LMFDB - Embedded newform 950.2.n.b.39.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(39,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("950.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.n (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.2
Character	$\chi$	$=$	950.39
Dual form			950.2.n.b.609.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 - 0.809017i) q^{2} +(-3.16378 - 1.02797i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(1.22578 - 1.87015i) q^{5} +(1.02797 + 3.16378i) q^{6} +4.52249i q^{7} +(0.951057 - 0.309017i) q^{8} +(6.52572 + 4.74121i) q^{9} +O(q^{10})$	\(q+(-0.587785 - 0.809017i) q^{2} +(-3.16378 - 1.02797i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(1.22578 - 1.87015i) q^{5} +(1.02797 + 3.16378i) q^{6} +4.52249i q^{7} +(0.951057 - 0.309017i) q^{8} +(6.52572 + 4.74121i) q^{9} +(-2.23348 + 0.107573i) q^{10} +(-1.31618 + 0.956259i) q^{11} +(1.95532 - 2.69127i) q^{12} +(2.78815 - 3.83755i) q^{13} +(3.65877 - 2.65825i) q^{14} +(-5.80056 + 4.65668i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-4.92873 + 1.60144i) q^{17} -8.06623i q^{18} +(-0.309017 - 0.951057i) q^{19} +(1.39983 + 1.74369i) q^{20} +(4.64900 - 14.3082i) q^{21} +(1.54726 + 0.502735i) q^{22} +(-3.69749 - 5.08916i) q^{23} -3.32659 q^{24} +(-1.99494 - 4.58478i) q^{25} -4.74348 q^{26} +(-9.90613 - 13.6346i) q^{27} +(-4.30114 - 1.39753i) q^{28} +(1.66178 - 5.11443i) q^{29} +(7.17682 + 1.95562i) q^{30} +(3.07181 + 9.45405i) q^{31} +1.00000i q^{32} +(5.14711 - 1.67240i) q^{33} +(4.19263 + 3.04612i) q^{34} +(8.45774 + 5.54356i) q^{35} +(-6.52572 + 4.74121i) q^{36} +(-2.49397 + 3.43266i) q^{37} +(-0.587785 + 0.809017i) q^{38} +(-12.7660 + 9.27503i) q^{39} +(0.587875 - 2.15741i) q^{40} +(0.0389637 + 0.0283088i) q^{41} +(-14.3082 + 4.64900i) q^{42} -1.42558i q^{43} +(-0.502735 - 1.54726i) q^{44} +(16.8659 - 6.39242i) q^{45} +(-1.94389 + 5.98267i) q^{46} +(-3.08310 - 1.00176i) q^{47} +(1.95532 + 2.69127i) q^{48} -13.4529 q^{49} +(-2.53657 + 4.30881i) q^{50} +17.2397 q^{51} +(2.78815 + 3.83755i) q^{52} +(-5.49183 - 1.78441i) q^{53} +(-5.20796 + 16.0284i) q^{54} +(0.175010 + 3.63361i) q^{55} +(1.39753 + 4.30114i) q^{56} +3.32659i q^{57} +(-5.11443 + 1.66178i) q^{58} +(-2.39512 - 1.74015i) q^{59} +(-2.63630 - 6.95565i) q^{60} +(0.495302 - 0.359858i) q^{61} +(5.84292 - 8.04209i) q^{62} +(-21.4421 + 29.5125i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-3.75916 - 9.91824i) q^{65} +(-4.37839 - 3.18109i) q^{66} +(-4.15030 + 1.34852i) q^{67} -5.18238i q^{68} +(6.46652 + 19.9019i) q^{69} +(-0.486499 - 10.1009i) q^{70} +(3.26509 - 10.0489i) q^{71} +(7.67144 + 2.49260i) q^{72} +(2.33652 + 3.21594i) q^{73} +4.24300 q^{74} +(1.59851 + 16.5560i) q^{75} +1.00000 q^{76} +(-4.32467 - 5.95240i) q^{77} +(15.0073 + 4.87617i) q^{78} +(1.40270 - 4.31708i) q^{79} +(-2.09092 + 0.792491i) q^{80} +(9.84696 + 30.3058i) q^{81} -0.0481618i q^{82} +(-11.8543 + 3.85168i) q^{83} +(12.1712 + 8.84293i) q^{84} +(-3.04659 + 11.1805i) q^{85} +(-1.15332 + 0.837933i) q^{86} +(-10.5150 + 14.4727i) q^{87} +(-0.956259 + 1.31618i) q^{88} +(-13.1027 + 9.51968i) q^{89} +(-15.0851 - 9.88741i) q^{90} +(17.3553 + 12.6094i) q^{91} +(5.98267 - 1.94389i) q^{92} -33.0683i q^{93} +(1.00176 + 3.08310i) q^{94} +(-2.15741 - 0.587875i) q^{95} +(1.02797 - 3.16378i) q^{96} +(0.199208 + 0.0647267i) q^{97} +(7.90741 + 10.8836i) q^{98} -13.1228 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 24 q^{4} + 8 q^{5} - 6 q^{6} + 34 q^{9}+O(q^{10}) $ 96 * q + 24 * q^4 + 8 * q^5 - 6 * q^6 + 34 * q^9	$ 96 q + 24 q^{4} + 8 q^{5} - 6 q^{6} + 34 q^{9} - 24 q^{11} + 10 q^{12} + 10 q^{14} - 8 q^{15} - 24 q^{16} + 30 q^{17} + 24 q^{19} + 2 q^{20} - 24 q^{24} - 60 q^{25} + 84 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} + 16 q^{30} - 14 q^{31} + 100 q^{33} + 8 q^{34} + 42 q^{35} - 34 q^{36} - 30 q^{37} + 32 q^{39} + 12 q^{41} + 10 q^{42} + 4 q^{44} - 18 q^{45} - 10 q^{46} + 10 q^{48} - 132 q^{49} - 36 q^{50} + 36 q^{51} + 30 q^{53} + 24 q^{54} - 4 q^{55} - 10 q^{56} + 60 q^{58} + 16 q^{59} + 8 q^{60} + 42 q^{61} - 110 q^{63} + 24 q^{64} + 12 q^{65} - 20 q^{66} + 130 q^{67} - 8 q^{69} + 20 q^{70} - 8 q^{71} - 120 q^{73} - 124 q^{74} - 24 q^{75} + 96 q^{76} - 50 q^{78} + 4 q^{79} - 2 q^{80} - 10 q^{81} - 70 q^{83} + 52 q^{85} - 44 q^{86} - 70 q^{87} + 10 q^{88} - 26 q^{89} + 32 q^{90} - 4 q^{91} - 10 q^{92} + 10 q^{94} + 2 q^{95} - 6 q^{96} - 10 q^{97} - 60 q^{98} - 184 q^{99}+O(q^{100}) $ 96 * q + 24 * q^4 + 8 * q^5 - 6 * q^6 + 34 * q^9 - 24 * q^11 + 10 * q^12 + 10 * q^14 - 8 * q^15 - 24 * q^16 + 30 * q^17 + 24 * q^19 + 2 * q^20 - 24 * q^24 - 60 * q^25 + 84 * q^26 - 30 * q^27 - 10 * q^28 - 4 * q^29 + 16 * q^30 - 14 * q^31 + 100 * q^33 + 8 * q^34 + 42 * q^35 - 34 * q^36 - 30 * q^37 + 32 * q^39 + 12 * q^41 + 10 * q^42 + 4 * q^44 - 18 * q^45 - 10 * q^46 + 10 * q^48 - 132 * q^49 - 36 * q^50 + 36 * q^51 + 30 * q^53 + 24 * q^54 - 4 * q^55 - 10 * q^56 + 60 * q^58 + 16 * q^59 + 8 * q^60 + 42 * q^61 - 110 * q^63 + 24 * q^64 + 12 * q^65 - 20 * q^66 + 130 * q^67 - 8 * q^69 + 20 * q^70 - 8 * q^71 - 120 * q^73 - 124 * q^74 - 24 * q^75 + 96 * q^76 - 50 * q^78 + 4 * q^79 - 2 * q^80 - 10 * q^81 - 70 * q^83 + 52 * q^85 - 44 * q^86 - 70 * q^87 + 10 * q^88 - 26 * q^89 + 32 * q^90 - 4 * q^91 - 10 * q^92 + 10 * q^94 + 2 * q^95 - 6 * q^96 - 10 * q^97 - 60 * q^98 - 184 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$3$	−3.16378	−	1.02797i	−1.82661	−	0.593501i	−0.999505	−	0.0314521i	$-0.989987\pi$
$3$	−3.16378	−	1.02797i	−1.82661	−	0.593501i	−0.827104	−	0.562049i	$-0.810013\pi$
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	1.22578	−	1.87015i	0.548184	−	0.836358i
$5$	1.22578	−	1.87015i	0.548184	−	0.836358i
$6$	1.02797	+	3.16378i	0.419669	+	1.29161i
$7$			4.52249i			1.70934i	0.519172	+	0.854670i	$0.326240\pi$
$7$			4.52249i			1.70934i	−0.519172	+	0.854670i	$0.673760\pi$
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$	6.52572	+	4.74121i	2.17524	+	1.58040i
$10$	−2.23348	+	0.107573i	−0.706288	+	0.0340177i
$11$	−1.31618	+	0.956259i	−0.396843	+	0.288323i	−0.768254	−	0.640145i	$-0.778874\pi$
$11$	−1.31618	+	0.956259i	−0.396843	+	0.288323i	0.371411	+	0.928469i	$0.378874\pi$
$12$	1.95532	−	2.69127i	0.564453	−	0.776903i
$13$	2.78815	−	3.83755i	0.773292	−	1.06435i	−0.222698	−	0.974887i	$-0.571486\pi$
$13$	2.78815	−	3.83755i	0.773292	−	1.06435i	0.995991	−	0.0894582i	$-0.0285136\pi$
$14$	3.65877	−	2.65825i	0.977847	−	0.710448i
$15$	−5.80056	+	4.65668i	−1.49770	+	1.20235i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−4.92873	+	1.60144i	−1.19539	+	0.388407i	−0.838064	−	0.545572i	$-0.816313\pi$
$17$	−4.92873	+	1.60144i	−1.19539	+	0.388407i	−0.357329	+	0.933979i	$0.616313\pi$
$18$		−	8.06623i		−	1.90123i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$20$	1.39983	+	1.74369i	0.313013	+	0.389901i
$21$	4.64900	−	14.3082i	1.01450	−	3.12230i
$22$	1.54726	+	0.502735i	0.329877	+	0.107184i
$23$	−3.69749	−	5.08916i	−0.770980	−	1.06116i	−0.996221	−	0.0868599i	$-0.972317\pi$
$23$	−3.69749	−	5.08916i	−0.770980	−	1.06116i	0.225240	−	0.974303i	$-0.427683\pi$
$24$	−3.32659			−0.679038
$25$	−1.99494	−	4.58478i	−0.398988	−	0.916956i
$26$	−4.74348			−0.930272
$27$	−9.90613	−	13.6346i	−1.90643	−	2.62398i
$28$	−4.30114	−	1.39753i	−0.812839	−	0.264107i
$29$	1.66178	−	5.11443i	0.308584	−	0.949725i	−0.669731	−	0.742604i	$-0.733591\pi$
$29$	1.66178	−	5.11443i	0.308584	−	0.949725i	0.978315	−	0.207121i	$-0.0664095\pi$
$30$	7.17682	+	1.95562i	1.31030	+	0.357046i
$31$	3.07181	+	9.45405i	0.551713	+	1.69800i	0.704471	+	0.709733i	$0.251184\pi$
$31$	3.07181	+	9.45405i	0.551713	+	1.69800i	−0.152758	+	0.988264i	$0.548816\pi$
$32$			1.00000i			0.176777i
$33$	5.14711	−	1.67240i	0.895996	−	0.291127i
$34$	4.19263	+	3.04612i	0.719030	+	0.522406i
$35$	8.45774	+	5.54356i	1.42962	+	0.937033i
$36$	−6.52572	+	4.74121i	−1.08762	+	0.790202i
$37$	−2.49397	+	3.43266i	−0.410007	+	0.564326i	−0.963220	−	0.268714i	$-0.913401\pi$
$37$	−2.49397	+	3.43266i	−0.410007	+	0.564326i	0.553213	+	0.833040i	$0.313401\pi$
$38$	−0.587785	+	0.809017i	−0.0953514	+	0.131240i
$39$	−12.7660	+	9.27503i	−2.04419	+	1.48519i
$40$	0.587875	−	2.15741i	0.0929511	−	0.341116i
$41$	0.0389637	+	0.0283088i	0.00608511	+	0.00442109i	0.590824	−	0.806801i	$-0.298803\pi$
$41$	0.0389637	+	0.0283088i	0.00608511	+	0.00442109i	−0.584739	+	0.811222i	$0.698803\pi$
$42$	−14.3082	+	4.64900i	−2.20780	+	0.717356i
$43$		−	1.42558i		−	0.217398i	−0.994075	−	0.108699i	$-0.965331\pi$
$43$		−	1.42558i		−	0.217398i	0.994075	−	0.108699i	$-0.0346685\pi$
$44$	−0.502735	−	1.54726i	−0.0757902	−	0.233258i
$45$	16.8659	−	6.39242i	2.51422	−	0.952926i
$46$	−1.94389	+	5.98267i	−0.286610	+	0.882096i
$47$	−3.08310	−	1.00176i	−0.449716	−	0.146122i	0.0753978	−	0.997154i	$-0.475977\pi$
$47$	−3.08310	−	1.00176i	−0.449716	−	0.146122i	−0.525114	+	0.851032i	$0.675977\pi$
$48$	1.95532	+	2.69127i	0.282227	+	0.388452i
$49$	−13.4529			−1.92184
$50$	−2.53657	+	4.30881i	−0.358725	+	0.609357i
$51$	17.2397			2.41404
$52$	2.78815	+	3.83755i	0.386646	+	0.532173i
$53$	−5.49183	−	1.78441i	−0.754361	−	0.245107i	−0.0935046	−	0.995619i	$-0.529807\pi$
$53$	−5.49183	−	1.78441i	−0.754361	−	0.245107i	−0.660857	+	0.750512i	$0.729807\pi$
$54$	−5.20796	+	16.0284i	−0.708713	+	2.18120i
$55$	0.175010	+	3.63361i	0.0235983	+	0.489956i
$56$	1.39753	+	4.30114i	0.186752	+	0.574764i
$57$			3.32659i			0.440618i
$58$	−5.11443	+	1.66178i	−0.671557	+	0.218202i
$59$	−2.39512	−	1.74015i	−0.311818	−	0.226549i	0.420858	−	0.907126i	$-0.361729\pi$
$59$	−2.39512	−	1.74015i	−0.311818	−	0.226549i	−0.732676	+	0.680578i	$0.761729\pi$
$60$	−2.63630	−	6.95565i	−0.340345	−	0.897971i
$61$	0.495302	−	0.359858i	0.0634169	−	0.0460751i	−0.555625	−	0.831433i	$-0.687521\pi$
$61$	0.495302	−	0.359858i	0.0634169	−	0.0460751i	0.619042	+	0.785358i	$0.287521\pi$
$62$	5.84292	−	8.04209i	0.742052	−	1.02135i
$63$	−21.4421	+	29.5125i	−2.70145	+	3.71822i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	−3.75916	−	9.91824i	−0.466267	−	1.23021i
$66$	−4.37839	−	3.18109i	−0.538943	−	0.391565i
$67$	−4.15030	+	1.34852i	−0.507040	+	0.164747i	−0.551356	−	0.834270i	$-0.685889\pi$
$67$	−4.15030	+	1.34852i	−0.507040	+	0.164747i	0.0443155	+	0.999018i	$0.485889\pi$
$68$		−	5.18238i		−	0.628455i
$69$	6.46652	+	19.9019i	0.778478	+	2.39591i
$70$	−0.486499	−	10.1009i	−0.0581478	−	1.20729i
$71$	3.26509	−	10.0489i	0.387494	−	1.19259i	−0.547160	−	0.837028i	$-0.684291\pi$
$71$	3.26509	−	10.0489i	0.387494	−	1.19259i	0.934655	−	0.355557i	$-0.115709\pi$
$72$	7.67144	+	2.49260i	0.904088	+	0.293756i
$73$	2.33652	+	3.21594i	0.273468	+	0.376397i	0.923557	−	0.383462i	$-0.125268\pi$
$73$	2.33652	+	3.21594i	0.273468	+	0.376397i	−0.650088	+	0.759859i	$0.725268\pi$
$74$	4.24300			0.493239
$75$	1.59851	+	16.5560i	0.184581	+	1.91172i
$76$	1.00000			0.114708
$77$	−4.32467	−	5.95240i	−0.492842	−	0.678339i
$78$	15.0073	+	4.87617i	1.69924	+	0.552118i
$79$	1.40270	−	4.31708i	0.157817	−	0.485709i	−0.840619	−	0.541627i	$-0.817808\pi$
$79$	1.40270	−	4.31708i	0.157817	−	0.485709i	0.998435	+	0.0559177i	$0.0178085\pi$
$80$	−2.09092	+	0.792491i	−0.233772	+	0.0886032i
$81$	9.84696	+	30.3058i	1.09411	+	3.36731i
$82$		−	0.0481618i		−	0.00531858i
$83$	−11.8543	+	3.85168i	−1.30117	+	0.422777i	−0.875990	−	0.482329i	$-0.839791\pi$
$83$	−11.8543	+	3.85168i	−1.30117	+	0.422777i	−0.425185	+	0.905107i	$0.639791\pi$
$84$	12.1712	+	8.84293i	1.32799	+	0.964842i
$85$	−3.04659	+	11.1805i	−0.330449	+	1.21269i
$86$	−1.15332	+	0.837933i	−0.124365	+	0.0903566i
$87$	−10.5150	+	14.4727i	−1.12733	+	1.55163i
$88$	−0.956259	+	1.31618i	−0.101938	+	0.140305i
$89$	−13.1027	+	9.51968i	−1.38888	+	1.00908i	−0.392898	+	0.919582i	$0.628528\pi$
$89$	−13.1027	+	9.51968i	−1.38888	+	1.00908i	−0.995987	+	0.0895019i	$0.971472\pi$
$90$	−15.0851	−	9.88741i	−1.59011	−	1.04222i
$91$	17.3553	+	12.6094i	1.81933	+	1.32182i
$92$	5.98267	−	1.94389i	0.623736	−	0.202664i
$93$		−	33.0683i		−	3.42902i
$94$	1.00176	+	3.08310i	0.103324	+	0.317997i
$95$	−2.15741	−	0.587875i	−0.221345	−	0.0603147i
$96$	1.02797	−	3.16378i	0.104917	−	0.322902i
$97$	0.199208	+	0.0647267i	0.0202266	+	0.00657201i	0.319113	−	0.947717i	$-0.396615\pi$
$97$	0.199208	+	0.0647267i	0.0202266	+	0.00657201i	−0.298886	+	0.954289i	$0.596615\pi$
$98$	7.90741	+	10.8836i	0.798769	+	1.09941i
$99$	−13.1228			−1.31889
$100$	4.97686	−	0.480526i	0.497686	−	0.0480526i
$101$	−6.14944			−0.611892			−0.305946	−	0.952049i	$-0.598973\pi$
$101$	−6.14944			−0.611892			−0.305946	+	0.952049i	$0.598973\pi$
$102$	−10.1332	−	13.9472i	−1.00334	−	1.38098i
$103$	6.33085	+	2.05702i	0.623797	+	0.202684i	0.603825	−	0.797117i	$-0.293642\pi$
$103$	6.33085	+	2.05702i	0.623797	+	0.202684i	0.0199716	+	0.999801i	$0.493642\pi$
$104$	1.46581	−	4.51131i	0.143735	−	0.442371i
$105$	−21.0598	−	26.2329i	−2.05522	−	2.56007i
$106$	1.78441	+	5.49183i	0.173317	+	0.533414i
$107$		−	14.0667i		−	1.35988i	−0.733268	−	0.679940i	$-0.762006\pi$
$107$		−	14.0667i		−	1.35988i	0.733268	−	0.679940i	$-0.237994\pi$
$108$	16.0284	−	5.20796i	1.54234	−	0.501136i
$109$	−11.1033	−	8.06699i	−1.06350	−	0.772677i	−0.0887664	−	0.996052i	$-0.528292\pi$
$109$	−11.1033	−	8.06699i	−1.06350	−	0.772677i	−0.974733	+	0.223375i	$0.928292\pi$
$110$	2.83679	−	2.27737i	0.270477	−	0.217139i
$111$	11.4191	−	8.29644i	1.08385	−	0.787464i
$112$	2.65825	−	3.65877i	0.251181	−	0.345721i
$113$	0.526720	−	0.724968i	0.0495496	−	0.0681992i	−0.783523	−	0.621363i	$-0.786579\pi$
$113$	0.526720	−	0.724968i	0.0495496	−	0.0681992i	0.833073	+	0.553163i	$0.186579\pi$
$114$	2.69127	−	1.95532i	0.252061	−	0.183133i
$115$	−14.0498	+	0.676695i	−1.31015	+	0.0631022i
$116$	4.35059	+	3.16089i	0.403942	+	0.293481i
$117$	36.3893	−	11.8236i	3.36419	−	1.09309i
$118$			2.96053i			0.272539i
$119$	−7.24250	−	22.2901i	−0.663919	−	2.04333i
$120$	−4.07766	+	6.22124i	−0.372238	+	0.567919i
$121$	−2.58129	+	7.94441i	−0.234663	+	0.722219i
$122$	−0.582262	−	0.189188i	−0.0527156	−	0.0171283i
$123$	−0.0941718	−	0.129616i	−0.00849119	−	0.0116871i
$124$	−9.94057			−0.892690
$125$	−11.0196	−	1.88908i	−0.985622	−	0.168964i
$126$	36.4794			3.24985
$127$	−4.68072	−	6.44246i	−0.415347	−	0.571676i	0.549166	−	0.835714i	$-0.314946\pi$
$127$	−4.68072	−	6.44246i	−0.415347	−	0.571676i	−0.964512	+	0.264038i	$0.914946\pi$
$128$	−0.951057	−	0.309017i	−0.0840623	−	0.0273135i
$129$	−1.46546	+	4.51021i	−0.129026	+	0.397102i
$130$	−5.81445	+	8.87102i	−0.509961	+	0.778040i
$131$	0.178215	+	0.548490i	0.0155707	+	0.0479218i	0.958540	−	0.284958i	$-0.0919797\pi$
$131$	0.178215	+	0.548490i	0.0155707	+	0.0479218i	−0.942969	+	0.332880i	$0.891980\pi$
$132$			5.41199i			0.471053i
$133$	4.30114	−	1.39753i	0.372956	−	0.121181i
$134$	3.53046	+	2.56503i	0.304985	+	0.221585i
$135$	−37.6415	+	1.81297i	−3.23966	+	0.156035i
$136$	−4.19263	+	3.04612i	−0.359515	+	0.261203i
$137$	−5.05825	+	6.96208i	−0.432155	+	0.594811i	−0.968446	−	0.249222i	$-0.919825\pi$
$137$	−5.05825	+	6.96208i	−0.432155	+	0.594811i	0.536291	+	0.844033i	$0.319825\pi$
$138$	12.3001	−	16.9296i	1.04705	−	1.44114i
$139$	−13.4767	+	9.79137i	−1.14308	+	0.830494i	−0.987545	−	0.157337i	$-0.949709\pi$
$139$	−13.4767	+	9.79137i	−1.14308	+	0.830494i	−0.155531	+	0.987831i	$0.549709\pi$
$140$	−7.88583	+	6.33073i	−0.666474	+	0.535045i
$141$	8.72447	+	6.33870i	0.734733	+	0.533814i
$142$	−10.0489	+	3.26509i	−0.843285	+	0.274000i
$143$			7.71709i			0.645336i
$144$	−2.49260	−	7.67144i	−0.207717	−	0.639287i
$145$	−7.52779	−	9.37693i	−0.625149	−	0.778711i
$146$	1.22838	−	3.78056i	0.101661	−	0.312882i
$147$	42.5620	+	13.8292i	3.51045	+	1.14062i
$148$	−2.49397	−	3.43266i	−0.205003	−	0.282163i
$149$	10.9524			0.897255			0.448627	−	0.893719i	$-0.351913\pi$
$149$	10.9524			0.897255			0.448627	+	0.893719i	$0.351913\pi$
$150$	12.4545	−	11.0246i	1.01690	−	0.900154i
$151$	−9.91741			−0.807067			−0.403534	−	0.914965i	$-0.632218\pi$
$151$	−9.91741			−0.807067			−0.403534	+	0.914965i	$0.632218\pi$
$152$	−0.587785	−	0.809017i	−0.0476757	−	0.0656199i
$153$	−39.7563	−	12.9176i	−3.21411	−	1.04433i
$154$	−2.27361	+	6.99746i	−0.183213	+	0.563872i
$155$	21.4459	+	5.84381i	1.72257	+	0.469386i
$156$	−4.87617	−	15.0073i	−0.390406	−	1.20155i
$157$			12.5654i			1.00283i	0.865207	+	0.501415i	$0.167187\pi$
$157$			12.5654i			1.00283i	−0.865207	+	0.501415i	$0.832813\pi$
$158$	−4.31708	+	1.40270i	−0.343448	+	0.111593i
$159$	15.5406	+	11.2909i	1.23245	+	0.895429i
$160$	1.87015	+	1.22578i	0.147849	+	0.0969062i
$161$	23.0157	−	16.7219i	1.81389	−	1.31787i
$162$	18.7300	−	25.7797i	1.47157	−	2.02544i
$163$	1.12475	−	1.54808i	0.0880971	−	0.121255i	−0.762694	−	0.646760i	$-0.776124\pi$
$163$	1.12475	−	1.54808i	0.0880971	−	0.121255i	0.850791	+	0.525505i	$0.176124\pi$
$164$	−0.0389637	+	0.0283088i	−0.00304255	+	0.00221054i
$165$	3.18157	−	11.6759i	0.247685	−	0.908965i
$166$	10.0838	+	7.32634i	0.782658	+	0.568634i
$167$	−2.27417	+	0.738923i	−0.175981	+	0.0571796i	−0.395682	−	0.918388i	$-0.629492\pi$
$167$	−2.27417	+	0.738923i	−0.175981	+	0.0571796i	0.219701	+	0.975567i	$0.429492\pi$
$168$		−	15.0445i		−	1.16071i
$169$	−2.93584	−	9.03558i	−0.225834	−	0.695044i
$170$	10.8359	−	4.10699i	0.831079	−	0.314992i
$171$	2.49260	−	7.67144i	0.190614	−	0.586650i
$172$	1.35580	+	0.440527i	0.103379	+	0.0335899i
$173$	0.832791	+	1.14624i	0.0633159	+	0.0871469i	0.839501	−	0.543359i	$-0.182848\pi$
$173$	0.832791	+	1.14624i	0.0633159	+	0.0871469i	−0.776185	+	0.630506i	$0.782848\pi$
$174$	17.8892			1.35618
$175$	20.7346	−	9.02209i	1.56739	−	0.682006i
$176$	1.62689			0.122631
$177$	5.78879	+	7.96758i	0.435112	+	0.598880i
$178$	15.4032	+	5.00479i	1.15452	+	0.375125i
$179$	−1.44942	+	4.46085i	−0.108335	+	0.333420i	−0.990499	−	0.137523i	$-0.956086\pi$
$179$	−1.44942	+	4.46085i	−0.108335	+	0.333420i	0.882164	+	0.470942i	$0.156086\pi$
$180$	0.867712	+	18.0158i	0.0646754	+	1.34282i
$181$	−2.34993	−	7.23235i	−0.174669	−	0.537577i	0.824949	−	0.565207i	$-0.191204\pi$
$181$	−2.34993	−	7.23235i	−0.174669	−	0.537577i	−0.999618	+	0.0276306i	$0.991204\pi$
$182$		−	21.4523i		−	1.59015i
$183$	−1.93695	+	0.629353i	−0.143184	+	0.0465231i
$184$	−5.08916	−	3.69749i	−0.375178	−	0.272583i
$185$	3.36254	+	8.87179i	0.247219	+	0.652267i
$186$	−26.7528	+	19.4370i	−1.96161	+	1.42519i
$187$	4.95570	−	6.82093i	0.362396	−	0.498796i
$188$	1.90546	−	2.62264i	0.138970	−	0.191276i
$189$	61.6624	−	44.8003i	4.48528	−	3.25874i
$190$	0.792491	+	2.09092i	0.0574934	+	0.151691i
$191$	−18.7145	−	13.5969i	−1.35414	−	0.983837i	−0.998794	−	0.0491011i	$-0.984364\pi$
$191$	−18.7145	−	13.5969i	−1.35414	−	0.983837i	−0.355342	−	0.934736i	$-0.615636\pi$
$192$	−3.16378	+	1.02797i	−0.228326	+	0.0741877i
$193$		−	9.10718i		−	0.655549i	−0.944756	−	0.327775i	$-0.893701\pi$
$193$		−	9.10718i		−	0.655549i	0.944756	−	0.327775i	$-0.106299\pi$
$194$	−0.0647267	−	0.199208i	−0.00464711	−	0.0143023i
$195$	1.69747	+	35.2435i	0.121558	+	2.52384i
$196$	4.15717	−	12.7945i	0.296941	−	0.913890i
$197$	5.60383	+	1.82079i	0.399256	+	0.129726i	0.501761	−	0.865006i	$-0.332686\pi$
$197$	5.60383	+	1.82079i	0.399256	+	0.129726i	−0.102505	+	0.994733i	$0.532686\pi$
$198$	7.71341	+	10.6166i	0.548168	+	0.754489i
$199$	5.07644			0.359859			0.179930	−	0.983680i	$-0.442413\pi$
$199$	5.07644			0.359859			0.179930	+	0.983680i	$0.442413\pi$
$200$	−3.31408	−	3.74392i	−0.234341	−	0.264735i
$201$	14.5169			1.02394
$202$	3.61455	+	4.97500i	0.254319	+	0.350040i
$203$	23.1299	+	7.51537i	1.62340	+	0.527476i
$204$	−5.32735	+	16.3959i	−0.372989	+	1.14794i
$205$	0.100703	−	0.0381678i	0.00703337	−	0.00266575i
$206$	−2.05702	−	6.33085i	−0.143319	−	0.441091i
$207$		−	50.7410i		−	3.52674i
$208$	−4.51131	+	1.46581i	−0.312803	+	0.101636i
$209$	1.31618	+	0.956259i	0.0910419	+	0.0661458i
$210$	−8.84427	+	32.4571i	−0.610313	+	2.23975i
$211$	−7.99832	+	5.81112i	−0.550627	+	0.400054i	−0.828017	−	0.560704i	$-0.810531\pi$
$211$	−7.99832	+	5.81112i	−0.550627	+	0.400054i	0.277390	+	0.960758i	$0.410531\pi$
$212$	3.39414	−	4.67163i	0.233111	−	0.320849i
$213$	−20.6600	+	28.4361i	−1.41560	+	1.94841i
$214$	−11.3802	+	8.26820i	−0.777935	+	0.565203i
$215$	−2.66605	−	1.74744i	−0.181823	−	0.119174i
$216$	−13.6346	−	9.90613i	−0.927718	−	0.674026i
$217$	−42.7558	+	13.8922i	−2.90245	+	0.943064i
$218$			13.7244i			0.929532i
$219$	−4.08632	−	12.5764i	−0.276128	−	0.849834i
$220$	−3.50985	−	0.956405i	−0.236634	−	0.0644808i
$221$	−7.59640	+	23.3793i	−0.510989	+	1.57266i
$222$	−13.4239	−	4.36170i	−0.900955	−	0.292738i
$223$	−1.90018	−	2.61538i	−0.127246	−	0.175139i	0.740641	−	0.671901i	$-0.234522\pi$
$223$	−1.90018	−	2.61538i	−0.127246	−	0.175139i	−0.867887	+	0.496763i	$0.834522\pi$
$224$	−4.52249			−0.302171
$225$	8.71900	−	39.3774i	0.581267	−	2.62516i
$226$	−0.896109			−0.0596083
$227$	−5.22736	−	7.19484i	−0.346952	−	0.477539i	0.599504	−	0.800372i	$-0.295365\pi$
$227$	−5.22736	−	7.19484i	−0.346952	−	0.477539i	−0.946456	+	0.322833i	$0.895365\pi$
$228$	−3.16378	−	1.02797i	−0.209526	−	0.0680793i
$229$	4.01852	−	12.3677i	0.265551	−	0.817282i	−0.726015	−	0.687679i	$-0.758630\pi$
$229$	4.01852	−	12.3677i	0.265551	−	0.817282i	0.991566	−	0.129603i	$-0.0413703\pi$
$230$	8.80573	+	10.9688i	0.580632	+	0.723260i
$231$	7.56339	+	23.2777i	0.497635	+	1.53156i
$232$		−	5.37763i		−	0.353059i
$233$	13.3868	−	4.34965i	0.877001	−	0.284955i	0.164289	−	0.986412i	$-0.447467\pi$
$233$	13.3868	−	4.34965i	0.877001	−	0.284955i	0.712711	+	0.701457i	$0.247467\pi$
$234$	−30.9546	−	22.4898i	−2.02357	−	1.47021i
$235$	−5.65264	+	4.53793i	−0.368737	+	0.296022i
$236$	2.39512	−	1.74015i	0.155909	−	0.113274i
$237$	−8.87569	+	12.2163i	−0.576538	+	0.793537i
$238$	−13.7761	+	18.9611i	−0.892969	+	1.22907i
$239$	13.9662	−	10.1471i	0.903401	−	0.656359i	−0.0359363	−	0.999354i	$-0.511441\pi$
$239$	13.9662	−	10.1471i	0.903401	−	0.656359i	0.939337	+	0.342995i	$0.111441\pi$
$240$	7.42988	−	0.357853i	0.479597	−	0.0230993i
$241$	−12.2336	−	8.88820i	−0.788032	−	0.572539i	0.119346	−	0.992853i	$-0.461920\pi$
$241$	−12.2336	−	8.88820i	−0.788032	−	0.572539i	−0.907379	+	0.420314i	$0.861920\pi$
$242$	7.94441	−	2.58129i	0.510686	−	0.165932i
$243$		−	55.4434i		−	3.55670i
$244$	0.189188	+	0.582262i	0.0121116	+	0.0372755i
$245$	−16.4902	+	25.1590i	−1.05352	+	1.60735i
$246$	−0.0495091	+	0.152373i	−0.00315658	+	0.00971496i
$247$	−4.51131	−	1.46581i	−0.287048	−	0.0932676i
$248$	5.84292	+	8.04209i	0.371026	+	0.510673i
$249$	41.4637			2.62766
$250$	4.94886	+	10.0254i	0.312993	+	0.634063i
$251$	−0.218574			−0.0137963			−0.00689815	−	0.999976i	$-0.502196\pi$
$251$	−0.218574			−0.0137963			−0.00689815	+	0.999976i	$0.502196\pi$
$252$	−21.4421	−	29.5125i	−1.35072	−	1.85911i
$253$	9.73311	+	3.16248i	0.611916	+	0.198823i
$254$	−2.46080	+	7.57357i	−0.154404	+	0.475208i
$255$	21.1320	−	32.2408i	1.32334	−	2.01900i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$			12.2724i			0.765534i	0.923845	+	0.382767i	$0.125029\pi$
$257$			12.2724i			0.765534i	−0.923845	+	0.382767i	$0.874971\pi$
$258$	4.51021	−	1.46546i	0.280793	−	0.0912353i
$259$	−15.5242	−	11.2790i	−0.964625	−	0.700841i
$260$	10.5945	−	0.510272i	0.657040	−	0.0316457i
$261$	35.0929	−	25.4965i	2.17220	−	1.57819i
$262$	0.338985	−	0.466573i	0.0209426	−	0.0288250i
$263$	−16.1743	+	22.2621i	−0.997353	+	1.37274i	−0.0704175	+	0.997518i	$0.522433\pi$
$263$	−16.1743	+	22.2621i	−0.997353	+	1.37274i	−0.926935	+	0.375221i	$0.877567\pi$
$264$	4.37839	−	3.18109i	0.269471	−	0.195782i
$265$	−10.0689	+	8.08328i	−0.618526	+	0.496552i
$266$	−3.65877	−	2.65825i	−0.224334	−	0.162988i
$267$	51.2401	−	16.6489i	3.13584	−	1.01890i
$268$		−	4.36389i		−	0.266567i
$269$	−1.43812	−	4.42608i	−0.0876838	−	0.269863i	0.897594	−	0.440823i	$-0.145313\pi$
$269$	−1.43812	−	4.42608i	−0.0876838	−	0.269863i	−0.985278	+	0.170960i	$0.945313\pi$
$270$	23.5918	+	29.3870i	1.43575	+	1.78843i
$271$	4.90393	−	15.0928i	0.297893	−	0.916820i	−0.684342	−	0.729162i	$-0.739910\pi$
$271$	4.90393	−	15.0928i	0.297893	−	0.916820i	0.982234	−	0.187658i	$-0.0600897\pi$
$272$	4.92873	+	1.60144i	0.298848	+	0.0971017i
$273$	−41.9462	−	57.7340i	−2.53870	−	3.49422i
$274$	8.60561			0.519884
$275$	7.00994	+	4.12671i	0.422715	+	0.248850i
$276$	−20.9261			−1.25960
$277$	−16.2107	−	22.3121i	−0.974005	−	1.34060i	−0.939998	−	0.341181i	$-0.889173\pi$
$277$	−16.2107	−	22.3121i	−0.974005	−	1.34060i	−0.0340069	−	0.999422i	$-0.510827\pi$
$278$	15.8428	+	5.14763i	0.950187	+	0.308734i
$279$	−24.7779	+	76.2585i	−1.48341	+	4.56548i
$280$	9.75684	+	2.65866i	0.583083	+	0.158885i
$281$	−2.28144	−	7.02155i	−0.136099	−	0.418871i	0.859660	−	0.510867i	$-0.170675\pi$
$281$	−2.28144	−	7.02155i	−0.136099	−	0.418871i	−0.995759	+	0.0919958i	$0.970675\pi$
$282$		−	10.7840i		−	0.642180i
$283$	−26.9992	+	8.77256i	−1.60493	+	0.521474i	−0.968321	−	0.249709i	$-0.919665\pi$
$283$	−26.9992	+	8.77256i	−1.60493	+	0.521474i	−0.636613	+	0.771184i	$0.719665\pi$
$284$	8.54810	+	6.21056i	0.507237	+	0.368529i
$285$	6.22124	+	4.07766i	0.368514	+	0.241540i
$286$	6.24326	−	4.53599i	0.369172	−	0.268219i
$287$	−0.128026	+	0.176213i	−0.00755714	+	0.0104015i
$288$	−4.74121	+	6.52572i	−0.279379	+	0.384532i
$289$	7.97450	−	5.79381i	0.469088	−	0.340813i
$290$	−3.16137	+	11.6017i	−0.185642	+	0.681277i
$291$	−0.563714	−	0.409562i	−0.0330455	−	0.0240090i
$292$	−3.78056	+	1.22838i	−0.221241	+	0.0718854i
$293$			21.5698i			1.26012i	0.776547	+	0.630060i	$0.216970\pi$
$293$			21.5698i			1.26012i	−0.776547	+	0.630060i	$0.783030\pi$
$294$	−13.8292	−	42.5620i	−0.806537	−	2.48227i
$295$	−6.19023	+	2.34619i	−0.360409	+	0.136601i
$296$	−1.31116	+	4.03534i	−0.0762096	+	0.234549i
$297$	26.0764	+	8.47275i	1.51311	+	0.491639i
$298$	−6.43765	−	8.86067i	−0.372923	−	0.513285i
$299$	−29.8391			−1.72564
$300$	−16.2396	−	3.59580i	−0.937596	−	0.207604i
$301$	6.44715			0.371608
$302$	5.82931	+	8.02335i	0.335439	+	0.461692i
$303$	19.4555	+	6.32146i	1.11769	+	0.363159i
$304$	−0.309017	+	0.951057i	−0.0177233	+	0.0545468i
$305$	−0.0658593	−	1.36740i	−0.00377109	−	0.0782968i
$306$	12.9176	+	39.7563i	0.738451	+	2.27272i
$307$			32.3467i			1.84612i	0.384651	+	0.923062i	$0.374322\pi$
$307$			32.3467i			1.84612i	−0.384651	+	0.923062i	$0.625678\pi$
$308$	6.99746	−	2.27361i	0.398718	−	0.129551i
$309$	−17.9148	−	13.0159i	−1.01914	−	0.740449i
$310$	−7.87782	−	20.7850i	−0.447430	−	1.18051i
$311$	−12.6386	+	9.18249i	−0.716670	+	0.520691i	−0.885319	−	0.464985i	$-0.846060\pi$
$311$	−12.6386	+	9.18249i	−0.716670	+	0.520691i	0.168649	+	0.985676i	$0.446060\pi$
$312$	−9.27503	+	12.7660i	−0.525095	+	0.722732i
$313$	0.919712	−	1.26588i	0.0519852	−	0.0715515i	−0.782233	−	0.622986i	$-0.785919\pi$
$313$	0.919712	−	1.26588i	0.0519852	−	0.0715515i	0.834218	+	0.551435i	$0.185919\pi$
$314$	10.1656	−	7.38577i	0.573680	−	0.416803i
$315$	28.9096	+	76.2757i	1.62887	+	4.29765i
$316$	3.67233	+	2.66810i	0.206585	+	0.150092i
$317$	24.5531	−	7.97779i	1.37904	−	0.448077i	0.476686	−	0.879074i	$-0.341838\pi$
$317$	24.5531	−	7.97779i	1.37904	−	0.448077i	0.902354	+	0.430996i	$0.141838\pi$
$318$		−	19.2093i		−	1.07720i
$319$	2.70352	+	8.32059i	0.151368	+	0.465863i
$320$	−0.107573	−	2.23348i	−0.00601353	−	0.124855i
$321$	−14.4602	+	44.5040i	−0.807090	+	2.48397i
$322$	−27.0565	−	8.79120i	−1.50780	−	0.489914i
$323$	3.04612	+	4.19263i	0.169491	+	0.233284i
$324$	−31.8654			−1.77030
$325$	−23.1565	−	5.12735i	−1.28449	−	0.284414i
$326$	−1.91354			−0.105981
$327$	26.8356	+	36.9360i	1.48401	+	2.04257i
$328$	0.0458046	+	0.0148828i	0.00252913	+	0.000821766i
$329$	4.53045	−	13.9433i	0.249772	−	0.768718i
$330$	−11.3161	+	4.28895i	−0.622928	+	0.236099i
$331$	−10.1155	−	31.1323i	−0.555998	−	1.71119i	−0.693293	−	0.720656i	$-0.743841\pi$
$331$	−10.1155	−	31.1323i	−0.555998	−	1.71119i	0.137295	−	0.990530i	$-0.456159\pi$
$332$		−	12.4643i		−	0.684068i
$333$	−32.5500	+	10.5761i	−1.78373	+	0.579568i
$334$	1.93453	+	1.40552i	0.105853	+	0.0769064i
$335$	−2.56542	+	9.41468i	−0.140164	+	0.514379i
$336$	−12.1712	+	8.84293i	−0.663996	+	0.482421i
$337$	10.3178	−	14.2012i	0.562045	−	0.773589i	−0.429539	−	0.903048i	$-0.641324\pi$
$337$	10.3178	−	14.2012i	0.562045	−	0.773589i	0.991585	+	0.129459i	$0.0413241\pi$
$338$	−5.58429	+	7.68612i	−0.303745	+	0.418070i
$339$	−2.41167	+	1.75218i	−0.130984	+	0.0951656i
$340$	−9.69183	−	6.35244i	−0.525613	−	0.344509i
$341$	−13.0836	−	9.50576i	−0.708515	−	0.514766i
$342$	−7.67144	+	2.49260i	−0.414824	+	0.134785i
$343$		−	29.1831i		−	1.57574i
$344$	−0.440527	−	1.35580i	−0.0237516	−	0.0731000i
$345$	45.1461	+	12.3019i	2.43058	+	0.662313i
$346$	0.437824	−	1.34748i	0.0235376	−	0.0724412i
$347$	19.4148	+	6.30825i	1.04224	+	0.338645i	0.779619	−	0.626254i	$-0.215413\pi$
$347$	19.4148	+	6.30825i	1.04224	+	0.338645i	0.262622	+	0.964899i	$0.415413\pi$
$348$	−10.5150	−	14.4727i	−0.563663	−	0.775816i
$349$	−6.45926			−0.345756			−0.172878	−	0.984943i	$-0.555307\pi$
$349$	−6.45926			−0.345756			−0.172878	+	0.984943i	$0.555307\pi$
$350$	−19.4865	−	11.4716i	−1.04160	−	0.613183i
$351$	−79.9433			−4.26706
$352$	−0.956259	−	1.31618i	−0.0509688	−	0.0701525i
$353$	22.7247	+	7.38370i	1.20951	+	0.392995i	0.843252	−	0.537518i	$-0.180638\pi$
$353$	22.7247	+	7.38370i	1.20951	+	0.392995i	0.366261	+	0.930512i	$0.380638\pi$
$354$	3.04334	−	9.36645i	0.161752	−	0.497821i
$355$	−14.7907	−	18.4239i	−0.785009	−	0.977840i
$356$	−5.00479	−	15.4032i	−0.265253	−	0.816366i
$357$			77.9662i			4.12641i
$358$	4.46085	−	1.44942i	0.235763	−	0.0766042i
$359$	−11.4170	−	8.29492i	−0.602565	−	0.437789i	0.244223	−	0.969719i	$-0.421467\pi$
$359$	−11.4170	−	8.29492i	−0.602565	−	0.437789i	−0.846789	+	0.531930i	$0.821467\pi$
$360$	14.0650	−	11.2914i	0.741292	−	0.595109i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	−4.46984	+	6.15221i	−0.234930	+	0.323353i
$363$	16.3333	−	22.4808i	0.857276	−	1.17994i
$364$	−17.3553	+	12.6094i	−0.909664	+	0.660910i
$365$	8.87834	−	0.427617i	0.464714	−	0.0223825i
$366$	1.64767	+	1.19710i	0.0861250	+	0.0625735i
$367$	25.3116	−	8.22424i	1.32126	−	0.429302i	0.438330	−	0.898814i	$-0.355570\pi$
$367$	25.3116	−	8.22424i	1.32126	−	0.429302i	0.882926	+	0.469512i	$0.155570\pi$
$368$			6.29055i			0.327917i
$369$	0.120048	+	0.369470i	0.00624946	+	0.0192339i
$370$	5.20098	−	7.93506i	0.270386	−	0.412524i
$371$	8.06995	−	24.8367i	0.418971	−	1.28946i
$372$	31.4498	+	10.2187i	1.63060	+	0.529812i
$373$	−1.32729	−	1.82685i	−0.0687243	−	0.0945908i	0.773271	−	0.634075i	$-0.218619\pi$
$373$	−1.32729	−	1.82685i	−0.0687243	−	0.0945908i	−0.841995	+	0.539485i	$0.818619\pi$
$374$	−8.43113			−0.435964
$375$	32.9216	+	17.3045i	1.70007	+	0.893600i
$376$	−3.24176			−0.167181
$377$	−14.9936	−	20.6369i	−0.772210	−	1.06286i
$378$	−72.4884	−	23.5529i	−3.72840	−	1.21143i
$379$	−7.77317	+	23.9234i	−0.399281	+	1.22886i	0.526296	+	0.850301i	$0.323580\pi$
$379$	−7.77317	+	23.9234i	−0.399281	+	1.22886i	−0.925577	+	0.378559i	$0.876420\pi$
$380$	1.22578	−	1.87015i	0.0628810	−	0.0959368i
$381$	8.18609	+	25.1942i	0.419386	+	1.29074i
$382$			23.1324i			1.18356i
$383$	−22.9187	+	7.44673i	−1.17109	+	0.380510i	−0.829049	−	0.559176i	$-0.811118\pi$
$383$	−22.9187	+	7.44673i	−1.17109	+	0.380510i	−0.342040	+	0.939685i	$0.611118\pi$
$384$	2.69127	+	1.95532i	0.137338	+	0.0997822i
$385$	−16.4330	+	0.791478i	−0.837502	+	0.0403375i
$386$	−7.36787	+	5.35307i	−0.375015	+	0.272464i
$387$	6.75896	−	9.30291i	0.343577	−	0.472894i
$388$	−0.123118	+	0.169457i	−0.00625035	+	0.00860287i
$389$	−13.3779	+	9.71960i	−0.678286	+	0.492803i	−0.872789	−	0.488099i	$-0.837691\pi$
$389$	−13.3779	+	9.71960i	−0.678286	+	0.492803i	0.194503	+	0.980902i	$0.437691\pi$
$390$	27.5148	−	22.0889i	1.39327	−	1.11851i
$391$	26.3739	+	19.1618i	1.33379	+	0.969053i
$392$	−12.7945	+	4.15717i	−0.646218	+	0.209969i
$393$		−	1.91850i		−	0.0967756i
$394$	−1.82079	−	5.60383i	−0.0917303	−	0.282317i
$395$	−6.35419	−	7.91505i	−0.319714	−	0.398249i
$396$	4.05518	−	12.4806i	0.203780	−	0.627172i
$397$	−27.4920	−	8.93271i	−1.37979	−	0.448320i	−0.477187	−	0.878802i	$-0.658344\pi$
$397$	−27.4920	−	8.93271i	−1.37979	−	0.448320i	−0.902599	+	0.430482i	$0.858344\pi$
$398$	−2.98385	−	4.10692i	−0.149567	−	0.205861i
$399$	−15.0445			−0.753166
$400$	−1.08093	+	4.88176i	−0.0540463	+	0.244088i
$401$	13.6769			0.682992			0.341496	−	0.939883i	$-0.389066\pi$
$401$	13.6769			0.682992			0.341496	+	0.939883i	$0.389066\pi$
$402$	−8.53281	−	11.7444i	−0.425578	−	0.585758i
$403$	44.8450	+	14.5710i	2.23389	+	0.725835i
$404$	1.90028	−	5.84846i	0.0945425	−	0.290972i
$405$	68.7467	+	18.7329i	3.41605	+	0.930844i
$406$	−7.51537	−	23.1299i	−0.372982	−	1.14792i
$407$		−	6.90288i		−	0.342163i
$408$	16.3959	−	5.32735i	0.811718	−	0.263743i
$409$	13.5441	+	9.84034i	0.669711	+	0.486574i	0.869928	−	0.493178i	$-0.164165\pi$
$409$	13.5441	+	9.84034i	0.669711	+	0.486574i	−0.200217	+	0.979751i	$0.564165\pi$
$410$	−0.0900699	−	0.0590356i	−0.00444823	−	0.00291556i
$411$	23.1600	−	16.8267i	1.14240	−	0.830002i
$412$	−3.91268	+	5.38534i	−0.192764	+	0.265317i
$413$	7.86982	−	10.8319i	0.387249	−	0.533002i
$414$	−41.0503	+	29.8248i	−2.01751	+	1.46581i
$415$	−7.32745	+	26.8906i	−0.359691	+	1.32001i
$416$	3.83755	+	2.78815i	0.188152	+	0.136700i
$417$	52.7025	−	17.1241i	2.58085	−	0.838570i
$418$		−	1.62689i		−	0.0795736i
$419$	6.69655	+	20.6098i	0.327148	+	1.00686i	0.970462	+	0.241255i	$0.0775589\pi$
$419$	6.69655	+	20.6098i	0.327148	+	1.00686i	−0.643314	+	0.765602i	$0.722441\pi$
$420$	31.4568	−	11.9226i	1.53494	−	0.581764i
$421$	8.75694	−	26.9511i	0.426787	−	1.31352i	−0.474485	−	0.880263i	$-0.657366\pi$
$421$	8.75694	−	26.9511i	0.426787	−	1.31352i	0.901273	−	0.433253i	$-0.142634\pi$
$422$	9.40259	+	3.05509i	0.457711	+	0.148719i
$423$	−15.3699	−	21.1548i	−0.747310	−	1.02858i
$424$	−5.77446			−0.280432
$425$	17.1748	+	19.4024i	0.833100	+	0.941154i
$426$	35.1489			1.70297
$427$	1.62745	+	2.24000i	0.0787580	+	0.108401i
$428$	13.3782	+	4.34685i	0.646661	+	0.210113i
$429$	7.93297	−	24.4152i	0.383008	−	1.17878i
$430$	0.153354	+	3.18399i	0.00739539	+	0.153546i
$431$	−6.02696	−	18.5491i	−0.290308	−	0.893477i	−0.984757	−	0.173935i	$-0.944352\pi$
$431$	−6.02696	−	18.5491i	−0.290308	−	0.893477i	0.694449	−	0.719542i	$-0.255648\pi$
$432$			16.8533i			0.810855i
$433$	4.38975	−	1.42632i	0.210958	−	0.0685444i	−0.201632	−	0.979461i	$-0.564624\pi$
$433$	4.38975	−	1.42632i	0.210958	−	0.0685444i	0.412590	+	0.910917i	$0.364624\pi$
$434$	36.3703	+	26.4245i	1.74583	+	1.26842i
$435$	14.1770	+	37.4049i	0.679736	+	1.79343i
$436$	11.1033	−	8.06699i	0.531749	−	0.386339i
$437$	−3.69749	+	5.08916i	−0.176875	+	0.243448i
$438$	−7.77264	+	10.6981i	−0.371391	+	0.511176i
$439$	16.7426	−	12.1642i	0.799081	−	0.580566i	−0.111564	−	0.993757i	$-0.535586\pi$
$439$	16.7426	−	12.1642i	0.799081	−	0.580566i	0.910644	+	0.413191i	$0.135586\pi$
$440$	1.28929	+	3.40169i	0.0614646	+	0.162169i
$441$	−87.7898	−	63.7830i	−4.18047	−	3.03729i
$442$	23.3793	−	7.59640i	1.11204	−	0.361324i
$443$			33.3327i			1.58369i	0.610724	+	0.791843i	$0.290878\pi$
$443$			33.3327i			1.58369i	−0.610724	+	0.791843i	$0.709122\pi$
$444$	4.36170	+	13.4239i	0.206997	+	0.637071i
$445$	1.74224	+	36.1731i	0.0825902	+	1.71477i
$446$	−0.998985	+	3.07456i	−0.0473033	+	0.145585i
$447$	−34.6510	−	11.2588i	−1.63893	−	0.532522i
$448$	2.65825	+	3.65877i	0.125591	+	0.172861i
$449$	−33.8812			−1.59895			−0.799476	−	0.600698i	$-0.794889\pi$
$449$	−33.8812			−1.59895			−0.799476	+	0.600698i	$0.794889\pi$
$450$	−36.9819	+	16.0917i	−1.74334	+	0.758568i
$451$	−0.0783537			−0.00368953
$452$	0.526720	+	0.724968i	0.0247748	+	0.0340996i
$453$	31.3765	+	10.1948i	1.47420	+	0.478995i
$454$	−2.74819	+	8.45805i	−0.128979	+	0.396956i
$455$	44.8551	−	17.0008i	2.10284	−	0.797008i
$456$	1.02797	+	3.16378i	0.0481393	+	0.148158i
$457$			14.1839i			0.663495i	0.943368	+	0.331748i	$0.107638\pi$
$457$			14.1839i			0.663495i	−0.943368	+	0.331748i	$0.892362\pi$
$458$	−12.3677	+	4.01852i	−0.577906	+	0.187773i
$459$	70.6597	+	51.3373i	3.29811	+	2.39622i
$460$	3.69805	−	13.5713i	0.172423	−	0.632764i
$461$	17.6265	−	12.8064i	0.820948	−	0.596454i	−0.0960359	−	0.995378i	$-0.530616\pi$
$461$	17.6265	−	12.8064i	0.820948	−	0.596454i	0.916984	+	0.398924i	$0.130616\pi$
$462$	14.3864	−	19.8012i	0.669317	−	0.921236i
$463$	−3.89003	+	5.35417i	−0.180785	+	0.248829i	−0.889786	−	0.456378i	$-0.849146\pi$
$463$	−3.89003	+	5.35417i	−0.180785	+	0.248829i	0.709001	+	0.705208i	$0.249146\pi$
$464$	−4.35059	+	3.16089i	−0.201971	+	0.146741i
$465$	−61.8427	−	40.5343i	−2.86789	−	1.87973i
$466$	−11.3875	−	8.27352i	−0.527517	−	0.383263i
$467$	30.1649	−	9.80118i	1.39587	−	0.453545i	0.488015	−	0.872835i	$-0.337721\pi$
$467$	30.1649	−	9.80118i	1.39587	−	0.453545i	0.907852	+	0.419290i	$0.137721\pi$
$468$			38.2620i			1.76866i
$469$	−6.09864	−	18.7697i	−0.281609	−	0.866704i
$470$	6.99380	+	1.90575i	0.322600	+	0.0879057i
$471$	12.9169	−	39.7542i	0.595181	−	1.83178i
$472$	−2.81563	−	0.914853i	−0.129600	−	0.0421095i
$473$	1.36322	+	1.87631i	0.0626810	+	0.0862729i
$474$	15.1002			0.693577
$475$	−3.74392	+	3.31408i	−0.171783	+	0.152060i
$476$	23.4372			1.07424
$477$	−27.3779	−	37.6825i	−1.25355	−	1.72536i
$478$	−16.4183	−	5.33463i	−0.750956	−	0.244000i
$479$	11.8569	−	36.4919i	0.541758	−	1.66736i	−0.186819	−	0.982394i	$-0.559818\pi$
$479$	11.8569	−	36.4919i	0.541758	−	1.66736i	0.728577	−	0.684964i	$-0.240182\pi$
$480$	−4.65668	−	5.80056i	−0.212548	−	0.264758i
$481$	6.21946	+	19.1415i	0.283583	+	0.872778i
$482$			15.1215i			0.688766i
$483$	−90.0061	+	29.2448i	−4.09542	+	1.33068i
$484$	−6.75792	−	4.90991i	−0.307178	−	0.223178i
$485$	0.365234	−	0.293210i	0.0165844	−	0.0133140i
$486$	−44.8547	+	32.5888i	−2.03465	+	1.47826i
$487$	8.61800	−	11.8617i	0.390519	−	0.537503i	−0.567814	−	0.823157i	$-0.692211\pi$
$487$	8.61800	−	11.8617i	0.390519	−	0.537503i	0.958333	+	0.285654i	$0.0922107\pi$
$488$	0.359858	−	0.495302i	0.0162900	−	0.0224213i
$489$	−5.14984	+	3.74158i	−0.232884	+	0.169200i
$490$	30.0467	−	1.44717i	1.35737	−	0.0653766i
$491$	5.60575	+	4.07281i	0.252984	+	0.183803i	0.707048	−	0.707165i	$-0.250026\pi$
$491$	5.60575	+	4.07281i	0.252984	+	0.183803i	−0.454064	+	0.890969i	$0.650026\pi$
$492$	0.152373	−	0.0495091i	0.00686952	−	0.00223204i
$493$			27.8689i			1.25515i
$494$	1.46581	+	4.51131i	0.0659501	+	0.202974i
$495$	−16.0857	+	24.5417i	−0.722997	+	1.10307i
$496$	3.07181	−	9.45405i	0.137928	−	0.424499i
$497$	45.4460	+	14.7663i	2.03853	+	0.662359i
$498$	−24.3718	−	33.5449i	−1.09212	−	1.50318i
$499$	−9.48945			−0.424806			−0.212403	−	0.977182i	$-0.568129\pi$
$499$	−9.48945			−0.424806			−0.212403	+	0.977182i	$0.568129\pi$
$500$	5.20186	−	9.89650i	0.232634	−	0.442585i
$501$	7.95457			0.355384
$502$	0.128475	+	0.176830i	0.00573411	+	0.00789233i
$503$	31.0950	+	10.1034i	1.38646	+	0.450488i	0.904787	−	0.425864i	$-0.140030\pi$
$503$	31.0950	+	10.1034i	1.38646	+	0.450488i	0.481672	+	0.876352i	$0.340030\pi$
$504$	−11.2728	+	34.6940i	−0.502129	+	1.54539i
$505$	−7.53784	+	11.5004i	−0.335429	+	0.511760i
$506$	−3.16248	−	9.73311i	−0.140589	−	0.432690i
$507$			31.6045i			1.40361i
$508$	7.57357	−	2.46080i	0.336023	−	0.109180i
$509$	−5.69386	−	4.13683i	−0.252376	−	0.183362i	0.454403	−	0.890796i	$-0.349853\pi$
$509$	−5.69386	−	4.13683i	−0.252376	−	0.183362i	−0.706779	+	0.707434i	$0.749853\pi$
$510$	−38.5044	+	1.85453i	−1.70500	+	0.0821199i
$511$	−14.5440	+	10.5669i	−0.643390	+	0.467450i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$	−9.90613	+	13.6346i	−0.437366	+	0.601983i
$514$	9.92861	−	7.21356i	0.437932	−	0.318176i
$515$	11.6071	−	9.31821i	0.511472	−	0.410609i
$516$	−3.83661	−	2.78746i	−0.168898	−	0.122711i
$517$	5.01585	−	1.62975i	0.220597	−	0.0716763i
$518$			19.1889i			0.843113i
$519$	−1.45646	−	4.48253i	−0.0639316	−	0.196761i
$520$	−6.64008	−	8.27116i	−0.291187	−	0.362714i
$521$	2.81977	−	8.67836i	0.123536	−	0.380206i	−0.870095	−	0.492884i	$-0.835943\pi$
$521$	2.81977	−	8.67836i	0.123536	−	0.380206i	0.993632	+	0.112678i	$0.0359428\pi$
$522$	−41.2542	−	13.4043i	−1.80565	−	0.586690i
$523$	−0.214089	−	0.294668i	−0.00936146	−	0.0128849i	0.804311	−	0.594209i	$-0.202535\pi$
$523$	−0.214089	−	0.294668i	−0.00936146	−	0.0128849i	−0.813672	+	0.581324i	$0.802535\pi$
$524$	−0.576716			−0.0251940
$525$	−74.8742	+	7.22926i	−3.26778	+	0.315511i
$526$	27.5174			1.19982
$527$	−30.2802	−	41.6771i	−1.31903	−	1.81548i
$528$	−5.14711	−	1.67240i	−0.223999	−	0.0727817i
$529$	−5.12072	+	15.7599i	−0.222640	+	0.685215i
$530$	12.4578	+	3.39466i	0.541134	+	0.147454i
$531$	−7.37942	−	22.7115i	−0.320239	−	0.985596i
$532$			4.52249i			0.196075i
$533$	0.217273	−	0.0705962i	0.00941113	−	0.00305786i
$534$	−43.5874	−	31.6681i	−1.88621	−	1.37041i
$535$	−26.3069	−	17.2426i	−1.13735	−	0.745465i
$536$	−3.53046	+	2.56503i	−0.152493	+	0.110792i
$537$	9.17129	−	12.6232i	0.395770	−	0.544731i
$538$	−2.73547	+	3.76505i	−0.117934	+	0.162323i
$539$	17.7064	−	12.8645i	0.762669	−	0.554111i
$540$	9.90763	−	36.3594i	0.426357	−	1.56466i
$541$	31.8689	+	23.1541i	1.37015	+	0.995471i	0.997725	+	0.0674085i	$0.0214731\pi$
$541$	31.8689	+	23.1541i	1.37015	+	0.995471i	0.372423	+	0.928063i	$0.378527\pi$
$542$	−15.0928	+	4.90393i	−0.648290	+	0.210642i
$543$			25.2972i			1.08561i
$544$	−1.60144	−	4.92873i	−0.0686613	−	0.211318i
$545$	−28.6966	+	10.8764i	−1.22923	+	0.465896i
$546$	−22.0524	+	67.8704i	−0.943757	+	2.90458i
$547$	−4.67733	−	1.51976i	−0.199988	−	0.0649801i	0.207310	−	0.978275i	$-0.433529\pi$
$547$	−4.67733	−	1.51976i	−0.199988	−	0.0649801i	−0.407298	+	0.913295i	$0.633529\pi$
$548$	−5.05825	−	6.96208i	−0.216078	−	0.297405i
$549$	4.93836			0.210764
$550$	−0.781760	−	8.09677i	−0.0333344	−	0.345248i
$551$	−5.37763			−0.229095
$552$	12.3001	+	16.9296i	0.523525	+	0.720570i
$553$	19.5239	+	6.34371i	0.830242	+	0.269762i
$554$	−8.52245	+	26.2294i	−0.362084	+	1.11438i
$555$	−1.51837	−	31.5250i	−0.0644513	−	1.33816i
$556$	−5.14763	−	15.8428i	−0.218308	−	0.671883i
$557$		−	8.86209i		−	0.375499i	−0.982217	−	0.187749i	$-0.939881\pi$
$557$		−	8.86209i		−	0.375499i	0.982217	−	0.187749i	$-0.0601193\pi$
$558$	76.2585	−	24.7779i	3.22828	−	1.04893i
$559$	−5.47073	−	3.97471i	−0.231387	−	0.168113i
$560$	−3.58403	−	9.45617i	−0.151453	−	0.399596i
$561$	−22.6905	+	16.4856i	−0.957992	+	0.696022i
$562$	−4.33956	+	5.97289i	−0.183053	+	0.251951i
$563$	7.90829	−	10.8848i	0.333295	−	0.458741i	−0.609173	−	0.793037i	$-0.708499\pi$
$563$	7.90829	−	10.8848i	0.333295	−	0.458741i	0.942468	+	0.334296i	$0.108499\pi$
$564$	−8.72447	+	6.33870i	−0.367366	+	0.266907i
$565$	−0.710159	−	1.87370i	−0.0298766	−	0.0788270i
$566$	22.9669	+	16.6864i	0.965369	+	0.701382i
$567$	−137.058	+	44.5327i	−5.75588	+	1.87020i
$568$		−	10.5660i		−	0.443341i
$569$	5.48718	+	16.8878i	0.230035	+	0.707974i	0.997741	+	0.0671726i	$0.0213978\pi$
$569$	5.48718	+	16.8878i	0.230035	+	0.707974i	−0.767707	+	0.640801i	$0.778602\pi$
$570$	−0.357853	−	7.42988i	−0.0149888	−	0.311203i
$571$	2.15722	−	6.63923i	0.0902767	−	0.277843i	−0.895717	−	0.444624i	$-0.853337\pi$
$571$	2.15722	−	6.63923i	0.0902767	−	0.277843i	0.985994	+	0.166781i	$0.0533373\pi$
$572$	−7.33939	−	2.38471i	−0.306875	−	0.0997099i
$573$	45.2314	+	62.2557i	1.88957	+	2.60077i
$574$	0.217811			0.00909126
$575$	−15.9564	+	27.1048i	−0.665428	+	1.13035i
$576$	8.06623			0.336093
$577$	9.64349	+	13.2731i	0.401464	+	0.552568i	0.961111	−	0.276164i	$-0.0890632\pi$
$577$	9.64349	+	13.2731i	0.401464	+	0.552568i	−0.559647	+	0.828731i	$0.689063\pi$
$578$	−9.37459	−	3.04599i	−0.389931	−	0.126696i
$579$	−9.36195	+	28.8131i	−0.389069	+	1.19743i
$580$	11.2442	−	4.26172i	0.466890	−	0.176958i
$581$	−17.4192	−	53.6108i	−0.722670	−	2.22415i
$582$			0.696789i			0.0288828i
$583$	8.93459	−	2.90302i	0.370033	−	0.120231i
$584$	3.21594	+	2.33652i	0.133076	+	0.0966857i
$585$	22.4932	−	82.5467i	0.929981	−	3.41288i
$586$	17.4503	−	12.6784i	0.720866	−	0.523740i
$587$	11.9944	−	16.5089i	0.495062	−	0.681395i	−0.486249	−	0.873820i	$-0.661635\pi$
$587$	11.9944	−	16.5089i	0.495062	−	0.681395i	0.981312	+	0.192425i	$0.0616353\pi$
$588$	−26.3048	+	36.2054i	−1.08479	+	1.49308i
$589$	8.04209	−	5.84292i	0.331369	−	0.240753i
$590$	5.53664	+	3.62895i	0.227940	+	0.149401i
$591$	−15.8575	−	11.5212i	−0.652292	−	0.473918i
$592$	4.03534	−	1.31116i	0.165851	−	0.0538883i
$593$		−	6.38598i		−	0.262241i	−0.991366	−	0.131120i	$-0.958143\pi$
$593$		−	6.38598i		−	0.262241i	0.991366	−	0.131120i	$-0.0418574\pi$
$594$	−8.47275	−	26.0764i	−0.347641	−	1.06993i
$595$	−50.5636	−	13.7782i	−2.07291	−	0.564849i
$596$	−3.38448	+	10.4163i	−0.138634	+	0.426670i
$597$	−16.0607	−	5.21845i	−0.657322	−	0.213577i
$598$	17.5390	+	24.1403i	0.717221	+	0.987171i
$599$	−29.8441			−1.21940			−0.609699	−	0.792633i	$-0.708710\pi$
$599$	−29.8441			−1.21940			−0.609699	+	0.792633i	$0.708710\pi$
$600$	6.63636	+	15.2517i	0.270928	+	0.622648i
$601$	31.8540			1.29935			0.649675	−	0.760212i	$-0.274905\pi$
$601$	31.8540			1.29935			0.649675	+	0.760212i	$0.274905\pi$
$602$	−3.78954	−	5.21585i	−0.154450	−	0.212582i
$603$	−33.4773	−	10.8774i	−1.36330	−	0.442964i
$604$	3.06465	−	9.43201i	0.124699	−	0.383783i
$605$	11.6932	+	14.5655i	0.475395	+	0.592171i
$606$	−6.32146	−	19.4555i	−0.256792	−	0.790324i
$607$			24.2976i			0.986208i	0.869970	+	0.493104i	$0.164138\pi$
$607$			24.2976i			0.986208i	−0.869970	+	0.493104i	$0.835862\pi$
$608$	0.951057	−	0.309017i	0.0385704	−	0.0125323i
$609$	−65.4524	−	47.5540i	−2.65227	−	1.92698i
$610$	−1.06754	+	0.857016i	−0.0432232	+	0.0346996i
$611$	−12.4404	+	9.03851i	−0.503286	+	0.365659i
$612$	24.5708	−	33.8187i	0.993214	−	1.36704i
$613$	−14.4029	+	19.8239i	−0.581728	+	0.800681i	−0.993884	−	0.110433i	$-0.964776\pi$
$613$	−14.4029	+	19.8239i	−0.581728	+	0.800681i	0.412155	+	0.911114i	$0.364776\pi$
$614$	26.1690	−	19.0129i	1.05610	−	0.767299i
$615$	−0.357836	+	0.0172348i	−0.0144293	+	0.000694976i
$616$	−5.95240	−	4.32467i	−0.239829	−	0.174246i
$617$	14.8570	−	4.82732i	0.598118	−	0.194340i	0.00571735	−	0.999984i	$-0.498180\pi$
$617$	14.8570	−	4.82732i	0.598118	−	0.194340i	0.592401	+	0.805643i	$0.298180\pi$
$618$			22.1440i			0.890761i
$619$	−6.81321	−	20.9689i	−0.273846	−	0.842811i	−0.989522	−	0.144379i	$-0.953882\pi$
$619$	−6.81321	−	20.9689i	−0.273846	−	0.842811i	0.715677	−	0.698432i	$-0.246118\pi$
$620$	−12.1849	+	18.5904i	−0.489358	+	0.746608i
$621$	−32.7609	+	100.828i	−1.31465	+	4.04608i
$622$	14.8576	+	4.82752i	0.595735	+	0.193566i
$623$	−43.0526	−	59.2569i	−1.72487	−	2.37408i
$624$	15.7796			0.631690
$625$	−17.0404	+	18.2927i	−0.681617	+	0.731709i
$626$	−1.56471			−0.0625383
$627$	−3.18109	−	4.37839i	−0.127040	−	0.174856i
$628$	−11.9504	−	3.88293i	−0.476874	−	0.154946i
$629$	6.79493	−	20.9126i	0.270931	−	0.833841i
$630$	44.7157	−	68.2221i	1.78151	−	2.71803i
$631$	−12.4371	−	38.2774i	−0.495112	−	1.52380i	−0.816782	−	0.576946i	$-0.804244\pi$
$631$	−12.4371	−	38.2774i	−0.495112	−	1.52380i	0.321670	−	0.946852i	$-0.395756\pi$
$632$		−	4.53925i		−	0.180562i
$633$	31.2786	−	10.1630i	1.24321	−	0.403944i
$634$	−20.8861	−	15.1747i	−0.829494	−	0.602662i
$635$	−17.7859	+	0.856641i	−0.705812	+	0.0339948i
$636$	−15.5406	+	11.2909i	−0.616226	+	0.447714i
$637$	−37.5086	+	51.6262i	−1.48615	+	2.04550i
$638$	5.14241	−	7.07791i	0.203590	−	0.280217i
$639$	68.9510	−	50.0958i	2.72766	−	1.98176i
$640$	−1.74369	+	1.39983i	−0.0689255	+	0.0553333i
$641$	11.7291	+	8.52167i	0.463270	+	0.336586i	0.794813	−	0.606855i	$-0.207569\pi$
$641$	11.7291	+	8.52167i	0.463270	+	0.336586i	−0.331543	+	0.943440i	$0.607569\pi$
$642$	44.5040	−	14.4602i	1.75643	−	0.570699i
$643$		−	41.6438i		−	1.64227i	−0.570734	−	0.821135i	$-0.693341\pi$
$643$		−	41.6438i		−	1.64227i	0.570734	−	0.821135i	$-0.306659\pi$
$644$	8.79120	+	27.0565i	0.346422	+	1.06618i
$645$	6.63846	+	8.26914i	0.261389	+	0.325597i
$646$	1.60144	−	4.92873i	0.0630079	−	0.193918i
$647$	0.632814	+	0.205614i	0.0248785	+	0.00808351i	0.321430	−	0.946933i	$-0.395837\pi$
$647$	0.632814	+	0.205614i	0.0248785	+	0.00808351i	−0.296551	+	0.955017i	$0.595837\pi$
$648$	18.7300	+	25.7797i	0.735785	+	1.01272i
$649$	4.81644			0.189062
$650$	9.46295	+	21.7478i	0.371167	+	0.853019i
$651$	149.551			5.86136
$652$	1.12475	+	1.54808i	0.0440485	+	0.0606276i
$653$	13.1199	+	4.26290i	0.513420	+	0.166820i	0.554257	−	0.832346i	$-0.313002\pi$
$653$	13.1199	+	4.26290i	0.513420	+	0.166820i	−0.0408371	+	0.999166i	$0.513002\pi$
$654$	14.1083	−	43.4209i	0.551678	−	1.69789i
$655$	1.24421	+	0.339037i	0.0486154	+	0.0132473i
$656$	−0.0148828	−	0.0458046i	−0.000581076	−	0.00178837i
$657$			32.0642i			1.25094i
$658$	−13.9433	+	4.53045i	−0.543566	+	0.176615i
$659$	2.90773	+	2.11259i	0.113269	+	0.0822949i	0.642978	−	0.765885i	$-0.277699\pi$
$659$	2.90773	+	2.11259i	0.113269	+	0.0822949i	−0.529709	+	0.848180i	$0.677699\pi$
$660$	10.1212	+	6.63389i	0.393969	+	0.258224i
$661$	12.2416	−	8.89405i	0.476143	−	0.345938i	−0.323687	−	0.946164i	$-0.604923\pi$
$661$	12.2416	−	8.89405i	0.476143	−	0.345938i	0.799831	+	0.600226i	$0.204923\pi$
$662$	−19.2408	+	26.4827i	−0.747816	+	1.02928i
$663$	48.0667	−	66.1581i	1.86676	−	2.56937i
$664$	−10.0838	+	7.32634i	−0.391329	+	0.284317i
$665$	2.65866	−	9.75684i	0.103098	−	0.378354i
$666$	27.6887	+	20.1170i	1.07291	+	0.779517i
$667$	−32.1725	+	10.4535i	−1.24573	+	0.404761i
$668$		−	2.39121i		−	0.0925185i
$669$	3.32322	+	10.2278i	0.128483	+	0.395430i
$670$	9.12455	−	3.45834i	0.352512	−	0.133607i
$671$	−0.307788	+	0.947274i	−0.0118820	+	0.0365691i
$672$	14.3082	+	4.64900i	0.551949	+	0.179339i
$673$	11.7683	+	16.1977i	0.453635	+	0.624375i	0.973174	−	0.230072i	$-0.0738961\pi$
$673$	11.7683	+	16.1977i	0.453635	+	0.624375i	−0.519539	+	0.854447i	$0.673896\pi$
$674$	−17.5537			−0.676142
$675$	−42.7496	+	72.6176i	−1.64543	+	2.79505i
$676$	9.50057			0.365406
$677$	6.48537	+	8.92634i	0.249253	+	0.343067i	0.915249	−	0.402888i	$-0.131993\pi$
$677$	6.48537	+	8.92634i	0.249253	+	0.343067i	−0.665997	+	0.745955i	$0.731993\pi$
$678$	2.83509	+	0.921177i	0.108881	+	0.0353776i
$679$	−0.292726	+	0.900918i	−0.0112338	+	0.0345740i
$680$	0.557486	+	11.5747i	0.0213786	+	0.443871i
$681$	9.14210	+	28.1365i	0.350326	+	1.07819i
$682$			16.1722i			0.619264i
$683$	30.5563	−	9.92836i	1.16921	−	0.379898i	0.340859	−	0.940114i	$-0.389282\pi$
$683$	30.5563	−	9.92836i	1.16921	−	0.379898i	0.828346	+	0.560216i	$0.189282\pi$
$684$	6.52572	+	4.74121i	0.249517	+	0.181285i
$685$	6.81987	+	17.9937i	0.260574	+	0.687502i
$686$	−23.6096	+	17.1534i	−0.901420	+	0.654920i
$687$	−25.4274	+	34.9978i	−0.970116	+	1.33525i
$688$	−0.837933	+	1.15332i	−0.0319459	+	0.0439697i
$689$	−22.1598	+	16.1000i	−0.844220	+	0.613362i
$690$	−16.5838	−	43.7549i	−0.631333	−	1.66572i
$691$	−5.92789	−	4.30686i	−0.225507	−	0.163841i	0.469295	−	0.883042i	$-0.344508\pi$
$691$	−5.92789	−	4.30686i	−0.225507	−	0.163841i	−0.694802	+	0.719201i	$0.744508\pi$
$692$	−1.34748	+	0.437824i	−0.0512236	+	0.0166436i
$693$		−	59.3479i		−	2.25444i
$694$	−6.30825	−	19.4148i	−0.239458	−	0.736976i
$695$	1.79197	+	37.2055i	0.0679731	+	1.41128i
$696$	−5.52806	+	17.0136i	−0.209541	+	0.644900i
$697$	−0.237377	−	0.0771283i	−0.00899128	−	0.00292144i
$698$	3.79666	+	5.22565i	0.143706	+	0.197794i
$699$	−46.8243			−1.77106
$700$	2.17317	+	22.5078i	0.0821382	+	0.850714i
$701$	−25.8753			−0.977298			−0.488649	−	0.872480i	$-0.662510\pi$
$701$	−25.8753			−0.977298			−0.488649	+	0.872480i	$0.662510\pi$
$702$	46.9895	+	64.6755i	1.77350	+	2.44102i
$703$	4.03534	+	1.31116i	0.152196	+	0.0494513i
$704$	−0.502735	+	1.54726i	−0.0189475	+	0.0583146i
$705$	22.5486	−	8.54625i	0.849229	−	0.321870i
$706$	−7.38370	−	22.7247i	−0.277889	−	0.855255i
$707$		−	27.8107i		−	1.04593i
$708$	−9.36645	+	3.04334i	−0.352013	+	0.114376i
$709$	32.6968	+	23.7556i	1.22795	+	0.892161i	0.996735	−	0.0807404i	$-0.0257285\pi$
$709$	32.6968	+	23.7556i	1.22795	+	0.892161i	0.231219	+	0.972902i	$0.425728\pi$
$710$	−6.21151	+	22.7952i	−0.233114	+	0.855490i
$711$	29.6219	−	21.5215i	1.11091	−	0.807121i
$712$	−9.51968	+	13.1027i	−0.356765	+	0.491045i
$713$	36.7552	−	50.5892i	1.37649	−	1.89458i
$714$	63.0760	−	45.8274i	2.36056	−	1.71505i
$715$	14.4321	+	9.45944i	0.539731	+	0.353763i
$716$	−3.79463	−	2.75696i	−0.141812	−	0.103032i
$717$	−54.6170	+	17.7461i	−2.03971	+	0.662742i
$718$			14.1122i			0.526661i
$719$	−7.63046	−	23.4841i	−0.284568	−	0.875810i	−0.986528	−	0.163594i	$-0.947691\pi$
$719$	−7.63046	−	23.4841i	−0.284568	−	0.875810i	0.701960	−	0.712217i	$-0.252309\pi$
$720$	−17.4021	−	4.74193i	−0.648540	−	0.176721i
$721$	−9.30283	+	28.6312i	−0.346456	+	1.06628i
$722$	0.951057	+	0.309017i	0.0353947	+	0.0115004i
$723$	29.5674	+	40.6961i	1.09962	+	1.51350i
$724$	7.60455			0.282621
$725$	−26.7637	+	2.58409i	−0.993978	+	0.0959706i
$726$	−27.7879			−1.03130
$727$	12.5890	+	17.3272i	0.466899	+	0.642631i	0.975921	−	0.218122i	$-0.0699931\pi$
$727$	12.5890	+	17.3272i	0.466899	+	0.642631i	−0.509023	+	0.860753i	$0.669993\pi$
$728$	20.4024	+	6.62913i	0.756162	+	0.245692i
$729$	−27.4536	+	84.4934i	−1.01680	+	3.12938i
$730$	−5.56451	−	6.93138i	−0.205952	−	0.256542i
$731$	2.28298	+	7.02629i	0.0844390	+	0.259877i
$732$		−	2.03663i		−	0.0752760i
$733$	−37.1808	+	12.0808i	−1.37330	+	0.446214i	−0.900462	−	0.434934i	$-0.856772\pi$
$733$	−37.1808	+	12.0808i	−1.37330	+	0.446214i	−0.472842	+	0.881147i	$0.656772\pi$
$734$	−21.5313	−	15.6434i	−0.794736	−	0.577410i
$735$	78.0343	−	62.6458i	2.87834	−	2.31073i
$736$	5.08916	−	3.69749i	0.187589	−	0.136291i
$737$	4.17301	−	5.74365i	0.153715	−	0.211570i
$738$	0.228345	−	0.314290i	0.00840550	−	0.0115692i
$739$	−22.9417	+	16.6681i	−0.843923	+	0.613146i	−0.923464	−	0.383686i	$-0.874655\pi$
$739$	−22.9417	+	16.6681i	−0.843923	+	0.613146i	0.0795409	+	0.996832i	$0.474655\pi$
$740$	−9.47666	+	0.456434i	−0.348369	+	0.0167789i
$741$	12.7660	+	9.27503i	0.468970	+	0.340727i
$742$	−24.8367	+	8.06995i	−0.911786	+	0.296257i
$743$		−	46.2637i		−	1.69725i	−0.528995	−	0.848625i	$-0.677431\pi$
$743$		−	46.2637i		−	1.69725i	0.528995	−	0.848625i	$-0.322569\pi$
$744$	−10.2187	−	31.4498i	−0.374634	−	1.15300i
$745$	13.4252	−	20.4826i	0.491861	−	0.750426i
$746$	−0.697795	+	2.14759i	−0.0255481	+	0.0786290i
$747$	−95.6193	−	31.0686i	−3.49853	−	1.13674i
$748$	4.95570	+	6.82093i	0.181198	+	0.249398i
$749$	63.6165			2.32450
$750$	−5.35123	−	36.8055i	−0.195399	−	1.34395i
$751$	−5.70683			−0.208245			−0.104123	−	0.994564i	$-0.533203\pi$
$751$	−5.70683			−0.208245			−0.104123	+	0.994564i	$0.533203\pi$
$752$	1.90546	+	2.62264i	0.0694850	+	0.0956379i
$753$	0.691521	+	0.224689i	0.0252004	+	0.00818812i
$754$	−7.88261	+	24.2602i	−0.287068	+	0.883503i
$755$	−12.1565	+	18.5471i	−0.442421	+	0.674997i
$756$	23.5529	+	72.4884i	0.856612	+	2.63638i
$757$		−	42.8558i		−	1.55762i	−0.627260	−	0.778810i	$-0.715824\pi$
$757$		−	42.8558i		−	1.55762i	0.627260	−	0.778810i	$-0.284176\pi$
$758$	23.9234	−	7.77317i	0.868936	−	0.282334i
$759$	−27.5425	−	20.0108i	−0.999729	−	0.726345i
$760$	−2.23348	+	0.107573i	−0.0810168	+	0.00390210i
$761$	−22.5405	+	16.3766i	−0.817092	+	0.593652i	−0.915878	−	0.401457i	$-0.868504\pi$
$761$	−22.5405	+	16.3766i	−0.817092	+	0.593652i	0.0987863	+	0.995109i	$0.468504\pi$
$762$	15.5709	−	21.4315i	0.564073	−	0.776380i
$763$	36.4828	−	50.2143i	1.32077	−	1.81788i
$764$	18.7145	−	13.5969i	0.677068	−	0.491919i
$765$	−72.8903	+	58.5162i	−2.63535	+	2.11566i
$766$	19.4958	+	14.1645i	0.704411	+	0.511785i
$767$	−13.3559	+	4.33958i	−0.482252	+	0.156693i
$768$		−	3.32659i		−	0.120038i
$769$	11.4639	+	35.2823i	0.413400	+	1.27231i	0.913675	+	0.406447i	$0.133232\pi$
$769$	11.4639	+	35.2823i	0.413400	+	1.27231i	−0.500275	+	0.865867i	$0.666768\pi$
$770$	10.2994	+	12.8293i	0.371164	+	0.462337i
$771$	12.6158	−	38.8273i	0.454345	−	1.39833i
$772$	8.66145	+	2.81427i	0.311732	+	0.101288i
$773$	−23.0661	−	31.7478i	−0.829631	−	1.14189i	−0.987992	−	0.154507i	$-0.950621\pi$
$773$	−23.0661	−	31.7478i	−0.829631	−	1.14189i	0.158361	−	0.987381i	$-0.449379\pi$
$774$	−11.4990			−0.413324
$775$	37.2167	−	32.9438i	1.33686	−	1.18338i
$776$	0.209460			0.00751918
$777$	37.5206	+	51.6426i	1.34604	+	1.85267i
$778$	15.7266	+	5.10990i	0.563828	+	0.183199i
$779$	0.0148828	−	0.0458046i	0.000533232	−	0.00164112i
$780$	−34.0431	−	9.27644i	−1.21894	−	0.332150i
$781$	5.31192	+	16.3484i	0.190075	+	0.584992i
$782$		−	32.6000i		−	1.16577i
$783$	−86.1950	+	28.0065i	−3.08036	+	1.00087i
$784$	10.8836	+	7.90741i	0.388701	+	0.282408i
$785$	23.4993	+	15.4024i	0.838725	+	0.549736i
$786$	−1.55210	+	1.12767i	−0.0553616	+	0.0402226i
$787$	29.6851	−	40.8580i	1.05816	−	1.45643i	0.176643	−	0.984275i	$-0.443476\pi$
$787$	29.6851	−	40.8580i	1.05816	−	1.45643i	0.881516	−	0.472155i	$-0.156524\pi$
$788$	−3.46336	+	4.76690i	−0.123377	+	0.169814i
$789$	74.0569	−	53.8055i	2.63650	−	1.91553i
$790$	−2.66851	+	9.79300i	−0.0949412	+	0.348419i
$791$	3.27866	+	2.38208i	0.116576	+	0.0846972i
$792$	−12.4806	+	4.05518i	−0.443477	+	0.144095i
$793$		−	2.90408i		−	0.103127i
$794$	8.93271	+	27.4920i	0.317010	+	0.975656i
$795$	40.1651	−	15.2232i	1.42451	−	0.539911i
$796$	−1.56871	+	4.82798i	−0.0556013	+	0.171123i
$797$	−22.3652	−	7.26688i	−0.792214	−	0.257406i	−0.115168	−	0.993346i	$-0.536741\pi$
$797$	−22.3652	−	7.26688i	−0.792214	−	0.257406i	−0.677047	+	0.735940i	$0.736741\pi$
$798$	8.84293	+	12.1712i	0.313036	+	0.430857i
$799$	16.8000			0.594343
$800$	4.58478	−	1.99494i	0.162096	−	0.0705318i
$801$	−130.639			−4.61592
$802$	−8.03908	−	11.0648i	−0.283870	−	0.390713i
$803$	−6.15054	−	1.99843i	−0.217048	−	0.0705231i
$804$	−4.48596	+	13.8064i	−0.158208	+	0.486914i
$805$	−3.06035	−	63.5401i	−0.107863	−	2.23949i
$806$	−14.5710	−	44.8450i	−0.513243	−	1.57960i
$807$			15.4815i			0.544975i
$808$	−5.84846	+	1.90028i	−0.205748	+	0.0668516i
$809$	11.4913	+	8.34894i	0.404014	+	0.293533i	0.771174	−	0.636625i	$-0.219670\pi$
$809$	11.4913	+	8.34894i	0.404014	+	0.293533i	−0.367160	+	0.930158i	$0.619670\pi$
$810$	−25.2531	−	66.6281i	−0.887302	−	2.34107i
$811$	−13.6451	+	9.91375i	−0.479145	+	0.348119i	−0.800994	−	0.598672i	$-0.795695\pi$
$811$	−13.6451	+	9.91375i	−0.479145	+	0.348119i	0.321850	+	0.946791i	$0.395695\pi$
$812$	−14.2951	+	19.6755i	−0.501659	+	0.690475i
$813$	−31.0299	+	42.7090i	−1.08827	+	1.49787i
$814$	−5.58455	+	4.05741i	−0.195738	+	0.142212i
$815$	−1.51646	−	4.00106i	−0.0531193	−	0.140151i
$816$	−13.9472	−	10.1332i	−0.488249	−	0.354734i
$817$	−1.35580	+	0.440527i	−0.0474336	+	0.0154121i
$818$		−	16.7414i		−	0.585349i
$819$	53.4721	+	164.570i	1.86847	+	5.75055i
$820$	0.00518092	+	0.107568i	0.000180926	+	0.00375645i
$821$	−9.95965	+	30.6527i	−0.347594	+	1.06979i	0.612586	+	0.790404i	$0.290129\pi$
$821$	−9.95965	+	30.6527i	−0.347594	+	1.06979i	−0.960180	+	0.279381i	$0.909871\pi$
$822$	−27.2262	−	8.84634i	−0.949624	−	0.308552i
$823$	28.1232	+	38.7083i	0.980314	+	1.34929i	0.936660	+	0.350240i	$0.113900\pi$
$823$	28.1232	+	38.7083i	0.980314	+	1.34929i	0.0436538	+	0.999047i	$0.486100\pi$
$824$	6.65665			0.231895
$825$	−17.9357	−	20.2620i	−0.624442	−	0.705433i
$826$	−13.3889			−0.465861
$827$	−13.5953	−	18.7123i	−0.472755	−	0.650692i	0.504337	−	0.863507i	$-0.331737\pi$
$827$	−13.5953	−	18.7123i	−0.472755	−	0.650692i	−0.977093	+	0.212815i	$0.931737\pi$
$828$	48.2576	+	15.6798i	1.67707	+	0.544912i
$829$	1.12797	−	3.47153i	0.0391760	−	0.120571i	−0.929556	−	0.368681i	$-0.879809\pi$
$829$	1.12797	−	3.47153i	0.0391760	−	0.120571i	0.968732	+	0.248110i	$0.0798094\pi$
$830$	26.0619	−	9.87786i	0.904622	−	0.342866i
$831$	28.3507	+	87.2546i	0.983476	+	3.02683i
$832$		−	4.74348i		−	0.164450i
$833$	66.3057	−	21.5440i	2.29736	−	0.746456i
$834$	−44.8314	−	32.5719i	−1.55239	−	1.12787i
$835$	−1.40573	+	5.15880i	−0.0486472	+	0.178528i
$836$	−1.31618	+	0.956259i	−0.0455210	+	0.0330729i
$837$	98.4725	−	135.536i	3.40371	−	4.68480i
$838$	12.7376	−	17.5318i	0.440013	−	0.605625i
$839$	−32.3048	+	23.4708i	−1.11529	+	0.810304i	−0.983488	−	0.180973i	$-0.942075\pi$
$839$	−32.3048	+	23.4708i	−1.11529	+	0.810304i	−0.131799	+	0.991276i	$0.542075\pi$
$840$	−28.1355	−	18.4412i	−0.970766	−	0.636281i
$841$	0.0656335	+	0.0476855i	0.00226322	+	0.00164433i
$842$	−26.9511	+	8.75694i	−0.928796	+	0.301784i
$843$			24.5599i			0.845888i
$844$	−3.05509	−	9.40259i	−0.105160	−	0.323650i
$845$	−20.4966	−	5.58514i	−0.705104	−	0.192135i
$846$	−8.08043	+	24.8690i	−0.277811	+	0.855014i
$847$	−35.9285	−	11.6739i	−1.23452	−	0.401119i
$848$	3.39414	+	4.67163i	0.116555	+	0.160425i
$849$	94.4374			3.24108
$850$	5.60177	−	25.2991i	0.192139	−	0.867753i
$851$	26.6908			0.914949
$852$	−20.6600	−	28.4361i	−0.707801	−	0.974204i
$853$	8.52162	+	2.76884i	0.291775	+	0.0948034i	0.451247	−	0.892399i	$-0.350979\pi$
$853$	8.52162	+	2.76884i	0.291775	+	0.0948034i	−0.159472	+	0.987202i	$0.550979\pi$
$854$	0.855603	−	2.63327i	0.0292781	−	0.0901088i
$855$	−11.2914	−	14.0650i	−0.386157	−	0.481014i
$856$	−4.34685	−	13.3782i	−0.148572	−	0.457259i
$857$			17.7688i			0.606972i	0.952836	+	0.303486i	$0.0981505\pi$
$857$			17.7688i			0.606972i	−0.952836	+	0.303486i	$0.901850\pi$
$858$	−24.4152	+	7.93297i	−0.833521	+	0.270827i
$859$	11.2092	+	8.14395i	0.382452	+	0.277868i	0.762356	−	0.647158i	$-0.224043\pi$
$859$	11.2092	+	8.14395i	0.382452	+	0.277868i	−0.379903	+	0.925026i	$0.624043\pi$
$860$	2.48577	−	1.99557i	0.0847639	−	0.0680484i
$861$	0.586189	−	0.425891i	0.0199773	−	0.0145143i
$862$	−11.4640	+	15.7788i	−0.390464	+	0.537427i
$863$	4.03276	−	5.55062i	0.137277	−	0.188945i	−0.734844	−	0.678237i	$-0.762744\pi$
$863$	4.03276	−	5.55062i	0.137277	−	0.188945i	0.872120	+	0.489291i	$0.162744\pi$
$864$	13.6346	−	9.90613i	0.463859	−	0.337013i
$865$	3.16446	−	0.152413i	0.107595	−	0.00518220i
$866$	−3.73415	−	2.71302i	−0.126891	−	0.0921920i
$867$	−31.1855	+	10.1328i	−1.05911	+	0.344127i
$868$		−	44.9561i		−	1.52591i
$869$	2.28204	+	7.02339i	0.0774129	+	0.238252i
$870$	21.9282	−	33.4555i	0.743434	−	1.13425i
$871$	−6.39665	+	19.6869i	−0.216742	+	0.667064i
$872$	−13.0527	−	4.24107i	−0.442019	−	0.143621i
$873$	0.993095	+	1.36688i	0.0336112	+	0.0462618i
$874$	6.29055			0.212781
$875$	8.54333	−	49.8360i	0.288817	−	1.68476i
$876$	13.2236			0.446784
$877$	19.8103	+	27.2665i	0.668945	+	0.920724i	0.999736	−	0.0229803i	$-0.00731551\pi$
$877$	19.8103	+	27.2665i	0.668945	+	0.920724i	−0.330791	+	0.943704i	$0.607316\pi$
$878$	−19.6821	−	6.39510i	−0.664239	−	0.215824i
$879$	22.1732	−	68.2420i	0.747883	−	2.30175i
$880$	1.99420	−	3.04252i	0.0672244	−	0.102563i
$881$	5.87995	+	18.0966i	0.198101	+	0.609691i	0.999926	+	0.0121331i	$0.00386217\pi$
$881$	5.87995	+	18.0966i	0.198101	+	0.609691i	−0.801826	+	0.597558i	$0.796138\pi$
$882$			108.514i			3.65386i
$883$	−19.3793	+	6.29671i	−0.652164	+	0.211901i	−0.616368	−	0.787458i	$-0.711397\pi$
$883$	−19.3793	+	6.29671i	−0.652164	+	0.211901i	−0.0357962	+	0.999359i	$0.511397\pi$
$884$	−19.8876	−	14.4492i	−0.668894	−	0.485980i
$885$	21.9964	−	1.05943i	0.739399	−	0.0356125i
$886$	26.9668	−	19.5925i	0.905966	−	0.658223i
$887$	−17.3972	+	23.9451i	−0.584139	+	0.803999i	−0.994142	−	0.108086i	$-0.965528\pi$
$887$	−17.3972	+	23.9451i	−0.584139	+	0.803999i	0.410002	+	0.912085i	$0.365528\pi$
$888$	8.29644	−	11.4191i	0.278410	−	0.383199i
$889$	29.1359	−	21.1685i	0.977188	−	0.709969i
$890$	28.2406	−	22.6715i	0.946626	−	0.759951i
$891$	−41.9406	−	30.4716i	−1.40506	−	1.02084i
$892$	3.07456	−	0.998985i	0.102944	−	0.0334485i
$893$			3.24176i			0.108481i
$894$	11.2588	+	34.6510i	0.376550	+	1.15890i
$895$	6.56581	+	8.17865i	0.219471	+	0.273382i
$896$	1.39753	−	4.30114i	0.0466880	−	0.143691i
$897$	94.4042	+	30.6738i	3.15206	+	1.02417i
$898$	19.9149	+	27.4105i	0.664568	+	0.914699i
$899$	53.4567			1.78288
$900$	34.7558	+	20.4606i	1.15853	+	0.682019i
$901$	29.9254			0.996960
$902$	0.0460551	+	0.0633895i	0.00153347	+	0.00211064i
$903$	−20.3974	−	6.62751i	−0.678782	−	0.220550i
$904$	0.276913	−	0.852251i	0.00920999	−	0.0283454i
$905$	−16.4061	−	4.47052i	−0.545357	−	0.148605i
$906$	−10.1948	−	31.3765i	−0.338701	−	1.04241i
$907$		−	29.7441i		−	0.987636i	−0.869565	−	0.493818i	$-0.835601\pi$
$907$		−	29.7441i		−	0.987636i	0.869565	−	0.493818i	$-0.164399\pi$
$908$	8.45805	−	2.74819i	0.280690	−	0.0912018i
$909$	−40.1295	−	29.1558i	−1.33101	−	0.967036i
$910$	−40.1191	−	26.2958i	−1.32993	−	0.871696i
$911$	35.9420	−	26.1134i	1.19081	−	0.865176i	0.197463	−	0.980310i	$-0.436730\pi$
$911$	35.9420	−	26.1134i	1.19081	−	0.865176i	0.993350	+	0.115134i	$0.0367299\pi$
$912$	1.95532	−	2.69127i	0.0647472	−	0.0891169i
$913$	11.9191	−	16.4053i	0.394465	−	0.542935i
$914$	11.4750	−	8.33709i	0.379560	−	0.275766i
$915$	−1.19728	+	4.39384i	−0.0395810	+	0.145256i
$916$	10.5206	+	7.64367i	0.347611	+	0.252554i
$917$	−2.48054	+	0.805976i	−0.0819146	+	0.0266157i
$918$		−	87.3402i		−	2.88266i
$919$	−5.64060	−	17.3600i	−0.186066	−	0.572653i	0.813899	−	0.581007i	$-0.197341\pi$
$919$	−5.64060	−	17.3600i	−0.186066	−	0.572653i	−0.999965	+	0.00835358i	$0.997341\pi$
$920$	−13.1530	+	4.98520i	−0.433643	+	0.164357i
$921$	33.2516	−	102.338i	1.09568	−	3.37215i
$922$	−20.7212	−	6.73272i	−0.682416	−	0.221730i
$923$	−29.4597	−	40.5477i	−0.969676	−	1.33464i
$924$	−24.4757			−0.805190
$925$	20.7133	+	4.58637i	0.681050	+	0.150799i
$926$	6.61812			0.217485
$927$	31.5606	+	43.4394i	1.03659	+	1.42674i
$928$	5.11443	+	1.66178i	0.167889	+	0.0545505i
$929$	−3.11334	+	9.58187i	−0.102145	+	0.314371i	−0.989050	−	0.147582i	$-0.952851\pi$
$929$	−3.11334	+	9.58187i	−0.102145	+	0.314371i	0.886905	+	0.461953i	$0.152851\pi$
$930$	3.55726	+	73.8572i	0.116647	+	2.42187i
$931$	4.15717	+	12.7945i	0.136246	+	0.419321i
$932$			14.0757i			0.461067i
$933$	49.4252	−	16.0592i	1.61811	−	0.525755i
$934$	−25.6598	−	18.6430i	−0.839615	−	0.610016i
$935$	−6.68160	−	17.6288i	−0.218512	−	0.576525i
$936$	30.9546	−	22.4898i	1.01178	−	0.735103i
$937$	−13.1014	+	18.0325i	−0.428003	+	0.589096i	−0.967494	−	0.252896i	$-0.918617\pi$
$937$	−13.1014	+	18.0325i	−0.428003	+	0.589096i	0.539490	+	0.841992i	$0.318617\pi$
$938$	−11.6003	+	15.9665i	−0.378764	+	0.521323i
$939$	−4.21105	+	3.05951i	−0.137423	+	0.0998433i
$940$	−2.56907	−	6.77828i	−0.0837938	−	0.221083i
$941$	−31.2866	−	22.7311i	−1.01992	−	0.741012i	−0.0536497	−	0.998560i	$-0.517085\pi$
$941$	−31.2866	−	22.7311i	−1.01992	−	0.741012i	−0.966266	+	0.257548i	$0.917085\pi$
$942$	−39.7542	+	12.9169i	−1.29526	+	0.420856i
$943$		−	0.302964i		−	0.00986586i
$944$	0.914853	+	2.81563i	0.0297759	+	0.0916409i
$945$	−8.19912	−	170.233i	−0.266717	−	5.53769i
$946$	0.716688	−	2.20574i	0.0233015	−	0.0717147i
$947$	−22.2329	−	7.22390i	−0.722471	−	0.234745i	−0.0753771	−	0.997155i	$-0.524016\pi$
$947$	−22.2329	−	7.22390i	−0.722471	−	0.234745i	−0.647094	+	0.762410i	$0.724016\pi$
$948$	−8.87569	−	12.2163i	−0.288269	−	0.396768i
$949$	18.8559			0.612088
$950$	4.88176	+	1.08093i	0.158385	+	0.0350699i
$951$	−85.8816			−2.78490
$952$	−13.7761	−	18.9611i	−0.446485	−	0.614533i
$953$	−33.0906	−	10.7518i	−1.07191	−	0.348284i	−0.280678	−	0.959802i	$-0.590559\pi$
$953$	−33.0906	−	10.7518i	−1.07191	−	0.348284i	−0.791231	+	0.611518i	$0.790559\pi$
$954$	−14.3934	+	44.2984i	−0.466004	+	1.43421i
$955$	−48.3681	+	18.3323i	−1.56516	+	0.593218i
$956$	5.33463	+	16.4183i	0.172534	+	0.531006i
$957$		−	29.1037i		−	0.940788i
$958$	−36.4919	+	11.8569i	−1.17900	+	0.383080i
$959$	−31.4859	−	22.8759i	−1.01673	−	0.738700i
$960$	−1.95562	+	7.17682i	−0.0631174	+	0.231631i
$961$	−54.8635	+	39.8606i	−1.76979	+	1.28583i
$962$	11.8301	−	16.2827i	0.381418	−	0.524977i
$963$	66.6932	−	91.7954i	2.14916	−	2.95806i
$964$	12.2336	−	8.88820i	0.394016	−	0.286270i
$965$	−17.0318	−	11.1634i	−0.548274	−	0.359362i
$966$	76.5638	+	55.6268i	2.46340	+	1.78976i
$967$	32.7451	−	10.6395i	1.05301	−	0.342144i	0.269161	−	0.963095i	$-0.413254\pi$
$967$	32.7451	−	10.6395i	1.05301	−	0.342144i	0.783849	+	0.620951i	$0.213254\pi$
$968$			8.35324i			0.268483i
$969$	−5.32735	−	16.3959i	−0.171139	−	0.526712i
$970$	−0.451891	−	0.123136i	−0.0145093	−	0.00395367i
$971$	−1.75737	+	5.40862i	−0.0563966	+	0.173571i	−0.975287	−	0.220942i	$-0.929087\pi$
$971$	−1.75737	+	5.40862i	−0.0563966	+	0.173571i	0.918890	+	0.394513i	$0.129087\pi$
$972$	52.7298	+	17.1330i	1.69131	+	0.549540i
$973$	−44.2814	−	60.9481i	−1.41960	−	1.95391i
$974$	−14.6618			−0.469795
$975$	67.9914	+	40.0261i	2.17747	+	1.28186i
$976$	−0.612227			−0.0195969
$977$	−21.8413	−	30.0620i	−0.698767	−	0.961770i	−0.999966	−	0.00820873i	$-0.997387\pi$
$977$	−21.8413	−	30.0620i	−0.698767	−	0.961770i	0.301200	−	0.953561i	$-0.402613\pi$
$978$	6.05401	+	1.96707i	0.193586	+	0.0628998i
$979$	8.14222	−	25.0592i	0.260227	−	0.800895i
$980$	−18.8318	−	23.4577i	−0.601560	−	0.749329i
$981$	−34.2094	−	105.286i	−1.09222	−	3.36152i
$982$		−	6.92908i		−	0.221116i
$983$	13.2653	−	4.31015i	0.423097	−	0.137473i	−0.0897269	−	0.995966i	$-0.528599\pi$
$983$	13.2653	−	4.31015i	0.423097	−	0.137473i	0.512824	+	0.858494i	$0.328599\pi$
$984$	−0.129616	−	0.0941718i	−0.00413202	−	0.00300209i
$985$	10.2742	−	8.24812i	0.327363	−	0.262807i
$986$	22.5464	−	16.3809i	0.718024	−	0.521675i
$987$	−28.6667	+	39.4563i	−0.912470	+	1.25591i
$988$	2.78815	−	3.83755i	0.0887027	−	0.122089i
$989$	−7.25499	+	5.27106i	−0.230695	+	0.167610i
$990$	29.3096	−	1.41167i	0.931520	−	0.0448658i
$991$	41.3493	+	30.0420i	1.31350	+	0.954316i	0.999989	+	0.00473307i	$0.00150659\pi$
$991$	41.3493	+	30.0420i	1.31350	+	0.954316i	0.313515	+	0.949583i	$0.398493\pi$
$992$	−9.45405	+	3.07181i	−0.300166	+	0.0975299i
$993$			108.894i			3.45565i
$994$	−14.7663	−	45.4460i	−0.468359	−	1.44146i
$995$	6.22258	−	9.49371i	0.197269	−	0.300971i
$996$	−12.8130	+	39.4343i	−0.405995	+	1.24952i
$997$	−8.38594	−	2.72476i	−0.265585	−	0.0862939i	0.173197	−	0.984887i	$-0.444590\pi$
$997$	−8.38594	−	2.72476i	−0.265585	−	0.0862939i	−0.438783	+	0.898593i	$0.644590\pi$
$998$	5.57776	+	7.67712i	0.176561	+	0.243015i
$999$	71.5086			2.26243

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.n.b.39.2	✓	96
25.9	even	10	inner	950.2.n.b.609.2	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.n.b.39.2	✓	96	1.1	even	1	trivial
950.2.n.b.609.2	yes	96	25.9	even	10	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-3.16378 - 1.02797i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(1.22578 - 1.87015i) q^{5} +(1.02797 + 3.16378i) q^{6} +4.52249i q^{7} +(0.951057 - 0.309017i) q^{8} +(6.52572 + 4.74121i) q^{9} +O(q^{10})\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-3.16378 - 1.02797i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(1.22578 - 1.87015i) q^{5} +(1.02797 + 3.16378i) q^{6} +4.52249i q^{7} +(0.951057 - 0.309017i) q^{8} +(6.52572 + 4.74121i) q^{9} +(-2.23348 + 0.107573i) q^{10} +(-1.31618 + 0.956259i) q^{11} +(1.95532 - 2.69127i) q^{12} +(2.78815 - 3.83755i) q^{13} +(3.65877 - 2.65825i) q^{14} +(-5.80056 + 4.65668i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-4.92873 + 1.60144i) q^{17} -8.06623i q^{18} +(-0.309017 - 0.951057i) q^{19} +(1.39983 + 1.74369i) q^{20} +(4.64900 - 14.3082i) q^{21} +(1.54726 + 0.502735i) q^{22} +(-3.69749 - 5.08916i) q^{23} -3.32659 q^{24} +(-1.99494 - 4.58478i) q^{25} -4.74348 q^{26} +(-9.90613 - 13.6346i) q^{27} +(-4.30114 - 1.39753i) q^{28} +(1.66178 - 5.11443i) q^{29} +(7.17682 + 1.95562i) q^{30} +(3.07181 + 9.45405i) q^{31} +1.00000i q^{32} +(5.14711 - 1.67240i) q^{33} +(4.19263 + 3.04612i) q^{34} +(8.45774 + 5.54356i) q^{35} +(-6.52572 + 4.74121i) q^{36} +(-2.49397 + 3.43266i) q^{37} +(-0.587785 + 0.809017i) q^{38} +(-12.7660 + 9.27503i) q^{39} +(0.587875 - 2.15741i) q^{40} +(0.0389637 + 0.0283088i) q^{41} +(-14.3082 + 4.64900i) q^{42} -1.42558i q^{43} +(-0.502735 - 1.54726i) q^{44} +(16.8659 - 6.39242i) q^{45} +(-1.94389 + 5.98267i) q^{46} +(-3.08310 - 1.00176i) q^{47} +(1.95532 + 2.69127i) q^{48} -13.4529 q^{49} +(-2.53657 + 4.30881i) q^{50} +17.2397 q^{51} +(2.78815 + 3.83755i) q^{52} +(-5.49183 - 1.78441i) q^{53} +(-5.20796 + 16.0284i) q^{54} +(0.175010 + 3.63361i) q^{55} +(1.39753 + 4.30114i) q^{56} +3.32659i q^{57} +(-5.11443 + 1.66178i) q^{58} +(-2.39512 - 1.74015i) q^{59} +(-2.63630 - 6.95565i) q^{60} +(0.495302 - 0.359858i) q^{61} +(5.84292 - 8.04209i) q^{62} +(-21.4421 + 29.5125i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-3.75916 - 9.91824i) q^{65} +(-4.37839 - 3.18109i) q^{66} +(-4.15030 + 1.34852i) q^{67} -5.18238i q^{68} +(6.46652 + 19.9019i) q^{69} +(-0.486499 - 10.1009i) q^{70} +(3.26509 - 10.0489i) q^{71} +(7.67144 + 2.49260i) q^{72} +(2.33652 + 3.21594i) q^{73} +4.24300 q^{74} +(1.59851 + 16.5560i) q^{75} +1.00000 q^{76} +(-4.32467 - 5.95240i) q^{77} +(15.0073 + 4.87617i) q^{78} +(1.40270 - 4.31708i) q^{79} +(-2.09092 + 0.792491i) q^{80} +(9.84696 + 30.3058i) q^{81} -0.0481618i q^{82} +(-11.8543 + 3.85168i) q^{83} +(12.1712 + 8.84293i) q^{84} +(-3.04659 + 11.1805i) q^{85} +(-1.15332 + 0.837933i) q^{86} +(-10.5150 + 14.4727i) q^{87} +(-0.956259 + 1.31618i) q^{88} +(-13.1027 + 9.51968i) q^{89} +(-15.0851 - 9.88741i) q^{90} +(17.3553 + 12.6094i) q^{91} +(5.98267 - 1.94389i) q^{92} -33.0683i q^{93} +(1.00176 + 3.08310i) q^{94} +(-2.15741 - 0.587875i) q^{95} +(1.02797 - 3.16378i) q^{96} +(0.199208 + 0.0647267i) q^{97} +(7.90741 + 10.8836i) q^{98} -13.1228 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{4} + 8 q^{5} - 6 q^{6} + 34 q^{9}+O(q^{10}) \) 96 * q + 24 * q^4 + 8 * q^5 - 6 * q^6 + 34 * q^9	\( 96 q + 24 q^{4} + 8 q^{5} - 6 q^{6} + 34 q^{9} - 24 q^{11} + 10 q^{12} + 10 q^{14} - 8 q^{15} - 24 q^{16} + 30 q^{17} + 24 q^{19} + 2 q^{20} - 24 q^{24} - 60 q^{25} + 84 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} + 16 q^{30} - 14 q^{31} + 100 q^{33} + 8 q^{34} + 42 q^{35} - 34 q^{36} - 30 q^{37} + 32 q^{39} + 12 q^{41} + 10 q^{42} + 4 q^{44} - 18 q^{45} - 10 q^{46} + 10 q^{48} - 132 q^{49} - 36 q^{50} + 36 q^{51} + 30 q^{53} + 24 q^{54} - 4 q^{55} - 10 q^{56} + 60 q^{58} + 16 q^{59} + 8 q^{60} + 42 q^{61} - 110 q^{63} + 24 q^{64} + 12 q^{65} - 20 q^{66} + 130 q^{67} - 8 q^{69} + 20 q^{70} - 8 q^{71} - 120 q^{73} - 124 q^{74} - 24 q^{75} + 96 q^{76} - 50 q^{78} + 4 q^{79} - 2 q^{80} - 10 q^{81} - 70 q^{83} + 52 q^{85} - 44 q^{86} - 70 q^{87} + 10 q^{88} - 26 q^{89} + 32 q^{90} - 4 q^{91} - 10 q^{92} + 10 q^{94} + 2 q^{95} - 6 q^{96} - 10 q^{97} - 60 q^{98} - 184 q^{99}+O(q^{100}) \) 96 * q + 24 * q^4 + 8 * q^5 - 6 * q^6 + 34 * q^9 - 24 * q^11 + 10 * q^12 + 10 * q^14 - 8 * q^15 - 24 * q^16 + 30 * q^17 + 24 * q^19 + 2 * q^20 - 24 * q^24 - 60 * q^25 + 84 * q^26 - 30 * q^27 - 10 * q^28 - 4 * q^29 + 16 * q^30 - 14 * q^31 + 100 * q^33 + 8 * q^34 + 42 * q^35 - 34 * q^36 - 30 * q^37 + 32 * q^39 + 12 * q^41 + 10 * q^42 + 4 * q^44 - 18 * q^45 - 10 * q^46 + 10 * q^48 - 132 * q^49 - 36 * q^50 + 36 * q^51 + 30 * q^53 + 24 * q^54 - 4 * q^55 - 10 * q^56 + 60 * q^58 + 16 * q^59 + 8 * q^60 + 42 * q^61 - 110 * q^63 + 24 * q^64 + 12 * q^65 - 20 * q^66 + 130 * q^67 - 8 * q^69 + 20 * q^70 - 8 * q^71 - 120 * q^73 - 124 * q^74 - 24 * q^75 + 96 * q^76 - 50 * q^78 + 4 * q^79 - 2 * q^80 - 10 * q^81 - 70 * q^83 + 52 * q^85 - 44 * q^86 - 70 * q^87 + 10 * q^88 - 26 * q^89 + 32 * q^90 - 4 * q^91 - 10 * q^92 + 10 * q^94 + 2 * q^95 - 6 * q^96 - 10 * q^97 - 60 * q^98 - 184 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more