LMFDB - Embedded newform 802.2.e.b.45.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [802,2,Mod(45,802)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(802, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("802.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 802 = 2 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	802.e (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.40400224211$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			45.3
Character	$\chi$	$=$	802.45
Dual form			802.2.e.b.303.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-2.43681 - 1.00936i) q^{3} +1.00000i q^{4} -3.88924 q^{5} +(-1.00936 - 2.43681i) q^{6} +(-0.0905001 + 0.0905001i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.79793 + 2.79793i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-2.43681 - 1.00936i) q^{3} +1.00000i q^{4} -3.88924 q^{5} +(-1.00936 - 2.43681i) q^{6} +(-0.0905001 + 0.0905001i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.79793 + 2.79793i) q^{9} +(-2.75011 - 2.75011i) q^{10} +(-1.34643 - 1.34643i) q^{11} +(1.00936 - 2.43681i) q^{12} +(-3.58743 + 1.48596i) q^{13} -0.127987 q^{14} +(9.47735 + 3.92565i) q^{15} -1.00000 q^{16} +(3.91861 - 1.62314i) q^{17} +3.95687i q^{18} +(-1.19157 - 2.87670i) q^{19} -3.88924i q^{20} +(0.311879 - 0.129185i) q^{21} -1.90414i q^{22} +(2.51214 + 6.06484i) q^{23} +(2.43681 - 1.00936i) q^{24} +10.1262 q^{25} +(-3.58743 - 1.48596i) q^{26} +(-0.965826 - 2.33171i) q^{27} +(-0.0905001 - 0.0905001i) q^{28} +5.61999 q^{29} +(3.92565 + 9.47735i) q^{30} +(-1.91626 - 4.62625i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.92196 + 4.64003i) q^{33} +(3.91861 + 1.62314i) q^{34} +(0.351977 - 0.351977i) q^{35} +(-2.79793 + 2.79793i) q^{36} +(2.37868 + 0.985281i) q^{37} +(1.19157 - 2.87670i) q^{38} +10.2418 q^{39} +(2.75011 - 2.75011i) q^{40} +1.98040 q^{41} +(0.311879 + 0.129185i) q^{42} +(7.14644 - 7.14644i) q^{43} +(1.34643 - 1.34643i) q^{44} +(-10.8818 - 10.8818i) q^{45} +(-2.51214 + 6.06484i) q^{46} +(1.06664 + 1.06664i) q^{47} +(2.43681 + 1.00936i) q^{48} +6.98362i q^{49} +(7.16029 + 7.16029i) q^{50} -11.1873 q^{51} +(-1.48596 - 3.58743i) q^{52} +(-1.95690 + 4.72438i) q^{53} +(0.965826 - 2.33171i) q^{54} +(5.23658 + 5.23658i) q^{55} -0.127987i q^{56} +8.21271i q^{57} +(3.97393 + 3.97393i) q^{58} +(3.68570 - 1.52667i) q^{59} +(-3.92565 + 9.47735i) q^{60} +(-0.999999 - 2.41421i) q^{61} +(1.91626 - 4.62625i) q^{62} -0.506426 q^{63} -1.00000i q^{64} +(13.9524 - 5.77926i) q^{65} +(-1.92196 + 4.64003i) q^{66} +(3.20823 - 7.74535i) q^{67} +(1.62314 + 3.91861i) q^{68} -17.3145i q^{69} +0.497770 q^{70} +(-2.45979 + 5.93845i) q^{71} -3.95687 q^{72} +(-2.64888 + 2.64888i) q^{73} +(0.985281 + 2.37868i) q^{74} +(-24.6756 - 10.2210i) q^{75} +(2.87670 - 1.19157i) q^{76} +0.243704 q^{77} +(7.24202 + 7.24202i) q^{78} +(-2.68573 - 6.48393i) q^{79} +3.88924 q^{80} -5.21380i q^{81} +(1.40035 + 1.40035i) q^{82} +8.44668 q^{83} +(0.129185 + 0.311879i) q^{84} +(-15.2404 + 6.31279i) q^{85} +10.1066 q^{86} +(-13.6949 - 5.67260i) q^{87} +1.90414 q^{88} +(-11.2906 + 11.2906i) q^{89} -15.3892i q^{90} +(0.190183 - 0.459142i) q^{91} +(-6.06484 + 2.51214i) q^{92} +13.2075i q^{93} +1.50846i q^{94} +(4.63430 + 11.1882i) q^{95} +(1.00936 + 2.43681i) q^{96} +(-2.13257 - 5.14847i) q^{97} +(-4.93816 + 4.93816i) q^{98} -7.53442i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{6} + 20 q^{9}+O(q^{10}) $ 68 * q + 4 * q^6 + 20 * q^9	$ 68 q + 4 q^{6} + 20 q^{9} - 4 q^{10} + 12 q^{11} - 4 q^{12} - 8 q^{13} + 8 q^{14} - 4 q^{15} - 68 q^{16} + 4 q^{17} + 20 q^{19} - 40 q^{21} - 16 q^{23} + 20 q^{25} - 8 q^{26} - 12 q^{27} + 16 q^{29} - 4 q^{30} - 8 q^{31} + 8 q^{33} + 4 q^{34} + 16 q^{35} - 20 q^{36} + 12 q^{37} - 20 q^{38} + 40 q^{39} + 4 q^{40} + 24 q^{41} - 40 q^{42} + 40 q^{43} - 12 q^{44} + 28 q^{45} + 16 q^{46} + 4 q^{47} - 8 q^{50} + 24 q^{51} + 4 q^{52} + 12 q^{53} + 12 q^{54} - 24 q^{55} - 4 q^{58} + 4 q^{59} + 4 q^{60} - 20 q^{61} + 8 q^{62} - 16 q^{63} + 36 q^{65} - 8 q^{66} + 48 q^{67} + 8 q^{68} - 16 q^{71} - 68 q^{72} + 40 q^{73} - 8 q^{74} - 96 q^{75} - 16 q^{77} + 32 q^{78} + 28 q^{79} - 16 q^{82} + 16 q^{83} - 4 q^{84} + 16 q^{85} - 32 q^{86} + 8 q^{87} + 8 q^{88} - 20 q^{89} - 4 q^{91} + 8 q^{92} - 24 q^{95} - 4 q^{96} + 24 q^{97} + 24 q^{98}+O(q^{100}) $ 68 * q + 4 * q^6 + 20 * q^9 - 4 * q^10 + 12 * q^11 - 4 * q^12 - 8 * q^13 + 8 * q^14 - 4 * q^15 - 68 * q^16 + 4 * q^17 + 20 * q^19 - 40 * q^21 - 16 * q^23 + 20 * q^25 - 8 * q^26 - 12 * q^27 + 16 * q^29 - 4 * q^30 - 8 * q^31 + 8 * q^33 + 4 * q^34 + 16 * q^35 - 20 * q^36 + 12 * q^37 - 20 * q^38 + 40 * q^39 + 4 * q^40 + 24 * q^41 - 40 * q^42 + 40 * q^43 - 12 * q^44 + 28 * q^45 + 16 * q^46 + 4 * q^47 - 8 * q^50 + 24 * q^51 + 4 * q^52 + 12 * q^53 + 12 * q^54 - 24 * q^55 - 4 * q^58 + 4 * q^59 + 4 * q^60 - 20 * q^61 + 8 * q^62 - 16 * q^63 + 36 * q^65 - 8 * q^66 + 48 * q^67 + 8 * q^68 - 16 * q^71 - 68 * q^72 + 40 * q^73 - 8 * q^74 - 96 * q^75 - 16 * q^77 + 32 * q^78 + 28 * q^79 - 16 * q^82 + 16 * q^83 - 4 * q^84 + 16 * q^85 - 32 * q^86 + 8 * q^87 + 8 * q^88 - 20 * q^89 - 4 * q^91 + 8 * q^92 - 24 * q^95 - 4 * q^96 + 24 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/802\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{8}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−2.43681	−	1.00936i	−1.40689	−	0.582755i	−0.455363	−	0.890306i	$-0.650491\pi$
$3$	−2.43681	−	1.00936i	−1.40689	−	0.582755i	−0.951532	+	0.307551i	$0.900491\pi$
$4$			1.00000i			0.500000i
$5$	−3.88924			−1.73932			−0.869660	−	0.493651i	$-0.835662\pi$
$5$	−3.88924			−1.73932			−0.869660	+	0.493651i	$0.835662\pi$
$6$	−1.00936	−	2.43681i	−0.412070	−	0.994825i
$7$	−0.0905001	+	0.0905001i	−0.0342058	+	0.0342058i	−0.724003	−	0.689797i	$-0.757700\pi$
$7$	−0.0905001	+	0.0905001i	−0.0342058	+	0.0342058i	0.689797	+	0.724003i	$0.257700\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.79793	+	2.79793i	0.932643	+	0.932643i
$10$	−2.75011	−	2.75011i	−0.869660	−	0.869660i
$11$	−1.34643	−	1.34643i	−0.405964	−	0.405964i	0.474365	−	0.880328i	$-0.342678\pi$
$11$	−1.34643	−	1.34643i	−0.405964	−	0.405964i	−0.880328	+	0.474365i	$0.842678\pi$
$12$	1.00936	−	2.43681i	0.291377	−	0.703447i
$13$	−3.58743	+	1.48596i	−0.994973	+	0.412131i	−0.819951	−	0.572433i	$-0.806000\pi$
$13$	−3.58743	+	1.48596i	−0.994973	+	0.412131i	−0.175022	+	0.984565i	$0.556000\pi$
$14$	−0.127987			−0.0342058
$15$	9.47735	+	3.92565i	2.44704	+	1.01360i
$16$	−1.00000			−0.250000
$17$	3.91861	−	1.62314i	0.950403	−	0.393670i	0.147021	−	0.989133i	$-0.453032\pi$
$17$	3.91861	−	1.62314i	0.950403	−	0.393670i	0.803382	+	0.595464i	$0.203032\pi$
$18$			3.95687i			0.932643i
$19$	−1.19157	−	2.87670i	−0.273365	−	0.659961i	0.726258	−	0.687422i	$-0.241258\pi$
$19$	−1.19157	−	2.87670i	−0.273365	−	0.659961i	−0.999623	+	0.0274611i	$0.991258\pi$
$20$		−	3.88924i		−	0.869660i
$21$	0.311879	−	0.129185i	0.0680576	−	0.0281904i
$22$		−	1.90414i		−	0.405964i
$23$	2.51214	+	6.06484i	0.523817	+	1.26461i	0.935515	+	0.353286i	$0.114936\pi$
$23$	2.51214	+	6.06484i	0.523817	+	1.26461i	−0.411698	+	0.911320i	$0.635064\pi$
$24$	2.43681	−	1.00936i	0.497412	−	0.206035i
$25$	10.1262			2.02524
$26$	−3.58743	−	1.48596i	−0.703552	−	0.291421i
$27$	−0.965826	−	2.33171i	−0.185873	−	0.448738i
$28$	−0.0905001	−	0.0905001i	−0.0171029	−	0.0171029i
$29$	5.61999			1.04361			0.521803	−	0.853066i	$-0.325260\pi$
$29$	5.61999			1.04361			0.521803	+	0.853066i	$0.325260\pi$
$30$	3.92565	+	9.47735i	0.716722	+	1.73032i
$31$	−1.91626	−	4.62625i	−0.344170	−	0.830900i	−0.997285	−	0.0736409i	$-0.976538\pi$
$31$	−1.91626	−	4.62625i	−0.344170	−	0.830900i	0.653115	−	0.757259i	$-0.273462\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	1.92196	+	4.64003i	0.334571	+	0.807725i
$34$	3.91861	+	1.62314i	0.672036	+	0.278367i
$35$	0.351977	−	0.351977i	0.0594949	−	0.0594949i
$36$	−2.79793	+	2.79793i	−0.466321	+	0.466321i
$37$	2.37868	+	0.985281i	0.391052	+	0.161979i	0.569541	−	0.821963i	$-0.307121\pi$
$37$	2.37868	+	0.985281i	0.391052	+	0.161979i	−0.178489	+	0.983942i	$0.557121\pi$
$38$	1.19157	−	2.87670i	0.193298	−	0.466663i
$39$	10.2418			1.63999
$40$	2.75011	−	2.75011i	0.434830	−	0.434830i
$41$	1.98040			0.309286			0.154643	−	0.987970i	$-0.450577\pi$
$41$	1.98040			0.309286			0.154643	+	0.987970i	$0.450577\pi$
$42$	0.311879	+	0.129185i	0.0481240	+	0.0199336i
$43$	7.14644	−	7.14644i	1.08982	−	1.08982i	0.0942765	−	0.995546i	$-0.469946\pi$
$43$	7.14644	−	7.14644i	1.08982	−	1.08982i	0.995546	−	0.0942765i	$-0.0300538\pi$
$44$	1.34643	−	1.34643i	0.202982	−	0.202982i
$45$	−10.8818	−	10.8818i	−1.62216	−	1.62216i
$46$	−2.51214	+	6.06484i	−0.370395	+	0.894212i
$47$	1.06664	+	1.06664i	0.155586	+	0.155586i	0.780608	−	0.625022i	$-0.214910\pi$
$47$	1.06664	+	1.06664i	0.155586	+	0.155586i	−0.625022	+	0.780608i	$0.714910\pi$
$48$	2.43681	+	1.00936i	0.351724	+	0.145689i
$49$			6.98362i			0.997660i
$50$	7.16029	+	7.16029i	1.01262	+	1.01262i
$51$	−11.1873			−1.56653
$52$	−1.48596	−	3.58743i	−0.206066	−	0.497486i
$53$	−1.95690	+	4.72438i	−0.268801	+	0.648943i	−0.999427	−	0.0338341i	$-0.989228\pi$
$53$	−1.95690	+	4.72438i	−0.268801	+	0.648943i	0.730626	+	0.682778i	$0.239228\pi$
$54$	0.965826	−	2.33171i	0.131432	−	0.317306i
$55$	5.23658	+	5.23658i	0.706101	+	0.706101i
$56$		−	0.127987i		−	0.0171029i
$57$			8.21271i			1.08780i
$58$	3.97393	+	3.97393i	0.521803	+	0.521803i
$59$	3.68570	−	1.52667i	0.479837	−	0.198755i	−0.129636	−	0.991562i	$-0.541381\pi$
$59$	3.68570	−	1.52667i	0.479837	−	0.198755i	0.609473	+	0.792807i	$0.291381\pi$
$60$	−3.92565	+	9.47735i	−0.506799	+	1.22352i
$61$	−0.999999	−	2.41421i	−0.128037	−	0.309108i	0.846842	−	0.531845i	$-0.178501\pi$
$61$	−0.999999	−	2.41421i	−0.128037	−	0.309108i	−0.974879	+	0.222737i	$0.928501\pi$
$62$	1.91626	−	4.62625i	0.243365	−	0.587535i
$63$	−0.506426			−0.0638037
$64$		−	1.00000i		−	0.125000i
$65$	13.9524	−	5.77926i	1.73058	−	0.716828i
$66$	−1.92196	+	4.64003i	−0.236577	+	0.571148i
$67$	3.20823	−	7.74535i	0.391948	−	0.946245i	−0.597568	−	0.801818i	$-0.703866\pi$
$67$	3.20823	−	7.74535i	0.391948	−	0.946245i	0.989515	−	0.144427i	$-0.0461339\pi$
$68$	1.62314	+	3.91861i	0.196835	+	0.475201i
$69$		−	17.3145i		−	2.08443i
$70$	0.497770			0.0594949
$71$	−2.45979	+	5.93845i	−0.291923	+	0.704765i	−0.999999	−	0.00137156i	$-0.999563\pi$
$71$	−2.45979	+	5.93845i	−0.291923	+	0.704765i	0.708076	+	0.706136i	$0.249563\pi$
$72$	−3.95687			−0.466321
$73$	−2.64888	+	2.64888i	−0.310028	+	0.310028i	−0.844920	−	0.534892i	$-0.820352\pi$
$73$	−2.64888	+	2.64888i	−0.310028	+	0.310028i	0.534892	+	0.844920i	$0.320352\pi$
$74$	0.985281	+	2.37868i	0.114537	+	0.276516i
$75$	−24.6756	−	10.2210i	−2.84929	−	1.18022i
$76$	2.87670	−	1.19157i	0.329981	−	0.136682i
$77$	0.243704			0.0277726
$78$	7.24202	+	7.24202i	0.819997	+	0.819997i
$79$	−2.68573	−	6.48393i	−0.302169	−	0.729499i	−0.999913	−	0.0131531i	$-0.995813\pi$
$79$	−2.68573	−	6.48393i	−0.302169	−	0.729499i	0.697745	−	0.716346i	$-0.254187\pi$
$80$	3.88924			0.434830
$81$		−	5.21380i		−	0.579311i
$82$	1.40035	+	1.40035i	0.154643	+	0.154643i
$83$	8.44668			0.927144			0.463572	−	0.886059i	$-0.346568\pi$
$83$	8.44668			0.927144			0.463572	+	0.886059i	$0.346568\pi$
$84$	0.129185	+	0.311879i	0.0140952	+	0.0340288i
$85$	−15.2404	+	6.31279i	−1.65306	+	0.684718i
$86$	10.1066			1.08982
$87$	−13.6949	−	5.67260i	−1.46824	−	0.608166i
$88$	1.90414			0.202982
$89$	−11.2906	+	11.2906i	−1.19680	+	1.19680i	−0.221683	+	0.975119i	$0.571155\pi$
$89$	−11.2906	+	11.2906i	−1.19680	+	1.19680i	−0.975119	+	0.221683i	$0.928845\pi$
$90$		−	15.3892i		−	1.62216i
$91$	0.190183	−	0.459142i	0.0199366	−	0.0481312i
$92$	−6.06484	+	2.51214i	−0.632303	+	0.261909i
$93$			13.2075i			1.36956i
$94$			1.50846i			0.155586i
$95$	4.63430	+	11.1882i	0.475469	+	1.14788i
$96$	1.00936	+	2.43681i	0.103017	+	0.248706i
$97$	−2.13257	−	5.14847i	−0.216529	−	0.522748i	0.777871	−	0.628424i	$-0.216300\pi$
$97$	−2.13257	−	5.14847i	−0.216529	−	0.522748i	−0.994401	+	0.105675i	$0.966300\pi$
$98$	−4.93816	+	4.93816i	−0.498830	+	0.498830i
$99$		−	7.53442i		−	0.757238i
$100$			10.1262i			1.01262i
$101$	−5.97657	+	14.4287i	−0.594691	+	1.43571i	0.284237	+	0.958754i	$0.408260\pi$
$101$	−5.97657	+	14.4287i	−0.594691	+	1.43571i	−0.878927	+	0.476956i	$0.841740\pi$
$102$	−7.91059	−	7.91059i	−0.783265	−	0.783265i
$103$	8.24789	−	8.24789i	0.812689	−	0.812689i	−0.172347	−	0.985036i	$-0.555135\pi$
$103$	8.24789	−	8.24789i	0.812689	−	0.812689i	0.985036	+	0.172347i	$0.0551352\pi$
$104$	1.48596	−	3.58743i	0.145710	−	0.351776i
$105$	−1.21297	+	0.502430i	−0.118374	+	0.0490321i
$106$	−4.72438	+	1.95690i	−0.458872	+	0.190071i
$107$	1.79187	−	0.742216i	0.173226	−	0.0717527i	−0.294385	−	0.955687i	$-0.595115\pi$
$107$	1.79187	−	0.742216i	0.173226	−	0.0717527i	0.467611	+	0.883934i	$0.345115\pi$
$108$	2.33171	−	0.965826i	0.224369	−	0.0929367i
$109$	−11.3465	−	11.3465i	−1.08680	−	1.08680i	−0.995856	−	0.0909411i	$-0.971012\pi$
$109$	−11.3465	−	11.3465i	−1.08680	−	1.08680i	−0.0909411	−	0.995856i	$-0.528988\pi$
$110$			7.40565i			0.706101i
$111$	−4.80189	−	4.80189i	−0.455775	−	0.455775i
$112$	0.0905001	−	0.0905001i	0.00855146	−	0.00855146i
$113$		−	0.426272i		−	0.0401003i	−0.999799	−	0.0200501i	$-0.993617\pi$
$113$		−	0.426272i		−	0.0401003i	0.999799	−	0.0200501i	$-0.00638259\pi$
$114$	−5.80727	+	5.80727i	−0.543900	+	0.543900i
$115$	−9.77031	−	23.5876i	−0.911086	−	2.19956i
$116$			5.61999i			0.521803i
$117$	−14.1950	−	5.87975i	−1.31233	−	0.543583i
$118$	3.68570	+	1.52667i	0.339296	+	0.140541i
$119$	−0.207740	+	0.501529i	−0.0190435	+	0.0459751i
$120$	−9.47735	+	3.92565i	−0.865160	+	0.358361i
$121$		−	7.37426i		−	0.670387i
$122$	0.999999	−	2.41421i	0.0905357	−	0.218572i
$123$	−4.82586	−	1.99894i	−0.435133	−	0.180238i
$124$	4.62625	−	1.91626i	0.415450	−	0.172085i
$125$	−19.9369			−1.78321
$126$	−0.358097	−	0.358097i	−0.0319018	−	0.0319018i
$127$	6.54426	+	15.7992i	0.580709	+	1.40196i	0.892171	+	0.451698i	$0.149181\pi$
$127$	6.54426	+	15.7992i	0.580709	+	1.40196i	−0.311462	+	0.950259i	$0.600819\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−24.6279	+	10.2012i	−2.16837	+	0.898166i
$130$	13.9524	+	5.77926i	1.22370	+	0.506874i
$131$	4.28501	−	10.3449i	0.374383	−	0.903840i	−0.618613	−	0.785696i	$-0.712305\pi$
$131$	4.28501	−	10.3449i	0.374383	−	0.903840i	0.992996	−	0.118145i	$-0.0376947\pi$
$132$	−4.64003	+	1.92196i	−0.403863	+	0.167285i
$133$	0.368179	+	0.152505i	0.0319252	+	0.0132238i
$134$	7.74535	−	3.20823i	0.669097	−	0.277149i
$135$	3.75633	+	9.06858i	0.323293	+	0.780499i
$136$	−1.62314	+	3.91861i	−0.139183	+	0.336018i
$137$	17.0327	+	7.05519i	1.45521	+	0.602766i	0.963431	−	0.267957i	$-0.0863484\pi$
$137$	17.0327	+	7.05519i	1.45521	+	0.602766i	0.491775	+	0.870723i	$0.336348\pi$
$138$	12.2432	−	12.2432i	1.04221	−	1.04221i
$139$	18.1667	−	7.52491i	1.54088	−	0.638254i	0.559244	−	0.829003i	$-0.311092\pi$
$139$	18.1667	−	7.52491i	1.54088	−	0.638254i	0.981639	+	0.190749i	$0.0610916\pi$
$140$	0.351977	+	0.351977i	0.0297475	+	0.0297475i
$141$	−1.52258	−	3.67584i	−0.128225	−	0.309562i
$142$	−5.93845	+	2.45979i	−0.498344	+	0.206421i
$143$	6.83095	+	2.82947i	0.571233	+	0.236612i
$144$	−2.79793	−	2.79793i	−0.233161	−	0.233161i
$145$	−21.8575			−1.81517
$146$	−3.74608			−0.310028
$147$	7.04899	−	17.0178i	0.581391	−	1.40360i
$148$	−0.985281	+	2.37868i	−0.0809896	+	0.195526i
$149$			0.161047i			0.0131935i	0.999978	+	0.00659676i	$0.00209983\pi$
$149$			0.161047i			0.0131935i	−0.999978	+	0.00659676i	$0.997900\pi$
$150$	−10.2210	−	24.6756i	−0.834539	−	2.01475i
$151$	5.31568	+	5.31568i	0.432584	+	0.432584i	0.889506	−	0.456923i	$-0.151048\pi$
$151$	5.31568	+	5.31568i	0.432584	+	0.432584i	−0.456923	+	0.889506i	$0.651048\pi$
$152$	2.87670	+	1.19157i	0.233331	+	0.0966491i
$153$	15.5054	+	6.42256i	1.25354	+	0.519233i
$154$	0.172325	+	0.172325i	0.0138863	+	0.0138863i
$155$	7.45278	+	17.9926i	0.598622	+	1.44520i
$156$			10.2418i			0.819997i
$157$	−0.0813988	+	0.0337165i	−0.00649633	+	0.00269087i	−0.385929	−	0.922528i	$-0.626119\pi$
$157$	−0.0813988	+	0.0337165i	−0.00649633	+	0.00269087i	0.379433	+	0.925219i	$0.376119\pi$
$158$	2.68573	−	6.48393i	0.213665	−	0.515834i
$159$	9.53721	−	9.53721i	0.756350	−	0.756350i
$160$	2.75011	+	2.75011i	0.217415	+	0.217415i
$161$	−0.776218	−	0.321520i	−0.0611745	−	0.0253393i
$162$	3.68671	−	3.68671i	0.289655	−	0.289655i
$163$	−0.227005	+	0.0940286i	−0.0177804	+	0.00736489i	−0.391556	−	0.920154i	$-0.628063\pi$
$163$	−0.227005	+	0.0940286i	−0.0177804	+	0.00736489i	0.373776	+	0.927519i	$0.378063\pi$
$164$			1.98040i			0.154643i
$165$	−7.47497	−	18.0462i	−0.581926	−	1.40489i
$166$	5.97271	+	5.97271i	0.463572	+	0.463572i
$167$	1.15795	+	2.79553i	0.0896047	+	0.216325i	0.962329	−	0.271889i	$-0.0876485\pi$
$167$	1.15795	+	2.79553i	0.0896047	+	0.216325i	−0.872724	+	0.488214i	$0.837648\pi$
$168$	−0.129185	+	0.311879i	−0.00996681	+	0.0240620i
$169$	1.46916	−	1.46916i	0.113012	−	0.113012i
$170$	−15.2404	−	6.31279i	−1.16889	−	0.484169i
$171$	4.71488	−	11.3827i	0.360556	−	0.870460i
$172$	7.14644	+	7.14644i	0.544911	+	0.544911i
$173$	9.48170			0.720880			0.360440	−	0.932782i	$-0.382626\pi$
$173$	9.48170			0.720880			0.360440	+	0.932782i	$0.382626\pi$
$174$	−5.67260	−	13.6949i	−0.430039	−	1.03821i
$175$	−0.916420	+	0.916420i	−0.0692749	+	0.0692749i
$176$	1.34643	+	1.34643i	0.101491	+	0.101491i
$177$	−10.5223			−0.790905
$178$	−15.9673			−1.19680
$179$			24.5419i			1.83435i	0.398489	+	0.917173i	$0.369535\pi$
$179$			24.5419i			1.83435i	−0.398489	+	0.917173i	$0.630465\pi$
$180$	10.8818	−	10.8818i	0.811082	−	0.811082i
$181$	−4.01730	+	4.01730i	−0.298603	+	0.298603i	−0.840467	−	0.541863i	$-0.817719\pi$
$181$	−4.01730	+	4.01730i	−0.298603	+	0.298603i	0.541863	+	0.840467i	$0.317719\pi$
$182$	0.459142	−	0.190183i	0.0340339	−	0.0140973i
$183$			6.89234i			0.509497i
$184$	−6.06484	−	2.51214i	−0.447106	−	0.185197i
$185$	−9.25125	−	3.83199i	−0.680165	−	0.281734i
$186$	−9.33912	+	9.33912i	−0.684778	+	0.684778i
$187$	−7.46157	−	3.09069i	−0.545644	−	0.226013i
$188$	−1.06664	+	1.06664i	−0.0777930	+	0.0777930i
$189$	0.298428	+	0.123613i	0.0217074	+	0.00899150i
$190$	−4.63430	+	11.1882i	−0.336207	+	0.811676i
$191$	−11.1810	−	4.63132i	−0.809028	−	0.335110i	−0.0604618	−	0.998171i	$-0.519257\pi$
$191$	−11.1810	−	4.63132i	−0.809028	−	0.335110i	−0.748566	+	0.663060i	$0.769257\pi$
$192$	−1.00936	+	2.43681i	−0.0728444	+	0.175862i
$193$	20.2572	−	8.39081i	1.45815	−	0.603984i	0.494025	−	0.869448i	$-0.335525\pi$
$193$	20.2572	−	8.39081i	1.45815	−	0.603984i	0.964121	+	0.265464i	$0.0855250\pi$
$194$	2.13257	−	5.14847i	0.153109	−	0.369639i
$195$	−39.8326			−2.85247
$196$	−6.98362			−0.498830
$197$			7.25140i			0.516641i	0.966059	+	0.258320i	$0.0831690\pi$
$197$			7.25140i			0.516641i	−0.966059	+	0.258320i	$0.916831\pi$
$198$	5.32764	−	5.32764i	0.378619	−	0.378619i
$199$	21.9431	−	9.08912i	1.55550	−	0.644311i	0.571203	−	0.820809i	$-0.306477\pi$
$199$	21.9431	−	9.08912i	1.55550	−	0.644311i	0.984301	+	0.176498i	$0.0564768\pi$
$200$	−7.16029	+	7.16029i	−0.506309	+	0.506309i
$201$	−15.6357	+	15.6357i	−1.10286	+	1.10286i
$202$	−14.4287	+	5.97657i	−1.01520	+	0.420510i
$203$	−0.508610	+	0.508610i	−0.0356974	+	0.0356974i
$204$		−	11.1873i		−	0.783265i
$205$	−7.70223			−0.537947
$206$	11.6643			0.812689
$207$	−9.94020	+	23.9978i	−0.690892	+	1.66796i
$208$	3.58743	−	1.48596i	0.248743	−	0.103033i
$209$	−2.26891	+	5.47764i	−0.156944	+	0.378896i
$210$	−1.21297	−	0.502430i	−0.0837031	−	0.0346709i
$211$	−6.25385	+	15.0981i	−0.430533	+	1.03940i	0.548583	+	0.836096i	$0.315167\pi$
$211$	−6.25385	+	15.0981i	−0.430533	+	1.03940i	−0.979116	+	0.203302i	$0.934833\pi$
$212$	−4.72438	−	1.95690i	−0.324472	−	0.134401i
$213$	11.9881	−	11.9881i	0.821410	−	0.821410i
$214$	1.79187	+	0.742216i	0.122490	+	0.0507368i
$215$	−27.7942	+	27.7942i	−1.89555	+	1.89555i
$216$	2.33171	+	0.965826i	0.158653	+	0.0657162i
$217$	0.592098	+	0.245255i	0.0401942	+	0.0166490i
$218$		−	16.0464i		−	1.08680i
$219$	9.12851	−	3.78115i	0.616848	−	0.255507i
$220$	−5.23658	+	5.23658i	−0.353050	+	0.353050i
$221$	−11.6458	+	11.6458i	−0.783381	+	0.783381i
$222$		−	6.79090i		−	0.455775i
$223$	18.7664			1.25669			0.628345	−	0.777935i	$-0.283733\pi$
$223$	18.7664			1.25669			0.628345	+	0.777935i	$0.283733\pi$
$224$	0.127987			0.00855146
$225$	28.3323	+	28.3323i	1.88882	+	1.88882i
$226$	0.301420	−	0.301420i	0.0200501	−	0.0200501i
$227$	−9.40332	−	22.7016i	−0.624120	−	1.50676i	−0.846824	−	0.531873i	$-0.821488\pi$
$227$	−9.40332	−	22.7016i	−0.624120	−	1.50676i	0.222704	−	0.974886i	$-0.428512\pi$
$228$	−8.21271			−0.543900
$229$	8.74780	+	8.74780i	0.578071	+	0.578071i	0.934371	−	0.356301i	$-0.115962\pi$
$229$	8.74780	+	8.74780i	0.578071	+	0.578071i	−0.356301	+	0.934371i	$0.615962\pi$
$230$	9.77031	−	23.5876i	0.644235	−	1.55532i
$231$	−0.593861	−	0.245985i	−0.0390732	−	0.0161846i
$232$	−3.97393	+	3.97393i	−0.260901	+	0.260901i
$233$	10.4932	−	25.3328i	0.687432	−	1.65961i	−0.0624589	−	0.998048i	$-0.519894\pi$
$233$	10.4932	−	25.3328i	0.687432	−	1.65961i	0.749891	−	0.661561i	$-0.230106\pi$
$234$	−5.87975	−	14.1950i	−0.384371	−	0.927954i
$235$	−4.14843	−	4.14843i	−0.270614	−	0.270614i
$236$	1.52667	+	3.68570i	0.0993774	+	0.239918i
$237$			18.5110i			1.20242i
$238$	−0.501529	+	0.207740i	−0.0325093	+	0.0134658i
$239$	12.7002	−	12.7002i	0.821509	−	0.821509i	−0.164816	−	0.986324i	$-0.552703\pi$
$239$	12.7002	−	12.7002i	0.821509	−	0.821509i	0.986324	+	0.164816i	$0.0527030\pi$
$240$	−9.47735	−	3.92565i	−0.611760	−	0.253399i
$241$	−1.61318	−	1.61318i	−0.103914	−	0.103914i	0.653238	−	0.757152i	$-0.273410\pi$
$241$	−1.61318	−	1.61318i	−0.103914	−	0.103914i	−0.757152	+	0.653238i	$0.773410\pi$
$242$	5.21439	−	5.21439i	0.335194	−	0.335194i
$243$	−8.16008	+	19.7002i	−0.523469	+	1.26377i
$244$	2.41421	−	0.999999i	0.154554	−	0.0640184i
$245$		−	27.1610i		−	1.73525i
$246$	−1.99894	−	4.82586i	−0.127447	−	0.307685i
$247$	8.54934	+	8.54934i	0.543981	+	0.543981i
$248$	4.62625	+	1.91626i	0.293767	+	0.121682i
$249$	−20.5830	−	8.52575i	−1.30439	−	0.540298i
$250$	−14.0975	−	14.0975i	−0.891607	−	0.891607i
$251$	0.0696472	+	0.168143i	0.00439609	+	0.0106131i	0.926062	−	0.377371i	$-0.123172\pi$
$251$	0.0696472	+	0.168143i	0.00439609	+	0.0106131i	−0.921666	+	0.387984i	$0.873172\pi$
$252$		−	0.506426i		−	0.0319018i
$253$	4.78346	−	11.5483i	0.300733	−	0.726035i
$254$	−6.54426	+	15.7992i	−0.410624	+	0.991333i
$255$	43.5099			2.72470
$256$	1.00000			0.0625000
$257$	14.4791	+	14.4791i	0.903181	+	0.903181i	0.995710	−	0.0925292i	$-0.0294952\pi$
$257$	14.4791	+	14.4791i	0.903181	+	0.903181i	−0.0925292	+	0.995710i	$0.529495\pi$
$258$	−24.6279	−	10.2012i	−1.53327	−	0.635099i
$259$	−0.304439	+	0.126103i	−0.0189169	+	0.00783564i
$260$	5.77926	+	13.9524i	0.358414	+	0.865288i
$261$	15.7243	+	15.7243i	0.973312	+	0.973312i
$262$	10.3449	−	4.28501i	0.639112	−	0.264729i
$263$	21.1017	−	21.1017i	1.30119	−	1.30119i	0.373593	−	0.927593i	$-0.378126\pi$
$263$	21.1017	−	21.1017i	1.30119	−	1.30119i	0.927593	−	0.373593i	$-0.121874\pi$
$264$	−4.64003	−	1.92196i	−0.285574	−	0.118289i
$265$	7.61086	−	18.3742i	0.467531	−	1.12872i
$266$	0.152505	+	0.368179i	0.00935067	+	0.0225745i
$267$	38.9094	−	16.1168i	2.38122	−	0.986332i
$268$	7.74535	+	3.20823i	0.473123	+	0.195974i
$269$	19.8079	−	8.20470i	1.20771	−	0.500250i	0.314227	−	0.949348i	$-0.398255\pi$
$269$	19.8079	−	8.20470i	1.20771	−	0.500250i	0.893482	+	0.449098i	$0.148255\pi$
$270$	−3.75633	+	9.06858i	−0.228603	+	0.551896i
$271$	−5.35577	−	2.21843i	−0.325340	−	0.134760i	0.214035	−	0.976826i	$-0.431339\pi$
$271$	−5.35577	−	2.21843i	−0.325340	−	0.134760i	−0.539375	+	0.842066i	$0.681339\pi$
$272$	−3.91861	+	1.62314i	−0.237601	+	0.0984174i
$273$	−0.926880	+	0.926880i	−0.0560974	+	0.0560974i
$274$	7.05519	+	17.0327i	0.426220	+	1.02899i
$275$	−13.6342	−	13.6342i	−0.822172	−	0.822172i
$276$	17.3145			1.04221
$277$	5.76841	−	2.38935i	0.346590	−	0.143562i	−0.202596	−	0.979262i	$-0.564938\pi$
$277$	5.76841	−	2.38935i	0.346590	−	0.143562i	0.549186	+	0.835700i	$0.314938\pi$
$278$	18.1667	+	7.52491i	1.08957	+	0.451314i
$279$	7.58238	−	18.3055i	0.453945	−	1.09592i
$280$			0.497770i			0.0297475i
$281$	−25.3899	+	10.5168i	−1.51464	+	0.627383i	−0.976508	−	0.215481i	$-0.930868\pi$
$281$	−25.3899	+	10.5168i	−1.51464	+	0.627383i	−0.538128	+	0.842863i	$0.680868\pi$
$282$	1.52258	−	3.67584i	0.0906685	−	0.218893i
$283$	5.73059	+	2.37369i	0.340648	+	0.141101i	0.546448	−	0.837493i	$-0.315980\pi$
$283$	5.73059	+	2.37369i	0.340648	+	0.141101i	−0.205800	+	0.978594i	$0.565980\pi$
$284$	−5.93845	−	2.45979i	−0.352382	−	0.145962i
$285$		−	31.9412i		−	1.89203i
$286$	2.82947	+	6.83095i	0.167310	+	0.403923i
$287$	−0.179226	+	0.179226i	−0.0105794	+	0.0105794i
$288$		−	3.95687i		−	0.233161i
$289$	0.700108	−	0.700108i	0.0411828	−	0.0411828i
$290$	−15.4556	−	15.4556i	−0.907583	−	0.907583i
$291$			14.6984i			0.861636i
$292$	−2.64888	−	2.64888i	−0.155014	−	0.155014i
$293$	−18.6779	+	7.73665i	−1.09118	+	0.451980i	−0.854417	−	0.519588i	$-0.826085\pi$
$293$	−18.6779	+	7.73665i	−1.09118	+	0.451980i	−0.236759	+	0.971568i	$0.576085\pi$
$294$	17.0178	−	7.04899i	0.992497	−	0.411106i
$295$	−14.3346	+	5.93757i	−0.834590	+	0.345698i
$296$	−2.37868	+	0.985281i	−0.138258	+	0.0572683i
$297$	−1.83907	+	4.43990i	−0.106713	+	0.257629i
$298$	−0.113878	+	0.113878i	−0.00659676	+	0.00659676i
$299$	−18.0242	−	18.0242i	−1.04237	−	1.04237i
$300$	10.2210	−	24.6756i	0.590108	−	1.42465i
$301$			1.29351i			0.0745566i
$302$			7.51751i			0.432584i
$303$	29.1276	−	29.1276i	1.67333	−	1.67333i
$304$	1.19157	+	2.87670i	0.0683412	+	0.164990i
$305$	3.88924	+	9.38945i	0.222697	+	0.537638i
$306$	6.42256	+	15.5054i	0.367153	+	0.886386i
$307$			5.09558i			0.290820i	0.989371	+	0.145410i	$0.0464502\pi$
$307$			5.09558i			0.290820i	−0.989371	+	0.145410i	$0.953550\pi$
$308$			0.243704i			0.0138863i
$309$	−28.4237	+	11.7735i	−1.61697	+	0.669769i
$310$	−7.45278	+	17.9926i	−0.423290	+	1.02191i
$311$		−	33.5051i		−	1.89990i	−0.312401	−	0.949950i	$-0.601133\pi$
$311$		−	33.5051i		−	1.89990i	0.312401	−	0.949950i	$-0.398867\pi$
$312$	−7.24202	+	7.24202i	−0.409998	+	0.409998i
$313$	−1.04515			−0.0590753			−0.0295377	−	0.999564i	$-0.509403\pi$
$313$	−1.04515			−0.0590753			−0.0295377	+	0.999564i	$0.509403\pi$
$314$	−0.0813988	−	0.0337165i	−0.00459360	−	0.00190273i
$315$	1.96961			0.110975
$316$	6.48393	−	2.68573i	0.364750	−	0.151084i
$317$	9.53200	+	23.0123i	0.535371	+	1.29250i	0.927924	+	0.372770i	$0.121592\pi$
$317$	9.53200	+	23.0123i	0.535371	+	1.29250i	−0.392553	+	0.919729i	$0.628408\pi$
$318$	13.4877			0.756350
$319$	−7.56691	−	7.56691i	−0.423666	−	0.423666i
$320$			3.88924i			0.217415i
$321$	−5.11561			−0.285525
$322$	−0.321520	−	0.776218i	−0.0179176	−	0.0432569i
$323$	−9.33860	−	9.33860i	−0.519613	−	0.519613i
$324$	5.21380			0.289655
$325$	−36.3269	+	15.0471i	−2.01505	+	0.834663i
$326$	−0.227005	−	0.0940286i	−0.0125727	−	0.00520777i
$327$	16.1966	+	39.1020i	0.895673	+	2.16235i
$328$	−1.40035	+	1.40035i	−0.0773215	+	0.0773215i
$329$	−0.193063			−0.0106439
$330$	7.47497	−	18.0462i	0.411484	−	0.993409i
$331$	15.9398			0.876133			0.438066	−	0.898943i	$-0.355663\pi$
$331$	15.9398			0.876133			0.438066	+	0.898943i	$0.355663\pi$
$332$			8.44668i			0.463572i
$333$	3.89863	+	9.41212i	0.213644	+	0.515781i
$334$	−1.15795	+	2.79553i	−0.0633601	+	0.152965i
$335$	−12.4776	+	30.1235i	−0.681723	+	1.64582i
$336$	−0.311879	+	0.129185i	−0.0170144	+	0.00704760i
$337$		−	32.1714i		−	1.75249i	−0.481868	−	0.876244i	$-0.660042\pi$
$337$		−	32.1714i		−	1.75249i	0.481868	−	0.876244i	$-0.339958\pi$
$338$	2.07770			0.113012
$339$	−0.430262	+	1.03875i	−0.0233686	+	0.0564169i
$340$	−6.31279	−	15.2404i	−0.342359	−	0.826528i
$341$	−3.64882	+	8.80902i	−0.197595	+	0.477035i
$342$	11.3827	−	4.71488i	0.615508	−	0.254952i
$343$	−1.26552	−	1.26552i	−0.0683316	−	0.0683316i
$344$			10.1066i			0.544911i
$345$			67.3404i			3.62548i
$346$	6.70458	+	6.70458i	0.360440	+	0.360440i
$347$	5.74147	−	13.8611i	0.308218	−	0.744105i	−0.691545	−	0.722334i	$-0.743069\pi$
$347$	5.74147	−	13.8611i	0.308218	−	0.744105i	0.999763	−	0.0217711i	$-0.00693050\pi$
$348$	5.67260	−	13.6949i	0.304083	−	0.734122i
$349$	5.48632	+	13.2452i	0.293676	+	0.708997i	0.999999	+	0.00110731i	$0.000352469\pi$
$349$	5.48632	+	13.2452i	0.293676	+	0.708997i	−0.706323	+	0.707889i	$0.749648\pi$
$350$	−1.29601			−0.0692749
$351$	6.92966	+	6.92966i	0.369878	+	0.369878i
$352$			1.90414i			0.101491i
$353$	20.5778	+	8.52361i	1.09525	+	0.453666i	0.855833	−	0.517251i	$-0.173045\pi$
$353$	20.5778	+	8.52361i	1.09525	+	0.453666i	0.239414	+	0.970918i	$0.423045\pi$
$354$	−7.44040	−	7.44040i	−0.395453	−	0.395453i
$355$	9.56670	−	23.0961i	0.507748	−	1.22581i
$356$	−11.2906	−	11.2906i	−0.598401	−	0.598401i
$357$	1.01245	−	1.01245i	0.0535845	−	0.0535845i
$358$	−17.3537	+	17.3537i	−0.917173	+	0.917173i
$359$	−17.2019	−	7.12527i	−0.907883	−	0.376057i	−0.120637	−	0.992697i	$-0.538494\pi$
$359$	−17.2019	−	7.12527i	−0.907883	−	0.376057i	−0.787246	+	0.616639i	$0.788494\pi$
$360$	15.3892			0.811082
$361$	6.57944	−	6.57944i	0.346287	−	0.346287i
$362$	−5.68131			−0.298603
$363$	−7.44329	+	17.9697i	−0.390671	+	0.943164i
$364$	0.459142	+	0.190183i	0.0240656	+	0.00996829i
$365$	10.3021	−	10.3021i	0.539238	−	0.539238i
$366$	−4.87362	+	4.87362i	−0.254748	+	0.254748i
$367$	−16.1679	−	6.69695i	−0.843956	−	0.349578i	−0.0815436	−	0.996670i	$-0.525985\pi$
$367$	−16.1679	−	6.69695i	−0.843956	−	0.349578i	−0.762412	+	0.647092i	$0.775985\pi$
$368$	−2.51214	−	6.06484i	−0.130954	−	0.316152i
$369$	5.54101	+	5.54101i	0.288453	+	0.288453i
$370$	−3.83199	−	9.25125i	−0.199216	−	0.480950i
$371$	−0.250457	−	0.604657i	−0.0130031	−	0.0313922i
$372$	−13.2075			−0.684778
$373$	25.3053	+	25.3053i	1.31026	+	1.31026i	0.921224	+	0.389033i	$0.127191\pi$
$373$	25.3053	+	25.3053i	1.31026	+	1.31026i	0.389033	+	0.921224i	$0.372809\pi$
$374$	−3.09069	−	7.46157i	−0.159816	−	0.385829i
$375$	48.5826	+	20.1236i	2.50879	+	1.03918i
$376$	−1.50846			−0.0777930
$377$	−20.1613	+	8.35108i	−1.03836	+	0.430103i
$378$	0.123613	+	0.298428i	0.00635795	+	0.0153495i
$379$		−	14.8207i		−	0.761288i	−0.924722	−	0.380644i	$-0.875702\pi$
$379$		−	14.8207i		−	0.761288i	0.924722	−	0.380644i	$-0.124298\pi$
$380$	−11.1882	+	4.63430i	−0.573942	+	0.237735i
$381$		−	45.1053i		−	2.31082i
$382$	−4.63132	−	11.1810i	−0.236959	−	0.572069i
$383$			24.5186i			1.25284i	0.779484	+	0.626422i	$0.215481\pi$
$383$			24.5186i			1.25284i	−0.779484	+	0.626422i	$0.784519\pi$
$384$	−2.43681	+	1.00936i	−0.124353	+	0.0515087i
$385$	−0.947823			−0.0483055
$386$	20.2572	+	8.39081i	1.03107	+	0.427081i
$387$	39.9905			2.03283
$388$	5.14847	−	2.13257i	0.261374	−	0.108265i
$389$	−9.28048	+	22.4051i	−0.470539	+	1.13598i	0.493387	+	0.869810i	$0.335759\pi$
$389$	−9.28048	+	22.4051i	−0.470539	+	1.13598i	−0.963926	+	0.266172i	$0.914241\pi$
$390$	−28.1659	−	28.1659i	−1.42624	−	1.42624i
$391$	19.6882	+	19.6882i	0.995675	+	0.995675i
$392$	−4.93816	−	4.93816i	−0.249415	−	0.249415i
$393$	−20.8835	+	20.8835i	−1.05343	+	1.05343i
$394$	−5.12751	+	5.12751i	−0.258320	+	0.258320i
$395$	10.4455	+	25.2176i	0.525568	+	1.26883i
$396$	7.53442			0.378619
$397$			27.7746i			1.39397i	0.717086	+	0.696984i	$0.245475\pi$
$397$			27.7746i			1.39397i	−0.717086	+	0.696984i	$0.754525\pi$
$398$	21.9431	+	9.08912i	1.09991	+	0.455597i
$399$	−0.743252	−	0.743252i	−0.0372091	−	0.0372091i
$400$	−10.1262			−0.506309
$401$	−14.8858	+	13.3945i	−0.743361	+	0.668890i
$401$	−14.8858	+	13.3945i	−0.743361	+	0.668890i
$402$	−22.1122			−1.10286
$403$	13.7489	+	13.7489i	0.684880	+	0.684880i
$404$	−14.4287	−	5.97657i	−0.717855	−	0.297345i
$405$			20.2777i			1.00761i
$406$	−0.719283			−0.0356974
$407$	−1.87611	−	4.52933i	−0.0929954	−	0.224511i
$408$	7.91059	−	7.91059i	0.391632	−	0.391632i
$409$	0.564726	−	0.564726i	0.0279239	−	0.0279239i	−0.693007	−	0.720931i	$-0.743715\pi$
$409$	0.564726	−	0.564726i	0.0279239	−	0.0279239i	0.720931	+	0.693007i	$0.243715\pi$
$410$	−5.44630	−	5.44630i	−0.268974	−	0.268974i
$411$	−34.3844	−	34.3844i	−1.69606	−	1.69606i
$412$	8.24789	+	8.24789i	0.406344	+	0.406344i
$413$	−0.195393	+	0.471719i	−0.00961464	+	0.0232118i
$414$	−23.9978	+	9.94020i	−1.17943	+	0.488534i
$415$	−32.8512			−1.61260
$416$	3.58743	+	1.48596i	0.175888	+	0.0728552i
$417$	−51.8643			−2.53981
$418$	−5.47764	+	2.26891i	−0.267920	+	0.110976i
$419$			32.3404i			1.57993i	0.613151	+	0.789965i	$0.289902\pi$
$419$			32.3404i			1.57993i	−0.613151	+	0.789965i	$0.710098\pi$
$420$	−0.502430	−	1.21297i	−0.0245161	−	0.0591870i
$421$			18.5449i			0.903825i	0.892062	+	0.451912i	$0.149258\pi$
$421$			18.5449i			0.903825i	−0.892062	+	0.451912i	$0.850742\pi$
$422$	−15.0981	+	6.25385i	−0.734966	+	0.304433i
$423$			5.96879i			0.290212i
$424$	−1.95690	−	4.72438i	−0.0950356	−	0.229436i
$425$	39.6806	−	16.4362i	1.92479	−	0.797274i
$426$	16.9537			0.821410
$427$	0.308987	+	0.127986i	0.0149529	+	0.00619370i
$428$	0.742216	+	1.79187i	0.0358763	+	0.0866132i
$429$	−13.7898	−	13.7898i	−0.665778	−	0.665778i
$430$	−39.3070			−1.89555
$431$	−7.75197	−	18.7149i	−0.373399	−	0.901466i	−0.993169	−	0.116682i	$-0.962774\pi$
$431$	−7.75197	−	18.7149i	−0.373399	−	0.901466i	0.619770	−	0.784784i	$-0.287226\pi$
$432$	0.965826	+	2.33171i	0.0464683	+	0.112184i
$433$	−25.6257	−	25.6257i	−1.23149	−	1.23149i	−0.963391	−	0.268100i	$-0.913604\pi$
$433$	−25.6257	−	25.6257i	−1.23149	−	1.23149i	−0.268100	−	0.963391i	$-0.586396\pi$
$434$	0.245255	+	0.592098i	0.0117726	+	0.0284216i
$435$	53.2626	+	22.0621i	2.55375	+	1.05780i
$436$	11.3465	−	11.3465i	0.543399	−	0.543399i
$437$	14.4534	−	14.4534i	0.691398	−	0.691398i
$438$	9.12851	+	3.78115i	0.436177	+	0.180670i
$439$	4.96518	−	11.9870i	0.236975	−	0.572108i	−0.759992	−	0.649932i	$-0.774797\pi$
$439$	4.96518	−	11.9870i	0.236975	−	0.572108i	0.996967	+	0.0778239i	$0.0247972\pi$
$440$	−7.40565			−0.353050
$441$	−19.5397	+	19.5397i	−0.930460	+	0.930460i
$442$	−16.4697			−0.783381
$443$	14.1782	+	5.87279i	0.673625	+	0.279025i	0.693159	−	0.720785i	$-0.256218\pi$
$443$	14.1782	+	5.87279i	0.673625	+	0.279025i	−0.0195342	+	0.999809i	$0.506218\pi$
$444$	4.80189	−	4.80189i	0.227888	−	0.227888i
$445$	43.9119	−	43.9119i	2.08162	−	2.08162i
$446$	13.2698	+	13.2698i	0.628345	+	0.628345i
$447$	0.162555	−	0.392443i	0.00768859	−	0.0185619i
$448$	0.0905001	+	0.0905001i	0.00427573	+	0.00427573i
$449$	18.6935	+	7.74312i	0.882203	+	0.365420i	0.777351	−	0.629068i	$-0.216563\pi$
$449$	18.6935	+	7.74312i	0.882203	+	0.365420i	0.104852	+	0.994488i	$0.466563\pi$
$450$			40.0680i			1.88882i
$451$	−2.66646	−	2.66646i	−0.125559	−	0.125559i
$452$	0.426272			0.0200501
$453$	−7.58788	−	18.3188i	−0.356510	−	0.860690i
$454$	9.40332	−	22.7016i	0.441320	−	1.06544i
$455$	−0.739667	+	1.78571i	−0.0346761	+	0.0837155i
$456$	−5.80727	−	5.80727i	−0.271950	−	0.271950i
$457$			36.0310i			1.68546i	0.538336	+	0.842730i	$0.319053\pi$
$457$			36.0310i			1.68546i	−0.538336	+	0.842730i	$0.680947\pi$
$458$			12.3713i			0.578071i
$459$	−7.56939	−	7.56939i	−0.353309	−	0.353309i
$460$	23.5876	−	9.77031i	1.09978	−	0.455543i
$461$	6.42491	−	15.5111i	0.299238	−	0.722424i	−0.700722	−	0.713435i	$-0.747139\pi$
$461$	6.42491	−	15.5111i	0.299238	−	0.722424i	0.999960	−	0.00898916i	$-0.00286138\pi$
$462$	−0.245985	−	0.593861i	−0.0114443	−	0.0276289i
$463$	−4.35928	+	10.5242i	−0.202593	+	0.489102i	−0.992222	−	0.124482i	$-0.960273\pi$
$463$	−4.35928	+	10.5242i	−0.202593	+	0.489102i	0.789629	+	0.613585i	$0.210273\pi$
$464$	−5.61999			−0.260901
$465$		−	51.3672i		−	2.38210i
$466$	25.3328	−	10.4932i	1.17352	−	0.486088i
$467$	−14.4419	+	34.8657i	−0.668289	+	1.61339i	0.116182	+	0.993228i	$0.462934\pi$
$467$	−14.4419	+	34.8657i	−0.668289	+	1.61339i	−0.784472	+	0.620165i	$0.787066\pi$
$468$	5.87975	−	14.1950i	0.271792	−	0.656163i
$469$	0.410610	+	0.991301i	0.0189602	+	0.0457740i
$470$		−	5.86677i		−	0.270614i
$471$	0.232386			0.0107078
$472$	−1.52667	+	3.68570i	−0.0702705	+	0.169648i
$473$	−19.2444			−0.884856
$474$	−13.0893	+	13.0893i	−0.601209	+	0.601209i
$475$	−12.0660	−	29.1300i	−0.553628	−	1.33658i
$476$	−0.501529	−	0.207740i	−0.0229876	−	0.00952176i
$477$	−18.6938	+	7.74321i	−0.855928	+	0.354537i
$478$	17.9608			0.821509
$479$	−14.4574	−	14.4574i	−0.660574	−	0.660574i	0.294942	−	0.955515i	$-0.404700\pi$
$479$	−14.4574	−	14.4574i	−0.660574	−	0.660574i	−0.955515	+	0.294942i	$0.904700\pi$
$480$	−3.92565	−	9.47735i	−0.179180	−	0.432580i
$481$	−9.99742			−0.455843
$482$		−	2.28138i		−	0.103914i
$483$	1.56697	+	1.56697i	0.0712995	+	0.0712995i
$484$	7.37426			0.335194
$485$	8.29407	+	20.0236i	0.376614	+	0.909227i
$486$	−19.7002	+	8.16008i	−0.893618	+	0.370149i
$487$	−2.58034			−0.116926			−0.0584632	−	0.998290i	$-0.518620\pi$
$487$	−2.58034			−0.116926			−0.0584632	+	0.998290i	$0.518620\pi$
$488$	2.41421	+	0.999999i	0.109286	+	0.0452678i
$489$	0.648078			0.0293071
$490$	19.2057	−	19.2057i	0.867625	−	0.867625i
$491$		−	19.7589i		−	0.891709i	−0.895106	−	0.445854i	$-0.852900\pi$
$491$		−	19.7589i		−	0.891709i	0.895106	−	0.445854i	$-0.147100\pi$
$492$	1.99894	−	4.82586i	0.0901190	−	0.217566i
$493$	22.0226	−	9.12204i	0.991846	−	0.410836i
$494$			12.0906i			0.543981i
$495$			29.3032i			1.31708i
$496$	1.91626	+	4.62625i	0.0860425	+	0.207725i
$497$	−0.314820	−	0.760042i	−0.0141216	−	0.0340925i
$498$	−8.52575	−	20.5830i	−0.382048	−	0.922346i
$499$	0.229518	−	0.229518i	0.0102746	−	0.0102746i	−0.701951	−	0.712225i	$-0.747687\pi$
$499$	0.229518	−	0.229518i	0.0102746	−	0.0102746i	0.712225	+	0.701951i	$0.247687\pi$
$500$		−	19.9369i		−	0.891607i
$501$		−	7.98098i		−	0.356564i
$502$	−0.0696472	+	0.168143i	−0.00310851	+	0.00750460i
$503$	6.25369	+	6.25369i	0.278838	+	0.278838i	0.832645	−	0.553807i	$-0.186825\pi$
$503$	6.25369	+	6.25369i	0.278838	+	0.278838i	−0.553807	+	0.832645i	$0.686825\pi$
$504$	0.358097	−	0.358097i	0.0159509	−	0.0159509i
$505$	23.2443	−	56.1167i	1.03436	−	2.49716i
$506$	11.5483	−	4.78346i	0.513384	−	0.212651i
$507$	−5.06297	+	2.09715i	−0.224855	+	0.0931378i
$508$	−15.7992	+	6.54426i	−0.700978	+	0.290355i
$509$	−20.0162	+	8.29096i	−0.887201	+	0.367490i	−0.779285	−	0.626670i	$-0.784418\pi$
$509$	−20.0162	+	8.29096i	−0.887201	+	0.367490i	−0.107915	+	0.994160i	$0.534418\pi$
$510$	30.7662	+	30.7662i	1.36235	+	1.36235i
$511$		−	0.479448i		−	0.0212095i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−5.55679	+	5.55679i	−0.245338	+	0.245338i
$514$			20.4765i			0.903181i
$515$	−32.0780	+	32.0780i	−1.41353	+	1.41353i
$516$	−10.2012	−	24.6279i	−0.449083	−	1.08418i
$517$		−	2.87232i		−	0.126324i
$518$	−0.304439	−	0.126103i	−0.0133763	−	0.00554063i
$519$	−23.1051	−	9.57046i	−1.01420	−	0.420097i
$520$	−5.77926	+	13.9524i	−0.253437	+	0.611851i
$521$	30.9938	−	12.8380i	1.35786	−	0.562445i	0.419392	−	0.907805i	$-0.362243\pi$
$521$	30.9938	−	12.8380i	1.35786	−	0.562445i	0.938470	+	0.345360i	$0.112243\pi$
$522$			22.2376i			0.973312i
$523$	3.37632	−	8.15116i	0.147636	−	0.356425i	−0.832710	−	0.553709i	$-0.813212\pi$
$523$	3.37632	−	8.15116i	0.147636	−	0.356425i	0.980346	+	0.197284i	$0.0632120\pi$
$524$	10.3449	+	4.28501i	0.451920	+	0.187191i
$525$	3.15814	−	1.30815i	0.137833	−	0.0570922i
$526$	29.8423			1.30119
$527$	−15.0181	−	15.0181i	−0.654200	−	0.654200i
$528$	−1.92196	−	4.64003i	−0.0836427	−	0.201931i
$529$	−14.2080	+	14.2080i	−0.617738	+	0.617738i
$530$	18.3742	−	7.61086i	0.798126	−	0.330595i
$531$	14.5838	+	6.04081i	0.632884	+	0.262149i
$532$	−0.152505	+	0.368179i	−0.00661192	+	0.0159626i
$533$	−7.10453	+	2.94279i	−0.307731	+	0.127466i
$534$	38.9094	+	16.1168i	1.68377	+	0.697442i
$535$	−6.96900	+	2.88665i	−0.301296	+	0.124801i
$536$	3.20823	+	7.74535i	0.138574	+	0.334548i
$537$	24.7716	−	59.8040i	1.06897	−	2.58073i
$538$	19.8079	+	8.20470i	0.853980	+	0.353730i
$539$	9.40295	−	9.40295i	0.405014	−	0.405014i
$540$	−9.06858	+	3.75633i	−0.390250	+	0.161647i
$541$	−14.9027	−	14.9027i	−0.640716	−	0.640716i	0.310015	−	0.950732i	$-0.399666\pi$
$541$	−14.9027	−	14.9027i	−0.640716	−	0.640716i	−0.950732	+	0.310015i	$0.899666\pi$
$542$	−2.21843	−	5.35577i	−0.0952898	−	0.230050i
$543$	13.8443	−	5.73450i	0.594116	−	0.246091i
$544$	−3.91861	−	1.62314i	−0.168009	−	0.0695916i
$545$	44.1292	+	44.1292i	1.89029	+	1.89029i
$546$	−1.31081			−0.0560974
$547$	−33.9468			−1.45146			−0.725731	−	0.687978i	$-0.758498\pi$
$547$	−33.9468			−1.45146			−0.725731	+	0.687978i	$0.758498\pi$
$548$	−7.05519	+	17.0327i	−0.301383	+	0.727603i
$549$	3.95687	−	9.55272i	0.168875	−	0.407700i
$550$		−	19.2816i		−	0.822172i
$551$	−6.69661	−	16.1670i	−0.285285	−	0.688739i
$552$	12.2432	+	12.2432i	0.521106	+	0.521106i
$553$	0.829856	+	0.343738i	0.0352891	+	0.0146172i
$554$	5.76841	+	2.38935i	0.245076	+	0.101514i
$555$	18.6757	+	18.6757i	0.792740	+	0.792740i
$556$	7.52491	+	18.1667i	0.319127	+	0.770441i
$557$		−	16.7627i		−	0.710259i	−0.934817	−	0.355130i	$-0.884437\pi$
$557$		−	16.7627i		−	0.710259i	0.934817	−	0.355130i	$-0.115563\pi$
$558$	18.3055	−	7.58238i	0.774933	−	0.320988i
$559$	−15.0180	+	36.2567i	−0.635194	+	1.53349i
$560$	−0.351977	+	0.351977i	−0.0148737	+	0.0148737i
$561$	15.0628	+	15.0628i	0.635954	+	0.635954i
$562$	−25.3899	−	10.5168i	−1.07101	−	0.443627i
$563$	3.81801	−	3.81801i	0.160910	−	0.160910i	−0.622060	−	0.782970i	$-0.713704\pi$
$563$	3.81801	−	3.81801i	0.160910	−	0.160910i	0.782970	+	0.622060i	$0.213704\pi$
$564$	3.67584	−	1.52258i	0.154781	−	0.0641123i
$565$			1.65787i			0.0697473i
$566$	2.37369	+	5.73059i	0.0997735	+	0.240874i
$567$	0.471849	+	0.471849i	0.0198158	+	0.0198158i
$568$	−2.45979	−	5.93845i	−0.103210	−	0.249172i
$569$	17.4380	−	42.0991i	0.731039	−	1.76488i	0.0919342	−	0.995765i	$-0.470695\pi$
$569$	17.4380	−	42.0991i	0.731039	−	1.76488i	0.639105	−	0.769120i	$-0.279305\pi$
$570$	22.5858	−	22.5858i	0.946017	−	0.946017i
$571$	−15.1673	−	6.28249i	−0.634730	−	0.262914i	0.0420310	−	0.999116i	$-0.486617\pi$
$571$	−15.1673	−	6.28249i	−0.634730	−	0.262914i	−0.676761	+	0.736202i	$0.736617\pi$
$572$	−2.82947	+	6.83095i	−0.118306	+	0.285616i
$573$	22.5713	+	22.5713i	0.942930	+	0.942930i
$574$	−0.253464			−0.0105794
$575$	25.4384	+	61.4136i	1.06085	+	2.56113i
$576$	2.79793	−	2.79793i	0.116580	−	0.116580i
$577$	−11.9350	−	11.9350i	−0.496859	−	0.496859i	0.413600	−	0.910459i	$-0.364271\pi$
$577$	−11.9350	−	11.9350i	−0.496859	−	0.496859i	−0.910459	+	0.413600i	$0.864271\pi$
$578$	0.990102			0.0411828
$579$	−57.8324			−2.40343
$580$		−	21.8575i		−	0.907583i
$581$	−0.764426	+	0.764426i	−0.0317137	+	0.0317137i
$582$	−10.3933	+	10.3933i	−0.430818	+	0.430818i
$583$	8.99587	−	3.72621i	0.372571	−	0.154324i
$584$		−	3.74608i		−	0.155014i
$585$	55.2076	+	22.8678i	2.28256	+	0.945465i
$586$	−18.6779	−	7.73665i	−0.771578	−	0.319598i
$587$	26.3191	−	26.3191i	1.08630	−	1.08630i	0.0903983	−	0.995906i	$-0.471186\pi$
$587$	26.3191	−	26.3191i	1.08630	−	1.08630i	0.995906	−	0.0903983i	$-0.0288140\pi$
$588$	17.0178	+	7.04899i	0.701801	+	0.290696i
$589$	−11.0250	+	11.0250i	−0.454277	+	0.454277i
$590$	−14.3346	−	5.93757i	−0.590144	−	0.244446i
$591$	7.31928	−	17.6703i	0.301075	−	0.726859i
$592$	−2.37868	−	0.985281i	−0.0977631	−	0.0404948i
$593$	−5.37065	+	12.9659i	−0.220546	+	0.532446i	−0.994964	−	0.100228i	$-0.968043\pi$
$593$	−5.37065	+	12.9659i	−0.220546	+	0.532446i	0.774418	+	0.632674i	$0.218043\pi$
$594$	−4.43990	+	1.83907i	−0.182171	+	0.0754578i
$595$	0.807951	−	1.95057i	0.0331228	−	0.0799655i
$596$	−0.161047			−0.00659676
$597$	−62.6454			−2.56391
$598$		−	25.4901i		−	1.04237i
$599$	24.1893	−	24.1893i	0.988347	−	0.988347i	−0.0115856	−	0.999933i	$-0.503688\pi$
$599$	24.1893	−	24.1893i	0.988347	−	0.988347i	0.999933	+	0.0115856i	$0.00368791\pi$
$600$	24.6756	−	10.2210i	1.00738	−	0.417269i
$601$	12.9775	−	12.9775i	0.529364	−	0.529364i	−0.391018	−	0.920383i	$-0.627877\pi$
$601$	12.9775	−	12.9775i	0.529364	−	0.529364i	0.920383	+	0.391018i	$0.127877\pi$
$602$	−0.914649	+	0.914649i	−0.0372783	+	0.0372783i
$603$	30.6473	−	12.6945i	1.24806	−	0.516962i
$604$	−5.31568	+	5.31568i	−0.216292	+	0.216292i
$605$			28.6803i			1.16602i
$606$	41.1926			1.67333
$607$	−20.2773			−0.823032			−0.411516	−	0.911403i	$-0.635001\pi$
$607$	−20.2773			−0.823032			−0.411516	+	0.911403i	$0.635001\pi$
$608$	−1.19157	+	2.87670i	−0.0483245	+	0.116666i
$609$	1.75276	−	0.726016i	0.0710253	−	0.0294197i
$610$	−3.88924	+	9.38945i	−0.157471	+	0.380168i
$611$	−5.41150	−	2.24152i	−0.218926	−	0.0906820i
$612$	−6.42256	+	15.5054i	−0.259617	+	0.626770i
$613$	−8.16611	−	3.38251i	−0.329826	−	0.136618i	0.211624	−	0.977351i	$-0.432125\pi$
$613$	−8.16611	−	3.38251i	−0.329826	−	0.136618i	−0.541451	+	0.840733i	$0.682125\pi$
$614$	−3.60312	+	3.60312i	−0.145410	+	0.145410i
$615$	18.7689	+	7.77434i	0.756835	+	0.313491i
$616$	−0.172325	+	0.172325i	−0.00694316	+	0.00694316i
$617$	16.4031	+	6.79440i	0.660365	+	0.273532i	0.687592	−	0.726097i	$-0.258668\pi$
$617$	16.4031	+	6.79440i	0.660365	+	0.273532i	−0.0272269	+	0.999629i	$0.508668\pi$
$618$	−28.4237	−	11.7735i	−1.14337	−	0.473598i
$619$			1.00275i			0.0403039i	0.999797	+	0.0201520i	$0.00641500\pi$
$619$			1.00275i			0.0403039i	−0.999797	+	0.0201520i	$0.993585\pi$
$620$	−17.9926	+	7.45278i	−0.722600	+	0.299311i
$621$	11.7152	−	11.7152i	0.470113	−	0.470113i
$622$	23.6917	−	23.6917i	0.949950	−	0.949950i
$623$		−	2.04360i		−	0.0818752i
$624$	−10.2418			−0.409998
$625$	26.9086			1.07634
$626$	−0.739032	−	0.739032i	−0.0295377	−	0.0295377i
$627$	11.0578	−	11.0578i	0.441607	−	0.441607i
$628$	−0.0337165	−	0.0813988i	−0.00134543	−	0.00324816i
$629$	10.9204			0.435424
$630$	1.39273	+	1.39273i	0.0554875	+	0.0554875i
$631$	−1.08476	+	2.61884i	−0.0431835	+	0.104254i	−0.944000	−	0.329947i	$-0.892969\pi$
$631$	−1.08476	+	2.61884i	−0.0431835	+	0.104254i	0.900816	+	0.434201i	$0.142969\pi$
$632$	6.48393	+	2.68573i	0.257917	+	0.106833i
$633$	30.4789	−	30.4789i	1.21143	−	1.21143i
$634$	−9.53200	+	23.0123i	−0.378564	+	0.913935i
$635$	−25.4522	−	61.4470i	−1.01004	−	2.43845i
$636$	9.53721	+	9.53721i	0.378175	+	0.378175i
$637$	−10.3774	−	25.0532i	−0.411167	−	0.992645i
$638$		−	10.7012i		−	0.423666i
$639$	−23.4977	+	9.73306i	−0.929554	+	0.385034i
$640$	−2.75011	+	2.75011i	−0.108708	+	0.108708i
$641$	−18.4219	−	7.63062i	−0.727623	−	0.301391i	−0.0120483	−	0.999927i	$-0.503835\pi$
$641$	−18.4219	−	7.63062i	−0.727623	−	0.301391i	−0.715575	+	0.698536i	$0.753835\pi$
$642$	−3.61728	−	3.61728i	−0.142763	−	0.142763i
$643$	−8.41655	+	8.41655i	−0.331917	+	0.331917i	−0.853314	−	0.521397i	$-0.825411\pi$
$643$	−8.41655	+	8.41655i	−0.331917	+	0.331917i	0.521397	+	0.853314i	$0.325411\pi$
$644$	0.321520	−	0.776218i	0.0126697	−	0.0305873i
$645$	95.7838	−	39.6749i	3.77148	−	1.56220i
$646$		−	13.2068i		−	0.519613i
$647$	10.1948	+	24.6123i	0.400797	+	0.967610i	0.987473	+	0.157788i	$0.0504363\pi$
$647$	10.1948	+	24.6123i	0.400797	+	0.967610i	−0.586676	+	0.809822i	$0.699564\pi$
$648$	3.68671	+	3.68671i	0.144828	+	0.144828i
$649$	−7.01807	−	2.90698i	−0.275483	−	0.114109i
$650$	−36.3269	−	15.0471i	−1.42486	−	0.590196i
$651$	−1.19528	−	1.19528i	−0.0468468	−	0.0468468i
$652$	−0.0940286	−	0.227005i	−0.00368245	−	0.00889021i
$653$		−	22.6301i		−	0.885586i	−0.896624	−	0.442793i	$-0.853988\pi$
$653$		−	22.6301i		−	0.885586i	0.896624	−	0.442793i	$-0.146012\pi$
$654$	−16.1966	+	39.1020i	−0.633337	+	1.52901i
$655$	−16.6654	+	40.2339i	−0.651172	+	1.57207i
$656$	−1.98040			−0.0773215
$657$	−14.8228			−0.578291
$658$	−0.136516	−	0.136516i	−0.00532195	−	0.00532195i
$659$	6.49747	+	2.69134i	0.253105	+	0.104840i	0.505629	−	0.862751i	$-0.331261\pi$
$659$	6.49747	+	2.69134i	0.253105	+	0.104840i	−0.252524	+	0.967591i	$0.581261\pi$
$660$	18.0462	−	7.47497i	0.702446	−	0.290963i
$661$	1.58920	+	3.83666i	0.0618126	+	0.149229i	0.951768	−	0.306819i	$-0.0992646\pi$
$661$	1.58920	+	3.83666i	0.0618126	+	0.149229i	−0.889955	+	0.456048i	$0.849265\pi$
$662$	11.2712	+	11.2712i	0.438066	+	0.438066i
$663$	40.1335	−	16.6238i	1.55865	−	0.645616i
$664$	−5.97271	+	5.97271i	−0.231786	+	0.231786i
$665$	−1.43194	−	0.593128i	−0.0555281	−	0.0230005i
$666$	−3.89863	+	9.41212i	−0.151069	+	0.364712i
$667$	14.1182	+	34.0843i	0.546659	+	1.31975i
$668$	−2.79553	+	1.15795i	−0.108162	+	0.0448023i
$669$	−45.7302	−	18.9421i	−1.76803	−	0.732342i
$670$	−30.1235	+	12.4776i	−1.16377	+	0.482051i
$671$	−1.90414	+	4.59699i	−0.0735084	+	0.177465i
$672$	−0.311879	−	0.129185i	−0.0120310	−	0.00498340i
$673$	−0.400698	+	0.165975i	−0.0154458	+	0.00639785i	−0.390393	−	0.920648i	$-0.627661\pi$
$673$	−0.400698	+	0.165975i	−0.0154458	+	0.00639785i	0.374947	+	0.927046i	$0.377661\pi$
$674$	22.7486	−	22.7486i	0.876244	−	0.876244i
$675$	−9.78013	−	23.6113i	−0.376437	−	0.908800i
$676$	1.46916	+	1.46916i	0.0565061	+	0.0565061i
$677$	17.8407			0.685676			0.342838	−	0.939395i	$-0.388612\pi$
$677$	17.8407			0.685676			0.342838	+	0.939395i	$0.388612\pi$
$678$	−1.03875	+	0.430262i	−0.0398928	+	0.0165241i
$679$	0.658935	+	0.272940i	0.0252876	+	0.0104745i
$680$	6.31279	−	15.2404i	0.242084	−	0.584443i
$681$			64.8110i			2.48356i
$682$	−8.80902	+	3.64882i	−0.337315	+	0.139720i
$683$	−15.2191	+	36.7421i	−0.582342	+	1.40590i	0.308342	+	0.951276i	$0.400226\pi$
$683$	−15.2191	+	36.7421i	−0.582342	+	1.40590i	−0.890684	+	0.454623i	$0.849774\pi$
$684$	11.3827	+	4.71488i	0.435230	+	0.180278i
$685$	−66.2444	−	27.4393i	−2.53107	−	1.04840i
$686$		−	1.78971i		−	0.0683316i
$687$	−12.4871	−	30.1464i	−0.476411	−	1.15016i
$688$	−7.14644	+	7.14644i	−0.272456	+	0.272456i
$689$		−	19.8562i		−	0.756463i
$690$	−47.6168	+	47.6168i	−1.81274	+	1.81274i
$691$	29.3933	+	29.3933i	1.11818	+	1.11818i	0.992009	+	0.126166i	$0.0402672\pi$
$691$	29.3933	+	29.3933i	1.11818	+	1.11818i	0.126166	+	0.992009i	$0.459733\pi$
$692$			9.48170i			0.360440i
$693$	0.681866	+	0.681866i	0.0259020	+	0.0259020i
$694$	13.8611	−	5.74147i	0.526162	−	0.217943i
$695$	−70.6548	+	29.2662i	−2.68009	+	1.11013i
$696$	13.6949	−	5.67260i	0.519103	−	0.215019i
$697$	7.76040	−	3.21446i	0.293946	−	0.121757i
$698$	−5.48632	+	13.2452i	−0.207660	+	0.501336i
$699$	−51.1399	+	51.1399i	−1.93429	+	1.93429i
$700$	−0.916420	−	0.916420i	−0.0346374	−	0.0346374i
$701$	2.38968	−	5.76921i	0.0902571	−	0.217900i	−0.872304	−	0.488963i	$-0.837375\pi$
$701$	2.38968	−	5.76921i	0.0902571	−	0.217900i	0.962562	+	0.271063i	$0.0873753\pi$
$702$			9.80002i			0.369878i
$703$		−	8.01679i		−	0.302359i
$704$	−1.34643	+	1.34643i	−0.0507454	+	0.0507454i
$705$	5.92169	+	14.2962i	0.223024	+	0.538427i
$706$	8.52361	+	20.5778i	0.320790	+	0.774457i
$707$	−0.764920	−	1.84668i	−0.0287678	−	0.0694516i
$708$		−	10.5223i		−	0.395453i
$709$		−	16.3592i		−	0.614382i	−0.951648	−	0.307191i	$-0.900611\pi$
$709$		−	16.3592i		−	0.614382i	0.951648	−	0.307191i	$-0.0993890\pi$
$710$	23.0961	−	9.56670i	0.866780	−	0.359032i
$711$	10.6271	−	25.6561i	0.398547	−	0.962178i
$712$		−	15.9673i		−	0.598401i
$713$	23.2436	−	23.2436i	0.870479	−	0.870479i
$714$	1.43182			0.0535845
$715$	−26.5672	−	11.0045i	−0.993557	−	0.411545i
$716$	−24.5419			−0.917173
$717$	−43.7672	+	18.1289i	−1.63451	+	0.677038i
$718$	−7.12527	−	17.2019i	−0.265913	−	0.641970i
$719$	4.58241			0.170895			0.0854475	−	0.996343i	$-0.472768\pi$
$719$	4.58241			0.170895			0.0854475	+	0.996343i	$0.472768\pi$
$720$	10.8818	+	10.8818i	0.405541	+	0.405541i
$721$			1.49287i			0.0555974i
$722$	9.30474			0.346287
$723$	2.30274	+	5.55930i	0.0856398	+	0.206753i
$724$	−4.01730	−	4.01730i	−0.149302	−	0.149302i
$725$	56.9090			2.11355
$726$	−17.9697	+	7.44329i	−0.666918	+	0.276246i
$727$	10.0212	+	4.15090i	0.371665	+	0.153949i	0.560694	−	0.828023i	$-0.310534\pi$
$727$	10.0212	+	4.15090i	0.371665	+	0.153949i	−0.189030	+	0.981971i	$0.560534\pi$
$728$	0.190183	+	0.459142i	0.00704865	+	0.0170169i
$729$	28.7091	−	28.7091i	1.06330	−	1.06330i
$730$	14.5694			0.539238
$731$	16.4044	−	39.6038i	0.606740	−	1.46480i
$732$	−6.89234			−0.254748
$733$		−	29.2720i		−	1.08119i	−0.841284	−	0.540593i	$-0.818200\pi$
$733$		−	29.2720i		−	1.08119i	0.841284	−	0.540593i	$-0.181800\pi$
$734$	−6.69695	−	16.1679i	−0.247189	−	0.596767i
$735$	−27.4152	+	66.1862i	−1.01123	+	2.44131i
$736$	2.51214	−	6.06484i	0.0925987	−	0.223553i
$737$	−14.7482	+	6.10891i	−0.543258	+	0.225025i
$738$			7.83617i			0.288453i
$739$	17.6690			0.649963			0.324982	−	0.945720i	$-0.394642\pi$
$739$	17.6690			0.649963			0.324982	+	0.945720i	$0.394642\pi$
$740$	3.83199	−	9.25125i	0.140867	−	0.340083i
$741$	−12.2038	−	29.4625i	−0.448317	−	1.08233i
$742$	0.250457	−	0.604657i	0.00919457	−	0.0221977i
$743$	−25.8778	+	10.7189i	−0.949364	+	0.393239i	−0.802992	−	0.595990i	$-0.796760\pi$
$743$	−25.8778	+	10.7189i	−0.949364	+	0.393239i	−0.146372	+	0.989230i	$0.546760\pi$
$744$	−9.33912	−	9.33912i	−0.342389	−	0.342389i
$745$		−	0.626352i		−	0.0229478i
$746$			35.7870i			1.31026i
$747$	23.6332	+	23.6332i	0.864694	+	0.864694i
$748$	3.09069	−	7.46157i	0.113007	−	0.272822i
$749$	−0.0949936	+	0.229335i	−0.00347099	+	0.00837971i
$750$	20.1236	+	48.5826i	0.734809	+	1.77399i
$751$	2.23729			0.0816397			0.0408199	−	0.999167i	$-0.487003\pi$
$751$	2.23729			0.0816397			0.0408199	+	0.999167i	$0.487003\pi$
$752$	−1.06664	−	1.06664i	−0.0388965	−	0.0388965i
$753$		−	0.480033i		−	0.0174934i
$754$	−20.1613	−	8.35108i	−0.734231	−	0.304128i
$755$	−20.6739	−	20.6739i	−0.752402	−	0.752402i
$756$	−0.123613	+	0.298428i	−0.00449575	+	0.0108537i
$757$	−15.0504	−	15.0504i	−0.547017	−	0.547017i	0.378560	−	0.925577i	$-0.376419\pi$
$757$	−15.0504	−	15.0504i	−0.547017	−	0.547017i	−0.925577	+	0.378560i	$0.876419\pi$
$758$	10.4798	−	10.4798i	0.380644	−	0.380644i
$759$	−23.3128	+	23.3128i	−0.846201	+	0.846201i
$760$	−11.1882	−	4.63430i	−0.405838	−	0.168104i
$761$	3.22960			0.117073			0.0585364	−	0.998285i	$-0.481357\pi$
$761$	3.22960			0.117073			0.0585364	+	0.998285i	$0.481357\pi$
$762$	31.8943	−	31.8943i	1.15541	−	1.15541i
$763$	2.05372			0.0743496
$764$	4.63132	−	11.1810i	0.167555	−	0.404514i
$765$	−60.3043	−	24.9789i	−2.18031	−	0.903113i
$766$	−17.3373	+	17.3373i	−0.626422	+	0.626422i
$767$	−10.9536	+	10.9536i	−0.395511	+	0.395511i
$768$	−2.43681	−	1.00936i	−0.0879309	−	0.0364222i
$769$	−8.94693	−	21.5998i	−0.322635	−	0.778909i	−0.999099	−	0.0424338i	$-0.986489\pi$
$769$	−8.94693	−	21.5998i	−0.322635	−	0.778909i	0.676465	−	0.736475i	$-0.263511\pi$
$770$	−0.670212	−	0.670212i	−0.0241528	−	0.0241528i
$771$	−20.6682	−	49.8975i	−0.744347	−	1.79701i
$772$	8.39081	+	20.2572i	0.301992	+	0.729073i
$773$	28.0041			1.00724			0.503619	−	0.863926i	$-0.332002\pi$
$773$	28.0041			1.00724			0.503619	+	0.863926i	$0.332002\pi$
$774$	28.2775	+	28.2775i	1.01642	+	1.01642i
$775$	−19.4044	−	46.8463i	−0.697025	−	1.68277i
$776$	5.14847	+	2.13257i	0.184819	+	0.0765547i
$777$	0.869144			0.0311804
$778$	−22.4051	+	9.28048i	−0.803260	+	0.332721i
$779$	−2.35978	−	5.69701i	−0.0845479	−	0.204117i
$780$		−	39.8326i		−	1.42624i
$781$	11.3076	−	4.68377i	0.404619	−	0.167599i
$782$			27.8433i			0.995675i
$783$	−5.42793	−	13.1042i	−0.193979	−	0.468306i
$784$		−	6.98362i		−	0.249415i
$785$	0.316579	−	0.131131i	0.0112992	−	0.00468028i
$786$	−29.5338			−1.05343
$787$	−48.5131	−	20.0948i	−1.72931	−	0.716302i	−0.999466	−	0.0326851i	$-0.989594\pi$
$787$	−48.5131	−	20.0948i	−1.72931	−	0.716302i	−0.729841	−	0.683617i	$-0.760406\pi$
$788$	−7.25140			−0.258320
$789$	−72.7201	+	30.1216i	−2.58890	+	1.07236i
$790$	−10.4455	+	25.2176i	−0.371633	+	0.897200i
$791$	0.0385777	+	0.0385777i	0.00137166	+	0.00137166i
$792$	5.32764	+	5.32764i	0.189309	+	0.189309i
$793$	7.17485	+	7.17485i	0.254786	+	0.254786i
$794$	−19.6396	+	19.6396i	−0.696984	+	0.696984i
$795$	−37.0925	+	37.0925i	−1.31554	+	1.31554i
$796$	9.08912	+	21.9431i	0.322155	+	0.777752i
$797$	30.8869			1.09407			0.547035	−	0.837110i	$-0.315757\pi$
$797$	30.8869			1.09407			0.547035	+	0.837110i	$0.315757\pi$
$798$		−	1.05112i		−	0.0372091i
$799$	5.91108	+	2.44845i	0.209119	+	0.0866199i
$800$	−7.16029	−	7.16029i	−0.253154	−	0.253154i
$801$	−63.1806			−2.23238
$802$	−19.9972	−	1.05450i	−0.706126	−	0.0372356i
$803$	7.13306			0.251720
$804$	−15.6357	−	15.6357i	−0.551429	−	0.551429i
$805$	3.01890	+	1.25047i	0.106402	+	0.0440732i
$806$			19.4438i			0.684880i
$807$	−56.5497			−1.99064
$808$	−5.97657	−	14.4287i	−0.210255	−	0.507600i
$809$	−3.91432	+	3.91432i	−0.137620	+	0.137620i	−0.772561	−	0.634941i	$-0.781025\pi$
$809$	−3.91432	+	3.91432i	−0.137620	+	0.137620i	0.634941	+	0.772561i	$0.281025\pi$
$810$	−14.3385	+	14.3385i	−0.503803	+	0.503803i
$811$	−37.1044	−	37.1044i	−1.30291	−	1.30291i	−0.926420	−	0.376491i	$-0.877130\pi$
$811$	−37.1044	−	37.1044i	−1.30291	−	1.30291i	−0.376491	−	0.926420i	$-0.622870\pi$
$812$	−0.508610	−	0.508610i	−0.0178487	−	0.0178487i
$813$	10.8118	+	10.8118i	0.379187	+	0.379187i
$814$	1.87611	−	4.52933i	0.0657576	−	0.158753i
$815$	0.882878	−	0.365700i	0.0309259	−	0.0128099i
$816$	11.1873			0.391632
$817$	−29.0737	−	12.0427i	−1.01716	−	0.421321i
$818$	0.798643			0.0279239
$819$	1.81677	−	0.752529i	0.0634829	−	0.0262955i
$820$		−	7.70223i		−	0.268974i
$821$	2.01343	+	4.86084i	0.0702691	+	0.169645i	0.955112	−	0.296245i	$-0.0957344\pi$
$821$	2.01343	+	4.86084i	0.0702691	+	0.169645i	−0.884843	+	0.465889i	$0.845734\pi$
$822$		−	48.6269i		−	1.69606i
$823$	−35.7669	+	14.8151i	−1.24675	+	0.516422i	−0.905819	−	0.423665i	$-0.860744\pi$
$823$	−35.7669	+	14.8151i	−1.24675	+	0.516422i	−0.340935	+	0.940087i	$0.610744\pi$
$824$			11.6643i			0.406344i
$825$	19.4621	+	46.9857i	0.677585	+	1.63583i
$826$	−0.471719	+	0.195393i	−0.0164132	+	0.00679858i
$827$	−53.3128			−1.85387			−0.926934	−	0.375224i	$-0.877566\pi$
$827$	−53.3128			−1.85387			−0.926934	+	0.375224i	$0.877566\pi$
$828$	−23.9978	−	9.94020i	−0.833980	−	0.345446i
$829$	−9.38302	−	22.6526i	−0.325886	−	0.786758i	−0.998889	−	0.0471184i	$-0.984996\pi$
$829$	−9.38302	−	22.6526i	−0.325886	−	0.786758i	0.673004	−	0.739639i	$-0.265004\pi$
$830$	−23.2293	−	23.2293i	−0.806300	−	0.806300i
$831$	−16.4683			−0.571277
$832$	1.48596	+	3.58743i	0.0515164	+	0.124372i
$833$	11.3354	+	27.3661i	0.392749	+	0.948179i
$834$	−36.6736	−	36.6736i	−1.26990	−	1.26990i
$835$	−4.50353	−	10.8725i	−0.155851	−	0.376258i
$836$	−5.47764	−	2.26891i	−0.189448	−	0.0784720i
$837$	−8.93631	+	8.93631i	−0.308884	+	0.308884i
$838$	−22.8681	+	22.8681i	−0.789965	+	0.789965i
$839$	22.0925	+	9.15103i	0.762719	+	0.315929i	0.729919	−	0.683533i	$-0.239558\pi$
$839$	22.0925	+	9.15103i	0.762719	+	0.315929i	0.0328000	+	0.999462i	$0.489558\pi$
$840$	0.502430	−	1.21297i	0.0173355	−	0.0418515i
$841$	2.58428			0.0891132
$842$	−13.1133	+	13.1133i	−0.451912	+	0.451912i
$843$	72.4858			2.49654
$844$	−15.0981	−	6.25385i	−0.519699	−	0.215266i
$845$	−5.71391	+	5.71391i	−0.196564	+	0.196564i
$846$	−4.22057	+	4.22057i	−0.145106	+	0.145106i
$847$	0.667371	+	0.667371i	0.0229312	+	0.0229312i
$848$	1.95690	−	4.72438i	0.0672003	−	0.162236i
$849$	−11.5685	−	11.5685i	−0.397029	−	0.397029i
$850$	39.6806	+	16.4362i	1.36103	+	0.563758i
$851$			16.9015i			0.579375i
$852$	11.9881	+	11.9881i	0.410705	+	0.410705i
$853$	−10.1052			−0.345996			−0.172998	−	0.984922i	$-0.555345\pi$
$853$	−10.1052			−0.345996			−0.172998	+	0.984922i	$0.555345\pi$
$854$	0.127986	+	0.308987i	0.00437960	+	0.0105733i
$855$	−18.3373	+	44.2702i	−0.627123	+	1.51401i
$856$	−0.742216	+	1.79187i	−0.0253684	+	0.0612448i
$857$	−25.3114	−	25.3114i	−0.864621	−	0.864621i	0.127250	−	0.991871i	$-0.459385\pi$
$857$	−25.3114	−	25.3114i	−0.864621	−	0.864621i	−0.991871	+	0.127250i	$0.959385\pi$
$858$		−	19.5017i		−	0.665778i
$859$		−	6.04570i		−	0.206277i	−0.994667	−	0.103138i	$-0.967112\pi$
$859$		−	6.04570i		−	0.206277i	0.994667	−	0.103138i	$-0.0328884\pi$
$860$	−27.7942	−	27.7942i	−0.947775	−	0.947775i
$861$	0.617645	−	0.255837i	0.0210493	−	0.00871889i
$862$	7.75197	−	18.7149i	0.264033	−	0.637433i
$863$	−3.76294	−	9.08453i	−0.128092	−	0.309241i	0.846803	−	0.531907i	$-0.178524\pi$
$863$	−3.76294	−	9.08453i	−0.128092	−	0.309241i	−0.974895	+	0.222666i	$0.928524\pi$
$864$	−0.965826	+	2.33171i	−0.0328581	+	0.0793264i
$865$	−36.8766			−1.25384
$866$		−	36.2402i		−	1.23149i
$867$	−2.41269	+	0.999371i	−0.0819394	+	0.0339404i
$868$	−0.245255	+	0.592098i	−0.00832450	+	0.0200971i
$869$	−5.11400	+	12.3463i	−0.173481	+	0.418819i
$870$	22.0621	+	53.2626i	0.747975	+	1.80577i
$871$			32.5532i			1.10302i
$872$	16.0464			0.543399
$873$	8.43829	−	20.3718i	0.285593	−	0.689482i
$874$	20.4401			0.691398
$875$	1.80429	−	1.80429i	0.0609963	−	0.0609963i
$876$	3.78115	+	9.12851i	0.127753	+	0.308424i
$877$	−17.8133	−	7.37849i	−0.601511	−	0.249154i	0.0610831	−	0.998133i	$-0.480545\pi$
$877$	−17.8133	−	7.37849i	−0.601511	−	0.249154i	−0.662594	+	0.748979i	$0.730545\pi$
$878$	11.9870	−	4.96518i	0.404542	−	0.167567i
$879$	53.3237			1.79856
$880$	−5.23658	−	5.23658i	−0.176525	−	0.176525i
$881$	7.99198	+	19.2943i	0.269256	+	0.650043i	0.999449	−	0.0331990i	$-0.0105695\pi$
$881$	7.99198	+	19.2943i	0.269256	+	0.650043i	−0.730192	+	0.683242i	$0.760570\pi$
$882$	−27.6333			−0.930460
$883$			30.2364i			1.01754i	0.860904	+	0.508768i	$0.169899\pi$
$883$			30.2364i			1.01754i	−0.860904	+	0.508768i	$0.830101\pi$
$884$	−11.6458	−	11.6458i	−0.391691	−	0.391691i
$885$	40.9238			1.37564
$886$	5.87279	+	14.1782i	0.197300	+	0.476325i
$887$	−18.5724	+	7.69292i	−0.623599	+	0.258303i	−0.672031	−	0.740523i	$-0.734578\pi$
$887$	−18.5724	+	7.69292i	−0.623599	+	0.258303i	0.0484317	+	0.998826i	$0.484578\pi$
$888$	6.79090			0.227888
$889$	−2.02209	−	0.837577i	−0.0678187	−	0.0280914i
$890$	62.1008			2.08162
$891$	−7.02000	+	7.02000i	−0.235179	+	0.235179i
$892$			18.7664i			0.628345i
$893$	1.79744	−	4.33940i	0.0601490	−	0.145212i
$894$	0.392443	−	0.162555i	0.0131252	−	0.00543666i
$895$		−	95.4492i		−	3.19052i
$896$			0.127987i			0.00427573i
$897$	25.7287	+	62.1146i	0.859057	+	2.07395i
$898$	7.74312	+	18.6935i	0.258391	+	0.623811i
$899$	−10.7693	−	25.9995i	−0.359178	−	0.867132i
$900$	−28.3323	+	28.3323i	−0.944411	+	0.944411i
$901$			21.6893i			0.722577i
$902$		−	3.77095i		−	0.125559i
$903$	1.30562	−	3.15204i	0.0434482	−	0.104893i
$904$	0.301420	+	0.301420i	0.0100251	+	0.0100251i
$905$	15.6242	−	15.6242i	0.519367	−	0.519367i
$906$	7.58788	−	18.3188i	0.252090	−	0.608600i
$907$	52.8028	−	21.8716i	1.75329	−	0.726235i	0.755846	−	0.654750i	$-0.227226\pi$
$907$	52.8028	−	21.8716i	1.75329	−	0.726235i	0.997442	−	0.0714855i	$-0.0227740\pi$
$908$	22.7016	−	9.40332i	0.753380	−	0.312060i
$909$	−57.0925	+	23.6485i	−1.89364	+	0.784371i
$910$	−1.78571	+	0.739667i	−0.0591958	+	0.0245197i
$911$	−40.6804	−	40.6804i	−1.34780	−	1.34780i	−0.888046	−	0.459754i	$-0.847938\pi$
$911$	−40.6804	−	40.6804i	−1.34780	−	1.34780i	−0.459754	−	0.888046i	$-0.652062\pi$
$912$		−	8.21271i		−	0.271950i
$913$	−11.3729	−	11.3729i	−0.376386	−	0.376386i
$914$	−25.4778	+	25.4778i	−0.842730	+	0.842730i
$915$		−	26.8060i		−	0.886178i
$916$	−8.74780	+	8.74780i	−0.289035	+	0.289035i
$917$	0.548423	+	1.32401i	0.0181105	+	0.0437227i
$918$		−	10.7047i		−	0.353309i
$919$	29.9411	+	12.4020i	0.987665	+	0.409104i	0.817259	−	0.576270i	$-0.195492\pi$
$919$	29.9411	+	12.4020i	0.987665	+	0.409104i	0.170405	+	0.985374i	$0.445492\pi$
$920$	23.5876	+	9.77031i	0.777660	+	0.322117i
$921$	5.14328	−	12.4170i	0.169477	−	0.409154i
$922$	15.5111	−	6.42491i	0.510831	−	0.211593i
$923$		−	24.9589i		−	0.821532i
$924$	0.245985	−	0.593861i	0.00809232	−	0.0195366i
$925$	24.0869	+	9.97713i	0.791973	+	0.328046i
$926$	−10.5242	+	4.35928i	−0.345848	+	0.143255i
$927$	46.1540			1.51590
$928$	−3.97393	−	3.97393i	−0.130451	−	0.130451i
$929$	17.8848	+	43.1778i	0.586782	+	1.41662i	0.886563	+	0.462608i	$0.153086\pi$
$929$	17.8848	+	43.1778i	0.586782	+	1.41662i	−0.299781	+	0.954008i	$0.596914\pi$
$930$	36.3221	−	36.3221i	1.19105	−	1.19105i
$931$	20.0898	−	8.32147i	0.658417	−	0.272725i
$932$	25.3328	+	10.4932i	0.829804	+	0.343716i
$933$	−33.8188	+	81.6457i	−1.10718	+	2.67296i
$934$	−34.8657	+	14.4419i	−1.14084	+	0.472552i
$935$	29.0198	+	12.0204i	0.949050	+	0.393110i
$936$	14.1950	−	5.87975i	0.463977	−	0.192186i
$937$	11.5967	+	27.9969i	0.378848	+	0.914620i	0.992182	+	0.124797i	$0.0398279\pi$
$937$	11.5967	+	27.9969i	0.378848	+	0.914620i	−0.613334	+	0.789824i	$0.710172\pi$
$938$	−0.410610	+	0.991301i	−0.0134069	+	0.0323671i
$939$	2.54683	+	1.05493i	0.0831128	+	0.0344264i
$940$	4.14843	−	4.14843i	0.135307	−	0.135307i
$941$	27.3485	−	11.3281i	0.891536	−	0.369286i	0.110576	−	0.993868i	$-0.464730\pi$
$941$	27.3485	−	11.3281i	0.891536	−	0.369286i	0.780960	+	0.624581i	$0.214730\pi$
$942$	0.164322	+	0.164322i	0.00535388	+	0.00535388i
$943$	4.97503	+	12.0108i	0.162009	+	0.391125i
$944$	−3.68570	+	1.52667i	−0.119959	+	0.0496887i
$945$	−1.16066	−	0.480759i	−0.0377561	−	0.0156391i
$946$	−13.6078	−	13.6078i	−0.442428	−	0.442428i
$947$	44.4531			1.44453			0.722266	−	0.691616i	$-0.243101\pi$
$947$	44.4531			1.44453			0.722266	+	0.691616i	$0.243101\pi$
$948$	−18.5110			−0.601209
$949$	5.56653	−	13.4388i	0.180697	−	0.436242i
$950$	12.0660	−	29.1300i	0.391474	−	0.945102i
$951$		−	65.6979i		−	2.13040i
$952$	−0.207740	−	0.501529i	−0.00673290	−	0.0162547i
$953$	32.9059	+	32.9059i	1.06593	+	1.06593i	0.997668	+	0.0682579i	$0.0217441\pi$
$953$	32.9059	+	32.9059i	1.06593	+	1.06593i	0.0682579	+	0.997668i	$0.478256\pi$
$954$	−18.6938	−	7.74321i	−0.605233	−	0.250696i
$955$	43.4855	+	18.0123i	1.40716	+	0.582864i
$956$	12.7002	+	12.7002i	0.410754	+	0.410754i
$957$	10.8014	+	26.0769i	0.349160	+	0.842947i
$958$		−	20.4458i		−	0.660574i
$959$	−2.17996	+	0.902970i	−0.0703946	+	0.0291584i
$960$	3.92565	−	9.47735i	0.126700	−	0.305880i
$961$	4.19013	−	4.19013i	0.135165	−	0.135165i
$962$	−7.06925	−	7.06925i	−0.227922	−	0.227922i
$963$	7.09018	+	2.93685i	0.228478	+	0.0946387i
$964$	1.61318	−	1.61318i	0.0519571	−	0.0519571i
$965$	−78.7851	+	32.6339i	−2.53618	+	1.05052i
$966$			2.21603i			0.0712995i
$967$	−7.96393	−	19.2266i	−0.256103	−	0.618287i	0.742571	−	0.669767i	$-0.233606\pi$
$967$	−7.96393	−	19.2266i	−0.256103	−	0.618287i	−0.998674	+	0.0514803i	$0.983606\pi$
$968$	5.21439	+	5.21439i	0.167597	+	0.167597i
$969$	13.3304	+	32.1824i	0.428234	+	1.03385i
$970$	−8.29407	+	20.0236i	−0.266306	+	0.642921i
$971$	2.26223	−	2.26223i	0.0725985	−	0.0725985i	−0.669875	−	0.742474i	$-0.733652\pi$
$971$	2.26223	−	2.26223i	0.0725985	−	0.0725985i	0.742474	+	0.669875i	$0.233652\pi$
$972$	−19.7002	−	8.16008i	−0.631884	−	0.261735i
$973$	−0.963087	+	2.32510i	−0.0308751	+	0.0745392i
$974$	−1.82458	−	1.82458i	−0.0584632	−	0.0584632i
$975$	103.710			3.32137
$976$	0.999999	+	2.41421i	0.0320092	+	0.0772770i
$977$	32.1808	−	32.1808i	1.02956	−	1.02956i	0.0300064	−	0.999550i	$-0.490447\pi$
$977$	32.1808	−	32.1808i	1.02956	−	1.02956i	0.999550	−	0.0300064i	$-0.00955276\pi$
$978$	0.458261	+	0.458261i	0.0146536	+	0.0146536i
$979$	30.4040			0.971716
$980$	27.1610			0.867625
$981$		−	63.4934i		−	2.02719i
$982$	13.9717	−	13.9717i	0.445854	−	0.445854i
$983$	−8.86243	+	8.86243i	−0.282667	+	0.282667i	−0.834172	−	0.551504i	$-0.814054\pi$
$983$	−8.86243	+	8.86243i	−0.282667	+	0.282667i	0.551504	+	0.834172i	$0.314054\pi$
$984$	4.82586	−	1.99894i	0.153843	−	0.0637237i
$985$		−	28.2024i		−	0.898604i
$986$	22.0226	+	9.12204i	0.701341	+	0.290505i
$987$	0.470458	+	0.194870i	0.0149748	+	0.00620278i
$988$	−8.54934	+	8.54934i	−0.271991	+	0.271991i
$989$	61.2949	+	25.3892i	1.94906	+	0.807329i
$990$	−20.7205	+	20.7205i	−0.658540	+	0.658540i
$991$	0.323406	+	0.133959i	0.0102733	+	0.00425535i	0.387814	−	0.921738i	$-0.373230\pi$
$991$	0.323406	+	0.133959i	0.0102733	+	0.00425535i	−0.377541	+	0.925993i	$0.623230\pi$
$992$	−1.91626	+	4.62625i	−0.0608412	+	0.146884i
$993$	−38.8424	−	16.0891i	−1.23263	−	0.510571i
$994$	0.314820	−	0.760042i	0.00998547	−	0.0241071i
$995$	−85.3419	+	35.3498i	−2.70552	+	1.12066i
$996$	8.52575	−	20.5830i	0.270149	−	0.652197i
$997$	−17.4854			−0.553767			−0.276884	−	0.960903i	$-0.589302\pi$
$997$	−17.4854			−0.553767			−0.276884	+	0.960903i	$0.589302\pi$
$998$	0.324588			0.0102746
$999$		−	6.49800i		−	0.205588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	802.2.e.b.45.3	✓	68
401.303	even	8	inner	802.2.e.b.303.3	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
802.2.e.b.45.3	✓	68	1.1	even	1	trivial
802.2.e.b.303.3	yes	68	401.303	even	8	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:	\( N \)	\(=\)	\( 802 = 2 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	802.e (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-2.43681 - 1.00936i) q^{3} +1.00000i q^{4} -3.88924 q^{5} +(-1.00936 - 2.43681i) q^{6} +(-0.0905001 + 0.0905001i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.79793 + 2.79793i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-2.43681 - 1.00936i) q^{3} +1.00000i q^{4} -3.88924 q^{5} +(-1.00936 - 2.43681i) q^{6} +(-0.0905001 + 0.0905001i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.79793 + 2.79793i) q^{9} +(-2.75011 - 2.75011i) q^{10} +(-1.34643 - 1.34643i) q^{11} +(1.00936 - 2.43681i) q^{12} +(-3.58743 + 1.48596i) q^{13} -0.127987 q^{14} +(9.47735 + 3.92565i) q^{15} -1.00000 q^{16} +(3.91861 - 1.62314i) q^{17} +3.95687i q^{18} +(-1.19157 - 2.87670i) q^{19} -3.88924i q^{20} +(0.311879 - 0.129185i) q^{21} -1.90414i q^{22} +(2.51214 + 6.06484i) q^{23} +(2.43681 - 1.00936i) q^{24} +10.1262 q^{25} +(-3.58743 - 1.48596i) q^{26} +(-0.965826 - 2.33171i) q^{27} +(-0.0905001 - 0.0905001i) q^{28} +5.61999 q^{29} +(3.92565 + 9.47735i) q^{30} +(-1.91626 - 4.62625i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.92196 + 4.64003i) q^{33} +(3.91861 + 1.62314i) q^{34} +(0.351977 - 0.351977i) q^{35} +(-2.79793 + 2.79793i) q^{36} +(2.37868 + 0.985281i) q^{37} +(1.19157 - 2.87670i) q^{38} +10.2418 q^{39} +(2.75011 - 2.75011i) q^{40} +1.98040 q^{41} +(0.311879 + 0.129185i) q^{42} +(7.14644 - 7.14644i) q^{43} +(1.34643 - 1.34643i) q^{44} +(-10.8818 - 10.8818i) q^{45} +(-2.51214 + 6.06484i) q^{46} +(1.06664 + 1.06664i) q^{47} +(2.43681 + 1.00936i) q^{48} +6.98362i q^{49} +(7.16029 + 7.16029i) q^{50} -11.1873 q^{51} +(-1.48596 - 3.58743i) q^{52} +(-1.95690 + 4.72438i) q^{53} +(0.965826 - 2.33171i) q^{54} +(5.23658 + 5.23658i) q^{55} -0.127987i q^{56} +8.21271i q^{57} +(3.97393 + 3.97393i) q^{58} +(3.68570 - 1.52667i) q^{59} +(-3.92565 + 9.47735i) q^{60} +(-0.999999 - 2.41421i) q^{61} +(1.91626 - 4.62625i) q^{62} -0.506426 q^{63} -1.00000i q^{64} +(13.9524 - 5.77926i) q^{65} +(-1.92196 + 4.64003i) q^{66} +(3.20823 - 7.74535i) q^{67} +(1.62314 + 3.91861i) q^{68} -17.3145i q^{69} +0.497770 q^{70} +(-2.45979 + 5.93845i) q^{71} -3.95687 q^{72} +(-2.64888 + 2.64888i) q^{73} +(0.985281 + 2.37868i) q^{74} +(-24.6756 - 10.2210i) q^{75} +(2.87670 - 1.19157i) q^{76} +0.243704 q^{77} +(7.24202 + 7.24202i) q^{78} +(-2.68573 - 6.48393i) q^{79} +3.88924 q^{80} -5.21380i q^{81} +(1.40035 + 1.40035i) q^{82} +8.44668 q^{83} +(0.129185 + 0.311879i) q^{84} +(-15.2404 + 6.31279i) q^{85} +10.1066 q^{86} +(-13.6949 - 5.67260i) q^{87} +1.90414 q^{88} +(-11.2906 + 11.2906i) q^{89} -15.3892i q^{90} +(0.190183 - 0.459142i) q^{91} +(-6.06484 + 2.51214i) q^{92} +13.2075i q^{93} +1.50846i q^{94} +(4.63430 + 11.1882i) q^{95} +(1.00936 + 2.43681i) q^{96} +(-2.13257 - 5.14847i) q^{97} +(-4.93816 + 4.93816i) q^{98} -7.53442i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{6} + 20 q^{9}+O(q^{10}) \) 68 * q + 4 * q^6 + 20 * q^9	\( 68 q + 4 q^{6} + 20 q^{9} - 4 q^{10} + 12 q^{11} - 4 q^{12} - 8 q^{13} + 8 q^{14} - 4 q^{15} - 68 q^{16} + 4 q^{17} + 20 q^{19} - 40 q^{21} - 16 q^{23} + 20 q^{25} - 8 q^{26} - 12 q^{27} + 16 q^{29} - 4 q^{30} - 8 q^{31} + 8 q^{33} + 4 q^{34} + 16 q^{35} - 20 q^{36} + 12 q^{37} - 20 q^{38} + 40 q^{39} + 4 q^{40} + 24 q^{41} - 40 q^{42} + 40 q^{43} - 12 q^{44} + 28 q^{45} + 16 q^{46} + 4 q^{47} - 8 q^{50} + 24 q^{51} + 4 q^{52} + 12 q^{53} + 12 q^{54} - 24 q^{55} - 4 q^{58} + 4 q^{59} + 4 q^{60} - 20 q^{61} + 8 q^{62} - 16 q^{63} + 36 q^{65} - 8 q^{66} + 48 q^{67} + 8 q^{68} - 16 q^{71} - 68 q^{72} + 40 q^{73} - 8 q^{74} - 96 q^{75} - 16 q^{77} + 32 q^{78} + 28 q^{79} - 16 q^{82} + 16 q^{83} - 4 q^{84} + 16 q^{85} - 32 q^{86} + 8 q^{87} + 8 q^{88} - 20 q^{89} - 4 q^{91} + 8 q^{92} - 24 q^{95} - 4 q^{96} + 24 q^{97} + 24 q^{98}+O(q^{100}) \) 68 * q + 4 * q^6 + 20 * q^9 - 4 * q^10 + 12 * q^11 - 4 * q^12 - 8 * q^13 + 8 * q^14 - 4 * q^15 - 68 * q^16 + 4 * q^17 + 20 * q^19 - 40 * q^21 - 16 * q^23 + 20 * q^25 - 8 * q^26 - 12 * q^27 + 16 * q^29 - 4 * q^30 - 8 * q^31 + 8 * q^33 + 4 * q^34 + 16 * q^35 - 20 * q^36 + 12 * q^37 - 20 * q^38 + 40 * q^39 + 4 * q^40 + 24 * q^41 - 40 * q^42 + 40 * q^43 - 12 * q^44 + 28 * q^45 + 16 * q^46 + 4 * q^47 - 8 * q^50 + 24 * q^51 + 4 * q^52 + 12 * q^53 + 12 * q^54 - 24 * q^55 - 4 * q^58 + 4 * q^59 + 4 * q^60 - 20 * q^61 + 8 * q^62 - 16 * q^63 + 36 * q^65 - 8 * q^66 + 48 * q^67 + 8 * q^68 - 16 * q^71 - 68 * q^72 + 40 * q^73 - 8 * q^74 - 96 * q^75 - 16 * q^77 + 32 * q^78 + 28 * q^79 - 16 * q^82 + 16 * q^83 - 4 * q^84 + 16 * q^85 - 32 * q^86 + 8 * q^87 + 8 * q^88 - 20 * q^89 - 4 * q^91 + 8 * q^92 - 24 * q^95 - 4 * q^96 + 24 * q^97 + 24 * q^98

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