LMFDB - Embedded newform 105.4.s.b.26.4

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			26.4
Character	$\chi$	$=$	105.26
Dual form			105.4.s.b.101.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.53626 - 2.04166i) q^{2} +(-5.19608 - 0.0272697i) q^{3} +(4.33676 + 7.51148i) q^{4} +(2.50000 - 4.33013i) q^{5} +(18.3190 + 10.7051i) q^{6} +(0.627588 + 18.5096i) q^{7} -2.75017i q^{8} +(26.9985 + 0.283391i) q^{9} +O(q^{10})$	\(q+(-3.53626 - 2.04166i) q^{2} +(-5.19608 - 0.0272697i) 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} +(26.9985 + 0.283391i) q^{9} +(-17.6813 + 10.2083i) q^{10} +(7.33279 - 4.23359i) q^{11} +(-22.3293 - 39.1485i) 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} +(-94.8952 - 56.1239i) q^{18} +(23.3904 + 13.5044i) q^{19} +43.3676 q^{20} +(-2.75625 - 96.1946i) q^{21} -34.5742 q^{22} +(2.98204 + 1.72168i) q^{23} +(-0.0749963 + 14.2901i) 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} +(92.1518 - 52.5610i) q^{30} +(242.287 - 139.885i) q^{31} +(-224.717 + 129.740i) q^{32} +(-38.2172 + 21.7981i) 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} +(0.150094 - 28.5996i) q^{39} +(-11.9086 - 6.87544i) q^{40} +221.251 q^{41} +(-186.650 + 345.796i) q^{42} +495.285 q^{43} +(63.6010 + 36.7201i) q^{44} +(68.7234 - 116.199i) 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} +(310.447 + 544.286i) q^{51} +(-41.3438 + 23.8699i) q^{52} +(63.3970 - 36.6023i) q^{53} +(491.553 + 294.212i) 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} +(-225.341 - 1.18262i) q^{60} +(-586.446 - 338.585i) q^{61} -1142.39 q^{62} +(11.6985 + 499.910i) q^{63} +594.275 q^{64} +(23.8334 + 13.7602i) q^{65} +(179.650 + 0.942827i) 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} +(0.779374 - 74.2506i) q^{72} +(881.784 - 509.098i) q^{73} +(-317.517 + 183.318i) q^{74} +(64.3606 + 112.839i) 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} +(728.839 + 15.3023i) q^{81} +(-782.400 - 451.719i) q^{82} +1419.66 q^{83} +(710.611 - 437.876i) q^{84} -602.944 q^{85} +(-1751.46 - 1011.20i) q^{86} +(-1.98413 + 378.066i) 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} +(-1262.76 + 720.245i) q^{93} +(-710.186 + 410.026i) q^{94} +(116.952 - 67.5222i) q^{95} +(1171.18 - 668.012i) 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} - 98 q^{9}+O(q^{10}) $ 32 * q + 2 * q^3 + 64 * q^4 + 80 * q^5 + 28 * q^6 + 46 * q^7 - 98 * q^9	\( 32 q + 2 q^{3} + 64 q^{4} + 80 q^{5} + 28 q^{6} + 46 q^{7} - 98 q^{9} - 36 q^{11} + 84 q^{12} - 18 q^{14} + 20 q^{15} - 376 q^{16} + 72 q^{17} + 260 q^{18} - 198 q^{19} + 640 q^{20} - 256 q^{21} + 204 q^{22} - 72 q^{23} - 94 q^{24} - 400 q^{25} + 312 q^{26} - 508 q^{27} + 350 q^{28} + 100 q^{30} + 510 q^{31} - 810 q^{32} + 454 q^{33} + 70 q^{35} - 612 q^{36} - 658 q^{37} + 192 q^{38} + 576 q^{39} + 1404 q^{41} - 1790 q^{42} + 332 q^{43} - 2034 q^{44} - 500 q^{45} - 468 q^{46} - 408 q^{47} - 2810 q^{48} + 980 q^{49} + 2748 q^{51} + 3378 q^{52} - 1152 q^{53} + 3322 q^{54} + 3354 q^{56} - 816 q^{57} - 1080 q^{58} + 48 q^{59} + 1230 q^{60} - 1662 q^{61} + 2076 q^{62} - 2306 q^{63} - 1952 q^{64} - 870 q^{65} - 3808 q^{66} - 1298 q^{67} - 1182 q^{68} - 2450 q^{69} - 450 q^{70} + 7678 q^{72} + 378 q^{73} - 2898 q^{74} + 50 q^{75} + 3528 q^{77} - 1896 q^{78} - 326 q^{79} + 1880 q^{80} + 1774 q^{81} - 2916 q^{82} + 1536 q^{83} - 10680 q^{84} + 720 q^{85} - 5202 q^{86} - 5666 q^{87} + 1668 q^{88} + 1590 q^{89} - 910 q^{90} + 2082 q^{91} + 4086 q^{93} - 1152 q^{94} - 990 q^{95} + 3996 q^{96} + 7830 q^{98} + 3128 q^{99}+O(q^{100}) \) 32 * q + 2 * q^3 + 64 * q^4 + 80 * q^5 + 28 * q^6 + 46 * q^7 - 98 * q^9 - 36 * q^11 + 84 * q^12 - 18 * q^14 + 20 * q^15 - 376 * q^16 + 72 * q^17 + 260 * q^18 - 198 * q^19 + 640 * q^20 - 256 * q^21 + 204 * q^22 - 72 * q^23 - 94 * q^24 - 400 * q^25 + 312 * q^26 - 508 * q^27 + 350 * q^28 + 100 * q^30 + 510 * q^31 - 810 * q^32 + 454 * q^33 + 70 * q^35 - 612 * q^36 - 658 * q^37 + 192 * q^38 + 576 * q^39 + 1404 * q^41 - 1790 * q^42 + 332 * q^43 - 2034 * q^44 - 500 * q^45 - 468 * q^46 - 408 * q^47 - 2810 * q^48 + 980 * q^49 + 2748 * q^51 + 3378 * q^52 - 1152 * q^53 + 3322 * q^54 + 3354 * q^56 - 816 * q^57 - 1080 * q^58 + 48 * q^59 + 1230 * q^60 - 1662 * q^61 + 2076 * q^62 - 2306 * q^63 - 1952 * q^64 - 870 * q^65 - 3808 * q^66 - 1298 * q^67 - 1182 * q^68 - 2450 * q^69 - 450 * q^70 + 7678 * q^72 + 378 * q^73 - 2898 * q^74 + 50 * q^75 + 3528 * q^77 - 1896 * q^78 - 326 * q^79 + 1880 * q^80 + 1774 * q^81 - 2916 * q^82 + 1536 * q^83 - 10680 * q^84 + 720 * q^85 - 5202 * q^86 - 5666 * q^87 + 1668 * q^88 + 1590 * q^89 - 910 * q^90 + 2082 * q^91 + 4086 * q^93 - 1152 * q^94 - 990 * q^95 + 3996 * 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	−0.279096	−	0.960263i	$-0.590035\pi$
$2$	−3.53626	−	2.04166i	−1.25026	−	0.721836i	−0.971160	+	0.238427i	$0.923368\pi$
$3$	−5.19608	−	0.0272697i	−0.999986	−	0.00524805i
$3$	−5.19608	−	0.0272697i	−0.999986	−	0.00524805i
$4$	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
$9$	26.9985	+	0.283391i	0.999945	+	0.0104960i
$10$	−17.6813	+	10.2083i	−0.559132	+	0.322815i
$11$	7.33279	−	4.23359i	0.200993	−	0.116043i	−0.396126	−	0.918196i	$-0.629646\pi$
$11$	7.33279	−	4.23359i	0.200993	−	0.116043i	0.597118	+	0.802153i	$0.296312\pi$
$12$	−22.3293	−	39.1485i	−0.537160	−	0.941767i
$13$			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	$-0.837000\pi$
$17$	−60.2944	−	104.433i	−0.860208	−	1.48992i	0.0115198	−	0.999934i	$-0.496333\pi$
$18$	−94.8952	−	56.1239i	−1.24261	−	0.734919i
$19$	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
$21$	−2.75625	−	96.1946i	−0.0286411	−	0.999590i
$22$	−34.5742			−0.335057
$23$	2.98204	+	1.72168i	0.0270347	+	0.0156085i	0.513456	−	0.858116i	$-0.328365\pi$
$23$	2.98204	+	1.72168i	0.0270347	+	0.0156085i	−0.486422	+	0.873724i	$0.661698\pi$
$24$	−0.0749963	+	14.2901i	−0.000637857	+	0.121540i
$25$	−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	$-0.925162\pi$
$29$		−	72.7598i		−	0.465902i	0.972489	−	0.232951i	$-0.0748381\pi$
$30$	92.1518	−	52.5610i	0.560818	−	0.319876i
$31$	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
$33$	−38.2172	+	21.7981i	−0.201599	+	0.114987i
$34$			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
$39$	0.150094	−	28.5996i	0.000616265	−	0.117426i
$40$	−11.9086	−	6.87544i	−0.0470729	−	0.0271775i
$41$	221.251			0.842770			0.421385	−	0.906882i	$-0.361544\pi$
$41$	221.251			0.842770			0.421385	+	0.906882i	$0.361544\pi$
$42$	−186.650	+	345.796i	−0.685731	+	1.27042i
$43$	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
$45$	68.7234	−	116.199i	0.227660	−	0.384930i
$46$	−7.03018	−	12.1766i	−0.0225336	−	0.0390293i
$47$	100.415	−	173.923i	0.311638	−	0.539773i	−0.667079	−	0.744987i	$-0.732456\pi$
$47$	100.415	−	173.923i	0.311638	−	0.539773i	0.978717	+	0.205214i	$0.0657889\pi$
$48$	−152.471	+	260.916i	−0.458485	+	0.784582i
$49$	−342.212	+	23.2328i	−0.997703	+	0.0677342i
$50$			102.083i			0.288734i
$51$	310.447	+	544.286i	0.852377	+	1.49442i
$52$	−41.3438	+	23.8699i	−0.110257	+	0.0636568i
$53$	63.3970	−	36.6023i	0.164307	−	0.0948625i	−0.415592	−	0.909551i	$-0.636426\pi$
$53$	63.3970	−	36.6023i	0.164307	−	0.0948625i	0.579899	+	0.814689i	$0.303092\pi$
$54$	491.553	+	294.212i	1.23874	+	0.741430i
$55$		−	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	0.595298	−	0.803505i	$-0.297034\pi$
$59$	−180.462	−	312.570i	−0.398207	−	0.689714i	−0.993505	+	0.113791i	$0.963701\pi$
$60$	−225.341	−	1.18262i	−0.484857	−	0.00254459i
$61$	−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
$63$	11.6985	+	499.910i	0.0233948	+	0.999726i
$64$	594.275			1.16069
$65$	23.8334	+	13.7602i	0.0454795	+	0.0262576i
$66$	179.650	+	0.942827i	0.335052	+	0.00175839i
$67$	−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	$0.233560\pi$
$71$			801.257i			1.33932i	−0.742668	+	0.669660i	$0.766440\pi$
$72$	0.779374	−	74.2506i	0.00127570	−	0.121535i
$73$	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
$75$	64.3606	+	112.839i	0.0990896	+	0.173728i
$76$			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
$81$	728.839	+	15.3023i	0.999780	+	0.0209908i
$82$	−782.400	−	451.719i	−1.05368	−	0.608342i
$83$	1419.66			1.87745			0.938724	−	0.344670i	$-0.112009\pi$
$83$	1419.66			1.87745			0.938724	+	0.344670i	$0.112009\pi$
$84$	710.611	−	437.876i	0.923024	−	0.568764i
$85$	−602.944			−0.769393
$86$	−1751.46	−	1011.20i	−2.19610	−	1.26792i
$87$	−1.98413	+	378.066i	−0.00244508	+	0.465895i
$88$	−11.6431	−	20.1664i	−0.0141041	−	0.0244290i
$89$	310.733	−	538.205i	0.370085	−	0.641007i	−0.619493	−	0.785002i	$-0.712662\pi$
$89$	310.733	−	538.205i	0.370085	−	0.641007i	0.989578	+	0.143995i	$0.0459951\pi$
$90$	−480.262	+	270.598i	−0.562489	+	0.316929i
$91$	−101.878	+	3.45429i	−0.117360	+	0.00397921i
$92$			29.8661i			0.0338451i
$93$	−1262.76	+	720.245i	−1.40798	+	0.803074i
$94$	−710.186	+	410.026i	−0.779256	+	0.449904i
$95$	116.952	−	67.5222i	0.126305	−	0.0729224i
$96$	1171.18	−	668.012i	1.24514	−	0.710195i
$97$			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	0.521660	−	0.853153i	$-0.325313\pi$
$101$	−485.210	−	840.409i	−0.478022	−	0.827959i	−0.999683	+	0.0251945i	$0.991979\pi$
$102$	13.4277	−	2558.56i	0.0130347	−	2.48368i
$103$	−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
$105$	−423.425	−	228.552i	−0.393544	−	0.212422i
$106$	−298.918			−0.273901
$107$	299.147	+	172.713i	0.270277	+	0.156045i	0.629014	−	0.777394i	$-0.283459\pi$
$107$	299.147	+	172.713i	0.270277	+	0.156045i	−0.358736	+	0.933439i	$0.616792\pi$
$108$	−591.764	−	1063.28i	−0.527245	−	0.947354i
$109$	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	$0.155427\pi$
$113$			1127.01i			0.938229i	−0.883137	+	0.469114i	$0.844573\pi$
$114$	283.923	+	497.783i	0.233261	+	0.408962i
$115$	14.9102	−	8.60841i	0.0120903	−	0.00698033i
$116$	546.534	−	315.541i	0.437452	−	0.252563i
$117$	−1.55981	+	148.602i	−0.00123251	+	0.117421i
$118$			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
$123$	−1149.64	−	6.03343i	−0.842758	−	0.00442290i
$124$	2101.48	+	1213.29i	1.52193	+	0.878684i
$125$	−125.000			−0.0894427
$126$	979.278	−	1791.70i	0.692389	−	1.26680i
$127$	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
$129$	−2573.54	−	13.5063i	−1.75649	−	0.00921829i
$130$	−56.1873	−	97.3193i	−0.0379073	−	0.0656574i
$131$	−1022.16	+	1770.44i	−0.681731	+	1.18079i	0.292721	+	0.956198i	$0.405439\pi$
$131$	−1022.16	+	1770.44i	−0.681731	+	1.18079i	−0.974452	+	0.224595i	$0.927894\pi$
$132$	−329.475	−	192.535i	−0.217251	−	0.126955i
$133$	−235.282	+	441.422i	−0.153395	+	0.287791i
$134$			3151.77i			2.03187i
$135$	−360.261	+	601.903i	−0.229677	+	0.383730i
$136$	−287.209	+	165.820i	−0.181088	+	0.104551i
$137$	−135.672	+	78.3304i	−0.0846078	+	0.0488483i	−0.541707	−	0.840567i	$-0.682222\pi$
$137$	−135.672	+	78.3304i	−0.0846078	+	0.0488483i	0.457099	+	0.889416i	$0.348888\pi$
$138$	36.1973	+	63.4625i	0.0223284	+	0.0391470i
$139$		−	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
$144$	799.367	−	1351.58i	0.462597	−	0.782165i
$145$	−315.059	−	181.899i	−0.180443	−	0.104179i
$146$	−4157.63			−2.35676
$147$	1778.80	−	111.388i	0.998045	−	0.0624973i
$148$	778.785			0.432539
$149$	−945.006	−	545.599i	−0.519583	−	0.299982i	0.217181	−	0.976131i	$-0.430314\pi$
$149$	−945.006	−	545.599i	−0.519583	−	0.299982i	−0.736764	+	0.676150i	$0.763647\pi$
$150$	2.78377	−	530.432i	0.00151529	−	0.288730i
$151$	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
$156$	215.477	−	122.902i	0.110589	−	0.0630773i
$157$	−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
$159$	−330.414	+	188.460i	−0.164802	+	0.0939989i
$160$			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
$165$	−1.15449	+	219.981i	−0.000544706	+	0.103791i
$166$	−5020.29	−	2898.47i	−2.34729	−	1.35521i
$167$	−3329.30			−1.54269			−0.771345	−	0.636417i	$-0.780416\pi$
$167$	−3329.30			−1.54269			−0.771345	+	0.636417i	$0.780416\pi$
$168$	−264.552	+	7.58016i	−0.121492	+	0.00348108i
$169$	2166.71			0.986211
$170$	2132.17	+	1231.01i	0.961939	+	0.555376i
$171$	627.678	+	371.228i	0.280700	+	0.166015i
$172$	2147.93	+	3720.33i	0.952199	+	1.64926i
$173$	134.286	−	232.590i	0.0590149	−	0.102217i	−0.835009	−	0.550237i	$-0.814537\pi$
$173$	134.286	−	232.590i	0.0590149	−	0.102217i	0.894023	+	0.448020i	$0.147871\pi$
$174$	778.898	−	1332.89i	0.339357	−	0.580724i
$175$	392.900	−	244.958i	0.169717	−	0.105812i
$176$		−	492.436i		−	0.210902i
$177$	929.174	+	1629.06i	0.394582	+	0.691795i
$178$	−2197.66	+	1268.82i	−0.925404	+	0.534282i
$179$	−1472.14	+	849.943i	−0.614711	+	0.354904i	−0.774807	−	0.632198i	$-0.782153\pi$
$179$	−1472.14	+	849.943i	−0.614711	+	0.354904i	0.160096	+	0.987101i	$0.448820\pi$
$180$	1170.86	+	12.2900i	0.484837	+	0.00508911i
$181$		−	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
$186$	5935.94	+	31.1525i	2.34002	+	0.0122807i
$187$	−884.252	−	510.523i	−0.345791	−	0.199642i
$188$	1741.90			0.675750
$189$	−47.1539	−	2597.89i	−0.0181478	−	0.999835i
$190$	−551.429			−0.210552
$191$	2142.24	+	1236.82i	0.811554	+	0.468551i	0.847495	−	0.530803i	$-0.178110\pi$
$191$	2142.24	+	1236.82i	0.811554	+	0.468551i	−0.0359413	+	0.999354i	$0.511443\pi$
$192$	−3087.90	−	16.2057i	−1.16068	−	0.00609138i
$193$	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	$-0.695579\pi$
$197$		−	4518.62i		−	1.63420i	0.576493	−	0.817102i	$-0.304421\pi$
$198$	−933.452	−	9.79801i	−0.335038	−	0.00351674i
$199$	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
$201$	1987.10	+	3483.86i	0.697311	+	1.22255i
$202$			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
$207$	80.0227	+	47.3279i	0.0268694	+	0.0158914i
$208$	277.221	+	160.054i	0.0924127	+	0.0533545i
$209$	228.689			0.0756877
$210$	1030.72	+	1672.71i	0.338697	+	0.549657i
$211$	−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
$213$	21.8500	−	4163.40i	0.00702882	−	1.33930i
$214$	−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
$219$	−4595.71	+	2621.27i	−1.41803	+	0.808808i
$220$	318.005	−	183.600i	0.0974541	−	0.0562652i
$221$	574.807	−	331.865i	0.174958	−	0.101012i
$222$	1654.84	−	943.878i	0.500296	−	0.285356i
$223$		−	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	0.904704	−	0.426041i	$-0.140092\pi$
$227$	285.201	+	493.982i	0.0833896	+	0.144435i	−0.821314	+	0.570476i	$0.806759\pi$
$228$	6.38824	−	1217.24i	0.00185558	−	0.353570i
$229$	−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
$231$	−427.459	−	693.706i	−0.121752	−	0.197587i
$232$	−200.102			−0.0566265
$233$	−588.268	−	339.637i	−0.165402	−	0.0954951i	0.415014	−	0.909815i	$-0.363777\pi$
$233$	−588.268	−	339.637i	−0.165402	−	0.0954951i	−0.580416	+	0.814320i	$0.697110\pi$
$234$	308.911	−	522.311i	0.0862997	−	0.145917i
$235$	−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	$-0.990874\pi$
$239$		−	211.837i		−	0.0573332i	0.999589	−	0.0286666i	$-0.00912611\pi$
$240$	748.620	+	1312.51i	0.201347	+	0.353008i
$241$	−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
$243$	−3786.69	−	99.3870i	−0.999656	−	0.0262374i
$244$		−	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
$249$	−7376.68	−	38.7137i	−1.87742	−	0.00985294i
$250$	442.033	+	255.208i	0.111826	+	0.0645630i
$251$	6671.72			1.67775			0.838875	−	0.544324i	$-0.183214\pi$
$251$	6671.72			1.67775			0.838875	+	0.544324i	$0.183214\pi$
$252$	−3704.33	+	2255.86i	−0.925996	+	0.563912i
$253$	29.1556			0.00724504
$254$	−6736.25	−	3889.17i	−1.66405	−	0.960742i
$255$	3132.95	+	16.4421i	0.769383	+	0.00403782i
$256$	−1660.94	−	2876.83i	−0.405502	−	0.702351i
$257$	1173.99	−	2033.40i	0.284946	−	0.493542i	−0.687650	−	0.726043i	$-0.741358\pi$
$257$	1173.99	−	2033.40i	0.284946	−	0.493542i	0.972596	+	0.232501i	$0.0746908\pi$
$258$	9073.14	+	5302.06i	2.18941	+	1.27943i
$259$	1467.47	+	782.178i	0.352063	+	0.187653i
$260$			238.699i			0.0569364i
$261$	20.6195	−	1964.41i	0.00489008	−	0.465876i
$262$	7229.26	−	4173.82i	1.70468	−	0.984196i
$263$	−6281.95	+	3626.88i	−1.47286	+	0.850354i	−0.999534	−	0.0305344i	$-0.990279\pi$
$263$	−6281.95	+	3626.88i	−1.47286	+	0.850354i	−0.473323	+	0.880889i	$0.656946\pi$
$264$	59.9486	+	105.104i	0.0139757	+	0.0245027i
$265$		−	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	0.942107	−	0.335313i	$-0.108842\pi$
$269$	797.075	+	1380.57i	0.180664	+	0.312918i	−0.761443	+	0.648232i	$0.775509\pi$
$270$	2502.86	−	1392.95i	0.564145	−	0.313972i
$271$	−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
$273$	529.463	−	15.1706i	0.117379	−	0.00336325i
$274$	639.697			0.141042
$275$	−183.320	−	105.840i	−0.0401985	−	0.0232086i
$276$	0.814438	−	155.186i	0.000177621	−	0.0338447i
$277$	−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	$-0.874223\pi$
$281$		−	3626.44i		−	0.769876i	0.922943	−	0.384938i	$-0.125777\pi$
$282$	3701.36	−	2111.16i	0.781606	−	0.445808i
$283$	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
$285$	−609.532	+	347.661i	−0.126686	+	0.0722585i
$286$		−	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
$291$	0.830126	−	158.176i	0.000167226	−	0.0318640i
$292$	7648.17	+	4415.67i	1.53279	+	0.884958i
$293$	1490.52			0.297191			0.148595	−	0.988898i	$-0.452525\pi$
$293$	1490.52			0.297191			0.148595	+	0.988898i	$0.452525\pi$
$294$	−6517.70	−	3237.80i	−1.29293	−	0.642287i
$295$	−1804.62			−0.356167
$296$	−213.852	−	123.467i	−0.0419929	−	0.0242446i
$297$	−1037.99	+	577.686i	−0.202795	+	0.112864i
$298$	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
$303$	2498.28	+	4380.07i	0.473670	+	0.830456i
$304$	1360.34	−	785.394i	0.256648	−	0.148176i
$305$	−2932.23	+	1692.92i	−0.550489	+	0.317825i
$306$	−139.542	+	13294.1i	−0.0260690	+	2.48358i
$307$			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	0.741950	−	0.670455i	$-0.233901\pi$
$311$	−1149.87	−	1991.63i	−0.209656	−	0.363136i	−0.951606	+	0.307320i	$0.900568\pi$
$312$	−78.6540	−	0.412786i	−0.0142721	−	7.49019e-5i
$313$	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
$315$	2193.92	+	1199.12i	0.392424	+	0.214485i
$316$	1680.55			0.299172
$317$	3604.26	+	2080.92i	0.638598	+	0.368694i	0.784074	−	0.620667i	$-0.213138\pi$
$317$	3604.26	+	2080.92i	0.638598	+	0.368694i	−0.145477	+	0.989362i	$0.546472\pi$
$318$	1553.20	+	8.15139i	0.273897	+	0.00143744i
$319$	−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
$324$	3045.86	+	5541.03i	0.522266	+	0.950108i
$325$	119.167	−	68.8010i	0.0203390	−	0.0117427i
$326$	−8831.68	+	5098.97i	−1.50043	+	0.866276i
$327$	−1966.75	−	3448.18i	−0.332604	−	0.583134i
$328$		−	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
$333$	1234.12	−	2086.67i	0.203091	−	0.343389i
$334$	11773.3	+	6797.31i	1.92876	+	1.11357i
$335$	−3859.32			−0.629424
$336$	−4925.14	−	2658.43i	−0.799668	−	0.431635i
$337$	−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
$339$	30.7331	−	5856.02i	0.00492387	−	0.938216i
$340$	−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
$345$	−77.7094	+	44.3234i	−0.0121268	+	0.00691679i
$346$	−949.741	+	548.333i	−0.147568	+	0.0851982i
$347$	8390.19	−	4844.08i	1.29801	−	0.749406i	0.317949	−	0.948108i	$-0.397006\pi$
$347$	8390.19	−	4844.08i	1.29801	−	0.749406i	0.980060	+	0.198702i	$0.0636727\pi$
$348$	−2848.44	+	1624.68i	−0.438771	+	0.250264i
$349$		−	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	$-0.973367\pi$
$353$	−3784.55	−	6555.03i	−0.570627	−	0.988355i	0.425875	−	0.904782i	$-0.359966\pi$
$354$	40.1893	−	7657.84i	0.00603400	−	1.14974i
$355$	3469.55	+	2003.14i	0.518716	+	0.299481i
$356$	5390.29			0.802485
$357$	−9879.70	+	6087.84i	−1.46468	+	0.902528i
$358$	6941.18			1.02473
$359$	8900.82	+	5138.89i	1.30854	+	0.755488i	0.981853	−	0.189643i	$-0.0607330\pi$
$359$	8900.82	+	5138.89i	1.30854	+	0.755488i	0.326691	+	0.945131i	$0.394066\pi$
$360$	−319.566	−	189.001i	−0.0467850	−	0.0276701i
$361$	−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
$366$	−7118.55	−	12480.5i	−1.01665	−	1.78242i
$367$	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
$369$	5973.44	+	62.7004i	0.842723	+	0.00884567i
$370$			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
$375$	649.510	+	3.40871i	0.0894415	+	0.000469400i
$376$	−478.320	−	276.158i	−0.0656050	−	0.0378770i
$377$	400.476			0.0547097
$378$	−5137.27	+	9283.10i	−0.699028	+	1.26315i
$379$	−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
$381$	−9898.05	−	51.9462i	−1.33095	−	0.00698500i
$382$	−5050.34	−	8747.44i	−0.676434	−	1.17162i
$383$	−5802.30	+	10049.9i	−0.774109	+	1.34080i	0.161186	+	0.986924i	$0.448468\pi$
$383$	−5802.30	+	10049.9i	−0.774109	+	1.34080i	−0.935294	+	0.353871i	$0.884865\pi$
$384$	1573.68	+	919.611i	0.209132	+	0.122210i
$385$	783.621	−	26.5695i	0.103733	−	0.00351716i
$386$		−	6852.82i		−	0.903625i
$387$	13372.0	+	140.359i	1.75642	+	0.0184363i
$388$	−228.660	+	132.017i	−0.0299187	+	0.0172735i
$389$	694.507	−	400.974i	0.0905217	−	0.0522627i	−0.454056	−	0.890973i	$-0.650023\pi$
$389$	694.507	−	400.974i	0.0905217	−	0.0522627i	0.544578	+	0.838711i	$0.316690\pi$
$390$	289.300	+	507.211i	0.0375622	+	0.0658555i
$391$		−	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
$396$	1706.73	+	1009.41i	0.216582	+	0.128093i
$397$	−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
$399$	1234.58	−	2287.25i	0.154904	−	0.286982i
$400$	−1453.96			−0.181745
$401$	−1886.94	−	1089.43i	−0.234986	−	0.135669i	0.377884	−	0.925853i	$-0.376652\pi$
$401$	−1886.94	−	1089.43i	−0.234986	−	0.135669i	−0.612870	+	0.790184i	$0.709985\pi$
$402$	85.9476	−	16376.8i	0.0106634	−	2.03185i
$403$	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
$408$	1496.88	−	853.782i	0.181634	−	0.103599i
$409$	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
$411$	707.100	−	403.312i	0.0848630	−	0.0484036i
$412$		−	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
$417$	−28.6791	+	5464.64i	−0.00336791	+	0.641737i
$418$	−808.703	−	466.905i	−0.0946291	−	0.0546341i
$419$	2105.13			0.245448			0.122724	−	0.992441i	$-0.460837\pi$
$419$	2105.13			0.245448			0.122724	+	0.992441i	$0.460837\pi$
$420$	−119.532	−	4171.73i	−0.0138870	−	0.484665i
$421$	−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
$423$	2760.34	−	4667.22i	0.317287	−	0.536473i
$424$	−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
$429$	−119.978	−	210.351i	−0.0135026	−	0.0236732i
$430$	−8757.28	+	5056.02i	−0.982125	+	0.567030i
$431$	−11007.2	+	6355.00i	−1.23016	+	0.710231i	−0.967062	−	0.254540i	$-0.918076\pi$
$431$	−11007.2	+	6355.00i	−1.23016	+	0.710231i	−0.263093	+	0.964770i	$0.584743\pi$
$432$	−4190.43	+	7001.12i	−0.466695	+	0.779726i
$433$			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
$438$	21603.4	+	113.377i	2.35673	+	0.0123684i
$439$	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
$441$	−9245.81	+	530.272i	−0.998359	+	0.0572586i
$442$	−2710.22			−0.291657
$443$	−9761.27	−	5635.67i	−1.04689	−	0.604421i	−0.125112	−	0.992143i	$-0.539929\pi$
$443$	−9761.27	−	5635.67i	−1.04689	−	0.604421i	−0.921777	+	0.387721i	$0.873262\pi$
$444$	−4046.63	−	21.2372i	−0.432533	−	0.00226998i
$445$	−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	$0.270975\pi$
$449$			14311.8i			1.50427i	−0.659012	+	0.752133i	$0.729025\pi$
$450$	−28.9294	+	2756.09i	−0.00303054	+	0.288719i
$451$	1622.38	−	936.684i	0.169391	−	0.0977977i
$452$	−8465.49	+	4887.55i	−0.880936	+	0.508609i
$453$	−8611.17	−	15097.4i	−0.893130	−	1.56587i
$454$		−	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
$459$	8227.35	+	14782.9i	0.836645	+	1.50328i
$460$	129.324	+	74.6652i	0.0131082	+	0.00756800i
$461$	18238.0			1.84258			0.921290	−	0.388877i	$-0.127137\pi$
$461$	18238.0			1.84258			0.921290	+	0.388877i	$0.127137\pi$
$462$	95.2950	+	3325.85i	0.00959637	+	0.334919i
$463$	−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
$465$	−38.1461	+	7268.52i	−0.00380426	+	0.724881i
$466$	1386.85	+	2402.09i	0.137864	+	0.238787i
$467$	3767.85	−	6526.10i	0.373352	−	0.646664i	−0.616727	−	0.787177i	$-0.711542\pi$
$467$	3767.85	−	6526.10i	0.373352	−	0.646664i	0.990079	+	0.140513i	$0.0448752\pi$
$468$	−1122.99	+	632.734i	−0.110919	+	0.0624960i
$469$	12130.6	−	7562.96i	1.19433	−	0.744617i
$470$			4100.26i			0.402406i
$471$	9474.08	−	5403.77i	0.926842	−	0.528646i
$472$	−859.622	+	496.303i	−0.0838291	+	0.0483987i
$473$	3631.82	−	2096.83i	0.353047	−	0.203832i
$474$	3571.01	−	2036.81i	0.346037	−	0.197371i
$475$		−	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	0.933643	−	0.358204i	$-0.116611\pi$
$479$	1641.79	+	2843.66i	0.156608	+	0.271253i	−0.777035	+	0.629457i	$0.783277\pi$
$480$	35.3797	−	6741.40i	0.00336428	−	0.641045i
$481$	427.994	+	247.102i	0.0405714	+	0.0234239i
$482$	467.858			0.0442123
$483$	157.397	−	291.602i	0.0148278	−	0.0274707i
$484$	−10922.6			−1.02579
$485$	131.815	+	76.1034i	0.0123410	+	0.00712511i
$486$	13187.8	+	8082.60i	1.23089	+	0.754391i
$487$	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	$0.0197253\pi$
$491$			1347.56i			0.123858i	−0.998081	+	0.0619292i	$0.980275\pi$
$492$	−4940.38	−	8661.64i	−0.452702	−	0.793693i
$493$	−7598.52	+	4387.01i	−0.694158	+	0.400772i
$494$	525.697	−	303.511i	0.0478790	−	0.0276429i
$495$	11.9976	−	1143.01i	0.00108940	−	0.103786i
$496$		−	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
$501$	17299.3	+	90.7890i	1.54267	+	0.00809611i
$502$	−23592.9	−	13621.4i	−2.09762	−	1.21106i
$503$	−3030.57			−0.268641			−0.134320	−	0.990938i	$-0.542885\pi$
$503$	−3030.57			−0.268641			−0.134320	+	0.990938i	$0.542885\pi$
$504$	1374.84	−	32.1729i	0.121508	−	0.00284344i
$505$	−4852.10			−0.427556
$506$	−103.102	−	59.5258i	−0.00905816	−	0.00522973i
$507$	−11258.4	−	59.0853i	−0.986197	−	0.00517568i
$508$	8261.12	+	14308.7i	0.721512	+	1.24969i
$509$	−6228.25	+	10787.7i	−0.542362	+	0.939399i	0.456405	+	0.889772i	$0.349137\pi$
$509$	−6228.25	+	10787.7i	−0.542362	+	0.939399i	−0.998768	+	0.0496273i	$0.984197\pi$
$510$	−11045.3	−	6454.55i	−0.959011	−	0.560417i
$511$	9976.62	+	16002.0i	0.863678	+	1.38530i
$512$			16370.5i			1.41305i
$513$	−3251.34	−	1946.05i	−0.279825	−	0.167486i
$514$	−8303.04	+	4793.76i	−0.712512	+	0.411369i
$515$	−4479.43	+	2586.20i	−0.383276	+	0.221285i
$516$	−11059.4	−	19389.7i	−0.943530	−	1.65423i
$517$		−	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	0.704551	−	0.709654i	$-0.251149\pi$
$521$	−3119.32	−	5402.82i	−0.262303	−	0.454322i	−0.966854	+	0.255332i	$0.917815\pi$
$522$	−4083.57	+	6904.55i	−0.342400	+	0.578935i
$523$	−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
$525$	−2048.22	+	1262.11i	−0.170270	+	0.104920i
$526$	29619.5			2.45527
$527$	−29217.1	−	16868.5i	−2.41503	−	1.39432i
$528$	−13.4286	+	2558.74i	−0.00110682	+	0.210899i
$529$	−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
$534$	11453.8	−	6532.97i	0.928195	−	0.529418i
$535$	1495.74	−	863.563i	0.120872	−	0.0697852i
$536$	−1838.36	+	1061.38i	−0.148144	+	0.0855310i
$537$	7672.56	−	4376.23i	0.616565	−	0.351673i
$538$		−	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
$543$	−71.5731	+	13637.8i	−0.00565653	+	1.07782i
$544$	27098.3	+	15645.2i	2.13572	+	1.23306i
$545$	3819.79			0.300224
$546$	−1903.29	−	1027.34i	−0.149182	−	0.0805237i
$547$	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
$549$	−15737.2	−	9307.48i	−1.22340	−	0.723559i
$550$	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
$555$	1155.77	+	2026.34i	0.0883961	+	0.154979i
$556$	7899.71	−	4560.90i	0.602558	−	0.347887i
$557$	863.961	−	498.808i	0.0657221	−	0.0379447i	−0.466779	−	0.884374i	$-0.654586\pi$
$557$	863.961	−	498.808i	0.0657221	−	0.0379447i	0.532501	+	0.846429i	$0.321252\pi$
$558$	−30842.8	−	323.742i	−2.33993	−	0.0245611i
$559$			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	0.997729	−	0.0673528i	$-0.0214553\pi$
$563$	5884.96	+	10193.0i	0.440535	+	0.763030i	−0.557194	+	0.830382i	$0.688122\pi$
$564$	−9051.04	−	47.5010i	−0.675741	−	0.00354637i
$565$	4880.08	+	2817.52i	0.363374	+	0.209794i
$566$	−3399.33			−0.252446
$567$	174.172	+	13500.1i	0.0129004	+	0.999917i
$568$	2203.60			0.162783
$569$	12969.2	+	7487.79i	0.955534	+	0.551678i	0.894796	−	0.446476i	$-0.147321\pi$
$569$	12969.2	+	7487.79i	0.955534	+	0.551678i	0.0607380	+	0.998154i	$0.480655\pi$
$570$	2865.27	+	15.0373i	0.210549	+	0.00110499i
$571$	−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
$576$	16044.5	+	168.412i	1.16063	+	0.0121826i
$577$	−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
$579$	−4320.52	−	7574.88i	−0.310111	−	0.543698i
$580$		−	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
$585$	639.566	+	378.259i	0.0452014	+	0.0267335i
$586$	−5270.85	−	3043.13i	−0.371565	−	0.214523i
$587$	−19139.8			−1.34580			−0.672900	−	0.739734i	$-0.734951\pi$
$587$	−19139.8			−1.34580			−0.672900	+	0.739734i	$0.734951\pi$
$588$	8550.89	+	12878.3i	0.599716	+	0.903221i
$589$	7556.25			0.528608
$590$	6381.62	+	3684.43i	0.445300	+	0.257094i
$591$	−123.221	+	23479.1i	−0.00857639	+	1.63418i
$592$	−2610.98	−	4522.35i	−0.181268	−	0.313966i
$593$	9205.87	−	15945.0i	0.637504	−	1.10419i	−0.348475	−	0.937318i	$-0.613300\pi$
$593$	9205.87	−	15945.0i	0.637504	−	1.10419i	0.985979	−	0.166871i	$-0.0533663\pi$
$594$	4850.02	+	76.3662i	0.335015	+	0.00527499i
$595$	−378.400	−	11160.3i	−0.0260721	−	0.768952i
$596$		−	9464.53i		−	0.650473i
$597$	−2305.44	+	1314.96i	−0.158049	+	0.0901472i
$598$	67.0211	−	38.6947i	0.00458311	−	0.00264606i
$599$	−9319.12	+	5380.39i	−0.635674	+	0.367007i	−0.782946	−	0.622089i	$-0.786284\pi$
$599$	−9319.12	+	5380.39i	−0.635674	+	0.367007i	0.147272	+	0.989096i	$0.452951\pi$
$600$	310.328	−	177.003i	0.0211151	−	0.0120435i
$601$			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
$606$	108.057	−	20589.7i	0.00724344	−	1.38020i
$607$	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
$609$	−6999.10	+	200.544i	−0.465711	+	0.0133439i
$610$	13825.5			0.917670
$611$	957.289	+	552.691i	0.0633842	+	0.0365949i
$612$	14376.0	−	24307.1i	0.949532	−	1.60548i
$613$	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	$0.190659\pi$
$617$			17281.4i			1.12759i	−0.825914	+	0.563796i	$0.809341\pi$
$618$	−10874.7	−	19065.8i	−0.707837	−	1.24100i
$619$	−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
$621$	−414.514	−	248.102i	−0.0267856	−	0.0160322i
$622$			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
$627$	−1188.29	−	6.23627i	−0.0756867	−	0.000397213i
$628$	−15766.8	−	9102.94i	−1.00185	−	0.578418i
$629$	−10827.5			−0.686362
$630$	−5310.08	−	8719.64i	−0.335807	−	0.551427i
$631$	−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
$633$	14856.9	+	77.9711i	0.932876	+	0.00489585i
$634$	−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
$639$	−227.069	+	21632.7i	−0.0140574	+	1.33925i
$640$	−1518.90	+	876.937i	−0.0938121	+	0.0541625i
$641$	−2290.70	+	1322.53i	−0.141150	+	0.0814929i	−0.568912	−	0.822399i	$-0.692635\pi$
$641$	−2290.70	+	1322.53i	−0.141150	+	0.0814929i	0.427762	+	0.903891i	$0.359302\pi$
$642$	3631.18	+	6366.32i	0.223226	+	0.391368i
$643$			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	0.617187	−	0.786817i	$-0.288272\pi$
$647$	−6135.42	−	10626.9i	−0.372810	−	0.645726i	−0.989997	+	0.141091i	$0.954939\pi$
$648$	42.0839	−	2004.44i	0.00255125	−	0.121515i
$649$	−2646.59	−	1528.01i	−0.160073	−	0.0924183i
$650$	−561.873			−0.0339054
$651$	−14124.0	−	22921.2i	−0.850325	−	1.37996i
$652$	21661.8			1.30114
$653$	−7275.75	−	4200.66i	−0.436022	−	0.251737i	0.265887	−	0.964004i	$-0.414335\pi$
$653$	−7275.75	−	4200.66i	−0.436022	−	0.251737i	−0.701909	+	0.712267i	$0.747669\pi$
$654$	−85.0673	+	16209.1i	−0.00508623	+	0.969153i
$655$	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	$-0.658925\pi$
$659$		−	29704.2i		−	1.75586i	0.478792	−	0.877929i	$-0.341075\pi$
$660$	−1657.39	+	945.331i	−0.0977481	+	0.0557529i
$661$	−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
$663$	−2995.79	+	1708.72i	−0.175486	+	0.100092i
$664$		−	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
$669$	−1.24712	+	237.631i	−7.20723e−5	+	0.0137330i
$670$	13647.5	+	7879.42i	0.786942	+	0.454341i
$671$	−5733.72			−0.329877
$672$	13099.7	+	21258.9i	0.751981	+	1.22036i
$673$	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
$675$	1705.66	+	3064.73i	0.0972607	+	0.174758i
$676$	9396.47	+	16275.2i	0.534620	+	0.925988i
$677$	−1264.76	+	2190.62i	−0.0718000	+	0.124361i	−0.899690	−	0.436529i	$-0.856208\pi$
$677$	−1264.76	+	2190.62i	−0.0718000	+	0.124361i	0.827890	+	0.560890i	$0.189541\pi$
$678$	−12064.7	+	20645.7i	−0.683394	+	1.16946i
$679$	−563.458	+	19.1046i	−0.0318461	+	0.00107978i
$680$			1658.20i			0.0935134i
$681$	−1468.46	−	2574.55i	−0.0826305	−	0.144871i
$682$	−8376.89	+	4836.40i	−0.470334	+	0.271547i
$683$	−9705.06	+	5603.22i	−0.543710	+	0.313911i	−0.746581	−	0.665294i	$-0.768306\pi$
$683$	−9705.06	+	5603.22i	−0.543710	+	0.313911i	0.202871	+	0.979205i	$0.434973\pi$
$684$	−66.3876	+	6324.72i	−0.00371110	+	0.353555i
$685$			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
$690$	365.294	+	1.91711i	0.0201543	+	0.000105772i
$691$	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
$693$	2202.20	+	3616.21i	0.120714	+	0.198223i
$694$	−39559.9			−2.16379
$695$	−4553.93	−	2629.21i	−0.248547	−	0.143499i
$696$	1039.75	+	5.45672i	0.0566257	+	0.000297179i
$697$	−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	$0.0525891\pi$
$701$			6104.85i			0.328926i	−0.986383	+	0.164463i	$0.947411\pi$
$702$	−1619.37	+	2705.54i	−0.0870643	+	0.145462i
$703$	2100.19	−	1212.55i	0.112675	−	0.0650528i
$704$	4357.70	−	2515.92i	0.233291	−	0.134691i
$705$	2585.10	+	4532.29i	0.138100	+	0.242122i
$706$			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
$711$	2663.12	−	4502.85i	0.140471	−	0.237510i
$712$	−1480.16	−	854.569i	−0.0779090	−	0.0449808i
$713$	963.348			0.0505998
$714$	47366.5	−	1357.18i	2.48270	−	0.0711363i
$715$	233.020			0.0121880
$716$	−12768.7	−	7371.99i	−0.666463	−	0.384783i
$717$	−5.77674	+	1100.72i	−0.000300887	+	0.0573324i
$718$	−20983.7	−	36344.9i	−1.09068	−	1.88911i
$719$	−10904.9	+	18887.9i	−0.565625	+	0.979691i	0.431366	+	0.902177i	$0.358032\pi$
$719$	−10904.9	+	18887.9i	−0.565625	+	0.979691i	−0.996991	+	0.0775144i	$0.975302\pi$
$720$	−3854.10	−	6840.31i	−0.199491	−	0.354060i
$721$	9011.67	−	16907.1i	0.465481	−	0.873307i
$722$			25028.8i			1.29013i
$723$	517.155	−	294.972i	0.0266020	−	0.0151731i
$724$	19714.9	−	11382.4i	1.01202	−	0.584288i
$725$	−1575.30	+	909.497i	−0.0806966	+	0.0465902i
$726$	−23209.5	+	13238.1i	−1.18648	+	0.676738i
$727$		−	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
$732$	−160.167	+	30518.9i	−0.00808734	+	1.54100i
$733$	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
$735$	3964.67	−	7980.88i	0.198965	−	0.400516i
$736$	−893.485			−0.0447477
$737$	−5659.91	−	3267.75i	−0.282884	−	0.163323i
$738$	−20995.6	−	12417.5i	−1.04724	−	0.619367i
$739$	−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	$-0.913693\pi$
$743$		−	10848.7i		−	0.535664i	0.963466	−	0.267832i	$-0.0863073\pi$
$744$	1980.80	+	3472.81i	0.0976070	+	0.171128i
$745$	−4725.03	+	2728.00i	−0.232365	+	0.134156i
$746$	−29810.2	+	17210.9i	−1.46304	+	0.844686i
$747$	38328.8	+	402.319i	1.87734	+	0.0197056i
$748$		−	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
$753$	−34666.8	−	181.936i	−1.67773	−	0.00880491i
$754$	−1416.19	−	817.635i	−0.0684011	−	0.0394914i
$755$	16724.5			0.806179
$756$	19309.5	−	11620.6i	0.928943	−	0.559045i
$757$	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
$759$	−151.495	−	0.795062i	−0.00724494	−	3.80223e-5i
$760$	−185.698	−	321.638i	−0.00886311	−	0.0153514i
$761$	−7619.87	+	13198.0i	−0.362970	+	0.628682i	−0.988448	−	0.151560i	$-0.951570\pi$
$761$	−7619.87	+	13198.0i	−0.362970	+	0.628682i	0.625478	+	0.780241i	$0.284904\pi$
$762$	34896.0	+	20392.2i	1.65899	+	0.969462i
$763$	−12006.4	+	7485.50i	−0.569672	+	0.355168i
$764$			21455.2i			1.01600i
$765$	−16278.6	−	170.869i	−0.769351	−	0.00807552i
$766$	41036.9	−	23692.6i	1.93567	−	1.11756i
$767$	1720.41	−	993.279i	0.0809914	−	0.0467604i
$768$	8551.92	+	14993.5i	0.401811	+	0.704469i
$769$		−	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	$0.218271\pi$
$773$	20102.7	+	34819.0i	0.935375	+	1.62012i	0.161412	+	0.986887i	$0.448395\pi$
$774$	−47000.2	−	27797.4i	−2.18267	−	1.29090i
$775$	−6057.18	−	3497.12i	−0.280749	−	0.162090i
$776$	83.7190			0.00387286
$777$	−7603.78	−	4104.28i	−0.351073	−	0.189498i
$778$	−3274.61			−0.150900
$779$	5175.14	+	2987.87i	0.238021	+	0.137422i
$780$	6.50923	−	1240.30i	0.000298805	−	0.0569356i
$781$	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
$786$	−37677.7	+	21490.4i	−1.70982	+	0.975236i
$787$	−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
$789$	32740.4	−	18674.3i	1.47730	−	0.842613i
$790$			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
$795$	−9.98132	+	1901.88i	−0.000445284	+	0.0848464i
$796$	3836.71	+	2215.13i	0.170840	+	0.0986346i
$797$	34131.6			1.51694			0.758471	−	0.651707i	$-0.225947\pi$
$797$	34131.6			1.51694			0.758471	+	0.651707i	$0.225947\pi$
$798$	−9035.60	+	5567.70i	−0.400823	+	0.246986i
$799$	−24217.8			−1.07230
$800$	5617.91	+	3243.50i	0.248279	+	0.143344i
$801$	8541.84	−	14442.7i	0.376793	−	0.637087i
$802$	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
$807$	−4104.02	−	7195.31i	−0.179019	−	0.313862i
$808$	−2311.27	+	1334.41i	−0.100632	+	0.0580996i
$809$	27867.5	−	16089.3i	1.21109	−	0.699222i	0.248091	−	0.968737i	$-0.420197\pi$
$809$	27867.5	−	16089.3i	1.21109	−	0.699222i	0.962996	+	0.269515i	$0.0868633\pi$
$810$	−13043.0	+	7169.65i	−0.565785	+	0.311007i
$811$			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
$816$	36441.3	+	191.249i	1.56336	+	0.00820470i
$817$	11584.9	+	6688.54i	0.496089	+	0.286417i
$818$	−11346.2			−0.484977
$819$	−2751.55	+	64.3894i	−0.117395	+	0.00274719i
$820$	9595.11			0.408629
$821$	319.413	+	184.413i	0.0135781	+	0.00783931i	0.506774	−	0.862079i	$-0.330838\pi$
$821$	319.413	+	184.413i	0.0135781	+	0.00783931i	−0.493196	+	0.869918i	$0.664171\pi$
$822$	−3323.92	−	17.4443i	−0.141040	−	0.000740195i
$823$	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	$-0.816029\pi$
$827$		−	25985.7i		−	1.09264i	0.837578	−	0.546318i	$-0.183971\pi$
$828$	−8.46377	+	806.339i	−0.000355237	+	0.0338433i
$829$	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
$831$	1345.47	+	2358.93i	0.0561659	+	0.0984721i
$832$			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
$837$	−34296.7	+	19087.7i	−1.41633	+	0.788252i
$838$	−7444.30	−	4297.97i	−0.306872	−	0.177173i
$839$	−26831.1			−1.10407			−0.552034	−	0.833822i	$-0.686148\pi$
$839$	−26831.1			−1.10407			−0.552034	+	0.833822i	$0.686148\pi$
$840$	−628.557	+	1164.49i	−0.0258182	+	0.0478320i
$841$	19095.0			0.782936
$842$	3229.41	+	1864.50i	0.132177	+	0.0763123i
$843$	−98.8917	+	18843.3i	−0.00404035	+	0.769865i
$844$	−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
$849$	−3757.51	+	2143.19i	−0.151893	+	0.0866360i
$850$	10660.8	−	6155.03i	0.430192	−	0.248372i
$851$	267.754	−	154.588i	0.0107855	−	0.00622703i
$852$	31368.0	−	17891.5i	1.26133	−	0.719429i
$853$			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	$0.225459\pi$
$857$	23661.3	+	40982.6i	0.943122	+	1.63353i	0.183652	+	0.982991i	$0.441208\pi$
$858$	−5.18939	+	988.810i	−0.000206484	+	0.0393443i
$859$	−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
$861$	−609.821	−	21283.1i	−0.0241378	−	0.842424i
$862$	51899.0			2.05068
$863$	9407.77	+	5431.58i	0.371082	+	0.214245i	0.673931	−	0.738794i	$-0.264604\pi$
$863$	9407.77	+	5431.58i	0.371082	+	0.214245i	−0.302849	+	0.953039i	$0.597938\pi$
$864$	31809.5	−	17703.4i	1.25253	−	0.697087i
$865$	−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
$870$	−3824.33	−	6704.95i	−0.149031	−	0.261286i
$871$	3679.22	−	2124.20i	0.143129	−	0.0826357i
$872$	1819.53	−	1050.51i	0.0706619	−	0.0407967i
$873$	−8.62680	+	821.871i	−0.000334448	+	0.0318627i
$874$		−	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
$879$	−7744.84	−	40.6459i	−0.297187	−	0.00155967i
$880$	−2132.31	−	1231.09i	−0.0816820	−	0.0471591i
$881$	30150.3			1.15299			0.576497	−	0.817099i	$-0.304419\pi$
$881$	30150.3			1.15299			0.576497	+	0.817099i	$0.304419\pi$
$882$	33778.2	+	17001.6i	1.28954	+	0.649064i
$883$	−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
$885$	9376.97	+	49.2115i	0.356162	+	0.00186918i
$886$	23012.2	+	39858.4i	0.872586	+	1.51136i
$887$	−11083.7	+	19197.6i	−0.419566	+	0.726710i	−0.995896	−	0.0905075i	$-0.971151\pi$
$887$	−11083.7	+	19197.6i	−0.419566	+	0.726710i	0.576330	+	0.817217i	$0.304484\pi$
$888$	1107.83	+	647.379i	0.0418651	+	0.0244646i
$889$	1195.50	+	35259.1i	0.0451020	+	1.33021i
$890$			12688.2i			0.477876i
$891$	5409.21	−	2973.40i	0.203384	−	0.111799i
$892$	343.521	−	198.332i	0.0128945	−	0.00744467i
$893$	4697.48	−	2712.09i	0.176030	−	0.101631i
$894$	−11470.9	−	20111.2i	−0.429132	−	0.752370i
$895$			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
$900$	2980.37	−	5039.25i	0.110384	−	0.186639i
$901$	−7644.97	−	4413.83i	−0.282676	−	0.163203i
$902$	−7649.57			−0.282376
$903$	−1365.13	−	47643.8i	−0.0503085	−	1.75580i
$904$	3099.46			0.114034
$905$	−11365.0	−	6561.60i	−0.417443	−	0.241011i
$906$	−372.456	+	70969.4i	−0.0136579	+	2.60243i
$907$	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	$0.218261\pi$
$911$			34821.8i			1.26641i	−0.773985	+	0.633204i	$0.781739\pi$
$912$	−7089.87	+	4043.88i	−0.257422	+	0.146827i
$913$	10410.1	−	6010.26i	0.377353	−	0.217865i
$914$	−5735.33	+	3311.29i	−0.207558	+	0.119834i
$915$	15282.3	−	8716.61i	0.552149	−	0.314931i
$916$		−	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
$921$	261.329	−	49794.8i	0.00934972	−	1.78154i
$922$	−64494.4	−	37235.8i	−2.30370	−	1.33004i
$923$	−4410.18			−0.157273
$924$	3356.97	−	6219.29i	0.119520	−	0.221428i
$925$	−2244.72			−0.0797902
$926$	52214.4	+	30146.0i	1.85299	+	1.06983i
$927$	−24041.0	−	14218.6i	−0.851791	−	0.503776i
$928$	9439.86	+	16350.3i	0.333921	+	0.578368i
$929$	19211.5	−	33275.3i	0.678482	−	1.17516i	−0.296957	−	0.954891i	$-0.595972\pi$
$929$	19211.5	−	33275.3i	0.678482	−	1.17516i	0.975438	−	0.220273i	$-0.0706950\pi$
$930$	14974.7	−	25625.5i	0.528001	−	0.903541i
$931$	−8318.22	−	4077.96i	−0.292823	−	0.143555i
$932$		−	5891.69i		−	0.207069i
$933$	5920.51	+	10380.0i	0.207748	+	0.364231i
$934$	−26648.2	+	15385.3i	−0.933571	+	0.538997i
$935$	−4421.26	+	2552.62i	−0.154642	+	0.0892828i
$936$	408.681	+	4.28974i	0.0142715	+	0.000149802i
$937$		−	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	0.807387	−	0.590023i	$-0.200881\pi$
$941$	−3096.77	−	5363.75i	−0.107281	−	0.185817i	−0.914668	+	0.404206i	$0.867548\pi$
$942$	−44535.5	−	233.728i	−1.54039	−	0.00808413i
$943$	659.779	+	380.923i	0.0227840	+	0.0131544i
$944$	−20990.8			−0.723719
$945$	−11367.1	−	6290.55i	−0.391293	−	0.216541i
$946$	−17124.1			−0.588533
$947$	−23917.9	−	13809.0i	−0.820726	−	0.473846i	0.0299408	−	0.999552i	$-0.490468\pi$
$947$	−23917.9	−	13809.0i	−0.820726	−	0.473846i	−0.850667	+	0.525705i	$0.823801\pi$
$948$	−8732.28	−	45.8280i	−0.299168	−	0.00157007i
$949$	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	$-0.845989\pi$
$953$		−	27371.0i		−	0.930361i	0.885216	−	0.465181i	$-0.154011\pi$
$954$	−8070.34	−	84.7106i	−0.273886	−	0.00287485i
$955$	10711.2	−	6184.10i	0.362938	−	0.209542i
$956$	1591.21	−	918.688i	0.0538321	−	0.0310800i
$957$	1586.02	+	2780.68i	0.0535725	+	0.0939253i
$958$		−	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
$963$	8027.58	+	4747.76i	0.268624	+	0.158873i
$964$	−860.649	−	496.896i	−0.0287548	−	0.0166016i
$965$	8391.23			0.279920
$966$	−1151.95	+	709.827i	−0.0383679	+	0.0236421i
$967$	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
$969$	−88.8164	+	16923.5i	−0.00294447	+	0.561052i
$970$	−310.755	−	538.243i	−0.0102863	−	0.0178164i
$971$	1836.88	−	3181.58i	0.0607090	−	0.105151i	−0.834074	−	0.551653i	$-0.813997\pi$
$971$	1836.88	−	3181.58i	0.0607090	−	0.105151i	0.894783	+	0.446502i	$0.147331\pi$
$972$	−15675.4	−	28874.7i	−0.517273	−	0.952835i
$973$	19466.3	−	660.024i	0.641377	−	0.0217466i
$974$		−	41708.8i		−	1.37211i
$975$	−621.077	+	354.246i	−0.0204004	+	0.0116358i
$976$	−34106.7	+	19691.5i	−1.11857	+	0.645809i
$977$	49808.3	−	28756.9i	1.63102	−	0.941672i	0.647245	−	0.762282i	$-0.275921\pi$
$977$	49808.3	−	28756.9i	1.63102	−	0.941672i	0.983778	−	0.179390i	$-0.0574122\pi$
$978$	46029.2	−	26253.8i	1.50496	−	0.858390i
$979$		−	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	0.995406	−	0.0957402i	$-0.0305218\pi$
$983$	12783.7	+	22142.1i	0.414790	+	0.718437i	−0.580617	+	0.814177i	$0.697188\pi$
$984$	−16.5930	+	3161.70i	−0.000537566	+	0.102430i
$985$	−19566.2	−	11296.5i	−0.632925	−	0.365419i
$986$	35827.1			1.15717
$987$	−17007.3	−	9179.98i	−0.548478	−	0.296051i
$988$	−1289.40			−0.0415194
$989$	1476.96	+	852.723i	0.0474870	+	0.0274166i
$990$	−2376.06	+	4017.47i	−0.0762788	+	0.128973i
$991$	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
$996$	−31700.1	−	55577.7i	−1.00849	−	1.76812i
$997$	−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
$999$	−6469.48	+	10808.8i	−0.204890	+	0.342319i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(-3.53626 - 2.04166i) q^{2} +(-5.19608 - 0.0272697i) q^{3} +(4.33676 + 7.51148i) q^{4} +(2.50000 - 4.33013i) q^{5} +(18.3190 + 10.7051i) q^{6} +(0.627588 + 18.5096i) q^{7} -2.75017i q^{8} +(26.9985 + 0.283391i) q^{9} +O(q^{10})\)	\(q+(-3.53626 - 2.04166i) q^{2} +(-5.19608 - 0.0272697i) 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} +(26.9985 + 0.283391i) q^{9} +(-17.6813 + 10.2083i) q^{10} +(7.33279 - 4.23359i) q^{11} +(-22.3293 - 39.1485i) 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} +(-94.8952 - 56.1239i) q^{18} +(23.3904 + 13.5044i) q^{19} +43.3676 q^{20} +(-2.75625 - 96.1946i) q^{21} -34.5742 q^{22} +(2.98204 + 1.72168i) q^{23} +(-0.0749963 + 14.2901i) 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} +(92.1518 - 52.5610i) q^{30} +(242.287 - 139.885i) q^{31} +(-224.717 + 129.740i) q^{32} +(-38.2172 + 21.7981i) 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} +(0.150094 - 28.5996i) q^{39} +(-11.9086 - 6.87544i) q^{40} +221.251 q^{41} +(-186.650 + 345.796i) q^{42} +495.285 q^{43} +(63.6010 + 36.7201i) q^{44} +(68.7234 - 116.199i) 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} +(310.447 + 544.286i) q^{51} +(-41.3438 + 23.8699i) q^{52} +(63.3970 - 36.6023i) q^{53} +(491.553 + 294.212i) 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} +(-225.341 - 1.18262i) q^{60} +(-586.446 - 338.585i) q^{61} -1142.39 q^{62} +(11.6985 + 499.910i) q^{63} +594.275 q^{64} +(23.8334 + 13.7602i) q^{65} +(179.650 + 0.942827i) 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} +(0.779374 - 74.2506i) q^{72} +(881.784 - 509.098i) q^{73} +(-317.517 + 183.318i) q^{74} +(64.3606 + 112.839i) 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} +(728.839 + 15.3023i) q^{81} +(-782.400 - 451.719i) q^{82} +1419.66 q^{83} +(710.611 - 437.876i) q^{84} -602.944 q^{85} +(-1751.46 - 1011.20i) q^{86} +(-1.98413 + 378.066i) 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} +(-1262.76 + 720.245i) q^{93} +(-710.186 + 410.026i) q^{94} +(116.952 - 67.5222i) q^{95} +(1171.18 - 668.012i) q^{96} +30.4414i q^{97} +(1257.59 + 616.524i) q^{98} +(199.174 - 112.223i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{3} + 64 q^{4} + 80 q^{5} + 28 q^{6} + 46 q^{7} - 98 q^{9}+O(q^{10}) \) 32 * q + 2 * q^3 + 64 * q^4 + 80 * q^5 + 28 * q^6 + 46 * q^7 - 98 * q^9	\( 32 q + 2 q^{3} + 64 q^{4} + 80 q^{5} + 28 q^{6} + 46 q^{7} - 98 q^{9} - 36 q^{11} + 84 q^{12} - 18 q^{14} + 20 q^{15} - 376 q^{16} + 72 q^{17} + 260 q^{18} - 198 q^{19} + 640 q^{20} - 256 q^{21} + 204 q^{22} - 72 q^{23} - 94 q^{24} - 400 q^{25} + 312 q^{26} - 508 q^{27} + 350 q^{28} + 100 q^{30} + 510 q^{31} - 810 q^{32} + 454 q^{33} + 70 q^{35} - 612 q^{36} - 658 q^{37} + 192 q^{38} + 576 q^{39} + 1404 q^{41} - 1790 q^{42} + 332 q^{43} - 2034 q^{44} - 500 q^{45} - 468 q^{46} - 408 q^{47} - 2810 q^{48} + 980 q^{49} + 2748 q^{51} + 3378 q^{52} - 1152 q^{53} + 3322 q^{54} + 3354 q^{56} - 816 q^{57} - 1080 q^{58} + 48 q^{59} + 1230 q^{60} - 1662 q^{61} + 2076 q^{62} - 2306 q^{63} - 1952 q^{64} - 870 q^{65} - 3808 q^{66} - 1298 q^{67} - 1182 q^{68} - 2450 q^{69} - 450 q^{70} + 7678 q^{72} + 378 q^{73} - 2898 q^{74} + 50 q^{75} + 3528 q^{77} - 1896 q^{78} - 326 q^{79} + 1880 q^{80} + 1774 q^{81} - 2916 q^{82} + 1536 q^{83} - 10680 q^{84} + 720 q^{85} - 5202 q^{86} - 5666 q^{87} + 1668 q^{88} + 1590 q^{89} - 910 q^{90} + 2082 q^{91} + 4086 q^{93} - 1152 q^{94} - 990 q^{95} + 3996 q^{96} + 7830 q^{98} + 3128 q^{99}+O(q^{100}) \) 32 * q + 2 * q^3 + 64 * q^4 + 80 * q^5 + 28 * q^6 + 46 * q^7 - 98 * q^9 - 36 * q^11 + 84 * q^12 - 18 * q^14 + 20 * q^15 - 376 * q^16 + 72 * q^17 + 260 * q^18 - 198 * q^19 + 640 * q^20 - 256 * q^21 + 204 * q^22 - 72 * q^23 - 94 * q^24 - 400 * q^25 + 312 * q^26 - 508 * q^27 + 350 * q^28 + 100 * q^30 + 510 * q^31 - 810 * q^32 + 454 * q^33 + 70 * q^35 - 612 * q^36 - 658 * q^37 + 192 * q^38 + 576 * q^39 + 1404 * q^41 - 1790 * q^42 + 332 * q^43 - 2034 * q^44 - 500 * q^45 - 468 * q^46 - 408 * q^47 - 2810 * q^48 + 980 * q^49 + 2748 * q^51 + 3378 * q^52 - 1152 * q^53 + 3322 * q^54 + 3354 * q^56 - 816 * q^57 - 1080 * q^58 + 48 * q^59 + 1230 * q^60 - 1662 * q^61 + 2076 * q^62 - 2306 * q^63 - 1952 * q^64 - 870 * q^65 - 3808 * q^66 - 1298 * q^67 - 1182 * q^68 - 2450 * q^69 - 450 * q^70 + 7678 * q^72 + 378 * q^73 - 2898 * q^74 + 50 * q^75 + 3528 * q^77 - 1896 * q^78 - 326 * q^79 + 1880 * q^80 + 1774 * q^81 - 2916 * q^82 + 1536 * q^83 - 10680 * q^84 + 720 * q^85 - 5202 * q^86 - 5666 * q^87 + 1668 * q^88 + 1590 * q^89 - 910 * q^90 + 2082 * q^91 + 4086 * q^93 - 1152 * q^94 - 990 * q^95 + 3996 * q^96 + 7830 * q^98 + 3128 * q^99

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