LMFDB - Embedded newform 570.2.k.b.77.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(77,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("570.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.4
Character	$\chi$	$=$	570.77
Dual form			570.2.k.b.533.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.0916341 - 1.72963i) q^{3} -1.00000i q^{4} +(-2.17182 - 0.532166i) q^{5} +(1.28782 + 1.15823i) q^{6} +(1.32508 + 1.32508i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.98321 + 0.316985i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.0916341 - 1.72963i) q^{3} -1.00000i q^{4} +(-2.17182 - 0.532166i) q^{5} +(1.28782 + 1.15823i) q^{6} +(1.32508 + 1.32508i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.98321 + 0.316985i) q^{9} +(1.91201 - 1.15941i) q^{10} +4.14708i q^{11} +(-1.72963 + 0.0916341i) q^{12} +(-3.92411 + 3.92411i) q^{13} -1.87395 q^{14} +(-0.721435 + 3.80520i) q^{15} -1.00000 q^{16} +(5.01690 - 5.01690i) q^{17} +(1.88530 - 2.33359i) q^{18} -1.00000i q^{19} +(-0.532166 + 2.17182i) q^{20} +(2.17047 - 2.41332i) q^{21} +(-2.93243 - 2.93243i) q^{22} +(5.46874 + 5.46874i) q^{23} +(1.15823 - 1.28782i) q^{24} +(4.43360 + 2.31154i) q^{25} -5.54954i q^{26} +(0.821629 + 5.13078i) q^{27} +(1.32508 - 1.32508i) q^{28} +0.0964393 q^{29} +(-2.18055 - 3.20081i) q^{30} +0.0111704 q^{31} +(0.707107 - 0.707107i) q^{32} +(7.17289 - 0.380013i) q^{33} +7.09497i q^{34} +(-2.17267 - 3.58300i) q^{35} +(0.316985 + 2.98321i) q^{36} +(1.55524 + 1.55524i) q^{37} +(0.707107 + 0.707107i) q^{38} +(7.14683 + 6.42767i) q^{39} +(-1.15941 - 1.91201i) q^{40} +8.45893i q^{41} +(0.171717 + 3.24123i) q^{42} +(0.130534 - 0.130534i) q^{43} +4.14708 q^{44} +(6.64767 + 0.899127i) q^{45} -7.73397 q^{46} +(-1.71433 + 1.71433i) q^{47} +(0.0916341 + 1.72963i) q^{48} -3.48832i q^{49} +(-4.76953 + 1.50052i) q^{50} +(-9.13708 - 8.21764i) q^{51} +(3.92411 + 3.92411i) q^{52} +(8.88222 + 8.88222i) q^{53} +(-4.20899 - 3.04703i) q^{54} +(2.20693 - 9.00670i) q^{55} +1.87395i q^{56} +(-1.72963 + 0.0916341i) q^{57} +(-0.0681929 + 0.0681929i) q^{58} -6.40826 q^{59} +(3.80520 + 0.721435i) q^{60} -10.2484 q^{61} +(-0.00789865 + 0.00789865i) q^{62} +(-4.37302 - 3.53296i) q^{63} +1.00000i q^{64} +(10.6107 - 6.43419i) q^{65} +(-4.80329 + 5.34071i) q^{66} +(4.77624 + 4.77624i) q^{67} +(-5.01690 - 5.01690i) q^{68} +(8.95775 - 9.95999i) q^{69} +(4.06987 + 0.997251i) q^{70} -9.47461i q^{71} +(-2.33359 - 1.88530i) q^{72} +(-4.04666 + 4.04666i) q^{73} -2.19944 q^{74} +(3.59182 - 7.88028i) q^{75} -1.00000 q^{76} +(-5.49521 + 5.49521i) q^{77} +(-9.59862 + 0.508527i) q^{78} +12.4743i q^{79} +(2.17182 + 0.532166i) q^{80} +(8.79904 - 1.89126i) q^{81} +(-5.98137 - 5.98137i) q^{82} +(1.43685 + 1.43685i) q^{83} +(-2.41332 - 2.17047i) q^{84} +(-13.5656 + 8.22598i) q^{85} +0.184604i q^{86} +(-0.00883712 - 0.166804i) q^{87} +(-2.93243 + 2.93243i) q^{88} -17.0881 q^{89} +(-5.33639 + 4.06484i) q^{90} -10.3995 q^{91} +(5.46874 - 5.46874i) q^{92} +(-0.00102359 - 0.0193206i) q^{93} -2.42443i q^{94} +(-0.532166 + 2.17182i) q^{95} +(-1.28782 - 1.15823i) q^{96} +(3.48454 + 3.48454i) q^{97} +(2.46662 + 2.46662i) q^{98} +(-1.31456 - 12.3716i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7}+O(q^{10}) $ 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7	$ 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} + 16 q^{21} - 4 q^{22} + 16 q^{25} - 44 q^{27} + 20 q^{28} + 32 q^{30} - 24 q^{31} - 4 q^{33} + 4 q^{36} - 8 q^{40} + 12 q^{42} - 8 q^{43} + 28 q^{45} - 16 q^{46} - 4 q^{48} + 40 q^{51} - 8 q^{52} - 36 q^{55} - 4 q^{57} + 44 q^{58} + 16 q^{60} - 120 q^{61} - 12 q^{63} + 80 q^{67} - 36 q^{70} + 44 q^{73} + 4 q^{75} - 36 q^{76} - 64 q^{78} + 36 q^{81} + 8 q^{82} - 24 q^{85} - 28 q^{87} - 4 q^{88} + 44 q^{90} - 72 q^{93} - 4 q^{96} + 92 q^{97}+O(q^{100}) $ 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 + 16 * q^21 - 4 * q^22 + 16 * q^25 - 44 * q^27 + 20 * q^28 + 32 * q^30 - 24 * q^31 - 4 * q^33 + 4 * q^36 - 8 * q^40 + 12 * q^42 - 8 * q^43 + 28 * q^45 - 16 * q^46 - 4 * q^48 + 40 * q^51 - 8 * q^52 - 36 * q^55 - 4 * q^57 + 44 * q^58 + 16 * q^60 - 120 * q^61 - 12 * q^63 + 80 * q^67 - 36 * q^70 + 44 * q^73 + 4 * q^75 - 36 * q^76 - 64 * q^78 + 36 * q^81 + 8 * q^82 - 24 * q^85 - 28 * q^87 - 4 * q^88 + 44 * q^90 - 72 * q^93 - 4 * q^96 + 92 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.0916341	−	1.72963i	−0.0529049	−	0.998600i
$3$	−0.0916341	−	1.72963i	−0.0529049	−	0.998600i
$4$		−	1.00000i		−	0.500000i
$5$	−2.17182	−	0.532166i	−0.971267	−	0.237992i
$5$	−2.17182	−	0.532166i	−0.971267	−	0.237992i
$6$	1.28782	+	1.15823i	0.525752	+	0.472847i
$7$	1.32508	+	1.32508i	0.500833	+	0.500833i	0.911697	−	0.410863i	$-0.134773\pi$
$7$	1.32508	+	1.32508i	0.500833	+	0.500833i	−0.410863	+	0.911697i	$0.634773\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.98321	+	0.316985i	−0.994402	+	0.105662i
$10$	1.91201	−	1.15941i	0.604630	−	0.366638i
$11$			4.14708i			1.25039i	0.780468	+	0.625195i	$0.214981\pi$
$11$			4.14708i			1.25039i	−0.780468	+	0.625195i	$0.785019\pi$
$12$	−1.72963	+	0.0916341i	−0.499300	+	0.0264525i
$13$	−3.92411	+	3.92411i	−1.08835	+	1.08835i	−0.0926554	+	0.995698i	$0.529536\pi$
$13$	−3.92411	+	3.92411i	−1.08835	+	1.08835i	−0.995698	+	0.0926554i	$0.970464\pi$
$14$	−1.87395			−0.500833
$15$	−0.721435	+	3.80520i	−0.186274	+	0.982498i
$16$	−1.00000			−0.250000
$17$	5.01690	−	5.01690i	1.21678	−	1.21678i	0.248024	−	0.968754i	$-0.420219\pi$
$17$	5.01690	−	5.01690i	1.21678	−	1.21678i	0.968754	−	0.248024i	$-0.0797813\pi$
$18$	1.88530	−	2.33359i	0.444370	−	0.550032i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	−0.532166	+	2.17182i	−0.118996	+	0.485634i
$21$	2.17047	−	2.41332i	0.473635	−	0.526629i
$22$	−2.93243	−	2.93243i	−0.625195	−	0.625195i
$23$	5.46874	+	5.46874i	1.14031	+	1.14031i	0.988393	+	0.151918i	$0.0485449\pi$
$23$	5.46874	+	5.46874i	1.14031	+	1.14031i	0.151918	+	0.988393i	$0.451455\pi$
$24$	1.15823	−	1.28782i	0.236424	−	0.262876i
$25$	4.43360	+	2.31154i	0.886720	+	0.462307i
$26$		−	5.54954i		−	1.08835i
$27$	0.821629	+	5.13078i	0.158123	+	0.987419i
$28$	1.32508	−	1.32508i	0.250417	−	0.250417i
$29$	0.0964393			0.0179083			0.00895416	−	0.999960i	$-0.497150\pi$
$29$	0.0964393			0.0179083			0.00895416	+	0.999960i	$0.497150\pi$
$30$	−2.18055	−	3.20081i	−0.398112	−	0.584386i
$31$	0.0111704			0.00200626			0.00100313	−	0.999999i	$-0.499681\pi$
$31$	0.0111704			0.00200626			0.00100313	+	0.999999i	$0.499681\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	7.17289	−	0.380013i	1.24864	−	0.0661519i
$34$			7.09497i			1.21678i
$35$	−2.17267	−	3.58300i	−0.367249	−	0.605637i
$36$	0.316985	+	2.98321i	0.0528309	+	0.497201i
$37$	1.55524	+	1.55524i	0.255679	+	0.255679i	0.823294	−	0.567615i	$-0.192134\pi$
$37$	1.55524	+	1.55524i	0.255679	+	0.255679i	−0.567615	+	0.823294i	$0.692134\pi$
$38$	0.707107	+	0.707107i	0.114708	+	0.114708i
$39$	7.14683	+	6.42767i	1.14441	+	1.02925i
$40$	−1.15941	−	1.91201i	−0.183319	−	0.302315i
$41$			8.45893i			1.32106i	0.750798	+	0.660532i	$0.229669\pi$
$41$			8.45893i			1.32106i	−0.750798	+	0.660532i	$0.770331\pi$
$42$	0.171717	+	3.24123i	0.0264966	+	0.500132i
$43$	0.130534	−	0.130534i	0.0199063	−	0.0199063i	−0.697084	−	0.716990i	$-0.745519\pi$
$43$	0.130534	−	0.130534i	0.0199063	−	0.0199063i	0.716990	+	0.697084i	$0.245519\pi$
$44$	4.14708			0.625195
$45$	6.64767	+	0.899127i	0.990977	+	0.134034i
$46$	−7.73397			−1.14031
$47$	−1.71433	+	1.71433i	−0.250061	+	0.250061i	−0.820996	−	0.570934i	$-0.806581\pi$
$47$	−1.71433	+	1.71433i	−0.250061	+	0.250061i	0.570934	+	0.820996i	$0.306581\pi$
$48$	0.0916341	+	1.72963i	0.0132262	+	0.249650i
$49$		−	3.48832i		−	0.498332i
$50$	−4.76953	+	1.50052i	−0.674514	+	0.212206i
$51$	−9.13708	−	8.21764i	−1.27945	−	1.15070i
$52$	3.92411	+	3.92411i	0.544177	+	0.544177i
$53$	8.88222	+	8.88222i	1.22007	+	1.22007i	0.967608	+	0.252459i	$0.0812392\pi$
$53$	8.88222	+	8.88222i	1.22007	+	1.22007i	0.252459	+	0.967608i	$0.418761\pi$
$54$	−4.20899	−	3.04703i	−0.572771	−	0.414648i
$55$	2.20693	−	9.00670i	0.297583	−	1.21446i
$56$			1.87395i			0.250417i
$57$	−1.72963	+	0.0916341i	−0.229094	+	0.0121372i
$58$	−0.0681929	+	0.0681929i	−0.00895416	+	0.00895416i
$59$	−6.40826			−0.834284			−0.417142	−	0.908841i	$-0.636968\pi$
$59$	−6.40826			−0.834284			−0.417142	+	0.908841i	$0.636968\pi$
$60$	3.80520	+	0.721435i	0.491249	+	0.0931369i
$61$	−10.2484			−1.31218			−0.656090	−	0.754683i	$-0.727791\pi$
$61$	−10.2484			−1.31218			−0.656090	+	0.754683i	$0.727791\pi$
$62$	−0.00789865	+	0.00789865i	−0.00100313	+	0.00100313i
$63$	−4.37302	−	3.53296i	−0.550949	−	0.445111i
$64$			1.00000i			0.125000i
$65$	10.6107	−	6.43419i	1.31610	−	0.798063i
$66$	−4.80329	+	5.34071i	−0.591244	+	0.657396i
$67$	4.77624	+	4.77624i	0.583511	+	0.583511i	0.935866	−	0.352355i	$-0.114619\pi$
$67$	4.77624	+	4.77624i	0.583511	+	0.583511i	−0.352355	+	0.935866i	$0.614619\pi$
$68$	−5.01690	−	5.01690i	−0.608389	−	0.608389i
$69$	8.95775	−	9.95999i	1.07839	−	1.19904i
$70$	4.06987	+	0.997251i	0.486443	+	0.119194i
$71$		−	9.47461i		−	1.12443i	−0.826991	−	0.562215i	$-0.809949\pi$
$71$		−	9.47461i		−	1.12443i	0.826991	−	0.562215i	$-0.190051\pi$
$72$	−2.33359	−	1.88530i	−0.275016	−	0.222185i
$73$	−4.04666	+	4.04666i	−0.473626	+	0.473626i	−0.903086	−	0.429460i	$-0.858704\pi$
$73$	−4.04666	+	4.04666i	−0.473626	+	0.473626i	0.429460	+	0.903086i	$0.358704\pi$
$74$	−2.19944			−0.255679
$75$	3.59182	−	7.88028i	0.414748	−	0.909936i
$76$	−1.00000			−0.114708
$77$	−5.49521	+	5.49521i	−0.626238	+	0.626238i
$78$	−9.59862	+	0.508527i	−1.08683	+	0.0575793i
$79$			12.4743i			1.40347i	0.712438	+	0.701735i	$0.247591\pi$
$79$			12.4743i			1.40347i	−0.712438	+	0.701735i	$0.752409\pi$
$80$	2.17182	+	0.532166i	0.242817	+	0.0594980i
$81$	8.79904	−	1.89126i	0.977671	−	0.210140i
$82$	−5.98137	−	5.98137i	−0.660532	−	0.660532i
$83$	1.43685	+	1.43685i	0.157715	+	0.157715i	0.781553	−	0.623838i	$-0.214428\pi$
$83$	1.43685	+	1.43685i	0.157715	+	0.157715i	−0.623838	+	0.781553i	$0.714428\pi$
$84$	−2.41332	−	2.17047i	−0.263314	−	0.236818i
$85$	−13.5656	+	8.22598i	−1.47140	+	0.892233i
$86$			0.184604i			0.0199063i
$87$	−0.00883712	−	0.166804i	−0.000947439	−	0.0178832i
$88$	−2.93243	+	2.93243i	−0.312598	+	0.312598i
$89$	−17.0881			−1.81134			−0.905668	−	0.423988i	$-0.860630\pi$
$89$	−17.0881			−1.81134			−0.905668	+	0.423988i	$0.860630\pi$
$90$	−5.33639	+	4.06484i	−0.562505	+	0.428471i
$91$	−10.3995			−1.09017
$92$	5.46874	−	5.46874i	0.570155	−	0.570155i
$93$	−0.00102359	−	0.0193206i	−0.000106141	−	0.00200345i
$94$		−	2.42443i		−	0.250061i
$95$	−0.532166	+	2.17182i	−0.0545991	+	0.222824i
$96$	−1.28782	−	1.15823i	−0.131438	−	0.118212i
$97$	3.48454	+	3.48454i	0.353801	+	0.353801i	0.861522	−	0.507721i	$-0.169512\pi$
$97$	3.48454	+	3.48454i	0.353801	+	0.353801i	−0.507721	+	0.861522i	$0.669512\pi$
$98$	2.46662	+	2.46662i	0.249166	+	0.249166i
$99$	−1.31456	−	12.3716i	−0.132118	−	1.24339i
$100$	2.31154	−	4.43360i	0.231154	−	0.443360i
$101$			16.2835i			1.62027i	0.586244	+	0.810135i	$0.300606\pi$
$101$			16.2835i			1.62027i	−0.586244	+	0.810135i	$0.699394\pi$
$102$	12.2716	−	0.650141i	1.21507	−	0.0643736i
$103$	2.44289	−	2.44289i	0.240705	−	0.240705i	−0.576437	−	0.817142i	$-0.695557\pi$
$103$	2.44289	−	2.44289i	0.240705	−	0.240705i	0.817142	+	0.576437i	$0.195557\pi$
$104$	−5.54954			−0.544177
$105$	−5.99815	+	4.08623i	−0.585360	+	0.398776i
$106$	−12.5614			−1.22007
$107$	1.32951	−	1.32951i	0.128529	−	0.128529i	−0.639916	−	0.768445i	$-0.721031\pi$
$107$	1.32951	−	1.32951i	0.128529	−	0.128529i	0.768445	+	0.639916i	$0.221031\pi$
$108$	5.13078	−	0.821629i	0.493710	−	0.0790613i
$109$			8.51296i			0.815394i	0.913117	+	0.407697i	$0.133668\pi$
$109$			8.51296i			0.815394i	−0.913117	+	0.407697i	$0.866332\pi$
$110$	4.80816	+	7.92924i	0.458440	+	0.756023i
$111$	2.54746	−	2.83249i	0.241795	−	0.268848i
$112$	−1.32508	−	1.32508i	−0.125208	−	0.125208i
$113$	−1.46934	−	1.46934i	−0.138224	−	0.138224i	0.634609	−	0.772833i	$-0.281161\pi$
$113$	−1.46934	−	1.46934i	−0.138224	−	0.138224i	−0.772833	+	0.634609i	$0.781161\pi$
$114$	1.15823	−	1.28782i	0.108479	−	0.120616i
$115$	−8.96684	−	14.7874i	−0.836162	−	1.37893i
$116$		−	0.0964393i		−	0.00895416i
$117$	10.4626	−	12.9503i	0.967264	−	1.19726i
$118$	4.53132	−	4.53132i	0.417142	−	0.417142i
$119$	13.2956			1.21881
$120$	−3.20081	+	2.18055i	−0.292193	+	0.199056i
$121$	−6.19825			−0.563477
$122$	7.24675	−	7.24675i	0.656090	−	0.656090i
$123$	14.6308	−	0.775126i	1.31921	−	0.0698908i
$124$		−	0.0111704i		−	0.00100313i
$125$	−8.39885	−	7.37965i	−0.751216	−	0.660056i
$126$	5.59037	−	0.594013i	0.498030	−	0.0529189i
$127$	−0.469960	−	0.469960i	−0.0417022	−	0.0417022i	0.685948	−	0.727650i	$-0.259388\pi$
$127$	−0.469960	−	0.469960i	−0.0417022	−	0.0417022i	−0.727650	+	0.685948i	$0.759388\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−0.237737	−	0.213814i	−0.0209316	−	0.0188253i
$130$	−2.95328	+	12.0526i	−0.259019	+	1.05708i
$131$		−	17.7953i		−	1.55478i	−0.629018	−	0.777391i	$-0.716543\pi$
$131$		−	17.7953i		−	1.55478i	0.629018	−	0.777391i	$-0.283457\pi$
$132$	−0.380013	−	7.17289i	−0.0330759	−	0.624320i
$133$	1.32508	−	1.32508i	0.114899	−	0.114899i
$134$	−6.75463			−0.583511
$135$	0.945999	−	11.5804i	0.0814186	−	0.996680i
$136$	7.09497			0.608389
$137$	9.30953	−	9.30953i	0.795367	−	0.795367i	−0.186994	−	0.982361i	$-0.559875\pi$
$137$	9.30953	−	9.30953i	0.795367	−	0.795367i	0.982361	+	0.186994i	$0.0598746\pi$
$138$	0.708695	+	13.3769i	0.0603281	+	1.13871i
$139$		−	12.4068i		−	1.05233i	−0.850383	−	0.526165i	$-0.823630\pi$
$139$		−	12.4068i		−	1.05233i	0.850383	−	0.526165i	$-0.176370\pi$
$140$	−3.58300	+	2.17267i	−0.302819	+	0.183624i
$141$	3.12225	+	2.80806i	0.262941	+	0.236482i
$142$	6.69956	+	6.69956i	0.562215	+	0.562215i
$143$	−16.2736	−	16.2736i	−1.36087	−	1.36087i
$144$	2.98321	−	0.316985i	0.248601	−	0.0264154i
$145$	−0.209449	−	0.0513217i	−0.0173938	−	0.00426204i
$146$		−	5.72284i		−	0.473626i
$147$	−6.03349	+	0.319649i	−0.497634	+	0.0263642i
$148$	1.55524	−	1.55524i	0.127840	−	0.127840i
$149$	10.8534			0.889142			0.444571	−	0.895744i	$-0.353356\pi$
$149$	10.8534			0.889142			0.444571	+	0.895744i	$0.353356\pi$
$150$	3.03240	+	8.11200i	0.247594	+	0.662342i
$151$	1.21233			0.0986577			0.0493288	−	0.998783i	$-0.484292\pi$
$151$	1.21233			0.0986577			0.0493288	+	0.998783i	$0.484292\pi$
$152$	0.707107	−	0.707107i	0.0573539	−	0.0573539i
$153$	−13.3762	+	16.5567i	−1.08140	+	1.33853i
$154$		−	7.77140i		−	0.626238i
$155$	−0.0242600	−	0.00594450i	−0.00194861	−	0.000477474i
$156$	6.42767	−	7.14683i	0.514625	−	0.572204i
$157$	10.0557	+	10.0557i	0.802530	+	0.802530i	0.983490	−	0.180960i	$-0.0579204\pi$
$157$	10.0557	+	10.0557i	0.802530	+	0.802530i	−0.180960	+	0.983490i	$0.557920\pi$
$158$	−8.82067	−	8.82067i	−0.701735	−	0.701735i
$159$	14.5490	−	16.1768i	1.15381	−	1.28291i
$160$	−1.91201	+	1.15941i	−0.151157	+	0.0916594i
$161$			14.4930i			1.14221i
$162$	−4.88454	+	7.55919i	−0.383765	+	0.593906i
$163$	−8.60942	+	8.60942i	−0.674342	+	0.674342i	−0.958714	−	0.284372i	$-0.908215\pi$
$163$	−8.60942	+	8.60942i	−0.674342	+	0.674342i	0.284372	+	0.958714i	$0.408215\pi$
$164$	8.45893			0.660532
$165$	−15.7804	−	2.99185i	−1.22851	−	0.232915i
$166$	−2.03202			−0.157715
$167$	−2.30123	+	2.30123i	−0.178074	+	0.178074i	−0.790516	−	0.612441i	$-0.790188\pi$
$167$	−2.30123	+	2.30123i	−0.178074	+	0.178074i	0.612441	+	0.790516i	$0.290188\pi$
$168$	3.24123	−	0.171717i	0.250066	−	0.0132483i
$169$		−	17.7974i		−	1.36903i
$170$	3.77570	−	15.4090i	0.289583	−	1.18182i
$171$	0.316985	+	2.98321i	0.0242405	+	0.228131i
$172$	−0.130534	−	0.130534i	−0.00995316	−	0.00995316i
$173$	−7.70257	−	7.70257i	−0.585616	−	0.585616i	0.350825	−	0.936441i	$-0.385901\pi$
$173$	−7.70257	−	7.70257i	−0.585616	−	0.585616i	−0.936441	+	0.350825i	$0.885901\pi$
$174$	0.124197	+	0.111699i	0.00941534	+	0.00846790i
$175$	2.81190	+	8.93785i	0.212560	+	0.675638i
$176$		−	4.14708i		−	0.312598i
$177$	0.587215	+	11.0839i	0.0441378	+	0.833116i
$178$	12.0831	−	12.0831i	0.905668	−	0.905668i
$179$	−9.05937			−0.677129			−0.338565	−	0.940943i	$-0.609941\pi$
$179$	−9.05937			−0.677129			−0.338565	+	0.940943i	$0.609941\pi$
$180$	0.899127	−	6.64767i	0.0670170	−	0.495488i
$181$	−17.9179			−1.33183			−0.665915	−	0.746028i	$-0.731959\pi$
$181$	−17.9179			−1.33183			−0.665915	+	0.746028i	$0.731959\pi$
$182$	7.35358	−	7.35358i	0.545084	−	0.545084i
$183$	0.939107	+	17.7260i	0.0694208	+	1.31034i
$184$			7.73397i			0.570155i
$185$	−2.55005	−	4.20534i	−0.187483	−	0.309183i
$186$	0.0143855	+	0.0129379i	0.00105480	+	0.000948654i
$187$	20.8055	+	20.8055i	1.52145	+	1.52145i
$188$	1.71433	+	1.71433i	0.125031	+	0.125031i
$189$	−5.70998	+	7.88743i	−0.415340	+	0.573726i
$190$	−1.15941	−	1.91201i	−0.0841124	−	0.138712i
$191$		−	8.41348i		−	0.608778i	−0.952548	−	0.304389i	$-0.901548\pi$
$191$		−	8.41348i		−	0.608778i	0.952548	−	0.304389i	$-0.0984522\pi$
$192$	1.72963	−	0.0916341i	0.124825	−	0.00661312i
$193$	0.408503	−	0.408503i	0.0294047	−	0.0294047i	−0.692252	−	0.721656i	$-0.743381\pi$
$193$	0.408503	−	0.408503i	0.0294047	−	0.0294047i	0.721656	+	0.692252i	$0.243381\pi$
$194$	−4.92788			−0.353801
$195$	−12.1010	−	17.7630i	−0.866573	−	1.27204i
$196$	−3.48832			−0.249166
$197$	3.06602	−	3.06602i	0.218445	−	0.218445i	−0.589398	−	0.807843i	$-0.700635\pi$
$197$	3.06602	−	3.06602i	0.218445	−	0.218445i	0.807843	+	0.589398i	$0.200635\pi$
$198$	9.67757	+	7.81850i	0.687755	+	0.555636i
$199$		−	21.9659i		−	1.55712i	−0.627570	−	0.778560i	$-0.715950\pi$
$199$		−	21.9659i		−	1.55712i	0.627570	−	0.778560i	$-0.284050\pi$
$200$	1.50052	+	4.76953i	0.106103	+	0.337257i
$201$	7.82344	−	8.69878i	0.551823	−	0.613564i
$202$	−11.5142	−	11.5142i	−0.810135	−	0.810135i
$203$	0.127790	+	0.127790i	0.00896909	+	0.00896909i
$204$	−8.21764	+	9.13708i	−0.575350	+	0.639724i
$205$	4.50156	−	18.3713i	0.314402	−	1.28311i
$206$			3.45477i			0.240705i
$207$	−18.0479	−	14.5809i	−1.25441	−	1.01344i
$208$	3.92411	−	3.92411i	0.272088	−	0.272088i
$209$	4.14708			0.286859
$210$	1.35193	−	7.13074i	0.0932921	−	0.492068i
$211$	10.9572			0.754327			0.377163	−	0.926147i	$-0.376899\pi$
$211$	10.9572			0.754327			0.377163	+	0.926147i	$0.376899\pi$
$212$	8.88222	−	8.88222i	0.610033	−	0.610033i
$213$	−16.3875	+	0.868197i	−1.12285	+	0.0594879i
$214$			1.88021i			0.128529i
$215$	−0.352963	+	0.214031i	−0.0240719	+	0.0145968i
$216$	−3.04703	+	4.20899i	−0.207324	+	0.286386i
$217$	0.0148017	+	0.0148017i	0.00100480	+	0.00100480i
$218$	−6.01957	−	6.01957i	−0.407697	−	0.407697i
$219$	7.37001	+	6.62839i	0.498019	+	0.447905i
$220$	−9.00670	−	2.20693i	−0.607232	−	0.148791i
$221$			39.3738i			2.64857i
$222$	0.201543	+	3.80420i	0.0135267	+	0.255321i
$223$	−3.81435	+	3.81435i	−0.255428	+	0.255428i	−0.823191	−	0.567764i	$-0.807809\pi$
$223$	−3.81435	+	3.81435i	−0.255428	+	0.255428i	0.567764	+	0.823191i	$0.307809\pi$
$224$	1.87395			0.125208
$225$	−13.9591	−	5.49041i	−0.930604	−	0.366027i
$226$	2.07797			0.138224
$227$	−8.48460	+	8.48460i	−0.563143	+	0.563143i	−0.930199	−	0.367056i	$-0.880366\pi$
$227$	−8.48460	+	8.48460i	−0.563143	+	0.563143i	0.367056	+	0.930199i	$0.380366\pi$
$228$	0.0916341	+	1.72963i	0.00606861	+	0.114547i
$229$			13.8975i			0.918372i	0.888340	+	0.459186i	$0.151859\pi$
$229$			13.8975i			0.918372i	−0.888340	+	0.459186i	$0.848141\pi$
$230$	16.7968	+	4.11575i	1.10755	+	0.271385i
$231$	10.0082	+	9.00111i	0.658492	+	0.592229i
$232$	0.0681929	+	0.0681929i	0.00447708	+	0.00447708i
$233$	21.1265	+	21.1265i	1.38404	+	1.38404i	0.837300	+	0.546744i	$0.184133\pi$
$233$	21.1265	+	21.1265i	1.38404	+	1.38404i	0.546744	+	0.837300i	$0.315867\pi$
$234$	1.75912	+	16.5554i	0.114997	+	1.08226i
$235$	4.63553	−	2.81091i	0.302389	−	0.183364i
$236$			6.40826i			0.417142i
$237$	21.5759	−	1.14307i	1.40150	−	0.0742505i
$238$	−9.40141	+	9.40141i	−0.609403	+	0.609403i
$239$	−3.09410			−0.200141			−0.100070	−	0.994980i	$-0.531907\pi$
$239$	−3.09410			−0.200141			−0.100070	+	0.994980i	$0.531907\pi$
$240$	0.721435	−	3.80520i	0.0465684	−	0.245624i
$241$	6.62578			0.426804			0.213402	−	0.976964i	$-0.431546\pi$
$241$	6.62578			0.426804			0.213402	+	0.976964i	$0.431546\pi$
$242$	4.38282	−	4.38282i	0.281738	−	0.281738i
$243$	−4.07747	−	15.0457i	−0.261570	−	0.965185i
$244$			10.2484i			0.656090i
$245$	−1.85637	+	7.57600i	−0.118599	+	0.484013i
$246$	−9.79743	+	10.8936i	−0.624661	+	0.694552i
$247$	3.92411	+	3.92411i	0.249685	+	0.249685i
$248$	0.00789865	+	0.00789865i	0.000501565	+	0.000501565i
$249$	2.35355	−	2.61688i	0.149150	−	0.165838i
$250$	11.1571	−	0.720684i	0.705636	−	0.0455800i
$251$			21.3523i			1.34775i	0.738847	+	0.673874i	$0.235371\pi$
$251$			21.3523i			1.34775i	−0.738847	+	0.673874i	$0.764629\pi$
$252$	−3.53296	+	4.37302i	−0.222555	+	0.275474i
$253$	−22.6793	+	22.6793i	−1.42583	+	1.42583i
$254$	0.664624			0.0417022
$255$	15.4709	+	22.7097i	0.968828	+	1.42214i
$256$	1.00000			0.0625000
$257$	2.86047	−	2.86047i	0.178431	−	0.178431i	−0.612240	−	0.790672i	$-0.709732\pi$
$257$	2.86047	−	2.86047i	0.178431	−	0.178431i	0.790672	+	0.612240i	$0.209732\pi$
$258$	0.319295	−	0.0169160i	0.0198784	−	0.00105314i
$259$			4.12163i			0.256106i
$260$	−6.43419	−	10.6107i	−0.399031	−	0.658051i
$261$	−0.287698	+	0.0305698i	−0.0178081	+	0.00189222i
$262$	12.5832	+	12.5832i	0.777391	+	0.777391i
$263$	−19.5180	−	19.5180i	−1.20353	−	1.20353i	−0.973085	−	0.230446i	$-0.925982\pi$
$263$	−19.5180	−	19.5180i	−1.20353	−	1.20353i	−0.230446	−	0.973085i	$-0.574018\pi$
$264$	5.34071	+	4.80329i	0.328698	+	0.295622i
$265$	−14.5638	−	24.0174i	−0.894644	−	1.47538i
$266$			1.87395i			0.114899i
$267$	1.56585	+	29.5560i	0.0958286	+	1.80880i
$268$	4.77624	−	4.77624i	0.291756	−	0.291756i
$269$	−9.59340			−0.584920			−0.292460	−	0.956278i	$-0.594474\pi$
$269$	−9.59340			−0.584920			−0.292460	+	0.956278i	$0.594474\pi$
$270$	7.51964	+	8.85748i	0.457631	+	0.539049i
$271$	30.4023			1.84681			0.923405	−	0.383828i	$-0.125394\pi$
$271$	30.4023			1.84681			0.923405	+	0.383828i	$0.125394\pi$
$272$	−5.01690	+	5.01690i	−0.304195	+	0.304195i
$273$	0.952952	+	17.9873i	0.0576753	+	1.08864i
$274$			13.1657i			0.795367i
$275$	−9.58612	+	18.3865i	−0.578065	+	1.10875i
$276$	−9.95999	−	8.95775i	−0.599521	−	0.539193i
$277$	−8.02745	−	8.02745i	−0.482323	−	0.482323i	0.423550	−	0.905873i	$-0.360784\pi$
$277$	−8.02745	−	8.02745i	−0.482323	−	0.482323i	−0.905873	+	0.423550i	$0.860784\pi$
$278$	8.77292	+	8.77292i	0.526165	+	0.526165i
$279$	−0.0333235	+	0.00354084i	−0.00199503	+	0.000211985i
$280$	0.997251	−	4.06987i	0.0595972	−	0.243222i
$281$			13.4543i			0.802618i	0.915943	+	0.401309i	$0.131445\pi$
$281$			13.4543i			0.802618i	−0.915943	+	0.401309i	$0.868555\pi$
$282$	−4.19336	+	0.222161i	−0.249711	+	0.0132295i
$283$	13.5068	−	13.5068i	0.802894	−	0.802894i	−0.180653	−	0.983547i	$-0.557821\pi$
$283$	13.5068	−	13.5068i	0.802894	−	0.802894i	0.983547	+	0.180653i	$0.0578209\pi$
$284$	−9.47461			−0.562215
$285$	3.80520	+	0.721435i	0.225400	+	0.0427341i
$286$	23.0144			1.36087
$287$	−11.2088	+	11.2088i	−0.661633	+	0.661633i
$288$	−1.88530	+	2.33359i	−0.111093	+	0.137508i
$289$		−	33.3387i		−	1.96110i
$290$	0.184392	−	0.111813i	0.0108279	−	0.00656586i
$291$	5.70764	−	6.34625i	0.334588	−	0.372024i
$292$	4.04666	+	4.04666i	0.236813	+	0.236813i
$293$	−1.92348	−	1.92348i	−0.112371	−	0.112371i	0.648686	−	0.761056i	$-0.275319\pi$
$293$	−1.92348	−	1.92348i	−0.112371	−	0.112371i	−0.761056	+	0.648686i	$0.775319\pi$
$294$	4.04030	−	4.49235i	0.235635	−	0.261999i
$295$	13.9176	+	3.41026i	0.810313	+	0.198553i
$296$			2.19944i			0.127840i
$297$	−21.2777	+	3.40736i	−1.23466	+	0.197715i
$298$	−7.67448	+	7.67448i	−0.444571	+	0.444571i
$299$	−42.9199			−2.48212
$300$	−7.88028	−	3.59182i	−0.454968	−	0.207374i
$301$	0.345937			0.0199395
$302$	−0.857244	+	0.857244i	−0.0493288	+	0.0493288i
$303$	28.1644	−	1.49212i	1.61800	−	0.0857203i
$304$			1.00000i			0.0573539i
$305$	22.2578	+	5.45388i	1.27448	+	0.312288i
$306$	−2.24900	−	21.1658i	−0.128567	−	1.20997i
$307$	−17.6649	−	17.6649i	−1.00819	−	1.00819i	−0.999966	−	0.00822043i	$-0.997383\pi$
$307$	−17.6649	−	17.6649i	−1.00819	−	1.00819i	−0.00822043	−	0.999966i	$-0.502617\pi$
$308$	5.49521	+	5.49521i	0.313119	+	0.313119i
$309$	−4.44913	−	4.00143i	−0.253102	−	0.227633i
$310$	0.0213578	−	0.0129510i	0.00121304	−	0.000735570i
$311$			9.64561i			0.546952i	0.961879	+	0.273476i	$0.0881735\pi$
$311$			9.64561i			0.546952i	−0.961879	+	0.273476i	$0.911827\pi$
$312$	0.508527	+	9.59862i	0.0287896	+	0.543415i
$313$	10.1110	−	10.1110i	0.571508	−	0.571508i	−0.361042	−	0.932550i	$-0.617579\pi$
$313$	10.1110	−	10.1110i	0.571508	−	0.571508i	0.932550	+	0.361042i	$0.117579\pi$
$314$	−14.2209			−0.802530
$315$	7.61729	+	10.0001i	0.429186	+	0.563443i
$316$	12.4743			0.701735
$317$	−9.56745	+	9.56745i	−0.537361	+	0.537361i	−0.922753	−	0.385392i	$-0.874066\pi$
$317$	−9.56745	+	9.56745i	−0.537361	+	0.537361i	0.385392	+	0.922753i	$0.374066\pi$
$318$	1.15105	+	21.7264i	0.0645475	+	1.21836i
$319$			0.399941i			0.0223924i
$320$	0.532166	−	2.17182i	0.0297490	−	0.121408i
$321$	−2.42138	−	2.17773i	−0.135148	−	0.121549i
$322$	−10.2481	−	10.2481i	−0.571106	−	0.571106i
$323$	−5.01690	−	5.01690i	−0.279148	−	0.279148i
$324$	−1.89126	−	8.79904i	−0.105070	−	0.488836i
$325$	−26.4687	+	8.32721i	−1.46822	+	0.461911i
$326$		−	12.1756i		−	0.674342i
$327$	14.7242	−	0.780077i	0.814252	−	0.0431384i
$328$	−5.98137	+	5.98137i	−0.330266	+	0.330266i
$329$	−4.54326			−0.250478
$330$	13.2740	−	9.04291i	0.730711	−	0.497796i
$331$	−10.8642			−0.597152			−0.298576	−	0.954386i	$-0.596512\pi$
$331$	−10.8642			−0.597152			−0.298576	+	0.954386i	$0.596512\pi$
$332$	1.43685	−	1.43685i	0.0788575	−	0.0788575i
$333$	−5.13258	−	4.14660i	−0.281264	−	0.227233i
$334$		−	3.25443i		−	0.178074i
$335$	−7.83138	−	12.9149i	−0.427874	−	0.705616i
$336$	−2.17047	+	2.41332i	−0.118409	+	0.131657i
$337$	2.83368	+	2.83368i	0.154361	+	0.154361i	0.780062	−	0.625702i	$-0.215187\pi$
$337$	2.83368	+	2.83368i	0.154361	+	0.154361i	−0.625702	+	0.780062i	$0.715187\pi$
$338$	12.5846	+	12.5846i	0.684514	+	0.684514i
$339$	−2.40677	+	2.67606i	−0.130718	+	0.145343i
$340$	8.22598	+	13.5656i	0.446117	+	0.735700i
$341$			0.0463244i			0.00250861i
$342$	−2.33359	−	1.88530i	−0.126186	−	0.101946i
$343$	13.8979	−	13.8979i	0.750415	−	0.750415i
$344$	0.184604			0.00995316
$345$	−24.7550	+	16.8643i	−1.33276	+	0.907943i
$346$	10.8931			0.585616
$347$	12.2836	−	12.2836i	0.659418	−	0.659418i	−0.295825	−	0.955242i	$-0.595594\pi$
$347$	12.2836	−	12.2836i	0.659418	−	0.659418i	0.955242	+	0.295825i	$0.0955944\pi$
$348$	−0.166804	+	0.00883712i	−0.00894162	+	0.000473719i
$349$			25.9576i			1.38948i	0.719261	+	0.694740i	$0.244480\pi$
$349$			25.9576i			1.38948i	−0.719261	+	0.694740i	$0.755520\pi$
$350$	−8.30833	−	4.33170i	−0.444099	−	0.231539i
$351$	−23.3579	−	16.9096i	−1.24675	−	0.902568i
$352$	2.93243	+	2.93243i	0.156299	+	0.156299i
$353$	−11.5702	−	11.5702i	−0.615818	−	0.615818i	0.328638	−	0.944456i	$-0.393410\pi$
$353$	−11.5702	−	11.5702i	−0.615818	−	0.615818i	−0.944456	+	0.328638i	$0.893410\pi$
$354$	−8.25271	−	7.42227i	−0.438627	−	0.394489i
$355$	−5.04207	+	20.5771i	−0.267605	+	1.09212i
$356$			17.0881i			0.905668i
$357$	−1.21833	−	22.9964i	−0.0644809	−	1.21710i
$358$	6.40594	−	6.40594i	0.338565	−	0.338565i
$359$	31.0266			1.63752			0.818760	−	0.574136i	$-0.194662\pi$
$359$	31.0266			1.63752			0.818760	+	0.574136i	$0.194662\pi$
$360$	4.06484	+	5.33639i	0.214236	+	0.281253i
$361$	−1.00000			−0.0526316
$362$	12.6699	−	12.6699i	0.665915	−	0.665915i
$363$	0.567970	+	10.7206i	0.0298107	+	0.562688i
$364$			10.3995i			0.545084i
$365$	10.9421	−	6.63512i	0.572736	−	0.347298i
$366$	−13.1982	−	11.8701i	−0.689881	−	0.620460i
$367$	13.0593	+	13.0593i	0.681690	+	0.681690i	0.960381	−	0.278691i	$-0.0899004\pi$
$367$	13.0593	+	13.0593i	0.681690	+	0.681690i	−0.278691	+	0.960381i	$0.589900\pi$
$368$	−5.46874	−	5.46874i	−0.285078	−	0.285078i
$369$	−2.68136	−	25.2347i	−0.139586	−	1.31367i
$370$	4.77678	+	1.17047i	0.248333	+	0.0608496i
$371$			23.5393i			1.22210i
$372$	−0.0193206	+	0.00102359i	−0.00100172	+	5.30705e-5i
$373$	21.2626	−	21.2626i	1.10093	−	1.10093i	0.106636	−	0.994298i	$-0.465992\pi$
$373$	21.2626	−	21.2626i	1.10093	−	1.10093i	0.994298	−	0.106636i	$-0.0340080\pi$
$374$	−29.4234			−1.52145
$375$	−11.9944	+	15.2031i	−0.619389	+	0.785084i
$376$	−2.42443			−0.125031
$377$	−0.378439	+	0.378439i	−0.0194906	+	0.0194906i
$378$	−1.53969	−	9.61481i	−0.0791931	−	0.494533i
$379$		−	27.4201i		−	1.40848i	−0.709963	−	0.704239i	$-0.751288\pi$
$379$		−	27.4201i		−	1.40848i	0.709963	−	0.704239i	$-0.248712\pi$
$380$	2.17182	+	0.532166i	0.111412	+	0.0272995i
$381$	−0.769791	+	0.855919i	−0.0394376	+	0.0438501i
$382$	5.94923	+	5.94923i	0.304389	+	0.304389i
$383$	1.51688	+	1.51688i	0.0775089	+	0.0775089i	0.744798	−	0.667290i	$-0.232546\pi$
$383$	1.51688	+	1.51688i	0.0775089	+	0.0775089i	−0.667290	+	0.744798i	$0.732546\pi$
$384$	−1.15823	+	1.28782i	−0.0591059	+	0.0657190i
$385$	14.8590	−	9.01024i	0.757283	−	0.459204i
$386$			0.577710i			0.0294047i
$387$	−0.348034	+	0.430789i	−0.0176916	+	0.0218982i
$388$	3.48454	−	3.48454i	0.176901	−	0.176901i
$389$	27.2165			1.37993			0.689966	−	0.723841i	$-0.257625\pi$
$389$	27.2165			1.37993			0.689966	+	0.723841i	$0.257625\pi$
$390$	21.1171	+	4.00363i	1.06931	+	0.202732i
$391$	54.8723			2.77501
$392$	2.46662	−	2.46662i	0.124583	−	0.124583i
$393$	−30.7792	+	1.63066i	−1.55260	+	0.0822557i
$394$			4.33601i			0.218445i
$395$	6.63841	−	27.0919i	0.334014	−	1.36314i
$396$	−12.3716	+	1.31456i	−0.621696	+	0.0660592i
$397$	11.0403	+	11.0403i	0.554095	+	0.554095i	0.927620	−	0.373525i	$-0.121851\pi$
$397$	11.0403	+	11.0403i	0.554095	+	0.554095i	−0.373525	+	0.927620i	$0.621851\pi$
$398$	15.5322	+	15.5322i	0.778560	+	0.778560i
$399$	−2.41332	−	2.17047i	−0.120817	−	0.108659i
$400$	−4.43360	−	2.31154i	−0.221680	−	0.115577i
$401$			9.33422i			0.466129i	0.972461	+	0.233064i	$0.0748753\pi$
$401$			9.33422i			0.466129i	−0.972461	+	0.233064i	$0.925125\pi$
$402$	0.618954	+	11.6830i	0.0308706	+	0.582694i
$403$	−0.0438339	+	0.0438339i	−0.00218352	+	0.00218352i
$404$	16.2835			0.810135
$405$	−20.1164	−	0.575067i	−0.999592	−	0.0285753i
$406$	−0.180722			−0.00896909
$407$	−6.44969	+	6.44969i	−0.319699	+	0.319699i
$408$	−0.650141	−	12.2716i	−0.0321868	−	0.607537i
$409$			15.1973i			0.751460i	0.926729	+	0.375730i	$0.122608\pi$
$409$			15.1973i			0.751460i	−0.926729	+	0.375730i	$0.877392\pi$
$410$	9.80737	+	16.1735i	0.484352	+	0.798754i
$411$	−16.9551	−	15.2489i	−0.836332	−	0.752174i
$412$	−2.44289	−	2.44289i	−0.120353	−	0.120353i
$413$	−8.49146	−	8.49146i	−0.417837	−	0.417837i
$414$	23.0720	−	2.45155i	1.13393	−	0.120487i
$415$	−2.35594	−	3.88523i	−0.115648	−	0.190718i
$416$			5.54954i			0.272088i
$417$	−21.4591	+	1.13688i	−1.05086	+	0.0556734i
$418$	−2.93243	+	2.93243i	−0.143430	+	0.143430i
$419$	3.37395			0.164828			0.0824142	−	0.996598i	$-0.473737\pi$
$419$	3.37395			0.164828			0.0824142	+	0.996598i	$0.473737\pi$
$420$	4.08623	+	5.99815i	0.199388	+	0.292680i
$421$	16.8556			0.821493			0.410746	−	0.911750i	$-0.365268\pi$
$421$	16.8556			0.821493			0.410746	+	0.911750i	$0.365268\pi$
$422$	−7.74793	+	7.74793i	−0.377163	+	0.377163i
$423$	4.57079	−	5.65763i	0.222240	−	0.275083i
$424$			12.5614i			0.610033i
$425$	33.8397	−	10.6462i	1.64147	−	0.516415i
$426$	10.9738	−	12.2016i	0.531683	−	0.591171i
$427$	−13.5800	−	13.5800i	−0.657183	−	0.657183i
$428$	−1.32951	−	1.32951i	−0.0642643	−	0.0642643i
$429$	−26.6560	+	29.6385i	−1.28696	+	1.43096i
$430$	0.0982398	−	0.400926i	0.00473754	−	0.0193344i
$431$		−	16.6210i		−	0.800607i	−0.916383	−	0.400303i	$-0.868905\pi$
$431$		−	16.6210i		−	0.800607i	0.916383	−	0.400303i	$-0.131095\pi$
$432$	−0.821629	−	5.13078i	−0.0395306	−	0.246855i
$433$	10.6960	−	10.6960i	0.514019	−	0.514019i	−0.401737	−	0.915755i	$-0.631593\pi$
$433$	10.6960	−	10.6960i	0.514019	−	0.514019i	0.915755	+	0.401737i	$0.131593\pi$
$434$	−0.0209327			−0.00100480
$435$	−0.0695747	+	0.366970i	−0.00333585	+	0.0175949i
$436$	8.51296			0.407697
$437$	5.46874	−	5.46874i	0.261605	−	0.261605i
$438$	−9.89837	+	0.524407i	−0.472962	+	0.0250571i
$439$			18.1152i			0.864593i	0.901731	+	0.432297i	$0.142297\pi$
$439$			18.1152i			0.864593i	−0.901731	+	0.432297i	$0.857703\pi$
$440$	7.92924	−	4.80816i	0.378012	−	0.229220i
$441$	1.10575	+	10.4064i	0.0526546	+	0.495542i
$442$	−27.8415	−	27.8415i	−1.32428	−	1.32428i
$443$	−15.6435	−	15.6435i	−0.743247	−	0.743247i	0.229955	−	0.973201i	$-0.426142\pi$
$443$	−15.6435	−	15.6435i	−0.743247	−	0.743247i	−0.973201	+	0.229955i	$0.926142\pi$
$444$	−2.83249	−	2.54746i	−0.134424	−	0.120897i
$445$	37.1123	+	9.09371i	1.75929	+	0.431083i
$446$		−	5.39430i		−	0.255428i
$447$	−0.994537	−	18.7722i	−0.0470400	−	0.887897i
$448$	−1.32508	+	1.32508i	−0.0626042	+	0.0626042i
$449$	4.48299			0.211565			0.105783	−	0.994389i	$-0.466265\pi$
$449$	4.48299			0.211565			0.105783	+	0.994389i	$0.466265\pi$
$450$	13.7529	−	5.98824i	0.648316	−	0.282288i
$451$	−35.0798			−1.65185
$452$	−1.46934	+	1.46934i	−0.0691122	+	0.0691122i
$453$	−0.111090	−	2.09687i	−0.00521948	−	0.0985195i
$454$		−	11.9990i		−	0.563143i
$455$	22.5859	+	5.53428i	1.05884	+	0.259451i
$456$	−1.28782	−	1.15823i	−0.0603079	−	0.0542393i
$457$	−6.38576	−	6.38576i	−0.298713	−	0.298713i	0.541797	−	0.840510i	$-0.317744\pi$
$457$	−6.38576	−	6.38576i	−0.298713	−	0.298713i	−0.840510	+	0.541797i	$0.817744\pi$
$458$	−9.82700	−	9.82700i	−0.459186	−	0.459186i
$459$	29.8627	+	21.6186i	1.39387	+	1.00907i
$460$	−14.7874	+	8.96684i	−0.689466	+	0.418081i
$461$			9.14050i			0.425716i	0.977083	+	0.212858i	$0.0682771\pi$
$461$			9.14050i			0.425716i	−0.977083	+	0.212858i	$0.931723\pi$
$462$	−13.4416	+	0.712125i	−0.625360	+	0.0331311i
$463$	−11.7522	+	11.7522i	−0.546170	+	0.546170i	−0.925331	−	0.379161i	$-0.876213\pi$
$463$	−11.7522	+	11.7522i	−0.546170	+	0.546170i	0.379161	+	0.925331i	$0.376213\pi$
$464$	−0.0964393			−0.00447708
$465$	−0.00805871	+	0.0425055i	−0.000373714	+	0.00197115i
$466$	−29.8774			−1.38404
$467$	10.8294	−	10.8294i	0.501124	−	0.501124i	−0.410663	−	0.911787i	$-0.634703\pi$
$467$	10.8294	−	10.8294i	0.501124	−	0.501124i	0.911787	+	0.410663i	$0.134703\pi$
$468$	−12.9503	−	10.4626i	−0.598629	−	0.483632i
$469$			12.6578i			0.584484i
$470$	−1.29020	+	5.26543i	−0.0595126	+	0.242876i
$471$	16.4711	−	18.3140i	0.758949	−	0.843864i
$472$	−4.53132	−	4.53132i	−0.208571	−	0.208571i
$473$	0.541336	+	0.541336i	0.0248907	+	0.0248907i
$474$	−14.4482	+	16.0647i	−0.663627	+	0.737877i
$475$	2.31154	−	4.43360i	0.106061	−	0.203427i
$476$		−	13.2956i		−	0.609403i
$477$	−29.3130	−	23.6820i	−1.34215	−	1.08432i
$478$	2.18786	−	2.18786i	0.100070	−	0.100070i
$479$	16.6381			0.760216			0.380108	−	0.924942i	$-0.375887\pi$
$479$	16.6381			0.760216			0.380108	+	0.924942i	$0.375887\pi$
$480$	2.18055	+	3.20081i	0.0995280	+	0.146096i
$481$	−12.2059			−0.556539
$482$	−4.68513	+	4.68513i	−0.213402	+	0.213402i
$483$	25.0675	−	1.32806i	1.14061	−	0.0604287i
$484$			6.19825i			0.281738i
$485$	−5.71343	−	9.42214i	−0.259434	−	0.427837i
$486$	13.5222	+	7.75574i	0.613377	+	0.351807i
$487$	6.95016	+	6.95016i	0.314942	+	0.314942i	0.846820	−	0.531879i	$-0.178514\pi$
$487$	6.95016	+	6.95016i	0.314942	+	0.314942i	−0.531879	+	0.846820i	$0.678514\pi$
$488$	−7.24675	−	7.24675i	−0.328045	−	0.328045i
$489$	15.6800	+	14.1022i	0.709073	+	0.637721i
$490$	−4.04439	−	6.66969i	−0.182707	−	0.301306i
$491$			3.80980i			0.171934i	0.996298	+	0.0859670i	$0.0273980\pi$
$491$			3.80980i			0.171934i	−0.996298	+	0.0859670i	$0.972602\pi$
$492$	−0.775126	−	14.6308i	−0.0349454	−	0.659607i
$493$	0.483827	−	0.483827i	0.0217905	−	0.0217905i
$494$	−5.54954			−0.249685
$495$	−3.72875	+	27.5684i	−0.167595	+	1.23911i
$496$	−0.0111704			−0.000501565
$497$	12.5546	−	12.5546i	0.563152	−	0.563152i
$498$	0.186202	+	3.51463i	0.00834390	+	0.157494i
$499$		−	12.0717i		−	0.540405i	−0.962804	−	0.270202i	$-0.912909\pi$
$499$		−	12.0717i		−	0.540405i	0.962804	−	0.270202i	$-0.0870906\pi$
$500$	−7.37965	+	8.39885i	−0.330028	+	0.375608i
$501$	4.19113	+	3.76939i	0.187246	+	0.168404i
$502$	−15.0984	−	15.0984i	−0.673874	−	0.673874i
$503$	−8.43285	−	8.43285i	−0.376002	−	0.376002i	0.493655	−	0.869658i	$-0.335660\pi$
$503$	−8.43285	−	8.43285i	−0.376002	−	0.376002i	−0.869658	+	0.493655i	$0.835660\pi$
$504$	−0.594013	−	5.59037i	−0.0264595	−	0.249015i
$505$	8.66553	−	35.3648i	0.385611	−	1.57371i
$506$		−	32.0733i		−	1.42583i
$507$	−30.7828	+	1.63084i	−1.36711	+	0.0724283i
$508$	−0.469960	+	0.469960i	−0.0208511	+	0.0208511i
$509$	14.4418			0.640120			0.320060	−	0.947397i	$-0.396297\pi$
$509$	14.4418			0.640120			0.320060	+	0.947397i	$0.396297\pi$
$510$	−26.9978	−	5.11856i	−1.19548	−	0.226654i
$511$	−10.7243			−0.474415
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	5.13078	−	0.821629i	0.226530	−	0.0362758i
$514$			4.04532i			0.178431i
$515$	−6.60554	+	4.00549i	−0.291075	+	0.176503i
$516$	−0.213814	+	0.237737i	−0.00941265	+	0.0104658i
$517$	−7.10947	−	7.10947i	−0.312674	−	0.312674i
$518$	−2.91443	−	2.91443i	−0.128053	−	0.128053i
$519$	−12.6167	+	14.0284i	−0.553814	+	0.615778i
$520$	12.0526	+	2.95328i	0.528541	+	0.129510i
$521$		−	36.0409i		−	1.57898i	−0.613762	−	0.789491i	$-0.710345\pi$
$521$		−	36.0409i		−	1.57898i	0.613762	−	0.789491i	$-0.289655\pi$
$522$	0.181817	−	0.225049i	0.00795792	−	0.00985015i
$523$	21.2547	−	21.2547i	0.929403	−	0.929403i	−0.0682644	−	0.997667i	$-0.521746\pi$
$523$	21.2547	−	21.2547i	0.929403	−	0.929403i	0.997667	+	0.0682644i	$0.0217461\pi$
$524$	−17.7953			−0.777391
$525$	15.2015	−	5.68255i	0.663446	−	0.248007i
$526$	27.6026			1.20353
$527$	0.0560407	−	0.0560407i	0.00244117	−	0.00244117i
$528$	−7.17289	+	0.380013i	−0.312160	+	0.0165380i
$529$			36.8142i			1.60062i
$530$	27.2810	+	6.68473i	1.18501	+	0.290366i
$531$	19.1172	−	2.03132i	0.829614	−	0.0881519i
$532$	−1.32508	−	1.32508i	−0.0574495	−	0.0574495i
$533$	−33.1938	−	33.1938i	−1.43778	−	1.43778i
$534$	−22.0065	−	19.7920i	−0.952314	−	0.856485i
$535$	−3.59497	+	2.17993i	−0.155424	+	0.0942468i
$536$			6.75463i			0.291756i
$537$	0.830147	+	15.6693i	0.0358235	+	0.676181i
$538$	6.78356	−	6.78356i	0.292460	−	0.292460i
$539$	14.4663			0.623109
$540$	−11.5804	−	0.945999i	−0.498340	−	0.0407093i
$541$	−10.6163			−0.456431			−0.228216	−	0.973611i	$-0.573289\pi$
$541$	−10.6163			−0.456431			−0.228216	+	0.973611i	$0.573289\pi$
$542$	−21.4977	+	21.4977i	−0.923405	+	0.923405i
$543$	1.64189	+	30.9913i	0.0704604	+	1.32996i
$544$		−	7.09497i		−	0.304195i
$545$	4.53031	−	18.4886i	0.194057	−	0.791965i
$546$	−13.3928	−	12.0451i	−0.573158	−	0.515483i
$547$	13.8661	+	13.8661i	0.592872	+	0.592872i	0.938406	−	0.345534i	$-0.112302\pi$
$547$	13.8661	+	13.8661i	0.592872	+	0.592872i	−0.345534	+	0.938406i	$0.612302\pi$
$548$	−9.30953	−	9.30953i	−0.397683	−	0.397683i
$549$	30.5732	−	3.24861i	1.30483	−	0.138647i
$550$	−6.22279	−	19.7796i	−0.265341	−	0.843406i
$551$		−	0.0964393i		−	0.00410845i
$552$	13.3769	−	0.708695i	0.569357	−	0.0301640i
$553$	−16.5295	+	16.5295i	−0.702905	+	0.702905i
$554$	11.3525			0.482323
$555$	−7.03999	+	4.79598i	−0.298831	+	0.203578i
$556$	−12.4068			−0.526165
$557$	−0.548599	+	0.548599i	−0.0232449	+	0.0232449i	−0.718634	−	0.695389i	$-0.755232\pi$
$557$	−0.548599	+	0.548599i	−0.0232449	+	0.0232449i	0.695389	+	0.718634i	$0.255232\pi$
$558$	0.0210596	−	0.0260671i	0.000891522	−	0.00110351i
$559$			1.02446i			0.0433302i
$560$	2.17267	+	3.58300i	0.0918122	+	0.151409i
$561$	34.0792	−	37.8922i	1.43883	−	1.59981i
$562$	−9.51365	−	9.51365i	−0.401309	−	0.401309i
$563$	−1.13682	−	1.13682i	−0.0479114	−	0.0479114i	0.682745	−	0.730657i	$-0.260786\pi$
$563$	−1.13682	−	1.13682i	−0.0479114	−	0.0479114i	−0.730657	+	0.682745i	$0.760786\pi$
$564$	2.80806	−	3.12225i	0.118241	−	0.131470i
$565$	2.40922	+	3.97309i	0.101356	+	0.167149i
$566$			19.1015i			0.802894i
$567$	14.1655	+	9.15336i	0.594896	+	0.384405i
$568$	6.69956	−	6.69956i	0.281107	−	0.281107i
$569$	25.5607			1.07156			0.535781	−	0.844357i	$-0.320017\pi$
$569$	25.5607			1.07156			0.535781	+	0.844357i	$0.320017\pi$
$570$	−3.20081	+	2.18055i	−0.134067	+	0.0913332i
$571$	−28.9943			−1.21337			−0.606686	−	0.794942i	$-0.707501\pi$
$571$	−28.9943			−1.21337			−0.606686	+	0.794942i	$0.707501\pi$
$572$	−16.2736	+	16.2736i	−0.680434	+	0.680434i
$573$	−14.5522	+	0.770961i	−0.607925	+	0.0322074i
$574$		−	15.8516i		−	0.661633i
$575$	11.6050	+	36.8874i	0.483962	+	1.53831i
$576$	−0.316985	−	2.98321i	−0.0132077	−	0.124300i
$577$	−28.4272	−	28.4272i	−1.18344	−	1.18344i	−0.978847	−	0.204594i	$-0.934413\pi$
$577$	−28.4272	−	28.4272i	−1.18344	−	1.18344i	−0.204594	−	0.978847i	$-0.565587\pi$
$578$	23.5740	+	23.5740i	0.980549	+	0.980549i
$579$	−0.743990	−	0.669124i	−0.0309192	−	0.0278079i
$580$	−0.0513217	+	0.209449i	−0.00213102	+	0.00869688i
$581$			3.80789i			0.157978i
$582$	0.451562	+	8.52339i	0.0187178	+	0.353306i
$583$	−36.8352	+	36.8352i	−1.52556	+	1.52556i
$584$	−5.72284			−0.236813
$585$	−29.6145	+	22.5580i	−1.22441	+	0.932657i
$586$	2.72021			0.112371
$587$	−23.4065	+	23.4065i	−0.966088	+	0.966088i	−0.999444	−	0.0333555i	$-0.989381\pi$
$587$	−23.4065	+	23.4065i	−0.966088	+	0.966088i	0.0333555	+	0.999444i	$0.489381\pi$
$588$	0.319649	+	6.03349i	0.0131821	+	0.248817i
$589$		−	0.0111704i		−	0.000460267i
$590$	−12.2526	+	7.42980i	−0.504433	+	0.305880i
$591$	−5.58402	−	5.02211i	−0.229696	−	0.206582i
$592$	−1.55524	−	1.55524i	−0.0639198	−	0.0639198i
$593$	17.7918	+	17.7918i	0.730620	+	0.730620i	0.970743	−	0.240122i	$-0.0771876\pi$
$593$	17.7918	+	17.7918i	0.730620	+	0.730620i	−0.240122	+	0.970743i	$0.577188\pi$
$594$	12.6363	−	17.4550i	0.518473	−	0.716188i
$595$	−28.8757	−	7.07547i	−1.18379	−	0.290066i
$596$		−	10.8534i		−	0.444571i
$597$	−37.9927	+	2.01282i	−1.55494	+	0.0823794i
$598$	30.3490	−	30.3490i	1.24106	−	1.24106i
$599$	−30.4391			−1.24371			−0.621854	−	0.783134i	$-0.713620\pi$
$599$	−30.4391			−1.24371			−0.621854	+	0.783134i	$0.713620\pi$
$600$	8.11200	−	3.03240i	0.331171	−	0.123797i
$601$	1.09778			0.0447792			0.0223896	−	0.999749i	$-0.492873\pi$
$601$	1.09778			0.0447792			0.0223896	+	0.999749i	$0.492873\pi$
$602$	−0.244615	+	0.244615i	−0.00996975	+	0.00996975i
$603$	−15.7625	−	12.7345i	−0.641899	−	0.518590i
$604$		−	1.21233i		−	0.0493288i
$605$	13.4615	+	3.29850i	0.547287	+	0.134103i
$606$	−18.8601	+	20.9703i	−0.766140	+	0.851860i
$607$	−8.70025	−	8.70025i	−0.353132	−	0.353132i	0.508141	−	0.861274i	$-0.330333\pi$
$607$	−8.70025	−	8.70025i	−0.353132	−	0.353132i	−0.861274	+	0.508141i	$0.830333\pi$
$608$	−0.707107	−	0.707107i	−0.0286770	−	0.0286770i
$609$	0.209319	−	0.232738i	0.00848202	−	0.00943104i
$610$	−19.5951	+	11.8822i	−0.793382	+	0.481094i
$611$		−	13.4545i		−	0.544310i
$612$	16.5567	+	13.3762i	0.669267	+	0.540700i
$613$	4.40309	−	4.40309i	0.177839	−	0.177839i	−0.612574	−	0.790413i	$-0.709866\pi$
$613$	4.40309	−	4.40309i	0.177839	−	0.177839i	0.790413	+	0.612574i	$0.209866\pi$
$614$	24.9819			1.00819
$615$	−32.1879	−	6.10257i	−1.29794	−	0.246079i
$616$	−7.77140			−0.313119
$617$	8.04047	−	8.04047i	0.323697	−	0.323697i	−0.526486	−	0.850183i	$-0.676491\pi$
$617$	8.04047	−	8.04047i	0.323697	−	0.323697i	0.850183	+	0.526486i	$0.176491\pi$
$618$	5.97545	−	0.316574i	0.240368	−	0.0127345i
$619$		−	23.1721i		−	0.931366i	−0.884952	−	0.465683i	$-0.845809\pi$
$619$		−	23.1721i		−	0.931366i	0.884952	−	0.465683i	$-0.154191\pi$
$620$	−0.00594450	+	0.0242600i	−0.000238737	+	0.000974307i
$621$	−23.5656	+	32.5522i	−0.945656	+	1.30627i
$622$	−6.82047	−	6.82047i	−0.273476	−	0.273476i
$623$	−22.6431	−	22.6431i	−0.907178	−	0.907178i
$624$	−7.14683	−	6.42767i	−0.286102	−	0.257313i
$625$	14.3136	+	20.4969i	0.572544	+	0.819874i
$626$			14.2991i			0.571508i
$627$	−0.380013	−	7.17289i	−0.0151763	−	0.286458i
$628$	10.0557	−	10.0557i	0.401265	−	0.401265i
$629$	15.6049			0.622210
$630$	−12.4574	−	1.68492i	−0.496314	−	0.0671287i
$631$	−16.4094			−0.653249			−0.326625	−	0.945154i	$-0.605911\pi$
$631$	−16.4094			−0.653249			−0.326625	+	0.945154i	$0.605911\pi$
$632$	−8.82067	+	8.82067i	−0.350867	+	0.350867i
$633$	−1.00406	−	18.9519i	−0.0399076	−	0.753271i
$634$		−	13.5304i		−	0.537361i
$635$	0.770572	+	1.27077i	0.0305792	+	0.0504288i
$636$	−16.1768	−	14.5490i	−0.641453	−	0.576905i
$637$	13.6886	+	13.6886i	0.542361	+	0.542361i
$638$	−0.282801	−	0.282801i	−0.0111962	−	0.0111962i
$639$	3.00331	+	28.2647i	0.118809	+	1.11813i
$640$	1.15941	+	1.91201i	0.0458297	+	0.0755787i
$641$		−	28.1764i		−	1.11290i	−0.830881	−	0.556450i	$-0.812163\pi$
$641$		−	28.1764i		−	1.11290i	0.830881	−	0.556450i	$-0.187837\pi$
$642$	3.25206	−	0.172291i	0.128349	−	0.00679980i
$643$	4.86470	−	4.86470i	0.191845	−	0.191845i	−0.604648	−	0.796493i	$-0.706686\pi$
$643$	4.86470	−	4.86470i	0.191845	−	0.191845i	0.796493	+	0.604648i	$0.206686\pi$
$644$	14.4930			0.571106
$645$	0.402537	+	0.590882i	0.0158499	+	0.0232659i
$646$	7.09497			0.279148
$647$	7.02609	−	7.02609i	0.276224	−	0.276224i	−0.555376	−	0.831600i	$-0.687425\pi$
$647$	7.02609	−	7.02609i	0.276224	−	0.276224i	0.831600	+	0.555376i	$0.187425\pi$
$648$	7.55919	+	4.88454i	0.296953	+	0.191883i
$649$		−	26.5755i		−	1.04318i
$650$	12.8280	−	24.6044i	0.503154	−	0.965065i
$651$	0.0242450	−	0.0269577i	0.000950236	−	0.00105655i
$652$	8.60942	+	8.60942i	0.337171	+	0.337171i
$653$	26.3564	+	26.3564i	1.03141	+	1.03141i	0.999491	+	0.0319150i	$0.0101606\pi$
$653$	26.3564	+	26.3564i	1.03141	+	1.03141i	0.0319150	+	0.999491i	$0.489839\pi$
$654$	−9.86001	+	10.9632i	−0.385557	+	0.428695i
$655$	−9.47005	+	38.6482i	−0.370026	+	1.51011i
$656$		−	8.45893i		−	0.330266i
$657$	10.7893	−	13.3547i	0.420930	−	0.521018i
$658$	3.21257	−	3.21257i	0.125239	−	0.125239i
$659$	−11.1631			−0.434853			−0.217426	−	0.976077i	$-0.569766\pi$
$659$	−11.1631			−0.434853			−0.217426	+	0.976077i	$0.569766\pi$
$660$	−2.99185	+	15.7804i	−0.116458	+	0.614253i
$661$	39.9360			1.55333			0.776665	−	0.629914i	$-0.216910\pi$
$661$	39.9360			1.55333			0.776665	+	0.629914i	$0.216910\pi$
$662$	7.68217	−	7.68217i	0.298576	−	0.298576i
$663$	68.1019	−	3.60798i	2.64486	−	0.140122i
$664$			2.03202i			0.0788575i
$665$	−3.58300	+	2.17267i	−0.138943	+	0.0842526i
$666$	6.56137	−	0.697189i	0.254248	−	0.0270155i
$667$	0.527401	+	0.527401i	0.0204211	+	0.0204211i
$668$	2.30123	+	2.30123i	0.0890372	+	0.0890372i
$669$	6.94691	+	6.24787i	0.268583	+	0.241556i
$670$	14.6698	+	3.59458i	0.566745	+	0.138871i
$671$		−	42.5011i		−	1.64074i
$672$	−0.171717	−	3.24123i	−0.00662414	−	0.125033i
$673$	−27.5847	+	27.5847i	−1.06331	+	1.06331i	−0.0654567	+	0.997855i	$0.520850\pi$
$673$	−27.5847	+	27.5847i	−1.06331	+	1.06331i	−0.997855	+	0.0654567i	$0.979150\pi$
$674$	−4.00743			−0.154361
$675$	−8.21722	+	24.6471i	−0.316281	+	0.948666i
$676$	−17.7974			−0.684514
$677$	18.4404	−	18.4404i	0.708721	−	0.708721i	−0.257545	−	0.966266i	$-0.582914\pi$
$677$	18.4404	−	18.4404i	0.708721	−	0.708721i	0.966266	+	0.257545i	$0.0829135\pi$
$678$	−0.190413	−	3.59410i	−0.00731275	−	0.138031i
$679$			9.23459i			0.354391i
$680$	−15.4090	−	3.77570i	−0.590908	−	0.144792i
$681$	15.4527	+	13.8977i	0.592147	+	0.532561i
$682$	−0.0327563	−	0.0327563i	−0.00125430	−	0.00125430i
$683$	−6.88800	−	6.88800i	−0.263562	−	0.263562i	0.562937	−	0.826500i	$-0.309671\pi$
$683$	−6.88800	−	6.88800i	−0.263562	−	0.263562i	−0.826500	+	0.562937i	$0.809671\pi$
$684$	2.98321	−	0.316985i	0.114066	−	0.0121202i
$685$	−25.1728	+	15.2644i	−0.961804	+	0.583223i
$686$			19.6546i			0.750415i
$687$	24.0374	−	1.27348i	0.917085	−	0.0485864i
$688$	−0.130534	+	0.130534i	−0.00497658	+	0.00497658i
$689$	−69.7097			−2.65573
$690$	5.57956	−	29.4293i	0.212410	−	1.12035i
$691$	−6.70656			−0.255129			−0.127565	−	0.991830i	$-0.540716\pi$
$691$	−6.70656			−0.255129			−0.127565	+	0.991830i	$0.540716\pi$
$692$	−7.70257	+	7.70257i	−0.292808	+	0.292808i
$693$	14.6515	−	18.1353i	0.556563	−	0.688901i
$694$			17.3716i			0.659418i
$695$	−6.60247	+	26.9453i	−0.250446	+	1.02209i
$696$	0.111699	−	0.124197i	0.00423395	−	0.00470767i
$697$	42.4377	+	42.4377i	1.60744	+	1.60744i
$698$	−18.3548	−	18.3548i	−0.694740	−	0.694740i
$699$	34.6050	−	38.4769i	1.30888	−	1.45533i
$700$	8.93785	−	2.81190i	0.337819	−	0.106280i
$701$		−	8.68700i		−	0.328104i	−0.986452	−	0.164052i	$-0.947544\pi$
$701$		−	8.68700i		−	0.328104i	0.986452	−	0.164052i	$-0.0524564\pi$
$702$	28.4735	−	4.55966i	1.07466	−	0.172093i
$703$	1.55524	−	1.55524i	0.0586569	−	0.0586569i
$704$	−4.14708			−0.156299
$705$	−5.28660	−	7.76016i	−0.199105	−	0.292265i
$706$	16.3627			0.615818
$707$	−21.5770	+	21.5770i	−0.811485	+	0.811485i
$708$	11.0839	−	0.587215i	0.416558	−	0.0220689i
$709$			20.6106i			0.774049i	0.922070	+	0.387024i	$0.126497\pi$
$709$			20.6106i			0.774049i	−0.922070	+	0.387024i	$0.873503\pi$
$710$	−10.9850	−	18.1155i	−0.412258	−	0.679863i
$711$	−3.95417	−	37.2134i	−0.148293	−	1.39561i
$712$	−12.0831	−	12.0831i	−0.452834	−	0.452834i
$713$	0.0610879	+	0.0610879i	0.00228776	+	0.00228776i
$714$	17.1224	+	15.3994i	0.640790	+	0.576309i
$715$	26.6831	+	44.0036i	0.997890	+	1.64564i
$716$			9.05937i			0.338565i
$717$	0.283525	+	5.35164i	0.0105884	+	0.199861i
$718$	−21.9391	+	21.9391i	−0.818760	+	0.818760i
$719$	39.9182			1.48870			0.744350	−	0.667790i	$-0.232760\pi$
$719$	39.9182			1.48870			0.744350	+	0.667790i	$0.232760\pi$
$720$	−6.64767	−	0.899127i	−0.247744	−	0.0335085i
$721$	6.47405			0.241106
$722$	0.707107	−	0.707107i	0.0263158	−	0.0263158i
$723$	−0.607147	−	11.4601i	−0.0225800	−	0.426206i
$724$			17.9179i			0.665915i
$725$	0.427573	+	0.222923i	0.0158797	+	0.00827915i
$726$	−7.98226	−	7.17902i	−0.296249	−	0.266439i
$727$	−4.40463	−	4.40463i	−0.163359	−	0.163359i	0.620694	−	0.784053i	$-0.286851\pi$
$727$	−4.40463	−	4.40463i	−0.163359	−	0.163359i	−0.784053	+	0.620694i	$0.786851\pi$
$728$	−7.35358	−	7.35358i	−0.272542	−	0.272542i
$729$	−25.6499	+	8.43120i	−0.949995	+	0.312267i
$730$	−3.04550	+	12.4290i	−0.112719	+	0.460017i
$731$		−	1.30976i		−	0.0484431i
$732$	17.7260	−	0.939107i	0.655171	−	0.0347104i
$733$	−13.9718	+	13.9718i	−0.516061	+	0.516061i	−0.916377	−	0.400316i	$-0.868900\pi$
$733$	−13.9718	+	13.9718i	−0.516061	+	0.516061i	0.400316	+	0.916377i	$0.368900\pi$
$734$	−18.4687			−0.681690
$735$	13.2738	+	2.51660i	0.489610	+	0.0928261i
$736$	7.73397			0.285078
$737$	−19.8074	+	19.8074i	−0.729617	+	0.729617i
$738$	19.7397	+	15.9477i	0.726627	+	0.587041i
$739$		−	38.9043i		−	1.43112i	−0.698553	−	0.715558i	$-0.746172\pi$
$739$		−	38.9043i		−	1.43112i	0.698553	−	0.715558i	$-0.253828\pi$
$740$	−4.20534	+	2.55005i	−0.154591	+	0.0937417i
$741$	6.42767	−	7.14683i	0.236126	−	0.262545i
$742$	−16.6448	−	16.6448i	−0.611050	−	0.611050i
$743$	31.6523	+	31.6523i	1.16121	+	1.16121i	0.984211	+	0.177000i	$0.0566393\pi$
$743$	31.6523	+	31.6523i	1.16121	+	1.16121i	0.177000	+	0.984211i	$0.443361\pi$
$744$	0.0129379	−	0.0143855i	0.000474327	−	0.000527398i
$745$	−23.5715	−	5.77579i	−0.863594	−	0.211609i
$746$			30.0698i			1.10093i
$747$	−4.74189	−	3.83097i	−0.173497	−	0.140168i
$748$	20.8055	−	20.8055i	0.760724	−	0.760724i
$749$	3.52342			0.128743
$750$	−2.26888	−	19.2315i	−0.0828479	−	0.702237i
$751$	−35.5821			−1.29841			−0.649205	−	0.760613i	$-0.724898\pi$
$751$	−35.5821			−1.29841			−0.649205	+	0.760613i	$0.724898\pi$
$752$	1.71433	−	1.71433i	0.0625153	−	0.0625153i
$753$	36.9315	−	1.95660i	1.34586	−	0.0713025i
$754$		−	0.535193i		−	0.0194906i
$755$	−2.63295	−	0.645159i	−0.0958230	−	0.0234797i
$756$	7.88743	+	5.70998i	0.286863	+	0.207670i
$757$	−11.1640	−	11.1640i	−0.405762	−	0.405762i	0.474496	−	0.880258i	$-0.342630\pi$
$757$	−11.1640	−	11.1640i	−0.405762	−	0.405762i	−0.880258	+	0.474496i	$0.842630\pi$
$758$	19.3890	+	19.3890i	0.704239	+	0.704239i
$759$	41.3049	+	37.1485i	1.49927	+	1.34840i
$760$	−1.91201	+	1.15941i	−0.0693558	+	0.0420562i
$761$			9.30941i			0.337466i	0.985662	+	0.168733i	$0.0539675\pi$
$761$			9.30941i			0.337466i	−0.985662	+	0.168733i	$0.946032\pi$
$762$	−0.0609022	−	1.14955i	−0.00220625	−	0.0416438i
$763$	−11.2804	+	11.2804i	−0.408377	+	0.408377i
$764$	−8.41348			−0.304389
$765$	37.8616	−	28.8399i	1.36889	−	1.04271i
$766$	−2.14519			−0.0775089
$767$	25.1467	−	25.1467i	0.907996	−	0.907996i
$768$	−0.0916341	−	1.72963i	−0.00330656	−	0.0624125i
$769$			36.9866i			1.33377i	0.745161	+	0.666885i	$0.232373\pi$
$769$			36.9866i			1.33377i	−0.745161	+	0.666885i	$0.767627\pi$
$770$	−4.13568	+	16.8781i	−0.149039	+	0.608244i
$771$	−5.20966	−	4.68542i	−0.187621	−	0.168741i
$772$	−0.408503	−	0.408503i	−0.0147023	−	0.0147023i
$773$	32.3504	+	32.3504i	1.16356	+	1.16356i	0.983690	+	0.179873i	$0.0575687\pi$
$773$	32.3504	+	32.3504i	1.16356	+	1.16356i	0.179873	+	0.983690i	$0.442431\pi$
$774$	−0.0585166	−	0.550711i	−0.00210334	−	0.0197949i
$775$	0.0495250	+	0.0258207i	0.00177899	+	0.000927509i
$776$			4.92788i			0.176901i
$777$	7.12887	−	0.377682i	0.255747	−	0.0135492i
$778$	−19.2450	+	19.2450i	−0.689966	+	0.689966i
$779$	8.45893			0.303073
$780$	−17.7630	+	12.1010i	−0.636018	+	0.433287i
$781$	39.2919			1.40598
$782$	−38.8006	+	38.8006i	−1.38751	+	1.38751i
$783$	0.0792373	+	0.494809i	0.00283171	+	0.0176830i
$784$			3.48832i			0.124583i
$785$	−16.4878	−	27.1904i	−0.588476	−	0.970467i
$786$	20.6111	−	22.9172i	0.735175	−	0.817430i
$787$	−6.93880	−	6.93880i	−0.247342	−	0.247342i	0.572537	−	0.819879i	$-0.305959\pi$
$787$	−6.93880	−	6.93880i	−0.247342	−	0.247342i	−0.819879	+	0.572537i	$0.805959\pi$
$788$	−3.06602	−	3.06602i	−0.109222	−	0.109222i
$789$	−31.9703	+	35.5473i	−1.13817	+	1.26552i
$790$	14.4628	+	23.8510i	0.514565	+	0.848579i
$791$		−	3.89400i		−	0.138455i
$792$	7.81850	−	9.67757i	0.277818	−	0.343877i
$793$	40.2161	−	40.2161i	1.42812	−	1.42812i
$794$	−15.6133			−0.554095
$795$	−40.2065	+	27.3906i	−1.42598	+	0.971446i
$796$	−21.9659			−0.778560
$797$	16.0617	−	16.0617i	0.568936	−	0.568936i	−0.362895	−	0.931830i	$-0.618212\pi$
$797$	16.0617	−	16.0617i	0.568936	−	0.568936i	0.931830	+	0.362895i	$0.118212\pi$
$798$	3.24123	−	0.171717i	0.114738	−	0.00607873i
$799$			17.2013i			0.608538i
$800$	4.76953	−	1.50052i	0.168628	−	0.0530515i
$801$	50.9774	−	5.41668i	1.80120	−	0.191389i
$802$	−6.60029	−	6.60029i	−0.233064	−	0.233064i
$803$	−16.7818	−	16.7818i	−0.592217	−	0.592217i
$804$	−8.69878	−	7.82344i	−0.306782	−	0.275912i
$805$	7.71271	−	31.4763i	0.271837	−	1.10939i
$806$		−	0.0619904i		−	0.00218352i
$807$	0.879082	+	16.5930i	0.0309451	+	0.584101i
$808$	−11.5142	+	11.5142i	−0.405067	+	0.405067i
$809$	10.5712			0.371665			0.185832	−	0.982581i	$-0.440502\pi$
$809$	10.5712			0.371665			0.185832	+	0.982581i	$0.440502\pi$
$810$	14.6311	−	13.8178i	0.514083	−	0.485508i
$811$	15.0113			0.527119			0.263560	−	0.964643i	$-0.415103\pi$
$811$	15.0113			0.527119			0.263560	+	0.964643i	$0.415103\pi$
$812$	0.127790	−	0.127790i	0.00448454	−	0.00448454i
$813$	−2.78589	−	52.5846i	−0.0977053	−	1.84422i
$814$		−	9.12123i		−	0.319699i
$815$	23.2797	−	14.1165i	0.815454	−	0.494478i
$816$	9.13708	+	8.21764i	0.319862	+	0.287675i
$817$	−0.130534	−	0.130534i	−0.00456682	−	0.00456682i
$818$	−10.7461	−	10.7461i	−0.375730	−	0.375730i
$819$	31.0240	−	3.29650i	1.08407	−	0.115189i
$820$	−18.3713	−	4.50156i	−0.641553	−	0.157201i
$821$		−	18.8147i		−	0.656638i	−0.944567	−	0.328319i	$-0.893518\pi$
$821$		−	18.8147i		−	0.656638i	0.944567	−	0.328319i	$-0.106482\pi$
$822$	22.7717	−	1.20642i	0.794253	−	0.0420788i
$823$	18.8387	−	18.8387i	0.656676	−	0.656676i	−0.297916	−	0.954592i	$-0.596292\pi$
$823$	18.8387	−	18.8387i	0.656676	−	0.656676i	0.954592	+	0.297916i	$0.0962916\pi$
$824$	3.45477			0.120353
$825$	32.6801	+	14.8956i	1.13778	+	0.518597i
$826$	12.0087			0.417837
$827$	−17.5079	+	17.5079i	−0.608810	+	0.608810i	−0.942635	−	0.333825i	$-0.891661\pi$
$827$	−17.5079	+	17.5079i	−0.608810	+	0.608810i	0.333825	+	0.942635i	$0.391661\pi$
$828$	−14.5809	+	18.0479i	−0.506720	+	0.627207i
$829$		−	39.9306i		−	1.38685i	−0.720530	−	0.693424i	$-0.756101\pi$
$829$		−	39.9306i		−	1.38685i	0.720530	−	0.693424i	$-0.243899\pi$
$830$	4.41317	+	1.08137i	0.153183	+	0.0375349i
$831$	−13.1489	+	14.6201i	−0.456130	+	0.507165i
$832$	−3.92411	−	3.92411i	−0.136044	−	0.136044i
$833$	−17.5006	−	17.5006i	−0.606359	−	0.606359i
$834$	14.3700	−	15.9778i	0.497591	−	0.553264i
$835$	6.22249	−	3.77322i	0.215338	−	0.130578i
$836$		−	4.14708i		−	0.143430i
$837$	0.00917791	+	0.0573128i	0.000317235	+	0.00198102i
$838$	−2.38575	+	2.38575i	−0.0824142	+	0.0824142i
$839$	−26.1082			−0.901355			−0.450678	−	0.892687i	$-0.648818\pi$
$839$	−26.1082			−0.901355			−0.450678	+	0.892687i	$0.648818\pi$
$840$	−7.13074	−	1.35193i	−0.246034	−	0.0466461i
$841$	−28.9907			−0.999679
$842$	−11.9187	+	11.9187i	−0.410746	+	0.410746i
$843$	23.2709	−	1.23287i	0.801494	−	0.0424625i
$844$		−	10.9572i		−	0.377163i
$845$	−9.47115	+	38.6526i	−0.325817	+	1.32969i
$846$	0.768510	+	7.23259i	0.0264219	+	0.248662i
$847$	−8.21318	−	8.21318i	−0.282208	−	0.282208i
$848$	−8.88222	−	8.88222i	−0.305017	−	0.305017i
$849$	−24.5993	−	22.1240i	−0.844247	−	0.759293i
$850$	−16.4003	+	31.4563i	−0.562526	+	1.07894i
$851$			17.0104i			0.583108i
$852$	0.868197	+	16.3875i	0.0297439	+	0.561427i
$853$	17.0198	−	17.0198i	0.582747	−	0.582747i	−0.352910	−	0.935657i	$-0.614808\pi$
$853$	17.0198	−	17.0198i	0.582747	−	0.582747i	0.935657	+	0.352910i	$0.114808\pi$
$854$	19.2050			0.657183
$855$	0.899127	−	6.64767i	0.0307495	−	0.227346i
$856$	1.88021			0.0642643
$857$	−22.2813	+	22.2813i	−0.761115	+	0.761115i	−0.976524	−	0.215409i	$-0.930891\pi$
$857$	−22.2813	+	22.2813i	−0.761115	+	0.761115i	0.215409	+	0.976524i	$0.430891\pi$
$858$	−2.10890	−	39.8062i	−0.0719966	−	1.35896i
$859$		−	54.5491i		−	1.86119i	−0.366051	−	0.930595i	$-0.619290\pi$
$859$		−	54.5491i		−	1.86119i	0.366051	−	0.930595i	$-0.380710\pi$
$860$	0.214031	+	0.352963i	0.00729841	+	0.0120359i
$861$	20.4141	+	18.3599i	0.695710	+	0.625703i
$862$	11.7528	+	11.7528i	0.400303	+	0.400303i
$863$	−27.3164	−	27.3164i	−0.929860	−	0.929860i	0.0678368	−	0.997696i	$-0.478390\pi$
$863$	−27.3164	−	27.3164i	−0.929860	−	0.929860i	−0.997696	+	0.0678368i	$0.978390\pi$
$864$	4.20899	+	3.04703i	0.143193	+	0.103662i
$865$	12.6295	+	20.8276i	0.429417	+	0.708161i
$866$			15.1265i			0.514019i
$867$	−57.6634	+	3.05496i	−1.95835	+	0.103752i
$868$	0.0148017	−	0.0148017i	0.000502401	−	0.000502401i
$869$	−51.7319			−1.75489
$870$	−0.210291	−	0.308684i	−0.00712952	−	0.0104654i
$871$	−37.4851			−1.27013
$872$	−6.01957	+	6.01957i	−0.203849	+	0.203849i
$873$	−11.4996	−	9.29055i	−0.389204	−	0.314437i
$874$			7.73397i			0.261605i
$875$	−1.35052	−	20.9078i	−0.0456560	−	0.706812i
$876$	6.62839	−	7.37001i	0.223953	−	0.249010i
$877$	−34.5098	−	34.5098i	−1.16531	−	1.16531i	−0.983295	−	0.182017i	$-0.941737\pi$
$877$	−34.5098	−	34.5098i	−1.16531	−	1.16531i	−0.182017	−	0.983295i	$-0.558263\pi$
$878$	−12.8094	−	12.8094i	−0.432297	−	0.432297i
$879$	−3.15064	+	3.50315i	−0.106269	+	0.118158i
$880$	−2.20693	+	9.00670i	−0.0743957	+	0.303616i
$881$			53.0461i			1.78717i	0.448895	+	0.893584i	$0.351818\pi$
$881$			53.0461i			1.78717i	−0.448895	+	0.893584i	$0.648182\pi$
$882$	−8.14031	−	6.57654i	−0.274098	−	0.221444i
$883$	−3.25237	+	3.25237i	−0.109451	+	0.109451i	−0.759711	−	0.650260i	$-0.774660\pi$
$883$	−3.25237	+	3.25237i	−0.109451	+	0.109451i	0.650260	+	0.759711i	$0.274660\pi$
$884$	39.3738			1.32428
$885$	4.62314	−	24.3847i	0.155405	−	0.819682i
$886$	22.1233			0.743247
$887$	−13.8916	+	13.8916i	−0.466434	+	0.466434i	−0.900757	−	0.434323i	$-0.856988\pi$
$887$	−13.8916	+	13.8916i	−0.466434	+	0.466434i	0.434323	+	0.900757i	$0.356988\pi$
$888$	3.80420	−	0.201543i	0.127661	−	0.00676335i
$889$		−	1.24547i		−	0.0417717i
$890$	−32.6726	+	19.8121i	−1.09519	+	0.664104i
$891$	7.84322	+	36.4903i	0.262758	+	1.22247i
$892$	3.81435	+	3.81435i	0.127714	+	0.127714i
$893$	1.71433	+	1.71433i	0.0573680	+	0.0573680i
$894$	13.9772	+	12.5707i	0.467468	+	0.420428i
$895$	19.6753	+	4.82109i	0.657673	+	0.161151i
$896$		−	1.87395i		−	0.0626042i
$897$	3.93293	+	74.2354i	0.131317	+	2.47865i
$898$	−3.16995	+	3.16995i	−0.105783	+	0.105783i
$899$	0.00107726			3.59287e−5
$900$	−5.49041	+	13.9591i	−0.183014	+	0.465302i
$901$	89.1225			2.96910
$902$	24.8052	−	24.8052i	0.825923	−	0.825923i
$903$	−0.0316997	−	0.598342i	−0.00105490	−	0.0199116i
$904$		−	2.07797i		−	0.0691122i
$905$	38.9145	+	9.53532i	1.29356	+	0.316965i
$906$	1.56126	+	1.40416i	0.0518695	+	0.0466500i
$907$	25.8006	+	25.8006i	0.856694	+	0.856694i	0.990947	−	0.134253i	$-0.0428636\pi$
$907$	25.8006	+	25.8006i	0.856694	+	0.856694i	−0.134253	+	0.990947i	$0.542864\pi$
$908$	8.48460	+	8.48460i	0.281571	+	0.281571i
$909$	−5.16163	−	48.5771i	−0.171200	−	1.61120i
$910$	−19.8840	+	12.0573i	−0.659148	+	0.399697i
$911$		−	14.3119i		−	0.474174i	−0.971488	−	0.237087i	$-0.923807\pi$
$911$		−	14.3119i		−	0.474174i	0.971488	−	0.237087i	$-0.0761926\pi$
$912$	1.72963	−	0.0916341i	0.0572736	−	0.00303431i
$913$	−5.95874	+	5.95874i	−0.197205	+	0.197205i
$914$	9.03082			0.298713
$915$	7.39359	−	38.9974i	0.244425	−	1.28921i
$916$	13.8975			0.459186
$917$	23.5802	−	23.5802i	0.778687	−	0.778687i
$918$	−36.4028	+	5.82944i	−1.20147	+	0.192400i
$919$			26.7468i			0.882295i	0.897435	+	0.441148i	$0.145428\pi$
$919$			26.7468i			0.882295i	−0.897435	+	0.441148i	$0.854572\pi$
$920$	4.11575	−	16.7968i	0.135692	−	0.553773i
$921$	−28.9349	+	32.1723i	−0.953437	+	1.06011i
$922$	−6.46331	−	6.46331i	−0.212858	−	0.212858i
$923$	37.1795	+	37.1795i	1.22378	+	1.22378i
$924$	9.00111	−	10.0082i	0.296115	−	0.329246i
$925$	3.30031	+	10.4903i	0.108513	+	0.344918i
$926$		−	16.6201i		−	0.546170i
$927$	−6.51328	+	8.06200i	−0.213924	+	0.264791i
$928$	0.0681929	−	0.0681929i	0.00223854	−	0.00223854i
$929$	−45.0802			−1.47903			−0.739517	−	0.673138i	$-0.764946\pi$
$929$	−45.0802			−1.47903			−0.739517	+	0.673138i	$0.764946\pi$
$930$	−0.0243576	−	0.0357543i	−0.000798716	−	0.00117243i
$931$	−3.48832			−0.114325
$932$	21.1265	−	21.1265i	0.692022	−	0.692022i
$933$	16.6833	−	0.883866i	0.546186	−	0.0289365i
$934$			15.3151i			0.501124i
$935$	−34.1138	−	56.2577i	−1.11564	−	1.83982i
$936$	16.5554	−	1.75912i	0.541131	−	0.0574987i
$937$	5.93609	+	5.93609i	0.193923	+	0.193923i	0.797389	−	0.603466i	$-0.206214\pi$
$937$	5.93609	+	5.93609i	0.193923	+	0.193923i	−0.603466	+	0.797389i	$0.706214\pi$
$938$	−8.95043	−	8.95043i	−0.292242	−	0.292242i
$939$	−18.4148	−	16.5617i	−0.600943	−	0.540472i
$940$	−2.81091	−	4.63553i	−0.0916819	−	0.151194i
$941$		−	2.12760i		−	0.0693578i	−0.999399	−	0.0346789i	$-0.988959\pi$
$941$		−	2.12760i		−	0.0693578i	0.999399	−	0.0346789i	$-0.0110409\pi$
$942$	1.30312	+	24.5968i	0.0424578	+	0.801407i
$943$	−46.2597	+	46.2597i	−1.50642	+	1.50642i
$944$	6.40826			0.208571
$945$	16.5985	−	14.0914i	0.539948	−	0.458394i
$946$	−0.765565			−0.0248907
$947$	−11.6968	+	11.6968i	−0.380097	+	0.380097i	−0.871137	−	0.491040i	$-0.836617\pi$
$947$	−11.6968	+	11.6968i	−0.380097	+	0.380097i	0.491040	+	0.871137i	$0.336617\pi$
$948$	−1.14307	−	21.5759i	−0.0371252	−	0.700752i
$949$		−	31.7591i		−	1.03094i
$950$	1.50052	+	4.76953i	0.0486834	+	0.154744i
$951$	17.4248	+	15.6714i	0.565038	+	0.508180i
$952$	9.40141	+	9.40141i	0.304702	+	0.304702i
$953$	−8.91128	−	8.91128i	−0.288665	−	0.288665i	0.547887	−	0.836552i	$-0.315432\pi$
$953$	−8.91128	−	8.91128i	−0.288665	−	0.288665i	−0.836552	+	0.547887i	$0.815432\pi$
$954$	37.4731	−	3.98176i	1.21324	−	0.128914i
$955$	−4.47737	+	18.2725i	−0.144884	+	0.591286i
$956$			3.09410i			0.100070i
$957$	0.691748	−	0.0366482i	0.0223610	−	0.00118467i
$958$	−11.7649	+	11.7649i	−0.380108	+	0.380108i
$959$	24.6718			0.796693
$960$	−3.80520	−	0.721435i	−0.122812	−	0.0232842i
$961$	−30.9999			−0.999996
$962$	8.63084	−	8.63084i	0.278270	−	0.278270i
$963$	−3.54477	+	4.38764i	−0.114229	+	0.141390i
$964$		−	6.62578i		−	0.213402i
$965$	−1.10459	+	0.669803i	−0.0355579	+	0.0215617i
$966$	−16.7863	+	18.6645i	−0.540092	+	0.600520i
$967$	23.9952	+	23.9952i	0.771633	+	0.771633i	0.978392	−	0.206759i	$-0.0662917\pi$
$967$	23.9952	+	23.9952i	0.771633	+	0.771633i	−0.206759	+	0.978392i	$0.566292\pi$
$968$	−4.38282	−	4.38282i	−0.140869	−	0.140869i
$969$	−8.21764	+	9.13708i	−0.263989	+	0.293525i
$970$	10.7025	+	2.62245i	0.343636	+	0.0842018i
$971$		−	11.1305i		−	0.357194i	−0.983922	−	0.178597i	$-0.942844\pi$
$971$		−	11.1305i		−	0.357194i	0.983922	−	0.178597i	$-0.0571558\pi$
$972$	−15.0457	+	4.07747i	−0.482592	+	0.130785i
$973$	16.4400	−	16.4400i	0.527042	−	0.527042i
$974$	−9.82901			−0.314942
$975$	16.8284	+	45.0179i	0.538940	+	1.44173i
$976$	10.2484			0.328045
$977$	12.3178	−	12.3178i	0.394082	−	0.394082i	−0.482058	−	0.876139i	$-0.660111\pi$
$977$	12.3178	−	12.3178i	0.394082	−	0.394082i	0.876139	+	0.482058i	$0.160111\pi$
$978$	−21.0592	+	1.11570i	−0.673397	+	0.0356760i
$979$		−	70.8657i		−	2.26488i
$980$	7.57600	+	1.85637i	0.242007	+	0.0592995i
$981$	−2.69848	−	25.3959i	−0.0861559	−	0.810830i
$982$	−2.69394	−	2.69394i	−0.0859670	−	0.0859670i
$983$	12.4846	+	12.4846i	0.398196	+	0.398196i	0.877596	−	0.479401i	$-0.159146\pi$
$983$	12.4846	+	12.4846i	0.398196	+	0.398196i	−0.479401	+	0.877596i	$0.659146\pi$
$984$	10.8936	+	9.79743i	0.347276	+	0.312331i
$985$	−8.29047	+	5.02721i	−0.264156	+	0.160180i
$986$			0.684234i			0.0217905i
$987$	0.416318	+	7.85814i	0.0132515	+	0.250127i
$988$	3.92411	−	3.92411i	0.124843	−	0.124843i
$989$	1.42772			0.0453988
$990$	−16.8572	−	22.1304i	−0.535757	−	0.703351i
$991$	−36.4365			−1.15744			−0.578721	−	0.815526i	$-0.696448\pi$
$991$	−36.4365			−1.15744			−0.578721	+	0.815526i	$0.696448\pi$
$992$	0.00789865	−	0.00789865i	0.000250782	−	0.000250782i
$993$	0.995534	+	18.7911i	0.0315923	+	0.596316i
$994$			17.7549i			0.563152i
$995$	−11.6895	+	47.7059i	−0.370582	+	1.51238i
$996$	−2.61688	−	2.35355i	−0.0829190	−	0.0745751i
$997$	39.4085	+	39.4085i	1.24808	+	1.24808i	0.956567	+	0.291511i	$0.0941581\pi$
$997$	39.4085	+	39.4085i	1.24808	+	1.24808i	0.291511	+	0.956567i	$0.405842\pi$
$998$	8.53600	+	8.53600i	0.270202	+	0.270202i
$999$	−6.70175	+	9.25741i	−0.212034	+	0.292891i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.k.b.77.4	✓	36
3.2	odd	2	inner	570.2.k.b.77.18	yes	36
5.3	odd	4	inner	570.2.k.b.533.18	yes	36
15.8	even	4	inner	570.2.k.b.533.4	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.k.b.77.4	✓	36	1.1	even	1	trivial
570.2.k.b.77.18	yes	36	3.2	odd	2	inner
570.2.k.b.533.4	yes	36	15.8	even	4	inner
570.2.k.b.533.18	yes	36	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.0916341 - 1.72963i) q^{3} -1.00000i q^{4} +(-2.17182 - 0.532166i) q^{5} +(1.28782 + 1.15823i) q^{6} +(1.32508 + 1.32508i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.98321 + 0.316985i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.0916341 - 1.72963i) q^{3} -1.00000i q^{4} +(-2.17182 - 0.532166i) q^{5} +(1.28782 + 1.15823i) q^{6} +(1.32508 + 1.32508i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.98321 + 0.316985i) q^{9} +(1.91201 - 1.15941i) q^{10} +4.14708i q^{11} +(-1.72963 + 0.0916341i) q^{12} +(-3.92411 + 3.92411i) q^{13} -1.87395 q^{14} +(-0.721435 + 3.80520i) q^{15} -1.00000 q^{16} +(5.01690 - 5.01690i) q^{17} +(1.88530 - 2.33359i) q^{18} -1.00000i q^{19} +(-0.532166 + 2.17182i) q^{20} +(2.17047 - 2.41332i) q^{21} +(-2.93243 - 2.93243i) q^{22} +(5.46874 + 5.46874i) q^{23} +(1.15823 - 1.28782i) q^{24} +(4.43360 + 2.31154i) q^{25} -5.54954i q^{26} +(0.821629 + 5.13078i) q^{27} +(1.32508 - 1.32508i) q^{28} +0.0964393 q^{29} +(-2.18055 - 3.20081i) q^{30} +0.0111704 q^{31} +(0.707107 - 0.707107i) q^{32} +(7.17289 - 0.380013i) q^{33} +7.09497i q^{34} +(-2.17267 - 3.58300i) q^{35} +(0.316985 + 2.98321i) q^{36} +(1.55524 + 1.55524i) q^{37} +(0.707107 + 0.707107i) q^{38} +(7.14683 + 6.42767i) q^{39} +(-1.15941 - 1.91201i) q^{40} +8.45893i q^{41} +(0.171717 + 3.24123i) q^{42} +(0.130534 - 0.130534i) q^{43} +4.14708 q^{44} +(6.64767 + 0.899127i) q^{45} -7.73397 q^{46} +(-1.71433 + 1.71433i) q^{47} +(0.0916341 + 1.72963i) q^{48} -3.48832i q^{49} +(-4.76953 + 1.50052i) q^{50} +(-9.13708 - 8.21764i) q^{51} +(3.92411 + 3.92411i) q^{52} +(8.88222 + 8.88222i) q^{53} +(-4.20899 - 3.04703i) q^{54} +(2.20693 - 9.00670i) q^{55} +1.87395i q^{56} +(-1.72963 + 0.0916341i) q^{57} +(-0.0681929 + 0.0681929i) q^{58} -6.40826 q^{59} +(3.80520 + 0.721435i) q^{60} -10.2484 q^{61} +(-0.00789865 + 0.00789865i) q^{62} +(-4.37302 - 3.53296i) q^{63} +1.00000i q^{64} +(10.6107 - 6.43419i) q^{65} +(-4.80329 + 5.34071i) q^{66} +(4.77624 + 4.77624i) q^{67} +(-5.01690 - 5.01690i) q^{68} +(8.95775 - 9.95999i) q^{69} +(4.06987 + 0.997251i) q^{70} -9.47461i q^{71} +(-2.33359 - 1.88530i) q^{72} +(-4.04666 + 4.04666i) q^{73} -2.19944 q^{74} +(3.59182 - 7.88028i) q^{75} -1.00000 q^{76} +(-5.49521 + 5.49521i) q^{77} +(-9.59862 + 0.508527i) q^{78} +12.4743i q^{79} +(2.17182 + 0.532166i) q^{80} +(8.79904 - 1.89126i) q^{81} +(-5.98137 - 5.98137i) q^{82} +(1.43685 + 1.43685i) q^{83} +(-2.41332 - 2.17047i) q^{84} +(-13.5656 + 8.22598i) q^{85} +0.184604i q^{86} +(-0.00883712 - 0.166804i) q^{87} +(-2.93243 + 2.93243i) q^{88} -17.0881 q^{89} +(-5.33639 + 4.06484i) q^{90} -10.3995 q^{91} +(5.46874 - 5.46874i) q^{92} +(-0.00102359 - 0.0193206i) q^{93} -2.42443i q^{94} +(-0.532166 + 2.17182i) q^{95} +(-1.28782 - 1.15823i) q^{96} +(3.48454 + 3.48454i) q^{97} +(2.46662 + 2.46662i) q^{98} +(-1.31456 - 12.3716i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7}+O(q^{10}) \) 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7	\( 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} + 16 q^{21} - 4 q^{22} + 16 q^{25} - 44 q^{27} + 20 q^{28} + 32 q^{30} - 24 q^{31} - 4 q^{33} + 4 q^{36} - 8 q^{40} + 12 q^{42} - 8 q^{43} + 28 q^{45} - 16 q^{46} - 4 q^{48} + 40 q^{51} - 8 q^{52} - 36 q^{55} - 4 q^{57} + 44 q^{58} + 16 q^{60} - 120 q^{61} - 12 q^{63} + 80 q^{67} - 36 q^{70} + 44 q^{73} + 4 q^{75} - 36 q^{76} - 64 q^{78} + 36 q^{81} + 8 q^{82} - 24 q^{85} - 28 q^{87} - 4 q^{88} + 44 q^{90} - 72 q^{93} - 4 q^{96} + 92 q^{97}+O(q^{100}) \) 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 + 16 * q^21 - 4 * q^22 + 16 * q^25 - 44 * q^27 + 20 * q^28 + 32 * q^30 - 24 * q^31 - 4 * q^33 + 4 * q^36 - 8 * q^40 + 12 * q^42 - 8 * q^43 + 28 * q^45 - 16 * q^46 - 4 * q^48 + 40 * q^51 - 8 * q^52 - 36 * q^55 - 4 * q^57 + 44 * q^58 + 16 * q^60 - 120 * q^61 - 12 * q^63 + 80 * q^67 - 36 * q^70 + 44 * q^73 + 4 * q^75 - 36 * q^76 - 64 * q^78 + 36 * q^81 + 8 * q^82 - 24 * q^85 - 28 * q^87 - 4 * q^88 + 44 * q^90 - 72 * q^93 - 4 * q^96 + 92 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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