LMFDB - Embedded newform 63.3.k.a.61.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,3,Mod(31,63)]

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([2, 1]))

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

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

chi := DirichletCharacter("63.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	63.k (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:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			61.4
Character	$\chi$	$=$	63.61
Dual form			63.3.k.a.31.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12025 - 1.94033i) q^{2} +(1.92745 - 2.29890i) q^{3} +(-0.509909 + 0.883189i) q^{4} -1.93444i q^{5} +(-6.61983 - 1.16455i) q^{6} +(3.87064 + 5.83251i) q^{7} -6.67708 q^{8} +(-1.56985 - 8.86203i) q^{9} +O(q^{10})$	\(q+(-1.12025 - 1.94033i) q^{2} +(1.92745 - 2.29890i) q^{3} +(-0.509909 + 0.883189i) q^{4} -1.93444i q^{5} +(-6.61983 - 1.16455i) q^{6} +(3.87064 + 5.83251i) q^{7} -6.67708 q^{8} +(-1.56985 - 8.86203i) q^{9} +(-3.75345 + 2.16706i) q^{10} -0.372337 q^{11} +(1.04753 + 2.87453i) q^{12} +(-5.01827 + 2.89730i) q^{13} +(6.98089 - 14.0442i) q^{14} +(-4.44709 - 3.72855i) q^{15} +(9.51962 + 16.4885i) q^{16} +(9.96576 - 5.75374i) q^{17} +(-15.4366 + 12.9737i) q^{18} +(18.2323 + 10.5264i) q^{19} +(1.70848 + 0.986391i) q^{20} +(20.8688 + 2.34369i) q^{21} +(0.417109 + 0.722455i) q^{22} +27.2835 q^{23} +(-12.8698 + 15.3499i) q^{24} +21.2579 q^{25} +(11.2434 + 6.49139i) q^{26} +(-23.3987 - 13.4722i) q^{27} +(-7.12488 + 0.444454i) q^{28} +(-20.1404 + 34.8842i) q^{29} +(-2.25276 + 12.8057i) q^{30} +(-42.2746 - 24.4073i) q^{31} +(7.97450 - 13.8122i) q^{32} +(-0.717662 + 0.855964i) q^{33} +(-22.3282 - 12.8912i) q^{34} +(11.2827 - 7.48753i) q^{35} +(8.62732 + 3.13236i) q^{36} +(14.7691 - 25.5809i) q^{37} -47.1687i q^{38} +(-3.01189 + 17.1209i) q^{39} +12.9164i q^{40} +(-19.6397 + 11.3390i) q^{41} +(-18.8307 - 43.1178i) q^{42} +(10.7407 - 18.6035i) q^{43} +(0.189858 - 0.328844i) q^{44} +(-17.1431 + 3.03679i) q^{45} +(-30.5642 - 52.9388i) q^{46} +(-46.1622 + 26.6518i) q^{47} +(56.2539 + 9.89612i) q^{48} +(-19.0363 + 45.1511i) q^{49} +(-23.8141 - 41.2473i) q^{50} +(5.98130 - 34.0003i) q^{51} -5.90944i q^{52} +(43.7300 + 75.7426i) q^{53} +(0.0718380 + 60.4933i) q^{54} +0.720265i q^{55} +(-25.8446 - 38.9441i) q^{56} +(59.3409 - 21.6249i) q^{57} +90.2490 q^{58} +(-7.99438 - 4.61556i) q^{59} +(5.56062 - 2.02639i) q^{60} +(-61.0848 + 35.2673i) q^{61} +109.369i q^{62} +(45.6115 - 43.4579i) q^{63} +40.4233 q^{64} +(5.60467 + 9.70757i) q^{65} +(2.46481 + 0.433606i) q^{66} +(37.7720 - 65.4230i) q^{67} +11.7355i q^{68} +(52.5876 - 62.7219i) q^{69} +(-27.1676 - 13.5041i) q^{70} -97.4729 q^{71} +(10.4820 + 59.1725i) q^{72} +(-75.3269 + 43.4900i) q^{73} -66.1804 q^{74} +(40.9737 - 48.8698i) q^{75} +(-18.5936 + 10.7350i) q^{76} +(-1.44118 - 2.17166i) q^{77} +(36.5942 - 13.3356i) q^{78} +(23.5997 + 40.8759i) q^{79} +(31.8960 - 18.4152i) q^{80} +(-76.0711 + 27.8241i) q^{81} +(44.0025 + 25.4049i) q^{82} +(81.1770 + 46.8676i) q^{83} +(-12.7111 + 17.2360i) q^{84} +(-11.1303 - 19.2782i) q^{85} -48.1291 q^{86} +(41.3755 + 113.538i) q^{87} +2.48612 q^{88} +(-25.6803 - 14.8266i) q^{89} +(25.0969 + 29.8612i) q^{90} +(-36.3225 - 18.0547i) q^{91} +(-13.9121 + 24.0965i) q^{92} +(-137.592 + 50.1411i) q^{93} +(103.426 + 59.7132i) q^{94} +(20.3627 - 35.2693i) q^{95} +(-16.3824 - 44.9550i) q^{96} +(-122.538 - 70.7471i) q^{97} +(108.933 - 13.6437i) q^{98} +(0.584513 + 3.29966i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{2} - 3 q^{3} - 23 q^{4} + 12 q^{6} - 16 q^{8} + 9 q^{9}+O(q^{10}) $ 28 * q + q^2 - 3 * q^3 - 23 * q^4 + 12 * q^6 - 16 * q^8 + 9 * q^9	\( 28 q + q^{2} - 3 q^{3} - 23 q^{4} + 12 q^{6} - 16 q^{8} + 9 q^{9} - 6 q^{10} - 14 q^{11} - 3 q^{12} + 15 q^{13} - 11 q^{14} - 18 q^{15} - 27 q^{16} - 33 q^{17} + 33 q^{18} - 6 q^{19} + 108 q^{20} + 12 q^{21} - 10 q^{22} - 68 q^{23} + 42 q^{24} - 62 q^{25} + 54 q^{26} - 81 q^{27} - 16 q^{28} + 70 q^{29} - 6 q^{30} + 45 q^{31} + 153 q^{32} - 114 q^{33} + 12 q^{34} + 18 q^{35} - 174 q^{36} + 9 q^{37} - 120 q^{39} - 234 q^{41} - 51 q^{42} + 30 q^{43} + 51 q^{44} + 276 q^{45} - 22 q^{46} - 111 q^{47} + 147 q^{48} + 34 q^{49} + 241 q^{50} - 6 q^{51} + 148 q^{53} + 378 q^{54} - 412 q^{56} + 189 q^{57} - 34 q^{58} + 42 q^{59} + 456 q^{60} + 120 q^{61} - 222 q^{63} - 48 q^{64} + 114 q^{65} - 447 q^{66} - 34 q^{67} + 78 q^{69} + 264 q^{70} - 350 q^{71} - 339 q^{72} - 6 q^{73} - 718 q^{74} - 123 q^{75} + 72 q^{76} - 32 q^{77} - 375 q^{78} - 82 q^{79} - 609 q^{80} - 3 q^{81} - 18 q^{82} + 738 q^{83} + 609 q^{84} + 3 q^{85} - 34 q^{86} + 3 q^{87} - 50 q^{88} + 21 q^{89} - 543 q^{90} + 39 q^{91} + 288 q^{92} + 252 q^{93} - 3 q^{94} + 507 q^{95} - 582 q^{96} - 57 q^{97} + 811 q^{98} - 162 q^{99}+O(q^{100}) \) 28 * q + q^2 - 3 * q^3 - 23 * q^4 + 12 * q^6 - 16 * q^8 + 9 * q^9 - 6 * q^10 - 14 * q^11 - 3 * q^12 + 15 * q^13 - 11 * q^14 - 18 * q^15 - 27 * q^16 - 33 * q^17 + 33 * q^18 - 6 * q^19 + 108 * q^20 + 12 * q^21 - 10 * q^22 - 68 * q^23 + 42 * q^24 - 62 * q^25 + 54 * q^26 - 81 * q^27 - 16 * q^28 + 70 * q^29 - 6 * q^30 + 45 * q^31 + 153 * q^32 - 114 * q^33 + 12 * q^34 + 18 * q^35 - 174 * q^36 + 9 * q^37 - 120 * q^39 - 234 * q^41 - 51 * q^42 + 30 * q^43 + 51 * q^44 + 276 * q^45 - 22 * q^46 - 111 * q^47 + 147 * q^48 + 34 * q^49 + 241 * q^50 - 6 * q^51 + 148 * q^53 + 378 * q^54 - 412 * q^56 + 189 * q^57 - 34 * q^58 + 42 * q^59 + 456 * q^60 + 120 * q^61 - 222 * q^63 - 48 * q^64 + 114 * q^65 - 447 * q^66 - 34 * q^67 + 78 * q^69 + 264 * q^70 - 350 * q^71 - 339 * q^72 - 6 * q^73 - 718 * q^74 - 123 * q^75 + 72 * q^76 - 32 * q^77 - 375 * q^78 - 82 * q^79 - 609 * q^80 - 3 * q^81 - 18 * q^82 + 738 * q^83 + 609 * q^84 + 3 * q^85 - 34 * q^86 + 3 * q^87 - 50 * q^88 + 21 * q^89 - 543 * q^90 + 39 * q^91 + 288 * q^92 + 252 * q^93 - 3 * q^94 + 507 * q^95 - 582 * q^96 - 57 * q^97 + 811 * q^98 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.12025	−	1.94033i	−0.560124	−	0.970163i	−0.997485	−	0.0708770i	$-0.977420\pi$
$2$	−1.12025	−	1.94033i	−0.560124	−	0.970163i	0.437361	−	0.899286i	$-0.355913\pi$
$3$	1.92745	−	2.29890i	0.642484	−	0.766299i
$3$	1.92745	−	2.29890i	0.642484	−	0.766299i
$4$	−0.509909	+	0.883189i	−0.127477	+	0.220797i
$5$		−	1.93444i		−	0.386889i	−0.981111	−	0.193444i	$-0.938034\pi$
$5$		−	1.93444i		−	0.386889i	0.981111	−	0.193444i	$-0.0619659\pi$
$6$	−6.61983	−	1.16455i	−1.10331	−	0.194092i
$7$	3.87064	+	5.83251i	0.552948	+	0.833216i
$7$	3.87064	+	5.83251i	0.552948	+	0.833216i
$8$	−6.67708			−0.834635
$9$	−1.56985	−	8.86203i	−0.174428	−	0.984670i
$10$	−3.75345	+	2.16706i	−0.375345	+	0.216706i
$11$	−0.372337			−0.0338488			−0.0169244	−	0.999857i	$-0.505387\pi$
$11$	−0.372337			−0.0338488			−0.0169244	+	0.999857i	$0.505387\pi$
$12$	1.04753	+	2.87453i	0.0872944	+	0.239544i
$13$	−5.01827	+	2.89730i	−0.386021	+	0.222869i	−0.680435	−	0.732809i	$-0.738209\pi$
$13$	−5.01827	+	2.89730i	−0.386021	+	0.222869i	0.294414	+	0.955678i	$0.404876\pi$
$14$	6.98089	−	14.0442i	0.498635	−	1.00315i
$15$	−4.44709	−	3.72855i	−0.296472	−	0.248570i
$16$	9.51962	+	16.4885i	0.594976	+	1.03053i
$17$	9.96576	−	5.75374i	0.586221	−	0.338455i	−0.177381	−	0.984142i	$-0.556762\pi$
$17$	9.96576	−	5.75374i	0.586221	−	0.338455i	0.763602	+	0.645687i	$0.223429\pi$
$18$	−15.4366	+	12.9737i	−0.857589	+	0.720760i
$19$	18.2323	+	10.5264i	0.959593	+	0.554021i	0.896048	−	0.443958i	$-0.146426\pi$
$19$	18.2323	+	10.5264i	0.959593	+	0.554021i	0.0635451	+	0.997979i	$0.479759\pi$
$20$	1.70848	+	0.986391i	0.0854239	+	0.0493195i
$21$	20.8688	+	2.34369i	0.993753	+	0.111604i
$22$	0.417109	+	0.722455i	0.0189595	+	0.0328389i
$23$	27.2835			1.18624			0.593119	−	0.805115i	$-0.297896\pi$
$23$	27.2835			1.18624			0.593119	+	0.805115i	$0.297896\pi$
$24$	−12.8698	+	15.3499i	−0.536240	+	0.639580i
$25$	21.2579			0.850317
$26$	11.2434	+	6.49139i	0.432439	+	0.249669i
$27$	−23.3987	−	13.4722i	−0.866619	−	0.498971i
$28$	−7.12488	+	0.444454i	−0.254460	+	0.0158734i
$29$	−20.1404	+	34.8842i	−0.694497	+	1.20290i	0.275853	+	0.961200i	$0.411040\pi$
$29$	−20.1404	+	34.8842i	−0.694497	+	1.20290i	−0.970350	+	0.241704i	$0.922294\pi$
$30$	−2.25276	+	12.8057i	−0.0750921	+	0.426856i
$31$	−42.2746	−	24.4073i	−1.36370	−	0.787331i	−0.373584	−	0.927596i	$-0.621871\pi$
$31$	−42.2746	−	24.4073i	−1.36370	−	0.787331i	−0.990114	+	0.140265i	$0.955205\pi$
$32$	7.97450	−	13.8122i	0.249203	−	0.431633i
$33$	−0.717662	+	0.855964i	−0.0217473	+	0.0259383i
$34$	−22.3282	−	12.8912i	−0.656713	−	0.379154i
$35$	11.2827	−	7.48753i	0.322362	−	0.213929i
$36$	8.62732	+	3.13236i	0.239648	+	0.0870099i
$37$	14.7691	−	25.5809i	0.399166	−	0.691376i	−0.594457	−	0.804127i	$-0.702633\pi$
$37$	14.7691	−	25.5809i	0.399166	−	0.691376i	0.993623	+	0.112751i	$0.0359663\pi$
$38$		−	47.1687i		−	1.24128i
$39$	−3.01189	+	17.1209i	−0.0772279	+	0.438998i
$40$			12.9164i			0.322911i
$41$	−19.6397	+	11.3390i	−0.479016	+	0.276560i	−0.720006	−	0.693968i	$-0.755861\pi$
$41$	−19.6397	+	11.3390i	−0.479016	+	0.276560i	0.240990	+	0.970528i	$0.422528\pi$
$42$	−18.8307	−	43.1178i	−0.448350	−	1.02661i
$43$	10.7407	−	18.6035i	0.249785	−	0.432639i	−0.713681	−	0.700470i	$-0.752974\pi$
$43$	10.7407	−	18.6035i	0.249785	−	0.432639i	0.963466	+	0.267831i	$0.0863069\pi$
$44$	0.189858	−	0.328844i	0.00431495	−	0.00747372i
$45$	−17.1431	+	3.03679i	−0.380958	+	0.0674841i
$46$	−30.5642	−	52.9388i	−0.664440	−	1.15084i
$47$	−46.1622	+	26.6518i	−0.982175	+	0.567059i	−0.902926	−	0.429796i	$-0.858586\pi$
$47$	−46.1622	+	26.6518i	−0.982175	+	0.567059i	−0.0792489	+	0.996855i	$0.525252\pi$
$48$	56.2539	+	9.89612i	1.17196	+	0.206169i
$49$	−19.0363	+	45.1511i	−0.388496	+	0.921450i
$50$	−23.8141	−	41.2473i	−0.476283	−	0.824946i
$51$	5.98130	−	34.0003i	0.117280	−	0.666673i
$52$		−	5.90944i		−	0.113643i
$53$	43.7300	+	75.7426i	0.825094	+	1.42911i	0.901847	+	0.432055i	$0.142211\pi$
$53$	43.7300	+	75.7426i	0.825094	+	1.42911i	−0.0767530	+	0.997050i	$0.524455\pi$
$54$	0.0718380	+	60.4933i	0.00133033	+	1.12025i
$55$			0.720265i			0.0130957i
$56$	−25.8446	−	38.9441i	−0.461510	−	0.695431i
$57$	59.3409	−	21.6249i	1.04107	−	0.379385i
$58$	90.2490			1.55602
$59$	−7.99438	−	4.61556i	−0.135498	−	0.0782298i	0.430719	−	0.902486i	$-0.358260\pi$
$59$	−7.99438	−	4.61556i	−0.135498	−	0.0782298i	−0.566217	+	0.824256i	$0.691593\pi$
$60$	5.56062	−	2.02639i	0.0926770	−	0.0337732i
$61$	−61.0848	+	35.2673i	−1.00139	+	0.578153i	−0.908659	−	0.417539i	$-0.862893\pi$
$61$	−61.0848	+	35.2673i	−1.00139	+	0.578153i	−0.0927306	+	0.995691i	$0.529560\pi$
$62$			109.369i			1.76401i
$63$	45.6115	−	43.4579i	0.723993	−	0.689808i
$64$	40.4233			0.631614
$65$	5.60467	+	9.70757i	0.0862256	+	0.149347i
$66$	2.46481	+	0.433606i	0.0373456	+	0.00656979i
$67$	37.7720	−	65.4230i	0.563761	−	0.976463i	−0.433403	−	0.901200i	$-0.642687\pi$
$67$	37.7720	−	65.4230i	0.563761	−	0.976463i	0.997164	−	0.0752625i	$-0.0239795\pi$
$68$			11.7355i			0.172581i
$69$	52.5876	−	62.7219i	0.762139	−	0.909013i
$70$	−27.1676	−	13.5041i	−0.388109	−	0.192916i
$71$	−97.4729			−1.37286			−0.686429	−	0.727197i	$-0.740823\pi$
$71$	−97.4729			−1.37286			−0.686429	+	0.727197i	$0.740823\pi$
$72$	10.4820	+	59.1725i	0.145584	+	0.821840i
$73$	−75.3269	+	43.4900i	−1.03188	+	0.595754i	−0.917521	−	0.397687i	$-0.869813\pi$
$73$	−75.3269	+	43.4900i	−1.03188	+	0.595754i	−0.114354	+	0.993440i	$0.536480\pi$
$74$	−66.1804			−0.894330
$75$	40.9737	−	48.8698i	0.546315	−	0.651597i
$76$	−18.5936	+	10.7350i	−0.244653	+	0.141250i
$77$	−1.44118	−	2.17166i	−0.0187166	−	0.0282033i
$78$	36.5942	−	13.3356i	0.469156	−	0.170969i
$79$	23.5997	+	40.8759i	0.298730	+	0.517416i	0.975846	−	0.218461i	$-0.0701036\pi$
$79$	23.5997	+	40.8759i	0.298730	+	0.517416i	−0.677115	+	0.735877i	$0.736770\pi$
$80$	31.8960	−	18.4152i	0.398700	−	0.230190i
$81$	−76.0711	+	27.8241i	−0.939150	+	0.343508i
$82$	44.0025	+	25.4049i	0.536616	+	0.309816i
$83$	81.1770	+	46.8676i	0.978036	+	0.564669i	0.901677	−	0.432411i	$-0.142337\pi$
$83$	81.1770	+	46.8676i	0.978036	+	0.564669i	0.0763594	+	0.997080i	$0.475670\pi$
$84$	−12.7111	+	17.2360i	−0.151323	+	0.205191i
$85$	−11.1303	−	19.2782i	−0.130944	−	0.226802i
$86$	−48.1291			−0.559641
$87$	41.3755	+	113.538i	0.475580	+	1.30504i
$88$	2.48612			0.0282514
$89$	−25.6803	−	14.8266i	−0.288543	−	0.166590i	0.348742	−	0.937219i	$-0.386609\pi$
$89$	−25.6803	−	14.8266i	−0.288543	−	0.166590i	−0.637285	+	0.770628i	$0.719942\pi$
$90$	25.0969	+	29.8612i	0.278854	+	0.331792i
$91$	−36.3225	−	18.0547i	−0.399148	−	0.198403i
$92$	−13.9121	+	24.0965i	−0.151218	+	0.261918i
$93$	−137.592	+	50.1411i	−1.47949	+	0.539152i
$94$	103.426	+	59.7132i	1.10028	+	0.635246i
$95$	20.3627	−	35.2693i	0.214345	−	0.371256i
$96$	−16.3824	−	44.9550i	−0.170650	−	0.468281i
$97$	−122.538	−	70.7471i	−1.26327	−	0.729351i	−0.289567	−	0.957158i	$-0.593511\pi$
$97$	−122.538	−	70.7471i	−1.26327	−	0.729351i	−0.973706	+	0.227806i	$0.926845\pi$
$98$	108.933	−	13.6437i	1.11156	−	0.139222i
$99$	0.584513	+	3.29966i	0.00590417	+	0.0333299i
$100$	−10.8396	+	18.7748i	−0.108396	+	0.187748i
$101$		−	46.9206i		−	0.464561i	−0.972649	−	0.232280i	$-0.925381\pi$
$101$		−	46.9206i		−	0.464561i	0.972649	−	0.232280i	$-0.0746187\pi$
$102$	−72.6722	+	26.4831i	−0.712473	+	0.259638i
$103$		−	131.547i		−	1.27715i	−0.769559	−	0.638576i	$-0.779524\pi$
$103$		−	131.547i		−	1.27715i	0.769559	−	0.638576i	$-0.220476\pi$
$104$	33.5074	−	19.3455i	0.322187	−	0.186015i
$105$	4.53373	−	40.3695i	0.0431784	−	0.384472i
$106$	97.9768	−	169.701i	0.924310	−	1.60095i
$107$	69.9586	−	121.172i	0.653819	−	1.13245i	−0.328369	−	0.944549i	$-0.606499\pi$
$107$	69.9586	−	121.172i	0.653819	−	1.13245i	0.982188	−	0.187899i	$-0.0601676\pi$
$108$	23.8297	−	13.7959i	0.220646	−	0.127739i
$109$	55.5420	+	96.2016i	0.509560	+	0.882583i	0.999939	+	0.0110739i	$0.00352500\pi$
$109$	55.5420	+	96.2016i	0.509560	+	0.882583i	−0.490379	+	0.871509i	$0.663142\pi$
$110$	1.39755	−	0.806875i	0.0127050	−	0.00733522i
$111$	−30.3410	−	83.2587i	−0.273343	−	0.750079i
$112$	−59.3221	+	119.344i	−0.529662	+	1.06557i
$113$	50.7636	+	87.9252i	0.449236	+	0.778099i	0.998336	−	0.0576571i	$-0.0183630\pi$
$113$	50.7636	+	87.9252i	0.449236	+	0.778099i	−0.549101	+	0.835756i	$0.685030\pi$
$114$	−108.436	−	90.9155i	−0.951193	−	0.797504i
$115$		−	52.7783i		−	0.458942i
$116$	−20.5396	−	35.5756i	−0.177065	−	0.306686i
$117$	33.5539	+	39.9238i	0.286786	+	0.341229i
$118$			20.6823i			0.175273i
$119$	72.1326	+	35.8548i	0.606156	+	0.301301i
$120$	29.6936	+	24.8958i	0.247446	+	0.207465i
$121$	−120.861			−0.998854
$122$	136.860	+	79.0162i	1.12180	+	0.647674i
$123$	−11.7874	+	67.0048i	−0.0958326	+	0.544755i
$124$	43.1125	−	24.8910i	0.347681	−	0.200734i
$125$		−	89.4834i		−	0.715867i
$126$	−135.419	−	39.8177i	−1.07475	−	0.316013i
$127$	−49.1014			−0.386625			−0.193312	−	0.981137i	$-0.561923\pi$
$127$	−49.1014			−0.386625			−0.193312	+	0.981137i	$0.561923\pi$
$128$	−77.1821	−	133.683i	−0.602985	−	1.04440i
$129$	−22.0653	−	60.5492i	−0.171048	−	0.469374i
$130$	12.5572	−	21.7498i	0.0965941	−	0.167306i
$131$		−	124.241i		−	0.948403i	−0.880416	−	0.474202i	$-0.842737\pi$
$131$		−	124.241i		−	0.948403i	0.880416	−	0.474202i	$-0.157263\pi$
$132$	−0.390035	−	1.07029i	−0.00295481	−	0.00810829i
$133$	9.17517	+	147.084i	0.0689863	+	1.10589i
$134$	−169.256			−1.26310
$135$	−26.0613	+	45.2635i	−0.193046	+	0.335285i
$136$	−66.5422	+	38.4182i	−0.489281	+	0.282487i
$137$	4.63071			0.0338008			0.0169004	−	0.999857i	$-0.494620\pi$
$137$	4.63071			0.0338008			0.0169004	+	0.999857i	$0.494620\pi$
$138$	−180.612	−	31.7731i	−1.30878	−	0.230240i
$139$	−37.7043	+	21.7686i	−0.271254	+	0.156608i	−0.629457	−	0.777035i	$-0.716723\pi$
$139$	−37.7043	+	21.7686i	−0.271254	+	0.156608i	0.358204	+	0.933644i	$0.383389\pi$
$140$	0.859772	+	13.7827i	0.00614123	+	0.0984477i
$141$	−27.7058	+	157.492i	−0.196495	+	1.11697i
$142$	109.194	+	189.129i	0.768970	+	1.33190i
$143$	1.86849	−	1.07877i	0.0130664	−	0.00754386i
$144$	131.177	−	110.248i	0.910951	−	0.765608i
$145$	67.4815	+	38.9605i	0.465390	+	0.268693i
$146$	168.770	+	97.4391i	1.15596	+	0.667391i
$147$	67.1060	+	130.789i	0.456504	+	0.889722i
$148$	15.0618	+	26.0879i	0.101769	+	0.176269i
$149$	−26.2607			−0.176246			−0.0881232	−	0.996110i	$-0.528087\pi$
$149$	−26.2607			−0.176246			−0.0881232	+	0.996110i	$0.528087\pi$
$150$	−140.724	−	24.7560i	−0.938159	−	0.165040i
$151$	119.873			0.793861			0.396931	−	0.917849i	$-0.370075\pi$
$151$	119.873			0.793861			0.396931	+	0.917849i	$0.370075\pi$
$152$	−121.738	−	70.2857i	−0.800910	−	0.462406i
$153$	−66.6345	−	79.2844i	−0.435520	−	0.518199i
$154$	−2.59924	+	5.22916i	−0.0168782	+	0.0339556i
$155$	−47.2145	+	81.7779i	−0.304610	+	0.527599i
$156$	−13.5852	−	11.3902i	−0.0870846	−	0.0730139i
$157$	169.702	+	97.9773i	1.08090	+	0.624059i	0.931140	−	0.364663i	$-0.118816\pi$
$157$	169.702	+	97.9773i	1.08090	+	0.624059i	0.149763	+	0.988722i	$0.452149\pi$
$158$	52.8750	−	91.5822i	0.334652	−	0.579634i
$159$	258.412	+	45.4595i	1.62523	+	0.285909i
$160$	−26.7190	−	15.4262i	−0.166994	−	0.0964139i
$161$	105.604	+	159.131i	0.655928	+	0.988392i
$162$	139.206	+	116.433i	0.859299	+	0.718722i
$163$	41.8418	−	72.4721i	0.256698	−	0.444614i	−0.708657	−	0.705553i	$-0.750699\pi$
$163$	41.8418	−	72.4721i	0.256698	−	0.444614i	0.965355	+	0.260939i	$0.0840321\pi$
$164$		−	23.1274i		−	0.141020i
$165$	1.65581	+	1.38828i	0.0100352	+	0.00841380i
$166$		−	210.013i		−	1.26514i
$167$	−215.835	+	124.612i	−1.29242	+	0.746181i	−0.979083	−	0.203460i	$-0.934781\pi$
$167$	−215.835	+	124.612i	−1.29242	+	0.746181i	−0.313340	+	0.949641i	$0.601448\pi$
$168$	−139.343	−	15.6490i	−0.829421	−	0.0931488i
$169$	−67.7113	+	117.279i	−0.400659	+	0.693961i
$170$	−24.9373	+	43.1927i	−0.146690	+	0.254075i
$171$	64.6634	−	178.100i	0.378148	−	1.04152i
$172$	10.9536	+	18.9722i	0.0636837	+	0.110303i
$173$	241.148	−	139.227i	1.39392	−	0.804779i	0.400171	−	0.916440i	$-0.368951\pi$
$173$	241.148	−	139.227i	1.39392	−	0.804779i	0.993746	+	0.111661i	$0.0356172\pi$
$174$	173.951	−	207.473i	0.999716	−	1.19237i
$175$	82.2818	+	123.987i	0.470181	+	0.708497i
$176$	−3.54451	−	6.13926i	−0.0201392	−	0.0348822i
$177$	−26.0195	+	9.48198i	−0.147003	+	0.0535705i
$178$			66.4376i			0.373245i
$179$	−128.758	−	223.015i	−0.719317	−	1.24589i	−0.961271	−	0.275605i	$-0.911122\pi$
$179$	−128.758	−	223.015i	−0.719317	−	1.24589i	0.241954	−	0.970288i	$-0.422212\pi$
$180$	6.05937	−	16.6891i	0.0336632	−	0.0927171i
$181$		−	29.2542i		−	0.161625i	−0.996729	−	0.0808126i	$-0.974248\pi$
$181$		−	29.2542i		−	0.161625i	0.996729	−	0.0808126i	$-0.0257515\pi$
$182$	5.65812	+	90.7032i	0.0310886	+	0.498369i
$183$	−36.6621	+	208.404i	−0.200340	+	1.13882i
$184$	−182.174			−0.990076
$185$	−49.4848	−	28.5701i	−0.267486	−	0.154433i
$186$	251.427	+	210.803i	1.35176	+	1.13335i
$187$	−3.71062	+	2.14233i	−0.0198429	+	0.0114563i
$188$		−	54.3599i		−	0.289149i
$189$	−11.9911	−	188.619i	−0.0634448	−	0.997985i
$190$	−91.2452			−0.480238
$191$	30.3852	+	52.6287i	0.159085	+	0.275543i	0.934539	−	0.355861i	$-0.115812\pi$
$191$	30.3852	+	52.6287i	0.159085	+	0.275543i	−0.775454	+	0.631404i	$0.782479\pi$
$192$	77.9140	−	92.9290i	0.405802	−	0.484005i
$193$	−12.4384	+	21.5439i	−0.0644474	+	0.111626i	−0.896449	−	0.443147i	$-0.853862\pi$
$193$	−12.4384	+	21.5439i	−0.0644474	+	0.111626i	0.832001	+	0.554774i	$0.187195\pi$
$194$			317.017i			1.63411i
$195$	33.1194	+	5.82633i	0.169843	+	0.0298786i
$196$	−30.1701	−	39.8356i	−0.153929	−	0.203243i
$197$	174.320			0.884873			0.442437	−	0.896800i	$-0.354114\pi$
$197$	174.320			0.884873			0.442437	+	0.896800i	$0.354114\pi$
$198$	5.74762	−	4.83058i	0.0290284	−	0.0243969i
$199$	250.227	−	144.468i	1.25742	−	0.725972i	0.284848	−	0.958573i	$-0.408057\pi$
$199$	250.227	−	144.468i	1.25742	−	0.725972i	0.972572	+	0.232600i	$0.0747234\pi$
$200$	−141.941			−0.709705
$201$	−77.5970	−	212.934i	−0.386055	−	1.05937i
$202$	−91.0413	+	52.5627i	−0.450699	+	0.260211i
$203$	−281.419	+	17.5551i	−1.38630	+	0.0864782i
$204$	26.9788	+	22.6197i	0.132249	+	0.110881i
$205$	21.9346	+	37.9918i	0.106998	+	0.185326i
$206$	−255.243	+	147.365i	−1.23905	+	0.715363i
$207$	−42.8310	−	241.787i	−0.206913	−	1.16805i
$208$	−95.5441	−	55.1624i	−0.459347	−	0.265204i
$209$	−6.78854	−	3.91937i	−0.0324811	−	0.0187530i
$210$	−83.4089	+	36.4270i	−0.397185	+	0.173462i
$211$	−149.601	−	259.116i	−0.709009	−	1.22804i	−0.965225	−	0.261419i	$-0.915809\pi$
$211$	−149.601	−	259.116i	−0.709009	−	1.22804i	0.256217	−	0.966619i	$-0.417524\pi$
$212$	−89.1933			−0.420723
$213$	−187.874	+	224.080i	−0.882039	+	1.05202i
$214$	−313.484			−1.46488
$215$	−35.9874	−	20.7773i	−0.167383	−	0.0966388i
$216$	156.235	+	89.9551i	0.723310	+	0.416459i
$217$	−21.2742	−	341.039i	−0.0980379	−	1.57161i
$218$	124.442	−	215.539i	0.570833	−	0.988712i
$219$	−45.2100	+	256.994i	−0.206439	+	1.17349i
$220$	−0.636130	−	0.367270i	−0.00289150	−	0.00166941i
$221$	−33.3406	+	57.7477i	−0.150863	+	0.261302i
$222$	−127.560	+	152.142i	−0.574593	+	0.685324i
$223$	−14.0772	−	8.12745i	−0.0631263	−	0.0364460i	0.468105	−	0.883673i	$-0.344937\pi$
$223$	−14.0772	−	8.12745i	−0.0631263	−	0.0364460i	−0.531231	+	0.847227i	$0.678270\pi$
$224$	111.426	−	6.95085i	0.497439	−	0.0310306i
$225$	−33.3718	−	188.388i	−0.148319	−	0.837282i
$226$	113.736	−	196.996i	0.503255	−	0.871664i
$227$			30.5448i			0.134559i	0.997734	+	0.0672793i	$0.0214319\pi$
$227$			30.5448i			0.134559i	−0.997734	+	0.0672793i	$0.978568\pi$
$228$	−11.1596	+	63.4360i	−0.0489456	+	0.278228i
$229$			182.597i			0.797368i	0.917088	+	0.398684i	$0.130533\pi$
$229$			182.597i			0.797368i	−0.917088	+	0.398684i	$0.869467\pi$
$230$	−102.407	+	59.1248i	−0.445249	+	0.257064i
$231$	−7.77023	−	0.872642i	−0.0336373	−	0.00377767i
$232$	134.479	−	232.925i	0.579652	−	1.00399i
$233$	174.898	−	302.932i	0.750635	−	1.30014i	−0.196880	−	0.980428i	$-0.563081\pi$
$233$	174.898	−	302.932i	0.750635	−	1.30014i	0.947515	−	0.319710i	$-0.103586\pi$
$234$	39.8764	−	109.830i	0.170412	−	0.469359i
$235$	51.5563	+	89.2982i	0.219389	+	0.379992i
$236$	8.15281	−	4.70703i	0.0345458	−	0.0199450i
$237$	139.457	+	24.5331i	0.588425	+	0.103515i
$238$	−11.2364	−	180.127i	−0.0472119	−	0.756836i
$239$	49.6154	+	85.9365i	0.207596	+	0.359567i	0.950957	−	0.309324i	$-0.100103\pi$
$239$	49.6154	+	85.9365i	0.207596	+	0.359567i	−0.743361	+	0.668891i	$0.766769\pi$
$240$	19.1435	−	108.820i	0.0797646	−	0.453417i
$241$		−	280.989i		−	1.16593i	−0.812498	−	0.582964i	$-0.801893\pi$
$241$		−	280.989i		−	1.16593i	0.812498	−	0.582964i	$-0.198107\pi$
$242$	135.395	+	234.510i	0.559482	+	0.969051i
$243$	−82.6588	+	228.509i	−0.340160	+	0.940368i
$244$		−	71.9325i		−	0.294805i
$245$	87.3422	+	36.8247i	0.356499	+	0.150305i
$246$	143.216	−	52.1906i	0.582179	−	0.212157i
$247$	−121.993			−0.493897
$248$	282.271	+	162.969i	1.13819	+	0.657135i
$249$	264.208	−	96.2825i	1.06108	−	0.386677i
$250$	−173.627	+	100.244i	−0.694507	+	0.400974i
$251$			16.5983i			0.0661286i	0.999453	+	0.0330643i	$0.0105266\pi$
$251$			16.5983i			0.0661286i	−0.999453	+	0.0330643i	$0.989473\pi$
$252$	15.1238	+	62.4432i	0.0600149	+	0.247790i
$253$	−10.1586			−0.0401527
$254$	55.0057	+	95.2726i	0.216558	+	0.375089i
$255$	−65.7717	−	11.5705i	−0.257928	−	0.0453744i
$256$	−92.0795	+	159.486i	−0.359686	+	0.622994i
$257$			85.2012i			0.331522i	0.986166	+	0.165761i	$0.0530080\pi$
$257$			85.2012i			0.331522i	−0.986166	+	0.165761i	$0.946992\pi$
$258$	−92.7666	+	110.644i	−0.359561	+	0.428852i
$259$	206.367	−	12.8733i	0.796783	−	0.0497038i
$260$	−11.4315			−0.0439672
$261$	340.762	+	123.722i	1.30560	+	0.474030i
$262$	−241.068	+	139.180i	−0.920105	+	0.531223i
$263$	−356.654			−1.35610			−0.678050	−	0.735016i	$-0.737175\pi$
$263$	−356.654			−1.35610			−0.678050	+	0.735016i	$0.737175\pi$
$264$	4.79189	−	5.71534i	0.0181511	−	0.0216490i
$265$	146.520	−	84.5932i	0.552905	−	0.319220i
$266$	275.112	−	182.573i	1.03426	−	0.686365i
$267$	−83.5824	+	30.4590i	−0.313043	+	0.114079i
$268$	38.5206	+	66.7196i	0.143733	+	0.248954i
$269$	−333.500	+	192.546i	−1.23978	+	0.715785i	−0.969048	−	0.246871i	$-0.920597\pi$
$269$	−333.500	+	192.546i	−1.23978	+	0.715785i	−0.270727	+	0.962656i	$0.587264\pi$
$270$	117.021	−	0.138967i	0.433411	−	0.000514691i
$271$	53.9536	+	31.1502i	0.199091	+	0.114945i	0.596231	−	0.802813i	$-0.296664\pi$
$271$	53.9536	+	31.1502i	0.199091	+	0.114945i	−0.397140	+	0.917758i	$0.629997\pi$
$272$	189.741	+	109.547i	0.697576	+	0.402746i
$273$	−111.516	+	48.7020i	−0.408483	+	0.178395i
$274$	−5.18755	−	8.98509i	−0.0189327	−	0.0327923i
$275$	−7.91511			−0.0287822
$276$	28.5803	+	78.4272i	0.103552	+	0.284157i
$277$	85.0115			0.306901			0.153450	−	0.988156i	$-0.450961\pi$
$277$	85.0115			0.306901			0.153450	+	0.988156i	$0.450961\pi$
$278$	84.4762	+	48.7724i	0.303871	+	0.175440i
$279$	−149.933	+	412.955i	−0.537395	+	1.48012i
$280$	−75.3352	+	49.9949i	−0.269054	+	0.178553i
$281$	73.8831	−	127.969i	0.262929	−	0.455407i	−0.704090	−	0.710111i	$-0.748645\pi$
$281$	73.8831	−	127.969i	0.262929	−	0.455407i	0.967019	+	0.254704i	$0.0819781\pi$
$282$	336.624	−	122.672i	1.19370	−	0.435007i
$283$	303.815	+	175.408i	1.07355	+	0.619815i	0.929150	−	0.369704i	$-0.120541\pi$
$283$	303.815	+	175.408i	1.07355	+	0.619815i	0.144402	+	0.989519i	$0.453874\pi$
$284$	49.7023	−	86.0869i	0.175008	−	0.303123i
$285$	−41.8322	−	114.792i	−0.146780	−	0.402778i
$286$	−4.18634	−	2.41698i	−0.0146375	−	0.00845099i
$287$	−142.153	−	70.6594i	−0.495305	−	0.246200i
$288$	−134.923	−	48.9871i	−0.468484	−	0.170094i
$289$	−78.2890	+	135.601i	−0.270896	+	0.469206i
$290$		−	174.582i		−	0.602005i
$291$	−398.826	+	145.339i	−1.37053	+	0.499448i
$292$		−	88.7038i		−	0.303780i
$293$	42.7689	−	24.6927i	0.145969	−	0.0842753i	−0.425237	−	0.905082i	$-0.639809\pi$
$293$	42.7689	−	24.6927i	0.145969	−	0.0842753i	0.571206	+	0.820807i	$0.306476\pi$
$294$	178.598	−	276.724i	0.607476	−	0.941237i
$295$	−8.92853	+	15.4647i	−0.0302662	+	0.0524226i
$296$	−98.6148	+	170.806i	−0.333158	+	0.577047i
$297$	8.71220	+	5.01620i	0.0293340	+	0.0168896i
$298$	29.4185	+	50.9544i	0.0987198	+	0.170988i
$299$	−136.916	+	79.0484i	−0.457913	+	0.264376i
$300$	22.2684	+	61.1066i	0.0742280	+	0.203689i
$301$	150.079	−	9.36199i	0.498600	−	0.0311030i
$302$	−134.288	−	232.593i	−0.444661	−	0.770175i
$303$	−107.866	−	90.4373i	−0.355992	−	0.298473i
$304$			400.829i			1.31852i
$305$	68.2226	+	118.165i	0.223681	+	0.387426i
$306$	−79.1904	+	218.111i	−0.258792	+	0.712781i
$307$			432.680i			1.40938i	0.709515	+	0.704691i	$0.248914\pi$
$307$			432.680i			1.40938i	−0.709515	+	0.704691i	$0.751086\pi$
$308$	2.65286	−	0.165487i	0.00861317	−	0.000537295i
$309$	−302.412	−	253.550i	−0.978680	−	0.820550i
$310$	211.568			0.682476
$311$	−144.790	−	83.5947i	−0.465563	−	0.268793i	0.248817	−	0.968550i	$-0.419958\pi$
$311$	−144.790	−	83.5947i	−0.465563	−	0.268793i	−0.714381	+	0.699757i	$0.753291\pi$
$312$	20.1106	−	114.318i	0.0644572	−	0.366403i
$313$	−223.941	+	129.293i	−0.715467	+	0.413075i	−0.813082	−	0.582149i	$-0.802212\pi$
$313$	−223.941	+	129.293i	−0.715467	+	0.413075i	0.0976148	+	0.995224i	$0.468879\pi$
$314$		−	439.035i		−	1.39820i
$315$	−84.0668	−	88.2330i	−0.266879	−	0.280105i
$316$	−48.1348			−0.152325
$317$	101.257	+	175.382i	0.319422	+	0.553255i	0.980368	−	0.197179i	$-0.0631780\pi$
$317$	101.257	+	175.382i	0.319422	+	0.553255i	−0.660946	+	0.750434i	$0.729845\pi$
$318$	−201.279	−	552.329i	−0.632953	−	1.73688i
$319$	7.49902	−	12.9887i	0.0235079	−	0.0407169i
$320$		−	78.1966i		−	0.244364i
$321$	−143.720	−	394.381i	−0.447725	−	1.22860i
$322$	190.463	−	383.173i	0.591500	−	1.18998i
$323$	242.265			0.750045
$324$	14.2154	−	81.3729i	0.0438748	−	0.251151i
$325$	−106.678	+	61.5906i	−0.328240	+	0.189510i
$326$	−187.493			−0.575131
$327$	328.212	+	57.7387i	1.00371	+	0.176571i
$328$	131.136	−	75.7112i	0.399804	−	0.230827i
$329$	−334.124	−	166.082i	−1.01557	−	0.504809i
$330$	0.838787	−	4.76803i	0.00254178	−	0.0144486i
$331$	−17.0781	−	29.5802i	−0.0515956	−	0.0893662i	0.839074	−	0.544017i	$-0.183097\pi$
$331$	−17.0781	−	29.5802i	−0.0515956	−	0.0893662i	−0.890670	+	0.454651i	$0.849764\pi$
$332$	−82.7858	+	47.7964i	−0.249355	+	0.143965i
$333$	−249.884	−	90.7264i	−0.750403	−	0.272452i
$334$	483.576	+	279.193i	1.44783	+	0.835907i
$335$	−126.557	−	73.0678i	−0.377783	−	0.218113i
$336$	160.019	+	366.406i	0.476248	+	1.09049i
$337$	205.854	+	356.550i	0.610844	+	1.05801i	0.991099	+	0.133130i	$0.0425029\pi$
$337$	205.854	+	356.550i	0.610844	+	1.05801i	−0.380255	+	0.924882i	$0.624164\pi$
$338$	303.414			0.897673
$339$	299.975	+	52.7713i	0.884883	+	0.155668i
$340$	22.7017			0.0667698
$341$	15.7404	+	9.08773i	0.0461595	+	0.0266502i
$342$	−418.010	+	74.0478i	−1.22225	+	0.216514i
$343$	−337.027	+	63.7340i	−0.982585	+	0.185813i
$344$	−71.7168	+	124.217i	−0.208479	+	0.361096i
$345$	−121.332	−	101.728i	−0.351687	−	0.294863i
$346$	−540.290	−	311.937i	−1.56153	−	0.901551i
$347$	298.744	−	517.439i	0.860933	−	1.49118i	−0.0100965	−	0.999949i	$-0.503214\pi$
$347$	298.744	−	517.439i	0.860933	−	1.49118i	0.871029	−	0.491231i	$-0.163453\pi$
$348$	−121.374	−	21.3519i	−0.348775	−	0.0613560i
$349$	72.8266	+	42.0465i	0.208672	+	0.120477i	0.600694	−	0.799479i	$-0.294891\pi$
$349$	72.8266	+	42.0465i	0.208672	+	0.120477i	−0.392022	+	0.919956i	$0.628224\pi$
$350$	148.399	−	298.550i	0.423998	−	0.852999i
$351$	156.454	−	0.185795i	0.445738	−	0.000529331i
$352$	−2.96920	+	5.14281i	−0.00843523	+	0.0146102i
$353$		−	458.436i		−	1.29869i	−0.760496	−	0.649343i	$-0.775044\pi$
$353$		−	458.436i		−	1.29869i	0.760496	−	0.649343i	$-0.224956\pi$
$354$	47.5464	+	39.8641i	0.134312	+	0.112610i
$355$			188.556i			0.531143i
$356$	26.1893	−	15.1204i	0.0735654	−	0.0424730i
$357$	221.459	−	96.7170i	0.620332	−	0.270916i
$358$	−288.481	+	499.664i	−0.805813	+	1.39571i
$359$	6.42758	−	11.1329i	0.0179041	−	0.0310109i	−0.856935	−	0.515425i	$-0.827634\pi$
$359$	6.42758	−	11.1329i	0.0179041	−	0.0310109i	0.874839	+	0.484414i	$0.160967\pi$
$360$	114.466	−	20.2769i	0.317961	−	0.0563247i
$361$	41.1103	+	71.2051i	0.113879	+	0.197244i
$362$	−56.7626	+	32.7719i	−0.156803	+	0.0905302i
$363$	−232.955	+	277.848i	−0.641748	+	0.765421i
$364$	34.4669	−	22.8733i	0.0946892	−	0.0628388i
$365$	84.1290	+	145.716i	0.230490	+	0.399221i
$366$	445.442	−	162.327i	1.21705	−	0.443517i
$367$		−	618.348i		−	1.68487i	−0.538796	−	0.842436i	$-0.681121\pi$
$367$		−	618.348i		−	1.68487i	0.538796	−	0.842436i	$-0.318879\pi$
$368$	259.728	+	449.863i	0.705784	+	1.22245i
$369$	131.318	+	156.247i	0.355874	+	0.423433i
$370$			128.022i			0.346006i
$371$	−272.506	+	548.228i	−0.734518	+	1.47770i
$372$	25.8754	−	147.087i	0.0695576	−	0.395396i
$373$	0.579265			0.00155299			0.000776495	−	1.00000i	$-0.499753\pi$
$373$	0.579265			0.00155299			0.000776495		1.00000i	$0.499753\pi$
$374$	8.31363	+	4.79988i	0.0222290	+	0.0128339i
$375$	−205.713	−	172.475i	−0.548568	−	0.459933i
$376$	308.229	−	177.956i	0.819758	−	0.473287i
$377$		−	233.411i		−	0.619128i
$378$	−352.550	+	234.567i	−0.932671	+	0.620547i
$379$	18.5015			0.0488165			0.0244083	−	0.999702i	$-0.492230\pi$
$379$	18.5015			0.0488165			0.0244083	+	0.999702i	$0.492230\pi$
$380$	20.7663	+	35.9683i	0.0546481	+	0.0946533i
$381$	−94.6406	+	112.879i	−0.248400	+	0.296270i
$382$	68.0779	−	117.914i	0.178214	−	0.308676i
$383$			56.6187i			0.147829i	0.997265	+	0.0739147i	$0.0235493\pi$
$383$			56.6187i			0.147829i	−0.997265	+	0.0739147i	$0.976451\pi$
$384$	−456.089	−	80.2347i	−1.18773	−	0.208944i
$385$	−4.20095	+	2.78788i	−0.0109116	+	0.00724126i
$386$	55.7361			0.144394
$387$	−181.726	−	65.9800i	−0.469576	−	0.170491i
$388$	124.966	−	72.1492i	0.322077	−	0.185951i
$389$	413.566			1.06315			0.531575	−	0.847011i	$-0.321600\pi$
$389$	413.566			1.06315			0.531575	+	0.847011i	$0.321600\pi$
$390$	−25.7970	−	70.7894i	−0.0661461	−	0.181511i
$391$	271.901	−	156.982i	0.695398	−	0.401488i
$392$	127.107	−	301.477i	0.324253	−	0.769075i
$393$	−285.617	−	239.468i	−0.726760	−	0.609334i
$394$	−195.282	−	338.238i	−0.495639	−	0.858471i
$395$	79.0721	−	45.6523i	0.200182	−	0.115575i
$396$	−3.21227	−	1.16629i	−0.00811180	−	0.00294518i
$397$	−540.503	−	312.059i	−1.36147	−	0.786044i	−0.371648	−	0.928374i	$-0.621207\pi$
$397$	−540.503	−	312.059i	−1.36147	−	0.786044i	−0.989819	+	0.142330i	$0.954541\pi$
$398$	−560.632	−	323.681i	−1.40862	−	0.813269i
$399$	355.815	+	262.404i	0.891767	+	0.657655i
$400$	202.367	+	350.511i	0.505919	+	0.876277i
$401$	126.874			0.316395			0.158198	−	0.987407i	$-0.449432\pi$
$401$	126.874			0.316395			0.158198	+	0.987407i	$0.449432\pi$
$402$	−326.233	+	389.102i	−0.811525	+	0.967915i
$403$	282.861			0.701888
$404$	41.4398	+	23.9253i	0.102574	+	0.0592209i
$405$	53.8242	+	147.155i	0.132899	+	0.363347i
$406$	349.321	+	526.378i	0.860397	+	1.29650i
$407$	−5.49910	+	9.52472i	−0.0135113	+	0.0234023i
$408$	−39.9376	+	227.023i	−0.0978863	+	0.556429i
$409$	−374.582	−	216.265i	−0.915848	−	0.528765i	−0.0335397	−	0.999437i	$-0.510678\pi$
$409$	−374.582	−	216.265i	−0.915848	−	0.528765i	−0.882308	+	0.470672i	$0.844011\pi$
$410$	49.1443	−	85.1205i	0.119864	−	0.207611i
$411$	8.92548	−	10.6455i	0.0217165	−	0.0259015i
$412$	116.181	+	67.0769i	0.281992	+	0.162808i
$413$	−4.02308	−	64.4924i	−0.00974110	−	0.156156i
$414$	−421.164	+	353.967i	−1.01730	+	0.854993i
$415$	90.6626	−	157.032i	0.218464	−	0.378391i
$416$			92.4181i			0.222159i
$417$	−22.6295	+	128.636i	−0.0542674	+	0.308480i
$418$			17.5626i			0.0420159i
$419$	150.801	−	87.0648i	0.359906	−	0.207792i	−0.309134	−	0.951019i	$-0.600039\pi$
$419$	150.801	−	87.0648i	0.359906	−	0.207792i	0.669040	+	0.743227i	$0.266706\pi$
$420$	33.3421	+	24.5889i	0.0793860	+	0.0585451i
$421$	−175.470	+	303.923i	−0.416793	+	0.721907i	−0.995615	−	0.0935470i	$-0.970179\pi$
$421$	−175.470	+	303.923i	−0.416793	+	0.721907i	0.578822	+	0.815454i	$0.303513\pi$
$422$	−335.180	+	580.549i	−0.794265	+	1.37571i
$423$	308.657	+	367.252i	0.729685	+	0.868207i
$424$	−291.989	−	505.739i	−0.688653	−	1.19278i
$425$	211.852	−	122.313i	0.498474	−	0.287794i
$426$	645.254	+	113.512i	1.51468	+	0.266461i
$427$	−442.134	−	219.770i	−1.03544	−	0.514685i
$428$	71.3451	+	123.573i	0.166694	+	0.288723i
$429$	1.12144	−	6.37474i	0.00261407	−	0.0148595i
$430$			93.1031i			0.216519i
$431$	367.837	+	637.113i	0.853451	+	1.47822i	0.878075	+	0.478524i	$0.158828\pi$
$431$	367.837	+	637.113i	0.853451	+	1.47822i	−0.0246236	+	0.999697i	$0.507839\pi$
$432$	−0.610464	−	514.059i	−0.00141311	−	1.18995i
$433$		−	134.778i		−	0.311266i	−0.987815	−	0.155633i	$-0.950258\pi$
$433$		−	134.778i		−	0.311266i	0.987815	−	0.155633i	$-0.0497417\pi$
$434$	−637.894	+	423.327i	−1.46980	+	0.975408i
$435$	219.634	−	80.0386i	0.504905	−	0.183997i
$436$	−113.285			−0.259829
$437$	497.439	+	287.197i	1.13831	+	0.657201i
$438$	549.298	−	200.174i	1.25410	−	0.457019i
$439$	5.06360	−	2.92347i	0.0115344	−	0.00665939i	−0.494222	−	0.869336i	$-0.664547\pi$
$439$	5.06360	−	2.92347i	0.0115344	−	0.00665939i	0.505756	+	0.862677i	$0.331214\pi$
$440$		−	4.80927i		−	0.0109302i
$441$	430.014	+	97.8200i	0.975089	+	0.221814i
$442$	149.399			0.338007
$443$	80.1590	+	138.839i	0.180946	+	0.313407i	0.942203	−	0.335043i	$-0.108751\pi$
$443$	80.1590	+	138.839i	0.180946	+	0.313407i	−0.761257	+	0.648450i	$0.775417\pi$
$444$	89.0043	+	15.6575i	0.200460	+	0.0352647i
$445$	−28.6811	+	49.6772i	−0.0644520	+	0.111634i
$446$			36.4190i			0.0816570i
$447$	−50.6163	+	60.3707i	−0.113236	+	0.135057i
$448$	156.464	+	235.769i	0.349250	+	0.526271i
$449$	46.7901			0.104209			0.0521047	−	0.998642i	$-0.483407\pi$
$449$	46.7901			0.104209			0.0521047	+	0.998642i	$0.483407\pi$
$450$	−328.150	+	275.794i	−0.729223	+	0.612875i
$451$	7.31257	−	4.22191i	0.0162141	−	0.00936122i
$452$	−103.539			−0.229069
$453$	231.050	−	275.576i	0.510044	−	0.608335i
$454$	59.2669	−	34.2177i	0.130544	−	0.0753695i
$455$	−34.9258	+	70.2638i	−0.0767601	+	0.154426i
$456$	−396.224	+	144.392i	−0.868913	+	0.316648i
$457$	−277.170	−	480.073i	−0.606499	−	1.05049i	−0.991813	−	0.127702i	$-0.959240\pi$
$457$	−277.170	−	480.073i	−0.606499	−	1.05049i	0.385314	−	0.922786i	$-0.374093\pi$
$458$	354.298	−	204.554i	0.773577	−	0.446625i
$459$	−310.702	+	0.368970i	−0.676910	+	0.000803855i
$460$	46.6132	+	26.9122i	0.101333	+	0.0585047i
$461$	117.654	+	67.9273i	0.255214	+	0.147348i	0.622149	−	0.782899i	$-0.286260\pi$
$461$	117.654	+	67.9273i	0.255214	+	0.147348i	−0.366935	+	0.930246i	$0.619593\pi$
$462$	7.01137	+	16.0543i	0.0151761	+	0.0347497i
$463$	0.952160	+	1.64919i	0.00205650	+	0.00356196i	0.867052	−	0.498218i	$-0.166012\pi$
$463$	0.952160	+	1.64919i	0.00205650	+	0.00356196i	−0.864995	+	0.501780i	$0.832679\pi$
$464$	−766.916			−1.65284
$465$	96.9952	+	266.164i	0.208592	+	0.572396i
$466$	−783.716			−1.68179
$467$	−89.3271	−	51.5730i	−0.191278	−	0.110435i	0.401302	−	0.915946i	$-0.368558\pi$
$467$	−89.3271	−	51.5730i	−0.191278	−	0.110435i	−0.592581	+	0.805511i	$0.701891\pi$
$468$	−52.3697	+	9.27694i	−0.111901	+	0.0198225i
$469$	527.782	−	32.9234i	1.12533	−	0.0701991i
$470$	115.512	−	200.072i	0.245770	−	0.425686i
$471$	552.332	−	201.280i	1.17268	−	0.427346i
$472$	53.3791	+	30.8184i	0.113091	+	0.0652933i
$473$	−3.99917	+	6.92677i	−0.00845491	+	0.0146443i
$474$	−108.624	−	298.075i	−0.229164	−	0.628849i
$475$	387.580	+	223.769i	0.815958	+	0.471094i
$476$	−68.4476	+	45.4240i	−0.143797	+	0.0954286i
$477$	602.583	−	506.441i	1.26328	−	1.06172i
$478$	111.163	−	192.540i	0.232559	−	0.402804i
$479$		−	191.432i		−	0.399649i	−0.979832	−	0.199825i	$-0.935963\pi$
$479$		−	191.432i		−	0.399649i	0.979832	−	0.199825i	$-0.0640372\pi$
$480$	−86.9629	+	31.6909i	−0.181173	+	0.0660227i
$481$			171.163i			0.355848i
$482$	−545.209	+	314.777i	−1.13114	+	0.653064i
$483$	569.374	+	63.9440i	1.17883	+	0.132389i
$484$	61.6283	−	106.743i	0.127331	−	0.220544i
$485$	−136.856	+	237.042i	−0.282178	+	0.488746i
$486$	535.981	−	95.6021i	1.10284	−	0.196712i
$487$	−224.406	−	388.683i	−0.460794	−	0.798118i	0.538207	−	0.842813i	$-0.319102\pi$
$487$	−224.406	−	388.683i	−0.460794	−	0.798118i	−0.999001	+	0.0446948i	$0.985768\pi$
$488$	407.868	−	235.483i	0.835795	−	0.482547i
$489$	−85.9578	−	235.876i	−0.175783	−	0.482365i
$490$	−26.3930	−	210.725i	−0.0538633	−	0.430051i
$491$	−40.8828	−	70.8111i	−0.0832644	−	0.144218i	0.821386	−	0.570373i	$-0.193201\pi$
$491$	−40.8828	−	70.8111i	−0.0832644	−	0.144218i	−0.904650	+	0.426155i	$0.859868\pi$
$492$	−53.1674	−	44.5769i	−0.108064	−	0.0906034i
$493$			463.530i			0.940224i
$494$	136.662	+	236.705i	0.276644	+	0.479161i
$495$	6.38301	−	1.13071i	0.0128950	−	0.00228426i
$496$		−	929.392i		−	1.87377i
$497$	−377.282	−	568.511i	−0.759119	−	1.14389i
$498$	−482.798	−	404.790i	−0.969474	−	0.812832i
$499$	−27.5430			−0.0551964			−0.0275982	−	0.999619i	$-0.508786\pi$
$499$	−27.5430			−0.0551964			−0.0275982	+	0.999619i	$0.508786\pi$
$500$	79.0307	+	45.6284i	0.158061	+	0.0912568i
$501$	−129.541	+	736.366i	−0.258564	+	1.46979i
$502$	32.2061	−	18.5942i	0.0641556	−	0.0370402i
$503$			49.4903i			0.0983902i	0.998789	+	0.0491951i	$0.0156656\pi$
$503$			49.4903i			0.0983902i	−0.998789	+	0.0491951i	$0.984334\pi$
$504$	−304.552	+	290.172i	−0.604270	+	0.575738i
$505$	−90.7653			−0.179733
$506$	11.3802	+	19.7111i	0.0224905	+	0.0389547i
$507$	139.103	+	381.712i	0.274365	+	0.752883i
$508$	25.0372	−	43.3658i	0.0492859	−	0.0853657i
$509$		−	125.689i		−	0.246934i	−0.992349	−	0.123467i	$-0.960599\pi$
$509$		−	125.689i		−	0.246934i	0.992349	−	0.123467i	$-0.0394013\pi$
$510$	51.2301	+	140.580i	0.100451	+	0.275648i
$511$	−545.219	−	271.011i	−1.06696	−	0.530354i
$512$	−204.849			−0.400097
$513$	−284.797	−	491.933i	−0.555160	−	0.958934i
$514$	165.318	−	95.4464i	0.321630	−	0.185693i
$515$	−254.470			−0.494116
$516$	64.7276	+	11.3868i	0.125441	+	0.0220675i
$517$	17.1879	−	9.92344i	0.0332454	−	0.0191943i
$518$	−256.160	−	385.998i	−0.494518	−	0.745169i
$519$	144.733	−	822.727i	0.278869	−	1.58522i
$520$	−37.4228	−	64.8182i	−0.0719670	−	0.124650i
$521$	−606.831	+	350.354i	−1.16474	+	0.672464i	−0.952436	−	0.304739i	$-0.901431\pi$
$521$	−606.831	+	350.354i	−1.16474	+	0.672464i	−0.212306	+	0.977203i	$0.568097\pi$
$522$	−141.677	−	799.789i	−0.271413	−	1.53216i
$523$	−302.754	−	174.795i	−0.578879	−	0.334216i	0.181809	−	0.983334i	$-0.441805\pi$
$523$	−302.754	−	174.795i	−0.578879	−	0.334216i	−0.760688	+	0.649118i	$0.775138\pi$
$524$	109.728	+	63.3515i	0.209405	+	0.120900i
$525$	443.628	+	49.8220i	0.845005	+	0.0948990i
$526$	399.541	+	692.026i	0.759584	+	1.31564i
$527$	−561.732			−1.06591
$528$	−20.9454	−	3.68469i	−0.0396693	−	0.00697858i
$529$	215.388			0.407160
$530$	−328.277	−	189.531i	−0.619390	−	0.357605i
$531$	−28.3532	+	78.0921i	−0.0533959	+	0.147066i
$532$	−134.581	−	66.8959i	−0.252972	−	0.125744i
$533$	65.7048	−	113.804i	0.123273	−	0.213516i
$534$	152.733	+	128.055i	0.286017	+	0.239804i
$535$	−234.400	−	135.331i	−0.438131	−	0.252955i
$536$	−252.207	+	436.835i	−0.470535	+	0.814990i
$537$	−760.862	−	133.850i	−1.41688	−	0.249255i
$538$	747.204	+	431.399i	1.38886	+	0.801856i
$539$	7.08792	−	16.8114i	0.0131501	−	0.0311900i
$540$	−26.6873	−	46.0973i	−0.0494209	−	0.0853653i
$541$	−350.723	+	607.469i	−0.648286	+	1.12286i	0.335246	+	0.942131i	$0.391180\pi$
$541$	−350.723	+	607.469i	−0.648286	+	1.12286i	−0.983532	+	0.180734i	$0.942153\pi$
$542$		−	139.584i		−	0.257534i
$543$	−67.2523	−	56.3860i	−0.123853	−	0.103842i
$544$		−	183.533i		−	0.337376i
$545$	186.096	−	107.443i	0.341461	−	0.197143i
$546$	219.423	+	161.819i	0.401873	+	0.296371i
$547$	−202.629	+	350.964i	−0.370437	+	0.641616i	−0.989633	−	0.143620i	$-0.954126\pi$
$547$	−202.629	+	350.964i	−0.370437	+	0.641616i	0.619195	+	0.785237i	$0.287459\pi$
$548$	−2.36124	+	4.08979i	−0.00430884	+	0.00746313i
$549$	408.434	+	485.971i	0.743960	+	0.885193i
$550$	8.86688	+	15.3579i	0.0161216	+	0.0279234i
$551$	−734.410	+	424.012i	−1.33287	+	0.769532i
$552$	−351.132	+	418.799i	−0.636108	+	0.758694i
$553$	−147.063	+	295.861i	−0.265937	+	0.535011i
$554$	−95.2339	−	164.950i	−0.171902	−	0.297744i
$555$	−161.059	+	58.6930i	−0.290197	+	0.105753i
$556$		−	44.4000i		−	0.0798560i
$557$	−51.7943	−	89.7104i	−0.0929880	−	0.161060i	0.815779	−	0.578364i	$-0.196308\pi$
$557$	−51.7943	−	89.7104i	−0.0929880	−	0.161060i	−0.908767	+	0.417304i	$0.862975\pi$
$558$	969.229	−	171.693i	1.73697	−	0.307693i
$559$			124.477i			0.222677i
$560$	230.865	+	114.755i	0.412258	+	0.204920i
$561$	−2.22706	+	12.6596i	−0.00396980	+	0.0225661i
$562$	−331.069			−0.589092
$563$	113.286	+	65.4059i	0.201219	+	0.116174i	0.597224	−	0.802074i	$-0.296270\pi$
$563$	113.286	+	65.4059i	0.201219	+	0.116174i	−0.396005	+	0.918248i	$0.629604\pi$
$564$	−124.968	−	104.776i	−0.221574	−	0.185773i
$565$	170.086	−	98.1994i	0.301038	−	0.173804i
$566$		−	786.000i		−	1.38869i
$567$	−456.728	−	335.988i	−0.805517	−	0.592572i
$568$	650.834			1.14584
$569$	317.790	+	550.428i	0.558506	+	0.967361i	0.997621	+	0.0689303i	$0.0219586\pi$
$569$	317.790	+	550.428i	0.558506	+	0.967361i	−0.439115	+	0.898431i	$0.644708\pi$
$570$	−175.871	+	209.763i	−0.308545	+	0.368006i
$571$	−86.0297	+	149.008i	−0.150665	+	0.260959i	−0.931472	−	0.363813i	$-0.881475\pi$
$571$	−86.0297	+	149.008i	−0.150665	+	0.260959i	0.780807	+	0.624772i	$0.214808\pi$
$572$			2.20030i			0.00384668i
$573$	179.554	+	31.5869i	0.313358	+	0.0551255i
$574$	22.1438	+	354.978i	0.0385780	+	0.618429i
$575$	579.990			1.00868
$576$	−63.4585	−	358.233i	−0.110171	−	0.621932i
$577$	27.4829	−	15.8672i	0.0476306	−	0.0274996i	−0.475996	−	0.879448i	$-0.657912\pi$
$577$	27.4829	−	15.8672i	0.0476306	−	0.0274996i	0.523626	+	0.851948i	$0.324579\pi$
$578$	350.812			0.606942
$579$	25.5528	+	70.1193i	0.0441326	+	0.121104i
$580$	−68.8189	+	39.7326i	−0.118653	+	0.0685045i
$581$	40.8514	+	654.873i	0.0703122	+	1.12715i
$582$	728.789	+	611.035i	1.25222	+	1.04989i
$583$	−16.2823	−	28.2017i	−0.0279285	−	0.0483735i
$584$	502.964	−	290.386i	0.861240	−	0.497237i
$585$	77.2303	−	64.9081i	0.132018	−	0.110954i
$586$	−95.8236	−	55.3238i	−0.163521	−	0.0944092i
$587$	780.765	+	450.775i	1.33009	+	0.767929i	0.985314	−	0.170754i	$-0.0546204\pi$
$587$	780.765	+	450.775i	1.33009	+	0.767929i	0.344779	+	0.938684i	$0.387954\pi$
$588$	−149.729	−	7.42327i	−0.254642	−	0.0126246i
$589$	−513.842	−	890.000i	−0.872396	−	1.51104i
$590$	40.0087			0.0678113
$591$	335.994	−	400.744i	0.568517	−	0.678077i
$592$	562.387			0.949978
$593$	−92.1847	−	53.2228i	−0.155455	−	0.0897518i	0.420255	−	0.907406i	$-0.361941\pi$
$593$	−92.1847	−	53.2228i	−0.155455	−	0.0897518i	−0.575709	+	0.817654i	$0.695274\pi$
$594$	−0.0267479	−	22.5239i	−4.50302e−5	−	0.0379190i
$595$	69.3590	−	139.536i	0.116570	−	0.234515i
$596$	13.3906	−	23.1932i	0.0224674	−	0.0389147i
$597$	150.182	−	853.702i	0.251561	−	1.42999i
$598$	306.759	+	177.108i	0.512976	+	0.296167i
$599$	407.540	−	705.880i	0.680367	−	1.17843i	−0.294501	−	0.955651i	$-0.595154\pi$
$599$	407.540	−	705.880i	0.680367	−	1.17843i	0.974869	−	0.222780i	$-0.0715131\pi$
$600$	−273.584	+	326.308i	−0.455974	+	0.543846i
$601$	222.029	+	128.189i	0.369433	+	0.213292i	0.673211	−	0.739451i	$-0.264915\pi$
$601$	222.029	+	128.189i	0.369433	+	0.213292i	−0.303778	+	0.952743i	$0.598248\pi$
$602$	−186.290	−	280.714i	−0.309453	−	0.466302i
$603$	−639.077	−	232.032i	−1.05983	−	0.384796i
$604$	−61.1244	+	105.871i	−0.101199	+	0.175282i
$605$			233.800i			0.386445i
$606$	−54.6416	+	310.607i	−0.0901676	+	0.512552i
$607$			323.825i			0.533485i	0.963768	+	0.266742i	$0.0859473\pi$
$607$			323.825i			0.533485i	−0.963768	+	0.266742i	$0.914053\pi$
$608$	290.786	−	167.886i	0.478267	−	0.276128i
$609$	−502.064	+	680.789i	−0.824407	+	1.11788i
$610$	152.852	−	264.748i	0.250578	−	0.434014i
$611$	154.436	−	267.492i	0.252760	−	0.437793i
$612$	104.001	−	18.4230i	0.169936	−	0.0301030i
$613$	310.620	+	538.010i	0.506721	+	0.877667i	0.999970	+	0.00777855i	$0.00247602\pi$
$613$	310.620	+	538.010i	0.506721	+	0.877667i	−0.493248	+	0.869888i	$0.664191\pi$
$614$	839.540	−	484.709i	1.36733	−	0.789428i
$615$	129.617	+	22.8021i	0.210759	+	0.0370766i
$616$	9.62289	+	14.5003i	0.0156216	+	0.0235395i
$617$	372.353	+	644.935i	0.603490	+	1.04527i	0.992288	+	0.123952i	$0.0395569\pi$
$617$	372.353	+	644.935i	0.603490	+	1.04527i	−0.388799	+	0.921323i	$0.627110\pi$
$618$	−153.193	+	870.817i	−0.247885	+	1.40909i
$619$			183.637i			0.296668i	0.988937	+	0.148334i	$0.0473910\pi$
$619$			183.637i			0.296668i	−0.988937	+	0.148334i	$0.952609\pi$
$620$	−48.1502	−	83.3986i	−0.0776616	−	0.134514i
$621$	−638.398	−	367.569i	−1.02802	−	0.591899i
$622$			374.587i			0.602230i
$623$	−12.9233	−	207.169i	−0.0207437	−	0.332535i
$624$	−310.970	+	113.323i	−0.498349	+	0.181607i
$625$	358.348			0.573356
$626$	501.739	+	289.679i	0.801501	+	0.462747i
$627$	−22.0948	+	8.05176i	−0.0352389	+	0.0128417i
$628$	−173.065	+	99.9191i	−0.275581	+	0.159107i
$629$		−	339.911i		−	0.540399i
$630$	−77.0250	+	261.960i	−0.122262	+	0.415809i
$631$	325.873			0.516439			0.258220	−	0.966086i	$-0.416864\pi$
$631$	325.873			0.516439			0.258220	+	0.966086i	$0.416864\pi$
$632$	−157.577	−	272.932i	−0.249331	−	0.431854i
$633$	−884.030	−	155.518i	−1.39657	−	0.245683i
$634$	226.865	−	392.942i	0.357831	−	0.619782i
$635$			94.9838i			0.149581i
$636$	−171.916	+	205.046i	−0.270308	+	0.322400i
$637$	−35.2868	−	281.734i	−0.0553953	−	0.442283i
$638$	−33.6030			−0.0526693
$639$	153.018	+	863.807i	0.239464	+	1.35181i
$640$	−258.603	+	149.304i	−0.404067	+	0.233288i
$641$	−178.662			−0.278725			−0.139362	−	0.990241i	$-0.544505\pi$
$641$	−178.662			−0.278725			−0.139362	+	0.990241i	$0.544505\pi$
$642$	−604.226	+	720.667i	−0.941162	+	1.12253i
$643$	60.1837	−	34.7471i	0.0935983	−	0.0540390i	−0.452470	−	0.891780i	$-0.649457\pi$
$643$	60.1837	−	34.7471i	0.0935983	−	0.0540390i	0.546069	+	0.837740i	$0.316124\pi$
$644$	−194.391	+	12.1263i	−0.301850	+	0.0188296i
$645$	−117.129	+	42.6840i	−0.181595	+	0.0661767i
$646$	−271.396	−	470.072i	−0.420118	−	0.727666i
$647$	−712.875	+	411.579i	−1.10182	+	0.636134i	−0.936697	−	0.350140i	$-0.886134\pi$
$647$	−712.875	+	411.579i	−1.10182	+	0.636134i	−0.165119	+	0.986274i	$0.552801\pi$
$648$	507.933	−	185.784i	0.783848	−	0.286704i
$649$	2.97660	+	1.71854i	0.00458644	+	0.00264798i
$650$	239.012	+	137.993i	0.367710	+	0.212298i
$651$	−825.018	−	608.429i	−1.26731	−	0.934607i
$652$	42.6710	+	73.9084i	0.0654463	+	0.113356i
$653$	782.435			1.19822			0.599108	−	0.800668i	$-0.295522\pi$
$653$	782.435			1.19822			0.599108	+	0.800668i	$0.295522\pi$
$654$	−255.647	−	701.520i	−0.390897	−	1.07266i
$655$	−240.337			−0.366926
$656$	−373.924	−	215.885i	−0.570006	−	0.329093i
$657$	503.662	+	599.276i	0.766608	+	0.912141i
$658$	52.0480	+	834.362i	0.0791004	+	1.26803i
$659$	90.6800	−	157.062i	0.137602	−	0.238334i	−0.788986	−	0.614411i	$-0.789394\pi$
$659$	90.6800	−	157.062i	0.137602	−	0.238334i	0.926589	+	0.376077i	$0.122727\pi$
$660$	−2.07042	+	0.754501i	−0.00313701	+	0.00114318i
$661$	−167.119	−	96.4862i	−0.252827	−	0.145970i	0.368231	−	0.929734i	$-0.379964\pi$
$661$	−167.119	−	96.4862i	−0.252827	−	0.145970i	−0.621058	+	0.783764i	$0.713297\pi$
$662$	−38.2635	+	66.2743i	−0.0577999	+	0.100112i
$663$	68.4934	+	187.953i	0.103308	+	0.283488i
$664$	−542.025	−	312.939i	−0.816303	−	0.471293i
$665$	284.525	−	17.7489i	0.427857	−	0.0266900i
$666$	103.893	+	586.493i	0.155996	+	0.880620i
$667$	−549.500	+	951.762i	−0.823839	+	1.42693i
$668$		−	254.164i		−	0.380484i
$669$	−45.8172	+	16.6966i	−0.0684861	+	0.0249576i
$670$			327.416i			0.488681i
$671$	22.7441	−	13.1313i	0.0338958	−	0.0195698i
$672$	198.790	−	269.555i	0.295818	−	0.401124i
$673$	−41.9447	+	72.6503i	−0.0623249	+	0.107950i	−0.895504	−	0.445053i	$-0.853185\pi$
$673$	−41.9447	+	72.6503i	−0.0623249	+	0.107950i	0.833179	+	0.553003i	$0.186518\pi$
$674$	461.215	−	798.849i	0.684296	−	1.18524i
$675$	−497.408	−	286.392i	−0.736901	−	0.424284i
$676$	−69.0532	−	119.604i	−0.102150	−	0.176929i
$677$	−179.443	+	103.601i	−0.265056	+	0.153030i	−0.626639	−	0.779310i	$-0.715570\pi$
$677$	−179.443	+	103.601i	−0.265056	+	0.153030i	0.361583	+	0.932340i	$0.382236\pi$
$678$	−233.653	−	641.167i	−0.344621	−	0.945674i
$679$	−61.6656	−	988.538i	−0.0908182	−	1.45587i
$680$	74.3178	+	128.722i	0.109291	+	0.189297i
$681$	70.2193	+	58.8737i	0.103112	+	0.0864518i
$682$		−	40.7220i		−	0.0597097i
$683$	−639.939	−	1108.41i	−0.936953	−	1.62285i	−0.771113	−	0.636698i	$-0.780300\pi$
$683$	−639.939	−	1108.41i	−0.936953	−	1.62285i	−0.165841	−	0.986153i	$-0.553034\pi$
$684$	124.323	+	147.925i	0.181759	+	0.216264i
$685$		−	8.95786i		−	0.0130772i
$686$	501.218	+	582.544i	0.730639	+	0.849189i
$687$	419.772	+	351.948i	0.611022	+	0.512296i
$688$	408.991			0.594464
$689$	−438.898	−	253.398i	−0.637007	−	0.367776i
$690$	−61.4632	+	349.384i	−0.0890771	+	0.506353i
$691$	1052.86	−	607.869i	1.52368	−	0.879695i	0.524069	−	0.851676i	$-0.324413\pi$
$691$	1052.86	−	607.869i	1.52368	−	0.879695i	0.999607	−	0.0280193i	$-0.00892000\pi$
$692$			283.972i			0.410364i
$693$	−16.9829	+	16.1810i	−0.0245063	+	0.0233492i
$694$	−1338.67			−1.92892
$695$	42.1101	+	72.9368i	0.0605900	+	0.104945i
$696$	−276.268	−	758.105i	−0.396936	−	1.08923i
$697$	−130.483	+	226.003i	−0.187206	+	0.324251i
$698$		−	188.410i		−	0.269928i
$699$	−359.302	−	985.960i	−0.514023	−	1.41053i
$700$	−151.460	+	9.44818i	−0.216372	+	0.0134974i
$701$	−1171.72			−1.67149			−0.835747	−	0.549114i	$-0.814965\pi$
$701$	−1171.72			−1.67149			−0.835747	+	0.549114i	$0.814965\pi$
$702$	−175.628	−	303.364i	−0.250182	−	0.432142i
$703$	538.550	−	310.932i	0.766074	−	0.442293i
$704$	−15.0511			−0.0213794
$705$	304.660	+	53.5954i	0.432142	+	0.0760218i
$706$	−889.515	+	513.562i	−1.25994	+	0.727425i
$707$	273.665	−	181.613i	0.387079	−	0.256878i
$708$	4.89319	−	27.8150i	0.00691129	−	0.0392868i
$709$	55.8366	+	96.7119i	0.0787540	+	0.136406i	0.902713	−	0.430244i	$-0.141572\pi$
$709$	55.8366	+	96.7119i	0.0787540	+	0.136406i	−0.823959	+	0.566650i	$0.808239\pi$
$710$	365.860	−	211.229i	0.515295	−	0.297506i
$711$	325.195	−	273.310i	0.457377	−	0.384403i
$712$	171.470	+	98.9981i	0.240828	+	0.139042i
$713$	−1153.40	−	665.915i	−1.61767	−	0.933962i
$714$	−435.751	−	321.355i	−0.610295	−	0.450077i
$715$	−2.08682	−	3.61448i	−0.00291863	−	0.00505522i
$716$	262.619			0.366786
$717$	293.190	+	51.5777i	0.408913	+	0.0719355i
$718$	−28.8019			−0.0401141
$719$	1204.35	+	695.331i	1.67503	+	0.967081i	0.964751	+	0.263164i	$0.0847662\pi$
$719$	1204.35	+	695.331i	1.67503	+	0.967081i	0.710283	+	0.703917i	$0.248567\pi$
$720$	−213.268	−	253.754i	−0.296205	−	0.352437i
$721$	767.247	−	509.170i	1.06414	−	0.706199i
$722$	92.1074	−	159.535i	0.127573	−	0.220962i
$723$	−645.964	−	541.592i	−0.893449	−	0.749090i
$724$	25.8370	+	14.9170i	0.0356864	+	0.0206036i
$725$	−428.143	+	741.566i	−0.590543	+	1.02285i
$726$	800.082	+	140.750i	1.10204	+	0.193870i
$727$	−570.198	−	329.204i	−0.784317	−	0.452826i	0.0536411	−	0.998560i	$-0.482917\pi$
$727$	−570.198	−	329.204i	−0.784317	−	0.452826i	−0.837958	+	0.545735i	$0.816251\pi$
$728$	242.528	+	120.553i	0.333143	+	0.165595i
$729$	365.998	+	630.465i	0.502055	+	0.864835i
$730$	188.491	−	326.475i	0.258206	−	0.447226i
$731$		−	247.197i		−	0.338163i
$732$	−165.365	−	138.647i	−0.225909	−	0.189408i
$733$			372.006i			0.507512i	0.967268	+	0.253756i	$0.0816659\pi$
$733$			372.006i			0.507512i	−0.967268	+	0.253756i	$0.918334\pi$
$734$	−1199.80	+	692.703i	−1.63460	+	0.943737i
$735$	253.004	−	129.813i	0.344223	−	0.176616i
$736$	217.572	−	376.846i	0.295614	−	0.512019i
$737$	−14.0639	+	24.3594i	−0.0190826	+	0.0330521i
$738$	156.061	−	429.834i	0.211465	−	0.582431i
$739$	470.172	+	814.362i	0.636227	+	1.10198i	0.986254	+	0.165238i	$0.0528393\pi$
$739$	470.172	+	814.362i	0.636227	+	1.10198i	−0.350026	+	0.936740i	$0.613827\pi$
$740$	50.4655	−	29.1363i	0.0681967	−	0.0393734i
$741$	−235.135	+	280.448i	−0.317321	+	0.378473i
$742$	1369.01	−	85.4000i	1.84503	−	0.115094i
$743$	−103.438	−	179.161i	−0.139217	−	0.241131i	0.787983	−	0.615697i	$-0.211125\pi$
$743$	−103.438	−	179.161i	−0.139217	−	0.241131i	−0.927201	+	0.374565i	$0.877792\pi$
$744$	918.714	−	334.797i	1.23483	−	0.449995i
$745$			50.7999i			0.0681878i
$746$	−0.648921	−	1.12396i	−0.000869867	−	0.00150665i
$747$	287.906	−	792.968i	0.385416	−	1.06154i
$748$		−	4.36957i		−	0.00584167i
$749$	977.521	−	60.9784i	1.30510	−	0.0814130i
$750$	−104.208	+	592.365i	−0.138944	+	0.789820i
$751$	1448.31			1.92850			0.964252	−	0.264986i	$-0.0853675\pi$
$751$	1448.31			1.92850			0.964252	+	0.264986i	$0.0853675\pi$
$752$	−878.894	−	507.430i	−1.16874	−	0.674773i
$753$	38.1578	+	31.9924i	0.0506743	+	0.0424866i
$754$	−452.894	+	261.478i	−0.600655	+	0.346788i
$755$		−	231.888i		−	0.307136i
$756$	172.701	+	85.5883i	0.228440	+	0.113212i
$757$	−296.987			−0.392321			−0.196161	−	0.980572i	$-0.562847\pi$
$757$	−296.987			−0.392321			−0.196161	+	0.980572i	$0.562847\pi$
$758$	−20.7262	−	35.8989i	−0.0273433	−	0.0473600i
$759$	−19.5803	+	23.3537i	−0.0257975	+	0.0307690i
$760$	−135.964	+	235.496i	−0.178900	+	0.309863i
$761$			294.080i			0.386439i	0.981156	+	0.193220i	$0.0618930\pi$
$761$			294.080i			0.386439i	−0.981156	+	0.193220i	$0.938107\pi$
$762$	325.043	+	57.1812i	0.426565	+	0.0750409i
$763$	−346.113	+	696.311i	−0.453622	+	0.912596i
$764$	−61.9748			−0.0811188
$765$	−153.371	+	128.901i	−0.200485	+	0.168498i
$766$	109.859	−	63.4270i	0.143419	−	0.0828028i
$767$	53.4906			0.0697401
$768$	189.164	+	519.084i	0.246307	+	0.675891i
$769$	−91.6783	+	52.9305i	−0.119218	+	0.0688303i	−0.558423	−	0.829556i	$-0.688593\pi$
$769$	−91.6783	+	52.9305i	−0.119218	+	0.0688303i	0.439205	+	0.898387i	$0.355260\pi$
$770$	10.1155	+	5.02809i	0.0131370	+	0.00652999i
$771$	195.869	+	164.221i	0.254045	+	0.212998i
$772$	−12.6849	−	21.9708i	−0.0164312	−	0.0284596i
$773$	−1070.93	+	618.299i	−1.38541	+	0.799869i	−0.992794	−	0.119832i	$-0.961765\pi$
$773$	−1070.93	+	618.299i	−1.38541	+	0.799869i	−0.392620	+	0.919701i	$0.628431\pi$
$774$	75.5555	+	426.522i	0.0976169	+	0.551062i
$775$	−898.671	−	518.848i	−1.15958	−	0.669481i
$776$	818.193	+	472.384i	1.05437	+	0.608742i
$777$	368.168	−	499.229i	0.473833	−	0.642508i
$778$	−463.296	−	802.452i	−0.595496	−	1.03143i
$779$	−477.434			−0.612880
$780$	−22.0336	+	26.2798i	−0.0282483	+	0.0336920i
$781$	36.2927			0.0464696
$782$	−609.192	−	351.717i	−0.779018	−	0.449766i
$783$	941.227	−	544.909i	1.20208	−	0.695925i
$784$	−925.690	+	115.941i	−1.18073	+	0.147884i
$785$	189.532	−	328.278i	0.241442	−	0.418189i
$786$	−144.685	+	822.453i	−0.184078	+	1.04638i
$787$	728.889	+	420.825i	0.926162	+	0.534720i	0.885596	−	0.464457i	$-0.153750\pi$
$787$	728.889	+	420.825i	0.926162	+	0.534720i	0.0405663	+	0.999177i	$0.487084\pi$
$788$	−88.8874	+	153.957i	−0.112801	+	0.195377i
$789$	−687.435	+	819.912i	−0.871273	+	1.03918i
$790$	−177.161	−	102.284i	−0.224254	−	0.129473i
$791$	−316.337	+	636.406i	−0.399920	+	0.804559i
$792$	−3.90284	−	22.0321i	−0.00492783	−	0.0278183i
$793$	204.360	−	353.962i	0.257705	−	0.446358i
$794$			1398.33i			1.76113i
$795$	87.9389	−	499.883i	0.110615	−	0.628784i
$796$			294.663i			0.370180i
$797$	−138.377	+	79.8921i	−0.173622	+	0.100241i	−0.584293	−	0.811543i	$-0.698628\pi$
$797$	−138.377	+	79.8921i	−0.173622	+	0.100241i	0.410670	+	0.911784i	$0.365295\pi$
$798$	110.549	−	984.355i	0.138532	−	1.23353i
$799$	−306.695	+	531.211i	−0.383848	+	0.664844i
$800$	169.521	−	293.620i	0.211902	−	0.367025i
$801$	−91.0791	+	250.855i	−0.113707	+	0.313178i
$802$	−142.131	−	246.178i	−0.177220	−	0.306955i
$803$	28.0470	−	16.1929i	0.0349277	−	0.0201655i
$804$	227.628	+	40.0441i	0.283119	+	0.0498061i
$805$	307.830	−	204.286i	0.382398	−	0.253771i
$806$	−316.874	−	548.842i	−0.393144	−	0.680946i
$807$	−200.161	+	1137.80i	−0.248031	+	1.40992i
$808$			313.293i			0.387739i
$809$	−17.7511	−	30.7458i	−0.0219420	−	0.0380046i	0.854846	−	0.518882i	$-0.173652\pi$
$809$	−17.7511	−	30.7458i	−0.0219420	−	0.0380046i	−0.876788	+	0.480877i	$0.840318\pi$
$810$	225.233	−	269.287i	0.278065	−	0.332453i
$811$			264.939i			0.326682i	0.986570	+	0.163341i	$0.0522271\pi$
$811$			264.939i			0.326682i	−0.986570	+	0.163341i	$0.947773\pi$
$812$	127.994	−	257.497i	0.157628	−	0.317115i
$813$	175.604	−	63.9934i	0.215995	−	0.0787127i
$814$	24.6414			0.0302720
$815$	−140.193	−	80.9406i	−0.172016	−	0.0993136i
$816$	617.553	−	225.048i	0.756805	−	0.275794i
$817$	391.656	−	226.123i	0.479383	−	0.276772i
$818$			969.081i			1.18470i
$819$	−102.981	+	350.234i	−0.125739	+	0.427636i
$820$	−44.7386			−0.0545592
$821$	−753.781	−	1305.59i	−0.918126	−	1.59024i	−0.802260	−	0.596975i	$-0.796369\pi$
$821$	−753.781	−	1305.59i	−0.918126	−	1.59024i	−0.115866	−	0.993265i	$-0.536964\pi$
$822$	−30.6546	−	5.39271i	−0.0372926	−	0.00656048i
$823$	−617.420	+	1069.40i	−0.750207	+	1.29940i	0.197515	+	0.980300i	$0.436713\pi$
$823$	−617.420	+	1069.40i	−0.750207	+	1.29940i	−0.947722	+	0.319097i	$0.896621\pi$
$824$			878.348i			1.06596i
$825$	−15.2560	+	18.1960i	−0.0184921	+	0.0220558i
$826$	−120.629	+	80.0535i	−0.146040	+	0.0969171i
$827$	642.770			0.777231			0.388616	−	0.921400i	$-0.372953\pi$
$827$	642.770			0.777231			0.388616	+	0.921400i	$0.372953\pi$
$828$	235.383	+	85.4616i	0.284279	+	0.103214i
$829$	831.340	−	479.974i	1.00282	−	0.578980i	0.0937403	−	0.995597i	$-0.470118\pi$
$829$	831.340	−	479.974i	1.00282	−	0.578980i	0.909082	+	0.416617i	$0.136784\pi$
$830$	−406.258			−0.489468
$831$	163.856	−	195.433i	0.197179	−	0.235178i
$832$	−202.855	+	117.119i	−0.243816	+	0.140767i
$833$	70.0759	+	559.495i	0.0841248	+	0.671662i
$834$	274.947	−	100.196i	0.329672	−	0.120139i
$835$	241.055	+	417.520i	0.288689	+	0.500024i
$836$	6.92308	−	3.99704i	0.00828120	−	0.00478115i
$837$	660.351	+	1140.63i	0.788950	+	1.36276i
$838$	−337.868	−	195.068i	−0.403184	−	0.232778i
$839$	409.757	+	236.574i	0.488388	+	0.281971i	0.723905	−	0.689899i	$-0.242345\pi$
$839$	409.757	+	236.574i	0.488388	+	0.281971i	−0.235518	+	0.971870i	$0.575679\pi$
$840$	−30.2721	+	269.551i	−0.0360382	+	0.320894i
$841$	−390.772	−	676.837i	−0.464652	−	0.804800i
$842$	786.279			0.933823
$843$	−151.782	−	416.504i	−0.180050	−	0.494074i
$844$	305.131			0.361530
$845$	226.870	+	130.984i	0.268486	+	0.155010i
$846$	366.816	−	1010.31i	0.433589	−	1.19422i
$847$	−467.811	−	704.925i	−0.552315	−	0.832261i
$848$	−832.586	+	1442.08i	−0.981823	+	1.70057i
$849$	988.833	−	360.349i	1.16470	−	0.424440i
$850$	−474.652	−	274.041i	−0.558414	−	0.322401i
$851$	402.954	−	697.936i	0.473506	−	0.820136i
$852$	−102.106	−	280.189i	−0.119843	−	0.328860i
$853$	−1068.57	−	616.937i	−1.25271	−	0.723255i	−0.281067	−	0.959688i	$-0.590688\pi$
$853$	−1068.57	−	616.937i	−1.25271	−	0.723255i	−0.971648	+	0.236433i	$0.924022\pi$
$854$	68.8733	+	1104.08i	0.0806479	+	1.29284i
$855$	−344.524	−	125.088i	−0.402952	−	0.146301i
$856$	−467.120	+	809.075i	−0.545701	+	0.945181i
$857$		−	397.309i		−	0.463605i	−0.972763	−	0.231802i	$-0.925538\pi$
$857$		−	397.309i		−	0.463605i	0.972763	−	0.231802i	$-0.0744622\pi$
$858$	−13.6254	+	4.96534i	−0.0158804	+	0.00578711i
$859$		−	546.401i		−	0.636090i	−0.948076	−	0.318045i	$-0.896974\pi$
$859$		−	546.401i		−	0.636090i	0.948076	−	0.318045i	$-0.103026\pi$
$860$	36.7006	−	21.1891i	0.0426752	−	0.0246385i
$861$	−436.431	+	190.601i	−0.506889	+	0.221372i
$862$	824.138	−	1427.45i	0.956076	−	1.65597i
$863$	−7.86960	+	13.6305i	−0.00911888	+	0.0157944i	−0.870549	−	0.492082i	$-0.836236\pi$
$863$	−7.86960	+	13.6305i	−0.00911888	+	0.0157944i	0.861430	+	0.507876i	$0.169569\pi$
$864$	−372.675	+	215.754i	−0.431336	+	0.249716i
$865$	−269.326	−	466.487i	−0.311360	−	0.539291i
$866$	−261.513	+	150.985i	−0.301978	+	0.174347i
$867$	160.833	+	441.342i	0.185505	+	0.509045i
$868$	312.050	+	155.110i	0.359504	+	0.178698i
$869$	−8.78704	−	15.2196i	−0.0101117	−	0.0175139i
$870$	−401.345	−	336.498i	−0.461316	−	0.386779i
$871$			437.747i			0.502580i
$872$	−370.858	−	642.346i	−0.425296	−	0.736635i
$873$	−434.597	+	1196.99i	−0.497820	+	1.37113i
$874$		−	1286.93i		−	1.47246i
$875$	521.912	−	346.358i	0.596471	−	0.395837i
$876$	−203.921	−	170.972i	−0.232786	−	0.195174i
$877$	−173.468			−0.197797			−0.0988984	−	0.995098i	$-0.531532\pi$
$877$	−173.468			−0.197797			−0.0988984	+	0.995098i	$0.531532\pi$
$878$	−11.3450	−	6.55002i	−0.0129214	−	0.00746017i
$879$	25.6692	−	145.915i	0.0292028	−	0.166001i
$880$	−11.8761	+	6.85665i	−0.0134955	+	0.00779164i
$881$			1381.76i			1.56840i	0.620507	+	0.784201i	$0.286927\pi$
$881$			1381.76i			1.56840i	−0.620507	+	0.784201i	$0.713073\pi$
$882$	−291.920	−	943.950i	−0.330975	−	1.07024i
$883$	1346.90			1.52537			0.762685	−	0.646771i	$-0.223881\pi$
$883$	1346.90			1.52537			0.762685	+	0.646771i	$0.223881\pi$
$884$	−34.0014	−	58.8921i	−0.0384631	−	0.0666200i
$885$	18.3424	+	50.3332i	0.0207258	+	0.0568737i
$886$	179.596	−	311.069i	0.202704	−	0.351094i
$887$			615.089i			0.693449i	0.937967	+	0.346724i	$0.112706\pi$
$887$			615.089i			0.693449i	−0.937967	+	0.346724i	$0.887294\pi$
$888$	202.590	+	555.926i	0.228141	+	0.626042i
$889$	−190.054	−	286.384i	−0.213784	−	0.322142i
$890$	128.520			0.144404
$891$	28.3241	−	10.3599i	0.0317891	−	0.0116273i
$892$	14.3561	−	8.28852i	0.0160943	−	0.00929206i
$893$	−1122.19			−1.25665
$894$	173.842	+	30.5820i	0.194454	+	0.0342081i
$895$	−431.410	+	249.074i	−0.482022	+	0.278295i
$896$	480.965	−	967.605i	0.536792	−	1.07992i
$897$	−82.1748	+	467.118i	−0.0916107	+	0.520756i
$898$	−52.4164	−	90.7880i	−0.0583702	−	0.101100i
$899$	1702.86	−	983.145i	1.89417	−	1.09360i
$900$	183.399	+	66.5874i	0.203777	+	0.0739860i
$901$	871.606	+	503.222i	0.967376	+	0.558515i
$902$	−16.3838	−	9.45917i	−0.0181638	−	0.0104869i
$903$	267.747	−	363.060i	0.296508	−	0.402060i
$904$	−338.953	−	587.084i	−0.374948	−	0.649429i
$905$	−56.5906			−0.0625310
$906$	−793.540	−	139.599i	−0.875872	−	0.154082i
$907$	−498.782			−0.549925			−0.274962	−	0.961455i	$-0.588665\pi$
$907$	−498.782			−0.549925			−0.274962	+	0.961455i	$0.588665\pi$
$908$	−26.9768	−	15.5751i	−0.0297102	−	0.0171532i
$909$	−415.812	+	73.6583i	−0.457439	+	0.0810323i
$910$	175.460	−	10.9453i	0.192813	−	0.0120278i
$911$	462.758	−	801.521i	0.507967	−	0.879825i	−0.491990	−	0.870601i	$-0.663730\pi$
$911$	462.758	−	801.521i	0.507967	−	0.879825i	0.999957	−	0.00922428i	$-0.00293622\pi$
$912$	921.465	+	772.580i	1.01038	+	0.847127i
$913$	−30.2252	−	17.4505i	−0.0331053	−	0.0191134i
$914$	−620.998	+	1075.60i	−0.679429	+	1.17681i
$915$	403.145	+	70.9208i	0.440596	+	0.0775091i
$916$	−161.268	−	93.1080i	−0.176057	−	0.101646i
$917$	724.636	−	480.891i	0.790224	−	0.524418i
$918$	348.779	+	602.449i	0.379933	+	0.656262i
$919$	544.947	−	943.877i	0.592979	−	1.02707i	−0.400850	−	0.916144i	$-0.631285\pi$
$919$	544.947	−	943.877i	0.592979	−	1.02707i	0.993829	−	0.110925i	$-0.0353815\pi$
$920$			352.405i			0.383049i
$921$	994.687	+	833.971i	1.08001	+	0.905505i
$922$		−	304.382i		−	0.330132i
$923$	489.146	−	282.408i	0.529952	−	0.305968i
$924$	4.73282	−	6.41761i	0.00512210	−	0.00694546i
$925$	313.961	−	543.797i	0.339418	−	0.587889i
$926$	2.13331	−	3.69500i	0.00230379	−	0.00399028i
$927$	−1165.77	+	206.509i	−1.25757	+	0.222771i
$928$	321.219	+	556.368i	0.346142	+	0.599535i
$929$	−465.713	+	268.879i	−0.501306	+	0.289429i	−0.729253	−	0.684245i	$-0.760132\pi$
$929$	−465.713	+	268.879i	−0.501306	+	0.289429i	0.227947	+	0.973674i	$0.426799\pi$
$930$	407.787	−	486.372i	0.438480	−	0.522981i
$931$	−822.353	+	622.822i	−0.883301	+	0.668982i
$932$	178.364	+	308.936i	0.191378	+	0.331476i
$933$	−471.252	+	171.733i	−0.505093	+	0.184065i
$934$			231.098i			0.247428i
$935$	4.14421	+	7.17799i	0.00443231	+	0.00767699i
$936$	−224.042	−	266.574i	−0.239361	−	0.284802i
$937$			647.389i			0.690917i	0.938434	+	0.345459i	$0.112277\pi$
$937$			647.389i			0.690917i	−0.938434	+	0.345459i	$0.887723\pi$
$938$	−655.129	−	987.187i	−0.698431	−	1.05244i
$939$	−134.406	+	764.023i	−0.143137	+	0.813656i
$940$	−105.156			−0.111868
$941$	−113.565	−	65.5667i	−0.120685	−	0.0696777i	0.438442	−	0.898759i	$-0.355530\pi$
$941$	−113.565	−	65.5667i	−0.120685	−	0.0696777i	−0.559127	+	0.829082i	$0.688864\pi$
$942$	−1009.30	−	846.220i	−1.07144	−	0.898323i
$943$	−535.838	+	309.366i	−0.568227	+	0.328066i
$944$		−	175.753i		−	0.186179i
$945$	−364.873	+	23.1960i	−0.386109	+	0.0245461i
$946$	17.9202			0.0189432
$947$	−209.492	−	362.851i	−0.221217	−	0.383159i	0.733961	−	0.679192i	$-0.237669\pi$
$947$	−209.492	−	362.851i	−0.221217	−	0.383159i	−0.955178	+	0.296033i	$0.904336\pi$
$948$	−92.7776	+	110.657i	−0.0978666	+	0.116727i
$949$	252.007	−	436.489i	0.265550	−	0.459947i
$950$		−	1002.71i		−	1.05548i
$951$	598.352	+	105.261i	0.629182	+	0.110685i
$952$	−481.635	−	239.405i	−0.505919	−	0.251476i
$953$	−1131.25			−1.18704			−0.593520	−	0.804819i	$-0.702262\pi$
$953$	−1131.25			−1.18704			−0.593520	+	0.804819i	$0.702262\pi$
$954$	−1657.70	−	601.869i	−1.73763	−	0.630890i
$955$	101.807	−	58.7785i	0.106604	−	0.0615481i
$956$	−101.197			−0.105855
$957$	−15.4056	−	42.2745i	−0.0160978	−	0.0441740i
$958$	−371.440	+	214.451i	−0.387725	+	0.223853i
$959$	17.9238	+	27.0087i	0.0186901	+	0.0281634i
$960$	−179.766	−	150.720i	−0.187256	−	0.157000i
$961$	710.930	+	1231.37i	0.739781	+	1.28134i
$962$	332.111	−	191.745i	0.345230	−	0.199319i
$963$	−1183.65	−	429.754i	−1.22913	−	0.446266i
$964$	248.166	+	143.279i	0.257433	+	0.148629i
$965$	41.6754	+	24.0613i	0.0431869	+	0.0249340i
$966$	−513.767	−	1176.40i	−0.531850	−	1.21781i
$967$	−115.840	−	200.640i	−0.119793	−	0.207488i	0.799893	−	0.600143i	$-0.204890\pi$
$967$	−115.840	−	200.640i	−0.119793	−	0.207488i	−0.919686	+	0.392656i	$0.871556\pi$
$968$	807.001			0.833679
$969$	466.954	−	556.941i	0.481892	−	0.574759i
$970$	613.251			0.632218
$971$	402.557	+	232.416i	0.414579	+	0.239358i	0.692755	−	0.721173i	$-0.256397\pi$
$971$	402.557	+	232.416i	0.414579	+	0.239358i	−0.278176	+	0.960530i	$0.589730\pi$
$972$	−159.668	−	189.522i	−0.164268	−	0.194982i
$973$	−272.905	−	135.652i	−0.280478	−	0.139416i
$974$	−502.782	+	870.843i	−0.516203	+	0.894089i
$975$	−64.0265	+	363.955i	−0.0656682	+	0.373287i
$976$	−1163.01	−	671.463i	−1.19161	−	0.687974i
$977$	889.489	−	1540.64i	0.910429	−	1.57691i	0.0969695	−	0.995287i	$-0.469085\pi$
$977$	889.489	−	1540.64i	0.910429	−	1.57691i	0.813459	−	0.581622i	$-0.197582\pi$
$978$	−361.383	+	431.026i	−0.369512	+	0.440722i
$979$	9.56174	+	5.52047i	0.00976684	+	0.00563889i
$980$	−77.0597	+	58.3624i	−0.0786324	+	0.0595535i
$981$	765.348	−	643.237i	0.780172	−	0.655695i
$982$	−91.5977	+	158.652i	−0.0932767	+	0.161560i
$983$		−	229.966i		−	0.233943i	−0.993135	−	0.116972i	$-0.962681\pi$
$983$		−	229.966i		−	0.233943i	0.993135	−	0.116972i	$-0.0373186\pi$
$984$	78.7055	−	447.397i	0.0799853	−	0.454672i
$985$		−	337.212i		−	0.342347i
$986$	899.400	−	519.269i	0.912170	−	0.526642i
$987$	−1025.81	+	448.001i	−1.03933	+	0.453902i
$988$	62.2052	−	107.743i	0.0629607	−	0.109051i
$989$	293.045	−	507.568i	0.296304	−	0.513213i
$990$	−9.34449	−	11.1184i	−0.00943888	−	0.0112307i
$991$	−561.974	−	973.368i	−0.567078	−	0.982208i	−0.996853	−	0.0792720i	$-0.974740\pi$
$991$	−561.974	−	973.368i	−0.567078	−	0.982208i	0.429775	−	0.902936i	$-0.358593\pi$
$992$	−674.238	+	389.272i	−0.679676	+	0.392411i
$993$	−100.919	−	17.7536i	−0.101631	−	0.0178787i
$994$	−680.448	+	1368.92i	−0.684555	+	1.37719i
$995$	−279.466	−	484.050i	−0.280870	−	0.486482i
$996$	−49.6867	+	282.441i	−0.0498863	+	0.283576i
$997$			639.933i			0.641858i	0.947103	+	0.320929i	$0.103995\pi$
$997$			639.933i			0.641858i	−0.947103	+	0.320929i	$0.896005\pi$
$998$	30.8550	+	53.4424i	0.0309168	+	0.0535495i
$999$	−690.211	+	399.587i	−0.690902	+	0.399987i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.3.k.a.61.4	yes	28
3.2	odd	2		189.3.k.a.19.11		28
7.2	even	3		441.3.l.a.97.4		28
7.3	odd	6		63.3.t.a.52.11	yes	28
7.4	even	3		441.3.t.a.178.11		28
7.5	odd	6		441.3.l.b.97.4		28
7.6	odd	2		441.3.k.b.313.4		28
9.4	even	3		63.3.t.a.40.11	yes	28
9.5	odd	6		189.3.t.a.145.4		28
21.17	even	6		189.3.t.a.73.4		28
63.4	even	3		441.3.k.b.31.4		28
63.13	odd	6		441.3.t.a.166.11		28
63.31	odd	6	inner	63.3.k.a.31.4	✓	28
63.40	odd	6		441.3.l.a.391.4		28
63.58	even	3		441.3.l.b.391.4		28
63.59	even	6		189.3.k.a.10.11		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.k.a.31.4	✓	28	63.31	odd	6	inner
63.3.k.a.61.4	yes	28	1.1	even	1	trivial
63.3.t.a.40.11	yes	28	9.4	even	3
63.3.t.a.52.11	yes	28	7.3	odd	6
189.3.k.a.10.11		28	63.59	even	6
189.3.k.a.19.11		28	3.2	odd	2
189.3.t.a.73.4		28	21.17	even	6
189.3.t.a.145.4		28	9.5	odd	6
441.3.k.b.31.4		28	63.4	even	3
441.3.k.b.313.4		28	7.6	odd	2
441.3.l.a.97.4		28	7.2	even	3
441.3.l.a.391.4		28	63.40	odd	6
441.3.l.b.97.4		28	7.5	odd	6
441.3.l.b.391.4		28	63.58	even	3
441.3.t.a.166.11		28	63.13	odd	6
441.3.t.a.178.11		28	7.4	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.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12025 - 1.94033i) q^{2} +(1.92745 - 2.29890i) q^{3} +(-0.509909 + 0.883189i) q^{4} -1.93444i q^{5} +(-6.61983 - 1.16455i) q^{6} +(3.87064 + 5.83251i) q^{7} -6.67708 q^{8} +(-1.56985 - 8.86203i) q^{9} +O(q^{10})\)	\(q+(-1.12025 - 1.94033i) q^{2} +(1.92745 - 2.29890i) q^{3} +(-0.509909 + 0.883189i) q^{4} -1.93444i q^{5} +(-6.61983 - 1.16455i) q^{6} +(3.87064 + 5.83251i) q^{7} -6.67708 q^{8} +(-1.56985 - 8.86203i) q^{9} +(-3.75345 + 2.16706i) q^{10} -0.372337 q^{11} +(1.04753 + 2.87453i) q^{12} +(-5.01827 + 2.89730i) q^{13} +(6.98089 - 14.0442i) q^{14} +(-4.44709 - 3.72855i) q^{15} +(9.51962 + 16.4885i) q^{16} +(9.96576 - 5.75374i) q^{17} +(-15.4366 + 12.9737i) q^{18} +(18.2323 + 10.5264i) q^{19} +(1.70848 + 0.986391i) q^{20} +(20.8688 + 2.34369i) q^{21} +(0.417109 + 0.722455i) q^{22} +27.2835 q^{23} +(-12.8698 + 15.3499i) q^{24} +21.2579 q^{25} +(11.2434 + 6.49139i) q^{26} +(-23.3987 - 13.4722i) q^{27} +(-7.12488 + 0.444454i) q^{28} +(-20.1404 + 34.8842i) q^{29} +(-2.25276 + 12.8057i) q^{30} +(-42.2746 - 24.4073i) q^{31} +(7.97450 - 13.8122i) q^{32} +(-0.717662 + 0.855964i) q^{33} +(-22.3282 - 12.8912i) q^{34} +(11.2827 - 7.48753i) q^{35} +(8.62732 + 3.13236i) q^{36} +(14.7691 - 25.5809i) q^{37} -47.1687i q^{38} +(-3.01189 + 17.1209i) q^{39} +12.9164i q^{40} +(-19.6397 + 11.3390i) q^{41} +(-18.8307 - 43.1178i) q^{42} +(10.7407 - 18.6035i) q^{43} +(0.189858 - 0.328844i) q^{44} +(-17.1431 + 3.03679i) q^{45} +(-30.5642 - 52.9388i) q^{46} +(-46.1622 + 26.6518i) q^{47} +(56.2539 + 9.89612i) q^{48} +(-19.0363 + 45.1511i) q^{49} +(-23.8141 - 41.2473i) q^{50} +(5.98130 - 34.0003i) q^{51} -5.90944i q^{52} +(43.7300 + 75.7426i) q^{53} +(0.0718380 + 60.4933i) q^{54} +0.720265i q^{55} +(-25.8446 - 38.9441i) q^{56} +(59.3409 - 21.6249i) q^{57} +90.2490 q^{58} +(-7.99438 - 4.61556i) q^{59} +(5.56062 - 2.02639i) q^{60} +(-61.0848 + 35.2673i) q^{61} +109.369i q^{62} +(45.6115 - 43.4579i) q^{63} +40.4233 q^{64} +(5.60467 + 9.70757i) q^{65} +(2.46481 + 0.433606i) q^{66} +(37.7720 - 65.4230i) q^{67} +11.7355i q^{68} +(52.5876 - 62.7219i) q^{69} +(-27.1676 - 13.5041i) q^{70} -97.4729 q^{71} +(10.4820 + 59.1725i) q^{72} +(-75.3269 + 43.4900i) q^{73} -66.1804 q^{74} +(40.9737 - 48.8698i) q^{75} +(-18.5936 + 10.7350i) q^{76} +(-1.44118 - 2.17166i) q^{77} +(36.5942 - 13.3356i) q^{78} +(23.5997 + 40.8759i) q^{79} +(31.8960 - 18.4152i) q^{80} +(-76.0711 + 27.8241i) q^{81} +(44.0025 + 25.4049i) q^{82} +(81.1770 + 46.8676i) q^{83} +(-12.7111 + 17.2360i) q^{84} +(-11.1303 - 19.2782i) q^{85} -48.1291 q^{86} +(41.3755 + 113.538i) q^{87} +2.48612 q^{88} +(-25.6803 - 14.8266i) q^{89} +(25.0969 + 29.8612i) q^{90} +(-36.3225 - 18.0547i) q^{91} +(-13.9121 + 24.0965i) q^{92} +(-137.592 + 50.1411i) q^{93} +(103.426 + 59.7132i) q^{94} +(20.3627 - 35.2693i) q^{95} +(-16.3824 - 44.9550i) q^{96} +(-122.538 - 70.7471i) q^{97} +(108.933 - 13.6437i) q^{98} +(0.584513 + 3.29966i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{2} - 3 q^{3} - 23 q^{4} + 12 q^{6} - 16 q^{8} + 9 q^{9}+O(q^{10}) \) 28 * q + q^2 - 3 * q^3 - 23 * q^4 + 12 * q^6 - 16 * q^8 + 9 * q^9	\( 28 q + q^{2} - 3 q^{3} - 23 q^{4} + 12 q^{6} - 16 q^{8} + 9 q^{9} - 6 q^{10} - 14 q^{11} - 3 q^{12} + 15 q^{13} - 11 q^{14} - 18 q^{15} - 27 q^{16} - 33 q^{17} + 33 q^{18} - 6 q^{19} + 108 q^{20} + 12 q^{21} - 10 q^{22} - 68 q^{23} + 42 q^{24} - 62 q^{25} + 54 q^{26} - 81 q^{27} - 16 q^{28} + 70 q^{29} - 6 q^{30} + 45 q^{31} + 153 q^{32} - 114 q^{33} + 12 q^{34} + 18 q^{35} - 174 q^{36} + 9 q^{37} - 120 q^{39} - 234 q^{41} - 51 q^{42} + 30 q^{43} + 51 q^{44} + 276 q^{45} - 22 q^{46} - 111 q^{47} + 147 q^{48} + 34 q^{49} + 241 q^{50} - 6 q^{51} + 148 q^{53} + 378 q^{54} - 412 q^{56} + 189 q^{57} - 34 q^{58} + 42 q^{59} + 456 q^{60} + 120 q^{61} - 222 q^{63} - 48 q^{64} + 114 q^{65} - 447 q^{66} - 34 q^{67} + 78 q^{69} + 264 q^{70} - 350 q^{71} - 339 q^{72} - 6 q^{73} - 718 q^{74} - 123 q^{75} + 72 q^{76} - 32 q^{77} - 375 q^{78} - 82 q^{79} - 609 q^{80} - 3 q^{81} - 18 q^{82} + 738 q^{83} + 609 q^{84} + 3 q^{85} - 34 q^{86} + 3 q^{87} - 50 q^{88} + 21 q^{89} - 543 q^{90} + 39 q^{91} + 288 q^{92} + 252 q^{93} - 3 q^{94} + 507 q^{95} - 582 q^{96} - 57 q^{97} + 811 q^{98} - 162 q^{99}+O(q^{100}) \) 28 * q + q^2 - 3 * q^3 - 23 * q^4 + 12 * q^6 - 16 * q^8 + 9 * q^9 - 6 * q^10 - 14 * q^11 - 3 * q^12 + 15 * q^13 - 11 * q^14 - 18 * q^15 - 27 * q^16 - 33 * q^17 + 33 * q^18 - 6 * q^19 + 108 * q^20 + 12 * q^21 - 10 * q^22 - 68 * q^23 + 42 * q^24 - 62 * q^25 + 54 * q^26 - 81 * q^27 - 16 * q^28 + 70 * q^29 - 6 * q^30 + 45 * q^31 + 153 * q^32 - 114 * q^33 + 12 * q^34 + 18 * q^35 - 174 * q^36 + 9 * q^37 - 120 * q^39 - 234 * q^41 - 51 * q^42 + 30 * q^43 + 51 * q^44 + 276 * q^45 - 22 * q^46 - 111 * q^47 + 147 * q^48 + 34 * q^49 + 241 * q^50 - 6 * q^51 + 148 * q^53 + 378 * q^54 - 412 * q^56 + 189 * q^57 - 34 * q^58 + 42 * q^59 + 456 * q^60 + 120 * q^61 - 222 * q^63 - 48 * q^64 + 114 * q^65 - 447 * q^66 - 34 * q^67 + 78 * q^69 + 264 * q^70 - 350 * q^71 - 339 * q^72 - 6 * q^73 - 718 * q^74 - 123 * q^75 + 72 * q^76 - 32 * q^77 - 375 * q^78 - 82 * q^79 - 609 * q^80 - 3 * q^81 - 18 * q^82 + 738 * q^83 + 609 * q^84 + 3 * q^85 - 34 * q^86 + 3 * q^87 - 50 * q^88 + 21 * q^89 - 543 * q^90 + 39 * q^91 + 288 * q^92 + 252 * q^93 - 3 * q^94 + 507 * q^95 - 582 * q^96 - 57 * q^97 + 811 * q^98 - 162 * q^99

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