LMFDB - Embedded newform 63.3.r.a.50.6

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			50.6
Character	$\chi$	$=$	63.50
Dual form			63.3.r.a.29.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.296130 - 0.170971i) q^{2} +(-2.98677 - 0.281486i) q^{3} +(-1.94154 + 3.36284i) q^{4} +(-7.71344 - 4.45336i) q^{5} +(-0.932598 + 0.427294i) q^{6} +(-1.32288 - 2.29129i) q^{7} +2.69555i q^{8} +(8.84153 + 1.68146i) q^{9} +O(q^{10})$	\(q+(0.296130 - 0.170971i) q^{2} +(-2.98677 - 0.281486i) q^{3} +(-1.94154 + 3.36284i) q^{4} +(-7.71344 - 4.45336i) q^{5} +(-0.932598 + 0.427294i) q^{6} +(-1.32288 - 2.29129i) q^{7} +2.69555i q^{8} +(8.84153 + 1.68146i) q^{9} -3.04558 q^{10} +(0.233142 - 0.134604i) q^{11} +(6.74551 - 9.49750i) q^{12} +(-9.41394 + 16.3054i) q^{13} +(-0.783487 - 0.452347i) q^{14} +(21.7847 + 15.4723i) q^{15} +(-7.30529 - 12.6531i) q^{16} -11.7696i q^{17} +(2.90573 - 1.01371i) q^{18} -0.353289 q^{19} +(29.9519 - 17.2927i) q^{20} +(3.30615 + 7.21591i) q^{21} +(0.0460269 - 0.0797209i) q^{22} +(-25.5250 - 14.7369i) q^{23} +(0.758760 - 8.05099i) q^{24} +(27.1647 + 47.0507i) q^{25} +6.43804i q^{26} +(-25.9343 - 7.51090i) q^{27} +10.2737 q^{28} +(-4.73941 + 2.73630i) q^{29} +(9.09643 + 0.857286i) q^{30} +(5.70693 - 9.88469i) q^{31} +(-13.6643 - 7.88909i) q^{32} +(-0.734228 + 0.336406i) q^{33} +(-2.01226 - 3.48534i) q^{34} +23.5649i q^{35} +(-22.8207 + 26.4681i) q^{36} -35.9222 q^{37} +(-0.104620 + 0.0604021i) q^{38} +(32.7070 - 46.0506i) q^{39} +(12.0043 - 20.7920i) q^{40} +(28.5616 + 16.4901i) q^{41} +(2.21276 + 1.57159i) q^{42} +(-11.8069 - 20.4501i) q^{43} +1.04536i q^{44} +(-60.7105 - 52.3443i) q^{45} -10.0783 q^{46} +(-37.1020 + 21.4209i) q^{47} +(18.2575 + 39.8483i) q^{48} +(-3.50000 + 6.06218i) q^{49} +(16.0886 + 9.28877i) q^{50} +(-3.31297 + 35.1530i) q^{51} +(-36.5550 - 63.3152i) q^{52} +67.4023i q^{53} +(-8.96407 + 2.20980i) q^{54} -2.39776 q^{55} +(6.17629 - 3.56588i) q^{56} +(1.05519 + 0.0994457i) q^{57} +(-0.935656 + 1.62060i) q^{58} +(-55.9985 - 32.3308i) q^{59} +(-94.3268 + 43.2183i) q^{60} +(27.4750 + 47.5881i) q^{61} -3.90287i q^{62} +(-7.84353 - 22.4829i) q^{63} +53.0471 q^{64} +(145.228 - 83.8473i) q^{65} +(-0.159912 + 0.225152i) q^{66} +(53.6141 - 92.8624i) q^{67} +(39.5793 + 22.8511i) q^{68} +(72.0891 + 51.2006i) q^{69} +(4.02892 + 6.97830i) q^{70} -2.36503i q^{71} +(-4.53247 + 23.8328i) q^{72} +120.760 q^{73} +(-10.6376 + 6.14165i) q^{74} +(-67.8906 - 148.176i) q^{75} +(0.685924 - 1.18805i) q^{76} +(-0.616835 - 0.356130i) q^{77} +(1.81222 - 19.2289i) q^{78} +(-9.18745 - 15.9131i) q^{79} +130.132i q^{80} +(75.3454 + 29.7334i) q^{81} +11.2773 q^{82} +(-98.3488 + 56.7817i) q^{83} +(-30.6850 - 2.89189i) q^{84} +(-52.4142 + 90.7841i) q^{85} +(-6.99274 - 4.03726i) q^{86} +(14.9257 - 6.83861i) q^{87} +(0.362833 + 0.628446i) q^{88} +24.4587i q^{89} +(-26.9276 - 5.12103i) q^{90} +49.8139 q^{91} +(99.1157 - 57.2245i) q^{92} +(-19.8276 + 27.9168i) q^{93} +(-7.32469 + 12.6867i) q^{94} +(2.72507 + 1.57332i) q^{95} +(38.5914 + 27.4092i) q^{96} +(-81.7611 - 141.614i) q^{97} +2.39359i q^{98} +(2.28766 - 0.798090i) 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 $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.296130	−	0.170971i	0.148065	−	0.0854855i	−0.424137	−	0.905598i	$-0.639423\pi$
$2$	0.296130	−	0.170971i	0.148065	−	0.0854855i	0.572202	+	0.820112i	$0.306089\pi$
$3$	−2.98677	−	0.281486i	−0.995588	−	0.0938285i
$3$	−2.98677	−	0.281486i	−0.995588	−	0.0938285i
$4$	−1.94154	+	3.36284i	−0.485384	+	0.840711i
$5$	−7.71344	−	4.45336i	−1.54269	−	0.890671i	−0.998668	−	0.0515985i	$-0.983568\pi$
$5$	−7.71344	−	4.45336i	−1.54269	−	0.890671i	−0.544020	−	0.839073i	$-0.683098\pi$
$6$	−0.932598	+	0.427294i	−0.155433	+	0.0712156i
$7$	−1.32288	−	2.29129i	−0.188982	−	0.327327i
$7$	−1.32288	−	2.29129i	−0.188982	−	0.327327i
$8$			2.69555i			0.336944i
$9$	8.84153	+	1.68146i	0.982392	+	0.186829i
$10$	−3.04558			−0.304558
$11$	0.233142	−	0.134604i	0.0211947	−	0.0122368i	−0.489365	−	0.872079i	$-0.662771\pi$
$11$	0.233142	−	0.134604i	0.0211947	−	0.0122368i	0.510560	+	0.859842i	$0.329438\pi$
$12$	6.74551	−	9.49750i	0.562126	−	0.791459i
$13$	−9.41394	+	16.3054i	−0.724149	+	1.25426i	0.235174	+	0.971953i	$0.424434\pi$
$13$	−9.41394	+	16.3054i	−0.724149	+	1.25426i	−0.959323	+	0.282310i	$0.908899\pi$
$14$	−0.783487	−	0.452347i	−0.0559634	−	0.0323105i
$15$	21.7847	+	15.4723i	1.45231	+	1.03149i
$16$	−7.30529	−	12.6531i	−0.456581	−	0.790821i
$17$		−	11.7696i		−	0.692329i	−0.938174	−	0.346165i	$-0.887484\pi$
$17$		−	11.7696i		−	0.692329i	0.938174	−	0.346165i	$-0.112516\pi$
$18$	2.90573	−	1.01371i	0.161429	−	0.0563174i
$19$	−0.353289			−0.0185941			−0.00929707	−	0.999957i	$-0.502959\pi$
$19$	−0.353289			−0.0185941			−0.00929707	+	0.999957i	$0.502959\pi$
$20$	29.9519	−	17.2927i	1.49759	−	0.864636i
$21$	3.30615	+	7.21591i	0.157436	+	0.343615i
$22$	0.0460269	−	0.0797209i	0.00209213	−	0.00362368i
$23$	−25.5250	−	14.7369i	−1.10978	−	0.640734i	−0.171011	−	0.985269i	$-0.554703\pi$
$23$	−25.5250	−	14.7369i	−1.10978	−	0.640734i	−0.938774	+	0.344535i	$0.888037\pi$
$24$	0.758760	−	8.05099i	0.0316150	−	0.335458i
$25$	27.1647	+	47.0507i	1.08659	+	1.88203i
$26$			6.43804i			0.247617i
$27$	−25.9343	−	7.51090i	−0.960529	−	0.278181i
$28$	10.2737			0.366916
$29$	−4.73941	+	2.73630i	−0.163428	+	0.0943552i	−0.579483	−	0.814984i	$-0.696746\pi$
$29$	−4.73941	+	2.73630i	−0.163428	+	0.0943552i	0.416055	+	0.909339i	$0.363412\pi$
$30$	9.09643	+	0.857286i	0.303214	+	0.0285762i
$31$	5.70693	−	9.88469i	0.184094	−	0.318861i	−0.759177	−	0.650885i	$-0.774398\pi$
$31$	5.70693	−	9.88469i	0.184094	−	0.318861i	0.943271	+	0.332024i	$0.107731\pi$
$32$	−13.6643	−	7.88909i	−0.427010	−	0.246534i
$33$	−0.734228	+	0.336406i	−0.0222493	+	0.0101941i
$34$	−2.01226	−	3.48534i	−0.0591841	−	0.102510i
$35$			23.5649i			0.673284i
$36$	−22.8207	+	26.4681i	−0.633907	+	0.735224i
$37$	−35.9222			−0.970869			−0.485435	−	0.874273i	$-0.661339\pi$
$37$	−35.9222			−0.970869			−0.485435	+	0.874273i	$0.661339\pi$
$38$	−0.104620	+	0.0604021i	−0.00275315	+	0.00158953i
$39$	32.7070	−	46.0506i	0.838640	−	1.18078i
$40$	12.0043	−	20.7920i	0.300107	−	0.519800i
$41$	28.5616	+	16.4901i	0.696625	+	0.402197i	0.806089	−	0.591794i	$-0.201580\pi$
$41$	28.5616	+	16.4901i	0.696625	+	0.402197i	−0.109464	+	0.993991i	$0.534914\pi$
$42$	2.21276	+	1.57159i	0.0526849	+	0.0374189i
$43$	−11.8069	−	20.4501i	−0.274578	−	0.475583i	0.695451	−	0.718574i	$-0.255205\pi$
$43$	−11.8069	−	20.4501i	−0.274578	−	0.475583i	−0.970029	+	0.242991i	$0.921871\pi$
$44$			1.04536i			0.0237581i
$45$	−60.7105	−	52.3443i	−1.34912	−	1.16321i
$46$	−10.0783			−0.219094
$47$	−37.1020	+	21.4209i	−0.789405	+	0.455763i	−0.839753	−	0.542969i	$-0.817300\pi$
$47$	−37.1020	+	21.4209i	−0.789405	+	0.455763i	0.0503482	+	0.998732i	$0.483967\pi$
$48$	18.2575	+	39.8483i	0.380365	+	0.830172i
$49$	−3.50000	+	6.06218i	−0.0714286	+	0.123718i
$50$	16.0886	+	9.28877i	0.321772	+	0.185775i
$51$	−3.31297	+	35.1530i	−0.0649602	+	0.689275i
$52$	−36.5550	−	63.3152i	−0.702982	−	1.21760i
$53$			67.4023i			1.27174i	0.771796	+	0.635870i	$0.219359\pi$
$53$			67.4023i			1.27174i	−0.771796	+	0.635870i	$0.780641\pi$
$54$	−8.96407	+	2.20980i	−0.166001	+	0.0409223i
$55$	−2.39776			−0.0435957
$56$	6.17629	−	3.56588i	0.110291	−	0.0636765i
$57$	1.05519	+	0.0994457i	0.0185121	+	0.00174466i
$58$	−0.935656	+	1.62060i	−0.0161320	+	0.0279415i
$59$	−55.9985	−	32.3308i	−0.949127	−	0.547979i	−0.0563175	−	0.998413i	$-0.517936\pi$
$59$	−55.9985	−	32.3308i	−0.949127	−	0.547979i	−0.892810	+	0.450434i	$0.851269\pi$
$60$	−94.3268	+	43.2183i	−1.57211	+	0.720304i
$61$	27.4750	+	47.5881i	0.450409	+	0.780132i	0.998411	−	0.0563451i	$-0.0179447\pi$
$61$	27.4750	+	47.5881i	0.450409	+	0.780132i	−0.548002	+	0.836477i	$0.684611\pi$
$62$		−	3.90287i		−	0.0629496i
$63$	−7.84353	−	22.4829i	−0.124501	−	0.356871i
$64$	53.0471			0.828861
$65$	145.228	−	83.8473i	2.23427	−	1.28996i
$66$	−0.159912	+	0.225152i	−0.00242291	+	0.00341139i
$67$	53.6141	−	92.8624i	0.800211	−	1.38601i	−0.119266	−	0.992862i	$-0.538054\pi$
$67$	53.6141	−	92.8624i	0.800211	−	1.38601i	0.919477	−	0.393144i	$-0.128613\pi$
$68$	39.5793	+	22.8511i	0.582049	+	0.336046i
$69$	72.0891	+	51.2006i	1.04477	+	0.742037i
$70$	4.02892	+	6.97830i	0.0575560	+	0.0996899i
$71$		−	2.36503i		−	0.0333102i	−0.999861	−	0.0166551i	$-0.994698\pi$
$71$		−	2.36503i		−	0.0333102i	0.999861	−	0.0166551i	$-0.00530174\pi$
$72$	−4.53247	+	23.8328i	−0.0629510	+	0.331012i
$73$	120.760			1.65425			0.827124	−	0.562020i	$-0.189975\pi$
$73$	120.760			1.65425			0.827124	+	0.562020i	$0.189975\pi$
$74$	−10.6376	+	6.14165i	−0.143752	+	0.0829952i
$75$	−67.8906	−	148.176i	−0.905208	−	1.97568i
$76$	0.685924	−	1.18805i	0.00902531	−	0.0156323i
$77$	−0.616835	−	0.356130i	−0.00801084	−	0.00462506i
$78$	1.81222	−	19.2289i	0.0232335	−	0.246525i
$79$	−9.18745	−	15.9131i	−0.116297	−	0.201432i	0.802001	−	0.597323i	$-0.203769\pi$
$79$	−9.18745	−	15.9131i	−0.116297	−	0.201432i	−0.918297	+	0.395891i	$0.870436\pi$
$80$			130.132i			1.62665i
$81$	75.3454	+	29.7334i	0.930190	+	0.367079i
$82$	11.2773			0.137528
$83$	−98.3488	+	56.7817i	−1.18493	+	0.684117i	−0.957149	−	0.289596i	$-0.906479\pi$
$83$	−98.3488	+	56.7817i	−1.18493	+	0.684117i	−0.227777	+	0.973713i	$0.573146\pi$
$84$	−30.6850	−	2.89189i	−0.365297	−	0.0344272i
$85$	−52.4142	+	90.7841i	−0.616638	+	1.06805i
$86$	−6.99274	−	4.03726i	−0.0813109	−	0.0469449i
$87$	14.9257	−	6.83861i	0.171560	−	0.0786048i
$88$	0.362833	+	0.628446i	0.00412311	+	0.00714143i
$89$			24.4587i			0.274817i	0.990514	+	0.137408i	$0.0438773\pi$
$89$			24.4587i			0.274817i	−0.990514	+	0.137408i	$0.956123\pi$
$90$	−26.9276	−	5.12103i	−0.299195	−	0.0569003i
$91$	49.8139			0.547405
$92$	99.1157	−	57.2245i	1.07734	−	0.622005i
$93$	−19.8276	+	27.9168i	−0.213200	+	0.300181i
$94$	−7.32469	+	12.6867i	−0.0779223	+	0.134965i
$95$	2.72507	+	1.57332i	0.0286850	+	0.0165613i
$96$	38.5914	+	27.4092i	0.401994	+	0.285512i
$97$	−81.7611	−	141.614i	−0.842898	−	1.45994i	−0.887434	−	0.460934i	$-0.847514\pi$
$97$	−81.7611	−	141.614i	−0.842898	−	1.45994i	0.0445362	−	0.999008i	$-0.485819\pi$
$98$			2.39359i			0.0244244i
$99$	2.28766	−	0.798090i	0.0231077	−	0.00806151i
$100$	−210.966			−2.10966
$101$	−65.6045	+	37.8768i	−0.649549	+	0.375017i	−0.788283	−	0.615312i	$-0.789030\pi$
$101$	−65.6045	+	37.8768i	−0.649549	+	0.375017i	0.138734	+	0.990330i	$0.455697\pi$
$102$	5.02908	+	10.9763i	0.0493047	+	0.107611i
$103$	26.4860	−	45.8751i	0.257146	−	0.445389i	−0.708330	−	0.705881i	$-0.750551\pi$
$103$	26.4860	−	45.8751i	0.257146	−	0.445389i	0.965476	+	0.260492i	$0.0838847\pi$
$104$	−43.9522	−	25.3758i	−0.422617	−	0.243998i
$105$	6.63319	−	70.3829i	0.0631733	−	0.670314i
$106$	11.5238	+	19.9599i	0.108715	+	0.188301i
$107$		−	103.882i		−	0.970863i	−0.874275	−	0.485431i	$-0.838663\pi$
$107$		−	103.882i		−	0.970863i	0.874275	−	0.485431i	$-0.161337\pi$
$108$	75.6103	−	72.6302i	0.700096	−	0.672502i
$109$	−45.5381			−0.417780			−0.208890	−	0.977939i	$-0.566985\pi$
$109$	−45.5381			−0.417780			−0.208890	+	0.977939i	$0.566985\pi$
$110$	−0.710051	+	0.409948i	−0.00645501	+	0.00372680i
$111$	107.291	+	10.1116i	0.966586	+	0.0910952i
$112$	−19.3280	+	33.4770i	−0.172571	+	0.298902i
$113$	−97.1815	−	56.1077i	−0.860013	−	0.496529i	0.00400362	−	0.999992i	$-0.498726\pi$
$113$	−97.1815	−	56.1077i	−0.860013	−	0.496529i	−0.864017	+	0.503463i	$0.832059\pi$
$114$	0.329476	−	0.150958i	0.00289014	−	0.00132419i
$115$	131.257	+	227.344i	1.14137	+	1.97691i
$116$		−	21.2505i		−	0.183194i
$117$	−110.651	+	128.336i	−0.945732	+	1.09689i
$118$	−22.1105			−0.187377
$119$	−26.9675	+	15.5697i	−0.226618	+	0.130838i
$120$	−41.7066	+	58.7218i	−0.347555	+	0.489348i
$121$	−60.4638	+	104.726i	−0.499701	+	0.865507i
$122$	16.2724	+	9.39485i	0.133380	+	0.0770069i
$123$	−80.6651	−	57.2916i	−0.655814	−	0.465786i
$124$	22.1604	+	38.3830i	0.178713	+	0.309540i
$125$		−	261.229i		−	2.08983i
$126$	−6.16663	−	5.31684i	−0.0489415	−	0.0421972i
$127$	−139.729			−1.10023			−0.550113	−	0.835090i	$-0.685415\pi$
$127$	−139.729			−1.10023			−0.550113	+	0.835090i	$0.685415\pi$
$128$	70.3661	−	40.6259i	0.549735	−	0.317390i
$129$	29.5079	+	64.4030i	0.228743	+	0.499248i
$130$	28.6709	−	49.6594i	0.220545	−	0.381996i
$131$	22.9642	+	13.2584i	0.175299	+	0.101209i	0.585082	−	0.810974i	$-0.301062\pi$
$131$	22.9642	+	13.2584i	0.175299	+	0.101209i	−0.409783	+	0.912183i	$0.634396\pi$
$132$	0.294253	−	3.12224i	0.00222919	−	0.0236533i
$133$	0.467357	+	0.809486i	0.00351396	+	0.00608636i
$134$		−	36.6659i		−	0.273626i
$135$	166.594	+	173.429i	1.23403	+	1.28466i
$136$	31.7256			0.233276
$137$	−16.5608	+	9.56137i	−0.120882	+	0.0697910i	−0.559222	−	0.829018i	$-0.688900\pi$
$137$	−16.5608	+	9.56137i	−0.120882	+	0.0697910i	0.438340	+	0.898809i	$0.355567\pi$
$138$	30.1016	+	2.83690i	0.218127	+	0.0205573i
$139$	−73.6084	+	127.494i	−0.529557	+	0.917220i	0.469849	+	0.882747i	$0.344309\pi$
$139$	−73.6084	+	127.494i	−0.529557	+	0.917220i	−0.999406	+	0.0344727i	$0.989025\pi$
$140$	−79.2452	−	45.7522i	−0.566037	−	0.326802i
$141$	116.845	−	53.5354i	0.828686	−	0.379684i
$142$	−0.404351	−	0.700357i	−0.00284754	−	0.00493209i
$143$			5.06863i			0.0354450i
$144$	−43.3142	−	124.157i	−0.300793	−	0.862199i
$145$	48.7429			0.336158
$146$	35.7607	−	20.6465i	0.244937	−	0.141414i
$147$	12.1601	−	17.1211i	0.0827217	−	0.116470i
$148$	69.7442	−	120.801i	0.471245	−	0.816220i
$149$	56.6131	+	32.6856i	0.379954	+	0.219366i	0.677798	−	0.735248i	$-0.262934\pi$
$149$	56.6131	+	32.6856i	0.379954	+	0.219366i	−0.297844	+	0.954614i	$0.596268\pi$
$150$	−45.4383	−	32.2721i	−0.302922	−	0.215147i
$151$	−14.3658	−	24.8824i	−0.0951380	−	0.164784i	0.814528	−	0.580124i	$-0.196996\pi$
$151$	−14.3658	−	24.8824i	−0.0951380	−	0.164784i	−0.909666	+	0.415340i	$0.863663\pi$
$152$		−	0.952309i		−	0.00626519i
$153$	19.7901	−	104.061i	0.129347	−	0.680139i
$154$	−0.243551			−0.00158150
$155$	−88.0400	+	50.8299i	−0.568000	+	0.327935i
$156$	91.3590	+	199.397i	0.585635	+	1.27819i
$157$	15.2370	−	26.3912i	0.0970507	−	0.168097i	−0.813412	−	0.581688i	$-0.802392\pi$
$157$	15.2370	−	26.3912i	0.0970507	−	0.168097i	0.910463	+	0.413591i	$0.135726\pi$
$158$	−5.44137	−	3.14157i	−0.0344390	−	0.0198834i
$159$	18.9728	−	201.315i	0.119326	−	1.26613i
$160$	70.2659	+	121.704i	0.439162	+	0.760650i
$161$			77.9803i			0.484350i
$162$	27.3956	−	4.07690i	0.169109	−	0.0251661i
$163$	59.6880			0.366184			0.183092	−	0.983096i	$-0.441389\pi$
$163$	59.6880			0.366184			0.183092	+	0.983096i	$0.441389\pi$
$164$	−110.907	+	64.0322i	−0.676262	+	0.390440i
$165$	7.16156	+	0.674936i	0.0434034	+	0.00409052i
$166$	−19.4161	+	33.6296i	−0.116964	+	0.202588i
$167$	279.108	+	161.143i	1.67131	+	0.964929i	0.966908	+	0.255125i	$0.0821165\pi$
$167$	279.108	+	161.143i	1.67131	+	0.964929i	0.704399	+	0.709805i	$0.251217\pi$
$168$	−19.4509	+	8.91192i	−0.115779	+	0.0530471i
$169$	−92.7446	−	160.638i	−0.548785	−	0.950523i
$170$			35.8452i			0.210854i
$171$	−3.12361	−	0.594042i	−0.0182667	−	0.00347393i
$172$	91.6938			0.533103
$173$	−231.968	+	133.927i	−1.34086	+	0.774144i	−0.986933	−	0.161131i	$-0.948486\pi$
$173$	−231.968	+	133.927i	−1.34086	+	0.774144i	−0.353923	+	0.935274i	$0.615153\pi$
$174$	3.25076	−	4.57699i	0.0186825	−	0.0263045i
$175$	71.8712	−	124.484i	0.410692	−	0.711340i
$176$	−3.40633	−	1.96665i	−0.0193542	−	0.0111741i
$177$	158.154	+	112.327i	0.893524	+	0.634617i
$178$	4.18173	+	7.24296i	0.0234929	+	0.0406908i
$179$		−	135.169i		−	0.755134i	−0.925982	−	0.377567i	$-0.876761\pi$
$179$		−	135.169i		−	0.755134i	0.925982	−	0.377567i	$-0.123239\pi$
$180$	293.897	−	102.531i	1.63276	−	0.569617i
$181$	−51.1768			−0.282745			−0.141372	−	0.989956i	$-0.545151\pi$
$181$	−51.1768			−0.282745			−0.141372	+	0.989956i	$0.545151\pi$
$182$	14.7514	−	8.51673i	0.0810517	−	0.0467952i
$183$	−68.6659	−	149.868i	−0.375224	−	0.818952i
$184$	39.7241	−	68.8041i	0.215892	−	0.373936i
$185$	277.083	+	159.974i	1.49775	+	0.864725i
$186$	−1.09860	+	11.6570i	−0.00590647	+	0.0626719i
$187$	−1.58424	−	2.74398i	−0.00847187	−	0.0146737i
$188$		−	166.358i		−	0.884881i
$189$	17.0982	+	69.3589i	0.0904666	+	0.366978i
$190$	1.07597			0.00566299
$191$	58.5429	−	33.7998i	0.306508	−	0.176962i	−0.338855	−	0.940839i	$-0.610040\pi$
$191$	58.5429	−	33.7998i	0.306508	−	0.176962i	0.645363	+	0.763876i	$0.276706\pi$
$192$	−158.439	−	14.9320i	−0.825204	−	0.0777708i
$193$	−138.701	+	240.238i	−0.718660	+	1.24475i	0.242871	+	0.970058i	$0.421911\pi$
$193$	−138.701	+	240.238i	−0.718660	+	1.24475i	−0.961531	+	0.274696i	$0.911423\pi$
$194$	−48.4239	−	27.9576i	−0.249608	−	0.144111i
$195$	−457.363	+	209.553i	−2.34545	+	1.07463i
$196$	−13.5908	−	23.5399i	−0.0693406	−	0.120102i
$197$		−	176.871i		−	0.897823i	−0.893576	−	0.448912i	$-0.851812\pi$
$197$		−	176.871i		−	0.897823i	0.893576	−	0.448912i	$-0.148188\pi$
$198$	0.540996	−	0.627462i	0.00273230	−	0.00316900i
$199$	−24.8351			−0.124799			−0.0623997	−	0.998051i	$-0.519875\pi$
$199$	−24.8351			−0.124799			−0.0623997	+	0.998051i	$0.519875\pi$
$200$	−126.828	+	73.2240i	−0.634139	+	0.366120i
$201$	−186.272	+	262.267i	−0.926728	+	1.30481i
$202$	−12.9517	+	22.4329i	−0.0641171	+	0.111054i
$203$	12.5393	+	7.23957i	0.0617700	+	0.0356629i
$204$	−111.782	−	79.3919i	−0.547950	−	0.389176i
$205$	−146.872	−	254.390i	−0.716450	−	1.24093i
$206$		−	18.1134i		−	0.0879289i
$207$	−200.901	−	173.216i	−0.970536	−	0.836793i
$208$	275.086			1.32253
$209$	−0.0823663	+	0.0475542i	−0.000394097	+	0.000227532i
$210$	−10.0692	−	21.9766i	−0.0479483	−	0.104651i
$211$	1.49387	−	2.58746i	0.00707996	−	0.0122629i	−0.862464	−	0.506119i	$-0.831080\pi$
$211$	1.49387	−	2.58746i	0.00707996	−	0.0122629i	0.869544	+	0.493856i	$0.164413\pi$
$212$	−226.663	−	130.864i	−1.06917	−	0.617283i
$213$	−0.665721	+	7.06378i	−0.00312545	+	0.0331633i
$214$	−17.7609	−	30.7627i	−0.0829947	−	0.143751i
$215$			210.320i			0.978235i
$216$	20.2460	−	69.9072i	0.0937316	−	0.323645i
$217$	−30.1982			−0.139162
$218$	−13.4852	+	7.78569i	−0.0618587	+	0.0357142i
$219$	−360.682	−	33.9922i	−1.64695	−	0.155216i
$220$	4.65535	−	8.06330i	0.0211607	−	0.0366514i
$221$	191.908	+	110.798i	0.868363	+	0.501350i
$222$	33.5009	−	15.3493i	0.150905	−	0.0691410i
$223$	3.69712	+	6.40359i	0.0165790	+	0.0287157i	0.874196	−	0.485573i	$-0.161389\pi$
$223$	3.69712	+	6.40359i	0.0165790	+	0.0287157i	−0.857617	+	0.514289i	$0.828056\pi$
$224$			41.7452i			0.186362i
$225$	161.064	+	461.677i	0.715840	+	2.05190i
$226$	−38.3712			−0.169784
$227$	−25.0445	+	14.4594i	−0.110328	+	0.0636980i	−0.554149	−	0.832418i	$-0.686956\pi$
$227$	−25.0445	+	14.4594i	−0.110328	+	0.0636980i	0.443821	+	0.896116i	$0.353623\pi$
$228$	−2.38311	+	3.35536i	−0.0104522	+	0.0147165i
$229$	84.0005	−	145.493i	0.366814	−	0.635341i	−0.622251	−	0.782818i	$-0.713782\pi$
$229$	84.0005	−	145.493i	0.366814	−	0.635341i	0.989066	+	0.147476i	$0.0471151\pi$
$230$	77.7385	+	44.8824i	0.337994	+	0.195141i
$231$	1.74210	+	1.23731i	0.00754154	+	0.00535630i
$232$	−7.37585	−	12.7753i	−0.0317925	−	0.0550661i
$233$			119.740i			0.513907i	0.966424	+	0.256954i	$0.0827188\pi$
$233$			119.740i			0.513907i	−0.966424	+	0.256954i	$0.917281\pi$
$234$	−10.8253	+	56.9222i	−0.0462621	+	0.243257i
$235$	381.579			1.62374
$236$	217.446	−	125.543i	0.921383	−	0.531961i
$237$	22.9614	+	50.1149i	0.0968837	+	0.211455i
$238$	−5.32394	+	9.22133i	−0.0223695	+	0.0387451i
$239$	145.941	+	84.2588i	0.610630	+	0.352547i	0.773212	−	0.634148i	$-0.218649\pi$
$239$	145.941	+	84.2588i	0.610630	+	0.352547i	−0.162582	+	0.986695i	$0.551982\pi$
$240$	36.6303	−	388.674i	0.152626	−	1.61948i
$241$	−62.7004	−	108.600i	−0.260168	−	0.450624i	0.706119	−	0.708094i	$-0.250445\pi$
$241$	−62.7004	−	108.600i	−0.260168	−	0.450624i	−0.966286	+	0.257470i	$0.917111\pi$
$242$			41.3502i			0.170869i
$243$	−216.669	−	110.015i	−0.891644	−	0.452738i
$244$	−213.375			−0.874487
$245$	53.9941	−	31.1735i	0.220384	−	0.127239i
$246$	−33.6826	−	3.17439i	−0.136921	−	0.0129040i
$247$	3.32584	−	5.76052i	0.0134649	−	0.0233220i
$248$	26.6447	+	15.3833i	0.107438	+	0.0620295i
$249$	309.728	−	141.910i	1.24389	−	0.569919i
$250$	−44.6626	−	77.3579i	−0.178650	−	0.309432i
$251$			34.3777i			0.136963i	0.997652	+	0.0684815i	$0.0218154\pi$
$251$			34.3777i			0.136963i	−0.997652	+	0.0684815i	$0.978185\pi$
$252$	90.8348	+	17.2748i	0.360456	+	0.0685507i
$253$	−7.93460			−0.0313621
$254$	−41.3779	+	23.8895i	−0.162905	+	0.0940533i
$255$	182.103	−	256.397i	0.714131	−	1.00548i
$256$	−92.2025	+	159.699i	−0.360166	+	0.623826i
$257$	−208.065	−	120.126i	−0.809590	−	0.467417i	0.0372233	−	0.999307i	$-0.488149\pi$
$257$	−208.065	−	120.126i	−0.809590	−	0.467417i	−0.846814	+	0.531890i	$0.821482\pi$
$258$	19.7492	+	14.0267i	0.0765474	+	0.0543670i
$259$	47.5205	+	82.3080i	0.183477	+	0.317792i
$260$			651.170i			2.50450i
$261$	−46.5047	+	16.2240i	−0.178179	+	0.0621607i
$262$	9.06719			0.0346076
$263$	−308.410	+	178.061i	−1.17266	+	0.677038i	−0.954306	−	0.298831i	$-0.903403\pi$
$263$	−308.410	+	178.061i	−1.17266	+	0.677038i	−0.218358	+	0.975869i	$0.570070\pi$
$264$	−0.906800	−	1.97915i	−0.00343485	−	0.00749679i
$265$	300.166	−	519.903i	1.13270	−	1.96190i
$266$	0.276797	+	0.159809i	0.00104059	+	0.000600786i
$267$	6.88477	−	73.0524i	0.0257857	−	0.273604i
$268$	208.188	+	360.592i	0.776820	+	1.34549i
$269$		−	231.361i		−	0.860078i	−0.902810	−	0.430039i	$-0.858500\pi$
$269$		−	231.361i		−	0.860078i	0.902810	−	0.430039i	$-0.141500\pi$
$270$	78.9848	+	22.8750i	0.292536	+	0.0847223i
$271$	−317.693			−1.17230			−0.586149	−	0.810203i	$-0.699357\pi$
$271$	−317.693			−1.17230			−0.586149	+	0.810203i	$0.699357\pi$
$272$	−148.922	+	85.9803i	−0.547508	+	0.316104i
$273$	−148.782	−	14.0219i	−0.544991	−	0.0513623i
$274$	−3.26943	+	5.66282i	−0.0119322	+	0.0206672i
$275$	12.6665	+	7.31299i	0.0460599	+	0.0265927i
$276$	−312.143	+	143.016i	−1.13095	+	0.518175i
$277$	−33.0785	−	57.2937i	−0.119417	−	0.206837i	0.800120	−	0.599840i	$-0.204769\pi$
$277$	−33.0785	−	57.2937i	−0.119417	−	0.206837i	−0.919537	+	0.393004i	$0.871436\pi$
$278$			50.3396i			0.181078i
$279$	67.0787	−	77.7998i	0.240425	−	0.278852i
$280$	−63.5206			−0.226859
$281$	437.977	−	252.866i	1.55864	−	0.899880i	0.561250	−	0.827646i	$-0.310321\pi$
$281$	437.977	−	252.866i	1.55864	−	0.899880i	0.997388	−	0.0722334i	$-0.0230126\pi$
$282$	25.4483	−	35.8305i	0.0902421	−	0.127059i
$283$	209.472	−	362.815i	0.740182	−	1.28203i	−0.212230	−	0.977220i	$-0.568072\pi$
$283$	209.472	−	362.815i	0.740182	−	1.28203i	0.952412	−	0.304814i	$-0.0985942\pi$
$284$	7.95321	+	4.59179i	0.0280043	+	0.0161683i
$285$	−7.69628	−	5.46621i	−0.0270045	−	0.0191797i
$286$	0.866589	+	1.50098i	0.00303003	+	0.00524817i
$287$		−	87.2572i		−	0.304032i
$288$	−107.548	−	92.7277i	−0.373431	−	0.321971i
$289$	150.477			0.520680
$290$	14.4343	−	8.33362i	0.0497733	−	0.0287366i
$291$	204.339	+	445.983i	0.702195	+	1.53259i
$292$	−234.460	+	406.097i	−0.802946	+	1.39074i
$293$	78.4211	+	45.2764i	0.267649	+	0.154527i	0.627819	−	0.778360i	$-0.283948\pi$
$293$	78.4211	+	45.2764i	0.267649	+	0.154527i	−0.360170	+	0.932887i	$0.617281\pi$
$294$	0.673762	−	7.14910i	0.00229171	−	0.0243167i
$295$	287.961	+	498.762i	0.976138	+	1.69072i
$296$		−	96.8301i		−	0.327129i
$297$	−7.05736	+	1.73976i	−0.0237621	+	0.00585779i
$298$	22.3531			0.0750105
$299$	480.583	−	277.464i	1.60730	−	0.927975i
$300$	630.104	+	59.3838i	2.10035	+	0.197946i
$301$	−31.2380	+	54.1058i	−0.103781	+	0.179753i
$302$	−8.50833	−	4.91228i	−0.0281733	−	0.0162658i
$303$	206.607	−	94.6623i	0.681871	−	0.312417i
$304$	2.58088	+	4.47021i	0.00848973	+	0.0147046i
$305$		−	489.423i		−	1.60467i
$306$	−11.9310	−	34.1993i	−0.0389902	−	0.111762i
$307$	183.384			0.597341			0.298670	−	0.954356i	$-0.403457\pi$
$307$	183.384			0.597341			0.298670	+	0.954356i	$0.403457\pi$
$308$	2.39522	−	1.38288i	0.00777668	−	0.00448987i
$309$	−92.0206	+	129.563i	−0.297801	+	0.419297i
$310$	−17.3809	+	30.1046i	−0.0560674	+	0.0971115i
$311$	−380.642	−	219.764i	−1.22393	−	0.706637i	−0.258177	−	0.966098i	$-0.583122\pi$
$311$	−380.642	−	219.764i	−1.22393	−	0.706637i	−0.965754	+	0.259461i	$0.916455\pi$
$312$	124.132	+	88.1634i	0.397859	+	0.282575i
$313$	−46.8554	−	81.1559i	−0.149698	−	0.259284i	0.781418	−	0.624008i	$-0.214497\pi$
$313$	−46.8554	−	81.1559i	−0.149698	−	0.259284i	−0.931116	+	0.364724i	$0.881163\pi$
$314$		−	10.4203i		−	0.0331857i
$315$	−39.6236	+	208.350i	−0.125789	+	0.661429i
$316$	71.3511			0.225795
$317$	106.213	−	61.3222i	0.335057	−	0.193445i	−0.323027	−	0.946390i	$-0.604700\pi$
$317$	106.213	−	61.3222i	0.335057	−	0.193445i	0.658084	+	0.752944i	$0.271367\pi$
$318$	−28.8006	−	62.8592i	−0.0905678	−	0.197670i
$319$	−0.736636	+	1.27589i	−0.00230920	+	0.00399966i
$320$	−409.175	−	236.238i	−1.27867	−	0.738242i
$321$	−29.2414	+	310.272i	−0.0910946	+	0.966580i
$322$	13.3324	+	23.0923i	0.0414049	+	0.0717153i
$323$			4.15807i			0.0128733i
$324$	−246.275	+	195.646i	−0.760107	+	0.603846i
$325$	−1022.91			−3.14741
$326$	17.6754	−	10.2049i	0.0542191	−	0.0313034i
$327$	136.011	+	12.8183i	0.415937	+	0.0391997i
$328$	−44.4499	+	76.9894i	−0.135518	+	0.234724i
$329$	98.1627	+	56.6743i	0.298367	+	0.172262i
$330$	2.23615	−	1.02455i	0.00677621	−	0.00310470i
$331$	−45.4975	−	78.8040i	−0.137455	−	0.238079i	0.789078	−	0.614293i	$-0.210559\pi$
$331$	−45.4975	−	78.8040i	−0.137455	−	0.238079i	−0.926533	+	0.376215i	$0.877226\pi$
$332$		−	440.975i		−	1.32824i
$333$	−317.607	−	60.4018i	−0.953774	−	0.181387i
$334$	110.203			0.329950
$335$	−827.099	+	477.526i	−2.46895	+	1.42545i
$336$	67.1514	−	94.5475i	0.199855	−	0.281391i
$337$	−237.627	+	411.582i	−0.705125	+	1.22131i	0.261521	+	0.965198i	$0.415776\pi$
$337$	−237.627	+	411.582i	−0.705125	+	1.22131i	−0.966646	+	0.256115i	$0.917558\pi$
$338$	−54.9290	−	31.7133i	−0.162512	−	0.0938262i
$339$	274.465	+	194.936i	0.809630	+	0.575032i
$340$	−203.528	−	352.521i	−0.598613	−	1.03683i
$341$		−	3.07271i		−	0.00901088i
$342$	−1.02656	+	0.358133i	−0.00300164	+	0.00104717i
$343$	18.5203			0.0539949
$344$	55.1243	−	31.8260i	0.160245	−	0.0925175i
$345$	−328.040	−	715.971i	−0.950842	−	2.07528i
$346$	−45.7952	+	79.3197i	−0.132356	+	0.229248i
$347$	346.315	+	199.945i	0.998025	+	0.576210i	0.907663	−	0.419699i	$-0.137864\pi$
$347$	346.315	+	199.945i	0.998025	+	0.576210i	0.0903618	+	0.995909i	$0.471198\pi$
$348$	−5.98172	+	63.4704i	−0.0171888	+	0.182386i
$349$	120.727	+	209.105i	0.345922	+	0.599154i	0.985521	−	0.169555i	$-0.0542330\pi$
$349$	120.727	+	209.105i	0.345922	+	0.599154i	−0.639599	+	0.768709i	$0.720900\pi$
$350$		−	49.1515i		−	0.140433i
$351$	366.612	−	352.162i	1.04448	−	1.00331i
$352$	−4.24763			−0.0120671
$353$	68.1235	−	39.3311i	0.192985	−	0.111420i	−0.400394	−	0.916343i	$-0.631127\pi$
$353$	68.1235	−	39.3311i	0.192985	−	0.111420i	0.593379	+	0.804923i	$0.297794\pi$
$354$	66.0388	+	6.22378i	0.186550	+	0.0175813i
$355$	−10.5323	+	18.2425i	−0.0296685	+	0.0513873i
$356$	−82.2507	−	47.4875i	−0.231041	−	0.133392i
$357$	84.9284	−	38.9121i	0.237895	−	0.108998i
$358$	−23.1100	−	40.0277i	−0.0645530	−	0.111809i
$359$			579.149i			1.61323i	0.591079	+	0.806614i	$0.298702\pi$
$359$			579.149i			1.61323i	−0.591079	+	0.806614i	$0.701298\pi$
$360$	141.097	−	163.648i	0.391936	−	0.454579i
$361$	−360.875			−0.999654
$362$	−15.1550	+	8.74975i	−0.0418647	+	0.0241706i
$363$	210.070	−	295.773i	0.578705	−	0.814802i
$364$	−96.7156	+	167.516i	−0.265702	+	0.460210i
$365$	−931.475	−	537.788i	−2.55199	−	1.47339i
$366$	−45.9572	−	32.6406i	−0.125566	−	0.0891821i
$367$	−94.4370	−	163.570i	−0.257321	−	0.445694i	0.708202	−	0.706010i	$-0.249507\pi$
$367$	−94.4370	−	163.570i	−0.257321	−	0.445694i	−0.965523	+	0.260316i	$0.916173\pi$
$368$			430.629i			1.17019i
$369$	224.801	+	193.823i	0.609217	+	0.525265i
$370$	109.404			0.295686
$371$	154.438	−	89.1648i	0.416275	−	0.240336i
$372$	−55.3837	−	120.879i	−0.148881	−	0.324943i
$373$	−13.7846	+	23.8757i	−0.0369561	+	0.0640099i	−0.883912	−	0.467653i	$-0.845100\pi$
$373$	−13.7846	+	23.8757i	−0.0369561	+	0.0640099i	0.846956	+	0.531663i	$0.178433\pi$
$374$	−0.938283	−	0.541718i	−0.00250878	−	0.00144844i
$375$	−73.5323	+	780.230i	−0.196086	+	2.08061i
$376$	−57.7411	−	100.011i	−0.153567	−	0.265985i
$377$		−	103.038i		−	0.273309i
$378$	16.9216	+	17.6160i	0.0447663	+	0.0466031i
$379$	9.25701			0.0244248			0.0122124	−	0.999925i	$-0.496113\pi$
$379$	9.25701			0.0244248			0.0122124	+	0.999925i	$0.496113\pi$
$380$	−10.5817	+	6.10932i	−0.0278465	+	0.0160772i
$381$	417.337	+	39.3316i	1.09537	+	0.103233i
$382$	11.5576	−	20.0183i	0.0302554	−	0.0524039i
$383$	419.680	+	242.302i	1.09577	+	0.632643i	0.935107	−	0.354366i	$-0.115303\pi$
$383$	419.680	+	242.302i	1.09577	+	0.632643i	0.160663	+	0.987009i	$0.448637\pi$
$384$	−221.603	+	101.533i	−0.577090	+	0.264409i
$385$	3.17194	+	5.49397i	0.00823882	+	0.0142700i
$386$			94.8556i			0.245740i
$387$	−70.0046	−	200.663i	−0.180891	−	0.518508i
$388$	634.969			1.63652
$389$	323.477	−	186.759i	0.831559	−	0.480101i	−0.0228270	−	0.999739i	$-0.507267\pi$
$389$	323.477	−	186.759i	0.831559	−	0.480101i	0.854386	+	0.519638i	$0.173933\pi$
$390$	−99.6116	+	140.251i	−0.255414	+	0.359617i
$391$	−173.447	+	300.420i	−0.443599	+	0.768336i
$392$	−16.3409	−	9.43444i	−0.0416860	−	0.0240674i
$393$	−64.8566	−	46.0638i	−0.165030	−	0.117211i
$394$	−30.2398	−	52.3769i	−0.0767509	−	0.132936i
$395$			163.660i			0.414329i
$396$	−1.75773	+	9.24257i	−0.00443871	+	0.0233398i
$397$	−35.3647			−0.0890800			−0.0445400	−	0.999008i	$-0.514182\pi$
$397$	−35.3647			−0.0890800			−0.0445400	+	0.999008i	$0.514182\pi$
$398$	−7.35442	+	4.24608i	−0.0184784	+	0.0106685i
$399$	−1.16803	−	2.54930i	−0.00292739	−	0.00638922i
$400$	396.893	−	687.438i	0.992232	−	1.71860i
$401$	−283.905	−	163.912i	−0.707992	−	0.408759i	0.102325	−	0.994751i	$-0.467372\pi$
$401$	−283.905	−	163.912i	−0.707992	−	0.408759i	−0.810317	+	0.585992i	$0.800705\pi$
$402$	−10.3209	+	109.512i	−0.0256739	+	0.272419i
$403$	107.449	+	186.108i	0.266624	+	0.461806i
$404$		−	294.157i		−	0.728111i
$405$	−448.758	−	564.887i	−1.10805	−	1.39478i
$406$	4.95103			0.0121947
$407$	−8.37495	+	4.83528i	−0.0205773	+	0.0118803i
$408$	−94.7569	−	8.93030i	−0.232247	−	0.0218880i
$409$	−294.569	+	510.209i	−0.720219	+	1.24746i	0.240693	+	0.970601i	$0.422625\pi$
$409$	−294.569	+	510.209i	−0.720219	+	1.24746i	−0.960912	+	0.276854i	$0.910708\pi$
$410$	−86.9866	−	50.2218i	−0.212163	−	0.122492i
$411$	52.1545	−	23.8959i	0.126897	−	0.0581410i
$412$	102.847	+	178.136i	0.249629	+	0.432370i
$413$			171.078i			0.414233i
$414$	−89.1078	−	16.9463i	−0.215236	−	0.0409332i
$415$	1011.48			2.43729
$416$	257.270	−	148.535i	0.618438	−	0.357055i
$417$	255.739	−	360.074i	0.613282	−	0.863486i
$418$	−0.0162608	+	0.0281645i	−3.89014e−5	+	6.73792e-5i
$419$	423.706	+	244.627i	1.01123	+	0.583835i	0.911552	−	0.411185i	$-0.134885\pi$
$419$	423.706	+	244.627i	1.01123	+	0.583835i	0.0996795	+	0.995020i	$0.468218\pi$
$420$	223.808	+	158.958i	0.532877	+	0.378470i
$421$	−41.7580	−	72.3270i	−0.0991876	−	0.171798i	0.812161	−	0.583433i	$-0.198291\pi$
$421$	−41.7580	−	72.3270i	−0.0991876	−	0.171798i	−0.911349	+	0.411635i	$0.864958\pi$
$422$		−	1.02164i		−	0.00242094i
$423$	−364.057	+	127.008i	−0.860655	+	0.300254i
$424$	−181.686			−0.428506
$425$	553.768	−	319.718i	1.30298	−	0.752278i
$426$	1.01056	+	2.20562i	0.00237221	+	0.00517751i
$427$	72.6919	−	125.906i	0.170239	−	0.294862i
$428$	349.340	+	201.691i	0.816215	+	0.471242i
$429$	1.42675	−	15.1388i	0.00332575	−	0.0352886i
$430$	35.9587	+	62.2823i	0.0836249	+	0.144843i
$431$		−	535.447i		−	1.24234i	−0.783677	−	0.621169i	$-0.786658\pi$
$431$		−	535.447i		−	1.24234i	0.783677	−	0.621169i	$-0.213342\pi$
$432$	94.4210	+	383.019i	0.218567	+	0.886618i
$433$	410.836			0.948814			0.474407	−	0.880306i	$-0.342663\pi$
$433$	410.836			0.948814			0.474407	+	0.880306i	$0.342663\pi$
$434$	−8.94261	+	5.16302i	−0.0206051	+	0.0118964i
$435$	−145.584	−	13.7204i	−0.334675	−	0.0315412i
$436$	88.4139	−	153.137i	0.202784	−	0.351232i
$437$	9.01771	+	5.20638i	0.0206355	+	0.0119139i
$438$	−112.621	+	51.6000i	−0.257125	+	0.117808i
$439$	−156.041	−	270.271i	−0.355446	−	0.615651i	0.631748	−	0.775174i	$-0.282338\pi$
$439$	−156.041	−	270.271i	−0.355446	−	0.615651i	−0.987194	+	0.159523i	$0.949004\pi$
$440$		−	6.46330i		−	0.0146893i
$441$	−41.1387	+	47.7138i	−0.0932850	+	0.108195i
$442$	75.7732			0.171433
$443$	−641.013	+	370.089i	−1.44698	+	0.835415i	−0.998300	−	0.0582763i	$-0.981440\pi$
$443$	−641.013	+	370.089i	−1.44698	+	0.835415i	−0.448681	+	0.893692i	$0.648106\pi$
$444$	−242.313	+	341.171i	−0.545751	+	0.768403i
$445$	108.923	−	188.661i	0.244771	−	0.423956i
$446$	2.18966	+	1.26420i	0.00490955	+	0.00283453i
$447$	−159.889	−	113.560i	−0.357695	−	0.254049i
$448$	−70.1747	−	121.546i	−0.156640	−	0.271308i
$449$			579.639i			1.29096i	0.763779	+	0.645478i	$0.223342\pi$
$449$			579.639i			1.29096i	−0.763779	+	0.645478i	$0.776658\pi$
$450$	126.629	+	109.179i	0.281398	+	0.242621i
$451$	8.87854			0.0196863
$452$	377.363	−	217.871i	0.834874	−	0.482015i
$453$	35.9034	+	78.3616i	0.0792569	+	0.172984i
$454$	−4.94429	+	8.56376i	−0.0108905	+	0.0188629i
$455$	−384.236	−	221.839i	−0.844476	−	0.487558i
$456$	−0.268061	+	2.84432i	−0.000587854	+	0.00623755i
$457$	161.167	+	279.150i	0.352663	+	0.610831i	0.986715	−	0.162460i	$-0.0519427\pi$
$457$	161.167	+	279.150i	0.352663	+	0.610831i	−0.634052	+	0.773291i	$0.718609\pi$
$458$		−	57.4466i		−	0.125429i
$459$	−88.4003	+	305.236i	−0.192593	+	0.665002i
$460$	−1019.36			−2.21601
$461$	450.196	−	259.921i	0.976563	−	0.563819i	0.0753323	−	0.997158i	$-0.475998\pi$
$461$	450.196	−	259.921i	0.976563	−	0.563819i	0.901231	+	0.433340i	$0.142665\pi$
$462$	0.727431	+	0.0685562i	0.00157453	+	0.000148390i
$463$	−48.0249	+	83.1815i	−0.103725	+	0.179658i	−0.913217	−	0.407474i	$-0.866410\pi$
$463$	−48.0249	+	83.1815i	−0.103725	+	0.179658i	0.809491	+	0.587132i	$0.199743\pi$
$464$	69.2456	+	39.9790i	0.149236	+	0.0861615i
$465$	277.263	−	127.035i	0.596264	−	0.273194i
$466$	20.4721	+	35.4588i	0.0439316	+	0.0760918i
$467$			777.866i			1.66567i	0.553525	+	0.832833i	$0.313282\pi$
$467$			777.866i			1.66567i	−0.553525	+	0.832833i	$0.686718\pi$
$468$	−216.740	−	621.269i	−0.463121	−	1.32750i
$469$	−283.699			−0.604903
$470$	112.997	−	65.2389i	0.240419	−	0.138806i
$471$	−52.9379	+	74.5353i	−0.112395	+	0.158249i
$472$	87.1493	−	150.947i	0.184638	−	0.319803i
$473$	−5.50534	−	3.17851i	−0.0116392	−	0.00671989i
$474$	15.3678	+	10.9148i	0.0324215	+	0.0230270i
$475$	−9.59700	−	16.6225i	−0.0202042	−	0.0349947i
$476$		−	120.917i		−	0.254027i
$477$	−113.334	+	595.939i	−0.237598	+	1.24935i
$478$	57.6233			0.120551
$479$	−72.6253	+	41.9303i	−0.151619	+	0.0875371i	−0.573890	−	0.818932i	$-0.694566\pi$
$479$	−72.6253	+	41.9303i	−0.151619	+	0.0875371i	0.422271	+	0.906469i	$0.361233\pi$
$480$	−175.610	−	383.280i	−0.365854	−	0.798501i
$481$	338.169	−	585.726i	0.703054	−	1.21773i
$482$	−37.1350	−	21.4399i	−0.0770436	−	0.0444811i
$483$	21.9503	−	232.909i	0.0454458	−	0.482213i
$484$	−234.785	−	406.660i	−0.485094	−	0.840207i
$485$			1456.44i			3.00298i
$486$	−82.9718	+	4.46528i	−0.170724	+	0.00918782i
$487$	−602.252			−1.23666			−0.618328	−	0.785920i	$-0.712190\pi$
$487$	−602.252			−1.23666			−0.618328	+	0.785920i	$0.712190\pi$
$488$	−128.276	+	74.0603i	−0.262861	+	0.151763i
$489$	−178.274	−	16.8013i	−0.364568	−	0.0343585i
$490$	10.6595	−	18.4628i	0.0217541	−	0.0376793i
$491$	−449.656	−	259.609i	−0.915796	−	0.528735i	−0.0335043	−	0.999439i	$-0.510667\pi$
$491$	−449.656	−	259.609i	−0.915796	−	0.528735i	−0.882291	+	0.470704i	$0.844000\pi$
$492$	349.277	−	160.030i	0.709913	−	0.325265i
$493$	32.2052	+	55.7810i	0.0653249	+	0.113146i
$494$		−	2.27449i		−	0.00460423i
$495$	−21.1999	−	4.03175i	−0.0428281	−	0.00814495i
$496$	−166.763			−0.336216
$497$	−5.41896	+	3.12864i	−0.0109033	+	0.00629504i
$498$	67.4574	−	94.9783i	0.135457	−	0.190720i
$499$	386.293	−	669.079i	0.774134	−	1.34084i	−0.161146	−	0.986931i	$-0.551519\pi$
$499$	386.293	−	669.079i	0.774134	−	1.34084i	0.935280	−	0.353909i	$-0.115148\pi$
$500$	878.473	+	507.187i	1.75695	+	1.01437i
$501$	−788.271	−	559.862i	−1.57340	−	1.11749i
$502$	5.87760	+	10.1803i	0.0117084	+	0.0202795i
$503$		−	322.324i		−	0.640803i	−0.947282	−	0.320401i	$-0.896182\pi$
$503$		−	322.324i		−	0.640803i	0.947282	−	0.320401i	$-0.103818\pi$
$504$	60.6038	−	21.1427i	0.120246	−	0.0419497i
$505$	674.715			1.33607
$506$	−2.34968	+	1.35659i	−0.00464363	+	0.00268100i
$507$	231.789	+	505.895i	0.457177	+	0.997821i
$508$	271.289	−	469.885i	0.534032	−	0.924971i
$509$	−652.096	−	376.488i	−1.28113	−	0.739662i	−0.304076	−	0.952648i	$-0.598348\pi$
$509$	−652.096	−	376.488i	−1.28113	−	0.739662i	−0.977055	+	0.212986i	$0.931681\pi$
$510$	10.0899	−	107.061i	0.0197842	−	0.209924i
$511$	−159.751	−	276.696i	−0.312623	−	0.541480i
$512$			388.063i			0.757935i
$513$	9.16229	+	2.65352i	0.0178602	+	0.00517255i
$514$	−82.1524			−0.159830
$515$	−408.596	+	235.903i	−0.793391	+	0.458064i
$516$	−273.868	−	25.8105i	−0.530752	−	0.0500203i
$517$	−5.76668	+	9.98819i	−0.0111541	+	0.0193195i
$518$	28.1446	+	16.2493i	0.0543331	+	0.0313692i
$519$	730.533	−	334.712i	1.40758	−	0.644918i
$520$	226.015	+	391.469i	0.434644	+	0.752825i
$521$		−	168.877i		−	0.324141i	−0.986779	−	0.162070i	$-0.948183\pi$
$521$		−	168.877i		−	0.324141i	0.986779	−	0.162070i	$-0.0518172\pi$
$522$	−10.9976	+	12.7554i	−0.0210682	+	0.0244355i
$523$	355.192			0.679143			0.339571	−	0.940580i	$-0.389718\pi$
$523$	355.192			0.679143			0.339571	+	0.940580i	$0.389718\pi$
$524$	−89.1717	+	51.4833i	−0.170175	+	0.0982506i
$525$	−249.703	+	351.575i	−0.475625	+	0.669667i
$526$	−60.8865	+	105.458i	−0.115754	+	0.200491i
$527$	−116.339	−	67.1682i	−0.220757	−	0.127454i
$528$	9.62034	+	6.83275i	0.0182203	+	0.0129408i
$529$	169.852	+	294.192i	0.321081	+	0.556129i
$530$		−	205.279i		−	0.387319i
$531$	−440.750	−	380.013i	−0.830037	−	0.715655i
$532$	−3.62957			−0.00682249
$533$	−537.755	+	310.473i	−1.00892	+	0.582501i
$534$	−10.4510	−	22.8101i	−0.0195712	−	0.0427156i
$535$	−462.625	+	801.290i	−0.864719	+	1.49774i
$536$	250.316	+	144.520i	0.467007	+	0.269627i
$537$	−38.0481	+	403.718i	−0.0708532	+	0.751803i
$538$	−39.5560	−	68.5130i	−0.0735242	−	0.127348i
$539$			1.88446i			0.00349622i
$540$	−906.664	+	223.509i	−1.67901	+	0.413905i
$541$	−460.295			−0.850822			−0.425411	−	0.905000i	$-0.639871\pi$
$541$	−460.295			−0.850822			−0.425411	+	0.905000i	$0.639871\pi$
$542$	−94.0785	+	54.3162i	−0.173577	+	0.100214i
$543$	152.853	+	14.4055i	0.281497	+	0.0265295i
$544$	−92.8515	+	160.823i	−0.170683	+	0.295631i
$545$	351.255	+	202.797i	0.644505	+	0.372105i
$546$	−46.4563	+	21.2852i	−0.0850849	+	0.0389838i
$547$	−119.739	−	207.394i	−0.218901	−	0.379148i	0.735571	−	0.677448i	$-0.236914\pi$
$547$	−119.739	−	207.394i	−0.218901	−	0.379148i	−0.954472	+	0.298300i	$0.903581\pi$
$548$		−	74.2550i		−	0.135502i
$549$	162.903	+	466.949i	0.296727	+	0.850545i
$550$	5.00123			0.00909315
$551$	1.67438	−	0.966705i	0.00303881	−	0.00175446i
$552$	−138.014	+	194.320i	−0.250025	+	0.352029i
$553$	−24.3077	+	42.1022i	−0.0439561	+	0.0761342i
$554$	−19.5911	−	11.3109i	−0.0353630	−	0.0204169i
$555$	−782.552	−	555.800i	−1.41000	−	1.00144i
$556$	−285.827	−	495.067i	−0.514078	−	0.890408i
$557$		−	495.790i		−	0.890107i	−0.895504	−	0.445053i	$-0.853185\pi$
$557$		−	495.790i		−	0.890107i	0.895504	−	0.445053i	$-0.146815\pi$
$558$	6.56254	−	34.5074i	0.0117608	−	0.0618412i
$559$	444.596			0.795342
$560$	298.170	−	172.149i	0.532447	−	0.307408i
$561$	3.95936	+	8.64157i	0.00705768	+	0.0154039i
$562$	86.4656	−	149.763i	0.153853	−	0.266482i
$563$	47.3877	+	27.3593i	0.0841699	+	0.0485955i	0.541494	−	0.840704i	$-0.317859\pi$
$563$	47.3877	+	27.3593i	0.0841699	+	0.0485955i	−0.457324	+	0.889300i	$0.651192\pi$
$564$	−46.8273	+	496.871i	−0.0830271	+	0.880978i
$565$	499.735	+	865.567i	0.884488	+	1.53198i
$566$		−	143.254i		−	0.253099i
$567$	−31.5447	−	211.972i	−0.0556345	−	0.373847i
$568$	6.37506			0.0112237
$569$	100.237	−	57.8721i	0.176164	−	0.101708i	−0.409325	−	0.912389i	$-0.634236\pi$
$569$	100.237	−	57.8721i	0.176164	−	0.101708i	0.585489	+	0.810680i	$0.300902\pi$
$570$	−3.21367	−	0.302870i	−0.00563801	−	0.000531350i
$571$	−150.608	+	260.861i	−0.263762	+	0.456850i	−0.967239	−	0.253869i	$-0.918297\pi$
$571$	−150.608	+	260.861i	−0.263762	+	0.456850i	0.703476	+	0.710719i	$0.251630\pi$
$572$	−17.0450	−	9.84094i	−0.0297990	−	0.0172044i
$573$	−184.368	+	84.4730i	−0.321759	+	0.147422i
$574$	−14.9184	−	25.8395i	−0.0259903	−	0.0450166i
$575$		−	1601.30i		−	2.78486i
$576$	469.018	+	89.1967i	0.814267	+	0.154855i
$577$	829.819			1.43816			0.719080	−	0.694927i	$-0.244563\pi$
$577$	829.819			1.43816			0.719080	+	0.694927i	$0.244563\pi$
$578$	44.5607	−	25.7271i	0.0770946	−	0.0445106i
$579$	481.892	−	678.491i	0.832283	−	1.17183i
$580$	−94.6362	+	163.915i	−0.163166	+	0.282611i
$581$	260.207	+	150.230i	0.447860	+	0.258572i
$582$	136.761	+	97.1333i	0.234985	+	0.166896i
$583$	9.07264	+	15.7143i	0.0155620	+	0.0269542i
$584$			325.515i			0.557389i
$585$	1425.02	−	497.143i	2.43593	−	0.849817i
$586$	30.9638			0.0528393
$587$	−726.950	+	419.705i	−1.23842	+	0.714999i	−0.968770	−	0.247961i	$-0.920240\pi$
$587$	−726.950	+	419.705i	−1.23842	+	0.714999i	−0.269645	+	0.962960i	$0.586906\pi$
$588$	33.9663	+	74.1337i	0.0577658	+	0.126078i
$589$	−2.01619	+	3.49215i	−0.00342308	+	0.00592894i
$590$	170.548	+	98.4658i	0.289064	+	0.166891i
$591$	−49.7867	+	528.273i	−0.0842415	+	0.893863i
$592$	262.422	+	454.528i	0.443280	+	0.767784i
$593$		−	238.642i		−	0.402432i	−0.979547	−	0.201216i	$-0.935511\pi$
$593$		−	238.642i		−	0.402432i	0.979547	−	0.201216i	$-0.0644893\pi$
$594$	−1.79245	+	1.72180i	−0.00301759	+	0.00289865i
$595$	277.350			0.466134
$596$	−219.833	+	126.921i	−0.368847	+	0.212954i
$597$	74.1765	+	6.99072i	0.124249	+	0.0117097i
$598$	94.8767	−	164.331i	0.158657	−	0.274802i
$599$	−622.617	−	359.468i	−1.03943	−	0.600113i	−0.119756	−	0.992803i	$-0.538211\pi$
$599$	−622.617	−	359.468i	−1.03943	−	0.600113i	−0.919671	+	0.392690i	$0.871544\pi$
$600$	399.416	−	183.003i	0.665694	−	0.305005i
$601$	−533.634	−	924.281i	−0.887910	−	1.53790i	−0.842342	−	0.538943i	$-0.818824\pi$
$601$	−533.634	−	924.281i	−0.887910	−	1.53790i	−0.0455677	−	0.998961i	$-0.514510\pi$
$602$			21.3632i			0.0354870i
$603$	630.176	−	730.896i	1.04507	−	1.21210i
$604$	111.567			0.184714
$605$	932.767	−	538.533i	1.54176	−	0.890138i
$606$	44.9981	−	63.3562i	0.0742543	−	0.104548i
$607$	−295.635	+	512.054i	−0.487042	+	0.843582i	−0.999889	−	0.0148982i	$-0.995258\pi$
$607$	−295.635	+	512.054i	−0.487042	+	0.843582i	0.512847	+	0.858480i	$0.328591\pi$
$608$	4.82745	+	2.78713i	0.00793988	+	0.00458409i
$609$	−35.4141	−	25.1525i	−0.0581513	−	0.0413014i
$610$	−83.6772	−	144.933i	−0.137176	−	0.237595i
$611$		−	806.619i		−	1.32016i
$612$	311.518	+	268.590i	0.509017	+	0.438873i
$613$	−375.965			−0.613319			−0.306660	−	0.951819i	$-0.599211\pi$
$613$	−375.965			−0.613319			−0.306660	+	0.951819i	$0.599211\pi$
$614$	54.3055	−	31.3533i	0.0884454	−	0.0510640i
$615$	367.066	+	801.146i	0.596855	+	1.30268i
$616$	0.959967	−	1.66271i	0.00155839	−	0.00269921i
$617$	1011.96	+	584.257i	1.64013	+	0.946932i	0.980784	+	0.195096i	$0.0625018\pi$
$617$	1011.96	+	584.257i	1.64013	+	0.946932i	0.659350	+	0.751836i	$0.270831\pi$
$618$	−5.09865	+	54.1003i	−0.00825024	+	0.0875410i
$619$	35.1546	+	60.8896i	0.0567926	+	0.0983677i	0.893024	−	0.450009i	$-0.148579\pi$
$619$	35.1546	+	60.8896i	0.0567926	+	0.0983677i	−0.836231	+	0.548377i	$0.815246\pi$
$620$		−	394.753i		−	0.636698i
$621$	551.286	+	573.907i	0.887739	+	0.924165i
$622$	−150.293			−0.241629
$623$	56.0419	−	32.3558i	0.0899549	−	0.0519355i
$624$	−821.618	−	77.4328i	−1.31670	−	0.124091i
$625$	−484.228	+	838.708i	−0.774765	+	1.34193i
$626$	−27.7506	−	16.0218i	−0.0443300	−	0.0255940i
$627$	0.259395	−	0.118848i	0.000413708	−	0.000189551i
$628$	59.1663	+	102.479i	0.0942138	+	0.163183i
$629$			422.789i			0.672161i
$630$	23.8881	+	68.4733i	0.0379176	+	0.108688i
$631$	−969.451			−1.53637			−0.768186	−	0.640226i	$-0.778840\pi$
$631$	−969.451			−1.53637			−0.768186	+	0.640226i	$0.778840\pi$
$632$	42.8947	−	24.7653i	0.0678714	−	0.0391856i
$633$	−5.19018	+	7.30764i	−0.00819934	+	0.0115445i
$634$	20.9686	−	36.3187i	0.0330736	−	0.0572851i
$635$	1077.79	+	622.261i	1.69730	+	0.979939i
$636$	640.153	+	454.663i	1.00653	+	0.714878i
$637$	−65.8976	−	114.138i	−0.103450	−	0.179180i
$638$			0.503774i			0.000789614i
$639$	3.97671	−	20.9105i	0.00622333	−	0.0327237i
$640$	−723.686			−1.13076
$641$	−943.411	+	544.678i	−1.47178	+	0.849732i	−0.999497	−	0.0317148i	$-0.989903\pi$
$641$	−943.411	+	544.678i	−1.47178	+	0.849732i	−0.472283	+	0.881447i	$0.656570\pi$
$642$	44.3883	+	96.8804i	0.0691406	+	0.150904i
$643$	−15.6731	+	27.1465i	−0.0243749	+	0.0422186i	−0.877956	−	0.478742i	$-0.841093\pi$
$643$	−15.6731	+	27.1465i	−0.0243749	+	0.0422186i	0.853581	+	0.520961i	$0.174426\pi$
$644$	−262.235	−	151.402i	−0.407198	−	0.235096i
$645$	59.2022	−	628.178i	0.0917863	−	0.973919i
$646$	0.710909	+	1.23133i	0.00110048	+	0.00190608i
$647$		−	415.409i		−	0.642054i	−0.947070	−	0.321027i	$-0.895972\pi$
$647$		−	415.409i		−	0.642054i	0.947070	−	0.321027i	$-0.104028\pi$
$648$	−80.1480	+	203.098i	−0.123685	+	0.313422i
$649$	−17.4074			−0.0268219
$650$	−302.915	+	174.888i	−0.466022	+	0.269058i
$651$	90.1950	+	8.50036i	0.138548	+	0.0130574i
$652$	−115.886	+	200.721i	−0.177740	+	0.307855i
$653$	−668.946	−	386.216i	−1.02442	−	0.591449i	−0.109038	−	0.994038i	$-0.534777\pi$
$653$	−668.946	−	386.216i	−1.02442	−	0.591449i	−0.915381	+	0.402589i	$0.868110\pi$
$654$	42.4687	−	19.4581i	0.0649369	−	0.0297525i
$655$	−118.089	−	204.535i	−0.180288	−	0.312268i
$656$		−	481.859i		−	0.734541i
$657$	1067.70	+	203.054i	1.62512	+	0.309062i
$658$	38.7586			0.0589037
$659$	704.509	−	406.749i	1.06906	−	0.617221i	0.141134	−	0.989991i	$-0.454925\pi$
$659$	704.509	−	406.749i	1.06906	−	0.617221i	0.927924	+	0.372770i	$0.121592\pi$
$660$	−16.1741	+	22.7728i	−0.0245063	+	0.0345042i
$661$	109.116	−	188.995i	0.165078	−	0.285923i	−0.771605	−	0.636102i	$-0.780546\pi$
$661$	109.116	−	188.995i	0.165078	−	0.285923i	0.936683	+	0.350179i	$0.113879\pi$
$662$	−26.9464	−	15.5575i	−0.0407045	−	0.0235008i
$663$	−541.997	−	384.948i	−0.817492	−	0.580615i
$664$	−153.058	−	265.105i	−0.230509	−	0.399254i
$665$		−	8.32523i		−	0.0125191i
$666$	−104.380	+	36.4148i	−0.156727	+	0.0546768i
$667$	161.298			0.241827
$668$	−1083.80	+	625.731i	−1.62245	+	0.936723i
$669$	−9.23990	−	20.1667i	−0.0138115	−	0.0301446i
$670$	−163.286	+	282.820i	−0.243711	+	0.422119i
$671$	12.8111	+	7.39650i	0.0190926	+	0.0110231i
$672$	11.7507	−	124.683i	0.0174861	−	0.185540i
$673$	358.122	+	620.286i	0.532128	+	0.921672i	0.999296	+	0.0375042i	$0.0119408\pi$
$673$	358.122	+	620.286i	0.532128	+	0.921672i	−0.467169	+	0.884168i	$0.654726\pi$
$674$			162.509i			0.241112i
$675$	−351.105	−	1424.26i	−0.520155	−	2.11001i
$676$	720.269			1.06549
$677$	−562.306	+	324.648i	−0.830585	+	0.479539i	−0.854053	−	0.520186i	$-0.825863\pi$
$677$	−562.306	+	324.648i	−0.830585	+	0.479539i	0.0234677	+	0.999725i	$0.492529\pi$
$678$	114.606	+	10.8009i	0.169035	+	0.0159306i
$679$	−216.320	+	374.676i	−0.318585	+	0.551806i
$680$	−244.713	−	141.285i	−0.359873	−	0.207773i
$681$	78.8721	−	36.1373i	0.115818	−	0.0530650i
$682$	−0.525344	−	0.909922i	−0.000770299	−	0.00133420i
$683$			952.353i			1.39437i	0.716892	+	0.697184i	$0.245564\pi$
$683$			952.353i			1.39437i	−0.716892	+	0.697184i	$0.754436\pi$
$684$	8.06228	−	9.35087i	0.0117870	−	0.0136709i
$685$	170.321			0.248643
$686$	5.48441	−	3.16643i	0.00799477	−	0.00461578i
$687$	−291.844	+	410.909i	−0.424809	+	0.598121i
$688$	−172.505	+	298.787i	−0.250734	+	0.434284i
$689$	−1099.02	−	634.521i	−1.59510	−	0.920930i
$690$	−219.553	−	155.935i	−0.318193	−	0.225993i
$691$	−294.245	−	509.647i	−0.425825	−	0.737551i	0.570672	−	0.821178i	$-0.306683\pi$
$691$	−294.245	−	509.647i	−0.425825	−	0.737551i	−0.996497	+	0.0836274i	$0.973349\pi$
$692$		−	1040.10i		−	1.50303i
$693$	−4.85495	−	4.18592i	−0.00700569	−	0.00604028i
$694$	136.739			0.197030
$695$	1135.55	−	655.609i	1.63388	−	0.943322i
$696$	18.4339	+	40.2332i	0.0264854	+	0.0578063i
$697$	194.081	−	336.159i	0.278452	−	0.482294i
$698$	71.5016	+	41.2815i	0.102438	+	0.0591425i
$699$	33.7052	−	357.636i	0.0482192	−	0.511640i
$700$	279.081	+	483.383i	0.398687	+	0.690547i
$701$		−	0.442274i		−	0.000630918i	−1.00000		0.000315459i	$-0.999900\pi$
$701$		−	0.442274i		−	0.000630918i	1.00000		0.000315459i	$-0.000100414\pi$
$702$	48.3555	−	166.966i	0.0688825	−	0.237843i
$703$	12.6909			0.0180525
$704$	12.3675	−	7.14037i	0.0175675	−	0.0101426i
$705$	−1139.69	−	107.409i	−1.61658	−	0.152353i
$706$	13.4490	−	23.2943i	0.0190495	−	0.0329948i
$707$	173.573	+	100.212i	0.245507	+	0.141743i
$708$	−684.800	+	313.759i	−0.967232	+	0.443162i
$709$	426.867	+	739.356i	0.602069	+	1.04281i	0.992507	+	0.122185i	$0.0389903\pi$
$709$	426.867	+	739.356i	0.602069	+	1.04281i	−0.390438	+	0.920629i	$0.627676\pi$
$710$			7.20288i			0.0101449i
$711$	−54.4738	−	156.145i	−0.0766158	−	0.219613i
$712$	−65.9297			−0.0925980
$713$	−291.339	+	168.205i	−0.408610	+	0.235911i
$714$	18.4970	−	26.0433i	0.0259062	−	0.0364753i
$715$	22.5724	−	39.0966i	0.0315698	−	0.0546805i
$716$	454.552	+	262.436i	0.634849	+	0.366530i
$717$	−412.173	−	292.742i	−0.574857	−	0.408287i
$718$	99.0176	+	171.504i	0.137908	+	0.238863i
$719$		−	1193.34i		−	1.65973i	−0.557968	−	0.829863i	$-0.688419\pi$
$719$		−	1193.34i		−	1.65973i	0.557968	−	0.829863i	$-0.311581\pi$
$720$	−218.812	+	1150.57i	−0.303906	+	1.59801i
$721$	−140.151			−0.194384
$722$	−106.866	+	61.6992i	−0.148014	+	0.0854559i
$723$	156.702	+	342.013i	0.216739	+	0.473047i
$724$	99.3617	−	172.100i	0.137240	−	0.237707i
$725$	−257.490	−	148.662i	−0.355159	−	0.205051i
$726$	11.6395	−	123.503i	0.0160323	−	0.170115i
$727$	268.082	+	464.331i	0.368751	+	0.638695i	0.989370	−	0.145417i	$-0.0464523\pi$
$727$	268.082	+	464.331i	0.368751	+	0.638695i	−0.620620	+	0.784112i	$0.713119\pi$
$728$			134.276i			0.184445i
$729$	616.173	+	389.579i	0.845230	+	0.534402i
$730$	−367.784			−0.503814
$731$	−240.689	+	138.962i	−0.329260	+	0.190098i
$732$	637.300	+	60.0619i	0.870629	+	0.0820518i
$733$	431.199	−	746.859i	0.588266	−	1.01891i	−0.406193	−	0.913787i	$-0.633144\pi$
$733$	431.199	−	746.859i	0.588266	−	1.01891i	0.994460	−	0.105120i	$-0.0335226\pi$
$734$	−55.9313	−	32.2920i	−0.0762007	−	0.0439945i
$735$	−170.042	+	77.9093i	−0.231350	+	0.105999i
$736$	232.521	+	402.739i	0.315926	+	0.547200i
$737$		−	28.8668i		−	0.0391680i
$738$	99.7085	+	18.9623i	0.135106	+	0.0256942i
$739$	−560.115			−0.757937			−0.378968	−	0.925410i	$-0.623721\pi$
$739$	−560.115			−0.757937			−0.378968	+	0.925410i	$0.623721\pi$
$740$	−1075.94	+	621.192i	−1.45397	+	0.839448i
$741$	−11.5550	+	16.2692i	−0.0155938	+	0.0219557i
$742$	30.4892	−	52.8088i	0.0410906	−	0.0711709i
$743$	298.646	+	172.423i	0.401946	+	0.232064i	0.687323	−	0.726352i	$-0.258786\pi$
$743$	298.646	+	172.423i	0.401946	+	0.232064i	−0.285377	+	0.958415i	$0.592119\pi$
$744$	−75.2513	−	53.4465i	−0.101144	−	0.0718367i
$745$	−291.121	−	504.236i	−0.390766	−	0.676827i
$746$			9.42709i			0.0126369i
$747$	−965.031	+	336.667i	−1.29187	+	0.450693i
$748$	12.3034			0.0164485
$749$	−238.024	+	137.423i	−0.317789	+	0.183476i
$750$	111.622	+	243.622i	0.148829	+	0.324829i
$751$	−19.3350	+	33.4893i	−0.0257457	+	0.0445929i	−0.878611	−	0.477538i	$-0.841529\pi$
$751$	−19.3350	+	33.4893i	−0.0257457	+	0.0445929i	0.852865	+	0.522131i	$0.174863\pi$
$752$	542.082	+	312.971i	0.720854	+	0.416185i
$753$	9.67684	−	102.678i	0.0128510	−	0.136359i
$754$	−17.6164	−	30.5125i	−0.0233640	−	0.0404676i
$755$			255.905i			0.338947i
$756$	−266.440	−	77.1644i	−0.352433	−	0.102069i
$757$	−613.583			−0.810546			−0.405273	−	0.914196i	$-0.632824\pi$
$757$	−613.583			−0.810546			−0.405273	+	0.914196i	$0.632824\pi$
$758$	2.74128	−	1.58268i	0.00361647	−	0.00208797i
$759$	23.6988	+	2.23348i	0.0312237	+	0.00294266i
$760$	−4.24097	+	7.34558i	−0.00558023	+	0.00966523i
$761$	231.197	+	133.482i	0.303807	+	0.175403i	0.644152	−	0.764898i	$-0.277211\pi$
$761$	231.197	+	133.482i	0.303807	+	0.175403i	−0.340345	+	0.940301i	$0.610544\pi$
$762$	130.311	−	59.7052i	0.171011	−	0.0783533i
$763$	60.2412	+	104.341i	0.0789531	+	0.136751i
$764$			262.494i			0.343579i
$765$	−616.072	+	714.538i	−0.805323	+	0.934036i
$766$	165.707			0.216327
$767$	1054.33	−	608.720i	1.37462	−	0.793637i
$768$	320.340	−	451.031i	0.417110	−	0.587280i
$769$	721.840	−	1250.26i	0.938674	−	1.62583i	0.170727	−	0.985318i	$-0.445388\pi$
$769$	721.840	−	1250.26i	0.938674	−	1.62583i	0.767947	−	0.640513i	$-0.221278\pi$
$770$	1.87862	+	1.08462i	0.00243976	+	0.00140860i
$771$	587.627	+	417.356i	0.762162	+	0.541318i
$772$	−538.588	−	932.861i	−0.697652	−	1.20837i
$773$			642.336i			0.830965i	0.909601	+	0.415483i	$0.136387\pi$
$773$			642.336i			0.830965i	−0.909601	+	0.415483i	$0.863613\pi$
$774$	−55.0380	−	47.4536i	−0.0711085	−	0.0613095i
$775$	620.109			0.800140
$776$	381.729	−	220.392i	0.491919	−	0.284010i
$777$	−118.764	−	259.211i	−0.152850	−	0.333605i
$778$	63.8608	−	110.610i	0.0820833	−	0.142172i
$779$	−10.0905	−	5.82575i	−0.0129531	−	0.00747850i
$780$	183.295	−	1944.89i	0.234994	−	2.49345i
$781$	−0.318343	−	0.551386i	−0.000407610	−	0.000706000i
$782$			118.618i			0.151685i
$783$	143.465	−	35.3667i	0.183225	−	0.0451682i
$784$	102.274			0.130452
$785$	−235.059	+	135.711i	−0.299438	+	0.172880i
$786$	−27.0816	−	2.55228i	−0.0344549	−	0.00324718i
$787$	230.924	−	399.972i	0.293423	−	0.508224i	−0.681194	−	0.732103i	$-0.738539\pi$
$787$	230.924	−	399.972i	0.293423	−	0.508224i	0.974617	+	0.223879i	$0.0718721\pi$
$788$	594.790	+	343.402i	0.754810	+	0.435790i
$789$	971.271	−	445.013i	1.23102	−	0.564021i
$790$	27.9811	+	48.4647i	0.0354191	+	0.0613477i
$791$			296.894i			0.375340i
$792$	2.15129	+	6.16652i	0.00271628	+	0.00778600i
$793$	−1034.59			−1.30465
$794$	−10.4726	+	6.04635i	−0.0131896	+	0.00761505i
$795$	−1042.87	+	1468.34i	−1.31179	+	1.84696i
$796$	48.2182	−	83.5164i	0.0605757	−	0.104920i
$797$	353.754	+	204.240i	0.443856	+	0.256261i	0.705232	−	0.708977i	$-0.250843\pi$
$797$	353.754	+	204.240i	0.443856	+	0.256261i	−0.261376	+	0.965237i	$0.584176\pi$
$798$	−0.781745	−	0.555226i	−0.000979630	−	0.000695773i
$799$	252.115	+	436.676i	0.315538	+	0.546528i
$800$		−	857.221i		−	1.07153i
$801$	−41.1264	+	216.252i	−0.0513438	+	0.269978i
$802$	−112.097			−0.139772
$803$	28.1542	−	16.2548i	0.0350613	−	0.0202426i
$804$	−520.307	−	1135.60i	−0.647148	−	1.41244i
$805$	347.274	−	601.496i	0.431396	−	0.747200i
$806$	63.6380	+	36.7414i	0.0789554	+	0.0455849i
$807$	−65.1248	+	691.021i	−0.0806998	+	0.856283i
$808$	−102.099	−	176.840i	−0.126360	−	0.218862i
$809$			1501.09i			1.85549i	0.373216	+	0.927744i	$0.378255\pi$
$809$			1501.09i			1.85549i	−0.373216	+	0.927744i	$0.621745\pi$
$810$	−229.470	−	90.5554i	−0.283297	−	0.111797i
$811$	−960.141			−1.18390			−0.591949	−	0.805975i	$-0.701641\pi$
$811$	−960.141			−1.18390			−0.591949	+	0.805975i	$0.701641\pi$
$812$	−48.6911	+	28.1118i	−0.0599644	+	0.0346205i
$813$	948.873	+	89.4259i	1.16713	+	0.109995i
$814$	−1.65338	+	2.86375i	−0.00203119	+	0.00351812i
$815$	−460.399	−	265.812i	−0.564907	−	0.326149i
$816$	468.998	−	214.884i	0.574753	−	0.263338i
$817$	4.17123	+	7.22478i	0.00510554	+	0.00884306i
$818$			201.451i			0.246273i
$819$	440.431	+	83.7602i	0.537767	+	0.102271i
$820$	1140.63			1.39101
$821$	52.9128	−	30.5492i	0.0644493	−	0.0372098i	−0.467429	−	0.884031i	$-0.654820\pi$
$821$	52.9128	−	30.5492i	0.0644493	−	0.0372098i	0.531878	+	0.846821i	$0.321486\pi$
$822$	11.3590	−	15.9932i	0.0138188	−	0.0194565i
$823$	59.1604	−	102.469i	0.0718839	−	0.124507i	−0.827843	−	0.560960i	$-0.810432\pi$
$823$	59.1604	−	102.469i	0.0718839	−	0.124507i	0.899727	+	0.436453i	$0.143766\pi$
$824$	123.659	+	71.3945i	0.150071	+	0.0866438i
$825$	−35.7733	−	25.4076i	−0.0433615	−	0.0307971i
$826$	29.2494	+	50.6615i	0.0354109	+	0.0613335i
$827$			1264.32i			1.52880i	0.644739	+	0.764402i	$0.276966\pi$
$827$			1264.32i			1.52880i	−0.644739	+	0.764402i	$0.723034\pi$
$828$	972.555	−	339.293i	1.17458	−	0.409774i
$829$	795.365			0.959427			0.479714	−	0.877425i	$-0.340741\pi$
$829$	795.365			0.959427			0.479714	+	0.877425i	$0.340741\pi$
$830$	299.529	−	172.933i	0.360878	−	0.208353i
$831$	82.6705	+	180.434i	0.0994831	+	0.217129i
$832$	−499.382	+	864.955i	−0.600219	+	1.03961i
$833$	71.3494	+	41.1936i	0.0856535	+	0.0494521i
$834$	14.1699	−	150.353i	0.0169903	−	0.180279i
$835$	−1435.26	−	2485.94i	−1.71887	−	2.97717i
$836$		−	0.369313i		−	0.000441762i
$837$	−222.248	+	213.488i	−0.265529	+	0.255063i
$838$	167.296			0.199638
$839$	927.762	−	535.643i	1.10579	−	0.638431i	0.168058	−	0.985777i	$-0.446251\pi$
$839$	927.762	−	535.643i	1.10579	−	0.638431i	0.937737	+	0.347346i	$0.112917\pi$
$840$	189.721	+	17.8801i	0.225858	+	0.0212859i
$841$	−405.525	+	702.390i	−0.482194	+	0.835185i
$842$	−24.7316	−	14.2788i	−0.0293725	−	0.0169582i
$843$	−1379.31	+	631.968i	−1.63620	+	0.749665i
$844$	5.80082	+	10.0473i	0.00687301	+	0.0119044i
$845$			1652.10i			1.95515i
$846$	−86.0938	+	99.8540i	−0.101766	+	0.118031i
$847$	319.944			0.377738
$848$	852.850	−	492.393i	1.00572	−	0.580652i
$849$	−727.770	+	1024.68i	−0.857208	+	1.20693i
$850$	109.325	−	189.357i	0.128618	−	0.222772i
$851$	916.915	+	529.381i	1.07746	+	0.622069i
$852$	−22.4619	−	15.9533i	−0.0263637	−	0.0187245i
$853$	643.378	+	1114.36i	0.754253	+	1.30640i	0.945745	+	0.324910i	$0.105334\pi$
$853$	643.378	+	1114.36i	0.754253	+	1.30640i	−0.191492	+	0.981494i	$0.561333\pi$
$854$		−	49.7129i		−	0.0582118i
$855$	21.4483	+	18.4927i	0.0250858	+	0.0216289i
$856$	280.020			0.327127
$857$	324.473	−	187.334i	0.378615	−	0.218593i	−0.298601	−	0.954378i	$-0.596520\pi$
$857$	324.473	−	187.334i	0.378615	−	0.218593i	0.677215	+	0.735785i	$0.263187\pi$
$858$	−2.16579	−	4.72699i	−0.00252424	−	0.00550932i
$859$	355.233	−	615.282i	0.413543	−	0.716277i	−0.581731	−	0.813381i	$-0.697625\pi$
$859$	355.233	−	615.282i	0.413543	−	0.716277i	0.995274	+	0.0971038i	$0.0309579\pi$
$860$	−707.274	−	408.345i	−0.822412	−	0.474820i
$861$	−24.5616	+	260.617i	−0.0285269	+	0.302691i
$862$	−91.5460	−	158.562i	−0.106202	−	0.183947i
$863$		−	1511.66i		−	1.75164i	−0.482640	−	0.875819i	$-0.660322\pi$
$863$		−	1511.66i		−	1.75164i	0.482640	−	0.875819i	$-0.339678\pi$
$864$	295.120	+	307.229i	0.341574	+	0.355589i
$865$	2385.70			2.75803
$866$	121.661	−	70.2411i	0.140486	−	0.0811098i
$867$	−449.438	−	42.3570i	−0.518383	−	0.0488547i
$868$	58.6310	−	101.552i	0.0675472	−	0.116995i
$869$	−4.28395	−	2.47334i	−0.00492975	−	0.00284619i
$870$	−45.4575	+	20.8275i	−0.0522500	+	0.0239397i
$871$	1009.44	+	1748.40i	1.15894	+	2.00735i
$872$		−	122.750i		−	0.140769i
$873$	−484.774	−	1389.57i	−0.555297	−	1.59171i
$874$	3.56056			0.00407387
$875$	−598.551	+	345.574i	−0.684059	+	0.394942i
$876$	814.588	−	1146.92i	0.929895	−	1.30927i
$877$	691.556	−	1197.81i	0.788547	−	1.36580i	−0.138310	−	0.990389i	$-0.544167\pi$
$877$	691.556	−	1197.81i	0.788547	−	1.36580i	0.926857	−	0.375415i	$-0.122500\pi$
$878$	−92.4170	−	53.3570i	−0.105259	−	0.0607710i
$879$	−221.481	−	157.304i	−0.251969	−	0.178958i
$880$	17.5164	+	30.3392i	0.0199050	+	0.0344764i
$881$		−	355.484i		−	0.403501i	−0.979437	−	0.201750i	$-0.935337\pi$
$881$		−	355.484i		−	0.403501i	0.979437	−	0.201750i	$-0.0646629\pi$
$882$	−4.02474	+	21.1630i	−0.00456320	+	0.0239944i
$883$	−260.696			−0.295238			−0.147619	−	0.989044i	$-0.547161\pi$
$883$	−260.696			−0.295238			−0.147619	+	0.989044i	$0.547161\pi$
$884$	−745.194	+	430.238i	−0.842980	+	0.486695i
$885$	−719.676	−	1570.74i	−0.813194	−	1.77485i
$886$	−126.549	+	219.189i	−0.142832	+	0.247392i
$887$	−723.191	−	417.535i	−0.815323	−	0.470727i	0.0334782	−	0.999439i	$-0.489342\pi$
$887$	−723.191	−	417.535i	−0.815323	−	0.470727i	−0.848801	+	0.528713i	$0.822675\pi$
$888$	−27.2563	+	289.209i	−0.0306940	+	0.325686i
$889$	184.844	+	320.159i	0.207923	+	0.360133i
$890$		−	74.4909i		−	0.0836976i
$891$	21.5684	−	3.20972i	0.0242069	−	0.00360238i
$892$	−28.7124			−0.0321888
$893$	13.1077	−	7.56775i	0.0146783	−	0.00847453i
$894$	−66.7636	−	6.29209i	−0.0746796	−	0.00703813i
$895$	−601.956	+	1042.62i	−0.672576	+	1.16494i
$896$	−186.171	−	107.486i	−0.207780	−	0.119962i
$897$	−1513.49	+	693.444i	−1.68728	+	0.773070i
$898$	99.1014	+	171.649i	0.110358	+	0.191146i
$899$			62.4635i			0.0694811i
$900$	−1865.26	−	354.731i	−2.07251	−	0.394145i
$901$	793.298			0.880464
$902$	2.62920	−	1.51797i	0.00291486	−	0.00168290i
$903$	108.531	−	152.808i	0.120189	−	0.169223i
$904$	151.241	−	261.958i	0.167303	−	0.289776i
$905$	394.749	+	227.909i	0.436187	+	0.251833i
$906$	24.0296	+	17.0668i	0.0265228	+	0.0188375i
$907$	−795.247	−	1377.41i	−0.876788	−	1.51864i	−0.854846	−	0.518882i	$-0.826348\pi$
$907$	−795.247	−	1377.41i	−0.876788	−	1.51864i	−0.0219419	−	0.999759i	$-0.506985\pi$
$908$		−	112.294i		−	0.123672i
$909$	−643.732	+	224.577i	−0.708176	+	0.247060i
$910$	−151.712			−0.166717
$911$	−1222.95	+	706.068i	−1.34242	+	0.775047i	−0.987162	−	0.159721i	$-0.948941\pi$
$911$	−1222.95	+	706.068i	−1.34242	+	0.775047i	−0.355259	+	0.934768i	$0.615607\pi$
$912$	−6.45017	−	14.0779i	−0.00707256	−	0.0154363i
$913$	−15.2861	+	26.4764i	−0.0167428	+	0.0289993i
$914$	95.4530	+	55.1098i	0.104434	+	0.0602952i
$915$	−137.766	+	1461.79i	−0.150564	+	1.59759i
$916$	326.180	+	564.961i	0.356092	+	0.616769i
$917$		−	70.1568i		−	0.0765068i
$918$	26.0085	+	105.504i	0.0283317	+	0.114928i
$919$	−1072.32			−1.16683			−0.583415	−	0.812175i	$-0.698284\pi$
$919$	−1072.32			−1.16683			−0.583415	+	0.812175i	$0.698284\pi$
$920$	−612.819	+	353.811i	−0.666107	+	0.384577i
$921$	−547.724	−	51.6199i	−0.594706	−	0.0560476i
$922$	88.8777	−	153.941i	0.0963967	−	0.166964i
$923$	38.5628	+	22.2642i	0.0417798	+	0.0241216i
$924$	−7.54321	+	3.45611i	−0.00816364	+	0.00374038i
$925$	−975.816	−	1690.16i	−1.05494	−	1.82720i
$926$			32.8434i			0.0354681i
$927$	311.314	−	361.071i	0.335830	−	0.389505i
$928$	86.3478			0.0930472
$929$	−42.7710	+	24.6938i	−0.0460398	+	0.0265811i	−0.522843	−	0.852429i	$-0.675129\pi$
$929$	−42.7710	+	24.6938i	−0.0460398	+	0.0265811i	0.476803	+	0.879010i	$0.341795\pi$
$930$	60.3866	−	85.0228i	0.0649319	−	0.0914224i
$931$	1.23651	−	2.14170i	0.00132815	−	0.00230043i
$932$	−402.668	−	232.481i	−0.432047	−	0.249443i
$933$	1075.03	+	763.529i	1.15223	+	0.818359i
$934$	132.992	+	230.350i	0.142390	+	0.246627i
$935$			28.2207i			0.0301826i
$936$	−345.936	−	298.265i	−0.369590	−	0.318659i
$937$	−1546.26			−1.65023			−0.825113	−	0.564968i	$-0.808889\pi$
$937$	−1546.26			−1.65023			−0.825113	+	0.564968i	$0.808889\pi$
$938$	−84.0120	+	48.5044i	−0.0895651	+	0.0517104i
$939$	117.102	+	255.583i	0.124709	+	0.272186i
$940$	−740.850	+	1283.19i	−0.788138	+	1.36510i
$941$	−63.8839	−	36.8834i	−0.0678894	−	0.0391960i	0.465671	−	0.884958i	$-0.345813\pi$
$941$	−63.8839	−	36.8834i	−0.0678894	−	0.0391960i	−0.533560	+	0.845762i	$0.679146\pi$
$942$	−2.93317	+	31.1230i	−0.00311377	+	0.0330393i
$943$	−486.024	−	841.819i	−0.515402	−	0.892703i
$944$			944.742i			1.00079i
$945$	176.994	−	611.140i	0.187295	−	0.646709i
$946$	−2.17373			−0.00229781
$947$	995.409	−	574.700i	1.05112	−	0.606863i	0.128156	−	0.991754i	$-0.459094\pi$
$947$	995.409	−	574.700i	1.05112	−	0.606863i	0.922962	+	0.384891i	$0.125761\pi$
$948$	−213.109	−	20.0843i	−0.224799	−	0.0211860i
$949$	−1136.83	+	1969.04i	−1.19792	+	2.07486i
$950$	−5.68393	−	3.28162i	−0.00598308	−	0.00345433i
$951$	−334.495	+	153.258i	−0.351730	+	0.161154i
$952$	−41.9690	−	72.6925i	−0.0440851	−	0.0763576i
$953$		−	1211.39i		−	1.27114i	−0.772045	−	0.635568i	$-0.780766\pi$
$953$		−	1211.39i		−	1.27114i	0.772045	−	0.635568i	$-0.219234\pi$
$954$	68.3266	+	195.853i	0.0716211	+	0.205296i
$955$	−602.090			−0.630460
$956$	−566.698	+	327.183i	−0.592781	+	0.342242i
$957$	2.55930	−	3.60344i	0.00267430	−	0.00376535i
$958$	−14.3377	+	24.8336i	−0.0149663	+	0.0259224i
$959$	43.8157	+	25.2970i	0.0456889	+	0.0263785i
$960$	1155.61	+	820.763i	1.20376	+	0.854962i
$961$	415.362	+	719.428i	0.432219	+	0.748624i
$962$		−	231.268i		−	0.240404i
$963$	174.674	−	918.479i	0.181386	−	0.953768i
$964$	486.941			0.505125
$965$	2139.73	−	1235.37i	2.21733	−	1.28018i
$966$	−33.3205	−	72.7243i	−0.0344933	−	0.0752839i
$967$	544.323	−	942.796i	0.562899	−	0.974970i	−0.434343	−	0.900748i	$-0.643019\pi$
$967$	544.323	−	942.796i	0.562899	−	0.974970i	0.997242	−	0.0742220i	$-0.0236473\pi$
$968$	−282.295	−	162.983i	−0.291628	−	0.168371i
$969$	1.17044	−	12.4192i	0.00120788	−	0.0128165i
$970$	249.010	+	431.298i	0.256711	+	0.444637i
$971$			336.566i			0.346617i	0.984868	+	0.173309i	$0.0554458\pi$
$971$			336.566i			0.346617i	−0.984868	+	0.173309i	$0.944554\pi$
$972$	790.636	−	515.026i	0.813412	−	0.529862i
$973$	389.499			0.400308
$974$	−178.345	+	102.968i	−0.183106	+	0.105716i
$975$	3055.19	+	287.934i	3.13353	+	0.295317i
$976$	401.425	−	695.289i	0.411296	−	0.712386i
$977$	−950.256	−	548.631i	−0.972627	−	0.561546i	−0.0725908	−	0.997362i	$-0.523127\pi$
$977$	−950.256	−	548.631i	−0.972627	−	0.561546i	−0.900036	+	0.435815i	$0.856460\pi$
$978$	−55.6649	+	25.5043i	−0.0569170	+	0.0260780i
$979$	3.29225	+	5.70234i	0.00336287	+	0.00582466i
$980$			242.098i			0.247039i
$981$	−402.626	−	76.5706i	−0.410424	−	0.0780536i
$982$	−177.542			−0.180797
$983$	−372.990	+	215.346i	−0.379440	+	0.219070i	−0.677575	−	0.735454i	$-0.736969\pi$
$983$	−372.990	+	215.346i	−0.379440	+	0.219070i	0.298134	+	0.954524i	$0.403636\pi$
$984$	154.433	−	217.437i	0.156944	−	0.220973i
$985$	−787.670	+	1364.29i	−0.799665	+	1.38506i
$986$	19.0739	+	11.0123i	0.0193447	+	0.0111687i
$987$	−277.236	−	196.904i	−0.280888	−	0.199498i
$988$	12.9145	+	22.3686i	0.0130713	+	0.0226402i
$989$			695.985i			0.703726i
$990$	−6.96725	+	2.43064i	−0.00703763	+	0.00245520i
$991$	−90.7080			−0.0915318			−0.0457659	−	0.998952i	$-0.514573\pi$
$991$	−90.7080			−0.0915318			−0.0457659	+	0.998952i	$0.514573\pi$
$992$	−155.962	+	90.0449i	−0.157220	+	0.0907711i
$993$	113.708	+	248.176i	0.114510	+	0.249926i
$994$	−1.06981	+	1.85297i	−0.00107627	+	0.00186415i
$995$	191.564	+	110.599i	0.192526	+	0.111155i
$996$	−124.128	+	1317.09i	−0.124627	+	1.32238i
$997$	−557.473	−	965.572i	−0.559151	−	0.968477i	−0.997568	−	0.0697057i	$-0.977794\pi$
$997$	−557.473	−	965.572i	−0.559151	−	0.968477i	0.438417	−	0.898772i	$-0.355539\pi$
$998$		−	264.179i		−	0.264709i
$999$	931.615	+	269.808i	0.932548	+	0.270078i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.3.r.a.50.6	yes	24
3.2	odd	2		189.3.r.a.71.7		24
7.2	even	3		441.3.n.g.410.7		24
7.3	odd	6		441.3.j.g.275.6		24
7.4	even	3		441.3.j.h.275.6		24
7.5	odd	6		441.3.n.h.410.7		24
7.6	odd	2		441.3.r.h.50.6		24
9.2	odd	6	inner	63.3.r.a.29.6	✓	24
9.4	even	3		567.3.b.a.323.13		24
9.5	odd	6		567.3.b.a.323.12		24
9.7	even	3		189.3.r.a.8.7		24
63.2	odd	6		441.3.j.h.263.7		24
63.11	odd	6		441.3.n.g.128.7		24
63.20	even	6		441.3.r.h.344.6		24
63.38	even	6		441.3.n.h.128.7		24
63.47	even	6		441.3.j.g.263.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.r.a.29.6	✓	24	9.2	odd	6	inner
63.3.r.a.50.6	yes	24	1.1	even	1	trivial
189.3.r.a.8.7		24	9.7	even	3
189.3.r.a.71.7		24	3.2	odd	2
441.3.j.g.263.7		24	63.47	even	6
441.3.j.g.275.6		24	7.3	odd	6
441.3.j.h.263.7		24	63.2	odd	6
441.3.j.h.275.6		24	7.4	even	3
441.3.n.g.128.7		24	63.11	odd	6
441.3.n.g.410.7		24	7.2	even	3
441.3.n.h.128.7		24	63.38	even	6
441.3.n.h.410.7		24	7.5	odd	6
441.3.r.h.50.6		24	7.6	odd	2
441.3.r.h.344.6		24	63.20	even	6
567.3.b.a.323.12		24	9.5	odd	6
567.3.b.a.323.13		24	9.4	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)

\(f(q)\)	\(=\)	\(q+(0.296130 - 0.170971i) q^{2} +(-2.98677 - 0.281486i) q^{3} +(-1.94154 + 3.36284i) q^{4} +(-7.71344 - 4.45336i) q^{5} +(-0.932598 + 0.427294i) q^{6} +(-1.32288 - 2.29129i) q^{7} +2.69555i q^{8} +(8.84153 + 1.68146i) q^{9} +O(q^{10})\)	\(q+(0.296130 - 0.170971i) q^{2} +(-2.98677 - 0.281486i) q^{3} +(-1.94154 + 3.36284i) q^{4} +(-7.71344 - 4.45336i) q^{5} +(-0.932598 + 0.427294i) q^{6} +(-1.32288 - 2.29129i) q^{7} +2.69555i q^{8} +(8.84153 + 1.68146i) q^{9} -3.04558 q^{10} +(0.233142 - 0.134604i) q^{11} +(6.74551 - 9.49750i) q^{12} +(-9.41394 + 16.3054i) q^{13} +(-0.783487 - 0.452347i) q^{14} +(21.7847 + 15.4723i) q^{15} +(-7.30529 - 12.6531i) q^{16} -11.7696i q^{17} +(2.90573 - 1.01371i) q^{18} -0.353289 q^{19} +(29.9519 - 17.2927i) q^{20} +(3.30615 + 7.21591i) q^{21} +(0.0460269 - 0.0797209i) q^{22} +(-25.5250 - 14.7369i) q^{23} +(0.758760 - 8.05099i) q^{24} +(27.1647 + 47.0507i) q^{25} +6.43804i q^{26} +(-25.9343 - 7.51090i) q^{27} +10.2737 q^{28} +(-4.73941 + 2.73630i) q^{29} +(9.09643 + 0.857286i) q^{30} +(5.70693 - 9.88469i) q^{31} +(-13.6643 - 7.88909i) q^{32} +(-0.734228 + 0.336406i) q^{33} +(-2.01226 - 3.48534i) q^{34} +23.5649i q^{35} +(-22.8207 + 26.4681i) q^{36} -35.9222 q^{37} +(-0.104620 + 0.0604021i) q^{38} +(32.7070 - 46.0506i) q^{39} +(12.0043 - 20.7920i) q^{40} +(28.5616 + 16.4901i) q^{41} +(2.21276 + 1.57159i) q^{42} +(-11.8069 - 20.4501i) q^{43} +1.04536i q^{44} +(-60.7105 - 52.3443i) q^{45} -10.0783 q^{46} +(-37.1020 + 21.4209i) q^{47} +(18.2575 + 39.8483i) q^{48} +(-3.50000 + 6.06218i) q^{49} +(16.0886 + 9.28877i) q^{50} +(-3.31297 + 35.1530i) q^{51} +(-36.5550 - 63.3152i) q^{52} +67.4023i q^{53} +(-8.96407 + 2.20980i) q^{54} -2.39776 q^{55} +(6.17629 - 3.56588i) q^{56} +(1.05519 + 0.0994457i) q^{57} +(-0.935656 + 1.62060i) q^{58} +(-55.9985 - 32.3308i) q^{59} +(-94.3268 + 43.2183i) q^{60} +(27.4750 + 47.5881i) q^{61} -3.90287i q^{62} +(-7.84353 - 22.4829i) q^{63} +53.0471 q^{64} +(145.228 - 83.8473i) q^{65} +(-0.159912 + 0.225152i) q^{66} +(53.6141 - 92.8624i) q^{67} +(39.5793 + 22.8511i) q^{68} +(72.0891 + 51.2006i) q^{69} +(4.02892 + 6.97830i) q^{70} -2.36503i q^{71} +(-4.53247 + 23.8328i) q^{72} +120.760 q^{73} +(-10.6376 + 6.14165i) q^{74} +(-67.8906 - 148.176i) q^{75} +(0.685924 - 1.18805i) q^{76} +(-0.616835 - 0.356130i) q^{77} +(1.81222 - 19.2289i) q^{78} +(-9.18745 - 15.9131i) q^{79} +130.132i q^{80} +(75.3454 + 29.7334i) q^{81} +11.2773 q^{82} +(-98.3488 + 56.7817i) q^{83} +(-30.6850 - 2.89189i) q^{84} +(-52.4142 + 90.7841i) q^{85} +(-6.99274 - 4.03726i) q^{86} +(14.9257 - 6.83861i) q^{87} +(0.362833 + 0.628446i) q^{88} +24.4587i q^{89} +(-26.9276 - 5.12103i) q^{90} +49.8139 q^{91} +(99.1157 - 57.2245i) q^{92} +(-19.8276 + 27.9168i) q^{93} +(-7.32469 + 12.6867i) q^{94} +(2.72507 + 1.57332i) q^{95} +(38.5914 + 27.4092i) q^{96} +(-81.7611 - 141.614i) q^{97} +2.39359i q^{98} +(2.28766 - 0.798090i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more