LMFDB - Embedded newform 63.3.r.a.29.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,3,Mod(29,63)]

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, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("63.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	63.r (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:	$1.71662566547$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.5
Character	$\chi$	$=$	63.29
Dual form			63.3.r.a.50.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.649615 - 0.375055i) q^{2} +(2.92707 + 0.657482i) q^{3} +(-1.71867 - 2.97682i) q^{4} +(2.68085 - 1.54779i) q^{5} +(-1.65487 - 1.52492i) q^{6} +(1.32288 - 2.29129i) q^{7} +5.57882i q^{8} +(8.13543 + 3.84899i) q^{9} +O(q^{10})$	\(q+(-0.649615 - 0.375055i) q^{2} +(2.92707 + 0.657482i) q^{3} +(-1.71867 - 2.97682i) q^{4} +(2.68085 - 1.54779i) q^{5} +(-1.65487 - 1.52492i) q^{6} +(1.32288 - 2.29129i) q^{7} +5.57882i q^{8} +(8.13543 + 3.84899i) q^{9} -2.32203 q^{10} +(5.13306 + 2.96357i) q^{11} +(-3.07345 - 9.84334i) q^{12} +(-8.50508 - 14.7312i) q^{13} +(-1.71872 + 0.992303i) q^{14} +(8.86467 - 2.76787i) q^{15} +(-4.78230 + 8.28319i) q^{16} +31.4021i q^{17} +(-3.84132 - 5.55160i) q^{18} -15.5536 q^{19} +(-9.21497 - 5.32027i) q^{20} +(5.37863 - 5.83698i) q^{21} +(-2.22301 - 3.85036i) q^{22} +(-9.27428 + 5.35451i) q^{23} +(-3.66798 + 16.3296i) q^{24} +(-7.70870 + 13.3519i) q^{25} +12.7595i q^{26} +(21.2823 + 16.6151i) q^{27} -9.09433 q^{28} +(-34.6895 - 20.0280i) q^{29} +(-6.79672 - 1.52669i) q^{30} +(6.78612 + 11.7539i) q^{31} +(25.5389 - 14.7449i) q^{32} +(13.0763 + 12.0495i) q^{33} +(11.7775 - 20.3993i) q^{34} -8.19013i q^{35} +(-2.52437 - 30.8328i) q^{36} +36.9276 q^{37} +(10.1038 + 5.83346i) q^{38} +(-15.2094 - 48.7112i) q^{39} +(8.63484 + 14.9560i) q^{40} +(15.1972 - 8.77413i) q^{41} +(-5.68323 + 1.77451i) q^{42} +(27.7990 - 48.1492i) q^{43} -20.3736i q^{44} +(27.7673 - 2.27338i) q^{45} +8.03294 q^{46} +(6.33896 + 3.65980i) q^{47} +(-19.4442 + 21.1012i) q^{48} +(-3.50000 - 6.06218i) q^{49} +(10.0154 - 5.78238i) q^{50} +(-20.6464 + 91.9162i) q^{51} +(-29.2348 + 50.6362i) q^{52} -7.18315i q^{53} +(-7.59371 - 18.7755i) q^{54} +18.3479 q^{55} +(12.7827 + 7.38009i) q^{56} +(-45.5264 - 10.2262i) q^{57} +(15.0232 + 26.0210i) q^{58} +(-0.793706 + 0.458247i) q^{59} +(-23.4749 - 21.6315i) q^{60} +(-37.1890 + 64.4133i) q^{61} -10.1807i q^{62} +(19.5813 - 13.5489i) q^{63} +16.1378 q^{64} +(-45.6017 - 26.3281i) q^{65} +(-3.97535 - 12.7319i) q^{66} +(-18.6154 - 32.2429i) q^{67} +(93.4785 - 53.9698i) q^{68} +(-30.6669 + 9.57532i) q^{69} +(-3.07175 + 5.32043i) q^{70} -9.30286i q^{71} +(-21.4728 + 45.3862i) q^{72} -8.55399 q^{73} +(-23.9887 - 13.8499i) q^{74} +(-31.3425 + 34.0134i) q^{75} +(26.7314 + 46.3002i) q^{76} +(13.5808 - 7.84088i) q^{77} +(-8.38914 + 37.3479i) q^{78} +(69.1244 - 119.727i) q^{79} +29.6080i q^{80} +(51.3706 + 62.6264i) q^{81} -13.1631 q^{82} +(-136.603 - 78.8678i) q^{83} +(-26.6197 - 5.97936i) q^{84} +(48.6039 + 84.1844i) q^{85} +(-36.1173 + 20.8523i) q^{86} +(-88.3704 - 81.4310i) q^{87} +(-16.5333 + 28.6364i) q^{88} +113.571i q^{89} +(-18.8907 - 8.93745i) q^{90} -45.0046 q^{91} +(31.8788 + 18.4052i) q^{92} +(12.1354 + 38.8662i) q^{93} +(-2.74525 - 4.75492i) q^{94} +(-41.6968 + 24.0737i) q^{95} +(84.4486 - 26.3679i) q^{96} +(8.04342 - 13.9316i) q^{97} +5.25078i q^{98} +(30.3529 + 43.8670i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{3} + 24 q^{4} - 18 q^{5} - 14 q^{6} + 26 q^{9}+O(q^{10}) $ 24 * q + 2 * q^3 + 24 * q^4 - 18 * q^5 - 14 * q^6 + 26 * q^9	$ 24 q + 2 q^{3} + 24 q^{4} - 18 q^{5} - 14 q^{6} + 26 q^{9} - 18 q^{11} + 4 q^{12} - 10 q^{15} - 48 q^{16} - 62 q^{18} - 24 q^{19} - 18 q^{20} - 14 q^{21} - 24 q^{22} + 72 q^{23} + 54 q^{24} + 54 q^{25} - 124 q^{27} + 54 q^{29} - 212 q^{30} + 30 q^{31} + 126 q^{32} - 178 q^{33} + 60 q^{34} + 124 q^{36} + 84 q^{37} - 144 q^{38} + 92 q^{39} - 60 q^{40} + 180 q^{41} + 140 q^{42} - 60 q^{43} - 118 q^{45} - 168 q^{46} + 378 q^{47} + 436 q^{48} - 84 q^{49} - 378 q^{50} + 168 q^{51} - 18 q^{52} + 514 q^{54} - 132 q^{55} - 232 q^{57} + 90 q^{58} - 90 q^{59} + 76 q^{60} + 28 q^{63} + 324 q^{64} + 126 q^{65} + 202 q^{66} + 6 q^{67} - 738 q^{68} - 432 q^{69} - 246 q^{72} - 72 q^{73} - 792 q^{74} + 40 q^{75} + 84 q^{76} + 28 q^{78} - 6 q^{79} - 34 q^{81} - 108 q^{82} - 558 q^{83} - 322 q^{84} + 126 q^{85} + 90 q^{86} + 428 q^{87} + 168 q^{88} - 488 q^{90} + 84 q^{91} + 774 q^{92} - 738 q^{93} - 354 q^{94} + 648 q^{95} - 280 q^{96} - 270 q^{97} + 296 q^{99}+O(q^{100}) $ 24 * q + 2 * q^3 + 24 * q^4 - 18 * q^5 - 14 * q^6 + 26 * q^9 - 18 * q^11 + 4 * q^12 - 10 * q^15 - 48 * q^16 - 62 * q^18 - 24 * q^19 - 18 * q^20 - 14 * q^21 - 24 * q^22 + 72 * q^23 + 54 * q^24 + 54 * q^25 - 124 * q^27 + 54 * q^29 - 212 * q^30 + 30 * q^31 + 126 * q^32 - 178 * q^33 + 60 * q^34 + 124 * q^36 + 84 * q^37 - 144 * q^38 + 92 * q^39 - 60 * q^40 + 180 * q^41 + 140 * q^42 - 60 * q^43 - 118 * q^45 - 168 * q^46 + 378 * q^47 + 436 * q^48 - 84 * q^49 - 378 * q^50 + 168 * q^51 - 18 * q^52 + 514 * q^54 - 132 * q^55 - 232 * q^57 + 90 * q^58 - 90 * q^59 + 76 * q^60 + 28 * q^63 + 324 * q^64 + 126 * q^65 + 202 * q^66 + 6 * q^67 - 738 * q^68 - 432 * q^69 - 246 * q^72 - 72 * q^73 - 792 * q^74 + 40 * q^75 + 84 * q^76 + 28 * q^78 - 6 * q^79 - 34 * q^81 - 108 * q^82 - 558 * q^83 - 322 * q^84 + 126 * q^85 + 90 * q^86 + 428 * q^87 + 168 * q^88 - 488 * q^90 + 84 * q^91 + 774 * q^92 - 738 * q^93 - 354 * q^94 + 648 * q^95 - 280 * q^96 - 270 * q^97 + 296 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.649615	−	0.375055i	−0.324807	−	0.187528i	0.328726	−	0.944425i	$-0.393381\pi$
$2$	−0.649615	−	0.375055i	−0.324807	−	0.187528i	−0.653533	+	0.756898i	$0.726714\pi$
$3$	2.92707	+	0.657482i	0.975689	+	0.219161i
$3$	2.92707	+	0.657482i	0.975689	+	0.219161i
$4$	−1.71867	−	2.97682i	−0.429667	−	0.744205i
$5$	2.68085	−	1.54779i	0.536170	−	0.309558i	−0.207355	−	0.978266i	$-0.566486\pi$
$5$	2.68085	−	1.54779i	0.536170	−	0.309558i	0.743525	+	0.668708i	$0.233152\pi$
$6$	−1.65487	−	1.52492i	−0.275812	−	0.254154i
$7$	1.32288	−	2.29129i	0.188982	−	0.327327i
$7$	1.32288	−	2.29129i	0.188982	−	0.327327i
$8$			5.57882i			0.697353i
$9$	8.13543	+	3.84899i	0.903937	+	0.427665i
$10$	−2.32203			−0.232203
$11$	5.13306	+	2.96357i	0.466642	+	0.269416i	0.714833	−	0.699295i	$-0.246503\pi$
$11$	5.13306	+	2.96357i	0.466642	+	0.269416i	−0.248191	+	0.968711i	$0.579836\pi$
$12$	−3.07345	−	9.84334i	−0.256121	−	0.820278i
$13$	−8.50508	−	14.7312i	−0.654237	−	1.13317i	−0.982085	−	0.188441i	$-0.939657\pi$
$13$	−8.50508	−	14.7312i	−0.654237	−	1.13317i	0.327848	−	0.944731i	$-0.393677\pi$
$14$	−1.71872	+	0.992303i	−0.122766	+	0.0708788i
$15$	8.86467	−	2.76787i	0.590978	−	0.184525i
$16$	−4.78230	+	8.28319i	−0.298894	+	0.517699i
$17$			31.4021i			1.84719i	0.383375	+	0.923593i	$0.374762\pi$
$17$			31.4021i			1.84719i	−0.383375	+	0.923593i	$0.625238\pi$
$18$	−3.84132	−	5.55160i	−0.213406	−	0.308422i
$19$	−15.5536			−0.818610			−0.409305	−	0.912398i	$-0.634229\pi$
$19$	−15.5536			−0.818610			−0.409305	+	0.912398i	$0.634229\pi$
$20$	−9.21497	−	5.32027i	−0.460749	−	0.266013i
$21$	5.37863	−	5.83698i	0.256125	−	0.277952i
$22$	−2.22301	−	3.85036i	−0.101046	−	0.175017i
$23$	−9.27428	+	5.35451i	−0.403229	+	0.232805i	−0.687876	−	0.725828i	$-0.741457\pi$
$23$	−9.27428	+	5.35451i	−0.403229	+	0.232805i	0.284647	+	0.958632i	$0.408124\pi$
$24$	−3.66798	+	16.3296i	−0.152832	+	0.680399i
$25$	−7.70870	+	13.3519i	−0.308348	+	0.534074i
$26$			12.7595i			0.490750i
$27$	21.2823	+	16.6151i	0.788234	+	0.615376i
$28$	−9.09433			−0.324798
$29$	−34.6895	−	20.0280i	−1.19619	−	0.690620i	−0.236486	−	0.971635i	$-0.575996\pi$
$29$	−34.6895	−	20.0280i	−1.19619	−	0.690620i	−0.959703	+	0.281015i	$0.909329\pi$
$30$	−6.79672	−	1.52669i	−0.226557	−	0.0508897i
$31$	6.78612	+	11.7539i	0.218907	+	0.379158i	0.954474	−	0.298294i	$-0.0964175\pi$
$31$	6.78612	+	11.7539i	0.218907	+	0.379158i	−0.735567	+	0.677452i	$0.763084\pi$
$32$	25.5389	−	14.7449i	0.798091	−	0.460778i
$33$	13.0763	+	12.0495i	0.396252	+	0.365136i
$34$	11.7775	−	20.3993i	0.346398	−	0.599980i
$35$		−	8.19013i		−	0.234004i
$36$	−2.52437	−	30.8328i	−0.0701213	−	0.856468i
$37$	36.9276			0.998043			0.499022	−	0.866590i	$-0.333693\pi$
$37$	36.9276			0.998043			0.499022	+	0.866590i	$0.333693\pi$
$38$	10.1038	+	5.83346i	0.265891	+	0.153512i
$39$	−15.2094	−	48.7112i	−0.389985	−	1.24901i
$40$	8.63484	+	14.9560i	0.215871	+	0.373900i
$41$	15.1972	−	8.77413i	0.370664	−	0.214003i	−0.303084	−	0.952964i	$-0.598016\pi$
$41$	15.1972	−	8.77413i	0.370664	−	0.214003i	0.673749	+	0.738961i	$0.264683\pi$
$42$	−5.68323	+	1.77451i	−0.135315	+	0.0422502i
$43$	27.7990	−	48.1492i	0.646488	−	1.11975i	−0.337468	−	0.941337i	$-0.609570\pi$
$43$	27.7990	−	48.1492i	0.646488	−	1.11975i	0.983956	−	0.178413i	$-0.0570962\pi$
$44$		−	20.3736i		−	0.463036i
$45$	27.7673	−	2.27338i	0.617051	−	0.0505196i
$46$	8.03294			0.174629
$47$	6.33896	+	3.65980i	0.134871	+	0.0778680i	0.565918	−	0.824462i	$-0.308522\pi$
$47$	6.33896	+	3.65980i	0.134871	+	0.0778680i	−0.431046	+	0.902330i	$0.641855\pi$
$48$	−19.4442	+	21.1012i	−0.405087	+	0.439607i
$49$	−3.50000	−	6.06218i	−0.0714286	−	0.123718i
$50$	10.0154	−	5.78238i	0.200307	−	0.115648i
$51$	−20.6464	+	91.9162i	−0.404830	+	1.80228i
$52$	−29.2348	+	50.6362i	−0.562208	+	0.973772i
$53$		−	7.18315i		−	0.135531i	−0.997701	−	0.0677656i	$-0.978413\pi$
$53$		−	7.18315i		−	0.135531i	0.997701	−	0.0677656i	$-0.0215870\pi$
$54$	−7.59371	−	18.7755i	−0.140624	−	0.347694i
$55$	18.3479			0.333599
$56$	12.7827	+	7.38009i	0.228262	+	0.131787i
$57$	−45.5264	−	10.2262i	−0.798709	−	0.179407i
$58$	15.0232	+	26.0210i	0.259021	+	0.448637i
$59$	−0.793706	+	0.458247i	−0.0134526	+	0.00776689i	−0.506711	−	0.862116i	$-0.669139\pi$
$59$	−0.793706	+	0.458247i	−0.0134526	+	0.00776689i	0.493259	+	0.869883i	$0.335806\pi$
$60$	−23.4749	−	21.6315i	−0.391248	−	0.360524i
$61$	−37.1890	+	64.4133i	−0.609656	+	1.05596i	0.381641	+	0.924311i	$0.375359\pi$
$61$	−37.1890	+	64.4133i	−0.609656	+	1.05596i	−0.991297	+	0.131645i	$0.957974\pi$
$62$		−	10.1807i		−	0.164204i
$63$	19.5813	−	13.5489i	0.310814	−	0.215062i
$64$	16.1378			0.252153
$65$	−45.6017	−	26.3281i	−0.701564	−	0.405048i
$66$	−3.97535	−	12.7319i	−0.0602326	−	0.192907i
$67$	−18.6154	−	32.2429i	−0.277842	−	0.481237i	0.693006	−	0.720932i	$-0.256286\pi$
$67$	−18.6154	−	32.2429i	−0.277842	−	0.481237i	−0.970848	+	0.239695i	$0.922953\pi$
$68$	93.4785	−	53.9698i	1.37468	−	0.793674i
$69$	−30.6669	+	9.57532i	−0.444448	+	0.138773i
$70$	−3.07175	+	5.32043i	−0.0438822	+	0.0760061i
$71$		−	9.30286i		−	0.131026i	−0.997852	−	0.0655131i	$-0.979132\pi$
$71$		−	9.30286i		−	0.131026i	0.997852	−	0.0655131i	$-0.0208684\pi$
$72$	−21.4728	+	45.3862i	−0.298234	+	0.630363i
$73$	−8.55399			−0.117178			−0.0585890	−	0.998282i	$-0.518660\pi$
$73$	−8.55399			−0.117178			−0.0585890	+	0.998282i	$0.518660\pi$
$74$	−23.9887	−	13.8499i	−0.324172	−	0.187161i
$75$	−31.3425	+	34.0134i	−0.417900	+	0.453513i
$76$	26.7314	+	46.3002i	0.351729	+	0.609213i
$77$	13.5808	−	7.84088i	0.176374	−	0.101830i
$78$	−8.38914	+	37.3479i	−0.107553	+	0.478819i
$79$	69.1244	−	119.727i	0.874993	−	1.51553i	0.0182218	−	0.999834i	$-0.494199\pi$
$79$	69.1244	−	119.727i	0.874993	−	1.51553i	0.856771	−	0.515698i	$-0.172467\pi$
$80$			29.6080i			0.370100i
$81$	51.3706	+	62.6264i	0.634205	+	0.773165i
$82$	−13.1631			−0.160526
$83$	−136.603	−	78.8678i	−1.64582	−	0.950214i	−0.978708	−	0.205256i	$-0.934197\pi$
$83$	−136.603	−	78.8678i	−1.64582	−	0.950214i	−0.667111	−	0.744958i	$-0.732469\pi$
$84$	−26.6197	−	5.97936i	−0.316901	−	0.0711829i
$85$	48.6039	+	84.1844i	0.571810	+	0.990405i
$86$	−36.1173	+	20.8523i	−0.419968	+	0.242469i
$87$	−88.3704	−	81.4310i	−1.01575	−	0.935988i
$88$	−16.5333	+	28.6364i	−0.187878	+	0.325414i
$89$			113.571i			1.27608i	0.770003	+	0.638040i	$0.220255\pi$
$89$			113.571i			1.27608i	−0.770003	+	0.638040i	$0.779745\pi$
$90$	−18.8907	−	8.93745i	−0.209897	−	0.0993050i
$91$	−45.0046			−0.494557
$92$	31.8788	+	18.4052i	0.346509	+	0.200057i
$93$	12.1354	+	38.8662i	0.130489	+	0.417916i
$94$	−2.74525	−	4.75492i	−0.0292048	−	0.0505842i
$95$	−41.6968	+	24.0737i	−0.438914	+	0.253407i
$96$	84.4486	−	26.3679i	0.879673	−	0.274666i
$97$	8.04342	−	13.9316i	0.0829218	−	0.143625i	−0.821582	−	0.570090i	$-0.806908\pi$
$97$	8.04342	−	13.9316i	0.0829218	−	0.143625i	0.904504	+	0.426466i	$0.140241\pi$
$98$			5.25078i			0.0535793i
$99$	30.3529	+	43.8670i	0.306595	+	0.443102i
$100$	52.9948			0.529948
$101$	113.254	+	65.3870i	1.12132	+	0.647396i	0.941738	−	0.336347i	$-0.109191\pi$
$101$	113.254	+	65.3870i	1.12132	+	0.647396i	0.179584	+	0.983743i	$0.442525\pi$
$102$	47.8858	−	51.9666i	0.469469	−	0.509476i
$103$	−74.2304	−	128.571i	−0.720683	−	1.24826i	−0.960726	−	0.277498i	$-0.910495\pi$
$103$	−74.2304	−	128.571i	−0.720683	−	1.24826i	0.240043	−	0.970762i	$-0.422839\pi$
$104$	82.1829	−	47.4483i	0.790221	−	0.456234i
$105$	5.38486	−	23.9730i	0.0512844	−	0.228315i
$106$	−2.69408	+	4.66628i	−0.0254159	+	0.0440215i
$107$		−	185.717i		−	1.73567i	−0.496850	−	0.867836i	$-0.665510\pi$
$107$		−	185.717i		−	1.73567i	0.496850	−	0.867836i	$-0.334490\pi$
$108$	12.8831	−	91.9095i	0.119288	−	0.851014i
$109$	−33.6651			−0.308854			−0.154427	−	0.988004i	$-0.549353\pi$
$109$	−33.6651			−0.308854			−0.154427	+	0.988004i	$0.549353\pi$
$110$	−11.9191	−	6.88150i	−0.108355	−	0.0625591i
$111$	108.090	+	24.2792i	0.973780	+	0.218732i
$112$	12.6528	+	21.9153i	0.112971	+	0.195672i
$113$	−71.5930	+	41.3343i	−0.633567	+	0.365790i	−0.782132	−	0.623113i	$-0.785868\pi$
$113$	−71.5930	+	41.3343i	−0.633567	+	0.365790i	0.148565	+	0.988903i	$0.452534\pi$
$114$	25.7392	+	23.7180i	0.225783	+	0.208053i
$115$	−16.5753	+	28.7092i	−0.144133	+	0.249646i
$116$			137.686i			1.18695i
$117$	−12.4922	−	152.581i	−0.106771	−	1.30411i
$118$	0.687471			0.00582603
$119$	71.9514	+	41.5411i	0.604633	+	0.349085i
$120$	15.4415	+	49.4544i	0.128679	+	0.412120i
$121$	−42.9345	−	74.3647i	−0.354830	−	0.614584i
$122$	48.3171	−	27.8959i	0.396042	−	0.228655i
$123$	50.2522	−	15.6906i	0.408554	−	0.127565i
$124$	23.3262	−	40.4021i	0.188114	−	0.325823i
$125$			125.115i			1.00092i
$126$	−17.8019	+	1.45749i	−0.141285	+	0.0115674i
$127$	2.37266			0.0186824			0.00934119	−	0.999956i	$-0.497027\pi$
$127$	2.37266			0.0186824			0.00934119	+	0.999956i	$0.497027\pi$
$128$	−112.639	−	65.0322i	−0.879992	−	0.508064i
$129$	113.027	−	122.659i	0.876176	−	0.950843i
$130$	19.7490	+	34.2063i	0.151915	+	0.263125i
$131$	−89.8328	+	51.8650i	−0.685747	+	0.395916i	−0.802017	−	0.597301i	$-0.796240\pi$
$131$	−89.8328	+	51.8650i	−0.685747	+	0.395916i	0.116270	+	0.993218i	$0.462906\pi$
$132$	13.3953	−	59.6348i	0.101479	−	0.451779i
$133$	−20.5755	+	35.6377i	−0.154703	+	0.267953i
$134$			27.9273i			0.208413i
$135$	82.7714	+	11.6022i	0.613122	+	0.0859419i
$136$	−175.187			−1.28814
$137$	173.072	+	99.9229i	1.26330	+	0.729364i	0.973711	−	0.227788i	$-0.0731492\pi$
$137$	173.072	+	99.9229i	1.26330	+	0.729364i	0.289585	+	0.957152i	$0.406483\pi$
$138$	23.5130	+	5.28152i	0.170384	+	0.0382719i
$139$	37.2118	+	64.4527i	0.267711	+	0.463689i	0.968270	−	0.249905i	$-0.0803995\pi$
$139$	37.2118	+	64.4527i	0.267711	+	0.463689i	−0.700559	+	0.713594i	$0.747066\pi$
$140$	−24.3805	+	14.0761i	−0.174147	+	0.100544i
$141$	16.1483	+	14.8802i	0.114527	+	0.105533i
$142$	−3.48909	+	6.04328i	−0.0245710	+	0.0425583i
$143$		−	100.822i		−	0.705047i
$144$	−70.7880	+	48.9803i	−0.491583	+	0.340141i
$145$	−123.996			−0.855147
$146$	5.55680	+	3.20822i	0.0380603	+	0.0219741i
$147$	−6.25896	−	20.0456i	−0.0425780	−	0.136365i
$148$	−63.4662	−	109.927i	−0.428826	−	0.742748i
$149$	−185.280	+	106.971i	−1.24349	+	0.717928i	−0.969803	−	0.243891i	$-0.921576\pi$
$149$	−185.280	+	106.971i	−1.24349	+	0.717928i	−0.273685	+	0.961819i	$0.588243\pi$
$150$	33.1175	−	10.3405i	0.220783	−	0.0689365i
$151$	30.4238	−	52.6956i	0.201482	−	0.348978i	−0.747524	−	0.664235i	$-0.768757\pi$
$151$	30.4238	−	52.6956i	0.201482	−	0.348978i	0.949006	+	0.315257i	$0.102091\pi$
$152$		−	86.7707i		−	0.570860i
$153$	−120.866	+	255.470i	−0.789977	+	1.66974i
$154$	−11.7631			−0.0763835
$155$	36.3851	+	21.0070i	0.234743	+	0.135529i
$156$	−118.865	+	128.994i	−0.761952	+	0.826885i
$157$	−90.2719	−	156.355i	−0.574980	−	0.995895i	−0.996044	−	0.0888637i	$-0.971676\pi$
$157$	−90.2719	−	156.355i	−0.574980	−	0.995895i	0.421064	−	0.907031i	$-0.361657\pi$
$158$	−89.8085	+	51.8510i	−0.568408	+	0.328171i
$159$	4.72279	−	21.0256i	0.0297031	−	0.132236i
$160$	45.6440	−	79.0577i	0.285275	−	0.494111i
$161$			28.3334i			0.175984i
$162$	−9.88275	−	59.9498i	−0.0610046	−	0.370061i
$163$	307.546			1.88679			0.943393	−	0.331677i	$-0.107615\pi$
$163$	307.546			1.88679			0.943393	+	0.331677i	$0.107615\pi$
$164$	−52.2380	−	30.1596i	−0.318524	−	0.183900i
$165$	53.7057	+	12.0634i	0.325489	+	0.0731118i
$166$	59.1596	+	102.467i	0.356383	+	0.617273i
$167$	−42.4273	+	24.4954i	−0.254056	+	0.146679i	−0.621620	−	0.783319i	$-0.713525\pi$
$167$	−42.4273	+	24.4954i	−0.254056	+	0.146679i	0.367564	+	0.929998i	$0.380192\pi$
$168$	32.5635	+	30.0064i	0.193830	+	0.178610i
$169$	−60.1727	+	104.222i	−0.356052	+	0.616700i
$170$		−	72.9166i		−	0.428921i
$171$	−126.535	−	59.8656i	−0.739972	−	0.350091i
$172$	−191.109			−1.11110
$173$	221.886	+	128.106i	1.28258	+	0.740498i	0.977319	−	0.211771i	$-0.0679231\pi$
$173$	221.886	+	128.106i	1.28258	+	0.740498i	0.305260	+	0.952269i	$0.401256\pi$
$174$	26.8656	+	86.0426i	0.154400	+	0.494497i
$175$	20.3953	+	35.3257i	0.116545	+	0.201861i
$176$	−49.0957	+	28.3454i	−0.278953	+	0.161053i
$177$	−2.62452	+	0.819470i	−0.0148278	+	0.00462978i
$178$	42.5955	−	73.7775i	0.239300	−	0.414480i
$179$		−	88.8872i		−	0.496576i	−0.968686	−	0.248288i	$-0.920132\pi$
$179$		−	88.8872i		−	0.496576i	0.968686	−	0.248288i	$-0.0798680\pi$
$180$	−54.4902	−	78.7510i	−0.302723	−	0.437506i
$181$	18.9731			0.104824			0.0524118	−	0.998626i	$-0.483309\pi$
$181$	18.9731			0.104824			0.0524118	+	0.998626i	$0.483309\pi$
$182$	29.2357	+	16.8792i	0.160636	+	0.0927430i
$183$	−151.205	+	164.091i	−0.826258	+	0.896671i
$184$	−29.8718	−	51.7396i	−0.162347	−	0.281193i
$185$	98.9973	−	57.1561i	0.535121	−	0.308952i
$186$	6.69361	−	29.7995i	0.0359872	−	0.160212i
$187$	−93.0626	+	161.189i	−0.497661	+	0.861974i
$188$		−	25.1599i		−	0.133829i
$189$	66.2239	−	26.7841i	0.350391	−	0.141715i
$190$	36.1158			0.190083
$191$	132.352	+	76.4133i	0.692941	+	0.400069i	0.804713	−	0.593664i	$-0.202319\pi$
$191$	132.352	+	76.4133i	0.692941	+	0.400069i	−0.111772	+	0.993734i	$0.535653\pi$
$192$	47.2364	+	10.6103i	0.246023	+	0.0552620i
$193$	76.2987	+	132.153i	0.395330	+	0.684732i	0.993143	−	0.116904i	$-0.0372969\pi$
$193$	76.2987	+	132.153i	0.395330	+	0.684732i	−0.597813	+	0.801636i	$0.703964\pi$
$194$	−10.4502	+	6.03345i	−0.0538673	+	0.0311003i
$195$	−116.169	−	107.046i	−0.595737	−	0.548956i
$196$	−12.0307	+	20.8377i	−0.0613810	+	0.106315i
$197$		−	342.825i		−	1.74023i	−0.492850	−	0.870114i	$-0.664045\pi$
$197$		−	342.825i		−	1.74023i	0.492850	−	0.870114i	$-0.335955\pi$
$198$	−3.26514	−	39.8807i	−0.0164906	−	0.201418i
$199$	150.484			0.756202			0.378101	−	0.925764i	$-0.376577\pi$
$199$	150.484			0.756202			0.378101	+	0.925764i	$0.376577\pi$
$200$	−74.4877	−	43.0055i	−0.372438	−	0.215027i
$201$	−33.2895	−	106.616i	−0.165619	−	0.530430i
$202$	−49.0475	−	84.9527i	−0.242809	−	0.420558i
$203$	−91.7798	+	52.9891i	−0.452117	+	0.261030i
$204$	309.102	−	96.5128i	1.51521	−	0.473102i
$205$	27.1610	−	47.0442i	0.132493	−	0.229484i
$206$			111.362i			0.540592i
$207$	−96.0597	+	7.86466i	−0.464056	+	0.0379935i
$208$	162.695			0.782189
$209$	−79.8375	−	46.0942i	−0.381998	−	0.220546i
$210$	−12.4893	+	13.5536i	−0.0594729	+	0.0645411i
$211$	83.7645	+	145.084i	0.396988	+	0.687604i	0.993353	−	0.115110i	$-0.0367220\pi$
$211$	83.7645	+	145.084i	0.396988	+	0.687604i	−0.596365	+	0.802714i	$0.703389\pi$
$212$	−21.3829	+	12.3454i	−0.100863	+	0.0582332i
$213$	6.11646	−	27.2301i	0.0287158	−	0.127841i
$214$	−69.6541	+	120.645i	−0.325487	+	0.563759i
$215$		−	172.108i		−	0.800501i
$216$	−92.6930	+	118.730i	−0.429134	+	0.549677i
$217$	35.9088			0.165478
$218$	21.8693	+	12.6263i	0.100318	+	0.0579186i
$219$	−25.0381	−	5.62410i	−0.114329	−	0.0256808i
$220$	−31.5340	−	54.6185i	−0.143336	−	0.248266i
$221$	462.592	−	267.078i	2.09318	−	1.20850i
$222$	−61.1105	−	56.3117i	−0.275273	−	0.253656i
$223$	36.0920	−	62.5132i	0.161848	−	0.280328i	−0.773684	−	0.633572i	$-0.781588\pi$
$223$	36.0920	−	62.5132i	0.161848	−	0.280328i	0.935531	+	0.353244i	$0.114921\pi$
$224$		−	78.0227i		−	0.348316i
$225$	−114.105	+	78.9525i	−0.507132	+	0.350900i
$226$	62.0105			0.274383
$227$	−60.3793	−	34.8600i	−0.265988	−	0.153568i	0.361075	−	0.932537i	$-0.382410\pi$
$227$	−60.3793	−	34.8600i	−0.265988	−	0.153568i	−0.627063	+	0.778968i	$0.715743\pi$
$228$	47.8031	+	153.099i	0.209663	+	0.671488i
$229$	35.5310	+	61.5416i	0.155157	+	0.268740i	0.933116	−	0.359575i	$-0.117078\pi$
$229$	35.5310	+	61.5416i	0.155157	+	0.268740i	−0.777959	+	0.628315i	$0.783745\pi$
$230$	21.5351	−	12.4333i	0.0936309	−	0.0540578i
$231$	44.9071	−	14.0216i	0.194403	−	0.0606997i
$232$	111.733	−	193.527i	0.481606	−	0.834166i
$233$		−	243.976i		−	1.04711i	−0.851993	−	0.523553i	$-0.824606\pi$
$233$		−	243.976i		−	1.04711i	0.851993	−	0.523553i	$-0.175394\pi$
$234$	−49.1112	+	103.804i	−0.209877	+	0.443607i
$235$	22.6584			0.0964186
$236$	2.72823	+	1.57515i	0.0115603	+	0.00667435i
$237$	281.050	−	305.001i	1.18587	−	1.28692i
$238$	−31.1605	−	53.9715i	−0.130926	−	0.226771i
$239$	−36.1941	+	20.8967i	−0.151440	+	0.0874337i	−0.573805	−	0.818992i	$-0.694533\pi$
$239$	−36.1941	+	20.8967i	−0.151440	+	0.0874337i	0.422365	+	0.906426i	$0.361200\pi$
$240$	−19.4667	+	86.6645i	−0.0811113	+	0.361102i
$241$	−204.125	+	353.555i	−0.846993	+	1.46703i	0.0368866	+	0.999319i	$0.488256\pi$
$241$	−204.125	+	353.555i	−0.846993	+	1.46703i	−0.883879	+	0.467715i	$0.845077\pi$
$242$			64.4112i			0.266162i
$243$	109.189	+	217.087i	0.449339	+	0.893361i
$244$	255.662			1.04780
$245$	−18.7659	−	10.8345i	−0.0765957	−	0.0442225i
$246$	−38.5294	−	8.65453i	−0.156624	−	0.0351810i
$247$	132.284	+	229.123i	0.535565	+	0.927625i
$248$	−65.5729	+	37.8586i	−0.264407	+	0.152655i
$249$	−347.992	−	320.665i	−1.39756	−	1.28781i
$250$	46.9251	−	81.2767i	0.187700	−	0.325107i
$251$			171.910i			0.684900i	0.939536	+	0.342450i	$0.111257\pi$
$251$			171.910i			0.684900i	−0.939536	+	0.342450i	$0.888743\pi$
$252$	−73.9863	−	35.0040i	−0.293597	−	0.138905i
$253$	−63.4739			−0.250885
$254$	−1.54132	−	0.889880i	−0.00606818	−	0.00350346i
$255$	86.9171	+	278.370i	0.340851	+	1.09165i
$256$	16.5058	+	28.5888i	0.0644756	+	0.111675i
$257$	−248.545	+	143.498i	−0.967102	+	0.558356i	−0.898351	−	0.439278i	$-0.855234\pi$
$257$	−248.545	+	143.498i	−0.967102	+	0.558356i	−0.0687502	+	0.997634i	$0.521901\pi$
$258$	−119.428	+	37.2896i	−0.462898	+	0.144534i
$259$	48.8506	−	84.6118i	0.188612	−	0.326686i
$260$			180.997i			0.696143i
$261$	−205.127	−	296.456i	−0.785926	−	1.13585i
$262$	77.8090			0.296981
$263$	−223.341	−	128.946i	−0.849205	−	0.490289i	0.0111774	−	0.999938i	$-0.496442\pi$
$263$	−223.341	−	128.946i	−0.849205	−	0.490289i	−0.860383	+	0.509649i	$0.829775\pi$
$264$	−67.2219	+	72.9504i	−0.254628	+	0.276327i
$265$	−11.1180	−	19.2569i	−0.0419547	−	0.0726677i
$266$	26.7323	−	15.4339i	0.100497	−	0.0580221i
$267$	−74.6710	+	332.430i	−0.279667	+	1.24506i
$268$	−63.9875	+	110.830i	−0.238759	+	0.413543i
$269$			23.4893i			0.0873206i	0.999046	+	0.0436603i	$0.0139019\pi$
$269$			23.4893i			0.0873206i	−0.999046	+	0.0436603i	$0.986098\pi$
$270$	−49.4181	−	38.5808i	−0.183030	−	0.142892i
$271$	−53.5143			−0.197470			−0.0987349	−	0.995114i	$-0.531480\pi$
$271$	−53.5143			−0.197470			−0.0987349	+	0.995114i	$0.531480\pi$
$272$	−260.110	−	150.174i	−0.956286	−	0.552112i
$273$	−131.732	−	29.5898i	−0.482533	−	0.108387i
$274$	−74.9533	−	129.823i	−0.273552	−	0.473806i
$275$	−79.1385	+	45.6906i	−0.287776	+	0.166148i
$276$	81.2102	+	74.8330i	0.294240	+	0.271134i
$277$	55.8696	−	96.7690i	0.201695	−	0.349347i	−0.747379	−	0.664398i	$-0.768688\pi$
$277$	55.8696	−	96.7690i	0.201695	−	0.349347i	0.949075	+	0.315051i	$0.102022\pi$
$278$		−	55.8259i		−	0.200813i
$279$	9.96740	+	121.743i	0.0357254	+	0.436354i
$280$	45.6913			0.163183
$281$	115.732	+	66.8180i	0.411858	+	0.237787i	0.691588	−	0.722292i	$-0.256911\pi$
$281$	115.732	+	66.8180i	0.411858	+	0.237787i	−0.279729	+	0.960079i	$0.590245\pi$
$282$	−4.90927	−	15.7229i	−0.0174087	−	0.0557550i
$283$	99.0115	+	171.493i	0.349864	+	0.605982i	0.986225	−	0.165409i	$-0.0528944\pi$
$283$	99.0115	+	171.493i	0.349864	+	0.605982i	−0.636361	+	0.771391i	$0.719561\pi$
$284$	−27.6929	+	15.9885i	−0.0975103	+	0.0562976i
$285$	−137.877	+	43.0503i	−0.483780	+	0.151054i
$286$	−37.8137	+	65.4953i	−0.132216	+	0.229005i
$287$		−	46.4283i		−	0.161771i
$288$	264.523	−	21.6572i	0.918483	−	0.0751986i
$289$	−697.095			−2.41209
$290$	80.5499	+	46.5055i	0.277758	+	0.160364i
$291$	32.7034	−	35.4903i	0.112383	−	0.121960i
$292$	14.7015	+	25.4637i	0.0503475	+	0.0872044i
$293$	230.738	−	133.217i	0.787501	−	0.454664i	−0.0515811	−	0.998669i	$-0.516426\pi$
$293$	230.738	−	133.217i	0.787501	−	0.454664i	0.839082	+	0.544005i	$0.183093\pi$
$294$	−3.45229	+	15.3694i	−0.0117425	+	0.0522768i
$295$	−1.41854	+	2.45698i	−0.00480860	+	0.00832874i
$296$			206.013i			0.695988i
$297$	60.0032	+	148.358i	0.202031	+	0.499523i
$298$	160.481			0.538525
$299$	157.757	+	91.0810i	0.527615	+	0.304619i
$300$	155.119	+	34.8431i	0.517064	+	0.116144i
$301$	−73.5492	−	127.391i	−0.244349	−	0.423226i
$302$	−39.5276	+	22.8213i	−0.130886	+	0.0755671i
$303$	288.510	+	265.854i	0.952178	+	0.877407i
$304$	74.3819	−	128.833i	0.244677	−	0.423794i
$305$			230.243i			0.754895i
$306$	174.332	−	120.626i	0.569713	−	0.394201i
$307$	−379.575			−1.23640			−0.618200	−	0.786021i	$-0.712138\pi$
$307$	−379.575			−1.23640			−0.618200	+	0.786021i	$0.712138\pi$
$308$	−46.6818	−	26.9517i	−0.151564	−	0.0875056i
$309$	−132.744	−	425.140i	−0.429593	−	1.37586i
$310$	−15.7575	−	27.2929i	−0.0508308	−	0.0880415i
$311$	−70.6629	+	40.7972i	−0.227212	+	0.131181i	−0.609285	−	0.792951i	$-0.708543\pi$
$311$	−70.6629	+	40.7972i	−0.227212	+	0.131181i	0.382073	+	0.924132i	$0.375210\pi$
$312$	271.751	−	84.8506i	0.870998	−	0.271957i
$313$	133.173	−	230.662i	0.425472	−	0.736939i	−0.570992	−	0.820955i	$-0.693441\pi$
$313$	133.173	−	230.662i	0.425472	−	0.736939i	0.996464	+	0.0840161i	$0.0267747\pi$
$314$			135.428i			0.431299i
$315$	31.5237	−	66.6303i	0.100075	−	0.211525i
$316$	−475.207			−1.50382
$317$	455.895	+	263.211i	1.43815	+	0.830319i	0.997722	−	0.0674662i	$-0.0214915\pi$
$317$	455.895	+	263.211i	1.43815	+	0.830319i	0.440433	+	0.897785i	$0.354825\pi$
$318$	−10.9537	+	11.8872i	−0.0344458	+	0.0373812i
$319$	−118.709	−	205.610i	−0.372128	−	0.644545i
$320$	43.2630	−	24.9779i	0.135197	−	0.0780559i
$321$	122.106	−	543.606i	0.380391	−	1.69348i
$322$	10.6266	−	18.4058i	0.0330018	−	0.0571608i
$323$		−	488.416i		−	1.51212i
$324$	98.1384	−	260.555i	0.302896	−	0.804181i
$325$	262.252			0.806930
$326$	−199.787	−	115.347i	−0.612842	−	0.353825i
$327$	−98.5399	−	22.1342i	−0.301345	−	0.0676886i
$328$	48.9493	+	84.7827i	0.149236	+	0.258484i
$329$	16.7713	−	9.68291i	0.0509766	−	0.0294314i
$330$	−30.3635	−	27.9792i	−0.0920107	−	0.0847854i
$331$	−28.2851	+	48.9912i	−0.0854534	+	0.148010i	−0.905584	−	0.424166i	$-0.860567\pi$
$331$	−28.2851	+	48.9912i	−0.0854534	+	0.148010i	0.820131	+	0.572176i	$0.193901\pi$
$332$			542.190i			1.63310i
$333$	300.422	+	142.134i	0.902168	+	0.426828i
$334$	36.7485			0.110026
$335$	−99.8104	−	57.6255i	−0.297941	−	0.172017i
$336$	22.6266	+	72.4664i	0.0673412	+	0.215674i
$337$	−73.3876	−	127.111i	−0.217767	−	0.377184i	0.736358	−	0.676592i	$-0.236544\pi$
$337$	−73.3876	−	127.111i	−0.217767	−	0.377184i	−0.954125	+	0.299408i	$0.903211\pi$
$338$	78.1782	−	45.1362i	0.231297	−	0.133539i
$339$	−236.734	+	73.9170i	−0.698331	+	0.218044i
$340$	167.068	−	289.370i	0.491376	−	0.851088i
$341$			80.4446i			0.235908i
$342$	59.7463	+	86.3473i	0.174697	+	0.252477i
$343$	−18.5203			−0.0539949
$344$	268.616	+	155.086i	0.780861	+	0.450830i
$345$	−67.3928	+	73.1359i	−0.195341	+	0.211988i
$346$	−96.0938	−	166.439i	−0.277728	−	0.481038i
$347$	−79.6250	+	45.9715i	−0.229467	+	0.132483i	−0.610326	−	0.792150i	$-0.708962\pi$
$347$	−79.6250	+	45.9715i	−0.229467	+	0.132483i	0.380859	+	0.924633i	$0.375628\pi$
$348$	−90.5259	+	403.015i	−0.260132	+	1.15809i
$349$	−103.383	+	179.065i	−0.296226	+	0.513079i	−0.975269	−	0.221019i	$-0.929062\pi$
$349$	−103.383	+	179.065i	−0.296226	+	0.513079i	0.679043	+	0.734099i	$0.262395\pi$
$350$		−	30.5975i		−	0.0874213i
$351$	63.7537	−	454.828i	0.181635	−	1.29581i
$352$	174.790			0.496564
$353$	−277.570	−	160.255i	−0.786316	−	0.453980i	0.0523479	−	0.998629i	$-0.483330\pi$
$353$	−277.570	−	160.255i	−0.786316	−	0.453980i	−0.838664	+	0.544649i	$0.816663\pi$
$354$	2.01227	+	0.452000i	0.00568439	+	0.00127684i
$355$	−14.3989	−	24.9396i	−0.0405602	−	0.0702523i
$356$	338.081	−	195.191i	0.949665	−	0.548289i
$357$	183.294	+	168.900i	0.513428	+	0.473110i
$358$	−33.3376	+	57.7424i	−0.0931218	+	0.161292i
$359$			569.688i			1.58687i	0.608652	+	0.793437i	$0.291710\pi$
$359$			569.688i			1.58687i	−0.608652	+	0.793437i	$0.708290\pi$
$360$	12.6828	+	154.909i	0.0352300	+	0.430302i
$361$	−119.086			−0.329878
$362$	−12.3252	−	7.11595i	−0.0340475	−	0.0196573i
$363$	−76.7786	−	245.899i	−0.211511	−	0.677408i
$364$	77.3480	+	133.971i	0.212495	+	0.368051i
$365$	−22.9320	+	13.2398i	−0.0628273	+	0.0362733i
$366$	159.768	−	49.8855i	0.436526	−	0.136299i
$367$	63.5720	−	110.110i	0.173221	−	0.300027i	−0.766323	−	0.642455i	$-0.777916\pi$
$367$	63.5720	−	110.110i	0.173221	−	0.300027i	0.939544	+	0.342428i	$0.111249\pi$
$368$		−	102.427i		−	0.278335i
$369$	157.408	−	12.8874i	0.426579	−	0.0349252i
$370$	−85.7468			−0.231748
$371$	−16.4587	−	9.50242i	−0.0443630	−	0.0256130i
$372$	94.8408	−	102.923i	0.254948	−	0.276675i
$373$	−118.719	−	205.628i	−0.318282	−	0.551281i	0.661847	−	0.749639i	$-0.269773\pi$
$373$	−118.719	−	205.628i	−0.318282	−	0.551281i	−0.980130	+	0.198357i	$0.936439\pi$
$374$	120.910	−	69.8072i	0.323288	−	0.186650i
$375$	−82.2610	+	366.220i	−0.219363	+	0.976588i
$376$	−20.4174	+	35.3639i	−0.0543015	+	0.0940530i
$377$			681.358i			1.80732i
$378$	−53.0656	−	7.43826i	−0.140385	−	0.0196779i
$379$	638.624			1.68502			0.842512	−	0.538678i	$-0.181076\pi$
$379$	638.624			1.68502			0.842512	+	0.538678i	$0.181076\pi$
$380$	143.326	+	82.7492i	0.377173	+	0.217761i
$381$	6.94494	+	1.55998i	0.0182282	+	0.00409444i
$382$	−57.3184	−	99.2784i	−0.150048	−	0.259891i
$383$	−349.399	+	201.726i	−0.912270	+	0.526699i	−0.881161	−	0.472817i	$-0.843237\pi$
$383$	−349.399	+	201.726i	−0.912270	+	0.526699i	−0.0311093	+	0.999516i	$0.509904\pi$
$384$	−286.944	−	264.412i	−0.747251	−	0.688572i
$385$	24.2721	−	42.0404i	0.0630443	−	0.109196i
$386$		−	114.465i		−	0.296541i
$387$	411.483	−	284.717i	1.06326	−	0.735703i
$388$	−55.2958			−0.142515
$389$	−535.101	−	308.941i	−1.37558	−	0.794192i	−0.383957	−	0.923351i	$-0.625439\pi$
$389$	−535.101	−	308.941i	−1.37558	−	0.794192i	−0.991624	+	0.129159i	$0.958772\pi$
$390$	35.3166	+	113.109i	0.0905555	+	0.290022i
$391$	−168.143	−	291.232i	−0.430033	−	0.744839i
$392$	33.8198	−	19.5259i	0.0862751	−	0.0498109i
$393$	−297.047	+	92.7489i	−0.755845	+	0.236002i
$394$	−128.578	+	222.704i	−0.326341	+	0.565239i
$395$		−	427.960i		−	1.08344i
$396$	78.4177	−	165.748i	0.198024	−	0.418556i
$397$	74.3330			0.187237			0.0936184	−	0.995608i	$-0.470157\pi$
$397$	74.3330			0.187237			0.0936184	+	0.995608i	$0.470157\pi$
$398$	−97.7568	−	56.4399i	−0.245620	−	0.141809i
$399$	−83.6569	+	90.7861i	−0.209666	+	0.227534i
$400$	−73.7306	−	127.705i	−0.184327	−	0.319263i
$401$	108.370	−	62.5673i	0.270249	−	0.156028i	−0.358752	−	0.933433i	$-0.616798\pi$
$401$	108.370	−	62.5673i	0.270249	−	0.156028i	0.629001	+	0.777405i	$0.283464\pi$
$402$	−18.3617	+	81.7450i	−0.0456758	+	0.203346i
$403$	115.433	−	199.936i	0.286434	−	0.496118i
$404$		−	449.514i		−	1.11266i
$405$	234.649	+	88.3810i	0.579381	+	0.218225i
$406$	79.4953			0.195801
$407$	189.552	+	109.438i	0.465729	+	0.268889i
$408$	−512.784	−	115.182i	−1.25682	−	0.282310i
$409$	296.975	+	514.377i	0.726101	+	1.25764i	0.958519	+	0.285028i	$0.0920030\pi$
$409$	296.975	+	514.377i	0.726101	+	1.25764i	−0.232418	+	0.972616i	$0.574664\pi$
$410$	−35.2884	+	20.3738i	−0.0860692	+	0.0496921i
$411$	440.894	+	406.273i	1.07274	+	0.988498i
$412$	−255.155	+	441.941i	−0.619307	+	1.07267i
$413$			2.42481i			0.00587122i
$414$	65.3515	+	30.9187i	0.157854	+	0.0746829i
$415$	−488.283			−1.17658
$416$	−434.421	−	250.813i	−1.04428	−	0.602916i
$417$	66.5449	+	213.123i	0.159580	+	0.511088i
$418$	34.5758	+	59.8870i	0.0827171	+	0.143270i
$419$	480.605	−	277.478i	1.14703	−	0.662238i	0.198868	−	0.980026i	$-0.436274\pi$
$419$	480.605	−	277.478i	1.14703	−	0.662238i	0.948162	+	0.317789i	$0.102940\pi$
$420$	−80.6182	+	25.1719i	−0.191948	+	0.0599332i
$421$	−13.8778	+	24.0370i	−0.0329638	+	0.0570949i	−0.882037	−	0.471181i	$-0.843828\pi$
$421$	−13.8778	+	24.0370i	−0.0329638	+	0.0570949i	0.849073	+	0.528276i	$0.177161\pi$
$422$		−	125.665i		−	0.297785i
$423$	37.4836	+	54.1726i	0.0886138	+	0.128068i
$424$	40.0735			0.0945131
$425$	−419.277	−	242.070i	−0.986534	−	0.569576i
$426$	−14.1861	+	15.3951i	−0.0333008	+	0.0361386i
$427$	98.3929	+	170.421i	0.230428	+	0.399114i
$428$	−552.846	+	319.186i	−1.29170	+	0.745761i
$429$	66.2885	−	295.112i	0.154519	−	0.687906i
$430$	−64.5499	+	111.804i	−0.150116	+	0.260009i
$431$			457.986i			1.06261i	0.847180	+	0.531306i	$0.178298\pi$
$431$			457.986i			1.06261i	−0.847180	+	0.531306i	$0.821702\pi$
$432$	−239.405	+	96.8268i	−0.554178	+	0.224136i
$433$	183.113			0.422893			0.211447	−	0.977390i	$-0.432183\pi$
$433$	183.113			0.422893			0.211447	+	0.977390i	$0.432183\pi$
$434$	−23.3269	−	13.4678i	−0.0537485	−	0.0310317i
$435$	−362.946	−	81.5254i	−0.834358	−	0.187415i
$436$	57.8590	+	100.215i	0.132704	+	0.229850i
$437$	144.248	−	83.2818i	0.330088	−	0.190576i
$438$	14.1558	+	13.0442i	0.0323191	+	0.0297812i
$439$	116.275	−	201.395i	0.264864	−	0.458758i	−0.702664	−	0.711522i	$-0.748006\pi$
$439$	116.275	−	201.395i	0.264864	−	0.458758i	0.967528	+	0.252764i	$0.0813396\pi$
$440$			102.360i			0.232636i
$441$	−5.14077	−	62.7899i	−0.0116571	−	0.142381i
$442$	−400.676			−0.906506
$443$	293.316	+	169.346i	0.662113	+	0.382271i	0.793082	−	0.609115i	$-0.208475\pi$
$443$	293.316	+	169.346i	0.662113	+	0.382271i	−0.130968	+	0.991387i	$0.541809\pi$
$444$	−113.495	−	363.491i	−0.255619	−	0.818673i
$445$	175.784	+	304.467i	0.395021	+	0.684196i
$446$	−46.8918	+	27.0730i	−0.105139	+	0.0607018i
$447$	−612.658	+	191.294i	−1.37060	+	0.427951i
$448$	21.3483	−	36.9763i	0.0476524	−	0.0825364i
$449$			393.080i			0.875456i	0.899107	+	0.437728i	$0.144217\pi$
$449$			393.080i			0.875456i	−0.899107	+	0.437728i	$0.855783\pi$
$450$	103.736	−	8.49312i	0.230524	−	0.0188736i
$451$	104.011			0.230623
$452$	246.089	+	142.080i	0.544445	+	0.314336i
$453$	123.699	−	134.241i	0.273066	−	0.296337i
$454$	26.1489	+	45.2912i	0.0575966	+	0.0997603i
$455$	−120.651	+	69.6577i	−0.265166	+	0.153094i
$456$	57.0502	−	253.984i	0.125110	−	0.556982i
$457$	−305.400	+	528.969i	−0.668272	+	1.15748i	0.310115	+	0.950699i	$0.399632\pi$
$457$	−305.400	+	528.969i	−0.668272	+	1.15748i	−0.978387	+	0.206782i	$0.933701\pi$
$458$		−	53.3044i		−	0.116385i
$459$	−521.751	+	668.310i	−1.13671	+	1.45601i
$460$	113.950			0.247717
$461$	112.674	+	65.0526i	0.244413	+	0.141112i	0.617203	−	0.786804i	$-0.288266\pi$
$461$	112.674	+	65.0526i	0.244413	+	0.141112i	−0.372790	+	0.927916i	$0.621599\pi$
$462$	−34.4312	−	7.73400i	−0.0745265	−	0.0167403i
$463$	372.157	+	644.594i	0.803794	+	1.39221i	0.917102	+	0.398652i	$0.130522\pi$
$463$	372.157	+	644.594i	0.803794	+	1.39221i	−0.113308	+	0.993560i	$0.536145\pi$
$464$	331.791	−	191.560i	0.715067	−	0.412844i
$465$	92.6899	+	85.4113i	0.199333	+	0.183680i
$466$	−91.5044	+	158.490i	−0.196361	+	0.340108i
$467$		−	418.622i		−	0.896408i	−0.893931	−	0.448204i	$-0.852064\pi$
$467$		−	418.622i		−	0.896408i	0.893931	−	0.448204i	$-0.147936\pi$
$468$	−432.736	+	299.423i	−0.924649	+	0.639792i
$469$	−98.5036			−0.210029
$470$	−14.7192	−	8.49814i	−0.0313175	−	0.0180812i
$471$	−161.431	−	517.015i	−0.342741	−	1.09770i
$472$	−2.55648	−	4.42795i	−0.00541626	−	0.00938125i
$473$	285.388	−	164.769i	0.603357	−	0.348348i
$474$	−296.967	+	92.7237i	−0.626512	+	0.195620i
$475$	119.898	−	207.669i	0.252417	−	0.437199i
$476$		−	285.582i		−	0.599961i
$477$	27.6479	−	58.4381i	0.0579620	−	0.122512i
$478$	31.3496			0.0655850
$479$	−277.454	−	160.188i	−0.579236	−	0.334422i	0.181594	−	0.983374i	$-0.441874\pi$
$479$	−277.454	−	160.188i	−0.579236	−	0.334422i	−0.760830	+	0.648952i	$0.775208\pi$
$480$	185.582	−	201.397i	0.386629	−	0.419577i
$481$	−314.072	−	543.989i	−0.652957	−	1.13095i
$482$	265.206	−	153.117i	0.550219	−	0.317669i
$483$	−18.6287	+	82.9337i	−0.0385687	+	0.171705i
$484$	−147.580	+	255.616i	−0.304917	+	0.528133i
$485$		−	49.7980i		−	0.102676i
$486$	10.4885	−	181.975i	0.0215813	−	0.374434i
$487$	804.446			1.65184			0.825920	−	0.563788i	$-0.190656\pi$
$487$	804.446			1.65184			0.825920	+	0.563788i	$0.190656\pi$
$488$	−359.350	−	207.471i	−0.736374	−	0.425145i
$489$	900.208	+	202.206i	1.84092	+	0.413509i
$490$	8.12709	+	14.0765i	0.0165859	+	0.0287276i
$491$	394.045	−	227.502i	0.802535	−	0.463344i	−0.0418218	−	0.999125i	$-0.513316\pi$
$491$	394.045	−	227.502i	0.802535	−	0.463344i	0.844357	+	0.535781i	$0.179983\pi$
$492$	−133.075	−	122.625i	−0.270477	−	0.249237i
$493$	628.922	−	1089.32i	1.27570	−	2.20958i
$494$		−	198.456i		−	0.401733i
$495$	149.269	+	70.6210i	0.301553	+	0.142669i
$496$	−129.813			−0.261720
$497$	−21.3155	−	12.3065i	−0.0428884	−	0.0247616i
$498$	105.794	+	338.825i	0.212437	+	0.680372i
$499$	−113.725	−	196.977i	−0.227905	−	0.394743i	0.729282	−	0.684213i	$-0.239854\pi$
$499$	−113.725	−	196.977i	−0.227905	−	0.394743i	−0.957187	+	0.289470i	$0.906521\pi$
$500$	372.445	−	215.031i	0.744890	−	0.430063i
$501$	−140.293	+	43.8045i	−0.280026	+	0.0874342i
$502$	64.4758	−	111.675i	0.128438	−	0.222461i
$503$			17.5431i			0.0348769i	0.999848	+	0.0174385i	$0.00555112\pi$
$503$			17.5431i			0.0348769i	−0.999848	+	0.0174385i	$0.994449\pi$
$504$	75.5869	+	109.241i	0.149974	+	0.216747i
$505$	404.821			0.801626
$506$	41.2336	+	23.8062i	0.0814893	+	0.0470479i
$507$	−244.654	+	265.503i	−0.482552	+	0.523674i
$508$	−4.07782	−	7.06298i	−0.00802720	−	0.0139035i
$509$	438.865	−	253.379i	0.862210	−	0.497797i	−0.00254144	−	0.999997i	$-0.500809\pi$
$509$	438.865	−	253.379i	0.862210	−	0.497797i	0.864752	+	0.502199i	$0.167476\pi$
$510$	47.9414	−	213.432i	0.0940027	−	0.418494i
$511$	−11.3159	+	19.5997i	−0.0221446	+	0.0383555i
$512$			495.495i			0.967764i
$513$	−331.016	−	258.425i	−0.645256	−	0.503753i
$514$	215.278			0.418829
$515$	−398.001	−	229.786i	−0.772817	−	0.446186i
$516$	−559.388	−	125.651i	−1.08409	−	0.243509i
$517$	21.6922	+	37.5719i	0.0419578	+	0.0726730i
$518$	−63.4682	+	36.6434i	−0.122525	+	0.0707401i
$519$	565.248	+	520.861i	1.08911	+	1.00359i
$520$	146.880	−	254.404i	0.282462	−	0.489238i
$521$		−	371.993i		−	0.713998i	−0.934105	−	0.356999i	$-0.883800\pi$
$521$		−	371.993i		−	0.713998i	0.934105	−	0.356999i	$-0.116200\pi$
$522$	22.0660	+	269.516i	0.0422720	+	0.516314i
$523$	564.688			1.07971			0.539855	−	0.841758i	$-0.318479\pi$
$523$	564.688			1.07971			0.539855	+	0.841758i	$0.318479\pi$
$524$	308.785	+	178.277i	0.589285	+	0.340224i
$525$	36.4724	+	116.810i	0.0694712	+	0.222496i
$526$	96.7238	+	167.530i	0.183885	+	0.318499i
$527$	−369.098	+	213.099i	−0.700375	+	0.404362i
$528$	−162.343	+	50.6893i	−0.307468	+	0.0960025i
$529$	−207.159	+	358.809i	−0.391604	+	0.678278i
$530$			16.6795i			0.0314707i
$531$	−8.22093	+	0.673069i	−0.0154820	+	0.00126755i
$532$	141.449			0.265882
$533$	−258.508	−	149.249i	−0.485005	−	0.280018i
$534$	173.187	−	187.946i	0.324321	−	0.351959i
$535$	−287.451	−	497.879i	−0.537291	−	0.930615i
$536$	179.877	−	103.852i	0.335592	−	0.193754i
$537$	58.4417	−	260.179i	0.108830	−	0.484504i
$538$	8.80977	−	15.2590i	0.0163750	−	0.0283624i
$539$		−	41.4900i		−	0.0769759i
$540$	−107.719	−	266.336i	−0.199480	−	0.493214i
$541$	−438.809			−0.811107			−0.405553	−	0.914071i	$-0.632921\pi$
$541$	−438.809			−0.811107			−0.405553	+	0.914071i	$0.632921\pi$
$542$	34.7637	+	20.0708i	0.0641396	+	0.0370310i
$543$	55.5355	+	12.4745i	0.102275	+	0.0229732i
$544$	463.022	+	801.977i	0.851143	+	1.47422i
$545$	−90.2510	+	52.1064i	−0.165598	+	0.0956081i
$546$	74.4770	+	68.6286i	0.136405	+	0.125693i
$547$	−186.766	+	323.489i	−0.341438	+	0.591387i	−0.984700	−	0.174259i	$-0.944247\pi$
$547$	−186.766	+	323.489i	−0.341438	+	0.591387i	0.643262	+	0.765646i	$0.277580\pi$
$548$		−	686.937i		−	1.25353i
$549$	−550.475	+	380.890i	−1.00269	+	0.693788i
$550$	68.5460			0.124629
$551$	539.546	+	311.507i	0.979212	+	0.565349i
$552$	−53.4190	−	171.085i	−0.0967736	−	0.309937i
$553$	−182.886	−	316.768i	−0.330716	−	0.572817i
$554$	−72.5875	+	41.9084i	−0.131024	+	0.0756470i
$555$	327.351	−	102.211i	0.589821	−	0.184164i
$556$	127.909	−	221.546i	0.230053	−	0.398463i
$557$			286.047i			0.513550i	0.966471	+	0.256775i	$0.0826599\pi$
$557$			286.047i			0.513550i	−0.966471	+	0.256775i	$0.917340\pi$
$558$	39.1853	−	82.8242i	0.0702246	−	0.148431i
$559$	−945.730			−1.69182
$560$	67.8404	+	39.1677i	0.121144	+	0.0699422i
$561$	−378.379	+	410.624i	−0.674473	+	0.731951i
$562$	−50.1209	−	86.8120i	−0.0891831	−	0.154470i
$563$	−697.167	+	402.509i	−1.23831	+	0.714937i	−0.968748	−	0.248047i	$-0.920211\pi$
$563$	−697.167	+	402.509i	−1.23831	+	0.714937i	−0.269559	+	0.962984i	$0.586878\pi$
$564$	16.5422	−	73.6447i	0.0293301	−	0.130576i
$565$	−127.953	+	221.622i	−0.226466	+	0.392251i
$566$		−	148.539i		−	0.262437i
$567$	211.452	−	34.8579i	0.372931	−	0.0614778i
$568$	51.8990			0.0913715
$569$	169.579	+	97.9065i	0.298030	+	0.172068i	0.641558	−	0.767075i	$-0.278289\pi$
$569$	169.579	+	97.9065i	0.298030	+	0.172068i	−0.343528	+	0.939143i	$0.611622\pi$
$570$	105.713	+	23.7455i	0.185462	+	0.0416588i
$571$	−81.3345	−	140.876i	−0.142442	−	0.246717i	0.785973	−	0.618260i	$-0.212162\pi$
$571$	−81.3345	−	140.876i	−0.142442	−	0.246717i	−0.928416	+	0.371543i	$0.878829\pi$
$572$	−300.128	+	173.279i	−0.524699	+	0.302935i
$573$	337.162	+	310.686i	0.588415	+	0.542209i
$574$	−17.4132	+	30.1605i	−0.0303366	+	0.0525445i
$575$		−	165.105i		−	0.287139i
$576$	131.288	+	62.1141i	0.227930	+	0.107837i
$577$	−55.0656			−0.0954343			−0.0477171	−	0.998861i	$-0.515195\pi$
$577$	−55.0656			−0.0954343			−0.0477171	+	0.998861i	$0.515195\pi$
$578$	452.843	+	261.449i	0.783466	+	0.452334i
$579$	136.443	+	436.986i	0.235653	+	0.754726i
$580$	213.108	+	369.115i	0.367428	+	0.636405i
$581$	−361.418	+	208.665i	−0.622061	+	0.359147i
$582$	−34.5555	+	10.7895i	−0.0593736	+	0.0185386i
$583$	21.2878	−	36.8716i	0.0365142	−	0.0632445i
$584$		−	47.7212i		−	0.0817144i
$585$	−269.653	−	389.711i	−0.460945	−	0.666173i
$586$	−199.854			−0.341048
$587$	−416.075	−	240.221i	−0.708816	−	0.409235i	0.101807	−	0.994804i	$-0.467538\pi$
$587$	−416.075	−	240.221i	−0.708816	−	0.409235i	−0.810622	+	0.585569i	$0.800871\pi$
$588$	−48.9150	+	53.0835i	−0.0831888	+	0.0902780i
$589$	−105.548	−	182.815i	−0.179199	−	0.310383i
$590$	1.84301	−	1.06406i	0.00312374	−	0.00180349i
$591$	225.401	−	1003.47i	0.381390	−	1.69792i
$592$	−176.599	+	305.878i	−0.298309	+	0.516686i
$593$			78.3292i			0.132090i	0.997817	+	0.0660449i	$0.0210380\pi$
$593$			78.3292i			0.132090i	−0.997817	+	0.0660449i	$0.978962\pi$
$594$	16.6636	−	118.880i	0.0280532	−	0.200135i
$595$	257.188			0.432248
$596$	636.868	+	367.696i	1.06857	+	0.616940i
$597$	440.477	+	98.9407i	0.737818	+	0.165730i
$598$	−68.3208	−	118.335i	−0.114249	−	0.197885i
$599$	−545.819	+	315.129i	−0.911217	+	0.526091i	−0.880822	−	0.473447i	$-0.843010\pi$
$599$	−545.819	+	315.129i	−0.911217	+	0.526091i	−0.0303943	+	0.999538i	$0.509676\pi$
$600$	−189.755	−	174.854i	−0.316258	−	0.291424i
$601$	26.8054	−	46.4283i	0.0446013	−	0.0772518i	−0.842863	−	0.538128i	$-0.819132\pi$
$601$	26.8054	−	46.4283i	0.0446013	−	0.0772518i	0.887464	+	0.460877i	$0.152465\pi$
$602$			110.340i			0.183289i
$603$	−27.3422	−	333.960i	−0.0453437	−	0.553832i
$604$	−209.154			−0.346281
$605$	−230.202	−	132.907i	−0.380498	−	0.219681i
$606$	−87.7103	−	280.910i	−0.144737	−	0.463548i
$607$	−407.662	−	706.091i	−0.671601	−	1.16325i	−0.977450	−	0.211168i	$-0.932273\pi$
$607$	−407.662	−	706.091i	−0.671601	−	1.16325i	0.305848	−	0.952080i	$-0.401060\pi$
$608$	−397.222	+	229.336i	−0.653325	+	0.377198i
$609$	−303.485	+	94.7590i	−0.498333	+	0.155598i
$610$	86.3539	−	149.569i	0.141564	−	0.245196i
$611$		−	124.507i		−	0.203777i
$612$	968.217	−	79.2705i	1.58205	−	0.129527i
$613$	−444.011			−0.724325			−0.362162	−	0.932115i	$-0.617961\pi$
$613$	−444.011			−0.724325			−0.362162	+	0.932115i	$0.617961\pi$
$614$	246.577	+	142.362i	0.401592	+	0.231859i
$615$	110.433	−	119.844i	0.179566	−	0.194868i
$616$	43.7429	+	75.7649i	0.0710112	+	0.122995i
$617$	−166.135	+	95.9183i	−0.269263	+	0.155459i	−0.628553	−	0.777767i	$-0.716352\pi$
$617$	−166.135	+	95.9183i	−0.269263	+	0.155459i	0.359290	+	0.933226i	$0.383019\pi$
$618$	−73.2185	+	325.964i	−0.118477	+	0.527450i
$619$	−156.042	+	270.273i	−0.252087	+	0.436628i	−0.964100	−	0.265538i	$-0.914450\pi$
$619$	−156.042	+	270.273i	−0.252087	+	0.436628i	0.712013	+	0.702166i	$0.247784\pi$
$620$		−	144.416i		−	0.232929i
$621$	−286.344	−	40.1371i	−0.461101	−	0.0646331i
$622$	61.2049			0.0984001
$623$	260.224	+	150.241i	0.417695	+	0.241157i
$624$	476.220	+	106.969i	0.763173	+	0.171425i
$625$	0.934393	+	1.61842i	0.00149503	+	0.00258947i
$626$	−173.022	+	99.8943i	−0.276393	+	0.159576i
$627$	−203.384	−	187.413i	−0.324376	−	0.298904i
$628$	−310.295	+	537.446i	−0.494100	+	0.855806i
$629$			1159.61i			1.84357i
$630$	−45.4683	+	31.4609i	−0.0721719	+	0.0499379i
$631$	−358.860			−0.568717			−0.284358	−	0.958718i	$-0.591781\pi$
$631$	−358.860			−0.568717			−0.284358	+	0.958718i	$0.591781\pi$
$632$	667.936	+	385.633i	1.05686	+	0.610179i
$633$	149.794	+	479.745i	0.236641	+	0.757892i
$634$	−197.438	−	341.972i	−0.311416	−	0.539388i
$635$	6.36075	−	3.67238i	0.0100169	−	0.00578328i
$636$	−70.7062	+	22.0770i	−0.111173	+	0.0347123i
$637$	−59.5356	+	103.119i	−0.0934624	+	0.161882i
$638$			178.090i			0.279137i
$639$	35.8066	−	75.6828i	0.0560354	−	0.118439i
$640$	−402.624			−0.629100
$641$	330.840	+	191.010i	0.516131	+	0.297988i	0.735350	−	0.677687i	$-0.237018\pi$
$641$	330.840	+	191.010i	0.516131	+	0.297988i	−0.219219	+	0.975676i	$0.570351\pi$
$642$	−283.204	+	307.338i	−0.441128	+	0.478720i
$643$	−10.4335	−	18.0714i	−0.0162263	−	0.0281048i	0.857798	−	0.513987i	$-0.171832\pi$
$643$	−10.4335	−	18.0714i	−0.0162263	−	0.0281048i	−0.874025	+	0.485882i	$0.838499\pi$
$644$	84.3433	−	48.6956i	0.130968	−	0.0756144i
$645$	113.158	−	503.771i	0.175438	−	0.781040i
$646$	−183.183	+	317.282i	−0.283565	+	0.491149i
$647$		−	169.301i		−	0.261671i	−0.991404	−	0.130835i	$-0.958234\pi$
$647$		−	169.301i		−	0.261671i	0.991404	−	0.130835i	$-0.0417659\pi$
$648$	−349.381	+	286.587i	−0.539169	+	0.442265i
$649$	−5.43219			−0.00837009
$650$	−170.363	−	98.3592i	−0.262097	−	0.151322i
$651$	105.107	+	23.6094i	0.161455	+	0.0362663i
$652$	−528.569	−	915.509i	−0.810689	−	1.40415i
$653$	−458.773	+	264.873i	−0.702563	+	0.405625i	−0.808301	−	0.588769i	$-0.799613\pi$
$653$	−458.773	+	264.873i	−0.702563	+	0.405625i	0.105738	+	0.994394i	$0.466279\pi$
$654$	55.7114	+	51.3366i	0.0851857	+	0.0784963i
$655$	−160.552	+	278.085i	−0.245118	+	0.424557i
$656$			167.842i			0.255857i
$657$	−69.5904	−	32.9242i	−0.105922	−	0.0501129i
$658$	−14.5265			−0.0220768
$659$	−343.159	−	198.123i	−0.520726	−	0.300642i	0.216505	−	0.976281i	$-0.430534\pi$
$659$	−343.159	−	198.123i	−0.520726	−	0.300642i	−0.737232	+	0.675640i	$0.763867\pi$
$660$	−56.3914	−	180.605i	−0.0854416	−	0.273644i
$661$	204.349	+	353.943i	0.309151	+	0.535466i	0.978177	−	0.207774i	$-0.0666218\pi$
$661$	204.349	+	353.943i	0.309151	+	0.535466i	−0.669026	+	0.743239i	$0.733288\pi$
$662$	36.7488	−	21.2170i	0.0555118	−	0.0320498i
$663$	1529.64	−	477.608i	2.30714	−	0.720374i
$664$	439.990	−	762.084i	0.662635	−	1.14772i
$665$			127.386i			0.191558i
$666$	−141.851	−	205.007i	−0.212989	−	0.307819i
$667$	428.960			0.643118
$668$	145.837	+	84.1989i	0.218319	+	0.126046i
$669$	146.745	−	159.250i	0.219350	−	0.238042i
$670$	43.2255	+	74.8688i	0.0645157	+	0.111744i
$671$	−381.787	+	220.425i	−0.568982	+	0.328502i
$672$	51.2985	−	228.378i	0.0763371	−	0.339848i
$673$	361.296	−	625.782i	0.536843	−	0.929840i	−0.462228	−	0.886761i	$-0.652950\pi$
$673$	361.296	−	625.782i	0.536843	−	0.929840i	0.999072	−	0.0430790i	$-0.0137167\pi$
$674$			110.098i			0.163350i
$675$	−385.902	+	156.077i	−0.571707	+	0.231226i
$676$	413.668			0.611934
$677$	−133.436	−	77.0393i	−0.197099	−	0.113795i	0.398203	−	0.917297i	$-0.369634\pi$
$677$	−133.436	−	77.0393i	−0.197099	−	0.113795i	−0.595302	+	0.803502i	$0.702967\pi$
$678$	181.509	+	40.7708i	0.267712	+	0.0601340i
$679$	−21.2809	−	36.8596i	−0.0313415	−	0.0542851i
$680$	−469.650	+	271.153i	−0.690662	+	0.398754i
$681$	−153.814	−	141.736i	−0.225865	−	0.208129i
$682$	30.1712	−	52.2580i	0.0442393	−	0.0766247i
$683$		−	965.184i		−	1.41315i	−0.707636	−	0.706577i	$-0.750239\pi$
$683$		−	965.184i		−	1.41315i	0.707636	−	0.706577i	$-0.249761\pi$
$684$	39.2629	+	479.561i	0.0574020	+	0.701113i
$685$	618.638			0.903122
$686$	12.0310	+	6.94612i	0.0175380	+	0.0101255i
$687$	63.5392	+	203.497i	0.0924879	+	0.296211i
$688$	265.886	+	460.528i	0.386462	+	0.669372i
$689$	−105.817	+	61.0933i	−0.153580	+	0.0886695i
$690$	71.2094	−	22.2341i	0.103202	−	0.0322234i
$691$	366.382	−	634.592i	0.530220	−	0.918367i	−0.469159	−	0.883114i	$-0.655443\pi$
$691$	366.382	−	634.592i	0.530220	−	0.918367i	0.999378	−	0.0352534i	$-0.0112238\pi$
$692$		−	880.687i		−	1.27267i
$693$	140.665	−	11.5166i	0.202980	−	0.0166185i
$694$	68.9674			0.0993767
$695$	199.518	+	115.192i	0.287077	+	0.165744i
$696$	454.289	−	493.003i	0.652714	−	0.708337i
$697$	275.527	+	477.226i	0.395304	+	0.684686i
$698$	134.318	−	77.5487i	0.192433	−	0.111101i
$699$	160.410	−	714.133i	0.229485	−	1.02165i
$700$	70.1055	−	121.426i	0.100151	−	0.173466i
$701$		−	783.811i		−	1.11813i	−0.829123	−	0.559066i	$-0.811160\pi$
$701$		−	783.811i		−	1.11813i	0.829123	−	0.559066i	$-0.188840\pi$
$702$	−212.001	+	271.552i	−0.301996	+	0.386826i
$703$	−574.357			−0.817008
$704$	82.8362	+	47.8255i	0.117665	+	0.0679340i
$705$	66.3226	+	14.8975i	0.0940746	+	0.0211312i
$706$	120.209	+	208.208i	0.170268	+	0.294912i
$707$	299.641	−	172.998i	0.423820	−	0.244693i
$708$	6.95009	+	6.40432i	0.00981651	+	0.00904565i
$709$	398.044	−	689.433i	0.561417	−	0.972402i	−0.435957	−	0.899968i	$-0.643590\pi$
$709$	398.044	−	689.433i	0.561417	−	0.972402i	0.997373	−	0.0724343i	$-0.0230768\pi$
$710$			21.6015i			0.0304246i
$711$	1023.18	−	707.972i	1.43908	−	0.995741i
$712$	−633.594			−0.889879
$713$	−125.873	−	72.6726i	−0.176539	−	0.101925i
$714$	−55.7234	−	178.466i	−0.0780440	−	0.249952i
$715$	−156.051	−	270.288i	−0.218253	−	0.378025i
$716$	−264.601	+	152.767i	−0.369554	+	0.213362i
$717$	−119.682	+	37.3689i	−0.166920	+	0.0521185i
$718$	213.664	−	370.078i	0.297583	−	0.515429i
$719$			592.329i			0.823823i	0.911224	+	0.411912i	$0.135139\pi$
$719$			592.329i			0.823823i	−0.911224	+	0.411912i	$0.864861\pi$
$720$	−113.961	+	240.874i	−0.158279	+	0.334547i
$721$	−392.790			−0.544785
$722$	77.3600	+	44.6638i	0.107147	+	0.0618612i
$723$	−829.944	+	900.671i	−1.14792	+	1.24574i
$724$	−32.6084	−	56.4794i	−0.0450392	−	0.0780102i
$725$	534.822	−	308.779i	0.737685	−	0.425903i
$726$	−42.3492	+	188.536i	−0.0583322	+	0.259691i
$727$	−310.376	+	537.587i	−0.426927	+	0.739460i	−0.996598	−	0.0824130i	$-0.973737\pi$
$727$	−310.376	+	537.587i	−0.426927	+	0.739460i	0.569671	+	0.821873i	$0.307071\pi$
$728$		−	251.073i		−	0.344881i
$729$	176.874	+	707.218i	0.242625	+	0.970120i
$730$	19.8626			0.0272090
$731$	1511.99	+	872.948i	2.06839	+	1.19418i
$732$	748.340	+	168.093i	1.02232	+	0.229636i
$733$	381.059	+	660.014i	0.519863	+	0.900429i	0.999733	+	0.0230894i	$0.00735024\pi$
$733$	381.059	+	660.014i	0.519863	+	0.900429i	−0.479871	+	0.877339i	$0.659316\pi$
$734$	−82.5947	+	47.6861i	−0.112527	+	0.0649674i
$735$	−47.8057	−	44.0516i	−0.0650417	−	0.0599342i
$736$	−157.903	+	273.497i	−0.214543	+	0.371599i
$737$		−	220.673i		−	0.299421i
$738$	−107.088	−	50.6648i	−0.145106	−	0.0686514i
$739$	−724.434			−0.980290			−0.490145	−	0.871641i	$-0.663056\pi$
$739$	−724.434			−0.980290			−0.490145	+	0.871641i	$0.663056\pi$
$740$	−340.287	−	196.465i	−0.459847	−	0.265493i
$741$	236.561	+	757.634i	0.319246	+	1.02245i
$742$	7.12787	+	12.3458i	0.00960629	+	0.0166386i
$743$	1004.86	−	580.154i	1.35243	−	0.780826i	0.363841	−	0.931461i	$-0.381465\pi$
$743$	1004.86	−	580.154i	1.35243	−	0.780826i	0.988589	+	0.150635i	$0.0481319\pi$
$744$	−216.828	+	67.7015i	−0.291435	+	0.0909966i
$745$	−331.138	+	573.548i	−0.444480	+	0.769862i
$746$			178.105i			0.238747i
$747$	−807.764	−	1167.41i	−1.08134	−	1.56279i
$748$	639.774			0.855313
$749$	−425.531	−	245.680i	−0.568132	−	0.328011i
$750$	190.791	−	207.050i	0.254388	−	0.276066i
$751$	−144.427	−	250.156i	−0.192314	−	0.333097i	0.753703	−	0.657215i	$-0.228266\pi$
$751$	−144.427	−	250.156i	−0.192314	−	0.333097i	−0.946017	+	0.324118i	$0.894932\pi$
$752$	−60.6296	+	35.0045i	−0.0806244	+	0.0465485i
$753$	−113.028	+	503.192i	−0.150103	+	0.668250i
$754$	255.547	−	442.621i	0.338922	−	0.587030i
$755$		−	188.359i		−	0.249482i
$756$	−193.548	−	151.104i	−0.256016	−	0.199873i
$757$	−65.8638			−0.0870064			−0.0435032	−	0.999053i	$-0.513852\pi$
$757$	−65.8638			−0.0870064			−0.0435032	+	0.999053i	$0.513852\pi$
$758$	−414.860	−	239.519i	−0.547308	−	0.315989i
$759$	−185.792	−	41.7329i	−0.244786	−	0.0549841i
$760$	−134.303	−	232.619i	−0.176714	−	0.306078i
$761$	−50.7672	+	29.3104i	−0.0667111	+	0.0385157i	−0.532985	−	0.846125i	$-0.678930\pi$
$761$	−50.7672	+	29.3104i	−0.0667111	+	0.0385157i	0.466273	+	0.884641i	$0.345596\pi$
$762$	−3.92646	−	3.61813i	−0.00515283	−	0.00474820i
$763$	−44.5347	+	77.1364i	−0.0583679	+	0.101096i
$764$		−	525.316i		−	0.687586i
$765$	71.3890	+	871.953i	0.0933190	+	1.13981i
$766$	302.633			0.395083
$767$	13.5011	+	7.79485i	0.0176024	+	0.0101628i
$768$	29.5168	+	94.5336i	0.0384334	+	0.123091i
$769$	−282.936	−	490.059i	−0.367927	−	0.637268i	0.621314	−	0.783561i	$-0.286599\pi$
$769$	−282.936	−	490.059i	−0.367927	−	0.637268i	−0.989241	+	0.146293i	$0.953266\pi$
$770$	−31.5350	+	18.2067i	−0.0409545	+	0.0236451i
$771$	−821.855	+	256.613i	−1.06596	+	0.332831i
$772$	262.264	−	454.255i	0.339720	−	0.588413i
$773$			872.441i			1.12864i	0.825555	+	0.564321i	$0.190862\pi$
$773$			872.441i			1.12864i	−0.825555	+	0.564321i	$0.809138\pi$
$774$	−374.090	+	30.6277i	−0.483320	+	0.0395707i
$775$	−209.249			−0.269998
$776$	77.7220	+	44.8728i	0.100157	+	0.0578258i
$777$	198.620	−	215.546i	0.255624	−	0.277408i
$778$	231.740	+	401.385i	0.297866	+	0.515919i
$779$	−236.372	+	136.469i	−0.303430	+	0.175185i
$780$	−119.002	+	529.791i	−0.152567	+	0.679219i
$781$	27.5697	−	47.7521i	0.0353005	−	0.0611423i
$782$			252.252i			0.322573i
$783$	−405.505	−	1002.61i	−0.517886	−	1.28048i
$784$	66.9522			0.0853982
$785$	−484.010	−	279.444i	−0.616574	−	0.355979i
$786$	227.752	+	51.1580i	0.289761	+	0.0650866i
$787$	724.706	+	1255.23i	0.920847	+	1.59495i	0.798108	+	0.602514i	$0.205834\pi$
$787$	724.706	+	1255.23i	0.920847	+	1.59495i	0.122739	+	0.992439i	$0.460832\pi$
$788$	−1020.53	+	589.202i	−1.29509	+	0.747718i
$789$	−568.954	−	524.276i	−0.721108	−	0.664482i
$790$	−160.509	+	278.009i	−0.203176	+	0.351910i
$791$			218.720i			0.276511i
$792$	−244.727	+	169.334i	−0.308998	+	0.213805i
$793$	1265.18			1.59544
$794$	−48.2878	−	27.8790i	−0.0608159	−	0.0351121i
$795$	−19.8820	−	63.6763i	−0.0250089	−	0.0800959i
$796$	−258.632	−	447.964i	−0.324915	−	0.562769i
$797$	976.039	−	563.516i	1.22464	−	0.707047i	0.258737	−	0.965948i	$-0.416694\pi$
$797$	976.039	−	563.516i	1.22464	−	0.707047i	0.965904	+	0.258901i	$0.0833602\pi$
$798$	88.3946	−	27.6000i	0.110770	−	0.0345865i
$799$	−114.926	+	199.057i	−0.143837	+	0.249132i
$800$			454.656i			0.568320i
$801$	−437.134	+	923.951i	−0.545735	+	1.15350i
$802$	−93.8648			−0.117038
$803$	−43.9082	−	25.3504i	−0.0546801	−	0.0315696i
$804$	−260.164	+	282.335i	−0.323587	+	0.351163i
$805$	43.8541	+	75.9575i	0.0544771	+	0.0943572i
$806$	−149.974	+	86.5875i	−0.186072	+	0.107429i
$807$	−15.4438	+	68.7546i	−0.0191373	+	0.0851978i
$808$	−364.782	+	631.822i	−0.451463	+	0.781958i
$809$		−	135.345i		−	0.167299i	−0.996495	−	0.0836497i	$-0.973342\pi$
$809$		−	135.345i		−	0.167299i	0.996495	−	0.0836497i	$-0.0266577\pi$
$810$	−119.284	−	145.420i	−0.147264	−	0.179531i
$811$	417.829			0.515202			0.257601	−	0.966251i	$-0.417068\pi$
$811$	417.829			0.515202			0.257601	+	0.966251i	$0.417068\pi$
$812$	315.478	+	182.141i	0.388519	+	0.224312i
$813$	−156.640	−	35.1847i	−0.192669	−	0.0432776i
$814$	−82.0904	−	142.185i	−0.100848	−	0.174674i
$815$	824.485	−	476.016i	1.01164	−	0.584069i
$816$	−662.622	−	610.588i	−0.812036	−	0.748270i
$817$	−432.374	+	748.894i	−0.529221	+	0.916638i
$818$		−	445.529i		−	0.544656i
$819$	−366.132	−	173.222i	−0.447048	−	0.211505i
$820$	−186.723			−0.227711
$821$	−1152.79	−	665.565i	−1.40413	−	0.810677i	−0.409319	−	0.912391i	$-0.634234\pi$
$821$	−1152.79	−	665.565i	−1.40413	−	0.810677i	−0.994814	+	0.101715i	$0.967567\pi$
$822$	−134.037	−	429.281i	−0.163062	−	0.522239i
$823$	−276.724	−	479.301i	−0.336239	−	0.582382i	0.647483	−	0.762080i	$-0.275822\pi$
$823$	−276.724	−	479.301i	−0.336239	−	0.582382i	−0.983722	+	0.179697i	$0.942488\pi$
$824$	717.274	−	414.118i	0.870478	−	0.502571i
$825$	−261.684	+	81.7073i	−0.317193	+	0.0990392i
$826$	0.909439	−	1.57519i	0.00110102	−	0.00190702i
$827$		−	256.869i		−	0.310603i	−0.987867	−	0.155302i	$-0.950365\pi$
$827$		−	256.869i		−	0.310603i	0.987867	−	0.155302i	$-0.0496350\pi$
$828$	188.506	+	272.436i	0.227665	+	0.329028i
$829$	−905.099			−1.09180			−0.545898	−	0.837852i	$-0.683811\pi$
$829$	−905.099			−1.09180			−0.545898	+	0.837852i	$0.683811\pi$
$830$	317.196	+	183.133i	0.382164	+	0.220642i
$831$	227.158	−	246.516i	0.273355	−	0.296650i
$832$	−137.253	−	237.729i	−0.164968	−	0.285732i
$833$	190.365	−	109.908i	0.228530	−	0.131942i
$834$	36.7046	−	163.406i	0.0440103	−	0.195931i
$835$	−75.8275	+	131.337i	−0.0908113	+	0.157290i
$836$			316.882i			0.379046i
$837$	−50.8684	+	362.903i	−0.0607747	+	0.433575i
$838$	−416.278			−0.496752
$839$	−289.365	−	167.065i	−0.344893	−	0.199124i	0.317541	−	0.948245i	$-0.397143\pi$
$839$	−289.365	−	167.065i	−0.344893	−	0.199124i	−0.662434	+	0.749121i	$0.730476\pi$
$840$	133.741	+	30.0412i	0.159216	+	0.0357633i
$841$	381.741	+	661.194i	0.453913	+	0.786200i
$842$	18.0304	−	10.4099i	0.0214138	−	0.0123632i
$843$	294.824	+	271.673i	0.349732	+	0.322269i
$844$	287.927	−	498.704i	0.341145	−	0.590881i
$845$			372.539i			0.440874i
$846$	−4.03221	−	49.2498i	−0.00476620	−	0.0582149i
$847$	−227.188			−0.268226
$848$	59.4994	+	34.3520i	0.0701644	+	0.0405094i
$849$	177.060	+	567.070i	0.208551	+	0.667927i
$850$	181.579	+	314.504i	0.213622	+	0.370005i
$851$	−342.477	+	197.729i	−0.402440	+	0.232349i
$852$	−91.5712	+	28.5919i	−0.107478	+	0.0335585i
$853$	236.657	−	409.902i	0.277441	−	0.480542i	−0.693307	−	0.720642i	$-0.743847\pi$
$853$	236.657	−	409.902i	0.277441	−	0.480542i	0.970748	+	0.240101i	$0.0771804\pi$
$854$		−	147.611i		−	0.172847i
$855$	−431.881	+	35.3592i	−0.505124	+	0.0413558i
$856$	1036.08			1.21038
$857$	367.809	+	212.355i	0.429182	+	0.247788i	0.698998	−	0.715124i	$-0.253630\pi$
$857$	367.809	+	212.355i	0.429182	+	0.247788i	−0.269816	+	0.962912i	$0.586963\pi$
$858$	−153.745	+	166.847i	−0.179190	+	0.194461i
$859$	472.355	+	818.143i	0.549890	+	0.952437i	0.998282	+	0.0585996i	$0.0186635\pi$
$859$	472.355	+	818.143i	0.549890	+	0.952437i	−0.448392	+	0.893837i	$0.648003\pi$
$860$	−512.334	+	295.796i	−0.595737	+	0.343949i
$861$	30.5258	−	135.899i	0.0354539	−	0.157838i
$862$	171.770	−	297.514i	0.199269	−	0.345144i
$863$		−	638.653i		−	0.740038i	−0.929024	−	0.370019i	$-0.879351\pi$
$863$		−	638.653i		−	0.740038i	0.929024	−	0.370019i	$-0.120649\pi$
$864$	788.516	+	110.527i	0.912634	+	0.127925i
$865$	793.125			0.916907
$866$	−118.953	−	68.6774i	−0.137359	−	0.0793042i
$867$	−2040.44	−	458.327i	−2.35345	−	0.528636i
$868$	−61.7152	−	106.894i	−0.0711005	−	0.123150i
$869$	709.640	−	409.711i	0.816616	−	0.471474i
$870$	205.198	+	189.085i	0.235860	+	0.217339i
$871$	−316.652	+	548.457i	−0.363549	+	0.629686i
$872$		−	187.811i		−	0.215380i
$873$	119.059	−	82.3807i	0.136379	−	0.0943650i
$874$	−124.941			−0.142953
$875$	286.675	+	165.512i	0.327628	+	0.189156i
$876$	26.2902	+	84.1998i	0.0300117	+	0.0961185i
$877$	702.130	+	1216.12i	0.800604	+	1.38669i	0.919219	+	0.393747i	$0.128821\pi$
$877$	702.130	+	1216.12i	0.800604	+	1.38669i	−0.118615	+	0.992940i	$0.537845\pi$
$878$	−151.068	+	87.2193i	−0.172060	+	0.0993387i
$879$	762.972	−	238.228i	0.868000	−	0.271021i
$880$	−87.7454	+	151.979i	−0.0997107	+	0.172704i
$881$		−	1098.35i		−	1.24671i	−0.781941	−	0.623353i	$-0.785770\pi$
$881$		−	1098.35i		−	1.24671i	0.781941	−	0.623353i	$-0.214230\pi$
$882$	−20.2102	+	42.7173i	−0.0229140	+	0.0484324i
$883$	970.081			1.09862			0.549310	−	0.835619i	$-0.314891\pi$
$883$	970.081			1.09862			0.549310	+	0.835619i	$0.314891\pi$
$884$	−1590.08	−	918.035i	−1.79874	−	1.03850i
$885$	−5.76757	+	6.25908i	−0.00651703	+	0.00707241i
$886$	−127.028	−	220.020i	−0.143373	−	0.248329i
$887$	41.9429	−	24.2157i	0.0472862	−	0.0273007i	−0.476171	−	0.879353i	$-0.657976\pi$
$887$	41.9429	−	24.2157i	0.0472862	−	0.0273007i	0.523457	+	0.852052i	$0.324642\pi$
$888$	−135.450	+	603.012i	−0.152533	+	0.679068i
$889$	3.13874	−	5.43645i	0.00353064	−	0.00611524i
$890$		−	263.715i		−	0.296309i
$891$	78.0905	+	473.706i	0.0876436	+	0.531656i
$892$	−248.121			−0.278162
$893$	−98.5935	−	56.9230i	−0.110407	−	0.0637435i
$894$	469.737	+	105.513i	0.525433	+	0.118024i
$895$	−137.579	−	238.293i	−0.153719	−	0.266249i
$896$	−298.015	+	172.059i	−0.332606	+	0.192030i
$897$	401.881	+	370.322i	0.448028	+	0.412846i
$898$	147.427	−	255.350i	0.164172	−	0.284355i
$899$		−	543.649i		−	0.604726i
$900$	431.135	+	203.976i	0.479039	+	0.226640i
$901$	225.566			0.250351
$902$	−67.5672	−	39.0099i	−0.0749082	−	0.0432483i
$903$	−131.526	−	421.239i	−0.145655	−	0.466488i
$904$	−230.597	−	399.405i	−0.255085	−	0.441820i
$905$	50.8639	−	29.3663i	0.0562033	−	0.0324490i
$906$	−130.704	+	40.8106i	−0.144265	+	0.0450449i
$907$	133.848	−	231.832i	0.147572	−	0.255603i	−0.782757	−	0.622327i	$-0.786187\pi$
$907$	133.848	−	231.832i	0.147572	−	0.255603i	0.930330	+	0.366724i	$0.119521\pi$
$908$			239.651i			0.263933i
$909$	669.693	+	967.863i	0.736736	+	1.06476i
$910$	104.502			0.114837
$911$	41.8883	+	24.1842i	0.0459805	+	0.0265469i	0.522814	−	0.852447i	$-0.324882\pi$
$911$	41.8883	+	24.1842i	0.0459805	+	0.0265469i	−0.476834	+	0.878994i	$0.658216\pi$
$912$	302.426	−	328.199i	0.331608	−	0.359867i
$913$	−467.461	−	809.666i	−0.512006	−	0.886820i
$914$	396.785	−	229.084i	0.434120	−	0.250639i
$915$	−151.381	+	673.936i	−0.165443	+	0.736543i
$916$	122.132	−	211.539i	0.133332	−	0.230938i
$917$			274.444i			0.299284i
$918$	589.591	−	238.459i	0.642256	−	0.259759i
$919$	−194.068			−0.211173			−0.105586	−	0.994410i	$-0.533672\pi$
$919$	−194.068			−0.211173			−0.105586	+	0.994410i	$0.533672\pi$
$920$	−160.164	−	92.4706i	−0.174091	−	0.100512i
$921$	−1111.04	−	249.564i	−1.20634	−	0.270970i
$922$	−48.7966	−	84.5183i	−0.0529248	−	0.0916684i
$923$	−137.043	+	79.1216i	−0.148475	+	0.0857222i
$924$	−118.920	−	109.582i	−0.128702	−	0.118595i
$925$	−284.664	+	493.052i	−0.307745	+	0.533029i
$926$		−	558.317i		−	0.602934i
$927$	−109.029	−	1331.69i	−0.117615	−	1.43656i
$928$	−1181.24			−1.27289
$929$	501.513	+	289.548i	0.539841	+	0.311678i	0.745015	−	0.667048i	$-0.232442\pi$
$929$	501.513	+	289.548i	0.539841	+	0.311678i	−0.205173	+	0.978726i	$0.565776\pi$
$930$	−28.1788	−	90.2483i	−0.0302998	−	0.0970412i
$931$	54.4376	+	94.2886i	0.0584721	+	0.101277i
$932$	−726.272	+	419.313i	−0.779261	+	0.449907i
$933$	−233.658	+	72.9566i	−0.250438	+	0.0781957i
$934$	−157.007	+	271.943i	−0.168101	+	0.291160i
$935$			576.165i			0.616219i
$936$	851.222	−	69.6918i	0.909425	−	0.0744570i
$937$	1387.72			1.48102			0.740511	−	0.672045i	$-0.234584\pi$
$937$	1387.72			1.48102			0.740511	+	0.672045i	$0.234584\pi$
$938$	63.9894	+	36.9443i	0.0682190	+	0.0393863i
$939$	541.462	−	587.604i	0.576637	−	0.625777i
$940$	−38.9422	−	67.4499i	−0.0414279	−	0.0717552i
$941$	−134.128	+	77.4391i	−0.142538	+	0.0822945i	−0.569573	−	0.821941i	$-0.692891\pi$
$941$	−134.128	+	77.4391i	−0.142538	+	0.0822945i	0.427035	+	0.904235i	$0.359558\pi$
$942$	−89.0414	+	396.406i	−0.0945237	+	0.420813i
$943$	−93.9623	+	162.747i	−0.0996419	+	0.172585i
$944$		−	8.76589i		−	0.00928590i
$945$	136.080	−	174.305i	0.144000	−	0.184450i
$946$	−247.189			−0.261300
$947$	−18.1551	−	10.4819i	−0.0191712	−	0.0110685i	0.490384	−	0.871507i	$-0.336857\pi$
$947$	−18.1551	−	10.4819i	−0.0191712	−	0.0110685i	−0.509555	+	0.860438i	$0.670190\pi$
$948$	−1390.96	−	312.440i	−1.46726	−	0.329578i
$949$	72.7524	+	126.011i	0.0766621	+	0.132783i
$950$	−155.775	+	89.9367i	−0.163974	+	0.0946702i
$951$	1161.38	+	1070.18i	1.22122	+	1.12532i
$952$	−231.751	+	401.404i	−0.243436	+	0.421643i
$953$			861.801i			0.904303i	0.891941	+	0.452152i	$0.149343\pi$
$953$			861.801i			0.904303i	−0.891941	+	0.452152i	$0.850657\pi$
$954$	−39.8780	+	27.5928i	−0.0418008	+	0.0289232i
$955$	473.086			0.495378
$956$	124.411	+	71.8288i	0.130137	+	0.0751347i
$957$	−212.284	−	679.882i	−0.221822	−	0.710431i
$958$	120.159	+	208.121i	0.125427	+	0.217245i
$959$	457.904	−	264.371i	0.477481	−	0.275674i
$960$	143.056	−	44.6673i	0.149017	−	0.0465284i
$961$	388.397	−	672.724i	0.404159	−	0.700025i
$962$			471.178i			0.489790i
$963$	714.822	−	1510.89i	0.742287	−	1.56894i
$964$	1403.29			1.45570
$965$	409.091	+	236.189i	0.423928	+	0.244755i
$966$	43.2062	−	46.8882i	0.0447269	−	0.0485385i
$967$	−300.030	−	519.667i	−0.310269	−	0.537401i	0.668152	−	0.744025i	$-0.267086\pi$
$967$	−300.030	−	519.667i	−0.310269	−	0.537401i	−0.978420	+	0.206624i	$0.933752\pi$
$968$	414.867	−	239.524i	0.428582	−	0.247442i
$969$	321.125	−	1429.63i	0.331398	−	1.47536i
$970$	−18.6770	+	32.3496i	−0.0192547	+	0.0333501i
$971$			1270.19i			1.30812i	0.756442	+	0.654061i	$0.226936\pi$
$971$			1270.19i			1.30812i	−0.756442	+	0.654061i	$0.773064\pi$
$972$	458.568	−	698.137i	0.471777	−	0.718248i
$973$	196.906			0.202370
$974$	−522.580	−	301.712i	−0.536530	−	0.309766i
$975$	767.630	+	172.426i	0.787313	+	0.176847i
$976$	−355.698	−	616.087i	−0.364445	−	0.631237i
$977$	1101.80	−	636.125i	1.12774	−	0.651100i	0.184373	−	0.982856i	$-0.440975\pi$
$977$	1101.80	−	636.125i	1.12774	−	0.651100i	0.943365	+	0.331757i	$0.107641\pi$
$978$	−508.950	−	468.984i	−0.520399	−	0.479534i
$979$	−336.577	+	582.968i	−0.343796	+	0.595473i
$980$			74.4837i			0.0760038i
$981$	−273.880	−	129.576i	−0.279184	−	0.132086i
$982$	−341.303			−0.347559
$983$	1025.26	+	591.932i	1.04299	+	0.602169i	0.920678	−	0.390324i	$-0.127637\pi$
$983$	1025.26	+	591.932i	1.04299	+	0.602169i	0.122309	+	0.992492i	$0.460970\pi$
$984$	87.5348	+	280.348i	0.0889582	+	0.284907i
$985$	−530.621	−	919.062i	−0.538701	−	0.933058i
$986$	−817.114	+	471.761i	−0.828716	+	0.478459i
$987$	55.4571	−	17.3157i	0.0561875	−	0.0175438i
$988$	454.706	−	787.574i	0.460229	−	0.797140i
$989$			595.399i			0.602021i
$990$	−70.4803	−	101.860i	−0.0711922	−	0.102889i
$991$	−1295.62			−1.30739			−0.653693	−	0.756760i	$-0.726781\pi$
$991$	−1295.62			−1.30739			−0.653693	+	0.756760i	$0.726781\pi$
$992$	346.620	+	200.121i	0.349416	+	0.201735i
$993$	−115.003	+	124.804i	−0.115814	+	0.125683i
$994$	9.23126	+	15.9890i	0.00928698	+	0.0160855i
$995$	403.426	−	232.918i	0.405453	−	0.234088i
$996$	−356.480	+	1587.03i	−0.357912	+	1.59340i
$997$	531.201	−	920.068i	0.532800	−	0.922836i	−0.466467	−	0.884539i	$-0.654473\pi$
$997$	531.201	−	920.068i	0.532800	−	0.922836i	0.999266	−	0.0382974i	$-0.0121934\pi$
$998$			170.612i			0.170954i
$999$	785.905	+	613.557i	0.786692	+	0.614172i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.3.r.a.29.5	✓	24
3.2	odd	2		189.3.r.a.8.8		24
7.2	even	3		441.3.j.h.263.8		24
7.3	odd	6		441.3.n.h.128.8		24
7.4	even	3		441.3.n.g.128.8		24
7.5	odd	6		441.3.j.g.263.8		24
7.6	odd	2		441.3.r.h.344.5		24
9.2	odd	6		567.3.b.a.323.10		24
9.4	even	3		189.3.r.a.71.8		24
9.5	odd	6	inner	63.3.r.a.50.5	yes	24
9.7	even	3		567.3.b.a.323.15		24
63.5	even	6		441.3.n.h.410.8		24
63.23	odd	6		441.3.n.g.410.8		24
63.32	odd	6		441.3.j.h.275.5		24
63.41	even	6		441.3.r.h.50.5		24
63.59	even	6		441.3.j.g.275.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.r.a.29.5	✓	24	1.1	even	1	trivial
63.3.r.a.50.5	yes	24	9.5	odd	6	inner
189.3.r.a.8.8		24	3.2	odd	2
189.3.r.a.71.8		24	9.4	even	3
441.3.j.g.263.8		24	7.5	odd	6
441.3.j.g.275.5		24	63.59	even	6
441.3.j.h.263.8		24	7.2	even	3
441.3.j.h.275.5		24	63.32	odd	6
441.3.n.g.128.8		24	7.4	even	3
441.3.n.g.410.8		24	63.23	odd	6
441.3.n.h.128.8		24	7.3	odd	6
441.3.n.h.410.8		24	63.5	even	6
441.3.r.h.50.5		24	63.41	even	6
441.3.r.h.344.5		24	7.6	odd	2
567.3.b.a.323.10		24	9.2	odd	6
567.3.b.a.323.15		24	9.7	even	3

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	63.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.649615 - 0.375055i) q^{2} +(2.92707 + 0.657482i) q^{3} +(-1.71867 - 2.97682i) q^{4} +(2.68085 - 1.54779i) q^{5} +(-1.65487 - 1.52492i) q^{6} +(1.32288 - 2.29129i) q^{7} +5.57882i q^{8} +(8.13543 + 3.84899i) q^{9} +O(q^{10})\)	\(q+(-0.649615 - 0.375055i) q^{2} +(2.92707 + 0.657482i) q^{3} +(-1.71867 - 2.97682i) q^{4} +(2.68085 - 1.54779i) q^{5} +(-1.65487 - 1.52492i) q^{6} +(1.32288 - 2.29129i) q^{7} +5.57882i q^{8} +(8.13543 + 3.84899i) q^{9} -2.32203 q^{10} +(5.13306 + 2.96357i) q^{11} +(-3.07345 - 9.84334i) q^{12} +(-8.50508 - 14.7312i) q^{13} +(-1.71872 + 0.992303i) q^{14} +(8.86467 - 2.76787i) q^{15} +(-4.78230 + 8.28319i) q^{16} +31.4021i q^{17} +(-3.84132 - 5.55160i) q^{18} -15.5536 q^{19} +(-9.21497 - 5.32027i) q^{20} +(5.37863 - 5.83698i) q^{21} +(-2.22301 - 3.85036i) q^{22} +(-9.27428 + 5.35451i) q^{23} +(-3.66798 + 16.3296i) q^{24} +(-7.70870 + 13.3519i) q^{25} +12.7595i q^{26} +(21.2823 + 16.6151i) q^{27} -9.09433 q^{28} +(-34.6895 - 20.0280i) q^{29} +(-6.79672 - 1.52669i) q^{30} +(6.78612 + 11.7539i) q^{31} +(25.5389 - 14.7449i) q^{32} +(13.0763 + 12.0495i) q^{33} +(11.7775 - 20.3993i) q^{34} -8.19013i q^{35} +(-2.52437 - 30.8328i) q^{36} +36.9276 q^{37} +(10.1038 + 5.83346i) q^{38} +(-15.2094 - 48.7112i) q^{39} +(8.63484 + 14.9560i) q^{40} +(15.1972 - 8.77413i) q^{41} +(-5.68323 + 1.77451i) q^{42} +(27.7990 - 48.1492i) q^{43} -20.3736i q^{44} +(27.7673 - 2.27338i) q^{45} +8.03294 q^{46} +(6.33896 + 3.65980i) q^{47} +(-19.4442 + 21.1012i) q^{48} +(-3.50000 - 6.06218i) q^{49} +(10.0154 - 5.78238i) q^{50} +(-20.6464 + 91.9162i) q^{51} +(-29.2348 + 50.6362i) q^{52} -7.18315i q^{53} +(-7.59371 - 18.7755i) q^{54} +18.3479 q^{55} +(12.7827 + 7.38009i) q^{56} +(-45.5264 - 10.2262i) q^{57} +(15.0232 + 26.0210i) q^{58} +(-0.793706 + 0.458247i) q^{59} +(-23.4749 - 21.6315i) q^{60} +(-37.1890 + 64.4133i) q^{61} -10.1807i q^{62} +(19.5813 - 13.5489i) q^{63} +16.1378 q^{64} +(-45.6017 - 26.3281i) q^{65} +(-3.97535 - 12.7319i) q^{66} +(-18.6154 - 32.2429i) q^{67} +(93.4785 - 53.9698i) q^{68} +(-30.6669 + 9.57532i) q^{69} +(-3.07175 + 5.32043i) q^{70} -9.30286i q^{71} +(-21.4728 + 45.3862i) q^{72} -8.55399 q^{73} +(-23.9887 - 13.8499i) q^{74} +(-31.3425 + 34.0134i) q^{75} +(26.7314 + 46.3002i) q^{76} +(13.5808 - 7.84088i) q^{77} +(-8.38914 + 37.3479i) q^{78} +(69.1244 - 119.727i) q^{79} +29.6080i q^{80} +(51.3706 + 62.6264i) q^{81} -13.1631 q^{82} +(-136.603 - 78.8678i) q^{83} +(-26.6197 - 5.97936i) q^{84} +(48.6039 + 84.1844i) q^{85} +(-36.1173 + 20.8523i) q^{86} +(-88.3704 - 81.4310i) q^{87} +(-16.5333 + 28.6364i) q^{88} +113.571i q^{89} +(-18.8907 - 8.93745i) q^{90} -45.0046 q^{91} +(31.8788 + 18.4052i) q^{92} +(12.1354 + 38.8662i) q^{93} +(-2.74525 - 4.75492i) q^{94} +(-41.6968 + 24.0737i) q^{95} +(84.4486 - 26.3679i) q^{96} +(8.04342 - 13.9316i) q^{97} +5.25078i q^{98} +(30.3529 + 43.8670i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{3} + 24 q^{4} - 18 q^{5} - 14 q^{6} + 26 q^{9}+O(q^{10}) \) 24 * q + 2 * q^3 + 24 * q^4 - 18 * q^5 - 14 * q^6 + 26 * q^9	\( 24 q + 2 q^{3} + 24 q^{4} - 18 q^{5} - 14 q^{6} + 26 q^{9} - 18 q^{11} + 4 q^{12} - 10 q^{15} - 48 q^{16} - 62 q^{18} - 24 q^{19} - 18 q^{20} - 14 q^{21} - 24 q^{22} + 72 q^{23} + 54 q^{24} + 54 q^{25} - 124 q^{27} + 54 q^{29} - 212 q^{30} + 30 q^{31} + 126 q^{32} - 178 q^{33} + 60 q^{34} + 124 q^{36} + 84 q^{37} - 144 q^{38} + 92 q^{39} - 60 q^{40} + 180 q^{41} + 140 q^{42} - 60 q^{43} - 118 q^{45} - 168 q^{46} + 378 q^{47} + 436 q^{48} - 84 q^{49} - 378 q^{50} + 168 q^{51} - 18 q^{52} + 514 q^{54} - 132 q^{55} - 232 q^{57} + 90 q^{58} - 90 q^{59} + 76 q^{60} + 28 q^{63} + 324 q^{64} + 126 q^{65} + 202 q^{66} + 6 q^{67} - 738 q^{68} - 432 q^{69} - 246 q^{72} - 72 q^{73} - 792 q^{74} + 40 q^{75} + 84 q^{76} + 28 q^{78} - 6 q^{79} - 34 q^{81} - 108 q^{82} - 558 q^{83} - 322 q^{84} + 126 q^{85} + 90 q^{86} + 428 q^{87} + 168 q^{88} - 488 q^{90} + 84 q^{91} + 774 q^{92} - 738 q^{93} - 354 q^{94} + 648 q^{95} - 280 q^{96} - 270 q^{97} + 296 q^{99}+O(q^{100}) \) 24 * q + 2 * q^3 + 24 * q^4 - 18 * q^5 - 14 * q^6 + 26 * q^9 - 18 * q^11 + 4 * q^12 - 10 * q^15 - 48 * q^16 - 62 * q^18 - 24 * q^19 - 18 * q^20 - 14 * q^21 - 24 * q^22 + 72 * q^23 + 54 * q^24 + 54 * q^25 - 124 * q^27 + 54 * q^29 - 212 * q^30 + 30 * q^31 + 126 * q^32 - 178 * q^33 + 60 * q^34 + 124 * q^36 + 84 * q^37 - 144 * q^38 + 92 * q^39 - 60 * q^40 + 180 * q^41 + 140 * q^42 - 60 * q^43 - 118 * q^45 - 168 * q^46 + 378 * q^47 + 436 * q^48 - 84 * q^49 - 378 * q^50 + 168 * q^51 - 18 * q^52 + 514 * q^54 - 132 * q^55 - 232 * q^57 + 90 * q^58 - 90 * q^59 + 76 * q^60 + 28 * q^63 + 324 * q^64 + 126 * q^65 + 202 * q^66 + 6 * q^67 - 738 * q^68 - 432 * q^69 - 246 * q^72 - 72 * q^73 - 792 * q^74 + 40 * q^75 + 84 * q^76 + 28 * q^78 - 6 * q^79 - 34 * q^81 - 108 * q^82 - 558 * q^83 - 322 * q^84 + 126 * q^85 + 90 * q^86 + 428 * q^87 + 168 * q^88 - 488 * q^90 + 84 * q^91 + 774 * q^92 - 738 * q^93 - 354 * q^94 + 648 * q^95 - 280 * q^96 - 270 * q^97 + 296 * q^99

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