LMFDB - Embedded newform 63.4.h.a.58.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(25,63)]

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([4, 4]))

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

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

chi := DirichletCharacter("63.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			58.6
Character	$\chi$	$=$	63.58
Dual form			63.4.h.a.25.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.93457 q^{2} +(-3.89946 + 3.43427i) q^{3} +0.611720 q^{4} +(1.84855 + 3.20179i) q^{5} +(11.4432 - 10.0781i) q^{6} +(-18.1273 + 3.79476i) q^{7} +21.6814 q^{8} +(3.41152 - 26.7836i) q^{9} +O(q^{10})$	\(q-2.93457 q^{2} +(-3.89946 + 3.43427i) q^{3} +0.611720 q^{4} +(1.84855 + 3.20179i) q^{5} +(11.4432 - 10.0781i) q^{6} +(-18.1273 + 3.79476i) q^{7} +21.6814 q^{8} +(3.41152 - 26.7836i) q^{9} +(-5.42471 - 9.39588i) q^{10} +(32.8537 - 56.9043i) q^{11} +(-2.38537 + 2.10081i) q^{12} +(2.73952 - 4.74498i) q^{13} +(53.1960 - 11.1360i) q^{14} +(-18.2042 - 6.13679i) q^{15} -68.5196 q^{16} +(-25.1343 - 43.5340i) q^{17} +(-10.0113 + 78.5985i) q^{18} +(0.769884 - 1.33348i) q^{19} +(1.13080 + 1.95860i) q^{20} +(57.6545 - 77.0517i) q^{21} +(-96.4115 + 166.990i) q^{22} +(60.0078 + 103.936i) q^{23} +(-84.5459 + 74.4600i) q^{24} +(55.6657 - 96.4158i) q^{25} +(-8.03931 + 13.9245i) q^{26} +(78.6792 + 116.158i) q^{27} +(-11.0888 + 2.32133i) q^{28} +(-39.2967 - 68.0640i) q^{29} +(53.4215 + 18.0089i) q^{30} -303.332 q^{31} +27.6241 q^{32} +(67.3133 + 334.724i) q^{33} +(73.7586 + 127.754i) q^{34} +(-45.6593 - 51.0250i) q^{35} +(2.08689 - 16.3841i) q^{36} +(96.6335 - 167.374i) q^{37} +(-2.25928 + 3.91319i) q^{38} +(5.61294 + 27.9111i) q^{39} +(40.0793 + 69.4194i) q^{40} +(196.671 - 340.645i) q^{41} +(-169.191 + 226.114i) q^{42} +(-138.067 - 239.139i) q^{43} +(20.0972 - 34.8095i) q^{44} +(92.0618 - 38.5880i) q^{45} +(-176.097 - 305.009i) q^{46} -252.760 q^{47} +(267.189 - 235.315i) q^{48} +(314.200 - 137.578i) q^{49} +(-163.355 + 282.939i) q^{50} +(247.518 + 83.4405i) q^{51} +(1.67582 - 2.90260i) q^{52} +(-204.244 - 353.761i) q^{53} +(-230.890 - 340.873i) q^{54} +242.927 q^{55} +(-393.027 + 82.2758i) q^{56} +(1.57740 + 7.84383i) q^{57} +(115.319 + 199.739i) q^{58} +262.830 q^{59} +(-11.1359 - 3.75400i) q^{60} -112.254 q^{61} +890.149 q^{62} +(39.7955 + 498.461i) q^{63} +467.092 q^{64} +20.2566 q^{65} +(-197.536 - 982.273i) q^{66} -98.2686 q^{67} +(-15.3752 - 26.6306i) q^{68} +(-590.944 - 199.213i) q^{69} +(133.991 + 149.737i) q^{70} -255.003 q^{71} +(73.9667 - 580.707i) q^{72} +(344.146 + 596.078i) q^{73} +(-283.578 + 491.172i) q^{74} +(114.052 + 567.141i) q^{75} +(0.470953 - 0.815715i) q^{76} +(-379.612 + 1156.19i) q^{77} +(-16.4716 - 81.9071i) q^{78} -1084.44 q^{79} +(-126.662 - 219.385i) q^{80} +(-705.723 - 182.746i) q^{81} +(-577.146 + 999.647i) q^{82} +(152.083 + 263.415i) q^{83} +(35.2684 - 47.1340i) q^{84} +(92.9243 - 160.950i) q^{85} +(405.167 + 701.771i) q^{86} +(386.986 + 130.457i) q^{87} +(712.315 - 1233.77i) q^{88} +(550.553 - 953.585i) q^{89} +(-270.162 + 113.239i) q^{90} +(-31.6540 + 96.4096i) q^{91} +(36.7079 + 63.5800i) q^{92} +(1182.83 - 1041.72i) q^{93} +741.742 q^{94} +5.69269 q^{95} +(-107.719 + 94.8686i) q^{96} +(493.784 + 855.260i) q^{97} +(-922.042 + 403.731i) q^{98} +(-1412.02 - 1074.07i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{2} - q^{3} + 158 q^{4} - 19 q^{5} - 20 q^{6} - 7 q^{7} - 24 q^{8} + 11 q^{9}+O(q^{10}) $ 44 * q - 2 * q^2 - q^3 + 158 * q^4 - 19 * q^5 - 20 * q^6 - 7 * q^7 - 24 * q^8 + 11 * q^9	\( 44 q - 2 q^{2} - q^{3} + 158 q^{4} - 19 q^{5} - 20 q^{6} - 7 q^{7} - 24 q^{8} + 11 q^{9} - 18 q^{10} + 5 q^{11} - 62 q^{12} - 14 q^{13} - 52 q^{14} + 119 q^{15} + 494 q^{16} - 162 q^{17} - 188 q^{18} + 58 q^{19} - 362 q^{20} - 59 q^{21} - 18 q^{22} - 93 q^{23} + 30 q^{24} - 349 q^{25} - 266 q^{26} + 272 q^{27} - 172 q^{28} + 248 q^{29} + 85 q^{30} - 122 q^{31} + 326 q^{32} + 77 q^{33} + 6 q^{34} + 289 q^{35} - 806 q^{36} - 86 q^{37} - 761 q^{38} - 256 q^{39} - 18 q^{40} - 692 q^{41} - 364 q^{42} - 86 q^{43} - 443 q^{44} + 527 q^{45} - 270 q^{46} + 2010 q^{47} - 1013 q^{48} + 317 q^{49} + 239 q^{50} + 1209 q^{51} - 335 q^{52} + 258 q^{53} + 577 q^{54} - 870 q^{55} - 1752 q^{56} + 566 q^{57} + 237 q^{58} + 3330 q^{59} + 1669 q^{60} - 878 q^{61} + 1812 q^{62} + 2872 q^{63} + 872 q^{64} + 1226 q^{65} + 1330 q^{66} - 590 q^{67} - 1374 q^{68} + 1389 q^{69} + 1251 q^{70} + 636 q^{71} - 5970 q^{72} - 338 q^{73} + 1119 q^{74} + 2737 q^{75} + 1006 q^{76} + 2269 q^{77} + 157 q^{78} - 266 q^{79} - 4817 q^{80} - 505 q^{81} + 6 q^{82} - 1356 q^{83} - 6013 q^{84} + 483 q^{85} - 3343 q^{86} - 5755 q^{87} + 369 q^{88} - 2200 q^{89} + 2665 q^{90} + 1552 q^{91} - 396 q^{92} - 129 q^{93} + 2382 q^{94} - 6166 q^{95} - 5941 q^{96} - 266 q^{97} + 3601 q^{98} - 5395 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 - q^3 + 158 * q^4 - 19 * q^5 - 20 * q^6 - 7 * q^7 - 24 * q^8 + 11 * q^9 - 18 * q^10 + 5 * q^11 - 62 * q^12 - 14 * q^13 - 52 * q^14 + 119 * q^15 + 494 * q^16 - 162 * q^17 - 188 * q^18 + 58 * q^19 - 362 * q^20 - 59 * q^21 - 18 * q^22 - 93 * q^23 + 30 * q^24 - 349 * q^25 - 266 * q^26 + 272 * q^27 - 172 * q^28 + 248 * q^29 + 85 * q^30 - 122 * q^31 + 326 * q^32 + 77 * q^33 + 6 * q^34 + 289 * q^35 - 806 * q^36 - 86 * q^37 - 761 * q^38 - 256 * q^39 - 18 * q^40 - 692 * q^41 - 364 * q^42 - 86 * q^43 - 443 * q^44 + 527 * q^45 - 270 * q^46 + 2010 * q^47 - 1013 * q^48 + 317 * q^49 + 239 * q^50 + 1209 * q^51 - 335 * q^52 + 258 * q^53 + 577 * q^54 - 870 * q^55 - 1752 * q^56 + 566 * q^57 + 237 * q^58 + 3330 * q^59 + 1669 * q^60 - 878 * q^61 + 1812 * q^62 + 2872 * q^63 + 872 * q^64 + 1226 * q^65 + 1330 * q^66 - 590 * q^67 - 1374 * q^68 + 1389 * q^69 + 1251 * q^70 + 636 * q^71 - 5970 * q^72 - 338 * q^73 + 1119 * q^74 + 2737 * q^75 + 1006 * q^76 + 2269 * q^77 + 157 * q^78 - 266 * q^79 - 4817 * q^80 - 505 * q^81 + 6 * q^82 - 1356 * q^83 - 6013 * q^84 + 483 * q^85 - 3343 * q^86 - 5755 * q^87 + 369 * q^88 - 2200 * q^89 + 2665 * q^90 + 1552 * q^91 - 396 * q^92 - 129 * q^93 + 2382 * q^94 - 6166 * q^95 - 5941 * q^96 - 266 * q^97 + 3601 * q^98 - 5395 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−2.93457			−1.03753			−0.518764	−	0.854917i	$-0.673608\pi$
$2$	−2.93457			−1.03753			−0.518764	+	0.854917i	$0.673608\pi$
$3$	−3.89946	+	3.43427i	−0.750451	+	0.660926i
$3$	−3.89946	+	3.43427i	−0.750451	+	0.660926i
$4$	0.611720			0.0764650
$5$	1.84855	+	3.20179i	0.165340	+	0.286377i	0.936776	−	0.349930i	$-0.113795\pi$
$5$	1.84855	+	3.20179i	0.165340	+	0.286377i	−0.771436	+	0.636307i	$0.780461\pi$
$6$	11.4432	−	10.0781i	0.778614	−	0.685730i
$7$	−18.1273	+	3.79476i	−0.978783	+	0.204898i
$7$	−18.1273	+	3.79476i	−0.978783	+	0.204898i
$8$	21.6814			0.958194
$9$	3.41152	−	26.7836i	0.126353	−	0.991985i
$10$	−5.42471	−	9.39588i	−0.171545	−	0.297124i
$11$	32.8537	−	56.9043i	0.900524	−	1.55975i	0.0737076	−	0.997280i	$-0.476517\pi$
$11$	32.8537	−	56.9043i	0.900524	−	1.55975i	0.826816	−	0.562473i	$-0.190150\pi$
$12$	−2.38537	+	2.10081i	−0.0573832	+	0.0505377i
$13$	2.73952	−	4.74498i	0.0584465	−	0.101232i	−0.835322	−	0.549761i	$-0.814719\pi$
$13$	2.73952	−	4.74498i	0.0584465	−	0.101232i	0.893768	+	0.448529i	$0.148052\pi$
$14$	53.1960	−	11.1360i	1.01552	−	0.212587i
$15$	−18.2042	−	6.13679i	−0.313353	−	0.105634i
$16$	−68.5196			−1.07062
$17$	−25.1343	−	43.5340i	−0.358587	−	0.621090i	0.629138	−	0.777293i	$-0.283408\pi$
$17$	−25.1343	−	43.5340i	−0.358587	−	0.621090i	−0.987725	+	0.156203i	$0.950075\pi$
$18$	−10.0113	+	78.5985i	−0.131094	+	1.02921i
$19$	0.769884	−	1.33348i	0.00929597	−	0.0161011i	−0.861340	−	0.508029i	$-0.830374\pi$
$19$	0.769884	−	1.33348i	0.00929597	−	0.0161011i	0.870636	+	0.491928i	$0.163708\pi$
$20$	1.13080	+	1.95860i	0.0126427	+	0.0218978i
$21$	57.6545	−	77.0517i	0.599107	−	0.800669i
$22$	−96.4115	+	166.990i	−0.934319	+	1.61829i
$23$	60.0078	+	103.936i	0.544021	+	0.942272i	0.998668	+	0.0516002i	$0.0164322\pi$
$23$	60.0078	+	103.936i	0.544021	+	0.942272i	−0.454647	+	0.890672i	$0.650235\pi$
$24$	−84.5459	+	74.4600i	−0.719077	+	0.633296i
$25$	55.6657	−	96.4158i	0.445326	−	0.771327i
$26$	−8.03931	+	13.9245i	−0.0606399	+	0.105031i
$27$	78.6792	+	116.158i	0.560808	+	0.827946i
$28$	−11.0888	+	2.32133i	−0.0748426	+	0.0156675i
$29$	−39.2967	−	68.0640i	−0.251628	−	0.435833i	0.712346	−	0.701829i	$-0.247633\pi$
$29$	−39.2967	−	68.0640i	−0.251628	−	0.435833i	−0.963974	+	0.265995i	$0.914299\pi$
$30$	53.4215	+	18.0089i	0.325113	+	0.109598i
$31$	−303.332			−1.75742			−0.878709	−	0.477358i	$-0.841595\pi$
$31$	−303.332			−1.75742			−0.878709	+	0.477358i	$0.841595\pi$
$32$	27.6241			0.152603
$33$	67.3133	+	334.724i	0.355083	+	1.76570i
$34$	73.7586	+	127.754i	0.372044	+	0.644399i
$35$	−45.6593	−	51.0250i	−0.220510	−	0.246423i
$36$	2.08689	−	16.3841i	0.00966154	−	0.0758521i
$37$	96.6335	−	167.374i	0.429363	−	0.743679i	−0.567453	−	0.823406i	$-0.692071\pi$
$37$	96.6335	−	167.374i	0.429363	−	0.743679i	0.996817	+	0.0797263i	$0.0254046\pi$
$38$	−2.25928	+	3.91319i	−0.00964484	+	0.0167053i
$39$	5.61294	+	27.9111i	0.0230459	+	0.114599i
$40$	40.0793	+	69.4194i	0.158427	+	0.274404i
$41$	196.671	−	340.645i	0.749144	−	1.29756i	−0.199090	−	0.979981i	$-0.563798\pi$
$41$	196.671	−	340.645i	0.749144	−	1.29756i	0.948233	−	0.317574i	$-0.102868\pi$
$42$	−169.191	+	226.114i	−0.621590	+	0.830717i
$43$	−138.067	−	239.139i	−0.489651	−	0.848101i	0.510278	−	0.860010i	$-0.329543\pi$
$43$	−138.067	−	239.139i	−0.489651	−	0.848101i	−0.999929	+	0.0119087i	$0.996209\pi$
$44$	20.0972	−	34.8095i	0.0688585	−	0.119266i
$45$	92.0618	−	38.5880i	0.304973	−	0.127830i
$46$	−176.097	−	305.009i	−0.564437	−	0.977634i
$47$	−252.760			−0.784443			−0.392221	−	0.919871i	$-0.628293\pi$
$47$	−252.760			−0.784443			−0.392221	+	0.919871i	$0.628293\pi$
$48$	267.189	−	235.315i	0.803446	−	0.707600i
$49$	314.200	−	137.578i	0.916034	−	0.401101i
$50$	−163.355	+	282.939i	−0.462038	+	0.800273i
$51$	247.518	+	83.4405i	0.679597	+	0.229098i
$52$	1.67582	−	2.90260i	0.00446911	−	0.00774073i
$53$	−204.244	−	353.761i	−0.529341	−	0.916845i	−0.999414	−	0.0342180i	$-0.989106\pi$
$53$	−204.244	−	353.761i	−0.529341	−	0.916845i	0.470074	−	0.882627i	$-0.344227\pi$
$54$	−230.890	−	340.873i	−0.581854	−	0.859017i
$55$	242.927			0.595569
$56$	−393.027	+	82.2758i	−0.937864	+	0.196332i
$57$	1.57740	+	7.84383i	0.00366547	+	0.0182270i
$58$	115.319	+	199.739i	0.261072	+	0.452189i
$59$	262.830			0.579959			0.289980	−	0.957033i	$-0.406351\pi$
$59$	262.830			0.579959			0.289980	+	0.957033i	$0.406351\pi$
$60$	−11.1359	−	3.75400i	−0.0239605	−	0.00807732i
$61$	−112.254			−0.235617			−0.117809	−	0.993036i	$-0.537587\pi$
$61$	−112.254			−0.235617			−0.117809	+	0.993036i	$0.537587\pi$
$62$	890.149			1.82337
$63$	39.7955	+	498.461i	0.0795836	+	0.996828i
$64$	467.092			0.912288
$65$	20.2566			0.0386541
$66$	−197.536	−	982.273i	−0.368409	−	1.83196i
$67$	−98.2686			−0.179185			−0.0895926	−	0.995978i	$-0.528557\pi$
$67$	−98.2686			−0.179185			−0.0895926	+	0.995978i	$0.528557\pi$
$68$	−15.3752	−	26.6306i	−0.0274193	−	0.0474916i
$69$	−590.944	−	199.213i	−1.03103	−	0.347571i
$70$	133.991	+	149.737i	0.228785	+	0.255671i
$71$	−255.003			−0.426243			−0.213122	−	0.977026i	$-0.568363\pi$
$71$	−255.003			−0.426243			−0.213122	+	0.977026i	$0.568363\pi$
$72$	73.9667	−	580.707i	0.121070	−	0.950514i
$73$	344.146	+	596.078i	0.551770	+	0.955694i	0.998147	+	0.0608488i	$0.0193808\pi$
$73$	344.146	+	596.078i	0.551770	+	0.955694i	−0.446377	+	0.894845i	$0.647286\pi$
$74$	−283.578	+	491.172i	−0.445477	+	0.771588i
$75$	114.052	+	567.141i	0.175595	+	0.873170i
$76$	0.470953	−	0.815715i	0.000710816	−	0.00123117i
$77$	−379.612	+	1156.19i	−0.561828	+	1.71117i
$78$	−16.4716	−	81.9071i	−0.0239108	−	0.118899i
$79$	−1084.44			−1.54442			−0.772211	−	0.635366i	$-0.780849\pi$
$79$	−1084.44			−1.54442			−0.772211	+	0.635366i	$0.780849\pi$
$80$	−126.662	−	219.385i	−0.177016	−	0.306600i
$81$	−705.723	−	182.746i	−0.968070	−	0.250680i
$82$	−577.146	+	999.647i	−0.777258	+	1.34625i
$83$	152.083	+	263.415i	0.201124	+	0.348356i	0.948891	−	0.315605i	$-0.102207\pi$
$83$	152.083	+	263.415i	0.201124	+	0.348356i	−0.747767	+	0.663961i	$0.768874\pi$
$84$	35.2684	−	47.1340i	0.0458107	−	0.0612231i
$85$	92.9243	−	160.950i	0.118577	−	0.205382i
$86$	405.167	+	701.771i	0.508027	+	0.879929i
$87$	386.986	+	130.457i	0.476888	+	0.160763i
$88$	712.315	−	1233.77i	0.862876	−	1.49455i
$89$	550.553	−	953.585i	0.655713	−	1.13573i	−0.326002	−	0.945369i	$-0.605701\pi$
$89$	550.553	−	953.585i	0.655713	−	1.13573i	0.981715	−	0.190359i	$-0.0609652\pi$
$90$	−270.162	+	113.239i	−0.316418	+	0.132627i
$91$	−31.6540	+	96.4096i	−0.0364642	+	0.111060i
$92$	36.7079	+	63.5800i	0.0415985	+	0.0720508i
$93$	1182.83	−	1041.72i	1.31886	−	1.16152i
$94$	741.742			0.813882
$95$	5.69269			0.00614797
$96$	−107.719	+	94.8686i	−0.114521	+	0.100859i
$97$	493.784	+	855.260i	0.516868	+	0.895242i	0.999808	+	0.0195884i	$0.00623557\pi$
$97$	493.784	+	855.260i	0.516868	+	0.895242i	−0.482940	+	0.875653i	$0.660431\pi$
$98$	−922.042	+	403.731i	−0.950411	+	0.416153i
$99$	−1412.02	−	1074.07i	−1.43347	−	1.09038i
$100$	34.0518	−	58.9795i	0.0340518	−	0.0589795i
$101$	−375.784	+	650.877i	−0.370217	+	0.641235i	−0.989599	−	0.143855i	$-0.954050\pi$
$101$	−375.784	+	650.877i	−0.370217	+	0.641235i	0.619382	+	0.785090i	$0.287383\pi$
$102$	−726.359	−	244.862i	−0.705101	−	0.237696i
$103$	276.520	+	478.947i	0.264528	+	0.458175i	0.967440	−	0.253102i	$-0.0814507\pi$
$103$	276.520	+	478.947i	0.264528	+	0.458175i	−0.702912	+	0.711277i	$0.748117\pi$
$104$	59.3967	−	102.878i	0.0560031	−	0.0970002i
$105$	353.281	+	42.1633i	0.328349	+	0.0391877i
$106$	599.369	+	1038.14i	0.549206	+	0.951253i
$107$	136.170	−	235.853i	0.123028	−	0.213091i	−0.797932	−	0.602747i	$-0.794073\pi$
$107$	136.170	−	235.853i	0.123028	−	0.213091i	0.920960	+	0.389656i	$0.127406\pi$
$108$	48.1296	+	71.0559i	0.0428822	+	0.0633088i
$109$	−218.698	−	378.796i	−0.192179	−	0.332863i	0.753793	−	0.657112i	$-0.228222\pi$
$109$	−218.698	−	378.796i	−0.192179	−	0.332863i	−0.945972	+	0.324248i	$0.894889\pi$
$110$	−712.888			−0.617920
$111$	197.991	+	984.534i	0.169301	+	0.841872i
$112$	1242.08	−	260.015i	1.04790	−	0.219367i
$113$	157.658	−	273.071i	0.131250	−	0.227331i	−0.792909	−	0.609340i	$-0.791434\pi$
$113$	157.658	−	273.071i	0.131250	−	0.227331i	0.924159	+	0.382009i	$0.124768\pi$
$114$	−4.62900	−	23.0183i	−0.00380303	−	0.0189111i
$115$	−221.855	+	384.264i	−0.179896	+	0.311590i
$116$	−24.0386	−	41.6361i	−0.0192408	−	0.0333260i
$117$	−117.742	−	89.5617i	−0.0930362	−	0.0707691i
$118$	−771.295			−0.601724
$119$	620.819	+	693.775i	0.478238	+	0.534439i
$120$	−394.693	−	133.055i	−0.300253	−	0.101218i
$121$	−1493.23	−	2586.35i	−1.12189	−	1.94316i
$122$	329.417			0.244459
$123$	402.956	+	2003.75i	0.295393	+	1.46888i
$124$	−185.554			−0.134381
$125$	873.742			0.625199
$126$	−116.783	−	1462.77i	−0.0825702	−	1.03424i
$127$	314.914			0.220032			0.110016	−	0.993930i	$-0.464910\pi$
$127$	314.914			0.220032			0.110016	+	0.993930i	$0.464910\pi$
$128$	−1591.71			−1.09913
$129$	1359.65	+	458.352i	0.927992	+	0.312834i
$130$	−59.4444			−0.0401047
$131$	−854.346	−	1479.77i	−0.569806	−	0.986932i	−0.996585	−	0.0825765i	$-0.973685\pi$
$131$	−854.346	−	1479.77i	−0.569806	−	0.986932i	0.426779	−	0.904356i	$-0.359648\pi$
$132$	41.1769	+	204.757i	0.0271514	+	0.135014i
$133$	−8.89571	+	27.0939i	−0.00579967	+	0.0176642i
$134$	288.376			0.185910
$135$	−226.469	+	466.638i	−0.144381	+	0.297495i
$136$	−544.949	−	943.879i	−0.343595	−	0.595125i
$137$	438.080	−	758.777i	0.273195	−	0.473188i	−0.696483	−	0.717573i	$-0.745253\pi$
$137$	438.080	−	758.777i	0.273195	−	0.473188i	0.969678	+	0.244385i	$0.0785862\pi$
$138$	1734.17	+	584.604i	1.06973	+	0.360615i
$139$	−368.183	+	637.712i	−0.224668	+	0.389137i	−0.956220	−	0.292649i	$-0.905463\pi$
$139$	−368.183	+	637.712i	−0.224668	+	0.389137i	0.731552	+	0.681786i	$0.238797\pi$
$140$	−27.9307	−	31.2130i	−0.0168613	−	0.0188427i
$141$	985.626	−	868.047i	0.588686	−	0.518459i
$142$	748.324			0.442239
$143$	−180.006	−	311.780i	−0.105265	−	0.182324i
$144$	−233.756	+	1835.20i	−0.135275	+	1.06204i
$145$	145.284	−	251.640i	0.0832083	−	0.144121i
$146$	−1009.92	−	1749.23i	−0.572477	−	0.991559i
$147$	−752.729	+	1615.53i	−0.422340	+	0.906437i
$148$	59.1126	−	102.386i	0.0328313	−	0.0568654i
$149$	161.831	+	280.300i	0.0889781	+	0.154115i	0.907079	−	0.420959i	$-0.138307\pi$
$149$	161.831	+	280.300i	0.0889781	+	0.154115i	−0.818101	+	0.575074i	$0.804973\pi$
$150$	−334.695	−	1664.32i	−0.182185	−	0.905939i
$151$	1375.69	−	2382.76i	0.741404	−	1.28415i	−0.210452	−	0.977604i	$-0.567494\pi$
$151$	1375.69	−	2382.76i	0.741404	−	1.28415i	0.951856	−	0.306545i	$-0.0991732\pi$
$152$	16.6922	−	28.9117i	0.00890734	−	0.0154280i
$153$	−1251.74	+	524.671i	−0.661421	+	0.277236i
$154$	1114.00	−	3392.93i	0.582913	−	1.77539i
$155$	−560.725	−	971.203i	−0.290571	−	0.503283i
$156$	3.43355	+	17.0738i	0.00176220	+	0.00876279i
$157$	−1710.03			−0.869267			−0.434634	−	0.900607i	$-0.643122\pi$
$157$	−1710.03			−0.869267			−0.434634	+	0.900607i	$0.643122\pi$
$158$	3182.38			1.60238
$159$	2011.35	+	678.045i	1.00321	+	0.338192i
$160$	51.0645	+	88.4464i	0.0252313	+	0.0437019i
$161$	−1482.19	−	1656.38i	−0.725548	−	0.810812i
$162$	2071.00	+	536.280i	1.00440	+	0.260087i
$163$	−1694.66	+	2935.24i	−0.814332	+	1.41046i	0.0954751	+	0.995432i	$0.469563\pi$
$163$	−1694.66	+	2935.24i	−0.814332	+	1.41046i	−0.909807	+	0.415032i	$0.863770\pi$
$164$	120.308	−	208.379i	0.0572833	−	0.0992175i
$165$	−947.284	+	834.279i	−0.446945	+	0.393627i
$166$	−446.298	−	773.011i	−0.208672	−	0.361430i
$167$	782.792	−	1355.83i	0.362720	−	0.628249i	−0.625688	−	0.780074i	$-0.715181\pi$
$167$	782.792	−	1355.83i	0.362720	−	0.628249i	0.988407	+	0.151824i	$0.0485148\pi$
$168$	1250.03	−	1670.59i	0.574060	−	0.767196i
$169$	1083.49	+	1876.66i	0.493168	+	0.854192i
$170$	−272.693	+	472.319i	−0.123027	+	0.213089i
$171$	−33.0889	−	25.1695i	−0.0147975	−	0.0112559i
$172$	−84.4583	−	146.286i	−0.0374412	−	0.0648500i
$173$	2848.83			1.25198			0.625991	−	0.779830i	$-0.284695\pi$
$173$	2848.83			1.25198			0.625991	+	0.779830i	$0.284695\pi$
$174$	−1135.64	−	382.835i	−0.494785	−	0.166797i
$175$	−643.196	+	1959.00i	−0.277834	+	0.846208i
$176$	−2251.12	+	3899.05i	−0.964117	+	1.66990i
$177$	−1024.90	+	902.631i	−0.435231	+	0.383310i
$178$	−1615.64	+	2798.37i	−0.680321	+	1.17835i
$179$	2004.75	+	3472.33i	0.837106	+	1.44991i	0.892304	+	0.451435i	$0.149088\pi$
$179$	2004.75	+	3472.33i	0.837106	+	1.44991i	−0.0551975	+	0.998475i	$0.517579\pi$
$180$	56.3160	−	23.6050i	0.0233197	−	0.00977452i
$181$	−4749.05			−1.95024			−0.975122	−	0.221668i	$-0.928850\pi$
$181$	−4749.05			−1.95024			−0.975122	+	0.221668i	$0.928850\pi$
$182$	92.8911	−	282.921i	0.0378327	−	0.115228i
$183$	437.729	−	385.511i	0.176819	−	0.155726i
$184$	1301.06	+	2253.49i	0.521278	+	0.902879i
$185$	714.529			0.283963
$186$	−3471.10	+	3057.01i	−1.36835	+	1.20511i
$187$	−3303.02			−1.29166
$188$	−154.618			−0.0599824
$189$	−1867.03	−	1807.06i	−0.718554	−	0.695472i
$190$	−16.7056			−0.00637869
$191$	3102.96			1.17551			0.587755	−	0.809039i	$-0.300012\pi$
$191$	3102.96			1.17551			0.587755	+	0.809039i	$0.300012\pi$
$192$	−1821.40	+	1604.12i	−0.684627	+	0.602955i
$193$	−2664.98			−0.993934			−0.496967	−	0.867769i	$-0.665553\pi$
$193$	−2664.98			−0.993934			−0.496967	+	0.867769i	$0.665553\pi$
$194$	−1449.05	−	2509.82i	−0.536265	−	0.928839i
$195$	−78.9896	+	69.5666i	−0.0290080	+	0.0255475i
$196$	192.202	−	84.1589i	0.0700445	−	0.0306701i
$197$	−1434.52			−0.518810			−0.259405	−	0.965769i	$-0.583526\pi$
$197$	−1434.52			−0.518810			−0.259405	+	0.965769i	$0.583526\pi$
$198$	4143.68	+	3151.94i	1.48726	+	1.13131i
$199$	1019.11	+	1765.15i	0.363030	+	0.628786i	0.988458	−	0.151496i	$-0.0484089\pi$
$199$	1019.11	+	1765.15i	0.363030	+	0.628786i	−0.625428	+	0.780282i	$0.715076\pi$
$200$	1206.91	−	2090.43i	0.426708	−	0.739080i
$201$	383.194	−	337.481i	0.134470	−	0.118428i
$202$	1102.77	−	1910.05i	0.384111	−	0.665299i
$203$	970.631	+	1084.70i	0.335591	+	0.375028i
$204$	151.412	+	51.0422i	0.0519653	+	0.0175180i
$205$	1454.23			0.495453
$206$	−811.468	−	1405.50i	−0.274455	−	0.475370i
$207$	2988.51	−	1252.64i	1.00346	−	0.420602i
$208$	−187.710	+	325.124i	−0.0625739	+	0.108381i
$209$	−50.5871	−	87.6193i	−0.0167425	−	0.0289988i
$210$	−1036.73	−	123.731i	−0.340671	−	0.0406584i
$211$	463.774	−	803.279i	0.151315	−	0.262085i	−0.780396	−	0.625286i	$-0.784983\pi$
$211$	463.774	−	803.279i	0.151315	−	0.262085i	0.931711	+	0.363200i	$0.118316\pi$
$212$	−124.940	−	216.403i	−0.0404760	−	0.0701065i
$213$	994.372	−	875.750i	0.319875	−	0.281715i
$214$	−399.600	+	692.128i	−0.127645	+	0.221088i
$215$	510.448	−	884.122i	0.161918	−	0.280449i
$216$	1705.88	+	2518.46i	0.537363	+	0.793333i
$217$	5498.59	−	1151.07i	1.72013	−	0.360091i
$218$	641.785	+	1111.60i	0.199391	+	0.345355i
$219$	−3389.08	−	1142.49i	−1.04572	−	0.352522i
$220$	148.603			0.0455402
$221$	−275.424			−0.0838326
$222$	−581.018	−	2889.19i	−0.175655	−	0.873466i
$223$	−2033.70	−	3522.47i	−0.610702	−	1.05777i	−0.991122	−	0.132953i	$-0.957554\pi$
$223$	−2033.70	−	3522.47i	−0.610702	−	1.05777i	0.380421	−	0.924814i	$-0.375779\pi$
$224$	−500.750	+	104.827i	−0.149365	+	0.0312679i
$225$	−2392.46	−	1819.85i	−0.708877	−	0.539216i
$226$	−462.658	+	801.348i	−0.136175	+	0.235862i
$227$	−380.784	+	659.537i	−0.111337	+	0.192842i	−0.916310	−	0.400471i	$-0.868847\pi$
$227$	−380.784	+	659.537i	−0.111337	+	0.192842i	0.804972	+	0.593312i	$0.202180\pi$
$228$	0.964927	+	4.79823i	0.000280280	+	0.00139373i
$229$	2566.92	+	4446.04i	0.740729	+	1.28298i	0.952164	+	0.305588i	$0.0988531\pi$
$229$	2566.92	+	4446.04i	0.740729	+	1.28298i	−0.211435	+	0.977392i	$0.567814\pi$
$230$	651.050	−	1127.65i	0.186648	−	0.323283i
$231$	−2490.41	−	5812.22i	−0.709336	−	1.65548i
$232$	−852.010	−	1475.73i	−0.241109	−	0.417613i
$233$	−718.366	+	1244.25i	−0.201982	+	0.349843i	−0.949167	−	0.314773i	$-0.898071\pi$
$233$	−718.366	+	1244.25i	−0.201982	+	0.349843i	0.747185	+	0.664616i	$0.231405\pi$
$234$	345.522	+	262.825i	0.0965277	+	0.0734249i
$235$	−467.240	−	809.284i	−0.129700	−	0.224646i
$236$	160.778			0.0443466
$237$	4228.74	−	3724.28i	1.15901	−	1.02075i
$238$	−1821.84	−	2035.93i	−0.496186	−	0.554496i
$239$	1361.15	−	2357.57i	0.368390	−	0.638070i	−0.620924	−	0.783871i	$-0.713242\pi$
$239$	1361.15	−	2357.57i	0.368390	−	0.638070i	0.989314	+	0.145801i	$0.0465758\pi$
$240$	1247.34	+	420.490i	0.335482	+	0.113094i
$241$	3094.96	−	5360.63i	0.827237	−	1.43282i	−0.0729607	−	0.997335i	$-0.523245\pi$
$241$	3094.96	−	5360.63i	0.827237	−	1.43282i	0.900198	−	0.435482i	$-0.143422\pi$
$242$	4381.99	+	7589.83i	1.16399	+	2.01609i
$243$	3379.53	−	1711.04i	0.892170	−	0.451700i
$244$	−68.6680			−0.0180165
$245$	1021.31	+	751.681i	0.266323	+	0.196013i
$246$	−1182.50	−	5880.16i	−0.306479	−	1.52400i
$247$	−4.21822	−	7.30617i	−0.00108663	−	0.00188211i
$248$	−6576.67			−1.68395
$249$	−1497.68	−	504.882i	−0.381171	−	0.128496i
$250$	−2564.06			−0.648662
$251$	−4822.76			−1.21279			−0.606394	−	0.795164i	$-0.707385\pi$
$251$	−4822.76			−1.21279			−0.606394	+	0.795164i	$0.707385\pi$
$252$	24.3437	+	304.918i	0.00608536	+	0.0762224i
$253$	7885.90			1.95961
$254$	−924.137			−0.228290
$255$	190.391	+	946.744i	0.0467559	+	0.232500i
$256$	934.248			0.228088
$257$	−2991.46	−	5181.36i	−0.726078	−	1.25760i	−0.958529	−	0.284995i	$-0.908008\pi$
$257$	−2991.46	−	5181.36i	−0.726078	−	1.25760i	0.232451	−	0.972608i	$-0.425325\pi$
$258$	−3990.01	−	1345.07i	−0.962818	−	0.324575i
$259$	−1116.56	+	3400.74i	−0.267876	+	0.815876i
$260$	12.3913			0.00295569
$261$	−1957.06	+	820.307i	−0.464134	+	0.194543i
$262$	2507.14	+	4342.50i	0.591190	+	1.02397i
$263$	−1874.95	+	3247.51i	−0.439598	+	0.761407i	−0.997658	−	0.0683939i	$-0.978213\pi$
$263$	−1874.95	+	3247.51i	−0.439598	+	0.761407i	0.558060	+	0.829801i	$0.311546\pi$
$264$	1459.45	+	7257.31i	0.340238	+	1.69188i
$265$	755.112	−	1307.89i	0.175042	−	0.303182i
$266$	26.1051	−	79.5091i	0.00601732	−	0.0183271i
$267$	1128.02	+	5609.21i	0.258553	+	1.28569i
$268$	−60.1128			−0.0137014
$269$	−599.355	−	1038.11i	−0.135849	−	0.235297i	0.790073	−	0.613013i	$-0.210043\pi$
$269$	−599.355	−	1038.11i	−0.135849	−	0.235297i	−0.925921	+	0.377716i	$0.876709\pi$
$270$	664.591	−	1369.38i	0.149799	−	0.308659i
$271$	2007.66	−	3477.37i	0.450024	−	0.779465i	−0.548362	−	0.836241i	$-0.684749\pi$
$271$	2007.66	−	3477.37i	0.450024	−	0.779465i	0.998387	+	0.0567755i	$0.0180819\pi$
$272$	1722.19	+	2982.93i	0.383909	+	0.664950i
$273$	−207.663	−	484.654i	−0.0460380	−	0.107445i
$274$	−1285.58	+	2226.69i	−0.283448	+	0.490946i
$275$	−3657.65	−	6335.23i	−0.802052	−	1.38920i
$276$	−361.492	−	121.862i	−0.0788379	−	0.0265770i
$277$	2209.33	−	3826.67i	0.479226	−	0.830044i	−0.520490	−	0.853868i	$-0.674251\pi$
$277$	2209.33	−	3826.67i	0.479226	−	0.830044i	0.999716	+	0.0238239i	$0.00758409\pi$
$278$	1080.46	−	1871.41i	0.233100	−	0.403741i
$279$	−1034.82	+	8124.31i	−0.222054	+	1.74333i
$280$	−989.960	−	1106.30i	−0.211291	−	0.236121i
$281$	786.552	+	1362.35i	0.166981	+	0.289220i	0.937357	−	0.348370i	$-0.113265\pi$
$281$	786.552	+	1362.35i	0.166981	+	0.289220i	−0.770376	+	0.637590i	$0.779931\pi$
$282$	−2892.39	+	2547.35i	−0.610778	+	0.537916i
$283$	4868.35			1.02259			0.511296	−	0.859405i	$-0.329166\pi$
$283$	4868.35			1.02259			0.511296	+	0.859405i	$0.329166\pi$
$284$	−155.990			−0.0325927
$285$	−22.1984	+	19.5502i	−0.00461375	+	0.00406336i
$286$	528.242	+	914.942i	0.109215	+	0.189167i
$287$	−2272.46	+	6921.30i	−0.467384	+	1.42352i
$288$	94.2400	−	739.872i	0.0192818	−	0.151380i
$289$	1193.03	−	2066.39i	0.242831	−	0.420596i
$290$	−426.347	+	738.455i	−0.0863310	+	0.149530i
$291$	−4862.69	−	1639.26i	−0.979573	−	0.330223i
$292$	210.521	+	364.633i	0.0421911	+	0.0730771i
$293$	−4379.03	+	7584.70i	−0.873125	+	1.51230i	−0.0143787	+	0.999897i	$0.504577\pi$
$293$	−4379.03	+	7584.70i	−0.873125	+	1.51230i	−0.858747	+	0.512401i	$0.828756\pi$
$294$	2208.94	−	4740.88i	0.438190	−	0.940454i
$295$	485.856	+	841.527i	0.0958902	+	0.166087i
$296$	2095.15	−	3628.91i	0.411413	−	0.712589i
$297$	9194.76	−	660.975i	1.79641	−	0.129137i
$298$	−474.906	−	822.561i	−0.0923173	−	0.159898i
$299$	657.569			0.127185
$300$	69.7681	+	346.931i	0.0134269	+	0.0667669i
$301$	3410.26	+	3811.02i	0.653036	+	0.729779i
$302$	−4037.06	+	6992.40i	−0.769228	+	1.33234i
$303$	−769.937	−	3828.61i	−0.145979	−	0.725901i
$304$	−52.7521	+	91.3693i	−0.00995244	+	0.0172381i
$305$	−207.507	−	359.413i	−0.0389569	−	0.0674752i
$306$	3673.33	−	1539.69i	0.686243	−	0.287641i
$307$	−5488.53			−1.02035			−0.510174	−	0.860071i	$-0.670419\pi$
$307$	−5488.53			−1.02035			−0.510174	+	0.860071i	$0.670419\pi$
$308$	−232.216	+	707.266i	−0.0429602	+	0.130845i
$309$	−2723.11	−	917.986i	−0.501335	−	0.169005i
$310$	1645.49	+	2850.07i	0.301475	+	0.522171i
$311$	1704.90			0.310855			0.155428	−	0.987847i	$-0.450324\pi$
$311$	1704.90			0.310855			0.155428	+	0.987847i	$0.450324\pi$
$312$	121.697	+	605.153i	0.0220824	+	0.109808i
$313$	−6652.59			−1.20136			−0.600681	−	0.799488i	$-0.705104\pi$
$313$	−6652.59			−1.20136			−0.600681	+	0.799488i	$0.705104\pi$
$314$	5018.20			0.901889
$315$	−1522.40	+	1048.85i	−0.272310	+	0.187606i
$316$	−663.375			−0.118094
$317$	−4225.84			−0.748728			−0.374364	−	0.927282i	$-0.622139\pi$
$317$	−4225.84			−0.748728			−0.374364	+	0.927282i	$0.622139\pi$
$318$	−5902.46	−	1989.77i	−1.04086	−	0.350884i
$319$	−5164.17			−0.906389
$320$	863.444	+	1495.53i	0.150837	+	0.261258i
$321$	278.996	+	1387.34i	0.0485110	+	0.241227i
$322$	4349.61	+	4860.76i	0.752777	+	0.841240i
$323$	−77.4021			−0.0133336
$324$	−431.705	−	111.789i	−0.0740234	−	0.0191682i
$325$	−304.994	−	528.265i	−0.0520555	−	0.0901627i
$326$	4973.11	−	8613.67i	0.844892	−	1.46340i
$327$	2153.69	+	726.030i	0.364219	+	0.122781i
$328$	4264.12	−	7385.67i	0.717825	−	1.24331i
$329$	4581.86	−	959.162i	0.767800	−	0.160730i
$330$	2779.87	−	2448.25i	0.463718	−	0.408399i
$331$	4414.80			0.733109			0.366555	−	0.930396i	$-0.380537\pi$
$331$	4414.80			0.733109			0.366555	+	0.930396i	$0.380537\pi$
$332$	93.0321	+	161.136i	0.0153789	+	0.0266371i
$333$	−4153.22	−	3159.19i	−0.683468	−	0.519888i
$334$	−2297.16	+	3978.80i	−0.376332	+	0.651827i
$335$	−181.655	−	314.635i	−0.0296264	−	0.0513145i
$336$	−3950.46	+	5279.55i	−0.641414	+	0.857211i
$337$	1290.74	−	2235.63i	0.208638	−	0.361372i	−0.742648	−	0.669682i	$-0.766430\pi$
$337$	1290.74	−	2235.63i	0.208638	−	0.361372i	0.951286	+	0.308311i	$0.0997636\pi$
$338$	−3179.58	−	5507.20i	−0.511676	−	0.886248i
$339$	323.022	+	1606.27i	0.0517527	+	0.257347i
$340$	56.8436	−	98.4561i	0.00906700	−	0.0157045i
$341$	−9965.56	+	17260.9i	−1.58260	+	2.74114i
$342$	97.1017	+	73.8616i	0.0153528	+	0.0116783i
$343$	−5173.53	+	3686.22i	−0.814414	+	0.580284i
$344$	−2993.49	−	5184.88i	−0.469181	−	0.812645i
$345$	−454.555	−	2260.33i	−0.0709345	−	0.352731i
$346$	−8360.11			−1.29897
$347$	6048.17			0.935685			0.467843	−	0.883812i	$-0.345031\pi$
$347$	6048.17			0.935685			0.467843	+	0.883812i	$0.345031\pi$
$348$	236.727	+	79.8029i	0.0364652	+	0.0122928i
$349$	5649.71	+	9785.58i	0.866538	+	1.50089i	0.865511	+	0.500889i	$0.166994\pi$
$349$	5649.71	+	9785.58i	0.866538	+	1.50089i	0.00102701	+	0.999999i	$0.499673\pi$
$350$	1887.50	−	5748.82i	0.288261	−	0.877965i
$351$	766.708	−	55.1157i	0.116592	−	0.00838136i
$352$	907.552	−	1571.93i	0.137422	−	0.238023i
$353$	−518.102	+	897.379i	−0.0781183	+	0.135305i	−0.902438	−	0.430820i	$-0.858225\pi$
$353$	−518.102	+	897.379i	−0.0781183	+	0.135305i	0.824320	+	0.566125i	$0.191558\pi$
$354$	3007.63	−	2648.84i	0.451564	−	0.397695i
$355$	−471.386	−	816.465i	−0.0704749	−	0.122066i
$356$	336.784	−	583.327i	0.0501391	−	0.0868434i
$357$	−4803.47	−	573.284i	−0.712119	−	0.0849899i
$358$	−5883.08	−	10189.8i	−0.868522	−	1.50432i
$359$	5156.80	−	8931.83i	0.758121	−	1.31310i	−0.185687	−	0.982609i	$-0.559451\pi$
$359$	5156.80	−	8931.83i	0.758121	−	1.31310i	0.943808	−	0.330495i	$-0.107216\pi$
$360$	1996.03	−	836.643i	0.292223	−	0.122486i
$361$	3428.31	+	5938.01i	0.499827	+	0.865726i
$362$	13936.4			2.02343
$363$	14705.0	+	4957.20i	2.12621	+	0.716764i
$364$	−19.3634	+	58.9756i	−0.00278824	+	0.00849221i
$365$	−1272.34	+	2203.76i	−0.182459	+	0.316028i
$366$	−1284.55	+	1131.31i	−0.183455	+	0.161570i
$367$	1033.03	−	1789.26i	0.146931	−	0.254493i	−0.783160	−	0.621820i	$-0.786394\pi$
$367$	1033.03	−	1789.26i	0.146931	−	0.254493i	0.930092	+	0.367327i	$0.119727\pi$
$368$	−4111.71	−	7121.68i	−0.582439	−	1.00881i
$369$	−8452.75	−	6429.68i	−1.19250	−	0.907089i
$370$	−2096.84			−0.294620
$371$	5044.83	+	5637.68i	0.705969	+	0.788932i
$372$	723.559	−	637.243i	0.100846	−	0.0888159i
$373$	−2409.82	−	4173.92i	−0.334519	−	0.579404i	0.648873	−	0.760896i	$-0.275240\pi$
$373$	−2409.82	−	4173.92i	−0.334519	−	0.579404i	−0.983392	+	0.181493i	$0.941907\pi$
$374$	9692.96			1.34014
$375$	−3407.12	+	3000.67i	−0.469181	+	0.413211i
$376$	−5480.20			−0.751648
$377$	−430.616			−0.0588272
$378$	5478.94	+	5302.94i	0.745520	+	0.721571i
$379$	−4459.20			−0.604363			−0.302182	−	0.953250i	$-0.597715\pi$
$379$	−4459.20			−0.604363			−0.302182	+	0.953250i	$0.597715\pi$
$380$	3.48233			0.000470104
$381$	−1227.99	+	1081.50i	−0.165123	+	0.145425i
$382$	−9105.87			−1.21963
$383$	−4505.18	−	7803.19i	−0.601054	−	1.04106i	−0.992662	−	0.120924i	$-0.961414\pi$
$383$	−4505.18	−	7803.19i	−0.601054	−	1.04106i	0.391608	−	0.920132i	$-0.371919\pi$
$384$	6206.79	−	5466.36i	0.824841	−	0.726443i
$385$	−4403.62	+	921.849i	−0.582933	+	0.122031i
$386$	7820.57			1.03124
$387$	−6876.02	+	2882.10i	−0.903173	+	0.378567i
$388$	302.058	+	523.179i	0.0395223	+	0.0684546i
$389$	−694.134	+	1202.28i	−0.0904730	+	0.156704i	−0.907710	−	0.419598i	$-0.862171\pi$
$389$	−694.134	+	1202.28i	−0.0904730	+	0.156704i	0.817237	+	0.576301i	$0.195505\pi$
$390$	231.801	−	204.148i	0.0300966	−	0.0265063i
$391$	3016.51	−	5224.75i	0.390157	−	0.675772i
$392$	6812.30	−	2982.88i	0.877738	−	0.384332i
$393$	8413.42	+	2836.24i	1.07990	+	0.364045i
$394$	4209.71			0.538280
$395$	−2004.65	−	3472.16i	−0.255354	−	0.442287i
$396$	−863.760	−	657.030i	−0.109610	−	0.0833762i
$397$	1056.07	−	1829.16i	0.133507	−	0.231242i	−0.791519	−	0.611145i	$-0.790709\pi$
$397$	1056.07	−	1829.16i	0.133507	−	0.231242i	0.925026	+	0.379903i	$0.124043\pi$
$398$	−2990.66	−	5179.97i	−0.376654	−	0.652384i
$399$	−58.3595	−	136.202i	−0.00732238	−	0.0170893i
$400$	−3814.19	+	6606.37i	−0.476774	+	0.825796i
$401$	7681.86	+	13305.4i	0.956642	+	1.65695i	0.730564	+	0.682844i	$0.239257\pi$
$401$	7681.86	+	13305.4i	0.956642	+	1.65695i	0.226078	+	0.974109i	$0.427409\pi$
$402$	−1124.51	+	990.363i	−0.139516	+	0.122873i
$403$	−830.982	+	1439.30i	−0.102715	+	0.177908i
$404$	−229.875	+	398.154i	−0.0283086	+	0.0490320i
$405$	−719.454	−	2597.39i	−0.0882715	−	0.318680i
$406$	−2848.39	−	3183.12i	−0.348185	−	0.389102i
$407$	−6349.53	−	10997.7i	−0.773304	−	1.33940i
$408$	5366.54	+	1809.11i	0.651185	+	0.219520i
$409$	2526.36			0.305429			0.152714	−	0.988270i	$-0.451199\pi$
$409$	2526.36			0.305429			0.152714	+	0.988270i	$0.451199\pi$
$410$	−4267.54			−0.514046
$411$	897.575	+	4463.31i	0.107723	+	0.535666i
$412$	169.153	+	292.981i	0.0202271	+	0.0350343i
$413$	−4764.41	+	997.377i	−0.567654	+	0.118832i
$414$	−8770.01	+	3675.97i	−1.04112	+	0.436387i
$415$	−562.267	+	973.874i	−0.0665074	+	0.115194i
$416$	75.6765	−	131.076i	0.00891911	−	0.0154483i
$417$	−754.364	−	3751.17i	−0.0885884	−	0.440517i
$418$	148.451	+	257.125i	0.0173708	+	0.0300871i
$419$	7146.27	−	12377.7i	0.833217	−	1.44317i	−0.0622570	−	0.998060i	$-0.519830\pi$
$419$	7146.27	−	12377.7i	0.833217	−	1.44317i	0.895474	−	0.445114i	$-0.146837\pi$
$420$	216.109	+	25.7921i	0.0251072	+	0.00299649i
$421$	4922.61	+	8526.22i	0.569866	+	0.987036i	0.996579	+	0.0826493i	$0.0263381\pi$
$421$	4922.61	+	8526.22i	0.569866	+	0.987036i	−0.426713	+	0.904387i	$0.640329\pi$
$422$	−1360.98	+	2357.28i	−0.156994	+	0.271921i
$423$	−862.295	+	6769.82i	−0.0991163	+	0.778156i
$424$	−4428.30	−	7670.05i	−0.507211	−	0.878515i
$425$	−5596.48			−0.638751
$426$	−2918.06	+	2569.95i	−0.331879	+	0.292288i
$427$	2034.86	−	425.976i	0.230618	−	0.0482774i
$428$	83.2977	−	144.276i	0.00940735	−	0.0162940i
$429$	1772.67	+	597.582i	0.199499	+	0.0672530i
$430$	−1497.95	+	2594.52i	−0.167994	+	0.290974i
$431$	−185.814	−	321.839i	−0.0207664	−	0.0359685i	0.855455	−	0.517876i	$-0.173277\pi$
$431$	−185.814	−	321.839i	−0.0207664	−	0.0359685i	−0.876222	+	0.481908i	$0.839944\pi$
$432$	−5391.06	−	7959.07i	−0.600411	−	0.886414i
$433$	−1175.51			−0.130466			−0.0652328	−	0.997870i	$-0.520779\pi$
$433$	−1175.51			−0.130466			−0.0652328	+	0.997870i	$0.520779\pi$
$434$	−16136.0	+	3377.90i	−1.78469	+	0.373604i
$435$	297.670	+	1480.20i	0.0328096	+	0.163150i
$436$	−133.782	−	231.717i	−0.0146949	−	0.0254524i
$437$	184.796			0.0202288
$438$	9945.49	+	3352.72i	1.08496	+	0.365751i
$439$	13454.2			1.46272			0.731358	−	0.681994i	$-0.238887\pi$
$439$	13454.2			1.46272			0.731358	+	0.681994i	$0.238887\pi$
$440$	5267.01			0.570670
$441$	−2612.92	−	8884.75i	−0.282143	−	0.959372i
$442$	808.251			0.0869787
$443$	6329.65			0.678851			0.339425	−	0.940633i	$-0.389767\pi$
$443$	6329.65			0.678851			0.339425	+	0.940633i	$0.389767\pi$
$444$	121.115	+	602.259i	0.0129456	+	0.0643737i
$445$	4070.90			0.433661
$446$	5968.03	+	10336.9i	0.633620	+	1.09746i
$447$	−1593.68	−	537.245i	−0.168632	−	0.0568474i
$448$	−8467.12	+	1772.50i	−0.892933	+	0.186926i
$449$	644.573			0.0677489			0.0338745	−	0.999426i	$-0.489215\pi$
$449$	644.573			0.0677489			0.0338745	+	0.999426i	$0.489215\pi$
$450$	7020.85	+	5340.49i	0.735480	+	0.559451i
$451$	−12922.8	−	22382.9i	−1.34924	−	2.33696i
$452$	96.4424	−	167.043i	0.0100360	−	0.0173828i
$453$	2818.63	+	14016.0i	0.292341	+	1.45370i
$454$	1117.44	−	1935.46i	0.115515	−	0.200079i
$455$	−367.197	+	76.8687i	−0.0378340	+	0.00792013i
$456$	34.2003	+	170.066i	0.00351223	+	0.0174650i
$457$	2638.21			0.270044			0.135022	−	0.990843i	$-0.456889\pi$
$457$	2638.21			0.270044			0.135022	+	0.990843i	$0.456889\pi$
$458$	−7532.82	−	13047.2i	−0.768527	−	1.33113i
$459$	3079.25	−	6344.76i	0.313131	−	0.645203i
$460$	−135.713	+	235.062i	−0.0137558	+	0.0238257i
$461$	1820.24	+	3152.75i	0.183898	+	0.318521i	0.943205	−	0.332212i	$-0.107795\pi$
$461$	1820.24	+	3152.75i	0.183898	+	0.318521i	−0.759307	+	0.650733i	$0.774462\pi$
$462$	7308.28	+	17056.4i	0.735957	+	1.71761i
$463$	−3186.10	+	5518.49i	−0.319807	+	0.553923i	−0.980448	−	0.196780i	$-0.936952\pi$
$463$	−3186.10	+	5518.49i	−0.319807	+	0.553923i	0.660640	+	0.750703i	$0.270285\pi$
$464$	2692.60	+	4663.71i	0.269398	+	0.466611i
$465$	5521.90	+	1861.48i	0.550692	+	0.185643i
$466$	2108.10	−	3651.33i	0.209562	−	0.362972i
$467$	2398.70	−	4154.67i	0.237684	−	0.411681i	−0.722365	−	0.691512i	$-0.756945\pi$
$467$	2398.70	−	4154.67i	0.237684	−	0.411681i	0.960049	+	0.279831i	$0.0902783\pi$
$468$	−72.0250	−	54.7867i	−0.00711401	−	0.00541135i
$469$	1781.35	−	372.905i	0.175384	−	0.0367146i
$470$	1371.15	+	2374.90i	0.134567	+	0.233077i
$471$	6668.17	−	5872.70i	0.652342	−	0.574522i
$472$	5698.54			0.555713
$473$	−18144.0			−1.76377
$474$	−12409.5	+	10929.2i	−1.20251	+	1.05906i
$475$	−85.7123	−	148.458i	−0.00827947	−	0.0143405i
$476$	379.767	+	424.396i	0.0365685	+	0.0408659i
$477$	−10171.8	+	4263.53i	−0.976381	+	0.409253i
$478$	−3994.38	+	6918.47i	−0.382215	+	0.662016i
$479$	−5969.99	+	10340.3i	−0.569470	+	0.986350i	0.427149	+	0.904181i	$0.359518\pi$
$479$	−5969.99	+	10340.3i	−0.569470	+	0.986350i	−0.996618	+	0.0821690i	$0.973815\pi$
$480$	−502.873	−	169.523i	−0.0478186	−	0.0161201i
$481$	−529.458	−	917.048i	−0.0501896	−	0.0869310i
$482$	−9082.40	+	15731.2i	−0.858282	+	1.48659i
$483$	11468.2	+	1368.70i	1.08037	+	0.128940i
$484$	−913.438	−	1582.12i	−0.0857849	−	0.148584i
$485$	−1825.57	+	3161.99i	−0.170918	+	0.296038i
$486$	−9917.49	+	5021.17i	−0.925651	+	0.468652i
$487$	4633.83	+	8026.04i	0.431168	+	0.746806i	0.996974	−	0.0777329i	$-0.0247681\pi$
$487$	4633.83	+	8026.04i	0.431168	+	0.746806i	−0.565806	+	0.824539i	$0.691435\pi$
$488$	−2433.83			−0.225767
$489$	−3472.16	−	17265.8i	−0.321097	−	1.59670i
$490$	−2997.11	−	2205.86i	−0.276317	−	0.203369i
$491$	2769.69	−	4797.25i	0.254571	−	0.440931i	−0.710208	−	0.703992i	$-0.751399\pi$
$491$	2769.69	−	4797.25i	0.254571	−	0.440931i	0.964779	+	0.263062i	$0.0847323\pi$
$492$	246.496	+	1225.73i	0.0225872	+	0.112318i
$493$	−1975.40	+	3421.49i	−0.180461	+	0.312568i
$494$	12.3787	+	21.4405i	0.00112741	+	0.00195274i
$495$	828.750	−	6506.47i	0.0752516	−	0.590796i
$496$	20784.1			1.88152
$497$	4622.52	−	967.673i	0.417200	−	0.0873362i
$498$	4395.05	+	1481.61i	0.395476	+	0.133319i
$499$	−2601.07	−	4505.19i	−0.233347	−	0.404168i	0.725444	−	0.688281i	$-0.241634\pi$
$499$	−2601.07	−	4505.19i	−0.233347	−	0.404168i	−0.958791	+	0.284113i	$0.908301\pi$
$500$	534.485			0.0478058
$501$	1603.85	+	7975.34i	0.143023	+	0.711201i
$502$	14152.7			1.25830
$503$	8925.34			0.791176			0.395588	−	0.918428i	$-0.370541\pi$
$503$	8925.34			0.791176			0.395588	+	0.918428i	$0.370541\pi$
$504$	862.825	+	10807.4i	0.0762565	+	0.955155i
$505$	−2778.63			−0.244846
$506$	−23141.8			−2.03316
$507$	−10670.0	−	3596.95i	−0.934656	−	0.315081i
$508$	192.639			0.0168247
$509$	−441.724	−	765.088i	−0.0384658	−	0.0666246i	0.846152	−	0.532942i	$-0.178914\pi$
$509$	−441.724	−	765.088i	−0.0384658	−	0.0666246i	−0.884617	+	0.466318i	$0.845580\pi$
$510$	−558.716	−	2778.29i	−0.0485105	−	0.241225i
$511$	−8500.41	−	9499.35i	−0.735883	−	0.822361i
$512$	9992.04			0.862480
$513$	215.467	−	15.4891i	0.0185441	−	0.00133306i
$514$	8778.65	+	15205.1i	0.753326	+	1.30480i
$515$	−1022.32	+	1770.72i	−0.0874738	+	0.151509i
$516$	831.727	+	280.383i	0.0709588	+	0.0239209i
$517$	−8304.09	+	14383.1i	−0.706409	+	1.22354i
$518$	3276.63	−	9979.73i	0.277929	−	0.846495i
$519$	−11108.9	+	9783.68i	−0.939550	+	0.827468i
$520$	439.192			0.0370381
$521$	3383.38	+	5860.18i	0.284507	+	0.492781i	0.972490	−	0.232946i	$-0.0748366\pi$
$521$	3383.38	+	5860.18i	0.284507	+	0.492781i	−0.687982	+	0.725728i	$0.741503\pi$
$522$	5743.14	−	2407.25i	0.481552	−	0.201844i
$523$	−2074.51	+	3593.15i	−0.173445	+	0.300416i	−0.939622	−	0.342214i	$-0.888823\pi$
$523$	−2074.51	+	3593.15i	−0.173445	+	0.300416i	0.766177	+	0.642630i	$0.222157\pi$
$524$	−522.620	−	905.205i	−0.0435702	−	0.0754658i
$525$	−4219.62	−	9847.94i	−0.350780	−	0.818665i
$526$	5502.18	−	9530.05i	0.456096	−	0.789981i
$527$	7624.04	+	13205.2i	0.630187	+	1.09152i
$528$	−4612.28	−	22935.2i	−0.380158	−	1.89039i
$529$	−1118.36	+	1937.06i	−0.0919177	+	0.159206i
$530$	−2215.93	+	3838.10i	−0.181611	+	0.314560i
$531$	896.650	−	7039.54i	0.0732793	−	0.575311i
$532$	−5.44168	+	16.5739i	−0.000443472	+	0.00135069i
$533$	−1077.57	−	1866.40i	−0.0875697	−	0.151675i
$534$	−3310.25	−	16460.6i	−0.268256	−	1.33394i
$535$	1006.87			0.0813658
$536$	−2130.60			−0.171694
$537$	−19742.4	−	6655.33i	−1.58649	−	0.534821i
$538$	1758.85	+	3046.42i	0.140947	+	0.244127i
$539$	2493.87	−	22399.2i	0.199293	−	1.78999i
$540$	−138.536	+	285.451i	−0.0110401	+	0.0227479i
$541$	525.578	−	910.327i	0.0417677	−	0.0723439i	−0.844386	−	0.535736i	$-0.820034\pi$
$541$	525.578	−	910.327i	0.0417677	−	0.0723439i	0.886154	+	0.463392i	$0.153368\pi$
$542$	−5891.62	+	10204.6i	−0.466913	+	0.808717i
$543$	18518.7	−	16309.5i	1.46356	−	1.28897i
$544$	−694.312	−	1202.58i	−0.0547213	−	0.0947801i
$545$	808.550	−	1400.45i	0.0635495	−	0.110071i
$546$	609.403	+	1422.25i	0.0477657	+	0.111478i
$547$	−8242.51	−	14276.4i	−0.644286	−	1.11594i	−0.984466	−	0.175575i	$-0.943821\pi$
$547$	−8242.51	−	14276.4i	−0.644286	−	1.11594i	0.340180	−	0.940360i	$-0.389512\pi$
$548$	267.982	−	464.159i	0.0208899	−	0.0361823i
$549$	−382.956	+	3006.57i	−0.0297708	+	0.233729i
$550$	10733.6	+	18591.2i	0.832152	+	1.44133i
$551$	−121.016			−0.00935652
$552$	−12812.5	−	4319.22i	−0.987930	−	0.333040i
$553$	19658.1	−	4115.20i	1.51166	−	0.316448i
$554$	−6483.43	+	11229.6i	−0.497211	+	0.861194i
$555$	−2786.27	+	2453.89i	−0.213100	+	0.187679i
$556$	−225.225	+	390.101i	−0.0171793	+	0.0297553i
$557$	−4592.38	−	7954.23i	−0.349345	−	0.605084i	0.636788	−	0.771039i	$-0.280263\pi$
$557$	−4592.38	−	7954.23i	−0.349345	−	0.605084i	−0.986133	+	0.165955i	$0.946929\pi$
$558$	3036.76	−	23841.4i	0.230388	−	1.80876i
$559$	−1512.95			−0.114474
$560$	3128.56	+	3496.21i	0.236082	+	0.263825i
$561$	12880.0	−	11343.5i	0.969329	−	0.853694i
$562$	−2308.19	−	3997.91i	−0.173248	−	0.300074i
$563$	19540.3			1.46275			0.731373	−	0.681977i	$-0.238880\pi$
$563$	19540.3			1.46275			0.731373	+	0.681977i	$0.238880\pi$
$564$	602.927	−	531.001i	0.0450138	−	0.0396440i
$565$	1165.76			0.0868030
$566$	−14286.5			−1.06097
$567$	13486.3	+	634.641i	0.998895	+	0.0470060i
$568$	−5528.83			−0.408424
$569$	18980.7			1.39844			0.699220	−	0.714906i	$-0.253531\pi$
$569$	18980.7			1.39844			0.699220	+	0.714906i	$0.253531\pi$
$570$	65.1428	−	57.3716i	0.00478690	−	0.00421585i
$571$	19907.7			1.45904			0.729519	−	0.683960i	$-0.239744\pi$
$571$	19907.7			1.45904			0.729519	+	0.683960i	$0.239744\pi$
$572$	−110.113	−	190.722i	−0.00804908	−	0.0139414i
$573$	−12099.9	+	10656.4i	−0.882163	+	0.776926i
$574$	6668.70	−	20311.1i	0.484924	−	1.47695i
$575$	13361.5			0.969066
$576$	1593.49	−	12510.4i	0.115270	−	0.904977i
$577$	759.050	+	1314.71i	0.0547655	+	0.0948566i	0.892108	−	0.451821i	$-0.149226\pi$
$577$	759.050	+	1314.71i	0.0547655	+	0.0948566i	−0.837343	+	0.546678i	$0.815892\pi$
$578$	−3501.03	+	6063.97i	−0.251944	+	0.436380i
$579$	10392.0	−	9152.27i	0.745899	−	0.656917i
$580$	88.8733	−	153.933i	0.00636252	−	0.0110202i
$581$	−3756.45	−	4197.90i	−0.268234	−	0.299756i
$582$	14269.9	+	4810.52i	1.01633	+	0.342616i
$583$	−26840.7			−1.90674
$584$	7461.58	+	12923.8i	0.528703	+	0.915740i
$585$	69.1056	−	542.544i	0.00488405	−	0.0383443i
$586$	12850.6	−	22257.9i	0.905892	−	1.56905i
$587$	49.6245	+	85.9522i	0.00348931	+	0.00604366i	0.867765	−	0.496975i	$-0.165556\pi$
$587$	49.6245	+	85.9522i	0.00348931	+	0.00604366i	−0.864275	+	0.503019i	$0.832223\pi$
$588$	−460.459	+	988.249i	−0.0322942	+	0.0693107i
$589$	−233.530	+	404.486i	−0.0163369	+	0.0282964i
$590$	−1425.78	−	2469.52i	−0.0994888	−	0.172320i
$591$	5593.86	−	4926.55i	0.389341	−	0.342895i
$592$	−6621.28	+	11468.4i	−0.459684	+	0.796196i
$593$	−1602.40	+	2775.44i	−0.110966	+	0.192199i	−0.916160	−	0.400813i	$-0.868728\pi$
$593$	−1602.40	+	2775.44i	−0.110966	+	0.192199i	0.805194	+	0.593011i	$0.202061\pi$
$594$	−26982.7	+	1939.68i	−1.86383	+	0.133983i
$595$	−1073.70	+	3270.21i	−0.0739792	+	0.225320i
$596$	98.9954	+	171.465i	0.00680371	+	0.0117844i
$597$	−10036.0	−	3383.23i	−0.688018	−	0.231937i
$598$	−1929.68			−0.131958
$599$	−19758.0			−1.34773			−0.673866	−	0.738854i	$-0.735368\pi$
$599$	−19758.0			−1.34773			−0.673866	+	0.738854i	$0.735368\pi$
$600$	2472.82	+	12296.4i	0.168254	+	0.836666i
$601$	745.047	+	1290.46i	0.0505676	+	0.0875856i	0.890201	−	0.455568i	$-0.150564\pi$
$601$	745.047	+	1290.46i	0.0505676	+	0.0875856i	−0.839634	+	0.543153i	$0.817230\pi$
$602$	−10007.6	−	11183.7i	−0.677544	−	0.757166i
$603$	−335.245	+	2631.99i	−0.0226405	+	0.177749i
$604$	841.536	−	1457.58i	0.0566914	−	0.0981925i
$605$	5520.63	−	9562.01i	0.370984	−	0.642563i
$606$	2259.44	+	11235.3i	0.151458	+	0.753143i
$607$	1207.26	+	2091.04i	0.0807269	+	0.139823i	0.903562	−	0.428457i	$-0.140942\pi$
$607$	1207.26	+	2091.04i	0.0807269	+	0.139823i	−0.822835	+	0.568280i	$0.807609\pi$
$608$	21.2673	−	36.8361i	0.00141859	−	0.00245707i
$609$	−7510.08	−	896.311i	−0.499710	−	0.0596394i
$610$	608.946	+	1054.72i	0.0404188	+	0.0700075i
$611$	−692.440	+	1199.34i	−0.0458480	+	0.0794110i
$612$	−765.716	+	320.952i	−0.0505755	+	0.0211989i
$613$	6831.31	+	11832.2i	0.450105	+	0.779604i	0.998392	−	0.0566858i	$-0.0180533\pi$
$613$	6831.31	+	11832.2i	0.450105	+	0.779604i	−0.548287	+	0.836290i	$0.684720\pi$
$614$	16106.5			1.05864
$615$	−5670.71	+	4994.22i	−0.371813	+	0.327458i
$616$	−8230.53	+	25067.9i	−0.538340	+	1.63964i
$617$	1876.84	−	3250.78i	0.122461	−	0.212109i	−0.798276	−	0.602291i	$-0.794255\pi$
$617$	1876.84	−	3250.78i	0.122461	−	0.212109i	0.920738	+	0.390182i	$0.127588\pi$
$618$	7991.17	+	2693.90i	0.520149	+	0.175347i
$619$	−12799.7	+	22169.7i	−0.831118	+	1.43954i	0.0660345	+	0.997817i	$0.478965\pi$
$619$	−12799.7	+	22169.7i	−0.831118	+	1.43954i	−0.897152	+	0.441721i	$0.854368\pi$
$620$	−343.006	−	594.104i	−0.0222185	−	0.0384836i
$621$	−7351.65	+	15148.0i	−0.475059	+	0.978854i
$622$	−5003.15			−0.322521
$623$	−6361.42	+	19375.2i	−0.409093	+	1.24599i
$624$	−384.596	−	1912.46i	−0.0246734	−	0.122692i
$625$	−5343.05	−	9254.44i	−0.341955	−	0.592284i
$626$	19522.5			1.24645
$627$	498.171	+	167.938i	0.0317305	+	0.0106966i
$628$	−1046.06			−0.0664685
$629$	−9715.27			−0.615856
$630$	4467.60	−	3077.92i	0.282529	−	0.194647i
$631$	718.485			0.0453288			0.0226644	−	0.999743i	$-0.492785\pi$
$631$	718.485			0.0453288			0.0226644	+	0.999743i	$0.492785\pi$
$632$	−23512.3			−1.47986
$633$	950.217	+	4725.08i	0.0596647	+	0.296690i
$634$	12401.0			0.776826
$635$	582.135	+	1008.29i	0.0363800	+	0.0630121i
$636$	1230.38	+	414.774i	0.0767105	+	0.0258598i
$637$	207.952	−	1867.77i	0.0129347	−	0.116175i
$638$	15154.6			0.940404
$639$	−869.947	+	6829.90i	−0.0538569	+	0.422827i
$640$	−2942.36	−	5096.31i	−0.181729	−	0.314765i
$641$	−4421.16	+	7657.67i	−0.272426	+	0.471856i	−0.969483	−	0.245160i	$-0.921159\pi$
$641$	−4421.16	+	7657.67i	−0.272426	+	0.471856i	0.697056	+	0.717016i	$0.254493\pi$
$642$	−818.733	−	4071.26i	−0.0503315	−	0.250280i
$643$	−15033.0	+	26037.9i	−0.921997	+	1.59695i	−0.125676	+	0.992071i	$0.540110\pi$
$643$	−15033.0	+	26037.9i	−0.921997	+	1.59695i	−0.796321	+	0.604874i	$0.793224\pi$
$644$	−906.687	−	1013.24i	−0.0554790	−	0.0619987i
$645$	1045.85	+	5200.61i	0.0638453	+	0.317479i
$646$	227.142			0.0138340
$647$	−2937.46	−	5087.84i	−0.178491	−	0.309155i	0.762873	−	0.646548i	$-0.223788\pi$
$647$	−2937.46	−	5087.84i	−0.178491	−	0.309155i	−0.941364	+	0.337393i	$0.890455\pi$
$648$	−15301.1	−	3962.19i	−0.927599	−	0.240200i
$649$	8634.94	−	14956.2i	0.522267	−	0.904593i
$650$	895.028	+	1550.23i	0.0540090	+	0.0935464i
$651$	−17488.4	+	23372.2i	−1.05288	+	1.40711i
$652$	−1036.66	+	1795.54i	−0.0622678	+	0.107851i
$653$	9099.17	+	15760.2i	0.545296	+	0.944480i	0.998588	+	0.0531181i	$0.0169160\pi$
$653$	9099.17	+	15760.2i	0.545296	+	0.944480i	−0.453292	+	0.891362i	$0.649751\pi$
$654$	−6320.17	−	2130.59i	−0.377887	−	0.127389i
$655$	3158.61	−	5470.87i	0.188423	−	0.326358i
$656$	−13475.8	+	23340.8i	−0.802047	+	1.38919i
$657$	17139.2	−	7183.93i	1.01775	−	0.426594i
$658$	−13445.8	+	2814.73i	−0.796614	+	0.166762i
$659$	−5816.45	−	10074.4i	−0.343819	−	0.595512i	0.641320	−	0.767274i	$-0.278387\pi$
$659$	−5816.45	−	10074.4i	−0.343819	−	0.595512i	−0.985138	+	0.171762i	$0.945054\pi$
$660$	−579.472	+	510.345i	−0.0341756	+	0.0300987i
$661$	−8940.79			−0.526107			−0.263053	−	0.964781i	$-0.584730\pi$
$661$	−8940.79			−0.526107			−0.263053	+	0.964781i	$0.584730\pi$
$662$	−12955.5			−0.760622
$663$	1074.00	−	945.881i	0.0629122	−	0.0554072i
$664$	3297.38	+	5711.22i	0.192715	+	0.333793i
$665$	−103.193	+	21.6024i	−0.00601753	+	0.00125970i
$666$	12187.9	+	9270.88i	0.709117	+	0.539399i
$667$	4716.22	−	8168.73i	0.273782	−	0.474205i
$668$	478.849	−	829.391i	0.0277354	−	0.0480391i
$669$	20027.4	+	6751.43i	1.15741	+	0.390173i
$670$	533.079	+	923.320i	0.0307383	+	0.0532402i
$671$	−3687.96	+	6387.73i	−0.212179	+	0.367504i
$672$	1592.65	−	2128.48i	0.0914253	−	0.122184i
$673$	5154.45	+	8927.77i	0.295229	+	0.511352i	0.975038	−	0.222037i	$-0.0712706\pi$
$673$	5154.45	+	8927.77i	0.295229	+	0.511352i	−0.679809	+	0.733389i	$0.737937\pi$
$674$	−3787.77	+	6560.61i	−0.216468	+	0.374933i
$675$	15579.2	−	1119.92i	0.888359	−	0.0638606i
$676$	662.792	+	1147.99i	0.0377101	+	0.0653158i
$677$	19108.4			1.08478			0.542389	−	0.840128i	$-0.317520\pi$
$677$	19108.4			1.08478			0.542389	+	0.840128i	$0.317520\pi$
$678$	−947.932	−	4713.72i	−0.0536949	−	0.267005i
$679$	−12196.5	−	13629.8i	−0.689335	−	0.770343i
$680$	2014.73	−	3489.62i	0.113620	−	0.196795i
$681$	−780.182	−	3879.55i	−0.0439011	−	0.218304i
$682$	29244.7	−	50653.2i	1.64199	−	2.84401i
$683$	−7772.25	−	13461.9i	−0.435427	−	0.754182i	0.561903	−	0.827203i	$-0.310069\pi$
$683$	−7772.25	−	13461.9i	−0.435427	−	0.754182i	−0.997330	+	0.0730208i	$0.976736\pi$
$684$	−20.2411	−	15.3967i	−0.00113149	−	0.000860681i
$685$	3239.26			0.180680
$686$	15182.1	−	10817.5i	0.844978	−	0.602061i
$687$	−25278.5	−	8521.62i	−1.40384	−	0.473246i
$688$	9460.28	+	16385.7i	0.524230	+	0.907992i
$689$	−2238.12			−0.123753
$690$	1333.92	+	6633.11i	0.0735966	+	0.365969i
$691$	13845.9			0.762261			0.381131	−	0.924521i	$-0.375535\pi$
$691$	13845.9			0.762261			0.381131	+	0.924521i	$0.375535\pi$
$692$	1742.69			0.0957327
$693$	29672.0	+	14111.7i	1.62647	+	0.773537i
$694$	−17748.8			−0.970800
$695$	−2722.43			−0.148586
$696$	8390.42	+	2828.49i	0.456951	+	0.154043i
$697$	−19772.8			−1.07453
$698$	−16579.5	−	28716.5i	−0.899058	−	1.55721i
$699$	−1471.85	−	7318.95i	−0.0796429	−	0.396035i
$700$	−393.455	+	1198.36i	−0.0212446	+	0.0647052i
$701$	21818.9			1.17559			0.587794	−	0.809011i	$-0.299997\pi$
$701$	21818.9			1.17559			0.587794	+	0.809011i	$0.299997\pi$
$702$	−2249.96	+	161.741i	−0.120968	+	0.00869590i
$703$	−148.793	−	257.717i	−0.00798270	−	0.0138264i
$704$	15345.7	−	26579.5i	0.821537	−	1.42294i
$705$	4601.28	+	1551.14i	0.245808	+	0.0828640i
$706$	1520.41	−	2633.42i	0.0810500	−	0.140383i
$707$	4342.04	−	13224.7i	0.230975	−	0.703486i
$708$	−626.949	+	552.157i	−0.0332799	+	0.0293098i
$709$	490.782			0.0259968			0.0129984	−	0.999916i	$-0.495862\pi$
$709$	490.782			0.0259968			0.0129984	+	0.999916i	$0.495862\pi$
$710$	1383.32	+	2395.98i	0.0731197	+	0.126647i
$711$	−3699.60	+	29045.3i	−0.195142	+	1.53204i
$712$	11936.8	−	20675.1i	0.628300	−	1.08825i
$713$	−18202.2	−	31527.2i	−0.956072	−	1.65597i
$714$	14096.1	+	1682.34i	0.738844	+	0.0881794i
$715$	665.503	−	1152.68i	0.0348089	−	0.0602909i
$716$	1226.34	+	2124.09i	0.0640093	+	0.110867i
$717$	2788.83	+	13867.8i	0.145259	+	0.722319i
$718$	−15133.0	+	26211.1i	−0.786572	+	1.36238i
$719$	−3069.85	+	5317.13i	−0.159229	+	0.275794i	−0.934591	−	0.355724i	$-0.884234\pi$
$719$	−3069.85	+	5317.13i	−0.159229	+	0.275794i	0.775362	+	0.631518i	$0.217568\pi$
$720$	−6308.03	+	2644.03i	−0.326509	+	0.136857i
$721$	−6830.05	−	7632.70i	−0.352794	−	0.394253i
$722$	−10060.6	−	17425.5i	−0.518585	−	0.898215i
$723$	6341.21	+	31532.5i	0.326186	+	1.62200i
$724$	−2905.09			−0.149125
$725$	−8749.92			−0.448226
$726$	−43152.9	−	14547.3i	−2.20600	−	0.743663i
$727$	−9687.53	−	16779.3i	−0.494210	−	0.855997i	0.505768	−	0.862670i	$-0.331209\pi$
$727$	−9687.53	−	16779.3i	−0.494210	−	0.855997i	−0.999978	+	0.00667304i	$0.997876\pi$
$728$	−686.306	+	2090.30i	−0.0349398	+	0.106417i
$729$	−7302.17	+	18278.4i	−0.370989	+	0.928637i
$730$	3733.79	−	6467.11i	0.189306	−	0.327888i
$731$	−6940.44	+	12021.2i	−0.351165	+	0.608235i
$732$	267.768	−	235.825i	0.0135205	−	0.0119076i
$733$	−4090.20	−	7084.44i	−0.206105	−	0.356985i	0.744379	−	0.667757i	$-0.232746\pi$
$733$	−4090.20	−	7084.44i	−0.206105	−	0.356985i	−0.950484	+	0.310773i	$0.899412\pi$
$734$	−3031.51	+	5250.72i	−0.152445	+	0.264043i
$735$	−6564.03	+	576.306i	−0.329412	+	0.0289216i
$736$	1657.66	+	2871.15i	0.0830191	+	0.143793i
$737$	−3228.48	+	5591.90i	−0.161361	+	0.279485i
$738$	24805.2	+	18868.4i	1.23725	+	0.941131i
$739$	−3994.83	−	6919.24i	−0.198853	−	0.344423i	0.749304	−	0.662226i	$-0.230388\pi$
$739$	−3994.83	−	6919.24i	−0.198853	−	0.344423i	−0.948157	+	0.317803i	$0.897055\pi$
$740$	437.091			0.0217132
$741$	41.5402	+	14.0036i	0.00205940	+	0.000694243i
$742$	−14804.4	−	16544.2i	−0.732463	−	0.818540i
$743$	11091.9	−	19211.7i	0.547674	−	0.948599i	−0.450760	−	0.892645i	$-0.648847\pi$
$743$	11091.9	−	19211.7i	0.547674	−	0.948599i	0.998433	−	0.0559534i	$-0.0178198\pi$
$744$	25645.4	−	22586.1i	1.26372	−	1.11297i
$745$	−598.308	+	1036.30i	−0.0294232	+	0.0509625i
$746$	7071.78	+	12248.7i	0.347073	+	0.601148i
$747$	7574.04	−	3174.68i	0.370977	−	0.155496i
$748$	−2020.52			−0.0987669
$749$	−1573.39	+	4792.11i	−0.0767562	+	0.233778i
$750$	9998.44	−	8805.69i	0.486789	−	0.428718i
$751$	−6605.32	−	11440.7i	−0.320947	−	0.555897i	0.659736	−	0.751497i	$-0.270668\pi$
$751$	−6605.32	−	11440.7i	−0.320947	−	0.555897i	−0.980684	+	0.195600i	$0.937335\pi$
$752$	17319.0			0.839839
$753$	18806.1	−	16562.7i	0.910138	−	0.801564i
$754$	1263.67			0.0610349
$755$	10172.1			0.490334
$756$	−1142.10	−	1105.41i	−0.0549442	−	0.0531792i
$757$	−5945.66			−0.285467			−0.142734	−	0.989761i	$-0.545589\pi$
$757$	−5945.66			−0.285467			−0.142734	+	0.989761i	$0.545589\pi$
$758$	13085.8			0.627044
$759$	−30750.7	+	27082.4i	−1.47059	+	1.29516i
$760$	123.426			0.00589095
$761$	−3981.91	−	6896.87i	−0.189677	−	0.328530i	0.755466	−	0.655188i	$-0.227411\pi$
$761$	−3981.91	−	6896.87i	−0.189677	−	0.328530i	−0.945142	+	0.326658i	$0.894077\pi$
$762$	3603.63	−	3173.74i	0.171320	−	0.150883i
$763$	5401.85	+	6036.65i	0.256304	+	0.286424i
$764$	1898.14			0.0898854
$765$	−3993.80	−	3037.93i	−0.188753	−	0.143577i
$766$	13220.8	+	22899.0i	0.623611	+	1.08013i
$767$	720.028	−	1247.12i	0.0338966	−	0.0587106i
$768$	−3643.06	+	3208.46i	−0.171169	+	0.150749i
$769$	11183.7	−	19370.7i	0.524439	−	0.908355i	−0.475156	−	0.879902i	$-0.657608\pi$
$769$	11183.7	−	19370.7i	0.524439	−	0.908355i	0.999595	−	0.0284535i	$-0.00905826\pi$
$770$	12922.7	−	2705.23i	0.604809	−	0.126610i
$771$	29459.3	+	9930.98i	1.37607	+	0.463885i
$772$	−1630.22			−0.0760012
$773$	−14269.9	−	24716.1i	−0.663974	−	1.15004i	−0.979562	−	0.201140i	$-0.935535\pi$
$773$	−14269.9	−	24716.1i	−0.663974	−	1.15004i	0.315589	−	0.948896i	$-0.397798\pi$
$774$	20178.2	−	8457.74i	0.937067	−	0.392774i
$775$	−16885.2	+	29246.0i	−0.782623	+	1.35554i
$776$	10706.0	+	18543.3i	0.495260	+	0.857815i
$777$	−7325.10	−	17095.6i	−0.338207	−	0.789321i
$778$	2036.99	−	3528.17i	0.0938683	−	0.162585i
$779$	−302.828	−	524.514i	−0.0139280	−	0.0241241i
$780$	−48.3195	+	42.5553i	−0.00221810	+	0.00195349i
$781$	−8377.78	+	14510.7i	−0.383842	+	0.664834i
$782$	−8852.17	+	15332.4i	−0.404799	+	0.701133i
$783$	4814.31	−	9919.83i	0.219731	−	0.452753i
$784$	−21528.8	+	9426.75i	−0.980723	+	0.429426i
$785$	−3161.07	−	5475.14i	−0.143724	−	0.248938i
$786$	−24689.8	−	8323.16i	−1.12043	−	0.377706i
$787$	−28114.7			−1.27342			−0.636711	−	0.771103i	$-0.719705\pi$
$787$	−28114.7			−1.27342			−0.636711	+	0.771103i	$0.719705\pi$
$788$	−877.526			−0.0396708
$789$	−3841.55	−	19102.6i	−0.173337	−	0.861940i
$790$	5882.80	+	10189.3i	0.264937	+	0.458885i
$791$	−1821.67	+	5548.32i	−0.0818853	+	0.249400i
$792$	−30614.6	−	23287.4i	−1.37354	−	1.04480i
$793$	−307.521	+	532.643i	−0.0137710	+	0.0238521i
$794$	−3099.10	+	5367.80i	−0.138518	+	0.239920i
$795$	1547.13	+	7693.33i	0.0690204	+	0.343213i
$796$	623.411	+	1079.78i	0.0277591	+	0.0480801i
$797$	798.238	−	1382.59i	0.0354769	−	0.0614477i	−0.847742	−	0.530409i	$-0.822038\pi$
$797$	798.238	−	1382.59i	0.0354769	−	0.0614477i	0.883219	+	0.468961i	$0.155372\pi$
$798$	171.260	+	399.694i	0.00759717	+	0.0177306i
$799$	6352.95	+	11003.6i	0.281291	+	0.487210i
$800$	1537.71	−	2663.40i	0.0679579	−	0.117707i
$801$	−23662.2	−	17999.0i	−1.04377	−	0.793960i
$802$	−22543.0	−	39045.6i	−0.992544	−	1.71914i
$803$	45225.8			1.98753
$804$	234.407	−	206.444i	0.0102822	−	0.00905561i
$805$	2563.45	−	7807.57i	0.112236	−	0.341839i
$806$	2438.58	−	4223.74i	0.106570	−	0.184584i
$807$	5902.33	+	1989.73i	0.257462	+	0.0867928i
$808$	−8147.54	+	14112.0i	−0.354740	+	0.614427i
$809$	17244.2	+	29867.8i	0.749411	+	1.29802i	0.948105	+	0.317956i	$0.102996\pi$
$809$	17244.2	+	29867.8i	0.749411	+	1.29802i	−0.198695	+	0.980061i	$0.563670\pi$
$810$	2111.29	+	7622.23i	0.0915842	+	0.330639i
$811$	13083.8			0.566504			0.283252	−	0.959046i	$-0.408587\pi$
$811$	13083.8			0.566504			0.283252	+	0.959046i	$0.408587\pi$
$812$	593.754	+	663.530i	0.0256609	+	0.0286765i
$813$	4113.46	+	20454.7i	0.177448	+	0.882383i
$814$	18633.2	+	32273.6i	0.802324	+	1.38967i
$815$	−12530.7			−0.538565
$816$	−16959.8	−	5717.31i	−0.727588	−	0.245277i
$817$	−425.182			−0.0182071
$818$	−7413.79			−0.316891
$819$	2474.21	+	1176.71i	0.105563	+	0.0502047i
$820$	889.581			0.0378848
$821$	27720.8			1.17839			0.589197	−	0.807990i	$-0.299444\pi$
$821$	27720.8			1.17839			0.589197	+	0.807990i	$0.299444\pi$
$822$	−2634.00	−	13097.9i	−0.111766	−	0.555769i
$823$	42033.0			1.78029			0.890144	−	0.455679i	$-0.150603\pi$
$823$	42033.0			1.78029			0.890144	+	0.455679i	$0.150603\pi$
$824$	5995.36	+	10384.3i	0.253469	+	0.439020i
$825$	36019.8	+	12142.6i	1.52006	+	0.512425i
$826$	13981.5	−	2926.87i	0.588957	−	0.123292i
$827$	−37151.6			−1.56214			−0.781069	−	0.624444i	$-0.785325\pi$
$827$	−37151.6			−1.56214			−0.781069	+	0.624444i	$0.785325\pi$
$828$	1828.13	−	766.266i	0.0767294	−	0.0321614i
$829$	−16093.7	−	27875.1i	−0.674254	−	1.16784i	−0.976686	−	0.214671i	$-0.931132\pi$
$829$	−16093.7	−	27875.1i	−0.674254	−	1.16784i	0.302432	−	0.953171i	$-0.402201\pi$
$830$	1650.01	−	2857.91i	0.0690033	−	0.119517i
$831$	4526.65	+	22509.4i	0.188962	+	0.939640i
$832$	1279.60	−	2216.34i	0.0533201	−	0.0923531i
$833$	−13886.5	−	10220.4i	−0.577597	−	0.425110i
$834$	2213.74	+	11008.1i	0.0919130	+	0.457049i
$835$	5788.13			0.239888
$836$	−30.9451	−	53.5985i	−0.00128021	−	0.00221739i
$837$	−23865.9	−	35234.3i	−0.985574	−	1.45505i
$838$	−20971.2	+	36323.2i	−0.864486	+	1.49733i
$839$	−10945.1	−	18957.4i	−0.450376	−	0.780075i	0.548033	−	0.836457i	$-0.315377\pi$
$839$	−10945.1	−	18957.4i	−0.450376	−	0.780075i	−0.998409	+	0.0563819i	$0.982044\pi$
$840$	7659.63	+	914.161i	0.314622	+	0.0375495i
$841$	9106.03	−	15772.1i	0.373366	−	0.646689i
$842$	−14445.8	−	25020.8i	−0.591252	−	1.02408i
$843$	−7745.80	−	2611.18i	−0.316465	−	0.106683i
$844$	283.699	−	491.382i	0.0115703	−	0.0200404i
$845$	−4005.78	+	6938.21i	−0.163080	+	0.282464i
$846$	2530.47	−	19866.5i	0.102836	−	0.807359i
$847$	36882.8	+	41217.1i	1.49623	+	1.67206i
$848$	13994.7	+	24239.5i	0.566722	+	0.981591i
$849$	−18983.9	+	16719.2i	−0.767404	+	0.675857i
$850$	16423.3			0.662722
$851$	23195.0			0.934331
$852$	608.277	−	535.713i	0.0244592	−	0.0215414i
$853$	−4501.76	−	7797.27i	−0.180700	−	0.312982i	0.761419	−	0.648260i	$-0.224503\pi$
$853$	−4501.76	−	7797.27i	−0.180700	−	0.312982i	−0.942119	+	0.335278i	$0.891170\pi$
$854$	−5971.46	+	1250.06i	−0.239273	+	0.0500891i
$855$	19.4207	−	152.471i	0.000776812	−	0.00609870i
$856$	2952.36	−	5113.63i	0.117885	−	0.204183i
$857$	14264.5	−	24706.8i	0.568571	−	0.984794i	−0.428136	−	0.903714i	$-0.640830\pi$
$857$	14264.5	−	24706.8i	0.568571	−	0.984794i	0.996708	−	0.0810802i	$-0.0258370\pi$
$858$	−5202.02	−	1753.65i	−0.206986	−	0.0697769i
$859$	−6163.02	−	10674.7i	−0.244796	−	0.423999i	0.717278	−	0.696787i	$-0.245388\pi$
$859$	−6163.02	−	10674.7i	−0.244796	−	0.423999i	−0.962074	+	0.272788i	$0.912054\pi$
$860$	312.251	−	540.835i	0.0123810	−	0.0214446i
$861$	−14908.3	−	34793.5i	−0.590096	−	1.37719i
$862$	545.284	+	944.459i	0.0215458	+	0.0373183i
$863$	1048.43	−	1815.93i	0.0413544	−	0.0716280i	−0.844607	−	0.535386i	$-0.820166\pi$
$863$	1048.43	−	1815.93i	0.0413544	−	0.0716280i	0.885962	+	0.463758i	$0.153499\pi$
$864$	2173.44	+	3208.74i	0.0855809	+	0.126347i
$865$	5266.22	+	9121.36i	0.207002	+	0.358538i
$866$	3449.63			0.135362
$867$	2444.38	+	12155.0i	0.0957502	+	0.476130i
$868$	3363.60	−	704.132i	0.131530	−	0.0275343i
$869$	−35628.0	+	61709.4i	−1.39079	+	2.40892i
$870$	−873.535	−	4343.77i	−0.0340409	−	0.169273i
$871$	−269.208	+	466.282i	−0.0104728	+	0.0181394i
$872$	−4741.69	−	8212.85i	−0.184144	−	0.318947i
$873$	24591.5	−	10307.6i	0.953374	−	0.399610i
$874$	−542.298			−0.0209880
$875$	−15838.6	+	3315.64i	−0.611935	+	0.128102i
$876$	−2073.17	−	698.883i	−0.0799609	−	0.0269556i
$877$	7105.35	+	12306.8i	0.273581	+	0.473856i	0.969776	−	0.243996i	$-0.0784585\pi$
$877$	7105.35	+	12306.8i	0.273581	+	0.473856i	−0.696195	+	0.717853i	$0.745125\pi$
$878$	−39482.2			−1.51761
$879$	−8972.11	−	44615.0i	−0.344280	−	1.71198i
$880$	−16645.3			−0.637627
$881$	19902.7			0.761112			0.380556	−	0.924758i	$-0.375733\pi$
$881$	19902.7			0.761112			0.380556	+	0.924758i	$0.375733\pi$
$882$	7667.82	+	26072.9i	0.292731	+	0.995376i
$883$	−34383.9			−1.31043			−0.655216	−	0.755442i	$-0.727422\pi$
$883$	−34383.9			−1.31043			−0.655216	+	0.755442i	$0.727422\pi$
$884$	−168.482			−0.00641026
$885$	−4784.61	−	1612.94i	−0.181732	−	0.0612635i
$886$	−18574.8			−0.704327
$887$	4300.61	+	7448.88i	0.162796	+	0.281972i	0.935871	−	0.352344i	$-0.114615\pi$
$887$	4300.61	+	7448.88i	0.162796	+	0.281972i	−0.773074	+	0.634316i	$0.781282\pi$
$888$	4292.72	+	21346.1i	0.162223	+	0.806677i
$889$	−5708.54	+	1195.02i	−0.215364	+	0.0450840i
$890$	−11946.4			−0.449936
$891$	−33584.6	+	34154.8i	−1.26277	+	1.28421i
$892$	−1244.05	−	2154.76i	−0.0466973	−	0.0808820i
$893$	−194.596	+	337.050i	−0.00729216	+	0.0126304i
$894$	4676.77	+	1576.58i	0.174961	+	0.0589808i
$895$	−7411.77	+	12837.6i	−0.276814	+	0.479455i
$896$	28853.4	−	6040.14i	1.07581	−	0.225209i
$897$	−2564.16	+	2258.27i	−0.0954458	+	0.0840597i
$898$	−1891.55			−0.0702914
$899$	11919.9	+	20646.0i	0.442216	+	0.765941i
$900$	−1463.51	−	1113.24i	−0.0542042	−	0.0412311i
$901$	−10267.1	+	17783.1i	−0.379629	+	0.657537i
$902$	37922.8	+	65684.2i	1.39988	+	2.42466i
$903$	−26386.2	−	3149.14i	−0.972402	−	0.116054i
$904$	3418.25	−	5920.58i	0.125762	−	0.217827i
$905$	−8778.88	−	15205.5i	−0.322453	−	0.558504i
$906$	−8271.46	−	41130.9i	−0.303312	−	1.50826i
$907$	−4418.11	+	7652.40i	−0.161743	+	0.280147i	−0.935494	−	0.353343i	$-0.885045\pi$
$907$	−4418.11	+	7652.40i	−0.161743	+	0.280147i	0.773751	+	0.633490i	$0.218378\pi$
$908$	−232.933	+	403.452i	−0.00851339	+	0.0147456i
$909$	16150.8	+	12285.3i	0.589318	+	0.448271i
$910$	1077.57	−	225.577i	0.0392539	−	0.00821736i
$911$	1061.16	+	1837.99i	0.0385926	+	0.0668443i	0.884677	−	0.466205i	$-0.154379\pi$
$911$	1061.16	+	1837.99i	0.0385926	+	0.0668443i	−0.846084	+	0.533050i	$0.821046\pi$
$912$	−108.083	−	537.456i	−0.00392432	−	0.0195142i
$913$	19985.9			0.724466
$914$	−7742.01			−0.280178
$915$	2043.49	+	688.879i	0.0738314	+	0.0248892i
$916$	1570.24	+	2719.73i	0.0566398	+	0.0981030i
$917$	21102.4	+	23582.2i	0.759936	+	0.849241i
$918$	−9036.28	+	18619.2i	−0.324882	+	0.669416i
$919$	8985.22	−	15562.9i	0.322519	−	0.558620i	−0.658488	−	0.752591i	$-0.728804\pi$
$919$	8985.22	−	15562.9i	0.322519	−	0.558620i	0.981007	+	0.193972i	$0.0621370\pi$
$920$	−4810.14	+	8331.41i	−0.172376	+	0.298563i
$921$	21402.3	−	18849.1i	0.765721	−	0.674375i
$922$	−5341.63	−	9251.97i	−0.190800	−	0.330474i
$923$	−698.584	+	1209.98i	−0.0249124	+	0.0431496i
$924$	−1523.43	−	3555.45i	−0.0542394	−	0.126586i
$925$	−10758.3	−	18634.0i	−0.382413	−	0.662359i
$926$	9349.85	−	16194.4i	0.331809	−	0.574710i
$927$	13771.3	−	5772.27i	0.487927	−	0.204516i
$928$	−1085.54	−	1880.20i	−0.0383992	−	0.0665094i
$929$	−48328.7			−1.70680			−0.853398	−	0.521260i	$-0.825462\pi$
$929$	−48328.7			−1.70680			−0.853398	+	0.521260i	$0.825462\pi$
$930$	−16204.4	−	5462.66i	−0.571359	−	0.192610i
$931$	58.4407	−	524.897i	0.00205727	−	0.0184778i
$932$	−439.439	+	761.130i	−0.0154445	+	0.0267507i
$933$	−6648.18	+	5855.09i	−0.233282	+	0.205452i
$934$	−7039.16	+	12192.2i	−0.246604	+	0.427131i
$935$	−6105.81	−	10575.6i	−0.213563	−	0.369902i
$936$	−2552.81	−	1941.83i	−0.0891467	−	0.0678105i
$937$	39874.3			1.39022			0.695111	−	0.718903i	$-0.255355\pi$
$937$	39874.3			1.39022			0.695111	+	0.718903i	$0.255355\pi$
$938$	−5227.49	+	1094.32i	−0.181965	+	0.0380925i
$939$	25941.5	−	22846.8i	0.901564	−	0.794012i
$940$	−285.820	−	495.055i	−0.00991747	−	0.0171776i
$941$	−28111.7			−0.973874			−0.486937	−	0.873437i	$-0.661886\pi$
$941$	−28111.7			−0.973874			−0.486937	+	0.873437i	$0.661886\pi$
$942$	−19568.2	+	17233.9i	−0.676823	+	0.596082i
$943$	47207.2			1.63020
$944$	−18009.0			−0.620915
$945$	2334.51	−	9318.29i	0.0803614	−	0.320766i
$946$	53245.0			1.82996
$947$	−31844.6			−1.09273			−0.546363	−	0.837549i	$-0.683988\pi$
$947$	−31844.6			−1.09273			−0.546363	+	0.837549i	$0.683988\pi$
$948$	2586.80	−	2278.21i	0.0886239	−	0.0780516i
$949$	3771.17			0.128996
$950$	251.529	+	435.661i	0.00859018	+	0.0148786i
$951$	16478.5	−	14512.7i	0.561883	−	0.494854i
$952$	13460.3	+	15042.1i	0.458245	+	0.512096i
$953$	20409.8			0.693745			0.346872	−	0.937912i	$-0.387244\pi$
$953$	20409.8			0.693745			0.346872	+	0.937912i	$0.387244\pi$
$954$	29849.8	−	12511.6i	1.01302	−	0.424611i
$955$	5735.99	+	9935.03i	0.194358	+	0.336639i
$956$	832.640	−	1442.17i	0.0281689	−	0.0487900i
$957$	20137.5	−	17735.2i	0.680200	−	0.599057i
$958$	17519.4	−	30344.5i	0.590841	−	1.02337i
$959$	−5061.85	+	15417.0i	−0.170444	+	0.519125i
$960$	−8503.02	−	2866.45i	−0.285868	−	0.0963689i
$961$	62219.0			2.08852
$962$	1553.73	+	2691.14i	0.0520731	+	0.0901933i
$963$	−5852.45	−	4451.73i	−0.195838	−	0.148967i
$964$	1893.25	−	3279.20i	0.0632546	−	0.109560i
$965$	−4926.35	−	8532.70i	−0.164337	−	0.284640i
$966$	−33654.3	−	4016.56i	−1.12092	−	0.133779i
$967$	−3545.97	+	6141.80i	−0.117922	+	0.204247i	−0.918944	−	0.394388i	$-0.870957\pi$
$967$	−3545.97	+	6141.80i	−0.117922	+	0.204247i	0.801022	+	0.598635i	$0.204290\pi$
$968$	−32375.4	−	56075.8i	−1.07498	−	1.86193i
$969$	301.826	−	265.820i	0.0100062	−	0.00881256i
$970$	5357.28	−	9279.08i	0.177332	−	0.307148i
$971$	−23512.6	+	40725.1i	−0.777092	+	1.34596i	0.156519	+	0.987675i	$0.449973\pi$
$971$	−23512.6	+	40725.1i	−0.777092	+	1.34596i	−0.933611	+	0.358289i	$0.883360\pi$
$972$	2067.33	−	1046.68i	0.0682197	−	0.0345392i
$973$	4254.22	−	12957.2i	0.140168	−	0.426915i
$974$	−13598.3	−	23553.0i	−0.447349	−	0.774832i
$975$	3003.52	+	1012.51i	0.0986560	+	0.0332578i
$976$	7691.59			0.252256
$977$	11732.9			0.384205			0.192103	−	0.981375i	$-0.438469\pi$
$977$	11732.9			0.384205			0.192103	+	0.981375i	$0.438469\pi$
$978$	10189.3	+	50667.6i	0.333147	+	1.65662i
$979$	−36175.4	−	62657.6i	−1.18097	−	2.04550i
$980$	624.755	+	459.818i	0.0203643	+	0.0149881i
$981$	−10891.6	+	4565.25i	−0.354478	+	0.148580i
$982$	−8127.87	+	14077.9i	−0.264125	+	0.457478i
$983$	−20528.6	+	35556.6i	−0.666084	+	1.15369i	0.312906	+	0.949784i	$0.398697\pi$
$983$	−20528.6	+	35556.6i	−0.666084	+	1.15369i	−0.978990	+	0.203907i	$0.934636\pi$
$984$	8736.68	+	43444.3i	0.283044	+	1.40747i
$985$	−2651.79	−	4593.04i	−0.0857799	−	0.148575i
$986$	5796.94	−	10040.6i	0.187234	−	0.324298i
$987$	−14572.7	+	19475.6i	−0.469965	+	0.628079i
$988$	−2.58037	−	4.46933i	−8.30895e−5	−	0.000143915i
$989$	16570.2	−	28700.4i	0.532761	−	0.922770i
$990$	−2432.03	+	19093.7i	−0.0780757	+	0.612967i
$991$	−12058.6	−	20886.1i	−0.386532	−	0.669493i	0.605449	−	0.795884i	$-0.292994\pi$
$991$	−12058.6	−	20886.1i	−0.386532	−	0.669493i	−0.991980	+	0.126392i	$0.959660\pi$
$992$	−8379.25			−0.268187
$993$	−17215.3	+	15161.6i	−0.550163	+	0.484531i
$994$	−13565.1	+	2839.71i	−0.432857	+	0.0906138i
$995$	−3767.77	+	6525.96i	−0.120046	+	0.207927i
$996$	−916.161	−	308.846i	−0.0291463	−	0.00982547i
$997$	5507.96	−	9540.06i	0.174964	−	0.303046i	−0.765185	−	0.643810i	$-0.777353\pi$
$997$	5507.96	−	9540.06i	0.174964	−	0.303046i	0.940149	+	0.340764i	$0.110686\pi$
$998$	7633.04	+	13220.8i	0.242104	+	0.419336i
$999$	27044.8	−	1944.15i	0.856517	−	0.0615716i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.h.a.58.6	yes	44
3.2	odd	2		189.4.h.a.37.17		44
7.4	even	3		63.4.g.a.4.17	✓	44
9.2	odd	6		189.4.g.a.100.6		44
9.7	even	3		63.4.g.a.16.17	yes	44
21.11	odd	6		189.4.g.a.172.6		44
63.11	odd	6		189.4.h.a.46.17		44
63.25	even	3	inner	63.4.h.a.25.6	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.g.a.4.17	✓	44	7.4	even	3
63.4.g.a.16.17	yes	44	9.7	even	3
63.4.h.a.25.6	yes	44	63.25	even	3	inner
63.4.h.a.58.6	yes	44	1.1	even	1	trivial
189.4.g.a.100.6		44	9.2	odd	6
189.4.g.a.172.6		44	21.11	odd	6
189.4.h.a.37.17		44	3.2	odd	2
189.4.h.a.46.17		44	63.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.93457 q^{2} +(-3.89946 + 3.43427i) q^{3} +0.611720 q^{4} +(1.84855 + 3.20179i) q^{5} +(11.4432 - 10.0781i) q^{6} +(-18.1273 + 3.79476i) q^{7} +21.6814 q^{8} +(3.41152 - 26.7836i) q^{9} +O(q^{10})\)	\(q-2.93457 q^{2} +(-3.89946 + 3.43427i) q^{3} +0.611720 q^{4} +(1.84855 + 3.20179i) q^{5} +(11.4432 - 10.0781i) q^{6} +(-18.1273 + 3.79476i) q^{7} +21.6814 q^{8} +(3.41152 - 26.7836i) q^{9} +(-5.42471 - 9.39588i) q^{10} +(32.8537 - 56.9043i) q^{11} +(-2.38537 + 2.10081i) q^{12} +(2.73952 - 4.74498i) q^{13} +(53.1960 - 11.1360i) q^{14} +(-18.2042 - 6.13679i) q^{15} -68.5196 q^{16} +(-25.1343 - 43.5340i) q^{17} +(-10.0113 + 78.5985i) q^{18} +(0.769884 - 1.33348i) q^{19} +(1.13080 + 1.95860i) q^{20} +(57.6545 - 77.0517i) q^{21} +(-96.4115 + 166.990i) q^{22} +(60.0078 + 103.936i) q^{23} +(-84.5459 + 74.4600i) q^{24} +(55.6657 - 96.4158i) q^{25} +(-8.03931 + 13.9245i) q^{26} +(78.6792 + 116.158i) q^{27} +(-11.0888 + 2.32133i) q^{28} +(-39.2967 - 68.0640i) q^{29} +(53.4215 + 18.0089i) q^{30} -303.332 q^{31} +27.6241 q^{32} +(67.3133 + 334.724i) q^{33} +(73.7586 + 127.754i) q^{34} +(-45.6593 - 51.0250i) q^{35} +(2.08689 - 16.3841i) q^{36} +(96.6335 - 167.374i) q^{37} +(-2.25928 + 3.91319i) q^{38} +(5.61294 + 27.9111i) q^{39} +(40.0793 + 69.4194i) q^{40} +(196.671 - 340.645i) q^{41} +(-169.191 + 226.114i) q^{42} +(-138.067 - 239.139i) q^{43} +(20.0972 - 34.8095i) q^{44} +(92.0618 - 38.5880i) q^{45} +(-176.097 - 305.009i) q^{46} -252.760 q^{47} +(267.189 - 235.315i) q^{48} +(314.200 - 137.578i) q^{49} +(-163.355 + 282.939i) q^{50} +(247.518 + 83.4405i) q^{51} +(1.67582 - 2.90260i) q^{52} +(-204.244 - 353.761i) q^{53} +(-230.890 - 340.873i) q^{54} +242.927 q^{55} +(-393.027 + 82.2758i) q^{56} +(1.57740 + 7.84383i) q^{57} +(115.319 + 199.739i) q^{58} +262.830 q^{59} +(-11.1359 - 3.75400i) q^{60} -112.254 q^{61} +890.149 q^{62} +(39.7955 + 498.461i) q^{63} +467.092 q^{64} +20.2566 q^{65} +(-197.536 - 982.273i) q^{66} -98.2686 q^{67} +(-15.3752 - 26.6306i) q^{68} +(-590.944 - 199.213i) q^{69} +(133.991 + 149.737i) q^{70} -255.003 q^{71} +(73.9667 - 580.707i) q^{72} +(344.146 + 596.078i) q^{73} +(-283.578 + 491.172i) q^{74} +(114.052 + 567.141i) q^{75} +(0.470953 - 0.815715i) q^{76} +(-379.612 + 1156.19i) q^{77} +(-16.4716 - 81.9071i) q^{78} -1084.44 q^{79} +(-126.662 - 219.385i) q^{80} +(-705.723 - 182.746i) q^{81} +(-577.146 + 999.647i) q^{82} +(152.083 + 263.415i) q^{83} +(35.2684 - 47.1340i) q^{84} +(92.9243 - 160.950i) q^{85} +(405.167 + 701.771i) q^{86} +(386.986 + 130.457i) q^{87} +(712.315 - 1233.77i) q^{88} +(550.553 - 953.585i) q^{89} +(-270.162 + 113.239i) q^{90} +(-31.6540 + 96.4096i) q^{91} +(36.7079 + 63.5800i) q^{92} +(1182.83 - 1041.72i) q^{93} +741.742 q^{94} +5.69269 q^{95} +(-107.719 + 94.8686i) q^{96} +(493.784 + 855.260i) q^{97} +(-922.042 + 403.731i) q^{98} +(-1412.02 - 1074.07i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{2} - q^{3} + 158 q^{4} - 19 q^{5} - 20 q^{6} - 7 q^{7} - 24 q^{8} + 11 q^{9}+O(q^{10}) \) 44 * q - 2 * q^2 - q^3 + 158 * q^4 - 19 * q^5 - 20 * q^6 - 7 * q^7 - 24 * q^8 + 11 * q^9	\( 44 q - 2 q^{2} - q^{3} + 158 q^{4} - 19 q^{5} - 20 q^{6} - 7 q^{7} - 24 q^{8} + 11 q^{9} - 18 q^{10} + 5 q^{11} - 62 q^{12} - 14 q^{13} - 52 q^{14} + 119 q^{15} + 494 q^{16} - 162 q^{17} - 188 q^{18} + 58 q^{19} - 362 q^{20} - 59 q^{21} - 18 q^{22} - 93 q^{23} + 30 q^{24} - 349 q^{25} - 266 q^{26} + 272 q^{27} - 172 q^{28} + 248 q^{29} + 85 q^{30} - 122 q^{31} + 326 q^{32} + 77 q^{33} + 6 q^{34} + 289 q^{35} - 806 q^{36} - 86 q^{37} - 761 q^{38} - 256 q^{39} - 18 q^{40} - 692 q^{41} - 364 q^{42} - 86 q^{43} - 443 q^{44} + 527 q^{45} - 270 q^{46} + 2010 q^{47} - 1013 q^{48} + 317 q^{49} + 239 q^{50} + 1209 q^{51} - 335 q^{52} + 258 q^{53} + 577 q^{54} - 870 q^{55} - 1752 q^{56} + 566 q^{57} + 237 q^{58} + 3330 q^{59} + 1669 q^{60} - 878 q^{61} + 1812 q^{62} + 2872 q^{63} + 872 q^{64} + 1226 q^{65} + 1330 q^{66} - 590 q^{67} - 1374 q^{68} + 1389 q^{69} + 1251 q^{70} + 636 q^{71} - 5970 q^{72} - 338 q^{73} + 1119 q^{74} + 2737 q^{75} + 1006 q^{76} + 2269 q^{77} + 157 q^{78} - 266 q^{79} - 4817 q^{80} - 505 q^{81} + 6 q^{82} - 1356 q^{83} - 6013 q^{84} + 483 q^{85} - 3343 q^{86} - 5755 q^{87} + 369 q^{88} - 2200 q^{89} + 2665 q^{90} + 1552 q^{91} - 396 q^{92} - 129 q^{93} + 2382 q^{94} - 6166 q^{95} - 5941 q^{96} - 266 q^{97} + 3601 q^{98} - 5395 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 - q^3 + 158 * q^4 - 19 * q^5 - 20 * q^6 - 7 * q^7 - 24 * q^8 + 11 * q^9 - 18 * q^10 + 5 * q^11 - 62 * q^12 - 14 * q^13 - 52 * q^14 + 119 * q^15 + 494 * q^16 - 162 * q^17 - 188 * q^18 + 58 * q^19 - 362 * q^20 - 59 * q^21 - 18 * q^22 - 93 * q^23 + 30 * q^24 - 349 * q^25 - 266 * q^26 + 272 * q^27 - 172 * q^28 + 248 * q^29 + 85 * q^30 - 122 * q^31 + 326 * q^32 + 77 * q^33 + 6 * q^34 + 289 * q^35 - 806 * q^36 - 86 * q^37 - 761 * q^38 - 256 * q^39 - 18 * q^40 - 692 * q^41 - 364 * q^42 - 86 * q^43 - 443 * q^44 + 527 * q^45 - 270 * q^46 + 2010 * q^47 - 1013 * q^48 + 317 * q^49 + 239 * q^50 + 1209 * q^51 - 335 * q^52 + 258 * q^53 + 577 * q^54 - 870 * q^55 - 1752 * q^56 + 566 * q^57 + 237 * q^58 + 3330 * q^59 + 1669 * q^60 - 878 * q^61 + 1812 * q^62 + 2872 * q^63 + 872 * q^64 + 1226 * q^65 + 1330 * q^66 - 590 * q^67 - 1374 * q^68 + 1389 * q^69 + 1251 * q^70 + 636 * q^71 - 5970 * q^72 - 338 * q^73 + 1119 * q^74 + 2737 * q^75 + 1006 * q^76 + 2269 * q^77 + 157 * q^78 - 266 * q^79 - 4817 * q^80 - 505 * q^81 + 6 * q^82 - 1356 * q^83 - 6013 * q^84 + 483 * q^85 - 3343 * q^86 - 5755 * q^87 + 369 * q^88 - 2200 * q^89 + 2665 * q^90 + 1552 * q^91 - 396 * q^92 - 129 * q^93 + 2382 * q^94 - 6166 * q^95 - 5941 * q^96 - 266 * q^97 + 3601 * q^98 - 5395 * q^99

Introduction

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