LMFDB - Embedded newform 174.4.f.a.17.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [174,4,Mod(17,174)] 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("174.17"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(174, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 174 = 2 \cdot 3 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	174.f (of order $4$, 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:	$10.2663323410$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.9
Character	$\chi$	$=$	174.17
Dual form			174.4.f.a.41.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41421 - 1.41421i) q^{2} +(0.762114 + 5.13996i) q^{3} +4.00000i q^{4} -8.24082 q^{5} +(6.19121 - 8.34679i) q^{6} +4.60548 q^{7} +(5.65685 - 5.65685i) q^{8} +(-25.8384 + 7.83447i) q^{9} +(11.6543 + 11.6543i) q^{10} +(12.6993 + 12.6993i) q^{11} +(-20.5598 + 3.04846i) q^{12} +35.0408i q^{13} +(-6.51313 - 6.51313i) q^{14} +(-6.28044 - 42.3575i) q^{15} -16.0000 q^{16} +(-90.2610 - 90.2610i) q^{17} +(47.6206 + 25.4614i) q^{18} +(-17.1416 + 17.1416i) q^{19} -32.9633i q^{20} +(3.50990 + 23.6720i) q^{21} -35.9191i q^{22} -204.945i q^{23} +(33.3872 + 24.7648i) q^{24} -57.0889 q^{25} +(49.5551 - 49.5551i) q^{26} +(-59.9606 - 126.837i) q^{27} +18.4219i q^{28} +(-142.530 - 63.8287i) q^{29} +(-51.0206 + 68.7844i) q^{30} +(-68.5989 + 68.5989i) q^{31} +(22.6274 + 22.6274i) q^{32} +(-55.5956 + 74.9522i) q^{33} +255.297i q^{34} -37.9529 q^{35} +(-31.3379 - 103.353i) q^{36} +(42.8414 + 42.8414i) q^{37} +48.4838 q^{38} +(-180.108 + 26.7050i) q^{39} +(-46.6171 + 46.6171i) q^{40} +(-23.5656 + 23.5656i) q^{41} +(28.5135 - 38.4410i) q^{42} +(197.932 - 197.932i) q^{43} +(-50.7972 + 50.7972i) q^{44} +(212.929 - 64.5625i) q^{45} +(-289.836 + 289.836i) q^{46} +(-410.374 + 410.374i) q^{47} +(-12.1938 - 82.2394i) q^{48} -321.790 q^{49} +(80.7359 + 80.7359i) q^{50} +(395.149 - 532.727i) q^{51} -140.163 q^{52} +242.810i q^{53} +(-94.5780 + 264.172i) q^{54} +(-104.653 - 104.653i) q^{55} +(26.0525 - 26.0525i) q^{56} +(-101.171 - 75.0433i) q^{57} +(111.301 + 291.836i) q^{58} -44.1380i q^{59} +(169.430 - 25.1218i) q^{60} +(153.359 - 153.359i) q^{61} +194.027 q^{62} +(-118.998 + 36.0815i) q^{63} -64.0000i q^{64} -288.765i q^{65} +(184.623 - 27.3744i) q^{66} -155.452i q^{67} +(361.044 - 361.044i) q^{68} +(1053.41 - 156.191i) q^{69} +(53.6735 + 53.6735i) q^{70} +325.633 q^{71} +(-101.845 + 190.482i) q^{72} +(837.309 + 837.309i) q^{73} -121.174i q^{74} +(-43.5082 - 293.435i) q^{75} +(-68.5664 - 68.5664i) q^{76} +(58.4864 + 58.4864i) q^{77} +(292.478 + 216.945i) q^{78} +(-52.9813 + 52.9813i) q^{79} +131.853 q^{80} +(606.242 - 404.860i) q^{81} +66.6536 q^{82} +358.507i q^{83} +(-94.6879 + 14.0396i) q^{84} +(743.825 + 743.825i) q^{85} -559.836 q^{86} +(219.453 - 781.245i) q^{87} +143.676 q^{88} +(149.821 + 149.821i) q^{89} +(-392.433 - 209.822i) q^{90} +161.379i q^{91} +819.779 q^{92} +(-404.876 - 300.315i) q^{93} +1160.71 q^{94} +(141.261 - 141.261i) q^{95} +(-99.0593 + 133.549i) q^{96} +(-735.966 - 735.966i) q^{97} +(455.079 + 455.079i) q^{98} +(-427.622 - 228.637i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 24 q^{10} + 88 q^{15} - 960 q^{16} + 48 q^{19} - 752 q^{21} + 64 q^{24} + 1500 q^{25} + 600 q^{27} + 312 q^{30} - 300 q^{31} - 224 q^{36} - 192 q^{37} - 172 q^{39} + 96 q^{40} + 888 q^{43} - 1532 q^{45}+ \cdots - 6000 q^{99}+O(q^{100}) $ 60 * q - 24 * q^10 + 88 * q^15 - 960 * q^16 + 48 * q^19 - 752 * q^21 + 64 * q^24 + 1500 * q^25 + 600 * q^27 + 312 * q^30 - 300 * q^31 - 224 * q^36 - 192 * q^37 - 172 * q^39 + 96 * q^40 + 888 * q^43 - 1532 * q^45 - 1104 * q^46 + 2292 * q^49 - 768 * q^52 - 1688 * q^54 + 2616 * q^55 - 1176 * q^58 - 352 * q^60 + 216 * q^61 + 192 * q^66 - 452 * q^69 + 192 * q^70 - 1668 * q^73 + 4840 * q^75 + 192 * q^76 - 1336 * q^78 + 3588 * q^79 - 280 * q^81 + 4224 * q^82 - 3008 * q^84 - 792 * q^85 - 4716 * q^87 - 800 * q^90 - 3072 * q^94 - 2916 * q^97 - 6000 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/174\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.41421	−	1.41421i	−0.500000	−	0.500000i
$2$	−1.41421	−	1.41421i	−0.500000	−	0.500000i
$3$	0.762114	+	5.13996i	0.146669	+	0.989186i
$3$	0.762114	+	5.13996i	0.146669	+	0.989186i
$4$			4.00000i			0.500000i
$5$	−8.24082			−0.737081			−0.368541	−	0.929612i	$-0.620142\pi$
$5$	−8.24082			−0.737081			−0.368541	+	0.929612i	$0.620142\pi$
$6$	6.19121	−	8.34679i	0.421258	−	0.567927i
$7$	4.60548			0.248672			0.124336	−	0.992240i	$-0.460320\pi$
$7$	4.60548			0.248672			0.124336	+	0.992240i	$0.460320\pi$
$8$	5.65685	−	5.65685i	0.250000	−	0.250000i
$9$	−25.8384	+	7.83447i	−0.956976	+	0.290166i
$10$	11.6543	+	11.6543i	0.368541	+	0.368541i
$11$	12.6993	+	12.6993i	0.348090	+	0.348090i	0.859398	−	0.511308i	$-0.170839\pi$
$11$	12.6993	+	12.6993i	0.348090	+	0.348090i	−0.511308	+	0.859398i	$0.670839\pi$
$12$	−20.5598	+	3.04846i	−0.494593	+	0.0733344i
$13$			35.0408i			0.747581i	0.927513	+	0.373791i	$0.121942\pi$
$13$			35.0408i			0.747581i	−0.927513	+	0.373791i	$0.878058\pi$
$14$	−6.51313	−	6.51313i	−0.124336	−	0.124336i
$15$	−6.28044	−	42.3575i	−0.108107	−	0.729110i
$16$	−16.0000			−0.250000
$17$	−90.2610	−	90.2610i	−1.28774	−	1.28774i	−0.936159	−	0.351578i	$-0.885645\pi$
$17$	−90.2610	−	90.2610i	−1.28774	−	1.28774i	−0.351578	−	0.936159i	$-0.614355\pi$
$18$	47.6206	+	25.4614i	0.623571	+	0.333405i
$19$	−17.1416	+	17.1416i	−0.206977	+	0.206977i	−0.802981	−	0.596005i	$-0.796754\pi$
$19$	−17.1416	+	17.1416i	−0.206977	+	0.206977i	0.596005	+	0.802981i	$0.296754\pi$
$20$		−	32.9633i		−	0.368541i
$21$	3.50990	+	23.6720i	0.0364725	+	0.245983i
$22$		−	35.9191i		−	0.348090i
$23$		−	204.945i		−	1.85800i	−0.370084	−	0.928998i	$-0.620671\pi$
$23$		−	204.945i		−	1.85800i	0.370084	−	0.928998i	$-0.379329\pi$
$24$	33.3872	+	24.7648i	0.283964	+	0.210629i
$25$	−57.0889			−0.456711
$26$	49.5551	−	49.5551i	0.373791	−	0.373791i
$27$	−59.9606	−	126.837i	−0.427386	−	0.904069i
$28$			18.4219i			0.124336i
$29$	−142.530	−	63.8287i	−0.912663	−	0.408713i
$29$	−142.530	−	63.8287i	−0.912663	−	0.408713i
$30$	−51.0206	+	68.7844i	−0.310502	+	0.418609i
$31$	−68.5989	+	68.5989i	−0.397443	+	0.397443i	−0.877330	−	0.479887i	$-0.840678\pi$
$31$	−68.5989	+	68.5989i	−0.397443	+	0.397443i	0.479887	+	0.877330i	$0.340678\pi$
$32$	22.6274	+	22.6274i	0.125000	+	0.125000i
$33$	−55.5956	+	74.9522i	−0.293271	+	0.395379i
$34$			255.297i			1.28774i
$35$	−37.9529			−0.183292
$36$	−31.3379	−	103.353i	−0.145083	−	0.478488i
$37$	42.8414	+	42.8414i	0.190354	+	0.190354i	0.795849	−	0.605495i	$-0.207025\pi$
$37$	42.8414	+	42.8414i	0.190354	+	0.190354i	−0.605495	+	0.795849i	$0.707025\pi$
$38$	48.4838			0.206977
$39$	−180.108	+	26.7050i	−0.739497	+	0.109647i
$40$	−46.6171	+	46.6171i	−0.184270	+	0.184270i
$41$	−23.5656	+	23.5656i	−0.0897641	+	0.0897641i	−0.750563	−	0.660799i	$-0.770218\pi$
$41$	−23.5656	+	23.5656i	−0.0897641	+	0.0897641i	0.660799	+	0.750563i	$0.270218\pi$
$42$	28.5135	−	38.4410i	0.104755	−	0.141228i
$43$	197.932	−	197.932i	0.701962	−	0.701962i	−0.262870	−	0.964831i	$-0.584669\pi$
$43$	197.932	−	197.932i	0.701962	−	0.701962i	0.964831	+	0.262870i	$0.0846689\pi$
$44$	−50.7972	+	50.7972i	−0.174045	+	0.174045i
$45$	212.929	−	64.5625i	0.705370	−	0.213876i
$46$	−289.836	+	289.836i	−0.928998	+	0.928998i
$47$	−410.374	+	410.374i	−1.27360	+	1.27360i	−0.329415	+	0.944185i	$0.606852\pi$
$47$	−410.374	+	410.374i	−1.27360	+	1.27360i	−0.944185	+	0.329415i	$0.893148\pi$
$48$	−12.1938	−	82.2394i	−0.0366672	−	0.247296i
$49$	−321.790			−0.938162
$50$	80.7359	+	80.7359i	0.228356	+	0.228356i
$51$	395.149	−	532.727i	1.08494	−	1.46268i
$52$	−140.163			−0.373791
$53$			242.810i			0.629292i	0.949209	+	0.314646i	$0.101886\pi$
$53$			242.810i			0.629292i	−0.949209	+	0.314646i	$0.898114\pi$
$54$	−94.5780	+	264.172i	−0.238341	+	0.665728i
$55$	−104.653	−	104.653i	−0.256570	−	0.256570i
$56$	26.0525	−	26.0525i	0.0621681	−	0.0621681i
$57$	−101.171	−	75.0433i	−0.235095	−	0.174381i
$58$	111.301	+	291.836i	0.251975	+	0.660688i
$59$		−	44.1380i		−	0.0973946i	−0.998814	−	0.0486973i	$-0.984493\pi$
$59$		−	44.1380i		−	0.0973946i	0.998814	−	0.0486973i	$-0.0155070\pi$
$60$	169.430	−	25.1218i	0.364555	−	0.0540535i
$61$	153.359	−	153.359i	0.321895	−	0.321895i	−0.527599	−	0.849494i	$-0.676907\pi$
$61$	153.359	−	153.359i	0.321895	−	0.321895i	0.849494	+	0.527599i	$0.176907\pi$
$62$	194.027			0.397443
$63$	−118.998	+	36.0815i	−0.237974	+	0.0721562i
$64$		−	64.0000i		−	0.125000i
$65$		−	288.765i		−	0.551028i
$66$	184.623	−	27.3744i	0.344325	−	0.0510539i
$67$		−	155.452i		−	0.283455i	−0.989906	−	0.141727i	$-0.954734\pi$
$67$		−	155.452i		−	0.283455i	0.989906	−	0.141727i	$-0.0452656\pi$
$68$	361.044	−	361.044i	0.643868	−	0.643868i
$69$	1053.41	−	156.191i	1.83790	−	0.272510i
$70$	53.6735	+	53.6735i	0.0916459	+	0.0916459i
$71$	325.633			0.544303			0.272152	−	0.962254i	$-0.412265\pi$
$71$	325.633			0.544303			0.272152	+	0.962254i	$0.412265\pi$
$72$	−101.845	+	190.482i	−0.166703	+	0.311785i
$73$	837.309	+	837.309i	1.34246	+	1.34246i	0.893604	+	0.448857i	$0.148169\pi$
$73$	837.309	+	837.309i	1.34246	+	1.34246i	0.448857	+	0.893604i	$0.351831\pi$
$74$		−	121.174i		−	0.190354i
$75$	−43.5082	−	293.435i	−0.0669853	−	0.451772i
$76$	−68.5664	−	68.5664i	−0.103488	−	0.103488i
$77$	58.4864	+	58.4864i	0.0865603	+	0.0865603i
$78$	292.478	+	216.945i	0.424572	+	0.314925i
$79$	−52.9813	+	52.9813i	−0.0754539	+	0.0754539i	−0.743827	−	0.668373i	$-0.766991\pi$
$79$	−52.9813	+	52.9813i	−0.0754539	+	0.0754539i	0.668373	+	0.743827i	$0.266991\pi$
$80$	131.853			0.184270
$81$	606.242	−	404.860i	0.831608	−	0.555363i
$82$	66.6536			0.0897641
$83$			358.507i			0.474111i	0.971496	+	0.237056i	$0.0761823\pi$
$83$			358.507i			0.474111i	−0.971496	+	0.237056i	$0.923818\pi$
$84$	−94.6879	+	14.0396i	−0.122992	+	0.0182363i
$85$	743.825	+	743.825i	0.949167	+	0.949167i
$86$	−559.836			−0.701962
$87$	219.453	−	781.245i	0.270434	−	0.962738i
$88$	143.676			0.174045
$89$	149.821	+	149.821i	0.178438	+	0.178438i	0.790675	−	0.612236i	$-0.209730\pi$
$89$	149.821	+	149.821i	0.178438	+	0.178438i	−0.612236	+	0.790675i	$0.709730\pi$
$90$	−392.433	−	209.822i	−0.459623	−	0.245747i
$91$			161.379i			0.185903i
$92$	819.779			0.928998
$93$	−404.876	−	300.315i	−0.451437	−	0.334852i
$94$	1160.71			1.27360
$95$	141.261	−	141.261i	0.152559	−	0.152559i
$96$	−99.0593	+	133.549i	−0.105315	+	0.141982i
$97$	−735.966	−	735.966i	−0.770372	−	0.770372i	0.207800	−	0.978171i	$-0.433370\pi$
$97$	−735.966	−	735.966i	−0.770372	−	0.770372i	−0.978171	+	0.207800i	$0.933370\pi$
$98$	455.079	+	455.079i	0.469081	+	0.469081i
$99$	−427.622	−	228.637i	−0.434117	−	0.232110i
$100$		−	228.356i		−	0.228356i
$101$	−363.410	−	363.410i	−0.358026	−	0.358026i	0.505059	−	0.863085i	$-0.331471\pi$
$101$	−363.410	−	363.410i	−0.358026	−	0.358026i	−0.863085	+	0.505059i	$0.831471\pi$
$102$	−1312.22	+	194.565i	−1.27381	+	0.188871i
$103$	−1764.22			−1.68771			−0.843853	−	0.536575i	$-0.819718\pi$
$103$	−1764.22			−1.68771			−0.843853	+	0.536575i	$0.819718\pi$
$104$	198.220	+	198.220i	0.186895	+	0.186895i
$105$	−28.9245	−	195.076i	−0.0268832	−	0.181310i
$106$	343.385	−	343.385i	0.314646	−	0.314646i
$107$			1108.90i			1.00188i	0.865482	+	0.500941i	$0.167012\pi$
$107$			1108.90i			1.00188i	−0.865482	+	0.500941i	$0.832988\pi$
$108$	507.350	−	239.843i	0.452035	−	0.213693i
$109$			993.771i			0.873266i	0.899640	+	0.436633i	$0.143829\pi$
$109$			993.771i			0.873266i	−0.899640	+	0.436633i	$0.856171\pi$
$110$			296.003i			0.256570i
$111$	−187.553	+	252.853i	−0.160376	+	0.216214i
$112$	−73.6877			−0.0621681
$113$	−481.710	+	481.710i	−0.401021	+	0.401021i	−0.878593	−	0.477571i	$-0.841517\pi$
$113$	−481.710	+	481.710i	−0.401021	+	0.401021i	0.477571	+	0.878593i	$0.341517\pi$
$114$	36.9502	+	249.205i	0.0303570	+	0.204738i
$115$			1688.91i			1.36949i
$116$	255.315	−	570.121i	0.204357	−	0.456331i
$117$	−274.526	−	905.396i	−0.216922	−	0.715418i
$118$	−62.4206	+	62.4206i	−0.0486973	+	0.0486973i
$119$	−415.695	−	415.695i	−0.320225	−	0.320225i
$120$	−275.138	−	204.083i	−0.209304	−	0.155251i
$121$		−	1008.46i		−	0.757667i
$122$	−433.765			−0.321895
$123$	−139.086	−	103.167i	−0.101959	−	0.0756277i
$124$	−274.396	−	274.396i	−0.198721	−	0.198721i
$125$	1500.56			1.07371
$126$	219.316	+	117.262i	0.155065	+	0.0829088i
$127$	247.225	−	247.225i	0.172738	−	0.172738i	−0.615443	−	0.788181i	$-0.711023\pi$
$127$	247.225	−	247.225i	0.172738	−	0.172738i	0.788181	+	0.615443i	$0.211023\pi$
$128$	−90.5097	+	90.5097i	−0.0625000	+	0.0625000i
$129$	1168.21	+	866.516i	0.797326	+	0.591414i
$130$	−408.375	+	408.375i	−0.275514	+	0.275514i
$131$	−1125.02	+	1125.02i	−0.750335	+	0.750335i	−0.974542	−	0.224207i	$-0.928021\pi$
$131$	−1125.02	+	1125.02i	−0.750335	+	0.750335i	0.224207	+	0.974542i	$0.428021\pi$
$132$	−299.809	−	222.382i	−0.197690	−	0.146636i
$133$	−78.9453	+	78.9453i	−0.0514694	+	0.0514694i
$134$	−219.842	+	219.842i	−0.141727	+	0.141727i
$135$	494.125	+	1045.24i	0.315018	+	0.666373i
$136$	−1021.19			−0.643868
$137$	968.152	+	968.152i	0.603758	+	0.603758i	0.941308	−	0.337550i	$-0.109598\pi$
$137$	968.152	+	968.152i	0.603758	+	0.603758i	−0.337550	+	0.941308i	$0.609598\pi$
$138$	−1710.63	−	1268.86i	−1.05521	−	0.782697i
$139$	−1135.68			−0.693003			−0.346501	−	0.938049i	$-0.612630\pi$
$139$	−1135.68			−0.693003			−0.346501	+	0.938049i	$0.612630\pi$
$140$		−	151.812i		−	0.0916459i
$141$	−2422.06	−	1796.55i	−1.44662	−	1.07303i
$142$	−460.514	−	460.514i	−0.272152	−	0.272152i
$143$	−444.993	+	444.993i	−0.260225	+	0.260225i
$144$	413.414	−	125.352i	0.239244	−	0.0725414i
$145$	1174.57	+	526.001i	0.672707	+	0.301255i
$146$		−	2368.27i		−	1.34246i
$147$	−245.240	−	1653.99i	−0.137599	−	0.928016i
$148$	−171.366	+	171.366i	−0.0951768	+	0.0951768i
$149$	−3436.03			−1.88920			−0.944599	−	0.328226i	$-0.893549\pi$
$149$	−3436.03			−1.88920			−0.944599	+	0.328226i	$0.893549\pi$
$150$	−353.449	+	476.509i	−0.192393	+	0.259379i
$151$			2291.63i			1.23504i	0.786557	+	0.617518i	$0.211862\pi$
$151$			2291.63i			1.23504i	−0.786557	+	0.617518i	$0.788138\pi$
$152$			193.935i			0.103488i
$153$	3039.35	+	1625.05i	1.60599	+	0.858677i
$154$		−	165.425i		−	0.0865603i
$155$	565.311	−	565.311i	0.292948	−	0.292948i
$156$	−106.820	−	720.432i	−0.0548235	−	0.369748i
$157$	−141.274	−	141.274i	−0.0718144	−	0.0718144i	0.670287	−	0.742102i	$-0.266171\pi$
$157$	−141.274	−	141.274i	−0.0718144	−	0.0718144i	−0.742102	+	0.670287i	$0.766171\pi$
$158$	149.854			0.0754539
$159$	−1248.03	+	185.049i	−0.622487	+	0.0922976i
$160$	−186.468	−	186.468i	−0.0921352	−	0.0921352i
$161$		−	943.869i		−	0.462033i
$162$	−1429.91	−	284.798i	−0.693486	−	0.138122i
$163$	−635.767	−	635.767i	−0.305504	−	0.305504i	0.537659	−	0.843163i	$-0.319309\pi$
$163$	−635.767	−	635.767i	−0.305504	−	0.305504i	−0.843163	+	0.537659i	$0.819309\pi$
$164$	−94.2624	−	94.2624i	−0.0448820	−	0.0448820i
$165$	458.153	−	617.668i	0.216165	−	0.291427i
$166$	507.005	−	507.005i	0.237056	−	0.237056i
$167$	470.718			0.218115			0.109058	−	0.994035i	$-0.465217\pi$
$167$	470.718			0.218115			0.109058	+	0.994035i	$0.465217\pi$
$168$	153.764	+	114.054i	0.0706139	+	0.0523777i
$169$	969.145			0.441122
$170$		−	2103.86i		−	0.949167i
$171$	308.616	−	577.206i	0.138014	−	0.258129i
$172$	791.728	+	791.728i	0.350981	+	0.350981i
$173$	1419.43			0.623798			0.311899	−	0.950115i	$-0.399035\pi$
$173$	1419.43			0.623798			0.311899	+	0.950115i	$0.399035\pi$
$174$	−1415.20	+	794.494i	−0.616586	+	0.346152i
$175$	−262.922			−0.113571
$176$	−203.189	−	203.189i	−0.0870224	−	0.0870224i
$177$	226.868	−	33.6382i	0.0963413	−	0.0142848i
$178$		−	423.758i		−	0.178438i
$179$	862.468			0.360133			0.180067	−	0.983654i	$-0.442369\pi$
$179$	862.468			0.360133			0.180067	+	0.983654i	$0.442369\pi$
$180$	258.250	+	851.717i	0.106938	+	0.352685i
$181$	861.720			0.353874			0.176937	−	0.984222i	$-0.443381\pi$
$181$	861.720			0.353874			0.176937	+	0.984222i	$0.443381\pi$
$182$	228.225	−	228.225i	0.0929515	−	0.0929515i
$183$	905.136	+	671.382i	0.365626	+	0.271202i
$184$	−1159.34	−	1159.34i	−0.464499	−	0.464499i
$185$	−353.048	−	353.048i	−0.140306	−	0.140306i
$186$	147.871	+	997.291i	0.0582925	+	0.393145i
$187$		−	2292.51i		−	0.896495i
$188$	−1641.50	−	1641.50i	−0.636800	−	0.636800i
$189$	−276.147	−	584.147i	−0.106279	−	0.224817i
$190$	−399.546			−0.152559
$191$	−1605.39	−	1605.39i	−0.608178	−	0.608178i	0.334292	−	0.942470i	$-0.391503\pi$
$191$	−1605.39	−	1605.39i	−0.608178	−	0.608178i	−0.942470	+	0.334292i	$0.891503\pi$
$192$	328.957	−	48.7753i	0.123648	−	0.0183336i
$193$	1542.76	−	1542.76i	0.575388	−	0.575388i	−0.358241	−	0.933629i	$-0.616623\pi$
$193$	1542.76	−	1542.76i	0.575388	−	0.575388i	0.933629	+	0.358241i	$0.116623\pi$
$194$			2081.63i			0.770372i
$195$	1484.24	−	220.072i	0.545069	−	0.0808187i
$196$		−	1287.16i		−	0.469081i
$197$		−	2986.12i		−	1.07996i	−0.841678	−	0.539980i	$-0.818432\pi$
$197$		−	2986.12i		−	1.07996i	0.841678	−	0.539980i	$-0.181568\pi$
$198$	281.407	+	928.090i	0.101004	+	0.333114i
$199$	−3578.36			−1.27469			−0.637345	−	0.770579i	$-0.719967\pi$
$199$	−3578.36			−1.27469			−0.637345	+	0.770579i	$0.719967\pi$
$200$	−322.943	+	322.943i	−0.114178	+	0.114178i
$201$	799.016	−	118.472i	0.280389	−	0.0415740i
$202$			1027.88i			0.358026i
$203$	−656.420	−	293.962i	−0.226954	−	0.101636i
$204$	2130.91	+	1580.60i	0.731341	+	0.542470i
$205$	194.200	−	194.200i	0.0661634	−	0.0661634i
$206$	2494.98	+	2494.98i	0.843853	+	0.843853i
$207$	1605.63	+	5295.44i	0.539127	+	1.77806i
$208$		−	560.652i		−	0.186895i
$209$	−435.373			−0.144093
$210$	−234.974	+	316.785i	−0.0772132	+	0.104096i
$211$	3103.73	+	3103.73i	1.01265	+	1.01265i	0.999919	+	0.0127319i	$0.00405281\pi$
$211$	3103.73	+	3103.73i	1.01265	+	1.01265i	0.0127319	+	0.999919i	$0.495947\pi$
$212$	−971.239			−0.314646
$213$	248.169	+	1673.74i	0.0798323	+	0.538417i
$214$	1568.22	−	1568.22i	0.500941	−	0.500941i
$215$	−1631.12	+	1631.12i	−0.517403	+	0.517403i
$216$	−1056.69	−	378.312i	−0.332864	−	0.119171i
$217$	−315.931	+	315.931i	−0.0988331	+	0.0988331i
$218$	1405.40	−	1405.40i	0.436633	−	0.436633i
$219$	−3665.61	+	4941.86i	−1.13105	+	1.52484i
$220$	418.611	−	418.611i	0.128285	−	0.128285i
$221$	3162.82	−	3162.82i	0.962688	−	0.962688i
$222$	622.828	−	92.3482i	0.188295	−	0.0279189i
$223$	1938.81			0.582208			0.291104	−	0.956691i	$-0.405977\pi$
$223$	1938.81			0.582208			0.291104	+	0.956691i	$0.405977\pi$
$224$	104.210	+	104.210i	0.0310841	+	0.0310841i
$225$	1475.08	−	447.261i	0.437062	−	0.132522i
$226$	1362.48			0.401021
$227$			4862.54i			1.42175i	0.703316	+	0.710877i	$0.251702\pi$
$227$			4862.54i			1.42175i	−0.703316	+	0.710877i	$0.748298\pi$
$228$	300.173	−	404.684i	0.0871906	−	0.117548i
$229$	−4888.21	−	4888.21i	−1.41058	−	1.41058i	−0.755975	−	0.654601i	$-0.772837\pi$
$229$	−4888.21	−	4888.21i	−1.41058	−	1.41058i	−0.654601	−	0.755975i	$-0.727163\pi$
$230$	2388.48	−	2388.48i	0.684747	−	0.684747i
$231$	−256.044	+	345.191i	−0.0729285	+	0.0983199i
$232$	−1167.34	+	445.204i	−0.330344	+	0.125987i
$233$			4183.02i			1.17613i	0.808813	+	0.588066i	$0.200110\pi$
$233$			4183.02i			1.17613i	−0.808813	+	0.588066i	$0.799890\pi$
$234$	−892.185	+	1668.66i	−0.249248	+	0.466170i
$235$	3381.82	−	3381.82i	0.938747	−	0.938747i
$236$	176.552			0.0486973
$237$	−312.699	−	231.944i	−0.0857046	−	0.0635712i
$238$			1175.76i			0.320225i
$239$			3698.40i			1.00096i	0.865748	+	0.500481i	$0.166843\pi$
$239$			3698.40i			1.00096i	−0.865748	+	0.500481i	$0.833157\pi$
$240$	100.487	+	677.720i	0.0270267	+	0.182278i
$241$		−	1726.78i		−	0.461543i	−0.973008	−	0.230771i	$-0.925875\pi$
$241$		−	1726.78i		−	0.461543i	0.973008	−	0.230771i	$-0.0741250\pi$
$242$	−1426.17	+	1426.17i	−0.378834	+	0.378834i
$243$	2542.99	+	2807.51i	0.671328	+	0.741160i
$244$	613.436	+	613.436i	0.160948	+	0.160948i
$245$	2651.81			0.691502
$246$	50.7976	+	342.597i	0.0131656	+	0.0887933i
$247$	−600.655	−	600.655i	−0.154732	−	0.154732i
$248$			776.108i			0.198721i
$249$	−1842.71	+	273.223i	−0.468984	+	0.0695373i
$250$	−2122.11	−	2122.11i	−0.536857	−	0.536857i
$251$	−3371.95	−	3371.95i	−0.847949	−	0.847949i	0.141928	−	0.989877i	$-0.454670\pi$
$251$	−3371.95	−	3371.95i	−0.847949	−	0.847949i	−0.989877	+	0.141928i	$0.954670\pi$
$252$	−144.326	−	475.992i	−0.0360781	−	0.118987i
$253$	2602.66	−	2602.66i	0.646749	−	0.646749i
$254$	−699.259			−0.172738
$255$	−3256.35	+	4390.11i	−0.799689	+	1.07812i
$256$	256.000			0.0625000
$257$			3277.94i			0.795612i	0.917469	+	0.397806i	$0.130228\pi$
$257$			3277.94i			0.795612i	−0.917469	+	0.397806i	$0.869772\pi$
$258$	−426.659	−	2877.54i	−0.102956	−	0.694370i
$259$	197.305	+	197.305i	0.0473357	+	0.0473357i
$260$	1155.06			0.275514
$261$	4182.81	+	532.580i	0.991991	+	0.126306i
$262$	3182.05			0.750335
$263$	−3264.73	−	3264.73i	−0.765444	−	0.765444i	0.211857	−	0.977301i	$-0.432049\pi$
$263$	−3264.73	−	3264.73i	−0.765444	−	0.765444i	−0.977301	+	0.211857i	$0.932049\pi$
$264$	109.498	+	738.490i	0.0255270	+	0.172163i
$265$		−	2000.95i		−	0.463840i
$266$	223.291			0.0514694
$267$	−655.894	+	884.255i	−0.150337	+	0.202680i
$268$	621.807			0.141727
$269$	−4260.77	+	4260.77i	−0.965738	+	0.965738i	−0.999432	−	0.0336942i	$-0.989273\pi$
$269$	−4260.77	+	4260.77i	−0.965738	+	0.965738i	0.0336942	+	0.999432i	$0.489273\pi$
$270$	779.400	−	2177.00i	0.175677	−	0.490695i
$271$	−4452.91	−	4452.91i	−0.998137	−	0.998137i	0.00186146	−	0.999998i	$-0.499407\pi$
$271$	−4452.91	−	4452.91i	−0.998137	−	0.998137i	−0.999998	+	0.00186146i	$0.999407\pi$
$272$	1444.18	+	1444.18i	0.321934	+	0.321934i
$273$	−829.484	+	122.990i	−0.183892	+	0.0272662i
$274$		−	2738.35i		−	0.603758i
$275$	−724.989	−	724.989i	−0.158976	−	0.158976i
$276$	624.765	+	4213.63i	0.136255	+	0.918952i
$277$	2717.42			0.589436			0.294718	−	0.955584i	$-0.404774\pi$
$277$	2717.42			0.589436			0.294718	+	0.955584i	$0.404774\pi$
$278$	1606.10	+	1606.10i	0.346501	+	0.346501i
$279$	1235.05	−	2309.92i	0.265019	−	0.495668i
$280$	−214.694	+	214.694i	−0.0458230	+	0.0458230i
$281$		−	8233.18i		−	1.74787i	−0.486046	−	0.873933i	$-0.661561\pi$
$281$		−	8233.18i		−	1.74787i	0.486046	−	0.873933i	$-0.338439\pi$
$282$	884.596	+	5966.02i	0.186798	+	1.25983i
$283$		−	5347.60i		−	1.12326i	−0.827389	−	0.561629i	$-0.810175\pi$
$283$		−	5347.60i		−	1.12326i	0.827389	−	0.561629i	$-0.189825\pi$
$284$			1302.53i			0.272152i
$285$	833.732	+	618.418i	0.173284	+	0.128533i
$286$	1258.63			0.260225
$287$	−108.531	+	108.531i	−0.0223219	+	0.0223219i
$288$	−761.929	−	407.382i	−0.155893	−	0.0833514i
$289$			11381.1i			2.31653i
$290$	−917.211	−	2404.97i	−0.185726	−	0.486981i
$291$	3221.95	−	4343.73i	0.649051	−	0.875030i
$292$	−3349.24	+	3349.24i	−0.671230	+	0.671230i
$293$	2021.49	+	2021.49i	0.403061	+	0.403061i	0.879310	−	0.476249i	$-0.158004\pi$
$293$	2021.49	+	2021.49i	0.403061	+	0.403061i	−0.476249	+	0.879310i	$0.658004\pi$
$294$	−1992.27	+	2685.91i	−0.395209	+	0.532808i
$295$			363.733i			0.0717877i
$296$	484.695			0.0951768
$297$	849.289	−	2372.21i	0.165928	−	0.463466i
$298$	4859.28	+	4859.28i	0.944599	+	0.944599i
$299$	7181.42			1.38900
$300$	1173.74	−	174.033i	0.225886	−	0.0334926i
$301$	911.572	−	911.572i	0.174559	−	0.174559i
$302$	3240.86	−	3240.86i	0.617518	−	0.617518i
$303$	1590.95	−	2144.87i	0.301643	−	0.406666i
$304$	274.266	−	274.266i	0.0517441	−	0.0517441i
$305$	−1263.80	+	1263.80i	−0.237263	+	0.237263i
$306$	−2000.11	−	6596.45i	−0.373657	−	1.23233i
$307$	−682.192	+	682.192i	−0.126823	+	0.126823i	−0.767669	−	0.640846i	$-0.778584\pi$
$307$	−682.192	+	682.192i	−0.126823	+	0.126823i	0.640846	+	0.767669i	$0.278584\pi$
$308$	−233.946	+	233.946i	−0.0432802	+	0.0432802i
$309$	−1344.54	−	9068.02i	−0.247534	−	1.66945i
$310$	−1598.94			−0.292948
$311$	589.772	+	589.772i	0.107533	+	0.107533i	0.758826	−	0.651293i	$-0.225773\pi$
$311$	589.772	+	589.772i	0.107533	+	0.107533i	−0.651293	+	0.758826i	$0.725773\pi$
$312$	−867.779	+	1169.91i	−0.157462	+	0.212286i
$313$	9591.31			1.73205			0.866027	−	0.499998i	$-0.166666\pi$
$313$	9591.31			1.73205			0.866027	+	0.499998i	$0.166666\pi$
$314$			399.582i			0.0718144i
$315$	980.641	−	297.341i	0.175406	−	0.0531850i
$316$	−211.925	−	211.925i	−0.0377269	−	0.0377269i
$317$	−457.637	+	457.637i	−0.0810835	+	0.0810835i	−0.746485	−	0.665402i	$-0.768260\pi$
$317$	−457.637	+	457.637i	−0.0810835	+	0.0810835i	0.665402	+	0.746485i	$0.268260\pi$
$318$	2026.68	+	1503.29i	0.357392	+	0.265095i
$319$	−999.456	−	2620.62i	−0.175419	−	0.459957i
$320$			527.413i			0.0921352i
$321$	−5699.69	+	845.107i	−0.991046	+	0.146945i
$322$	−1334.83	+	1334.83i	−0.231016	+	0.231016i
$323$	3094.44			0.533062
$324$	1619.44	+	2424.97i	0.277682	+	0.415804i
$325$		−	2000.44i		−	0.341429i
$326$			1798.22i			0.305504i
$327$	−5107.94	+	757.366i	−0.863822	+	0.128081i
$328$			266.614i			0.0448820i
$329$	−1889.97	+	1889.97i	−0.316709	+	0.316709i
$330$	−1521.44	+	225.588i	−0.253796	+	0.0376309i
$331$	−601.873	−	601.873i	−0.0999455	−	0.0999455i	0.655366	−	0.755311i	$-0.272514\pi$
$331$	−601.873	−	601.873i	−0.0999455	−	0.0999455i	−0.755311	+	0.655366i	$0.772514\pi$
$332$	−1434.03			−0.237056
$333$	−1442.59	−	771.312i	−0.237398	−	0.126930i
$334$	−665.696	−	665.696i	−0.109058	−	0.109058i
$335$			1281.05i			0.208929i
$336$	−56.1584	−	378.752i	−0.00911813	−	0.0614958i
$337$	−2317.42	−	2317.42i	−0.374593	−	0.374593i	0.494554	−	0.869147i	$-0.335332\pi$
$337$	−2317.42	−	2317.42i	−0.374593	−	0.374593i	−0.869147	+	0.494554i	$0.835332\pi$
$338$	−1370.58	−	1370.58i	−0.220561	−	0.220561i
$339$	−2843.09	−	2108.85i	−0.455502	−	0.337867i
$340$	−2975.30	+	2975.30i	−0.474583	+	0.474583i
$341$	−1742.32			−0.276691
$342$	−1252.74	+	379.845i	−0.198072	+	0.0600574i
$343$	−3061.67			−0.481968
$344$		−	2239.35i		−	0.350981i
$345$	−8680.94	+	1287.14i	−1.35468	+	0.200862i
$346$	−2007.37	−	2007.37i	−0.311899	−	0.311899i
$347$	−9157.78			−1.41676			−0.708379	−	0.705832i	$-0.750573\pi$
$347$	−9157.78			−1.41676			−0.708379	+	0.705832i	$0.750573\pi$
$348$	3124.98	+	877.810i	0.481369	+	0.135217i
$349$	712.847			0.109335			0.0546673	−	0.998505i	$-0.482590\pi$
$349$	712.847			0.109335			0.0546673	+	0.998505i	$0.482590\pi$
$350$	371.827	+	371.827i	0.0567857	+	0.0567857i
$351$	4444.48	−	2101.07i	0.675865	−	0.319506i
$352$			574.705i			0.0870224i
$353$	10185.9			1.53581			0.767904	−	0.640565i	$-0.221300\pi$
$353$	10185.9			1.53581			0.767904	+	0.640565i	$0.221300\pi$
$354$	−368.411	−	273.268i	−0.0553130	−	0.0410283i
$355$	−2683.48			−0.401196
$356$	−599.284	+	599.284i	−0.0892191	+	0.0892191i
$357$	1819.85	−	2453.46i	0.269795	−	0.363729i
$358$	−1219.71	−	1219.71i	−0.180067	−	0.180067i
$359$	−6676.28	−	6676.28i	−0.981506	−	0.981506i	0.0183257	−	0.999832i	$-0.494166\pi$
$359$	−6676.28	−	6676.28i	−0.981506	−	0.981506i	−0.999832	+	0.0183257i	$0.994166\pi$
$360$	839.290	−	1569.73i	0.122873	−	0.229811i
$361$			6271.33i			0.914321i
$362$	−1218.66	−	1218.66i	−0.176937	−	0.176937i
$363$	5183.42	−	768.558i	0.749474	−	0.111126i
$364$	−645.518			−0.0929515
$365$	−6900.11	−	6900.11i	−0.989503	−	0.989503i
$366$	−330.578	−	2229.53i	−0.0472120	−	0.318414i
$367$	1458.99	−	1458.99i	0.207517	−	0.207517i	−0.595694	−	0.803211i	$-0.703123\pi$
$367$	1458.99	−	1458.99i	0.207517	−	0.207517i	0.803211	+	0.595694i	$0.203123\pi$
$368$			3279.12i			0.464499i
$369$	424.273	−	793.520i	0.0598557	−	0.111949i
$370$			998.571i			0.140306i
$371$			1118.26i			0.156488i
$372$	1201.26	−	1619.50i	0.167426	−	0.225719i
$373$	−5959.73			−0.827300			−0.413650	−	0.910436i	$-0.635746\pi$
$373$	−5959.73			−0.827300			−0.413650	+	0.910436i	$0.635746\pi$
$374$	−3242.09	+	3242.09i	−0.448248	+	0.448248i
$375$	1143.60	+	7712.83i	0.157481	+	1.06210i
$376$			4642.85i			0.636800i
$377$	2236.61	−	4994.37i	0.305547	−	0.682290i
$378$	−435.577	+	1216.64i	−0.0592690	+	0.165548i
$379$	5440.07	−	5440.07i	0.737303	−	0.737303i	−0.234753	−	0.972055i	$-0.575428\pi$
$379$	5440.07	−	5440.07i	0.737303	−	0.737303i	0.972055	+	0.234753i	$0.0754280\pi$
$380$	565.044	+	565.044i	0.0762793	+	0.0762793i
$381$	1459.14	+	1082.31i	0.196205	+	0.145534i
$382$			4540.73i			0.608178i
$383$	3194.01			0.426126			0.213063	−	0.977038i	$-0.431656\pi$
$383$	3194.01			0.426126			0.213063	+	0.977038i	$0.431656\pi$
$384$	−534.195	−	396.237i	−0.0709909	−	0.0526573i
$385$	−481.976	−	481.976i	−0.0638020	−	0.0638020i
$386$	−4363.57			−0.575388
$387$	−3563.55	+	6664.93i	−0.468076	+	0.875446i
$388$	2943.86	−	2943.86i	0.385186	−	0.385186i
$389$	3982.78	−	3982.78i	0.519113	−	0.519113i	−0.398190	−	0.917303i	$-0.630362\pi$
$389$	3982.78	−	3982.78i	0.519113	−	0.519113i	0.917303	+	0.398190i	$0.130362\pi$
$390$	−2410.26	−	1787.80i	−0.312944	−	0.232125i
$391$	−18498.5	+	18498.5i	−2.39261	+	2.39261i
$392$	−1820.32	+	1820.32i	−0.234541	+	0.234541i
$393$	−6639.98	−	4925.18i	−0.852271	−	0.632170i
$394$	−4223.01	+	4223.01i	−0.539980	+	0.539980i
$395$	436.609	−	436.609i	0.0556157	−	0.0556157i
$396$	914.548	−	1710.49i	0.116055	−	0.217059i
$397$	9302.53			1.17602			0.588011	−	0.808853i	$-0.299911\pi$
$397$	9302.53			1.17602			0.588011	+	0.808853i	$0.299911\pi$
$398$	5060.57	+	5060.57i	0.637345	+	0.637345i
$399$	−465.941	−	345.610i	−0.0584617	−	0.0433638i
$400$	913.422			0.114178
$401$			8886.30i			1.10663i	0.832971	+	0.553317i	$0.186638\pi$
$401$			8886.30i			1.10663i	−0.832971	+	0.553317i	$0.813362\pi$
$402$	−1297.52	−	962.434i	−0.160982	−	0.119408i
$403$	−2403.76	−	2403.76i	−0.297121	−	0.297121i
$404$	1453.64	−	1453.64i	0.179013	−	0.179013i
$405$	−4995.93	+	3336.38i	−0.612963	+	0.409348i
$406$	512.594	+	1344.04i	0.0626592	+	0.164295i
$407$			1088.11i			0.132520i
$408$	−778.261	−	5248.86i	−0.0944354	−	0.636905i
$409$	−5041.86	+	5041.86i	−0.609545	+	0.609545i	−0.942827	−	0.333282i	$-0.891844\pi$
$409$	−5041.86	+	5041.86i	−0.609545	+	0.609545i	0.333282	+	0.942827i	$0.391844\pi$
$410$	−549.280			−0.0661634
$411$	−4238.42	+	5714.10i	−0.508676	+	0.685781i
$412$		−	7056.88i		−	0.843853i
$413$		−	203.277i		−	0.0242194i
$414$	5218.17	−	9759.59i	0.619466	−	1.15859i
$415$		−	2954.39i		−	0.349458i
$416$	−792.882	+	792.882i	−0.0934477	+	0.0934477i
$417$	−865.520	−	5837.36i	−0.101642	−	0.685508i
$418$	615.710	+	615.710i	0.0720464	+	0.0720464i
$419$	1256.60			0.146513			0.0732565	−	0.997313i	$-0.476661\pi$
$419$	1256.60			0.146513			0.0732565	+	0.997313i	$0.476661\pi$
$420$	780.306	−	115.698i	0.0906548	−	0.0134416i
$421$	−62.6636	−	62.6636i	−0.00725424	−	0.00725424i	0.703470	−	0.710725i	$-0.251633\pi$
$421$	−62.6636	−	62.6636i	−0.00725424	−	0.00725424i	−0.710725	+	0.703470i	$0.751633\pi$
$422$		−	8778.66i		−	1.01265i
$423$	7388.33	−	13818.5i	0.849251	−	1.58836i
$424$	1373.54	+	1373.54i	0.157323	+	0.157323i
$425$	5152.90	+	5152.90i	0.588123	+	0.588123i
$426$	2016.06	−	2717.99i	0.229292	−	0.309125i
$427$	706.292	−	706.292i	0.0800465	−	0.0800465i
$428$	−4435.59			−0.500941
$429$	−2626.38	−	1948.11i	−0.295578	−	0.219244i
$430$	4613.51			0.517403
$431$		−	15119.7i		−	1.68976i	−0.534953	−	0.844882i	$-0.679671\pi$
$431$		−	15119.7i		−	1.68976i	0.534953	−	0.844882i	$-0.320329\pi$
$432$	959.370	+	2029.40i	0.106847	+	0.226017i
$433$	3031.13	+	3031.13i	0.336413	+	0.336413i	0.855016	−	0.518602i	$-0.173547\pi$
$433$	3031.13	+	3031.13i	0.336413	+	0.336413i	−0.518602	+	0.855016i	$0.673547\pi$
$434$	893.587			0.0988331
$435$	−1808.47	+	6438.10i	−0.199332	+	0.709617i
$436$	−3975.08			−0.436633
$437$	3513.08	+	3513.08i	0.384562	+	0.384562i
$438$	12172.8	−	1804.89i	1.32794	−	0.196897i
$439$			9089.77i			0.988226i	0.869398	+	0.494113i	$0.164507\pi$
$439$			9089.77i			0.988226i	−0.869398	+	0.494113i	$0.835493\pi$
$440$	−1184.01			−0.128285
$441$	8314.52	−	2521.05i	0.897799	−	0.272222i
$442$	−8945.79			−0.962688
$443$	6878.83	−	6878.83i	0.737750	−	0.737750i	−0.234392	−	0.972142i	$-0.575310\pi$
$443$	6878.83	−	6878.83i	0.737750	−	0.737750i	0.972142	+	0.234392i	$0.0753101\pi$
$444$	−1011.41	−	750.212i	−0.108107	−	0.0801880i
$445$	−1234.65	−	1234.65i	−0.131524	−	0.131524i
$446$	−2741.89	−	2741.89i	−0.291104	−	0.291104i
$447$	−2618.65	−	17661.1i	−0.277087	−	1.86877i
$448$		−	294.751i		−	0.0310841i
$449$	10181.2	+	10181.2i	1.07011	+	1.07011i	0.997349	+	0.0727619i	$0.0231813\pi$
$449$	10181.2	+	10181.2i	1.07011	+	1.07011i	0.0727619	+	0.997349i	$0.476819\pi$
$450$	−2718.61	−	1453.56i	−0.284792	−	0.152270i
$451$	−598.534			−0.0624919
$452$	−1926.84	−	1926.84i	−0.200511	−	0.200511i
$453$	−11778.9	+	1746.49i	−1.22168	+	0.181141i
$454$	6876.67	−	6876.67i	0.710877	−	0.710877i
$455$		−	1329.90i		−	0.137026i
$456$	−996.819	+	147.801i	−0.102369	+	0.0151785i
$457$			7606.81i			0.778625i	0.921106	+	0.389313i	$0.127287\pi$
$457$			7606.81i			0.778625i	−0.921106	+	0.389313i	$0.872713\pi$
$458$			13825.9i			1.41058i
$459$	−6036.37	+	16860.6i	−0.613842	+	1.71456i
$460$	−6755.65			−0.684747
$461$	−6387.87	+	6387.87i	−0.645364	+	0.645364i	−0.951869	−	0.306505i	$-0.900840\pi$
$461$	−6387.87	+	6387.87i	−0.645364	+	0.645364i	0.306505	+	0.951869i	$0.400840\pi$
$462$	850.275	−	126.072i	0.0856242	−	0.0126957i
$463$			9518.04i			0.955380i	0.878529	+	0.477690i	$0.158526\pi$
$463$			9518.04i			0.955380i	−0.878529	+	0.477690i	$0.841474\pi$
$464$	2280.49	+	1021.26i	0.228166	+	0.102178i
$465$	3336.51	+	2474.84i	0.332746	+	0.246813i
$466$	5915.68	−	5915.68i	0.588066	−	0.588066i
$467$	−6859.88	−	6859.88i	−0.679738	−	0.679738i	0.280203	−	0.959941i	$-0.409598\pi$
$467$	−6859.88	−	6859.88i	−0.679738	−	0.679738i	−0.959941	+	0.280203i	$0.909598\pi$
$468$	3621.58	−	1098.10i	0.357709	−	0.108461i
$469$		−	715.930i		−	0.0704873i
$470$	−9565.23			−0.938747
$471$	618.474	−	833.807i	0.0605048	−	0.0815707i
$472$	−249.682	−	249.682i	−0.0243486	−	0.0243486i
$473$	5027.20			0.488691
$474$	114.206	+	770.242i	0.0110667	+	0.0746379i
$475$	978.595	−	978.595i	0.0945285	−	0.0945285i
$476$	1662.78	−	1662.78i	0.160112	−	0.160112i
$477$	−1902.29	−	6273.81i	−0.182599	−	0.602218i
$478$	5230.33	−	5230.33i	0.500481	−	0.500481i
$479$	4237.88	−	4237.88i	0.404245	−	0.404245i	−0.475481	−	0.879726i	$-0.657726\pi$
$479$	4237.88	−	4237.88i	0.404245	−	0.404245i	0.879726	+	0.475481i	$0.157726\pi$
$480$	816.330	−	1100.55i	0.0776254	−	0.104652i
$481$	−1501.19	+	1501.19i	−0.142305	+	0.142305i
$482$	−2442.04	+	2442.04i	−0.230771	+	0.230771i
$483$	4851.45	−	719.335i	0.457036	−	0.0677658i
$484$	4033.82			0.378834
$485$	6064.97	+	6064.97i	0.567827	+	0.567827i
$486$	374.092	−	7566.75i	0.0349159	−	0.706244i
$487$	9488.03			0.882841			0.441421	−	0.897300i	$-0.354475\pi$
$487$	9488.03			0.882841			0.441421	+	0.897300i	$0.354475\pi$
$488$		−	1735.06i		−	0.160948i
$489$	2783.29	−	3752.34i	0.257392	−	0.347008i
$490$	−3750.23	−	3750.23i	−0.345751	−	0.345751i
$491$	3090.67	−	3090.67i	0.284074	−	0.284074i	−0.550658	−	0.834731i	$-0.685623\pi$
$491$	3090.67	−	3090.67i	0.284074	−	0.284074i	0.834731	+	0.550658i	$0.185623\pi$
$492$	412.666	−	556.343i	0.0378139	−	0.0509795i
$493$	7103.69	+	18626.2i	0.648954	+	1.70158i
$494$			1698.91i			0.154732i
$495$	3523.95	+	1884.16i	0.319980	+	0.171084i
$496$	1097.58	−	1097.58i	0.0993607	−	0.0993607i
$497$	1499.70			0.135353
$498$	2992.38	+	2219.59i	0.269261	+	0.199723i
$499$		−	11969.9i		−	1.07384i	−0.843634	−	0.536918i	$-0.819588\pi$
$499$		−	11969.9i		−	1.07384i	0.843634	−	0.536918i	$-0.180412\pi$
$500$			6002.25i			0.536857i
$501$	358.741	+	2419.47i	0.0319907	+	0.215756i
$502$			9537.30i			0.847949i
$503$	−9938.85	+	9938.85i	−0.881017	+	0.881017i	−0.993638	−	0.112621i	$-0.964075\pi$
$503$	−9938.85	+	9938.85i	−0.881017	+	0.881017i	0.112621	+	0.993638i	$0.464075\pi$
$504$	−469.047	+	877.262i	−0.0414544	+	0.0775325i
$505$	2994.80	+	2994.80i	0.263894	+	0.263894i
$506$	−7361.42			−0.646749
$507$	738.599	+	4981.37i	0.0646989	+	0.436352i
$508$	988.901	+	988.901i	0.0863689	+	0.0863689i
$509$			16304.4i			1.41981i	0.704300	+	0.709903i	$0.251261\pi$
$509$			16304.4i			1.41981i	−0.704300	+	0.709903i	$0.748739\pi$
$510$	10813.7	−	1603.38i	0.938902	−	0.139213i
$511$	3856.21	+	3856.21i	0.333833	+	0.333833i
$512$	−362.039	−	362.039i	−0.0312500	−	0.0312500i
$513$	3202.02	+	1146.38i	0.275580	+	0.0986622i
$514$	4635.71	−	4635.71i	0.397806	−	0.397806i
$515$	14538.6			1.24398
$516$	−3466.06	+	4672.84i	−0.295707	+	0.398663i
$517$	−10422.9			−0.886654
$518$		−	558.063i		−	0.0473357i
$519$	1081.77	+	7295.80i	0.0914918	+	0.617052i
$520$	−1633.50	−	1633.50i	−0.137757	−	0.137757i
$521$	−867.452			−0.0729438			−0.0364719	−	0.999335i	$-0.511612\pi$
$521$	−867.452			−0.0729438			−0.0364719	+	0.999335i	$0.511612\pi$
$522$	−5162.21	−	6668.57i	−0.432843	−	0.559149i
$523$	21914.3			1.83221			0.916107	−	0.400935i	$-0.131315\pi$
$523$	21914.3			1.83221			0.916107	+	0.400935i	$0.131315\pi$
$524$	−4500.10	−	4500.10i	−0.375167	−	0.375167i
$525$	−200.376	−	1351.41i	−0.0166574	−	0.112343i
$526$			9234.04i			0.765444i
$527$	12383.6			1.02360
$528$	889.530	−	1199.24i	0.0733178	−	0.0988448i
$529$	−29835.3			−2.45215
$530$	−2829.77	+	2829.77i	−0.231920	+	0.231920i
$531$	345.798	+	1140.45i	0.0282606	+	0.0932043i
$532$	−315.781	−	315.781i	−0.0257347	−	0.0257347i
$533$	−825.756	−	825.756i	−0.0671060	−	0.0671060i
$534$	2178.10	−	322.952i	0.176509	−	0.0261713i
$535$		−	9138.23i		−	0.738468i
$536$	−879.368	−	879.368i	−0.0708636	−	0.0708636i
$537$	657.299	+	4433.05i	0.0528203	+	0.356239i
$538$	12051.3			0.965738
$539$	−4086.50	−	4086.50i	−0.326564	−	0.326564i
$540$	−4180.98	+	1976.50i	−0.333186	+	0.157509i
$541$	8072.98	−	8072.98i	0.641561	−	0.641561i	−0.309378	−	0.950939i	$-0.600121\pi$
$541$	8072.98	−	8072.98i	0.641561	−	0.641561i	0.950939	+	0.309378i	$0.100121\pi$
$542$			12594.7i			0.998137i
$543$	656.729	+	4429.21i	0.0519023	+	0.350047i
$544$		−	4084.75i		−	0.321934i
$545$		−	8189.49i		−	0.643668i
$546$	1347.00	+	999.134i	0.105579	+	0.0783132i
$547$	19144.5			1.49645			0.748225	−	0.663445i	$-0.230906\pi$
$547$	19144.5			1.49645			0.748225	+	0.663445i	$0.230906\pi$
$548$	−3872.61	+	3872.61i	−0.301879	+	0.301879i
$549$	−2761.06	+	5164.03i	−0.214643	+	0.401449i
$550$			2050.58i			0.158976i
$551$	3537.33	−	1349.07i	0.273494	−	0.104306i
$552$	5075.42	−	6842.52i	0.391348	−	0.527604i
$553$	−244.004	+	244.004i	−0.0187633	+	0.0187633i
$554$	−3843.01	−	3843.01i	−0.294718	−	0.294718i
$555$	1545.59	−	2083.72i	0.118210	−	0.159367i
$556$		−	4542.73i		−	0.346501i
$557$	−10070.8			−0.766096			−0.383048	−	0.923729i	$-0.625126\pi$
$557$	−10070.8			−0.766096			−0.383048	+	0.923729i	$0.625126\pi$
$558$	−5013.34	+	1520.10i	−0.380343	+	0.115324i
$559$	6935.69	+	6935.69i	0.524773	+	0.524773i
$560$	607.247			0.0458230
$561$	11783.4	−	1747.15i	0.886800	−	0.131488i
$562$	−11643.5	+	11643.5i	−0.873933	+	0.873933i
$563$	8696.58	−	8696.58i	0.651007	−	0.651007i	−0.302228	−	0.953236i	$-0.597730\pi$
$563$	8696.58	−	8696.58i	0.651007	−	0.651007i	0.953236	+	0.302228i	$0.0977304\pi$
$564$	7186.22	−	9688.23i	0.536515	−	0.723312i
$565$	3969.68	−	3969.68i	0.295585	−	0.295585i
$566$	−7562.65	+	7562.65i	−0.561629	+	0.561629i
$567$	2792.04	−	1864.57i	0.206798	−	0.138104i
$568$	1842.06	−	1842.06i	0.136076	−	0.136076i
$569$	6753.06	−	6753.06i	0.497545	−	0.497545i	−0.413128	−	0.910673i	$-0.635564\pi$
$569$	6753.06	−	6753.06i	0.497545	−	0.497545i	0.910673	+	0.413128i	$0.135564\pi$
$570$	−304.500	−	2053.65i	−0.0223756	−	0.150909i
$571$	−8878.30			−0.650692			−0.325346	−	0.945595i	$-0.605481\pi$
$571$	−8878.30			−0.650692			−0.325346	+	0.945595i	$0.605481\pi$
$572$	−1779.97	−	1779.97i	−0.130113	−	0.130113i
$573$	7028.15	−	9475.13i	0.512400	−	0.690802i
$574$	306.972			0.0223219
$575$			11700.1i			0.848568i
$576$	501.406	+	1653.66i	0.0362707	+	0.119622i
$577$	−3505.86	−	3505.86i	−0.252948	−	0.252948i	0.569230	−	0.822178i	$-0.307241\pi$
$577$	−3505.86	−	3505.86i	−0.252948	−	0.252948i	−0.822178	+	0.569230i	$0.807241\pi$
$578$	16095.3	−	16095.3i	1.15827	−	1.15827i
$579$	9105.45	+	6753.94i	0.653557	+	0.484774i
$580$	−2104.00	+	4698.27i	−0.150628	+	0.336353i
$581$			1651.09i			0.117898i
$582$	−10699.5	+	1586.44i	−0.762041	+	0.112990i
$583$	−3083.52	+	3083.52i	−0.219050	+	0.219050i
$584$	9473.07			0.671230
$585$	2262.32	+	7461.21i	0.159889	+	0.527321i
$586$		−	5717.65i		−	0.403061i
$587$			964.987i			0.0678522i	0.999424	+	0.0339261i	$0.0108011\pi$
$587$			964.987i			0.0678522i	−0.999424	+	0.0339261i	$0.989199\pi$
$588$	6615.94	−	980.961i	0.464008	−	0.0687996i
$589$		−	2351.79i		−	0.164523i
$590$	514.397	−	514.397i	0.0358939	−	0.0358939i
$591$	15348.5	−	2275.76i	1.06828	−	0.158396i
$592$	−685.462	−	685.462i	−0.0475884	−	0.0475884i
$593$	−3231.55			−0.223784			−0.111892	−	0.993720i	$-0.535691\pi$
$593$	−3231.55			−0.223784			−0.111892	+	0.993720i	$0.535691\pi$
$594$	−4555.88	+	2153.73i	−0.314697	+	0.148769i
$595$	3425.67	+	3425.67i	0.236032	+	0.236032i
$596$		−	13744.1i		−	0.944599i
$597$	−2727.12	−	18392.6i	−0.186957	−	1.26090i
$598$	−10156.1	−	10156.1i	−0.694502	−	0.694502i
$599$	−17636.4	−	17636.4i	−1.20301	−	1.20301i	−0.973246	−	0.229765i	$-0.926204\pi$
$599$	−17636.4	−	17636.4i	−1.20301	−	1.20301i	−0.229765	−	0.973246i	$-0.573796\pi$
$600$	−1906.04	−	1413.80i	−0.129689	−	0.0961967i
$601$	−17742.0	+	17742.0i	−1.20418	+	1.20418i	−0.231295	+	0.972884i	$0.574296\pi$
$601$	−17742.0	+	17742.0i	−1.20418	+	1.20418i	−0.972884	+	0.231295i	$0.925704\pi$
$602$	−2578.31			−0.174559
$603$	1217.88	+	4016.62i	0.0822487	+	0.271259i
$604$	−9166.53			−0.617518
$605$			8310.50i			0.558462i
$606$	−5283.25	+	783.361i	−0.354154	+	0.0525113i
$607$	212.781	+	212.781i	0.0142282	+	0.0142282i	0.714185	−	0.699957i	$-0.246797\pi$
$607$	212.781	+	212.781i	0.0142282	+	0.0142282i	−0.699957	+	0.714185i	$0.746797\pi$
$608$	−775.740			−0.0517441
$609$	1010.68	−	3598.01i	0.0672496	−	0.239407i
$610$	3574.58			0.237263
$611$	−14379.8	−	14379.8i	−0.952120	−	0.952120i
$612$	−6500.20	+	12157.4i	−0.429338	+	0.802995i
$613$		−	22134.7i		−	1.45842i	−0.684291	−	0.729209i	$-0.739888\pi$
$613$		−	22134.7i		−	1.45842i	0.684291	−	0.729209i	$-0.260112\pi$
$614$	1929.53			0.126823
$615$	1146.18	+	850.177i	0.0751520	+	0.0557438i
$616$	661.698			0.0432802
$617$	12934.9	−	12934.9i	0.843987	−	0.843987i	−0.145387	−	0.989375i	$-0.546443\pi$
$617$	12934.9	−	12934.9i	0.843987	−	0.843987i	0.989375	+	0.145387i	$0.0464428\pi$
$618$	−10922.6	+	14725.6i	−0.710960	+	0.958494i
$619$	−857.139	−	857.139i	−0.0556564	−	0.0556564i	0.678731	−	0.734387i	$-0.262530\pi$
$619$	−857.139	−	857.139i	−0.0556564	−	0.0556564i	−0.734387	+	0.678731i	$0.762530\pi$
$620$	2261.24	+	2261.24i	0.146474	+	0.146474i
$621$	−25994.7	+	12288.6i	−1.67976	+	0.794082i
$622$		−	1668.13i		−	0.107533i
$623$	689.998	+	689.998i	0.0443727	+	0.0443727i
$624$	2881.73	−	427.281i	0.184874	−	0.0274117i
$625$	−5229.75			−0.334704
$626$	−13564.2	−	13564.2i	−0.866027	−	0.866027i
$627$	−331.804	−	2237.80i	−0.0211339	−	0.142534i
$628$	565.094	−	565.094i	0.0359072	−	0.0359072i
$629$		−	7733.82i		−	0.490250i
$630$	−1807.34	−	966.333i	−0.114295	−	0.0611105i
$631$			13527.0i			0.853410i	0.904391	+	0.426705i	$0.140326\pi$
$631$			13527.0i			0.853410i	−0.904391	+	0.426705i	$0.859674\pi$
$632$			599.414i			0.0377269i
$633$	−13587.6	+	18318.4i	−0.853175	+	1.15022i
$634$	1294.39			0.0810835
$635$	−2037.34	+	2037.34i	−0.127322	+	0.127322i
$636$	−740.195	−	4992.13i	−0.0461488	−	0.311243i
$637$		−	11275.8i		−	0.701352i
$638$	−2292.67	+	5119.56i	−0.142269	+	0.317688i
$639$	−8413.82	+	2551.16i	−0.520885	+	0.157938i
$640$	745.874	−	745.874i	0.0460676	−	0.0460676i
$641$	−1777.13	−	1777.13i	−0.109504	−	0.109504i	0.650232	−	0.759736i	$-0.274672\pi$
$641$	−1777.13	−	1777.13i	−0.109504	−	0.109504i	−0.759736	+	0.650232i	$0.774672\pi$
$642$	9255.75	+	6865.42i	0.568996	+	0.422051i
$643$			6490.78i			0.398089i	0.979990	+	0.199045i	$0.0637838\pi$
$643$			6490.78i			0.398089i	−0.979990	+	0.199045i	$0.936216\pi$
$644$	3775.47			0.231016
$645$	−9627.00	−	7140.80i	−0.587694	−	0.435921i
$646$	−4376.20	−	4376.20i	−0.266531	−	0.266531i
$647$	6133.94			0.372720			0.186360	−	0.982481i	$-0.440331\pi$
$647$	6133.94			0.372720			0.186360	+	0.982481i	$0.440331\pi$
$648$	1139.19	−	5719.66i	0.0690612	−	0.346743i
$649$	560.522	−	560.522i	0.0339020	−	0.0339020i
$650$	−2829.05	+	2829.05i	−0.170714	+	0.170714i
$651$	−1864.65	−	1383.10i	−0.112260	−	0.0832685i
$652$	2543.07	−	2543.07i	0.152752	−	0.152752i
$653$	−9675.82	+	9675.82i	−0.579853	+	0.579853i	−0.934863	−	0.355009i	$-0.884478\pi$
$653$	−9675.82	+	9675.82i	−0.579853	+	0.579853i	0.355009	+	0.934863i	$0.384478\pi$
$654$	8294.80	+	6152.64i	0.495951	+	0.367871i
$655$	9271.12	−	9271.12i	0.553058	−	0.553058i
$656$	377.050	−	377.050i	0.0224410	−	0.0224410i
$657$	−28194.6	−	15074.8i	−1.67424	−	0.895167i
$658$	5345.64			0.316709
$659$	−19410.7	−	19410.7i	−1.14740	−	1.14740i	−0.987063	−	0.160335i	$-0.948743\pi$
$659$	−19410.7	−	19410.7i	−1.14740	−	1.14740i	−0.160335	−	0.987063i	$-0.551257\pi$
$660$	2470.67	+	1832.61i	0.145713	+	0.108082i
$661$	−17947.3			−1.05608			−0.528040	−	0.849219i	$-0.677073\pi$
$661$	−17947.3			−1.05608			−0.528040	+	0.849219i	$0.677073\pi$
$662$			1702.35i			0.0999455i
$663$	18667.2	+	13846.3i	1.09347	+	0.811081i
$664$	2028.02	+	2028.02i	0.118528	+	0.118528i
$665$	650.574	−	650.574i	0.0379371	−	0.0379371i
$666$	949.332	+	3130.93i	0.0552340	+	0.182164i
$667$	−13081.4	+	29210.8i	−0.759388	+	1.69572i
$668$			1882.87i			0.109058i
$669$	1477.59	+	9965.41i	0.0853918	+	0.575912i
$670$	1811.68	−	1811.68i	0.104465	−	0.104465i
$671$	3895.11			0.224097
$672$	−456.216	+	615.056i	−0.0261888	+	0.0353070i
$673$		−	12839.7i		−	0.735412i	−0.929942	−	0.367706i	$-0.880143\pi$
$673$		−	12839.7i		−	0.735412i	0.929942	−	0.367706i	$-0.119857\pi$
$674$			6554.66i			0.374593i
$675$	3423.08	+	7241.00i	0.195192	+	0.412898i
$676$			3876.58i			0.220561i
$677$	−19449.8	+	19449.8i	−1.10416	+	1.10416i	−0.110256	+	0.993903i	$0.535167\pi$
$677$	−19449.8	+	19449.8i	−1.10416	+	1.10416i	−0.993903	+	0.110256i	$0.964833\pi$
$678$	1038.37	+	7003.09i	0.0588174	+	0.396685i
$679$	−3389.48	−	3389.48i	−0.191570	−	0.191570i
$680$	8415.42			0.474583
$681$	−24993.3	+	3705.81i	−1.40638	+	0.208527i
$682$	2464.01	+	2464.01i	0.138346	+	0.138346i
$683$			10360.6i			0.580437i	0.956960	+	0.290218i	$0.0937279\pi$
$683$			10360.6i			0.580437i	−0.956960	+	0.290218i	$0.906272\pi$
$684$	2308.83	+	1234.46i	0.129065	+	0.0690071i
$685$	−7978.36	−	7978.36i	−0.445018	−	0.445018i
$686$	4329.86	+	4329.86i	0.240984	+	0.240984i
$687$	21399.8	−	28850.6i	1.18843	−	1.60221i
$688$	−3166.91	+	3166.91i	−0.175490	+	0.175490i
$689$	−8508.24			−0.470447
$690$	14097.0	+	10456.4i	0.777774	+	0.576911i
$691$	−21300.4			−1.17265			−0.586327	−	0.810075i	$-0.699427\pi$
$691$	−21300.4			−1.17265			−0.586327	+	0.810075i	$0.699427\pi$
$692$			5677.71i			0.311899i
$693$	−1969.40	−	1052.98i	−0.107953	−	0.0577194i
$694$	12951.1	+	12951.1i	0.708379	+	0.708379i
$695$	9358.96			0.510799
$696$	−3177.98	−	5660.80i	−0.173076	−	0.308293i
$697$	4254.11			0.231185
$698$	−1008.12	−	1008.12i	−0.0546673	−	0.0546673i
$699$	−21500.6	+	3187.94i	−1.16341	+	0.172502i
$700$		−	1051.69i		−	0.0567857i
$701$	26053.1			1.40372			0.701862	−	0.712313i	$-0.252352\pi$
$701$	26053.1			1.40372			0.701862	+	0.712313i	$0.252352\pi$
$702$	−9256.80	−	3314.09i	−0.497686	−	0.178180i
$703$	−1468.74			−0.0787974
$704$	812.756	−	812.756i	0.0435112	−	0.0435112i
$705$	19959.7	+	14805.1i	1.06628	+	0.790910i
$706$	−14405.0	−	14405.0i	−0.767904	−	0.767904i
$707$	−1673.68	−	1673.68i	−0.0890313	−	0.0890313i
$708$	134.553	+	907.470i	0.00714238	+	0.0481707i
$709$		−	22513.4i		−	1.19254i	−0.802785	−	0.596268i	$-0.796649\pi$
$709$		−	22513.4i		−	1.19254i	0.802785	−	0.596268i	$-0.203351\pi$
$710$	3795.02	+	3795.02i	0.200598	+	0.200598i
$711$	953.869	−	1784.03i	0.0503135	−	0.0941017i
$712$	1695.03			0.0892191
$713$	14059.0	+	14059.0i	0.738447	+	0.738447i
$714$	−6043.38	+	896.066i	−0.316762	+	0.0469670i
$715$	3667.11	−	3667.11i	0.191807	−	0.191807i
$716$			3449.87i			0.180067i
$717$	−19009.6	+	2818.61i	−0.990137	+	0.146810i
$718$			18883.4i			0.981506i
$719$		−	30026.4i		−	1.55743i	−0.627376	−	0.778717i	$-0.715871\pi$
$719$		−	30026.4i		−	1.55743i	0.627376	−	0.778717i	$-0.284129\pi$
$720$	−3406.87	+	1033.00i	−0.176342	+	0.0534689i
$721$	−8125.07			−0.419686
$722$	8869.00	−	8869.00i	0.457161	−	0.457161i
$723$	8875.59	−	1316.00i	0.456552	−	0.0676940i
$724$			3446.88i			0.176937i
$725$	8136.90	+	3643.91i	0.416823	+	0.186664i
$726$	−8417.37	−	6243.56i	−0.430300	−	0.319174i
$727$	15853.5	−	15853.5i	0.808765	−	0.808765i	−0.175682	−	0.984447i	$-0.556213\pi$
$727$	15853.5	−	15853.5i	0.808765	−	0.808765i	0.984447	+	0.175682i	$0.0562130\pi$
$728$	912.900	+	912.900i	0.0464757	+	0.0464757i
$729$	−12492.4	+	15210.5i	−0.634682	+	0.772773i
$730$			19516.5i			0.989503i
$731$	−35731.1			−1.80788
$732$	−2685.53	+	3620.54i	−0.135601	+	0.182813i
$733$	−6978.55	−	6978.55i	−0.351649	−	0.351649i	0.509074	−	0.860723i	$-0.329988\pi$
$733$	−6978.55	−	6978.55i	−0.351649	−	0.351649i	−0.860723	+	0.509074i	$0.829988\pi$
$734$	−4126.65			−0.207517
$735$	2020.98	+	13630.2i	0.101422	+	0.684024i
$736$	4637.37	−	4637.37i	0.232250	−	0.232250i
$737$	1974.13	−	1974.13i	0.0986676	−	0.0986676i
$738$	−1722.22	+	522.195i	−0.0859021	+	0.0260464i
$739$	22616.9	−	22616.9i	1.12581	−	1.12581i	0.134963	−	0.990851i	$-0.456908\pi$
$739$	22616.9	−	22616.9i	1.12581	−	1.12581i	0.990851	−	0.134963i	$-0.0430916\pi$
$740$	1412.19	−	1412.19i	0.0701530	−	0.0701530i
$741$	2629.57	−	3545.11i	0.130364	−	0.175753i
$742$	1581.45	−	1581.45i	0.0782438	−	0.0782438i
$743$	−16618.7	+	16618.7i	−0.820568	+	0.820568i	−0.986189	−	0.165621i	$-0.947037\pi$
$743$	−16618.7	+	16618.7i	−0.820568	+	0.820568i	0.165621	+	0.986189i	$0.447037\pi$
$744$	−3989.16	+	591.483i	−0.196572	+	0.0291462i
$745$	28315.7			1.39249
$746$	8428.33	+	8428.33i	0.413650	+	0.413650i
$747$	−2808.71	−	9263.23i	−0.137571	−	0.453713i
$748$	9170.02			0.448248
$749$			5107.01i			0.249140i
$750$	9290.29	−	12524.9i	0.452311	−	0.609792i
$751$	−25543.5	−	25543.5i	−1.24114	−	1.24114i	−0.959529	−	0.281610i	$-0.909132\pi$
$751$	−25543.5	−	25543.5i	−1.24114	−	1.24114i	−0.281610	−	0.959529i	$-0.590868\pi$
$752$	6565.99	−	6565.99i	0.318400	−	0.318400i
$753$	14761.9	−	19901.5i	0.714412	−	0.963147i
$754$	−10226.1	+	3900.07i	−0.493918	+	0.188372i
$755$		−	18884.9i		−	0.910322i
$756$	2336.59	−	1104.59i	0.112409	−	0.0531396i
$757$	13680.4	−	13680.4i	0.656833	−	0.656833i	−0.297796	−	0.954629i	$-0.596252\pi$
$757$	13680.4	−	13680.4i	0.656833	−	0.656833i	0.954629	+	0.297796i	$0.0962516\pi$
$758$	−15386.8			−0.737303
$759$	15361.1	+	11394.0i	0.734613	+	0.544897i
$760$		−	1598.18i		−	0.0762793i
$761$			30151.3i			1.43624i	0.695917	+	0.718122i	$0.254998\pi$
$761$			30151.3i			1.43624i	−0.695917	+	0.718122i	$0.745002\pi$
$762$	−532.915	−	3594.16i	−0.0253353	−	0.170870i
$763$			4576.79i			0.217157i
$764$	6421.56	−	6421.56i	0.304089	−	0.304089i
$765$	−25046.7	−	13391.7i	−1.18375	−	0.632915i
$766$	−4517.01	−	4517.01i	−0.213063	−	0.213063i
$767$	1546.63			0.0728104
$768$	195.101	+	1315.83i	0.00916681	+	0.0618241i
$769$	−20123.2	−	20123.2i	−0.943641	−	0.943641i	0.0548535	−	0.998494i	$-0.482531\pi$
$769$	−20123.2	−	20123.2i	−0.943641	−	0.943641i	−0.998494	+	0.0548535i	$0.982531\pi$
$770$			1363.23i			0.0638020i
$771$	−16848.5	+	2498.17i	−0.787008	+	0.116692i
$772$	6171.02	+	6171.02i	0.287694	+	0.287694i
$773$	−8756.08	−	8756.08i	−0.407418	−	0.407418i	0.473419	−	0.880837i	$-0.343020\pi$
$773$	−8756.08	−	8756.08i	−0.407418	−	0.407418i	−0.880837	+	0.473419i	$0.843020\pi$
$774$	14465.3	−	4386.02i	0.671761	−	0.203685i
$775$	3916.23	−	3916.23i	0.181516	−	0.181516i
$776$	−8326.51			−0.385186
$777$	−863.771	+	1164.51i	−0.0398811	+	0.0537664i
$778$	−11265.0			−0.519113
$779$		−	807.904i		−	0.0371581i
$780$	880.286	+	5936.95i	0.0404094	+	0.272535i
$781$	4135.31	+	4135.31i	0.189466	+	0.189466i
$782$	52321.7			2.39261
$783$	450.344	+	21905.4i	0.0205543	+	0.999789i
$784$	5148.63			0.234541
$785$	1164.21	+	1164.21i	0.0529330	+	0.0529330i
$786$	2425.08	+	16355.6i	0.110051	+	0.742220i
$787$			17263.1i			0.781910i	0.920410	+	0.390955i	$0.127855\pi$
$787$			17263.1i			0.781910i	−0.920410	+	0.390955i	$0.872145\pi$
$788$	11944.5			0.539980
$789$	14292.5	−	19268.7i	0.644899	−	0.869433i
$790$	−1234.92			−0.0556157
$791$	−2218.50	+	2218.50i	−0.0997230	+	0.0997230i
$792$	−3712.36	+	1125.63i	−0.166557	+	0.0505018i
$793$	5373.82	+	5373.82i	0.240643	+	0.240643i
$794$	−13155.8	−	13155.8i	−0.588011	−	0.588011i
$795$	10284.8	−	1524.95i	0.458823	−	0.0680308i
$796$		−	14313.4i		−	0.637345i
$797$	−9765.83	−	9765.83i	−0.434032	−	0.434032i	0.455965	−	0.889998i	$-0.349294\pi$
$797$	−9765.83	−	9765.83i	−0.434032	−	0.434032i	−0.889998	+	0.455965i	$0.849294\pi$
$798$	170.173	+	1147.71i	0.00754895	+	0.0509128i
$799$	74081.6			3.28012
$800$	−1291.77	−	1291.77i	−0.0570889	−	0.0570889i
$801$	−5044.90	−	2697.36i	−0.222538	−	0.118985i
$802$	12567.1	−	12567.1i	0.553317	−	0.553317i
$803$			21266.5i			0.934593i
$804$	473.888	+	3196.06i	0.0207870	+	0.140195i
$805$			7778.25i			0.340556i
$806$			6798.85i			0.297121i
$807$	−25147.4	−	18653.0i	−1.09694	−	0.813650i
$808$	−4111.51			−0.179013
$809$	−4580.93	+	4580.93i	−0.199081	+	0.199081i	−0.799606	−	0.600525i	$-0.794958\pi$
$809$	−4580.93	+	4580.93i	−0.199081	+	0.199081i	0.600525	+	0.799606i	$0.294958\pi$
$810$	11783.7	+	2346.97i	0.511155	+	0.101807i
$811$			17596.9i			0.761913i	0.924593	+	0.380956i	$0.124405\pi$
$811$			17596.9i			0.761913i	−0.924593	+	0.380956i	$0.875595\pi$
$812$	1175.85	−	2625.68i	0.0508179	−	0.113477i
$813$	19494.2	−	26281.4i	0.840947	−	1.13374i
$814$	1538.82	−	1538.82i	0.0662601	−	0.0662601i
$815$	5239.24	+	5239.24i	0.225181	+	0.225181i
$816$	−6322.38	+	8523.64i	−0.271235	+	0.365670i
$817$			6785.75i			0.290579i
$818$	14260.5			0.609545
$819$	−1264.32	−	4169.78i	−0.0539426	−	0.177905i
$820$	776.799	+	776.799i	0.0330817	+	0.0330817i
$821$	14456.9			0.614555			0.307277	−	0.951620i	$-0.400582\pi$
$821$	14456.9			0.614555			0.307277	+	0.951620i	$0.400582\pi$
$822$	14075.0	−	2086.93i	0.597228	−	0.0885524i
$823$	24947.6	−	24947.6i	1.05665	−	1.05665i	0.0583500	−	0.998296i	$-0.481416\pi$
$823$	24947.6	−	24947.6i	1.05665	−	1.05665i	0.998296	−	0.0583500i	$-0.0185839\pi$
$824$	−9979.93	+	9979.93i	−0.421926	+	0.421926i
$825$	3173.89	−	4278.94i	0.133940	−	0.180574i
$826$	−287.477	+	287.477i	−0.0121097	+	0.0121097i
$827$	28593.5	−	28593.5i	1.20229	−	1.20229i	0.228822	−	0.973468i	$-0.426513\pi$
$827$	28593.5	−	28593.5i	1.20229	−	1.20229i	0.973468	−	0.228822i	$-0.0734873\pi$
$828$	−21181.7	+	6422.53i	−0.889030	+	0.269563i
$829$	27229.5	−	27229.5i	1.14080	−	1.14080i	0.152491	−	0.988305i	$-0.451271\pi$
$829$	27229.5	−	27229.5i	1.14080	−	1.14080i	0.988305	−	0.152491i	$-0.0487294\pi$
$830$	−4178.14	+	4178.14i	−0.174729	+	0.174729i
$831$	2070.98	+	13967.4i	0.0864520	+	0.583062i
$832$	2242.61			0.0934477
$833$	29045.1	+	29045.1i	1.20811	+	1.20811i
$834$	−7031.25	+	9479.31i	−0.291933	+	0.393575i
$835$	−3879.10			−0.160769
$836$		−	1741.49i		−	0.0720464i
$837$	12814.1	+	4587.67i	0.529177	+	0.189454i
$838$	−1777.10	−	1777.10i	−0.0732565	−	0.0732565i
$839$	−23743.9	+	23743.9i	−0.977032	+	0.977032i	−0.999742	−	0.0227099i	$-0.992771\pi$
$839$	−23743.9	+	23743.9i	−0.977032	+	0.977032i	0.0227099	+	0.999742i	$0.492771\pi$
$840$	−1267.14	−	939.898i	−0.0520482	−	0.0386066i
$841$	16240.8	+	18195.1i	0.665907	+	0.746035i
$842$			177.239i			0.00725424i
$843$	42318.2	−	6274.62i	1.72896	−	0.256358i
$844$	−12414.9	+	12414.9i	−0.506325	+	0.506325i
$845$	−7986.55			−0.325143
$846$	−29990.9	+	9093.57i	−1.21881	+	0.369555i
$847$		−	4644.42i		−	0.188411i
$848$		−	3884.96i		−	0.157323i
$849$	27486.4	−	4075.48i	1.11111	−	0.164747i
$850$		−	14574.6i		−	0.588123i
$851$	8780.12	−	8780.12i	0.353676	−	0.353676i
$852$	−6694.96	+	992.677i	−0.269208	+	0.0399162i
$853$	−21419.2	−	21419.2i	−0.859766	−	0.859766i	0.131544	−	0.991310i	$-0.458006\pi$
$853$	−21419.2	−	21419.2i	−0.859766	−	0.859766i	−0.991310	+	0.131544i	$0.958006\pi$
$854$	−1997.69			−0.0800465
$855$	−2543.25	+	4756.65i	−0.101728	+	0.190262i
$856$	6272.88	+	6272.88i	0.250470	+	0.250470i
$857$			46702.1i			1.86151i	0.365644	+	0.930755i	$0.380849\pi$
$857$			46702.1i			1.86151i	−0.365644	+	0.930755i	$0.619151\pi$
$858$	959.220	+	6469.31i	0.0381670	+	0.257411i
$859$	−5502.22	−	5502.22i	−0.218549	−	0.218549i	0.589338	−	0.807887i	$-0.299389\pi$
$859$	−5502.22	−	5502.22i	−0.218549	−	0.218549i	−0.807887	+	0.589338i	$0.799389\pi$
$860$	−6524.49	−	6524.49i	−0.258701	−	0.258701i
$861$	−640.557	−	475.131i	−0.0253544	−	0.0188065i
$862$	−21382.4	+	21382.4i	−0.844882	+	0.844882i
$863$	−29460.8			−1.16206			−0.581029	−	0.813883i	$-0.697350\pi$
$863$	−29460.8			−1.16206			−0.581029	+	0.813883i	$0.697350\pi$
$864$	1513.25	−	4226.76i	0.0595854	−	0.166432i
$865$	−11697.3			−0.459790
$866$		−	8573.34i		−	0.336413i
$867$	−58498.5	+	8673.70i	−2.29148	+	0.339763i
$868$	−1263.72	−	1263.72i	−0.0494165	−	0.0494165i
$869$	−1345.65			−0.0525294
$870$	11662.4	−	6547.29i	0.454474	−	0.255142i
$871$	5447.15			0.211905
$872$	5621.62	+	5621.62i	0.218316	+	0.218316i
$873$	24782.1	+	13250.3i	0.960763	+	0.513692i
$874$		−	9936.49i		−	0.384562i
$875$	6910.81			0.267003
$876$	−19767.4	−	14662.4i	−0.762420	−	0.565523i
$877$	−32019.6			−1.23287			−0.616433	−	0.787407i	$-0.711423\pi$
$877$	−32019.6			−1.23287			−0.616433	+	0.787407i	$0.711423\pi$
$878$	12854.9	−	12854.9i	0.494113	−	0.494113i
$879$	−8849.79	+	11931.0i	−0.339586	+	0.457819i
$880$	1674.44	+	1674.44i	0.0641426	+	0.0641426i
$881$	18501.1	+	18501.1i	0.707511	+	0.707511i	0.966011	−	0.258500i	$-0.0832281\pi$
$881$	18501.1	+	18501.1i	0.707511	+	0.707511i	−0.258500	+	0.966011i	$0.583228\pi$
$882$	−15323.8	−	8193.20i	−0.585011	−	0.312788i
$883$			38898.6i			1.48249i	0.671232	+	0.741247i	$0.265765\pi$
$883$			38898.6i			1.48249i	−0.671232	+	0.741247i	$0.734235\pi$
$884$	12651.3	+	12651.3i	0.481344	+	0.481344i
$885$	−1869.58	+	277.206i	−0.0710114	+	0.0105290i
$886$	−19456.3			−0.737750
$887$	491.626	+	491.626i	0.0186101	+	0.0186101i	0.716351	−	0.697740i	$-0.245811\pi$
$887$	491.626	+	491.626i	0.0186101	+	0.0186101i	−0.697740	+	0.716351i	$0.745811\pi$
$888$	369.393	+	2491.31i	0.0139595	+	0.0941475i
$889$	1138.59	−	1138.59i	0.0429551	−	0.0429551i
$890$			3492.11i			0.131524i
$891$	12840.3	+	2557.42i	0.482790	+	0.0961579i
$892$			7755.24i			0.291104i
$893$		−	14068.9i		−	0.527211i
$894$	−21273.2	+	28679.8i	−0.795841	+	1.07293i
$895$	−7107.44			−0.265448
$896$	−416.840	+	416.840i	−0.0155420	+	0.0155420i
$897$	5473.06	+	36912.2i	0.203724	+	1.37398i
$898$		−	28796.7i		−	1.07011i
$899$	14156.0	−	5398.85i	0.525171	−	0.200291i
$900$	1789.04	+	5900.33i	0.0662609	+	0.218531i
$901$	21916.3	−	21916.3i	0.810362	−	0.810362i
$902$	846.454	+	846.454i	0.0312459	+	0.0312459i
$903$	5380.16	+	3990.72i	0.198273	+	0.147069i
$904$			5449.92i			0.200511i
$905$	−7101.28			−0.260834
$906$	19127.8	+	14188.0i	0.701411	+	0.520269i
$907$	−32957.0	−	32957.0i	−1.20653	−	1.20653i	−0.972145	−	0.234380i	$-0.924694\pi$
$907$	−32957.0	−	32957.0i	−1.20653	−	1.20653i	−0.234380	−	0.972145i	$-0.575306\pi$
$908$	−19450.2			−0.710877
$909$	12237.0	+	6542.80i	0.446510	+	0.238736i
$910$	−1880.76	+	1880.76i	−0.0685128	+	0.0685128i
$911$	−10207.4	+	10207.4i	−0.371226	+	0.371226i	−0.867924	−	0.496698i	$-0.834546\pi$
$911$	−10207.4	+	10207.4i	−0.371226	+	0.371226i	0.496698	+	0.867924i	$0.334546\pi$
$912$	1618.74	+	1200.69i	0.0587738	+	0.0435953i
$913$	−4552.79	+	4552.79i	−0.165033	+	0.165033i
$914$	10757.7	−	10757.7i	0.389313	−	0.389313i
$915$	−7459.06	−	5532.74i	−0.269496	−	0.199898i
$916$	19552.8	−	19552.8i	0.705288	−	0.705288i
$917$	−5181.28	+	5181.28i	−0.186588	+	0.186588i
$918$	32381.2	−	15307.8i	1.16420	−	0.550361i
$919$	−9575.65			−0.343712			−0.171856	−	0.985122i	$-0.554976\pi$
$919$	−9575.65			−0.343712			−0.171856	+	0.985122i	$0.554976\pi$
$920$	9553.93	+	9553.93i	0.342374	+	0.342374i
$921$	−4026.35	−	2986.53i	−0.144053	−	0.106851i
$922$	18067.6			0.645364
$923$			11410.4i			0.406911i
$924$	−1380.76	−	1024.18i	−0.0491600	−	0.0364643i
$925$	−2445.77	−	2445.77i	−0.0869366	−	0.0869366i
$926$	13460.5	−	13460.5i	0.477690	−	0.477690i
$927$	45584.5	−	13821.7i	1.61509	−	0.489714i
$928$	−1780.81	−	4669.37i	−0.0629937	−	0.165172i
$929$		−	36175.2i		−	1.27758i	−0.769382	−	0.638788i	$-0.779436\pi$
$929$		−	36175.2i		−	1.27758i	0.769382	−	0.638788i	$-0.220564\pi$
$930$	−1218.58	−	8218.49i	−0.0429663	−	0.289780i
$931$	5515.99	−	5515.99i	0.194178	−	0.194178i
$932$	−16732.1			−0.588066
$933$	−2581.93	+	3480.87i	−0.0905987	+	0.122142i
$934$			19402.7i			0.679738i
$935$			18892.1i			0.660790i
$936$	−6674.64	−	3568.74i	−0.233085	−	0.124624i
$937$			29592.1i			1.03173i	0.856669	+	0.515866i	$0.172530\pi$
$937$			29592.1i			1.03173i	−0.856669	+	0.515866i	$0.827470\pi$
$938$	−1012.48	+	1012.48i	−0.0352437	+	0.0352437i
$939$	7309.67	+	49298.9i	0.254038	+	1.71332i
$940$	13527.3	+	13527.3i	0.469374	+	0.469374i
$941$	−25766.8			−0.892639			−0.446320	−	0.894874i	$-0.647266\pi$
$941$	−25766.8			−0.892639			−0.446320	+	0.894874i	$0.647266\pi$
$942$	−2053.83	+	304.527i	−0.0710377	+	0.0105329i
$943$	4829.64	+	4829.64i	0.166781	+	0.166781i
$944$			706.208i			0.0243486i
$945$	2275.68	+	4813.85i	0.0783364	+	0.165709i
$946$	−7109.53	−	7109.53i	−0.244346	−	0.244346i
$947$	−28176.3	−	28176.3i	−0.966851	−	0.966851i	0.0326167	−	0.999468i	$-0.489616\pi$
$947$	−28176.3	−	28176.3i	−0.966851	−	0.966851i	−0.999468	+	0.0326167i	$0.989616\pi$
$948$	927.775	−	1250.80i	0.0317856	−	0.0428523i
$949$	−29339.9	+	29339.9i	−1.00360	+	1.00360i
$950$	−2767.88			−0.0945285
$951$	−2701.01	−	2003.47i	−0.0920991	−	0.0683142i
$952$	−4703.06			−0.160112
$953$			18923.3i			0.643219i	0.946872	+	0.321609i	$0.104224\pi$
$953$			18923.3i			0.643219i	−0.946872	+	0.321609i	$0.895776\pi$
$954$	−6182.26	+	11562.7i	−0.209809	+	0.392408i
$955$	13229.7	+	13229.7i	0.448277	+	0.448277i
$956$	−14793.6			−0.500481
$957$	12708.2	−	7134.37i	0.429255	−	0.240984i
$958$	−11986.5			−0.404245
$959$	4458.80	+	4458.80i	0.150138	+	0.150138i
$960$	−2710.88	+	401.948i	−0.0911388	+	0.0135134i
$961$			20379.4i			0.684079i
$962$	4246.02			0.142305
$963$	−8687.63	−	28652.1i	−0.290711	−	0.958777i
$964$	6907.13			0.230771
$965$	−12713.6	+	12713.6i	−0.424108	+	0.424108i
$966$	−7878.27	−	5843.69i	−0.262401	−	0.194635i
$967$	−39736.7	−	39736.7i	−1.32146	−	1.32146i	−0.912599	−	0.408857i	$-0.865928\pi$
$967$	−39736.7	−	39736.7i	−1.32146	−	1.32146i	−0.408857	−	0.912599i	$-0.634072\pi$
$968$	−5704.68	−	5704.68i	−0.189417	−	0.189417i
$969$	2358.31	+	15905.3i	0.0781837	+	0.527298i
$970$		−	17154.3i		−	0.567827i
$971$	15258.8	+	15258.8i	0.504304	+	0.504304i	0.912772	−	0.408468i	$-0.133937\pi$
$971$	15258.8	+	15258.8i	0.504304	+	0.504304i	−0.408468	+	0.912772i	$0.633937\pi$
$972$	−11230.0	+	10172.0i	−0.370580	+	0.335664i
$973$	−5230.36			−0.172331
$974$	−13418.1	−	13418.1i	−0.441421	−	0.441421i
$975$	10282.2	−	1524.56i	0.337736	−	0.0500770i
$976$	−2453.74	+	2453.74i	−0.0804738	+	0.0804738i
$977$		−	3050.43i		−	0.0998894i	−0.998752	−	0.0499447i	$-0.984095\pi$
$977$		−	3050.43i		−	0.0998894i	0.998752	−	0.0499447i	$-0.0159045\pi$
$978$	−9242.78	+	1370.45i	−0.302200	+	0.0448079i
$979$			3805.25i			0.124225i
$980$			10607.2i			0.345751i
$981$	−7785.67	−	25677.4i	−0.253392	−	0.835695i
$982$	−8741.74			−0.284074
$983$	5573.62	−	5573.62i	0.180845	−	0.180845i	−0.610879	−	0.791724i	$-0.709184\pi$
$983$	5573.62	−	5573.62i	0.180845	−	0.180845i	0.791724	+	0.610879i	$0.209184\pi$
$984$	−1370.39	+	203.190i	−0.0443967	+	0.00658280i
$985$			24608.1i			0.796018i
$986$	16295.3	−	36387.5i	0.526315	−	1.17527i
$987$	−11154.7	−	8273.99i	−0.359736	−	0.266833i
$988$	2402.62	−	2402.62i	0.0773659	−	0.0773659i
$989$	−40565.1	−	40565.1i	−1.30424	−	1.30424i
$990$	−2319.02	−	7648.22i	−0.0744479	−	0.245532i
$991$			33551.2i			1.07547i	0.843115	+	0.537733i	$0.180719\pi$
$991$			33551.2i			1.07547i	−0.843115	+	0.537733i	$0.819281\pi$
$992$	−3104.43			−0.0993607
$993$	2634.91	−	3552.30i	0.0842057	−	0.113524i
$994$	−2120.89	−	2120.89i	−0.0676766	−	0.0676766i
$995$	29488.6			0.939550
$996$	−1092.89	−	7370.84i	−0.0347687	−	0.234492i
$997$	12169.9	−	12169.9i	0.386585	−	0.386585i	−0.486883	−	0.873467i	$-0.661866\pi$
$997$	12169.9	−	12169.9i	0.386585	−	0.386585i	0.873467	+	0.486883i	$0.161866\pi$
$998$	−16927.9	+	16927.9i	−0.536918	+	0.536918i
$999$	2865.09	−	8002.69i	0.0907383	−	0.253447i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	174.4.f.a.17.9	✓	60
3.2	odd	2	inner	174.4.f.a.17.16	yes	60
29.12	odd	4	inner	174.4.f.a.41.16	yes	60
87.41	even	4	inner	174.4.f.a.41.9	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
174.4.f.a.17.9	✓	60	1.1	even	1	trivial
174.4.f.a.17.16	yes	60	3.2	odd	2	inner
174.4.f.a.41.9	yes	60	87.41	even	4	inner
174.4.f.a.41.16	yes	60	29.12	odd	4	inner

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:	\( N \)	\(=\)	\( 174 = 2 \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	174.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41421 - 1.41421i) q^{2} +(0.762114 + 5.13996i) q^{3} +4.00000i q^{4} -8.24082 q^{5} +(6.19121 - 8.34679i) q^{6} +4.60548 q^{7} +(5.65685 - 5.65685i) q^{8} +(-25.8384 + 7.83447i) q^{9} +(11.6543 + 11.6543i) q^{10} +(12.6993 + 12.6993i) q^{11} +(-20.5598 + 3.04846i) q^{12} +35.0408i q^{13} +(-6.51313 - 6.51313i) q^{14} +(-6.28044 - 42.3575i) q^{15} -16.0000 q^{16} +(-90.2610 - 90.2610i) q^{17} +(47.6206 + 25.4614i) q^{18} +(-17.1416 + 17.1416i) q^{19} -32.9633i q^{20} +(3.50990 + 23.6720i) q^{21} -35.9191i q^{22} -204.945i q^{23} +(33.3872 + 24.7648i) q^{24} -57.0889 q^{25} +(49.5551 - 49.5551i) q^{26} +(-59.9606 - 126.837i) q^{27} +18.4219i q^{28} +(-142.530 - 63.8287i) q^{29} +(-51.0206 + 68.7844i) q^{30} +(-68.5989 + 68.5989i) q^{31} +(22.6274 + 22.6274i) q^{32} +(-55.5956 + 74.9522i) q^{33} +255.297i q^{34} -37.9529 q^{35} +(-31.3379 - 103.353i) q^{36} +(42.8414 + 42.8414i) q^{37} +48.4838 q^{38} +(-180.108 + 26.7050i) q^{39} +(-46.6171 + 46.6171i) q^{40} +(-23.5656 + 23.5656i) q^{41} +(28.5135 - 38.4410i) q^{42} +(197.932 - 197.932i) q^{43} +(-50.7972 + 50.7972i) q^{44} +(212.929 - 64.5625i) q^{45} +(-289.836 + 289.836i) q^{46} +(-410.374 + 410.374i) q^{47} +(-12.1938 - 82.2394i) q^{48} -321.790 q^{49} +(80.7359 + 80.7359i) q^{50} +(395.149 - 532.727i) q^{51} -140.163 q^{52} +242.810i q^{53} +(-94.5780 + 264.172i) q^{54} +(-104.653 - 104.653i) q^{55} +(26.0525 - 26.0525i) q^{56} +(-101.171 - 75.0433i) q^{57} +(111.301 + 291.836i) q^{58} -44.1380i q^{59} +(169.430 - 25.1218i) q^{60} +(153.359 - 153.359i) q^{61} +194.027 q^{62} +(-118.998 + 36.0815i) q^{63} -64.0000i q^{64} -288.765i q^{65} +(184.623 - 27.3744i) q^{66} -155.452i q^{67} +(361.044 - 361.044i) q^{68} +(1053.41 - 156.191i) q^{69} +(53.6735 + 53.6735i) q^{70} +325.633 q^{71} +(-101.845 + 190.482i) q^{72} +(837.309 + 837.309i) q^{73} -121.174i q^{74} +(-43.5082 - 293.435i) q^{75} +(-68.5664 - 68.5664i) q^{76} +(58.4864 + 58.4864i) q^{77} +(292.478 + 216.945i) q^{78} +(-52.9813 + 52.9813i) q^{79} +131.853 q^{80} +(606.242 - 404.860i) q^{81} +66.6536 q^{82} +358.507i q^{83} +(-94.6879 + 14.0396i) q^{84} +(743.825 + 743.825i) q^{85} -559.836 q^{86} +(219.453 - 781.245i) q^{87} +143.676 q^{88} +(149.821 + 149.821i) q^{89} +(-392.433 - 209.822i) q^{90} +161.379i q^{91} +819.779 q^{92} +(-404.876 - 300.315i) q^{93} +1160.71 q^{94} +(141.261 - 141.261i) q^{95} +(-99.0593 + 133.549i) q^{96} +(-735.966 - 735.966i) q^{97} +(455.079 + 455.079i) q^{98} +(-427.622 - 228.637i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 24 q^{10} + 88 q^{15} - 960 q^{16} + 48 q^{19} - 752 q^{21} + 64 q^{24} + 1500 q^{25} + 600 q^{27} + 312 q^{30} - 300 q^{31} - 224 q^{36} - 192 q^{37} - 172 q^{39} + 96 q^{40} + 888 q^{43} - 1532 q^{45}+ \cdots - 6000 q^{99}+O(q^{100}) \) 60 * q - 24 * q^10 + 88 * q^15 - 960 * q^16 + 48 * q^19 - 752 * q^21 + 64 * q^24 + 1500 * q^25 + 600 * q^27 + 312 * q^30 - 300 * q^31 - 224 * q^36 - 192 * q^37 - 172 * q^39 + 96 * q^40 + 888 * q^43 - 1532 * q^45 - 1104 * q^46 + 2292 * q^49 - 768 * q^52 - 1688 * q^54 + 2616 * q^55 - 1176 * q^58 - 352 * q^60 + 216 * q^61 + 192 * q^66 - 452 * q^69 + 192 * q^70 - 1668 * q^73 + 4840 * q^75 + 192 * q^76 - 1336 * q^78 + 3588 * q^79 - 280 * q^81 + 4224 * q^82 - 3008 * q^84 - 792 * q^85 - 4716 * q^87 - 800 * q^90 - 3072 * q^94 - 2916 * q^97 - 6000 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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