LMFDB - Embedded newform 63.4.f.b.22.3

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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 58 x^{14} - 129 x^{13} + 2107 x^{12} - 4455 x^{11} + 42901 x^{10} - 76404 x^{9} + \cdots + 21307456 $ x^16 - 3x^15 + 58x^14 - 129x^13 + 2107x^12 - 4455x^11 + 42901x^10 - 76404x^9 + 599392x^8 - 1089732x^7 + 4808401x^6 - 7939134x^5 + 26225236x^4 - 39450864x^3 + 62254768x^2 - 39660672*x + 21307456
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.3
Root			$1.30789 + 2.26533i$ of defining polynomial
Character	$\chi$	$=$	63.22
Dual form			63.4.f.b.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30789 - 2.26533i) q^{2} +(-3.13193 - 4.14620i) q^{3} +(0.578868 - 1.00263i) q^{4} +(6.77153 - 11.7286i) q^{5} +(-5.29628 + 12.5176i) q^{6} +(3.50000 + 6.06218i) q^{7} -23.9546 q^{8} +(-7.38198 + 25.9713i) q^{9} +O(q^{10})$	\(q+(-1.30789 - 2.26533i) q^{2} +(-3.13193 - 4.14620i) q^{3} +(0.578868 - 1.00263i) q^{4} +(6.77153 - 11.7286i) q^{5} +(-5.29628 + 12.5176i) q^{6} +(3.50000 + 6.06218i) q^{7} -23.9546 q^{8} +(-7.38198 + 25.9713i) q^{9} -35.4255 q^{10} +(-12.0346 - 20.8445i) q^{11} +(-5.97007 + 0.740063i) q^{12} +(-11.9972 + 20.7798i) q^{13} +(9.15520 - 15.8573i) q^{14} +(-69.8372 + 8.65717i) q^{15} +(26.6989 + 46.2438i) q^{16} +79.6971 q^{17} +(68.4881 - 17.2449i) q^{18} -50.0463 q^{19} +(-7.83963 - 13.5786i) q^{20} +(14.1732 - 33.4980i) q^{21} +(-31.4798 + 54.5245i) q^{22} +(75.8039 - 131.296i) q^{23} +(75.0241 + 99.3204i) q^{24} +(-29.2071 - 50.5883i) q^{25} +62.7639 q^{26} +(130.802 - 50.7331i) q^{27} +8.10415 q^{28} +(-128.062 - 221.810i) q^{29} +(110.950 + 146.881i) q^{30} +(1.36254 - 2.35999i) q^{31} +(-25.9800 + 44.9987i) q^{32} +(-48.7341 + 115.182i) q^{33} +(-104.235 - 180.540i) q^{34} +94.8014 q^{35} +(21.7663 + 22.4353i) q^{36} +319.617 q^{37} +(65.4548 + 113.371i) q^{38} +(123.732 - 15.3380i) q^{39} +(-162.209 + 280.954i) q^{40} +(-82.3892 + 142.702i) q^{41} +(-94.4210 + 11.7046i) q^{42} +(-211.384 - 366.129i) q^{43} -27.8657 q^{44} +(254.620 + 262.446i) q^{45} -396.571 q^{46} +(-50.0386 - 86.6693i) q^{47} +(108.117 - 255.532i) q^{48} +(-24.5000 + 42.4352i) q^{49} +(-76.3992 + 132.327i) q^{50} +(-249.606 - 330.440i) q^{51} +(13.8896 + 24.0575i) q^{52} +194.981 q^{53} +(-286.001 - 229.956i) q^{54} -325.970 q^{55} +(-83.8409 - 145.217i) q^{56} +(156.742 + 207.502i) q^{57} +(-334.981 + 580.204i) q^{58} +(-288.258 + 499.277i) q^{59} +(-31.7466 + 75.0321i) q^{60} +(21.5192 + 37.2723i) q^{61} -7.12819 q^{62} +(-183.279 + 46.1485i) q^{63} +563.098 q^{64} +(162.479 + 281.422i) q^{65} +(324.662 - 40.2458i) q^{66} +(508.257 - 880.326i) q^{67} +(46.1341 - 79.9065i) q^{68} +(-781.793 + 96.9127i) q^{69} +(-123.989 - 214.756i) q^{70} -509.305 q^{71} +(176.832 - 622.130i) q^{72} +1039.67 q^{73} +(-418.023 - 724.037i) q^{74} +(-118.274 + 279.538i) q^{75} +(-28.9702 + 50.1778i) q^{76} +(84.2422 - 145.912i) q^{77} +(-196.572 - 260.232i) q^{78} +(447.071 + 774.349i) q^{79} +723.169 q^{80} +(-620.013 - 383.439i) q^{81} +431.023 q^{82} +(-7.23057 - 12.5237i) q^{83} +(-25.3816 - 33.6014i) q^{84} +(539.671 - 934.738i) q^{85} +(-552.934 + 957.709i) q^{86} +(-518.587 + 1225.66i) q^{87} +(288.283 + 499.321i) q^{88} +1532.12 q^{89} +(261.511 - 920.046i) q^{90} -167.961 q^{91} +(-87.7608 - 152.006i) q^{92} +(-14.0524 + 1.74196i) q^{93} +(-130.889 + 226.707i) q^{94} +(-338.890 + 586.974i) q^{95} +(267.941 - 33.2146i) q^{96} +(887.575 + 1537.32i) q^{97} +128.173 q^{98} +(630.198 - 158.680i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} + 2 q^{3} - 43 q^{4} - 30 q^{5} + 19 q^{6} + 56 q^{7} + 12 q^{8} - 124 q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 + 2 * q^3 - 43 * q^4 - 30 * q^5 + 19 * q^6 + 56 * q^7 + 12 * q^8 - 124 * q^9	\( 16 q - 3 q^{2} + 2 q^{3} - 43 q^{4} - 30 q^{5} + 19 q^{6} + 56 q^{7} + 12 q^{8} - 124 q^{9} - 28 q^{10} - 24 q^{11} + 268 q^{12} - 68 q^{13} + 21 q^{14} + 56 q^{15} - 103 q^{16} + 336 q^{17} - 479 q^{18} + 352 q^{19} - 330 q^{20} + 70 q^{21} - 151 q^{22} - 228 q^{23} - 195 q^{24} - 244 q^{25} + 1590 q^{26} + 272 q^{27} - 602 q^{28} - 618 q^{29} + 1030 q^{30} - 72 q^{31} - 786 q^{32} - 700 q^{33} + 261 q^{34} - 420 q^{35} + 727 q^{36} + 420 q^{37} - 1032 q^{38} - 22 q^{39} + 375 q^{40} - 420 q^{41} - 175 q^{42} + 2 q^{43} + 774 q^{44} + 1406 q^{45} + 804 q^{46} - 570 q^{47} + 1864 q^{48} - 392 q^{49} - 1110 q^{50} - 2940 q^{51} + 431 q^{52} + 1056 q^{53} + 2269 q^{54} - 1676 q^{55} + 42 q^{56} + 122 q^{57} - 37 q^{58} + 150 q^{59} - 6350 q^{60} - 578 q^{61} + 2340 q^{62} - 350 q^{63} - 224 q^{64} + 366 q^{65} + 5812 q^{66} + 898 q^{67} - 2526 q^{68} - 2166 q^{69} - 98 q^{70} + 1764 q^{71} + 1350 q^{72} + 1944 q^{73} + 222 q^{74} - 2096 q^{75} - 1423 q^{76} + 168 q^{77} - 5558 q^{78} + 158 q^{79} + 4950 q^{80} + 476 q^{81} - 422 q^{82} - 2958 q^{83} + 1715 q^{84} + 774 q^{85} + 114 q^{86} + 44 q^{87} - 1317 q^{88} + 8760 q^{89} - 3659 q^{90} - 952 q^{91} - 4629 q^{92} + 3954 q^{93} + 3234 q^{94} - 930 q^{95} - 5923 q^{96} + 60 q^{97} + 294 q^{98} + 1214 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + 2 * q^3 - 43 * q^4 - 30 * q^5 + 19 * q^6 + 56 * q^7 + 12 * q^8 - 124 * q^9 - 28 * q^10 - 24 * q^11 + 268 * q^12 - 68 * q^13 + 21 * q^14 + 56 * q^15 - 103 * q^16 + 336 * q^17 - 479 * q^18 + 352 * q^19 - 330 * q^20 + 70 * q^21 - 151 * q^22 - 228 * q^23 - 195 * q^24 - 244 * q^25 + 1590 * q^26 + 272 * q^27 - 602 * q^28 - 618 * q^29 + 1030 * q^30 - 72 * q^31 - 786 * q^32 - 700 * q^33 + 261 * q^34 - 420 * q^35 + 727 * q^36 + 420 * q^37 - 1032 * q^38 - 22 * q^39 + 375 * q^40 - 420 * q^41 - 175 * q^42 + 2 * q^43 + 774 * q^44 + 1406 * q^45 + 804 * q^46 - 570 * q^47 + 1864 * q^48 - 392 * q^49 - 1110 * q^50 - 2940 * q^51 + 431 * q^52 + 1056 * q^53 + 2269 * q^54 - 1676 * q^55 + 42 * q^56 + 122 * q^57 - 37 * q^58 + 150 * q^59 - 6350 * q^60 - 578 * q^61 + 2340 * q^62 - 350 * q^63 - 224 * q^64 + 366 * q^65 + 5812 * q^66 + 898 * q^67 - 2526 * q^68 - 2166 * q^69 - 98 * q^70 + 1764 * q^71 + 1350 * q^72 + 1944 * q^73 + 222 * q^74 - 2096 * q^75 - 1423 * q^76 + 168 * q^77 - 5558 * q^78 + 158 * q^79 + 4950 * q^80 + 476 * q^81 - 422 * q^82 - 2958 * q^83 + 1715 * q^84 + 774 * q^85 + 114 * q^86 + 44 * q^87 - 1317 * q^88 + 8760 * q^89 - 3659 * q^90 - 952 * q^91 - 4629 * q^92 + 3954 * q^93 + 3234 * q^94 - 930 * q^95 - 5923 * q^96 + 60 * q^97 + 294 * q^98 + 1214 * 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 $

$2$	−1.30789	−	2.26533i	−0.462408	−	0.800913i	0.536673	−	0.843790i	$-0.319681\pi$
$2$	−1.30789	−	2.26533i	−0.462408	−	0.800913i	−0.999080	+	0.0428770i	$0.986348\pi$
$3$	−3.13193	−	4.14620i	−0.602741	−	0.797937i
$3$	−3.13193	−	4.14620i	−0.602741	−	0.797937i
$4$	0.578868	−	1.00263i	0.0723584	−	0.125328i
$5$	6.77153	−	11.7286i	0.605664	−	1.04904i	−0.386282	−	0.922381i	$-0.626241\pi$
$5$	6.77153	−	11.7286i	0.605664	−	1.04904i	0.991946	−	0.126660i	$-0.0404257\pi$
$6$	−5.29628	+	12.5176i	−0.360366	+	0.851715i
$7$	3.50000	+	6.06218i	0.188982	+	0.327327i
$7$	3.50000	+	6.06218i	0.188982	+	0.327327i
$8$	−23.9546			−1.05865
$9$	−7.38198	+	25.9713i	−0.273407	+	0.961899i
$10$	−35.4255			−1.12025
$11$	−12.0346	−	20.8445i	−0.329870	−	0.571351i	0.652616	−	0.757689i	$-0.273671\pi$
$11$	−12.0346	−	20.8445i	−0.329870	−	0.571351i	−0.982486	+	0.186338i	$0.940338\pi$
$12$	−5.97007	+	0.740063i	−0.143618	+	0.0178031i
$13$	−11.9972	+	20.7798i	−0.255956	+	0.443329i	−0.965155	−	0.261680i	$-0.915724\pi$
$13$	−11.9972	+	20.7798i	−0.255956	+	0.443329i	0.709199	+	0.705009i	$0.249057\pi$
$14$	9.15520	−	15.8573i	0.174774	−	0.302717i
$15$	−69.8372	+	8.65717i	−1.20213	+	0.149018i
$16$	26.6989	+	46.2438i	0.417170	+	0.722560i
$17$	79.6971			1.13702			0.568511	−	0.822675i	$-0.307520\pi$
$17$	79.6971			1.13702			0.568511	+	0.822675i	$0.307520\pi$
$18$	68.4881	−	17.2449i	0.896823	−	0.225814i
$19$	−50.0463			−0.604284			−0.302142	−	0.953263i	$-0.597702\pi$
$19$	−50.0463			−0.604284			−0.302142	+	0.953263i	$0.597702\pi$
$20$	−7.83963	−	13.5786i	−0.0876498	−	0.151814i
$21$	14.1732	−	33.4980i	0.147279	−	0.348089i
$22$	−31.4798	+	54.5245i	−0.305069	+	0.528394i
$23$	75.8039	−	131.296i	0.687226	−	1.19031i	−0.285506	−	0.958377i	$-0.592162\pi$
$23$	75.8039	−	131.296i	0.687226	−	1.19031i	0.972732	−	0.231933i	$-0.0745051\pi$
$24$	75.0241	+	99.3204i	0.638093	+	0.844737i
$25$	−29.2071	−	50.5883i	−0.233657	−	0.404706i
$26$	62.7639			0.473424
$27$	130.802	−	50.7331i	0.932328	−	0.361614i
$28$	8.10415			0.0546978
$29$	−128.062	−	221.810i	−0.820018	−	1.42031i	−0.905668	−	0.423987i	$-0.860630\pi$
$29$	−128.062	−	221.810i	−0.820018	−	1.42031i	0.0856508	−	0.996325i	$-0.472703\pi$
$30$	110.950	+	146.881i	0.675223	+	0.893892i
$31$	1.36254	−	2.35999i	0.00789417	−	0.0136731i	−0.862051	−	0.506821i	$-0.830821\pi$
$31$	1.36254	−	2.35999i	0.00789417	−	0.0136731i	0.869946	+	0.493148i	$0.164154\pi$
$32$	−25.9800	+	44.9987i	−0.143521	+	0.248585i
$33$	−48.7341	+	115.182i	−0.257076	+	0.607592i
$34$	−104.235	−	180.540i	−0.525768	−	0.910657i
$35$	94.8014			0.457839
$36$	21.7663	+	22.4353i	0.100770	+	0.103867i
$37$	319.617			1.42013			0.710065	−	0.704137i	$-0.248666\pi$
$37$	319.617			1.42013			0.710065	+	0.704137i	$0.248666\pi$
$38$	65.4548	+	113.371i	0.279426	+	0.483979i
$39$	123.732	−	15.3380i	0.508023	−	0.0629756i
$40$	−162.209	+	280.954i	−0.641187	+	1.11057i
$41$	−82.3892	+	142.702i	−0.313830	+	0.543570i	−0.979188	−	0.202955i	$-0.934946\pi$
$41$	−82.3892	+	142.702i	−0.313830	+	0.543570i	0.665358	+	0.746524i	$0.268279\pi$
$42$	−94.4210	+	11.7046i	−0.346892	+	0.0430015i
$43$	−211.384	−	366.129i	−0.749670	−	1.29847i	−0.947981	−	0.318328i	$-0.896879\pi$
$43$	−211.384	−	366.129i	−0.749670	−	1.29847i	0.198310	−	0.980139i	$-0.436455\pi$
$44$	−27.8657			−0.0954754
$45$	254.620	+	262.446i	0.843478	+	0.869402i
$46$	−396.571			−1.27111
$47$	−50.0386	−	86.6693i	−0.155295	−	0.268979i	0.777871	−	0.628424i	$-0.216300\pi$
$47$	−50.0386	−	86.6693i	−0.155295	−	0.268979i	−0.933166	+	0.359444i	$0.882966\pi$
$48$	108.117	−	255.532i	0.325112	−	0.768392i
$49$	−24.5000	+	42.4352i	−0.0714286	+	0.123718i
$50$	−76.3992	+	132.327i	−0.216090	+	0.374278i
$51$	−249.606	−	330.440i	−0.685330	−	0.907272i
$52$	13.8896	+	24.0575i	0.0370411	+	0.0641571i
$53$	194.981			0.505333			0.252667	−	0.967553i	$-0.418692\pi$
$53$	194.981			0.505333			0.252667	+	0.967553i	$0.418692\pi$
$54$	−286.001	−	229.956i	−0.720737	−	0.579501i
$55$	−325.970			−0.799160
$56$	−83.8409	−	145.217i	−0.200066	−	0.346525i
$57$	156.742	+	207.502i	0.364227	+	0.482181i
$58$	−334.981	+	580.204i	−0.758365	+	1.31353i
$59$	−288.258	+	499.277i	−0.636067	+	1.10170i	0.350221	+	0.936667i	$0.386106\pi$
$59$	−288.258	+	499.277i	−0.636067	+	1.10170i	−0.986288	+	0.165033i	$0.947227\pi$
$60$	−31.7466	+	75.0321i	−0.0683078	+	0.161443i
$61$	21.5192	+	37.2723i	0.0451680	+	0.0782332i	0.887726	−	0.460373i	$-0.152284\pi$
$61$	21.5192	+	37.2723i	0.0451680	+	0.0782332i	−0.842558	+	0.538606i	$0.818951\pi$
$62$	−7.12819			−0.0146013
$63$	−183.279	+	46.1485i	−0.366524	+	0.0922884i
$64$	563.098			1.09980
$65$	162.479	+	281.422i	0.310046	+	0.537016i
$66$	324.662	−	40.2458i	0.605502	−	0.0750594i
$67$	508.257	−	880.326i	0.926768	−	1.60521i	0.138074	−	0.990422i	$-0.455909\pi$
$67$	508.257	−	880.326i	0.926768	−	1.60521i	0.788693	−	0.614787i	$-0.210758\pi$
$68$	46.1341	−	79.9065i	0.0822732	−	0.142501i
$69$	−781.793	+	96.9127i	−1.36401	+	0.169086i
$70$	−123.989	−	214.756i	−0.211708	−	0.366689i
$71$	−509.305			−0.851315			−0.425657	−	0.904884i	$-0.639957\pi$
$71$	−509.305			−0.851315			−0.425657	+	0.904884i	$0.639957\pi$
$72$	176.832	−	622.130i	0.289442	−	1.01832i
$73$	1039.67			1.66690			0.833452	−	0.552592i	$-0.186361\pi$
$73$	1039.67			1.66690			0.833452	+	0.552592i	$0.186361\pi$
$74$	−418.023	−	724.037i	−0.656678	−	1.13740i
$75$	−118.274	+	279.538i	−0.182095	+	0.430377i
$76$	−28.9702	+	50.1778i	−0.0437251	+	0.0757341i
$77$	84.2422	−	145.912i	0.124679	−	0.215950i
$78$	−196.572	−	260.232i	−0.285352	−	0.377762i
$79$	447.071	+	774.349i	0.636701	+	1.10280i	0.986152	+	0.165844i	$0.0530347\pi$
$79$	447.071	+	774.349i	0.636701	+	1.10280i	−0.349451	+	0.936955i	$0.613632\pi$
$80$	723.169			1.01066
$81$	−620.013	−	383.439i	−0.850498	−	0.525979i
$82$	431.023			0.580470
$83$	−7.23057	−	12.5237i	−0.00956214	−	0.0165621i	0.861205	−	0.508258i	$-0.169710\pi$
$83$	−7.23057	−	12.5237i	−0.00956214	−	0.0165621i	−0.870767	+	0.491696i	$0.836377\pi$
$84$	−25.3816	−	33.6014i	−0.0329686	−	0.0436454i
$85$	539.671	−	934.738i	0.688653	−	1.19278i
$86$	−552.934	+	957.709i	−0.693307	+	1.20084i
$87$	−518.587	+	1225.66i	−0.639061	+	1.51040i
$88$	288.283	+	499.321i	0.349217	+	0.604862i
$89$	1532.12			1.82477			0.912384	−	0.409336i	$-0.134240\pi$
$89$	1532.12			1.82477			0.912384	+	0.409336i	$0.134240\pi$
$90$	261.511	−	920.046i	0.306285	−	1.07757i
$91$	−167.961			−0.193484
$92$	−87.7608	−	152.006i	−0.0994532	−	0.172258i
$93$	−14.0524	+	1.74196i	−0.0156684	+	0.00194229i
$94$	−130.889	+	226.707i	−0.143619	+	0.248756i
$95$	−338.890	+	586.974i	−0.365993	+	0.633919i
$96$	267.941	−	33.2146i	0.284861	−	0.0353119i
$97$	887.575	+	1537.32i	0.929067	+	1.60919i	0.784886	+	0.619641i	$0.212722\pi$
$97$	887.575	+	1537.32i	0.929067	+	1.60919i	0.144182	+	0.989551i	$0.453945\pi$
$98$	128.173			0.132116
$99$	630.198	−	158.680i	0.639770	−	0.161090i
$100$	−67.6283			−0.0676283
$101$	−169.349	−	293.320i	−0.166840	−	0.288975i	0.770467	−	0.637480i	$-0.220023\pi$
$101$	−169.349	−	293.320i	−0.166840	−	0.288975i	−0.937307	+	0.348504i	$0.886690\pi$
$102$	−422.098	+	997.617i	−0.409745	+	0.968420i
$103$	225.235	−	390.119i	0.215467	−	0.373200i	−0.737950	−	0.674855i	$-0.764206\pi$
$103$	225.235	−	390.119i	0.215467	−	0.373200i	0.953417	+	0.301656i	$0.0975393\pi$
$104$	287.388	−	497.770i	0.270968	−	0.469331i
$105$	−296.912	−	393.066i	−0.275958	−	0.365326i
$106$	−255.013	−	441.695i	−0.233670	−	0.404728i
$107$	−581.208			−0.525117			−0.262558	−	0.964916i	$-0.584566\pi$
$107$	−581.208			−0.525117			−0.262558	+	0.964916i	$0.584566\pi$
$108$	24.8506	−	160.513i	0.0221412	−	0.143013i
$109$	−1381.38			−1.21388			−0.606938	−	0.794749i	$-0.707602\pi$
$109$	−1381.38			−1.21388			−0.606938	+	0.794749i	$0.707602\pi$
$110$	426.332	+	738.429i	0.369538	+	0.640058i
$111$	−1001.02	−	1325.20i	−0.855970	−	1.13317i
$112$	−186.892	+	323.707i	−0.157675	+	0.273102i
$113$	−749.878	+	1298.83i	−0.624271	+	1.08127i	0.364410	+	0.931239i	$0.381271\pi$
$113$	−749.878	+	1298.83i	−0.624271	+	1.08127i	−0.988681	+	0.150031i	$0.952063\pi$
$114$	265.059	−	626.460i	0.217764	−	0.514678i
$115$	−1026.62	−	1778.15i	−0.832456	−	1.44186i
$116$	−296.524			−0.237341
$117$	−451.114	−	464.978i	−0.356457	−	0.367413i
$118$	1508.03			1.17649
$119$	278.940	+	483.138i	0.214877	+	0.372178i
$120$	1672.92	−	207.379i	1.27263	−	0.157758i
$121$	375.837	−	650.969i	0.282372	−	0.489083i
$122$	56.2892	−	97.4958i	0.0417720	−	0.0723513i
$123$	849.710	−	105.332i	0.622892	−	0.0772150i
$124$	−1.57746	−	2.73224i	−0.00114242	−	0.00197873i
$125$	901.774			0.645257
$126$	344.250	+	354.830i	0.243399	+	0.250879i
$127$	−908.229			−0.634585			−0.317292	−	0.948328i	$-0.602774\pi$
$127$	−908.229			−0.634585			−0.317292	+	0.948328i	$0.602774\pi$
$128$	−528.628	−	915.610i	−0.365035	−	0.632260i
$129$	−856.001	+	2023.13i	−0.584238	+	1.38083i
$130$	425.008	−	736.135i	0.286736	−	0.496641i
$131$	309.932	−	536.818i	0.206709	−	0.358030i	−0.743967	−	0.668216i	$-0.767058\pi$
$131$	309.932	−	536.818i	0.206709	−	0.358030i	0.950676	+	0.310186i	$0.100391\pi$
$132$	87.2737	+	115.537i	0.0575469	+	0.0761834i
$133$	−175.162	−	303.389i	−0.114199	−	0.197798i
$134$	−2658.97			−1.71418
$135$	290.700	−	1877.67i	0.185329	−	1.19707i
$136$	−1909.11			−1.20371
$137$	381.288	+	660.410i	0.237778	+	0.411844i	0.960076	−	0.279738i	$-0.0902475\pi$
$137$	381.288	+	660.410i	0.237778	+	0.411844i	−0.722298	+	0.691582i	$0.756914\pi$
$138$	1242.03	+	1644.26i	0.766152	+	1.01427i
$139$	−696.068	+	1205.63i	−0.424746	+	0.735682i	−0.996397	−	0.0848153i	$-0.972970\pi$
$139$	−696.068	+	1205.63i	−0.424746	+	0.735682i	0.571651	+	0.820497i	$0.306303\pi$
$140$	54.8774	−	95.0505i	0.0331285	−	0.0573802i
$141$	−202.631	+	478.913i	−0.121026	+	0.286041i
$142$	666.113	+	1153.74i	0.393654	+	0.681830i
$143$	577.526			0.337728
$144$	−1398.10	+	352.033i	−0.809086	+	0.203723i
$145$	−3468.70			−1.98662
$146$	−1359.77	−	2355.19i	−0.770789	−	1.33505i
$147$	252.677	−	31.3224i	0.141772	−	0.0175744i
$148$	185.016	−	320.457i	0.102758	−	0.177983i
$149$	−521.124	+	902.613i	−0.286525	+	0.496275i	−0.972978	−	0.230899i	$-0.925833\pi$
$149$	−521.124	+	902.613i	−0.286525	+	0.496275i	0.686453	+	0.727174i	$0.259167\pi$
$150$	787.933	−	97.6739i	0.428897	−	0.0531669i
$151$	−49.9139	−	86.4533i	−0.0269002	−	0.0465925i	0.852262	−	0.523115i	$-0.175230\pi$
$151$	−49.9139	−	86.4533i	−0.0269002	−	0.0465925i	−0.879162	+	0.476523i	$0.841897\pi$
$152$	1198.84			0.639727
$153$	−588.322	+	2069.83i	−0.310870	+	1.09370i
$154$	−440.717			−0.230610
$155$	−18.4529	−	31.9614i	−0.00956243	−	0.0165626i
$156$	56.2459	−	132.935i	0.0288671	−	0.0682266i
$157$	−246.721	+	427.334i	−0.125417	+	0.217229i	−0.921896	−	0.387438i	$-0.873360\pi$
$157$	−246.721	+	427.334i	−0.125417	+	0.217229i	0.796479	+	0.604666i	$0.206694\pi$
$158$	1169.43	−	2025.52i	0.588831	−	1.01988i
$159$	−610.667	−	808.430i	−0.304585	−	0.403224i
$160$	351.848	+	609.419i	0.173850	+	0.301118i
$161$	1061.25			0.519494
$162$	−57.7075	+	1906.02i	−0.0279872	+	0.924392i
$163$	2174.81			1.04506			0.522529	−	0.852622i	$-0.324989\pi$
$163$	2174.81			1.04506			0.522529	+	0.852622i	$0.324989\pi$
$164$	95.3849	+	165.211i	0.0454165	+	0.0786637i
$165$	1020.92	+	1351.54i	0.481687	+	0.637680i
$166$	−18.9135	+	32.7592i	−0.00884321	+	0.0153169i
$167$	−1150.10	+	1992.04i	−0.532921	+	0.923045i	0.466340	+	0.884605i	$0.345572\pi$
$167$	−1150.10	+	1992.04i	−0.532921	+	0.923045i	−0.999261	+	0.0384401i	$0.987761\pi$
$168$	−339.514	+	802.431i	−0.155917	+	0.368505i
$169$	810.634	+	1404.06i	0.368973	+	0.639080i
$170$	−2823.31			−1.27375
$171$	369.441	−	1299.76i	0.165215	−	0.581260i
$172$	−489.454			−0.216980
$173$	156.272	+	270.672i	0.0686773	+	0.118953i	0.898319	−	0.439343i	$-0.144789\pi$
$173$	156.272	+	270.672i	0.0686773	+	0.118953i	−0.829642	+	0.558296i	$0.811455\pi$
$174$	3454.78	−	428.262i	1.50521	−	0.186589i
$175$	204.450	−	354.118i	0.0883141	−	0.152965i
$176$	642.620	−	1113.05i	0.275224	−	0.476701i
$177$	2972.91	−	368.528i	1.26247	−	0.156499i
$178$	−2003.84	−	3470.75i	−0.843786	−	1.46148i
$179$	4345.85			1.81466			0.907329	−	0.420421i	$-0.138118\pi$
$179$	4345.85			1.81466			0.907329	+	0.420421i	$0.138118\pi$
$180$	410.527	−	103.368i	0.169994	−	0.0428033i
$181$	−110.995			−0.0455812			−0.0227906	−	0.999740i	$-0.507255\pi$
$181$	−110.995			−0.0455812			−0.0227906	+	0.999740i	$0.507255\pi$
$182$	219.674	+	380.486i	0.0894687	+	0.154964i
$183$	87.1418	−	205.957i	0.0352006	−	0.0831956i
$184$	−1815.85	+	3145.14i	−0.727533	+	1.26012i
$185$	2164.30	−	3748.67i	0.860121	−	1.48977i
$186$	22.3250	+	29.5549i	0.00880080	+	0.0116509i
$187$	−959.122	−	1661.25i	−0.375069	−	0.649639i
$188$	−115.863			−0.0449477
$189$	765.360	+	615.379i	0.294559	+	0.236837i
$190$	1772.92			0.676952
$191$	−1102.94	−	1910.35i	−0.417833	−	0.723707i	0.577889	−	0.816116i	$-0.303877\pi$
$191$	−1102.94	−	1910.35i	−0.417833	−	0.723707i	−0.995721	+	0.0924083i	$0.970543\pi$
$192$	−1763.58	−	2334.72i	−0.662895	−	0.877571i
$193$	219.259	−	379.767i	0.0817750	−	0.141639i	−0.822237	−	0.569145i	$-0.807274\pi$
$193$	219.259	−	379.767i	0.0817750	−	0.141639i	0.904012	+	0.427506i	$0.140608\pi$
$194$	2321.69	−	4021.29i	0.859216	−	1.48821i
$195$	657.958	−	1555.06i	0.241627	−	0.571079i
$196$	28.3645	+	49.1288i	0.0103369	+	0.0179041i
$197$	2536.01			0.917173			0.458587	−	0.888650i	$-0.348356\pi$
$197$	2536.01			0.917173			0.458587	+	0.888650i	$0.348356\pi$
$198$	−1183.69	−	1220.07i	−0.424854	−	0.437911i
$199$	2797.01			0.996356			0.498178	−	0.867075i	$-0.334003\pi$
$199$	2797.01			0.996356			0.498178	+	0.867075i	$0.334003\pi$
$200$	699.644	+	1211.82i	0.247361	+	0.428443i
$201$	−5241.84	+	649.789i	−1.83946	+	0.228023i
$202$	−442.978	+	767.260i	−0.154296	+	0.267248i
$203$	896.434	−	1552.67i	0.309937	−	0.536827i
$204$	−475.797	+	58.9808i	−0.163296	+	0.0202426i
$205$	1115.80	+	1932.62i	0.380151	+	0.658441i
$206$	−1178.33			−0.398534
$207$	2850.34	+	2937.95i	0.957065	+	0.986480i
$208$	−1281.25			−0.427109
$209$	602.287	+	1043.19i	0.199335	+	0.345259i
$210$	−502.095	+	1186.69i	−0.164990	+	0.389948i
$211$	−944.079	+	1635.19i	−0.308024	+	0.533514i	−0.977930	−	0.208932i	$-0.933001\pi$
$211$	−944.079	+	1635.19i	−0.308024	+	0.533514i	0.669906	+	0.742446i	$0.266334\pi$
$212$	112.868	−	195.493i	0.0365651	−	0.0633327i
$213$	1595.11	+	2111.68i	0.513122	+	0.679296i
$214$	760.154	+	1316.62i	0.242818	+	0.420573i
$215$	−5725.58			−1.81619
$216$	−3133.30	+	1215.29i	−0.987010	+	0.382824i
$217$	19.0756			0.00596743
$218$	1806.69	+	3129.28i	0.561305	+	0.972210i
$219$	−3256.17	−	4310.67i	−1.00471	−	1.33008i
$220$	−188.694	+	326.827i	−0.0578260	+	0.100158i
$221$	−956.142	+	1656.09i	−0.291028	+	0.504075i
$222$	−1692.78	+	4000.85i	−0.511767	+	1.20955i
$223$	−674.874	−	1168.92i	−0.202659	−	0.351015i	0.746725	−	0.665132i	$-0.231625\pi$
$223$	−674.874	−	1168.92i	−0.202659	−	0.351015i	−0.949384	+	0.314117i	$0.898292\pi$
$224$	−363.720			−0.108491
$225$	1529.45	−	385.105i	0.453170	−	0.114105i
$226$	3923.02			1.15467
$227$	−1242.53	−	2152.13i	−0.363303	−	0.629260i	0.625199	−	0.780465i	$-0.285018\pi$
$227$	−1242.53	−	2152.13i	−0.363303	−	0.629260i	−0.988502	+	0.151206i	$0.951684\pi$
$228$	298.780	−	37.0374i	0.0867859	−	0.0107582i
$229$	931.009	−	1612.56i	0.268659	−	0.465330i	−0.699857	−	0.714283i	$-0.746753\pi$
$229$	931.009	−	1612.56i	0.268659	−	0.465330i	0.968516	+	0.248953i	$0.0800863\pi$
$230$	−2685.39	+	4651.24i	−0.769868	+	1.33345i
$231$	−868.820	+	107.701i	−0.247464	+	0.0306761i
$232$	3067.67	+	5313.35i	0.868113	+	1.50362i
$233$	−4094.94			−1.15137			−0.575684	−	0.817672i	$-0.695264\pi$
$233$	−4094.94			−1.15137			−0.575684	+	0.817672i	$0.695264\pi$
$234$	−463.322	+	1630.06i	−0.129437	+	0.455386i
$235$	−1355.35			−0.376227
$236$	333.726	+	578.030i	0.0920496	+	0.159435i
$237$	1810.41	−	4278.85i	0.496198	−	1.17275i
$238$	729.643	−	1263.78i	0.198722	−	0.344196i
$239$	1061.36	−	1838.33i	0.287254	−	0.497538i	−0.685900	−	0.727696i	$-0.740591\pi$
$239$	1061.36	−	1838.33i	0.287254	−	0.497538i	0.973153	+	0.230158i	$0.0739244\pi$
$240$	−2264.92	−	2998.40i	−0.609166	−	0.806442i
$241$	−2644.98	−	4581.25i	−0.706964	−	1.22450i	−0.965978	−	0.258624i	$-0.916731\pi$
$241$	−2644.98	−	4581.25i	−0.706964	−	1.22450i	0.259014	−	0.965874i	$-0.416603\pi$
$242$	−1966.21			−0.522284
$243$	352.024	+	3771.60i	0.0929315	+	0.995673i
$244$	49.8270			0.0130731
$245$	331.805	+	574.703i	0.0865234	+	0.149863i
$246$	−1349.93	−	1787.11i	−0.349873	−	0.463178i
$247$	600.416	−	1039.95i	0.154670	−	0.267897i
$248$	−32.6390	+	56.5325i	−0.00835718	+	0.0144751i
$249$	−29.2802	+	69.2028i	−0.00745203	+	0.0176127i
$250$	−1179.42	−	2042.81i	−0.298372	−	0.516795i
$251$	−4632.56			−1.16496			−0.582480	−	0.812845i	$-0.697918\pi$
$251$	−4632.56			−1.16496			−0.582480	+	0.812845i	$0.697918\pi$
$252$	−59.8247	+	210.475i	−0.0149548	+	0.0526138i
$253$	−3649.07			−0.906780
$254$	1187.86	+	2057.43i	0.293437	+	0.508248i
$255$	−5565.82	+	689.951i	−1.36684	+	0.169437i
$256$	869.621	−	1506.23i	0.212310	−	0.367731i
$257$	−1578.23	+	2733.58i	−0.383065	+	0.663487i	−0.991499	−	0.130117i	$-0.958465\pi$
$257$	−1578.23	+	2733.58i	−0.383065	+	0.663487i	0.608434	+	0.793604i	$0.291798\pi$
$258$	5702.61	−	706.907i	1.37608	−	0.170582i
$259$	1118.66	+	1937.58i	0.268379	+	0.464846i
$260$	376.215			0.0897379
$261$	6706.03	−	1688.53i	1.59039	−	0.400451i
$262$	−1621.42			−0.382335
$263$	894.284	+	1548.95i	0.209673	+	0.363164i	0.951611	−	0.307304i	$-0.0994268\pi$
$263$	894.284	+	1548.95i	0.209673	+	0.363164i	−0.741939	+	0.670468i	$0.766093\pi$
$264$	1167.40	−	2759.12i	0.272154	−	0.643228i
$265$	1320.32	−	2286.86i	0.306062	−	0.530115i
$266$	−458.184	+	793.598i	−0.105613	+	0.182927i
$267$	−4798.50	−	6352.47i	−1.09986	−	1.45605i
$268$	−588.427	−	1019.18i	−0.134119	−	0.232301i
$269$	5780.38			1.31017			0.655085	−	0.755555i	$-0.272633\pi$
$269$	5780.38			1.31017			0.655085	+	0.755555i	$0.272633\pi$
$270$	−4633.73	+	1797.25i	−1.04444	+	0.405100i
$271$	5745.97			1.28798			0.643991	−	0.765033i	$-0.277277\pi$
$271$	5745.97			1.28798			0.643991	+	0.765033i	$0.277277\pi$
$272$	2127.82	+	3685.50i	0.474332	+	0.821567i
$273$	526.042	+	696.400i	0.116621	+	0.154388i
$274$	997.362	−	1727.48i	0.219901	−	0.380879i
$275$	−702.992	+	1217.62i	−0.154153	+	0.267001i
$276$	−355.387	+	839.947i	−0.0775065	+	0.183184i
$277$	−1746.81	−	3025.57i	−0.378902	−	0.656278i	0.612001	−	0.790857i	$-0.290365\pi$
$277$	−1746.81	−	3025.57i	−0.378902	−	0.656278i	−0.990903	+	0.134579i	$0.957032\pi$
$278$	3641.51			0.785623
$279$	51.2336	+	52.8083i	0.0109938	+	0.0113317i
$280$	−2270.92			−0.484692
$281$	−927.263	−	1606.07i	−0.196854	−	0.340961i	0.750653	−	0.660697i	$-0.229739\pi$
$281$	−927.263	−	1606.07i	−0.196854	−	0.340961i	−0.947507	+	0.319736i	$0.896406\pi$
$282$	1349.91	−	167.338i	0.285057	−	0.0353362i
$283$	−2710.16	+	4694.13i	−0.569266	+	0.985997i	0.427373	+	0.904075i	$0.359439\pi$
$283$	−2710.16	+	4694.13i	−0.569266	+	0.985997i	−0.996639	+	0.0819218i	$0.973894\pi$
$284$	−294.820	+	510.643i	−0.0615998	+	0.106694i
$285$	3495.09	−	433.259i	0.726426	−	0.0900493i
$286$	−755.338	−	1308.28i	−0.156168	−	0.270491i
$287$	−1153.45			−0.237233
$288$	−976.888	−	1006.91i	−0.199874	−	0.206017i
$289$	1438.63			0.292820
$290$	4536.66	+	7857.73i	0.918628	+	1.59111i
$291$	3594.23	−	8494.86i	0.724047	−	1.71126i
$292$	601.830	−	1042.40i	0.120615	−	0.208911i
$293$	−707.626	+	1225.64i	−0.141092	+	0.244379i	−0.927908	−	0.372809i	$-0.878395\pi$
$293$	−707.626	+	1225.64i	−0.141092	+	0.244379i	0.786816	+	0.617188i	$0.211728\pi$
$294$	−401.429	−	531.431i	−0.0796320	−	0.105421i
$295$	3903.89	+	6761.73i	0.770485	+	1.33452i
$296$	−7656.29			−1.50342
$297$	−2631.66	−	2115.95i	−0.514155	−	0.413401i
$298$	2726.28			0.529964
$299$	1818.87	+	3150.37i	0.351799	+	0.609334i
$300$	211.807	+	280.400i	0.0407623	+	0.0539631i
$301$	1479.69	−	2562.90i	0.283349	−	0.490775i
$302$	−130.563	+	226.142i	−0.0248777	+	0.0430895i
$303$	−685.777	+	1620.81i	−0.130023	+	0.307305i
$304$	−1336.18	−	2314.33i	−0.252089	−	0.436632i
$305$	582.870			0.109426
$306$	5458.31	−	1374.37i	1.01971	−	0.256756i
$307$	6596.15			1.22626			0.613131	−	0.789982i	$-0.289910\pi$
$307$	6596.15			1.22626			0.613131	+	0.789982i	$0.289910\pi$
$308$	−97.5301	−	168.927i	−0.0180432	−	0.0312517i
$309$	−2322.94	+	287.956i	−0.427661	+	0.0530137i
$310$	−48.2687	+	83.6039i	−0.00884348	+	0.0153174i
$311$	379.003	−	656.452i	0.0691037	−	0.119691i	−0.829403	−	0.558650i	$-0.811319\pi$
$311$	379.003	−	656.452i	0.0691037	−	0.119691i	0.898507	+	0.438959i	$0.144653\pi$
$312$	−2963.93	+	367.416i	−0.537820	+	0.0666693i
$313$	−3552.76	−	6153.56i	−0.641578	−	1.11125i	−0.985081	−	0.172094i	$-0.944947\pi$
$313$	−3552.76	−	6153.56i	−0.641578	−	1.11125i	0.343503	−	0.939152i	$-0.388387\pi$
$314$	1290.73			0.231975
$315$	−699.822	+	2462.11i	−0.125176	+	0.440394i
$316$	1035.18			0.184283
$317$	2629.69	+	4554.75i	0.465924	+	0.807005i	0.999243	−	0.0389100i	$-0.0123886\pi$
$317$	2629.69	+	4554.75i	0.465924	+	0.807005i	−0.533318	+	0.845915i	$0.679055\pi$
$318$	−1032.67	+	2440.69i	−0.182105	+	0.430400i
$319$	−3082.35	+	5338.78i	−0.540998	+	0.937036i
$320$	3813.03	−	6604.36i	0.666109	−	1.15373i
$321$	1820.30	+	2409.81i	0.316509	+	0.419010i
$322$	−1388.00	−	2404.09i	−0.240218	−	0.416070i
$323$	−3988.54			−0.687085
$324$	−743.352	+	399.682i	−0.127461	+	0.0685325i
$325$	1401.62			0.239224
$326$	−2844.41	−	4926.66i	−0.483243	−	0.837001i
$327$	4326.40	+	5727.49i	0.731653	+	0.968596i
$328$	1973.60	−	3418.37i	0.332237	−	0.575451i
$329$	350.270	−	606.685i	0.0586961	−	0.101665i
$330$	1726.43	−	4080.37i	0.287991	−	0.680657i
$331$	2126.09	+	3682.50i	0.353053	+	0.611507i	0.986783	−	0.162048i	$-0.0518100\pi$
$331$	2126.09	+	3682.50i	0.353053	+	0.611507i	−0.633729	+	0.773555i	$0.718477\pi$
$332$	−16.7422			−0.00276761
$333$	−2359.41	+	8300.87i	−0.388273	+	1.36602i
$334$	6016.82			0.985706
$335$	−6883.35	−	11922.3i	−1.12262	−	1.94443i
$336$	1927.49	−	238.935i	0.312956	−	0.0387946i
$337$	−1296.08	+	2244.87i	−0.209501	+	0.362867i	−0.951558	−	0.307471i	$-0.900517\pi$
$337$	−1296.08	+	2244.87i	−0.209501	+	0.362867i	0.742056	+	0.670338i	$0.233851\pi$
$338$	2120.43	−	3672.70i	0.341232	−	0.591031i
$339$	7733.77	−	958.694i	1.23906	−	0.153596i
$340$	−624.796	−	1082.18i	−0.0996598	−	0.172616i
$341$	−65.5905			−0.0104162
$342$	−3427.58	+	863.041i	−0.541936	+	0.136456i
$343$	−343.000			−0.0539949
$344$	5063.62	+	8770.45i	0.793640	+	1.37462i
$345$	−4157.28	+	9825.60i	−0.648755	+	1.53331i
$346$	408.773	−	708.016i	0.0635138	−	0.110009i
$347$	245.989	−	426.066i	0.0380559	−	0.0659148i	−0.846370	−	0.532595i	$-0.821217\pi$
$347$	245.989	−	426.066i	0.0380559	−	0.0659148i	0.884426	+	0.466680i	$0.154550\pi$
$348$	928.692	+	1229.45i	0.143055	+	0.189383i
$349$	5958.75	+	10320.9i	0.913939	+	1.58299i	0.808448	+	0.588568i	$0.200308\pi$
$349$	5958.75	+	10320.9i	0.913939	+	1.58299i	0.105491	+	0.994420i	$0.466358\pi$
$350$	−1069.59			−0.163348
$351$	−515.036	+	3326.69i	−0.0783208	+	0.505885i
$352$	1250.63			0.189372
$353$	−4039.98	−	6997.45i	−0.609140	−	1.05506i	−0.991382	−	0.130999i	$-0.958181\pi$
$353$	−4039.98	−	6997.45i	−0.609140	−	1.05506i	0.382242	−	0.924062i	$-0.375152\pi$
$354$	−4723.06	−	6252.61i	−0.709118	−	0.938764i
$355$	−3448.77	+	5973.45i	−0.515611	+	0.893064i
$356$	886.894	−	1536.15i	0.132037	−	0.228695i
$357$	1129.57	−	2669.70i	0.167459	−	0.395785i
$358$	−5683.87	−	9844.76i	−0.839112	−	1.45338i
$359$	−6675.40			−0.981376			−0.490688	−	0.871335i	$-0.663255\pi$
$359$	−6675.40			−0.981376			−0.490688	+	0.871335i	$0.663255\pi$
$360$	−6099.31	−	6286.77i	−0.892949	−	0.920394i
$361$	−4354.37			−0.634840
$362$	145.169	+	251.440i	0.0210771	+	0.0365066i
$363$	−3876.15	+	480.495i	−0.560454	+	0.0694751i
$364$	−97.2271	+	168.402i	−0.0140002	+	0.0242491i
$365$	7040.14	−	12193.9i	1.00958	−	1.74865i
$366$	−580.532	+	71.9639i	−0.0829095	+	0.0102776i
$367$	5888.45	+	10199.1i	0.837532	+	1.45065i	0.891952	+	0.452130i	$0.149336\pi$
$367$	5888.45	+	10199.1i	0.837532	+	1.45065i	−0.0544197	+	0.998518i	$0.517331\pi$
$368$	8095.51			1.14676
$369$	−3097.96	−	3193.18i	−0.437055	−	0.450488i
$370$	−11322.6			−1.59091
$371$	682.433	+	1182.01i	0.0954991	+	0.165409i
$372$	−6.38792	+	15.0977i	−0.000890318	+	0.00210424i
$373$	−741.638	+	1284.55i	−0.102950	+	0.178315i	−0.912899	−	0.408185i	$-0.866162\pi$
$373$	−741.638	+	1284.55i	−0.102950	+	0.178315i	0.809949	+	0.586501i	$0.199495\pi$
$374$	−2508.85	+	4345.45i	−0.346870	+	0.600796i
$375$	−2824.30	−	3738.94i	−0.388923	−	0.514874i
$376$	1198.65	+	2076.12i	0.164403	+	0.284755i
$377$	6145.54			0.839553
$378$	393.030	−	2538.63i	0.0534796	−	0.345432i
$379$	−13400.9			−1.81625			−0.908124	−	0.418701i	$-0.862486\pi$
$379$	−13400.9			−1.81625			−0.908124	+	0.418701i	$0.862486\pi$
$380$	392.344	+	679.561i	0.0529654	+	0.0917387i
$381$	2844.51	+	3765.70i	0.382490	+	0.506359i
$382$	−2885.04	+	4997.04i	−0.386418	+	0.669296i
$383$	−5883.57	+	10190.6i	−0.784952	+	1.35958i	0.144076	+	0.989567i	$0.453979\pi$
$383$	−5883.57	+	10190.6i	−0.784952	+	1.35958i	−0.929028	+	0.370010i	$0.879354\pi$
$384$	−2140.68	+	5059.43i	−0.284482	+	0.672364i
$385$	−1140.90	−	1976.09i	−0.151027	−	0.261587i
$386$	−1147.06			−0.151254
$387$	11069.3	−	2787.17i	1.45396	−	0.366097i
$388$	2055.15			0.268903
$389$	−3900.97	−	6756.68i	−0.508450	−	0.880661i	−0.999952	−	0.00978494i	$-0.996885\pi$
$389$	−3900.97	−	6756.68i	−0.508450	−	0.880661i	0.491502	−	0.870876i	$-0.336448\pi$
$390$	−4383.26	+	543.358i	−0.569115	+	0.0705487i
$391$	6041.35	−	10463.9i	0.781391	−	1.35341i
$392$	586.886	−	1016.52i	0.0756180	−	0.130974i
$393$	−3196.44	+	396.237i	−0.410278	+	0.0508589i
$394$	−3316.81	−	5744.88i	−0.424108	−	0.734576i
$395$	12109.4			1.54251
$396$	205.704	−	723.708i	0.0261036	−	0.0918377i
$397$	−6197.81			−0.783525			−0.391762	−	0.920066i	$-0.628134\pi$
$397$	−6197.81			−0.783525			−0.391762	+	0.920066i	$0.628134\pi$
$398$	−3658.17	−	6336.14i	−0.460723	−	0.797995i
$399$	−709.318	+	1676.45i	−0.0889983	+	0.210345i
$400$	1559.60	−	2701.30i	0.194950	−	0.337662i
$401$	−500.722	+	867.276i	−0.0623563	+	0.108004i	−0.895518	−	0.445025i	$-0.853195\pi$
$401$	−500.722	+	867.276i	−0.0623563	+	0.108004i	0.833162	+	0.553029i	$0.186528\pi$
$402$	8327.71	+	11024.6i	1.03321	+	1.36781i
$403$	32.6933	+	56.6265i	0.00404112	+	0.00699943i
$404$	−392.122			−0.0482891
$405$	−8695.64	+	4675.43i	−1.06689	+	0.573640i
$406$	−4689.73			−0.573270
$407$	−3846.47	−	6662.27i	−0.468458	−	0.811392i
$408$	5979.20	+	7915.55i	0.725526	+	0.960485i
$409$	−5054.60	+	8754.82i	−0.611085	+	1.05843i	0.379973	+	0.924998i	$0.375933\pi$
$409$	−5054.60	+	8754.82i	−0.611085	+	1.05843i	−0.991058	+	0.133433i	$0.957400\pi$
$410$	2918.68	−	5055.31i	0.351569	−	0.608936i
$411$	1544.02	−	3649.26i	0.185307	−	0.437967i
$412$	−260.763	−	451.655i	−0.0311817	−	0.0540083i
$413$	−4035.61			−0.480821
$414$	2927.48	−	10299.5i	0.347531	−	1.22268i
$415$	−195.848			−0.0231658
$416$	−623.375	−	1079.72i	−0.0734699	−	0.127254i
$417$	7178.80	−	889.899i	0.843040	−	0.104505i
$418$	1575.44	−	2728.75i	0.184348	−	0.319300i
$419$	−178.252	+	308.741i	−0.0207832	+	0.0359976i	−0.876230	−	0.481893i	$-0.839949\pi$
$419$	−178.252	+	308.741i	−0.0207832	+	0.0359976i	0.855447	+	0.517891i	$0.173283\pi$
$420$	−565.971	+	70.1590i	−0.0657537	+	0.00815097i
$421$	1435.87	+	2487.00i	0.166223	+	0.287907i	0.937089	−	0.349091i	$-0.113509\pi$
$421$	1435.87	+	2487.00i	0.166223	+	0.287907i	−0.770866	+	0.636998i	$0.780176\pi$
$422$	4938.99			0.569731
$423$	2620.30	−	659.773i	0.301189	−	0.0758375i
$424$	−4670.68			−0.534972
$425$	−2327.72	−	4031.74i	−0.265673	−	0.460160i
$426$	2697.42	−	6375.28i	0.306785	−	0.725078i
$427$	−150.634	+	260.906i	−0.0170719	+	0.0295694i
$428$	−336.442	+	582.735i	−0.0379966	+	0.0658121i
$429$	−1808.77	−	2394.54i	−0.203563	−	0.269486i
$430$	7488.41	+	12970.3i	0.839821	+	1.45461i
$431$	−3224.02			−0.360314			−0.180157	−	0.983638i	$-0.557661\pi$
$431$	−3224.02			−0.360314			−0.180157	+	0.983638i	$0.557661\pi$
$432$	5838.36	+	4694.27i	0.650227	+	0.522808i
$433$	−14285.5			−1.58549			−0.792744	−	0.609555i	$-0.791348\pi$
$433$	−14285.5			−1.58549			−0.792744	+	0.609555i	$0.791348\pi$
$434$	−24.9487	−	43.2123i	−0.00275939	−	0.00477940i
$435$	10863.7	+	14381.9i	1.19742	+	1.58520i
$436$	−799.638	+	1385.01i	−0.0878342	+	0.152133i
$437$	−3793.70	+	6570.88i	−0.415280	+	0.719286i
$438$	−5506.38	+	13014.2i	−0.600696	+	1.41973i
$439$	−1757.57	−	3044.19i	−0.191080	−	0.330960i	0.754528	−	0.656267i	$-0.227866\pi$
$439$	−1757.57	−	3044.19i	−0.191080	−	0.330960i	−0.945608	+	0.325307i	$0.894532\pi$
$440$	7808.47			0.846032
$441$	−921.238	−	949.552i	−0.0994750	−	0.102532i
$442$	5002.10			0.538294
$443$	3991.41	+	6913.33i	0.428076	+	0.741449i	0.996702	−	0.0811467i	$-0.0258582\pi$
$443$	3991.41	+	6913.33i	0.428076	+	0.741449i	−0.568626	+	0.822596i	$0.692525\pi$
$444$	−1908.14	+	236.537i	−0.203956	+	0.0252828i
$445$	10374.8	−	17969.7i	1.10520	−	1.91425i
$446$	−1765.32	+	3057.62i	−0.187422	+	0.324624i
$447$	5374.54	−	666.240i	0.568696	−	0.0704968i
$448$	1970.84	+	3413.60i	0.207843	+	0.359994i
$449$	3502.50			0.368137			0.184068	−	0.982913i	$-0.441073\pi$
$449$	3502.50			0.368137			0.184068	+	0.982913i	$0.441073\pi$
$450$	−2872.73	−	2961.02i	−0.300937	−	0.310187i
$451$	3966.08			0.414092
$452$	868.161	+	1503.70i	0.0903426	+	0.156478i
$453$	−202.126	+	477.719i	−0.0209640	+	0.0495479i
$454$	−3250.19	+	5629.49i	−0.335988	+	0.581949i
$455$	−1137.35	+	1969.95i	−0.117187	+	0.202973i
$456$	−3754.68	−	4970.62i	−0.385589	−	0.510461i
$457$	−6531.24	−	11312.4i	−0.668531	−	1.15793i	−0.978315	−	0.207123i	$-0.933590\pi$
$457$	−6531.24	−	11312.4i	−0.668531	−	1.15793i	0.309784	−	0.950807i	$-0.399743\pi$
$458$	−4870.62			−0.496919
$459$	10424.5	−	4043.28i	1.06008	−	0.411164i
$460$	−2377.10			−0.240941
$461$	−3357.21	−	5814.86i	−0.339178	−	0.587473i	0.645101	−	0.764098i	$-0.276815\pi$
$461$	−3357.21	−	5814.86i	−0.339178	−	0.587473i	−0.984278	+	0.176625i	$0.943482\pi$
$462$	1380.30	+	1827.30i	0.138998	+	0.184012i
$463$	3048.84	−	5280.74i	0.306029	−	0.530058i	−0.671461	−	0.741040i	$-0.734333\pi$
$463$	3048.84	−	5280.74i	0.306029	−	0.530058i	0.977490	+	0.210982i	$0.0676661\pi$
$464$	6838.22	−	11844.1i	0.684174	−	1.18502i
$465$	−74.7252	+	176.611i	−0.00745225	+	0.0176132i
$466$	5355.72	+	9276.38i	0.532401	+	0.922146i
$467$	−11929.4			−1.18207			−0.591033	−	0.806647i	$-0.701280\pi$
$467$	−11929.4			−1.18207			−0.591033	+	0.806647i	$0.701280\pi$
$468$	−727.335	+	183.138i	−0.0718399	+	0.0180888i
$469$	7115.59			0.700571
$470$	1772.64	+	3070.31i	0.173970	+	0.301325i
$471$	2544.53	−	315.425i	0.248929	−	0.0308578i
$472$	6905.08	−	11960.0i	0.673373	−	1.16632i
$473$	−5087.85	+	8812.42i	−0.494587	+	0.856650i
$474$	−12060.8	+	1495.08i	−1.16872	+	0.144876i
$475$	1461.71	+	2531.75i	0.141195	+	0.244558i
$476$	645.877			0.0621927
$477$	−1439.34	+	5063.90i	−0.138162	+	0.486080i
$478$	−5552.55			−0.531313
$479$	3745.00	+	6486.54i	0.357231	+	0.618742i	0.987497	−	0.157637i	$-0.0503876\pi$
$479$	3745.00	+	6486.54i	0.357231	+	0.618742i	−0.630266	+	0.776379i	$0.717054\pi$
$480$	1424.81	−	3367.50i	0.135486	−	0.320218i
$481$	−3834.52	+	6641.58i	−0.363490	+	0.629584i
$482$	−6918.68	+	11983.5i	−0.653811	+	1.13243i
$483$	−3323.78	−	4400.17i	−0.313120	−	0.414523i
$484$	−435.120	−	753.650i	−0.0408640	−	0.0707785i
$485$	24040.9			2.25081
$486$	8083.50	−	5730.28i	0.754475	−	0.534837i
$487$	14200.8			1.32135			0.660675	−	0.750672i	$-0.270270\pi$
$487$	14200.8			1.32135			0.660675	+	0.750672i	$0.270270\pi$
$488$	−515.482	−	892.841i	−0.0478172	−	0.0828217i
$489$	−6811.37	−	9017.21i	−0.629899	−	0.833890i
$490$	867.926	−	1503.29i	0.0800181	−	0.138595i
$491$	−5395.93	+	9346.03i	−0.495957	+	0.859023i	−0.999989	−	0.00466183i	$-0.998516\pi$
$491$	−5395.93	+	9346.03i	−0.495957	+	0.859023i	0.504032	+	0.863685i	$0.331849\pi$
$492$	386.261	−	912.916i	0.0353943	−	0.0836533i
$493$	−10206.2	−	17677.6i	−0.932378	−	1.61493i
$494$	−3141.10			−0.286083
$495$	2406.31	−	8465.86i	0.218496	−	0.768711i
$496$	145.513			0.0131729
$497$	−1782.57	−	3087.50i	−0.160883	−	0.278658i
$498$	195.062	−	24.1803i	0.0175521	−	0.00217579i
$499$	−3170.09	+	5490.75i	−0.284394	+	0.492585i	−0.972462	−	0.233061i	$-0.925126\pi$
$499$	−3170.09	+	5490.75i	−0.284394	+	0.492585i	0.688068	+	0.725646i	$0.258459\pi$
$500$	522.008	−	904.144i	0.0466898	−	0.0808691i
$501$	11861.4	−	1470.37i	1.05775	−	0.131120i
$502$	6058.87	+	10494.3i	0.538686	+	0.933032i
$503$	18901.4			1.67549			0.837747	−	0.546059i	$-0.183873\pi$
$503$	18901.4			1.67549			0.837747	+	0.546059i	$0.183873\pi$
$504$	4390.37	−	1105.47i	0.388021	−	0.0977012i
$505$	−4587.00			−0.404195
$506$	4772.57	+	8266.34i	0.419302	+	0.726252i
$507$	3282.66	−	7758.47i	0.287551	−	0.679617i
$508$	−525.744	+	910.616i	−0.0459176	+	0.0795316i
$509$	6838.35	−	11844.4i	0.595491	−	1.03142i	−0.397987	−	0.917391i	$-0.630291\pi$
$509$	6838.35	−	11844.4i	0.595491	−	1.03142i	0.993477	−	0.114029i	$-0.0363757\pi$
$510$	8842.43	+	11706.0i	0.767744	+	1.01638i
$511$	3638.84	+	6302.65i	0.315015	+	0.545622i
$512$	−13007.5			−1.12277
$513$	−6546.15	+	2539.00i	−0.563391	+	0.218518i
$514$	8256.61			0.708528
$515$	−3050.38	−	5283.40i	−0.261001	−	0.452067i
$516$	1532.94	+	2029.38i	0.130783	+	0.173136i
$517$	−1204.39	+	2086.06i	−0.102454	+	0.177456i
$518$	2926.16	−	5068.26i	0.248201	−	0.429897i
$519$	632.825	−	1495.66i	0.0535220	−	0.126498i
$520$	−3892.11	−	6741.33i	−0.328231	−	0.568513i
$521$	−10323.9			−0.868139			−0.434069	−	0.900879i	$-0.642923\pi$
$521$	−10323.9			−0.868139			−0.434069	+	0.900879i	$0.642923\pi$
$522$	−12595.8	−	12982.9i	−1.05614	−	1.08860i
$523$	9294.18			0.777067			0.388534	−	0.921435i	$-0.372982\pi$
$523$	9294.18			0.777067			0.388534	+	0.921435i	$0.372982\pi$
$524$	−358.819	−	621.493i	−0.0299143	−	0.0518130i
$525$	−2108.57	+	261.382i	−0.175287	+	0.0217289i
$526$	2339.24	−	4051.69i	0.193909	−	0.335859i
$527$	108.590	−	188.084i	0.00897585	−	0.0155466i
$528$	−6627.58	+	821.569i	−0.546266	+	0.0677163i
$529$	−5408.95	−	9368.57i	−0.444559	−	0.769999i
$530$	−6907.30			−0.566102
$531$	−10838.9	−	11172.1i	−0.885819	−	0.913044i
$532$	−405.582			−0.0330531
$533$	−1976.88	−	3424.06i	−0.160653	−	0.278260i
$534$	−8114.54	+	19178.5i	−0.657585	+	1.55418i
$535$	−3935.66	+	6816.77i	−0.318044	+	0.550869i
$536$	−12175.1	+	21087.8i	−0.981124	+	1.69936i
$537$	−13610.9	−	18018.8i	−1.09377	−	1.44798i
$538$	−7560.08	−	13094.4i	−0.605833	−	1.04933i
$539$	1179.39			0.0942485
$540$	−1714.33	−	1378.38i	−0.136616	−	0.109845i
$541$	4432.55			0.352256			0.176128	−	0.984367i	$-0.443643\pi$
$541$	4432.55			0.352256			0.176128	+	0.984367i	$0.443643\pi$
$542$	−7515.08	−	13016.5i	−0.595572	−	1.03156i
$543$	347.629	+	460.208i	0.0274736	+	0.0363709i
$544$	−2070.53	+	3586.26i	−0.163186	+	0.282647i
$545$	−9354.07	+	16201.7i	−0.735201	+	1.27340i
$546$	889.569	−	2102.47i	0.0697253	−	0.164794i
$547$	−2164.18	−	3748.47i	−0.169166	−	0.293004i	0.768961	−	0.639296i	$-0.220774\pi$
$547$	−2164.18	−	3748.47i	−0.169166	−	0.293004i	−0.938127	+	0.346292i	$0.887441\pi$
$548$	882.860			0.0688210
$549$	−1126.86	+	283.737i	−0.0876017	+	0.0220575i
$550$	3677.74			0.285126
$551$	6409.02	+	11100.8i	0.495524	+	0.858272i
$552$	18727.5	−	2321.50i	1.44401	−	0.179003i
$553$	−3129.49	+	5420.44i	−0.240650	+	0.416819i
$554$	−4569.27	+	7914.21i	−0.350415	+	0.606936i
$555$	−22321.2	+	2766.98i	−1.70717	+	0.211625i
$556$	805.862	+	1395.79i	0.0614679	+	0.106466i
$557$	6102.88			0.464250			0.232125	−	0.972686i	$-0.425432\pi$
$557$	6102.88			0.464250			0.232125	+	0.972686i	$0.425432\pi$
$558$	52.6202	−	185.128i	0.00399209	−	0.0140450i
$559$	10144.1			0.767530
$560$	2531.09	+	4383.98i	0.190997	+	0.330816i
$561$	−3883.96	+	9179.63i	−0.292301	+	0.690846i
$562$	−2425.51	+	4201.11i	−0.182053	+	0.315326i
$563$	−2428.85	+	4206.89i	−0.181819	+	0.314919i	−0.942500	−	0.334207i	$-0.891532\pi$
$563$	−2428.85	+	4206.89i	−0.181819	+	0.314919i	0.760681	+	0.649126i	$0.224865\pi$
$564$	362.875	+	480.390i	0.0270918	+	0.0358654i
$565$	10155.6	+	17590.1i	0.756197	+	1.30977i
$566$	14178.3			1.05293
$567$	154.429	−	5100.66i	0.0114381	−	0.377791i
$568$	12200.2			0.901246
$569$	−1501.30	−	2600.33i	−0.110611	−	0.191585i	0.805406	−	0.592724i	$-0.201948\pi$
$569$	−1501.30	−	2600.33i	−0.110611	−	0.191585i	−0.916017	+	0.401140i	$0.868614\pi$
$570$	−5552.66	−	7350.87i	−0.408027	−	0.540165i
$571$	−9682.85	+	16771.2i	−0.709658	+	1.22916i	0.255326	+	0.966855i	$0.417817\pi$
$571$	−9682.85	+	16771.2i	−0.709658	+	1.22916i	−0.964984	+	0.262309i	$0.915516\pi$
$572$	334.311	−	579.044i	0.0244375	−	0.0423270i
$573$	−4466.36	+	10556.1i	−0.325628	+	0.769612i
$574$	1508.58	+	2612.94i	0.109698	+	0.190003i
$575$	−8856.06			−0.642301
$576$	−4156.78	+	14624.4i	−0.300693	+	1.05790i
$577$	9688.50			0.699025			0.349512	−	0.936932i	$-0.386347\pi$
$577$	9688.50			0.699025			0.349512	+	0.936932i	$0.386347\pi$
$578$	−1881.56	−	3258.96i	−0.135402	−	0.234524i
$579$	−2261.29	+	280.315i	−0.162308	+	0.0201200i
$580$	−2007.92	+	3477.82i	−0.143749	+	0.248980i
$581$	50.6140	−	87.6660i	0.00361415	−	0.00625989i
$582$	−23944.5	+	2968.21i	−1.70538	+	0.211402i
$583$	−2346.52	−	4064.28i	−0.166694	−	0.288723i
$584$	−24904.8			−1.76467
$585$	−8508.29	+	2142.33i	−0.601324	+	0.151409i
$586$	3701.98			0.260968
$587$	872.314	+	1510.89i	0.0613360	+	0.106237i	0.895063	−	0.445940i	$-0.147131\pi$
$587$	872.314	+	1510.89i	0.0613360	+	0.106237i	−0.833727	+	0.552177i	$0.813797\pi$
$588$	114.862	−	271.473i	0.00805583	−	0.0190397i
$589$	−68.1900	+	118.109i	−0.00477033	+	0.00826245i
$590$	10211.7	−	17687.2i	0.712556	−	1.23418i
$591$	−7942.61	−	10514.8i	−0.552818	−	0.731846i
$592$	8533.43	+	14780.3i	0.592435	+	1.02613i
$593$	20857.6			1.44438			0.722192	−	0.691692i	$-0.243135\pi$
$593$	20857.6			1.44438			0.722192	+	0.691692i	$0.243135\pi$
$594$	−1351.42	+	8728.98i	−0.0933490	+	0.602954i
$595$	7555.39			0.520573
$596$	603.324	+	1044.99i	0.0414649	+	0.0718194i
$597$	−8760.06	−	11597.0i	−0.600545	−	0.795030i
$598$	4757.75	−	8240.66i	0.325349	−	0.563521i
$599$	−3598.35	+	6232.52i	−0.245450	+	0.425132i	−0.962258	−	0.272139i	$-0.912269\pi$
$599$	−3598.35	+	6232.52i	−0.245450	+	0.425132i	0.716808	+	0.697271i	$0.245602\pi$
$600$	2833.21	−	6696.20i	0.192775	−	0.455619i
$601$	−5649.25	−	9784.79i	−0.383424	−	0.664110i	0.608125	−	0.793841i	$-0.291922\pi$
$601$	−5649.25	−	9784.79i	−0.383424	−	0.664110i	−0.991549	+	0.129731i	$0.958589\pi$
$602$	−7741.07			−0.524091
$603$	19111.2	+	19698.6i	1.29066	+	1.33033i
$604$	−115.574			−0.00778583
$605$	−5089.98	−	8816.11i	−0.342045	−	0.592439i
$606$	4568.59	−	566.332i	0.306248	−	0.0379631i
$607$	9204.31	−	15942.3i	0.615472	−	1.06603i	−0.374829	−	0.927094i	$-0.622299\pi$
$607$	9204.31	−	15942.3i	0.615472	−	1.06603i	0.990301	−	0.138935i	$-0.0443680\pi$
$608$	1300.20	−	2252.02i	0.0867272	−	0.150216i
$609$	−9245.25	+	1146.06i	−0.615166	+	0.0762573i
$610$	−762.328	−	1320.39i	−0.0505996	−	0.0876411i
$611$	2401.29			0.158995
$612$	1734.71	+	1788.03i	0.114578	+	0.118099i
$613$	−8745.01			−0.576195			−0.288098	−	0.957601i	$-0.593023\pi$
$613$	−8745.01			−0.576195			−0.288098	+	0.957601i	$0.593023\pi$
$614$	−8627.01	−	14942.4i	−0.567032	−	0.982129i
$615$	4518.44	−	10679.2i	0.296262	−	0.700206i
$616$	−2017.98	+	3495.25i	−0.131992	+	0.228616i
$617$	14619.8	−	25322.2i	0.953923	−	1.65224i	0.217110	−	0.976147i	$-0.430337\pi$
$617$	14619.8	−	25322.2i	0.953923	−	1.65224i	0.736813	−	0.676096i	$-0.236330\pi$
$618$	3690.45	+	4885.59i	0.240213	+	0.318005i
$619$	−1289.82	−	2234.04i	−0.0837518	−	0.145062i	0.821107	−	0.570775i	$-0.193357\pi$
$619$	−1289.82	−	2234.04i	−0.0837518	−	0.145062i	−0.904859	+	0.425712i	$0.860024\pi$
$620$	−42.7273			−0.00276769
$621$	3254.24	−	21019.6i	0.210287	−	1.35827i
$622$	−1982.77			−0.127816
$623$	5362.42	+	9287.98i	0.344849	+	0.597295i
$624$	4012.78	+	5312.31i	0.257436	+	0.340806i
$625$	9757.28	−	16900.1i	0.624466	−	1.08161i
$626$	−9293.21	+	16096.3i	−0.593341	+	1.02770i
$627$	2438.96	−	5764.41i	0.155347	−	0.367158i
$628$	285.638	+	494.739i	0.0181500	+	0.0314367i
$629$	25472.6			1.61472
$630$	6492.77	−	1634.84i	0.410600	−	0.103386i
$631$	15166.5			0.956847			0.478424	−	0.878129i	$-0.341208\pi$
$631$	15166.5			0.956847			0.478424	+	0.878129i	$0.341208\pi$
$632$	−10709.4	−	18549.2i	−0.674044	−	1.16748i
$633$	9736.64	−	1206.97i	0.611369	−	0.0757866i
$634$	6878.67	−	11914.2i	0.430894	−	0.746330i
$635$	−6150.10	+	10652.3i	−0.384345	+	0.665705i
$636$	−1164.05	+	144.298i	−0.0725748	+	0.00899652i
$637$	−587.863	−	1018.21i	−0.0365651	−	0.0633327i
$638$	16125.4			1.00065
$639$	3759.68	−	13227.3i	0.232755	−	0.818879i
$640$	−14318.5			−0.884355
$641$	5784.05	+	10018.3i	0.356406	+	0.617313i	0.987357	−	0.158509i	$-0.0506688\pi$
$641$	5784.05	+	10018.3i	0.356406	+	0.617313i	−0.630952	+	0.775822i	$0.717335\pi$
$642$	3078.24	−	7275.33i	0.189234	−	0.447250i
$643$	26.3640	−	45.6638i	0.00161694	−	0.00280063i	−0.865216	−	0.501400i	$-0.832819\pi$
$643$	26.3640	−	45.6638i	0.00161694	−	0.00280063i	0.866833	+	0.498599i	$0.166152\pi$
$644$	614.325	−	1064.04i	0.0375898	−	0.0651074i
$645$	17932.1	+	23739.4i	1.09469	+	1.44921i
$646$	5216.56	+	9035.35i	0.317713	+	0.550296i
$647$	−13568.7			−0.824484			−0.412242	−	0.911074i	$-0.635254\pi$
$647$	−13568.7			−0.824484			−0.412242	+	0.911074i	$0.635254\pi$
$648$	14852.1	+	9185.10i	0.900381	+	0.556829i
$649$	13876.3			0.839277
$650$	−1833.15	−	3175.12i	−0.110619	−	0.191597i
$651$	−59.7434	−	79.0911i	−0.00359682	−	0.00476164i
$652$	1258.93	−	2180.53i	0.0756188	−	0.130976i
$653$	7707.15	−	13349.2i	0.461875	−	0.799990i	−0.537180	−	0.843468i	$-0.680510\pi$
$653$	7707.15	−	13349.2i	0.461875	−	0.799990i	0.999054	+	0.0434774i	$0.0138437\pi$
$654$	7316.20	−	17291.6i	0.437440	−	1.03388i
$655$	−4197.42	−	7270.15i	−0.250392	−	0.433692i
$656$	−8798.80			−0.523682
$657$	−7674.81	+	27001.5i	−0.455743	+	1.60339i
$658$	−1832.45			−0.108566
$659$	9417.53	+	16311.6i	0.556684	+	0.964206i	0.997770	+	0.0667409i	$0.0212601\pi$
$659$	9417.53	+	16311.6i	0.556684	+	0.964206i	−0.441086	+	0.897465i	$0.645407\pi$
$660$	1946.07	−	241.238i	0.114774	−	0.0142276i
$661$	−4509.40	+	7810.50i	−0.265348	+	0.459597i	−0.967655	−	0.252278i	$-0.918820\pi$
$661$	−4509.40	+	7810.50i	−0.265348	+	0.459597i	0.702307	+	0.711875i	$0.252154\pi$
$662$	5561.38	−	9632.59i	0.326509	−	0.565531i
$663$	9861.05	−	1222.40i	0.577634	−	0.0716047i
$664$	173.205	+	300.000i	0.0101230	+	0.0175335i
$665$	−4744.46			−0.276665
$666$	21890.0	−	5511.76i	1.27360	−	0.320685i
$667$	−38830.4			−2.25415
$668$	1331.52	+	2306.25i	0.0771226	+	0.133580i
$669$	−2732.90	+	6459.13i	−0.157937	+	0.373280i
$670$	−18005.3	+	31186.0i	−1.03822	+	1.79824i
$671$	517.949	−	897.114i	0.0297991	−	0.0516136i
$672$	1139.15	+	1508.06i	0.0653922	+	0.0865693i
$673$	−11519.7	−	19952.8i	−0.659812	−	1.14283i	−0.980664	−	0.195699i	$-0.937303\pi$
$673$	−11519.7	−	19952.8i	−0.659812	−	1.14283i	0.320852	−	0.947129i	$-0.396031\pi$
$674$	6780.49			0.387500
$675$	−6386.85	−	5135.27i	−0.364193	−	0.292825i
$676$	1877.00			0.106793
$677$	14577.1	+	25248.3i	0.827539	+	1.43334i	0.899963	+	0.435965i	$0.143593\pi$
$677$	14577.1	+	25248.3i	0.827539	+	1.43334i	−0.0724245	+	0.997374i	$0.523074\pi$
$678$	−12286.6	−	16265.6i	−0.695967	−	0.921354i
$679$	−6213.02	+	10761.3i	−0.351154	+	0.608217i
$680$	−12927.6	+	22391.2i	−0.729044	+	1.26274i
$681$	−5031.64	+	11892.1i	−0.283132	+	0.669174i
$682$	85.7848	+	148.584i	0.00481653	+	0.00834247i
$683$	−8818.55			−0.494045			−0.247022	−	0.969010i	$-0.579452\pi$
$683$	−8818.55			−0.494045			−0.247022	+	0.969010i	$0.579452\pi$
$684$	−1089.32	−	1122.80i	−0.0608937	−	0.0627653i
$685$	10327.6			0.576054
$686$	448.605	+	777.007i	0.0249677	+	0.0432453i
$687$	−9601.84	+	1190.26i	−0.533236	+	0.0661010i
$688$	11287.5	−	19550.5i	0.625480	−	1.08336i
$689$	−2339.23	+	4051.66i	−0.129343	+	0.224029i
$690$	27695.4	−	3433.18i	1.52804	−	0.189419i
$691$	4721.50	+	8177.88i	0.259934	+	0.450219i	0.966224	−	0.257704i	$-0.0829659\pi$
$691$	4721.50	+	8177.88i	0.259934	+	0.450219i	−0.706290	+	0.707923i	$0.749633\pi$
$692$	361.844			0.0198775
$693$	3167.64	+	3264.99i	0.173634	+	0.178971i
$694$	−1286.90			−0.0703894
$695$	9426.88	+	16327.8i	0.514507	+	0.891152i
$696$	12422.5	−	29360.2i	0.676543	−	1.59899i
$697$	−6566.18	+	11373.0i	−0.356832	+	0.618051i
$698$	15586.7	−	26997.0i	0.845225	−	1.46397i
$699$	12825.1	+	16978.5i	0.693977	+	0.918719i
$700$	−236.699	−	409.975i	−0.0127805	−	0.0221365i
$701$	−11255.0			−0.606411			−0.303205	−	0.952925i	$-0.598057\pi$
$701$	−11255.0			−0.606411			−0.303205	+	0.952925i	$0.598057\pi$
$702$	8209.64	−	3184.21i	0.441386	−	0.171197i
$703$	−15995.7			−0.858162
$704$	−6776.65	−	11737.5i	−0.362791	−	0.628372i
$705$	4244.87	+	5619.55i	0.226767	+	0.300205i
$706$	−10567.7	+	18303.7i	−0.563342	+	0.975737i
$707$	1185.44	−	2053.24i	0.0630595	−	0.109222i
$708$	1351.42	−	3194.05i	0.0717367	−	0.169548i
$709$	−11242.5	−	19472.6i	−0.595515	−	1.03146i	−0.993474	−	0.114060i	$-0.963615\pi$
$709$	−11242.5	−	19472.6i	−0.595515	−	1.03146i	0.397958	−	0.917403i	$-0.369719\pi$
$710$	18042.4			0.953689
$711$	−23411.1	+	5894.76i	−1.23486	+	0.310929i
$712$	−36701.2			−1.93179
$713$	−206.572	−	357.792i	−0.0108502	−	0.0187930i
$714$	−7525.08	+	932.824i	−0.394424	+	0.0488937i
$715$	3910.73	−	6773.59i	0.204550	−	0.354291i
$716$	2515.67	−	4357.27i	0.131306	−	0.227428i
$717$	−10946.2	+	1356.91i	−0.570143	+	0.0706762i
$718$	8730.66	+	15121.9i	0.453796	+	0.785997i
$719$	−27322.6			−1.41719			−0.708595	−	0.705615i	$-0.750671\pi$
$719$	−27322.6			−1.41719			−0.708595	+	0.705615i	$0.750671\pi$
$720$	−5338.42	+	18781.6i	−0.276321	+	0.972152i
$721$	3153.30			0.162878
$722$	5695.02	+	9864.06i	0.293555	+	0.508452i
$723$	−10710.9	+	25314.8i	−0.550956	+	1.30217i
$724$	−64.2514	+	111.287i	−0.00329818	+	0.00571262i
$725$	−7480.65	+	12956.9i	−0.383206	+	0.663732i
$726$	6158.03	+	8152.30i	0.314802	+	0.416750i
$727$	388.538	+	672.967i	0.0198213	+	0.0343315i	0.875766	−	0.482736i	$-0.160357\pi$
$727$	388.538	+	672.967i	0.0198213	+	0.0343315i	−0.855945	+	0.517068i	$0.827024\pi$
$728$	4023.43			0.204833
$729$	14535.3	−	13272.0i	0.738470	−	0.674286i
$730$	−36830.8			−1.86736
$731$	−16846.7	−	29179.4i	−0.852392	−	1.47639i
$732$	−156.055	−	206.593i	−0.00787972	−	0.0104315i
$733$	12682.6	−	21966.9i	0.639075	−	1.10691i	−0.346561	−	0.938028i	$-0.612651\pi$
$733$	12682.6	−	21966.9i	0.639075	−	1.10691i	0.985636	−	0.168883i	$-0.0540161\pi$
$734$	15402.8	−	26678.5i	0.774563	−	1.34158i
$735$	1343.64	−	3175.66i	0.0674300	−	0.159369i
$736$	3938.77	+	6822.15i	0.197262	+	0.341668i
$737$	−24466.7			−1.22285
$738$	−3181.80	+	11194.2i	−0.158704	+	0.558353i
$739$	851.804			0.0424007			0.0212004	−	0.999775i	$-0.493251\pi$
$739$	851.804			0.0424007			0.0212004	+	0.999775i	$0.493251\pi$
$740$	−2505.68	−	4339.97i	−0.124474	−	0.215595i
$741$	−6192.31	+	767.611i	−0.306991	+	0.0380552i
$742$	1785.09	−	3091.86i	0.0883190	−	0.152973i
$743$	16910.0	−	29289.0i	0.834950	−	1.44618i	−0.0591206	−	0.998251i	$-0.518830\pi$
$743$	16910.0	−	29289.0i	0.834950	−	1.44618i	0.894071	−	0.447926i	$-0.147837\pi$
$744$	336.618	−	41.7279i	0.0165874	−	0.00205621i
$745$	7057.61	+	12224.1i	0.347075	+	0.601152i
$746$	3879.91			0.190420
$747$	378.632	−	95.3371i	0.0185454	−	0.00466962i
$748$	−2220.82			−0.108558
$749$	−2034.23	−	3523.39i	−0.0992377	−	0.171885i
$750$	−4776.05	+	11288.1i	−0.232529	+	0.549575i
$751$	376.630	−	652.341i	0.0183001	−	0.0316968i	−0.856730	−	0.515765i	$-0.827508\pi$
$751$	376.630	−	652.341i	0.0183001	−	0.0316968i	0.875030	+	0.484068i	$0.160841\pi$
$752$	2671.95	−	4627.95i	0.129569	−	0.224420i
$753$	14508.9	+	19207.5i	0.702169	+	0.929564i
$754$	−8037.67	−	13921.7i	−0.388216	−	0.672409i
$755$	−1351.97			−0.0651699
$756$	1060.04	−	411.148i	0.0509963	−	0.0197795i
$757$	−8507.90			−0.408487			−0.204244	−	0.978920i	$-0.565473\pi$
$757$	−8507.90			−0.408487			−0.204244	+	0.978920i	$0.565473\pi$
$758$	17526.9	+	30357.4i	0.839847	+	1.45466i
$759$	11428.7	+	15129.8i	0.546553	+	0.723553i
$760$	8117.95	−	14060.7i	0.387459	−	0.671099i
$761$	−1839.97	+	3186.93i	−0.0876466	+	0.151808i	−0.906516	−	0.422172i	$-0.861268\pi$
$761$	−1839.97	+	3186.93i	−0.0876466	+	0.151808i	0.818869	+	0.573980i	$0.194601\pi$
$762$	4810.24	−	11368.9i	0.228683	−	0.540486i
$763$	−4834.84	−	8374.19i	−0.229401	−	0.397334i
$764$	−2553.83			−0.120935
$765$	20292.5	+	20916.2i	0.959053	+	0.988529i
$766$	30780.2			1.45187
$767$	−6916.57	−	11979.9i	−0.325610	−	0.563973i
$768$	−8968.72	+	1111.78i	−0.421394	+	0.0522369i
$769$	−10837.0	+	18770.3i	−0.508184	+	0.880201i	0.491771	+	0.870725i	$0.336350\pi$
$769$	−10837.0	+	18770.3i	−0.508184	+	0.880201i	−0.999955	+	0.00947643i	$0.996984\pi$
$770$	−2984.32	+	5169.00i	−0.139672	+	0.241919i
$771$	16276.9	−	2017.72i	0.760310	−	0.0942496i
$772$	−253.843	−	439.670i	−0.0118342	−	0.0204975i
$773$	16219.4			0.754685			0.377342	−	0.926074i	$-0.376838\pi$
$773$	16219.4			0.754685			0.377342	+	0.926074i	$0.376838\pi$
$774$	−20791.2	−	21430.2i	−0.965534	−	0.995209i
$775$	−159.184			−0.00737812
$776$	−21261.4	−	36825.9i	−0.983559	−	1.70357i
$777$	4530.02	−	10706.6i	0.209155	−	0.494332i
$778$	−10204.1	+	17673.9i	−0.470222	+	0.814449i
$779$	4123.27	−	7141.72i	0.189643	−	0.328471i
$780$	−1178.28	−	1559.86i	−0.0540887	−	0.0716052i
$781$	6129.28	+	10616.2i	0.280823	+	0.486400i
$782$	−31605.6			−1.44529
$783$	−28003.9	−	22516.2i	−1.27813	−	1.02767i
$784$	−2616.49			−0.119191
$785$	3341.36	+	5787.40i	0.151921	+	0.263135i
$786$	5078.19	+	6722.74i	0.230449	+	0.305079i
$787$	12981.2	−	22484.0i	0.587965	−	1.01838i	−0.406534	−	0.913636i	$-0.633263\pi$
$787$	12981.2	−	22484.0i	0.587965	−	1.01838i	0.994499	−	0.104749i	$-0.0334039\pi$
$788$	1468.01	−	2542.67i	0.0663652	−	0.114948i
$789$	3621.40	−	8559.08i	0.163404	−	0.386199i
$790$	−15837.7	−	27431.7i	−0.713267	−	1.23541i
$791$	−10498.3			−0.471905
$792$	−15096.1	+	3801.10i	−0.677294	+	0.170538i
$793$	−1032.68			−0.0462440
$794$	8106.03	+	14040.1i	0.362308	+	0.627535i
$795$	−13616.9	+	1687.98i	−0.607475	+	0.0753038i
$796$	1619.10	−	2804.36i	0.0720948	−	0.124872i
$797$	−13877.2	+	24036.1i	−0.616759	+	1.06826i	0.373314	+	0.927705i	$0.378221\pi$
$797$	−13877.2	+	24036.1i	−0.616759	+	1.06826i	−0.990073	+	0.140553i	$0.955112\pi$
$798$	4725.42	−	585.773i	0.209622	−	0.0259851i
$799$	−3987.93	−	6907.29i	−0.176574	−	0.305835i
$800$	3035.21			0.134138
$801$	−11310.1	+	39791.1i	−0.498904	+	1.75524i
$802$	2619.55			0.115336
$803$	−12512.0	−	21671.4i	−0.549861	−	0.952387i
$804$	−2382.83	+	5631.75i	−0.104522	+	0.247036i
$805$	7186.31	−	12447.1i	0.314639	−	0.544970i
$806$	85.5183	−	148.122i	0.00373729	−	0.00647318i
$807$	−18103.8	−	23966.6i	−0.789693	−	1.04543i
$808$	4056.67	+	7026.36i	0.176625	+	0.305924i
$809$	−3816.68			−0.165868			−0.0829340	−	0.996555i	$-0.526429\pi$
$809$	−3816.68			−0.165868			−0.0829340	+	0.996555i	$0.526429\pi$
$810$	21964.3	+	13583.5i	0.952773	+	0.589230i
$811$	20419.0			0.884103			0.442051	−	0.896990i	$-0.354251\pi$
$811$	20419.0			0.884103			0.442051	+	0.896990i	$0.354251\pi$
$812$	−1037.83	−	1797.58i	−0.0448532	−	0.0776880i
$813$	−17996.0	−	23824.0i	−0.776319	−	1.02773i
$814$	−10061.5	+	17427.0i	−0.433237	+	0.750388i
$815$	14726.8	−	25507.6i	0.632954	−	1.09631i
$816$	8616.62	−	20365.1i	0.369659	−	0.873679i
$817$	10579.0	+	18323.4i	0.453014	+	0.784644i
$818$	26443.4			1.13028
$819$	1239.88	−	4362.16i	0.0529000	−	0.186112i
$820$	2583.60			0.110029
$821$	10976.3	+	19011.5i	0.466597	+	0.808169i	0.999272	−	0.0381503i	$-0.0121466\pi$
$821$	10976.3	+	19011.5i	0.466597	+	0.808169i	−0.532675	+	0.846320i	$0.678813\pi$
$822$	−10286.2	+	1275.09i	−0.436461	+	0.0541046i
$823$	−5875.21	+	10176.2i	−0.248842	+	0.431007i	−0.963205	−	0.268769i	$-0.913383\pi$
$823$	−5875.21	+	10176.2i	−0.248842	+	0.431007i	0.714363	+	0.699775i	$0.246717\pi$
$824$	−5395.41	+	9345.13i	−0.228105	+	0.395089i
$825$	7250.22	−	898.752i	0.305964	−	0.0379279i
$826$	5278.11	+	9141.96i	0.222335	+	0.385096i
$827$	−7326.79			−0.308074			−0.154037	−	0.988065i	$-0.549228\pi$
$827$	−7326.79			−0.308074			−0.154037	+	0.988065i	$0.549228\pi$
$828$	4595.64	−	1157.15i	0.192886	−	0.0485674i
$829$	−13574.8			−0.568725			−0.284362	−	0.958717i	$-0.591782\pi$
$829$	−13574.8			−0.568725			−0.284362	+	0.958717i	$0.591782\pi$
$830$	256.147	+	443.659i	0.0107120	+	0.0185538i
$831$	−7073.72	+	16718.5i	−0.295288	+	0.697906i
$832$	−6755.60	+	11701.0i	−0.281500	+	0.487573i
$833$	−1952.58	+	3381.97i	−0.0812159	+	0.140670i
$834$	−11405.0	−	15098.4i	−0.473527	−	0.626878i
$835$	15575.9	+	26978.3i	0.645541	+	1.11811i
$836$	1394.58			0.0576943
$837$	58.4934	−	377.817i	0.00241557	−	0.0156025i
$838$	932.533			0.0384413
$839$	13920.6	+	24111.3i	0.572818	+	0.992149i	0.996275	+	0.0862330i	$0.0274830\pi$
$839$	13920.6	+	24111.3i	0.572818	+	0.992149i	−0.423457	+	0.905916i	$0.639184\pi$
$840$	7112.38	+	9415.71i	0.292144	+	0.386753i
$841$	−20605.2	+	35689.3i	−0.844858	+	1.46334i
$842$	3755.90	−	6505.42i	0.153726	−	0.266261i
$843$	−3754.95	+	8874.72i	−0.153413	+	0.362588i
$844$	1092.99	+	1893.12i	0.0445763	+	0.0772084i
$845$	21956.9			0.893895
$846$	−4921.65	−	5072.91i	−0.200012	−	0.206159i
$847$	5261.72			0.213453
$848$	5205.77	+	9016.66i	0.210810	+	0.365134i
$849$	27950.9	−	3464.85i	1.12988	−	0.140063i
$850$	−6088.80	+	10546.1i	−0.245699	+	0.425563i
$851$	24228.2	−	41964.5i	0.975950	−	1.69039i
$852$	3040.59	−	376.917i	0.122264	−	0.0151561i
$853$	10653.1	+	18451.7i	0.427613	+	0.740648i	0.996661	−	0.0816568i	$-0.0260211\pi$
$853$	10653.1	+	18451.7i	0.427613	+	0.740648i	−0.569047	+	0.822305i	$0.692688\pi$
$854$	788.049			0.0315767
$855$	−12742.8	−	13134.4i	−0.509700	−	0.525366i
$856$	13922.6			0.555916
$857$	1460.33	+	2529.37i	0.0582077	+	0.100819i	0.893661	−	0.448743i	$-0.148128\pi$
$857$	1460.33	+	2529.37i	0.0582077	+	0.100819i	−0.835453	+	0.549562i	$0.814795\pi$
$858$	−3058.74	+	7229.25i	−0.121706	+	0.287648i
$859$	13786.5	−	23879.0i	0.547602	−	0.948475i	−0.450836	−	0.892607i	$-0.648874\pi$
$859$	13786.5	−	23879.0i	0.547602	−	0.948475i	0.998438	−	0.0558681i	$-0.0177926\pi$
$860$	−3314.35	+	5740.63i	−0.131417	+	0.227621i
$861$	3612.52	+	4782.43i	0.142990	+	0.189297i
$862$	4216.64	+	7303.44i	0.166612	+	0.288580i
$863$	2361.13			0.0931329			0.0465664	−	0.998915i	$-0.485172\pi$
$863$	2361.13			0.0931329			0.0465664	+	0.998915i	$0.485172\pi$
$864$	−1115.31	+	7203.96i	−0.0439164	+	0.283662i
$865$	4232.81			0.166381
$866$	18683.8	+	32361.2i	0.733141	+	1.26984i
$867$	−4505.68	−	5964.84i	−0.176495	−	0.233652i
$868$	11.0422	−	19.1257i	0.000431794	−	0.000747890i
$869$	10760.6	−	18638.0i	0.420057	−	0.727560i
$870$	18371.2	−	43419.8i	0.715911	−	1.69203i
$871$	12195.3	+	21122.9i	0.474423	+	0.821725i
$872$	33090.4			1.28507
$873$	−46478.3	+	11702.9i	−1.80189	+	0.453705i
$874$	19846.9			0.768114
$875$	3156.21	+	5466.71i	0.121942	+	0.211210i
$876$	−6206.90	+	769.420i	−0.239397	+	0.0296761i
$877$	22493.5	−	38959.8i	0.866078	−	1.50009i	0.000106172	−	1.00000i	$-0.499966\pi$
$877$	22493.5	−	38959.8i	0.866078	−	1.50009i	0.865972	−	0.500092i	$-0.166700\pi$
$878$	−4597.39	+	7962.92i	−0.176714	+	0.306077i
$879$	7298.01	−	904.676i	0.280041	−	0.0347144i
$880$	−8703.04	−	15074.1i	−0.333386	−	0.577441i
$881$	−39465.4			−1.50922			−0.754610	−	0.656173i	$-0.772174\pi$
$881$	−39465.4			−1.50922			−0.754610	+	0.656173i	$0.772174\pi$
$882$	−946.170	+	3328.81i	−0.0361215	+	0.127083i
$883$	−33583.8			−1.27994			−0.639968	−	0.768402i	$-0.721052\pi$
$883$	−33583.8			−1.27994			−0.639968	+	0.768402i	$0.721052\pi$
$884$	1106.96	+	1917.31i	0.0421166	+	0.0729481i
$885$	15808.8	−	37363.6i	0.600460	−	1.41917i
$886$	10440.6	−	18083.7i	0.395891	−	0.685704i
$887$	−11710.5	+	20283.2i	−0.443293	+	0.767807i	−0.997932	−	0.0642850i	$-0.979523\pi$
$887$	−11710.5	+	20283.2i	−0.443293	+	0.767807i	0.554638	+	0.832092i	$0.312857\pi$
$888$	23979.0	+	31744.5i	0.906174	+	1.19964i
$889$	−3178.80	−	5505.84i	−0.119925	−	0.207717i
$890$	−54276.1			−2.04420
$891$	−530.999	+	17538.4i	−0.0199653	+	0.659437i
$892$	−1562.65			−0.0586563
$893$	2504.24	+	4337.48i	0.0938425	+	0.162540i
$894$	−8538.54	−	11303.7i	−0.319431	−	0.422878i
$895$	29428.0	−	50970.8i	1.09907	−	1.90365i
$896$	3700.39	−	6409.27i	0.137970	−	0.238972i
$897$	7365.51	−	17408.2i	0.274166	−	0.647984i
$898$	−4580.88	−	7934.31i	−0.170229	−	0.294846i
$899$	−697.958			−0.0258934
$900$	499.231	−	1756.39i	0.0184900	−	0.0650515i
$901$	15539.4			0.574576
$902$	−5187.18	−	8984.47i	−0.191479	−	0.331652i
$903$	−15260.6	+	1891.74i	−0.562393	+	0.0697154i
$904$	17963.0	−	31112.8i	0.660886	−	1.14469i
$905$	−751.606	+	1301.82i	−0.0276069	+	0.0478165i
$906$	1346.55	−	166.921i	0.0493775	−	0.00612094i
$907$	−2380.08	−	4122.42i	−0.0871327	−	0.150918i	0.819165	−	0.573557i	$-0.194437\pi$
$907$	−2380.08	−	4122.42i	−0.0871327	−	0.150918i	−0.906298	+	0.422639i	$0.861104\pi$
$908$	−2877.05			−0.105152
$909$	8868.03	−	2232.91i	0.323580	−	0.0814752i
$910$	5950.11			0.216752
$911$	4403.96	+	7627.89i	0.160164	+	0.277413i	0.934928	−	0.354839i	$-0.115464\pi$
$911$	4403.96	+	7627.89i	0.160164	+	0.277413i	−0.774763	+	0.632252i	$0.782131\pi$
$912$	−5410.86	+	12788.4i	−0.196460	+	0.464327i
$913$	−174.034	+	301.435i	−0.00630852	+	0.0109267i
$914$	−17084.2	+	29590.8i	−0.618268	+	1.07087i
$915$	−1825.51	−	2416.70i	−0.0659558	−	0.0873154i
$916$	−1077.86	−	1866.91i	−0.0388794	−	0.0673412i
$917$	4339.05			0.156257
$918$	−22793.4	−	18326.8i	−0.819494	−	0.658905i
$919$	50540.1			1.81411			0.907054	−	0.421015i	$-0.138326\pi$
$919$	50540.1			1.81411			0.907054	+	0.421015i	$0.138326\pi$
$920$	24592.1	+	42594.8i	0.881280	+	1.52642i
$921$	−20658.7	−	27349.0i	−0.739118	−	0.978479i
$922$	−8781.70	+	15210.4i	−0.313677	+	0.543304i
$923$	6110.23	−	10583.2i	0.217899	−	0.377412i
$924$	−394.948	+	933.448i	−0.0140615	+	0.0332340i
$925$	−9335.11	−	16168.9i	−0.331823	−	0.574735i
$926$	−15950.1			−0.566041
$927$	8469.20	+	8729.50i	0.300070	+	0.309293i
$928$	13308.2			0.470757
$929$	−2533.05	−	4387.36i	−0.0894580	−	0.154946i	0.817824	−	0.575468i	$-0.195180\pi$
$929$	−2533.05	−	4387.36i	−0.0894580	−	0.154946i	−0.907282	+	0.420522i	$0.861847\pi$
$930$	497.813	−	61.7099i	0.0175526	−	0.00217586i
$931$	1226.13	−	2123.73i	0.0431632	−	0.0747608i
$932$	−2370.43	+	4105.71i	−0.0833112	+	0.144299i
$933$	−3908.79	+	484.542i	−0.137158	+	0.0170023i
$934$	15602.2	+	27023.9i	0.546597	+	0.946733i
$935$	−25978.9			−0.908663
$936$	10806.2	+	11138.4i	0.377364	+	0.388962i
$937$	−17496.0			−0.609999			−0.305000	−	0.952352i	$-0.598656\pi$
$937$	−17496.0			−0.609999			−0.305000	+	0.952352i	$0.598656\pi$
$938$	−9306.39	−	16119.1i	−0.323949	−	0.561096i
$939$	−14386.9	+	34003.0i	−0.499999	+	1.18173i
$940$	−784.568	+	1358.91i	−0.0272232	+	0.0471519i
$941$	−15930.8	+	27592.9i	−0.551890	+	0.955902i	0.446248	+	0.894909i	$0.352760\pi$
$941$	−15930.8	+	27592.9i	−0.551890	+	0.955902i	−0.998138	+	0.0609927i	$0.980573\pi$
$942$	−4042.49	−	5351.64i	−0.139821	−	0.185102i
$943$	12490.8	+	21634.8i	0.431344	+	0.747110i
$944$	−30784.6			−1.06139
$945$	12400.2	−	4809.57i	0.426856	−	0.165561i
$946$	26617.3			0.914803
$947$	−6020.36	−	10427.6i	−0.206584	−	0.357814i	0.744052	−	0.668122i	$-0.232901\pi$
$947$	−6020.36	−	10427.6i	−0.206584	−	0.357814i	−0.950636	+	0.310307i	$0.899568\pi$
$948$	−3242.11	−	4292.06i	−0.111075	−	0.147046i
$949$	−12473.1	+	21604.1i	−0.426654	+	0.738986i
$950$	3823.50	−	6622.49i	0.130580	−	0.226171i
$951$	10648.9	−	25168.4i	0.363107	−	0.858193i
$952$	−6681.88	−	11573.4i	−0.227480	−	0.394007i
$953$	56064.5			1.90567			0.952837	−	0.303482i	$-0.0981494\pi$
$953$	56064.5			1.90567			0.952837	+	0.303482i	$0.0981494\pi$
$954$	13353.9	−	3362.42i	0.453195	−	0.114111i
$955$	−29874.4			−1.01226
$956$	−1228.77	−	2128.30i	−0.0415705	−	0.0720021i
$957$	31789.4	−	3940.68i	1.07378	−	0.133108i
$958$	9796.08	−	16967.3i	0.330373	−	0.572222i
$959$	−2669.01	+	4622.87i	−0.0898717	+	0.155662i
$960$	−39325.2	+	4874.83i	−1.32210	+	0.163890i
$961$	14891.8	+	25793.3i	0.499875	+	0.865810i
$962$	20060.4			0.672323
$963$	4290.47	−	15094.7i	0.143570	−	0.505109i
$964$	−6124.38			−0.204619
$965$	−2969.43	−	5143.21i	−0.0990563	−	0.171571i
$966$	−5620.70	+	13284.4i	−0.187208	+	0.442461i
$967$	−17575.4	+	30441.6i	−0.584476	+	1.01234i	0.410465	+	0.911877i	$0.365367\pi$
$967$	−17575.4	+	30441.6i	−0.584476	+	1.01234i	−0.994941	+	0.100466i	$0.967967\pi$
$968$	−9003.01	+	15593.7i	−0.298934	+	0.517768i
$969$	12491.9	+	16537.3i	0.414134	+	0.548251i
$970$	−31442.8	−	54460.5i	−1.04079	−	1.80270i
$971$	5008.69			0.165537			0.0827685	−	0.996569i	$-0.473624\pi$
$971$	5008.69			0.165537			0.0827685	+	0.996569i	$0.473624\pi$
$972$	3985.29	+	1830.31i	0.131511	+	0.0603983i
$973$	−9744.95			−0.321078
$974$	−18573.0	−	32169.3i	−0.611003	−	1.05829i
$975$	−4389.77	−	5811.39i	−0.144190	−	0.190885i
$976$	−1149.08	+	1990.26i	−0.0376855	+	0.0652731i
$977$	−7504.08	+	12997.4i	−0.245729	+	0.425614i	−0.962336	−	0.271862i	$-0.912361\pi$
$977$	−7504.08	+	12997.4i	−0.245729	+	0.425614i	0.716608	+	0.697476i	$0.245694\pi$
$978$	−11518.4	+	27223.5i	−0.376604	+	0.890092i
$979$	−18438.4	−	31936.3i	−0.601935	−	1.04258i
$980$	768.284			0.0250428
$981$	10197.3	−	35876.3i	0.331882	−	1.16763i
$982$	28229.1			0.917338
$983$	17493.7	+	30299.9i	0.567611	+	0.983131i	0.996802	+	0.0799169i	$0.0254655\pi$
$983$	17493.7	+	30299.9i	0.567611	+	0.983131i	−0.429191	+	0.903214i	$0.641201\pi$
$984$	−20354.4	+	2523.18i	−0.659426	+	0.0817438i
$985$	17172.7	−	29743.9i	0.555499	−	0.962152i
$986$	−26697.0	+	46240.6i	−0.862278	+	1.49351i
$987$	−3612.46	+	447.808i	−0.116500	+	0.0144416i
$988$	−695.122	−	1203.99i	−0.0223834	−	0.0387692i
$989$	−64095.0			−2.06077
$990$	−22325.1	+	5621.31i	−0.716705	+	0.180462i
$991$	−34764.1			−1.11435			−0.557173	−	0.830396i	$-0.688114\pi$
$991$	−34764.1			−1.11435			−0.557173	+	0.830396i	$0.688114\pi$
$992$	70.7976	+	122.625i	0.00226595	+	0.00392474i
$993$	8609.61	−	20348.6i	0.275144	−	0.650294i
$994$	−4662.79	+	8076.19i	−0.148787	+	0.257707i
$995$	18940.0	−	32805.1i	0.603457	−	1.04522i
$996$	52.4353	+	69.4164i	0.00166815	+	0.00220838i
$997$	15164.0	+	26264.9i	0.481695	+	0.834320i	0.999779	−	0.0210097i	$-0.00668810\pi$
$997$	15164.0	+	26264.9i	0.481695	+	0.834320i	−0.518085	+	0.855329i	$0.673355\pi$
$998$	16584.4			0.526024
$999$	41806.6	−	16215.2i	1.32403	−	0.513539i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.f.b.22.3	✓	16
3.2	odd	2		189.4.f.b.64.6		16
9.2	odd	6		189.4.f.b.127.6		16
9.4	even	3		567.4.a.i.1.6		8
9.5	odd	6		567.4.a.g.1.3		8
9.7	even	3	inner	63.4.f.b.43.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.f.b.22.3	✓	16	1.1	even	1	trivial
63.4.f.b.43.3	yes	16	9.7	even	3	inner
189.4.f.b.64.6		16	3.2	odd	2
189.4.f.b.127.6		16	9.2	odd	6
567.4.a.g.1.3		8	9.5	odd	6
567.4.a.i.1.6		8	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.30789 - 2.26533i) q^{2} +(-3.13193 - 4.14620i) q^{3} +(0.578868 - 1.00263i) q^{4} +(6.77153 - 11.7286i) q^{5} +(-5.29628 + 12.5176i) q^{6} +(3.50000 + 6.06218i) q^{7} -23.9546 q^{8} +(-7.38198 + 25.9713i) q^{9} +O(q^{10})\)	\(q+(-1.30789 - 2.26533i) q^{2} +(-3.13193 - 4.14620i) q^{3} +(0.578868 - 1.00263i) q^{4} +(6.77153 - 11.7286i) q^{5} +(-5.29628 + 12.5176i) q^{6} +(3.50000 + 6.06218i) q^{7} -23.9546 q^{8} +(-7.38198 + 25.9713i) q^{9} -35.4255 q^{10} +(-12.0346 - 20.8445i) q^{11} +(-5.97007 + 0.740063i) q^{12} +(-11.9972 + 20.7798i) q^{13} +(9.15520 - 15.8573i) q^{14} +(-69.8372 + 8.65717i) q^{15} +(26.6989 + 46.2438i) q^{16} +79.6971 q^{17} +(68.4881 - 17.2449i) q^{18} -50.0463 q^{19} +(-7.83963 - 13.5786i) q^{20} +(14.1732 - 33.4980i) q^{21} +(-31.4798 + 54.5245i) q^{22} +(75.8039 - 131.296i) q^{23} +(75.0241 + 99.3204i) q^{24} +(-29.2071 - 50.5883i) q^{25} +62.7639 q^{26} +(130.802 - 50.7331i) q^{27} +8.10415 q^{28} +(-128.062 - 221.810i) q^{29} +(110.950 + 146.881i) q^{30} +(1.36254 - 2.35999i) q^{31} +(-25.9800 + 44.9987i) q^{32} +(-48.7341 + 115.182i) q^{33} +(-104.235 - 180.540i) q^{34} +94.8014 q^{35} +(21.7663 + 22.4353i) q^{36} +319.617 q^{37} +(65.4548 + 113.371i) q^{38} +(123.732 - 15.3380i) q^{39} +(-162.209 + 280.954i) q^{40} +(-82.3892 + 142.702i) q^{41} +(-94.4210 + 11.7046i) q^{42} +(-211.384 - 366.129i) q^{43} -27.8657 q^{44} +(254.620 + 262.446i) q^{45} -396.571 q^{46} +(-50.0386 - 86.6693i) q^{47} +(108.117 - 255.532i) q^{48} +(-24.5000 + 42.4352i) q^{49} +(-76.3992 + 132.327i) q^{50} +(-249.606 - 330.440i) q^{51} +(13.8896 + 24.0575i) q^{52} +194.981 q^{53} +(-286.001 - 229.956i) q^{54} -325.970 q^{55} +(-83.8409 - 145.217i) q^{56} +(156.742 + 207.502i) q^{57} +(-334.981 + 580.204i) q^{58} +(-288.258 + 499.277i) q^{59} +(-31.7466 + 75.0321i) q^{60} +(21.5192 + 37.2723i) q^{61} -7.12819 q^{62} +(-183.279 + 46.1485i) q^{63} +563.098 q^{64} +(162.479 + 281.422i) q^{65} +(324.662 - 40.2458i) q^{66} +(508.257 - 880.326i) q^{67} +(46.1341 - 79.9065i) q^{68} +(-781.793 + 96.9127i) q^{69} +(-123.989 - 214.756i) q^{70} -509.305 q^{71} +(176.832 - 622.130i) q^{72} +1039.67 q^{73} +(-418.023 - 724.037i) q^{74} +(-118.274 + 279.538i) q^{75} +(-28.9702 + 50.1778i) q^{76} +(84.2422 - 145.912i) q^{77} +(-196.572 - 260.232i) q^{78} +(447.071 + 774.349i) q^{79} +723.169 q^{80} +(-620.013 - 383.439i) q^{81} +431.023 q^{82} +(-7.23057 - 12.5237i) q^{83} +(-25.3816 - 33.6014i) q^{84} +(539.671 - 934.738i) q^{85} +(-552.934 + 957.709i) q^{86} +(-518.587 + 1225.66i) q^{87} +(288.283 + 499.321i) q^{88} +1532.12 q^{89} +(261.511 - 920.046i) q^{90} -167.961 q^{91} +(-87.7608 - 152.006i) q^{92} +(-14.0524 + 1.74196i) q^{93} +(-130.889 + 226.707i) q^{94} +(-338.890 + 586.974i) q^{95} +(267.941 - 33.2146i) q^{96} +(887.575 + 1537.32i) q^{97} +128.173 q^{98} +(630.198 - 158.680i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} + 2 q^{3} - 43 q^{4} - 30 q^{5} + 19 q^{6} + 56 q^{7} + 12 q^{8} - 124 q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 + 2 * q^3 - 43 * q^4 - 30 * q^5 + 19 * q^6 + 56 * q^7 + 12 * q^8 - 124 * q^9	\( 16 q - 3 q^{2} + 2 q^{3} - 43 q^{4} - 30 q^{5} + 19 q^{6} + 56 q^{7} + 12 q^{8} - 124 q^{9} - 28 q^{10} - 24 q^{11} + 268 q^{12} - 68 q^{13} + 21 q^{14} + 56 q^{15} - 103 q^{16} + 336 q^{17} - 479 q^{18} + 352 q^{19} - 330 q^{20} + 70 q^{21} - 151 q^{22} - 228 q^{23} - 195 q^{24} - 244 q^{25} + 1590 q^{26} + 272 q^{27} - 602 q^{28} - 618 q^{29} + 1030 q^{30} - 72 q^{31} - 786 q^{32} - 700 q^{33} + 261 q^{34} - 420 q^{35} + 727 q^{36} + 420 q^{37} - 1032 q^{38} - 22 q^{39} + 375 q^{40} - 420 q^{41} - 175 q^{42} + 2 q^{43} + 774 q^{44} + 1406 q^{45} + 804 q^{46} - 570 q^{47} + 1864 q^{48} - 392 q^{49} - 1110 q^{50} - 2940 q^{51} + 431 q^{52} + 1056 q^{53} + 2269 q^{54} - 1676 q^{55} + 42 q^{56} + 122 q^{57} - 37 q^{58} + 150 q^{59} - 6350 q^{60} - 578 q^{61} + 2340 q^{62} - 350 q^{63} - 224 q^{64} + 366 q^{65} + 5812 q^{66} + 898 q^{67} - 2526 q^{68} - 2166 q^{69} - 98 q^{70} + 1764 q^{71} + 1350 q^{72} + 1944 q^{73} + 222 q^{74} - 2096 q^{75} - 1423 q^{76} + 168 q^{77} - 5558 q^{78} + 158 q^{79} + 4950 q^{80} + 476 q^{81} - 422 q^{82} - 2958 q^{83} + 1715 q^{84} + 774 q^{85} + 114 q^{86} + 44 q^{87} - 1317 q^{88} + 8760 q^{89} - 3659 q^{90} - 952 q^{91} - 4629 q^{92} + 3954 q^{93} + 3234 q^{94} - 930 q^{95} - 5923 q^{96} + 60 q^{97} + 294 q^{98} + 1214 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + 2 * q^3 - 43 * q^4 - 30 * q^5 + 19 * q^6 + 56 * q^7 + 12 * q^8 - 124 * q^9 - 28 * q^10 - 24 * q^11 + 268 * q^12 - 68 * q^13 + 21 * q^14 + 56 * q^15 - 103 * q^16 + 336 * q^17 - 479 * q^18 + 352 * q^19 - 330 * q^20 + 70 * q^21 - 151 * q^22 - 228 * q^23 - 195 * q^24 - 244 * q^25 + 1590 * q^26 + 272 * q^27 - 602 * q^28 - 618 * q^29 + 1030 * q^30 - 72 * q^31 - 786 * q^32 - 700 * q^33 + 261 * q^34 - 420 * q^35 + 727 * q^36 + 420 * q^37 - 1032 * q^38 - 22 * q^39 + 375 * q^40 - 420 * q^41 - 175 * q^42 + 2 * q^43 + 774 * q^44 + 1406 * q^45 + 804 * q^46 - 570 * q^47 + 1864 * q^48 - 392 * q^49 - 1110 * q^50 - 2940 * q^51 + 431 * q^52 + 1056 * q^53 + 2269 * q^54 - 1676 * q^55 + 42 * q^56 + 122 * q^57 - 37 * q^58 + 150 * q^59 - 6350 * q^60 - 578 * q^61 + 2340 * q^62 - 350 * q^63 - 224 * q^64 + 366 * q^65 + 5812 * q^66 + 898 * q^67 - 2526 * q^68 - 2166 * q^69 - 98 * q^70 + 1764 * q^71 + 1350 * q^72 + 1944 * q^73 + 222 * q^74 - 2096 * q^75 - 1423 * q^76 + 168 * q^77 - 5558 * q^78 + 158 * q^79 + 4950 * q^80 + 476 * q^81 - 422 * q^82 - 2958 * q^83 + 1715 * q^84 + 774 * q^85 + 114 * q^86 + 44 * q^87 - 1317 * q^88 + 8760 * q^89 - 3659 * q^90 - 952 * q^91 - 4629 * q^92 + 3954 * q^93 + 3234 * q^94 - 930 * q^95 - 5923 * q^96 + 60 * q^97 + 294 * q^98 + 1214 * q^99

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