0.106544	−	0.146645i	−0.752415	−	0.658689i	$-0.771111\pi$
$547$	2.49185	−	3.42974i	0.106544	−	0.146645i	0.858959	+	0.512044i	$0.171111\pi$
$548$	6.46570	+	2.10083i	0.276201	+	0.0897431i
$549$	3.59634			0.153488
$550$	16.3310	+	4.51202i	0.696358	+	0.192393i
$551$	−65.4625			−2.78880
$552$	−0.192904	−	0.0626784i	−0.00821055	−	0.00266777i
$553$	3.75342	−	5.16613i	0.159611	−	0.219686i
$554$	18.3710	+	13.3473i	0.780509	+	0.567073i
$555$	−0.374913	−	0.492542i	−0.0159142	−	0.0209072i
$556$	−12.3763	+	8.99190i	−0.524871	+	0.381341i
$557$		−	17.7289i		−	0.751197i	−0.926783	−	0.375598i	$-0.877437\pi$
$557$		−	17.7289i		−	0.751197i	0.926783	−	0.375598i	$-0.122563\pi$
$558$	−6.53807	−	8.99888i	−0.276778	−	0.380953i
$559$	3.82233	+	11.7639i	0.161667	+	0.497561i
$560$	0.643393	−	2.14151i	0.0271883	−	0.0904951i
$561$	3.35797	−	10.3348i	0.141774	−	0.436334i
$562$	2.49247	−	0.809852i	0.105138	−	0.0341615i
$563$	35.4481	−	11.5178i	1.49396	−	0.485417i	0.555710	−	0.831376i	$-0.312447\pi$
$563$	35.4481	−	11.5178i	1.49396	−	0.485417i	0.938249	+	0.345959i	$0.112447\pi$
$564$	1.12023	−	3.44771i	0.0471701	−	0.145175i
$565$	−10.8618	+	36.1531i	−0.456960	+	1.52097i
$566$	−3.28610	−	10.1136i	−0.138125	−	0.425105i
$567$	−2.33355	−	3.21185i	−0.0979998	−	0.134885i
$568$			8.43515i			0.353931i
$569$	13.5659	−	9.85624i	0.568714	−	0.413195i	−0.265924	−	0.963994i	$-0.585677\pi$
$569$	13.5659	−	9.85624i	0.568714	−	0.413195i	0.834638	+	0.550799i	$0.185677\pi$
$570$	6.98523	+	9.17685i	0.292579	+	0.384376i
$571$	12.5229	+	9.09841i	0.524067	+	0.380757i	0.818134	−	0.575028i	$-0.195009\pi$
$571$	12.5229	+	9.09841i	0.524067	+	0.380757i	−0.294067	+	0.955785i	$0.595009\pi$
$572$	−10.5853	+	14.5695i	−0.442595	+	0.609180i
$573$	15.5155	+	5.04128i	0.648168	+	0.210603i
$574$	−0.823177			−0.0343588
$575$	0.0584353	+	1.30938i	0.00243692	+	0.0546049i
$576$	−2.40129			−0.100054
$577$	−29.8930	−	9.71281i	−1.24446	−	0.404350i	−0.388527	−	0.921437i	$-0.627016\pi$
$577$	−29.8930	−	9.71281i	−1.24446	−	0.404350i	−0.855932	+	0.517088i	$0.827016\pi$
$578$	−0.103835	+	0.142916i	−0.00431896	+	0.00594453i
$579$	10.9735	+	7.97273i	0.456044	+	0.331335i
$580$	21.0313	+	6.31863i	0.873277	+	0.262367i
$581$	4.49600	−	3.26654i	0.186526	−	0.135519i
$582$		−	14.9636i		−	0.620261i
$583$	2.11716	+	2.91402i	0.0876836	+	0.120686i
$584$	−0.448330	−	1.37982i	−0.0185520	−	0.0570973i
$585$	−28.5293	+	0.636290i	−1.17954	+	0.0263073i
$586$	−4.42244	+	13.6109i	−0.182689	+	0.562260i
$587$	−24.3521	+	7.91247i	−1.00512	+	0.326583i	−0.764909	−	0.644138i	$-0.777216\pi$
$587$	−24.3521	+	7.91247i	−1.00512	+	0.326583i	−0.240209	+	0.970721i	$0.577216\pi$
$588$	−0.735893	+	0.239106i	−0.0303477	+	0.00986056i
$589$	−9.54145	+	29.3655i	−0.393148	+	1.20999i
$590$	2.90920	+	2.01611i	0.119770	+	0.0830018i
$591$	4.37094	+	13.4524i	0.179797	+	0.553357i
$592$	−0.210288	−	0.289436i	−0.00864278	−	0.0118958i
$593$		−	8.09401i		−	0.332381i	−0.986094	−	0.166191i	$-0.946853\pi$
$593$		−	8.09401i		−	0.332381i	0.986094	−	0.166191i	$-0.0531467\pi$
$594$	−11.4573	+	8.32418i	−0.470097	+	0.341545i
$595$	0.206638	+	9.26502i	0.00847134	+	0.379829i
$596$	−9.93893	−	7.22106i	−0.407114	−	0.295786i
$597$	−10.7016	+	14.7295i	−0.437987	+	0.602838i
$598$	−1.32496	−	0.430506i	−0.0541816	−	0.0176047i
$599$	47.5661			1.94350			0.971749	−	0.236015i	$-0.0758414\pi$
$599$	47.5661			1.94350			0.971749	+	0.236015i	$0.0758414\pi$
$600$	−1.35839	−	3.62250i	−0.0554559	−	0.147888i
$601$	39.8486			1.62546			0.812730	−	0.582641i	$-0.197981\pi$
$601$	39.8486			1.62546			0.812730	+	0.582641i	$0.197981\pi$
$602$	−2.21352	−	0.719216i	−0.0902163	−	0.0293131i
$603$	−11.2559	+	15.4924i	−0.458376	+	0.630901i
$604$	−9.59238	−	6.96927i	−0.390309	−	0.283576i
$605$	1.01830	−	0.356157i	0.0413997	−	0.0144799i
$606$	−6.25782	+	4.54657i	−0.254207	+	0.184692i
$607$			24.3793i			0.989526i	0.869028	+	0.494763i	$0.164745\pi$
$607$			24.3793i			0.989526i	−0.869028	+	0.494763i	$0.835255\pi$
$608$	3.91800	+	5.39266i	0.158896	+	0.218701i
$609$	−2.34821	−	7.22705i	−0.0951543	−	0.292855i
$610$	1.10562	+	3.16112i	0.0447654	+	0.127990i
$611$	7.69427	−	23.6805i	0.311277	−	0.958011i
$612$	9.46499	−	3.07536i	0.382600	−	0.124314i
$613$	−31.2901	+	10.1668i	−1.26380	+	0.410632i	−0.862846	−	0.505468i	$-0.831320\pi$
$613$	−31.2901	+	10.1668i	−1.26380	+	0.410632i	−0.400950	+	0.916100i	$0.631320\pi$
$614$	3.74813	−	11.5356i	0.151262	−	0.465537i
$615$	−1.13329	+	0.862638i	−0.0456987	+	0.0347849i
$616$	−1.04713	−	3.22273i	−0.0421900	−	0.129847i
$617$	21.3728	+	29.4171i	0.860435	+	1.18429i	0.981466	+	0.191638i	$0.0613801\pi$
$617$	21.3728	+	29.4171i	0.860435	+	1.18429i	−0.121031	+	0.992649i	$0.538620\pi$
$618$		−	5.47998i		−	0.220437i
$619$	−20.8135	+	15.1219i	−0.836566	+	0.607800i	−0.921409	−	0.388594i	$-0.872961\pi$
$619$	−20.8135	+	15.1219i	−0.836566	+	0.607800i	0.0848436	+	0.996394i	$0.472961\pi$
$620$	5.89985	−	8.51337i	0.236944	−	0.341905i
$621$	−0.886320	−	0.643949i	−0.0355668	−	0.0258408i
$622$	−12.8717	+	17.7163i	−0.516107	+	0.710360i
$623$	13.5171	+	4.39198i	0.541553	+	0.175961i
$624$	4.11223			0.164621
$625$	−18.8360	+	16.4379i	−0.753441	+	0.657515i
$626$	15.7216			0.628363
$627$	16.6218	+	5.40074i	0.663810	+	0.215685i
$628$	−10.8728	+	14.9652i	−0.433874	+	0.597176i
$629$	1.19956	+	0.871532i	0.0478296	+	0.0347503i
$630$	3.05844	−	4.41327i	0.121851	−	0.175829i
$631$	−27.2144	+	19.7724i	−1.08339	+	0.787128i	−0.978271	−	0.207331i	$-0.933522\pi$
$631$	−27.2144	+	19.7724i	−1.08339	+	0.787128i	−0.105118	+	0.994460i	$0.533522\pi$
$632$		−	6.38569i		−	0.254009i
$633$	−5.79479	−	7.97584i	−0.230322	−	0.317011i
$634$	−6.17764	−	19.0128i	−0.245345	−	0.755095i
$635$	−26.5120	+	20.1804i	−1.05210	+	0.800834i
$636$	0.254160	−	0.782224i	0.0100781	−	0.0310172i
$637$	−5.05447	+	1.64230i	−0.200265	+	0.0650701i
$638$	31.6498	−	10.2836i	1.25303	−	0.407133i
$639$	−6.25922	+	19.2639i	−0.247611	+	0.762068i
$640$	−0.738230	−	2.11069i	−0.0291811	−	0.0834324i
$641$	−2.33946	−	7.20012i	−0.0924031	−	0.284388i	0.894165	−	0.447737i	$-0.147770\pi$
$641$	−2.33946	−	7.20012i	−0.0924031	−	0.284388i	−0.986568	+	0.163350i	$0.947770\pi$
$642$	1.55414	+	2.13908i	0.0613369	+	0.0844229i
$643$		−	9.71266i		−	0.383030i	−0.981490	−	0.191515i	$-0.938660\pi$
$643$		−	9.71266i		−	0.383030i	0.981490	−	0.191515i	$-0.0613400\pi$
$644$	0.212073	−	0.154080i	0.00835684	−	0.00607160i
$645$	−3.80110	+	1.32946i	−0.149668	+	0.0523476i
$646$	−22.3498	−	16.2380i	−0.879339	−	0.638877i
$647$	2.05909	−	2.83410i	0.0809513	−	0.111420i	−0.766621	−	0.642100i	$-0.778063\pi$
$647$	2.05909	−	2.83410i	0.0809513	−	0.111420i	0.847572	+	0.530680i	$0.178063\pi$
$648$	−3.77576	−	1.22682i	−0.148326	−	0.0481940i
$649$	5.36384			0.210549
$650$	−9.33005	−	24.8811i	−0.365955	−	0.975917i
$651$	−3.58422			−0.140476
$652$	−14.2234	−	4.62146i	−0.557031	−	0.180990i
$653$	23.3370	−	32.1206i	0.913247	−	1.25698i	−0.0527982	−	0.998605i	$-0.516814\pi$
$653$	23.3370	−	32.1206i	0.913247	−	1.25698i	0.966046	−	0.258372i	$-0.0831860\pi$
$654$	−12.8858	−	9.36210i	−0.503876	−	0.366087i
$655$	−0.877125	−	39.3276i	−0.0342721	−	1.53666i
$656$	−0.665965	+	0.483852i	−0.0260015	+	0.0188912i
$657$		−	3.48386i		−	0.135918i
$658$	2.75381	+	3.79030i	0.107355	+	0.147761i
$659$	−9.70302	−	29.8628i	−0.377976	−	1.16329i	−0.941449	−	0.337156i	$-0.890535\pi$
$659$	−9.70302	−	29.8628i	−0.377976	−	1.16329i	0.563473	−	0.826135i	$-0.309465\pi$
$660$	−4.81882	−	3.33949i	−0.187572	−	0.129990i
$661$	5.00190	−	15.3943i	0.194551	−	0.598768i	−0.805430	−	0.592691i	$-0.798066\pi$
$661$	5.00190	−	15.3943i	0.194551	−	0.598768i	0.999982	−	0.00607707i	$-0.00193440\pi$
$662$	2.13768	−	0.694573i	0.0830831	−	0.0269953i
$663$	−16.2089	+	5.26658i	−0.629500	+	0.204537i
$664$	1.71732	−	5.28537i	0.0666449	−	0.205112i
$665$	−14.9013	+	0.332343i	−0.577846	+	0.0128877i
$666$	−0.265474	−	0.817046i	−0.0102869	−	0.0316599i
$667$	1.51319	+	2.08272i	0.0585909	+	0.0806434i
$668$		−	13.0662i		−	0.505546i
$669$	8.00234	−	5.81404i	0.309388	−	0.224784i
$670$	−17.0780	−	5.13090i	−0.659780	−	0.198224i
$671$	4.10573	+	2.98299i	0.158500	+	0.115157i
$672$	−0.454807	+	0.625988i	−0.0175445	+	0.0241480i
$673$	22.6345	+	7.35438i	0.872494	+	0.283491i	0.710837	−	0.703356i	$-0.248316\pi$
$673$	22.6345	+	7.35438i	0.872494	+	0.283491i	0.161657	+	0.986847i	$0.448316\pi$
$674$	−8.34039			−0.321260
$675$	−0.931652	−	20.8758i	−0.0358593	−	0.803511i
$676$	15.2448			0.586337
$677$	5.47601	+	1.77926i	0.210460	+	0.0683827i	0.412350	−	0.911026i	$-0.364708\pi$
$677$	5.47601	+	1.77926i	0.210460	+	0.0683827i	−0.201889	+	0.979408i	$0.564708\pi$
$678$	7.67808	−	10.5680i	0.294875	−	0.405861i
$679$	15.6454	+	11.3670i	0.600414	+	0.436226i
$680$	5.61302	+	7.37410i	0.215249	+	0.282784i
$681$	0.734986	−	0.533999i	0.0281647	−	0.0204629i
$682$		−	15.6965i		−	0.601051i
$683$	−10.3190	−	14.2029i	−0.394845	−	0.543457i	0.564596	−	0.825367i	$-0.309032\pi$
$683$	−10.3190	−	14.2029i	−0.394845	−	0.543457i	−0.959441	+	0.281910i	$0.909032\pi$
$684$	4.94621	+	15.2229i	0.189123	+	0.582061i
$685$	−4.37406	+	14.5589i	−0.167124	+	0.556266i
$686$	0.309017	−	0.951057i	0.0117983	−	0.0363115i
$687$	4.56608	−	1.48361i	0.174207	−	0.0566032i
$688$	−2.21352	+	0.719216i	−0.0843896	+	0.0274199i
$689$	1.74569	−	5.37270i	0.0665057	−	0.204683i
$690$	0.130500	−	0.434365i	0.00496806	−	0.0165360i
$691$	3.62060	+	11.1430i	0.137734	+	0.423901i	0.996005	−	0.0892948i	$-0.0284613\pi$
$691$	3.62060	+	11.1430i	0.137734	+	0.423901i	−0.858271	+	0.513196i	$0.828461\pi$
$692$	−7.17391	−	9.87404i	−0.272711	−	0.375355i
$693$		−	8.13696i		−	0.309097i
$694$	−5.28936	+	3.84294i	−0.200781	+	0.145876i
$695$	−20.7186	−	27.2190i	−0.785900	−	1.03248i
$696$	−6.14770	−	4.46656i	−0.233028	−	0.169305i
$697$	2.00531	−	2.76007i	0.0759565	−	0.104545i
$698$	−7.03090	−	2.28448i	−0.266123	−	0.0864687i
$699$	−8.48503			−0.320933
$700$	4.81944	+	1.33154i	0.182158	+	0.0503275i
$701$	−37.4802			−1.41561			−0.707803	−	0.706410i	$-0.750314\pi$
$701$	−37.4802			−1.41561			−0.707803	+	0.706410i	$0.750314\pi$
$702$	21.1242	+	6.86368i	0.797283	+	0.259053i
$703$	−1.40172	+	1.92930i	−0.0528667	+	0.0727648i
$704$	−2.74142	−	1.99176i	−0.103321	−	0.0750671i
$705$	7.76324	+	2.33238i	0.292381	+	0.0878427i
$706$	13.1813	−	9.57677i	0.496085	−	0.360427i
$707$		−	9.99672i		−	0.375965i
$708$	−0.719921	−	0.990887i	−0.0270563	−	0.0372398i
$709$	−2.30098	−	7.08169i	−0.0864151	−	0.265958i	0.898506	−	0.438961i	$-0.144653\pi$
$709$	−2.30098	−	7.08169i	−0.0864151	−	0.265958i	−0.984921	+	0.173002i	$0.944653\pi$
$710$	−18.8569	+	0.420566i	−0.707686	+	0.0157836i
$711$	4.73844	−	14.5834i	0.177705	−	0.546920i
$712$	13.5171	−	4.39198i	0.506576	−	0.164597i
$713$	1.15483	−	0.375229i	0.0432489	−	0.0140524i
$714$	0.990968	−	3.04989i	0.0370861	−	0.114139i
$715$	−33.0980	−	22.9372i	−1.23780	−	0.857804i
$716$	6.73832	+	20.7384i	0.251823	+	0.775031i
$717$	8.88715	+	12.2321i	0.331897	+	0.456817i
$718$		−	3.88147i		−	0.144855i
$719$	20.3456	−	14.7820i	0.758764	−	0.551274i	−0.139767	−	0.990184i	$-0.544635\pi$
$719$	20.3456	−	14.7820i	0.758764	−	0.551274i	0.898531	+	0.438910i	$0.144635\pi$
$720$	−0.119725	−	5.36811i	−0.00446190	−	0.200058i
$721$	5.72966	+	4.16284i	0.213384	+	0.155032i
$722$	14.9483	−	20.5746i	0.556318	−	0.765706i
$723$	−8.38002	−	2.72283i	−0.311656	−	0.101263i
$724$	−12.4131			−0.461327
$725$	−13.0768	+	47.3308i	−0.485660	+	1.75782i
$726$	−0.373301			−0.0138545
$727$	29.8718	+	9.70593i	1.10788	+	0.359973i	0.805131	−	0.593097i	$-0.202095\pi$
$727$	29.8718	+	9.70593i	1.10788	+	0.359973i	0.302751	+	0.953070i	$0.402095\pi$
$728$	−3.12383	+	4.29959i	−0.115777	+	0.159353i
$729$	0.136017	+	0.0988218i	0.00503765	+	0.00366007i
$730$	3.06225	−	1.07104i	0.113339	−	0.0396411i
$731$	7.80376	−	5.66976i	0.288633	−	0.209704i
$732$		−	1.15884i		−	0.0428320i
$733$	−6.28770	−	8.65428i	−0.232241	−	0.319653i	0.676952	−	0.736027i	$-0.263301\pi$
$733$	−6.28770	−	8.65428i	−0.232241	−	0.319653i	−0.909193	+	0.416374i	$0.863301\pi$
$734$	−9.26507	−	28.5150i	−0.341980	−	1.05251i
$735$	−0.571215	−	1.63318i	−0.0210696	−	0.0602406i
$736$	0.0810046	−	0.249307i	0.00298587	−	0.00918956i
$737$	−25.7005	+	8.35059i	−0.946689	+	0.307598i
$738$	−1.87994	+	0.610830i	−0.0692016	+	0.0224850i
$739$	−0.608242	+	1.87198i	−0.0223745	+	0.0688618i	−0.961620	−	0.274384i	$-0.911526\pi$
$739$	−0.608242	+	1.87198i	−0.0223745	+	0.0688618i	0.939246	+	0.343245i	$0.111526\pi$
$740$	0.636554	−	0.484532i	0.0234002	−	0.0178117i
$741$	−8.47042	−	26.0693i	−0.311169	−	0.957679i
$742$	0.624792	+	0.859953i	0.0229368	+	0.0315699i
$743$		−	38.8897i		−	1.42672i	−0.700796	−	0.713362i	$-0.747171\pi$
$743$		−	38.8897i		−	1.42672i	0.700796	−	0.713362i	$-0.252829\pi$
$744$	−2.89969	+	2.10675i	−0.106308	+	0.0772372i
$745$	15.6472	−	22.5786i	0.573270	−	0.827217i
$746$	−29.6359	−	21.5318i	−1.08505	−	0.788334i
$747$	7.84390	−	10.7962i	0.286993	−	0.395013i
$748$	13.3565	+	4.33979i	0.488362	+	0.158679i
$749$	−3.41714			−0.124859
$750$	8.03042	−	3.21730i	0.293230	−	0.117479i
$751$	−25.8651			−0.943830			−0.471915	−	0.881644i	$-0.656437\pi$
$751$	−25.8651			−0.943830			−0.471915	+	0.881644i	$0.656437\pi$
$752$	4.45577	+	1.44777i	0.162485	+	0.0527946i
$753$	7.41055	−	10.1997i	0.270055	−	0.371699i
$754$	−42.2254	−	30.6785i	−1.53776	−	1.11725i
$755$	15.1016	−	21.7914i	0.549605	−	0.793069i
$756$	−3.38114	+	2.45654i	−0.122971	+	0.0893436i
$757$			25.8619i			0.939967i	0.882675	+	0.469983i	$0.155740\pi$
$757$			25.8619i			0.939967i	−0.882675	+	0.469983i	$0.844260\pi$
$758$	8.44587	+	11.6247i	0.306768	+	0.422230i
$759$	−0.212391	−	0.653671i	−0.00770929	−	0.0237267i
$760$	−11.8600	+	9.02761i	−0.430208	+	0.327466i
$761$	5.33509	−	16.4197i	0.193397	−	0.595214i	−0.806595	−	0.591105i	$-0.798692\pi$
$761$	5.33509	−	16.4197i	0.193397	−	0.595214i	0.999992	−	0.00410939i	$-0.00130806\pi$
$762$	10.9652	−	3.56281i	0.397227	−	0.129067i
$763$	19.5773	−	6.36105i	0.708746	−	0.230286i
$764$	−6.51528	+	20.0520i	−0.235714	+	0.725455i
$765$	7.34692	+	21.0058i	0.265629	+	0.759465i
$766$	0.889297	+	2.73697i	0.0321316	+	0.0988909i
$767$	−4.94477	−	6.80589i	−0.178545	−	0.245746i
$768$			0.773763i			0.0279208i
$769$	−19.3225	+	14.0386i	−0.696786	+	0.506244i	−0.878884	−	0.477036i	$-0.841711\pi$
$769$	−19.3225	+	14.0386i	−0.696786	+	0.506244i	0.182098	+	0.983280i	$0.441711\pi$
$770$	7.15224	−	2.50155i	0.257749	−	0.0901495i
$771$	2.39719	+	1.74166i	0.0863329	+	0.0627245i
$772$	−10.3038	+	14.1820i	−0.370843	+	0.510422i
$773$	−7.32098	−	2.37873i	−0.263317	−	0.0855570i	0.174383	−	0.984678i	$-0.444207\pi$
$773$	−7.32098	−	2.37873i	−0.263317	−	0.0855570i	−0.437700	+	0.899121i	$0.644207\pi$
$774$	−5.58884			−0.200887
$775$	19.3259	+	12.7647i	0.694207	+	0.458522i
$776$	19.3387			0.694220
$777$	−0.263275	−	0.0855433i	−0.00944494	−	0.00306885i
$778$	6.51804	−	8.97132i	0.233683	−	0.321637i
$779$	4.43912	+	3.22521i	0.159048	+	0.115555i
$780$	0.205030	+	9.19293i	0.00734126	+	0.329160i
$781$	−23.1243	+	16.8008i	−0.827451	+	0.601179i
$782$			1.08642i			0.0388502i
$783$	−24.1252	−	33.2055i	−0.862165	−	1.18667i
$784$	−0.309017	−	0.951057i	−0.0110363	−	0.0339663i
$785$	−33.9970	−	23.5602i	−1.21340	−	0.840901i
$786$	−4.20640	+	12.9460i	−0.150037	+	0.461767i
$787$	21.7606	−	7.07045i	0.775682	−	0.252034i	0.105686	−	0.994400i	$-0.466296\pi$
$787$	21.7606	−	7.07045i	0.775682	−	0.252034i	0.669995	+	0.742365i	$0.266296\pi$
$788$	−17.3857	+	5.64894i	−0.619338	+	0.201235i
$789$	−3.97938	+	12.2473i	−0.141670	+	0.436014i
$790$	14.2753	−	0.318382i	0.507892	−	0.0113275i
$791$	5.21685	+	16.0558i	0.185490	+	0.570879i
$792$	−4.78278	−	6.58294i	−0.169949	−	0.233914i
$793$		−	7.95949i		−	0.282650i
$794$	−14.2565	+	10.3580i	−0.505945	+	0.367591i
$795$	1.76134	+	0.529177i	0.0624684	+	0.0187680i
$796$	−19.0362	−	13.8306i	−0.674719	−	0.490212i
$797$	−10.0965	+	13.8967i	−0.357637	+	0.492245i	−0.949489	−	0.313802i	$-0.898397\pi$
$797$	−10.0965	+	13.8967i	−0.357637	+	0.492245i	0.591851	+	0.806047i	$0.298397\pi$
$798$	4.90524	+	1.59381i	0.173644	+	0.0564202i
$799$	−19.4171			−0.686929
$800$	4.68167	−	1.75556i	0.165522	−	0.0620683i
$801$	34.1290			1.20589
$802$	−9.98229	−	3.24344i	−0.352487	−	0.114530i
$803$	2.88969	−	3.97732i	0.101975	−	0.140357i
$804$	4.99210	+	3.62697i	0.176058	+	0.127913i
$805$	0.355021	+	0.466409i	0.0125129	+	0.0164388i
$806$	−19.9165	+	14.4702i	−0.701528	+	0.509690i
$807$			10.5697i			0.372070i
$808$	−5.87592	−	8.08752i	−0.206714	−	0.284518i
$809$	−7.37053	−	22.6842i	−0.259134	−	0.797532i	−0.992987	−	0.118224i	$-0.962280\pi$
$809$	−7.37053	−	22.6842i	−0.259134	−	0.797532i	0.733853	−	0.679308i	$-0.237720\pi$
$810$	2.55431	−	8.50192i	0.0897494	−	0.298727i
$811$	−14.4735	+	44.5449i	−0.508234	+	1.56418i	0.287032	+	0.957921i	$0.407331\pi$
$811$	−14.4735	+	44.5449i	−0.508234	+	1.56418i	−0.795265	+	0.606261i	$0.792669\pi$
$812$	9.34014	−	3.03479i	0.327774	−	0.106500i
$813$	−19.4695	+	6.32602i	−0.682824	+	0.221863i
$814$	0.374624	−	1.15297i	0.0131305	−	0.0404117i
$815$	9.62217	−	32.0270i	0.337050	−	1.12186i
$816$	−0.990968	−	3.04989i	−0.0346908	−	0.106767i
$817$	9.11888	+	12.5511i	0.319029	+	0.439106i
$818$			3.46639i			0.121199i
$819$	−10.3246	+	7.50123i	−0.360769	+	0.262114i
$820$	−1.11486	−	1.46465i	−0.0389326	−	0.0511477i
$821$	−7.64981	−	5.55791i	−0.266980	−	0.193972i	0.446238	−	0.894914i	$-0.352763\pi$
$821$	−7.64981	−	5.55791i	−0.266980	−	0.193972i	−0.713219	+	0.700942i	$0.752763\pi$
$822$	3.09197	−	4.25574i	0.107845	−	0.148436i
$823$	−22.8185	−	7.41419i	−0.795404	−	0.258443i	−0.117001	−	0.993132i	$-0.537328\pi$
$823$	−22.8185	−	7.41419i	−0.795404	−	0.258443i	−0.678404	+	0.734689i	$0.737328\pi$
$824$	7.08225			0.246722
$825$	7.22521	−	10.9390i	0.251550	−	0.380848i
$826$	1.58292			0.0550767
$827$	−47.3400	−	15.3817i	−1.64617	−	0.534875i	−0.668269	−	0.743920i	$-0.732964\pi$
$827$	−47.3400	−	15.3817i	−1.64617	−	0.534875i	−0.977906	+	0.209045i	$0.932964\pi$
$828$	0.369991	−	0.509249i	0.0128581	−	0.0176976i
$829$	−34.3585	−	24.9629i	−1.19332	−	0.866997i	−0.199708	−	0.979856i	$-0.563999\pi$
$829$	−34.3585	−	24.9629i	−1.19332	−	0.866997i	−0.993611	+	0.112859i	$0.963999\pi$
$830$	11.9011	+	3.57557i	0.413094	+	0.124110i
$831$	14.2148	−	10.3277i	0.493106	−	0.358262i
$832$			5.31458i			0.184250i
$833$	2.43606	+	3.35295i	0.0844045	+	0.116173i
$834$	3.65783	+	11.2576i	0.126660	+	0.389820i
$835$	29.2096	−	0.651464i	1.01084	−	0.0225448i
$836$	−6.97984	+	21.4817i	−0.241403	+	0.742961i
$837$	−18.4119	+	5.98238i	−0.636407	+	0.206781i
$838$	12.9461	−	4.20644i	0.447216	−	0.145309i
$839$	−1.03815	+	3.19509i	−0.0358409	+	0.110307i	−0.967376	−	0.253344i	$-0.918470\pi$
$839$	−1.03815	+	3.19509i	−0.0358409	+	0.110307i	0.931536	+	0.363650i	$0.118470\pi$
$840$	−1.42208	−	0.985515i	−0.0490664	−	0.0340035i
$841$	20.8426	+	64.1470i	0.718711	+	2.21196i
$842$	21.2987	+	29.3151i	0.734001	+	1.01027i
$843$		−	2.02783i		−	0.0698421i
$844$	10.3079	−	7.48910i	0.354811	−	0.257785i
$845$	0.760084	+	34.0798i	0.0261477	+	1.17238i
$846$	9.10161	+	6.61271i	0.312920	+	0.227350i
$847$	0.283576	−	0.390309i	0.00974378	−	0.0134112i
$848$	1.01094	+	0.328473i	0.0347157	+	0.0112798i
$849$	−8.22823			−0.282392
$850$	−16.2050	+	12.9156i	−0.555828	+	0.443002i
$851$	0.0937827			0.00321483
$852$	6.20737	+	2.01690i	0.212661	+	0.0690977i
$853$	20.9267	−	28.8031i	0.716515	−	0.986198i	−0.283117	−	0.959085i	$-0.591369\pi$
$853$	20.9267	−	28.8031i	0.716515	−	0.986198i	0.999632	−	0.0271130i	$-0.00863139\pi$
$854$	1.21164	+	0.880308i	0.0414615	+	0.0301235i
$855$	−33.7843	+	11.8163i	−1.15540	+	0.404109i
$856$	−2.76452	+	2.00854i	−0.0944894	+	0.0686506i
$857$			44.6335i			1.52465i	0.647194	+	0.762325i	$0.275942\pi$
$857$			44.6335i			1.52465i	−0.647194	+	0.762325i	$0.724058\pi$
$858$	8.19055	+	11.2733i	0.279621	+	0.384865i
$859$	−5.90154	−	18.1631i	−0.201358	−	0.619716i	−0.999843	−	0.0177018i	$-0.994365\pi$
$859$	−5.90154	−	18.1631i	−0.201358	−	0.619716i	0.798485	−	0.602014i	$-0.205635\pi$
$860$	−1.71818	−	4.91249i	−0.0585894	−	0.167515i
$861$	−0.196827	+	0.605770i	−0.00670783	+	0.0206446i
$862$	34.9662	−	11.3612i	1.19095	−	0.386964i
$863$	42.1522	−	13.6961i	1.43488	−	0.466220i	0.514582	−	0.857441i	$-0.327947\pi$
$863$	42.1522	−	13.6961i	1.43488	−	0.466220i	0.920297	+	0.391221i	$0.127947\pi$
$864$	−1.29148	+	3.97477i	−0.0439371	+	0.135224i
$865$	21.7159	−	16.5297i	0.738362	−	0.562026i
$866$	−1.04163	−	3.20581i	−0.0353960	−	0.108938i
$867$	0.0803435	+	0.110583i	0.00272861	+	0.00375561i
$868$		−	4.63219i		−	0.157227i
$869$	17.5058	−	12.7187i	0.593845	−	0.431454i
$870$	9.67854	−	13.9660i	0.328133	−	0.473490i
$871$	34.2882	+	24.9118i	1.16181	+	0.844104i
$872$	12.0994	−	16.6534i	0.409739	−	0.563957i
$873$	44.1651	+	14.3501i	1.49476	+	0.485678i
$874$	−1.74732			−0.0591041
$875$	−2.73638	+	10.8403i	−0.0925066	+	0.366469i
$876$	−1.12260			−0.0379290
$877$	12.0673	+	3.92090i	0.407484	+	0.132399i	0.505585	−	0.862777i	$-0.331277\pi$
$877$	12.0673	+	3.92090i	0.407484	+	0.132399i	−0.0981010	+	0.995176i	$0.531277\pi$
$878$	−7.61758	+	10.4847i	−0.257081	+	0.353841i
$879$	8.95871	+	6.50889i	0.302170	+	0.219539i
$880$	4.31591	−	6.22777i	0.145489	−	0.209938i
$881$	−20.5022	+	14.8957i	−0.690737	+	0.501850i	−0.876902	−	0.480669i	$-0.840394\pi$
$881$	−20.5022	+	14.8957i	−0.690737	+	0.501850i	0.186166	+	0.982518i	$0.440394\pi$
$882$		−	2.40129i		−	0.0808557i
$883$	22.3187	+	30.7191i	0.751084	+	1.03378i	0.997904	+	0.0647172i	$0.0206145\pi$
$883$	22.3187	+	30.7191i	0.751084	+	1.03378i	−0.246819	+	0.969061i	$0.579385\pi$
$884$	−6.80645	−	20.9481i	−0.228926	−	0.704561i
$885$	2.17924	−	1.65880i	0.0732545	−	0.0557599i
$886$	−4.00330	+	12.3209i	−0.134493	+	0.413928i
$887$	−1.65216	+	0.536820i	−0.0554742	+	0.0180247i	−0.336623	−	0.941640i	$-0.609285\pi$
$887$	−1.65216	+	0.536820i	−0.0554742	+	0.0180247i	0.281148	+	0.959664i	$0.409285\pi$
$888$	−0.263275	+	0.0855433i	−0.00883493	+	0.00287064i
$889$	−4.60452	+	14.1713i	−0.154431	+	0.475289i
$890$	10.4923	+	29.9987i	0.351702	+	1.00556i
$891$	−4.15717	−	12.7944i	−0.139270	−	0.428630i
$892$	7.51398	+	10.3421i	0.251587	+	0.346279i
$893$		−	31.2293i		−	1.04505i
$894$	−7.69038	+	5.58739i	−0.257205	+	0.186870i
$895$	−46.0250	+	16.0976i	−1.53845	+	0.538083i
$896$	−0.809017	−	0.587785i	−0.0270274	−	0.0196365i
$897$	−0.633612	+	0.872092i	−0.0211557	+	0.0291183i
$898$	−31.3802	−	10.1961i	−1.04717	−	0.340247i
$899$	45.4918			1.51724
$900$	11.9945	−	0.535295i	0.399817	−	0.0178432i
$901$	−4.40541			−0.146765
$902$	−2.65288	−	0.861972i	−0.0883311	−	0.0287005i
$903$	−1.05853	+	1.45694i	−0.0352257	+	0.0484840i
$904$	13.6579	+	9.92304i	0.454255	+	0.330035i
$905$	−0.618899	−	27.7495i	−0.0205729	−	0.922425i
$906$	−7.42223	+	5.39257i	−0.246587	+	0.179156i
$907$			50.7967i			1.68668i	0.537382	+	0.843339i	$0.319413\pi$
$907$			50.7967i			1.68668i	−0.537382	+	0.843339i	$0.680587\pi$
$908$	0.690132	+	0.949885i	0.0229028	+	0.0315230i
$909$	−7.41796	−	22.8301i	−0.246038	−	0.757228i
$910$	−9.76753	−	6.76899i	−0.323790	−	0.224390i
$911$	11.7035	−	36.0197i	0.387755	−	1.19339i	−0.546707	−	0.837324i	$-0.684119\pi$
$911$	11.7035	−	36.0197i	0.387755	−	1.19339i	0.934462	−	0.356063i	$-0.115881\pi$
$912$	4.90524	−	1.59381i	0.162429	−	0.0527763i
$913$	17.9099	−	5.81927i	0.592730	−	0.192590i
$914$	1.16031	−	3.57105i	0.0383795	−	0.118120i
$915$	2.59060	−	0.0577784i	0.0856427	−	0.00191009i
$916$	1.91739	+	5.90113i	0.0633525	+	0.194979i
$917$	−10.3404	−	14.2324i	−0.341471	−	0.469995i
$918$		−	17.3211i		−	0.571681i
$919$	2.90361	−	2.10959i	0.0957812	−	0.0695891i	−0.538864	−	0.842393i	$-0.681146\pi$
$919$	2.90361	−	2.10959i	0.0957812	−	0.0695891i	0.634645	+	0.772804i	$0.281146\pi$
$920$	0.561367	+	0.168657i	0.0185077	+	0.00556045i
$921$	−7.59273	−	5.51644i	−0.250189	−	0.181773i
$922$	−7.55347	+	10.3965i	−0.248760	+	0.342389i
$923$	42.6352	+	13.8530i	1.40335	+	0.455978i
$924$	−2.62196			−0.0862560
$925$	1.11491	+	1.39887i	0.0366582	+	0.0459944i
$926$	−19.6416			−0.645464
$927$	16.1742	+	5.25531i	0.531230	+	0.172607i
$928$	5.77252	−	7.94519i	0.189492	−	0.260814i
$929$	−15.6287	−	11.3549i	−0.512759	−	0.372542i	0.301110	−	0.953589i	$-0.402643\pi$
$929$	−15.6287	−	11.3549i	−0.512759	−	0.372542i	−0.813869	+	0.581048i	$0.802643\pi$
$930$	−4.85424	−	6.37726i	−0.159177	−	0.209118i
$931$	−5.39266	+	3.91800i	−0.176737	+	0.128407i
$932$		−	10.9659i		−	0.359201i
$933$	9.95963	+	13.7082i	0.326064	+	0.448788i
$934$	−3.67331	−	11.3053i	−0.120194	−	0.369920i
$935$	−9.03572	+	30.0750i	−0.295500	+	0.983558i
$936$	−3.94363	+	12.1372i	−0.128902	+	0.396718i
$937$	−5.33328	+	1.73289i	−0.174231	+	0.0566109i	−0.394833	−	0.918753i	$-0.629198\pi$
$937$	−5.33328	+	1.73289i	−0.174231	+	0.0566109i	0.220603	+	0.975364i	$0.429198\pi$
$938$	−7.58445	+	2.46434i	−0.247641	+	0.0804634i
$939$	3.75914	−	11.5694i	0.122675	−	0.377554i
$940$	−3.01434	+	10.0331i	−0.0983169	+	0.327244i
$941$	3.79715	+	11.6864i	0.123784	+	0.380966i	0.993677	−	0.112272i	$-0.0358129\pi$
$941$	3.79715	+	11.6864i	0.123784	+	0.380966i	−0.869894	+	0.493239i	$0.835813\pi$
$942$	8.41301	+	11.5795i	0.274111	+	0.377281i
$943$		−	0.215785i		−	0.00702692i
$944$	1.28061	−	0.930416i	0.0416802	−	0.0302824i
$945$	−5.66021	−	7.43610i	−0.184127	−	0.241896i
$946$	−6.38046	−	4.63567i	−0.207447	−	0.150719i
$947$	9.30462	−	12.8067i	0.302360	−	0.416162i	−0.630620	−	0.776092i	$-0.717199\pi$
$947$	9.30462	−	12.8067i	0.302360	−	0.416162i	0.932980	+	0.359930i	$0.117199\pi$
$948$	−4.69918	−	1.52686i	−0.152622	−	0.0495900i
$949$	−7.71053			−0.250295
$950$	−20.7727	−	26.0631i	−0.673954	−	0.845599i
$951$	−15.4685			−0.501600
$952$	3.94163	+	1.28071i	0.127749	+	0.0415081i
$953$	14.6690	−	20.1901i	0.475174	−	0.654021i	−0.502394	−	0.864639i	$-0.667547\pi$
$953$	14.6690	−	20.1901i	0.475174	−	0.654021i	0.977569	+	0.210617i	$0.0675474\pi$
$954$	2.06500	+	1.50031i	0.0668567	+	0.0485743i
$955$	−45.1512	−	13.5652i	−1.46106	−	0.438960i
$956$	−15.8086	+	11.4856i	−0.511287	+	0.371472i
$957$		−	25.7497i		−	0.832370i
$958$	20.7090	+	28.5035i	0.669077	+	0.920906i
$959$	2.10083	+	6.46570i	0.0678394	+	0.208788i
$960$	−1.72976	+	0.0385788i	−0.0558277	+	0.00124513i
$961$	−2.94890	+	9.07579i	−0.0951259	+	0.292767i
$962$	−1.80830	+	0.587553i	−0.0583020	+	0.0189435i
$963$	−7.80393	+	2.53565i	−0.251478	+	0.0817102i
$964$	3.51895	−	10.8302i	0.113338	−	0.348818i
$965$	−32.2178	−	22.3273i	−1.03713	−	0.718740i
$966$	−0.0626784	−	0.192904i	−0.00201664	−	0.00620659i
$967$	18.5595	+	25.5450i	0.596834	+	0.821472i	0.995414	−	0.0956617i	$-0.0304967\pi$
$967$	18.5595	+	25.5450i	0.596834	+	0.821472i	−0.398579	+	0.917134i	$0.630497\pi$
$968$		−	0.482448i		−	0.0155065i
$969$	−17.2934	+	12.5644i	−0.555545	+	0.403627i
$970$	0.964205	+	43.2320i	0.0309587	+	1.38810i
$971$	30.4968	+	22.1572i	0.978688	+	0.711059i	0.957415	−	0.288715i	$-0.0932280\pi$
$971$	30.4968	+	22.1572i	0.978688	+	0.711059i	0.0212732	+	0.999774i	$0.493228\pi$
$972$	−9.17524	+	12.6286i	−0.294296	+	0.405064i
$973$	−14.5492	−	4.72732i	−0.466426	−	0.151551i
$974$	30.0594			0.963165
$975$	−20.5407	+	0.916696i	−0.657828	+	0.0293578i
$976$	1.49767			0.0479392
$977$	39.2612	+	12.7567i	1.25608	+	0.408124i	0.860095	−	0.510134i	$-0.170404\pi$
$977$	39.2612	+	12.7567i	1.25608	+	0.408124i	0.395982	+	0.918258i	$0.370404\pi$
$978$	−6.80180	+	9.36187i	−0.217498	+	0.299360i
$979$	38.9631	+	28.3083i	1.24527	+	0.904738i
$980$	2.11069	−	0.738230i	0.0674236	−	0.0235819i
$981$	39.9898	−	29.0543i	1.27678	−	0.927631i
$982$			14.9505i			0.477091i
$983$	−31.7877	−	43.7520i	−1.01387	−	1.39547i	−0.916413	−	0.400234i	$-0.868929\pi$
$983$	−31.7877	−	43.7520i	−1.01387	−	1.39547i	−0.0974577	−	0.995240i	$-0.531071\pi$
$984$	0.196827	+	0.605770i	0.00627460	+	0.0193112i
$985$	−13.4951	−	38.5842i	−0.429990	−	1.22939i
$986$	−12.5776	+	38.7099i	−0.400553	+	1.23278i
$987$	3.44771	−	1.12023i	0.109742	−	0.0356572i
$988$	33.6916	−	10.9470i	1.07187	−	0.348272i
$989$	0.188533	−	0.580244i	0.00599499	−	0.0184507i
$990$	14.4778	−	11.0202i	0.460134	−	0.350244i
$991$	−9.32667	−	28.7045i	−0.296271	−	0.911830i	−0.982791	−	0.184719i	$-0.940863\pi$
$991$	−9.32667	−	28.7045i	−0.296271	−	0.911830i	0.686520	−	0.727111i	$-0.259137\pi$
$992$	−2.72273	−	3.74752i	−0.0864468	−	0.118984i
$993$		−	1.73918i		−	0.0551911i
$994$	−6.82418	+	4.95806i	−0.216450	+	0.157260i
$995$	29.9693	−	43.2452i	0.950092	−	1.37096i
$996$	−3.47884	−	2.52753i	−0.110231	−	0.0800877i
$997$	1.34911	−	1.85690i	0.0427269	−	0.0588085i	−0.787119	−	0.616801i	$-0.788428\pi$
$997$	1.34911	−	1.85690i	0.0427269	−	0.0588085i	0.829846	+	0.557993i	$0.188428\pi$
$998$	22.4617	+	7.29826i	0.711014	+	0.231023i
$999$	−1.49521			−0.0473062

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.m.b.29.8	✓	40
25.12	odd	20		8750.2.a.be.1.12		20
25.13	odd	20		8750.2.a.bf.1.9		20
25.19	even	10	inner	350.2.m.b.169.8	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.m.b.29.8	✓	40	1.1	even	1	trivial
350.2.m.b.169.8	yes	40	25.19	even	10	inner
8750.2.a.be.1.12		20	25.12	odd	20
8750.2.a.bf.1.9		20	25.13	odd	20

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 + 0.309017i) q^{2} +(0.454807 - 0.625988i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.27366 + 1.83787i) q^{5} +(0.625988 - 0.454807i) q^{6} +1.00000i q^{7} +(0.587785 + 0.809017i) q^{8} +(0.742040 + 2.28376i) q^{9} +O(q^{10})\)	\(q+(0.951057 + 0.309017i) q^{2} +(0.454807 - 0.625988i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.27366 + 1.83787i) q^{5} +(0.625988 - 0.454807i) q^{6} +1.00000i q^{7} +(0.587785 + 0.809017i) q^{8} +(0.742040 + 2.28376i) q^{9} +(-1.77926 + 1.35434i) q^{10} +(-1.04713 + 3.22273i) q^{11} +(0.735893 - 0.239106i) q^{12} +(5.05447 - 1.64230i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(0.571215 + 1.63318i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-2.43606 - 3.35295i) q^{17} +2.40129i q^{18} +(5.39266 - 3.91800i) q^{19} +(-2.11069 + 0.738230i) q^{20} +(0.625988 + 0.454807i) q^{21} +(-1.99176 + 2.74142i) q^{22} +(-0.249307 - 0.0810046i) q^{23} +0.773763 q^{24} +(-1.75556 - 4.68167i) q^{25} +5.31458 q^{26} +(3.97477 + 1.29148i) q^{27} +(-0.587785 + 0.809017i) q^{28} +(-7.94519 - 5.77252i) q^{29} +(0.0385788 + 1.72976i) q^{30} +(-3.74752 + 2.72273i) q^{31} +1.00000i q^{32} +(1.54115 + 2.12121i) q^{33} +(-1.28071 - 3.94163i) q^{34} +(-1.83787 - 1.27366i) q^{35} +(-0.742040 + 2.28376i) q^{36} +(-0.340253 + 0.110555i) q^{37} +(6.33946 - 2.05981i) q^{38} +(1.27075 - 3.91096i) q^{39} +(-2.23551 + 0.0498587i) q^{40} +(0.254376 + 0.782888i) q^{41} +(0.454807 + 0.625988i) q^{42} +2.32743i q^{43} +(-2.74142 + 1.99176i) q^{44} +(-5.14238 - 1.54497i) q^{45} +(-0.212073 - 0.154080i) q^{46} +(2.75381 - 3.79030i) q^{47} +(0.735893 + 0.239106i) q^{48} -1.00000 q^{49} +(-0.222920 - 4.99503i) q^{50} -3.20684 q^{51} +(5.05447 + 1.64230i) q^{52} +(0.624792 - 0.859953i) q^{53} +(3.38114 + 2.45654i) q^{54} +(-4.58928 - 6.02916i) q^{55} +(-0.809017 + 0.587785i) q^{56} -5.15767i q^{57} +(-5.77252 - 7.94519i) q^{58} +(-0.489148 - 1.50544i) q^{59} +(-0.497834 + 1.65702i) q^{60} +(0.462805 - 1.42437i) q^{61} +(-4.40547 + 1.43142i) q^{62} +(-2.28376 + 0.742040i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-3.41936 + 11.3812i) q^{65} +(0.810229 + 2.49363i) q^{66} +(4.68745 + 6.45172i) q^{67} -4.14447i q^{68} +(-0.164094 + 0.119221i) q^{69} +(-1.35434 - 1.77926i) q^{70} +(6.82418 + 4.95806i) q^{71} +(-1.41144 + 1.94268i) q^{72} +(-1.37982 - 0.448330i) q^{73} -0.357763 q^{74} +(-3.72911 - 1.03030i) q^{75} +6.66570 q^{76} +(-3.22273 - 1.04713i) q^{77} +(2.41711 - 3.32686i) q^{78} +(-5.16613 - 3.75342i) q^{79} +(-2.14151 - 0.643393i) q^{80} +(-3.21185 + 2.33355i) q^{81} +0.823177i q^{82} +(-3.26654 - 4.49600i) q^{83} +(0.239106 + 0.735893i) q^{84} +(9.26502 - 0.206638i) q^{85} +(-0.719216 + 2.21352i) q^{86} +(-7.22705 + 2.34821i) q^{87} +(-3.22273 + 1.04713i) q^{88} +(4.39198 - 13.5171i) q^{89} +(-4.41327 - 3.05844i) q^{90} +(1.64230 + 5.05447i) q^{91} +(-0.154080 - 0.212073i) q^{92} +3.58422i q^{93} +(3.79030 - 2.75381i) q^{94} +(0.332343 + 14.9013i) q^{95} +(0.625988 + 0.454807i) q^{96} +(11.3670 - 15.6454i) q^{97} +(-0.951057 - 0.309017i) q^{98} -8.13696 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9}+O(q^{10}) \) 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9	\( 40 q + 10 q^{4} + 6 q^{5} - 2 q^{6} + 20 q^{9} - 4 q^{10} - 6 q^{11} + 10 q^{12} + 10 q^{14} - 12 q^{15} - 10 q^{16} - 2 q^{19} + 4 q^{20} - 2 q^{21} - 10 q^{22} - 10 q^{23} - 8 q^{24} - 10 q^{25} + 12 q^{26} - 30 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{31} - 60 q^{33} - 4 q^{35} - 20 q^{36} + 10 q^{37} + 10 q^{38} + 36 q^{39} - 6 q^{40} - 34 q^{41} + 6 q^{44} + 112 q^{45} - 6 q^{46} + 30 q^{47} + 10 q^{48} - 40 q^{49} - 16 q^{50} + 44 q^{51} + 10 q^{53} + 20 q^{54} + 34 q^{55} - 10 q^{56} + 20 q^{58} + 12 q^{59} + 2 q^{60} + 2 q^{61} + 10 q^{64} - 106 q^{65} + 10 q^{66} - 30 q^{67} + 84 q^{69} + 4 q^{70} + 16 q^{71} - 110 q^{73} - 60 q^{74} + 10 q^{75} + 32 q^{76} + 20 q^{77} - 20 q^{78} + 4 q^{79} - 4 q^{80} - 20 q^{81} + 10 q^{83} + 2 q^{84} - 42 q^{85} - 14 q^{86} - 20 q^{87} + 20 q^{88} - 38 q^{90} + 2 q^{91} - 30 q^{92} + 6 q^{94} + 64 q^{95} - 2 q^{96} + 30 q^{97} - 72 q^{99}+O(q^{100}) \) 40 * q + 10 * q^4 + 6 * q^5 - 2 * q^6 + 20 * q^9 - 4 * q^10 - 6 * q^11 + 10 * q^12 + 10 * q^14 - 12 * q^15 - 10 * q^16 - 2 * q^19 + 4 * q^20 - 2 * q^21 - 10 * q^22 - 10 * q^23 - 8 * q^24 - 10 * q^25 + 12 * q^26 - 30 * q^27 + 4 * q^29 - 22 * q^30 - 24 * q^31 - 60 * q^33 - 4 * q^35 - 20 * q^36 + 10 * q^37 + 10 * q^38 + 36 * q^39 - 6 * q^40 - 34 * q^41 + 6 * q^44 + 112 * q^45 - 6 * q^46 + 30 * q^47 + 10 * q^48 - 40 * q^49 - 16 * q^50 + 44 * q^51 + 10 * q^53 + 20 * q^54 + 34 * q^55 - 10 * q^56 + 20 * q^58 + 12 * q^59 + 2 * q^60 + 2 * q^61 + 10 * q^64 - 106 * q^65 + 10 * q^66 - 30 * q^67 + 84 * q^69 + 4 * q^70 + 16 * q^71 - 110 * q^73 - 60 * q^74 + 10 * q^75 + 32 * q^76 + 20 * q^77 - 20 * q^78 + 4 * q^79 - 4 * q^80 - 20 * q^81 + 10 * q^83 + 2 * q^84 - 42 * q^85 - 14 * q^86 - 20 * q^87 + 20 * q^88 - 38 * q^90 + 2 * q^91 - 30 * q^92 + 6 * q^94 + 64 * q^95 - 2 * q^96 + 30 * q^97 - 72 * q^99

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