LMFDB - Embedded newform 63.4.f.c.22.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(22,63)]

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, 0]))

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

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

chi := DirichletCharacter("63.22");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.f (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:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 6 x^{16} - 23 x^{15} - 6 x^{14} + 255 x^{13} - 56 x^{12} - 81 x^{11} + \cdots + 387420489 $ x^18 - 3x^17 + 6x^16 - 23x^15 - 6x^14 + 255x^13 - 56x^12 - 81x^11 + 5832x^10 - 32373x^9 + 52488x^8 - 6561x^7 - 40824x^6 + 1673055x^5 - 354294x^4 - 12223143x^3 + 28697814x^2 - 129140163*x + 387420489
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.1
Root			$0.960810 + 2.84198i$ of defining polynomial
Character	$\chi$	$=$	63.22
Dual form			63.4.f.c.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.32254 - 4.02275i) q^{2} +(3.90244 - 3.43088i) q^{3} +(-6.78835 + 11.7578i) q^{4} +(8.24268 - 14.2767i) q^{5} +(-22.8651 - 7.73020i) q^{6} +(-3.50000 - 6.06218i) q^{7} +25.9042 q^{8} +(3.45809 - 26.7776i) q^{9} +O(q^{10})$	\(q+(-2.32254 - 4.02275i) q^{2} +(3.90244 - 3.43088i) q^{3} +(-6.78835 + 11.7578i) q^{4} +(8.24268 - 14.2767i) q^{5} +(-22.8651 - 7.73020i) q^{6} +(-3.50000 - 6.06218i) q^{7} +25.9042 q^{8} +(3.45809 - 26.7776i) q^{9} -76.5757 q^{10} +(23.3916 + 40.5154i) q^{11} +(13.8484 + 69.1741i) q^{12} +(-20.8079 + 36.0404i) q^{13} +(-16.2578 + 28.1593i) q^{14} +(-16.8153 - 83.9939i) q^{15} +(-5.85664 - 10.1440i) q^{16} -49.9526 q^{17} +(-115.751 + 48.2810i) q^{18} +27.2795 q^{19} +(111.909 + 193.831i) q^{20} +(-34.4572 - 11.6492i) q^{21} +(108.656 - 188.197i) q^{22} +(93.7666 - 162.409i) q^{23} +(101.090 - 88.8743i) q^{24} +(-73.3837 - 127.104i) q^{25} +193.309 q^{26} +(-78.3759 - 116.362i) q^{27} +95.0369 q^{28} +(95.7669 + 165.873i) q^{29} +(-298.832 + 262.722i) q^{30} +(30.1489 - 52.2194i) q^{31} +(76.4123 - 132.350i) q^{32} +(230.288 + 77.8552i) q^{33} +(116.017 + 200.947i) q^{34} -115.398 q^{35} +(291.371 + 222.435i) q^{36} -82.4348 q^{37} +(-63.3577 - 109.739i) q^{38} +(42.4486 + 212.035i) q^{39} +(213.520 - 369.828i) q^{40} +(114.266 - 197.915i) q^{41} +(33.1662 + 165.668i) q^{42} +(163.319 + 282.876i) q^{43} -635.161 q^{44} +(-353.794 - 270.090i) q^{45} -871.106 q^{46} +(-268.821 - 465.612i) q^{47} +(-57.6581 - 19.4929i) q^{48} +(-24.5000 + 42.4352i) q^{49} +(-340.873 + 590.409i) q^{50} +(-194.937 + 171.381i) q^{51} +(-282.503 - 489.309i) q^{52} +554.989 q^{53} +(-286.066 + 585.543i) q^{54} +771.237 q^{55} +(-90.6647 - 157.036i) q^{56} +(106.457 - 93.5928i) q^{57} +(444.844 - 770.493i) q^{58} +(-241.962 + 419.090i) q^{59} +(1101.73 + 372.470i) q^{60} +(365.426 + 632.937i) q^{61} -280.087 q^{62} +(-174.434 + 72.7581i) q^{63} -803.588 q^{64} +(343.026 + 594.139i) q^{65} +(-221.660 - 1107.21i) q^{66} +(-171.978 + 297.875i) q^{67} +(339.096 - 587.331i) q^{68} +(-191.286 - 955.492i) q^{69} +(268.015 + 464.216i) q^{70} -231.562 q^{71} +(89.5792 - 693.653i) q^{72} +420.350 q^{73} +(191.458 + 331.615i) q^{74} +(-722.455 - 244.246i) q^{75} +(-185.183 + 320.746i) q^{76} +(163.741 - 283.608i) q^{77} +(754.375 - 663.219i) q^{78} +(8.45685 + 14.6477i) q^{79} -193.098 q^{80} +(-705.083 - 185.199i) q^{81} -1061.55 q^{82} +(-273.529 - 473.766i) q^{83} +(370.876 - 326.061i) q^{84} +(-411.743 + 713.160i) q^{85} +(758.627 - 1313.98i) q^{86} +(942.816 + 318.745i) q^{87} +(605.940 + 1049.52i) q^{88} -189.407 q^{89} +(-264.806 + 2050.52i) q^{90} +291.311 q^{91} +(1273.04 + 2204.97i) q^{92} +(-61.5043 - 307.220i) q^{93} +(-1248.69 + 2162.80i) q^{94} +(224.856 - 389.463i) q^{95} +(-155.883 - 778.649i) q^{96} +(39.9090 + 69.1245i) q^{97} +227.609 q^{98} +(1165.80 - 486.265i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9}+O(q^{10}) $ 18 * q + 6 * q^2 + 9 * q^3 - 36 * q^4 + 24 * q^5 - 63 * q^7 - 150 * q^8 + 63 * q^9	\( 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9} + 111 q^{11} - 18 q^{13} + 42 q^{14} - 36 q^{15} - 144 q^{16} - 546 q^{17} - 45 q^{18} + 90 q^{19} + 402 q^{20} - 63 q^{21} + 162 q^{22} + 312 q^{23} - 36 q^{24} - 279 q^{25} + 102 q^{26} + 432 q^{27} + 504 q^{28} + 378 q^{29} - 864 q^{30} - 18 q^{31} + 891 q^{32} + 513 q^{33} + 324 q^{34} - 336 q^{35} + 414 q^{36} - 72 q^{37} + 147 q^{38} - 810 q^{39} - 405 q^{40} + 477 q^{41} + 315 q^{42} + 171 q^{43} - 1896 q^{44} - 720 q^{45} - 756 q^{46} + 654 q^{47} - 2709 q^{48} - 441 q^{49} + 429 q^{50} + 1341 q^{51} - 747 q^{52} - 1896 q^{53} - 108 q^{54} - 432 q^{55} + 525 q^{56} - 1143 q^{57} - 297 q^{58} + 957 q^{59} + 5400 q^{60} + 198 q^{61} - 600 q^{62} - 504 q^{63} + 4770 q^{64} + 2478 q^{65} - 2646 q^{66} + 333 q^{67} + 1443 q^{68} + 3366 q^{69} - 5652 q^{71} - 3681 q^{72} + 306 q^{73} + 2100 q^{74} - 4113 q^{75} + 144 q^{76} + 777 q^{77} + 6336 q^{78} - 1152 q^{79} - 8418 q^{80} - 1917 q^{81} - 6048 q^{82} + 1890 q^{83} + 1008 q^{84} + 648 q^{85} + 3837 q^{86} + 4212 q^{87} + 2268 q^{88} - 2604 q^{89} - 135 q^{90} + 252 q^{91} + 987 q^{92} + 378 q^{93} - 324 q^{94} + 3144 q^{95} + 5643 q^{96} + 1737 q^{97} - 588 q^{98} + 720 q^{99}+O(q^{100}) \) 18 * q + 6 * q^2 + 9 * q^3 - 36 * q^4 + 24 * q^5 - 63 * q^7 - 150 * q^8 + 63 * q^9 + 111 * q^11 - 18 * q^13 + 42 * q^14 - 36 * q^15 - 144 * q^16 - 546 * q^17 - 45 * q^18 + 90 * q^19 + 402 * q^20 - 63 * q^21 + 162 * q^22 + 312 * q^23 - 36 * q^24 - 279 * q^25 + 102 * q^26 + 432 * q^27 + 504 * q^28 + 378 * q^29 - 864 * q^30 - 18 * q^31 + 891 * q^32 + 513 * q^33 + 324 * q^34 - 336 * q^35 + 414 * q^36 - 72 * q^37 + 147 * q^38 - 810 * q^39 - 405 * q^40 + 477 * q^41 + 315 * q^42 + 171 * q^43 - 1896 * q^44 - 720 * q^45 - 756 * q^46 + 654 * q^47 - 2709 * q^48 - 441 * q^49 + 429 * q^50 + 1341 * q^51 - 747 * q^52 - 1896 * q^53 - 108 * q^54 - 432 * q^55 + 525 * q^56 - 1143 * q^57 - 297 * q^58 + 957 * q^59 + 5400 * q^60 + 198 * q^61 - 600 * q^62 - 504 * q^63 + 4770 * q^64 + 2478 * q^65 - 2646 * q^66 + 333 * q^67 + 1443 * q^68 + 3366 * q^69 - 5652 * q^71 - 3681 * q^72 + 306 * q^73 + 2100 * q^74 - 4113 * q^75 + 144 * q^76 + 777 * q^77 + 6336 * q^78 - 1152 * q^79 - 8418 * q^80 - 1917 * q^81 - 6048 * q^82 + 1890 * q^83 + 1008 * q^84 + 648 * q^85 + 3837 * q^86 + 4212 * q^87 + 2268 * q^88 - 2604 * q^89 - 135 * q^90 + 252 * q^91 + 987 * q^92 + 378 * q^93 - 324 * q^94 + 3144 * q^95 + 5643 * q^96 + 1737 * q^97 - 588 * q^98 + 720 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−2.32254	−	4.02275i	−0.821141	−	1.42226i	−0.904833	−	0.425766i	$-0.860005\pi$
$2$	−2.32254	−	4.02275i	−0.821141	−	1.42226i	0.0836927	−	0.996492i	$-0.473329\pi$
$3$	3.90244	−	3.43088i	0.751025	−	0.660274i
$3$	3.90244	−	3.43088i	0.751025	−	0.660274i
$4$	−6.78835	+	11.7578i	−0.848544	+	1.46972i
$5$	8.24268	−	14.2767i	0.737248	−	1.27695i	−0.216482	−	0.976287i	$-0.569458\pi$
$5$	8.24268	−	14.2767i	0.737248	−	1.27695i	0.953730	−	0.300665i	$-0.0972085\pi$
$6$	−22.8651	−	7.73020i	−1.55578	−	0.525974i
$7$	−3.50000	−	6.06218i	−0.188982	−	0.327327i
$7$	−3.50000	−	6.06218i	−0.188982	−	0.327327i
$8$	25.9042			1.14481
$9$	3.45809	−	26.7776i	0.128078	−	0.991764i
$10$	−76.5757			−2.42154
$11$	23.3916	+	40.5154i	0.641166	+	1.11053i	0.985173	+	0.171565i	$0.0548822\pi$
$11$	23.3916	+	40.5154i	0.641166	+	1.11053i	−0.344007	+	0.938967i	$0.611784\pi$
$12$	13.8484	+	69.1741i	0.333140	+	1.66407i
$13$	−20.8079	+	36.0404i	−0.443929	+	0.768907i	−0.997977	−	0.0635773i	$-0.979749\pi$
$13$	−20.8079	+	36.0404i	−0.443929	+	0.768907i	0.554048	+	0.832485i	$0.313082\pi$
$14$	−16.2578	+	28.1593i	−0.310362	+	0.537563i
$15$	−16.8153	−	83.9939i	−0.289445	−	1.44581i
$16$	−5.85664	−	10.1440i	−0.0915101	−	0.158500i
$17$	−49.9526			−0.712663			−0.356332	−	0.934360i	$-0.615973\pi$
$17$	−49.9526			−0.712663			−0.356332	+	0.934360i	$0.615973\pi$
$18$	−115.751	+	48.2810i	−1.51571	+	0.632219i
$19$	27.2795			0.329387			0.164693	−	0.986345i	$-0.447337\pi$
$19$	27.2795			0.329387			0.164693	+	0.986345i	$0.447337\pi$
$20$	111.909	+	193.831i	1.25118	+	2.16710i
$21$	−34.4572	−	11.6492i	−0.358056	−	0.121051i
$22$	108.656	−	188.197i	1.05297	−	1.82381i
$23$	93.7666	−	162.409i	0.850074	−	1.47237i	−0.0310674	−	0.999517i	$-0.509891\pi$
$23$	93.7666	−	162.409i	0.850074	−	1.47237i	0.881141	−	0.472853i	$-0.156776\pi$
$24$	101.090	−	88.8743i	0.859785	−	0.755891i
$25$	−73.3837	−	127.104i	−0.587070	−	1.01683i
$26$	193.309			1.45811
$27$	−78.3759	−	116.362i	−0.558646	−	0.829406i
$28$	95.0369			0.641439
$29$	95.7669	+	165.873i	0.613223	+	1.06213i	0.990694	+	0.136112i	$0.0434606\pi$
$29$	95.7669	+	165.873i	0.613223	+	1.06213i	−0.377471	+	0.926022i	$0.623206\pi$
$30$	−298.832	+	262.722i	−1.81864	+	1.59888i
$31$	30.1489	−	52.2194i	0.174674	−	0.302544i	−0.765374	−	0.643585i	$-0.777446\pi$
$31$	30.1489	−	52.2194i	0.174674	−	0.302544i	0.940048	+	0.341041i	$0.110780\pi$
$32$	76.4123	−	132.350i	0.422122	−	0.731137i
$33$	230.288	+	77.8552i	1.21479	+	0.410692i
$34$	116.017	+	200.947i	0.585197	+	1.01359i
$35$	−115.398			−0.557307
$36$	291.371	+	222.435i	1.34894	+	1.02979i
$37$	−82.4348			−0.366276			−0.183138	−	0.983087i	$-0.558625\pi$
$37$	−82.4348			−0.366276			−0.183138	+	0.983087i	$0.558625\pi$
$38$	−63.3577	−	109.739i	−0.270473	−	0.468473i
$39$	42.4486	+	212.035i	0.174287	+	0.870583i
$40$	213.520	−	369.828i	0.844013	−	1.46187i
$41$	114.266	−	197.915i	0.435254	−	0.753882i	−0.562063	−	0.827095i	$-0.689992\pi$
$41$	114.266	−	197.915i	0.435254	−	0.753882i	0.997316	+	0.0732131i	$0.0233253\pi$
$42$	33.1662	+	165.668i	0.121849	+	0.608647i
$43$	163.319	+	282.876i	0.579206	+	1.00321i	0.995571	+	0.0940168i	$0.0299707\pi$
$43$	163.319	+	282.876i	0.579206	+	1.00321i	−0.416364	+	0.909198i	$0.636696\pi$
$44$	−635.161			−2.17623
$45$	−353.794	−	270.090i	−1.17201	−	0.894725i
$46$	−871.106			−2.79212
$47$	−268.821	−	465.612i	−0.834290	−	1.44503i	−0.894607	−	0.446853i	$-0.852545\pi$
$47$	−268.821	−	465.612i	−0.834290	−	1.44503i	0.0603174	−	0.998179i	$-0.480789\pi$
$48$	−57.6581	−	19.4929i	−0.173380	−	0.0586159i
$49$	−24.5000	+	42.4352i	−0.0714286	+	0.123718i
$50$	−340.873	+	590.409i	−0.964133	+	1.66993i
$51$	−194.937	+	171.381i	−0.535228	+	0.470553i
$52$	−282.503	−	489.309i	−0.753386	−	1.30490i
$53$	554.989			1.43837			0.719185	−	0.694819i	$-0.244515\pi$
$53$	554.989			1.43837			0.719185	+	0.694819i	$0.244515\pi$
$54$	−286.066	+	585.543i	−0.720902	+	1.47560i
$55$	771.237			1.89079
$56$	−90.6647	−	157.036i	−0.216350	−	0.374729i
$57$	106.457	−	93.5928i	0.247378	−	0.217485i
$58$	444.844	−	770.493i	1.00708	−	1.74432i
$59$	−241.962	+	419.090i	−0.533911	+	0.924761i	0.465304	+	0.885151i	$0.345945\pi$
$59$	−241.962	+	419.090i	−0.533911	+	0.924761i	−0.999215	+	0.0396100i	$0.987388\pi$
$60$	1101.73	+	372.470i	2.37054	+	0.801428i
$61$	365.426	+	632.937i	0.767017	+	1.32851i	0.939174	+	0.343443i	$0.111593\pi$
$61$	365.426	+	632.937i	0.767017	+	1.32851i	−0.172156	+	0.985070i	$0.555073\pi$
$62$	−280.087			−0.573728
$63$	−174.434	+	72.7581i	−0.348835	+	0.145503i
$64$	−803.588			−1.56951
$65$	343.026	+	594.139i	0.654571	+	1.13375i
$66$	−221.660	−	1107.21i	−0.413400	−	2.06498i
$67$	−171.978	+	297.875i	−0.313589	+	0.543152i	−0.979137	−	0.203204i	$-0.934865\pi$
$67$	−171.978	+	297.875i	−0.313589	+	0.543152i	0.665548	+	0.746355i	$0.268198\pi$
$68$	339.096	−	587.331i	0.604726	−	1.04742i
$69$	−191.286	−	955.492i	−0.333741	−	1.66707i
$70$	268.015	+	464.216i	0.457628	+	0.792634i
$71$	−231.562			−0.387061			−0.193531	−	0.981094i	$-0.561994\pi$
$71$	−231.562			−0.387061			−0.193531	+	0.981094i	$0.561994\pi$
$72$	89.5792	−	693.653i	0.146625	−	1.13539i
$73$	420.350			0.673949			0.336974	−	0.941514i	$-0.390596\pi$
$73$	420.350			0.673949			0.336974	+	0.941514i	$0.390596\pi$
$74$	191.458	+	331.615i	0.300764	+	0.520938i
$75$	−722.455	−	244.246i	−1.11229	−	0.376042i
$76$	−185.183	+	320.746i	−0.279499	+	0.484107i
$77$	163.741	−	283.608i	0.242338	−	0.419742i
$78$	754.375	−	663.219i	1.09508	−	0.962753i
$79$	8.45685	+	14.6477i	0.0120439	+	0.0208607i	0.871985	−	0.489533i	$-0.162833\pi$
$79$	8.45685	+	14.6477i	0.0120439	+	0.0208607i	−0.859941	+	0.510394i	$0.829500\pi$
$80$	−193.098			−0.269862
$81$	−705.083	−	185.199i	−0.967192	−	0.254045i
$82$	−1061.55			−1.42962
$83$	−273.529	−	473.766i	−0.361731	−	0.626537i	0.626515	−	0.779410i	$-0.284481\pi$
$83$	−273.529	−	473.766i	−0.361731	−	0.626537i	−0.988246	+	0.152873i	$0.951147\pi$
$84$	370.876	−	326.061i	0.481737	−	0.423525i
$85$	−411.743	+	713.160i	−0.525410	+	0.910036i
$86$	758.627	−	1313.98i	0.951220	−	1.64756i
$87$	942.816	+	318.745i	1.16184	+	0.392794i
$88$	605.940	+	1049.52i	0.734016	+	1.27135i
$89$	−189.407			−0.225585			−0.112793	−	0.993619i	$-0.535980\pi$
$89$	−189.407			−0.225585			−0.112793	+	0.993619i	$0.535980\pi$
$90$	−264.806	+	2050.52i	−0.310145	+	2.40159i
$91$	291.311			0.335579
$92$	1273.04	+	2204.97i	1.44265	+	2.49874i
$93$	−61.5043	−	307.220i	−0.0685774	−	0.342551i
$94$	−1248.69	+	2162.80i	−1.37014	+	2.37315i
$95$	224.856	−	389.463i	0.242840	−	0.420611i
$96$	−155.883	−	778.649i	−0.165726	−	0.827819i
$97$	39.9090	+	69.1245i	0.0417747	+	0.0723559i	0.886157	−	0.463386i	$-0.153365\pi$
$97$	39.9090	+	69.1245i	0.0417747	+	0.0723559i	−0.844382	+	0.535741i	$0.820032\pi$
$98$	227.609			0.234612
$99$	1165.80	−	486.265i	1.18350	−	0.493651i
$100$	1992.62			1.99262
$101$	−101.809	−	176.338i	−0.100301	−	0.173726i	0.811508	−	0.584342i	$-0.198647\pi$
$101$	−101.809	−	176.338i	−0.100301	−	0.173726i	−0.911809	+	0.410616i	$0.865314\pi$
$102$	1142.17	+	386.143i	1.10874	+	0.374842i
$103$	−439.251	+	760.805i	−0.420201	+	0.727810i	−0.995959	−	0.0898107i	$-0.971374\pi$
$103$	−439.251	+	760.805i	−0.420201	+	0.727810i	0.575758	+	0.817620i	$0.304707\pi$
$104$	−539.012	+	933.597i	−0.508216	+	0.880257i
$105$	−450.332	+	395.916i	−0.418552	+	0.367975i
$106$	−1288.98	−	2232.58i	−1.18110	−	2.04573i
$107$	−831.738			−0.751469			−0.375734	−	0.926727i	$-0.622610\pi$
$107$	−831.738			−0.751469			−0.375734	+	0.926727i	$0.622610\pi$
$108$	1900.21	−	131.617i	1.69303	−	0.117267i
$109$	740.887			0.651047			0.325523	−	0.945534i	$-0.394460\pi$
$109$	740.887			0.651047			0.325523	+	0.945534i	$0.394460\pi$
$110$	−1791.23	−	3102.50i	−1.55261	−	2.68919i
$111$	−321.697	+	282.824i	−0.275082	+	0.241842i
$112$	−40.9965	+	71.0080i	−0.0345875	+	0.0599074i
$113$	−698.168	+	1209.26i	−0.581222	+	1.00671i	0.414113	+	0.910226i	$0.364092\pi$
$113$	−698.168	+	1209.26i	−0.581222	+	1.00671i	−0.995335	+	0.0964805i	$0.969241\pi$
$114$	−623.750	−	210.876i	−0.512452	−	0.173249i
$115$	−1545.78	−	2677.37i	−1.25343	−	2.17101i
$116$	−2600.40			−2.08139
$117$	893.120	+	681.817i	0.705717	+	0.538753i
$118$	2247.86			1.75366
$119$	174.834	+	302.821i	0.134681	+	0.233274i
$120$	−435.586	−	2175.79i	−0.331361	−	1.65518i
$121$	−428.831	+	742.757i	−0.322187	+	0.558044i
$122$	1697.43	−	2940.04i	1.25966	−	2.18179i
$123$	−233.106	−	1164.39i	−0.170882	−	0.853571i
$124$	409.322	+	708.967i	0.296437	+	0.513444i
$125$	−358.844			−0.256768
$126$	697.817	+	532.722i	0.493385	+	0.376656i
$127$	−1291.70			−0.902515			−0.451257	−	0.892394i	$-0.649024\pi$
$127$	−1291.70			−0.902515			−0.451257	+	0.892394i	$0.649024\pi$
$128$	1255.06	+	2173.83i	0.866664	+	1.50111i
$129$	1607.86	+	543.581i	1.09739	+	0.371005i
$130$	1593.38	−	2759.82i	1.07499	−	1.86194i
$131$	−690.089	+	1195.27i	−0.460255	+	0.797185i	−0.998973	−	0.0453010i	$-0.985575\pi$
$131$	−690.089	+	1195.27i	−0.460255	+	0.797185i	0.538718	+	0.842486i	$0.318909\pi$
$132$	−2478.68	+	2179.16i	−1.63440	+	1.43691i
$133$	−95.4783	−	165.373i	−0.0622483	−	0.107817i
$134$	1597.70			1.03000
$135$	−2307.31	+	159.814i	−1.47097	+	0.101886i
$136$	−1293.98			−0.815868
$137$	924.171	+	1600.71i	0.576330	+	0.998234i	0.995896	+	0.0905085i	$0.0288492\pi$
$137$	924.171	+	1600.71i	0.576330	+	0.998234i	−0.419565	+	0.907725i	$0.637817\pi$
$138$	−3399.44	+	2988.66i	−2.09695	+	1.84356i
$139$	1097.93	−	1901.67i	0.669965	−	1.16041i	−0.307948	−	0.951403i	$-0.599642\pi$
$139$	1097.93	−	1901.67i	0.669965	−	1.16041i	0.977913	−	0.209011i	$-0.0670244\pi$
$140$	783.360	−	1356.82i	0.472900	−	0.819086i
$141$	−2646.52	−	894.730i	−1.58069	−	0.534396i
$142$	537.811	+	931.516i	0.317832	+	0.550501i
$143$	−1946.92			−1.13853
$144$	−291.885	+	121.748i	−0.168915	+	0.0704561i
$145$	3157.50			1.80839
$146$	−976.279	−	1690.96i	−0.553407	−	0.958529i
$147$	49.9805	+	249.658i	0.0280430	+	0.140078i
$148$	559.597	−	969.250i	0.310801	−	0.538323i
$149$	−1336.03	+	2314.07i	−0.734575	+	1.27232i	0.220335	+	0.975424i	$0.429285\pi$
$149$	−1336.03	+	2314.07i	−0.734575	+	1.27232i	−0.954910	+	0.296897i	$0.904048\pi$
$150$	695.387	+	3473.53i	0.378521	+	1.89075i
$151$	558.011	+	966.504i	0.300731	+	0.520881i	0.976302	−	0.216414i	$-0.0694362\pi$
$151$	558.011	+	966.504i	0.300731	+	0.520881i	−0.675571	+	0.737295i	$0.736103\pi$
$152$	706.654			0.377087
$153$	−172.741	+	1337.61i	−0.0912762	+	0.706794i
$154$	−1521.18			−0.795974
$155$	−497.015	−	860.855i	−0.257556	−	0.446100i
$156$	−2781.21	−	940.267i	−1.42741	−	0.482574i
$157$	−74.6969	+	129.379i	−0.0379711	+	0.0657679i	−0.884386	−	0.466755i	$-0.845423\pi$
$157$	−74.6969	+	129.379i	−0.0379711	+	0.0657679i	0.846415	+	0.532523i	$0.178756\pi$
$158$	39.2827	−	68.0396i	0.0197795	−	0.0342591i
$159$	2165.81	−	1904.10i	1.08025	−	0.949717i
$160$	−1259.68	−	2181.84i	−0.622418	−	1.07806i
$161$	−1312.73			−0.642595
$162$	892.571	+	3266.51i	0.432883	+	1.58420i
$163$	1384.19			0.665143			0.332571	−	0.943078i	$-0.392084\pi$
$163$	1384.19			0.665143			0.332571	+	0.943078i	$0.392084\pi$
$164$	1551.36	+	2687.04i	0.738664	+	1.27940i
$165$	3009.71	−	2646.02i	1.42003	−	1.24844i
$166$	−1270.56	+	2200.68i	−0.594064	+	1.02895i
$167$	1614.41	−	2796.24i	0.748066	−	1.29569i	−0.200683	−	0.979656i	$-0.564316\pi$
$167$	1614.41	−	2796.24i	0.748066	−	1.29569i	0.948749	−	0.316032i	$-0.102351\pi$
$168$	−892.585	−	301.763i	−0.409907	−	0.138581i
$169$	232.562	+	402.809i	0.105854	+	0.183345i
$170$	3825.15			1.72574
$171$	94.3351	−	730.481i	0.0421871	−	0.326674i
$172$	−4434.66			−1.96593
$173$	1382.32	+	2394.25i	0.607491	+	1.05221i	0.991652	+	0.128940i	$0.0411575\pi$
$173$	1382.32	+	2394.25i	0.607491	+	1.05221i	−0.384161	+	0.923266i	$0.625509\pi$
$174$	−907.492	−	4533.01i	−0.395384	−	1.97498i
$175$	−513.686	+	889.730i	−0.221891	+	0.384327i
$176$	273.992	−	474.568i	0.117346	−	0.203250i
$177$	493.607	+	2465.62i	0.209615	+	1.04705i
$178$	439.905	+	761.937i	0.185237	+	0.320841i
$179$	−2595.28			−1.08369			−0.541844	−	0.840479i	$-0.682274\pi$
$179$	−2595.28			−1.08369			−0.541844	+	0.840479i	$0.682274\pi$
$180$	5577.33	−	2326.36i	2.30950	−	0.963314i
$181$	−632.683			−0.259818			−0.129909	−	0.991526i	$-0.541468\pi$
$181$	−632.683			−0.259818			−0.129909	+	0.991526i	$0.541468\pi$
$182$	−676.580	−	1171.87i	−0.275557	−	0.477279i
$183$	3597.59	+	1216.26i	1.45323	+	0.491305i
$184$	2428.95	−	4207.06i	0.973177	−	1.68559i
$185$	−679.484	+	1176.90i	−0.270036	+	0.467716i
$186$	−1093.02	+	960.947i	−0.430884	+	0.378817i
$187$	−1168.47	−	2023.85i	−0.456935	−	0.791435i
$188$	7299.42			2.83173
$189$	−431.094	+	882.397i	−0.165913	+	0.339603i
$190$	−2088.95			−0.797623
$191$	179.915	+	311.623i	0.0681582	+	0.118054i	0.898091	−	0.439810i	$-0.144954\pi$
$191$	179.915	+	311.623i	0.0681582	+	0.118054i	−0.829932	+	0.557864i	$0.811621\pi$
$192$	−3135.95	+	2757.01i	−1.17874	+	1.03630i
$193$	−943.654	+	1634.46i	−0.351947	+	0.609590i	−0.986591	−	0.163215i	$-0.947814\pi$
$193$	−943.654	+	1634.46i	−0.351947	+	0.609590i	0.634644	+	0.772805i	$0.281147\pi$
$194$	185.380	−	321.088i	0.0686058	−	0.118829i
$195$	3377.06	+	1141.71i	1.24019	+	0.419279i
$196$	−332.629	−	576.131i	−0.121221	−	0.209960i
$197$	2678.12			0.968570			0.484285	−	0.874910i	$-0.339080\pi$
$197$	2678.12			0.968570			0.484285	+	0.874910i	$0.339080\pi$
$198$	−4663.73	−	3560.34i	−1.67392	−	1.27789i
$199$	2529.75			0.901151			0.450575	−	0.892738i	$-0.351219\pi$
$199$	2529.75			0.901151			0.450575	+	0.892738i	$0.351219\pi$
$200$	−1900.95	−	3292.54i	−0.672086	−	1.16409i
$201$	350.839	+	1752.47i	0.123116	+	0.614975i
$202$	−472.911	+	819.105i	−0.164722	+	0.285307i
$203$	670.368	−	1161.11i	0.231776	−	0.401449i
$204$	−691.762	−	3455.42i	−0.237417	−	1.18592i
$205$	−1883.72	−	3262.70i	−0.641780	−	1.11160i
$206$	4080.71			1.38018
$207$	−4024.66	−	3072.47i	−1.35137	−	1.03165i
$208$	487.458			0.162496
$209$	638.111	+	1105.24i	0.211192	+	0.365794i
$210$	2638.58	+	892.047i	0.867045	+	0.293129i
$211$	1803.46	−	3123.69i	0.588414	−	1.01916i	−0.406026	−	0.913861i	$-0.633086\pi$
$211$	1803.46	−	3123.69i	0.588414	−	1.01916i	0.994440	−	0.105302i	$-0.0335809\pi$
$212$	−3767.46	+	6525.43i	−1.22052	+	2.11400i
$213$	−903.657	+	794.462i	−0.290693	+	0.255566i
$214$	1931.74	+	3345.88i	0.617062	+	1.06878i
$215$	5384.74			1.70807
$216$	−2030.27	−	3014.28i	−0.639547	−	0.949516i
$217$	−422.084			−0.132041
$218$	−1720.74	−	2980.40i	−0.534601	−	0.925956i
$219$	1640.39	−	1442.17i	0.506152	−	0.444991i
$220$	−5235.43	+	9068.03i	−1.60442	+	2.77894i
$221$	1039.41	−	1800.31i	0.316372	−	0.547972i
$222$	1884.88	+	637.238i	0.569843	+	0.192651i
$223$	1515.64	+	2625.17i	0.455135	+	0.788316i	0.998696	−	0.0510533i	$-0.0162578\pi$
$223$	1515.64	+	2625.17i	0.455135	+	0.788316i	−0.543561	+	0.839369i	$0.682924\pi$
$224$	−1069.77			−0.319094
$225$	−3657.32	+	1525.50i	−1.08365	+	0.452001i
$226$	6486.08			1.90906
$227$	−1089.45	−	1886.99i	−0.318544	−	0.551735i	0.661640	−	0.749821i	$-0.269861\pi$
$227$	−1089.45	−	1886.99i	−0.318544	−	0.551735i	−0.980185	+	0.198087i	$0.936527\pi$
$228$	377.777	+	1887.03i	0.109732	+	0.548122i
$229$	181.260	−	313.951i	0.0523056	−	0.0905960i	−0.838687	−	0.544614i	$-0.816676\pi$
$229$	181.260	−	313.951i	0.0523056	−	0.0905960i	0.890993	+	0.454018i	$0.150010\pi$
$230$	−7180.25	+	12436.6i	−2.05849	+	3.56540i
$231$	−334.035	−	1668.54i	−0.0951424	−	0.475246i
$232$	2480.77	+	4296.81i	0.702027	+	1.21595i
$233$	−5643.69			−1.58683			−0.793414	−	0.608683i	$-0.791698\pi$
$233$	−5643.69			−1.58683			−0.793414	+	0.608683i	$0.791698\pi$
$234$	668.479	−	5176.34i	0.186751	−	1.44610i
$235$	−8863.24			−2.46031
$236$	−3285.04	−	5689.86i	−0.906094	−	1.56940i
$237$	83.2569	+	28.1473i	0.0228191	+	0.00771462i
$238$	812.117	−	1406.63i	0.221184	−	0.383101i
$239$	−186.760	+	323.477i	−0.0505459	+	0.0875481i	−0.890191	−	0.455587i	$-0.849429\pi$
$239$	−186.760	+	323.477i	−0.0505459	+	0.0875481i	0.839645	+	0.543135i	$0.182763\pi$
$240$	−753.553	+	662.496i	−0.202673	+	0.178183i
$241$	70.7323	+	122.512i	0.0189057	+	0.0327456i	0.875323	−	0.483538i	$-0.160648\pi$
$241$	70.7323	+	122.512i	0.0189057	+	0.0327456i	−0.856418	+	0.516283i	$0.827315\pi$
$242$	3983.90			1.05824
$243$	−3386.94	+	1696.33i	−0.894125	+	0.447817i
$244$	−9922.57			−2.60339
$245$	403.892	+	699.561i	0.105321	+	0.182422i
$246$	−4142.64	+	3642.06i	−1.07368	+	0.943939i
$247$	−567.630	+	983.163i	−0.146224	+	0.253268i
$248$	780.982	−	1352.70i	0.199969	−	0.346357i
$249$	−2692.86	−	910.398i	−0.685355	−	0.231703i
$250$	833.427	+	1443.54i	0.210842	+	0.365190i
$251$	−940.514			−0.236513			−0.118256	−	0.992983i	$-0.537730\pi$
$251$	−940.514			−0.236513			−0.118256	+	0.992983i	$0.537730\pi$
$252$	328.647	−	2544.86i	0.0821539	−	0.636156i
$253$	8773.39			2.18015
$254$	3000.01	+	5196.17i	0.741092	+	1.28361i
$255$	839.965	+	4195.71i	0.206277	+	1.03037i
$256$	2615.51	−	4530.20i	0.638552	−	1.10601i
$257$	2586.02	−	4479.11i	0.627670	−	1.08716i	−0.360347	−	0.932818i	$-0.617342\pi$
$257$	2586.02	−	4479.11i	0.627670	−	1.08716i	0.988018	−	0.154339i	$-0.0493248\pi$
$258$	−1547.62	−	7730.50i	−0.373451	−	1.86542i
$259$	288.522	+	499.735i	0.0692196	+	0.119892i
$260$	−9314.33			−2.22173
$261$	4772.86	−	1990.81i	1.13193	−	0.472137i
$262$	6411.03			1.51174
$263$	−2061.70	−	3570.96i	−0.483383	−	0.837243i	0.516435	−	0.856326i	$-0.327259\pi$
$263$	−2061.70	−	3570.96i	−0.483383	−	0.837243i	−0.999818	+	0.0190831i	$0.993925\pi$
$264$	5965.42	+	2016.78i	1.39071	+	0.470167i
$265$	4574.60	−	7923.44i	1.06044	−	1.83673i
$266$	−443.504	+	768.171i	−0.102229	+	0.177066i
$267$	−739.150	+	649.833i	−0.169420	+	0.148948i
$268$	−2334.89	−	4044.15i	−0.532188	−	0.921776i
$269$	−5076.62			−1.15066			−0.575329	−	0.817922i	$-0.695126\pi$
$269$	−5076.62			−1.15066			−0.575329	+	0.817922i	$0.695126\pi$
$270$	6001.69	+	8910.54i	1.35278	+	2.00844i
$271$	−7398.87			−1.65849			−0.829243	−	0.558888i	$-0.811228\pi$
$271$	−7398.87			−1.65849			−0.829243	+	0.558888i	$0.811228\pi$
$272$	292.554	+	506.719i	0.0652159	+	0.112957i
$273$	1136.82	−	999.453i	0.252028	−	0.221574i
$274$	4292.84	−	7435.42i	0.946497	−	1.63938i
$275$	3433.12	−	5946.34i	0.752818	−	1.30392i
$276$	12533.0	+	4237.12i	2.73332	+	0.924075i
$277$	483.855	+	838.062i	0.104953	+	0.181784i	0.913719	−	0.406346i	$-0.133197\pi$
$277$	483.855	+	838.062i	0.104953	+	0.181784i	−0.808766	+	0.588131i	$0.799864\pi$
$278$	−10199.9			−2.20054
$279$	−1294.05	−	987.894i	−0.277681	−	0.211985i
$280$	−2989.28			−0.638014
$281$	−3383.85	−	5861.00i	−0.718376	−	1.24426i	−0.961643	−	0.274305i	$-0.911552\pi$
$281$	−3383.85	−	5861.00i	−0.718376	−	1.24426i	0.243267	−	0.969959i	$-0.421781\pi$
$282$	2547.36	+	12724.3i	0.537920	+	2.68696i
$283$	−2614.35	+	4528.19i	−0.549142	+	0.951142i	0.449192	+	0.893435i	$0.351712\pi$
$283$	−2614.35	+	4528.19i	−0.549142	+	0.951142i	−0.998334	+	0.0577064i	$0.981621\pi$
$284$	1571.92	−	2722.65i	0.328438	−	0.568872i
$285$	−458.712	−	2291.31i	−0.0953395	−	0.476230i
$286$	4521.79	+	7831.97i	0.934892	+	1.61928i
$287$	−1599.73			−0.329021
$288$	−3279.78	−	2503.82i	−0.671051	−	0.512288i
$289$	−2417.74			−0.492111
$290$	−7333.42	−	12701.9i	−1.48494	−	2.57200i
$291$	392.901	+	132.831i	0.0791486	+	0.0267584i
$292$	−2853.48	+	4942.38i	−0.571875	+	0.990517i
$293$	−1424.37	+	2467.08i	−0.284002	+	0.491905i	−0.972367	−	0.233459i	$-0.924995\pi$
$293$	−1424.37	+	2467.08i	−0.284002	+	0.491905i	0.688365	+	0.725365i	$0.258329\pi$
$294$	888.229	−	780.898i	0.176199	−	0.154908i
$295$	3988.83	+	6908.86i	0.787250	+	1.36356i
$296$	−2135.41			−0.419318
$297$	2881.13	−	5897.33i	0.562897	−	1.15218i
$298$	12411.9			2.41276
$299$	3902.18	+	6758.77i	0.754745	+	1.30726i
$300$	7776.07	−	6836.44i	1.49651	−	1.31567i
$301$	1143.23	−	1980.13i	0.218919	−	0.379180i
$302$	2592.00	−	4489.48i	0.493884	−	0.855433i
$303$	−1002.30	−	338.856i	−0.190035	−	0.0642467i
$304$	−159.766	−	276.723i	−0.0301422	−	0.0522078i
$305$	12048.4			2.26193
$306$	5782.07	−	2411.76i	1.08019	−	0.450559i
$307$	−1414.13			−0.262895			−0.131448	−	0.991323i	$-0.541963\pi$
$307$	−1414.13			−0.262895			−0.131448	+	0.991323i	$0.541963\pi$
$308$	2223.06	+	3850.46i	0.411269	+	0.712338i
$309$	896.082	+	4476.02i	0.164972	+	0.824051i
$310$	−2308.67	+	3998.74i	−0.422980	+	0.732622i
$311$	786.849	−	1362.86i	0.143467	−	0.248492i	−0.785333	−	0.619073i	$-0.787508\pi$
$311$	786.849	−	1362.86i	0.143467	−	0.248492i	0.928800	+	0.370582i	$0.120842\pi$
$312$	1099.60	+	5492.59i	0.199527	+	0.996657i
$313$	−3576.47	−	6194.62i	−0.645859	−	1.11866i	−0.984102	−	0.177602i	$-0.943166\pi$
$313$	−3576.47	−	6194.62i	−0.645859	−	1.11866i	0.338244	−	0.941059i	$-0.390167\pi$
$314$	693.946			0.124719
$315$	−399.056	+	3090.07i	−0.0713785	+	0.552717i
$316$	−229.632			−0.0408792
$317$	3745.66	+	6487.67i	0.663650	+	1.14948i	0.979650	+	0.200716i	$0.0643268\pi$
$317$	3745.66	+	6487.67i	0.663650	+	1.14948i	−0.316000	+	0.948759i	$0.602340\pi$
$318$	−12689.9	−	4290.18i	−2.23778	−	0.756544i
$319$	−4480.28	+	7760.06i	−0.786355	+	1.36201i
$320$	−6623.72	+	11472.6i	−1.15712	+	2.00418i
$321$	−3245.81	+	2853.60i	−0.564372	+	0.496175i
$322$	3048.87	+	5280.80i	0.527661	+	0.913936i
$323$	−1362.68			−0.234742
$324$	6963.88	−	7033.01i	1.19408	−	1.20593i
$325$	6107.85			1.04247
$326$	−3214.84	−	5568.26i	−0.546176	−	0.946004i
$327$	2891.27	−	2541.90i	0.488952	−	0.429869i
$328$	2959.98	−	5126.83i	0.498285	−	0.863055i
$329$	−1881.75	+	3259.29i	−0.315332	+	0.546171i
$330$	−17634.5	−	5961.82i	−2.94165	−	0.994507i
$331$	−300.335	−	520.195i	−0.0498727	−	0.0863821i	0.840011	−	0.542569i	$-0.182548\pi$
$331$	−300.335	−	520.195i	−0.0498727	−	0.0863821i	−0.889884	+	0.456187i	$0.849215\pi$
$332$	7427.24			1.22778
$333$	−285.067	+	2207.41i	−0.0469117	+	0.363259i
$334$	−14998.1			−2.45707
$335$	2835.12	+	4910.57i	0.462386	+	0.800875i
$336$	83.6337	+	417.759i	0.0135792	+	0.0678292i
$337$	−2027.33	+	3511.44i	−0.327702	+	0.567597i	−0.982056	−	0.188592i	$-0.939608\pi$
$337$	−2027.33	+	3511.44i	−0.327702	+	0.567597i	0.654353	+	0.756189i	$0.272941\pi$
$338$	1080.27	−	1871.08i	0.173843	−	0.301104i
$339$	1424.28	+	7114.40i	0.228189	+	1.13983i
$340$	−5590.12	−	9682.37i	−0.891667	−	1.54441i
$341$	2820.92			0.447980
$342$	−3157.64	+	1317.08i	−0.499256	+	0.208244i
$343$	343.000			0.0539949
$344$	4230.64	+	7327.69i	0.663084	+	1.14850i
$345$	−15218.0	−	5144.88i	−2.37482	−	0.802872i
$346$	6420.99	−	11121.5i	0.997672	−	1.72802i
$347$	−690.011	+	1195.13i	−0.106748	+	0.184894i	−0.914451	−	0.404696i	$-0.867377\pi$
$347$	−690.011	+	1195.13i	−0.106748	+	0.184894i	0.807703	+	0.589590i	$0.200711\pi$
$348$	−10147.9	+	8921.66i	−1.56317	+	1.37428i
$349$	−951.344	−	1647.78i	−0.145915	−	0.252732i	0.783799	−	0.621015i	$-0.213279\pi$
$349$	−951.344	−	1647.78i	−0.145915	−	0.252732i	−0.929714	+	0.368283i	$0.879946\pi$
$350$	4772.22			0.728816
$351$	5824.58	−	403.436i	0.885736	−	0.0613499i
$352$	7149.61			1.08260
$353$	−1365.00	−	2364.24i	−0.205811	−	0.356476i	0.744580	−	0.667534i	$-0.232650\pi$
$353$	−1365.00	−	2364.24i	−0.205811	−	0.356476i	−0.950391	+	0.311058i	$0.899317\pi$
$354$	8772.14	−	7712.14i	1.31705	−	1.15790i
$355$	−1908.69	+	3305.95i	−0.285360	+	0.494258i
$356$	1285.76	−	2227.00i	0.191419	−	0.331548i
$357$	1721.22	+	581.908i	0.255173	+	0.0862684i
$358$	6027.63	+	10440.2i	0.889860	+	1.54128i
$359$	11525.7			1.69444			0.847219	−	0.531244i	$-0.178275\pi$
$359$	11525.7			1.69444			0.847219	+	0.531244i	$0.178275\pi$
$360$	−9164.74	−	6996.46i	−1.34173	−	1.02429i
$361$	−6114.83			−0.891504
$362$	1469.43	+	2545.13i	0.213347	+	0.369527i
$363$	874.824	+	4369.83i	0.126491	+	0.631837i
$364$	−1977.52	+	3425.17i	−0.284753	+	0.493207i
$365$	3464.81	−	6001.23i	0.496867	−	0.860600i
$366$	−3462.80	−	17297.0i	−0.494545	−	2.47030i
$367$	−833.694	−	1444.00i	−0.118579	−	0.205385i	0.800626	−	0.599165i	$-0.204501\pi$
$367$	−833.694	−	1444.00i	−0.118579	−	0.205385i	−0.919205	+	0.393780i	$0.871167\pi$
$368$	−2196.63			−0.311161
$369$	−4904.55	−	3744.19i	−0.691927	−	0.528224i
$370$	6312.51			0.886951
$371$	−1942.46	−	3364.44i	−0.271826	−	0.470817i
$372$	4029.74	+	1362.36i	0.561646	+	0.189880i
$373$	−1807.99	+	3131.53i	−0.250976	+	0.434703i	−0.963795	−	0.266645i	$-0.914085\pi$
$373$	−1807.99	+	3131.53i	−0.250976	+	0.434703i	0.712819	+	0.701348i	$0.247418\pi$
$374$	−5427.62	+	9400.92i	−0.750416	+	1.29976i
$375$	−1400.37	+	1231.15i	−0.192839	+	0.169537i
$376$	−6963.60	−	12061.3i	−0.955108	−	1.65429i
$377$	−7970.83			−1.08891
$378$	4550.90	−	315.215i	0.619240	−	0.0428913i
$379$	−8281.46			−1.12240			−0.561201	−	0.827680i	$-0.689660\pi$
$379$	−8281.46			−1.12240			−0.561201	+	0.827680i	$0.689660\pi$
$380$	3052.81	+	5287.62i	0.412121	+	0.713814i
$381$	−5040.76	+	4431.65i	−0.677811	+	0.595907i
$382$	835.720	−	1447.51i	0.111935	−	0.193877i
$383$	5283.33	−	9150.99i	0.704871	−	1.22087i	−0.261867	−	0.965104i	$-0.584338\pi$
$383$	5283.33	−	9150.99i	0.704871	−	1.22087i	0.966738	−	0.255768i	$-0.0823284\pi$
$384$	12356.0	+	4177.28i	1.64203	+	0.555133i
$385$	−2699.33	−	4675.38i	−0.357326	−	0.618907i
$386$	8766.69			1.15599
$387$	8139.53	−	3395.08i	1.06914	−	0.445947i
$388$	−1083.67			−0.141791
$389$	3701.95	+	6411.97i	0.482510	+	0.835732i	0.999798	−	0.0200791i	$-0.00639182\pi$
$389$	3701.95	+	6411.97i	0.482510	+	0.835732i	−0.517288	+	0.855811i	$0.673058\pi$
$390$	−3250.53	−	16236.7i	−0.422044	−	2.10815i
$391$	−4683.88	+	8112.72i	−0.605816	+	1.04930i
$392$	−634.653	+	1099.25i	−0.0817725	+	0.141634i
$393$	1407.80	+	7032.09i	0.180697	+	0.902600i
$394$	−6220.03	−	10773.4i	−0.795332	−	1.37756i
$395$	278.829			0.0355174
$396$	−2196.45	+	17008.1i	−0.278726	+	2.15831i
$397$	12432.1			1.57166			0.785831	−	0.618441i	$-0.212236\pi$
$397$	12432.1			1.57166			0.785831	+	0.618441i	$0.212236\pi$
$398$	−5875.43	−	10176.5i	−0.739971	−	1.28167i
$399$	−939.975	−	317.785i	−0.117939	−	0.0398725i
$400$	−859.564	+	1488.81i	−0.107446	+	0.186101i
$401$	1982.83	−	3434.36i	0.246927	−	0.427690i	−0.715745	−	0.698362i	$-0.753913\pi$
$401$	1982.83	−	3434.36i	0.246927	−	0.427690i	0.962672	+	0.270672i	$0.0872460\pi$
$402$	6234.93	−	5481.52i	0.773558	−	0.680083i
$403$	1254.67	+	2173.15i	0.155086	+	0.268616i
$404$	2764.46			0.340439
$405$	−8455.82	+	8539.76i	−1.03746	+	1.04776i
$406$	−6227.82			−0.761284
$407$	−1928.28	−	3339.88i	−0.234843	−	0.406761i
$408$	−5049.69	+	4439.50i	−0.612737	+	0.538696i
$409$	−872.444	+	1511.12i	−0.105476	+	0.182689i	−0.913933	−	0.405866i	$-0.866970\pi$
$409$	−872.444	+	1511.12i	−0.105476	+	0.182689i	0.808457	+	0.588556i	$0.200303\pi$
$410$	−8750.03	+	15155.5i	−1.05398	+	1.82555i
$411$	9098.38	+	3075.96i	1.09195	+	0.369163i
$412$	−5963.58	−	10329.2i	−0.713118	−	1.23516i
$413$	3387.47			0.403599
$414$	−3012.37	+	23326.1i	−0.357608	+	2.76912i
$415$	−9018.44			−1.06674
$416$	3179.96	+	5507.85i	0.374784	+	0.649146i
$417$	−2239.80	−	11188.0i	−0.263030	−	1.31386i
$418$	2964.07	−	5133.92i	0.346836	−	0.600737i
$419$	−1842.02	+	3190.47i	−0.214770	+	0.371992i	−0.953201	−	0.302336i	$-0.902234\pi$
$419$	−1842.02	+	3190.47i	−0.214770	+	0.371992i	0.738431	+	0.674329i	$0.235567\pi$
$420$	−1598.07	−	7982.52i	−0.185662	−	0.927398i
$421$	1831.91	+	3172.96i	0.212071	+	0.367318i	0.952362	−	0.304968i	$-0.0986459\pi$
$421$	1831.91	+	3172.96i	0.212071	+	0.367318i	−0.740292	+	0.672286i	$0.765313\pi$
$422$	−16754.4			−1.93268
$423$	−13397.6	+	5588.27i	−1.53999	+	0.642343i
$424$	14376.5			1.64667
$425$	3665.70	+	6349.18i	0.418383	+	0.724660i
$426$	5294.70	+	1790.02i	0.602181	+	0.203584i
$427$	2557.98	−	4430.56i	0.289905	−	0.502131i
$428$	5646.13	−	9779.39i	0.637654	−	1.10445i
$429$	−7597.74	+	6679.65i	−0.855063	+	0.751740i
$430$	−12506.3	−	21661.5i	−1.40257	−	2.42932i
$431$	−2735.58			−0.305727			−0.152864	−	0.988247i	$-0.548849\pi$
$431$	−2735.58			−0.305727			−0.152864	+	0.988247i	$0.548849\pi$
$432$	−721.361	+	1476.54i	−0.0803392	+	0.164444i
$433$	−1654.76			−0.183655			−0.0918276	−	0.995775i	$-0.529271\pi$
$433$	−1654.76			−0.183655			−0.0918276	+	0.995775i	$0.529271\pi$
$434$	980.306	+	1697.94i	0.108424	+	0.187796i
$435$	12322.0	−	10833.0i	1.35815	−	1.19403i
$436$	−5029.40	+	8711.18i	−0.552442	+	0.956857i
$437$	2557.91	−	4430.43i	0.280003	−	0.484979i
$438$	−9611.37	−	3249.39i	−1.04851	−	0.354479i
$439$	5043.53	+	8735.66i	0.548325	+	0.949727i	0.998389	+	0.0567310i	$0.0180677\pi$
$439$	5043.53	+	8735.66i	0.548325	+	0.949727i	−0.450064	+	0.892996i	$0.648599\pi$
$440$	19978.3			2.16461
$441$	1051.59	+	802.797i	0.113551	+	0.0866858i
$442$	−9656.26			−1.03914
$443$	−4260.01	−	7378.55i	−0.456883	−	0.791344i	0.541911	−	0.840436i	$-0.317701\pi$
$443$	−4260.01	−	7378.55i	−0.456883	−	0.791344i	−0.998794	+	0.0490913i	$0.984367\pi$
$444$	−1141.59	−	5702.35i	−0.122021	−	0.609508i
$445$	−1561.22	+	2704.12i	−0.166312	+	0.288062i
$446$	7040.28	−	12194.1i	0.747459	−	1.29464i
$447$	2725.53	+	13614.3i	0.288396	+	1.44057i
$448$	2812.56	+	4871.49i	0.296609	+	0.513742i
$449$	−16614.0			−1.74624			−0.873120	−	0.487506i	$-0.837907\pi$
$449$	−16614.0			−1.74624			−0.873120	+	0.487506i	$0.837907\pi$
$450$	14631.0	+	11169.5i	1.53269	+	1.17007i
$451$	10691.5			1.11628
$452$	−9478.82	−	16417.8i	−0.986385	−	1.70847i
$453$	5493.57	+	1857.25i	0.569780	+	0.192630i
$454$	−5060.59	+	8765.20i	−0.523139	+	0.906104i
$455$	2401.18	−	4158.97i	0.247405	−	0.428518i
$456$	2757.68	−	2424.45i	0.283202	−	0.248981i
$457$	−159.393	−	276.078i	−0.0163153	−	0.0282590i	0.857752	−	0.514063i	$-0.171860\pi$
$457$	−159.393	−	276.078i	−0.0163153	−	0.0282590i	−0.874068	+	0.485804i	$0.838527\pi$
$458$	−1683.93			−0.171801
$459$	3915.08	+	5812.60i	0.398127	+	0.591087i
$460$	41973.1			4.25436
$461$	−131.110	−	227.090i	−0.0132460	−	0.0229428i	0.859326	−	0.511428i	$-0.170883\pi$
$461$	−131.110	−	227.090i	−0.0132460	−	0.0229428i	−0.872572	+	0.488485i	$0.837550\pi$
$462$	−5936.31	+	5218.98i	−0.597796	+	0.525561i
$463$	9451.23	−	16370.0i	0.948674	−	1.64315i	0.200451	−	0.979704i	$-0.435759\pi$
$463$	9451.23	−	16370.0i	0.948674	−	1.64315i	0.748223	−	0.663447i	$-0.230907\pi$
$464$	1121.74	−	1942.92i	0.112232	−	0.194392i
$465$	−4893.07	−	1654.24i	−0.487979	−	0.164975i
$466$	13107.7	+	22703.2i	1.30301	+	2.25688i
$467$	−7702.12			−0.763194			−0.381597	−	0.924329i	$-0.624626\pi$
$467$	−7702.12			−0.763194			−0.381597	+	0.924329i	$0.624626\pi$
$468$	−14079.5	+	5872.68i	−1.39065	+	0.580053i
$469$	2407.69			0.237051
$470$	20585.2	+	35654.6i	2.02026	+	3.49920i
$471$	152.383	+	761.170i	0.0149075	+	0.0744647i
$472$	−6267.83	+	10856.2i	−0.611229	+	1.05868i
$473$	−7640.56	+	13233.8i	−0.742734	+	1.28645i
$474$	−80.1375	−	400.295i	−0.00776548	−	0.0387894i
$475$	−2001.87	−	3467.34i	−0.193373	−	0.334932i
$476$	−4747.34			−0.457130
$477$	1919.20	−	14861.3i	0.184223	−	1.42652i
$478$	1735.02			0.166021
$479$	−8242.50	−	14276.4i	−0.786241	−	1.36181i	−0.928255	−	0.371944i	$-0.878691\pi$
$479$	−8242.50	−	14276.4i	−0.786241	−	1.36181i	0.142014	−	0.989865i	$-0.454642\pi$
$480$	−12401.5	−	4192.66i	−1.17927	−	0.398683i
$481$	1715.30	−	2970.98i	0.162600	−	0.281632i
$482$	328.557	−	569.077i	0.0310484	−	0.0537775i
$483$	−5122.86	+	4503.83i	−0.482605	+	0.424289i
$484$	−5822.11	−	10084.2i	−0.546780	−	0.947051i
$485$	1315.83			0.123193
$486$	14690.2	+	9685.04i	1.37111	+	0.903955i
$487$	13193.2			1.22760			0.613799	−	0.789462i	$-0.289640\pi$
$487$	13193.2			1.22760			0.613799	+	0.789462i	$0.289640\pi$
$488$	9466.08	+	16395.7i	0.878093	+	1.52090i
$489$	5401.73	−	4749.00i	0.499539	−	0.439176i
$490$	1876.11	−	3249.51i	0.172967	−	0.299588i
$491$	−101.859	+	176.426i	−0.00936222	+	0.0162158i	−0.870669	−	0.491870i	$-0.836313\pi$
$491$	−101.859	+	176.426i	−0.00936222	+	0.0162158i	0.861306	+	0.508086i	$0.169647\pi$
$492$	15273.0	+	5163.46i	1.39951	+	0.473144i
$493$	−4783.80	−	8285.79i	−0.437021	−	0.756943i
$494$	5273.36			0.480283
$495$	2667.01	−	20651.9i	0.242168	−	1.87522i
$496$	−706.284			−0.0639377
$497$	810.467	+	1403.77i	0.0731477	+	0.126696i
$498$	2591.97	+	12947.2i	0.233231	+	1.16501i
$499$	8315.90	−	14403.6i	0.746034	−	1.29217i	−0.203676	−	0.979038i	$-0.565289\pi$
$499$	8315.90	−	14403.6i	0.746034	−	1.29217i	0.949710	−	0.313130i	$-0.101378\pi$
$500$	2435.96	−	4219.20i	0.217879	−	0.377377i
$501$	−3293.44	−	16451.0i	−0.293692	−	1.46702i
$502$	2184.38	+	3783.46i	0.194210	+	0.336382i
$503$	−921.507			−0.0816858			−0.0408429	−	0.999166i	$-0.513004\pi$
$503$	−921.507			−0.0816858			−0.0408429	+	0.999166i	$0.513004\pi$
$504$	−4518.58	+	1884.74i	−0.399352	+	0.166574i
$505$	−3356.72			−0.295786
$506$	−20376.5	−	35293.2i	−1.79021	−	3.10074i
$507$	2289.55	+	774.046i	0.200557	+	0.0678039i
$508$	8768.48	−	15187.5i	0.765824	−	1.32645i
$509$	1883.93	−	3263.06i	0.164054	−	0.284151i	−0.772265	−	0.635301i	$-0.780876\pi$
$509$	1883.93	−	3263.06i	0.164054	−	0.284151i	0.936319	+	0.351150i	$0.114209\pi$
$510$	14927.4	−	13123.7i	1.29607	−	1.13946i
$511$	−1471.23	−	2548.24i	−0.127364	−	0.220602i
$512$	−4217.47			−0.364038
$513$	−2138.06	−	3174.31i	−0.184011	−	0.273195i
$514$	−24024.5			−2.06162
$515$	7241.22	+	12542.2i	0.619585	+	1.07315i
$516$	−17306.0	+	15214.8i	−1.47646	+	1.29805i
$517$	12576.3	−	21782.8i	1.06984	−	1.85301i
$518$	1340.21	−	2321.30i	0.113678	−	0.196896i
$519$	13608.8	+	4600.84i	1.15099	+	0.389123i
$520$	8885.82	+	15390.7i	0.749363	+	1.29794i
$521$	6192.75			0.520748			0.260374	−	0.965508i	$-0.416154\pi$
$521$	6192.75			0.520748			0.260374	+	0.965508i	$0.416154\pi$
$522$	−19093.7	−	14576.3i	−1.60097	−	1.22220i
$523$	−15499.3			−1.29586			−0.647932	−	0.761698i	$-0.724366\pi$
$523$	−15499.3			−1.29586			−0.647932	+	0.761698i	$0.724366\pi$
$524$	−9369.14	−	16227.8i	−0.781093	−	1.35289i
$525$	1047.93	+	5234.51i	0.0871151	+	0.435149i
$526$	−9576.73	+	16587.4i	−0.793850	+	1.37499i
$527$	−1506.01	+	2608.49i	−0.124484	+	0.215612i
$528$	−558.950	−	2792.01i	−0.0460704	−	0.230126i
$529$	−11500.9	−	19920.1i	−0.945250	−	1.63722i
$530$	−42498.7			−3.48307
$531$	10385.5	+	7928.42i	0.848763	+	0.647955i
$532$	2592.56			0.211282
$533$	4755.29	+	8236.40i	0.386443	+	0.669340i
$534$	4330.82	+	1464.15i	0.350960	+	0.118652i
$535$	−6855.76	+	11874.5i	−0.554019	+	0.959589i
$536$	−4454.95	+	7716.20i	−0.359001	+	0.621808i
$537$	−10127.9	+	8904.09i	−0.813877	+	0.715530i
$538$	11790.6	+	20422.0i	0.944852	+	1.63653i
$539$	−2292.37			−0.183190
$540$	13783.7	−	28213.6i	1.09844	−	2.24837i
$541$	−12060.5			−0.958447			−0.479224	−	0.877693i	$-0.659082\pi$
$541$	−12060.5			−0.958447			−0.479224	+	0.877693i	$0.659082\pi$
$542$	17184.2	+	29763.8i	1.36185	+	2.35879i
$543$	−2469.01	+	2170.66i	−0.195129	+	0.171551i
$544$	−3816.99	+	6611.22i	−0.300831	+	0.521055i
$545$	6106.90	−	10577.5i	0.479983	−	0.831355i
$546$	−6660.86	−	2251.89i	−0.522085	−	0.176506i
$547$	−1424.68	−	2467.61i	−0.111362	−	0.192884i	0.804958	−	0.593332i	$-0.202188\pi$
$547$	−1424.68	−	2467.61i	−0.111362	−	0.192884i	−0.916319	+	0.400448i	$0.868854\pi$
$548$	−25094.4			−1.95617
$549$	18212.2	−	7596.50i	1.41581	−	0.590547i
$550$	−31894.2			−2.47268
$551$	2612.47	+	4524.94i	0.201988	+	0.349853i
$552$	−4955.11	−	24751.3i	−0.382072	−	1.90849i
$553$	59.1980	−	102.534i	0.00455218	−	0.00788460i
$554$	2247.54	−	3892.86i	0.172363	−	0.298541i
$555$	1386.16	+	6924.02i	0.106017	+	0.529564i
$556$	14906.3	+	25818.4i	1.13699	+	1.96932i
$557$	−7878.87			−0.599351			−0.299675	−	0.954041i	$-0.596878\pi$
$557$	−7878.87			−0.599351			−0.299675	+	0.954041i	$0.596878\pi$
$558$	−968.568	+	7500.07i	−0.0734816	+	0.569003i
$559$	−13593.3			−1.02851
$560$	675.843	+	1170.59i	0.0509992	+	0.0883332i
$561$	−11503.5	−	3889.07i	−0.865734	−	0.292685i
$562$	−15718.2	+	27224.8i	−1.17978	+	2.04343i
$563$	−4529.86	+	7845.94i	−0.339095	+	0.587331i	−0.984263	−	0.176711i	$-0.943454\pi$
$563$	−4529.86	+	7845.94i	−0.339095	+	0.587331i	0.645167	+	0.764041i	$0.276788\pi$
$564$	28485.5	−	25043.4i	2.12670	−	1.86971i
$565$	11509.6	+	19935.1i	0.857010	+	1.48438i
$566$	24287.7			1.80369
$567$	1345.08	+	4922.54i	0.0996263	+	0.364598i
$568$	−5998.43			−0.443113
$569$	8421.86	+	14587.1i	0.620497	+	1.07473i	0.989393	+	0.145262i	$0.0464024\pi$
$569$	8421.86	+	14587.1i	0.620497	+	1.07473i	−0.368896	+	0.929471i	$0.620264\pi$
$570$	−8152.00	+	7166.94i	−0.599035	+	0.526649i
$571$	−6768.99	+	11724.2i	−0.496100	+	0.859271i	−0.999990	−	0.00449711i	$-0.998569\pi$
$571$	−6768.99	+	11724.2i	−0.496100	+	0.859271i	0.503890	+	0.863768i	$0.331902\pi$
$572$	13216.4	−	22891.4i	0.966091	−	1.67332i
$573$	1771.25	+	598.820i	0.129136	+	0.0436581i
$574$	3715.43	+	6435.31i	0.270172	+	0.467952i
$575$	−27523.8			−1.99621
$576$	−2778.88	+	21518.2i	−0.201019	+	1.55658i
$577$	−2596.01			−0.187302			−0.0936509	−	0.995605i	$-0.529854\pi$
$577$	−2596.01			−0.187302			−0.0936509	+	0.995605i	$0.529854\pi$
$578$	5615.29	+	9725.97i	0.404092	+	0.699909i
$579$	1925.08	+	9615.94i	0.138175	+	0.690198i
$580$	−21434.3	+	37125.2i	−1.53450	+	2.65783i
$581$	−1914.70	+	3316.36i	−0.136721	+	0.236809i
$582$	−378.180	−	1889.05i	−0.0269348	−	0.134542i
$583$	12982.1	+	22485.6i	0.922233	+	1.59735i
$584$	10888.8			0.771547
$585$	17095.8	−	7130.84i	1.20825	−	0.503972i
$586$	13232.6			0.932821
$587$	−9735.16	−	16861.8i	−0.684519	−	1.18562i	−0.973588	−	0.228314i	$-0.926679\pi$
$587$	−9735.16	−	16861.8i	−0.684519	−	1.18562i	0.289068	−	0.957309i	$-0.406655\pi$
$588$	−3274.70	−	1107.10i	−0.229671	−	0.0776466i
$589$	822.446	−	1424.52i	0.0575353	−	0.0996541i
$590$	18528.4	−	32092.1i	1.29289	−	2.23934i
$591$	10451.2	−	9188.32i	0.727420	−	0.639521i
$592$	482.791	+	836.219i	0.0335179	+	0.0580547i
$593$	3741.32			0.259085			0.129543	−	0.991574i	$-0.458649\pi$
$593$	3741.32			0.259085			0.129543	+	0.991574i	$0.458649\pi$
$594$	−30415.0	+	2106.68i	−2.10092	+	0.145519i
$595$	5764.40			0.397172
$596$	−18138.9	−	31417.4i	−1.24664	−	2.15924i
$597$	9872.19	−	8679.26i	0.676787	−	0.595006i
$598$	18125.9	−	31395.0i	1.23950	−	2.14688i
$599$	8082.46	−	13999.2i	0.551320	−	0.954914i	−0.446860	−	0.894604i	$-0.647458\pi$
$599$	8082.46	−	13999.2i	0.551320	−	0.954914i	0.998180	−	0.0603099i	$-0.0192089\pi$
$600$	−18714.6	−	6327.00i	−1.27337	−	0.430498i
$601$	8534.25	+	14781.8i	0.579234	+	1.00326i	0.995567	+	0.0940503i	$0.0299815\pi$
$601$	8534.25	+	14781.8i	0.579234	+	1.00326i	−0.416334	+	0.909212i	$0.636685\pi$
$602$	−10620.8			−0.719054
$603$	7381.66	+	5635.24i	0.498515	+	0.380572i
$604$	−15151.9			−1.02073
$605$	7069.44	+	12244.6i	0.475064	+	0.822834i
$606$	964.748	+	4819.01i	0.0646703	+	0.323034i
$607$	9765.88	−	16915.0i	0.653023	−	1.13107i	−0.329363	−	0.944203i	$-0.606834\pi$
$607$	9765.88	−	16915.0i	0.653023	−	1.13107i	0.982386	−	0.186865i	$-0.0598328\pi$
$608$	2084.49	−	3610.44i	0.139041	−	0.240827i
$609$	−1367.57	−	6831.12i	−0.0909960	−	0.454534i
$610$	−27982.8	−	48467.6i	−1.85736	−	3.21704i
$611$	22374.4			1.48146
$612$	−14554.7	−	11111.2i	−0.961338	−	0.733896i
$613$	−6738.59			−0.443995			−0.221997	−	0.975047i	$-0.571258\pi$
$613$	−6738.59			−0.443995			−0.221997	+	0.975047i	$0.571258\pi$
$614$	3284.38	+	5688.71i	0.215874	+	0.373905i
$615$	−18545.1	−	6269.68i	−1.21595	−	0.411086i
$616$	4241.58	−	7346.63i	0.277432	−	0.480526i
$617$	−5865.77	+	10159.8i	−0.382734	+	0.662915i	−0.991452	−	0.130472i	$-0.958351\pi$
$617$	−5865.77	+	10159.8i	−0.382734	+	0.662915i	0.608718	+	0.793387i	$0.291684\pi$
$618$	15924.7	−	14000.4i	1.03655	−	0.911294i
$619$	2542.46	+	4403.67i	0.165089	+	0.285943i	0.936687	−	0.350168i	$-0.113875\pi$
$619$	2542.46	+	4403.67i	0.165089	+	0.285943i	−0.771598	+	0.636111i	$0.780542\pi$
$620$	13495.7			0.874191
$621$	−26247.3	+	1818.00i	−1.69608	+	0.117478i
$622$	−7309.95			−0.471225
$623$	662.925	+	1148.22i	0.0426316	+	0.0738402i
$624$	1902.28	−	1672.41i	0.122038	−	0.107292i
$625$	6215.13	−	10764.9i	0.397768	−	0.688955i
$626$	−16612.9	+	28774.5i	−1.06068	+	1.83715i
$627$	6282.14	+	2123.85i	0.400135	+	0.135277i
$628$	−1014.14	−	1756.54i	−0.0644403	−	0.111614i
$629$	4117.83			0.261031
$630$	13357.4	−	5571.51i	0.844718	−	0.352340i
$631$	−17996.7			−1.13540			−0.567701	−	0.823235i	$-0.692167\pi$
$631$	−17996.7			−1.13540			−0.567701	+	0.823235i	$0.692167\pi$
$632$	219.068	+	379.437i	0.0137881	+	0.0238816i
$633$	−3679.10	−	18377.5i	−0.231013	−	1.15393i
$634$	17398.8	−	30135.7i	1.08990	−	1.88776i
$635$	−10647.0	+	18441.2i	−0.665377	+	1.15247i
$636$	7685.70	+	38390.8i	0.479179	+	2.39355i
$637$	−1019.59	−	1765.98i	−0.0634184	−	0.109844i
$638$	41622.4			2.58283
$639$	−800.763	+	6200.68i	−0.0495738	+	0.383873i
$640$	41380.4			2.55579
$641$	5981.17	+	10359.7i	0.368552	+	0.638351i	0.989339	−	0.145628i	$-0.0465203\pi$
$641$	5981.17	+	10359.7i	0.368552	+	0.638351i	−0.620787	+	0.783979i	$0.713187\pi$
$642$	19017.8	+	6429.50i	1.16912	+	0.395253i
$643$	3790.45	−	6565.25i	0.232474	−	0.402656i	−0.726062	−	0.687630i	$-0.758651\pi$
$643$	3790.45	−	6565.25i	0.232474	−	0.402656i	0.958536	+	0.284973i	$0.0919847\pi$
$644$	8911.29	−	15434.8i	0.545270	−	0.944436i
$645$	21013.6	−	18474.4i	1.28281	−	1.12780i
$646$	3164.88	+	5481.73i	0.192756	+	0.333863i
$647$	−16686.5			−1.01393			−0.506966	−	0.861966i	$-0.669233\pi$
$647$	−16686.5			−1.01393			−0.506966	+	0.861966i	$0.669233\pi$
$648$	−18264.6	−	4797.44i	−1.10726	−	0.290835i
$649$	−22639.5			−1.36930
$650$	−14185.7	−	24570.3i	−0.856013	−	1.48266i
$651$	−1647.16	+	1448.12i	−0.0991662	+	0.0871833i
$652$	−9396.38	+	16275.0i	−0.564403	+	0.977574i
$653$	−4809.52	+	8330.33i	−0.288225	+	0.499221i	−0.973386	−	0.229171i	$-0.926398\pi$
$653$	−4809.52	+	8330.33i	−0.288225	+	0.499221i	0.685161	+	0.728392i	$0.259732\pi$
$654$	−16940.5	−	5727.20i	−1.01288	−	0.342433i
$655$	11376.4	+	19704.5i	0.678644	+	1.17545i
$656$	−2676.87			−0.159320
$657$	1453.61	−	11256.0i	0.0863177	−	0.668398i
$658$	17481.7			1.03573
$659$	1378.91	+	2388.35i	0.0815096	+	0.141179i	0.903899	−	0.427747i	$-0.140693\pi$
$659$	1378.91	+	2388.35i	0.0815096	+	0.141179i	−0.822389	+	0.568926i	$0.807359\pi$
$660$	10680.4	+	53349.6i	0.629899	+	3.14641i
$661$	11522.4	−	19957.4i	0.678018	−	1.17436i	−0.297559	−	0.954703i	$-0.596173\pi$
$661$	11522.4	−	19957.4i	0.678018	−	1.17436i	0.975577	−	0.219658i	$-0.0704942\pi$
$662$	−1395.08	+	2416.34i	−0.0819051	+	0.141864i
$663$	−2120.42	−	10591.7i	−0.124208	−	0.620433i
$664$	−7085.54	−	12272.5i	−0.414115	−	0.717268i
$665$	−3147.99			−0.183570
$666$	9541.94	−	3980.03i	0.555169	−	0.231566i
$667$	35919.0			2.08514
$668$	21918.4	+	37963.8i	1.26953	+	2.19890i
$669$	14921.4	+	5044.58i	0.862322	+	0.291532i
$670$	13169.3	−	22810.0i	0.759367	−	1.31526i
$671$	−17095.8	+	29610.8i	−0.983570	+	1.70359i
$672$	−4174.72	+	3670.26i	−0.239648	+	0.210690i
$673$	12301.0	+	21306.0i	0.704562	+	1.22034i	0.966849	+	0.255348i	$0.0821899\pi$
$673$	12301.0	+	21306.0i	0.704562	+	1.22034i	−0.262287	+	0.964990i	$0.584477\pi$
$674$	18834.2			1.07636
$675$	−9038.65	+	18501.0i	−0.515404	+	1.05497i
$676$	−6314.85			−0.359288
$677$	−8381.07	−	14516.4i	−0.475791	−	0.824094i	0.523824	−	0.851826i	$-0.324505\pi$
$677$	−8381.07	−	14516.4i	−0.475791	−	0.824094i	−0.999615	+	0.0277321i	$0.991171\pi$
$678$	25311.5	−	22253.0i	1.43375	−	1.26050i
$679$	279.363	−	483.871i	0.0157894	−	0.0273480i
$680$	−10665.9	+	18473.8i	−0.601497	+	1.04182i
$681$	−10725.6	−	3626.08i	−0.603531	−	0.204040i
$682$	−6551.68	−	11347.8i	−0.367855	−	0.637143i
$683$	21242.2			1.19006			0.595029	−	0.803704i	$-0.297140\pi$
$683$	21242.2			1.19006			0.595029	+	0.803704i	$0.297140\pi$
$684$	7948.45	+	6067.93i	0.444322	+	0.339201i
$685$	30470.6			1.69959
$686$	−796.630	−	1379.80i	−0.0443374	−	0.0767947i
$687$	−369.774	−	1847.06i	−0.0205353	−	0.102576i
$688$	1913.00	−	3313.41i	0.106006	−	0.183608i
$689$	−11548.2	+	20002.0i	−0.638534	+	1.10597i
$690$	14647.9	+	73167.5i	0.808166	+	4.03687i
$691$	−15131.7	−	26208.8i	−0.833048	−	1.44288i	−0.895610	−	0.444840i	$-0.853261\pi$
$691$	−15131.7	−	26208.8i	−0.833048	−	1.44288i	0.0625624	−	0.998041i	$-0.480073\pi$
$692$	−37534.8			−2.06193
$693$	−7028.11	−	5365.34i	−0.385247	−	0.294101i
$694$	6410.30			0.350622
$695$	−18099.8	−	31349.7i	−0.987861	−	1.71103i
$696$	24422.9	+	8256.84i	1.33010	+	0.449676i
$697$	−5707.90	+	9886.37i	−0.310189	+	0.537264i
$698$	−4419.06	+	7654.04i	−0.239633	+	0.415057i
$699$	−22024.2	+	19362.9i	−1.19175	+	1.04774i
$700$	−6974.16	−	12079.6i	−0.376569	−	0.652237i
$701$	−27335.4			−1.47282			−0.736409	−	0.676537i	$-0.763480\pi$
$701$	−27335.4			−1.47282			−0.736409	+	0.676537i	$0.763480\pi$
$702$	−15150.7	−	22493.9i	−0.814569	−	1.20937i
$703$	−2248.78			−0.120646
$704$	−18797.2	−	32557.7i	−1.00631	−	1.74299i
$705$	−34588.3	+	30408.7i	−1.84776	+	1.62448i
$706$	−6340.51	+	10982.1i	−0.338000	+	0.585434i
$707$	−712.663	+	1234.37i	−0.0379101	+	0.0656623i
$708$	−32340.9	−	10933.8i	−1.71673	−	0.580389i
$709$	−821.479	−	1422.84i	−0.0435138	−	0.0753682i	0.843448	−	0.537210i	$-0.180522\pi$
$709$	−821.479	−	1422.84i	−0.0435138	−	0.0753682i	−0.886962	+	0.461842i	$0.847189\pi$
$710$	17732.0			0.937283
$711$	421.475	−	175.801i	0.0222314	−	0.00927295i
$712$	−4906.44			−0.258254
$713$	−5653.91	−	9792.87i	−0.296972	−	0.514370i
$714$	−1656.74	−	8275.56i	−0.0868372	−	0.433760i
$715$	−16047.8	+	27795.7i	−0.839378	+	1.45384i
$716$	17617.7	−	30514.7i	0.919557	−	1.59272i
$717$	380.994	+	1903.10i	0.0198444	+	0.0991249i
$718$	−26768.9	−	46365.0i	−1.39137	−	2.40993i
$719$	28119.4			1.45852			0.729260	−	0.684237i	$-0.239865\pi$
$719$	28119.4			1.45852			0.729260	+	0.684237i	$0.239865\pi$
$720$	−667.750	+	5170.70i	−0.0345633	+	0.267640i
$721$	6149.52			0.317642
$722$	14201.9	+	24598.4i	0.732050	+	1.26795i
$723$	696.353	+	235.421i	0.0358197	+	0.0121098i
$724$	4294.88	−	7438.94i	0.220467	−	0.381859i
$725$	14055.5	−	24344.8i	0.720009	−	1.24709i
$726$	15546.9	−	13668.3i	0.794768	−	0.698730i
$727$	−13306.3	−	23047.1i	−0.678820	−	1.17575i	−0.975337	−	0.220723i	$-0.929158\pi$
$727$	−13306.3	−	23047.1i	−0.678820	−	1.17575i	0.296516	−	0.955028i	$-0.404175\pi$
$728$	7546.17			0.384176
$729$	−7397.44	+	18240.0i	−0.375829	+	0.926689i
$730$	−32188.6			−1.63199
$731$	−8158.19	−	14130.4i	−0.412779	−	0.714954i
$732$	−38722.2	+	34043.2i	−1.95521	+	1.71895i
$733$	6205.35	−	10748.0i	0.312687	−	0.541591i	−0.666256	−	0.745723i	$-0.732104\pi$
$733$	6205.35	−	10748.0i	0.312687	−	0.541591i	0.978943	+	0.204133i	$0.0654374\pi$
$734$	−3872.57	+	6707.49i	−0.194740	+	0.337300i
$735$	3976.27	+	1344.29i	0.199547	+	0.0674624i
$736$	−14329.8	−	24820.0i	−0.717670	−	1.24304i
$737$	−16091.3			−0.804250
$738$	−3670.94	+	28425.8i	−0.183102	+	1.41784i
$739$	9958.14			0.495692			0.247846	−	0.968799i	$-0.420277\pi$
$739$	9958.14			0.495692			0.247846	+	0.968799i	$0.420277\pi$
$740$	−9225.16	−	15978.4i	−0.458275	−	0.793756i
$741$	1157.98	+	5784.21i	0.0574080	+	0.286759i
$742$	−9022.87	+	15628.1i	−0.446415	+	0.773214i
$743$	4866.25	−	8428.59i	0.240276	−	0.416171i	−0.720517	−	0.693438i	$-0.756095\pi$
$743$	4866.25	−	8428.59i	0.240276	−	0.416171i	0.960793	+	0.277267i	$0.0894286\pi$
$744$	−1593.22	−	7958.29i	−0.0785085	−	0.392157i
$745$	22024.9	+	38148.3i	1.08313	+	1.87603i
$746$	16796.5			0.824346
$747$	−13632.2	+	5686.13i	−0.667706	+	0.278507i
$748$	31727.9			1.55092
$749$	2911.08	+	5042.14i	0.142014	+	0.245976i
$750$	8205.01	+	2773.93i	0.399473	+	0.135053i
$751$	−12499.0	+	21648.9i	−0.607318	+	1.05191i	0.384363	+	0.923182i	$0.374421\pi$
$751$	−12499.0	+	21648.9i	−0.607318	+	1.05191i	−0.991681	+	0.128723i	$0.958912\pi$
$752$	−3148.78	+	5453.85i	−0.152692	+	0.264470i
$753$	−3670.30	+	3226.79i	−0.177627	+	0.156163i
$754$	18512.6	+	32064.7i	0.894148	+	1.54871i
$755$	18398.0			0.886852
$756$	−7448.61	−	11058.7i	−0.358338	−	0.532013i
$757$	10673.8			0.512476			0.256238	−	0.966614i	$-0.417517\pi$
$757$	10673.8			0.512476			0.256238	+	0.966614i	$0.417517\pi$
$758$	19234.0	+	33314.3i	0.921650	+	1.59634i
$759$	34237.7	−	30100.5i	1.63735	−	1.43950i
$760$	5824.73	−	10088.7i	0.278007	−	0.481522i
$761$	4652.73	−	8058.77i	0.221631	−	0.383877i	−0.733672	−	0.679504i	$-0.762195\pi$
$761$	4652.73	−	8058.77i	0.221631	−	0.383877i	0.955303	+	0.295627i	$0.0955285\pi$
$762$	29534.8	+	9985.06i	1.40411	+	0.474699i
$763$	−2593.10	−	4491.39i	−0.123036	−	0.213105i
$764$	−4885.32			−0.231341
$765$	17672.9	+	13491.7i	0.835248	+	0.637638i
$766$	−49082.9			−2.31519
$767$	−10069.4	−	17440.8i	−0.474037	−	0.821056i
$768$	−5335.70	−	26652.3i	−0.250697	−	1.25226i
$769$	9966.38	−	17262.3i	0.467356	−	0.809484i	−0.531948	−	0.846777i	$-0.678540\pi$
$769$	9966.38	−	17262.3i	0.467356	−	0.809484i	0.999304	+	0.0372924i	$0.0118733\pi$
$770$	−12538.6	+	21717.5i	−0.586830	+	1.01642i
$771$	−5275.53	−	26351.8i	−0.246425	−	1.23092i
$772$	−12811.7	−	22190.5i	−0.597285	−	1.03453i
$773$	8411.00			0.391362			0.195681	−	0.980668i	$-0.437308\pi$
$773$	8411.00			0.391362			0.195681	+	0.980668i	$0.437308\pi$
$774$	−32561.9	−	24858.1i	−1.51216	−	1.15440i
$775$	−8849.74			−0.410183
$776$	1033.81	+	1790.61i	0.0478243	+	0.0828342i
$777$	2840.47	+	960.300i	0.131147	+	0.0443379i
$778$	17195.8	−	29784.1i	0.792417	−	1.37251i
$779$	3117.13	−	5399.03i	0.143367	−	0.248319i
$780$	−36348.6	+	31956.4i	−1.66858	+	1.46695i
$781$	−5416.60	−	9381.82i	−0.248170	−	0.429844i
$782$	43514.0			1.98984
$783$	11795.6	−	24144.1i	0.538365	−	1.10197i
$784$	573.951			0.0261457
$785$	1231.41	+	2132.86i	0.0559883	+	0.0969745i
$786$	25018.7	−	21995.5i	1.13535	−	0.998159i
$787$	−19208.8	+	33270.7i	−0.870039	+	1.50695i	−0.00808446	+	0.999967i	$0.502573\pi$
$787$	−19208.8	+	33270.7i	−0.870039	+	1.50695i	−0.861955	+	0.506985i	$0.830760\pi$
$788$	−18180.0	+	31488.7i	−0.821874	+	1.42353i
$789$	−20297.2	−	6862.03i	−0.915842	−	0.309626i
$790$	−647.590	−	1121.66i	−0.0291648	−	0.0505150i
$791$	9774.35			0.439363
$792$	30199.0	−	12596.3i	1.35489	−	0.565139i
$793$	−30415.0			−1.36200
$794$	−28874.0	−	50011.3i	−1.29056	−	2.23531i
$795$	−9332.28	−	46615.7i	−0.416329	−	2.07961i
$796$	−17172.8	+	29744.2i	−0.764666	+	1.32444i
$797$	12750.6	−	22084.7i	0.566686	−	0.981529i	−0.430205	−	0.902731i	$-0.641559\pi$
$797$	12750.6	−	22084.7i	0.566686	−	0.981529i	0.996891	−	0.0787975i	$-0.0251080\pi$
$798$	904.757	+	4519.35i	0.0401354	+	0.200480i
$799$	13428.3	+	23258.5i	0.594568	+	1.02982i
$800$	−22429.7			−0.991260
$801$	−654.987	+	5071.87i	−0.0288924	+	0.223728i
$802$	−18420.7			−0.811046
$803$	9832.65	+	17030.6i	0.432113	+	0.748441i
$804$	−22986.8	−	7771.33i	−1.00831	−	0.340888i
$805$	−10820.4	+	18741.6i	−0.473752	+	0.820563i
$806$	5828.03	−	10094.4i	0.254694	−	0.441144i
$807$	−19811.2	+	17417.3i	−0.864173	+	0.759749i
$808$	−2637.28	−	4567.91i	−0.114826	−	0.198884i
$809$	−30218.6			−1.31326			−0.656631	−	0.754212i	$-0.728019\pi$
$809$	−30218.6			−1.31326			−0.656631	+	0.754212i	$0.728019\pi$
$810$	53992.3	+	14181.8i	2.34209	+	0.615181i
$811$	3754.20			0.162550			0.0812749	−	0.996692i	$-0.474101\pi$
$811$	3754.20			0.162550			0.0812749	+	0.996692i	$0.474101\pi$
$812$	9101.39	+	15764.1i	0.393345	+	0.681294i
$813$	−28873.7	+	25384.7i	−1.24556	+	1.09505i
$814$	−8957.00	+	15514.0i	−0.385679	+	0.668016i
$815$	11409.5	−	19761.8i	0.490375	−	0.849355i
$816$	2880.17	+	973.721i	0.123561	+	0.0417734i
$817$	4455.25	+	7716.73i	0.190783	+	0.330446i
$818$	8105.14			0.346442
$819$	1007.38	−	7800.61i	0.0429801	−	0.332815i
$820$	51149.5			2.17831
$821$	18975.6	+	32866.6i	0.806641	+	1.39714i	0.915178	+	0.403050i	$0.132050\pi$
$821$	18975.6	+	32866.6i	0.806641	+	1.39714i	−0.108537	+	0.994092i	$0.534617\pi$
$822$	−8757.49	−	43744.5i	−0.371597	−	1.85616i
$823$	2535.80	−	4392.13i	0.107403	−	0.186027i	−0.807315	−	0.590121i	$-0.799080\pi$
$823$	2535.80	−	4392.13i	0.107403	−	0.186027i	0.914717	+	0.404094i	$0.132413\pi$
$824$	−11378.5	+	19708.1i	−0.481052	+	0.833207i
$825$	−7003.64	−	34983.9i	−0.295558	−	1.47634i
$826$	−7867.51	−	13626.9i	−0.331411	−	0.574021i
$827$	31431.5			1.32162			0.660811	−	0.750552i	$-0.270212\pi$
$827$	31431.5			1.32162			0.660811	+	0.750552i	$0.270212\pi$
$828$	63446.3	−	26464.0i	2.66293	−	1.11074i
$829$	28002.8			1.17319			0.586597	−	0.809879i	$-0.300467\pi$
$829$	28002.8			1.17319			0.586597	+	0.809879i	$0.300467\pi$
$830$	20945.7	+	36279.0i	0.875945	+	1.51718i
$831$	4763.51	+	1610.44i	0.198850	+	0.0672268i
$832$	16721.0	−	28961.6i	0.696750	−	1.20681i
$833$	1223.84	−	2119.75i	0.0509045	−	0.0881692i
$834$	−39804.6	+	34994.8i	−1.65266	+	1.45296i
$835$	−26614.2	−	46097.1i	−1.10302	−	1.91049i
$836$	−17326.9			−0.716821
$837$	−8439.32	+	584.544i	−0.348513	+	0.0241395i
$838$	17112.6			0.705425
$839$	11772.5	+	20390.6i	0.484425	+	0.839048i	0.999840	−	0.0178924i	$-0.00569565\pi$
$839$	11772.5	+	20390.6i	0.484425	+	0.839048i	−0.515415	+	0.856941i	$0.672362\pi$
$840$	−11665.5	+	10255.9i	−0.479164	+	0.421264i
$841$	−6148.09	+	10648.8i	−0.252085	+	0.436623i
$842$	8509.36	−	14738.6i	0.348280	−	0.603239i
$843$	−33313.7	−	11262.6i	−1.36107	−	0.460149i
$844$	24485.1	+	42409.4i	0.998591	+	1.72961i
$845$	7667.74			0.312163
$846$	53596.6	+	40916.3i	2.17812	+	1.66280i
$847$	6003.63			0.243551
$848$	−3250.37	−	5629.81i	−0.131625	−	0.227982i
$849$	5333.34	+	26640.5i	0.215594	+	1.07692i
$850$	17027.5	−	29492.4i	0.687102	−	1.19010i
$851$	−7729.64	+	13388.1i	−0.311361	+	0.539294i
$852$	−3206.76	−	16018.1i	−0.128946	−	0.644097i
$853$	−6850.13	−	11864.8i	−0.274964	−	0.476251i	0.695162	−	0.718853i	$-0.255332\pi$
$853$	−6850.13	−	11864.8i	−0.274964	−	0.476251i	−0.970126	+	0.242602i	$0.921999\pi$
$854$	−23764.0			−0.952212
$855$	−9651.32	−	7367.92i	−0.386044	−	0.294711i
$856$	−21545.5			−0.860293
$857$	−1295.81	−	2244.41i	−0.0516500	−	0.0894605i	0.839044	−	0.544063i	$-0.183115\pi$
$857$	−1295.81	−	2244.41i	−0.0516500	−	0.0894605i	−0.890694	+	0.454602i	$0.849781\pi$
$858$	44516.6	+	15050.1i	1.77129	+	0.598836i
$859$	−732.309	+	1268.40i	−0.0290874	+	0.0503808i	−0.880203	−	0.474598i	$-0.842593\pi$
$859$	−732.309	+	1268.40i	−0.0290874	+	0.0503808i	0.851115	+	0.524979i	$0.175927\pi$
$860$	−36553.5	+	63312.5i	−1.44938	+	2.51039i
$861$	−6242.85	+	5488.48i	−0.247103	+	0.217244i
$862$	6353.49	+	11004.6i	0.251045	+	0.434823i
$863$	−35034.9			−1.38193			−0.690963	−	0.722890i	$-0.742813\pi$
$863$	−35034.9			−1.38193			−0.690963	+	0.722890i	$0.742813\pi$
$864$	−21389.4	+	1481.53i	−0.842227	+	0.0583363i
$865$	45576.2			1.79149
$866$	3843.24	+	6656.69i	0.150807	+	0.261205i
$867$	−9435.09	+	8294.99i	−0.369588	+	0.324928i
$868$	2865.25	−	4962.77i	0.112043	−	0.194064i
$869$	−395.638	+	685.265i	−0.0154443	+	0.0267503i
$870$	−72196.8	−	24408.1i	−2.81345	−	0.951165i
$871$	−7157.00	−	12396.3i	−0.278422	−	0.482242i
$872$	19192.1			0.745328
$873$	1989.00	−	829.630i	0.0771104	−	0.0321635i
$874$	−23763.3			−0.919688
$875$	1255.95	+	2175.37i	0.0485245	+	0.0840469i
$876$	5821.17	+	29077.3i	0.224520	+	1.12150i
$877$	−10817.4	+	18736.3i	−0.416508	+	0.721413i	−0.995585	−	0.0938596i	$-0.970080\pi$
$877$	−10817.4	+	18736.3i	−0.416508	+	0.721413i	0.579078	+	0.815272i	$0.303413\pi$
$878$	23427.6	−	40577.8i	0.900504	−	1.55972i
$879$	2905.74	+	14514.5i	0.111500	+	0.556952i
$880$	−4516.86	−	7823.43i	−0.173027	−	0.299691i
$881$	47035.2			1.79870			0.899350	−	0.437229i	$-0.144040\pi$
$881$	47035.2			1.79870			0.899350	+	0.437229i	$0.144040\pi$
$882$	787.092	−	6094.82i	0.0300485	−	0.232679i
$883$	3997.99			0.152371			0.0761853	−	0.997094i	$-0.475726\pi$
$883$	3997.99			0.152371			0.0761853	+	0.997094i	$0.475726\pi$
$884$	14111.7	+	24442.3i	0.536911	+	0.929957i
$885$	39269.6	+	13276.2i	1.49156	+	0.504265i
$886$	−19788.1	+	34273.9i	−0.750330	+	1.29961i
$887$	−23060.1	+	39941.4i	−0.872925	+	1.51195i	−0.0139672	+	0.999902i	$0.504446\pi$
$887$	−23060.1	+	39941.4i	−0.872925	+	1.51195i	−0.858957	+	0.512047i	$0.828887\pi$
$888$	−8333.31	+	7326.34i	−0.314918	+	0.276865i
$889$	4520.93	+	7830.49i	0.170559	+	0.295417i
$890$	14504.0			0.546264
$891$	−8989.59	−	32898.8i	−0.338005	−	1.23698i
$892$	−41154.9			−1.54481
$893$	−7333.32	−	12701.7i	−0.274804	−	0.475975i
$894$	48436.7	−	42583.8i	1.81204	−	1.59308i
$895$	−21392.1	+	37052.1i	−0.798947	+	1.38382i
$896$	8785.44	−	15216.8i	0.327568	−	0.567365i
$897$	38416.5	+	12987.8i	1.42998	+	0.483444i
$898$	38586.5	+	66833.9i	1.43391	+	2.48360i
$899$	11549.0			0.428456
$900$	6890.66	−	53357.6i	0.255210	−	1.97621i
$901$	−27723.1			−1.02507
$902$	−24831.3	−	43009.2i	−0.916622	−	1.58764i
$903$	−2332.22	−	11649.6i	−0.0859482	−	0.429320i
$904$	−18085.5	+	31325.0i	−0.665392	+	1.15249i
$905$	−5215.01	+	9032.66i	−0.191550	+	0.331774i
$906$	−5287.74	−	26412.8i	−0.193900	−	0.968550i
$907$	1720.44	+	2979.88i	0.0629837	+	0.109091i	0.895798	−	0.444462i	$-0.146605\pi$
$907$	1720.44	+	2979.88i	0.0629837	+	0.109091i	−0.832814	+	0.553553i	$0.813272\pi$
$908$	29582.4			1.08120
$909$	−5073.99	+	2116.41i	−0.185142	+	0.0772243i
$910$	−22307.3			−0.812616
$911$	−14161.7	−	24528.9i	−0.515038	−	0.892072i	−0.999848	−	0.0174523i	$-0.994444\pi$
$911$	−14161.7	−	24528.9i	−0.515038	−	0.892072i	0.484810	−	0.874620i	$-0.338889\pi$
$912$	−1572.88	−	531.757i	−0.0571090	−	0.0193073i
$913$	12796.5	−	22164.2i	0.463859	−	0.803428i
$914$	−740.394	+	1282.40i	−0.0267944	+	0.0464092i
$915$	47018.1	−	41336.6i	1.69876	−	1.49349i
$916$	2460.91	+	4262.42i	0.0887672	+	0.153749i
$917$	9661.25			0.347920
$918$	14289.7	−	29249.4i	0.513760	−	1.05160i
$919$	20114.3			0.721993			0.360996	−	0.932567i	$-0.382437\pi$
$919$	20114.3			0.721993			0.360996	+	0.932567i	$0.382437\pi$
$920$	−40042.1	−	69355.0i	−1.43495	−	2.48540i
$921$	−5518.57	+	4851.72i	−0.197441	+	0.173583i
$922$	−609.017	+	1054.85i	−0.0217537	+	0.0376785i
$923$	4818.32	−	8345.57i	0.171828	−	0.297614i
$924$	21885.8	+	7399.12i	0.779211	+	0.263434i
$925$	6049.37	+	10477.8i	0.215029	+	0.372442i
$926$	−87803.3			−3.11598
$927$	18853.6	+	14393.0i	0.667997	+	0.509956i
$928$	29271.1			1.03542
$929$	−18614.8	−	32241.8i	−0.657409	−	1.13867i	−0.981284	−	0.192566i	$-0.938319\pi$
$929$	−18614.8	−	32241.8i	−0.657409	−	1.13867i	0.323875	−	0.946100i	$-0.395014\pi$
$930$	4709.74	+	23525.6i	0.166063	+	0.829500i
$931$	−668.348	+	1157.61i	−0.0235276	+	0.0407510i
$932$	38311.4	−	66357.3i	1.34649	−	2.33219i
$933$	−1605.19	−	8018.08i	−0.0563253	−	0.281351i
$934$	17888.5	+	30983.7i	0.626690	+	1.08546i
$935$	−38525.3			−1.34750
$936$	23135.6	+	17661.9i	0.807916	+	0.616772i
$937$	−27280.4			−0.951133			−0.475566	−	0.879680i	$-0.657757\pi$
$937$	−27280.4			−0.951133			−0.475566	+	0.879680i	$0.657757\pi$
$938$	−5591.95	−	9685.54i	−0.194652	−	0.337147i
$939$	−35210.0	−	11903.7i	−1.22368	−	0.413698i
$940$	60166.8	−	104212.i	2.08769	−	3.61598i
$941$	−403.808	+	699.415i	−0.0139891	+	0.0242298i	−0.872935	−	0.487836i	$-0.837786\pi$
$941$	−403.808	+	699.415i	−0.0139891	+	0.0242298i	0.858946	+	0.512066i	$0.171120\pi$
$942$	2708.08	−	2380.85i	0.0936667	−	0.0823483i
$943$	−21428.7	−	37115.7i	−0.739996	−	1.28171i
$944$	5668.34			0.195433
$945$	9044.39	+	13427.9i	0.311338	+	0.462234i
$946$	70981.9			2.43956
$947$	1590.43	+	2754.70i	0.0545744	+	0.0945257i	0.892022	−	0.451992i	$-0.149286\pi$
$947$	1590.43	+	2754.70i	0.0545744	+	0.0945257i	−0.837448	+	0.546518i	$0.815953\pi$
$948$	−896.127	+	787.842i	−0.0307013	+	0.0269915i
$949$	−8746.61	+	15149.6i	−0.299185	+	0.518204i
$950$	−9298.84	+	16106.1i	−0.317573	+	0.550052i
$951$	36875.6	+	12466.8i	1.25739	+	0.425094i
$952$	4528.93	+	7844.35i	0.154184	+	0.267055i
$953$	−35239.3			−1.19781			−0.598906	−	0.800819i	$-0.704398\pi$
$953$	−35239.3			−1.19781			−0.598906	+	0.800819i	$0.704398\pi$
$954$	−64240.7	+	26795.4i	−2.18016	+	0.909364i
$955$	5931.94			0.200998
$956$	−2535.58	−	4391.75i	−0.0857809	−	0.148577i
$957$	9139.86	+	45654.5i	0.308725	+	1.54211i
$958$	−38287.0	+	66315.0i	−1.29123	+	2.23647i
$959$	6469.20	−	11205.0i	0.217832	−	0.377297i
$960$	13512.5	+	67496.4i	0.454286	+	2.26921i
$961$	13077.6	+	22651.1i	0.438978	+	0.760332i
$962$	−15935.4			−0.534071
$963$	−2876.23	+	22272.0i	−0.0962463	+	0.745280i
$964$	−1920.62			−0.0641692
$965$	15556.5	+	26944.6i	0.518944	+	0.898838i
$966$	30015.8	+	10147.7i	0.999735	+	0.337988i
$967$	−7961.06	+	13789.0i	−0.264747	+	0.458556i	−0.967497	−	0.252881i	$-0.918622\pi$
$967$	−7961.06	+	13789.0i	−0.264747	+	0.458556i	0.702750	+	0.711437i	$0.251955\pi$
$968$	−11108.5	+	19240.5i	−0.368845	+	0.638858i
$969$	−5317.78	+	4675.20i	−0.176297	+	0.154994i
$970$	−3056.06	−	5293.26i	−0.101159	−	0.175213i
$971$	9265.09			0.306211			0.153105	−	0.988210i	$-0.451073\pi$
$971$	9265.09			0.306211			0.153105	+	0.988210i	$0.451073\pi$
$972$	3046.71	−	51338.2i	0.100538	−	1.69411i
$973$	−15371.0			−0.506446
$974$	−30641.7	−	53072.9i	−1.00803	−	1.74596i
$975$	23835.5	−	20955.3i	0.782920	−	0.688314i
$976$	4280.34	−	7413.77i	0.140380	−	0.243145i
$977$	8299.12	−	14374.5i	0.271763	−	0.470707i	−0.697550	−	0.716536i	$-0.745727\pi$
$977$	8299.12	−	14374.5i	0.271763	−	0.470707i	0.969313	+	0.245828i	$0.0790600\pi$
$978$	−31649.7	−	10700.1i	−1.03481	−	0.349847i
$979$	−4430.53	−	7673.90i	−0.144638	−	0.250520i
$980$	−10967.0			−0.357479
$981$	2562.06	−	19839.2i	0.0833845	−	0.645685i
$982$	946.289			0.0307508
$983$	9492.78	+	16442.0i	0.308009	+	0.533487i	0.977927	−	0.208948i	$-0.0670041\pi$
$983$	9492.78	+	16442.0i	0.308009	+	0.533487i	−0.669918	+	0.742435i	$0.733671\pi$
$984$	−6038.42	−	30162.5i	−0.195628	−	0.977180i
$985$	22074.9	−	38234.9i	0.714076	−	1.23682i
$986$	−22221.1	+	38488.1i	−0.717712	+	1.24311i
$987$	3838.81	+	19175.2i	0.123800	+	0.618393i
$988$	−7706.54	−	13348.1i	−0.248156	−	0.429818i
$989$	61255.4			1.96947
$990$	−89271.7	+	37236.1i	−2.86590	+	1.19539i
$991$	48866.0			1.56638			0.783189	−	0.621784i	$-0.213592\pi$
$991$	48866.0			1.56638			0.783189	+	0.621784i	$0.213592\pi$
$992$	−4607.49	−	7980.40i	−0.147468	−	0.255421i
$993$	−2956.76	−	999.617i	−0.0944915	−	0.0319455i
$994$	3764.68	−	6520.61i	0.120129	−	0.208070i
$995$	20851.9	−	36116.6i	0.664372	−	1.15073i
$996$	28984.4	−	25482.0i	0.922093	−	0.810670i
$997$	−30130.8	−	52188.1i	−0.957124	−	1.65779i	−0.729431	−	0.684054i	$-0.760215\pi$
$997$	−30130.8	−	52188.1i	−0.957124	−	1.65779i	−0.227692	−	0.973733i	$-0.573118\pi$
$998$	−77256.0			−2.45040
$999$	6460.90	+	9592.32i	0.204619	+	0.303791i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.f.c.22.1	✓	18
3.2	odd	2		189.4.f.c.64.9		18
9.2	odd	6		189.4.f.c.127.9		18
9.4	even	3		567.4.a.j.1.9		9
9.5	odd	6		567.4.a.k.1.1		9
9.7	even	3	inner	63.4.f.c.43.1	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.f.c.22.1	✓	18	1.1	even	1	trivial
63.4.f.c.43.1	yes	18	9.7	even	3	inner
189.4.f.c.64.9		18	3.2	odd	2
189.4.f.c.127.9		18	9.2	odd	6
567.4.a.j.1.9		9	9.4	even	3
567.4.a.k.1.1		9	9.5	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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.32254 - 4.02275i) q^{2} +(3.90244 - 3.43088i) q^{3} +(-6.78835 + 11.7578i) q^{4} +(8.24268 - 14.2767i) q^{5} +(-22.8651 - 7.73020i) q^{6} +(-3.50000 - 6.06218i) q^{7} +25.9042 q^{8} +(3.45809 - 26.7776i) q^{9} +O(q^{10})\)	\(q+(-2.32254 - 4.02275i) q^{2} +(3.90244 - 3.43088i) q^{3} +(-6.78835 + 11.7578i) q^{4} +(8.24268 - 14.2767i) q^{5} +(-22.8651 - 7.73020i) q^{6} +(-3.50000 - 6.06218i) q^{7} +25.9042 q^{8} +(3.45809 - 26.7776i) q^{9} -76.5757 q^{10} +(23.3916 + 40.5154i) q^{11} +(13.8484 + 69.1741i) q^{12} +(-20.8079 + 36.0404i) q^{13} +(-16.2578 + 28.1593i) q^{14} +(-16.8153 - 83.9939i) q^{15} +(-5.85664 - 10.1440i) q^{16} -49.9526 q^{17} +(-115.751 + 48.2810i) q^{18} +27.2795 q^{19} +(111.909 + 193.831i) q^{20} +(-34.4572 - 11.6492i) q^{21} +(108.656 - 188.197i) q^{22} +(93.7666 - 162.409i) q^{23} +(101.090 - 88.8743i) q^{24} +(-73.3837 - 127.104i) q^{25} +193.309 q^{26} +(-78.3759 - 116.362i) q^{27} +95.0369 q^{28} +(95.7669 + 165.873i) q^{29} +(-298.832 + 262.722i) q^{30} +(30.1489 - 52.2194i) q^{31} +(76.4123 - 132.350i) q^{32} +(230.288 + 77.8552i) q^{33} +(116.017 + 200.947i) q^{34} -115.398 q^{35} +(291.371 + 222.435i) q^{36} -82.4348 q^{37} +(-63.3577 - 109.739i) q^{38} +(42.4486 + 212.035i) q^{39} +(213.520 - 369.828i) q^{40} +(114.266 - 197.915i) q^{41} +(33.1662 + 165.668i) q^{42} +(163.319 + 282.876i) q^{43} -635.161 q^{44} +(-353.794 - 270.090i) q^{45} -871.106 q^{46} +(-268.821 - 465.612i) q^{47} +(-57.6581 - 19.4929i) q^{48} +(-24.5000 + 42.4352i) q^{49} +(-340.873 + 590.409i) q^{50} +(-194.937 + 171.381i) q^{51} +(-282.503 - 489.309i) q^{52} +554.989 q^{53} +(-286.066 + 585.543i) q^{54} +771.237 q^{55} +(-90.6647 - 157.036i) q^{56} +(106.457 - 93.5928i) q^{57} +(444.844 - 770.493i) q^{58} +(-241.962 + 419.090i) q^{59} +(1101.73 + 372.470i) q^{60} +(365.426 + 632.937i) q^{61} -280.087 q^{62} +(-174.434 + 72.7581i) q^{63} -803.588 q^{64} +(343.026 + 594.139i) q^{65} +(-221.660 - 1107.21i) q^{66} +(-171.978 + 297.875i) q^{67} +(339.096 - 587.331i) q^{68} +(-191.286 - 955.492i) q^{69} +(268.015 + 464.216i) q^{70} -231.562 q^{71} +(89.5792 - 693.653i) q^{72} +420.350 q^{73} +(191.458 + 331.615i) q^{74} +(-722.455 - 244.246i) q^{75} +(-185.183 + 320.746i) q^{76} +(163.741 - 283.608i) q^{77} +(754.375 - 663.219i) q^{78} +(8.45685 + 14.6477i) q^{79} -193.098 q^{80} +(-705.083 - 185.199i) q^{81} -1061.55 q^{82} +(-273.529 - 473.766i) q^{83} +(370.876 - 326.061i) q^{84} +(-411.743 + 713.160i) q^{85} +(758.627 - 1313.98i) q^{86} +(942.816 + 318.745i) q^{87} +(605.940 + 1049.52i) q^{88} -189.407 q^{89} +(-264.806 + 2050.52i) q^{90} +291.311 q^{91} +(1273.04 + 2204.97i) q^{92} +(-61.5043 - 307.220i) q^{93} +(-1248.69 + 2162.80i) q^{94} +(224.856 - 389.463i) q^{95} +(-155.883 - 778.649i) q^{96} +(39.9090 + 69.1245i) q^{97} +227.609 q^{98} +(1165.80 - 486.265i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9}+O(q^{10}) \) 18 * q + 6 * q^2 + 9 * q^3 - 36 * q^4 + 24 * q^5 - 63 * q^7 - 150 * q^8 + 63 * q^9	\( 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9} + 111 q^{11} - 18 q^{13} + 42 q^{14} - 36 q^{15} - 144 q^{16} - 546 q^{17} - 45 q^{18} + 90 q^{19} + 402 q^{20} - 63 q^{21} + 162 q^{22} + 312 q^{23} - 36 q^{24} - 279 q^{25} + 102 q^{26} + 432 q^{27} + 504 q^{28} + 378 q^{29} - 864 q^{30} - 18 q^{31} + 891 q^{32} + 513 q^{33} + 324 q^{34} - 336 q^{35} + 414 q^{36} - 72 q^{37} + 147 q^{38} - 810 q^{39} - 405 q^{40} + 477 q^{41} + 315 q^{42} + 171 q^{43} - 1896 q^{44} - 720 q^{45} - 756 q^{46} + 654 q^{47} - 2709 q^{48} - 441 q^{49} + 429 q^{50} + 1341 q^{51} - 747 q^{52} - 1896 q^{53} - 108 q^{54} - 432 q^{55} + 525 q^{56} - 1143 q^{57} - 297 q^{58} + 957 q^{59} + 5400 q^{60} + 198 q^{61} - 600 q^{62} - 504 q^{63} + 4770 q^{64} + 2478 q^{65} - 2646 q^{66} + 333 q^{67} + 1443 q^{68} + 3366 q^{69} - 5652 q^{71} - 3681 q^{72} + 306 q^{73} + 2100 q^{74} - 4113 q^{75} + 144 q^{76} + 777 q^{77} + 6336 q^{78} - 1152 q^{79} - 8418 q^{80} - 1917 q^{81} - 6048 q^{82} + 1890 q^{83} + 1008 q^{84} + 648 q^{85} + 3837 q^{86} + 4212 q^{87} + 2268 q^{88} - 2604 q^{89} - 135 q^{90} + 252 q^{91} + 987 q^{92} + 378 q^{93} - 324 q^{94} + 3144 q^{95} + 5643 q^{96} + 1737 q^{97} - 588 q^{98} + 720 q^{99}+O(q^{100}) \) 18 * q + 6 * q^2 + 9 * q^3 - 36 * q^4 + 24 * q^5 - 63 * q^7 - 150 * q^8 + 63 * q^9 + 111 * q^11 - 18 * q^13 + 42 * q^14 - 36 * q^15 - 144 * q^16 - 546 * q^17 - 45 * q^18 + 90 * q^19 + 402 * q^20 - 63 * q^21 + 162 * q^22 + 312 * q^23 - 36 * q^24 - 279 * q^25 + 102 * q^26 + 432 * q^27 + 504 * q^28 + 378 * q^29 - 864 * q^30 - 18 * q^31 + 891 * q^32 + 513 * q^33 + 324 * q^34 - 336 * q^35 + 414 * q^36 - 72 * q^37 + 147 * q^38 - 810 * q^39 - 405 * q^40 + 477 * q^41 + 315 * q^42 + 171 * q^43 - 1896 * q^44 - 720 * q^45 - 756 * q^46 + 654 * q^47 - 2709 * q^48 - 441 * q^49 + 429 * q^50 + 1341 * q^51 - 747 * q^52 - 1896 * q^53 - 108 * q^54 - 432 * q^55 + 525 * q^56 - 1143 * q^57 - 297 * q^58 + 957 * q^59 + 5400 * q^60 + 198 * q^61 - 600 * q^62 - 504 * q^63 + 4770 * q^64 + 2478 * q^65 - 2646 * q^66 + 333 * q^67 + 1443 * q^68 + 3366 * q^69 - 5652 * q^71 - 3681 * q^72 + 306 * q^73 + 2100 * q^74 - 4113 * q^75 + 144 * q^76 + 777 * q^77 + 6336 * q^78 - 1152 * q^79 - 8418 * q^80 - 1917 * q^81 - 6048 * q^82 + 1890 * q^83 + 1008 * q^84 + 648 * q^85 + 3837 * q^86 + 4212 * q^87 + 2268 * q^88 - 2604 * q^89 - 135 * q^90 + 252 * q^91 + 987 * q^92 + 378 * q^93 - 324 * q^94 + 3144 * q^95 + 5643 * q^96 + 1737 * q^97 - 588 * q^98 + 720 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more