LMFDB - Embedded newform 63.4.s.a.47.10

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			47.10
Character	$\chi$	$=$	63.47
Dual form			63.4.s.a.59.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.998155 + 0.576285i) q^{2} +(-1.29916 + 5.03112i) q^{3} +(-3.33579 + 5.77776i) q^{4} +0.274718 q^{5} +(-1.60260 - 5.77053i) q^{6} +(-9.15344 - 16.1001i) q^{7} -16.9100i q^{8} +(-23.6244 - 13.0725i) q^{9} +O(q^{10})$	\(q+(-0.998155 + 0.576285i) q^{2} +(-1.29916 + 5.03112i) q^{3} +(-3.33579 + 5.77776i) q^{4} +0.274718 q^{5} +(-1.60260 - 5.77053i) q^{6} +(-9.15344 - 16.1001i) q^{7} -16.9100i q^{8} +(-23.6244 - 13.0725i) q^{9} +(-0.274212 + 0.158316i) q^{10} +26.2387i q^{11} +(-24.7349 - 24.2890i) q^{12} +(-39.6128 + 22.8704i) q^{13} +(18.4148 + 10.7954i) q^{14} +(-0.356904 + 1.38214i) q^{15} +(-16.9413 - 29.3432i) q^{16} +(30.2340 + 52.3669i) q^{17} +(31.1143 - 0.566004i) q^{18} +(-38.8827 - 22.4489i) q^{19} +(-0.916403 + 1.58726i) q^{20} +(92.8936 - 25.1354i) q^{21} +(-15.1209 - 26.1902i) q^{22} +127.767i q^{23} +(85.0764 + 21.9689i) q^{24} -124.925 q^{25} +(26.3598 - 45.6565i) q^{26} +(96.4611 - 101.874i) q^{27} +(123.557 + 0.820329i) q^{28} +(58.2779 + 33.6468i) q^{29} +(-0.440263 - 1.58527i) q^{30} +(85.6986 + 49.4781i) q^{31} +(150.976 + 87.1662i) q^{32} +(-132.010 - 34.0883i) q^{33} +(-60.3565 - 34.8469i) q^{34} +(-2.51462 - 4.42301i) q^{35} +(154.336 - 92.8888i) q^{36} +(-123.714 + 214.278i) q^{37} +51.7480 q^{38} +(-63.6006 - 229.009i) q^{39} -4.64550i q^{40} +(134.234 + 232.500i) q^{41} +(-78.2370 + 78.6222i) q^{42} +(-72.4990 + 125.572i) q^{43} +(-151.601 - 87.5267i) q^{44} +(-6.49005 - 3.59125i) q^{45} +(-73.6304 - 127.532i) q^{46} +(-250.874 - 434.526i) q^{47} +(169.639 - 47.1123i) q^{48} +(-175.429 + 294.743i) q^{49} +(124.694 - 71.9922i) q^{50} +(-302.743 + 84.0781i) q^{51} -305.164i q^{52} +(-333.839 + 192.742i) q^{53} +(-37.5748 + 157.275i) q^{54} +7.20824i q^{55} +(-272.254 + 154.785i) q^{56} +(163.458 - 166.459i) q^{57} -77.5605 q^{58} +(274.307 - 475.113i) q^{59} +(-6.79513 - 6.67264i) q^{60} +(189.637 - 109.487i) q^{61} -114.054 q^{62} +(5.77539 + 500.014i) q^{63} +70.1309 q^{64} +(-10.8824 + 6.28293i) q^{65} +(151.411 - 42.0499i) q^{66} +(378.858 - 656.202i) q^{67} -403.418 q^{68} +(-642.813 - 165.990i) q^{69} +(5.05889 + 2.96571i) q^{70} +1109.53i q^{71} +(-221.056 + 399.489i) q^{72} +(-125.762 + 72.6086i) q^{73} -285.177i q^{74} +(162.297 - 628.510i) q^{75} +(259.409 - 149.770i) q^{76} +(422.446 - 240.174i) q^{77} +(195.458 + 191.934i) q^{78} +(445.950 + 772.407i) q^{79} +(-4.65409 - 8.06113i) q^{80} +(387.221 + 617.658i) q^{81} +(-267.972 - 154.714i) q^{82} +(745.760 - 1291.69i) q^{83} +(-164.647 + 620.563i) q^{84} +(8.30585 + 14.3862i) q^{85} -167.120i q^{86} +(-244.993 + 249.491i) q^{87} +443.696 q^{88} +(-145.205 + 251.503i) q^{89} +(8.54766 - 0.155492i) q^{90} +(730.810 + 428.428i) q^{91} +(-738.209 - 426.205i) q^{92} +(-360.267 + 366.880i) q^{93} +(500.822 + 289.150i) q^{94} +(-10.6818 - 6.16714i) q^{95} +(-634.686 + 646.337i) q^{96} +(144.917 + 83.6676i) q^{97} +(5.24921 - 395.297i) q^{98} +(343.004 - 619.871i) 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 $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.998155	+	0.576285i	−0.352901	+	0.203748i	−0.665962	−	0.745985i	$-0.731979\pi$
$2$	−0.998155	+	0.576285i	−0.352901	+	0.203748i	0.313061	+	0.949733i	$0.398646\pi$
$3$	−1.29916	+	5.03112i	−0.250024	+	0.968240i
$3$	−1.29916	+	5.03112i	−0.250024	+	0.968240i
$4$	−3.33579	+	5.77776i	−0.416974	+	0.722220i
$5$	0.274718			0.0245716			0.0122858	−	0.999925i	$-0.496089\pi$
$5$	0.274718			0.0245716			0.0122858	+	0.999925i	$0.496089\pi$
$6$	−1.60260	−	5.77053i	−0.109043	−	0.392635i
$7$	−9.15344	−	16.1001i	−0.494239	−	0.869326i
$7$	−9.15344	−	16.1001i	−0.494239	−	0.869326i
$8$		−	16.9100i		−	0.747325i
$9$	−23.6244	−	13.0725i	−0.874976	−	0.484166i
$10$	−0.274212	+	0.158316i	−0.00867133	+	0.00500640i
$11$			26.2387i			0.719205i	0.933106	+	0.359602i	$0.117088\pi$
$11$			26.2387i			0.719205i	−0.933106	+	0.359602i	$0.882912\pi$
$12$	−24.7349	−	24.2890i	−0.595029	−	0.584303i
$13$	−39.6128	+	22.8704i	−0.845123	+	0.487932i	−0.859002	−	0.511972i	$-0.828915\pi$
$13$	−39.6128	+	22.8704i	−0.845123	+	0.487932i	0.0138792	+	0.999904i	$0.495582\pi$
$14$	18.4148	+	10.7954i	0.351541	+	0.206086i
$15$	−0.356904	+	1.38214i	−0.00614348	+	0.0237912i
$16$	−16.9413	−	29.3432i	−0.264708	−	0.458488i
$17$	30.2340	+	52.3669i	0.431343	+	0.747108i	0.996989	−	0.0775399i	$-0.0247065\pi$
$17$	30.2340	+	52.3669i	0.431343	+	0.747108i	−0.565646	+	0.824648i	$0.691373\pi$
$18$	31.1143	−	0.566004i	0.407428	−	0.00741158i
$19$	−38.8827	−	22.4489i	−0.469490	−	0.271060i	0.246536	−	0.969134i	$-0.420708\pi$
$19$	−38.8827	−	22.4489i	−0.469490	−	0.271060i	−0.716026	+	0.698074i	$0.754041\pi$
$20$	−0.916403	+	1.58726i	−0.0102457	+	0.0177461i
$21$	92.8936	−	25.1354i	0.965287	−	0.261190i
$22$	−15.1209	−	26.1902i	−0.146536	−	0.253808i
$23$			127.767i			1.15832i	0.815214	+	0.579159i	$0.196619\pi$
$23$			127.767i			1.15832i	−0.815214	+	0.579159i	$0.803381\pi$
$24$	85.0764	+	21.9689i	0.723590	+	0.186849i
$25$	−124.925			−0.999396
$26$	26.3598	−	45.6565i	0.198830	−	0.344384i
$27$	96.4611	−	101.874i	0.687554	−	0.726134i
$28$	123.557	+	0.820329i	0.833929	+	0.00553670i
$29$	58.2779	+	33.6468i	0.373170	+	0.215450i	0.674843	−	0.737962i	$-0.264212\pi$
$29$	58.2779	+	33.6468i	0.373170	+	0.215450i	−0.301672	+	0.953412i	$0.597545\pi$
$30$	−0.440263	−	1.58527i	−0.00267935	−	0.00964765i
$31$	85.6986	+	49.4781i	0.496513	+	0.286662i	0.727273	−	0.686349i	$-0.240788\pi$
$31$	85.6986	+	49.4781i	0.496513	+	0.286662i	−0.230759	+	0.973011i	$0.574121\pi$
$32$	150.976	+	87.1662i	0.834034	+	0.481530i
$33$	−132.010	−	34.0883i	−0.696363	−	0.179818i
$34$	−60.3565	−	34.8469i	−0.304443	−	0.175770i
$35$	−2.51462	−	4.42301i	−0.0121442	−	0.0213607i
$36$	154.336	−	92.8888i	0.714516	−	0.430041i
$37$	−123.714	+	214.278i	−0.549686	+	0.952085i	0.448610	+	0.893728i	$0.351919\pi$
$37$	−123.714	+	214.278i	−0.549686	+	0.952085i	−0.998296	+	0.0583567i	$0.981414\pi$
$38$	51.7480			0.220911
$39$	−63.6006	−	229.009i	−0.261134	−	0.940276i
$40$		−	4.64550i		−	0.0183629i
$41$	134.234	+	232.500i	0.511312	+	0.885618i	0.999914	+	0.0131112i	$0.00417355\pi$
$41$	134.234	+	232.500i	0.511312	+	0.885618i	−0.488602	+	0.872507i	$0.662493\pi$
$42$	−78.2370	+	78.6222i	−0.287434	+	0.288849i
$43$	−72.4990	+	125.572i	−0.257116	+	0.445338i	−0.965468	−	0.260521i	$-0.916106\pi$
$43$	−72.4990	+	125.572i	−0.257116	+	0.445338i	0.708352	+	0.705859i	$0.249439\pi$
$44$	−151.601	−	87.5267i	−0.519424	−	0.299890i
$45$	−6.49005	−	3.59125i	−0.0214995	−	0.0118967i
$46$	−73.6304	−	127.532i	−0.236005	−	0.408772i
$47$	−250.874	−	434.526i	−0.778589	−	1.34856i	−0.932755	−	0.360511i	$-0.882602\pi$
$47$	−250.874	−	434.526i	−0.778589	−	1.34856i	0.154166	−	0.988045i	$-0.450731\pi$
$48$	169.639	−	47.1123i	0.510110	−	0.141668i
$49$	−175.429	+	294.743i	−0.511455	+	0.859310i
$50$	124.694	−	71.9922i	0.352688	−	0.203625i
$51$	−302.743	+	84.0781i	−0.831226	+	0.230849i
$52$		−	305.164i		−	0.813820i
$53$	−333.839	+	192.742i	−0.865213	+	0.499531i	−0.865755	−	0.500469i	$-0.833161\pi$
$53$	−333.839	+	192.742i	−0.865213	+	0.499531i	0.000541270		1.00000i	$0.499828\pi$
$54$	−37.5748	+	157.275i	−0.0946904	+	0.396341i
$55$			7.20824i			0.0176720i
$56$	−272.254	+	154.785i	−0.649669	+	0.369357i
$57$	163.458	−	166.459i	0.379835	−	0.386807i
$58$	−77.5605			−0.175590
$59$	274.307	−	475.113i	0.605283	−	1.04838i	−0.386724	−	0.922195i	$-0.626393\pi$
$59$	274.307	−	475.113i	0.605283	−	1.04838i	0.992007	−	0.126185i	$-0.0402732\pi$
$60$	−6.79513	−	6.67264i	−0.0146208	−	0.0143572i
$61$	189.637	−	109.487i	0.398041	−	0.229809i	−0.287597	−	0.957751i	$-0.592857\pi$
$61$	189.637	−	109.487i	0.398041	−	0.229809i	0.685638	+	0.727942i	$0.259523\pi$
$62$	−114.054			−0.233627
$63$	5.77539	+	500.014i	0.0115497	+	0.999933i
$64$	70.1309			0.136974
$65$	−10.8824	+	6.28293i	−0.0207660	+	0.0119893i
$66$	151.411	−	42.0499i	0.282385	−	0.0784241i
$67$	378.858	−	656.202i	0.690819	−	1.19653i	−0.280750	−	0.959781i	$-0.590583\pi$
$67$	378.858	−	656.202i	0.690819	−	1.19653i	0.971570	−	0.236753i	$-0.0760834\pi$
$68$	−403.418			−0.719435
$69$	−642.813	−	165.990i	−1.12153	−	0.289607i
$70$	5.05889	+	2.96571i	0.00863790	+	0.00506386i
$71$			1109.53i			1.85461i	0.374306	+	0.927305i	$0.377881\pi$
$71$			1109.53i			1.85461i	−0.374306	+	0.927305i	$0.622119\pi$
$72$	−221.056	+	399.489i	−0.361829	+	0.653891i
$73$	−125.762	+	72.6086i	−0.201634	+	0.116414i	−0.597418	−	0.801930i	$-0.703806\pi$
$73$	−125.762	+	72.6086i	−0.201634	+	0.116414i	0.395783	+	0.918344i	$0.370473\pi$
$74$		−	285.177i		−	0.447989i
$75$	162.297	−	628.510i	0.249873	−	0.967655i
$76$	259.409	−	149.770i	0.391530	−	0.226050i
$77$	422.446	−	240.174i	0.625223	−	0.355459i
$78$	195.458	+	191.934i	0.283734	+	0.278619i
$79$	445.950	+	772.407i	0.635104	+	1.10003i	0.986493	+	0.163803i	$0.0523763\pi$
$79$	445.950	+	772.407i	0.635104	+	1.10003i	−0.351389	+	0.936230i	$0.614290\pi$
$80$	−4.65409	−	8.06113i	−0.00650429	−	0.0112658i
$81$	387.221	+	617.658i	0.531167	+	0.847267i
$82$	−267.972	−	154.714i	−0.360885	−	0.208357i
$83$	745.760	−	1291.69i	0.986238	−	1.70821i	0.349939	−	0.936772i	$-0.386202\pi$
$83$	745.760	−	1291.69i	0.986238	−	1.70821i	0.636299	−	0.771442i	$-0.280464\pi$
$84$	−164.647	+	620.563i	−0.213863	+	0.806059i
$85$	8.30585	+	14.3862i	0.0105988	+	0.0183576i
$86$		−	167.120i		−	0.209547i
$87$	−244.993	+	249.491i	−0.301909	+	0.307451i
$88$	443.696			0.537480
$89$	−145.205	+	251.503i	−0.172941	+	0.299542i	−0.939447	−	0.342695i	$-0.888660\pi$
$89$	−145.205	+	251.503i	−0.172941	+	0.299542i	0.766506	+	0.642237i	$0.221994\pi$
$90$	8.54766	−	0.155492i	0.0100111	−	0.000182114i
$91$	730.810	+	428.428i	0.841865	+	0.493532i
$92$	−738.209	−	426.205i	−0.836561	−	0.482989i
$93$	−360.267	+	366.880i	−0.401698	+	0.409072i
$94$	500.822	+	289.150i	0.549530	+	0.317271i
$95$	−10.6818	−	6.16714i	−0.0115361	−	0.00666037i
$96$	−634.686	+	646.337i	−0.674765	+	0.687151i
$97$	144.917	+	83.6676i	0.151691	+	0.0875789i	0.573924	−	0.818908i	$-0.305420\pi$
$97$	144.917	+	83.6676i	0.151691	+	0.0875789i	−0.422233	+	0.906487i	$0.638754\pi$
$98$	5.24921	−	395.297i	0.00541072	−	0.407459i
$99$	343.004	−	619.871i	0.348214	−	0.629287i
$100$	416.722	−	721.784i	0.416722	−	0.721784i
$101$	945.019			0.931019			0.465510	−	0.885043i	$-0.345871\pi$
$101$	945.019			0.931019			0.465510	+	0.885043i	$0.345871\pi$
$102$	253.732	−	258.389i	0.246306	−	0.250827i
$103$		−	836.645i		−	0.800360i	−0.916437	−	0.400180i	$-0.868948\pi$
$103$		−	836.645i		−	0.800360i	0.916437	−	0.400180i	$-0.131052\pi$
$104$	386.740	+	669.853i	0.364644	+	0.631582i
$105$	25.5196	−	6.90515i	0.0237186	−	0.00641785i
$106$	222.149	−	384.773i	0.203557	−	0.352570i
$107$	−1220.83	−	704.848i	−1.10301	−	0.636825i	−0.166002	−	0.986125i	$-0.553086\pi$
$107$	−1220.83	−	704.848i	−1.10301	−	0.636825i	−0.937011	+	0.349301i	$0.886419\pi$
$108$	266.828	+	897.158i	0.237736	+	0.799344i
$109$	7.79612	+	13.5033i	0.00685076	+	0.0118659i	0.869430	−	0.494055i	$-0.164486\pi$
$109$	7.79612	+	13.5033i	0.00685076	+	0.0118659i	−0.862580	+	0.505921i	$0.831153\pi$
$110$	−4.15400	−	7.19494i	−0.00360062	−	0.00623646i
$111$	−917.336	−	900.800i	−0.784411	−	0.770272i
$112$	−317.359	+	541.349i	−0.267746	+	0.456721i
$113$	−382.754	+	220.983i	−0.318641	+	0.183968i	−0.650787	−	0.759261i	$-0.725561\pi$
$113$	−382.754	+	220.983i	−0.318641	+	0.183968i	0.332146	+	0.943228i	$0.392227\pi$
$114$	−67.2290	+	260.350i	−0.0552331	+	0.213895i
$115$			35.1000i			0.0284617i
$116$	−388.806	+	224.477i	−0.311204	+	0.179674i
$117$	1234.80	−	22.4624i	0.975703	−	0.0177492i
$118$			632.315i			0.493299i
$119$	566.369	−	966.110i	0.436294	−	0.744228i
$120$	23.3721	+	6.03525i	0.0177797	+	0.00459117i
$121$	642.533			0.482745
$122$	−126.191	+	218.570i	−0.0936461	+	0.162200i
$123$	−1344.12	+	373.291i	−0.985330	+	0.273647i
$124$	−571.745	+	330.097i	−0.414066	+	0.239061i
$125$	−68.6589			−0.0491283
$126$	−293.915	−	495.763i	−0.207810	−	0.350524i
$127$	−2019.56			−1.41108			−0.705539	−	0.708671i	$-0.749295\pi$
$127$	−2019.56			−1.41108			−0.705539	+	0.708671i	$0.749295\pi$
$128$	−1277.81	+	737.745i	−0.882372	+	0.509438i
$129$	−537.580	−	527.889i	−0.366909	−	0.360295i
$130$	7.24152	−	12.5427i	0.00488556	−	0.00846204i
$131$	954.174			0.636386			0.318193	−	0.948026i	$-0.396924\pi$
$131$	954.174			0.636386			0.318193	+	0.948026i	$0.396924\pi$
$132$	637.311	−	649.010i	0.420233	−	0.427947i
$133$	−5.52058	+	831.502i	−0.00359921	+	0.542108i
$134$			873.322i			0.563011i
$135$	26.4996	−	27.9866i	0.0168943	−	0.0178422i
$136$	885.526	−	511.259i	0.558333	−	0.322353i
$137$			1382.02i			0.861857i	0.902386	+	0.430928i	$0.141814\pi$
$137$			1382.02i			0.861857i	−0.902386	+	0.430928i	$0.858186\pi$
$138$	737.285	−	204.759i	0.454796	−	0.126306i
$139$	−2724.54	+	1573.02i	−1.66254	+	0.959867i	−0.691041	+	0.722815i	$0.742848\pi$
$139$	−2724.54	+	1573.02i	−1.66254	+	0.959867i	−0.971497	+	0.237052i	$0.923819\pi$
$140$	33.9433	+	0.225359i	0.0204909	+	0.000136045i
$141$	2512.08	−	697.656i	1.50039	−	0.416690i
$142$	−639.407	−	1107.49i	−0.377872	−	0.654494i
$143$	−600.089	−	1039.39i	−0.350923	−	0.607817i
$144$	16.6391	+	914.680i	0.00962910	+	0.529329i
$145$	16.0100	+	9.24339i	0.00916938	+	0.00529394i
$146$	83.6865	−	144.949i	0.0474380	−	0.0821650i
$147$	−1254.98	−	1265.52i	−0.704142	−	0.710059i
$148$	−825.365	−	1429.57i	−0.458410	−	0.793989i
$149$			363.709i			0.199975i	0.994989	+	0.0999873i	$0.0318802\pi$
$149$			363.709i			0.199975i	−0.994989	+	0.0999873i	$0.968120\pi$
$150$	200.203	+	720.880i	0.108977	+	0.392398i
$151$	−516.508			−0.278363			−0.139181	−	0.990267i	$-0.544447\pi$
$151$	−516.508			−0.278363			−0.139181	+	0.990267i	$0.544447\pi$
$152$	−379.612	+	657.508i	−0.202570	+	0.350861i
$153$	−29.6947	−	1632.37i	−0.0156907	−	0.862544i
$154$	−283.258	+	483.180i	−0.148218	+	0.252830i
$155$	23.5430	+	13.5925i	0.0122001	+	0.00704374i
$156$	1535.32	+	396.457i	0.787973	+	0.203474i
$157$	−1002.39	−	578.732i	−0.509552	−	0.294190i	0.223097	−	0.974796i	$-0.428383\pi$
$157$	−1002.39	−	578.732i	−0.509552	−	0.294190i	−0.732650	+	0.680606i	$0.761717\pi$
$158$	−890.254	−	513.988i	−0.448258	−	0.258802i
$159$	−535.998	−	1929.99i	−0.267342	−	0.962629i
$160$	41.4760	+	23.9462i	0.0204935	+	0.0118319i
$161$	2057.07	−	1169.51i	1.00696	−	0.572487i
$162$	−742.453	−	393.369i	−0.360078	−	0.190778i
$163$	1783.72	−	3089.49i	0.857126	−	1.48459i	−0.0175321	−	0.999846i	$-0.505581\pi$
$163$	1783.72	−	3089.49i	0.857126	−	1.48459i	0.874658	−	0.484740i	$-0.161086\pi$
$164$	−1791.10			−0.852814
$165$	−36.2655	−	9.36467i	−0.0171107	−	0.00441842i
$166$			1719.08i			0.803775i
$167$	1874.87	+	3247.37i	0.868754	+	1.50473i	0.863271	+	0.504741i	$0.168412\pi$
$167$	1874.87	+	3247.37i	0.868754	+	1.50473i	0.00548318	+	0.999985i	$0.498255\pi$
$168$	−425.040	−	1570.83i	−0.195194	−	0.721383i
$169$	−52.3864	+	90.7359i	−0.0238445	+	0.0412999i
$170$	−16.5811	−	9.57308i	−0.00748064	−	0.00431895i
$171$	625.116	+	1038.64i	0.279554	+	0.464482i
$172$	−483.683	−	837.763i	−0.214421	−	0.371389i
$173$	1176.24	+	2037.30i	0.516922	+	0.895335i	0.999807	+	0.0196514i	$0.00625564\pi$
$173$	1176.24	+	2037.30i	0.516922	+	0.895335i	−0.482885	+	0.875684i	$0.660411\pi$
$174$	100.764	−	390.216i	0.0439016	−	0.170013i
$175$	1143.49	+	2011.30i	0.493941	+	0.868801i
$176$	769.927	−	444.518i	0.329747	−	0.190379i
$177$	2033.98	+	1997.32i	0.863748	+	0.848179i
$178$		−	334.718i		−	0.140945i
$179$	1977.18	−	1141.53i	0.825595	−	0.476657i	−0.0267473	−	0.999642i	$-0.508515\pi$
$179$	1977.18	−	1141.53i	0.825595	−	0.476657i	0.852342	+	0.522985i	$0.175182\pi$
$180$	42.3988	−	25.5183i	0.0175568	−	0.0105668i
$181$			3446.80i			1.41546i	0.706482	+	0.707731i	$0.250281\pi$
$181$			3446.80i			1.41546i	−0.706482	+	0.707731i	$0.749719\pi$
$182$	−976.359	−	6.48233i	−0.397651	−	0.00264012i
$183$	304.473	+	1096.33i	0.122991	+	0.442857i
$184$	2160.55			0.865640
$185$	−33.9864	+	58.8662i	−0.0135067	+	0.0233942i
$186$	148.175	−	573.819i	0.0584123	−	0.226207i
$187$	−1374.04	+	793.301i	−0.537324	+	0.310224i
$188$	3347.45			1.29861
$189$	−2523.13	−	620.542i	−0.971063	−	0.238824i
$190$	14.2161			0.00542814
$191$	1540.99	−	889.689i	0.583780	−	0.337045i	−0.178854	−	0.983876i	$-0.557239\pi$
$191$	1540.99	−	889.689i	0.583780	−	0.337045i	0.762634	+	0.646830i	$0.223906\pi$
$192$	−91.1113	+	352.837i	−0.0342468	+	0.132624i
$193$	249.570	−	432.268i	0.0930800	−	0.161219i	−0.815726	−	0.578439i	$-0.803662\pi$
$193$	249.570	−	432.268i	0.0930800	−	0.161219i	0.908806	+	0.417220i	$0.136995\pi$
$194$	−192.866			−0.0713760
$195$	−17.4722	−	62.9130i	−0.00641648	−	0.0231041i
$196$	−1117.76	−	1996.79i	−0.407347	−	0.727693i
$197$			4333.51i			1.56726i	0.621229	+	0.783629i	$0.286634\pi$
$197$			4333.51i			1.56726i	−0.621229	+	0.783629i	$0.713366\pi$
$198$	14.8512	+	816.396i	0.00533044	+	0.293024i
$199$	−1426.57	+	823.632i	−0.508176	+	0.293396i	−0.732084	−	0.681215i	$-0.761452\pi$
$199$	−1426.57	+	823.632i	−0.508176	+	0.293396i	0.223907	+	0.974610i	$0.428119\pi$
$200$			2112.48i			0.746874i
$201$	2809.23	+	2758.59i	0.985811	+	0.968041i
$202$	−943.276	+	544.601i	−0.328558	+	0.189693i
$203$	8.27433	−	1246.27i	0.00286081	−	0.430890i
$204$	524.105	−	2029.64i	0.179876	−	0.696586i
$205$	36.8765	+	63.8719i	0.0125637	+	0.0217610i
$206$	482.146	+	835.102i	0.163071	+	0.282448i
$207$	1670.24	−	3018.42i	0.560818	−	1.01350i
$208$	1342.19	+	774.911i	0.447422	+	0.258319i
$209$	589.030	−	1020.23i	0.194948	−	0.337659i
$210$	−21.4932	+	21.5990i	−0.00706271	+	0.00709748i
$211$	−1023.38	−	1772.54i	−0.333897	−	0.578327i	0.649375	−	0.760468i	$-0.275031\pi$
$211$	−1023.38	−	1772.54i	−0.333897	−	0.578327i	−0.983272	+	0.182141i	$0.941697\pi$
$212$		−	2571.79i		−	0.833166i
$213$	−5582.19	−	1441.46i	−1.79571	−	0.463697i
$214$	1624.77			0.519006
$215$	−19.9168	+	34.4969i	−0.00631775	+	0.0109427i
$216$	−1722.69	−	1631.16i	−0.542658	−	0.513826i
$217$	12.1675	−	1832.65i	0.00380638	−	0.573312i
$218$	−15.5635	−	8.98558i	−0.00483528	−	0.00279165i
$219$	−201.918	−	727.053i	−0.0623029	−	0.224336i
$220$	−41.6475	−	24.0452i	−0.0127631	−	0.00736876i
$221$	−2395.31	−	1382.93i	−0.729076	−	0.420932i
$222$	1434.76	+	370.491i	0.433761	+	0.112008i
$223$	−1682.84	−	971.590i	−0.505343	−	0.291760i	0.225574	−	0.974226i	$-0.427574\pi$
$223$	−1682.84	−	971.590i	−0.505343	−	0.291760i	−0.730917	+	0.682466i	$0.760908\pi$
$224$	21.4357	−	3228.61i	0.00639389	−	0.963038i
$225$	2951.26	+	1633.07i	0.874448	+	0.483874i
$226$	254.699	−	441.151i	0.0749659	−	0.129845i
$227$	−3979.61			−1.16359			−0.581797	−	0.813334i	$-0.697650\pi$
$227$	−3979.61			−1.16359			−0.581797	+	0.813334i	$0.697650\pi$
$228$	416.496	+	1499.69i	0.120979	+	0.435613i
$229$		−	3742.04i		−	1.07983i	−0.841720	−	0.539915i	$-0.818456\pi$
$229$		−	3742.04i		−	1.07983i	0.841720	−	0.539915i	$-0.181544\pi$
$230$	−20.2276	−	35.0353i	−0.00579900	−	0.0100442i
$231$	659.519	+	2437.40i	0.187849	+	0.694239i
$232$	568.968	−	985.481i	0.161011	−	0.278879i
$233$	−4212.14	−	2431.88i	−1.18432	−	0.683767i	−0.227309	−	0.973823i	$-0.572993\pi$
$233$	−4212.14	−	2431.88i	−1.18432	−	0.683767i	−0.957010	+	0.290056i	$0.906326\pi$
$234$	−1219.58	+	734.017i	−0.340710	+	0.205061i
$235$	−68.9196	−	119.372i	−0.0191311	−	0.0331361i
$236$	1830.06	+	3169.75i	0.504774	+	0.874294i
$237$	−4465.44	+	1240.14i	−1.22389	+	0.339899i
$238$	−8.56945	+	1290.72i	−0.00233393	+	0.351533i
$239$	−3994.45	+	2306.19i	−1.08108	+	0.624165i	−0.931189	−	0.364537i	$-0.881227\pi$
$239$	−3994.45	+	2306.19i	−1.08108	+	0.624165i	−0.149896	+	0.988702i	$0.547894\pi$
$240$	46.6029	−	12.9426i	0.0125342	−	0.00348101i
$241$			945.401i			0.252691i	0.991986	+	0.126346i	$0.0403248\pi$
$241$			945.401i			0.252691i	−0.991986	+	0.126346i	$0.959675\pi$
$242$	−641.348	+	370.282i	−0.170361	+	0.0983580i
$243$	−3610.57	+	1145.72i	−0.953162	+	0.302460i
$244$			1460.90i			0.383297i
$245$	−48.1936	+	80.9714i	−0.0125672	+	0.0211146i
$246$	1126.52	−	1147.20i	0.291969	−	0.297329i
$247$	2053.67			0.529036
$248$	836.676	−	1449.17i	0.214230	−	0.371057i
$249$	5529.81	+	5430.13i	1.40738	+	1.38201i
$250$	68.5322	−	39.5671i	0.0173374	−	0.0100098i
$251$	−478.897			−0.120429			−0.0602146	−	0.998185i	$-0.519178\pi$
$251$	−478.897			−0.120429			−0.0602146	+	0.998185i	$0.519178\pi$
$252$	−2908.22	−	1634.57i	−0.726988	−	0.408605i
$253$	−3352.44			−0.833068
$254$	2015.83	−	1163.84i	0.497971	−	0.287504i
$255$	−83.1691	+	23.0978i	−0.0204245	+	0.00567231i
$256$	569.780	−	986.887i	0.139106	−	0.240939i
$257$	−4135.57			−1.00377			−0.501887	−	0.864933i	$-0.667361\pi$
$257$	−4135.57			−1.00377			−0.501887	+	0.864933i	$0.667361\pi$
$258$	840.803	+	217.116i	0.202892	+	0.0523918i
$259$	4582.31	+	30.4233i	1.09935	+	0.00729889i
$260$		−	83.8342i		−	0.0199968i
$261$	−936.932	−	1556.72i	−0.222202	−	0.369190i
$262$	−952.414	+	549.876i	−0.224581	+	0.129662i
$263$			1336.33i			0.313315i	0.987653	+	0.156658i	$0.0500719\pi$
$263$			1336.33i			0.313315i	−0.987653	+	0.156658i	$0.949928\pi$
$264$	−576.433	+	2232.29i	−0.134383	+	0.520409i
$265$	−91.7117	+	52.9498i	−0.0212596	+	0.0122743i
$266$	−473.672	−	833.150i	−0.109183	−	0.192044i
$267$	−1076.70	−	1057.29i	−0.246789	−	0.242341i
$268$	2527.58	+	4377.90i	0.576107	+	0.997847i
$269$	−1094.02	−	1894.90i	−0.247969	−	0.429494i	0.714993	−	0.699131i	$-0.246430\pi$
$269$	−1094.02	−	1894.90i	−0.247969	−	0.429494i	−0.962962	+	0.269637i	$0.913096\pi$
$270$	−10.3225	+	43.2063i	−0.00232669	+	0.00973871i
$271$	3642.53	+	2103.02i	0.816488	+	0.471400i	0.849204	−	0.528065i	$-0.177082\pi$
$271$	3642.53	+	2103.02i	0.816488	+	0.471400i	−0.0327159	+	0.999465i	$0.510416\pi$
$272$	1024.41	−	1774.33i	0.228360	−	0.395531i
$273$	−3104.91	+	3120.20i	−0.688344	+	0.691732i
$274$	−796.440	−	1379.48i	−0.175601	−	0.304150i
$275$		−	3277.85i		−	0.718770i
$276$	3103.34	−	3160.31i	0.676809	−	0.689233i
$277$	−2108.80			−0.457421			−0.228710	−	0.973495i	$-0.573451\pi$
$277$	−2108.80			−0.457421			−0.228710	+	0.973495i	$0.573451\pi$
$278$	1813.01	−	3140.23i	0.391141	−	0.677476i
$279$	−1377.77	−	2289.18i	−0.295645	−	0.491217i
$280$	−74.7932	+	42.5223i	−0.0159634	+	0.00907569i
$281$	5062.18	+	2922.65i	1.07468	+	0.620465i	0.929455	−	0.368934i	$-0.120277\pi$
$281$	5062.18	+	2922.65i	1.07468	+	0.620465i	0.145221	+	0.989399i	$0.453611\pi$
$282$	−2105.39	+	2144.04i	−0.444590	+	0.452751i
$283$	6556.08	+	3785.15i	1.37710	+	0.795067i	0.991809	−	0.127729i	$-0.0407688\pi$
$283$	6556.08	+	3785.15i	1.37710	+	0.795067i	0.385288	+	0.922796i	$0.374102\pi$
$284$	−6410.61	−	3701.17i	−1.33944	−	0.773324i
$285$	44.9050	−	45.7293i	0.00933313	−	0.00950446i
$286$	1197.96	+	691.645i	0.247682	+	0.142999i
$287$	2514.58	−	4289.35i	0.517180	−	0.882204i
$288$	−2427.24	−	4032.88i	−0.496620	−	0.825138i
$289$	628.305	−	1088.26i	0.127886	−	0.221505i
$290$	−21.3073			−0.00431451
$291$	−609.212	+	620.395i	−0.122724	+	0.124977i
$292$		−	968.828i		−	0.194166i
$293$	92.9288	+	160.957i	0.0185289	+	0.0320930i	0.875141	−	0.483868i	$-0.160768\pi$
$293$	92.9288	+	160.957i	0.0185289	+	0.0320930i	−0.856612	+	0.515961i	$0.827435\pi$
$294$	1981.97	+	539.964i	0.393165	+	0.107113i
$295$	75.3571	−	130.522i	0.0148727	−	0.0257603i
$296$	3623.45	+	2092.00i	0.711516	+	0.410794i
$297$	2673.03	+	2531.01i	0.522239	+	0.494492i
$298$	−209.600	−	363.038i	−0.0407444	−	0.0705713i
$299$	−2922.09	−	5061.22i	−0.565181	−	0.978922i
$300$	3089.99	+	3034.29i	0.594669	+	0.583950i
$301$	2685.34	+	17.8288i	0.514221	+	0.00341406i
$302$	515.555	−	297.656i	0.0982346	−	0.0567158i
$303$	−1227.73	+	4754.51i	−0.232777	+	0.901450i
$304$			1521.26i			0.287007i
$305$	52.0967	−	30.0780i	0.00978049	−	0.00564677i
$306$	970.350	+	1612.24i	0.181278	+	0.301196i
$307$			2608.06i			0.484853i	0.970170	+	0.242427i	$0.0779434\pi$
$307$			2608.06i			0.484853i	−0.970170	+	0.242427i	$0.922057\pi$
$308$	−21.5243	+	3241.96i	−0.00398202	+	0.599766i
$309$	4209.26	+	1086.94i	0.774940	+	0.200109i
$310$	−31.3327			−0.00574058
$311$	1846.85	−	3198.84i	0.336738	−	0.583247i	−0.647079	−	0.762423i	$-0.724010\pi$
$311$	1846.85	−	3198.84i	0.336738	−	0.583247i	0.983817	+	0.179176i	$0.0573431\pi$
$312$	−3872.55	+	1075.49i	−0.702692	+	0.195152i
$313$	5911.47	−	3412.99i	1.06753	−	0.616337i	0.140023	−	0.990148i	$-0.455282\pi$
$313$	5911.47	−	3412.99i	1.06753	−	0.616337i	0.927505	+	0.373811i	$0.121949\pi$
$314$	1334.06			0.239762
$315$	1.58661	+	137.363i	0.000283794	+	0.0245699i
$316$	−5950.38			−1.05929
$317$	−2657.16	+	1534.11i	−0.470791	+	0.271811i	−0.716571	−	0.697514i	$-0.754289\pi$
$317$	−2657.16	+	1534.11i	−0.470791	+	0.271811i	0.245780	+	0.969326i	$0.420956\pi$
$318$	1647.23	+	1617.54i	0.290479	+	0.285242i
$319$	−882.846	+	1529.13i	−0.154953	+	0.268386i
$320$	19.2662			0.00336567
$321$	5132.24	−	5226.45i	0.892379	−	0.908760i
$322$	−1379.31	+	2352.81i	−0.238713	+	0.407196i
$323$		−	2714.89i		−	0.467680i
$324$	−4860.37	+	176.890i	−0.833396	+	0.0303309i
$325$	4948.60	−	2857.08i	0.844613	−	0.487638i
$326$			4111.72i			0.698550i
$327$	−78.0650	+	21.6803i	−0.0132019	+	0.00366643i
$328$	3931.57	−	2269.90i	0.661844	−	0.382116i
$329$	−4699.57	+	8016.51i	−0.787525	+	1.34336i
$330$	41.5954	−	11.5519i	0.00693863	−	0.00192700i
$331$	−455.469	−	788.896i	−0.0756340	−	0.131002i	0.825728	−	0.564069i	$-0.190765\pi$
$331$	−455.469	−	788.896i	−0.0756340	−	0.131002i	−0.901362	+	0.433067i	$0.857431\pi$
$332$	4975.40	+	8617.64i	0.822471	+	1.42456i
$333$	5723.80	−	3444.94i	0.941929	−	0.566912i
$334$	−3742.83	−	2160.92i	−0.613169	−	0.354013i
$335$	104.079	−	180.271i	0.0169745	−	0.0294007i
$336$	−2311.29	−	2299.97i	−0.375272	−	0.373434i
$337$	−2379.71	−	4121.79i	−0.384663	−	0.666255i	0.607060	−	0.794656i	$-0.292349\pi$
$337$	−2379.71	−	4121.79i	−0.384663	−	0.666255i	−0.991722	+	0.128401i	$0.959016\pi$
$338$		−	120.758i		−	0.0194330i
$339$	−614.533	−	2212.77i	−0.0984568	−	0.354517i
$340$	−110.826			−0.0176776
$341$	−1298.24	+	2248.61i	−0.206169	+	0.357095i
$342$	−1222.51	−	676.474i	−0.193292	−	0.106958i
$343$	6351.19	+	126.517i	0.999802	+	0.0199163i
$344$	2123.43	+	1225.96i	0.332812	+	0.192149i
$345$	−176.593	−	45.6006i	−0.0275577	−	0.00711610i
$346$	−2348.13	−	1355.69i	−0.364845	−	0.210643i
$347$	2185.79	+	1261.97i	0.338154	+	0.195233i	0.659455	−	0.751744i	$-0.270787\pi$
$347$	2185.79	+	1261.97i	0.338154	+	0.195233i	−0.321302	+	0.946977i	$0.604120\pi$
$348$	−624.250	−	2247.76i	−0.0961590	−	0.346243i
$349$	−6370.82	−	3678.20i	−0.977142	−	0.564153i	−0.0757357	−	0.997128i	$-0.524131\pi$
$349$	−6370.82	−	3678.20i	−0.977142	−	0.564153i	−0.901406	+	0.432975i	$0.857464\pi$
$350$	−2300.46	−	1348.62i	−0.351328	−	0.205962i
$351$	−1491.19	+	6241.61i	−0.226763	+	0.949152i
$352$	−2287.12	+	3961.41i	−0.346318	+	0.599841i
$353$	−192.834			−0.0290752			−0.0145376	−	0.999894i	$-0.504628\pi$
$353$	−192.834			−0.0290752			−0.0145376	+	0.999894i	$0.504628\pi$
$354$	−3181.25	−	821.480i	−0.477632	−	0.123337i
$355$			304.809i			0.0455707i
$356$	−968.748	−	1677.92i	−0.144223	−	0.249802i
$357$	4124.81	+	4104.60i	0.611507	+	0.608512i
$358$	−1315.69	+	2278.84i	−0.194236	+	0.336426i
$359$	−3707.83	−	2140.72i	−0.545103	−	0.314715i	0.202042	−	0.979377i	$-0.435242\pi$
$359$	−3707.83	−	2140.72i	−0.545103	−	0.314715i	−0.747144	+	0.664662i	$0.768576\pi$
$360$	−60.7282	+	109.747i	−0.00889071	+	0.0160671i
$361$	−2421.59	−	4194.32i	−0.353053	−	0.611506i
$362$	−1986.34	−	3440.44i	−0.288397	−	0.499518i
$363$	−834.754	+	3232.66i	−0.120698	+	0.467412i
$364$	−4913.18	+	2793.30i	−0.707475	+	0.402222i
$365$	−34.5491	+	19.9469i	−0.00495447	+	0.00286046i
$366$	−935.708	−	918.841i	−0.133634	−	0.131226i
$367$		−	5775.69i		−	0.821495i	−0.911749	−	0.410747i	$-0.865268\pi$
$367$		−	5775.69i		−	0.821495i	0.911749	−	0.410747i	$-0.134732\pi$
$368$	3749.11	−	2164.55i	0.531075	−	0.306616i
$369$	−131.839	−	7247.42i	−0.0185996	−	1.02245i
$370$		−	78.3435i		−	0.0110078i
$371$	6158.95	+	3610.60i	0.861878	+	0.505264i
$372$	−917.969	−	3305.37i	−0.127942	−	0.460686i
$373$	−12373.8			−1.71767			−0.858834	−	0.512255i	$-0.828810\pi$
$373$	−12373.8			−1.71767			−0.858834	+	0.512255i	$0.828810\pi$
$374$	914.335	−	1583.67i	0.126415	−	0.218957i
$375$	89.1990	−	345.431i	0.0122832	−	0.0475680i
$376$	−7347.85	+	4242.28i	−1.00781	+	0.581859i
$377$	−3078.07			−0.420500
$378$	2876.09	−	834.647i	0.391349	−	0.113570i
$379$	9640.94			1.30665			0.653327	−	0.757076i	$-0.273373\pi$
$379$	9640.94			1.30665			0.653327	+	0.757076i	$0.273373\pi$
$380$	71.2645	−	41.1446i	0.00962050	−	0.00555440i
$381$	2623.73	−	10160.6i	0.352803	−	1.36626i
$382$	−1025.43	+	1776.10i	−0.137344	+	0.237887i
$383$	10541.8			1.40642			0.703212	−	0.710980i	$-0.251748\pi$
$383$	10541.8			1.40642			0.703212	+	0.710980i	$0.251748\pi$
$384$	−2051.60	−	7387.28i	−0.272644	−	0.981720i
$385$	116.054	−	65.9802i	0.0153627	−	0.00873419i
$386$			575.294i			0.0758593i
$387$	3354.28	−	2018.81i	0.440588	−	0.265173i
$388$	−966.822	+	558.195i	−0.126503	+	0.0730363i
$389$			1429.20i			0.186281i	0.995653	+	0.0931406i	$0.0296906\pi$
$389$			1429.20i			0.186281i	−0.995653	+	0.0931406i	$0.970309\pi$
$390$	53.6958	+	52.7279i	0.00697178	+	0.00684611i
$391$	−6690.78	+	3862.92i	−0.865389	+	0.499633i
$392$	4984.12	+	2966.51i	0.642184	+	0.382223i
$393$	−1239.63	+	4800.57i	−0.159112	+	0.616174i
$394$	−2497.34	−	4325.52i	−0.319325	−	0.553087i
$395$	122.511	+	212.195i	0.0156055	+	0.0270295i
$396$	2437.28	+	4049.56i	0.309287	+	0.513884i
$397$	−5532.85	−	3194.39i	−0.699460	−	0.403834i	0.107686	−	0.994185i	$-0.465656\pi$
$397$	−5532.85	−	3194.39i	−0.699460	−	0.403834i	−0.807146	+	0.590351i	$0.798989\pi$
$398$	949.294	−	1644.23i	0.119557	−	0.207079i
$399$	−4176.22	−	1108.03i	−0.523991	−	0.139025i
$400$	2116.39	+	3665.69i	0.264548	+	0.458211i
$401$			15077.6i			1.87765i	0.344396	+	0.938825i	$0.388084\pi$
$401$			15077.6i			1.87765i	−0.344396	+	0.938825i	$0.611916\pi$
$402$	−4393.79	−	1134.59i	−0.545130	−	0.140766i
$403$	−4526.34			−0.559487
$404$	−3152.39	+	5460.09i	−0.388211	+	0.672401i
$405$	106.377	+	169.682i	0.0130516	+	0.0208187i
$406$	709.946	+	1248.74i	0.0867833	+	0.152645i
$407$	−5622.37	−	3246.08i	−0.684744	−	0.395337i
$408$	1421.76	+	5119.40i	0.172519	+	0.621196i
$409$	5666.97	+	3271.83i	0.685119	+	0.395554i	0.801781	−	0.597618i	$-0.203886\pi$
$409$	5666.97	+	3271.83i	0.685119	+	0.395554i	−0.116662	+	0.993172i	$0.537219\pi$
$410$	−73.6169	−	42.5027i	−0.00886751	−	0.00511966i
$411$	−6953.13	−	1795.47i	−0.834484	−	0.215485i
$412$	4833.93	+	2790.87i	0.578036	+	0.333729i
$413$	−10160.2	−	67.4567i	−1.21054	−	0.00803712i
$414$	72.3168	+	3975.38i	0.00858497	+	0.471931i
$415$	204.874	−	354.852i	0.0242334	−	0.0419735i
$416$	−7974.12			−0.939815
$417$	−4374.41	−	15751.1i	−0.513707	−	1.84973i
$418$			1357.80i			0.158880i
$419$	3808.29	+	6596.15i	0.444027	+	0.769077i	0.997984	−	0.0634684i	$-0.0202162\pi$
$419$	3808.29	+	6596.15i	0.444027	+	0.769077i	−0.553957	+	0.832545i	$0.686883\pi$
$420$	−45.2316	+	170.480i	−0.00525495	+	0.0198061i
$421$	2874.27	−	4978.38i	0.332739	−	0.576321i	−0.650309	−	0.759670i	$-0.725360\pi$
$421$	2874.27	−	4978.38i	0.332739	−	0.576321i	0.983048	+	0.183349i	$0.0586938\pi$
$422$	2042.98	+	1179.52i	0.235665	+	0.136061i
$423$	246.398	+	13544.9i	0.0283222	+	1.55692i
$424$	3259.27	+	5645.23i	0.373312	+	0.646595i
$425$	−3776.97	−	6541.91i	−0.431083	−	0.746657i
$426$	6402.59	−	1778.13i	0.728184	−	0.202232i
$427$	−3498.58	−	2051.00i	−0.396506	−	0.232447i
$428$	8144.89	−	4702.45i	0.919855	−	0.531079i
$429$	6008.89	−	1668.79i	0.676251	−	0.187809i
$430$		−	45.9111i		−	0.00514890i
$431$	11353.0	−	6554.64i	1.26880	−	0.732543i	0.294040	−	0.955793i	$-0.405000\pi$
$431$	11353.0	−	6554.64i	1.26880	−	0.732543i	0.974761	+	0.223251i	$0.0716668\pi$
$432$	−4623.48	−	1104.60i	−0.514925	−	0.123022i
$433$		−	12018.7i		−	1.33390i	−0.745102	−	0.666951i	$-0.767599\pi$
$433$		−	12018.7i		−	1.33390i	0.745102	−	0.666951i	$-0.232401\pi$
$434$	1043.99	+	1836.28i	0.115468	+	0.203098i
$435$	−67.3042	+	68.5397i	−0.00741837	+	0.00755454i
$436$	−104.025			−0.0114263
$437$	2868.24	−	4967.94i	0.313974	−	0.543819i
$438$	620.535	+	609.350i	0.0676948	+	0.0664745i
$439$	−3519.12	+	2031.76i	−0.382593	+	0.220890i	−0.678946	−	0.734188i	$-0.737563\pi$
$439$	−3519.12	+	2031.76i	−0.382593	+	0.220890i	0.296353	+	0.955079i	$0.404230\pi$
$440$	121.892			0.0132067
$441$	7997.43	−	4669.83i	0.863560	−	0.504247i
$442$	3187.85			0.343056
$443$	−5733.91	+	3310.47i	−0.614958	+	0.355046i	−0.774903	−	0.632080i	$-0.782201\pi$
$443$	−5733.91	+	3310.47i	−0.614958	+	0.355046i	0.159946	+	0.987126i	$0.448868\pi$
$444$	8264.65	−	2295.26i	0.883385	−	0.245334i
$445$	−39.8905	+	69.0924i	−0.00424942	+	0.00736021i
$446$	2239.65			0.237782
$447$	−1829.87	−	472.517i	−0.193623	−	0.0499984i
$448$	−641.939	−	1129.12i	−0.0676981	−	0.119075i
$449$			3211.25i			0.337524i	0.985657	+	0.168762i	$0.0539769\pi$
$449$			3211.25i			0.337524i	−0.985657	+	0.168762i	$0.946023\pi$
$450$	−3886.93	+	70.7078i	−0.407182	+	0.00740710i
$451$	−6100.48	+	3522.11i	−0.636940	+	0.367738i
$452$		−	2948.61i		−	0.306839i
$453$	671.027	−	2598.61i	0.0695973	−	0.269522i
$454$	3972.26	−	2293.39i	0.410634	−	0.237079i
$455$	200.767	+	117.697i	0.0206859	+	0.0121269i
$456$	−2814.82	−	2764.08i	−0.289071	−	0.283860i
$457$	3926.69	+	6801.23i	0.401932	+	0.696166i	0.993959	−	0.109752i	$-0.0350056\pi$
$457$	3926.69	+	6801.23i	0.401932	+	0.696166i	−0.592027	+	0.805918i	$0.701672\pi$
$458$	2156.48	+	3735.14i	0.220013	+	0.381073i
$459$	8251.22	+	1971.31i	0.839072	+	0.200464i
$460$	−202.800	−	117.086i	−0.0205556	−	0.0118678i
$461$	2992.54	−	5183.22i	0.302335	−	0.523659i	−0.674330	−	0.738430i	$-0.735567\pi$
$461$	2992.54	−	5183.22i	0.302335	−	0.523659i	0.976664	+	0.214771i	$0.0689006\pi$
$462$	−2062.94	−	2052.83i	−0.207742	−	0.206724i
$463$	9378.59	+	16244.2i	0.941383	+	1.63052i	0.762837	+	0.646591i	$0.223806\pi$
$463$	9378.59	+	16244.2i	0.941383	+	1.63052i	0.178546	+	0.983932i	$0.442861\pi$
$464$		−	2280.08i		−	0.228125i
$465$	−98.9719	+	100.789i	−0.00987034	+	0.0100515i
$466$	5605.82			0.557263
$467$	−4572.53	+	7919.86i	−0.453087	+	0.784770i	−0.998576	−	0.0533484i	$-0.983011\pi$
$467$	−4572.53	+	7919.86i	−0.453087	+	0.784770i	0.545489	+	0.838118i	$0.316344\pi$
$468$	−3989.25	+	7209.30i	−0.394024	+	0.712073i
$469$	−14032.8	−	93.1678i	−1.38161	−	0.00917290i
$470$	137.585	+	79.4347i	0.0135028	+	0.00779585i
$471$	4213.94	−	4291.30i	0.412247	−	0.419814i
$472$	−8034.17	−	4638.53i	−0.783480	−	0.452343i
$473$	−3294.84	−	1902.28i	−0.320289	−	0.184919i
$474$	3742.52	−	3811.22i	0.362658	−	0.369315i
$475$	4857.40	+	2804.42i	0.469206	+	0.270896i
$476$	3692.66	+	6495.08i	0.355573	+	0.625424i
$477$	10406.3	−	189.303i	0.998897	−	0.0181711i
$478$	2658.05	−	4603.88i	0.254344	−	0.440537i
$479$	−40.6827			−0.00388067			−0.00194033	−	0.999998i	$-0.500618\pi$
$479$	−40.6827			−0.00388067			−0.00194033	+	0.999998i	$0.500618\pi$
$480$	−174.360	+	177.561i	−0.0165800	+	0.0168844i
$481$		−	11317.5i		−	1.07284i
$482$	−544.820	−	943.657i	−0.0514852	−	0.0891751i
$483$	3211.48	+	11868.8i	0.302541	+	1.11811i
$484$	−2143.36	+	3712.40i	−0.201292	+	0.348648i
$485$	39.8112	+	22.9850i	0.00372729	+	0.00215195i
$486$	2943.65	−	3224.32i	0.274747	−	0.300943i
$487$	5493.67	+	9515.32i	0.511174	+	0.885380i	0.999916	+	0.0129516i	$0.00412273\pi$
$487$	5493.67	+	9515.32i	0.511174	+	0.885380i	−0.488742	+	0.872429i	$0.662544\pi$
$488$	−1851.43	−	3206.76i	−0.171742	−	0.297466i
$489$	13226.3	+	12987.8i	1.22313	+	1.20109i
$490$	1.44206	−	108.595i	0.000132950	−	0.0100119i
$491$	−2232.83	+	1289.12i	−0.205226	+	0.118488i	−0.599091	−	0.800681i	$-0.704471\pi$
$491$	−2232.83	+	1289.12i	−0.205226	+	0.118488i	0.393865	+	0.919168i	$0.371138\pi$
$492$	2326.93	−	9011.25i	0.213224	−	0.825729i
$493$			4069.11i			0.371731i
$494$	−2049.88	+	1183.50i	−0.186697	+	0.107790i
$495$	94.2296	−	170.290i	0.00855617	−	0.0154626i
$496$		−	3352.90i		−	0.303527i
$497$	17863.6	−	10156.0i	1.61226	−	0.916621i
$498$	−8648.91	−	2233.36i	−0.778247	−	0.200963i
$499$	−1096.63			−0.0983809			−0.0491904	−	0.998789i	$-0.515664\pi$
$499$	−1096.63			−0.0983809			−0.0491904	+	0.998789i	$0.515664\pi$
$500$	229.032	−	396.694i	0.0204852	−	0.0354814i
$501$	−18773.7	+	5213.84i	−1.67414	+	0.464945i
$502$	478.014	−	275.981i	0.0424996	−	0.0245372i
$503$	−22314.6			−1.97805			−0.989024	−	0.147755i	$-0.952795\pi$
$503$	−22314.6			−1.97805			−0.989024	+	0.147755i	$0.952795\pi$
$504$	8455.25	−	97.6620i	0.747275	−	0.00863137i
$505$	259.614			0.0228766
$506$	3346.26	−	1931.96i	0.293991	−	0.169736i
$507$	−388.445	−	381.443i	−0.0340265	−	0.0334132i
$508$	6736.82	−	11668.5i	0.588382	−	1.01911i
$509$	5432.23			0.473044			0.236522	−	0.971626i	$-0.423993\pi$
$509$	5432.23			0.473044			0.236522	+	0.971626i	$0.423993\pi$
$510$	69.7048	−	70.9843i	0.00605212	−	0.00616321i
$511$	2320.16	+	1360.16i	0.200857	+	0.117750i
$512$		−	10490.5i		−	0.905506i
$513$	−6037.63	+	1795.68i	−0.519625	+	0.154544i
$514$	4127.94	−	2383.27i	0.354233	−	0.204516i
$515$		−	229.842i		−	0.0196661i
$516$	4843.27	−	1345.08i	0.413204	−	0.114755i
$517$	11401.4	−	6582.59i	0.969888	−	0.559965i
$518$	−4591.39	+	2610.35i	−0.389448	+	0.221414i
$519$	−11778.0	+	3271.00i	−0.996142	+	0.276649i
$520$	106.245	+	184.021i	0.00895987	+	0.0155189i
$521$	5784.74	+	10019.5i	0.486438	+	0.842535i	0.999878	−	0.0155903i	$-0.00496276\pi$
$521$	5784.74	+	10019.5i	0.486438	+	0.842535i	−0.513441	+	0.858125i	$0.671629\pi$
$522$	1832.32	+	1013.91i	0.153637	+	0.0850145i
$523$	9256.60	+	5344.30i	0.773925	+	0.446826i	0.834273	−	0.551352i	$-0.185888\pi$
$523$	9256.60	+	5344.30i	0.773925	+	0.446826i	−0.0603481	+	0.998177i	$0.519221\pi$
$524$	−3182.93	+	5512.99i	−0.265356	+	0.459611i
$525$	−11604.7	+	3140.03i	−0.964705	+	0.261032i
$526$	−770.110	−	1333.87i	−0.0638372	−	0.110569i
$527$			5983.69i			0.494599i
$528$	1236.16	+	4451.10i	0.101888	+	0.366873i
$529$	−4157.49			−0.341702
$530$	61.0284	−	105.704i	0.00500170	−	0.00866320i
$531$	−12691.2	+	7638.37i	−1.03720	+	0.624250i
$532$	−4785.80	−	2805.61i	−0.390020	−	0.228644i
$533$	−10634.7	−	6139.97i	−0.864243	−	0.498971i
$534$	1684.01	+	434.853i	0.136468	+	0.0352396i
$535$	−335.385	−	193.635i	−0.0271028	−	0.0156478i
$536$	−11096.4	−	6406.50i	−0.894200	−	0.516266i
$537$	3174.48	+	11430.5i	0.255100	+	0.918549i
$538$	2184.00	+	1260.94i	0.175017	+	0.101046i
$539$	−7733.67	−	4603.02i	−0.618020	−	0.367841i
$540$	73.3025	+	246.466i	0.00584155	+	0.0196411i
$541$	−6142.32	+	10638.8i	−0.488131	+	0.845468i	−0.999907	−	0.0136513i	$-0.995655\pi$
$541$	−6142.32	+	10638.8i	−0.488131	+	0.845468i	0.511776	+	0.859119i	$0.328988\pi$
$542$	−4847.75			−0.384186
$543$	−17341.3	−	4477.95i	−1.37051	−	0.353899i
$544$			10541.5i			0.830818i
$545$	2.14174	+	3.70960i	0.000168334	+	0.000291563i
$546$	1301.06	−	4903.76i	0.101979	−	0.384362i
$547$	2319.96	−	4018.29i	0.181342	−	0.314094i	−0.760996	−	0.648757i	$-0.775289\pi$
$547$	2319.96	−	4018.29i	0.181342	−	0.314094i	0.942338	+	0.334663i	$0.108622\pi$
$548$	−7985.01	−	4610.15i	−0.622450	−	0.359372i
$549$	−5911.31	+	107.534i	−0.459542	+	0.00835960i
$550$	1888.98	+	3271.80i	0.146448	+	0.253655i
$551$	−1510.67	−	2616.56i	−0.116800	−	0.202303i
$552$	−2806.90	+	10870.0i	−0.216431	+	0.838147i
$553$	8353.89	−	14250.0i	0.642394	−	1.09579i
$554$	2104.91	−	1215.27i	0.161424	−	0.0931983i
$555$	−252.009	−	247.466i	−0.0192742	−	0.0189268i
$556$		−	20989.0i		−	1.60096i
$557$	−918.666	+	530.392i	−0.0698835	+	0.0403473i	−0.534535	−	0.845147i	$-0.679513\pi$
$557$	−918.666	+	530.392i	−0.0698835	+	0.0403473i	0.464651	+	0.885494i	$0.346180\pi$
$558$	2694.45	+	1490.97i	0.204418	+	0.113114i
$559$		−	6632.33i		−	0.501821i
$560$	−87.1843	+	148.719i	−0.00657895	+	0.0112223i
$561$	−2206.10	−	7943.57i	−0.166027	−	0.597822i
$562$	−6737.12			−0.505673
$563$	9805.04	−	16982.8i	0.733984	−	1.27130i	−0.221183	−	0.975232i	$-0.570992\pi$
$563$	9805.04	−	16982.8i	0.733984	−	1.27130i	0.955168	−	0.296066i	$-0.0956748\pi$
$564$	−4348.88	+	16841.4i	−0.324682	+	1.25736i
$565$	−105.150	+	60.7081i	−0.00782951	+	0.00452037i
$566$	−8725.31			−0.647972
$567$	6399.98	−	11888.0i	0.474028	−	0.880510i
$568$	18762.2			1.38600
$569$	18029.9	−	10409.6i	1.32839	−	0.766945i	0.343337	−	0.939212i	$-0.388443\pi$
$569$	18029.9	−	10409.6i	1.32839	−	0.766945i	0.985050	+	0.172267i	$0.0551093\pi$
$570$	−18.4690	+	71.5230i	−0.00135716	+	0.00525574i
$571$	−7362.92	+	12753.0i	−0.539630	+	0.934667i	0.459294	+	0.888285i	$0.348103\pi$
$571$	−7362.92	+	12753.0i	−0.539630	+	0.934667i	−0.998924	+	0.0463823i	$0.985231\pi$
$572$	8007.09			0.585303
$573$	2474.14	+	8908.74i	0.180382	+	0.649508i
$574$	−38.0468	+	5730.55i	−0.00276663	+	0.416705i
$575$		−	15961.3i		−	1.15762i
$576$	−1656.80	−	916.784i	−0.119849	−	0.0663183i
$577$	−14296.1	+	8253.86i	−1.03146	+	0.595516i	−0.917404	−	0.397958i	$-0.869719\pi$
$577$	−14296.1	+	8253.86i	−1.03146	+	0.595516i	−0.114060	+	0.993474i	$0.536386\pi$
$578$			1448.33i			0.104226i
$579$	1850.56	+	1817.20i	0.132827	+	0.130432i
$580$	−106.812	+	61.6680i	−0.00764678	+	0.00441487i
$581$	−27622.7	−	183.395i	−1.97243	−	0.0130956i
$582$	250.564	−	970.330i	0.0178457	−	0.0691091i
$583$	−5057.29	−	8759.48i	−0.359265	−	0.622266i
$584$	1227.81	+	2126.64i	0.0869988	+	0.150686i
$585$	339.222	−	6.17084i	0.0239745	−	0.000436124i
$586$	−185.515	−	107.107i	−0.0130777	−	0.00755043i
$587$	6104.52	−	10573.3i	0.429234	−	0.743456i	−0.567571	−	0.823324i	$-0.692117\pi$
$587$	6104.52	−	10573.3i	0.429234	−	0.743456i	0.996805	+	0.0798686i	$0.0254501\pi$
$588$	11498.2	−	3029.44i	0.806428	−	0.212469i
$589$	−2221.46	−	3847.68i	−0.155405	−	0.269170i
$590$			173.709i			0.0121211i
$591$	−21802.4	−	5629.93i	−1.51748	−	0.391852i
$592$	8383.49			0.582026
$593$	−4385.09	+	7595.19i	−0.303666	+	0.525965i	−0.976963	−	0.213407i	$-0.931544\pi$
$593$	−4385.09	+	7595.19i	−0.303666	+	0.525965i	0.673298	+	0.739372i	$0.264877\pi$
$594$	−4126.68	−	985.912i	−0.285050	−	0.0681018i
$595$	155.592	−	265.408i	0.0107204	−	0.0182868i
$596$	−2101.42	−	1213.26i	−0.144426	−	0.0833842i
$597$	−2290.44	−	8247.29i	−0.157021	−	0.565392i
$598$	5833.41	+	3367.92i	0.398906	+	0.230308i
$599$	19136.2	+	11048.3i	1.30531	+	0.753623i	0.981310	−	0.192433i	$-0.0616377\pi$
$599$	19136.2	+	11048.3i	1.30531	+	0.753623i	0.324003	+	0.946056i	$0.394971\pi$
$600$	−10628.1	−	2744.45i	−0.723153	−	0.186736i
$601$	10189.4	+	5882.86i	0.691572	+	0.399279i	0.804201	−	0.594358i	$-0.202594\pi$
$601$	10189.4	+	5882.86i	0.691572	+	0.399279i	−0.112629	+	0.993637i	$0.535927\pi$
$602$	−2690.66	+	1529.73i	−0.182165	+	0.103566i
$603$	−17528.5	+	10549.7i	−1.18377	+	0.712468i
$604$	1722.96	−	2984.26i	0.116070	−	0.201039i
$605$	176.516			0.0118618
$606$	−1514.48	−	5453.26i	−0.101521	−	0.365550i
$607$			8352.53i			0.558515i	0.960216	+	0.279258i	$0.0900884\pi$
$607$			8352.53i			0.558515i	−0.960216	+	0.279258i	$0.909912\pi$
$608$	−3913.58	−	6778.52i	−0.261047	−	0.452147i
$609$	6259.37	+	1660.73i	0.416490	+	0.110503i
$610$	−34.6671	+	60.0451i	−0.00230103	+	0.00398550i
$611$	19875.6	+	11475.2i	1.31601	+	0.759797i
$612$	9530.49	+	5273.67i	0.629489	+	0.348326i
$613$	−6844.06	−	11854.3i	−0.450945	−	0.781059i	0.547500	−	0.836805i	$-0.315579\pi$
$613$	−6844.06	−	11854.3i	−0.450945	−	0.781059i	−0.998445	+	0.0557466i	$0.982246\pi$
$614$	−1502.99	−	2603.25i	−0.0987877	−	0.171105i
$615$	−369.256	+	102.550i	−0.0242111	+	0.00672393i
$616$	−4061.35	−	7143.58i	−0.265644	−	0.467245i
$617$	2227.88	−	1286.27i	0.145366	−	0.0839274i	−0.425553	−	0.904934i	$-0.639920\pi$
$617$	2227.88	−	1286.27i	0.145366	−	0.0839274i	0.570919	+	0.821006i	$0.306587\pi$
$618$	−4827.88	+	1340.80i	−0.314249	+	0.0872735i
$619$			27393.3i			1.77872i	0.457206	+	0.889361i	$0.348850\pi$
$619$			27393.3i			1.77872i	−0.457206	+	0.889361i	$0.651150\pi$
$620$	−157.069	+	90.6838i	−0.0101743	+	0.00587411i
$621$	13016.1	+	12324.6i	0.841094	+	0.796406i
$622$			4257.26i			0.274438i
$623$	5378.36	+	35.7085i	0.345874	+	0.00229636i
$624$	−5642.39	+	5745.96i	−0.361981	+	0.368626i
$625$	15596.7			0.998189
$626$	−3933.71	+	6813.39i	−0.251154	+	0.435012i
$627$	4367.65	+	4288.92i	0.278194	+	0.273179i
$628$	6687.55	−	3861.06i	0.424940	−	0.245339i
$629$	−14961.5			−0.948414
$630$	−80.7439	−	136.195i	−0.00510621	−	0.00861293i
$631$	−15166.2			−0.956822			−0.478411	−	0.878136i	$-0.658787\pi$
$631$	−15166.2			−0.956822			−0.478411	+	0.878136i	$0.658787\pi$
$632$	13061.4	−	7541.02i	0.822082	−	0.474629i
$633$	10247.4	−	2845.92i	0.643441	−	0.178697i
$634$	1768.17	−	3062.56i	0.110762	−	0.191845i
$635$	−554.810			−0.0346724
$636$	12939.0	+	3341.17i	0.806704	+	0.208311i
$637$	208.320	−	15687.7i	0.0129575	−	0.975778i
$638$		−	2035.08i		−	0.126285i
$639$	14504.3	−	26212.0i	0.897939	−	1.62274i
$640$	−351.038	+	202.672i	−0.0216813	+	0.0125177i
$641$			22415.6i			1.38122i	0.723226	+	0.690612i	$0.242659\pi$
$641$			22415.6i			1.38122i	−0.723226	+	0.690612i	$0.757341\pi$
$642$	−2110.84	+	8174.44i	−0.129764	+	0.502522i
$643$	14768.9	−	8526.82i	0.905798	−	0.522963i	0.0267213	−	0.999643i	$-0.491493\pi$
$643$	14768.9	−	8526.82i	0.905798	−	0.522963i	0.879077	+	0.476680i	$0.158160\pi$
$644$	−104.811	+	15786.5i	−0.00641326	+	0.965956i
$645$	−147.683	−	145.021i	−0.00901553	−	0.00885302i
$646$	1564.55	+	2709.88i	0.0952886	+	0.165045i
$647$	13132.8	+	22746.6i	0.797995	+	1.38217i	0.920920	+	0.389752i	$0.127439\pi$
$647$	13132.8	+	22746.6i	0.797995	+	1.38217i	−0.122925	+	0.992416i	$0.539227\pi$
$648$	10444.6	−	6547.91i	0.633184	−	0.396954i
$649$	12466.3	+	7197.43i	0.754000	+	0.435322i
$650$	−3292.98	+	5703.62i	−0.198710	+	0.344176i
$651$	9204.49	+	2442.13i	0.554151	+	0.147027i
$652$	11900.2	+	20611.8i	0.714798	+	1.23807i
$653$			153.742i			0.00921345i	0.999989	+	0.00460672i	$0.00146637\pi$
$653$			153.742i			0.00921345i	−0.999989	+	0.00460672i	$0.998534\pi$
$654$	65.4270	−	66.6280i	0.00391192	−	0.00398373i
$655$	262.129			0.0156370
$656$	4548.19	−	7877.70i	0.270697	−	0.468861i
$657$	3920.22	−	71.3132i	0.232789	−	0.00423469i
$658$	71.1069	−	10710.0i	0.00421282	−	0.634529i
$659$	−9292.80	−	5365.20i	−0.549311	−	0.317145i	0.199533	−	0.979891i	$-0.436058\pi$
$659$	−9292.80	−	5365.20i	−0.549311	−	0.317145i	−0.748844	+	0.662746i	$0.769391\pi$
$660$	175.081	−	178.295i	0.0103258	−	0.0105153i
$661$	−27734.8	−	16012.7i	−1.63201	−	0.942243i	−0.983471	−	0.181063i	$-0.942046\pi$
$661$	−27734.8	−	16012.7i	−1.63201	−	0.942243i	−0.648541	−	0.761180i	$-0.724621\pi$
$662$	909.258	+	524.960i	0.0533826	+	0.0308205i
$663$	10069.6	−	10254.4i	0.589850	−	0.600677i
$664$	−21842.6	−	12610.8i	−1.27659	−	0.737040i
$665$	−1.51661	+	228.429i	−8.84383e−5	+	0.0133204i
$666$	−3727.97	+	6737.13i	−0.216901	+	0.391980i
$667$	−4298.96	+	7446.01i	−0.249560	+	0.432250i
$668$	−25016.7			−1.44899
$669$	7074.47	−	7204.34i	0.408841	−	0.416346i
$670$			239.918i			0.0138341i
$671$	2872.79	+	4975.81i	0.165280	+	0.286273i
$672$	16215.7	+	4302.33i	0.930853	+	0.246973i
$673$	−6229.97	+	10790.6i	−0.356831	+	0.618050i	−0.987430	−	0.158059i	$-0.949476\pi$
$673$	−6229.97	+	10790.6i	−0.356831	+	0.618050i	0.630598	+	0.776110i	$0.282810\pi$
$674$	4750.65	+	2742.79i	0.271496	+	0.156748i
$675$	−12050.4	+	12726.5i	−0.687138	+	0.725695i
$676$	−349.500	−	605.352i	−0.0198851	−	0.0344420i
$677$	4805.25	+	8322.94i	0.272793	+	0.472491i	0.969576	−	0.244791i	$-0.0787193\pi$
$677$	4805.25	+	8322.94i	0.272793	+	0.472491i	−0.696783	+	0.717282i	$0.745386\pi$
$678$	1888.59	+	1854.55i	0.106978	+	0.105049i
$679$	20.5753	−	3099.02i	0.00116290	−	0.175154i
$680$	243.270	−	140.452i	0.0137191	−	0.00792073i
$681$	5170.15	−	20021.9i	0.290926	−	1.12664i
$682$		−	2992.62i		−	0.168026i
$683$	24434.5	−	14107.2i	1.36890	−	0.790335i	0.378113	−	0.925760i	$-0.376573\pi$
$683$	24434.5	−	14107.2i	1.36890	−	0.790335i	0.990788	+	0.135425i	$0.0432398\pi$
$684$	−8086.24	+	147.098i	−0.452025	+	0.00822285i
$685$			379.668i			0.0211772i
$686$	−6412.38	+	3533.81i	−0.356889	+	0.196679i
$687$	18826.7	+	4861.52i	1.04553	+	0.269983i
$688$	4912.92			0.272243
$689$	8816.19	−	15270.1i	0.487475	−	0.844331i
$690$	202.546	−	56.2512i	0.0111751	−	0.00310354i
$691$	2458.51	−	1419.42i	0.135349	−	0.0781439i	−0.430796	−	0.902449i	$-0.641767\pi$
$691$	2458.51	−	1419.42i	0.135349	−	0.0781439i	0.566146	+	0.824305i	$0.308434\pi$
$692$	−15694.7			−0.862172
$693$	−13119.7	+	151.538i	−0.719157	+	0.00830659i
$694$	−2909.01			−0.159113
$695$	−748.483	+	432.137i	−0.0408512	+	0.0235854i
$696$	4218.89	+	4142.85i	0.229766	+	0.225624i
$697$	−8116.85	+	14058.8i	−0.441102	+	0.764010i
$698$	8478.76			0.459779
$699$	17707.3	−	18032.4i	0.958158	−	0.975746i
$700$	−15435.3	−	102.479i	−0.833426	−	0.00553336i
$701$		−	5765.47i		−	0.310640i	−0.987864	−	0.155320i	$-0.950359\pi$
$701$		−	5765.47i		−	0.310640i	0.987864	−	0.155320i	$-0.0496409\pi$
$702$	−2108.50	−	7089.44i	−0.113362	−	0.381159i
$703$	9620.64	−	5554.48i	0.516144	−	0.297996i
$704$			1840.14i			0.0985126i
$705$	690.114	−	191.659i	0.0368670	−	0.0102387i
$706$	192.479	−	111.128i	0.0102607	−	0.00592399i
$707$	−8650.18	−	15214.9i	−0.460146	−	0.809359i
$708$	−18325.0	+	5089.22i	−0.972732	+	0.270148i
$709$	−2400.73	−	4158.18i	−0.127167	−	0.220259i	0.795411	−	0.606070i	$-0.207255\pi$
$709$	−2400.73	−	4158.18i	−0.127167	−	0.220259i	−0.922578	+	0.385811i	$0.873922\pi$
$710$	−175.657	−	304.247i	−0.00928492	−	0.0160819i
$711$	−437.994	−	24077.3i	−0.0231027	−	1.27000i
$712$	4252.92	+	2455.42i	0.223855	+	0.129243i
$713$	−6321.68	+	10949.5i	−0.332046	+	0.575121i
$714$	−6482.62	−	1719.96i	−0.339784	−	0.0901513i
$715$	−164.856	−	285.538i	−0.00862273	−	0.0149350i
$716$			15231.6i			0.795014i
$717$	−6413.31	−	23092.7i	−0.334044	−	1.20281i
$718$	4934.65			0.256490
$719$	2528.38	−	4379.29i	0.131144	−	0.227149i	−0.792974	−	0.609256i	$-0.791468\pi$
$719$	2528.38	−	4379.29i	0.131144	−	0.227149i	0.924118	+	0.382107i	$0.124802\pi$
$720$	4.57106	+	251.280i	0.000236602	+	0.0130064i
$721$	−13470.1	+	7658.18i	−0.695774	+	0.395569i
$722$	4834.25	+	2791.05i	0.249186	+	0.143867i
$723$	−4756.43	−	1228.23i	−0.244666	−	0.0631788i
$724$	−19914.8	−	11497.8i	−1.02228	−	0.590211i
$725$	−7280.34	−	4203.31i	−0.372945	−	0.215320i
$726$	−1029.72	−	3707.75i	−0.0526398	−	0.189542i
$727$	−8680.56	−	5011.72i	−0.442839	−	0.255673i	0.261962	−	0.965078i	$-0.415630\pi$
$727$	−8680.56	−	5011.72i	−0.442839	−	0.255673i	−0.704801	+	0.709405i	$0.748964\pi$
$728$	7244.73	−	12358.0i	0.368829	−	0.629147i
$729$	−1073.52	−	19653.7i	−0.0545403	−	0.998512i
$730$	22.9902	−	39.8202i	0.00116563	−	0.00201892i
$731$	−8767.75			−0.443621
$732$	−7349.97	−	1897.95i	−0.371124	−	0.0958335i
$733$			31917.2i			1.60831i	0.594422	+	0.804153i	$0.297381\pi$
$733$			31917.2i			1.60831i	−0.594422	+	0.804153i	$0.702619\pi$
$734$	3328.44	+	5765.03i	0.167378	+	0.289906i
$735$	−344.766	−	347.663i	−0.0173019	−	0.0174473i
$736$	−11137.0	+	19289.8i	−0.557765	+	0.966077i
$737$	17217.8	+	9940.73i	0.860553	+	0.496841i
$738$	4308.18	+	7158.07i	0.214886	+	0.357036i
$739$	4191.82	+	7260.45i	0.208659	+	0.361407i	0.951292	−	0.308291i	$-0.0997569\pi$
$739$	4191.82	+	7260.45i	0.208659	+	0.361407i	−0.742634	+	0.669698i	$0.766424\pi$
$740$	−226.743	−	392.731i	−0.0112638	−	0.0195095i
$741$	−2668.05	+	10332.3i	−0.132271	+	0.512233i
$742$	−8228.32	−	54.6302i	−0.407104	−	0.00270288i
$743$	14035.0	−	8103.09i	0.692992	−	0.400099i	−0.111740	−	0.993737i	$-0.535642\pi$
$743$	14035.0	−	8103.09i	0.692992	−	0.400099i	0.804732	+	0.593638i	$0.202309\pi$
$744$	6203.95	+	6092.12i	0.305709	+	0.300199i
$745$			99.9176i			0.00491369i
$746$	12351.0	−	7130.82i	0.606167	−	0.349971i
$747$	−34503.7	+	20766.5i	−1.68999	+	1.01714i
$748$		−	10585.1i		−	0.517421i
$749$	−173.334	+	26107.4i	−0.00845594	+	1.27362i
$750$	110.032	+	396.198i	0.00535709	+	0.0192895i
$751$	−29812.4			−1.44856			−0.724281	−	0.689505i	$-0.757828\pi$
$751$	−29812.4			−1.44856			−0.724281	+	0.689505i	$0.757828\pi$
$752$	−8500.26	+	14722.9i	−0.412198	+	0.713948i
$753$	622.165	−	2409.39i	0.0301102	−	0.116604i
$754$	3072.39	−	1773.84i	0.148395	−	0.0856758i
$755$	−141.894			−0.00683981
$756$	12002.0	−	12508.1i	0.577391	−	0.601737i
$757$	29462.2			1.41456			0.707281	−	0.706933i	$-0.249922\pi$
$757$	29462.2			1.41456			0.707281	+	0.706933i	$0.249922\pi$
$758$	−9623.15	+	5555.93i	−0.461120	+	0.266227i
$759$	4355.36	−	16866.5i	0.208287	−	0.806610i
$760$	−104.286	+	180.630i	−0.00497746	+	0.00862121i
$761$	−1305.63			−0.0621931			−0.0310965	−	0.999516i	$-0.509900\pi$
$761$	−1305.63			−0.0621931			−0.0310965	+	0.999516i	$0.509900\pi$
$762$	3236.54	+	11653.9i	0.153868	+	0.554038i
$763$	146.043	−	249.120i	0.00692939	−	0.0118201i
$764$			11871.3i			0.562156i
$765$	−8.15767	−	448.442i	−0.000385544	−	0.0211940i
$766$	−10522.3	+	6075.08i	−0.496329	+	0.286556i
$767$			25094.0i			1.18135i
$768$	4224.91	+	4148.76i	0.198507	+	0.194929i
$769$	−1387.38	+	801.002i	−0.0650586	+	0.0375616i	−0.532176	−	0.846633i	$-0.678626\pi$
$769$	−1387.38	+	801.002i	−0.0650586	+	0.0375616i	0.467118	+	0.884195i	$0.345292\pi$
$770$	−77.8162	+	132.739i	−0.00364195	+	0.00621242i
$771$	5372.77	−	20806.6i	0.250967	−	0.971893i
$772$	1665.03	+	2883.91i	0.0776239	+	0.134449i
$773$	−9429.57	−	16332.5i	−0.438755	−	0.759947i	0.558838	−	0.829277i	$-0.311247\pi$
$773$	−9429.57	−	16332.5i	−0.438755	−	0.759947i	−0.997594	+	0.0693300i	$0.977914\pi$
$774$	−2184.68	+	3948.11i	−0.101456	+	0.183349i
$775$	−10705.9	−	6181.03i	−0.496214	−	0.286489i
$776$	1414.82	−	2450.54i	0.0654499	−	0.113363i
$777$	−6106.23	+	23014.7i	−0.281930	+	1.06261i
$778$	−823.627	−	1426.56i	−0.0379543	−	0.0657388i
$779$		−	12053.6i		−	0.554385i
$780$	421.780	+	108.914i	0.0193617	+	0.00499968i
$781$	−29112.7			−1.33384
$782$	4452.29	−	7711.59i	0.203598	−	0.352642i
$783$	9049.27	−	2691.39i	0.413020	−	0.122838i
$784$	11620.7	+	154.314i	0.529370	+	0.00702959i
$785$	−275.376	−	158.988i	−0.0125205	−	0.00722872i
$786$	−1529.16	−	5506.09i	−0.0693933	−	0.249867i
$787$	20329.8	+	11737.4i	0.920810	+	0.531630i	0.883893	−	0.467689i	$-0.154913\pi$
$787$	20329.8	+	11737.4i	0.920810	+	0.531630i	0.0369165	+	0.999318i	$0.488246\pi$
$788$	−25038.0	−	14455.7i	−1.13190	−	0.653506i
$789$	−6723.26	−	1736.11i	−0.303364	−	0.0783362i
$790$	−244.569	−	141.202i	−0.0110144	−	0.00635917i
$791$	7061.37	+	4139.64i	0.317413	+	0.186079i
$792$	−10482.0	−	5800.21i	−0.470282	−	0.260229i
$793$	−5008.02	+	8674.15i	−0.224262	+	0.388434i
$794$	7363.52			0.329120
$795$	−147.248	−	530.203i	−0.00656901	−	0.0236533i
$796$		−	10989.9i		−	0.489353i
$797$	15759.6	+	27296.5i	0.700420	+	1.21316i	0.968319	+	0.249715i	$0.0803371\pi$
$797$	15759.6	+	27296.5i	0.700420	+	1.21316i	−0.267900	+	0.963447i	$0.586330\pi$
$798$	4807.05	−	1300.70i	0.213243	−	0.0576998i
$799$	15169.9	−	26275.0i	0.671678	−	1.16338i
$800$	−18860.6	−	10889.2i	−0.833530	−	0.481239i
$801$	6718.14	−	4043.40i	0.296347	−	0.178360i
$802$	−8688.97	−	15049.7i	−0.382566	−	0.662625i
$803$	−1905.15	−	3299.82i	−0.0837252	−	0.145016i
$804$	−25309.5	+	7028.97i	−1.11020	+	0.308324i
$805$	565.116	−	321.286i	0.0247425	−	0.0140669i
$806$	4517.99	−	2608.46i	0.197444	−	0.113994i
$807$	10954.8	−	3042.37i	0.477852	−	0.132709i
$808$		−	15980.3i		−	0.695774i
$809$	14756.8	−	8519.85i	0.641312	−	0.370262i	−0.143807	−	0.989606i	$-0.545935\pi$
$809$	14756.8	−	8519.85i	0.641312	−	0.370262i	0.785120	+	0.619344i	$0.212601\pi$
$810$	−203.966	−	108.066i	−0.00884768	−	0.00468771i
$811$		−	9916.81i		−	0.429379i	−0.976682	−	0.214689i	$-0.931126\pi$
$811$		−	9916.81i		−	0.429379i	0.976682	−	0.214689i	$-0.0688739\pi$
$812$	7173.03	+	4205.09i	0.310005	+	0.181736i
$813$	−15312.8	+	15593.9i	−0.660569	+	0.672695i
$814$	7482.67			0.322196
$815$	490.020	−	848.740i	0.0210609	−	0.0364786i
$816$	7595.99	+	7459.07i	0.325874	+	0.320000i
$817$	5637.91	−	3255.05i	0.241427	−	0.139388i
$818$	−7542.02			−0.322372
$819$	−11664.3	−	19674.8i	−0.497660	−	0.839431i
$820$	−492.049			−0.0209550
$821$	1740.83	−	1005.07i	0.0740018	−	0.0427250i	−0.462543	−	0.886597i	$-0.653063\pi$
$821$	1740.83	−	1005.07i	0.0740018	−	0.0427250i	0.536544	+	0.843872i	$0.319729\pi$
$822$	7975.01	−	2214.83i	0.338395	−	0.0939793i
$823$	−5316.32	+	9208.13i	−0.225170	+	0.390006i	−0.956371	−	0.292157i	$-0.905627\pi$
$823$	−5316.32	+	9208.13i	−0.225170	+	0.390006i	0.731200	+	0.682163i	$0.238961\pi$
$824$	−14147.7			−0.598129
$825$	16491.3	+	4258.46i	0.695942	+	0.179710i
$826$	10180.4	−	5787.86i	0.428838	−	0.243808i
$827$			5725.20i			0.240731i	0.992730	+	0.120366i	$0.0384067\pi$
$827$			5725.20i			0.240731i	−0.992730	+	0.120366i	$0.961593\pi$
$828$	11868.2	+	19719.0i	0.498124	+	0.827638i
$829$	16983.1	−	9805.21i	0.711517	−	0.410795i	−0.100105	−	0.994977i	$-0.531918\pi$
$829$	16983.1	−	9805.21i	0.711517	−	0.410795i	0.811623	+	0.584182i	$0.198585\pi$
$830$			472.263i			0.0197500i
$831$	2739.67	−	10609.6i	0.114366	−	0.442893i
$832$	−2778.08	+	1603.92i	−0.115760	+	0.0668342i
$833$	−20738.7	−	275.393i	−0.862610	−	0.0114547i
$834$	13443.5	+	13201.1i	0.558165	+	0.548104i
$835$	515.062	+	892.113i	0.0213466	+	0.0369735i
$836$	3929.76	+	6806.55i	0.162576	+	0.281590i
$837$	13307.1	−	3957.72i	0.549535	−	0.163440i
$838$	−7602.53	−	4389.32i	−0.313395	−	0.180939i
$839$	14243.5	−	24670.5i	0.586104	−	1.01516i	−0.408633	−	0.912699i	$-0.633995\pi$
$839$	14243.5	−	24670.5i	0.586104	−	1.01516i	0.994737	−	0.102462i	$-0.0326722\pi$
$840$	−116.766	−	431.537i	−0.00479622	−	0.0177255i
$841$	−9930.29	−	17199.8i	−0.407163	−	0.705226i
$842$			6625.59i			0.271179i
$843$	−21280.8	+	21671.4i	−0.869453	+	0.885413i
$844$	13655.1			0.556906
$845$	−14.3915	+	24.9268i	−0.000585897	+	0.00101480i
$846$	−8051.69	−	13378.0i	−0.327214	−	0.543668i
$847$	−5881.39	−	10344.9i	−0.238591	−	0.419662i
$848$	11311.3	+	6530.61i	0.458058	+	0.264460i
$849$	−27561.0	+	28066.9i	−1.11412	+	1.13457i
$850$	7540.01	+	4353.23i	0.304259	+	0.175664i
$851$	−27377.8	−	15806.6i	−1.10282	−	0.636712i
$852$	26949.5	−	27444.2i	1.08365	−	1.10355i
$853$	20170.8	+	11645.6i	0.809652	+	0.467453i	0.846835	−	0.531856i	$-0.178505\pi$
$853$	20170.8	+	11645.6i	0.809652	+	0.467453i	−0.0371829	+	0.999308i	$0.511838\pi$
$854$	4674.09	+	31.0326i	0.187288	+	0.00124346i
$855$	171.731	+	285.332i	0.00686909	+	0.0114130i
$856$	−11919.0	+	20644.3i	−0.475915	+	0.824309i
$857$	34729.8			1.38430			0.692152	−	0.721752i	$-0.256663\pi$
$857$	34729.8			1.38430			0.692152	+	0.721752i	$0.256663\pi$
$858$	−5036.10	+	5128.55i	−0.200384	+	0.204063i
$859$		−	38761.1i		−	1.53960i	−0.638288	−	0.769798i	$-0.720357\pi$
$859$		−	38761.1i		−	1.53960i	0.638288	−	0.769798i	$-0.279643\pi$
$860$	−132.877	−	230.149i	−0.00526867	−	0.00912560i
$861$	18313.4	+	18223.7i	0.724877	+	0.721326i
$862$	−7554.68	+	13085.1i	−0.298508	+	0.517030i
$863$	−6375.08	−	3680.65i	−0.251460	−	0.145181i	0.368972	−	0.929440i	$-0.379710\pi$
$863$	−6375.08	−	3680.65i	−0.251460	−	0.145181i	−0.620433	+	0.784260i	$0.713043\pi$
$864$	23443.3	−	6972.37i	0.923098	−	0.274543i
$865$	323.134	+	559.684i	0.0127016	+	0.0219998i
$866$	6926.17	+	11996.5i	0.271779	+	0.470736i
$867$	4658.88	+	4574.90i	0.182496	+	0.179206i
$868$	10548.0	+	6183.65i	0.412470	+	0.241805i
$869$	−20266.9	+	11701.1i	−0.791149	+	0.456770i
$870$	27.6816	−	107.200i	0.00107873	−	0.00417748i
$871$			34658.6i			1.34829i
$872$	228.341	−	131.833i	0.00886765	−	0.00511974i
$873$	−2329.82	−	3871.01i	−0.0903234	−	0.150073i
$874$			6611.70i			0.255886i
$875$	628.465	+	1105.42i	0.0242811	+	0.0427085i
$876$	4874.29	+	1258.66i	0.187999	+	0.0485460i
$877$	−1980.37			−0.0762512			−0.0381256	−	0.999273i	$-0.512139\pi$
$877$	−1980.37			−0.0762512			−0.0381256	+	0.999273i	$0.512139\pi$
$878$	2341.75	−	4056.03i	0.0900117	−	0.155905i
$879$	−930.526	+	258.426i	−0.0357063	+	0.00991639i
$880$	211.513	−	122.117i	0.00810239	−	0.00467792i
$881$	30117.5			1.15174			0.575870	−	0.817541i	$-0.304663\pi$
$881$	30117.5			1.15174			0.575870	+	0.817541i	$0.304663\pi$
$882$	−5291.52	+	9270.01i	−0.202012	+	0.353897i
$883$	3739.43			0.142516			0.0712580	−	0.997458i	$-0.477299\pi$
$883$	3739.43			0.142516			0.0712580	+	0.997458i	$0.477299\pi$
$884$	15980.5	−	9226.34i	0.608011	−	0.351036i
$885$	558.772	+	548.700i	0.0212236	+	0.0208411i
$886$	3815.55	−	6608.73i	0.144680	−	0.250592i
$887$	−35778.8			−1.35438			−0.677190	−	0.735809i	$-0.736802\pi$
$887$	−35778.8			−1.35438			−0.677190	+	0.735809i	$0.736802\pi$
$888$	−15232.6	+	15512.2i	−0.575643	+	0.586210i
$889$	18485.9	+	32515.2i	0.697410	+	1.22669i
$890$		−	91.9533i		−	0.00346324i
$891$	−16206.5	+	10160.1i	−0.609359	+	0.382018i
$892$	11227.2	−	6482.04i	0.421430	−	0.243313i
$893$			22527.4i			0.844177i
$894$	2098.79	−	582.879i	0.0785170	−	0.0218058i
$895$	543.168	−	313.598i	0.0202861	−	0.0117122i
$896$	23574.2	+	13820.0i	0.878971	+	0.515285i
$897$	29259.9	−	8126.07i	1.08914	−	0.302477i
$898$	−1850.60	−	3205.33i	−0.0687697	−	0.119113i
$899$	3329.56	+	5766.96i	0.123523	+	0.213948i
$900$	−19280.3	+	11604.1i	−0.714085	+	0.429781i
$901$	−20186.6	−	11654.7i	−0.746408	−	0.430939i
$902$	4059.48	−	7031.23i	0.149851	−	0.259550i
$903$	−3578.39	+	13487.1i	−0.131873	+	0.497035i
$904$	3736.83	+	6472.38i	0.137484	+	0.238128i
$905$			946.900i			0.0347801i
$906$	827.753	+	2980.52i	0.0303535	+	0.109295i
$907$	30813.7			1.12806			0.564031	−	0.825753i	$-0.309250\pi$
$907$	30813.7			1.12806			0.564031	+	0.825753i	$0.309250\pi$
$908$	13275.1	−	22993.2i	0.485188	−	0.840370i
$909$	−22325.5	−	12353.7i	−0.814620	−	0.450768i
$910$	−268.224	−	1.78082i	−0.00977091	−	6.48719e-5i
$911$	−10135.1	−	5851.50i	−0.368595	−	0.212809i	0.304249	−	0.952592i	$-0.401594\pi$
$911$	−10135.1	−	5851.50i	−0.368595	−	0.212809i	−0.672845	+	0.739784i	$0.734928\pi$
$912$	−7653.64	−	1976.36i	−0.277892	−	0.0717586i
$913$	33892.3	+	19567.7i	1.22856	+	0.709307i
$914$	−7838.89	−	4525.79i	−0.283684	−	0.163785i
$915$	83.6442	+	301.181i	0.00302207	+	0.0108817i
$916$	21620.6	+	12482.7i	0.779875	+	0.450261i
$917$	−8733.98	−	15362.3i	−0.314527	−	0.553227i
$918$	−9372.04	+	2787.38i	−0.336954	+	0.100215i
$919$	9866.32	−	17089.0i	0.354146	−	0.613398i	−0.632826	−	0.774294i	$-0.718105\pi$
$919$	9866.32	−	17089.0i	0.354146	−	0.613398i	0.986971	+	0.160896i	$0.0514384\pi$
$920$	593.543			0.0212701
$921$	−13121.5	−	3388.29i	−0.469454	−	0.121225i
$922$			6898.22i			0.246400i
$923$	−25375.5	−	43951.7i	−0.904924	−	1.56737i
$924$	−16282.7	−	4320.12i	−0.579722	−	0.153811i
$925$	15454.9	−	26768.6i	0.549354	−	0.951510i
$926$	−18722.6	−	10809.5i	−0.664430	−	0.383609i
$927$	−10937.0	+	19765.2i	−0.387507	+	0.700296i
$928$	5865.72	+	10159.7i	0.207491	+	0.359385i
$929$	−8592.29	−	14882.3i	−0.303449	−	0.525589i	0.673466	−	0.739218i	$-0.264805\pi$
$929$	−8592.29	−	14882.3i	−0.303449	−	0.525589i	−0.976915	+	0.213629i	$0.931471\pi$
$930$	40.7063	−	157.639i	0.00143528	−	0.00555826i
$931$	13437.8	−	7522.22i	0.473047	−	0.264802i
$932$	28101.6	−	16224.5i	0.987660	−	0.570226i
$933$	13694.4	+	13447.6i	0.480530	+	0.471868i
$934$		−	10540.3i		−	0.369261i
$935$	−377.473	+	217.934i	−0.0132029	+	0.00762269i
$936$	−379.840	−	20880.5i	−0.0132644	−	0.729167i
$937$			16777.3i			0.584940i	0.956275	+	0.292470i	$0.0944772\pi$
$937$			16777.3i			0.584940i	−0.956275	+	0.292470i	$0.905523\pi$
$938$	14060.6	−	7993.90i	0.489440	−	0.278262i
$939$	9491.21	+	34175.4i	0.329855	+	1.18772i
$940$	919.606			0.0319088
$941$	4512.78	−	7816.36i	0.156336	−	0.270782i	−0.777209	−	0.629243i	$-0.783365\pi$
$941$	4512.78	−	7816.36i	0.156336	−	0.270782i	0.933545	+	0.358461i	$0.116698\pi$
$942$	−1733.16	+	6711.82i	−0.0599463	+	0.232147i
$943$	−29705.8	+	17150.7i	−1.02583	+	0.592262i
$944$	−18588.5			−0.640893
$945$	−693.151	−	170.474i	−0.0238605	−	0.00586829i
$946$	4385.01			0.150707
$947$	−49093.6	+	28344.2i	−1.68461	+	0.972611i	−0.726088	+	0.687602i	$0.758663\pi$
$947$	−49093.6	+	28344.2i	−1.68461	+	0.972611i	−0.958525	+	0.285009i	$0.908003\pi$
$948$	7730.50	−	29937.1i	0.264847	−	1.02564i
$949$	3321.18	−	5752.45i	0.113604	−	0.196768i
$950$	−6464.59			−0.220778
$951$	−4266.22	−	15361.5i	−0.145470	−	0.523798i
$952$	−16336.9	−	9577.32i	−0.556180	−	0.326053i
$953$		−	2869.91i		−	0.0975503i	−0.998810	−	0.0487751i	$-0.984468\pi$
$953$		−	2869.91i		−	0.0975503i	0.998810	−	0.0487751i	$-0.0155318\pi$
$954$	−10278.1	+	6185.98i	−0.348810	+	0.209935i
$955$	423.338	−	244.414i	0.0143444	−	0.00828173i
$956$		−	30771.9i		−	1.04104i
$957$	−6546.30	−	6428.30i	−0.221120	−	0.217134i
$958$	40.6077	−	23.4448i	0.00136949	−	0.000790677i
$959$	22250.8	−	12650.3i	0.749234	−	0.425963i
$960$	−25.0300	+	96.9308i	−0.000841498	+	0.00325878i
$961$	−9999.34	−	17319.4i	−0.335650	−	0.581362i
$962$	6522.13	+	11296.7i	0.218588	+	0.378606i
$963$	19627.3	+	32610.9i	0.656781	+	1.09125i
$964$	−5462.30	−	3153.66i	−0.182499	−	0.105366i
$965$	68.5615	−	118.752i	0.00228712	−	0.00396141i
$966$	−10045.3	−	9996.14i	−0.334579	−	0.332940i
$967$	−20201.6	−	34990.2i	−0.671810	−	1.16361i	−0.977390	−	0.211443i	$-0.932184\pi$
$967$	−20201.6	−	34990.2i	−0.671810	−	1.16361i	0.305580	−	0.952166i	$-0.401150\pi$
$968$		−	10865.3i		−	0.360767i
$969$	13658.9	+	3527.08i	0.452826	+	0.116931i
$970$	−52.9837			−0.00175382
$971$	−15681.9	+	27161.9i	−0.518288	+	0.897701i	0.481486	+	0.876454i	$0.340097\pi$
$971$	−15681.9	+	27161.9i	−0.518288	+	0.897701i	−0.999774	+	0.0212472i	$0.993236\pi$
$972$	5424.45	−	24682.9i	0.179001	−	0.814510i
$973$	50264.7	+	29467.0i	1.65613	+	0.970884i
$974$	−10967.1	−	6331.84i	−0.360788	−	0.208301i
$975$	7945.27	+	28608.8i	0.260977	+	0.939709i
$976$	−6425.39	−	3709.70i	−0.210729	−	0.121665i
$977$	−20718.0	−	11961.5i	−0.678430	−	0.391692i	0.120833	−	0.992673i	$-0.461443\pi$
$977$	−20718.0	−	11961.5i	−0.678430	−	0.391692i	−0.799263	+	0.600981i	$0.794777\pi$
$978$	−20686.6	−	5341.79i	−0.676363	−	0.174654i
$979$	−6599.09	−	3809.99i	−0.215432	−	0.124380i
$980$	−307.070	−	548.555i	−0.0100092	−	0.0178805i
$981$	−7.65703	−	420.921i	−0.000249205	−	0.0136993i
$982$	1485.81	−	2573.49i	0.0482831	−	0.0836288i
$983$	−39291.6			−1.27488			−0.637440	−	0.770500i	$-0.720007\pi$
$983$	−39291.6			−1.27488			−0.637440	+	0.770500i	$0.720007\pi$
$984$	6312.37	+	22729.2i	0.204503	+	0.736362i
$985$			1190.50i			0.0385100i
$986$	−2344.97	−	4061.61i	−0.0757394	−	0.131184i
$987$	−34226.5	−	34058.9i	−1.10379	−	1.09838i
$988$	−6850.61	+	11865.6i	−0.220594	+	0.382080i
$989$	−16044.0	−	9263.00i	−0.515844	−	0.297822i
$990$	4.07989	+	224.279i	0.000130977	+	0.00720006i
$991$	12281.2	+	21271.6i	0.393667	+	0.681852i	0.992930	−	0.118700i	$-0.0378728\pi$
$991$	12281.2	+	21271.6i	0.393667	+	0.681852i	−0.599263	+	0.800552i	$0.704539\pi$
$992$	8625.63	+	14940.0i	0.276073	+	0.478172i
$993$	4560.76	−	1266.62i	0.145752	−	0.0404782i
$994$	−11977.9	+	20431.9i	−0.382209	+	0.651971i
$995$	−391.906	+	226.267i	−0.0124867	+	0.00720919i
$996$	−49820.2	+	13836.1i	−1.58495	+	0.440175i
$997$			10337.6i			0.328379i	0.986429	+	0.164190i	$0.0525009\pi$
$997$			10337.6i			0.328379i	−0.986429	+	0.164190i	$0.947499\pi$
$998$	1094.61	−	631.974i	0.0347187	−	0.0200449i
$999$	9895.78	+	33272.7i	0.313402	+	1.05375i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.s.a.47.10	yes	44
3.2	odd	2		189.4.s.a.89.13		44
7.3	odd	6		63.4.i.a.38.10	yes	44
9.4	even	3		189.4.i.a.152.10		44
9.5	odd	6		63.4.i.a.5.13	✓	44
21.17	even	6		189.4.i.a.143.13		44
63.31	odd	6		189.4.s.a.17.13		44
63.59	even	6	inner	63.4.s.a.59.10	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.13	✓	44	9.5	odd	6
63.4.i.a.38.10	yes	44	7.3	odd	6
63.4.s.a.47.10	yes	44	1.1	even	1	trivial
63.4.s.a.59.10	yes	44	63.59	even	6	inner
189.4.i.a.143.13		44	21.17	even	6
189.4.i.a.152.10		44	9.4	even	3
189.4.s.a.17.13		44	63.31	odd	6
189.4.s.a.89.13		44	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.998155 + 0.576285i) q^{2} +(-1.29916 + 5.03112i) q^{3} +(-3.33579 + 5.77776i) q^{4} +0.274718 q^{5} +(-1.60260 - 5.77053i) q^{6} +(-9.15344 - 16.1001i) q^{7} -16.9100i q^{8} +(-23.6244 - 13.0725i) q^{9} +O(q^{10})\)	\(q+(-0.998155 + 0.576285i) q^{2} +(-1.29916 + 5.03112i) q^{3} +(-3.33579 + 5.77776i) q^{4} +0.274718 q^{5} +(-1.60260 - 5.77053i) q^{6} +(-9.15344 - 16.1001i) q^{7} -16.9100i q^{8} +(-23.6244 - 13.0725i) q^{9} +(-0.274212 + 0.158316i) q^{10} +26.2387i q^{11} +(-24.7349 - 24.2890i) q^{12} +(-39.6128 + 22.8704i) q^{13} +(18.4148 + 10.7954i) q^{14} +(-0.356904 + 1.38214i) q^{15} +(-16.9413 - 29.3432i) q^{16} +(30.2340 + 52.3669i) q^{17} +(31.1143 - 0.566004i) q^{18} +(-38.8827 - 22.4489i) q^{19} +(-0.916403 + 1.58726i) q^{20} +(92.8936 - 25.1354i) q^{21} +(-15.1209 - 26.1902i) q^{22} +127.767i q^{23} +(85.0764 + 21.9689i) q^{24} -124.925 q^{25} +(26.3598 - 45.6565i) q^{26} +(96.4611 - 101.874i) q^{27} +(123.557 + 0.820329i) q^{28} +(58.2779 + 33.6468i) q^{29} +(-0.440263 - 1.58527i) q^{30} +(85.6986 + 49.4781i) q^{31} +(150.976 + 87.1662i) q^{32} +(-132.010 - 34.0883i) q^{33} +(-60.3565 - 34.8469i) q^{34} +(-2.51462 - 4.42301i) q^{35} +(154.336 - 92.8888i) q^{36} +(-123.714 + 214.278i) q^{37} +51.7480 q^{38} +(-63.6006 - 229.009i) q^{39} -4.64550i q^{40} +(134.234 + 232.500i) q^{41} +(-78.2370 + 78.6222i) q^{42} +(-72.4990 + 125.572i) q^{43} +(-151.601 - 87.5267i) q^{44} +(-6.49005 - 3.59125i) q^{45} +(-73.6304 - 127.532i) q^{46} +(-250.874 - 434.526i) q^{47} +(169.639 - 47.1123i) q^{48} +(-175.429 + 294.743i) q^{49} +(124.694 - 71.9922i) q^{50} +(-302.743 + 84.0781i) q^{51} -305.164i q^{52} +(-333.839 + 192.742i) q^{53} +(-37.5748 + 157.275i) q^{54} +7.20824i q^{55} +(-272.254 + 154.785i) q^{56} +(163.458 - 166.459i) q^{57} -77.5605 q^{58} +(274.307 - 475.113i) q^{59} +(-6.79513 - 6.67264i) q^{60} +(189.637 - 109.487i) q^{61} -114.054 q^{62} +(5.77539 + 500.014i) q^{63} +70.1309 q^{64} +(-10.8824 + 6.28293i) q^{65} +(151.411 - 42.0499i) q^{66} +(378.858 - 656.202i) q^{67} -403.418 q^{68} +(-642.813 - 165.990i) q^{69} +(5.05889 + 2.96571i) q^{70} +1109.53i q^{71} +(-221.056 + 399.489i) q^{72} +(-125.762 + 72.6086i) q^{73} -285.177i q^{74} +(162.297 - 628.510i) q^{75} +(259.409 - 149.770i) q^{76} +(422.446 - 240.174i) q^{77} +(195.458 + 191.934i) q^{78} +(445.950 + 772.407i) q^{79} +(-4.65409 - 8.06113i) q^{80} +(387.221 + 617.658i) q^{81} +(-267.972 - 154.714i) q^{82} +(745.760 - 1291.69i) q^{83} +(-164.647 + 620.563i) q^{84} +(8.30585 + 14.3862i) q^{85} -167.120i q^{86} +(-244.993 + 249.491i) q^{87} +443.696 q^{88} +(-145.205 + 251.503i) q^{89} +(8.54766 - 0.155492i) q^{90} +(730.810 + 428.428i) q^{91} +(-738.209 - 426.205i) q^{92} +(-360.267 + 366.880i) q^{93} +(500.822 + 289.150i) q^{94} +(-10.6818 - 6.16714i) q^{95} +(-634.686 + 646.337i) q^{96} +(144.917 + 83.6676i) q^{97} +(5.24921 - 395.297i) q^{98} +(343.004 - 619.871i) 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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