LMFDB - Embedded newform 272.3.x.a.155.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [272,3,Mod(155,272)] 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("272.155"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(272, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 2, 7])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 272 = 2^{4} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	272.x (of order $8$, degree $4$, 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:	$7.41146319060$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$70$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			155.20
Character	$\chi$	$=$	272.155
Dual form			272.3.x.a.179.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37735 - 1.45014i) q^{2} +(-2.31294 - 0.958051i) q^{3} +(-0.205791 + 3.99470i) q^{4} +(-2.57391 + 6.21396i) q^{5} +(1.79643 + 4.67366i) q^{6} +(-3.91405 + 9.44936i) q^{7} +(6.07631 - 5.20370i) q^{8} +(-1.93213 - 1.93213i) q^{9} +(12.5563 - 4.82631i) q^{10} +(2.21125 - 0.915929i) q^{11} +(4.30311 - 9.04235i) q^{12} +(-2.67910 - 2.67910i) q^{13} +(19.0939 - 7.33921i) q^{14} +(11.9066 - 11.9066i) q^{15} +(-15.9153 - 1.64415i) q^{16} +(-9.64295 - 14.0005i) q^{17} +(-0.140625 + 5.46308i) q^{18} -23.0344i q^{19} +(-24.2933 - 11.5608i) q^{20} +(18.1059 - 18.1059i) q^{21} +(-4.37390 - 1.94505i) q^{22} +(30.2283 + 12.5210i) q^{23} +(-19.0396 + 6.21442i) q^{24} +(-14.3107 - 14.3107i) q^{25} +(-0.194991 + 7.57514i) q^{26} +(11.2403 + 27.1364i) q^{27} +(-36.9419 - 17.5801i) q^{28} +(-5.45495 - 2.25952i) q^{29} +(-33.6658 - 0.866588i) q^{30} +(0.199048 + 0.480544i) q^{31} +(19.5368 + 25.3439i) q^{32} -5.99199 q^{33} +(-7.02084 + 33.2672i) q^{34} +(-48.6436 - 48.6436i) q^{35} +(8.11590 - 7.32067i) q^{36} +(-40.6070 - 16.8200i) q^{37} +(-33.4030 + 31.7265i) q^{38} +(3.62989 + 8.76332i) q^{39} +(16.6957 + 51.1518i) q^{40} +(-27.2162 - 11.2733i) q^{41} +(-51.1944 - 1.31779i) q^{42} -47.0216i q^{43} +(3.20381 + 9.02177i) q^{44} +(16.9793 - 7.03306i) q^{45} +(-23.4779 - 61.0809i) q^{46} +75.0974 q^{47} +(35.2360 + 19.0505i) q^{48} +(-39.3224 - 39.3224i) q^{49} +(-1.04156 + 40.4633i) q^{50} +(8.89040 + 41.6207i) q^{51} +(11.2536 - 10.1509i) q^{52} -1.90490i q^{53} +(23.8697 - 53.6764i) q^{54} +16.0981i q^{55} +(25.3886 + 77.7848i) q^{56} +(-22.0682 + 53.2772i) q^{57} +(4.23680 + 11.0226i) q^{58} -40.0758i q^{59} +(45.1130 + 50.0136i) q^{60} +(-26.6454 - 64.3277i) q^{61} +(0.422695 - 0.950525i) q^{62} +(25.8199 - 10.6949i) q^{63} +(9.84310 - 63.2385i) q^{64} +(23.5436 - 9.75208i) q^{65} +(8.25310 + 8.68921i) q^{66} +(-16.4701 - 16.4701i) q^{67} +(57.9122 - 35.6396i) q^{68} +(-57.9205 - 57.9205i) q^{69} +(-3.54039 + 137.539i) q^{70} +(-59.0533 + 24.4607i) q^{71} +(-21.7944 - 1.68601i) q^{72} +(124.003 - 51.3637i) q^{73} +(31.5390 + 82.0527i) q^{74} +(19.3894 + 46.8101i) q^{75} +(92.0156 + 4.74027i) q^{76} +24.4799i q^{77} +(7.70837 - 17.3340i) q^{78} +(-52.1521 + 125.906i) q^{79} +(51.1812 - 94.6652i) q^{80} -48.9418i q^{81} +(21.1385 + 54.9946i) q^{82} +5.61797i q^{83} +(68.6018 + 76.0539i) q^{84} +(111.819 - 23.8850i) q^{85} +(-68.1877 + 64.7654i) q^{86} +(10.4522 + 10.4522i) q^{87} +(8.67002 - 17.0721i) q^{88} -10.7697 q^{89} +(-33.5854 - 14.9353i) q^{90} +(35.8020 - 14.8297i) q^{91} +(-56.2382 + 118.176i) q^{92} -1.30217i q^{93} +(-103.436 - 108.902i) q^{94} +(143.135 + 59.2885i) q^{95} +(-20.9066 - 77.3362i) q^{96} +(-3.02256 - 7.29710i) q^{97} +(-2.86197 + 111.184i) q^{98} +(-6.04211 - 2.50273i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q - 4 q^{2} - 4 q^{3} - 4 q^{5} + 12 q^{6} - 8 q^{7} - 4 q^{8} + 12 q^{10} - 4 q^{11} - 24 q^{12} + 40 q^{14} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 4 q^{20} + 4 q^{22} - 8 q^{23} - 324 q^{24} - 132 q^{26}+ \cdots + 284 q^{99}+O(q^{100}) $ 280 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 + 12 * q^6 - 8 * q^7 - 4 * q^8 + 12 * q^10 - 4 * q^11 - 24 * q^12 + 40 * q^14 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 4 * q^20 + 4 * q^22 - 8 * q^23 - 324 * q^24 - 132 * q^26 - 40 * q^27 + 212 * q^28 - 4 * q^29 - 256 * q^31 - 124 * q^32 - 16 * q^33 - 148 * q^34 - 8 * q^35 - 164 * q^36 - 4 * q^37 + 32 * q^38 - 8 * q^39 - 40 * q^40 + 448 * q^42 - 40 * q^44 - 68 * q^45 - 228 * q^46 - 48 * q^48 - 8 * q^49 - 8 * q^50 - 164 * q^51 - 8 * q^52 - 48 * q^54 + 176 * q^56 + 72 * q^57 - 20 * q^58 - 552 * q^60 - 68 * q^61 + 176 * q^62 - 640 * q^63 + 24 * q^65 + 228 * q^66 - 8 * q^67 - 368 * q^68 - 8 * q^69 + 560 * q^70 + 504 * q^71 + 520 * q^72 - 156 * q^74 + 60 * q^75 + 664 * q^76 + 600 * q^78 + 304 * q^80 + 212 * q^82 - 8 * q^84 - 4 * q^85 + 1136 * q^86 - 8 * q^87 + 408 * q^88 - 200 * q^90 + 384 * q^91 + 60 * q^92 + 584 * q^94 + 200 * q^95 - 112 * q^96 - 8 * q^97 - 624 * q^98 + 284 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/272\mathbb{Z}\right)^\times$.

$n$	$69$	$239$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{7}{8}\right)$

Coefficient data

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

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

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

$2$	−1.37735	−	1.45014i	−0.688677	−	0.725068i
$2$	−1.37735	−	1.45014i	−0.688677	−	0.725068i
$3$	−2.31294	−	0.958051i	−0.770980	−	0.319350i	−0.0377108	−	0.999289i	$-0.512007\pi$
$3$	−2.31294	−	0.958051i	−0.770980	−	0.319350i	−0.733269	+	0.679938i	$0.762007\pi$
$4$	−0.205791	+	3.99470i	−0.0514477	+	0.998676i
$5$	−2.57391	+	6.21396i	−0.514782	+	1.24279i	0.426290	+	0.904586i	$0.359820\pi$
$5$	−2.57391	+	6.21396i	−0.514782	+	1.24279i	−0.941072	+	0.338206i	$0.890180\pi$
$6$	1.79643	+	4.67366i	0.299406	+	0.778943i
$7$	−3.91405	+	9.44936i	−0.559151	+	1.34991i	0.351289	+	0.936267i	$0.385743\pi$
$7$	−3.91405	+	9.44936i	−0.559151	+	1.34991i	−0.910440	+	0.413642i	$0.864257\pi$
$8$	6.07631	−	5.20370i	0.759539	−	0.650462i
$9$	−1.93213	−	1.93213i	−0.214681	−	0.214681i
$10$	12.5563	−	4.82631i	1.25563	−	0.482631i
$11$	2.21125	−	0.915929i	0.201023	−	0.0832663i	−0.279901	−	0.960029i	$-0.590302\pi$
$11$	2.21125	−	0.915929i	0.201023	−	0.0832663i	0.480923	+	0.876763i	$0.340302\pi$
$12$	4.30311	−	9.04235i	0.358593	−	0.753529i
$13$	−2.67910	−	2.67910i	−0.206085	−	0.206085i	0.596516	−	0.802601i	$-0.296551\pi$
$13$	−2.67910	−	2.67910i	−0.206085	−	0.206085i	−0.802601	+	0.596516i	$0.796551\pi$
$14$	19.0939	−	7.33921i	1.36385	−	0.524229i
$15$	11.9066	−	11.9066i	0.793773	−	0.793773i
$16$	−15.9153	−	1.64415i	−0.994706	−	0.102759i
$17$	−9.64295	−	14.0005i	−0.567233	−	0.823558i
$17$	−9.64295	−	14.0005i	−0.567233	−	0.823558i
$18$	−0.140625	+	5.46308i	−0.00781248	+	0.303504i
$19$		−	23.0344i		−	1.21234i	−0.795336	−	0.606169i	$-0.792706\pi$
$19$		−	23.0344i		−	1.21234i	0.795336	−	0.606169i	$-0.207294\pi$
$20$	−24.2933	−	11.5608i	−1.21466	−	0.578039i
$21$	18.1059	−	18.1059i	0.862188	−	0.862188i
$22$	−4.37390	−	1.94505i	−0.198813	−	0.0884115i
$23$	30.2283	+	12.5210i	1.31427	+	0.544390i	0.926128	−	0.377209i	$-0.123116\pi$
$23$	30.2283	+	12.5210i	1.31427	+	0.544390i	0.388144	+	0.921599i	$0.373116\pi$
$24$	−19.0396	+	6.21442i	−0.793315	+	0.258934i
$25$	−14.3107	−	14.3107i	−0.572427	−	0.572427i
$26$	−0.194991	+	7.57514i	−0.00749965	+	0.291351i
$27$	11.2403	+	27.1364i	0.416307	+	1.00505i
$28$	−36.9419	−	17.5801i	−1.31935	−	0.627860i
$29$	−5.45495	−	2.25952i	−0.188102	−	0.0779143i	0.286644	−	0.958037i	$-0.407460\pi$
$29$	−5.45495	−	2.25952i	−0.188102	−	0.0779143i	−0.474746	+	0.880123i	$0.657460\pi$
$30$	−33.6658	−	0.866588i	−1.12219	−	0.0288863i
$31$	0.199048	+	0.480544i	0.00642089	+	0.0155014i	0.927057	−	0.374919i	$-0.122330\pi$
$31$	0.199048	+	0.480544i	0.00642089	+	0.0155014i	−0.920637	+	0.390421i	$0.872330\pi$
$32$	19.5368	+	25.3439i	0.610524	+	0.791998i
$33$	−5.99199			−0.181576
$34$	−7.02084	+	33.2672i	−0.206495	+	0.978448i
$35$	−48.6436	−	48.6436i	−1.38982	−	1.38982i
$36$	8.11590	−	7.32067i	0.225442	−	0.203352i
$37$	−40.6070	−	16.8200i	−1.09749	−	0.454594i	−0.240875	−	0.970556i	$-0.577434\pi$
$37$	−40.6070	−	16.8200i	−1.09749	−	0.454594i	−0.856611	+	0.515963i	$0.827434\pi$
$38$	−33.4030	+	31.7265i	−0.879027	+	0.834909i
$39$	3.62989	+	8.76332i	0.0930740	+	0.224701i
$40$	16.6957	+	51.1518i	0.417393	+	1.27880i
$41$	−27.2162	−	11.2733i	−0.663811	−	0.274959i	0.0252303	−	0.999682i	$-0.491968\pi$
$41$	−27.2162	−	11.2733i	−0.663811	−	0.274959i	−0.689041	+	0.724722i	$0.741968\pi$
$42$	−51.1944	−	1.31779i	−1.21891	−	0.0313760i
$43$		−	47.0216i		−	1.09353i	−0.837288	−	0.546763i	$-0.815860\pi$
$43$		−	47.0216i		−	1.09353i	0.837288	−	0.546763i	$-0.184140\pi$
$44$	3.20381	+	9.02177i	0.0728139	+	0.205040i
$45$	16.9793	−	7.03306i	0.377318	−	0.156290i
$46$	−23.4779	−	61.0809i	−0.510390	−	1.32785i
$47$	75.0974			1.59782			0.798909	−	0.601452i	$-0.205411\pi$
$47$	75.0974			1.59782			0.798909	+	0.601452i	$0.205411\pi$
$48$	35.2360	+	19.0505i	0.734083	+	0.396885i
$49$	−39.3224	−	39.3224i	−0.802498	−	0.802498i
$50$	−1.04156	+	40.4633i	−0.0208312	+	0.809266i
$51$	8.89040	+	41.6207i	0.174322	+	0.816093i
$52$	11.2536	−	10.1509i	0.216414	−	0.195209i
$53$		−	1.90490i		−	0.0359414i	−0.999839	−	0.0179707i	$-0.994279\pi$
$53$		−	1.90490i		−	0.0359414i	0.999839	−	0.0179707i	$-0.00572056\pi$
$54$	23.8697	−	53.6764i	0.442031	−	0.994008i
$55$			16.0981i			0.292693i
$56$	25.3886	+	77.7848i	0.453368	+	1.38901i
$57$	−22.0682	+	53.2772i	−0.387161	+	0.934688i
$58$	4.23680	+	11.0226i	0.0730482	+	0.190044i
$59$		−	40.0758i		−	0.679252i	−0.940561	−	0.339626i	$-0.889700\pi$
$59$		−	40.0758i		−	0.679252i	0.940561	−	0.339626i	$-0.110300\pi$
$60$	45.1130	+	50.0136i	0.751884	+	0.833559i
$61$	−26.6454	−	64.3277i	−0.436810	−	1.05455i	−0.977044	−	0.213038i	$-0.931664\pi$
$61$	−26.6454	−	64.3277i	−0.436810	−	1.05455i	0.540234	−	0.841515i	$-0.318336\pi$
$62$	0.422695	−	0.950525i	0.00681766	−	0.0153311i
$63$	25.8199	−	10.6949i	0.409839	−	0.169761i
$64$	9.84310	−	63.2385i	0.153798	−	0.988102i
$65$	23.5436	−	9.75208i	0.362209	−	0.150032i
$66$	8.25310	+	8.68921i	0.125047	+	0.131655i
$67$	−16.4701	−	16.4701i	−0.245822	−	0.245822i	0.573432	−	0.819253i	$-0.305612\pi$
$67$	−16.4701	−	16.4701i	−0.245822	−	0.245822i	−0.819253	+	0.573432i	$0.805612\pi$
$68$	57.9122	−	35.6396i	0.851650	−	0.524111i
$69$	−57.9205	−	57.9205i	−0.839427	−	0.839427i
$70$	−3.54039	+	137.539i	−0.0505769	+	1.96485i
$71$	−59.0533	+	24.4607i	−0.831737	+	0.344517i	−0.757590	−	0.652731i	$-0.773623\pi$
$71$	−59.0533	+	24.4607i	−0.831737	+	0.344517i	−0.0741467	+	0.997247i	$0.523623\pi$
$72$	−21.7944	−	1.68601i	−0.302700	−	0.0234167i
$73$	124.003	−	51.3637i	1.69867	−	0.703612i	0.698739	−	0.715376i	$-0.253745\pi$
$73$	124.003	−	51.3637i	1.69867	−	0.703612i	0.999931	+	0.0117642i	$0.00374474\pi$
$74$	31.5390	+	82.0527i	0.426202	+	1.10882i
$75$	19.3894	+	46.8101i	0.258525	+	0.624135i
$76$	92.0156	+	4.74027i	1.21073	+	0.0623720i
$77$			24.4799i			0.317921i
$78$	7.70837	−	17.3340i	0.0988253	−	0.222231i
$79$	−52.1521	+	125.906i	−0.660153	+	1.59375i	0.137410	+	0.990514i	$0.456122\pi$
$79$	−52.1521	+	125.906i	−0.660153	+	1.59375i	−0.797563	+	0.603236i	$0.793878\pi$
$80$	51.1812	−	94.6652i	0.639765	−	1.18332i
$81$		−	48.9418i		−	0.604219i
$82$	21.1385	+	54.9946i	0.257787	+	0.670666i
$83$			5.61797i			0.0676864i	0.999427	+	0.0338432i	$0.0107747\pi$
$83$			5.61797i			0.0676864i	−0.999427	+	0.0338432i	$0.989225\pi$
$84$	68.6018	+	76.0539i	0.816689	+	0.905404i
$85$	111.819	−	23.8850i	1.31551	−	0.281000i
$86$	−68.1877	+	64.7654i	−0.792881	+	0.753086i
$87$	10.4522	+	10.4522i	0.120141	+	0.120141i
$88$	8.67002	−	17.0721i	0.0985229	−	0.194002i
$89$	−10.7697			−0.121008			−0.0605040	−	0.998168i	$-0.519271\pi$
$89$	−10.7697			−0.121008			−0.0605040	+	0.998168i	$0.519271\pi$
$90$	−33.5854	−	14.9353i	−0.373171	−	0.165948i
$91$	35.8020	−	14.8297i	0.393428	−	0.162963i
$92$	−56.2382	+	118.176i	−0.611285	+	1.28452i
$93$		−	1.30217i		−	0.0140018i
$94$	−103.436	−	108.902i	−1.10038	−	1.15853i
$95$	143.135	+	59.2885i	1.50668	+	0.624089i
$96$	−20.9066	−	77.3362i	−0.217777	−	0.805586i
$97$	−3.02256	−	7.29710i	−0.0311604	−	0.0752278i	0.907533	−	0.419980i	$-0.137963\pi$
$97$	−3.02256	−	7.29710i	−0.0311604	−	0.0752278i	−0.938694	+	0.344752i	$0.887963\pi$
$98$	−2.86197	+	111.184i	−0.0292038	+	1.13453i
$99$	−6.04211	−	2.50273i	−0.0610314	−	0.0252801i
$100$	60.1119	−	54.2219i	0.601119	−	0.542219i
$101$	−68.0039	−	68.0039i	−0.673306	−	0.673306i	0.285170	−	0.958477i	$-0.407950\pi$
$101$	−68.0039	−	68.0039i	−0.673306	−	0.673306i	−0.958477	+	0.285170i	$0.907950\pi$
$102$	48.1105	−	70.2188i	0.471672	−	0.688419i
$103$	−27.6147			−0.268104			−0.134052	−	0.990974i	$-0.542799\pi$
$103$	−27.6147			−0.268104			−0.134052	+	0.990974i	$0.542799\pi$
$104$	−30.2203	−	2.33783i	−0.290580	−	0.0224791i
$105$	65.9067	+	159.113i	0.627683	+	1.51536i
$106$	−2.76236	+	2.62372i	−0.0260600	+	0.0247520i
$107$	54.4529	+	22.5551i	0.508906	+	0.210796i	0.622336	−	0.782750i	$-0.286184\pi$
$107$	54.4529	+	22.5551i	0.508906	+	0.210796i	−0.113430	+	0.993546i	$0.536184\pi$
$108$	−110.715	+	39.3172i	−1.02514	+	0.364048i
$109$	−81.9903	−	197.942i	−0.752204	−	1.81598i	−0.546706	−	0.837325i	$-0.684118\pi$
$109$	−81.9903	−	197.942i	−0.752204	−	1.81598i	−0.205499	−	0.978657i	$-0.565882\pi$
$110$	23.3445	−	22.1728i	0.212223	−	0.201571i
$111$	77.8071	+	77.8071i	0.700965	+	0.700965i
$112$	77.8295	−	143.954i	0.694906	−	1.28531i
$113$	137.026	+	56.7580i	1.21262	+	0.502283i	0.895056	−	0.445955i	$-0.147136\pi$
$113$	137.026	+	56.7580i	1.21262	+	0.502283i	0.317562	+	0.948237i	$0.397136\pi$
$114$	107.655	−	41.3798i	0.944341	−	0.362981i
$115$	−155.610	+	155.610i	−1.35313	+	1.35313i
$116$	10.1487	−	21.3259i	0.0874885	−	0.183844i
$117$			10.3527i			0.0884850i
$118$	−58.1154	+	55.1986i	−0.492504	+	0.467785i
$119$	170.039	−	36.3211i	1.42890	−	0.305220i
$120$	10.3899	−	134.306i	0.0865823	−	1.11922i
$121$	−81.5092	+	81.5092i	−0.673630	+	0.673630i
$122$	−56.5838	+	127.242i	−0.463801	+	1.04296i
$123$	52.1491	+	52.1491i	0.423977	+	0.423977i
$124$	−1.96059	+	0.696245i	−0.0158112	+	0.00561488i
$125$	−29.5887	+	12.2561i	−0.236710	+	0.0980484i
$126$	−51.0722	−	22.7116i	−0.405335	−	0.180251i
$127$	−105.583	−	105.583i	−0.831360	−	0.831360i	0.156343	−	0.987703i	$-0.450029\pi$
$127$	−105.583	−	105.583i	−0.831360	−	0.831360i	−0.987703	+	0.156343i	$0.950029\pi$
$128$	−105.262	+	72.8280i	−0.822359	+	0.568969i
$129$	−45.0491	+	108.758i	−0.349218	+	0.843087i
$130$	−46.5697	−	20.7094i	−0.358229	−	0.159303i
$131$	−33.0348	+	79.7530i	−0.252174	+	0.608802i	−0.998379	−	0.0569144i	$-0.981874\pi$
$131$	−33.0348	+	79.7530i	−0.252174	+	0.608802i	0.746205	+	0.665716i	$0.231874\pi$
$132$	1.23310	−	23.9362i	0.00934165	−	0.181335i
$133$	217.661	+	90.1579i	1.63655	+	0.677879i
$134$	−1.19873	+	46.5689i	−0.00894572	+	0.347529i
$135$	−197.556			−1.46338
$136$	−131.448	−	34.8923i	−0.966528	−	0.256561i
$137$			12.7888i			0.0933489i	0.998910	+	0.0466744i	$0.0148623\pi$
$137$			12.7888i			0.0933489i	−0.998910	+	0.0466744i	$0.985138\pi$
$138$	−4.21558	+	163.770i	−0.0305477	+	1.18674i
$139$	96.5540	−	233.102i	0.694633	−	1.67699i	−0.0405981	−	0.999176i	$-0.512926\pi$
$139$	96.5540	−	233.102i	0.694633	−	1.67699i	0.735231	−	0.677817i	$-0.237074\pi$
$140$	204.327	−	184.306i	1.45948	−	1.31647i
$141$	−173.696	−	71.9472i	−1.23189	−	0.510264i
$142$	116.809	+	51.9443i	0.822596	+	0.365805i
$143$	−8.37803	−	3.47029i	−0.0585876	−	0.0242678i
$144$	27.5737	+	33.9271i	0.191484	+	0.235605i
$145$	28.0811	−	28.0811i	0.193663	−	0.193663i
$146$	−245.280	−	109.075i	−1.68000	−	0.747090i
$147$	53.2775	+	128.623i	0.362432	+	0.874988i
$148$	75.5473	−	158.751i	0.510455	−	1.07264i
$149$	−56.9961	+	56.9961i	−0.382524	+	0.382524i	−0.872011	−	0.489487i	$-0.837184\pi$
$149$	−56.9961	+	56.9961i	−0.382524	+	0.382524i	0.489487	+	0.872011i	$0.337184\pi$
$150$	41.1750	−	92.5913i	0.274500	−	0.617275i
$151$	−46.4442	−	46.4442i	−0.307577	−	0.307577i	0.536392	−	0.843969i	$-0.319787\pi$
$151$	−46.4442	−	46.4442i	−0.307577	−	0.307577i	−0.843969	+	0.536392i	$0.819787\pi$
$152$	−119.864	−	139.964i	−0.788579	−	0.920817i
$153$	−8.41931	+	45.6822i	−0.0550282	+	0.298576i
$154$	35.4992	−	33.7175i	0.230514	−	0.218945i
$155$	−3.49841			−0.0225704
$156$	−35.7539	+	12.6969i	−0.229191	+	0.0813904i
$157$	−18.3119	−	18.3119i	−0.116636	−	0.116636i	0.646380	−	0.763016i	$-0.276282\pi$
$157$	−18.3119	−	18.3119i	−0.116636	−	0.116636i	−0.763016	+	0.646380i	$0.776282\pi$
$158$	254.413	−	97.7899i	1.61021	−	0.618923i
$159$	−1.82499	+	4.40591i	−0.0114779	+	0.0277101i
$160$	−207.772	+	56.1678i	−1.29858	+	0.351049i
$161$	−236.630	+	236.630i	−1.46975	+	1.46975i
$162$	−70.9722	+	67.4101i	−0.438100	+	0.416112i
$163$	−239.534	+	99.2184i	−1.46954	+	0.608702i	−0.966753	−	0.255711i	$-0.917690\pi$
$163$	−239.534	+	99.2184i	−1.46954	+	0.608702i	−0.502782	+	0.864413i	$0.667690\pi$
$164$	50.6345	−	106.401i	0.308747	−	0.648786i
$165$	15.4228	−	37.2340i	0.0934718	−	0.225661i
$166$	8.14682	−	7.73794i	0.0490773	−	0.0466141i
$167$	251.470	−	104.162i	1.50581	−	0.623726i	0.531119	−	0.847297i	$-0.321772\pi$
$167$	251.470	−	104.162i	1.50581	−	0.623726i	0.974688	+	0.223571i	$0.0717715\pi$
$168$	15.7995	−	204.235i	0.0940448	−	1.21569i
$169$		−	154.645i		−	0.915058i
$170$	−188.650	−	129.254i	−1.10971	−	0.760318i
$171$	−44.5055	+	44.5055i	−0.260266	+	0.260266i
$172$	187.837	+	9.67662i	1.09208	+	0.0562594i
$173$	−8.63288	+	20.8416i	−0.0499010	+	0.120472i	−0.946864	−	0.321633i	$-0.895768\pi$
$173$	−8.63288	+	20.8416i	−0.0499010	+	0.120472i	0.896963	+	0.442105i	$0.145768\pi$
$174$	0.760737	−	29.5536i	0.00437205	−	0.169848i
$175$	191.239	−	79.2140i	1.09280	−	0.452651i
$176$	−36.6986	+	10.9417i	−0.208515	+	0.0621686i
$177$	−38.3947	+	92.6931i	−0.216919	+	0.523690i
$178$	14.8337	+	15.6175i	0.0833354	+	0.0877390i
$179$	−6.78623			−0.0379119			−0.0189559	−	0.999820i	$-0.506034\pi$
$179$	−6.78623			−0.0379119			−0.0189559	+	0.999820i	$0.506034\pi$
$180$	24.6008	+	69.2746i	0.136671	+	0.384859i
$181$	91.1142	+	219.969i	0.503393	+	1.21530i	0.947625	+	0.319386i	$0.103477\pi$
$181$	91.1142	+	219.969i	0.503393	+	1.21530i	−0.444231	+	0.895912i	$0.646523\pi$
$182$	−70.8170	−	31.4920i	−0.389104	−	0.173033i
$183$			174.314i			0.952535i
$184$	248.832	−	81.2175i	1.35235	−	0.441399i
$185$	209.037	−	209.037i	1.12993	−	1.12993i
$186$	−1.88832	+	1.79354i	−0.0101523	+	0.00964271i
$187$	−34.1464	−	22.1263i	−0.182601	−	0.118322i
$188$	−15.4544	+	299.992i	−0.0822041	+	1.59570i
$189$	−300.417			−1.58951
$190$	−111.171	−	289.226i	−0.585112	−	1.52224i
$191$	197.320			1.03309			0.516546	−	0.856260i	$-0.327218\pi$
$191$	197.320			1.03309			0.516546	+	0.856260i	$0.327218\pi$
$192$	−83.3523	+	136.837i	−0.434126	+	0.712692i
$193$	−270.263	−	111.947i	−1.40033	−	0.580035i	−0.450491	−	0.892781i	$-0.648751\pi$
$193$	−270.263	−	111.947i	−1.40033	−	0.580035i	−0.949837	+	0.312746i	$0.898751\pi$
$194$	−6.41865	+	14.4338i	−0.0330858	+	0.0744011i
$195$	−63.7980			−0.327169
$196$	165.174	−	148.989i	0.842722	−	0.760149i
$197$	−230.287	+	95.3881i	−1.16897	+	0.484204i	−0.880852	−	0.473391i	$-0.843030\pi$
$197$	−230.287	+	95.3881i	−1.16897	+	0.484204i	−0.288119	+	0.957595i	$0.593030\pi$
$198$	4.69284	+	12.2090i	0.0237012	+	0.0616618i
$199$	−113.894	−	274.965i	−0.572334	−	1.38174i	−0.899563	−	0.436791i	$-0.856115\pi$
$199$	−113.894	−	274.965i	−0.572334	−	1.38174i	0.327229	−	0.944945i	$-0.393885\pi$
$200$	−161.424	−	12.4877i	−0.807122	−	0.0624385i
$201$	22.3151	+	53.8734i	0.111020	+	0.268027i
$202$	−4.94948	+	192.281i	−0.0245024	+	0.951884i
$203$	42.7020	−	42.7020i	0.210354	−	0.210354i
$204$	−168.092	+	26.9493i	−0.823980	+	0.132105i
$205$	140.104	−	140.104i	0.683435	−	0.683435i
$206$	38.0353	+	40.0451i	0.184637	+	0.194394i
$207$	−34.2128	−	82.5971i	−0.165279	−	0.399020i
$208$	38.2339	+	47.0436i	0.183817	+	0.226171i
$209$	−21.0979	−	50.9348i	−0.100947	−	0.243707i
$210$	139.958	−	314.728i	0.666468	−	1.49871i
$211$	−97.5911	+	40.4236i	−0.462517	+	0.191581i	−0.601759	−	0.798678i	$-0.705533\pi$
$211$	−97.5911	+	40.4236i	−0.462517	+	0.191581i	0.139242	+	0.990258i	$0.455533\pi$
$212$	7.60949	+	0.392010i	0.0358938	+	0.00184911i
$213$	160.021			0.751274
$214$	−42.2929	−	110.031i	−0.197630	−	0.514161i
$215$	292.191	+	121.029i	1.35903	+	0.562927i
$216$	209.509	+	106.398i	0.969950	+	0.492585i
$217$	−5.31991			−0.0245157
$218$	−174.113	+	391.533i	−0.798685	+	1.79602i
$219$	−336.020			−1.53434
$220$	−64.3073	−	3.31285i	−0.292306	−	0.0150584i
$221$	−11.6743	+	63.3432i	−0.0528247	+	0.286621i
$222$	5.66297	−	219.999i	0.0255089	−	0.990986i
$223$	−89.4011	+	89.4011i	−0.400902	+	0.400902i	−0.878551	−	0.477649i	$-0.841489\pi$
$223$	−89.4011	+	89.4011i	−0.400902	+	0.400902i	0.477649	+	0.878551i	$0.341489\pi$
$224$	−315.952	+	85.4125i	−1.41050	+	0.381306i
$225$			55.3002i			0.245778i
$226$	−106.426	−	276.882i	−0.470913	−	1.22514i
$227$	−73.8981	−	178.406i	−0.325542	−	0.785929i	−0.998913	−	0.0466234i	$-0.985154\pi$
$227$	−73.8981	−	178.406i	−0.325542	−	0.785929i	0.673370	−	0.739306i	$-0.264846\pi$
$228$	−208.285	−	99.1197i	−0.913532	−	0.434735i
$229$	81.3352			0.355176			0.177588	−	0.984105i	$-0.443171\pi$
$229$	81.3352			0.355176			0.177588	+	0.984105i	$0.443171\pi$
$230$	439.985	+	11.3256i	1.91298	+	0.0492418i
$231$	23.4530	−	56.6205i	0.101528	−	0.245111i
$232$	−44.9038	+	14.6564i	−0.193551	+	0.0631741i
$233$	−226.945	+	94.0039i	−0.974014	+	0.403450i	−0.812205	−	0.583372i	$-0.801733\pi$
$233$	−226.945	+	94.0039i	−0.974014	+	0.403450i	−0.161809	+	0.986822i	$0.551733\pi$
$234$	15.0129	−	14.2594i	0.0641577	−	0.0609376i
$235$	−193.294	+	466.653i	−0.822527	+	1.98576i
$236$	160.091	+	8.24725i	0.678352	+	0.0349460i
$237$	241.249	−	241.249i	1.01793	−	1.01793i
$238$	−286.874	−	196.552i	−1.20535	−	0.825850i
$239$			179.910i			0.752761i	0.926465	+	0.376380i	$0.122831\pi$
$239$			179.910i			0.752761i	−0.926465	+	0.376380i	$0.877169\pi$
$240$	−209.073	+	169.921i	−0.871138	+	0.708003i
$241$	−186.456	+	77.2326i	−0.773676	+	0.320467i	−0.734361	−	0.678760i	$-0.762518\pi$
$241$	−186.456	+	77.2326i	−0.773676	+	0.320467i	−0.0393158	+	0.999227i	$0.512518\pi$
$242$	230.467	+	5.93242i	0.952341	+	0.0245141i
$243$	54.2738	−	131.029i	0.223349	−	0.539212i
$244$	262.453	−	93.2024i	1.07563	−	0.381977i
$245$	345.560	−	143.136i	1.41045	−	0.584228i
$246$	3.79553	−	147.451i	0.0154290	−	0.599395i
$247$	−61.7116	+	61.7116i	−0.249844	+	0.249844i
$248$	3.71008	+	1.88415i	0.0149600	+	0.00759737i
$249$	5.38230	−	12.9940i	0.0216157	−	0.0521849i
$250$	58.5271	+	26.0268i	0.234108	+	0.104107i
$251$	57.8777	+	57.8777i	0.230588	+	0.230588i	0.812938	−	0.582350i	$-0.197867\pi$
$251$	57.8777	+	57.8777i	0.230588	+	0.230588i	−0.582350	+	0.812938i	$0.697867\pi$
$252$	37.4096	+	105.344i	0.148451	+	0.418030i
$253$	78.3105			0.309528
$254$	−7.68454	+	298.534i	−0.0302541	+	1.17533i
$255$	−281.513	−	51.8833i	−1.10397	−	0.203464i
$256$	250.594	+	52.3342i	0.978881	+	0.204430i
$257$	287.707	+	287.707i	1.11948	+	1.11948i	0.991817	+	0.127665i	$0.0407481\pi$
$257$	287.707	+	287.707i	1.11948	+	1.11948i	0.127665	+	0.991817i	$0.459252\pi$
$258$	219.763	−	84.4712i	0.851794	−	0.327408i
$259$	317.876	−	317.876i	1.22732	−	1.22732i
$260$	34.1116	+	96.0566i	0.131198	+	0.369448i
$261$	6.17400	+	14.9054i	0.0236552	+	0.0571086i
$262$	161.153	−	61.9432i	0.615089	−	0.236424i
$263$	84.7918	−	84.7918i	0.322402	−	0.322402i	−0.527286	−	0.849688i	$-0.676790\pi$
$263$	84.7918	−	84.7918i	0.322402	−	0.322402i	0.849688	+	0.527286i	$0.176790\pi$
$264$	−36.4092	+	31.1805i	−0.137914	+	0.118108i
$265$	11.8370	+	4.90303i	0.0446678	+	0.0185020i
$266$	−169.054	−	439.817i	−0.635543	−	1.65345i
$267$	24.9097	+	10.3179i	0.0932948	+	0.0386440i
$268$	69.1824	−	62.4036i	0.258143	−	0.232849i
$269$	145.671	−	351.682i	0.541530	−	1.30737i	−0.382114	−	0.924115i	$-0.624804\pi$
$269$	145.671	−	351.682i	0.541530	−	1.30737i	0.923643	−	0.383253i	$-0.125196\pi$
$270$	272.105	+	286.484i	1.00780	+	1.06105i
$271$			376.373i			1.38883i	0.719575	+	0.694415i	$0.244337\pi$
$271$			376.373i			1.38883i	−0.719575	+	0.694415i	$0.755663\pi$
$272$	130.452	+	238.676i	0.479602	+	0.877486i
$273$	−97.0154			−0.355368
$274$	18.5455	−	17.6147i	0.0676843	−	0.0642872i
$275$	−44.7520	−	18.5369i	−0.162735	−	0.0674069i
$276$	243.295	−	219.456i	0.881502	−	0.795129i
$277$	94.2773	−	227.605i	0.340351	−	0.821680i	−0.657329	−	0.753604i	$-0.728314\pi$
$277$	94.2773	−	227.605i	0.340351	−	0.821680i	0.997680	−	0.0680766i	$-0.0216862\pi$
$278$	−471.019	+	181.047i	−1.69431	+	0.651250i
$279$	0.543887	−	1.31306i	0.00194941	−	0.00470630i
$280$	−548.700	−	42.4471i	−1.95964	−	0.151597i
$281$	−293.463	−	293.463i	−1.04435	−	1.04435i	−0.998970	−	0.0453808i	$-0.985550\pi$
$281$	−293.463	−	293.463i	−1.04435	−	1.04435i	−0.0453808	−	0.998970i	$-0.514450\pi$
$282$	134.908	+	350.979i	0.478395	+	1.24461i
$283$	−114.683	+	47.5033i	−0.405241	+	0.167856i	−0.575987	−	0.817459i	$-0.695382\pi$
$283$	−114.683	+	47.5033i	−0.405241	+	0.167856i	0.170746	+	0.985315i	$0.445382\pi$
$284$	−85.5605	−	240.934i	−0.301269	−	0.848360i
$285$	−274.261	−	274.261i	−0.962321	−	0.962321i
$286$	6.50712	+	16.9291i	0.0227522	+	0.0591927i
$287$	213.052	−	213.052i	0.742341	−	0.742341i
$288$	11.2202	−	86.7153i	0.0389590	−	0.301095i
$289$	−103.027	+	270.012i	−0.356495	+	0.934297i
$290$	−79.3990	−	2.04380i	−0.273790	−	0.00704760i
$291$			19.7735i			0.0679502i
$292$	179.664	+	505.925i	0.615288	+	1.73262i
$293$	−81.5361	+	81.5361i	−0.278280	+	0.278280i	−0.832422	−	0.554142i	$-0.813046\pi$
$293$	−81.5361	+	81.5361i	−0.278280	+	0.278280i	0.554142	+	0.832422i	$0.313046\pi$
$294$	113.139	−	254.419i	0.384828	−	0.865372i
$295$	249.030	+	103.152i	0.844169	+	0.349666i
$296$	−334.267	+	109.103i	−1.12928	+	0.368591i
$297$	49.7101	+	49.7101i	0.167374	+	0.167374i
$298$	161.156	+	4.14830i	0.540791	+	0.0139205i
$299$	−47.4397	−	114.530i	−0.158661	−	0.383042i
$300$	−190.983	+	67.8217i	−0.636609	+	0.226072i
$301$	444.324	+	184.045i	1.47616	+	0.611446i
$302$	−3.38031	+	131.321i	−0.0111931	+	0.434836i
$303$	92.1378	+	222.440i	0.304085	+	0.734127i
$304$	−37.8720	+	366.600i	−0.124579	+	1.20592i
$305$	468.313			1.53545
$306$	77.8418	−	50.7114i	0.254385	−	0.165724i
$307$	346.818	+	346.818i	1.12970	+	1.12970i	0.990226	+	0.139475i	$0.0445415\pi$
$307$	346.818	+	346.818i	1.12970	+	1.12970i	0.139475	+	0.990226i	$0.455459\pi$
$308$	−97.7899	−	5.03774i	−0.317500	−	0.0163563i
$309$	63.8712	+	26.4563i	0.206703	+	0.0856192i
$310$	4.81855	+	5.07317i	0.0155437	+	0.0163651i
$311$	−174.120	−	420.364i	−0.559873	−	1.35165i	−0.909867	−	0.414901i	$-0.863816\pi$
$311$	−174.120	−	420.364i	−0.559873	−	1.35165i	0.349994	−	0.936752i	$-0.386184\pi$
$312$	67.6580	+	34.3598i	0.216852	+	0.110128i
$313$	403.783	+	167.252i	1.29004	+	0.534353i	0.918998	−	0.394263i	$-0.129000\pi$
$313$	403.783	+	167.252i	1.29004	+	0.534353i	0.371044	+	0.928615i	$0.379000\pi$
$314$	−1.33278	+	51.7768i	−0.00424453	+	0.164894i
$315$			187.971i			0.596735i
$316$	−492.226	−	234.242i	−1.55768	−	0.741273i
$317$	190.381	−	78.8583i	0.600570	−	0.248764i	−0.0616206	−	0.998100i	$-0.519627\pi$
$317$	190.381	−	78.8583i	0.600570	−	0.248764i	0.662191	+	0.749335i	$0.269627\pi$
$318$	8.90283	−	3.42202i	0.0279963	−	0.0107611i
$319$	−14.1318			−0.0443004
$320$	367.627	+	223.935i	1.14883	+	0.699797i
$321$	−104.337	−	104.337i	−0.325038	−	0.325038i
$322$	669.070	+	17.2225i	2.07786	+	0.0534859i
$323$	−322.493	+	222.120i	−0.998430	+	0.687677i
$324$	195.508	+	10.0718i	0.603419	+	0.0310857i
$325$			76.6795i			0.235937i
$326$	473.804	+	210.699i	1.45339	+	0.646315i
$327$			536.379i			1.64030i
$328$	−224.037	+	73.1248i	−0.683041	+	0.222941i
$329$	−293.935	+	709.623i	−0.893421	+	2.15691i
$330$	−75.2371	+	28.9192i	−0.227991	+	0.0876340i
$331$		−	443.754i		−	1.34065i	−0.742069	−	0.670323i	$-0.766156\pi$
$331$		−	443.754i		−	1.34065i	0.742069	−	0.670323i	$-0.233844\pi$
$332$	−22.4421	−	1.15613i	−0.0675968	−	0.00348231i
$333$	45.9596	+	110.956i	0.138017	+	0.333202i
$334$	−497.412	−	221.197i	−1.48926	−	0.662267i
$335$	144.737	−	59.9519i	0.432050	−	0.178961i
$336$	−317.930	+	258.393i	−0.946222	+	0.769026i
$337$	−153.403	+	63.5417i	−0.455202	+	0.188551i	−0.598490	−	0.801130i	$-0.704232\pi$
$337$	−153.403	+	63.5417i	−0.455202	+	0.188551i	0.143288	+	0.989681i	$0.454232\pi$
$338$	−224.256	+	213.001i	−0.663480	+	0.630180i
$339$	−262.556	−	262.556i	−0.774500	−	0.774500i
$340$	72.4023	+	451.597i	0.212948	+	1.32823i
$341$	0.880288	+	0.880288i	0.00258149	+	0.00258149i
$342$	125.839	+	3.23921i	0.367950	+	0.00947136i
$343$	62.4630	−	25.8730i	0.182108	−	0.0754315i
$344$	−244.686	−	285.718i	−0.711297	−	0.830575i
$345$	508.998	−	210.834i	1.47536	−	0.611112i
$346$	42.1137	−	16.1874i	0.121716	−	0.0467845i
$347$	−151.430	−	365.584i	−0.436397	−	1.05356i	−0.977184	−	0.212396i	$-0.931873\pi$
$347$	−151.430	−	365.584i	−0.436397	−	1.05356i	0.540787	−	0.841160i	$-0.318127\pi$
$348$	−43.9046	+	39.6026i	−0.126163	+	0.113801i
$349$		−	143.470i		−	0.411088i	−0.978648	−	0.205544i	$-0.934104\pi$
$349$		−	143.470i		−	0.411088i	0.978648	−	0.205544i	$-0.0658964\pi$
$350$	−378.276	−	168.218i	−1.08079	−	0.480622i
$351$	42.5874	−	102.815i	0.121332	−	0.292921i
$352$	66.4139	+	38.1474i	0.188676	+	0.108373i
$353$			312.935i			0.886500i	0.896398	+	0.443250i	$0.146175\pi$
$353$			312.935i			0.886500i	−0.896398	+	0.443250i	$0.853825\pi$
$354$	187.301	−	71.9936i	0.529098	−	0.203372i
$355$		−	429.915i		−	1.21103i
$356$	2.21631	−	43.0218i	0.00622559	−	0.120848i
$357$	−428.087	−	78.8972i	−1.19912	−	0.221000i
$358$	9.34704	+	9.84095i	0.0261090	+	0.0274887i
$359$	−479.711	−	479.711i	−1.33624	−	1.33624i	−0.899670	−	0.436572i	$-0.856193\pi$
$359$	−479.711	−	479.711i	−1.33624	−	1.33624i	−0.436572	−	0.899670i	$-0.643807\pi$
$360$	66.5736	−	131.090i	0.184927	−	0.364139i
$361$	−169.584			−0.469762
$362$	193.489	−	435.103i	0.534499	−	1.20194i
$363$	266.616	−	110.436i	0.734479	−	0.304231i
$364$	51.8724	+	146.070i	0.142506	+	0.401291i
$365$			902.755i			2.47330i
$366$	252.779	−	240.092i	0.690652	−	0.655989i
$367$	153.953	+	63.7693i	0.419490	+	0.173758i	0.582436	−	0.812877i	$-0.302100\pi$
$367$	153.953	+	63.7693i	0.419490	+	0.173758i	−0.162946	+	0.986635i	$0.552100\pi$
$368$	−460.506	−	248.975i	−1.25137	−	0.676561i
$369$	30.8038	+	74.3669i	0.0834790	+	0.201536i
$370$	−591.051	−	15.2142i	−1.59743	−	0.0411194i
$371$	18.0001	+	7.45587i	0.0485177	+	0.0200967i
$372$	5.20177	+	0.267974i	0.0139833	+	0.000720361i
$373$	−421.818	−	421.818i	−1.13088	−	1.13088i	−0.990031	−	0.140847i	$-0.955017\pi$
$373$	−421.818	−	421.818i	−1.13088	−	1.13088i	−0.140847	−	0.990031i	$-0.544983\pi$
$374$	14.9456	+	79.9927i	0.0399615	+	0.213884i
$375$	80.1789			0.213810
$376$	456.315	−	390.784i	1.21360	−	1.03932i
$377$	8.56090	+	20.6678i	0.0227080	+	0.0548219i
$378$	413.781	+	435.646i	1.09466	+	1.15250i
$379$	147.976	+	61.2938i	0.390439	+	0.161725i	0.569262	−	0.822156i	$-0.307229\pi$
$379$	147.976	+	61.2938i	0.390439	+	0.161725i	−0.178823	+	0.983881i	$0.557229\pi$
$380$	−266.296	+	559.581i	−0.700778	+	1.47258i
$381$	143.053	+	345.360i	0.375467	+	0.906457i
$382$	−271.780	−	286.141i	−0.711466	−	0.749062i
$383$	−204.822	−	204.822i	−0.534783	−	0.534783i	0.387209	−	0.921992i	$-0.373439\pi$
$383$	−204.822	−	204.822i	−0.534783	−	0.534783i	−0.921992	+	0.387209i	$0.873439\pi$
$384$	313.238	−	67.6005i	0.815723	−	0.176043i
$385$	−152.117	−	63.0090i	−0.395109	−	0.163660i
$386$	209.910	+	546.109i	0.543809	+	1.41479i
$387$	−90.8518	+	90.8518i	−0.234759	+	0.234759i
$388$	29.7717	−	10.5725i	0.0767313	−	0.0272488i
$389$		−	41.3895i		−	0.106400i	−0.998584	−	0.0531999i	$-0.983058\pi$
$389$		−	41.3895i		−	0.106400i	0.998584	−	0.0531999i	$-0.0169420\pi$
$390$	87.8724	+	92.5157i	0.225314	+	0.237220i
$391$	−116.190	−	543.949i	−0.297162	−	1.39117i
$392$	−443.557	−	34.3133i	−1.13152	−	0.0875340i
$393$	152.815	−	152.815i	0.388842	−	0.388842i
$394$	455.513	+	202.565i	1.15612	+	0.514124i
$395$	−648.142	−	648.142i	−1.64087	−	1.64087i
$396$	11.2411	−	23.6214i	0.0283865	−	0.0596500i
$397$	63.7639	−	26.4119i	0.160614	−	0.0665287i	−0.300928	−	0.953647i	$-0.597296\pi$
$397$	63.7639	−	26.4119i	0.160614	−	0.0665287i	0.461542	+	0.887118i	$0.347296\pi$
$398$	−241.864	+	543.887i	−0.607700	+	1.36655i
$399$	−417.060	−	417.060i	−1.04526	−	1.04526i
$400$	204.230	+	251.288i	0.510574	+	0.628219i
$401$	173.410	−	418.649i	0.432445	−	1.04401i	−0.546052	−	0.837751i	$-0.683870\pi$
$401$	173.410	−	418.649i	0.432445	−	1.04401i	0.978497	−	0.206262i	$-0.0661300\pi$
$402$	47.3880	−	106.563i	0.117881	−	0.265081i
$403$	0.754156	−	1.82069i	0.00187136	−	0.00451785i
$404$	285.650	−	257.661i	0.707055	−	0.637775i
$405$	304.122	+	125.972i	0.750919	+	0.311041i
$406$	−120.739	−	3.10794i	−0.297388	−	0.00765503i
$407$	−105.198			−0.258472
$408$	270.602	+	206.638i	0.663241	+	0.506465i
$409$		−	197.736i		−	0.483462i	−0.970343	−	0.241731i	$-0.922285\pi$
$409$		−	197.736i		−	0.483462i	0.970343	−	0.241731i	$-0.0777152\pi$
$410$	−396.143	−	10.1971i	−0.966203	−	0.0248710i
$411$	12.2523	−	29.5797i	0.0298110	−	0.0719701i
$412$	5.68286	−	110.313i	0.0137934	−	0.267749i
$413$	378.691	+	156.859i	0.916928	+	0.379804i
$414$	−72.6538	+	163.379i	−0.175492	+	0.394634i
$415$	−34.9099	−	14.4601i	−0.0841202	−	0.0348437i
$416$	15.5580	−	120.240i	0.0373990	−	0.289038i
$417$	−446.647	+	446.647i	−1.07110	+	1.07110i
$418$	−44.8032	+	100.750i	−0.107185	+	0.241029i
$419$	−74.2100	−	179.159i	−0.177112	−	0.427587i	0.810246	−	0.586089i	$-0.199333\pi$
$419$	−74.2100	−	179.159i	−0.177112	−	0.427587i	−0.987359	+	0.158503i	$0.949333\pi$
$420$	−649.171	+	230.534i	−1.54565	+	0.548889i
$421$	−442.880	+	442.880i	−1.05197	+	1.05197i	−0.0533988	+	0.998573i	$0.517005\pi$
$421$	−442.880	+	442.880i	−1.05197	+	1.05197i	−0.998573	+	0.0533988i	$0.982995\pi$
$422$	193.037	+	85.8428i	0.457434	+	0.203419i
$423$	−145.098	−	145.098i	−0.343021	−	0.343021i
$424$	−9.91250	−	11.5747i	−0.0233785	−	0.0272989i
$425$	−62.3592	+	338.353i	−0.146727	+	0.796126i
$426$	−220.406	−	232.053i	−0.517385	−	0.544725i
$427$	712.147			1.66779
$428$	−101.307	+	212.882i	−0.236699	+	0.497387i
$429$	16.0532	+	16.0532i	0.0374200	+	0.0374200i
$430$	−226.941	−	590.416i	−0.527770	−	1.37306i
$431$	−77.0481	+	186.011i	−0.178766	+	0.431579i	−0.987708	−	0.156309i	$-0.950040\pi$
$431$	−77.0481	+	186.011i	−0.178766	+	0.431579i	0.808942	+	0.587888i	$0.200040\pi$
$432$	−134.276	−	450.365i	−0.310824	−	1.04251i
$433$	21.1111	−	21.1111i	0.0487555	−	0.0487555i	−0.682309	−	0.731064i	$-0.739024\pi$
$433$	21.1111	−	21.1111i	0.0487555	−	0.0487555i	0.731064	+	0.682309i	$0.239024\pi$
$434$	7.32741	+	7.71460i	0.0168834	+	0.0177756i
$435$	−91.8530	+	38.0468i	−0.211156	+	0.0874638i
$436$	807.593	−	286.792i	1.85228	−	0.657780i
$437$	288.413	−	696.290i	0.659984	−	1.59334i
$438$	462.819	+	487.275i	1.05666	+	1.11250i
$439$	100.441	−	41.6041i	0.228795	−	0.0947701i	−0.265341	−	0.964155i	$-0.585484\pi$
$439$	100.441	−	41.6041i	0.228795	−	0.0947701i	0.494136	+	0.869385i	$0.335484\pi$
$440$	83.7698	+	97.8173i	0.190386	+	0.222312i
$441$			151.952i			0.344562i
$442$	107.936	−	70.3167i	0.244199	−	0.159088i
$443$	−2.45250	+	2.45250i	−0.00553611	+	0.00553611i	−0.709869	−	0.704333i	$-0.751246\pi$
$443$	−2.45250	+	2.45250i	−0.00553611	+	0.00553611i	0.704333	+	0.709869i	$0.251246\pi$
$444$	−326.828	+	294.804i	−0.736100	+	0.663974i
$445$	27.7202	−	66.9226i	0.0622927	−	0.150388i
$446$	252.781	+	6.50681i	0.566773	+	0.0145893i
$447$	186.434	−	77.2233i	0.417078	−	0.172759i
$448$	559.038	+	340.530i	1.24785	+	0.760112i
$449$	124.304	−	300.095i	0.276845	−	0.668364i	−0.722899	−	0.690953i	$-0.757191\pi$
$449$	124.304	−	300.095i	0.276845	−	0.668364i	0.999745	+	0.0225894i	$0.00719105\pi$
$450$	80.1928	−	76.1679i	0.178206	−	0.169262i
$451$	−70.5075			−0.156336
$452$	−254.930	+	535.697i	−0.564004	+	1.18517i
$453$	62.9267	+	151.919i	0.138911	+	0.335361i
$454$	−156.929	+	352.890i	−0.345658	+	0.777292i
$455$			260.642i			0.572840i
$456$	143.146	+	438.565i	0.313916	+	0.961765i
$457$	172.991	−	172.991i	0.378536	−	0.378536i	−0.492038	−	0.870574i	$-0.663748\pi$
$457$	172.991	−	172.991i	0.378536	−	0.378536i	0.870574	+	0.492038i	$0.163748\pi$
$458$	−112.027	−	117.947i	−0.244601	−	0.257527i
$459$	271.534	−	419.045i	0.591577	−	0.912952i
$460$	−589.591	−	653.637i	−1.28172	−	1.42095i
$461$	−633.088			−1.37329			−0.686646	−	0.726992i	$-0.740918\pi$
$461$	−633.088			−1.37329			−0.686646	+	0.726992i	$0.740918\pi$
$462$	−114.411	+	43.9765i	−0.247642	+	0.0951872i
$463$	−61.1027			−0.131971			−0.0659856	−	0.997821i	$-0.521019\pi$
$463$	−61.1027			−0.131971			−0.0659856	+	0.997821i	$0.521019\pi$
$464$	83.1022	+	44.9296i	0.179100	+	0.0968310i
$465$	8.09162	+	3.35166i	0.0174013	+	0.00720787i
$466$	448.903	+	199.625i	0.963310	+	0.428380i
$467$	76.0617			0.162873			0.0814365	−	0.996679i	$-0.474049\pi$
$467$	76.0617			0.162873			0.0814365	+	0.996679i	$0.474049\pi$
$468$	−41.3561	−	2.13050i	−0.0883678	−	0.00455235i
$469$	220.096	−	91.1668i	0.469288	−	0.194386i
$470$	942.944	−	362.444i	2.00626	−	0.771156i
$471$	24.8106	+	59.8981i	0.0526765	+	0.127172i
$472$	−208.543	−	243.513i	−0.441827	−	0.515918i
$473$	−43.0685	−	103.976i	−0.0910538	−	0.219823i
$474$	−682.130	−	17.5587i	−1.43909	−	0.0370436i
$475$	−329.638	+	329.638i	−0.693975	+	0.693975i
$476$	110.100	+	686.728i	0.231302	+	1.44271i
$477$	−3.68051	+	3.68051i	−0.00771595	+	0.00771595i
$478$	260.894	−	247.800i	0.545803	−	0.518409i
$479$	−125.261	−	302.408i	−0.261506	−	0.631332i	0.737526	−	0.675319i	$-0.235994\pi$
$479$	−125.261	−	302.408i	−0.261506	−	0.631332i	−0.999032	+	0.0439872i	$0.985994\pi$
$480$	534.376	+	69.1435i	1.11328	+	0.144049i
$481$	63.7279	+	153.853i	0.132490	+	0.319860i
$482$	368.814	+	164.010i	0.765174	+	0.340270i
$483$	774.015	−	320.608i	1.60252	−	0.663784i
$484$	−308.831	−	342.379i	−0.638081	−	0.707395i
$485$	53.1237			0.109533
$486$	−264.764	+	101.768i	−0.544781	+	0.209400i
$487$	−518.916	−	214.942i	−1.06554	−	0.441360i	−0.220123	−	0.975472i	$-0.570646\pi$
$487$	−518.916	−	214.942i	−1.06554	−	0.441360i	−0.845414	+	0.534112i	$0.820646\pi$
$488$	−496.648	−	252.221i	−1.01772	−	0.516845i
$489$	649.085			1.32737
$490$	−683.525	−	303.961i	−1.39495	−	0.620328i
$491$	252.822			0.514912			0.257456	−	0.966290i	$-0.417116\pi$
$491$	252.822			0.514912			0.257456	+	0.966290i	$0.417116\pi$
$492$	−219.052	+	197.588i	−0.445228	+	0.401602i
$493$	20.9675	+	98.1603i	0.0425305	+	0.199108i
$494$	174.489	+	4.49150i	0.353216	+	0.00909211i
$495$	31.1037	−	31.1037i	0.0628357	−	0.0628357i
$496$	−2.37782	−	7.97526i	−0.00479399	−	0.0160792i
$497$		−	653.757i		−	1.31541i
$498$	−26.2565	+	10.0923i	−0.0527238	+	0.0202657i
$499$	−18.2824	−	44.1376i	−0.0366381	−	0.0884521i	0.904501	−	0.426471i	$-0.140243\pi$
$499$	−18.2824	−	44.1376i	−0.0366381	−	0.0884521i	−0.941139	+	0.338019i	$0.890243\pi$
$500$	−42.8702	−	120.720i	−0.0857404	−	0.241441i
$501$	−681.427			−1.36013
$502$	4.21246	−	163.649i	0.00839136	−	0.325993i
$503$	42.4940	−	102.590i	0.0844811	−	0.203955i	−0.875994	−	0.482323i	$-0.839793\pi$
$503$	42.4940	−	102.590i	0.0844811	−	0.203955i	0.960475	+	0.278367i	$0.0897933\pi$
$504$	101.236	−	199.344i	0.200866	−	0.395525i
$505$	597.610	−	247.538i	1.18339	−	0.490175i
$506$	−107.861	−	113.561i	−0.213165	−	0.224429i
$507$	−148.158	+	357.684i	−0.292224	+	0.705492i
$508$	443.499	−	400.043i	0.873030	−	0.787487i
$509$	603.758	−	603.758i	1.18617	−	1.18617i	0.208046	−	0.978119i	$-0.433290\pi$
$509$	603.758	−	603.758i	1.18617	−	1.18617i	0.978119	−	0.208046i	$-0.0667104\pi$
$510$	312.505	+	479.694i	0.612755	+	0.940576i
$511$			1372.79i			2.68648i
$512$	−269.264	−	435.478i	−0.525907	−	0.850542i
$513$	625.072	−	258.913i	1.21846	−	0.504704i
$514$	20.9399	−	813.488i	0.0407392	−	1.58266i
$515$	71.0778	−	171.597i	0.138015	−	0.333198i
$516$	−425.186	−	202.339i	−0.824004	−	0.392130i
$517$	166.059	−	68.7839i	0.321197	−	0.133044i
$518$	−898.791	−	23.1357i	−1.73512	−	0.0446635i
$519$	39.9347	−	39.9347i	0.0769454	−	0.0769454i
$520$	92.3114	−	181.770i	0.177522	−	0.349559i
$521$	360.990	−	871.508i	0.692880	−	1.67276i	−0.0460163	−	0.998941i	$-0.514653\pi$
$521$	360.990	−	871.508i	0.692880	−	1.67276i	0.738896	−	0.673819i	$-0.235347\pi$
$522$	13.1110	−	29.4831i	0.0251169	−	0.0564810i
$523$	−478.525	−	478.525i	−0.914961	−	0.914961i	0.0816961	−	0.996657i	$-0.473966\pi$
$523$	−478.525	−	478.525i	−0.914961	−	0.914961i	−0.996657	+	0.0816961i	$0.973966\pi$
$524$	−311.791	−	148.377i	−0.595022	−	0.283161i
$525$	−518.217			−0.987079
$526$	−239.748	−	6.17133i	−0.455795	−	0.0117326i
$527$	4.80843	−	7.42062i	0.00912416	−	0.0140809i
$528$	95.3644	+	9.85172i	0.180614	+	0.0186586i
$529$	382.914	+	382.914i	0.723846	+	0.723846i
$530$	−9.19362	−	23.9184i	−0.0173465	−	0.0451291i
$531$	−77.4317	+	77.4317i	−0.145822	+	0.145822i
$532$	−404.947	+	850.935i	−0.761178	+	1.59950i
$533$	42.7127	+	103.118i	0.0801364	+	0.193466i
$534$	−19.3471	−	50.3339i	−0.0362305	−	0.0942583i
$535$	−280.314	+	280.314i	−0.523951	+	0.523951i
$536$	−185.782	−	14.3720i	−0.346609	−	0.0268135i
$537$	15.6961	+	6.50155i	0.0292293	+	0.0121072i
$538$	−710.628	+	273.147i	−1.32087	+	0.507709i
$539$	−122.968	−	50.9351i	−0.228141	−	0.0944992i
$540$	40.6553	−	789.179i	0.0752876	−	1.46144i
$541$	−368.395	+	889.383i	−0.680951	+	1.64396i	0.0813069	+	0.996689i	$0.474091\pi$
$541$	−368.395	+	889.383i	−0.680951	+	1.64396i	−0.762258	+	0.647273i	$0.775909\pi$
$542$	545.792	−	518.399i	1.00700	−	0.956456i
$543$		−	596.067i		−	1.09773i
$544$	166.435	−	517.914i	0.305947	−	0.952049i
$545$	1441.04			2.64411
$546$	133.625	+	140.686i	0.244734	+	0.257666i
$547$	−384.423	−	159.233i	−0.702784	−	0.291103i	0.00253086	−	0.999997i	$-0.499194\pi$
$547$	−384.423	−	159.233i	−0.702784	−	0.291103i	−0.705315	+	0.708894i	$0.749194\pi$
$548$	−51.0874	−	2.63182i	−0.0932253	−	0.00480259i
$549$	−72.8071	+	175.772i	−0.132618	+	0.320167i
$550$	34.7584	+	90.4284i	0.0631970	+	0.164415i
$551$	−52.0466	+	125.652i	−0.0944585	+	0.228043i
$552$	−653.343	−	50.5423i	−1.18359	−	0.0915621i
$553$	−985.608	−	985.608i	−1.78229	−	1.78229i
$554$	−459.912	+	176.778i	−0.830166	+	0.319095i
$555$	−683.759	+	283.222i	−1.23200	+	0.510311i
$556$	911.303	+	433.675i	1.63903	+	0.779990i
$557$	−180.533	−	180.533i	−0.324116	−	0.324116i	0.526228	−	0.850344i	$-0.323606\pi$
$557$	−180.533	−	180.533i	−0.324116	−	0.324116i	−0.850344	+	0.526228i	$0.823606\pi$
$558$	−2.65324	+	1.01984i	−0.00475491	+	0.00182766i
$559$	−125.976	+	125.976i	−0.225359	+	0.225359i
$560$	694.200	+	854.154i	1.23964	+	1.52528i
$561$	57.7805	+	83.8908i	0.102996	+	0.149538i
$562$	−21.3588	+	829.762i	−0.0380051	+	1.47645i
$563$			739.561i			1.31361i	0.754061	+	0.656804i	$0.228092\pi$
$563$			739.561i			1.31361i	−0.754061	+	0.656804i	$0.771908\pi$
$564$	323.153	−	679.057i	0.572966	−	1.20400i
$565$	−705.384	+	705.384i	−1.24847	+	1.24847i
$566$	226.846	+	100.877i	0.400787	+	0.178228i
$567$	462.468	+	191.561i	0.815641	+	0.337850i
$568$	−231.540	+	455.926i	−0.407641	+	0.802687i
$569$	−335.800	−	335.800i	−0.590158	−	0.590158i	0.347516	−	0.937674i	$-0.387025\pi$
$569$	−335.800	−	335.800i	−0.590158	−	0.590158i	−0.937674	+	0.347516i	$0.887025\pi$
$570$	−19.9613	+	775.471i	−0.0350199	+	1.36048i
$571$	403.923	+	975.156i	0.707395	+	1.70780i	0.706409	+	0.707804i	$0.250314\pi$
$571$	403.923	+	975.156i	0.707395	+	1.70780i	0.000985901		1.00000i	$0.499686\pi$
$572$	15.5869	−	32.7536i	0.0272498	−	0.0572615i
$573$	−456.390	−	189.043i	−0.796493	−	0.329918i
$574$	−602.402	−	15.5064i	−1.04948	−	0.0270146i
$575$	−253.404	−	611.770i	−0.440702	−	1.06395i
$576$	−141.203	+	103.167i	−0.245144	+	0.179109i
$577$	−1036.72			−1.79674			−0.898372	−	0.439236i	$-0.855249\pi$
$577$	−1036.72			−1.79674			−0.898372	+	0.439236i	$0.855249\pi$
$578$	533.459	−	222.499i	0.922939	−	0.384946i
$579$	517.852	+	517.852i	0.894391	+	0.894391i
$580$	106.397	+	117.954i	0.183443	+	0.203370i
$581$	−53.0863	−	21.9890i	−0.0913705	−	0.0378469i
$582$	28.6743	−	27.2351i	0.0492685	−	0.0467958i
$583$	−1.74475	−	4.21220i	−0.00299271	−	0.00722504i
$584$	486.199	−	957.375i	0.832533	−	1.63934i
$585$	−64.3316	−	26.6470i	−0.109969	−	0.0455505i
$586$	230.543	+	5.93437i	0.393417	+	0.0101269i
$587$			935.477i			1.59366i	0.604206	+	0.796828i	$0.293491\pi$
$587$			935.477i			1.59366i	−0.604206	+	0.796828i	$0.706509\pi$
$588$	−524.776	+	186.358i	−0.892476	+	0.316936i
$589$	11.0690	−	4.58495i	0.0187929	−	0.00778429i
$590$	−193.419	−	503.203i	−0.327828	−	0.852887i
$591$	624.028			1.05588
$592$	618.618	+	334.459i	1.04496	+	0.564964i
$593$	−122.823	−	122.823i	−0.207122	−	0.207122i	0.595921	−	0.803043i	$-0.296787\pi$
$593$	−122.823	−	122.823i	−0.207122	−	0.207122i	−0.803043	+	0.595921i	$0.796787\pi$
$594$	3.61801	−	140.555i	0.00609093	−	0.236624i
$595$	−211.966	+	1150.10i	−0.356245	+	1.93294i
$596$	−215.953	−	239.412i	−0.362337	−	0.401697i
$597$			745.095i			1.24807i
$598$	−100.742	+	226.542i	−0.168465	+	0.378832i
$599$			520.026i			0.868156i	0.900875	+	0.434078i	$0.142926\pi$
$599$			520.026i			0.868156i	−0.900875	+	0.434078i	$0.857074\pi$
$600$	361.401	+	183.536i	0.602336	+	0.305894i
$601$	−359.658	+	868.291i	−0.598432	+	1.44474i	0.276746	+	0.960943i	$0.410744\pi$
$601$	−359.658	+	868.291i	−0.598432	+	1.44474i	−0.875178	+	0.483801i	$0.839256\pi$
$602$	−345.101	−	897.826i	−0.573258	−	1.49141i
$603$			63.6446i			0.105547i
$604$	195.089	−	175.973i	0.322994	−	0.291346i
$605$	−296.698	−	716.293i	−0.490410	−	1.18395i
$606$	195.662	−	439.992i	0.322875	−	0.726059i
$607$	−291.833	+	120.881i	−0.480779	+	0.199145i	−0.609892	−	0.792485i	$-0.708787\pi$
$607$	−291.833	+	120.881i	−0.480779	+	0.199145i	0.129113	+	0.991630i	$0.458787\pi$
$608$	583.783	−	450.018i	0.960169	−	0.740161i
$609$	−139.678	+	57.8564i	−0.229356	+	0.0950023i
$610$	−645.033	−	679.117i	−1.05743	−	1.11331i
$611$	−201.194	−	201.194i	−0.329286	−	0.329286i
$612$	−180.754	−	43.0336i	−0.295350	−	0.0703164i
$613$	60.5000	+	60.5000i	0.0986949	+	0.0986949i	0.754730	−	0.656035i	$-0.227768\pi$
$613$	60.5000	+	60.5000i	0.0986949	+	0.0986949i	−0.656035	+	0.754730i	$0.727768\pi$
$614$	25.2422	−	980.625i	0.0411110	−	1.59711i
$615$	−458.280	+	189.826i	−0.745170	+	0.308660i
$616$	127.386	+	148.747i	0.206795	+	0.241473i
$617$	−688.256	+	285.085i	−1.11549	+	0.462050i	−0.862824	−	0.505504i	$-0.831306\pi$
$617$	−688.256	+	285.085i	−1.11549	+	0.462050i	−0.252663	+	0.967554i	$0.581306\pi$
$618$	−49.6080	−	129.062i	−0.0802719	−	0.208838i
$619$	11.8572	+	28.6258i	0.0191554	+	0.0462453i	0.933168	−	0.359441i	$-0.117033\pi$
$619$	11.8572	+	28.6258i	0.0191554	+	0.0462453i	−0.914012	+	0.405686i	$0.867033\pi$
$620$	0.719941	−	13.9751i	0.00116120	−	0.0225405i
$621$			961.027i			1.54755i
$622$	−369.760	+	831.489i	−0.594469	+	1.33680i
$623$	42.1532	−	101.767i	0.0676617	−	0.163350i
$624$	−43.3625	−	145.439i	−0.0694913	−	0.233075i
$625$		−	721.368i		−	1.15419i
$626$	−313.613	−	815.906i	−0.500980	−	1.30336i
$627$			138.022i			0.220131i
$628$	76.9191	−	69.3823i	0.122483	−	0.110481i
$629$	156.084	+	730.711i	0.248146	+	1.16170i
$630$	272.584	−	258.903i	0.432673	−	0.410957i
$631$	421.009	+	421.009i	0.667208	+	0.667208i	0.957069	−	0.289860i	$-0.0936089\pi$
$631$	421.009	+	421.009i	0.667208	+	0.667208i	−0.289860	+	0.957069i	$0.593609\pi$
$632$	338.286	+	1036.43i	0.535262	+	1.63992i
$633$	264.450			0.417773
$634$	−376.577	−	167.462i	−0.593970	−	0.264136i
$635$	927.847	−	384.327i	1.46118	−	0.605239i
$636$	−17.2247	−	8.19698i	−0.0270829	−	0.0128883i
$637$			210.698i			0.330765i
$638$	19.4645	+	20.4931i	0.0305086	+	0.0321208i
$639$	161.360	+	66.8374i	0.252519	+	0.104597i
$640$	−181.616	−	841.547i	−0.283775	−	1.31492i
$641$	−120.699	−	291.394i	−0.188299	−	0.454593i	0.801334	−	0.598218i	$-0.204124\pi$
$641$	−120.699	−	291.394i	−0.188299	−	0.454593i	−0.989632	+	0.143625i	$0.954124\pi$
$642$	−7.59390	+	295.013i	−0.0118285	+	0.459522i
$643$	−304.350	−	126.066i	−0.473328	−	0.196059i	0.133250	−	0.991082i	$-0.457459\pi$
$643$	−304.350	−	126.066i	−0.473328	−	0.196059i	−0.606579	+	0.795023i	$0.707459\pi$
$644$	−896.571	−	993.964i	−1.39219	−	1.54342i
$645$	−559.867	−	559.867i	−0.868011	−	0.868011i
$646$	766.291	+	161.721i	1.18621	+	0.250342i
$647$	150.479			0.232580			0.116290	−	0.993215i	$-0.462900\pi$
$647$	150.479			0.232580			0.116290	+	0.993215i	$0.462900\pi$
$648$	−254.678	−	297.385i	−0.393022	−	0.458928i
$649$	−36.7066	−	88.6177i	−0.0565588	−	0.136545i
$650$	111.196	−	105.615i	0.171070	−	0.162484i
$651$	12.3046	+	5.09675i	0.0189011	+	0.00782911i
$652$	−347.054	−	977.287i	−0.532291	−	1.49891i
$653$	417.823	+	1008.71i	0.639852	+	1.54474i	0.826877	+	0.562383i	$0.190115\pi$
$653$	417.823	+	1008.71i	0.639852	+	1.54474i	−0.187025	+	0.982355i	$0.559885\pi$
$654$	777.823	−	738.784i	1.18933	−	1.12964i
$655$	−410.554	−	410.554i	−0.626800	−	0.626800i
$656$	414.620	+	224.166i	0.632042	+	0.341717i
$657$	−338.831	−	140.348i	−0.515725	−	0.213620i
$658$	1433.90	−	551.156i	2.17918	−	0.837622i
$659$	526.928	−	526.928i	0.799588	−	0.799588i	−0.183443	−	0.983030i	$-0.558724\pi$
$659$	526.928	−	526.928i	0.799588	−	0.799588i	0.983030	+	0.183443i	$0.0587241\pi$
$660$	145.565	+	69.2721i	0.220553	+	0.104958i
$661$		−	1045.88i		−	1.58228i	−0.611638	−	0.791138i	$-0.709489\pi$
$661$		−	1045.88i		−	1.58228i	0.611638	−	0.791138i	$-0.290511\pi$
$662$	−643.504	+	611.206i	−0.972060	+	0.923272i
$663$	87.6879	−	135.324i	0.132259	−	0.204109i
$664$	29.2342	+	34.1365i	0.0440274	+	0.0514105i
$665$	−1120.48	+	1120.48i	−1.68493	+	1.68493i
$666$	97.5991	−	219.474i	0.146545	−	0.329540i
$667$	−136.602	−	136.602i	−0.204801	−	0.204801i
$668$	364.347	+	1025.98i	0.545429	+	1.53590i
$669$	292.430	−	121.129i	0.437116	−	0.181059i
$670$	−286.292	−	127.313i	−0.427302	−	0.190019i
$671$	−117.839	−	117.839i	−0.175617	−	0.175617i
$672$	812.608	+	105.144i	1.20924	+	0.156465i
$673$	291.748	−	704.342i	0.433503	−	1.04657i	−0.544646	−	0.838666i	$-0.683336\pi$
$673$	291.748	−	704.342i	0.433503	−	1.04657i	0.978149	−	0.207904i	$-0.0666641\pi$
$674$	303.434	+	134.936i	0.450200	+	0.200202i
$675$	227.485	−	549.197i	0.337014	−	0.813625i
$676$	617.760	+	31.8245i	0.913846	+	0.0470777i
$677$	630.412	+	261.125i	0.931185	+	0.385710i	0.796128	−	0.605128i	$-0.206878\pi$
$677$	630.412	+	261.125i	0.931185	+	0.385710i	0.135057	+	0.990838i	$0.456878\pi$
$678$	−19.1094	+	742.373i	−0.0281849	+	1.09495i
$679$	80.7834			0.118974
$680$	555.154	−	727.002i	0.816403	−	1.06912i
$681$			483.440i			0.709898i
$682$	0.0640693	−	2.48901i	9.39432e−5	−	0.00364957i
$683$	57.6607	−	139.205i	0.0844227	−	0.203814i	−0.876031	−	0.482255i	$-0.839818\pi$
$683$	57.6607	−	139.205i	0.0844227	−	0.203814i	0.960453	+	0.278441i	$0.0898177\pi$
$684$	−168.627	−	186.945i	−0.246531	−	0.273311i
$685$	−79.4691	−	32.9172i	−0.116013	−	0.0480543i
$686$	−123.553	−	54.9435i	−0.180106	−	0.0800926i
$687$	−188.124	−	77.9233i	−0.273833	−	0.113426i
$688$	−77.3104	+	748.363i	−0.112370	+	1.08774i
$689$	−5.10341	+	5.10341i	−0.00740698	+	0.00740698i
$690$	−1006.81	−	447.723i	−1.45914	−	0.648874i
$691$	383.656	+	926.226i	0.555218	+	1.34041i	0.913514	+	0.406807i	$0.133358\pi$
$691$	383.656	+	926.226i	0.555218	+	1.34041i	−0.358296	+	0.933608i	$0.616642\pi$
$692$	−81.4795	−	38.7748i	−0.117745	−	0.0560330i
$693$	47.2983	−	47.2983i	0.0682515	−	0.0682515i
$694$	−321.574	+	723.132i	−0.463363	+	1.04198i
$695$	1199.97	+	1199.97i	1.72657	+	1.72657i
$696$	117.901	+	9.12079i	0.169399	+	0.0131046i
$697$	104.613	+	489.749i	0.150090	+	0.702652i
$698$	−208.051	+	197.609i	−0.298067	+	0.283107i
$699$	614.972			0.879788
$700$	277.081	+	780.246i	0.395830	+	1.11464i
$701$	371.722	+	371.722i	0.530274	+	0.530274i	0.920654	−	0.390380i	$-0.127656\pi$
$701$	371.722	+	371.722i	0.530274	+	0.530274i	−0.390380	+	0.920654i	$0.627656\pi$
$702$	−207.754	+	79.8553i	−0.295946	+	0.113754i
$703$	−387.438	+	935.358i	−0.551121	+	1.33052i
$704$	−36.1565	−	148.852i	−0.0513586	−	0.211437i
$705$	894.154	−	894.154i	1.26830	−	1.26830i
$706$	453.798	−	431.022i	0.642773	−	0.610512i
$707$	908.765	−	376.423i	1.28538	−	0.532423i
$708$	−362.380	−	172.451i	−0.511836	−	0.243575i
$709$	−297.400	+	717.988i	−0.419464	+	1.01268i	0.563039	+	0.826431i	$0.309632\pi$
$709$	−297.400	+	717.988i	−0.419464	+	1.01268i	−0.982503	+	0.186246i	$0.940368\pi$
$710$	−623.435	+	592.145i	−0.878077	+	0.834007i
$711$	344.032	−	142.503i	0.483870	−	0.200426i
$712$	−65.4401	+	56.0423i	−0.0919103	+	0.0787111i
$713$			17.0183i			0.0238685i
$714$	475.215	+	729.454i	0.665568	+	1.02164i
$715$	43.1286	−	43.1286i	0.0603197	−	0.0603197i
$716$	1.39654	−	27.1090i	0.00195048	−	0.0378617i
$717$	172.363	−	416.121i	0.240395	−	0.580364i
$718$	−34.9144	+	1356.38i	−0.0486273	+	1.88910i
$719$	492.070	−	203.822i	0.684381	−	0.283480i	−0.0132760	−	0.999912i	$-0.504226\pi$
$719$	492.070	−	203.822i	0.684381	−	0.283480i	0.697657	+	0.716432i	$0.254226\pi$
$720$	−281.794	+	84.0168i	−0.391381	+	0.116690i
$721$	108.086	−	260.942i	0.149911	−	0.361916i
$722$	233.578	+	245.920i	0.323515	+	0.340610i
$723$	505.254			0.698830
$724$	−897.461	+	318.706i	−1.23959	+	0.440202i
$725$	45.7289	+	110.399i	0.0630743	+	0.152275i
$726$	−527.372	−	234.520i	−0.726408	−	0.323030i
$727$		−	140.017i		−	0.192595i	−0.995353	−	0.0962975i	$-0.969300\pi$
$727$		−	140.017i		−	0.192595i	0.995353	−	0.0962975i	$-0.0307000\pi$
$728$	140.375	−	276.412i	0.192823	−	0.379687i
$729$	−562.528	+	562.528i	−0.771643	+	0.771643i
$730$	1309.12	−	1243.41i	1.79331	−	1.70331i
$731$	−658.325	+	453.427i	−0.900581	+	0.620283i
$732$	−696.332	−	35.8722i	−0.951273	−	0.0490057i
$733$	−35.7790			−0.0488117			−0.0244058	−	0.999702i	$-0.507769\pi$
$733$	−35.7790			−0.0488117			−0.0244058	+	0.999702i	$0.507769\pi$
$734$	−119.573	−	311.085i	−0.162906	−	0.423822i
$735$	−936.392			−1.27400
$736$	273.232	+	1010.72i	0.371240	+	1.37326i
$737$	−51.5048	−	21.3340i	−0.0698844	−	0.0289471i
$738$	65.4144	−	147.099i	0.0886374	−	0.199321i
$739$	1116.12			1.51031			0.755156	−	0.655546i	$-0.227561\pi$
$739$	1116.12			1.51031			0.755156	+	0.655546i	$0.227561\pi$
$740$	792.024	+	878.060i	1.07030	+	1.18657i
$741$	201.858	−	83.6123i	0.272413	−	0.112837i
$742$	−13.9804	−	36.3719i	−0.0188415	−	0.0490187i
$743$	7.51415	+	18.1408i	0.0101133	+	0.0244155i	0.928856	−	0.370442i	$-0.120794\pi$
$743$	7.51415	+	18.1408i	0.0101133	+	0.0244155i	−0.918742	+	0.394858i	$0.870794\pi$
$744$	−6.77608	−	7.91237i	−0.00910763	−	0.0106349i
$745$	−207.469	−	500.874i	−0.278482	−	0.672314i
$746$	−30.7008	+	1192.69i	−0.0411539	+	1.59877i
$747$	10.8546	−	10.8546i	0.0145310	−	0.0145310i
$748$	95.4149	−	131.851i	0.127560	−	0.176272i
$749$	−426.263	+	426.263i	−0.569110	+	0.569110i
$750$	−110.435	−	116.270i	−0.147246	−	0.155027i
$751$	500.340	+	1207.93i	0.666232	+	1.60843i	0.787863	+	0.615851i	$0.211188\pi$
$751$	500.340	+	1207.93i	0.666232	+	1.60843i	−0.121631	+	0.992575i	$0.538812\pi$
$752$	−1195.20	−	123.471i	−1.58936	−	0.164190i
$753$	−78.4178	−	189.317i	−0.104141	−	0.251417i
$754$	18.1798	−	40.8814i	0.0241111	−	0.0542194i
$755$	408.146	−	169.059i	0.540590	−	0.223920i
$756$	61.8231	−	1200.08i	0.0817766	−	1.58740i
$757$	1276.35			1.68606			0.843031	−	0.537865i	$-0.180769\pi$
$757$	1276.35			1.68606			0.843031	+	0.537865i	$0.180769\pi$
$758$	−114.931	−	299.009i	−0.151625	−	0.394471i
$759$	−181.128	−	75.0255i	−0.238640	−	0.0988478i
$760$	1178.25	−	384.576i	1.55033	−	0.506021i
$761$	963.648			1.26629			0.633146	−	0.774033i	$-0.281763\pi$
$761$	963.648			1.26629			0.633146	+	0.774033i	$0.281763\pi$
$762$	303.785	−	683.129i	0.398668	−	0.896495i
$763$	2191.34			2.87201
$764$	−40.6068	+	788.236i	−0.0531502	+	1.03172i
$765$	−262.197	−	169.899i	−0.342741	−	0.222090i
$766$	−14.9074	+	579.132i	−0.0194613	+	0.756046i
$767$	−107.367	+	107.367i	−0.139983	+	0.139983i
$768$	−529.469	−	361.127i	−0.689413	−	0.470218i
$769$		−	566.116i		−	0.736172i	−0.929792	−	0.368086i	$-0.880013\pi$
$769$		−	566.116i		−	0.736172i	0.929792	−	0.368086i	$-0.119987\pi$
$770$	118.148	+	307.376i	0.153438	+	0.399190i
$771$	−389.811	−	941.087i	−0.505591	−	1.22061i
$772$	502.812	−	1056.58i	0.651310	−	1.36863i
$773$	1010.37			1.30708			0.653540	−	0.756892i	$-0.273283\pi$
$773$	1010.37			1.30708			0.653540	+	0.756892i	$0.273283\pi$
$774$	256.883	+	6.61239i	0.331890	+	0.00854315i
$775$	4.02840	−	9.72541i	0.00519793	−	0.0125489i
$776$	−56.3379	−	28.6110i	−0.0726003	−	0.0368698i
$777$	−1039.77	+	430.687i	−1.33818	+	0.554294i
$778$	−60.0204	+	57.0080i	−0.0771471	+	0.0732751i
$779$	−259.675	+	626.910i	−0.333344	+	0.804763i
$780$	13.1290	−	254.854i	0.0168321	−	0.326736i
$781$	−108.177	+	108.177i	−0.138511	+	0.138511i
$782$	−628.765	+	917.703i	−0.804048	+	1.17353i
$783$		−	173.426i		−	0.221489i
$784$	561.176	+	690.480i	0.715786	+	0.880714i
$785$	160.923	−	66.6564i	0.204997	−	0.0849126i
$786$	−432.083	−	11.1222i	−0.549724	−	0.0141504i
$787$	357.960	−	864.192i	0.454841	−	1.09808i	−0.515618	−	0.856819i	$-0.672438\pi$
$787$	357.960	−	864.192i	0.454841	−	1.09808i	0.970459	−	0.241265i	$-0.0775624\pi$
$788$	−333.656	−	939.559i	−0.423422	−	1.19233i
$789$	−277.353	+	114.883i	−0.351525	+	0.145606i
$790$	−47.1732	+	1832.62i	−0.0597129	+	2.31977i
$791$	−1072.65	+	1072.65i	−1.35607	+	1.35607i
$792$	−49.7372	+	16.2340i	−0.0627995	+	0.0204975i
$793$	−100.955	+	243.726i	−0.127307	+	0.307347i
$794$	−126.126	−	56.0879i	−0.158849	−	0.0706396i
$795$	−22.6808	−	22.6808i	−0.0285293	−	0.0285293i
$796$	1121.84	−	398.389i	1.40935	−	0.500489i
$797$	−936.400			−1.17491			−0.587453	−	0.809259i	$-0.699869\pi$
$797$	−936.400			−1.17491			−0.587453	+	0.809259i	$0.699869\pi$
$798$	−30.3545	+	1179.23i	−0.0380383	+	1.47774i
$799$	−724.161	−	1051.40i	−0.906334	−	1.31589i
$800$	83.1044	−	642.273i	0.103880	−	0.802841i
$801$	20.8085	+	20.8085i	0.0259781	+	0.0259781i
$802$	−845.946	+	325.160i	−1.05480	+	0.405436i
$803$	227.156	−	227.156i	0.282884	−	0.282884i
$804$	−219.801	+	78.0555i	−0.273384	+	0.0970840i
$805$	−861.347	−	2079.48i	−1.07000	−	2.58320i
$806$	−3.67900	+	1.41411i	−0.00456451	+	0.00175448i
$807$	−673.859	+	673.859i	−0.835017	+	0.835017i
$808$	−767.085	−	59.3413i	−0.949363	−	0.0734422i
$809$	−368.399	−	152.596i	−0.455375	−	0.188623i	0.143192	−	0.989695i	$-0.454263\pi$
$809$	−368.399	−	152.596i	−0.455375	−	0.188623i	−0.598568	+	0.801072i	$0.704263\pi$
$810$	−236.208	−	614.526i	−0.291615	−	0.758674i
$811$	−356.885	−	147.827i	−0.440056	−	0.182277i	0.151644	−	0.988435i	$-0.451543\pi$
$811$	−356.885	−	147.827i	−0.440056	−	0.182277i	−0.591700	+	0.806158i	$0.701543\pi$
$812$	161.794	+	179.369i	0.199254	+	0.220898i
$813$	360.585	−	870.528i	0.443524	−	1.07076i
$814$	144.895	+	152.551i	0.178004	+	0.187410i
$815$		−	1743.84i		−	2.13968i
$816$	−73.0627	−	677.023i	−0.0895377	−	0.829686i
$817$	−1083.12			−1.32572
$818$	−286.744	+	272.353i	−0.350543	+	0.332949i
$819$	−97.8269	−	40.5212i	−0.119447	−	0.0494764i
$820$	530.843	+	588.507i	0.647369	+	0.717691i
$821$	129.325	−	312.219i	0.157522	−	0.380291i	−0.825340	−	0.564636i	$-0.809017\pi$
$821$	129.325	−	312.219i	0.157522	−	0.380291i	0.982862	+	0.184346i	$0.0590165\pi$
$822$	−59.7704	+	22.9742i	−0.0727134	+	0.0279492i
$823$	42.8106	−	103.354i	0.0520177	−	0.125582i	−0.895734	−	0.444589i	$-0.853350\pi$
$823$	42.8106	−	103.354i	0.0520177	−	0.125582i	0.947752	+	0.319008i	$0.103350\pi$
$824$	−167.796	+	143.699i	−0.203636	+	0.174392i
$825$	85.7495	+	85.7495i	0.103939	+	0.103939i
$826$	−294.125	−	765.204i	−0.356083	−	0.926398i
$827$	277.928	−	115.122i	0.336068	−	0.139204i	−0.208267	−	0.978072i	$-0.566782\pi$
$827$	277.928	−	115.122i	0.336068	−	0.139204i	0.544335	+	0.838868i	$0.316782\pi$
$828$	336.991	−	119.672i	0.406994	−	0.144532i
$829$	−58.8368	−	58.8368i	−0.0709732	−	0.0709732i	0.670729	−	0.741702i	$-0.265981\pi$
$829$	−58.8368	−	58.8368i	−0.0709732	−	0.0709732i	−0.741702	+	0.670729i	$0.765981\pi$
$830$	27.1141	+	70.5408i	0.0326676	+	0.0849889i
$831$	−436.115	+	436.115i	−0.524808	+	0.524808i
$832$	−195.793	+	143.052i	−0.235328	+	0.171937i
$833$	−171.348	+	929.717i	−0.205700	+	1.11611i
$834$	1262.89	+	32.5080i	1.51426	+	0.0389784i
$835$			1830.73i			2.19249i
$836$	207.811	−	73.7979i	0.248578	−	0.0882750i
$837$	−10.8029	+	10.8029i	−0.0129067	+	0.0129067i
$838$	−157.591	+	354.380i	−0.188056	+	0.422888i
$839$	795.683	+	329.583i	0.948370	+	0.392828i	0.802618	−	0.596493i	$-0.203440\pi$
$839$	795.683	+	329.583i	0.948370	+	0.392828i	0.145752	+	0.989321i	$0.453440\pi$
$840$	1228.44	+	623.860i	1.46243	+	0.742691i
$841$	−570.026	−	570.026i	−0.677795	−	0.677795i
$842$	1252.24	+	32.2338i	1.48722	+	0.0382824i
$843$	397.609	+	959.913i	0.471660	+	1.13869i
$844$	−141.397	−	398.166i	−0.167532	−	0.471761i
$845$	960.957	+	398.042i	1.13723	+	0.471055i
$846$	−10.5605	+	410.263i	−0.0124829	+	0.484945i
$847$	−451.179	−	1089.24i	−0.532679	−	1.28600i
$848$	−3.13193	+	30.3170i	−0.00369331	+	0.0357512i
$849$	310.766			0.366038
$850$	576.549	−	375.603i	0.678293	−	0.441886i
$851$	−1016.88	−	1016.88i	−1.19492	−	1.19492i
$852$	−32.9309	+	639.238i	−0.0386513	+	0.750279i
$853$	−799.923	−	331.339i	−0.937776	−	0.388440i	−0.139153	−	0.990271i	$-0.544438\pi$
$853$	−799.923	−	331.339i	−0.937776	−	0.388440i	−0.798623	+	0.601831i	$0.794438\pi$
$854$	−980.879	−	1032.71i	−1.14857	−	1.20926i
$855$	−162.002	−	391.108i	−0.189476	−	0.457437i
$856$	448.243	−	146.304i	0.523648	−	0.170916i
$857$	109.607	+	45.4007i	0.127896	+	0.0529763i	0.445714	−	0.895176i	$-0.352950\pi$
$857$	109.607	+	45.4007i	0.127896	+	0.0529763i	−0.317818	+	0.948152i	$0.602950\pi$
$858$	1.16838	−	45.3902i	0.00136175	−	0.0529023i
$859$			424.122i			0.493739i	0.969049	+	0.246869i	$0.0794019\pi$
$859$			424.122i			0.493739i	−0.969049	+	0.246869i	$0.920598\pi$
$860$	−543.606	+	1142.31i	−0.632100	+	1.32826i
$861$	−696.890	+	288.661i	−0.809397	+	0.335263i
$862$	375.863	−	144.472i	0.436036	−	0.167601i
$863$	−482.643			−0.559262			−0.279631	−	0.960107i	$-0.590212\pi$
$863$	−482.643			−0.559262			−0.279631	+	0.960107i	$0.590212\pi$
$864$	−468.145	+	815.031i	−0.541835	+	0.943323i
$865$	−107.289	−	107.289i	−0.124033	−	0.124033i
$866$	−59.6916	−	1.53652i	−0.0689279	−	0.00177427i
$867$	496.980	−	525.817i	0.573218	−	0.606478i
$868$	1.09479	−	21.2515i	0.00126128	−	0.0244833i
$869$			326.178i			0.375348i
$870$	181.687	+	80.7955i	0.208836	+	0.0928684i
$871$			88.2499i			0.101320i
$872$	−1528.23	−	776.105i	−1.75256	−	0.890029i
$873$	−8.25896	+	19.9389i	−0.00946044	+	0.0228395i
$874$	−1406.96	+	540.800i	−1.60980	+	0.618765i
$875$		−	327.566i		−	0.374361i
$876$	69.1500	−	1342.30i	0.0789383	−	1.53231i
$877$	133.662	+	322.687i	0.152408	+	0.367945i	0.981581	−	0.191047i	$-0.0611883\pi$
$877$	133.662	+	322.687i	0.152408	+	0.367945i	−0.829173	+	0.558992i	$0.811188\pi$
$878$	−198.675	−	88.3498i	−0.226281	−	0.100626i
$879$	266.704	−	110.472i	0.303417	−	0.125680i
$880$	26.4677	−	256.207i	0.0300769	−	0.291144i
$881$	3.82434	−	1.58409i	0.00434091	−	0.00179806i	−0.380512	−	0.924776i	$-0.624252\pi$
$881$	3.82434	−	1.58409i	0.00434091	−	0.00179806i	0.384853	+	0.922978i	$0.374252\pi$
$882$	220.351	−	209.292i	0.249831	−	0.237292i
$883$	−154.406	−	154.406i	−0.174865	−	0.174865i	0.614248	−	0.789113i	$-0.289460\pi$
$883$	−154.406	−	154.406i	−0.174865	−	0.174865i	−0.789113	+	0.614248i	$0.789460\pi$
$884$	−250.635	−	59.6707i	−0.283523	−	0.0675007i
$885$	−477.167	−	477.167i	−0.539172	−	0.539172i
$886$	6.93441	+	0.178498i	0.00782665	+	0.000201465i
$887$	−984.827	+	407.929i	−1.11029	+	0.459897i	−0.861037	−	0.508542i	$-0.830185\pi$
$887$	−984.827	+	407.929i	−1.11029	+	0.459897i	−0.249252	+	0.968439i	$0.580185\pi$
$888$	877.665	+	67.8957i	0.988362	+	0.0764591i
$889$	1410.95	−	584.433i	1.58711	−	0.657405i
$890$	−135.227	+	51.9780i	−0.151941	+	0.0584022i
$891$	−44.8272	−	108.222i	−0.0503111	−	0.121462i
$892$	−338.733	−	375.529i	−0.379746	−	0.420997i
$893$		−	1729.83i		−	1.93709i
$894$	−368.770	−	163.990i	−0.412494	−	0.183434i
$895$	17.4671	−	42.1694i	0.0195163	−	0.0471166i
$896$	−276.177	−	1279.71i	−0.308234	−	1.42825i
$897$			310.350i			0.345986i
$898$	−606.389	+	233.080i	−0.675266	+	0.259555i
$899$		−	3.07109i		−	0.00341612i
$900$	−220.908	−	11.3803i	−0.245453	−	0.0126447i
$901$	−26.6695	+	18.3688i	−0.0295998	+	0.0203872i
$902$	97.1138	+	102.245i	0.107665	+	0.113354i
$903$	−851.371	−	851.371i	−0.942825	−	0.942825i
$904$	1127.96	−	368.162i	1.24775	−	0.407259i
$905$	−1601.40			−1.76950
$906$	133.630	−	300.498i	0.147495	−	0.331676i
$907$	−1108.81	+	459.284i	−1.22250	+	0.506377i	−0.898204	−	0.439579i	$-0.855128\pi$
$907$	−1108.81	+	459.284i	−1.22250	+	0.506377i	−0.324297	+	0.945955i	$0.605128\pi$
$908$	727.886	−	258.487i	0.801637	−	0.284677i
$909$			262.785i			0.289092i
$910$	377.967	−	358.997i	0.415348	−	0.394502i
$911$	1014.81	+	420.349i	1.11395	+	0.461415i	0.862298	−	0.506402i	$-0.169025\pi$
$911$	1014.81	+	420.349i	1.11395	+	0.461415i	0.251657	+	0.967817i	$0.419025\pi$
$912$	438.817	−	811.640i	0.481159	−	0.889956i
$913$	5.14566	+	12.4227i	0.00563600	+	0.0136065i
$914$	−489.130	−	12.5907i	−0.535154	−	0.0137753i
$915$	−1083.18	−	448.668i	−1.18380	−	0.490347i
$916$	−16.7381	+	324.910i	−0.0182730	+	0.354705i
$917$	−624.315	−	624.315i	−0.680824	−	0.680824i
$918$	−981.670	+	183.412i	−1.06936	+	0.199795i
$919$	−254.976			−0.277449			−0.138725	−	0.990331i	$-0.544300\pi$
$919$	−254.976			−0.277449			−0.138725	+	0.990331i	$0.544300\pi$
$920$	−135.787	+	1755.28i	−0.147595	+	1.90791i
$921$	−469.900	−	1134.44i	−0.510206	−	1.23175i
$922$	871.986	+	918.063i	0.945755	+	0.995730i
$923$	223.743	+	92.6772i	0.242408	+	0.100409i
$924$	221.356	+	105.340i	0.239563	+	0.114004i
$925$	340.408	+	821.818i	0.368009	+	0.888452i
$926$	84.1600	+	88.6072i	0.0908855	+	0.0956881i
$927$	53.3552	+	53.3552i	0.0575569	+	0.0575569i
$928$	−49.3071	−	182.394i	−0.0531327	−	0.196545i
$929$	−964.002	−	399.303i	−1.03768	−	0.429820i	−0.202199	−	0.979344i	$-0.564809\pi$
$929$	−964.002	−	399.303i	−1.03768	−	0.429820i	−0.835478	+	0.549525i	$0.814809\pi$
$930$	−6.28466	−	16.3504i	−0.00675770	−	0.0175810i
$931$	−905.769	+	905.769i	−0.972899	+	0.972899i
$932$	−328.814	−	925.924i	−0.352805	−	0.993481i
$933$			1139.09i			1.22089i
$934$	−104.764	−	110.300i	−0.112167	−	0.118094i
$935$	225.382	−	155.234i	0.241050	−	0.166025i
$936$	53.8725	+	62.9065i	0.0575561	+	0.0672078i
$937$	1317.53	−	1317.53i	1.40612	−	1.40612i	0.627517	−	0.778603i	$-0.284071\pi$
$937$	1317.53	−	1317.53i	1.40612	−	1.40612i	0.778603	−	0.627517i	$-0.215929\pi$
$938$	−435.355	−	193.601i	−0.464131	−	0.206397i
$939$	−773.690	−	773.690i	−0.823951	−	0.823951i
$940$	−1824.36	−	868.184i	−1.94081	−	0.923600i
$941$	1235.22	−	511.643i	1.31266	−	0.543723i	0.387003	−	0.922079i	$-0.373510\pi$
$941$	1235.22	−	511.643i	1.31266	−	0.543723i	0.925660	+	0.378356i	$0.123510\pi$
$942$	52.6875	−	118.480i	0.0559315	−	0.125775i
$943$	−681.547	−	681.547i	−0.722743	−	0.722743i
$944$	−65.8906	+	637.819i	−0.0697994	+	0.675656i
$945$	773.246	−	1866.78i	0.818250	−	1.97543i
$946$	−91.4595	+	205.668i	−0.0966803	+	0.217408i
$947$	−507.352	+	1224.86i	−0.535747	+	1.29341i	0.391921	+	0.919999i	$0.371811\pi$
$947$	−507.352	+	1224.86i	−0.535747	+	1.29341i	−0.927667	+	0.373408i	$0.878189\pi$
$948$	914.072	+	1013.37i	0.964211	+	1.06895i
$949$	−469.825	−	194.608i	−0.495074	−	0.205066i
$950$	932.048	+	23.9918i	0.981103	+	0.0252545i
$951$	−515.890			−0.542471
$952$	844.204	−	1105.53i	0.886769	−	1.16127i
$953$			530.860i			0.557041i	0.960430	+	0.278520i	$0.0898440\pi$
$953$			530.860i			0.557041i	−0.960430	+	0.278520i	$0.910156\pi$
$954$	10.4066	+	0.267875i	0.0109084	+	0.000280792i
$955$	−507.885	+	1226.14i	−0.531816	+	1.28392i
$956$	−718.686	−	37.0238i	−0.751764	−	0.0387278i
$957$	32.6860	+	13.5390i	0.0341547	+	0.0141473i
$958$	−266.003	+	598.169i	−0.277665	+	0.624393i
$959$	−120.846	−	50.0560i	−0.126013	−	0.0521961i
$960$	−635.758	−	870.153i	−0.662248	−	0.906410i
$961$	679.338	−	679.338i	0.706908	−	0.706908i
$962$	135.332	−	304.324i	0.140677	−	0.316345i
$963$	−61.6306	−	148.790i	−0.0639986	−	0.154506i
$964$	−270.150	−	760.730i	−0.280239	−	0.789139i
$965$	1391.27	−	1391.27i	1.44173	−	1.44173i
$966$	−1531.02	−	680.838i	−1.58490	−	0.704801i
$967$	760.832	+	760.832i	0.786797	+	0.786797i	0.980968	−	0.194171i	$-0.0622017\pi$
$967$	760.832	+	760.832i	0.786797	+	0.786797i	−0.194171	+	0.980968i	$0.562202\pi$
$968$	−71.1262	+	919.425i	−0.0734775	+	0.949819i
$969$	958.709	−	204.785i	0.989380	−	0.211337i
$970$	−73.1701	−	77.0366i	−0.0754331	−	0.0794191i
$971$	−1109.06			−1.14219			−0.571093	−	0.820885i	$-0.693480\pi$
$971$	−1109.06			−1.14219			−0.571093	+	0.820885i	$0.693480\pi$
$972$	512.251	+	243.772i	0.527008	+	0.250795i
$973$	1824.75	+	1824.75i	1.87538	+	1.87538i
$974$	403.036	+	1048.55i	0.413795	+	1.07654i
$975$	73.4629	−	177.355i	0.0753466	−	0.181903i
$976$	318.305	+	1067.60i	0.326133	+	1.09386i
$977$	−933.522	+	933.522i	−0.955499	+	0.955499i	−0.999051	−	0.0435523i	$-0.986132\pi$
$977$	−933.522	+	933.522i	−0.955499	+	0.955499i	0.0435523	+	0.999051i	$0.486132\pi$
$978$	−894.020	−	941.262i	−0.914131	−	0.962435i
$979$	−23.8145	+	9.86429i	−0.0243253	+	0.0100759i
$980$	500.672	+	1409.87i	0.510889	+	1.43864i
$981$	−224.034	+	540.866i	−0.228373	+	0.551341i
$982$	−348.225	−	366.626i	−0.354608	−	0.373346i
$983$	329.256	−	136.382i	0.334950	−	0.138741i	−0.208868	−	0.977944i	$-0.566978\pi$
$983$	329.256	−	136.382i	0.334950	−	0.138741i	0.543819	+	0.839203i	$0.316978\pi$
$984$	588.242	+	45.5061i	0.597807	+	0.0462460i
$985$		−	1676.52i		−	1.70205i
$986$	113.466	−	165.607i	0.115077	−	0.167959i
$987$	1359.71	−	1359.71i	1.37762	−	1.37762i
$988$	−233.820	−	259.219i	−0.236660	−	0.262367i
$989$	588.756	−	1421.38i	0.595304	−	1.43719i
$990$	−87.9454	−	2.26379i	−0.0888337	−	0.00228666i
$991$	−439.029	+	181.852i	−0.443016	+	0.183503i	−0.593029	−	0.805181i	$-0.702068\pi$
$991$	−439.029	+	181.852i	−0.443016	+	0.183503i	0.150014	+	0.988684i	$0.452068\pi$
$992$	−8.29012	+	14.4329i	−0.00835697	+	0.0145493i
$993$	−425.139	+	1026.38i	−0.428136	+	1.03361i
$994$	−948.036	+	900.454i	−0.953759	+	0.905890i
$995$	2001.78			2.01184
$996$	50.7997	+	24.1748i	0.0510037	+	0.0242718i
$997$	389.342	+	939.956i	0.390514	+	0.942784i	0.989828	+	0.142270i	$0.0454401\pi$
$997$	389.342	+	939.956i	0.390514	+	0.942784i	−0.599314	+	0.800514i	$0.704560\pi$
$998$	−38.8242	+	87.3051i	−0.0389020	+	0.0874800i
$999$		−	1290.99i		−	1.29228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	272.3.x.a.155.20	✓	280
16.3	odd	4		272.3.z.a.19.17	yes	280
17.9	even	8		272.3.z.a.43.17	yes	280
272.179	odd	8	inner	272.3.x.a.179.20	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
272.3.x.a.155.20	✓	280	1.1	even	1	trivial
272.3.x.a.179.20	yes	280	272.179	odd	8	inner
272.3.z.a.19.17	yes	280	16.3	odd	4
272.3.z.a.43.17	yes	280	17.9	even	8

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:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	272.x (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37735 - 1.45014i) q^{2} +(-2.31294 - 0.958051i) q^{3} +(-0.205791 + 3.99470i) q^{4} +(-2.57391 + 6.21396i) q^{5} +(1.79643 + 4.67366i) q^{6} +(-3.91405 + 9.44936i) q^{7} +(6.07631 - 5.20370i) q^{8} +(-1.93213 - 1.93213i) q^{9} +(12.5563 - 4.82631i) q^{10} +(2.21125 - 0.915929i) q^{11} +(4.30311 - 9.04235i) q^{12} +(-2.67910 - 2.67910i) q^{13} +(19.0939 - 7.33921i) q^{14} +(11.9066 - 11.9066i) q^{15} +(-15.9153 - 1.64415i) q^{16} +(-9.64295 - 14.0005i) q^{17} +(-0.140625 + 5.46308i) q^{18} -23.0344i q^{19} +(-24.2933 - 11.5608i) q^{20} +(18.1059 - 18.1059i) q^{21} +(-4.37390 - 1.94505i) q^{22} +(30.2283 + 12.5210i) q^{23} +(-19.0396 + 6.21442i) q^{24} +(-14.3107 - 14.3107i) q^{25} +(-0.194991 + 7.57514i) q^{26} +(11.2403 + 27.1364i) q^{27} +(-36.9419 - 17.5801i) q^{28} +(-5.45495 - 2.25952i) q^{29} +(-33.6658 - 0.866588i) q^{30} +(0.199048 + 0.480544i) q^{31} +(19.5368 + 25.3439i) q^{32} -5.99199 q^{33} +(-7.02084 + 33.2672i) q^{34} +(-48.6436 - 48.6436i) q^{35} +(8.11590 - 7.32067i) q^{36} +(-40.6070 - 16.8200i) q^{37} +(-33.4030 + 31.7265i) q^{38} +(3.62989 + 8.76332i) q^{39} +(16.6957 + 51.1518i) q^{40} +(-27.2162 - 11.2733i) q^{41} +(-51.1944 - 1.31779i) q^{42} -47.0216i q^{43} +(3.20381 + 9.02177i) q^{44} +(16.9793 - 7.03306i) q^{45} +(-23.4779 - 61.0809i) q^{46} +75.0974 q^{47} +(35.2360 + 19.0505i) q^{48} +(-39.3224 - 39.3224i) q^{49} +(-1.04156 + 40.4633i) q^{50} +(8.89040 + 41.6207i) q^{51} +(11.2536 - 10.1509i) q^{52} -1.90490i q^{53} +(23.8697 - 53.6764i) q^{54} +16.0981i q^{55} +(25.3886 + 77.7848i) q^{56} +(-22.0682 + 53.2772i) q^{57} +(4.23680 + 11.0226i) q^{58} -40.0758i q^{59} +(45.1130 + 50.0136i) q^{60} +(-26.6454 - 64.3277i) q^{61} +(0.422695 - 0.950525i) q^{62} +(25.8199 - 10.6949i) q^{63} +(9.84310 - 63.2385i) q^{64} +(23.5436 - 9.75208i) q^{65} +(8.25310 + 8.68921i) q^{66} +(-16.4701 - 16.4701i) q^{67} +(57.9122 - 35.6396i) q^{68} +(-57.9205 - 57.9205i) q^{69} +(-3.54039 + 137.539i) q^{70} +(-59.0533 + 24.4607i) q^{71} +(-21.7944 - 1.68601i) q^{72} +(124.003 - 51.3637i) q^{73} +(31.5390 + 82.0527i) q^{74} +(19.3894 + 46.8101i) q^{75} +(92.0156 + 4.74027i) q^{76} +24.4799i q^{77} +(7.70837 - 17.3340i) q^{78} +(-52.1521 + 125.906i) q^{79} +(51.1812 - 94.6652i) q^{80} -48.9418i q^{81} +(21.1385 + 54.9946i) q^{82} +5.61797i q^{83} +(68.6018 + 76.0539i) q^{84} +(111.819 - 23.8850i) q^{85} +(-68.1877 + 64.7654i) q^{86} +(10.4522 + 10.4522i) q^{87} +(8.67002 - 17.0721i) q^{88} -10.7697 q^{89} +(-33.5854 - 14.9353i) q^{90} +(35.8020 - 14.8297i) q^{91} +(-56.2382 + 118.176i) q^{92} -1.30217i q^{93} +(-103.436 - 108.902i) q^{94} +(143.135 + 59.2885i) q^{95} +(-20.9066 - 77.3362i) q^{96} +(-3.02256 - 7.29710i) q^{97} +(-2.86197 + 111.184i) q^{98} +(-6.04211 - 2.50273i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q - 4 q^{2} - 4 q^{3} - 4 q^{5} + 12 q^{6} - 8 q^{7} - 4 q^{8} + 12 q^{10} - 4 q^{11} - 24 q^{12} + 40 q^{14} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 4 q^{20} + 4 q^{22} - 8 q^{23} - 324 q^{24} - 132 q^{26}+ \cdots + 284 q^{99}+O(q^{100}) \) 280 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 + 12 * q^6 - 8 * q^7 - 4 * q^8 + 12 * q^10 - 4 * q^11 - 24 * q^12 + 40 * q^14 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 4 * q^20 + 4 * q^22 - 8 * q^23 - 324 * q^24 - 132 * q^26 - 40 * q^27 + 212 * q^28 - 4 * q^29 - 256 * q^31 - 124 * q^32 - 16 * q^33 - 148 * q^34 - 8 * q^35 - 164 * q^36 - 4 * q^37 + 32 * q^38 - 8 * q^39 - 40 * q^40 + 448 * q^42 - 40 * q^44 - 68 * q^45 - 228 * q^46 - 48 * q^48 - 8 * q^49 - 8 * q^50 - 164 * q^51 - 8 * q^52 - 48 * q^54 + 176 * q^56 + 72 * q^57 - 20 * q^58 - 552 * q^60 - 68 * q^61 + 176 * q^62 - 640 * q^63 + 24 * q^65 + 228 * q^66 - 8 * q^67 - 368 * q^68 - 8 * q^69 + 560 * q^70 + 504 * q^71 + 520 * q^72 - 156 * q^74 + 60 * q^75 + 664 * q^76 + 600 * q^78 + 304 * q^80 + 212 * q^82 - 8 * q^84 - 4 * q^85 + 1136 * q^86 - 8 * q^87 + 408 * q^88 - 200 * q^90 + 384 * q^91 + 60 * q^92 + 584 * q^94 + 200 * q^95 - 112 * q^96 - 8 * q^97 - 624 * q^98 + 284 * q^99

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