LMFDB - Embedded newform 210.3.w.b.17.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(17,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("210.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.w (of order $12$, 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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			17.5
Character	$\chi$	$=$	210.17
Dual form			210.3.w.b.173.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 + 0.366025i) q^{2} +(-1.72513 + 2.45437i) q^{3} +(1.73205 + 1.00000i) q^{4} +(2.34013 + 4.41857i) q^{5} +(-3.25493 + 2.72129i) q^{6} +(-6.07917 + 3.47039i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-3.04785 - 8.46821i) q^{9} +O(q^{10})$	\(q+(1.36603 + 0.366025i) q^{2} +(-1.72513 + 2.45437i) q^{3} +(1.73205 + 1.00000i) q^{4} +(2.34013 + 4.41857i) q^{5} +(-3.25493 + 2.72129i) q^{6} +(-6.07917 + 3.47039i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-3.04785 - 8.46821i) q^{9} +(1.57936 + 6.89243i) q^{10} +(5.23131 + 3.02030i) q^{11} +(-5.44238 + 2.52596i) q^{12} +(-7.33446 - 7.33446i) q^{13} +(-9.57456 + 2.51551i) q^{14} +(-14.8818 - 1.87909i) q^{15} +(2.00000 + 3.46410i) q^{16} +(-22.5211 + 6.03451i) q^{17} +(-1.06386 - 12.6834i) q^{18} +(17.0920 + 29.6042i) q^{19} +(-0.365356 + 9.99332i) q^{20} +(1.96974 - 20.9074i) q^{21} +(6.04060 + 6.04060i) q^{22} +(7.11456 - 26.5519i) q^{23} +(-8.35900 + 1.45848i) q^{24} +(-14.0476 + 20.6801i) q^{25} +(-7.33446 - 12.7037i) q^{26} +(26.0420 + 7.12823i) q^{27} +(-13.9998 - 0.0682753i) q^{28} +6.86667 q^{29} +(-19.6412 - 8.01401i) q^{30} +(38.9114 + 22.4655i) q^{31} +(1.46410 + 5.46410i) q^{32} +(-16.4376 + 7.62915i) q^{33} -32.9732 q^{34} +(-29.5602 - 18.7401i) q^{35} +(3.18919 - 17.7152i) q^{36} +(-9.14352 + 34.1241i) q^{37} +(12.5122 + 46.6962i) q^{38} +(30.6544 - 5.34857i) q^{39} +(-4.15690 + 13.5174i) q^{40} -18.2221 q^{41} +(10.3434 - 27.8391i) q^{42} +(17.2571 - 17.2571i) q^{43} +(6.04060 + 10.4626i) q^{44} +(30.2851 - 33.2838i) q^{45} +(19.4373 - 33.6664i) q^{46} +(6.24890 - 23.3212i) q^{47} +(-11.9524 - 1.06729i) q^{48} +(24.9127 - 42.1943i) q^{49} +(-26.7588 + 23.1077i) q^{50} +(24.0409 - 65.6854i) q^{51} +(-5.36920 - 20.0381i) q^{52} +(77.2906 - 20.7100i) q^{53} +(32.9650 + 19.2694i) q^{54} +(-1.10348 + 30.1828i) q^{55} +(-19.0991 - 5.21756i) q^{56} +(-102.145 - 9.12106i) q^{57} +(9.38005 + 2.51338i) q^{58} +(97.9689 + 56.5624i) q^{59} +(-23.8970 - 18.1365i) q^{60} +(16.8856 - 9.74888i) q^{61} +(44.9310 + 44.9310i) q^{62} +(47.9164 + 40.9025i) q^{63} +8.00000i q^{64} +(15.2443 - 49.5715i) q^{65} +(-25.2467 + 4.40503i) q^{66} +(10.9297 - 2.92860i) q^{67} +(-45.0422 - 12.0690i) q^{68} +(52.8946 + 63.2672i) q^{69} +(-33.5207 - 36.4193i) q^{70} -80.6556i q^{71} +(10.8407 - 23.0321i) q^{72} +(-1.93873 + 0.519481i) q^{73} +(-24.9805 + 43.2676i) q^{74} +(-26.5225 - 70.1538i) q^{75} +68.3679i q^{76} +(-42.2837 - 0.206212i) q^{77} +(43.8324 + 3.91400i) q^{78} +(-73.1841 + 42.2528i) q^{79} +(-10.6261 + 16.9436i) q^{80} +(-62.4212 + 51.6196i) q^{81} +(-24.8919 - 6.66976i) q^{82} +(4.56113 - 4.56113i) q^{83} +(24.3191 - 34.2430i) q^{84} +(-79.3662 - 85.3897i) q^{85} +(29.8902 - 17.2571i) q^{86} +(-11.8459 + 16.8533i) q^{87} +(4.42202 + 16.5032i) q^{88} +(21.5716 - 12.4544i) q^{89} +(53.5529 - 34.3815i) q^{90} +(70.0410 + 19.1340i) q^{91} +(38.8747 - 38.8747i) q^{92} +(-122.266 + 56.7469i) q^{93} +(17.0723 - 29.5701i) q^{94} +(-90.8109 + 144.800i) q^{95} +(-15.9367 - 5.83284i) q^{96} +(38.4454 - 38.4454i) q^{97} +(49.4756 - 48.5197i) q^{98} +(9.63229 - 53.5053i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{2} + 6 q^{3} + 12 q^{5} + 4 q^{7} + 128 q^{8} + 16 q^{9}+O(q^{10}) $ 64 * q + 32 * q^2 + 6 * q^3 + 12 * q^5 + 4 * q^7 + 128 * q^8 + 16 * q^9	$ 64 q + 32 q^{2} + 6 q^{3} + 12 q^{5} + 4 q^{7} + 128 q^{8} + 16 q^{9} + 24 q^{10} - 12 q^{12} + 16 q^{14} + 68 q^{15} + 128 q^{16} - 12 q^{18} + 36 q^{21} + 16 q^{22} + 12 q^{23} - 16 q^{25} + 8 q^{28} + 112 q^{29} + 22 q^{30} - 128 q^{32} + 30 q^{33} + 16 q^{36} - 32 q^{37} - 24 q^{38} - 64 q^{39} - 88 q^{42} + 32 q^{43} + 16 q^{44} - 474 q^{45} - 24 q^{46} + 96 q^{47} - 40 q^{50} - 84 q^{51} - 56 q^{53} + 72 q^{54} - 220 q^{57} + 56 q^{58} - 672 q^{59} + 24 q^{60} + 600 q^{61} - 114 q^{63} - 28 q^{65} + 16 q^{67} + 40 q^{72} - 624 q^{73} + 64 q^{74} - 144 q^{75} - 208 q^{77} - 248 q^{78} + 48 q^{80} - 64 q^{81} - 192 q^{82} - 160 q^{84} - 152 q^{85} - 672 q^{87} - 16 q^{88} - 144 q^{89} - 232 q^{91} - 48 q^{92} - 202 q^{93} - 136 q^{95} - 48 q^{96} - 128 q^{98} - 160 q^{99}+O(q^{100}) $ 64 * q + 32 * q^2 + 6 * q^3 + 12 * q^5 + 4 * q^7 + 128 * q^8 + 16 * q^9 + 24 * q^10 - 12 * q^12 + 16 * q^14 + 68 * q^15 + 128 * q^16 - 12 * q^18 + 36 * q^21 + 16 * q^22 + 12 * q^23 - 16 * q^25 + 8 * q^28 + 112 * q^29 + 22 * q^30 - 128 * q^32 + 30 * q^33 + 16 * q^36 - 32 * q^37 - 24 * q^38 - 64 * q^39 - 88 * q^42 + 32 * q^43 + 16 * q^44 - 474 * q^45 - 24 * q^46 + 96 * q^47 - 40 * q^50 - 84 * q^51 - 56 * q^53 + 72 * q^54 - 220 * q^57 + 56 * q^58 - 672 * q^59 + 24 * q^60 + 600 * q^61 - 114 * q^63 - 28 * q^65 + 16 * q^67 + 40 * q^72 - 624 * q^73 + 64 * q^74 - 144 * q^75 - 208 * q^77 - 248 * q^78 + 48 * q^80 - 64 * q^81 - 192 * q^82 - 160 * q^84 - 152 * q^85 - 672 * q^87 - 16 * q^88 - 144 * q^89 - 232 * q^91 - 48 * q^92 - 202 * q^93 - 136 * q^95 - 48 * q^96 - 128 * q^98 - 160 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.36603	+	0.366025i	0.683013	+	0.183013i
$2$	1.36603	+	0.366025i	0.683013	+	0.183013i
$3$	−1.72513	+	2.45437i	−0.575044	+	0.818123i
$3$	−1.72513	+	2.45437i	−0.575044	+	0.818123i
$4$	1.73205	+	1.00000i	0.433013	+	0.250000i
$5$	2.34013	+	4.41857i	0.468025	+	0.883715i
$5$	2.34013	+	4.41857i	0.468025	+	0.883715i
$6$	−3.25493	+	2.72129i	−0.542489	+	0.453548i
$7$	−6.07917	+	3.47039i	−0.868454	+	0.495771i
$7$	−6.07917	+	3.47039i	−0.868454	+	0.495771i
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$	−3.04785	−	8.46821i	−0.338650	−	0.940913i
$10$	1.57936	+	6.89243i	0.157936	+	0.689243i
$11$	5.23131	+	3.02030i	0.475574	+	0.274573i	0.718570	−	0.695455i	$-0.244797\pi$
$11$	5.23131	+	3.02030i	0.475574	+	0.274573i	−0.242996	+	0.970027i	$0.578130\pi$
$12$	−5.44238	+	2.52596i	−0.453532	+	0.210497i
$13$	−7.33446	−	7.33446i	−0.564189	−	0.564189i	0.366305	−	0.930495i	$-0.380623\pi$
$13$	−7.33446	−	7.33446i	−0.564189	−	0.564189i	−0.930495	+	0.366305i	$0.880623\pi$
$14$	−9.57456	+	2.51551i	−0.683897	+	0.179680i
$15$	−14.8818	−	1.87909i	−0.992122	−	0.125272i
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	−22.5211	+	6.03451i	−1.32477	+	0.354971i	−0.850763	−	0.525549i	$-0.823860\pi$
$17$	−22.5211	+	6.03451i	−1.32477	+	0.354971i	−0.474008	+	0.880520i	$0.657193\pi$
$18$	−1.06386	−	12.6834i	−0.0591032	−	0.704632i
$19$	17.0920	+	29.6042i	0.899578	+	1.55811i	0.828034	+	0.560678i	$0.189459\pi$
$19$	17.0920	+	29.6042i	0.899578	+	1.55811i	0.0715438	+	0.997437i	$0.477207\pi$
$20$	−0.365356	+	9.99332i	−0.0182678	+	0.499666i
$21$	1.96974	−	20.9074i	0.0937974	−	0.995591i
$22$	6.04060	+	6.04060i	0.274573	+	0.274573i
$23$	7.11456	−	26.5519i	0.309329	−	1.15443i	−0.619826	−	0.784739i	$-0.712797\pi$
$23$	7.11456	−	26.5519i	0.309329	−	1.15443i	0.929155	−	0.369691i	$-0.120536\pi$
$24$	−8.35900	+	1.45848i	−0.348292	+	0.0607698i
$25$	−14.0476	+	20.6801i	−0.561904	+	0.827202i
$26$	−7.33446	−	12.7037i	−0.282095	−	0.488602i
$27$	26.0420	+	7.12823i	0.964520	+	0.264009i
$28$	−13.9998	−	0.0682753i	−0.499994	−	0.00243840i
$29$	6.86667			0.236782			0.118391	−	0.992967i	$-0.462226\pi$
$29$	6.86667			0.236782			0.118391	+	0.992967i	$0.462226\pi$
$30$	−19.6412	−	8.01401i	−0.654706	−	0.267134i
$31$	38.9114	+	22.4655i	1.25520	+	0.724693i	0.972138	−	0.234407i	$-0.0753150\pi$
$31$	38.9114	+	22.4655i	1.25520	+	0.724693i	0.283066	+	0.959100i	$0.408648\pi$
$32$	1.46410	+	5.46410i	0.0457532	+	0.170753i
$33$	−16.4376	+	7.62915i	−0.498110	+	0.231186i
$34$	−32.9732			−0.969800
$35$	−29.5602	−	18.7401i	−0.844578	−	0.535432i
$36$	3.18919	−	17.7152i	0.0885885	−	0.492090i
$37$	−9.14352	+	34.1241i	−0.247122	+	0.922272i	0.725183	+	0.688556i	$0.241755\pi$
$37$	−9.14352	+	34.1241i	−0.247122	+	0.922272i	−0.972305	+	0.233716i	$0.924911\pi$
$38$	12.5122	+	46.6962i	0.329268	+	1.22885i
$39$	30.6544	−	5.34857i	0.786010	−	0.137143i
$40$	−4.15690	+	13.5174i	−0.103922	+	0.337935i
$41$	−18.2221			−0.444442			−0.222221	−	0.974996i	$-0.571331\pi$
$41$	−18.2221			−0.444442			−0.222221	+	0.974996i	$0.571331\pi$
$42$	10.3434	−	27.8391i	0.246271	−	0.662835i
$43$	17.2571	−	17.2571i	0.401329	−	0.401329i	−0.477372	−	0.878701i	$-0.658411\pi$
$43$	17.2571	−	17.2571i	0.401329	−	0.401329i	0.878701	+	0.477372i	$0.158411\pi$
$44$	6.04060	+	10.4626i	0.137286	+	0.237787i
$45$	30.2851	−	33.2838i	0.673002	−	0.739641i
$46$	19.4373	−	33.6664i	0.422551	−	0.731879i
$47$	6.24890	−	23.3212i	0.132955	−	0.496196i	−0.867043	−	0.498234i	$-0.833982\pi$
$47$	6.24890	−	23.3212i	0.132955	−	0.496196i	0.999998	+	0.00203792i	$0.000648691\pi$
$48$	−11.9524	−	1.06729i	−0.249009	−	0.0222352i
$49$	24.9127	−	42.1943i	0.508423	−	0.861107i
$50$	−26.7588	+	23.1077i	−0.535176	+	0.462154i
$51$	24.0409	−	65.6854i	0.471391	−	1.28795i
$52$	−5.36920	−	20.0381i	−0.103254	−	0.385349i
$53$	77.2906	−	20.7100i	1.45831	−	0.390754i	0.559407	−	0.828893i	$-0.311029\pi$
$53$	77.2906	−	20.7100i	1.45831	−	0.390754i	0.898907	+	0.438139i	$0.144362\pi$
$54$	32.9650	+	19.2694i	0.610463	+	0.356841i
$55$	−1.10348	+	30.1828i	−0.0200633	+	0.548779i
$56$	−19.0991	−	5.21756i	−0.341056	−	0.0931707i
$57$	−102.145	−	9.12106i	−1.79203	−	0.160019i
$58$	9.38005	+	2.51338i	0.161725	+	0.0433341i
$59$	97.9689	+	56.5624i	1.66049	+	0.958684i	0.972481	+	0.232982i	$0.0748484\pi$
$59$	97.9689	+	56.5624i	1.66049	+	0.958684i	0.688009	+	0.725702i	$0.258485\pi$
$60$	−23.8970	−	18.1365i	−0.398284	−	0.302275i
$61$	16.8856	−	9.74888i	0.276812	−	0.159818i	−0.355167	−	0.934803i	$-0.615576\pi$
$61$	16.8856	−	9.74888i	0.276812	−	0.159818i	0.631979	+	0.774985i	$0.282243\pi$
$62$	44.9310	+	44.9310i	0.724693	+	0.724693i
$63$	47.9164	+	40.9025i	0.760578	+	0.649246i
$64$			8.00000i			0.125000i
$65$	15.2443	−	49.5715i	0.234528	−	0.762638i
$66$	−25.2467	+	4.40503i	−0.382525	+	0.0667429i
$67$	10.9297	−	2.92860i	0.163130	−	0.0437104i	−0.176330	−	0.984331i	$-0.556423\pi$
$67$	10.9297	−	2.92860i	0.163130	−	0.0437104i	0.339459	+	0.940621i	$0.389756\pi$
$68$	−45.0422	−	12.0690i	−0.662386	−	0.177486i
$69$	52.8946	+	63.2672i	0.766588	+	0.916916i
$70$	−33.5207	−	36.4193i	−0.478867	−	0.520275i
$71$		−	80.6556i		−	1.13599i	−0.823030	−	0.567997i	$-0.807718\pi$
$71$		−	80.6556i		−	1.13599i	0.823030	−	0.567997i	$-0.192282\pi$
$72$	10.8407	−	23.0321i	0.150566	−	0.319891i
$73$	−1.93873	+	0.519481i	−0.0265579	+	0.00711618i	−0.272074	−	0.962276i	$-0.587709\pi$
$73$	−1.93873	+	0.519481i	−0.0265579	+	0.00711618i	0.245516	+	0.969393i	$0.421043\pi$
$74$	−24.9805	+	43.2676i	−0.337575	+	0.584697i
$75$	−26.5225	−	70.1538i	−0.353633	−	0.935384i
$76$			68.3679i			0.899578i
$77$	−42.2837	−	0.206212i	−0.549139	−	0.00267807i
$78$	43.8324	+	3.91400i	0.561954	+	0.0501796i
$79$	−73.1841	+	42.2528i	−0.926381	+	0.534846i	−0.885665	−	0.464325i	$-0.846297\pi$
$79$	−73.1841	+	42.2528i	−0.926381	+	0.534846i	−0.0407156	+	0.999171i	$0.512964\pi$
$80$	−10.6261	+	16.9436i	−0.132827	+	0.211795i
$81$	−62.4212	+	51.6196i	−0.770633	+	0.637280i
$82$	−24.8919	−	6.66976i	−0.303559	−	0.0813385i
$83$	4.56113	−	4.56113i	0.0549533	−	0.0549533i	−0.679096	−	0.734049i	$-0.737628\pi$
$83$	4.56113	−	4.56113i	0.0549533	−	0.0549533i	0.734049	+	0.679096i	$0.237628\pi$
$84$	24.3191	−	34.2430i	0.289513	−	0.407654i
$85$	−79.3662	−	85.3897i	−0.933720	−	1.00458i
$86$	29.8902	−	17.2571i	0.347561	−	0.200664i
$87$	−11.8459	+	16.8533i	−0.136160	+	0.193717i
$88$	4.42202	+	16.5032i	0.0502503	+	0.187537i
$89$	21.5716	−	12.4544i	0.242377	−	0.139937i	−0.373892	−	0.927472i	$-0.621977\pi$
$89$	21.5716	−	12.4544i	0.242377	−	0.139937i	0.616269	+	0.787536i	$0.288643\pi$
$90$	53.5529	−	34.3815i	0.595032	−	0.382016i
$91$	70.0410	+	19.1340i	0.769681	+	0.210264i
$92$	38.8747	−	38.8747i	0.422551	−	0.422551i
$93$	−122.266	+	56.7469i	−1.31469	+	0.610182i
$94$	17.0723	−	29.5701i	0.181620	−	0.314576i
$95$	−90.8109	+	144.800i	−0.955904	+	1.52421i
$96$	−15.9367	−	5.83284i	−0.166007	−	0.0607588i
$97$	38.4454	−	38.4454i	0.396345	−	0.396345i	−0.480597	−	0.876942i	$-0.659580\pi$
$97$	38.4454	−	38.4454i	0.396345	−	0.396345i	0.876942	+	0.480597i	$0.159580\pi$
$98$	49.4756	−	48.5197i	0.504853	−	0.495099i
$99$	9.63229	−	53.5053i	0.0972959	−	0.540457i
$100$	−45.0112	+	21.7713i	−0.450112	+	0.217713i
$101$	11.7303	−	20.3175i	0.116142	−	0.201163i	−0.802094	−	0.597198i	$-0.796281\pi$
$101$	11.7303	−	20.3175i	0.116142	−	0.201163i	0.918235	+	0.396035i	$0.129614\pi$
$102$	56.8831	−	80.9284i	0.557677	−	0.793416i
$103$	−48.6683	+	181.632i	−0.472507	+	1.76342i	0.158207	+	0.987406i	$0.449429\pi$
$103$	−48.6683	+	181.632i	−0.472507	+	1.76342i	−0.630714	+	0.776015i	$0.717238\pi$
$104$		−	29.3379i		−	0.282095i
$105$	96.9904	−	40.2226i	0.923719	−	0.383072i
$106$	113.161			1.06756
$107$	−80.3041	−	21.5174i	−0.750506	−	0.201097i	−0.136763	−	0.990604i	$-0.543670\pi$
$107$	−80.3041	−	21.5174i	−0.750506	−	0.201097i	−0.613742	+	0.789506i	$0.710337\pi$
$108$	37.9779	+	38.3885i	0.351647	+	0.355449i
$109$	28.9994	+	16.7428i	0.266049	+	0.153604i	0.627091	−	0.778946i	$-0.284245\pi$
$109$	28.9994	+	16.7428i	0.266049	+	0.153604i	−0.361042	+	0.932550i	$0.617579\pi$
$110$	−12.5551	+	40.8266i	−0.114137	+	0.371151i
$111$	−67.9793	−	81.3100i	−0.612426	−	0.732523i
$112$	−24.1801	−	14.1181i	−0.215894	−	0.126054i
$113$	−12.6123	−	12.6123i	−0.111613	−	0.111613i	0.649095	−	0.760708i	$-0.275148\pi$
$113$	−12.6123	−	12.6123i	−0.111613	−	0.111613i	−0.760708	+	0.649095i	$0.775148\pi$
$114$	−136.195	−	49.8474i	−1.19469	−	0.437258i
$115$	133.970	−	30.6986i	1.16496	−	0.266944i
$116$	11.8934	+	6.86667i	0.102530	+	0.0591954i
$117$	−39.7555	+	84.4641i	−0.339790	+	0.721916i
$118$	113.125	+	113.125i	0.958684	+	0.958684i
$119$	115.968	−	114.842i	0.974518	−	0.965059i
$120$	−26.0055	−	33.5218i	−0.216713	−	0.279349i
$121$	−42.2556	−	73.1888i	−0.349220	−	0.604866i
$122$	26.6344	−	7.13668i	0.218315	−	0.0584973i
$123$	31.4355	−	44.7238i	0.255573	−	0.363608i
$124$	44.9310	+	77.8227i	0.362346	+	0.627602i
$125$	−124.250	−	13.6764i	−0.993997	−	0.109412i
$126$	50.4837	+	73.4125i	0.400664	+	0.582639i
$127$	147.938	+	147.938i	1.16486	+	1.16486i	0.983397	+	0.181467i	$0.0580847\pi$
$127$	147.938	+	147.938i	1.16486	+	1.16486i	0.181467	+	0.983397i	$0.441915\pi$
$128$	−2.92820	+	10.9282i	−0.0228766	+	0.0853766i
$129$	12.5846	+	72.1262i	0.0975547	+	0.559118i
$130$	38.9685	−	62.1361i	0.299758	−	0.477970i
$131$	−74.8356	−	129.619i	−0.571264	−	0.989459i	−0.996436	−	0.0843465i	$-0.973120\pi$
$131$	−74.8356	−	129.619i	−0.571264	−	0.989459i	0.425172	−	0.905113i	$-0.360214\pi$
$132$	−36.0999	−	3.22354i	−0.273484	−	0.0244207i
$133$	−206.643	−	120.653i	−1.55371	−	0.907166i
$134$	16.0022			0.119419
$135$	29.4451	+	131.750i	0.218112	+	0.975924i
$136$	−57.1113	−	32.9732i	−0.419936	−	0.242450i
$137$	−6.54134	−	24.4126i	−0.0477470	−	0.178194i	0.937934	−	0.346813i	$-0.112736\pi$
$137$	−6.54134	−	24.4126i	−0.0477470	−	0.178194i	−0.985681	+	0.168619i	$0.946069\pi$
$138$	49.0979	+	105.785i	0.355782	+	0.766561i
$139$	−237.437			−1.70818			−0.854090	−	0.520125i	$-0.825885\pi$
$139$	−237.437			−1.70818			−0.854090	+	0.520125i	$0.825885\pi$
$140$	−32.4597	−	62.0191i	−0.231855	−	0.442993i
$141$	46.4587	+	55.5693i	0.329494	+	0.394108i
$142$	29.5220	−	110.178i	0.207901	−	0.775899i
$143$	−16.2166	−	60.5211i	−0.113403	−	0.423225i
$144$	23.2391	−	27.4945i	0.161382	−	0.190934i
$145$	16.0689	+	30.3409i	0.110820	+	0.209248i
$146$	−2.83850			−0.0194418
$147$	60.5826	+	133.936i	0.412126	+	0.911127i
$148$	−49.9611	+	49.9611i	−0.337575	+	0.337575i
$149$	−19.6566	−	34.0462i	−0.131924	−	0.228498i	0.792494	−	0.609879i	$-0.208782\pi$
$149$	−19.6566	−	34.0462i	−0.131924	−	0.228498i	−0.924418	+	0.381381i	$0.875449\pi$
$150$	−10.5523	−	105.540i	−0.0703490	−	0.703599i
$151$	−19.0601	+	33.0130i	−0.126226	+	0.218629i	−0.922211	−	0.386686i	$-0.873620\pi$
$151$	−19.0601	+	33.0130i	−0.126226	+	0.218629i	0.795986	+	0.605315i	$0.206953\pi$
$152$	−25.0244	+	93.3923i	−0.164634	+	0.614423i
$153$	119.742	+	172.321i	0.782631	+	1.12628i
$154$	−57.6851	−	15.7586i	−0.374579	−	0.102329i
$155$	−8.20789	+	224.505i	−0.0529541	+	1.44842i
$156$	58.4435	+	21.3904i	0.374638	+	0.137118i
$157$	15.5225	+	57.9306i	0.0988692	+	0.368985i	0.997578	−	0.0695618i	$-0.0221601\pi$
$157$	15.5225	+	57.9306i	0.0988692	+	0.368985i	−0.898708	+	0.438547i	$0.855493\pi$
$158$	−115.437	+	30.9312i	−0.730613	+	0.195767i
$159$	−82.5066	+	225.427i	−0.518909	+	1.41778i
$160$	−20.7174	+	19.2559i	−0.129483	+	0.120350i
$161$	48.8949	+	186.104i	0.303695	+	1.15592i
$162$	−104.163	+	47.6660i	−0.642982	+	0.294234i
$163$	5.64718	+	1.51316i	0.0346453	+	0.00928317i	0.276100	−	0.961129i	$-0.410958\pi$
$163$	5.64718	+	1.51316i	0.0346453	+	0.00928317i	−0.241455	+	0.970412i	$0.577625\pi$
$164$	−31.5616	−	18.2221i	−0.192449	−	0.111110i
$165$	−72.1761	−	54.7777i	−0.437431	−	0.331986i
$166$	7.90010	−	4.56113i	0.0475910	−	0.0274767i
$167$	6.13829	+	6.13829i	0.0367562	+	0.0367562i	0.725246	−	0.688490i	$-0.241726\pi$
$167$	6.13829	+	6.13829i	0.0367562	+	0.0367562i	−0.688490	+	0.725246i	$0.741726\pi$
$168$	45.7543	−	37.8753i	0.272347	−	0.225448i
$169$		−	61.4113i		−	0.363381i
$170$	−77.1615	−	145.695i	−0.453891	−	0.857027i
$171$	198.601	−	234.968i	1.16141	−	1.37408i
$172$	47.1474	−	12.6331i	0.274113	−	0.0734483i
$173$	−194.574	−	52.1359i	−1.12470	−	0.301363i	−0.351918	−	0.936031i	$-0.614470\pi$
$173$	−194.574	−	52.1359i	−1.12470	−	0.301363i	−0.772785	+	0.634668i	$0.781137\pi$
$174$	−22.3506	+	18.6862i	−0.128451	+	0.107392i
$175$	13.6299	−	174.468i	0.0778852	−	0.996962i
$176$			24.1624i			0.137286i
$177$	−307.834	+	142.874i	−1.73918	+	0.807199i
$178$	34.0259	−	9.11722i	0.191157	−	0.0512203i
$179$	17.6436	−	30.5596i	0.0985676	−	0.170724i	−0.812524	−	0.582927i	$-0.801907\pi$
$179$	17.6436	−	30.5596i	0.0985676	−	0.170724i	0.911092	+	0.412203i	$0.135241\pi$
$180$	85.7391	−	27.3642i	0.476329	−	0.152023i
$181$		−	194.579i		−	1.07502i	−0.843258	−	0.537510i	$-0.819365\pi$
$181$		−	194.579i		−	1.07502i	0.843258	−	0.537510i	$-0.180635\pi$
$182$	88.6742	+	51.7743i	0.487221	+	0.284474i
$183$	−5.20245	+	58.2615i	−0.0284287	+	0.318369i
$184$	67.3329	−	38.8747i	0.365940	−	0.211275i
$185$	−172.177	+	39.4533i	−0.930685	+	0.213261i
$186$	−187.789	+	32.7653i	−1.00962	+	0.176158i
$187$	−136.041	−	36.4521i	−0.727492	−	0.194931i
$188$	34.1446	−	34.1446i	0.181620	−	0.181620i
$189$	−183.052	+	47.0424i	−0.968529	+	0.248902i
$190$	−177.050	+	164.561i	−0.931844	+	0.866111i
$191$	114.428	−	66.0651i	0.599100	−	0.345890i	−0.169588	−	0.985515i	$-0.554244\pi$
$191$	114.428	−	66.0651i	0.599100	−	0.345890i	0.768687	+	0.639625i	$0.220910\pi$
$192$	−19.6349	−	13.8010i	−0.102265	−	0.0718804i
$193$	54.3985	+	203.018i	0.281858	+	1.05191i	0.951105	+	0.308867i	$0.0999498\pi$
$193$	54.3985	+	203.018i	0.281858	+	1.05191i	−0.669248	+	0.743039i	$0.733383\pi$
$194$	66.5894	−	38.4454i	0.343244	−	0.198172i
$195$	95.3682	+	122.932i	0.489068	+	0.630422i
$196$	85.3444	−	48.1699i	0.435430	−	0.245765i
$197$	94.5121	−	94.5121i	0.479757	−	0.479757i	−0.425297	−	0.905054i	$-0.639830\pi$
$197$	94.5121	−	94.5121i	0.479757	−	0.479757i	0.905054	+	0.425297i	$0.139830\pi$
$198$	32.7422	−	69.5639i	0.165365	−	0.351333i
$199$	182.775	−	316.575i	0.918465	−	1.59083i	0.116717	−	0.993165i	$-0.462763\pi$
$199$	182.775	−	316.575i	0.918465	−	1.59083i	0.801748	−	0.597663i	$-0.203904\pi$
$200$	−69.4553	+	13.2649i	−0.347277	+	0.0663245i
$201$	−11.6673	+	31.8777i	−0.0580461	+	0.158595i
$202$	23.4606	−	23.4606i	0.116142	−	0.116142i
$203$	−41.7437	+	23.8301i	−0.205634	+	0.117389i
$204$	107.326	−	89.7296i	0.526106	−	0.439851i
$205$	−42.6421	−	80.5158i	−0.208010	−	0.392760i
$206$	−132.964	+	230.301i	−0.645457	+	1.11796i
$207$	−246.531	+	20.6785i	−1.19097	+	0.0998963i
$208$	10.7384	−	40.0763i	0.0516269	−	0.192674i
$209$			206.492i			0.987998i
$210$	147.214	−	19.4441i	0.701019	−	0.0925908i
$211$	49.4419			0.234322			0.117161	−	0.993113i	$-0.462621\pi$
$211$	49.4419			0.234322			0.117161	+	0.993113i	$0.462621\pi$
$212$	154.581	+	41.4199i	0.729157	+	0.195377i
$213$	197.959	+	139.141i	0.929383	+	0.653246i
$214$	−101.822	−	58.7867i	−0.475801	−	0.274704i
$215$	116.636	+	35.8681i	0.542492	+	0.166828i
$216$	37.8276	+	66.3406i	0.175128	+	0.307132i
$217$	−314.513	−	1.53384i	−1.44937	−	0.00706837i
$218$	33.4856	+	33.4856i	0.153604	+	0.153604i
$219$	2.06956	−	5.65453i	0.00945006	−	0.0258198i
$220$	−32.0941	+	51.1747i	−0.145882	+	0.232612i
$221$	209.440	+	120.920i	0.947693	+	0.547151i
$222$	−63.0999	−	135.954i	−0.284234	−	0.612404i
$223$	−147.669	−	147.669i	−0.662195	−	0.662195i	0.293702	−	0.955897i	$-0.405113\pi$
$223$	−147.669	−	147.669i	−0.662195	−	0.662195i	−0.955897	+	0.293702i	$0.905113\pi$
$224$	−27.8631	−	28.1362i	−0.124389	−	0.125608i
$225$	217.938	+	55.9285i	0.968614	+	0.248571i
$226$	−12.6123	−	21.8451i	−0.0558066	−	0.0966599i
$227$	212.531	−	56.9475i	0.936259	−	0.250870i	0.241738	−	0.970342i	$-0.422283\pi$
$227$	212.531	−	56.9475i	0.936259	−	0.250870i	0.694522	+	0.719472i	$0.255616\pi$
$228$	−167.800	−	117.944i	−0.735965	−	0.517297i
$229$	149.624	+	259.157i	0.653380	+	1.13169i	0.982297	+	0.187329i	$0.0599831\pi$
$229$	149.624	+	259.157i	0.653380	+	1.13169i	−0.328917	+	0.944359i	$0.606684\pi$
$230$	194.244	+	7.10154i	0.844537	+	0.0308762i
$231$	73.4510	−	103.424i	0.317970	−	0.447723i
$232$	13.7333	+	13.7333i	0.0591954	+	0.0591954i
$233$	31.0526	−	115.890i	0.133273	−	0.497381i	−0.866726	−	0.498784i	$-0.833780\pi$
$233$	31.0526	−	115.890i	0.133273	−	0.497381i	0.999999	+	0.00140324i	$0.000446666\pi$
$234$	−85.2230	+	100.829i	−0.364201	+	0.430892i
$235$	117.670	−	26.9634i	0.500722	−	0.114738i
$236$	113.125	+	195.938i	0.479342	+	0.830245i
$237$	22.5481	−	252.512i	0.0951395	−	1.06545i
$238$	200.450	−	114.430i	0.842226	−	0.480798i
$239$	395.609			1.65527			0.827634	−	0.561268i	$-0.189686\pi$
$239$	395.609			1.65527			0.827634	+	0.561268i	$0.189686\pi$
$240$	−23.2543	−	55.3104i	−0.0968930	−	0.230460i
$241$	−191.579	−	110.608i	−0.794934	−	0.458956i	0.0467624	−	0.998906i	$-0.485110\pi$
$241$	−191.579	−	110.608i	−0.794934	−	0.458956i	−0.841697	+	0.539950i	$0.818443\pi$
$242$	−30.9332	−	115.444i	−0.127823	−	0.477043i
$243$	−19.0088	−	242.255i	−0.0782256	−	0.996936i
$244$	38.9955			0.159818
$245$	244.737	+	11.3388i	0.998928	+	0.0462808i
$246$	59.3118	−	49.5876i	0.241105	−	0.201576i
$247$	91.7703	−	342.491i	0.371540	−	1.38660i
$248$	32.8917	+	122.754i	0.132628	+	0.494974i
$249$	3.32615	+	19.0632i	0.0133580	+	0.0765591i
$250$	−164.722	−	64.1609i	−0.658889	−	0.256644i
$251$	−231.794			−0.923482			−0.461741	−	0.887015i	$-0.652775\pi$
$251$	−231.794			−0.923482			−0.461741	+	0.887015i	$0.652775\pi$
$252$	42.0912	+	118.762i	0.167029	+	0.471276i
$253$	117.413	−	117.413i	0.464083	−	0.464083i
$254$	147.938	+	256.236i	0.582432	+	1.00880i
$255$	346.495	−	47.4856i	1.35880	−	0.186218i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−8.34872	+	31.1578i	−0.0324853	+	0.121237i	−0.980264	−	0.197691i	$-0.936656\pi$
$257$	−8.34872	+	31.1578i	−0.0324853	+	0.121237i	0.947779	+	0.318927i	$0.103323\pi$
$258$	−9.20920	+	103.132i	−0.0356946	+	0.399738i
$259$	−62.8389	−	239.178i	−0.242621	−	0.923466i
$260$	75.9753	−	70.6160i	0.292213	−	0.271600i
$261$	−20.9286	−	58.1484i	−0.0801861	−	0.222791i
$262$	−54.7835	−	204.455i	−0.209097	−	0.780362i
$263$	161.425	−	43.2538i	0.613785	−	0.164463i	0.0614840	−	0.998108i	$-0.480417\pi$
$263$	161.425	−	43.2538i	0.613785	−	0.164463i	0.552301	+	0.833645i	$0.313750\pi$
$264$	−48.1335	−	17.6169i	−0.182324	−	0.0667308i
$265$	272.378	+	293.051i	1.02784	+	1.10585i
$266$	−238.118	−	240.452i	−0.895180	−	0.903954i
$267$	−6.64621	+	74.4300i	−0.0248922	+	0.278764i
$268$	21.8594	+	5.85720i	0.0815648	+	0.0218552i
$269$	−302.162	−	174.453i	−1.12328	−	0.648526i	−0.181043	−	0.983475i	$-0.557947\pi$
$269$	−302.162	−	174.453i	−1.12328	−	0.648526i	−0.942236	+	0.334949i	$0.891281\pi$
$270$	−8.00101	+	190.751i	−0.0296334	+	0.706486i
$271$	17.0749	−	9.85817i	0.0630068	−	0.0363770i	−0.468166	−	0.883641i	$-0.655085\pi$
$271$	17.0749	−	9.85817i	0.0630068	−	0.0363770i	0.531172	+	0.847264i	$0.321752\pi$
$272$	−65.9464	−	65.9464i	−0.242450	−	0.242450i
$273$	−167.792	+	138.898i	−0.614622	+	0.508783i
$274$		−	35.7425i		−	0.130447i
$275$	−135.947	+	65.7558i	−0.494354	+	0.239112i
$276$	28.3489	+	162.477i	0.102713	+	0.588683i
$277$	216.453	−	57.9983i	0.781417	−	0.209380i	0.154008	−	0.988070i	$-0.450782\pi$
$277$	216.453	−	57.9983i	0.781417	−	0.209380i	0.627409	+	0.778690i	$0.284115\pi$
$278$	−324.345	−	86.9080i	−1.16671	−	0.312619i
$279$	71.6466	−	397.981i	0.256798	−	1.42646i
$280$	−21.6402	−	96.6007i	−0.0772865	−	0.345003i
$281$		−	226.986i		−	0.807780i	−0.914808	−	0.403890i	$-0.867658\pi$
$281$		−	226.986i		−	0.807780i	0.914808	−	0.403890i	$-0.132342\pi$
$282$	43.1240	+	92.9141i	0.152922	+	0.329483i
$283$	−92.5997	+	24.8120i	−0.327208	+	0.0876750i	−0.418683	−	0.908132i	$-0.637508\pi$
$283$	−92.5997	+	24.8120i	−0.327208	+	0.0876750i	0.0914758	+	0.995807i	$0.470842\pi$
$284$	80.6556	−	139.700i	0.283999	−	0.491900i
$285$	−198.731	−	472.682i	−0.697303	−	1.65853i
$286$		−	88.6091i		−	0.309822i
$287$	110.775	−	63.2379i	0.385977	−	0.220341i
$288$	41.8088	−	29.0521i	0.145169	−	0.100875i
$289$	220.504	−	127.308i	0.762989	−	0.440512i
$290$	10.8450	+	47.3281i	0.0373964	+	0.163200i
$291$	28.0358	+	160.683i	0.0963431	+	0.552174i
$292$	−3.87746	−	1.03896i	−0.0132790	−	0.00355809i
$293$	190.809	−	190.809i	0.651224	−	0.651224i	−0.302064	−	0.953288i	$-0.597675\pi$
$293$	190.809	−	190.809i	0.651224	−	0.651224i	0.953288	+	0.302064i	$0.0976755\pi$
$294$	33.7335	+	205.134i	0.114740	+	0.697735i
$295$	−20.6654	+	565.246i	−0.0700521	+	1.91609i
$296$	−86.5352	+	49.9611i	−0.292349	+	0.168787i
$297$	114.705	+	115.945i	0.386211	+	0.390386i
$298$	−14.3896	−	53.7028i	−0.0482874	−	0.180211i
$299$	−246.925	+	142.562i	−0.825837	+	0.476797i
$300$	24.2155	−	148.032i	0.0807182	−	0.493442i
$301$	−45.0201	+	164.798i	−0.149568	+	0.547502i
$302$	−38.1201	+	38.1201i	−0.126226	+	0.126226i
$303$	29.6303	+	63.8407i	0.0977896	+	0.210696i
$304$	−68.3679	+	118.417i	−0.224895	+	0.389529i
$305$	82.5905	+	51.7965i	0.270789	+	0.169824i
$306$	100.497	+	279.224i	0.328423	+	0.912497i
$307$	−34.1553	+	34.1553i	−0.111255	+	0.111255i	−0.760543	−	0.649288i	$-0.775067\pi$
$307$	−34.1553	+	34.1553i	−0.111255	+	0.111255i	0.649288	+	0.760543i	$0.275067\pi$
$308$	−73.0313	−	42.6408i	−0.237114	−	0.138444i
$309$	−361.834	−	432.789i	−1.17098	−	1.40061i
$310$	−93.3866	+	303.675i	−0.301247	+	0.979597i
$311$	−272.168	+	471.409i	−0.875139	+	1.51579i	−0.0185247	+	0.999828i	$0.505897\pi$
$311$	−272.168	+	471.409i	−0.875139	+	1.51579i	−0.856614	+	0.515957i	$0.827436\pi$
$312$	72.0059	+	50.6116i	0.230788	+	0.162217i
$313$	118.989	−	444.072i	0.380155	−	1.41876i	−0.465509	−	0.885043i	$-0.654129\pi$
$313$	118.989	−	444.072i	0.380155	−	1.41876i	0.845664	−	0.533716i	$-0.179205\pi$
$314$			84.8163i			0.270116i
$315$	−68.6002	+	307.439i	−0.217779	+	0.975998i
$316$	−169.011			−0.534846
$317$	−17.9678	−	4.81445i	−0.0566806	−	0.0151875i	0.230367	−	0.973104i	$-0.426007\pi$
$317$	−17.9678	−	4.81445i	−0.0566806	−	0.0151875i	−0.287048	+	0.957916i	$0.592674\pi$
$318$	−195.218	+	277.740i	−0.613894	+	0.873395i
$319$	35.9217	+	20.7394i	0.112607	+	0.0650138i
$320$	−35.3486	+	18.7210i	−0.110464	+	0.0585032i
$321$	191.347	−	159.975i	0.596096	−	0.498366i
$322$	−1.32709	+	272.119i	−0.00412139	+	0.845091i
$323$	−563.577	−	563.577i	−1.74482	−	1.74482i
$324$	−159.736	+	26.9866i	−0.493014	+	0.0832920i
$325$	254.709	−	48.6454i	0.783719	−	0.149678i
$326$	7.16033	+	4.13402i	0.0219642	+	0.0126810i
$327$	−91.1208	+	42.2917i	−0.278657	+	0.129332i
$328$	−36.4442	−	36.4442i	−0.111110	−	0.111110i
$329$	42.9457	+	163.460i	0.130534	+	0.496839i
$330$	−78.5444	−	101.246i	−0.238013	−	0.306806i
$331$	−82.1070	−	142.213i	−0.248057	−	0.429648i	0.714929	−	0.699197i	$-0.246459\pi$
$331$	−82.1070	−	142.213i	−0.248057	−	0.429648i	−0.962987	+	0.269549i	$0.913125\pi$
$332$	12.4612	−	3.33898i	0.0375338	−	0.0100572i
$333$	316.838	−	26.5757i	0.951465	−	0.0798070i
$334$	6.13829	+	10.6318i	0.0183781	+	0.0318318i
$335$	38.5171	+	41.4403i	0.114976	+	0.123702i
$336$	76.3649	−	34.9914i	0.227277	−	0.104141i
$337$	182.945	+	182.945i	0.542865	+	0.542865i	0.924368	−	0.381503i	$-0.124593\pi$
$337$	182.945	+	182.945i	0.542865	+	0.542865i	−0.381503	+	0.924368i	$0.624593\pi$
$338$	22.4781	−	83.8894i	0.0665033	−	0.248194i
$339$	52.7131	−	9.19736i	0.155496	−	0.0271309i
$340$	−52.0766	−	227.266i	−0.153167	−	0.668428i
$341$	135.705	+	235.048i	0.397962	+	0.689290i
$342$	357.298	−	248.279i	1.04473	−	0.725961i
$343$	−5.01807	+	342.963i	−0.0146300	+	0.999893i
$344$	69.0285			0.200664
$345$	−155.771	+	381.772i	−0.451510	+	1.10659i
$346$	−246.710	−	142.438i	−0.713033	−	0.411670i
$347$	19.7736	+	73.7960i	0.0569844	+	0.212669i	0.988547	−	0.150912i	$-0.0482209\pi$
$347$	19.7736	+	73.7960i	0.0569844	+	0.212669i	−0.931563	+	0.363580i	$0.881554\pi$
$348$	−37.3710	+	17.3449i	−0.107388	+	0.0498418i
$349$	−601.421			−1.72327			−0.861634	−	0.507529i	$-0.830559\pi$
$349$	−601.421			−1.72327			−0.861634	+	0.507529i	$0.830559\pi$
$350$	82.4787	−	233.339i	0.235653	−	0.666684i
$351$	−138.723	−	243.286i	−0.395221	−	0.693123i
$352$	−8.84405	+	33.0064i	−0.0251251	+	0.0937683i
$353$	−117.673	−	439.162i	−0.333351	−	1.24408i	−0.905645	−	0.424036i	$-0.860613\pi$
$353$	−117.673	−	439.162i	−0.333351	−	1.24408i	0.572294	−	0.820048i	$-0.306054\pi$
$354$	−472.805	+	82.4948i	−1.33561	+	0.233036i
$355$	356.383	−	188.744i	1.00390	−	0.531674i
$356$	49.8174			0.139937
$357$	81.8053	+	482.745i	0.229146	+	1.35223i
$358$	35.2872	−	35.2872i	0.0985676	−	0.0985676i
$359$	99.2457	+	171.899i	0.276450	+	0.478826i	0.970500	−	0.241101i	$-0.0775085\pi$
$359$	99.2457	+	171.899i	0.276450	+	0.478826i	−0.694050	+	0.719927i	$0.744175\pi$
$360$	127.138	−	5.99752i	0.353161	−	0.0166598i
$361$	−403.772	+	699.353i	−1.11848	+	1.93727i
$362$	71.2207	−	265.799i	0.196742	−	0.734252i
$363$	252.529	+	22.5495i	0.695672	+	0.0621199i
$364$	102.180	+	103.182i	0.280716	+	0.283467i
$365$	−6.83224	−	7.35077i	−0.0187185	−	0.0201391i
$366$	−28.4319	+	77.6824i	−0.0776827	+	0.212247i
$367$	121.793	+	454.536i	0.331860	+	1.23852i	0.907233	+	0.420628i	$0.138190\pi$
$367$	121.793	+	454.536i	0.331860	+	1.23852i	−0.575373	+	0.817891i	$0.695143\pi$
$368$	106.208	−	28.4582i	0.288607	−	0.0773321i
$369$	55.5382	+	154.309i	0.150510	+	0.418181i
$370$	−249.639	−	9.12678i	−0.674699	−	0.0246670i
$371$	−397.992	+	394.129i	−1.07275	+	1.06234i
$372$	−268.517	−	23.9772i	−0.721821	−	0.0644549i
$373$	261.696	+	70.1213i	0.701599	+	0.187993i	0.591947	−	0.805977i	$-0.298360\pi$
$373$	261.696	+	70.1213i	0.701599	+	0.187993i	0.109652	+	0.993970i	$0.465026\pi$
$374$	−172.493	−	99.5889i	−0.461211	−	0.266281i
$375$	247.914	−	281.361i	0.661103	−	0.750295i
$376$	59.1402	−	34.1446i	0.157288	−	0.0908102i
$377$	−50.3633	−	50.3633i	−0.133590	−	0.133590i
$378$	−267.272	−	2.74053i	−0.707070	−	0.00725009i
$379$			478.536i			1.26263i	0.775528	+	0.631314i	$0.217484\pi$
$379$			478.536i			1.26263i	−0.775528	+	0.631314i	$0.782516\pi$
$380$	−302.089	+	159.990i	−0.794971	+	0.421025i
$381$	−618.306	+	107.882i	−1.62285	+	0.283154i
$382$	180.493	−	48.3630i	0.472495	−	0.126605i
$383$	412.087	+	110.418i	1.07595	+	0.288299i	0.752934	−	0.658096i	$-0.228638\pi$
$383$	412.087	+	110.418i	1.07595	+	0.288299i	0.323012	+	0.946395i	$0.395305\pi$
$384$	−21.7703	−	26.0395i	−0.0566935	−	0.0678111i
$385$	−98.0380	−	187.316i	−0.254644	−	0.486535i
$386$			297.239i			0.770049i
$387$	−198.734	−	93.5400i	−0.513525	−	0.241705i
$388$	105.035	−	28.1440i	0.270708	−	0.0725361i
$389$	−116.515	+	201.810i	−0.299524	+	0.518791i	−0.976027	−	0.217649i	$-0.930161\pi$
$389$	−116.515	+	201.810i	−0.299524	+	0.518791i	0.676503	+	0.736440i	$0.263495\pi$
$390$	85.2790	+	202.836i	0.218664	+	0.520092i
$391$			640.911i			1.63916i
$392$	134.214	−	34.5631i	0.342383	−	0.0881711i
$393$	447.234	+	39.9357i	1.13800	+	0.101618i
$394$	163.700	−	94.5121i	0.415482	−	0.239878i
$395$	−357.957	−	224.492i	−0.906221	−	0.568335i
$396$	70.1889	−	83.0415i	0.177245	−	0.209701i
$397$	52.8700	+	14.1665i	0.133174	+	0.0356838i	0.324790	−	0.945786i	$-0.394706\pi$
$397$	52.8700	+	14.1665i	0.133174	+	0.0356838i	−0.191616	+	0.981470i	$0.561373\pi$
$398$	365.549	−	365.549i	0.918465	−	0.918465i
$399$	652.614	−	299.037i	1.63562	−	0.749465i
$400$	−99.7330	−	7.30223i	−0.249333	−	0.0182556i
$401$	396.262	−	228.782i	0.988184	−	0.570528i	0.0834527	−	0.996512i	$-0.473405\pi$
$401$	396.262	−	228.782i	0.988184	−	0.570528i	0.904731	+	0.425984i	$0.140072\pi$
$402$	−27.6058	+	39.2752i	−0.0686712	+	0.0976995i
$403$	−120.622	−	450.166i	−0.299309	−	1.11704i
$404$	40.6349	−	23.4606i	0.100582	−	0.0580708i
$405$	−374.159	−	155.016i	−0.923849	−	0.382757i
$406$	−65.7453	+	17.2732i	−0.161934	+	0.0425449i
$407$	−150.897	+	150.897i	−0.370755	+	0.370755i
$408$	179.453	−	83.2890i	0.439835	−	0.204140i
$409$	−166.436	+	288.276i	−0.406935	+	0.704832i	−0.994545	−	0.104312i	$-0.966736\pi$
$409$	−166.436	+	288.276i	−0.406935	+	0.704832i	0.587609	+	0.809145i	$0.300069\pi$
$410$	−28.7793	−	125.595i	−0.0701935	−	0.306329i
$411$	71.2022	+	26.0601i	0.173241	+	0.0634066i
$412$	−265.928	+	265.928i	−0.645457	+	0.645457i
$413$	−791.864	−	3.86181i	−1.91735	−	0.00935064i
$414$	−344.337	−	61.9892i	−0.831731	−	0.149732i
$415$	30.8273	+	9.48006i	0.0742827	+	0.0228435i
$416$	29.3379	−	50.8146i	0.0705237	−	0.122151i
$417$	409.610	−	582.758i	0.982278	−	1.39750i
$418$	−75.5812	+	282.073i	−0.180816	+	0.674815i
$419$			377.243i			0.900341i	0.892943	+	0.450171i	$0.148637\pi$
$419$			377.243i			0.900341i	−0.892943	+	0.450171i	$0.851363\pi$
$420$	208.215	+	27.3229i	0.495750	+	0.0650546i
$421$	197.759			0.469736			0.234868	−	0.972027i	$-0.424534\pi$
$421$	197.759			0.469736			0.234868	+	0.972027i	$0.424534\pi$
$422$	67.5389	+	18.0970i	0.160045	+	0.0428839i
$423$	−216.535	+	18.1625i	−0.511902	+	0.0429374i
$424$	196.001	+	113.161i	0.462267	+	0.266890i
$425$	191.574	−	550.508i	0.450762	−	1.29531i
$426$	219.487	+	262.529i	0.515228	+	0.616265i
$427$	−68.8178	+	117.865i	−0.161166	+	0.276030i
$428$	−117.573	−	117.573i	−0.274704	−	0.274704i
$429$	176.517	+	64.6054i	0.411461	+	0.150595i
$430$	146.199	+	91.6883i	0.339997	+	0.213229i
$431$	142.518	+	82.2828i	0.330668	+	0.190911i	0.656138	−	0.754641i	$-0.272189\pi$
$431$	142.518	+	82.2828i	0.330668	+	0.190911i	−0.325469	+	0.945553i	$0.605522\pi$
$432$	27.3912	+	104.469i	0.0634055	+	0.241826i
$433$	−346.623	−	346.623i	−0.800515	−	0.800515i	0.182661	−	0.983176i	$-0.441529\pi$
$433$	−346.623	−	346.623i	−0.800515	−	0.800515i	−0.983176	+	0.182661i	$0.941529\pi$
$434$	−429.071	−	117.215i	−0.988644	−	0.270081i
$435$	−102.189	−	12.9031i	−0.234916	−	0.0296622i
$436$	33.4856	+	57.9988i	0.0768019	+	0.133025i
$437$	907.649	−	243.204i	2.07700	−	0.556530i
$438$	4.89678	−	6.96672i	0.0111799	−	0.0159057i
$439$	−269.647	−	467.043i	−0.614230	−	1.06388i	−0.990519	−	0.137376i	$-0.956133\pi$
$439$	−269.647	−	467.043i	−0.614230	−	1.06388i	0.376289	−	0.926502i	$-0.377200\pi$
$440$	−62.5726	+	58.1587i	−0.142210	+	0.132179i
$441$	−433.240	−	82.3646i	−0.982404	−	0.186768i
$442$	241.841	+	241.841i	0.547151	+	0.547151i
$443$	−91.4437	+	341.272i	−0.206419	+	0.770367i	0.782593	+	0.622533i	$0.213897\pi$
$443$	−91.4437	+	341.272i	−0.206419	+	0.770367i	−0.989012	+	0.147833i	$0.952770\pi$
$444$	−36.4335	−	208.812i	−0.0820575	−	0.470298i
$445$	105.511	+	66.1709i	0.237103	+	0.148699i
$446$	−147.669	−	255.771i	−0.331097	−	0.573478i
$447$	117.472	+	10.4897i	0.262801	+	0.0234668i
$448$	−27.7632	−	48.6334i	−0.0619713	−	0.108557i
$449$	−436.761			−0.972742			−0.486371	−	0.873752i	$-0.661680\pi$
$449$	−436.761			−0.972742			−0.486371	+	0.873752i	$0.661680\pi$
$450$	277.238	+	156.171i	0.616084	+	0.347046i
$451$	−95.3255	−	55.0362i	−0.211365	−	0.122032i
$452$	−9.23284	−	34.4574i	−0.0204266	−	0.0762333i
$453$	−48.1450	−	103.732i	−0.106280	−	0.228989i
$454$	311.167			0.685389
$455$	79.3597	+	354.257i	0.174417	+	0.778587i
$456$	−186.049	−	222.533i	−0.408002	−	0.488011i
$457$	−8.13289	+	30.3524i	−0.0177963	+	0.0664166i	−0.974253	−	0.225458i	$-0.927612\pi$
$457$	−8.13289	+	30.3524i	−0.0177963	+	0.0664166i	0.956457	+	0.291874i	$0.0942789\pi$
$458$	109.532	+	408.781i	0.239154	+	0.892534i
$459$	−629.511	−	3.38462i	−1.37148	−	0.00737389i
$460$	262.742	+	80.7989i	0.571179	+	0.175650i
$461$	154.115			0.334305			0.167152	−	0.985931i	$-0.446543\pi$
$461$	154.115			0.334305			0.167152	+	0.985931i	$0.446543\pi$
$462$	138.192	−	114.395i	0.299116	−	0.247608i
$463$	−200.474	+	200.474i	−0.432989	+	0.432989i	−0.889644	−	0.456655i	$-0.849047\pi$
$463$	−200.474	+	200.474i	−0.432989	+	0.432989i	0.456655	+	0.889644i	$0.349047\pi$
$464$	13.7333	+	23.7868i	0.0295977	+	0.0512648i
$465$	−536.858	−	407.445i	−1.15453	−	0.876227i
$466$	84.8372	−	146.942i	0.182054	−	0.315327i
$467$	25.0817	−	93.6060i	0.0537081	−	0.200441i	−0.933858	−	0.357643i	$-0.883581\pi$
$467$	25.0817	−	93.6060i	0.0537081	−	0.200441i	0.987567	+	0.157202i	$0.0502472\pi$
$468$	−153.323	+	106.541i	−0.327612	+	0.227651i
$469$	−56.2800	+	55.7338i	−0.120000	+	0.118835i
$470$	170.609	+	6.23747i	0.362998	+	0.0132712i
$471$	−168.961	−	61.8400i	−0.358729	−	0.131295i
$472$	82.8131	+	309.063i	0.175451	+	0.654794i
$473$	142.399	−	38.1557i	0.301055	−	0.0806675i
$474$	123.227	−	336.685i	0.259973	−	0.710306i
$475$	−852.318	−	62.4048i	−1.79435	−	0.131379i
$476$	315.704	−	82.9446i	0.663243	−	0.174253i
$477$	−410.947	−	591.393i	−0.861523	−	1.23982i
$478$	540.412	+	144.803i	1.13057	+	0.302935i
$479$	92.7005	+	53.5207i	0.193529	+	0.111734i	0.593634	−	0.804735i	$-0.297693\pi$
$479$	92.7005	+	53.5207i	0.193529	+	0.111734i	−0.400104	+	0.916470i	$0.631026\pi$
$480$	−11.5210	−	84.0670i	−0.0240021	−	0.175140i
$481$	317.344	−	183.219i	0.659760	−	0.380912i
$482$	−221.217	−	221.217i	−0.458956	−	0.458956i
$483$	−541.117	−	201.047i	−1.12033	−	0.416247i
$484$		−	169.022i		−	0.349220i
$485$	259.841	+	79.9068i	0.535755	+	0.164756i
$486$	62.7051	−	337.885i	0.129023	−	0.695236i
$487$	456.200	−	122.238i	0.936756	−	0.251003i	0.242023	−	0.970271i	$-0.422189\pi$
$487$	456.200	−	122.238i	0.936756	−	0.251003i	0.694733	+	0.719268i	$0.255522\pi$
$488$	53.2689	+	14.2734i	0.109158	+	0.0292487i
$489$	−13.4560	+	11.2499i	−0.0275173	+	0.0230059i
$490$	330.167	+	105.069i	0.673811	+	0.214427i
$491$			228.035i			0.464431i	0.972664	+	0.232215i	$0.0745974\pi$
$491$			228.035i			0.464431i	−0.972664	+	0.232215i	$0.925403\pi$
$492$	99.1717	−	46.0283i	0.201569	−	0.0935535i
$493$	−154.645	+	41.4370i	−0.313682	+	0.0840508i
$494$	250.721	−	434.262i	0.507532	−	0.879072i
$495$	258.958	−	82.6481i	0.523147	−	0.166966i
$496$			179.724i			0.362346i
$497$	279.907	+	490.320i	0.563193	+	0.986559i
$498$	−2.43403	+	27.2583i	−0.00488760	+	0.0547356i
$499$	706.586	−	407.948i	1.41600	−	0.817530i	0.420059	−	0.907497i	$-0.362009\pi$
$499$	706.586	−	407.948i	1.41600	−	0.817530i	0.995945	+	0.0899668i	$0.0286761\pi$
$500$	−201.530	−	147.938i	−0.403060	−	0.295876i
$501$	−25.6550	+	4.47627i	−0.0512075	+	0.00893467i
$502$	−316.636	−	84.8425i	−0.630750	−	0.169009i
$503$	−493.203	+	493.203i	−0.980522	+	0.980522i	−0.999814	−	0.0192915i	$-0.993859\pi$
$503$	−493.203	+	493.203i	−0.980522	+	0.980522i	0.0192915	+	0.999814i	$0.493859\pi$
$504$	14.0279	+	177.638i	0.0278330	+	0.352456i
$505$	117.225	+	4.28573i	0.232128	+	0.00848659i
$506$	203.365	−	117.413i	0.401908	−	0.232042i
$507$	150.726	+	105.943i	0.297290	+	0.208960i
$508$	108.298	+	404.174i	0.213185	+	0.795617i
$509$	715.344	−	413.004i	1.40539	−	0.811403i	0.410452	−	0.911882i	$-0.365371\pi$
$509$	715.344	−	413.004i	1.40539	−	0.811403i	0.994939	+	0.100479i	$0.0320376\pi$
$510$	490.702	+	61.9595i	0.962160	+	0.121489i
$511$	9.98307	−	9.88617i	0.0195363	−	0.0193467i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	234.085	+	892.789i	0.456306	+	1.74033i
$514$	−22.8091	+	39.5066i	−0.0443757	+	0.0768610i
$515$	−916.446	+	209.999i	−1.77951	+	0.407764i
$516$	−50.3291	+	137.511i	−0.0975370	+	0.266494i
$517$	103.127	−	103.127i	0.199472	−	0.199472i
$518$	1.70555	−	349.724i	0.00329258	−	0.675142i
$519$	463.626	−	387.614i	0.893306	−	0.746848i
$520$	129.631	−	68.6543i	0.249291	−	0.132028i
$521$	70.0727	−	121.369i	0.134497	−	0.232955i	−0.790908	−	0.611934i	$-0.790392\pi$
$521$	70.0727	−	121.369i	0.134497	−	0.232955i	0.925405	+	0.378980i	$0.123725\pi$
$522$	−7.30515	−	87.0926i	−0.0139945	−	0.166844i
$523$	−44.3611	+	165.558i	−0.0848204	+	0.316554i	−0.995280	−	0.0970437i	$-0.969061\pi$
$523$	−44.3611	+	165.558i	−0.0848204	+	0.316554i	0.910460	+	0.413598i	$0.135728\pi$
$524$		−	299.343i		−	0.571264i
$525$	404.696	+	334.434i	0.770850	+	0.637016i
$526$	236.343			0.449322
$527$	−1011.90	−	271.137i	−1.92011	−	0.514491i
$528$	−59.3034	−	41.6833i	−0.112317	−	0.0789456i
$529$	−196.258	−	113.310i	−0.370999	−	0.214196i
$530$	264.812	+	500.012i	0.499645	+	0.943419i
$531$	180.388	−	1002.02i	0.339714	−	1.88703i
$532$	−237.264	−	415.621i	−0.445984	−	0.781242i
$533$	133.649	+	133.649i	0.250749	+	0.250749i
$534$	−36.3222	+	99.2406i	−0.0680190	+	0.185844i
$535$	−92.8455	−	405.183i	−0.173543	−	0.757352i
$536$	27.7166	+	16.0022i	0.0517100	+	0.0298548i
$537$	44.5670	+	96.0233i	0.0829926	+	0.178814i
$538$	−348.907	−	348.907i	−0.648526	−	0.648526i
$539$	257.765	−	145.487i	0.478229	−	0.269921i
$540$	−80.7493	+	257.642i	−0.149536	+	0.477115i
$541$	271.403	+	470.083i	0.501669	+	0.868916i	0.999998	+	0.00192801i	$0.000613704\pi$
$541$	271.403	+	470.083i	0.501669	+	0.868916i	−0.498329	+	0.866988i	$0.666053\pi$
$542$	26.9330	−	7.21668i	0.0496919	−	0.0133149i
$543$	477.567	+	335.673i	0.879498	+	0.618183i
$544$	−65.9464	−	114.223i	−0.121225	−	0.209968i
$545$	−6.11708	+	167.316i	−0.0112240	+	0.307002i
$546$	−280.048	+	128.322i	−0.512908	+	0.235021i
$547$	−764.656	−	764.656i	−1.39791	−	1.39791i	−0.806017	−	0.591892i	$-0.798381\pi$
$547$	−764.656	−	764.656i	−1.39791	−	1.39791i	−0.591892	−	0.806017i	$-0.701619\pi$
$548$	13.0827	−	48.8252i	0.0238735	−	0.0890971i
$549$	−134.020	−	113.277i	−0.244117	−	0.206334i
$550$	−209.776	+	40.0639i	−0.381411	+	0.0728435i
$551$	117.365	+	203.282i	0.213004	+	0.368933i
$552$	−20.7453	+	232.324i	−0.0375821	+	0.420876i
$553$	298.265	−	510.840i	0.539358	−	0.923761i
$554$	316.909			0.572037
$555$	200.194	−	490.647i	0.360710	−	0.884049i
$556$	−411.253	−	237.437i	−0.739664	−	0.427045i
$557$	0.745171	+	2.78102i	0.00133783	+	0.00499285i	0.966592	−	0.256322i	$-0.0825107\pi$
$557$	0.745171	+	2.78102i	0.00133783	+	0.00499285i	−0.965254	+	0.261315i	$0.915844\pi$
$558$	243.542	−	517.428i	0.436456	−	0.927290i
$559$	−253.144			−0.452851
$560$	5.79721	−	139.880i	0.0103522	−	0.249786i
$561$	324.155	−	271.010i	0.577817	−	0.483084i
$562$	83.0827	−	310.069i	0.147834	−	0.551724i
$563$	−58.0850	−	216.776i	−0.103171	−	0.385038i	0.894961	−	0.446145i	$-0.147203\pi$
$563$	−58.0850	−	216.776i	−0.103171	−	0.385038i	−0.998131	+	0.0611074i	$0.980537\pi$
$564$	24.8996	+	142.707i	0.0441481	+	0.253027i
$565$	26.2140	−	85.2428i	0.0463965	−	0.150872i
$566$	−135.575			−0.239533
$567$	200.329	−	530.431i	0.353314	−	0.935505i
$568$	161.311	−	161.311i	0.283999	−	0.283999i
$569$	395.156	+	684.429i	0.694474	+	1.20286i	0.970358	+	0.241673i	$0.0776961\pi$
$569$	395.156	+	684.429i	0.694474	+	1.20286i	−0.275884	+	0.961191i	$0.588971\pi$
$570$	−98.4584	−	718.436i	−0.172734	−	1.26041i
$571$	−124.910	+	216.351i	−0.218757	+	0.378899i	−0.954428	−	0.298440i	$-0.903534\pi$
$571$	−124.910	+	216.351i	−0.218757	+	0.378899i	0.735671	+	0.677339i	$0.236867\pi$
$572$	32.4332	−	121.042i	0.0567013	−	0.211612i
$573$	−35.2553	+	394.820i	−0.0615277	+	0.689039i
$574$	174.469	−	45.8380i	0.303953	−	0.0798571i
$575$	449.152	+	520.120i	0.781134	+	0.904556i
$576$	67.7457	−	24.3828i	0.117614	−	0.0423312i
$577$	22.1831	+	82.7885i	0.0384456	+	0.143481i	0.982481	−	0.186364i	$-0.0596703\pi$
$577$	22.1831	+	82.7885i	0.0384456	+	0.143481i	−0.944035	+	0.329845i	$0.893004\pi$
$578$	347.812	−	93.1959i	0.601751	−	0.161239i
$579$	−592.125	−	216.719i	−1.02267	−	0.374298i
$580$	−2.50878	+	68.6209i	−0.00432548	+	0.118312i
$581$	−11.8990	+	43.5568i	−0.0204802	+	0.0749687i
$582$	−20.5162	+	229.758i	−0.0352513	+	0.394774i
$583$	466.882	+	125.101i	0.800826	+	0.214581i
$584$	−4.91642	−	2.83850i	−0.00841853	−	0.00486044i
$585$	−466.244	+	21.9943i	−0.796998	+	0.0375971i
$586$	330.490	−	190.809i	0.563977	−	0.325612i
$587$	198.002	+	198.002i	0.337312	+	0.337312i	0.855355	−	0.518043i	$-0.173339\pi$
$587$	198.002	+	198.002i	0.337312	+	0.337312i	−0.518043	+	0.855355i	$0.673339\pi$
$588$	−29.0036	+	292.566i	−0.0493258	+	0.497561i
$589$			1535.92i			2.60767i
$590$	−235.124	+	764.577i	−0.398515	+	1.29589i
$591$	68.9218	+	395.013i	0.116619	+	0.668381i
$592$	−136.496	+	36.5741i	−0.230568	+	0.0617805i
$593$	957.421	+	256.540i	1.61454	+	0.432614i	0.949391	−	0.314097i	$-0.101702\pi$
$593$	957.421	+	256.540i	1.61454	+	0.432614i	0.665148	+	0.746712i	$0.268369\pi$
$594$	114.251	+	200.368i	0.192341	+	0.337320i
$595$	778.817	+	243.667i	1.30894	+	0.409524i
$596$		−	78.6264i		−	0.131924i
$597$	461.681	+	994.729i	0.773335	+	1.66621i
$598$	−389.488	+	104.363i	−0.651317	+	0.174520i
$599$	58.5042	−	101.332i	0.0976698	−	0.169169i	−0.813050	−	0.582194i	$-0.802194\pi$
$599$	58.5042	−	101.332i	0.0976698	−	0.169169i	0.910720	+	0.413025i	$0.135528\pi$
$600$	87.2626	−	193.353i	0.145438	−	0.322254i
$601$			258.350i			0.429867i	0.976629	+	0.214933i	$0.0689534\pi$
$601$			258.350i			0.429867i	−0.976629	+	0.214933i	$0.931047\pi$
$602$	−121.819	+	208.640i	−0.202357	+	0.346578i
$603$	−58.1120	−	83.6289i	−0.0963715	−	0.138688i
$604$	−66.0260	+	38.1201i	−0.109315	+	0.0631128i
$605$	224.507	−	357.981i	0.371086	−	0.591704i
$606$	17.1083	+	98.0535i	0.0282316	+	0.161804i
$607$	−920.381	−	246.615i	−1.51628	−	0.406285i	−0.597763	−	0.801673i	$-0.703944\pi$
$607$	−920.381	−	246.615i	−1.51628	−	0.406285i	−0.918514	+	0.395387i	$0.870610\pi$
$608$	−136.736	+	136.736i	−0.224895	+	0.224895i
$609$	13.5256	−	143.564i	0.0222095	−	0.235738i
$610$	93.8619	+	100.986i	0.153872	+	0.165550i
$611$	−216.881	+	125.216i	−0.354961	+	0.204937i
$612$	35.0788	+	418.212i	0.0573182	+	0.683353i
$613$	60.5569	+	226.001i	0.0987878	+	0.368681i	0.997566	−	0.0697216i	$-0.0222111\pi$
$613$	60.5569	+	226.001i	0.0987878	+	0.368681i	−0.898779	+	0.438403i	$0.855544\pi$
$614$	−59.1587	+	34.1553i	−0.0963497	+	0.0556275i
$615$	271.179	+	34.2409i	0.440941	+	0.0556763i
$616$	−84.1549	−	84.9798i	−0.136615	−	0.137954i
$617$	−722.963	+	722.963i	−1.17174	+	1.17174i	−0.189945	+	0.981795i	$0.560831\pi$
$617$	−722.963	+	722.963i	−1.17174	+	1.17174i	−0.981795	+	0.189945i	$0.939169\pi$
$618$	−335.862	−	723.642i	−0.543466	−	1.17094i
$619$	164.472	−	284.874i	0.265706	−	0.460217i	−0.702042	−	0.712135i	$-0.747728\pi$
$619$	164.472	−	284.874i	0.265706	−	0.460217i	0.967748	+	0.251919i	$0.0810616\pi$
$620$	−238.721	+	380.646i	−0.385034	+	0.613945i
$621$	374.546	−	640.751i	0.603133	−	1.03181i
$622$	−544.337	+	544.337i	−0.875139	+	0.875139i
$623$	−87.9159	+	150.574i	−0.141117	+	0.241692i
$624$	79.8367	+	95.4928i	0.127943	+	0.153033i
$625$	−230.329	−	581.011i	−0.368527	−	0.929617i
$626$	325.083	−	563.060i	0.519302	−	0.899457i
$627$	−506.806	−	356.225i	−0.808304	−	0.568142i
$628$	−31.0449	+	115.861i	−0.0494346	+	0.184492i
$629$		−	823.689i		−	1.30952i
$630$	−206.240	+	394.861i	−0.327366	+	0.626763i
$631$	−184.344			−0.292145			−0.146073	−	0.989274i	$-0.546663\pi$
$631$	−184.344			−0.292145			−0.146073	+	0.989274i	$0.546663\pi$
$632$	−230.874	−	61.8625i	−0.365307	−	0.0978836i
$633$	−85.2938	+	121.349i	−0.134745	+	0.191704i
$634$	−22.7822	−	13.1533i	−0.0359341	−	0.0207465i
$635$	−307.481	+	999.867i	−0.484222	+	1.57459i
$636$	−368.333	+	307.945i	−0.579139	+	0.484190i
$637$	−492.194	+	126.751i	−0.772675	+	0.198981i
$638$	41.4788	+	41.4788i	0.0650138	+	0.0650138i
$639$	−683.009	+	245.826i	−1.06887	+	0.384704i
$640$	−55.1395	+	12.6349i	−0.0861554	+	0.0197420i
$641$	−706.892	−	408.124i	−1.10280	−	0.636699i	−0.165841	−	0.986152i	$-0.553034\pi$
$641$	−706.892	−	408.124i	−1.10280	−	0.636699i	−0.936954	+	0.349453i	$0.886367\pi$
$642$	319.940	−	148.493i	0.498348	−	0.231297i
$643$	18.6427	+	18.6427i	0.0289933	+	0.0289933i	0.721455	−	0.692462i	$-0.243474\pi$
$643$	18.6427	+	18.6427i	0.0289933	+	0.0289933i	−0.692462	+	0.721455i	$0.743474\pi$
$644$	−101.415	+	371.236i	−0.157477	+	0.576454i
$645$	−289.245	+	224.390i	−0.448443	+	0.347892i
$646$	−563.577	−	976.145i	−0.872411	−	1.51106i
$647$	936.314	−	250.884i	1.44716	−	0.387766i	0.552126	−	0.833761i	$-0.313817\pi$
$647$	936.314	−	250.884i	1.44716	−	0.387766i	0.895036	+	0.445995i	$0.147150\pi$
$648$	−228.082	−	21.6032i	−0.351978	−	0.0333383i
$649$	341.671	+	591.791i	0.526457	+	0.911850i
$650$	365.744	+	26.7790i	0.562683	+	0.0411984i
$651$	546.341	−	769.285i	0.839233	−	1.18170i
$652$	8.26804	+	8.26804i	0.0126810	+	0.0126810i
$653$	−15.6346	+	58.3491i	−0.0239427	+	0.0893554i	−0.976863	−	0.213864i	$-0.931395\pi$
$653$	−15.6346	+	58.3491i	−0.0239427	+	0.0893554i	0.952921	+	0.303220i	$0.0980616\pi$
$654$	−139.953	+	24.4190i	−0.213996	+	0.0373379i
$655$	397.607	−	633.992i	0.607033	−	0.967927i
$656$	−36.4442	−	63.1233i	−0.0555552	−	0.0962245i
$657$	10.3080	+	14.8343i	0.0156895	+	0.0225788i
$658$	−1.16562	+	239.010i	−0.00177145	+	0.363236i
$659$	−397.461			−0.603127			−0.301564	−	0.953446i	$-0.597509\pi$
$659$	−397.461			−0.603127			−0.301564	+	0.953446i	$0.597509\pi$
$660$	−70.2350	−	167.054i	−0.106417	−	0.253112i
$661$	417.970	+	241.315i	0.632330	+	0.365076i	0.781654	−	0.623712i	$-0.214376\pi$
$661$	417.970	+	241.315i	0.632330	+	0.365076i	−0.149324	+	0.988788i	$0.547710\pi$
$662$	−60.1065	−	224.320i	−0.0907953	−	0.338853i
$663$	−658.095	+	305.440i	−0.992602	+	0.460694i
$664$	18.2445			0.0274767
$665$	49.5429	−	1195.41i	0.0745007	−	1.79761i
$666$	442.536	+	79.6676i	0.664468	+	0.119621i
$667$	48.8533	−	182.323i	0.0732434	−	0.273348i
$668$	4.49354	+	16.7701i	0.00672685	+	0.0251050i
$669$	617.184	−	107.686i	0.922548	−	0.160966i
$670$	37.4471	+	70.7068i	0.0558912	+	0.105532i
$671$	117.778			0.175526
$672$	117.124	−	19.8477i	0.174292	−	0.0295353i
$673$	594.528	−	594.528i	0.883400	−	0.883400i	−0.110479	−	0.993879i	$-0.535238\pi$
$673$	594.528	−	594.528i	0.883400	−	0.883400i	0.993879	+	0.110479i	$0.0352384\pi$
$674$	182.945	+	316.871i	0.271432	+	0.470135i
$675$	−513.241	+	438.416i	−0.760357	+	0.649506i
$676$	61.4113	−	106.368i	0.0908451	−	0.157348i
$677$	−28.8163	+	107.544i	−0.0425647	+	0.158854i	−0.983937	−	0.178516i	$-0.942870\pi$
$677$	−28.8163	+	107.544i	−0.0425647	+	0.158854i	0.941372	+	0.337369i	$0.109537\pi$
$678$	75.3739	+	6.73050i	0.111171	+	0.00992699i
$679$	−100.296	+	367.137i	−0.147711	+	0.540703i
$680$	12.0469	−	329.512i	0.0177161	−	0.484576i
$681$	−226.873	+	619.871i	−0.333147	+	0.910236i
$682$	99.3429	+	370.753i	0.145664	+	0.543626i
$683$	−380.211	+	101.877i	−0.556678	+	0.149161i	−0.526180	−	0.850373i	$-0.676376\pi$
$683$	−380.211	+	101.877i	−0.556678	+	0.149161i	−0.0304984	+	0.999535i	$0.509709\pi$
$684$	578.954	−	208.375i	0.846424	−	0.304642i
$685$	92.5614	−	86.0320i	0.135126	−	0.125594i
$686$	−132.388	+	466.660i	−0.192986	+	0.680262i
$687$	−894.187	−	79.8463i	−1.30158	−	0.116225i
$688$	94.2947	+	25.2662i	0.137056	+	0.0367241i
$689$	−718.782	−	414.989i	−1.04322	−	0.602306i
$690$	−352.525	+	464.494i	−0.510906	+	0.673180i
$691$	675.459	−	389.977i	0.977510	−	0.564366i	0.0759924	−	0.997108i	$-0.475788\pi$
$691$	675.459	−	389.977i	0.977510	−	0.564366i	0.901517	+	0.432743i	$0.142454\pi$
$692$	−284.876	−	284.876i	−0.411670	−	0.411670i
$693$	127.128	+	358.696i	0.183446	+	0.517598i
$694$			108.045i			0.155684i
$695$	−555.633	−	1049.13i	−0.799472	−	1.50954i
$696$	−57.3985	+	10.0149i	−0.0824691	+	0.0143892i
$697$	410.382	−	109.962i	0.588784	−	0.157764i
$698$	−821.556	−	220.135i	−1.17701	−	0.315380i
$699$	230.866	+	276.139i	0.330281	+	0.395049i
$700$	198.076	−	288.558i	0.282966	−	0.412226i
$701$		−	1193.31i		−	1.70229i	−0.524928	−	0.851147i	$-0.675908\pi$
$701$		−	1193.31i		−	1.70229i	0.524928	−	0.851147i	$-0.324092\pi$
$702$	−100.450	−	383.111i	−0.143091	−	0.545742i
$703$	−1166.50	+	312.562i	−1.65931	+	0.444611i
$704$	−24.1624	+	41.8505i	−0.0343216	+	0.0594467i
$705$	−136.818	+	335.320i	−0.194068	+	0.475632i
$706$		−	642.977i		−	0.910733i
$707$	−0.800889	+	164.222i	−0.00113280	+	0.232280i
$708$	−676.059	−	60.3685i	−0.954885	−	0.0852663i
$709$	−787.987	+	454.944i	−1.11141	+	0.641671i	−0.939193	−	0.343389i	$-0.888425\pi$
$709$	−787.987	+	454.944i	−1.11141	+	0.641671i	−0.172213	+	0.985060i	$0.555092\pi$
$710$	555.913	−	127.384i	0.782977	−	0.179415i
$711$	580.860	+	490.958i	0.816962	+	0.690518i
$712$	68.0519	+	18.2344i	0.0955785	+	0.0256102i
$713$	873.338	−	873.338i	1.22488	−	1.22488i
$714$	−64.9488	+	689.384i	−0.0909647	+	0.965525i
$715$	229.468	−	213.281i	0.320935	−	0.298296i
$716$	61.1192	−	35.2872i	0.0853621	−	0.0492838i
$717$	−682.478	+	970.971i	−0.951852	+	1.35421i
$718$	72.6529	+	271.144i	0.101188	+	0.377638i
$719$	276.671	−	159.736i	0.384800	−	0.222164i	−0.295105	−	0.955465i	$-0.595355\pi$
$719$	276.671	−	159.736i	0.384800	−	0.222164i	0.679905	+	0.733301i	$0.262021\pi$
$720$	175.869	+	38.3429i	0.244262	+	0.0532540i
$721$	−334.473	−	1273.07i	−0.463902	−	1.76570i
$722$	−807.544	+	807.544i	−1.11848	+	1.11848i
$723$	601.973	−	279.392i	0.832604	−	0.386435i
$724$	194.579	−	337.020i	0.268755	−	0.465497i
$725$	−96.4603	+	142.003i	−0.133049	+	0.195866i
$726$	336.707	+	123.235i	0.463784	+	0.169745i
$727$	962.101	−	962.101i	1.32338	−	1.32338i	0.412367	−	0.911018i	$-0.364702\pi$
$727$	962.101	−	962.101i	1.32338	−	1.32338i	0.911018	−	0.412367i	$-0.135298\pi$
$728$	101.814	+	178.350i	0.139854	+	0.244986i
$729$	627.377	+	371.268i	0.860599	+	0.509283i
$730$	−6.64244	−	12.5421i	−0.00909924	−	0.0171810i
$731$	−284.511	+	492.788i	−0.389209	+	0.674129i
$732$	−67.2724	+	95.7094i	−0.0919021	+	0.130751i
$733$	−101.038	+	377.079i	−0.137842	+	0.514433i	0.862128	+	0.506690i	$0.169131\pi$
$733$	−101.038	+	377.079i	−0.137842	+	0.514433i	−0.999970	+	0.00774251i	$0.997535\pi$
$734$			665.487i			0.906658i
$735$	−450.034	+	581.115i	−0.612291	+	0.790633i
$736$	155.499			0.211275
$737$	66.0218	+	17.6905i	0.0895818	+	0.0240034i
$738$	19.3857	+	231.118i	0.0262679	+	0.313168i
$739$	−665.653	−	384.315i	−0.900749	−	0.520047i	−0.0233056	−	0.999728i	$-0.507419\pi$
$739$	−665.653	−	384.315i	−0.900749	−	0.520047i	−0.877443	+	0.479681i	$0.840752\pi$
$740$	−337.672	−	103.842i	−0.456314	−	0.140326i
$741$	682.284	+	816.080i	0.920761	+	1.10132i
$742$	−687.928	+	392.715i	−0.927126	+	0.529265i
$743$	411.294	+	411.294i	0.553559	+	0.553559i	0.927466	−	0.373907i	$-0.121982\pi$
$743$	411.294	+	411.294i	0.553559	+	0.553559i	−0.373907	+	0.927466i	$0.621982\pi$
$744$	−358.025	−	131.038i	−0.481217	−	0.176126i
$745$	104.437	−	166.527i	0.140184	−	0.223526i
$746$	331.818	+	191.575i	0.444796	+	0.256803i
$747$	−52.5262	−	24.7230i	−0.0703162	−	0.0330963i
$748$	−199.178	−	199.178i	−0.266281	−	0.266281i
$749$	562.857	−	147.879i	0.751477	−	0.197435i
$750$	441.642	−	293.603i	0.588856	−	0.391471i
$751$	569.327	+	986.103i	0.758091	+	1.31305i	0.943823	+	0.330452i	$0.107201\pi$
$751$	569.327	+	986.103i	0.758091	+	1.31305i	−0.185731	+	0.982601i	$0.559465\pi$
$752$	93.2849	−	24.9956i	0.124049	−	0.0332388i
$753$	399.875	−	568.908i	0.531042	−	0.755522i
$754$	−50.3633	−	87.2319i	−0.0667949	−	0.115692i
$755$	−190.473	−	6.96370i	−0.252283	−	0.00922345i
$756$	−364.098	−	101.572i	−0.481611	−	0.134355i
$757$	−264.443	−	264.443i	−0.349331	−	0.349331i	0.510530	−	0.859860i	$-0.329449\pi$
$757$	−264.443	−	264.443i	−0.349331	−	0.349331i	−0.859860	+	0.510530i	$0.829449\pi$
$758$	−175.156	+	653.692i	−0.231077	+	0.862390i
$759$	85.6220	+	490.728i	0.112809	+	0.646545i
$760$	−471.221	+	107.978i	−0.620028	+	0.142076i
$761$	−692.515	−	1199.47i	−0.910006	−	1.57618i	−0.814052	−	0.580792i	$-0.802743\pi$
$761$	−692.515	−	1199.47i	−0.910006	−	1.57618i	−0.0959541	−	0.995386i	$-0.530590\pi$
$762$	−884.109	−	78.9464i	−1.16025	−	0.103604i
$763$	−234.397	−	1.14312i	−0.307204	−	0.00149819i
$764$	264.260			0.345890
$765$	−481.202	+	932.345i	−0.629022	+	1.21875i
$766$	522.505	+	301.669i	0.682122	+	0.393823i
$767$	−303.695	−	1133.40i	−0.395951	−	1.47771i
$768$	−20.2077	−	43.5391i	−0.0263121	−	0.0566915i
$769$	1084.88			1.41077			0.705386	−	0.708823i	$-0.250773\pi$
$769$	1084.88			1.41077			0.705386	+	0.708823i	$0.250773\pi$
$770$	−65.3600	−	291.763i	−0.0848831	−	0.378913i
$771$	−62.0702	−	74.2422i	−0.0805061	−	0.0962933i
$772$	−108.797	+	406.036i	−0.140929	+	0.525953i
$773$	371.358	+	1385.93i	0.480411	+	1.79292i	0.599891	+	0.800082i	$0.295211\pi$
$773$	371.358	+	1385.93i	0.480411	+	1.79292i	−0.119480	+	0.992837i	$0.538123\pi$
$774$	−237.238	−	200.520i	−0.306509	−	0.259069i
$775$	−1011.20	+	489.103i	−1.30477	+	0.631100i
$776$	153.782			0.198172
$777$	695.436	+	258.383i	0.895027	+	0.332539i
$778$	−233.030	+	233.030i	−0.299524	+	0.299524i
$779$	−311.452	−	539.451i	−0.399810	−	0.692492i
$780$	42.2502	+	308.293i	0.0541669	+	0.395248i
$781$	243.604	−	421.935i	0.311913	−	0.540249i
$782$	−234.590	+	875.501i	−0.299987	+	1.11957i
$783$	178.822	+	48.9472i	0.228381	+	0.0625124i
$784$	195.991	+	1.91169i	0.249988	+	0.00243837i
$785$	−219.646	+	204.152i	−0.279804	+	0.260066i
$786$	596.316	+	218.252i	0.758672	+	0.277675i
$787$	−127.483	−	475.774i	−0.161986	−	0.604542i	−0.998405	−	0.0564509i	$-0.982022\pi$
$787$	−127.483	−	475.774i	−0.161986	−	0.604542i	0.836419	−	0.548091i	$-0.184645\pi$
$788$	258.212	−	69.1876i	0.327680	−	0.0878016i
$789$	−172.319	+	470.816i	−0.218402	+	0.596725i
$790$	−406.809	−	437.684i	−0.514948	−	0.554030i
$791$	120.442	+	32.9027i	0.152265	+	0.0415963i
$792$	126.275	−	87.7459i	0.159438	−	0.110790i
$793$	−195.349	−	52.3437i	−0.246342	−	0.0660072i
$794$	67.0365	+	38.7035i	0.0844288	+	0.0487450i
$795$	−1189.14	+	162.967i	−1.49578	+	0.204989i
$796$	633.149	−	365.549i	0.795414	−	0.459232i
$797$	−183.570	−	183.570i	−0.230326	−	0.230326i	0.582503	−	0.812829i	$-0.302074\pi$
$797$	−183.570	−	183.570i	−0.230326	−	0.230326i	−0.812829	+	0.582503i	$0.802074\pi$
$798$	1000.94	−	169.618i	1.25431	−	0.212554i
$799$			562.929i			0.704542i
$800$	−133.565	−	46.4799i	−0.166956	−	0.0580998i
$801$	−171.213	−	144.714i	−0.213749	−	0.180666i
$802$	625.043	−	167.480i	0.779356	−	0.208828i
$803$	−11.7111	−	3.13798i	−0.0145842	−	0.00390781i
$804$	−52.0860	+	43.5465i	−0.0647836	+	0.0541623i
$805$	−707.894	+	651.552i	−0.879371	+	0.809382i
$806$		−	659.089i		−	0.817728i
$807$	949.442	−	440.662i	1.17651	−	0.546050i
$808$	64.0955	−	17.1743i	0.0793261	−	0.0212554i
$809$	−554.415	+	960.275i	−0.685309	+	1.18699i	0.288030	+	0.957621i	$0.407000\pi$
$809$	−554.415	+	960.275i	−0.685309	+	1.18699i	−0.973340	+	0.229369i	$0.926334\pi$
$810$	−454.371	−	348.708i	−0.560951	−	0.430504i
$811$			715.199i			0.881873i	0.897538	+	0.440937i	$0.145354\pi$
$811$			715.199i			0.881873i	−0.897538	+	0.440937i	$0.854646\pi$
$812$	−96.1323	−	0.468824i	−0.118389	−	0.000577369i
$813$	−5.26077	+	58.9146i	−0.00647081	+	0.0724657i
$814$	−261.362	+	150.897i	−0.321084	+	0.185378i
$815$	6.52912	+	28.4935i	0.00801119	+	0.0349613i
$816$	275.623	−	48.0906i	0.337773	−	0.0589346i
$817$	805.842	+	215.925i	0.986343	+	0.264290i
$818$	−332.873	+	332.873i	−0.406935	+	0.406935i
$819$	−51.4434	−	651.439i	−0.0628124	−	0.795408i
$820$	6.65755	−	182.100i	0.00811897	−	0.222073i
$821$	1269.36	−	732.866i	1.54612	−	0.892650i	0.547683	−	0.836686i	$-0.315510\pi$
$821$	1269.36	−	732.866i	1.54612	−	0.892650i	0.998433	−	0.0559644i	$-0.0178233\pi$
$822$	87.7254	+	61.6606i	0.106722	+	0.0750129i
$823$	251.704	+	939.371i	0.305837	+	1.14140i	0.932223	+	0.361885i	$0.117867\pi$
$823$	251.704	+	939.371i	0.305837	+	1.14140i	−0.626386	+	0.779513i	$0.715467\pi$
$824$	−460.601	+	265.928i	−0.558982	+	0.322728i
$825$	73.1379	−	447.102i	0.0886520	−	0.541942i
$826$	−1080.29	−	295.118i	−1.30786	−	0.357285i
$827$	618.411	−	618.411i	0.747776	−	0.747776i	−0.226285	−	0.974061i	$-0.572658\pi$
$827$	618.411	−	618.411i	0.747776	−	0.747776i	0.974061	+	0.226285i	$0.0726581\pi$
$828$	−447.683	−	210.715i	−0.540680	−	0.254486i
$829$	678.323	−	1174.89i	0.818242	−	1.41724i	−0.0887341	−	0.996055i	$-0.528282\pi$
$829$	678.323	−	1174.89i	0.818242	−	1.41724i	0.906976	−	0.421182i	$-0.138385\pi$
$830$	38.6409	+	24.2336i	0.0465553	+	0.0291971i
$831$	−231.060	+	631.309i	−0.278050	+	0.759698i
$832$	58.6757	−	58.6757i	0.0705237	−	0.0705237i
$833$	−306.440	+	1100.60i	−0.367876	+	1.32125i
$834$	772.842	−	646.135i	0.926669	−	0.774742i
$835$	−12.7581	+	41.4868i	−0.0152792	+	0.0496848i
$836$	−206.492	+	357.654i	−0.246999	+	0.427816i
$837$	853.192	+	862.416i	1.01935	+	1.03037i
$838$	−138.080	+	515.323i	−0.164774	+	0.614944i
$839$		−	1498.76i		−	1.78637i	−0.449693	−	0.893183i	$-0.648467\pi$
$839$		−	1498.76i		−	1.78637i	0.449693	−	0.893183i	$-0.351533\pi$
$840$	274.426	+	113.536i	0.326698	+	0.135162i
$841$	−793.849			−0.943934
$842$	270.143	+	72.3847i	0.320835	+	0.0859676i
$843$	557.108	+	391.581i	0.660863	+	0.464509i
$844$	85.6360	+	49.4419i	0.101464	+	0.0585805i
$845$	271.350	−	143.710i	0.321125	−	0.170071i
$846$	−302.440	−	54.4468i	−0.357494	−	0.0643579i
$847$	510.873	+	298.284i	0.603156	+	0.352165i
$848$	226.323	+	226.323i	0.266890	+	0.266890i
$849$	98.8488	−	270.078i	0.116430	−	0.318113i
$850$	463.195	−	681.888i	0.544935	−	0.802221i
$851$	841.006	+	485.555i	0.988256	+	0.570570i
$852$	203.733	+	438.959i	0.239123	+	0.515210i
$853$	4.38891	+	4.38891i	0.00514527	+	0.00514527i	0.709675	−	0.704529i	$-0.248842\pi$
$853$	4.38891	+	4.38891i	0.00514527	+	0.00514527i	−0.704529	+	0.709675i	$0.748842\pi$
$854$	−137.148	+	135.817i	−0.160595	+	0.159036i
$855$	1502.97	+	327.678i	1.75786	+	0.383249i
$856$	−117.573	−	203.643i	−0.137352	−	0.237901i
$857$	−741.882	+	198.787i	−0.865673	+	0.231956i	−0.664216	−	0.747541i	$-0.731234\pi$
$857$	−741.882	+	198.787i	−0.865673	+	0.231956i	−0.201457	+	0.979497i	$0.564568\pi$
$858$	217.479	+	152.862i	0.253472	+	0.178161i
$859$	−506.657	−	877.555i	−0.589821	−	1.02160i	−0.994255	−	0.107033i	$-0.965865\pi$
$859$	−506.657	−	877.555i	−0.589821	−	1.02160i	0.404434	−	0.914567i	$-0.367469\pi$
$860$	166.151	+	178.761i	0.193199	+	0.207862i
$861$	−35.8929	+	380.977i	−0.0416875	+	0.442482i
$862$	164.566	+	164.566i	0.190911	+	0.190911i
$863$	226.732	−	846.176i	0.262726	−	0.980505i	−0.700902	−	0.713257i	$-0.747219\pi$
$863$	226.732	−	846.176i	0.262726	−	0.980505i	0.963628	−	0.267248i	$-0.0861142\pi$
$864$	−0.821180	+	152.733i	−0.000950440	+	0.176774i
$865$	−224.961	−	981.743i	−0.260070	−	1.13496i
$866$	−346.623	−	600.369i	−0.400258	−	0.693267i
$867$	−67.9374	+	760.821i	−0.0783591	+	0.877533i
$868$	−543.219	−	317.170i	−0.625828	−	0.365403i
$869$	−510.465			−0.587416
$870$	−134.869	−	55.0296i	−0.155022	−	0.0632524i
$871$	−101.643	−	58.6836i	−0.116697	−	0.0673750i
$872$	24.5132	+	91.4844i	0.0281114	+	0.104913i
$873$	−442.740	−	208.388i	−0.507148	−	0.238704i
$874$	1328.89			1.52047
$875$	802.797	−	348.053i	0.917483	−	0.397775i
$876$	9.23912	−	7.72437i	0.0105469	−	0.00881777i
$877$	332.001	−	1239.04i	0.378564	−	1.41282i	−0.469502	−	0.882931i	$-0.655567\pi$
$877$	332.001	−	1239.04i	0.378564	−	1.41282i	0.848067	−	0.529890i	$-0.177767\pi$
$878$	−197.395	−	736.690i	−0.224824	−	0.839054i
$879$	139.145	+	797.485i	0.158299	+	0.907264i
$880$	−106.763	+	56.5431i	−0.121322	+	0.0642535i
$881$	−1186.25			−1.34648			−0.673241	−	0.739423i	$-0.735098\pi$
$881$	−1186.25			−1.34648			−0.673241	+	0.739423i	$0.735098\pi$
$882$	−561.670	−	271.089i	−0.636814	−	0.307357i
$883$	459.415	−	459.415i	0.520289	−	0.520289i	−0.397369	−	0.917659i	$-0.630077\pi$
$883$	459.415	−	459.415i	0.520289	−	0.520289i	0.917659	+	0.397369i	$0.130077\pi$
$884$	241.841	+	418.880i	0.273575	+	0.473847i
$885$	−1351.67	−	1025.84i	−1.52731	−	1.15915i
$886$	−249.829	+	432.716i	−0.281974	+	0.488393i
$887$	−231.193	+	862.823i	−0.260646	+	0.972743i	0.704216	+	0.709986i	$0.251299\pi$
$887$	−231.193	+	862.823i	−0.260646	+	0.972743i	−0.964862	+	0.262758i	$0.915368\pi$
$888$	26.6615	−	298.579i	0.0300242	−	0.336237i
$889$	−1412.74	−	385.937i	−1.58914	−	0.434125i
$890$	119.910	+	129.011i	0.134730	+	0.144956i
$891$	−482.452	+	81.5076i	−0.541472	+	0.0914788i
$892$	−108.102	−	403.441i	−0.121190	−	0.452288i
$893$	797.212	−	213.612i	0.892734	−	0.239207i
$894$	156.631	+	57.3270i	0.175202	+	0.0641241i
$895$	176.318	+	6.44619i	0.197004	+	0.00720245i
$896$	−20.1241	−	76.5965i	−0.0224600	−	0.0854871i
$897$	76.0778	−	851.984i	0.0848136	−	0.949815i
$898$	−596.627	−	159.866i	−0.664395	−	0.178024i
$899$	267.191	+	154.263i	0.297210	+	0.171594i
$900$	321.551	+	314.809i	0.357279	+	0.349788i
$901$	−1615.70	+	932.823i	−1.79323	+	1.03532i
$902$	−110.072	−	110.072i	−0.122032	−	0.122032i
$903$	−326.810	−	394.794i	−0.361916	−	0.437203i
$904$		−	50.4492i		−	0.0558066i
$905$	859.760	−	455.339i	0.950011	−	0.503137i
$906$	−27.7986	−	159.323i	−0.0306828	−	0.175853i
$907$	−607.910	+	162.889i	−0.670242	+	0.179591i	−0.577864	−	0.816133i	$-0.696114\pi$
$907$	−607.910	+	162.889i	−0.670242	+	0.179591i	−0.0923782	+	0.995724i	$0.529447\pi$
$908$	425.062	+	113.895i	0.468130	+	0.125435i
$909$	−207.805	−	37.4101i	−0.228608	−	0.0411552i
$910$	−21.2597	+	512.972i	−0.0233623	+	0.563706i
$911$		−	911.280i		−	1.00031i	−0.865937	−	0.500154i	$-0.833277\pi$
$911$		−	911.280i		−	1.00031i	0.865937	−	0.500154i	$-0.166723\pi$
$912$	−172.695	−	372.084i	−0.189358	−	0.407987i
$913$	37.6366	−	10.0847i	0.0412230	−	0.0110457i
$914$	−22.2195	+	38.4853i	−0.0243102	+	0.0421064i
$915$	−269.607	+	113.352i	−0.294653	+	0.123882i
$916$			598.496i			0.653380i
$917$	904.768	+	528.268i	0.986661	+	0.576083i
$918$	−858.690	−	235.041i	−0.935392	−	0.256036i
$919$	687.784	−	397.092i	0.748404	−	0.432092i	−0.0767126	−	0.997053i	$-0.524442\pi$
$919$	687.784	−	397.092i	0.748404	−	0.432092i	0.825117	+	0.564962i	$0.191109\pi$
$920$	329.338	+	206.544i	0.357976	+	0.224504i
$921$	−24.9073	−	142.752i	−0.0270438	−	0.154997i
$922$	210.524	+	56.4099i	0.228335	+	0.0611821i
$923$	−591.566	+	591.566i	−0.640916	+	0.640916i
$924$	230.645	−	105.685i	0.249616	−	0.114377i
$925$	−577.243	−	668.450i	−0.624046	−	0.722649i
$926$	−347.231	+	200.474i	−0.374979	+	0.216494i
$927$	1686.44	−	141.455i	1.81924	−	0.152594i
$928$	10.0535	+	37.5202i	0.0108335	+	0.0404312i
$929$	−445.001	+	256.922i	−0.479011	+	0.276557i	−0.720004	−	0.693970i	$-0.755860\pi$
$929$	−445.001	+	256.922i	−0.479011	+	0.276557i	0.240993	+	0.970527i	$0.422527\pi$
$930$	−584.226	−	753.084i	−0.628200	−	0.809768i
$931$	1674.93	+	16.3372i	1.79907	+	0.0175481i
$932$	169.674	−	169.674i	0.182054	−	0.182054i
$933$	−687.486	−	1481.24i	−0.736855	−	1.58761i
$934$	68.5244	−	118.688i	0.0733666	−	0.127075i
$935$	−157.287	−	686.410i	−0.168221	−	0.734128i
$936$	−248.439	+	89.4173i	−0.265426	+	0.0955313i
$937$	−35.0323	+	35.0323i	−0.0373877	+	0.0373877i	−0.725553	−	0.688166i	$-0.758416\pi$
$937$	−35.0323	+	35.0323i	−0.0373877	+	0.0373877i	0.688166	+	0.725553i	$0.258416\pi$
$938$	−97.2799	+	55.5338i	−0.103710	+	0.0592045i
$939$	884.644	+	1058.12i	0.942113	+	1.12686i
$940$	230.773	+	70.9678i	0.245504	+	0.0754977i
$941$	−423.536	+	733.586i	−0.450091	+	0.779581i	−0.998391	−	0.0567009i	$-0.981942\pi$
$941$	−423.536	+	733.586i	−0.450091	+	0.779581i	0.548300	+	0.836282i	$0.315275\pi$
$942$	−208.170	−	146.319i	−0.220988	−	0.155328i
$943$	−129.642	+	483.832i	−0.137479	+	0.513077i
$944$			452.499i			0.479342i
$945$	−636.225	−	698.743i	−0.673254	−	0.739411i
$946$	208.487			0.220388
$947$	−1461.39	−	391.578i	−1.54318	−	0.413493i	−0.615887	−	0.787835i	$-0.711202\pi$
$947$	−1461.39	−	391.578i	−1.54318	−	0.413493i	−0.927291	+	0.374341i	$0.877869\pi$
$948$	291.567	−	414.816i	0.307560	−	0.437570i
$949$	18.0297	+	10.4094i	0.0189986	+	0.0109688i
$950$	−1141.45	−	397.216i	−1.20152	−	0.418123i
$951$	42.8132	−	35.7939i	0.0450191	−	0.0376382i
$952$	461.619	+	2.25125i	0.484894	+	0.00236476i
$953$	88.2376	+	88.2376i	0.0925893	+	0.0925893i	0.751884	−	0.659295i	$-0.229145\pi$
$953$	88.2376	+	88.2376i	0.0925893	+	0.0925893i	−0.659295	+	0.751884i	$0.729145\pi$
$954$	−344.899	−	958.274i	−0.361529	−	1.00448i
$955$	559.690	+	351.008i	0.586063	+	0.367548i
$956$	685.215	+	395.609i	0.716752	+	0.413817i
$957$	−112.872	+	52.3869i	−0.117943	+	0.0547407i
$958$	107.041	+	107.041i	0.111734	+	0.111734i
$959$	124.487	+	125.708i	0.129810	+	0.131082i
$960$	15.0327	−	119.055i	0.0156590	−	0.124015i
$961$	528.896	+	916.074i	0.550360	+	0.953251i
$962$	500.563	−	134.126i	0.520336	−	0.139424i
$963$	62.5406	+	745.614i	0.0649435	+	0.774262i
$964$	−221.217	−	383.158i	−0.229478	−	0.397467i
$965$	−769.751	+	715.452i	−0.797669	+	0.741401i
$966$	−665.592	−	472.699i	−0.689018	−	0.489336i
$967$	−11.0507	−	11.0507i	−0.0114278	−	0.0114278i	0.701370	−	0.712798i	$-0.252572\pi$
$967$	−11.0507	−	11.0507i	−0.0114278	−	0.0114278i	−0.712798	+	0.701370i	$0.752572\pi$
$968$	61.8665	−	230.889i	0.0639117	−	0.238522i
$969$	2355.47	−	410.982i	2.43083	−	0.424130i
$970$	325.702	+	204.263i	0.335775	+	0.210581i
$971$	−528.106	−	914.707i	−0.543879	−	0.942025i	−0.998677	−	0.0514307i	$-0.983622\pi$
$971$	−528.106	−	914.707i	−0.543879	−	0.942025i	0.454798	−	0.890595i	$-0.349711\pi$
$972$	209.331	−	438.607i	0.215361	−	0.451242i
$973$	1443.42	−	824.000i	1.48348	−	0.846866i
$974$	667.923			0.685753
$975$	−320.012	+	709.069i	−0.328218	+	0.727250i
$976$	67.5422	+	38.9955i	0.0692031	+	0.0399544i
$977$	−414.973	−	1548.70i	−0.424743	−	1.58516i	−0.764484	−	0.644642i	$-0.777006\pi$
$977$	−414.973	−	1548.70i	−0.424743	−	1.58516i	0.339742	−	0.940519i	$-0.389660\pi$
$978$	−22.4989	+	10.4424i	−0.0230050	+	0.0106773i
$979$	150.463			0.153691
$980$	412.559	+	264.377i	0.420979	+	0.269772i
$981$	53.3959	−	296.603i	0.0544301	−	0.302347i
$982$	−83.4668	+	311.502i	−0.0849967	+	0.317212i
$983$	203.226	+	758.449i	0.206740	+	0.771565i	0.988912	+	0.148502i	$0.0474453\pi$
$983$	203.226	+	758.449i	0.206740	+	0.771565i	−0.782172	+	0.623063i	$0.785888\pi$
$984$	152.319	−	26.5765i	0.154795	−	0.0270086i
$985$	638.779	+	196.438i	0.648507	+	0.199430i
$986$	−226.416			−0.229631
$987$	−475.278	−	176.585i	−0.481538	−	0.178911i
$988$	501.442	−	501.442i	0.507532	−	0.507532i
$989$	−335.433	−	580.986i	−0.339163	−	0.587448i
$990$	383.994	−	18.1143i	0.387873	−	0.0182973i
$991$	517.260	−	895.920i	0.521957	−	0.904056i	−0.477717	−	0.878514i	$-0.658535\pi$
$991$	517.260	−	895.920i	0.521957	−	0.904056i	0.999674	−	0.0255424i	$-0.00813127\pi$
$992$	−65.7835	+	245.507i	−0.0663140	+	0.247487i
$993$	490.690	+	43.8160i	0.494149	+	0.0441249i
$994$	202.890	+	772.242i	0.204115	+	0.776903i
$995$	1826.52	+	66.7777i	1.83570	+	0.0671133i
$996$	−13.3022	+	36.3446i	−0.0133556	+	0.0364906i
$997$	50.5660	+	188.715i	0.0507181	+	0.189283i	0.986637	−	0.162932i	$-0.0520953\pi$
$997$	50.5660	+	188.715i	0.0507181	+	0.189283i	−0.935919	+	0.352215i	$0.885429\pi$
$998$	1114.53	−	298.638i	1.11677	−	0.299237i
$999$	−481.360	+	823.483i	−0.481842	+	0.824308i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.w.b.17.5	yes	64
3.2	odd	2		210.3.w.a.17.2	✓	64
5.3	odd	4		210.3.w.a.143.3	yes	64
7.5	odd	6	inner	210.3.w.b.47.11	yes	64
15.8	even	4	inner	210.3.w.b.143.11	yes	64
21.5	even	6		210.3.w.a.47.3	yes	64
35.33	even	12		210.3.w.a.173.2	yes	64
105.68	odd	12	inner	210.3.w.b.173.5	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.w.a.17.2	✓	64	3.2	odd	2
210.3.w.a.47.3	yes	64	21.5	even	6
210.3.w.a.143.3	yes	64	5.3	odd	4
210.3.w.a.173.2	yes	64	35.33	even	12
210.3.w.b.17.5	yes	64	1.1	even	1	trivial
210.3.w.b.47.11	yes	64	7.5	odd	6	inner
210.3.w.b.143.11	yes	64	15.8	even	4	inner
210.3.w.b.173.5	yes	64	105.68	odd	12	inner

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 + 0.366025i) q^{2} +(-1.72513 + 2.45437i) q^{3} +(1.73205 + 1.00000i) q^{4} +(2.34013 + 4.41857i) q^{5} +(-3.25493 + 2.72129i) q^{6} +(-6.07917 + 3.47039i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-3.04785 - 8.46821i) q^{9} +O(q^{10})\)	\(q+(1.36603 + 0.366025i) q^{2} +(-1.72513 + 2.45437i) q^{3} +(1.73205 + 1.00000i) q^{4} +(2.34013 + 4.41857i) q^{5} +(-3.25493 + 2.72129i) q^{6} +(-6.07917 + 3.47039i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-3.04785 - 8.46821i) q^{9} +(1.57936 + 6.89243i) q^{10} +(5.23131 + 3.02030i) q^{11} +(-5.44238 + 2.52596i) q^{12} +(-7.33446 - 7.33446i) q^{13} +(-9.57456 + 2.51551i) q^{14} +(-14.8818 - 1.87909i) q^{15} +(2.00000 + 3.46410i) q^{16} +(-22.5211 + 6.03451i) q^{17} +(-1.06386 - 12.6834i) q^{18} +(17.0920 + 29.6042i) q^{19} +(-0.365356 + 9.99332i) q^{20} +(1.96974 - 20.9074i) q^{21} +(6.04060 + 6.04060i) q^{22} +(7.11456 - 26.5519i) q^{23} +(-8.35900 + 1.45848i) q^{24} +(-14.0476 + 20.6801i) q^{25} +(-7.33446 - 12.7037i) q^{26} +(26.0420 + 7.12823i) q^{27} +(-13.9998 - 0.0682753i) q^{28} +6.86667 q^{29} +(-19.6412 - 8.01401i) q^{30} +(38.9114 + 22.4655i) q^{31} +(1.46410 + 5.46410i) q^{32} +(-16.4376 + 7.62915i) q^{33} -32.9732 q^{34} +(-29.5602 - 18.7401i) q^{35} +(3.18919 - 17.7152i) q^{36} +(-9.14352 + 34.1241i) q^{37} +(12.5122 + 46.6962i) q^{38} +(30.6544 - 5.34857i) q^{39} +(-4.15690 + 13.5174i) q^{40} -18.2221 q^{41} +(10.3434 - 27.8391i) q^{42} +(17.2571 - 17.2571i) q^{43} +(6.04060 + 10.4626i) q^{44} +(30.2851 - 33.2838i) q^{45} +(19.4373 - 33.6664i) q^{46} +(6.24890 - 23.3212i) q^{47} +(-11.9524 - 1.06729i) q^{48} +(24.9127 - 42.1943i) q^{49} +(-26.7588 + 23.1077i) q^{50} +(24.0409 - 65.6854i) q^{51} +(-5.36920 - 20.0381i) q^{52} +(77.2906 - 20.7100i) q^{53} +(32.9650 + 19.2694i) q^{54} +(-1.10348 + 30.1828i) q^{55} +(-19.0991 - 5.21756i) q^{56} +(-102.145 - 9.12106i) q^{57} +(9.38005 + 2.51338i) q^{58} +(97.9689 + 56.5624i) q^{59} +(-23.8970 - 18.1365i) q^{60} +(16.8856 - 9.74888i) q^{61} +(44.9310 + 44.9310i) q^{62} +(47.9164 + 40.9025i) q^{63} +8.00000i q^{64} +(15.2443 - 49.5715i) q^{65} +(-25.2467 + 4.40503i) q^{66} +(10.9297 - 2.92860i) q^{67} +(-45.0422 - 12.0690i) q^{68} +(52.8946 + 63.2672i) q^{69} +(-33.5207 - 36.4193i) q^{70} -80.6556i q^{71} +(10.8407 - 23.0321i) q^{72} +(-1.93873 + 0.519481i) q^{73} +(-24.9805 + 43.2676i) q^{74} +(-26.5225 - 70.1538i) q^{75} +68.3679i q^{76} +(-42.2837 - 0.206212i) q^{77} +(43.8324 + 3.91400i) q^{78} +(-73.1841 + 42.2528i) q^{79} +(-10.6261 + 16.9436i) q^{80} +(-62.4212 + 51.6196i) q^{81} +(-24.8919 - 6.66976i) q^{82} +(4.56113 - 4.56113i) q^{83} +(24.3191 - 34.2430i) q^{84} +(-79.3662 - 85.3897i) q^{85} +(29.8902 - 17.2571i) q^{86} +(-11.8459 + 16.8533i) q^{87} +(4.42202 + 16.5032i) q^{88} +(21.5716 - 12.4544i) q^{89} +(53.5529 - 34.3815i) q^{90} +(70.0410 + 19.1340i) q^{91} +(38.8747 - 38.8747i) q^{92} +(-122.266 + 56.7469i) q^{93} +(17.0723 - 29.5701i) q^{94} +(-90.8109 + 144.800i) q^{95} +(-15.9367 - 5.83284i) q^{96} +(38.4454 - 38.4454i) q^{97} +(49.4756 - 48.5197i) q^{98} +(9.63229 - 53.5053i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{2} + 6 q^{3} + 12 q^{5} + 4 q^{7} + 128 q^{8} + 16 q^{9}+O(q^{10}) \) 64 * q + 32 * q^2 + 6 * q^3 + 12 * q^5 + 4 * q^7 + 128 * q^8 + 16 * q^9	\( 64 q + 32 q^{2} + 6 q^{3} + 12 q^{5} + 4 q^{7} + 128 q^{8} + 16 q^{9} + 24 q^{10} - 12 q^{12} + 16 q^{14} + 68 q^{15} + 128 q^{16} - 12 q^{18} + 36 q^{21} + 16 q^{22} + 12 q^{23} - 16 q^{25} + 8 q^{28} + 112 q^{29} + 22 q^{30} - 128 q^{32} + 30 q^{33} + 16 q^{36} - 32 q^{37} - 24 q^{38} - 64 q^{39} - 88 q^{42} + 32 q^{43} + 16 q^{44} - 474 q^{45} - 24 q^{46} + 96 q^{47} - 40 q^{50} - 84 q^{51} - 56 q^{53} + 72 q^{54} - 220 q^{57} + 56 q^{58} - 672 q^{59} + 24 q^{60} + 600 q^{61} - 114 q^{63} - 28 q^{65} + 16 q^{67} + 40 q^{72} - 624 q^{73} + 64 q^{74} - 144 q^{75} - 208 q^{77} - 248 q^{78} + 48 q^{80} - 64 q^{81} - 192 q^{82} - 160 q^{84} - 152 q^{85} - 672 q^{87} - 16 q^{88} - 144 q^{89} - 232 q^{91} - 48 q^{92} - 202 q^{93} - 136 q^{95} - 48 q^{96} - 128 q^{98} - 160 q^{99}+O(q^{100}) \) 64 * q + 32 * q^2 + 6 * q^3 + 12 * q^5 + 4 * q^7 + 128 * q^8 + 16 * q^9 + 24 * q^10 - 12 * q^12 + 16 * q^14 + 68 * q^15 + 128 * q^16 - 12 * q^18 + 36 * q^21 + 16 * q^22 + 12 * q^23 - 16 * q^25 + 8 * q^28 + 112 * q^29 + 22 * q^30 - 128 * q^32 + 30 * q^33 + 16 * q^36 - 32 * q^37 - 24 * q^38 - 64 * q^39 - 88 * q^42 + 32 * q^43 + 16 * q^44 - 474 * q^45 - 24 * q^46 + 96 * q^47 - 40 * q^50 - 84 * q^51 - 56 * q^53 + 72 * q^54 - 220 * q^57 + 56 * q^58 - 672 * q^59 + 24 * q^60 + 600 * q^61 - 114 * q^63 - 28 * q^65 + 16 * q^67 + 40 * q^72 - 624 * q^73 + 64 * q^74 - 144 * q^75 - 208 * q^77 - 248 * q^78 + 48 * q^80 - 64 * q^81 - 192 * q^82 - 160 * q^84 - 152 * q^85 - 672 * q^87 - 16 * q^88 - 144 * q^89 - 232 * q^91 - 48 * q^92 - 202 * q^93 - 136 * q^95 - 48 * q^96 - 128 * q^98 - 160 * q^99

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