LMFDB - Embedded newform 585.2.i.h.391.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(196,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("585.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			391.3
Character	$\chi$	$=$	585.391
Dual form			585.2.i.h.196.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09333 - 1.89370i) q^{2} +(1.72789 - 0.119945i) q^{3} +(-1.39073 + 2.40882i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.11629 - 3.14097i) q^{6} +(2.12668 + 3.68352i) q^{7} +1.70880 q^{8} +(2.97123 - 0.414503i) q^{9} +O(q^{10})$	\(q+(-1.09333 - 1.89370i) q^{2} +(1.72789 - 0.119945i) q^{3} +(-1.39073 + 2.40882i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.11629 - 3.14097i) q^{6} +(2.12668 + 3.68352i) q^{7} +1.70880 q^{8} +(2.97123 - 0.414503i) q^{9} -2.18666 q^{10} +(0.344526 + 0.596736i) q^{11} +(-2.11411 + 4.32900i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(4.65033 - 8.05460i) q^{14} +(0.760071 - 1.55637i) q^{15} +(0.913186 + 1.58168i) q^{16} +2.89736 q^{17} +(-4.03347 - 5.17342i) q^{18} +1.63191 q^{19} +(1.39073 + 2.40882i) q^{20} +(4.11650 + 6.10965i) q^{21} +(0.753360 - 1.30486i) q^{22} +(0.480072 - 0.831510i) q^{23} +(2.95263 - 0.204962i) q^{24} +(-0.500000 - 0.866025i) q^{25} +2.18666 q^{26} +(5.08424 - 1.07260i) q^{27} -11.8306 q^{28} +(-1.58191 - 2.73995i) q^{29} +(-3.77831 + 0.262278i) q^{30} +(-0.953545 + 1.65159i) q^{31} +(3.70563 - 6.41833i) q^{32} +(0.666879 + 0.989773i) q^{33} +(-3.16777 - 5.48673i) q^{34} +4.25337 q^{35} +(-3.13372 + 7.73362i) q^{36} +5.34441 q^{37} +(-1.78422 - 3.09035i) q^{38} +(-0.760071 + 1.55637i) q^{39} +(0.854401 - 1.47987i) q^{40} +(-3.93651 + 6.81823i) q^{41} +(7.06916 - 14.4753i) q^{42} +(-3.78779 - 6.56064i) q^{43} -1.91658 q^{44} +(1.12664 - 2.78041i) q^{45} -2.09951 q^{46} +(-4.08424 - 7.07411i) q^{47} +(1.76760 + 2.62345i) q^{48} +(-5.54556 + 9.60519i) q^{49} +(-1.09333 + 1.89370i) q^{50} +(5.00633 - 0.347523i) q^{51} +(-1.39073 - 2.40882i) q^{52} +11.5941 q^{53} +(-7.58993 - 8.45533i) q^{54} +0.689052 q^{55} +(3.63408 + 6.29441i) q^{56} +(2.81977 - 0.195739i) q^{57} +(-3.45909 + 5.99132i) q^{58} +(-1.44118 + 2.49620i) q^{59} +(2.69196 + 3.99537i) q^{60} +(-2.50678 - 4.34187i) q^{61} +4.17015 q^{62} +(7.84569 + 10.0631i) q^{63} -12.5531 q^{64} +(0.500000 + 0.866025i) q^{65} +(1.14521 - 2.34502i) q^{66} +(-2.77964 + 4.81448i) q^{67} +(-4.02946 + 6.97923i) q^{68} +(0.729778 - 1.49434i) q^{69} +(-4.65033 - 8.05460i) q^{70} -6.84175 q^{71} +(5.07724 - 0.708304i) q^{72} -12.5995 q^{73} +(-5.84320 - 10.1207i) q^{74} +(-0.967822 - 1.43643i) q^{75} +(-2.26956 + 3.93099i) q^{76} +(-1.46539 + 2.53814i) q^{77} +(3.77831 - 0.262278i) q^{78} +(-6.12760 - 10.6133i) q^{79} +1.82637 q^{80} +(8.65637 - 2.46317i) q^{81} +17.2156 q^{82} +(-7.07700 - 12.2577i) q^{83} +(-20.4420 + 1.41902i) q^{84} +(1.44868 - 2.50919i) q^{85} +(-8.28259 + 14.3459i) q^{86} +(-3.06201 - 4.54459i) q^{87} +(0.588727 + 1.01970i) q^{88} -16.7769 q^{89} +(-6.49705 + 0.906377i) q^{90} -4.25337 q^{91} +(1.33531 + 2.31282i) q^{92} +(-1.44952 + 2.96814i) q^{93} +(-8.93083 + 15.4686i) q^{94} +(0.815956 - 1.41328i) q^{95} +(5.63308 - 11.5347i) q^{96} +(6.83463 + 11.8379i) q^{97} +24.2525 q^{98} +(1.27101 + 1.63023i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9}+O(q^{10}) $ 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9} + 2 q^{10} + 9 q^{11} + 18 q^{12} - 15 q^{13} + 3 q^{14} + 2 q^{15} - 33 q^{16} + 6 q^{17} + 9 q^{18} + 30 q^{19} + 21 q^{20} + 9 q^{21} - 10 q^{22} - 6 q^{23} + 24 q^{24} - 15 q^{25} - 2 q^{26} - 2 q^{27} + 70 q^{28} + 8 q^{29} - 6 q^{30} - 22 q^{31} + 21 q^{32} - 20 q^{33} - 9 q^{34} - 20 q^{35} - 7 q^{36} + 8 q^{37} - 14 q^{38} - 2 q^{39} + 13 q^{41} + 21 q^{42} - 24 q^{43} + 10 q^{44} - 7 q^{45} - 6 q^{46} - q^{47} - 27 q^{48} - 37 q^{49} + q^{50} - q^{51} - 21 q^{52} + 14 q^{53} - 24 q^{54} + 18 q^{55} + 17 q^{56} - 55 q^{57} - 22 q^{58} + 19 q^{59} + 9 q^{60} - 16 q^{61} + 26 q^{62} + 4 q^{63} + 72 q^{64} + 15 q^{65} + 24 q^{66} - 11 q^{67} - 28 q^{68} + 44 q^{69} - 3 q^{70} - 56 q^{71} - 18 q^{72} + 52 q^{73} + 8 q^{74} + q^{75} - 18 q^{76} - 24 q^{77} + 6 q^{78} - 44 q^{79} - 66 q^{80} + 37 q^{81} + 70 q^{82} - 3 q^{83} - 139 q^{84} + 3 q^{85} + 40 q^{86} + 60 q^{87} - 37 q^{88} - 8 q^{89} - 12 q^{90} + 20 q^{91} - 74 q^{92} - 55 q^{93} - 2 q^{94} + 15 q^{95} + 55 q^{96} - 33 q^{97} + 6 q^{98} + 26 q^{99}+O(q^{100}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9 + 2 * q^10 + 9 * q^11 + 18 * q^12 - 15 * q^13 + 3 * q^14 + 2 * q^15 - 33 * q^16 + 6 * q^17 + 9 * q^18 + 30 * q^19 + 21 * q^20 + 9 * q^21 - 10 * q^22 - 6 * q^23 + 24 * q^24 - 15 * q^25 - 2 * q^26 - 2 * q^27 + 70 * q^28 + 8 * q^29 - 6 * q^30 - 22 * q^31 + 21 * q^32 - 20 * q^33 - 9 * q^34 - 20 * q^35 - 7 * q^36 + 8 * q^37 - 14 * q^38 - 2 * q^39 + 13 * q^41 + 21 * q^42 - 24 * q^43 + 10 * q^44 - 7 * q^45 - 6 * q^46 - q^47 - 27 * q^48 - 37 * q^49 + q^50 - q^51 - 21 * q^52 + 14 * q^53 - 24 * q^54 + 18 * q^55 + 17 * q^56 - 55 * q^57 - 22 * q^58 + 19 * q^59 + 9 * q^60 - 16 * q^61 + 26 * q^62 + 4 * q^63 + 72 * q^64 + 15 * q^65 + 24 * q^66 - 11 * q^67 - 28 * q^68 + 44 * q^69 - 3 * q^70 - 56 * q^71 - 18 * q^72 + 52 * q^73 + 8 * q^74 + q^75 - 18 * q^76 - 24 * q^77 + 6 * q^78 - 44 * q^79 - 66 * q^80 + 37 * q^81 + 70 * q^82 - 3 * q^83 - 139 * q^84 + 3 * q^85 + 40 * q^86 + 60 * q^87 - 37 * q^88 - 8 * q^89 - 12 * q^90 + 20 * q^91 - 74 * q^92 - 55 * q^93 - 2 * q^94 + 15 * q^95 + 55 * q^96 - 33 * q^97 + 6 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.09333	−	1.89370i	−0.773100	−	1.33905i	−0.935856	−	0.352382i	$-0.885372\pi$
$2$	−1.09333	−	1.89370i	−0.773100	−	1.33905i	0.162756	−	0.986666i	$-0.447962\pi$
$3$	1.72789	−	0.119945i	0.997599	−	0.0692501i
$3$	1.72789	−	0.119945i	0.997599	−	0.0692501i
$4$	−1.39073	+	2.40882i	−0.695367	+	1.20441i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−2.11629	−	3.14097i	−0.863973	−	1.28230i
$7$	2.12668	+	3.68352i	0.803811	+	1.39224i	0.917091	+	0.398678i	$0.130531\pi$
$7$	2.12668	+	3.68352i	0.803811	+	1.39224i	−0.113281	+	0.993563i	$0.536136\pi$
$8$	1.70880			0.604153
$9$	2.97123	−	0.414503i	0.990409	−	0.138168i
$10$	−2.18666			−0.691482
$11$	0.344526	+	0.596736i	0.103878	+	0.179923i	0.913279	−	0.407334i	$-0.133541\pi$
$11$	0.344526	+	0.596736i	0.103878	+	0.179923i	−0.809401	+	0.587256i	$0.800208\pi$
$12$	−2.11411	+	4.32900i	−0.610292	+	1.24967i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$	4.65033	−	8.05460i	1.24285	−	2.15268i
$15$	0.760071	−	1.55637i	0.196250	−	0.401853i
$16$	0.913186	+	1.58168i	0.228297	+	0.395421i
$17$	2.89736			0.702713			0.351357	−	0.936242i	$-0.385720\pi$
$17$	2.89736			0.702713			0.351357	+	0.936242i	$0.385720\pi$
$18$	−4.03347	−	5.17342i	−0.950698	−	1.21939i
$19$	1.63191			0.374386			0.187193	−	0.982323i	$-0.440061\pi$
$19$	1.63191			0.374386			0.187193	+	0.982323i	$0.440061\pi$
$20$	1.39073	+	2.40882i	0.310978	+	0.538629i
$21$	4.11650	+	6.10965i	0.898294	+	1.33323i
$22$	0.753360	−	1.30486i	0.160617	−	0.278197i
$23$	0.480072	−	0.831510i	0.100102	−	0.173382i	−0.811624	−	0.584179i	$-0.801416\pi$
$23$	0.480072	−	0.831510i	0.100102	−	0.173382i	0.911727	+	0.410798i	$0.134750\pi$
$24$	2.95263	−	0.204962i	0.602702	−	0.0418377i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	2.18666			0.428839
$27$	5.08424	−	1.07260i	0.978463	−	0.206422i
$28$	−11.8306			−2.23577
$29$	−1.58191	−	2.73995i	−0.293753	−	0.508795i	0.680941	−	0.732338i	$-0.261571\pi$
$29$	−1.58191	−	2.73995i	−0.293753	−	0.508795i	−0.974694	+	0.223543i	$0.928238\pi$
$30$	−3.77831	+	0.262278i	−0.689822	+	0.0478852i
$31$	−0.953545	+	1.65159i	−0.171262	+	0.296634i	−0.938861	−	0.344296i	$-0.888118\pi$
$31$	−0.953545	+	1.65159i	−0.171262	+	0.296634i	0.767599	+	0.640930i	$0.221451\pi$
$32$	3.70563	−	6.41833i	0.655068	−	1.13461i
$33$	0.666879	+	0.989773i	0.116089	+	0.172297i
$34$	−3.16777	−	5.48673i	−0.543268	−	0.940967i
$35$	4.25337			0.718950
$36$	−3.13372	+	7.73362i	−0.522287	+	1.28894i
$37$	5.34441			0.878616			0.439308	−	0.898337i	$-0.355224\pi$
$37$	5.34441			0.878616			0.439308	+	0.898337i	$0.355224\pi$
$38$	−1.78422	−	3.09035i	−0.289438	−	0.501321i
$39$	−0.760071	+	1.55637i	−0.121709	+	0.249219i
$40$	0.854401	−	1.47987i	0.135093	−	0.233987i
$41$	−3.93651	+	6.81823i	−0.614779	+	1.06483i	0.375644	+	0.926764i	$0.377422\pi$
$41$	−3.93651	+	6.81823i	−0.614779	+	1.06483i	−0.990423	+	0.138065i	$0.955912\pi$
$42$	7.06916	−	14.4753i	1.09079	−	2.23358i
$43$	−3.78779	−	6.56064i	−0.577632	−	1.00049i	−0.995750	−	0.0920953i	$-0.970644\pi$
$43$	−3.78779	−	6.56064i	−0.577632	−	1.00049i	0.418118	−	0.908393i	$-0.362690\pi$
$44$	−1.91658			−0.288935
$45$	1.12664	−	2.78041i	0.167950	−	0.414479i
$46$	−2.09951			−0.309555
$47$	−4.08424	−	7.07411i	−0.595747	−	1.03186i	−0.993441	−	0.114346i	$-0.963523\pi$
$47$	−4.08424	−	7.07411i	−0.595747	−	1.03186i	0.397694	−	0.917518i	$-0.369811\pi$
$48$	1.76760	+	2.62345i	0.255131	+	0.378662i
$49$	−5.54556	+	9.60519i	−0.792223	+	1.37217i
$50$	−1.09333	+	1.89370i	−0.154620	+	0.267810i
$51$	5.00633	−	0.347523i	0.701026	−	0.0486630i
$52$	−1.39073	−	2.40882i	−0.192860	−	0.334043i
$53$	11.5941			1.59257			0.796287	−	0.604919i	$-0.206795\pi$
$53$	11.5941			1.59257			0.796287	+	0.604919i	$0.206795\pi$
$54$	−7.58993	−	8.45533i	−1.03286	−	1.15062i
$55$	0.689052			0.0929117
$56$	3.63408	+	6.29441i	0.485624	+	0.841126i
$57$	2.81977	−	0.195739i	0.373488	−	0.0259263i
$58$	−3.45909	+	5.99132i	−0.454201	+	0.786699i
$59$	−1.44118	+	2.49620i	−0.187626	+	0.324978i	−0.944458	−	0.328631i	$-0.893413\pi$
$59$	−1.44118	+	2.49620i	−0.187626	+	0.324978i	0.756832	+	0.653609i	$0.226746\pi$
$60$	2.69196	+	3.99537i	0.347531	+	0.515801i
$61$	−2.50678	−	4.34187i	−0.320961	−	0.555920i	0.659726	−	0.751506i	$-0.270672\pi$
$61$	−2.50678	−	4.34187i	−0.320961	−	0.555920i	−0.980686	+	0.195586i	$0.937339\pi$
$62$	4.17015			0.529610
$63$	7.84569	+	10.0631i	0.988464	+	1.26783i
$64$	−12.5531			−1.56914
$65$	0.500000	+	0.866025i	0.0620174	+	0.107417i
$66$	1.14521	−	2.34502i	0.140966	−	0.288652i
$67$	−2.77964	+	4.81448i	−0.339587	+	0.588182i	−0.984355	−	0.176196i	$-0.943621\pi$
$67$	−2.77964	+	4.81448i	−0.339587	+	0.588182i	0.644768	+	0.764378i	$0.276954\pi$
$68$	−4.02946	+	6.97923i	−0.488644	+	0.846356i
$69$	0.729778	−	1.49434i	0.0878550	−	0.179898i
$70$	−4.65033	−	8.05460i	−0.555820	−	0.962709i
$71$	−6.84175			−0.811966			−0.405983	−	0.913881i	$-0.633071\pi$
$71$	−6.84175			−0.811966			−0.405983	+	0.913881i	$0.633071\pi$
$72$	5.07724	−	0.708304i	0.598358	−	0.0834745i
$73$	−12.5995			−1.47465			−0.737327	−	0.675536i	$-0.763912\pi$
$73$	−12.5995			−1.47465			−0.737327	+	0.675536i	$0.763912\pi$
$74$	−5.84320	−	10.1207i	−0.679258	−	1.17651i
$75$	−0.967822	−	1.43643i	−0.111754	−	0.165864i
$76$	−2.26956	+	3.93099i	−0.260336	+	0.450915i
$77$	−1.46539	+	2.53814i	−0.166997	+	0.289248i
$78$	3.77831	−	0.262278i	0.427809	−	0.0296971i
$79$	−6.12760	−	10.6133i	−0.689409	−	1.19409i	−0.972029	−	0.234859i	$-0.924537\pi$
$79$	−6.12760	−	10.6133i	−0.689409	−	1.19409i	0.282620	−	0.959232i	$-0.408796\pi$
$80$	1.82637			0.204195
$81$	8.65637	−	2.46317i	0.961819	−	0.273685i
$82$	17.2156			1.90114
$83$	−7.07700	−	12.2577i	−0.776802	−	1.34546i	−0.933776	−	0.357858i	$-0.883507\pi$
$83$	−7.07700	−	12.2577i	−0.776802	−	1.34546i	0.156974	−	0.987603i	$-0.449826\pi$
$84$	−20.4420	+	1.41902i	−2.23041	+	0.154828i
$85$	1.44868	−	2.50919i	0.157131	−	0.272160i
$86$	−8.28259	+	14.3459i	−0.893134	+	1.54695i
$87$	−3.06201	−	4.54459i	−0.328282	−	0.487231i
$88$	0.588727	+	1.01970i	0.0627585	+	0.108701i
$89$	−16.7769			−1.77835			−0.889176	−	0.457564i	$-0.848722\pi$
$89$	−16.7769			−1.77835			−0.889176	+	0.457564i	$0.848722\pi$
$90$	−6.49705	+	0.906377i	−0.684849	+	0.0955405i
$91$	−4.25337			−0.445874
$92$	1.33531	+	2.31282i	0.139215	+	0.241128i
$93$	−1.44952	+	2.96814i	−0.150309	+	0.307782i
$94$	−8.93083	+	15.4686i	−0.921144	+	1.59547i
$95$	0.815956	−	1.41328i	0.0837153	−	0.144999i
$96$	5.63308	−	11.5347i	0.574924	−	1.17725i
$97$	6.83463	+	11.8379i	0.693952	+	1.20196i	0.970533	+	0.240969i	$0.0774653\pi$
$97$	6.83463	+	11.8379i	0.693952	+	1.20196i	−0.276581	+	0.960991i	$0.589201\pi$
$98$	24.2525			2.44987
$99$	1.27101	+	1.63023i	0.127742	+	0.163844i
$100$	2.78147			0.278147
$101$	7.30116	+	12.6460i	0.726493	+	1.25832i	0.958357	+	0.285574i	$0.0921844\pi$
$101$	7.30116	+	12.6460i	0.726493	+	1.25832i	−0.231863	+	0.972748i	$0.574482\pi$
$102$	−6.13167	−	9.10053i	−0.607126	−	0.901087i
$103$	8.91125	−	15.4347i	0.878051	−	1.52083i	0.0245745	−	0.999698i	$-0.492177\pi$
$103$	8.91125	−	15.4347i	0.878051	−	1.52083i	0.853477	−	0.521131i	$-0.174490\pi$
$104$	−0.854401	+	1.47987i	−0.0837809	+	0.145113i
$105$	7.34936	−	0.510169i	0.717224	−	0.0497874i
$106$	−12.6762	−	21.9558i	−1.23122	−	2.13253i
$107$	7.01124			0.677802			0.338901	−	0.940822i	$-0.389945\pi$
$107$	7.01124			0.677802			0.338901	+	0.940822i	$0.389945\pi$
$108$	−4.48713	+	13.7387i	−0.431774	+	1.32201i
$109$	−1.29945			−0.124464			−0.0622322	−	0.998062i	$-0.519822\pi$
$109$	−1.29945			−0.124464			−0.0622322	+	0.998062i	$0.519822\pi$
$110$	−0.753360	−	1.30486i	−0.0718301	−	0.124413i
$111$	9.23457	−	0.641034i	0.876507	−	0.0608443i
$112$	−3.88411	+	6.72748i	−0.367014	+	0.635687i
$113$	0.778397	−	1.34822i	0.0732254	−	0.126830i	−0.827088	−	0.562073i	$-0.810004\pi$
$113$	0.778397	−	1.34822i	0.0732254	−	0.126830i	0.900313	+	0.435243i	$0.143337\pi$
$114$	−3.45361	−	5.12579i	−0.323460	−	0.480074i
$115$	−0.480072	−	0.831510i	−0.0447670	−	0.0775387i
$116$	8.80006			0.817065
$117$	−1.12664	+	2.78041i	−0.104158	+	0.257049i
$118$	6.30274			0.580215
$119$	6.16177	+	10.6725i	0.564848	+	0.978346i
$120$	1.29881	−	2.65953i	0.118565	−	0.242781i
$121$	5.26260	−	9.11510i	0.478419	−	0.828645i
$122$	−5.48147	+	9.49419i	−0.496269	+	0.859563i
$123$	−5.98405	+	12.2533i	−0.539564	+	1.10485i
$124$	−2.65226	−	4.59384i	−0.238180	−	0.412539i
$125$	−1.00000			−0.0894427
$126$	10.4785	−	25.8596i	0.933500	−	2.30376i
$127$	5.95367			0.528303			0.264152	−	0.964481i	$-0.414908\pi$
$127$	5.95367			0.528303			0.264152	+	0.964481i	$0.414908\pi$
$128$	6.31343	+	10.9352i	0.558034	+	0.966543i
$129$	−7.33180	−	10.8818i	−0.645529	−	0.958085i
$130$	1.09333	−	1.89370i	0.0958912	−	0.166089i
$131$	−1.94294	+	3.36528i	−0.169756	+	0.294026i	−0.938334	−	0.345730i	$-0.887631\pi$
$131$	−1.94294	+	3.36528i	−0.169756	+	0.294026i	0.768578	+	0.639756i	$0.220965\pi$
$132$	−3.31164	+	0.229883i	−0.288241	+	0.0200088i
$133$	3.47056	+	6.01119i	0.300936	+	0.521236i
$134$	12.1562			1.05014
$135$	1.61322	−	4.93938i	0.138844	−	0.425114i
$136$	4.95102			0.424546
$137$	8.13046	+	14.0824i	0.694632	+	1.20314i	0.970305	+	0.241886i	$0.0777660\pi$
$137$	8.13046	+	14.0824i	0.694632	+	1.20314i	−0.275673	+	0.961252i	$0.588901\pi$
$138$	−3.62772	+	0.251825i	−0.308812	+	0.0214368i
$139$	−9.36970	+	16.2288i	−0.794727	+	1.37651i	0.128285	+	0.991737i	$0.459053\pi$
$139$	−9.36970	+	16.2288i	−0.794727	+	1.37651i	−0.923012	+	0.384771i	$0.874280\pi$
$140$	−5.91530	+	10.2456i	−0.499934	+	0.865911i
$141$	−7.90563	−	11.7334i	−0.665774	−	0.988132i
$142$	7.48028	+	12.9562i	0.627731	+	1.08726i
$143$	−0.689052			−0.0576214
$144$	3.36890	+	4.32102i	0.280741	+	0.360085i
$145$	−3.16382			−0.262741
$146$	13.7753	+	23.8596i	1.14006	+	1.97463i
$147$	−8.43004	+	17.2619i	−0.695298	+	1.42374i
$148$	−7.43266	+	12.8737i	−0.610961	+	1.05821i
$149$	0.342103	−	0.592539i	0.0280261	−	0.0485427i	−0.851672	−	0.524075i	$-0.824411\pi$
$149$	0.342103	−	0.592539i	0.0280261	−	0.0485427i	0.879698	+	0.475532i	$0.157745\pi$
$150$	−1.66201	+	3.40325i	−0.135703	+	0.277874i
$151$	5.42725	+	9.40027i	0.441663	+	0.764983i	0.997813	−	0.0660989i	$-0.0210553\pi$
$151$	5.42725	+	9.40027i	0.441663	+	0.764983i	−0.556150	+	0.831082i	$0.687722\pi$
$152$	2.78862			0.226187
$153$	8.60872	−	1.20097i	0.695973	−	0.0970924i
$154$	6.40863			0.516422
$155$	0.953545	+	1.65159i	0.0765906	+	0.132659i
$156$	−2.69196	−	3.99537i	−0.215530	−	0.319886i
$157$	−9.01254	+	15.6102i	−0.719279	+	1.24583i	0.242006	+	0.970275i	$0.422195\pi$
$157$	−9.01254	+	15.6102i	−0.719279	+	1.24583i	−0.961286	+	0.275554i	$0.911139\pi$
$158$	−13.3990	+	23.2077i	−1.06596	+	1.84630i
$159$	20.0334	−	1.39065i	1.58875	−	0.110286i
$160$	−3.70563	−	6.41833i	−0.292956	−	0.507414i
$161$	4.08385			0.321852
$162$	−14.1288	−	13.6995i	−1.11006	−	1.07634i
$163$	13.1672			1.03134			0.515669	−	0.856788i	$-0.327544\pi$
$163$	13.1672			1.03134			0.515669	+	0.856788i	$0.327544\pi$
$164$	−10.9493	−	18.9647i	−0.854994	−	1.48089i
$165$	1.19061	−	0.0826482i	0.0926887	−	0.00643415i
$166$	−15.4750	+	26.8034i	−1.20109	+	2.08035i
$167$	0.599138	−	1.03774i	0.0463627	−	0.0803026i	−0.841913	−	0.539614i	$-0.818570\pi$
$167$	0.599138	−	1.03774i	0.0463627	−	0.0803026i	0.888276	+	0.459311i	$0.151904\pi$
$168$	7.03428	+	10.4402i	0.542707	+	0.805477i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	−6.33553			−0.485913
$171$	4.84878	−	0.676433i	0.370796	−	0.0517281i
$172$	21.0712			1.60666
$173$	−7.17684	−	12.4307i	−0.545645	−	0.945086i	−0.998566	−	0.0535347i	$-0.982951\pi$
$173$	−7.17684	−	12.4307i	−0.545645	−	0.945086i	0.452921	−	0.891551i	$-0.350382\pi$
$174$	−5.25831	+	10.7673i	−0.398631	+	0.816264i
$175$	2.12668	−	3.68352i	0.160762	−	0.278448i
$176$	−0.629233	+	1.08986i	−0.0474302	+	0.0821515i
$177$	−2.19080	+	4.48603i	−0.164671	+	0.337191i
$178$	18.3427	+	31.7705i	1.37484	+	2.38130i
$179$	−14.3886			−1.07545			−0.537727	−	0.843119i	$-0.680717\pi$
$179$	−14.3886			−1.07545			−0.537727	+	0.843119i	$0.680717\pi$
$180$	5.13065	+	6.58069i	0.382416	+	0.490496i
$181$	17.5268			1.30276			0.651379	−	0.758752i	$-0.274191\pi$
$181$	17.5268			1.30276			0.651379	+	0.758752i	$0.274191\pi$
$182$	4.65033	+	8.05460i	0.344705	+	0.597047i
$183$	−4.85224	−	7.20162i	−0.358688	−	0.532359i
$184$	0.820349	−	1.42089i	0.0604769	−	0.104749i
$185$	2.67221	−	4.62840i	0.196465	−	0.340286i
$186$	7.20558	−	0.500188i	0.528338	−	0.0366756i
$187$	0.998216	+	1.72896i	0.0729968	+	0.126434i
$188$	22.7204			1.65705
$189$	14.7635	+	16.4468i	1.07389	+	1.19633i
$190$	−3.56843			−0.258881
$191$	−6.93881	−	12.0184i	−0.502075	−	0.869619i	−0.999997	−	0.00239740i	$-0.999237\pi$
$191$	−6.93881	−	12.0184i	−0.502075	−	0.869619i	0.497922	−	0.867222i	$-0.334096\pi$
$192$	−21.6904	+	1.50568i	−1.56537	+	0.108663i
$193$	1.64162	−	2.84336i	0.118166	−	0.204670i	−0.800875	−	0.598832i	$-0.795632\pi$
$193$	1.64162	−	2.84336i	0.118166	−	0.204670i	0.919041	+	0.394162i	$0.128965\pi$
$194$	14.9450	−	25.8855i	1.07299	−	1.85847i
$195$	0.967822	+	1.43643i	0.0693071	+	0.102865i
$196$	−15.4248	−	26.7165i	−1.10177	−	1.90832i
$197$	−0.446318			−0.0317989			−0.0158994	−	0.999874i	$-0.505061\pi$
$197$	−0.446318			−0.0317989			−0.0158994	+	0.999874i	$0.505061\pi$
$198$	1.69754	−	4.18930i	0.120639	−	0.297720i
$199$	20.1948			1.43157			0.715786	−	0.698320i	$-0.246069\pi$
$199$	20.1948			1.43157			0.715786	+	0.698320i	$0.246069\pi$
$200$	−0.854401	−	1.47987i	−0.0604153	−	0.104642i
$201$	−4.22545	+	8.65231i	−0.298040	+	0.610287i
$202$	15.9651	−	27.6524i	1.12330	−	1.94562i
$203$	6.72844	−	11.6540i	0.472244	−	0.817950i
$204$	−6.12535	+	12.5427i	−0.428860	+	0.878162i
$205$	3.93651	+	6.81823i	0.274938	+	0.476206i
$206$	−38.9717			−2.71529
$207$	1.08174	−	2.66960i	0.0751862	−	0.185550i
$208$	−1.82637			−0.126636
$209$	0.562236	+	0.973822i	0.0388907	+	0.0673606i
$210$	−9.00137	−	13.3597i	−0.621154	−	0.921907i
$211$	−7.62202	+	13.2017i	−0.524721	+	0.908844i	0.474864	+	0.880059i	$0.342497\pi$
$211$	−7.62202	+	13.2017i	−0.524721	+	0.908844i	−0.999586	+	0.0287851i	$0.990836\pi$
$212$	−16.1243	+	27.9282i	−1.10742	+	1.91811i
$213$	−11.8218	+	0.820632i	−0.810017	+	0.0562288i
$214$	−7.66558	−	13.2772i	−0.524008	−	0.907609i
$215$	−7.57557			−0.516650
$216$	8.68797	−	1.83286i	0.591141	−	0.124710i
$217$	−8.11155			−0.550648
$218$	1.42072	+	2.46076i	0.0962234	+	0.166664i
$219$	−21.7705	+	1.51124i	−1.47111	+	0.102120i
$220$	−0.958288	+	1.65980i	−0.0646078	+	0.111904i
$221$	−1.44868	+	2.50919i	−0.0974488	+	0.168786i
$222$	−11.3103	−	16.7866i	−0.759101	−	1.12665i
$223$	−7.82617	−	13.5553i	−0.524079	−	0.907732i	−0.999607	−	0.0280311i	$-0.991076\pi$
$223$	−7.82617	−	13.5553i	−0.524079	−	0.907732i	0.475528	−	0.879701i	$-0.342257\pi$
$224$	31.5228			2.10620
$225$	−1.84458	−	2.36591i	−0.122972	−	0.157727i
$226$	−3.40417			−0.226442
$227$	−9.64199	−	16.7004i	−0.639961	−	1.10845i	−0.985441	−	0.170019i	$-0.945617\pi$
$227$	−9.64199	−	16.7004i	−0.639961	−	1.10845i	0.345479	−	0.938426i	$-0.387716\pi$
$228$	−3.45005	+	7.06454i	−0.228485	+	0.467861i
$229$	8.38050	−	14.5155i	0.553799	−	0.959208i	−0.444197	−	0.895929i	$-0.646511\pi$
$229$	8.38050	−	14.5155i	0.553799	−	0.959208i	0.997996	−	0.0632791i	$-0.0201558\pi$
$230$	−1.04975	+	1.81823i	−0.0692187	+	0.119890i
$231$	−2.22761	+	4.56140i	−0.146566	+	0.300118i
$232$	−2.70317	−	4.68203i	−0.177472	−	0.307390i
$233$	−18.0229			−1.18072			−0.590358	−	0.807141i	$-0.701014\pi$
$233$	−18.0229			−1.18072			−0.590358	+	0.807141i	$0.701014\pi$
$234$	6.49705	−	0.906377i	0.424726	−	0.0592517i
$235$	−8.16848			−0.532853
$236$	−4.00860	−	6.94311i	−0.260938	−	0.451958i
$237$	−11.8608	−	17.6037i	−0.770445	−	1.14348i
$238$	13.4737	−	23.3371i	0.873368	−	1.51272i
$239$	−9.22727	+	15.9821i	−0.596863	+	1.03380i	0.396418	+	0.918070i	$0.370253\pi$
$239$	−9.22727	+	15.9821i	−0.596863	+	1.03380i	−0.993281	+	0.115727i	$0.963080\pi$
$240$	3.15578	−	0.219064i	0.203704	−	0.0141405i
$241$	−1.84614	−	3.19760i	−0.118920	−	0.205976i	0.800420	−	0.599440i	$-0.204610\pi$
$241$	−1.84614	−	3.19760i	−0.118920	−	0.205976i	−0.919340	+	0.393464i	$0.871277\pi$
$242$	−23.0150			−1.47946
$243$	14.6618	−	5.29438i	0.940558	−	0.339634i
$244$	13.9451			0.892741
$245$	5.54556	+	9.60519i	0.354293	+	0.613653i
$246$	29.7467	−	2.06492i	1.89658	−	0.131654i
$247$	−0.815956	+	1.41328i	−0.0519180	+	0.0899247i
$248$	−1.62942	+	2.82224i	−0.103468	+	0.179212i
$249$	−13.6986	−	20.3312i	−0.868110	−	1.28844i
$250$	1.09333	+	1.89370i	0.0691482	+	0.119768i
$251$	−10.5672			−0.666997			−0.333499	−	0.942751i	$-0.608229\pi$
$251$	−10.5672			−0.666997			−0.333499	+	0.942751i	$0.608229\pi$
$252$	−35.1514	+	4.90382i	−2.21433	+	0.308912i
$253$	0.661590			0.0415938
$254$	−6.50932	−	11.2745i	−0.408431	−	0.707423i
$255$	2.20220	−	4.50937i	0.137907	−	0.282388i
$256$	1.25219	−	2.16885i	0.0782617	−	0.135553i
$257$	10.2856	−	17.8151i	0.641596	−	1.11128i	−0.343480	−	0.939160i	$-0.611606\pi$
$257$	10.2856	−	17.8151i	0.641596	−	1.11128i	0.985076	−	0.172117i	$-0.0550608\pi$
$258$	−12.5907	+	25.7816i	−0.783864	+	1.60509i
$259$	11.3659	+	19.6863i	0.706241	+	1.22324i
$260$	−2.78147			−0.172499
$261$	−5.83593	−	7.48529i	−0.361235	−	0.463328i
$262$	8.49711			0.524953
$263$	−4.37556	−	7.57869i	−0.269808	−	0.467322i	0.699004	−	0.715118i	$-0.253627\pi$
$263$	−4.37556	−	7.57869i	−0.269808	−	0.467322i	−0.968812	+	0.247796i	$0.920294\pi$
$264$	1.13956	+	1.69133i	0.0701354	+	0.104094i
$265$	5.79706	−	10.0408i	0.356110	−	0.616801i
$266$	7.58892	−	13.1444i	0.465307	−	0.805935i
$267$	−28.9888	+	2.01231i	−1.77408	+	0.123151i
$268$	−7.73148	−	13.3913i	−0.472275	−	0.818005i
$269$	−14.5794			−0.888919			−0.444459	−	0.895799i	$-0.646604\pi$
$269$	−14.5794			−0.888919			−0.444459	+	0.895799i	$0.646604\pi$
$270$	−11.1175	+	2.34541i	−0.676589	+	0.142737i
$271$	−12.5060			−0.759687			−0.379844	−	0.925051i	$-0.624022\pi$
$271$	−12.5060			−0.759687			−0.379844	+	0.925051i	$0.624022\pi$
$272$	2.64583	+	4.58271i	0.160427	+	0.277868i
$273$	−7.34936	+	0.510169i	−0.444803	+	0.0308768i
$274$	17.7785	−	30.7933i	1.07404	−	1.86029i
$275$	0.344526	−	0.596736i	0.0207757	−	0.0359846i
$276$	2.58468	+	3.83614i	0.155579	+	0.230908i
$277$	−1.06039	−	1.83664i	−0.0637125	−	0.110353i	0.832410	−	0.554161i	$-0.186961\pi$
$277$	−1.06039	−	1.83664i	−0.0637125	−	0.110353i	−0.896122	+	0.443807i	$0.853627\pi$
$278$	40.9766			2.45762
$279$	−2.14861	+	5.30249i	−0.128634	+	0.317452i
$280$	7.26816			0.434356
$281$	−10.7282	−	18.5818i	−0.639991	−	1.10850i	−0.985434	−	0.170057i	$-0.945605\pi$
$281$	−10.7282	−	18.5818i	−0.639991	−	1.10850i	0.345443	−	0.938440i	$-0.387729\pi$
$282$	−13.5761	+	27.7994i	−0.808447	+	1.65543i
$283$	−6.77940	+	11.7423i	−0.402994	+	0.698005i	−0.994086	−	0.108599i	$-0.965364\pi$
$283$	−6.77940	+	11.7423i	−0.402994	+	0.698005i	0.591092	+	0.806604i	$0.298697\pi$
$284$	9.51506	−	16.4806i	0.564615	−	0.977941i
$285$	1.24037	−	2.53986i	0.0734731	−	0.150448i
$286$	0.753360	+	1.30486i	0.0445471	+	0.0771579i
$287$	−33.4868			−1.97666
$288$	8.34983	−	20.6063i	0.492019	−	1.21424i
$289$	−8.60530			−0.506194
$290$	3.45909	+	5.99132i	0.203125	+	0.351823i
$291$	13.2294	+	19.6349i	0.775522	+	1.15102i
$292$	17.5225	−	30.3498i	1.02543	−	1.77609i
$293$	−3.43491	+	5.94944i	−0.200670	+	0.347570i	−0.948744	−	0.316044i	$-0.897645\pi$
$293$	−3.43491	+	5.94944i	−0.200670	+	0.347570i	0.748075	+	0.663615i	$0.230978\pi$
$294$	41.9057	−	2.90896i	2.44399	−	0.169654i
$295$	1.44118	+	2.49620i	0.0839089	+	0.145335i
$296$	9.13254			0.530818
$297$	2.39171	+	2.66441i	0.138781	+	0.154605i
$298$	−1.49612			−0.0866680
$299$	0.480072	+	0.831510i	0.0277633	+	0.0480875i
$300$	4.80608	−	0.333623i	0.277479	−	0.0192617i
$301$	16.1108	−	27.9048i	0.928613	−	1.60841i
$302$	11.8675	−	20.5552i	0.682900	−	1.18282i
$303$	14.1324	+	20.9752i	0.811888	+	1.20499i
$304$	1.49024	+	2.58117i	0.0854711	+	0.148040i
$305$	−5.01356			−0.287076
$306$	−11.6864	−	14.9893i	−0.668068	−	0.856880i
$307$	25.0619			1.43036			0.715180	−	0.698940i	$-0.246345\pi$
$307$	25.0619			1.43036			0.715180	+	0.698940i	$0.246345\pi$
$308$	−4.07595	−	7.05975i	−0.232249	−	0.402267i
$309$	13.5464	−	27.7384i	0.770626	−	1.57798i
$310$	2.08508	−	3.61146i	0.118424	−	0.205117i
$311$	−10.0538	+	17.4137i	−0.570100	+	0.987442i	0.426455	+	0.904509i	$0.359762\pi$
$311$	−10.0538	+	17.4137i	−0.570100	+	0.987442i	−0.996555	+	0.0829334i	$0.973571\pi$
$312$	−1.29881	+	2.65953i	−0.0735307	+	0.150566i
$313$	12.5881	+	21.8032i	0.711521	+	1.23239i	0.964286	+	0.264863i	$0.0853267\pi$
$313$	12.5881	+	21.8032i	0.711521	+	1.23239i	−0.252765	+	0.967528i	$0.581340\pi$
$314$	39.4147			2.22430
$315$	12.6377	−	1.76303i	0.712054	−	0.0993357i
$316$	34.0874			1.91757
$317$	0.567820	+	0.983493i	0.0318920	+	0.0552385i	0.881531	−	0.472126i	$-0.156513\pi$
$317$	0.567820	+	0.983493i	0.0318920	+	0.0552385i	−0.849639	+	0.527365i	$0.823180\pi$
$318$	−24.5366	−	36.4168i	−1.37594	−	2.04215i
$319$	1.09002	−	1.88797i	0.0610292	−	0.105706i
$320$	−6.27656	+	10.8713i	−0.350870	+	0.607725i
$321$	12.1147	−	0.840961i	0.676175	−	0.0469379i
$322$	−4.46499	−	7.73358i	−0.248824	−	0.430976i
$323$	4.72824			0.263086
$324$	−6.10538	+	24.2773i	−0.339188	+	1.34874i
$325$	1.00000			0.0554700
$326$	−14.3961	−	24.9348i	−0.797327	−	1.38101i
$327$	−2.24530	+	0.155862i	−0.124166	+	0.00861918i
$328$	−6.72671	+	11.6510i	−0.371421	+	0.643319i
$329$	17.3718	−	30.0888i	0.957736	−	1.65885i
$330$	−1.45824	−	2.16429i	−0.0802733	−	0.119140i
$331$	−3.74544	−	6.48729i	−0.205868	−	0.356574i	0.744541	−	0.667577i	$-0.232668\pi$
$331$	−3.74544	−	6.48729i	−0.205868	−	0.356574i	−0.950409	+	0.311003i	$0.899335\pi$
$332$	39.3689			2.16065
$333$	15.8795	−	2.21528i	0.870189	−	0.121396i
$334$	−2.62022			−0.143372
$335$	2.77964	+	4.81448i	0.151868	+	0.263043i
$336$	−5.90441	+	12.0902i	−0.322112	+	0.659577i
$337$	3.38164	−	5.85718i	0.184210	−	0.319061i	−0.759100	−	0.650974i	$-0.774361\pi$
$337$	3.38164	−	5.85718i	0.184210	−	0.319061i	0.943310	+	0.331913i	$0.107694\pi$
$338$	−1.09333	+	1.89370i	−0.0594692	+	0.103004i
$339$	1.18327	−	2.42295i	0.0642666	−	0.131597i
$340$	4.02946	+	6.97923i	0.218528	+	0.378502i
$341$	−1.31408			−0.0711617
$342$	−6.58227	−	8.44257i	−0.355929	−	0.456522i
$343$	−17.4010			−0.939567
$344$	−6.47258	−	11.2108i	−0.348978	−	0.604448i
$345$	−0.929249	−	1.37918i	−0.0500291	−	0.0742524i
$346$	−15.6933	+	27.1816i	−0.843677	+	1.46129i
$347$	−18.1026	+	31.3546i	−0.971797	+	1.68320i	−0.281672	+	0.959511i	$0.590889\pi$
$347$	−18.1026	+	31.3546i	−0.971797	+	1.68320i	−0.690125	+	0.723691i	$0.742444\pi$
$348$	15.2056	−	1.05552i	0.815103	−	0.0565818i
$349$	2.52269	+	4.36942i	0.135036	+	0.233890i	0.925611	−	0.378475i	$-0.123552\pi$
$349$	2.52269	+	4.36942i	0.135036	+	0.233890i	−0.790575	+	0.612365i	$0.790218\pi$
$350$	−9.30065			−0.497141
$351$	−1.61322	+	4.93938i	−0.0861074	+	0.263645i
$352$	5.10674			0.272190
$353$	−7.28971	−	12.6261i	−0.387992	−	0.672022i	0.604187	−	0.796842i	$-0.293498\pi$
$353$	−7.28971	−	12.6261i	−0.387992	−	0.672022i	−0.992179	+	0.124820i	$0.960165\pi$
$354$	10.8905	−	0.755981i	0.578822	−	0.0401800i
$355$	−3.42088	+	5.92513i	−0.181561	+	0.314473i
$356$	23.3323	−	40.4127i	1.23661	−	2.14187i
$357$	11.9270	+	17.7019i	0.631243	+	0.936882i
$358$	15.7314	+	27.2477i	0.831433	+	1.44008i
$359$	−27.3341			−1.44264			−0.721320	−	0.692602i	$-0.756464\pi$
$359$	−27.3341			−1.44264			−0.721320	+	0.692602i	$0.756464\pi$
$360$	1.92521	−	4.75117i	0.101467	−	0.250409i
$361$	−16.3369			−0.859835
$362$	−19.1626	−	33.1905i	−1.00716	−	1.74446i
$363$	7.99991	−	16.3811i	0.419886	−	0.859786i
$364$	5.91530	−	10.2456i	0.310046	−	0.537015i
$365$	−6.29973	+	10.9114i	−0.329743	+	0.571131i
$366$	−8.33262	+	17.0624i	−0.435553	+	0.891867i
$367$	−18.1241	−	31.3919i	−0.946072	−	1.63865i	−0.753590	−	0.657345i	$-0.771680\pi$
$367$	−18.1241	−	31.3919i	−0.946072	−	1.63865i	−0.192482	−	0.981300i	$-0.561654\pi$
$368$	1.75358			0.0914118
$369$	−8.87008	+	21.8902i	−0.461758	+	1.13956i
$370$	−11.6864			−0.607547
$371$	24.6570	+	42.7072i	1.28013	+	2.21725i
$372$	−5.13382	−	7.61954i	−0.266176	−	0.395055i
$373$	−3.29989	+	5.71558i	−0.170862	+	0.295942i	−0.938721	−	0.344677i	$-0.887989\pi$
$373$	−3.29989	+	5.71558i	−0.170862	+	0.295942i	0.767860	+	0.640618i	$0.221322\pi$
$374$	2.18276	−	3.78064i	0.112868	−	0.195492i
$375$	−1.72789	+	0.119945i	−0.0892280	+	0.00619392i
$376$	−6.97915	−	12.0883i	−0.359922	−	0.623404i
$377$	3.16382			0.162945
$378$	15.0040	−	45.9395i	0.771723	−	2.36287i
$379$	−33.0304			−1.69666			−0.848328	−	0.529471i	$-0.822390\pi$
$379$	−33.0304			−1.69666			−0.848328	+	0.529471i	$0.822390\pi$
$380$	2.26956	+	3.93099i	0.116426	+	0.201655i
$381$	10.2873	−	0.714112i	0.527035	−	0.0365851i
$382$	−15.1728	+	26.2801i	−0.776308	+	1.34460i
$383$	5.72853	−	9.92210i	0.292714	−	0.506996i	−0.681736	−	0.731598i	$-0.738775\pi$
$383$	5.72853	−	9.92210i	0.292714	−	0.506996i	0.974451	+	0.224602i	$0.0721083\pi$
$384$	12.2206	+	18.1376i	0.623627	+	0.925579i
$385$	1.46539	+	2.53814i	0.0746834	+	0.129356i
$386$	−7.17931			−0.365417
$387$	−13.9738	−	17.9231i	−0.710327	−	0.911082i
$388$	−38.0206			−1.93020
$389$	−1.50802	−	2.61197i	−0.0764599	−	0.132432i	0.825260	−	0.564753i	$-0.191028\pi$
$389$	−1.50802	−	2.61197i	−0.0764599	−	0.132432i	−0.901720	+	0.432320i	$0.857695\pi$
$390$	1.66201	−	3.40325i	0.0841594	−	0.172330i
$391$	1.39094	−	2.40918i	0.0703430	−	0.121838i
$392$	−9.47626	+	16.4134i	−0.478624	+	0.829000i
$393$	−2.95355	+	6.04789i	−0.148987	+	0.305076i
$394$	0.487972	+	0.845193i	0.0245837	+	0.0425802i
$395$	−12.2552			−0.616626
$396$	−5.69458	+	0.794427i	−0.286163	+	0.0399215i
$397$	13.8542			0.695322			0.347661	−	0.937620i	$-0.386976\pi$
$397$	13.8542			0.695322			0.347661	+	0.937620i	$0.386976\pi$
$398$	−22.0796	−	38.2429i	−1.10675	−	1.91694i
$399$	6.71777	+	9.97041i	0.336309	+	0.499145i
$400$	0.913186	−	1.58168i	0.0456593	−	0.0790842i
$401$	3.57066	−	6.18456i	0.178310	−	0.308842i	−0.762992	−	0.646408i	$-0.776270\pi$
$401$	3.57066	−	6.18456i	0.178310	−	0.308842i	0.941302	+	0.337566i	$0.109604\pi$
$402$	21.0047	−	1.45808i	1.04762	−	0.0727223i
$403$	−0.953545	−	1.65159i	−0.0474995	−	0.0822715i
$404$	−40.6159			−2.02072
$405$	2.19502	−	8.72822i	0.109072	−	0.433709i
$406$	−29.4256			−1.46037
$407$	1.84129	+	3.18921i	0.0912693	+	0.158083i
$408$	8.55483	−	0.593849i	0.423527	−	0.0293999i
$409$	−10.0719	+	17.4450i	−0.498022	+	0.862599i	−0.999997	−	0.00228263i	$-0.999273\pi$
$409$	−10.0719	+	17.4450i	−0.498022	+	0.862599i	0.501976	+	0.864882i	$0.332607\pi$
$410$	8.60779	−	14.9091i	0.425109	−	0.736310i
$411$	15.7377	+	23.3576i	0.776282	+	1.15215i
$412$	24.7863	+	42.9312i	1.22114	+	2.11507i
$413$	−12.2598			−0.603263
$414$	−6.23811	+	0.870253i	−0.306586	+	0.0427706i
$415$	−14.1540			−0.694793
$416$	3.70563	+	6.41833i	0.181683	+	0.314685i
$417$	−14.2433	+	29.1655i	−0.697496	+	1.42824i
$418$	1.22942	−	2.12941i	0.0601328	−	0.104153i
$419$	16.8782	−	29.2339i	0.824553	−	1.42817i	−0.0777074	−	0.996976i	$-0.524760\pi$
$419$	16.8782	−	29.2339i	0.824553	−	1.42817i	0.902260	−	0.431191i	$-0.141907\pi$
$420$	−8.99210	+	18.4128i	−0.438769	+	0.898453i
$421$	0.814846	+	1.41135i	0.0397132	+	0.0687852i	0.885199	−	0.465213i	$-0.154022\pi$
$421$	0.814846	+	1.41135i	0.0397132	+	0.0687852i	−0.845486	+	0.533998i	$0.820689\pi$
$422$	33.3335			1.62265
$423$	−15.0674	−	19.3258i	−0.732604	−	0.939655i
$424$	19.8120			0.962158
$425$	−1.44868	−	2.50919i	−0.0702713	−	0.121714i
$426$	14.4792	+	21.4897i	0.701517	+	1.04118i
$427$	10.6623	−	18.4676i	0.515983	−	0.893709i
$428$	−9.75076	+	16.8888i	−0.471321	+	0.816352i
$429$	−1.19061	+	0.0826482i	−0.0574831	+	0.00399029i
$430$	8.28259	+	14.3459i	0.399422	+	0.691819i
$431$	22.6923			1.09305			0.546524	−	0.837443i	$-0.315951\pi$
$431$	22.6923			1.09305			0.546524	+	0.837443i	$0.315951\pi$
$432$	6.33938	+	7.06219i	0.305003	+	0.339780i
$433$	35.0666			1.68519			0.842596	−	0.538546i	$-0.181026\pi$
$433$	35.0666			1.68519			0.842596	+	0.538546i	$0.181026\pi$
$434$	8.86859	+	15.3608i	0.425706	+	0.737344i
$435$	−5.46674	+	0.379483i	−0.262110	+	0.0181948i
$436$	1.80718	−	3.13014i	0.0865485	−	0.149906i
$437$	0.783436	−	1.35695i	0.0374768	−	0.0649118i
$438$	26.6641	+	39.5745i	1.27406	+	1.89094i
$439$	−19.2721	−	33.3803i	−0.919808	−	1.59315i	−0.799706	−	0.600392i	$-0.795011\pi$
$439$	−19.2721	−	33.3803i	−0.919808	−	1.59315i	−0.120102	−	0.992762i	$-0.538322\pi$
$440$	1.17745			0.0561329
$441$	−12.4957	+	30.8378i	−0.595035	+	1.46847i
$442$	6.33553			0.301351
$443$	17.4558	+	30.2343i	0.829348	+	1.43647i	0.898550	+	0.438870i	$0.144621\pi$
$443$	17.4558	+	30.2343i	0.829348	+	1.43647i	−0.0692025	+	0.997603i	$0.522045\pi$
$444$	−11.2987	+	23.1359i	−0.536212	+	1.09798i
$445$	−8.38847	+	14.5293i	−0.397652	+	0.688753i
$446$	−17.1131	+	29.6408i	−0.810331	+	1.40353i
$447$	0.520045	−	1.06488i	0.0245973	−	0.0503670i
$448$	−26.6965	−	46.2397i	−1.26129	−	2.18462i
$449$	23.3933			1.10400			0.551999	−	0.833845i	$-0.313865\pi$
$449$	23.3933			1.10400			0.551999	+	0.833845i	$0.313865\pi$
$450$	−2.46358	+	6.07980i	−0.116134	+	0.286605i
$451$	−5.42492			−0.255449
$452$	2.16509	+	3.75004i	0.101837	+	0.176387i
$453$	10.5052	+	15.5917i	0.493578	+	0.732561i
$454$	−21.0837	+	36.5181i	−0.989508	+	1.71388i
$455$	−2.12668	+	3.68352i	−0.0997004	+	0.172686i
$456$	4.81843	−	0.334480i	0.225644	−	0.0156635i
$457$	−13.9765	−	24.2081i	−0.653795	−	1.13241i	−0.982194	−	0.187867i	$-0.939842\pi$
$457$	−13.9765	−	24.2081i	−0.653795	−	1.13241i	0.328399	−	0.944539i	$-0.393491\pi$
$458$	−36.6506			−1.71257
$459$	14.7309	−	3.10771i	0.687579	−	0.145056i
$460$	2.67061			0.124518
$461$	12.4888	+	21.6312i	0.581661	+	1.00747i	0.995283	+	0.0970176i	$0.0309303\pi$
$461$	12.4888	+	21.6312i	0.581661	+	1.00747i	−0.413622	+	0.910449i	$0.635736\pi$
$462$	11.0734	−	0.768682i	0.515182	−	0.0357623i
$463$	2.81602	−	4.87749i	0.130872	−	0.226676i	−0.793141	−	0.609038i	$-0.791556\pi$
$463$	2.81602	−	4.87749i	0.130872	−	0.226676i	0.924013	+	0.382361i	$0.124889\pi$
$464$	2.88915	−	5.00416i	0.134126	−	0.232312i
$465$	1.84572	+	2.73940i	0.0855934	+	0.127036i
$466$	19.7049	+	34.1299i	0.912812	+	1.58104i
$467$	−13.0634			−0.604502			−0.302251	−	0.953228i	$-0.597738\pi$
$467$	−13.0634			−0.604502			−0.302251	+	0.953228i	$0.597738\pi$
$468$	−5.13065	−	6.58069i	−0.237164	−	0.304193i
$469$	−23.6457			−1.09185
$470$	8.93083	+	15.4686i	0.411948	+	0.713515i
$471$	−13.7004	+	28.0537i	−0.631279	+	1.29265i
$472$	−2.46270	+	4.26552i	−0.113355	+	0.196336i
$473$	2.60998	−	4.52062i	0.120007	−	0.207858i
$474$	−20.3683	+	41.7075i	−0.935548	+	1.91569i
$475$	−0.815956	−	1.41328i	−0.0374386	−	0.0648456i
$476$	−34.2775			−1.57111
$477$	34.4487	−	4.80580i	1.57730	−	0.220042i
$478$	40.3538			1.84574
$479$	17.9564	+	31.1013i	0.820447	+	1.42106i	0.905350	+	0.424667i	$0.139609\pi$
$479$	17.9564	+	31.1013i	0.820447	+	1.42106i	−0.0849029	+	0.996389i	$0.527058\pi$
$480$	−7.17277	−	10.6457i	−0.327391	−	0.485908i
$481$	−2.67221	+	4.62840i	−0.121842	+	0.211037i
$482$	−4.03687	+	6.99206i	−0.183874	+	0.318479i
$483$	7.05645	−	0.489836i	0.321080	−	0.0222883i
$484$	14.6378	+	25.3533i	0.665353	+	1.15242i
$485$	13.6693			0.620689
$486$	−26.0562	−	21.9766i	−1.18193	−	0.996881i
$487$	12.5269			0.567649			0.283825	−	0.958876i	$-0.408397\pi$
$487$	12.5269			0.567649			0.283825	+	0.958876i	$0.408397\pi$
$488$	−4.28359	−	7.41940i	−0.193909	−	0.335861i
$489$	22.7516	−	1.57934i	1.02886	−	0.0714202i
$490$	12.1262	−	21.0033i	0.547807	−	0.948830i
$491$	10.6425	−	18.4333i	0.480289	−	0.831885i	−0.519455	−	0.854498i	$-0.673865\pi$
$491$	10.6425	−	18.4333i	0.480289	−	0.831885i	0.999744	+	0.0226124i	$0.00719835\pi$
$492$	−21.1939	−	31.4556i	−0.955494	−	1.41813i
$493$	−4.58336	−	7.93861i	−0.206424	−	0.357537i
$494$	3.56843			0.160551
$495$	2.04733	−	0.285614i	0.0920206	−	0.0128374i
$496$	−3.48306			−0.156394
$497$	−14.5502	−	25.2017i	−0.652667	−	1.13045i
$498$	−23.5242	+	48.1696i	−1.05414	+	2.15853i
$499$	−1.45213	+	2.51516i	−0.0650062	+	0.112594i	−0.896697	−	0.442645i	$-0.854040\pi$
$499$	−1.45213	+	2.51516i	−0.0650062	+	0.112594i	0.831691	+	0.555239i	$0.187373\pi$
$500$	1.39073	−	2.40882i	0.0621955	−	0.107726i
$501$	0.910776	−	1.86496i	0.0406905	−	0.0833204i
$502$	11.5534	+	20.0112i	0.515656	+	0.893142i
$503$	−34.3097			−1.52979			−0.764897	−	0.644152i	$-0.777210\pi$
$503$	−34.3097			−1.52979			−0.764897	+	0.644152i	$0.777210\pi$
$504$	13.4067	+	17.1958i	0.597183	+	0.765961i
$505$	14.6023			0.649795
$506$	−0.723335	−	1.25285i	−0.0321562	−	0.0556961i
$507$	−0.967822	−	1.43643i	−0.0429825	−	0.0637939i
$508$	−8.27998	+	14.3413i	−0.367365	+	0.636294i
$509$	8.42417	−	14.5911i	0.373395	−	0.646739i	−0.616690	−	0.787206i	$-0.711527\pi$
$509$	8.42417	−	14.5911i	0.373395	−	0.646739i	0.990085	+	0.140467i	$0.0448603\pi$
$510$	−10.9471	+	0.759914i	−0.484747	+	0.0336496i
$511$	−26.7950	−	46.4104i	−1.18534	−	2.05307i
$512$	19.7775			0.874051
$513$	8.29704	−	1.75039i	0.366323	−	0.0772816i
$514$	−44.9820			−1.98407
$515$	−8.91125	−	15.4347i	−0.392676	−	0.680135i
$516$	36.4088	−	2.52738i	1.60281	−	0.111262i
$517$	2.81425	−	4.87443i	0.123771	−	0.214377i
$518$	24.8533	−	43.0471i	1.09199	−	1.89138i
$519$	−13.8918	−	20.6180i	−0.609783	−	0.905031i
$520$	0.854401	+	1.47987i	0.0374680	+	0.0648964i
$521$	−12.2903			−0.538449			−0.269225	−	0.963077i	$-0.586767\pi$
$521$	−12.2903			−0.538449			−0.269225	+	0.963077i	$0.586767\pi$
$522$	−7.79432	+	19.2354i	−0.341148	+	0.841910i
$523$	6.75486			0.295369			0.147685	−	0.989034i	$-0.452818\pi$
$523$	6.75486			0.295369			0.147685	+	0.989034i	$0.452818\pi$
$524$	−5.40424	−	9.36042i	−0.236085	−	0.408912i
$525$	3.23286	−	6.61982i	0.141094	−	0.288912i
$526$	−9.56784	+	16.5720i	−0.417178	+	0.722573i
$527$	−2.76276	+	4.78525i	−0.120348	+	0.208449i
$528$	−0.956523	+	1.95864i	−0.0416273	+	0.0852388i
$529$	11.0391	+	19.1202i	0.479959	+	0.831314i
$530$	−25.3523			−1.10124
$531$	−3.24740	+	8.01416i	−0.140925	+	0.347785i
$532$	−19.3065			−0.837043
$533$	−3.93651	−	6.81823i	−0.170509	−	0.295330i
$534$	35.5049	+	52.6959i	1.53645	+	2.28038i
$535$	3.50562	−	6.07191i	0.151561	−	0.262511i
$536$	−4.74986	+	8.22699i	−0.205163	+	0.355352i
$537$	−24.8619	+	1.72584i	−1.07287	+	0.0744753i
$538$	15.9400	+	27.6089i	0.687223	+	1.19031i
$539$	−7.64236			−0.329180
$540$	9.65453	+	10.7553i	0.415465	+	0.462836i
$541$	40.4080			1.73728			0.868638	−	0.495448i	$-0.164996\pi$
$541$	40.4080			1.73728			0.868638	+	0.495448i	$0.164996\pi$
$542$	13.6732	+	23.6827i	0.587314	+	1.01726i
$543$	30.2845	−	2.10225i	1.29963	−	0.0902162i
$544$	10.7365	−	18.5962i	0.460325	−	0.797307i
$545$	−0.649723	+	1.12535i	−0.0278311	+	0.0482049i
$546$	9.00137	+	13.3597i	0.385223	+	0.571742i
$547$	−22.9471	−	39.7456i	−0.981148	−	1.69940i	−0.657940	−	0.753070i	$-0.728572\pi$
$547$	−22.9471	−	39.7456i	−0.981148	−	1.69940i	−0.323208	−	0.946328i	$-0.604761\pi$
$548$	−45.2292			−1.93210
$549$	−9.24794	−	11.8616i	−0.394692	−	0.506242i
$550$	−1.50672			−0.0642468
$551$	−2.58154	−	4.47135i	−0.109977	−	0.190486i
$552$	1.24705	−	2.55353i	0.0530778	−	0.108686i
$553$	26.0629	−	45.1423i	1.10831	−	1.91965i
$554$	−2.31870	+	4.01611i	−0.0985123	+	0.170628i
$555$	4.06213	−	8.31789i	0.172428	−	0.353075i
$556$	−26.0615	−	45.1399i	−1.10525	−	1.91436i
$557$	26.7832			1.13484			0.567420	−	0.823428i	$-0.307942\pi$
$557$	26.7832			1.13484			0.567420	+	0.823428i	$0.307942\pi$
$558$	12.3905	−	1.72854i	0.524530	−	0.0731750i
$559$	7.57557			0.320413
$560$	3.88411	+	6.72748i	0.164134	+	0.284288i
$561$	1.93219	+	2.86773i	0.0815771	+	0.121076i
$562$	−23.4589	+	40.6320i	−0.989554	+	1.71396i
$563$	−2.05791	+	3.56440i	−0.0867305	+	0.150222i	−0.906127	−	0.423005i	$-0.860975\pi$
$563$	−2.05791	+	3.56440i	−0.0867305	+	0.150222i	0.819397	+	0.573227i	$0.194309\pi$
$564$	39.2583	−	2.72519i	1.65307	−	0.114751i
$565$	−0.778397	−	1.34822i	−0.0327474	−	0.0567202i
$566$	29.6484			1.24622
$567$	27.4825	+	26.6476i	1.15416	+	1.11909i
$568$	−11.6912			−0.490552
$569$	14.9788	+	25.9441i	0.627944	+	1.08763i	0.987964	+	0.154687i	$0.0494368\pi$
$569$	14.9788	+	25.9441i	0.627944	+	1.08763i	−0.360019	+	0.932945i	$0.617230\pi$
$570$	−6.16587	+	0.428015i	−0.258260	+	0.0179276i
$571$	2.07204	−	3.58888i	0.0867122	−	0.150190i	−0.819407	−	0.573212i	$-0.805697\pi$
$571$	2.07204	−	3.58888i	0.0867122	−	0.150190i	0.906120	+	0.423022i	$0.139031\pi$
$572$	0.958288	−	1.65980i	0.0400680	−	0.0693999i
$573$	−13.4311	−	19.9342i	−0.561091	−	0.832763i
$574$	36.6121	+	63.4140i	1.52816	+	2.64685i
$575$	−0.960145			−0.0400408
$576$	−37.2982	+	5.20331i	−1.55409	+	0.216805i
$577$	0.0706668			0.00294190			0.00147095	−	0.999999i	$-0.499532\pi$
$577$	0.0706668			0.00294190			0.00147095	+	0.999999i	$0.499532\pi$
$578$	9.40842	+	16.2959i	0.391339	+	0.677818i
$579$	2.49549	−	5.10993i	0.103709	−	0.212361i
$580$	4.40003	−	7.62107i	0.182701	−	0.316448i
$581$	30.1011	−	52.1366i	1.24880	−	2.16299i
$582$	22.7185	−	46.5199i	0.941713	−	1.92831i
$583$	3.99447	+	6.91863i	0.165434	+	0.286540i
$584$	−21.5300			−0.890917
$585$	1.84458	+	2.36591i	0.0762642	+	0.0978182i
$586$	15.0219			0.620551
$587$	7.18330	+	12.4418i	0.296487	+	0.513530i	0.975330	−	0.220753i	$-0.0708516\pi$
$587$	7.18330	+	12.4418i	0.296487	+	0.513530i	−0.678843	+	0.734284i	$0.737518\pi$
$588$	−29.8569	−	44.3132i	−1.23128	−	1.82744i
$589$	−1.55610	+	2.69525i	−0.0641181	+	0.111056i
$590$	3.15137	−	5.45834i	0.129740	−	0.224716i
$591$	−0.771190	+	0.0535335i	−0.0317225	+	0.00220208i
$592$	4.88044	+	8.45318i	0.200585	+	0.347423i
$593$	−15.6563			−0.642928			−0.321464	−	0.946922i	$-0.604175\pi$
$593$	−15.6563			−0.642928			−0.321464	+	0.946922i	$0.604175\pi$
$594$	2.43067	−	7.44227i	0.0997318	−	0.305360i
$595$	12.3235			0.505216
$596$	0.951548	+	1.64813i	0.0389769	+	0.0675100i
$597$	34.8945	−	2.42226i	1.42813	−	0.0991366i
$598$	1.04975	−	1.81823i	0.0429276	−	0.0743528i
$599$	9.28176	−	16.0765i	0.379243	−	0.656867i	−0.611710	−	0.791082i	$-0.709518\pi$
$599$	9.28176	−	16.0765i	0.379243	−	0.656867i	0.990952	+	0.134215i	$0.0428513\pi$
$600$	−1.65382	−	2.45457i	−0.0675167	−	0.100207i
$601$	1.91582	+	3.31829i	0.0781478	+	0.135356i	0.902451	−	0.430793i	$-0.141766\pi$
$601$	1.91582	+	3.31829i	0.0781478	+	0.135356i	−0.824303	+	0.566149i	$0.808433\pi$
$602$	−70.4578			−2.87164
$603$	−6.26332	+	15.4571i	−0.255062	+	0.629461i
$604$	−30.1914			−1.22847
$605$	−5.26260	−	9.11510i	−0.213955	−	0.370581i
$606$	24.2693	−	49.6954i	0.985872	−	2.01874i
$607$	−12.7813	+	22.1379i	−0.518777	+	0.898549i	0.480985	+	0.876729i	$0.340279\pi$
$607$	−12.7813	+	22.1379i	−0.518777	+	0.898549i	−0.999762	+	0.0218196i	$0.993054\pi$
$608$	6.04726	−	10.4742i	0.245249	−	0.424783i
$609$	10.2282	−	20.9439i	0.414467	−	0.848689i
$610$	5.48147	+	9.49419i	0.221938	+	0.384408i
$611$	8.16848			0.330461
$612$	−9.07952	+	22.4071i	−0.367018	+	0.905753i
$613$	−18.9425			−0.765080			−0.382540	−	0.923939i	$-0.624951\pi$
$613$	−18.9425			−0.765080			−0.382540	+	0.923939i	$0.624951\pi$
$614$	−27.4009	−	47.4598i	−1.10581	−	1.91532i
$615$	7.61967	+	11.3090i	0.307255	+	0.456023i
$616$	−2.50407	+	4.33718i	−0.100892	+	0.174750i
$617$	−6.52475	+	11.3012i	−0.262677	+	0.454969i	−0.966952	−	0.254957i	$-0.917939\pi$
$617$	−6.52475	+	11.3012i	−0.262677	+	0.454969i	0.704276	+	0.709927i	$0.251272\pi$
$618$	−67.3389	+	4.67445i	−2.70877	+	0.188034i
$619$	−2.83676	−	4.91341i	−0.114019	−	0.197487i	0.803368	−	0.595483i	$-0.203039\pi$
$619$	−2.83676	−	4.91341i	−0.114019	−	0.197487i	−0.917387	+	0.397996i	$0.869706\pi$
$620$	−5.30451			−0.213034
$621$	1.54893	−	4.74252i	0.0621563	−	0.190311i
$622$	43.9685			1.76298
$623$	−35.6792	−	61.7983i	−1.42946	−	2.47590i
$624$	−3.15578	+	0.219064i	−0.126332	+	0.00876957i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	27.5258	−	47.6761i	1.10015	−	1.90552i
$627$	1.08829	+	1.61522i	0.0434621	+	0.0645058i
$628$	−25.0681	−	43.4192i	−1.00033	−	1.73262i
$629$	15.4847			0.617415
$630$	−17.1558	−	22.0045i	−0.683505	−	0.876679i
$631$	−3.54731			−0.141216			−0.0706080	−	0.997504i	$-0.522494\pi$
$631$	−3.54731			−0.141216			−0.0706080	+	0.997504i	$0.522494\pi$
$632$	−10.4709	−	18.1361i	−0.416508	−	0.721414i
$633$	−11.5866	+	23.7254i	−0.460524	+	0.942999i
$634$	1.24163	−	2.15056i	0.0493113	−	0.0854098i
$635$	2.97684	−	5.15603i	0.118132	−	0.204611i
$636$	−24.5113	+	50.1909i	−0.971935	+	1.99020i
$637$	−5.54556	−	9.60519i	−0.219723	−	0.380571i
$638$	−4.76699			−0.188727
$639$	−20.3284	+	2.83593i	−0.804179	+	0.112188i
$640$	12.6269			0.499121
$641$	9.80157	+	16.9768i	0.387139	+	0.670544i	0.992063	−	0.125739i	$-0.0401301\pi$
$641$	9.80157	+	16.9768i	0.387139	+	0.670544i	−0.604925	+	0.796283i	$0.706797\pi$
$642$	−14.8378	−	22.0221i	−0.585603	−	0.869143i
$643$	−1.25121	+	2.16715i	−0.0493428	+	0.0854642i	−0.889642	−	0.456659i	$-0.849046\pi$
$643$	−1.25121	+	2.16715i	−0.0493428	+	0.0854642i	0.840299	+	0.542123i	$0.182379\pi$
$644$	−5.67955	+	9.83726i	−0.223805	+	0.387642i
$645$	−13.0898	+	0.908650i	−0.515409	+	0.0357781i
$646$	−5.16952	−	8.95387i	−0.203392	−	0.352285i
$647$	−14.2685			−0.560951			−0.280475	−	0.959861i	$-0.590492\pi$
$647$	−14.2685			−0.560951			−0.280475	+	0.959861i	$0.590492\pi$
$648$	14.7920	−	4.20906i	0.581086	−	0.165348i
$649$	−1.98610			−0.0779612
$650$	−1.09333	−	1.89370i	−0.0428839	−	0.0742770i
$651$	−14.0159	+	0.972938i	−0.549326	+	0.0381325i
$652$	−18.3121	+	31.7175i	−0.717158	+	1.24215i
$653$	4.50803	−	7.80813i	0.176413	−	0.305556i	−0.764237	−	0.644936i	$-0.776884\pi$
$653$	4.50803	−	7.80813i	0.176413	−	0.305556i	0.940649	+	0.339380i	$0.110217\pi$
$654$	2.75001	+	4.08153i	0.107534	+	0.159600i
$655$	1.94294	+	3.36528i	0.0759171	+	0.131492i
$656$	−14.3791			−0.561408
$657$	−37.4358	+	5.22252i	−1.46051	+	0.203750i
$658$	−75.9721			−2.96170
$659$	25.2282	+	43.6965i	0.982751	+	1.70218i	0.651531	+	0.758622i	$0.274127\pi$
$659$	25.2282	+	43.6965i	0.982751	+	1.70218i	0.331220	+	0.943554i	$0.392540\pi$
$660$	−1.45673	+	2.98290i	−0.0567033	+	0.116109i
$661$	3.27473	−	5.67200i	0.127372	−	0.220615i	−0.795285	−	0.606235i	$-0.792679\pi$
$661$	3.27473	−	5.67200i	0.127372	−	0.220615i	0.922658	+	0.385620i	$0.126012\pi$
$662$	−8.18998	+	14.1855i	−0.318313	+	0.551334i
$663$	−2.20220	+	4.50937i	−0.0855264	+	0.175129i
$664$	−12.0932	−	20.9460i	−0.469307	−	0.812864i
$665$	6.94112			0.269165
$666$	−21.5565	−	27.6489i	−0.835299	−	1.07137i
$667$	−3.03772			−0.117621
$668$	1.66648	+	2.88644i	0.0644782	+	0.111680i
$669$	−15.1487	−	22.4834i	−0.585682	−	0.869260i
$670$	6.07812	−	10.5276i	0.234818	−	0.406717i
$671$	1.72730	−	2.99178i	0.0666818	−	0.115496i
$672$	54.4680	−	3.78099i	2.10115	−	0.145855i
$673$	17.9173	+	31.0336i	0.690660	+	1.19626i	0.971622	+	0.236540i	$0.0760134\pi$
$673$	17.9173	+	31.0336i	0.690660	+	1.19626i	−0.280961	+	0.959719i	$0.590653\pi$
$674$	−14.7890			−0.569651
$675$	−3.47102	−	3.86678i	−0.133600	−	0.148833i
$676$	2.78147			0.106980
$677$	7.79008	+	13.4928i	0.299397	+	0.518571i	0.975998	−	0.217779i	$-0.0698811\pi$
$677$	7.79008	+	13.4928i	0.299397	+	0.518571i	−0.676601	+	0.736350i	$0.736548\pi$
$678$	−5.88205	+	0.408313i	−0.225899	+	0.0156812i
$679$	−29.0702	+	50.3511i	−1.11561	+	1.93230i
$680$	2.47551	−	4.28771i	0.0949314	−	0.164426i
$681$	−18.6635	−	27.7000i	−0.715185	−	1.06147i
$682$	1.43673	+	2.48848i	0.0550151	+	0.0952889i
$683$	−40.4896			−1.54929			−0.774645	−	0.632396i	$-0.782071\pi$
$683$	−40.4896			−1.54929			−0.774645	+	0.632396i	$0.782071\pi$
$684$	−5.11396	+	12.6206i	−0.195537	+	0.482560i
$685$	16.2609			0.621298
$686$	19.0250	+	32.9523i	0.726379	+	1.25813i
$687$	12.7396	−	26.0863i	0.486044	−	0.995256i
$688$	6.91791	−	11.9822i	0.263743	−	0.456816i
$689$	−5.79706	+	10.0408i	−0.220850	+	0.382524i
$690$	−1.59578	+	3.26761i	−0.0607501	+	0.124396i
$691$	−8.56765	−	14.8396i	−0.325929	−	0.564525i	0.655771	−	0.754960i	$-0.272344\pi$
$691$	−8.56765	−	14.8396i	−0.325929	−	0.564525i	−0.981700	+	0.190434i	$0.939010\pi$
$692$	39.9243			1.51770
$693$	−3.30195	+	8.14879i	−0.125431	+	0.309547i
$694$	79.1682			3.00518
$695$	9.36970	+	16.2288i	0.355413	+	0.615593i
$696$	−5.23237	−	7.76581i	−0.198332	−	0.294362i
$697$	−11.4055	+	19.7549i	−0.432014	+	0.748269i
$698$	5.51625	−	9.55443i	0.208793	−	0.361641i
$699$	−31.1416	+	2.16175i	−1.17788	+	0.0817648i
$700$	5.91530	+	10.2456i	0.223577	+	0.387247i
$701$	12.0524			0.455212			0.227606	−	0.973753i	$-0.426910\pi$
$701$	12.0524			0.455212			0.227606	+	0.973753i	$0.426910\pi$
$702$	11.1175	−	2.34541i	0.419603	−	0.0885218i
$703$	8.72161			0.328942
$704$	−4.32488	−	7.49091i	−0.163000	−	0.282324i
$705$	−14.1143	+	0.979766i	−0.531573	+	0.0369001i
$706$	−15.9401	+	27.6090i	−0.599913	+	1.03908i
$707$	−31.0545	+	53.7880i	−1.16793	+	2.02291i
$708$	−7.75923	−	11.5161i	−0.291610	−	0.432803i
$709$	−13.7320	−	23.7845i	−0.515715	−	0.893245i	−0.999834	−	0.0182427i	$-0.994193\pi$
$709$	−13.7320	−	23.7845i	−0.515715	−	0.893245i	0.484118	−	0.875003i	$-0.339140\pi$
$710$	14.9606			0.561460
$711$	−22.6057	−	28.9947i	−0.847782	−	1.08738i
$712$	−28.6685			−1.07440
$713$	0.915542	+	1.58576i	0.0342873	+	0.0593873i
$714$	20.4819	−	41.9401i	0.766516	−	1.56957i
$715$	−0.344526	+	0.596736i	−0.0128845	+	0.0223167i
$716$	20.0107	−	34.6595i	0.747835	−	1.29529i
$717$	−14.0268	+	28.7221i	−0.523839	+	1.07265i
$718$	29.8852	+	51.7627i	1.11531	+	1.93177i
$719$	32.5517			1.21397			0.606987	−	0.794711i	$-0.292378\pi$
$719$	32.5517			1.21397			0.606987	+	0.794711i	$0.292378\pi$
$720$	5.42657	−	0.757037i	0.202236	−	0.0282131i
$721$	75.8056			2.82315
$722$	17.8616	+	30.9371i	0.664738	+	1.15136i
$723$	−3.57346	−	5.30368i	−0.132898	−	0.197246i
$724$	−24.3751	+	42.2190i	−0.905895	+	1.56906i
$725$	−1.58191	+	2.73995i	−0.0587506	+	0.101759i
$726$	−39.7675	+	2.76053i	−1.47591	+	0.102453i
$727$	−14.1082	−	24.4360i	−0.523243	−	0.906283i	−0.999634	−	0.0270494i	$-0.991389\pi$
$727$	−14.1082	−	24.4360i	−0.523243	−	0.906283i	0.476392	−	0.879233i	$-0.341944\pi$
$728$	−7.26816			−0.269376
$729$	24.6991	−	10.9067i	0.914780	−	0.403953i
$730$	27.5507			1.01970
$731$	−10.9746	−	19.0085i	−0.405910	−	0.703056i
$732$	24.0956	−	1.67264i	0.890598	−	0.0618225i
$733$	−10.9287	+	18.9290i	−0.403660	+	0.699160i	−0.994165	−	0.107875i	$-0.965596\pi$
$733$	−10.9287	+	18.9290i	−0.403660	+	0.699160i	0.590504	+	0.807034i	$0.298929\pi$
$734$	−39.6313	+	68.6434i	−1.46282	+	2.53367i
$735$	10.7342	+	15.9316i	0.395938	+	0.587645i
$736$	−3.55794	−	6.16253i	−0.131147	−	0.227154i
$737$	−3.83063			−0.141103
$738$	51.1514	−	7.13592i	1.88291	−	0.262677i
$739$	−1.75791			−0.0646657			−0.0323329	−	0.999477i	$-0.510294\pi$
$739$	−1.75791			−0.0646657			−0.0323329	+	0.999477i	$0.510294\pi$
$740$	7.43266	+	12.8737i	0.273230	+	0.473248i
$741$	−1.24037	+	2.53986i	−0.0455661	+	0.0933041i
$742$	53.9164	−	93.3859i	1.97933	−	3.42831i
$743$	4.98732	−	8.63829i	0.182967	−	0.316908i	−0.759923	−	0.650014i	$-0.774763\pi$
$743$	4.98732	−	8.63829i	0.182967	−	0.316908i	0.942890	+	0.333105i	$0.108097\pi$
$744$	−2.47695	+	5.07197i	−0.0908094	+	0.185947i
$745$	−0.342103	−	0.592539i	−0.0125337	−	0.0217090i
$746$	14.4315			0.528373
$747$	−26.1082	−	33.4870i	−0.955251	−	1.22523i
$748$	−5.55301			−0.203038
$749$	14.9107	+	25.8260i	0.544824	+	0.943663i
$750$	2.11629	+	3.14097i	0.0772761	+	0.114692i
$751$	−0.798870	+	1.38368i	−0.0291512	+	0.0504913i	−0.880233	−	0.474542i	$-0.842614\pi$
$751$	−0.798870	+	1.38368i	−0.0291512	+	0.0504913i	0.851082	+	0.525033i	$0.175947\pi$
$752$	7.45934	−	12.9200i	0.272014	−	0.471142i
$753$	−18.2590	+	1.26748i	−0.665396	+	0.0461897i
$754$	−3.45909	−	5.99132i	−0.125973	−	0.218191i
$755$	10.8545			0.395036
$756$	−60.1496	+	12.6895i	−2.18762	+	0.461513i
$757$	10.4955			0.381467			0.190733	−	0.981642i	$-0.438913\pi$
$757$	10.4955			0.381467			0.190733	+	0.981642i	$0.438913\pi$
$758$	36.1130	+	62.5496i	1.31168	+	2.27190i
$759$	1.14316	−	0.0793542i	0.0414939	−	0.00288038i
$760$	1.39431	−	2.41501i	0.0505769	−	0.0876017i
$761$	−15.1730	+	26.2804i	−0.550020	+	0.952662i	0.448253	+	0.893907i	$0.352046\pi$
$761$	−15.1730	+	26.2804i	−0.550020	+	0.952662i	−0.998272	+	0.0587552i	$0.981287\pi$
$762$	−12.5997	−	18.7003i	−0.456440	−	0.677441i
$763$	−2.76351	−	4.78654i	−0.100046	−	0.173284i
$764$	38.6002			1.39650
$765$	3.26429	−	8.05585i	0.118021	−	0.291260i
$766$	−25.0526			−0.905189
$767$	−1.44118	−	2.49620i	−0.0520381	−	0.0901326i
$768$	1.90350	−	3.89774i	0.0686867	−	0.140647i
$769$	22.5420	−	39.0439i	0.812885	−	1.40796i	−0.0979509	−	0.995191i	$-0.531229\pi$
$769$	22.5420	−	39.0439i	0.812885	−	1.40796i	0.910836	−	0.412768i	$-0.135438\pi$
$770$	3.20432	−	5.55004i	0.115476	−	0.200009i
$771$	15.6355	−	32.0163i	0.563100	−	1.15304i
$772$	4.56610	+	7.90872i	0.164338	+	0.284641i
$773$	−0.573929			−0.0206428			−0.0103214	−	0.999947i	$-0.503285\pi$
$773$	−0.573929			−0.0206428			−0.0103214	+	0.999947i	$0.503285\pi$
$774$	−18.6630	+	46.0580i	−0.670829	+	1.65552i
$775$	1.90709			0.0685047
$776$	11.6790	+	20.2287i	0.419253	+	0.726167i
$777$	22.0003	+	32.6525i	0.789255	+	1.17140i
$778$	−3.29753	+	5.71149i	−0.118222	+	0.204767i
$779$	−6.42404	+	11.1268i	−0.230165	+	0.398657i
$780$	−4.80608	+	0.333623i	−0.172085	+	0.0119456i
$781$	−2.35716	−	4.08272i	−0.0843459	−	0.146091i
$782$	−6.08303			−0.217529
$783$	−10.9817	−	12.2338i	−0.392453	−	0.437200i
$784$	−20.2565			−0.723447
$785$	9.01254	+	15.6102i	0.321672	+	0.557151i
$786$	14.6821	−	1.01918i	0.523693	−	0.0363531i
$787$	−23.7225	+	41.0886i	−0.845616	+	1.46465i	0.0394691	+	0.999221i	$0.487433\pi$
$787$	−23.7225	+	41.0886i	−0.845616	+	1.46465i	−0.885085	+	0.465429i	$0.845900\pi$
$788$	0.620710	−	1.07510i	0.0221119	−	0.0382989i
$789$	−8.46952	−	12.5703i	−0.301523	−	0.447516i
$790$	13.3990	+	23.2077i	0.476714	+	0.825692i
$791$	6.62161			0.235437
$792$	2.17191	+	2.78574i	0.0771755	+	0.0989871i
$793$	5.01356			0.178037
$794$	−15.1472	−	26.2357i	−0.537554	−	0.931070i
$795$	8.81235	−	18.0447i	0.312542	−	0.639981i
$796$	−28.0856	+	48.6457i	−0.995468	+	1.72420i
$797$	9.16331	−	15.8713i	0.324581	−	0.562191i	−0.656846	−	0.754024i	$-0.728110\pi$
$797$	9.16331	−	15.8713i	0.324581	−	0.562191i	0.981427	+	0.191834i	$0.0614434\pi$
$798$	11.5362	−	23.6224i	0.408379	−	0.836223i
$799$	−11.8335	−	20.4962i	−0.418640	−	0.725105i
$800$	−7.41125			−0.262027
$801$	−49.8481	+	6.95410i	−1.76130	+	0.245711i
$802$	−15.6156			−0.551406
$803$	−4.34084	−	7.51855i	−0.153185	−	0.265324i
$804$	−14.9654	−	22.2114i	−0.527789	−	0.783336i
$805$	2.04192	−	3.53672i	0.0719684	−	0.124653i
$806$	−2.08508	+	3.61146i	−0.0734437	+	0.127208i
$807$	−25.1916	+	1.74872i	−0.886785	+	0.0615578i
$808$	12.4762	+	21.6095i	0.438913	+	0.760219i
$809$	17.2623			0.606911			0.303455	−	0.952846i	$-0.401860\pi$
$809$	17.2623			0.606911			0.303455	+	0.952846i	$0.401860\pi$
$810$	−18.9285	+	5.38610i	−0.665080	+	0.189248i
$811$	−1.38400			−0.0485988			−0.0242994	−	0.999705i	$-0.507735\pi$
$811$	−1.38400			−0.0485988			−0.0242994	+	0.999705i	$0.507735\pi$
$812$	18.7149	+	32.4152i	0.656765	+	1.13755i
$813$	−21.6091	+	1.50003i	−0.757863	+	0.0526084i
$814$	4.02627	−	6.97370i	0.141121	−	0.244428i
$815$	6.58362	−	11.4032i	0.230614	−	0.399435i
$816$	5.12138	+	7.60108i	0.179284	+	0.266091i
$817$	−6.18134	−	10.7064i	−0.216258	−	0.374569i
$818$	44.0474			1.54008
$819$	−12.6377	+	1.76303i	−0.441597	+	0.0616054i
$820$	−21.8985			−0.764730
$821$	−4.40630	−	7.63194i	−0.153781	−	0.266357i	0.778833	−	0.627231i	$-0.215812\pi$
$821$	−4.40630	−	7.63194i	−0.153781	−	0.266357i	−0.932615	+	0.360874i	$0.882478\pi$
$822$	27.0259	−	55.3400i	0.942636	−	1.93020i
$823$	21.4196	−	37.0999i	0.746642	−	1.29322i	−0.202782	−	0.979224i	$-0.564998\pi$
$823$	21.4196	−	37.0999i	0.746642	−	1.29322i	0.949424	−	0.313998i	$-0.101668\pi$
$824$	15.2276	−	26.3749i	0.530477	−	0.918813i
$825$	0.523728	−	1.07242i	0.0182339	−	0.0373369i
$826$	13.4039	+	23.2163i	0.466383	+	0.807798i
$827$	32.4485			1.12834			0.564172	−	0.825657i	$-0.309195\pi$
$827$	32.4485			1.12834			0.564172	+	0.825657i	$0.309195\pi$
$828$	4.92617	+	6.31842i	0.171196	+	0.219580i
$829$	27.3127			0.948610			0.474305	−	0.880361i	$-0.342699\pi$
$829$	27.3127			0.948610			0.474305	+	0.880361i	$0.342699\pi$
$830$	15.4750	+	26.8034i	0.537144	+	0.930361i
$831$	−2.05253	−	3.04634i	−0.0712015	−	0.105676i
$832$	6.27656	−	10.8713i	0.217601	−	0.376895i
$833$	−16.0675	+	27.8297i	−0.556705	+	0.964242i
$834$	70.8032	−	4.91493i	2.45172	−	0.170190i
$835$	−0.599138	−	1.03774i	−0.0207340	−	0.0359124i
$836$	−3.12768			−0.108173
$837$	−3.07656	+	9.41985i	−0.106341	+	0.325598i
$838$	−73.8136			−2.54985
$839$	14.9182	+	25.8392i	0.515035	+	0.892067i	0.999848	+	0.0174488i	$0.00555441\pi$
$839$	14.9182	+	25.8392i	0.515035	+	0.892067i	−0.484813	+	0.874618i	$0.661112\pi$
$840$	12.5586	−	0.871778i	0.433313	−	0.0300792i
$841$	9.49513	−	16.4460i	0.327418	−	0.567105i
$842$	1.78179	−	3.08615i	0.0614045	−	0.106356i
$843$	−20.7660	−	30.8206i	−0.715218	−	1.06152i
$844$	−21.2004	−	36.7202i	−0.729748	−	1.26396i
$845$	−1.00000			−0.0344010
$846$	−20.1237	+	49.6627i	−0.691867	+	1.70744i
$847$	44.7676			1.53823
$848$	10.5876	+	18.3382i	0.363579	+	0.629738i
$849$	−10.3057	+	21.1025i	−0.353689	+	0.724237i
$850$	−3.16777	+	5.48673i	−0.108654	+	0.188193i
$851$	2.56571	−	4.44393i	0.0879512	−	0.152336i
$852$	14.4642	−	29.6179i	0.495537	−	1.01469i
$853$	12.3729	+	21.4305i	0.423640	+	0.733766i	0.996292	−	0.0860325i	$-0.0274189\pi$
$853$	12.3729	+	21.4305i	0.423640	+	0.733766i	−0.572652	+	0.819798i	$0.694086\pi$
$854$	−46.6294			−1.59563
$855$	1.83858	−	4.53738i	0.0628782	−	0.155175i
$856$	11.9808			0.409496
$857$	−8.97560	−	15.5462i	−0.306601	−	0.531048i	0.671016	−	0.741443i	$-0.265858\pi$
$857$	−8.97560	−	15.5462i	−0.306601	−	0.531048i	−0.977616	+	0.210395i	$0.932525\pi$
$858$	1.45824	+	2.16429i	0.0497834	+	0.0738877i
$859$	−17.1792	+	29.7552i	−0.586145	+	1.01523i	0.408587	+	0.912720i	$0.366022\pi$
$859$	−17.1792	+	29.7552i	−0.586145	+	1.01523i	−0.994732	+	0.102514i	$0.967312\pi$
$860$	10.5356	−	18.2482i	0.359261	−	0.622259i
$861$	−57.8616	+	4.01657i	−1.97192	+	0.136884i
$862$	−24.8101	−	42.9724i	−0.845036	−	1.46364i
$863$	9.72994			0.331211			0.165605	−	0.986192i	$-0.447042\pi$
$863$	9.72994			0.331211			0.165605	+	0.986192i	$0.447042\pi$
$864$	11.9560	−	36.6070i	0.406751	−	1.24540i
$865$	−14.3537			−0.488040
$866$	−38.3393	−	66.4056i	−1.30282	−	2.25655i
$867$	−14.8690	+	1.03216i	−0.504979	+	0.0350540i
$868$	11.2810	−	19.5393i	0.382902	−	0.663207i
$869$	4.22223	−	7.31313i	0.143230	−	0.248081i
$870$	6.69557	+	9.93746i	0.227001	+	0.336911i
$871$	−2.77964	−	4.81448i	−0.0941845	−	0.163132i
$872$	−2.22050			−0.0751955
$873$	25.2141	+	32.3402i	0.853368	+	1.09455i
$874$	−3.42621			−0.115893
$875$	−2.12668	−	3.68352i	−0.0718950	−	0.124526i
$876$	26.6367	−	54.5430i	0.899970	−	1.84284i
$877$	26.5218	−	45.9371i	0.895578	−	1.55119i	0.0624902	−	0.998046i	$-0.480096\pi$
$877$	26.5218	−	45.9371i	0.895578	−	1.55119i	0.833088	−	0.553141i	$-0.186571\pi$
$878$	−42.1415	+	72.9912i	−1.42221	+	2.46333i
$879$	−5.22155	+	10.6920i	−0.176119	+	0.360632i
$880$	0.629233	+	1.08986i	0.0212114	+	0.0367393i
$881$	−10.3953			−0.350226			−0.175113	−	0.984548i	$-0.556029\pi$
$881$	−10.3953			−0.350226			−0.175113	+	0.984548i	$0.556029\pi$
$882$	72.0596	−	10.0527i	2.42637	−	0.338493i
$883$	−16.6781			−0.561263			−0.280632	−	0.959816i	$-0.590544\pi$
$883$	−16.6781			−0.561263			−0.280632	+	0.959816i	$0.590544\pi$
$884$	−4.02946	−	6.97923i	−0.135525	−	0.234737i
$885$	2.78962	+	4.14031i	0.0937719	+	0.139175i
$886$	38.1697	−	66.1119i	1.28234	−	2.22107i
$887$	−27.2728	+	47.2379i	−0.915731	+	1.58609i	−0.109902	+	0.993942i	$0.535054\pi$
$887$	−27.2728	+	47.2379i	−0.915731	+	1.58609i	−0.805828	+	0.592149i	$0.798280\pi$
$888$	15.7801	−	1.09540i	0.529544	−	0.0367592i
$889$	12.6616	+	21.9305i	0.424656	+	0.735525i
$890$	36.6854			1.22970
$891$	4.45221	+	4.31695i	0.149155	+	0.144623i
$892$	43.5365			1.45771
$893$	−6.66512	−	11.5443i	−0.223040	−	0.386316i
$894$	−2.58514	+	0.179452i	−0.0864600	+	0.00600177i
$895$	−7.19429	+	12.4609i	−0.240479	+	0.416521i
$896$	−26.8533	+	46.5113i	−0.897107	+	1.55383i
$897$	0.929249	+	1.37918i	0.0310267	+	0.0460494i
$898$	−25.5766	−	44.2999i	−0.853501	−	1.47831i
$899$	6.03368			0.201235
$900$	8.26437	−	1.15293i	0.275479	−	0.0384309i
$901$	33.5923			1.11912
$902$	5.93122	+	10.2732i	0.197488	+	0.342059i
$903$	24.4908	−	50.1489i	0.815002	−	1.66885i
$904$	1.33013	−	2.30385i	0.0442393	−	0.0766248i
$905$	8.76341	−	15.1787i	0.291306	−	0.504556i
$906$	18.0403	−	36.9406i	0.599350	−	1.22727i
$907$	5.38054	+	9.31937i	0.178658	+	0.309444i	0.941421	−	0.337233i	$-0.109491\pi$
$907$	5.38054	+	9.31937i	0.178658	+	0.309444i	−0.762763	+	0.646678i	$0.776158\pi$
$908$	53.6378			1.78003
$909$	26.9352	+	34.5477i	0.893385	+	1.14588i
$910$	9.30065			0.308314
$911$	−3.85961	−	6.68504i	−0.127875	−	0.221485i	0.794978	−	0.606638i	$-0.207482\pi$
$911$	−3.85961	−	6.68504i	−0.127875	−	0.221485i	−0.922853	+	0.385152i	$0.874149\pi$
$912$	2.88457	+	4.28124i	0.0955177	+	0.141766i
$913$	4.87642	−	8.44621i	0.161386	−	0.279529i
$914$	−30.5619	+	52.9348i	−1.01090	+	1.75093i
$915$	−8.66290	+	0.601351i	−0.286387	+	0.0198800i
$916$	23.3101	+	40.3743i	0.770187	+	1.33400i
$917$	−16.5281			−0.545806
$918$	−21.9908	−	24.4981i	−0.725804	−	0.808559i
$919$	−16.4050			−0.541150			−0.270575	−	0.962699i	$-0.587214\pi$
$919$	−16.4050			−0.541150			−0.270575	+	0.962699i	$0.587214\pi$
$920$	−0.820349	−	1.42089i	−0.0270461	−	0.0468452i
$921$	43.3044	−	3.00605i	1.42693	−	0.0990527i
$922$	27.3087	−	47.3001i	0.899364	−	1.55774i
$923$	3.42088	−	5.92513i	0.112599	−	0.195028i
$924$	−7.88958	−	11.7096i	−0.259548	−	0.385218i
$925$	−2.67221	−	4.62840i	−0.0878616	−	0.152181i
$926$	−12.3153			−0.404707
$927$	20.0796	−	49.5538i	0.659500	−	1.62756i
$928$	−23.4478			−0.769713
$929$	−28.2090	−	48.8595i	−0.925509	−	1.60303i	−0.790741	−	0.612151i	$-0.790304\pi$
$929$	−28.2090	−	48.8595i	−0.925509	−	1.60303i	−0.134768	−	0.990877i	$-0.543029\pi$
$930$	3.16961	−	6.49031i	0.103936	−	0.212825i
$931$	−9.04987	+	15.6748i	−0.296597	+	0.513722i
$932$	25.0650	−	43.4139i	0.821031	−	1.42207i
$933$	−15.2832	+	31.2950i	−0.500351	+	1.02455i
$934$	14.2826	+	24.7382i	0.467340	+	0.809457i
$935$	1.99643			0.0652903
$936$	−1.92521	+	4.75117i	−0.0629274	+	0.155297i
$937$	−10.4036			−0.339870			−0.169935	−	0.985455i	$-0.554356\pi$
$937$	−10.4036			−0.339870			−0.169935	+	0.985455i	$0.554356\pi$
$938$	25.8525	+	44.7778i	0.844113	+	1.46205i
$939$	24.3661	+	36.1637i	0.795156	+	1.18016i
$940$	11.3602	−	19.6764i	0.370528	−	0.641774i
$941$	18.4943	−	32.0331i	0.602898	−	1.04425i	−0.389482	−	0.921034i	$-0.627346\pi$
$941$	18.4943	−	32.0331i	0.602898	−	1.04425i	0.992380	−	0.123216i	$-0.0393208\pi$
$942$	68.1043	−	4.72759i	2.21896	−	0.154033i
$943$	3.77962	+	6.54649i	0.123081	+	0.213183i
$944$	−5.26427			−0.171337
$945$	21.6251	−	4.56216i	0.703466	−	0.148407i
$946$	−11.4143			−0.371110
$947$	24.3801	+	42.2275i	0.792246	+	1.37221i	0.924573	+	0.381004i	$0.124422\pi$
$947$	24.3801	+	42.2275i	0.792246	+	1.37221i	−0.132328	+	0.991206i	$0.542245\pi$
$948$	58.8995	−	4.08861i	1.91297	−	0.132792i
$949$	6.29973	−	10.9114i	0.204498	−	0.354201i
$950$	−1.78422	+	3.09035i	−0.0578876	+	0.100264i
$951$	1.09910	+	1.63126i	0.0356407	+	0.0528974i
$952$	10.5292	+	18.2372i	0.341255	+	0.591070i
$953$	35.5681			1.15216			0.576082	−	0.817392i	$-0.304581\pi$
$953$	35.5681			1.15216			0.576082	+	0.817392i	$0.304581\pi$
$954$	−46.7645	−	59.9813i	−1.51406	−	1.94197i
$955$	−13.8776			−0.449069
$956$	−25.6654	−	44.4537i	−0.830077	−	1.43774i
$957$	1.65698	−	3.39294i	0.0535626	−	0.109678i
$958$	39.2644	−	68.0079i	1.26857	−	2.19724i
$959$	−34.5818	+	59.8974i	−1.11670	+	1.93419i
$960$	−9.54127	+	19.5373i	−0.307943	+	0.630564i
$961$	13.6815	+	23.6971i	0.441339	+	0.764421i
$962$	11.6864			0.376785
$963$	20.8320	−	2.90618i	0.671301	−	0.0936504i
$964$	10.2699			0.330772
$965$	−1.64162	−	2.84336i	−0.0528455	−	0.0915311i
$966$	−8.64262	−	12.8273i	−0.278072	−	0.412710i
$967$	4.63654	−	8.03073i	0.149101	−	0.258251i	−0.781794	−	0.623536i	$-0.785695\pi$
$967$	4.63654	−	8.03073i	0.149101	−	0.258251i	0.930896	+	0.365286i	$0.119029\pi$
$968$	8.99275	−	15.5759i	0.289038	−	0.500628i
$969$	8.16989	−	0.567128i	0.262455	−	0.0182188i
$970$	−14.9450	−	25.8855i	−0.479855	−	0.831133i
$971$	−1.93319			−0.0620390			−0.0310195	−	0.999519i	$-0.509875\pi$
$971$	−1.93319			−0.0620390			−0.0310195	+	0.999519i	$0.509875\pi$
$972$	−7.63751	+	42.6808i	−0.244973	+	1.36899i
$973$	−79.7055			−2.55524
$974$	−13.6960	−	23.7222i	−0.438850	−	0.760110i
$975$	1.72789	−	0.119945i	0.0553369	−	0.00384131i
$976$	4.57832	−	7.92988i	0.146548	−	0.253829i
$977$	12.1237	−	20.9989i	0.387873	−	0.671815i	−0.604291	−	0.796764i	$-0.706543\pi$
$977$	12.1237	−	20.9989i	0.387873	−	0.671815i	0.992163	+	0.124949i	$0.0398767\pi$
$978$	−27.8657	−	41.3579i	−0.891048	−	1.32248i
$979$	−5.78009	−	10.0114i	−0.184733	−	0.319966i
$980$	−30.8496			−0.985454
$981$	−3.86095	+	0.538625i	−0.123271	+	0.0171970i
$982$	−46.5430			−1.48525
$983$	22.6000	+	39.1443i	0.720827	+	1.24851i	0.960669	+	0.277697i	$0.0895711\pi$
$983$	22.6000	+	39.1443i	0.720827	+	1.24851i	−0.239842	+	0.970812i	$0.577096\pi$
$984$	−10.2256	+	20.9385i	−0.325979	+	0.667496i
$985$	−0.223159	+	0.386523i	−0.00711044	+	0.0123156i
$986$	−10.0222	+	17.3590i	−0.319173	+	0.552824i
$987$	26.4075	−	54.0738i	0.840561	−	1.72119i
$988$	−2.26956	−	3.93099i	−0.0722042	−	0.125061i
$989$	−7.27365			−0.231289
$990$	−2.77927	−	3.56476i	−0.0883310	−	0.113295i
$991$	37.2801			1.18424			0.592121	−	0.805849i	$-0.298291\pi$
$991$	37.2801			1.18424			0.592121	+	0.805849i	$0.298291\pi$
$992$	7.06696	+	12.2403i	0.224376	+	0.388631i
$993$	−7.24983	−	10.7601i	−0.230066	−	0.341461i
$994$	−31.8164	+	55.1076i	−1.00915	+	1.74791i
$995$	10.0974	−	17.4892i	0.320109	−	0.554445i
$996$	68.0253	−	4.72209i	2.15546	−	0.149625i
$997$	−4.43560	−	7.68268i	−0.140477	−	0.243313i	0.787199	−	0.616698i	$-0.211530\pi$
$997$	−4.43560	−	7.68268i	−0.140477	−	0.243313i	−0.927676	+	0.373385i	$0.878197\pi$
$998$	6.35062			0.201025
$999$	27.1723	−	5.73242i	0.859693	−	0.181366i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.h.391.3	yes	30
3.2	odd	2		1755.2.i.h.1171.13		30
9.2	odd	6		1755.2.i.h.586.13		30
9.4	even	3		5265.2.a.bk.1.13		15
9.5	odd	6		5265.2.a.bl.1.3		15
9.7	even	3	inner	585.2.i.h.196.3	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.h.196.3	✓	30	9.7	even	3	inner
585.2.i.h.391.3	yes	30	1.1	even	1	trivial
1755.2.i.h.586.13		30	9.2	odd	6
1755.2.i.h.1171.13		30	3.2	odd	2
5265.2.a.bk.1.13		15	9.4	even	3
5265.2.a.bl.1.3		15	9.5	odd	6

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09333 - 1.89370i) q^{2} +(1.72789 - 0.119945i) q^{3} +(-1.39073 + 2.40882i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.11629 - 3.14097i) q^{6} +(2.12668 + 3.68352i) q^{7} +1.70880 q^{8} +(2.97123 - 0.414503i) q^{9} +O(q^{10})\)	\(q+(-1.09333 - 1.89370i) q^{2} +(1.72789 - 0.119945i) q^{3} +(-1.39073 + 2.40882i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.11629 - 3.14097i) q^{6} +(2.12668 + 3.68352i) q^{7} +1.70880 q^{8} +(2.97123 - 0.414503i) q^{9} -2.18666 q^{10} +(0.344526 + 0.596736i) q^{11} +(-2.11411 + 4.32900i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(4.65033 - 8.05460i) q^{14} +(0.760071 - 1.55637i) q^{15} +(0.913186 + 1.58168i) q^{16} +2.89736 q^{17} +(-4.03347 - 5.17342i) q^{18} +1.63191 q^{19} +(1.39073 + 2.40882i) q^{20} +(4.11650 + 6.10965i) q^{21} +(0.753360 - 1.30486i) q^{22} +(0.480072 - 0.831510i) q^{23} +(2.95263 - 0.204962i) q^{24} +(-0.500000 - 0.866025i) q^{25} +2.18666 q^{26} +(5.08424 - 1.07260i) q^{27} -11.8306 q^{28} +(-1.58191 - 2.73995i) q^{29} +(-3.77831 + 0.262278i) q^{30} +(-0.953545 + 1.65159i) q^{31} +(3.70563 - 6.41833i) q^{32} +(0.666879 + 0.989773i) q^{33} +(-3.16777 - 5.48673i) q^{34} +4.25337 q^{35} +(-3.13372 + 7.73362i) q^{36} +5.34441 q^{37} +(-1.78422 - 3.09035i) q^{38} +(-0.760071 + 1.55637i) q^{39} +(0.854401 - 1.47987i) q^{40} +(-3.93651 + 6.81823i) q^{41} +(7.06916 - 14.4753i) q^{42} +(-3.78779 - 6.56064i) q^{43} -1.91658 q^{44} +(1.12664 - 2.78041i) q^{45} -2.09951 q^{46} +(-4.08424 - 7.07411i) q^{47} +(1.76760 + 2.62345i) q^{48} +(-5.54556 + 9.60519i) q^{49} +(-1.09333 + 1.89370i) q^{50} +(5.00633 - 0.347523i) q^{51} +(-1.39073 - 2.40882i) q^{52} +11.5941 q^{53} +(-7.58993 - 8.45533i) q^{54} +0.689052 q^{55} +(3.63408 + 6.29441i) q^{56} +(2.81977 - 0.195739i) q^{57} +(-3.45909 + 5.99132i) q^{58} +(-1.44118 + 2.49620i) q^{59} +(2.69196 + 3.99537i) q^{60} +(-2.50678 - 4.34187i) q^{61} +4.17015 q^{62} +(7.84569 + 10.0631i) q^{63} -12.5531 q^{64} +(0.500000 + 0.866025i) q^{65} +(1.14521 - 2.34502i) q^{66} +(-2.77964 + 4.81448i) q^{67} +(-4.02946 + 6.97923i) q^{68} +(0.729778 - 1.49434i) q^{69} +(-4.65033 - 8.05460i) q^{70} -6.84175 q^{71} +(5.07724 - 0.708304i) q^{72} -12.5995 q^{73} +(-5.84320 - 10.1207i) q^{74} +(-0.967822 - 1.43643i) q^{75} +(-2.26956 + 3.93099i) q^{76} +(-1.46539 + 2.53814i) q^{77} +(3.77831 - 0.262278i) q^{78} +(-6.12760 - 10.6133i) q^{79} +1.82637 q^{80} +(8.65637 - 2.46317i) q^{81} +17.2156 q^{82} +(-7.07700 - 12.2577i) q^{83} +(-20.4420 + 1.41902i) q^{84} +(1.44868 - 2.50919i) q^{85} +(-8.28259 + 14.3459i) q^{86} +(-3.06201 - 4.54459i) q^{87} +(0.588727 + 1.01970i) q^{88} -16.7769 q^{89} +(-6.49705 + 0.906377i) q^{90} -4.25337 q^{91} +(1.33531 + 2.31282i) q^{92} +(-1.44952 + 2.96814i) q^{93} +(-8.93083 + 15.4686i) q^{94} +(0.815956 - 1.41328i) q^{95} +(5.63308 - 11.5347i) q^{96} +(6.83463 + 11.8379i) q^{97} +24.2525 q^{98} +(1.27101 + 1.63023i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9}+O(q^{10}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9} + 2 q^{10} + 9 q^{11} + 18 q^{12} - 15 q^{13} + 3 q^{14} + 2 q^{15} - 33 q^{16} + 6 q^{17} + 9 q^{18} + 30 q^{19} + 21 q^{20} + 9 q^{21} - 10 q^{22} - 6 q^{23} + 24 q^{24} - 15 q^{25} - 2 q^{26} - 2 q^{27} + 70 q^{28} + 8 q^{29} - 6 q^{30} - 22 q^{31} + 21 q^{32} - 20 q^{33} - 9 q^{34} - 20 q^{35} - 7 q^{36} + 8 q^{37} - 14 q^{38} - 2 q^{39} + 13 q^{41} + 21 q^{42} - 24 q^{43} + 10 q^{44} - 7 q^{45} - 6 q^{46} - q^{47} - 27 q^{48} - 37 q^{49} + q^{50} - q^{51} - 21 q^{52} + 14 q^{53} - 24 q^{54} + 18 q^{55} + 17 q^{56} - 55 q^{57} - 22 q^{58} + 19 q^{59} + 9 q^{60} - 16 q^{61} + 26 q^{62} + 4 q^{63} + 72 q^{64} + 15 q^{65} + 24 q^{66} - 11 q^{67} - 28 q^{68} + 44 q^{69} - 3 q^{70} - 56 q^{71} - 18 q^{72} + 52 q^{73} + 8 q^{74} + q^{75} - 18 q^{76} - 24 q^{77} + 6 q^{78} - 44 q^{79} - 66 q^{80} + 37 q^{81} + 70 q^{82} - 3 q^{83} - 139 q^{84} + 3 q^{85} + 40 q^{86} + 60 q^{87} - 37 q^{88} - 8 q^{89} - 12 q^{90} + 20 q^{91} - 74 q^{92} - 55 q^{93} - 2 q^{94} + 15 q^{95} + 55 q^{96} - 33 q^{97} + 6 q^{98} + 26 q^{99}+O(q^{100}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9 + 2 * q^10 + 9 * q^11 + 18 * q^12 - 15 * q^13 + 3 * q^14 + 2 * q^15 - 33 * q^16 + 6 * q^17 + 9 * q^18 + 30 * q^19 + 21 * q^20 + 9 * q^21 - 10 * q^22 - 6 * q^23 + 24 * q^24 - 15 * q^25 - 2 * q^26 - 2 * q^27 + 70 * q^28 + 8 * q^29 - 6 * q^30 - 22 * q^31 + 21 * q^32 - 20 * q^33 - 9 * q^34 - 20 * q^35 - 7 * q^36 + 8 * q^37 - 14 * q^38 - 2 * q^39 + 13 * q^41 + 21 * q^42 - 24 * q^43 + 10 * q^44 - 7 * q^45 - 6 * q^46 - q^47 - 27 * q^48 - 37 * q^49 + q^50 - q^51 - 21 * q^52 + 14 * q^53 - 24 * q^54 + 18 * q^55 + 17 * q^56 - 55 * q^57 - 22 * q^58 + 19 * q^59 + 9 * q^60 - 16 * q^61 + 26 * q^62 + 4 * q^63 + 72 * q^64 + 15 * q^65 + 24 * q^66 - 11 * q^67 - 28 * q^68 + 44 * q^69 - 3 * q^70 - 56 * q^71 - 18 * q^72 + 52 * q^73 + 8 * q^74 + q^75 - 18 * q^76 - 24 * q^77 + 6 * q^78 - 44 * q^79 - 66 * q^80 + 37 * q^81 + 70 * q^82 - 3 * q^83 - 139 * q^84 + 3 * q^85 + 40 * q^86 + 60 * q^87 - 37 * q^88 - 8 * q^89 - 12 * q^90 + 20 * q^91 - 74 * q^92 - 55 * q^93 - 2 * q^94 + 15 * q^95 + 55 * q^96 - 33 * q^97 + 6 * q^98 + 26 * q^99

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