LMFDB - Embedded newform 48.4.j.a.37.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,4,Mod(13,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("48.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	48.j (of order $4$, 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:	$2.83209168028$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.4
Character	$\chi$	$=$	48.37
Dual form			48.4.j.a.13.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40656 - 2.45389i) q^{2} +(-2.12132 + 2.12132i) q^{3} +(-4.04315 + 6.90311i) q^{4} +(3.22588 + 3.22588i) q^{5} +(8.18926 + 2.22171i) q^{6} +24.6080i q^{7} +(22.6264 + 0.211795i) q^{8} -9.00000i q^{9} +O(q^{10})$	\(q+(-1.40656 - 2.45389i) q^{2} +(-2.12132 + 2.12132i) q^{3} +(-4.04315 + 6.90311i) q^{4} +(3.22588 + 3.22588i) q^{5} +(8.18926 + 2.22171i) q^{6} +24.6080i q^{7} +(22.6264 + 0.211795i) q^{8} -9.00000i q^{9} +(3.37855 - 12.4534i) q^{10} +(23.7522 + 23.7522i) q^{11} +(-6.06688 - 23.2205i) q^{12} +(-18.6720 + 18.6720i) q^{13} +(60.3853 - 34.6127i) q^{14} -13.6863 q^{15} +(-31.3058 - 55.8207i) q^{16} -3.55065 q^{17} +(-22.0850 + 12.6591i) q^{18} +(-109.089 + 109.089i) q^{19} +(-35.3113 + 9.22587i) q^{20} +(-52.2014 - 52.2014i) q^{21} +(24.8763 - 91.6943i) q^{22} -36.5653i q^{23} +(-48.4472 + 47.5486i) q^{24} -104.187i q^{25} +(72.0826 + 19.5557i) q^{26} +(19.0919 + 19.0919i) q^{27} +(-169.872 - 99.4939i) q^{28} +(68.8087 - 68.8087i) q^{29} +(19.2506 + 33.5846i) q^{30} +306.914 q^{31} +(-92.9442 + 155.336i) q^{32} -100.772 q^{33} +(4.99422 + 8.71292i) q^{34} +(-79.3824 + 79.3824i) q^{35} +(62.1280 + 36.3884i) q^{36} +(92.9951 + 92.9951i) q^{37} +(421.132 + 114.251i) q^{38} -79.2188i q^{39} +(72.3069 + 73.6734i) q^{40} -385.594i q^{41} +(-54.6719 + 201.521i) q^{42} +(150.610 + 150.610i) q^{43} +(-259.998 + 67.9302i) q^{44} +(29.0329 - 29.0329i) q^{45} +(-89.7271 + 51.4314i) q^{46} -114.406 q^{47} +(184.823 + 52.0039i) q^{48} -262.553 q^{49} +(-255.664 + 146.546i) q^{50} +(7.53207 - 7.53207i) q^{51} +(-53.4012 - 204.389i) q^{52} +(451.631 + 451.631i) q^{53} +(19.9954 - 73.7033i) q^{54} +153.243i q^{55} +(-5.21185 + 556.791i) q^{56} -462.824i q^{57} +(-265.633 - 72.0652i) q^{58} +(-544.327 - 544.327i) q^{59} +(55.3356 - 94.4777i) q^{60} +(179.921 - 179.921i) q^{61} +(-431.694 - 753.133i) q^{62} +221.472 q^{63} +(511.910 + 9.58434i) q^{64} -120.468 q^{65} +(141.742 + 247.283i) q^{66} +(-283.133 + 283.133i) q^{67} +(14.3558 - 24.5105i) q^{68} +(77.5666 + 77.5666i) q^{69} +(306.452 + 83.1393i) q^{70} -930.296i q^{71} +(1.90616 - 203.638i) q^{72} +701.187i q^{73} +(97.3962 - 359.003i) q^{74} +(221.015 + 221.015i) q^{75} +(-311.988 - 1194.11i) q^{76} +(-584.494 + 584.494i) q^{77} +(-194.394 + 111.426i) q^{78} +779.471 q^{79} +(79.0820 - 281.060i) q^{80} -81.0000 q^{81} +(-946.205 + 542.363i) q^{82} +(-296.734 + 296.734i) q^{83} +(571.410 - 149.294i) q^{84} +(-11.4540 - 11.4540i) q^{85} +(157.738 - 581.423i) q^{86} +291.931i q^{87} +(532.397 + 542.458i) q^{88} +865.485i q^{89} +(-112.080 - 30.4069i) q^{90} +(-459.481 - 459.481i) q^{91} +(252.414 + 147.839i) q^{92} +(-651.062 + 651.062i) q^{93} +(160.919 + 280.740i) q^{94} -703.813 q^{95} +(-132.354 - 526.683i) q^{96} -542.420 q^{97} +(369.298 + 644.276i) q^{98} +(213.770 - 213.770i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{4} + 84 q^{8}+O(q^{10}) $ 24 * q - 20 * q^4 + 84 * q^8	$ 24 q - 20 q^{4} + 84 q^{8} + 72 q^{10} - 40 q^{11} - 24 q^{12} - 348 q^{14} + 120 q^{15} - 192 q^{16} - 36 q^{18} + 24 q^{19} + 80 q^{20} + 704 q^{22} + 228 q^{24} - 20 q^{26} - 344 q^{28} + 400 q^{29} - 408 q^{30} - 744 q^{31} - 960 q^{32} - 704 q^{34} - 456 q^{35} + 108 q^{36} + 16 q^{37} + 1256 q^{38} + 1744 q^{40} + 660 q^{42} + 1240 q^{43} - 200 q^{44} - 1432 q^{46} - 528 q^{48} - 1176 q^{49} + 708 q^{50} + 744 q^{51} + 1008 q^{52} + 752 q^{53} + 108 q^{54} + 1344 q^{56} + 1936 q^{58} - 1376 q^{59} - 1224 q^{60} - 912 q^{61} - 996 q^{62} - 504 q^{63} - 56 q^{64} + 976 q^{65} - 1368 q^{66} - 2256 q^{67} - 1568 q^{68} - 528 q^{69} - 1760 q^{70} - 612 q^{72} - 2740 q^{74} + 1104 q^{75} - 1880 q^{76} + 1904 q^{77} + 1692 q^{78} + 5992 q^{79} + 712 q^{80} - 1944 q^{81} - 40 q^{82} + 2680 q^{83} + 1800 q^{84} - 240 q^{85} - 1712 q^{86} - 3936 q^{88} + 648 q^{90} - 3496 q^{91} + 5296 q^{92} + 5272 q^{94} - 7728 q^{95} + 2880 q^{96} + 6760 q^{98} - 360 q^{99}+O(q^{100}) $ 24 * q - 20 * q^4 + 84 * q^8 + 72 * q^10 - 40 * q^11 - 24 * q^12 - 348 * q^14 + 120 * q^15 - 192 * q^16 - 36 * q^18 + 24 * q^19 + 80 * q^20 + 704 * q^22 + 228 * q^24 - 20 * q^26 - 344 * q^28 + 400 * q^29 - 408 * q^30 - 744 * q^31 - 960 * q^32 - 704 * q^34 - 456 * q^35 + 108 * q^36 + 16 * q^37 + 1256 * q^38 + 1744 * q^40 + 660 * q^42 + 1240 * q^43 - 200 * q^44 - 1432 * q^46 - 528 * q^48 - 1176 * q^49 + 708 * q^50 + 744 * q^51 + 1008 * q^52 + 752 * q^53 + 108 * q^54 + 1344 * q^56 + 1936 * q^58 - 1376 * q^59 - 1224 * q^60 - 912 * q^61 - 996 * q^62 - 504 * q^63 - 56 * q^64 + 976 * q^65 - 1368 * q^66 - 2256 * q^67 - 1568 * q^68 - 528 * q^69 - 1760 * q^70 - 612 * q^72 - 2740 * q^74 + 1104 * q^75 - 1880 * q^76 + 1904 * q^77 + 1692 * q^78 + 5992 * q^79 + 712 * q^80 - 1944 * q^81 - 40 * q^82 + 2680 * q^83 + 1800 * q^84 - 240 * q^85 - 1712 * q^86 - 3936 * q^88 + 648 * q^90 - 3496 * q^91 + 5296 * q^92 + 5272 * q^94 - 7728 * q^95 + 2880 * q^96 + 6760 * q^98 - 360 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.40656	−	2.45389i	−0.497295	−	0.867581i
$2$	−1.40656	−	2.45389i	−0.497295	−	0.867581i
$3$	−2.12132	+	2.12132i	−0.408248	+	0.408248i
$3$	−2.12132	+	2.12132i	−0.408248	+	0.408248i
$4$	−4.04315	+	6.90311i	−0.505394	+	0.862888i
$5$	3.22588	+	3.22588i	0.288531	+	0.288531i	0.836499	−	0.547968i	$-0.184598\pi$
$5$	3.22588	+	3.22588i	0.288531	+	0.288531i	−0.547968	+	0.836499i	$0.684598\pi$
$6$	8.18926	+	2.22171i	0.557209	+	0.151169i
$7$			24.6080i			1.32871i	0.747419	+	0.664353i	$0.231293\pi$
$7$			24.6080i			1.32871i	−0.747419	+	0.664353i	$0.768707\pi$
$8$	22.6264	+	0.211795i	0.999956	+	0.00936012i
$9$		−	9.00000i		−	0.333333i
$10$	3.37855	−	12.4534i	0.106839	−	0.393810i
$11$	23.7522	+	23.7522i	0.651051	+	0.651051i	0.953246	−	0.302195i	$-0.0977195\pi$
$11$	23.7522	+	23.7522i	0.651051	+	0.651051i	−0.302195	+	0.953246i	$0.597720\pi$
$12$	−6.06688	−	23.2205i	−0.145946	−	0.558599i
$13$	−18.6720	+	18.6720i	−0.398361	+	0.398361i	−0.877655	−	0.479294i	$-0.840893\pi$
$13$	−18.6720	+	18.6720i	−0.398361	+	0.398361i	0.479294	+	0.877655i	$0.340893\pi$
$14$	60.3853	−	34.6127i	1.15276	−	0.660760i
$15$	−13.6863			−0.235585
$16$	−31.3058	−	55.8207i	−0.489153	−	0.872198i
$17$	−3.55065			−0.0506565			−0.0253282	−	0.999679i	$-0.508063\pi$
$17$	−3.55065			−0.0506565			−0.0253282	+	0.999679i	$0.508063\pi$
$18$	−22.0850	+	12.6591i	−0.289194	+	0.165765i
$19$	−109.089	+	109.089i	−1.31719	+	1.31719i	−0.401202	+	0.915990i	$0.631407\pi$
$19$	−109.089	+	109.089i	−1.31719	+	1.31719i	−0.915990	+	0.401202i	$0.868593\pi$
$20$	−35.3113	+	9.22587i	−0.394793	+	0.103148i
$21$	−52.2014	−	52.2014i	−0.542442	−	0.542442i
$22$	24.8763	−	91.6943i	0.241075	−	0.888604i
$23$		−	36.5653i		−	0.331495i	−0.986168	−	0.165747i	$-0.946996\pi$
$23$		−	36.5653i		−	0.331495i	0.986168	−	0.165747i	$-0.0530037\pi$
$24$	−48.4472	+	47.5486i	−0.412052	+	0.404409i
$25$		−	104.187i		−	0.833499i
$26$	72.0826	+	19.5557i	0.543714	+	0.147507i
$27$	19.0919	+	19.0919i	0.136083	+	0.136083i
$28$	−169.872	−	99.4939i	−1.14653	−	0.671521i
$29$	68.8087	−	68.8087i	0.440602	−	0.440602i	−0.451612	−	0.892214i	$-0.649151\pi$
$29$	68.8087	−	68.8087i	0.440602	−	0.440602i	0.892214	+	0.451612i	$0.149151\pi$
$30$	19.2506	+	33.5846i	0.117155	+	0.204389i
$31$	306.914			1.77817			0.889086	−	0.457740i	$-0.151341\pi$
$31$	306.914			1.77817			0.889086	+	0.457740i	$0.151341\pi$
$32$	−92.9442	+	155.336i	−0.513449	+	0.858120i
$33$	−100.772			−0.531581
$34$	4.99422	+	8.71292i	0.0251912	+	0.0439486i
$35$	−79.3824	+	79.3824i	−0.383374	+	0.383374i
$36$	62.1280	+	36.3884i	0.287629	+	0.168465i
$37$	92.9951	+	92.9951i	0.413197	+	0.413197i	0.882851	−	0.469654i	$-0.155621\pi$
$37$	92.9951	+	92.9951i	0.413197	+	0.413197i	−0.469654	+	0.882851i	$0.655621\pi$
$38$	421.132	+	114.251i	1.79780	+	0.487737i
$39$		−	79.2188i		−	0.325260i
$40$	72.3069	+	73.6734i	0.285818	+	0.291220i
$41$		−	385.594i		−	1.46877i	−0.678732	−	0.734386i	$-0.737470\pi$
$41$		−	385.594i		−	1.46877i	0.678732	−	0.734386i	$-0.262530\pi$
$42$	−54.6719	+	201.521i	−0.200859	+	0.740367i
$43$	150.610	+	150.610i	0.534135	+	0.534135i	0.921800	−	0.387665i	$-0.126718\pi$
$43$	150.610	+	150.610i	0.534135	+	0.534135i	−0.387665	+	0.921800i	$0.626718\pi$
$44$	−259.998	+	67.9302i	−0.890821	+	0.232747i
$45$	29.0329	−	29.0329i	0.0961772	−	0.0961772i
$46$	−89.7271	+	51.4314i	−0.287599	+	0.164851i
$47$	−114.406			−0.355060			−0.177530	−	0.984115i	$-0.556811\pi$
$47$	−114.406			−0.355060			−0.177530	+	0.984115i	$0.556811\pi$
$48$	184.823	+	52.0039i	0.555769	+	0.156377i
$49$	−262.553			−0.765460
$50$	−255.664	+	146.546i	−0.723128	+	0.414495i
$51$	7.53207	−	7.53207i	0.0206804	−	0.0206804i
$52$	−53.4012	−	204.389i	−0.142412	−	0.545070i
$53$	451.631	+	451.631i	1.17050	+	1.17050i	0.982092	+	0.188404i	$0.0603315\pi$
$53$	451.631	+	451.631i	1.17050	+	1.17050i	0.188404	+	0.982092i	$0.439669\pi$
$54$	19.9954	−	73.7033i	0.0503895	−	0.185736i
$55$			153.243i			0.375697i
$56$	−5.21185	+	556.791i	−0.0124368	+	1.32865i
$57$		−	462.824i		−	1.07548i
$58$	−265.633	−	72.0652i	−0.601368	−	0.163149i
$59$	−544.327	−	544.327i	−1.20111	−	1.20111i	−0.973830	−	0.227276i	$-0.927018\pi$
$59$	−544.327	−	544.327i	−1.20111	−	1.20111i	−0.227276	−	0.973830i	$-0.572982\pi$
$60$	55.3356	−	94.4777i	0.119063	−	0.203284i
$61$	179.921	−	179.921i	0.377647	−	0.377647i	−0.492605	−	0.870253i	$-0.663955\pi$
$61$	179.921	−	179.921i	0.377647	−	0.377647i	0.870253	+	0.492605i	$0.163955\pi$
$62$	−431.694	−	753.133i	−0.884277	−	1.54271i
$63$	221.472			0.442902
$64$	511.910	+	9.58434i	0.999825	+	0.0187194i
$65$	−120.468			−0.229879
$66$	141.742	+	247.283i	0.264353	+	0.461189i
$67$	−283.133	+	283.133i	−0.516272	+	0.516272i	−0.916441	−	0.400170i	$-0.868951\pi$
$67$	−283.133	+	283.133i	−0.516272	+	0.516272i	0.400170	+	0.916441i	$0.368951\pi$
$68$	14.3558	−	24.5105i	0.0256015	−	0.0437109i
$69$	77.5666	+	77.5666i	0.135332	+	0.135332i
$70$	306.452	+	83.1393i	0.523258	+	0.141958i
$71$		−	930.296i		−	1.55501i	−0.628876	−	0.777505i	$-0.716485\pi$
$71$		−	930.296i		−	1.55501i	0.628876	−	0.777505i	$-0.283515\pi$
$72$	1.90616	−	203.638i	0.00312004	−	0.333319i
$73$			701.187i			1.12422i	0.827064	+	0.562108i	$0.190009\pi$
$73$			701.187i			1.12422i	−0.827064	+	0.562108i	$0.809991\pi$
$74$	97.3962	−	359.003i	0.153001	−	0.563963i
$75$	221.015	+	221.015i	0.340275	+	0.340275i
$76$	−311.988	−	1194.11i	−0.470888	−	1.80229i
$77$	−584.494	+	584.494i	−0.865055	+	0.865055i
$78$	−194.394	+	111.426i	−0.282190	+	0.161751i
$79$	779.471			1.11009			0.555046	−	0.831819i	$-0.312701\pi$
$79$	779.471			1.11009			0.555046	+	0.831819i	$0.312701\pi$
$80$	79.0820	−	281.060i	0.110521	−	0.392793i
$81$	−81.0000			−0.111111
$82$	−946.205	+	542.363i	−1.27428	+	0.730414i
$83$	−296.734	+	296.734i	−0.392419	+	0.392419i	−0.875549	−	0.483129i	$-0.839500\pi$
$83$	−296.734	+	296.734i	−0.392419	+	0.392419i	0.483129	+	0.875549i	$0.339500\pi$
$84$	571.410	−	149.294i	0.742214	−	0.193920i
$85$	−11.4540	−	11.4540i	−0.0146160	−	0.0146160i
$86$	157.738	−	581.423i	0.197783	−	0.729028i
$87$			291.931i			0.359750i
$88$	532.397	+	542.458i	0.644928	+	0.657116i
$89$			865.485i			1.03080i	0.856950	+	0.515400i	$0.172357\pi$
$89$			865.485i			1.03080i	−0.856950	+	0.515400i	$0.827643\pi$
$90$	−112.080	−	30.4069i	−0.131270	−	0.0356130i
$91$	−459.481	−	459.481i	−0.529305	−	0.529305i
$92$	252.414	+	147.839i	0.286043	+	0.167536i
$93$	−651.062	+	651.062i	−0.725936	+	0.725936i
$94$	160.919	+	280.740i	0.176570	+	0.308044i
$95$	−703.813			−0.760103
$96$	−132.354	−	526.683i	−0.140711	−	0.559941i
$97$	−542.420			−0.567778			−0.283889	−	0.958857i	$-0.591625\pi$
$97$	−542.420			−0.567778			−0.283889	+	0.958857i	$0.591625\pi$
$98$	369.298	+	644.276i	0.380660	+	0.664099i
$99$	213.770	−	213.770i	0.217017	−	0.217017i
$100$	719.217	+	421.246i	0.719217	+	0.421246i
$101$	1109.76	+	1109.76i	1.09331	+	1.09331i	0.995172	+	0.0981421i	$0.0312900\pi$
$101$	1109.76	+	1109.76i	1.09331	+	1.09331i	0.0981421	+	0.995172i	$0.468710\pi$
$102$	−29.0772	−	7.88854i	−0.0282262	−	0.00765766i
$103$		−	806.968i		−	0.771970i	−0.922505	−	0.385985i	$-0.873862\pi$
$103$		−	806.968i		−	0.771970i	0.922505	−	0.385985i	$-0.126138\pi$
$104$	−426.436	+	418.527i	−0.402072	+	0.394615i
$105$		−	336.791i		−	0.313023i
$106$	473.005	−	1743.50i	0.433418	−	1.59758i
$107$	345.828	+	345.828i	0.312453	+	0.312453i	0.845859	−	0.533406i	$-0.179088\pi$
$107$	345.828	+	345.828i	0.312453	+	0.312453i	−0.533406	+	0.845859i	$0.679088\pi$
$108$	−208.985	+	54.6019i	−0.186200	+	0.0486488i
$109$	251.854	−	251.854i	0.221314	−	0.221314i	−0.587738	−	0.809052i	$-0.699981\pi$
$109$	251.854	−	251.854i	0.221314	−	0.221314i	0.809052	+	0.587738i	$0.199981\pi$
$110$	376.043	−	215.547i	0.325948	−	0.186832i
$111$	−394.545			−0.337374
$112$	1373.63	−	770.373i	1.15889	−	0.649941i
$113$	1692.35			1.40888			0.704439	−	0.709764i	$-0.251199\pi$
$113$	1692.35			1.40888			0.704439	+	0.709764i	$0.251199\pi$
$114$	−1135.72	+	650.991i	−0.933068	+	0.534833i
$115$	117.955	−	117.955i	0.0956467	−	0.0956467i
$116$	196.790	+	753.199i	0.157513	+	0.602868i
$117$	168.048	+	168.048i	0.132787	+	0.132787i
$118$	−570.087	+	2101.35i	−0.444753	+	1.63936i
$119$		−	87.3744i		−	0.0673076i
$120$	−309.671	−	2.89868i	−0.235575	−	0.00220510i
$121$		−	202.667i		−	0.152266i
$122$	−694.576	−	188.436i	−0.515442	−	0.139837i
$123$	817.968	+	817.968i	0.599624	+	0.599624i
$124$	−1240.90	+	2118.66i	−0.898678	+	1.53436i
$125$	739.331	−	739.331i	0.529022	−	0.529022i
$126$	−311.514	−	543.468i	−0.220253	−	0.384254i
$127$	507.618			0.354676			0.177338	−	0.984150i	$-0.443251\pi$
$127$	507.618			0.354676			0.177338	+	0.984150i	$0.443251\pi$
$128$	−696.516	−	1269.65i	−0.480968	−	0.876738i
$129$	−638.984			−0.436119
$130$	169.445	+	295.614i	0.114318	+	0.199439i
$131$	848.697	−	848.697i	0.566038	−	0.566038i	−0.364978	−	0.931016i	$-0.618924\pi$
$131$	848.697	−	848.697i	0.566038	−	0.566038i	0.931016	+	0.364978i	$0.118924\pi$
$132$	407.437	−	695.640i	0.268658	−	0.458695i
$133$	−2684.45	−	2684.45i	−1.75016	−	1.75016i
$134$	1093.02	+	296.533i	0.704647	+	0.191168i
$135$			123.176i			0.0785283i
$136$	−80.3386	−	0.752012i	−0.0506543	−	0.000474151i
$137$		−	784.731i		−	0.489373i	−0.969602	−	0.244687i	$-0.921315\pi$
$137$		−	784.731i		−	0.489373i	0.969602	−	0.244687i	$-0.0786851\pi$
$138$	81.2376	−	299.442i	0.0501116	−	0.184712i
$139$	−1487.40	−	1487.40i	−0.907623	−	0.907623i	0.0884574	−	0.996080i	$-0.471806\pi$
$139$	−1487.40	−	1487.40i	−0.907623	−	0.907623i	−0.996080	+	0.0884574i	$0.971806\pi$
$140$	−227.030	−	868.941i	−0.137054	−	0.524564i
$141$	242.692	−	242.692i	0.144953	−	0.144953i
$142$	−2282.84	+	1308.52i	−1.34910	+	0.773300i
$143$	−887.004			−0.518706
$144$	−502.386	+	281.752i	−0.290733	+	0.163051i
$145$	443.937			0.254255
$146$	1720.64	−	986.265i	0.975349	−	0.559067i
$147$	556.959	−	556.959i	0.312498	−	0.312498i
$148$	−1017.95	+	265.962i	−0.565371	+	0.147716i
$149$	−1440.83	−	1440.83i	−0.792199	−	0.792199i	0.189652	−	0.981851i	$-0.439264\pi$
$149$	−1440.83	−	1440.83i	−0.792199	−	0.792199i	−0.981851	+	0.189652i	$0.939264\pi$
$150$	231.475	−	853.218i	0.125999	−	0.464433i
$151$			1416.10i			0.763180i	0.924332	+	0.381590i	$0.124623\pi$
$151$			1416.10i			0.763180i	−0.924332	+	0.381590i	$0.875377\pi$
$152$	−2491.39	+	2445.18i	−1.32946	+	1.30480i
$153$			31.9559i			0.0168855i
$154$	2256.41	+	612.155i	1.18069	+	0.320317i
$155$	990.067	+	990.067i	0.513059	+	0.513059i
$156$	546.856	+	320.294i	0.280663	+	0.164385i
$157$	1700.27	−	1700.27i	0.864309	−	0.864309i	−0.127526	−	0.991835i	$-0.540704\pi$
$157$	1700.27	−	1700.27i	0.864309	−	0.864309i	0.991835	+	0.127526i	$0.0407037\pi$
$158$	−1096.38	−	1912.74i	−0.552044	−	0.963095i
$159$	−1916.11			−0.955706
$160$	−800.923	+	201.270i	−0.395741	+	0.0994485i
$161$	899.797			0.440459
$162$	113.932	+	198.765i	0.0552551	+	0.0963979i
$163$	−1041.45	+	1041.45i	−0.500445	+	0.500445i	−0.911576	−	0.411131i	$-0.865134\pi$
$163$	−1041.45	+	1041.45i	−0.500445	+	0.500445i	0.411131	+	0.911576i	$0.365134\pi$
$164$	2661.80	+	1559.02i	1.26739	+	0.742309i
$165$	−325.078	−	325.078i	−0.153378	−	0.153378i
$166$	1145.53	+	310.778i	0.535604	+	0.145307i
$167$			3044.20i			1.41058i	0.708917	+	0.705292i	$0.249184\pi$
$167$			3044.20i			1.41058i	−0.708917	+	0.705292i	$0.750816\pi$
$168$	−1170.08	−	1192.19i	−0.537341	−	0.547496i
$169$			1499.71i			0.682617i
$170$	−11.9961	+	44.2176i	−0.00541209	+	0.0199490i
$171$	981.797	+	981.797i	0.439064	+	0.439064i
$172$	−1648.62	+	430.737i	−0.730848	+	0.190950i
$173$	−1410.58	+	1410.58i	−0.619912	+	0.619912i	−0.945509	−	0.325597i	$-0.894435\pi$
$173$	−1410.58	+	1410.58i	−0.619912	+	0.619912i	0.325597	+	0.945509i	$0.394435\pi$
$174$	716.366	−	410.619i	0.312112	−	0.178902i
$175$	2563.84			1.10748
$176$	582.282	−	2069.44i	0.249382	−	0.886308i
$177$	2309.38			0.980699
$178$	2123.81	−	1217.36i	0.894303	−	0.512613i
$179$	2160.33	−	2160.33i	0.902069	−	0.902069i	−0.0935459	−	0.995615i	$-0.529820\pi$
$179$	2160.33	−	2160.33i	0.902069	−	0.902069i	0.995615	+	0.0935459i	$0.0298202\pi$
$180$	83.0328	+	317.802i	0.0343828	+	0.131598i
$181$	−214.307	−	214.307i	−0.0880074	−	0.0880074i	0.661733	−	0.749740i	$-0.269821\pi$
$181$	−214.307	−	214.307i	−0.0880074	−	0.0880074i	−0.749740	+	0.661733i	$0.769821\pi$
$182$	−481.227	+	1773.81i	−0.195994	+	0.722436i
$183$			763.339i			0.308348i
$184$	7.74435	−	827.341i	0.00310283	−	0.331480i
$185$			599.982i			0.238441i
$186$	2513.40	+	681.875i	0.990813	+	0.268804i
$187$	−84.3358	−	84.3358i	−0.0329799	−	0.0329799i
$188$	462.561	−	789.757i	0.179445	−	0.306377i
$189$	−469.813	+	469.813i	−0.180814	+	0.180814i
$190$	989.959	+	1727.08i	0.377996	+	0.659451i
$191$	−3267.16			−1.23772			−0.618858	−	0.785503i	$-0.712404\pi$
$191$	−3267.16			−1.23772			−0.618858	+	0.785503i	$0.712404\pi$
$192$	−1106.26	+	1065.59i	−0.415819	+	0.400535i
$193$	−694.819			−0.259141			−0.129570	−	0.991570i	$-0.541360\pi$
$193$	−694.819			−0.259141			−0.129570	+	0.991570i	$0.541360\pi$
$194$	762.949	+	1331.04i	0.282353	+	0.492593i
$195$	255.550	−	255.550i	0.0938479	−	0.0938479i
$196$	1061.54	−	1812.43i	0.386859	−	0.660507i
$197$	−597.455	−	597.455i	−0.216076	−	0.216076i	0.590767	−	0.806842i	$-0.298825\pi$
$197$	−597.455	−	597.455i	−0.216076	−	0.216076i	−0.806842	+	0.590767i	$0.798825\pi$
$198$	−825.248	−	223.887i	−0.296201	−	0.0803582i
$199$			3359.58i			1.19676i	0.801214	+	0.598378i	$0.204188\pi$
$199$			3359.58i			1.19676i	−0.801214	+	0.598378i	$0.795812\pi$
$200$	22.0664	−	2357.39i	0.00780165	−	0.833463i
$201$		−	1201.23i		−	0.421534i
$202$	1162.28	−	4284.16i	0.404839	−	1.49224i
$203$	1693.24	+	1693.24i	0.585431	+	0.585431i
$204$	21.5414	+	82.4481i	0.00739313	+	0.0282967i
$205$	1243.88	−	1243.88i	0.423787	−	0.423787i
$206$	−1980.21	+	1135.05i	−0.669747	+	0.383897i
$207$	−329.087			−0.110498
$208$	1626.83	+	457.743i	0.542309	+	0.152590i
$209$	−5182.19			−1.71512
$210$	−826.448	+	473.718i	−0.271573	+	0.155665i
$211$	1339.88	−	1339.88i	0.437161	−	0.437161i	−0.453894	−	0.891055i	$-0.649966\pi$
$211$	1339.88	−	1339.88i	0.437161	−	0.437161i	0.891055	+	0.453894i	$0.149966\pi$
$212$	−4943.67	+	1291.64i	−1.60157	+	0.418445i
$213$	1973.45	+	1973.45i	0.634831	+	0.634831i
$214$	362.195	−	1335.05i	0.115697	−	0.426460i
$215$			971.699i			0.308230i
$216$	427.938	+	436.025i	0.134803	+	0.137351i
$217$			7552.53i			2.36267i
$218$	−972.269	−	263.773i	−0.302066	−	0.0819493i
$219$	−1487.44	−	1487.44i	−0.458959	−	0.458959i
$220$	−1057.86	−	619.587i	−0.324185	−	0.189875i
$221$	66.2980	−	66.2980i	0.0201796	−	0.0201796i
$222$	554.952	+	968.169i	0.167775	+	0.292699i
$223$	−2495.66			−0.749424			−0.374712	−	0.927141i	$-0.622258\pi$
$223$	−2495.66			−0.749424			−0.374712	+	0.927141i	$0.622258\pi$
$224$	−3822.51	−	2287.17i	−1.14019	−	0.682223i
$225$	−937.687			−0.277833
$226$	−2380.40	−	4152.85i	−0.700629	−	1.22232i
$227$	−1729.68	+	1729.68i	−0.505741	+	0.505741i	−0.913216	−	0.407475i	$-0.866409\pi$
$227$	−1729.68	+	1729.68i	−0.505741	+	0.505741i	0.407475	+	0.913216i	$0.366409\pi$
$228$	3194.92	+	1871.27i	0.928021	+	0.543543i
$229$	−1283.18	−	1283.18i	−0.370284	−	0.370284i	0.497296	−	0.867581i	$-0.334326\pi$
$229$	−1283.18	−	1283.18i	−0.370284	−	0.370284i	−0.867581	+	0.497296i	$0.834326\pi$
$230$	−455.360	−	123.538i	−0.130546	−	0.0354166i
$231$		−	2479.80i		−	0.706314i
$232$	1571.47	−	1542.32i	0.444707	−	0.436459i
$233$		−	6515.45i		−	1.83194i	−0.401252	−	0.915968i	$-0.631425\pi$
$233$		−	6515.45i		−	1.83194i	0.401252	−	0.915968i	$-0.368575\pi$
$234$	176.001	−	648.743i	0.0491691	−	0.181238i
$235$	−369.060	−	369.060i	−0.102446	−	0.102446i
$236$	5958.34	−	1556.75i	1.64345	−	0.429388i
$237$	−1653.51	+	1653.51i	−0.453193	+	0.453193i
$238$	−214.407	+	122.898i	−0.0583948	+	0.0334718i
$239$	761.174			0.206009			0.103005	−	0.994681i	$-0.467154\pi$
$239$	761.174			0.206009			0.103005	+	0.994681i	$0.467154\pi$
$240$	428.459	+	763.976i	0.115237	+	0.205477i
$241$	6225.86			1.66408			0.832040	−	0.554716i	$-0.187173\pi$
$241$	6225.86			1.66408			0.832040	+	0.554716i	$0.187173\pi$
$242$	−497.322	+	285.064i	−0.132104	+	0.0757214i
$243$	171.827	−	171.827i	0.0453609	−	0.0453609i
$244$	514.565	+	1969.46i	0.135007	+	0.516728i
$245$	−846.964	−	846.964i	−0.220859	−	0.220859i
$246$	856.680	−	3157.73i	0.222032	−	0.818412i
$247$		−	4073.81i		−	1.04944i
$248$	6944.36	+	65.0029i	1.77809	+	0.0166439i
$249$		−	1258.94i		−	0.320409i
$250$	−2854.15	−	774.321i	−0.722050	−	0.195889i
$251$	−275.380	−	275.380i	−0.0692502	−	0.0692502i	0.671633	−	0.740884i	$-0.265593\pi$
$251$	−275.380	−	275.380i	−0.0692502	−	0.0692502i	−0.740884	+	0.671633i	$0.765593\pi$
$252$	−895.445	+	1528.84i	−0.223840	+	0.382175i
$253$	868.505	−	868.505i	0.215820	−	0.215820i
$254$	−713.998	−	1245.64i	−0.176379	−	0.307710i
$255$	48.5951			0.0119339
$256$	−2135.89	+	3495.02i	−0.521459	+	0.853277i
$257$	1993.21			0.483786			0.241893	−	0.970303i	$-0.422232\pi$
$257$	1993.21			0.483786			0.241893	+	0.970303i	$0.422232\pi$
$258$	898.772	+	1568.00i	0.216880	+	0.378369i
$259$	−2288.42	+	2288.42i	−0.549018	+	0.549018i
$260$	487.069	−	831.600i	0.116180	−	0.198360i
$261$	−619.279	−	619.279i	−0.146867	−	0.146867i
$262$	−3276.35	−	888.862i	−0.772572	−	0.209596i
$263$		−	4385.21i		−	1.02815i	−0.857745	−	0.514075i	$-0.828135\pi$
$263$		−	4385.21i		−	1.02815i	0.857745	−	0.514075i	$-0.171865\pi$
$264$	−2280.11	−	21.3430i	−0.531557	−	0.00497566i
$265$			2913.81i			0.675450i
$266$	−2811.50	+	10363.2i	−0.648060	+	2.38875i
$267$	−1835.97	−	1835.97i	−0.420823	−	0.420823i
$268$	−809.747	−	3099.25i	−0.184564	−	0.706406i
$269$	−1683.14	+	1683.14i	−0.381498	+	0.381498i	−0.871642	−	0.490144i	$-0.836944\pi$
$269$	−1683.14	+	1683.14i	−0.381498	+	0.381498i	0.490144	+	0.871642i	$0.336944\pi$
$270$	302.261	−	173.255i	0.0681297	−	0.0390518i
$271$	2381.69			0.533866			0.266933	−	0.963715i	$-0.413990\pi$
$271$	2381.69			0.533866			0.266933	+	0.963715i	$0.413990\pi$
$272$	111.156	+	198.200i	0.0247788	+	0.0441825i
$273$	1949.41			0.432176
$274$	−1925.64	+	1103.77i	−0.424571	+	0.243363i
$275$	2474.68	−	2474.68i	0.542650	−	0.542650i
$276$	−849.065	+	221.837i	−0.185173	+	0.0483805i
$277$	5711.88	+	5711.88i	1.23897	+	1.23897i	0.960424	+	0.278543i	$0.0898516\pi$
$277$	5711.88	+	5711.88i	1.23897	+	1.23897i	0.278543	+	0.960424i	$0.410148\pi$
$278$	−1557.79	+	5742.04i	−0.336080	+	1.23879i
$279$		−	2762.22i		−	0.592724i
$280$	−1812.95	+	1779.33i	−0.386945	+	0.379768i
$281$			1996.19i			0.423781i	0.977293	+	0.211890i	$0.0679620\pi$
$281$			1996.19i			0.423781i	−0.977293	+	0.211890i	$0.932038\pi$
$282$	−936.900	−	254.177i	−0.197843	−	0.0536739i
$283$	−1457.11	−	1457.11i	−0.306065	−	0.306065i	0.537316	−	0.843381i	$-0.319438\pi$
$283$	−1457.11	−	1457.11i	−0.306065	−	0.306065i	−0.843381	+	0.537316i	$0.819438\pi$
$284$	6421.93	+	3761.33i	1.34180	+	0.785894i
$285$	1493.01	−	1493.01i	0.310311	−	0.310311i
$286$	1247.63	+	2176.61i	0.257950	+	0.450020i
$287$	9488.69			1.95157
$288$	1398.03	+	836.498i	0.286040	+	0.171150i
$289$	−4900.39			−0.997434
$290$	−624.427	−	1089.37i	−0.126440	−	0.220587i
$291$	1150.65	−	1150.65i	0.231794	−	0.231794i
$292$	−4840.37	−	2835.01i	−0.970073	−	0.568172i
$293$	−1542.07	−	1542.07i	−0.307470	−	0.307470i	0.536458	−	0.843927i	$-0.319762\pi$
$293$	−1542.07	−	1542.07i	−0.307470	−	0.307470i	−0.843927	+	0.536458i	$0.819762\pi$
$294$	−2150.11	−	583.318i	−0.426521	−	0.115714i
$295$		−	3511.86i		−	0.693114i
$296$	2084.45	+	2123.84i	0.409312	+	0.417047i
$297$			906.948i			0.177194i
$298$	−1509.02	+	5562.27i	−0.293340	+	1.08125i
$299$	682.748	+	682.748i	0.132055	+	0.132055i
$300$	−2419.29	+	632.092i	−0.465592	+	0.121646i
$301$	−3706.21	+	3706.21i	−0.709708	+	0.709708i
$302$	3474.94	−	1991.83i	0.662121	−	0.379526i
$303$	−4708.29			−0.892688
$304$	9504.50	+	2674.29i	1.79316	+	0.504544i
$305$	1160.81			0.217926
$306$	78.4162	−	44.9480i	0.0146495	−	0.00839708i
$307$	−3256.35	+	3256.35i	−0.605373	+	0.605373i	−0.941733	−	0.336360i	$-0.890804\pi$
$307$	−3256.35	+	3256.35i	−0.605373	+	0.605373i	0.336360	+	0.941733i	$0.390804\pi$
$308$	−1671.62	−	6398.02i	−0.309252	−	1.18364i
$309$	1711.84	+	1711.84i	0.315156	+	0.315156i
$310$	1036.92	−	3822.11i	0.189978	−	0.700262i
$311$		−	1839.43i		−	0.335384i	−0.985839	−	0.167692i	$-0.946369\pi$
$311$		−	1839.43i		−	0.335384i	0.985839	−	0.167692i	$-0.0536314\pi$
$312$	16.7782	−	1792.44i	0.00304447	−	0.325246i
$313$		−	3421.32i		−	0.617841i	−0.951088	−	0.308921i	$-0.900032\pi$
$313$		−	3421.32i		−	0.617841i	0.951088	−	0.308921i	$-0.0999678\pi$
$314$	−6563.82	−	1780.74i	−1.17968	−	0.320041i
$315$	714.442	+	714.442i	0.127791	+	0.127791i
$316$	−3151.52	+	5380.77i	−0.561035	+	0.957886i
$317$	729.653	−	729.653i	0.129279	−	0.129279i	−0.639507	−	0.768786i	$-0.720861\pi$
$317$	729.653	−	729.653i	0.129279	−	0.129279i	0.768786	+	0.639507i	$0.220861\pi$
$318$	2695.13	+	4701.92i	0.475268	+	0.829152i
$319$	3268.72			0.573708
$320$	1620.44	+	1682.28i	0.283080	+	0.293882i
$321$	−1467.22			−0.255117
$322$	−1265.62	−	2208.00i	−0.219038	−	0.382134i
$323$	387.336	−	387.336i	0.0667243	−	0.0667243i
$324$	327.496	−	559.152i	0.0561549	−	0.0958765i
$325$	1945.39	+	1945.39i	0.332034	+	0.332034i
$326$	4020.46	+	1090.74i	0.683046	+	0.185308i
$327$			1068.52i			0.180702i
$328$	81.6670	−	8724.61i	0.0137479	−	1.46871i
$329$		−	2815.30i		−	0.471771i
$330$	−340.463	+	1254.95i	−0.0567936	+	0.209342i
$331$	−2768.78	−	2768.78i	−0.459776	−	0.459776i	0.438806	−	0.898582i	$-0.355402\pi$
$331$	−2768.78	−	2768.78i	−0.459776	−	0.459776i	−0.898582	+	0.438806i	$0.855402\pi$
$332$	−848.646	−	3248.13i	−0.140288	−	0.536941i
$333$	836.956	−	836.956i	0.137732	−	0.137732i
$334$	7470.14	−	4281.87i	1.22380	−	0.701477i
$335$	−1826.71			−0.297921
$336$	−1279.71	+	4548.13i	−0.207780	+	0.738454i
$337$	−2334.75			−0.377394			−0.188697	−	0.982035i	$-0.560426\pi$
$337$	−2334.75			−0.377394			−0.188697	+	0.982035i	$0.560426\pi$
$338$	3680.12	−	2109.44i	0.592226	−	0.339462i
$339$	−3590.03	+	3590.03i	−0.575172	+	0.575172i
$340$	125.378	−	32.7579i	0.0199988	−	0.00522513i
$341$	7289.88	+	7289.88i	1.15768	+	1.15768i
$342$	1028.26	−	3790.18i	0.162579	−	0.599268i
$343$			1979.64i			0.311634i
$344$	3375.87	+	3439.66i	0.529112	+	0.539111i
$345$			500.441i			0.0780952i
$346$	5445.50	+	1477.34i	0.846103	+	0.229544i
$347$	1047.15	+	1047.15i	0.161999	+	0.161999i	0.783452	−	0.621453i	$-0.213457\pi$
$347$	1047.15	+	1047.15i	0.161999	+	0.161999i	−0.621453	+	0.783452i	$0.713457\pi$
$348$	−2015.23	−	1180.32i	−0.310424	−	0.181816i
$349$	692.953	−	692.953i	0.106284	−	0.106284i	−0.651965	−	0.758249i	$-0.726055\pi$
$349$	692.953	−	692.953i	0.106284	−	0.106284i	0.758249	+	0.651965i	$0.226055\pi$
$350$	−3606.21	−	6291.39i	−0.550743	−	0.960825i
$351$	−712.969			−0.108420
$352$	−5897.21	+	1481.95i	−0.892961	+	0.224398i
$353$	−11254.7			−1.69695			−0.848477	−	0.529233i	$-0.822480\pi$
$353$	−11254.7			−1.69695			−0.848477	+	0.529233i	$0.822480\pi$
$354$	−3248.29	−	5666.97i	−0.487697	−	0.850836i
$355$	3001.02	−	3001.02i	0.448670	−	0.448670i
$356$	−5974.54	−	3499.29i	−0.889466	−	0.520961i
$357$	185.349	+	185.349i	0.0274782	+	0.0274782i
$358$	−8339.84	−	2262.57i	−1.23121	−	0.334023i
$359$			3855.05i			0.566746i	0.959010	+	0.283373i	$0.0914534\pi$
$359$			3855.05i			0.566746i	−0.959010	+	0.283373i	$0.908547\pi$
$360$	663.060	−	650.762i	0.0970732	−	0.0952727i
$361$		−	16941.6i		−	2.46999i
$362$	−224.450	+	827.324i	−0.0325879	+	0.120119i
$363$	429.921	+	429.921i	0.0621625	+	0.0621625i
$364$	5029.60	−	1314.09i	0.724239	−	0.189223i
$365$	−2261.95	+	2261.95i	−0.324372	+	0.324372i
$366$	1873.15	−	1073.69i	0.267517	−	0.153340i
$367$	−1173.47			−0.166907			−0.0834534	−	0.996512i	$-0.526595\pi$
$367$	−1173.47			−0.166907			−0.0834534	+	0.996512i	$0.526595\pi$
$368$	−2041.10	+	1144.70i	−0.289129	+	0.162152i
$369$	−3470.35			−0.489591
$370$	1472.29	−	843.913i	0.206867	−	0.118576i
$371$	−11113.7	+	11113.7i	−1.55525	+	1.55525i
$372$	−1862.01	−	7126.70i	−0.259518	−	0.993286i
$373$	1645.82	+	1645.82i	0.228464	+	0.228464i	0.812051	−	0.583587i	$-0.198351\pi$
$373$	1645.82	+	1645.82i	0.228464	+	0.228464i	−0.583587	+	0.812051i	$0.698351\pi$
$374$	−88.3271	+	325.575i	−0.0122120	+	0.0450135i
$375$			3136.72i			0.431945i
$376$	−2588.60	−	24.2306i	−0.355045	−	0.00332340i
$377$			2569.60i			0.351037i
$378$	1813.69	+	492.047i	0.246789	+	0.0669529i
$379$	1829.15	+	1829.15i	0.247908	+	0.247908i	0.820111	−	0.572204i	$-0.193911\pi$
$379$	1829.15	+	1829.15i	0.247908	+	0.247908i	−0.572204	+	0.820111i	$0.693911\pi$
$380$	2845.63	−	4858.50i	0.384152	−	0.655884i
$381$	−1076.82	+	1076.82i	−0.144796	+	0.144796i
$382$	4595.47	+	8017.26i	0.615510	+	1.07382i
$383$	3425.39			0.456995			0.228498	−	0.973544i	$-0.426619\pi$
$383$	3425.39			0.456995			0.228498	+	0.973544i	$0.426619\pi$
$384$	4170.87	+	1215.81i	0.554281	+	0.161573i
$385$	−3771.01			−0.499191
$386$	977.307	+	1705.01i	0.128870	+	0.224826i
$387$	1355.49	−	1355.49i	0.178045	−	0.178045i
$388$	2193.09	−	3744.38i	0.286952	−	0.489929i
$389$	−6327.26	−	6327.26i	−0.824691	−	0.824691i	0.162086	−	0.986777i	$-0.448178\pi$
$389$	−6327.26	−	6327.26i	−0.824691	−	0.824691i	−0.986777	+	0.162086i	$0.948178\pi$
$390$	−986.540	−	267.644i	−0.128091	−	0.0347505i
$391$			129.831i			0.0167924i
$392$	−5940.63	−	55.6075i	−0.765427	−	0.00716480i
$393$			3600.72i			0.462168i
$394$	−625.731	+	2306.45i	−0.0800098	+	0.294917i
$395$	2514.48	+	2514.48i	0.320297	+	0.320297i
$396$	611.371	+	2339.98i	0.0775822	+	0.296940i
$397$	−536.835	+	536.835i	−0.0678664	+	0.0678664i	−0.740225	−	0.672359i	$-0.765281\pi$
$397$	−536.835	+	536.835i	−0.0678664	+	0.0678664i	0.672359	+	0.740225i	$0.265281\pi$
$398$	8244.05	−	4725.47i	1.03828	−	0.595141i
$399$	11389.2			1.42900
$400$	−5815.81	+	3261.67i	−0.726976	+	0.407709i
$401$	8145.45			1.01437			0.507187	−	0.861836i	$-0.330685\pi$
$401$	8145.45			1.01437			0.507187	+	0.861836i	$0.330685\pi$
$402$	−2947.69	+	1689.61i	−0.365715	+	0.209627i
$403$	−5730.71	+	5730.71i	−0.708354	+	0.708354i
$404$	−12147.7	+	3173.85i	−1.49596	+	0.390853i
$405$	−261.296	−	261.296i	−0.0320591	−	0.0320591i
$406$	1773.38	−	6536.69i	0.216777	−	0.799041i
$407$			4417.67i			0.538025i
$408$	172.019	−	168.829i	0.0208731	−	0.0204859i
$409$			1931.84i			0.233554i	0.993158	+	0.116777i	$0.0372562\pi$
$409$			1931.84i			0.233554i	−0.993158	+	0.116777i	$0.962744\pi$
$410$	−4801.94	−	1302.75i	−0.578417	−	0.156922i
$411$	1664.67	+	1664.67i	0.199786	+	0.199786i
$412$	5570.59	+	3262.70i	0.666124	+	0.390149i
$413$	13394.8	−	13394.8i	1.59592	−	1.59592i
$414$	462.882	+	807.544i	0.0549503	+	0.0958663i
$415$	−1914.46			−0.226451
$416$	−1164.99	−	4635.90i	−0.137304	−	0.546380i
$417$	6310.50			0.741071
$418$	7289.08	+	12716.5i	0.852920	+	1.48800i
$419$	−3381.69	+	3381.69i	−0.394287	+	0.394287i	−0.876212	−	0.481925i	$-0.839938\pi$
$419$	−3381.69	+	3381.69i	−0.394287	+	0.394287i	0.481925	+	0.876212i	$0.339938\pi$
$420$	2324.90	+	1361.70i	0.270104	+	0.158200i
$421$	−2730.44	−	2730.44i	−0.316089	−	0.316089i	0.531174	−	0.847263i	$-0.321751\pi$
$421$	−2730.44	−	2730.44i	−0.316089	−	0.316089i	−0.847263	+	0.531174i	$0.821751\pi$
$422$	−5172.54	−	1403.29i	−0.596671	−	0.161875i
$423$			1029.65i			0.118353i
$424$	10123.1	+	10314.4i	1.15949	+	1.18140i
$425$			369.933i			0.0422221i
$426$	2066.85	−	7618.43i	0.235069	−	0.866465i
$427$	4427.49	+	4427.49i	0.501782	+	0.501782i
$428$	−3785.52	+	989.052i	−0.427524	+	0.111700i
$429$	1881.62	−	1881.62i	0.211761	−	0.211761i
$430$	2384.44	−	1366.76i	0.267414	−	0.153281i
$431$	−6404.91			−0.715809			−0.357905	−	0.933758i	$-0.616509\pi$
$431$	−6404.91			−0.715809			−0.357905	+	0.933758i	$0.616509\pi$
$432$	468.035	−	1663.41i	0.0521258	−	0.185256i
$433$	5169.70			0.573764			0.286882	−	0.957966i	$-0.407381\pi$
$433$	5169.70			0.573764			0.286882	+	0.957966i	$0.407381\pi$
$434$	18533.1	−	10623.1i	2.04981	−	1.17494i
$435$	−941.734	+	941.734i	−0.103799	+	0.103799i
$436$	720.289	+	2756.86i	0.0791184	+	0.302820i
$437$	3988.85	+	3988.85i	0.436642	+	0.436642i
$438$	−1557.84	+	5742.20i	−0.169946	+	0.626423i
$439$		−	463.177i		−	0.0503559i	−0.999683	−	0.0251780i	$-0.991985\pi$
$439$		−	463.177i		−	0.0503559i	0.999683	−	0.0251780i	$-0.00801524\pi$
$440$	−32.4562	+	3467.35i	−0.00351657	+	0.375681i
$441$			2362.98i			0.255153i
$442$	−255.940	−	69.4356i	−0.0275426	−	0.00747220i
$443$	−8274.66	−	8274.66i	−0.887452	−	0.887452i	0.106826	−	0.994278i	$-0.465931\pi$
$443$	−8274.66	−	8274.66i	−0.887452	−	0.887452i	−0.994278	+	0.106826i	$0.965931\pi$
$444$	1595.21	−	2723.58i	0.170507	−	0.291116i
$445$	−2791.95	+	2791.95i	−0.297418	+	0.297418i
$446$	3510.30	+	6124.07i	0.372685	+	0.650187i
$447$	6112.94			0.646828
$448$	−235.851	+	12597.1i	−0.0248726	+	1.32847i
$449$	−6245.19			−0.656412			−0.328206	−	0.944606i	$-0.606444\pi$
$449$	−6245.19			−0.656412			−0.328206	+	0.944606i	$0.606444\pi$
$450$	1318.92	+	2300.98i	0.138165	+	0.241043i
$451$	9158.70	−	9158.70i	0.956245	−	0.956245i
$452$	−6842.45	+	11682.5i	−0.712039	+	1.21571i
$453$	−3003.99	−	3003.99i	−0.311567	−	0.311567i
$454$	6677.37	+	1811.54i	0.690274	+	0.187269i
$455$		−	2964.46i		−	0.305442i
$456$	98.0239	−	10472.0i	0.0100666	−	1.07544i
$457$		−	17086.8i		−	1.74899i	−0.485037	−	0.874494i	$-0.661194\pi$
$457$		−	17086.8i		−	1.74899i	0.485037	−	0.874494i	$-0.338806\pi$
$458$	−1343.91	+	4953.67i	−0.137111	+	0.505393i
$459$	−67.7887	−	67.7887i	−0.00689347	−	0.00689347i
$460$	337.346	+	1291.17i	0.0341931	+	0.130872i
$461$	−9796.68	+	9796.68i	−0.989755	+	0.989755i	−0.999948	−	0.0101932i	$-0.996755\pi$
$461$	−9796.68	+	9796.68i	−0.989755	+	0.989755i	0.0101932	+	0.999948i	$0.496755\pi$
$462$	−6085.15	+	3487.99i	−0.612785	+	0.351247i
$463$	−10699.4			−1.07396			−0.536980	−	0.843595i	$-0.680435\pi$
$463$	−10699.4			−1.07396			−0.536980	+	0.843595i	$0.680435\pi$
$464$	−5995.06	−	1686.84i	−0.599814	−	0.168770i
$465$	−4200.50			−0.418911
$466$	−15988.2	+	9164.39i	−1.58935	+	0.911013i
$467$	11145.1	−	11145.1i	1.10435	−	1.10435i	0.110473	−	0.993879i	$-0.464764\pi$
$467$	11145.1	−	11145.1i	1.10435	−	1.10435i	0.993879	−	0.110473i	$-0.0352364\pi$
$468$	−1839.50	+	480.610i	−0.181690	+	0.0474706i
$469$	−6967.33	−	6967.33i	−0.685973	−	0.685973i
$470$	−386.526	+	1424.74i	−0.0379343	+	0.139826i
$471$			7213.64i			0.705705i
$472$	−12200.9	−	12431.4i	−1.18981	−	1.21230i
$473$			7154.63i			0.695498i
$474$	6383.29	+	1731.76i	0.618553	+	0.167811i
$475$	11365.7	+	11365.7i	1.09788	+	1.09788i
$476$	603.155	+	353.268i	0.0580789	+	0.0340169i
$477$	4064.68	−	4064.68i	0.390165	−	0.390165i
$478$	−1070.64	−	1867.84i	−0.102447	−	0.178730i
$479$	2322.90			0.221579			0.110789	−	0.993844i	$-0.464662\pi$
$479$	2322.90			0.221579			0.110789	+	0.993844i	$0.464662\pi$
$480$	1272.06	−	2125.97i	0.120961	−	0.202160i
$481$	−3472.82			−0.329203
$482$	−8757.08	−	15277.6i	−0.827539	−	1.44372i
$483$	−1908.76	+	1908.76i	−0.179817	+	0.179817i
$484$	1399.03	+	819.413i	0.131389	+	0.0769546i
$485$	−1749.78	−	1749.78i	−0.163822	−	0.163822i
$486$	−663.330	−	179.959i	−0.0619121	−	0.0167965i
$487$		−	6238.14i		−	0.580446i	−0.956959	−	0.290223i	$-0.906271\pi$
$487$		−	6238.14i		−	0.580446i	0.956959	−	0.290223i	$-0.0937295\pi$
$488$	4109.07	−	4032.86i	0.381166	−	0.374096i
$489$		−	4418.49i		−	0.408612i
$490$	−887.048	+	3269.67i	−0.0817811	+	0.301446i
$491$	−7481.69	−	7481.69i	−0.687666	−	0.687666i	0.274049	−	0.961716i	$-0.411637\pi$
$491$	−7481.69	−	7481.69i	−0.687666	−	0.687666i	−0.961716	+	0.274049i	$0.911637\pi$
$492$	−8953.69	+	2339.35i	−0.820455	+	0.214362i
$493$	−244.316	+	244.316i	−0.0223194	+	0.0223194i
$494$	−9996.69	+	5730.08i	−0.910470	+	0.521880i
$495$	1379.19			0.125232
$496$	−9608.18	−	17132.1i	−0.869798	−	1.55092i
$497$	22892.7			2.06615
$498$	−3089.29	+	1770.78i	−0.277981	+	0.159338i
$499$	14385.4	−	14385.4i	1.29054	−	1.29054i	0.356084	−	0.934454i	$-0.384112\pi$
$499$	14385.4	−	14385.4i	1.29054	−	1.29054i	0.934454	−	0.356084i	$-0.115888\pi$
$500$	2114.45	+	8092.91i	0.189122	+	0.723852i
$501$	−6457.73	−	6457.73i	−0.575868	−	0.575868i
$502$	−288.412	+	1063.09i	−0.0256424	+	0.0945180i
$503$		−	10411.3i		−	0.922892i	−0.887168	−	0.461446i	$-0.847331\pi$
$503$		−	10411.3i		−	0.922892i	0.887168	−	0.461446i	$-0.152669\pi$
$504$	5011.12	+	46.9067i	0.442883	+	0.00414562i
$505$			7159.87i			0.630911i
$506$	−3352.82	−	909.608i	−0.294568	−	0.0799150i
$507$	−3181.36	−	3181.36i	−0.278677	−	0.278677i
$508$	−2052.38	+	3504.14i	−0.179251	+	0.306046i
$509$	−2836.55	+	2836.55i	−0.247010	+	0.247010i	−0.819742	−	0.572733i	$-0.805883\pi$
$509$	−2836.55	+	2836.55i	−0.247010	+	0.247010i	0.572733	+	0.819742i	$0.305883\pi$
$510$	−68.3522	−	119.247i	−0.00593468	−	0.0103536i
$511$	−17254.8			−1.49375
$512$	11580.7	+	325.280i	0.999606	+	0.0280771i
$513$	−4165.41			−0.358494
$514$	−2803.58	−	4891.11i	−0.240584	−	0.419723i
$515$	2603.18	−	2603.18i	0.222738	−	0.222738i
$516$	2583.51	−	4410.98i	0.220412	−	0.376322i
$517$	−2717.39	−	2717.39i	−0.231162	−	0.231162i
$518$	8834.35	+	2396.72i	0.749342	+	0.203293i
$519$		−	5984.60i		−	0.506156i
$520$	−2725.75	−	25.5145i	−0.229869	−	0.00215170i
$521$			9858.27i			0.828980i	0.910054	+	0.414490i	$0.136040\pi$
$521$			9858.27i			0.828980i	−0.910054	+	0.414490i	$0.863960\pi$
$522$	−648.587	+	2390.70i	−0.0543829	+	0.200456i
$523$	−174.291	−	174.291i	−0.0145721	−	0.0145721i	0.699783	−	0.714355i	$-0.253280\pi$
$523$	−174.291	−	174.291i	−0.0145721	−	0.0145721i	−0.714355	+	0.699783i	$0.753280\pi$
$524$	2427.23	+	9290.06i	0.202355	+	0.774500i
$525$	−5438.73	+	5438.73i	−0.452125	+	0.452125i
$526$	−10760.8	+	6168.08i	−0.892004	+	0.511294i
$527$	−1089.74			−0.0900759
$528$	3154.75	+	5625.16i	0.260024	+	0.463643i
$529$	10830.0			0.890111
$530$	7150.18	−	4098.47i	0.586008	−	0.335898i
$531$	−4898.94	+	4898.94i	−0.400369	+	0.400369i
$532$	29384.7	−	7677.40i	2.39472	−	0.625672i
$533$	7199.83	+	7199.83i	0.585101	+	0.585101i
$534$	−1922.86	+	7087.68i	−0.155825	+	0.574371i
$535$			2231.20i			0.180305i
$536$	−6466.25	+	6346.32i	−0.521081	+	0.511417i
$537$			9165.49i			0.736536i
$538$	6497.69	+	1762.80i	0.520698	+	0.141263i
$539$	−6236.21	−	6236.21i	−0.498353	−	0.498353i
$540$	−850.299	−	498.021i	−0.0677612	−	0.0396878i
$541$	4401.08	−	4401.08i	0.349755	−	0.349755i	−0.510263	−	0.860018i	$-0.670452\pi$
$541$	4401.08	−	4401.08i	0.349755	−	0.349755i	0.860018	+	0.510263i	$0.170452\pi$
$542$	−3350.01	−	5844.42i	−0.265489	−	0.463172i
$543$	909.229			0.0718577
$544$	330.013	−	551.546i	0.0260095	−	0.0434693i
$545$	1624.90			0.127712
$546$	−2741.98	−	4783.65i	−0.214919	−	0.374947i
$547$	−873.908	+	873.908i	−0.0683101	+	0.0683101i	−0.740436	−	0.672126i	$-0.765381\pi$
$547$	−873.908	+	873.908i	−0.0683101	+	0.0683101i	0.672126	+	0.740436i	$0.265381\pi$
$548$	5417.08	+	3172.79i	0.422274	+	0.247326i
$549$	−1619.29	−	1619.29i	−0.125882	−	0.125882i
$550$	−9553.39	−	2591.80i	−0.740650	−	0.200936i
$551$			15012.5i			1.16071i
$552$	1738.63	+	1771.48i	0.134060	+	0.136593i
$553$			19181.2i			1.47499i
$554$	5982.21	−	22050.5i	0.458772	−	1.69104i
$555$	−1272.75	−	1272.75i	−0.0973431	−	0.0973431i
$556$	16281.5	−	4253.89i	1.24188	−	0.324470i
$557$	11487.1	−	11487.1i	0.873830	−	0.873830i	−0.119057	−	0.992887i	$-0.537987\pi$
$557$	11487.1	−	11487.1i	0.873830	−	0.873830i	0.992887	+	0.119057i	$0.0379872\pi$
$558$	−6778.19	+	3885.24i	−0.514236	+	0.294759i
$559$	−5624.39			−0.425557
$560$	6916.31	+	1946.05i	0.521906	+	0.146849i
$561$	357.807			0.0269280
$562$	4898.42	−	2807.76i	0.367664	−	0.210744i
$563$	−4674.36	+	4674.36i	−0.349912	+	0.349912i	−0.860077	−	0.510164i	$-0.829585\pi$
$563$	−4674.36	+	4674.36i	−0.349912	+	0.349912i	0.510164	+	0.860077i	$0.329585\pi$
$564$	694.087	+	2656.57i	0.0518197	+	0.198336i
$565$	5459.33	+	5459.33i	0.406506	+	0.406506i
$566$	−1526.07	+	5625.11i	−0.113331	+	0.417741i
$567$		−	1993.25i		−	0.147634i
$568$	197.032	−	21049.3i	0.0145551	−	1.55494i
$569$			21013.7i			1.54823i	0.633048	+	0.774113i	$0.281804\pi$
$569$			21013.7i			1.54823i	−0.633048	+	0.774113i	$0.718196\pi$
$570$	−5763.71	−	1563.67i	−0.423536	−	0.114904i
$571$	6974.02	+	6974.02i	0.511127	+	0.511127i	0.914872	−	0.403745i	$-0.132292\pi$
$571$	6974.02	+	6974.02i	0.511127	+	0.511127i	−0.403745	+	0.914872i	$0.632292\pi$
$572$	3586.29	−	6123.08i	0.262151	−	0.447586i
$573$	6930.70	−	6930.70i	0.505295	−	0.505295i
$574$	−13346.4	−	23284.2i	−0.970505	−	1.69314i
$575$	−3809.64			−0.276301
$576$	86.2591	−	4607.19i	0.00623980	−	0.333275i
$577$	−1772.18			−0.127863			−0.0639315	−	0.997954i	$-0.520364\pi$
$577$	−1772.18			−0.127863			−0.0639315	+	0.997954i	$0.520364\pi$
$578$	6892.72	+	12025.0i	0.496019	+	0.865355i
$579$	1473.93	−	1473.93i	0.105794	−	0.105794i
$580$	−1794.91	+	3064.55i	−0.128499	+	0.219394i
$581$	−7302.03	−	7302.03i	−0.521410	−	0.521410i
$582$	−4442.02	−	1205.10i	−0.316371	−	0.0858301i
$583$			21454.4i			1.52410i
$584$	−148.508	+	15865.4i	−0.0105228	+	1.12417i
$585$			1084.21i			0.0766265i
$586$	−1615.05	+	5953.09i	−0.113852	+	0.419658i
$587$	−707.518	−	707.518i	−0.0497485	−	0.0497485i	0.681795	−	0.731543i	$-0.261200\pi$
$587$	−707.518	−	707.518i	−0.0497485	−	0.0497485i	−0.731543	+	0.681795i	$0.761200\pi$
$588$	1592.88	+	6096.62i	0.111716	+	0.427586i
$589$	−33480.8	+	33480.8i	−2.34219	+	2.34219i
$590$	−8617.73	+	4939.66i	−0.601333	+	0.344682i
$591$	2534.79			0.176425
$592$	2279.76	−	8102.33i	0.158273	−	0.562506i
$593$	7025.73			0.486530			0.243265	−	0.969960i	$-0.421782\pi$
$593$	7025.73			0.486530			0.243265	+	0.969960i	$0.421782\pi$
$594$	2225.55	−	1275.68i	0.153730	−	0.0881175i
$595$	281.859	−	281.859i	0.0194204	−	0.0194204i
$596$	15771.7	−	4120.72i	1.08395	−	0.283207i
$597$	−7126.75	−	7126.75i	−0.488574	−	0.488574i
$598$	715.060	−	2635.72i	0.0488979	−	0.180238i
$599$		−	25562.9i		−	1.74369i	−0.489781	−	0.871846i	$-0.662923\pi$
$599$		−	25562.9i		−	1.74369i	0.489781	−	0.871846i	$-0.337077\pi$
$600$	4953.97	+	5047.59i	0.337075	+	0.343445i
$601$		−	6395.84i		−	0.434096i	−0.976161	−	0.217048i	$-0.930357\pi$
$601$		−	6395.84i		−	0.434096i	0.976161	−	0.217048i	$-0.0696428\pi$
$602$	14307.6	+	3881.61i	0.968665	+	0.262795i
$603$	2548.20	+	2548.20i	0.172091	+	0.172091i
$604$	−9775.46	−	5725.49i	−0.658539	−	0.385707i
$605$	653.778	−	653.778i	0.0439337	−	0.0439337i
$606$	6622.52	+	11553.6i	0.443930	+	0.774479i
$607$	9420.38			0.629920			0.314960	−	0.949105i	$-0.398009\pi$
$607$	9420.38			0.629920			0.314960	+	0.949105i	$0.398009\pi$
$608$	−6806.27	−	27084.6i	−0.453998	−	1.80662i
$609$	−7183.83			−0.478002
$610$	−1632.75	−	2848.49i	−0.108374	−	0.189069i
$611$	2136.19	−	2136.19i	0.141442	−	0.141442i
$612$	−220.595	−	129.203i	−0.0145703	−	0.00853383i
$613$	10149.0	+	10149.0i	0.668700	+	0.668700i	0.957415	−	0.288715i	$-0.0932281\pi$
$613$	10149.0	+	10149.0i	0.668700	+	0.668700i	−0.288715	+	0.957415i	$0.593228\pi$
$614$	12571.0	+	3410.46i	0.826260	+	0.224161i
$615$			5277.33i			0.346021i
$616$	−13348.8	+	13101.2i	−0.873114	+	0.856920i
$617$			9621.85i			0.627814i	0.949454	+	0.313907i	$0.101638\pi$
$617$			9621.85i			0.627814i	−0.949454	+	0.313907i	$0.898362\pi$
$618$	1792.85	−	6608.47i	0.116698	−	0.430148i
$619$	3235.21	+	3235.21i	0.210071	+	0.210071i	0.804298	−	0.594227i	$-0.202542\pi$
$619$	3235.21	+	3235.21i	0.210071	+	0.210071i	−0.594227	+	0.804298i	$0.702542\pi$
$620$	−10837.5	+	2831.55i	−0.702009	+	0.183415i
$621$	698.100	−	698.100i	0.0451107	−	0.0451107i
$622$	−4513.75	+	2587.27i	−0.290973	+	0.166785i
$623$	−21297.8			−1.36963
$624$	−4422.04	+	2480.01i	−0.283691	+	0.159102i
$625$	−8253.44			−0.528220
$626$	−8395.54	+	4812.30i	−0.536028	+	0.307250i
$627$	10993.1	−	10993.1i	0.700193	−	0.700193i
$628$	4862.70	+	18611.6i	0.308985	+	1.18262i
$629$	−330.193	−	330.193i	−0.0209311	−	0.0209311i
$630$	748.254	−	2758.07i	0.0473193	−	0.174419i
$631$			371.400i			0.0234314i	0.999931	+	0.0117157i	$0.00372930\pi$
$631$			371.400i			0.0234314i	−0.999931	+	0.0117157i	$0.996271\pi$
$632$	17636.6	+	165.088i	1.11004	+	0.0103906i
$633$			5684.62i			0.356941i
$634$	−2816.79	−	764.185i	−0.176450	−	0.0478701i
$635$	1637.52	+	1637.52i	0.102335	+	0.102335i
$636$	7747.12	−	13227.1i	0.483008	−	0.824667i
$637$	4902.40	−	4902.40i	0.304930	−	0.304930i
$638$	−4597.66	−	8021.07i	−0.285303	−	0.497739i
$639$	−8372.66			−0.518337
$640$	1848.87	−	6342.62i	0.114192	−	0.391741i
$641$	−9470.43			−0.583556			−0.291778	−	0.956486i	$-0.594247\pi$
$641$	−9470.43			−0.583556			−0.291778	+	0.956486i	$0.594247\pi$
$642$	2063.74	+	3600.41i	0.126868	+	0.221334i
$643$	6234.89	−	6234.89i	0.382395	−	0.382395i	−0.489569	−	0.871964i	$-0.662846\pi$
$643$	6234.89	−	6234.89i	0.382395	−	0.382395i	0.871964	+	0.489569i	$0.162846\pi$
$644$	−3638.02	+	6211.40i	−0.222606	+	0.380067i
$645$	−2061.29	−	2061.29i	−0.125834	−	0.125834i
$646$	−1495.29	−	405.667i	−0.0910704	−	0.0247071i
$647$			27954.8i			1.69863i	0.527884	+	0.849316i	$0.322986\pi$
$647$			27954.8i			1.69863i	−0.527884	+	0.849316i	$0.677014\pi$
$648$	−1832.74	−	17.1554i	−0.111106	−	0.00104001i
$649$		−	25857.9i		−	1.56396i
$650$	2037.46	−	7510.09i	0.122947	−	0.453185i
$651$	−16021.3	−	16021.3i	−0.964555	−	0.964555i
$652$	−2978.49	−	11400.0i	−0.178906	−	0.684750i
$653$	15041.2	−	15041.2i	0.901387	−	0.901387i	−0.0941690	−	0.995556i	$-0.530019\pi$
$653$	15041.2	−	15041.2i	0.901387	−	0.901387i	0.995556	+	0.0941690i	$0.0300194\pi$
$654$	2622.04	−	1502.95i	0.156774	−	0.0898623i
$655$	5475.59			0.326640
$656$	−21524.1	+	12071.3i	−1.28106	+	0.718454i
$657$	6310.69			0.374739
$658$	−6908.44	+	3959.90i	−0.409299	+	0.234609i
$659$	17971.9	−	17971.9i	1.06234	−	1.06234i	0.0644201	−	0.997923i	$-0.479480\pi$
$659$	17971.9	−	17971.9i	1.06234	−	1.06234i	0.997923	−	0.0644201i	$-0.0205198\pi$
$660$	3558.39	−	929.709i	0.209864	−	0.0548316i
$661$	18445.8	+	18445.8i	1.08541	+	1.08541i	0.995994	+	0.0894197i	$0.0285012\pi$
$661$	18445.8	+	18445.8i	1.08541	+	1.08541i	0.0894197	+	0.995994i	$0.471499\pi$
$662$	−2899.82	+	10688.8i	−0.170249	+	0.627538i
$663$			281.278i			0.0164765i
$664$	−6776.88	+	6651.19i	−0.396075	+	0.388729i
$665$		−	17319.4i		−	1.00995i
$666$	−3231.03	−	876.566i	−0.187988	−	0.0510003i
$667$	−2516.01	−	2516.01i	−0.146057	−	0.146057i
$668$	−21014.5	−	12308.2i	−1.21718	−	0.712901i
$669$	5294.09	−	5294.09i	0.305951	−	0.305951i
$670$	2569.38	+	4482.54i	0.148155	+	0.258471i
$671$	8547.02			0.491735
$672$	12960.6	−	3256.96i	0.743997	−	0.186964i
$673$	8934.70			0.511749			0.255875	−	0.966710i	$-0.417637\pi$
$673$	8934.70			0.511749			0.255875	+	0.966710i	$0.417637\pi$
$674$	3283.97	+	5729.22i	0.187676	+	0.327420i
$675$	1989.13	−	1989.13i	0.113425	−	0.113425i
$676$	−10352.7	−	6063.56i	−0.589022	−	0.344991i
$677$	−16188.7	−	16188.7i	−0.919030	−	0.919030i	0.0779287	−	0.996959i	$-0.475169\pi$
$677$	−16188.7	−	16188.7i	−0.919030	−	0.919030i	−0.996959	+	0.0779287i	$0.975169\pi$
$678$	13859.1	+	3759.93i	0.785039	+	0.212978i
$679$		−	13347.9i		−	0.754410i
$680$	−256.737	−	261.589i	−0.0144785	−	0.0147522i
$681$		−	7338.43i		−	0.412936i
$682$	7634.88	−	28142.2i	0.428672	−	1.58009i
$683$	−4013.46	−	4013.46i	−0.224848	−	0.224848i	0.585689	−	0.810536i	$-0.300824\pi$
$683$	−4013.46	−	4013.46i	−0.224848	−	0.224848i	−0.810536	+	0.585689i	$0.800824\pi$
$684$	−10747.0	+	2807.89i	−0.600764	+	0.156963i
$685$	2531.45	−	2531.45i	0.141200	−	0.141200i
$686$	4857.82	−	2784.49i	0.270368	−	0.154974i
$687$	5444.09			0.302336
$688$	3692.18	−	13122.1i	0.204598	−	0.727145i
$689$	−16865.7			−0.932560
$690$	1228.03	−	703.903i	0.0677539	−	0.0388364i
$691$	−5748.83	+	5748.83i	−0.316492	+	0.316492i	−0.847418	−	0.530926i	$-0.821844\pi$
$691$	−5748.83	+	5748.83i	−0.316492	+	0.316492i	0.530926	+	0.847418i	$0.321844\pi$
$692$	−4034.20	−	15440.6i	−0.221615	−	0.848215i
$693$	5260.44	+	5260.44i	0.288352	+	0.288352i
$694$	1096.70	−	4042.46i	0.0599860	−	0.221109i
$695$		−	9596.34i		−	0.523755i
$696$	−61.8295	+	6605.35i	−0.00336730	+	0.359734i
$697$			1369.11i			0.0744028i
$698$	−2675.12	−	725.748i	−0.145064	−	0.0393553i
$699$	13821.3	+	13821.3i	0.747885	+	0.747885i
$700$	−10366.0	+	17698.5i	−0.559712	+	0.955628i
$701$	−12548.7	+	12548.7i	−0.676119	+	0.676119i	−0.959120	−	0.283001i	$-0.908670\pi$
$701$	−12548.7	+	12548.7i	−0.676119	+	0.676119i	0.283001	+	0.959120i	$0.408670\pi$
$702$	1002.84	+	1749.55i	0.0539168	+	0.0940633i
$703$	−20289.4			−1.08852
$704$	11931.3	+	12386.6i	0.638749	+	0.663124i
$705$	1565.79			0.0836468
$706$	15830.4	+	27617.7i	0.843887	+	1.47225i
$707$	−27308.8	+	27308.8i	−1.45269	+	1.45269i
$708$	−9337.19	+	15941.9i	−0.495640	+	0.846234i
$709$	−18950.0	−	18950.0i	−1.00378	−	1.00378i	−0.999993	−	0.00379062i	$-0.998793\pi$
$709$	−18950.0	−	18950.0i	−1.00378	−	1.00378i	−0.00379062	−	0.999993i	$-0.501207\pi$
$710$	−11585.3	−	3143.05i	−0.612379	−	0.166136i
$711$		−	7015.24i		−	0.370031i
$712$	−183.306	+	19582.8i	−0.00964841	+	1.03076i
$713$		−	11222.4i		−	0.589455i
$714$	194.121	−	715.532i	0.0101748	−	0.0375044i
$715$	−2861.37	−	2861.37i	−0.149663	−	0.149663i
$716$	6178.43	+	23647.5i	0.322484	+	1.23429i
$717$	−1614.69	+	1614.69i	−0.0841029	+	0.0841029i
$718$	9459.87	−	5422.38i	0.491698	−	0.281840i
$719$	33244.6			1.72436			0.862180	−	0.506603i	$-0.169099\pi$
$719$	33244.6			1.72436			0.862180	+	0.506603i	$0.169099\pi$
$720$	−2529.54	−	711.738i	−0.130931	−	0.0368402i
$721$	19857.9			1.02572
$722$	−41572.9	+	23829.5i	−2.14291	+	1.22831i
$723$	−13207.1	+	13207.1i	−0.679358	+	0.679358i
$724$	2345.86	−	612.909i	0.120419	−	0.0314621i
$725$	−7169.00	−	7169.00i	−0.367242	−	0.367242i
$726$	450.267	−	1659.69i	0.0230179	−	0.0848442i
$727$			25543.7i			1.30312i	0.758599	+	0.651558i	$0.225884\pi$
$727$			25543.7i			1.30312i	−0.758599	+	0.651558i	$0.774116\pi$
$728$	−10299.1	−	10493.7i	−0.524327	−	0.534236i
$729$			729.000i			0.0370370i
$730$	8732.14	+	2369.00i	0.442727	+	0.120110i
$731$	−534.764	−	534.764i	−0.0270574	−	0.0270574i
$732$	−5269.41	−	3086.30i	−0.266070	−	0.155837i
$733$	17290.1	−	17290.1i	0.871246	−	0.871246i	−0.121363	−	0.992608i	$-0.538726\pi$
$733$	17290.1	−	17290.1i	0.871246	−	0.871246i	0.992608	+	0.121363i	$0.0387264\pi$
$734$	1650.57	+	2879.58i	0.0830020	+	0.144805i
$735$	3593.37			0.180331
$736$	5679.91	+	3398.53i	0.284462	+	0.170206i
$737$	−13450.1			−0.672238
$738$	4881.26	+	8515.85i	0.243471	+	0.424760i
$739$	−2931.71	+	2931.71i	−0.145933	+	0.145933i	−0.776299	−	0.630365i	$-0.782905\pi$
$739$	−2931.71	+	2931.71i	−0.145933	+	0.145933i	0.630365	+	0.776299i	$0.282905\pi$
$740$	−4141.74	−	2425.82i	−0.205748	−	0.120507i
$741$	8641.86	+	8641.86i	0.428430	+	0.428430i
$742$	42904.0	+	11639.7i	2.12272	+	0.575885i
$743$		−	23349.2i		−	1.15289i	−0.817135	−	0.576446i	$-0.804439\pi$
$743$		−	23349.2i		−	1.15289i	0.817135	−	0.576446i	$-0.195561\pi$
$744$	−14869.1	+	14593.3i	−0.732699	+	0.719109i
$745$		−	9295.91i		−	0.457149i
$746$	1723.71	−	6353.60i	0.0845970	−	0.311825i
$747$	2670.61	+	2670.61i	0.130806	+	0.130806i
$748$	923.162	−	241.196i	0.0451259	−	0.0117901i
$749$	−8510.13	+	8510.13i	−0.415158	+	0.415158i
$750$	7697.16	−	4411.99i	0.374747	−	0.214804i
$751$	18998.3			0.923115			0.461557	−	0.887110i	$-0.347291\pi$
$751$	18998.3			0.923115			0.461557	+	0.887110i	$0.347291\pi$
$752$	3581.57	+	6386.22i	0.173679	+	0.309683i
$753$	1168.34			0.0565426
$754$	6305.51	−	3614.31i	0.304553	−	0.174569i
$755$	−4568.15	+	4568.15i	−0.220201	+	0.220201i
$756$	−1343.64	−	5142.69i	−0.0646399	−	0.247405i
$757$	−2302.76	−	2302.76i	−0.110562	−	0.110562i	0.649662	−	0.760224i	$-0.274911\pi$
$757$	−2302.76	−	2302.76i	−0.110562	−	0.110562i	−0.760224	+	0.649662i	$0.774911\pi$
$758$	1915.71	−	7061.34i	0.0917966	−	0.338363i
$759$			3684.75i			0.176216i
$760$	−15924.8	−	149.064i	−0.760069	−	0.00711465i
$761$		−	23935.6i		−	1.14016i	−0.821588	−	0.570082i	$-0.806912\pi$
$761$		−	23935.6i		−	1.14016i	0.821588	−	0.570082i	$-0.193088\pi$
$762$	4157.02	+	1127.78i	0.197629	+	0.0536158i
$763$	6197.61	+	6197.61i	0.294061	+	0.294061i
$764$	13209.6	−	22553.6i	0.625534	−	1.06801i
$765$	−103.086	+	103.086i	−0.00487200	+	0.00487200i
$766$	−4818.03	−	8405.52i	−0.227262	−	0.396480i
$767$	20327.4			0.956948
$768$	−2883.14	−	11945.0i	−0.135464	−	0.561233i
$769$	−10382.5			−0.486867			−0.243434	−	0.969918i	$-0.578274\pi$
$769$	−10382.5			−0.486867			−0.243434	+	0.969918i	$0.578274\pi$
$770$	5304.17	+	9253.65i	0.248246	+	0.433089i
$771$	−4228.23	+	4228.23i	−0.197505	+	0.197505i
$772$	2809.26	−	4796.41i	0.130968	−	0.223610i
$773$	12250.4	+	12250.4i	0.570009	+	0.570009i	0.932131	−	0.362122i	$-0.117948\pi$
$773$	12250.4	+	12250.4i	0.570009	+	0.570009i	−0.362122	+	0.932131i	$0.617948\pi$
$774$	−5232.81	−	1419.64i	−0.243009	−	0.0659275i
$775$		−	31976.5i		−	1.48211i
$776$	−12273.0	−	114.882i	−0.567753	−	0.00531446i
$777$		−	9708.95i		−	0.448271i
$778$	−6626.70	+	24426.1i	−0.305371	+	1.12560i
$779$	42063.9	+	42063.9i	1.93465	+	1.93465i
$780$	730.862	+	2797.32i	0.0335501	+	0.128410i
$781$	22096.6	−	22096.6i	1.01239	−	1.01239i
$782$	318.590	−	182.615i	0.0145687	−	0.00835077i
$783$	2627.38			0.119917
$784$	8219.43	+	14655.9i	0.374427	+	0.667633i
$785$	10969.7			0.498761
$786$	8835.76	−	5064.64i	0.400968	−	0.229834i
$787$	−16691.8	+	16691.8i	−0.756033	+	0.756033i	−0.975598	−	0.219565i	$-0.929536\pi$
$787$	−16691.8	+	16691.8i	−0.756033	+	0.756033i	0.219565	+	0.975598i	$0.429536\pi$
$788$	6539.90	−	1708.69i	0.295653	−	0.0772458i
$789$	9302.43	+	9302.43i	0.419741	+	0.419741i
$790$	2633.48	−	9707.03i	0.118601	−	0.437165i
$791$			41645.4i			1.87199i
$792$	4882.12	−	4791.57i	0.219039	−	0.214976i
$793$			6718.97i			0.300880i
$794$	2072.43	+	562.241i	0.0926293	+	0.0251300i
$795$	−6181.13	−	6181.13i	−0.275751	−	0.275751i
$796$	−23191.6	−	13583.3i	−1.03267	−	0.604834i
$797$	−6753.90	+	6753.90i	−0.300170	+	0.300170i	−0.841080	−	0.540910i	$-0.818080\pi$
$797$	−6753.90	+	6753.90i	−0.300170	+	0.300170i	0.540910	+	0.841080i	$0.318080\pi$
$798$	−16019.6	−	27947.7i	−0.710635	−	1.23977i
$799$	406.216			0.0179861
$800$	16184.1	+	9683.61i	0.715242	+	0.427959i
$801$	7789.37			0.343600
$802$	−11457.1	−	19988.0i	−0.504444	−	0.880053i
$803$	−16654.7	+	16654.7i	−0.731921	+	0.731921i
$804$	8292.23	+	4856.76i	0.363737	+	0.213041i
$805$	2902.64	+	2902.64i	0.127086	+	0.127086i
$806$	22123.1	+	6001.92i	0.966816	+	0.262294i
$807$		−	7140.97i		−	0.311492i
$808$	24874.8	+	25344.8i	1.08303	+	1.10350i
$809$		−	13717.0i		−	0.596125i	−0.954546	−	0.298063i	$-0.903660\pi$
$809$		−	13717.0i		−	0.596125i	0.954546	−	0.298063i	$-0.0963404\pi$
$810$	−273.662	+	1008.72i	−0.0118710	+	0.0437567i
$811$	−4025.22	−	4025.22i	−0.174284	−	0.174284i	0.614574	−	0.788859i	$-0.289328\pi$
$811$	−4025.22	−	4025.22i	−0.174284	−	0.174284i	−0.788859	+	0.614574i	$0.789328\pi$
$812$	−18534.7	+	4842.60i	−0.801035	+	0.209288i
$813$	−5052.34	+	5052.34i	−0.217950	+	0.217950i
$814$	10840.5	−	6213.74i	0.466780	−	0.267557i
$815$	−6719.18			−0.288788
$816$	−656.243	−	184.648i	−0.0281533	−	0.00792153i
$817$	−32859.7			−1.40712
$818$	4740.53	−	2717.26i	0.202627	−	0.116145i
$819$	−4135.33	+	4135.33i	−0.176435	+	0.176435i
$820$	3557.44	+	13615.8i	0.151501	+	0.579860i
$821$	1800.87	+	1800.87i	0.0765539	+	0.0765539i	0.744347	−	0.667793i	$-0.232761\pi$
$821$	1800.87	+	1800.87i	0.0765539	+	0.0765539i	−0.667793	+	0.744347i	$0.732761\pi$
$822$	1743.45	−	6426.37i	0.0739778	−	0.272683i
$823$		−	35700.7i		−	1.51209i	−0.654522	−	0.756043i	$-0.727130\pi$
$823$		−	35700.7i		−	1.51209i	0.654522	−	0.756043i	$-0.272870\pi$
$824$	170.912	−	18258.8i	0.00722573	−	0.771936i
$825$			10499.2i			0.443072i
$826$	−51709.9	−	14028.7i	−2.17823	−	0.590946i
$827$	−20857.1	−	20857.1i	−0.876994	−	0.876994i	0.116229	−	0.993222i	$-0.462920\pi$
$827$	−20857.1	−	20857.1i	−0.876994	−	0.876994i	−0.993222	+	0.116229i	$0.962920\pi$
$828$	1330.55	−	2271.73i	0.0558452	−	0.0953477i
$829$	−9907.55	+	9907.55i	−0.415083	+	0.415083i	−0.883505	−	0.468422i	$-0.844823\pi$
$829$	−9907.55	+	9907.55i	−0.415083	+	0.415083i	0.468422	+	0.883505i	$0.344823\pi$
$830$	2692.81	+	4697.87i	0.112613	+	0.196464i
$831$	−24233.5			−1.01161
$832$	−9737.37	+	9379.45i	−0.405748	+	0.390834i
$833$	932.235			0.0387755
$834$	−8876.12	−	15485.3i	−0.368531	−	0.642939i
$835$	−9820.23	+	9820.23i	−0.406998	+	0.406998i
$836$	20952.4	−	35773.2i	0.866810	−	1.47995i
$837$	5859.56	+	5859.56i	0.241979	+	0.241979i
$838$	13054.9	+	3541.73i	0.538154	+	0.145999i
$839$			15663.0i			0.644513i	0.946652	+	0.322257i	$0.104441\pi$
$839$			15663.0i			0.644513i	−0.946652	+	0.322257i	$0.895559\pi$
$840$	71.3307	−	7620.38i	0.00292993	−	0.313010i
$841$			14919.7i			0.611740i
$842$	−2859.66	+	10540.7i	−0.117043	+	0.431422i
$843$	−4234.55	−	4234.55i	−0.173008	−	0.173008i
$844$	3831.99	+	14666.7i	0.156283	+	0.598160i
$845$	−4837.88	+	4837.88i	−0.196957	+	0.196957i
$846$	2526.66	−	1448.27i	0.102681	−	0.0588566i
$847$	4987.22			0.202317
$848$	11071.7	−	39349.0i	0.448352	−	1.59346i
$849$	6182.00			0.249901
$850$	907.776	−	520.335i	0.0366311	−	0.0209969i
$851$	3400.39	−	3400.39i	0.136973	−	0.136973i
$852$	−21602.0	+	5643.99i	−0.868628	+	0.226948i
$853$	4808.17	+	4808.17i	0.192999	+	0.192999i	0.796991	−	0.603991i	$-0.206424\pi$
$853$	4808.17	+	4808.17i	0.192999	+	0.192999i	−0.603991	+	0.796991i	$0.706424\pi$
$854$	4637.02	−	17092.1i	0.185803	−	0.684871i
$855$			6334.32i			0.253368i
$856$	7751.61	+	7898.10i	0.309515	+	0.315364i
$857$		−	19827.2i		−	0.790298i	−0.918617	−	0.395149i	$-0.870693\pi$
$857$		−	19827.2i		−	0.790298i	0.918617	−	0.395149i	$-0.129307\pi$
$858$	−7263.91	−	1970.67i	−0.289028	−	0.0784120i
$859$	−25818.2	−	25818.2i	−1.02550	−	1.02550i	−0.999666	−	0.0258367i	$-0.991775\pi$
$859$	−25818.2	−	25818.2i	−1.02550	−	1.02550i	−0.0258367	−	0.999666i	$-0.508225\pi$
$860$	−6707.75	−	3928.73i	−0.265968	−	0.155777i
$861$	−20128.5	+	20128.5i	−0.796724	+	0.796724i
$862$	9008.92	+	15717.0i	0.355969	+	0.621023i
$863$	−633.059			−0.0249706			−0.0124853	−	0.999922i	$-0.503974\pi$
$863$	−633.059			−0.0249706			−0.0124853	+	0.999922i	$0.503974\pi$
$864$	−4740.14	+	1191.18i	−0.186647	+	0.0469038i
$865$	−9100.75			−0.357728
$866$	−7271.52	−	12685.9i	−0.285330	−	0.497787i
$867$	10395.3	−	10395.3i	0.407201	−	0.407201i
$868$	−52135.9	−	30536.0i	−2.03872	−	1.19408i
$869$	18514.1	+	18514.1i	0.722726	+	0.722726i
$870$	3635.52	+	986.302i	0.141673	+	0.0384354i
$871$		−	10573.3i		−	0.411325i
$872$	5751.89	−	5645.21i	0.223376	−	0.219233i
$873$			4881.78i			0.189259i
$874$	4177.63	−	15398.8i	0.161682	−	0.595963i
$875$	18193.4	+	18193.4i	0.702915	+	0.702915i
$876$	16281.9	−	4254.02i	0.627986	−	0.164075i
$877$	−22480.1	+	22480.1i	−0.865563	+	0.865563i	−0.991977	−	0.126415i	$-0.959653\pi$
$877$	−22480.1	+	22480.1i	−0.865563	+	0.865563i	0.126415	+	0.991977i	$0.459653\pi$
$878$	−1136.59	+	651.489i	−0.0436878	+	0.0250418i
$879$	6542.45			0.251048
$880$	8554.15	−	4797.41i	0.327682	−	0.183773i
$881$	−37603.1			−1.43800			−0.719001	−	0.695009i	$-0.755400\pi$
$881$	−37603.1			−1.43800			−0.719001	+	0.695009i	$0.755400\pi$
$882$	5798.49	−	3323.68i	0.221366	−	0.126887i
$883$	−11054.8	+	11054.8i	−0.421316	+	0.421316i	−0.885657	−	0.464341i	$-0.846291\pi$
$883$	−11054.8	+	11054.8i	−0.421316	+	0.421316i	0.464341	+	0.885657i	$0.346291\pi$
$884$	189.609	+	725.715i	0.00721407	+	0.0276113i
$885$	7449.79	+	7449.79i	0.282963	+	0.282963i
$886$	−8666.27	+	31944.0i	−0.328611	+	1.21126i
$887$		−	20920.6i		−	0.791935i	−0.918264	−	0.395968i	$-0.870409\pi$
$887$		−	20920.6i		−	0.791935i	0.918264	−	0.395968i	$-0.129591\pi$
$888$	−8927.14	−	83.5627i	−0.337359	−	0.00315786i
$889$			12491.5i			0.471260i
$890$	10778.2	+	2924.08i	0.405940	+	0.110130i
$891$	−1923.93	−	1923.93i	−0.0723389	−	0.0723389i
$892$	10090.3	−	17227.8i	0.378755	−	0.646670i
$893$	12480.4	−	12480.4i	0.467682	−	0.467682i
$894$	−8598.24	−	15000.5i	−0.321665	−	0.561176i
$895$	13937.9			0.520551
$896$	31243.6	−	17139.8i	1.16493	−	0.639065i
$897$	−2896.65			−0.107822
$898$	8784.26	+	15325.0i	0.326431	+	0.569490i
$899$	21118.3	−	21118.3i	0.783467	−	0.783467i
$900$	3791.21	−	6472.95i	0.140415	−	0.239739i
$901$	−1603.58	−	1603.58i	−0.0592932	−	0.0592932i
$902$	−35356.7	−	9592.15i	−1.30516	−	0.354084i
$903$		−	15724.1i		−	0.579475i
$904$	38291.9	+	358.433i	1.40882	+	0.0131873i
$905$		−	1382.66i		−	0.0507858i
$906$	−3146.16	+	11596.8i	−0.115369	+	0.425250i
$907$	−32396.8	−	32396.8i	−1.18602	−	1.18602i	−0.978159	−	0.207859i	$-0.933351\pi$
$907$	−32396.8	−	32396.8i	−1.18602	−	1.18602i	−0.207859	−	0.978159i	$-0.566649\pi$
$908$	−4946.82	−	18933.6i	−0.180799	−	0.691997i
$909$	9987.80	−	9987.80i	0.364438	−	0.364438i
$910$	−7274.47	+	4169.71i	−0.264996	+	0.151895i
$911$	11273.7			0.410006			0.205003	−	0.978761i	$-0.434280\pi$
$911$	11273.7			0.410006			0.205003	+	0.978761i	$0.434280\pi$
$912$	−25835.1	+	14489.1i	−0.938034	+	0.526076i
$913$	−14096.2			−0.510970
$914$	−41929.1	+	24033.7i	−1.51739	+	0.869763i
$915$	−2462.44	+	2462.44i	−0.0889680	+	0.0889680i
$916$	14046.1	−	3669.84i	0.506654	−	0.132374i
$917$	20884.7	+	20884.7i	0.752098	+	0.752098i
$918$	−70.9969	+	261.695i	−0.00255255	+	0.00940874i
$919$			44241.7i			1.58803i	0.607898	+	0.794015i	$0.292013\pi$
$919$			44241.7i			1.58803i	−0.607898	+	0.794015i	$0.707987\pi$
$920$	2693.89	−	2643.92i	0.0965378	−	0.0947473i
$921$		−	13815.5i		−	0.494285i
$922$	37819.6	+	10260.3i	1.35089	+	0.366492i
$923$	17370.5	+	17370.5i	0.619456	+	0.619456i
$924$	17118.3	+	10026.2i	0.609471	+	0.356967i
$925$	9688.92	−	9688.92i	0.344400	−	0.344400i
$926$	15049.4	+	26255.2i	0.534076	+	0.931748i
$927$	−7262.71			−0.257323
$928$	4293.12	+	17083.9i	0.151863	+	0.604316i
$929$	7271.46			0.256802			0.128401	−	0.991722i	$-0.459016\pi$
$929$	7271.46			0.256802			0.128401	+	0.991722i	$0.459016\pi$
$930$	5908.27	+	10307.6i	0.208322	+	0.363439i
$931$	28641.5	−	28641.5i	1.00826	−	1.00826i
$932$	44976.8	+	26343.0i	1.58076	+	0.925850i
$933$	3902.02	+	3902.02i	0.136920	+	0.136920i
$934$	−43025.0	−	11672.5i	−1.50730	−	0.408926i
$935$		−	544.114i		−	0.0190315i
$936$	3766.74	+	3837.93i	0.131538	+	0.134024i
$937$			26357.3i			0.918948i	0.888191	+	0.459474i	$0.151962\pi$
$937$			26357.3i			0.918948i	−0.888191	+	0.459474i	$0.848038\pi$
$938$	−7297.07	+	26897.1i	−0.254006	+	0.936269i
$939$	7257.71	+	7257.71i	0.252233	+	0.252233i
$940$	4039.83	−	1055.49i	0.140175	−	0.0366239i
$941$	−19843.2	+	19843.2i	−0.687427	+	0.687427i	−0.961663	−	0.274235i	$-0.911575\pi$
$941$	−19843.2	+	19843.2i	−0.687427	+	0.687427i	0.274235	+	0.961663i	$0.411575\pi$
$942$	17701.5	−	10146.5i	0.612257	−	0.350944i
$943$	−14099.3			−0.486890
$944$	−13344.1	+	47425.2i	−0.460078	+	1.63513i
$945$	−3031.12			−0.104341
$946$	17556.7	−	10063.5i	0.603401	−	0.345868i
$947$	24241.9	−	24241.9i	0.831845	−	0.831845i	−0.155924	−	0.987769i	$-0.549836\pi$
$947$	24241.9	−	24241.9i	0.831845	−	0.831845i	0.987769	+	0.155924i	$0.0498355\pi$
$948$	−4728.95	−	18099.7i	−0.162014	−	0.620097i
$949$	−13092.6	−	13092.6i	−0.447844	−	0.447844i
$950$	11903.5	−	43876.6i	0.406529	−	1.49847i
$951$			3095.66i			0.105556i
$952$	18.5055	−	1976.97i	0.000630007	−	0.0673046i
$953$			42596.4i			1.44788i	0.689861	+	0.723942i	$0.257672\pi$
$953$			42596.4i			1.44788i	−0.689861	+	0.723942i	$0.742328\pi$
$954$	−15691.5	−	4257.04i	−0.532527	−	0.144473i
$955$	−10539.5	−	10539.5i	−0.357120	−	0.357120i
$956$	−3077.54	+	5254.46i	−0.104116	+	0.177763i
$957$	−6934.00	+	6934.00i	−0.234216	+	0.234216i
$958$	−3267.31	−	5700.15i	−0.110190	−	0.192237i
$959$	19310.7			0.650233
$960$	−7006.13	−	131.174i	−0.235544	−	0.00441001i
$961$	64405.1			2.16190
$962$	4884.74	+	8521.91i	0.163711	+	0.285611i
$963$	3112.45	−	3112.45i	0.104151	−	0.104151i
$964$	−25172.1	+	42977.8i	−0.841016	+	1.43592i
$965$	−2241.40	−	2241.40i	−0.0747703	−	0.0747703i
$966$	7368.67	+	1999.09i	0.245428	+	0.0665836i
$967$		−	38631.7i		−	1.28471i	−0.766409	−	0.642353i	$-0.777958\pi$
$967$		−	38631.7i		−	1.28471i	0.766409	−	0.642353i	$-0.222042\pi$
$968$	42.9238	−	4585.62i	0.00142523	−	0.152260i
$969$			1643.33i			0.0544802i
$970$	−1832.59	+	6754.95i	−0.0606608	+	0.223596i
$971$	−1713.62	−	1713.62i	−0.0566351	−	0.0566351i	0.678222	−	0.734857i	$-0.262751\pi$
$971$	−1713.62	−	1713.62i	−0.0566351	−	0.0566351i	−0.734857	+	0.678222i	$0.762751\pi$
$972$	491.417	+	1880.86i	0.0162163	+	0.0620666i
$973$	36601.9	−	36601.9i	1.20596	−	1.20596i
$974$	−15307.7	+	8774.35i	−0.503584	+	0.288653i
$975$	−8253.60			−0.271104
$976$	−15675.9	−	4410.73i	−0.514111	−	0.144656i
$977$	26738.5			0.875579			0.437789	−	0.899078i	$-0.355762\pi$
$977$	26738.5			0.875579			0.437789	+	0.899078i	$0.355762\pi$
$978$	−10842.5	+	6214.89i	−0.354504	+	0.203201i
$979$	−20557.2	+	20557.2i	−0.671103	+	0.671103i
$980$	9271.09	−	2422.28i	0.302198	−	0.0789560i
$981$	−2266.68	−	2266.68i	−0.0737713	−	0.0737713i
$982$	−7835.77	+	28882.7i	−0.254633	+	0.938580i
$983$		−	35262.6i		−	1.14415i	−0.820201	−	0.572076i	$-0.806138\pi$
$983$		−	35262.6i		−	1.14415i	0.820201	−	0.572076i	$-0.193862\pi$
$984$	18334.5	+	18680.9i	0.593985	+	0.605210i
$985$		−	3854.64i		−	0.124689i
$986$	943.171	+	255.879i	0.0304632	+	0.00826454i
$987$	5972.15	+	5972.15i	0.192600	+	0.192600i
$988$	28122.0	+	16471.1i	0.905546	+	0.530379i
$989$	5507.09	−	5507.09i	0.177063	−	0.177063i
$990$	−1939.92	−	3384.38i	−0.0622775	−	0.108649i
$991$	48515.7			1.55515			0.777574	−	0.628791i	$-0.216450\pi$
$991$	48515.7			1.55515			0.777574	+	0.628791i	$0.216450\pi$
$992$	−28525.9	+	47674.9i	−0.913001	+	1.52589i
$993$	11746.9			0.375406
$994$	−32200.0	−	56176.2i	−1.02749	−	1.79256i
$995$	−10837.6	+	10837.6i	−0.345302	+	0.345302i
$996$	8690.58	+	5090.08i	0.276477	+	0.161933i
$997$	11465.5	+	11465.5i	0.364208	+	0.364208i	0.865360	−	0.501151i	$-0.167090\pi$
$997$	11465.5	+	11465.5i	0.364208	+	0.364208i	−0.501151	+	0.865360i	$0.667090\pi$
$998$	−55534.1	−	15066.2i	−1.76142	−	0.477868i
$999$			3550.90i			0.112458i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.4.j.a.37.4	yes	24
3.2	odd	2		144.4.k.b.37.9		24
4.3	odd	2		192.4.j.a.49.11		24
8.3	odd	2		384.4.j.a.97.3		24
8.5	even	2		384.4.j.b.97.10		24
12.11	even	2		576.4.k.b.433.4		24
16.3	odd	4		192.4.j.a.145.11		24
16.5	even	4		384.4.j.b.289.10		24
16.11	odd	4		384.4.j.a.289.3		24
16.13	even	4	inner	48.4.j.a.13.4	✓	24
48.29	odd	4		144.4.k.b.109.9		24
48.35	even	4		576.4.k.b.145.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.j.a.13.4	✓	24	16.13	even	4	inner
48.4.j.a.37.4	yes	24	1.1	even	1	trivial
144.4.k.b.37.9		24	3.2	odd	2
144.4.k.b.109.9		24	48.29	odd	4
192.4.j.a.49.11		24	4.3	odd	2
192.4.j.a.145.11		24	16.3	odd	4
384.4.j.a.97.3		24	8.3	odd	2
384.4.j.a.289.3		24	16.11	odd	4
384.4.j.b.97.10		24	8.5	even	2
384.4.j.b.289.10		24	16.5	even	4
576.4.k.b.145.4		24	48.35	even	4
576.4.k.b.433.4		24	12.11	even	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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	48.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40656 - 2.45389i) q^{2} +(-2.12132 + 2.12132i) q^{3} +(-4.04315 + 6.90311i) q^{4} +(3.22588 + 3.22588i) q^{5} +(8.18926 + 2.22171i) q^{6} +24.6080i q^{7} +(22.6264 + 0.211795i) q^{8} -9.00000i q^{9} +O(q^{10})\)	\(q+(-1.40656 - 2.45389i) q^{2} +(-2.12132 + 2.12132i) q^{3} +(-4.04315 + 6.90311i) q^{4} +(3.22588 + 3.22588i) q^{5} +(8.18926 + 2.22171i) q^{6} +24.6080i q^{7} +(22.6264 + 0.211795i) q^{8} -9.00000i q^{9} +(3.37855 - 12.4534i) q^{10} +(23.7522 + 23.7522i) q^{11} +(-6.06688 - 23.2205i) q^{12} +(-18.6720 + 18.6720i) q^{13} +(60.3853 - 34.6127i) q^{14} -13.6863 q^{15} +(-31.3058 - 55.8207i) q^{16} -3.55065 q^{17} +(-22.0850 + 12.6591i) q^{18} +(-109.089 + 109.089i) q^{19} +(-35.3113 + 9.22587i) q^{20} +(-52.2014 - 52.2014i) q^{21} +(24.8763 - 91.6943i) q^{22} -36.5653i q^{23} +(-48.4472 + 47.5486i) q^{24} -104.187i q^{25} +(72.0826 + 19.5557i) q^{26} +(19.0919 + 19.0919i) q^{27} +(-169.872 - 99.4939i) q^{28} +(68.8087 - 68.8087i) q^{29} +(19.2506 + 33.5846i) q^{30} +306.914 q^{31} +(-92.9442 + 155.336i) q^{32} -100.772 q^{33} +(4.99422 + 8.71292i) q^{34} +(-79.3824 + 79.3824i) q^{35} +(62.1280 + 36.3884i) q^{36} +(92.9951 + 92.9951i) q^{37} +(421.132 + 114.251i) q^{38} -79.2188i q^{39} +(72.3069 + 73.6734i) q^{40} -385.594i q^{41} +(-54.6719 + 201.521i) q^{42} +(150.610 + 150.610i) q^{43} +(-259.998 + 67.9302i) q^{44} +(29.0329 - 29.0329i) q^{45} +(-89.7271 + 51.4314i) q^{46} -114.406 q^{47} +(184.823 + 52.0039i) q^{48} -262.553 q^{49} +(-255.664 + 146.546i) q^{50} +(7.53207 - 7.53207i) q^{51} +(-53.4012 - 204.389i) q^{52} +(451.631 + 451.631i) q^{53} +(19.9954 - 73.7033i) q^{54} +153.243i q^{55} +(-5.21185 + 556.791i) q^{56} -462.824i q^{57} +(-265.633 - 72.0652i) q^{58} +(-544.327 - 544.327i) q^{59} +(55.3356 - 94.4777i) q^{60} +(179.921 - 179.921i) q^{61} +(-431.694 - 753.133i) q^{62} +221.472 q^{63} +(511.910 + 9.58434i) q^{64} -120.468 q^{65} +(141.742 + 247.283i) q^{66} +(-283.133 + 283.133i) q^{67} +(14.3558 - 24.5105i) q^{68} +(77.5666 + 77.5666i) q^{69} +(306.452 + 83.1393i) q^{70} -930.296i q^{71} +(1.90616 - 203.638i) q^{72} +701.187i q^{73} +(97.3962 - 359.003i) q^{74} +(221.015 + 221.015i) q^{75} +(-311.988 - 1194.11i) q^{76} +(-584.494 + 584.494i) q^{77} +(-194.394 + 111.426i) q^{78} +779.471 q^{79} +(79.0820 - 281.060i) q^{80} -81.0000 q^{81} +(-946.205 + 542.363i) q^{82} +(-296.734 + 296.734i) q^{83} +(571.410 - 149.294i) q^{84} +(-11.4540 - 11.4540i) q^{85} +(157.738 - 581.423i) q^{86} +291.931i q^{87} +(532.397 + 542.458i) q^{88} +865.485i q^{89} +(-112.080 - 30.4069i) q^{90} +(-459.481 - 459.481i) q^{91} +(252.414 + 147.839i) q^{92} +(-651.062 + 651.062i) q^{93} +(160.919 + 280.740i) q^{94} -703.813 q^{95} +(-132.354 - 526.683i) q^{96} -542.420 q^{97} +(369.298 + 644.276i) q^{98} +(213.770 - 213.770i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{4} + 84 q^{8}+O(q^{10}) \) 24 * q - 20 * q^4 + 84 * q^8	\( 24 q - 20 q^{4} + 84 q^{8} + 72 q^{10} - 40 q^{11} - 24 q^{12} - 348 q^{14} + 120 q^{15} - 192 q^{16} - 36 q^{18} + 24 q^{19} + 80 q^{20} + 704 q^{22} + 228 q^{24} - 20 q^{26} - 344 q^{28} + 400 q^{29} - 408 q^{30} - 744 q^{31} - 960 q^{32} - 704 q^{34} - 456 q^{35} + 108 q^{36} + 16 q^{37} + 1256 q^{38} + 1744 q^{40} + 660 q^{42} + 1240 q^{43} - 200 q^{44} - 1432 q^{46} - 528 q^{48} - 1176 q^{49} + 708 q^{50} + 744 q^{51} + 1008 q^{52} + 752 q^{53} + 108 q^{54} + 1344 q^{56} + 1936 q^{58} - 1376 q^{59} - 1224 q^{60} - 912 q^{61} - 996 q^{62} - 504 q^{63} - 56 q^{64} + 976 q^{65} - 1368 q^{66} - 2256 q^{67} - 1568 q^{68} - 528 q^{69} - 1760 q^{70} - 612 q^{72} - 2740 q^{74} + 1104 q^{75} - 1880 q^{76} + 1904 q^{77} + 1692 q^{78} + 5992 q^{79} + 712 q^{80} - 1944 q^{81} - 40 q^{82} + 2680 q^{83} + 1800 q^{84} - 240 q^{85} - 1712 q^{86} - 3936 q^{88} + 648 q^{90} - 3496 q^{91} + 5296 q^{92} + 5272 q^{94} - 7728 q^{95} + 2880 q^{96} + 6760 q^{98} - 360 q^{99}+O(q^{100}) \) 24 * q - 20 * q^4 + 84 * q^8 + 72 * q^10 - 40 * q^11 - 24 * q^12 - 348 * q^14 + 120 * q^15 - 192 * q^16 - 36 * q^18 + 24 * q^19 + 80 * q^20 + 704 * q^22 + 228 * q^24 - 20 * q^26 - 344 * q^28 + 400 * q^29 - 408 * q^30 - 744 * q^31 - 960 * q^32 - 704 * q^34 - 456 * q^35 + 108 * q^36 + 16 * q^37 + 1256 * q^38 + 1744 * q^40 + 660 * q^42 + 1240 * q^43 - 200 * q^44 - 1432 * q^46 - 528 * q^48 - 1176 * q^49 + 708 * q^50 + 744 * q^51 + 1008 * q^52 + 752 * q^53 + 108 * q^54 + 1344 * q^56 + 1936 * q^58 - 1376 * q^59 - 1224 * q^60 - 912 * q^61 - 996 * q^62 - 504 * q^63 - 56 * q^64 + 976 * q^65 - 1368 * q^66 - 2256 * q^67 - 1568 * q^68 - 528 * q^69 - 1760 * q^70 - 612 * q^72 - 2740 * q^74 + 1104 * q^75 - 1880 * q^76 + 1904 * q^77 + 1692 * q^78 + 5992 * q^79 + 712 * q^80 - 1944 * q^81 - 40 * q^82 + 2680 * q^83 + 1800 * q^84 - 240 * q^85 - 1712 * q^86 - 3936 * q^88 + 648 * q^90 - 3496 * q^91 + 5296 * q^92 + 5272 * q^94 - 7728 * q^95 + 2880 * q^96 + 6760 * q^98 - 360 * q^99

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