LMFDB - Embedded newform 105.4.s.a.26.13

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			26.13
Character	$\chi$	$=$	105.26
Dual form			105.4.s.a.101.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.53626 + 2.04166i) q^{2} +(-2.57442 + 4.51357i) q^{3} +(4.33676 + 7.51148i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-18.3190 + 10.7051i) q^{6} +(0.627588 + 18.5096i) q^{7} +2.75017i q^{8} +(-13.7447 - 23.2397i) q^{9} +O(q^{10})$	\(q+(3.53626 + 2.04166i) q^{2} +(-2.57442 + 4.51357i) q^{3} +(4.33676 + 7.51148i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-18.3190 + 10.7051i) q^{6} +(0.627588 + 18.5096i) q^{7} +2.75017i q^{8} +(-13.7447 - 23.2397i) q^{9} +(-17.6813 + 10.2083i) q^{10} +(-7.33279 + 4.23359i) q^{11} +(-45.0683 + 0.236524i) q^{12} +5.50408i q^{13} +(-35.5711 + 66.7362i) q^{14} +(-13.1083 - 22.4315i) q^{15} +(29.0791 - 50.3665i) q^{16} +(60.2944 + 104.433i) q^{17} +(-1.15718 - 110.244i) q^{18} +(23.3904 + 13.5044i) q^{19} -43.3676 q^{20} +(-85.1602 - 44.8190i) q^{21} -34.5742 q^{22} +(-2.98204 - 1.72168i) q^{23} +(-12.4131 - 7.08012i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(-11.2375 + 19.4639i) q^{26} +(140.279 - 2.20876i) q^{27} +(-136.313 + 84.9859i) q^{28} +72.7598i q^{29} +(-0.556754 - 106.086i) q^{30} +(242.287 - 139.885i) q^{31} +(224.717 - 129.740i) q^{32} +(-0.230897 - 43.9961i) q^{33} +492.403i q^{34} +(-81.7180 - 43.5565i) q^{35} +(114.957 - 204.028i) q^{36} +(44.8944 - 77.7594i) q^{37} +(55.1429 + 95.5104i) q^{38} +(-24.8431 - 14.1698i) q^{39} +(-11.9086 - 6.87544i) q^{40} -221.251 q^{41} +(-209.644 - 332.360i) q^{42} +495.285 q^{43} +(-63.6010 - 36.7201i) q^{44} +(134.993 - 1.41695i) q^{45} +(-7.03018 - 12.1766i) q^{46} +(-100.415 + 173.923i) q^{47} +(152.471 + 260.916i) q^{48} +(-342.212 + 23.2328i) q^{49} -102.083i q^{50} +(-626.589 + 3.28842i) q^{51} +(-41.3438 + 23.8699i) q^{52} +(-63.3970 + 36.6023i) q^{53} +(500.572 + 278.591i) q^{54} -42.3359i q^{55} +(-50.9047 + 1.72598i) q^{56} +(-121.170 + 70.8080i) q^{57} +(-148.551 + 257.297i) q^{58} +(180.462 + 312.570i) q^{59} +(111.647 - 195.743i) q^{60} +(-586.446 - 338.585i) q^{61} +1142.39 q^{62} +(421.532 - 268.994i) q^{63} +594.275 q^{64} +(-23.8334 - 13.7602i) q^{65} +(89.0086 - 156.053i) q^{66} +(-385.932 - 668.453i) q^{67} +(-522.964 + 905.801i) q^{68} +(15.4480 - 9.02732i) q^{69} +(-200.048 - 320.868i) q^{70} -801.257i q^{71} +(63.9132 - 37.8003i) q^{72} +(881.784 - 509.098i) q^{73} +(317.517 - 183.318i) q^{74} +(129.902 - 0.681742i) q^{75} +234.262i q^{76} +(-82.9641 - 133.070i) q^{77} +(-58.9215 - 100.829i) q^{78} +(96.8783 - 167.798i) q^{79} +(145.396 + 251.833i) q^{80} +(-351.168 + 638.845i) q^{81} +(-782.400 - 451.719i) q^{82} -1419.66 q^{83} +(-32.6623 - 834.048i) q^{84} -602.944 q^{85} +(1751.46 + 1011.20i) q^{86} +(-328.407 - 187.315i) q^{87} +(-11.6431 - 20.1664i) q^{88} +(-310.733 + 538.205i) q^{89} +(480.262 + 270.598i) q^{90} +(-101.878 + 3.45429i) q^{91} -29.8661i q^{92} +(7.62922 + 1453.70i) q^{93} +(-710.186 + 410.026i) q^{94} +(-116.952 + 67.5222i) q^{95} +(7.07594 + 1348.28i) q^{96} +30.4414i q^{97} +(-1257.59 - 616.524i) q^{98} +(199.174 + 112.223i) 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 $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	3.53626	+	2.04166i	1.25026	+	0.721836i	0.971160	−	0.238427i	$-0.0766318\pi$
$2$	3.53626	+	2.04166i	1.25026	+	0.721836i	0.279096	+	0.960263i	$0.409965\pi$
$3$	−2.57442	+	4.51357i	−0.495448	+	0.868638i
$3$	−2.57442	+	4.51357i	−0.495448	+	0.868638i
$4$	4.33676	+	7.51148i	0.542095	+	0.938935i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$	−18.3190	+	10.7051i	−1.24645	+	0.728388i
$7$	0.627588	+	18.5096i	0.0338866	+	0.999426i
$7$	0.627588	+	18.5096i	0.0338866	+	0.999426i
$8$			2.75017i			0.121542i
$9$	−13.7447	−	23.2397i	−0.509062	−	0.860730i
$10$	−17.6813	+	10.2083i	−0.559132	+	0.322815i
$11$	−7.33279	+	4.23359i	−0.200993	+	0.116043i	−0.597118	−	0.802153i	$-0.703688\pi$
$11$	−7.33279	+	4.23359i	−0.200993	+	0.116043i	0.396126	+	0.918196i	$0.370354\pi$
$12$	−45.0683	+	0.236524i	−1.08417	+	0.00568988i
$13$			5.50408i			0.117427i	0.998275	+	0.0587137i	$0.0186999\pi$
$13$			5.50408i			0.117427i	−0.998275	+	0.0587137i	$0.981300\pi$
$14$	−35.5711	+	66.7362i	−0.679055	+	1.27400i
$15$	−13.1083	−	22.4315i	−0.225636	−	0.386120i
$16$	29.0791	−	50.3665i	0.454361	−	0.786977i
$17$	60.2944	+	104.433i	0.860208	+	1.48992i	0.871728	+	0.489990i	$0.163000\pi$
$17$	60.2944	+	104.433i	0.860208	+	1.48992i	−0.0115198	+	0.999934i	$0.503667\pi$
$18$	−1.15718	−	110.244i	−0.0151527	−	1.44359i
$19$	23.3904	+	13.5044i	0.282427	+	0.163059i	0.634522	−	0.772905i	$-0.281197\pi$
$19$	23.3904	+	13.5044i	0.282427	+	0.163059i	−0.352095	+	0.935964i	$0.614530\pi$
$20$	−43.3676			−0.484864
$21$	−85.1602	−	44.8190i	−0.884928	−	0.465728i
$22$	−34.5742			−0.335057
$23$	−2.98204	−	1.72168i	−0.0270347	−	0.0156085i	0.486422	−	0.873724i	$-0.338302\pi$
$23$	−2.98204	−	1.72168i	−0.0270347	−	0.0156085i	−0.513456	+	0.858116i	$0.671635\pi$
$24$	−12.4131	−	7.08012i	−0.105576	−	0.0602176i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	−11.2375	+	19.4639i	−0.0847634	+	0.146814i
$27$	140.279	−	2.20876i	0.999876	−	0.0157436i
$28$	−136.313	+	84.9859i	−0.920026	+	0.573601i
$29$			72.7598i			0.465902i	0.972489	+	0.232951i	$0.0748381\pi$
$29$			72.7598i			0.465902i	−0.972489	+	0.232951i	$0.925162\pi$
$30$	−0.556754	−	106.086i	−0.00338830	−	0.645621i
$31$	242.287	−	139.885i	1.40374	−	0.810452i	0.408970	−	0.912548i	$-0.365888\pi$
$31$	242.287	−	139.885i	1.40374	−	0.810452i	0.994775	+	0.102095i	$0.0325546\pi$
$32$	224.717	−	129.740i	1.24140	−	0.716720i
$33$	−0.230897	−	43.9961i	−0.00121800	−	0.232083i
$34$			492.403i			2.48372i
$35$	−81.7180	−	43.5565i	−0.394653	−	0.210354i
$36$	114.957	−	204.028i	0.532210	−	0.944574i
$37$	44.8944	−	77.7594i	0.199476	−	0.345502i	−0.748883	−	0.662702i	$-0.769409\pi$
$37$	44.8944	−	77.7594i	0.199476	−	0.345502i	0.948359	+	0.317200i	$0.102743\pi$
$38$	55.1429	+	95.5104i	0.235404	+	0.407732i
$39$	−24.8431	−	14.1698i	−0.102002	−	0.0581792i
$40$	−11.9086	−	6.87544i	−0.0470729	−	0.0271775i
$41$	−221.251			−0.842770			−0.421385	−	0.906882i	$-0.638456\pi$
$41$	−221.251			−0.842770			−0.421385	+	0.906882i	$0.638456\pi$
$42$	−209.644	−	332.360i	−0.770207	−	1.22105i
$43$	495.285			1.75652			0.878259	−	0.478185i	$-0.158705\pi$
$43$	495.285			1.75652			0.878259	+	0.478185i	$0.158705\pi$
$44$	−63.6010	−	36.7201i	−0.217914	−	0.125813i
$45$	134.993	−	1.41695i	0.447189	−	0.00469393i
$46$	−7.03018	−	12.1766i	−0.0225336	−	0.0390293i
$47$	−100.415	+	173.923i	−0.311638	+	0.539773i	−0.978717	−	0.205214i	$-0.934211\pi$
$47$	−100.415	+	173.923i	−0.311638	+	0.539773i	0.667079	+	0.744987i	$0.267544\pi$
$48$	152.471	+	260.916i	0.458485	+	0.784582i
$49$	−342.212	+	23.2328i	−0.997703	+	0.0677342i
$50$		−	102.083i		−	0.288734i
$51$	−626.589	+	3.28842i	−1.72039	+	0.00902883i
$52$	−41.3438	+	23.8699i	−0.110257	+	0.0636568i
$53$	−63.3970	+	36.6023i	−0.164307	+	0.0948625i	−0.579899	−	0.814689i	$-0.696908\pi$
$53$	−63.3970	+	36.6023i	−0.164307	+	0.0948625i	0.415592	+	0.909551i	$0.363574\pi$
$54$	500.572	+	278.591i	1.26147	+	0.702063i
$55$		−	42.3359i		−	0.103792i
$56$	−50.9047	+	1.72598i	−0.121472	+	0.00411863i
$57$	−121.170	+	70.8080i	−0.281568	+	0.164539i
$58$	−148.551	+	257.297i	−0.336305	+	0.582497i
$59$	180.462	+	312.570i	0.398207	+	0.689714i	0.993505	−	0.113791i	$-0.0362993\pi$
$59$	180.462	+	312.570i	0.398207	+	0.689714i	−0.595298	+	0.803505i	$0.702966\pi$
$60$	111.647	−	195.743i	0.240225	−	0.421171i
$61$	−586.446	−	338.585i	−1.23093	−	0.710678i	−0.263706	−	0.964603i	$-0.584945\pi$
$61$	−586.446	−	338.585i	−1.23093	−	0.710678i	−0.967224	+	0.253925i	$0.918278\pi$
$62$	1142.39			2.34006
$63$	421.532	−	268.994i	0.842985	−	0.537937i
$64$	594.275			1.16069
$65$	−23.8334	−	13.7602i	−0.0454795	−	0.0262576i
$66$	89.0086	−	156.053i	0.166003	−	0.291043i
$67$	−385.932	−	668.453i	−0.703717	−	1.21887i	−0.967152	−	0.254197i	$-0.918189\pi$
$67$	−385.932	−	668.453i	−0.703717	−	1.21887i	0.263435	−	0.964677i	$-0.415145\pi$
$68$	−522.964	+	905.801i	−0.932628	+	1.61536i
$69$	15.4480	−	9.02732i	0.0269524	−	0.0157502i
$70$	−200.048	−	320.868i	−0.341577	−	0.547872i
$71$		−	801.257i		−	1.33932i	−0.742668	−	0.669660i	$-0.766440\pi$
$71$		−	801.257i		−	1.33932i	0.742668	−	0.669660i	$-0.233560\pi$
$72$	63.9132	−	37.8003i	0.104615	−	0.0618723i
$73$	881.784	−	509.098i	1.41377	−	0.816239i	0.418027	−	0.908435i	$-0.362722\pi$
$73$	881.784	−	509.098i	1.41377	−	0.816239i	0.995741	+	0.0921954i	$0.0293884\pi$
$74$	317.517	−	183.318i	0.498791	−	0.287977i
$75$	129.902	−	0.681742i	0.199997	−	0.00104961i
$76$			234.262i			0.353575i
$77$	−82.9641	−	133.070i	−0.122787	−	0.196945i
$78$	−58.9215	−	100.829i	−0.0855327	−	0.146368i
$79$	96.8783	−	167.798i	0.137970	−	0.238972i	−0.788758	−	0.614704i	$-0.789275\pi$
$79$	96.8783	−	167.798i	0.137970	−	0.238972i	0.926728	+	0.375732i	$0.122609\pi$
$80$	145.396	+	251.833i	0.203197	+	0.351947i
$81$	−351.168	+	638.845i	−0.481711	+	0.876330i
$82$	−782.400	−	451.719i	−1.05368	−	0.608342i
$83$	−1419.66			−1.87745			−0.938724	−	0.344670i	$-0.887991\pi$
$83$	−1419.66			−1.87745			−0.938724	+	0.344670i	$0.887991\pi$
$84$	−32.6623	−	834.048i	−0.0424255	−	1.08336i
$85$	−602.944			−0.769393
$86$	1751.46	+	1011.20i	2.19610	+	1.26792i
$87$	−328.407	−	187.315i	−0.404700	−	0.230830i
$88$	−11.6431	−	20.1664i	−0.0141041	−	0.0244290i
$89$	−310.733	+	538.205i	−0.370085	+	0.641007i	−0.989578	−	0.143995i	$-0.954005\pi$
$89$	−310.733	+	538.205i	−0.370085	+	0.641007i	0.619493	+	0.785002i	$0.287338\pi$
$90$	480.262	+	270.598i	0.562489	+	0.316929i
$91$	−101.878	+	3.45429i	−0.117360	+	0.00397921i
$92$		−	29.8661i		−	0.0338451i
$93$	7.62922	+	1453.70i	0.00850659	+	1.62088i
$94$	−710.186	+	410.026i	−0.779256	+	0.449904i
$95$	−116.952	+	67.5222i	−0.126305	+	0.0729224i
$96$	7.07594	+	1348.28i	0.00752276	+	1.43342i
$97$			30.4414i			0.0318644i	0.999873	+	0.0159322i	$0.00507160\pi$
$97$			30.4414i			0.0318644i	−0.999873	+	0.0159322i	$0.994928\pi$
$98$	−1257.59	−	616.524i	−1.29628	−	0.635493i
$99$	199.174	+	112.223i	0.202200	+	0.113927i
$100$	108.419	−	187.787i	0.108419	−	0.187787i
$101$	485.210	+	840.409i	0.478022	+	0.827959i	0.999683	−	0.0251945i	$-0.00802050\pi$
$101$	485.210	+	840.409i	0.478022	+	0.827959i	−0.521660	+	0.853153i	$0.674687\pi$
$102$	−2222.50	−	1267.65i	−2.15745	−	1.23055i
$103$	−895.886	−	517.240i	−0.857032	−	0.494808i	0.00598542	−	0.999982i	$-0.498095\pi$
$103$	−895.886	−	517.240i	−0.857032	−	0.494808i	−0.863017	+	0.505175i	$0.831428\pi$
$104$	−15.1372			−0.0142723
$105$	406.972	−	256.707i	0.378252	−	0.238591i
$106$	−298.918			−0.273901
$107$	−299.147	−	172.713i	−0.270277	−	0.156045i	0.358736	−	0.933439i	$-0.383208\pi$
$107$	−299.147	−	172.713i	−0.270277	−	0.156045i	−0.629014	+	0.777394i	$0.716541\pi$
$108$	624.946	+	1044.12i	0.556810	+	0.930285i
$109$	381.979	+	661.607i	0.335660	+	0.581380i	0.983611	−	0.180301i	$-0.0577073\pi$
$109$	381.979	+	661.607i	0.335660	+	0.581380i	−0.647951	+	0.761682i	$0.724374\pi$
$110$	86.4355	−	149.711i	0.0749209	−	0.129767i
$111$	235.396	+	402.820i	0.201286	+	0.344450i
$112$	950.515	+	506.634i	0.801922	+	0.427433i
$113$		−	1127.01i		−	0.938229i	−0.883137	−	0.469114i	$-0.844573\pi$
$113$		−	1127.01i		−	0.938229i	0.883137	−	0.469114i	$-0.155427\pi$
$114$	−573.054	+	3.00746i	−0.470802	+	0.00247083i
$115$	14.9102	−	8.60841i	0.0120903	−	0.00698033i
$116$	−546.534	+	315.541i	−0.437452	+	0.252563i
$117$	127.913	−	75.6518i	0.101073	−	0.0597779i
$118$			1473.77i			1.14976i
$119$	−1895.17	+	1181.57i	−1.45992	+	0.910202i
$120$	61.6906	−	36.0501i	0.0469296	−	0.0274242i
$121$	−629.653	+	1090.59i	−0.473068	+	0.819378i
$122$	−1382.55	−	2394.65i	−1.02599	−	1.77706i
$123$	569.593	−	998.631i	0.417549	−	0.732061i
$124$	2101.48	+	1213.29i	1.52193	+	0.878684i
$125$	125.000			0.0894427
$126$	2039.84	−	90.6064i	1.44225	−	0.0640624i
$127$	1904.91			1.33097			0.665485	−	0.746411i	$-0.268225\pi$
$127$	1904.91			1.33097			0.665485	+	0.746411i	$0.268225\pi$
$128$	303.780	+	175.387i	0.209770	+	0.121111i
$129$	−1275.07	+	2235.51i	−0.870264	+	1.52578i
$130$	−56.1873	−	97.3193i	−0.0379073	−	0.0656574i
$131$	1022.16	−	1770.44i	0.681731	−	1.18079i	−0.292721	−	0.956198i	$-0.594561\pi$
$131$	1022.16	−	1770.44i	0.681731	−	1.18079i	0.974452	−	0.224595i	$-0.0721058\pi$
$132$	329.475	−	192.535i	0.217251	−	0.126955i
$133$	−235.282	+	441.422i	−0.153395	+	0.287791i
$134$		−	3151.77i		−	2.03187i
$135$	−341.133	+	612.947i	−0.217482	+	0.390771i
$136$	−287.209	+	165.820i	−0.181088	+	0.104551i
$137$	135.672	−	78.3304i	0.0846078	−	0.0488483i	−0.457099	−	0.889416i	$-0.651112\pi$
$137$	135.672	−	78.3304i	0.0846078	−	0.0488483i	0.541707	+	0.840567i	$0.317778\pi$
$138$	73.0588	−	0.383421i	0.0450665	−	0.000236514i
$139$		−	1051.68i		−	0.641746i	−0.947122	−	0.320873i	$-0.896024\pi$
$139$		−	1051.68i		−	0.641746i	0.947122	−	0.320873i	$-0.103976\pi$
$140$	−27.2170	−	802.717i	−0.0164304	−	0.484586i
$141$	−526.506	−	900.982i	−0.314467	−	0.538130i
$142$	1635.90	−	2833.45i	0.966770	−	1.67449i
$143$	−23.3020	−	40.3603i	−0.0136267	−	0.0236021i
$144$	−1570.19	+	16.4815i	−0.908673	+	0.00953791i
$145$	−315.059	−	181.899i	−0.180443	−	0.104179i
$146$	4157.63			2.35676
$147$	776.136	−	1604.41i	0.435474	−	0.900201i
$148$	778.785			0.432539
$149$	945.006	+	545.599i	0.519583	+	0.299982i	0.736764	−	0.676150i	$-0.236353\pi$
$149$	945.006	+	545.599i	0.519583	+	0.299982i	−0.217181	+	0.976131i	$0.569686\pi$
$150$	460.759	+	262.805i	0.250806	+	0.143053i
$151$	1672.45	+	2896.76i	0.901336	+	1.56116i	0.825762	+	0.564019i	$0.190745\pi$
$151$	1672.45	+	2896.76i	0.901336	+	1.56116i	0.0755736	+	0.997140i	$0.475921\pi$
$152$	−37.1395	+	64.3276i	−0.0198185	+	0.0343267i
$153$	1598.26	−	2836.62i	0.844522	−	1.49887i
$154$	−21.6983	−	639.955i	−0.0113539	−	0.334864i
$155$			1398.85i			0.724891i
$156$	−1.30185	−	248.059i	−0.000668148	−	0.127312i
$157$	−1817.80	+	1049.51i	−0.924055	+	0.533503i	−0.884926	−	0.465731i	$-0.845791\pi$
$157$	−1817.80	+	1049.51i	−0.924055	+	0.533503i	−0.0391283	+	0.999234i	$0.512458\pi$
$158$	685.174	−	395.585i	0.344997	−	0.199184i
$159$	−1.99626	−	380.377i	−0.000995686	−	0.189722i
$160$			1297.40i			0.641054i
$161$	29.9962	−	56.2769i	0.0146834	−	0.0275481i
$162$	−2546.12	+	1542.16i	−1.23483	+	0.747921i
$163$	1248.73	−	2162.87i	0.600050	−	1.03932i	−0.392762	−	0.919640i	$-0.628480\pi$
$163$	1248.73	−	2162.87i	0.600050	−	1.03932i	0.992813	−	0.119678i	$-0.0381862\pi$
$164$	−959.511	−	1661.92i	−0.456861	−	0.791306i
$165$	191.086	+	108.990i	0.0901577	+	0.0514236i
$166$	−5020.29	−	2898.47i	−2.34729	−	1.35521i
$167$	3329.30			1.54269			0.771345	−	0.636417i	$-0.219584\pi$
$167$	3329.30			1.54269			0.771345	+	0.636417i	$0.219584\pi$
$168$	123.260	−	234.205i	0.0566054	−	0.107556i
$169$	2166.71			0.986211
$170$	−2132.17	−	1231.01i	−0.961939	−	0.555376i
$171$	−7.65406	−	729.199i	−0.00342293	−	0.326101i
$172$	2147.93	+	3720.33i	0.952199	+	1.64926i
$173$	−134.286	+	232.590i	−0.0590149	+	0.102217i	−0.894023	−	0.448020i	$-0.852129\pi$
$173$	−134.286	+	232.590i	−0.0590149	+	0.102217i	0.835009	+	0.550237i	$0.185463\pi$
$174$	−778.898	−	1332.89i	−0.339357	−	0.580724i
$175$	392.900	−	244.958i	0.169717	−	0.105812i
$176$			492.436i			0.210902i
$177$	−1875.39	+	9.84230i	−0.796403	+	0.00417962i
$178$	−2197.66	+	1268.82i	−0.925404	+	0.534282i
$179$	1472.14	−	849.943i	0.614711	−	0.354904i	−0.160096	−	0.987101i	$-0.551180\pi$
$179$	1472.14	−	849.943i	0.614711	−	0.354904i	0.774807	+	0.632198i	$0.217847\pi$
$180$	596.073	+	1007.85i	0.246826	+	0.417337i
$181$		−	2624.64i		−	1.07783i	−0.842359	−	0.538917i	$-0.818834\pi$
$181$		−	2624.64i		−	1.07783i	0.842359	−	0.538917i	$-0.181166\pi$
$182$	−367.321	−	195.786i	−0.149603	−	0.0797397i
$183$	3037.99	−	1775.31i	1.22718	−	0.717128i
$184$	4.73493	−	8.20113i	0.00189708	−	0.00328584i
$185$	224.472	+	388.797i	0.0892082	+	0.154513i
$186$	−2940.99	+	5156.25i	−1.15938	+	2.03266i
$187$	−884.252	−	510.523i	−0.345791	−	0.199642i
$188$	−1741.90			−0.675750
$189$	128.921	+	2595.12i	0.0496169	+	0.998768i
$190$	−551.429			−0.210552
$191$	−2142.24	−	1236.82i	−0.811554	−	0.468551i	0.0359413	−	0.999354i	$-0.488557\pi$
$191$	−2142.24	−	1236.82i	−0.811554	−	0.468551i	−0.847495	+	0.530803i	$0.821890\pi$
$192$	−1529.92	+	2682.30i	−0.575064	+	1.00822i
$193$	839.123	+	1453.40i	0.312961	+	0.542064i	0.979002	−	0.203851i	$-0.0653459\pi$
$193$	839.123	+	1453.40i	0.312961	+	0.542064i	−0.666041	+	0.745915i	$0.732013\pi$
$194$	−62.1509	+	107.649i	−0.0230009	+	0.0398387i
$195$	123.465	−	72.1490i	0.0453410	−	0.0264959i
$196$	−1658.60	−	2469.77i	−0.604448	−	0.900061i
$197$			4518.62i			1.63420i	0.576493	+	0.817102i	$0.304421\pi$
$197$			4518.62i			1.63420i	−0.576493	+	0.817102i	$0.695579\pi$
$198$	475.211	+	803.494i	0.170565	+	0.288393i
$199$	442.348	−	255.390i	0.157574	−	0.0909754i	−0.419140	−	0.907922i	$-0.637668\pi$
$199$	442.348	−	255.390i	0.157574	−	0.0909754i	0.576714	+	0.816946i	$0.304335\pi$
$200$	59.5430	−	34.3772i	0.0210516	−	0.0121542i
$201$	4010.66	−	21.0485i	1.40742	−	0.00738629i
$202$			3962.54i			1.38021i
$203$	−1346.76	+	45.6632i	−0.465634	+	0.0157878i
$204$	−2742.07	−	4692.35i	−0.941093	−	1.61044i
$205$	553.127	−	958.044i	0.188449	−	0.326403i
$206$	−2112.06	−	3658.19i	−0.714340	−	1.23727i
$207$	0.975818	+	92.9657i	0.000327652	+	0.0312153i
$208$	277.221	+	160.054i	0.0924127	+	0.0533545i
$209$	−228.689			−0.0756877
$210$	1963.27	−	76.8838i	0.645135	−	0.0252642i
$211$	−2859.26			−0.932889			−0.466444	−	0.884550i	$-0.654465\pi$
$211$	−2859.26			−0.932889			−0.466444	+	0.884550i	$0.654465\pi$
$212$	−549.875	−	317.471i	−0.178140	−	0.102849i
$213$	3616.53	+	2062.78i	1.16338	+	0.663564i
$214$	−705.241	−	1221.51i	−0.225277	−	0.390191i
$215$	−1238.21	+	2144.65i	−0.392769	+	0.680296i
$216$	6.07448	+	385.791i	0.00191350	+	0.121527i
$217$	2741.27	+	4396.86i	0.857555	+	1.37548i
$218$			3119.49i			0.969166i
$219$	27.7659	+	5290.63i	0.00856733	+	1.63246i
$220$	318.005	−	183.600i	0.0974541	−	0.0562652i
$221$	−574.807	+	331.865i	−0.174958	+	0.101012i
$222$	9.99806	+	1905.07i	0.00302264	+	0.575947i
$223$		−	45.7328i		−	0.0137332i	−0.999976	−	0.00686658i	$-0.997814\pi$
$223$		−	45.7328i		−	0.0137332i	0.999976	−	0.00686658i	$-0.00218572\pi$
$224$	2542.47	+	4077.99i	0.758375	+	1.21640i
$225$	−331.346	+	588.077i	−0.0981765	+	0.174245i
$226$	2300.96	−	3985.39i	0.677247	−	1.17303i
$227$	−285.201	−	493.982i	−0.0833896	−	0.144435i	0.821314	−	0.570476i	$-0.193241\pi$
$227$	−285.201	−	493.982i	−0.0833896	−	0.144435i	−0.904704	+	0.426041i	$0.859908\pi$
$228$	−1057.36	−	603.089i	−0.307128	−	0.175178i
$229$	−4897.01	−	2827.29i	−1.41311	−	0.815862i	−0.417434	−	0.908707i	$-0.637071\pi$
$229$	−4897.01	−	2827.29i	−1.41311	−	0.815862i	−0.995681	+	0.0928450i	$0.970404\pi$
$230$	70.3018			0.0201546
$231$	814.207	−	31.8852i	0.231909	−	0.00908180i
$232$	−200.102			−0.0566265
$233$	588.268	+	339.637i	0.165402	+	0.0954951i	0.580416	−	0.814320i	$-0.302890\pi$
$233$	588.268	+	339.637i	0.165402	+	0.0954951i	−0.415014	+	0.909815i	$0.636223\pi$
$234$	606.790	−	6.36919i	0.169517	−	0.00177935i
$235$	−502.074	−	869.617i	−0.139369	−	0.241394i
$236$	−1565.24	+	2711.08i	−0.431732	+	0.747781i
$237$	507.963	+	869.251i	0.139223	+	0.238244i
$238$	−9114.19	+	309.026i	−2.48229	+	0.0841646i
$239$			211.837i			0.0573332i	0.999589	+	0.0286666i	$0.00912611\pi$
$239$			211.837i			0.0573332i	−0.999589	+	0.0286666i	$0.990874\pi$
$240$	−1510.98	+	7.92978i	−0.406388	+	0.00213277i
$241$	−99.2273	+	57.2889i	−0.0265220	+	0.0153125i	−0.513202	−	0.858268i	$-0.671541\pi$
$241$	−99.2273	+	57.2889i	−0.0265220	+	0.0153125i	0.486680	+	0.873580i	$0.338208\pi$
$242$	−4453.24	+	2571.08i	−1.18291	+	0.682955i
$243$	−1979.42	−	3229.68i	−0.522550	−	0.852609i
$244$		−	5873.44i		−	1.54102i
$245$	754.930	−	1539.90i	0.196860	−	0.401555i
$246$	4053.10	−	2368.50i	1.05047	−	0.613863i
$247$	−74.3295	+	128.742i	−0.0191477	+	0.0331647i
$248$	384.707	+	666.332i	0.0985038	+	0.170614i
$249$	3654.81	−	6407.75i	0.930178	−	1.63082i
$250$	442.033	+	255.208i	0.111826	+	0.0645630i
$251$	−6671.72			−1.67775			−0.838875	−	0.544324i	$-0.816786\pi$
$251$	−6671.72			−1.67775			−0.838875	+	0.544324i	$0.816786\pi$
$252$	3848.62	+	1999.77i	0.962066	+	0.499896i
$253$	29.1556			0.00724504
$254$	6736.25	+	3889.17i	1.66405	+	0.960742i
$255$	1552.23	−	2721.43i	0.381195	−	0.668324i
$256$	−1660.94	−	2876.83i	−0.405502	−	0.702351i
$257$	−1173.99	+	2033.40i	−0.284946	+	0.493542i	−0.972596	−	0.232501i	$-0.925309\pi$
$257$	−1173.99	+	2033.40i	−0.284946	+	0.493542i	0.687650	+	0.726043i	$0.258642\pi$
$258$	−9073.14	+	5302.06i	−2.18941	+	1.27943i
$259$	1467.47	+	782.178i	0.352063	+	0.187653i
$260$		−	238.699i		−	0.0569364i
$261$	1690.92	−	1000.06i	0.401016	−	0.237173i
$262$	7229.26	−	4173.82i	1.70468	−	0.984196i
$263$	6281.95	−	3626.88i	1.47286	−	0.850354i	0.473323	−	0.880889i	$-0.343054\pi$
$263$	6281.95	−	3626.88i	1.47286	−	0.850354i	0.999534	+	0.0305344i	$0.00972091\pi$
$264$	120.997	−	0.635007i	0.0282078	−	0.000148038i
$265$		−	366.023i		−	0.0848476i
$266$	−1733.25	+	1080.62i	−0.399521	+	0.249086i
$267$	−1629.27	−	2788.08i	−0.373444	−	0.639056i
$268$	3347.38	−	5797.84i	0.762963	−	1.32149i
$269$	−797.075	−	1380.57i	−0.180664	−	0.312918i	0.761443	−	0.648232i	$-0.224491\pi$
$269$	−797.075	−	1380.57i	−0.180664	−	0.312918i	−0.942107	+	0.335313i	$0.891158\pi$
$270$	−2457.76	+	1471.06i	−0.553980	+	0.331578i
$271$	−2302.55	−	1329.38i	−0.516124	−	0.297984i	0.219223	−	0.975675i	$-0.429648\pi$
$271$	−2302.55	−	1329.38i	−0.516124	−	0.297984i	−0.735347	+	0.677690i	$0.762981\pi$
$272$	7013.23			1.56338
$273$	246.687	−	468.729i	0.0546893	−	0.103915i
$274$	639.697			0.141042
$275$	183.320	+	105.840i	0.0401985	+	0.0232086i
$276$	134.803	+	76.8879i	0.0293992	+	0.0167685i
$277$	−261.315	−	452.611i	−0.0566820	−	0.0981760i	0.836292	−	0.548284i	$-0.184719\pi$
$277$	−261.315	−	452.611i	−0.0566820	−	0.0981760i	−0.892974	+	0.450108i	$0.851385\pi$
$278$	2147.18	−	3719.03i	0.463235	−	0.802347i
$279$	−6581.04	−	3708.02i	−1.41217	−	0.795674i
$280$	119.788	−	224.739i	0.0255668	−	0.0479668i
$281$			3626.44i			0.769876i	0.922943	+	0.384938i	$0.125777\pi$
$281$			3626.44i			0.769876i	−0.922943	+	0.384938i	$0.874223\pi$
$282$	−22.3625	−	4261.05i	−0.00472223	−	0.899795i
$283$	720.958	−	416.246i	0.151437	−	0.0874319i	−0.422367	−	0.906425i	$-0.638801\pi$
$283$	720.958	−	416.246i	0.151437	−	0.0874319i	0.573804	+	0.818993i	$0.305467\pi$
$284$	6018.63	−	3474.86i	1.25754	−	0.726038i
$285$	−3.68261	−	701.701i	−0.000765401	−	0.145843i
$286$		−	190.299i		−	0.0393448i
$287$	−138.854	−	4095.27i	−0.0285586	−	0.842286i
$288$	−6103.78	−	3439.11i	−1.24885	−	0.703651i
$289$	−4814.33	+	8338.66i	−0.979916	+	1.69726i
$290$	−742.754	−	1286.49i	−0.150400	−	0.260501i
$291$	−137.399	−	78.3690i	−0.0276787	−	0.0157872i
$292$	7648.17	+	4415.67i	1.53279	+	0.884958i
$293$	−1490.52			−0.297191			−0.148595	−	0.988898i	$-0.547475\pi$
$293$	−1490.52			−0.297191			−0.148595	+	0.988898i	$0.547475\pi$
$294$	6020.28	−	4089.01i	1.19425	−	0.811142i
$295$	−1804.62			−0.356167
$296$	213.852	+	123.467i	0.0419929	+	0.0242446i
$297$	−1019.28	+	610.079i	−0.199141	+	0.119193i
$298$	2227.86	+	3858.76i	0.433075	+	0.750108i
$299$	9.47627	−	16.4134i	0.00183287	−	0.00317462i
$300$	568.474	+	972.800i	0.109403	+	0.187216i
$301$	310.835	+	9167.54i	0.0595223	+	1.75551i
$302$			13658.3i			2.60247i
$303$	−5042.39	+	26.4631i	−0.956031	+	0.00501737i
$304$	1360.34	−	785.394i	0.256648	−	0.148176i
$305$	2932.23	−	1692.92i	0.550489	−	0.317825i
$306$	11443.3	−	6767.92i	2.13781	−	1.26437i
$307$			9583.15i			1.78156i	0.454434	+	0.890780i	$0.349841\pi$
$307$			9583.15i			1.78156i	−0.454434	+	0.890780i	$0.650159\pi$
$308$	639.760	−	1200.28i	0.118356	−	0.222052i
$309$	4640.99	−	2712.05i	0.854423	−	0.499298i
$310$	−2855.97	+	4946.69i	−0.523252	+	0.906300i
$311$	1149.87	+	1991.63i	0.209656	+	0.363136i	0.951606	−	0.307320i	$-0.0994321\pi$
$311$	1149.87	+	1991.63i	0.209656	+	0.363136i	−0.741950	+	0.670455i	$0.766099\pi$
$312$	38.9695	−	68.3228i	0.00707120	−	0.0123975i
$313$	4770.46	+	2754.23i	0.861478	+	0.497374i	0.864507	−	0.502621i	$-0.167631\pi$
$313$	4770.46	+	2754.23i	0.861478	+	0.497374i	−0.00302927	+	0.999995i	$0.500964\pi$
$314$	−8570.97			−1.54041
$315$	110.947	+	2497.77i	0.0198449	+	0.446773i
$316$	1680.55			0.299172
$317$	−3604.26	−	2080.92i	−0.638598	−	0.368694i	0.145477	−	0.989362i	$-0.453528\pi$
$317$	−3604.26	−	2080.92i	−0.638598	−	0.368694i	−0.784074	+	0.620667i	$0.786862\pi$
$318$	769.541	−	1349.19i	0.135704	−	0.237920i
$319$	−308.035	−	533.532i	−0.0540647	−	0.0936428i
$320$	−1485.69	+	2573.29i	−0.259539	+	0.449535i
$321$	1549.68	−	905.587i	0.269454	−	0.157461i
$322$	220.973	−	137.768i	0.0382433	−	0.0238432i
$323$			3256.97i			0.561060i
$324$	−6321.60	+	132.724i	−1.08395	+	0.0227579i
$325$	119.167	−	68.8010i	0.0203390	−	0.0117427i
$326$	8831.68	−	5098.97i	1.50043	−	0.866276i
$327$	−3969.59	+	20.8329i	−0.671311	+	0.00352312i
$328$		−	608.478i		−	0.102432i
$329$	−3282.28	−	1749.49i	−0.550024	−	0.293168i
$330$	453.208	+	775.552i	0.0756009	+	0.129372i
$331$	−2185.70	+	3785.75i	−0.362952	+	0.628651i	−0.988445	−	0.151578i	$-0.951564\pi$
$331$	−2185.70	+	3785.75i	−0.362952	+	0.628651i	0.625493	+	0.780229i	$0.284898\pi$
$332$	−6156.73	−	10663.8i	−1.01775	−	1.76280i
$333$	−2424.17	+	25.4453i	−0.398929	+	0.00418737i
$334$	11773.3	+	6797.31i	1.92876	+	1.11357i
$335$	3859.32			0.629424
$336$	−4733.76	+	2985.93i	−0.768595	+	0.484809i
$337$	−3888.74			−0.628584			−0.314292	−	0.949326i	$-0.601767\pi$
$337$	−3888.74			−0.628584			−0.314292	+	0.949326i	$0.601767\pi$
$338$	7662.03	+	4423.68i	1.23302	+	0.711883i
$339$	5086.83	+	2901.39i	0.814981	+	0.464844i
$340$	−2614.82	−	4529.00i	−0.417084	−	0.722411i
$341$	−1184.43	+	2051.49i	−0.188095	+	0.325790i
$342$	1461.71	−	2594.27i	0.231112	−	0.410181i
$343$	−644.799	−	6319.64i	−0.101504	−	0.994835i
$344$			1362.12i			0.213490i
$345$	0.469497	+	89.4600i	7.32663e−5	+	0.0139605i
$346$	−949.741	+	548.333i	−0.147568	+	0.0851982i
$347$	−8390.19	+	4844.08i	−1.29801	+	0.749406i	−0.980060	−	0.198702i	$-0.936327\pi$
$347$	−8390.19	+	4844.08i	−1.29801	+	0.749406i	−0.317949	+	0.948108i	$0.602994\pi$
$348$	−17.2094	−	3279.16i	−0.00265092	−	0.505119i
$349$		−	5564.36i		−	0.853447i	−0.904382	−	0.426724i	$-0.859668\pi$
$349$		−	5564.36i		−	0.853447i	0.904382	−	0.426724i	$-0.140332\pi$
$350$	1889.52	−	64.0661i	0.288569	−	0.00978422i
$351$	12.1572	+	772.105i	0.00184873	+	0.117413i
$352$	−1098.53	+	1902.71i	−0.166341	+	0.288111i
$353$	3784.55	+	6555.03i	0.570627	+	0.988355i	0.996502	+	0.0835727i	$0.0266331\pi$
$353$	3784.55	+	6555.03i	0.570627	+	0.988355i	−0.425875	+	0.904782i	$0.640034\pi$
$354$	−6651.98	−	3794.11i	−0.998725	−	0.569647i
$355$	3469.55	+	2003.14i	0.518716	+	0.299481i
$356$	−5390.29			−0.802485
$357$	−454.107	−	11595.9i	−0.0673218	−	1.71910i
$358$	6941.18			1.02473
$359$	−8900.82	−	5138.89i	−1.30854	−	0.755488i	−0.326691	−	0.945131i	$-0.605934\pi$
$359$	−8900.82	−	5138.89i	−1.30854	−	0.755488i	−0.981853	+	0.189643i	$0.939267\pi$
$360$	3.89687	+	371.253i	0.000570509	+	0.0543521i
$361$	−3064.76	−	5308.32i	−0.446823	−	0.773921i
$362$	5358.62	−	9281.41i	0.778019	−	1.34757i
$363$	−3301.47	−	5649.63i	−0.477362	−	0.816884i
$364$	−467.769	−	750.278i	−0.0673565	−	0.108036i
$365$			5090.98i			0.730067i
$366$	14367.7	−	75.4034i	2.05194	−	0.0107689i
$367$	5323.65	−	3073.61i	0.757199	−	0.437169i	−0.0710901	−	0.997470i	$-0.522648\pi$
$367$	5323.65	−	3073.61i	0.757199	−	0.437169i	0.828289	+	0.560301i	$0.189314\pi$
$368$	−173.430	+	100.130i	−0.0245671	+	0.0141838i
$369$	3041.02	+	5141.80i	0.429022	+	0.725397i
$370$			1833.18i			0.257575i
$371$	−717.282	−	1150.48i	−0.100376	−	0.160998i
$372$	−10886.4	+	6361.67i	−1.51729	+	0.886659i
$373$	4214.93	−	7300.47i	0.585096	−	1.01342i	−0.409768	−	0.912190i	$-0.634390\pi$
$373$	4214.93	−	7300.47i	0.585096	−	1.01342i	0.994864	−	0.101225i	$-0.0322764\pi$
$374$	−2084.63	−	3610.68i	−0.288218	−	0.499209i
$375$	−321.803	+	564.197i	−0.0443142	+	0.0776933i
$376$	−478.320	−	276.158i	−0.0656050	−	0.0378770i
$377$	−400.476			−0.0547097
$378$	−4842.46	+	9440.23i	−0.658913	+	1.28453i
$379$	−7676.46			−1.04040			−0.520202	−	0.854043i	$-0.674143\pi$
$379$	−7676.46			−1.04040			−0.520202	+	0.854043i	$0.674143\pi$
$380$	−1014.38	−	585.654i	−0.136939	−	0.0790617i
$381$	−4904.04	+	8597.94i	−0.659427	+	1.15613i
$382$	−5050.34	−	8747.44i	−0.676434	−	1.17162i
$383$	5802.30	−	10049.9i	0.774109	−	1.34080i	−0.161186	−	0.986924i	$-0.551532\pi$
$383$	5802.30	−	10049.9i	0.774109	−	1.34080i	0.935294	−	0.353871i	$-0.115135\pi$
$384$	−1573.68	+	919.611i	−0.209132	+	0.122210i
$385$	783.621	−	26.5695i	0.103733	−	0.00351716i
$386$			6852.82i			0.903625i
$387$	−6807.54	−	11510.3i	−0.894177	−	1.51189i
$388$	−228.660	+	132.017i	−0.0299187	+	0.0172735i
$389$	−694.507	+	400.974i	−0.0905217	+	0.0522627i	−0.544578	−	0.838711i	$-0.683310\pi$
$389$	−694.507	+	400.974i	−0.0905217	+	0.0522627i	0.454056	+	0.890973i	$0.349977\pi$
$390$	583.908	−	3.06442i	0.0758136	−	0.000397879i
$391$		−	415.231i		−	0.0537062i
$392$	−63.8943	−	941.143i	−0.00823253	−	0.121263i
$393$	5359.52	+	9171.46i	0.687918	+	1.17720i
$394$	−9225.49	+	15979.0i	−1.17963	+	2.04318i
$395$	484.391	+	838.991i	0.0617022	+	0.106871i
$396$	20.8123	+	1982.78i	0.00264105	+	0.251612i
$397$	−7984.56	−	4609.89i	−1.00940	−	0.582780i	−0.0983871	−	0.995148i	$-0.531368\pi$
$397$	−7984.56	−	4609.89i	−1.00940	−	0.582780i	−0.911017	+	0.412368i	$0.864702\pi$
$398$	2085.68			0.262677
$399$	−1386.67	−	2198.37i	−0.173986	−	0.275830i
$400$	−1453.96			−0.181745
$401$	1886.94	+	1089.43i	0.234986	+	0.135669i	0.612870	−	0.790184i	$-0.290015\pi$
$401$	1886.94	+	1089.43i	0.234986	+	0.135669i	−0.377884	+	0.925853i	$0.623348\pi$
$402$	14225.7	+	8113.98i	1.76496	+	1.00669i
$403$	769.936	+	1333.57i	0.0951694	+	0.164838i
$404$	−4208.48	+	7289.30i	−0.518267	+	0.897664i
$405$	−1888.36	−	3117.71i	−0.231687	−	0.382519i
$406$	−4855.71	−	2588.14i	−0.593559	−	0.316373i
$407$			760.258i			0.0925911i
$408$	−9.04372	−	1723.23i	−0.00109738	−	0.209099i
$409$	2406.40	−	1389.34i	0.290926	−	0.167966i	−0.347433	−	0.937705i	$-0.612947\pi$
$409$	2406.40	−	1389.34i	0.290926	−	0.167966i	0.638360	+	0.769738i	$0.279613\pi$
$410$	3912.00	−	2258.59i	0.471219	−	0.272059i
$411$	4.27209	+	814.022i	0.000512717	+	0.0976953i
$412$		−	8972.58i		−	1.07293i
$413$	−5672.30	+	3536.46i	−0.675825	+	0.421350i
$414$	−186.354	+	330.743i	−0.0221227	+	0.0392636i
$415$	3549.15	−	6147.32i	0.419810	−	0.727132i
$416$	714.100	+	1236.86i	0.0841626	+	0.145774i
$417$	4746.85	+	2707.48i	0.557445	+	0.317952i
$418$	−808.703	−	466.905i	−0.0946291	−	0.0546341i
$419$	−2105.13			−0.245448			−0.122724	−	0.992441i	$-0.539163\pi$
$419$	−2105.13			−0.245448			−0.122724	+	0.992441i	$0.539163\pi$
$420$	3693.19	+	1943.69i	0.429070	+	0.225815i
$421$	−913.228			−0.105720			−0.0528599	−	0.998602i	$-0.516834\pi$
$421$	−913.228			−0.105720			−0.0528599	+	0.998602i	$0.516834\pi$
$422$	−10111.1	−	5837.64i	−1.16635	−	0.673393i
$423$	5422.10	−	56.9132i	0.623242	−	0.00654188i
$424$	−100.663	−	174.353i	−0.0115297	−	0.0199701i
$425$	1507.36	−	2610.82i	0.172042	−	0.297985i
$426$	8577.51	+	14678.2i	0.975544	+	1.66940i
$427$	5899.03	−	11067.4i	0.668558	−	1.25431i
$428$		−	2996.05i		−	0.338364i
$429$	242.158	−	1.27088i	0.0272529	−	0.000143027i
$430$	−8757.28	+	5056.02i	−0.982125	+	0.567030i
$431$	11007.2	−	6355.00i	1.23016	−	0.710231i	0.263093	−	0.964770i	$-0.415257\pi$
$431$	11007.2	−	6355.00i	1.23016	−	0.710231i	0.967062	+	0.254540i	$0.0819240\pi$
$432$	3967.94	−	7129.58i	0.441915	−	0.794033i
$433$			3578.00i			0.397108i	0.980090	+	0.198554i	$0.0636245\pi$
$433$			3578.00i			0.397108i	−0.980090	+	0.198554i	$0.936375\pi$
$434$	716.949	+	21145.2i	0.0792964	+	2.33871i
$435$	1632.11	−	953.756i	0.179894	−	0.105124i
$436$	−3313.10	+	5738.46i	−0.363919	+	0.630326i
$437$	−46.5007	−	80.5415i	−0.00509023	−	0.00881653i
$438$	−10703.5	+	18765.7i	−1.16765	+	2.04717i
$439$	11240.4	+	6489.62i	1.22203	+	0.705542i	0.965351	−	0.260954i	$-0.0840371\pi$
$439$	11240.4	+	6489.62i	1.22203	+	0.705542i	0.256683	+	0.966496i	$0.417370\pi$
$440$	116.431			0.0126151
$441$	5243.52	+	7633.58i	0.566194	+	0.824272i
$442$	−2710.22			−0.291657
$443$	9761.27	+	5635.67i	1.04689	+	0.604421i	0.921777	−	0.387721i	$-0.126738\pi$
$443$	9761.27	+	5635.67i	1.04689	+	0.604421i	0.125112	+	0.992143i	$0.460071\pi$
$444$	−2004.92	+	3515.10i	−0.214300	+	0.375719i
$445$	−1553.66	−	2691.02i	−0.165507	−	0.286667i
$446$	93.3708	−	161.723i	0.00991308	−	0.0171700i
$447$	−4895.45	+	2860.75i	−0.518002	+	0.302704i
$448$	372.960	+	10999.8i	0.0393319	+	1.16003i
$449$		−	14311.8i		−	1.50427i	−0.659012	−	0.752133i	$-0.729025\pi$
$449$		−	14311.8i		−	1.50427i	0.659012	−	0.752133i	$-0.270975\pi$
$450$	−2372.38	+	1403.10i	−0.248522	+	0.146984i
$451$	1622.38	−	936.684i	0.169391	−	0.0977977i
$452$	8465.49	−	4887.55i	0.880936	−	0.508609i
$453$	−17380.3	+	91.2141i	−1.80265	+	0.00946051i
$454$		−	2329.13i		−	0.240774i
$455$	239.739	−	449.782i	0.0247014	−	0.0463431i
$456$	−194.734	−	333.239i	−0.0199984	−	0.0342222i
$457$	810.931	−	1404.57i	0.0830061	−	0.143771i	−0.821534	−	0.570160i	$-0.806881\pi$
$457$	810.931	−	1404.57i	0.0830061	−	0.143771i	0.904540	+	0.426389i	$0.140215\pi$
$458$	−11544.7	−	19996.0i	−1.17784	−	2.04007i
$459$	8688.69	+	14516.5i	0.883558	+	1.47620i
$460$	129.324	+	74.6652i	0.0131082	+	0.00756800i
$461$	−18238.0			−1.84258			−0.921290	−	0.388877i	$-0.872863\pi$
$461$	−18238.0			−1.84258			−0.921290	+	0.388877i	$0.872863\pi$
$462$	2944.35	+	1549.58i	0.296501	+	0.156045i
$463$	−14765.4			−1.48209			−0.741046	−	0.671455i	$-0.765670\pi$
$463$	−14765.4			−1.48209			−0.741046	+	0.671455i	$0.765670\pi$
$464$	3664.66	+	2115.79i	0.366654	+	0.211688i
$465$	−6313.80	−	3601.22i	−0.629667	−	0.359146i
$466$	1386.85	+	2402.09i	0.137864	+	0.238787i
$467$	−3767.85	+	6526.10i	−0.373352	+	0.646664i	−0.990079	−	0.140513i	$-0.955125\pi$
$467$	−3767.85	+	6526.10i	−0.373352	+	0.646664i	0.616727	+	0.787177i	$0.288458\pi$
$468$	1122.99	+	632.734i	0.110919	+	0.0624960i
$469$	12130.6	−	7562.96i	1.19433	−	0.744617i
$470$		−	4100.26i		−	0.402406i
$471$	−57.2396	−	10906.7i	−0.00559970	−	1.06699i
$472$	−859.622	+	496.303i	−0.0838291	+	0.0483987i
$473$	−3631.82	+	2096.83i	−0.353047	+	0.203832i
$474$	21.5750	+	4110.99i	0.00209065	+	0.398362i
$475$		−	675.222i		−	0.0652238i
$476$	−17094.2	−	9111.40i	−1.64604	−	0.877354i
$477$	1722.00	+	970.241i	0.165293	+	0.0931327i
$478$	−432.500	+	749.112i	−0.0413851	+	0.0716812i
$479$	−1641.79	−	2843.66i	−0.156608	−	0.271253i	0.777035	−	0.629457i	$-0.216723\pi$
$479$	−1641.79	−	2843.66i	−0.156608	−	0.271253i	−0.933643	+	0.358204i	$0.883389\pi$
$480$	−5855.92	−	3340.06i	−0.556843	−	0.317609i
$481$	427.994	+	247.102i	0.0405714	+	0.0234239i
$482$	−467.858			−0.0442123
$483$	176.787	+	280.271i	0.0166544	+	0.0264032i
$484$	−10922.6			−1.02579
$485$	−131.815	−	76.1034i	−0.0123410	−	0.00712511i
$486$	−405.829	−	15462.3i	−0.0378781	−	1.44318i
$487$	5107.21	+	8845.95i	0.475215	+	0.823097i	0.999597	−	0.0283864i	$-0.00903690\pi$
$487$	5107.21	+	8845.95i	0.475215	+	0.823097i	−0.524382	+	0.851483i	$0.675704\pi$
$488$	931.168	−	1612.83i	0.0863770	−	0.149609i
$489$	6547.49	+	11204.4i	0.605497	+	1.03615i
$490$	5813.59	−	3904.19i	0.535982	−	0.359946i
$491$		−	1347.56i		−	0.123858i	−0.998081	−	0.0619292i	$-0.980275\pi$
$491$		−	1347.56i		−	0.123858i	0.998081	−	0.0619292i	$-0.0197253\pi$
$492$	9971.39	−	52.3311i	0.913709	−	0.00479526i
$493$	−7598.52	+	4387.01i	−0.694158	+	0.400772i
$494$	−525.697	+	303.511i	−0.0478790	+	0.0276429i
$495$	−983.873	+	581.893i	−0.0893370	+	0.0528367i
$496$		−	16270.9i		−	1.47295i
$497$	14831.0	−	502.859i	1.33855	−	0.0453849i
$498$	26006.8	−	15197.6i	2.34015	−	1.36751i
$499$	6255.74	−	10835.3i	0.561213	−	0.972050i	−0.436178	−	0.899861i	$-0.643668\pi$
$499$	6255.74	−	10835.3i	0.561213	−	0.972050i	0.997391	−	0.0721893i	$-0.0229986\pi$
$500$	542.095	+	938.935i	0.0484864	+	0.0839809i
$501$	−8571.04	+	15027.1i	−0.764323	+	1.34004i
$502$	−23592.9	−	13621.4i	−2.09762	−	1.21106i
$503$	3030.57			0.268641			0.134320	−	0.990938i	$-0.457115\pi$
$503$	3030.57			0.268641			0.134320	+	0.990938i	$0.457115\pi$
$504$	739.780	+	1159.29i	0.0653818	+	0.102458i
$505$	−4852.10			−0.427556
$506$	103.102	+	59.5258i	0.00905816	+	0.00522973i
$507$	−5578.02	+	9779.58i	−0.488616	+	0.856660i
$508$	8261.12	+	14308.7i	0.721512	+	1.24969i
$509$	6228.25	−	10787.7i	0.542362	−	0.939399i	−0.456405	−	0.889772i	$-0.650863\pi$
$509$	6228.25	−	10787.7i	0.542362	−	0.939399i	0.998768	−	0.0496273i	$-0.0158034\pi$
$510$	11045.3	−	6454.55i	0.959011	−	0.560417i
$511$	9976.62	+	16002.0i	0.863678	+	1.38530i
$512$		−	16370.5i		−	1.41305i
$513$	3311.00	+	1842.72i	0.284959	+	0.158593i
$514$	−8303.04	+	4793.76i	−0.712512	+	0.411369i
$515$	4479.43	−	2586.20i	0.383276	−	0.221285i
$516$	−22321.6	+	117.147i	−1.90437	+	0.00999437i
$517$		−	1700.46i		−	0.144654i
$518$	3592.42	+	5762.07i	0.304714	+	0.488746i
$519$	−704.104	−	1204.90i	−0.0595506	−	0.101906i
$520$	37.8429	−	65.5459i	0.00319139	−	0.00552765i
$521$	3119.32	+	5402.82i	0.262303	+	0.454322i	0.966854	−	0.255332i	$-0.0821847\pi$
$521$	3119.32	+	5402.82i	0.262303	+	0.454322i	−0.704551	+	0.709654i	$0.748851\pi$
$522$	8021.30	−	84.1958i	0.672572	−	0.00705968i
$523$	−6897.77	−	3982.43i	−0.576708	−	0.332962i	0.183116	−	0.983091i	$-0.441382\pi$
$523$	−6897.77	−	3982.43i	−0.576708	−	0.332962i	−0.759824	+	0.650129i	$0.774715\pi$
$524$	17731.5			1.47825
$525$	94.1437	+	2404.01i	0.00782623	+	0.199847i
$526$	29619.5			2.45527
$527$	29217.1	+	16868.5i	2.41503	+	1.39432i
$528$	−2222.65	−	1267.74i	−0.183197	−	0.104491i
$529$	−6077.57	−	10526.7i	−0.499513	−	0.865181i
$530$	747.295	−	1294.35i	0.0612461	−	0.106081i
$531$	4783.64	−	8490.07i	0.390946	−	0.693856i
$532$	−4336.10	+	147.020i	−0.353372	+	0.0119814i
$533$		−	1217.78i		−	0.0989643i
$534$	−69.2007	−	13185.8i	−0.00560788	−	1.06855i
$535$	1495.74	−	863.563i	0.120872	−	0.0697852i
$536$	1838.36	−	1061.38i	0.148144	−	0.0855310i
$537$	46.3553	+	8832.75i	0.00372510	+	0.709797i
$538$		−	6509.42i		−	0.521638i
$539$	2411.01	−	1619.15i	0.192671	−	0.129391i
$540$	−6083.55	+	95.7886i	−0.484804	+	0.00763349i
$541$	3018.33	−	5227.90i	0.239867	−	0.415462i	−0.720809	−	0.693134i	$-0.756229\pi$
$541$	3018.33	−	5227.90i	0.239867	−	0.415462i	0.960676	+	0.277672i	$0.0895627\pi$
$542$	−5428.27	−	9402.03i	−0.430192	−	0.745114i
$543$	11846.5	+	6756.94i	0.936247	+	0.534011i
$544$	27098.3	+	15645.2i	2.13572	+	1.23306i
$545$	−3819.79			−0.300224
$546$	1829.33	−	1153.89i	0.143385	−	0.0904435i
$547$	620.134			0.0484735			0.0242368	−	0.999706i	$-0.492284\pi$
$547$	620.134			0.0484735			0.0242368	+	0.999706i	$0.492284\pi$
$548$	1176.76	+	679.400i	0.0917308	+	0.0529608i
$549$	191.904	+	18282.6i	0.0149185	+	1.42128i
$550$	432.177	+	748.553i	0.0335057	+	0.0580335i
$551$	−982.580	+	1701.88i	−0.0759697	+	0.131583i
$552$	24.8267	+	42.4846i	0.00191430	+	0.00327584i
$553$	3166.68	+	1687.87i	0.243510	+	0.129793i
$554$		−	2134.07i		−	0.163660i
$555$	−2332.75	+	12.2426i	−0.178414	+	0.000936338i
$556$	7899.71	−	4560.90i	0.602558	−	0.347887i
$557$	−863.961	+	498.808i	−0.0657221	+	0.0379447i	−0.532501	−	0.846429i	$-0.678748\pi$
$557$	−863.961	+	498.808i	−0.0657221	+	0.0379447i	0.466779	+	0.884374i	$0.345414\pi$
$558$	−15701.8	−	26548.8i	−1.19123	−	2.01416i
$559$			2726.09i			0.206263i
$560$	−4570.08	+	2849.27i	−0.344859	+	0.215006i
$561$	4580.72	−	2676.83i	0.344738	−	0.201454i
$562$	−7403.95	+	12824.0i	−0.555724	+	0.962542i
$563$	−5884.96	−	10193.0i	−0.440535	−	0.763030i	0.557194	−	0.830382i	$-0.311878\pi$
$563$	−5884.96	−	10193.0i	−0.440535	−	0.763030i	−0.997729	+	0.0673528i	$0.978545\pi$
$564$	4484.38	−	7862.18i	0.334799	−	0.586982i
$565$	4880.08	+	2817.52i	0.363374	+	0.209794i
$566$	3399.33			0.252446
$567$	−12045.2	−	6099.05i	−0.892150	−	0.451739i
$568$	2203.60			0.162783
$569$	−12969.2	−	7487.79i	−0.955534	−	0.551678i	−0.0607380	−	0.998154i	$-0.519345\pi$
$569$	−12969.2	−	7487.79i	−0.955534	−	0.551678i	−0.894796	+	0.446476i	$0.852679\pi$
$570$	1419.61	−	2488.92i	0.104318	−	0.182893i
$571$	−3729.38	−	6459.47i	−0.273327	−	0.473416i	0.696385	−	0.717669i	$-0.254791\pi$
$571$	−3729.38	−	6459.47i	−0.273327	−	0.473416i	−0.969712	+	0.244253i	$0.921457\pi$
$572$	202.110	−	350.065i	0.0147739	−	0.0255891i
$573$	11097.5	−	6485.04i	0.809084	−	0.472804i
$574$	7870.12	−	14765.4i	0.572287	−	1.07369i
$575$			86.0841i			0.00624340i
$576$	−8168.12	−	13810.8i	−0.590865	−	0.999044i
$577$	−15285.7	+	8825.21i	−1.10286	+	0.636739i	−0.936972	−	0.349405i	$-0.886384\pi$
$577$	−15285.7	+	8825.21i	−1.10286	+	0.636739i	−0.165892	+	0.986144i	$0.553050\pi$
$578$	−34049.4	+	19658.4i	−2.45029	+	1.41468i
$579$	−8720.30	+	45.7652i	−0.625912	+	0.00328486i
$580$		−	3155.41i		−	0.225899i
$581$	−890.963	−	26277.4i	−0.0636202	−	1.87637i
$582$	−325.877	−	557.656i	−0.0232097	−	0.0397175i
$583$	309.918	−	536.794i	0.0220163	−	0.0381333i
$584$	1400.11	+	2425.06i	0.0992071	+	0.171832i
$585$	7.79903	+	743.010i	0.000551197	+	0.0525123i
$586$	−5270.85	−	3043.13i	−0.371565	−	0.214523i
$587$	19139.8			1.34580			0.672900	−	0.739734i	$-0.265049\pi$
$587$	19139.8			1.34580			0.672900	+	0.739734i	$0.265049\pi$
$588$	15417.4	−	1128.00i	1.08130	−	0.0791125i
$589$	7556.25			0.528608
$590$	−6381.62	−	3684.43i	−0.445300	−	0.257094i
$591$	−20395.1	−	11632.8i	−1.41953	−	0.809664i
$592$	−2610.98	−	4522.35i	−0.181268	−	0.313966i
$593$	−9205.87	+	15945.0i	−0.637504	+	1.10419i	0.348475	+	0.937318i	$0.386700\pi$
$593$	−9205.87	+	15945.0i	−0.637504	+	1.10419i	−0.985979	+	0.166871i	$0.946634\pi$
$594$	−4850.02	+	76.3662i	−0.335015	+	0.00527499i
$595$	−378.400	−	11160.3i	−0.0260721	−	0.768952i
$596$			9464.53i			0.650473i
$597$	13.9288	+	2654.05i	0.000954887	+	0.181948i
$598$	67.0211	−	38.6947i	0.00458311	−	0.00264606i
$599$	9319.12	−	5380.39i	0.635674	−	0.367007i	−0.147272	−	0.989096i	$-0.547049\pi$
$599$	9319.12	−	5380.39i	0.635674	−	0.367007i	0.782946	+	0.622089i	$0.213716\pi$
$600$	1.87491	+	357.253i	0.000127571	+	0.0243080i
$601$			16893.6i			1.14660i	0.819347	+	0.573298i	$0.194336\pi$
$601$			16893.6i			1.14660i	−0.819347	+	0.573298i	$0.805664\pi$
$602$	−17617.8	+	33053.4i	−1.19277	+	2.23780i
$603$	−10230.1	+	18156.6i	−0.690885	+	1.22619i
$604$	−14506.0	+	25125.1i	−0.977218	+	1.69259i
$605$	−3148.27	−	5452.96i	−0.211562	−	0.366437i
$606$	−17885.2	−	10201.3i	−1.19891	−	0.683825i
$607$	10522.5	+	6075.17i	0.703617	+	0.406233i	0.808693	−	0.588231i	$-0.200175\pi$
$607$	10522.5	+	6075.17i	0.703617	+	0.406233i	−0.105076	+	0.994464i	$0.533509\pi$
$608$	7008.27			0.467472
$609$	3261.02	−	6196.24i	0.216984	−	0.412289i
$610$	13825.5			0.917670
$611$	−957.289	−	552.691i	−0.0633842	−	0.0365949i
$612$	28238.5	−	296.406i	1.86515	−	0.0195776i
$613$	10068.8	+	17439.6i	0.663416	+	1.14907i	0.979712	+	0.200410i	$0.0642274\pi$
$613$	10068.8	+	17439.6i	0.663416	+	1.14907i	−0.316296	+	0.948661i	$0.602439\pi$
$614$	−19565.5	+	33888.5i	−1.28599	+	2.22741i
$615$	2900.22	+	4962.99i	0.190159	+	0.325410i
$616$	365.966	−	228.166i	0.0239370	−	0.0149238i
$617$		−	17281.4i		−	1.12759i	−0.825914	−	0.563796i	$-0.809341\pi$
$617$		−	17281.4i		−	1.12759i	0.825914	−	0.563796i	$-0.190659\pi$
$618$	21948.8	−	115.190i	1.42866	−	0.00749778i
$619$	−12324.5	+	7115.55i	−0.800264	+	0.462033i	−0.843563	−	0.537030i	$-0.819546\pi$
$619$	−12324.5	+	7115.55i	−0.800264	+	0.462033i	0.0432995	+	0.999062i	$0.486213\pi$
$620$	−10507.4	+	6066.46i	−0.680626	+	0.392959i
$621$	−422.120	−	234.929i	−0.0272771	−	0.0151809i
$622$			9390.58i			0.605350i
$623$	−10157.0	−	5413.77i	−0.653180	−	0.348151i
$624$	−1436.10	+	839.213i	−0.0921315	+	0.0538388i
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	11246.4	+	19479.3i	0.718045	+	1.24369i
$627$	588.742	−	1032.20i	0.0374993	−	0.0657452i
$628$	−15766.8	−	9102.94i	−1.00185	−	0.578418i
$629$	10827.5			0.686362
$630$	−4707.27	+	9059.29i	−0.297686	+	0.572906i
$631$	−17950.2			−1.13247			−0.566233	−	0.824245i	$-0.691600\pi$
$631$	−17950.2			−1.13247			−0.566233	+	0.824245i	$0.691600\pi$
$632$	461.474	+	266.432i	0.0290450	+	0.0167692i
$633$	7360.95	−	12905.5i	0.462198	−	0.810342i
$634$	−8497.07	−	14717.4i	−0.532274	−	0.921926i
$635$	−4762.27	+	8248.49i	−0.297614	+	0.515482i
$636$	2848.54	−	1664.60i	0.177597	−	0.103782i
$637$	−127.875	−	1883.56i	−0.00795385	−	0.117158i
$638$		−	2515.61i		−	0.156103i
$639$	−18621.0	+	11013.0i	−1.15279	+	0.681797i
$640$	−1518.90	+	876.937i	−0.0938121	+	0.0541625i
$641$	2290.70	−	1322.53i	0.141150	−	0.0814929i	−0.427762	−	0.903891i	$-0.640698\pi$
$641$	2290.70	−	1322.53i	0.141150	−	0.0814929i	0.568912	+	0.822399i	$0.307365\pi$
$642$	7328.98	−	38.4634i	0.450548	−	0.00236453i
$643$			9632.67i			0.590786i	0.955376	+	0.295393i	$0.0954506\pi$
$643$			9632.67i			0.590786i	−0.955376	+	0.295393i	$0.904549\pi$
$644$	552.810	−	18.7436i	0.0338257	−	0.00114690i
$645$	−6492.34	−	11110.0i	−0.396334	−	0.678226i
$646$	−6649.62	+	11517.5i	−0.404993	+	0.701469i
$647$	6135.42	+	10626.9i	0.372810	+	0.645726i	0.989997	−	0.141091i	$-0.0450609\pi$
$647$	6135.42	+	10626.9i	0.372810	+	0.645726i	−0.617187	+	0.786817i	$0.711728\pi$
$648$	−1756.93	−	965.772i	−0.106511	−	0.0585480i
$649$	−2646.59	−	1528.01i	−0.160073	−	0.0924183i
$650$	561.873			0.0339054
$651$	−26902.7	+	1053.54i	−1.61966	+	0.0634278i
$652$	21661.8			1.30114
$653$	7275.75	+	4200.66i	0.436022	+	0.251737i	0.701909	−	0.712267i	$-0.252331\pi$
$653$	7275.75	+	4200.66i	0.436022	+	0.251737i	−0.265887	+	0.964004i	$0.585665\pi$
$654$	−14080.0	−	8030.88i	−0.841854	−	0.480172i
$655$	5110.81	+	8852.19i	0.304879	+	0.528066i
$656$	−6433.78	+	11143.6i	−0.382922	+	0.663241i
$657$	−23951.1	−	13495.0i	−1.42226	−	0.801355i
$658$	−8035.13	−	12887.9i	−0.476051	−	0.763563i
$659$			29704.2i			1.75586i	0.478792	+	0.877929i	$0.341075\pi$
$659$			29704.2i			1.75586i	−0.478792	+	0.877929i	$0.658925\pi$
$660$	10.0134	+	1908.00i	0.000590565	+	0.112529i
$661$	−1377.33	+	795.203i	−0.0810469	+	0.0467924i	−0.539976	−	0.841681i	$-0.681567\pi$
$661$	−1377.33	+	795.203i	−0.0810469	+	0.0467924i	0.458929	+	0.888473i	$0.348233\pi$
$662$	−15458.4	+	8924.93i	−0.907566	+	0.523984i
$663$	−18.0997	−	3448.80i	−0.00106023	−	0.202021i
$664$		−	3904.32i		−	0.228188i
$665$	−1323.21	−	2122.36i	−0.0771606	−	0.123762i
$666$	−8624.43	−	4859.34i	−0.501787	−	0.282726i
$667$	125.269	−	216.973i	0.00727203	−	0.0125955i
$668$	14438.4	+	25008.0i	0.836284	+	1.44849i
$669$	206.418	+	117.736i	0.0119291	+	0.00680407i
$670$	13647.5	+	7879.42i	0.786942	+	0.454341i
$671$	5733.72			0.329877
$672$	−24951.7	+	977.137i	−1.43234	+	0.0560921i
$673$	12890.7			0.738338			0.369169	−	0.929362i	$-0.379642\pi$
$673$	12890.7			0.738338			0.369169	+	0.929362i	$0.379642\pi$
$674$	−13751.6	−	7939.48i	−0.785892	−	0.453735i
$675$	−1801.31	−	3009.51i	−0.102714	−	0.171609i
$676$	9396.47	+	16275.2i	0.534620	+	0.925988i
$677$	1264.76	−	2190.62i	0.0718000	−	0.124361i	−0.827890	−	0.560890i	$-0.810459\pi$
$677$	1264.76	−	2190.62i	0.0718000	−	0.124361i	0.899690	+	0.436529i	$0.143792\pi$
$678$	12064.7	+	20645.7i	0.683394	+	1.16946i
$679$	−563.458	+	19.1046i	−0.0318461	+	0.00107978i
$680$		−	1658.20i		−	0.0935134i
$681$	2963.85	−	15.5547i	0.166777	−	0.000875266i
$682$	−8376.89	+	4836.40i	−0.470334	+	0.271547i
$683$	9705.06	−	5603.22i	0.543710	−	0.313911i	−0.202871	−	0.979205i	$-0.565027\pi$
$683$	9705.06	−	5603.22i	0.543710	−	0.313911i	0.746581	+	0.665294i	$0.231694\pi$
$684$	5444.17	−	3219.85i	0.304332	−	0.179991i
$685$			783.304i			0.0436913i
$686$	10622.4	−	23664.3i	0.591202	−	1.31707i
$687$	25368.1	−	14824.4i	1.40881	−	0.823267i
$688$	14402.5	−	24945.8i	0.798094	−	1.38234i
$689$	−201.462	−	348.942i	−0.0111395	−	0.0192941i
$690$	−180.987	+	317.312i	−0.00998557	+	0.0175071i
$691$	6536.69	+	3773.96i	0.359866	+	0.207769i	0.669022	−	0.743243i	$-0.266713\pi$
$691$	6536.69	+	3773.96i	0.359866	+	0.207769i	−0.309156	+	0.951011i	$0.600046\pi$
$692$	−2329.47			−0.127967
$693$	−1952.20	+	3757.07i	−0.107010	+	0.205944i
$694$	−39559.9			−2.16379
$695$	4553.93	+	2629.21i	0.248547	+	0.143499i
$696$	515.148	−	903.175i	0.0280555	−	0.0491879i
$697$	−13340.2	−	23105.9i	−0.724957	−	1.25566i
$698$	11360.5	−	19677.0i	0.616049	−	1.06703i
$699$	−3047.43	+	1780.82i	−0.164899	+	0.0963618i
$700$	3543.91	+	1888.94i	0.191353	+	0.101993i
$701$		−	6104.85i		−	0.328926i	−0.986383	−	0.164463i	$-0.947411\pi$
$701$		−	6104.85i		−	0.328926i	0.986383	−	0.164463i	$-0.0525891\pi$
$702$	−1533.39	+	2755.19i	−0.0824415	+	0.148131i
$703$	2100.19	−	1212.55i	0.112675	−	0.0650528i
$704$	−4357.70	+	2515.92i	−0.233291	+	0.134691i
$705$	5217.63	−	27.3828i	0.278734	−	0.00146283i
$706$			30907.1i			1.64760i
$707$	−15251.1	+	9508.49i	−0.811285	+	0.505804i
$708$	−8207.06	−	14044.3i	−0.435650	−	0.745505i
$709$	9505.45	−	16463.9i	0.503505	−	0.872096i	−0.496487	−	0.868044i	$-0.665377\pi$
$709$	9505.45	−	16463.9i	0.503505	−	0.872096i	0.999992	−	0.00405149i	$-0.00128963\pi$
$710$	8179.48	+	14167.3i	0.432352	+	0.748856i
$711$	−5231.14	+	54.9088i	−0.275926	+	0.00289626i
$712$	−1480.16	−	854.569i	−0.0779090	−	0.0449808i
$713$	−963.348			−0.0505998
$714$	22069.0	−	41933.1i	1.15674	−	2.19791i
$715$	233.020			0.0121880
$716$	12768.7	+	7371.99i	0.666463	+	0.384783i
$717$	−956.144	−	545.359i	−0.0498017	−	0.0284056i
$718$	−20983.7	−	36344.9i	−1.09068	−	1.88911i
$719$	10904.9	−	18887.9i	0.565625	−	0.979691i	−0.431366	−	0.902177i	$-0.641968\pi$
$719$	10904.9	−	18887.9i	0.565625	−	0.979691i	0.996991	−	0.0775144i	$-0.0246984\pi$
$720$	3854.10	−	6840.31i	0.199491	−	0.354060i
$721$	9011.67	−	16907.1i	0.465481	−	0.873307i
$722$		−	25028.8i		−	1.29013i
$723$	−3.12450	−	595.356i	−0.000160721	−	0.0306245i
$724$	19714.9	−	11382.4i	1.01202	−	0.584288i
$725$	1575.30	−	909.497i	0.0806966	−	0.0465902i
$726$	−140.225	−	26719.1i	−0.00716836	−	1.36589i
$727$		−	1336.38i		−	0.0681757i	−0.999419	−	0.0340878i	$-0.989147\pi$
$727$		−	1336.38i		−	0.0681757i	0.999419	−	0.0340878i	$-0.0108526\pi$
$728$	−9.49991	−	280.183i	−0.000483640	−	0.0142641i
$729$	19673.2	−	619.685i	0.999504	−	0.0314832i
$730$	−10394.1	+	18003.0i	−0.526988	+	0.912771i
$731$	29862.9	+	51724.1i	1.51097	+	2.61708i
$732$	26510.2	+	15120.7i	1.33859	+	0.763495i
$733$	4426.94	+	2555.90i	0.223074	+	0.128792i	0.607373	−	0.794417i	$-0.292224\pi$
$733$	4426.94	+	2555.90i	0.223074	+	0.128792i	−0.384299	+	0.923209i	$0.625557\pi$
$734$	25101.1			1.26226
$735$	5006.96	+	7371.80i	0.251272	+	0.369949i
$736$	−893.485			−0.0447477
$737$	5659.91	+	3267.75i	0.282884	+	0.163323i
$738$	256.026	+	24391.5i	0.0127703	+	1.21662i
$739$	−12541.2	−	21721.9i	−0.624268	−	1.08126i	−0.988682	−	0.150027i	$-0.952064\pi$
$739$	−12541.2	−	21721.9i	−0.624268	−	1.08126i	0.364414	−	0.931237i	$-0.381269\pi$
$740$	−1946.96	+	3372.24i	−0.0967186	+	0.167521i
$741$	−389.733	−	666.929i	−0.0193214	−	0.0330638i
$742$	−187.597	−	5532.86i	−0.00928155	−	0.273743i
$743$			10848.7i			0.535664i	0.963466	+	0.267832i	$0.0863073\pi$
$743$			10848.7i			0.535664i	−0.963466	+	0.267832i	$0.913693\pi$
$744$	−3997.94	+	20.9817i	−0.197005	+	0.00103391i
$745$	−4725.03	+	2728.00i	−0.232365	+	0.134156i
$746$	29810.2	−	17210.9i	1.46304	−	0.844686i
$747$	19512.8	+	32992.5i	0.955738	+	1.61597i
$748$		−	8856.06i		−	0.432900i
$749$	3009.11	−	5645.49i	0.146796	−	0.275410i
$750$	−2289.88	+	1338.13i	−0.111486	+	0.0651490i
$751$	8500.44	−	14723.2i	0.413030	−	0.715389i	−0.582189	−	0.813053i	$-0.697804\pi$
$751$	8500.44	−	14723.2i	0.413030	−	0.715389i	0.995219	+	0.0976641i	$0.0311371\pi$
$752$	5839.95	+	10115.1i	0.283193	+	0.490504i
$753$	17175.8	−	30113.3i	0.831238	−	1.45736i
$754$	−1416.19	−	817.635i	−0.0684011	−	0.0394914i
$755$	−16724.5			−0.806179
$756$	−18934.1	+	12222.8i	−0.910882	+	0.588014i
$757$	4378.07			0.210203			0.105102	−	0.994461i	$-0.466483\pi$
$757$	4378.07			0.210203			0.105102	+	0.994461i	$0.466483\pi$
$758$	−27146.0	−	15672.7i	−1.30077	−	0.751001i
$759$	−75.0588	+	131.596i	−0.00358954	+	0.00629331i
$760$	−185.698	−	321.638i	−0.00886311	−	0.0153514i
$761$	7619.87	−	13198.0i	0.362970	−	0.628682i	−0.625478	−	0.780241i	$-0.715096\pi$
$761$	7619.87	−	13198.0i	0.362970	−	0.628682i	0.988448	+	0.151560i	$0.0484295\pi$
$762$	−34896.0	+	20392.2i	−1.65899	+	0.969462i
$763$	−12006.4	+	7485.50i	−0.569672	+	0.355168i
$764$		−	21455.2i		−	1.01600i
$765$	8287.27	+	14012.2i	0.391669	+	0.662240i
$766$	41036.9	−	23692.6i	1.93567	−	1.11756i
$767$	−1720.41	+	993.279i	−0.0809914	+	0.0467604i
$768$	17260.7	−	90.5865i	0.810994	−	0.00425619i
$769$		−	16240.8i		−	0.761583i	−0.924661	−	0.380792i	$-0.875652\pi$
$769$		−	16240.8i		−	0.761583i	0.924661	−	0.380792i	$-0.124348\pi$
$770$	2825.33	+	1505.93i	0.132231	+	0.0704805i
$771$	−6155.58	−	10533.7i	−0.287533	−	0.492040i
$772$	−7278.14	+	12606.1i	−0.339308	+	0.587699i
$773$	−20102.7	−	34819.0i	−0.935375	−	1.62012i	−0.773963	−	0.633230i	$-0.781729\pi$
$773$	−20102.7	−	34819.0i	−0.935375	−	1.62012i	−0.161412	−	0.986887i	$-0.551605\pi$
$774$	−573.132	−	54602.0i	−0.0266160	−	2.53570i
$775$	−6057.18	−	3497.12i	−0.280749	−	0.162090i
$776$	−83.7190			−0.00387286
$777$	−7308.31	+	4609.89i	−0.337432	+	0.212843i
$778$	−3274.61			−0.150900
$779$	−5175.14	−	2987.87i	−0.238021	−	0.137422i
$780$	1077.38	+	614.511i	0.0494571	+	0.0282090i
$781$	3392.19	+	5875.45i	0.155419	+	0.269193i
$782$	847.761	−	1468.36i	0.0387671	−	0.0671466i
$783$	160.709	+	10206.6i	0.00733496	+	0.465844i
$784$	−8781.08	+	17911.6i	−0.400013	+	0.815946i
$785$		−	10495.1i		−	0.477180i
$786$	227.637	+	43375.0i	0.0103302	+	1.96836i
$787$	−5358.79	+	3093.90i	−0.242719	+	0.140134i	−0.616426	−	0.787413i	$-0.711420\pi$
$787$	−5358.79	+	3093.90i	−0.242719	+	0.140134i	0.373707	+	0.927547i	$0.378087\pi$
$788$	−33941.5	+	19596.2i	−1.53441	+	0.885894i
$789$	197.808	+	37691.2i	0.00892540	+	1.70069i
$790$			3955.85i			0.178156i
$791$	20860.5	−	707.296i	0.937690	−	0.0317933i
$792$	−308.631	+	547.764i	−0.0138469	+	0.0245757i
$793$	1863.60	−	3227.85i	0.0834531	−	0.144545i
$794$	−18823.7	−	32603.5i	−0.841343	−	1.45725i
$795$	1652.07	+	942.298i	0.0737018	+	0.0420376i
$796$	3836.71	+	2215.13i	0.170840	+	0.0986346i
$797$	−34131.6			−1.51694			−0.758471	−	0.651707i	$-0.774053\pi$
$797$	−34131.6			−1.51694			−0.758471	+	0.651707i	$0.774053\pi$
$798$	−415.309	−	10605.1i	−0.0184233	−	0.470448i
$799$	−24217.8			−1.07230
$800$	−5617.91	−	3243.50i	−0.248279	−	0.143344i
$801$	16778.6	−	176.118i	0.740130	−	0.00776880i
$802$	4448.48	+	7705.00i	0.195862	+	0.339243i
$803$	−4310.63	+	7466.22i	−0.189438	+	0.328116i
$804$	17551.4	+	30034.8i	0.769888	+	1.31747i
$805$	168.696	+	270.580i	0.00738602	+	0.0118468i
$806$			6287.80i			0.274787i
$807$	8283.33	−	43.4719i	0.361322	−	0.00189626i
$808$	−2311.27	+	1334.41i	−0.100632	+	0.0580996i
$809$	−27867.5	+	16089.3i	−1.21109	+	0.699222i	−0.962996	−	0.269515i	$-0.913137\pi$
$809$	−27867.5	+	16089.3i	−1.21109	+	0.699222i	−0.248091	+	0.968737i	$0.579803\pi$
$810$	−312.420	−	14880.4i	−0.0135523	−	0.645488i
$811$			19444.4i			0.841906i	0.907083	+	0.420953i	$0.138304\pi$
$811$			19444.4i			0.841906i	−0.907083	+	0.420953i	$0.861696\pi$
$812$	−6183.55	−	9918.11i	−0.267242	−	0.428642i
$813$	11928.0	−	6970.33i	0.514553	−	0.300689i
$814$	−1552.19	+	2688.47i	−0.0668356	+	0.115763i
$815$	6243.66	+	10814.3i	0.268351	+	0.464797i
$816$	−18055.0	+	31654.7i	−0.774575	+	1.35801i
$817$	11584.9	+	6688.54i	0.496089	+	0.286417i
$818$	11346.2			0.484977
$819$	1480.56	+	2320.15i	0.0631686	+	0.0989896i
$820$	9595.11			0.408629
$821$	−319.413	−	184.413i	−0.0135781	−	0.00783931i	0.493196	−	0.869918i	$-0.335829\pi$
$821$	−319.413	−	184.413i	−0.0135781	−	0.00783931i	−0.506774	+	0.862079i	$0.669162\pi$
$822$	−1646.85	+	2887.32i	−0.0698790	+	0.122514i
$823$	6812.44	+	11799.5i	0.288538	+	0.499762i	0.973461	−	0.228853i	$-0.0734975\pi$
$823$	6812.44	+	11799.5i	0.288538	+	0.499762i	−0.684923	+	0.728615i	$0.740164\pi$
$824$	1422.50	−	2463.84i	0.0601397	−	0.104165i
$825$	−949.658	+	554.951i	−0.0400762	+	0.0234193i
$826$	−27279.0	+	924.921i	−1.14910	+	0.0389614i
$827$			25985.7i			1.09264i	0.837578	+	0.546318i	$0.183971\pi$
$827$			25985.7i			1.09264i	−0.837578	+	0.546318i	$0.816029\pi$
$828$	−694.078	+	410.499i	−0.0291315	+	0.0172293i
$829$	20752.9	−	11981.7i	0.869455	−	0.501980i	0.00228780	−	0.999997i	$-0.499272\pi$
$829$	20752.9	−	11981.7i	0.869455	−	0.501980i	0.867167	+	0.498017i	$0.165938\pi$
$830$	25101.5	−	14492.3i	1.04974	−	0.606068i
$831$	2715.63	−	14.2520i	0.113362	−	0.000594939i
$832$			3270.94i			0.136297i
$833$	−23059.8	−	34337.4i	−0.959151	−	1.42824i
$834$	11258.3	+	19265.8i	0.467440	+	0.799905i
$835$	−8323.26	+	14416.3i	−0.344956	+	0.597481i
$836$	−991.768	−	1717.79i	−0.0410299	−	0.0710659i
$837$	33678.8	−	20158.0i	1.39081	−	0.832452i
$838$	−7444.30	−	4297.97i	−0.306872	−	0.177173i
$839$	26831.1			1.10407			0.552034	−	0.833822i	$-0.313852\pi$
$839$	26831.1			1.10407			0.552034	+	0.833822i	$0.313852\pi$
$840$	705.989	+	1119.24i	0.0289987	+	0.0459733i
$841$	19095.0			0.782936
$842$	−3229.41	−	1864.50i	−0.132177	−	0.0763123i
$843$	−16368.2	−	9335.98i	−0.668743	−	0.381433i
$844$	−12399.9	−	21477.3i	−0.505714	−	0.875922i
$845$	−5416.76	+	9382.11i	−0.220523	+	0.381958i
$846$	19290.2	+	10868.8i	0.783935	+	0.441700i
$847$	−20581.6	−	10970.2i	−0.834938	−	0.445030i
$848$			4257.45i			0.172407i
$849$	22.7018	+	4325.69i	0.000917694	+	0.174861i
$850$	10660.8	−	6155.03i	0.430192	−	0.248372i
$851$	−267.754	+	154.588i	−0.0107855	+	0.00622703i
$852$	189.516	+	36111.3i	0.00762057	+	1.45206i
$853$			27485.0i			1.10324i	0.834094	+	0.551622i	$0.185991\pi$
$853$			27485.0i			1.10324i	−0.834094	+	0.551622i	$0.814009\pi$
$854$	43456.4	−	27093.4i	1.74127	−	1.08562i
$855$	3176.66	+	1789.86i	0.127064	+	0.0715927i
$856$	474.990	−	822.707i	0.0189659	−	0.0328499i
$857$	−23661.3	−	40982.6i	−0.943122	−	1.63353i	−0.759469	−	0.650543i	$-0.774541\pi$
$857$	−23661.3	−	40982.6i	−0.943122	−	1.63353i	−0.183652	−	0.982991i	$-0.558792\pi$
$858$	858.929	+	489.911i	0.0341764	+	0.0194933i
$859$	−24680.1	−	14249.1i	−0.980295	−	0.565974i	−0.0779360	−	0.996958i	$-0.524833\pi$
$859$	−24680.1	−	14249.1i	−0.980295	−	0.565974i	−0.902359	+	0.430985i	$0.858166\pi$
$860$	−21479.3			−0.851673
$861$	18841.8	+	9916.23i	0.745790	+	0.392502i
$862$	51899.0			2.05068
$863$	−9407.77	−	5431.58i	−0.371082	−	0.214245i	0.302849	−	0.953039i	$-0.402062\pi$
$863$	−9407.77	−	5431.58i	−0.371082	−	0.214245i	−0.673931	+	0.738794i	$0.735396\pi$
$864$	31236.4	−	18696.1i	1.22996	−	0.736175i
$865$	−671.431	−	1162.95i	−0.0263923	−	0.0457128i
$866$	−7305.06	+	12652.7i	−0.286647	+	0.496487i
$867$	−25243.0	−	43197.1i	−0.988810	−	1.69210i
$868$	−21138.7	+	39659.1i	−0.826606	+	1.55083i
$869$			1640.57i			0.0640421i
$870$	7718.82	−	40.5093i	0.300796	−	0.00157861i
$871$	3679.22	−	2124.20i	0.143129	−	0.0826357i
$872$	−1819.53	+	1050.51i	−0.0706619	+	0.0407967i
$873$	707.448	−	418.407i	0.0274267	−	0.0162210i
$874$		−	379.754i		−	0.0146972i
$875$	78.4485	+	2313.70i	0.00303091	+	0.0893914i
$876$	−39620.1	+	23152.8i	−1.52813	+	0.892990i
$877$	1474.02	−	2553.08i	0.0567550	−	0.0983026i	−0.836252	−	0.548345i	$-0.815258\pi$
$877$	1474.02	−	2553.08i	0.0567550	−	0.0983026i	0.893007	+	0.450043i	$0.148591\pi$
$878$	26499.2	+	45898.0i	1.01857	+	1.76422i
$879$	3837.22	−	6727.55i	0.147243	−	0.258151i
$880$	−2132.31	−	1231.09i	−0.0816820	−	0.0471591i
$881$	−30150.3			−1.15299			−0.576497	−	0.817099i	$-0.695581\pi$
$881$	−30150.3			−1.15299			−0.576497	+	0.817099i	$0.695581\pi$
$882$	2957.27	+	37699.8i	0.112898	+	1.43925i
$883$	−13452.4			−0.512693			−0.256347	−	0.966585i	$-0.582519\pi$
$883$	−13452.4			−0.512693			−0.256347	+	0.966585i	$0.582519\pi$
$884$	−4985.60	−	2878.44i	−0.189688	−	0.109516i
$885$	4645.87	−	8145.30i	0.176462	−	0.309380i
$886$	23012.2	+	39858.4i	0.872586	+	1.51136i
$887$	11083.7	−	19197.6i	0.419566	−	0.726710i	−0.576330	−	0.817217i	$-0.695516\pi$
$887$	11083.7	−	19197.6i	0.419566	−	0.726710i	0.995896	+	0.0905075i	$0.0288489\pi$
$888$	−1107.83	+	647.379i	−0.0418651	+	0.0244646i
$889$	1195.50	+	35259.1i	0.0451020	+	1.33021i
$890$		−	12688.2i		−	0.477876i
$891$	−129.567	−	6171.21i	−0.00487167	−	0.232035i
$892$	343.521	−	198.332i	0.0128945	−	0.00744467i
$893$	−4697.48	+	2712.09i	−0.176030	+	0.101631i
$894$	−23152.3	+	121.506i	−0.866138	+	0.00454560i
$895$			8499.43i			0.317435i
$896$	−3055.71	+	5732.92i	−0.113933	+	0.213754i
$897$	49.6871	+	85.0269i	0.00184950	+	0.00316496i
$898$	29219.8	−	50610.2i	1.08583	−	1.88072i
$899$	10178.0	+	17628.8i	0.377591	+	0.654007i
$900$	−5854.30	+	61.4498i	−0.216826	+	0.00227592i
$901$	−7644.97	−	4413.83i	−0.282676	−	0.163203i
$902$	7649.57			0.282376
$903$	−42178.6	−	22198.2i	−1.55439	−	0.818060i
$904$	3099.46			0.114034
$905$	11365.0	+	6561.60i	0.417443	+	0.241011i
$906$	−61647.6	−	35162.2i	−2.26060	−	1.28939i
$907$	6575.84	+	11389.7i	0.240736	+	0.416966i	0.960924	−	0.276812i	$-0.0892780\pi$
$907$	6575.84	+	11389.7i	0.240736	+	0.416966i	−0.720188	+	0.693778i	$0.755945\pi$
$908$	2473.69	−	4284.56i	0.0904101	−	0.156595i
$909$	12861.8	−	22827.3i	0.469306	−	0.832930i
$910$	1766.08	−	1101.08i	0.0643352	−	0.0401105i
$911$		−	34821.8i		−	1.26641i	−0.773985	−	0.633204i	$-0.781739\pi$
$911$		−	34821.8i		−	1.26641i	0.773985	−	0.633204i	$-0.218261\pi$
$912$	42.8349	+	8161.95i	0.00155527	+	0.296348i
$913$	10410.1	−	6010.26i	0.377353	−	0.217865i
$914$	5735.33	−	3311.29i	0.207558	−	0.119834i
$915$	92.3310	+	17593.1i	0.00333592	+	0.635641i
$916$		−	49045.0i		−	1.76910i
$917$	33411.6	+	17808.7i	1.20322	+	0.641326i
$918$	1087.60	+	69073.6i	0.0391026	+	2.48341i
$919$	−10471.5	+	18137.1i	−0.375867	+	0.651021i	−0.990456	−	0.137826i	$-0.955988\pi$
$919$	−10471.5	+	18137.1i	−0.375867	+	0.651021i	0.614589	+	0.788847i	$0.289322\pi$
$920$	23.6746	+	41.0057i	0.000848401	+	0.00146947i
$921$	−43254.2	−	24671.1i	−1.54753	−	0.882671i
$922$	−64494.4	−	37235.8i	−2.30370	−	1.33004i
$923$	4410.18			0.157273
$924$	3770.52	+	5977.62i	0.134244	+	0.212824i
$925$	−2244.72			−0.0797902
$926$	−52214.4	−	30146.0i	−1.85299	−	1.06983i
$927$	293.162	+	27929.4i	0.0103870	+	0.989561i
$928$	9439.86	+	16350.3i	0.333921	+	0.578368i
$929$	−19211.5	+	33275.3i	−0.678482	+	1.17516i	0.296957	+	0.954891i	$0.404028\pi$
$929$	−19211.5	+	33275.3i	−0.678482	+	1.17516i	−0.975438	+	0.220273i	$0.929305\pi$
$930$	−14974.7	−	25625.5i	−0.528001	−	0.903541i
$931$	−8318.22	−	4077.96i	−0.292823	−	0.143555i
$932$			5891.69i			0.207069i
$933$	−11949.6	+	62.7131i	−0.419307	+	0.00220057i
$934$	−26648.2	+	15385.3i	−0.933571	+	0.538997i
$935$	4421.26	−	2552.62i	0.154642	−	0.0892828i
$936$	208.056	+	351.784i	0.00726551	+	0.0122846i
$937$		−	2693.78i		−	0.0939188i	−0.998897	−	0.0469594i	$-0.985047\pi$
$937$		−	2693.78i		−	0.0939188i	0.998897	−	0.0469594i	$-0.0149531\pi$
$938$	58338.0	−	1978.01i	2.03071	−	0.0688532i
$939$	−24712.6	+	14441.3i	−0.858855	+	0.501889i
$940$	4354.74	−	7542.64i	0.151102	−	0.261717i
$941$	3096.77	+	5363.75i	0.107281	+	0.185817i	0.914668	−	0.404206i	$-0.132452\pi$
$941$	3096.77	+	5363.75i	0.107281	+	0.185817i	−0.807387	+	0.590023i	$0.799119\pi$
$942$	22065.3	−	38685.7i	0.763192	−	1.33806i
$943$	659.779	+	380.923i	0.0227840	+	0.0131544i
$944$	20990.8			0.723719
$945$	−11559.5	−	5929.56i	−0.397916	−	0.204115i
$946$	−17124.1			−0.588533
$947$	23917.9	+	13809.0i	0.820726	+	0.473846i	0.850667	−	0.525705i	$-0.176199\pi$
$947$	23917.9	+	13809.0i	0.820726	+	0.473846i	−0.0299408	+	0.999552i	$0.509532\pi$
$948$	−4326.45	+	7585.29i	−0.148224	+	0.259872i
$949$	2802.12	+	4853.41i	0.0958489	+	0.166015i
$950$	1378.57	−	2387.76i	0.0470809	−	0.0815465i
$951$	18671.3	−	10910.9i	0.636654	−	0.372041i
$952$	−3249.52	−	5212.06i	−0.110628	−	0.177441i
$953$			27371.0i			0.930361i	0.885216	+	0.465181i	$0.154011\pi$
$953$			27371.0i			0.930361i	−0.885216	+	0.465181i	$0.845989\pi$
$954$	4108.53	+	6946.76i	0.139432	+	0.235754i
$955$	10711.2	−	6184.10i	0.362938	−	0.209542i
$956$	−1591.21	+	918.688i	−0.0538321	+	0.0310800i
$957$	3201.15	−	16.8000i	0.108128	−	0.000567469i
$958$		−	13407.9i		−	0.452181i
$959$	1535.01	+	2462.08i	0.0516873	+	0.0829039i
$960$	−7789.93	−	13330.5i	−0.261895	−	0.448167i
$961$	24239.9	−	41984.8i	0.813666	−	1.40931i
$962$	1009.00	+	1747.64i	0.0338165	+	0.0585718i
$963$	97.8904	+	9325.97i	0.00327567	+	0.312072i
$964$	−860.649	−	496.896i	−0.0287548	−	0.0166016i
$965$	−8391.23			−0.279920
$966$	52.9478	+	1352.05i	0.00176353	+	0.0450326i
$967$	46696.9			1.55292			0.776458	−	0.630169i	$-0.217014\pi$
$967$	46696.9			1.55292			0.776458	+	0.630169i	$0.217014\pi$
$968$	−2999.32	−	1731.66i	−0.0995886	−	0.0574975i
$969$	−14700.6	−	8384.81i	−0.487358	−	0.277976i
$970$	−310.755	−	538.243i	−0.0102863	−	0.0178164i
$971$	−1836.88	+	3181.58i	−0.0607090	+	0.105151i	−0.894783	−	0.446502i	$-0.852669\pi$
$971$	−1836.88	+	3181.58i	−0.0607090	+	0.105151i	0.834074	+	0.551653i	$0.186003\pi$
$972$	15675.4	−	28874.7i	0.517273	−	0.952835i
$973$	19466.3	−	660.024i	0.641377	−	0.0217466i
$974$			41708.8i			1.37211i
$975$	3.75236	+	714.991i	0.000123253	+	0.0234852i
$976$	−34106.7	+	19691.5i	−1.11857	+	0.645809i
$977$	−49808.3	+	28756.9i	−1.63102	+	0.941672i	−0.647245	+	0.762282i	$0.724079\pi$
$977$	−49808.3	+	28756.9i	−1.63102	+	0.941672i	−0.983778	+	0.179390i	$0.942588\pi$
$978$	278.095	+	52989.4i	0.00909252	+	1.73253i
$979$		−	5262.06i		−	0.171784i
$980$	14840.9	−	1007.55i	0.483751	−	0.0328419i
$981$	10125.4	−	17970.7i	0.329539	−	0.584871i
$982$	2751.26	−	4765.32i	0.0894055	−	0.154855i
$983$	−12783.7	−	22142.1i	−0.414790	−	0.718437i	0.580617	−	0.814177i	$-0.302812\pi$
$983$	−12783.7	−	22142.1i	−0.414790	−	0.718437i	−0.995406	+	0.0957402i	$0.969478\pi$
$984$	2746.41	+	1566.48i	0.0889760	+	0.0507496i
$985$	−19566.2	−	11296.5i	−0.632925	−	0.365419i
$986$	−35827.1			−1.15717
$987$	16346.4	−	10310.9i	0.527165	−	0.332522i
$988$	−1289.40			−0.0415194
$989$	−1476.96	−	852.723i	−0.0474870	−	0.0274166i
$990$	−4667.26	+	48.9900i	−0.149834	+	0.00157273i
$991$	12003.2	+	20790.2i	0.384757	+	0.666419i	0.991736	−	0.128299i	$-0.0409518\pi$
$991$	12003.2	+	20790.2i	0.384757	+	0.666419i	−0.606978	+	0.794719i	$0.707618\pi$
$992$	36297.3	−	62868.8i	1.16173	−	2.01218i
$993$	−11460.3	−	19611.4i	−0.366246	−	0.626738i
$994$	53472.8	+	28501.6i	1.70629	+	0.909471i
$995$			2553.90i			0.0813709i
$996$	63981.7	−	335.784i	2.03548	−	0.0106824i
$997$	−49562.8	+	28615.1i	−1.57439	+	0.908976i	−0.578771	+	0.815490i	$0.696468\pi$
$997$	−49562.8	+	28615.1i	−1.57439	+	0.908976i	−0.995621	+	0.0934855i	$0.970199\pi$
$998$	44243.9	−	25544.2i	1.40332	−	0.810208i
$999$	6125.98	−	11007.2i	0.194011	−	0.348600i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.s.a.26.13	✓	32
3.2	odd	2		105.4.s.b.26.4	yes	32
7.3	odd	6		105.4.s.b.101.4	yes	32
21.17	even	6	inner	105.4.s.a.101.13	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.s.a.26.13	✓	32	1.1	even	1	trivial
105.4.s.a.101.13	yes	32	21.17	even	6	inner
105.4.s.b.26.4	yes	32	3.2	odd	2
105.4.s.b.101.4	yes	32	7.3	odd	6

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)

\(f(q)\)	\(=\)	\(q+(3.53626 + 2.04166i) q^{2} +(-2.57442 + 4.51357i) q^{3} +(4.33676 + 7.51148i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-18.3190 + 10.7051i) q^{6} +(0.627588 + 18.5096i) q^{7} +2.75017i q^{8} +(-13.7447 - 23.2397i) q^{9} +O(q^{10})\)	\(q+(3.53626 + 2.04166i) q^{2} +(-2.57442 + 4.51357i) q^{3} +(4.33676 + 7.51148i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-18.3190 + 10.7051i) q^{6} +(0.627588 + 18.5096i) q^{7} +2.75017i q^{8} +(-13.7447 - 23.2397i) q^{9} +(-17.6813 + 10.2083i) q^{10} +(-7.33279 + 4.23359i) q^{11} +(-45.0683 + 0.236524i) q^{12} +5.50408i q^{13} +(-35.5711 + 66.7362i) q^{14} +(-13.1083 - 22.4315i) q^{15} +(29.0791 - 50.3665i) q^{16} +(60.2944 + 104.433i) q^{17} +(-1.15718 - 110.244i) q^{18} +(23.3904 + 13.5044i) q^{19} -43.3676 q^{20} +(-85.1602 - 44.8190i) q^{21} -34.5742 q^{22} +(-2.98204 - 1.72168i) q^{23} +(-12.4131 - 7.08012i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(-11.2375 + 19.4639i) q^{26} +(140.279 - 2.20876i) q^{27} +(-136.313 + 84.9859i) q^{28} +72.7598i q^{29} +(-0.556754 - 106.086i) q^{30} +(242.287 - 139.885i) q^{31} +(224.717 - 129.740i) q^{32} +(-0.230897 - 43.9961i) q^{33} +492.403i q^{34} +(-81.7180 - 43.5565i) q^{35} +(114.957 - 204.028i) q^{36} +(44.8944 - 77.7594i) q^{37} +(55.1429 + 95.5104i) q^{38} +(-24.8431 - 14.1698i) q^{39} +(-11.9086 - 6.87544i) q^{40} -221.251 q^{41} +(-209.644 - 332.360i) q^{42} +495.285 q^{43} +(-63.6010 - 36.7201i) q^{44} +(134.993 - 1.41695i) q^{45} +(-7.03018 - 12.1766i) q^{46} +(-100.415 + 173.923i) q^{47} +(152.471 + 260.916i) q^{48} +(-342.212 + 23.2328i) q^{49} -102.083i q^{50} +(-626.589 + 3.28842i) q^{51} +(-41.3438 + 23.8699i) q^{52} +(-63.3970 + 36.6023i) q^{53} +(500.572 + 278.591i) q^{54} -42.3359i q^{55} +(-50.9047 + 1.72598i) q^{56} +(-121.170 + 70.8080i) q^{57} +(-148.551 + 257.297i) q^{58} +(180.462 + 312.570i) q^{59} +(111.647 - 195.743i) q^{60} +(-586.446 - 338.585i) q^{61} +1142.39 q^{62} +(421.532 - 268.994i) q^{63} +594.275 q^{64} +(-23.8334 - 13.7602i) q^{65} +(89.0086 - 156.053i) q^{66} +(-385.932 - 668.453i) q^{67} +(-522.964 + 905.801i) q^{68} +(15.4480 - 9.02732i) q^{69} +(-200.048 - 320.868i) q^{70} -801.257i q^{71} +(63.9132 - 37.8003i) q^{72} +(881.784 - 509.098i) q^{73} +(317.517 - 183.318i) q^{74} +(129.902 - 0.681742i) q^{75} +234.262i q^{76} +(-82.9641 - 133.070i) q^{77} +(-58.9215 - 100.829i) q^{78} +(96.8783 - 167.798i) q^{79} +(145.396 + 251.833i) q^{80} +(-351.168 + 638.845i) q^{81} +(-782.400 - 451.719i) q^{82} -1419.66 q^{83} +(-32.6623 - 834.048i) q^{84} -602.944 q^{85} +(1751.46 + 1011.20i) q^{86} +(-328.407 - 187.315i) q^{87} +(-11.6431 - 20.1664i) q^{88} +(-310.733 + 538.205i) q^{89} +(480.262 + 270.598i) q^{90} +(-101.878 + 3.45429i) q^{91} -29.8661i q^{92} +(7.62922 + 1453.70i) q^{93} +(-710.186 + 410.026i) q^{94} +(-116.952 + 67.5222i) q^{95} +(7.07594 + 1348.28i) q^{96} +30.4414i q^{97} +(-1257.59 - 616.524i) q^{98} +(199.174 + 112.223i) 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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