LMFDB - Embedded newform 63.4.i.a.38.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [63,4,Mod(5,63)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("63.5"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(63, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 5])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.i (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			38.5
Character	$\chi$	$=$	63.38
Dual form			63.4.i.a.5.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.64983i q^{2} +(-4.97539 - 1.49850i) q^{3} -5.32127 q^{4} +(-6.11568 + 10.5927i) q^{5} +(-5.46929 + 18.1593i) q^{6} +(-17.8879 + 4.79841i) q^{7} -9.77690i q^{8} +(22.5090 + 14.9113i) q^{9} +(38.6615 + 22.3212i) q^{10} +(8.67010 - 5.00569i) q^{11} +(26.4754 + 7.97395i) q^{12} +(-57.0263 + 32.9241i) q^{13} +(17.5134 + 65.2877i) q^{14} +(46.3010 - 43.5383i) q^{15} -78.2542 q^{16} +(38.6818 - 66.9989i) q^{17} +(54.4237 - 82.1539i) q^{18} +(-104.262 + 60.1959i) q^{19} +(32.5432 - 56.3665i) q^{20} +(96.1894 + 2.93108i) q^{21} +(-18.2699 - 31.6444i) q^{22} +(-106.180 - 61.3030i) q^{23} +(-14.6507 + 48.6439i) q^{24} +(-12.3031 - 21.3096i) q^{25} +(120.168 + 208.136i) q^{26} +(-89.6462 - 107.919i) q^{27} +(95.1861 - 25.5337i) q^{28} +(-50.3417 - 29.0648i) q^{29} +(-158.907 - 168.991i) q^{30} -201.468i q^{31} +207.400i q^{32} +(-50.6382 + 11.9130i) q^{33} +(-244.535 - 141.182i) q^{34} +(58.5684 - 218.826i) q^{35} +(-119.776 - 79.3470i) q^{36} +(82.9121 + 143.608i) q^{37} +(219.705 + 380.540i) q^{38} +(333.065 - 78.3562i) q^{39} +(103.563 + 59.7924i) q^{40} +(112.422 + 194.721i) q^{41} +(10.6979 - 351.075i) q^{42} +(152.402 - 263.969i) q^{43} +(-46.1360 + 26.6366i) q^{44} +(-295.608 + 147.237i) q^{45} +(-223.746 + 387.539i) q^{46} +22.5866 q^{47} +(389.345 + 117.264i) q^{48} +(296.951 - 171.667i) q^{49} +(-77.7763 + 44.9042i) q^{50} +(-292.855 + 275.381i) q^{51} +(303.452 - 175.198i) q^{52} +(-360.132 - 207.922i) q^{53} +(-393.887 + 327.194i) q^{54} +122.453i q^{55} +(46.9136 + 174.888i) q^{56} +(608.949 - 143.260i) q^{57} +(-106.082 + 183.739i) q^{58} +360.669 q^{59} +(-246.381 + 231.679i) q^{60} +734.031i q^{61} -735.324 q^{62} +(-474.188 - 158.724i) q^{63} +130.940 q^{64} -805.414i q^{65} +(43.4806 + 184.821i) q^{66} -111.291 q^{67} +(-205.837 + 356.519i) q^{68} +(436.423 + 464.117i) q^{69} +(-798.677 - 213.765i) q^{70} +455.487i q^{71} +(145.786 - 220.068i) q^{72} +(-662.747 - 382.637i) q^{73} +(524.145 - 302.615i) q^{74} +(29.2801 + 124.460i) q^{75} +(554.808 - 320.319i) q^{76} +(-131.070 + 131.144i) q^{77} +(-285.987 - 1215.63i) q^{78} -43.1365 q^{79} +(478.578 - 828.921i) q^{80} +(284.307 + 671.275i) q^{81} +(710.697 - 410.321i) q^{82} +(200.064 - 346.522i) q^{83} +(-511.850 - 15.5971i) q^{84} +(473.131 + 819.488i) q^{85} +(-963.441 - 556.243i) q^{86} +(206.916 + 220.046i) q^{87} +(-48.9401 - 84.7667i) q^{88} +(-347.632 - 602.117i) q^{89} +(537.392 + 1078.92i) q^{90} +(862.094 - 862.577i) q^{91} +(565.012 + 326.210i) q^{92} +(-301.901 + 1002.38i) q^{93} -82.4373i q^{94} -1472.55i q^{95} +(310.789 - 1031.89i) q^{96} +(955.178 + 551.472i) q^{97} +(-626.554 - 1083.82i) q^{98} +(269.796 + 16.6095i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 3 q^{3} - 162 q^{4} - 3 q^{5} + 24 q^{6} + 5 q^{7} - 45 q^{9} - 6 q^{10} + 9 q^{11} + 186 q^{12} - 36 q^{13} + 54 q^{14} - 141 q^{15} + 526 q^{16} - 72 q^{17} - 54 q^{18} - 6 q^{19} + 24 q^{20} - 81 q^{21}+ \cdots + 4335 q^{99}+O(q^{100}) $ 44 * q - 3 * q^3 - 162 * q^4 - 3 * q^5 + 24 * q^6 + 5 * q^7 - 45 * q^9 - 6 * q^10 + 9 * q^11 + 186 * q^12 - 36 * q^13 + 54 * q^14 - 141 * q^15 + 526 * q^16 - 72 * q^17 - 54 * q^18 - 6 * q^19 + 24 * q^20 - 81 * q^21 + 14 * q^22 - 285 * q^23 - 114 * q^24 - 349 * q^25 - 96 * q^26 + 432 * q^27 - 156 * q^28 - 132 * q^29 - 447 * q^30 - 3 * q^33 + 24 * q^34 + 765 * q^35 + 1122 * q^36 + 82 * q^37 - 873 * q^38 + 306 * q^39 + 420 * q^40 + 618 * q^41 - 282 * q^42 + 82 * q^43 + 603 * q^44 + 291 * q^45 + 266 * q^46 - 402 * q^47 - 1569 * q^48 - 79 * q^49 - 1845 * q^50 + 453 * q^51 + 189 * q^52 + 564 * q^53 - 2385 * q^54 + 66 * q^56 + 1170 * q^57 + 269 * q^58 + 1494 * q^59 + 2265 * q^60 - 2904 * q^62 - 636 * q^63 - 1144 * q^64 - 372 * q^66 - 590 * q^67 + 3504 * q^68 - 1005 * q^69 - 105 * q^70 + 1830 * q^72 - 6 * q^73 + 1515 * q^74 - 33 * q^75 - 144 * q^76 - 4443 * q^77 - 5985 * q^78 + 1102 * q^79 - 4239 * q^80 - 4017 * q^81 + 18 * q^82 + 1830 * q^83 + 3165 * q^84 - 237 * q^85 + 1209 * q^86 + 2013 * q^87 - 623 * q^88 + 4266 * q^89 + 9993 * q^90 - 1140 * q^91 + 7896 * q^92 - 729 * q^93 + 3975 * q^96 - 792 * q^97 + 5667 * q^98 + 4335 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$		−	3.64983i		−	1.29041i	−0.764009	−	0.645205i	$-0.776772\pi$
$2$		−	3.64983i		−	1.29041i	0.764009	−	0.645205i	$-0.223228\pi$
$3$	−4.97539	−	1.49850i	−0.957514	−	0.288387i
$3$	−4.97539	−	1.49850i	−0.957514	−	0.288387i
$4$	−5.32127			−0.665159
$5$	−6.11568	+	10.5927i	−0.547003	+	0.947437i	0.451475	+	0.892284i	$0.350898\pi$
$5$	−6.11568	+	10.5927i	−0.547003	+	0.947437i	−0.998478	+	0.0551532i	$0.982435\pi$
$6$	−5.46929	+	18.1593i	−0.372138	+	1.23559i
$7$	−17.8879	+	4.79841i	−0.965853	+	0.259090i
$7$	−17.8879	+	4.79841i	−0.965853	+	0.259090i
$8$		−	9.77690i		−	0.432082i
$9$	22.5090	+	14.9113i	0.833665	+	0.552270i
$10$	38.6615	+	22.3212i	1.22258	+	0.705858i
$11$	8.67010	−	5.00569i	0.237649	−	0.137206i	−0.376447	−	0.926438i	$-0.622854\pi$
$11$	8.67010	−	5.00569i	0.237649	−	0.137206i	0.614096	+	0.789232i	$0.289521\pi$
$12$	26.4754	+	7.97395i	0.636899	+	0.191823i
$13$	−57.0263	+	32.9241i	−1.21663	+	0.702424i	−0.964196	−	0.265189i	$-0.914566\pi$
$13$	−57.0263	+	32.9241i	−1.21663	+	0.702424i	−0.252437	+	0.967613i	$0.581232\pi$
$14$	17.5134	+	65.2877i	0.334332	+	1.24635i
$15$	46.3010	−	43.5383i	0.796992	−	0.749435i
$16$	−78.2542			−1.22272
$17$	38.6818	−	66.9989i	0.551866	−	0.955860i	−0.446274	−	0.894896i	$-0.647249\pi$
$17$	38.6818	−	66.9989i	0.551866	−	0.955860i	0.998140	−	0.0609637i	$-0.0194174\pi$
$18$	54.4237	−	82.1539i	0.712655	−	1.07577i
$19$	−104.262	+	60.1959i	−1.25892	+	0.726836i	−0.972864	−	0.231378i	$-0.925677\pi$
$19$	−104.262	+	60.1959i	−1.25892	+	0.726836i	−0.286053	+	0.958214i	$0.592343\pi$
$20$	32.5432	−	56.3665i	0.363844	−	0.630196i
$21$	96.1894	+	2.93108i	0.999536	+	0.0304578i
$22$	−18.2699	−	31.6444i	−0.177053	−	0.306664i
$23$	−106.180	−	61.3030i	−0.962610	−	0.555763i	−0.0656346	−	0.997844i	$-0.520907\pi$
$23$	−106.180	−	61.3030i	−0.962610	−	0.555763i	−0.896975	+	0.442081i	$0.854241\pi$
$24$	−14.6507	+	48.6439i	−0.124607	+	0.413725i
$25$	−12.3031	−	21.3096i	−0.0984247	−	0.170477i
$26$	120.168	+	208.136i	0.906415	+	1.56996i
$27$	−89.6462	−	107.919i	−0.638979	−	0.769225i
$28$	95.1861	−	25.5337i	0.642446	−	0.172336i
$29$	−50.3417	−	29.0648i	−0.322352	−	0.186110i	0.330088	−	0.943950i	$-0.392922\pi$
$29$	−50.3417	−	29.0648i	−0.322352	−	0.186110i	−0.652441	+	0.757840i	$0.726255\pi$
$30$	−158.907	−	168.991i	−0.967079	−	1.02845i
$31$		−	201.468i		−	1.16725i	−0.812024	−	0.583624i	$-0.801634\pi$
$31$		−	201.468i		−	1.16725i	0.812024	−	0.583624i	$-0.198366\pi$
$32$			207.400i			1.14573i
$33$	−50.6382	+	11.9130i	−0.267120	+	0.0628422i
$34$	−244.535	−	141.182i	−1.23345	−	0.712134i
$35$	58.5684	−	218.826i	0.282853	−	1.05681i
$36$	−119.776	−	79.3470i	−0.554520	−	0.367347i
$37$	82.9121	+	143.608i	0.368396	+	0.638081i	0.989315	−	0.145794i	$-0.0465737\pi$
$37$	82.9121	+	143.608i	0.368396	+	0.638081i	−0.620919	+	0.783875i	$0.713240\pi$
$38$	219.705	+	380.540i	0.937917	+	1.62452i
$39$	333.065	−	78.3562i	1.36751	−	0.321719i
$40$	103.563	+	59.7924i	0.409371	+	0.236350i
$41$	112.422	+	194.721i	0.428228	+	0.741713i	0.996716	−	0.0809786i	$-0.0258046\pi$
$41$	112.422	+	194.721i	0.428228	+	0.741713i	−0.568487	+	0.822692i	$0.692471\pi$
$42$	10.6979	−	351.075i	0.0393031	−	1.28981i
$43$	152.402	−	263.969i	0.540492	−	0.936159i	−0.458384	−	0.888754i	$-0.651572\pi$
$43$	152.402	−	263.969i	0.540492	−	0.936159i	0.998876	−	0.0474048i	$-0.0150951\pi$
$44$	−46.1360	+	26.6366i	−0.158074	+	0.0912641i
$45$	−295.608	+	147.237i	−0.979258	+	0.487752i
$46$	−223.746	+	387.539i	−0.717163	+	1.24216i
$47$	22.5866			0.0700977			0.0350489	−	0.999386i	$-0.488841\pi$
$47$	22.5866			0.0700977			0.0350489	+	0.999386i	$0.488841\pi$
$48$	389.345	+	117.264i	1.17077	+	0.352618i
$49$	296.951	−	171.667i	0.865745	−	0.500485i
$50$	−77.7763	+	44.9042i	−0.219985	+	0.127008i
$51$	−292.855	+	275.381i	−0.804077	+	0.756098i
$52$	303.452	−	175.198i	0.809255	−	0.467224i
$53$	−360.132	−	207.922i	−0.933358	−	0.538875i	−0.0454860	−	0.998965i	$-0.514484\pi$
$53$	−360.132	−	207.922i	−0.933358	−	0.538875i	−0.887872	+	0.460090i	$0.847817\pi$
$54$	−393.887	+	327.194i	−0.992615	+	0.824545i
$55$			122.453i			0.300209i
$56$	46.9136	+	174.888i	0.111948	+	0.417328i
$57$	608.949	−	143.260i	1.41504	−	0.332900i
$58$	−106.082	+	183.739i	−0.240159	+	0.415967i
$59$	360.669			0.795849			0.397924	−	0.917418i	$-0.369731\pi$
$59$	360.669			0.795849			0.397924	+	0.917418i	$0.369731\pi$
$60$	−246.381	+	231.679i	−0.530126	+	0.498494i
$61$			734.031i			1.54071i	0.637618	+	0.770353i	$0.279920\pi$
$61$			734.031i			1.54071i	−0.637618	+	0.770353i	$0.720080\pi$
$62$	−735.324			−1.50623
$63$	−474.188	−	158.724i	−0.948286	−	0.317417i
$64$	130.940			0.255742
$65$		−	805.414i		−	1.53691i
$66$	43.4806	+	184.821i	0.0810923	+	0.344695i
$67$	−111.291			−0.202931			−0.101466	−	0.994839i	$-0.532353\pi$
$67$	−111.291			−0.202931			−0.101466	+	0.994839i	$0.532353\pi$
$68$	−205.837	+	356.519i	−0.367079	+	0.635799i
$69$	436.423	+	464.117i	0.761437	+	0.809755i
$70$	−798.677	−	213.765i	−1.36372	−	0.364997i
$71$			455.487i			0.761358i	0.924707	+	0.380679i	$0.124310\pi$
$71$			455.487i			0.761358i	−0.924707	+	0.380679i	$0.875690\pi$
$72$	145.786	−	220.068i	0.238626	−	0.360212i
$73$	−662.747	−	382.637i	−1.06258	−	0.613483i	−0.136438	−	0.990649i	$-0.543565\pi$
$73$	−662.747	−	382.637i	−1.06258	−	0.613483i	−0.926146	+	0.377166i	$0.876899\pi$
$74$	524.145	−	302.615i	0.823386	−	0.475382i
$75$	29.2801	+	124.460i	0.0450797	+	0.191618i
$76$	554.808	−	320.319i	0.837380	−	0.483462i
$77$	−131.070	+	131.144i	−0.193985	+	0.194094i
$78$	−285.987	−	1215.63i	−0.415149	−	1.76465i
$79$	−43.1365			−0.0614334			−0.0307167	−	0.999528i	$-0.509779\pi$
$79$	−43.1365			−0.0614334			−0.0307167	+	0.999528i	$0.509779\pi$
$80$	478.578	−	828.921i	0.668833	−	1.15845i
$81$	284.307	+	671.275i	0.389996	+	0.920816i
$82$	710.697	−	410.321i	0.957115	−	0.552590i
$83$	200.064	−	346.522i	0.264577	−	0.458262i	−0.702875	−	0.711313i	$-0.748101\pi$
$83$	200.064	−	346.522i	0.264577	−	0.458262i	0.967453	+	0.253051i	$0.0814342\pi$
$84$	−511.850	−	15.5971i	−0.664851	−	0.0202593i
$85$	473.131	+	819.488i	0.603745	+	1.04572i
$86$	−963.441	−	556.243i	−1.20803	−	0.697456i
$87$	206.916	+	220.046i	0.254985	+	0.271166i
$88$	−48.9401	−	84.7667i	−0.0592845	−	0.102684i
$89$	−347.632	−	602.117i	−0.414033	−	0.717127i	0.581293	−	0.813694i	$-0.302547\pi$
$89$	−347.632	−	602.117i	−0.414033	−	0.717127i	−0.995326	+	0.0965674i	$0.969214\pi$
$90$	537.392	+	1078.92i	0.629401	+	1.26365i
$91$	862.094	−	862.577i	0.993099	−	0.993656i
$92$	565.012	+	326.210i	0.640289	+	0.369671i
$93$	−301.901	+	1002.38i	−0.336620	+	1.11766i
$94$		−	82.4373i		−	0.0904548i
$95$		−	1472.55i		−	1.59033i
$96$	310.789	−	1031.89i	0.330415	−	1.09705i
$97$	955.178	+	551.472i	0.999831	+	0.577253i	0.908198	−	0.418540i	$-0.137458\pi$
$97$	955.178	+	551.472i	0.999831	+	0.577253i	0.0916328	+	0.995793i	$0.470791\pi$
$98$	−626.554	−	1083.82i	−0.645832	−	1.11717i
$99$	269.796	+	16.6095i	0.273894	+	0.0168618i
$100$	65.4681	+	113.394i	0.0654681	+	0.113394i
$101$	−352.193	−	610.017i	−0.346976	−	0.600979i	0.638735	−	0.769427i	$-0.279458\pi$
$101$	−352.193	−	610.017i	−0.346976	−	0.600979i	−0.985711	+	0.168447i	$0.946125\pi$
$102$	1005.09	+	1068.87i	0.975677	+	1.03759i
$103$	−899.558	−	519.360i	−0.860545	−	0.496836i	0.00364978	−	0.999993i	$-0.498838\pi$
$103$	−899.558	−	519.360i	−0.860545	−	0.496836i	−0.864195	+	0.503157i	$0.832172\pi$
$104$	321.896	+	557.540i	0.303505	+	0.525686i
$105$	−619.312	+	1000.98i	−0.575606	+	0.930337i
$106$	−758.882	+	1314.42i	−0.695369	+	1.20442i
$107$	−50.4942	+	29.1528i	−0.0456211	+	0.0263394i	−0.522637	−	0.852555i	$-0.675052\pi$
$107$	−50.4942	+	29.1528i	−0.0456211	+	0.0263394i	0.477016	+	0.878895i	$0.341718\pi$
$108$	477.032	+	574.268i	0.425022	+	0.511657i
$109$	−444.694	+	770.232i	−0.390770	+	0.676834i	−0.992551	−	0.121827i	$-0.961125\pi$
$109$	−444.694	+	770.232i	−0.390770	+	0.676834i	0.601781	+	0.798661i	$0.294458\pi$
$110$	446.932			0.387393
$111$	−197.323	−	838.749i	−0.168730	−	0.717212i
$112$	1399.80	−	375.496i	1.18097	−	0.316795i
$113$	−2032.03	+	1173.20i	−1.69166	+	0.976681i	−0.738481	+	0.674274i	$0.764457\pi$
$113$	−2032.03	+	1173.20i	−1.69166	+	0.976681i	−0.953179	+	0.302407i	$0.902210\pi$
$114$	−522.876	−	2222.56i	−0.429577	−	1.82598i
$115$	1298.72	−	749.819i	1.05310	−	0.608008i
$116$	267.882	+	154.662i	0.214416	+	0.123793i
$117$	−1774.54	−	109.247i	−1.40219	−	0.0863236i
$118$		−	1316.38i		−	1.02697i
$119$	−370.447	+	1384.08i	−0.285368	+	1.06620i
$120$	−425.669	−	452.681i	−0.323818	−	0.344366i
$121$	−615.386	+	1065.88i	−0.462349	+	0.800812i
$122$	2679.09			1.98814
$123$	−267.553	−	1137.28i	−0.196134	−	0.833696i
$124$			1072.07i			0.776406i
$125$	−1227.95			−0.878652
$126$	−579.314	+	1730.70i	−0.409599	+	1.22368i
$127$	−1026.54			−0.717251			−0.358625	−	0.933482i	$-0.616754\pi$
$127$	−1026.54			−0.717251			−0.358625	+	0.933482i	$0.616754\pi$
$128$			1181.29i			0.815720i
$129$	−1153.82	+	1084.97i	−0.787505	+	0.740514i
$130$	−2939.62			−1.98325
$131$	−715.576	+	1239.41i	−0.477253	+	0.826627i	−0.999660	−	0.0260695i	$-0.991701\pi$
$131$	−715.576	+	1239.41i	−0.477253	+	0.826627i	0.522407	+	0.852696i	$0.325034\pi$
$132$	269.460	−	63.3925i	0.177678	−	0.0418001i
$133$	1576.18	−	1577.07i	1.02761	−	1.02819i
$134$			406.195i			0.261865i
$135$	1691.40	−	289.593i	1.07832	−	0.184624i
$136$	−655.042	−	378.189i	−0.413010	−	0.238451i
$137$	2188.83	−	1263.72i	1.36500	−	0.788081i	0.374713	−	0.927141i	$-0.377741\pi$
$137$	2188.83	−	1263.72i	1.36500	−	0.788081i	0.990284	+	0.139060i	$0.0444080\pi$
$138$	1693.95	−	1592.87i	1.04492	−	0.982567i
$139$	247.028	−	142.622i	0.150739	−	0.0870290i	−0.422734	−	0.906254i	$-0.638929\pi$
$139$	247.028	−	142.622i	0.150739	−	0.0870290i	0.573472	+	0.819225i	$0.305596\pi$
$140$	−311.659	+	1164.43i	−0.188143	+	0.702946i
$141$	−112.377	−	33.8461i	−0.0671195	−	0.0202153i
$142$	1662.45			0.982464
$143$	−329.616	+	570.911i	−0.192754	+	0.333860i
$144$	−1761.42	−	1166.87i	−1.01934	−	0.675273i
$145$	615.748	−	355.502i	0.352656	−	0.203606i
$146$	−1396.56	+	2418.91i	−0.791645	+	1.37117i
$147$	−1734.69	+	409.126i	−0.973296	+	0.229552i
$148$	−441.198	−	764.177i	−0.245042	−	0.424425i
$149$	1631.83	+	942.139i	0.897215	+	0.518007i	0.876296	−	0.481774i	$-0.160007\pi$
$149$	1631.83	+	942.139i	0.897215	+	0.518007i	0.0209192	+	0.999781i	$0.493341\pi$
$150$	454.257	−	106.868i	0.247266	−	0.0581713i
$151$	200.223	+	346.797i	0.107907	+	0.186900i	0.914922	−	0.403630i	$-0.132252\pi$
$151$	200.223	+	346.797i	0.107907	+	0.186900i	−0.807015	+	0.590531i	$0.798918\pi$
$152$	588.529	+	1019.36i	0.314053	+	0.543955i
$153$	1869.73	−	931.280i	0.987964	−	0.492089i
$154$	478.652	+	478.384i	0.250460	+	0.250320i
$155$	2134.08	+	1232.11i	1.10589	+	0.638489i
$156$	−1772.33	+	416.955i	−0.909614	+	0.213994i
$157$			1961.83i			0.997268i	0.866813	+	0.498634i	$0.166165\pi$
$157$			1961.83i			0.997268i	−0.866813	+	0.498634i	$0.833835\pi$
$158$			157.441i			0.0792743i
$159$	1480.23	+	1574.15i	0.738299	+	0.785148i
$160$	−2196.92	−	1268.39i	−1.08551	−	0.626719i
$161$	2193.49	+	587.084i	1.07373	+	0.287383i
$162$	2450.04	−	1037.67i	1.18823	−	0.503255i
$163$	1092.64	+	1892.50i	0.525043	+	0.909400i	0.999575	+	0.0291623i	$0.00928395\pi$
$163$	1092.64	+	1892.50i	0.525043	+	0.909400i	−0.474532	+	0.880238i	$0.657383\pi$
$164$	−598.228	−	1036.16i	−0.284840	−	0.493357i
$165$	183.496	−	609.250i	0.0865766	−	0.287455i
$166$	−1264.75	−	730.202i	−0.591345	−	0.341413i
$167$	−724.771	−	1255.34i	−0.335835	−	0.581683i	0.647810	−	0.761802i	$-0.275685\pi$
$167$	−724.771	−	1255.34i	−0.335835	−	0.581683i	−0.983645	+	0.180119i	$0.942352\pi$
$168$	28.6569	−	940.435i	0.0131603	−	0.431882i
$169$	1069.50	−	1852.42i	0.486798	−	0.843160i
$170$	2990.99	−	1726.85i	1.34940	−	0.779079i
$171$	−3244.44	−	199.738i	−1.45092	−	0.0893237i
$172$	−810.975	+	1404.65i	−0.359513	+	0.622695i
$173$	−1845.93			−0.811233			−0.405617	−	0.914043i	$-0.632943\pi$
$173$	−1845.93			−0.811233			−0.405617	+	0.914043i	$0.632943\pi$
$174$	803.131	−	755.208i	0.349915	−	0.329035i
$175$	322.328	+	322.147i	0.139233	+	0.139154i
$176$	−678.472	+	391.716i	−0.290578	+	0.167765i
$177$	−1794.47	−	540.464i	−0.762036	−	0.229513i
$178$	−2197.63	+	1268.80i	−0.925388	+	0.534273i
$179$	−389.538	−	224.900i	−0.162656	−	0.0939096i	0.416462	−	0.909153i	$-0.363270\pi$
$179$	−389.538	−	224.900i	−0.162656	−	0.0939096i	−0.579118	+	0.815243i	$0.696603\pi$
$180$	1573.01	−	783.490i	0.651363	−	0.324433i
$181$		−	3067.12i		−	1.25954i	−0.776781	−	0.629771i	$-0.783149\pi$
$181$		−	3067.12i		−	1.25954i	0.776781	−	0.629771i	$-0.216851\pi$
$182$	−3148.26	−	3146.50i	−1.28222	−	1.28151i
$183$	1099.95	−	3652.09i	0.444320	−	1.47525i
$184$	−599.353	+	1038.11i	−0.240135	+	0.415927i
$185$	−2028.25			−0.806055
$186$	3658.52	+	1101.89i	1.44224	+	0.434378i
$187$		−	774.517i		−	0.302878i
$188$	−120.189			−0.0466261
$189$	2121.42	+	1500.28i	0.816458	+	0.577405i
$190$	−5374.58			−2.05217
$191$		−	5200.53i		−	1.97014i	−0.172147	−	0.985071i	$-0.555070\pi$
$191$		−	5200.53i		−	1.97014i	0.172147	−	0.985071i	$-0.444930\pi$
$192$	−651.476	−	196.214i	−0.244876	−	0.0737527i
$193$	2376.22			0.886239			0.443119	−	0.896463i	$-0.353872\pi$
$193$	2376.22			0.886239			0.443119	+	0.896463i	$0.353872\pi$
$194$	2012.78	−	3486.24i	0.744893	−	1.29019i
$195$	−1206.92	+	4007.25i	−0.443226	+	1.47161i
$196$	−1580.15	+	913.484i	−0.575858	+	0.332902i
$197$			148.115i			0.0535672i	0.999641	+	0.0267836i	$0.00852651\pi$
$197$			148.115i			0.0535672i	−0.999641	+	0.0267836i	$0.991473\pi$
$198$	60.6220	−	984.711i	0.0217587	−	0.353436i
$199$	−1479.37	−	854.117i	−0.526985	−	0.304255i	0.212803	−	0.977095i	$-0.431741\pi$
$199$	−1479.37	−	854.117i	−0.526985	−	0.304255i	−0.739788	+	0.672840i	$0.765074\pi$
$200$	−208.342	+	120.286i	−0.0736599	+	0.0425275i
$201$	553.718	+	166.771i	0.194310	+	0.0585228i
$202$	−2226.46	+	1285.45i	−0.775510	+	0.447741i
$203$	1039.97	+	278.347i	0.359564	+	0.0962370i
$204$	1558.36	−	1465.38i	0.534839	−	0.502926i
$205$	−2750.15			−0.936969
$206$	−1895.58	+	3283.24i	−0.641122	+	1.11046i
$207$	−1475.89	−	2963.14i	−0.495564	−	0.994941i
$208$	4462.55	−	2576.45i	1.48761	−	0.858869i
$209$	−602.643	+	1043.81i	−0.199453	+	0.345463i
$210$	3653.40	+	2260.38i	1.20052	+	0.742768i
$211$	545.976	+	945.659i	0.178135	+	0.308540i	0.941242	−	0.337733i	$-0.109660\pi$
$211$	545.976	+	945.659i	0.178135	+	0.308540i	−0.763106	+	0.646273i	$0.776327\pi$
$212$	1916.36	+	1106.41i	0.620832	+	0.358437i
$213$	682.550	−	2266.23i	0.219566	−	0.729010i
$214$	106.403	+	184.295i	0.0339886	+	0.0588700i
$215$	1864.09	+	3228.70i	0.591301	+	1.02416i
$216$	−1055.12	+	876.462i	−0.332368	+	0.276091i
$217$	966.726	+	3603.83i	0.302422	+	1.12739i
$218$	2811.22	+	1623.06i	0.873393	+	0.504254i
$219$	2724.04	+	2896.90i	0.840518	+	0.893854i
$220$		−	651.604i		−	0.199687i
$221$			5094.26i			1.55058i
$222$	−3061.29	+	720.194i	−0.925498	+	0.217731i
$223$	−1063.36	−	613.931i	−0.319317	−	0.184358i	0.331771	−	0.943360i	$-0.392354\pi$
$223$	−1063.36	−	613.931i	−0.319317	−	0.184358i	−0.651088	+	0.759002i	$0.725687\pi$
$224$	−995.188	−	3709.93i	−0.296847	−	1.10661i
$225$	40.8233	−	663.111i	0.0120958	−	0.196477i
$226$	4281.96	+	7416.58i	1.26032	+	2.18294i
$227$	−1131.73	−	1960.21i	−0.330905	−	0.573144i	0.651785	−	0.758404i	$-0.274021\pi$
$227$	−1131.73	−	1960.21i	−0.330905	−	0.573144i	−0.982689	+	0.185260i	$0.940687\pi$
$228$	−3240.39	+	762.327i	−0.941227	+	0.221431i
$229$	−4462.12	−	2576.20i	−1.28762	−	0.743408i	−0.309391	−	0.950935i	$-0.600125\pi$
$229$	−4462.12	−	2576.20i	−1.28762	−	0.743408i	−0.978229	+	0.207527i	$0.933458\pi$
$230$	−2736.71	−	4740.12i	−0.784580	−	1.35893i
$231$	848.644	−	456.081i	0.241717	−	0.129905i
$232$	−284.164	+	492.186i	−0.0804149	+	0.139283i
$233$	361.488	−	208.705i	0.101639	−	0.0586812i	−0.448319	−	0.893874i	$-0.647977\pi$
$233$	361.488	−	208.705i	0.101639	−	0.0586812i	0.549958	+	0.835192i	$0.314644\pi$
$234$	−398.732	+	6476.78i	−0.111393	+	1.80940i
$235$	−138.132	+	239.252i	−0.0383437	+	0.0664132i
$236$	−1919.22			−0.529366
$237$	214.621	+	64.6403i	0.0588233	+	0.0177166i
$238$	5051.65	+	1352.07i	1.37584	+	0.368242i
$239$	4832.69	−	2790.15i	1.30795	−	0.755146i	0.326198	−	0.945302i	$-0.394233\pi$
$239$	4832.69	−	2790.15i	1.30795	−	0.755146i	0.981754	+	0.190155i	$0.0608992\pi$
$240$	−3623.25	+	3407.05i	−0.974500	+	0.916351i
$241$	2402.23	−	1386.93i	0.642079	−	0.370704i	−0.143336	−	0.989674i	$-0.545783\pi$
$241$	2402.23	−	1386.93i	0.642079	−	0.370704i	0.785415	+	0.618970i	$0.212450\pi$
$242$	3890.28	+	2246.06i	1.03338	+	0.596620i
$243$	−408.630	−	3765.89i	−0.107875	−	0.994164i
$244$		−	3905.98i		−	1.02481i
$245$	2.35213	+	4195.36i	0.000613356	+	1.09401i
$246$	−4150.86	+	976.524i	−1.07581	+	0.253093i
$247$	3963.79	−	6865.49i	1.02109	−	1.76859i
$248$	−1969.73			−0.504347
$249$	−1514.66	+	1424.28i	−0.385493	+	0.362491i
$250$			4481.82i			1.13382i
$251$	−3751.34			−0.943357			−0.471678	−	0.881771i	$-0.656352\pi$
$251$	−3751.34			−0.943357			−0.471678	+	0.881771i	$0.656352\pi$
$252$	2523.28	+	844.612i	0.630761	+	0.211133i
$253$	−1227.45			−0.305017
$254$			3746.70i			0.925548i
$255$	−1126.01	−	4786.26i	−0.276523	−	1.17540i
$256$	5359.02			1.30836
$257$	3755.86	−	6505.34i	0.911612	−	1.57896i	0.0998242	−	0.995005i	$-0.468172\pi$
$257$	3755.86	−	6505.34i	0.911612	−	1.57896i	0.811788	−	0.583953i	$-0.198495\pi$
$258$	3959.96	+	4211.25i	0.955567	+	1.01620i
$259$	−2172.21	−	2170.99i	−0.521137	−	0.520845i
$260$			4285.83i			1.02229i
$261$	−699.746	−	1404.88i	−0.165951	−	0.333179i
$262$	4523.65	+	2611.73i	1.06669	+	0.615852i
$263$	−4793.38	+	2767.46i	−1.12385	+	0.648854i	−0.942381	−	0.334542i	$-0.891418\pi$
$263$	−4793.38	+	2767.46i	−1.12385	+	0.648854i	−0.181468	+	0.983397i	$0.558085\pi$
$264$	116.473	+	495.084i	0.0271530	+	0.115418i
$265$	4404.91	−	2543.17i	1.02110	−	0.589532i
$266$	−5756.03	−	5752.81i	−1.32679	−	1.32604i
$267$	827.331	+	3516.70i	0.189632	+	0.806061i
$268$	592.212			0.134982
$269$	411.958	−	713.532i	0.0933737	−	0.161728i	−0.815555	−	0.578680i	$-0.803568\pi$
$269$	411.958	−	713.532i	0.0933737	−	0.161728i	0.908929	+	0.416952i	$0.136902\pi$
$270$	−1056.97	−	6173.33i	−0.238241	−	1.39147i
$271$	−3757.66	+	2169.49i	−0.842294	+	0.486299i	−0.858043	−	0.513577i	$-0.828320\pi$
$271$	−3757.66	+	2169.49i	−0.842294	+	0.486299i	0.0157492	+	0.999876i	$0.494987\pi$
$272$	−3027.02	+	5242.95i	−0.674779	+	1.16875i
$273$	−5581.83	+	2999.80i	−1.23746	+	0.665042i
$274$	−4612.38	−	7988.87i	−1.01695	−	1.76141i
$275$	−213.338	−	123.171i	−0.0467810	−	0.0270090i
$276$	−2322.33	−	2469.69i	−0.506477	−	0.538616i
$277$	1321.28	+	2288.52i	0.286599	+	0.496405i	0.972996	−	0.230823i	$-0.0741418\pi$
$277$	1321.28	+	2288.52i	0.286599	+	0.496405i	−0.686396	+	0.727228i	$0.740808\pi$
$278$	−520.546	−	901.612i	−0.112303	−	0.194515i
$279$	3004.15	−	4534.84i	0.644636	−	0.973095i
$280$	−2139.44	−	572.618i	−0.456628	−	0.122216i
$281$	−3315.71	−	1914.33i	−0.703910	−	0.406403i	0.104892	−	0.994484i	$-0.466550\pi$
$281$	−3315.71	−	1914.33i	−0.703910	−	0.406403i	−0.808802	+	0.588081i	$0.799884\pi$
$282$	−123.533	+	410.157i	−0.0260860	+	0.0866118i
$283$			7192.67i			1.51081i	0.655257	+	0.755406i	$0.272560\pi$
$283$			7192.67i			1.51081i	−0.655257	+	0.755406i	$0.727440\pi$
$284$		−	2423.77i		−	0.506424i
$285$	−2206.63	+	7326.53i	−0.458630	+	1.52276i
$286$	2083.73	+	1203.04i	0.430816	+	0.248732i
$287$	−2945.34	−	2943.69i	−0.605776	−	0.605437i
$288$	−3092.59	+	4668.35i	−0.632753	+	0.955157i
$289$	−536.069	−	928.499i	−0.109112	−	0.188988i
$290$	−1297.52	−	2247.38i	−0.262735	−	0.455070i
$291$	−3926.00	−	4175.13i	−0.790880	−	0.841066i
$292$	3526.66	+	2036.12i	0.706787	+	0.408064i
$293$	1871.73	+	3241.93i	0.373199	+	0.646400i	0.990056	−	0.140675i	$-0.0449274\pi$
$293$	1871.73	+	3241.93i	0.373199	+	0.646400i	−0.616856	+	0.787076i	$0.711594\pi$
$294$	1493.24	+	6331.32i	0.296216	+	1.25595i
$295$	−2205.74	+	3820.45i	−0.435332	+	0.754017i
$296$	1404.04	−	810.623i	0.275703	−	0.159177i
$297$	−1317.45	−	486.930i	−0.257395	−	0.0951331i
$298$	3438.65	−	5955.92i	0.668442	−	1.15778i
$299$	8073.39			1.56153
$300$	−155.808	−	662.283i	−0.0299852	−	0.127457i
$301$	−1459.52	+	5453.12i	−0.279486	+	1.04423i
$302$	1265.75	−	730.781i	0.241178	−	0.139244i
$303$	838.185	+	3562.83i	0.158919	+	0.675509i
$304$	8158.97	−	4710.58i	1.53931	−	0.888719i
$305$	−7775.35	−	4489.10i	−1.45972	−	0.842771i
$306$	−3399.02	−	6824.19i	−0.634996	−	1.27488i
$307$		−	4199.35i		−	0.780682i	−0.920670	−	0.390341i	$-0.872357\pi$
$307$		−	4199.35i		−	0.780682i	0.920670	−	0.390341i	$-0.127643\pi$
$308$	697.460	−	697.851i	0.129031	−	0.129103i
$309$	3697.39	+	3932.01i	0.680703	+	0.723898i
$310$	4497.01	−	7789.05i	0.823913	−	1.42706i
$311$	2483.35			0.452791			0.226395	−	0.974036i	$-0.427306\pi$
$311$	2483.35			0.452791			0.226395	+	0.974036i	$0.427306\pi$
$312$	−766.081	−	3256.34i	−0.139009	−	0.590878i
$313$			820.556i			0.148181i	0.997252	+	0.0740904i	$0.0236053\pi$
$313$			820.556i			0.148181i	−0.997252	+	0.0740904i	$0.976395\pi$
$314$	7160.35			1.28688
$315$	4581.29	−	4052.21i	0.819448	−	0.724813i
$316$	229.541			0.0408630
$317$		−	4133.49i		−	0.732365i	−0.930543	−	0.366183i	$-0.880665\pi$
$317$		−	4133.49i		−	0.732365i	0.930543	−	0.366183i	$-0.119335\pi$
$318$	5745.40	−	5402.57i	1.01316	−	0.952708i
$319$	−581.957			−0.102142
$320$	−800.786	+	1387.00i	−0.139892	+	0.242299i
$321$	294.914	−	69.3809i	0.0512788	−	0.0120638i
$322$	2142.76	−	8005.86i	0.370842	−	1.38556i
$323$			9313.95i			1.60446i
$324$	−1512.88	−	3572.04i	−0.259410	−	0.612490i
$325$	1403.20	+	810.137i	0.239494	+	0.138272i
$326$	6907.32	−	3987.94i	1.17350	−	0.677520i
$327$	3366.72	−	3165.83i	0.569358	−	0.535384i
$328$	1903.76	−	1099.14i	0.320481	−	0.185030i
$329$	−404.026	+	108.380i	−0.0677041	+	0.0181616i
$330$	−2223.66	−	669.729i	−0.370935	−	0.111719i
$331$	−8888.38			−1.47598			−0.737991	−	0.674811i	$-0.764225\pi$
$331$	−8888.38			−1.47598			−0.737991	+	0.674811i	$0.764225\pi$
$332$	−1064.60	+	1843.94i	−0.175986	+	0.304817i
$333$	−275.113	+	4468.79i	−0.0452736	+	0.735400i
$334$	−4581.78	+	2645.29i	−0.750610	+	0.433365i
$335$	680.622	−	1178.87i	0.111004	−	0.192265i
$336$	−7527.23	−	229.369i	−1.22216	−	0.0372414i
$337$	1800.32	+	3118.24i	0.291007	+	0.504040i	0.974048	−	0.226341i	$-0.0726763\pi$
$337$	1800.32	+	3118.24i	0.291007	+	0.504040i	−0.683041	+	0.730380i	$0.739343\pi$
$338$	−6761.03	−	3903.48i	−1.08802	−	0.628170i
$339$	11868.2	−	2792.09i	1.90145	−	0.447332i
$340$	−2517.66	−	4360.72i	−0.401586	−	0.695568i
$341$	−1008.49	−	1746.75i	−0.160154	−	0.277395i
$342$	−729.010	+	11841.6i	−0.115264	+	1.87229i
$343$	−4488.08	+	4495.64i	−0.706512	+	0.707701i
$344$	−2580.80	−	1490.02i	−0.404498	−	0.233537i
$345$	−7585.26	+	1784.49i	−1.18370	+	0.278475i
$346$			6737.33i			1.04682i
$347$			9358.55i			1.44782i	0.689895	+	0.723909i	$0.257657\pi$
$347$			9358.55i			1.44782i	−0.689895	+	0.723909i	$0.742343\pi$
$348$	−1101.06	−	1170.92i	−0.169606	−	0.180368i
$349$	3496.96	+	2018.97i	0.536355	+	0.309665i	0.743601	−	0.668624i	$-0.233116\pi$
$349$	3496.96	+	2018.97i	0.536355	+	0.309665i	−0.207245	+	0.978289i	$0.566450\pi$
$350$	1175.78	−	1176.44i	0.179566	−	0.179667i
$351$	8665.33	+	3202.71i	1.31772	+	0.487031i
$352$	1038.18	+	1798.18i	0.157202	+	0.272282i
$353$	−2179.09	−	3774.29i	−0.328558	−	0.569080i	0.653668	−	0.756782i	$-0.273229\pi$
$353$	−2179.09	−	3774.29i	−0.328558	−	0.569080i	−0.982226	+	0.187702i	$0.939896\pi$
$354$	−1972.60	+	6549.50i	−0.296166	+	0.983340i
$355$	−4824.82	−	2785.61i	−0.721338	−	0.416465i
$356$	1849.85	+	3204.03i	0.275398	+	0.477003i
$357$	3917.16	−	6331.21i	0.580723	−	0.938608i
$358$	−820.847	+	1421.75i	−0.121182	+	0.209893i
$359$	3099.17	−	1789.31i	0.455621	−	0.263053i	−0.254580	−	0.967052i	$-0.581937\pi$
$359$	3099.17	−	1789.31i	0.455621	−	0.263053i	0.710201	+	0.703999i	$0.248604\pi$
$360$	1439.53	+	2890.13i	0.210749	+	0.423120i
$361$	3817.59	−	6612.26i	0.556581	−	0.964026i
$362$	−11194.5			−1.62532
$363$	4659.01	−	4381.01i	0.673649	−	0.633453i
$364$	−4587.44	+	4590.01i	−0.660569	+	0.660939i
$365$	8106.29	−	4680.17i	1.16247	−	0.671154i
$366$	−13329.5	−	4014.63i	−1.90367	−	0.573355i
$367$	−8884.14	+	5129.26i	−1.26362	+	0.729551i	−0.973773	−	0.227522i	$-0.926938\pi$
$367$	−8884.14	+	5129.26i	−1.26362	+	0.729551i	−0.289847	+	0.957073i	$0.593604\pi$
$368$	8309.02	+	4797.22i	1.17700	+	0.679544i
$369$	−373.031	+	6059.32i	−0.0526266	+	0.854838i
$370$			7402.79i			1.04014i
$371$	7439.69	+	1991.22i	1.04110	+	0.278650i
$372$	1606.50	−	5333.94i	0.223906	−	0.743420i
$373$	−4926.89	+	8533.62i	−0.683927	+	1.18460i	0.289846	+	0.957073i	$0.406396\pi$
$373$	−4926.89	+	8533.62i	−0.683927	+	1.18460i	−0.973773	+	0.227522i	$0.926937\pi$
$374$	−2826.86			−0.390837
$375$	6109.54	+	1840.09i	0.841321	+	0.253392i
$376$		−	220.827i		−	0.0302880i
$377$	3827.73			0.522913
$378$	5475.78	−	7742.82i	0.745090	−	1.05357i
$379$	−11181.0			−1.51538			−0.757688	−	0.652617i	$-0.773671\pi$
$379$	−11181.0			−1.51538			−0.757688	+	0.652617i	$0.773671\pi$
$380$			7835.87i			1.05782i
$381$	5107.44	+	1538.28i	0.686778	+	0.206846i
$382$	−18981.1			−2.54229
$383$	−4495.30	+	7786.09i	−0.599737	+	1.03877i	0.393123	+	0.919486i	$0.371395\pi$
$383$	−4495.30	+	7786.09i	−0.599737	+	1.03877i	−0.992860	+	0.119288i	$0.961939\pi$
$384$	1770.17	−	5877.37i	0.235243	−	0.781063i
$385$	−587.578	−	2190.42i	−0.0777812	−	0.289958i
$386$		−	8672.81i		−	1.14361i
$387$	7366.53	−	3669.15i	0.967601	−	0.481946i
$388$	−5082.76	−	2934.53i	−0.665047	−	0.383965i
$389$	−1635.32	+	944.155i	−0.213147	+	0.123061i	−0.602773	−	0.797913i	$-0.705938\pi$
$389$	−1635.32	+	944.155i	−0.213147	+	0.123061i	0.389626	+	0.920973i	$0.372604\pi$
$390$	14625.8	+	4405.04i	1.89899	+	0.571943i
$391$	−8214.46	+	4742.62i	−1.06246	+	0.613414i
$392$	−1678.37	−	2903.26i	−0.216251	−	0.374073i
$393$	5417.54	−	5094.27i	0.695365	−	0.653873i
$394$	540.594			0.0691237
$395$	263.809	−	456.931i	0.0336043	−	0.0582043i
$396$	−1435.66	−	88.3839i	−0.182183	−	0.0112158i
$397$	9137.13	−	5275.32i	1.15511	−	0.666904i	0.204984	−	0.978765i	$-0.434286\pi$
$397$	9137.13	−	5275.32i	1.15511	−	0.666904i	0.950128	+	0.311861i	$0.100952\pi$
$398$	−3117.38	+	5399.47i	−0.392614	+	0.680027i
$399$	−10205.4	+	5484.61i	−1.28047	+	0.688155i
$400$	962.768	+	1667.56i	0.120346	+	0.208445i
$401$	−1788.09	−	1032.35i	−0.222676	−	0.128562i	0.384513	−	0.923120i	$-0.374369\pi$
$401$	−1788.09	−	1032.35i	−0.222676	−	0.128562i	−0.607189	+	0.794558i	$0.707703\pi$
$402$	608.685	−	2020.98i	0.0755185	−	0.250739i
$403$	6633.16	+	11489.0i	0.819903	+	1.42011i
$404$	1874.12	+	3246.07i	0.230794	+	0.399747i
$405$	−8849.33	−	1093.73i	−1.08574	−	0.134193i
$406$	1015.92	−	3795.72i	0.124185	−	0.463986i
$407$	1437.71	+	830.064i	0.175098	+	0.101093i
$408$	2692.37	+	2863.22i	0.326696	+	0.347427i
$409$		−	143.871i		−	0.0173935i	−0.999962	−	0.00869676i	$-0.997232\pi$
$409$		−	143.871i		−	0.0173935i	0.999962	−	0.00869676i	$-0.00276830\pi$
$410$			10037.6i			1.20907i
$411$	−12784.0	+	3007.54i	−1.53428	+	0.360951i
$412$	4786.80	+	2763.66i	0.572399	+	0.330475i
$413$	−6451.59	+	1730.64i	−0.768673	+	0.206196i
$414$	−10815.0	+	5386.76i	−1.28388	+	0.639480i
$415$	2447.06	+	4238.43i	0.289449	+	0.501341i
$416$	−6828.45	−	11827.2i	−0.804789	−	1.39394i
$417$	−1442.78	+	339.426i	−0.169432	+	0.0398604i
$418$	3809.73	+	2199.55i	0.445789	+	0.257376i
$419$	−1974.15	−	3419.34i	−0.230176	−	0.398677i	0.727684	−	0.685913i	$-0.240597\pi$
$419$	−1974.15	−	3419.34i	−0.230176	−	0.398677i	−0.957860	+	0.287236i	$0.907264\pi$
$420$	3295.53	−	5326.47i	0.382870	−	0.618822i
$421$	5518.29	−	9557.95i	0.638824	−	1.10648i	−0.346868	−	0.937914i	$-0.612755\pi$
$421$	5518.29	−	9557.95i	0.638824	−	1.10648i	0.985691	−	0.168561i	$-0.0539120\pi$
$422$	3451.50	−	1992.72i	0.398143	−	0.229868i
$423$	508.401	+	336.795i	0.0584381	+	0.0387129i
$424$	−2032.84	+	3520.98i	−0.232838	+	0.403287i
$425$	−1903.62			−0.217269
$426$	−8271.34	−	2491.19i	−0.940723	−	0.283330i
$427$	−3522.18	−	13130.2i	−0.399181	−	1.48810i
$428$	268.694	−	155.130i	0.0303453	−	0.0175199i
$429$	2495.48	−	2346.57i	0.280846	−	0.264088i
$430$	11784.2	−	6803.61i	1.32159	−	0.763021i
$431$	−1481.18	−	855.162i	−0.165536	−	0.0955724i	0.414943	−	0.909847i	$-0.363801\pi$
$431$	−1481.18	−	855.162i	−0.165536	−	0.0955724i	−0.580479	+	0.814275i	$0.697135\pi$
$432$	7015.20	+	8445.14i	0.781293	+	0.940548i
$433$		−	11599.1i		−	1.28734i	−0.765303	−	0.643670i	$-0.777411\pi$
$433$		−	11599.1i		−	1.28734i	0.765303	−	0.643670i	$-0.222589\pi$
$434$	13153.4	−	3528.39i	1.45480	−	0.390249i
$435$	−3596.30	+	846.060i	−0.396390	+	0.0932539i
$436$	2366.34	−	4098.62i	0.259924	−	0.450202i
$437$	14760.7			1.61579
$438$	10573.2	−	9942.28i	1.15344	−	1.08461i
$439$			4279.83i			0.465297i	0.972561	+	0.232648i	$0.0747391\pi$
$439$			4279.83i			0.465297i	−0.972561	+	0.232648i	$0.925261\pi$
$440$	1197.21			0.129715
$441$	9243.82	+	563.878i	0.998145	+	0.0608873i
$442$	18593.2			2.00088
$443$			9281.52i			0.995436i	0.867339	+	0.497718i	$0.165829\pi$
$443$			9281.52i			0.995436i	−0.867339	+	0.497718i	$0.834171\pi$
$444$	1050.01	+	4463.21i	0.112232	+	0.477060i
$445$	8504.04			0.905910
$446$	−2240.74	+	3881.08i	−0.237898	+	0.412051i
$447$	−6707.20	−	7132.82i	−0.709709	−	0.754744i
$448$	−2342.23	+	628.303i	−0.247009	+	0.0662601i
$449$		−	6876.47i		−	0.722763i	−0.932418	−	0.361382i	$-0.882305\pi$
$449$		−	6876.47i		−	0.722763i	0.932418	−	0.361382i	$-0.117695\pi$
$450$	−2420.24	−	148.998i	−0.253536	−	0.0156085i
$451$	1949.42	+	1125.50i	0.203536	+	0.117511i
$452$	10813.0	−	6242.89i	1.12522	−	0.649648i
$453$	−476.512	−	2025.48i	−0.0494227	−	0.210079i
$454$	−7154.43	+	4130.61i	−0.739590	+	0.427003i
$455$	3864.71	+	14407.1i	0.398198	+	1.48443i
$456$	−1400.64	−	5953.64i	−0.143840	−	0.611414i
$457$	−11161.5			−1.14248			−0.571239	−	0.820784i	$-0.693537\pi$
$457$	−11161.5			−1.14248			−0.571239	+	0.820784i	$0.693537\pi$
$458$	−9402.71	+	16286.0i	−0.959301	+	1.66156i
$459$	−10698.1	+	1831.68i	−1.08790	+	0.186265i
$460$	−6910.87	+	3989.99i	−0.700480	+	0.404422i
$461$	−193.554	+	335.245i	−0.0195547	+	0.0338697i	−0.875637	−	0.482970i	$-0.839558\pi$
$461$	−193.554	+	335.245i	−0.0195547	+	0.0338697i	0.856082	+	0.516839i	$0.172892\pi$
$462$	−1664.62	−	3097.41i	−0.167630	−	0.311915i
$463$	−2485.01	−	4304.16i	−0.249435	−	0.432033i	0.713934	−	0.700213i	$-0.246911\pi$
$463$	−2485.01	−	4304.16i	−0.249435	−	0.432033i	−0.963369	+	0.268179i	$0.913578\pi$
$464$	3939.45	+	2274.44i	0.394148	+	0.227561i
$465$	−8771.56	−	9328.18i	−0.874778	−	0.930288i
$466$	−761.738	−	1319.37i	−0.0757228	−	0.131156i
$467$	4548.20	+	7877.72i	0.450676	+	0.780594i	0.998428	−	0.0560470i	$-0.0178497\pi$
$467$	4548.20	+	7877.72i	0.450676	+	0.780594i	−0.547752	+	0.836641i	$0.684516\pi$
$468$	9442.83	+	581.331i	0.932681	+	0.0574189i
$469$	1990.76	−	534.021i	0.196002	−	0.0525774i
$470$	873.231	+	504.160i	0.0857003	+	0.0494791i
$471$	2939.81	−	9760.86i	0.287599	−	0.954898i
$472$		−	3526.22i		−	0.343872i
$473$		−	3051.51i		−	0.296636i
$474$	235.926	−	783.330i	0.0228617	−	0.0759062i
$475$	2565.50	+	1481.19i	0.247817	+	0.143077i
$476$	1971.25	−	7365.06i	0.189815	−	0.709195i
$477$	−5005.82	−	10050.2i	−0.480504	−	0.964707i
$478$	−10183.6	−	17638.5i	−0.974449	−	1.68779i
$479$	6929.05	+	12001.5i	0.660953	+	1.14480i	0.980366	+	0.197188i	$0.0631810\pi$
$479$	6929.05	+	12001.5i	0.660953	+	1.14480i	−0.319413	+	0.947616i	$0.603486\pi$
$480$	9029.82	+	9602.82i	0.858652	+	0.913139i
$481$	−9456.33	−	5459.61i	−0.896407	−	0.517541i
$482$	−5062.05	−	8767.72i	−0.478361	−	0.828545i
$483$	−10033.7	−	6207.92i	−0.945236	−	0.584824i
$484$	3274.64	−	5671.84i	0.307536	−	0.532667i
$485$	−11683.1	+	6745.26i	−1.09382	+	0.631518i
$486$	−13744.9	+	1491.43i	−1.28288	+	0.139203i
$487$	−681.295	+	1180.04i	−0.0633931	+	0.109800i	−0.895980	−	0.444094i	$-0.853526\pi$
$487$	−681.295	+	1180.04i	−0.0633931	+	0.109800i	0.832587	+	0.553894i	$0.186859\pi$
$488$	7176.55			0.665711
$489$	−2600.37	−	11053.3i	−0.240476	−	1.02218i
$490$	15312.3	−	8.58489i	1.41172	−	0.000791481i
$491$	−15324.0	+	8847.30i	−1.40847	+	0.813183i	−0.995241	−	0.0974422i	$-0.968934\pi$
$491$	−15324.0	+	8847.30i	−1.40847	+	0.813183i	−0.413233	+	0.910625i	$0.635601\pi$
$492$	1423.72	+	6051.75i	0.130460	+	0.554541i
$493$	−3894.62	+	2248.56i	−0.355791	+	0.205416i
$494$	−25057.9	−	14467.2i	−2.28220	−	1.31763i
$495$	−1825.93	+	2756.28i	−0.165797	+	0.250274i
$496$			15765.7i			1.42722i
$497$	−2185.61	−	8147.69i	−0.197260	−	0.735360i
$498$	5198.39	+	5528.26i	0.467762	+	0.497445i
$499$	7078.88	−	12261.0i	0.635059	−	1.09995i	−0.351444	−	0.936209i	$-0.614309\pi$
$499$	7078.88	−	12261.0i	0.635059	−	1.09995i	0.986503	−	0.163745i	$-0.0523575\pi$
$500$	6534.27			0.584443
$501$	1724.88	+	7331.88i	0.153817	+	0.653821i
$502$			13691.8i			1.21732i
$503$	5337.01			0.473093			0.236546	−	0.971620i	$-0.423985\pi$
$503$	5337.01			0.473093			0.236546	+	0.971620i	$0.423985\pi$
$504$	−1551.82	+	4636.09i	−0.137150	+	0.409737i
$505$	8615.60			0.759187
$506$			4480.00i			0.393597i
$507$	−8097.02	+	7613.87i	−0.709273	+	0.666950i
$508$	5462.51			0.477086
$509$	−760.691	+	1317.56i	−0.0662417	+	0.114734i	−0.897244	−	0.441535i	$-0.854434\pi$
$509$	−760.691	+	1317.56i	−0.0662417	+	0.114734i	0.831002	+	0.556269i	$0.187768\pi$
$510$	−17469.0	+	4109.73i	−1.51675	+	0.356828i
$511$	13691.2	+	3664.42i	1.18525	+	0.317230i
$512$		−	10109.2i		−	0.872595i
$513$	15843.0	+	5855.58i	1.36352	+	0.503957i
$514$	−23743.4	−	13708.3i	−2.03750	−	1.17635i
$515$	11002.8	−	6352.48i	0.941441	−	0.543541i
$516$	6139.79	−	5773.42i	0.523816	−	0.492560i
$517$	195.828	−	113.061i	0.0166586	−	0.00961786i
$518$	−7923.75	+	7928.20i	−0.672104	+	0.672481i
$519$	9184.21	+	2766.13i	0.776767	+	0.233949i
$520$	−7874.45			−0.664072
$521$	8290.88	−	14360.2i	0.697178	−	1.20755i	−0.272262	−	0.962223i	$-0.587772\pi$
$521$	8290.88	−	14360.2i	0.697178	−	1.20755i	0.969441	−	0.245325i	$-0.0788948\pi$
$522$	−5127.57	+	2553.96i	−0.429938	+	0.214145i
$523$	8034.14	−	4638.51i	0.671718	−	0.387816i	−0.125009	−	0.992156i	$-0.539896\pi$
$523$	8034.14	−	4638.51i	0.671718	−	0.387816i	0.796727	+	0.604339i	$0.206563\pi$
$524$	3807.78	−	6595.26i	0.317449	−	0.549838i
$525$	−1120.97	−	2085.82i	−0.0931867	−	0.173395i
$526$	10100.8	+	17495.0i	0.837288	+	1.45023i
$527$	−13498.1	−	7793.15i	−1.11573	−	0.644165i
$528$	3962.65	−	932.246i	0.326614	−	0.0768386i
$529$	1432.61	+	2481.35i	0.117745	+	0.203941i
$530$	−9282.16	−	16077.2i	−0.760738	−	1.31764i
$531$	8118.28	+	5378.04i	0.663472	+	0.439523i
$532$	−8387.31	+	8392.01i	−0.683526	+	0.683910i
$533$	−12822.0	−	7402.79i	−1.04199	−	0.601596i
$534$	12835.3	−	3019.62i	1.04015	−	0.244704i
$535$		−	713.158i		−	0.0576309i
$536$			1088.08i			0.0876830i
$537$	1601.09	+	1702.69i	0.128663	+	0.136828i
$538$	−2604.27	−	1503.58i	−0.208695	−	0.120490i
$539$	1715.28	−	2974.81i	0.137073	−	0.237725i
$540$	−9000.40	+	1541.00i	−0.717251	+	0.122804i
$541$	6256.31	+	10836.2i	0.497190	+	0.861158i	0.999995	−	0.00324160i	$-0.00103183\pi$
$541$	6256.31	+	10836.2i	0.497190	+	0.861158i	−0.502805	+	0.864400i	$0.667699\pi$
$542$	7918.26	+	13714.8i	0.627525	+	1.08691i
$543$	−4596.09	+	15260.1i	−0.363236	+	1.20603i
$544$	13895.5	+	8022.60i	1.09516	+	0.632290i
$545$	−5439.21	−	9420.99i	−0.427505	−	0.740460i
$546$	10948.8	+	20372.7i	0.858177	+	1.59684i
$547$	4213.76	−	7298.44i	0.329373	−	0.570491i	−0.653014	−	0.757346i	$-0.726496\pi$
$547$	4213.76	−	7298.44i	0.329373	−	0.570491i	0.982388	+	0.186854i	$0.0598292\pi$
$548$	−11647.4	+	6724.61i	−0.907940	+	0.524199i
$549$	−10945.3	+	16522.3i	−0.850885	+	1.28443i
$550$	−449.553	+	778.648i	−0.0348527	+	0.0603666i
$551$	6998.33			0.541087
$552$	4537.63	−	4266.87i	0.349881	−	0.329003i
$553$	771.620	−	206.987i	0.0593357	−	0.0159168i
$554$	8352.73	−	4822.45i	0.640566	−	0.369831i
$555$	10091.4	+	3039.35i	0.771809	+	0.232456i
$556$	−1314.51	+	758.930i	−0.100265	+	0.0578881i
$557$	−17760.6	−	10254.1i	−1.35106	−	0.780035i	−0.362662	−	0.931921i	$-0.618132\pi$
$557$	−17760.6	−	10254.1i	−1.35106	−	0.780035i	−0.988398	+	0.151886i	$0.951465\pi$
$558$	−16551.4	−	10964.6i	−1.25569	−	0.831845i
$559$			20070.9i			1.51862i
$560$	−4583.23	+	17124.0i	−0.345851	+	1.29218i
$561$	−1160.62	+	3853.52i	−0.0873463	+	0.290010i
$562$	−6986.97	+	12101.8i	−0.524426	+	0.908333i
$563$	4511.91			0.337752			0.168876	−	0.985637i	$-0.445986\pi$
$563$	4511.91			0.337752			0.168876	+	0.985637i	$0.445986\pi$
$564$	597.989	+	180.104i	0.0446452	+	0.0134464i
$565$		−	28699.5i		−	2.13699i
$566$	26252.0			1.94957
$567$	−8306.70	−	10643.4i	−0.615253	−	0.788330i
$568$	4453.25			0.328969
$569$		−	12855.6i		−	0.947164i	−0.880750	−	0.473582i	$-0.842961\pi$
$569$		−	12855.6i		−	0.947164i	0.880750	−	0.473582i	$-0.157039\pi$
$570$	26740.6	+	8053.83i	1.96498	+	0.591821i
$571$	6198.78			0.454310			0.227155	−	0.973859i	$-0.427058\pi$
$571$	6198.78			0.454310			0.227155	+	0.973859i	$0.427058\pi$
$572$	1753.98	−	3037.97i	0.128212	−	0.222070i
$573$	−7793.02	+	25874.7i	−0.568164	+	1.88644i
$574$	−10744.0	+	10750.0i	−0.781262	+	0.781700i
$575$			3016.86i			0.218803i
$576$	2947.32	+	1952.48i	0.213203	+	0.141238i
$577$	15660.3	+	9041.50i	1.12989	+	0.652344i	0.943908	−	0.330209i	$-0.107119\pi$
$577$	15660.3	+	9041.50i	1.12989	+	0.652344i	0.185985	+	0.982553i	$0.440452\pi$
$578$	−3388.86	+	1956.56i	−0.243872	+	0.140800i
$579$	−11822.6	−	3560.78i	−0.848586	−	0.255580i
$580$	−3276.56	+	1891.72i	−0.234572	+	0.135430i
$581$	−1915.97	+	7158.52i	−0.136812	+	0.511163i
$582$	−15238.5	+	14329.2i	−1.08532	+	1.02056i
$583$	−4163.18			−0.295748
$584$	−3741.00	+	6479.61i	−0.265075	+	0.459123i
$585$	12009.8	−	18129.0i	0.848790	−	1.28127i
$586$	11832.5	−	6831.49i	0.834122	−	0.481580i
$587$	2442.51	−	4230.56i	0.171743	−	0.297468i	−0.767286	−	0.641305i	$-0.778393\pi$
$587$	2442.51	−	4230.56i	0.171743	−	0.297468i	0.939029	+	0.343837i	$0.111727\pi$
$588$	9230.74	−	2177.07i	0.647397	−	0.152689i
$589$	12127.5	+	21005.5i	0.848398	+	1.46947i
$590$	13944.0	+	8050.56i	0.972991	+	0.561757i
$591$	221.951	−	736.928i	0.0154481	−	0.0512913i
$592$	−6488.22	−	11237.9i	−0.450446	−	0.780196i
$593$	1304.78	+	2259.95i	0.0903557	+	0.156501i	0.907661	−	0.419704i	$-0.137866\pi$
$593$	1304.78	+	2259.95i	0.0903557	+	0.156501i	−0.817305	+	0.576205i	$0.804533\pi$
$594$	−1777.21	+	4808.48i	−0.122761	+	0.332145i
$595$	−12395.5	−	12388.6i	−0.854063	−	0.853585i
$596$	−8683.43	−	5013.38i	−0.596791	−	0.344557i
$597$	6080.56	+	6466.41i	0.416852	+	0.443304i
$598$		−	29466.5i		−	2.01501i
$599$		−	16046.5i		−	1.09456i	−0.836948	−	0.547282i	$-0.815663\pi$
$599$		−	16046.5i		−	1.09456i	0.836948	−	0.547282i	$-0.184337\pi$
$600$	1216.83	−	286.269i	0.0827947	−	0.0194781i
$601$	−6848.07	−	3953.74i	−0.464790	−	0.268347i	0.249266	−	0.968435i	$-0.419811\pi$
$601$	−6848.07	−	3953.74i	−0.464790	−	0.268347i	−0.714056	+	0.700088i	$0.753144\pi$
$602$	19903.0	+	5327.01i	1.34748	+	0.360652i
$603$	−2505.05	−	1659.50i	−0.169177	−	0.112073i
$604$	−1065.44	−	1845.40i	−0.0717753	−	0.124318i
$605$	−7527.01	−	13037.2i	−0.505812	−	0.876093i
$606$	13003.7	−	3059.24i	0.871685	−	0.205071i
$607$	3207.15	+	1851.65i	0.214455	+	0.123816i	0.603380	−	0.797454i	$-0.293820\pi$
$607$	3207.15	+	1851.65i	0.214455	+	0.123816i	−0.388925	+	0.921269i	$0.627153\pi$
$608$	−12484.6	−	21624.0i	−0.832759	−	1.44238i
$609$	−4757.15	−	2943.28i	−0.316534	−	0.195842i
$610$	−16384.5	+	28378.7i	−1.08752	+	1.88364i
$611$	−1288.03	+	743.644i	−0.0852833	+	0.0492383i
$612$	−9949.33	+	4955.60i	−0.657154	+	0.327317i
$613$	−4872.57	+	8439.53i	−0.321046	+	0.556068i	−0.980704	−	0.195498i	$-0.937368\pi$
$613$	−4872.57	+	8439.53i	−0.321046	+	0.556068i	0.659658	+	0.751566i	$0.270701\pi$
$614$	−15326.9			−1.00740
$615$	13683.0	+	4121.11i	0.897161	+	0.270210i
$616$	1282.18	+	1281.46i	0.0838644	+	0.0838174i
$617$	−22722.4	+	13118.8i	−1.48261	+	0.855985i	−0.999805	−	0.0197440i	$-0.993715\pi$
$617$	−22722.4	+	13118.8i	−1.48261	+	0.855985i	−0.482804	+	0.875729i	$0.660382\pi$
$618$	14351.2	−	13494.8i	0.934125	−	0.878386i
$619$	−4473.09	+	2582.54i	−0.290450	+	0.167692i	−0.638145	−	0.769916i	$-0.720298\pi$
$619$	−4473.09	+	2582.54i	−0.290450	+	0.167692i	0.347695	+	0.937608i	$0.386965\pi$
$620$	−11356.0	−	6556.41i	−0.735596	−	0.424697i
$621$	2902.85	+	16954.4i	0.187581	+	1.09558i
$622$		−	9063.81i		−	0.584286i
$623$	9107.60	+	9102.50i	0.585696	+	0.585367i
$624$	−26063.7	+	6131.70i	−1.67209	+	0.393373i
$625$	9047.65	−	15671.0i	0.579050	−	1.00294i
$626$	2994.89			0.191214
$627$	4562.54	−	4290.29i	0.290606	−	0.273266i
$628$		−	10439.4i		−	0.663342i
$629$	12828.8			0.813221
$630$	−14789.9	−	16720.9i	−0.935306	−	1.05742i
$631$	1350.06			0.0851743			0.0425871	−	0.999093i	$-0.486440\pi$
$631$	1350.06			0.0851743			0.0425871	+	0.999093i	$0.486440\pi$
$632$			421.742i			0.0265443i
$633$	−1299.37	−	5523.17i	−0.0815882	−	0.346803i
$634$	−15086.5			−0.945052
$635$	6278.00	−	10873.8i	0.392338	−	0.679550i
$636$	−7876.68	−	8376.51i	−0.491086	−	0.522249i
$637$	−11282.0	+	19566.3i	−0.701742	+	1.21703i
$638$			2124.05i			0.131805i
$639$	−6791.90	+	10252.5i	−0.420475	+	0.634717i
$640$	−12513.0	−	7224.38i	−0.772843	−	0.446201i
$641$	15660.2	−	9041.44i	0.964964	−	0.557122i	0.0672665	−	0.997735i	$-0.478572\pi$
$641$	15660.2	−	9041.44i	0.964964	−	0.557122i	0.897697	+	0.440613i	$0.145239\pi$
$642$	−253.229	−	1076.39i	−0.0155672	−	0.0661707i
$643$	16884.0	−	9748.00i	1.03552	−	0.597859i	0.116961	−	0.993137i	$-0.462685\pi$
$643$	16884.0	−	9748.00i	1.03552	−	0.597859i	0.918562	+	0.395277i	$0.129351\pi$
$644$	−11672.1	−	3124.03i	−0.714203	−	0.191156i
$645$	−4436.35	−	18857.4i	−0.270823	−	1.15117i
$646$	33994.3			2.07042
$647$	−8503.93	+	14729.2i	−0.516730	+	0.895002i	0.483082	+	0.875575i	$0.339517\pi$
$647$	−8503.93	+	14729.2i	−0.516730	+	0.895002i	−0.999811	+	0.0194267i	$0.993816\pi$
$648$	6562.99	−	2779.64i	0.397868	−	0.168510i
$649$	3127.04	−	1805.40i	0.189132	−	0.109196i
$650$	2956.86	−	5121.44i	0.178427	−	0.309045i
$651$	590.518	−	19379.1i	0.0355518	−	1.16671i
$652$	−5814.22	−	10070.5i	−0.349237	−	0.604896i
$653$	3751.19	+	2165.75i	0.224801	+	0.129789i	0.608172	−	0.793806i	$-0.291903\pi$
$653$	3751.19	+	2165.75i	0.224801	+	0.129789i	−0.383370	+	0.923595i	$0.625237\pi$
$654$	−11554.7	−	12288.0i	−0.690866	−	0.734706i
$655$	−8752.47	−	15159.7i	−0.522118	−	0.904335i
$656$	−8797.50	−	15237.7i	−0.523604	−	0.906909i
$657$	−9212.13	−	18495.2i	−0.547031	−	1.09827i
$658$	395.568	+	1474.63i	0.0234359	+	0.0873661i
$659$	2674.86	+	1544.33i	0.158115	+	0.0912875i	0.576970	−	0.816766i	$-0.304235\pi$
$659$	2674.86	+	1544.33i	0.158115	+	0.0912875i	−0.418855	+	0.908053i	$0.637568\pi$
$660$	−976.432	+	3241.98i	−0.0575872	+	0.191203i
$661$		−	22587.6i		−	1.32913i	−0.747231	−	0.664564i	$-0.768617\pi$
$661$		−	22587.6i		−	1.32913i	0.747231	−	0.664564i	$-0.231383\pi$
$662$			32441.1i			1.90462i
$663$	7633.78	−	25345.9i	0.447166	−	1.48470i
$664$	−3387.91	−	1956.01i	−0.198007	−	0.114319i
$665$	7065.92	+	26340.8i	0.412037	+	1.53602i
$666$	16310.3	+	1004.12i	0.948968	+	0.0584216i
$667$	3563.52	+	6172.19i	0.206866	+	0.358303i
$668$	3856.70	+	6680.01i	0.223384	+	0.386912i
$669$	4370.65	+	4647.99i	0.252584	+	0.268612i
$670$	−4302.69	−	2484.16i	−0.248100	−	0.143241i
$671$	3674.33	+	6364.12i	0.211395	+	0.366146i
$672$	−607.904	+	19949.7i	−0.0348965	+	1.14520i
$673$	3978.45	−	6890.88i	0.227872	−	0.394686i	−0.729305	−	0.684189i	$-0.760156\pi$
$673$	3978.45	−	6890.88i	0.227872	−	0.394686i	0.957177	+	0.289502i	$0.0934898\pi$
$674$	11381.0	−	6570.85i	0.650418	−	0.375519i
$675$	−1196.79	+	3238.06i	−0.0682435	+	0.184642i
$676$	−5691.08	+	9857.24i	−0.323798	+	0.560835i
$677$	−11105.5			−0.630458			−0.315229	−	0.949016i	$-0.602081\pi$
$677$	−11105.5			−0.630458			−0.315229	+	0.949016i	$0.602081\pi$
$678$	−10190.7	−	43316.9i	−0.577241	−	2.45365i
$679$	−19732.3	−	5281.32i	−1.11525	−	0.298495i
$680$	8012.05	−	4625.76i	0.451836	−	0.260867i
$681$	2693.40	+	11448.7i	0.151558	+	0.644222i
$682$	−6375.34	+	3680.80i	−0.357953	+	0.206665i
$683$	−16295.7	−	9408.31i	−0.912938	−	0.527085i	−0.0315626	−	0.999502i	$-0.510048\pi$
$683$	−16295.7	−	9408.31i	−0.912938	−	0.527085i	−0.881375	+	0.472417i	$0.843382\pi$
$684$	17264.5	+	1062.86i	0.965096	+	0.0594145i
$685$			30914.1i			1.72433i
$686$	16408.3	+	16380.7i	0.913225	+	0.911690i
$687$	18340.3	+	19504.1i	1.01852	+	1.08316i
$688$	−11926.1	+	20656.7i	−0.660871	+	1.14466i
$689$	27382.7			1.51407
$690$	6513.11	+	27684.9i	0.359347	+	1.52746i
$691$			14695.2i			0.809016i	0.914534	+	0.404508i	$0.132557\pi$
$691$			14695.2i			0.809016i	−0.914534	+	0.404508i	$0.867443\pi$
$692$	9822.69			0.539599
$693$	−4905.78	+	997.484i	−0.268911	+	0.0546772i
$694$	34157.1			1.86828
$695$			3488.92i			0.190421i
$696$	2151.37	−	2023.00i	0.117166	−	0.110174i
$697$	17394.8			0.945299
$698$	7368.91	−	12763.3i	0.399595	−	0.692119i
$699$	−2111.29	+	496.697i	−0.114243	+	0.0268767i
$700$	−1715.19	−	1714.23i	−0.0926118	−	0.0925599i
$701$			2167.47i			0.116782i	0.998294	+	0.0583910i	$0.0185970\pi$
$701$			2167.47i			0.116782i	−0.998294	+	0.0583910i	$0.981403\pi$
$702$	11689.3	−	31627.0i	0.628470	−	1.70041i
$703$	−17289.2	−	9981.93i	−0.927560	−	0.535527i
$704$	1135.26	−	655.443i	0.0607767	−	0.0350894i
$705$	1045.78	−	983.381i	0.0558673	−	0.0525337i
$706$	−13775.5	+	7953.30i	−0.734346	+	0.423975i
$707$	9227.09	+	9221.92i	0.490835	+	0.490560i
$708$	9548.85	+	2875.96i	0.506875	+	0.152663i
$709$	34298.2			1.81678			0.908388	−	0.418128i	$-0.137314\pi$
$709$	34298.2			1.81678			0.908388	+	0.418128i	$0.137314\pi$
$710$	−10167.0	+	17609.8i	−0.537411	+	0.930823i
$711$	−970.959	−	643.221i	−0.0512149	−	0.0339278i
$712$	−5886.84	+	3398.77i	−0.309858	+	0.178896i
$713$	−12350.6	+	21391.8i	−0.648714	+	1.12361i
$714$	−23107.8	−	14297.0i	−1.21119	−	0.749372i
$715$	−4031.65	−	6983.02i	−0.210874	−	0.365245i
$716$	2072.84	+	1196.75i	0.108192	+	0.0624648i
$717$	−28225.5	+	6640.29i	−1.47016	+	0.345866i
$718$	−6530.67	−	11311.5i	−0.339446	−	0.587939i
$719$	7330.37	+	12696.6i	0.380218	+	0.658557i	0.991093	−	0.133170i	$-0.0425157\pi$
$719$	7330.37	+	12696.6i	0.380218	+	0.658557i	−0.610875	+	0.791727i	$0.709182\pi$
$720$	23132.6	−	11521.9i	1.19736	−	0.596386i
$721$	18583.3	+	4973.79i	0.959885	+	0.256912i
$722$	−24133.6	−	13933.6i	−1.24399	−	0.718218i
$723$	−14030.3	+	3300.75i	−0.721706	+	0.169787i
$724$			16321.0i			0.837795i
$725$			1430.35i			0.0732714i
$726$	−15989.9	−	17004.6i	−0.817414	−	0.869284i
$727$	9274.34	+	5354.55i	0.473131	+	0.273162i	0.717550	−	0.696507i	$-0.245264\pi$
$727$	9274.34	+	5354.55i	0.473131	+	0.273162i	−0.244418	+	0.969670i	$0.578597\pi$
$728$	−8433.33	−	8428.61i	−0.429341	−	0.429100i
$729$	−3610.11	+	19349.1i	−0.183413	+	0.983036i
$730$	−17081.8	−	29586.6i	−0.866064	−	1.50007i
$731$	−11790.4	−	20421.6i	−0.596558	−	1.03327i
$732$	−5853.13	+	19433.8i	−0.295543	+	0.981274i
$733$	−13175.9	−	7607.11i	−0.663933	−	0.383322i	0.129841	−	0.991535i	$-0.458553\pi$
$733$	−13175.9	−	7607.11i	−0.663933	−	0.383322i	−0.793774	+	0.608213i	$0.791887\pi$
$734$	18720.9	+	32425.6i	0.941421	+	1.63059i
$735$	6275.06	−	20877.0i	0.314910	−	1.04770i
$736$	12714.2	−	22021.7i	0.636755	−	1.10289i
$737$	−964.907	+	557.089i	−0.0482263	+	0.0278435i
$738$	22115.5	+	1361.50i	1.10309	+	0.0679100i
$739$	4828.54	−	8363.28i	0.240353	−	0.416304i	−0.720462	−	0.693495i	$-0.756070\pi$
$739$	4828.54	−	8363.28i	0.240353	−	0.416304i	0.960815	+	0.277191i	$0.0894035\pi$
$740$	10792.9			0.536155
$741$	−30009.4	+	28218.7i	−1.48775	+	1.39898i
$742$	7267.63	−	27153.6i	0.359573	−	1.34345i
$743$	−4935.72	+	2849.64i	−0.243706	+	0.140704i	−0.616879	−	0.787058i	$-0.711603\pi$
$743$	−4935.72	+	2849.64i	−0.243706	+	0.140704i	0.373173	+	0.927762i	$0.378270\pi$
$744$	9800.18	+	2951.65i	0.482920	+	0.145447i
$745$	−19959.5	+	11523.6i	−0.981558	+	0.566703i
$746$	31146.3	+	17982.3i	1.52861	+	0.882546i
$747$	9670.33	−	4816.63i	0.473653	−	0.235919i
$748$			4121.41i			0.201462i
$749$	763.346	−	763.774i	0.0372390	−	0.0372599i
$750$	6716.03	−	22298.8i	0.326980	−	1.08565i
$751$	−17407.8	+	30151.2i	−0.845833	+	1.46503i	0.0390625	+	0.999237i	$0.487563\pi$
$751$	−17407.8	+	30151.2i	−0.845833	+	1.46503i	−0.884896	+	0.465789i	$0.845770\pi$
$752$	−1767.50			−0.0857101
$753$	18664.4	+	5621.40i	0.903277	+	0.272052i
$754$		−	13970.6i		−	0.674773i
$755$	−4898.01			−0.236102
$756$	−11288.6	−	7983.42i	−0.543074	−	0.384066i
$757$	−12225.4			−0.586976			−0.293488	−	0.955963i	$-0.594816\pi$
$757$	−12225.4			−0.586976			−0.293488	+	0.955963i	$0.594816\pi$
$758$			40808.6i			1.95546i
$759$	6107.06	+	1839.34i	0.292058	+	0.0879631i
$760$	−14397.0			−0.687151
$761$	5694.19	−	9862.63i	0.271241	−	0.469803i	−0.697939	−	0.716157i	$-0.745899\pi$
$761$	5694.19	−	9862.63i	0.271241	−	0.469803i	0.969180	+	0.246354i	$0.0792327\pi$
$762$	5614.45	−	18641.3i	0.266916	−	0.886225i
$763$	4258.73	−	15911.6i	0.202066	−	0.754967i
$764$			27673.4i			1.31046i
$765$	−1569.91	+	25500.8i	−0.0741965	+	1.20521i
$766$	28417.9	+	16407.1i	1.34045	+	0.773906i
$767$	−20567.6	+	11874.7i	−0.968257	+	0.559023i
$768$	−26663.2	−	8030.52i	−1.25277	−	0.377313i
$769$	−5063.88	+	2923.63i	−0.237462	+	0.137099i	−0.614010	−	0.789299i	$-0.710444\pi$
$769$	−5063.88	+	2923.63i	−0.237462	+	0.137099i	0.376548	+	0.926397i	$0.377111\pi$
$770$	−7994.65	+	2144.56i	−0.374165	+	0.100370i
$771$	−28435.2	+	26738.4i	−1.32823	+	1.24898i
$772$	−12644.5			−0.589490
$773$	2151.82	−	3727.06i	0.100124	−	0.173419i	−0.811612	−	0.584197i	$-0.801410\pi$
$773$	2151.82	−	3727.06i	0.100124	−	0.173419i	0.911735	+	0.410778i	$0.134743\pi$
$774$	−13391.8	−	26886.6i	−0.621908	−	1.24860i
$775$	−4293.20	+	2478.68i	−0.198989	+	0.114886i
$776$	5391.69	−	9338.68i	0.249421	−	0.432009i
$777$	7554.34	+	14056.6i	0.348791	+	0.649005i
$778$	3446.01	+	5968.66i	0.158799	+	0.275047i
$779$	−23442.8	−	13534.7i	−1.07821	−	0.622503i
$780$	6422.33	−	21323.6i	0.294816	−	0.978858i
$781$	2280.03	+	3949.12i	0.104463	+	0.180936i
$782$	17309.8	+	29981.4i	0.791555	+	1.37101i
$783$	1376.29	+	8038.39i	0.0628157	+	0.366882i
$784$	−23237.6	+	13433.6i	−1.05857	+	0.611955i
$785$	−20781.0	−	11997.9i	−0.944848	−	0.545509i
$786$	−18593.2	−	19773.1i	−0.843764	−	0.897307i
$787$			28346.1i			1.28390i	0.766747	+	0.641949i	$0.221874\pi$
$787$			28346.1i			1.28390i	−0.766747	+	0.641949i	$0.778126\pi$
$788$		−	788.159i		−	0.0356307i
$789$	27996.0	−	6586.27i	1.26322	−	0.297183i
$790$	−1667.72	−	962.859i	−0.0751074	−	0.0433633i
$791$	30719.2	−	30736.5i	1.38085	−	1.38162i
$792$	162.390	−	2637.77i	0.00728570	−	0.118345i
$793$	−24167.3	−	41859.0i	−1.08223	−	1.87447i
$794$	−19254.0	−	33349.0i	−0.860580	−	1.49057i
$795$	−25727.1	+	6052.51i	−1.14773	+	0.270013i
$796$	7872.16	+	4544.99i	0.350529	+	0.202378i
$797$	−4002.70	−	6932.88i	−0.177896	−	0.308124i	0.763264	−	0.646087i	$-0.223596\pi$
$797$	−4002.70	−	6932.88i	−0.177896	−	0.308124i	−0.941160	+	0.337963i	$0.890262\pi$
$798$	20017.9	+	37247.9i	0.888002	+	1.65233i
$799$	873.691	−	1513.28i	0.0386846	−	0.0670036i
$800$	4419.60	−	2551.65i	0.195320	−	0.112768i
$801$	1153.49	−	18736.7i	0.0508822	−	0.826502i
$802$	−3767.92	+	6526.23i	−0.165898	+	0.287343i
$803$	−7661.44			−0.336695
$804$	−2946.48	−	887.432i	−0.129247	−	0.0389270i
$805$	−19633.4	+	19644.5i	−0.859612	+	0.860095i
$806$	41932.8	−	24209.9i	1.83253	−	1.05801i
$807$	−3118.88	+	2932.78i	−0.136047	+	0.127929i
$808$	−5964.07	+	3443.36i	−0.259672	+	0.149922i
$809$	9857.91	+	5691.47i	0.428412	+	0.247344i	0.698670	−	0.715444i	$-0.253776\pi$
$809$	9857.91	+	5691.47i	0.428412	+	0.247344i	−0.270258	+	0.962788i	$0.587109\pi$
$810$	−3991.94	+	32298.6i	−0.173163	+	1.40106i
$811$			3510.72i			0.152008i	0.997108	+	0.0760038i	$0.0242161\pi$
$811$			3510.72i			0.152008i	−0.997108	+	0.0760038i	$0.975784\pi$
$812$	−5533.96	−	1481.16i	−0.239168	−	0.0640129i
$813$	21946.8	−	5163.17i	0.946751	−	0.222731i
$814$	3029.59	−	5247.41i	0.130451	−	0.225948i
$815$	−26728.9			−1.14880
$816$	22917.2	−	21549.7i	0.983163	−	0.924498i
$817$			36696.0i			1.57139i
$818$	−525.104			−0.0224448
$819$	32267.0	−	6560.80i	1.37668	−	0.279918i
$820$	14634.3			0.623233
$821$			12755.0i			0.542209i	0.962550	+	0.271105i	$0.0873889\pi$
$821$			12755.0i			0.542209i	−0.962550	+	0.271105i	$0.912611\pi$
$822$	10977.0	+	46659.4i	0.465775	+	1.97985i
$823$	−9671.52			−0.409633			−0.204817	−	0.978800i	$-0.565660\pi$
$823$	−9671.52			−0.409633			−0.204817	+	0.978800i	$0.565660\pi$
$824$	−5077.74	+	8794.90i	−0.214674	+	0.371826i
$825$	876.867	+	932.510i	0.0370044	+	0.0393525i
$826$	6316.53	+	23547.2i	0.266078	+	0.991904i
$827$		−	41804.8i		−	1.75779i	−0.477011	−	0.878897i	$-0.658280\pi$
$827$		−	41804.8i		−	1.75779i	0.477011	−	0.878897i	$-0.341720\pi$
$828$	7853.63	+	15767.7i	0.329629	+	0.661794i
$829$	12794.2	+	7386.73i	0.536020	+	0.309471i	0.743465	−	0.668775i	$-0.233181\pi$
$829$	12794.2	+	7386.73i	0.536020	+	0.309471i	−0.207444	+	0.978247i	$0.566515\pi$
$830$	15469.6	−	8931.36i	0.646936	−	0.373508i
$831$	−3144.52	−	13366.2i	−0.131266	−	0.557966i
$832$	−7467.01	+	4311.08i	−0.311144	+	0.179639i
$833$	−14.8773	−	26535.7i	−0.000618809	−	1.10373i
$834$	1238.85	+	5265.91i	0.0514362	+	0.218637i
$835$	17729.9			0.734811
$836$	3206.83	−	5554.39i	0.132668	−	0.229788i
$837$	−21742.3	+	18060.8i	−0.897877	+	0.745847i
$838$	−12480.0	+	7205.33i	−0.514457	+	0.297022i
$839$	746.315	−	1292.66i	0.0307100	−	0.0531912i	−0.850262	−	0.526360i	$-0.823557\pi$
$839$	746.315	−	1292.66i	0.0307100	−	0.0531912i	0.880972	+	0.473169i	$0.156890\pi$
$840$	9786.46	+	6054.95i	0.401982	+	0.248709i
$841$	−10505.0	−	18195.1i	−0.430726	−	0.746039i
$842$	−34884.9	−	20140.8i	−1.42781	−	0.824345i
$843$	13628.3	+	14493.1i	0.556802	+	0.592135i
$844$	−2905.29	−	5032.11i	−0.118488	−	0.205228i
$845$	13081.4	+	22657.6i	0.532560	+	0.922422i
$846$	1229.25	−	1855.58i	0.0499555	−	0.0754091i
$847$	5893.41	−	22019.2i	0.239079	−	0.893256i
$848$	28181.9	+	16270.8i	1.14124	+	0.658894i
$849$	10778.2	−	35786.3i	0.435699	−	1.44662i
$850$			6947.91i			0.280366i
$851$		−	20331.0i		−	0.818964i
$852$	−3632.03	+	12059.2i	−0.146046	+	0.484908i
$853$	−3660.40	−	2113.34i	−0.146928	−	0.0848291i	0.424734	−	0.905318i	$-0.360368\pi$
$853$	−3660.40	−	2113.34i	−0.146928	−	0.0848291i	−0.571662	+	0.820489i	$0.693701\pi$
$854$	−47923.2	+	12855.4i	−1.92025	+	0.515107i
$855$	21957.7	−	33145.7i	0.878289	−	1.32580i
$856$	285.025	+	493.677i	0.0113808	+	0.0197121i
$857$	3364.40	+	5827.31i	0.134102	+	0.232272i	0.925254	−	0.379348i	$-0.123852\pi$
$857$	3364.40	+	5827.31i	0.134102	+	0.232272i	−0.791152	+	0.611620i	$0.790518\pi$
$858$	−8564.60	−	9108.08i	−0.340782	−	0.362406i
$859$	34244.2	+	19770.9i	1.36018	+	0.785302i	0.989648	−	0.143517i	$-0.0458412\pi$
$859$	34244.2	+	19770.9i	1.36018	+	0.785302i	0.370535	+	0.928819i	$0.379175\pi$
$860$	−9919.32	−	17180.8i	−0.393309	−	0.681232i
$861$	10243.1	+	19059.6i	0.405439	+	0.754412i
$862$	−3121.20	+	5406.07i	−0.123328	+	0.213610i
$863$	22905.9	−	13224.7i	0.903508	−	0.521640i	0.0251711	−	0.999683i	$-0.491987\pi$
$863$	22905.9	−	13224.7i	0.903508	−	0.521640i	0.878337	+	0.478043i	$0.158654\pi$
$864$	22382.4	−	18592.6i	0.881325	−	0.732098i
$865$	11289.1	−	19553.3i	0.443747	−	0.768592i
$866$	−42334.9			−1.66120
$867$	1275.79	+	5422.94i	0.0499748	+	0.212425i
$868$	−5144.21	−	19177.0i	−0.201159	−	0.749895i
$869$	−373.998	+	215.928i	−0.0145996	+	0.00842906i
$870$	3087.98	+	13125.9i	0.120336	+	0.511506i
$871$	6346.53	−	3664.17i	0.246893	−	0.142544i
$872$	7530.49	+	4347.73i	0.292448	+	0.168845i
$873$	13276.9	+	26656.0i	0.514725	+	1.03341i
$874$		−	53874.2i		−	2.08504i
$875$	21965.4	−	5892.22i	0.848649	−	0.227650i
$876$	−14495.3	−	15415.2i	−0.559078	−	0.594555i
$877$	−1213.18	+	2101.29i	−0.0467117	+	0.0809070i	−0.888436	−	0.459001i	$-0.848208\pi$
$877$	−1213.18	+	2101.29i	−0.0467117	+	0.0809070i	0.841724	+	0.539908i	$0.181541\pi$
$878$	15620.7			0.600424
$879$	−4454.52	−	18934.6i	−0.170930	−	0.726563i
$880$		−	9582.44i		−	0.367073i
$881$	−22112.5			−0.845616			−0.422808	−	0.906219i	$-0.638956\pi$
$881$	−22112.5			−0.845616			−0.422808	+	0.906219i	$0.638956\pi$
$882$	2058.06	−	33738.4i	0.0785696	−	1.28802i
$883$	−50385.7			−1.92029			−0.960144	−	0.279506i	$-0.909829\pi$
$883$	−50385.7			−1.92029			−0.960144	+	0.279506i	$0.909829\pi$
$884$		−	27108.0i		−	1.03138i
$885$	16699.3	−	15702.9i	0.634285	−	0.596437i
$886$	33876.0			1.28452
$887$	5162.50	−	8941.71i	0.195422	−	0.338482i	−0.751616	−	0.659600i	$-0.770726\pi$
$887$	5162.50	−	8941.71i	0.195422	−	0.338482i	0.947039	+	0.321119i	$0.104059\pi$
$888$	−8200.37	+	1929.20i	−0.309895	+	0.0729052i
$889$	18362.6	−	4925.77i	0.692759	−	0.185832i
$890$		−	31038.3i		−	1.16900i
$891$	5825.17	+	4396.87i	0.219024	+	0.165321i
$892$	5658.42	+	3266.89i	0.212397	+	0.122627i
$893$	−2354.93	+	1359.62i	−0.0882472	+	0.0509495i
$894$	−26033.6	+	24480.2i	−0.973930	+	0.915816i
$895$	4764.58	−	2750.83i	0.177947	−	0.102738i
$896$	−5668.31	−	21130.7i	−0.211345	−	0.787866i
$897$	−40168.2	−	12098.0i	−1.49518	−	0.450324i
$898$	−25098.0			−0.932661
$899$	−5855.63	+	10142.2i	−0.217237	+	0.376266i
$900$	−217.232	+	3528.60i	−0.00804562	+	0.130689i
$901$	−27861.2	+	16085.6i	−1.03018	+	0.594773i
$902$	4107.88	−	7115.06i	0.151638	−	0.262645i
$903$	15433.2	−	24944.3i	0.568754	−	0.919262i
$904$	11470.2	+	19867.0i	0.422006	+	0.730936i
$905$	32488.9	+	18757.5i	1.19334	+	0.688973i
$906$	−7392.68	+	1739.19i	−0.271088	+	0.0637755i
$907$	2439.23	+	4224.86i	0.0892979	+	0.154668i	0.907215	−	0.420668i	$-0.138204\pi$
$907$	2439.23	+	4224.86i	0.0892979	+	0.154668i	−0.817917	+	0.575337i	$0.804871\pi$
$908$	6022.23	+	10430.8i	0.220104	+	0.381232i
$909$	1168.62	−	18982.5i	0.0426412	−	0.692640i
$910$	52583.6	−	14105.5i	1.91553	−	0.513839i
$911$	26279.5	+	15172.5i	0.955741	+	0.551797i	0.894860	−	0.446348i	$-0.147276\pi$
$911$	26279.5	+	15172.5i	0.955741	+	0.551797i	0.0608814	+	0.998145i	$0.480609\pi$
$912$	−47652.9	+	11210.7i	−1.73020	+	0.407044i
$913$		−	4005.84i		−	0.145207i
$914$			40737.6i			1.47427i
$915$	31958.4	+	33986.4i	1.15466	+	1.22793i
$916$	23744.1	+	13708.7i	0.856472	+	0.494484i
$917$	6852.90	−	25604.1i	0.246786	−	0.922052i
$918$	6685.34	+	39046.4i	0.240359	+	1.40384i
$919$	−14141.6	−	24493.9i	−0.507603	−	0.879194i	−0.999961	−	0.00880146i	$-0.997198\pi$
$919$	−14141.6	−	24493.9i	−0.507603	−	0.879194i	0.492358	−	0.870393i	$-0.336135\pi$
$920$	−7330.90	−	12697.5i	−0.262709	−	0.455026i
$921$	−6292.74	+	20893.4i	−0.225139	+	0.747514i
$922$	1223.59	+	706.439i	0.0437058	+	0.0252335i
$923$	−14996.5	−	25974.7i	−0.534796	−	0.926293i
$924$	−4515.87	+	2426.93i	−0.160780	+	0.0864072i
$925$	2040.15	−	3533.64i	0.0725185	−	0.125606i
$926$	−15709.5	+	9069.87i	−0.557500	+	0.321873i
$927$	−12503.8	−	25103.8i	−0.443019	−	0.889448i
$928$	6028.03	−	10440.9i	0.213232	−	0.369329i
$929$	−21710.9			−0.766752			−0.383376	−	0.923592i	$-0.625239\pi$
$929$	−21710.9			−0.766752			−0.383376	+	0.923592i	$0.625239\pi$
$930$	−34046.3	+	32014.7i	−1.20045	+	1.12882i
$931$	−20627.1	+	35773.5i	−0.726130	+	1.25932i
$932$	−1923.57	+	1110.58i	−0.0676060	+	0.0390323i
$933$	−12355.6	−	3721.31i	−0.433553	−	0.130579i
$934$	28752.3	−	16600.2i	1.00729	−	0.581557i
$935$	8204.20	+	4736.70i	0.286958	+	0.165675i
$936$	−1068.09	+	17349.5i	−0.0372989	+	0.605863i
$937$			6528.34i			0.227611i	0.993503	+	0.113805i	$0.0363041\pi$
$937$			6528.34i			0.227611i	−0.993503	+	0.113805i	$0.963696\pi$
$938$	−1949.09	−	7265.95i	−0.0678465	−	0.252923i
$939$	1229.61	−	4082.59i	0.0427335	−	0.141885i
$940$	735.040	−	1273.13i	0.0255046	−	0.0441753i
$941$	2996.66			0.103813			0.0519066	−	0.998652i	$-0.483470\pi$
$941$	2996.66			0.103813			0.0519066	+	0.998652i	$0.483470\pi$
$942$	−35625.5	−	10729.8i	−1.23221	−	0.371121i
$943$		−	27567.2i		−	0.951974i
$944$	−28223.9			−0.973102
$945$	−28865.9	+	13296.2i	−0.993660	+	0.457700i
$946$	−11137.5			−0.382782
$947$			5770.97i			0.198027i	0.995086	+	0.0990133i	$0.0315686\pi$
$947$			5770.97i			0.198027i	−0.995086	+	0.0990133i	$0.968431\pi$
$948$	−1142.06	−	343.969i	−0.0391269	−	0.0117844i
$949$	50391.9			1.72370
$950$	5406.09	−	9363.63i	0.184628	−	0.319786i
$951$	−6194.05	+	20565.7i	−0.211205	+	0.701250i
$952$	13532.0	+	3621.82i	0.460687	+	0.123302i
$953$			38807.0i			1.31908i	0.751670	+	0.659540i	$0.229249\pi$
$953$			38807.0i			1.31908i	−0.751670	+	0.659540i	$0.770751\pi$
$954$	−36681.4	+	18270.4i	−1.24487	+	0.620048i
$955$	55087.5	+	31804.8i	1.86659	+	1.07767i
$956$	−25716.0	+	14847.2i	−0.869996	+	0.502292i
$957$	2895.46	+	872.065i	0.0978025	+	0.0294565i
$958$	43803.3	−	25289.9i	1.47727	−	0.852900i
$959$	−33089.6	+	33108.2i	−1.11420	+	1.11483i
$960$	6062.65	−	5700.89i	0.203824	−	0.191662i
$961$	−10798.3			−0.362470
$962$	−19926.7	+	34514.0i	−0.667840	+	1.15673i
$963$	−1571.28	−	96.7331i	−0.0525792	−	0.00323695i
$964$	−12782.9	+	7380.21i	−0.427085	+	0.246577i
$965$	−14532.2	+	25170.5i	−0.484775	+	0.839656i
$966$	−22657.9	+	36621.3i	−0.754663	+	1.21974i
$967$	−27150.0	−	47025.2i	−0.902880	−	1.56383i	−0.823738	−	0.566970i	$-0.808115\pi$
$967$	−27150.0	−	47025.2i	−0.902880	−	1.56383i	−0.0791416	−	0.996863i	$-0.525218\pi$
$968$	10421.0	+	6016.57i	0.346016	+	0.199773i
$969$	13957.0	−	46340.5i	0.462707	−	1.53630i
$970$	24619.0	+	42641.4i	0.814918	+	1.41148i
$971$	−17624.4	−	30526.3i	−0.582485	−	1.00889i	−0.995184	−	0.0980262i	$-0.968747\pi$
$971$	−17624.4	−	30526.3i	−0.582485	−	1.00889i	0.412699	−	0.910868i	$-0.364586\pi$
$972$	2174.43	+	20039.3i	0.0717540	+	0.661278i
$973$	−3734.45	+	3736.54i	−0.123043	+	0.123112i
$974$	4306.94	+	2486.61i	0.141687	+	0.0818031i
$975$	−5767.46	−	6133.44i	−0.189443	−	0.201464i
$976$		−	57441.0i		−	1.88386i
$977$		−	49431.6i		−	1.61869i	−0.587335	−	0.809344i	$-0.699823\pi$
$977$		−	49431.6i		−	1.61869i	0.587335	−	0.809344i	$-0.300177\pi$
$978$	−40342.5	+	9490.91i	−1.31903	+	0.310313i
$979$	−6028.02	−	3480.28i	−0.196789	−	0.113616i
$980$	−12.5163	−	22324.6i	−0.000407980	−	0.727688i
$981$	−21494.8	+	10706.2i	−0.699566	+	0.348442i
$982$	32291.1	+	55929.9i	1.04934	+	1.81751i
$983$	21423.7	+	37107.0i	0.695128	+	1.20400i	0.970138	+	0.242555i	$0.0779855\pi$
$983$	21423.7	+	37107.0i	0.695128	+	1.20400i	−0.275010	+	0.961441i	$0.588681\pi$
$984$	−11119.0	+	2615.84i	−0.360225	+	0.0847459i
$985$	−1568.93	−	905.822i	−0.0507516	−	0.0293014i
$986$	8206.87	+	14214.7i	0.265071	+	0.459116i
$987$	2172.59	+	66.2031i	0.0700652	+	0.00213502i
$988$	−21092.4	+	36533.2i	−0.679190	+	1.17639i
$989$	−32364.1	+	18685.4i	−1.04057	+	0.600771i
$990$	10060.0	+	6664.33i	0.322956	+	0.213946i
$991$	15056.3	−	26078.3i	0.482623	−	0.835927i	−0.517178	−	0.855878i	$-0.673018\pi$
$991$	15056.3	−	26078.3i	0.482623	−	0.835927i	0.999801	+	0.0199505i	$0.00635086\pi$
$992$	41784.4			1.33735
$993$	44223.2	+	13319.3i	1.41327	+	0.425654i
$994$	−29737.7	+	7977.13i	−0.948916	+	0.254546i
$995$	18094.8	−	10447.0i	0.576525	−	0.332857i
$996$	8059.93	−	7579.00i	0.256414	−	0.241114i
$997$	−6236.09	+	3600.41i	−0.198093	+	0.114369i	−0.595766	−	0.803158i	$-0.703151\pi$
$997$	−6236.09	+	3600.41i	−0.198093	+	0.114369i	0.397673	+	0.917527i	$0.369818\pi$
$998$	−44750.5	−	25836.7i	−1.41939	−	0.819487i
$999$	8065.30	−	21821.7i	0.255430	−	0.691099i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.i.a.38.5	yes	44
3.2	odd	2		189.4.i.a.143.18		44
7.5	odd	6		63.4.s.a.47.5	yes	44
9.4	even	3		189.4.s.a.17.18		44
9.5	odd	6		63.4.s.a.59.5	yes	44
21.5	even	6		189.4.s.a.89.18		44
63.5	even	6	inner	63.4.i.a.5.18	✓	44
63.40	odd	6		189.4.i.a.152.5		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.18	✓	44	63.5	even	6	inner
63.4.i.a.38.5	yes	44	1.1	even	1	trivial
63.4.s.a.47.5	yes	44	7.5	odd	6
63.4.s.a.59.5	yes	44	9.5	odd	6
189.4.i.a.143.18		44	3.2	odd	2
189.4.i.a.152.5		44	63.40	odd	6
189.4.s.a.17.18		44	9.4	even	3
189.4.s.a.89.18		44	21.5	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-3.64983i q^{2} +(-4.97539 - 1.49850i) q^{3} -5.32127 q^{4} +(-6.11568 + 10.5927i) q^{5} +(-5.46929 + 18.1593i) q^{6} +(-17.8879 + 4.79841i) q^{7} -9.77690i q^{8} +(22.5090 + 14.9113i) q^{9} +(38.6615 + 22.3212i) q^{10} +(8.67010 - 5.00569i) q^{11} +(26.4754 + 7.97395i) q^{12} +(-57.0263 + 32.9241i) q^{13} +(17.5134 + 65.2877i) q^{14} +(46.3010 - 43.5383i) q^{15} -78.2542 q^{16} +(38.6818 - 66.9989i) q^{17} +(54.4237 - 82.1539i) q^{18} +(-104.262 + 60.1959i) q^{19} +(32.5432 - 56.3665i) q^{20} +(96.1894 + 2.93108i) q^{21} +(-18.2699 - 31.6444i) q^{22} +(-106.180 - 61.3030i) q^{23} +(-14.6507 + 48.6439i) q^{24} +(-12.3031 - 21.3096i) q^{25} +(120.168 + 208.136i) q^{26} +(-89.6462 - 107.919i) q^{27} +(95.1861 - 25.5337i) q^{28} +(-50.3417 - 29.0648i) q^{29} +(-158.907 - 168.991i) q^{30} -201.468i q^{31} +207.400i q^{32} +(-50.6382 + 11.9130i) q^{33} +(-244.535 - 141.182i) q^{34} +(58.5684 - 218.826i) q^{35} +(-119.776 - 79.3470i) q^{36} +(82.9121 + 143.608i) q^{37} +(219.705 + 380.540i) q^{38} +(333.065 - 78.3562i) q^{39} +(103.563 + 59.7924i) q^{40} +(112.422 + 194.721i) q^{41} +(10.6979 - 351.075i) q^{42} +(152.402 - 263.969i) q^{43} +(-46.1360 + 26.6366i) q^{44} +(-295.608 + 147.237i) q^{45} +(-223.746 + 387.539i) q^{46} +22.5866 q^{47} +(389.345 + 117.264i) q^{48} +(296.951 - 171.667i) q^{49} +(-77.7763 + 44.9042i) q^{50} +(-292.855 + 275.381i) q^{51} +(303.452 - 175.198i) q^{52} +(-360.132 - 207.922i) q^{53} +(-393.887 + 327.194i) q^{54} +122.453i q^{55} +(46.9136 + 174.888i) q^{56} +(608.949 - 143.260i) q^{57} +(-106.082 + 183.739i) q^{58} +360.669 q^{59} +(-246.381 + 231.679i) q^{60} +734.031i q^{61} -735.324 q^{62} +(-474.188 - 158.724i) q^{63} +130.940 q^{64} -805.414i q^{65} +(43.4806 + 184.821i) q^{66} -111.291 q^{67} +(-205.837 + 356.519i) q^{68} +(436.423 + 464.117i) q^{69} +(-798.677 - 213.765i) q^{70} +455.487i q^{71} +(145.786 - 220.068i) q^{72} +(-662.747 - 382.637i) q^{73} +(524.145 - 302.615i) q^{74} +(29.2801 + 124.460i) q^{75} +(554.808 - 320.319i) q^{76} +(-131.070 + 131.144i) q^{77} +(-285.987 - 1215.63i) q^{78} -43.1365 q^{79} +(478.578 - 828.921i) q^{80} +(284.307 + 671.275i) q^{81} +(710.697 - 410.321i) q^{82} +(200.064 - 346.522i) q^{83} +(-511.850 - 15.5971i) q^{84} +(473.131 + 819.488i) q^{85} +(-963.441 - 556.243i) q^{86} +(206.916 + 220.046i) q^{87} +(-48.9401 - 84.7667i) q^{88} +(-347.632 - 602.117i) q^{89} +(537.392 + 1078.92i) q^{90} +(862.094 - 862.577i) q^{91} +(565.012 + 326.210i) q^{92} +(-301.901 + 1002.38i) q^{93} -82.4373i q^{94} -1472.55i q^{95} +(310.789 - 1031.89i) q^{96} +(955.178 + 551.472i) q^{97} +(-626.554 - 1083.82i) q^{98} +(269.796 + 16.6095i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 3 q^{3} - 162 q^{4} - 3 q^{5} + 24 q^{6} + 5 q^{7} - 45 q^{9} - 6 q^{10} + 9 q^{11} + 186 q^{12} - 36 q^{13} + 54 q^{14} - 141 q^{15} + 526 q^{16} - 72 q^{17} - 54 q^{18} - 6 q^{19} + 24 q^{20} - 81 q^{21}+ \cdots + 4335 q^{99}+O(q^{100}) \) 44 * q - 3 * q^3 - 162 * q^4 - 3 * q^5 + 24 * q^6 + 5 * q^7 - 45 * q^9 - 6 * q^10 + 9 * q^11 + 186 * q^12 - 36 * q^13 + 54 * q^14 - 141 * q^15 + 526 * q^16 - 72 * q^17 - 54 * q^18 - 6 * q^19 + 24 * q^20 - 81 * q^21 + 14 * q^22 - 285 * q^23 - 114 * q^24 - 349 * q^25 - 96 * q^26 + 432 * q^27 - 156 * q^28 - 132 * q^29 - 447 * q^30 - 3 * q^33 + 24 * q^34 + 765 * q^35 + 1122 * q^36 + 82 * q^37 - 873 * q^38 + 306 * q^39 + 420 * q^40 + 618 * q^41 - 282 * q^42 + 82 * q^43 + 603 * q^44 + 291 * q^45 + 266 * q^46 - 402 * q^47 - 1569 * q^48 - 79 * q^49 - 1845 * q^50 + 453 * q^51 + 189 * q^52 + 564 * q^53 - 2385 * q^54 + 66 * q^56 + 1170 * q^57 + 269 * q^58 + 1494 * q^59 + 2265 * q^60 - 2904 * q^62 - 636 * q^63 - 1144 * q^64 - 372 * q^66 - 590 * q^67 + 3504 * q^68 - 1005 * q^69 - 105 * q^70 + 1830 * q^72 - 6 * q^73 + 1515 * q^74 - 33 * q^75 - 144 * q^76 - 4443 * q^77 - 5985 * q^78 + 1102 * q^79 - 4239 * q^80 - 4017 * q^81 + 18 * q^82 + 1830 * q^83 + 3165 * q^84 - 237 * q^85 + 1209 * q^86 + 2013 * q^87 - 623 * q^88 + 4266 * q^89 + 9993 * q^90 - 1140 * q^91 + 7896 * q^92 - 729 * q^93 + 3975 * q^96 - 792 * q^97 + 5667 * q^98 + 4335 * q^99

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