LMFDB - Embedded newform 210.3.k.b.83.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(83,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 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("210.83");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			83.12
Character	$\chi$	$=$	210.83
Dual form			210.3.k.b.167.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(1.94039 + 2.28799i) q^{3} +2.00000i q^{4} +(-4.58449 + 1.99562i) q^{5} +(-0.347606 + 4.22838i) q^{6} +(5.57668 + 4.23091i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.46981 + 8.87917i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(1.94039 + 2.28799i) q^{3} +2.00000i q^{4} +(-4.58449 + 1.99562i) q^{5} +(-0.347606 + 4.22838i) q^{6} +(5.57668 + 4.23091i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.46981 + 8.87917i) q^{9} +(-6.58010 - 2.58887i) q^{10} -14.6047i q^{11} +(-4.57598 + 3.88077i) q^{12} +(-3.48167 + 3.48167i) q^{13} +(1.34578 + 9.80759i) q^{14} +(-13.4616 - 6.61700i) q^{15} -4.00000 q^{16} +(-20.1653 + 20.1653i) q^{17} +(-10.3490 + 7.40936i) q^{18} +26.4132 q^{19} +(-3.99123 - 9.16897i) q^{20} +(1.14063 + 20.9690i) q^{21} +(14.6047 - 14.6047i) q^{22} +(2.68095 - 2.68095i) q^{23} +(-8.45675 - 0.695213i) q^{24} +(17.0350 - 18.2978i) q^{25} -6.96334 q^{26} +(-23.1675 + 13.8661i) q^{27} +(-8.46182 + 11.1534i) q^{28} +28.5159 q^{29} +(-6.84462 - 20.0786i) q^{30} -15.6511i q^{31} +(-4.00000 - 4.00000i) q^{32} +(33.4154 - 28.3387i) q^{33} -40.3306 q^{34} +(-34.0095 - 8.26762i) q^{35} +(-17.7583 - 2.93962i) q^{36} +(7.69844 - 7.69844i) q^{37} +(26.4132 + 26.4132i) q^{38} +(-14.7218 - 1.21025i) q^{39} +(5.17774 - 13.1602i) q^{40} +37.9832 q^{41} +(-19.8284 + 22.1096i) q^{42} +(41.7817 + 41.7817i) q^{43} +29.2094 q^{44} +(-10.9811 - 43.6396i) q^{45} +5.36190 q^{46} +(21.0822 - 21.0822i) q^{47} +(-7.76154 - 9.15197i) q^{48} +(13.1988 + 47.1889i) q^{49} +(35.3328 - 1.26273i) q^{50} +(-85.2664 - 7.00958i) q^{51} +(-6.96334 - 6.96334i) q^{52} +(-47.4934 + 47.4934i) q^{53} +(-37.0336 - 9.30137i) q^{54} +(29.1453 + 66.9549i) q^{55} +(-19.6152 + 2.69155i) q^{56} +(51.2518 + 60.4332i) q^{57} +(28.5159 + 28.5159i) q^{58} -61.6589i q^{59} +(13.2340 - 26.9232i) q^{60} -54.1777i q^{61} +(15.6511 - 15.6511i) q^{62} +(-45.7636 + 43.2977i) q^{63} -8.00000i q^{64} +(9.01359 - 22.9098i) q^{65} +(61.7541 + 5.07668i) q^{66} +(68.9882 - 68.9882i) q^{67} +(-40.3306 - 40.3306i) q^{68} +(11.3361 + 0.931915i) q^{69} +(-25.7419 - 42.2771i) q^{70} -65.9594i q^{71} +(-14.8187 - 20.6980i) q^{72} +(6.51081 - 6.51081i) q^{73} +15.3969 q^{74} +(74.9196 + 3.47129i) q^{75} +52.8265i q^{76} +(61.7911 - 81.4457i) q^{77} +(-13.5116 - 15.9321i) q^{78} +42.7301i q^{79} +(18.3379 - 7.98247i) q^{80} +(-76.6793 - 26.1014i) q^{81} +(37.9832 + 37.9832i) q^{82} +(9.52614 + 9.52614i) q^{83} +(-41.9380 + 2.28126i) q^{84} +(52.2053 - 132.690i) q^{85} +83.5634i q^{86} +(55.3318 + 65.2441i) q^{87} +(29.2094 + 29.2094i) q^{88} +19.3830i q^{89} +(32.6585 - 54.6207i) q^{90} +(-34.1468 + 4.68555i) q^{91} +(5.36190 + 5.36190i) q^{92} +(35.8096 - 30.3692i) q^{93} +42.1644 q^{94} +(-121.091 + 52.7107i) q^{95} +(1.39043 - 16.9135i) q^{96} +(-84.6391 - 84.6391i) q^{97} +(-33.9901 + 60.3877i) q^{98} +(129.677 + 21.4661i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{2} - 4 q^{7} - 64 q^{8} + 16 q^{9}+O(q^{10}) $ 32 * q + 32 * q^2 - 4 * q^7 - 64 * q^8 + 16 * q^9	$ 32 q + 32 q^{2} - 4 q^{7} - 64 q^{8} + 16 q^{9} - 8 q^{14} - 4 q^{15} - 128 q^{16} - 4 q^{18} + 12 q^{21} - 40 q^{22} - 24 q^{23} + 16 q^{25} - 8 q^{28} + 112 q^{29} + 28 q^{30} - 128 q^{32} + 48 q^{35} - 40 q^{36} + 32 q^{37} - 64 q^{39} - 20 q^{42} - 32 q^{43} - 80 q^{44} - 48 q^{46} + 8 q^{50} + 84 q^{51} + 136 q^{53} + 340 q^{57} + 112 q^{58} + 64 q^{60} + 168 q^{63} + 200 q^{65} + 32 q^{67} - 72 q^{72} + 64 q^{74} - 88 q^{77} - 4 q^{78} + 76 q^{81} - 64 q^{84} - 40 q^{85} - 80 q^{88} - 272 q^{91} - 48 q^{92} - 388 q^{93} - 544 q^{95} - 128 q^{98} - 160 q^{99}+O(q^{100}) $ 32 * q + 32 * q^2 - 4 * q^7 - 64 * q^8 + 16 * q^9 - 8 * q^14 - 4 * q^15 - 128 * q^16 - 4 * q^18 + 12 * q^21 - 40 * q^22 - 24 * q^23 + 16 * q^25 - 8 * q^28 + 112 * q^29 + 28 * q^30 - 128 * q^32 + 48 * q^35 - 40 * q^36 + 32 * q^37 - 64 * q^39 - 20 * q^42 - 32 * q^43 - 80 * q^44 - 48 * q^46 + 8 * q^50 + 84 * q^51 + 136 * q^53 + 340 * q^57 + 112 * q^58 + 64 * q^60 + 168 * q^63 + 200 * q^65 + 32 * q^67 - 72 * q^72 + 64 * q^74 - 88 * q^77 - 4 * q^78 + 76 * q^81 - 64 * q^84 - 40 * q^85 - 80 * q^88 - 272 * q^91 - 48 * q^92 - 388 * q^93 - 544 * q^95 - 128 * q^98 - 160 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$31$	$71$	$127$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$	1.94039	+	2.28799i	0.646795	+	0.762664i
$3$	1.94039	+	2.28799i	0.646795	+	0.762664i
$4$			2.00000i			0.500000i
$5$	−4.58449	+	1.99562i	−0.916897	+	0.399123i
$5$	−4.58449	+	1.99562i	−0.916897	+	0.399123i
$6$	−0.347606	+	4.22838i	−0.0579344	+	0.704729i
$7$	5.57668	+	4.23091i	0.796669	+	0.604416i
$7$	5.57668	+	4.23091i	0.796669	+	0.604416i
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$	−1.46981	+	8.87917i	−0.163312	+	0.986574i
$10$	−6.58010	−	2.58887i	−0.658010	−	0.258887i
$11$		−	14.6047i		−	1.32770i	−0.747867	−	0.663849i	$-0.768922\pi$
$11$		−	14.6047i		−	1.32770i	0.747867	−	0.663849i	$-0.231078\pi$
$12$	−4.57598	+	3.88077i	−0.381332	+	0.323398i
$13$	−3.48167	+	3.48167i	−0.267821	+	0.267821i	−0.828222	−	0.560401i	$-0.810647\pi$
$13$	−3.48167	+	3.48167i	−0.267821	+	0.267821i	0.560401	+	0.828222i	$0.310647\pi$
$14$	1.34578	+	9.80759i	0.0961268	+	0.700542i
$15$	−13.4616	−	6.61700i	−0.897442	−	0.441133i
$16$	−4.00000			−0.250000
$17$	−20.1653	+	20.1653i	−1.18619	+	1.18619i	−0.208081	+	0.978112i	$0.566722\pi$
$17$	−20.1653	+	20.1653i	−1.18619	+	1.18619i	−0.978112	+	0.208081i	$0.933278\pi$
$18$	−10.3490	+	7.40936i	−0.574943	+	0.411631i
$19$	26.4132			1.39017			0.695085	−	0.718928i	$-0.255367\pi$
$19$	26.4132			1.39017			0.695085	+	0.718928i	$0.255367\pi$
$20$	−3.99123	−	9.16897i	−0.199562	−	0.458449i
$21$	1.14063	+	20.9690i	0.0543157	+	0.998524i
$22$	14.6047	−	14.6047i	0.663849	−	0.663849i
$23$	2.68095	−	2.68095i	0.116563	−	0.116563i	−0.646419	−	0.762982i	$-0.723734\pi$
$23$	2.68095	−	2.68095i	0.116563	−	0.116563i	0.762982	+	0.646419i	$0.223734\pi$
$24$	−8.45675	−	0.695213i	−0.352365	−	0.0289672i
$25$	17.0350	−	18.2978i	0.681401	−	0.731910i
$26$	−6.96334			−0.267821
$27$	−23.1675	+	13.8661i	−0.858054	+	0.513559i
$28$	−8.46182	+	11.1534i	−0.302208	+	0.398335i
$29$	28.5159			0.983306			0.491653	−	0.870791i	$-0.336393\pi$
$29$	28.5159			0.983306			0.491653	+	0.870791i	$0.336393\pi$
$30$	−6.84462	−	20.0786i	−0.228154	−	0.669287i
$31$		−	15.6511i		−	0.504875i	−0.967613	−	0.252438i	$-0.918768\pi$
$31$		−	15.6511i		−	0.504875i	0.967613	−	0.252438i	$-0.0812322\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	33.4154	−	28.3387i	1.01259	−	0.858748i
$34$	−40.3306			−1.18619
$35$	−34.0095	−	8.26762i	−0.971700	−	0.236218i
$36$	−17.7583	−	2.93962i	−0.493287	−	0.0816562i
$37$	7.69844	−	7.69844i	0.208066	−	0.208066i	−0.595379	−	0.803445i	$-0.702998\pi$
$37$	7.69844	−	7.69844i	0.208066	−	0.208066i	0.803445	+	0.595379i	$0.202998\pi$
$38$	26.4132	+	26.4132i	0.695085	+	0.695085i
$39$	−14.7218	−	1.21025i	−0.377483	−	0.0310321i
$40$	5.17774	−	13.1602i	0.129443	−	0.329005i
$41$	37.9832			0.926419			0.463209	−	0.886249i	$-0.346698\pi$
$41$	37.9832			0.926419			0.463209	+	0.886249i	$0.346698\pi$
$42$	−19.8284	+	22.1096i	−0.472104	+	0.526420i
$43$	41.7817	+	41.7817i	0.971667	+	0.971667i	0.999610	−	0.0279426i	$-0.00889555\pi$
$43$	41.7817	+	41.7817i	0.971667	+	0.971667i	−0.0279426	+	0.999610i	$0.508896\pi$
$44$	29.2094			0.663849
$45$	−10.9811	−	43.6396i	−0.244024	−	0.969769i
$46$	5.36190			0.116563
$47$	21.0822	−	21.0822i	0.448558	−	0.448558i	−0.446317	−	0.894875i	$-0.647265\pi$
$47$	21.0822	−	21.0822i	0.448558	−	0.448558i	0.894875	+	0.446317i	$0.147265\pi$
$48$	−7.76154	−	9.15197i	−0.161699	−	0.190666i
$49$	13.1988	+	47.1889i	0.269364	+	0.963039i
$50$	35.3328	−	1.26273i	0.706656	−	0.0252547i
$51$	−85.2664	−	7.00958i	−1.67189	−	0.137443i
$52$	−6.96334	−	6.96334i	−0.133910	−	0.133910i
$53$	−47.4934	+	47.4934i	−0.896102	+	0.896102i	−0.995089	−	0.0989866i	$-0.968440\pi$
$53$	−47.4934	+	47.4934i	−0.896102	+	0.896102i	0.0989866	+	0.995089i	$0.468440\pi$
$54$	−37.0336	−	9.30137i	−0.685807	−	0.172248i
$55$	29.1453	+	66.9549i	0.529915	+	1.21736i
$56$	−19.6152	+	2.69155i	−0.350271	+	0.0480634i
$57$	51.2518	+	60.4332i	0.899155	+	1.06023i
$58$	28.5159	+	28.5159i	0.491653	+	0.491653i
$59$		−	61.6589i		−	1.04507i	−0.852619	−	0.522533i	$-0.824987\pi$
$59$		−	61.6589i		−	1.04507i	0.852619	−	0.522533i	$-0.175013\pi$
$60$	13.2340	−	26.9232i	0.220567	−	0.448721i
$61$		−	54.1777i		−	0.888159i	−0.895987	−	0.444080i	$-0.853531\pi$
$61$		−	54.1777i		−	0.888159i	0.895987	−	0.444080i	$-0.146469\pi$
$62$	15.6511	−	15.6511i	0.252438	−	0.252438i
$63$	−45.7636	+	43.2977i	−0.726407	+	0.687265i
$64$		−	8.00000i		−	0.125000i
$65$	9.01359	−	22.9098i	0.138671	−	0.352458i
$66$	61.7541	+	5.07668i	0.935668	+	0.0769194i
$67$	68.9882	−	68.9882i	1.02967	−	1.02967i	0.0301280	−	0.999546i	$-0.490409\pi$
$67$	68.9882	−	68.9882i	1.02967	−	1.02967i	0.999546	−	0.0301280i	$-0.00959148\pi$
$68$	−40.3306	−	40.3306i	−0.593096	−	0.593096i
$69$	11.3361	+	0.931915i	0.164291	+	0.0135060i
$70$	−25.7419	−	42.2771i	−0.367741	−	0.603959i
$71$		−	65.9594i		−	0.929006i	−0.885572	−	0.464503i	$-0.846233\pi$
$71$		−	65.9594i		−	0.929006i	0.885572	−	0.464503i	$-0.153767\pi$
$72$	−14.8187	−	20.6980i	−0.205816	−	0.287472i
$73$	6.51081	−	6.51081i	0.0891892	−	0.0891892i	−0.661105	−	0.750294i	$-0.729912\pi$
$73$	6.51081	−	6.51081i	0.0891892	−	0.0891892i	0.750294	+	0.661105i	$0.229912\pi$
$74$	15.3969			0.208066
$75$	74.9196	+	3.47129i	0.998928	+	0.0462839i
$76$			52.8265i			0.695085i
$77$	61.7911	−	81.4457i	0.802481	−	1.05774i
$78$	−13.5116	−	15.9321i	−0.173225	−	0.204257i
$79$			42.7301i			0.540887i	0.962736	+	0.270443i	$0.0871703\pi$
$79$			42.7301i			0.540887i	−0.962736	+	0.270443i	$0.912830\pi$
$80$	18.3379	−	7.98247i	0.229224	−	0.0997809i
$81$	−76.6793	−	26.1014i	−0.946658	−	0.322240i
$82$	37.9832	+	37.9832i	0.463209	+	0.463209i
$83$	9.52614	+	9.52614i	0.114773	+	0.114773i	0.762161	−	0.647388i	$-0.224139\pi$
$83$	9.52614	+	9.52614i	0.114773	+	0.114773i	−0.647388	+	0.762161i	$0.724139\pi$
$84$	−41.9380	+	2.28126i	−0.499262	+	0.0271579i
$85$	52.2053	−	132.690i	0.614180	−	1.56105i
$86$			83.5634i			0.971667i
$87$	55.3318	+	65.2441i	0.635998	+	0.749932i
$88$	29.2094	+	29.2094i	0.331924	+	0.331924i
$89$			19.3830i			0.217786i	0.994053	+	0.108893i	$0.0347306\pi$
$89$			19.3830i			0.217786i	−0.994053	+	0.108893i	$0.965269\pi$
$90$	32.6585	−	54.6207i	0.362872	−	0.606897i
$91$	−34.1468	+	4.68555i	−0.375240	+	0.0514895i
$92$	5.36190	+	5.36190i	0.0582815	+	0.0582815i
$93$	35.8096	−	30.3692i	0.385050	−	0.326551i
$94$	42.1644			0.448558
$95$	−121.091	+	52.7107i	−1.27464	+	0.554849i
$96$	1.39043	−	16.9135i	0.0144836	−	0.176182i
$97$	−84.6391	−	84.6391i	−0.872568	−	0.872568i	0.120184	−	0.992752i	$-0.461652\pi$
$97$	−84.6391	−	84.6391i	−0.872568	−	0.872568i	−0.992752	+	0.120184i	$0.961652\pi$
$98$	−33.9901	+	60.3877i	−0.346837	+	0.616201i
$99$	129.677	+	21.4661i	1.30987	+	0.216829i
$100$	36.5955	+	34.0700i	0.365955	+	0.340700i
$101$	−112.859			−1.11741			−0.558707	−	0.829365i	$-0.688702\pi$
$101$	−112.859			−1.11741			−0.558707	+	0.829365i	$0.688702\pi$
$102$	−78.2568	−	92.2760i	−0.767224	−	0.904666i
$103$	−82.5883	+	82.5883i	−0.801828	+	0.801828i	−0.983381	−	0.181553i	$-0.941888\pi$
$103$	−82.5883	+	82.5883i	−0.801828	+	0.801828i	0.181553	+	0.983381i	$0.441888\pi$
$104$		−	13.9267i		−	0.133910i
$105$	−47.0753	−	93.8558i	−0.448336	−	0.893865i
$106$	−94.9868			−0.896102
$107$	125.554	+	125.554i	1.17340	+	1.17340i	0.981393	+	0.192011i	$0.0615011\pi$
$107$	125.554	+	125.554i	1.17340	+	1.17340i	0.192011	+	0.981393i	$0.438499\pi$
$108$	−27.7322	−	46.3349i	−0.256780	−	0.429027i
$109$		−	1.60754i		−	0.0147481i	−0.999973	−	0.00737405i	$-0.997653\pi$
$109$		−	1.60754i		−	0.0147481i	0.999973	−	0.00737405i	$-0.00234725\pi$
$110$	−37.8096	+	96.1003i	−0.343724	+	0.873639i
$111$	32.5519	+	2.67603i	0.293261	+	0.0241084i
$112$	−22.3067	−	16.9236i	−0.199167	−	0.151104i
$113$	141.505	−	141.505i	1.25226	−	1.25226i	0.297556	−	0.954704i	$-0.403828\pi$
$113$	141.505	−	141.505i	1.25226	−	1.25226i	0.954704	−	0.297556i	$-0.0961715\pi$
$114$	−9.18141	+	111.685i	−0.0805387	+	0.979694i
$115$	−6.94062	+	17.6409i	−0.0603532	+	0.153399i
$116$			57.0318i			0.491653i
$117$	−25.7970	−	36.0318i	−0.220487	−	0.307964i
$118$	61.6589	−	61.6589i	0.522533	−	0.522533i
$119$	−197.773	+	27.1379i	−1.66196	+	0.228050i
$120$	40.1572	−	13.6892i	0.334644	−	0.114077i
$121$	−92.2966			−0.762782
$122$	54.1777	−	54.1777i	0.444080	−	0.444080i
$123$	73.7020	+	86.9052i	0.599203	+	0.706546i
$124$	31.3023			0.252438
$125$	−41.5815	+	117.881i	−0.332652	+	0.943050i
$126$	−89.0613	−	2.46594i	−0.706836	−	0.0195710i
$127$	−39.5166	+	39.5166i	−0.311154	+	0.311154i	−0.845357	−	0.534202i	$-0.820612\pi$
$127$	−39.5166	+	39.5166i	−0.311154	+	0.311154i	0.534202	+	0.845357i	$0.320612\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$	−14.5236	+	176.669i	−0.112586	+	1.36952i
$130$	31.9234	−	13.8962i	0.245564	−	0.106894i
$131$	−122.046			−0.931652			−0.465826	−	0.884876i	$-0.654243\pi$
$131$	−122.046			−0.931652			−0.465826	+	0.884876i	$0.654243\pi$
$132$	56.6774	+	66.8308i	0.429374	+	0.506294i
$133$	147.298	+	111.752i	1.10751	+	0.840240i
$134$	137.976			1.02967
$135$	78.5395	−	109.802i	0.581774	−	0.813350i
$136$		−	80.6611i		−	0.593096i
$137$	−141.949	−	141.949i	−1.03612	−	1.03612i	−0.999323	−	0.0368001i	$-0.988284\pi$
$137$	−141.949	−	141.949i	−1.03612	−	1.03612i	−0.0368001	−	0.999323i	$-0.511716\pi$
$138$	10.4041	+	12.2680i	0.0753924	+	0.0888984i
$139$	41.4554			0.298240			0.149120	−	0.988819i	$-0.452356\pi$
$139$	41.4554			0.298240			0.149120	+	0.988819i	$0.452356\pi$
$140$	16.5352	−	68.0190i	0.118109	−	0.485850i
$141$	89.1435	+	7.32831i	0.632224	+	0.0519739i
$142$	65.9594	−	65.9594i	0.464503	−	0.464503i
$143$	50.8487	+	50.8487i	0.355585	+	0.355585i
$144$	5.87924	−	35.5167i	0.0408281	−	0.246644i
$145$	−130.731	+	56.9068i	−0.901591	+	0.392461i
$146$	13.0216			0.0891892
$147$	−82.3570	+	121.763i	−0.560252	+	0.828322i
$148$	15.3969	+	15.3969i	0.104033	+	0.104033i
$149$	−189.375			−1.27097			−0.635485	−	0.772113i	$-0.719200\pi$
$149$	−189.375			−1.27097			−0.635485	+	0.772113i	$0.719200\pi$
$150$	71.4483	+	78.3909i	0.476322	+	0.522606i
$151$	−117.328			−0.777007			−0.388503	−	0.921447i	$-0.627008\pi$
$151$	−117.328			−0.777007			−0.388503	+	0.921447i	$0.627008\pi$
$152$	−52.8265	+	52.8265i	−0.347542	+	0.347542i
$153$	−149.412	−	208.690i	−0.976548	−	1.36399i
$154$	143.237	−	19.6546i	0.930109	−	0.127627i
$155$	31.2337	+	71.7524i	0.201507	+	0.462919i
$156$	2.42050	−	29.4436i	0.0155160	−	0.188741i
$157$	−123.504	−	123.504i	−0.786651	−	0.786651i	0.194293	−	0.980944i	$-0.437759\pi$
$157$	−123.504	−	123.504i	−0.786651	−	0.786651i	−0.980944	+	0.194293i	$0.937759\pi$
$158$	−42.7301	+	42.7301i	−0.270443	+	0.270443i
$159$	−200.820	−	16.5090i	−1.26302	−	0.103830i
$160$	26.3204	+	10.3555i	0.164503	+	0.0647217i
$161$	26.2937	−	3.60795i	0.163315	−	0.0224096i
$162$	−50.5779	−	102.781i	−0.312209	−	0.634449i
$163$	−173.541	−	173.541i	−1.06467	−	1.06467i	−0.997759	−	0.0669121i	$-0.978685\pi$
$163$	−173.541	−	173.541i	−1.06467	−	1.06467i	−0.0669121	−	0.997759i	$-0.521315\pi$
$164$			75.9663i			0.463209i
$165$	−96.6391	+	196.603i	−0.585692	+	1.19153i
$166$			19.0523i			0.114773i
$167$	−32.6021	+	32.6021i	−0.195222	+	0.195222i	−0.797948	−	0.602726i	$-0.794081\pi$
$167$	−32.6021	+	32.6021i	−0.195222	+	0.195222i	0.602726	+	0.797948i	$0.294081\pi$
$168$	−44.2193	−	39.6567i	−0.263210	−	0.236052i
$169$			144.756i			0.856544i
$170$	184.895	−	80.4844i	1.08762	−	0.473437i
$171$	−38.8225	+	234.528i	−0.227032	+	1.37151i
$172$	−83.5634	+	83.5634i	−0.485833	+	0.485833i
$173$	122.097	+	122.097i	0.705761	+	0.705761i	0.965641	−	0.259880i	$-0.0836830\pi$
$173$	122.097	+	122.097i	0.705761	+	0.705761i	−0.259880	+	0.965641i	$0.583683\pi$
$174$	−9.91231	+	120.576i	−0.0569673	+	0.692965i
$175$	172.415	−	29.9672i	0.985229	−	0.171241i
$176$			58.4187i			0.331924i
$177$	141.075	−	119.642i	0.797034	−	0.675943i
$178$	−19.3830	+	19.3830i	−0.108893	+	0.108893i
$179$	48.8414			0.272857			0.136429	−	0.990650i	$-0.456438\pi$
$179$	48.8414			0.272857			0.136429	+	0.990650i	$0.456438\pi$
$180$	87.2792	−	21.9622i	0.484885	−	0.122012i
$181$		−	74.5578i		−	0.411921i	−0.978560	−	0.205961i	$-0.933968\pi$
$181$		−	74.5578i		−	0.411921i	0.978560	−	0.205961i	$-0.0660319\pi$
$182$	−38.8324	−	29.4613i	−0.213365	−	0.161875i
$183$	123.958	−	105.126i	0.677367	−	0.574457i
$184$			10.7238i			0.0582815i
$185$	−19.9303	+	50.6565i	−0.107731	+	0.273819i
$186$	66.1789	+	5.44043i	0.355800	+	0.0292496i
$187$	294.507	+	294.507i	1.57491	+	1.57491i
$188$	42.1644	+	42.1644i	0.224279	+	0.224279i
$189$	−187.864	−	20.6926i	−0.993988	−	0.109485i
$190$	−173.802	−	68.3804i	−0.914746	−	0.359897i
$191$		−	22.0006i		−	0.115187i	−0.998340	−	0.0575933i	$-0.981657\pi$
$191$		−	22.0006i		−	0.115187i	0.998340	−	0.0575933i	$-0.0183427\pi$
$192$	18.3039	−	15.5231i	0.0953330	−	0.0808494i
$193$	−73.7660	−	73.7660i	−0.382207	−	0.382207i	0.489690	−	0.871897i	$-0.337110\pi$
$193$	−73.7660	−	73.7660i	−0.382207	−	0.382207i	−0.871897	+	0.489690i	$0.837110\pi$
$194$		−	169.278i		−	0.872568i
$195$	69.9072	−	23.8307i	0.358498	−	0.122209i
$196$	−94.3778	+	26.3976i	−0.481519	+	0.134682i
$197$	124.480	+	124.480i	0.631878	+	0.631878i	0.948539	−	0.316661i	$-0.102562\pi$
$197$	124.480	+	124.480i	0.631878	+	0.631878i	−0.316661	+	0.948539i	$0.602562\pi$
$198$	108.211	+	151.144i	0.546522	+	0.763351i
$199$	−324.188			−1.62908			−0.814542	−	0.580104i	$-0.803012\pi$
$199$	−324.188			−1.62908			−0.814542	+	0.580104i	$0.803012\pi$
$200$	2.52547	+	70.6656i	0.0126273	+	0.353328i
$201$	291.708	+	23.9807i	1.45128	+	0.119307i
$202$	−112.859	−	112.859i	−0.558707	−	0.558707i
$203$	159.024	+	120.648i	0.783370	+	0.594326i
$204$	14.0192	−	170.533i	0.0687214	−	0.835945i
$205$	−174.133	+	75.7999i	−0.849431	+	0.369755i
$206$	−165.177			−0.801828
$207$	19.8641	+	27.7451i	0.0959619	+	0.134034i
$208$	13.9267	−	13.9267i	0.0669552	−	0.0669552i
$209$		−	385.757i		−	1.84573i
$210$	46.7805	−	140.931i	0.222764	−	0.671101i
$211$	29.3640			0.139166			0.0695828	−	0.997576i	$-0.477833\pi$
$211$	29.3640			0.139166			0.0695828	+	0.997576i	$0.477833\pi$
$212$	−94.9868	−	94.9868i	−0.448051	−	0.448051i
$213$	150.915	−	127.987i	0.708519	−	0.600876i
$214$			251.108i			1.17340i
$215$	−274.928	−	108.167i	−1.27873	−	0.503104i
$216$	18.6027	−	74.0671i	0.0861238	−	0.342903i
$217$	66.2185	−	87.2814i	0.305154	−	0.402218i
$218$	1.60754	−	1.60754i	0.00737405	−	0.00737405i
$219$	27.5302	+	2.26320i	0.125709	+	0.0103342i
$220$	−133.910	+	58.2907i	−0.608681	+	0.264958i
$221$		−	140.418i		−	0.635375i
$222$	29.8759	+	35.2279i	0.134576	+	0.158684i
$223$	−203.552	+	203.552i	−0.912788	+	0.912788i	−0.996491	−	0.0837032i	$-0.973325\pi$
$223$	−203.552	+	203.552i	−0.912788	+	0.912788i	0.0837032	+	0.996491i	$0.473325\pi$
$224$	−5.38310	−	39.2304i	−0.0240317	−	0.175136i
$225$	137.431	+	178.151i	0.610803	+	0.791783i
$226$	283.011			1.25226
$227$	152.211	−	152.211i	0.670535	−	0.670535i	−0.287305	−	0.957839i	$-0.592759\pi$
$227$	152.211	−	152.211i	0.670535	−	0.670535i	0.957839	+	0.287305i	$0.0927592\pi$
$228$	−120.866	+	102.504i	−0.530116	+	0.449577i
$229$	219.445			0.958275			0.479138	−	0.877740i	$-0.340949\pi$
$229$	219.445			0.958275			0.479138	+	0.877740i	$0.340949\pi$
$230$	−24.5815	+	10.7003i	−0.106876	+	0.0465230i
$231$	306.245	−	16.6585i	1.32574	−	0.0721149i
$232$	−57.0318	+	57.0318i	−0.245827	+	0.245827i
$233$	216.913	−	216.913i	0.930957	−	0.930957i	−0.0668091	−	0.997766i	$-0.521282\pi$
$233$	216.913	−	216.913i	0.930957	−	0.930957i	0.997766	+	0.0668091i	$0.0212819\pi$
$234$	10.2348	−	61.8287i	0.0437385	−	0.264225i
$235$	−54.5791	+	138.723i	−0.232251	+	0.590311i
$236$	123.318			0.522533
$237$	−97.7660	+	82.9128i	−0.412515	+	0.349843i
$238$	−224.911	−	170.635i	−0.945003	−	0.716953i
$239$	261.894			1.09579			0.547896	−	0.836547i	$-0.315429\pi$
$239$	261.894			1.09579			0.547896	+	0.836547i	$0.315429\pi$
$240$	53.8465	+	26.4680i	0.224360	+	0.110283i
$241$		−	187.969i		−	0.779955i	−0.920824	−	0.389978i	$-0.872483\pi$
$241$		−	187.969i		−	0.779955i	0.920824	−	0.389978i	$-0.127517\pi$
$242$	−92.2966	−	92.2966i	−0.381391	−	0.381391i
$243$	−89.0676	−	226.088i	−0.366533	−	0.930405i
$244$	108.355			0.444080
$245$	−154.681	−	189.997i	−0.631350	−	0.775498i
$246$	−13.2032	+	160.607i	−0.0536715	+	0.652875i
$247$	−91.9622	+	91.9622i	−0.372317	+	0.372317i
$248$	31.3023	+	31.3023i	0.126219	+	0.126219i
$249$	−3.31135	+	40.2801i	−0.0132986	+	0.161768i
$250$	−159.463	+	76.2997i	−0.637851	+	0.305199i
$251$	406.255			1.61855			0.809273	−	0.587433i	$-0.199861\pi$
$251$	406.255			1.61855			0.809273	+	0.587433i	$0.199861\pi$
$252$	−86.5954	−	91.5273i	−0.343632	−	0.363203i
$253$	−39.1544	−	39.1544i	−0.154760	−	0.154760i
$254$	−79.0332			−0.311154
$255$	404.891	−	138.024i	1.58781	−	0.541270i
$256$	16.0000			0.0625000
$257$	−55.7465	+	55.7465i	−0.216912	+	0.216912i	−0.807196	−	0.590284i	$-0.799016\pi$
$257$	−55.7465	+	55.7465i	−0.216912	+	0.216912i	0.590284	+	0.807196i	$0.299016\pi$
$258$	−191.192	+	162.145i	−0.741055	+	0.628469i
$259$	75.5032	−	10.3604i	0.291518	−	0.0400014i
$260$	45.8195	+	18.0272i	0.176229	+	0.0693353i
$261$	−41.9130	+	253.197i	−0.160586	+	0.970105i
$262$	−122.046	−	122.046i	−0.465826	−	0.465826i
$263$	−96.5716	+	96.5716i	−0.367192	+	0.367192i	−0.866452	−	0.499260i	$-0.833605\pi$
$263$	−96.5716	+	96.5716i	−0.367192	+	0.367192i	0.499260	+	0.866452i	$0.333605\pi$
$264$	−10.1534	+	123.508i	−0.0384597	+	0.467834i
$265$	122.954	−	312.512i	0.463978	−	1.17929i
$266$	35.5463	+	259.050i	0.133633	+	0.973873i
$267$	−44.3481	+	37.6105i	−0.166098	+	0.140863i
$268$	137.976	+	137.976i	0.514837	+	0.514837i
$269$		−	100.672i		−	0.374246i	−0.982336	−	0.187123i	$-0.940084\pi$
$269$		−	100.672i		−	0.374246i	0.982336	−	0.187123i	$-0.0599163\pi$
$270$	188.342	−	31.2628i	0.697562	−	0.115788i
$271$		−	299.070i		−	1.10358i	−0.833983	−	0.551790i	$-0.813945\pi$
$271$		−	299.070i		−	1.10358i	0.833983	−	0.551790i	$-0.186055\pi$
$272$	80.6611	−	80.6611i	0.296548	−	0.296548i
$273$	−76.9785	−	69.0359i	−0.281972	−	0.252879i
$274$		−	283.898i		−	1.03612i
$275$	−267.233	−	248.791i	−0.971756	−	0.904695i
$276$	−1.86383	+	22.6721i	−0.00675301	+	0.0821454i
$277$	−310.502	+	310.502i	−1.12095	+	1.12095i	−0.129348	+	0.991599i	$0.541288\pi$
$277$	−310.502	+	310.502i	−1.12095	+	1.12095i	−0.991599	+	0.129348i	$0.958712\pi$
$278$	41.4554	+	41.4554i	0.149120	+	0.149120i
$279$	138.969	+	23.0042i	0.498097	+	0.0824523i
$280$	84.5542	−	51.4838i	0.301979	−	0.183871i
$281$		−	229.692i		−	0.817409i	−0.912667	−	0.408704i	$-0.865981\pi$
$281$		−	229.692i		−	0.817409i	0.912667	−	0.408704i	$-0.134019\pi$
$282$	81.8152	+	96.4718i	0.290125	+	0.342099i
$283$	170.587	−	170.587i	0.602781	−	0.602781i	−0.338269	−	0.941049i	$-0.609841\pi$
$283$	170.587	−	170.587i	0.602781	−	0.602781i	0.941049	+	0.338269i	$0.109841\pi$
$284$	131.919			0.464503
$285$	−355.565	−	174.776i	−1.24760	−	0.613250i
$286$			101.697i			0.355585i
$287$	211.820	+	160.703i	0.738049	+	0.559942i
$288$	41.3959	−	29.6374i	0.143736	−	0.102908i
$289$		−	524.277i		−	1.81411i
$290$	−187.637	−	73.8239i	−0.647026	−	0.254565i
$291$	29.4211	−	357.886i	0.101103	−	1.22985i
$292$	13.0216	+	13.0216i	0.0445946	+	0.0445946i
$293$	186.419	+	186.419i	0.636243	+	0.636243i	0.949627	−	0.313384i	$-0.101463\pi$
$293$	186.419	+	186.419i	0.636243	+	0.636243i	−0.313384	+	0.949627i	$0.601463\pi$
$294$	−204.120	+	39.4064i	−0.694287	+	0.134035i
$295$	123.047	+	282.674i	0.417110	+	0.958218i
$296$			30.7938i			0.104033i
$297$	202.510	+	338.353i	0.681851	+	1.13924i
$298$	−189.375	−	189.375i	−0.635485	−	0.635485i
$299$			18.6684i			0.0624360i
$300$	−6.94259	+	149.839i	−0.0231420	+	0.499464i
$301$	56.2287	+	409.778i	0.186806	+	1.36139i
$302$	−117.328	−	117.328i	−0.388503	−	0.388503i
$303$	−218.990	−	258.220i	−0.722738	−	0.852211i
$304$	−105.653			−0.347542
$305$	108.118	+	248.377i	0.354485	+	0.814351i
$306$	59.2783	−	358.102i	0.193720	−	1.17027i
$307$	−9.77168	−	9.77168i	−0.0318296	−	0.0318296i	0.691013	−	0.722842i	$-0.257165\pi$
$307$	−9.77168	−	9.77168i	−0.0318296	−	0.0318296i	−0.722842	+	0.691013i	$0.757165\pi$
$308$	162.891	+	123.582i	0.528868	+	0.401241i
$309$	−349.215	−	28.7082i	−1.13014	−	0.0929069i
$310$	−40.5187	+	102.986i	−0.130706	+	0.332213i
$311$	−145.632			−0.468271			−0.234136	−	0.972204i	$-0.575226\pi$
$311$	−145.632			−0.468271			−0.234136	+	0.972204i	$0.575226\pi$
$312$	31.8641	−	27.0231i	0.102129	−	0.0866126i
$313$	354.096	−	354.096i	1.13130	−	1.13130i	0.141335	−	0.989962i	$-0.454861\pi$
$313$	354.096	−	354.096i	1.13130	−	1.13130i	0.989962	−	0.141335i	$-0.0451395\pi$
$314$		−	247.008i		−	0.786651i
$315$	123.397	−	289.824i	0.391737	−	0.920077i
$316$	−85.4601			−0.270443
$317$	136.486	+	136.486i	0.430556	+	0.430556i	0.888817	−	0.458262i	$-0.151528\pi$
$317$	136.486	+	136.486i	0.430556	+	0.430556i	−0.458262	+	0.888817i	$0.651528\pi$
$318$	−184.311	−	217.329i	−0.579594	−	0.683425i
$319$		−	416.465i		−	1.30553i
$320$	15.9649	+	36.6759i	0.0498904	+	0.114612i
$321$	−43.6435	+	530.891i	−0.135961	+	1.65386i
$322$	29.9016	+	22.6857i	0.0928621	+	0.0704525i
$323$	−532.630	+	532.630i	−1.64901	+	1.64901i
$324$	52.2028	−	153.359i	0.161120	−	0.473329i
$325$	4.39643	+	123.017i	0.0135275	+	0.378514i
$326$		−	347.083i		−	1.06467i
$327$	3.67804	−	3.11925i	0.0112478	−	0.00953899i
$328$	−75.9663	+	75.9663i	−0.231605	+	0.231605i
$329$	206.766	−	28.3719i	0.628467	−	0.0862368i
$330$	−293.242	+	99.9635i	−0.888612	+	0.302920i
$331$	317.945			0.960559			0.480279	−	0.877116i	$-0.340535\pi$
$331$	317.945			0.960559			0.480279	+	0.877116i	$0.340535\pi$
$332$	−19.0523	+	19.0523i	−0.0573864	+	0.0573864i
$333$	57.0405	+	79.6710i	0.171293	+	0.239252i
$334$	−65.2042			−0.195222
$335$	−178.601	+	453.949i	−0.533138	+	1.35507i
$336$	−4.56252	−	83.8760i	−0.0135789	−	0.249631i
$337$	95.8647	−	95.8647i	0.284465	−	0.284465i	−0.550422	−	0.834887i	$-0.685533\pi$
$337$	95.8647	−	95.8647i	0.284465	−	0.284465i	0.834887	+	0.550422i	$0.185533\pi$
$338$	−144.756	+	144.756i	−0.428272	+	0.428272i
$339$	598.338	+	49.1882i	1.76501	+	0.145098i
$340$	265.379	+	104.411i	0.780527	+	0.307090i
$341$	−228.580			−0.670322
$342$	−273.350	+	195.705i	−0.799269	+	0.572237i
$343$	−126.046	+	319.001i	−0.367482	+	0.930031i
$344$	−167.127			−0.485833
$345$	−53.8298	+	18.3501i	−0.156028	+	0.0531886i
$346$			244.193i			0.705761i
$347$	76.3053	+	76.3053i	0.219900	+	0.219900i	0.808456	−	0.588556i	$-0.200303\pi$
$347$	76.3053	+	76.3053i	0.219900	+	0.219900i	−0.588556	+	0.808456i	$0.700303\pi$
$348$	−130.488	+	110.664i	−0.374966	+	0.317999i
$349$	−27.7850			−0.0796133			−0.0398067	−	0.999207i	$-0.512674\pi$
$349$	−27.7850			−0.0796133			−0.0398067	+	0.999207i	$0.512674\pi$
$350$	202.382	+	142.448i	0.578235	+	0.406994i
$351$	32.3843	−	128.939i	0.0922630	−	0.367347i
$352$	−58.4187	+	58.4187i	−0.165962	+	0.165962i
$353$	188.774	+	188.774i	0.534769	+	0.534769i	0.921988	−	0.387218i	$-0.126564\pi$
$353$	188.774	+	188.774i	0.534769	+	0.534769i	−0.387218	+	0.921988i	$0.626564\pi$
$354$	260.717	+	21.4330i	0.736488	+	0.0605452i
$355$	131.630	+	302.390i	0.370788	+	0.851803i
$356$	−38.7660			−0.108893
$357$	−445.847	−	399.845i	−1.24887	−	1.12001i
$358$	48.8414	+	48.8414i	0.136429	+	0.136429i
$359$	−171.974			−0.479037			−0.239519	−	0.970892i	$-0.576990\pi$
$359$	−171.974			−0.479037			−0.239519	+	0.970892i	$0.576990\pi$
$360$	109.241	+	65.3170i	0.303448	+	0.181436i
$361$	336.659			0.932572
$362$	74.5578	−	74.5578i	0.205961	−	0.205961i
$363$	−179.091	−	211.174i	−0.493364	−	0.581746i
$364$	−9.37109	−	68.2936i	−0.0257448	−	0.187620i
$365$	−16.8556	+	42.8418i	−0.0461798	+	0.117375i
$366$	229.084	+	18.8325i	0.625912	+	0.0514550i
$367$	−181.555	−	181.555i	−0.494700	−	0.494700i	0.415083	−	0.909784i	$-0.363753\pi$
$367$	−181.555	−	181.555i	−0.494700	−	0.494700i	−0.909784	+	0.415083i	$0.863753\pi$
$368$	−10.7238	+	10.7238i	−0.0291407	+	0.0291407i
$369$	−55.8281	+	337.259i	−0.151296	+	0.913981i
$370$	−70.5868	+	30.7263i	−0.190775	+	0.0830440i
$371$	−465.796	+	63.9154i	−1.25552	+	0.172279i
$372$	60.7384	+	71.6193i	0.163275	+	0.192525i
$373$	−104.153	−	104.153i	−0.279231	−	0.279231i	0.553571	−	0.832802i	$-0.313265\pi$
$373$	−104.153	−	104.153i	−0.279231	−	0.279231i	−0.832802	+	0.553571i	$0.813265\pi$
$374$			589.015i			1.57491i
$375$	−350.395	+	133.597i	−0.934388	+	0.356258i
$376$			84.3288i			0.224279i
$377$	−99.2830	+	99.2830i	−0.263350	+	0.263350i
$378$	−167.171	−	208.556i	−0.442252	−	0.551737i
$379$			339.431i			0.895596i	0.894135	+	0.447798i	$0.147792\pi$
$379$			339.431i			0.895596i	−0.894135	+	0.447798i	$0.852208\pi$
$380$	−105.421	−	242.182i	−0.277425	−	0.637321i
$381$	−167.091	−	13.7362i	−0.438559	−	0.0360531i
$382$	22.0006	−	22.0006i	0.0575933	−	0.0575933i
$383$	−187.161	−	187.161i	−0.488670	−	0.488670i	0.419217	−	0.907886i	$-0.362305\pi$
$383$	−187.161	−	187.161i	−0.488670	−	0.488670i	−0.907886	+	0.419217i	$0.862305\pi$
$384$	33.8270	+	2.78085i	0.0880912	+	0.00724180i
$385$	−120.746	+	496.698i	−0.313626	+	1.29012i
$386$		−	147.532i		−	0.382207i
$387$	−432.398	+	309.575i	−1.11731	+	0.799937i
$388$	169.278	−	169.278i	0.436284	−	0.436284i
$389$	511.312			1.31443			0.657214	−	0.753704i	$-0.271735\pi$
$389$	511.312			1.31443			0.657214	+	0.753704i	$0.271735\pi$
$390$	93.7379	+	46.0764i	0.240354	+	0.118145i
$391$			108.124i			0.276532i
$392$	−120.775	−	67.9801i	−0.308101	−	0.173419i
$393$	−236.817	−	279.241i	−0.602588	−	0.710537i
$394$			248.960i			0.631878i
$395$	−85.2729	−	195.895i	−0.215881	−	0.495938i
$396$	−42.9322	+	259.355i	−0.108415	+	0.654936i
$397$	448.583	+	448.583i	1.12993	+	1.12993i	0.990188	+	0.139744i	$0.0446280\pi$
$397$	448.583	+	448.583i	1.12993	+	1.12993i	0.139744	+	0.990188i	$0.455372\pi$
$398$	−324.188	−	324.188i	−0.814542	−	0.814542i
$399$	30.1277	+	553.859i	0.0755081	+	1.38812i
$400$	−68.1401	+	73.1910i	−0.170350	+	0.182978i
$401$			44.3430i			0.110581i	0.998470	+	0.0552905i	$0.0176085\pi$
$401$			44.3430i			0.110581i	−0.998470	+	0.0552905i	$0.982391\pi$
$402$	267.727	+	315.689i	0.665988	+	0.785295i
$403$	54.4921	+	54.4921i	0.135216	+	0.135216i
$404$		−	225.718i		−	0.558707i
$405$	403.624	−	33.3610i	0.996602	−	0.0823729i
$406$	38.3760	+	279.672i	0.0945221	+	0.688848i
$407$	−112.433	−	112.433i	−0.276249	−	0.276249i
$408$	184.552	−	156.514i	0.452333	−	0.383612i
$409$	−392.358			−0.959311			−0.479656	−	0.877457i	$-0.659238\pi$
$409$	−392.358			−0.959311			−0.479656	+	0.877457i	$0.659238\pi$
$410$	−249.933	−	98.3335i	−0.609593	−	0.239838i
$411$	49.3423	−	600.213i	0.120054	−	1.46037i
$412$	−165.177	−	165.177i	−0.400914	−	0.400914i
$413$	260.873	−	343.852i	0.631654	−	0.832571i
$414$	−7.88097	+	47.6092i	−0.0190362	+	0.114998i
$415$	−62.6830	−	24.6619i	−0.151043	−	0.0594263i
$416$	27.8534			0.0669552
$417$	80.4394	+	94.8495i	0.192900	+	0.227457i
$418$	385.757	−	385.757i	0.922863	−	0.922863i
$419$			383.324i			0.914855i	0.889247	+	0.457427i	$0.151229\pi$
$419$			383.324i			0.914855i	−0.889247	+	0.457427i	$0.848771\pi$
$420$	187.712	−	94.1506i	0.446933	−	0.224168i
$421$	809.373			1.92250			0.961250	−	0.275678i	$-0.0889023\pi$
$421$	809.373			1.92250			0.961250	+	0.275678i	$0.0889023\pi$
$422$	29.3640	+	29.3640i	0.0695828	+	0.0695828i
$423$	156.206	+	218.179i	0.369281	+	0.515791i
$424$		−	189.974i		−	0.448051i
$425$	25.4634	+	712.495i	0.0599139	+	1.67646i
$426$	278.901	+	22.9279i	0.654698	+	0.0538214i
$427$	229.221	−	302.132i	0.536817	−	0.707569i
$428$	−251.108	+	251.108i	−0.586702	+	0.586702i
$429$	−17.6753	+	215.007i	−0.0412012	+	0.501183i
$430$	−166.760	−	383.095i	−0.387815	−	0.890919i
$431$			432.674i			1.00388i	0.864902	+	0.501942i	$0.167381\pi$
$431$			432.674i			1.00388i	−0.864902	+	0.501942i	$0.832619\pi$
$432$	92.6699	−	55.4644i	0.214514	−	0.128390i
$433$	−288.449	+	288.449i	−0.666163	+	0.666163i	−0.956826	−	0.290662i	$-0.906124\pi$
$433$	−288.449	+	288.449i	−0.666163	+	0.666163i	0.290662	+	0.956826i	$0.406124\pi$
$434$	153.500	−	21.0629i	0.353686	−	0.0485320i
$435$	−383.870	−	188.690i	−0.882460	−	0.433769i
$436$	3.21508			0.00737405
$437$	70.8125	−	70.8125i	0.162042	−	0.162042i
$438$	25.2670	+	29.7934i	0.0576871	+	0.0680214i
$439$	−652.665			−1.48671			−0.743354	−	0.668898i	$-0.766766\pi$
$439$	−652.665			−1.48671			−0.743354	+	0.668898i	$0.766766\pi$
$440$	−192.201	−	75.6192i	−0.436819	−	0.171862i
$441$	−438.398	+	47.8358i	−0.994100	+	0.108471i
$442$	140.418	−	140.418i	0.317687	−	0.317687i
$443$	−429.708	+	429.708i	−0.969996	+	0.969996i	−0.999563	−	0.0295673i	$-0.990587\pi$
$443$	−429.708	+	429.708i	−0.969996	+	0.969996i	0.0295673	+	0.999563i	$0.490587\pi$
$444$	−5.35206	+	65.1038i	−0.0120542	+	0.146630i
$445$	−38.6810	−	88.8610i	−0.0869236	−	0.199688i
$446$	−407.103			−0.912788
$447$	−367.460	−	433.287i	−0.822057	−	0.969323i
$448$	33.8473	−	44.6135i	0.0755519	−	0.0995836i
$449$	−544.342			−1.21234			−0.606171	−	0.795334i	$-0.707295\pi$
$449$	−544.342			−1.21234			−0.606171	+	0.795334i	$0.707295\pi$
$450$	−40.7205	+	315.582i	−0.0904900	+	0.701293i
$451$		−	554.732i		−	1.23000i
$452$	283.011	+	283.011i	0.626130	+	0.626130i
$453$	−227.662	−	268.446i	−0.502564	−	0.592595i
$454$	304.423			0.670535
$455$	147.195	−	89.6248i	0.323506	−	0.196978i
$456$	−223.370	−	18.3628i	−0.489847	−	0.0402693i
$457$	−100.300	+	100.300i	−0.219475	+	0.219475i	−0.808277	−	0.588802i	$-0.799600\pi$
$457$	−100.300	+	100.300i	−0.219475	+	0.219475i	0.588802	+	0.808277i	$0.299600\pi$
$458$	219.445	+	219.445i	0.479138	+	0.479138i
$459$	187.565	−	746.792i	0.408638	−	1.62700i
$460$	−35.2818	−	13.8812i	−0.0766996	−	0.0301766i
$461$	−16.3102			−0.0353801			−0.0176900	−	0.999844i	$-0.505631\pi$
$461$	−16.3102			−0.0353801			−0.0176900	+	0.999844i	$0.505631\pi$
$462$	322.904	+	289.587i	0.698926	+	0.626812i
$463$	−401.469	−	401.469i	−0.867104	−	0.867104i	0.125047	−	0.992151i	$-0.460092\pi$
$463$	−401.469	−	401.469i	−0.867104	−	0.867104i	−0.992151	+	0.125047i	$0.960092\pi$
$464$	−114.064			−0.245827
$465$	−103.564	+	210.690i	−0.222717	+	0.453096i
$466$	433.826			0.930957
$467$	371.481	−	371.481i	0.795462	−	0.795462i	−0.186914	−	0.982376i	$-0.559849\pi$
$467$	371.481	−	371.481i	0.795462	−	0.795462i	0.982376	+	0.186914i	$0.0598486\pi$
$468$	72.0635	−	51.5939i	0.153982	−	0.110243i
$469$	676.608	−	92.8425i	1.44266	−	0.197959i
$470$	−193.302	+	84.1441i	−0.411281	+	0.179030i
$471$	42.9309	−	522.222i	0.0911483	−	1.10875i
$472$	123.318	+	123.318i	0.261266	+	0.261266i
$473$	610.208	−	610.208i	1.29008	−	1.29008i
$474$	−180.679	−	14.8532i	−0.381179	−	0.0313360i
$475$	449.950	−	483.303i	0.947263	−	1.01748i
$476$	−54.2759	−	395.546i	−0.114025	−	0.830978i
$477$	−351.896	−	491.508i	−0.737727	−	1.03042i
$478$	261.894	+	261.894i	0.547896	+	0.547896i
$479$		−	615.307i		−	1.28457i	−0.766467	−	0.642283i	$-0.777987\pi$
$479$		−	615.307i		−	1.28457i	0.766467	−	0.642283i	$-0.222013\pi$
$480$	27.3785	+	80.3145i	0.0570385	+	0.167322i
$481$			53.6069i			0.111449i
$482$	187.969	−	187.969i	0.389978	−	0.389978i
$483$	59.2748	+	53.1588i	0.122722	+	0.110060i
$484$		−	184.593i		−	0.381391i
$485$	556.934	+	219.119i	1.14832	+	0.451793i
$486$	137.021	−	315.156i	0.281936	−	0.648469i
$487$	597.102	−	597.102i	1.22608	−	1.22608i	0.260649	−	0.965434i	$-0.416064\pi$
$487$	597.102	−	597.102i	1.22608	−	1.22608i	0.965434	−	0.260649i	$-0.0839364\pi$
$488$	108.355	+	108.355i	0.222040	+	0.222040i
$489$	60.3241	−	733.798i	0.123362	−	1.50061i
$490$	35.3163	−	344.678i	0.0720740	−	0.703424i
$491$			11.7151i			0.0238597i	0.999929	+	0.0119298i	$0.00379747\pi$
$491$			11.7151i			0.0238597i	−0.999929	+	0.0119298i	$0.996203\pi$
$492$	−173.810	+	147.404i	−0.353273	+	0.299602i
$493$	−575.031	+	575.031i	−1.16639	+	1.16639i
$494$	−183.924			−0.372317
$495$	−637.342	+	160.375i	−1.28756	+	0.323991i
$496$			62.6045i			0.126219i
$497$	279.068	−	367.835i	0.561506	−	0.740110i
$498$	−43.5915	+	36.9688i	−0.0875330	+	0.0742345i
$499$			11.1783i			0.0224014i	0.999937	+	0.0112007i	$0.00356537\pi$
$499$			11.1783i			0.0224014i	−0.999937	+	0.0112007i	$0.996435\pi$
$500$	−235.762	−	83.1630i	−0.471525	−	0.166326i
$501$	−137.854	−	11.3327i	−0.275157	−	0.0226201i
$502$	406.255	+	406.255i	0.809273	+	0.809273i
$503$	15.0212	+	15.0212i	0.0298632	+	0.0298632i	0.721881	−	0.692017i	$-0.243278\pi$
$503$	15.0212	+	15.0212i	0.0298632	+	0.0298632i	−0.692017	+	0.721881i	$0.743278\pi$
$504$	4.93189	−	178.123i	0.00978549	−	0.353418i
$505$	517.400	−	225.223i	1.02455	−	0.445986i
$506$		−	78.3088i		−	0.154760i
$507$	−331.200	+	280.882i	−0.653255	+	0.554008i
$508$	−79.0332	−	79.0332i	−0.155577	−	0.155577i
$509$		−	62.6374i		−	0.123060i	−0.998105	−	0.0615298i	$-0.980402\pi$
$509$		−	62.6374i		−	0.123060i	0.998105	−	0.0615298i	$-0.0195979\pi$
$510$	542.915	+	266.867i	1.06454	+	0.523269i
$511$	63.8554	−	8.76209i	0.124962	−	0.0171469i
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	−611.928	+	366.248i	−1.19284	+	0.713934i
$514$	−111.493			−0.216912
$515$	213.810	−	543.440i	0.415166	−	1.05522i
$516$	−353.337	−	29.0472i	−0.684762	−	0.0562930i
$517$	−307.899	−	307.899i	−0.595549	−	0.595549i
$518$	85.8636	+	65.1428i	0.165760	+	0.125758i
$519$	−42.4416	+	516.271i	−0.0817757	+	0.994741i
$520$	27.7923	+	63.8467i	0.0534468	+	0.122782i
$521$	2.86685			0.00550258			0.00275129	−	0.999996i	$-0.499124\pi$
$521$	2.86685			0.00550258			0.00275129	+	0.999996i	$0.499124\pi$
$522$	−295.110	+	211.284i	−0.565345	+	0.404759i
$523$	216.205	−	216.205i	0.413394	−	0.413394i	−0.469525	−	0.882919i	$-0.655575\pi$
$523$	216.205	−	216.205i	0.413394	−	0.413394i	0.882919	+	0.469525i	$0.155575\pi$
$524$		−	244.093i		−	0.465826i
$525$	403.116	+	336.336i	0.767841	+	0.640641i
$526$	−193.143			−0.367192
$527$	315.609	+	315.609i	0.598879	+	0.598879i
$528$	−133.662	+	113.355i	−0.253147	+	0.214687i
$529$			514.625i			0.972826i
$530$	435.466	−	189.557i	0.821634	−	0.357655i
$531$	547.479	+	90.6269i	1.03103	+	0.170672i
$532$	−223.504	+	294.596i	−0.420120	+	0.553753i
$533$	−132.245	+	132.245i	−0.248114	+	0.248114i
$534$	−81.9586	−	6.73765i	−0.153480	−	0.0126173i
$535$	−826.160	−	325.043i	−1.54422	−	0.607558i
$536$			275.953i			0.514837i
$537$	94.7712	+	111.749i	0.176483	+	0.208098i
$538$	100.672	−	100.672i	0.187123	−	0.187123i
$539$	689.179	−	192.764i	1.27862	−	0.357633i
$540$	219.605	+	157.079i	0.406675	+	0.290887i
$541$	−544.738			−1.00691			−0.503454	−	0.864022i	$-0.667938\pi$
$541$	−544.738			−1.00691			−0.503454	+	0.864022i	$0.667938\pi$
$542$	299.070	−	299.070i	0.551790	−	0.551790i
$543$	170.588	−	144.671i	0.314158	−	0.266429i
$544$	161.322			0.296548
$545$	3.20804	+	7.36976i	0.00588631	+	0.0135225i
$546$	−7.94260	−	146.014i	−0.0145469	−	0.267426i
$547$	−644.286	+	644.286i	−1.17785	+	1.17785i	−0.197564	+	0.980290i	$0.563303\pi$
$547$	−644.286	+	644.286i	−1.17785	+	1.17785i	−0.980290	+	0.197564i	$0.936697\pi$
$548$	283.898	−	283.898i	0.518061	−	0.518061i
$549$	481.053	+	79.6310i	0.876235	+	0.145047i
$550$	−18.4418	−	516.024i	−0.0335306	−	0.938225i
$551$	753.197			1.36696
$552$	−24.5359	+	20.8083i	−0.0444492	+	0.0376962i
$553$	−180.787	+	238.292i	−0.326921	+	0.430908i
$554$	−621.005			−1.12095
$555$	−154.574	+	52.6929i	−0.278512	+	0.0949423i
$556$			82.9107i			0.149120i
$557$	−180.720	−	180.720i	−0.324452	−	0.324452i	0.526020	−	0.850472i	$-0.323684\pi$
$557$	−180.720	−	180.720i	−0.324452	−	0.324452i	−0.850472	+	0.526020i	$0.823684\pi$
$558$	115.965	+	161.973i	0.207822	+	0.290275i
$559$	−290.940			−0.520465
$560$	136.038	+	33.0705i	0.242925	+	0.0590544i
$561$	−102.373	+	1245.29i	−0.182482	+	2.21977i
$562$	229.692	−	229.692i	0.408704	−	0.408704i
$563$	−16.4783	−	16.4783i	−0.0292687	−	0.0292687i	0.692321	−	0.721590i	$-0.256588\pi$
$563$	−16.4783	−	16.4783i	−0.0292687	−	0.0292687i	−0.721590	+	0.692321i	$0.756588\pi$
$564$	−14.6566	+	178.287i	−0.0259869	+	0.316112i
$565$	−366.339	+	931.120i	−0.648388	+	1.64800i
$566$	341.174			0.602781
$567$	−317.184	−	469.982i	−0.559407	−	0.828893i
$568$	131.919	+	131.919i	0.232251	+	0.232251i
$569$	−354.571			−0.623147			−0.311574	−	0.950222i	$-0.600856\pi$
$569$	−354.571			−0.623147			−0.311574	+	0.950222i	$0.600856\pi$
$570$	−180.789	−	530.341i	−0.317173	−	0.930423i
$571$	−110.075			−0.192777			−0.0963883	−	0.995344i	$-0.530729\pi$
$571$	−110.075			−0.192777			−0.0963883	+	0.995344i	$0.530729\pi$
$572$	−101.697	+	101.697i	−0.177793	+	0.177793i
$573$	50.3372	−	42.6897i	0.0878486	−	0.0745021i
$574$	51.1168	+	372.524i	0.0890537	+	0.648996i
$575$	−3.38533	−	94.7254i	−0.00588752	−	0.164740i
$576$	71.0334	+	11.7585i	0.123322	+	0.0204140i
$577$	212.392	+	212.392i	0.368097	+	0.368097i	0.866783	−	0.498686i	$-0.166184\pi$
$577$	212.392	+	212.392i	0.368097	+	0.368097i	−0.498686	+	0.866783i	$0.666184\pi$
$578$	524.277	−	524.277i	0.907054	−	0.907054i
$579$	25.6415	−	311.910i	0.0442859	−	0.538705i
$580$	−113.814	−	261.461i	−0.196230	−	0.450795i
$581$	12.8200	+	93.4285i	0.0220655	+	0.160806i
$582$	387.307	−	328.465i	0.665476	−	0.564372i
$583$	693.626	+	693.626i	1.18975	+	1.18975i
$584$			26.0432i			0.0445946i
$585$	190.171	+	113.706i	0.325079	+	0.194370i
$586$			372.838i			0.636243i
$587$	−277.047	+	277.047i	−0.471972	+	0.471972i	−0.902552	−	0.430580i	$-0.858309\pi$
$587$	−277.047	+	277.047i	−0.471972	+	0.471972i	0.430580	+	0.902552i	$0.358309\pi$
$588$	−243.527	−	164.714i	−0.414161	−	0.280126i
$589$		−	413.397i		−	0.701862i
$590$	−159.627	+	405.722i	−0.270554	+	0.687664i
$591$	−43.2700	+	526.348i	−0.0732150	+	0.890606i
$592$	−30.7938	+	30.7938i	−0.0520165	+	0.0520165i
$593$	118.407	+	118.407i	0.199674	+	0.199674i	0.799860	−	0.600186i	$-0.204907\pi$
$593$	118.407	+	118.407i	0.199674	+	0.199674i	−0.600186	+	0.799860i	$0.704907\pi$
$594$	−135.844	+	540.863i	−0.228693	+	0.910544i
$595$	852.530	−	519.092i	1.43282	−	0.872424i
$596$		−	378.749i		−	0.635485i
$597$	−629.049	−	741.739i	−1.05368	−	1.24244i
$598$	−18.6684	+	18.6684i	−0.0312180	+	0.0312180i
$599$	254.409			0.424722			0.212361	−	0.977191i	$-0.431885\pi$
$599$	254.409			0.424722			0.212361	+	0.977191i	$0.431885\pi$
$600$	−156.782	+	142.897i	−0.261303	+	0.238161i
$601$			335.032i			0.557458i	0.960370	+	0.278729i	$0.0899131\pi$
$601$			335.032i			0.557458i	−0.960370	+	0.278729i	$0.910087\pi$
$602$	−353.549	+	466.006i	−0.587291	+	0.774097i
$603$	511.158	+	713.957i	0.847692	+	1.18401i
$604$		−	234.656i		−	0.388503i
$605$	423.132	−	184.189i	0.699393	−	0.304444i
$606$	39.2304	−	477.210i	0.0647367	−	0.787474i
$607$	537.196	+	537.196i	0.885002	+	0.885002i	0.994038	−	0.109036i	$-0.0347763\pi$
$607$	537.196	+	537.196i	0.885002	+	0.885002i	−0.109036	+	0.994038i	$0.534776\pi$
$608$	−105.653	−	105.653i	−0.173771	−	0.173771i
$609$	32.5261	+	597.950i	0.0534090	+	0.981855i
$610$	−140.259	+	356.495i	−0.229933	+	0.584418i
$611$			146.803i			0.240266i
$612$	417.380	−	298.824i	0.681994	−	0.488274i
$613$	−155.599	−	155.599i	−0.253832	−	0.253832i	0.568708	−	0.822540i	$-0.307444\pi$
$613$	−155.599	−	155.599i	−0.253832	−	0.253832i	−0.822540	+	0.568708i	$0.807444\pi$
$614$		−	19.5434i		−	0.0318296i
$615$	−511.315	−	251.335i	−0.831407	−	0.408674i
$616$	39.3092	+	286.473i	0.0638137	+	0.465054i
$617$	−533.777	−	533.777i	−0.865116	−	0.865116i	0.126811	−	0.991927i	$-0.459526\pi$
$617$	−533.777	−	533.777i	−0.865116	−	0.865116i	−0.991927	+	0.126811i	$0.959526\pi$
$618$	−320.506	−	377.923i	−0.518619	−	0.611526i
$619$	−96.5213			−0.155931			−0.0779655	−	0.996956i	$-0.524842\pi$
$619$	−96.5213			−0.155931			−0.0779655	+	0.996956i	$0.524842\pi$
$620$	−143.505	+	62.4673i	−0.231459	+	0.100754i
$621$	−24.9365	+	99.2851i	−0.0401554	+	0.159879i
$622$	−145.632	−	145.632i	−0.234136	−	0.234136i
$623$	−82.0076	+	108.093i	−0.131633	+	0.173504i
$624$	58.8873	+	4.84101i	0.0943706	+	0.00775802i
$625$	−44.6159	−	623.406i	−0.0713855	−	0.997449i
$626$	708.192			1.13130
$627$	882.608	−	748.516i	1.40767	−	1.19381i
$628$	247.008	−	247.008i	0.393326	−	0.393326i
$629$			310.482i			0.493613i
$630$	413.221	−	166.427i	0.655907	−	0.264170i
$631$	−797.287			−1.26353			−0.631765	−	0.775160i	$-0.717669\pi$
$631$	−797.287			−1.26353			−0.631765	+	0.775160i	$0.717669\pi$
$632$	−85.4601	−	85.4601i	−0.135222	−	0.135222i
$633$	56.9774	+	67.1845i	0.0900117	+	0.106137i
$634$			272.972i			0.430556i
$635$	102.303	−	260.023i	0.161108	−	0.409485i
$636$	33.0180	−	401.640i	0.0519151	−	0.631510i
$637$	−210.250	−	118.342i	−0.330063	−	0.185781i
$638$	416.465	−	416.465i	0.652767	−	0.652767i
$639$	585.665	+	96.9479i	0.916533	+	0.151718i
$640$	−20.7110	+	52.6408i	−0.0323609	+	0.0822513i
$641$			816.250i			1.27340i	0.771111	+	0.636701i	$0.219701\pi$
$641$			816.250i			1.27340i	−0.771111	+	0.636701i	$0.780299\pi$
$642$	−574.534	+	487.247i	−0.894913	+	0.758952i
$643$	397.740	−	397.740i	0.618569	−	0.618569i	−0.326595	−	0.945164i	$-0.605901\pi$
$643$	397.740	−	397.740i	0.618569	−	0.618569i	0.945164	+	0.326595i	$0.105901\pi$
$644$	7.21591	+	52.5873i	0.0112048	+	0.0816573i
$645$	−285.980	−	838.919i	−0.443380	−	1.30065i
$646$	−1065.26			−1.64901
$647$	−593.146	+	593.146i	−0.916763	+	0.916763i	−0.996792	−	0.0800295i	$-0.974499\pi$
$647$	−593.146	+	593.146i	−0.916763	+	0.916763i	0.0800295	+	0.996792i	$0.474499\pi$
$648$	205.561	−	101.156i	0.317224	−	0.156105i
$649$	−900.508			−1.38753
$650$	−118.621	+	127.414i	−0.182493	+	0.196021i
$651$	328.189	−	17.8522i	0.504130	−	0.0274227i
$652$	347.083	−	347.083i	0.532335	−	0.532335i
$653$	525.550	−	525.550i	0.804824	−	0.804824i	−0.179021	−	0.983845i	$-0.557293\pi$
$653$	525.550	−	525.550i	0.804824	−	0.804824i	0.983845	+	0.179021i	$0.0572930\pi$
$654$	6.79729	+	0.558792i	0.0103934	+	0.000854422i
$655$	559.520	−	243.558i	0.854229	−	0.371844i
$656$	−151.933			−0.231605
$657$	48.2409	+	67.3803i	0.0734261	+	0.102557i
$658$	235.138	+	178.394i	0.357352	+	0.271115i
$659$	−415.401			−0.630350			−0.315175	−	0.949034i	$-0.602063\pi$
$659$	−415.401			−0.630350			−0.315175	+	0.949034i	$0.602063\pi$
$660$	−393.205	−	193.278i	−0.595766	−	0.292846i
$661$		−	723.547i		−	1.09462i	−0.836929	−	0.547312i	$-0.815651\pi$
$661$		−	723.547i		−	1.09462i	0.836929	−	0.547312i	$-0.184349\pi$
$662$	317.945	+	317.945i	0.480279	+	0.480279i
$663$	321.275	−	272.465i	0.484577	−	0.410957i
$664$	−38.1046			−0.0573864
$665$	−898.301	−	218.374i	−1.35083	−	0.328383i
$666$	−22.6305	+	136.712i	−0.0339797	+	0.205273i
$667$	76.4496	−	76.4496i	0.114617	−	0.114617i
$668$	−65.2042	−	65.2042i	−0.0976110	−	0.0976110i
$669$	−860.693	−	70.7559i	−1.28654	−	0.105764i
$670$	−632.550	+	275.348i	−0.944105	+	0.410967i
$671$	−791.248			−1.17921
$672$	79.3135	−	88.4385i	0.118026	−	0.131605i
$673$	95.8909	+	95.8909i	0.142483	+	0.142483i	0.774750	−	0.632267i	$-0.217876\pi$
$673$	95.8909	+	95.8909i	0.142483	+	0.142483i	−0.632267	+	0.774750i	$0.717876\pi$
$674$	191.729			0.284465
$675$	−140.940	+	660.122i	−0.208800	+	0.977958i
$676$	−289.512			−0.428272
$677$	−90.8203	+	90.8203i	−0.134151	+	0.134151i	−0.770994	−	0.636843i	$-0.780240\pi$
$677$	−90.8203	+	90.8203i	−0.134151	+	0.134151i	0.636843	+	0.770994i	$0.280240\pi$
$678$	549.150	+	647.526i	0.809956	+	0.955054i
$679$	−113.905	−	830.106i	−0.167754	−	1.22254i
$680$	160.969	+	369.790i	0.236719	+	0.543808i
$681$	643.607	+	52.9096i	0.945091	+	0.0776940i
$682$	−228.580	−	228.580i	−0.335161	−	0.335161i
$683$	−572.076	+	572.076i	−0.837593	+	0.837593i	−0.988542	−	0.150948i	$-0.951767\pi$
$683$	−572.076	+	572.076i	−0.837593	+	0.837593i	0.150948	+	0.988542i	$0.451767\pi$
$684$	−469.055	−	77.6449i	−0.685753	−	0.113516i
$685$	934.038	+	367.487i	1.36356	+	0.536477i
$686$	−445.047	+	192.954i	−0.648756	+	0.281274i
$687$	425.808	+	502.088i	0.619808	+	0.730842i
$688$	−167.127	−	167.127i	−0.242917	−	0.242917i
$689$		−	330.713i		−	0.479990i
$690$	−72.1798	−	35.4797i	−0.104608	−	0.0514198i
$691$		−	941.057i		−	1.36188i	−0.732340	−	0.680939i	$-0.761572\pi$
$691$		−	941.057i		−	1.36188i	0.732340	−	0.680939i	$-0.238428\pi$
$692$	−244.193	+	244.193i	−0.352880	+	0.352880i
$693$	632.349	+	668.363i	0.912480	+	0.964449i
$694$			152.611i			0.219900i
$695$	−190.052	+	82.7290i	−0.273455	+	0.119035i
$696$	−241.152	−	19.8246i	−0.346482	−	0.0284836i
$697$	−765.941	+	765.941i	−1.09891	+	1.09891i
$698$	−27.7850	−	27.7850i	−0.0398067	−	0.0398067i
$699$	917.189	+	75.4003i	1.31215	+	0.107869i
$700$	59.9344	+	344.830i	0.0856205	+	0.492615i
$701$		−	305.599i		−	0.435947i	−0.975955	−	0.217973i	$-0.930055\pi$
$701$		−	305.599i		−	0.435947i	0.975955	−	0.217973i	$-0.0699446\pi$
$702$	161.323	−	96.5544i	0.229805	−	0.137542i
$703$	203.341	−	203.341i	0.289247	−	0.289247i
$704$	−116.837			−0.165962
$705$	−423.302	+	144.300i	−0.600428	+	0.204681i
$706$			377.547i			0.534769i
$707$	−629.378	−	477.495i	−0.890209	−	0.675382i
$708$	239.284	+	282.150i	0.337972	+	0.398517i
$709$			976.020i			1.37661i	0.725419	+	0.688307i	$0.241646\pi$
$709$			976.020i			1.37661i	−0.725419	+	0.688307i	$0.758354\pi$
$710$	−170.760	+	434.020i	−0.240507	+	0.611295i
$711$	−379.408	−	62.8051i	−0.533625	−	0.0883335i
$712$	−38.7660	−	38.7660i	−0.0544466	−	0.0544466i
$713$	−41.9599	−	41.9599i	−0.0588497	−	0.0588497i
$714$	−46.0023	−	845.691i	−0.0644289	−	1.18444i
$715$	−334.590	−	131.641i	−0.467958	−	0.184113i
$716$			97.6829i			0.136429i
$717$	508.176	+	599.212i	0.708753	+	0.835721i
$718$	−171.974	−	171.974i	−0.239519	−	0.239519i
$719$			792.968i			1.10288i	0.834216	+	0.551438i	$0.185921\pi$
$719$			792.968i			1.10288i	−0.834216	+	0.551438i	$0.814079\pi$
$720$	43.9244	+	174.558i	0.0610061	+	0.242442i
$721$	−809.993	+	111.145i	−1.12343	+	0.154154i
$722$	336.659	+	336.659i	0.466286	+	0.466286i
$723$	430.072	−	364.733i	0.594844	−	0.504471i
$724$	149.116			0.205961
$725$	485.769	−	521.777i	0.670026	−	0.719692i
$726$	32.0829	−	390.265i	0.0441913	−	0.537555i
$727$	−666.489	−	666.489i	−0.916767	−	0.916767i	0.0800261	−	0.996793i	$-0.474500\pi$
$727$	−666.489	−	666.489i	−0.916767	−	0.916767i	−0.996793	+	0.0800261i	$0.974500\pi$
$728$	58.9226	−	77.6647i	0.0809376	−	0.106682i
$729$	344.463	−	642.484i	0.472514	−	0.881323i
$730$	−59.6975	+	25.9862i	−0.0817773	+	0.0355975i
$731$	−1685.08			−2.30517
$732$	210.251	+	247.916i	0.287228	+	0.338683i
$733$	338.466	−	338.466i	0.461754	−	0.461754i	−0.437476	−	0.899230i	$-0.644127\pi$
$733$	338.466	−	338.466i	0.461754	−	0.461754i	0.899230	+	0.437476i	$0.144127\pi$
$734$		−	363.110i		−	0.494700i
$735$	134.571	−	722.576i	0.183090	−	0.983096i
$736$	−21.4476			−0.0291407
$737$	−1007.55	−	1007.55i	−1.36710	−	1.36710i
$738$	−393.087	+	281.431i	−0.532638	+	0.381343i
$739$			1021.49i			1.38226i	0.722730	+	0.691130i	$0.242887\pi$
$739$			1021.49i			1.38226i	−0.722730	+	0.691130i	$0.757113\pi$
$740$	−101.313	−	39.8605i	−0.136910	−	0.0538656i
$741$	−388.851	−	31.9667i	−0.524765	−	0.0431399i
$742$	−529.712	−	401.881i	−0.713897	−	0.541618i
$743$	−262.382	+	262.382i	−0.353138	+	0.353138i	−0.861276	−	0.508138i	$-0.830334\pi$
$743$	−262.382	+	262.382i	−0.353138	+	0.353138i	0.508138	+	0.861276i	$0.330334\pi$
$744$	−10.8809	+	132.358i	−0.0146248	+	0.177900i
$745$	868.185	−	377.919i	1.16535	−	0.507274i
$746$		−	208.307i		−	0.279231i
$747$	−98.5858	+	70.5826i	−0.131976	+	0.0944881i
$748$	−589.015	+	589.015i	−0.787453	+	0.787453i
$749$	168.968	+	1231.38i	0.225591	+	1.64404i
$750$	−483.992	−	216.799i	−0.645323	−	0.289065i
$751$	−429.513			−0.571922			−0.285961	−	0.958241i	$-0.592313\pi$
$751$	−429.513			−0.571922			−0.285961	+	0.958241i	$0.592313\pi$
$752$	−84.3288	+	84.3288i	−0.112139	+	0.112139i
$753$	788.291	+	929.508i	1.04687	+	1.23441i
$754$	−198.566			−0.263350
$755$	537.889	−	234.142i	0.712436	−	0.310122i
$756$	41.3852	−	375.728i	0.0547424	−	0.496994i
$757$	439.564	−	439.564i	0.580666	−	0.580666i	−0.354420	−	0.935086i	$-0.615322\pi$
$757$	439.564	−	439.564i	0.580666	−	0.580666i	0.935086	+	0.354420i	$0.115322\pi$
$758$	−339.431	+	339.431i	−0.447798	+	0.447798i
$759$	13.6103	−	165.559i	0.0179319	−	0.218128i
$760$	136.761	−	347.604i	0.179948	−	0.457373i
$761$	1005.16			1.32084			0.660420	−	0.750897i	$-0.270378\pi$
$761$	1005.16			1.32084			0.660420	+	0.750897i	$0.270378\pi$
$762$	−153.355	−	180.827i	−0.201253	−	0.237306i
$763$	6.80137	−	8.96476i	0.00891398	−	0.0117494i
$764$	44.0013			0.0575933
$765$	1101.44	+	658.568i	1.43979	+	0.860873i
$766$		−	374.321i		−	0.488670i
$767$	214.676	+	214.676i	0.279890	+	0.279890i
$768$	31.0462	+	36.6079i	0.0404247	+	0.0476665i
$769$	156.235			0.203167			0.101583	−	0.994827i	$-0.467609\pi$
$769$	156.235			0.203167			0.101583	+	0.994827i	$0.467609\pi$
$770$	−617.444	+	375.952i	−0.801875	+	0.488249i
$771$	−235.717	−	19.3778i	−0.305729	−	0.0251334i
$772$	147.532	−	147.532i	0.191104	−	0.191104i
$773$	−95.1552	−	95.1552i	−0.123099	−	0.123099i	0.642874	−	0.765972i	$-0.277742\pi$
$773$	−95.1552	−	95.1552i	−0.123099	−	0.123099i	−0.765972	+	0.642874i	$0.777742\pi$
$774$	−741.973	−	122.822i	−0.958622	−	0.158685i
$775$	−286.381	−	266.617i	−0.369523	−	0.344022i
$776$	338.556			0.436284
$777$	170.210	+	152.648i	0.219060	+	0.196458i
$778$	511.312	+	511.312i	0.657214	+	0.657214i
$779$	1003.26			1.28788
$780$	47.6615	+	139.814i	0.0611045	+	0.179249i
$781$	−963.316			−1.23344
$782$	−108.124	+	108.124i	−0.138266	+	0.138266i
$783$	−660.641	+	395.404i	−0.843730	+	0.504986i
$784$	−52.7953	−	188.756i	−0.0673409	−	0.240760i
$785$	812.671	+	319.736i	1.03525	+	0.407307i
$786$	42.4241	−	516.058i	0.0539747	−	0.656563i
$787$	909.207	+	909.207i	1.15528	+	1.15528i	0.985478	+	0.169804i	$0.0543133\pi$
$787$	909.207	+	909.207i	1.15528	+	1.15528i	0.169804	+	0.985478i	$0.445687\pi$
$788$	−248.960	+	248.960i	−0.315939	+	0.315939i
$789$	−408.341	−	33.5689i	−0.517543	−	0.0425462i
$790$	110.623	−	281.168i	0.140029	−	0.355909i
$791$	1387.83	−	190.434i	1.75452	−	0.240752i
$792$	−302.287	+	216.423i	−0.381676	+	0.273261i
$793$	188.629	+	188.629i	0.237868	+	0.237868i
$794$			897.166i			1.12993i
$795$	953.602	−	325.075i	1.19950	−	0.408899i
$796$		−	648.376i		−	0.814542i
$797$	−8.09283	+	8.09283i	−0.0101541	+	0.0101541i	−0.712166	−	0.702011i	$-0.752285\pi$
$797$	−8.09283	+	8.09283i	−0.0101541	+	0.0101541i	0.702011	+	0.712166i	$0.252285\pi$
$798$	−523.731	+	583.987i	−0.656305	+	0.731813i
$799$			850.257i			1.06415i
$800$	−141.331	+	5.05094i	−0.176664	+	0.00631367i
$801$	−172.105	−	28.4893i	−0.214862	−	0.0355672i
$802$	−44.3430	+	44.3430i	−0.0552905	+	0.0552905i
$803$	−95.0883	−	95.0883i	−0.118416	−	0.118416i
$804$	−47.9615	+	583.416i	−0.0596536	+	0.725642i
$805$	−113.343	+	69.0127i	−0.140798	+	0.0857300i
$806$			108.984i			0.135216i
$807$	230.337	−	195.343i	0.285424	−	0.242061i
$808$	225.718	−	225.718i	0.279353	−	0.279353i
$809$	−1556.68			−1.92421			−0.962103	−	0.272686i	$-0.912088\pi$
$809$	−1556.68			−1.92421			−0.962103	+	0.272686i	$0.912088\pi$
$810$	436.985	+	370.263i	0.539487	+	0.457114i
$811$			849.941i			1.04802i	0.851713	+	0.524008i	$0.175564\pi$
$811$			849.941i			1.04802i	−0.851713	+	0.524008i	$0.824436\pi$
$812$	−241.296	+	318.048i	−0.297163	+	0.391685i
$813$	684.270	−	580.312i	0.841661	−	0.713790i
$814$		−	224.867i		−	0.276249i
$815$	1141.92	+	449.276i	1.40113	+	0.551259i
$816$	341.066	+	28.0383i	0.417973	+	0.0343607i
$817$	1103.59	+	1103.59i	1.35078	+	1.35078i
$818$	−392.358	−	392.358i	−0.479656	−	0.479656i
$819$	8.58561	−	310.082i	0.0104830	−	0.378611i
$820$	−151.600	−	348.267i	−0.184878	−	0.424715i
$821$			164.509i			0.200376i	0.994969	+	0.100188i	$0.0319445\pi$
$821$			164.509i			0.200376i	−0.994969	+	0.100188i	$0.968056\pi$
$822$	649.555	−	550.871i	0.790213	−	0.670159i
$823$	−90.7701	−	90.7701i	−0.110292	−	0.110292i	0.649807	−	0.760099i	$-0.274850\pi$
$823$	−90.7701	−	90.7701i	−0.110292	−	0.110292i	−0.760099	+	0.649807i	$0.774850\pi$
$824$		−	330.353i		−	0.400914i
$825$	50.6971	−	1094.18i	0.0614511	−	1.32628i
$826$	604.725	−	82.9790i	0.732113	−	0.100459i
$827$	369.738	+	369.738i	0.447083	+	0.447083i	0.894384	−	0.447300i	$-0.147615\pi$
$827$	369.738	+	369.738i	0.447083	+	0.447083i	−0.447300	+	0.894384i	$0.647615\pi$
$828$	−55.4902	+	39.7282i	−0.0670171	+	0.0479809i
$829$	−61.7867			−0.0745316			−0.0372658	−	0.999305i	$-0.511865\pi$
$829$	−61.7867			−0.0745316			−0.0372658	+	0.999305i	$0.511865\pi$
$830$	−38.0211	−	87.3449i	−0.0458085	−	0.105235i
$831$	−1312.92	−	107.933i	−1.57993	−	0.129883i
$832$	27.8534	+	27.8534i	0.0334776	+	0.0334776i
$833$	−1217.73	−	685.419i	−1.46187	−	0.822832i
$834$	−14.4102	+	175.289i	−0.0172784	+	0.210179i
$835$	84.4025	−	214.525i	0.101081	−	0.256916i
$836$	771.513			0.922863
$837$	217.020	+	362.597i	0.259283	+	0.433210i
$838$	−383.324	+	383.324i	−0.457427	+	0.457427i
$839$			77.9554i			0.0929146i	0.998920	+	0.0464573i	$0.0147931\pi$
$839$			77.9554i			0.0929146i	−0.998920	+	0.0464573i	$0.985207\pi$
$840$	281.862	+	93.5610i	0.335550	+	0.111382i
$841$	−27.8443			−0.0331086
$842$	809.373	+	809.373i	0.961250	+	0.961250i
$843$	525.533	−	445.691i	0.623408	−	0.528696i
$844$			58.7279i			0.0695828i
$845$	−288.877	−	663.631i	−0.341867	−	0.785363i
$846$	−61.9737	+	374.385i	−0.0732550	+	0.442536i
$847$	−514.709	−	390.499i	−0.607685	−	0.461037i
$848$	189.974	−	189.974i	0.224026	−	0.224026i
$849$	721.306	+	59.2971i	0.849594	+	0.0698435i
$850$	−687.032	+	737.959i	−0.808273	+	0.868187i
$851$		−	41.2783i		−	0.0485056i
$852$	255.973	+	301.829i	0.300438	+	0.354260i
$853$	−1148.30	+	1148.30i	−1.34620	+	1.34620i	−0.456443	+	0.889753i	$0.650877\pi$
$853$	−1148.30	+	1148.30i	−1.34620	+	1.34620i	−0.889753	+	0.456443i	$0.849123\pi$
$854$	531.353	−	72.9110i	0.622193	−	0.0853759i
$855$	−290.046	−	1152.66i	−0.339235	−	1.34814i
$856$	−502.217			−0.586702
$857$	663.238	−	663.238i	0.773906	−	0.773906i	−0.204881	−	0.978787i	$-0.565681\pi$
$857$	663.238	−	663.238i	0.773906	−	0.773906i	0.978787	+	0.204881i	$0.0656806\pi$
$858$	−232.683	+	197.332i	−0.271192	+	0.229991i
$859$	726.339			0.845564			0.422782	−	0.906231i	$-0.361054\pi$
$859$	726.339			0.845564			0.422782	+	0.906231i	$0.361054\pi$
$860$	216.335	−	549.856i	0.251552	−	0.639367i
$861$	43.3248	+	796.469i	0.0503191	+	0.925051i
$862$	−432.674	+	432.674i	−0.501942	+	0.501942i
$863$	−881.430	+	881.430i	−1.02136	+	1.02136i	−0.0215890	+	0.999767i	$0.506873\pi$
$863$	−881.430	+	881.430i	−1.02136	+	1.02136i	−0.999767	+	0.0215890i	$0.993127\pi$
$864$	148.134	+	37.2055i	0.171452	+	0.0430619i
$865$	−803.408	−	316.092i	−0.928796	−	0.365424i
$866$	−576.898			−0.666163
$867$	1199.54	−	1017.30i	1.38355	−	1.17336i
$868$	174.563	+	132.437i	0.201109	+	0.152577i
$869$	624.059			0.718134
$870$	−195.181	−	572.560i	−0.224345	−	0.658115i
$871$			480.388i			0.551536i
$872$	3.21508	+	3.21508i	0.00368702	+	0.00368702i
$873$	875.928	−	627.121i	1.00335	−	0.718352i
$874$	141.625			0.162042
$875$	−730.632	+	481.459i	−0.835008	+	0.550238i
$876$	−4.52640	+	55.0603i	−0.00516712	+	0.0628543i
$877$	1201.58	−	1201.58i	1.37010	−	1.37010i	0.509822	−	0.860280i	$-0.329711\pi$
$877$	1201.58	−	1201.58i	1.37010	−	1.37010i	0.860280	−	0.509822i	$-0.170289\pi$
$878$	−652.665	−	652.665i	−0.743354	−	0.743354i
$879$	−64.8005	+	788.251i	−0.0737207	+	0.896759i
$880$	−116.581	−	267.820i	−0.132479	−	0.304341i
$881$	−403.967			−0.458533			−0.229266	−	0.973364i	$-0.573633\pi$
$881$	−403.967			−0.458533			−0.229266	+	0.973364i	$0.573633\pi$
$882$	−486.234	−	390.562i	−0.551285	−	0.442814i
$883$	−740.709	−	740.709i	−0.838855	−	0.838855i	0.149853	−	0.988708i	$-0.452120\pi$
$883$	−740.709	−	740.709i	−0.838855	−	0.838855i	−0.988708	+	0.149853i	$0.952120\pi$
$884$	280.836			0.317687
$885$	−407.997	+	830.028i	−0.461013	+	0.937885i
$886$	−859.416			−0.969996
$887$	703.405	−	703.405i	0.793016	−	0.793016i	−0.188968	−	0.981983i	$-0.560514\pi$
$887$	703.405	−	703.405i	0.793016	−	0.793016i	0.981983	+	0.188968i	$0.0605142\pi$
$888$	−70.4559	+	59.7518i	−0.0793422	+	0.0672880i
$889$	−387.563	+	53.1804i	−0.435954	+	0.0598205i
$890$	50.1800	−	127.542i	0.0563820	−	0.143306i
$891$	−381.203	+	1119.88i	−0.427837	+	1.25688i
$892$	−407.103	−	407.103i	−0.456394	−	0.456394i
$893$	556.849	−	556.849i	0.623571	−	0.623571i
$894$	65.8278	−	800.747i	0.0736329	−	0.895690i
$895$	−223.913	+	97.4688i	−0.250182	+	0.108904i
$896$	78.4607	−	10.7662i	0.0875678	−	0.0120158i
$897$	−42.7131	+	36.2238i	−0.0476177	+	0.0403833i
$898$	−544.342	−	544.342i	−0.606171	−	0.606171i
$899$		−	446.306i		−	0.496447i
$900$	−356.302	+	274.861i	−0.395891	+	0.305401i
$901$		−	1915.44i		−	2.12590i
$902$	554.732	−	554.732i	0.615002	−	0.615002i
$903$	−828.463	+	923.778i	−0.917456	+	1.02301i
$904$			566.022i			0.626130i
$905$	148.789	+	341.809i	0.164407	+	0.377690i
$906$	40.7840	−	496.107i	0.0450154	−	0.547580i
$907$	−141.537	+	141.537i	−0.156050	+	0.156050i	−0.780814	−	0.624764i	$-0.785195\pi$
$907$	−141.537	+	141.537i	−0.156050	+	0.156050i	0.624764	+	0.780814i	$0.285195\pi$
$908$	304.423	+	304.423i	0.335267	+	0.335267i
$909$	165.881	−	1002.09i	0.182487	−	1.10241i
$910$	236.820	+	57.5703i	0.260242	+	0.0632640i
$911$		−	379.247i		−	0.416298i	−0.978097	−	0.208149i	$-0.933256\pi$
$911$		−	379.247i		−	0.416298i	0.978097	−	0.208149i	$-0.0667439\pi$
$912$	−205.007	−	241.733i	−0.224789	−	0.265058i
$913$	139.126	−	139.126i	0.152384	−	0.152384i
$914$	−200.600			−0.219475
$915$	−358.494	+	729.320i	−0.391797	+	0.797071i
$916$			438.890i			0.479138i
$917$	−680.614	−	516.367i	−0.742219	−	0.563105i
$918$	934.357	−	559.227i	1.01782	−	0.609180i
$919$		−	589.717i		−	0.641695i	−0.947131	−	0.320847i	$-0.896032\pi$
$919$		−	589.717i		−	0.641695i	0.947131	−	0.320847i	$-0.103968\pi$
$920$	−21.4006	−	49.1631i	−0.0232615	−	0.0534381i
$921$	3.39670	−	41.3184i	0.00368806	−	0.0448625i
$922$	−16.3102	−	16.3102i	−0.0176900	−	0.0176900i
$923$	229.649	+	229.649i	0.248807	+	0.248807i
$924$	33.3171	+	612.491i	0.0360574	+	0.662869i
$925$	−9.72109	−	272.007i	−0.0105093	−	0.294062i
$926$		−	802.938i		−	0.867104i
$927$	−611.927	−	854.705i	−0.660115	−	0.922012i
$928$	−114.064	−	114.064i	−0.122913	−	0.122913i
$929$			409.557i			0.440858i	0.975403	+	0.220429i	$0.0707457\pi$
$929$			409.557i			0.440858i	−0.975403	+	0.220429i	$0.929254\pi$
$930$	−314.253	+	107.126i	−0.337907	+	0.115189i
$931$	348.623	+	1246.41i	0.374461	+	1.33879i
$932$	433.826	+	433.826i	0.465478	+	0.465478i
$933$	−282.583	−	333.206i	−0.302875	−	0.357134i
$934$	742.962			0.795462
$935$	−1937.89	−	762.441i	−2.07261	−	0.815445i
$936$	123.657	+	20.4696i	0.132113	+	0.0218692i
$937$	−275.806	−	275.806i	−0.294350	−	0.294350i	0.544446	−	0.838796i	$-0.316740\pi$
$937$	−275.806	−	275.806i	−0.294350	−	0.294350i	−0.838796	+	0.544446i	$0.816740\pi$
$938$	769.450	+	583.765i	0.820310	+	0.622351i
$939$	1497.25	+	123.086i	1.59452	+	0.131082i
$940$	−277.446	−	109.158i	−0.295156	−	0.116126i
$941$	769.189			0.817416			0.408708	−	0.912665i	$-0.365979\pi$
$941$	769.189			0.817416			0.408708	+	0.912665i	$0.365979\pi$
$942$	565.153	−	479.291i	0.599950	−	0.508802i
$943$	101.831	−	101.831i	0.107986	−	0.107986i
$944$			246.635i			0.261266i
$945$	902.554	−	280.039i	0.955083	−	0.296338i
$946$	1220.42			1.29008
$947$	−148.857	−	148.857i	−0.157188	−	0.157188i	0.624132	−	0.781319i	$-0.285453\pi$
$947$	−148.857	−	148.857i	−0.157188	−	0.157188i	−0.781319	+	0.624132i	$0.785453\pi$
$948$	−165.826	−	195.532i	−0.174921	−	0.206257i
$949$			45.3370i			0.0477735i
$950$	933.253	−	33.3529i	0.982371	−	0.0351083i
$951$	−47.4435	+	577.115i	−0.0498880	+	0.606851i
$952$	341.270	−	449.822i	0.358477	−	0.472502i
$953$	99.9670	−	99.9670i	0.104897	−	0.104897i	−0.652710	−	0.757608i	$-0.726368\pi$
$953$	99.9670	−	99.9670i	0.104897	−	0.104897i	0.757608	+	0.652710i	$0.226368\pi$
$954$	139.613	−	843.404i	0.146345	−	0.884071i
$955$	43.9048	+	100.862i	0.0459736	+	0.105614i
$956$			523.788i			0.547896i
$957$	952.869	−	808.103i	0.995683	−	0.844413i
$958$	615.307	−	615.307i	0.642283	−	0.642283i
$959$	−191.031	−	1392.18i	−0.199198	−	1.45170i
$960$	−52.9360	+	107.693i	−0.0551417	+	0.112180i
$961$	716.042			0.745101
$962$	−53.6069	+	53.6069i	−0.0557244	+	0.0557244i
$963$	−1299.36	+	930.276i	−1.34928	+	0.966019i
$964$	375.938			0.389978
$965$	485.388	+	190.970i	0.502992	+	0.197897i
$966$	6.11594	+	112.434i	0.00633120	+	0.116391i
$967$	−452.536	+	452.536i	−0.467979	+	0.467979i	−0.901259	−	0.433280i	$-0.857356\pi$
$967$	−452.536	+	452.536i	−0.467979	+	0.467979i	0.433280	+	0.901259i	$0.357356\pi$
$968$	184.593	−	184.593i	0.190695	−	0.190695i
$969$	−2252.16	−	185.146i	−2.32421	−	0.191069i
$970$	337.814	+	776.053i	0.348262	+	0.800055i
$971$	625.077			0.643746			0.321873	−	0.946783i	$-0.395688\pi$
$971$	625.077			0.643746			0.321873	+	0.946783i	$0.395688\pi$
$972$	452.177	−	178.135i	0.465202	−	0.183267i
$973$	231.183	+	175.394i	0.237599	+	0.180261i
$974$	1194.20			1.22608
$975$	−272.931	+	248.760i	−0.279930	+	0.255138i
$976$			216.711i			0.222040i
$977$	−172.179	−	172.179i	−0.176232	−	0.176232i	0.613479	−	0.789711i	$-0.289770\pi$
$977$	−172.179	−	172.179i	−0.176232	−	0.176232i	−0.789711	+	0.613479i	$0.789770\pi$
$978$	794.122	−	673.474i	0.811986	−	0.688624i
$979$	283.082			0.289154
$980$	379.994	−	309.361i	0.387749	−	0.315675i
$981$	14.2736	+	2.36278i	0.0145501	+	0.00240855i
$982$	−11.7151	+	11.7151i	−0.0119298	+	0.0119298i
$983$	−612.197	−	612.197i	−0.622785	−	0.622785i	0.323458	−	0.946243i	$-0.395155\pi$
$983$	−612.197	−	612.197i	−0.622785	−	0.622785i	−0.946243	+	0.323458i	$0.895155\pi$
$984$	−321.214	−	26.4064i	−0.326437	−	0.0268358i
$985$	−819.091	−	322.262i	−0.831565	−	0.327170i
$986$	−1150.06			−1.16639
$987$	466.120	+	418.026i	0.472259	+	0.423532i
$988$	−183.924	−	183.924i	−0.186158	−	0.186158i
$989$	224.029			0.226521
$990$	−797.718	−	476.967i	−0.805776	−	0.481785i
$991$	1736.43			1.75220			0.876102	−	0.482125i	$-0.160135\pi$
$991$	1736.43			1.75220			0.876102	+	0.482125i	$0.160135\pi$
$992$	−62.6045	+	62.6045i	−0.0631094	+	0.0631094i
$993$	616.936	+	727.455i	0.621285	+	0.732583i
$994$	646.903	−	88.7665i	0.650808	−	0.0893024i
$995$	1486.23	−	646.955i	1.49370	−	0.650206i
$996$	−80.5602	−	6.62270i	−0.0808838	−	0.00664929i
$997$	−817.471	−	817.471i	−0.819930	−	0.819930i	0.166167	−	0.986098i	$-0.446861\pi$
$997$	−817.471	−	817.471i	−0.819930	−	0.819930i	−0.986098	+	0.166167i	$0.946861\pi$
$998$	−11.1783	+	11.1783i	−0.0112007	+	0.0112007i
$999$	−71.6061	+	285.101i	−0.0716778	+	0.285386i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.k.b.83.12	yes	32
3.2	odd	2		210.3.k.a.83.4	✓	32
5.2	odd	4		210.3.k.a.167.13	yes	32
7.6	odd	2	inner	210.3.k.b.83.5	yes	32
15.2	even	4	inner	210.3.k.b.167.5	yes	32
21.20	even	2		210.3.k.a.83.13	yes	32
35.27	even	4		210.3.k.a.167.4	yes	32
105.62	odd	4	inner	210.3.k.b.167.12	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.k.a.83.4	✓	32	3.2	odd	2
210.3.k.a.83.13	yes	32	21.20	even	2
210.3.k.a.167.4	yes	32	35.27	even	4
210.3.k.a.167.13	yes	32	5.2	odd	4
210.3.k.b.83.5	yes	32	7.6	odd	2	inner
210.3.k.b.83.12	yes	32	1.1	even	1	trivial
210.3.k.b.167.5	yes	32	15.2	even	4	inner
210.3.k.b.167.12	yes	32	105.62	odd	4	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.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.94039 + 2.28799i) q^{3} +2.00000i q^{4} +(-4.58449 + 1.99562i) q^{5} +(-0.347606 + 4.22838i) q^{6} +(5.57668 + 4.23091i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.46981 + 8.87917i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.94039 + 2.28799i) q^{3} +2.00000i q^{4} +(-4.58449 + 1.99562i) q^{5} +(-0.347606 + 4.22838i) q^{6} +(5.57668 + 4.23091i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.46981 + 8.87917i) q^{9} +(-6.58010 - 2.58887i) q^{10} -14.6047i q^{11} +(-4.57598 + 3.88077i) q^{12} +(-3.48167 + 3.48167i) q^{13} +(1.34578 + 9.80759i) q^{14} +(-13.4616 - 6.61700i) q^{15} -4.00000 q^{16} +(-20.1653 + 20.1653i) q^{17} +(-10.3490 + 7.40936i) q^{18} +26.4132 q^{19} +(-3.99123 - 9.16897i) q^{20} +(1.14063 + 20.9690i) q^{21} +(14.6047 - 14.6047i) q^{22} +(2.68095 - 2.68095i) q^{23} +(-8.45675 - 0.695213i) q^{24} +(17.0350 - 18.2978i) q^{25} -6.96334 q^{26} +(-23.1675 + 13.8661i) q^{27} +(-8.46182 + 11.1534i) q^{28} +28.5159 q^{29} +(-6.84462 - 20.0786i) q^{30} -15.6511i q^{31} +(-4.00000 - 4.00000i) q^{32} +(33.4154 - 28.3387i) q^{33} -40.3306 q^{34} +(-34.0095 - 8.26762i) q^{35} +(-17.7583 - 2.93962i) q^{36} +(7.69844 - 7.69844i) q^{37} +(26.4132 + 26.4132i) q^{38} +(-14.7218 - 1.21025i) q^{39} +(5.17774 - 13.1602i) q^{40} +37.9832 q^{41} +(-19.8284 + 22.1096i) q^{42} +(41.7817 + 41.7817i) q^{43} +29.2094 q^{44} +(-10.9811 - 43.6396i) q^{45} +5.36190 q^{46} +(21.0822 - 21.0822i) q^{47} +(-7.76154 - 9.15197i) q^{48} +(13.1988 + 47.1889i) q^{49} +(35.3328 - 1.26273i) q^{50} +(-85.2664 - 7.00958i) q^{51} +(-6.96334 - 6.96334i) q^{52} +(-47.4934 + 47.4934i) q^{53} +(-37.0336 - 9.30137i) q^{54} +(29.1453 + 66.9549i) q^{55} +(-19.6152 + 2.69155i) q^{56} +(51.2518 + 60.4332i) q^{57} +(28.5159 + 28.5159i) q^{58} -61.6589i q^{59} +(13.2340 - 26.9232i) q^{60} -54.1777i q^{61} +(15.6511 - 15.6511i) q^{62} +(-45.7636 + 43.2977i) q^{63} -8.00000i q^{64} +(9.01359 - 22.9098i) q^{65} +(61.7541 + 5.07668i) q^{66} +(68.9882 - 68.9882i) q^{67} +(-40.3306 - 40.3306i) q^{68} +(11.3361 + 0.931915i) q^{69} +(-25.7419 - 42.2771i) q^{70} -65.9594i q^{71} +(-14.8187 - 20.6980i) q^{72} +(6.51081 - 6.51081i) q^{73} +15.3969 q^{74} +(74.9196 + 3.47129i) q^{75} +52.8265i q^{76} +(61.7911 - 81.4457i) q^{77} +(-13.5116 - 15.9321i) q^{78} +42.7301i q^{79} +(18.3379 - 7.98247i) q^{80} +(-76.6793 - 26.1014i) q^{81} +(37.9832 + 37.9832i) q^{82} +(9.52614 + 9.52614i) q^{83} +(-41.9380 + 2.28126i) q^{84} +(52.2053 - 132.690i) q^{85} +83.5634i q^{86} +(55.3318 + 65.2441i) q^{87} +(29.2094 + 29.2094i) q^{88} +19.3830i q^{89} +(32.6585 - 54.6207i) q^{90} +(-34.1468 + 4.68555i) q^{91} +(5.36190 + 5.36190i) q^{92} +(35.8096 - 30.3692i) q^{93} +42.1644 q^{94} +(-121.091 + 52.7107i) q^{95} +(1.39043 - 16.9135i) q^{96} +(-84.6391 - 84.6391i) q^{97} +(-33.9901 + 60.3877i) q^{98} +(129.677 + 21.4661i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{2} - 4 q^{7} - 64 q^{8} + 16 q^{9}+O(q^{10}) \) 32 * q + 32 * q^2 - 4 * q^7 - 64 * q^8 + 16 * q^9	\( 32 q + 32 q^{2} - 4 q^{7} - 64 q^{8} + 16 q^{9} - 8 q^{14} - 4 q^{15} - 128 q^{16} - 4 q^{18} + 12 q^{21} - 40 q^{22} - 24 q^{23} + 16 q^{25} - 8 q^{28} + 112 q^{29} + 28 q^{30} - 128 q^{32} + 48 q^{35} - 40 q^{36} + 32 q^{37} - 64 q^{39} - 20 q^{42} - 32 q^{43} - 80 q^{44} - 48 q^{46} + 8 q^{50} + 84 q^{51} + 136 q^{53} + 340 q^{57} + 112 q^{58} + 64 q^{60} + 168 q^{63} + 200 q^{65} + 32 q^{67} - 72 q^{72} + 64 q^{74} - 88 q^{77} - 4 q^{78} + 76 q^{81} - 64 q^{84} - 40 q^{85} - 80 q^{88} - 272 q^{91} - 48 q^{92} - 388 q^{93} - 544 q^{95} - 128 q^{98} - 160 q^{99}+O(q^{100}) \) 32 * q + 32 * q^2 - 4 * q^7 - 64 * q^8 + 16 * q^9 - 8 * q^14 - 4 * q^15 - 128 * q^16 - 4 * q^18 + 12 * q^21 - 40 * q^22 - 24 * q^23 + 16 * q^25 - 8 * q^28 + 112 * q^29 + 28 * q^30 - 128 * q^32 + 48 * q^35 - 40 * q^36 + 32 * q^37 - 64 * q^39 - 20 * q^42 - 32 * q^43 - 80 * q^44 - 48 * q^46 + 8 * q^50 + 84 * q^51 + 136 * q^53 + 340 * q^57 + 112 * q^58 + 64 * q^60 + 168 * q^63 + 200 * q^65 + 32 * q^67 - 72 * q^72 + 64 * q^74 - 88 * q^77 - 4 * q^78 + 76 * q^81 - 64 * q^84 - 40 * q^85 - 80 * q^88 - 272 * q^91 - 48 * q^92 - 388 * q^93 - 544 * q^95 - 128 * q^98 - 160 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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