LMFDB - Embedded newform 570.2.k.b.533.18

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			533.18
Character	$\chi$	$=$	570.533
Dual form			570.2.k.b.77.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(1.72963 - 0.0916341i) q^{3} +1.00000i q^{4} +(2.17182 - 0.532166i) q^{5} +(1.28782 + 1.15823i) q^{6} +(1.32508 - 1.32508i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.98321 - 0.316985i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(1.72963 - 0.0916341i) 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} +(0.0916341 + 1.72963i) q^{12} +(-3.92411 - 3.92411i) q^{13} +1.87395 q^{14} +(3.70767 - 1.11946i) q^{15} -1.00000 q^{16} +(-5.01690 - 5.01690i) q^{17} +(2.33359 + 1.88530i) 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} +(5.13078 - 0.821629i) q^{27} +(1.32508 + 1.32508i) q^{28} -0.0964393 q^{29} +(3.41330 + 1.83014i) q^{30} +0.0111704 q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.380013 + 7.17289i) 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} +(3.24123 - 0.171717i) q^{42} +(0.130534 + 0.130534i) q^{43} -4.14708 q^{44} +(6.31030 - 2.27600i) q^{45} -7.73397 q^{46} +(1.71433 + 1.71433i) q^{47} +(-1.72963 + 0.0916341i) 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} +(0.0916341 + 1.72963i) q^{57} +(-0.0681929 - 0.0681929i) q^{58} +6.40826 q^{59} +(1.11946 + 3.70767i) q^{60} -10.2484 q^{61} +(0.00789865 + 0.00789865i) q^{62} +(3.53296 - 4.37302i) 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} +(-1.88530 + 2.33359i) q^{72} +(-4.04666 - 4.04666i) q^{73} +2.19944 q^{74} +(7.45665 - 4.40436i) q^{75} -1.00000 q^{76} +(5.49521 + 5.49521i) q^{77} +(-0.508527 - 9.59862i) 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} +(-0.166804 + 0.00883712i) q^{87} +(-2.93243 - 2.93243i) q^{88} +17.0881 q^{89} +(6.07143 + 2.85268i) q^{90} -10.3995 q^{91} +(-5.46874 - 5.46874i) q^{92} +(0.0193206 - 0.00102359i) 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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	1.72963	−	0.0916341i	0.998600	−	0.0529049i
$3$	1.72963	−	0.0916341i	0.998600	−	0.0529049i
$4$			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	−0.410863	−	0.911697i	$-0.634773\pi$
$7$	1.32508	−	1.32508i	0.500833	−	0.500833i	0.911697	+	0.410863i	$0.134773\pi$
$8$	−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	$0.785019\pi$
$12$	0.0916341	+	1.72963i	0.0264525	+	0.499300i
$13$	−3.92411	−	3.92411i	−1.08835	−	1.08835i	−0.995698	−	0.0926554i	$-0.970464\pi$
$13$	−3.92411	−	3.92411i	−1.08835	−	1.08835i	−0.0926554	−	0.995698i	$-0.529536\pi$
$14$	1.87395			0.500833
$15$	3.70767	−	1.11946i	0.957316	−	0.289043i
$16$	−1.00000			−0.250000
$17$	−5.01690	−	5.01690i	−1.21678	−	1.21678i	−0.968754	−	0.248024i	$-0.920219\pi$
$17$	−5.01690	−	5.01690i	−1.21678	−	1.21678i	−0.248024	−	0.968754i	$-0.579781\pi$
$18$	2.33359	+	1.88530i	0.550032	+	0.444370i
$19$			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	−0.151918	+	0.988393i	$0.548545\pi$
$23$	−5.46874	+	5.46874i	−1.14031	+	1.14031i	−0.988393	+	0.151918i	$0.951455\pi$
$24$	−1.15823	+	1.28782i	−0.236424	+	0.262876i
$25$	4.43360	−	2.31154i	0.886720	−	0.462307i
$26$		−	5.54954i		−	1.08835i
$27$	5.13078	−	0.821629i	0.987419	−	0.158123i
$28$	1.32508	+	1.32508i	0.250417	+	0.250417i
$29$	−0.0964393			−0.0179083			−0.00895416	−	0.999960i	$-0.502850\pi$
$29$	−0.0964393			−0.0179083			−0.00895416	+	0.999960i	$0.502850\pi$
$30$	3.41330	+	1.83014i	0.623180	+	0.334136i
$31$	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
$33$	0.380013	+	7.17289i	0.0661519	+	1.24864i
$34$		−	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	−0.567615	−	0.823294i	$-0.692134\pi$
$37$	1.55524	−	1.55524i	0.255679	−	0.255679i	0.823294	+	0.567615i	$0.192134\pi$
$38$	−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	$0.770331\pi$
$42$	3.24123	−	0.171717i	0.500132	−	0.0264966i
$43$	0.130534	+	0.130534i	0.0199063	+	0.0199063i	0.716990	−	0.697084i	$-0.245519\pi$
$43$	0.130534	+	0.130534i	0.0199063	+	0.0199063i	−0.697084	+	0.716990i	$0.745519\pi$
$44$	−4.14708			−0.625195
$45$	6.31030	−	2.27600i	0.940683	−	0.339285i
$46$	−7.73397			−1.14031
$47$	1.71433	+	1.71433i	0.250061	+	0.250061i	0.820996	−	0.570934i	$-0.193419\pi$
$47$	1.71433	+	1.71433i	0.250061	+	0.250061i	−0.570934	+	0.820996i	$0.693419\pi$
$48$	−1.72963	+	0.0916341i	−0.249650	+	0.0132262i
$49$			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	−0.252459	+	0.967608i	$0.581239\pi$
$53$	−8.88222	+	8.88222i	−1.22007	+	1.22007i	−0.967608	+	0.252459i	$0.918761\pi$
$54$	4.20899	+	3.04703i	0.572771	+	0.414648i
$55$	2.20693	+	9.00670i	0.297583	+	1.21446i
$56$			1.87395i			0.250417i
$57$	0.0916341	+	1.72963i	0.0121372	+	0.229094i
$58$	−0.0681929	−	0.0681929i	−0.00895416	−	0.00895416i
$59$	6.40826			0.834284			0.417142	−	0.908841i	$-0.363032\pi$
$59$	6.40826			0.834284			0.417142	+	0.908841i	$0.363032\pi$
$60$	1.11946	+	3.70767i	0.144522	+	0.478658i
$61$	−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
$63$	3.53296	−	4.37302i	0.445111	−	0.550949i
$64$		−	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	−0.352355	−	0.935866i	$-0.614619\pi$
$67$	4.77624	−	4.77624i	0.583511	−	0.583511i	0.935866	+	0.352355i	$0.114619\pi$
$68$	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	$-0.190051\pi$
$72$	−1.88530	+	2.33359i	−0.222185	+	0.275016i
$73$	−4.04666	−	4.04666i	−0.473626	−	0.473626i	0.429460	−	0.903086i	$-0.358704\pi$
$73$	−4.04666	−	4.04666i	−0.473626	−	0.473626i	−0.903086	+	0.429460i	$0.858704\pi$
$74$	2.19944			0.255679
$75$	7.45665	−	4.40436i	0.861020	−	0.508572i
$76$	−1.00000			−0.114708
$77$	5.49521	+	5.49521i	0.626238	+	0.626238i
$78$	−0.508527	−	9.59862i	−0.0575793	−	1.08683i
$79$		−	12.4743i		−	1.40347i	−0.712438	−	0.701735i	$-0.752409\pi$
$79$		−	12.4743i		−	1.40347i	0.712438	−	0.701735i	$-0.247591\pi$
$80$	−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	$-0.785572\pi$
$83$	−1.43685	+	1.43685i	−0.157715	+	0.157715i	0.623838	+	0.781553i	$0.285572\pi$
$84$	2.41332	+	2.17047i	0.263314	+	0.236818i
$85$	−13.5656	−	8.22598i	−1.47140	−	0.892233i
$86$			0.184604i			0.0199063i
$87$	−0.166804	+	0.00883712i	−0.0178832	+	0.000947439i
$88$	−2.93243	−	2.93243i	−0.312598	−	0.312598i
$89$	17.0881			1.81134			0.905668	−	0.423988i	$-0.139370\pi$
$89$	17.0881			1.81134			0.905668	+	0.423988i	$0.139370\pi$
$90$	6.07143	+	2.85268i	0.639984	+	0.300699i
$91$	−10.3995			−1.09017
$92$	−5.46874	−	5.46874i	−0.570155	−	0.570155i
$93$	0.0193206	−	0.00102359i	0.00200345	−	0.000106141i
$94$			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	−0.507721	−	0.861522i	$-0.669512\pi$
$97$	3.48454	−	3.48454i	0.353801	−	0.353801i	0.861522	+	0.507721i	$0.169512\pi$
$98$	−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	$0.699394\pi$
$102$	−0.650141	−	12.2716i	−0.0643736	−	1.21507i
$103$	2.44289	+	2.44289i	0.240705	+	0.240705i	0.817142	−	0.576437i	$-0.195557\pi$
$103$	2.44289	+	2.44289i	0.240705	+	0.240705i	−0.576437	+	0.817142i	$0.695557\pi$
$104$	5.54954			0.544177
$105$	3.42959	−	6.39634i	0.334693	−	0.624219i
$106$	−12.5614			−1.22007
$107$	−1.32951	−	1.32951i	−0.128529	−	0.128529i	0.639916	−	0.768445i	$-0.278969\pi$
$107$	−1.32951	−	1.32951i	−0.128529	−	0.128529i	−0.768445	+	0.639916i	$0.778969\pi$
$108$	0.821629	+	5.13078i	0.0790613	+	0.493710i
$109$		−	8.51296i		−	0.815394i	−0.913117	−	0.407697i	$-0.866332\pi$
$109$		−	8.51296i		−	0.815394i	0.913117	−	0.407697i	$-0.133668\pi$
$110$	−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	$-0.718839\pi$
$113$	1.46934	−	1.46934i	0.138224	−	0.138224i	0.772833	+	0.634609i	$0.218839\pi$
$114$	−1.15823	+	1.28782i	−0.108479	+	0.120616i
$115$	−8.96684	+	14.7874i	−0.836162	+	1.37893i
$116$		−	0.0964393i		−	0.00895416i
$117$	−12.9503	−	10.4626i	−1.19726	−	0.967264i
$118$	4.53132	+	4.53132i	0.417142	+	0.417142i
$119$	−13.2956			−1.21881
$120$	−1.83014	+	3.41330i	−0.167068	+	0.311590i
$121$	−6.19825			−0.563477
$122$	−7.24675	−	7.24675i	−0.656090	−	0.656090i
$123$	0.775126	+	14.6308i	0.0698908	+	1.31921i
$124$			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	−0.727650	−	0.685948i	$-0.759388\pi$
$127$	−0.469960	+	0.469960i	−0.0417022	+	0.0417022i	0.685948	+	0.727650i	$0.259388\pi$
$128$	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	$-0.283457\pi$
$132$	−7.17289	+	0.380013i	−0.624320	+	0.0330759i
$133$	1.32508	+	1.32508i	0.114899	+	0.114899i
$134$	6.75463			0.583511
$135$	10.7059	−	4.51486i	0.921416	−	0.388577i
$136$	7.09497			0.608389
$137$	−9.30953	−	9.30953i	−0.795367	−	0.795367i	0.186994	−	0.982361i	$-0.440125\pi$
$137$	−9.30953	−	9.30953i	−0.795367	−	0.795367i	−0.982361	+	0.186994i	$0.940125\pi$
$138$	−13.3769	+	0.708695i	−1.13871	+	0.0603281i
$139$			12.4068i			1.05233i	0.850383	+	0.526165i	$0.176370\pi$
$139$			12.4068i			1.05233i	−0.850383	+	0.526165i	$0.823630\pi$
$140$	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
$147$	0.319649	+	6.03349i	0.0263642	+	0.497634i
$148$	1.55524	+	1.55524i	0.127840	+	0.127840i
$149$	−10.8534			−0.889142			−0.444571	−	0.895744i	$-0.646644\pi$
$149$	−10.8534			−0.889142			−0.444571	+	0.895744i	$0.646644\pi$
$150$	8.38700	+	2.15829i	0.684796	+	0.176224i
$151$	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
$153$	−16.5567	−	13.3762i	−1.33853	−	1.08140i
$154$			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	−0.180960	−	0.983490i	$-0.557920\pi$
$157$	10.0557	−	10.0557i	0.802530	−	0.802530i	0.983490	+	0.180960i	$0.0579204\pi$
$158$	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
$162$	7.55919	+	4.88454i	0.593906	+	0.383765i
$163$	−8.60942	−	8.60942i	−0.674342	−	0.674342i	0.284372	−	0.958714i	$-0.408215\pi$
$163$	−8.60942	−	8.60942i	−0.674342	−	0.674342i	−0.958714	+	0.284372i	$0.908215\pi$
$164$	−8.45893			−0.660532
$165$	4.64249	+	15.3760i	0.361417	+	1.19702i
$166$	−2.03202			−0.157715
$167$	2.30123	+	2.30123i	0.178074	+	0.178074i	0.790516	−	0.612441i	$-0.209812\pi$
$167$	2.30123	+	2.30123i	0.178074	+	0.178074i	−0.612441	+	0.790516i	$0.709812\pi$
$168$	0.171717	+	3.24123i	0.0132483	+	0.250066i
$169$			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	$-0.614099\pi$
$173$	7.70257	−	7.70257i	0.585616	−	0.585616i	0.936441	+	0.350825i	$0.114099\pi$
$174$	−0.124197	−	0.111699i	−0.00941534	−	0.00846790i
$175$	2.81190	−	8.93785i	0.212560	−	0.675638i
$176$		−	4.14708i		−	0.312598i
$177$	11.0839	−	0.587215i	0.833116	−	0.0441378i
$178$	12.0831	+	12.0831i	0.905668	+	0.905668i
$179$	9.05937			0.677129			0.338565	−	0.940943i	$-0.390059\pi$
$179$	9.05937			0.677129			0.338565	+	0.940943i	$0.390059\pi$
$180$	2.27600	+	6.31030i	0.169643	+	0.470342i
$181$	−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
$183$	−17.7260	+	0.939107i	−1.31034	+	0.0694208i
$184$		−	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	$-0.0984522\pi$
$192$	−0.0916341	−	1.72963i	−0.00661312	−	0.124825i
$193$	0.408503	+	0.408503i	0.0294047	+	0.0294047i	0.721656	−	0.692252i	$-0.243381\pi$
$193$	0.408503	+	0.408503i	0.0294047	+	0.0294047i	−0.692252	+	0.721656i	$0.743381\pi$
$194$	4.92788			0.353801
$195$	−18.9422	−	10.1564i	−1.35648	−	0.727317i
$196$	−3.48832			−0.249166
$197$	−3.06602	−	3.06602i	−0.218445	−	0.218445i	0.589398	−	0.807843i	$-0.299365\pi$
$197$	−3.06602	−	3.06602i	−0.218445	−	0.218445i	−0.807843	+	0.589398i	$0.799365\pi$
$198$	−7.81850	+	9.67757i	−0.555636	+	0.687755i
$199$			21.9659i			1.55712i	0.627570	+	0.778560i	$0.284050\pi$
$199$			21.9659i			1.55712i	−0.627570	+	0.778560i	$0.715950\pi$
$200$	−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
$207$	−14.5809	+	18.0479i	−1.01344	+	1.25441i
$208$	3.92411	+	3.92411i	0.272088	+	0.272088i
$209$	−4.14708			−0.286859
$210$	6.94798	−	2.09781i	0.479456	−	0.144763i
$211$	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
$213$	−0.868197	−	16.3875i	−0.0594879	−	1.12285i
$214$		−	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
$222$	3.80420	−	0.201543i	0.255321	−	0.0135267i
$223$	−3.81435	−	3.81435i	−0.255428	−	0.255428i	0.567764	−	0.823191i	$-0.307809\pi$
$223$	−3.81435	−	3.81435i	−0.255428	−	0.255428i	−0.823191	+	0.567764i	$0.807809\pi$
$224$	−1.87395			−0.125208
$225$	12.4936	−	8.30118i	0.832908	−	0.553412i
$226$	2.07797			0.138224
$227$	8.48460	+	8.48460i	0.563143	+	0.563143i	0.930199	−	0.367056i	$-0.119634\pi$
$227$	8.48460	+	8.48460i	0.563143	+	0.563143i	−0.367056	+	0.930199i	$0.619634\pi$
$228$	−1.72963	+	0.0916341i	−0.114547	+	0.00606861i
$229$		−	13.8975i		−	0.918372i	−0.888340	−	0.459186i	$-0.848141\pi$
$229$		−	13.8975i		−	0.918372i	0.888340	−	0.459186i	$-0.151859\pi$
$230$	−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	−0.546744	+	0.837300i	$0.684133\pi$
$233$	−21.1265	+	21.1265i	−1.38404	+	1.38404i	−0.837300	+	0.546744i	$0.815867\pi$
$234$	−1.75912	−	16.5554i	−0.114997	−	1.08226i
$235$	4.63553	+	2.81091i	0.302389	+	0.183364i
$236$			6.40826i			0.417142i
$237$	−1.14307	−	21.5759i	−0.0742505	−	1.40150i
$238$	−9.40141	−	9.40141i	−0.609403	−	0.609403i
$239$	3.09410			0.200141			0.100070	−	0.994980i	$-0.468093\pi$
$239$	3.09410			0.200141			0.100070	+	0.994980i	$0.468093\pi$
$240$	−3.70767	+	1.11946i	−0.239329	+	0.0722609i
$241$	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
$243$	15.0457	−	4.07747i	0.965185	−	0.261570i
$244$		−	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	$0.764629\pi$
$252$	4.37302	+	3.53296i	0.275474	+	0.222555i
$253$	−22.6793	−	22.6793i	−1.42583	−	1.42583i
$254$	−0.664624			−0.0417022
$255$	−24.2172	−	12.9848i	−1.51654	−	0.813139i
$256$	1.00000			0.0625000
$257$	−2.86047	−	2.86047i	−0.178431	−	0.178431i	0.612240	−	0.790672i	$-0.290268\pi$
$257$	−2.86047	−	2.86047i	−0.178431	−	0.178431i	−0.790672	+	0.612240i	$0.790268\pi$
$258$	0.0169160	+	0.319295i	0.00105314	+	0.0198784i
$259$		−	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	0.230446	−	0.973085i	$-0.425982\pi$
$263$	19.5180	−	19.5180i	1.20353	−	1.20353i	0.973085	−	0.230446i	$-0.0740184\pi$
$264$	−5.34071	−	4.80329i	−0.328698	−	0.295622i
$265$	−14.5638	+	24.0174i	−0.894644	+	1.47538i
$266$			1.87395i			0.114899i
$267$	29.5560	−	1.56585i	1.80880	−	0.0958286i
$268$	4.77624	+	4.77624i	0.291756	+	0.291756i
$269$	9.59340			0.584920			0.292460	−	0.956278i	$-0.405526\pi$
$269$	9.59340			0.584920			0.292460	+	0.956278i	$0.405526\pi$
$270$	10.7627	+	4.37772i	0.654997	+	0.266420i
$271$	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
$273$	−17.9873	+	0.952952i	−1.08864	+	0.0576753i
$274$		−	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	−0.905873	−	0.423550i	$-0.860784\pi$
$277$	−8.02745	+	8.02745i	−0.482323	+	0.482323i	0.423550	+	0.905873i	$0.360784\pi$
$278$	−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	$0.868555\pi$
$282$	0.222161	+	4.19336i	0.0132295	+	0.249711i
$283$	13.5068	+	13.5068i	0.802894	+	0.802894i	0.983547	−	0.180653i	$-0.0578209\pi$
$283$	13.5068	+	13.5068i	0.802894	+	0.802894i	−0.180653	+	0.983547i	$0.557821\pi$
$284$	9.47461			0.562215
$285$	1.11946	+	3.70767i	0.0663111	+	0.219623i
$286$	23.0144			1.36087
$287$	11.2088	+	11.2088i	0.661633	+	0.661633i
$288$	−2.33359	−	1.88530i	−0.137508	−	0.111093i
$289$			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	$-0.724681\pi$
$293$	1.92348	−	1.92348i	0.112371	−	0.112371i	0.761056	+	0.648686i	$0.224681\pi$
$294$	−4.04030	+	4.49235i	−0.235635	+	0.261999i
$295$	13.9176	−	3.41026i	0.810313	−	0.198553i
$296$			2.19944i			0.127840i
$297$	3.40736	+	21.2777i	0.197715	+	1.23466i
$298$	−7.67448	−	7.67448i	−0.444571	−	0.444571i
$299$	42.9199			2.48212
$300$	4.40436	+	7.45665i	0.254286	+	0.430510i
$301$	0.345937			0.0199395
$302$	0.857244	+	0.857244i	0.0493288	+	0.0493288i
$303$	1.49212	+	28.1644i	0.0857203	+	1.61800i
$304$		−	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	−0.00822043	+	0.999966i	$0.502617\pi$
$307$	−17.6649	+	17.6649i	−1.00819	+	1.00819i	−0.999966	+	0.00822043i	$0.997383\pi$
$308$	−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	$0.911827\pi$
$312$	9.59862	−	0.508527i	0.543415	−	0.0287896i
$313$	10.1110	+	10.1110i	0.571508	+	0.571508i	0.932550	−	0.361042i	$-0.117579\pi$
$313$	10.1110	+	10.1110i	0.571508	+	0.571508i	−0.361042	+	0.932550i	$0.617579\pi$
$314$	14.2209			0.802530
$315$	5.34577	−	11.3775i	0.301200	−	0.641051i
$316$	12.4743			0.701735
$317$	9.56745	+	9.56745i	0.537361	+	0.537361i	0.922753	−	0.385392i	$-0.125934\pi$
$317$	9.56745	+	9.56745i	0.537361	+	0.537361i	−0.385392	+	0.922753i	$0.625934\pi$
$318$	−21.7264	+	1.15105i	−1.21836	+	0.0645475i
$319$		−	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
$327$	−0.780077	−	14.7242i	−0.0431384	−	0.814252i
$328$	−5.98137	−	5.98137i	−0.330266	−	0.330266i
$329$	4.54326			0.250478
$330$	−7.58973	+	14.1552i	−0.417801	+	0.779218i
$331$	−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
$333$	4.14660	−	5.13258i	0.227233	−	0.281264i
$334$			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	−0.625702	−	0.780062i	$-0.715187\pi$
$337$	2.83368	−	2.83368i	0.154361	−	0.154361i	0.780062	+	0.625702i	$0.215187\pi$
$338$	−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
$342$	−1.88530	+	2.33359i	−0.101946	+	0.126186i
$343$	13.8979	+	13.8979i	0.750415	+	0.750415i
$344$	−0.184604			−0.00995316
$345$	−14.1542	+	26.3983i	−0.762038	+	1.42124i
$346$	10.8931			0.585616
$347$	−12.2836	−	12.2836i	−0.659418	−	0.659418i	0.295825	−	0.955242i	$-0.404406\pi$
$347$	−12.2836	−	12.2836i	−0.659418	−	0.659418i	−0.955242	+	0.295825i	$0.904406\pi$
$348$	−0.00883712	−	0.166804i	−0.000473719	−	0.00894162i
$349$		−	25.9576i		−	1.38948i	−0.719261	−	0.694740i	$-0.755520\pi$
$349$		−	25.9576i		−	1.38948i	0.719261	−	0.694740i	$-0.244480\pi$
$350$	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	$-0.606590\pi$
$353$	11.5702	−	11.5702i	0.615818	−	0.615818i	0.944456	+	0.328638i	$0.106590\pi$
$354$	8.25271	+	7.42227i	0.438627	+	0.394489i
$355$	−5.04207	−	20.5771i	−0.267605	−	1.09212i
$356$			17.0881i			0.905668i
$357$	−22.9964	+	1.21833i	−1.21710	+	0.0644809i
$358$	6.40594	+	6.40594i	0.338565	+	0.338565i
$359$	−31.0266			−1.63752			−0.818760	−	0.574136i	$-0.805338\pi$
$359$	−31.0266			−1.63752			−0.818760	+	0.574136i	$0.805338\pi$
$360$	−2.85268	+	6.07143i	−0.150350	+	0.319992i
$361$	−1.00000			−0.0526316
$362$	−12.6699	−	12.6699i	−0.665915	−	0.665915i
$363$	−10.7206	+	0.567970i	−0.562688	+	0.0298107i
$364$		−	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	−0.278691	−	0.960381i	$-0.589900\pi$
$367$	13.0593	−	13.0593i	0.681690	−	0.681690i	0.960381	+	0.278691i	$0.0899004\pi$
$368$	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
$372$	0.00102359	+	0.0193206i	5.30705e−5	+	0.00100172i
$373$	21.2626	+	21.2626i	1.10093	+	1.10093i	0.994298	+	0.106636i	$0.0340080\pi$
$373$	21.2626	+	21.2626i	1.10093	+	1.10093i	0.106636	+	0.994298i	$0.465992\pi$
$374$	29.4234			1.52145
$375$	13.8506	−	13.5337i	0.715244	−	0.698875i
$376$	−2.42443			−0.125031
$377$	0.378439	+	0.378439i	0.0194906	+	0.0194906i
$378$	9.61481	−	1.53969i	0.494533	−	0.0791931i
$379$			27.4201i			1.40848i	0.709963	+	0.704239i	$0.248712\pi$
$379$			27.4201i			1.40848i	−0.709963	+	0.704239i	$0.751288\pi$
$380$	−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	$-0.767454\pi$
$383$	−1.51688	+	1.51688i	−0.0775089	+	0.0775089i	0.667290	+	0.744798i	$0.267454\pi$
$384$	1.15823	−	1.28782i	0.0591059	−	0.0657190i
$385$	14.8590	+	9.01024i	0.757283	+	0.459204i
$386$			0.577710i			0.0294047i
$387$	0.430789	+	0.348034i	0.0218982	+	0.0176916i
$388$	3.48454	+	3.48454i	0.176901	+	0.176901i
$389$	−27.2165			−1.37993			−0.689966	−	0.723841i	$-0.742375\pi$
$389$	−27.2165			−1.37993			−0.689966	+	0.723841i	$0.742375\pi$
$390$	−6.21249	−	20.5758i	−0.314582	−	1.04190i
$391$	54.8723			2.77501
$392$	−2.46662	−	2.46662i	−0.124583	−	0.124583i
$393$	−1.63066	−	30.7792i	−0.0822557	−	1.55260i
$394$		−	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	−0.373525	−	0.927620i	$-0.621851\pi$
$397$	11.0403	−	11.0403i	0.554095	−	0.554095i	0.927620	+	0.373525i	$0.121851\pi$
$398$	−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	$0.925125\pi$
$402$	11.6830	−	0.618954i	0.582694	−	0.0308706i
$403$	−0.0438339	−	0.0438339i	−0.00218352	−	0.00218352i
$404$	−16.2835			−0.810135
$405$	18.1035	−	8.79004i	0.899568	−	0.436780i
$406$	−0.180722			−0.00896909
$407$	6.44969	+	6.44969i	0.319699	+	0.319699i
$408$	12.2716	−	0.650141i	0.607537	−	0.0321868i
$409$		−	15.1973i		−	0.751460i	−0.926729	−	0.375730i	$-0.877392\pi$
$409$		−	15.1973i		−	0.751460i	0.926729	−	0.375730i	$-0.122608\pi$
$410$	−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
$417$	1.13688	+	21.4591i	0.0556734	+	1.05086i
$418$	−2.93243	−	2.93243i	−0.143430	−	0.143430i
$419$	−3.37395			−0.164828			−0.0824142	−	0.996598i	$-0.526263\pi$
$419$	−3.37395			−0.164828			−0.0824142	+	0.996598i	$0.526263\pi$
$420$	6.39634	+	3.42959i	0.312109	+	0.167347i
$421$	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
$423$	5.65763	+	4.57079i	0.275083	+	0.222240i
$424$		−	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	$-0.131095\pi$
$432$	−5.13078	+	0.821629i	−0.246855	+	0.0395306i
$433$	10.6960	+	10.6960i	0.514019	+	0.514019i	0.915755	−	0.401737i	$-0.131593\pi$
$433$	10.6960	+	10.6960i	0.514019	+	0.514019i	−0.401737	+	0.915755i	$0.631593\pi$
$434$	0.0209327			0.00100480
$435$	−0.357565	+	0.107960i	−0.0171439	+	0.00517628i
$436$	8.51296			0.407697
$437$	−5.46874	−	5.46874i	−0.261605	−	0.261605i
$438$	−0.524407	−	9.89837i	−0.0250571	−	0.472962i
$439$		−	18.1152i		−	0.864593i	−0.901731	−	0.432297i	$-0.857703\pi$
$439$		−	18.1152i		−	0.864593i	0.901731	−	0.432297i	$-0.142297\pi$
$440$	−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	$-0.573858\pi$
$443$	15.6435	−	15.6435i	0.743247	−	0.743247i	0.973201	+	0.229955i	$0.0738578\pi$
$444$	2.83249	+	2.54746i	0.134424	+	0.120897i
$445$	37.1123	−	9.09371i	1.75929	−	0.431083i
$446$		−	5.39430i		−	0.255428i
$447$	−18.7722	+	0.994537i	−0.887897	+	0.0470400i
$448$	−1.32508	−	1.32508i	−0.0626042	−	0.0626042i
$449$	−4.48299			−0.211565			−0.105783	−	0.994389i	$-0.533735\pi$
$449$	−4.48299			−0.211565			−0.105783	+	0.994389i	$0.533735\pi$
$450$	14.7041	+	2.96450i	0.693160	+	0.139748i
$451$	−35.0798			−1.65185
$452$	1.46934	+	1.46934i	0.0691122	+	0.0691122i
$453$	2.09687	−	0.111090i	0.0985195	−	0.00521948i
$454$			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	−0.840510	−	0.541797i	$-0.817744\pi$
$457$	−6.38576	+	6.38576i	−0.298713	+	0.298713i	0.541797	+	0.840510i	$0.317744\pi$
$458$	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	$0.931723\pi$
$462$	0.712125	+	13.4416i	0.0331311	+	0.625360i
$463$	−11.7522	−	11.7522i	−0.546170	−	0.546170i	0.379161	−	0.925331i	$-0.376213\pi$
$463$	−11.7522	−	11.7522i	−0.546170	−	0.546170i	−0.925331	+	0.379161i	$0.876213\pi$
$464$	0.0964393			0.00447708
$465$	0.0414161	−	0.0125048i	0.00192062	−	0.000579896i
$466$	−29.8774			−1.38404
$467$	−10.8294	−	10.8294i	−0.501124	−	0.501124i	0.410663	−	0.911787i	$-0.365297\pi$
$467$	−10.8294	−	10.8294i	−0.501124	−	0.501124i	−0.911787	+	0.410663i	$0.865297\pi$
$468$	10.4626	−	12.9503i	0.483632	−	0.598629i
$469$		−	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
$477$	−23.6820	+	29.3130i	−1.08432	+	1.34215i
$478$	2.18786	+	2.18786i	0.100070	+	0.100070i
$479$	−16.6381			−0.760216			−0.380108	−	0.924942i	$-0.624113\pi$
$479$	−16.6381			−0.760216			−0.380108	+	0.924942i	$0.624113\pi$
$480$	−3.41330	−	1.83014i	−0.155795	−	0.0835341i
$481$	−12.2059			−0.556539
$482$	4.68513	+	4.68513i	0.213402	+	0.213402i
$483$	1.32806	+	25.0675i	0.0604287	+	1.14061i
$484$		−	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	−0.531879	−	0.846820i	$-0.678514\pi$
$487$	6.95016	−	6.95016i	0.314942	−	0.314942i	0.846820	+	0.531879i	$0.178514\pi$
$488$	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	$0.972602\pi$
$492$	−14.6308	+	0.775126i	−0.659607	+	0.0349454i
$493$	0.483827	+	0.483827i	0.0217905	+	0.0217905i
$494$	5.54954			0.249685
$495$	9.43873	+	26.1693i	0.424239	+	1.17622i
$496$	−0.0111704			−0.000501565
$497$	−12.5546	−	12.5546i	−0.563152	−	0.563152i
$498$	−3.51463	+	0.186202i	−0.157494	+	0.00834390i
$499$			12.0717i			0.540405i	0.962804	+	0.270202i	$0.0870906\pi$
$499$			12.0717i			0.540405i	−0.962804	+	0.270202i	$0.912909\pi$
$500$	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	$-0.664340\pi$
$503$	8.43285	−	8.43285i	0.376002	−	0.376002i	0.869658	+	0.493655i	$0.164340\pi$
$504$	0.594013	+	5.59037i	0.0264595	+	0.249015i
$505$	8.66553	+	35.3648i	0.385611	+	1.57371i
$506$		−	32.0733i		−	1.42583i
$507$	1.63084	+	30.7828i	0.0724283	+	1.36711i
$508$	−0.469960	−	0.469960i	−0.0208511	−	0.0208511i
$509$	−14.4418			−0.640120			−0.320060	−	0.947397i	$-0.603703\pi$
$509$	−14.4418			−0.640120			−0.320060	+	0.947397i	$0.603703\pi$
$510$	−7.94254	−	26.3058i	−0.351702	−	1.16484i
$511$	−10.7243			−0.474415
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	0.821629	+	5.13078i	0.0362758	+	0.226530i
$514$		−	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	$-0.289655\pi$
$522$	−0.225049	−	0.181817i	−0.00985015	−	0.00795792i
$523$	21.2547	+	21.2547i	0.929403	+	0.929403i	0.997667	−	0.0682644i	$-0.0217461\pi$
$523$	21.2547	+	21.2547i	0.929403	+	0.929403i	−0.0682644	+	0.997667i	$0.521746\pi$
$524$	17.7953			0.777391
$525$	4.04453	−	15.7168i	0.176518	−	0.685937i
$526$	27.6026			1.20353
$527$	−0.0560407	−	0.0560407i	−0.00244117	−	0.00244117i
$528$	−0.380013	−	7.17289i	−0.0165380	−	0.312160i
$529$		−	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
$537$	15.6693	−	0.830147i	0.676181	−	0.0358235i
$538$	6.78356	+	6.78356i	0.292460	+	0.292460i
$539$	−14.4663			−0.623109
$540$	4.51486	+	10.7059i	0.194289	+	0.460708i
$541$	−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
$543$	−30.9913	+	1.64189i	−1.32996	+	0.0704604i
$544$			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	−0.345534	−	0.938406i	$-0.612302\pi$
$547$	13.8661	−	13.8661i	0.592872	−	0.592872i	0.938406	+	0.345534i	$0.112302\pi$
$548$	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
$552$	−0.708695	−	13.3769i	−0.0301640	−	0.569357i
$553$	−16.5295	−	16.5295i	−0.702905	−	0.702905i
$554$	−11.3525			−0.482323
$555$	4.02528	−	7.50733i	0.170863	−	0.318668i
$556$	−12.4068			−0.526165
$557$	0.548599	+	0.548599i	0.0232449	+	0.0232449i	0.718634	−	0.695389i	$-0.244768\pi$
$557$	0.548599	+	0.548599i	0.0232449	+	0.0232449i	−0.695389	+	0.718634i	$0.744768\pi$
$558$	0.0260671	+	0.0210596i	0.00110351	+	0.000891522i
$559$		−	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	$-0.739214\pi$
$563$	1.13682	−	1.13682i	0.0479114	−	0.0479114i	0.730657	+	0.682745i	$0.239214\pi$
$564$	−2.80806	+	3.12225i	−0.118241	+	0.131470i
$565$	2.40922	−	3.97309i	0.101356	−	0.167149i
$566$			19.1015i			0.802894i
$567$	9.15336	−	14.1655i	0.384405	−	0.594896i
$568$	6.69956	+	6.69956i	0.281107	+	0.281107i
$569$	−25.5607			−1.07156			−0.535781	−	0.844357i	$-0.679983\pi$
$569$	−25.5607			−1.07156			−0.535781	+	0.844357i	$0.679983\pi$
$570$	−1.83014	+	3.41330i	−0.0766561	+	0.142967i
$571$	−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
$573$	−0.770961	−	14.5522i	−0.0322074	−	0.607925i
$574$			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	−0.204594	+	0.978847i	$0.565587\pi$
$577$	−28.4272	+	28.4272i	−1.18344	+	1.18344i	−0.978847	+	0.204594i	$0.934413\pi$
$578$	−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
$582$	8.52339	−	0.451562i	0.353306	−	0.0187178i
$583$	−36.8352	−	36.8352i	−1.52556	−	1.52556i
$584$	5.72284			0.236813
$585$	−33.6936	−	15.8311i	−1.39306	−	0.654534i
$586$	2.72021			0.112371
$587$	23.4065	+	23.4065i	0.966088	+	0.966088i	0.999444	−	0.0333555i	$-0.0106194\pi$
$587$	23.4065	+	23.4065i	0.966088	+	0.966088i	−0.0333555	+	0.999444i	$0.510619\pi$
$588$	−6.03349	+	0.319649i	−0.248817	+	0.0131821i
$589$			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	$-0.922812\pi$
$593$	−17.7918	+	17.7918i	−0.730620	+	0.730620i	0.240122	+	0.970743i	$0.422812\pi$
$594$	−12.6363	+	17.4550i	−0.518473	+	0.716188i
$595$	−28.8757	+	7.07547i	−1.18379	+	0.290066i
$596$		−	10.8534i		−	0.444571i
$597$	2.01282	+	37.9927i	0.0823794	+	1.55494i
$598$	30.3490	+	30.3490i	1.24106	+	1.24106i
$599$	30.4391			1.24371			0.621854	−	0.783134i	$-0.286380\pi$
$599$	30.4391			1.24371			0.621854	+	0.783134i	$0.286380\pi$
$600$	−2.15829	+	8.38700i	−0.0881119	+	0.342398i
$601$	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
$603$	12.7345	−	15.7625i	0.518590	−	0.641899i
$604$			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	−0.861274	−	0.508141i	$-0.830333\pi$
$607$	−8.70025	+	8.70025i	−0.353132	+	0.353132i	0.508141	+	0.861274i	$0.330333\pi$
$608$	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
$612$	13.3762	−	16.5567i	0.540700	−	0.669267i
$613$	4.40309	+	4.40309i	0.177839	+	0.177839i	0.790413	−	0.612574i	$-0.209866\pi$
$613$	4.40309	+	4.40309i	0.177839	+	0.177839i	−0.612574	+	0.790413i	$0.709866\pi$
$614$	−24.9819			−1.00819
$615$	9.46944	+	31.3629i	0.381845	+	1.26468i
$616$	−7.77140			−0.313119
$617$	−8.04047	−	8.04047i	−0.323697	−	0.323697i	0.526486	−	0.850183i	$-0.323509\pi$
$617$	−8.04047	−	8.04047i	−0.323697	−	0.323697i	−0.850183	+	0.526486i	$0.823509\pi$
$618$	0.316574	+	5.97545i	0.0127345	+	0.240368i
$619$			23.1721i			0.931366i	0.884952	+	0.465683i	$0.154191\pi$
$619$			23.1721i			0.931366i	−0.884952	+	0.465683i	$0.845809\pi$
$620$	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
$627$	−7.17289	+	0.380013i	−0.286458	+	0.0151763i
$628$	10.0557	+	10.0557i	0.401265	+	0.401265i
$629$	−15.6049			−0.622210
$630$	11.8252	−	4.26510i	0.471126	−	0.169925i
$631$	−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
$633$	18.9519	−	1.00406i	0.753271	−	0.0399076i
$634$			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	$-0.187837\pi$
$642$	−0.172291	−	3.25206i	−0.00679980	−	0.128349i
$643$	4.86470	+	4.86470i	0.191845	+	0.191845i	0.796493	−	0.604648i	$-0.206686\pi$
$643$	4.86470	+	4.86470i	0.191845	+	0.191845i	−0.604648	+	0.796493i	$0.706686\pi$
$644$	−14.4930			−0.571106
$645$	0.630107	+	0.337850i	0.0248104	+	0.0133028i
$646$	7.09497			0.279148
$647$	−7.02609	−	7.02609i	−0.276224	−	0.276224i	0.555376	−	0.831600i	$-0.312575\pi$
$647$	−7.02609	−	7.02609i	−0.276224	−	0.276224i	−0.831600	+	0.555376i	$0.812575\pi$
$648$	−4.88454	+	7.55919i	−0.191883	+	0.296953i
$649$			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	−0.0319150	+	0.999491i	$0.510161\pi$
$653$	−26.3564	+	26.3564i	−1.03141	+	1.03141i	−0.999491	+	0.0319150i	$0.989839\pi$
$654$	9.86001	−	10.9632i	0.385557	−	0.428695i
$655$	−9.47005	−	38.6482i	−0.370026	−	1.51011i
$656$		−	8.45893i		−	0.330266i
$657$	−13.3547	−	10.7893i	−0.521018	−	0.420930i
$658$	3.21257	+	3.21257i	0.125239	+	0.125239i
$659$	11.1631			0.434853			0.217426	−	0.976077i	$-0.430234\pi$
$659$	11.1631			0.434853			0.217426	+	0.976077i	$0.430234\pi$
$660$	−15.3760	+	4.64249i	−0.598510	+	0.180709i
$661$	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
$663$	3.60798	+	68.1019i	0.140122	+	2.64486i
$664$		−	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
$672$	−3.24123	+	0.171717i	−0.125033	+	0.00662414i
$673$	−27.5847	−	27.5847i	−1.06331	−	1.06331i	−0.997855	−	0.0654567i	$-0.979150\pi$
$673$	−27.5847	−	27.5847i	−1.06331	−	1.06331i	−0.0654567	−	0.997855i	$-0.520850\pi$
$674$	4.00743			0.154361
$675$	20.8486	−	15.5028i	0.802463	−	0.596702i
$676$	−17.7974			−0.684514
$677$	−18.4404	−	18.4404i	−0.708721	−	0.708721i	0.257545	−	0.966266i	$-0.417086\pi$
$677$	−18.4404	−	18.4404i	−0.708721	−	0.708721i	−0.966266	+	0.257545i	$0.917086\pi$
$678$	3.59410	−	0.190413i	0.138031	−	0.00731275i
$679$		−	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	$-0.690329\pi$
$683$	6.88800	−	6.88800i	0.263562	−	0.263562i	0.826500	+	0.562937i	$0.190329\pi$
$684$	−2.98321	+	0.316985i	−0.114066	+	0.0121202i
$685$	−25.1728	−	15.2644i	−0.961804	−	0.583223i
$686$			19.6546i			0.750415i
$687$	−1.27348	−	24.0374i	−0.0485864	−	0.917085i
$688$	−0.130534	−	0.130534i	−0.00497658	−	0.00497658i
$689$	69.7097			2.65573
$690$	−28.6750	+	8.65787i	−1.09164	+	0.329599i
$691$	−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
$693$	18.1353	+	14.6515i	0.688901	+	0.556563i
$694$		−	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	$-0.0524564\pi$
$702$	−4.55966	−	28.4735i	−0.172093	−	1.07466i
$703$	1.55524	+	1.55524i	0.0586569	+	0.0586569i
$704$	4.14708			0.156299
$705$	8.27531	+	4.43705i	0.311666	+	0.167109i
$706$	16.3627			0.615818
$707$	21.5770	+	21.5770i	0.811485	+	0.811485i
$708$	0.587215	+	11.0839i	0.0220689	+	0.416558i
$709$		−	20.6106i		−	0.774049i	−0.922070	−	0.387024i	$-0.873503\pi$
$709$		−	20.6106i		−	0.774049i	0.922070	−	0.387024i	$-0.126497\pi$
$710$	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
$717$	5.35164	−	0.283525i	0.199861	−	0.0105884i
$718$	−21.9391	−	21.9391i	−0.818760	−	0.818760i
$719$	−39.9182			−1.48870			−0.744350	−	0.667790i	$-0.767240\pi$
$719$	−39.9182			−1.48870			−0.744350	+	0.667790i	$0.767240\pi$
$720$	−6.31030	+	2.27600i	−0.235171	+	0.0848214i
$721$	6.47405			0.241106
$722$	−0.707107	−	0.707107i	−0.0263158	−	0.0263158i
$723$	11.4601	−	0.607147i	0.426206	−	0.0225800i
$724$		−	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	−0.784053	−	0.620694i	$-0.786851\pi$
$727$	−4.40463	+	4.40463i	−0.163359	+	0.163359i	0.620694	+	0.784053i	$0.286851\pi$
$728$	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
$732$	−0.939107	−	17.7260i	−0.0347104	−	0.655171i
$733$	−13.9718	−	13.9718i	−0.516061	−	0.516061i	0.400316	−	0.916377i	$-0.368900\pi$
$733$	−13.9718	−	13.9718i	−0.516061	−	0.516061i	−0.916377	+	0.400316i	$0.868900\pi$
$734$	18.4687			0.681690
$735$	3.90504	+	12.9335i	0.144040	+	0.477061i
$736$	7.73397			0.285078
$737$	19.8074	+	19.8074i	0.729617	+	0.729617i
$738$	−15.9477	+	19.7397i	−0.587041	+	0.726627i
$739$			38.9043i			1.43112i	0.698553	+	0.715558i	$0.253828\pi$
$739$			38.9043i			1.43112i	−0.698553	+	0.715558i	$0.746172\pi$
$740$	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	−0.177000	+	0.984211i	$0.556639\pi$
$743$	−31.6523	+	31.6523i	−1.16121	+	1.16121i	−0.984211	+	0.177000i	$0.943361\pi$
$744$	−0.0129379	+	0.0143855i	−0.000474327	+	0.000527398i
$745$	−23.5715	+	5.77579i	−0.863594	+	0.211609i
$746$			30.0698i			1.10093i
$747$	−3.83097	+	4.74189i	−0.140168	+	0.173497i
$748$	20.8055	+	20.8055i	0.760724	+	0.760724i
$749$	−3.52342			−0.128743
$750$	19.3636	+	0.224143i	0.707059	+	0.00818456i
$751$	−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
$753$	1.95660	+	36.9315i	0.0713025	+	1.34586i
$754$			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	−0.880258	−	0.474496i	$-0.842630\pi$
$757$	−11.1640	+	11.1640i	−0.405762	+	0.405762i	0.474496	+	0.880258i	$0.342630\pi$
$758$	−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	$0.946032\pi$
$762$	−1.14955	+	0.0609022i	−0.0416438	+	0.00220625i
$763$	−11.2804	−	11.2804i	−0.408377	−	0.408377i
$764$	8.41348			0.304389
$765$	−43.0766	−	20.2397i	−1.55744	−	0.731768i
$766$	−2.14519			−0.0775089
$767$	−25.1467	−	25.1467i	−0.907996	−	0.907996i
$768$	1.72963	−	0.0916341i	0.0624125	−	0.00330656i
$769$		−	36.9866i		−	1.33377i	−0.745161	−	0.666885i	$-0.767627\pi$
$769$		−	36.9866i		−	1.33377i	0.745161	−	0.666885i	$-0.232373\pi$
$770$	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	−0.179873	+	0.983690i	$0.557569\pi$
$773$	−32.3504	+	32.3504i	−1.16356	+	1.16356i	−0.983690	+	0.179873i	$0.942431\pi$
$774$	0.0585166	+	0.550711i	0.00210334	+	0.0197949i
$775$	0.0495250	−	0.0258207i	0.00177899	−	0.000927509i
$776$			4.92788i			0.176901i
$777$	−0.377682	−	7.12887i	−0.0135492	−	0.255747i
$778$	−19.2450	−	19.2450i	−0.689966	−	0.689966i
$779$	−8.45893			−0.303073
$780$	10.1564	−	18.9422i	0.363658	−	0.678240i
$781$	39.2919			1.40598
$782$	38.8006	+	38.8006i	1.38751	+	1.38751i
$783$	−0.494809	+	0.0792373i	−0.0176830	+	0.00283171i
$784$		−	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	−0.819879	−	0.572537i	$-0.805959\pi$
$787$	−6.93880	+	6.93880i	−0.247342	+	0.247342i	0.572537	+	0.819879i	$0.305959\pi$
$788$	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
$792$	−9.67757	−	7.81850i	−0.343877	−	0.277818i
$793$	40.2161	+	40.2161i	1.42812	+	1.42812i
$794$	15.6133			0.554095
$795$	−22.9890	+	42.8756i	−0.815337	+	1.52064i
$796$	−21.9659			−0.778560
$797$	−16.0617	−	16.0617i	−0.568936	−	0.568936i	0.362895	−	0.931830i	$-0.381788\pi$
$797$	−16.0617	−	16.0617i	−0.568936	−	0.568936i	−0.931830	+	0.362895i	$0.881788\pi$
$798$	0.171717	+	3.24123i	0.00607873	+	0.114738i
$799$		−	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
$807$	16.5930	−	0.879082i	0.584101	−	0.0309451i
$808$	−11.5142	−	11.5142i	−0.405067	−	0.405067i
$809$	−10.5712			−0.371665			−0.185832	−	0.982581i	$-0.559498\pi$
$809$	−10.5712			−0.371665			−0.185832	+	0.982581i	$0.559498\pi$
$810$	19.0166	+	6.58559i	0.668174	+	0.231394i
$811$	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
$813$	52.5846	−	2.78589i	1.84422	−	0.0977053i
$814$			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	$-0.106482\pi$
$822$	−1.20642	−	22.7717i	−0.0420788	−	0.794253i
$823$	18.8387	+	18.8387i	0.656676	+	0.656676i	0.954592	−	0.297916i	$-0.0962916\pi$
$823$	18.8387	+	18.8387i	0.656676	+	0.656676i	−0.297916	+	0.954592i	$0.596292\pi$
$824$	−3.45477			−0.120353
$825$	18.2652	+	30.9233i	0.635914	+	1.07661i
$826$	12.0087			0.417837
$827$	17.5079	+	17.5079i	0.608810	+	0.608810i	0.942635	−	0.333825i	$-0.108339\pi$
$827$	17.5079	+	17.5079i	0.608810	+	0.608810i	−0.333825	+	0.942635i	$0.608339\pi$
$828$	−18.0479	−	14.5809i	−0.627207	−	0.506720i
$829$			39.9306i			1.38685i	0.720530	+	0.693424i	$0.243899\pi$
$829$			39.9306i			1.38685i	−0.720530	+	0.693424i	$0.756101\pi$
$830$	−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
$837$	0.0573128	−	0.00917791i	0.00198102	−	0.000317235i
$838$	−2.38575	−	2.38575i	−0.0824142	−	0.0824142i
$839$	26.1082			0.901355			0.450678	−	0.892687i	$-0.351182\pi$
$839$	26.1082			0.901355			0.450678	+	0.892687i	$0.351182\pi$
$840$	2.09781	+	6.94798i	0.0723813	+	0.239728i
$841$	−28.9907			−0.999679
$842$	11.9187	+	11.9187i	0.410746	+	0.410746i
$843$	1.23287	+	23.2709i	0.0424625	+	0.801494i
$844$			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
$852$	16.3875	−	0.868197i	0.561427	−	0.0297439i
$853$	17.0198	+	17.0198i	0.582747	+	0.582747i	0.935657	−	0.352910i	$-0.114808\pi$
$853$	17.0198	+	17.0198i	0.582747	+	0.582747i	−0.352910	+	0.935657i	$0.614808\pi$
$854$	−19.2050			−0.657183
$855$	2.27600	+	6.31030i	0.0778374	+	0.215808i
$856$	1.88021			0.0642643
$857$	22.2813	+	22.2813i	0.761115	+	0.761115i	0.976524	−	0.215409i	$-0.0691085\pi$
$857$	22.2813	+	22.2813i	0.761115	+	0.761115i	−0.215409	+	0.976524i	$0.569109\pi$
$858$	39.8062	−	2.10890i	1.35896	−	0.0719966i
$859$			54.5491i			1.86119i	0.366051	+	0.930595i	$0.380710\pi$
$859$			54.5491i			1.86119i	−0.366051	+	0.930595i	$0.619290\pi$
$860$	−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	$-0.521610\pi$
$863$	27.3164	−	27.3164i	0.929860	−	0.929860i	0.997696	+	0.0678368i	$0.0216097\pi$
$864$	−4.20899	−	3.04703i	−0.143193	−	0.103662i
$865$	12.6295	−	20.8276i	0.429417	−	0.708161i
$866$			15.1265i			0.514019i
$867$	3.05496	+	57.6634i	0.103752	+	1.95835i
$868$	0.0148017	+	0.0148017i	0.000502401	+	0.000502401i
$869$	51.7319			1.75489
$870$	−0.329176	−	0.176497i	−0.0111601	−	0.00598382i
$871$	−37.4851			−1.27013
$872$	6.01957	+	6.01957i	0.203849	+	0.203849i
$873$	9.29055	−	11.4996i	0.314437	−	0.389204i
$874$		−	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	−0.182017	+	0.983295i	$0.558263\pi$
$877$	−34.5098	+	34.5098i	−1.16531	+	1.16531i	−0.983295	+	0.182017i	$0.941737\pi$
$878$	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	$0.648182\pi$
$882$	−6.57654	+	8.14031i	−0.221444	+	0.274098i
$883$	−3.25237	−	3.25237i	−0.109451	−	0.109451i	0.650260	−	0.759711i	$-0.274660\pi$
$883$	−3.25237	−	3.25237i	−0.109451	−	0.109451i	−0.759711	+	0.650260i	$0.774660\pi$
$884$	−39.3738			−1.32428
$885$	23.7597	−	7.17379i	0.798673	−	0.241144i
$886$	22.1233			0.743247
$887$	13.8916	+	13.8916i	0.466434	+	0.466434i	0.900757	−	0.434323i	$-0.143012\pi$
$887$	13.8916	+	13.8916i	0.466434	+	0.466434i	−0.434323	+	0.900757i	$0.643012\pi$
$888$	0.201543	+	3.80420i	0.00676335	+	0.127661i
$889$			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
$897$	74.2354	−	3.93293i	2.47865	−	0.131317i
$898$	−3.16995	−	3.16995i	−0.105783	−	0.105783i
$899$	−0.00107726			−3.59287e−5
$900$	8.30118	+	12.4936i	0.276706	+	0.416454i
$901$	89.1225			2.96910
$902$	−24.8052	−	24.8052i	−0.825923	−	0.825923i
$903$	0.598342	−	0.0316997i	0.0199116	−	0.00105490i
$904$			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	−0.134253	−	0.990947i	$-0.542864\pi$
$907$	25.8006	−	25.8006i	0.856694	−	0.856694i	0.990947	+	0.134253i	$0.0428636\pi$
$908$	−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	$-0.0761926\pi$
$912$	−0.0916341	−	1.72963i	−0.00303431	−	0.0572736i
$913$	−5.95874	−	5.95874i	−0.197205	−	0.197205i
$914$	−9.03082			−0.298713
$915$	−37.9978	+	11.4727i	−1.25617	+	0.379277i
$916$	13.8975			0.459186
$917$	−23.5802	−	23.5802i	−0.778687	−	0.778687i
$918$	−5.82944	−	36.4028i	−0.192400	−	1.20147i
$919$		−	26.7468i		−	0.882295i	−0.897435	−	0.441148i	$-0.854572\pi$
$919$		−	26.7468i		−	0.882295i	0.897435	−	0.441148i	$-0.145428\pi$
$920$	−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
$927$	8.06200	+	6.51328i	0.264791	+	0.213924i
$928$	0.0681929	+	0.0681929i	0.00223854	+	0.00223854i
$929$	45.0802			1.47903			0.739517	−	0.673138i	$-0.235054\pi$
$929$	45.0802			1.47903			0.739517	+	0.673138i	$0.235054\pi$
$930$	0.0381278	+	0.0204434i	0.00125026	+	0.000670364i
$931$	−3.48832			−0.114325
$932$	−21.1265	−	21.1265i	−0.692022	−	0.692022i
$933$	0.883866	+	16.6833i	0.0289365	+	0.546186i
$934$		−	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	−0.603466	−	0.797389i	$-0.706214\pi$
$937$	5.93609	−	5.93609i	0.193923	−	0.193923i	0.797389	+	0.603466i	$0.206214\pi$
$938$	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	$-0.0110409\pi$
$942$	24.5968	−	1.30312i	0.801407	−	0.0424578i
$943$	−46.2597	−	46.2597i	−1.50642	−	1.50642i
$944$	−6.40826			−0.208571
$945$	8.20362	−	20.1687i	0.266864	−	0.656088i
$946$	−0.765565			−0.0248907
$947$	11.6968	+	11.6968i	0.380097	+	0.380097i	0.871137	−	0.491040i	$-0.163383\pi$
$947$	11.6968	+	11.6968i	0.380097	+	0.380097i	−0.491040	+	0.871137i	$0.663383\pi$
$948$	21.5759	−	1.14307i	0.700752	−	0.0371252i
$949$			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	$-0.684568\pi$
$953$	8.91128	−	8.91128i	0.288665	−	0.288665i	0.836552	+	0.547887i	$0.184568\pi$
$954$	−37.4731	+	3.98176i	−1.21324	+	0.128914i
$955$	−4.47737	−	18.2725i	−0.144884	−	0.591286i
$956$			3.09410i			0.100070i
$957$	−0.0366482	−	0.691748i	−0.00118467	−	0.0223610i
$958$	−11.7649	−	11.7649i	−0.380108	−	0.380108i
$959$	−24.6718			−0.796693
$960$	−1.11946	−	3.70767i	−0.0361304	−	0.119664i
$961$	−30.9999			−0.999996
$962$	−8.63084	−	8.63084i	−0.278270	−	0.278270i
$963$	−4.38764	−	3.54477i	−0.141390	−	0.114229i
$964$			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	−0.206759	−	0.978392i	$-0.566292\pi$
$967$	23.9952	−	23.9952i	0.771633	−	0.771633i	0.978392	+	0.206759i	$0.0662917\pi$
$968$	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	$-0.0571558\pi$
$972$	4.07747	+	15.0457i	0.130785	+	0.482592i
$973$	16.4400	+	16.4400i	0.527042	+	0.527042i
$974$	9.82901			0.314942
$975$	−46.5440	−	11.9775i	−1.49060	−	0.383588i
$976$	10.2484			0.328045
$977$	−12.3178	−	12.3178i	−0.394082	−	0.394082i	0.482058	−	0.876139i	$-0.339889\pi$
$977$	−12.3178	−	12.3178i	−0.394082	−	0.394082i	−0.876139	+	0.482058i	$0.839889\pi$
$978$	−1.11570	−	21.0592i	−0.0356760	−	0.673397i
$979$			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	$-0.840854\pi$
$983$	−12.4846	+	12.4846i	−0.398196	+	0.398196i	0.479401	+	0.877596i	$0.340854\pi$
$984$	−10.8936	−	9.79743i	−0.347276	−	0.312331i
$985$	−8.29047	−	5.02721i	−0.264156	−	0.160180i
$986$			0.684234i			0.0217905i
$987$	7.85814	−	0.416318i	0.250127	−	0.0132515i
$988$	3.92411	+	3.92411i	0.124843	+	0.124843i
$989$	−1.42772			−0.0453988
$990$	−11.8303	+	25.1787i	−0.375991	+	0.800231i
$991$	−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
$993$	−18.7911	+	0.995534i	−0.596316	+	0.0315923i
$994$		−	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	0.291511	−	0.956567i	$-0.405842\pi$
$997$	39.4085	−	39.4085i	1.24808	−	1.24808i	0.956567	−	0.291511i	$-0.0941581\pi$
$998$	−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.533.18	yes	36
3.2	odd	2	inner	570.2.k.b.533.4	yes	36
5.2	odd	4	inner	570.2.k.b.77.4	✓	36
15.2	even	4	inner	570.2.k.b.77.18	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.k.b.77.4	✓	36	5.2	odd	4	inner
570.2.k.b.77.18	yes	36	15.2	even	4	inner
570.2.k.b.533.4	yes	36	3.2	odd	2	inner
570.2.k.b.533.18	yes	36	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.72963 - 0.0916341i) q^{3} +1.00000i q^{4} +(2.17182 - 0.532166i) q^{5} +(1.28782 + 1.15823i) q^{6} +(1.32508 - 1.32508i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.98321 - 0.316985i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.72963 - 0.0916341i) 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} +(0.0916341 + 1.72963i) q^{12} +(-3.92411 - 3.92411i) q^{13} +1.87395 q^{14} +(3.70767 - 1.11946i) q^{15} -1.00000 q^{16} +(-5.01690 - 5.01690i) q^{17} +(2.33359 + 1.88530i) 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} +(5.13078 - 0.821629i) q^{27} +(1.32508 + 1.32508i) q^{28} -0.0964393 q^{29} +(3.41330 + 1.83014i) q^{30} +0.0111704 q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.380013 + 7.17289i) 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} +(3.24123 - 0.171717i) q^{42} +(0.130534 + 0.130534i) q^{43} -4.14708 q^{44} +(6.31030 - 2.27600i) q^{45} -7.73397 q^{46} +(1.71433 + 1.71433i) q^{47} +(-1.72963 + 0.0916341i) 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} +(0.0916341 + 1.72963i) q^{57} +(-0.0681929 - 0.0681929i) q^{58} +6.40826 q^{59} +(1.11946 + 3.70767i) q^{60} -10.2484 q^{61} +(0.00789865 + 0.00789865i) q^{62} +(3.53296 - 4.37302i) 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} +(-1.88530 + 2.33359i) q^{72} +(-4.04666 - 4.04666i) q^{73} +2.19944 q^{74} +(7.45665 - 4.40436i) q^{75} -1.00000 q^{76} +(5.49521 + 5.49521i) q^{77} +(-0.508527 - 9.59862i) 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} +(-0.166804 + 0.00883712i) q^{87} +(-2.93243 - 2.93243i) q^{88} +17.0881 q^{89} +(6.07143 + 2.85268i) q^{90} -10.3995 q^{91} +(-5.46874 - 5.46874i) q^{92} +(0.0193206 - 0.00102359i) 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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