LMFDB - Embedded newform 175.2.n.a.64.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(29,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([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("175.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.4
Character	$\chi$	$=$	175.64
Dual form			175.2.n.a.134.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.635734 - 0.875013i) q^{2} +(-3.03925 - 0.987513i) q^{3} +(0.256544 - 0.789562i) q^{4} +(0.574707 - 2.16095i) q^{5} +(1.06807 + 3.28718i) q^{6} -1.00000i q^{7} +(-2.91125 + 0.945922i) q^{8} +(5.83482 + 4.23925i) q^{9} +O(q^{10})$	\(q+(-0.635734 - 0.875013i) q^{2} +(-3.03925 - 0.987513i) q^{3} +(0.256544 - 0.789562i) q^{4} +(0.574707 - 2.16095i) q^{5} +(1.06807 + 3.28718i) q^{6} -1.00000i q^{7} +(-2.91125 + 0.945922i) q^{8} +(5.83482 + 4.23925i) q^{9} +(-2.25622 + 0.870914i) q^{10} +(-3.82981 + 2.78252i) q^{11} +(-1.55941 + 2.14634i) q^{12} +(0.888450 - 1.22285i) q^{13} +(-0.875013 + 0.635734i) q^{14} +(-3.88065 + 6.00015i) q^{15} +(1.33519 + 0.970074i) q^{16} +(-0.595592 + 0.193520i) q^{17} -7.80058i q^{18} +(-0.975363 - 3.00186i) q^{19} +(-1.55877 - 1.00815i) q^{20} +(-0.987513 + 3.03925i) q^{21} +(4.86949 + 1.58219i) q^{22} +(3.61147 + 4.97076i) q^{23} +9.78213 q^{24} +(-4.33942 - 2.48383i) q^{25} -1.63482 q^{26} +(-7.91211 - 10.8901i) q^{27} +(-0.789562 - 0.256544i) q^{28} +(1.68504 - 5.18603i) q^{29} +(7.71727 - 0.418880i) q^{30} +(-0.975100 - 3.00105i) q^{31} +4.33712i q^{32} +(14.3875 - 4.67480i) q^{33} +(0.547970 + 0.398124i) q^{34} +(-2.16095 - 0.574707i) q^{35} +(4.84404 - 3.51940i) q^{36} +(0.491351 - 0.676287i) q^{37} +(-2.00659 + 2.76184i) q^{38} +(-3.90780 + 2.83918i) q^{39} +(0.370976 + 6.83470i) q^{40} +(-3.59928 - 2.61503i) q^{41} +(3.28718 - 1.06807i) q^{42} -4.43071i q^{43} +(1.21446 + 3.73771i) q^{44} +(12.5141 - 10.1724i) q^{45} +(2.05355 - 6.32016i) q^{46} +(-10.0035 - 3.25033i) q^{47} +(-3.10003 - 4.26682i) q^{48} -1.00000 q^{49} +(0.585337 + 5.37611i) q^{50} +2.00126 q^{51} +(-0.737586 - 1.01520i) q^{52} +(-10.2598 - 3.33360i) q^{53} +(-4.49897 + 13.8464i) q^{54} +(3.81187 + 9.87518i) q^{55} +(0.945922 + 2.91125i) q^{56} +10.0866i q^{57} +(-5.60908 + 1.82250i) q^{58} +(-1.92813 - 1.40087i) q^{59} +(3.74193 + 4.60332i) q^{60} +(-4.88772 + 3.55114i) q^{61} +(-2.00605 + 2.76109i) q^{62} +(4.23925 - 5.83482i) q^{63} +(6.46542 - 4.69740i) q^{64} +(-2.13191 - 2.62268i) q^{65} +(-13.2372 - 9.61736i) q^{66} +(11.1026 - 3.60747i) q^{67} +0.519903i q^{68} +(-6.06747 - 18.6738i) q^{69} +(0.870914 + 2.25622i) q^{70} +(-0.968731 + 2.98145i) q^{71} +(-20.9966 - 6.82222i) q^{72} +(6.22462 + 8.56745i) q^{73} -0.904129 q^{74} +(10.7358 + 11.8342i) q^{75} -2.62038 q^{76} +(2.78252 + 3.82981i) q^{77} +(4.96864 + 1.61441i) q^{78} +(2.31523 - 7.12553i) q^{79} +(2.86363 - 2.32778i) q^{80} +(6.60669 + 20.3333i) q^{81} +4.81187i q^{82} +(7.95931 - 2.58614i) q^{83} +(2.14634 + 1.55941i) q^{84} +(0.0758954 + 1.39826i) q^{85} +(-3.87693 + 2.81675i) q^{86} +(-10.2425 + 14.0976i) q^{87} +(8.51749 - 11.7233i) q^{88} +(10.3651 - 7.53070i) q^{89} +(-16.8567 - 4.48305i) q^{90} +(-1.22285 - 0.888450i) q^{91} +(4.85122 - 1.57626i) q^{92} +10.0839i q^{93} +(3.51547 + 10.8195i) q^{94} +(-7.04742 + 0.382522i) q^{95} +(4.28296 - 13.1816i) q^{96} +(11.7732 + 3.82534i) q^{97} +(0.635734 + 0.875013i) q^{98} -34.1421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 12 q^{4} - 6 q^{5} + 6 q^{9}+O(q^{10}) $ 56 * q + 12 * q^4 - 6 * q^5 + 6 * q^9	$ 56 q + 12 q^{4} - 6 q^{5} + 6 q^{9} - 4 q^{10} + 8 q^{11} - 40 q^{12} - 4 q^{14} - 18 q^{15} - 32 q^{16} + 12 q^{19} + 12 q^{20} + 4 q^{21} - 30 q^{22} + 10 q^{23} - 28 q^{24} + 4 q^{25} + 12 q^{26} + 30 q^{27} - 2 q^{29} + 28 q^{30} + 12 q^{31} + 20 q^{33} + 2 q^{35} - 14 q^{36} - 70 q^{37} - 70 q^{38} - 4 q^{39} - 30 q^{40} + 4 q^{41} + 50 q^{42} + 22 q^{44} - 52 q^{45} - 4 q^{46} - 10 q^{47} + 30 q^{48} - 56 q^{49} - 54 q^{50} - 44 q^{51} - 20 q^{53} + 54 q^{54} - 2 q^{55} + 12 q^{56} + 10 q^{58} - 6 q^{59} + 16 q^{60} - 4 q^{61} + 50 q^{62} + 20 q^{63} + 24 q^{64} - 18 q^{65} - 74 q^{66} + 10 q^{67} - 78 q^{69} + 8 q^{70} - 8 q^{71} + 140 q^{72} + 40 q^{73} + 60 q^{74} - 8 q^{75} + 52 q^{76} - 20 q^{77} - 90 q^{78} + 124 q^{80} - 72 q^{81} - 30 q^{83} - 12 q^{84} + 96 q^{85} - 20 q^{86} + 30 q^{87} + 140 q^{88} + 38 q^{89} - 8 q^{90} + 8 q^{91} + 80 q^{92} + 88 q^{94} - 70 q^{95} - 28 q^{96} - 30 q^{97} + 60 q^{99}+O(q^{100}) $ 56 * q + 12 * q^4 - 6 * q^5 + 6 * q^9 - 4 * q^10 + 8 * q^11 - 40 * q^12 - 4 * q^14 - 18 * q^15 - 32 * q^16 + 12 * q^19 + 12 * q^20 + 4 * q^21 - 30 * q^22 + 10 * q^23 - 28 * q^24 + 4 * q^25 + 12 * q^26 + 30 * q^27 - 2 * q^29 + 28 * q^30 + 12 * q^31 + 20 * q^33 + 2 * q^35 - 14 * q^36 - 70 * q^37 - 70 * q^38 - 4 * q^39 - 30 * q^40 + 4 * q^41 + 50 * q^42 + 22 * q^44 - 52 * q^45 - 4 * q^46 - 10 * q^47 + 30 * q^48 - 56 * q^49 - 54 * q^50 - 44 * q^51 - 20 * q^53 + 54 * q^54 - 2 * q^55 + 12 * q^56 + 10 * q^58 - 6 * q^59 + 16 * q^60 - 4 * q^61 + 50 * q^62 + 20 * q^63 + 24 * q^64 - 18 * q^65 - 74 * q^66 + 10 * q^67 - 78 * q^69 + 8 * q^70 - 8 * q^71 + 140 * q^72 + 40 * q^73 + 60 * q^74 - 8 * q^75 + 52 * q^76 - 20 * q^77 - 90 * q^78 + 124 * q^80 - 72 * q^81 - 30 * q^83 - 12 * q^84 + 96 * q^85 - 20 * q^86 + 30 * q^87 + 140 * q^88 + 38 * q^89 - 8 * q^90 + 8 * q^91 + 80 * q^92 + 88 * q^94 - 70 * q^95 - 28 * q^96 - 30 * q^97 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.635734	−	0.875013i	−0.449532	−	0.618728i	0.522765	−	0.852477i	$-0.324901\pi$
$2$	−0.635734	−	0.875013i	−0.449532	−	0.618728i	−0.972297	+	0.233749i	$0.924901\pi$
$3$	−3.03925	−	0.987513i	−1.75471	−	0.570141i	−0.758083	−	0.652159i	$-0.773864\pi$
$3$	−3.03925	−	0.987513i	−1.75471	−	0.570141i	−0.996631	+	0.0820177i	$0.973864\pi$
$4$	0.256544	−	0.789562i	0.128272	−	0.394781i
$5$	0.574707	−	2.16095i	0.257017	−	0.966407i
$5$	0.574707	−	2.16095i	0.257017	−	0.966407i
$6$	1.06807	+	3.28718i	0.436038	+	1.34199i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−2.91125	+	0.945922i	−1.02928	+	0.334434i
$9$	5.83482	+	4.23925i	1.94494	+	1.41308i
$10$	−2.25622	+	0.870914i	−0.713480	+	0.275407i
$11$	−3.82981	+	2.78252i	−1.15473	+	0.838962i	−0.989103	−	0.147226i	$-0.952966\pi$
$11$	−3.82981	+	2.78252i	−1.15473	+	0.838962i	−0.165629	+	0.986188i	$0.552966\pi$
$12$	−1.55941	+	2.14634i	−0.450162	+	0.619594i
$13$	0.888450	−	1.22285i	0.246412	−	0.339157i	−0.667839	−	0.744306i	$-0.732780\pi$
$13$	0.888450	−	1.22285i	0.246412	−	0.339157i	0.914251	+	0.405149i	$0.132780\pi$
$14$	−0.875013	+	0.635734i	−0.233857	+	0.169907i
$15$	−3.88065	+	6.00015i	−1.00198	+	1.54923i
$16$	1.33519	+	0.970074i	0.333798	+	0.242518i
$17$	−0.595592	+	0.193520i	−0.144452	+	0.0469354i	−0.380351	−	0.924842i	$-0.624197\pi$
$17$	−0.595592	+	0.193520i	−0.144452	+	0.0469354i	0.235898	+	0.971778i	$0.424197\pi$
$18$		−	7.80058i		−	1.83861i
$19$	−0.975363	−	3.00186i	−0.223764	−	0.688674i	−0.998415	−	0.0562849i	$-0.982074\pi$
$19$	−0.975363	−	3.00186i	−0.223764	−	0.688674i	0.774651	−	0.632389i	$-0.217926\pi$
$20$	−1.55877	−	1.00815i	−0.348551	−	0.225428i
$21$	−0.987513	+	3.03925i	−0.215493	+	0.663219i
$22$	4.86949	+	1.58219i	1.03818	+	0.337324i
$23$	3.61147	+	4.97076i	0.753043	+	1.03647i	0.997761	+	0.0668806i	$0.0213047\pi$
$23$	3.61147	+	4.97076i	0.753043	+	1.03647i	−0.244718	+	0.969594i	$0.578695\pi$
$24$	9.78213			1.99677
$25$	−4.33942	−	2.48383i	−0.867885	−	0.496766i
$26$	−1.63482			−0.320615
$27$	−7.91211	−	10.8901i	−1.52269	−	2.09580i
$28$	−0.789562	−	0.256544i	−0.149213	−	0.0484823i
$29$	1.68504	−	5.18603i	0.312904	−	0.963021i	−0.663704	−	0.747995i	$-0.731017\pi$
$29$	1.68504	−	5.18603i	0.312904	−	0.963021i	0.976608	−	0.215026i	$-0.0689835\pi$
$30$	7.71727	−	0.418880i	1.40897	−	0.0764767i
$31$	−0.975100	−	3.00105i	−0.175133	−	0.539004i	0.824506	−	0.565853i	$-0.191453\pi$
$31$	−0.975100	−	3.00105i	−0.175133	−	0.539004i	−0.999640	+	0.0268483i	$0.991453\pi$
$32$			4.33712i			0.766702i
$33$	14.3875	−	4.67480i	2.50455	−	0.813778i
$34$	0.547970	+	0.398124i	0.0939762	+	0.0682777i
$35$	−2.16095	−	0.574707i	−0.365267	−	0.0971433i
$36$	4.84404	−	3.51940i	0.807340	−	0.586567i
$37$	0.491351	−	0.676287i	0.0807777	−	0.111181i	−0.766716	−	0.641986i	$-0.778111\pi$
$37$	0.491351	−	0.676287i	0.0807777	−	0.111181i	0.847494	+	0.530806i	$0.178111\pi$
$38$	−2.00659	+	2.76184i	−0.325513	+	0.448030i
$39$	−3.90780	+	2.83918i	−0.625749	+	0.454633i
$40$	0.370976	+	6.83470i	0.0586564	+	1.08066i
$41$	−3.59928	−	2.61503i	−0.562112	−	0.408399i	0.270119	−	0.962827i	$-0.412937\pi$
$41$	−3.59928	−	2.61503i	−0.562112	−	0.408399i	−0.832231	+	0.554428i	$0.812937\pi$
$42$	3.28718	−	1.06807i	0.507223	−	0.164807i
$43$		−	4.43071i		−	0.675677i	−0.941204	−	0.337838i	$-0.890304\pi$
$43$		−	4.43071i		−	0.675677i	0.941204	−	0.337838i	$-0.109696\pi$
$44$	1.21446	+	3.73771i	0.183086	+	0.563482i
$45$	12.5141	−	10.1724i	1.86550	−	1.51642i
$46$	2.05355	−	6.32016i	0.302779	−	0.931857i
$47$	−10.0035	−	3.25033i	−1.45916	−	0.474109i	−0.531344	−	0.847156i	$-0.678313\pi$
$47$	−10.0035	−	3.25033i	−1.45916	−	0.474109i	−0.927812	+	0.373047i	$0.878313\pi$
$48$	−3.10003	−	4.26682i	−0.447450	−	0.615862i
$49$	−1.00000			−0.142857
$50$	0.585337	+	5.37611i	0.0827791	+	0.760296i
$51$	2.00126			0.280232
$52$	−0.737586	−	1.01520i	−0.102285	−	0.140783i
$53$	−10.2598	−	3.33360i	−1.40929	−	0.457905i	−0.497104	−	0.867691i	$-0.665603\pi$
$53$	−10.2598	−	3.33360i	−1.40929	−	0.457905i	−0.912182	+	0.409786i	$0.865603\pi$
$54$	−4.49897	+	13.8464i	−0.612232	+	1.88426i
$55$	3.81187	+	9.87518i	0.513993	+	1.33157i
$56$	0.945922	+	2.91125i	0.126404	+	0.389032i
$57$			10.0866i			1.33600i
$58$	−5.60908	+	1.82250i	−0.736508	+	0.239306i
$59$	−1.92813	−	1.40087i	−0.251021	−	0.182377i	0.455158	−	0.890410i	$-0.349583\pi$
$59$	−1.92813	−	1.40087i	−0.251021	−	0.182377i	−0.706179	+	0.708033i	$0.749583\pi$
$60$	3.74193	+	4.60332i	0.483081	+	0.594285i
$61$	−4.88772	+	3.55114i	−0.625809	+	0.454677i	−0.854946	−	0.518718i	$-0.826410\pi$
$61$	−4.88772	+	3.55114i	−0.625809	+	0.454677i	0.229137	+	0.973394i	$0.426410\pi$
$62$	−2.00605	+	2.76109i	−0.254769	+	0.350659i
$63$	4.23925	−	5.83482i	0.534095	−	0.735119i
$64$	6.46542	−	4.69740i	0.808177	−	0.587175i
$65$	−2.13191	−	2.62268i	−0.264431	−	0.325303i
$66$	−13.2372	−	9.61736i	−1.62938	−	1.18382i
$67$	11.1026	−	3.60747i	1.35640	−	0.440722i	0.461563	−	0.887107i	$-0.347289\pi$
$67$	11.1026	−	3.60747i	1.35640	−	0.440722i	0.894841	+	0.446385i	$0.147289\pi$
$68$			0.519903i			0.0630475i
$69$	−6.06747	−	18.6738i	−0.730438	−	2.24806i
$70$	0.870914	+	2.25622i	0.104094	+	0.269670i
$71$	−0.968731	+	2.98145i	−0.114967	+	0.353833i	−0.991940	−	0.126707i	$-0.959559\pi$
$71$	−0.968731	+	2.98145i	−0.114967	+	0.353833i	0.876973	+	0.480540i	$0.159559\pi$
$72$	−20.9966	−	6.82222i	−2.47448	−	0.804006i
$73$	6.22462	+	8.56745i	0.728536	+	1.00274i	0.999197	+	0.0400692i	$0.0127578\pi$
$73$	6.22462	+	8.56745i	0.728536	+	1.00274i	−0.270661	+	0.962675i	$0.587242\pi$
$74$	−0.904129			−0.105103
$75$	10.7358	+	11.8342i	1.23966	+	1.36650i
$76$	−2.62038			−0.300578
$77$	2.78252	+	3.82981i	0.317098	+	0.436448i
$78$	4.96864	+	1.61441i	0.562588	+	0.182796i
$79$	2.31523	−	7.12553i	0.260483	−	0.801685i	−0.732216	−	0.681072i	$-0.761514\pi$
$79$	2.31523	−	7.12553i	0.260483	−	0.801685i	0.992700	−	0.120613i	$-0.0384860\pi$
$80$	2.86363	−	2.32778i	0.320163	−	0.260253i
$81$	6.60669	+	20.3333i	0.734076	+	2.25925i
$82$			4.81187i			0.531383i
$83$	7.95931	−	2.58614i	0.873648	−	0.283865i	0.162331	−	0.986736i	$-0.448099\pi$
$83$	7.95931	−	2.58614i	0.873648	−	0.283865i	0.711317	+	0.702871i	$0.248099\pi$
$84$	2.14634	+	1.55941i	0.234185	+	0.170145i
$85$	0.0758954	+	1.39826i	0.00823201	+	0.151663i
$86$	−3.87693	+	2.81675i	−0.418060	+	0.303738i
$87$	−10.2425	+	14.0976i	−1.09812	+	1.51143i
$88$	8.51749	−	11.7233i	0.907968	−	1.24971i
$89$	10.3651	−	7.53070i	1.09870	−	0.798253i	0.117853	−	0.993031i	$-0.462399\pi$
$89$	10.3651	−	7.53070i	1.09870	−	0.798253i	0.980847	+	0.194778i	$0.0623987\pi$
$90$	−16.8567	−	4.48305i	−1.77685	−	0.472555i
$91$	−1.22285	−	0.888450i	−0.128189	−	0.0931348i
$92$	4.85122	−	1.57626i	0.505775	−	0.164336i
$93$			10.0839i			1.04565i
$94$	3.51547	+	10.8195i	0.362593	+	1.11595i
$95$	−7.04742	+	0.382522i	−0.723050	+	0.0392460i
$96$	4.28296	−	13.1816i	0.437128	−	1.34534i
$97$	11.7732	+	3.82534i	1.19539	+	0.388404i	0.838061	−	0.545576i	$-0.183689\pi$
$97$	11.7732	+	3.82534i	1.19539	+	0.388404i	0.357324	+	0.933980i	$0.383689\pi$
$98$	0.635734	+	0.875013i	0.0642188	+	0.0883897i
$99$	−34.1421			−3.43141
$100$	−3.07439	+	2.78903i	−0.307439	+	0.278903i
$101$	−6.84519			−0.681122			−0.340561	−	0.940222i	$-0.610617\pi$
$101$	−6.84519			−0.681122			−0.340561	+	0.940222i	$0.610617\pi$
$102$	−1.27227	−	1.75113i	−0.125973	−	0.173387i
$103$	−5.72986	−	1.86175i	−0.564580	−	0.183443i	0.0128009	−	0.999918i	$-0.495925\pi$
$103$	−5.72986	−	1.86175i	−0.564580	−	0.183443i	−0.577381	+	0.816475i	$0.695925\pi$
$104$	−1.42978	+	4.40042i	−0.140202	+	0.431496i
$105$	6.00015	+	3.88065i	0.585554	+	0.378713i
$106$	3.60554	+	11.0967i	0.350201	+	1.07781i
$107$		−	6.71648i		−	0.649307i	−0.945833	−	0.324653i	$-0.894752\pi$
$107$		−	6.71648i		−	0.649307i	0.945833	−	0.324653i	$-0.105248\pi$
$108$	−10.6282	+	3.45331i	−1.02270	+	0.332295i
$109$	−9.78078	−	7.10616i	−0.936829	−	0.680646i	0.0108262	−	0.999941i	$-0.496554\pi$
$109$	−9.78078	−	7.10616i	−0.936829	−	0.680646i	−0.947655	+	0.319295i	$0.896554\pi$
$110$	6.21757	−	9.61343i	0.592822	−	0.916604i
$111$	−2.16118	+	1.57019i	−0.205130	+	0.149036i
$112$	0.970074	−	1.33519i	0.0916633	−	0.126164i
$113$	−4.84382	+	6.66695i	−0.455668	+	0.627174i	−0.973603	−	0.228246i	$-0.926701\pi$
$113$	−4.84382	+	6.66695i	−0.455668	+	0.627174i	0.517935	+	0.855420i	$0.326701\pi$
$114$	8.82590	−	6.41239i	0.826621	−	0.600576i
$115$	12.8171	−	4.94748i	1.19520	−	0.461354i
$116$	−3.66240	−	2.66089i	−0.340045	−	0.247057i
$117$	10.3679	−	3.36873i	0.958512	−	0.311440i
$118$			2.57771i			0.237298i
$119$	0.193520	+	0.595592i	0.0177399	+	0.0545978i
$120$	5.62186	−	21.1387i	0.513204	−	1.92969i
$121$	3.52585	−	10.8515i	0.320532	−	0.986496i
$122$	6.21458	+	2.01924i	0.562642	+	0.182813i
$123$	8.35673	+	11.5021i	0.753501	+	1.03711i
$124$	−2.61967			−0.235253
$125$	−7.86133	+	7.94981i	−0.703139	+	0.711052i
$126$	−7.80058			−0.694931
$127$	−4.41613	−	6.07828i	−0.391868	−	0.539360i	0.566812	−	0.823847i	$-0.308177\pi$
$127$	−4.41613	−	6.07828i	−0.391868	−	0.539360i	−0.958680	+	0.284487i	$0.908177\pi$
$128$	0.0291157	+	0.00946027i	0.00257349	+	0.000836177i
$129$	−4.37538	+	13.4660i	−0.385231	+	1.18562i
$130$	−0.939545	+	3.53278i	−0.0824036	+	0.309845i
$131$	0.890551	+	2.74083i	0.0778078	+	0.239468i	0.982393	−	0.186824i	$-0.0598196\pi$
$131$	0.890551	+	2.74083i	0.0778078	+	0.239468i	−0.904586	+	0.426292i	$0.859820\pi$
$132$		−	12.5592i		−	1.09313i
$133$	−3.00186	+	0.975363i	−0.260294	+	0.0845747i
$134$	−10.2149	−	7.42157i	−0.882434	−	0.641126i
$135$	−28.0801	+	10.8391i	−2.41675	+	0.932879i
$136$	1.55086	−	1.12677i	0.132985	−	0.0966196i
$137$	9.09664	−	12.5205i	0.777179	−	1.06969i	−0.218409	−	0.975857i	$-0.570087\pi$
$137$	9.09664	−	12.5205i	0.777179	−	1.06969i	0.995588	−	0.0938373i	$-0.0299134\pi$
$138$	−12.4825	+	17.1807i	−1.06258	+	1.46252i
$139$	−4.94263	+	3.59103i	−0.419228	+	0.304587i	−0.777327	−	0.629097i	$-0.783425\pi$
$139$	−4.94263	+	3.59103i	−0.419228	+	0.304587i	0.358099	+	0.933684i	$0.383425\pi$
$140$	−1.00815	+	1.55877i	−0.0852039	+	0.131740i
$141$	27.1933	+	19.7571i	2.29009	+	1.66385i
$142$	3.22466	−	1.04776i	0.270607	−	0.0879257i
$143$			7.15540i			0.598365i
$144$	3.67823	+	11.3204i	0.306519	+	0.943368i
$145$	−10.2383	−	6.62174i	−0.850248	−	0.549906i
$146$	3.53943	−	10.8932i	0.292925	−	0.901531i
$147$	3.03925	+	0.987513i	0.250673	+	0.0814487i
$148$	−0.407917	−	0.561450i	−0.0335306	−	0.0461509i
$149$	23.5516			1.92942			0.964710	−	0.263316i	$-0.0848161\pi$
$149$	23.5516			1.92942			0.964710	+	0.263316i	$0.0848161\pi$
$150$	3.52999	−	16.9174i	0.288222	−	1.38130i
$151$	5.35326			0.435642			0.217821	−	0.975989i	$-0.430105\pi$
$151$	5.35326			0.435642			0.217821	+	0.975989i	$0.430105\pi$
$152$	5.67905	+	7.81655i	0.460632	+	0.634006i
$153$	−4.29555	−	1.39571i	−0.347275	−	0.112836i
$154$	1.58219	−	4.86949i	0.127497	−	0.392394i
$155$	−7.04552	+	0.382419i	−0.565910	+	0.0307166i
$156$	1.23919	+	3.81383i	0.0992144	+	0.305350i
$157$		−	7.56734i		−	0.603940i	−0.953317	−	0.301970i	$-0.902356\pi$
$157$		−	7.56734i		−	0.603940i	0.953317	−	0.301970i	$-0.0976442\pi$
$158$	−7.70680	+	2.50409i	−0.613120	+	0.199215i
$159$	27.8900	+	20.2633i	2.21182	+	1.60698i
$160$	9.37230	+	2.49257i	0.740946	+	0.197055i
$161$	4.97076	−	3.61147i	0.391751	−	0.284624i
$162$	13.5918	−	18.7075i	1.06787	−	1.46980i
$163$	1.99706	−	2.74872i	0.156422	−	0.215296i	−0.723612	−	0.690207i	$-0.757520\pi$
$163$	1.99706	−	2.74872i	0.156422	−	0.215296i	0.880034	+	0.474910i	$0.157520\pi$
$164$	−2.98810	+	2.17098i	−0.233331	+	0.169525i
$165$	−1.83338	−	33.7774i	−0.142729	−	2.62957i
$166$	−7.32291	−	5.32040i	−0.568368	−	0.412943i
$167$	11.3040	−	3.67288i	0.874728	−	0.284216i	0.162961	−	0.986632i	$-0.447895\pi$
$167$	11.3040	−	3.67288i	0.874728	−	0.284216i	0.711767	+	0.702416i	$0.247895\pi$
$168$		−	9.78213i		−	0.754708i
$169$	3.31121	+	10.1909i	0.254709	+	0.783912i
$170$	1.17525	−	0.955333i	0.0901375	−	0.0732707i
$171$	7.03455	−	21.6501i	0.537946	−	1.65563i
$172$	−3.49832	−	1.13667i	−0.266744	−	0.0866705i
$173$	−15.0399	−	20.7007i	−1.14346	−	1.57384i	−0.759515	−	0.650490i	$-0.774563\pi$
$173$	−15.0399	−	20.7007i	−1.14346	−	1.57384i	−0.383950	−	0.923354i	$-0.625437\pi$
$174$	18.8472			1.42880
$175$	−2.48383	+	4.33942i	−0.187760	+	0.328030i
$176$	−7.81279			−0.588911
$177$	4.47669	+	6.16163i	0.336489	+	0.463137i
$178$	−13.1789	−	4.28209i	−0.987802	−	0.320956i
$179$	2.87123	−	8.83672i	0.214605	−	0.660488i	−0.784576	−	0.620033i	$-0.787119\pi$
$179$	2.87123	−	8.83672i	0.214605	−	0.660488i	0.999181	−	0.0404549i	$-0.0128807\pi$
$180$	−4.82135	−	12.4904i	−0.359362	−	0.930976i
$181$	1.22697	+	3.77621i	0.0911996	+	0.280684i	0.986245	−	0.165292i	$-0.0528567\pi$
$181$	1.22697	+	3.77621i	0.0911996	+	0.280684i	−0.895045	+	0.445976i	$0.852857\pi$
$182$			1.63482i			0.121181i
$183$	18.3618	−	5.96612i	1.35734	−	0.441028i
$184$	−15.2158	−	11.0550i	−1.12173	−	0.814982i
$185$	−1.17904	−	1.45045i	−0.0866848	−	0.106639i
$186$	8.82352	−	6.41066i	0.646972	−	0.470053i
$187$	1.74253	−	2.39839i	0.127427	−	0.175388i
$188$	−5.13267	+	7.06451i	−0.374338	+	0.515232i
$189$	−10.8901	+	7.91211i	−0.792137	+	0.575521i
$190$	4.81500	+	5.92340i	0.349317	+	0.429729i
$191$	7.92919	+	5.76089i	0.573736	+	0.416844i	0.836460	−	0.548027i	$-0.184621\pi$
$191$	7.92919	+	5.76089i	0.573736	+	0.416844i	−0.262724	+	0.964871i	$0.584621\pi$
$192$	−24.2888	+	7.89191i	−1.75289	+	0.569549i
$193$			6.32794i			0.455495i	0.973720	+	0.227748i	$0.0731361\pi$
$193$			6.32794i			0.455495i	−0.973720	+	0.227748i	$0.926864\pi$
$194$	−4.13739	−	12.7336i	−0.297048	−	0.914218i
$195$	3.88950	+	10.0763i	0.278533	+	0.721576i
$196$	−0.256544	+	0.789562i	−0.0183246	+	0.0563973i
$197$	12.8845	+	4.18643i	0.917983	+	0.298271i	0.729639	−	0.683832i	$-0.239688\pi$
$197$	12.8845	+	4.18643i	0.917983	+	0.298271i	0.188344	+	0.982103i	$0.439688\pi$
$198$	21.7053	+	29.8748i	1.54253	+	2.12311i
$199$	−19.5717			−1.38740			−0.693702	−	0.720262i	$-0.744021\pi$
$199$	−19.5717			−1.38740			−0.693702	+	0.720262i	$0.744021\pi$
$200$	14.9827	+	3.12629i	1.05943	+	0.221062i
$201$	−37.3062			−2.63137
$202$	4.35172	+	5.98963i	0.306186	+	0.421429i
$203$	−5.18603	−	1.68504i	−0.363988	−	0.118267i
$204$	0.513411	−	1.58012i	0.0359460	−	0.110630i
$205$	−7.71947	+	6.27498i	−0.539152	+	0.438264i
$206$	2.01362	+	6.19728i	0.140295	+	0.431785i
$207$			44.3134i			3.08000i
$208$	2.37250	−	0.770873i	0.164503	−	0.0534504i
$209$	12.0882	+	8.78259i	0.836158	+	0.607505i
$210$	−0.418880	−	7.71727i	−0.0289055	−	0.532542i
$211$	5.75133	−	4.17859i	0.395938	−	0.287666i	−0.371946	−	0.928254i	$-0.621309\pi$
$211$	5.75133	−	4.17859i	0.395938	−	0.287666i	0.767884	+	0.640588i	$0.221309\pi$
$212$	−5.26416	+	7.24550i	−0.361544	+	0.497623i
$213$	5.88844	−	8.10474i	0.403469	−	0.555327i
$214$	−5.87701	+	4.26990i	−0.401744	+	0.291884i
$215$	−9.57455	−	2.54636i	−0.652979	−	0.173660i
$216$	33.3353	+	24.2195i	2.26818	+	1.64793i
$217$	−3.00105	+	0.975100i	−0.203725	+	0.0661941i
$218$			13.0759i			0.885614i
$219$	−10.4577	−	32.1855i	−0.706667	−	2.17490i
$220$	8.77498	−	0.476291i	0.591609	−	0.0321115i
$221$	−0.292509	+	0.900250i	−0.0196763	+	0.0605574i
$222$	2.74788	+	0.892839i	0.184425	+	0.0599234i
$223$	5.09800	+	7.01680i	0.341388	+	0.469880i	0.944846	−	0.327515i	$-0.106211\pi$
$223$	5.09800	+	7.01680i	0.341388	+	0.469880i	−0.603458	+	0.797394i	$0.706211\pi$
$224$	4.33712			0.289786
$225$	−14.7902	−	32.8886i	−0.986014	−	2.19257i
$226$	8.91305			0.592887
$227$	3.91664	+	5.39080i	0.259957	+	0.357800i	0.918967	−	0.394334i	$-0.129025\pi$
$227$	3.91664	+	5.39080i	0.259957	+	0.357800i	−0.659010	+	0.752134i	$0.729025\pi$
$228$	7.96399	+	2.58766i	0.527428	+	0.171372i
$229$	−4.04355	+	12.4448i	−0.267205	+	0.822373i	0.723972	+	0.689830i	$0.242315\pi$
$229$	−4.04355	+	12.4448i	−0.267205	+	0.822373i	−0.991177	+	0.132544i	$0.957685\pi$
$230$	−12.4774	−	8.06985i	−0.822734	−	0.532110i
$231$	−4.67480	−	14.3875i	−0.307579	−	0.946631i
$232$			16.6917i			1.09587i
$233$	−16.2048	+	5.26526i	−1.06161	+	0.344939i	−0.787216	−	0.616678i	$-0.788478\pi$
$233$	−16.2048	+	5.26526i	−1.06161	+	0.344939i	−0.274397	+	0.961617i	$0.588478\pi$
$234$	−9.53891	−	6.93043i	−0.623578	−	0.453056i
$235$	−12.7729	+	19.7490i	−0.833210	+	1.28828i
$236$	−1.60072	+	1.16299i	−0.104198	+	0.0757043i
$237$	−14.0731	+	19.3700i	−0.914147	+	1.25822i
$238$	0.398124	−	0.547970i	0.0258065	−	0.0355196i
$239$	21.1591	−	15.3730i	1.36867	−	0.994398i	0.370831	−	0.928700i	$-0.379073\pi$
$239$	21.1591	−	15.3730i	1.36867	−	0.994398i	0.997840	−	0.0656974i	$-0.0209272\pi$
$240$	−11.0020	+	4.24683i	−0.710176	+	0.274132i
$241$	6.89901	+	5.01242i	0.444404	+	0.322879i	0.787382	−	0.616465i	$-0.211436\pi$
$241$	6.89901	+	5.01242i	0.444404	+	0.322879i	−0.342978	+	0.939343i	$0.611436\pi$
$242$	−11.7367	+	3.81348i	−0.754462	+	0.245139i
$243$		−	27.9395i		−	1.79232i
$244$	1.54993	+	4.77018i	0.0992239	+	0.305380i
$245$	−0.574707	+	2.16095i	−0.0367167	+	0.138058i
$246$	4.75179	−	14.6245i	0.302963	−	0.932424i
$247$	−4.53737	−	1.47428i	−0.288706	−	0.0938063i
$248$	5.67752	+	7.81444i	0.360523	+	0.496217i
$249$	−26.7442			−1.69484
$250$	11.9539	+	1.82480i	0.756031	+	0.115411i
$251$	−6.38022			−0.402716			−0.201358	−	0.979518i	$-0.564535\pi$
$251$	−6.38022			−0.402716			−0.201358	+	0.979518i	$0.564535\pi$
$252$	−3.51940	−	4.84404i	−0.221701	−	0.305146i
$253$	−27.6625	−	8.98809i	−1.73913	−	0.565076i
$254$	−2.51109	+	7.72834i	−0.157560	+	0.484919i
$255$	1.15014	−	4.32462i	0.0720244	−	0.270818i
$256$	−4.94937	−	15.2326i	−0.309336	−	0.952038i
$257$		−	15.4987i		−	0.966781i	−0.875405	−	0.483390i	$-0.839405\pi$
$257$		−	15.4987i		−	0.966781i	0.875405	−	0.483390i	$-0.160595\pi$
$258$	14.5645	−	4.73231i	0.906749	−	0.294621i
$259$	−0.676287	−	0.491351i	−0.0420224	−	0.0305311i
$260$	−2.61769	+	1.01044i	−0.162343	+	0.0626651i
$261$	31.8168	−	23.1162i	1.96941	−	1.43086i
$262$	1.83211	−	2.52168i	0.113188	−	0.155790i
$263$	4.34650	−	5.98245i	0.268017	−	0.368893i	−0.653702	−	0.756752i	$-0.726785\pi$
$263$	4.34650	−	5.98245i	0.268017	−	0.368893i	0.921719	+	0.387859i	$0.126785\pi$
$264$	−37.4637	+	27.2190i	−2.30573	+	1.67521i
$265$	−13.1001	+	20.2550i	−0.804733	+	1.24425i
$266$	2.76184	+	2.00659i	0.169339	+	0.123032i
$267$	−38.9389	+	12.6520i	−2.38302	+	0.774291i
$268$		−	9.69170i		−	0.592015i
$269$	4.53999	+	13.9727i	0.276808	+	0.851928i	0.988735	+	0.149674i	$0.0478226\pi$
$269$	4.53999	+	13.9727i	0.276808	+	0.851928i	−0.711927	+	0.702253i	$0.752177\pi$
$270$	27.3358	+	17.6797i	1.66360	+	1.07595i
$271$	−0.681130	+	2.09630i	−0.0413757	+	0.127341i	−0.969611	−	0.244653i	$-0.921326\pi$
$271$	−0.681130	+	2.09630i	−0.0413757	+	0.127341i	0.928235	+	0.371994i	$0.121326\pi$
$272$	−0.982958	−	0.319382i	−0.0596006	−	0.0193654i
$273$	2.83918	+	3.90780i	0.171835	+	0.236511i
$274$	−16.7386			−1.01122
$275$	23.5305	−	2.56194i	1.41894	−	0.154491i
$276$	−16.3007			−0.981185
$277$	4.89326	+	6.73499i	0.294007	+	0.404666i	0.930311	−	0.366773i	$-0.119537\pi$
$277$	4.89326	+	6.73499i	0.294007	+	0.404666i	−0.636303	+	0.771439i	$0.719537\pi$
$278$	6.28439	+	2.04192i	0.376913	+	0.122466i
$279$	7.03266	−	21.6443i	0.421034	−	1.29581i
$280$	6.83470	−	0.370976i	0.408451	−	0.0221701i
$281$	−7.91576	−	24.3622i	−0.472215	−	1.45333i	−0.849678	−	0.527302i	$-0.823203\pi$
$281$	−7.91576	−	24.3622i	−0.472215	−	1.45333i	0.377463	−	0.926025i	$-0.376797\pi$
$282$		−	36.3548i		−	2.16490i
$283$	15.5992	−	5.06847i	0.927274	−	0.301289i	0.193826	−	0.981036i	$-0.437910\pi$
$283$	15.5992	−	5.06847i	0.927274	−	0.301289i	0.733447	+	0.679746i	$0.237910\pi$
$284$	2.10551	+	1.52975i	0.124939	+	0.0907737i
$285$	21.7966	+	5.79684i	1.29112	+	0.343375i
$286$	6.26107	−	4.54893i	0.370225	−	0.268984i
$287$	−2.61503	+	3.59928i	−0.154360	+	0.212458i
$288$	−18.3861	+	25.3063i	−1.08341	+	1.49119i
$289$	−13.4360	+	9.76183i	−0.790353	+	0.574225i
$290$	0.714756	+	13.1684i	0.0419719	+	0.773272i
$291$	−32.0041	−	23.2523i	−1.87611	−	1.36308i
$292$	8.36142	−	2.71679i	0.489315	−	0.158988i
$293$			8.33846i			0.487138i	0.969884	+	0.243569i	$0.0783182\pi$
$293$			8.33846i			0.487138i	−0.969884	+	0.243569i	$0.921682\pi$
$294$	−1.06807	−	3.28718i	−0.0622911	−	0.191712i
$295$	−4.13531	+	3.36150i	−0.240767	+	0.195714i
$296$	−0.790731	+	2.43362i	−0.0459603	+	0.141451i
$297$	60.6038	+	19.6914i	3.51659	+	1.14261i
$298$	−14.9725	−	20.6079i	−0.867336	−	1.19379i
$299$	9.28708			0.537086
$300$	12.0981	−	5.44057i	0.698482	−	0.314111i
$301$	−4.43071			−0.255382
$302$	−3.40325	−	4.68417i	−0.195835	−	0.269544i
$303$	20.8043	+	6.75972i	1.19517	+	0.388336i
$304$	1.60973	−	4.95423i	0.0923242	−	0.284145i
$305$	4.86483	+	12.6030i	0.278559	+	0.721645i
$306$	1.50957	+	4.64597i	0.0862961	+	0.265592i
$307$		−	25.6753i		−	1.46537i	−0.680569	−	0.732684i	$-0.738268\pi$
$307$		−	25.6753i		−	1.46537i	0.680569	−	0.732684i	$-0.261732\pi$
$308$	3.73771	−	1.21446i	0.212976	−	0.0692001i
$309$	15.5760	+	11.3166i	0.886088	+	0.643780i
$310$	4.81370	+	5.92180i	0.273400	+	0.336336i
$311$	9.11025	−	6.61898i	0.516595	−	0.375328i	−0.298725	−	0.954339i	$-0.596561\pi$
$311$	9.11025	−	6.61898i	0.516595	−	0.375328i	0.815320	+	0.579011i	$0.196561\pi$
$312$	8.69094	−	11.9620i	0.492027	−	0.677218i
$313$	−1.15753	+	1.59320i	−0.0654274	+	0.0900531i	−0.840477	−	0.541848i	$-0.817725\pi$
$313$	−1.15753	+	1.59320i	−0.0654274	+	0.0900531i	0.775049	+	0.631901i	$0.217725\pi$
$314$	−6.62152	+	4.81082i	−0.373674	+	0.271490i
$315$	−10.1724	−	12.5141i	−0.573152	−	0.705091i
$316$	−5.03209	−	3.65603i	−0.283077	−	0.205668i
$317$	−29.2692	+	9.51016i	−1.64392	+	0.534144i	−0.977411	−	0.211349i	$-0.932214\pi$
$317$	−29.2692	+	9.51016i	−1.64392	+	0.534144i	−0.666514	+	0.745492i	$0.732214\pi$
$318$		−	37.2862i		−	2.09091i
$319$	7.97684	+	24.5502i	0.446617	+	1.37455i
$320$	−6.43513	−	16.6711i	−0.359735	−	0.931942i
$321$	−6.63261	+	20.4131i	−0.370196	+	1.13935i
$322$	−6.32016	−	2.05355i	−0.352209	−	0.114440i
$323$	1.16184	+	1.59913i	0.0646464	+	0.0889781i
$324$	17.7493			0.986072
$325$	−6.89270	+	3.09969i	−0.382338	+	0.171940i
$326$	−3.67477			−0.203527
$327$	22.7089	+	31.2561i	1.25580	+	1.72846i
$328$	12.9520	+	4.20836i	0.715155	+	0.232368i
$329$	−3.25033	+	10.0035i	−0.179196	+	0.551509i
$330$	−28.3901	+	23.0777i	−1.56283	+	1.27039i
$331$	8.21432	+	25.2811i	0.451500	+	1.38957i	0.875195	+	0.483770i	$0.160733\pi$
$331$	8.21432	+	25.2811i	0.451500	+	1.38957i	−0.423695	+	0.905805i	$0.639267\pi$
$332$		−	6.94783i		−	0.381312i
$333$	5.73390	−	1.86306i	0.314216	−	0.102095i
$334$	−10.4001	−	7.55615i	−0.569071	−	0.413454i
$335$	−1.41479	−	26.0655i	−0.0772984	−	1.42411i
$336$	−4.26682	+	3.10003i	−0.232774	+	0.169120i
$337$	4.39177	−	6.04475i	0.239235	−	0.329278i	−0.672470	−	0.740124i	$-0.734767\pi$
$337$	4.39177	−	6.04475i	0.239235	−	0.329278i	0.911705	+	0.410846i	$0.134767\pi$
$338$	6.81208	−	9.37603i	0.370529	−	0.509989i
$339$	21.3053	−	15.4792i	1.15715	−	0.840715i
$340$	1.12349	+	0.298792i	0.0609296	+	0.0162043i
$341$	12.0849	+	8.78022i	0.654436	+	0.475476i
$342$	−23.4163	+	7.60840i	−1.26621	+	0.411415i
$343$			1.00000i			0.0539949i
$344$	4.19111	+	12.8989i	0.225969	+	0.695462i
$345$	−43.8401	+	2.37957i	−2.36027	+	0.128112i
$346$	−8.55197	+	26.3203i	−0.459757	+	1.41499i
$347$	−6.04244	−	1.96331i	−0.324375	−	0.105396i	0.142303	−	0.989823i	$-0.454549\pi$
$347$	−6.04244	−	1.96331i	−0.324375	−	0.105396i	−0.466678	+	0.884427i	$0.654549\pi$
$348$	8.50330	+	11.7038i	0.455825	+	0.627389i
$349$	3.14477			0.168336			0.0841679	−	0.996452i	$-0.473177\pi$
$349$	3.14477			0.168336			0.0841679	+	0.996452i	$0.473177\pi$
$350$	5.37611	−	0.585337i	0.287365	−	0.0312876i
$351$	−20.3464			−1.08601
$352$	−12.0681	−	16.6104i	−0.643233	−	0.885335i
$353$	7.71854	+	2.50790i	0.410816	+	0.133482i	0.507132	−	0.861869i	$-0.330706\pi$
$353$	7.71854	+	2.50790i	0.410816	+	0.133482i	−0.0963155	+	0.995351i	$0.530706\pi$
$354$	2.54553	−	7.83432i	0.135293	−	0.416389i
$355$	5.88603	+	3.80684i	0.312398	+	0.202046i
$356$	−3.28684	−	10.1159i	−0.174202	−	0.536140i
$357$		−	2.00126i		−	0.105918i
$358$	−9.55758	+	3.10545i	−0.505134	+	0.164128i
$359$	−10.0273	−	7.28529i	−0.529223	−	0.384503i	0.290844	−	0.956770i	$-0.406064\pi$
$359$	−10.0273	−	7.28529i	−0.529223	−	0.384503i	−0.820067	+	0.572268i	$0.806064\pi$
$360$	−26.8094	+	41.4519i	−1.41298	+	2.18471i
$361$	7.31149	−	5.31211i	0.384815	−	0.279585i
$362$	2.52421	−	3.47428i	0.132670	−	0.182604i
$363$	−21.4319	+	29.4985i	−1.12488	+	1.54827i
$364$	−1.01520	+	0.737586i	−0.0532110	+	0.0386600i
$365$	22.0912	−	8.52732i	1.15630	−	0.446340i
$366$	−16.8937	−	12.2740i	−0.883046	−	0.641570i
$367$	6.41517	−	2.08442i	0.334869	−	0.108806i	−0.136756	−	0.990605i	$-0.543668\pi$
$367$	6.41517	−	2.08442i	0.334869	−	0.108806i	0.471625	+	0.881799i	$0.343668\pi$
$368$			10.1403i			0.528600i
$369$	−9.91539	−	30.5164i	−0.516175	−	1.58862i
$370$	−0.519609	+	1.95378i	−0.0270132	+	0.101572i
$371$	−3.33360	+	10.2598i	−0.173072	+	0.532660i
$372$	7.96184	+	2.58696i	0.412802	+	0.134128i
$373$	−12.8198	−	17.6450i	−0.663785	−	0.913621i	0.335814	−	0.941928i	$-0.390988\pi$
$373$	−12.8198	−	17.6450i	−0.663785	−	0.913621i	−0.999599	+	0.0283067i	$0.990988\pi$
$374$	−3.20641			−0.165800
$375$	31.7431	−	16.3983i	1.63921	−	0.846805i
$376$	32.1972			1.66044
$377$	−4.84464	−	6.66807i	−0.249512	−	0.343423i
$378$	13.8464	+	4.49897i	0.712182	+	0.231402i
$379$	4.39393	−	13.5231i	0.225701	−	0.694637i	−0.772519	−	0.634992i	$-0.781003\pi$
$379$	4.39393	−	13.5231i	0.225701	−	0.694637i	0.998220	−	0.0596445i	$-0.0189967\pi$
$380$	−1.50595	+	5.66251i	−0.0772536	+	0.290481i
$381$	7.41935	+	22.8344i	0.380105	+	1.16984i
$382$		−	10.6005i		−	0.542371i
$383$	21.0466	−	6.83844i	1.07543	−	0.349428i	0.282829	−	0.959170i	$-0.408727\pi$
$383$	21.0466	−	6.83844i	1.07543	−	0.349428i	0.792600	+	0.609742i	$0.208727\pi$
$384$	−0.0791479	−	0.0575043i	−0.00403900	−	0.00293450i
$385$	9.87518	−	3.81187i	0.503286	−	0.194271i
$386$	5.53703	−	4.02289i	0.281827	−	0.204760i
$387$	18.7829	−	25.8524i	0.954787	−	1.31415i
$388$	6.04068	−	8.31429i	0.306669	−	0.422094i
$389$	14.2282	−	10.3374i	0.721399	−	0.524127i	−0.165432	−	0.986221i	$-0.552902\pi$
$389$	14.2282	−	10.3374i	0.721399	−	0.524127i	0.886831	+	0.462094i	$0.152902\pi$
$390$	6.34418	−	9.80919i	0.321250	−	0.496707i
$391$	−3.11290	−	2.26166i	−0.157426	−	0.114377i
$392$	2.91125	−	0.945922i	0.147040	−	0.0477763i
$393$		−	9.20951i		−	0.464559i
$394$	−4.52794	−	13.9356i	−0.228114	−	0.702064i
$395$	−14.0674	−	9.09819i	−0.707805	−	0.457779i
$396$	−8.75896	+	26.9573i	−0.440154	+	1.35465i
$397$	−14.9413	−	4.85473i	−0.749883	−	0.243652i	−0.0909522	−	0.995855i	$-0.528991\pi$
$397$	−14.9413	−	4.85473i	−0.749883	−	0.243652i	−0.658931	+	0.752203i	$0.728991\pi$
$398$	12.4424	+	17.1255i	0.623682	+	0.858425i
$399$	10.0866			0.504961
$400$	−3.38447	−	7.52595i	−0.169223	−	0.376297i
$401$	0.840486			0.0419719			0.0209859	−	0.999780i	$-0.493319\pi$
$401$	0.840486			0.0419719			0.0209859	+	0.999780i	$0.493319\pi$
$402$	23.7168	+	32.6434i	1.18289	+	1.62810i
$403$	−4.53615	−	1.47388i	−0.225962	−	0.0734194i
$404$	−1.75609	+	5.40470i	−0.0873690	+	0.268894i
$405$	47.7362	−	2.59104i	2.37203	−	0.128750i
$406$	1.82250	+	5.60908i	0.0904492	+	0.278374i
$407$			3.95725i			0.196154i
$408$	−5.82616	+	1.89304i	−0.288438	+	0.0937192i
$409$	−15.7099	−	11.4139i	−0.776804	−	0.564381i	0.127214	−	0.991875i	$-0.459397\pi$
$409$	−15.7099	−	11.4139i	−0.776804	−	0.564381i	−0.904018	+	0.427494i	$0.859397\pi$
$410$	10.3982	+	2.76542i	0.513532	+	0.136574i
$411$	−40.0111	+	29.0698i	−1.97360	+	1.43391i
$412$	−2.93993	+	4.04646i	−0.144840	+	0.199355i
$413$	−1.40087	+	1.92813i	−0.0689321	+	0.0948769i
$414$	38.7748	−	28.1715i	1.90568	−	1.38456i
$415$	−1.01424	−	18.6860i	−0.0497872	−	0.917258i
$416$	5.30363	+	3.85331i	0.260032	+	0.188924i
$417$	18.5681	−	6.03313i	0.909283	−	0.295444i
$418$		−	16.1607i		−	0.790447i
$419$	9.64569	+	29.6864i	0.471223	+	1.45027i	0.850985	+	0.525191i	$0.176006\pi$
$419$	9.64569	+	29.6864i	0.471223	+	1.45027i	−0.379762	+	0.925084i	$0.623994\pi$
$420$	4.60332	−	3.74193i	0.224619	−	0.182587i
$421$	−3.26385	+	10.0451i	−0.159070	+	0.489568i	−0.998551	−	0.0538223i	$-0.982860\pi$
$421$	−3.26385	+	10.0451i	−0.159070	+	0.489568i	0.839480	+	0.543390i	$0.182860\pi$
$422$	−7.31264	−	2.37602i	−0.355974	−	0.115663i
$423$	−44.5896	−	61.3723i	−2.16802	−	2.98402i
$424$	33.0220			1.60369
$425$	3.06520	+	0.639586i	0.148684	+	0.0310245i
$426$	−10.8352			−0.524968
$427$	3.55114	+	4.88772i	0.171852	+	0.236533i
$428$	−5.30308	−	1.72307i	−0.256334	−	0.0832879i
$429$	7.06606	−	21.7471i	0.341152	−	1.04996i
$430$	3.85877	+	9.99666i	0.186086	+	0.482082i
$431$	−0.198095	−	0.609672i	−0.00954188	−	0.0293669i	0.946172	−	0.323664i	$-0.104915\pi$
$431$	−0.198095	−	0.609672i	−0.00954188	−	0.0293669i	−0.955714	+	0.294297i	$0.904915\pi$
$432$		−	22.2157i		−	1.06885i
$433$	−3.06461	+	0.995751i	−0.147276	+	0.0478528i	−0.381727	−	0.924275i	$-0.624671\pi$
$433$	−3.06461	+	0.995751i	−0.147276	+	0.0478528i	0.234451	+	0.972128i	$0.424671\pi$
$434$	2.76109	+	2.00605i	0.132537	+	0.0962936i
$435$	24.5779	+	30.2356i	1.17842	+	1.44969i
$436$	−8.11995	+	5.89949i	−0.388875	+	0.282534i
$437$	11.3990	−	15.6894i	0.545289	−	0.750527i
$438$	−21.5144	+	29.6121i	−1.02800	+	1.41492i
$439$	−3.95294	+	2.87198i	−0.188664	+	0.137072i	−0.678108	−	0.734963i	$-0.737200\pi$
$439$	−3.95294	+	2.87198i	−0.188664	+	0.137072i	0.489444	+	0.872035i	$0.337200\pi$
$440$	−20.4385	−	25.1434i	−0.974366	−	1.19866i
$441$	−5.83482	−	4.23925i	−0.277849	−	0.201869i
$442$	0.973689	−	0.316371i	0.0463136	−	0.0150482i
$443$			30.6647i			1.45692i	0.685087	+	0.728461i	$0.259764\pi$
$443$			30.6647i			1.45692i	−0.685087	+	0.728461i	$0.740236\pi$
$444$	0.685324	+	2.10921i	0.0325241	+	0.100099i
$445$	−10.3166	−	26.7265i	−0.489052	−	1.26696i
$446$	2.89882	−	8.92164i	0.137263	−	0.422452i
$447$	−71.5792	−	23.2575i	−3.38558	−	1.10004i
$448$	−4.69740	−	6.46542i	−0.221931	−	0.305462i
$449$	16.0918			0.759420			0.379710	−	0.925105i	$-0.376024\pi$
$449$	16.0918			0.759420			0.379710	+	0.925105i	$0.376024\pi$
$450$	−19.3753	+	33.8500i	−0.913361	+	1.59571i
$451$	21.0609			0.991720
$452$	4.02131	+	5.53487i	0.189147	+	0.260338i
$453$	−16.2699	−	5.28641i	−0.764426	−	0.248377i
$454$	2.22707	−	6.85423i	0.104522	−	0.321685i
$455$	−2.62268	+	2.13191i	−0.122953	+	0.0999456i
$456$	−9.54114	−	29.3646i	−0.446805	−	1.37512i
$457$		−	4.65892i		−	0.217935i	−0.994045	−	0.108968i	$-0.965246\pi$
$457$		−	4.65892i		−	0.217935i	0.994045	−	0.108968i	$-0.0347545\pi$
$458$	13.4600	−	4.37340i	0.628942	−	0.204356i
$459$	6.81984	+	4.95490i	0.318323	+	0.231275i
$460$	−0.618184	−	11.3891i	−0.0288230	−	0.531022i
$461$	22.8070	−	16.5703i	1.06223	−	0.771754i	0.0877288	−	0.996144i	$-0.472039\pi$
$461$	22.8070	−	16.5703i	1.06223	−	0.771754i	0.974499	+	0.224391i	$0.0720391\pi$
$462$	−9.61736	+	13.2372i	−0.447440	+	0.615849i
$463$	11.8262	−	16.2774i	0.549610	−	0.756473i	−0.440349	−	0.897826i	$-0.645145\pi$
$463$	11.8262	−	16.2774i	0.549610	−	0.756473i	0.989959	+	0.141354i	$0.0451455\pi$
$464$	7.28068	−	5.28973i	0.337997	−	0.245569i
$465$	21.7908	+	5.79528i	1.01052	+	0.268749i
$466$	14.9091	+	10.8321i	0.690652	+	0.501788i
$467$	−10.8999	+	3.54158i	−0.504385	+	0.163885i	−0.550147	−	0.835068i	$-0.685428\pi$
$467$	−10.8999	+	3.54158i	−0.504385	+	0.163885i	0.0457619	+	0.998952i	$0.485428\pi$
$468$		−	9.05033i		−	0.418351i
$469$	−3.60747	−	11.1026i	−0.166577	−	0.512673i
$470$	25.4008	−	1.37871i	1.17165	−	0.0635953i
$471$	−7.47285	+	22.9991i	−0.344331	+	1.05974i
$472$	6.93837	+	2.25441i	0.319364	+	0.103768i
$473$	12.3285	+	16.9688i	0.566867	+	0.780226i
$474$	25.8957			1.18943
$475$	−3.22359	+	15.4490i	−0.147909	+	0.708848i
$476$	0.519903			0.0238297
$477$	−45.7319	−	62.9446i	−2.09392	−	2.88204i
$478$	−26.9032	−	8.74137i	−1.23052	−	0.399821i
$479$	−5.30740	+	16.3345i	−0.242501	+	0.746343i	0.753536	+	0.657407i	$0.228347\pi$
$479$	−5.30740	+	16.3345i	−0.242501	+	0.746343i	−0.996037	+	0.0889360i	$0.971653\pi$
$480$	−26.0234	−	16.8308i	−1.18780	−	0.768219i
$481$	−0.390454	−	1.20169i	−0.0178032	−	0.0547925i
$482$		−	9.22329i		−	0.420109i
$483$	−18.6738	+	6.06747i	−0.849686	+	0.276080i
$484$	−7.66336	−	5.56776i	−0.348335	−	0.253080i
$485$	15.0325	−	23.2428i	0.682591	−	1.05540i
$486$	−24.4475	+	17.7621i	−1.10896	+	0.805706i
$487$	−4.17404	+	5.74507i	−0.189144	+	0.260334i	−0.893049	−	0.449960i	$-0.851438\pi$
$487$	−4.17404	+	5.74507i	−0.189144	+	0.260334i	0.703905	+	0.710294i	$0.251438\pi$
$488$	10.8703	−	14.9617i	0.492074	−	0.677282i
$489$	−8.78398	+	6.38193i	−0.397225	+	0.288601i
$490$	2.25622	−	0.870914i	0.101926	−	0.0393439i
$491$	−0.533590	−	0.387676i	−0.0240806	−	0.0174956i	0.575680	−	0.817675i	$-0.304737\pi$
$491$	−0.533590	−	0.387676i	−0.0240806	−	0.0174956i	−0.599760	+	0.800180i	$0.704737\pi$
$492$	11.2255	−	3.64737i	0.506083	−	0.164436i
$493$			3.41485i			0.153797i
$494$	1.59455	+	4.90751i	0.0717421	+	0.220799i
$495$	−19.6217	+	73.7794i	−0.881930	+	3.31614i
$496$	1.60929	−	4.95290i	0.0722594	−	0.222392i
$497$	2.98145	+	0.968731i	0.133736	+	0.0434535i
$498$	17.0022	+	23.4015i	0.761887	+	1.04865i
$499$	−9.78180			−0.437894			−0.218947	−	0.975737i	$-0.570262\pi$
$499$	−9.78180			−0.437894			−0.218947	+	0.975737i	$0.570262\pi$
$500$	4.26009	+	8.24649i	0.190517	+	0.368794i
$501$	−37.9827			−1.69694
$502$	4.05612	+	5.58277i	0.181034	+	0.249171i
$503$	−13.6592	−	4.43813i	−0.609032	−	0.197886i	−0.0117673	−	0.999931i	$-0.503746\pi$
$503$	−13.6592	−	4.43813i	−0.609032	−	0.197886i	−0.597265	+	0.802044i	$0.703746\pi$
$504$	−6.82222	+	20.9966i	−0.303886	+	0.935264i
$505$	−3.93398	+	14.7921i	−0.175060	+	0.658241i
$506$	9.72130	+	29.9191i	0.432164	+	1.33007i
$507$		−	34.2425i		−	1.52076i
$508$	−5.93211	+	1.92746i	−0.263195	+	0.0855172i
$509$	−18.9394	−	13.7603i	−0.839476	−	0.609915i	0.0827485	−	0.996570i	$-0.473630\pi$
$509$	−18.9394	−	13.7603i	−0.839476	−	0.609915i	−0.922224	+	0.386656i	$0.873630\pi$
$510$	−4.51528	+	1.74292i	−0.199940	+	0.0771780i
$511$	8.56745	−	6.22462i	0.379002	−	0.275361i
$512$	−10.1462	+	13.9651i	−0.448405	+	0.617177i
$513$	−24.9733	+	34.3728i	−1.10260	+	1.51760i
$514$	−13.5615	+	9.85303i	−0.598174	+	0.434599i
$515$	−7.31613	+	11.3120i	−0.322387	+	0.498466i
$516$	9.50979	+	6.90927i	0.418645	+	0.304164i
$517$	47.3555	−	15.3867i	2.08269	−	0.676708i
$518$			0.904129i			0.0397251i
$519$	25.2679	+	77.7667i	1.10914	+	3.41358i
$520$	8.68738	+	5.61864i	0.380967	+	0.246394i
$521$	−10.5241	+	32.3899i	−0.461070	+	1.41903i	0.402789	+	0.915293i	$0.368041\pi$
$521$	−10.5241	+	32.3899i	−0.461070	+	1.41903i	−0.863859	+	0.503734i	$0.831959\pi$
$522$	−40.4540	−	13.1443i	−1.77062	−	0.575311i
$523$	21.8453	+	30.0675i	0.955230	+	1.31476i	0.949165	+	0.314779i	$0.101931\pi$
$523$	21.8453	+	30.0675i	0.955230	+	1.31476i	0.00606484	+	0.999982i	$0.498069\pi$
$524$	2.39252			0.104518
$525$	11.8342	−	10.7358i	0.516488	−	0.468548i
$526$	−7.99794			−0.348727
$527$	1.16152	+	1.59870i	0.0505968	+	0.0696405i
$528$	23.7450	+	7.71523i	1.03337	+	0.335762i
$529$	−4.55835	+	14.0292i	−0.198189	+	0.609964i
$530$	26.0516	−	1.41404i	1.13161	−	0.0614218i
$531$	−5.31166	−	16.3476i	−0.230506	−	0.709426i
$532$			2.62038i			0.113608i
$533$	−6.39555	+	2.07804i	−0.277022	+	0.0900099i
$534$	35.8255	+	26.0287i	1.55032	+	1.12637i
$535$	−14.5140	−	3.86001i	−0.627494	−	0.166883i
$536$	−28.9102	+	21.0045i	−1.24873	+	0.907255i
$537$	−17.4528	+	24.0217i	−0.753142	+	1.03661i
$538$	9.34003	−	12.8554i	0.402677	−	0.554237i
$539$	3.82981	−	2.78252i	0.164962	−	0.119852i
$540$	1.35433	+	24.9517i	0.0582813	+	1.07375i
$541$	8.65467	+	6.28799i	0.372093	+	0.270342i	0.758078	−	0.652163i	$-0.226138\pi$
$541$	8.65467	+	6.28799i	0.372093	+	0.270342i	−0.385985	+	0.922505i	$0.626138\pi$
$542$	2.26731	−	0.736694i	0.0973893	−	0.0316437i
$543$		−	12.6885i		−	0.544516i
$544$	−0.839318	−	2.58315i	−0.0359854	−	0.110752i
$545$	−20.9771	+	17.0518i	−0.898562	+	0.730421i
$546$	1.61441	−	4.96864i	0.0690904	−	0.212638i
$547$	−14.1854	−	4.60912i	−0.606524	−	0.197072i	−0.0103761	−	0.999946i	$-0.503303\pi$
$547$	−14.1854	−	4.60912i	−0.606524	−	0.197072i	−0.596148	+	0.802875i	$0.703303\pi$
$548$	−7.55198	−	10.3944i	−0.322605	−	0.444027i
$549$	−43.5732			−1.85966
$550$	−17.2009	−	18.9608i	−0.733447	−	0.808490i
$551$	−17.2113			−0.733224
$552$	35.3279	+	48.6246i	1.50365	+	2.06960i
$553$	−7.12553	−	2.31523i	−0.303008	−	0.0984534i
$554$	2.78239	−	8.56333i	0.118213	−	0.363821i
$555$	2.15106	+	5.57261i	0.0913074	+	0.236544i
$556$	1.56734	+	4.82377i	0.0664699	+	0.204573i
$557$			25.0829i			1.06280i	0.847122	+	0.531399i	$0.178334\pi$
$557$			25.0829i			1.06280i	−0.847122	+	0.531399i	$0.821666\pi$
$558$	−23.4099	+	7.60635i	−0.991021	+	0.322002i
$559$	−5.41807	−	3.93646i	−0.229160	−	0.166495i
$560$	−2.32778	−	2.86363i	−0.0983665	−	0.121010i
$561$	−7.66445	+	5.56855i	−0.323593	+	0.235104i
$562$	−16.2849	+	22.4143i	−0.686938	+	0.945489i
$563$	19.6004	−	26.9777i	0.826059	−	1.13697i	−0.162585	−	0.986695i	$-0.551983\pi$
$563$	19.6004	−	26.9777i	0.826059	−	1.13697i	0.988644	−	0.150278i	$-0.0480169\pi$
$564$	22.5758	−	16.4023i	0.950611	−	0.690659i
$565$	11.6232	+	14.2988i	0.488991	+	0.601555i
$566$	−14.3519	−	10.4273i	−0.603255	−	0.438291i
$567$	20.3333	−	6.60669i	0.853918	−	0.277455i
$568$		−	9.59608i		−	0.402643i
$569$	−0.330852	−	1.01826i	−0.0138700	−	0.0426876i	0.943882	−	0.330283i	$-0.107144\pi$
$569$	−0.330852	−	1.01826i	−0.0138700	−	0.0426876i	−0.957752	+	0.287595i	$0.907144\pi$
$570$	−8.78456	−	22.7576i	−0.367945	−	0.953211i
$571$	8.55331	−	26.3244i	0.357945	−	1.10164i	−0.596337	−	0.802734i	$-0.703378\pi$
$571$	8.55331	−	26.3244i	0.357945	−	1.10164i	0.954282	−	0.298907i	$-0.0966221\pi$
$572$	5.64963	+	1.83568i	0.236223	+	0.0767535i
$573$	−18.4099	−	25.3390i	−0.769083	−	1.05855i
$574$	4.81187			0.200844
$575$	−3.32517	−	30.5405i	−0.138669	−	1.27363i
$576$	57.6380			2.40158
$577$	−14.9951	−	20.6390i	−0.624254	−	0.859213i	0.373400	−	0.927671i	$-0.378192\pi$
$577$	−14.9951	−	20.6390i	−0.624254	−	0.859213i	−0.997654	+	0.0684580i	$0.978192\pi$
$578$	17.0835	+	5.55075i	0.710578	+	0.230881i
$579$	6.24892	−	19.2322i	0.259696	−	0.799263i
$580$	−7.85486	+	6.38504i	−0.326155	+	0.265124i
$581$	−2.58614	−	7.95931i	−0.107291	−	0.330208i
$582$			42.7863i			1.77355i
$583$	48.5688	−	15.7809i	2.01151	−	0.653580i
$584$	−26.2256	−	19.0540i	−1.08522	−	0.788459i
$585$	−1.32116	−	24.3406i	−0.0546234	−	1.00636i
$586$	7.29626	−	5.30104i	0.301406	−	0.218984i
$587$	7.33260	−	10.0925i	0.302649	−	0.416561i	−0.630422	−	0.776252i	$-0.717118\pi$
$587$	7.33260	−	10.0925i	0.302649	−	0.416561i	0.933071	+	0.359692i	$0.117118\pi$
$588$	1.55941	−	2.14634i	0.0643088	−	0.0885135i
$589$	−8.05765	+	5.85423i	−0.332010	+	0.241219i
$590$	5.57031	+	1.48143i	0.229326	+	0.0609895i
$591$	−35.0251	−	25.4472i	−1.44074	−	1.04676i
$592$	1.31210	−	0.426326i	0.0539268	−	0.0175219i
$593$		−	12.0433i		−	0.494561i	−0.968944	−	0.247280i	$-0.920463\pi$
$593$		−	12.0433i		−	0.494561i	0.968944	−	0.247280i	$-0.0795368\pi$
$594$	−21.2977	−	65.5476i	−0.873855	−	2.68945i
$595$	1.39826	−	0.0758954i	0.0573232	−	0.00311141i
$596$	6.04202	−	18.5954i	0.247491	−	0.761698i
$597$	59.4835	+	19.3273i	2.43450	+	0.791016i
$598$	−5.90411	−	8.12632i	−0.241437	−	0.332310i
$599$	−2.89855			−0.118431			−0.0592157	−	0.998245i	$-0.518860\pi$
$599$	−2.89855			−0.118431			−0.0592157	+	0.998245i	$0.518860\pi$
$600$	−42.4488	−	24.2972i	−1.73297	−	0.991927i
$601$	4.30169			0.175470			0.0877348	−	0.996144i	$-0.472037\pi$
$601$	4.30169			0.175470			0.0877348	+	0.996144i	$0.472037\pi$
$602$	2.81675	+	3.87693i	0.114802	+	0.158012i
$603$	80.0749	+	26.0179i	3.26090	+	1.05953i
$604$	1.37335	−	4.22673i	0.0558807	−	0.171983i
$605$	−21.4231	−	13.8556i	−0.870975	−	0.563311i
$606$	−7.31115	−	22.5014i	−0.296995	−	0.914057i
$607$			32.8653i			1.33396i	0.745076	+	0.666980i	$0.232413\pi$
$607$			32.8653i			1.33396i	−0.745076	+	0.666980i	$0.767587\pi$
$608$	13.0194	−	4.23027i	0.528007	−	0.171560i
$609$	14.0976	+	10.2425i	0.571265	+	0.415049i
$610$	7.93505	−	12.2689i	0.321281	−	0.496755i
$611$	−12.8622	+	9.34496i	−0.520350	+	0.378057i
$612$	−2.20400	+	3.03354i	−0.0890914	+	0.122624i
$613$	−0.802562	+	1.10463i	−0.0324152	+	0.0446157i	−0.824917	−	0.565254i	$-0.808778\pi$
$613$	−0.802562	+	1.10463i	−0.0324152	+	0.0446157i	0.792502	+	0.609870i	$0.208778\pi$
$614$	−22.4662	+	16.3227i	−0.906663	+	0.658729i
$615$	29.6581	−	11.4482i	1.19593	−	0.461635i
$616$	−11.7233	−	8.51749i	−0.472346	−	0.343180i
$617$	−34.0130	+	11.0515i	−1.36931	+	0.444917i	−0.899141	−	0.437659i	$-0.855808\pi$
$617$	−34.0130	+	11.0515i	−1.36931	+	0.444917i	−0.470171	+	0.882575i	$0.655808\pi$
$618$		−	20.8236i		−	0.837647i
$619$	7.09355	+	21.8317i	0.285114	+	0.877490i	0.986364	+	0.164576i	$0.0526254\pi$
$619$	7.09355	+	21.8317i	0.285114	+	0.877490i	−0.701251	+	0.712915i	$0.747375\pi$
$620$	−1.50554	+	5.66098i	−0.0604641	+	0.227350i
$621$	25.5577	−	78.6584i	1.02559	−	3.15645i
$622$	−11.5834	−	3.76367i	−0.464452	−	0.150909i
$623$	−7.53070	−	10.3651i	−0.301711	−	0.415270i
$624$	−7.97188			−0.319131
$625$	12.6612	+	21.5568i	0.506447	+	0.862271i
$626$	2.12995			0.0851300
$627$	−28.0662	−	38.6298i	−1.12086	−	1.54272i
$628$	−5.97488	−	1.94136i	−0.238424	−	0.0774686i
$629$	−0.161770	+	0.497877i	−0.00645020	+	0.0198517i
$630$	−4.48305	+	16.8567i	−0.178609	+	0.671586i
$631$	15.2414	+	46.9081i	0.606749	+	1.86738i	0.484291	+	0.874907i	$0.339078\pi$
$631$	15.2414	+	46.9081i	0.606749	+	1.86738i	0.122458	+	0.992474i	$0.460922\pi$
$632$			22.9342i			0.912275i
$633$	−21.6062	+	7.02027i	−0.858768	+	0.279031i
$634$	26.9290	+	19.5650i	1.06949	+	0.777027i
$635$	−15.6729	+	6.04981i	−0.621958	+	0.240079i
$636$	23.1541	−	16.8225i	0.918122	−	0.667054i
$637$	−0.888450	+	1.22285i	−0.0352017	+	0.0484509i
$638$	16.4106	−	22.5872i	0.649701	−	0.894237i
$639$	−18.2915	+	13.2895i	−0.723599	+	0.525726i
$640$	0.0371762	−	0.0574807i	0.00146952	−	0.00227213i
$641$	18.9868	+	13.7947i	0.749932	+	0.544857i	0.895806	−	0.444446i	$-0.146599\pi$
$641$	18.9868	+	13.7947i	0.749932	+	0.544857i	−0.145874	+	0.989303i	$0.546599\pi$
$642$	22.0783	−	7.17367i	0.871360	−	0.283122i
$643$			29.2544i			1.15368i	0.816857	+	0.576840i	$0.195714\pi$
$643$			29.2544i			1.15368i	−0.816857	+	0.576840i	$0.804286\pi$
$644$	−1.57626	−	4.85122i	−0.0621133	−	0.191165i
$645$	26.5849	+	17.1940i	1.04678	+	0.677014i
$646$	0.660642	−	2.03325i	0.0259926	−	0.0799970i
$647$	−5.10046	−	1.65724i	−0.200520	−	0.0651529i	0.207035	−	0.978334i	$-0.433619\pi$
$647$	−5.10046	−	1.65724i	−0.200520	−	0.0651529i	−0.407555	+	0.913181i	$0.633619\pi$
$648$	−38.4674	−	52.9459i	−1.51114	−	2.07991i
$649$	11.2823			0.442869
$650$	7.09419	+	4.06062i	0.278257	+	0.159271i
$651$	10.0839			0.395218
$652$	−1.65795	−	2.28197i	−0.0649304	−	0.0893690i
$653$	20.1160	+	6.53608i	0.787199	+	0.255776i	0.674911	−	0.737899i	$-0.264182\pi$
$653$	20.1160	+	6.53608i	0.787199	+	0.255776i	0.112288	+	0.993676i	$0.464182\pi$
$654$	12.9127	−	39.7411i	0.504925	−	1.55400i
$655$	6.43461	−	0.349260i	0.251421	−	0.0136467i
$656$	−2.26895	−	6.98312i	−0.0885878	−	0.272645i
$657$			76.3773i			2.97976i
$658$	10.8195	−	3.51547i	0.421788	−	0.137047i
$659$	−34.2703	−	24.8988i	−1.33498	−	0.969920i	−0.999613	−	0.0278334i	$-0.991139\pi$
$659$	−34.2703	−	24.8988i	−1.33498	−	0.969920i	−0.335368	−	0.942087i	$-0.608861\pi$
$660$	−27.1397	−	7.21784i	−1.05641	−	0.280954i
$661$	−32.6672	+	23.7341i	−1.27061	+	0.923150i	−0.999227	−	0.0393227i	$-0.987480\pi$
$661$	−32.6672	+	23.7341i	−1.27061	+	0.923150i	−0.271380	+	0.962472i	$0.587480\pi$
$662$	16.8992	−	23.2597i	0.656804	−	0.904014i
$663$	1.77802	−	2.44723i	0.0690525	−	0.0950426i
$664$	−20.7253	+	15.0578i	−0.804296	+	0.584355i
$665$	0.382522	+	7.04742i	0.0148336	+	0.273287i
$666$	−5.27543	−	3.83283i	−0.204419	−	0.148519i
$667$	31.8640	−	10.3532i	1.23378	−	0.400879i
$668$		−	9.86745i		−	0.381783i
$669$	−8.56494	−	26.3602i	−0.331140	−	1.01914i
$670$	−21.9082	+	17.8087i	−0.846389	+	0.688010i
$671$	8.83794	−	27.2004i	0.341185	−	1.05006i
$672$	−13.1816	−	4.28296i	−0.508491	−	0.165219i
$673$	20.4874	+	28.1985i	0.789732	+	1.08697i	0.994141	+	0.108087i	$0.0344725\pi$
$673$	20.4874	+	28.1985i	0.789732	+	1.08697i	−0.204410	+	0.978885i	$0.565528\pi$
$674$	−8.08123			−0.311277
$675$	7.28488	+	66.9090i	0.280395	+	2.57533i
$676$	8.89579			0.342146
$677$	−11.5868	−	15.9478i	−0.445316	−	0.612925i	0.526067	−	0.850443i	$-0.323666\pi$
$677$	−11.5868	−	15.9478i	−0.445316	−	0.612925i	−0.971383	+	0.237518i	$0.923666\pi$
$678$	−27.0890	−	8.80175i	−1.04035	−	0.338029i
$679$	3.82534	−	11.7732i	0.146803	−	0.451813i
$680$	−1.54360	−	3.99890i	−0.0591943	−	0.153351i
$681$	−6.58019	−	20.2517i	−0.252153	−	0.776048i
$682$		−	16.1564i		−	0.618659i
$683$	20.6930	−	6.72356i	0.791795	−	0.257270i	0.114927	−	0.993374i	$-0.463337\pi$
$683$	20.6930	−	6.72356i	0.791795	−	0.257270i	0.676868	+	0.736104i	$0.263337\pi$
$684$	−15.2894	−	11.1084i	−0.584607	−	0.424742i
$685$	−21.8282	−	26.8530i	−0.834012	−	1.02600i
$686$	0.875013	−	0.635734i	0.0334081	−	0.0242724i
$687$	24.5787	−	33.8297i	0.937737	−	1.29068i
$688$	4.29811	−	5.91585i	0.163864	−	0.225539i
$689$	−13.1918	+	9.58437i	−0.502566	+	0.365135i
$690$	29.9528	+	36.8479i	1.14028	+	1.40278i
$691$	27.8070	+	20.2030i	1.05783	+	0.768558i	0.973686	−	0.227896i	$-0.0731845\pi$
$691$	27.8070	+	20.2030i	1.05783	+	0.768558i	0.0841438	+	0.996454i	$0.473184\pi$
$692$	−20.2029	+	6.56431i	−0.767998	+	0.249538i
$693$			34.1421i			1.29695i
$694$	2.12346	+	6.53535i	0.0806056	+	0.248078i
$695$	4.91947	+	12.7446i	0.186606	+	0.483429i
$696$	16.4833	−	50.7304i	0.624798	−	1.92293i
$697$	2.64976	+	0.860959i	0.100367	+	0.0326111i
$698$	−1.99924	−	2.75172i	−0.0756723	−	0.104154i
$699$	54.4500			2.05949
$700$	2.78903	+	3.07439i	0.105415	+	0.116201i
$701$	23.4591			0.886039			0.443020	−	0.896512i	$-0.353907\pi$
$701$	23.4591			0.886039			0.443020	+	0.896512i	$0.353907\pi$
$702$	12.9349	+	17.8034i	0.488197	+	0.671945i
$703$	−2.50937	−	0.815342i	−0.0946425	−	0.0307512i
$704$	−11.6907	+	35.9803i	−0.440611	+	1.35606i
$705$	58.3224	−	47.4089i	2.19655	−	1.78552i
$706$	−2.71249	−	8.34818i	−0.102086	−	0.314188i
$707$			6.84519i			0.257440i
$708$	6.01346	−	1.95389i	0.226000	−	0.0734317i
$709$	16.4621	+	11.9604i	0.618248	+	0.449183i	0.852309	−	0.523039i	$-0.175202\pi$
$709$	16.4621	+	11.9604i	0.618248	+	0.449183i	−0.234061	+	0.972222i	$0.575202\pi$
$710$	−0.410913	−	7.57049i	−0.0154213	−	0.284115i
$711$	43.7158	−	31.7614i	1.63947	−	1.19115i
$712$	−23.0520	+	31.7283i	−0.863910	+	1.18907i
$713$	11.3960	−	15.6852i	0.426782	−	0.587415i
$714$	−1.75113	+	1.27227i	−0.0655343	+	0.0476134i
$715$	15.4625	+	4.11226i	0.578264	+	0.153790i
$716$	−6.24054	−	4.53402i	−0.233220	−	0.169444i
$717$	−79.4890	+	25.8275i	−2.96857	+	0.964548i
$718$			13.4056i			0.500291i
$719$	−5.61288	−	17.2747i	−0.209325	−	0.644236i	−0.999508	−	0.0313653i	$-0.990014\pi$
$719$	−5.61288	−	17.2747i	−0.209325	−	0.644236i	0.790183	−	0.612871i	$-0.209986\pi$
$720$	26.5768	−	1.44254i	0.990458	−	0.0537604i
$721$	−1.86175	+	5.72986i	−0.0693350	+	0.213391i
$722$	−9.29633	−	3.02056i	−0.345974	−	0.112414i
$723$	−16.0180	−	22.0469i	−0.595716	−	0.819932i
$724$	3.29632			0.122507
$725$	−20.1933	+	18.3190i	−0.749961	+	0.680351i
$726$	39.4366			1.46363
$727$	−14.3079	−	19.6931i	−0.530650	−	0.730377i	0.456580	−	0.889683i	$-0.349074\pi$
$727$	−14.3079	−	19.6931i	−0.530650	−	0.730377i	−0.987229	+	0.159306i	$0.949074\pi$
$728$	4.40042	+	1.42978i	0.163090	+	0.0529912i
$729$	−7.77060	+	23.9154i	−0.287800	+	0.885757i
$730$	−21.5056	−	13.9090i	−0.795959	−	0.514794i
$731$	0.857429	+	2.63890i	0.0317132	+	0.0976031i
$732$		−	16.0284i		−	0.592425i
$733$	−35.8871	+	11.6604i	−1.32552	+	0.430688i	−0.884388	−	0.466753i	$-0.845424\pi$
$733$	−35.8871	+	11.6604i	−1.32552	+	0.430688i	−0.441134	+	0.897441i	$0.645424\pi$
$734$	−5.90223	−	4.28822i	−0.217855	−	0.158281i
$735$	3.88065	−	6.00015i	0.143140	−	0.221319i
$736$	−21.5588	+	15.6634i	−0.794667	+	0.577359i
$737$	−32.4832	+	44.7093i	−1.19653	+	1.64689i
$738$	−20.3987	+	28.0764i	−0.750887	+	1.03351i
$739$	−33.0253	+	23.9943i	−1.21486	+	0.882645i	−0.995663	−	0.0930368i	$-0.970343\pi$
$739$	−33.0253	+	23.9943i	−1.21486	+	0.882645i	−0.219193	+	0.975681i	$0.570343\pi$
$740$	−1.44770	+	0.558820i	−0.0532185	+	0.0205426i
$741$	12.3344	+	8.96143i	0.453114	+	0.329206i
$742$	11.0967	−	3.60554i	0.407373	−	0.132363i
$743$		−	24.9128i		−	0.913962i	−0.889476	−	0.456981i	$-0.848931\pi$
$743$		−	24.9128i		−	0.913962i	0.889476	−	0.456981i	$-0.151069\pi$
$744$	−9.53856	−	29.3567i	−0.349701	−	1.07627i
$745$	13.5353	−	50.8938i	0.495893	−	1.86460i
$746$	−7.28958	+	22.4350i	−0.266890	+	0.821404i
$747$	57.4045	+	18.6518i	2.10032	+	0.682435i
$748$	−1.44664	−	1.99113i	−0.0528945	−	0.0728030i
$749$	−6.71648			−0.245415
$750$	−34.5289	−	17.3507i	−1.26082	−	0.633557i
$751$	12.0413			0.439393			0.219697	−	0.975568i	$-0.429493\pi$
$751$	12.0413			0.439393			0.219697	+	0.975568i	$0.429493\pi$
$752$	−10.2035	−	14.0439i	−0.372083	−	0.512129i
$753$	19.3911	+	6.30055i	0.706651	+	0.229605i
$754$	−2.75475	+	8.47824i	−0.100322	+	0.308759i
$755$	3.07655	−	11.5681i	0.111967	−	0.421007i
$756$	3.45331	+	10.6282i	0.125596	+	0.386544i
$757$		−	0.867358i		−	0.0315247i	−0.999876	−	0.0157623i	$-0.994982\pi$
$757$		−	0.867358i		−	0.0315247i	0.999876	−	0.0157623i	$-0.00501751\pi$
$758$	−14.6263	+	4.75237i	−0.531251	+	0.172614i
$759$	75.1975	+	54.6342i	2.72949	+	1.98309i
$760$	20.1550	−	7.77993i	0.731098	−	0.282208i
$761$	−11.3657	+	8.25768i	−0.412007	+	0.299340i	−0.774414	−	0.632679i	$-0.781955\pi$
$761$	−11.3657	+	8.25768i	−0.412007	+	0.299340i	0.362407	+	0.932020i	$0.381955\pi$
$762$	15.2637	−	21.0086i	0.552945	−	0.761063i
$763$	−7.10616	+	9.78078i	−0.257260	+	0.354088i
$764$	6.58277	−	4.78266i	0.238156	−	0.173031i
$765$	−5.48475	+	8.48036i	−0.198301	+	0.306608i
$766$	−19.3637	−	14.0686i	−0.699640	−	0.508318i
$767$	−3.42609	+	1.11320i	−0.123709	+	0.0401954i
$768$			51.1833i			1.84692i
$769$	−12.6101	−	38.8098i	−0.454731	−	1.39952i	−0.871450	−	0.490484i	$-0.836820\pi$
$769$	−12.6101	−	38.8098i	−0.454731	−	1.39952i	0.416719	−	0.909035i	$-0.363180\pi$
$770$	−9.61343	−	6.21757i	−0.346444	−	0.224066i
$771$	−15.3051	+	47.1044i	−0.551201	+	1.69642i
$772$	4.99630	+	1.62340i	0.179821	+	0.0584273i
$773$	12.9905	+	17.8798i	0.467234	+	0.643093i	0.975989	−	0.217819i	$-0.0698942\pi$
$773$	12.9905	+	17.8798i	0.467234	+	0.643093i	−0.508755	+	0.860911i	$0.669894\pi$
$774$	−34.5621			−1.24231
$775$	−3.22272	+	15.4448i	−0.115764	+	0.554794i
$776$	−37.8932			−1.36028
$777$	1.57019	+	2.16118i	0.0563303	+	0.0775320i
$778$	−18.0907	−	5.87803i	−0.648583	−	0.210738i
$779$	−4.33934	+	13.3551i	−0.155473	+	0.478497i
$780$	8.95366	−	0.485990i	0.320593	−	0.0174012i
$781$	−4.58588	−	14.1139i	−0.164096	−	0.505035i
$782$			4.16164i			0.148820i
$783$	−69.8085	+	22.6822i	−2.49475	+	0.810594i
$784$	−1.33519	−	0.970074i	−0.0476854	−	0.0346455i
$785$	−16.3527	−	4.34901i	−0.583651	−	0.155223i
$786$	−8.05844	+	5.85480i	−0.287435	+	0.208834i
$787$	18.7878	−	25.8592i	0.669713	−	0.921781i	−0.330041	−	0.943967i	$-0.607062\pi$
$787$	18.7878	−	25.8592i	0.669713	−	0.921781i	0.999754	+	0.0221854i	$0.00706242\pi$
$788$	6.61089	−	9.09911i	0.235503	−	0.324142i
$789$	−19.1179	+	13.8899i	−0.680614	+	0.494495i
$790$	0.982065	+	18.0931i	0.0349403	+	0.643725i
$791$	6.66695	+	4.84382i	0.237049	+	0.172227i
$792$	99.3961	−	32.2958i	3.53189	−	1.14758i
$793$			9.13194i			0.324285i
$794$	5.25075	+	16.1602i	0.186342	+	0.573503i
$795$	59.8166	−	48.6235i	2.12148	−	1.72450i
$796$	−5.02102	+	15.4531i	−0.177965	+	0.547721i
$797$	19.8463	+	6.44844i	0.702991	+	0.228416i	0.638633	−	0.769511i	$-0.279500\pi$
$797$	19.8463	+	6.44844i	0.702991	+	0.228416i	0.0643577	+	0.997927i	$0.479500\pi$
$798$	−6.41239	−	8.82590i	−0.226996	−	0.312434i
$799$	6.58699			0.233031
$800$	10.7727	−	18.8206i	0.380871	−	0.665408i
$801$	92.4032			3.26491
$802$	−0.534325	−	0.735436i	−0.0188677	−	0.0259691i
$803$	−47.6782	−	15.4916i	−1.68253	−	0.546687i
$804$	−9.57068	+	29.4555i	−0.337532	+	1.03882i
$805$	−4.94748	−	12.8171i	−0.174376	−	0.451744i
$806$	1.59412	+	4.90619i	0.0561504	+	0.172813i
$807$		−	46.9497i		−	1.65271i
$808$	19.9281	−	6.47502i	0.701067	−	0.227790i
$809$	−20.6875	−	15.0303i	−0.727333	−	0.528438i	0.161386	−	0.986891i	$-0.448404\pi$
$809$	−20.6875	−	15.0303i	−0.727333	−	0.528438i	−0.888719	+	0.458453i	$0.848404\pi$
$810$	−32.6147	−	40.1225i	−1.14596	−	1.40976i
$811$	−41.5595	+	30.1947i	−1.45935	+	1.06028i	−0.475819	+	0.879543i	$0.657848\pi$
$811$	−41.5595	+	30.1947i	−1.45935	+	1.06028i	−0.983531	+	0.180737i	$0.942152\pi$
$812$	−2.66089	+	3.66240i	−0.0933789	+	0.128525i
$813$	4.14025	−	5.69857i	0.145205	−	0.199858i
$814$	3.46264	−	2.51576i	0.121366	−	0.0881773i
$815$	−4.79213	−	5.89527i	−0.167861	−	0.206502i
$816$	2.67206	+	1.94137i	0.0935410	+	0.0679615i
$817$	−13.3004	+	4.32155i	−0.465321	+	0.151192i
$818$			21.0026i			0.734338i
$819$	−3.36873	−	10.3679i	−0.117713	−	0.362284i
$820$	2.97410	+	7.70481i	0.103860	+	0.269064i
$821$	11.5240	−	35.4673i	0.402191	−	1.23782i	−0.521028	−	0.853540i	$-0.674451\pi$
$821$	11.5240	−	35.4673i	0.402191	−	1.23782i	0.923218	−	0.384276i	$-0.125549\pi$
$822$	50.8729	+	16.5296i	1.77439	+	0.576536i
$823$	−15.7566	−	21.6872i	−0.549242	−	0.755967i	0.440667	−	0.897671i	$-0.354742\pi$
$823$	−15.7566	−	21.6872i	−0.549242	−	0.755967i	−0.989909	+	0.141704i	$0.954742\pi$
$824$	18.4421			0.642462
$825$	−74.0451	−	15.4503i	−2.57792	−	0.537910i
$826$	2.57771			0.0896901
$827$	−4.48937	−	6.17908i	−0.156111	−	0.214868i	0.723797	−	0.690013i	$-0.242395\pi$
$827$	−4.48937	−	6.17908i	−0.156111	−	0.214868i	−0.879907	+	0.475146i	$0.842395\pi$
$828$	34.9882	+	11.3684i	1.21592	+	0.395077i
$829$	10.2779	−	31.6322i	0.356967	−	1.09863i	−0.597892	−	0.801576i	$-0.703995\pi$
$829$	10.2779	−	31.6322i	0.356967	−	1.09863i	0.954860	−	0.297056i	$-0.0960050\pi$
$830$	−15.7057	+	12.7668i	−0.545152	+	0.443141i
$831$	−8.22095	−	25.3015i	−0.285182	−	0.877699i
$832$		−	12.0796i		−	0.418785i
$833$	0.595592	−	0.193520i	0.0206360	−	0.00670506i
$834$	−17.0834	−	12.4118i	−0.591551	−	0.429787i
$835$	−1.44045	−	26.5382i	−0.0498487	−	0.918392i
$836$	10.0356	−	7.29126i	0.347087	−	0.252174i
$837$	−24.9666	+	34.3636i	−0.862971	+	1.18778i
$838$	19.8439	−	27.3128i	0.685495	−	0.943503i
$839$	17.0630	−	12.3970i	0.589081	−	0.427992i	−0.252906	−	0.967491i	$-0.581386\pi$
$839$	17.0630	−	12.3970i	0.589081	−	0.427992i	0.841986	+	0.539499i	$0.181386\pi$
$840$	−21.1387	−	5.62186i	−0.729355	−	0.193973i
$841$	−0.594011	−	0.431574i	−0.0204831	−	0.0148819i
$842$	10.8645	−	3.53010i	0.374416	−	0.121655i
$843$			81.8598i			2.81940i
$844$	−1.82378	−	5.61302i	−0.0627772	−	0.193208i
$845$	23.9249	−	1.29861i	0.823043	−	0.0446734i
$846$	−25.3544	+	78.0329i	−0.871703	+	2.68283i
$847$	−10.8515	−	3.52585i	−0.372861	−	0.121150i
$848$	−10.4649	−	14.4037i	−0.359366	−	0.494626i
$849$	−52.4150			−1.79888
$850$	−1.38900	−	3.08869i	−0.0476424	−	0.105941i
$851$	5.13616			0.176065
$852$	−4.88855	−	6.72851i	−0.167479	−	0.230515i
$853$	33.0192	+	10.7286i	1.13056	+	0.367340i	0.813787	−	0.581163i	$-0.197402\pi$
$853$	33.0192	+	10.7286i	1.13056	+	0.367340i	0.316768	+	0.948503i	$0.397402\pi$
$854$	2.01924	−	6.21458i	0.0690970	−	0.212659i
$855$	−42.7421	−	27.6438i	−1.46175	−	0.945399i
$856$	6.35327	+	19.5533i	0.217150	+	0.668320i
$857$			43.3883i			1.48212i	0.671441	+	0.741058i	$0.265676\pi$
$857$			43.3883i			1.48212i	−0.671441	+	0.741058i	$0.734324\pi$
$858$	−23.5211	+	7.64247i	−0.802997	+	0.260910i
$859$	42.1658	+	30.6353i	1.43868	+	1.04526i	0.988316	+	0.152417i	$0.0487055\pi$
$859$	42.1658	+	30.6353i	1.43868	+	1.04526i	0.450363	+	0.892845i	$0.351294\pi$
$860$	−4.46680	+	6.90644i	−0.152317	+	0.235508i
$861$	11.5021	−	8.35673i	0.391989	−	0.284797i
$862$	−0.407536	+	0.560925i	−0.0138807	+	0.0191052i
$863$	−19.3874	+	26.6845i	−0.659955	+	0.908350i	−0.999480	−	0.0322468i	$-0.989734\pi$
$863$	−19.3874	+	26.6845i	−0.659955	+	0.908350i	0.339525	+	0.940597i	$0.389734\pi$
$864$	47.2316	−	34.3158i	1.60685	−	1.16745i
$865$	−53.3767	+	20.6037i	−1.81486	+	0.700548i
$866$	2.81957	+	2.04854i	0.0958129	+	0.0696122i
$867$	50.4754	−	16.4004i	1.71423	−	0.556988i
$868$			2.61967i			0.0889174i
$869$	10.9601	+	33.7316i	0.371795	+	1.14427i
$870$	10.8316	−	40.7278i	0.367225	−	1.38080i
$871$	5.45276	−	16.7819i	0.184760	−	0.568632i
$872$	35.1962	+	11.4359i	1.19189	+	0.387269i
$873$	52.4779	+	72.2296i	1.77611	+	2.44460i
$874$	−20.9752			−0.709497
$875$	7.94981	+	7.86133i	0.268753	+	0.265762i
$876$	−28.0953			−0.949253
$877$	12.1055	+	16.6617i	0.408772	+	0.562627i	0.962918	−	0.269793i	$-0.0869551\pi$
$877$	12.1055	+	16.6617i	0.408772	+	0.562627i	−0.554146	+	0.832419i	$0.686955\pi$
$878$	5.02604	+	1.63306i	0.169621	+	0.0551131i
$879$	8.23434	−	25.3427i	0.277737	−	0.854787i
$880$	−4.49007	+	16.8831i	−0.151360	+	0.569128i
$881$	−6.83622	−	21.0397i	−0.230318	−	0.708847i	−0.997708	−	0.0676657i	$-0.978445\pi$
$881$	−6.83622	−	21.0397i	−0.230318	−	0.708847i	0.767390	−	0.641181i	$-0.221555\pi$
$882$			7.80058i			0.262659i
$883$	−52.5956	+	17.0894i	−1.76998	+	0.575102i	−0.998154	−	0.0607278i	$-0.980658\pi$
$883$	−52.5956	+	17.0894i	−1.76998	+	0.575102i	−0.771829	+	0.635830i	$0.780658\pi$
$884$	0.635762	+	0.461908i	0.0213830	+	0.0155356i
$885$	15.8878	−	6.13277i	0.534062	−	0.206151i
$886$	26.8320	−	19.4946i	0.901438	−	0.654933i
$887$	13.5839	−	18.6966i	0.456102	−	0.627770i	−0.517593	−	0.855627i	$-0.673172\pi$
$887$	13.5839	−	18.6966i	0.456102	−	0.627770i	0.973695	+	0.227857i	$0.0731718\pi$
$888$	4.80646	−	6.61553i	0.161294	−	0.222003i
$889$	−6.07828	+	4.41613i	−0.203859	+	0.148112i
$890$	−16.8274	+	26.0181i	−0.564056	+	0.872127i
$891$	−81.8802	−	59.4894i	−2.74309	−	1.99297i
$892$	6.84806	−	2.22507i	0.229290	−	0.0745009i
$893$			33.1993i			1.11097i
$894$	25.1547	+	77.4183i	0.841300	+	2.58925i
$895$	−17.4456	−	11.2831i	−0.583143	−	0.377153i
$896$	0.00946027	−	0.0291157i	0.000316045	−	0.000972687i
$897$	−28.2258	−	9.17112i	−0.942432	−	0.306215i
$898$	−10.2301	−	14.0806i	−0.341384	−	0.469874i
$899$	−17.2066			−0.573872
$900$	−29.7619	+	3.24040i	−0.992064	+	0.108013i
$901$	6.75575			0.225067
$902$	−13.3891	−	18.4286i	−0.445810	−	0.613604i
$903$	13.4660	+	4.37538i	0.448122	+	0.145604i
$904$	7.79516	−	23.9910i	0.259263	−	0.797930i
$905$	8.86535	−	0.481197i	0.294694	−	0.0159955i
$906$	5.71765	+	17.5971i	0.189956	+	0.584625i
$907$			41.7280i			1.38555i	0.721152	+	0.692777i	$0.243613\pi$
$907$			41.7280i			1.38555i	−0.721152	+	0.692777i	$0.756387\pi$
$908$	5.26116	−	1.70945i	0.174598	−	0.0567302i
$909$	−39.9405	−	29.0185i	−1.32474	−	0.962482i
$910$	3.53278	+	0.939545i	0.117110	+	0.0311456i
$911$	−0.539553	+	0.392008i	−0.0178762	+	0.0129878i	−0.596687	−	0.802474i	$-0.703517\pi$
$911$	−0.539553	+	0.392008i	−0.0178762	+	0.0129878i	0.578811	+	0.815462i	$0.303517\pi$
$912$	−9.78474	+	13.4675i	−0.324005	+	0.445955i
$913$	−23.2867	+	32.0514i	−0.770677	+	1.06075i
$914$	−4.07662	+	2.96184i	−0.134843	+	0.0979688i
$915$	−2.33982	−	43.1078i	−0.0773520	−	1.42510i
$916$	8.78856	+	6.38527i	0.290382	+	0.210975i
$917$	2.74083	−	0.890551i	0.0905103	−	0.0294086i
$918$		−	9.11744i		−	0.300920i
$919$	0.640781	+	1.97212i	0.0211374	+	0.0650543i	0.961069	−	0.276309i	$-0.0891113\pi$
$919$	0.640781	+	1.97212i	0.0211374	+	0.0650543i	−0.939931	+	0.341363i	$0.889111\pi$
$920$	−32.6339	+	26.5273i	−1.07591	+	0.874580i
$921$	−25.3547	+	78.0338i	−0.835466	+	2.57130i
$922$	−28.9984	−	9.42214i	−0.955011	−	0.310302i
$923$	2.78518	+	3.83347i	0.0916754	+	0.126180i
$924$	−12.5592			−0.413166
$925$	−3.81196	+	1.71426i	−0.125337	+	0.0563646i
$926$	−21.7612			−0.715118
$927$	−25.5403	−	35.1533i	−0.838855	−	1.15458i
$928$	22.4924	+	7.30823i	0.738350	+	0.239904i
$929$	14.8296	−	45.6410i	0.486545	−	1.49743i	−0.343186	−	0.939267i	$-0.611506\pi$
$929$	14.8296	−	45.6410i	0.486545	−	1.49743i	0.829731	−	0.558164i	$-0.188494\pi$
$930$	−8.78219	−	22.7515i	−0.287979	−	0.746049i
$931$	0.975363	+	3.00186i	0.0319662	+	0.0983820i
$932$			14.1455i			0.463350i
$933$	−34.2247	+	11.1203i	−1.12047	+	0.364061i
$934$	10.0283	+	7.28602i	0.328137	+	0.238406i
$935$	−4.18136	−	5.14391i	−0.136745	−	0.168224i
$936$	−26.9970	+	19.6145i	−0.882424	+	0.641118i
$937$	10.0803	−	13.8744i	0.329310	−	0.453256i	−0.611971	−	0.790880i	$-0.709623\pi$
$937$	10.0803	−	13.8744i	0.329310	−	0.453256i	0.941281	+	0.337624i	$0.109623\pi$
$938$	−7.42157	+	10.2149i	−0.242323	+	0.333529i
$939$	5.09133	−	3.69907i	0.166149	−	0.120715i
$940$	12.3163	+	15.1515i	0.401713	+	0.494186i
$941$	−29.3666	−	21.3361i	−0.957324	−	0.695536i	−0.00479596	−	0.999988i	$-0.501527\pi$
$941$	−29.3666	−	21.3361i	−0.957324	−	0.695536i	−0.952528	+	0.304452i	$0.901527\pi$
$942$	24.8752	−	8.08245i	0.810479	−	0.263340i
$943$		−	27.3352i		−	0.890157i
$944$	−1.21548	−	3.74085i	−0.0395604	−	0.121754i
$945$	10.8391	+	28.0801i	0.352595	+	0.913445i
$946$	7.01023	−	21.5753i	0.227922	−	0.701473i
$947$	−20.9363	−	6.80262i	−0.680338	−	0.221055i	−0.0515949	−	0.998668i	$-0.516430\pi$
$947$	−20.9363	−	6.80262i	−0.680338	−	0.221055i	−0.628744	+	0.777613i	$0.716430\pi$
$948$	11.6834	+	16.0808i	0.379460	+	0.522282i
$949$	16.0069			0.519607
$950$	15.5674	−	7.00076i	0.505073	−	0.227134i
$951$	98.3480			3.18915
$952$	−1.12677	−	1.55086i	−0.0365188	−	0.0502638i
$953$	−42.9320	−	13.9495i	−1.39071	−	0.451867i	−0.484532	−	0.874774i	$-0.661010\pi$
$953$	−42.9320	−	13.9495i	−1.39071	−	0.451867i	−0.906173	+	0.422906i	$0.861010\pi$
$954$	−26.0040	+	80.0321i	−0.841910	+	2.59113i
$955$	17.0060	−	13.8238i	0.550300	−	0.447327i
$956$	−6.70969	−	20.6503i	−0.217007	−	0.667879i
$957$		−	82.4914i		−	2.66657i
$958$	17.6670	−	5.74036i	0.570795	−	0.185463i
$959$	−12.5205	−	9.09664i	−0.404307	−	0.293746i
$960$	3.09508	+	57.0224i	0.0998933	+	1.84039i
$961$	17.0240	−	12.3687i	0.549163	−	0.398990i
$962$	−0.803273	+	1.10561i	−0.0258986	+	0.0356463i
$963$	28.4728	−	39.1895i	0.917524	−	1.26286i
$964$	5.72752	−	4.16129i	0.184471	−	0.134026i
$965$	13.6744	+	3.63671i	0.440194	+	0.117070i
$966$	17.1807	+	12.4825i	0.552779	+	0.401617i
$967$	58.4019	−	18.9759i	1.87808	−	0.610225i	0.890072	−	0.455819i	$-0.150654\pi$
$967$	58.4019	−	18.9759i	1.87808	−	0.610225i	0.988008	−	0.154406i	$-0.0493463\pi$
$968$			34.9265i			1.12258i
$969$	−1.95195	−	6.00750i	−0.0627058	−	0.192989i
$970$	−29.8945	+	1.62262i	−0.959853	+	0.0520992i
$971$	−13.9420	+	42.9091i	−0.447421	+	1.37702i	0.432386	+	0.901688i	$0.357672\pi$
$971$	−13.9420	+	42.9091i	−0.447421	+	1.37702i	−0.879807	+	0.475331i	$0.842328\pi$
$972$	−22.0600	−	7.16773i	−0.707575	−	0.229905i
$973$	3.59103	+	4.94263i	0.115123	+	0.158453i
$974$	7.68059			0.246102
$975$	24.0096	−	2.61411i	0.768924	−	0.0837185i
$976$	−9.97091			−0.319161
$977$	4.76573	+	6.55947i	0.152469	+	0.209856i	0.878418	−	0.477892i	$-0.158599\pi$
$977$	4.76573	+	6.55947i	0.152469	+	0.209856i	−0.725949	+	0.687749i	$0.758599\pi$
$978$	11.1685	+	3.62888i	0.357131	+	0.116039i
$979$	−18.7421	+	57.6824i	−0.599001	+	1.84354i
$980$	1.55877	+	1.00815i	0.0497930	+	0.0322041i
$981$	−26.9444	−	82.9263i	−0.860268	−	2.64763i
$982$			0.713357i			0.0227641i
$983$	−19.9882	+	6.49456i	−0.637525	+	0.207144i	−0.609905	−	0.792474i	$-0.708793\pi$
$983$	−19.9882	+	6.49456i	−0.637525	+	0.207144i	−0.0276192	+	0.999619i	$0.508793\pi$
$984$	−35.2086	−	25.5805i	−1.12241	−	0.815478i
$985$	16.4515	−	25.4368i	0.524188	−	0.810485i
$986$	2.98803	−	2.17093i	0.0951584	−	0.0691366i
$987$	19.7571	−	27.1933i	0.628876	−	0.865574i
$988$	−2.32807	+	3.20432i	−0.0740659	+	0.101943i
$989$	22.0240	−	16.0014i	0.700322	−	0.508814i
$990$	77.0321	−	29.7348i	2.44824	−	0.945035i
$991$	−10.1275	−	7.35808i	−0.321712	−	0.233737i	0.415194	−	0.909733i	$-0.363714\pi$
$991$	−10.1275	−	7.35808i	−0.321712	−	0.233737i	−0.736905	+	0.675996i	$0.763714\pi$
$992$	13.0159	−	4.22913i	0.413256	−	0.134275i
$993$		−	84.9474i		−	2.69572i
$994$	−1.04776	−	3.22466i	−0.0332328	−	0.102280i
$995$	−11.2480	+	42.2936i	−0.356586	+	1.34080i
$996$	−6.86107	+	21.1162i	−0.217401	+	0.669093i
$997$	−33.4473	−	10.8677i	−1.05929	−	0.344183i	−0.272980	−	0.962020i	$-0.588009\pi$
$997$	−33.4473	−	10.8677i	−1.05929	−	0.344183i	−0.786307	+	0.617837i	$0.788009\pi$
$998$	6.21862	+	8.55920i	0.196847	+	0.270937i
$999$	−11.2524			−0.356012

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.n.a.64.4	✓	56
5.2	odd	4		875.2.h.e.176.9		56
5.3	odd	4		875.2.h.d.176.6		56
5.4	even	2		875.2.n.c.449.11		56
25.3	odd	20		4375.2.a.p.1.18		28
25.9	even	10	inner	175.2.n.a.134.4	yes	56
25.12	odd	20		875.2.h.e.701.9		56
25.13	odd	20		875.2.h.d.701.6		56
25.16	even	5		875.2.n.c.799.11		56
25.22	odd	20		4375.2.a.o.1.11		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.n.a.64.4	✓	56	1.1	even	1	trivial
175.2.n.a.134.4	yes	56	25.9	even	10	inner
875.2.h.d.176.6		56	5.3	odd	4
875.2.h.d.701.6		56	25.13	odd	20
875.2.h.e.176.9		56	5.2	odd	4
875.2.h.e.701.9		56	25.12	odd	20
875.2.n.c.449.11		56	5.4	even	2
875.2.n.c.799.11		56	25.16	even	5
4375.2.a.o.1.11		28	25.22	odd	20
4375.2.a.p.1.18		28	25.3	odd	20

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.635734 - 0.875013i) q^{2} +(-3.03925 - 0.987513i) q^{3} +(0.256544 - 0.789562i) q^{4} +(0.574707 - 2.16095i) q^{5} +(1.06807 + 3.28718i) q^{6} -1.00000i q^{7} +(-2.91125 + 0.945922i) q^{8} +(5.83482 + 4.23925i) q^{9} +O(q^{10})\)	\(q+(-0.635734 - 0.875013i) q^{2} +(-3.03925 - 0.987513i) q^{3} +(0.256544 - 0.789562i) q^{4} +(0.574707 - 2.16095i) q^{5} +(1.06807 + 3.28718i) q^{6} -1.00000i q^{7} +(-2.91125 + 0.945922i) q^{8} +(5.83482 + 4.23925i) q^{9} +(-2.25622 + 0.870914i) q^{10} +(-3.82981 + 2.78252i) q^{11} +(-1.55941 + 2.14634i) q^{12} +(0.888450 - 1.22285i) q^{13} +(-0.875013 + 0.635734i) q^{14} +(-3.88065 + 6.00015i) q^{15} +(1.33519 + 0.970074i) q^{16} +(-0.595592 + 0.193520i) q^{17} -7.80058i q^{18} +(-0.975363 - 3.00186i) q^{19} +(-1.55877 - 1.00815i) q^{20} +(-0.987513 + 3.03925i) q^{21} +(4.86949 + 1.58219i) q^{22} +(3.61147 + 4.97076i) q^{23} +9.78213 q^{24} +(-4.33942 - 2.48383i) q^{25} -1.63482 q^{26} +(-7.91211 - 10.8901i) q^{27} +(-0.789562 - 0.256544i) q^{28} +(1.68504 - 5.18603i) q^{29} +(7.71727 - 0.418880i) q^{30} +(-0.975100 - 3.00105i) q^{31} +4.33712i q^{32} +(14.3875 - 4.67480i) q^{33} +(0.547970 + 0.398124i) q^{34} +(-2.16095 - 0.574707i) q^{35} +(4.84404 - 3.51940i) q^{36} +(0.491351 - 0.676287i) q^{37} +(-2.00659 + 2.76184i) q^{38} +(-3.90780 + 2.83918i) q^{39} +(0.370976 + 6.83470i) q^{40} +(-3.59928 - 2.61503i) q^{41} +(3.28718 - 1.06807i) q^{42} -4.43071i q^{43} +(1.21446 + 3.73771i) q^{44} +(12.5141 - 10.1724i) q^{45} +(2.05355 - 6.32016i) q^{46} +(-10.0035 - 3.25033i) q^{47} +(-3.10003 - 4.26682i) q^{48} -1.00000 q^{49} +(0.585337 + 5.37611i) q^{50} +2.00126 q^{51} +(-0.737586 - 1.01520i) q^{52} +(-10.2598 - 3.33360i) q^{53} +(-4.49897 + 13.8464i) q^{54} +(3.81187 + 9.87518i) q^{55} +(0.945922 + 2.91125i) q^{56} +10.0866i q^{57} +(-5.60908 + 1.82250i) q^{58} +(-1.92813 - 1.40087i) q^{59} +(3.74193 + 4.60332i) q^{60} +(-4.88772 + 3.55114i) q^{61} +(-2.00605 + 2.76109i) q^{62} +(4.23925 - 5.83482i) q^{63} +(6.46542 - 4.69740i) q^{64} +(-2.13191 - 2.62268i) q^{65} +(-13.2372 - 9.61736i) q^{66} +(11.1026 - 3.60747i) q^{67} +0.519903i q^{68} +(-6.06747 - 18.6738i) q^{69} +(0.870914 + 2.25622i) q^{70} +(-0.968731 + 2.98145i) q^{71} +(-20.9966 - 6.82222i) q^{72} +(6.22462 + 8.56745i) q^{73} -0.904129 q^{74} +(10.7358 + 11.8342i) q^{75} -2.62038 q^{76} +(2.78252 + 3.82981i) q^{77} +(4.96864 + 1.61441i) q^{78} +(2.31523 - 7.12553i) q^{79} +(2.86363 - 2.32778i) q^{80} +(6.60669 + 20.3333i) q^{81} +4.81187i q^{82} +(7.95931 - 2.58614i) q^{83} +(2.14634 + 1.55941i) q^{84} +(0.0758954 + 1.39826i) q^{85} +(-3.87693 + 2.81675i) q^{86} +(-10.2425 + 14.0976i) q^{87} +(8.51749 - 11.7233i) q^{88} +(10.3651 - 7.53070i) q^{89} +(-16.8567 - 4.48305i) q^{90} +(-1.22285 - 0.888450i) q^{91} +(4.85122 - 1.57626i) q^{92} +10.0839i q^{93} +(3.51547 + 10.8195i) q^{94} +(-7.04742 + 0.382522i) q^{95} +(4.28296 - 13.1816i) q^{96} +(11.7732 + 3.82534i) q^{97} +(0.635734 + 0.875013i) q^{98} -34.1421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 12 q^{4} - 6 q^{5} + 6 q^{9}+O(q^{10}) \) 56 * q + 12 * q^4 - 6 * q^5 + 6 * q^9	\( 56 q + 12 q^{4} - 6 q^{5} + 6 q^{9} - 4 q^{10} + 8 q^{11} - 40 q^{12} - 4 q^{14} - 18 q^{15} - 32 q^{16} + 12 q^{19} + 12 q^{20} + 4 q^{21} - 30 q^{22} + 10 q^{23} - 28 q^{24} + 4 q^{25} + 12 q^{26} + 30 q^{27} - 2 q^{29} + 28 q^{30} + 12 q^{31} + 20 q^{33} + 2 q^{35} - 14 q^{36} - 70 q^{37} - 70 q^{38} - 4 q^{39} - 30 q^{40} + 4 q^{41} + 50 q^{42} + 22 q^{44} - 52 q^{45} - 4 q^{46} - 10 q^{47} + 30 q^{48} - 56 q^{49} - 54 q^{50} - 44 q^{51} - 20 q^{53} + 54 q^{54} - 2 q^{55} + 12 q^{56} + 10 q^{58} - 6 q^{59} + 16 q^{60} - 4 q^{61} + 50 q^{62} + 20 q^{63} + 24 q^{64} - 18 q^{65} - 74 q^{66} + 10 q^{67} - 78 q^{69} + 8 q^{70} - 8 q^{71} + 140 q^{72} + 40 q^{73} + 60 q^{74} - 8 q^{75} + 52 q^{76} - 20 q^{77} - 90 q^{78} + 124 q^{80} - 72 q^{81} - 30 q^{83} - 12 q^{84} + 96 q^{85} - 20 q^{86} + 30 q^{87} + 140 q^{88} + 38 q^{89} - 8 q^{90} + 8 q^{91} + 80 q^{92} + 88 q^{94} - 70 q^{95} - 28 q^{96} - 30 q^{97} + 60 q^{99}+O(q^{100}) \) 56 * q + 12 * q^4 - 6 * q^5 + 6 * q^9 - 4 * q^10 + 8 * q^11 - 40 * q^12 - 4 * q^14 - 18 * q^15 - 32 * q^16 + 12 * q^19 + 12 * q^20 + 4 * q^21 - 30 * q^22 + 10 * q^23 - 28 * q^24 + 4 * q^25 + 12 * q^26 + 30 * q^27 - 2 * q^29 + 28 * q^30 + 12 * q^31 + 20 * q^33 + 2 * q^35 - 14 * q^36 - 70 * q^37 - 70 * q^38 - 4 * q^39 - 30 * q^40 + 4 * q^41 + 50 * q^42 + 22 * q^44 - 52 * q^45 - 4 * q^46 - 10 * q^47 + 30 * q^48 - 56 * q^49 - 54 * q^50 - 44 * q^51 - 20 * q^53 + 54 * q^54 - 2 * q^55 + 12 * q^56 + 10 * q^58 - 6 * q^59 + 16 * q^60 - 4 * q^61 + 50 * q^62 + 20 * q^63 + 24 * q^64 - 18 * q^65 - 74 * q^66 + 10 * q^67 - 78 * q^69 + 8 * q^70 - 8 * q^71 + 140 * q^72 + 40 * q^73 + 60 * q^74 - 8 * q^75 + 52 * q^76 - 20 * q^77 - 90 * q^78 + 124 * q^80 - 72 * q^81 - 30 * q^83 - 12 * q^84 + 96 * q^85 - 20 * q^86 + 30 * q^87 + 140 * q^88 + 38 * q^89 - 8 * q^90 + 8 * q^91 + 80 * q^92 + 88 * q^94 - 70 * q^95 - 28 * q^96 - 30 * q^97 + 60 * q^99

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