LMFDB - Embedded newform 63.4.s.a.59.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(47,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("63.47");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.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:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			59.17
Character	$\chi$	$=$	63.59
Dual form			63.4.s.a.47.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.52419 + 1.45734i) q^{2} +(-4.29460 - 2.92513i) q^{3} +(0.247680 + 0.428994i) q^{4} +17.2113 q^{5} +(-6.57748 - 13.6423i) q^{6} +(17.7231 + 5.37495i) q^{7} -21.8736i q^{8} +(9.88725 + 25.1245i) q^{9} +O(q^{10})$	\(q+(2.52419 + 1.45734i) q^{2} +(-4.29460 - 2.92513i) q^{3} +(0.247680 + 0.428994i) q^{4} +17.2113 q^{5} +(-6.57748 - 13.6423i) q^{6} +(17.7231 + 5.37495i) q^{7} -21.8736i q^{8} +(9.88725 + 25.1245i) q^{9} +(43.4446 + 25.0828i) q^{10} -35.6923i q^{11} +(0.191176 - 2.56686i) q^{12} +(-8.99430 - 5.19286i) q^{13} +(36.9034 + 39.3960i) q^{14} +(-73.9159 - 50.3454i) q^{15} +(33.8587 - 58.6451i) q^{16} +(-64.1402 + 111.094i) q^{17} +(-11.6577 + 77.8281i) q^{18} +(-84.7576 + 48.9348i) q^{19} +(4.26290 + 7.38356i) q^{20} +(-60.3915 - 74.9258i) q^{21} +(52.0158 - 90.0941i) q^{22} +25.5640i q^{23} +(-63.9832 + 93.9386i) q^{24} +171.230 q^{25} +(-15.1355 - 26.2155i) q^{26} +(31.0307 - 136.821i) q^{27} +(2.08385 + 8.93439i) q^{28} +(-14.1366 + 8.16176i) q^{29} +(-113.207 - 234.802i) q^{30} +(160.589 - 92.7160i) q^{31} +(19.3867 - 11.1929i) q^{32} +(-104.405 + 153.284i) q^{33} +(-323.804 + 186.948i) q^{34} +(305.039 + 92.5101i) q^{35} +(-8.32941 + 10.4644i) q^{36} +(-0.462855 - 0.801688i) q^{37} -285.259 q^{38} +(23.4372 + 48.6108i) q^{39} -376.474i q^{40} +(-231.546 + 401.049i) q^{41} +(-43.2471 - 277.138i) q^{42} +(-43.2469 - 74.9058i) q^{43} +(15.3118 - 8.84027i) q^{44} +(170.173 + 432.427i) q^{45} +(-37.2555 + 64.5283i) q^{46} +(-143.746 + 248.976i) q^{47} +(-316.954 + 152.816i) q^{48} +(285.220 + 190.522i) q^{49} +(432.217 + 249.541i) q^{50} +(600.421 - 289.487i) q^{51} -5.14467i q^{52} +(-334.811 - 193.303i) q^{53} +(277.723 - 300.141i) q^{54} -614.313i q^{55} +(117.570 - 387.669i) q^{56} +(507.141 + 37.7712i) q^{57} -47.5778 q^{58} +(-45.2274 - 78.3362i) q^{59} +(3.29040 - 44.1790i) q^{60} +(120.761 + 69.7214i) q^{61} +540.475 q^{62} +(40.1900 + 498.429i) q^{63} -476.492 q^{64} +(-154.804 - 89.3761i) q^{65} +(-486.924 + 234.765i) q^{66} +(-151.612 - 262.599i) q^{67} -63.5449 q^{68} +(74.7780 - 109.787i) q^{69} +(635.157 + 678.059i) q^{70} -351.969i q^{71} +(549.565 - 216.270i) q^{72} +(761.691 + 439.763i) q^{73} -2.69815i q^{74} +(-735.367 - 500.871i) q^{75} +(-41.9855 - 24.2403i) q^{76} +(191.844 - 632.580i) q^{77} +(-11.6826 + 156.859i) q^{78} +(7.12361 - 12.3385i) q^{79} +(582.755 - 1009.36i) q^{80} +(-533.485 + 496.825i) q^{81} +(-1168.93 + 674.881i) q^{82} +(-125.688 - 217.699i) q^{83} +(17.1850 - 44.4652i) q^{84} +(-1103.94 + 1912.08i) q^{85} -252.102i q^{86} +(84.5852 + 6.29979i) q^{87} -780.720 q^{88} +(-505.658 - 875.825i) q^{89} +(-200.645 + 1339.53i) q^{90} +(-131.496 - 140.378i) q^{91} +(-10.9668 + 6.33169i) q^{92} +(-960.871 - 71.5644i) q^{93} +(-725.684 + 418.974i) q^{94} +(-1458.79 + 842.234i) q^{95} +(-115.999 - 8.63945i) q^{96} +(1125.76 - 649.959i) q^{97} +(442.293 + 896.575i) q^{98} +(896.753 - 352.899i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 3 q^{2} - 3 q^{3} + 81 q^{4} - 6 q^{5} - 24 q^{6} + 5 q^{7} - 3 q^{9}+O(q^{10}) $ 44 * q - 3 * q^2 - 3 * q^3 + 81 * q^4 - 6 * q^5 - 24 * q^6 + 5 * q^7 - 3 * q^9	\( 44 q - 3 q^{2} - 3 q^{3} + 81 q^{4} - 6 q^{5} - 24 q^{6} + 5 q^{7} - 3 q^{9} - 6 q^{10} - 3 q^{12} + 36 q^{13} + 129 q^{14} - 141 q^{15} - 263 q^{16} + 72 q^{17} - 15 q^{18} - 6 q^{19} - 24 q^{20} - 306 q^{21} + 14 q^{22} - 66 q^{24} + 698 q^{25} + 96 q^{26} - 432 q^{27} - 156 q^{28} - 132 q^{29} + 852 q^{30} + 177 q^{31} - 501 q^{32} + 849 q^{33} - 24 q^{34} - 765 q^{35} + 1122 q^{36} + 82 q^{37} - 1746 q^{38} - 645 q^{39} - 618 q^{41} - 963 q^{42} + 82 q^{43} - 603 q^{44} + 303 q^{45} + 266 q^{46} - 201 q^{47} + 1569 q^{48} + 515 q^{49} - 1845 q^{50} + 417 q^{51} - 564 q^{53} - 684 q^{54} + 3600 q^{56} + 1170 q^{57} - 538 q^{58} + 747 q^{59} - 516 q^{60} - 1209 q^{61} + 2904 q^{62} + 1557 q^{63} - 1144 q^{64} - 831 q^{65} + 1029 q^{66} + 295 q^{67} + 7008 q^{68} + 1005 q^{69} - 390 q^{70} - 1119 q^{72} - 6 q^{73} - 1788 q^{75} + 144 q^{76} - 1203 q^{77} - 5985 q^{78} - 551 q^{79} + 4239 q^{80} + 3741 q^{81} + 18 q^{82} - 1830 q^{83} - 7725 q^{84} - 237 q^{85} - 2130 q^{87} + 1246 q^{88} - 4266 q^{89} - 9993 q^{90} - 1140 q^{91} + 7896 q^{92} - 1479 q^{93} - 3 q^{94} - 1053 q^{95} + 5034 q^{96} + 792 q^{97} - 5667 q^{98} + 4335 q^{99}+O(q^{100}) \) 44 * q - 3 * q^2 - 3 * q^3 + 81 * q^4 - 6 * q^5 - 24 * q^6 + 5 * q^7 - 3 * q^9 - 6 * q^10 - 3 * q^12 + 36 * q^13 + 129 * q^14 - 141 * q^15 - 263 * q^16 + 72 * q^17 - 15 * q^18 - 6 * q^19 - 24 * q^20 - 306 * q^21 + 14 * q^22 - 66 * q^24 + 698 * q^25 + 96 * q^26 - 432 * q^27 - 156 * q^28 - 132 * q^29 + 852 * q^30 + 177 * q^31 - 501 * q^32 + 849 * q^33 - 24 * q^34 - 765 * q^35 + 1122 * q^36 + 82 * q^37 - 1746 * q^38 - 645 * q^39 - 618 * q^41 - 963 * q^42 + 82 * q^43 - 603 * q^44 + 303 * q^45 + 266 * q^46 - 201 * q^47 + 1569 * q^48 + 515 * q^49 - 1845 * q^50 + 417 * q^51 - 564 * q^53 - 684 * q^54 + 3600 * q^56 + 1170 * q^57 - 538 * q^58 + 747 * q^59 - 516 * q^60 - 1209 * q^61 + 2904 * q^62 + 1557 * q^63 - 1144 * q^64 - 831 * q^65 + 1029 * q^66 + 295 * q^67 + 7008 * q^68 + 1005 * q^69 - 390 * q^70 - 1119 * q^72 - 6 * q^73 - 1788 * q^75 + 144 * q^76 - 1203 * q^77 - 5985 * q^78 - 551 * q^79 + 4239 * q^80 + 3741 * q^81 + 18 * q^82 - 1830 * q^83 - 7725 * q^84 - 237 * q^85 - 2130 * q^87 + 1246 * q^88 - 4266 * q^89 - 9993 * q^90 - 1140 * q^91 + 7896 * q^92 - 1479 * q^93 - 3 * q^94 - 1053 * q^95 + 5034 * q^96 + 792 * q^97 - 5667 * q^98 + 4335 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	2.52419	+	1.45734i	0.892435	+	0.515248i	0.874738	−	0.484596i	$-0.161033\pi$
$2$	2.52419	+	1.45734i	0.892435	+	0.515248i	0.0176967	+	0.999843i	$0.494367\pi$
$3$	−4.29460	−	2.92513i	−0.826497	−	0.562941i
$3$	−4.29460	−	2.92513i	−0.826497	−	0.562941i
$4$	0.247680	+	0.428994i	0.0309600	+	0.0536243i
$5$	17.2113			1.53943			0.769715	−	0.638388i	$-0.220398\pi$
$5$	17.2113			1.53943			0.769715	+	0.638388i	$0.220398\pi$
$6$	−6.57748	−	13.6423i	−0.447541	−	0.928239i
$7$	17.7231	+	5.37495i	0.956960	+	0.290220i
$7$	17.7231	+	5.37495i	0.956960	+	0.290220i
$8$		−	21.8736i		−	0.966687i
$9$	9.88725	+	25.1245i	0.366194	+	0.930538i
$10$	43.4446	+	25.0828i	1.37384	+	0.793187i
$11$		−	35.6923i		−	0.978331i	−0.872191	−	0.489165i	$-0.837301\pi$
$11$		−	35.6923i		−	0.978331i	0.872191	−	0.489165i	$-0.162699\pi$
$12$	0.191176	−	2.56686i	0.00459898	−	0.0617489i
$13$	−8.99430	−	5.19286i	−0.191890	−	0.110788i	0.400977	−	0.916088i	$-0.368671\pi$
$13$	−8.99430	−	5.19286i	−0.191890	−	0.110788i	−0.592867	+	0.805300i	$0.702004\pi$
$14$	36.9034	+	39.3960i	0.704489	+	0.752074i
$15$	−73.9159	−	50.3454i	−1.27233	−	0.866608i
$16$	33.8587	−	58.6451i	0.529043	−	0.916329i
$17$	−64.1402	+	111.094i	−0.915075	+	1.58496i	−0.108285	+	0.994120i	$0.534536\pi$
$17$	−64.1402	+	111.094i	−0.915075	+	1.58496i	−0.806791	+	0.590837i	$0.798798\pi$
$18$	−11.6577	+	77.8281i	−0.152653	+	1.01913i
$19$	−84.7576	+	48.9348i	−1.02341	+	0.590864i	−0.915089	−	0.403253i	$-0.867880\pi$
$19$	−84.7576	+	48.9348i	−1.02341	+	0.590864i	−0.108317	+	0.994116i	$0.534546\pi$
$20$	4.26290	+	7.38356i	0.0476607	+	0.0825508i
$21$	−60.3915	−	74.9258i	−0.627548	−	0.778578i
$22$	52.0158	−	90.0941i	0.504082	−	0.873096i
$23$			25.5640i			0.231759i	0.993263	+	0.115880i	$0.0369687\pi$
$23$			25.5640i			0.231759i	−0.993263	+	0.115880i	$0.963031\pi$
$24$	−63.9832	+	93.9386i	−0.544188	+	0.798964i
$25$	171.230			1.36984
$26$	−15.1355	−	26.2155i	−0.114166	−	0.197742i
$27$	31.0307	−	136.821i	0.221180	−	0.975233i
$28$	2.08385	+	8.93439i	0.0140646	+	0.0603015i
$29$	−14.1366	+	8.16176i	−0.0905206	+	0.0522621i	−0.544577	−	0.838711i	$-0.683310\pi$
$29$	−14.1366	+	8.16176i	−0.0905206	+	0.0522621i	0.454056	+	0.890973i	$0.349976\pi$
$30$	−113.207	−	234.802i	−0.688957	−	1.42896i
$31$	160.589	−	92.7160i	0.930406	−	0.537170i	0.0434664	−	0.999055i	$-0.486160\pi$
$31$	160.589	−	92.7160i	0.930406	−	0.537170i	0.886940	+	0.461884i	$0.152827\pi$
$32$	19.3867	−	11.1929i	0.107097	−	0.0618327i
$33$	−104.405	+	153.284i	−0.550743	+	0.808587i
$34$	−323.804	+	186.948i	−1.63329	+	0.942981i
$35$	305.039	+	92.5101i	1.47317	+	0.446773i
$36$	−8.32941	+	10.4644i	−0.0385621	+	0.0484464i
$37$	−0.462855	−	0.801688i	−0.00205656	−	0.00356207i	0.864995	−	0.501780i	$-0.167321\pi$
$37$	−0.462855	−	0.801688i	−0.00205656	−	0.00356207i	−0.867052	+	0.498218i	$0.833988\pi$
$38$	−285.259			−1.21776
$39$	23.4372	+	48.6108i	0.0962295	+	0.199589i
$40$		−	376.474i		−	1.48815i
$41$	−231.546	+	401.049i	−0.881984	+	1.52764i	−0.0328523	+	0.999460i	$0.510459\pi$
$41$	−231.546	+	401.049i	−0.881984	+	1.52764i	−0.849132	+	0.528181i	$0.822874\pi$
$42$	−43.2471	−	277.138i	−0.158885	−	1.01817i
$43$	−43.2469	−	74.9058i	−0.153374	−	0.265652i	0.779092	−	0.626910i	$-0.215681\pi$
$43$	−43.2469	−	74.9058i	−0.153374	−	0.265652i	−0.932466	+	0.361258i	$0.882347\pi$
$44$	15.3118	−	8.84027i	0.0524623	−	0.0302891i
$45$	170.173	+	432.427i	0.563730	+	1.43250i
$46$	−37.2555	+	64.5283i	−0.119413	+	0.206830i
$47$	−143.746	+	248.976i	−0.446118	+	0.772698i	−0.998129	−	0.0611380i	$-0.980527\pi$
$47$	−143.746	+	248.976i	−0.446118	+	0.772698i	0.552012	+	0.833836i	$0.313860\pi$
$48$	−316.954	+	152.816i	−0.953092	+	0.459523i
$49$	285.220	+	190.522i	0.831545	+	0.555458i
$50$	432.217	+	249.541i	1.22250	+	0.705808i
$51$	600.421	−	289.487i	1.64854	−	0.794828i
$52$		−	5.14467i		−	0.0137200i
$53$	−334.811	−	193.303i	−0.867732	−	0.500985i	−0.00113806	−	0.999999i	$-0.500362\pi$
$53$	−334.811	−	193.303i	−0.867732	−	0.500985i	−0.866594	+	0.499014i	$0.833696\pi$
$54$	277.723	−	300.141i	0.699875	−	0.756369i
$55$		−	614.313i		−	1.50607i
$56$	117.570	−	387.669i	0.280552	−	0.925081i
$57$	507.141	+	37.7712i	1.17846	+	0.0877704i
$58$	−47.5778			−0.107712
$59$	−45.2274	−	78.3362i	−0.0997985	−	0.172856i	0.811803	−	0.583932i	$-0.198486\pi$
$59$	−45.2274	−	78.3362i	−0.0997985	−	0.172856i	−0.911601	+	0.411076i	$0.865153\pi$
$60$	3.29040	−	44.1790i	0.00707980	−	0.0950581i
$61$	120.761	+	69.7214i	0.253473	+	0.146343i	0.621354	−	0.783530i	$-0.286583\pi$
$61$	120.761	+	69.7214i	0.253473	+	0.146343i	−0.367880	+	0.929873i	$0.619916\pi$
$62$	540.475			1.10710
$63$	40.1900	+	498.429i	0.0803725	+	0.996765i
$64$	−476.492			−0.930649
$65$	−154.804	−	89.3761i	−0.295401	−	0.170550i
$66$	−486.924	+	234.765i	−0.908124	+	0.437843i
$67$	−151.612	−	262.599i	−0.276452	−	0.478830i	0.694048	−	0.719929i	$-0.255826\pi$
$67$	−151.612	−	262.599i	−0.276452	−	0.478830i	−0.970501	+	0.241099i	$0.922492\pi$
$68$	−63.5449			−0.113323
$69$	74.7780	−	109.787i	0.130467	−	0.191548i
$70$	635.157	+	678.059i	1.08451	+	1.15776i
$71$		−	351.969i		−	0.588325i	−0.955755	−	0.294163i	$-0.904959\pi$
$71$		−	351.969i		−	0.588325i	0.955755	−	0.294163i	$-0.0950407\pi$
$72$	549.565	−	216.270i	0.899539	−	0.353995i
$73$	761.691	+	439.763i	1.22122	+	0.705073i	0.965179	−	0.261592i	$-0.0842475\pi$
$73$	761.691	+	439.763i	1.22122	+	0.705073i	0.256044	+	0.966665i	$0.417581\pi$
$74$		−	2.69815i		−	0.00423856i
$75$	−735.367	−	500.871i	−1.13217	−	0.771141i
$76$	−41.9855	−	24.2403i	−0.0633693	−	0.0365863i
$77$	191.844	−	632.580i	0.283931	−	0.936223i
$78$	−11.6826	+	156.859i	−0.0169589	+	0.227702i
$79$	7.12361	−	12.3385i	0.0101452	−	0.0175720i	−0.860908	−	0.508760i	$-0.830104\pi$
$79$	7.12361	−	12.3385i	0.0101452	−	0.0175720i	0.871053	+	0.491188i	$0.163437\pi$
$80$	582.755	−	1009.36i	0.814424	−	1.41062i
$81$	−533.485	+	496.825i	−0.731803	+	0.681516i
$82$	−1168.93	+	674.881i	−1.57423	+	0.908880i
$83$	−125.688	−	217.699i	−0.166218	−	0.287898i	0.770869	−	0.636994i	$-0.219822\pi$
$83$	−125.688	−	217.699i	−0.166218	−	0.287898i	−0.937087	+	0.349095i	$0.886489\pi$
$84$	17.1850	−	44.4652i	0.0223218	−	0.0577565i
$85$	−1103.94	+	1912.08i	−1.40869	+	2.43993i
$86$		−	252.102i		−	0.316102i
$87$	84.5852	+	6.29979i	0.104235	+	0.00776332i
$88$	−780.720			−0.945739
$89$	−505.658	−	875.825i	−0.602243	−	1.04312i	−0.992481	−	0.122401i	$-0.960940\pi$
$89$	−505.658	−	875.825i	−0.602243	−	1.04312i	0.390238	−	0.920714i	$-0.372393\pi$
$90$	−200.645	+	1339.53i	−0.234999	+	1.56887i
$91$	−131.496	−	140.378i	−0.151478	−	0.161710i
$92$	−10.9668	+	6.33169i	−0.0124279	+	0.00717527i
$93$	−960.871	−	71.5644i	−1.07137	−	0.0797945i
$94$	−725.684	+	418.974i	−0.796262	+	0.459722i
$95$	−1458.79	+	842.234i	−1.57546	+	0.909593i
$96$	−115.999	−	8.63945i	−0.123324	−	0.00918500i
$97$	1125.76	−	649.959i	1.17839	−	0.680344i	0.222748	−	0.974876i	$-0.428497\pi$
$97$	1125.76	−	649.959i	1.17839	−	0.680344i	0.955642	+	0.294532i	$0.0951638\pi$
$98$	442.293	+	896.575i	0.455901	+	0.924161i
$99$	896.753	−	352.899i	0.910374	−	0.358259i
$100$	42.4103	+	73.4568i	0.0424103	+	0.0734568i
$101$	−852.814			−0.840180			−0.420090	−	0.907482i	$-0.638002\pi$
$101$	−852.814			−0.840180			−0.420090	+	0.907482i	$0.638002\pi$
$102$	1937.46	+	144.299i	1.88075	+	0.140076i
$103$		−	42.6846i		−	0.0408334i	−0.999792	−	0.0204167i	$-0.993501\pi$
$103$		−	42.6846i		−	0.0408334i	0.999792	−	0.0204167i	$-0.00649929\pi$
$104$	−113.587	+	196.738i	−0.107097	+	0.185498i
$105$	−1039.42	−	1289.57i	−0.966065	−	1.19857i
$106$	−563.417	−	975.866i	−0.516263	−	0.894193i
$107$	718.939	−	415.080i	0.649556	−	0.375021i	−0.138730	−	0.990330i	$-0.544302\pi$
$107$	718.939	−	415.080i	0.649556	−	0.375021i	0.788286	+	0.615309i	$0.210969\pi$
$108$	66.3813	−	20.5759i	0.0591439	−	0.0183326i
$109$	689.418	−	1194.11i	0.605819	−	1.04931i	−0.386103	−	0.922456i	$-0.626179\pi$
$109$	689.418	−	1194.11i	0.605819	−	1.04931i	0.991921	−	0.126853i	$-0.0404877\pi$
$110$	895.262	−	1550.64i	0.775999	−	1.34407i
$111$	−0.357262	+	4.79684i	−0.000305494	+	0.00410177i
$112$	915.298	−	857.386i	0.772210	−	0.723352i
$113$	1325.63	+	765.354i	1.10358	+	0.637155i	0.937160	−	0.348900i	$-0.113445\pi$
$113$	1325.63	+	765.354i	1.10358	+	0.637155i	0.166424	+	0.986054i	$0.446778\pi$
$114$	1225.07	+	834.418i	1.00648	+	0.685530i
$115$			439.991i			0.356777i
$116$	−7.00269	−	4.04301i	−0.00560503	−	0.00323607i
$117$	41.5394	−	277.321i	0.0328232	−	0.219131i
$118$		−	263.647i		−	0.205684i
$119$	−1733.89	+	1624.19i	−1.33568	+	1.25117i
$120$	−1101.24	+	1616.81i	−0.837739	+	1.22995i
$121$	57.0592			0.0428694
$122$	203.216	+	351.980i	0.150806	+	0.261203i
$123$	2167.52	−	1045.04i	1.58893	−	0.766086i
$124$	79.5492	+	45.9278i	0.0576107	+	0.0332616i
$125$	795.686			0.569347
$126$	−624.934	+	1316.70i	−0.441853	+	0.930959i
$127$	106.298			0.0742710			0.0371355	−	0.999310i	$-0.488177\pi$
$127$	106.298			0.0742710			0.0371355	+	0.999310i	$0.488177\pi$
$128$	−1357.85	−	783.955i	−0.937641	−	0.541347i
$129$	−33.3808	+	448.193i	−0.0227831	+	0.305901i
$130$	−260.503	−	451.204i	−0.175751	−	0.304409i
$131$	−27.2836			−0.0181968			−0.00909841	−	0.999959i	$-0.502896\pi$
$131$	−27.2836			−0.0181968			−0.00909841	+	0.999959i	$0.502896\pi$
$132$	−91.6170	−	6.82351i	−0.0604109	−	0.00449932i
$133$	−1765.19	+	411.711i	−1.15084	+	0.268420i
$134$		−	883.799i		−	0.569766i
$135$	534.080	−	2354.88i	0.340491	−	1.50130i
$136$	2430.03	+	1402.98i	1.53216	+	0.884591i
$137$			86.9719i			0.0542373i	0.999632	+	0.0271186i	$0.00863319\pi$
$137$			86.9719i			0.0542373i	−0.999632	+	0.0271186i	$0.991367\pi$
$138$	348.751	−	168.147i	0.215128	−	0.103722i
$139$	−248.393	−	143.410i	−0.151572	−	0.0875099i	0.422296	−	0.906458i	$-0.361224\pi$
$139$	−248.393	−	143.410i	−0.151572	−	0.0875099i	−0.573868	+	0.818948i	$0.694558\pi$
$140$	35.8658	+	153.773i	0.0216515	+	0.0928299i
$141$	1345.62	−	648.776i	0.803699	−	0.387495i
$142$	512.939	−	888.437i	0.303133	−	0.525042i
$143$	−185.345	+	321.027i	−0.108387	+	0.187732i
$144$	1808.20	+	270.847i	1.04641	+	0.156740i
$145$	−243.310	+	140.475i	−0.139350	+	0.0804538i
$146$	1281.77	+	2220.09i	0.726574	+	1.25846i
$147$	−667.605	−	1652.52i	−0.374579	−	0.927195i
$148$	0.229280	−	0.397124i	0.000127342	−	0.000220563i
$149$			2020.90i			1.11113i	0.831473	+	0.555566i	$0.187498\pi$
$149$			2020.90i			1.11113i	−0.831473	+	0.555566i	$0.812502\pi$
$150$	−1126.26	−	2335.97i	−0.613060	−	1.27154i
$151$	−1919.05			−1.03424			−0.517120	−	0.855913i	$-0.672996\pi$
$151$	−1919.05			−1.03424			−0.517120	+	0.855913i	$0.672996\pi$
$152$	1070.38	+	1853.95i	0.571180	+	0.989313i
$153$	−3425.36	−	513.078i	−1.80996	−	0.271111i
$154$	1406.14	−	1317.17i	0.735777	−	0.689223i
$155$	2763.95	−	1595.77i	1.43230	−	0.826936i
$156$	−15.0488	+	22.0943i	−0.00772353	+	0.0113395i
$157$	784.058	−	452.676i	0.398565	−	0.230111i	−0.287300	−	0.957841i	$-0.592758\pi$
$157$	784.058	−	452.676i	0.398565	−	0.230111i	0.685864	+	0.727729i	$0.259424\pi$
$158$	35.9626	−	20.7630i	0.0181078	−	0.0104545i
$159$	872.443	+	1809.52i	0.435152	+	0.902545i
$160$	333.671	−	192.645i	0.164869	−	0.0951871i
$161$	−137.405	+	453.075i	−0.0672612	+	0.221784i
$162$	−2070.66	+	476.610i	−1.00424	+	0.231148i
$163$	1124.59	+	1947.85i	0.540397	+	0.935995i	0.998881	+	0.0472926i	$0.0150593\pi$
$163$	1124.59	+	1947.85i	0.540397	+	0.935995i	−0.458484	+	0.888703i	$0.651607\pi$
$164$	−229.397			−0.109225
$165$	−1796.94	+	2638.23i	−0.847829	+	1.24476i
$166$		−	732.683i		−	0.342574i
$167$	1097.47	−	1900.88i	0.508534	−	0.880807i	−0.491417	−	0.870924i	$-0.663521\pi$
$167$	1097.47	−	1900.88i	0.508534	−	0.880807i	0.999951	−	0.00988229i	$-0.00314568\pi$
$168$	−1638.90	+	1320.98i	−0.752641	+	0.606642i
$169$	−1044.57	−	1809.25i	−0.475452	−	0.823507i
$170$	−5573.10	+	3217.63i	−2.51434	+	1.45165i
$171$	−2067.48	−	1645.66i	−0.924587	−	0.735948i
$172$	21.4228	−	37.1053i	0.00949692	−	0.0164491i
$173$	−1351.18	+	2340.32i	−0.593807	+	1.02850i	0.399908	+	0.916555i	$0.369042\pi$
$173$	−1351.18	+	2340.32i	−0.593807	+	1.02850i	−0.993714	+	0.111948i	$0.964291\pi$
$174$	204.328	+	139.171i	0.0890233	+	0.0606353i
$175$	3034.74	+	920.354i	1.31088	+	0.397556i
$176$	−2093.18	−	1208.50i	−0.896473	−	0.517579i
$177$	−34.9096	+	468.719i	−0.0148247	+	0.199046i
$178$		−	2947.66i		−	1.24122i
$179$	351.098	+	202.707i	0.146605	+	0.0846425i	0.571508	−	0.820596i	$-0.306359\pi$
$179$	351.098	+	202.707i	0.146605	+	0.0846425i	−0.424903	+	0.905239i	$0.639692\pi$
$180$	−143.360	+	180.107i	−0.0593636	+	0.0745797i
$181$		−	3023.81i		−	1.24176i	−0.783907	−	0.620878i	$-0.786776\pi$
$181$		−	3023.81i		−	1.24176i	0.783907	−	0.620878i	$-0.213224\pi$
$182$	−127.342	−	545.974i	−0.0518639	−	0.222364i
$183$	−314.677	−	652.667i	−0.127112	−	0.263642i
$184$	559.178			0.224039
$185$	−7.96635	−	13.7981i	−0.00316593	−	0.00548356i
$186$	−2321.13	−	1580.96i	−0.915017	−	0.623234i
$187$	3965.20	+	2289.31i	1.55061	+	0.895246i
$188$	−142.412			−0.0552472
$189$	1285.37	−	2258.12i	0.494692	−	0.869068i
$190$	−4909.68			−1.87466
$191$	−890.669	−	514.228i	−0.337416	−	0.194807i	0.321713	−	0.946837i	$-0.395742\pi$
$191$	−890.669	−	514.228i	−0.337416	−	0.194807i	−0.659129	+	0.752030i	$0.729075\pi$
$192$	2046.35	+	1393.80i	0.769179	+	0.523901i
$193$	2051.01	+	3552.46i	0.764948	+	1.32493i	0.940274	+	0.340419i	$0.110569\pi$
$193$	2051.01	+	3552.46i	0.764948	+	1.32493i	−0.175326	+	0.984510i	$0.556098\pi$
$194$	3788.85			1.40218
$195$	403.385	+	836.657i	0.148139	+	0.307253i
$196$	−11.0896	+	169.546i	−0.00404140	+	0.0617879i
$197$		−	805.333i		−	0.291257i	−0.989339	−	0.145628i	$-0.953480\pi$
$197$		−	805.333i		−	0.291257i	0.989339	−	0.145628i	$-0.0465204\pi$
$198$	2777.86	+	416.092i	0.997042	+	0.149345i
$199$	−1923.11	−	1110.31i	−0.685054	−	0.395516i	0.116702	−	0.993167i	$-0.462768\pi$
$199$	−1923.11	−	1110.31i	−0.685054	−	0.395516i	−0.801757	+	0.597651i	$0.796101\pi$
$200$		−	3745.43i		−	1.32421i
$201$	−117.024	+	1571.24i	−0.0410659	+	0.551378i
$202$	−2152.66	−	1242.84i	−0.749806	−	0.432901i
$203$	−294.414	+	68.6687i	−0.101792	+	0.0237418i
$204$	272.900	+	185.877i	0.0936610	+	0.0637941i
$205$	−3985.21	+	6902.59i	−1.35775	+	2.35170i
$206$	62.2060	−	107.744i	0.0210393	−	0.0364411i
$207$	−642.284	+	252.758i	−0.215661	+	0.0848690i
$208$	−609.072	+	351.648i	−0.203036	+	0.117223i
$209$	1746.60	+	3025.19i	0.578060	+	1.00123i
$210$	−744.340	−	4769.91i	−0.244592	−	1.56740i
$211$	1123.34	−	1945.68i	0.366511	−	0.634816i	−0.622506	−	0.782615i	$-0.713885\pi$
$211$	1123.34	−	1945.68i	0.366511	−	0.634816i	0.989017	+	0.147799i	$0.0472188\pi$
$212$		−	191.509i		−	0.0620420i
$213$	−1029.56	+	1511.57i	−0.331193	+	0.486249i
$214$	2419.65			0.772915
$215$	−744.337	−	1289.23i	−0.236109	−	0.408952i
$216$	−2992.78	−	678.754i	−0.942745	−	0.213812i
$217$	3344.48	−	780.062i	1.04626	−	0.244028i
$218$	3480.44	−	2009.43i	1.08131	−	0.624293i
$219$	−1984.80	−	4116.65i	−0.612422	−	1.27022i
$220$	263.536	−	152.153i	0.0807619	−	0.0466279i
$221$	1153.79	−	666.142i	0.351188	−	0.202758i
$222$	−7.89242	+	11.5875i	−0.00238606	+	0.00350315i
$223$	3632.93	−	2097.48i	1.09094	−	0.629854i	0.157112	−	0.987581i	$-0.449782\pi$
$223$	3632.93	−	2097.48i	1.09094	−	0.629854i	0.933826	+	0.357727i	$0.116448\pi$
$224$	403.755	−	94.1712i	0.120433	−	0.0280896i
$225$	1693.00	+	4302.08i	0.501629	+	1.27469i
$226$	2230.76	+	3863.79i	0.656585	+	1.13724i
$227$	−2341.01			−0.684487			−0.342243	−	0.939611i	$-0.611187\pi$
$227$	−2341.01			−0.684487			−0.342243	+	0.939611i	$0.611187\pi$
$228$	109.405	+	226.916i	0.0317786	+	0.0659116i
$229$		−	3060.73i		−	0.883225i	−0.897206	−	0.441613i	$-0.854407\pi$
$229$		−	3060.73i		−	0.883225i	0.897206	−	0.441613i	$-0.145593\pi$
$230$	−641.217	+	1110.62i	−0.183829	+	0.318400i
$231$	−2674.27	+	2155.51i	−0.761707	+	0.613949i
$232$	178.527	+	309.218i	0.0505211	+	0.0875051i
$233$	2201.24	−	1270.89i	0.618920	−	0.357333i	−0.157529	−	0.987514i	$-0.550353\pi$
$233$	2201.24	−	1270.89i	0.618920	−	0.357333i	0.776448	+	0.630181i	$0.217019\pi$
$234$	509.004	−	639.473i	0.142199	−	0.178648i
$235$	−2474.06	+	4285.20i	−0.686766	+	1.18951i
$236$	22.4039	−	38.8046i	0.00617952	−	0.0107032i
$237$	−66.6846	+	32.1513i	−0.0182769	+	0.00881203i
$238$	−6743.66	+	1572.88i	−1.83667	+	0.428381i
$239$	−1543.33	−	891.040i	−0.417697	−	0.241157i	0.276395	−	0.961044i	$-0.410860\pi$
$239$	−1543.33	−	891.040i	−0.417697	−	0.241157i	−0.694091	+	0.719887i	$0.744194\pi$
$240$	−5455.21	+	2630.17i	−1.46722	+	0.707404i
$241$		−	1610.36i		−	0.430426i	−0.976567	−	0.215213i	$-0.930955\pi$
$241$		−	1610.36i		−	0.430426i	0.976567	−	0.215213i	$-0.0690445\pi$
$242$	144.028	+	83.1547i	0.0382582	+	0.0220884i
$243$	3744.38	−	573.155i	0.988487	−	0.151308i
$244$			69.0743i			0.0181231i
$245$	4909.02	+	3279.14i	1.28010	+	0.855088i
$246$	6994.20	+	520.919i	1.81274	+	0.135010i
$247$	1016.45			0.261842
$248$	−2028.03	−	3512.66i	−0.519276	−	0.899412i
$249$	−97.0148	+	1302.58i	−0.0246910	+	0.331518i
$250$	2008.46	+	1159.59i	0.508105	+	0.293355i
$251$	−603.105			−0.151664			−0.0758320	−	0.997121i	$-0.524161\pi$
$251$	−603.105			−0.151664			−0.0758320	+	0.997121i	$0.524161\pi$
$252$	−203.869	+	140.692i	−0.0509625	+	0.0351697i
$253$	912.439			0.226737
$254$	268.316	+	154.912i	0.0662820	+	0.0382679i
$255$	10334.1	−	4982.46i	2.53782	−	1.22358i
$256$	−379.008	−	656.461i	−0.0925312	−	0.160269i
$257$	−1336.18			−0.324313			−0.162157	−	0.986765i	$-0.551845\pi$
$257$	−1336.18			−0.324313			−0.162157	+	0.986765i	$0.551845\pi$
$258$	−737.429	+	1082.68i	−0.177947	+	0.261258i
$259$	−3.89421	−	16.6962i	−0.000934264	−	0.00400562i
$260$		−	88.5467i		−	0.0211209i
$261$	−344.832	−	274.478i	−0.0817800	−	0.0650948i
$262$	−68.8690	−	39.7615i	−0.0162395	−	0.00937587i
$263$		−	5754.61i		−	1.34922i	−0.738175	−	0.674609i	$-0.764312\pi$
$263$		−	5754.61i		−	1.34922i	0.738175	−	0.674609i	$-0.235688\pi$
$264$	3352.88	+	2283.71i	0.781651	+	0.532396i
$265$	−5762.54	−	3327.01i	−1.33581	−	0.771231i
$266$	−5055.68	−	1533.25i	−1.16535	−	0.353420i
$267$	−390.301	+	5240.44i	−0.0894608	+	1.20116i
$268$	75.1023	−	130.081i	0.0171179	−	0.0296491i
$269$	−926.438	+	1604.64i	−0.209985	+	0.363704i	−0.951709	−	0.307000i	$-0.900675\pi$
$269$	−926.438	+	1604.64i	−0.209985	+	0.363704i	0.741725	+	0.670705i	$0.234008\pi$
$270$	4779.98	−	5165.82i	1.07741	−	1.16438i
$271$	−6459.12	+	3729.17i	−1.44784	+	0.835908i	−0.998352	−	0.0573809i	$-0.981725\pi$
$271$	−6459.12	+	3729.17i	−1.44784	+	0.835908i	−0.449483	+	0.893289i	$0.648392\pi$
$272$	4343.41	+	7523.01i	0.968228	+	1.67702i
$273$	154.100	+	987.510i	0.0341632	+	0.218926i
$274$	−126.748	+	219.533i	−0.0279456	+	0.0484032i
$275$		−	6111.61i		−	1.34016i
$276$	65.6191	+	4.88723i	0.0143109	+	0.00106586i
$277$	1370.01			0.297169			0.148585	−	0.988900i	$-0.452528\pi$
$277$	1370.01			0.297169			0.148585	+	0.988900i	$0.452528\pi$
$278$	−417.994	−	723.987i	−0.0901785	−	0.156194i
$279$	3917.23	+	3118.01i	0.840567	+	0.669070i
$280$	2023.53	−	6672.31i	0.431890	−	1.42410i
$281$	−3574.32	+	2063.63i	−0.758811	+	0.438100i	−0.828869	−	0.559443i	$-0.811015\pi$
$281$	−3574.32	+	2063.63i	−0.758811	+	0.438100i	0.0700574	+	0.997543i	$0.477682\pi$
$282$	4342.08	+	323.392i	0.916904	+	0.0682898i
$283$	−1647.02	+	950.906i	−0.345954	+	0.199737i	−0.662902	−	0.748706i	$-0.730675\pi$
$283$	−1647.02	+	950.906i	−0.345954	+	0.199737i	0.316948	+	0.948443i	$0.397342\pi$
$284$	150.993	−	87.1758i	0.0315485	−	0.0182145i
$285$	8728.57	+	650.093i	1.81416	+	0.135116i
$286$	−935.692	+	540.222i	−0.193457	+	0.111692i
$287$	−6259.33	+	5863.30i	−1.28738	+	1.20592i
$288$	472.898	+	376.415i	0.0967562	+	0.0770155i
$289$	−5771.43	−	9996.41i	−1.17473	−	2.03469i
$290$	−818.878			−0.165814
$291$	−6735.92	−	501.682i	−1.35693	−	0.101062i
$292$			435.681i			0.0873162i
$293$	3959.77	−	6858.52i	0.789530	−	1.36751i	−0.136726	−	0.990609i	$-0.543658\pi$
$293$	3959.77	−	6858.52i	0.789530	−	1.36751i	0.926255	−	0.376896i	$-0.123009\pi$
$294$	723.126	−	5144.20i	0.143447	−	1.02046i
$295$	−778.425	−	1348.27i	−0.153633	−	0.266100i
$296$	−17.5358	+	10.1243i	−0.00344341	+	0.00198805i
$297$	−4883.47	−	1107.56i	−0.954100	−	0.216387i
$298$	−2945.14	+	5101.13i	−0.572508	+	0.991612i
$299$	132.750	−	229.930i	0.0256761	−	0.0444723i
$300$	32.7351	−	439.523i	0.00629988	−	0.0845863i
$301$	−363.856	−	1560.02i	−0.0696754	−	0.298730i
$302$	−4844.05	−	2796.71i	−0.922993	−	0.532890i
$303$	3662.50	+	2494.59i	0.694406	+	0.472972i
$304$			6627.48i			1.25037i
$305$	2078.46	+	1200.00i	0.390204	+	0.225284i
$306$	−7898.51	−	6287.02i	−1.47558	−	1.17453i
$307$			1709.99i			0.317896i	0.987287	+	0.158948i	$0.0508102\pi$
$307$			1709.99i			0.317896i	−0.987287	+	0.158948i	$0.949190\pi$
$308$	318.889	−	74.3772i	0.0589948	−	0.0137599i
$309$	−124.858	+	183.313i	−0.0229868	+	0.0337487i
$310$	9302.30			1.70431
$311$	5182.89	+	8977.03i	0.944999	+	1.63679i	0.755753	+	0.654856i	$0.227271\pi$
$311$	5182.89	+	8977.03i	0.944999	+	1.63679i	0.189245	+	0.981930i	$0.439396\pi$
$312$	1063.29	−	512.656i	0.192940	−	0.0930238i
$313$	−7088.96	−	4092.81i	−1.28016	−	0.739103i	−0.303286	−	0.952899i	$-0.598084\pi$
$313$	−7088.96	−	4092.81i	−1.28016	−	0.739103i	−0.976878	+	0.213796i	$0.931417\pi$
$314$	2638.81			0.474257
$315$	691.724	+	8578.64i	0.123728	+	1.53445i
$316$	7.05750			0.00125638
$317$	3116.43	+	1799.27i	0.552165	+	0.318792i	0.749995	−	0.661444i	$-0.230056\pi$
$317$	3116.43	+	1799.27i	0.552165	+	0.318792i	−0.197830	+	0.980236i	$0.563389\pi$
$318$	−434.883	+	5839.02i	−0.0766887	+	1.02967i
$319$	291.312	+	504.567i	0.0511296	+	0.0885591i
$320$	−8201.07			−1.43267
$321$	−4301.72	−	320.386i	−0.747971	−	0.0557079i
$322$	−1007.12	+	943.399i	−0.174300	+	0.163272i
$323$		−	12554.7i		−	2.16274i
$324$	−345.268	−	105.808i	−0.0592024	−	0.0181427i
$325$	−1540.10	−	889.176i	−0.262859	−	0.151762i
$326$			6555.64i			1.11375i
$327$	−6453.69	+	3111.58i	−1.09141	+	0.526210i
$328$	8772.39	+	5064.74i	1.47675	+	0.852602i
$329$	−3885.86	+	3640.00i	−0.651169	+	0.609969i
$330$	−8380.62	+	4040.63i	−1.39799	+	0.674028i
$331$	−3992.83	+	6915.79i	−0.663039	+	1.14842i	0.316773	+	0.948501i	$0.397401\pi$
$331$	−3992.83	+	6915.79i	−0.663039	+	1.14842i	−0.979813	+	0.199917i	$0.935933\pi$
$332$	62.2610	−	107.839i	0.0102922	−	0.0178266i
$333$	15.5657	−	19.5555i	0.00256154	−	0.00321812i
$334$	5540.46	−	3198.79i	0.907667	−	0.524042i
$335$	−2609.44	−	4519.68i	−0.425579	−	0.737125i
$336$	−6438.81	+	1004.77i	−1.04543	+	0.163139i
$337$	−4758.03	+	8241.15i	−0.769100	+	1.33212i	0.168952	+	0.985624i	$0.445962\pi$
$337$	−4758.03	+	8241.15i	−0.769100	+	1.33212i	−0.938052	+	0.346495i	$0.887372\pi$
$338$		−	6089.17i		−	0.979902i
$339$	−3454.31	−	7164.54i	−0.553428	−	1.14786i
$340$	−1093.69			−0.174453
$341$	−3309.25	−	5731.78i	−0.525530	−	0.910245i
$342$	−2820.42	−	7166.99i	−0.445938	−	1.13318i
$343$	4030.95	+	4909.69i	0.634550	+	0.772882i
$344$	−1638.46	+	945.966i	−0.256802	+	0.148265i
$345$	1287.03	−	1889.59i	0.200845	−	0.294875i
$346$	−6821.28	+	3938.27i	−1.05987	+	0.611915i
$347$	6785.01	−	3917.33i	1.04968	−	0.606032i	0.127119	−	0.991887i	$-0.459427\pi$
$347$	6785.01	−	3917.33i	1.04968	−	0.606032i	0.922559	+	0.385855i	$0.126094\pi$
$348$	18.2475	+	37.8469i	0.00281083	+	0.00582990i
$349$	5127.39	−	2960.30i	0.786427	−	0.454044i	−0.0522759	−	0.998633i	$-0.516648\pi$
$349$	5127.39	−	2960.30i	0.786427	−	0.454044i	0.838703	+	0.544589i	$0.183314\pi$
$350$	6318.98	+	6745.80i	0.965040	+	1.03022i
$351$	−989.594	+	1069.47i	−0.150486	+	0.162633i
$352$	−399.501	−	691.956i	−0.0604928	−	0.104777i
$353$	4592.76			0.692487			0.346244	−	0.938145i	$-0.387457\pi$
$353$	4592.76			0.692487			0.346244	+	0.938145i	$0.387457\pi$
$354$	−771.201	+	1132.26i	−0.115788	+	0.169997i
$355$		−	6057.87i		−	0.905685i
$356$	250.483	−	433.849i	0.0372909	−	0.0645897i
$357$	12197.3	−	1903.38i	1.80827	−	0.282178i
$358$	590.825	+	1023.34i	0.0872237	+	0.151076i
$359$	−10030.3	+	5790.97i	−1.47459	+	0.851353i	−0.999590	−	0.0286338i	$-0.990884\pi$
$359$	−10030.3	+	5790.97i	−1.47459	+	0.851353i	−0.474997	+	0.879987i	$0.657551\pi$
$360$	9458.75	−	3722.30i	1.38478	−	0.544951i
$361$	1359.73	−	2355.12i	0.198240	−	0.343362i
$362$	4406.72	−	7632.66i	0.639812	−	1.10819i
$363$	−245.047	−	166.905i	−0.0354314	−	0.0241330i
$364$	27.6523	−	91.1797i	0.00398180	−	0.0131294i
$365$	13109.7	+	7568.91i	1.87999	+	1.08541i
$366$	156.855	−	2106.04i	0.0224015	−	0.300778i
$367$		−	4647.15i		−	0.660979i	−0.943810	−	0.330490i	$-0.892786\pi$
$367$		−	4647.15i		−	0.660979i	0.943810	−	0.330490i	$-0.107214\pi$
$368$	1499.20	+	865.565i	0.212368	+	0.122611i
$369$	−12365.5	−	1852.21i	−1.74451	−	0.261307i
$370$		−	46.4387i		−	0.00652496i
$371$	−4894.91	−	5225.53i	−0.684989	−	0.731256i
$372$	−207.288	−	429.933i	−0.0288908	−	0.0599220i
$373$	13272.9			1.84247			0.921237	−	0.389001i	$-0.127180\pi$
$373$	13272.9			1.84247			0.921237	+	0.389001i	$0.127180\pi$
$374$	6672.61	+	11557.3i	0.922547	+	1.59790i
$375$	−3417.16	−	2327.48i	−0.470563	−	0.320509i
$376$	5446.00	+	3144.25i	0.746957	+	0.431256i
$377$	169.532			0.0231600
$378$	6535.36	−	3826.69i	0.889266	−	0.520698i
$379$	11820.6			1.60207			0.801033	−	0.598620i	$-0.204284\pi$
$379$	11820.6			1.60207			0.801033	+	0.598620i	$0.204284\pi$
$380$	−722.626	−	417.209i	−0.0975525	−	0.0563220i
$381$	−456.507	−	310.935i	−0.0613847	−	0.0418102i
$382$	−1498.81	−	2596.02i	−0.200748	−	0.347706i
$383$	4630.60			0.617787			0.308894	−	0.951097i	$-0.400041\pi$
$383$	4630.60			0.617787			0.308894	+	0.951097i	$0.400041\pi$
$384$	3538.26	+	7338.66i	0.470211	+	0.975259i
$385$	3301.90	−	10887.6i	0.437092	−	1.44125i
$386$			11956.1i			1.57655i
$387$	1454.38	−	1827.17i	0.191034	−	0.240001i
$388$	557.657	+	321.964i	0.0729659	+	0.0421269i
$389$		−	8332.61i		−	1.08607i	−0.839711	−	0.543034i	$-0.817276\pi$
$389$		−	8332.61i		−	1.08607i	0.839711	−	0.543034i	$-0.182724\pi$
$390$	−201.074	+	2699.75i	−0.0261071	+	0.350531i
$391$	−2840.01	−	1639.68i	−0.367329	−	0.212077i
$392$	4167.41	−	6238.79i	0.536954	−	0.803843i
$393$	117.172	+	79.8082i	0.0150396	+	0.0102437i
$394$	1173.64	−	2032.81i	0.150069	−	0.259928i
$395$	122.607	−	212.361i	0.0156178	−	0.0270508i
$396$	373.499	+	297.296i	0.0473965	+	0.0377264i
$397$	5613.15	−	3240.75i	0.709611	−	0.409694i	−0.101306	−	0.994855i	$-0.532302\pi$
$397$	5613.15	−	3240.75i	0.709611	−	0.409694i	0.810917	+	0.585161i	$0.198969\pi$
$398$	−3236.20	−	5605.26i	−0.407577	−	0.705945i
$399$	8785.11	+	3395.28i	1.10227	+	0.426006i
$400$	5797.65	−	10041.8i	0.724706	−	1.25523i
$401$		−	1709.94i		−	0.212944i	−0.994316	−	0.106472i	$-0.966045\pi$
$401$		−	1709.94i		−	0.212944i	0.994316	−	0.106472i	$-0.0339554\pi$
$402$	−2585.23	+	3795.57i	−0.320745	+	0.470910i
$403$	−1925.85			−0.238048
$404$	−211.225	−	365.852i	−0.0260120	−	0.0450540i
$405$	−9181.99	+	8551.02i	−1.12656	+	1.04915i
$406$	−843.229	−	255.728i	−0.103076	−	0.0312601i
$407$	−28.6141	+	16.5203i	−0.00348488	+	0.00201200i
$408$	−6332.12	−	13133.4i	−0.768350	−	1.59363i
$409$	−5376.61	+	3104.19i	−0.650016	+	0.375287i	−0.788462	−	0.615083i	$-0.789122\pi$
$409$	−5376.61	+	3104.19i	−0.650016	+	0.375287i	0.138447	+	0.990370i	$0.455789\pi$
$410$	−20118.8	+	11615.6i	−2.42341	+	1.39916i
$411$	254.404	−	373.510i	0.0305324	−	0.0448269i
$412$	18.3114	−	10.5721i	0.00218966	−	0.00126420i
$413$	−380.519	−	1631.46i	−0.0453369	−	0.194380i
$414$	−1989.60	−	298.019i	−0.236192	−	0.0353788i
$415$	−2163.27	−	3746.89i	−0.255881	−	0.443199i
$416$	−232.493			−0.0274012
$417$	647.259	+	1342.47i	0.0760105	+	0.157653i
$418$			10181.5i			1.19138i
$419$	−5926.05	+	10264.2i	−0.690946	+	1.19675i	0.280582	+	0.959830i	$0.409473\pi$
$419$	−5926.05	+	10264.2i	−0.690946	+	1.19675i	−0.971528	+	0.236924i	$0.923861\pi$
$420$	295.776	−	765.306i	0.0343629	−	0.0889121i
$421$	−218.101	−	377.763i	−0.0252485	−	0.0437317i	0.853125	−	0.521706i	$-0.174704\pi$
$421$	−218.101	−	377.763i	−0.0252485	−	0.0437317i	−0.878374	+	0.477975i	$0.841371\pi$
$422$	5671.04	−	3274.17i	0.654175	−	0.377688i
$423$	−7676.65	−	1149.87i	−0.882391	−	0.132172i
$424$	−4228.24	+	7323.52i	−0.484296	+	0.838825i
$425$	−10982.7	+	19022.7i	−1.25351	+	2.17114i
$426$	−4801.66	+	2315.07i	−0.546106	+	0.263299i
$427$	1765.52	+	1884.77i	0.200092	+	0.213607i
$428$	356.133	+	205.614i	0.0402205	+	0.0232213i
$429$	1735.03	−	836.527i	0.195264	−	0.0941443i
$430$		−	4339.01i		−	0.486617i
$431$	10890.9	+	6287.86i	1.21716	+	0.702728i	0.964309	−	0.264778i	$-0.0852986\pi$
$431$	10890.9	+	6287.86i	1.21716	+	0.702728i	0.252850	+	0.967505i	$0.418632\pi$
$432$	−6973.24	−	6452.40i	−0.776621	−	0.718614i
$433$			15488.3i			1.71898i	0.511149	+	0.859492i	$0.329220\pi$
$433$			15488.3i			1.71898i	−0.511149	+	0.859492i	$0.670780\pi$
$434$	9578.92	+	2905.02i	1.05945	+	0.321303i
$435$	1455.83	+	108.428i	0.160463	+	0.0119511i
$436$	683.020			0.0750246
$437$	−1250.97	−	2166.74i	−0.136938	−	0.237184i
$438$	989.355	−	13283.7i	0.107930	−	1.44913i
$439$	−10844.1	−	6260.84i	−1.17895	−	0.680669i	−0.223181	−	0.974777i	$-0.571644\pi$
$439$	−10844.1	−	6260.84i	−1.17895	−	0.680669i	−0.955772	+	0.294108i	$0.904977\pi$
$440$	−13437.2			−1.45590
$441$	−1966.74	+	9049.75i	−0.212368	+	0.977190i
$442$	3883.18			0.417883
$443$	705.907	+	407.556i	0.0757080	+	0.0437100i	0.537376	−	0.843343i	$-0.319416\pi$
$443$	705.907	+	407.556i	0.0757080	+	0.0437100i	−0.461668	+	0.887053i	$0.652749\pi$
$444$	−2.14630	+	1.03482i	−0.000229412	+	0.000110609i
$445$	−8703.05	−	15074.1i	−0.927111	−	1.60580i
$446$	12226.9			1.29812
$447$	5911.39	−	8678.96i	0.625502	−	0.918347i
$448$	−8444.95	−	2561.12i	−0.890594	−	0.270093i
$449$		−	5276.20i		−	0.554565i	−0.960788	−	0.277282i	$-0.910566\pi$
$449$		−	5276.20i		−	0.554565i	0.960788	−	0.277282i	$-0.0894337\pi$
$450$	−1996.16	+	13326.5i	−0.209111	+	1.39604i
$451$	14314.4	+	8264.40i	1.49454	+	0.862872i
$452$			758.251i			0.0789052i
$453$	8241.58	+	5613.48i	0.854797	+	0.582217i
$454$	−5909.15	−	3411.65i	−0.610860	−	0.352680i
$455$	−2263.22	−	2416.09i	−0.233190	−	0.248941i
$456$	826.192	−	11093.0i	0.0848465	−	1.13921i
$457$	4560.82	−	7899.58i	0.466841	−	0.808592i	−0.532442	−	0.846467i	$-0.678725\pi$
$457$	4560.82	−	7899.58i	0.466841	−	0.808592i	0.999283	+	0.0378745i	$0.0120587\pi$
$458$	4460.52	−	7725.85i	0.455080	−	0.788221i
$459$	13209.7	+	12223.1i	1.34331	+	1.24297i
$460$	−188.754	+	108.977i	−0.0191319	+	0.0110458i
$461$	−420.112	−	727.655i	−0.0424437	−	0.0735147i	0.844023	−	0.536307i	$-0.180181\pi$
$461$	−420.112	−	727.655i	−0.0424437	−	0.0735147i	−0.886467	+	0.462792i	$0.846848\pi$
$462$	−9891.68	+	1543.59i	−0.996109	+	0.155442i
$463$	−1889.21	+	3272.21i	−0.189631	+	0.328450i	−0.945127	−	0.326703i	$-0.894062\pi$
$463$	−1889.21	+	3272.21i	−0.189631	+	0.328450i	0.755496	+	0.655153i	$0.227396\pi$
$464$			1105.39i			0.110596i
$465$	−16537.9	−	1231.72i	−1.64930	−	0.122838i
$466$	7408.47			0.736461
$467$	3197.40	+	5538.05i	0.316826	+	0.548759i	0.979824	−	0.199862i	$-0.0640495\pi$
$467$	3197.40	+	5538.05i	0.316826	+	0.548759i	−0.662998	+	0.748621i	$0.730716\pi$
$468$	129.257	−	50.8666i	0.0127669	−	0.00502417i
$469$	−1275.58	−	5468.99i	−0.125588	−	0.538453i
$470$	−12490.0	+	7211.10i	−1.22579	+	0.707709i
$471$	−4691.36	−	349.406i	−0.458952	−	0.0341821i
$472$	−1713.50	+	989.288i	−0.167098	+	0.0964739i
$473$	−2673.56	+	1543.58i	−0.259895	+	0.150051i
$474$	−215.180	−	16.0263i	−0.0208513	−	0.00155298i
$475$	−14513.1	+	8379.12i	−1.40191	+	0.809390i
$476$	−1126.22	−	341.551i	−0.108445	−	0.0328886i
$477$	1546.29	−	10323.2i	0.148428	−	0.990916i
$478$	−2597.10	−	4498.30i	−0.248511	−	0.430434i
$479$	−17221.8			−1.64276			−0.821382	−	0.570379i	$-0.806797\pi$
$479$	−17221.8			−1.64276			−0.821382	+	0.570379i	$0.806797\pi$
$480$	−1996.50	−	148.696i	−0.189848	−	0.0141397i
$481$			9.61416i			0.000911368i
$482$	2346.85	−	4064.86i	0.221776	−	0.384127i
$483$	1915.40	−	1543.85i	0.180443	−	0.145440i
$484$	14.1324	+	24.4781i	0.00132724	+	0.00229884i
$485$	19375.9	−	11186.7i	1.81405	−	1.04734i
$486$	10286.8	+	4010.09i	0.960121	+	0.374282i
$487$	1435.74	−	2486.77i	0.133592	−	0.231389i	−0.791466	−	0.611213i	$-0.790682\pi$
$487$	1435.74	−	2486.77i	0.133592	−	0.231389i	0.925059	+	0.379824i	$0.124015\pi$
$488$	1525.06	−	2641.48i	0.141468	−	0.245029i
$489$	868.035	−	11654.8i	0.0802738	−	1.07781i
$490$	7612.45	+	15431.3i	0.701828	+	1.42268i
$491$	−4900.34	−	2829.21i	−0.450406	−	0.260042i	0.257596	−	0.966253i	$-0.417070\pi$
$491$	−4900.34	−	2829.21i	−0.450406	−	0.260042i	−0.708002	+	0.706211i	$0.750403\pi$
$492$	985.168	+	671.015i	0.0902740	+	0.0614872i
$493$		−	2093.99i		−	0.191295i
$494$	2565.70	+	1481.31i	0.233677	+	0.134913i
$495$	15434.3	−	6073.86i	1.40146	−	0.551514i
$496$		−	12557.0i		−	1.13674i
$497$	1891.82	−	6238.01i	0.170744	−	0.563004i
$498$	−2143.19	+	3146.58i	−0.192849	+	0.283136i
$499$	−18601.4			−1.66876			−0.834380	−	0.551190i	$-0.814174\pi$
$499$	−18601.4			−1.66876			−0.834380	+	0.551190i	$0.814174\pi$
$500$	197.075	+	341.345i	0.0176270	+	0.0305308i
$501$	−10273.5	+	4953.28i	−0.916144	+	0.441709i
$502$	−1522.35	−	878.930i	−0.135350	−	0.0781445i
$503$	−14649.8			−1.29862			−0.649308	−	0.760526i	$-0.724941\pi$
$503$	−14649.8			−1.29862			−0.649308	+	0.760526i	$0.724941\pi$
$504$	10902.5	−	879.101i	0.963559	−	0.0776950i
$505$	−14678.1			−1.29340
$506$	2303.17	+	1329.73i	0.202348	+	0.116826i
$507$	−806.268	+	10825.5i	−0.0706265	+	0.948278i
$508$	26.3279	+	45.6012i	0.00229943	+	0.00398273i
$509$	−2629.20			−0.228953			−0.114477	−	0.993426i	$-0.536519\pi$
$509$	−2629.20			−0.228953			−0.114477	+	0.993426i	$0.536519\pi$
$510$	33346.2	+	2483.58i	2.89529	+	0.215637i
$511$	11135.9	+	11888.0i	0.964035	+	1.02915i
$512$			10333.9i			0.891989i
$513$	4065.24	+	13115.1i	0.349873	+	1.12875i
$514$	−3372.76	−	1947.27i	−0.289428	−	0.167102i
$515$		−	734.659i		−	0.0628601i
$516$	−200.540	+	96.6882i	−0.0171091	+	0.00824896i
$517$	8886.51	+	5130.63i	0.755954	+	0.436450i
$518$	14.5024	−	47.8196i	0.00123011	−	0.00405613i
$519$	12648.5	−	6098.35i	1.06977	−	0.515776i
$520$	−1954.98	+	3386.13i	−0.164868	+	0.285560i
$521$	8915.56	−	15442.2i	0.749708	−	1.29853i	−0.198255	−	0.980151i	$-0.563527\pi$
$521$	8915.56	−	15442.2i	0.749708	−	1.29853i	0.947963	−	0.318382i	$-0.103139\pi$
$522$	−470.414	−	1195.37i	−0.0394434	−	0.100230i
$523$	−18929.9	+	10929.2i	−1.58269	+	0.913766i	−0.588224	+	0.808698i	$0.700173\pi$
$523$	−18929.9	+	10929.2i	−1.58269	+	0.913766i	−0.994465	+	0.105068i	$0.966494\pi$
$524$	−6.75761	−	11.7045i	−0.000563373	−	0.000975791i
$525$	−10340.9	−	12829.6i	−0.859642	−	1.06653i
$526$	8386.42	−	14525.7i	0.695181	−	1.20409i
$527$			23787.3i			1.96621i
$528$	5454.36	+	11312.8i	0.449566	+	0.932439i
$529$	11513.5			0.946288
$530$	−9697.16	−	16796.0i	−0.794750	−	1.37655i
$531$	1520.99	−	1910.85i	0.124304	−	0.156165i
$532$	−613.824	−	655.285i	−0.0500238	−	0.0534026i
$533$	4165.18	−	2404.77i	0.338488	−	0.195426i
$534$	−8622.29	+	12659.0i	−0.698732	+	1.02586i
$535$	12373.9	−	7144.08i	0.999945	−	0.577319i
$536$	−5744.00	+	3316.30i	−0.462878	+	0.267243i
$537$	−914.885	−	1897.55i	−0.0735199	−	0.152487i
$538$	−4677.01	+	2700.27i	−0.374796	+	0.216388i
$539$	6800.17	−	10180.2i	0.543421	−	0.813526i
$540$	1142.51	−	354.139i	0.0910478	−	0.0282217i
$541$	−5561.14	−	9632.17i	−0.441944	−	0.765470i	0.555889	−	0.831256i	$-0.312378\pi$
$541$	−5561.14	−	9632.17i	−0.441944	−	0.765470i	−0.997834	+	0.0657862i	$0.979044\pi$
$542$	−21738.7			−1.72280
$543$	−8845.03	+	12986.1i	−0.699036	+	1.02631i
$544$			2871.66i			0.226326i
$545$	11865.8	−	20552.2i	0.932615	−	1.61534i
$546$	−1050.16	+	2717.24i	−0.0823126	+	0.212980i
$547$	7533.25	+	13048.0i	0.588845	+	1.01991i	0.994384	+	0.105832i	$0.0337506\pi$
$547$	7533.25	+	13048.0i	0.588845	+	1.01991i	−0.405539	+	0.914078i	$0.632916\pi$
$548$	−37.3104	+	21.5412i	−0.00290843	+	0.00167919i
$549$	−557.724	+	3723.42i	−0.0433572	+	0.289456i
$550$	8906.69	−	15426.8i	0.690514	−	1.19600i
$551$	798.788	−	1383.54i	0.0617596	−	0.106971i
$552$	−2401.45	−	1635.67i	−0.185167	−	0.126121i
$553$	192.571	−	180.387i	0.0148083	−	0.0138713i
$554$	3458.16	+	1996.57i	0.265204	+	0.153116i
$555$	−6.14896	+	82.5601i	−0.000470287	+	0.00631438i
$556$		−	142.079i		−	0.0108372i
$557$	6994.00	+	4037.99i	0.532038	+	0.307172i	0.741846	−	0.670570i	$-0.233951\pi$
$557$	6994.00	+	4037.99i	0.532038	+	0.307172i	−0.209808	+	0.977743i	$0.567284\pi$
$558$	5343.81	+	13579.2i	0.405415	+	1.03020i
$559$			898.300i			0.0679679i
$560$	15753.5	−	14756.8i	1.18876	−	1.11355i
$561$	−10332.4	−	21430.4i	−0.777605	−	1.61282i
$562$	−12029.7			−0.902920
$563$	4491.15	+	7778.89i	0.336198	+	0.582311i	0.983714	−	0.179740i	$-0.0575257\pi$
$563$	4491.15	+	7778.89i	0.336198	+	0.582311i	−0.647517	+	0.762051i	$0.724192\pi$
$564$	611.603	+	416.574i	0.0456616	+	0.0311009i
$565$	22815.9	+	13172.8i	1.69889	+	0.980855i
$566$	−5543.18			−0.411656
$567$	−12125.4	+	5937.85i	−0.898096	+	0.439799i
$568$	−7698.85			−0.568726
$569$	9591.95	+	5537.92i	0.706706	+	0.408017i	0.809840	−	0.586651i	$-0.199554\pi$
$569$	9591.95	+	5537.92i	0.706706	+	0.408017i	−0.103134	+	0.994667i	$0.532887\pi$
$570$	21085.1	+	14361.5i	1.54940	+	1.05532i
$571$	11164.3	+	19337.1i	0.818233	+	1.41722i	0.906983	+	0.421167i	$0.138380\pi$
$571$	11164.3	+	19337.1i	0.818233	+	1.41722i	−0.0887498	+	0.996054i	$0.528287\pi$
$572$	−183.625			−0.0134226
$573$	2320.89	+	4813.73i	0.169209	+	0.350953i
$574$	−24344.5	+	5678.09i	−1.77025	+	0.412890i
$575$			4377.33i			0.317474i
$576$	−4711.20	−	11971.7i	−0.340798	−	0.866005i
$577$	2753.56	+	1589.77i	0.198669	+	0.114702i	0.596035	−	0.802959i	$-0.296742\pi$
$577$	2753.56	+	1589.77i	0.198669	+	0.114702i	−0.397365	+	0.917660i	$0.630075\pi$
$578$		−	33643.7i		−	2.42110i
$579$	1583.11	−	21255.9i	0.113630	−	1.52567i
$580$	−120.526	−	69.5856i	−0.00862855	−	0.00498170i
$581$	−1057.47	−	4533.87i	−0.0755102	−	0.323747i
$582$	−16271.6	−	11082.9i	−1.15890	−	0.789346i
$583$	−6899.43	+	11950.2i	−0.490129	+	0.848929i
$584$	9619.21	−	16661.0i	0.681585	−	1.18054i
$585$	714.949	−	4773.06i	0.0505291	−	0.337337i
$586$	19990.4	−	11541.5i	1.40921	−	0.813606i
$587$	9230.28	+	15987.3i	0.649019	+	1.12413i	0.983357	+	0.181681i	$0.0581540\pi$
$587$	9230.28	+	15987.3i	0.649019	+	1.12413i	−0.334338	+	0.942453i	$0.608513\pi$
$588$	543.570	−	695.695i	0.0381232	−	0.0487925i
$589$	−9074.08	+	15716.8i	−0.634789	+	1.09949i
$590$		−	4537.72i		−	0.316636i
$591$	−2355.70	+	3458.58i	−0.163960	+	0.240723i
$592$	−62.6867			−0.00435204
$593$	4842.31	+	8387.12i	0.335328	+	0.580806i	0.983548	−	0.180648i	$-0.0578194\pi$
$593$	4842.31	+	8387.12i	0.335328	+	0.580806i	−0.648220	+	0.761453i	$0.724486\pi$
$594$	−10712.7	−	9912.56i	−0.739979	−	0.684709i
$595$	−29842.6	+	27954.4i	−2.05618	+	1.92608i
$596$	−866.954	+	500.536i	−0.0595836	+	0.0344006i
$597$	5011.21	+	10393.7i	0.343543	+	0.712538i
$598$	670.174	−	386.925i	0.0458285	−	0.0264591i
$599$	−3303.93	+	1907.53i	−0.225367	+	0.130116i	−0.608433	−	0.793605i	$-0.708202\pi$
$599$	−3303.93	+	1907.53i	−0.225367	+	0.130116i	0.383066	+	0.923721i	$0.374868\pi$
$600$	−10955.9	+	16085.1i	−0.745452	+	1.09445i
$601$	7609.28	−	4393.22i	0.516454	−	0.298175i	−0.219029	−	0.975718i	$-0.570289\pi$
$601$	7609.28	−	4393.22i	0.516454	−	0.298175i	0.735483	+	0.677544i	$0.236955\pi$
$602$	1355.03	−	4468.03i	0.0917392	−	0.302497i
$603$	5098.66	−	6405.56i	0.344334	−	0.432594i
$604$	−475.311	−	823.263i	−0.0320201	−	0.0554604i
$605$	982.066			0.0659944
$606$	5609.37	+	11634.3i	0.376015	+	0.779888i
$607$		−	11742.5i		−	0.785194i	−0.919711	−	0.392597i	$-0.871577\pi$
$607$		−	11742.5i		−	0.785194i	0.919711	−	0.392597i	$-0.128423\pi$
$608$	−1095.45	+	1897.37i	−0.0730694	+	0.126560i
$609$	1465.26	+	566.293i	0.0974961	+	0.0376804i
$610$	3497.61	+	6058.04i	0.232154	+	0.402103i
$611$	2585.79	−	1492.91i	0.171211	−	0.0988487i
$612$	−628.284	−	1596.54i	−0.0414982	−	0.105451i
$613$	9443.86	−	16357.2i	0.622241	−	1.07775i	−0.366826	−	0.930289i	$-0.619556\pi$
$613$	9443.86	−	16357.2i	0.622241	−	1.07775i	0.989067	−	0.147464i	$-0.0471110\pi$
$614$	−2492.03	+	4316.33i	−0.163795	+	0.283702i
$615$	37305.9	−	17986.6i	2.44604	−	1.17933i
$616$	−13836.8	−	4196.33i	−0.905035	−	0.274472i
$617$	−10726.8	−	6193.11i	−0.699909	−	0.404093i	0.107404	−	0.994215i	$-0.465746\pi$
$617$	−10726.8	−	6193.11i	−0.699909	−	0.404093i	−0.807314	+	0.590123i	$0.799079\pi$
$618$	−582.315	+	280.757i	−0.0379031	+	0.0182746i
$619$		−	2663.48i		−	0.172947i	−0.996254	−	0.0864735i	$-0.972440\pi$
$619$		−	2663.48i		−	0.172947i	0.996254	−	0.0864735i	$-0.0275598\pi$
$620$	1369.15	+	790.479i	0.0886877	+	0.0512038i
$621$	3497.70	+	793.269i	0.226019	+	0.0512605i
$622$			30212.9i			1.94763i
$623$	−4254.33	−	18240.3i	−0.273590	−	1.17300i
$624$	3644.34	+	271.425i	0.233798	+	0.0174130i
$625$	−7708.96			−0.493374
$626$	−11929.2	−	20662.0i	−0.761642	−	1.31920i
$627$	1348.14	−	18101.0i	0.0858685	−	1.15293i
$628$	388.391	+	224.238i	0.0246791	+	0.0142485i
$629$	118.750			0.00752764
$630$	−10756.0	+	22662.2i	−0.680202	+	1.43315i
$631$	20380.6			1.28580			0.642898	−	0.765952i	$-0.277732\pi$
$631$	20380.6			1.28580			0.642898	+	0.765952i	$0.277732\pi$
$632$	−269.887	−	155.819i	−0.0169866	−	0.00980720i
$633$	−10515.7	+	5070.02i	−0.660284	+	0.318349i
$634$	5244.30	+	9083.40i	0.328514	+	0.569003i
$635$	1829.53			0.114335
$636$	−560.189	+	822.456i	−0.0349260	+	0.0512775i
$637$	−1576.00	−	3194.72i	−0.0980272	−	0.198712i
$638$			1698.16i			0.105378i
$639$	8843.07	−	3480.01i	0.547459	−	0.215441i
$640$	−23370.4	−	13492.9i	−1.44343	−	0.833366i
$641$			20778.8i			1.28036i	0.768224	+	0.640181i	$0.221141\pi$
$641$			20778.8i			1.28036i	−0.768224	+	0.640181i	$0.778859\pi$
$642$	−10391.4	−	7077.78i	−0.638812	−	0.435106i
$643$	−6344.01	−	3662.72i	−0.389088	−	0.224640i	0.292677	−	0.956211i	$-0.405454\pi$
$643$	−6344.01	−	3662.72i	−0.389088	−	0.224640i	−0.681765	+	0.731572i	$0.738787\pi$
$644$	−228.399	+	53.2714i	−0.0139754	+	0.00325961i
$645$	−574.529	+	7714.01i	−0.0350730	+	0.470913i
$646$	18296.5	−	31690.5i	1.11435	−	1.93010i
$647$	5424.13	−	9394.87i	0.329590	−	0.570866i	−0.652841	−	0.757495i	$-0.726423\pi$
$647$	5424.13	−	9394.87i	0.329590	−	0.570866i	0.982430	+	0.186629i	$0.0597562\pi$
$648$	10867.4	+	11669.2i	0.658812	+	0.707425i
$649$	−2796.00	+	1614.27i	−0.169110	+	0.0976359i
$650$	−2591.66	−	4488.89i	−0.156390	−	0.270875i
$651$	−16645.0	−	6432.98i	−1.00210	−	0.387294i
$652$	−557.077	+	964.885i	−0.0334614	+	0.0579568i
$653$			11896.6i			0.712941i	0.934307	+	0.356470i	$0.116020\pi$
$653$			11896.6i			0.712941i	−0.934307	+	0.356470i	$0.883980\pi$
$654$	−20825.0	−	1551.02i	−1.24514	−	0.0927362i
$655$	−469.588			−0.0280127
$656$	15679.7	+	27158.0i	0.933215	+	1.61638i
$657$	−3517.80	+	23485.2i	−0.208893	+	1.39459i
$658$	−15113.4	+	3525.02i	−0.895411	+	0.208844i
$659$	−24001.0	+	13857.0i	−1.41874	+	0.819108i	−0.996188	−	0.0872319i	$-0.972198\pi$
$659$	−24001.0	+	13857.0i	−1.41874	+	0.819108i	−0.422549	+	0.906340i	$0.638865\pi$
$660$	−1576.85	−	117.442i	−0.0929983	−	0.00692639i
$661$	24782.6	−	14308.3i	1.45829	−	0.841947i	0.459367	−	0.888246i	$-0.348076\pi$
$661$	24782.6	−	14308.3i	1.45829	−	0.841947i	0.998928	+	0.0462996i	$0.0147429\pi$
$662$	−20157.3	+	11637.8i	−1.18344	+	0.683259i
$663$	−6903.63	−	514.174i	−0.404397	−	0.0301189i
$664$	−4761.86	+	2749.26i	−0.278307	+	0.160681i
$665$	−30381.3	+	7086.10i	−1.77164	+	0.413214i
$666$	67.7897	−	26.6772i	0.00394414	−	0.00155213i
$667$	−208.647	−	361.388i	−0.0121122	−	0.0209790i
$668$	1087.29			0.0629768
$669$	−21737.4	−	1618.97i	−1.25623	−	0.0935622i
$670$		−	15211.4i		−	0.877114i
$671$	2488.52	−	4310.24i	0.143172	−	0.247981i
$672$	−2009.43	−	776.606i	−0.115350	−	0.0445807i
$673$	−3408.12	−	5903.03i	−0.195205	−	0.338106i	0.751762	−	0.659434i	$-0.229204\pi$
$673$	−3408.12	−	5903.03i	−0.195205	−	0.338106i	−0.946968	+	0.321328i	$0.895871\pi$
$674$	−24020.3	+	13868.1i	−1.37274	+	0.792553i
$675$	5313.40	−	23428.0i	0.302982	−	1.33592i
$676$	517.437	−	896.227i	0.0294400	−	0.0509915i
$677$	−2806.77	+	4861.47i	−0.159340	+	0.275984i	−0.934631	−	0.355620i	$-0.884270\pi$
$677$	−2806.77	+	4861.47i	−0.159340	+	0.275984i	0.775291	+	0.631604i	$0.217603\pi$
$678$	1721.85	−	23118.7i	0.0975330	−	1.30954i
$679$	23445.5	−	5468.41i	1.32512	−	0.309069i
$680$	41824.1	+	24147.1i	2.35865	+	1.36177i
$681$	10053.7	+	6847.76i	0.565726	+	0.385326i
$682$		−	19290.8i		−	1.08311i
$683$	−8374.35	−	4834.94i	−0.469159	−	0.270869i	0.246728	−	0.969085i	$-0.420644\pi$
$683$	−8374.35	−	4834.94i	−0.469159	−	0.270869i	−0.715888	+	0.698215i	$0.753978\pi$
$684$	193.906	−	1294.54i	0.0108395	−	0.0723652i
$685$			1496.90i			0.0834945i
$686$	3019.77	+	18267.4i	0.168069	+	1.01670i
$687$	−8953.02	+	13144.6i	−0.497204	+	0.729983i
$688$	−5857.14			−0.324566
$689$	2007.59	+	3477.25i	0.111006	+	0.192268i
$690$	6002.48	−	2894.03i	0.331174	−	0.159672i
$691$	3737.34	+	2157.76i	0.205753	+	0.118792i	0.599336	−	0.800497i	$-0.295431\pi$
$691$	3737.34	+	2157.76i	0.205753	+	0.118792i	−0.393583	+	0.919289i	$0.628765\pi$
$692$	−1338.64			−0.0735370
$693$	17790.1	−	1434.47i	0.975166	−	0.0786308i
$694$	22835.5			1.24903
$695$	−4275.18	−	2468.28i	−0.233334	−	0.134715i
$696$	137.799	−	1850.19i	0.00750470	−	0.100763i
$697$	−29702.8	−	51446.7i	−1.61416	−	2.79581i
$698$	17256.7			0.935780
$699$	−13171.0	−	980.957i	−0.712693	−	0.0530804i
$700$	356.818	+	1529.84i	0.0192663	+	0.0826035i
$701$			22520.8i			1.21341i	0.794929	+	0.606703i	$0.207508\pi$
$701$			22520.8i			1.21341i	−0.794929	+	0.606703i	$0.792492\pi$
$702$	−4056.51	+	1257.38i	−0.218096	+	0.0676022i
$703$	78.4608	+	45.2994i	0.00420940	+	0.00243030i
$704$			17007.1i			0.910483i
$705$	23159.9	−	11166.3i	1.23724	−	0.596521i
$706$	11593.0	+	6693.21i	0.618000	+	0.356802i
$707$	−15114.6	−	4583.83i	−0.804019	−	0.243837i
$708$	−209.724	+	101.116i	−0.0111327	+	0.00536749i
$709$	1407.50	−	2437.87i	0.0745556	−	0.129134i	−0.826337	−	0.563175i	$-0.809579\pi$
$709$	1407.50	−	2437.87i	0.0745556	−	0.129134i	0.900893	+	0.434041i	$0.142913\pi$
$710$	8828.37	−	15291.2i	0.466652	−	0.808265i
$711$	380.431	+	56.9841i	0.0200665	+	0.00300572i
$712$	−19157.5	+	11060.6i	−1.00837	+	0.582180i
$713$	2370.19	+	4105.29i	0.124494	+	0.215630i
$714$	33562.2	+	12971.2i	1.75915	+	0.679879i
$715$	−3190.04	+	5525.31i	−0.166854	+	0.289000i
$716$			200.826i			0.0104821i
$717$	4021.57	+	8341.09i	0.209468	+	0.434455i
$718$	−33757.7			−1.75463
$719$	−5377.34	−	9313.82i	−0.278916	−	0.483097i	0.692199	−	0.721706i	$-0.256642\pi$
$719$	−5377.34	−	9313.82i	−0.278916	−	0.483097i	−0.971116	+	0.238609i	$0.923309\pi$
$720$	31121.6	+	4661.64i	1.61088	+	0.241291i
$721$	229.428	−	756.505i	0.0118507	−	0.0390759i
$722$	6864.42	−	3963.17i	0.353833	−	0.204285i
$723$	−4710.52	+	6915.87i	−0.242304	+	0.355745i
$724$	1297.20	−	748.936i	0.0665883	−	0.0384447i
$725$	−2420.61	+	1397.54i	−0.123999	+	0.0715908i
$726$	−375.306	−	778.417i	−0.0191858	−	0.0397931i
$727$	5477.81	−	3162.62i	0.279451	−	0.161341i	−0.353724	−	0.935350i	$-0.615085\pi$
$727$	5477.81	−	3162.62i	0.279451	−	0.161341i	0.633175	+	0.774009i	$0.281751\pi$
$728$	−3070.57	+	2876.29i	−0.156323	+	0.146432i
$729$	−17757.2	−	8491.33i	−0.902159	−	0.431404i
$730$	22060.9	+	38210.7i	1.11851	+	1.93732i
$731$	11095.4			0.561395
$732$	202.051	−	296.647i	0.0102022	−	0.0149787i
$733$			14798.7i			0.745706i	0.927890	+	0.372853i	$0.121620\pi$
$733$			14798.7i			0.745706i	−0.927890	+	0.372853i	$0.878380\pi$
$734$	6772.48	−	11730.3i	0.340568	−	0.589881i
$735$	−11490.4	−	28442.1i	−0.576638	−	1.42735i
$736$	286.136	+	495.602i	0.0143303	+	0.0248208i
$737$	−9372.77	+	5411.37i	−0.468454	+	0.270462i
$738$	−28513.6	−	22696.1i	−1.42222	−	1.13205i
$739$	12825.4	−	22214.3i	0.638418	−	1.10577i	−0.347362	−	0.937731i	$-0.612923\pi$
$739$	12825.4	−	22214.3i	0.638418	−	1.10577i	0.985780	−	0.168041i	$-0.0537441\pi$
$740$	3.94621	−	6.83503i	0.000196034	−	0.000339542i
$741$	−4365.24	−	2973.24i	−0.216412	−	0.147402i
$742$	−4740.28	−	20323.8i	−0.234530	−	1.00554i
$743$	−30440.0	−	17574.5i	−1.50301	−	0.867761i	−0.999994	−	0.00348188i	$-0.998892\pi$
$743$	−30440.0	−	17574.5i	−1.50301	−	0.867761i	−0.503012	−	0.864279i	$-0.667775\pi$
$744$	−1565.37	+	21017.7i	−0.0771363	+	1.03568i
$745$			34782.4i			1.71051i
$746$	33503.2	+	19343.1i	1.64429	+	0.949331i
$747$	4226.87	−	5310.30i	0.207032	−	0.260099i
$748$			2268.07i			0.110867i
$749$	14972.9	−	3492.26i	0.730438	−	0.170366i
$750$	−5233.61	−	10855.0i	−0.254806	−	0.528490i
$751$	−15906.4			−0.772881			−0.386440	−	0.922314i	$-0.626295\pi$
$751$	−15906.4			−0.772881			−0.386440	+	0.922314i	$0.626295\pi$
$752$	9734.13	+	16860.0i	0.472031	+	0.817581i
$753$	2590.10	+	1764.16i	0.125350	+	0.0853780i
$754$	427.929	+	247.065i	0.0206688	+	0.0119331i
$755$	−33029.5			−1.59214
$756$	1287.08	−	7.87423i	0.0619188	−	0.000378814i
$757$	8886.22			0.426651			0.213326	−	0.976981i	$-0.431570\pi$
$757$	8886.22			0.426651			0.213326	+	0.976981i	$0.431570\pi$
$758$	29837.4	+	17226.6i	1.42974	+	0.825461i
$759$	−3918.56	−	2669.00i	−0.187398	−	0.127640i
$760$	18422.7	+	31909.1i	0.879292	+	1.52298i
$761$	6896.64			0.328519			0.164259	−	0.986417i	$-0.447477\pi$
$761$	6896.64			0.328519			0.164259	+	0.986417i	$0.447477\pi$
$762$	−699.172	−	1450.14i	−0.0332393	−	0.0689412i
$763$	18636.9	−	17457.7i	0.884275	−	0.828326i
$764$		−	509.456i		−	0.0241249i
$765$	−58955.0	−	8830.77i	−2.78630	−	0.417356i
$766$	11688.5	+	6748.35i	0.551335	+	0.318313i
$767$			939.440i			0.0442258i
$768$	−292.544	+	3927.88i	−0.0137451	+	0.184551i
$769$	23996.6	+	13854.4i	1.12528	+	0.649680i	0.942743	−	0.333519i	$-0.108236\pi$
$769$	23996.6	+	13854.4i	1.12528	+	0.649680i	0.182536	+	0.983199i	$0.441569\pi$
$770$	24201.5	−	22670.2i	1.13268	−	1.06101i
$771$	5738.36	+	3908.49i	0.268044	+	0.182569i
$772$	−1015.99	+	1759.74i	−0.0473656	+	0.0820396i
$773$	−17922.3	+	31042.4i	−0.833921	+	1.44439i	0.0609846	+	0.998139i	$0.480576\pi$
$773$	−17922.3	+	31042.4i	−0.833921	+	1.44439i	−0.894906	+	0.446255i	$0.852757\pi$
$774$	6333.93	−	2492.59i	0.294145	−	0.115755i
$775$	27497.7	−	15875.8i	1.27451	−	0.735839i
$776$	−14217.0	−	24624.5i	−0.657679	−	1.13913i
$777$	−32.1146	+	83.0948i	−0.00148276	+	0.00383656i
$778$	12143.5	−	21033.1i	0.559594	−	0.969245i
$779$		−	45322.5i		−	2.08453i
$780$	−259.010	+	380.273i	−0.0118898	+	0.0174564i
$781$	−12562.6			−0.575577
$782$	−4779.14	−	8277.72i	−0.218545	−	0.378530i
$783$	678.035	+	2187.45i	0.0309464	+	0.0998380i
$784$	20830.4	−	10275.9i	0.948905	−	0.468108i
$785$	13494.7	−	7791.17i	0.613562	−	0.354240i
$786$	179.458	+	372.211i	0.00814381	+	0.0168910i
$787$	7049.71	−	4070.15i	0.319307	−	0.184352i	−0.331776	−	0.943358i	$-0.607648\pi$
$787$	7049.71	−	4070.15i	0.319307	−	0.184352i	0.651084	+	0.759006i	$0.274315\pi$
$788$	345.483	−	199.465i	0.0156184	−	0.00901730i
$789$	−16833.0	+	24713.8i	−0.759530	+	1.11512i
$790$	618.965	−	357.360i	0.0278757	−	0.0160940i
$791$	19380.6	+	20689.7i	0.871171	+	0.930014i
$792$	−7719.17	−	19615.2i	−0.346324	−	0.880047i
$793$	−724.107	−	1254.19i	−0.0324260	−	0.0561635i
$794$	18891.5			0.844376
$795$	15015.9	+	31144.3i	0.669887	+	1.38940i
$796$		−	1100.00i		−	0.0489807i
$797$	−2028.87	+	3514.10i	−0.0901708	+	0.156180i	−0.907583	−	0.419873i	$-0.862075\pi$
$797$	−2028.87	+	3514.10i	−0.0901708	+	0.156180i	0.817412	+	0.576053i	$0.195408\pi$
$798$	17227.2	+	21373.2i	0.764205	+	0.948125i
$799$	−18439.8	−	31938.7i	−0.816462	−	1.41415i
$800$	3319.59	−	1916.57i	0.146707	−	0.0847011i
$801$	17005.1	−	21363.9i	0.750121	−	0.942393i
$802$	2491.97	−	4316.21i	0.109719	−	0.190038i
$803$	15696.1	−	27186.5i	0.689794	−	1.19476i
$804$	−703.039	+	338.963i	−0.0308386	+	0.0148685i
$805$	−2364.93	+	7798.03i	−0.103544	+	0.341421i
$806$	−4861.19	−	2806.61i	−0.212442	−	0.122653i
$807$	8672.46	−	4181.33i	0.378296	−	0.182391i
$808$			18654.1i			0.812191i
$809$	1680.09	+	970.002i	0.0730148	+	0.0421551i	0.536063	−	0.844178i	$-0.319911\pi$
$809$	1680.09	+	970.002i	0.0730148	+	0.0421551i	−0.463048	+	0.886333i	$0.653244\pi$
$810$	−35638.8	+	8203.11i	−1.54595	+	0.355837i
$811$		−	35635.2i		−	1.54294i	−0.636268	−	0.771468i	$-0.719523\pi$
$811$		−	35635.2i		−	1.54294i	0.636268	−	0.771468i	$-0.280477\pi$
$812$	−102.379	−	109.294i	−0.00442462	−	0.00472348i
$813$	38647.7	+	2878.43i	1.66720	+	0.124171i
$814$	−96.3031			−0.00414671
$815$	19355.7	+	33525.1i	0.831903	+	1.44090i
$816$	3352.54	−	45013.4i	0.143826	−	1.93111i
$817$	7331.00	+	4232.55i	0.313928	+	0.181246i
$818$	−18095.4			−0.773462
$819$	2226.79	−	4691.73i	0.0950067	−	0.200174i
$820$	−3948.23			−0.168144
$821$	22330.0	+	12892.2i	0.949234	+	0.548040i	0.892843	−	0.450368i	$-0.148707\pi$
$821$	22330.0	+	12892.2i	0.949234	+	0.548040i	0.0563908	+	0.998409i	$0.482041\pi$
$822$	1186.49	−	572.055i	0.0503452	−	0.0242734i
$823$	18894.9	+	32726.9i	0.800284	+	1.38613i	0.919429	+	0.393255i	$0.128651\pi$
$823$	18894.9	+	32726.9i	0.800284	+	1.38613i	−0.119146	+	0.992877i	$0.538016\pi$
$824$	−933.667			−0.0394731
$825$	−17877.2	+	26246.9i	−0.754431	+	1.10764i
$826$	1417.09	−	4672.66i	0.0596935	−	0.196831i
$827$			9246.54i			0.388795i	0.980923	+	0.194398i	$0.0622752\pi$
$827$			9246.54i			0.388795i	−0.980923	+	0.194398i	$0.937725\pi$
$828$	−267.512	−	212.933i	−0.0112279	−	0.00893712i
$829$	−22476.1	−	12976.6i	−0.941649	−	0.543661i	−0.0511721	−	0.998690i	$-0.516296\pi$
$829$	−22476.1	−	12976.6i	−0.941649	−	0.543661i	−0.890477	+	0.455029i	$0.849629\pi$
$830$		−	12610.5i		−	0.527368i
$831$	−5883.65	−	4007.45i	−0.245609	−	0.167289i
$832$	4285.72	+	2474.36i	0.178582	+	0.103105i
$833$	−39459.9	+	19466.1i	−1.64130	+	0.809677i
$834$	−322.636	+	4331.93i	−0.0133957	+	0.179859i
$835$	18889.0	−	32716.7i	0.782852	−	1.35594i
$836$	−865.193	+	1498.56i	−0.0357935	+	0.0619961i
$837$	−7702.35	−	24849.0i	−0.318079	−	1.02617i
$838$	−29916.9	+	17272.5i	−1.23325	+	0.712017i
$839$	−16562.3	−	28686.7i	−0.681518	−	1.18042i	−0.974517	−	0.224312i	$-0.927987\pi$
$839$	−16562.3	−	28686.7i	−0.681518	−	1.18042i	0.292999	−	0.956113i	$-0.405347\pi$
$840$	−28207.6	+	22735.9i	−1.15864	+	0.933883i
$841$	−12061.3	+	20890.7i	−0.494537	+	0.856564i
$842$		−	1271.39i		−	0.0520369i
$843$	21386.7	+	1592.85i	0.873780	+	0.0650780i
$844$	1112.91			0.0453887
$845$	−17978.4	−	31139.5i	−0.731925	−	1.26773i
$846$	−17701.5	−	14090.0i	−0.719375	−	0.572605i
$847$	1011.27	+	306.690i	0.0410243	+	0.0124416i
$848$	−22672.5	+	13090.0i	−0.918135	+	0.530085i
$849$	9854.81	+	733.973i	0.398370	+	0.0296701i
$850$	−55445.0	+	32011.2i	−2.23735	+	1.29174i
$851$	20.4944	−	11.8324i	0.000825543	−	0.000476628i
$852$	−903.455	−	67.2881i	−0.0363285	−	0.00270570i
$853$	−33036.5	+	19073.6i	−1.32608	+	0.765614i	−0.984691	−	0.174307i	$-0.944232\pi$
$853$	−33036.5	+	19073.6i	−1.32608	+	0.765614i	−0.341392	+	0.939921i	$0.610898\pi$
$854$	1709.75	+	7330.46i	0.0685086	+	0.293727i
$855$	−35584.2	−	28324.1i	−1.42334	−	1.13294i
$856$	−9079.30	−	15725.8i	−0.362528	−	0.627917i
$857$	−29314.0			−1.16843			−0.584217	−	0.811598i	$-0.698598\pi$
$857$	−29314.0			−1.16843			−0.584217	+	0.811598i	$0.698598\pi$
$858$	5598.65	+	416.980i	0.222768	+	0.0165914i
$859$			30802.0i			1.22346i	0.791067	+	0.611729i	$0.209526\pi$
$859$			30802.0i			1.22346i	−0.791067	+	0.611729i	$0.790474\pi$
$860$	368.714	−	638.632i	0.0146198	−	0.0253223i
$861$	44032.3	−	6871.20i	1.74288	−	0.271974i
$862$	18327.1	+	31743.5i	0.724157	+	1.25428i
$863$	10009.9	−	5779.21i	0.394832	−	0.227957i	−0.289419	−	0.957202i	$-0.593462\pi$
$863$	10009.9	−	5779.21i	0.394832	−	0.227957i	0.684252	+	0.729246i	$0.260129\pi$
$864$	−929.848	−	2999.84i	−0.0366135	−	0.118121i
$865$	−23255.7	+	40280.0i	−0.914123	+	1.58331i
$866$	−22571.7	+	39095.4i	−0.885702	+	1.53408i
$867$	−4454.78	+	59812.8i	−0.174501	+	2.34296i
$868$	1163.00	+	1241.56i	0.0454780	+	0.0485498i
$869$	−440.388	−	254.258i	−0.0171912	−	0.00992533i
$870$	3516.76	+	2395.32i	0.137045	+	0.0933438i
$871$			3149.19i			0.122510i
$872$	−26119.4	−	15080.1i	−1.01435	−	0.585637i
$873$	27460.6	+	21857.9i	1.06461	+	0.847399i
$874$		−	7292.35i		−	0.282228i
$875$	14102.1	+	4276.77i	0.544842	+	0.165236i
$876$	1274.42	−	1871.08i	0.0491539	−	0.0721666i
$877$	−8118.17			−0.312578			−0.156289	−	0.987711i	$-0.549953\pi$
$877$	−8118.17			−0.312578			−0.156289	+	0.987711i	$0.549953\pi$
$878$	−18248.3	−	31607.1i	−0.701426	−	1.21490i
$879$	−37067.7	+	17871.8i	−1.42237	+	0.685780i
$880$	−36026.4	−	20799.9i	−1.38006	−	0.796776i
$881$	20509.9			0.784331			0.392165	−	0.919895i	$-0.371726\pi$
$881$	20509.9			0.784331			0.392165	+	0.919895i	$0.371726\pi$
$882$	−18153.0	+	19977.1i	−0.693019	+	0.762656i
$883$	−12792.6			−0.487549			−0.243774	−	0.969832i	$-0.578386\pi$
$883$	−12792.6			−0.487549			−0.243774	+	0.969832i	$0.578386\pi$
$884$	571.542	+	329.980i	0.0217455	+	0.0125548i
$885$	−600.841	+	8067.29i	−0.0228215	+	0.306417i
$886$	1187.89	+	2057.49i	0.0450430	+	0.0780167i
$887$	1469.19			0.0556150			0.0278075	−	0.999613i	$-0.491147\pi$
$887$	1469.19			0.0556150			0.0278075	+	0.999613i	$0.491147\pi$
$888$	104.924	+	7.81462i	0.00396512	+	0.000295317i
$889$	1883.93	+	571.346i	0.0710743	+	0.0215549i
$890$		−	50733.2i		−	1.91077i
$891$	17732.8	+	19041.3i	0.666748	+	0.715946i
$892$	1799.61	+	1039.00i	0.0675509	+	0.0390005i
$893$		−	28136.7i		−	1.05438i
$894$	27569.7	−	13292.4i	1.03140	−	0.497276i
$895$	6042.87	+	3488.86i	0.225688	+	0.130301i
$896$	−19851.7	−	21192.5i	−0.740175	−	0.790170i
$897$	−1242.69	+	599.148i	−0.0462565	+	0.0223021i
$898$	7689.22	−	13318.1i	0.285738	−	0.494913i
$899$	−1513.45	+	2621.37i	−0.0561473	+	0.0972500i
$900$	−1426.25	+	1791.82i	−0.0528240	+	0.0663639i
$901$	42949.7	−	24797.0i	1.58808	−	0.916879i
$902$	24088.1	+	41721.8i	0.889185	+	1.54011i
$903$	−3000.63	+	7763.97i	−0.110581	+	0.286123i
$904$	16741.1	−	28996.4i	0.615929	−	1.06682i
$905$		−	52043.8i		−	1.91160i
$906$	12622.5	+	26180.3i	0.462865	+	0.960023i
$907$	−9286.67			−0.339977			−0.169988	−	0.985446i	$-0.554373\pi$
$907$	−9286.67			−0.339977			−0.169988	+	0.985446i	$0.554373\pi$
$908$	−579.822	−	1004.28i	−0.0211917	−	0.0367051i
$909$	−8431.98	−	21426.6i	−0.307669	−	0.781820i
$910$	−2191.73	−	9396.95i	−0.0798409	−	0.342314i
$911$	17555.0	−	10135.4i	0.638444	−	0.368606i	−0.145571	−	0.989348i	$-0.546502\pi$
$911$	17555.0	−	10135.4i	0.638444	−	0.368606i	0.784015	+	0.620742i	$0.213169\pi$
$912$	19386.2	−	28462.4i	0.703884	−	1.03343i
$913$	−7770.17	+	4486.11i	−0.281659	+	0.162616i
$914$	23024.7	−	13293.3i	0.833250	−	0.481077i
$915$	−5416.01	−	11233.3i	−0.195681	−	0.405859i
$916$	1313.03	−	758.081i	0.0473623	−	0.0273446i
$917$	−483.552	−	146.648i	−0.0174136	−	0.00528108i
$918$	15530.7	+	50104.4i	0.558375	+	1.80141i
$919$	18209.8	+	31540.4i	0.653632	+	1.13212i	0.982235	+	0.187655i	$0.0600887\pi$
$919$	18209.8	+	31540.4i	0.653632	+	1.13212i	−0.328603	+	0.944468i	$0.606578\pi$
$920$	9624.20			0.344892
$921$	5001.93	−	7343.72i	0.178957	−	0.262740i
$922$		−	2448.98i		−	0.0874761i
$923$	−1827.73	+	3165.72i	−0.0651792	+	0.112894i
$924$	−1587.07	−	613.371i	−0.0565050	−	0.0218381i
$925$	−79.2547	−	137.273i	−0.00281717	−	0.00487948i
$926$	−9537.45	+	5506.45i	−0.338467	+	0.195414i
$927$	1072.43	−	422.033i	0.0379970	−	0.0149530i
$928$	−182.708	+	316.459i	−0.00646301	+	0.0111943i
$929$	−10201.3	+	17669.2i	−0.360275	+	0.624014i	−0.988006	−	0.154416i	$-0.950650\pi$
$929$	−10201.3	+	17669.2i	−0.360275	+	0.624014i	0.627731	+	0.778430i	$0.283984\pi$
$930$	−39949.7	−	27210.4i	−1.40860	−	0.959425i
$931$	−33497.7	−	2191.00i	−1.17921	−	0.0771291i
$932$	1090.41	+	629.547i	0.0383235	+	0.0221261i
$933$	4000.50	−	53713.4i	0.140376	−	1.88478i
$934$			18638.8i			0.652976i
$935$	68246.5	+	39402.1i	2.38706	+	1.37817i
$936$	−6066.01	−	908.617i	−0.211831	−	0.0317298i
$937$			18280.7i			0.637357i	0.947863	+	0.318679i	$0.103239\pi$
$937$			18280.7i			0.637357i	−0.947863	+	0.318679i	$0.896761\pi$
$938$	4750.37	−	15663.7i	0.165357	−	0.545243i
$939$	18472.3	+	38313.1i	0.641980	+	1.33152i
$940$	−2451.10			−0.0850491
$941$	20474.1	+	35462.2i	0.709286	+	1.22852i	0.965122	+	0.261799i	$0.0843157\pi$
$941$	20474.1	+	35462.2i	0.709286	+	1.22852i	−0.255837	+	0.966720i	$0.582351\pi$
$942$	−11332.7	−	7718.87i	−0.391972	−	0.266979i
$943$	−10252.4	−	5919.23i	−0.354045	−	0.204408i
$944$	−6125.38			−0.211191
$945$	22122.9	−	38865.2i	0.761544	−	1.33787i
$946$	−8998.08			−0.309253
$947$	−29968.9	−	17302.6i	−1.02836	−	0.593725i	−0.111847	−	0.993725i	$-0.535677\pi$
$947$	−29968.9	−	17302.6i	−1.02836	−	0.593725i	−0.916515	+	0.400001i	$0.869010\pi$
$948$	−30.3092	−	20.6441i	−0.00103839	−	0.000707267i
$949$	−4567.26	−	7910.72i	−0.156227	−	0.270593i
$950$	−48844.9			−1.66815
$951$	−8120.74	−	16843.1i	−0.276901	−	0.574317i
$952$	35526.8	+	37926.5i	1.20949	+	1.29118i
$953$		−	35792.0i		−	1.21660i	−0.793709	−	0.608298i	$-0.791853\pi$
$953$		−	35792.0i		−	1.21660i	0.793709	−	0.608298i	$-0.208147\pi$
$954$	18947.5	−	23804.2i	0.643029	−	0.807851i
$955$	−15329.6	−	8850.55i	−0.519429	−	0.299892i
$956$		−	882.771i		−	0.0298649i
$957$	224.854	−	3019.04i	0.00759509	−	0.101977i
$958$	−43471.0	−	25098.0i	−1.46606	−	0.846430i
$959$	−467.469	+	1541.42i	−0.0157407	+	0.0519029i
$960$	35220.4	+	23989.2i	1.18410	+	0.806508i
$961$	2297.01	−	3978.54i	0.0771041	−	0.133548i
$962$	−14.0111	+	24.2679i	−0.000469580	+	0.000813337i
$963$	17537.0	+	13959.0i	0.586835	+	0.467106i
$964$	690.836	−	398.854i	0.0230813	−	0.0133260i
$965$	35300.7	+	61142.5i	1.17758	+	2.03963i
$966$	7084.75	−	1105.57i	0.235971	−	0.0368231i
$967$	−2517.30	+	4360.10i	−0.0837135	+	0.144996i	−0.904842	−	0.425747i	$-0.860011\pi$
$967$	−2517.30	+	4360.10i	−0.0837135	+	0.144996i	0.821129	+	0.570743i	$0.193345\pi$
$968$		−	1248.09i		−	0.0414413i
$969$	−36724.3	+	53917.7i	−1.21750	+	1.78750i
$970$	65211.1			2.15856
$971$	−5636.92	−	9763.43i	−0.186300	−	0.322681i	0.757714	−	0.652587i	$-0.226316\pi$
$971$	−5636.92	−	9763.43i	−0.186300	−	0.322681i	−0.944014	+	0.329906i	$0.892983\pi$
$972$	1173.29	+	1464.36i	0.0387173	+	0.0483224i
$973$	−3631.49	−	3876.78i	−0.119651	−	0.127733i
$974$	7248.14	−	4184.72i	0.238445	−	0.137666i
$975$	4013.16	+	8323.64i	0.131819	+	0.273405i
$976$	8177.63	−	4721.36i	0.268196	−	0.154843i
$977$	28739.0	−	16592.5i	0.941087	−	0.543337i	0.0507863	−	0.998710i	$-0.483827\pi$
$977$	28739.0	−	16592.5i	0.941087	−	0.543337i	0.890301	+	0.455373i	$0.150494\pi$
$978$	19176.1	−	28153.9i	0.626978	−	0.920514i
$979$	−31260.2	+	18048.1i	−1.02051	+	0.589193i
$980$	−190.867	+	2918.12i	−0.00622145	+	0.0951182i
$981$	36817.8	+	5514.88i	1.19827	+	0.179487i
$982$	−8246.25	−	14282.9i	−0.267972	−	0.464141i
$983$	46854.4			1.52027			0.760134	−	0.649767i	$-0.225133\pi$
$983$	46854.4			1.52027			0.760134	+	0.649767i	$0.225133\pi$
$984$	−22858.9	−	47411.4i	−0.740565	−	1.53600i
$985$		−	13860.9i		−	0.448369i
$986$	3051.65	−	5285.62i	0.0985643	−	0.170718i
$987$	27335.7	−	4265.72i	0.881566	−	0.137568i
$988$	251.753	+	436.050i	0.00810662	+	0.0140411i
$989$	1914.89	−	1105.56i	0.0615673	−	0.0355459i
$990$	47810.8	+	7161.49i	1.53488	+	0.229906i
$991$	−3756.98	+	6507.28i	−0.120428	+	0.208588i	−0.919937	−	0.392067i	$-0.871760\pi$
$991$	−3756.98	+	6507.28i	−0.120428	+	0.208588i	0.799508	+	0.600655i	$0.205093\pi$
$992$	2075.52	−	3594.91i	0.0664294	−	0.115059i
$993$	37377.2	−	18021.0i	1.19449	−	0.575912i
$994$	13866.2	−	12988.9i	0.442464	−	0.414469i
$995$	−33099.3	−	19109.9i	−1.05459	−	0.608869i
$996$	−582.830	+	281.005i	−0.0185418	+	0.00893975i
$997$		−	33471.9i		−	1.06325i	−0.846978	−	0.531627i	$-0.821581\pi$
$997$		−	33471.9i		−	1.06325i	0.846978	−	0.531627i	$-0.178419\pi$
$998$	−46953.3	−	27108.5i	−1.48926	−	0.859824i
$999$	−124.051	+	38.4515i	−0.00392872	+	0.00121777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.s.a.59.17	yes	44
3.2	odd	2		189.4.s.a.17.6		44
7.5	odd	6		63.4.i.a.5.6	✓	44
9.2	odd	6		63.4.i.a.38.17	yes	44
9.7	even	3		189.4.i.a.143.6		44
21.5	even	6		189.4.i.a.152.17		44
63.47	even	6	inner	63.4.s.a.47.17	yes	44
63.61	odd	6		189.4.s.a.89.6		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.6	✓	44	7.5	odd	6
63.4.i.a.38.17	yes	44	9.2	odd	6
63.4.s.a.47.17	yes	44	63.47	even	6	inner
63.4.s.a.59.17	yes	44	1.1	even	1	trivial
189.4.i.a.143.6		44	9.7	even	3
189.4.i.a.152.17		44	21.5	even	6
189.4.s.a.17.6		44	3.2	odd	2
189.4.s.a.89.6		44	63.61	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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.52419 + 1.45734i) q^{2} +(-4.29460 - 2.92513i) q^{3} +(0.247680 + 0.428994i) q^{4} +17.2113 q^{5} +(-6.57748 - 13.6423i) q^{6} +(17.7231 + 5.37495i) q^{7} -21.8736i q^{8} +(9.88725 + 25.1245i) q^{9} +O(q^{10})\)	\(q+(2.52419 + 1.45734i) q^{2} +(-4.29460 - 2.92513i) q^{3} +(0.247680 + 0.428994i) q^{4} +17.2113 q^{5} +(-6.57748 - 13.6423i) q^{6} +(17.7231 + 5.37495i) q^{7} -21.8736i q^{8} +(9.88725 + 25.1245i) q^{9} +(43.4446 + 25.0828i) q^{10} -35.6923i q^{11} +(0.191176 - 2.56686i) q^{12} +(-8.99430 - 5.19286i) q^{13} +(36.9034 + 39.3960i) q^{14} +(-73.9159 - 50.3454i) q^{15} +(33.8587 - 58.6451i) q^{16} +(-64.1402 + 111.094i) q^{17} +(-11.6577 + 77.8281i) q^{18} +(-84.7576 + 48.9348i) q^{19} +(4.26290 + 7.38356i) q^{20} +(-60.3915 - 74.9258i) q^{21} +(52.0158 - 90.0941i) q^{22} +25.5640i q^{23} +(-63.9832 + 93.9386i) q^{24} +171.230 q^{25} +(-15.1355 - 26.2155i) q^{26} +(31.0307 - 136.821i) q^{27} +(2.08385 + 8.93439i) q^{28} +(-14.1366 + 8.16176i) q^{29} +(-113.207 - 234.802i) q^{30} +(160.589 - 92.7160i) q^{31} +(19.3867 - 11.1929i) q^{32} +(-104.405 + 153.284i) q^{33} +(-323.804 + 186.948i) q^{34} +(305.039 + 92.5101i) q^{35} +(-8.32941 + 10.4644i) q^{36} +(-0.462855 - 0.801688i) q^{37} -285.259 q^{38} +(23.4372 + 48.6108i) q^{39} -376.474i q^{40} +(-231.546 + 401.049i) q^{41} +(-43.2471 - 277.138i) q^{42} +(-43.2469 - 74.9058i) q^{43} +(15.3118 - 8.84027i) q^{44} +(170.173 + 432.427i) q^{45} +(-37.2555 + 64.5283i) q^{46} +(-143.746 + 248.976i) q^{47} +(-316.954 + 152.816i) q^{48} +(285.220 + 190.522i) q^{49} +(432.217 + 249.541i) q^{50} +(600.421 - 289.487i) q^{51} -5.14467i q^{52} +(-334.811 - 193.303i) q^{53} +(277.723 - 300.141i) q^{54} -614.313i q^{55} +(117.570 - 387.669i) q^{56} +(507.141 + 37.7712i) q^{57} -47.5778 q^{58} +(-45.2274 - 78.3362i) q^{59} +(3.29040 - 44.1790i) q^{60} +(120.761 + 69.7214i) q^{61} +540.475 q^{62} +(40.1900 + 498.429i) q^{63} -476.492 q^{64} +(-154.804 - 89.3761i) q^{65} +(-486.924 + 234.765i) q^{66} +(-151.612 - 262.599i) q^{67} -63.5449 q^{68} +(74.7780 - 109.787i) q^{69} +(635.157 + 678.059i) q^{70} -351.969i q^{71} +(549.565 - 216.270i) q^{72} +(761.691 + 439.763i) q^{73} -2.69815i q^{74} +(-735.367 - 500.871i) q^{75} +(-41.9855 - 24.2403i) q^{76} +(191.844 - 632.580i) q^{77} +(-11.6826 + 156.859i) q^{78} +(7.12361 - 12.3385i) q^{79} +(582.755 - 1009.36i) q^{80} +(-533.485 + 496.825i) q^{81} +(-1168.93 + 674.881i) q^{82} +(-125.688 - 217.699i) q^{83} +(17.1850 - 44.4652i) q^{84} +(-1103.94 + 1912.08i) q^{85} -252.102i q^{86} +(84.5852 + 6.29979i) q^{87} -780.720 q^{88} +(-505.658 - 875.825i) q^{89} +(-200.645 + 1339.53i) q^{90} +(-131.496 - 140.378i) q^{91} +(-10.9668 + 6.33169i) q^{92} +(-960.871 - 71.5644i) q^{93} +(-725.684 + 418.974i) q^{94} +(-1458.79 + 842.234i) q^{95} +(-115.999 - 8.63945i) q^{96} +(1125.76 - 649.959i) q^{97} +(442.293 + 896.575i) q^{98} +(896.753 - 352.899i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 3 q^{2} - 3 q^{3} + 81 q^{4} - 6 q^{5} - 24 q^{6} + 5 q^{7} - 3 q^{9}+O(q^{10}) \) 44 * q - 3 * q^2 - 3 * q^3 + 81 * q^4 - 6 * q^5 - 24 * q^6 + 5 * q^7 - 3 * q^9	\( 44 q - 3 q^{2} - 3 q^{3} + 81 q^{4} - 6 q^{5} - 24 q^{6} + 5 q^{7} - 3 q^{9} - 6 q^{10} - 3 q^{12} + 36 q^{13} + 129 q^{14} - 141 q^{15} - 263 q^{16} + 72 q^{17} - 15 q^{18} - 6 q^{19} - 24 q^{20} - 306 q^{21} + 14 q^{22} - 66 q^{24} + 698 q^{25} + 96 q^{26} - 432 q^{27} - 156 q^{28} - 132 q^{29} + 852 q^{30} + 177 q^{31} - 501 q^{32} + 849 q^{33} - 24 q^{34} - 765 q^{35} + 1122 q^{36} + 82 q^{37} - 1746 q^{38} - 645 q^{39} - 618 q^{41} - 963 q^{42} + 82 q^{43} - 603 q^{44} + 303 q^{45} + 266 q^{46} - 201 q^{47} + 1569 q^{48} + 515 q^{49} - 1845 q^{50} + 417 q^{51} - 564 q^{53} - 684 q^{54} + 3600 q^{56} + 1170 q^{57} - 538 q^{58} + 747 q^{59} - 516 q^{60} - 1209 q^{61} + 2904 q^{62} + 1557 q^{63} - 1144 q^{64} - 831 q^{65} + 1029 q^{66} + 295 q^{67} + 7008 q^{68} + 1005 q^{69} - 390 q^{70} - 1119 q^{72} - 6 q^{73} - 1788 q^{75} + 144 q^{76} - 1203 q^{77} - 5985 q^{78} - 551 q^{79} + 4239 q^{80} + 3741 q^{81} + 18 q^{82} - 1830 q^{83} - 7725 q^{84} - 237 q^{85} - 2130 q^{87} + 1246 q^{88} - 4266 q^{89} - 9993 q^{90} - 1140 q^{91} + 7896 q^{92} - 1479 q^{93} - 3 q^{94} - 1053 q^{95} + 5034 q^{96} + 792 q^{97} - 5667 q^{98} + 4335 q^{99}+O(q^{100}) \) 44 * q - 3 * q^2 - 3 * q^3 + 81 * q^4 - 6 * q^5 - 24 * q^6 + 5 * q^7 - 3 * q^9 - 6 * q^10 - 3 * q^12 + 36 * q^13 + 129 * q^14 - 141 * q^15 - 263 * q^16 + 72 * q^17 - 15 * q^18 - 6 * q^19 - 24 * q^20 - 306 * q^21 + 14 * q^22 - 66 * q^24 + 698 * q^25 + 96 * q^26 - 432 * q^27 - 156 * q^28 - 132 * q^29 + 852 * q^30 + 177 * q^31 - 501 * q^32 + 849 * q^33 - 24 * q^34 - 765 * q^35 + 1122 * q^36 + 82 * q^37 - 1746 * q^38 - 645 * q^39 - 618 * q^41 - 963 * q^42 + 82 * q^43 - 603 * q^44 + 303 * q^45 + 266 * q^46 - 201 * q^47 + 1569 * q^48 + 515 * q^49 - 1845 * q^50 + 417 * q^51 - 564 * q^53 - 684 * q^54 + 3600 * q^56 + 1170 * q^57 - 538 * q^58 + 747 * q^59 - 516 * q^60 - 1209 * q^61 + 2904 * q^62 + 1557 * q^63 - 1144 * q^64 - 831 * q^65 + 1029 * q^66 + 295 * q^67 + 7008 * q^68 + 1005 * q^69 - 390 * q^70 - 1119 * q^72 - 6 * q^73 - 1788 * q^75 + 144 * q^76 - 1203 * q^77 - 5985 * q^78 - 551 * q^79 + 4239 * q^80 + 3741 * q^81 + 18 * q^82 - 1830 * q^83 - 7725 * q^84 - 237 * q^85 - 2130 * q^87 + 1246 * q^88 - 4266 * q^89 - 9993 * q^90 - 1140 * q^91 + 7896 * q^92 - 1479 * q^93 - 3 * q^94 - 1053 * q^95 + 5034 * q^96 + 792 * q^97 - 5667 * q^98 + 4335 * q^99

Introduction

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