LMFDB - Embedded newform 117.4.r.a.43.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,4,Mod(43,117)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("117.43");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	117.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.90322347067$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.8
Character	$\chi$	$=$	117.43
Dual form			117.4.r.a.49.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.44134 + 1.98686i) q^{2} +(-0.951787 - 5.10824i) q^{3} +(3.89522 - 6.74672i) q^{4} +(-9.30367 + 5.37147i) q^{5} +(13.4248 + 15.6881i) q^{6} -16.8418i q^{7} -0.832741i q^{8} +(-25.1882 + 9.72391i) q^{9} +(21.3447 - 36.9702i) q^{10} +(-11.4307 + 6.59955i) q^{11} +(-38.1713 - 13.4763i) q^{12} +(44.2653 - 15.4136i) q^{13} +(33.4623 + 57.9585i) q^{14} +(36.2939 + 42.4129i) q^{15} +(32.8163 + 56.8395i) q^{16} +(49.0702 + 84.9920i) q^{17} +(67.3612 - 83.5087i) q^{18} +(-56.0776 + 32.3764i) q^{19} +83.6923i q^{20} +(-86.0321 + 16.0298i) q^{21} +(26.2247 - 45.4226i) q^{22} -98.5778 q^{23} +(-4.25384 + 0.792592i) q^{24} +(-4.79452 + 8.30436i) q^{25} +(-121.707 + 140.993i) q^{26} +(73.6458 + 119.412i) q^{27} +(-113.627 - 65.6026i) q^{28} +(152.065 + 263.385i) q^{29} +(-209.168 - 73.8463i) q^{30} +(86.6932 - 50.0523i) q^{31} +(-220.095 - 127.072i) q^{32} +(44.5917 + 52.1096i) q^{33} +(-337.734 - 194.991i) q^{34} +(90.4654 + 156.691i) q^{35} +(-32.5091 + 207.814i) q^{36} +(197.075 + 113.781i) q^{37} +(128.655 - 222.837i) q^{38} +(-120.868 - 211.447i) q^{39} +(4.47305 + 7.74755i) q^{40} -48.2835i q^{41} +(264.217 - 226.098i) q^{42} -171.010 q^{43} +102.827i q^{44} +(182.111 - 225.766i) q^{45} +(339.240 - 195.860i) q^{46} +(-23.5689 - 13.6075i) q^{47} +(259.116 - 221.733i) q^{48} +59.3529 q^{49} -38.1042i q^{50} +(387.455 - 331.556i) q^{51} +(68.4317 - 358.685i) q^{52} +611.664 q^{53} +(-490.696 - 264.614i) q^{54} +(70.8986 - 122.800i) q^{55} -14.0249 q^{56} +(218.760 + 255.642i) q^{57} +(-1046.62 - 604.264i) q^{58} +(-709.861 - 409.839i) q^{59} +(427.520 - 79.6572i) q^{60} +36.6653 q^{61} +(-198.894 + 344.494i) q^{62} +(163.768 + 424.215i) q^{63} +484.834 q^{64} +(-329.036 + 381.173i) q^{65} +(-256.990 - 90.7296i) q^{66} -107.753i q^{67} +764.556 q^{68} +(93.8251 + 503.559i) q^{69} +(-622.645 - 359.484i) q^{70} +(-93.2300 + 53.8263i) q^{71} +(8.09750 + 20.9753i) q^{72} +553.128i q^{73} -904.271 q^{74} +(46.9840 + 16.5876i) q^{75} +504.453i q^{76} +(111.148 + 192.515i) q^{77} +(836.063 + 487.515i) q^{78} +(-395.090 + 684.315i) q^{79} +(-610.624 - 352.544i) q^{80} +(539.891 - 489.856i) q^{81} +(95.9325 + 166.160i) q^{82} +(-14.9734 - 8.64491i) q^{83} +(-226.965 + 642.874i) q^{84} +(-913.065 - 527.158i) q^{85} +(588.505 - 339.774i) q^{86} +(1200.70 - 1027.47i) q^{87} +(5.49571 + 9.51886i) q^{88} +(-43.2247 - 24.9558i) q^{89} +(-178.141 + 1138.77i) q^{90} +(-259.594 - 745.509i) q^{91} +(-383.982 + 665.077i) q^{92} +(-338.193 - 395.210i) q^{93} +108.145 q^{94} +(347.818 - 602.439i) q^{95} +(-439.629 + 1245.24i) q^{96} +1396.78i q^{97} +(-204.254 + 117.926i) q^{98} +(223.747 - 277.382i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 3 q^{2} - q^{3} + 153 q^{4} - 3 q^{6} - 17 q^{9} - 10 q^{10} - 3 q^{11} - 101 q^{12} - 13 q^{13} + 126 q^{14} - 84 q^{15} - 551 q^{16} - 138 q^{17} + 168 q^{18} - 96 q^{19} + 249 q^{21} - 31 q^{22}+ \cdots + 2331 q^{99}+O(q^{100}) $ 80 * q - 3 * q^2 - q^3 + 153 * q^4 - 3 * q^6 - 17 * q^9 - 10 * q^10 - 3 * q^11 - 101 * q^12 - 13 * q^13 + 126 * q^14 - 84 * q^15 - 551 * q^16 - 138 * q^17 + 168 * q^18 - 96 * q^19 + 249 * q^21 - 31 * q^22 + 654 * q^23 - 834 * q^24 + 798 * q^25 + 510 * q^26 - 364 * q^27 + 18 * q^28 + 201 * q^29 + 87 * q^30 - 180 * q^31 + 117 * q^32 + 231 * q^33 - 24 * q^34 + 297 * q^35 + 251 * q^36 + 246 * q^37 - 768 * q^38 - 560 * q^39 + 328 * q^40 + 1212 * q^42 + 166 * q^43 - 603 * q^45 - 6 * q^46 - 372 * q^47 - 1288 * q^48 - 3226 * q^49 + 186 * q^51 + 186 * q^52 - 2568 * q^53 + 480 * q^54 - 127 * q^55 + 4596 * q^56 - 1332 * q^57 - 3 * q^58 - 531 * q^59 - 711 * q^60 + 838 * q^61 + 135 * q^62 + 2895 * q^63 - 3178 * q^64 - 2337 * q^65 + 6228 * q^66 - 3900 * q^68 + 591 * q^69 + 1005 * q^70 - 2598 * q^71 + 1821 * q^72 - 942 * q^74 - 494 * q^75 - 1584 * q^77 + 2631 * q^78 - 260 * q^79 - 1332 * q^80 - 2357 * q^81 - 1273 * q^82 - 1194 * q^83 + 8196 * q^84 + 3936 * q^85 + 2910 * q^86 - 363 * q^87 + 781 * q^88 - 1056 * q^89 + 2559 * q^90 + 537 * q^91 + 1056 * q^92 + 1830 * q^93 - 1078 * q^94 - 5292 * q^95 - 6777 * q^96 - 6339 * q^98 + 2331 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−3.44134	+	1.98686i	−1.21670	+	0.702461i	−0.964210	−	0.265139i	$-0.914582\pi$
$2$	−3.44134	+	1.98686i	−1.21670	+	0.702461i	−0.252488	+	0.967600i	$0.581249\pi$
$3$	−0.951787	−	5.10824i	−0.183171	−	0.983081i
$3$	−0.951787	−	5.10824i	−0.183171	−	0.983081i
$4$	3.89522	−	6.74672i	0.486902	−	0.843340i
$5$	−9.30367	+	5.37147i	−0.832145	+	0.480439i	−0.854587	−	0.519309i	$-0.826189\pi$
$5$	−9.30367	+	5.37147i	−0.832145	+	0.480439i	0.0224414	+	0.999748i	$0.492856\pi$
$6$	13.4248	+	15.6881i	0.913440	+	1.06744i
$7$		−	16.8418i		−	0.909373i	−0.890652	−	0.454687i	$-0.849751\pi$
$7$		−	16.8418i		−	0.909373i	0.890652	−	0.454687i	$-0.150249\pi$
$8$		−	0.832741i		−	0.0368023i
$9$	−25.1882	+	9.72391i	−0.932896	+	0.360145i
$10$	21.3447	−	36.9702i	0.674980	−	1.16910i
$11$	−11.4307	+	6.59955i	−0.313318	+	0.180894i	−0.648410	−	0.761291i	$-0.724566\pi$
$11$	−11.4307	+	6.59955i	−0.313318	+	0.180894i	0.335092	+	0.942185i	$0.391233\pi$
$12$	−38.1713	−	13.4763i	−0.918258	−	0.324189i
$13$	44.2653	−	15.4136i	0.944384	−	0.328844i
$13$	44.2653	−	15.4136i	0.944384	−	0.328844i
$14$	33.4623	+	57.9585i	0.638799	+	1.10643i
$15$	36.2939	+	42.4129i	0.624736	+	0.730063i
$16$	32.8163	+	56.8395i	0.512755	+	0.888117i
$17$	49.0702	+	84.9920i	0.700074	+	1.21256i	0.968440	+	0.249247i	$0.0801832\pi$
$17$	49.0702	+	84.9920i	0.700074	+	1.21256i	−0.268366	+	0.963317i	$0.586484\pi$
$18$	67.3612	−	83.5087i	0.882065	−	1.09351i
$19$	−56.0776	+	32.3764i	−0.677110	+	0.390929i	−0.798765	−	0.601643i	$-0.794513\pi$
$19$	−56.0776	+	32.3764i	−0.677110	+	0.390929i	0.121655	+	0.992572i	$0.461180\pi$
$20$			83.6923i			0.935708i
$21$	−86.0321	+	16.0298i	−0.893987	+	0.166571i
$22$	26.2247	−	45.4226i	0.254142	−	0.440188i
$23$	−98.5778			−0.893691			−0.446846	−	0.894611i	$-0.647453\pi$
$23$	−98.5778			−0.893691			−0.446846	+	0.894611i	$0.647453\pi$
$24$	−4.25384	+	0.792592i	−0.0361797	+	0.00674113i
$25$	−4.79452	+	8.30436i	−0.0383562	+	0.0664349i
$26$	−121.707	+	140.993i	−0.918030	+	1.06350i
$27$	73.6458	+	119.412i	0.524931	+	0.851144i
$28$	−113.627	−	65.6026i	−0.766910	−	0.442776i
$29$	152.065	+	263.385i	0.973717	+	1.68653i	0.684106	+	0.729383i	$0.260193\pi$
$29$	152.065	+	263.385i	0.973717	+	1.68653i	0.289611	+	0.957144i	$0.406474\pi$
$30$	−209.168	−	73.8463i	−1.27296	−	0.449414i
$31$	86.6932	−	50.0523i	0.502276	−	0.289989i	−0.227377	−	0.973807i	$-0.573015\pi$
$31$	86.6932	−	50.0523i	0.502276	−	0.289989i	0.729653	+	0.683818i	$0.239682\pi$
$32$	−220.095	−	127.072i	−1.21586	−	0.701979i
$33$	44.5917	+	52.1096i	0.235225	+	0.274883i
$34$	−337.734	−	194.991i	−1.70356	−	0.983550i
$35$	90.4654	+	156.691i	0.436899	+	0.756731i
$36$	−32.5091	+	207.814i	−0.150505	+	0.962104i
$37$	197.075	+	113.781i	0.875648	+	0.505556i	0.869221	−	0.494424i	$-0.164621\pi$
$37$	197.075	+	113.781i	0.875648	+	0.505556i	0.00642714	+	0.999979i	$0.497954\pi$
$38$	128.655	−	222.837i	0.549225	−	0.951286i
$39$	−120.868	−	211.447i	−0.496265	−	0.868171i
$40$	4.47305	+	7.74755i	0.0176813	+	0.0306249i
$41$		−	48.2835i		−	0.183917i	−0.995763	−	0.0919587i	$-0.970687\pi$
$41$		−	48.2835i		−	0.183917i	0.995763	−	0.0919587i	$-0.0293128\pi$
$42$	264.217	−	226.098i	0.970703	−	0.830658i
$43$	−171.010			−0.606485			−0.303242	−	0.952913i	$-0.598069\pi$
$43$	−171.010			−0.606485			−0.303242	+	0.952913i	$0.598069\pi$
$44$			102.827i			0.352312i
$45$	182.111	−	225.766i	0.603278	−	0.747893i
$46$	339.240	−	195.860i	1.08735	−	0.627783i
$47$	−23.5689	−	13.6075i	−0.0731465	−	0.0422311i	0.462981	−	0.886368i	$-0.346780\pi$
$47$	−23.5689	−	13.6075i	−0.0731465	−	0.0422311i	−0.536127	+	0.844137i	$0.680113\pi$
$48$	259.116	−	221.733i	0.779169	−	0.666757i
$49$	59.3529			0.173041
$50$		−	38.1042i		−	0.107775i
$51$	387.455	−	331.556i	1.06382	−	0.910337i
$52$	68.4317	−	358.685i	0.182496	−	0.956552i
$53$	611.664			1.58525			0.792627	−	0.609707i	$-0.208713\pi$
$53$	611.664			1.58525			0.792627	+	0.609707i	$0.208713\pi$
$54$	−490.696	−	264.614i	−1.23658	−	0.666842i
$55$	70.8986	−	122.800i	0.173818	−	0.301061i
$56$	−14.0249			−0.0334670
$57$	218.760	+	255.642i	0.508343	+	0.594047i
$58$	−1046.62	−	604.264i	−2.36944	−	1.36800i
$59$	−709.861	−	409.839i	−1.56637	−	0.904346i	−0.996587	−	0.0825539i	$-0.973692\pi$
$59$	−709.861	−	409.839i	−1.56637	−	0.904346i	−0.569787	−	0.821792i	$-0.692974\pi$
$60$	427.520	−	79.6572i	0.919877	−	0.171395i
$61$	36.6653			0.0769592			0.0384796	−	0.999259i	$-0.487749\pi$
$61$	36.6653			0.0769592			0.0384796	+	0.999259i	$0.487749\pi$
$62$	−198.894	+	344.494i	−0.407412	+	0.705658i
$63$	163.768	+	424.215i	0.327506	+	0.848351i
$64$	484.834			0.946941
$65$	−329.036	+	381.173i	−0.627875	+	0.727365i
$66$	−256.990	−	90.7296i	−0.479292	−	0.169213i
$67$		−	107.753i		−	0.196480i	−0.995163	−	0.0982401i	$-0.968679\pi$
$67$		−	107.753i		−	0.196480i	0.995163	−	0.0982401i	$-0.0313213\pi$
$68$	764.556			1.36347
$69$	93.8251	+	503.559i	0.163699	+	0.878571i
$70$	−622.645	−	359.484i	−1.06315	−	0.613808i
$71$	−93.2300	+	53.8263i	−0.155836	+	0.0899720i	−0.575890	−	0.817527i	$-0.695344\pi$
$71$	−93.2300	+	53.8263i	−0.155836	+	0.0899720i	0.420054	+	0.907499i	$0.362011\pi$
$72$	8.09750	+	20.9753i	0.0132542	+	0.0343327i
$73$			553.128i			0.886832i	0.896316	+	0.443416i	$0.146234\pi$
$73$			553.128i			0.886832i	−0.896316	+	0.443416i	$0.853766\pi$
$74$	−904.271			−1.42053
$75$	46.9840	+	16.5876i	0.0723366	+	0.0255383i
$76$			504.453i			0.761378i
$77$	111.148	+	192.515i	0.164500	+	0.284923i
$78$	836.063	+	487.515i	1.21366	+	0.707696i
$79$	−395.090	+	684.315i	−0.562672	+	0.974576i	0.434591	+	0.900628i	$0.356893\pi$
$79$	−395.090	+	684.315i	−0.562672	+	0.974576i	−0.997262	+	0.0739476i	$0.976440\pi$
$80$	−610.624	−	352.544i	−0.853373	−	0.492695i
$81$	539.891	−	489.856i	0.740591	−	0.671956i
$82$	95.9325	+	166.160i	0.129195	+	0.223772i
$83$	−14.9734	−	8.64491i	−0.0198018	−	0.0114326i	0.490066	−	0.871685i	$-0.336973\pi$
$83$	−14.9734	−	8.64491i	−0.0198018	−	0.0114326i	−0.509868	+	0.860253i	$0.670306\pi$
$84$	−226.965	+	642.874i	−0.294808	+	0.835039i
$85$	−913.065	−	527.158i	−1.16513	−	0.672686i
$86$	588.505	−	339.774i	0.737909	−	0.426032i
$87$	1200.70	−	1027.47i	1.47964	−	1.26617i
$88$	5.49571	+	9.51886i	0.00665733	+	0.0115308i
$89$	−43.2247	−	24.9558i	−0.0514810	−	0.0297226i	0.474039	−	0.880504i	$-0.342796\pi$
$89$	−43.2247	−	24.9558i	−0.0514810	−	0.0297226i	−0.525520	+	0.850782i	$0.676129\pi$
$90$	−178.141	+	1138.77i	−0.208641	+	1.33374i
$91$	−259.594	−	745.509i	−0.299042	−	0.858798i
$92$	−383.982	+	665.077i	−0.435140	+	0.753685i
$93$	−338.193	−	395.210i	−0.377085	−	0.440660i
$94$	108.145			0.118663
$95$	347.818	−	602.439i	0.375636	−	0.650620i
$96$	−439.629	+	1245.24i	−0.467391	+	1.32387i
$97$			1396.78i			1.46208i	0.682336	+	0.731039i	$0.260964\pi$
$97$			1396.78i			1.46208i	−0.682336	+	0.731039i	$0.739036\pi$
$98$	−204.254	+	117.926i	−0.210538	+	0.121554i
$99$	223.747	−	277.382i	0.227145	−	0.281596i
$100$	37.3514	+	64.6946i	0.0373514	+	0.0646946i
$101$	−853.648	−	1478.56i	−0.841001	−	1.45666i	−0.889049	−	0.457812i	$-0.848633\pi$
$101$	−853.648	−	1478.56i	−0.841001	−	1.45666i	0.0480479	−	0.998845i	$-0.484700\pi$
$102$	−674.610	+	1910.82i	−0.654866	+	1.85489i
$103$	237.262	+	410.949i	0.226972	+	0.393127i	0.956909	−	0.290387i	$-0.0937842\pi$
$103$	237.262	+	410.949i	0.226972	+	0.393127i	−0.729937	+	0.683514i	$0.760451\pi$
$104$	−12.8356	−	36.8616i	−0.0121022	−	0.0347555i
$105$	714.310	−	611.255i	0.663900	−	0.568118i
$106$	−2104.94	+	1215.29i	−1.92878	+	1.11358i
$107$	−675.268	+	1169.60i	−0.610099	+	1.05672i	0.381124	+	0.924524i	$0.375537\pi$
$107$	−675.268	+	1169.60i	−0.610099	+	1.05672i	−0.991223	+	0.132199i	$0.957796\pi$
$108$	1092.51	−	31.7308i	0.973394	−	0.0282713i
$109$			1212.35i			1.06534i	0.846324	+	0.532669i	$0.178811\pi$
$109$			1212.35i			1.06534i	−0.846324	+	0.532669i	$0.821189\pi$
$110$			563.462i			0.488400i
$111$	393.649	−	1115.00i	0.336608	−	0.953436i
$112$	957.281	−	552.686i	0.807630	−	0.466285i
$113$	234.740	−	406.582i	0.195420	−	0.338478i	−0.751618	−	0.659599i	$-0.770726\pi$
$113$	234.740	−	406.582i	0.195420	−	0.338478i	0.947038	+	0.321121i	$0.104060\pi$
$114$	−1260.75	−	445.106i	−1.03579	−	0.365684i
$115$	917.135	−	529.508i	0.743681	−	0.429364i
$116$	2369.31			1.89642
$117$	−965.083	+	818.674i	−0.762581	+	0.646893i
$118$	3257.17			2.54107
$119$	1431.42	−	826.431i	1.10267	−	0.636629i
$120$	35.3189	−	30.2234i	0.0268680	−	0.0229917i
$121$	−578.392	+	1001.80i	−0.434554	+	0.752670i
$122$	−126.178	+	72.8488i	−0.0936361	+	0.0540608i
$123$	−246.644	+	45.9556i	−0.180806	+	0.0336884i
$124$		−	779.859i		−	0.564786i
$125$		−	1445.88i		−	1.03459i
$126$	−1406.44	−	1134.48i	−0.994409	−	0.802127i
$127$	−226.697	+	392.651i	−0.158395	+	0.274347i	−0.934290	−	0.356514i	$-0.883965\pi$
$127$	−226.697	+	392.651i	−0.158395	+	0.274347i	0.775895	+	0.630862i	$0.217298\pi$
$128$	92.2787	−	53.2772i	0.0637216	−	0.0367897i
$129$	162.766	+	873.562i	0.111091	+	0.596224i
$130$	374.987	−	1965.50i	0.252989	−	1.32604i
$131$	817.565	+	1416.06i	0.545274	+	0.944443i	0.998590	+	0.0530927i	$0.0169079\pi$
$131$	817.565	+	1416.06i	0.545274	+	0.944443i	−0.453315	+	0.891350i	$0.649759\pi$
$132$	525.263	−	97.8691i	0.346351	−	0.0645334i
$133$	545.278	+	944.449i	0.355501	+	0.615745i
$134$	214.091	+	370.816i	0.138020	+	0.239057i
$135$	−1326.60	−	715.385i	−0.845742	−	0.456078i
$136$	70.7764	−	40.8628i	0.0446252	−	0.0257644i
$137$			923.932i			0.576181i	0.957603	+	0.288091i	$0.0930205\pi$
$137$			923.932i			0.576181i	−0.957603	+	0.288091i	$0.906980\pi$
$138$	−1323.39	−	1546.50i	−0.816334	−	0.953963i
$139$	271.659	−	470.526i	0.165768	−	0.287119i	−0.771160	−	0.636642i	$-0.780323\pi$
$139$	271.659	−	470.526i	0.165768	−	0.287119i	0.936928	+	0.349523i	$0.113656\pi$
$140$	1409.53			0.850908
$141$	−47.0779	+	133.347i	−0.0281183	+	0.0796444i
$142$	213.891	−	370.470i	0.126404	−	0.218937i
$143$	−404.263	+	468.321i	−0.236407	+	0.273867i
$144$	−1379.29	−	1112.58i	−0.798198	−	0.643855i
$145$	−2829.53	−	1633.63i	−1.62055	−	0.935624i
$146$	−1098.99	−	1903.50i	−0.622965	−	1.07901i
$147$	−56.4913	−	303.189i	−0.0316961	−	0.170113i
$148$	1535.30	−	886.408i	0.852710	−	0.492313i
$149$	−1063.04	−	613.745i	−0.584479	−	0.337449i	0.178432	−	0.983952i	$-0.442897\pi$
$149$	−1063.04	−	613.745i	−0.584479	−	0.337449i	−0.762911	+	0.646503i	$0.776231\pi$
$150$	−194.645	+	36.2670i	−0.105951	+	0.0197413i
$151$	2856.94	+	1649.45i	1.53970	+	0.888945i	0.998856	+	0.0478207i	$0.0152276\pi$
$151$	2856.94	+	1649.45i	1.53970	+	0.888945i	0.540842	+	0.841124i	$0.318106\pi$
$152$	26.9612	+	46.6981i	0.0143871	+	0.0249192i
$153$	−2062.44	−	1663.64i	−1.08980	−	0.879069i
$154$	−764.999	−	441.672i	−0.400295	−	0.231110i
$155$	−537.710	+	931.340i	−0.278644	+	0.482626i
$156$	−1897.38	−	8.17366i	−0.973796	−	0.00419498i
$157$	765.027	+	1325.07i	0.388891	+	0.673578i	0.992301	−	0.123853i	$-0.0395251\pi$
$157$	765.027	+	1325.07i	0.388891	+	0.673578i	−0.603410	+	0.797431i	$0.706192\pi$
$158$		−	3139.95i		−	1.58102i
$159$	−582.174	−	3124.52i	−0.290373	−	1.55843i
$160$	2730.25			1.34903
$161$			1660.23i			0.812699i
$162$	−884.676	+	2758.45i	−0.429054	+	1.33780i
$163$	−659.353	+	380.678i	−0.316838	+	0.182926i	−0.649982	−	0.759950i	$-0.725224\pi$
$163$	−659.353	+	380.678i	−0.316838	+	0.182926i	0.333145	+	0.942876i	$0.391890\pi$
$164$	−325.755	−	188.075i	−0.155105	−	0.0895498i
$165$	−694.772	−	245.288i	−0.327806	−	0.115731i
$166$	68.7049			0.0321237
$167$			3331.51i			1.54371i	0.635797	+	0.771857i	$0.280672\pi$
$167$			3331.51i			1.54371i	−0.635797	+	0.771857i	$0.719328\pi$
$168$	13.3487	+	71.6424i	0.00613021	+	0.0329008i
$169$	1721.84	−	1364.58i	0.783723	−	0.621110i
$170$	4189.56			1.89014
$171$	1097.67	−	1360.80i	0.490882	−	0.608554i
$172$	−666.123	+	1153.76i	−0.295299	+	0.511473i
$173$	−763.868			−0.335698			−0.167849	−	0.985813i	$-0.553682\pi$
$173$	−763.868			−0.335698			−0.167849	+	0.985813i	$0.553682\pi$
$174$	−2090.57	+	5921.50i	−0.910837	+	2.57993i
$175$	139.861	+	80.7485i	0.0604141	+	0.0348801i
$176$	−750.230	−	433.145i	−0.321311	−	0.185509i
$177$	−1417.92	+	4016.22i	−0.602131	+	1.70552i
$178$	198.334			0.0835157
$179$	624.714	−	1082.04i	0.260857	−	0.451817i	−0.705613	−	0.708597i	$-0.749328\pi$
$179$	624.714	−	1082.04i	0.260857	−	0.451817i	0.966470	+	0.256780i	$0.0826617\pi$
$180$	−813.816	−	2108.06i	−0.336990	−	0.872919i
$181$	−1721.72			−0.707040			−0.353520	−	0.935427i	$-0.615015\pi$
$181$	−1721.72			−0.707040			−0.353520	+	0.935427i	$0.615015\pi$
$182$	2374.57	+	2049.77i	0.967115	+	0.834832i
$183$	−34.8976	−	187.295i	−0.0140967	−	0.0756571i
$184$			82.0898i			0.0328899i
$185$	−2444.70			−0.971555
$186$	1949.06	+	688.112i	0.768345	+	0.271262i
$187$	−1121.82	−	647.682i	−0.438692	−	0.253279i
$188$	−183.612	+	106.009i	−0.0712304	+	0.0411249i
$189$	2011.12	−	1240.33i	0.774008	−	0.477359i
$190$			2764.26i			1.05548i
$191$	−4964.26			−1.88064			−0.940318	−	0.340298i	$-0.889472\pi$
$191$	−4964.26			−1.88064			−0.940318	+	0.340298i	$0.889472\pi$
$192$	−461.459	−	2476.65i	−0.173453	−	0.930920i
$193$		−	3018.63i		−	1.12583i	−0.826514	−	0.562916i	$-0.809679\pi$
$193$		−	3018.63i		−	1.12583i	0.826514	−	0.562916i	$-0.190321\pi$
$194$	−2775.21	−	4806.80i	−1.02705	−	1.77891i
$195$	2260.30	+	1318.00i	0.830068	+	0.484020i
$196$	231.193	−	400.437i	0.0842538	−	0.145932i
$197$	480.686	+	277.524i	0.173845	+	0.100369i	0.584398	−	0.811467i	$-0.301331\pi$
$197$	480.686	+	277.524i	0.173845	+	0.100369i	−0.410553	+	0.911837i	$0.634664\pi$
$198$	−218.869	+	1399.12i	−0.0785573	+	0.502177i
$199$	−2047.37	−	3546.14i	−0.729316	−	1.26321i	−0.957173	−	0.289518i	$-0.906505\pi$
$199$	−2047.37	−	3546.14i	−0.729316	−	1.26321i	0.227856	−	0.973695i	$-0.426828\pi$
$200$	6.91538	+	3.99260i	0.00244496	+	0.00141160i
$201$	−550.430	+	102.558i	−0.193156	+	0.0359896i
$202$	5875.39	+	3392.16i	2.04649	+	1.18154i
$203$	4435.88	−	2561.05i	1.53368	−	0.885472i
$204$	−727.695	−	3905.54i	−0.249749	−	1.34040i
$205$	259.353	+	449.213i	0.0883611	+	0.153046i
$206$	−1633.00	−	942.811i	−0.552312	−	0.318877i
$207$	2483.00	−	958.562i	0.833722	−	0.321858i
$208$	2328.73	+	2010.20i	0.776289	+	0.670107i
$209$	427.339	−	740.174i	0.141434	−	0.244971i
$210$	−1243.71	+	3522.77i	−0.408685	+	1.15759i
$211$	2502.58			0.816514			0.408257	−	0.912867i	$-0.366137\pi$
$211$	2502.58			0.816514			0.408257	+	0.912867i	$0.366137\pi$
$212$	2382.56	−	4126.72i	0.771864	−	1.33691i
$213$	363.693	+	425.010i	0.116994	+	0.136719i
$214$		−	5366.65i		−	1.71428i
$215$	1591.02	−	918.578i	0.504684	−	0.291379i
$216$	99.4395	−	61.3279i	0.0313241	−	0.0193187i
$217$	−842.972	−	1460.07i	−0.263708	−	0.456756i
$218$	−2408.76	−	4172.10i	−0.748358	−	1.29619i
$219$	2825.51	−	526.460i	0.871828	−	0.162442i
$220$	−552.331	−	956.665i	−0.169264	−	0.293174i
$221$	3482.14	+	3005.85i	1.05988	+	0.914911i
$222$	860.673	+	4619.23i	0.260201	+	1.39650i
$223$	−5163.13	+	2980.93i	−1.55044	+	0.895149i	−0.552338	+	0.833620i	$0.686264\pi$
$223$	−5163.13	+	2980.93i	−1.55044	+	0.895149i	−0.998105	+	0.0615282i	$0.980403\pi$
$224$	−2140.12	+	3706.80i	−0.638361	+	1.10567i
$225$	40.0146	−	255.793i	0.0118562	−	0.0757906i
$226$			1865.58i			0.549100i
$227$		−	85.2586i		−	0.0249287i	−0.999922	−	0.0124643i	$-0.996032\pi$
$227$		−	85.2586i		−	0.0249287i	0.999922	−	0.0124643i	$-0.00396763\pi$
$228$	2576.87	−	480.132i	0.748496	−	0.139463i
$229$	−5514.11	+	3183.57i	−1.59119	+	0.918674i	−0.598087	+	0.801431i	$0.704072\pi$
$229$	−5514.11	+	3183.57i	−1.59119	+	0.918674i	−0.993103	+	0.117243i	$0.962594\pi$
$230$	−2104.12	+	3644.44i	−0.603223	+	1.04481i
$231$	877.621	−	751.006i	0.249971	−	0.213907i
$232$	219.331	−	126.631i	0.0620681	−	0.0358350i
$233$	1809.23			0.508698			0.254349	−	0.967112i	$-0.418139\pi$
$233$	1809.23			0.508698			0.254349	+	0.967112i	$0.418139\pi$
$234$	1694.59	−	4734.82i	0.473414	−	1.32276i
$235$	292.370			0.0811580
$236$	−5530.13	+	3192.82i	−1.52534	+	0.880657i
$237$	3871.69	+	1366.89i	1.06115	+	0.374637i
$238$	−3284.00	+	5688.06i	−0.894414	+	1.54917i
$239$	2866.58	−	1655.02i	0.775832	−	0.447927i	−0.0591193	−	0.998251i	$-0.518829\pi$
$239$	2866.58	−	1655.02i	0.775832	−	0.447927i	0.834951	+	0.550324i	$0.185496\pi$
$240$	−1219.69	+	3454.76i	−0.328045	+	0.929182i
$241$		−	1185.31i		−	0.316817i	−0.987374	−	0.158408i	$-0.949364\pi$
$241$		−	1185.31i		−	0.316817i	0.987374	−	0.158408i	$-0.0506362\pi$
$242$		−	4596.73i		−	1.22103i
$243$	−3016.16	−	2291.65i	−0.796242	−	0.604978i
$244$	142.819	−	247.370i	0.0374716	−	0.0649027i
$245$	−552.200	+	318.813i	−0.143995	+	0.0831355i
$246$	757.477	−	648.195i	0.196321	−	0.167998i
$247$	−1983.26	+	2297.51i	−0.510897	+	0.591851i
$248$	−41.6806	−	72.1930i	−0.0106723	−	0.0184849i
$249$	−29.9088	+	84.7159i	−0.00761201	+	0.0215609i
$250$	2872.77	+	4975.78i	0.726759	+	1.25878i
$251$	−197.379	−	341.871i	−0.0496353	−	0.0859708i	0.840140	−	0.542369i	$-0.182473\pi$
$251$	−197.379	−	341.871i	−0.0496353	−	0.0859708i	−0.889776	+	0.456398i	$0.849139\pi$
$252$	3499.97	+	547.513i	0.874911	+	0.136865i
$253$	1126.82	−	650.569i	0.280010	−	0.161664i
$254$		−	1801.66i		−	0.445064i
$255$	−1823.81	+	5165.90i	−0.447887	+	1.26863i
$256$	−2151.04	+	3725.72i	−0.525157	+	0.909599i
$257$	6666.70			1.61812			0.809061	−	0.587725i	$-0.199976\pi$
$257$	6666.70			1.61812			0.809061	+	0.587725i	$0.199976\pi$
$258$	−2295.78	−	2682.83i	−0.553988	−	0.647387i
$259$	1916.29	−	3319.11i	0.459739	−	0.796291i
$260$	1290.00	+	3704.67i	0.307702	+	0.883668i
$261$	−6391.38	−	5155.52i	−1.51577	−	1.22268i
$262$	−5627.04	−	3248.77i	−1.32687	−	0.766068i
$263$	2050.29	+	3551.20i	0.480708	+	0.832610i	0.999755	−	0.0221353i	$-0.00704648\pi$
$263$	2050.29	+	3551.20i	0.480708	+	0.832610i	−0.519047	+	0.854746i	$0.673713\pi$
$264$	43.3938	−	37.1333i	0.0101163	−	0.00865682i
$265$	−5690.72	+	3285.54i	−1.31916	+	0.761619i
$266$	−3752.98	−	2166.78i	−0.865074	−	0.499451i
$267$	−86.3394	+	244.555i	−0.0197898	+	0.0560543i
$268$	−726.982	−	419.723i	−0.165700	−	0.0956667i
$269$	1263.72	+	2188.83i	0.286433	+	0.496116i	0.972956	−	0.230992i	$-0.0741972\pi$
$269$	1263.72	+	2188.83i	0.286433	+	0.496116i	−0.686523	+	0.727108i	$0.740864\pi$
$270$	5986.64	−	173.876i	1.34939	−	0.0391917i
$271$	−292.278	−	168.747i	−0.0655152	−	0.0378252i	0.466885	−	0.884318i	$-0.345376\pi$
$271$	−292.278	−	168.747i	−0.0655152	−	0.0378252i	−0.532400	+	0.846493i	$0.678710\pi$
$272$	−3220.60	+	5578.25i	−0.717933	+	1.24350i
$273$	−3561.16	+	2035.63i	−0.789492	+	0.451290i
$274$	−1835.72	−	3179.57i	−0.404745	−	0.701039i
$275$		−	126.567i		−	0.0277537i
$276$	3762.84	+	1328.46i	0.820639	+	0.289725i
$277$	−7253.84			−1.57343			−0.786716	−	0.617315i	$-0.788220\pi$
$277$	−7253.84			−1.57343			−0.786716	+	0.617315i	$0.788220\pi$
$278$			2158.99i			0.465783i
$279$	−1696.94	+	2103.72i	−0.364133	+	0.451422i
$280$	130.483	−	75.3343i	0.0278494	−	0.0160789i
$281$	544.880	+	314.587i	0.115676	+	0.0667853i	0.556721	−	0.830699i	$-0.312059\pi$
$281$	544.880	+	314.587i	0.115676	+	0.0667853i	−0.441046	+	0.897485i	$0.645392\pi$
$282$	−102.931	−	552.431i	−0.0217356	−	0.116655i
$283$	5485.14			1.15215			0.576074	−	0.817398i	$-0.304584\pi$
$283$	5485.14			1.15215			0.576074	+	0.817398i	$0.304584\pi$
$284$			838.662i			0.175230i
$285$	−3408.45	−	1203.35i	−0.708418	−	0.250105i
$286$	460.720	−	2414.86i	0.0952550	−	0.499279i
$287$	−813.182			−0.167250
$288$	6779.42	+	1060.53i	1.38709	+	0.216987i
$289$	−2359.26	+	4086.36i	−0.480208	+	0.831745i
$290$	12983.2			2.62896
$291$	7135.09	−	1329.44i	1.43734	−	0.267811i
$292$	3731.80	+	2154.56i	0.747901	+	0.431801i
$293$	−6701.50	−	3869.11i	−1.33620	−	0.771454i	−0.349957	−	0.936766i	$-0.613804\pi$
$293$	−6701.50	−	3869.11i	−1.33620	−	0.771454i	−0.986241	+	0.165312i	$0.947137\pi$
$294$	796.799	+	931.136i	0.158062	+	0.184711i
$295$	8805.75			1.73793
$296$	94.7505	−	164.113i	0.0186056	−	0.0322259i
$297$	−1629.89	−	878.942i	−0.318438	−	0.171722i
$298$	4877.70			0.948179
$299$	−4363.58	+	1519.44i	−0.843988	+	0.293885i
$300$	294.925	−	252.375i	0.0567583	−	0.0485697i
$301$			2880.13i			0.551521i
$302$	−13108.9			−2.49780
$303$	−6740.35	+	5767.91i	−1.27796	+	1.09359i
$304$	−3680.52	−	2124.95i	−0.694382	−	0.400902i
$305$	−341.122	+	196.947i	−0.0640412	+	0.0369742i
$306$	10403.0	+	1627.38i	1.94346	+	0.304022i
$307$		−	7239.21i		−	1.34581i	−0.739729	−	0.672904i	$-0.765047\pi$
$307$		−	7239.21i		−	1.34581i	0.739729	−	0.672904i	$-0.234953\pi$
$308$	1731.79			0.320383
$309$	1873.40	−	1603.13i	0.344900	−	0.295141i
$310$		−	4273.41i		−	0.782947i
$311$	3437.27	+	5953.53i	0.626719	+	1.08551i	0.988206	+	0.153132i	$0.0489361\pi$
$311$	3437.27	+	5953.53i	0.626719	+	1.08551i	−0.361486	+	0.932377i	$0.617731\pi$
$312$	−176.081	+	100.652i	−0.0319507	+	0.0182637i
$313$	5164.67	−	8945.48i	0.932667	−	1.61543i	0.153924	−	0.988083i	$-0.450809\pi$
$313$	5164.67	−	8945.48i	0.932667	−	1.61543i	0.778743	−	0.627343i	$-0.215858\pi$
$314$	−5265.44	−	3040.00i	−0.946325	−	0.546361i
$315$	−3802.31	−	3067.08i	−0.680114	−	0.548604i
$316$	3077.92	+	5331.12i	0.547932	+	0.949046i
$317$	2643.50	+	1526.23i	0.468372	+	0.270415i	0.715558	−	0.698553i	$-0.246173\pi$
$317$	2643.50	+	1526.23i	0.468372	+	0.270415i	−0.247186	+	0.968968i	$0.579506\pi$
$318$	8211.45	+	9595.86i	1.44804	+	1.69217i
$319$	−3476.44	−	2007.12i	−0.610167	−	0.352280i
$320$	−4510.73	+	2604.27i	−0.787993	+	0.454948i
$321$	6617.30	+	2336.22i	1.15060	+	0.406216i
$322$	−3298.65	−	5713.42i	−0.570889	−	0.988809i
$323$	−5503.48	−	3177.43i	−0.948054	−	0.547359i
$324$	−1201.92	−	5550.59i	−0.206091	−	0.951747i
$325$	−84.2308	+	441.496i	−0.0143763	+	0.0753532i
$326$	1512.71	−	2620.08i	0.256997	−	0.445132i
$327$	6192.96	−	1153.90i	1.04731	−	0.195140i
$328$	−40.2076			−0.00676858
$329$	−229.176	+	396.944i	−0.0384039	+	0.0665174i
$330$	2878.30	−	536.296i	0.480137	−	0.0894609i
$331$		−	311.413i		−	0.0517124i	−0.999666	−	0.0258562i	$-0.991769\pi$
$331$		−	311.413i		−	0.0517124i	0.999666	−	0.0258562i	$-0.00823121\pi$
$332$	−116.650	+	67.3476i	−0.0192831	+	0.0111331i
$333$	−6070.37	−	949.609i	−0.998962	−	0.156271i
$334$	−6619.24	−	11464.9i	−1.08440	−	1.87823i
$335$	578.795	+	1002.50i	0.0943968	+	0.163500i
$336$	−3734.38	−	4363.98i	−0.606331	−	0.708555i
$337$	−4866.45	−	8428.95i	−0.786625	−	1.36247i	−0.928023	−	0.372522i	$-0.878493\pi$
$337$	−4866.45	−	8428.95i	−0.786625	−	1.36247i	0.141398	−	0.989953i	$-0.454840\pi$
$338$	−3214.21	+	8117.04i	−0.517248	+	1.30624i
$339$	−2300.34	−	812.129i	−0.368546	−	0.130114i
$340$	−7113.18	+	4106.79i	−1.13461	+	0.655065i
$341$	−660.645	+	1144.27i	−0.104915	+	0.181718i
$342$	−1073.74	+	6863.88i	−0.169770	+	1.08525i
$343$		−	6776.36i		−	1.06673i
$344$			142.407i			0.0223200i
$345$	−3577.77	−	4180.97i	−0.558321	−	0.652451i
$346$	2628.73	−	1517.70i	0.408444	−	0.235815i
$347$	1056.66	−	1830.20i	0.163472	−	0.283142i	−0.772640	−	0.634845i	$-0.781064\pi$
$347$	1056.66	−	1830.20i	0.163472	−	0.283142i	0.936112	+	0.351703i	$0.114397\pi$
$348$	−2255.08	−	12103.0i	−0.347370	−	1.86433i
$349$	−2013.35	+	1162.41i	−0.308803	+	0.178287i	−0.646391	−	0.763007i	$-0.723722\pi$
$349$	−2013.35	+	1162.41i	−0.308803	+	0.178287i	0.337588	+	0.941294i	$0.390389\pi$
$350$	−641.744			−0.0980076
$351$	5100.54	+	4150.67i	0.775631	+	0.631187i
$352$	3354.46			0.507936
$353$	4164.21	−	2404.21i	0.627871	−	0.362501i	−0.152056	−	0.988372i	$-0.548590\pi$
$353$	4164.21	−	2404.21i	0.627871	−	0.362501i	0.779927	+	0.625871i	$0.215256\pi$
$354$	−3100.13	−	16638.4i	−0.465452	−	2.49808i
$355$	578.254	−	1001.56i	0.0864522	−	0.149740i
$356$	−336.739	+	194.416i	−0.0501324	+	0.0289440i
$357$	−5584.02	−	6525.45i	−0.827836	−	0.967405i
$358$			4964.88i			0.732966i
$359$			7076.66i			1.04037i	0.854055	+	0.520184i	$0.174136\pi$
$359$			7076.66i			1.04037i	−0.854055	+	0.520184i	$0.825864\pi$
$360$	−188.004	−	151.651i	−0.0275242	−	0.0222020i
$361$	−1333.03	+	2308.88i	−0.194348	+	0.336621i
$362$	5925.02	−	3420.81i	0.860254	−	0.496668i
$363$	5667.96	+	2001.06i	0.819534	+	0.289334i
$364$	−6040.91	−	1152.51i	−0.869862	−	0.165957i
$365$	−2971.11	−	5146.12i	−0.426069	−	0.737973i
$366$	492.223	+	575.210i	0.0702976	+	0.0821495i
$367$	5129.51	+	8884.57i	0.729587	+	1.26368i	0.957058	+	0.289896i	$0.0936208\pi$
$367$	5129.51	+	8884.57i	0.729587	+	1.26368i	−0.227472	+	0.973785i	$0.573046\pi$
$368$	−3234.96	−	5603.11i	−0.458244	−	0.793702i
$369$	469.504	+	1216.17i	0.0662369	+	0.171576i
$370$	8413.04	−	4857.27i	1.18209	−	0.682480i
$371$		−	10301.5i		−	1.44159i
$372$	−3983.71	+	742.260i	−0.555230	+	0.103453i
$373$	−371.142	+	642.838i	−0.0515202	+	0.0892356i	−0.890635	−	0.454718i	$-0.849740\pi$
$373$	−371.142	+	642.838i	−0.0515202	+	0.0892356i	0.839115	+	0.543954i	$0.183073\pi$
$374$	5147.41			0.711674
$375$	−7385.92	+	1376.17i	−1.01709	+	0.189507i
$376$	−11.3316	+	19.6268i	−0.00155420	+	0.00269196i
$377$	10790.9	+	9314.93i	1.47417	+	1.27253i
$378$	−4456.59	+	8264.21i	−0.606408	+	1.12451i
$379$	−1383.08	−	798.523i	−0.187452	−	0.108225i	0.403337	−	0.915051i	$-0.367850\pi$
$379$	−1383.08	−	798.523i	−0.187452	−	0.108225i	−0.590789	+	0.806826i	$0.701183\pi$
$380$	−2709.66	−	4693.26i	−0.365796	−	0.633577i
$381$	2221.52	+	784.303i	0.298719	+	0.105462i
$382$	17083.7	−	9863.29i	2.28816	−	1.32107i
$383$	10290.4	+	5941.17i	1.37288	+	0.792635i	0.991290	−	0.131694i	$-0.0420417\pi$
$383$	10290.4	+	5941.17i	1.37288	+	0.792635i	0.381595	+	0.924330i	$0.375375\pi$
$384$	−359.982	−	420.673i	−0.0478392	−	0.0559047i
$385$	−2068.18	−	1194.06i	−0.273777	−	0.158065i
$386$	5997.59	+	10388.1i	0.790853	+	1.36980i
$387$	4307.45	−	1662.89i	0.565788	−	0.218422i
$388$	9423.68	+	5440.77i	1.23303	+	0.711889i
$389$	21.4339	−	37.1246i	0.00279368	−	0.00483879i	−0.864625	−	0.502417i	$-0.832444\pi$
$389$	21.4339	−	37.1246i	0.00279368	−	0.00483879i	0.867419	+	0.497579i	$0.165777\pi$
$390$	−10397.1	−	44.7894i	−1.34995	−	0.00581538i
$391$	−4837.23	−	8378.33i	−0.625650	−	1.08366i
$392$		−	49.4256i		−	0.00636829i
$393$	6455.44	−	5524.11i	0.828585	−	0.709044i
$394$	−2205.61			−0.282022
$395$		−	8488.86i		−	1.08132i
$396$	−999.878	−	2590.02i	−0.126883	−	0.328670i
$397$	6201.11	−	3580.21i	0.783941	−	0.452609i	−0.0538839	−	0.998547i	$-0.517160\pi$
$397$	6201.11	−	3580.21i	0.783941	−	0.452609i	0.837825	+	0.545938i	$0.183827\pi$
$398$	14091.4	+	8135.65i	1.77471	+	1.02463i
$399$	4305.48	−	3684.32i	0.540210	−	0.462273i
$400$	−629.354			−0.0786692
$401$			12404.6i			1.54478i	0.635151	+	0.772388i	$0.280938\pi$
$401$			12404.6i			1.54478i	−0.635151	+	0.772388i	$0.719062\pi$
$402$	1690.45	−	1446.56i	0.209731	−	0.179473i
$403$	3066.01	−	3551.84i	0.378980	−	0.439032i
$404$	−13300.6			−1.63794
$405$	−2391.72	+	7457.47i	−0.293446	+	0.914974i
$406$	−10176.9	+	17626.9i	−1.24402	+	2.15470i
$407$	−3003.62			−0.365809
$408$	−276.101	−	322.650i	−0.0335025	−	0.0391509i
$409$	6263.58	+	3616.28i	0.757247	+	0.437197i	0.828306	−	0.560276i	$-0.189305\pi$
$409$	6263.58	+	3616.28i	0.757247	+	0.437197i	−0.0710597	+	0.997472i	$0.522638\pi$
$410$	−1785.05	−	1030.60i	−0.215018	−	0.124140i
$411$	4719.67	−	879.387i	0.566433	−	0.105540i
$412$	3696.74			0.442052
$413$	−6902.43	+	11955.4i	−0.822388	+	1.42442i
$414$	−6640.32	+	8232.11i	−0.788294	+	0.977261i
$415$	185.744			0.0219706
$416$	−11701.2	−	2232.41i	−1.37908	−	0.263108i
$417$	−2662.12	−	939.856i	−0.312625	−	0.110372i
$418$			3396.25i			0.397407i
$419$	−5671.17			−0.661228			−0.330614	−	0.943766i	$-0.607256\pi$
$419$	−5671.17			−0.661228			−0.330614	+	0.943766i	$0.607256\pi$
$420$	−1341.57	−	7200.22i	−0.155862	−	0.836511i
$421$	−5489.27	−	3169.23i	−0.635465	−	0.366886i	0.147401	−	0.989077i	$-0.452909\pi$
$421$	−5489.27	−	3169.23i	−0.635465	−	0.366886i	−0.782865	+	0.622191i	$0.786243\pi$
$422$	−8612.22	+	4972.27i	−0.993451	+	0.573569i
$423$	725.978	+	113.567i	0.0834474	+	0.0130540i
$424$		−	509.358i		−	0.0583410i
$425$	−941.072			−0.107409
$426$	−2096.03	−	739.997i	−0.238387	−	0.0841619i
$427$		−	617.511i		−	0.0699846i
$428$	5260.63	+	9111.69i	0.594118	+	1.02904i
$429$	2777.07	+	1619.33i	0.312536	+	0.182242i
$430$	−3650.17	+	6322.28i	−0.409365	+	0.709041i
$431$	−6644.54	−	3836.23i	−0.742590	−	0.428734i	0.0804203	−	0.996761i	$-0.474374\pi$
$431$	−6644.54	−	3836.23i	−0.742590	−	0.428734i	−0.823010	+	0.568027i	$0.807707\pi$
$432$	−4370.55	+	8104.66i	−0.486755	+	0.902629i
$433$	8922.12	+	15453.6i	0.990230	+	1.71513i	0.615878	+	0.787842i	$0.288802\pi$
$433$	8922.12	+	15453.6i	0.990230	+	1.71513i	0.374352	+	0.927287i	$0.377865\pi$
$434$	5801.91	+	3349.74i	0.641707	+	0.370489i
$435$	−5651.86	+	16008.8i	−0.622956	+	1.76451i
$436$	8179.37	+	4722.36i	0.898442	+	0.518716i
$437$	5528.01	−	3191.60i	0.605127	−	0.349370i
$438$	−8677.55	+	7425.62i	−0.946642	+	0.810068i
$439$	4850.18	+	8400.76i	0.527304	+	0.913318i	0.999494	+	0.0318208i	$0.0101306\pi$
$439$	4850.18	+	8400.76i	0.527304	+	0.913318i	−0.472189	+	0.881497i	$0.656536\pi$
$440$	−102.261	−	59.0402i	−0.0110797	−	0.00639689i
$441$	−1494.99	+	577.142i	−0.161429	+	0.0623196i
$442$	−17955.4	−	3425.63i	−1.93225	−	0.368644i
$443$	−653.632	+	1132.12i	−0.0701016	+	0.121420i	−0.898946	−	0.438060i	$-0.855666\pi$
$443$	−653.632	+	1132.12i	−0.0701016	+	0.121420i	0.828844	+	0.559480i	$0.188999\pi$
$444$	−5989.26	−	6999.02i	−0.640175	−	0.748106i
$445$	536.197			0.0571195
$446$	11845.4	−	20516.8i	1.25761	−	2.17825i
$447$	−2123.37	+	6014.40i	−0.224680	+	0.636401i
$448$		−	8165.49i		−	0.861123i
$449$	−874.196	+	504.717i	−0.0918839	+	0.0530492i	−0.545238	−	0.838281i	$-0.683561\pi$
$449$	−874.196	+	504.717i	−0.0918839	+	0.0530492i	0.453354	+	0.891331i	$0.350227\pi$
$450$	370.521	+	959.775i	0.0388146	+	0.100543i
$451$	318.649	+	551.916i	0.0332696	+	0.0576247i
$452$	−1828.73	−	3167.45i	−0.190301	−	0.329611i
$453$	5706.61	−	16163.9i	0.591876	−	1.67648i
$454$	169.397	+	293.404i	0.0175114	+	0.0303307i
$455$	6419.66	+	5541.57i	0.661447	+	0.570973i
$456$	212.884	−	182.171i	0.0218623	−	0.0187082i
$457$	−830.380	+	479.420i	−0.0849968	+	0.0490729i	−0.541896	−	0.840446i	$-0.682293\pi$
$457$	−830.380	+	479.420i	−0.0849968	+	0.0490729i	0.456899	+	0.889518i	$0.348960\pi$
$458$	12650.6	−	21911.5i	1.29067	−	2.23550i
$459$	−6535.28	+	12118.9i	−0.664576	+	1.23238i
$460$		−	8250.20i		−	0.836234i
$461$			1286.92i			0.130017i	0.997885	+	0.0650083i	$0.0207074\pi$
$461$			1286.92i			0.130017i	−0.997885	+	0.0650083i	$0.979293\pi$
$462$	−1528.05	+	4328.18i	−0.153878	+	0.435855i
$463$	−13747.3	+	7937.03i	−1.37990	+	0.796685i	−0.992147	−	0.125078i	$-0.960082\pi$
$463$	−13747.3	+	7937.03i	−1.37990	+	0.796685i	−0.387752	+	0.921764i	$0.626748\pi$
$464$	−9980.43	+	17286.6i	−0.998556	+	1.72955i
$465$	5269.29	+	1860.31i	0.525500	+	0.185527i
$466$	−6226.18	+	3594.69i	−0.618932	+	0.357341i
$467$	14009.8			1.38822			0.694108	−	0.719871i	$-0.255799\pi$
$467$	14009.8			1.38822			0.694108	+	0.719871i	$0.255799\pi$
$468$	1764.15	+	9700.06i	0.174248	+	0.958088i
$469$	−1814.76			−0.178674
$470$	−1006.15	+	580.898i	−0.0987447	+	0.0570103i
$471$	6040.61	−	5169.12i	0.590948	−	0.505691i
$472$	−341.289	+	591.131i	−0.0332820	+	0.0576462i
$473$	1954.78	−	1128.59i	0.190023	−	0.109710i
$474$	−16039.6	+	2988.56i	−1.55427	+	0.289598i
$475$		−	620.918i		−	0.0599783i
$476$		−	12876.5i		−	1.23990i
$477$	−15406.7	+	5947.76i	−1.47888	+	0.570921i
$478$	−6576.59	+	11391.0i	−0.629302	+	1.08998i
$479$	5490.42	−	3169.89i	0.523724	−	0.302372i	−0.214733	−	0.976673i	$-0.568888\pi$
$479$	5490.42	−	3169.89i	0.523724	−	0.302372i	0.738457	+	0.674301i	$0.235555\pi$
$480$	−2598.62	−	13946.8i	−0.247104	−	1.32621i
$481$	10477.4	+	1998.93i	0.993197	+	0.189487i
$482$	2355.05	+	4079.07i	0.222551	+	0.385470i
$483$	8480.86	−	1580.19i	0.798949	−	0.148863i
$484$	4505.93	+	7804.49i	0.423171	+	0.732954i
$485$	−7502.77	−	12995.2i	−0.702440	−	1.21666i
$486$	14932.8	+	1893.68i	1.39376	+	0.176747i
$487$	17214.5	−	9938.82i	1.60178	−	0.924786i	0.610645	−	0.791904i	$-0.290910\pi$
$487$	17214.5	−	9938.82i	1.60178	−	0.924786i	0.991132	−	0.132882i	$-0.0424231\pi$
$488$		−	30.5327i		−	0.00283228i
$489$	2572.16	+	3005.81i	0.237867	+	0.277970i
$490$	1266.87	−	2194.29i	0.116799	−	0.202302i
$491$	−15731.2			−1.44591			−0.722954	−	0.690896i	$-0.757216\pi$
$491$	−15731.2			−1.44591			−0.722954	+	0.690896i	$0.757216\pi$
$492$	−650.681	+	1843.04i	−0.0596239	+	0.168884i
$493$	−14923.7	+	25848.7i	−1.36335	+	2.36139i
$494$	2260.22	−	11847.0i	0.205855	−	1.07899i
$495$	−591.712	+	3782.52i	−0.0537283	+	0.343458i
$496$	5689.90	+	3285.06i	0.515088	+	0.297386i
$497$	906.534	+	1570.16i	0.0818181	+	0.141713i
$498$	−65.3924	−	350.961i	−0.00588414	−	0.0315802i
$499$	−5543.66	+	3200.63i	−0.497331	+	0.287134i	−0.727611	−	0.685990i	$-0.759369\pi$
$499$	−5543.66	+	3200.63i	−0.497331	+	0.287134i	0.230280	+	0.973125i	$0.426036\pi$
$500$	−9754.97	−	5632.03i	−0.872511	−	0.503744i
$501$	17018.2	−	3170.89i	1.51759	−	0.282764i
$502$	1358.50	+	784.329i	0.120782	+	0.0697337i
$503$	−7906.80	−	13695.0i	−0.700889	−	1.21397i	−0.968155	−	0.250352i	$-0.919454\pi$
$503$	−7906.80	−	13695.0i	−0.700889	−	1.21397i	0.267266	−	0.963623i	$-0.413880\pi$
$504$	353.262	−	136.377i	0.0312213	−	0.0120530i
$505$	15884.1	+	9170.69i	1.39967	+	0.808100i
$506$	−2585.18	+	4477.66i	−0.227125	+	0.393392i
$507$	−8609.42	−	7496.78i	−0.754158	−	0.656694i
$508$	1766.07	+	3058.92i	0.154245	+	0.267161i
$509$		−	14670.9i		−	1.27756i	−0.769390	−	0.638779i	$-0.779440\pi$
$509$		−	14670.9i		−	1.27756i	0.769390	−	0.638779i	$-0.220560\pi$
$510$	−3987.57	−	21401.3i	−0.346220	−	1.85816i
$511$	9315.69			0.806462
$512$		−	16242.9i		−	1.40203i
$513$	−7996.02	−	4311.96i	−0.688174	−	0.371107i
$514$	−22942.4	+	13245.8i	−1.96877	+	1.13667i
$515$	−4414.81	−	2548.89i	−0.377747	−	0.218092i
$516$	6527.69	+	2304.58i	0.556910	+	0.196616i
$517$	359.214			0.0305575
$518$			15229.6i			1.29179i
$519$	727.040	+	3902.02i	0.0614904	+	0.330019i
$520$	317.419	+	274.002i	0.0267687	+	0.0231073i
$521$	4671.22			0.392802			0.196401	−	0.980524i	$-0.437075\pi$
$521$	4671.22			0.392802			0.196401	+	0.980524i	$0.437075\pi$
$522$	32238.2	+	5043.13i	2.70312	+	0.422858i
$523$	2987.41	−	5174.35i	0.249771	−	0.432617i	−0.713691	−	0.700461i	$-0.752978\pi$
$523$	2987.41	−	5174.35i	0.249771	−	0.432617i	0.963462	+	0.267844i	$0.0863112\pi$
$524$	12738.4			1.06198
$525$	279.365	−	791.296i	0.0232238	−	0.0657810i
$526$	−14111.5	−	8147.26i	−1.16975	−	0.675357i
$527$	8508.10	+	4912.15i	0.703261	+	0.406028i
$528$	−1498.55	+	4244.61i	−0.123515	+	0.349854i
$529$	−2449.41			−0.201316
$530$	13055.8	−	22613.3i	1.07001	−	1.85332i
$531$	21865.4	+	3420.47i	1.78696	+	0.279540i
$532$	8495.91			0.692377
$533$	−744.224	−	2137.28i	−0.0604802	−	0.173689i
$534$	−188.772	−	1013.14i	−0.0152977	−	0.0821027i
$535$		−	14508.7i		−	1.17246i
$536$	−89.7307			−0.00723092
$537$	−6121.90	−	2161.32i	−0.491954	−	0.173683i
$538$	−8697.78	−	5021.67i	−0.697004	−	0.402415i
$539$	−678.448	+	391.702i	−0.0542168	+	0.0313021i
$540$	−9993.88	+	6163.59i	−0.796423	+	0.491183i
$541$		−	744.548i		−	0.0591694i	−0.999562	−	0.0295847i	$-0.990582\pi$
$541$		−	744.548i		−	0.0591694i	0.999562	−	0.0295847i	$-0.00941847\pi$
$542$	1341.10			0.106283
$543$	1638.71	+	8794.94i	0.129510	+	0.695078i
$544$		−	24941.7i		−	1.96575i
$545$	−6512.10	−	11279.3i	−0.511830	−	0.886516i
$546$	8210.65	−	14080.8i	0.643559	−	1.10367i
$547$	11128.6	−	19275.3i	0.869882	−	1.50668i	0.00776623	−	0.999970i	$-0.497528\pi$
$547$	11128.6	−	19275.3i	0.869882	−	1.50668i	0.862116	−	0.506711i	$-0.169139\pi$
$548$	6233.51	+	3598.92i	0.485917	+	0.280544i
$549$	−923.533	+	356.530i	−0.0717950	+	0.0277165i
$550$	251.470	+	435.559i	0.0194959	+	0.0337678i
$551$	−17054.9	−	9846.65i	−1.31863	−	0.761309i
$552$	419.334	−	78.1320i	0.0323334	−	0.00602449i
$553$	11525.1	+	6654.03i	0.886253	+	0.511678i
$554$	24962.9	−	14412.3i	1.91439	−	1.10527i
$555$	2326.83	+	12488.1i	0.177961	+	0.955118i
$556$	−2116.34	−	3665.61i	−0.161426	−	0.279598i
$557$	−2730.61	−	1576.52i	−0.207719	−	0.119927i	0.392532	−	0.919739i	$-0.371599\pi$
$557$	−2730.61	−	1576.52i	−0.207719	−	0.119927i	−0.600251	+	0.799812i	$0.704933\pi$
$558$	1659.95	−	10611.2i	0.125934	−	0.805033i
$559$	−7569.84	+	2635.89i	−0.572755	+	0.199439i
$560$	−5937.48	+	10284.0i	−0.448043	+	0.776034i
$561$	−2240.78	+	6346.97i	−0.168638	+	0.477663i
$562$	−2500.16			−0.187656
$563$	−1590.79	+	2755.33i	−0.119083	+	0.206258i	−0.919405	−	0.393313i	$-0.871329\pi$
$563$	−1590.79	+	2755.33i	−0.119083	+	0.206258i	0.800322	+	0.599571i	$0.204662\pi$
$564$	716.277	+	837.038i	0.0534764	+	0.0624923i
$565$			5043.60i			0.375550i
$566$	−18876.2	+	10898.2i	−1.40182	+	0.809339i
$567$	−8250.06	−	9092.75i	−0.611058	−	0.673474i
$568$	44.8234	+	77.6364i	0.00331118	+	0.00573513i
$569$	3992.80	+	6915.73i	0.294177	+	0.509530i	0.974793	−	0.223110i	$-0.0716210\pi$
$569$	3992.80	+	6915.73i	0.294177	+	0.509530i	−0.680616	+	0.732640i	$0.738288\pi$
$570$	14120.5	−	2630.99i	1.03762	−	0.193333i
$571$	−742.326	−	1285.75i	−0.0544052	−	0.0942326i	0.837540	−	0.546376i	$-0.183993\pi$
$571$	−742.326	−	1285.75i	−0.0544052	−	0.0942326i	−0.891945	+	0.452143i	$0.850660\pi$
$572$	1584.93	+	4551.66i	0.115856	+	0.332717i
$573$	4724.92	+	25358.6i	0.344479	+	1.84882i
$574$	2798.44	−	1615.68i	0.203492	−	0.117486i
$575$	472.634	−	818.626i	0.0342786	−	0.0593723i
$576$	−12212.1	+	4714.48i	−0.883398	+	0.341036i
$577$			2749.63i			0.198386i	0.995068	+	0.0991930i	$0.0316261\pi$
$577$			2749.63i			0.198386i	−0.995068	+	0.0991930i	$0.968374\pi$
$578$		−	18750.1i		−	1.34931i
$579$	−15419.9	+	2873.09i	−1.10678	+	0.206220i
$580$	−22043.3	+	12726.7i	−1.57810	+	0.911115i
$581$	−145.596	+	252.180i	−0.0103965	+	0.0180072i
$582$	−21912.9	+	18751.5i	−1.56068	+	1.33552i
$583$	−6991.78	+	4036.70i	−0.496689	+	0.286764i
$584$	460.613			0.0326375
$585$	4581.33	−	12800.6i	0.323786	−	0.904683i
$586$	30749.5			2.16767
$587$	20144.3	−	11630.3i	1.41643	−	0.817777i	0.420448	−	0.907317i	$-0.361873\pi$
$587$	20144.3	−	11630.3i	1.41643	−	0.817777i	0.995983	+	0.0895401i	$0.0285397\pi$
$588$	−2265.58	−	799.856i	−0.158896	−	0.0560978i
$589$	−3241.03	+	5613.63i	−0.226731	+	0.392709i
$590$	−30303.6	+	17495.8i	−2.11454	+	1.22083i
$591$	960.149	−	2719.60i	0.0668279	−	0.189289i
$592$			14935.5i			1.03690i
$593$			16160.4i			1.11910i	0.828796	+	0.559551i	$0.189027\pi$
$593$			16160.4i			1.11910i	−0.828796	+	0.559551i	$0.810973\pi$
$594$	7355.36	−	213.629i	0.508071	−	0.0147564i
$595$	−8878.31	+	15377.7i	−0.611723	+	1.05954i
$596$	−8281.52	+	4781.34i	−0.569168	+	0.328610i
$597$	−16165.9	+	13833.6i	−1.10825	+	0.948361i
$598$	11997.7	−	13898.7i	0.820436	−	0.950438i
$599$	−10780.2	−	18671.9i	−0.735340	−	1.27365i	−0.954574	−	0.297974i	$-0.903689\pi$
$599$	−10780.2	−	18671.9i	−0.735340	−	1.27365i	0.219234	−	0.975672i	$-0.429644\pi$
$600$	13.8132	−	39.1255i	0.000939867	−	0.00266215i
$601$	1349.64	+	2337.65i	0.0916024	+	0.158660i	0.908186	−	0.418568i	$-0.137468\pi$
$601$	1349.64	+	2337.65i	0.0916024	+	0.158660i	−0.816583	+	0.577228i	$0.804134\pi$
$602$	−5722.41	−	9911.51i	−0.387422	−	0.671035i
$603$	1047.78	+	2714.11i	0.0707613	+	0.183296i
$604$	22256.8	−	12850.0i	1.49937	−	0.865659i
$605$		−	12427.3i		−	0.835108i
$606$	11735.8	−	33241.5i	0.786692	−	2.22829i
$607$	4590.33	−	7950.69i	0.306945	−	0.531645i	−0.670747	−	0.741686i	$-0.734026\pi$
$607$	4590.33	−	7950.69i	0.306945	−	0.531645i	0.977693	+	0.210041i	$0.0673597\pi$
$608$	16456.5			1.09770
$609$	−17304.5	−	20221.9i	−1.15142	−	1.34554i
$610$	782.611	−	1355.52i	0.0519459	−	0.0899729i
$611$	−1253.03	−	239.059i	−0.0829658	−	0.0158286i
$612$	−19257.8	+	7434.47i	−1.27198	+	0.491047i
$613$	−15016.1	−	8669.55i	−0.989388	−	0.571223i	−0.0842964	−	0.996441i	$-0.526864\pi$
$613$	−15016.1	−	8669.55i	−0.989388	−	0.571223i	−0.905091	+	0.425218i	$0.860198\pi$
$614$	14383.3	+	24912.6i	0.945378	+	1.63744i
$615$	2047.84	−	1752.39i	0.134271	−	0.114900i
$616$	160.315	−	92.5579i	0.0104858	−	0.00605400i
$617$	−20811.0	−	12015.2i	−1.35789	−	0.783978i	−0.368550	−	0.929608i	$-0.620146\pi$
$617$	−20811.0	−	12015.2i	−1.35789	−	0.783978i	−0.989339	+	0.145630i	$0.953479\pi$
$618$	−3261.84	+	9239.09i	−0.212315	+	0.601377i
$619$	4252.29	+	2455.06i	0.276113	+	0.159414i	0.631662	−	0.775244i	$-0.282373\pi$
$619$	4252.29	+	2455.06i	0.276113	+	0.159414i	−0.355550	+	0.934657i	$0.615706\pi$
$620$	4188.99	+	7255.55i	0.271345	+	0.469984i
$621$	−7259.85	−	11771.4i	−0.469127	−	0.760661i
$622$	−23657.6	−	13658.7i	−1.52506	−	0.880492i
$623$	−420.301	+	727.982i	−0.0270289	+	0.0468154i
$624$	8052.13	−	13809.0i	0.516576	−	0.885900i
$625$	7167.21	+	12414.0i	0.458701	+	0.794494i
$626$			41045.9i			2.62065i
$627$	−4187.72	−	1478.46i	−0.266733	−	0.0941693i
$628$	11919.8			0.757407
$629$			22333.1i			1.41571i
$630$	19178.9	+	3000.22i	1.21287	+	0.189733i
$631$	−5594.69	+	3230.10i	−0.352965	+	0.203785i	−0.665991	−	0.745960i	$-0.731991\pi$
$631$	−5594.69	+	3230.10i	−0.352965	+	0.203785i	0.313025	+	0.949745i	$0.398658\pi$
$632$	569.858	+	329.007i	0.0358666	+	0.0207076i
$633$	−2381.92	−	12783.8i	−0.149562	−	0.802699i
$634$	−12129.6			−0.759823
$635$		−	4870.79i		−	0.304396i
$636$	−23348.0	−	8242.95i	−1.45567	−	0.513922i
$637$	2627.28	−	914.844i	0.163417	−	0.0569034i
$638$	15951.5			0.989851
$639$	1824.89	−	2262.35i	0.112976	−	0.140058i
$640$	−572.354	+	991.346i	−0.0353504	+	0.0612287i
$641$	−4728.60			−0.291371			−0.145685	−	0.989331i	$-0.546539\pi$
$641$	−4728.60			−0.291371			−0.145685	+	0.989331i	$0.546539\pi$
$642$	−27414.1	+	5107.91i	−1.68528	+	0.314008i
$643$	4147.64	+	2394.64i	0.254381	+	0.146867i	0.621769	−	0.783201i	$-0.286414\pi$
$643$	4147.64	+	2394.64i	0.254381	+	0.146867i	−0.367388	+	0.930068i	$0.619748\pi$
$644$	11201.1	+	6466.96i	0.685381	+	0.395705i
$645$	−6206.63	−	7253.04i	−0.378893	−	0.442772i
$646$	25252.4			1.53799
$647$	−11606.9	+	20103.8i	−0.705278	+	1.22158i	0.261313	+	0.965254i	$0.415844\pi$
$647$	−11606.9	+	20103.8i	−0.705278	+	1.22158i	−0.966591	+	0.256323i	$0.917489\pi$
$648$	−407.923	−	449.590i	−0.0247295	−	0.0272555i
$649$	10819.0			0.654365
$650$	−587.324	−	1686.69i	−0.0354411	−	0.101781i
$651$	−6656.06	+	5695.78i	−0.400724	+	0.342911i
$652$			5931.29i			0.356269i
$653$	7457.80			0.446932			0.223466	−	0.974712i	$-0.428263\pi$
$653$	7457.80			0.446932			0.223466	+	0.974712i	$0.428263\pi$
$654$	−19019.5	+	16275.5i	−1.13719	+	0.973123i
$655$	−15212.7	−	8783.05i	−0.907495	−	0.523942i
$656$	2744.41	−	1584.48i	0.163340	−	0.0943045i
$657$	−5378.57	−	13932.3i	−0.319388	−	0.827323i
$658$		−	1821.36i		−	0.107909i
$659$	−6276.37			−0.371006			−0.185503	−	0.982644i	$-0.559391\pi$
$659$	−6276.37			−0.371006			−0.185503	+	0.982644i	$0.559391\pi$
$660$	−4361.17	+	3731.98i	−0.257210	+	0.220102i
$661$			22131.6i			1.30230i	0.758950	+	0.651149i	$0.225713\pi$
$661$			22131.6i			1.30230i	−0.758950	+	0.651149i	$0.774287\pi$
$662$	618.734	+	1071.68i	0.0363260	+	0.0629184i
$663$	12040.3	−	20648.5i	0.705291	−	1.20954i
$664$	−7.19897	+	12.4690i	−0.000420745	+	0.000728751i
$665$	−10146.2	−	5857.89i	−0.591657	−	0.341593i
$666$	22777.0	−	8793.05i	1.32521	−	0.511597i
$667$	−14990.3	−	25963.9i	−0.870202	−	1.50723i
$668$	22476.8	+	12977.0i	1.30187	+	0.751638i
$669$	20141.5	+	23537.3i	1.16400	+	1.36025i
$670$	−3983.66	−	2299.97i	−0.229705	−	0.132620i
$671$	−419.112	+	241.974i	−0.0241127	+	0.0139215i
$672$	20972.1	+	7404.16i	1.20390	+	0.425032i
$673$	−1717.73	−	2975.19i	−0.0983855	−	0.170409i	0.812631	−	0.582779i	$-0.198035\pi$
$673$	−1717.73	−	2975.19i	−0.0983855	−	0.170409i	−0.911017	+	0.412370i	$0.864701\pi$
$674$	33494.3	+	19337.9i	1.91417	+	1.10515i
$675$	−1344.74	+	39.0566i	−0.0766800	+	0.00222710i
$676$	−2499.49	−	16932.1i	−0.142210	−	0.963365i
$677$	9949.28	−	17232.7i	0.564818	−	0.978294i	−0.432248	−	0.901755i	$-0.642280\pi$
$677$	9949.28	−	17232.7i	0.564818	−	0.978294i	0.997067	−	0.0765395i	$-0.0243871\pi$
$678$	9529.83	−	1775.64i	0.539810	−	0.100579i
$679$	23524.3			1.32957
$680$	−438.986	+	760.347i	−0.0247564	+	0.0428794i
$681$	−435.521	+	81.1480i	−0.0245069	+	0.00456623i
$682$		−	5250.44i		−	0.294794i
$683$	−24354.1	+	14060.9i	−1.36440	+	0.787736i	−0.990206	−	0.139615i	$-0.955413\pi$
$683$	−24354.1	+	14060.9i	−1.36440	+	0.787736i	−0.374193	+	0.927351i	$0.622080\pi$
$684$	−4905.25	−	12706.3i	−0.274206	−	0.710287i
$685$	−4962.88	−	8595.96i	−0.276820	−	0.479467i
$686$	13463.7	+	23319.8i	0.749337	+	1.29789i
$687$	21510.7	+	25137.3i	1.19459	+	1.39599i
$688$	−5611.93	−	9720.15i	−0.310978	−	0.538630i
$689$	27075.5	−	9427.96i	1.49709	−	0.521302i
$690$	20619.3	+	7279.60i	1.13763	+	0.401637i
$691$	7998.38	−	4617.87i	0.440337	−	0.254229i	−0.263404	−	0.964686i	$-0.584845\pi$
$691$	7998.38	−	4617.87i	0.440337	−	0.254229i	0.703740	+	0.710457i	$0.251512\pi$
$692$	−2975.43	+	5153.60i	−0.163452	+	0.283108i
$693$	−4671.62	−	3768.30i	−0.256075	−	0.206560i
$694$			8397.78i			0.459330i
$695$			5836.83i			0.318566i
$696$	−855.618	−	999.870i	−0.0465978	−	0.0544540i
$697$	4103.71	−	2369.28i	0.223012	−	0.128756i
$698$	4619.08	−	8000.49i	0.250480	−	0.433844i
$699$	−1722.00	−	9241.99i	−0.0931790	−	0.500092i
$700$	1089.57	−	629.066i	0.0588315	−	0.0339664i
$701$	6671.95			0.359481			0.179741	−	0.983714i	$-0.442474\pi$
$701$	6671.95			0.359481			0.179741	+	0.983714i	$0.442474\pi$
$702$	−25799.5	−	4149.84i	−1.38709	−	0.223113i
$703$	−14735.4			−0.790547
$704$	−5542.01	+	3199.68i	−0.296694	+	0.171296i
$705$	−278.274	−	1493.50i	−0.0148658	−	0.0797849i
$706$	−9553.64	+	16547.4i	−0.509286	+	0.882109i
$707$	−24901.7	+	14377.0i	−1.32464	+	0.764784i
$708$	21573.2	+	25210.3i	1.14516	+	1.33822i
$709$		−	29245.3i		−	1.54913i	−0.632495	−	0.774564i	$-0.717969\pi$
$709$		−	29245.3i		−	1.54913i	0.632495	−	0.774564i	$-0.282031\pi$
$710$			4595.63i			0.242917i
$711$	3297.38	−	21078.5i	0.173926	−	1.11182i
$712$	−20.7817	+	35.9950i	−0.00109386	+	0.00189462i
$713$	−8546.03	+	4934.05i	−0.448880	+	0.259161i
$714$	32181.7	+	11361.7i	1.68679	+	0.595517i
$715$	1245.56	−	6528.59i	0.0651484	−	0.341476i
$716$	−4866.80	−	8429.54i	−0.254023	−	0.439982i
$717$	−11182.6	−	13068.0i	−0.582458	−	0.680658i
$718$	−14060.3	−	24353.2i	−0.730817	−	1.26581i
$719$	1136.47	+	1968.42i	0.0589473	+	0.102100i	0.893993	−	0.448081i	$-0.147892\pi$
$719$	1136.47	+	1968.42i	0.0589473	+	0.102100i	−0.835046	+	0.550180i	$0.814559\pi$
$720$	18808.6	+	2942.29i	0.973550	+	0.152296i
$721$	6921.14	−	3995.92i	0.357499	−	0.206402i
$722$		−	10594.2i		−	0.546088i
$723$	−6054.87	+	1128.17i	−0.311456	+	0.0580318i
$724$	−6706.47	+	11615.9i	−0.344259	+	0.596275i
$725$	−2916.32			−0.149392
$726$	−23481.2	+	4375.11i	−1.20037	+	0.223658i
$727$	−11663.3	+	20201.4i	−0.595004	+	1.03058i	0.398542	+	0.917150i	$0.369516\pi$
$727$	−11663.3	+	20201.4i	−0.595004	+	1.03058i	−0.993546	+	0.113428i	$0.963817\pi$
$728$	−620.816	+	216.174i	−0.0316057	+	0.0110054i
$729$	−8835.58	+	17588.4i	−0.448894	+	0.893585i
$730$	20449.2	+	11806.4i	1.03679	+	0.598594i
$731$	−8391.51	−	14534.5i	−0.424585	−	0.735402i
$732$	−1399.56	−	494.112i	−0.0706684	−	0.0249493i
$733$	15695.3	−	9061.68i	0.790885	−	0.456618i	−0.0493889	−	0.998780i	$-0.515727\pi$
$733$	15695.3	−	9061.68i	0.790885	−	0.456618i	0.840274	+	0.542162i	$0.182394\pi$
$734$	−35304.8	−	20383.2i	−1.77537	−	1.02501i
$735$	2154.15	+	2517.33i	0.108105	+	0.126331i
$736$	21696.5	+	12526.5i	1.08661	+	0.627352i
$737$	711.124	+	1231.70i	0.0355422	+	0.0615608i
$738$	−4032.09	−	3252.43i	−0.201116	−	0.162227i
$739$	−4511.88	−	2604.94i	−0.224590	−	0.129667i	0.383484	−	0.923548i	$-0.374724\pi$
$739$	−4511.88	−	2604.94i	−0.224590	−	0.129667i	−0.608074	+	0.793880i	$0.708058\pi$
$740$	−9522.63	+	16493.7i	−0.473053	+	0.819351i
$741$	13623.9	+	7944.20i	0.675419	+	0.393843i
$742$	20467.7	+	35451.1i	1.01266	+	1.75398i
$743$			28289.3i			1.39681i	0.715701	+	0.698407i	$0.246107\pi$
$743$			28289.3i			1.39681i	−0.715701	+	0.698407i	$0.753893\pi$
$744$	−329.108	+	281.627i	−0.0162173	+	0.0138776i
$745$	13186.9			0.648495
$746$		−	2949.63i		−	0.144764i
$747$	461.216	+	72.1496i	0.0225904	+	0.00353389i
$748$	−8739.45	+	5045.72i	−0.427200	+	0.246644i
$749$	19698.2	+	11372.7i	0.960956	+	0.554808i
$750$	22683.2	−	19410.7i	1.10436	−	0.945036i
$751$	−884.841			−0.0429938			−0.0214969	−	0.999769i	$-0.506843\pi$
$751$	−884.841			−0.0429938			−0.0214969	+	0.999769i	$0.506843\pi$
$752$		−	1786.20i		−	0.0866168i
$753$	−1558.49	+	1333.65i	−0.0754245	+	0.0645429i
$754$	−55642.7	−	10615.8i	−2.68752	−	0.512738i
$755$	−35440.0			−1.70834
$756$	−534.405	−	18399.8i	−0.0257091	−	0.885179i
$757$	11514.6	−	19943.9i	0.552847	−	0.957559i	−0.445221	−	0.895421i	$-0.646875\pi$
$757$	11514.6	−	19943.9i	0.552847	−	0.957559i	0.998068	−	0.0621380i	$-0.0197919\pi$
$758$	6346.21			0.304096
$759$	−4395.75	−	5136.86i	−0.210218	−	0.245660i
$760$	−501.676	−	289.643i	−0.0239443	−	0.0138243i
$761$	7860.59	+	4538.32i	0.374437	+	0.216181i	0.675395	−	0.737456i	$-0.263973\pi$
$761$	7860.59	+	4538.32i	0.374437	+	0.216181i	−0.300958	+	0.953637i	$0.597307\pi$
$762$	−9203.31	+	1714.80i	−0.437534	+	0.0815230i
$763$	20418.2			0.968790
$764$	−19336.9	+	33492.5i	−0.915686	+	1.58601i
$765$	28124.5	+	4399.61i	1.32921	+	0.207932i
$766$	−47217.0			−2.22718
$767$	−37739.3	−	7200.10i	−1.77665	−	0.338957i
$768$	21079.2	+	7441.96i	0.990403	+	0.349660i
$769$		−	15240.5i		−	0.714677i	−0.933975	−	0.357338i	$-0.883684\pi$
$769$		−	15240.5i		−	0.714677i	0.933975	−	0.357338i	$-0.116316\pi$
$770$	9489.73			0.444138
$771$	−6345.28	−	34055.1i	−0.296394	−	1.59075i
$772$	−20365.8	−	11758.2i	−0.949459	−	0.548170i
$773$	7248.35	−	4184.84i	0.337264	−	0.194719i	−0.321797	−	0.946809i	$-0.604287\pi$
$773$	7248.35	−	4184.84i	0.337264	−	0.194719i	0.659061	+	0.752089i	$0.270954\pi$
$774$	−11519.5	+	14280.9i	−0.534959	+	0.663198i
$775$			959.908i			0.0444915i
$776$	1163.16			0.0538078
$777$	−18778.7	−	6629.77i	−0.867030	−	0.306103i
$778$			170.344i			0.00784980i
$779$	1563.25	+	2707.62i	0.0718987	+	0.124532i
$780$	17696.5	−	10115.7i	0.812355	−	0.464359i
$781$	710.459	−	1230.55i	0.0325509	−	0.0563797i
$782$	33293.1	+	19221.8i	1.52245	+	0.878990i
$783$	−20252.4	+	37555.6i	−0.924344	+	1.71408i
$784$	1947.74	+	3373.59i	0.0887273	+	0.153680i
$785$	−14235.1	−	8218.65i	−0.647227	−	0.373677i
$786$	−11239.8	+	31836.4i	−0.510062	+	1.44474i
$787$	−725.187	−	418.687i	−0.0328464	−	0.0189639i	0.483487	−	0.875352i	$-0.339370\pi$
$787$	−725.187	−	418.687i	−0.0328464	−	0.0189639i	−0.516333	+	0.856388i	$0.672703\pi$
$788$	3744.75	−	2162.03i	0.169291	−	0.0977402i
$789$	16188.9	−	13853.3i	0.730471	−	0.625085i
$790$	16866.2	+	29213.0i	0.759584	+	1.31564i
$791$	−6847.58	−	3953.45i	−0.307803	−	0.177710i
$792$	−230.988	−	186.323i	−0.0103634	−	0.00835947i
$793$	1623.00	−	565.146i	0.0726790	−	0.0253076i
$794$	−14226.8	+	24641.5i	−0.635880	+	1.10138i
$795$	22199.7	+	25942.4i	0.990366	+	1.15734i
$796$	−31899.8			−1.42042
$797$	19475.6	−	33732.6i	0.865570	−	1.49921i	−0.000909600	−	1.00000i	$-0.500290\pi$
$797$	19475.6	−	33732.6i	0.865570	−	1.49921i	0.866480	−	0.499212i	$-0.166377\pi$
$798$	−7496.40	+	21233.4i	−0.332544	+	0.941923i
$799$		−	2670.90i		−	0.118260i
$800$	2110.50	−	1218.50i	0.0932717	−	0.0538505i
$801$	1331.42	+	208.278i	0.0587308	+	0.00918746i
$802$	−24646.2	−	42688.4i	−1.08514	−	1.87953i
$803$	−3650.40	−	6322.67i	−0.160423	−	0.277861i
$804$	−1452.11	+	4113.08i	−0.0636967	+	0.180419i
$805$	−8917.89	−	15446.2i	−0.390452	−	0.676284i
$806$	−3494.19	+	18314.8i	−0.152702	+	0.800387i
$807$	9978.26	−	8538.68i	0.435256	−	0.372461i
$808$	−1231.26	+	710.868i	−0.0536083	+	0.0309508i
$809$	11894.2	−	20601.3i	0.516906	−	0.895308i	−0.482901	−	0.875675i	$-0.660417\pi$
$809$	11894.2	−	20601.3i	0.516906	−	0.895308i	0.999807	−	0.0196331i	$-0.00624981\pi$
$810$	−6586.21	−	30415.7i	−0.285698	−	1.31938i
$811$			35866.7i			1.55296i	0.630143	+	0.776479i	$0.282996\pi$
$811$			35866.7i			1.55296i	−0.630143	+	0.776479i	$0.717004\pi$
$812$		−	39903.5i		−	1.72455i
$813$	−583.812	+	1653.64i	−0.0251847	+	0.0713353i
$814$	10336.5	−	5967.78i	0.445079	−	0.256966i
$815$	4089.60	−	7083.40i	0.175770	−	0.304442i
$816$	31560.3	+	11142.3i	1.35396	+	0.478013i
$817$	9589.86	−	5536.71i	0.410657	−	0.237093i
$818$	−28740.1			−1.22845
$819$	13788.0	+	16253.8i	0.588267	+	0.693471i
$820$	4040.95			0.172093
$821$	189.064	−	109.156i	0.00803702	−	0.00464017i	−0.495976	−	0.868336i	$-0.665190\pi$
$821$	189.064	−	109.156i	0.00803702	−	0.00464017i	0.504013	+	0.863696i	$0.331856\pi$
$822$	−14494.8	+	12403.6i	−0.615040	+	0.526307i
$823$	−8398.14	+	14546.0i	−0.355700	+	0.616090i	−0.987237	−	0.159255i	$-0.949091\pi$
$823$	−8398.14	+	14546.0i	−0.355700	+	0.616090i	0.631538	+	0.775345i	$0.282424\pi$
$824$	342.214	−	197.578i	0.0144680	−	0.00835308i
$825$	−646.533	+	120.465i	−0.0272841	+	0.00508368i
$826$		−	54856.6i		−	2.31078i
$827$		−	5954.17i		−	0.250359i	−0.992134	−	0.125180i	$-0.960049\pi$
$827$		−	5954.17i		−	0.250359i	0.992134	−	0.125180i	$-0.0399507\pi$
$828$	3204.68	−	20485.9i	0.134505	−	0.859824i
$829$	−10443.7	+	18089.0i	−0.437544	+	0.757848i	−0.997499	−	0.0706747i	$-0.977485\pi$
$829$	−10443.7	+	18089.0i	−0.437544	+	0.757848i	0.559956	+	0.828523i	$0.310818\pi$
$830$	−639.207	+	369.047i	−0.0267316	+	0.0154335i
$831$	6904.11	+	37054.3i	0.288208	+	1.54681i
$832$	21461.3	−	7473.05i	0.894276	−	0.311396i
$833$	2912.46	+	5044.52i	0.121141	+	0.209823i
$834$	11028.6	−	2054.90i	0.457902	−	0.0853181i
$835$	−17895.1	−	30995.3i	−0.741660	−	1.28459i
$836$	−3329.16	−	5766.28i	−0.137729	−	0.238554i
$837$	12361.5	+	6666.08i	0.510483	+	0.275285i
$838$	19516.4	−	11267.8i	0.804515	−	0.464487i
$839$			35558.1i			1.46317i	0.681749	+	0.731586i	$0.261220\pi$
$839$			35558.1i			1.46317i	−0.681749	+	0.731586i	$0.738780\pi$
$840$	−509.017	−	594.835i	−0.0209081	−	0.0244331i
$841$	−34053.1	+	58981.7i	−1.39625	+	2.41837i
$842$	25187.3			1.03089
$843$	1088.37	−	3082.80i	0.0444669	−	0.125952i
$844$	9748.08	−	16884.2i	0.397563	−	0.688599i
$845$	−8689.62	+	21944.4i	−0.353766	+	0.893385i
$846$	−2723.98	+	1051.59i	−0.110700	+	0.0427358i
$847$	16872.2	+	9741.18i	0.684458	+	0.395172i
$848$	20072.5	+	34766.7i	0.812846	+	1.40789i
$849$	−5220.69	−	28019.4i	−0.211041	−	1.13265i
$850$	3238.55	−	1869.78i	0.130684	−	0.0754504i
$851$	−19427.3	−	11216.3i	−0.782559	−	0.451811i
$852$	4284.08	−	798.227i	0.172266	−	0.0320972i
$853$	−4359.17	−	2516.77i	−0.174977	−	0.101023i	0.409954	−	0.912106i	$-0.365545\pi$
$853$	−4359.17	−	2516.77i	−0.174977	−	0.101023i	−0.584930	+	0.811084i	$0.698878\pi$
$854$	1226.91	+	2125.06i	0.0491615	+	0.0851501i
$855$	−2902.86	+	18556.5i	−0.116112	+	0.742245i
$856$	973.973	+	562.324i	0.0388899	+	0.0224531i
$857$	21165.7	−	36660.1i	0.843649	−	1.46124i	−0.0431411	−	0.999069i	$-0.513737\pi$
$857$	21165.7	−	36660.1i	0.843649	−	1.46124i	0.886790	−	0.462173i	$-0.152930\pi$
$858$	−12774.2	−	55.0295i	−0.508280	−	0.00218960i
$859$	5920.82	+	10255.2i	0.235176	+	0.407336i	0.959324	−	0.282308i	$-0.0911002\pi$
$859$	5920.82	+	10255.2i	0.235176	+	0.407336i	−0.724148	+	0.689644i	$0.757767\pi$
$860$		−	14312.3i		−	0.567493i
$861$	773.976	+	4153.93i	0.0306353	+	0.164420i
$862$	30488.2			1.20468
$863$			3264.28i			0.128757i	0.997926	+	0.0643785i	$0.0205065\pi$
$863$			3264.28i			0.128757i	−0.997926	+	0.0643785i	$0.979494\pi$
$864$	−1035.14	−	35640.3i	−0.0407594	−	1.40337i
$865$	7106.78	−	4103.10i	0.279350	−	0.161283i
$866$	−61408.1	−	35454.0i	−2.40962	−	1.39120i
$867$	23119.6	+	8162.33i	0.905633	+	0.319732i
$868$	−13134.2			−0.513601
$869$		−	10429.6i		−	0.407136i
$870$	−12357.2	−	66321.1i	−0.481550	−	2.58448i
$871$	−1660.87	−	4769.74i	−0.0646114	−	0.185553i
$872$	1009.57			0.0392069
$873$	−13582.2	−	35182.4i	−0.526560	−	1.36397i
$874$	−12682.5	+	21966.8i	−0.490838	+	0.850156i
$875$	−24351.3			−0.940828
$876$	7454.11	−	21113.6i	0.287501	−	0.814341i
$877$	−14844.1	−	8570.23i	−0.571549	−	0.329984i	0.186219	−	0.982508i	$-0.440377\pi$
$877$	−14844.1	−	8570.23i	−0.571549	−	0.329984i	−0.757768	+	0.652524i	$0.773710\pi$
$878$	−33382.3	−	19273.3i	−1.28314	−	0.740821i
$879$	−13386.0	+	37915.4i	−0.513649	+	1.45490i
$880$	9306.51			0.356503
$881$	16988.8	−	29425.4i	0.649678	−	1.12527i	−0.333522	−	0.942742i	$-0.608237\pi$
$881$	16988.8	−	29425.4i	0.649678	−	1.12527i	0.983200	−	0.182533i	$-0.0584295\pi$
$882$	3998.08	−	4956.48i	0.152633	−	0.189222i
$883$	−8053.03			−0.306915			−0.153458	−	0.988155i	$-0.549041\pi$
$883$	−8053.03			−0.306915			−0.153458	+	0.988155i	$0.549041\pi$
$884$	33843.3	−	11784.6i	1.28764	−	0.448370i
$885$	−8381.20	−	44981.9i	−0.318340	−	1.70853i
$886$		−	5194.70i		−	0.196975i
$887$	32712.3			1.23830			0.619149	−	0.785273i	$-0.287477\pi$
$887$	32712.3			1.23830			0.619149	+	0.785273i	$0.287477\pi$
$888$	−928.509	−	327.808i	−0.0350887	−	0.0123880i
$889$	6612.96	+	3817.99i	0.249484	+	0.144040i
$890$	−1845.24	+	1065.35i	−0.0694972	+	0.0401242i
$891$	−2938.54	+	9162.45i	−0.110488	+	0.344505i
$892$			46445.6i			1.74340i
$893$	1762.25			0.0660376
$894$	−4642.53	−	24916.4i	−0.173679	−	0.932137i
$895$			13422.5i			0.501303i
$896$	−897.285	−	1554.14i	−0.0334555	−	0.0579467i
$897$	11914.9	+	20844.0i	0.443507	+	0.775877i
$898$	2005.60	−	3473.81i	0.0745299	−	0.129090i
$899$	26366.0	+	15222.4i	0.978149	+	0.564735i
$900$	−1569.90	−	1266.34i	−0.0581444	−	0.0469014i
$901$	30014.4	+	51986.5i	1.10980	+	1.92222i
$902$	−2193.16	−	1266.22i	−0.0809581	−	0.0467412i
$903$	14712.4	−	2741.27i	0.542190	−	0.101023i
$904$	−338.577	−	195.478i	−0.0124568	−	0.00719191i
$905$	16018.3	−	9248.16i	0.588360	−	0.339690i
$906$	12476.9	+	66963.6i	0.457525	+	2.45554i
$907$	−18190.4	−	31506.7i	−0.665935	−	1.15343i	−0.979031	−	0.203711i	$-0.934700\pi$
$907$	−18190.4	−	31506.7i	−0.665935	−	1.15343i	0.313096	−	0.949721i	$-0.398634\pi$
$908$	−575.216	−	332.101i	−0.0210234	−	0.0121378i
$909$	35879.2	+	28941.5i	1.30917	+	1.05603i
$910$	−33102.5	−	6315.46i	−1.20587	−	0.230061i
$911$	2145.59	−	3716.27i	0.0780314	−	0.135154i	−0.824369	−	0.566053i	$-0.808470\pi$
$911$	2145.59	−	3716.27i	0.0780314	−	0.135154i	0.902400	+	0.430898i	$0.141803\pi$
$912$	−7351.67	+	20823.5i	−0.266928	+	0.756068i
$913$	228.210			0.00827234
$914$	1905.08	−	3299.70i	0.0689436	−	0.119414i
$915$	1330.73	+	1555.08i	0.0480792	+	0.0561851i
$916$			49602.8i			1.78922i
$917$	23849.1	−	13769.3i	0.858851	−	0.495858i
$918$	−1588.41	−	54689.9i	−0.0571084	−	1.96627i
$919$	−1282.45	−	2221.27i	−0.0460329	−	0.0797313i	0.842091	−	0.539336i	$-0.181325\pi$
$919$	−1282.45	−	2221.27i	−0.0460329	−	0.0797313i	−0.888124	+	0.459604i	$0.847991\pi$
$920$	−440.943	−	763.737i	−0.0158016	−	0.0273692i
$921$	−36979.6	+	6890.18i	−1.32304	+	0.246514i
$922$	−2556.92	−	4428.72i	−0.0913316	−	0.158191i
$923$	−3297.20	+	3819.65i	−0.117582	+	0.136214i
$924$	−1648.29	−	8846.39i	−0.0586850	−	0.314962i
$925$	−1889.76	+	1091.06i	−0.0671730	+	0.0387824i
$926$	31539.5	−	54628.1i	1.11928	−	1.93865i
$927$	−9972.23	−	8043.96i	−0.353324	−	0.285004i
$928$		−	77292.7i		−	2.73411i
$929$		−	7977.71i		−	0.281744i	−0.990028	−	0.140872i	$-0.955009\pi$
$929$		−	7977.71i		−	0.281744i	0.990028	−	0.140872i	$-0.0449906\pi$
$930$	−21829.6	+	4067.38i	−0.769700	+	0.143414i
$931$	−3328.37	+	1921.63i	−0.117167	+	0.0676467i
$932$	7047.35	−	12206.4i	0.247686	−	0.429005i
$933$	27140.5	−	23224.9i	0.952347	−	0.814950i
$934$	−48212.6	+	27835.5i	−1.68904	+	0.975168i
$935$	13916.0			0.486741
$936$	681.744	+	803.665i	0.0238071	+	0.0280647i
$937$	−22558.1			−0.786490			−0.393245	−	0.919434i	$-0.628648\pi$
$937$	−22558.1			−0.786490			−0.393245	+	0.919434i	$0.628648\pi$
$938$	6245.22	−	3605.68i	0.217392	−	0.125511i
$939$	−50611.3	−	17868.2i	−1.75893	−	0.620987i
$940$	1138.85	−	1972.54i	0.0395160	−	0.0684437i
$941$	−4724.10	+	2727.46i	−0.163657	+	0.0944874i	−0.579592	−	0.814907i	$-0.696788\pi$
$941$	−4724.10	+	2727.46i	−0.163657	+	0.0944874i	0.415935	+	0.909395i	$0.363455\pi$
$942$	−10517.5	+	29790.6i	−0.363777	+	1.03039i
$943$			4759.68i			0.164365i
$944$		−	53797.5i		−	1.85483i
$945$	−12048.4	+	22342.3i	−0.414745	+	0.769095i
$946$	−4484.71	+	7767.74i	−0.154134	+	0.266967i
$947$	−2966.02	+	1712.43i	−0.101777	+	0.0587609i	−0.550024	−	0.835149i	$-0.685382\pi$
$947$	−2966.02	+	1712.43i	−0.101777	+	0.0587609i	0.448248	+	0.893909i	$0.352048\pi$
$948$	24303.1	−	20796.8i	0.832624	−	0.712500i
$949$	8525.72	+	24484.4i	0.291630	+	0.837511i
$950$	1233.68	+	2136.79i	0.0421324	+	0.0729754i
$951$	5280.28	−	14956.3i	0.180047	−	0.509980i
$952$	−688.203	−	1192.00i	−0.0234294	−	0.0405809i
$953$	16363.6	+	28342.7i	0.556212	+	0.963388i	0.997808	+	0.0661741i	$0.0210793\pi$
$953$	16363.6	+	28342.7i	0.556212	+	0.963388i	−0.441596	+	0.897214i	$0.645587\pi$
$954$	41202.4	−	51079.3i	1.39830	−	1.73349i
$955$	46185.8	−	26665.4i	1.56496	−	0.903531i
$956$		−	25786.7i		−	0.872386i
$957$	−6944.03	+	19668.8i	−0.234554	+	0.664371i
$958$	−12596.3	+	21817.4i	−0.424809	+	0.735791i
$959$	15560.7			0.523964
$960$	17596.5	+	20563.2i	0.591588	+	0.691327i
$961$	−9885.03	+	17121.4i	−0.331813	+	0.574716i
$962$	−40027.9	+	13938.1i	−1.34153	+	0.467134i
$963$	5635.72	−	36026.3i	0.188586	−	1.20554i
$964$	−7996.98	−	4617.06i	−0.267184	−	0.154259i
$965$	16214.5	+	28084.3i	0.540894	+	0.936856i
$966$	−26045.9	+	22288.2i	−0.867509	+	0.742352i
$967$	49213.4	−	28413.4i	1.63660	−	0.944893i	0.654612	−	0.755965i	$-0.272832\pi$
$967$	49213.4	−	28413.4i	1.63660	−	0.944893i	0.981991	−	0.188928i	$-0.0605014\pi$
$968$	834.244	+	481.651i	0.0277000	+	0.0159926i
$969$	−10992.9	+	31137.3i	−0.364442	+	1.03227i
$970$	51639.2	+	29813.9i	1.70931	+	0.986873i
$971$	20615.6	+	35707.3i	0.681346	+	1.18013i	0.974570	+	0.224083i	$0.0719386\pi$
$971$	20615.6	+	35707.3i	0.681346	+	1.18013i	−0.293224	+	0.956044i	$0.594728\pi$
$972$	−27209.8	+	11422.7i	−0.897894	+	0.376937i
$973$	−7924.52	−	4575.23i	−0.261098	−	0.150745i
$974$	−39494.1	+	68405.7i	−1.29925	+	2.25037i
$975$	2335.44	+	10.0607i	0.0767117	+	0.000330463i
$976$	1203.22	+	2084.04i	0.0394612	+	0.0683488i
$977$			25235.3i			0.826355i	0.910651	+	0.413177i	$0.135581\pi$
$977$			25235.3i			0.826355i	−0.910651	+	0.413177i	$0.864419\pi$
$978$	−14823.8	−	5233.50i	−0.484675	−	0.171113i
$979$	658.787			0.0215066
$980$			4967.38i			0.161915i
$981$	−11788.8	−	30536.9i	−0.383676	−	0.993850i
$982$	54136.6	−	31255.8i	1.75923	−	1.01569i
$983$	−11991.4	−	6923.25i	−0.389081	−	0.224636i	0.292681	−	0.956210i	$-0.405453\pi$
$983$	−11991.4	−	6923.25i	−0.389081	−	0.224636i	−0.681762	+	0.731574i	$0.738786\pi$
$984$	38.2691	+	205.390i	0.00123981	+	0.00665407i
$985$	−5962.86			−0.192886
$986$		−	118605.i		−	3.83080i
$987$	2245.81	+	792.878i	0.0724265	+	0.0255700i
$988$	7775.46	+	22329.8i	0.250375	+	0.719033i
$989$	16857.8			0.542010
$990$	−5479.05	−	14192.6i	−0.175895	−	0.455627i
$991$	−2076.06	+	3595.85i	−0.0665473	+	0.115263i	−0.897379	−	0.441260i	$-0.854532\pi$
$991$	−2076.06	+	3595.85i	−0.0665473	+	0.115263i	0.830832	+	0.556523i	$0.187865\pi$
$992$	−25440.9			−0.814265
$993$	−1590.77	+	296.399i	−0.0508375	+	0.00947224i
$994$	−6239.39	−	3602.31i	−0.199096	−	0.114948i
$995$	38096.0	+	21994.7i	1.21379	+	0.700784i
$996$	455.053	+	531.773i	0.0144768	+	0.0169175i
$997$	−37626.2			−1.19522			−0.597610	−	0.801787i	$-0.703883\pi$
$997$	−37626.2			−1.19522			−0.597610	+	0.801787i	$0.703883\pi$
$998$	12718.4	−	22028.9i	0.403401	−	0.698711i
$999$	926.874	+	31912.7i	0.0293544	+	1.01069i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.4.r.a.43.8	yes	80
3.2	odd	2		351.4.r.a.316.33		80
9.4	even	3		117.4.l.a.4.8	✓	80
9.5	odd	6		351.4.l.a.199.33		80
13.10	even	6		117.4.l.a.88.33	yes	80
39.23	odd	6		351.4.l.a.127.8		80
117.23	odd	6		351.4.r.a.10.33		80
117.49	even	6	inner	117.4.r.a.49.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.4.l.a.4.8	✓	80	9.4	even	3
117.4.l.a.88.33	yes	80	13.10	even	6
117.4.r.a.43.8	yes	80	1.1	even	1	trivial
117.4.r.a.49.8	yes	80	117.49	even	6	inner
351.4.l.a.127.8		80	39.23	odd	6
351.4.l.a.199.33		80	9.5	odd	6
351.4.r.a.10.33		80	117.23	odd	6
351.4.r.a.316.33		80	3.2	odd	2

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	117.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.44134 + 1.98686i) q^{2} +(-0.951787 - 5.10824i) q^{3} +(3.89522 - 6.74672i) q^{4} +(-9.30367 + 5.37147i) q^{5} +(13.4248 + 15.6881i) q^{6} -16.8418i q^{7} -0.832741i q^{8} +(-25.1882 + 9.72391i) q^{9} +(21.3447 - 36.9702i) q^{10} +(-11.4307 + 6.59955i) q^{11} +(-38.1713 - 13.4763i) q^{12} +(44.2653 - 15.4136i) q^{13} +(33.4623 + 57.9585i) q^{14} +(36.2939 + 42.4129i) q^{15} +(32.8163 + 56.8395i) q^{16} +(49.0702 + 84.9920i) q^{17} +(67.3612 - 83.5087i) q^{18} +(-56.0776 + 32.3764i) q^{19} +83.6923i q^{20} +(-86.0321 + 16.0298i) q^{21} +(26.2247 - 45.4226i) q^{22} -98.5778 q^{23} +(-4.25384 + 0.792592i) q^{24} +(-4.79452 + 8.30436i) q^{25} +(-121.707 + 140.993i) q^{26} +(73.6458 + 119.412i) q^{27} +(-113.627 - 65.6026i) q^{28} +(152.065 + 263.385i) q^{29} +(-209.168 - 73.8463i) q^{30} +(86.6932 - 50.0523i) q^{31} +(-220.095 - 127.072i) q^{32} +(44.5917 + 52.1096i) q^{33} +(-337.734 - 194.991i) q^{34} +(90.4654 + 156.691i) q^{35} +(-32.5091 + 207.814i) q^{36} +(197.075 + 113.781i) q^{37} +(128.655 - 222.837i) q^{38} +(-120.868 - 211.447i) q^{39} +(4.47305 + 7.74755i) q^{40} -48.2835i q^{41} +(264.217 - 226.098i) q^{42} -171.010 q^{43} +102.827i q^{44} +(182.111 - 225.766i) q^{45} +(339.240 - 195.860i) q^{46} +(-23.5689 - 13.6075i) q^{47} +(259.116 - 221.733i) q^{48} +59.3529 q^{49} -38.1042i q^{50} +(387.455 - 331.556i) q^{51} +(68.4317 - 358.685i) q^{52} +611.664 q^{53} +(-490.696 - 264.614i) q^{54} +(70.8986 - 122.800i) q^{55} -14.0249 q^{56} +(218.760 + 255.642i) q^{57} +(-1046.62 - 604.264i) q^{58} +(-709.861 - 409.839i) q^{59} +(427.520 - 79.6572i) q^{60} +36.6653 q^{61} +(-198.894 + 344.494i) q^{62} +(163.768 + 424.215i) q^{63} +484.834 q^{64} +(-329.036 + 381.173i) q^{65} +(-256.990 - 90.7296i) q^{66} -107.753i q^{67} +764.556 q^{68} +(93.8251 + 503.559i) q^{69} +(-622.645 - 359.484i) q^{70} +(-93.2300 + 53.8263i) q^{71} +(8.09750 + 20.9753i) q^{72} +553.128i q^{73} -904.271 q^{74} +(46.9840 + 16.5876i) q^{75} +504.453i q^{76} +(111.148 + 192.515i) q^{77} +(836.063 + 487.515i) q^{78} +(-395.090 + 684.315i) q^{79} +(-610.624 - 352.544i) q^{80} +(539.891 - 489.856i) q^{81} +(95.9325 + 166.160i) q^{82} +(-14.9734 - 8.64491i) q^{83} +(-226.965 + 642.874i) q^{84} +(-913.065 - 527.158i) q^{85} +(588.505 - 339.774i) q^{86} +(1200.70 - 1027.47i) q^{87} +(5.49571 + 9.51886i) q^{88} +(-43.2247 - 24.9558i) q^{89} +(-178.141 + 1138.77i) q^{90} +(-259.594 - 745.509i) q^{91} +(-383.982 + 665.077i) q^{92} +(-338.193 - 395.210i) q^{93} +108.145 q^{94} +(347.818 - 602.439i) q^{95} +(-439.629 + 1245.24i) q^{96} +1396.78i q^{97} +(-204.254 + 117.926i) q^{98} +(223.747 - 277.382i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 3 q^{2} - q^{3} + 153 q^{4} - 3 q^{6} - 17 q^{9} - 10 q^{10} - 3 q^{11} - 101 q^{12} - 13 q^{13} + 126 q^{14} - 84 q^{15} - 551 q^{16} - 138 q^{17} + 168 q^{18} - 96 q^{19} + 249 q^{21} - 31 q^{22}+ \cdots + 2331 q^{99}+O(q^{100}) \) 80 * q - 3 * q^2 - q^3 + 153 * q^4 - 3 * q^6 - 17 * q^9 - 10 * q^10 - 3 * q^11 - 101 * q^12 - 13 * q^13 + 126 * q^14 - 84 * q^15 - 551 * q^16 - 138 * q^17 + 168 * q^18 - 96 * q^19 + 249 * q^21 - 31 * q^22 + 654 * q^23 - 834 * q^24 + 798 * q^25 + 510 * q^26 - 364 * q^27 + 18 * q^28 + 201 * q^29 + 87 * q^30 - 180 * q^31 + 117 * q^32 + 231 * q^33 - 24 * q^34 + 297 * q^35 + 251 * q^36 + 246 * q^37 - 768 * q^38 - 560 * q^39 + 328 * q^40 + 1212 * q^42 + 166 * q^43 - 603 * q^45 - 6 * q^46 - 372 * q^47 - 1288 * q^48 - 3226 * q^49 + 186 * q^51 + 186 * q^52 - 2568 * q^53 + 480 * q^54 - 127 * q^55 + 4596 * q^56 - 1332 * q^57 - 3 * q^58 - 531 * q^59 - 711 * q^60 + 838 * q^61 + 135 * q^62 + 2895 * q^63 - 3178 * q^64 - 2337 * q^65 + 6228 * q^66 - 3900 * q^68 + 591 * q^69 + 1005 * q^70 - 2598 * q^71 + 1821 * q^72 - 942 * q^74 - 494 * q^75 - 1584 * q^77 + 2631 * q^78 - 260 * q^79 - 1332 * q^80 - 2357 * q^81 - 1273 * q^82 - 1194 * q^83 + 8196 * q^84 + 3936 * q^85 + 2910 * q^86 - 363 * q^87 + 781 * q^88 - 1056 * q^89 + 2559 * q^90 + 537 * q^91 + 1056 * q^92 + 1830 * q^93 - 1078 * q^94 - 5292 * q^95 - 6777 * q^96 - 6339 * q^98 + 2331 * q^99

Introduction

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