LMFDB - Embedded newform 50.4.e.a.39.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,4,Mod(9,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("50.9");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	50.e (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:	$2.95009550029$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.6
Character	$\chi$	$=$	50.39
Dual form			50.4.e.a.9.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17557 + 1.61803i) q^{2} +(-4.16531 - 1.35339i) q^{3} +(-1.23607 + 3.80423i) q^{4} +(-1.15597 + 11.1204i) q^{5} +(-2.70679 - 8.33063i) q^{6} +31.2051i q^{7} +(-7.60845 + 2.47214i) q^{8} +(-6.32528 - 4.59559i) q^{9} +O(q^{10})$	\(q+(1.17557 + 1.61803i) q^{2} +(-4.16531 - 1.35339i) q^{3} +(-1.23607 + 3.80423i) q^{4} +(-1.15597 + 11.1204i) q^{5} +(-2.70679 - 8.33063i) q^{6} +31.2051i q^{7} +(-7.60845 + 2.47214i) q^{8} +(-6.32528 - 4.59559i) q^{9} +(-19.3521 + 11.2024i) q^{10} +(12.0574 - 8.76021i) q^{11} +(10.2972 - 14.1729i) q^{12} +(25.0832 - 34.5241i) q^{13} +(-50.4909 + 36.6838i) q^{14} +(19.8653 - 44.7556i) q^{15} +(-12.9443 - 9.40456i) q^{16} +(27.6773 - 8.99290i) q^{17} -15.6370i q^{18} +(15.9076 + 48.9587i) q^{19} +(-40.8757 - 18.1432i) q^{20} +(42.2328 - 129.979i) q^{21} +(28.3486 + 9.21103i) q^{22} +(109.187 + 150.283i) q^{23} +35.0374 q^{24} +(-122.327 - 25.7097i) q^{25} +85.3482 q^{26} +(89.6334 + 123.370i) q^{27} +(-118.711 - 38.5716i) q^{28} +(23.7789 - 73.1839i) q^{29} +(95.7691 - 20.4707i) q^{30} +(-80.3709 - 247.356i) q^{31} -32.0000i q^{32} +(-62.0789 + 20.1706i) q^{33} +(47.0875 + 34.2110i) q^{34} +(-347.014 - 36.0721i) q^{35} +(25.3011 - 18.3823i) q^{36} +(70.7618 - 97.3953i) q^{37} +(-60.5163 + 83.2935i) q^{38} +(-151.204 + 109.856i) q^{39} +(-18.6961 - 87.4669i) q^{40} +(248.032 + 180.206i) q^{41} +(259.958 - 84.4656i) q^{42} +504.394i q^{43} +(18.4221 + 56.6973i) q^{44} +(58.4167 - 65.0275i) q^{45} +(-114.806 + 353.337i) q^{46} +(-186.822 - 60.7022i) q^{47} +(41.1889 + 56.6917i) q^{48} -630.759 q^{49} +(-102.205 - 228.154i) q^{50} -127.456 q^{51} +(100.333 + 138.096i) q^{52} +(430.808 + 139.978i) q^{53} +(-94.2462 + 290.060i) q^{54} +(83.4793 + 144.210i) q^{55} +(-77.1433 - 237.423i) q^{56} -225.458i q^{57} +(146.368 - 47.5578i) q^{58} +(51.9655 + 37.7552i) q^{59} +(145.706 + 130.893i) q^{60} +(110.566 - 80.3305i) q^{61} +(305.749 - 420.827i) q^{62} +(143.406 - 197.381i) q^{63} +(51.7771 - 37.6183i) q^{64} +(354.927 + 318.844i) q^{65} +(-105.615 - 76.7337i) q^{66} +(-223.555 + 72.6375i) q^{67} +116.407i q^{68} +(-251.407 - 773.750i) q^{69} +(-349.574 - 603.886i) q^{70} +(166.664 - 512.939i) q^{71} +(59.4865 + 19.3283i) q^{72} +(-614.830 - 846.241i) q^{73} +240.774 q^{74} +(474.737 + 272.646i) q^{75} -205.913 q^{76} +(273.363 + 376.252i) q^{77} +(-355.502 - 115.510i) q^{78} +(-109.157 + 335.949i) q^{79} +(119.546 - 133.074i) q^{80} +(-141.150 - 434.416i) q^{81} +613.169i q^{82} +(928.944 - 301.832i) q^{83} +(442.267 + 321.326i) q^{84} +(68.0108 + 318.179i) q^{85} +(-816.127 + 592.951i) q^{86} +(-198.093 + 272.652i) q^{87} +(-70.0817 + 96.4592i) q^{88} +(891.118 - 647.435i) q^{89} +(173.890 + 18.0758i) q^{90} +(1077.33 + 782.724i) q^{91} +(-706.674 + 229.612i) q^{92} +1139.09i q^{93} +(-121.404 - 373.644i) q^{94} +(-562.830 + 120.305i) q^{95} +(-43.3086 + 133.290i) q^{96} +(-1379.77 - 448.316i) q^{97} +(-741.502 - 1020.59i) q^{98} -116.525 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} - 30 q^{5} - 12 q^{6} + 26 q^{9}+O(q^{10}) $ 32 * q + 32 * q^4 - 30 * q^5 - 12 * q^6 + 26 * q^9	\( 32 q + 32 q^{4} - 30 q^{5} - 12 q^{6} + 26 q^{9} - 40 q^{10} - 106 q^{11} + 80 q^{12} + 56 q^{14} + 260 q^{15} - 128 q^{16} + 320 q^{17} + 110 q^{19} - 160 q^{20} - 36 q^{21} - 360 q^{22} - 370 q^{23} - 192 q^{24} - 1050 q^{25} + 808 q^{26} - 1200 q^{27} - 120 q^{28} - 10 q^{29} + 160 q^{30} - 486 q^{31} + 2560 q^{33} + 616 q^{34} + 340 q^{35} - 104 q^{36} + 680 q^{37} + 1012 q^{39} + 160 q^{40} - 96 q^{41} - 1020 q^{42} - 136 q^{44} - 1500 q^{45} - 832 q^{46} + 1040 q^{47} + 320 q^{48} - 2076 q^{49} + 400 q^{50} + 884 q^{51} - 2550 q^{53} - 120 q^{54} + 720 q^{55} - 224 q^{56} + 2250 q^{59} + 360 q^{60} + 934 q^{61} + 4200 q^{62} + 4660 q^{63} + 512 q^{64} + 1670 q^{65} + 16 q^{66} - 3780 q^{67} - 628 q^{69} - 2440 q^{70} - 2616 q^{71} - 600 q^{73} - 2584 q^{74} - 4500 q^{75} + 800 q^{76} - 4320 q^{77} - 6640 q^{78} - 2800 q^{79} + 160 q^{80} - 5268 q^{81} + 4050 q^{83} + 624 q^{84} - 1420 q^{85} - 692 q^{86} + 9390 q^{87} - 1680 q^{88} + 4520 q^{89} + 9220 q^{90} + 3764 q^{91} + 1280 q^{92} + 656 q^{94} - 4860 q^{95} - 192 q^{96} + 1710 q^{97} + 3280 q^{98} - 2108 q^{99}+O(q^{100}) \) 32 * q + 32 * q^4 - 30 * q^5 - 12 * q^6 + 26 * q^9 - 40 * q^10 - 106 * q^11 + 80 * q^12 + 56 * q^14 + 260 * q^15 - 128 * q^16 + 320 * q^17 + 110 * q^19 - 160 * q^20 - 36 * q^21 - 360 * q^22 - 370 * q^23 - 192 * q^24 - 1050 * q^25 + 808 * q^26 - 1200 * q^27 - 120 * q^28 - 10 * q^29 + 160 * q^30 - 486 * q^31 + 2560 * q^33 + 616 * q^34 + 340 * q^35 - 104 * q^36 + 680 * q^37 + 1012 * q^39 + 160 * q^40 - 96 * q^41 - 1020 * q^42 - 136 * q^44 - 1500 * q^45 - 832 * q^46 + 1040 * q^47 + 320 * q^48 - 2076 * q^49 + 400 * q^50 + 884 * q^51 - 2550 * q^53 - 120 * q^54 + 720 * q^55 - 224 * q^56 + 2250 * q^59 + 360 * q^60 + 934 * q^61 + 4200 * q^62 + 4660 * q^63 + 512 * q^64 + 1670 * q^65 + 16 * q^66 - 3780 * q^67 - 628 * q^69 - 2440 * q^70 - 2616 * q^71 - 600 * q^73 - 2584 * q^74 - 4500 * q^75 + 800 * q^76 - 4320 * q^77 - 6640 * q^78 - 2800 * q^79 + 160 * q^80 - 5268 * q^81 + 4050 * q^83 + 624 * q^84 - 1420 * q^85 - 692 * q^86 + 9390 * q^87 - 1680 * q^88 + 4520 * q^89 + 9220 * q^90 + 3764 * q^91 + 1280 * q^92 + 656 * q^94 - 4860 * q^95 - 192 * q^96 + 1710 * q^97 + 3280 * q^98 - 2108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	1.17557	+	1.61803i	0.415627	+	0.572061i
$2$	1.17557	+	1.61803i	0.415627	+	0.572061i
$3$	−4.16531	−	1.35339i	−0.801615	−	0.260461i	−0.120573	−	0.992704i	$-0.538473\pi$
$3$	−4.16531	−	1.35339i	−0.801615	−	0.260461i	−0.681042	+	0.732244i	$0.738473\pi$
$4$	−1.23607	+	3.80423i	−0.154508	+	0.475528i
$5$	−1.15597	+	11.1204i	−0.103393	+	0.994641i
$5$	−1.15597	+	11.1204i	−0.103393	+	0.994641i
$6$	−2.70679	−	8.33063i	−0.184173	−	0.566828i
$7$			31.2051i			1.68492i	0.538761	+	0.842459i	$0.318893\pi$
$7$			31.2051i			1.68492i	−0.538761	+	0.842459i	$0.681107\pi$
$8$	−7.60845	+	2.47214i	−0.336249	+	0.109254i
$9$	−6.32528	−	4.59559i	−0.234270	−	0.170207i
$10$	−19.3521	+	11.2024i	−0.611968	+	0.354252i
$11$	12.0574	−	8.76021i	0.330495	−	0.240118i	−0.410146	−	0.912020i	$-0.634522\pi$
$11$	12.0574	−	8.76021i	0.330495	−	0.240118i	0.740640	+	0.671902i	$0.234522\pi$
$12$	10.2972	−	14.1729i	0.247713	−	0.340947i
$13$	25.0832	−	34.5241i	0.535141	−	0.736558i	−0.452762	−	0.891631i	$-0.649561\pi$
$13$	25.0832	−	34.5241i	0.535141	−	0.736558i	0.987903	+	0.155073i	$0.0495613\pi$
$14$	−50.4909	+	36.6838i	−0.963876	+	0.700297i
$15$	19.8653	−	44.7556i	0.341946	−	0.770389i
$16$	−12.9443	−	9.40456i	−0.202254	−	0.146946i
$17$	27.6773	−	8.99290i	0.394867	−	0.128300i	−0.104852	−	0.994488i	$-0.533437\pi$
$17$	27.6773	−	8.99290i	0.394867	−	0.128300i	0.499718	+	0.866188i	$0.333437\pi$
$18$		−	15.6370i		−	0.204759i
$19$	15.9076	+	48.9587i	0.192077	+	0.591152i	0.999998	+	0.00186182i	$0.000592636\pi$
$19$	15.9076	+	48.9587i	0.192077	+	0.591152i	−0.807921	+	0.589290i	$0.799407\pi$
$20$	−40.8757	−	18.1432i	−0.457005	−	0.202847i
$21$	42.2328	−	129.979i	0.438855	−	1.35066i
$22$	28.3486	+	9.21103i	0.274725	+	0.0892636i
$23$	109.187	+	150.283i	0.989874	+	1.36244i	0.931337	+	0.364159i	$0.118644\pi$
$23$	109.187	+	150.283i	0.989874	+	1.36244i	0.0585368	+	0.998285i	$0.481356\pi$
$24$	35.0374			0.297999
$25$	−122.327	−	25.7097i	−0.978620	−	0.205677i
$26$	85.3482			0.643775
$27$	89.6334	+	123.370i	0.638887	+	0.879353i
$28$	−118.711	−	38.5716i	−0.801226	−	0.260334i
$29$	23.7789	−	73.1839i	0.152263	−	0.468618i	−0.845610	−	0.533801i	$-0.820763\pi$
$29$	23.7789	−	73.1839i	0.152263	−	0.468618i	0.997873	+	0.0651831i	$0.0207631\pi$
$30$	95.7691	−	20.4707i	0.582832	−	0.124581i
$31$	−80.3709	−	247.356i	−0.465646	−	1.43311i	−0.858168	−	0.513369i	$-0.828397\pi$
$31$	−80.3709	−	247.356i	−0.465646	−	1.43311i	0.392522	−	0.919743i	$-0.371603\pi$
$32$		−	32.0000i		−	0.176777i
$33$	−62.0789	+	20.1706i	−0.327471	+	0.106402i
$34$	47.0875	+	34.2110i	0.237513	+	0.172563i
$35$	−347.014	−	36.0721i	−1.67589	−	0.174208i
$36$	25.3011	−	18.3823i	0.117135	−	0.0851035i
$37$	70.7618	−	97.3953i	0.314410	−	0.432748i	−0.622340	−	0.782747i	$-0.713818\pi$
$37$	70.7618	−	97.3953i	0.314410	−	0.432748i	0.936750	+	0.349999i	$0.113818\pi$
$38$	−60.5163	+	83.2935i	−0.258343	+	0.355579i
$39$	−151.204	+	109.856i	−0.620821	+	0.451053i
$40$	−18.6961	−	87.4669i	−0.0739027	−	0.345743i
$41$	248.032	+	180.206i	0.944783	+	0.686425i	0.949567	−	0.313563i	$-0.101523\pi$
$41$	248.032	+	180.206i	0.944783	+	0.686425i	−0.00478394	+	0.999989i	$0.501523\pi$
$42$	259.958	−	84.4656i	0.955058	−	0.310317i
$43$			504.394i			1.78882i	0.447246	+	0.894411i	$0.352405\pi$
$43$			504.394i			1.78882i	−0.447246	+	0.894411i	$0.647595\pi$
$44$	18.4221	+	56.6973i	0.0631189	+	0.194260i
$45$	58.4167	−	65.0275i	0.193516	−	0.215416i
$46$	−114.806	+	353.337i	−0.367984	+	1.13254i
$47$	−186.822	−	60.7022i	−0.579804	−	0.188390i	0.00440862	−	0.999990i	$-0.498597\pi$
$47$	−186.822	−	60.7022i	−0.579804	−	0.188390i	−0.584213	+	0.811600i	$0.698597\pi$
$48$	41.1889	+	56.6917i	0.123856	+	0.170474i
$49$	−630.759			−1.83895
$50$	−102.205	−	228.154i	−0.289081	−	0.645316i
$51$	−127.456			−0.349948
$52$	100.333	+	138.096i	0.267570	+	0.368279i
$53$	430.808	+	139.978i	1.11653	+	0.362782i	0.808442	−	0.588576i	$-0.200311\pi$
$53$	430.808	+	139.978i	1.11653	+	0.362782i	0.308087	+	0.951358i	$0.400311\pi$
$54$	−94.2462	+	290.060i	−0.237505	+	0.730966i
$55$	83.4793	+	144.210i	0.204661	+	0.353550i
$56$	−77.1433	−	237.423i	−0.184084	−	0.566552i
$57$		−	225.458i		−	0.523905i
$58$	146.368	−	47.5578i	0.331363	−	0.107666i
$59$	51.9655	+	37.7552i	0.114667	+	0.0833102i	0.643641	−	0.765328i	$-0.277423\pi$
$59$	51.9655	+	37.7552i	0.114667	+	0.0833102i	−0.528974	+	0.848638i	$0.677423\pi$
$60$	145.706	+	130.893i	0.313508	+	0.281637i
$61$	110.566	−	80.3305i	0.232073	−	0.168611i	−0.465671	−	0.884958i	$-0.654187\pi$
$61$	110.566	−	80.3305i	0.232073	−	0.168611i	0.697744	+	0.716347i	$0.254187\pi$
$62$	305.749	−	420.827i	0.626293	−	0.862018i
$63$	143.406	−	197.381i	0.286785	−	0.394725i
$64$	51.7771	−	37.6183i	0.101127	−	0.0734732i
$65$	354.927	+	318.844i	0.677281	+	0.608428i
$66$	−105.615	−	76.7337i	−0.196974	−	0.143110i
$67$	−223.555	+	72.6375i	−0.407636	+	0.132449i	−0.505656	−	0.862735i	$-0.668749\pi$
$67$	−223.555	+	72.6375i	−0.407636	+	0.132449i	0.0980193	+	0.995185i	$0.468749\pi$
$68$			116.407i			0.207594i
$69$	−251.407	−	773.750i	−0.438635	−	1.34998i
$70$	−349.574	−	603.886i	−0.596886	−	1.03112i
$71$	166.664	−	512.939i	0.278583	−	0.857390i	−0.709666	−	0.704538i	$-0.751154\pi$
$71$	166.664	−	512.939i	0.278583	−	0.857390i	0.988249	−	0.152852i	$-0.0488458\pi$
$72$	59.4865	+	19.3283i	0.0973688	+	0.0316370i
$73$	−614.830	−	846.241i	−0.985759	−	1.35678i	−0.933668	−	0.358139i	$-0.883411\pi$
$73$	−614.830	−	846.241i	−0.985759	−	1.35678i	−0.0520909	−	0.998642i	$-0.516589\pi$
$74$	240.774			0.378236
$75$	474.737	+	272.646i	0.730906	+	0.419766i
$76$	−205.913			−0.310787
$77$	273.363	+	376.252i	0.404580	+	0.556856i
$78$	−355.502	−	115.510i	−0.516060	−	0.167678i
$79$	−109.157	+	335.949i	−0.155457	+	0.478446i	−0.998207	−	0.0598585i	$-0.980935\pi$
$79$	−109.157	+	335.949i	−0.155457	+	0.478446i	0.842750	+	0.538305i	$0.180935\pi$
$80$	119.546	−	133.074i	0.167070	−	0.185977i
$81$	−141.150	−	434.416i	−0.193622	−	0.595907i
$82$			613.169i			0.825771i
$83$	928.944	−	301.832i	1.22849	−	0.399161i	0.378325	−	0.925673i	$-0.376500\pi$
$83$	928.944	−	301.832i	1.22849	−	0.399161i	0.850168	+	0.526512i	$0.176500\pi$
$84$	442.267	+	321.326i	0.574468	+	0.417376i
$85$	68.0108	+	318.179i	0.0867860	+	0.406016i
$86$	−816.127	+	592.951i	−1.02332	+	0.743483i
$87$	−198.093	+	272.652i	−0.244113	+	0.335993i
$88$	−70.0817	+	96.4592i	−0.0848947	+	0.116848i
$89$	891.118	−	647.435i	1.06133	−	0.771101i	0.0869953	−	0.996209i	$-0.472273\pi$
$89$	891.118	−	647.435i	1.06133	−	0.771101i	0.974334	+	0.225108i	$0.0722735\pi$
$90$	173.890	+	18.0758i	0.203662	+	0.0211706i
$91$	1077.33	+	782.724i	1.24104	+	0.901668i
$92$	−706.674	+	229.612i	−0.800825	+	0.260204i
$93$			1139.09i			1.27009i
$94$	−121.404	−	373.644i	−0.133212	−	0.409984i
$95$	−562.830	+	120.305i	−0.607843	+	0.129927i
$96$	−43.3086	+	133.290i	−0.0460434	+	0.141707i
$97$	−1379.77	−	448.316i	−1.44428	−	0.469274i	−0.521048	−	0.853527i	$-0.674459\pi$
$97$	−1379.77	−	448.316i	−1.44428	−	0.469274i	−0.923228	+	0.384253i	$0.874459\pi$
$98$	−741.502	−	1020.59i	−0.764316	−	1.05199i
$99$	−116.525			−0.118295
$100$	249.010	−	433.583i	0.249010	−	0.433583i
$101$	−305.774			−0.301244			−0.150622	−	0.988591i	$-0.548128\pi$
$101$	−305.774			−0.301244			−0.150622	+	0.988591i	$0.548128\pi$
$102$	−149.833	−	206.228i	−0.145448	−	0.200192i
$103$	−337.914	−	109.795i	−0.323259	−	0.105033i	0.142892	−	0.989738i	$-0.454360\pi$
$103$	−337.914	−	109.795i	−0.323259	−	0.105033i	−0.466151	+	0.884705i	$0.654360\pi$
$104$	−105.496	+	324.684i	−0.0994688	+	0.306133i
$105$	1396.60	+	619.898i	1.29804	+	0.576151i
$106$	279.956	+	861.616i	0.256526	+	0.789505i
$107$			254.177i			0.229647i	0.993386	+	0.114823i	$0.0366302\pi$
$107$			254.177i			0.229647i	−0.993386	+	0.114823i	$0.963370\pi$
$108$	−580.120	+	188.492i	−0.516871	+	0.167942i
$109$	723.625	+	525.744i	0.635878	+	0.461992i	0.858432	−	0.512928i	$-0.171439\pi$
$109$	723.625	+	525.744i	0.635878	+	0.461992i	−0.222554	+	0.974920i	$0.571439\pi$
$110$	−135.201	+	304.601i	−0.117190	+	0.264023i
$111$	−426.559	+	309.914i	−0.364750	+	0.265006i
$112$	293.470	−	403.927i	0.247592	−	0.340782i
$113$	785.716	−	1081.45i	0.654106	−	0.900300i	−0.345163	−	0.938543i	$-0.612176\pi$
$113$	785.716	−	1081.45i	0.654106	−	0.900300i	0.999268	+	0.0382434i	$0.0121762\pi$
$114$	364.798	−	265.041i	0.299706	−	0.217749i
$115$	−1797.43	+	1040.48i	−1.45749	+	0.843702i
$116$	249.016	+	180.921i	0.199315	+	0.144811i
$117$	−317.317	+	103.102i	−0.250735	+	0.0814686i
$118$			128.466i			0.100222i
$119$	280.625	+	863.674i	0.216175	+	0.665318i
$120$	−40.5020	+	389.630i	−0.0308109	+	0.296402i
$121$	−342.662	+	1054.61i	−0.257447	+	0.792341i
$122$	259.955	+	84.4645i	0.192912	+	0.0626808i
$123$	−789.243	−	1086.30i	−0.578566	−	0.796328i
$124$	1040.34			0.753431
$125$	427.309	−	1330.61i	0.305757	−	0.952110i
$126$	487.953			0.345002
$127$	−891.078	−	1226.46i	−0.622601	−	0.856937i	0.374938	−	0.927050i	$-0.377664\pi$
$127$	−891.078	−	1226.46i	−0.622601	−	0.856937i	−0.997539	+	0.0701127i	$0.977664\pi$
$128$	121.735	+	39.5542i	0.0840623	+	0.0273135i
$129$	682.643	−	2100.96i	0.465918	−	1.43395i
$130$	−98.6596	+	949.108i	−0.0665617	+	0.640325i
$131$	−385.607	−	1186.78i	−0.257180	−	0.791519i	−0.993392	−	0.114768i	$-0.963387\pi$
$131$	−385.607	−	1186.78i	−0.257180	−	0.791519i	0.736212	−	0.676751i	$-0.236613\pi$
$132$		−	261.094i		−	0.172162i
$133$	−1527.76	+	496.400i	−0.996043	+	0.323634i
$134$	−380.335	−	276.330i	−0.245194	−	0.178144i
$135$	−1475.54	+	854.150i	−0.940697	+	0.544545i
$136$	−188.350	+	136.844i	−0.118756	+	0.0862815i
$137$	−1405.06	+	1933.90i	−0.876222	+	1.20602i	0.101231	+	0.994863i	$0.467722\pi$
$137$	−1405.06	+	1933.90i	−0.876222	+	1.20602i	−0.977453	+	0.211154i	$0.932278\pi$
$138$	956.408	−	1316.38i	0.589962	−	0.812014i
$139$	1423.34	−	1034.12i	0.868534	−	0.631027i	−0.0616594	−	0.998097i	$-0.519639\pi$
$139$	1423.34	−	1034.12i	0.868534	−	0.631027i	0.930193	+	0.367071i	$0.119639\pi$
$140$	566.159	−	1275.53i	0.341780	−	0.770015i
$141$	696.019	+	505.687i	0.415712	+	0.302032i
$142$	1025.88	−	333.328i	0.606266	−	0.196988i
$143$		−	636.005i		−	0.371926i
$144$	38.6567	+	118.973i	0.0223708	+	0.0688501i
$145$	786.349	+	349.030i	0.450363	+	0.199899i
$146$	646.471	−	1989.63i	0.366454	−	1.12783i
$147$	2627.31	+	853.665i	1.47413	+	0.478973i
$148$	283.047	+	389.581i	0.157205	+	0.216374i
$149$	−391.623			−0.215322			−0.107661	−	0.994188i	$-0.534336\pi$
$149$	−391.623			−0.215322			−0.107661	+	0.994188i	$0.534336\pi$
$150$	116.937	+	1088.66i	0.0636523	+	0.592589i
$151$	1937.43			1.04414			0.522072	−	0.852901i	$-0.325159\pi$
$151$	1937.43			1.04414			0.522072	+	0.852901i	$0.325159\pi$
$152$	−242.065	−	333.174i	−0.129172	−	0.177789i
$153$	−216.394	−	70.3108i	−0.114343	−	0.0371522i
$154$	−287.431	+	884.622i	−0.150402	+	0.462889i
$155$	2843.61	−	607.823i	1.47358	−	0.314977i
$156$	−231.019	−	711.004i	−0.118566	−	0.364910i
$157$		−	1798.13i		−	0.914052i	−0.889453	−	0.457026i	$-0.848915\pi$
$157$		−	1798.13i		−	0.914052i	0.889453	−	0.457026i	$-0.151085\pi$
$158$	−671.899	+	218.313i	−0.338313	+	0.109924i
$159$	−1605.01	−	1166.10i	−0.800536	−	0.581623i
$160$	355.853	+	36.9909i	0.175829	+	0.0182774i
$161$	−4689.60	+	3407.20i	−2.29561	+	1.66786i
$162$	536.968	−	739.073i	0.260421	−	0.358439i
$163$	784.182	−	1079.33i	0.376821	−	0.518650i	−0.577917	−	0.816095i	$-0.696134\pi$
$163$	784.182	−	1079.33i	0.376821	−	0.518650i	0.954739	+	0.297445i	$0.0961345\pi$
$164$	−992.129	+	720.824i	−0.472392	+	0.343213i
$165$	−152.545	−	713.659i	−0.0719734	−	0.336717i
$166$	1580.41	+	1148.24i	0.738939	+	0.536871i
$167$	−1535.29	+	498.847i	−0.711404	+	0.231149i	−0.642292	−	0.766460i	$-0.722016\pi$
$167$	−1535.29	+	498.847i	−0.711404	+	0.231149i	−0.0691116	+	0.997609i	$0.522016\pi$
$168$			1093.35i			0.502104i
$169$	116.166	+	357.522i	0.0528748	+	0.162732i
$170$	−434.873	+	484.085i	−0.196195	+	0.218398i
$171$	124.374	−	382.782i	0.0556204	−	0.171182i
$172$	−1918.83	−	623.465i	−0.850636	−	0.276388i
$173$	1941.29	+	2671.96i	0.853142	+	1.17425i	0.983162	+	0.182738i	$0.0584960\pi$
$173$	1941.29	+	2671.96i	0.853142	+	1.17425i	−0.130020	+	0.991511i	$0.541504\pi$
$174$	−674.033			−0.293668
$175$	802.273	−	3817.24i	0.346549	−	1.64889i
$176$	−238.460			−0.102128
$177$	−165.355	−	227.592i	−0.0702195	−	0.0966489i
$178$	2095.14	+	680.753i	0.882234	+	0.286655i
$179$	−854.933	+	2631.21i	−0.356987	+	1.09869i	0.597861	+	0.801600i	$0.296017\pi$
$179$	−854.933	+	2631.21i	−0.356987	+	1.09869i	−0.954848	+	0.297094i	$0.903983\pi$
$180$	175.172	+	302.609i	0.0725365	+	0.125306i
$181$	−1009.96	−	3108.33i	−0.414749	−	1.27647i	−0.912475	−	0.409132i	$-0.865832\pi$
$181$	−1009.96	−	3108.33i	−0.414749	−	1.27647i	0.497726	−	0.867334i	$-0.334168\pi$
$182$			2663.30i			1.08471i
$183$	−569.259	+	184.963i	−0.229950	+	0.0747153i
$184$	−1202.27	−	873.497i	−0.481697	−	0.349973i
$185$	1001.28	+	899.487i	0.397921	+	0.357468i
$186$	−1843.09	+	1339.08i	−0.726568	+	0.527882i
$187$	254.937	−	350.890i	0.0996941	−	0.137217i
$188$	461.850	−	635.681i	0.179169	−	0.246605i
$189$	−3849.77	+	2797.02i	−1.48164	+	1.07647i
$190$	−856.304	−	769.251i	−0.326962	−	0.293723i
$191$	−286.949	−	208.481i	−0.108706	−	0.0789797i	0.532104	−	0.846679i	$-0.321401\pi$
$191$	−286.949	−	208.481i	−0.108706	−	0.0789797i	−0.640810	+	0.767699i	$0.721401\pi$
$192$	−266.580	+	86.6171i	−0.100202	+	0.0325576i
$193$			2907.82i			1.08451i	0.840216	+	0.542253i	$0.182428\pi$
$193$			2907.82i			1.08451i	−0.840216	+	0.542253i	$0.817572\pi$
$194$	−896.631	−	2759.55i	−0.331827	−	1.02126i
$195$	−1046.86	−	1808.44i	−0.384447	−	0.664130i
$196$	779.661	−	2399.55i	0.284133	−	0.874472i
$197$	3974.94	+	1291.54i	1.43758	+	0.467098i	0.921142	−	0.389228i	$-0.127258\pi$
$197$	3974.94	+	1291.54i	1.43758	+	0.467098i	0.516437	+	0.856325i	$0.327258\pi$
$198$	−136.983	−	188.541i	−0.0491665	−	0.0676718i
$199$	1052.08			0.374772			0.187386	−	0.982286i	$-0.439998\pi$
$199$	1052.08			0.374772			0.187386	+	0.982286i	$0.439998\pi$
$200$	994.281	−	106.799i	0.351531	−	0.0377593i
$201$	1029.49			0.361265
$202$	−359.459	−	494.753i	−0.125205	−	0.172330i
$203$	2283.71	+	742.023i	0.789583	+	0.256551i
$204$	157.544	−	484.870i	0.0540700	−	0.166410i
$205$	−2290.68	+	2549.91i	−0.780430	+	0.868749i
$206$	−219.590	−	675.828i	−0.0742697	−	0.228579i
$207$		−	1452.36i		−	0.487663i
$208$	−649.368	+	210.992i	−0.216469	+	0.0703350i
$209$	620.693	+	450.960i	0.205427	+	0.149251i
$210$	638.790	+	2988.48i	0.209908	+	0.982024i
$211$	1074.58	−	780.728i	0.350602	−	0.254727i	−0.398519	−	0.917160i	$-0.630476\pi$
$211$	1074.58	−	780.728i	0.350602	−	0.254727i	0.749122	+	0.662432i	$0.230476\pi$
$212$	−1065.02	+	1465.87i	−0.345026	+	0.474888i
$213$	−1388.42	+	1910.99i	−0.446633	+	0.614737i
$214$	−411.267	+	298.803i	−0.131372	+	0.0954474i
$215$	−5609.07	−	583.062i	−1.77924	−	0.184951i
$216$	−986.959	−	717.067i	−0.310898	−	0.225881i
$217$	7718.77	−	2507.98i	2.41468	−	0.784576i
$218$			1788.90i			0.555778i
$219$	1415.66	+	4356.97i	0.436812	+	1.34437i
$220$	−651.793	+	139.321i	−0.199745	+	0.0426955i
$221$	383.764	−	1181.10i	0.116809	−	0.359501i
$222$	−1002.90	−	325.862i	−0.303200	−	0.0985155i
$223$	−2625.59	−	3613.82i	−0.788442	−	1.08520i	−0.994300	−	0.106616i	$-0.965999\pi$
$223$	−2625.59	−	3613.82i	−0.788442	−	1.08520i	0.205858	−	0.978582i	$-0.434001\pi$
$224$	998.564			0.297854
$225$	655.605	+	724.787i	0.194253	+	0.214752i
$226$	2673.48			0.786891
$227$	1085.71	+	1494.35i	0.317449	+	0.436931i	0.937686	−	0.347483i	$-0.112964\pi$
$227$	1085.71	+	1494.35i	0.317449	+	0.436931i	−0.620237	+	0.784414i	$0.712964\pi$
$228$	857.692	+	278.681i	0.249132	+	0.0809478i
$229$	80.0296	−	246.306i	0.0230939	−	0.0710757i	−0.938845	−	0.344339i	$-0.888103\pi$
$229$	80.0296	−	246.306i	0.0230939	−	0.0710757i	0.961939	+	0.273263i	$0.0881030\pi$
$230$	−3796.54	−	1685.14i	−1.08842	−	0.483108i
$231$	−629.427	−	1937.18i	−0.179278	−	0.551762i
$232$			615.601i			0.174208i
$233$	−3222.33	+	1047.00i	−0.906018	+	0.294383i	−0.724719	−	0.689045i	$-0.758030\pi$
$233$	−3222.33	+	1047.00i	−0.906018	+	0.294383i	−0.181299	+	0.983428i	$0.558030\pi$
$234$	−539.852	−	392.225i	−0.150817	−	0.109575i
$235$	890.994	−	2007.37i	0.247328	−	0.557219i
$236$	−207.862	+	151.021i	−0.0573333	+	0.0416551i
$237$	909.343	−	1251.60i	0.249233	−	0.343040i
$238$	−1067.56	+	1469.37i	−0.290755	+	0.400189i
$239$	2332.67	−	1694.79i	0.631330	−	0.458688i	−0.225530	−	0.974236i	$-0.572411\pi$
$239$	2332.67	−	1694.79i	0.631330	−	0.458688i	0.856861	+	0.515548i	$0.172411\pi$
$240$	−678.048	+	392.504i	−0.182366	+	0.105567i
$241$	5114.13	+	3715.63i	1.36693	+	0.993133i	0.997970	+	0.0636877i	$0.0202861\pi$
$241$	5114.13	+	3715.63i	1.36693	+	0.993133i	0.368960	+	0.929445i	$0.379714\pi$
$242$	−2109.21	+	685.324i	−0.560270	+	0.182043i
$243$		−	2116.81i		−	0.558821i
$244$	168.929	+	519.910i	0.0443220	+	0.136409i
$245$	729.136	−	7014.31i	0.190134	−	1.82909i
$246$	829.859	−	2554.04i	0.215081	−	0.661951i
$247$	2089.27	+	678.844i	0.538206	+	0.174874i
$248$	1223.00	+	1683.31i	0.313146	+	0.431009i
$249$	−4277.84			−1.08874
$250$	2655.31	−	872.830i	0.671746	−	0.220811i
$251$	1232.70			0.309990			0.154995	−	0.987915i	$-0.450464\pi$
$251$	1232.70			0.309990			0.154995	+	0.987915i	$0.450464\pi$
$252$	573.623	+	789.525i	0.143392	+	0.197363i
$253$	2633.02	+	855.522i	0.654296	+	0.212594i
$254$	936.935	−	2883.59i	0.231451	−	0.712332i
$255$	147.334	−	1417.36i	0.0361821	−	0.348073i
$256$	79.1084	+	243.470i	0.0193136	+	0.0594410i
$257$		−	6483.90i		−	1.57375i	−0.617110	−	0.786877i	$-0.711697\pi$
$257$		−	6483.90i		−	1.57375i	0.617110	−	0.786877i	$-0.288303\pi$
$258$	4201.92	−	1365.29i	1.01395	−	0.329454i
$259$	3039.23	+	2208.13i	0.729145	+	0.529755i
$260$	−1651.67	+	956.109i	−0.393970	+	0.228059i
$261$	−486.731	+	353.631i	−0.115433	+	0.0838667i
$262$	1466.93	−	2019.06i	0.345907	−	0.476100i
$263$	−469.694	+	646.478i	−0.110124	+	0.151572i	−0.860521	−	0.509414i	$-0.829862\pi$
$263$	−469.694	+	646.478i	−0.110124	+	0.151572i	0.750398	+	0.660987i	$0.229862\pi$
$264$	422.459	−	306.935i	0.0984870	−	0.0715550i
$265$	−2054.61	+	4628.95i	−0.476279	+	1.07304i
$266$	−2599.18	−	1888.42i	−0.599121	−	0.435287i
$267$	−4588.02	+	1490.74i	−1.05162	+	0.341692i
$268$		−	940.240i		−	0.214307i
$269$	−1260.60	−	3879.74i	−0.285727	−	0.879376i	−0.986180	−	0.165678i	$-0.947019\pi$
$269$	−1260.60	−	3879.74i	−0.285727	−	0.879376i	0.700453	−	0.713698i	$-0.252981\pi$
$270$	−3116.64	−	1383.36i	−0.702492	−	0.311809i
$271$	135.829	−	418.040i	0.0304467	−	0.0937052i	−0.934678	−	0.355494i	$-0.884313\pi$
$271$	135.829	−	418.040i	0.0304467	−	0.0937052i	0.965125	+	0.261789i	$0.0843125\pi$
$272$	−442.837	−	143.886i	−0.0987167	−	0.0320750i
$273$	−3428.08	−	4718.34i	−0.759987	−	1.04603i
$274$	−4780.86			−1.05410
$275$	−1700.17	+	761.623i	−0.372816	+	0.167009i
$276$	3254.28			0.709726
$277$	37.7190	+	51.9157i	0.00818164	+	0.0112611i	0.813088	−	0.582140i	$-0.197785\pi$
$277$	37.7190	+	51.9157i	0.00818164	+	0.0112611i	−0.804907	+	0.593402i	$0.797785\pi$
$278$	3346.47	+	1087.34i	0.721972	+	0.234583i
$279$	−628.378	+	1933.95i	−0.134839	+	0.414991i
$280$	2729.41	−	583.413i	0.582549	−	0.124520i
$281$	−552.262	−	1699.69i	−0.117243	−	0.360836i	0.875166	−	0.483824i	$-0.160752\pi$
$281$	−552.262	−	1699.69i	−0.117243	−	0.360836i	−0.992408	+	0.122988i	$0.960752\pi$
$282$			1720.65i			0.363345i
$283$	−5937.78	+	1929.30i	−1.24722	+	0.405248i	−0.856926	−	0.515440i	$-0.827628\pi$
$283$	−5937.78	+	1929.30i	−1.24722	+	0.405248i	−0.390299	+	0.920688i	$0.627628\pi$
$284$	1745.33	+	1268.06i	0.364670	+	0.264948i
$285$	2507.18	+	260.621i	0.521097	+	0.0541680i
$286$	1029.08	−	747.668i	0.212764	−	0.154582i
$287$	−5623.35	+	7739.87i	−1.15657	+	1.59188i
$288$	−147.059	+	202.409i	−0.0300886	+	0.0414134i
$289$	−3289.54	+	2389.99i	−0.669558	+	0.486462i
$290$	359.667	+	1682.65i	0.0728288	+	0.340719i
$291$	5140.44	+	3734.75i	1.03553	+	0.752354i
$292$	3979.26	−	1292.94i	0.797496	−	0.259122i
$293$			2442.29i			0.486963i	0.969905	+	0.243482i	$0.0782896\pi$
$293$			2442.29i			0.486963i	−0.969905	+	0.243482i	$0.921710\pi$
$294$	1707.33	+	5254.62i	0.338685	+	1.04237i
$295$	−479.924	+	534.235i	−0.0947194	+	0.105438i
$296$	−297.614	+	915.960i	−0.0584407	+	0.179862i
$297$	2161.49	+	702.311i	0.422298	+	0.137213i
$298$	−460.381	−	633.660i	−0.0894937	−	0.123178i
$299$	7927.15			1.53324
$300$	−1624.01	+	1469.00i	−0.312542	+	0.282709i
$301$	−15739.7			−3.01402
$302$	2277.59	+	3134.83i	0.433975	+	0.597315i
$303$	1273.65	+	413.832i	0.241482	+	0.0784622i
$304$	254.522	−	783.339i	0.0480193	−	0.147788i
$305$	765.499	+	1322.39i	0.143713	+	0.248263i
$306$	−140.622	−	432.789i	−0.0262706	−	0.0808526i
$307$			6382.66i			1.18657i	0.804992	+	0.593286i	$0.202170\pi$
$307$			6382.66i			1.18657i	−0.804992	+	0.593286i	$0.797830\pi$
$308$	−1769.24	+	574.862i	−0.327312	+	0.106350i
$309$	1258.92	+	914.661i	0.231772	+	0.168392i
$310$	4326.34	+	3886.52i	0.792644	+	0.712063i
$311$	−2487.41	+	1807.21i	−0.453531	+	0.329510i	−0.790988	−	0.611831i	$-0.790433\pi$
$311$	−2487.41	+	1807.21i	−0.453531	+	0.329510i	0.337457	+	0.941341i	$0.390433\pi$
$312$	878.850	−	1209.63i	0.159471	−	0.219494i
$313$	3265.88	−	4495.09i	0.589771	−	0.811750i	−0.404953	−	0.914337i	$-0.632712\pi$
$313$	3265.88	−	4495.09i	0.589771	−	0.811750i	0.994724	+	0.102587i	$0.0327122\pi$
$314$	2909.43	−	2113.82i	0.522894	−	0.379904i
$315$	2029.19	+	1822.90i	0.362958	+	0.326059i
$316$	−1143.10	−	830.513i	−0.203495	−	0.147848i
$317$	−3164.57	+	1028.23i	−0.560693	+	0.182180i	−0.575633	−	0.817708i	$-0.695244\pi$
$317$	−3164.57	+	1028.23i	−0.560693	+	0.182180i	0.0149397	+	0.999888i	$0.495244\pi$
$318$		−	3967.79i		−	0.699694i
$319$	−354.395	−	1090.72i	−0.0622016	−	0.191437i
$320$	358.478	+	619.268i	0.0626236	+	0.108182i
$321$	344.001	−	1058.73i	0.0598140	−	0.184088i
$322$	−11025.9	−	3582.54i	−1.90823	−	0.620022i
$323$	880.562	+	1211.99i	0.151690	+	0.208783i
$324$	1827.09			0.313287
$325$	−3955.97	+	3578.36i	−0.675193	+	0.610744i
$326$	2668.26			0.453317
$327$	−2302.59	−	3169.24i	−0.389399	−	0.535961i
$328$	−2332.63	−	757.919i	−0.392677	−	0.127589i
$329$	1894.22	−	5829.80i	0.317421	−	0.976923i
$330$	975.398	−	1085.78i	0.162709	−	0.181122i
$331$	−266.427	−	819.978i	−0.0442422	−	0.136163i	0.926495	−	0.376306i	$-0.122806\pi$
$331$	−266.427	−	819.978i	−0.0442422	−	0.136163i	−0.970738	+	0.240143i	$0.922806\pi$
$332$			3907.00i			0.645857i
$333$	−895.177	+	290.861i	−0.147313	+	0.0478651i
$334$	−2611.99	−	1897.73i	−0.427910	−	0.310895i
$335$	−549.337	−	2570.00i	−0.0895926	−	0.419146i
$336$	−1769.07	+	1285.30i	−0.287234	+	0.208688i
$337$	3366.82	−	4634.03i	0.544221	−	0.749056i	−0.444993	−	0.895534i	$-0.646794\pi$
$337$	3366.82	−	4634.03i	0.544221	−	0.749056i	0.989214	+	0.146478i	$0.0467939\pi$
$338$	−441.921	+	608.253i	−0.0711164	+	0.0978834i
$339$	−4736.38	+	3441.18i	−0.758834	+	0.551325i
$340$	−1294.49	−	134.562i	−0.206481	−	0.0214637i
$341$	−3135.95	−	2278.40i	−0.498010	−	0.361826i
$342$	765.565	−	248.747i	0.121044	−	0.0393295i
$343$		−	8979.56i		−	1.41356i
$344$	−1246.93	−	3837.66i	−0.195436	−	0.601490i
$345$	8895.04	−	1901.32i	1.38810	−	0.296706i
$346$	−2041.19	+	6282.15i	−0.317154	+	0.976099i
$347$	−2202.29	−	715.567i	−0.340706	−	0.110702i	0.133666	−	0.991026i	$-0.457325\pi$
$347$	−2202.29	−	715.567i	−0.340706	−	0.110702i	−0.474373	+	0.880324i	$0.657325\pi$
$348$	−792.373	−	1090.61i	−0.122056	−	0.167996i
$349$	4454.14			0.683166			0.341583	−	0.939852i	$-0.389037\pi$
$349$	4454.14			0.683166			0.341583	+	0.939852i	$0.389037\pi$
$350$	7119.56	−	3189.33i	1.08730	−	0.487077i
$351$	6507.52			0.989589
$352$	−280.327	−	385.837i	−0.0424473	−	0.0584238i
$353$	7220.26	+	2346.00i	1.08866	+	0.353726i	0.797727	−	0.603019i	$-0.206036\pi$
$353$	7220.26	+	2346.00i	1.08866	+	0.353726i	0.290929	+	0.956745i	$0.406036\pi$
$354$	173.865	−	535.101i	0.0261040	−	0.0803398i
$355$	5511.44	+	2446.31i	0.823991	+	0.365738i
$356$	1361.51	+	4190.29i	0.202696	+	0.623834i
$357$		−	3977.27i		−	0.589634i
$358$	−5262.43	+	1709.87i	−0.776894	+	0.252428i
$359$	−7535.11	−	5474.58i	−1.10777	−	0.804839i	−0.125455	−	0.992099i	$-0.540039\pi$
$359$	−7535.11	−	5474.58i	−1.10777	−	0.804839i	−0.982310	+	0.187261i	$0.940039\pi$
$360$	−283.704	+	639.172i	−0.0415347	+	0.0935759i
$361$	3405.15	−	2473.98i	0.496450	−	0.360692i
$362$	3842.11	−	5288.21i	0.557836	−	0.767796i
$363$	2854.59	−	3929.01i	0.412747	−	0.568098i
$364$	−4309.31	+	3130.90i	−0.620520	+	0.450834i
$365$	10121.3	−	5858.94i	1.45143	−	0.840195i
$366$	−968.481	−	703.643i	−0.138315	−	0.100492i
$367$	−7331.03	+	2382.00i	−1.04272	+	0.338799i	−0.779806	−	0.626022i	$-0.784682\pi$
$367$	−7331.03	+	2382.00i	−1.04272	+	0.338799i	−0.262910	+	0.964820i	$0.584682\pi$
$368$		−	2972.16i		−	0.421018i
$369$	−740.722	−	2279.71i	−0.104500	−	0.321617i
$370$	−278.327	+	2677.51i	−0.0391068	+	0.376209i
$371$	−4368.03	+	13443.4i	−0.611258	+	1.88126i
$372$	−4333.35	−	1407.99i	−0.603962	−	0.196239i
$373$	5249.03	+	7224.67i	0.728644	+	1.00289i	0.999192	+	0.0401863i	$0.0127951\pi$
$373$	5249.03	+	7224.67i	0.728644	+	1.00289i	−0.270548	+	0.962707i	$0.587205\pi$
$374$	867.448			0.119932
$375$	−3580.72	+	4964.11i	−0.493087	+	0.683588i
$376$	1571.49			0.215541
$377$	−1930.16	−	2656.63i	−0.263682	−	0.362927i
$378$	−9051.35	−	2940.96i	−1.23162	−	0.400177i
$379$	1311.50	−	4036.39i	0.177750	−	0.547059i	−0.821998	−	0.569490i	$-0.807141\pi$
$379$	1311.50	−	4036.39i	0.177750	−	0.547059i	0.999748	+	0.0224313i	$0.00714069\pi$
$380$	238.028	−	2289.84i	0.0321331	−	0.309122i
$381$	2051.73	+	6314.59i	0.275888	+	0.849097i
$382$		−	709.377i		−	0.0950127i
$383$	5191.55	−	1686.84i	0.692626	−	0.225048i	0.0585112	−	0.998287i	$-0.481365\pi$
$383$	5191.55	−	1686.84i	0.692626	−	0.225048i	0.634115	+	0.773239i	$0.281365\pi$
$384$	−453.533	−	329.511i	−0.0602715	−	0.0437898i
$385$	−4500.08	+	2604.98i	−0.595703	+	0.344837i
$386$	−4704.95	+	3418.35i	−0.620403	+	0.450749i
$387$	2317.99	−	3190.43i	0.304470	−	0.419067i
$388$	3410.99	−	4694.82i	0.446306	−	0.614287i
$389$	10460.1	−	7599.69i	1.36336	−	0.990538i	0.365136	−	0.930954i	$-0.381023\pi$
$389$	10460.1	−	7599.69i	1.36336	−	0.990538i	0.998223	−	0.0595840i	$-0.0189774\pi$
$390$	1695.46	−	3819.81i	0.220136	−	0.495958i
$391$	4373.49	+	3177.53i	0.565670	+	0.410983i
$392$	4799.10	−	1559.32i	0.618345	−	0.200912i
$393$			5465.17i			0.701479i
$394$	2583.07	+	7949.89i	0.330288	+	1.01652i
$395$	−3609.72	−	1602.21i	−0.459809	−	0.204091i
$396$	144.032	−	443.286i	0.0182775	−	0.0562525i
$397$	−1933.04	−	628.083i	−0.244374	−	0.0794020i	0.184269	−	0.982876i	$-0.441008\pi$
$397$	−1933.04	−	628.083i	−0.244374	−	0.0794020i	−0.428643	+	0.903474i	$0.641008\pi$
$398$	1236.79	+	1702.29i	0.155765	+	0.214393i
$399$	7035.43			0.882737
$400$	1341.65	+	1483.23i	0.167707	+	0.185404i
$401$	−8972.43			−1.11736			−0.558681	−	0.829383i	$-0.688692\pi$
$401$	−8972.43			−1.11736			−0.558681	+	0.829383i	$0.688692\pi$
$402$	1210.23	+	1665.74i	0.150152	+	0.206666i
$403$	−10555.7	−	3429.75i	−1.30476	−	0.423941i
$404$	377.958	−	1163.23i	0.0465448	−	0.143250i
$405$	4994.06	−	1067.48i	0.612733	−	0.130972i
$406$	1484.05	+	4567.43i	0.181409	+	0.558319i
$407$		−	1794.22i		−	0.218517i
$408$	969.740	−	315.088i	0.117670	−	0.0382332i
$409$	−7002.65	−	5087.72i	−0.846599	−	0.615090i	0.0776075	−	0.996984i	$-0.475272\pi$
$409$	−7002.65	−	5087.72i	−0.846599	−	0.615090i	−0.924206	+	0.381894i	$0.875272\pi$
$410$	−6818.70	−	708.803i	−0.821345	−	0.0853787i
$411$	8469.85	−	6153.71i	1.01651	−	0.738540i
$412$	835.370	−	1149.79i	0.0998925	−	0.137490i
$413$	−1178.15	+	1621.59i	−0.140371	+	0.193204i
$414$	2349.97	−	1707.35i	0.278973	−	0.202686i
$415$	2282.67	+	10679.2i	0.270005	+	1.26318i
$416$	−1104.77	−	802.663i	−0.130206	−	0.0946004i
$417$	−7328.23	+	2381.09i	−0.860587	+	0.279622i
$418$			1534.44i			0.179550i
$419$	1774.40	+	5461.04i	0.206886	+	0.636729i	0.999631	+	0.0271754i	$0.00865126\pi$
$419$	1774.40	+	5461.04i	0.206886	+	0.636729i	−0.792745	+	0.609554i	$0.791349\pi$
$420$	−4084.53	+	4546.76i	−0.474535	+	0.528236i
$421$	1139.25	−	3506.25i	0.131885	−	0.405901i	−0.863207	−	0.504850i	$-0.831548\pi$
$421$	1139.25	−	3506.25i	0.131885	−	0.405901i	0.995093	+	0.0989486i	$0.0315479\pi$
$422$	2526.49	+	820.905i	0.291440	+	0.0946944i
$423$	902.740	+	1242.52i	0.103765	+	0.142821i
$424$	−3623.83			−0.415067
$425$	−3616.90	+	388.505i	−0.412813	+	0.0443418i
$426$	−4724.23			−0.537300
$427$	2506.72	+	3450.21i	0.284096	+	0.391024i
$428$	−966.947	−	314.180i	−0.109204	−	0.0354824i
$429$	−860.764	+	2649.16i	−0.0968720	+	0.298141i
$430$	−5650.45	−	9761.10i	−0.633695	−	1.09470i
$431$	−2973.01	−	9149.99i	−0.332262	−	1.02260i	−0.968055	−	0.250738i	$-0.919327\pi$
$431$	−2973.01	−	9149.99i	−0.332262	−	1.02260i	0.635793	−	0.771859i	$-0.280673\pi$
$432$		−	2439.90i		−	0.271735i
$433$	−1505.50	+	489.167i	−0.167090	+	0.0542907i	−0.391367	−	0.920235i	$-0.627998\pi$
$433$	−1505.50	+	489.167i	−0.167090	+	0.0542907i	0.224278	+	0.974525i	$0.427998\pi$
$434$	13132.0	+	9540.93i	1.45243	+	1.05525i
$435$	−2803.02	−	2518.06i	−0.308952	−	0.277544i
$436$	−2894.50	+	2102.98i	−0.317939	+	0.230996i
$437$	−5620.76	+	7736.31i	−0.615280	+	0.846860i
$438$	−5385.51	+	7412.52i	−0.587510	+	0.808639i
$439$	1345.66	−	977.681i	0.146298	−	0.106292i	−0.512229	−	0.858849i	$-0.671180\pi$
$439$	1345.66	−	977.681i	0.146298	−	0.106292i	0.658527	+	0.752557i	$0.271180\pi$
$440$	−991.654	−	890.841i	−0.107444	−	0.0965209i
$441$	3989.73	+	2898.71i	0.430810	+	0.313002i
$442$	2362.21	−	767.528i	0.254205	−	0.0825964i
$443$		−	6466.22i		−	0.693497i	−0.937958	−	0.346748i	$-0.887286\pi$
$443$		−	6466.22i		−	0.693497i	0.937958	−	0.346748i	$-0.112714\pi$
$444$	−651.725	−	2005.80i	−0.0696610	−	0.214395i
$445$	6169.65	+	10658.0i	0.657234	+	1.13537i
$446$	2760.71	−	8496.59i	0.293102	−	0.902075i
$447$	1631.23	+	530.020i	0.172606	+	0.0560830i
$448$	1173.88	+	1615.71i	0.123796	+	0.170391i
$449$	−5559.14			−0.584303			−0.292151	−	0.956372i	$-0.594371\pi$
$449$	−5559.14			−0.584303			−0.292151	+	0.956372i	$0.594371\pi$
$450$	−402.021	+	1912.83i	−0.0421143	+	0.200381i
$451$	4569.26			0.477069
$452$	3142.87	+	4325.78i	0.327053	+	0.450150i
$453$	−8070.01	−	2622.11i	−0.837002	−	0.271959i
$454$	−1141.58	+	3513.42i	−0.118011	+	0.363201i
$455$	−9949.58	+	11075.5i	−1.02515	+	1.14116i
$456$	557.362	+	1715.38i	0.0572387	+	0.176163i
$457$			1317.36i			0.134843i	0.997725	+	0.0674216i	$0.0214773\pi$
$457$			1317.36i			0.134843i	−0.997725	+	0.0674216i	$0.978523\pi$
$458$	492.611	−	160.059i	0.0502581	−	0.0163299i
$459$	3590.27	+	2608.48i	0.365096	+	0.265258i
$460$	−1736.49	−	8123.94i	−0.176010	−	0.823436i
$461$	6845.97	−	4973.89i	0.691646	−	0.502510i	−0.185555	−	0.982634i	$-0.559408\pi$
$461$	6845.97	−	4973.89i	0.691646	−	0.502510i	0.877201	+	0.480124i	$0.159408\pi$
$462$	2394.48	−	3295.72i	0.241129	−	0.331885i
$463$	−7458.64	+	10265.9i	−0.748666	+	1.03045i	0.249407	+	0.968399i	$0.419764\pi$
$463$	−7458.64	+	10265.9i	−0.748666	+	1.03045i	−0.998073	+	0.0620519i	$0.980236\pi$
$464$	−996.064	+	723.683i	−0.0996575	+	0.0724054i
$465$	−12667.2	−	1316.75i	−1.26328	−	0.131318i
$466$	−5482.16	−	3983.02i	−0.544971	−	0.395944i
$467$	781.175	−	253.819i	0.0774057	−	0.0251506i	−0.270058	−	0.962844i	$-0.587043\pi$
$467$	781.175	−	253.819i	0.0774057	−	0.0251506i	0.347464	+	0.937693i	$0.387043\pi$
$468$		−	1334.59i		−	0.131819i
$469$	−2266.66	−	6976.07i	−0.223166	−	0.686834i
$470$	4295.42	−	918.147i	0.421559	−	0.0901085i
$471$	−2433.57	+	7489.76i	−0.238074	+	0.732718i
$472$	−488.713	−	158.792i	−0.0476586	−	0.0154852i
$473$	4418.60	+	6081.68i	0.429529	+	0.591196i
$474$	3094.13			0.299828
$475$	−687.231	−	6397.97i	−0.0663838	−	0.618019i
$476$	−3632.48			−0.349778
$477$	−2081.70	−	2865.21i	−0.199821	−	0.275030i
$478$	5484.44	+	1782.00i	0.524796	+	0.170517i
$479$	−3405.28	+	10480.4i	−0.324825	+	0.999710i	0.646694	+	0.762750i	$0.276151\pi$
$479$	−3405.28	+	10480.4i	−0.324825	+	0.999710i	−0.971519	+	0.236960i	$0.923849\pi$
$480$	−1432.18	−	635.688i	−0.136187	−	0.0604481i
$481$	−1587.55	−	4885.97i	−0.150491	−	0.463163i
$482$			12642.8i			1.19474i
$483$	24145.0	−	7845.17i	2.27460	−	0.739064i
$484$	−3588.40	−	2607.13i	−0.337003	−	0.244847i
$485$	6580.43	−	14825.4i	0.616086	−	1.38802i
$486$	3425.07	−	2488.46i	0.319680	−	0.232261i
$487$	−4616.73	+	6354.39i	−0.429577	+	0.591262i	−0.967856	−	0.251504i	$-0.919075\pi$
$487$	−4616.73	+	6354.39i	−0.429577	+	0.591262i	0.538279	+	0.842767i	$0.319075\pi$
$488$	−642.644	+	884.524i	−0.0596130	+	0.0820503i
$489$	−4727.13	+	3434.46i	−0.437154	+	0.317611i
$490$	12206.5	−	7066.04i	1.12538	−	0.651452i
$491$	−16604.1	−	12063.6i	−1.52614	−	1.10881i	−0.958337	−	0.285641i	$-0.907794\pi$
$491$	−16604.1	−	12063.6i	−1.52614	−	1.10881i	−0.567803	−	0.823164i	$-0.692206\pi$
$492$	5108.09	−	1659.72i	0.468070	−	0.152085i
$493$		−	2239.38i		−	0.204577i
$494$	1357.69	+	4178.54i	0.123654	+	0.380569i
$495$	134.699	−	1295.80i	0.0122308	−	0.117661i
$496$	−1285.93	+	3957.70i	−0.116412	+	0.358278i
$497$	16006.3	+	5200.77i	1.44463	+	0.469389i
$498$	−5028.91	−	6921.70i	−0.452511	−	0.622829i
$499$	−20672.7			−1.85458			−0.927291	−	0.374341i	$-0.877869\pi$
$499$	−20672.7			−1.85458			−0.927291	+	0.374341i	$0.877869\pi$
$500$	4533.77	+	3270.31i	0.405513	+	0.292505i
$501$	7070.11			0.630477
$502$	1449.13	+	1994.55i	0.128840	+	0.177333i
$503$	3087.72	+	1003.26i	0.273707	+	0.0889329i	0.442655	−	0.896692i	$-0.354037\pi$
$503$	3087.72	+	1003.26i	0.273707	+	0.0889329i	−0.168947	+	0.985625i	$0.554037\pi$
$504$	−603.143	+	1856.28i	−0.0533058	+	0.164058i
$505$	353.464	−	3400.34i	0.0311465	−	0.299630i
$506$	1711.04	+	5266.05i	0.150326	+	0.462657i
$507$		−	1646.41i		−	0.144220i
$508$	5767.18	−	1873.87i	0.503695	−	0.163660i
$509$	43.4872	+	31.5953i	0.00378691	+	0.00275135i	0.589677	−	0.807639i	$-0.299255\pi$
$509$	43.4872	+	31.5953i	0.00378691	+	0.00275135i	−0.585890	+	0.810390i	$0.699255\pi$
$510$	2466.54	−	1427.81i	0.214157	−	0.123970i
$511$	26407.1	−	19185.8i	2.28606	−	1.66092i
$512$	−300.946	+	414.217i	−0.0259767	+	0.0357538i
$513$	−4614.17	+	6350.86i	−0.397116	+	0.546583i
$514$	10491.2	−	7622.28i	0.900284	−	0.654094i
$515$	1611.58	−	3630.83i	0.137893	−	0.310667i
$516$	7148.73	+	5193.86i	0.609894	+	0.443114i
$517$	−2784.35	+	904.691i	−0.236858	+	0.0769599i
$518$			7513.39i			0.637296i
$519$	−4469.88	−	13756.9i	−0.378046	−	1.16351i
$520$	−3488.67	−	1548.49i	−0.294208	−	0.130588i
$521$	1555.45	−	4787.17i	0.130797	−	0.402553i	−0.864115	−	0.503294i	$-0.832121\pi$
$521$	1555.45	−	4787.17i	0.130797	−	0.402553i	0.994913	+	0.100741i	$0.0321214\pi$
$522$	−1144.37	−	371.830i	−0.0959538	−	0.0311773i
$523$	−3493.99	−	4809.07i	−0.292126	−	0.402076i	0.637577	−	0.770386i	$-0.279937\pi$
$523$	−3493.99	−	4809.07i	−0.292126	−	0.402076i	−0.929703	+	0.368310i	$0.879937\pi$
$524$	4991.40			0.416126
$525$	−8507.95	+	14814.2i	−0.707271	+	1.23152i
$526$	−1598.18			−0.132479
$527$	−4448.90	−	6123.38i	−0.367736	−	0.506146i
$528$	993.262	+	322.730i	0.0818677	+	0.0266004i
$529$	−6903.40	+	21246.5i	−0.567387	+	1.74624i
$530$	−9905.15	+	2117.23i	−0.811796	+	0.173522i
$531$	−155.189	−	477.624i	−0.0126830	−	0.0390341i
$532$		−	6425.53i		−	0.523651i
$533$	12442.9	−	4042.94i	1.01118	−	0.328554i
$534$	−7805.61	−	5671.10i	−0.632550	−	0.459574i
$535$	−2826.55	−	293.820i	−0.228416	−	0.0237438i
$536$	1521.34	−	1105.32i	0.122597	−	0.0890718i
$537$	7122.13	−	9802.77i	0.572333	−	0.787748i
$538$	4795.63	−	6600.61i	0.384301	−	0.528945i
$539$	−7605.31	+	5525.58i	−0.607762	+	0.441565i
$540$	−1425.52	−	6669.07i	−0.113601	−	0.531465i
$541$	−16453.2	−	11953.9i	−1.30754	−	0.949982i	−0.307539	−	0.951535i	$-0.599505\pi$
$541$	−16453.2	−	11953.9i	−1.30754	−	0.949982i	−0.999999	+	0.00155356i	$0.999505\pi$
$542$	836.080	−	271.659i	0.0662596	−	0.0215290i
$543$			14314.0i			1.13126i
$544$	−287.773	−	885.674i	−0.0226804	−	0.0698032i
$545$	−6682.98	+	7439.27i	−0.525262	+	0.584703i
$546$	3604.49	−	11093.5i	0.282524	−	0.869519i
$547$	17348.4	+	5636.82i	1.35606	+	0.440609i	0.894724	−	0.446619i	$-0.147372\pi$
$547$	17348.4	+	5636.82i	1.35606	+	0.440609i	0.461331	+	0.887228i	$0.347372\pi$
$548$	−5620.24	−	7735.60i	−0.438111	−	0.603008i
$549$	−1068.52			−0.0830665
$550$	−3231.00	−	1855.60i	−0.250492	−	0.143860i
$551$	3961.26			0.306271
$552$	3825.63	+	5265.53i	0.294981	+	0.406007i
$553$	−10483.3	−	3406.24i	−0.806143	−	0.261932i
$554$	−39.6601	+	122.061i	−0.00304151	+	0.00936080i
$555$	−2953.28	−	5101.77i	−0.225873	−	0.390195i
$556$	2174.67	+	6692.95i	0.165875	+	0.510511i
$557$		−	2617.19i		−	0.199092i	−0.995033	−	0.0995458i	$-0.968261\pi$
$557$		−	2617.19i		−	0.199092i	0.995033	−	0.0995458i	$-0.0317390\pi$
$558$	−3867.90	+	1256.76i	−0.293443	+	0.0953454i
$559$	17413.7	+	12651.8i	1.31757	+	0.957272i
$560$	4152.60	+	3730.44i	0.313356	+	0.281500i
$561$	−1536.78	+	1116.54i	−0.115656	+	0.0840290i
$562$	2100.93	−	2891.68i	0.157691	−	0.217043i
$563$	−9201.70	+	12665.1i	−0.688820	+	0.948079i	−0.999997	−	0.00227286i	$-0.999277\pi$
$563$	−9201.70	+	12665.1i	−0.688820	+	0.948079i	0.311178	+	0.950352i	$0.399277\pi$
$564$	−2784.08	+	2022.75i	−0.207856	+	0.151016i
$565$	11117.9	+	9987.61i	0.827845	+	0.743685i
$566$	−10102.0	−	7339.50i	−0.750207	−	0.545057i
$567$	13556.0	−	4404.62i	1.00405	−	0.326237i
$568$			4314.69i			0.318733i
$569$	−2209.54	−	6800.27i	−0.162792	−	0.501023i	0.836075	−	0.548616i	$-0.184845\pi$
$569$	−2209.54	−	6800.27i	−0.162792	−	0.501023i	−0.998867	+	0.0475929i	$0.984845\pi$
$570$	2525.68	+	4363.09i	0.185595	+	0.320613i
$571$	2342.24	−	7208.67i	0.171663	−	0.528325i	−0.827802	−	0.561020i	$-0.810409\pi$
$571$	2342.24	−	7208.67i	0.171663	−	0.528325i	0.999465	+	0.0326951i	$0.0104090\pi$
$572$	2419.51	+	786.145i	0.176861	+	0.0574657i
$573$	913.076	+	1256.74i	0.0665695	+	0.0916250i
$574$	−19134.0			−1.39136
$575$	−9492.86	−	21190.9i	−0.688486	−	1.53691i
$576$	−500.383			−0.0361967
$577$	4557.21	+	6272.46i	0.328803	+	0.452558i	0.941129	−	0.338047i	$-0.109766\pi$
$577$	4557.21	+	6272.46i	0.328803	+	0.452558i	−0.612327	+	0.790605i	$0.709766\pi$
$578$	−7734.17	−	2512.98i	−0.556573	−	0.180841i
$579$	3935.42	−	12112.0i	0.282471	−	0.869356i
$580$	−2299.77	+	2560.02i	−0.164643	+	0.183274i
$581$	9418.71	+	28987.8i	0.672554	+	2.06991i
$582$			12707.9i			0.905083i
$583$	6420.66	−	2086.20i	0.456117	−	0.148202i
$584$	6769.93	+	4918.64i	0.479695	+	0.348519i
$585$	−779.735	−	3647.88i	−0.0551078	−	0.257814i
$586$	−3951.71	+	2871.09i	−0.278573	+	0.202395i
$587$	−5047.27	+	6946.97i	−0.354894	+	0.488470i	−0.948717	−	0.316126i	$-0.897618\pi$
$587$	−5047.27	+	6946.97i	−0.354894	+	0.488470i	0.593823	+	0.804596i	$0.297618\pi$
$588$	−6495.07	+	8939.70i	−0.455531	+	0.626984i
$589$	10831.7	−	7869.70i	0.757747	−	0.550536i
$590$	−1428.59	−	148.502i	−0.0996852	−	0.0103623i
$591$	−14808.9	−	10759.3i	−1.03072	−	0.748865i
$592$	−1831.92	+	595.227i	−0.127182	+	0.0413238i
$593$			7557.43i			0.523350i	0.965156	+	0.261675i	$0.0842748\pi$
$593$			7557.43i			0.523350i	−0.965156	+	0.261675i	$0.915725\pi$
$594$	1404.62	+	4322.98i	0.0970241	+	0.298610i
$595$	−9928.81	+	2122.29i	−0.684103	+	0.146227i
$596$	484.073	−	1489.82i	0.0332691	−	0.102392i
$597$	−4382.22	−	1423.87i	−0.300423	−	0.0976133i
$598$	9318.93	+	12826.4i	0.637256	+	0.877108i
$599$	1555.67			0.106115			0.0530577	−	0.998591i	$-0.483103\pi$
$599$	1555.67			0.106115			0.0530577	+	0.998591i	$0.483103\pi$
$600$	−4286.03	−	900.799i	−0.291628	−	0.0612916i
$601$	3958.20			0.268650			0.134325	−	0.990937i	$-0.457113\pi$
$601$	3958.20			0.268650			0.134325	+	0.990937i	$0.457113\pi$
$602$	−18503.1	−	25467.3i	−1.25271	−	1.72420i
$603$	1747.86	+	567.915i	0.118041	+	0.0383537i
$604$	−2394.80	+	7370.42i	−0.161329	+	0.496520i
$605$	−11331.6	−	5029.64i	−0.761476	−	0.337990i
$606$	827.665	+	2547.29i	0.0554812	+	0.170753i
$607$		−	23128.2i		−	1.54653i	−0.634081	−	0.773266i	$-0.718622\pi$
$607$		−	23128.2i		−	1.54653i	0.634081	−	0.773266i	$-0.281378\pi$
$608$	1566.68	−	509.045i	0.104502	−	0.0339547i
$609$	−8508.14	−	6181.52i	−0.566120	−	0.411310i
$610$	−1239.78	+	2793.17i	−0.0822906	+	0.185397i
$611$	−6781.78	+	4927.25i	−0.449037	+	0.326244i
$612$	534.957	−	736.305i	0.0353339	−	0.0486329i
$613$	5456.58	−	7510.33i	0.359525	−	0.494844i	−0.590491	−	0.807044i	$-0.701066\pi$
$613$	5456.58	−	7510.33i	0.359525	−	0.494844i	0.950016	+	0.312200i	$0.101066\pi$
$614$	−10327.4	+	7503.26i	−0.678792	+	0.493171i
$615$	12992.4	−	7520.99i	0.851880	−	0.493131i
$616$	−3010.02	−	2186.91i	−0.196878	−	0.143041i
$617$	5259.91	−	1709.05i	0.343203	−	0.111513i	−0.132344	−	0.991204i	$-0.542250\pi$
$617$	5259.91	−	1709.05i	0.343203	−	0.111513i	0.475547	+	0.879691i	$0.342250\pi$
$618$			3112.23i			0.202576i
$619$	4872.99	+	14997.5i	0.316417	+	0.973831i	0.975167	+	0.221469i	$0.0710853\pi$
$619$	4872.99	+	14997.5i	0.316417	+	0.973831i	−0.658750	+	0.752361i	$0.728915\pi$
$620$	−1202.60	+	11569.0i	−0.0778993	+	0.749394i
$621$	−8753.60	+	26940.8i	−0.565652	+	1.74090i
$622$	−5848.26	−	1900.21i	−0.377000	−	0.122495i
$623$	20203.3	+	27807.4i	1.29924	+	1.78825i
$624$	2990.38			0.191844
$625$	14303.0	+	6290.00i	0.915394	+	0.402560i
$626$	11112.5			0.709496
$627$	−1975.06	−	2718.43i	−0.125799	−	0.173148i
$628$	6840.48	+	2222.61i	0.434657	+	0.141229i
$629$	1082.63	−	3331.99i	0.0686285	−	0.211217i
$630$	−564.057	+	5426.24i	−0.0356708	+	0.343153i
$631$	6785.23	+	20882.8i	0.428075	+	1.31748i	0.900019	+	0.435852i	$0.143553\pi$
$631$	6785.23	+	20882.8i	0.428075	+	1.31748i	−0.471943	+	0.881629i	$0.656447\pi$
$632$		−	2825.90i		−	0.177861i
$633$	−5532.59	+	1797.65i	−0.347395	+	0.112875i
$634$	−5383.88	−	3911.62i	−0.337258	−	0.245032i
$635$	14668.8	−	8491.41i	0.916717	−	0.530664i
$636$	6420.02	−	4664.42i	0.400268	−	0.290812i
$637$	−15821.5	+	21776.4i	−0.984096	+	1.35449i
$638$	1348.20	−	1855.64i	0.0836610	−	0.115149i
$639$	−3411.45	+	2478.57i	−0.211197	+	0.153444i
$640$	−580.581	+	1308.02i	−0.0358586	+	0.0807878i
$641$	23240.6	+	16885.3i	1.43205	+	1.04045i	0.989630	+	0.143643i	$0.0458817\pi$
$641$	23240.6	+	16885.3i	1.43205	+	1.04045i	0.442425	+	0.896806i	$0.354118\pi$
$642$	2117.45	−	688.003i	0.130170	−	0.0422949i
$643$		−	19485.8i		−	1.19509i	−0.801834	−	0.597547i	$-0.796142\pi$
$643$		−	19485.8i		−	1.19509i	0.801834	−	0.597547i	$-0.203858\pi$
$644$	−7165.08	−	22051.8i	−0.438422	−	1.34932i
$645$	22574.4	+	10019.9i	1.37809	+	0.611680i
$646$	−925.877	+	2849.56i	−0.0563903	+	0.173552i
$647$	−17212.8	−	5592.78i	−1.04591	−	0.339838i	−0.264850	−	0.964290i	$-0.585322\pi$
$647$	−17212.8	−	5592.78i	−1.04591	−	0.339838i	−0.781063	+	0.624452i	$0.785322\pi$
$648$	2147.87	+	2956.29i	0.130211	+	0.179219i
$649$	957.312			0.0579010
$650$	−10440.4	−	2194.27i	−0.630011	−	0.132410i
$651$	−35545.4			−2.13999
$652$	3136.73	+	4317.34i	0.188411	+	0.259325i
$653$	−25011.1	−	8126.61i	−1.49887	−	0.487012i	−0.559181	−	0.829045i	$-0.688885\pi$
$653$	−25011.1	−	8126.61i	−1.49887	−	0.487012i	−0.939688	+	0.342033i	$0.888885\pi$
$654$	2421.08	−	7451.33i	0.144758	−	0.445520i
$655$	13643.2	−	2916.24i	0.813868	−	0.173965i
$656$	−1515.84	−	4665.27i	−0.0902188	−	0.277665i
$657$			8178.22i			0.485636i
$658$	11659.6	−	3788.44i	0.690789	−	0.224451i
$659$	−832.956	−	605.178i	−0.0492373	−	0.0357730i	0.562894	−	0.826529i	$-0.309688\pi$
$659$	−832.956	−	605.178i	−0.0492373	−	0.0357730i	−0.612132	+	0.790756i	$0.709688\pi$
$660$	2903.48	+	301.816i	0.171239	+	0.0178003i
$661$	3435.86	−	2496.30i	0.202178	−	0.146891i	−0.482090	−	0.876122i	$-0.660122\pi$
$661$	3435.86	−	2496.30i	0.202178	−	0.146891i	0.684267	+	0.729231i	$0.260122\pi$
$662$	1013.55	−	1395.03i	0.0595056	−	0.0819024i
$663$	−3197.00	+	4400.29i	−0.187272	+	0.257757i
$664$	−6321.66	+	4592.95i	−0.369470	+	0.268435i
$665$	−3754.13	−	17563.2i	−0.218916	−	1.02417i
$666$	−1522.97	−	1106.50i	−0.0886092	−	0.0643784i
$667$	13594.7	−	4417.18i	0.789187	−	0.256422i
$668$		−	6457.21i		−	0.374007i
$669$	6045.50	+	18606.1i	0.349376	+	1.07527i
$670$	3512.56	−	3910.06i	0.202540	−	0.225461i
$671$	629.420	−	1937.15i	0.0362123	−	0.111450i
$672$	−4159.33	−	1351.45i	−0.238764	−	0.0775793i
$673$	−8195.71	−	11280.4i	−0.469422	−	0.646105i	0.507007	−	0.861942i	$-0.330752\pi$
$673$	−8195.71	−	11280.4i	−0.469422	−	0.646105i	−0.976429	+	0.215837i	$0.930752\pi$
$674$	11456.0			0.654699
$675$	−7792.84	−	17396.0i	−0.444365	−	0.991957i
$676$	−1503.68			−0.0855532
$677$	−7907.76	−	10884.1i	−0.448921	−	0.617887i	0.523244	−	0.852183i	$-0.324722\pi$
$677$	−7907.76	−	10884.1i	−0.448921	−	0.617887i	−0.972165	+	0.234296i	$0.924722\pi$
$678$	−11135.9	−	3618.27i	−0.630784	−	0.204954i
$679$	13989.7	−	43056.0i	0.790688	−	2.43349i
$680$	−1304.04	−	2252.72i	−0.0735406	−	0.127041i
$681$	−2499.87	−	7693.82i	−0.140669	−	0.432934i
$682$		−	7752.51i		−	0.435277i
$683$	−18301.2	+	5946.43i	−1.02530	+	0.333139i	−0.772928	−	0.634493i	$-0.781209\pi$
$683$	−18301.2	+	5946.43i	−1.02530	+	0.333139i	−0.252367	+	0.967632i	$0.581209\pi$
$684$	1302.46	+	946.290i	0.0728080	+	0.0528981i
$685$	−19881.6	−	17860.4i	−1.10896	−	0.996220i
$686$	14529.2	−	10556.1i	0.808642	−	0.587513i
$687$	−666.697	+	917.629i	−0.0370248	+	0.0509603i
$688$	4743.61	−	6529.01i	0.262861	−	0.361797i
$689$	15638.7	−	11362.1i	0.864710	−	0.628249i
$690$	13533.1	+	12157.3i	0.746664	+	0.670757i
$691$	−18585.0	−	13502.8i	−1.02316	−	0.743373i	−0.0562356	−	0.998418i	$-0.517910\pi$
$691$	−18585.0	−	13502.8i	−1.02316	−	0.743373i	−0.966929	+	0.255045i	$0.917910\pi$
$692$	−12564.3	+	4082.39i	−0.690206	+	0.224262i
$693$		−	3636.17i		−	0.199317i
$694$	−1431.13	−	4404.58i	−0.0782783	−	0.240916i
$695$	9854.49	+	17023.6i	0.537845	+	0.929122i
$696$	833.150	−	2564.17i	0.0453743	−	0.139648i
$697$	8485.44	+	2757.09i	0.461132	+	0.149831i
$698$	5236.16	+	7206.96i	0.283942	+	0.390813i
$699$	14839.0			0.802953
$700$	13530.0	+	7770.40i	0.730551	+	0.419562i
$701$	−4226.67			−0.227730			−0.113865	−	0.993496i	$-0.536323\pi$
$701$	−4226.67			−0.227730			−0.113865	+	0.993496i	$0.536323\pi$
$702$	7650.05	+	10529.4i	0.411300	+	0.566106i
$703$	5894.00	+	1915.08i	0.316211	+	0.102743i
$704$	294.753	−	907.156i	0.0157797	−	0.0485650i
$705$	−6428.03	+	7155.47i	−0.343395	+	0.382256i
$706$	4692.01	+	14440.5i	0.250122	+	0.769796i
$707$		−	9541.71i		−	0.507572i
$708$	1070.20	−	347.729i	0.0568088	−	0.0184583i
$709$	18626.9	+	13533.2i	0.986668	+	0.716856i	0.959189	−	0.282766i	$-0.0912520\pi$
$709$	18626.9	+	13533.2i	0.986668	+	0.716856i	0.0274791	+	0.999622i	$0.491252\pi$
$710$	2520.87	+	11793.5i	0.133249	+	0.623384i
$711$	2234.33	−	1623.34i	0.117854	−	0.0856257i
$712$	−5179.48	+	7128.94i	−0.272625	+	0.375236i
$713$	28398.0	−	39086.5i	1.49160	−	2.05302i
$714$	6435.35	−	4675.56i	0.337307	−	0.245068i
$715$	7072.64	+	735.200i	0.369932	+	0.0384544i
$716$	−8952.98	−	6504.72i	−0.467302	−	0.339515i
$717$	−12010.0	+	3902.29i	−0.625554	+	0.203255i
$718$		−	18627.8i		−	0.968222i
$719$	1901.30	+	5851.59i	0.0986181	+	0.303515i	0.988180	−	0.153300i	$-0.0489901\pi$
$719$	1901.30	+	5851.59i	0.0986181	+	0.303515i	−0.889562	+	0.456815i	$0.848990\pi$
$720$	−1367.72	+	292.350i	−0.0707941	+	0.0151323i
$721$	3426.16	−	10544.7i	0.176972	−	0.544665i
$722$	8005.98	+	2601.30i	0.412676	+	0.134086i
$723$	−16273.3	−	22398.2i	−0.837080	−	1.15214i
$724$	13073.2			0.671078
$725$	−4790.35	+	8341.06i	−0.245392	+	0.427282i
$726$	9713.04			0.496536
$727$	16997.0	+	23394.3i	0.867101	+	1.19346i	0.979829	+	0.199836i	$0.0640410\pi$
$727$	16997.0	+	23394.3i	0.867101	+	1.19346i	−0.112729	+	0.993626i	$0.535959\pi$
$728$	−10131.8	−	3292.02i	−0.515810	−	0.167597i
$729$	−6675.94	+	20546.4i	−0.339173	+	1.04387i
$730$	21378.2	+	9488.97i	1.08390	+	0.481100i
$731$	4535.97	+	13960.3i	0.229506	+	0.706346i
$732$		−	2394.22i		−	0.120892i
$733$	−10380.1	+	3372.68i	−0.523051	+	0.169949i	−0.558629	−	0.829417i	$-0.688673\pi$
$733$	−10380.1	+	3372.68i	−0.523051	+	0.169949i	0.0355788	+	0.999367i	$0.488673\pi$
$734$	−12472.3	−	9061.65i	−0.627194	−	0.455683i
$735$	−12530.2	+	28230.0i	−0.628821	+	1.41671i
$736$	4809.06	−	3493.99i	0.240848	−	0.174987i
$737$	−2059.17	+	2834.21i	−0.102918	+	0.141655i
$738$	2817.87	−	3878.47i	0.140552	−	0.193453i
$739$	−11697.6	+	8498.82i	−0.582278	+	0.423050i	−0.839545	−	0.543290i	$-0.817178\pi$
$739$	−11697.6	+	8498.82i	−0.582278	+	0.423050i	0.257266	+	0.966341i	$0.417178\pi$
$740$	−4659.50	+	2697.26i	−0.231468	+	0.133991i
$741$	−7783.72	−	5655.20i	−0.385887	−	0.280363i
$742$	−26886.8	+	8736.06i	−1.33025	+	0.432225i
$743$		−	22720.1i		−	1.12183i	−0.827874	−	0.560915i	$-0.810450\pi$
$743$		−	22720.1i		−	1.12183i	0.827874	−	0.560915i	$-0.189550\pi$
$744$	−2815.98	−	8666.71i	−0.138762	−	0.427066i
$745$	452.703	−	4355.01i	0.0222628	−	0.214168i
$746$	−5519.15	+	16986.2i	−0.270872	+	0.833659i
$747$	−7262.93	−	2359.87i	−0.355739	−	0.115586i
$748$	1019.75	+	1403.56i	0.0498471	+	0.0686086i
$749$	−7931.62			−0.386936
$750$	−12241.5	+	41.9359i	−0.595994	+	0.00204171i
$751$	400.556			0.0194627			0.00973135	−	0.999953i	$-0.496902\pi$
$751$	400.556			0.0194627			0.00973135	+	0.999953i	$0.496902\pi$
$752$	1847.40	+	2542.73i	0.0895847	+	0.123303i
$753$	−5134.59	−	1668.33i	−0.248493	−	0.0807401i
$754$	2029.49	−	6246.12i	0.0980233	−	0.301685i
$755$	−2239.60	+	21545.0i	−0.107957	+	1.03855i
$756$	−5881.92	−	18102.7i	−0.282968	−	0.870885i
$757$			8445.77i			0.405504i	0.979230	+	0.202752i	$0.0649886\pi$
$757$			8445.77i			0.405504i	−0.979230	+	0.202752i	$0.935011\pi$
$758$	8072.77	−	2623.00i	0.386829	−	0.125688i
$759$	−9809.52	−	7127.03i	−0.469121	−	0.340837i
$760$	3984.85	−	2306.73i	0.190192	−	0.110097i
$761$	−7569.25	+	5499.38i	−0.360559	+	0.261961i	−0.753285	−	0.657694i	$-0.771532\pi$
$761$	−7569.25	+	5499.38i	−0.360559	+	0.261961i	0.392726	+	0.919655i	$0.371532\pi$
$762$	−7805.26	+	10743.0i	−0.371069	+	0.510733i
$763$	−16405.9	+	22580.8i	−0.778419	+	1.07140i
$764$	1147.80	−	833.922i	0.0543531	−	0.0394898i
$765$	1032.03	−	2325.12i	0.0487754	−	0.109889i
$766$	8832.39	+	6417.11i	0.416615	+	0.302689i
$767$	2606.92	−	847.041i	0.122726	−	0.0398760i
$768$		−	1121.20i		−	0.0526793i
$769$	3534.39	+	10877.7i	0.165739	+	0.510092i	0.999090	−	0.0426520i	$-0.0135807\pi$
$769$	3534.39	+	10877.7i	0.165739	+	0.510092i	−0.833351	+	0.552744i	$0.813581\pi$
$770$	−9505.11	−	4218.95i	−0.444858	−	0.197455i
$771$	−8775.26	+	27007.5i	−0.409901	+	1.26154i
$772$	−11062.0	−	3594.26i	−0.515713	−	0.167565i
$773$	−2210.68	−	3042.74i	−0.102862	−	0.141578i	0.754483	−	0.656320i	$-0.227888\pi$
$773$	−2210.68	−	3042.74i	−0.102862	−	0.141578i	−0.857345	+	0.514742i	$0.827888\pi$
$774$	7887.19			0.366278
$775$	3472.13	+	32324.8i	0.160932	+	1.49824i
$776$	11606.2			0.536907
$777$	−9670.89	−	13310.8i	−0.446514	−	0.614573i
$778$	24593.1	+	7990.78i	1.13330	+	0.368231i
$779$	−4877.04	+	15010.0i	−0.224311	+	0.690357i
$780$	8173.72	−	1747.13i	0.375213	−	0.0802019i
$781$	−2483.92	−	7644.72i	−0.113805	−	0.350256i
$782$			10811.9i			0.494413i
$783$	11160.1	−	3626.13i	0.509360	−	0.165501i
$784$	8164.72	+	5932.01i	0.371935	+	0.270227i
$785$	19995.9	+	2078.57i	0.909153	+	0.0945063i
$786$	−8842.83	+	6424.69i	−0.401289	+	0.291554i
$787$	13423.6	−	18476.0i	0.608005	−	0.836848i	−0.388406	−	0.921488i	$-0.626974\pi$
$787$	13423.6	−	18476.0i	0.608005	−	0.836848i	0.996412	+	0.0846407i	$0.0269742\pi$
$788$	−9826.60	+	13525.2i	−0.444236	+	0.611439i
$789$	2831.36	−	2057.10i	0.127756	−	0.0928198i
$790$	−1651.04	−	7724.16i	−0.0743562	−	0.347865i
$791$	33746.6	+	24518.4i	1.51693	+	1.10211i
$792$	886.573	−	288.065i	0.0397765	−	0.0129242i
$793$		−	5832.12i		−	0.261166i
$794$	−1256.17	−	3866.08i	−0.0561457	−	0.172799i
$795$	14822.9	−	16500.4i	0.661276	−	0.736110i
$796$	−1300.44	+	4002.33i	−0.0579055	+	0.178215i
$797$	−153.415	−	49.8475i	−0.00681836	−	0.00221542i	0.305606	−	0.952158i	$-0.401141\pi$
$797$	−153.415	−	49.8475i	−0.00681836	−	0.00221542i	−0.312424	+	0.949943i	$0.601141\pi$
$798$	8270.65	+	11383.6i	0.366889	+	0.504980i
$799$	−5716.62			−0.253116
$800$	−822.709	+	3914.48i	−0.0363589	+	0.172997i
$801$	−8611.91			−0.379884
$802$	−10547.7	−	14517.7i	−0.464405	−	0.639199i
$803$	−14826.5	−	4817.42i	−0.651576	−	0.211710i
$804$	−1272.51	+	3916.40i	−0.0558185	+	0.171792i
$805$	−32468.4	−	56089.0i	−1.42157	−	2.45575i
$806$	−6859.51	−	21111.4i	−0.299772	−	0.922602i
$807$			17866.4i			0.779342i
$808$	2326.47	−	755.915i	0.101293	−	0.0329121i
$809$	8390.60	+	6096.13i	0.364645	+	0.264930i	0.754987	−	0.655740i	$-0.227643\pi$
$809$	8390.60	+	6096.13i	0.364645	+	0.264930i	−0.390342	+	0.920670i	$0.627643\pi$
$810$	7598.09	+	6825.66i	0.329592	+	0.296085i
$811$	−34337.8	+	24947.9i	−1.48676	+	1.08020i	−0.511463	+	0.859305i	$0.670896\pi$
$811$	−34337.8	+	24947.9i	−1.48676	+	1.08020i	−0.975299	+	0.220890i	$0.929104\pi$
$812$	−5645.65	+	7770.57i	−0.243994	+	0.335830i
$813$	−1131.54	+	1557.44i	−0.0488130	+	0.0671854i
$814$	2903.11	−	2109.23i	0.125005	−	0.0908214i
$815$	11096.2	+	9968.11i	0.476910	+	0.428427i
$816$	1649.82	+	1198.66i	0.0707785	+	0.0514236i
$817$	−24694.5	+	8023.72i	−1.05747	+	0.343592i
$818$		−	17311.5i		−	0.739954i
$819$	−3217.32	−	9901.91i	−0.137268	−	0.422467i
$820$	−6869.00	−	11866.1i	−0.292531	−	0.505346i
$821$	8552.50	−	26321.9i	0.363562	−	1.11893i	−0.587315	−	0.809359i	$-0.699815\pi$
$821$	8552.50	−	26321.9i	0.363562	−	1.11893i	0.950877	−	0.309570i	$-0.100185\pi$
$822$	19913.8	+	6470.39i	0.844980	+	0.274551i
$823$	−6684.48	−	9200.39i	−0.283118	−	0.389679i	0.643645	−	0.765324i	$-0.277421\pi$
$823$	−6684.48	−	9200.39i	−0.283118	−	0.389679i	−0.926764	+	0.375645i	$0.877421\pi$
$824$	2842.43			0.120171
$825$	8112.53	−	871.398i	0.342354	−	0.0367736i
$826$	−4008.79			−0.168866
$827$	1946.09	+	2678.57i	0.0818287	+	0.112628i	0.847969	−	0.530046i	$-0.177825\pi$
$827$	1946.09	+	2678.57i	0.0818287	+	0.112628i	−0.766140	+	0.642673i	$0.777825\pi$
$828$	5525.12	+	1795.22i	0.231897	+	0.0753480i
$829$	7520.64	−	23146.2i	0.315082	−	0.969722i	−0.660639	−	0.750704i	$-0.729715\pi$
$829$	7520.64	−	23146.2i	0.315082	−	0.969722i	0.975721	−	0.219018i	$-0.0702854\pi$
$830$	−14595.8	+	16247.5i	−0.610395	+	0.679471i
$831$	−86.8491	−	267.294i	−0.00362547	−	0.0111580i
$832$		−	2731.14i		−	0.113804i
$833$	−17457.7	+	5672.36i	−0.726139	+	0.235937i
$834$	−12467.5	−	9058.19i	−0.517644	−	0.376090i
$835$	−3772.64	−	17649.7i	−0.156356	−	0.731490i
$836$	−2482.77	+	1803.84i	−0.102713	+	0.0746257i
$837$	23312.4	−	32086.7i	0.962716	−	1.32506i
$838$	−6750.22	+	9290.88i	−0.278261	+	0.382993i
$839$	−11147.2	+	8098.89i	−0.458692	+	0.333260i	−0.793018	−	0.609198i	$-0.791491\pi$
$839$	−11147.2	+	8098.89i	−0.458692	+	0.333260i	0.334326	+	0.942458i	$0.391491\pi$
$840$	−12158.5	−	1263.87i	−0.499413	−	0.0519139i
$841$	14940.7	+	10855.0i	0.612598	+	0.445079i
$842$	7012.51	−	2278.50i	0.287015	−	0.0932570i
$843$			7827.16i			0.319789i
$844$	1641.81	+	5052.97i	0.0669591	+	0.206079i
$845$	−4110.08	+	878.530i	−0.167327	+	0.0357661i
$846$	−949.197	+	2921.33i	−0.0385746	+	0.118720i
$847$	−32909.1	−	10692.8i	−1.33503	−	0.433777i
$848$	−4260.06	−	5863.47i	−0.172513	−	0.237444i
$849$	27343.8			1.10535
$850$	−4880.54	−	5395.55i	−0.196942	−	0.217725i
$851$	22363.2			0.900822
$852$	−5553.67	−	7643.97i	−0.223316	−	0.307369i
$853$	12442.5	+	4042.80i	0.499439	+	0.162278i	0.547894	−	0.836548i	$-0.315430\pi$
$853$	12442.5	+	4042.80i	0.499439	+	0.162278i	−0.0484548	+	0.998825i	$0.515430\pi$
$854$	−2635.73	+	8111.93i	−0.105612	+	0.325040i
$855$	4112.93	+	1825.57i	0.164514	+	0.0730213i
$856$	−628.360	−	1933.89i	−0.0250898	−	0.0772186i
$857$			17624.7i			0.702508i	0.936280	+	0.351254i	$0.114245\pi$
$857$			17624.7i			0.702508i	−0.936280	+	0.351254i	$0.885755\pi$
$858$	−5298.32	+	1721.53i	−0.210818	+	0.0684988i
$859$	−834.395	−	606.224i	−0.0331423	−	0.0240793i	0.571091	−	0.820887i	$-0.306520\pi$
$859$	−834.395	−	606.224i	−0.0331423	−	0.0240793i	−0.604233	+	0.796808i	$0.706520\pi$
$860$	9151.30	−	20617.5i	0.362857	−	0.817500i
$861$	33898.1	−	24628.4i	1.34175	−	0.974836i
$862$	11310.0	−	15566.9i	0.446891	−	0.615093i
$863$	−21765.5	+	29957.6i	−0.858523	+	1.18166i	0.123396	+	0.992357i	$0.460621\pi$
$863$	−21765.5	+	29957.6i	−0.858523	+	1.18166i	−0.981920	+	0.189299i	$0.939379\pi$
$864$	3947.83	−	2868.27i	0.155449	−	0.112940i
$865$	−31957.4	+	18499.3i	−1.25616	+	0.727161i
$866$	−2561.31	−	1860.90i	−0.100505	−	0.0730209i
$867$	16936.6	−	5503.02i	0.663432	−	0.215562i
$868$			32464.0i			1.26947i
$869$	1626.84	+	5006.91i	0.0635062	+	0.195452i
$870$	779.159	−	7495.53i	0.0303632	−	0.292094i
$871$	−3099.74	+	9540.02i	−0.120586	+	0.371127i
$872$	−6805.38	−	2211.20i	−0.264288	−	0.0858724i
$873$	6667.18	+	9176.59i	0.258477	+	0.355762i
$874$	−19125.2			−0.740183
$875$	41521.9	+	13334.2i	1.60423	+	0.515176i
$876$	−18324.7			−0.706776
$877$	24803.1	+	34138.6i	0.955008	+	1.31446i	0.949267	+	0.314472i	$0.101827\pi$
$877$	24803.1	+	34138.6i	0.955008	+	1.31446i	0.00574075	+	0.999984i	$0.498173\pi$
$878$	3163.84	+	1027.99i	0.121611	+	0.0395138i
$879$	3305.38	−	10172.9i	0.126835	−	0.390357i
$880$	275.652	−	2651.78i	0.0105593	−	0.101581i
$881$	−2050.56	−	6310.96i	−0.0784165	−	0.241341i	0.904162	−	0.427190i	$-0.140497\pi$
$881$	−2050.56	−	6310.96i	−0.0784165	−	0.241341i	−0.982578	+	0.185849i	$0.940497\pi$
$882$			9863.15i			0.376542i
$883$	−5354.36	+	1739.74i	−0.204064	+	0.0663044i	−0.409266	−	0.912415i	$-0.634215\pi$
$883$	−5354.36	+	1739.74i	−0.204064	+	0.0663044i	0.205202	+	0.978720i	$0.434215\pi$
$884$	4018.83	+	2919.85i	0.152905	+	0.111092i
$885$	2722.06	−	1575.73i	0.103391	−	0.0598504i
$886$	10462.6	−	7601.49i	0.396723	−	0.288236i
$887$	19343.9	−	26624.6i	0.732250	−	1.00786i	−0.266777	−	0.963758i	$-0.585959\pi$
$887$	19343.9	−	26624.6i	0.732250	−	1.00786i	0.999027	−	0.0440972i	$-0.0140411\pi$
$888$	2479.31	−	3412.47i	0.0936938	−	0.128959i
$889$	38271.9	−	27806.2i	1.44387	−	1.04903i
$890$	−9992.18	+	22511.9i	−0.376335	+	0.847868i
$891$	−5507.49	−	4001.42i	−0.207079	−	0.150452i
$892$	16993.2	−	5521.42i	0.637863	−	0.207254i
$893$		−	10112.2i		−	0.378938i
$894$	1060.04	+	3262.47i	0.0396567	+	0.122051i
$895$	−28271.9	−	12548.8i	−1.05590	−	0.468671i
$896$	−1234.29	+	3798.76i	−0.0460210	+	0.141638i
$897$	−33019.1	−	10728.6i	−1.22907	−	0.399349i
$898$	−6535.16	−	8994.87i	−0.242852	−	0.334257i
$899$	−20013.6			−0.742483
$900$	−3567.63	+	1598.18i	−0.132134	+	0.0591920i
$901$	13182.4			0.487425
$902$	5371.49	+	7393.22i	0.198283	+	0.272913i
$903$	65560.7	+	21302.0i	2.41608	+	0.785033i
$904$	−3304.60	+	10170.5i	−0.121581	+	0.374189i
$905$	35733.4	−	7638.03i	1.31251	−	0.280549i
$906$	−5244.21	−	16140.0i	−0.192304	−	0.591850i
$907$		−	23738.5i		−	0.869046i	−0.900661	−	0.434523i	$-0.856917\pi$
$907$		−	23738.5i		−	0.869046i	0.900661	−	0.434523i	$-0.143083\pi$
$908$	−7026.85	+	2283.16i	−0.256822	+	0.0834464i
$909$	1934.11	+	1405.21i	0.0705724	+	0.0512738i
$910$	−29617.0	−	3078.69i	−1.07890	−	0.112151i
$911$	−10584.2	+	7689.85i	−0.384928	+	0.279666i	−0.763374	−	0.645957i	$-0.776459\pi$
$911$	−10584.2	+	7689.85i	−0.384928	+	0.279666i	0.378446	+	0.925623i	$0.376459\pi$
$912$	−2120.33	+	2918.39i	−0.0769859	+	0.105962i
$913$	8556.53	−	11777.1i	0.310164	−	0.426904i
$914$	−2131.53	+	1548.65i	−0.0771386	+	0.0560445i
$915$	−1398.83	−	6544.21i	−0.0505397	−	0.236443i
$916$	838.081	+	608.901i	0.0302303	+	0.0219636i
$917$	37033.5	−	12032.9i	1.33364	−	0.433328i
$918$			8875.62i			0.319106i
$919$	983.027	+	3025.45i	0.0352852	+	0.108597i	0.967148	−	0.254215i	$-0.0818170\pi$
$919$	983.027	+	3025.45i	0.0352852	+	0.108597i	−0.931863	+	0.362811i	$0.881817\pi$
$920$	11103.4	−	12360.0i	0.397901	−	0.442930i
$921$	8638.24	−	26585.8i	0.309055	−	0.951174i
$922$	16095.8	+	5229.86i	0.574933	+	0.186807i
$923$	−13528.3	−	18620.1i	−0.482436	−	0.664017i
$924$	8147.48			0.290078
$925$	−11160.1	+	10094.9i	−0.396694	+	0.358829i
$926$	−25378.8			−0.900647
$927$	1632.83	+	2247.40i	0.0578524	+	0.0796270i
$928$	−2341.89	−	760.925i	−0.0828407	−	0.0269166i
$929$	−12964.0	+	39899.2i	−0.457843	+	1.40910i	0.409921	+	0.912121i	$0.365556\pi$
$929$	−12964.0	+	39899.2i	−0.457843	+	1.40910i	−0.867764	+	0.496976i	$0.834444\pi$
$930$	−12760.6	−	22043.8i	−0.449931	−	0.777253i
$931$	−10033.9	−	30881.1i	−0.353220	−	1.08710i
$932$		−	13552.7i		−	0.476322i
$933$	12806.7	−	4161.16i	0.449382	−	0.146013i
$934$	1329.01	+	965.585i	0.0465596	+	0.0338275i
$935$	3607.35	+	3240.62i	0.126174	+	0.113347i
$936$	2159.41	−	1568.90i	0.0754085	−	0.0547875i
$937$	−2442.49	+	3361.80i	−0.0851577	+	0.117210i	−0.849470	−	0.527636i	$-0.823078\pi$
$937$	−2442.49	+	3361.80i	−0.0851577	+	0.117210i	0.764313	+	0.644846i	$0.223078\pi$
$938$	8622.90	−	11868.4i	0.300157	−	0.413131i
$939$	−19687.0	+	14303.5i	−0.684198	+	0.497099i
$940$	6535.16	+	5870.79i	0.226759	+	0.203706i
$941$	−14793.5	−	10748.1i	−0.512490	−	0.372346i	0.301277	−	0.953537i	$-0.402587\pi$
$941$	−14793.5	−	10748.1i	−0.512490	−	0.372346i	−0.813767	+	0.581191i	$0.802587\pi$
$942$	−14979.5	+	4867.14i	−0.518110	+	0.168344i
$943$			56951.2i			1.96669i
$944$	−317.585	−	977.426i	−0.0109497	−	0.0336997i
$945$	−26653.8	−	46044.3i	−0.917513	−	1.58500i
$946$	−4645.99	+	14298.9i	−0.159677	+	0.491434i
$947$	46162.9	+	14999.2i	1.58405	+	0.514688i	0.963096	−	0.269160i	$-0.0867459\pi$
$947$	46162.9	+	14999.2i	1.58405	+	0.514688i	0.620953	+	0.783848i	$0.286746\pi$
$948$	3637.37	+	5006.41i	0.124616	+	0.171520i
$949$	−44637.6			−1.52687
$950$	9544.25	−	8633.23i	0.325954	−	0.294841i
$951$	14573.0			0.496911
$952$	−4270.24	−	5877.48i	−0.145377	−	0.200095i
$953$	32652.7	+	10609.5i	1.10989	+	0.360625i	0.805900	−	0.592051i	$-0.201682\pi$
$953$	32652.7	+	10609.5i	1.10989	+	0.360625i	0.303988	+	0.952676i	$0.401682\pi$
$954$	2188.83	−	6736.52i	0.0742830	−	0.228620i
$955$	2650.09	−	2950.00i	0.0897958	−	0.0999577i
$956$	3564.01	+	10968.9i	0.120573	+	0.371087i
$957$			5022.81i			0.169660i
$958$	−20960.8	+	6810.57i	−0.706902	+	0.229686i
$959$	−60347.6	−	43845.1i	−2.03204	−	1.47636i
$960$	−655.061	−	3064.61i	−0.0220229	−	0.103031i
$961$	−30624.1	+	22249.7i	−1.02797	+	0.746861i
$962$	6039.39	−	8312.51i	0.202409	−	0.278593i
$963$	1168.09	−	1607.74i	0.0390875	−	0.0537993i
$964$	−20456.5	+	14862.5i	−0.683465	+	0.496566i
$965$	−32336.2	−	3361.34i	−1.07869	−	0.112130i
$966$	41077.9	+	29844.8i	1.36818	+	0.994038i
$967$	−6186.33	+	2010.06i	−0.205728	+	0.0668451i	−0.410068	−	0.912055i	$-0.634495\pi$
$967$	−6186.33	+	2010.06i	−0.205728	+	0.0668451i	0.204340	+	0.978900i	$0.434495\pi$
$968$		−	8871.02i		−	0.294551i
$969$	−2027.52	−	6240.06i	−0.0672170	−	0.206873i
$970$	31723.8	−	6780.97i	1.05009	−	0.224458i
$971$	8528.41	−	26247.7i	0.281864	−	0.867487i	−0.705457	−	0.708752i	$-0.749258\pi$
$971$	8528.41	−	26247.7i	0.281864	−	0.867487i	0.987321	−	0.158735i	$-0.0507416\pi$
$972$	8052.83	+	2616.52i	0.265735	+	0.0863426i
$973$	32269.8	+	44415.5i	1.06323	+	1.46341i
$974$	−15708.9			−0.516782
$975$	21320.8	−	9551.03i	0.700320	−	0.313721i
$976$	−2186.66			−0.0717146
$977$	−11978.4	−	16486.8i	−0.392244	−	0.539877i	0.566533	−	0.824039i	$-0.308285\pi$
$977$	−11978.4	−	16486.8i	−0.392244	−	0.539877i	−0.958776	+	0.284162i	$0.908285\pi$
$978$	−11114.1	−	3611.21i	−0.363386	−	0.118071i
$979$	5072.89	−	15612.8i	0.165608	−	0.509689i
$980$	25782.7	+	11444.0i	0.840408	+	0.373024i
$981$	−2161.03	−	6650.96i	−0.0703327	−	0.216462i
$982$		−	41047.7i		−	1.33390i
$983$	−4843.95	+	1573.89i	−0.157170	+	0.0510675i	−0.386545	−	0.922270i	$-0.626332\pi$
$983$	−4843.95	+	1573.89i	−0.157170	+	0.0510675i	0.229375	+	0.973338i	$0.426332\pi$
$984$	8690.40	+	6313.94i	0.281544	+	0.204554i
$985$	−18957.3	+	42710.1i	−0.613229	+	1.38158i
$986$	3623.39	−	2632.54i	0.117031	−	0.0850277i
$987$	−15780.0	+	21719.3i	−0.508900	+	0.700440i
$988$	−5164.96	+	7108.95i	−0.166315	+	0.228913i
$989$	−75801.9	+	55073.3i	−2.43717	+	1.77071i
$990$	2255.00	−	1305.36i	0.0723926	−	0.0419062i
$991$	−1089.49	−	791.563i	−0.0349232	−	0.0253732i	0.570187	−	0.821515i	$-0.306871\pi$
$991$	−1089.49	−	791.563i	−0.0349232	−	0.0253732i	−0.605110	+	0.796142i	$0.706871\pi$
$992$	−7915.39	+	2571.87i	−0.253341	+	0.0823154i
$993$			3776.05i			0.120674i
$994$	10401.5	+	32012.7i	0.331908	+	1.02151i
$995$	−1216.16	+	11699.5i	−0.0387487	+	0.372763i
$996$	5287.71	−	16273.9i	0.168220	−	0.517729i
$997$	−21308.2	−	6923.45i	−0.676868	−	0.219928i	−0.0496443	−	0.998767i	$-0.515809\pi$
$997$	−21308.2	−	6923.45i	−0.676868	−	0.219928i	−0.627224	+	0.778839i	$0.715809\pi$
$998$	−24302.2	−	33449.1i	−0.770814	−	1.06093i
$999$	18358.3			0.581411

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.4.e.a.39.6	yes	32
5.2	odd	4		250.4.d.c.51.3		32
5.3	odd	4		250.4.d.d.51.6		32
5.4	even	2		250.4.e.b.199.3		32
25.3	odd	20		1250.4.a.m.1.12		16
25.9	even	10	inner	50.4.e.a.9.6	✓	32
25.12	odd	20		250.4.d.c.201.3		32
25.13	odd	20		250.4.d.d.201.6		32
25.16	even	5		250.4.e.b.49.3		32
25.22	odd	20		1250.4.a.n.1.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.4.e.a.9.6	✓	32	25.9	even	10	inner
50.4.e.a.39.6	yes	32	1.1	even	1	trivial
250.4.d.c.51.3		32	5.2	odd	4
250.4.d.c.201.3		32	25.12	odd	20
250.4.d.d.51.6		32	5.3	odd	4
250.4.d.d.201.6		32	25.13	odd	20
250.4.e.b.49.3		32	25.16	even	5
250.4.e.b.199.3		32	5.4	even	2
1250.4.a.m.1.12		16	25.3	odd	20
1250.4.a.n.1.5		16	25.22	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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	50.e (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.17557 + 1.61803i) q^{2} +(-4.16531 - 1.35339i) q^{3} +(-1.23607 + 3.80423i) q^{4} +(-1.15597 + 11.1204i) q^{5} +(-2.70679 - 8.33063i) q^{6} +31.2051i q^{7} +(-7.60845 + 2.47214i) q^{8} +(-6.32528 - 4.59559i) q^{9} +O(q^{10})\)	\(q+(1.17557 + 1.61803i) q^{2} +(-4.16531 - 1.35339i) q^{3} +(-1.23607 + 3.80423i) q^{4} +(-1.15597 + 11.1204i) q^{5} +(-2.70679 - 8.33063i) q^{6} +31.2051i q^{7} +(-7.60845 + 2.47214i) q^{8} +(-6.32528 - 4.59559i) q^{9} +(-19.3521 + 11.2024i) q^{10} +(12.0574 - 8.76021i) q^{11} +(10.2972 - 14.1729i) q^{12} +(25.0832 - 34.5241i) q^{13} +(-50.4909 + 36.6838i) q^{14} +(19.8653 - 44.7556i) q^{15} +(-12.9443 - 9.40456i) q^{16} +(27.6773 - 8.99290i) q^{17} -15.6370i q^{18} +(15.9076 + 48.9587i) q^{19} +(-40.8757 - 18.1432i) q^{20} +(42.2328 - 129.979i) q^{21} +(28.3486 + 9.21103i) q^{22} +(109.187 + 150.283i) q^{23} +35.0374 q^{24} +(-122.327 - 25.7097i) q^{25} +85.3482 q^{26} +(89.6334 + 123.370i) q^{27} +(-118.711 - 38.5716i) q^{28} +(23.7789 - 73.1839i) q^{29} +(95.7691 - 20.4707i) q^{30} +(-80.3709 - 247.356i) q^{31} -32.0000i q^{32} +(-62.0789 + 20.1706i) q^{33} +(47.0875 + 34.2110i) q^{34} +(-347.014 - 36.0721i) q^{35} +(25.3011 - 18.3823i) q^{36} +(70.7618 - 97.3953i) q^{37} +(-60.5163 + 83.2935i) q^{38} +(-151.204 + 109.856i) q^{39} +(-18.6961 - 87.4669i) q^{40} +(248.032 + 180.206i) q^{41} +(259.958 - 84.4656i) q^{42} +504.394i q^{43} +(18.4221 + 56.6973i) q^{44} +(58.4167 - 65.0275i) q^{45} +(-114.806 + 353.337i) q^{46} +(-186.822 - 60.7022i) q^{47} +(41.1889 + 56.6917i) q^{48} -630.759 q^{49} +(-102.205 - 228.154i) q^{50} -127.456 q^{51} +(100.333 + 138.096i) q^{52} +(430.808 + 139.978i) q^{53} +(-94.2462 + 290.060i) q^{54} +(83.4793 + 144.210i) q^{55} +(-77.1433 - 237.423i) q^{56} -225.458i q^{57} +(146.368 - 47.5578i) q^{58} +(51.9655 + 37.7552i) q^{59} +(145.706 + 130.893i) q^{60} +(110.566 - 80.3305i) q^{61} +(305.749 - 420.827i) q^{62} +(143.406 - 197.381i) q^{63} +(51.7771 - 37.6183i) q^{64} +(354.927 + 318.844i) q^{65} +(-105.615 - 76.7337i) q^{66} +(-223.555 + 72.6375i) q^{67} +116.407i q^{68} +(-251.407 - 773.750i) q^{69} +(-349.574 - 603.886i) q^{70} +(166.664 - 512.939i) q^{71} +(59.4865 + 19.3283i) q^{72} +(-614.830 - 846.241i) q^{73} +240.774 q^{74} +(474.737 + 272.646i) q^{75} -205.913 q^{76} +(273.363 + 376.252i) q^{77} +(-355.502 - 115.510i) q^{78} +(-109.157 + 335.949i) q^{79} +(119.546 - 133.074i) q^{80} +(-141.150 - 434.416i) q^{81} +613.169i q^{82} +(928.944 - 301.832i) q^{83} +(442.267 + 321.326i) q^{84} +(68.0108 + 318.179i) q^{85} +(-816.127 + 592.951i) q^{86} +(-198.093 + 272.652i) q^{87} +(-70.0817 + 96.4592i) q^{88} +(891.118 - 647.435i) q^{89} +(173.890 + 18.0758i) q^{90} +(1077.33 + 782.724i) q^{91} +(-706.674 + 229.612i) q^{92} +1139.09i q^{93} +(-121.404 - 373.644i) q^{94} +(-562.830 + 120.305i) q^{95} +(-43.3086 + 133.290i) q^{96} +(-1379.77 - 448.316i) q^{97} +(-741.502 - 1020.59i) q^{98} -116.525 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} - 30 q^{5} - 12 q^{6} + 26 q^{9}+O(q^{10}) \) 32 * q + 32 * q^4 - 30 * q^5 - 12 * q^6 + 26 * q^9	\( 32 q + 32 q^{4} - 30 q^{5} - 12 q^{6} + 26 q^{9} - 40 q^{10} - 106 q^{11} + 80 q^{12} + 56 q^{14} + 260 q^{15} - 128 q^{16} + 320 q^{17} + 110 q^{19} - 160 q^{20} - 36 q^{21} - 360 q^{22} - 370 q^{23} - 192 q^{24} - 1050 q^{25} + 808 q^{26} - 1200 q^{27} - 120 q^{28} - 10 q^{29} + 160 q^{30} - 486 q^{31} + 2560 q^{33} + 616 q^{34} + 340 q^{35} - 104 q^{36} + 680 q^{37} + 1012 q^{39} + 160 q^{40} - 96 q^{41} - 1020 q^{42} - 136 q^{44} - 1500 q^{45} - 832 q^{46} + 1040 q^{47} + 320 q^{48} - 2076 q^{49} + 400 q^{50} + 884 q^{51} - 2550 q^{53} - 120 q^{54} + 720 q^{55} - 224 q^{56} + 2250 q^{59} + 360 q^{60} + 934 q^{61} + 4200 q^{62} + 4660 q^{63} + 512 q^{64} + 1670 q^{65} + 16 q^{66} - 3780 q^{67} - 628 q^{69} - 2440 q^{70} - 2616 q^{71} - 600 q^{73} - 2584 q^{74} - 4500 q^{75} + 800 q^{76} - 4320 q^{77} - 6640 q^{78} - 2800 q^{79} + 160 q^{80} - 5268 q^{81} + 4050 q^{83} + 624 q^{84} - 1420 q^{85} - 692 q^{86} + 9390 q^{87} - 1680 q^{88} + 4520 q^{89} + 9220 q^{90} + 3764 q^{91} + 1280 q^{92} + 656 q^{94} - 4860 q^{95} - 192 q^{96} + 1710 q^{97} + 3280 q^{98} - 2108 q^{99}+O(q^{100}) \) 32 * q + 32 * q^4 - 30 * q^5 - 12 * q^6 + 26 * q^9 - 40 * q^10 - 106 * q^11 + 80 * q^12 + 56 * q^14 + 260 * q^15 - 128 * q^16 + 320 * q^17 + 110 * q^19 - 160 * q^20 - 36 * q^21 - 360 * q^22 - 370 * q^23 - 192 * q^24 - 1050 * q^25 + 808 * q^26 - 1200 * q^27 - 120 * q^28 - 10 * q^29 + 160 * q^30 - 486 * q^31 + 2560 * q^33 + 616 * q^34 + 340 * q^35 - 104 * q^36 + 680 * q^37 + 1012 * q^39 + 160 * q^40 - 96 * q^41 - 1020 * q^42 - 136 * q^44 - 1500 * q^45 - 832 * q^46 + 1040 * q^47 + 320 * q^48 - 2076 * q^49 + 400 * q^50 + 884 * q^51 - 2550 * q^53 - 120 * q^54 + 720 * q^55 - 224 * q^56 + 2250 * q^59 + 360 * q^60 + 934 * q^61 + 4200 * q^62 + 4660 * q^63 + 512 * q^64 + 1670 * q^65 + 16 * q^66 - 3780 * q^67 - 628 * q^69 - 2440 * q^70 - 2616 * q^71 - 600 * q^73 - 2584 * q^74 - 4500 * q^75 + 800 * q^76 - 4320 * q^77 - 6640 * q^78 - 2800 * q^79 + 160 * q^80 - 5268 * q^81 + 4050 * q^83 + 624 * q^84 - 1420 * q^85 - 692 * q^86 + 9390 * q^87 - 1680 * q^88 + 4520 * q^89 + 9220 * q^90 + 3764 * q^91 + 1280 * q^92 + 656 * q^94 - 4860 * q^95 - 192 * q^96 + 1710 * q^97 + 3280 * q^98 - 2108 * q^99

Introduction

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