LMFDB - Embedded newform 275.3.bk.c.82.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,3,Mod(82,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 8])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.82"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	275.bk (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [128] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.49320726991$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			82.5
Character	$\chi$	$=$	275.82
Dual form			275.3.bk.c.218.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.807274 + 1.58436i) q^{2} +(0.0974353 - 0.0154322i) q^{3} +(0.492622 + 0.678036i) q^{4} +(-0.0542067 + 0.166831i) q^{6} +(-2.29002 - 0.362704i) q^{7} +(-8.49706 + 1.34580i) q^{8} +(-8.55025 + 2.77815i) q^{9} +(10.4743 - 3.35998i) q^{11} +(0.0584623 + 0.0584623i) q^{12} +(-10.0820 - 5.13704i) q^{13} +(2.42333 - 3.33543i) q^{14} +(3.69127 - 11.3606i) q^{16} +(-23.3644 + 11.9048i) q^{17} +(2.50080 - 15.7894i) q^{18} +(-6.52576 + 8.98194i) q^{19} -0.228726 q^{21} +(-3.13218 + 19.3075i) q^{22} +(-2.20560 + 2.20560i) q^{23} +(-0.807145 + 0.262257i) q^{24} +(16.2779 - 11.8266i) q^{26} +(-1.58130 + 0.805713i) q^{27} +(-0.882189 - 1.73139i) q^{28} +(9.68796 + 13.3343i) q^{29} +(-7.66619 - 23.5941i) q^{31} +(-9.31350 - 9.31350i) q^{32} +(0.968712 - 0.489022i) q^{33} -46.6282i q^{34} +(-6.09572 - 4.42880i) q^{36} +(-22.0420 - 3.49111i) q^{37} +(-8.96259 - 17.5901i) q^{38} +(-1.06162 - 0.344941i) q^{39} +(-42.0056 - 30.5189i) q^{41} +(0.184645 - 0.362386i) q^{42} +(22.3480 - 22.3480i) q^{43} +(7.43805 + 5.44673i) q^{44} +(-1.71395 - 5.27500i) q^{46} +(0.432857 + 2.73295i) q^{47} +(0.184341 - 1.16388i) q^{48} +(-41.4891 - 13.4806i) q^{49} +(-2.09280 + 1.52051i) q^{51} +(-1.48352 - 9.36658i) q^{52} +(72.8878 + 37.1382i) q^{53} -3.15579i q^{54} +19.9466 q^{56} +(-0.497228 + 0.975864i) q^{57} +(-28.9473 + 4.58480i) q^{58} +(27.6110 + 38.0033i) q^{59} +(-15.8306 + 48.7215i) q^{61} +(43.5704 + 6.90087i) q^{62} +(20.5879 - 3.26081i) q^{63} +(67.7168 - 22.0025i) q^{64} +(-0.00722659 + 1.92957i) q^{66} +(-1.56835 - 1.56835i) q^{67} +(-19.5817 - 9.97737i) q^{68} +(-0.180866 + 0.248941i) q^{69} +(-33.2289 + 102.268i) q^{71} +(68.9132 - 35.1130i) q^{72} +(-12.5990 + 79.5472i) q^{73} +(23.3252 - 32.1043i) q^{74} -9.30481 q^{76} +(-25.2050 + 3.89537i) q^{77} +(1.40353 - 1.40353i) q^{78} +(-80.4790 + 26.1492i) q^{79} +(65.3179 - 47.4562i) q^{81} +(82.2631 - 41.9151i) q^{82} +(-6.21119 - 12.1901i) q^{83} +(-0.112676 - 0.155085i) q^{84} +(17.3664 + 53.4484i) q^{86} +(1.14973 + 1.14973i) q^{87} +(-84.4787 + 42.6463i) q^{88} +92.0338i q^{89} +(21.2248 + 15.4207i) q^{91} +(-2.58200 - 0.408949i) q^{92} +(-1.11107 - 2.18059i) q^{93} +(-4.67942 - 1.52044i) q^{94} +(-1.05119 - 0.763735i) q^{96} +(69.8642 - 137.116i) q^{97} +(54.8513 - 54.8513i) q^{98} +(-80.2232 + 57.8278i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 48 q^{6} + 32 q^{11} + 280 q^{16} - 8 q^{21} + 528 q^{26} - 16 q^{31} + 336 q^{36} - 604 q^{41} - 1152 q^{46} - 1024 q^{51} - 992 q^{56} - 320 q^{61} + 1624 q^{66} + 536 q^{71} + 1776 q^{76} + 3680 q^{81}+ \cdots - 6584 q^{96}+O(q^{100}) $ 128 * q - 48 * q^6 + 32 * q^11 + 280 * q^16 - 8 * q^21 + 528 * q^26 - 16 * q^31 + 336 * q^36 - 604 * q^41 - 1152 * q^46 - 1024 * q^51 - 992 * q^56 - 320 * q^61 + 1624 * q^66 + 536 * q^71 + 1776 * q^76 + 3680 * q^81 + 872 * q^86 - 448 * q^91 - 6584 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.807274	+	1.58436i	−0.403637	+	0.792182i	−0.999944	−	0.0105742i	$-0.996634\pi$
$2$	−0.807274	+	1.58436i	−0.403637	+	0.792182i	0.596307	+	0.802756i	$0.296634\pi$
$3$	0.0974353	−	0.0154322i	0.0324784	−	0.00514408i	−0.140174	−	0.990127i	$-0.544766\pi$
$3$	0.0974353	−	0.0154322i	0.0324784	−	0.00514408i	0.172653	+	0.984983i	$0.444766\pi$
$4$	0.492622	+	0.678036i	0.123155	+	0.169509i
$5$		0			0
$5$		0			0
$6$	−0.0542067	+	0.166831i	−0.00903445	+	0.0278052i
$7$	−2.29002	−	0.362704i	−0.327146	−	0.0518148i	−0.00929877	−	0.999957i	$-0.502960\pi$
$7$	−2.29002	−	0.362704i	−0.327146	−	0.0518148i	−0.317847	+	0.948142i	$0.602960\pi$
$8$	−8.49706	+	1.34580i	−1.06213	+	0.168225i
$9$	−8.55025	+	2.77815i	−0.950028	+	0.308683i
$10$		0			0
$11$	10.4743	−	3.35998i	0.952207	−	0.305453i
$11$	10.4743	−	3.35998i	0.952207	−	0.305453i
$12$	0.0584623	+	0.0584623i	0.00487186	+	0.00487186i
$13$	−10.0820	−	5.13704i	−0.775539	−	0.395157i	0.0209727	−	0.999780i	$-0.493324\pi$
$13$	−10.0820	−	5.13704i	−0.775539	−	0.395157i	−0.796512	+	0.604623i	$0.793324\pi$
$14$	2.42333	−	3.33543i	0.173095	−	0.238245i
$15$		0			0
$16$	3.69127	−	11.3606i	0.230704	−	0.710035i
$17$	−23.3644	+	11.9048i	−1.37438	+	0.700281i	−0.976169	−	0.217013i	$-0.930368\pi$
$17$	−23.3644	+	11.9048i	−1.37438	+	0.700281i	−0.398210	+	0.917294i	$0.630368\pi$
$18$	2.50080	−	15.7894i	0.138933	−	0.877191i
$19$	−6.52576	+	8.98194i	−0.343461	+	0.472734i	−0.945448	−	0.325772i	$-0.894376\pi$
$19$	−6.52576	+	8.98194i	−0.343461	+	0.472734i	0.601987	+	0.798506i	$0.294376\pi$
$20$		0			0
$21$	−0.228726			−0.0108917
$22$	−3.13218	+	19.3075i	−0.142372	+	0.877614i
$23$	−2.20560	+	2.20560i	−0.0958957	+	0.0958957i	−0.753427	−	0.657531i	$-0.771601\pi$
$23$	−2.20560	+	2.20560i	−0.0958957	+	0.0958957i	0.657531	+	0.753427i	$0.271601\pi$
$24$	−0.807145	+	0.262257i	−0.0336310	+	0.0109274i
$25$		0			0
$26$	16.2779	−	11.8266i	0.626072	−	0.454868i
$27$	−1.58130	+	0.805713i	−0.0585667	+	0.0298412i
$28$	−0.882189	−	1.73139i	−0.0315067	−	0.0618355i
$29$	9.68796	+	13.3343i	0.334068	+	0.459805i	0.942697	−	0.333650i	$-0.108280\pi$
$29$	9.68796	+	13.3343i	0.334068	+	0.459805i	−0.608629	+	0.793455i	$0.708280\pi$
$30$		0			0
$31$	−7.66619	−	23.5941i	−0.247297	−	0.761101i	−0.995250	−	0.0973497i	$-0.968963\pi$
$31$	−7.66619	−	23.5941i	−0.247297	−	0.761101i	0.747954	−	0.663751i	$-0.231037\pi$
$32$	−9.31350	−	9.31350i	−0.291047	−	0.291047i
$33$	0.968712	−	0.489022i	0.0293549	−	0.0148189i
$34$		−	46.6282i		−	1.37142i
$35$		0			0
$36$	−6.09572	−	4.42880i	−0.169326	−	0.123022i
$37$	−22.0420	−	3.49111i	−0.595730	−	0.0943544i	−0.148714	−	0.988880i	$-0.547513\pi$
$37$	−22.0420	−	3.49111i	−0.595730	−	0.0943544i	−0.447016	+	0.894526i	$0.647513\pi$
$38$	−8.96259	−	17.5901i	−0.235858	−	0.462897i
$39$	−1.06162	−	0.344941i	−0.0272210	−	0.00884464i
$40$		0			0
$41$	−42.0056	−	30.5189i	−1.02453	−	0.744363i	−0.0573217	−	0.998356i	$-0.518256\pi$
$41$	−42.0056	−	30.5189i	−1.02453	−	0.744363i	−0.967206	+	0.253993i	$0.918256\pi$
$42$	0.184645	−	0.362386i	0.00439630	−	0.00862823i
$43$	22.3480	−	22.3480i	0.519722	−	0.519722i	−0.397765	−	0.917487i	$-0.630214\pi$
$43$	22.3480	−	22.3480i	0.519722	−	0.519722i	0.917487	+	0.397765i	$0.130214\pi$
$44$	7.43805	+	5.44673i	0.169046	+	0.123789i
$45$		0			0
$46$	−1.71395	−	5.27500i	−0.0372598	−	0.114674i
$47$	0.432857	+	2.73295i	0.00920972	+	0.0581479i	0.991865	−	0.127293i	$-0.0406288\pi$
$47$	0.432857	+	2.73295i	0.00920972	+	0.0581479i	−0.982655	+	0.185441i	$0.940629\pi$
$48$	0.184341	−	1.16388i	0.00384044	−	0.0242476i
$49$	−41.4891	−	13.4806i	−0.846717	−	0.275115i
$50$		0			0
$51$	−2.09280	+	1.52051i	−0.0410353	+	0.0298139i
$52$	−1.48352	−	9.36658i	−0.0285292	−	0.180126i
$53$	72.8878	+	37.1382i	1.37524	+	0.700721i	0.976334	−	0.216270i	$-0.0693892\pi$
$53$	72.8878	+	37.1382i	1.37524	+	0.700721i	0.398908	+	0.916991i	$0.369389\pi$
$54$		−	3.15579i		−	0.0584405i
$55$		0			0
$56$	19.9466			0.356189
$57$	−0.497228	+	0.975864i	−0.00872329	+	0.0171204i
$58$	−28.9473	+	4.58480i	−0.499091	+	0.0790483i
$59$	27.6110	+	38.0033i	0.467983	+	0.644124i	0.976140	−	0.217141i	$-0.0696731\pi$
$59$	27.6110	+	38.0033i	0.467983	+	0.644124i	−0.508157	+	0.861264i	$0.669673\pi$
$60$		0			0
$61$	−15.8306	+	48.7215i	−0.259518	+	0.798713i	0.733388	+	0.679810i	$0.237938\pi$
$61$	−15.8306	+	48.7215i	−0.259518	+	0.798713i	−0.992906	+	0.118903i	$0.962062\pi$
$62$	43.5704	+	6.90087i	0.702748	+	0.111304i
$63$	20.5879	−	3.26081i	0.326792	−	0.0517588i
$64$	67.7168	−	22.0025i	1.05807	−	0.343789i
$65$		0			0
$66$	−0.00722659	+	1.92957i	−0.000109494	+	0.0292359i
$67$	−1.56835	−	1.56835i	−0.0234081	−	0.0234081i	0.695306	−	0.718714i	$-0.255269\pi$
$67$	−1.56835	−	1.56835i	−0.0234081	−	0.0234081i	−0.718714	+	0.695306i	$0.755269\pi$
$68$	−19.5817	−	9.97737i	−0.287966	−	0.146726i
$69$	−0.180866	+	0.248941i	−0.00262124	+	0.00360783i
$70$		0			0
$71$	−33.2289	+	102.268i	−0.468013	+	1.44040i	0.387140	+	0.922021i	$0.373463\pi$
$71$	−33.2289	+	102.268i	−0.468013	+	1.44040i	−0.855153	+	0.518375i	$0.826537\pi$
$72$	68.9132	−	35.1130i	0.957128	−	0.487681i
$73$	−12.5990	+	79.5472i	−0.172590	+	1.08969i	0.737522	+	0.675323i	$0.235996\pi$
$73$	−12.5990	+	79.5472i	−0.172590	+	1.08969i	−0.910111	+	0.414364i	$0.864004\pi$
$74$	23.3252	−	32.1043i	0.315205	−	0.433842i
$75$		0			0
$76$	−9.30481			−0.122432
$77$	−25.2050	+	3.89537i	−0.327338	+	0.0505893i
$78$	1.40353	−	1.40353i	0.0179940	−	0.0179940i
$79$	−80.4790	+	26.1492i	−1.01872	+	0.331003i	−0.770322	−	0.637655i	$-0.779904\pi$
$79$	−80.4790	+	26.1492i	−1.01872	+	0.331003i	−0.248399	+	0.968658i	$0.579904\pi$
$80$		0			0
$81$	65.3179	−	47.4562i	0.806394	−	0.585879i
$82$	82.2631	−	41.9151i	1.00321	−	0.511160i
$83$	−6.21119	−	12.1901i	−0.0748336	−	0.146869i	0.850558	−	0.525881i	$-0.176264\pi$
$83$	−6.21119	−	12.1901i	−0.0748336	−	0.146869i	−0.925392	+	0.379011i	$0.876264\pi$
$84$	−0.112676	−	0.155085i	−0.00134138	−	0.00184624i
$85$		0			0
$86$	17.3664	+	53.4484i	0.201935	+	0.621493i
$87$	1.14973	+	1.14973i	0.0132153	+	0.0132153i
$88$	−84.4787	+	42.6463i	−0.959986	+	0.484617i
$89$			92.0338i			1.03409i	0.855959	+	0.517044i	$0.172968\pi$
$89$			92.0338i			1.03409i	−0.855959	+	0.517044i	$0.827032\pi$
$90$		0			0
$91$	21.2248	+	15.4207i	0.233239	+	0.169458i
$92$	−2.58200	−	0.408949i	−0.0280652	−	0.00444510i
$93$	−1.11107	−	2.18059i	−0.0119470	−	0.0234472i
$94$	−4.67942	−	1.52044i	−0.0497811	−	0.0161749i
$95$		0			0
$96$	−1.05119	−	0.763735i	−0.0109499	−	0.00795557i
$97$	69.8642	−	137.116i	0.720249	−	1.41357i	−0.182414	−	0.983222i	$-0.558391\pi$
$97$	69.8642	−	137.116i	0.720249	−	1.41357i	0.902664	−	0.430347i	$-0.141609\pi$
$98$	54.8513	−	54.8513i	0.559707	−	0.559707i
$99$	−80.2232	+	57.8278i	−0.810335	+	0.584119i
$100$		0			0
$101$	54.3328	+	167.219i	0.537948	+	1.65563i	0.737191	+	0.675684i	$0.236152\pi$
$101$	54.3328	+	167.219i	0.537948	+	1.65563i	−0.199243	+	0.979950i	$0.563848\pi$
$102$	−0.719577	−	4.54323i	−0.00705468	−	0.0445415i
$103$	−19.9427	+	125.913i	−0.193619	+	1.22246i	0.679030	+	0.734111i	$0.262401\pi$
$103$	−19.9427	+	125.913i	−0.193619	+	1.22246i	−0.872649	+	0.488349i	$0.837599\pi$
$104$	92.5809	+	30.0813i	0.890201	+	0.289244i
$105$		0			0
$106$	−117.681	+	85.5002i	−1.11020	+	0.806605i
$107$	25.9863	+	164.071i	0.242863	+	1.53338i	0.744101	+	0.668067i	$0.232878\pi$
$107$	25.9863	+	164.071i	0.242863	+	1.53338i	−0.501238	+	0.865310i	$0.667122\pi$
$108$	−1.32529	−	0.675267i	−0.0122712	−	0.00625247i
$109$		−	95.5708i		−	0.876796i	−0.898781	−	0.438398i	$-0.855546\pi$
$109$		−	95.5708i		−	0.876796i	0.898781	−	0.438398i	$-0.144454\pi$
$110$		0			0
$111$	−2.20155			−0.0198337
$112$	−12.5736	+	24.6771i	−0.112264	+	0.220331i
$113$	115.722	−	18.3285i	1.02408	−	0.162199i	0.378272	−	0.925695i	$-0.376519\pi$
$113$	115.722	−	18.3285i	1.02408	−	0.162199i	0.645813	+	0.763496i	$0.276519\pi$
$114$	−1.14473	−	1.57558i	−0.0100415	−	0.0138209i
$115$		0			0
$116$	−4.26865	+	13.1376i	−0.0367987	+	0.113255i
$117$	100.475	+	15.9137i	0.858762	+	0.136015i
$118$	−82.5007	+	13.0668i	−0.699159	+	0.110736i
$119$	57.8230	−	18.7878i	0.485907	−	0.157881i
$120$		0			0
$121$	98.4210	−	70.3868i	0.813397	−	0.581709i
$122$	−64.4130	−	64.4130i	−0.527976	−	0.527976i
$123$	−4.56380	−	2.32537i	−0.0371041	−	0.0189055i
$124$	12.2211	−	16.8209i	0.0985574	−	0.135653i
$125$		0			0
$126$	−11.4538	+	35.2511i	−0.0909031	+	0.279771i
$127$	4.81465	−	2.45318i	0.0379106	−	0.0193164i	−0.434932	−	0.900463i	$-0.643228\pi$
$127$	4.81465	−	2.45318i	0.0379106	−	0.0193164i	0.472843	+	0.881147i	$0.343228\pi$
$128$	−11.5642	+	73.0136i	−0.0903455	+	0.570419i
$129$	1.83261	−	2.52237i	0.0142063	−	0.0195532i
$130$		0			0
$131$	−86.8414			−0.662912			−0.331456	−	0.943471i	$-0.607540\pi$
$131$	−86.8414			−0.662912			−0.331456	+	0.943471i	$0.607540\pi$
$132$	0.808783	+	0.415918i	0.00612714	+	0.00315090i
$133$	18.2019	−	18.2019i	0.136857	−	0.136857i
$134$	3.75092	−	1.21875i	0.0279919	−	0.00909512i
$135$		0			0
$136$	182.508	−	132.600i	1.34197	−	0.974996i
$137$	−81.2550	+	41.4015i	−0.593102	+	0.302201i	−0.724659	−	0.689108i	$-0.758002\pi$
$137$	−81.2550	+	41.4015i	−0.593102	+	0.302201i	0.131557	+	0.991309i	$0.458002\pi$
$138$	−0.248404	−	0.487521i	−0.00180003	−	0.00353276i
$139$	−56.9198	−	78.3433i	−0.409495	−	0.563621i	0.553600	−	0.832782i	$-0.313253\pi$
$139$	−56.9198	−	78.3433i	−0.409495	−	0.563621i	−0.963095	+	0.269161i	$0.913253\pi$
$140$		0			0
$141$	0.0843510	+	0.259606i	0.000598234	+	0.00184117i
$142$	−135.205	−	135.205i	−0.952149	−	0.952149i
$143$	−122.862	−	19.9314i	−0.859175	−	0.139380i
$144$			107.391i			0.745768i
$145$		0			0
$146$	−115.861	−	84.1778i	−0.793568	−	0.576561i
$147$	−4.25054	−	0.673219i	−0.0289152	−	0.00457972i
$148$	−8.49128	−	16.6651i	−0.0573735	−	0.112602i
$149$	−46.3778	−	15.0691i	−0.311260	−	0.101135i	0.149221	−	0.988804i	$-0.452323\pi$
$149$	−46.3778	−	15.0691i	−0.311260	−	0.101135i	−0.460482	+	0.887669i	$0.652323\pi$
$150$		0			0
$151$	−233.936	−	169.964i	−1.54924	−	1.12559i	−0.944188	−	0.329409i	$-0.893151\pi$
$151$	−233.936	−	169.964i	−1.54924	−	1.12559i	−0.605056	−	0.796183i	$-0.706849\pi$
$152$	43.3619	−	85.1025i	0.285275	−	0.559885i
$153$	166.699	−	166.699i	1.08953	−	1.08953i
$154$	14.1757	−	43.0786i	0.0920497	−	0.279731i
$155$		0			0
$156$	−0.289094	−	0.889741i	−0.00185317	−	0.00570347i
$157$	0.989679	+	6.24859i	0.00630369	+	0.0397999i	0.990640	−	0.136503i	$-0.0435863\pi$
$157$	0.989679	+	6.24859i	0.00630369	+	0.0397999i	−0.984336	+	0.176303i	$0.943586\pi$
$158$	23.5387	−	148.618i	0.148979	−	0.940618i
$159$	7.67497	+	2.49375i	0.0482702	+	0.0156839i
$160$		0			0
$161$	5.85085	−	4.25089i	0.0363407	−	0.0264031i
$162$	22.4585	+	141.797i	0.138633	+	0.875293i
$163$	204.201	+	104.046i	1.25277	+	0.638318i	0.949255	−	0.314509i	$-0.101840\pi$
$163$	204.201	+	104.046i	1.25277	+	0.638318i	0.303515	+	0.952827i	$0.401840\pi$
$164$		−	43.5156i		−	0.265339i
$165$		0			0
$166$	24.3278			0.146553
$167$	−71.4859	+	140.299i	−0.428059	+	0.840114i	0.571747	+	0.820430i	$0.306266\pi$
$167$	−71.4859	+	140.299i	−0.428059	+	0.840114i	−0.999806	+	0.0196836i	$0.993734\pi$
$168$	1.94350	−	0.307820i	0.0115685	−	0.00183226i
$169$	−24.0780	−	33.1406i	−0.142474	−	0.196098i
$170$		0			0
$171$	30.8438	−	94.9274i	0.180373	−	0.555131i
$172$	26.1619	+	4.14364i	0.152104	+	0.0240909i
$173$	10.8143	−	1.71282i	0.0625104	−	0.00990068i	−0.125101	−	0.992144i	$-0.539925\pi$
$173$	10.8143	−	1.71282i	0.0625104	−	0.00990068i	0.187611	+	0.982243i	$0.439925\pi$
$174$	−2.74973	+	0.893442i	−0.0158031	+	0.00513473i
$175$		0			0
$176$	0.492103	−	131.396i	0.00279604	−	0.746570i
$177$	3.27676	+	3.27676i	0.0185128	+	0.0185128i
$178$	−145.815	−	74.2965i	−0.819186	−	0.417396i
$179$	8.66776	−	11.9301i	0.0484232	−	0.0666488i	−0.784119	−	0.620611i	$-0.786885\pi$
$179$	8.66776	−	11.9301i	0.0484232	−	0.0666488i	0.832542	+	0.553962i	$0.186885\pi$
$180$		0			0
$181$	−52.5269	+	161.661i	−0.290204	+	0.893156i	0.694586	+	0.719409i	$0.255587\pi$
$181$	−52.5269	+	161.661i	−0.290204	+	0.893156i	−0.984790	+	0.173747i	$0.944413\pi$
$182$	−41.5663	+	21.1791i	−0.228386	+	0.116368i
$183$	−0.790575	+	4.99149i	−0.00432008	+	0.0272759i
$184$	15.7728	−	21.7094i	0.0857219	−	0.117986i
$185$		0			0
$186$	4.35179			0.0233967
$187$	−204.726	+	203.198i	−1.09479	+	1.08662i
$188$	−1.63980	+	1.63980i	−0.00872235	+	0.00872235i
$189$	3.91345	−	1.27156i	0.0207061	−	0.00672782i
$190$		0			0
$191$	284.824	−	206.937i	1.49123	−	1.08344i	0.517511	−	0.855676i	$-0.326859\pi$
$191$	284.824	−	206.937i	1.49123	−	1.08344i	0.973716	−	0.227764i	$-0.0731414\pi$
$192$	6.25845	−	3.18884i	0.0325961	−	0.0166085i
$193$	−49.7456	−	97.6313i	−0.257749	−	0.505861i	0.725478	−	0.688245i	$-0.241619\pi$
$193$	−49.7456	−	97.6313i	−0.257749	−	0.505861i	−0.983227	+	0.182384i	$0.941619\pi$
$194$	160.842	+	221.381i	0.829085	+	1.14114i
$195$		0			0
$196$	−11.2981	−	34.7720i	−0.0576433	−	0.177408i
$197$	−117.931	−	117.931i	−0.598636	−	0.598636i	0.341313	−	0.939950i	$-0.389128\pi$
$197$	−117.931	−	117.931i	−0.598636	−	0.598636i	−0.939950	+	0.341313i	$0.889128\pi$
$198$	−26.8582	−	173.786i	−0.135647	−	0.877705i
$199$		−	299.028i		−	1.50265i	−0.659931	−	0.751326i	$-0.729415\pi$
$199$		−	299.028i		−	1.50265i	0.659931	−	0.751326i	$-0.270585\pi$
$200$		0			0
$201$	−0.177015	−	0.128609i	−0.000880673	−	0.000639846i
$202$	−308.797	−	48.9087i	−1.52870	−	0.242122i
$203$	−17.3492	−	34.0498i	−0.0854642	−	0.167733i
$204$	−2.06192	−	0.669958i	−0.0101075	−	0.00328411i
$205$		0			0
$206$	−183.393	−	133.243i	−0.890259	−	0.646811i
$207$	12.7310	−	24.9859i	0.0615022	−	0.120705i
$208$	−95.5750	+	95.5750i	−0.459495	+	0.459495i
$209$	−38.1735	+	116.006i	−0.182648	+	0.555052i
$210$		0			0
$211$	−46.9412	−	144.470i	−0.222470	−	0.684693i	−0.998539	−	0.0540442i	$-0.982789\pi$
$211$	−46.9412	−	144.470i	−0.222470	−	0.684693i	0.776068	−	0.630649i	$-0.217211\pi$
$212$	10.7251	+	67.7156i	0.0505901	+	0.319413i
$213$	−1.65944	+	10.4773i	−0.00779082	+	0.0491893i
$214$	−280.927	−	91.2787i	−1.31274	−	0.426536i
$215$		0			0
$216$	12.3521	−	8.97432i	0.0571856	−	0.0415478i
$217$	8.99808	+	56.8116i	0.0414658	+	0.261805i
$218$	151.419	+	77.1518i	0.694582	+	0.353907i
$219$			7.94513i			0.0362791i
$220$		0			0
$221$	296.716			1.34260
$222$	1.77725	−	3.48805i	0.00800563	−	0.0157119i
$223$	−304.194	+	48.1796i	−1.36410	+	0.216052i	−0.795196	−	0.606353i	$-0.792632\pi$
$223$	−304.194	+	48.1796i	−1.36410	+	0.216052i	−0.568903	+	0.822405i	$0.692632\pi$
$224$	17.9501	+	24.7062i	0.0801343	+	0.110295i
$225$		0			0
$226$	−64.3800	+	198.141i	−0.284867	+	0.876731i
$227$	370.529	+	58.6861i	1.63229	+	0.258529i	0.904249	−	0.427006i	$-0.140432\pi$
$227$	370.529	+	58.6861i	1.63229	+	0.258529i	0.728040	+	0.685535i	$0.240432\pi$
$228$	−0.906616	+	0.143594i	−0.00397639	+	0.000629798i
$229$	118.770	−	38.5907i	0.518646	−	0.168518i	−0.0379849	−	0.999278i	$-0.512094\pi$
$229$	118.770	−	38.5907i	0.518646	−	0.168518i	0.556631	+	0.830760i	$0.312094\pi$
$230$		0			0
$231$	−2.39574	+	0.768516i	−0.0103712	+	0.00332691i
$232$	−100.265	−	100.265i	−0.432175	−	0.432175i
$233$	−227.137	−	115.732i	−0.974837	−	0.496704i	−0.107381	−	0.994218i	$-0.534246\pi$
$233$	−227.137	−	115.732i	−0.974837	−	0.496704i	−0.867456	+	0.497514i	$0.834246\pi$
$234$	−106.324	+	146.343i	−0.454376	+	0.625395i
$235$		0			0
$236$	−12.1658	+	37.4425i	−0.0515500	+	0.158655i
$237$	−7.43795	+	3.78982i	−0.0313837	+	0.0159908i
$238$	−16.9122	+	106.780i	−0.0710598	+	0.448654i
$239$	−146.021	+	200.980i	−0.610965	+	0.840921i	−0.996656	−	0.0817069i	$-0.973963\pi$
$239$	−146.021	+	200.980i	−0.610965	+	0.840921i	0.385692	+	0.922628i	$0.373963\pi$
$240$		0			0
$241$	287.218			1.19177			0.595887	−	0.803068i	$-0.296800\pi$
$241$	287.218			1.19177			0.595887	+	0.803068i	$0.296800\pi$
$242$	32.0656	+	212.756i	0.132502	+	0.879158i
$243$	16.9263	−	16.9263i	0.0696554	−	0.0696554i
$244$	−40.8334	+	13.2676i	−0.167350	+	0.0543753i
$245$		0			0
$246$	7.36848	−	5.35352i	0.0299532	−	0.0217623i
$247$	111.933	−	57.0329i	0.453171	−	0.230902i
$248$	96.8932	+	190.164i	0.390698	+	0.766788i
$249$	−0.793310	−	1.09190i	−0.00318598	−	0.00438513i
$250$		0			0
$251$	64.7604	+	199.312i	0.258010	+	0.794072i	0.993222	+	0.116235i	$0.0370825\pi$
$251$	64.7604	+	199.312i	0.258010	+	0.794072i	−0.735212	+	0.677837i	$0.762917\pi$
$252$	12.3530	+	12.3530i	0.0490198	+	0.0490198i
$253$	−15.6913	+	30.5129i	−0.0620209	+	0.120604i
$254$			9.60854i			0.0378289i
$255$		0			0
$256$	124.069	+	90.1411i	0.484643	+	0.352114i
$257$	−331.611	−	52.5220i	−1.29031	−	0.204366i	−0.526707	−	0.850047i	$-0.676574\pi$
$257$	−331.611	−	52.5220i	−1.29031	−	0.204366i	−0.763607	+	0.645681i	$0.776574\pi$
$258$	2.51693	+	4.93976i	0.00975555	+	0.0191464i
$259$	49.2105	+	15.9895i	0.190002	+	0.0617354i
$260$		0			0
$261$	−119.879	−	87.0974i	−0.459307	−	0.333706i
$262$	70.1048	−	137.588i	0.267576	−	0.525147i
$263$	191.280	−	191.280i	0.727299	−	0.727299i	−0.242782	−	0.970081i	$-0.578060\pi$
$263$	191.280	−	191.280i	0.727299	−	0.727299i	0.970081	+	0.242782i	$0.0780600\pi$
$264$	−7.57308	+	5.45895i	−0.0286859	+	0.0206778i
$265$		0			0
$266$	14.1445	+	43.5324i	0.0531750	+	0.163656i
$267$	1.42029	+	8.96734i	0.00531943	+	0.0335855i
$268$	0.290793	−	1.83600i	0.00108505	−	0.00685073i
$269$	19.6590	+	6.38760i	0.0730818	+	0.0237457i	0.345330	−	0.938481i	$-0.387767\pi$
$269$	19.6590	+	6.38760i	0.0730818	+	0.0237457i	−0.272248	+	0.962227i	$0.587767\pi$
$270$		0			0
$271$	−371.981	+	270.260i	−1.37262	+	0.997269i	−0.375096	+	0.926986i	$0.622390\pi$
$271$	−371.981	+	270.260i	−1.37262	+	0.997269i	−0.997527	+	0.0702831i	$0.977610\pi$
$272$	49.0005	+	309.377i	0.180149	+	1.13741i
$273$	2.30602	+	1.17498i	0.00844696	+	0.00430394i
$274$		−	162.160i		−	0.591824i
$275$		0			0
$276$	−0.257889			−0.000934381
$277$	174.111	−	341.712i	0.628559	−	1.23362i	−0.328713	−	0.944430i	$-0.606615\pi$
$277$	174.111	−	341.712i	0.628559	−	1.23362i	0.957273	−	0.289187i	$-0.0933851\pi$
$278$	170.074	−	26.9371i	0.611778	−	0.0968961i
$279$	131.096	+	180.438i	0.469877	+	0.646731i
$280$		0			0
$281$	−58.9055	+	181.292i	−0.209628	+	0.645169i	0.789863	+	0.613283i	$0.210151\pi$
$281$	−58.9055	+	181.292i	−0.209628	+	0.645169i	−0.999492	+	0.0318861i	$0.989849\pi$
$282$	−0.479404	−	0.0759302i	−0.00170002	−	0.000269256i
$283$	−548.838	+	86.9274i	−1.93936	+	0.307164i	−0.999416	−	0.0341733i	$-0.989120\pi$
$283$	−548.838	+	86.9274i	−1.93936	+	0.307164i	−0.939941	+	0.341337i	$0.889120\pi$
$284$	−85.7107	+	27.8491i	−0.301798	+	0.0980602i
$285$		0			0
$286$	130.762	−	178.568i	0.457210	−	0.624364i
$287$	85.1245	+	85.1245i	0.296601	+	0.296601i
$288$	105.507	+	53.7585i	0.366344	+	0.186662i
$289$	234.303	−	322.491i	0.810738	−	1.11588i
$290$		0			0
$291$	4.69123	−	14.4381i	0.0161211	−	0.0496155i
$292$	−60.1424	+	30.6441i	−0.205967	+	0.104945i
$293$	−24.4572	+	154.417i	−0.0834718	+	0.527020i	0.910152	+	0.414274i	$0.135965\pi$
$293$	−24.4572	+	154.417i	−0.0834718	+	0.527020i	−0.993624	+	0.112746i	$0.964035\pi$
$294$	4.49797	−	6.19093i	0.0152992	−	0.0210576i
$295$		0			0
$296$	191.991			0.648618
$297$	−13.8558	+	13.7524i	−0.0466526	+	0.0463044i
$298$	61.3145	−	61.3145i	0.205753	−	0.205753i
$299$	33.5671	−	10.9066i	0.112265	−	0.0364770i
$300$		0			0
$301$	−59.2832	+	43.0718i	−0.196954	+	0.143096i
$302$	458.136	−	233.432i	1.51701	−	0.772953i
$303$	7.87449	+	15.4546i	0.0259884	+	0.0510051i
$304$	77.9515	+	107.291i	0.256419	+	0.352931i
$305$		0			0
$306$	129.540	+	398.683i	0.423333	+	1.30289i
$307$	23.5348	+	23.5348i	0.0766605	+	0.0766605i	0.744397	−	0.667737i	$-0.232737\pi$
$307$	23.5348	+	23.5348i	0.0766605	+	0.0766605i	−0.667737	+	0.744397i	$0.732737\pi$
$308$	−15.0577	−	15.1710i	−0.0488888	−	0.0492563i
$309$			12.5762i			0.0406995i
$310$		0			0
$311$	−134.134	−	97.4541i	−0.431299	−	0.313357i	0.350869	−	0.936425i	$-0.385886\pi$
$311$	−134.134	−	97.4541i	−0.431299	−	0.313357i	−0.782168	+	0.623067i	$0.785886\pi$
$312$	9.48486	+	1.50225i	0.0304002	+	0.00481492i
$313$	233.885	+	459.024i	0.747235	+	1.46653i	0.879794	+	0.475356i	$0.157681\pi$
$313$	233.885	+	459.024i	0.747235	+	1.46653i	−0.132559	+	0.991175i	$0.542319\pi$
$314$	−10.6990	−	3.47631i	−0.0340732	−	0.0110711i
$315$		0			0
$316$	−57.3758	−	41.6859i	−0.181569	−	0.131918i
$317$	263.414	−	516.979i	0.830958	−	1.63085i	0.0563462	−	0.998411i	$-0.482055\pi$
$317$	263.414	−	516.979i	0.830958	−	1.63085i	0.774612	−	0.632436i	$-0.217945\pi$
$318$	−10.1468	+	10.1468i	−0.0319082	+	0.0319082i
$319$	146.278	+	107.116i	0.458550	+	0.335787i
$320$		0			0
$321$	5.06397	+	15.5853i	0.0157756	+	0.0485523i
$322$	2.01172	+	12.7015i	0.00624759	+	0.0394457i
$323$	45.5428	−	287.546i	0.140999	−	0.890234i
$324$	64.3540	+	20.9099i	0.198623	+	0.0645367i
$325$		0			0
$326$	−329.693	+	239.536i	−1.01133	+	0.734773i
$327$	−1.47487	−	9.31196i	−0.00451031	−	0.0284770i
$328$	397.997	+	202.790i	1.21341	+	0.618261i
$329$		−	6.41551i		−	0.0195000i
$330$		0			0
$331$	−337.154			−1.01859			−0.509296	−	0.860592i	$-0.670094\pi$
$331$	−337.154			−1.01859			−0.509296	+	0.860592i	$0.670094\pi$
$332$	5.20559	−	10.2165i	0.0156795	−	0.0307727i
$333$	198.164	−	31.3861i	0.595086	−	0.0942524i
$334$	−164.576	−	226.519i	−0.492742	−	0.678202i
$335$		0			0
$336$	−0.844290	+	2.59846i	−0.00251277	+	0.00773351i
$337$	139.008	+	22.0167i	0.412487	+	0.0653315i	0.359229	−	0.933249i	$-0.383040\pi$
$337$	139.008	+	22.0167i	0.412487	+	0.0653315i	0.0532574	+	0.998581i	$0.483040\pi$
$338$	71.9443	−	11.3949i	0.212853	−	0.0337126i
$339$	10.9925	−	3.57168i	0.0324263	−	0.0105359i
$340$		0			0
$341$	−159.574	−	221.373i	−0.467958	−	0.649188i
$342$	125.500	+	125.500i	0.366960	+	0.366960i
$343$	191.349	+	97.4970i	0.557868	+	0.284248i
$344$	−159.817	+	219.969i	−0.464583	+	0.639444i
$345$		0			0
$346$	−6.01638	+	18.5165i	−0.0173884	+	0.0535159i
$347$	315.980	−	161.000i	0.910606	−	0.463977i	0.0650608	−	0.997881i	$-0.479276\pi$
$347$	315.980	−	161.000i	0.910606	−	0.463977i	0.845545	+	0.533905i	$0.179276\pi$
$348$	−0.213175	+	1.34594i	−0.000612573	+	0.00386763i
$349$	−48.1418	+	66.2614i	−0.137942	+	0.189861i	−0.872399	−	0.488794i	$-0.837437\pi$
$349$	−48.1418	+	66.2614i	−0.137942	+	0.189861i	0.734457	+	0.678655i	$0.237437\pi$
$350$		0			0
$351$	20.0817			0.0572127
$352$	−128.845	−	66.2590i	−0.366038	−	0.188236i
$353$	197.329	−	197.329i	0.559006	−	0.559006i	−0.370018	−	0.929025i	$-0.620649\pi$
$353$	197.329	−	197.329i	0.559006	−	0.559006i	0.929025	+	0.370018i	$0.120649\pi$
$354$	−7.83683	+	2.54634i	−0.0221379	+	0.00719305i
$355$		0			0
$356$	−62.4022	+	45.3379i	−0.175287	+	0.127354i
$357$	5.34406	−	2.72293i	0.0149694	−	0.00762727i
$358$	11.9044	+	23.3638i	0.0332526	+	0.0652619i
$359$	−183.112	−	252.032i	−0.510060	−	0.702038i	0.473869	−	0.880595i	$-0.342857\pi$
$359$	−183.112	−	252.032i	−0.510060	−	0.702038i	−0.983930	+	0.178557i	$0.942857\pi$
$360$		0			0
$361$	73.4655	+	226.103i	0.203505	+	0.626325i
$362$	−213.727	−	213.727i	−0.590405	−	0.590405i
$363$	8.50345	−	8.37701i	0.0234255	−	0.0230772i
$364$			21.9877i			0.0604059i
$365$		0			0
$366$	−7.27013	−	5.28206i	−0.0198638	−	0.0144319i
$367$	−100.232	−	15.8753i	−0.273113	−	0.0432568i	0.0183757	−	0.999831i	$-0.494151\pi$
$367$	−100.232	−	15.8753i	−0.273113	−	0.0432568i	−0.291489	+	0.956574i	$0.594151\pi$
$368$	16.9154	+	33.1983i	0.0459657	+	0.0902128i
$369$	443.945	+	144.246i	1.20310	+	0.390912i
$370$		0			0
$371$	−153.445	−	111.484i	−0.413597	−	0.300496i
$372$	0.931184	−	1.82755i	0.00250318	−	0.00491277i
$373$	−212.910	+	212.910i	−0.570803	+	0.570803i	−0.932353	−	0.361550i	$-0.882248\pi$
$373$	−212.910	+	212.910i	−0.570803	+	0.570803i	0.361550	+	0.932353i	$0.382248\pi$
$374$	−156.670	−	488.397i	−0.418904	−	1.30587i
$375$		0			0
$376$	−7.35602	−	22.6395i	−0.0195639	−	0.0602114i
$377$	−29.1751	−	184.204i	−0.0773875	−	0.488605i
$378$	−1.14462	+	7.22683i	−0.00302809	+	0.0191186i
$379$	570.872	+	185.487i	1.50626	+	0.489413i	0.941836	−	0.336073i	$-0.109099\pi$
$379$	570.872	+	185.487i	1.50626	+	0.489413i	0.564422	+	0.825486i	$0.309099\pi$
$380$		0			0
$381$	0.431258	−	0.313327i	0.00113191	−	0.000822381i
$382$	97.9324	+	618.321i	0.256367	+	1.61864i
$383$	−543.751	−	277.055i	−1.41972	−	0.723381i	−0.435473	−	0.900202i	$-0.643419\pi$
$383$	−543.751	−	277.055i	−1.41972	−	0.723381i	−0.984243	+	0.176821i	$0.943419\pi$
$384$			7.29256i			0.0189910i
$385$		0			0
$386$	194.842			0.504772
$387$	−128.995	+	253.168i	−0.333321	+	0.654180i
$388$	127.386	−	20.1760i	0.328315	−	0.0520000i
$389$	−230.163	−	316.792i	−0.591679	−	0.814376i	0.403236	−	0.915096i	$-0.367885\pi$
$389$	−230.163	−	316.792i	−0.591679	−	0.814376i	−0.994915	+	0.100720i	$0.967885\pi$
$390$		0			0
$391$	25.2754	−	77.7898i	0.0646430	−	0.198951i
$392$	370.678	+	58.7096i	0.945607	+	0.149769i
$393$	−8.46142	+	1.34016i	−0.0215303	+	0.00341007i
$394$	282.049	−	91.6433i	0.715861	−	0.232597i
$395$		0			0
$396$	−78.7290	−	25.9070i	−0.198811	−	0.0654217i
$397$	−437.032	−	437.032i	−1.10084	−	1.10084i	−0.994310	−	0.106526i	$-0.966027\pi$
$397$	−437.032	−	437.032i	−1.10084	−	1.10084i	−0.106526	−	0.994310i	$-0.533973\pi$
$398$	473.769	+	241.397i	1.19037	+	0.606526i
$399$	1.49261	−	2.05440i	0.00374088	−	0.00514888i
$400$		0			0
$401$	−67.2375	+	206.936i	−0.167675	+	0.516049i	−0.999223	−	0.0394025i	$-0.987455\pi$
$401$	−67.2375	+	206.936i	−0.167675	+	0.516049i	0.831549	+	0.555452i	$0.187455\pi$
$402$	0.346663	−	0.176634i	0.000862347	−	0.000439388i
$403$	−43.9133	+	277.258i	−0.108966	+	0.687984i
$404$	−86.6150	+	119.215i	−0.214393	+	0.295087i
$405$		0			0
$406$	67.9529			0.167372
$407$	−242.604	+	37.4939i	−0.596080	+	0.0921227i
$408$	15.7364	−	15.7364i	0.0385695	−	0.0385695i
$409$	158.994	−	51.6604i	0.388739	−	0.126309i	−0.108125	−	0.994137i	$-0.534485\pi$
$409$	158.994	−	51.6604i	0.388739	−	0.126309i	0.496864	+	0.867828i	$0.334485\pi$
$410$		0			0
$411$	−7.27818	+	5.28791i	−0.0177085	+	0.0128660i
$412$	−95.1979	+	48.5058i	−0.231063	+	0.117732i
$413$	−49.4459	−	97.0430i	−0.119724	−	0.234971i
$414$	29.3094	+	40.3410i	0.0707957	+	0.0974420i
$415$		0			0
$416$	46.0549	+	141.743i	0.110709	+	0.340727i
$417$	−6.75500	−	6.75500i	−0.0161990	−	0.0161990i
$418$	−152.979	−	154.129i	−0.365978	−	0.368730i
$419$			187.271i			0.446948i	0.974710	+	0.223474i	$0.0717398\pi$
$419$			187.271i			0.446948i	−0.974710	+	0.223474i	$0.928260\pi$
$420$		0			0
$421$	215.858	+	156.830i	0.512726	+	0.372517i	0.813857	−	0.581066i	$-0.197364\pi$
$421$	215.858	+	156.830i	0.512726	+	0.372517i	−0.301131	+	0.953583i	$0.597364\pi$
$422$	266.788	+	42.2551i	0.632199	+	0.100130i
$423$	−11.2936	−	22.1649i	−0.0266987	−	0.0523992i
$424$	−669.313	−	217.473i	−1.57857	−	0.512908i
$425$		0			0
$426$	−15.2603	−	11.0872i	−0.0358222	−	0.0260264i
$427$	53.9239	−	105.832i	0.126285	−	0.247849i
$428$	−98.4448	+	98.4448i	−0.230011	+	0.230011i
$429$	−12.2787	−	0.0459859i	−0.0286216	−	0.000107193i
$430$		0			0
$431$	−133.538	−	410.989i	−0.309834	−	0.953570i	−0.977829	−	0.209404i	$-0.932847\pi$
$431$	−133.538	−	410.989i	−0.309834	−	0.953570i	0.667996	−	0.744165i	$-0.267153\pi$
$432$	3.31634	+	20.9386i	0.00767672	+	0.0484689i
$433$	107.820	−	680.747i	0.249006	−	1.57216i	−0.473497	−	0.880795i	$-0.657009\pi$
$433$	107.820	−	680.747i	0.249006	−	1.57216i	0.722503	−	0.691368i	$-0.242991\pi$
$434$	−97.2742	−	31.6063i	−0.224134	−	0.0728256i
$435$		0			0
$436$	64.8004	−	47.0802i	0.148625	−	0.107982i
$437$	−5.41735	−	34.2038i	−0.0123967	−	0.0782695i
$438$	−12.5880	−	6.41390i	−0.0287397	−	0.0146436i
$439$			620.821i			1.41417i	0.707129	+	0.707085i	$0.249990\pi$
$439$			620.821i			1.41417i	−0.707129	+	0.707085i	$0.750010\pi$
$440$		0			0
$441$	392.194			0.889328
$442$	−239.531	+	470.106i	−0.541925	+	1.06359i
$443$	−700.851	+	111.004i	−1.58206	+	0.250573i	−0.884703	−	0.466154i	$-0.845639\pi$
$443$	−700.851	+	111.004i	−1.58206	+	0.250573i	−0.697353	+	0.716728i	$0.745639\pi$
$444$	−1.08453	−	1.49273i	−0.00244263	−	0.00336200i
$445$		0			0
$446$	169.234	−	520.848i	0.379448	−	1.16782i
$447$	−4.75138	−	0.752545i	−0.0106295	−	0.00168355i
$448$	−163.053	+	25.8251i	−0.363958	+	0.0576453i
$449$	−346.705	+	112.651i	−0.772173	+	0.250894i	−0.668495	−	0.743717i	$-0.733061\pi$
$449$	−346.705	+	112.651i	−0.772173	+	0.250894i	−0.103678	+	0.994611i	$0.533061\pi$
$450$		0			0
$451$	−542.522	−	178.525i	−1.20293	−	0.395843i
$452$	69.4343	+	69.4343i	0.153616	+	0.153616i
$453$	−25.4165	−	12.9504i	−0.0561071	−	0.0285880i
$454$	−392.099	+	539.678i	−0.863654	+	1.18872i
$455$		0			0
$456$	2.91165	−	8.96115i	0.00638521	−	0.0196516i
$457$	382.378	−	194.831i	0.836713	−	0.426327i	0.0175216	−	0.999846i	$-0.494422\pi$
$457$	382.378	−	194.831i	0.836713	−	0.426327i	0.819192	+	0.573520i	$0.194422\pi$
$458$	−34.7381	+	219.328i	−0.0758475	+	0.478882i
$459$	27.3544	−	37.6501i	0.0595956	−	0.0820263i
$460$		0			0
$461$	721.637			1.56537			0.782687	−	0.622416i	$-0.213849\pi$
$461$	721.637			1.56537			0.782687	+	0.622416i	$0.213849\pi$
$462$	0.716411	−	4.41613i	0.00155067	−	0.00955873i
$463$	−180.799	+	180.799i	−0.390494	+	0.390494i	−0.874863	−	0.484370i	$-0.839049\pi$
$463$	−180.799	+	180.799i	−0.390494	+	0.390494i	0.484370	+	0.874863i	$0.339049\pi$
$464$	187.246	−	60.8400i	0.403548	−	0.131121i
$465$		0			0
$466$	366.724	−	266.440i	0.786961	−	0.571760i
$467$	−513.866	+	261.828i	−1.10036	+	0.560659i	−0.907281	−	0.420525i	$-0.861846\pi$
$467$	−513.866	+	261.828i	−1.10036	+	0.560659i	−0.193075	+	0.981184i	$0.561846\pi$
$468$	38.7062	+	75.9652i	0.0827055	+	0.162319i
$469$	3.02270	+	4.16039i	0.00644499	+	0.00887077i
$470$		0			0
$471$	0.192859	+	0.593560i	0.000409468	+	0.00126021i
$472$	−285.757	−	285.757i	−0.605418	−	0.605418i
$473$	158.991	−	309.169i	0.336132	−	0.653634i
$474$		−	14.8438i		−	0.0313161i
$475$		0			0
$476$	41.2237	+	29.9508i	0.0866044	+	0.0629218i
$477$	−726.385	−	115.048i	−1.52282	−	0.241191i
$478$	−200.547	−	393.596i	−0.419555	−	0.823422i
$479$	232.826	+	75.6499i	0.486068	+	0.157933i	0.541791	−	0.840513i	$-0.317746\pi$
$479$	232.826	+	75.6499i	0.486068	+	0.157933i	−0.0557233	+	0.998446i	$0.517746\pi$
$480$		0			0
$481$	204.294	+	148.428i	0.424727	+	0.308582i
$482$	−231.863	+	455.058i	−0.481044	+	0.944103i
$483$	0.504479	−	0.504479i	0.00104447	−	0.00104447i
$484$	96.2091	+	32.0589i	0.198779	+	0.0662374i
$485$		0			0
$486$	13.1532	+	40.4815i	0.0270643	+	0.0832953i
$487$	133.328	+	841.801i	0.273775	+	1.72855i	0.614968	+	0.788552i	$0.289169\pi$
$487$	133.328	+	841.801i	0.273775	+	1.72855i	−0.341193	+	0.939993i	$0.610831\pi$
$488$	68.9439	−	435.295i	0.141278	−	0.891997i
$489$	21.5021	+	6.98645i	0.0439715	+	0.0142872i
$490$		0			0
$491$	349.478	−	253.910i	0.711767	−	0.517129i	−0.171976	−	0.985101i	$-0.555015\pi$
$491$	349.478	−	253.910i	0.711767	−	0.517129i	0.883743	+	0.467972i	$0.155015\pi$
$492$	−0.671542	−	4.23995i	−0.00136492	−	0.00861779i
$493$	−385.096	−	196.216i	−0.781128	−	0.398004i
$494$			223.384i			0.452195i
$495$		0			0
$496$	−296.340			−0.597460
$497$	113.188	−	222.144i	0.227743	−	0.446970i
$498$	2.37038	−	0.375432i	0.00475980	−	0.000753879i
$499$	−464.030	−	638.682i	−0.929919	−	1.27992i	−0.959891	−	0.280373i	$-0.909542\pi$
$499$	−464.030	−	638.682i	−0.929919	−	1.27992i	0.0299719	−	0.999551i	$-0.490458\pi$
$500$		0			0
$501$	−4.80012	+	14.7733i	−0.00958108	+	0.0294875i
$502$	−368.062	−	58.2953i	−0.733192	−	0.116126i
$503$	−213.537	+	33.8209i	−0.424527	+	0.0672385i	−0.365043	−	0.930991i	$-0.618946\pi$
$503$	−213.537	+	33.8209i	−0.424527	+	0.0672385i	−0.0594843	+	0.998229i	$0.518946\pi$
$504$	−170.548	+	55.4145i	−0.338390	+	0.109949i
$505$		0			0
$506$	−35.6763	−	49.4930i	−0.0705065	−	0.0978122i
$507$	−2.85748	−	2.85748i	−0.00563606	−	0.00563606i
$508$	4.03515	+	2.05601i	0.00794320	+	0.00404726i
$509$	342.653	−	471.621i	0.673188	−	0.926564i	−0.326639	−	0.945149i	$-0.605916\pi$
$509$	342.653	−	471.621i	0.673188	−	0.926564i	0.999827	+	0.0185853i	$0.00591622\pi$
$510$		0			0
$511$	57.7042	−	177.595i	0.112924	−	0.347544i
$512$	−506.440	+	258.044i	−0.989140	+	0.503992i
$513$	3.08233	−	19.4610i	0.00600843	−	0.0379358i
$514$	350.915	−	482.993i	0.682713	−	0.939674i
$515$		0			0
$516$	2.61304			0.00506402
$517$	13.7165	+	27.1713i	0.0265310	+	0.0525557i
$518$	−65.0595	+	65.0595i	−0.125597	+	0.125597i
$519$	1.02726	−	0.333778i	0.00197931	−	0.000643117i
$520$		0			0
$521$	−212.021	+	154.042i	−0.406950	+	0.295666i	−0.772366	−	0.635178i	$-0.780927\pi$
$521$	−212.021	+	154.042i	−0.406950	+	0.295666i	0.365416	+	0.930844i	$0.380927\pi$
$522$	234.769	−	119.621i	0.449750	−	0.229159i
$523$	−49.0341	−	96.2349i	−0.0937555	−	0.184006i	0.839366	−	0.543567i	$-0.182926\pi$
$523$	−49.0341	−	96.2349i	−0.0937555	−	0.184006i	−0.933122	+	0.359561i	$0.882926\pi$
$524$	−42.7800	−	58.8816i	−0.0816412	−	0.112369i
$525$		0			0
$526$	148.642	+	457.472i	0.282588	+	0.869718i
$527$	459.999	+	459.999i	0.872863	+	0.872863i
$528$	−1.97979	−	12.8102i	−0.00374960	−	0.0242618i
$529$			519.271i			0.981608i
$530$		0			0
$531$	−341.660	−	248.230i	−0.643427	−	0.467477i
$532$	21.3082	+	3.37489i	0.0400530	+	0.00634378i
$533$	266.724	+	523.476i	0.500421	+	0.982132i
$534$	−15.3541	−	4.98885i	−0.0287530	−	0.00934241i
$535$		0			0
$536$	15.4370	+	11.2156i	0.0288004	+	0.0209247i
$537$	0.660436	−	1.29618i	0.00122986	−	0.00241374i
$538$	−25.9905	+	25.9905i	−0.0483095	+	0.0483095i
$539$	−479.863	−	1.79718i	−0.890284	−	0.00333428i
$540$		0			0
$541$	−202.598	−	623.533i	−0.374488	−	1.15256i	−0.943823	−	0.330450i	$-0.892799\pi$
$541$	−202.598	−	623.533i	−0.374488	−	1.15256i	0.569335	−	0.822105i	$-0.307201\pi$
$542$	−127.900	−	807.527i	−0.235977	−	1.48990i
$543$	−2.62318	+	16.5621i	−0.00483090	+	0.0305011i
$544$	328.480	+	106.730i	0.603823	+	0.196194i
$545$		0			0
$546$	−3.72318	+	2.70505i	−0.00681901	+	0.00495430i
$547$	30.6938	+	193.793i	0.0561130	+	0.354283i	0.999730	+	0.0232437i	$0.00739937\pi$
$547$	30.6938	+	193.793i	0.0561130	+	0.354283i	−0.943617	+	0.331040i	$0.892601\pi$
$548$	−68.0996	−	34.6985i	−0.124269	−	0.0633184i
$549$		−	460.561i		−	0.838909i
$550$		0			0
$551$	−182.989			−0.332104
$552$	1.20180	−	2.35867i	0.00217718	−	0.00427296i
$553$	193.783	−	30.6922i	0.350421	−	0.0555013i
$554$	400.841	+	551.710i	0.723540	+	0.995867i
$555$		0			0
$556$	25.0797	−	77.1872i	0.0451073	−	0.138826i
$557$	−22.3245	−	3.53585i	−0.0400799	−	0.00634803i	0.136362	−	0.990659i	$-0.456459\pi$
$557$	−22.3245	−	3.53585i	−0.0400799	−	0.00634803i	−0.176442	+	0.984311i	$0.556459\pi$
$558$	−391.710	+	62.0407i	−0.701989	+	0.111184i
$559$	−340.116	+	110.510i	−0.608436	+	0.197693i
$560$		0			0
$561$	−16.8117	+	22.9580i	−0.0299674	+	0.0409234i
$562$	−239.680	−	239.680i	−0.426478	−	0.426478i
$563$	−67.0356	−	34.1564i	−0.119069	−	0.0606685i	0.393442	−	0.919350i	$-0.371284\pi$
$563$	−67.0356	−	34.1564i	−0.119069	−	0.0606685i	−0.512510	+	0.858681i	$0.671284\pi$
$564$	−0.134469	+	0.185080i	−0.000238420	+	0.000328157i
$565$		0			0
$566$	305.338	−	939.734i	0.539466	−	1.66031i
$567$	−166.792	+	84.9847i	−0.294166	+	0.149885i
$568$	144.716	−	913.698i	0.254781	−	1.60862i
$569$	−322.832	+	444.341i	−0.567368	+	0.780915i	−0.992240	−	0.124338i	$-0.960319\pi$
$569$	−322.832	+	444.341i	−0.567368	+	0.780915i	0.424872	+	0.905253i	$0.360319\pi$
$570$		0			0
$571$	451.066			0.789957			0.394979	−	0.918690i	$-0.370752\pi$
$571$	451.066			0.789957			0.394979	+	0.918690i	$0.370752\pi$
$572$	−47.0103	−	93.1235i	−0.0821859	−	0.162803i
$573$	24.5584	−	24.5584i	0.0428594	−	0.0428594i
$574$	−203.587	+	66.1495i	−0.354681	+	0.115243i
$575$		0			0
$576$	−517.869	+	376.254i	−0.899079	+	0.653219i
$577$	−36.5804	+	18.6386i	−0.0633975	+	0.0323026i	−0.485402	−	0.874291i	$-0.661327\pi$
$577$	−36.5804	+	18.6386i	−0.0633975	+	0.0323026i	0.422004	+	0.906594i	$0.361327\pi$
$578$	321.796	+	631.560i	0.556740	+	1.09266i
$579$	−6.35364	−	8.74504i	−0.0109735	−	0.0151037i
$580$		0			0
$581$	9.80235	+	30.1685i	0.0168715	+	0.0519252i
$582$	19.0881	+	19.0881i	0.0327975	+	0.0327975i
$583$	888.231	+	144.094i	1.52355	+	0.247160i
$584$		−	692.873i		−	1.18643i
$585$		0			0
$586$	−224.909	−	163.406i	−0.383804	−	0.278850i
$587$	−9.99314	−	1.58276i	−0.0170241	−	0.00269635i	0.147917	−	0.989000i	$-0.452743\pi$
$587$	−9.99314	−	1.58276i	−0.0170241	−	0.00269635i	−0.164941	+	0.986303i	$0.552743\pi$
$588$	−1.63744	−	3.21366i	−0.00278476	−	0.00546541i
$589$	261.949	+	85.1123i	0.444735	+	0.144503i
$590$		0			0
$591$	−13.3106	−	9.67073i	−0.0225222	−	0.0163633i
$592$	−121.024	+	237.523i	−0.204433	+	0.401221i
$593$	239.814	−	239.814i	0.404408	−	0.404408i	−0.475375	−	0.879783i	$-0.657688\pi$
$593$	239.814	−	239.814i	0.404408	−	0.404408i	0.879783	+	0.475375i	$0.157688\pi$
$594$	−10.6034	−	33.0546i	−0.0178508	−	0.0556475i
$595$		0			0
$596$	−12.6294	−	38.8692i	−0.0211902	−	0.0652167i
$597$	−4.61466	−	29.1358i	−0.00772976	−	0.0488038i
$598$	−9.81781	+	61.9872i	−0.0164177	+	0.103658i
$599$	−336.022	−	109.180i	−0.560971	−	0.182271i	0.0147869	−	0.999891i	$-0.495293\pi$
$599$	−336.022	−	109.180i	−0.560971	−	0.182271i	−0.575758	+	0.817620i	$0.695293\pi$
$600$		0			0
$601$	−276.836	+	201.133i	−0.460626	+	0.334664i	−0.793777	−	0.608209i	$-0.791888\pi$
$601$	−276.836	+	201.133i	−0.460626	+	0.334664i	0.333151	+	0.942873i	$0.391888\pi$
$602$	−20.3836	−	128.697i	−0.0338598	−	0.213782i
$603$	17.7668	+	9.05266i	0.0294641	+	0.0150127i
$604$		−	242.345i		−	0.401233i
$605$		0			0
$606$	−30.8425			−0.0508952
$607$	227.460	−	446.416i	0.374728	−	0.735446i	−0.624222	−	0.781247i	$-0.714584\pi$
$607$	227.460	−	446.416i	0.374728	−	0.735446i	0.998951	+	0.0458010i	$0.0145840\pi$
$608$	144.431	−	22.8756i	0.237551	−	0.0376244i
$609$	−2.21589	−	3.04991i	−0.00363857	−	0.00500807i
$610$		0			0
$611$	9.67520	−	29.7772i	0.0158350	−	0.0487352i
$612$	195.147	+	30.9082i	0.318868	+	0.0505037i
$613$	527.169	−	83.4954i	0.859983	−	0.136208i	0.289160	−	0.957281i	$-0.406624\pi$
$613$	527.169	−	83.4954i	0.859983	−	0.136208i	0.570823	+	0.821073i	$0.306624\pi$
$614$	−56.2866	+	18.2886i	−0.0916720	+	0.0297861i
$615$		0			0
$616$	208.926	−	67.0202i	0.339166	−	0.108799i
$617$	194.972	+	194.972i	0.316001	+	0.316001i	0.847229	−	0.531228i	$-0.178269\pi$
$617$	194.972	+	194.972i	0.316001	+	0.316001i	−0.531228	+	0.847229i	$0.678269\pi$
$618$	−19.9252	−	10.1524i	−0.0322414	−	0.0164278i
$619$	483.351	−	665.276i	0.780858	−	1.07476i	−0.214329	−	0.976762i	$-0.568756\pi$
$619$	483.351	−	665.276i	0.780858	−	1.07476i	0.995187	−	0.0979970i	$-0.0312436\pi$
$620$		0			0
$621$	1.71064	−	5.26480i	0.00275465	−	0.00847794i
$622$	262.686	−	133.845i	0.422324	−	0.215185i
$623$	33.3810	−	210.760i	0.0535811	−	0.338298i
$624$	−7.83744	+	10.7873i	−0.0125600	+	0.0172874i
$625$		0			0
$626$	−916.071			−1.46337
$627$	−1.92921	+	11.8922i	−0.00307690	+	0.0189668i
$628$	−3.74923	+	3.74923i	−0.00597011	+	0.00597011i
$629$	556.560	−	180.837i	0.884834	−	0.287500i
$630$		0			0
$631$	−645.846	+	469.235i	−1.02353	+	0.743637i	−0.967003	−	0.254764i	$-0.918002\pi$
$631$	−645.846	+	469.235i	−1.02353	+	0.743637i	−0.0565250	+	0.998401i	$0.518002\pi$
$632$	648.643	−	330.500i	1.02633	−	0.522943i
$633$	−6.80323	−	13.3521i	−0.0107476	−	0.0210933i
$634$	606.436	+	834.687i	0.956523	+	1.31654i
$635$		0			0
$636$	2.09001	+	6.43238i	0.00328617	+	0.0101138i
$637$	349.043	+	349.043i	0.547948	+	0.547948i
$638$	−287.797	+	145.285i	−0.451093	+	0.227719i
$639$		−	966.733i		−	1.51288i
$640$		0			0
$641$	534.242	+	388.150i	0.833451	+	0.605538i	0.920534	−	0.390663i	$-0.127754\pi$
$641$	534.242	+	388.150i	0.833451	+	0.605538i	−0.0870824	+	0.996201i	$0.527754\pi$
$642$	−28.7808	−	4.55843i	−0.0448299	−	0.00710036i
$643$	186.876	+	366.766i	0.290632	+	0.570398i	0.989445	−	0.144907i	$-0.0462882\pi$
$643$	186.876	+	366.766i	0.290632	+	0.570398i	−0.698813	+	0.715304i	$0.746288\pi$
$644$	5.76452	+	1.87300i	0.00895111	+	0.00290839i
$645$		0			0
$646$	418.812	+	304.284i	0.648315	+	0.471028i
$647$	−16.7738	+	32.9204i	−0.0259255	+	0.0508816i	−0.903606	−	0.428365i	$-0.859090\pi$
$647$	−16.7738	+	32.9204i	−0.0259255	+	0.0508816i	0.877681	+	0.479246i	$0.159090\pi$
$648$	−491.143	+	491.143i	−0.757937	+	0.757937i
$649$	416.896	+	305.285i	0.642366	+	0.470392i
$650$		0			0
$651$	1.75346	+	5.39659i	0.00269349	+	0.00828970i
$652$	30.0473	+	189.711i	0.0460848	+	0.290968i
$653$	−73.3615	+	463.186i	−0.112345	+	0.709320i	0.865643	+	0.500661i	$0.166910\pi$
$653$	−73.3615	+	463.186i	−0.112345	+	0.709320i	−0.977988	+	0.208659i	$0.933090\pi$
$654$	15.9442	+	5.18057i	0.0243795	+	0.00792137i
$655$		0			0
$656$	−501.766	+	364.554i	−0.764887	+	0.555723i
$657$	−113.269	−	715.151i	−0.172403	−	1.08851i
$658$	10.1645	+	5.17908i	0.0154476	+	0.00787094i
$659$			476.130i			0.722504i	0.932468	+	0.361252i	$0.117651\pi$
$659$			476.130i			0.722504i	−0.932468	+	0.361252i	$0.882349\pi$
$660$		0			0
$661$	−23.2329			−0.0351481			−0.0175740	−	0.999846i	$-0.505594\pi$
$661$	−23.2329			−0.0351481			−0.0175740	+	0.999846i	$0.505594\pi$
$662$	272.175	−	534.174i	0.411141	−	0.806910i
$663$	28.9106	−	4.57898i	0.0436057	−	0.00690646i
$664$	69.1824	+	95.2214i	0.104190	+	0.143406i
$665$		0			0
$666$	−110.245	+	339.301i	−0.165534	+	0.509461i
$667$	−50.7780	−	8.04244i	−0.0761289	−	0.0120576i
$668$	−130.343	+	20.6443i	−0.195125	+	0.0309047i
$669$	−28.8957	+	9.38878i	−0.0431924	+	0.0140341i
$670$		0			0
$671$	−2.11046	+	563.513i	−0.00314525	+	0.839811i
$672$	2.13024	+	2.13024i	0.00317000	+	0.00317000i
$673$	566.940	+	288.871i	0.842408	+	0.429228i	0.821264	−	0.570548i	$-0.193269\pi$
$673$	566.940	+	288.871i	0.842408	+	0.429228i	0.0211437	+	0.999776i	$0.493269\pi$
$674$	−147.100	+	202.466i	−0.218249	+	0.300394i
$675$		0			0
$676$	10.6091	−	32.6515i	0.0156940	−	0.0483011i
$677$	−470.522	+	239.743i	−0.695010	+	0.354125i	−0.765543	−	0.643384i	$-0.777530\pi$
$677$	−470.522	+	239.743i	−0.695010	+	0.354125i	0.0705336	+	0.997509i	$0.477530\pi$
$678$	−3.21512	+	20.2995i	−0.00474206	+	0.0299402i
$679$	−209.723	+	288.659i	−0.308871	+	0.425124i
$680$		0			0
$681$	37.0083			0.0543440
$682$	479.555	−	74.1141i	0.703160	−	0.108672i
$683$	−18.9735	+	18.9735i	−0.0277797	+	0.0277797i	−0.720860	−	0.693081i	$-0.756253\pi$
$683$	−18.9735	+	18.9735i	−0.0277797	+	0.0277797i	0.693081	+	0.720860i	$0.256253\pi$
$684$	79.5584	−	25.8501i	0.116314	−	0.0377926i
$685$		0			0
$686$	−308.942	+	224.459i	−0.450352	+	0.327200i
$687$	10.9768	−	5.59298i	0.0159779	−	0.00814116i
$688$	−171.394	−	336.379i	−0.249119	−	0.488923i
$689$	−544.075	−	748.855i	−0.789659	−	1.08687i
$690$		0			0
$691$	26.2414	+	80.7627i	0.0379759	+	0.116878i	0.968247	−	0.249994i	$-0.0804287\pi$
$691$	26.2414	+	80.7627i	0.0379759	+	0.116878i	−0.930271	+	0.366872i	$0.880429\pi$
$692$	6.48871	+	6.48871i	0.00937675	+	0.00937675i
$693$	204.687	−	103.330i	0.295364	−	0.149105i
$694$			630.599i			0.908644i
$695$		0			0
$696$	−11.3166	−	8.22200i	−0.0162595	−	0.0118132i
$697$	1344.76	+	212.989i	1.92935	+	0.305579i
$698$	−66.1187	−	129.765i	−0.0947259	−	0.185910i
$699$	−23.9172	−	7.77116i	−0.0342162	−	0.0111175i
$700$		0			0
$701$	300.312	+	218.189i	0.428405	+	0.311254i	0.781011	−	0.624517i	$-0.214704\pi$
$701$	300.312	+	218.189i	0.428405	+	0.311254i	−0.352606	+	0.935772i	$0.614704\pi$
$702$	−16.2114	+	31.8167i	−0.0230932	+	0.0453229i
$703$	175.198	−	175.198i	0.249215	−	0.249215i
$704$	635.356	−	457.988i	0.902495	−	0.650551i
$705$		0			0
$706$	153.343	+	471.940i	0.217199	+	0.668471i
$707$	−63.7722	−	402.642i	−0.0902012	−	0.569508i
$708$	−0.607557	+	3.83596i	−0.000858131	+	0.00541803i
$709$	−613.715	−	199.408i	−0.865607	−	0.281253i	−0.157639	−	0.987497i	$-0.550388\pi$
$709$	−613.715	−	199.408i	−0.865607	−	0.281253i	−0.707968	+	0.706244i	$0.750388\pi$
$710$		0			0
$711$	615.469	−	447.165i	0.865639	−	0.628923i
$712$	−123.859	−	782.017i	−0.173960	−	1.09834i
$713$	68.9478	+	35.1306i	0.0967009	+	0.0492716i
$714$			10.6651i			0.0149371i
$715$		0			0
$716$	12.3590			0.0172612
$717$	−11.1260	+	21.8360i	−0.0155174	+	0.0304546i
$718$	547.131	−	86.6571i	0.762021	−	0.120692i
$719$	409.022	+	562.970i	0.568876	+	0.782991i	0.992421	−	0.122885i	$-0.0392145\pi$
$719$	409.022	+	562.970i	0.568876	+	0.782991i	−0.423545	+	0.905875i	$0.639214\pi$
$720$		0			0
$721$	91.3385	−	281.111i	0.126683	−	0.389890i
$722$	−417.537	−	66.1314i	−0.578306	−	0.0915947i
$723$	27.9851	−	4.43241i	0.0387070	−	0.00613058i
$724$	−135.488	+	44.0227i	−0.187138	+	0.0608048i
$725$		0			0
$726$	6.40762	+	20.2351i	0.00882592	+	0.0278721i
$727$	840.761	+	840.761i	1.15648	+	1.15648i	0.985227	+	0.171254i	$0.0547818\pi$
$727$	840.761	+	840.761i	1.15648	+	1.15648i	0.171254	+	0.985227i	$0.445218\pi$
$728$	−201.102	−	102.466i	−0.276239	−	0.140751i
$729$	−425.718	+	585.950i	−0.583975	+	0.803773i
$730$		0			0
$731$	−256.101	+	788.198i	−0.350343	+	1.07825i
$732$	−3.77386	+	1.92288i	−0.00515555	+	0.00262689i
$733$	−85.4375	+	539.431i	−0.116559	+	0.735922i	0.858308	+	0.513134i	$0.171516\pi$
$733$	−85.4375	+	539.431i	−0.116559	+	0.735922i	−0.974867	+	0.222788i	$0.928484\pi$
$734$	106.067	−	145.989i	0.144506	−	0.198895i
$735$		0			0
$736$	41.0837			0.0558203
$737$	−21.6969	−	11.1577i	−0.0294395	−	0.0151393i
$738$	−586.924	+	586.924i	−0.795290	+	0.795290i
$739$	−1133.64	+	368.342i	−1.53402	+	0.498433i	−0.949719	−	0.313105i	$-0.898631\pi$
$739$	−1133.64	+	368.342i	−1.53402	+	0.498433i	−0.584300	+	0.811538i	$0.698631\pi$
$740$		0			0
$741$	10.0261	−	7.28439i	0.0135305	−	0.00983049i
$742$	300.503	−	153.114i	0.404991	−	0.206353i
$743$	125.677	+	246.656i	0.169149	+	0.331973i	0.959983	−	0.280057i	$-0.0903533\pi$
$743$	125.677	+	246.656i	0.169149	+	0.331973i	−0.790835	+	0.612030i	$0.790353\pi$
$744$	12.3755	+	17.0334i	0.0166337	+	0.0228943i
$745$		0			0
$746$	−165.450	−	509.203i	−0.221783	−	0.682578i
$747$	86.9733	+	86.9733i	0.116430	+	0.116430i
$748$	−238.628	−	38.7116i	−0.319021	−	0.0517535i
$749$		−	385.152i		−	0.514222i
$750$		0			0
$751$	579.889	+	421.314i	0.772156	+	0.561004i	0.902615	−	0.430450i	$-0.141645\pi$
$751$	579.889	+	421.314i	0.772156	+	0.561004i	−0.130459	+	0.991454i	$0.541645\pi$
$752$	32.6456	+	5.17056i	0.0434117	+	0.00687574i
$753$	9.38578	+	18.4206i	0.0124645	+	0.0244630i
$754$	315.399	+	102.479i	0.418301	+	0.135914i
$755$		0			0
$756$	2.79001	+	2.02706i	0.00369049	+	0.00268130i
$757$	−149.714	+	293.829i	−0.197772	+	0.388150i	−0.968500	−	0.249015i	$-0.919893\pi$
$757$	−149.714	+	293.829i	−0.197772	+	0.388150i	0.770727	+	0.637165i	$0.219893\pi$
$758$	−754.730	+	754.730i	−0.995686	+	0.995686i
$759$	−1.05800	+	3.21518i	−0.00139394	+	0.00423607i
$760$		0			0
$761$	157.983	+	486.220i	0.207599	+	0.638923i	0.999597	+	0.0283993i	$0.00904099\pi$
$761$	157.983	+	486.220i	0.207599	+	0.638923i	−0.791998	+	0.610524i	$0.790959\pi$
$762$	0.148281	+	0.936211i	0.000194595	+	0.00122862i
$763$	−34.6639	+	218.859i	−0.0454311	+	0.286840i
$764$	280.621	+	91.1794i	0.367306	+	0.119345i
$765$		0			0
$766$	877.912	−	637.841i	1.14610	−	0.832690i
$767$	−83.1500	−	524.988i	−0.108409	−	0.684470i
$768$	13.4797	+	6.86827i	0.0175517	+	0.00894306i
$769$			1149.32i			1.49456i	0.664507	+	0.747282i	$0.268642\pi$
$769$			1149.32i			1.49456i	−0.664507	+	0.747282i	$0.731358\pi$
$770$		0			0
$771$	−33.1211			−0.0429586
$772$	41.6917	−	81.8246i	0.0540048	−	0.105990i
$773$	−1425.52	+	225.780i	−1.84413	+	0.292082i	−0.978136	−	0.207965i	$-0.933316\pi$
$773$	−1425.52	+	225.780i	−1.84413	+	0.292082i	−0.865998	+	0.500047i	$0.833316\pi$
$774$	−296.975	−	408.751i	−0.383689	−	0.528102i
$775$		0			0
$776$	−409.109	+	1259.11i	−0.527202	+	1.62256i
$777$	5.04159	+	0.798509i	0.00648853	+	0.00102768i
$778$	687.719	−	108.924i	0.883958	−	0.140005i
$779$	548.237	−	178.133i	0.703771	−	0.228669i
$780$		0			0
$781$	−4.42993	+	1182.83i	−0.00567212	+	1.51451i
$782$	102.843	+	102.843i	0.131513	+	0.131513i
$783$	−26.0632	−	13.2799i	−0.0332864	−	0.0169603i
$784$	−306.295	+	421.579i	−0.390682	+	0.537728i
$785$		0			0
$786$	4.70739	−	14.4878i	0.00598904	−	0.0184324i
$787$	686.578	−	349.829i	0.872399	−	0.444510i	0.0403333	−	0.999186i	$-0.487158\pi$
$787$	686.578	−	349.829i	0.872399	−	0.444510i	0.832066	+	0.554677i	$0.187158\pi$
$788$	21.8661	−	138.057i	0.0277489	−	0.175199i
$789$	15.6855	−	21.5892i	0.0198802	−	0.0273628i
$790$		0			0
$791$	−271.653			−0.343430
$792$	603.837	−	599.331i	0.762420	−	0.756731i
$793$	409.888	−	409.888i	0.516883	−	0.516883i
$794$	1045.22	−	339.613i	1.31640	−	0.427725i
$795$		0			0
$796$	202.751	−	147.308i	0.254713	−	0.185060i
$797$	−1366.39	+	696.209i	−1.71441	+	0.873537i	−0.733350	+	0.679851i	$0.762044\pi$
$797$	−1366.39	+	696.209i	−1.71441	+	0.873537i	−0.981064	+	0.193686i	$0.937956\pi$
$798$	2.04998	+	4.02331i	0.00256890	+	0.00504174i
$799$	−42.6486	−	58.7008i	−0.0533775	−	0.0734678i
$800$		0			0
$801$	−255.683	−	786.913i	−0.319205	−	0.982413i
$802$	−273.582	−	273.582i	−0.341125	−	0.341125i
$803$	135.311	+	875.532i	0.168507	+	1.09033i
$804$		−	0.183378i		−	0.000228082i
$805$		0			0
$806$	−403.827	−	293.397i	−0.501026	−	0.364017i
$807$	2.01406	+	0.318995i	0.00249573	+	0.000395285i
$808$	−686.713	−	1347.75i	−0.849892	−	1.66801i
$809$	−408.675	−	132.787i	−0.505161	−	0.164137i	0.0453394	−	0.998972i	$-0.485563\pi$
$809$	−408.675	−	132.787i	−0.505161	−	0.164137i	−0.550500	+	0.834835i	$0.685563\pi$
$810$		0			0
$811$	−66.5901	−	48.3805i	−0.0821086	−	0.0596554i	0.545974	−	0.837802i	$-0.316160\pi$
$811$	−66.5901	−	48.3805i	−0.0821086	−	0.0596554i	−0.628082	+	0.778147i	$0.716160\pi$
$812$	14.5404	−	28.5371i	0.0179068	−	0.0351442i
$813$	−32.0733	+	32.0733i	−0.0394506	+	0.0394506i
$814$	136.444	−	414.642i	0.167622	−	0.509388i
$815$		0			0
$816$	9.54875	+	29.3880i	0.0117019	+	0.0360147i
$817$	54.8908	+	346.567i	0.0671858	+	0.424194i
$818$	−46.5031	+	293.609i	−0.0568497	+	0.358935i
$819$	−224.318	−	72.8855i	−0.273893	−	0.0889932i
$820$		0			0
$821$	231.122	−	167.920i	0.281513	−	0.204531i	−0.438064	−	0.898944i	$-0.644336\pi$
$821$	231.122	−	167.920i	0.281513	−	0.204531i	0.719577	+	0.694412i	$0.244336\pi$
$822$	−2.50249	−	15.8001i	−0.00304439	−	0.0192215i
$823$	−67.9203	−	34.6071i	−0.0825277	−	0.0420500i	0.412240	−	0.911076i	$-0.364747\pi$
$823$	−67.9203	−	34.6071i	−0.0825277	−	0.0420500i	−0.494767	+	0.869026i	$0.664747\pi$
$824$		−	1096.73i		−	1.33099i
$825$		0			0
$826$	193.668			0.234465
$827$	−469.154	+	920.766i	−0.567296	+	1.11338i	0.412044	+	0.911164i	$0.364815\pi$
$827$	−469.154	+	920.766i	−0.567296	+	1.11338i	−0.979341	+	0.202218i	$0.935185\pi$
$828$	23.2129	−	3.67656i	0.0280349	−	0.00444029i
$829$	−181.436	−	249.725i	−0.218861	−	0.301237i	0.685442	−	0.728127i	$-0.259609\pi$
$829$	−181.436	−	249.725i	−0.218861	−	0.301237i	−0.904303	+	0.426890i	$0.859609\pi$
$830$		0			0
$831$	11.6912	−	35.9817i	0.0140688	−	0.0432993i
$832$	−795.748	−	126.034i	−0.956428	−	0.151483i
$833$	1129.85	−	178.951i	1.35637	−	0.214827i
$834$	16.1555	−	5.24925i	0.0193711	−	0.00629406i
$835$		0			0
$836$	−97.4611	+	31.2640i	−0.116580	+	0.0373971i
$837$	31.1327	+	31.1327i	0.0371955	+	0.0371955i
$838$	−296.706	−	151.179i	−0.354065	−	0.180405i
$839$	206.489	−	284.207i	0.246113	−	0.338745i	−0.668032	−	0.744132i	$-0.732863\pi$
$839$	206.489	−	284.207i	0.246113	−	0.338745i	0.914145	+	0.405387i	$0.132863\pi$
$840$		0			0
$841$	175.935	−	541.473i	0.209198	−	0.643845i
$842$	−422.732	+	215.392i	−0.502057	+	0.255811i
$843$	−2.94172	+	18.5733i	−0.00348959	+	0.0220324i
$844$	74.8317	−	102.997i	0.0886632	−	0.122034i
$845$		0			0
$846$	44.2342			0.0522863
$847$	−250.916	+	125.490i	−0.296241	+	0.148158i
$848$	690.959	−	690.959i	0.814810	−	0.814810i
$849$	−52.1347	+	16.9396i	−0.0614072	+	0.0199524i
$850$		0			0
$851$	56.3159	−	40.9159i	0.0661762	−	0.0480798i
$852$	−7.92147	+	4.03619i	−0.00929750	+	0.00473731i
$853$	−529.736	−	1039.67i	−0.621027	−	1.21883i	−0.960516	−	0.278224i	$-0.910254\pi$
$853$	−529.736	−	1039.67i	−0.621027	−	1.21883i	0.339489	−	0.940610i	$-0.389746\pi$
$854$	124.144	+	170.870i	0.145368	+	0.200082i
$855$		0			0
$856$	−441.615	−	1359.15i	−0.515906	−	1.58779i
$857$	242.005	+	242.005i	0.282387	+	0.282387i	0.834060	−	0.551673i	$-0.186011\pi$
$857$	242.005	+	242.005i	0.282387	+	0.282387i	−0.551673	+	0.834060i	$0.686011\pi$
$858$	9.98512	−	19.4168i	0.0116377	−	0.0226303i
$859$			1371.72i			1.59688i	0.602076	+	0.798439i	$0.294340\pi$
$859$			1371.72i			1.59688i	−0.602076	+	0.798439i	$0.705660\pi$
$860$		0			0
$861$	9.60779	+	6.98047i	0.0111589	+	0.00810740i
$862$	758.958	+	120.207i	0.880461	+	0.139451i
$863$	−62.2624	−	122.197i	−0.0721465	−	0.141595i	0.852116	−	0.523353i	$-0.175319\pi$
$863$	−62.2624	−	122.197i	−0.0721465	−	0.141595i	−0.924263	+	0.381757i	$0.875319\pi$
$864$	22.2315	+	7.22344i	0.0257309	+	0.00836046i
$865$		0			0
$866$	991.511	+	720.375i	1.14493	+	0.831841i
$867$	17.8526	−	35.0378i	0.0205913	−	0.0404127i
$868$	−34.0877	+	34.0877i	−0.0392715	+	0.0392715i
$869$	−755.098	+	544.302i	−0.868928	+	0.626354i
$870$		0			0
$871$	7.75542	+	23.8687i	0.00890404	+	0.0274038i
$872$	128.619	+	812.071i	0.147499	+	0.931274i
$873$	−216.428	+	1366.47i	−0.247913	+	1.56526i
$874$	58.5645	+	19.0288i	0.0670075	+	0.0217721i
$875$		0			0
$876$	−5.38708	+	3.91394i	−0.00614964	+	0.00446797i
$877$	−89.6933	−	566.301i	−0.102273	−	0.645726i	−0.984564	−	0.175022i	$-0.944000\pi$
$877$	−89.6933	−	566.301i	−0.102273	−	0.645726i	0.882292	−	0.470703i	$-0.156000\pi$
$878$	−983.606	−	501.172i	−1.12028	−	0.570811i
$879$			15.4231i			0.0175462i
$880$		0			0
$881$	−340.367			−0.386341			−0.193171	−	0.981165i	$-0.561877\pi$
$881$	−340.367			−0.386341			−0.193171	+	0.981165i	$0.561877\pi$
$882$	−316.608	+	621.378i	−0.358966	+	0.704510i
$883$	1480.77	−	234.531i	1.67698	−	0.265607i	0.755814	−	0.654787i	$-0.227242\pi$
$883$	1480.77	−	234.531i	1.67698	−	0.265607i	0.921162	+	0.389180i	$0.127242\pi$
$884$	146.169	+	201.184i	0.165349	+	0.227583i
$885$		0			0
$886$	389.908	−	1200.01i	0.440077	−	1.35442i
$887$	−1427.16	−	226.040i	−1.60898	−	0.254837i	−0.713734	−	0.700417i	$-0.752997\pi$
$887$	−1427.16	−	226.040i	−1.60898	−	0.254837i	−0.895242	+	0.445581i	$0.852997\pi$
$888$	18.7067	−	2.96285i	0.0210661	−	0.00333654i
$889$	−11.9154	+	3.87156i	−0.0134032	+	0.00435496i
$890$		0			0
$891$	524.706	−	716.537i	0.588895	−	0.804194i
$892$	−182.520	−	182.520i	−0.204619	−	0.204619i
$893$	−27.3719	−	13.9467i	−0.0306516	−	0.0156178i
$894$	5.02797	−	6.92041i	0.00562413	−	0.00774095i
$895$		0			0
$896$	52.9646	−	163.008i	0.0591123	−	0.181929i
$897$	3.10231	−	1.58070i	0.00345854	−	0.00176221i
$898$	101.405	−	640.248i	0.112924	−	0.712972i
$899$	240.342	−	330.803i	0.267344	−	0.367967i
$900$		0			0
$901$	−2145.10			−2.38080
$902$	720.812	−	715.433i	0.799127	−	0.793164i
$903$	−5.11158	+	5.11158i	−0.00566067	+	0.00566067i
$904$	−958.627	+	311.477i	−1.06043	+	0.344554i
$905$		0			0
$906$	41.0362	−	29.8145i	0.0452938	−	0.0329079i
$907$	−556.910	+	283.760i	−0.614013	+	0.312855i	−0.733196	−	0.680017i	$-0.761972\pi$
$907$	−556.910	+	283.760i	−0.614013	+	0.312855i	0.119183	+	0.992872i	$0.461972\pi$
$908$	142.740	+	280.142i	0.157202	+	0.308527i
$909$	−929.118	−	1278.82i	−1.02213	−	1.40684i
$910$		0			0
$911$	−430.867	−	1326.07i	−0.472961	−	1.45562i	−0.848688	−	0.528894i	$-0.822607\pi$
$911$	−430.867	−	1326.07i	−0.472961	−	1.45562i	0.375727	−	0.926730i	$-0.377393\pi$
$912$	9.25096	+	9.25096i	0.0101436	+	0.0101436i
$913$	−106.016	−	106.814i	−0.116119	−	0.116992i
$914$			763.108i			0.834911i
$915$		0			0
$916$	84.6745	+	61.5196i	0.0924394	+	0.0671611i
$917$	198.869	+	31.4977i	0.216869	+	0.0343487i
$918$	37.5690	+	73.7332i	0.0409248	+	0.0803194i
$919$	526.505	+	171.072i	0.572911	+	0.186150i	0.581122	−	0.813816i	$-0.302614\pi$
$919$	526.505	+	171.072i	0.572911	+	0.186150i	−0.00821145	+	0.999966i	$0.502614\pi$
$920$		0			0
$921$	2.65631	+	1.92992i	0.00288416	+	0.00209546i
$922$	−582.559	+	1143.34i	−0.631843	+	1.24006i
$923$	860.369	−	860.369i	0.932145	−	0.932145i
$924$	−1.70128	−	1.24581i	−0.00184121	−	0.00134828i
$925$		0			0
$926$	−140.497	−	432.405i	−0.151724	−	0.466960i
$927$	−179.290	−	1131.99i	−0.193409	−	1.22114i
$928$	33.9605	−	214.418i	0.0365954	−	0.231054i
$929$	409.865	+	133.173i	0.441190	+	0.143351i	0.521184	−	0.853444i	$-0.325490\pi$
$929$	409.865	+	133.173i	0.441190	+	0.143351i	−0.0799947	+	0.996795i	$0.525490\pi$
$930$		0			0
$931$	391.830	−	284.681i	0.420870	−	0.305780i
$932$	−33.4221	−	211.019i	−0.0358607	−	0.226415i
$933$	−14.5733	−	7.42548i	−0.0156198	−	0.00795871i
$934$		−	1025.52i		−	1.09798i
$935$		0			0
$936$	−875.160			−0.935000
$937$	376.319	−	738.568i	0.401622	−	0.788227i	−0.598293	−	0.801277i	$-0.704154\pi$
$937$	376.319	−	738.568i	0.401622	−	0.788227i	0.999915	+	0.0130505i	$0.00415422\pi$
$938$	−9.03172	+	1.43048i	−0.00962870	+	0.00152504i
$939$	29.8724	+	41.1158i	0.0318130	+	0.0437868i
$940$		0			0
$941$	275.334	−	847.390i	0.292597	−	0.900520i	−0.691421	−	0.722452i	$-0.743015\pi$
$941$	275.334	−	847.390i	0.292597	−	0.900520i	0.984018	−	0.178069i	$-0.0569849\pi$
$942$	−1.09611	−	0.173606i	−0.00116359	−	0.000184295i
$943$	159.960	−	25.3352i	0.169629	−	0.0268666i
$944$	533.658	−	173.396i	0.565316	−	0.183682i
$945$		0			0
$946$	361.487	+	501.483i	0.382121	+	0.530109i
$947$	−604.866	−	604.866i	−0.638718	−	0.638718i	0.311521	−	0.950239i	$-0.399162\pi$
$947$	−604.866	−	604.866i	−0.638718	−	0.638718i	−0.950239	+	0.311521i	$0.899162\pi$
$948$	−6.23373	−	3.17624i	−0.00657566	−	0.00335047i
$949$	535.661	−	737.273i	0.564447	−	0.776895i
$950$		0			0
$951$	17.6877	−	54.4370i	0.0185990	−	0.0572419i
$952$	−466.041	+	237.460i	−0.489539	+	0.249432i
$953$	90.1909	−	569.443i	0.0946389	−	0.597527i	−0.894099	−	0.447869i	$-0.852183\pi$
$953$	90.1909	−	569.443i	0.0946389	−	0.597527i	0.988738	−	0.149657i	$-0.0478170\pi$
$954$	768.669	−	1057.98i	0.805733	−	1.10900i
$955$		0			0
$956$	−208.205			−0.217787
$957$	15.9056	+	8.17950i	0.0166203	+	0.00854702i
$958$	−307.812	+	307.812i	−0.321306	+	0.321306i
$959$	201.092	−	65.3388i	0.209689	−	0.0681322i
$960$		0			0
$961$	279.553	−	203.107i	0.290898	−	0.211350i
$962$	−400.085	+	203.854i	−0.415889	+	0.211906i
$963$	−678.004	−	1330.66i	−0.704054	−	1.38178i
$964$	141.490	+	194.744i	0.146774	+	0.202016i
$965$		0			0
$966$	0.392026	+	1.20653i	0.000405824	+	0.00124900i
$967$	792.160	+	792.160i	0.819193	+	0.819193i	0.985991	−	0.166798i	$-0.0533428\pi$
$967$	792.160	+	792.160i	0.819193	+	0.819193i	−0.166798	+	0.985991i	$0.553343\pi$
$968$	−741.563	+	730.536i	−0.766077	+	0.754686i
$969$		−	28.7199i		−	0.0296387i
$970$		0			0
$971$	−924.936	−	672.005i	−0.952560	−	0.692075i	−0.00114909	−	0.999999i	$-0.500366\pi$
$971$	−924.936	−	672.005i	−0.952560	−	0.692075i	−0.951411	+	0.307924i	$0.900366\pi$
$972$	19.8149	+	3.13836i	0.0203856	+	0.00322877i
$973$	101.932	+	200.053i	0.104761	+	0.205604i
$974$	−1441.35	−	468.324i	−1.47983	−	0.480825i
$975$		0			0
$976$	495.069	+	359.688i	0.507242	+	0.368533i
$977$	−607.003	+	1191.31i	−0.621293	+	1.21936i	0.339112	+	0.940746i	$0.389874\pi$
$977$	−607.003	+	1191.31i	−0.621293	+	1.21936i	−0.960404	+	0.278610i	$0.910126\pi$
$978$	−28.4271	+	28.4271i	−0.0290666	+	0.0290666i
$979$	309.232	+	963.988i	0.315865	+	0.984666i
$980$		0			0
$981$	265.510	+	817.154i	0.270652	+	0.832981i
$982$	120.162	+	758.675i	0.122365	+	0.772582i
$983$	−131.614	+	830.976i	−0.133890	+	0.845346i	0.825734	+	0.564060i	$0.190761\pi$
$983$	−131.614	+	830.976i	−0.133890	+	0.845346i	−0.959624	+	0.281287i	$0.909239\pi$
$984$	41.9084	+	13.6169i	0.0425899	+	0.0138383i
$985$		0			0
$986$	621.756	−	451.732i	0.630584	−	0.458146i
$987$	−0.0990057	−	0.625097i	−0.000100310	−	0.000633330i
$988$	93.8111	+	47.7991i	0.0949505	+	0.0483797i
$989$			98.5817i			0.0996782i
$990$		0			0
$991$	−190.257			−0.191985			−0.0959925	−	0.995382i	$-0.530602\pi$
$991$	−190.257			−0.191985			−0.0959925	+	0.995382i	$0.530602\pi$
$992$	−148.345	+	291.143i	−0.149541	+	0.293491i
$993$	−32.8507	+	5.20303i	−0.0330822	+	0.00523971i
$994$	260.583	+	358.662i	0.262156	+	0.360827i
$995$		0			0
$996$	0.349544	−	1.07578i	0.000350947	−	0.00108011i
$997$	−1063.21	−	168.395i	−1.06641	−	0.168902i	−0.401522	−	0.915849i	$-0.631519\pi$
$997$	−1063.21	−	168.395i	−1.06641	−	0.168902i	−0.664883	+	0.746947i	$0.731519\pi$
$998$	1386.50	−	219.601i	1.38928	−	0.220041i
$999$	37.6679	−	12.2391i	0.0377056	−	0.0122513i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.3.bk.c.82.5	✓	128
5.2	odd	4	inner	275.3.bk.c.93.5	yes	128
5.3	odd	4	inner	275.3.bk.c.93.12	yes	128
5.4	even	2	inner	275.3.bk.c.82.12	yes	128
11.9	even	5	inner	275.3.bk.c.207.12	yes	128
55.9	even	10	inner	275.3.bk.c.207.5	yes	128
55.42	odd	20	inner	275.3.bk.c.218.12	yes	128
55.53	odd	20	inner	275.3.bk.c.218.5	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.3.bk.c.82.5	✓	128	1.1	even	1	trivial
275.3.bk.c.82.12	yes	128	5.4	even	2	inner
275.3.bk.c.93.5	yes	128	5.2	odd	4	inner
275.3.bk.c.93.12	yes	128	5.3	odd	4	inner
275.3.bk.c.207.5	yes	128	55.9	even	10	inner
275.3.bk.c.207.12	yes	128	11.9	even	5	inner
275.3.bk.c.218.5	yes	128	55.53	odd	20	inner
275.3.bk.c.218.12	yes	128	55.42	odd	20	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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	275.bk (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.807274 + 1.58436i) q^{2} +(0.0974353 - 0.0154322i) q^{3} +(0.492622 + 0.678036i) q^{4} +(-0.0542067 + 0.166831i) q^{6} +(-2.29002 - 0.362704i) q^{7} +(-8.49706 + 1.34580i) q^{8} +(-8.55025 + 2.77815i) q^{9} +(10.4743 - 3.35998i) q^{11} +(0.0584623 + 0.0584623i) q^{12} +(-10.0820 - 5.13704i) q^{13} +(2.42333 - 3.33543i) q^{14} +(3.69127 - 11.3606i) q^{16} +(-23.3644 + 11.9048i) q^{17} +(2.50080 - 15.7894i) q^{18} +(-6.52576 + 8.98194i) q^{19} -0.228726 q^{21} +(-3.13218 + 19.3075i) q^{22} +(-2.20560 + 2.20560i) q^{23} +(-0.807145 + 0.262257i) q^{24} +(16.2779 - 11.8266i) q^{26} +(-1.58130 + 0.805713i) q^{27} +(-0.882189 - 1.73139i) q^{28} +(9.68796 + 13.3343i) q^{29} +(-7.66619 - 23.5941i) q^{31} +(-9.31350 - 9.31350i) q^{32} +(0.968712 - 0.489022i) q^{33} -46.6282i q^{34} +(-6.09572 - 4.42880i) q^{36} +(-22.0420 - 3.49111i) q^{37} +(-8.96259 - 17.5901i) q^{38} +(-1.06162 - 0.344941i) q^{39} +(-42.0056 - 30.5189i) q^{41} +(0.184645 - 0.362386i) q^{42} +(22.3480 - 22.3480i) q^{43} +(7.43805 + 5.44673i) q^{44} +(-1.71395 - 5.27500i) q^{46} +(0.432857 + 2.73295i) q^{47} +(0.184341 - 1.16388i) q^{48} +(-41.4891 - 13.4806i) q^{49} +(-2.09280 + 1.52051i) q^{51} +(-1.48352 - 9.36658i) q^{52} +(72.8878 + 37.1382i) q^{53} -3.15579i q^{54} +19.9466 q^{56} +(-0.497228 + 0.975864i) q^{57} +(-28.9473 + 4.58480i) q^{58} +(27.6110 + 38.0033i) q^{59} +(-15.8306 + 48.7215i) q^{61} +(43.5704 + 6.90087i) q^{62} +(20.5879 - 3.26081i) q^{63} +(67.7168 - 22.0025i) q^{64} +(-0.00722659 + 1.92957i) q^{66} +(-1.56835 - 1.56835i) q^{67} +(-19.5817 - 9.97737i) q^{68} +(-0.180866 + 0.248941i) q^{69} +(-33.2289 + 102.268i) q^{71} +(68.9132 - 35.1130i) q^{72} +(-12.5990 + 79.5472i) q^{73} +(23.3252 - 32.1043i) q^{74} -9.30481 q^{76} +(-25.2050 + 3.89537i) q^{77} +(1.40353 - 1.40353i) q^{78} +(-80.4790 + 26.1492i) q^{79} +(65.3179 - 47.4562i) q^{81} +(82.2631 - 41.9151i) q^{82} +(-6.21119 - 12.1901i) q^{83} +(-0.112676 - 0.155085i) q^{84} +(17.3664 + 53.4484i) q^{86} +(1.14973 + 1.14973i) q^{87} +(-84.4787 + 42.6463i) q^{88} +92.0338i q^{89} +(21.2248 + 15.4207i) q^{91} +(-2.58200 - 0.408949i) q^{92} +(-1.11107 - 2.18059i) q^{93} +(-4.67942 - 1.52044i) q^{94} +(-1.05119 - 0.763735i) q^{96} +(69.8642 - 137.116i) q^{97} +(54.8513 - 54.8513i) q^{98} +(-80.2232 + 57.8278i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 48 q^{6} + 32 q^{11} + 280 q^{16} - 8 q^{21} + 528 q^{26} - 16 q^{31} + 336 q^{36} - 604 q^{41} - 1152 q^{46} - 1024 q^{51} - 992 q^{56} - 320 q^{61} + 1624 q^{66} + 536 q^{71} + 1776 q^{76} + 3680 q^{81}+ \cdots - 6584 q^{96}+O(q^{100}) \) 128 * q - 48 * q^6 + 32 * q^11 + 280 * q^16 - 8 * q^21 + 528 * q^26 - 16 * q^31 + 336 * q^36 - 604 * q^41 - 1152 * q^46 - 1024 * q^51 - 992 * q^56 - 320 * q^61 + 1624 * q^66 + 536 * q^71 + 1776 * q^76 + 3680 * q^81 + 872 * q^86 - 448 * q^91 - 6584 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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