LMFDB - Embedded newform 175.2.n.a.134.4

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			134.4
Character	$\chi$	$=$	175.134
Dual form			175.2.n.a.64.4

$q$-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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$

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	−0.972297	−	0.233749i	$-0.924901\pi$
$2$	−0.635734	+	0.875013i	−0.449532	+	0.618728i	0.522765	+	0.852477i	$0.324901\pi$
$3$	−3.03925	+	0.987513i	−1.75471	+	0.570141i	−0.996631	−	0.0820177i	$-0.973864\pi$
$3$	−3.03925	+	0.987513i	−1.75471	+	0.570141i	−0.758083	+	0.652159i	$0.773864\pi$
$4$	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	−0.165629	−	0.986188i	$-0.552966\pi$
$11$	−3.82981	−	2.78252i	−1.15473	−	0.838962i	−0.989103	+	0.147226i	$0.952966\pi$
$12$	−1.55941	−	2.14634i	−0.450162	−	0.619594i
$13$	0.888450	+	1.22285i	0.246412	+	0.339157i	0.914251	−	0.405149i	$-0.132780\pi$
$13$	0.888450	+	1.22285i	0.246412	+	0.339157i	−0.667839	+	0.744306i	$0.732780\pi$
$14$	−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	0.235898	−	0.971778i	$-0.424197\pi$
$17$	−0.595592	−	0.193520i	−0.144452	−	0.0469354i	−0.380351	+	0.924842i	$0.624197\pi$
$18$			7.80058i			1.83861i
$19$	−0.975363	+	3.00186i	−0.223764	+	0.688674i	0.774651	+	0.632389i	$0.217926\pi$
$19$	−0.975363	+	3.00186i	−0.223764	+	0.688674i	−0.998415	+	0.0562849i	$0.982074\pi$
$20$	−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	−0.244718	−	0.969594i	$-0.578695\pi$
$23$	3.61147	−	4.97076i	0.753043	−	1.03647i	0.997761	−	0.0668806i	$-0.0213047\pi$
$24$	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	0.976608	+	0.215026i	$0.0689835\pi$
$29$	1.68504	+	5.18603i	0.312904	+	0.963021i	−0.663704	+	0.747995i	$0.731017\pi$
$30$	7.71727	+	0.418880i	1.40897	+	0.0764767i
$31$	−0.975100	+	3.00105i	−0.175133	+	0.539004i	−0.999640	−	0.0268483i	$-0.991453\pi$
$31$	−0.975100	+	3.00105i	−0.175133	+	0.539004i	0.824506	+	0.565853i	$0.191453\pi$
$32$		−	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	0.847494	−	0.530806i	$-0.178111\pi$
$37$	0.491351	+	0.676287i	0.0807777	+	0.111181i	−0.766716	+	0.641986i	$0.778111\pi$
$38$	−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	−0.832231	−	0.554428i	$-0.812937\pi$
$41$	−3.59928	+	2.61503i	−0.562112	+	0.408399i	0.270119	+	0.962827i	$0.412937\pi$
$42$	3.28718	+	1.06807i	0.507223	+	0.164807i
$43$			4.43071i			0.675677i	0.941204	+	0.337838i	$0.109696\pi$
$43$			4.43071i			0.675677i	−0.941204	+	0.337838i	$0.890304\pi$
$44$	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	−0.927812	−	0.373047i	$-0.878313\pi$
$47$	−10.0035	+	3.25033i	−1.45916	+	0.474109i	−0.531344	+	0.847156i	$0.678313\pi$
$48$	−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	−0.912182	−	0.409786i	$-0.865603\pi$
$53$	−10.2598	+	3.33360i	−1.40929	+	0.457905i	−0.497104	+	0.867691i	$0.665603\pi$
$54$	−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	−0.706179	−	0.708033i	$-0.749583\pi$
$59$	−1.92813	+	1.40087i	−0.251021	+	0.182377i	0.455158	+	0.890410i	$0.349583\pi$
$60$	3.74193	−	4.60332i	0.483081	−	0.594285i
$61$	−4.88772	−	3.55114i	−0.625809	−	0.454677i	0.229137	−	0.973394i	$-0.426410\pi$
$61$	−4.88772	−	3.55114i	−0.625809	−	0.454677i	−0.854946	+	0.518718i	$0.826410\pi$
$62$	−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	0.894841	−	0.446385i	$-0.147289\pi$
$67$	11.1026	+	3.60747i	1.35640	+	0.440722i	0.461563	+	0.887107i	$0.347289\pi$
$68$		−	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	0.876973	−	0.480540i	$-0.159559\pi$
$71$	−0.968731	−	2.98145i	−0.114967	−	0.353833i	−0.991940	+	0.126707i	$0.959559\pi$
$72$	−20.9966	+	6.82222i	−2.47448	+	0.804006i
$73$	6.22462	−	8.56745i	0.728536	−	1.00274i	−0.270661	−	0.962675i	$-0.587242\pi$
$73$	6.22462	−	8.56745i	0.728536	−	1.00274i	0.999197	−	0.0400692i	$-0.0127578\pi$
$74$	−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	0.992700	+	0.120613i	$0.0384860\pi$
$79$	2.31523	+	7.12553i	0.260483	+	0.801685i	−0.732216	+	0.681072i	$0.761514\pi$
$80$	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	0.711317	−	0.702871i	$-0.248099\pi$
$83$	7.95931	+	2.58614i	0.873648	+	0.283865i	0.162331	+	0.986736i	$0.448099\pi$
$84$	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	0.980847	−	0.194778i	$-0.0623987\pi$
$89$	10.3651	+	7.53070i	1.09870	+	0.798253i	0.117853	+	0.993031i	$0.462399\pi$
$90$	−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	0.357324	−	0.933980i	$-0.383689\pi$
$97$	11.7732	−	3.82534i	1.19539	−	0.388404i	0.838061	+	0.545576i	$0.183689\pi$
$98$	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	−0.577381	−	0.816475i	$-0.695925\pi$
$103$	−5.72986	+	1.86175i	−0.564580	+	0.183443i	0.0128009	+	0.999918i	$0.495925\pi$
$104$	−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	$0.105248\pi$
$107$			6.71648i			0.649307i	−0.945833	+	0.324653i	$0.894752\pi$
$108$	−10.6282	−	3.45331i	−1.02270	−	0.332295i
$109$	−9.78078	+	7.10616i	−0.936829	+	0.680646i	−0.947655	−	0.319295i	$-0.896554\pi$
$109$	−9.78078	+	7.10616i	−0.936829	+	0.680646i	0.0108262	+	0.999941i	$0.496554\pi$
$110$	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	0.517935	−	0.855420i	$-0.326701\pi$
$113$	−4.84382	−	6.66695i	−0.455668	−	0.627174i	−0.973603	+	0.228246i	$0.926701\pi$
$114$	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	−0.958680	−	0.284487i	$-0.908177\pi$
$127$	−4.41613	+	6.07828i	−0.391868	+	0.539360i	0.566812	+	0.823847i	$0.308177\pi$
$128$	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	−0.904586	−	0.426292i	$-0.859820\pi$
$131$	0.890551	−	2.74083i	0.0778078	−	0.239468i	0.982393	+	0.186824i	$0.0598196\pi$
$132$			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	0.995588	+	0.0938373i	$0.0299134\pi$
$137$	9.09664	+	12.5205i	0.777179	+	1.06969i	−0.218409	+	0.975857i	$0.570087\pi$
$138$	−12.4825	−	17.1807i	−1.06258	−	1.46252i
$139$	−4.94263	−	3.59103i	−0.419228	−	0.304587i	0.358099	−	0.933684i	$-0.383425\pi$
$139$	−4.94263	−	3.59103i	−0.419228	−	0.304587i	−0.777327	+	0.629097i	$0.783425\pi$
$140$	−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	$0.0976442\pi$
$157$			7.56734i			0.603940i	−0.953317	+	0.301970i	$0.902356\pi$
$158$	−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	0.880034	−	0.474910i	$-0.157520\pi$
$163$	1.99706	+	2.74872i	0.156422	+	0.215296i	−0.723612	+	0.690207i	$0.757520\pi$
$164$	−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	0.711767	−	0.702416i	$-0.247895\pi$
$167$	11.3040	+	3.67288i	0.874728	+	0.284216i	0.162961	+	0.986632i	$0.447895\pi$
$168$			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	−0.383950	+	0.923354i	$0.625437\pi$
$173$	−15.0399	+	20.7007i	−1.14346	+	1.57384i	−0.759515	+	0.650490i	$0.774563\pi$
$174$	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	0.999181	+	0.0404549i	$0.0128807\pi$
$179$	2.87123	+	8.83672i	0.214605	+	0.660488i	−0.784576	+	0.620033i	$0.787119\pi$
$180$	−4.82135	+	12.4904i	−0.359362	+	0.930976i
$181$	1.22697	−	3.77621i	0.0911996	−	0.280684i	−0.895045	−	0.445976i	$-0.852857\pi$
$181$	1.22697	−	3.77621i	0.0911996	−	0.280684i	0.986245	+	0.165292i	$0.0528567\pi$
$182$		−	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	−0.262724	−	0.964871i	$-0.584621\pi$
$191$	7.92919	−	5.76089i	0.573736	−	0.416844i	0.836460	+	0.548027i	$0.184621\pi$
$192$	−24.2888	−	7.89191i	−1.75289	−	0.569549i
$193$		−	6.32794i		−	0.455495i	−0.973720	−	0.227748i	$-0.926864\pi$
$193$		−	6.32794i		−	0.455495i	0.973720	−	0.227748i	$-0.0731361\pi$
$194$	−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	0.188344	−	0.982103i	$-0.439688\pi$
$197$	12.8845	−	4.18643i	0.917983	−	0.298271i	0.729639	+	0.683832i	$0.239688\pi$
$198$	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	0.767884	−	0.640588i	$-0.221309\pi$
$211$	5.75133	+	4.17859i	0.395938	+	0.287666i	−0.371946	+	0.928254i	$0.621309\pi$
$212$	−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	−0.603458	−	0.797394i	$-0.706211\pi$
$223$	5.09800	−	7.01680i	0.341388	−	0.469880i	0.944846	+	0.327515i	$0.106211\pi$
$224$	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	−0.659010	−	0.752134i	$-0.729025\pi$
$227$	3.91664	−	5.39080i	0.259957	−	0.357800i	0.918967	+	0.394334i	$0.129025\pi$
$228$	7.96399	−	2.58766i	0.527428	−	0.171372i
$229$	−4.04355	−	12.4448i	−0.267205	−	0.822373i	−0.991177	−	0.132544i	$-0.957685\pi$
$229$	−4.04355	−	12.4448i	−0.267205	−	0.822373i	0.723972	−	0.689830i	$-0.242315\pi$
$230$	−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	−0.274397	−	0.961617i	$-0.588478\pi$
$233$	−16.2048	−	5.26526i	−1.06161	−	0.344939i	−0.787216	+	0.616678i	$0.788478\pi$
$234$	−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	0.997840	+	0.0656974i	$0.0209272\pi$
$239$	21.1591	+	15.3730i	1.36867	+	0.994398i	0.370831	+	0.928700i	$0.379073\pi$
$240$	−11.0020	−	4.24683i	−0.710176	−	0.274132i
$241$	6.89901	−	5.01242i	0.444404	−	0.322879i	−0.342978	−	0.939343i	$-0.611436\pi$
$241$	6.89901	−	5.01242i	0.444404	−	0.322879i	0.787382	+	0.616465i	$0.211436\pi$
$242$	−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	$0.160595\pi$
$257$			15.4987i			0.966781i	−0.875405	+	0.483390i	$0.839405\pi$
$258$	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	0.921719	−	0.387859i	$-0.126785\pi$
$263$	4.34650	+	5.98245i	0.268017	+	0.368893i	−0.653702	+	0.756752i	$0.726785\pi$
$264$	−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	−0.711927	−	0.702253i	$-0.752177\pi$
$269$	4.53999	−	13.9727i	0.276808	−	0.851928i	0.988735	−	0.149674i	$-0.0478226\pi$
$270$	27.3358	−	17.6797i	1.66360	−	1.07595i
$271$	−0.681130	−	2.09630i	−0.0413757	−	0.127341i	0.928235	−	0.371994i	$-0.121326\pi$
$271$	−0.681130	−	2.09630i	−0.0413757	−	0.127341i	−0.969611	+	0.244653i	$0.921326\pi$
$272$	−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	−0.636303	−	0.771439i	$-0.719537\pi$
$277$	4.89326	−	6.73499i	0.294007	−	0.404666i	0.930311	+	0.366773i	$0.119537\pi$
$278$	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	0.377463	+	0.926025i	$0.376797\pi$
$281$	−7.91576	+	24.3622i	−0.472215	+	1.45333i	−0.849678	+	0.527302i	$0.823203\pi$
$282$			36.3548i			2.16490i
$283$	15.5992	+	5.06847i	0.927274	+	0.301289i	0.733447	−	0.679746i	$-0.237910\pi$
$283$	15.5992	+	5.06847i	0.927274	+	0.301289i	0.193826	+	0.981036i	$0.437910\pi$
$284$	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	$-0.921682\pi$
$293$		−	8.33846i		−	0.487138i	0.969884	−	0.243569i	$-0.0783182\pi$
$294$	−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	$0.261732\pi$
$307$			25.6753i			1.46537i	−0.680569	+	0.732684i	$0.738268\pi$
$308$	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	0.815320	−	0.579011i	$-0.196561\pi$
$311$	9.11025	+	6.61898i	0.516595	+	0.375328i	−0.298725	+	0.954339i	$0.596561\pi$
$312$	8.69094	+	11.9620i	0.492027	+	0.677218i
$313$	−1.15753	−	1.59320i	−0.0654274	−	0.0900531i	0.775049	−	0.631901i	$-0.217725\pi$
$313$	−1.15753	−	1.59320i	−0.0654274	−	0.0900531i	−0.840477	+	0.541848i	$0.817725\pi$
$314$	−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	−0.666514	−	0.745492i	$-0.732214\pi$
$317$	−29.2692	−	9.51016i	−1.64392	−	0.534144i	−0.977411	+	0.211349i	$0.932214\pi$
$318$			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	−0.423695	−	0.905805i	$-0.639267\pi$
$331$	8.21432	−	25.2811i	0.451500	−	1.38957i	0.875195	−	0.483770i	$-0.160733\pi$
$332$			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	0.911705	−	0.410846i	$-0.134767\pi$
$337$	4.39177	+	6.04475i	0.239235	+	0.329278i	−0.672470	+	0.740124i	$0.734767\pi$
$338$	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	−0.466678	−	0.884427i	$-0.654549\pi$
$347$	−6.04244	+	1.96331i	−0.324375	+	0.105396i	0.142303	+	0.989823i	$0.454549\pi$
$348$	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	−0.0963155	−	0.995351i	$-0.530706\pi$
$353$	7.71854	−	2.50790i	0.410816	−	0.133482i	0.507132	+	0.861869i	$0.330706\pi$
$354$	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	−0.820067	−	0.572268i	$-0.806064\pi$
$359$	−10.0273	+	7.28529i	−0.529223	+	0.384503i	0.290844	+	0.956770i	$0.406064\pi$
$360$	−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	0.471625	−	0.881799i	$-0.343668\pi$
$367$	6.41517	+	2.08442i	0.334869	+	0.108806i	−0.136756	+	0.990605i	$0.543668\pi$
$368$		−	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	−0.999599	−	0.0283067i	$-0.990988\pi$
$373$	−12.8198	+	17.6450i	−0.663785	+	0.913621i	0.335814	+	0.941928i	$0.390988\pi$
$374$	−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	0.998220	+	0.0596445i	$0.0189967\pi$
$379$	4.39393	+	13.5231i	0.225701	+	0.694637i	−0.772519	+	0.634992i	$0.781003\pi$
$380$	−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	0.792600	−	0.609742i	$-0.208727\pi$
$383$	21.0466	+	6.83844i	1.07543	+	0.349428i	0.282829	+	0.959170i	$0.408727\pi$
$384$	−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	0.886831	−	0.462094i	$-0.152902\pi$
$389$	14.2282	+	10.3374i	0.721399	+	0.524127i	−0.165432	+	0.986221i	$0.552902\pi$
$390$	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	−0.658931	−	0.752203i	$-0.728991\pi$
$397$	−14.9413	+	4.85473i	−0.749883	+	0.243652i	−0.0909522	+	0.995855i	$0.528991\pi$
$398$	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	−0.904018	−	0.427494i	$-0.859397\pi$
$409$	−15.7099	+	11.4139i	−0.776804	+	0.564381i	0.127214	+	0.991875i	$0.459397\pi$
$410$	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	−0.379762	−	0.925084i	$-0.623994\pi$
$419$	9.64569	−	29.6864i	0.471223	−	1.45027i	0.850985	−	0.525191i	$-0.176006\pi$
$420$	4.60332	+	3.74193i	0.224619	+	0.182587i
$421$	−3.26385	−	10.0451i	−0.159070	−	0.489568i	0.839480	−	0.543390i	$-0.182860\pi$
$421$	−3.26385	−	10.0451i	−0.159070	−	0.489568i	−0.998551	+	0.0538223i	$0.982860\pi$
$422$	−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	−0.955714	−	0.294297i	$-0.904915\pi$
$431$	−0.198095	+	0.609672i	−0.00954188	+	0.0293669i	0.946172	+	0.323664i	$0.104915\pi$
$432$			22.2157i			1.06885i
$433$	−3.06461	−	0.995751i	−0.147276	−	0.0478528i	0.234451	−	0.972128i	$-0.424671\pi$
$433$	−3.06461	−	0.995751i	−0.147276	−	0.0478528i	−0.381727	+	0.924275i	$0.624671\pi$
$434$	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	0.489444	−	0.872035i	$-0.337200\pi$
$439$	−3.95294	−	2.87198i	−0.188664	−	0.137072i	−0.678108	+	0.734963i	$0.737200\pi$
$440$	−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	$-0.740236\pi$
$443$		−	30.6647i		−	1.45692i	0.685087	−	0.728461i	$-0.259764\pi$
$444$	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	$0.0347545\pi$
$457$			4.65892i			0.217935i	−0.994045	+	0.108968i	$0.965246\pi$
$458$	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	0.974499	−	0.224391i	$-0.0720391\pi$
$461$	22.8070	+	16.5703i	1.06223	+	0.771754i	0.0877288	+	0.996144i	$0.472039\pi$
$462$	−9.61736	−	13.2372i	−0.447440	−	0.615849i
$463$	11.8262	+	16.2774i	0.549610	+	0.756473i	0.989959	−	0.141354i	$-0.0451455\pi$
$463$	11.8262	+	16.2774i	0.549610	+	0.756473i	−0.440349	+	0.897826i	$0.645145\pi$
$464$	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	0.0457619	−	0.998952i	$-0.485428\pi$
$467$	−10.8999	−	3.54158i	−0.504385	−	0.163885i	−0.550147	+	0.835068i	$0.685428\pi$
$468$			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	−0.996037	−	0.0889360i	$-0.971653\pi$
$479$	−5.30740	−	16.3345i	−0.242501	−	0.746343i	0.753536	−	0.657407i	$-0.228347\pi$
$480$	−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	0.703905	−	0.710294i	$-0.251438\pi$
$487$	−4.17404	−	5.74507i	−0.189144	−	0.260334i	−0.893049	+	0.449960i	$0.851438\pi$
$488$	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	−0.599760	−	0.800180i	$-0.704737\pi$
$491$	−0.533590	+	0.387676i	−0.0240806	+	0.0174956i	0.575680	+	0.817675i	$0.304737\pi$
$492$	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	−0.597265	−	0.802044i	$-0.703746\pi$
$503$	−13.6592	+	4.43813i	−0.609032	+	0.197886i	−0.0117673	+	0.999931i	$0.503746\pi$
$504$	−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	−0.922224	−	0.386656i	$-0.873630\pi$
$509$	−18.9394	+	13.7603i	−0.839476	+	0.609915i	0.0827485	+	0.996570i	$0.473630\pi$
$510$	−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	−0.863859	−	0.503734i	$-0.831959\pi$
$521$	−10.5241	−	32.3899i	−0.461070	−	1.41903i	0.402789	−	0.915293i	$-0.368041\pi$
$522$	−40.4540	+	13.1443i	−1.77062	+	0.575311i
$523$	21.8453	−	30.0675i	0.955230	−	1.31476i	0.00606484	−	0.999982i	$-0.498069\pi$
$523$	21.8453	−	30.0675i	0.955230	−	1.31476i	0.949165	−	0.314779i	$-0.101931\pi$
$524$	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	−0.385985	−	0.922505i	$-0.626138\pi$
$541$	8.65467	−	6.28799i	0.372093	−	0.270342i	0.758078	+	0.652163i	$0.226138\pi$
$542$	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	−0.596148	−	0.802875i	$-0.703303\pi$
$547$	−14.1854	+	4.60912i	−0.606524	+	0.197072i	−0.0103761	+	0.999946i	$0.503303\pi$
$548$	−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	$-0.821666\pi$
$557$		−	25.0829i		−	1.06280i	0.847122	−	0.531399i	$-0.178334\pi$
$558$	−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	0.988644	+	0.150278i	$0.0480169\pi$
$563$	19.6004	+	26.9777i	0.826059	+	1.13697i	−0.162585	+	0.986695i	$0.551983\pi$
$564$	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	−0.957752	−	0.287595i	$-0.907144\pi$
$569$	−0.330852	+	1.01826i	−0.0138700	+	0.0426876i	0.943882	+	0.330283i	$0.107144\pi$
$570$	−8.78456	+	22.7576i	−0.367945	+	0.953211i
$571$	8.55331	+	26.3244i	0.357945	+	1.10164i	0.954282	+	0.298907i	$0.0966221\pi$
$571$	8.55331	+	26.3244i	0.357945	+	1.10164i	−0.596337	+	0.802734i	$0.703378\pi$
$572$	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	−0.997654	−	0.0684580i	$-0.978192\pi$
$577$	−14.9951	+	20.6390i	−0.624254	+	0.859213i	0.373400	+	0.927671i	$0.378192\pi$
$578$	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	0.933071	−	0.359692i	$-0.117118\pi$
$587$	7.33260	+	10.0925i	0.302649	+	0.416561i	−0.630422	+	0.776252i	$0.717118\pi$
$588$	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	$0.0795368\pi$
$593$			12.0433i			0.494561i	−0.968944	+	0.247280i	$0.920463\pi$
$594$	−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	$-0.767587\pi$
$607$		−	32.8653i		−	1.33396i	0.745076	−	0.666980i	$-0.232413\pi$
$608$	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	0.792502	−	0.609870i	$-0.208778\pi$
$613$	−0.802562	−	1.10463i	−0.0324152	−	0.0446157i	−0.824917	+	0.565254i	$0.808778\pi$
$614$	−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	−0.470171	−	0.882575i	$-0.655808\pi$
$617$	−34.0130	−	11.0515i	−1.36931	−	0.444917i	−0.899141	+	0.437659i	$0.855808\pi$
$618$			20.8236i			0.837647i
$619$	7.09355	−	21.8317i	0.285114	−	0.877490i	−0.701251	−	0.712915i	$-0.747375\pi$
$619$	7.09355	−	21.8317i	0.285114	−	0.877490i	0.986364	−	0.164576i	$-0.0526254\pi$
$620$	−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	0.122458	−	0.992474i	$-0.460922\pi$
$631$	15.2414	−	46.9081i	0.606749	−	1.86738i	0.484291	−	0.874907i	$-0.339078\pi$
$632$		−	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	−0.145874	−	0.989303i	$-0.546599\pi$
$641$	18.9868	−	13.7947i	0.749932	−	0.544857i	0.895806	+	0.444446i	$0.146599\pi$
$642$	22.0783	+	7.17367i	0.871360	+	0.283122i
$643$		−	29.2544i		−	1.15368i	−0.816857	−	0.576840i	$-0.804286\pi$
$643$		−	29.2544i		−	1.15368i	0.816857	−	0.576840i	$-0.195714\pi$
$644$	−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	−0.407555	−	0.913181i	$-0.633619\pi$
$647$	−5.10046	+	1.65724i	−0.200520	+	0.0651529i	0.207035	+	0.978334i	$0.433619\pi$
$648$	−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	0.112288	−	0.993676i	$-0.464182\pi$
$653$	20.1160	−	6.53608i	0.787199	−	0.255776i	0.674911	+	0.737899i	$0.264182\pi$
$654$	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	−0.335368	+	0.942087i	$0.608861\pi$
$659$	−34.2703	+	24.8988i	−1.33498	+	0.969920i	−0.999613	+	0.0278334i	$0.991139\pi$
$660$	−27.1397	+	7.21784i	−1.05641	+	0.280954i
$661$	−32.6672	−	23.7341i	−1.27061	−	0.923150i	−0.271380	−	0.962472i	$-0.587480\pi$
$661$	−32.6672	−	23.7341i	−1.27061	−	0.923150i	−0.999227	+	0.0393227i	$0.987480\pi$
$662$	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	−0.204410	−	0.978885i	$-0.565528\pi$
$673$	20.4874	−	28.1985i	0.789732	−	1.08697i	0.994141	−	0.108087i	$-0.0344725\pi$
$674$	−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	−0.971383	−	0.237518i	$-0.923666\pi$
$677$	−11.5868	+	15.9478i	−0.445316	+	0.612925i	0.526067	+	0.850443i	$0.323666\pi$
$678$	−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	0.676868	−	0.736104i	$-0.263337\pi$
$683$	20.6930	+	6.72356i	0.791795	+	0.257270i	0.114927	+	0.993374i	$0.463337\pi$
$684$	−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	0.0841438	−	0.996454i	$-0.473184\pi$
$691$	27.8070	−	20.2030i	1.05783	−	0.768558i	0.973686	+	0.227896i	$0.0731845\pi$
$692$	−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	−0.234061	−	0.972222i	$-0.575202\pi$
$709$	16.4621	−	11.9604i	0.618248	−	0.449183i	0.852309	+	0.523039i	$0.175202\pi$
$710$	−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	0.790183	+	0.612871i	$0.209986\pi$
$719$	−5.61288	+	17.2747i	−0.209325	+	0.644236i	−0.999508	+	0.0313653i	$0.990014\pi$
$720$	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	−0.987229	−	0.159306i	$-0.949074\pi$
$727$	−14.3079	+	19.6931i	−0.530650	+	0.730377i	0.456580	+	0.889683i	$0.349074\pi$
$728$	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	−0.441134	−	0.897441i	$-0.645424\pi$
$733$	−35.8871	−	11.6604i	−1.32552	−	0.430688i	−0.884388	+	0.466753i	$0.845424\pi$
$734$	−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	−0.219193	−	0.975681i	$-0.570343\pi$
$739$	−33.0253	−	23.9943i	−1.21486	−	0.882645i	−0.995663	+	0.0930368i	$0.970343\pi$
$740$	−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	$0.151069\pi$
$743$			24.9128i			0.913962i	−0.889476	+	0.456981i	$0.848931\pi$
$744$	−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	$0.00501751\pi$
$757$			0.867358i			0.0315247i	−0.999876	+	0.0157623i	$0.994982\pi$
$758$	−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	0.362407	−	0.932020i	$-0.381955\pi$
$761$	−11.3657	−	8.25768i	−0.412007	−	0.299340i	−0.774414	+	0.632679i	$0.781955\pi$
$762$	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	0.416719	+	0.909035i	$0.363180\pi$
$769$	−12.6101	+	38.8098i	−0.454731	+	1.39952i	−0.871450	+	0.490484i	$0.836820\pi$
$770$	−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	−0.508755	−	0.860911i	$-0.669894\pi$
$773$	12.9905	−	17.8798i	0.467234	−	0.643093i	0.975989	+	0.217819i	$0.0698942\pi$
$774$	−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	0.999754	−	0.0221854i	$-0.00706242\pi$
$787$	18.7878	+	25.8592i	0.669713	+	0.921781i	−0.330041	+	0.943967i	$0.607062\pi$
$788$	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	0.0643577	−	0.997927i	$-0.479500\pi$
$797$	19.8463	−	6.44844i	0.702991	−	0.228416i	0.638633	+	0.769511i	$0.279500\pi$
$798$	−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	−0.888719	−	0.458453i	$-0.848404\pi$
$809$	−20.6875	+	15.0303i	−0.727333	+	0.528438i	0.161386	+	0.986891i	$0.448404\pi$
$810$	−32.6147	+	40.1225i	−1.14596	+	1.40976i
$811$	−41.5595	−	30.1947i	−1.45935	−	1.06028i	−0.983531	−	0.180737i	$-0.942152\pi$
$811$	−41.5595	−	30.1947i	−1.45935	−	1.06028i	−0.475819	−	0.879543i	$-0.657848\pi$
$812$	−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	0.923218	+	0.384276i	$0.125549\pi$
$821$	11.5240	+	35.4673i	0.402191	+	1.23782i	−0.521028	+	0.853540i	$0.674451\pi$
$822$	50.8729	−	16.5296i	1.77439	−	0.576536i
$823$	−15.7566	+	21.6872i	−0.549242	+	0.755967i	−0.989909	−	0.141704i	$-0.954742\pi$
$823$	−15.7566	+	21.6872i	−0.549242	+	0.755967i	0.440667	+	0.897671i	$0.354742\pi$
$824$	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	−0.879907	−	0.475146i	$-0.842395\pi$
$827$	−4.48937	+	6.17908i	−0.156111	+	0.214868i	0.723797	+	0.690013i	$0.242395\pi$
$828$	34.9882	−	11.3684i	1.21592	−	0.395077i
$829$	10.2779	+	31.6322i	0.356967	+	1.09863i	0.954860	+	0.297056i	$0.0960050\pi$
$829$	10.2779	+	31.6322i	0.356967	+	1.09863i	−0.597892	+	0.801576i	$0.703995\pi$
$830$	−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	0.841986	−	0.539499i	$-0.181386\pi$
$839$	17.0630	+	12.3970i	0.589081	+	0.427992i	−0.252906	+	0.967491i	$0.581386\pi$
$840$	−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	0.316768	−	0.948503i	$-0.397402\pi$
$853$	33.0192	−	10.7286i	1.13056	−	0.367340i	0.813787	+	0.581163i	$0.197402\pi$
$854$	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	$-0.734324\pi$
$857$		−	43.3883i		−	1.48212i	0.671441	−	0.741058i	$-0.265676\pi$
$858$	−23.5211	−	7.64247i	−0.802997	−	0.260910i
$859$	42.1658	−	30.6353i	1.43868	−	1.04526i	0.450363	−	0.892845i	$-0.351294\pi$
$859$	42.1658	−	30.6353i	1.43868	−	1.04526i	0.988316	−	0.152417i	$-0.0487055\pi$
$860$	−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	0.339525	−	0.940597i	$-0.389734\pi$
$863$	−19.3874	−	26.6845i	−0.659955	−	0.908350i	−0.999480	+	0.0322468i	$0.989734\pi$
$864$	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	−0.554146	−	0.832419i	$-0.686955\pi$
$877$	12.1055	−	16.6617i	0.408772	−	0.562627i	0.962918	+	0.269793i	$0.0869551\pi$
$878$	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	0.767390	+	0.641181i	$0.221555\pi$
$881$	−6.83622	+	21.0397i	−0.230318	+	0.708847i	−0.997708	+	0.0676657i	$0.978445\pi$
$882$		−	7.80058i		−	0.262659i
$883$	−52.5956	−	17.0894i	−1.76998	−	0.575102i	−0.771829	−	0.635830i	$-0.780658\pi$
$883$	−52.5956	−	17.0894i	−1.76998	−	0.575102i	−0.998154	+	0.0607278i	$0.980658\pi$
$884$	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	0.973695	−	0.227857i	$-0.0731718\pi$
$887$	13.5839	+	18.6966i	0.456102	+	0.627770i	−0.517593	+	0.855627i	$0.673172\pi$
$888$	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	$-0.756387\pi$
$907$		−	41.7280i		−	1.38555i	0.721152	−	0.692777i	$-0.243613\pi$
$908$	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	0.578811	−	0.815462i	$-0.303517\pi$
$911$	−0.539553	−	0.392008i	−0.0178762	−	0.0129878i	−0.596687	+	0.802474i	$0.703517\pi$
$912$	−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	−0.939931	−	0.341363i	$-0.889111\pi$
$919$	0.640781	−	1.97212i	0.0211374	−	0.0650543i	0.961069	+	0.276309i	$0.0891113\pi$
$920$	−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	0.829731	+	0.558164i	$0.188494\pi$
$929$	14.8296	+	45.6410i	0.486545	+	1.49743i	−0.343186	+	0.939267i	$0.611506\pi$
$930$	−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	0.941281	−	0.337624i	$-0.109623\pi$
$937$	10.0803	+	13.8744i	0.329310	+	0.453256i	−0.611971	+	0.790880i	$0.709623\pi$
$938$	−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	−0.952528	−	0.304452i	$-0.901527\pi$
$941$	−29.3666	+	21.3361i	−0.957324	+	0.695536i	−0.00479596	+	0.999988i	$0.501527\pi$
$942$	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	−0.628744	−	0.777613i	$-0.716430\pi$
$947$	−20.9363	+	6.80262i	−0.680338	+	0.221055i	−0.0515949	+	0.998668i	$0.516430\pi$
$948$	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	−0.906173	−	0.422906i	$-0.861010\pi$
$953$	−42.9320	+	13.9495i	−1.39071	+	0.451867i	−0.484532	+	0.874774i	$0.661010\pi$
$954$	−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	0.988008	+	0.154406i	$0.0493463\pi$
$967$	58.4019	+	18.9759i	1.87808	+	0.610225i	0.890072	+	0.455819i	$0.150654\pi$
$968$		−	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	−0.879807	−	0.475331i	$-0.842328\pi$
$971$	−13.9420	−	42.9091i	−0.447421	−	1.37702i	0.432386	−	0.901688i	$-0.357672\pi$
$972$	−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	−0.725949	−	0.687749i	$-0.758599\pi$
$977$	4.76573	−	6.55947i	0.152469	−	0.209856i	0.878418	+	0.477892i	$0.158599\pi$
$978$	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	−0.0276192	−	0.999619i	$-0.508793\pi$
$983$	−19.9882	−	6.49456i	−0.637525	−	0.207144i	−0.609905	+	0.792474i	$0.708793\pi$
$984$	−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	−0.736905	−	0.675996i	$-0.763714\pi$
$991$	−10.1275	+	7.35808i	−0.321712	+	0.233737i	0.415194	+	0.909733i	$0.363714\pi$
$992$	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	−0.786307	−	0.617837i	$-0.788009\pi$
$997$	−33.4473	+	10.8677i	−1.05929	+	0.344183i	−0.272980	+	0.962020i	$0.588009\pi$
$998$	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.134.4	yes	56
5.2	odd	4		875.2.h.d.701.6		56
5.3	odd	4		875.2.h.e.701.9		56
5.4	even	2		875.2.n.c.799.11		56
25.2	odd	20		875.2.h.d.176.6		56
25.8	odd	20		4375.2.a.o.1.11		28
25.11	even	5		875.2.n.c.449.11		56
25.14	even	10	inner	175.2.n.a.64.4	✓	56
25.17	odd	20		4375.2.a.p.1.18		28
25.23	odd	20		875.2.h.e.176.9		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.n.a.64.4	✓	56	25.14	even	10	inner
175.2.n.a.134.4	yes	56	1.1	even	1	trivial
875.2.h.d.176.6		56	25.2	odd	20
875.2.h.d.701.6		56	5.2	odd	4
875.2.h.e.176.9		56	25.23	odd	20
875.2.h.e.701.9		56	5.3	odd	4
875.2.n.c.449.11		56	25.11	even	5
875.2.n.c.799.11		56	5.4	even	2
4375.2.a.o.1.11		28	25.8	odd	20
4375.2.a.p.1.18		28	25.17	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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