LMFDB - Embedded newform 105.4.s.a.101.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(26,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("105.26");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.8
Character	$\chi$	$=$	105.101
Dual form			105.4.s.a.26.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.133140 + 0.0768685i) q^{2} +(2.47104 - 4.57099i) q^{3} +(-3.98818 + 6.90773i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(0.0223714 + 0.798528i) q^{6} +(-15.0457 - 10.7995i) q^{7} -2.45616i q^{8} +(-14.7880 - 22.5902i) q^{9} +O(q^{10})$	\(q+(-0.133140 + 0.0768685i) q^{2} +(2.47104 - 4.57099i) q^{3} +(-3.98818 + 6.90773i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(0.0223714 + 0.798528i) q^{6} +(-15.0457 - 10.7995i) q^{7} -2.45616i q^{8} +(-14.7880 - 22.5902i) q^{9} +(0.665701 + 0.384343i) q^{10} +(-14.9856 - 8.65197i) q^{11} +(21.7203 + 35.2992i) q^{12} -36.4846i q^{13} +(2.83332 + 0.281303i) q^{14} +(-25.9706 + 0.727588i) q^{15} +(-31.7167 - 54.9349i) q^{16} +(-14.8621 + 25.7418i) q^{17} +(3.70535 + 1.87093i) q^{18} +(-112.843 + 65.1498i) q^{19} +39.8818 q^{20} +(-86.5426 + 42.0878i) q^{21} +2.66026 q^{22} +(134.961 - 77.9197i) q^{23} +(-11.2271 - 6.06926i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(2.80452 + 4.85757i) q^{26} +(-139.801 + 11.7746i) q^{27} +(134.605 - 60.8612i) q^{28} -165.529i q^{29} +(3.40180 - 2.09319i) q^{30} +(12.9990 + 7.50496i) q^{31} +(25.4623 + 14.7007i) q^{32} +(-76.5782 + 47.1200i) q^{33} -4.56970i q^{34} +(-9.14885 + 92.1482i) q^{35} +(215.024 - 12.0576i) q^{36} +(-16.8835 - 29.2431i) q^{37} +(10.0159 - 17.3481i) q^{38} +(-166.771 - 90.1547i) q^{39} +(-10.6355 + 6.14040i) q^{40} +274.227 q^{41} +(8.28707 - 12.2560i) q^{42} +248.354 q^{43} +(119.531 - 69.0113i) q^{44} +(-60.8484 + 120.509i) q^{45} +(-11.9791 + 20.7485i) q^{46} +(229.515 + 397.532i) q^{47} +(-329.480 + 9.23066i) q^{48} +(109.744 + 324.970i) q^{49} -3.84343i q^{50} +(80.9411 + 131.543i) q^{51} +(252.026 + 145.507i) q^{52} +(-211.972 - 122.382i) q^{53} +(17.7081 - 12.3140i) q^{54} +86.5197i q^{55} +(-26.5252 + 36.9545i) q^{56} +(18.9609 + 676.791i) q^{57} +(12.7239 + 22.0385i) q^{58} +(292.478 - 506.587i) q^{59} +(98.5494 - 182.300i) q^{60} +(-221.862 + 128.092i) q^{61} -2.30758 q^{62} +(-21.4667 + 499.586i) q^{63} +502.946 q^{64} +(-157.983 + 91.2115i) q^{65} +(6.57359 - 12.1600i) q^{66} +(-137.355 + 237.906i) q^{67} +(-118.545 - 205.326i) q^{68} +(-22.6774 - 809.448i) q^{69} +(-5.86522 - 12.9719i) q^{70} -1069.38i q^{71} +(-55.4851 + 36.3216i) q^{72} +(-861.294 - 497.268i) q^{73} +(4.49574 + 2.59562i) q^{74} +(68.0770 + 110.637i) q^{75} -1039.32i q^{76} +(132.032 + 292.011i) q^{77} +(29.1340 - 0.816213i) q^{78} +(-5.81624 - 10.0740i) q^{79} +(-158.583 + 274.674i) q^{80} +(-291.632 + 668.126i) q^{81} +(-36.5107 + 21.0794i) q^{82} +584.631 q^{83} +(54.4163 - 765.667i) q^{84} +148.621 q^{85} +(-33.0660 + 19.0906i) q^{86} +(-756.630 - 409.027i) q^{87} +(-21.2506 + 36.8071i) q^{88} +(-548.569 - 950.149i) q^{89} +(-1.16200 - 20.7220i) q^{90} +(-394.014 + 548.935i) q^{91} +1243.03i q^{92} +(66.4260 - 40.8732i) q^{93} +(-61.1154 - 35.2850i) q^{94} +(564.214 + 325.749i) q^{95} +(130.115 - 80.0621i) q^{96} -1117.90i q^{97} +(-39.5912 - 34.8307i) q^{98} +(26.1578 + 466.473i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{3} + 64 q^{4} - 80 q^{5} - 28 q^{6} + 46 q^{7} + 100 q^{9}+O(q^{10}) $ 32 * q - 2 * q^3 + 64 * q^4 - 80 * q^5 - 28 * q^6 + 46 * q^7 + 100 * q^9	\( 32 q - 2 q^{3} + 64 q^{4} - 80 q^{5} - 28 q^{6} + 46 q^{7} + 100 q^{9} + 36 q^{11} + 246 q^{12} + 18 q^{14} + 20 q^{15} - 376 q^{16} - 72 q^{17} - 442 q^{18} - 198 q^{19} - 640 q^{20} - 218 q^{21} + 204 q^{22} + 72 q^{23} - 50 q^{24} - 400 q^{25} - 312 q^{26} + 508 q^{27} + 350 q^{28} + 40 q^{30} + 510 q^{31} + 810 q^{32} + 290 q^{33} - 70 q^{35} - 612 q^{36} - 658 q^{37} - 192 q^{38} - 648 q^{39} - 1404 q^{41} + 1892 q^{42} + 332 q^{43} + 2034 q^{44} - 490 q^{45} - 468 q^{46} + 408 q^{47} + 2810 q^{48} + 980 q^{49} - 888 q^{51} + 3378 q^{52} + 1152 q^{53} + 2714 q^{54} - 3354 q^{56} - 816 q^{57} - 1080 q^{58} - 48 q^{59} - 420 q^{60} - 1662 q^{61} - 2076 q^{62} + 874 q^{63} - 1952 q^{64} + 870 q^{65} - 1892 q^{66} - 1298 q^{67} + 1182 q^{68} + 2450 q^{69} - 450 q^{70} - 2708 q^{72} + 378 q^{73} + 2898 q^{74} - 50 q^{75} - 3528 q^{77} - 1896 q^{78} - 326 q^{79} - 1880 q^{80} - 3308 q^{81} - 2916 q^{82} - 1536 q^{83} + 1380 q^{84} + 720 q^{85} + 5202 q^{86} - 1090 q^{87} + 1668 q^{88} - 1590 q^{89} + 910 q^{90} + 2082 q^{91} - 4950 q^{93} - 1152 q^{94} + 990 q^{95} + 7416 q^{96} - 7830 q^{98} + 3128 q^{99}+O(q^{100}) \) 32 * q - 2 * q^3 + 64 * q^4 - 80 * q^5 - 28 * q^6 + 46 * q^7 + 100 * q^9 + 36 * q^11 + 246 * q^12 + 18 * q^14 + 20 * q^15 - 376 * q^16 - 72 * q^17 - 442 * q^18 - 198 * q^19 - 640 * q^20 - 218 * q^21 + 204 * q^22 + 72 * q^23 - 50 * q^24 - 400 * q^25 - 312 * q^26 + 508 * q^27 + 350 * q^28 + 40 * q^30 + 510 * q^31 + 810 * q^32 + 290 * q^33 - 70 * q^35 - 612 * q^36 - 658 * q^37 - 192 * q^38 - 648 * q^39 - 1404 * q^41 + 1892 * q^42 + 332 * q^43 + 2034 * q^44 - 490 * q^45 - 468 * q^46 + 408 * q^47 + 2810 * q^48 + 980 * q^49 - 888 * q^51 + 3378 * q^52 + 1152 * q^53 + 2714 * q^54 - 3354 * q^56 - 816 * q^57 - 1080 * q^58 - 48 * q^59 - 420 * q^60 - 1662 * q^61 - 2076 * q^62 + 874 * q^63 - 1952 * q^64 + 870 * q^65 - 1892 * q^66 - 1298 * q^67 + 1182 * q^68 + 2450 * q^69 - 450 * q^70 - 2708 * q^72 + 378 * q^73 + 2898 * q^74 - 50 * q^75 - 3528 * q^77 - 1896 * q^78 - 326 * q^79 - 1880 * q^80 - 3308 * q^81 - 2916 * q^82 - 1536 * q^83 + 1380 * q^84 + 720 * q^85 + 5202 * q^86 - 1090 * q^87 + 1668 * q^88 - 1590 * q^89 + 910 * q^90 + 2082 * q^91 - 4950 * q^93 - 1152 * q^94 + 990 * q^95 + 7416 * q^96 - 7830 * q^98 + 3128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.133140	+	0.0768685i	−0.0470722	+	0.0271771i	−0.523351	−	0.852117i	$-0.675318\pi$
$2$	−0.133140	+	0.0768685i	−0.0470722	+	0.0271771i	0.476279	+	0.879294i	$0.341985\pi$
$3$	2.47104	−	4.57099i	0.475551	−	0.879688i
$3$	2.47104	−	4.57099i	0.475551	−	0.879688i
$4$	−3.98818	+	6.90773i	−0.498523	+	0.863467i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$6$	0.0223714	+	0.798528i	0.00152218	+	0.0543329i
$7$	−15.0457	−	10.7995i	−0.812389	−	0.583116i
$7$	−15.0457	−	10.7995i	−0.812389	−	0.583116i
$8$		−	2.45616i		−	0.108548i
$9$	−14.7880	−	22.5902i	−0.547703	−	0.836673i
$10$	0.665701	+	0.384343i	0.0210513	+	0.0121540i
$11$	−14.9856	−	8.65197i	−0.410758	−	0.237152i	0.280357	−	0.959896i	$-0.409547\pi$
$11$	−14.9856	−	8.65197i	−0.410758	−	0.237152i	−0.691116	+	0.722744i	$0.742880\pi$
$12$	21.7203	+	35.2992i	0.522509	+	0.849167i
$13$		−	36.4846i		−	0.778385i	−0.921156	−	0.389192i	$-0.872754\pi$
$13$		−	36.4846i		−	0.778385i	0.921156	−	0.389192i	$-0.127246\pi$
$14$	2.83332	+	0.281303i	0.0540883	+	0.00537011i
$15$	−25.9706	+	0.727588i	−0.447038	+	0.0125242i
$16$	−31.7167	−	54.9349i	−0.495573	−	0.858357i
$17$	−14.8621	+	25.7418i	−0.212034	+	0.367254i	−0.952351	−	0.305004i	$-0.901342\pi$
$17$	−14.8621	+	25.7418i	−0.212034	+	0.367254i	0.740317	+	0.672258i	$0.234675\pi$
$18$	3.70535	+	1.87093i	0.0485199	+	0.0244990i
$19$	−112.843	+	65.1498i	−1.36252	+	0.786652i	−0.989959	−	0.141355i	$-0.954854\pi$
$19$	−112.843	+	65.1498i	−1.36252	+	0.786652i	−0.372562	+	0.928007i	$0.621521\pi$
$20$	39.8818			0.445892
$21$	−86.5426	+	42.0878i	−0.899292	+	0.437348i
$22$	2.66026			0.0257804
$23$	134.961	−	77.9197i	1.22353	−	0.706408i	0.257865	−	0.966181i	$-0.416981\pi$
$23$	134.961	−	77.9197i	1.22353	−	0.706408i	0.965670	+	0.259773i	$0.0836478\pi$
$24$	−11.2271	−	6.06926i	−0.0954883	−	0.0516201i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	2.80452	+	4.85757i	0.0211543	+	0.0366403i
$27$	−139.801	+	11.7746i	−0.996472	+	0.0839268i
$28$	134.605	−	60.8612i	0.908495	−	0.410775i
$29$		−	165.529i		−	1.05993i	−0.848021	−	0.529963i	$-0.822206\pi$
$29$		−	165.529i		−	1.05993i	0.848021	−	0.529963i	$-0.177794\pi$
$30$	3.40180	−	2.09319i	0.0207027	−	0.0127388i
$31$	12.9990	+	7.50496i	0.0753123	+	0.0434816i	0.537183	−	0.843466i	$-0.319488\pi$
$31$	12.9990	+	7.50496i	0.0753123	+	0.0434816i	−0.461871	+	0.886947i	$0.652822\pi$
$32$	25.4623	+	14.7007i	0.140661	+	0.0812105i
$33$	−76.5782	+	47.1200i	−0.403956	+	0.248562i
$34$		−	4.56970i		−	0.0230499i
$35$	−9.14885	+	92.1482i	−0.0441839	+	0.445026i
$36$	215.024	−	12.0576i	0.995482	−	0.0558224i
$37$	−16.8835	−	29.2431i	−0.0750170	−	0.129933i	0.826077	−	0.563558i	$-0.190568\pi$
$37$	−16.8835	−	29.2431i	−0.0750170	−	0.129933i	−0.901094	+	0.433625i	$0.857234\pi$
$38$	10.0159	−	17.3481i	0.0427579	−	0.0740588i
$39$	−166.771	−	90.1547i	−0.684736	−	0.370162i
$40$	−10.6355	+	6.14040i	−0.0420404	+	0.0242721i
$41$	274.227			1.04456			0.522282	−	0.852773i	$-0.325081\pi$
$41$	274.227			1.04456			0.522282	+	0.852773i	$0.325081\pi$
$42$	8.28707	−	12.2560i	0.0304458	−	0.0450271i
$43$	248.354			0.880784			0.440392	−	0.897806i	$-0.354840\pi$
$43$	248.354			0.880784			0.440392	+	0.897806i	$0.354840\pi$
$44$	119.531	−	69.0113i	0.409545	−	0.236451i
$45$	−60.8484	+	120.509i	−0.201572	+	0.399210i
$46$	−11.9791	+	20.7485i	−0.0383963	+	0.0665043i
$47$	229.515	+	397.532i	0.712302	+	1.23374i	0.963991	+	0.265936i	$0.0856808\pi$
$47$	229.515	+	397.532i	0.712302	+	1.23374i	−0.251689	+	0.967808i	$0.580986\pi$
$48$	−329.480	+	9.23066i	−0.990757	+	0.0277569i
$49$	109.744	+	324.970i	0.319953	+	0.947434i
$50$		−	3.84343i		−	0.0108709i
$51$	80.9411	+	131.543i	0.222236	+	0.361172i
$52$	252.026	+	145.507i	0.672110	+	0.388043i
$53$	−211.972	−	122.382i	−0.549371	−	0.317179i	0.199497	−	0.979898i	$-0.436069\pi$
$53$	−211.972	−	122.382i	−0.549371	−	0.317179i	−0.748868	+	0.662719i	$0.769402\pi$
$54$	17.7081	−	12.3140i	0.0446252	−	0.0310319i
$55$			86.5197i			0.212115i
$56$	−26.5252	+	36.9545i	−0.0632960	+	0.0881832i
$57$	18.9609	+	676.791i	0.0440602	+	1.57269i
$58$	12.7239	+	22.0385i	0.0288058	+	0.0498931i
$59$	292.478	−	506.587i	0.645379	−	1.11783i	−0.338834	−	0.940846i	$-0.610033\pi$
$59$	292.478	−	506.587i	0.645379	−	1.11783i	0.984214	−	0.176984i	$-0.0566340\pi$
$60$	98.5494	−	182.300i	0.212045	−	0.392246i
$61$	−221.862	+	128.092i	−0.465680	+	0.268861i	−0.714430	−	0.699707i	$-0.753314\pi$
$61$	−221.862	+	128.092i	−0.465680	+	0.268861i	0.248749	+	0.968568i	$0.419980\pi$
$62$	−2.30758			−0.00472682
$63$	−21.4667	+	499.586i	−0.0429294	+	0.999078i
$64$	502.946			0.982317
$65$	−157.983	+	91.2115i	−0.301467	+	0.174052i
$66$	6.57359	−	12.1600i	0.0122599	−	0.0226787i
$67$	−137.355	+	237.906i	−0.250457	+	0.433804i	−0.963652	−	0.267162i	$-0.913914\pi$
$67$	−137.355	+	237.906i	−0.250457	+	0.433804i	0.713195	+	0.700966i	$0.247248\pi$
$68$	−118.545	−	205.326i	−0.211408	−	0.366169i
$69$	−22.6774	−	809.448i	−0.0395657	−	1.41226i
$70$	−5.86522	−	12.9719i	−0.0100147	−	0.0221491i
$71$		−	1069.38i		−	1.78750i	−0.448569	−	0.893748i	$-0.648066\pi$
$71$		−	1069.38i		−	1.78750i	0.448569	−	0.893748i	$-0.351934\pi$
$72$	−55.4851	+	36.3216i	−0.0908191	+	0.0594520i
$73$	−861.294	−	497.268i	−1.38092	−	0.797272i	−0.388648	−	0.921386i	$-0.627058\pi$
$73$	−861.294	−	497.268i	−1.38092	−	0.797272i	−0.992268	+	0.124114i	$0.960391\pi$
$74$	4.49574	+	2.59562i	0.00706242	+	0.00407749i
$75$	68.0770	+	110.637i	0.104811	+	0.170337i
$76$		−	1039.32i		−	1.56866i
$77$	132.032	+	292.011i	0.195409	+	0.432179i
$78$	29.1340	−	0.816213i	0.0422919	−	0.00118485i
$79$	−5.81624	−	10.0740i	−0.00828327	−	0.0143470i	0.861854	−	0.507156i	$-0.169303\pi$
$79$	−5.81624	−	10.0740i	−0.00828327	−	0.0143470i	−0.870137	+	0.492809i	$0.835970\pi$
$80$	−158.583	+	274.674i	−0.221627	+	0.383869i
$81$	−291.632	+	668.126i	−0.400044	+	0.916496i
$82$	−36.5107	+	21.0794i	−0.0491699	+	0.0283882i
$83$	584.631			0.773152			0.386576	−	0.922258i	$-0.373658\pi$
$83$	584.631			0.773152			0.386576	+	0.922258i	$0.373658\pi$
$84$	54.4163	−	765.667i	0.0706822	−	0.994537i
$85$	148.621			0.189649
$86$	−33.0660	+	19.0906i	−0.0414604	+	0.0239372i
$87$	−756.630	−	409.027i	−0.932405	−	0.504049i
$88$	−21.2506	+	36.8071i	−0.0257423	+	0.0445870i
$89$	−548.569	−	950.149i	−0.653350	−	1.13164i	−0.982305	−	0.187290i	$-0.940030\pi$
$89$	−548.569	−	950.149i	−0.653350	−	1.13164i	0.328955	−	0.944346i	$-0.393304\pi$
$90$	−1.16200	−	20.7220i	−0.00136095	−	0.0242698i
$91$	−394.014	+	548.935i	−0.453888	+	0.632352i
$92$			1243.03i			1.40864i
$93$	66.4260	−	40.8732i	0.0740651	−	0.0455737i
$94$	−61.1154	−	35.2850i	−0.0670592	−	0.0387167i
$95$	564.214	+	325.749i	0.609338	+	0.351801i
$96$	130.115	−	80.0621i	0.138331	−	0.0851178i
$97$		−	1117.90i		−	1.17016i	−0.810976	−	0.585079i	$-0.801064\pi$
$97$		−	1117.90i		−	1.17016i	0.810976	−	0.585079i	$-0.198936\pi$
$98$	−39.5912	−	34.8307i	−0.0408094	−	0.0359024i
$99$	26.1578	+	466.473i	0.0265552	+	0.473559i
$100$	−99.7046	−	172.693i	−0.0997046	−	0.172693i
$101$	−864.575	+	1497.49i	−0.851767	+	1.47530i	0.0278458	+	0.999612i	$0.491135\pi$
$101$	−864.575	+	1497.49i	−0.851767	+	1.47530i	−0.879612	+	0.475691i	$0.842198\pi$
$102$	−20.8881	−	11.2919i	−0.0202767	−	0.0109614i
$103$	−977.085	+	564.120i	−0.934709	+	0.539655i	−0.888298	−	0.459268i	$-0.848112\pi$
$103$	−977.085	+	564.120i	−0.934709	+	0.539655i	−0.0464113	+	0.998922i	$0.514778\pi$
$104$	−89.6120			−0.0844921
$105$	398.602	+	269.521i	0.370472	+	0.250500i
$106$	37.6294			0.0344801
$107$	−882.249	+	509.367i	−0.797105	+	0.460209i	−0.842458	−	0.538762i	$-0.818892\pi$
$107$	−882.249	+	509.367i	−0.797105	+	0.460209i	0.0453528	+	0.998971i	$0.485559\pi$
$108$	476.217	−	1012.67i	0.424296	−	0.902260i
$109$	73.1821	−	126.755i	0.0643080	−	0.111385i	−0.832079	−	0.554657i	$-0.812849\pi$
$109$	73.1821	−	126.755i	0.0643080	−	0.111385i	0.896387	+	0.443273i	$0.146183\pi$
$110$	−6.65064	−	11.5192i	−0.00576467	−	0.00998470i
$111$	−175.390	+	4.91369i	−0.149975	+	0.00420168i
$112$	−116.068	+	1169.05i	−0.0979235	+	0.986296i
$113$		−	911.520i		−	0.758837i	−0.925225	−	0.379419i	$-0.876124\pi$
$113$		−	911.520i		−	0.758837i	0.925225	−	0.379419i	$-0.123876\pi$
$114$	−54.5484	−	88.6506i	−0.0448151	−	0.0728324i
$115$	−674.804	−	389.598i	−0.547181	−	0.315915i
$116$	1143.43	+	660.158i	0.915212	+	0.528398i
$117$	−824.193	+	539.533i	−0.651254	+	0.426323i
$118$			89.9294i			0.0701582i
$119$	501.607	−	226.801i	0.386405	−	0.174713i
$120$	1.78707	+	63.7879i	0.00135947	+	0.0485251i
$121$	−515.787	−	893.369i	−0.387518	−	0.671201i
$122$	19.6925	−	34.1084i	0.0146137	−	0.0253117i
$123$	677.625	−	1253.49i	0.496743	−	0.918890i
$124$	−103.684	+	59.8623i	−0.0750898	+	0.0433531i
$125$	125.000			0.0894427
$126$	−35.5444	−	68.1651i	−0.0251313	−	0.0481955i
$127$	2237.94			1.56366			0.781830	−	0.623491i	$-0.214286\pi$
$127$	2237.94			1.56366			0.781830	+	0.623491i	$0.214286\pi$
$128$	−270.661	+	156.266i	−0.186900	+	0.107907i
$129$	613.693	−	1135.23i	0.418858	−	0.774815i
$130$	14.0226	−	24.2878i	0.00946048	−	0.0163860i
$131$	−700.695	−	1213.64i	−0.467329	−	0.809437i	0.531975	−	0.846760i	$-0.321450\pi$
$131$	−700.695	−	1213.64i	−0.467329	−	0.809437i	−0.999303	+	0.0373234i	$0.988117\pi$
$132$	−20.0847	−	716.905i	−0.0132436	−	0.472716i
$133$	2401.38	+	238.418i	1.56561	+	0.155440i
$134$		−	42.2332i		−	0.0272268i
$135$	400.488	+	575.920i	0.255323	+	0.367165i
$136$	63.2261	+	36.5036i	0.0398646	+	0.0230159i
$137$	−775.480	−	447.724i	−0.483604	−	0.279209i	0.238313	−	0.971188i	$-0.423405\pi$
$137$	−775.480	−	447.724i	−0.483604	−	0.279209i	−0.721917	+	0.691980i	$0.756739\pi$
$138$	65.2403	+	106.027i	0.0402437	+	0.0654029i
$139$			430.880i			0.262926i	0.991321	+	0.131463i	$0.0419675\pi$
$139$			430.880i			0.262926i	−0.991321	+	0.131463i	$0.958032\pi$
$140$	−600.048	−	430.702i	−0.362238	−	0.260007i
$141$	2384.25	−	66.7969i	1.42405	−	0.0398959i
$142$	82.2018	+	142.378i	0.0485790	+	0.0841414i
$143$	−315.664	+	546.745i	−0.184595	+	0.319728i
$144$	−771.963	+	1528.86i	−0.446738	+	0.884757i
$145$	−716.760	+	413.821i	−0.410508	+	0.237007i
$146$	152.897			0.0866703
$147$	1756.62	+	301.374i	0.985600	+	0.169094i
$148$	269.338			0.149591
$149$	−1266.00	+	730.926i	−0.696073	+	0.401878i	−0.805883	−	0.592075i	$-0.798309\pi$
$149$	−1266.00	+	730.926i	−0.696073	+	0.401878i	0.109810	+	0.993953i	$0.464976\pi$
$150$	−17.5683	−	9.49724i	−0.00956296	−	0.00516964i
$151$	−757.698	+	1312.37i	−0.408348	+	0.707280i	−0.994705	−	0.102773i	$-0.967228\pi$
$151$	−757.698	+	1312.37i	−0.408348	+	0.707280i	0.586357	+	0.810053i	$0.300562\pi$
$152$	160.018	+	277.160i	0.0853895	+	0.147899i
$153$	801.292	−	44.9331i	0.423403	−	0.0237426i
$154$	−40.0253	−	28.7293i	−0.0209437	−	0.0150329i
$155$		−	75.0496i		−	0.0388911i
$156$	1287.88	−	792.455i	0.660979	−	0.406713i
$157$	1490.94	+	860.793i	0.757897	+	0.437572i	0.828540	−	0.559930i	$-0.189172\pi$
$157$	1490.94	+	860.793i	0.757897	+	0.437572i	−0.0706433	+	0.997502i	$0.522505\pi$
$158$	1.54875	+	0.894172i	0.000779823	+	0.000450231i
$159$	−1083.20	+	666.513i	−0.540273	+	0.332440i
$160$		−	147.007i		−	0.0726368i
$161$	−2872.07	−	285.150i	−1.40590	−	0.139584i
$162$	−12.5299	−	111.372i	−0.00607680	−	0.0540135i
$163$	480.549	+	832.334i	0.230917	+	0.399960i	0.958078	−	0.286507i	$-0.0924941\pi$
$163$	480.549	+	832.334i	0.230917	+	0.399960i	−0.727161	+	0.686467i	$0.759161\pi$
$164$	−1093.67	+	1894.29i	−0.520739	+	0.901946i
$165$	395.481	+	213.793i	0.186595	+	0.100871i
$166$	−77.8379	+	44.9398i	−0.0363940	+	0.0210121i
$167$	41.4822			0.0192215			0.00961075	−	0.999954i	$-0.496941\pi$
$167$	41.4822			0.0192215			0.00961075	+	0.999954i	$0.496941\pi$
$168$	103.374	+	212.562i	0.0474732	+	0.0976163i
$169$	865.875			0.394117
$170$	−19.7874	+	11.4242i	−0.00892719	+	0.00515412i
$171$	3140.46	+	1585.70i	1.40443	+	0.709134i
$172$	−990.483	+	1715.57i	−0.439091	+	0.760528i
$173$	1109.55	+	1921.80i	0.487616	+	0.844575i	0.999899	−	0.0142416i	$-0.00453340\pi$
$173$	1109.55	+	1921.80i	0.487616	+	0.844575i	−0.512283	+	0.858817i	$0.671200\pi$
$174$	132.179	−	3.70311i	0.0575889	−	0.00161340i
$175$	421.886	−	190.755i	0.182237	−	0.0823984i
$176$			1097.65i			0.470103i
$177$	−1592.88	−	2588.71i	−0.676431	−	1.09932i
$178$	146.073	+	84.3353i	0.0615092	+	0.0355124i
$179$	454.441	+	262.372i	0.189757	+	0.109556i	0.591869	−	0.806034i	$-0.298390\pi$
$179$	454.441	+	262.372i	0.189757	+	0.109556i	−0.402112	+	0.915591i	$0.631724\pi$
$180$	−589.771	−	900.937i	−0.244216	−	0.373066i
$181$		−	3053.58i		−	1.25398i	−0.779026	−	0.626992i	$-0.784286\pi$
$181$		−	3053.58i		−	1.25398i	0.779026	−	0.626992i	$-0.215714\pi$
$182$	10.2632	−	103.373i	0.00418001	−	0.0421015i
$183$	37.2793	+	1330.65i	0.0150588	+	0.537510i
$184$	−191.383	−	331.485i	−0.0766791	−	0.132812i
$185$	−84.4174	+	146.215i	−0.0335486	+	0.0581079i
$186$	−5.70211	+	10.5479i	−0.00224784	+	0.00415813i
$187$	445.435	−	257.172i	0.174190	−	0.100568i
$188$	−3661.39			−1.42040
$189$	2230.56	+	1332.62i	0.858462	+	0.512877i
$190$	−100.159			−0.0382438
$191$	3214.37	−	1855.82i	1.21772	−	0.703049i	0.253287	−	0.967391i	$-0.418488\pi$
$191$	3214.37	−	1855.82i	1.21772	−	0.703049i	0.964429	+	0.264343i	$0.0851550\pi$
$192$	1242.80	−	2298.97i	0.467142	−	0.864133i
$193$	1684.11	−	2916.97i	0.628109	−	1.08792i	−0.359822	−	0.933021i	$-0.617163\pi$
$193$	1684.11	−	2916.97i	0.628109	−	1.08792i	0.987931	−	0.154895i	$-0.0495041\pi$
$194$	85.9311	+	148.837i	0.0318015	+	0.0550819i
$195$	26.5457	+	947.526i	0.00974862	+	0.347968i
$196$	−2682.48	−	537.958i	−0.977581	−	0.196049i
$197$		−	4539.50i		−	1.64176i	−0.571103	−	0.820879i	$-0.693484\pi$
$197$		−	4539.50i		−	1.64176i	0.571103	−	0.820879i	$-0.306516\pi$
$198$	−39.3398	−	60.0957i	−0.0141200	−	0.0215698i
$199$	−618.443	−	357.058i	−0.220303	−	0.127192i	0.385788	−	0.922588i	$-0.373930\pi$
$199$	−618.443	−	357.058i	−0.220303	−	0.127192i	−0.606090	+	0.795396i	$0.707263\pi$
$200$	53.1774	+	30.7020i	0.0188011	+	0.0108548i
$201$	748.059	+	1215.73i	0.262508	+	0.426620i
$202$		−	265.834i		−	0.0925943i
$203$	−1787.62	+	2490.49i	−0.618060	+	0.861073i
$204$	−1231.47	+	34.5008i	−0.422649	+	0.0118409i
$205$	−685.568	−	1187.44i	−0.233571	−	0.404558i
$206$	86.7262	−	150.214i	0.0293325	−	0.0508054i
$207$	−3756.02	−	1896.52i	−1.26117	−	0.636797i
$208$	−2004.28	+	1157.17i	−0.668132	+	0.385746i
$209$	2254.70			0.746223
$210$	−73.7876	−	5.24412i	−0.0242468	−	0.00172323i
$211$	−3219.39			−1.05039			−0.525194	−	0.850983i	$-0.676007\pi$
$211$	−3219.39			−1.05039			−0.525194	+	0.850983i	$0.676007\pi$
$212$	1690.77	−	976.166i	0.547748	−	0.316242i
$213$	−4888.14	−	2642.48i	−1.57244	−	0.850046i
$214$	78.3086	−	135.634i	0.0250143	−	0.0433261i
$215$	−620.886	−	1075.41i	−0.196949	−	0.341126i
$216$	28.9203	+	343.374i	0.00911008	+	0.108165i
$217$	−114.529	−	253.299i	−0.0358281	−	0.0792398i
$218$			22.5016i			0.00699083i
$219$	−4401.30	+	2708.20i	−1.35805	+	0.835632i
$220$	−597.655	−	345.056i	−0.183154	−	0.105744i
$221$	939.180	+	542.236i	0.285865	+	0.165044i
$222$	22.9737	−	14.1361i	0.00694547	−	0.00427368i
$223$			4724.84i			1.41883i	0.704792	+	0.709414i	$0.251040\pi$
$223$			4724.84i			1.41883i	−0.704792	+	0.709414i	$0.748960\pi$
$224$	−224.338	−	496.160i	−0.0669161	−	0.147996i
$225$	673.941	−	37.7918i	0.199686	−	0.0111976i
$226$	70.0672	+	121.360i	0.0206230	+	0.0357201i
$227$	1390.18	−	2407.86i	0.406474	−	0.704033i	−0.588018	−	0.808848i	$-0.700092\pi$
$227$	1390.18	−	2407.86i	0.406474	−	0.704033i	0.994492	+	0.104814i	$0.0334249\pi$
$228$	−4750.71	−	2568.19i	−1.37993	−	0.745976i
$229$	2545.85	−	1469.85i	0.734649	−	0.424150i	−0.0854716	−	0.996341i	$-0.527240\pi$
$229$	2545.85	−	1469.85i	0.734649	−	0.424150i	0.820120	+	0.572191i	$0.193906\pi$
$230$	119.791			0.0343427
$231$	1661.04	+	118.051i	0.473110	+	0.0336241i
$232$	−406.564			−0.115053
$233$	5228.24	−	3018.53i	1.47002	−	0.848714i	0.470582	−	0.882356i	$-0.344044\pi$
$233$	5228.24	−	3018.53i	1.47002	−	0.848714i	0.999434	+	0.0336426i	$0.0107108\pi$
$234$	68.2601	−	135.188i	0.0190697	−	0.0377672i
$235$	1147.58	−	1987.66i	0.318551	−	0.551747i
$236$	2332.91	+	4040.72i	0.643473	+	1.11453i
$237$	−60.4205	+	1.69273i	−0.0165600	+	0.000463944i
$238$	−49.3502	+	68.7541i	−0.0134408	+	0.0187255i
$239$			4322.85i			1.16996i	0.811046	+	0.584982i	$0.198899\pi$
$239$			4322.85i			1.16996i	−0.811046	+	0.584982i	$0.801101\pi$
$240$	863.670	+	1403.61i	0.232290	+	0.377512i
$241$	−3915.54	−	2260.64i	−1.04657	−	0.604235i	−0.124880	−	0.992172i	$-0.539854\pi$
$241$	−3915.54	−	2260.64i	−1.04657	−	0.604235i	−0.921686	+	0.387937i	$0.873188\pi$
$242$	137.344	+	79.2956i	0.0364827	+	0.0210633i
$243$	2333.37	+	2984.01i	0.615989	+	0.787754i
$244$		−	2043.42i		−	0.536133i
$245$	1132.80	−	1287.63i	0.295396	−	0.335770i
$246$	6.13486	+	218.978i	0.00159002	+	0.0567542i
$247$	2376.96	+	4117.02i	0.612318	+	1.06057i
$248$	18.4334	−	31.9275i	0.00471984	−	0.00817500i
$249$	1444.64	−	2672.35i	0.367673	−	0.680133i
$250$	−16.6425	+	9.60857i	−0.00421026	+	0.00243080i
$251$	−3711.55			−0.933352			−0.466676	−	0.884428i	$-0.654549\pi$
$251$	−3711.55			−0.933352			−0.466676	+	0.884428i	$0.654549\pi$
$252$	−3365.39	−	2140.73i	−0.841270	−	0.535131i
$253$	−2696.64			−0.670103
$254$	−297.960	+	172.027i	−0.0736049	+	0.0424958i
$255$	367.247	−	679.344i	0.0901878	−	0.166832i
$256$	−1987.76	+	3442.90i	−0.485293	+	0.840553i
$257$	−1628.67	−	2820.94i	−0.395307	−	0.684691i	0.597834	−	0.801620i	$-0.296028\pi$
$257$	−1628.67	−	2820.94i	−0.395307	−	0.684691i	−0.993140	+	0.116929i	$0.962695\pi$
$258$	5.55605	+	198.318i	0.00134072	+	0.0478556i
$259$	−61.7858	+	622.314i	−0.0148231	+	0.149300i
$260$		−	1455.07i		−	0.347076i
$261$	−3739.32	+	2447.83i	−0.886812	+	0.580525i
$262$	186.581	+	107.723i	0.0439963	+	0.0254013i
$263$	3190.09	+	1841.80i	0.747945	+	0.431826i	0.824951	−	0.565204i	$-0.191203\pi$
$263$	3190.09	+	1841.80i	0.747945	+	0.431826i	−0.0770059	+	0.997031i	$0.524536\pi$
$264$	115.734	+	188.088i	0.0269809	+	0.0438486i
$265$			1223.82i			0.283694i
$266$	−338.047	+	152.847i	−0.0779209	+	0.0352318i
$267$	−5698.66	+	159.653i	−1.30619	+	0.0365940i
$268$	−1095.60	−	1897.63i	−0.249717	−	0.432523i
$269$	−2305.20	+	3992.72i	−0.522492	+	0.904984i	0.477165	+	0.878814i	$0.341664\pi$
$269$	−2305.20	+	3992.72i	−0.522492	+	0.904984i	−0.999658	+	0.0261698i	$0.991669\pi$
$270$	−97.5912	−	45.8932i	−0.0219971	−	0.0103443i
$271$	4246.10	−	2451.49i	0.951780	−	0.549510i	0.0581466	−	0.998308i	$-0.481481\pi$
$271$	4246.10	−	2451.49i	0.951780	−	0.549510i	0.893633	+	0.448798i	$0.148148\pi$
$272$	1885.50			0.420313
$273$	1535.56	+	3157.47i	0.340425	+	0.699996i
$274$	137.663			0.0303524
$275$	374.641	−	216.299i	0.0821517	−	0.0474303i
$276$	5681.89	+	3071.58i	1.23917	+	0.669881i
$277$	1735.84	−	3006.55i	0.376521	−	0.652153i	−0.614033	−	0.789281i	$-0.710454\pi$
$277$	1735.84	−	3006.55i	0.376521	−	0.652153i	0.990553	+	0.137128i	$0.0437870\pi$
$278$	−33.1211	−	57.3674i	−0.00714558	−	0.0123765i
$279$	−22.6900	−	404.632i	−0.00486888	−	0.0868268i
$280$	226.331	+	22.4710i	0.0483066	+	0.00479607i
$281$		−	5764.29i		−	1.22373i	−0.790962	−	0.611866i	$-0.790419\pi$
$281$		−	5764.29i		−	1.22373i	0.790962	−	0.611866i	$-0.209581\pi$
$282$	−312.306	+	192.168i	−0.0659487	+	0.0405795i
$283$	1522.02	+	878.739i	0.319699	+	0.184578i	0.651258	−	0.758856i	$-0.274241\pi$
$283$	1522.02	+	878.739i	0.319699	+	0.184578i	−0.331559	+	0.943434i	$0.607575\pi$
$284$	7387.01	+	4264.89i	1.54344	+	0.891108i
$285$	2883.19	−	1774.08i	0.599247	−	0.368728i
$286$		−	97.0584i		−	0.0200671i
$287$	−4125.93	−	2961.50i	−0.848592	−	0.609101i
$288$	−44.4451	−	792.591i	−0.00909359	−	0.162166i
$289$	2014.74	+	3489.63i	0.410083	+	0.710285i
$290$	63.6197	−	110.193i	0.0128823	−	0.0223129i
$291$	−5109.90	−	2762.36i	−1.02937	−	0.556470i
$292$	6870.00	−	3966.39i	1.37684	−	0.794917i
$293$	3080.27			0.614168			0.307084	−	0.951682i	$-0.400647\pi$
$293$	3080.27			0.614168			0.307084	+	0.951682i	$0.400647\pi$
$294$	−257.042	+	94.9035i	−0.0509898	+	0.0188261i
$295$	−2924.78			−0.577245
$296$	−71.8256	+	41.4685i	−0.0141040	+	0.00814294i
$297$	2196.88	+	1033.11i	0.429213	+	0.201841i
$298$	112.370	−	194.631i	0.0218438	−	0.0378345i
$299$	−2842.87	−	4923.99i	−0.549857	−	0.952381i
$300$	−1035.75	+	29.0175i	−0.199331	+	0.00558443i
$301$	−3736.66	−	2682.09i	−0.715539	−	0.513599i
$302$		−	232.973i		−	0.0443909i
$303$	4708.61	+	7652.31i	0.892748	+	1.45087i
$304$	7157.99	+	4132.67i	1.35046	+	0.779687i
$305$	1109.31	+	640.460i	0.208259	+	0.120238i
$306$	−103.230	+	67.5766i	−0.0192852	+	0.0126245i
$307$			8885.73i			1.65191i	0.563738	+	0.825953i	$0.309363\pi$
$307$			8885.73i			1.65191i	−0.563738	+	0.825953i	$0.690637\pi$
$308$	−2543.71	−	252.549i	−0.470588	−	0.0467219i
$309$	164.179	+	5860.21i	0.0302259	+	1.07889i
$310$	5.76895	+	9.99211i	0.00105695	+	0.00183069i
$311$	−920.877	+	1595.01i	−0.167904	+	0.290818i	−0.937683	−	0.347493i	$-0.887033\pi$
$311$	−920.877	+	1595.01i	−0.167904	+	0.290818i	0.769779	+	0.638311i	$0.220367\pi$
$312$	−221.434	+	409.616i	−0.0401803	+	0.0743267i
$313$	374.901	−	216.449i	0.0677017	−	0.0390876i	−0.465767	−	0.884907i	$-0.654222\pi$
$313$	374.901	−	216.449i	0.0677017	−	0.0390876i	0.533469	+	0.845820i	$0.320888\pi$
$314$	−264.672			−0.0475678
$315$	2216.94	−	1156.01i	0.396541	−	0.206774i
$316$	92.7850			0.0165176
$317$	3607.61	−	2082.86i	0.639192	−	0.369037i	−0.145112	−	0.989415i	$-0.546354\pi$
$317$	3607.61	−	2082.86i	0.639192	−	0.369037i	0.784303	+	0.620378i	$0.213021\pi$
$318$	92.9836	−	172.004i	0.0163970	−	0.0303317i
$319$	−1432.15	+	2480.55i	−0.251363	+	0.435374i
$320$	−1257.37	−	2177.82i	−0.219653	−	0.380450i
$321$	148.244	+	5291.42i	0.0257762	+	0.920057i
$322$	404.306	−	182.807i	0.0699724	−	0.0316379i
$323$		−	3873.04i		−	0.667188i
$324$	−3452.15	−	4679.12i	−0.591933	−	0.802319i
$325$	789.914	+	456.057i	0.134820	+	0.0778385i
$326$	−127.961	−	73.8781i	−0.0217395	−	0.0125513i
$327$	−398.561	−	647.731i	−0.0674021	−	0.109540i
$328$		−	673.546i		−	0.113385i
$329$	839.919	−	8459.76i	0.140748	−	1.41763i
$330$	−69.0884	+	1.93557i	−0.0115248	+	0.000322878i
$331$	90.4559	+	156.674i	0.0150209	+	0.0260169i	0.873438	−	0.486935i	$-0.161885\pi$
$331$	90.4559	+	156.674i	0.0150209	+	0.0260169i	−0.858417	+	0.512952i	$0.828552\pi$
$332$	−2331.62	+	4038.48i	−0.385434	+	0.667591i
$333$	−410.933	+	813.846i	−0.0676246	+	0.133929i
$334$	−5.52295	+	3.18868i	−0.000904797	+	0.000522385i
$335$	1373.55			0.224016
$336$	5056.93	+	3419.32i	0.821066	+	0.555176i
$337$	1270.88			0.205428			0.102714	−	0.994711i	$-0.467247\pi$
$337$	1270.88			0.205428			0.102714	+	0.994711i	$0.467247\pi$
$338$	−115.283	+	66.5585i	−0.0185519	+	0.0107110i
$339$	−4166.55	−	2252.40i	−0.667540	−	0.360866i
$340$	−592.726	+	1026.63i	−0.0945443	+	0.163756i
$341$	−129.865	−	224.933i	−0.0206235	−	0.0357209i
$342$	−540.012	+	30.2816i	−0.0853816	+	0.00478784i
$343$	1858.33	−	6074.56i	0.292537	−	0.956254i
$344$		−	609.998i		−	0.0956073i
$345$	−3448.32	+	2121.82i	−0.538119	+	0.331115i
$346$	−295.451	−	170.579i	−0.0459063	−	0.0265040i
$347$	7237.61	+	4178.64i	1.11970	+	0.646458i	0.941324	−	0.337505i	$-0.109583\pi$
$347$	7237.61	+	4178.64i	1.11970	+	0.646458i	0.178374	+	0.983963i	$0.442916\pi$
$348$	5843.03	−	3595.32i	0.900055	−	0.553821i
$349$			8009.35i			1.22845i	0.789129	+	0.614227i	$0.210532\pi$
$349$			8009.35i			1.22845i	−0.789129	+	0.614227i	$0.789468\pi$
$350$	−41.5069	+	57.8269i	−0.00633896	+	0.00883136i
$351$	429.591	+	5100.59i	0.0653273	+	0.775639i
$352$	−254.379	−	440.598i	−0.0385184	−	0.0667158i
$353$	−1606.90	+	2783.23i	−0.242285	+	0.419649i	−0.961365	−	0.275278i	$-0.911230\pi$
$353$	−1606.90	+	2783.23i	−0.242285	+	0.419649i	0.719080	+	0.694927i	$0.244563\pi$
$354$	411.067	+	222.219i	0.0617174	+	0.0333638i
$355$	−4630.56	+	2673.45i	−0.692295	+	0.399696i
$356$	8751.17			1.30284
$357$	202.784	−	2853.28i	0.0300629	−	0.423001i
$358$	−80.6725			−0.0119097
$359$	−6481.42	+	3742.05i	−0.952859	+	0.550134i	−0.893968	−	0.448131i	$-0.852090\pi$
$359$	−6481.42	+	3742.05i	−0.952859	+	0.550134i	−0.0588913	+	0.998264i	$0.518757\pi$
$360$	295.990	+	149.453i	0.0433334	+	0.0218802i
$361$	5059.49	−	8763.30i	0.737643	−	1.27763i
$362$	234.725	+	406.555i	0.0340797	+	0.0590278i
$363$	−5358.11	+	150.112i	−0.774733	+	0.0217048i
$364$	−2220.50	−	4910.99i	−0.319741	−	0.707159i
$365$			4972.68i			0.713102i
$366$	−107.248	−	174.297i	−0.0153168	−	0.0248925i
$367$	−1091.71	−	630.297i	−0.155277	−	0.0896491i	0.420348	−	0.907363i	$-0.361908\pi$
$367$	−1091.71	−	630.297i	−0.155277	−	0.0896491i	−0.575625	+	0.817714i	$0.695241\pi$
$368$	−8561.02	−	4942.70i	−1.21270	−	0.700153i
$369$	−4055.26	−	6194.84i	−0.572110	−	0.873958i
$370$		−	25.9562i		−	0.00364702i
$371$	1867.60	+	4130.51i	0.261351	+	0.578020i
$372$	17.4220	+	621.863i	0.00242820	+	0.0866723i
$373$	−4319.97	−	7482.40i	−0.599676	−	1.03867i	−0.992869	−	0.119214i	$-0.961963\pi$
$373$	−4319.97	−	7482.40i	−0.599676	−	1.03867i	0.393192	−	0.919456i	$-0.371371\pi$
$374$	−39.5369	+	68.4799i	−0.00546632	+	0.00946794i
$375$	308.879	−	571.374i	0.0425346	−	0.0786817i
$376$	976.401	−	563.726i	0.133920	−	0.0773190i
$377$	−6039.24			−0.825031
$378$	−399.414	−	5.96532i	−0.0543482	−	0.000811701i
$379$	−14223.5			−1.92773			−0.963867	−	0.266384i	$-0.914171\pi$
$379$	−14223.5			−1.92773			−0.963867	+	0.266384i	$0.914171\pi$
$380$	−4500.37	+	2598.29i	−0.607538	+	0.350762i
$381$	5530.02	−	10229.6i	0.743600	−	1.37553i
$382$	−285.308	+	494.168i	−0.0382137	+	0.0661880i
$383$	5208.11	+	9020.72i	0.694836	+	1.20349i	0.970236	+	0.242162i	$0.0778564\pi$
$383$	5208.11	+	9020.72i	0.694836	+	1.20349i	−0.275400	+	0.961330i	$0.588810\pi$
$384$	45.4789	+	1623.33i	0.00604385	+	0.215729i
$385$	934.365	−	1301.75i	0.123687	−	0.172320i
$386$			517.821i			0.0682808i
$387$	−3672.66	−	5610.37i	−0.482408	−	0.736928i
$388$	7722.14	+	4458.38i	1.01039	+	0.583350i
$389$	10797.5	+	6233.94i	1.40734	+	0.812528i	0.995131	−	0.0985609i	$-0.0314239\pi$
$389$	10797.5	+	6233.94i	1.40734	+	0.812528i	0.412209	+	0.911089i	$0.364757\pi$
$390$	−76.3692	−	124.113i	−0.00991565	−	0.0161147i
$391$			4632.19i			0.599130i
$392$	798.177	−	269.548i	0.102842	−	0.0347302i
$393$	−7278.98	+	203.927i	−0.934291	+	0.0261750i
$394$	348.945	+	604.390i	0.0446183	+	0.0772811i
$395$	−29.0812	+	50.3701i	−0.00370439	+	0.00641620i
$396$	−3326.60	−	1679.69i	−0.422141	−	0.213150i
$397$	−8261.81	+	4769.96i	−1.04445	+	0.603016i	−0.921092	−	0.389346i	$-0.872701\pi$
$397$	−8261.81	+	4769.96i	−1.04445	+	0.603016i	−0.123363	+	0.992362i	$0.539368\pi$
$398$	109.786			0.0138268
$399$	7023.69	−	10387.5i	0.881264	−	1.30333i
$400$	1585.83			0.198229
$401$	774.728	−	447.290i	0.0964790	−	0.0557022i	−0.450984	−	0.892532i	$-0.648927\pi$
$401$	774.728	−	447.290i	0.0964790	−	0.0557022i	0.547463	+	0.836830i	$0.315594\pi$
$402$	−193.048	−	104.360i	−0.0239511	−	0.0129477i
$403$	273.815	−	474.262i	0.0338454	−	0.0586220i
$404$	−6896.17	−	11944.5i	−0.849250	−	1.47094i
$405$	3622.15	−	407.511i	0.444410	−	0.0499984i
$406$	46.5637	−	468.995i	0.00569192	−	0.0573297i
$407$			584.302i			0.0711616i
$408$	323.091	−	198.804i	0.0392044	−	0.0241232i
$409$	−2148.44	−	1240.40i	−0.259739	−	0.149961i	0.364476	−	0.931213i	$-0.381248\pi$
$409$	−2148.44	−	1240.40i	−0.259739	−	0.149961i	−0.624216	+	0.781252i	$0.714581\pi$
$410$	182.553	+	105.397i	0.0219894	+	0.0126956i
$411$	−3962.78	+	2438.37i	−0.475595	+	0.292643i
$412$		−	8999.26i		−	1.07612i
$413$	−9871.38	+	4463.33i	−1.17612	+	0.531782i
$414$	645.859	−	36.2170i	0.0766721	−	0.00429944i
$415$	−1461.58	−	2531.53i	−0.172882	−	0.299441i
$416$	536.348	−	928.981i	0.0632130	−	0.109488i
$417$	1969.55	+	1064.72i	0.231293	+	0.125035i
$418$	−300.191	+	173.315i	−0.0351263	+	0.0202802i
$419$	2031.63			0.236878			0.118439	−	0.992961i	$-0.462211\pi$
$419$	2031.63			0.236878			0.118439	+	0.992961i	$0.462211\pi$
$420$	−3451.48	+	1678.54i	−0.400988	+	0.195010i
$421$	−8997.00			−1.04154			−0.520768	−	0.853698i	$-0.674354\pi$
$421$	−8997.00			−1.04154			−0.520768	+	0.853698i	$0.674354\pi$
$422$	428.630	−	247.470i	0.0494440	−	0.0285465i
$423$	5586.25	−	11063.5i	0.642110	−	1.27169i
$424$	−300.590	+	520.638i	−0.0344292	+	0.0596331i
$425$	−371.551	−	643.546i	−0.0424068	−	0.0734507i
$426$	853.931	−	23.9236i	0.0971200	−	0.00272090i
$427$	4721.38	+	468.758i	0.535090	+	0.0531259i
$428$		−	8125.79i		−	0.917698i
$429$	1719.15	+	2793.92i	0.193477	+	0.314433i
$430$	165.330	+	95.4532i	0.0185417	+	0.0107050i
$431$	−13741.2	−	7933.48i	−1.53571	−	0.886642i	−0.999083	−	0.0428210i	$-0.986365\pi$
$431$	−13741.2	−	7933.48i	−1.53571	−	0.886642i	−0.536625	−	0.843821i	$-0.680301\pi$
$432$	5080.86	+	7306.51i	0.565864	+	0.813737i
$433$			6147.48i			0.682284i	0.940012	+	0.341142i	$0.110814\pi$
$433$			6147.48i			0.682284i	−0.940012	+	0.341142i	$0.889186\pi$
$434$	34.7191	+	24.9206i	0.00384002	+	0.00275628i
$435$	120.437	+	4298.87i	0.0132747	+	0.473828i
$436$	583.727	+	1011.05i	0.0641180	+	0.111056i
$437$	−10152.9	+	17585.3i	−1.11139	+	1.92499i
$438$	377.814	−	698.892i	0.0412161	−	0.0762428i
$439$	5458.01	−	3151.19i	0.593387	−	0.342592i	−0.173049	−	0.984913i	$-0.555362\pi$
$439$	5458.01	−	3151.19i	0.593387	−	0.342592i	0.766436	+	0.642321i	$0.222028\pi$
$440$	212.506			0.0230246
$441$	5718.24	−	7284.77i	0.617453	−	0.786607i
$442$	−166.724			−0.0179417
$443$	12071.4	−	6969.45i	1.29465	−	0.747468i	0.315178	−	0.949033i	$-0.397936\pi$
$443$	12071.4	−	6969.45i	1.29465	−	0.747468i	0.979475	+	0.201565i	$0.0646026\pi$
$444$	665.543	−	1231.14i	0.0711380	−	0.131593i
$445$	−2742.84	+	4750.74i	−0.292187	+	0.506083i
$446$	−363.191	−	629.066i	−0.0385597	−	0.0667873i
$447$	212.725	+	7593.03i	0.0225091	+	0.803441i
$448$	−7567.16	−	5431.55i	−0.798024	−	0.572804i
$449$		−	11463.6i		−	1.20490i	−0.798157	−	0.602449i	$-0.794192\pi$
$449$		−	11463.6i		−	1.20490i	0.798157	−	0.602449i	$-0.205808\pi$
$450$	−86.8237	+	56.8365i	−0.00909535	+	0.00595399i
$451$	−4109.47	−	2372.60i	−0.429063	−	0.247720i
$452$	6296.54	+	3635.31i	0.655231	+	0.378298i
$453$	4126.54	+	6706.35i	0.427995	+	0.695567i
$454$			427.445i			0.0441872i
$455$	3361.99	+	333.792i	0.346401	+	0.0343921i
$456$	1662.31	−	46.5710i	0.170712	−	0.00478264i
$457$	489.645	+	848.089i	0.0501195	+	0.0868095i	0.889997	−	0.455967i	$-0.150706\pi$
$457$	489.645	+	848.089i	0.0501195	+	0.0868095i	−0.839877	+	0.542776i	$0.817373\pi$
$458$	−225.970	+	391.392i	−0.0230543	+	0.0399313i
$459$	1774.63	−	3773.73i	0.180464	−	0.383753i
$460$	5382.49	−	3107.58i	0.545565	−	0.314982i
$461$	−9965.28			−1.00679			−0.503394	−	0.864057i	$-0.667916\pi$
$461$	−9965.28			−1.00679			−0.503394	+	0.864057i	$0.667916\pi$
$462$	−230.225	+	111.964i	−0.0231841	+	0.0112750i
$463$	8423.87			0.845552			0.422776	−	0.906234i	$-0.361056\pi$
$463$	8423.87			0.845552			0.422776	+	0.906234i	$0.361056\pi$
$464$	−9093.29	+	5250.01i	−0.909796	+	0.525271i
$465$	−343.051	−	185.450i	−0.0342121	−	0.0184947i
$466$	−464.060	+	803.775i	−0.0461312	+	0.0799016i
$467$	3656.16	+	6332.66i	0.362285	+	0.627495i	0.988336	−	0.152286i	$-0.0486635\pi$
$467$	3656.16	+	6332.66i	0.362285	+	0.627495i	−0.626052	+	0.779781i	$0.715330\pi$
$468$	−439.918	−	7845.06i	−0.0434513	−	0.774868i
$469$	4635.86	−	2096.10i	0.456427	−	0.206373i
$470$			352.850i			0.0346292i
$471$	7618.84	−	4688.02i	0.745345	−	0.458625i
$472$	−1244.26	−	718.373i	−0.121338	−	0.0700546i
$473$	−3721.75	−	2148.76i	−0.361789	−	0.208879i
$474$	7.91428	−	4.86980i	0.000766909	−	0.000471893i
$475$		−	3257.49i		−	0.314661i
$476$	−433.821	+	4369.49i	−0.0417734	+	0.420747i
$477$	370.003	+	6598.28i	0.0355163	+	0.633364i
$478$	−332.291	−	575.544i	−0.0317963	−	0.0550728i
$479$	−251.793	+	436.117i	−0.0240182	+	0.0416007i	−0.877785	−	0.479055i	$-0.840979\pi$
$479$	−251.793	+	436.117i	−0.0240182	+	0.0416007i	0.853767	+	0.520656i	$0.174313\pi$
$480$	−671.966	−	363.259i	−0.0638978	−	0.0345425i
$481$	−1066.92	+	615.987i	−0.101138	+	0.0583921i
$482$	695.088			0.0656855
$483$	−8400.39	+	12423.6i	−0.791369	+	1.17038i
$484$	8228.21			0.772747
$485$	−4840.64	+	2794.74i	−0.453200	+	0.261655i
$486$	−540.041	−	217.929i	−0.0504049	−	0.0203405i
$487$	1580.86	−	2738.13i	0.147096	−	0.254778i	−0.783057	−	0.621950i	$-0.786341\pi$
$487$	1580.86	−	2738.13i	0.147096	−	0.254778i	0.930153	+	0.367172i	$0.119674\pi$
$488$	314.614	+	544.928i	0.0291843	+	0.0505486i
$489$	4992.05	−	139.857i	0.461653	−	0.0129336i
$490$	−51.8432	+	258.512i	−0.00477967	+	0.0238334i
$491$			6402.37i			0.588462i	0.955734	+	0.294231i	$0.0950636\pi$
$491$			6402.37i			0.588462i	−0.955734	+	0.294231i	$0.904936\pi$
$492$	5956.29	+	9680.00i	0.545793	+	0.887009i
$493$	4261.01	+	2460.09i	0.389262	+	0.224741i
$494$	−632.939	−	365.427i	−0.0576463	−	0.0332821i
$495$	1954.49	−	1279.45i	0.177471	−	0.116176i
$496$		−	952.128i		−	0.0861932i
$497$	−11548.7	+	16089.6i	−1.04232	+	1.45214i
$498$	13.0791	+	466.844i	0.00117688	+	0.0420076i
$499$	1960.50	+	3395.69i	0.175880	+	0.304633i	0.940465	−	0.339889i	$-0.110390\pi$
$499$	1960.50	+	3395.69i	0.175880	+	0.304633i	−0.764585	+	0.644522i	$0.777056\pi$
$500$	−498.523	+	863.467i	−0.0445892	+	0.0772308i
$501$	102.504	−	189.615i	0.00914080	−	0.0169089i
$502$	494.157	−	285.302i	0.0439349	−	0.0253658i
$503$	−5461.33			−0.484113			−0.242056	−	0.970262i	$-0.577822\pi$
$503$	−5461.33			−0.484113			−0.242056	+	0.970262i	$0.577822\pi$
$504$	1227.06	+	52.7257i	0.108448	+	0.00465990i
$505$	8645.75			0.761843
$506$	359.031	−	207.286i	0.0315432	−	0.0182115i
$507$	2139.61	−	3957.91i	0.187423	−	0.346700i
$508$	−8925.31	+	15459.1i	−0.779521	+	1.35017i
$509$	−7459.40	−	12920.1i	−0.649572	−	1.12509i	−0.983225	−	0.182395i	$-0.941615\pi$
$509$	−7459.40	−	12920.1i	−0.649572	−	1.12509i	0.333654	−	0.942696i	$-0.391718\pi$
$510$	3.32486	+	118.678i	0.000288681	+	0.0103042i
$511$	7588.51	+	16783.2i	0.656939	+	1.45293i
$512$		−	3111.44i		−	0.268570i
$513$	15008.4	−	10436.7i	1.29169	−	0.898229i
$514$	433.683	+	250.387i	0.0372159	+	0.0214866i
$515$	4885.42	+	2820.60i	0.418015	+	0.241341i
$516$	5394.33	+	8766.72i	0.460217	+	0.747933i
$517$		−	7943.03i		−	0.675694i
$518$	−39.6102	−	87.6043i	−0.00335979	−	0.00743072i
$519$	11526.3	−	322.918i	0.974849	−	0.0273112i
$520$	224.030	+	388.031i	0.0188930	+	0.0327236i
$521$	4021.29	−	6965.07i	0.338149	−	0.585692i	−0.645935	−	0.763392i	$-0.723532\pi$
$521$	4021.29	−	6965.07i	0.338149	−	0.585692i	0.984085	+	0.177700i	$0.0568658\pi$
$522$	309.692	−	613.341i	0.0259672	−	0.0514276i
$523$	2018.19	−	1165.20i	0.168737	−	0.0974203i	−0.413253	−	0.910616i	$-0.635608\pi$
$523$	2018.19	−	1165.20i	0.168737	−	0.0974203i	0.581990	+	0.813196i	$0.302274\pi$
$524$	11178.0			0.931896
$525$	170.555	−	2399.80i	0.0141783	−	0.199497i
$526$	−566.306			−0.0469432
$527$	−386.383	+	223.078i	−0.0319376	+	0.0184392i
$528$	5017.33	+	2712.32i	0.413544	+	0.223558i
$529$	6059.46	−	10495.3i	0.498024	−	0.862603i
$530$	−94.0735	−	162.940i	−0.00770998	−	0.0133541i
$531$	−15769.0	+	884.260i	−1.28873	+	0.0722667i
$532$	−11224.1	+	15637.2i	−0.914708	+	1.27436i
$533$		−	10005.1i		−	0.813072i
$534$	746.448	−	459.303i	0.0604906	−	0.0372210i
$535$	4411.25	+	2546.83i	0.356476	+	0.205812i
$536$	584.336	+	337.367i	0.0470886	+	0.0271866i
$537$	2322.24	−	1428.92i	0.186615	−	0.114827i
$538$		−	708.789i		−	0.0567994i
$539$	1167.05	−	5819.38i	0.0932621	−	0.465044i
$540$	−5575.52	+	469.592i	−0.444319	+	0.0374223i
$541$	9042.88	+	15662.7i	0.718639	+	1.24472i	0.961539	+	0.274668i	$0.0885680\pi$
$541$	9042.88	+	15662.7i	0.718639	+	1.24472i	−0.242900	+	0.970051i	$0.578099\pi$
$542$	−376.885	+	652.783i	−0.0298682	+	0.0517333i
$543$	−13957.9	−	7545.52i	−1.10312	−	0.596333i
$544$	−756.844	+	436.964i	−0.0596497	+	0.0344388i
$545$	−731.821			−0.0575189
$546$	−447.154	−	302.350i	−0.0350484	−	0.0236985i
$547$	6873.98			0.537313			0.268657	−	0.963236i	$-0.413420\pi$
$547$	6873.98			0.537313			0.268657	+	0.963236i	$0.413420\pi$
$548$	6185.51	−	3571.21i	0.482175	−	0.278384i
$549$	6174.51	+	3117.68i	0.480003	+	0.242366i
$550$	−33.2532	+	57.5962i	−0.00257804	+	0.00446530i
$551$	10784.1	+	18678.7i	0.833793	+	1.44417i
$552$	−1988.13	+	55.6992i	−0.153298	+	0.00429478i
$553$	−21.2848	+	214.383i	−0.00163675	+	0.0164855i
$554$			533.724i			0.0409310i
$555$	459.751	+	747.175i	0.0351628	+	0.0571456i
$556$	−2976.40	−	1718.43i	−0.227028	−	0.131075i
$557$	−10589.9	−	6114.09i	−0.805582	−	0.465103i	0.0398376	−	0.999206i	$-0.487316\pi$
$557$	−10589.9	−	6114.09i	−0.805582	−	0.465103i	−0.845419	+	0.534103i	$0.820649\pi$
$558$	34.1244	+	52.1286i	0.00258889	+	0.00395480i
$559$		−	9061.11i		−	0.685589i
$560$	5352.32	−	2420.04i	0.403887	−	0.182617i
$561$	−74.8461	−	2671.56i	−0.00563281	−	0.201058i
$562$	443.092	+	767.458i	0.0332575	+	0.0576037i
$563$	1734.41	−	3004.09i	0.129835	−	0.224880i	−0.793778	−	0.608208i	$-0.791889\pi$
$563$	1734.41	−	3004.09i	0.129835	−	0.224880i	0.923612	+	0.383328i	$0.125222\pi$
$564$	−9047.43	+	16736.2i	−0.675471	+	1.24951i
$565$	−3947.00	+	2278.80i	−0.293896	+	0.169681i
$566$	−270.190			−0.0200652
$567$	11603.2	−	6902.93i	0.859414	−	0.511280i
$568$	−2626.57			−0.194029
$569$	−9690.69	+	5594.92i	−0.713980	+	0.412217i	−0.812533	−	0.582915i	$-0.801912\pi$
$569$	−9690.69	+	5594.92i	−0.713980	+	0.412217i	0.0985529	+	0.995132i	$0.468579\pi$
$570$	−247.497	+	457.828i	−0.0181869	+	0.0336426i
$571$	9458.91	−	16383.3i	0.693245	−	1.20074i	−0.277523	−	0.960719i	$-0.589514\pi$
$571$	9458.91	−	16383.3i	0.693245	−	1.20074i	0.970769	−	0.240017i	$-0.0771530\pi$
$572$	−2517.85	−	4361.04i	−0.184050	−	0.318784i
$573$	−540.108	−	19278.7i	−0.0393776	−	1.40555i
$574$	776.973	+	77.1410i	0.0564987	+	0.00560941i
$575$			3895.98i			0.282563i
$576$	−7437.56	−	11361.6i	−0.538018	−	0.821878i
$577$	−16834.9	−	9719.64i	−1.21464	−	0.701272i	−0.250872	−	0.968020i	$-0.580717\pi$
$577$	−16834.9	−	9719.64i	−1.21464	−	0.701272i	−0.963766	+	0.266749i	$0.914051\pi$
$578$	−536.485	−	309.740i	−0.0386070	−	0.0222898i
$579$	−9171.94	−	14906.0i	−0.658329	−	1.06990i
$580$		−	6601.58i		−	0.472613i
$581$	−8796.16	−	6313.70i	−0.628100	−	0.450837i
$582$	892.672	−	25.0090i	0.0635781	−	0.00178120i
$583$	2117.70	+	3667.96i	0.150439	+	0.260568i
$584$	−1221.37	+	2115.48i	−0.0865422	+	0.149896i
$585$	4396.73	+	2220.03i	0.310739	+	0.156901i
$586$	−410.107	+	236.776i	−0.0289102	+	0.0166913i
$587$	22159.7			1.55814			0.779070	−	0.626937i	$-0.215692\pi$
$587$	22159.7			1.55814			0.779070	+	0.626937i	$0.215692\pi$
$588$	−9087.51	+	10932.3i	−0.637351	+	0.766735i
$589$	−1955.79			−0.136820
$590$	389.406	−	224.824i	0.0271722	−	0.0156879i
$591$	−20750.0	−	11217.3i	−1.44423	−	0.780739i
$592$	−1070.98	+	1854.98i	−0.0743528	+	0.128783i
$593$	9285.64	+	16083.2i	0.643028	+	1.11376i	0.984753	+	0.173957i	$0.0556553\pi$
$593$	9285.64	+	16083.2i	0.643028	+	1.11376i	−0.341726	+	0.939800i	$0.611011\pi$
$594$	−371.907	+	31.3235i	−0.0256894	+	0.00216367i
$595$	−2236.09	−	1605.02i	−0.154069	−	0.110587i
$596$		−	11660.3i		−	0.801381i
$597$	−3160.31	+	1944.60i	−0.216654	+	0.133312i
$598$	757.000	+	437.054i	0.0517659	+	0.0298871i
$599$	16435.0	+	9488.76i	1.12106	+	0.647246i	0.941672	−	0.336532i	$-0.109254\pi$
$599$	16435.0	+	9488.76i	1.12106	+	0.647246i	0.179391	+	0.983778i	$0.442587\pi$
$600$	271.742	−	167.208i	0.0184897	−	0.0113771i
$601$			6978.97i			0.473674i	0.971549	+	0.236837i	$0.0761107\pi$
$601$			6978.97i			0.473674i	−0.971549	+	0.236837i	$0.923889\pi$
$602$	703.668	+	69.8630i	0.0476401	+	0.00472990i
$603$	7405.56	−	415.272i	0.500129	−	0.0280451i
$604$	−6043.68	−	10468.0i	−0.407142	−	0.705190i
$605$	−2578.93	+	4466.85i	−0.173303	+	0.300170i
$606$	−1215.13	−	656.886i	−0.0814541	−	0.0440333i
$607$	−8863.71	+	5117.47i	−0.592697	+	0.342194i	−0.766163	−	0.642646i	$-0.777837\pi$
$607$	−8863.71	+	5117.47i	−0.592697	+	0.342194i	0.173466	+	0.984840i	$0.444503\pi$
$608$	−3830.98			−0.255538
$609$	6966.73	+	14325.3i	0.463557	+	0.953184i
$610$	−196.925			−0.0130709
$611$	14503.8	−	8373.76i	0.960328	−	0.554445i
$612$	−2885.31	+	5714.32i	−0.190575	+	0.377431i
$613$	−5480.10	+	9491.81i	−0.361075	+	0.625401i	−0.988138	−	0.153568i	$-0.950924\pi$
$613$	−5480.10	+	9491.81i	−0.361075	+	0.625401i	0.627063	+	0.778969i	$0.284257\pi$
$614$	−683.033	−	1183.05i	−0.0448941	−	0.0777588i
$615$	−7121.84	+	199.524i	−0.466960	+	0.0130823i
$616$	717.227	−	324.293i	0.0469121	−	0.0212112i
$617$		−	7305.62i		−	0.476682i	−0.971181	−	0.238341i	$-0.923396\pi$
$617$		−	7305.62i		−	0.476682i	0.971181	−	0.238341i	$-0.0766037\pi$
$618$	−472.325	−	767.609i	−0.0307438	−	0.0499640i
$619$	−26035.4	−	15031.5i	−1.69055	−	0.976040i	−0.954071	−	0.299582i	$-0.903153\pi$
$619$	−26035.4	−	15031.5i	−1.69055	−	0.976040i	−0.736481	−	0.676459i	$-0.763514\pi$
$620$	518.422	+	299.311i	0.0335812	+	0.0193881i
$621$	−17950.2	+	12482.4i	−1.15993	+	0.806603i
$622$		−	283.146i		−	0.0182526i
$623$	−2007.51	+	20219.9i	−0.129100	+	1.30031i
$624$	336.777	+	12020.9i	0.0216056	+	0.771190i
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	−33.2762	+	57.6361i	−0.00212458	+	0.00367988i
$627$	5571.43	−	10306.2i	0.354867	−	0.656443i
$628$	−11892.3	+	6866.00i	−0.755658	+	0.436279i
$629$	1003.69			0.0636246
$630$	−206.303	+	324.324i	−0.0130465	+	0.0205101i
$631$	25464.3			1.60653			0.803263	−	0.595624i	$-0.203095\pi$
$631$	25464.3			1.60653			0.803263	+	0.595624i	$0.203095\pi$
$632$	−24.7434	+	14.2856i	−0.00155734	+	0.000899132i
$633$	−7955.22	+	14715.8i	−0.499513	+	0.924014i
$634$	−320.212	+	554.624i	−0.0200588	+	0.0347428i
$635$	−5594.85	−	9690.56i	−0.349645	−	0.605603i
$636$	−284.099	−	10140.6i	−0.0177126	−	0.632236i
$637$	11856.4	−	4003.95i	0.737468	−	0.249046i
$638$		−	440.348i		−	0.0273253i
$639$	−24157.5	+	15814.0i	−1.49555	+	0.979017i
$640$	1353.30	+	781.330i	0.0835844	+	0.0482575i
$641$	11576.8	+	6683.87i	0.713348	+	0.411852i	0.812300	−	0.583240i	$-0.198215\pi$
$641$	11576.8	+	6683.87i	0.713348	+	0.411852i	−0.0989513	+	0.995092i	$0.531549\pi$
$642$	−426.481	−	693.105i	−0.0262178	−	0.0426085i
$643$		−	27659.7i		−	1.69641i	−0.529666	−	0.848207i	$-0.677683\pi$
$643$		−	27659.7i		−	1.69641i	0.529666	−	0.848207i	$-0.322317\pi$
$644$	13424.1	−	18702.2i	0.821401	−	1.14437i
$645$	−6449.91	+	180.700i	−0.393744	+	0.0110311i
$646$	297.715	+	515.657i	0.0181323	+	0.0314060i
$647$	11868.7	−	20557.2i	0.721186	−	1.24913i	−0.239339	−	0.970936i	$-0.576931\pi$
$647$	11868.7	−	20557.2i	0.721186	−	1.24913i	0.960525	−	0.278194i	$-0.0897360\pi$
$648$	1641.02	+	716.295i	0.0994838	+	0.0434239i
$649$	−8765.94	+	5061.02i	−0.530190	+	0.306105i
$650$	−140.226			−0.00846171
$651$	−1440.83	−	102.401i	−0.0867444	−	0.00616496i
$652$	−7666.06			−0.460469
$653$	7869.60	−	4543.51i	0.471610	−	0.272284i	−0.245304	−	0.969446i	$-0.578888\pi$
$653$	7869.60	−	4543.51i	0.471610	−	0.272284i	0.716913	+	0.697162i	$0.245554\pi$
$654$	102.855	+	55.6023i	0.00614975	+	0.00332450i
$655$	−3503.48	+	6068.20i	−0.208996	+	0.361991i
$656$	−8697.57	−	15064.6i	−0.517657	−	0.896608i
$657$	1503.41	+	26810.4i	0.0892750	+	1.59204i
$658$	538.463	+	1190.90i	0.0319019	+	0.0705563i
$659$			25926.8i			1.53257i	0.642499	+	0.766287i	$0.277898\pi$
$659$			25926.8i			1.53257i	−0.642499	+	0.766287i	$0.722102\pi$
$660$	−3054.08	+	1879.23i	−0.180121	+	0.110832i
$661$	5148.52	+	2972.50i	0.302957	+	0.174912i	0.643770	−	0.765219i	$-0.277369\pi$
$661$	5148.52	+	2972.50i	0.302957	+	0.174912i	−0.340814	+	0.940131i	$0.610703\pi$
$662$	−24.0866	−	13.9064i	−0.00141413	−	0.000816448i
$663$	4799.31	−	2953.10i	0.281131	−	0.172985i
$664$		−	1435.95i		−	0.0839241i
$665$	−4971.06	−	10994.3i	−0.289879	−	0.641114i
$666$	−7.84744	−	139.944i	−0.000456580	−	0.00814219i
$667$	−12897.9	−	22339.9i	−0.748741	−	1.29686i
$668$	−165.439	+	286.548i	−0.00958235	+	0.0165971i
$669$	21597.2	+	11675.2i	1.24813	+	0.674725i
$670$	−182.875	+	105.583i	−0.0105449	+	0.00608810i
$671$	4432.99			0.255043
$672$	−2822.29	−	200.582i	−0.162012	−	0.0115143i
$673$	10966.0			0.628095			0.314047	−	0.949407i	$-0.398315\pi$
$673$	10966.0			0.628095			0.314047	+	0.949407i	$0.398315\pi$
$674$	−169.205	+	97.6905i	−0.00966992	+	0.00558293i
$675$	1492.59	−	3173.97i	0.0851107	−	0.180987i
$676$	−3453.27	+	5981.23i	−0.196476	+	0.340307i
$677$	−796.434	−	1379.46i	−0.0452134	−	0.0783118i	0.842533	−	0.538645i	$-0.181063\pi$
$677$	−796.434	−	1379.46i	−0.0452134	−	0.0783118i	−0.887746	+	0.460333i	$0.847730\pi$
$678$	727.874	−	20.3920i	0.0412299	−	0.00115509i
$679$	−12072.7	+	16819.5i	−0.682337	+	0.950623i
$680$		−	365.036i		−	0.0205860i
$681$	−7571.15	−	12304.4i	−0.426031	−	0.692374i
$682$	34.5806	+	19.9651i	0.00194158	+	0.00112097i
$683$	−22933.5	−	13240.7i	−1.28481	−	0.741788i	−0.307089	−	0.951681i	$-0.599355\pi$
$683$	−22933.5	−	13240.7i	−1.28481	−	0.741788i	−0.977724	+	0.209893i	$0.932688\pi$
$684$	−23478.4	+	15369.4i	−1.31245	+	0.859157i
$685$			4477.24i			0.249732i
$686$	219.524	+	951.615i	0.0122179	+	0.0529633i
$687$	−427.777	−	15269.1i	−0.0237565	−	0.847967i
$688$	−7876.97	−	13643.3i	−0.436492	−	0.756027i
$689$	−4465.07	+	7733.72i	−0.246888	+	0.427622i
$690$	296.009	−	547.566i	0.0163317	−	0.0302108i
$691$	1461.64	−	843.876i	0.0804678	−	0.0464581i	−0.459226	−	0.888319i	$-0.651873\pi$
$691$	1461.64	−	843.876i	0.0804678	−	0.0464581i	0.539694	+	0.841861i	$0.318540\pi$
$692$	−17700.3			−0.972350
$693$	4644.10	−	7300.89i	0.254567	−	0.400199i
$694$	−1284.82			−0.0702755
$695$	1865.76	−	1077.20i	0.101831	−	0.0587921i
$696$	−1004.64	+	1858.40i	−0.0547135	+	0.101211i
$697$	−4075.58	+	7059.11i	−0.221483	+	0.383620i
$698$	−615.667	−	1066.37i	−0.0333859	−	0.0578260i
$699$	−878.498	−	31357.2i	−0.0475362	−	1.69676i
$700$	−364.873	+	3675.04i	−0.0197013	+	0.198434i
$701$			4560.98i			0.245743i	0.992423	+	0.122871i	$0.0392103\pi$
$701$			4560.98i			0.245743i	−0.992423	+	0.122871i	$0.960790\pi$
$702$	−449.271	−	646.071i	−0.0241547	−	0.0347356i
$703$	3810.36	+	2199.91i	0.204424	+	0.118025i
$704$	−7536.98	−	4351.48i	−0.403495	−	0.232958i
$705$	−6249.88	−	10157.1i	−0.333878	−	0.542610i
$706$		−	494.079i		−	0.0263384i
$707$	29180.1	−	13193.8i	1.55224	−	0.701842i
$708$	24234.8	−	678.959i	1.28644	−	0.0360407i
$709$	−2799.16	−	4848.29i	−0.148272	−	0.256815i	0.782317	−	0.622881i	$-0.214038\pi$
$709$	−2799.16	−	4848.29i	−0.148272	−	0.256815i	−0.930589	+	0.366066i	$0.880704\pi$
$710$	411.009	−	711.889i	0.0217252	−	0.0376292i
$711$	−141.564	+	280.364i	−0.00746702	+	0.0147883i
$712$	−2333.72	+	1347.37i	−0.122837	+	0.0709198i
$713$	2339.14			0.122863
$714$	192.329	+	395.473i	0.0100808	+	0.0207286i
$715$	3156.64			0.165107
$716$	−3624.79	+	2092.77i	−0.189196	+	0.109233i
$717$	19759.7	+	10681.9i	1.02920	+	0.556378i
$718$	575.292	−	996.435i	0.0299021	−	0.0517920i
$719$	−2130.26	−	3689.72i	−0.110494	−	0.191382i	0.805475	−	0.592629i	$-0.201910\pi$
$719$	−2130.26	−	3689.72i	−0.110494	−	0.191382i	−0.915970	+	0.401248i	$0.868577\pi$
$720$	8550.07	−	479.451i	0.442559	−	0.0248168i
$721$	20793.1	+	2064.42i	1.07403	+	0.106634i
$722$			1555.66i			0.0801881i
$723$	−20008.8	+	12311.8i	−1.02923	+	0.633307i
$724$	21093.4	+	12178.3i	1.08277	+	0.625140i
$725$	3583.80	+	2069.11i	0.183585	+	0.105993i
$726$	701.841	−	431.856i	0.0358785	−	0.0220767i
$727$		−	32435.0i		−	1.65467i	−0.561707	−	0.827336i	$-0.689855\pi$
$727$		−	32435.0i		−	1.65467i	0.561707	−	0.827336i	$-0.310145\pi$
$728$	1348.27	+	967.760i	0.0686405	+	0.0492686i
$729$	19405.7	−	3292.20i	0.985913	−	0.167261i
$730$	−382.243	−	662.064i	−0.0193801	−	0.0335672i
$731$	−3691.06	+	6393.10i	−0.186756	+	0.323471i
$732$	−9340.45	−	5049.35i	−0.471629	−	0.254958i
$733$	1426.04	−	823.323i	0.0718579	−	0.0414872i	−0.463641	−	0.886023i	$-0.653457\pi$
$733$	1426.04	−	823.323i	0.0718579	−	0.0414872i	0.535498	+	0.844536i	$0.320124\pi$
$734$	193.800			0.00974563
$735$	−3086.55	−	8359.80i	−0.154897	−	0.419532i
$736$	4581.89			0.229471
$737$	4116.72	−	2376.79i	0.205755	−	0.118793i
$738$	1016.11	+	513.060i	0.0506821	+	0.0255908i
$739$	−3446.71	+	5969.88i	−0.171569	+	0.297166i	−0.938969	−	0.344003i	$-0.888217\pi$
$739$	−3446.71	+	5969.88i	−0.171569	+	0.297166i	0.767400	+	0.641169i	$0.221550\pi$
$740$	−673.344	−	1166.27i	−0.0334495	−	0.0579362i
$741$	24692.4	−	691.780i	1.22416	−	0.0342958i
$742$	−566.159	−	406.377i	−0.0280113	−	0.0201059i
$743$			15079.0i			0.744545i	0.928124	+	0.372272i	$0.121421\pi$
$743$			15079.0i			0.744545i	−0.928124	+	0.372272i	$0.878579\pi$
$744$	−100.391	−	163.153i	−0.00494693	−	0.00803962i
$745$	6330.01	+	3654.63i	0.311293	+	0.179725i
$746$	1150.32	+	664.139i	0.0564562	+	0.0325950i
$747$	−8645.51	−	13206.9i	−0.423457	−	0.646876i
$748$			4102.60i			0.200543i
$749$	18774.9	+	1864.05i	0.915915	+	0.0909357i
$750$	2.79643	+	99.8160i	0.000136148	+	0.00485969i
$751$	7920.87	+	13719.4i	0.384869	+	0.666613i	0.991751	−	0.128179i	$-0.0409132\pi$
$751$	7920.87	+	13719.4i	0.384869	+	0.666613i	−0.606882	+	0.794792i	$0.707580\pi$
$752$	14558.9	−	25216.8i	0.705995	−	1.22282i
$753$	−9171.38	+	16965.5i	−0.443856	+	0.821058i
$754$	804.066	−	464.228i	0.0388360	−	0.0224220i
$755$	7576.98			0.365238
$756$	−18101.3	+	10093.4i	−0.870815	+	0.485573i
$757$	21422.4			1.02855			0.514273	−	0.857627i	$-0.328062\pi$
$757$	21422.4			1.02855			0.514273	+	0.857627i	$0.328062\pi$
$758$	1893.72	−	1093.34i	0.0907426	−	0.0523903i
$759$	−6663.48	+	12326.3i	−0.318668	+	0.589482i
$760$	800.091	−	1385.80i	0.0381873	−	0.0661424i
$761$	1309.82	+	2268.67i	0.0623927	+	0.108067i	0.895534	−	0.444992i	$-0.146794\pi$
$761$	1309.82	+	2268.67i	0.0623927	+	0.108067i	−0.833142	+	0.553060i	$0.813460\pi$
$762$	50.0659	+	1787.06i	0.00238018	+	0.0849583i
$763$	−2469.96	+	1116.79i	−0.117193	+	0.0529888i
$764$			29605.4i			1.40194i
$765$	−2197.80	−	3357.36i	−0.103871	−	0.158674i
$766$	−1386.82	−	800.680i	−0.0654149	−	0.0377673i
$767$	−18482.6	−	10670.9i	−0.870102	−	0.502354i
$768$	10825.7	+	17593.6i	0.508643	+	0.826633i
$769$			35239.7i			1.65250i	0.563301	+	0.826252i	$0.309531\pi$
$769$			35239.7i			1.65250i	−0.563301	+	0.826252i	$0.690469\pi$
$770$	−24.3383	+	245.138i	−0.00113908	+	0.0114729i
$771$	−16919.0	+	474.001i	−0.790303	+	0.0221410i
$772$	13433.1	+	23266.8i	0.626253	+	1.08470i
$773$	10841.0	−	18777.1i	0.504427	−	0.873693i	−0.495560	−	0.868574i	$-0.665037\pi$
$773$	10841.0	−	18777.1i	0.504427	−	0.873693i	0.999987	−	0.00511943i	$-0.00162957\pi$
$774$	920.240	+	464.654i	0.0427356	+	0.0215784i
$775$	−324.974	+	187.624i	−0.0150625	+	0.00869632i
$776$	−2745.73			−0.127018
$777$	2691.92	+	1820.18i	0.124288	+	0.0840394i
$778$	−1916.78			−0.0883288
$779$	−30944.5	+	17865.8i	−1.42324	+	0.821708i
$780$	−6651.12	−	3595.53i	−0.305319	−	0.165052i
$781$	−9252.26	+	16025.4i	−0.423908	+	0.734229i
$782$	−356.070	−	616.730i	−0.0162826	−	0.0282023i
$783$	1949.03	+	23141.1i	0.0889562	+	1.05619i
$784$	14371.5	−	16335.7i	0.654677	−	0.744156i
$785$		−	8607.93i		−	0.391376i
$786$	953.450	−	586.676i	0.0432677	−	0.0266234i
$787$	−9043.80	−	5221.44i	−0.409627	−	0.236498i	0.281002	−	0.959707i	$-0.409333\pi$
$787$	−9043.80	−	5221.44i	−0.409627	−	0.236498i	−0.690629	+	0.723209i	$0.742666\pi$
$788$	31357.7	+	18104.4i	1.41760	+	0.818454i
$789$	16301.7	−	10030.7i	0.735558	−	0.452603i
$790$		−	8.94172i		−	0.000402699i
$791$	−9843.92	+	13714.4i	−0.442490	+	0.616471i
$792$	1145.73	−	64.2478i	0.0514039	−	0.00288251i
$793$	4673.38	+	8094.54i	0.209277	+	0.362478i
$794$	733.319	−	1270.15i	0.0327765	−	0.0567705i
$795$	5594.09	+	3024.11i	0.249562	+	0.134911i
$796$	4932.93	−	2848.03i	0.219652	−	0.126816i
$797$	−29378.6			−1.30570			−0.652850	−	0.757487i	$-0.726427\pi$
$797$	−29378.6			−1.30570			−0.652850	+	0.757487i	$0.726427\pi$
$798$	−136.661	+	1922.90i	−0.00606235	+	0.0853006i
$799$	−13644.3			−0.604129
$800$	−636.557	+	367.517i	−0.0281321	+	0.0162421i
$801$	−13351.8	+	26443.0i	−0.588967	+	1.16644i
$802$	−68.7650	+	119.104i	−0.00302765	+	0.00524405i
$803$	8604.70	+	14903.8i	0.378149	+	0.654972i
$804$	−11381.3	+	318.857i	−0.499238	+	0.0139866i
$805$	5945.43	+	13149.3i	0.260309	+	0.575716i
$806$			84.1911i			0.00367929i
$807$	12554.5	+	20403.2i	0.547632	+	0.889996i
$808$	3678.07	+	2123.53i	0.160141	+	0.0924575i
$809$	11033.8	+	6370.39i	0.479517	+	0.276849i	0.720215	−	0.693751i	$-0.244043\pi$
$809$	11033.8	+	6370.39i	0.479517	+	0.276849i	−0.240698	+	0.970600i	$0.577376\pi$
$810$	−450.929	+	332.685i	−0.0195605	+	0.0144313i
$811$		−	9282.79i		−	0.401927i	−0.979599	−	0.200964i	$-0.935593\pi$
$811$		−	9282.79i		−	0.401927i	0.979599	−	0.200964i	$-0.0644073\pi$
$812$	−10074.3	−	22280.9i	−0.435391	−	0.962939i
$813$	−713.469	−	25466.6i	−0.0307779	−	1.09859i
$814$	−44.9144	−	77.7940i	−0.00193397	−	0.00334973i
$815$	2402.74	−	4161.67i	0.103269	−	0.178868i
$816$	4659.13	−	8618.60i	0.199880	−	0.369745i
$817$	−28025.0	+	16180.2i	−1.20009	+	0.692870i
$818$	381.391			0.0163020
$819$	18227.2	+	783.205i	0.777667	+	0.0334156i
$820$	10936.7			0.465763
$821$	8268.85	−	4774.02i	0.351504	−	0.202941i	−0.313843	−	0.949475i	$-0.601617\pi$
$821$	8268.85	−	4774.02i	0.351504	−	0.202941i	0.665348	+	0.746534i	$0.268283\pi$
$822$	340.171	−	629.259i	0.0144341	−	0.0267006i
$823$	16940.8	−	29342.4i	0.717521	−	1.24278i	−0.244458	−	0.969660i	$-0.578610\pi$
$823$	16940.8	−	29342.4i	0.717521	−	1.24278i	0.961979	−	0.273123i	$-0.0880565\pi$
$824$	1385.57	+	2399.88i	0.0585784	+	0.101461i
$825$	−62.9507	−	2246.97i	−0.00265656	−	0.0948234i
$826$	971.188	−	1353.05i	0.0409104	−	0.0569958i
$827$			5465.50i			0.229811i	0.993376	+	0.114906i	$0.0366566\pi$
$827$			5465.50i			0.229811i	−0.993376	+	0.114906i	$0.963343\pi$
$828$	28080.3	−	18381.9i	1.17857	−	0.771517i
$829$	−98.9858	−	57.1495i	−0.00414707	−	0.00239431i	0.497925	−	0.867220i	$-0.334095\pi$
$829$	−98.9858	−	57.1495i	−0.00414707	−	0.00239431i	−0.502072	+	0.864826i	$0.667429\pi$
$830$	389.190	+	224.699i	0.0162759	+	0.00939688i
$831$	−9453.63	−	15363.8i	−0.394636	−	0.641353i
$832$		−	18349.8i		−	0.764621i
$833$	−9996.34	−	2004.71i	−0.415789	−	0.0833844i
$834$	−344.070	+	9.63941i	−0.0142856	+	0.000400222i
$835$	−103.705	−	179.623i	−0.00429806	−	0.00744445i
$836$	−8992.14	+	15574.8i	−0.372009	+	0.644339i
$837$	−1905.64	−	896.144i	−0.0786959	−	0.0370075i
$838$	−270.492	+	156.169i	−0.0111503	+	0.00643765i
$839$	3786.86			0.155825			0.0779123	−	0.996960i	$-0.475175\pi$
$839$	3786.86			0.155825			0.0779123	+	0.996960i	$0.475175\pi$
$840$	661.986	−	979.030i	0.0271913	−	0.0402140i
$841$	−3010.69			−0.123445
$842$	1197.86	−	691.586i	0.0490274	−	0.0283060i
$843$	−26348.5	−	14243.8i	−1.07650	−	0.581946i
$844$	12839.5	−	22238.7i	0.523642	−	0.906975i
$845$	−2164.69	−	3749.35i	−0.0881272	−	0.152641i
$846$	106.678	+	1902.40i	0.00433532	+	0.0773119i
$847$	−1887.54	+	19011.5i	−0.0765723	+	0.771245i
$848$			15526.2i			0.628742i
$849$	7777.68	−	4785.75i	0.314404	−	0.193459i
$850$	98.9369	+	57.1212i	0.00399236	+	0.00230499i
$851$	−4557.22	−	2631.11i	−0.183572	−	0.105985i
$852$	37748.3	−	23227.3i	1.51788	−	0.933982i
$853$			17751.9i			0.712559i	0.934379	+	0.356280i	$0.115955\pi$
$853$			17751.9i			0.712559i	−0.934379	+	0.356280i	$0.884045\pi$
$854$	−664.638	+	300.515i	−0.0266317	+	0.0120415i
$855$	−984.850	−	17562.9i	−0.0393932	−	0.702499i
$856$	1251.09	+	2166.94i	0.0499547	+	0.0865241i
$857$	6500.24	−	11258.7i	0.259094	−	0.448765i	−0.706905	−	0.707308i	$-0.749909\pi$
$857$	6500.24	−	11258.7i	0.259094	−	0.448765i	0.966000	+	0.258544i	$0.0832426\pi$
$858$	−443.653	−	239.835i	−0.0176528	−	0.00954291i
$859$	15348.1	−	8861.23i	0.609628	−	0.351969i	−0.163192	−	0.986594i	$-0.552179\pi$
$859$	15348.1	−	8861.23i	0.609628	−	0.351969i	0.772820	+	0.634625i	$0.218846\pi$
$860$	9904.83			0.392735
$861$	−23732.3	+	11541.6i	−0.939368	+	0.456838i
$862$	2439.34			0.0963855
$863$	1571.32	−	907.201i	0.0619795	−	0.0357839i	−0.468690	−	0.883363i	$-0.655274\pi$
$863$	1571.32	−	907.201i	0.0619795	−	0.0357839i	0.530670	+	0.847579i	$0.321941\pi$
$864$	−3732.75	−	1755.36i	−0.146980	−	0.0691188i
$865$	5547.75	−	9608.98i	0.218068	−	0.377705i
$866$	−472.548	−	818.476i	−0.0185425	−	0.0321166i
$867$	20929.6	−	586.360i	0.819845	−	0.0229687i
$868$	2206.48	+	219.068i	0.0862821	+	0.00856643i
$869$			201.288i			0.00785756i
$870$	−346.483	−	563.095i	−0.0135021	−	0.0219433i
$871$	8679.92	+	5011.35i	0.337667	+	0.194952i
$872$	−311.331	−	179.747i	−0.0120906	−	0.00698051i
$873$	−25253.5	+	16531.4i	−0.979039	+	0.640898i
$874$		−	3121.76i		−	0.120818i
$875$	−1880.71	−	1349.93i	−0.0726623	−	0.0521554i
$876$	−1154.36	−	41203.8i	−0.0445231	−	1.58921i
$877$	−19242.8	−	33329.5i	−0.740916	−	1.28330i	−0.952079	−	0.305854i	$-0.901058\pi$
$877$	−19242.8	−	33329.5i	−0.740916	−	1.28330i	0.211162	−	0.977451i	$-0.432275\pi$
$878$	−484.454	+	839.099i	−0.0186213	+	0.0322531i
$879$	7611.45	−	14079.9i	0.292068	−	0.540276i
$880$	4752.95	−	2744.12i	0.182070	−	0.105118i
$881$	−8924.43			−0.341285			−0.170642	−	0.985333i	$-0.554584\pi$
$881$	−8924.43			−0.341285			−0.170642	+	0.985333i	$0.554584\pi$
$882$	−201.357	+	1409.45i	−0.00768714	+	0.0538079i
$883$	−48075.7			−1.83225			−0.916124	−	0.400894i	$-0.868699\pi$
$883$	−48075.7			−1.83225			−0.916124	+	0.400894i	$0.868699\pi$
$884$	−7491.25	+	4325.07i	−0.285020	+	0.164556i
$885$	−7227.23	+	13369.1i	−0.274509	+	0.507796i
$886$	−1071.46	+	1855.83i	−0.0406281	+	0.0703699i
$887$	6260.47	+	10843.4i	0.236985	+	0.410470i	0.959848	−	0.280521i	$-0.0905074\pi$
$887$	6260.47	+	10843.4i	0.236985	+	0.410470i	−0.722863	+	0.690992i	$0.757174\pi$
$888$	12.0688	+	430.785i	0.000456084	+	0.0162795i
$889$	−33671.3	−	24168.5i	−1.27030	−	0.911795i
$890$		−	843.353i		−	0.0317632i
$891$	10150.9	−	7489.11i	0.381670	−	0.281588i
$892$	−32637.9	−	18843.5i	−1.22511	−	0.707318i
$893$	−51798.2	−	29905.7i	−1.94105	−	1.12067i
$894$	−611.987	−	994.586i	−0.0228948	−	0.0372080i
$895$		−	2623.72i		−	0.0979901i
$896$	5759.86	+	571.862i	0.214758	+	0.0213221i
$897$	−29532.4	+	827.375i	−1.09928	+	0.0307974i
$898$	881.188	+	1526.26i	0.0327457	+	0.0567172i
$899$	1242.28	−	2151.70i	0.0460873	−	0.0798256i
$900$	−2426.75	+	4806.13i	−0.0898795	+	0.178005i
$901$	6300.69	−	3637.71i	0.232971	−	0.134506i
$902$	729.515			0.0269292
$903$	−21493.2	+	10452.7i	−0.792082	+	0.385209i
$904$	−2238.84			−0.0823702
$905$	−13222.4	+	7633.96i	−0.485666	+	0.280399i
$906$	−1064.92	−	575.683i	−0.0390502	−	0.0211102i
$907$	−10558.3	+	18287.5i	−0.386529	+	0.669488i	−0.991980	−	0.126395i	$-0.959659\pi$
$907$	−10558.3	+	18287.5i	−0.386529	+	0.669488i	0.605451	+	0.795882i	$0.292993\pi$
$908$	11088.6	+	19206.0i	0.405273	+	0.701953i
$909$	46613.8	−	2613.90i	1.70086	−	0.0953770i
$910$	−473.274	+	213.990i	−0.0172405	+	0.00779528i
$911$		−	26013.1i		−	0.946050i	−0.881049	−	0.473025i	$-0.843162\pi$
$911$		−	26013.1i		−	0.946050i	0.881049	−	0.473025i	$-0.156838\pi$
$912$	36578.0	−	22507.2i	1.32809	−	0.817200i
$913$	−8761.08	−	5058.21i	−0.317579	−	0.183354i
$914$	−130.383	−	75.2765i	−0.00471847	−	0.00272421i
$915$	5668.68	−	3488.05i	0.204810	−	0.126023i
$916$			23448.1i			0.845793i
$917$	−2564.22	+	25827.1i	−0.0923425	+	0.930084i
$918$	53.8064	+	638.849i	0.00193450	+	0.0229686i
$919$	13097.3	+	22685.3i	0.470121	+	0.814274i	0.999416	−	0.0341639i	$-0.0108768\pi$
$919$	13097.3	+	22685.3i	0.470121	+	0.814274i	−0.529295	+	0.848438i	$0.677543\pi$
$920$	−956.916	+	1657.43i	−0.0342919	+	0.0593954i
$921$	40616.6	+	21957.0i	1.45316	+	0.785566i
$922$	1326.78	−	766.016i	0.0473917	−	0.0273616i
$923$	−39016.0			−1.39136
$924$	−7439.99	+	11003.2i	−0.264889	+	0.391752i
$925$	844.174			0.0300068
$926$	−1121.56	+	647.531i	−0.0398020	+	0.0229797i
$927$	27192.7	+	13730.3i	0.963457	+	0.486476i
$928$	2433.38	−	4214.74i	0.0860771	−	0.149090i
$929$	−7499.33	−	12989.2i	−0.264849	−	0.458732i	0.702675	−	0.711511i	$-0.251989\pi$
$929$	−7499.33	−	12989.2i	−0.264849	−	0.458732i	−0.967524	+	0.252779i	$0.918656\pi$
$930$	59.9292	−	1.67897i	0.00211307	−	5.91995e-5i
$931$	−33555.5	−	29520.7i	−1.18124	−	1.03921i
$932$			48153.8i			1.69241i
$933$	5015.24	+	8150.64i	0.175982	+	0.286002i
$934$	−973.564	−	562.087i	−0.0341071	−	0.0196917i
$935$	−2227.18	−	1285.86i	−0.0778999	−	0.0449755i
$936$	1325.18	+	2024.35i	0.0462765	+	0.0706923i
$937$			8484.86i			0.295825i	0.989000	+	0.147913i	$0.0472555\pi$
$937$			8484.86i			0.295825i	−0.989000	+	0.147913i	$0.952745\pi$
$938$	−456.096	+	635.427i	−0.0158764	+	0.0221188i
$939$	−62.9943	−	2248.52i	−0.00218929	−	0.0781445i
$940$	9153.48	+	15854.3i	0.317610	+	0.550117i
$941$	4495.58	−	7786.57i	0.155740	−	0.269750i	−0.777588	−	0.628774i	$-0.783557\pi$
$941$	4495.58	−	7786.57i	0.155740	−	0.269750i	0.933328	+	0.359024i	$0.116890\pi$
$942$	−654.013	+	1209.81i	−0.0226209	+	0.0418448i
$943$	37009.9	−	21367.7i	1.27806	−	0.737888i
$944$	−37105.7			−1.27933
$945$	194.011	−	12990.2i	0.00667848	−	0.447164i
$946$	660.687			0.0227070
$947$	−5302.79	+	3061.57i	−0.181961	+	0.105056i	−0.588214	−	0.808705i	$-0.700169\pi$
$947$	−5302.79	+	3061.57i	−0.181961	+	0.105056i	0.406252	+	0.913761i	$0.366835\pi$
$948$	229.275	−	424.119i	0.00785496	−	0.0145303i
$949$	−18142.6	+	31424.0i	−0.620584	+	1.07488i
$950$	250.398	+	433.703i	0.00855158	+	0.0148118i
$951$	−606.184	−	21637.2i	−0.0206697	−	0.737785i
$952$	−557.059	−	1232.03i	−0.0189647	−	0.0419435i
$953$		−	228.212i		−	0.00775711i	−0.999992	−	0.00387855i	$-0.998765\pi$
$953$		−	228.212i		−	0.00775711i	0.999992	−	0.00387855i	$-0.00123459\pi$
$954$	−556.462	−	850.055i	−0.0188848	−	0.0288486i
$955$	−16071.9	−	9279.09i	−0.544579	−	0.314413i
$956$	−29861.1	−	17240.3i	−1.01023	−	0.583254i
$957$	7799.70	+	12675.9i	0.263457	+	0.428164i
$958$		−	77.4197i		−	0.00261098i
$959$	6832.44	+	15111.1i	0.230064	+	0.508823i
$960$	−13061.8	+	365.938i	−0.439133	+	0.0123027i
$961$	−14782.9	−	25604.6i	−0.496219	−	0.859476i
$962$	94.7001	−	164.025i	0.00317386	−	0.00549729i
$963$	24553.4	+	12397.7i	0.821621	+	0.414859i
$964$	31231.8	−	18031.7i	1.04347	−	0.602450i
$965$	−16841.1			−0.561798
$966$	163.448	−	2299.80i	0.00544395	−	0.0765993i
$967$	2427.96			0.0807425			0.0403712	−	0.999185i	$-0.487146\pi$
$967$	2427.96			0.0807425			0.0403712	+	0.999185i	$0.487146\pi$
$968$	−2194.26	+	1266.85i	−0.0728575	+	0.0420643i
$969$	−17703.6	−	9570.42i	−0.586917	−	0.317282i
$970$	429.656	−	744.186i	0.0142221	−	0.0246334i
$971$	29081.4	+	50370.5i	0.961140	+	1.66474i	0.719645	+	0.694342i	$0.244305\pi$
$971$	29081.4	+	50370.5i	0.961140	+	1.66474i	0.241495	+	0.970402i	$0.422362\pi$
$972$	−29918.6	+	4217.49i	−0.987285	+	0.139173i
$973$	4653.27	−	6482.87i	0.153316	−	0.213599i
$974$			486.074i			0.0159906i
$975$	4036.54	−	2483.76i	0.132587	−	0.0815836i
$976$	14073.4	+	8125.30i	0.461557	+	0.266480i
$977$	−18454.9	−	10655.0i	−0.604326	−	0.348908i	0.166416	−	0.986056i	$-0.446781\pi$
$977$	−18454.9	−	10655.0i	−0.604326	−	0.348908i	−0.770741	+	0.637148i	$0.780114\pi$
$978$	−653.892	+	402.352i	−0.0213795	+	0.0131552i
$979$			18984.8i			0.619772i
$980$	4376.78	+	12960.4i	0.142664	+	0.422453i
$981$	−3945.64	+	221.254i	−0.128414	+	0.00720093i
$982$	−492.141	−	852.413i	−0.0159927	−	0.0277002i
$983$	2012.71	−	3486.11i	0.0653056	−	0.113113i	−0.831524	−	0.555489i	$-0.812531\pi$
$983$	2012.71	−	3486.11i	0.0653056	−	0.113113i	0.896830	+	0.442376i	$0.145864\pi$
$984$	−3078.77	−	1664.36i	−0.0997436	−	0.0539204i
$985$	−19656.6	+	11348.8i	−0.635850	+	0.367108i
$986$	−756.415			−0.0244312
$987$	−36594.1	−	24743.6i	−1.18014	−	0.797972i
$988$	−37919.1			−1.22102
$989$	33518.1	−	19351.7i	1.07767	−	0.622193i
$990$	−161.872	+	320.585i	−0.00519661	+	0.0102918i
$991$	−2914.75	+	5048.50i	−0.0934311	+	0.161827i	−0.908953	−	0.416899i	$-0.863117\pi$
$991$	−2914.75	+	5048.50i	−0.0934311	+	0.161827i	0.815522	+	0.578727i	$0.196450\pi$
$992$	220.656	+	382.187i	0.00706232	+	0.0122323i
$993$	939.677	−	26.3259i	0.0300300	−	0.000841315i
$994$	300.821	−	3029.90i	0.00959905	−	0.0966827i
$995$			3570.58i			0.113764i
$996$	12698.4	+	20637.0i	0.403979	+	0.656535i
$997$	39114.3	+	22582.7i	1.24249	+	0.717352i	0.969601	−	0.244693i	$-0.0786872\pi$
$997$	39114.3	+	22582.7i	1.24249	+	0.717352i	0.272890	+	0.962045i	$0.412021\pi$
$998$	−522.043	−	301.402i	−0.0165581	−	0.00955983i
$999$	2704.66	+	3889.42i	0.0856572	+	0.123179i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.s.a.101.8	yes	32
3.2	odd	2		105.4.s.b.101.9	yes	32
7.5	odd	6		105.4.s.b.26.9	yes	32
21.5	even	6	inner	105.4.s.a.26.8	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.s.a.26.8	✓	32	21.5	even	6	inner
105.4.s.a.101.8	yes	32	1.1	even	1	trivial
105.4.s.b.26.9	yes	32	7.5	odd	6
105.4.s.b.101.9	yes	32	3.2	odd	2

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.133140 + 0.0768685i) q^{2} +(2.47104 - 4.57099i) q^{3} +(-3.98818 + 6.90773i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(0.0223714 + 0.798528i) q^{6} +(-15.0457 - 10.7995i) q^{7} -2.45616i q^{8} +(-14.7880 - 22.5902i) q^{9} +O(q^{10})\)	\(q+(-0.133140 + 0.0768685i) q^{2} +(2.47104 - 4.57099i) q^{3} +(-3.98818 + 6.90773i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(0.0223714 + 0.798528i) q^{6} +(-15.0457 - 10.7995i) q^{7} -2.45616i q^{8} +(-14.7880 - 22.5902i) q^{9} +(0.665701 + 0.384343i) q^{10} +(-14.9856 - 8.65197i) q^{11} +(21.7203 + 35.2992i) q^{12} -36.4846i q^{13} +(2.83332 + 0.281303i) q^{14} +(-25.9706 + 0.727588i) q^{15} +(-31.7167 - 54.9349i) q^{16} +(-14.8621 + 25.7418i) q^{17} +(3.70535 + 1.87093i) q^{18} +(-112.843 + 65.1498i) q^{19} +39.8818 q^{20} +(-86.5426 + 42.0878i) q^{21} +2.66026 q^{22} +(134.961 - 77.9197i) q^{23} +(-11.2271 - 6.06926i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(2.80452 + 4.85757i) q^{26} +(-139.801 + 11.7746i) q^{27} +(134.605 - 60.8612i) q^{28} -165.529i q^{29} +(3.40180 - 2.09319i) q^{30} +(12.9990 + 7.50496i) q^{31} +(25.4623 + 14.7007i) q^{32} +(-76.5782 + 47.1200i) q^{33} -4.56970i q^{34} +(-9.14885 + 92.1482i) q^{35} +(215.024 - 12.0576i) q^{36} +(-16.8835 - 29.2431i) q^{37} +(10.0159 - 17.3481i) q^{38} +(-166.771 - 90.1547i) q^{39} +(-10.6355 + 6.14040i) q^{40} +274.227 q^{41} +(8.28707 - 12.2560i) q^{42} +248.354 q^{43} +(119.531 - 69.0113i) q^{44} +(-60.8484 + 120.509i) q^{45} +(-11.9791 + 20.7485i) q^{46} +(229.515 + 397.532i) q^{47} +(-329.480 + 9.23066i) q^{48} +(109.744 + 324.970i) q^{49} -3.84343i q^{50} +(80.9411 + 131.543i) q^{51} +(252.026 + 145.507i) q^{52} +(-211.972 - 122.382i) q^{53} +(17.7081 - 12.3140i) q^{54} +86.5197i q^{55} +(-26.5252 + 36.9545i) q^{56} +(18.9609 + 676.791i) q^{57} +(12.7239 + 22.0385i) q^{58} +(292.478 - 506.587i) q^{59} +(98.5494 - 182.300i) q^{60} +(-221.862 + 128.092i) q^{61} -2.30758 q^{62} +(-21.4667 + 499.586i) q^{63} +502.946 q^{64} +(-157.983 + 91.2115i) q^{65} +(6.57359 - 12.1600i) q^{66} +(-137.355 + 237.906i) q^{67} +(-118.545 - 205.326i) q^{68} +(-22.6774 - 809.448i) q^{69} +(-5.86522 - 12.9719i) q^{70} -1069.38i q^{71} +(-55.4851 + 36.3216i) q^{72} +(-861.294 - 497.268i) q^{73} +(4.49574 + 2.59562i) q^{74} +(68.0770 + 110.637i) q^{75} -1039.32i q^{76} +(132.032 + 292.011i) q^{77} +(29.1340 - 0.816213i) q^{78} +(-5.81624 - 10.0740i) q^{79} +(-158.583 + 274.674i) q^{80} +(-291.632 + 668.126i) q^{81} +(-36.5107 + 21.0794i) q^{82} +584.631 q^{83} +(54.4163 - 765.667i) q^{84} +148.621 q^{85} +(-33.0660 + 19.0906i) q^{86} +(-756.630 - 409.027i) q^{87} +(-21.2506 + 36.8071i) q^{88} +(-548.569 - 950.149i) q^{89} +(-1.16200 - 20.7220i) q^{90} +(-394.014 + 548.935i) q^{91} +1243.03i q^{92} +(66.4260 - 40.8732i) q^{93} +(-61.1154 - 35.2850i) q^{94} +(564.214 + 325.749i) q^{95} +(130.115 - 80.0621i) q^{96} -1117.90i q^{97} +(-39.5912 - 34.8307i) q^{98} +(26.1578 + 466.473i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{3} + 64 q^{4} - 80 q^{5} - 28 q^{6} + 46 q^{7} + 100 q^{9}+O(q^{10}) \) 32 * q - 2 * q^3 + 64 * q^4 - 80 * q^5 - 28 * q^6 + 46 * q^7 + 100 * q^9	\( 32 q - 2 q^{3} + 64 q^{4} - 80 q^{5} - 28 q^{6} + 46 q^{7} + 100 q^{9} + 36 q^{11} + 246 q^{12} + 18 q^{14} + 20 q^{15} - 376 q^{16} - 72 q^{17} - 442 q^{18} - 198 q^{19} - 640 q^{20} - 218 q^{21} + 204 q^{22} + 72 q^{23} - 50 q^{24} - 400 q^{25} - 312 q^{26} + 508 q^{27} + 350 q^{28} + 40 q^{30} + 510 q^{31} + 810 q^{32} + 290 q^{33} - 70 q^{35} - 612 q^{36} - 658 q^{37} - 192 q^{38} - 648 q^{39} - 1404 q^{41} + 1892 q^{42} + 332 q^{43} + 2034 q^{44} - 490 q^{45} - 468 q^{46} + 408 q^{47} + 2810 q^{48} + 980 q^{49} - 888 q^{51} + 3378 q^{52} + 1152 q^{53} + 2714 q^{54} - 3354 q^{56} - 816 q^{57} - 1080 q^{58} - 48 q^{59} - 420 q^{60} - 1662 q^{61} - 2076 q^{62} + 874 q^{63} - 1952 q^{64} + 870 q^{65} - 1892 q^{66} - 1298 q^{67} + 1182 q^{68} + 2450 q^{69} - 450 q^{70} - 2708 q^{72} + 378 q^{73} + 2898 q^{74} - 50 q^{75} - 3528 q^{77} - 1896 q^{78} - 326 q^{79} - 1880 q^{80} - 3308 q^{81} - 2916 q^{82} - 1536 q^{83} + 1380 q^{84} + 720 q^{85} + 5202 q^{86} - 1090 q^{87} + 1668 q^{88} - 1590 q^{89} + 910 q^{90} + 2082 q^{91} - 4950 q^{93} - 1152 q^{94} + 990 q^{95} + 7416 q^{96} - 7830 q^{98} + 3128 q^{99}+O(q^{100}) \) 32 * q - 2 * q^3 + 64 * q^4 - 80 * q^5 - 28 * q^6 + 46 * q^7 + 100 * q^9 + 36 * q^11 + 246 * q^12 + 18 * q^14 + 20 * q^15 - 376 * q^16 - 72 * q^17 - 442 * q^18 - 198 * q^19 - 640 * q^20 - 218 * q^21 + 204 * q^22 + 72 * q^23 - 50 * q^24 - 400 * q^25 - 312 * q^26 + 508 * q^27 + 350 * q^28 + 40 * q^30 + 510 * q^31 + 810 * q^32 + 290 * q^33 - 70 * q^35 - 612 * q^36 - 658 * q^37 - 192 * q^38 - 648 * q^39 - 1404 * q^41 + 1892 * q^42 + 332 * q^43 + 2034 * q^44 - 490 * q^45 - 468 * q^46 + 408 * q^47 + 2810 * q^48 + 980 * q^49 - 888 * q^51 + 3378 * q^52 + 1152 * q^53 + 2714 * q^54 - 3354 * q^56 - 816 * q^57 - 1080 * q^58 - 48 * q^59 - 420 * q^60 - 1662 * q^61 - 2076 * q^62 + 874 * q^63 - 1952 * q^64 + 870 * q^65 - 1892 * q^66 - 1298 * q^67 + 1182 * q^68 + 2450 * q^69 - 450 * q^70 - 2708 * q^72 + 378 * q^73 + 2898 * q^74 - 50 * q^75 - 3528 * q^77 - 1896 * q^78 - 326 * q^79 - 1880 * q^80 - 3308 * q^81 - 2916 * q^82 - 1536 * q^83 + 1380 * q^84 + 720 * q^85 + 5202 * q^86 - 1090 * q^87 + 1668 * q^88 - 1590 * q^89 + 910 * q^90 + 2082 * q^91 - 4950 * q^93 - 1152 * q^94 + 990 * q^95 + 7416 * q^96 - 7830 * q^98 + 3128 * q^99

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