LMFDB - Embedded newform 72.3.j.a.29.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,3,Mod(5,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("72.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	72.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.96185790339$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.6
Character	$\chi$	$=$	72.29
Dual form			72.3.j.a.5.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.54182 - 1.27389i) q^{2} +(-1.07504 + 2.80077i) q^{3} +(0.754413 + 3.92821i) q^{4} +(-3.98823 - 6.90782i) q^{5} +(5.22538 - 2.94880i) q^{6} +(5.64852 - 9.78353i) q^{7} +(3.84094 - 7.01763i) q^{8} +(-6.68859 - 6.02186i) q^{9} +O(q^{10})$	\(q+(-1.54182 - 1.27389i) q^{2} +(-1.07504 + 2.80077i) q^{3} +(0.754413 + 3.92821i) q^{4} +(-3.98823 - 6.90782i) q^{5} +(5.22538 - 2.94880i) q^{6} +(5.64852 - 9.78353i) q^{7} +(3.84094 - 7.01763i) q^{8} +(-6.68859 - 6.02186i) q^{9} +(-2.65067 + 15.7312i) q^{10} +(1.06057 - 1.83697i) q^{11} +(-11.8130 - 2.11004i) q^{12} +(-6.03586 + 3.48480i) q^{13} +(-21.1721 + 7.88884i) q^{14} +(23.6347 - 3.74395i) q^{15} +(-14.8617 + 5.92699i) q^{16} -4.29594i q^{17} +(2.64142 + 17.8051i) q^{18} -11.2235i q^{19} +(24.1266 - 20.8780i) q^{20} +(21.3290 + 26.3378i) q^{21} +(-3.97530 + 1.48122i) q^{22} +(-3.40068 + 1.96338i) q^{23} +(15.5256 + 18.3018i) q^{24} +(-19.3120 + 33.4494i) q^{25} +(13.7455 + 2.31608i) q^{26} +(24.0563 - 12.2595i) q^{27} +(42.6931 + 14.8078i) q^{28} +(0.512348 - 0.887412i) q^{29} +(-41.2098 - 24.3355i) q^{30} +(4.18829 + 7.25434i) q^{31} +(30.4644 + 9.79383i) q^{32} +(4.00476 + 4.94522i) q^{33} +(-5.47255 + 6.62356i) q^{34} -90.1105 q^{35} +(18.6092 - 30.8172i) q^{36} -58.9714i q^{37} +(-14.2975 + 17.3046i) q^{38} +(-3.27135 - 20.6513i) q^{39} +(-63.7951 + 1.45543i) q^{40} +(-48.6696 + 28.0994i) q^{41} +(0.666016 - 67.7790i) q^{42} +(49.8518 + 28.7820i) q^{43} +(8.01611 + 2.78033i) q^{44} +(-14.9222 + 70.2202i) q^{45} +(7.74436 + 1.30491i) q^{46} +(44.8348 + 25.8854i) q^{47} +(-0.623225 - 47.9960i) q^{48} +(-39.3116 - 68.0897i) q^{49} +(72.3864 - 26.9715i) q^{50} +(12.0319 + 4.61829i) q^{51} +(-18.2426 - 21.0812i) q^{52} +42.6170 q^{53} +(-52.7077 - 11.7432i) q^{54} -16.9193 q^{55} +(-46.9616 - 77.2172i) q^{56} +(31.4344 + 12.0657i) q^{57} +(-1.92041 + 0.715555i) q^{58} +(25.6501 + 44.4272i) q^{59} +(32.5374 + 90.0177i) q^{60} +(-42.9355 - 24.7888i) q^{61} +(2.78363 - 16.5203i) q^{62} +(-96.6956 + 31.4234i) q^{63} +(-34.4944 - 53.9086i) q^{64} +(48.1448 + 27.7964i) q^{65} +(0.125052 - 12.7263i) q^{66} +(85.1906 - 49.1848i) q^{67} +(16.8754 - 3.24091i) q^{68} +(-1.84312 - 11.6352i) q^{69} +(138.934 + 114.791i) q^{70} -31.4710i q^{71} +(-67.9497 + 23.8085i) q^{72} +85.4715 q^{73} +(-75.1230 + 90.9232i) q^{74} +(-72.9228 - 90.0478i) q^{75} +(44.0883 - 8.46716i) q^{76} +(-11.9813 - 20.7523i) q^{77} +(-21.2637 + 36.0080i) q^{78} +(-6.61671 + 11.4605i) q^{79} +(100.215 + 79.0239i) q^{80} +(8.47451 + 80.5555i) q^{81} +(110.835 + 18.6755i) q^{82} +(-41.8804 + 72.5390i) q^{83} +(-87.3698 + 103.655i) q^{84} +(-29.6756 + 17.1332i) q^{85} +(-40.1975 - 107.882i) q^{86} +(1.93464 + 2.38897i) q^{87} +(-8.81756 - 14.4984i) q^{88} -105.027i q^{89} +(112.460 - 89.2575i) q^{90} +78.7360i q^{91} +(-10.2781 - 11.8774i) q^{92} +(-24.8203 + 3.93176i) q^{93} +(-36.1520 - 97.0251i) q^{94} +(-77.5300 + 44.7620i) q^{95} +(-60.1806 + 74.7950i) q^{96} +(-9.54179 + 16.5269i) q^{97} +(-26.1273 + 155.061i) q^{98} +(-18.1557 + 5.90010i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) $ 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9	$ 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9} + 4 q^{10} + 14 q^{12} - 48 q^{14} + 14 q^{15} - q^{16} - 38 q^{18} - 66 q^{20} + 7 q^{22} - 6 q^{23} - 47 q^{24} - 72 q^{25} + 28 q^{28} + 16 q^{30} - 2 q^{31} - 93 q^{32} + 30 q^{33} + 9 q^{34} - 105 q^{36} + 99 q^{38} - 118 q^{39} - 56 q^{40} + 66 q^{41} + 236 q^{42} + 72 q^{46} - 6 q^{47} + 117 q^{48} - 72 q^{49} + 189 q^{50} - 42 q^{52} + 139 q^{54} + 92 q^{55} + 270 q^{56} - 8 q^{57} - 38 q^{58} + 456 q^{60} - 226 q^{63} + 2 q^{64} - 6 q^{65} - 258 q^{66} + 387 q^{68} - 4 q^{70} + 259 q^{72} - 8 q^{73} - 432 q^{74} - 63 q^{76} - 620 q^{78} - 2 q^{79} - 44 q^{81} + 186 q^{82} - 232 q^{84} - 615 q^{86} + 174 q^{87} - 77 q^{88} - 554 q^{90} - 624 q^{92} - 186 q^{94} + 144 q^{95} - 794 q^{96} - 2 q^{97}+O(q^{100}) $ 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9 + 4 * q^10 + 14 * q^12 - 48 * q^14 + 14 * q^15 - q^16 - 38 * q^18 - 66 * q^20 + 7 * q^22 - 6 * q^23 - 47 * q^24 - 72 * q^25 + 28 * q^28 + 16 * q^30 - 2 * q^31 - 93 * q^32 + 30 * q^33 + 9 * q^34 - 105 * q^36 + 99 * q^38 - 118 * q^39 - 56 * q^40 + 66 * q^41 + 236 * q^42 + 72 * q^46 - 6 * q^47 + 117 * q^48 - 72 * q^49 + 189 * q^50 - 42 * q^52 + 139 * q^54 + 92 * q^55 + 270 * q^56 - 8 * q^57 - 38 * q^58 + 456 * q^60 - 226 * q^63 + 2 * q^64 - 6 * q^65 - 258 * q^66 + 387 * q^68 - 4 * q^70 + 259 * q^72 - 8 * q^73 - 432 * q^74 - 63 * q^76 - 620 * q^78 - 2 * q^79 - 44 * q^81 + 186 * q^82 - 232 * q^84 - 615 * q^86 + 174 * q^87 - 77 * q^88 - 554 * q^90 - 624 * q^92 - 186 * q^94 + 144 * q^95 - 794 * q^96 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.54182	−	1.27389i	−0.770910	−	0.636945i
$2$	−1.54182	−	1.27389i	−0.770910	−	0.636945i
$3$	−1.07504	+	2.80077i	−0.358346	+	0.933589i
$3$	−1.07504	+	2.80077i	−0.358346	+	0.933589i
$4$	0.754413	+	3.92821i	0.188603	+	0.982053i
$5$	−3.98823	−	6.90782i	−0.797647	−	1.38156i	−0.921145	−	0.389220i	$-0.872745\pi$
$5$	−3.98823	−	6.90782i	−0.797647	−	1.38156i	0.123498	−	0.992345i	$-0.460589\pi$
$6$	5.22538	−	2.94880i	0.870897	−	0.491466i
$7$	5.64852	−	9.78353i	0.806932	−	1.39765i	−0.108047	−	0.994146i	$-0.534460\pi$
$7$	5.64852	−	9.78353i	0.806932	−	1.39765i	0.914979	−	0.403501i	$-0.132207\pi$
$8$	3.84094	−	7.01763i	0.480117	−	0.877204i
$9$	−6.68859	−	6.02186i	−0.743177	−	0.669095i
$10$	−2.65067	+	15.7312i	−0.265067	+	1.57312i
$11$	1.06057	−	1.83697i	0.0964157	−	0.166997i	−0.813783	−	0.581169i	$-0.802596\pi$
$11$	1.06057	−	1.83697i	0.0964157	−	0.166997i	0.910199	+	0.414172i	$0.135929\pi$
$12$	−11.8130	−	2.11004i	−0.984419	−	0.175837i
$13$	−6.03586	+	3.48480i	−0.464297	+	0.268062i	−0.713849	−	0.700299i	$-0.753050\pi$
$13$	−6.03586	+	3.48480i	−0.464297	+	0.268062i	0.249552	+	0.968361i	$0.419716\pi$
$14$	−21.1721	+	7.88884i	−1.51229	+	0.563489i
$15$	23.6347	−	3.74395i	1.57565	−	0.249597i
$16$	−14.8617	+	5.92699i	−0.928858	+	0.370437i
$17$		−	4.29594i		−	0.252702i	−0.991986	−	0.126351i	$-0.959673\pi$
$17$		−	4.29594i		−	0.252702i	0.991986	−	0.126351i	$-0.0403266\pi$
$18$	2.64142	+	17.8051i	0.146746	+	0.989174i
$19$		−	11.2235i		−	0.590711i	−0.955387	−	0.295356i	$-0.904562\pi$
$19$		−	11.2235i		−	0.590711i	0.955387	−	0.295356i	$-0.0954381\pi$
$20$	24.1266	−	20.8780i	1.20633	−	1.04390i
$21$	21.3290	+	26.3378i	1.01567	+	1.25418i
$22$	−3.97530	+	1.48122i	−0.180696	+	0.0673281i
$23$	−3.40068	+	1.96338i	−0.147856	+	0.0853645i	−0.572103	−	0.820182i	$-0.693872\pi$
$23$	−3.40068	+	1.96338i	−0.147856	+	0.0853645i	0.424247	+	0.905546i	$0.360539\pi$
$24$	15.5256	+	18.3018i	0.646900	+	0.762575i
$25$	−19.3120	+	33.4494i	−0.772480	+	1.33798i
$26$	13.7455	+	2.31608i	0.528671	+	0.0890798i
$27$	24.0563	−	12.2595i	0.890974	−	0.454054i
$28$	42.6931	+	14.8078i	1.52475	+	0.528849i
$29$	0.512348	−	0.887412i	0.0176672	−	0.0306004i	−0.857057	−	0.515222i	$-0.827709\pi$
$29$	0.512348	−	0.887412i	0.0176672	−	0.0306004i	0.874724	+	0.484622i	$0.161043\pi$
$30$	−41.2098	−	24.3355i	−1.37366	−	0.811183i
$31$	4.18829	+	7.25434i	0.135106	+	0.234011i	0.925638	−	0.378410i	$-0.123529\pi$
$31$	4.18829	+	7.25434i	0.135106	+	0.234011i	−0.790532	+	0.612421i	$0.790196\pi$
$32$	30.4644	+	9.79383i	0.952013	+	0.306057i
$33$	4.00476	+	4.94522i	0.121356	+	0.149855i
$34$	−5.47255	+	6.62356i	−0.160957	+	0.194811i
$35$	−90.1105			−2.57459
$36$	18.6092	−	30.8172i	0.516921	−	0.856033i
$37$		−	58.9714i		−	1.59382i	−0.604097	−	0.796911i	$-0.706466\pi$
$37$		−	58.9714i		−	1.59382i	0.604097	−	0.796911i	$-0.293534\pi$
$38$	−14.2975	+	17.3046i	−0.376250	+	0.455385i
$39$	−3.27135	−	20.6513i	−0.0838809	−	0.529521i
$40$	−63.7951	+	1.45543i	−1.59488	+	0.0363858i
$41$	−48.6696	+	28.0994i	−1.18706	+	0.685351i	−0.957638	−	0.287975i	$-0.907018\pi$
$41$	−48.6696	+	28.0994i	−1.18706	+	0.685351i	−0.229425	+	0.973326i	$0.573685\pi$
$42$	0.666016	−	67.7790i	0.0158575	−	1.61379i
$43$	49.8518	+	28.7820i	1.15935	+	0.669348i	0.951147	−	0.308738i	$-0.0999068\pi$
$43$	49.8518	+	28.7820i	1.15935	+	0.669348i	0.208198	+	0.978087i	$0.433240\pi$
$44$	8.01611	+	2.78033i	0.182184	+	0.0631892i
$45$	−14.9222	+	70.2202i	−0.331606	+	1.56045i
$46$	7.74436	+	1.30491i	0.168356	+	0.0283675i
$47$	44.8348	+	25.8854i	0.953931	+	0.550752i	0.894300	−	0.447468i	$-0.147674\pi$
$47$	44.8348	+	25.8854i	0.953931	+	0.550752i	0.0596311	+	0.998220i	$0.481008\pi$
$48$	−0.623225	−	47.9960i	−0.0129839	−	0.999916i
$49$	−39.3116	−	68.0897i	−0.802278	−	1.38959i
$50$	72.3864	−	26.9715i	1.44773	−	0.539431i
$51$	12.0319	+	4.61829i	0.235920	+	0.0905547i
$52$	−18.2426	−	21.0812i	−0.350819	−	0.405407i
$53$	42.6170			0.804094			0.402047	−	0.915619i	$-0.368299\pi$
$53$	42.6170			0.804094			0.402047	+	0.915619i	$0.368299\pi$
$54$	−52.7077	−	11.7432i	−0.976068	−	0.217466i
$55$	−16.9193			−0.307623
$56$	−46.9616	−	77.2172i	−0.838600	−	1.37888i
$57$	31.4344	+	12.0657i	0.551481	+	0.211679i
$58$	−1.92041	+	0.715555i	−0.0331106	+	0.0123372i
$59$	25.6501	+	44.4272i	0.434747	+	0.753003i	0.997275	−	0.0737746i	$-0.0235046\pi$
$59$	25.6501	+	44.4272i	0.434747	+	0.753003i	−0.562528	+	0.826778i	$0.690171\pi$
$60$	32.5374	+	90.0177i	0.542289	+	1.50029i
$61$	−42.9355	−	24.7888i	−0.703861	−	0.406374i	0.104923	−	0.994480i	$-0.466540\pi$
$61$	−42.9355	−	24.7888i	−0.703861	−	0.406374i	−0.808784	+	0.588106i	$0.799874\pi$
$62$	2.78363	−	16.5203i	0.0448973	−	0.266456i
$63$	−96.6956	+	31.4234i	−1.53485	+	0.498785i
$64$	−34.4944	−	53.9086i	−0.538975	−	0.842322i
$65$	48.1448	+	27.7964i	0.740689	+	0.427637i
$66$	0.125052	−	12.7263i	0.00189473	−	0.192822i
$67$	85.1906	−	49.1848i	1.27150	−	0.734102i	0.296231	−	0.955116i	$-0.404270\pi$
$67$	85.1906	−	49.1848i	1.27150	−	0.734102i	0.975271	+	0.221014i	$0.0709367\pi$
$68$	16.8754	−	3.24091i	0.248167	−	0.0476605i
$69$	−1.84312	−	11.6352i	−0.0267119	−	0.168626i
$70$	138.934	+	114.791i	1.98477	+	1.63987i
$71$		−	31.4710i		−	0.443254i	−0.975132	−	0.221627i	$-0.928863\pi$
$71$		−	31.4710i		−	0.443254i	0.975132	−	0.221627i	$-0.0711367\pi$
$72$	−67.9497	+	23.8085i	−0.943745	+	0.330674i
$73$	85.4715			1.17084			0.585421	−	0.810729i	$-0.300929\pi$
$73$	85.4715			1.17084			0.585421	+	0.810729i	$0.300929\pi$
$74$	−75.1230	+	90.9232i	−1.01518	+	1.22869i
$75$	−72.9228	−	90.0478i	−0.972304	−	1.20064i
$76$	44.0883	−	8.46716i	0.580110	−	0.111410i
$77$	−11.9813	−	20.7523i	−0.155602	−	0.269510i
$78$	−21.2637	+	36.0080i	−0.272611	+	0.461640i
$79$	−6.61671	+	11.4605i	−0.0837558	+	0.145069i	−0.904860	−	0.425708i	$-0.860025\pi$
$79$	−6.61671	+	11.4605i	−0.0837558	+	0.145069i	0.821105	+	0.570778i	$0.193358\pi$
$80$	100.215	+	79.0239i	1.25268	+	0.987799i
$81$	8.47451	+	80.5555i	0.104624	+	0.994512i
$82$	110.835	+	18.6755i	1.35165	+	0.227750i
$83$	−41.8804	+	72.5390i	−0.504583	+	0.873964i	0.495403	+	0.868663i	$0.335021\pi$
$83$	−41.8804	+	72.5390i	−0.504583	+	0.873964i	−0.999986	+	0.00530047i	$0.998313\pi$
$84$	−87.3698	+	103.655i	−1.04012	+	1.23398i
$85$	−29.6756	+	17.1332i	−0.349124	+	0.201567i
$86$	−40.1975	−	107.882i	−0.467413	−	1.25445i
$87$	1.93464	+	2.38897i	0.0222373	+	0.0274594i
$88$	−8.81756	−	14.4984i	−0.100200	−	0.164754i
$89$		−	105.027i		−	1.18008i	−0.807374	−	0.590040i	$-0.799112\pi$
$89$		−	105.027i		−	1.18008i	0.807374	−	0.590040i	$-0.200888\pi$
$90$	112.460	−	89.2575i	1.24956	−	0.991750i
$91$			78.7360i			0.865230i
$92$	−10.2781	−	11.8774i	−0.111719	−	0.129102i
$93$	−24.8203	+	3.93176i	−0.266885	+	0.0422769i
$94$	−36.1520	−	97.0251i	−0.384596	−	1.03218i
$95$	−77.5300	+	44.7620i	−0.816105	+	0.471179i
$96$	−60.1806	+	74.7950i	−0.626881	+	0.779115i
$97$	−9.54179	+	16.5269i	−0.0983690	+	0.170380i	−0.911010	−	0.412385i	$-0.864696\pi$
$97$	−9.54179	+	16.5269i	−0.0983690	+	0.170380i	0.812641	+	0.582765i	$0.198029\pi$
$98$	−26.1273	+	155.061i	−0.266605	+	1.58225i
$99$	−18.1557	+	5.90010i	−0.183391	+	0.0595970i
$100$	−145.966	−	50.6270i	−1.45966	−	0.506270i
$101$	53.0235	−	91.8395i	0.524985	−	0.909302i	−0.474591	−	0.880206i	$-0.657404\pi$
$101$	53.0235	−	91.8395i	0.524985	−	0.909302i	0.999577	−	0.0290952i	$-0.00926259\pi$
$102$	−12.6679	−	22.4479i	−0.124195	−	0.220077i
$103$	−30.5290	−	52.8778i	−0.296398	−	0.513376i	0.678911	−	0.734220i	$-0.262452\pi$
$103$	−30.5290	−	52.8778i	−0.296398	−	0.513376i	−0.975309	+	0.220844i	$0.929119\pi$
$104$	1.27171	+	55.7424i	0.0122280	+	0.535984i
$105$	96.8721	−	252.379i	0.922592	−	2.40360i
$106$	−65.7077	−	54.2893i	−0.619884	−	0.512163i
$107$	7.01531			0.0655636			0.0327818	−	0.999463i	$-0.489563\pi$
$107$	7.01531			0.0655636			0.0327818	+	0.999463i	$0.489563\pi$
$108$	66.3062	+	85.2496i	0.613946	+	0.789348i
$109$			38.1403i			0.349911i	0.984576	+	0.174956i	$0.0559782\pi$
$109$			38.1403i			0.349911i	−0.984576	+	0.174956i	$0.944022\pi$
$110$	26.0864	+	21.5533i	0.237149	+	0.195939i
$111$	165.165	+	63.3964i	1.48797	+	0.571139i
$112$	−25.9599	+	178.879i	−0.231785	+	1.59713i
$113$	120.801	−	69.7442i	1.06903	−	0.617205i	0.141115	−	0.989993i	$-0.454931\pi$
$113$	120.801	−	69.7442i	1.06903	−	0.617205i	0.927917	+	0.372788i	$0.121598\pi$
$114$	−33.0959	−	58.6471i	−0.290315	−	0.514448i
$115$	27.1254	+	15.6609i	0.235873	+	0.136181i
$116$	3.87247	+	1.34314i	0.0333833	+	0.0115788i
$117$	61.3564	+	13.0386i	0.524413	+	0.111441i
$118$	17.0476	−	101.174i	0.144471	−	0.857407i
$119$	−42.0294	−	24.2657i	−0.353188	−	0.203913i
$120$	64.5058	−	180.240i	0.537548	−	1.50200i
$121$	58.2504	+	100.893i	0.481408	+	0.833823i
$122$	34.6206	+	92.9150i	0.283775	+	0.761598i
$123$	−26.3783	−	166.520i	−0.214457	−	1.35382i
$124$	−25.3369	+	21.9253i	−0.204330	+	0.176817i
$125$	108.672			0.869373
$126$	189.117	+	74.7303i	1.50093	+	0.593097i
$127$	−11.3165			−0.0891066			−0.0445533	−	0.999007i	$-0.514186\pi$
$127$	−11.3165			−0.0891066			−0.0445533	+	0.999007i	$0.514186\pi$
$128$	−15.4895	+	127.059i	−0.121012	+	0.992651i
$129$	−134.204	+	108.682i	−1.04034	+	0.842494i
$130$	−38.8210	−	104.188i	−0.298623	−	0.801448i
$131$	−33.8613	−	58.6494i	−0.258483	−	0.447705i	0.707353	−	0.706861i	$-0.249889\pi$
$131$	−33.8613	−	58.6494i	−0.258483	−	0.447705i	−0.965836	+	0.259155i	$0.916556\pi$
$132$	−16.4047	+	19.4623i	−0.124278	+	0.147442i
$133$	−109.806	−	63.3962i	−0.825605	−	0.476664i
$134$	−194.005	−	32.6893i	−1.44780	−	0.243950i
$135$	−180.628	−	117.283i	−1.33799	−	0.868763i
$136$	−30.1473	−	16.5004i	−0.221671	−	0.121327i
$137$	−12.4238	−	7.17291i	−0.0906850	−	0.0523570i	0.453972	−	0.891016i	$-0.350007\pi$
$137$	−12.4238	−	7.17291i	−0.0906850	−	0.0523570i	−0.544657	+	0.838659i	$0.683340\pi$
$138$	−11.9802	+	20.2873i	−0.0868131	+	0.147010i
$139$	−182.816	+	105.549i	−1.31522	+	0.759342i	−0.982955	−	0.183844i	$-0.941146\pi$
$139$	−182.816	+	105.549i	−1.31522	+	0.759342i	−0.332264	+	0.943186i	$0.607813\pi$
$140$	−67.9806	−	353.973i	−0.485575	−	2.52838i
$141$	−120.698	+	97.7440i	−0.856013	+	0.693220i
$142$	−40.0906	+	48.5226i	−0.282328	+	0.341709i
$143$			14.7836i			0.103382i
$144$	135.095	+	49.8519i	0.938163	+	0.346194i
$145$	−8.17345			−0.0563686
$146$	−131.782	−	108.881i	−0.902614	−	0.745762i
$147$	232.965	−	36.9037i	1.58479	−	0.251046i
$148$	231.652	−	44.4888i	1.56522	−	0.300600i
$149$	91.6036	+	158.662i	0.614789	+	1.06485i	0.990421	+	0.138077i	$0.0440922\pi$
$149$	91.6036	+	158.662i	0.614789	+	1.06485i	−0.375632	+	0.926769i	$0.622574\pi$
$150$	−2.27708	+	231.733i	−0.0151805	+	1.54489i
$151$	78.9656	−	136.772i	0.522951	−	0.905778i	−0.476692	−	0.879070i	$-0.658164\pi$
$151$	78.9656	−	136.772i	0.522951	−	0.905778i	0.999643	−	0.0267076i	$-0.00850231\pi$
$152$	−78.7625	−	43.1088i	−0.518174	−	0.283611i
$153$	−25.8695	+	28.7338i	−0.169082	+	0.187802i
$154$	−7.96306	+	47.2592i	−0.0517082	+	0.306878i
$155$	33.4078	−	57.8640i	0.215534	−	0.373316i
$156$	78.6549	−	28.4302i	0.504198	−	0.182245i
$157$	−137.812	+	79.5658i	−0.877784	+	0.506789i	−0.869927	−	0.493180i	$-0.835834\pi$
$157$	−137.812	+	79.5658i	−0.877784	+	0.506789i	−0.00785670	+	0.999969i	$0.502501\pi$
$158$	24.8011	−	9.24103i	0.156969	−	0.0584875i
$159$	−45.8148	+	119.360i	−0.288143	+	0.750693i
$160$	−53.8451	−	249.503i	−0.336532	−	1.55939i
$161$			44.3608i			0.275533i
$162$	89.5526	−	134.998i	0.552794	−	0.833318i
$163$			127.443i			0.781861i	0.920420	+	0.390930i	$0.127847\pi$
$163$			127.443i			0.781861i	−0.920420	+	0.390930i	$0.872153\pi$
$164$	−147.097	−	169.986i	−0.896935	−	1.03650i
$165$	18.1888	−	47.3869i	0.110235	−	0.287193i
$166$	156.979	−	58.4910i	0.945655	−	0.352356i
$167$	−14.9753	+	8.64602i	−0.0896727	+	0.0517726i	−0.544166	−	0.838978i	$-0.683154\pi$
$167$	−14.9753	+	8.64602i	−0.0896727	+	0.0517726i	0.454493	+	0.890750i	$0.349820\pi$
$168$	266.753	−	48.5171i	1.58781	−	0.288792i
$169$	−60.2123	+	104.291i	−0.356286	+	0.617105i
$170$	67.5802	+	11.3871i	0.397530	+	0.0669829i
$171$	−67.5864	+	75.0695i	−0.395242	+	0.439003i
$172$	−75.4529	+	217.542i	−0.438679	+	1.26478i
$173$	122.607	−	212.361i	0.708709	−	1.22752i	−0.256627	−	0.966510i	$-0.582611\pi$
$173$	122.607	−	212.361i	0.708709	−	1.22752i	0.965336	−	0.261009i	$-0.0840554\pi$
$174$	0.0604108	−	6.14788i	0.000347189	−	0.0353326i
$175$	218.169	+	377.879i	1.24668	+	2.15931i
$176$	−4.87426	+	33.5865i	−0.0276946	+	0.190832i
$177$	−152.005	+	24.0790i	−0.858785	+	0.136039i
$178$	−133.793	+	161.933i	−0.751646	+	0.909735i
$179$	245.877			1.37361			0.686807	−	0.726840i	$-0.259012\pi$
$179$	245.877			1.37361			0.686807	+	0.726840i	$0.259012\pi$
$180$	−287.097	−	5.64275i	−1.59499	−	0.0313486i
$181$			53.7077i			0.296728i	0.988933	+	0.148364i	$0.0474007\pi$
$181$			53.7077i			0.296728i	−0.988933	+	0.148364i	$0.952599\pi$
$182$	100.301	−	121.397i	0.551104	−	0.667014i
$183$	115.585	−	93.6034i	0.631612	−	0.511494i
$184$	0.716500	+	31.4059i	0.00389402	+	0.170685i
$185$	−407.364	+	235.192i	−2.20197	+	1.27131i
$186$	43.2770	+	25.5562i	0.232672	+	0.137399i
$187$	−7.89149	−	4.55615i	−0.0422005	−	0.0243645i
$188$	−67.8593	+	195.649i	−0.360954	+	1.04068i
$189$	15.9417	−	304.603i	0.0843475	−	1.61166i
$190$	176.559	+	29.7498i	0.929258	+	0.156578i
$191$	208.549	+	120.406i	1.09188	+	0.630396i	0.934076	−	0.357075i	$-0.116226\pi$
$191$	208.549	+	120.406i	1.09188	+	0.630396i	0.157802	+	0.987471i	$0.449559\pi$
$192$	188.068	−	38.6569i	0.979522	−	0.201338i
$193$	−124.900	−	216.333i	−0.647151	−	1.12090i	−0.983800	−	0.179268i	$-0.942627\pi$
$193$	−124.900	−	216.333i	−0.647151	−	1.12090i	0.336650	−	0.941630i	$-0.390706\pi$
$194$	35.7651	−	13.3263i	0.184356	−	0.0686920i
$195$	−129.609	+	104.960i	−0.664660	+	0.538258i
$196$	237.814	−	205.792i	1.21334	−	1.04996i
$197$	−327.726			−1.66359			−0.831793	−	0.555086i	$-0.812685\pi$
$197$	−327.726			−1.66359			−0.831793	+	0.555086i	$0.812685\pi$
$198$	35.5089	+	14.0314i	0.179338	+	0.0708659i
$199$	−229.254			−1.15203			−0.576016	−	0.817439i	$-0.695393\pi$
$199$	−229.254			−1.15203			−0.576016	+	0.817439i	$0.695393\pi$
$200$	160.559	+	264.002i	0.802796	+	1.32001i
$201$	46.1722	+	291.475i	0.229712	+	1.45012i
$202$	−198.746	+	74.0537i	−0.983891	+	0.366603i
$203$	−5.78801	−	10.0251i	−0.0285124	−	0.0493849i
$204$	−9.06459	+	50.7480i	−0.0444343	+	0.248765i
$205$	388.211	+	224.134i	1.89371	+	1.09334i
$206$	−20.2902	+	120.418i	−0.0984962	+	0.584556i
$207$	34.5690	+	7.34613i	0.167000	+	0.0354886i
$208$	69.0488	−	87.5647i	0.331966	−	0.420984i
$209$	−20.6172	−	11.9034i	−0.0986469	−	0.0569538i
$210$	−470.862	+	265.718i	−2.24220	+	1.26532i
$211$	135.544	−	78.2563i	0.642388	−	0.370883i	−0.143146	−	0.989702i	$-0.545722\pi$
$211$	135.544	−	78.2563i	0.642388	−	0.370883i	0.785534	+	0.618819i	$0.212388\pi$
$212$	32.1508	+	167.409i	0.151655	+	0.789663i
$213$	88.1430	+	33.8325i	0.413817	+	0.158838i
$214$	−10.8163	−	8.93672i	−0.0505436	−	0.0417604i
$215$		−	459.157i		−	2.13561i
$216$	6.36631	−	215.906i	0.0294737	−	0.999566i
$217$	94.6307			0.436086
$218$	48.5866	−	58.8055i	0.222874	−	0.269750i
$219$	−91.8850	+	239.386i	−0.419566	+	1.09309i
$220$	−12.7641	−	66.4624i	−0.0580187	−	0.302102i
$221$	14.9705	+	25.9297i	0.0677398	+	0.117329i
$222$	−173.895	−	308.148i	−0.783310	−	1.38805i
$223$	120.451	−	208.628i	0.540140	−	0.935550i	−0.458755	−	0.888563i	$-0.651705\pi$
$223$	120.451	−	208.628i	0.540140	−	0.935550i	0.998895	−	0.0469875i	$-0.0149621\pi$
$224$	267.897	−	242.729i	1.19597	−	1.08361i
$225$	330.598	−	107.435i	1.46932	−	0.477489i
$226$	−275.099	−	46.3535i	−1.21725	−	0.205104i
$227$	44.5553	−	77.1721i	0.196279	−	0.339965i	−0.751040	−	0.660257i	$-0.770448\pi$
$227$	44.5553	−	77.1721i	0.196279	−	0.339965i	0.947319	+	0.320291i	$0.103781\pi$
$228$	−23.6820	+	132.584i	−0.103869	+	0.581507i
$229$	144.631	−	83.5027i	0.631576	−	0.364641i	−0.149786	−	0.988718i	$-0.547858\pi$
$229$	144.631	−	83.5027i	0.631576	−	0.364641i	0.781362	+	0.624078i	$0.214525\pi$
$230$	−21.8723	−	58.7010i	−0.0950968	−	0.255222i
$231$	71.0027	−	11.2475i	0.307371	−	0.0486903i
$232$	−4.25964	−	7.00397i	−0.0183605	−	0.0301895i
$233$		−	136.581i		−	0.586185i	−0.956084	−	0.293092i	$-0.905316\pi$
$233$		−	136.581i		−	0.586185i	0.956084	−	0.293092i	$-0.0946844\pi$
$234$	−77.9907	−	98.2644i	−0.333293	−	0.419933i
$235$		−	412.947i		−	1.75722i
$236$	−155.169	+	134.275i	−0.657495	+	0.568963i
$237$	−24.9849	−	30.8523i	−0.105422	−	0.130178i
$238$	33.8900	+	90.9541i	0.142395	+	0.382160i
$239$	133.564	−	77.1130i	0.558844	−	0.322648i	−0.193838	−	0.981034i	$-0.562094\pi$
$239$	133.564	−	77.1130i	0.558844	−	0.322648i	0.752681	+	0.658385i	$0.228760\pi$
$240$	−329.062	+	195.724i	−1.37109	+	0.815517i
$241$	−31.9120	+	55.2732i	−0.132415	+	0.229350i	−0.924607	−	0.380922i	$-0.875606\pi$
$241$	−31.9120	+	55.2732i	−0.132415	+	0.229350i	0.792192	+	0.610272i	$0.208940\pi$
$242$	38.7144	−	229.763i	0.159977	−	0.949432i
$243$	−234.727	−	62.8650i	−0.965957	−	0.258704i
$244$	64.9847	−	187.361i	0.266331	−	0.767872i
$245$	−313.568	+	543.115i	−1.27987	+	2.21680i
$246$	−171.458	+	290.347i	−0.696982	+	1.18027i
$247$	39.1117	+	67.7435i	0.158347	+	0.274265i
$248$	66.9953	−	1.52844i	0.270142	−	0.00616307i
$249$	−158.142	−	195.279i	−0.635108	−	0.784255i
$250$	−167.552	−	138.436i	−0.670208	−	0.553742i
$251$	−99.6131			−0.396865			−0.198432	−	0.980115i	$-0.563585\pi$
$251$	−99.6131			−0.396865			−0.198432	+	0.980115i	$0.563585\pi$
$252$	−196.386	−	356.135i	−0.779311	−	1.41323i
$253$			8.32924i			0.0329219i
$254$	17.4481	+	14.4160i	0.0686931	+	0.0567559i
$255$	−16.0838	−	101.533i	−0.0630736	−	0.398169i
$256$	185.742	−	176.171i	0.725553	−	0.688166i
$257$	258.303	−	149.131i	1.00507	−	0.580277i	0.0953248	−	0.995446i	$-0.469611\pi$
$257$	258.303	−	149.131i	1.00507	−	0.580277i	0.909744	+	0.415169i	$0.136278\pi$
$258$	345.367	+	3.39368i	1.33863	+	0.0131538i
$259$	−576.948	−	333.101i	−2.22760	−	1.28611i
$260$	−72.8692	+	210.093i	−0.280266	+	0.808050i
$261$	−8.77075	+	2.85025i	−0.0336044	+	0.0109205i
$262$	−22.5049	+	133.562i	−0.0858966	+	0.509780i
$263$	26.4361	+	15.2629i	0.100518	+	0.0580338i	0.549416	−	0.835549i	$-0.314850\pi$
$263$	26.4361	+	15.2629i	0.100518	+	0.0580338i	−0.448899	+	0.893583i	$0.648184\pi$
$264$	50.0858	−	9.10963i	0.189719	−	0.0345062i
$265$	−169.966	−	294.390i	−0.641383	−	1.11091i
$266$	88.5405	+	237.626i	0.332859	+	0.893329i
$267$	294.157	+	112.908i	1.10171	+	0.422877i
$268$	257.477	+	297.541i	0.960737	+	1.11023i
$269$	−218.092			−0.810749			−0.405375	−	0.914151i	$-0.632859\pi$
$269$	−218.092			−0.810749			−0.405375	+	0.914151i	$0.632859\pi$
$270$	129.091	+	410.930i	0.478114	+	1.52196i
$271$	−343.470			−1.26742			−0.633709	−	0.773572i	$-0.718468\pi$
$271$	−343.470			−1.26742			−0.633709	+	0.773572i	$0.718468\pi$
$272$	25.4620	+	63.8450i	0.0936102	+	0.234724i
$273$	−220.521	−	84.6441i	−0.807770	−	0.310052i
$274$	10.0178	+	26.8859i	0.0365614	+	0.0981238i
$275$	40.9636	+	70.9510i	0.148959	+	0.258004i
$276$	44.3151	−	16.0179i	0.160562	−	0.0580360i
$277$	−110.463	−	63.7759i	−0.398784	−	0.230238i	0.287175	−	0.957878i	$-0.407284\pi$
$277$	−110.463	−	63.7759i	−0.398784	−	0.230238i	−0.685959	+	0.727640i	$0.740617\pi$
$278$	416.326	+	70.1499i	1.49757	+	0.252338i
$279$	15.6708	−	73.7426i	0.0561677	−	0.264310i
$280$	−346.109	+	632.362i	−1.23610	+	2.25844i
$281$	336.249	+	194.134i	1.19662	+	0.690867i	0.959799	−	0.280687i	$-0.0905623\pi$
$281$	336.249	+	194.134i	1.19662	+	0.690867i	0.236818	+	0.971554i	$0.423896\pi$
$282$	310.609	+	3.05214i	1.10145	+	0.0108232i
$283$	215.980	−	124.696i	0.763180	−	0.440622i	−0.0672566	−	0.997736i	$-0.521425\pi$
$283$	215.980	−	124.696i	0.763180	−	0.440622i	0.830436	+	0.557114i	$0.188091\pi$
$284$	123.625	−	23.7421i	0.435299	−	0.0835991i
$285$	−42.0202	−	265.264i	−0.147439	−	0.930752i
$286$	18.8326	−	22.7936i	0.0658483	−	0.0796978i
$287$			634.880i			2.21213i
$288$	−144.787	−	248.959i	−0.502733	−	0.864442i
$289$	270.545			0.936142
$290$	12.6020	+	10.4121i	0.0434551	+	0.0359037i
$291$	−36.0301	−	44.4913i	−0.123815	−	0.152891i
$292$	64.4808	+	335.750i	0.220825	+	1.14983i
$293$	−56.0435	−	97.0701i	−0.191275	−	0.331297i	0.754398	−	0.656417i	$-0.227929\pi$
$293$	−56.0435	−	97.0701i	−0.191275	−	0.331297i	−0.945673	+	0.325120i	$0.894595\pi$
$294$	−406.201	−	239.872i	−1.38164	−	0.815893i
$295$	204.597	−	354.372i	0.693549	−	1.20126i
$296$	−413.840	−	226.506i	−1.39811	−	0.765222i
$297$	2.99323	−	57.1927i	0.0100782	−	0.192568i
$298$	60.8817	−	361.321i	0.204301	−	1.21249i
$299$	13.6840	−	23.7014i	0.0457659	−	0.0792689i
$300$	298.713	−	354.390i	0.995710	−	1.18130i
$301$	563.179	−	325.151i	1.87102	−	1.08024i
$302$	−295.984	+	110.285i	−0.980078	+	0.365182i
$303$	200.219	+	247.237i	0.660788	+	0.815965i
$304$	66.5217	+	166.801i	0.218821	+	0.548686i
$305$			395.454i			1.29657i
$306$	76.4897	−	11.3474i	0.249966	−	0.0370830i
$307$			425.029i			1.38446i	0.721678	+	0.692229i	$0.243371\pi$
$307$			425.029i			1.38446i	−0.721678	+	0.692229i	$0.756629\pi$
$308$	72.4805	−	62.7211i	0.235326	−	0.203640i
$309$	180.918	−	28.6590i	0.585495	−	0.0927477i
$310$	−125.221	+	46.6580i	−0.403939	+	0.150510i
$311$	−257.225	+	148.509i	−0.827089	+	0.477520i	−0.852855	−	0.522148i	$-0.825131\pi$
$311$	−257.225	+	148.509i	−0.827089	+	0.477520i	0.0257662	+	0.999668i	$0.491797\pi$
$312$	−157.488	−	56.3633i	−0.504771	−	0.180652i
$313$	−101.171	+	175.234i	−0.323231	+	0.559852i	−0.981153	−	0.193234i	$-0.938102\pi$
$313$	−101.171	+	175.234i	−0.323231	+	0.559852i	0.657922	+	0.753086i	$0.271436\pi$
$314$	313.839	+	52.8811i	0.999488	+	0.168411i
$315$	602.712	+	542.632i	1.91337	+	1.72264i
$316$	−50.0109	−	17.3459i	−0.158262	−	0.0548921i
$317$	−21.4220	+	37.1039i	−0.0675772	+	0.117047i	−0.897834	−	0.440333i	$-0.854860\pi$
$317$	−21.4220	+	37.1039i	−0.0675772	+	0.117047i	0.830257	+	0.557381i	$0.188194\pi$
$318$	222.690	−	125.669i	0.700282	−	0.395185i
$319$	−1.08676	−	1.88233i	−0.00340678	−	0.00590072i
$320$	−234.820	+	453.281i	−0.733811	+	1.41650i
$321$	−7.54171	+	19.6482i	−0.0234944	+	0.0612095i
$322$	56.5108	−	68.3964i	0.175499	−	0.212411i
$323$	−48.2155			−0.149274
$324$	−310.046	+	94.0618i	−0.956931	+	0.290314i
$325$		−	269.194i		−	0.828290i
$326$	162.349	−	196.495i	0.498002	−	0.602744i
$327$	−106.822	−	41.0023i	−0.326673	−	0.125389i
$328$	10.2544	+	449.473i	0.0312633	+	1.37035i
$329$	506.500	−	292.428i	1.53951	−	0.888839i
$330$	−88.4095	+	49.8915i	−0.267908	+	0.151186i
$331$	184.989	+	106.804i	0.558880	+	0.322669i	0.752696	−	0.658369i	$-0.228753\pi$
$331$	184.989	+	106.804i	0.558880	+	0.322669i	−0.193816	+	0.981038i	$0.562087\pi$
$332$	−316.544	−	109.791i	−0.953445	−	0.330695i
$333$	−355.117	+	394.436i	−1.06642	+	1.18449i
$334$	34.1033	+	5.74633i	0.102106	+	0.0172046i
$335$	−679.520	−	392.321i	−2.02842	−	1.17111i
$336$	−473.090	−	265.009i	−1.40801	−	0.788717i
$337$	111.390	+	192.934i	0.330535	+	0.572504i	0.982617	−	0.185645i	$-0.0594374\pi$
$337$	111.390	+	192.934i	0.330535	+	0.572504i	−0.652082	+	0.758149i	$0.726104\pi$
$338$	225.691	−	84.0937i	0.667726	−	0.248798i
$339$	65.4723	+	413.312i	0.193134	+	1.21921i
$340$	−89.6905	−	103.646i	−0.263796	−	0.304843i
$341$	17.7680			0.0521055
$342$	199.836	−	29.6460i	0.584316	−	0.0866843i
$343$	−334.655			−0.975670
$344$	393.459	−	239.292i	1.14378	−	0.695617i
$345$	−73.0232	+	59.1359i	−0.211661	+	0.171408i
$346$	−459.562	+	171.235i	−1.32821	+	0.494899i
$347$	−72.3481	−	125.311i	−0.208496	−	0.361126i	0.742745	−	0.669574i	$-0.233523\pi$
$347$	−72.3481	−	125.311i	−0.208496	−	0.361126i	−0.951241	+	0.308449i	$0.900190\pi$
$348$	−7.92485	+	9.40196i	−0.0227726	+	0.0270171i
$349$	191.412	+	110.512i	0.548458	+	0.316652i	0.748500	−	0.663135i	$-0.230774\pi$
$349$	191.412	+	110.512i	0.548458	+	0.316652i	−0.200042	+	0.979787i	$0.564108\pi$
$350$	145.000	−	860.544i	0.414284	−	2.45870i
$351$	−102.479	+	157.828i	−0.291962	+	0.449652i
$352$	50.3007	−	45.5750i	0.142900	−	0.129475i
$353$	−600.193	−	346.521i	−1.70026	−	0.981647i	−0.945485	−	0.325666i	$-0.894411\pi$
$353$	−600.193	−	346.521i	−1.70026	−	0.981647i	−0.754778	−	0.655981i	$-0.772255\pi$
$354$	265.038	+	156.512i	0.748695	+	0.442125i
$355$	−217.396	+	125.514i	−0.612384	+	0.353560i
$356$	412.569	−	79.2339i	1.15890	−	0.222567i
$357$	113.146	−	91.6281i	0.316935	−	0.256661i
$358$	−379.098	−	313.220i	−1.05893	−	0.874916i
$359$			287.752i			0.801537i	0.916179	+	0.400769i	$0.131257\pi$
$359$			287.752i			0.801537i	−0.916179	+	0.400769i	$0.868743\pi$
$360$	435.464	+	374.430i	1.20962	+	1.04008i
$361$	235.033			0.651060
$362$	68.4177	−	82.8076i	0.188999	−	0.228750i
$363$	−345.198	+	54.6824i	−0.950959	+	0.150640i
$364$	−309.292	+	59.3995i	−0.849702	+	0.163185i
$365$	−340.880	−	590.422i	−0.933919	−	1.61759i
$366$	−297.452	−	2.92285i	−0.812709	−	0.00798592i
$367$	−328.424	+	568.847i	−0.894888	+	1.54999i	−0.0609450	+	0.998141i	$0.519411\pi$
$367$	−328.424	+	568.847i	−0.894888	+	1.54999i	−0.833943	+	0.551851i	$0.813922\pi$
$368$	38.9030	−	49.3350i	0.105715	−	0.134063i
$369$	494.741	+	105.136i	1.34076	+	0.284921i
$370$	927.690	+	156.313i	2.50727	+	0.422469i
$371$	240.723	−	416.944i	0.648849	−	1.12384i
$372$	−34.1695	−	94.5332i	−0.0918536	−	0.254122i
$373$	−320.900	+	185.272i	−0.860322	+	0.496707i	−0.864120	−	0.503286i	$-0.832124\pi$
$373$	−320.900	+	185.272i	−0.860322	+	0.496707i	0.00379823	+	0.999993i	$0.498791\pi$
$374$	6.36322	+	17.0777i	0.0170140	+	0.0456622i
$375$	−116.826	+	304.364i	−0.311536	+	0.811637i
$376$	353.862	−	215.210i	0.941121	−	0.572367i
$377$			7.14173i			0.0189436i
$378$	−412.610	+	449.335i	−1.09156	+	1.18872i
$379$		−	603.632i		−	1.59270i	−0.604839	−	0.796348i	$-0.706762\pi$
$379$		−	603.632i		−	1.59270i	0.604839	−	0.796348i	$-0.293238\pi$
$380$	−234.324	−	270.785i	−0.616643	−	0.712593i
$381$	12.1657	−	31.6950i	0.0319310	−	0.0831889i
$382$	−168.161	−	451.311i	−0.440212	−	1.18144i
$383$	285.312	−	164.725i	0.744939	−	0.430091i	−0.0789230	−	0.996881i	$-0.525148\pi$
$383$	285.312	−	164.725i	0.744939	−	0.430091i	0.823862	+	0.566790i	$0.191815\pi$
$384$	−339.212	−	179.976i	−0.883364	−	0.468687i
$385$	−95.5688	+	165.530i	−0.248231	+	0.429948i
$386$	−83.0113	+	492.656i	−0.215055	+	1.27631i
$387$	−160.118	−	492.711i	−0.413741	−	1.27316i
$388$	−72.1195	−	25.0141i	−0.185875	−	0.0644693i
$389$	−298.296	+	516.663i	−0.766827	+	1.32818i	0.172449	+	0.985019i	$0.444832\pi$
$389$	−298.296	+	516.663i	−0.766827	+	1.32818i	−0.939275	+	0.343164i	$0.888501\pi$
$390$	333.541	+	3.27747i	0.855233	+	0.00840377i
$391$	8.43457	+	14.6091i	0.0215718	+	0.0373634i
$392$	−628.822	+	14.3460i	−1.60414	+	0.0365971i
$393$	200.665	−	31.7872i	0.510599	−	0.0808835i
$394$	505.295	+	417.487i	1.28247	+	1.05961i
$395$	105.556			0.267230
$396$	−36.8737	−	66.8683i	−0.0931155	−	0.168859i
$397$			777.319i			1.95798i	0.203902	+	0.978991i	$0.434637\pi$
$397$			777.319i			1.95798i	−0.203902	+	0.978991i	$0.565363\pi$
$398$	353.469	+	292.044i	0.888112	+	0.733780i
$399$	295.603	−	239.386i	0.740860	−	0.599966i
$400$	88.7555	−	611.578i	0.221889	−	1.52894i
$401$	−433.690	+	250.391i	−1.08152	+	0.624417i	−0.931307	−	0.364236i	$-0.881330\pi$
$401$	−433.690	+	250.391i	−1.08152	+	0.624417i	−0.150215	+	0.988653i	$0.547997\pi$
$402$	300.117	−	508.219i	0.746560	−	1.26423i
$403$	−50.5599	−	29.1908i	−0.125459	−	0.0724337i
$404$	400.767	+	139.003i	0.991997	+	0.344066i
$405$	522.665	−	379.814i	1.29053	−	0.937813i
$406$	−3.84684	+	22.8302i	−0.00947497	+	0.0562321i
$407$	−108.328	−	62.5435i	−0.266163	−	0.153669i
$408$	78.6233	−	66.6970i	0.192704	−	0.163473i
$409$	−210.054	−	363.824i	−0.513579	−	0.889546i	−0.999876	−	0.0157518i	$-0.994986\pi$
$409$	−210.054	−	363.824i	−0.513579	−	0.889546i	0.486297	−	0.873794i	$-0.338347\pi$
$410$	−313.030	−	840.112i	−0.763488	−	2.04905i
$411$	33.4457	−	27.0852i	0.0813765	−	0.0659006i
$412$	184.684	−	159.816i	0.448261	−	0.387903i
$413$	579.540			1.40324
$414$	−43.9409	−	55.3634i	−0.106138	−	0.133728i
$415$	668.115			1.60992
$416$	−218.008	+	47.0483i	−0.524059	+	0.113097i
$417$	−99.0836	−	625.492i	−0.237611	−	1.49998i
$418$	16.6245	+	44.6169i	0.0397714	+	0.106739i
$419$	103.906	+	179.970i	0.247985	+	0.429523i	0.962967	−	0.269620i	$-0.0868982\pi$
$419$	103.906	+	179.970i	0.247985	+	0.429523i	−0.714981	+	0.699143i	$0.753565\pi$
$420$	1064.48	+	190.137i	2.53447	+	0.452706i
$421$	82.2587	+	47.4921i	0.195389	+	0.112808i	0.594503	−	0.804094i	$-0.297349\pi$
$421$	82.2587	+	47.4921i	0.195389	+	0.112808i	−0.399114	+	0.916901i	$0.630682\pi$
$422$	−308.674	−	52.0108i	−0.731455	−	0.123248i
$423$	−144.003	−	443.125i	−0.340434	−	1.04758i
$424$	163.689	−	299.070i	0.386059	−	0.705354i
$425$	143.696	+	82.9632i	0.338109	+	0.195207i
$426$	−92.8017	−	164.448i	−0.217844	−	0.386028i
$427$	−485.044	+	280.040i	−1.13594	+	0.655832i
$428$	5.29244	+	27.5576i	0.0123655	+	0.0643870i
$429$	−41.4053	−	15.8929i	−0.0965158	−	0.0370463i
$430$	−584.915	+	707.937i	−1.36027	+	1.64637i
$431$		−	239.645i		−	0.556021i	−0.960578	−	0.278010i	$-0.910325\pi$
$431$		−	239.645i		−	0.556021i	0.960578	−	0.278010i	$-0.0896750\pi$
$432$	−284.856	+	324.778i	−0.659389	+	0.751802i
$433$	41.9180			0.0968083			0.0484042	−	0.998828i	$-0.484586\pi$
$433$	41.9180			0.0968083			0.0484042	+	0.998828i	$0.484586\pi$
$434$	−145.903	−	120.549i	−0.336183	−	0.277763i
$435$	8.78676	−	22.8919i	0.0201994	−	0.0526251i
$436$	−149.823	+	28.7736i	−0.343632	+	0.0659944i
$437$	22.0360	+	38.1676i	0.0504257	+	0.0873399i
$438$	446.621	−	252.038i	1.01968	−	0.575430i
$439$	−265.485	+	459.834i	−0.604749	+	1.04746i	0.387342	+	0.921936i	$0.373393\pi$
$439$	−265.485	+	459.834i	−0.604749	+	1.04746i	−0.992091	+	0.125521i	$0.959940\pi$
$440$	−64.9858	+	118.733i	−0.147695	+	0.269848i
$441$	−147.087	+	692.153i	−0.333531	+	1.56951i
$442$	9.94971	−	59.0496i	0.0225107	−	0.133596i
$443$	−146.570	+	253.866i	−0.330857	+	0.573061i	−0.982680	−	0.185310i	$-0.940671\pi$
$443$	−146.570	+	253.866i	−0.330857	+	0.573061i	0.651823	+	0.758371i	$0.274004\pi$
$444$	−124.432	+	696.631i	−0.280252	+	1.56899i
$445$	−725.509	+	418.873i	−1.63036	+	0.941287i
$446$	−451.483	+	168.225i	−1.01229	+	0.377185i
$447$	−542.853	+	85.9927i	−1.21444	+	0.192377i
$448$	−722.259	+	32.9726i	−1.61218	+	0.0735996i
$449$			268.273i			0.597491i	0.954333	+	0.298746i	$0.0965682\pi$
$449$			268.273i			0.597491i	−0.954333	+	0.298746i	$0.903432\pi$
$450$	−646.582	−	255.499i	−1.43685	−	0.567776i
$451$			119.206i			0.264315i
$452$	365.104	+	421.914i	0.807751	+	0.933439i
$453$	298.177	+	368.200i	0.658227	+	0.812803i
$454$	−167.005	+	62.2269i	−0.367852	+	0.137064i
$455$	543.894	−	314.017i	1.19537	−	0.690148i
$456$	205.410	−	174.252i	0.450461	−	0.382131i
$457$	372.941	−	645.954i	0.816064	−	1.41347i	−0.0924966	−	0.995713i	$-0.529485\pi$
$457$	372.941	−	645.954i	0.816064	−	1.41347i	0.908561	−	0.417752i	$-0.137182\pi$
$458$	−329.368	−	55.4977i	−0.719144	−	0.121174i
$459$	−52.6659	−	103.344i	−0.114741	−	0.225151i
$460$	−41.0554	+	118.369i	−0.0892509	+	0.257324i
$461$	331.542	−	574.248i	0.719180	−	1.24566i	−0.242145	−	0.970240i	$-0.577851\pi$
$461$	331.542	−	574.248i	0.719180	−	1.24566i	0.961325	−	0.275416i	$-0.0888157\pi$
$462$	−123.801	−	73.1080i	−0.267968	−	0.158242i
$463$	−142.342	−	246.544i	−0.307435	−	0.532493i	0.670366	−	0.742031i	$-0.266137\pi$
$463$	−142.342	−	246.544i	−0.307435	−	0.532493i	−0.977800	+	0.209538i	$0.932804\pi$
$464$	−2.35468	+	16.2252i	−0.00507475	+	0.0349680i
$465$	126.149	+	155.773i	0.271288	+	0.334997i
$466$	−173.989	+	210.583i	−0.373367	+	0.451895i
$467$	174.804			0.374313			0.187157	−	0.982330i	$-0.440073\pi$
$467$	174.804			0.374313			0.187157	+	0.982330i	$0.440073\pi$
$468$	−4.93047	+	250.857i	−0.0105352	+	0.536020i
$469$		−	1111.29i		−	2.36948i
$470$	−526.049	+	636.690i	−1.11925	+	1.35466i
$471$	−74.6923	−	471.516i	−0.158582	−	1.00109i
$472$	410.294	−	9.36052i	0.869267	−	0.0198316i
$473$	105.743	−	61.0508i	0.223558	−	0.129071i
$474$	−0.780175	+	79.3967i	−0.00164594	+	0.167504i
$475$	375.420	+	216.749i	0.790357	+	0.456313i
$476$	63.6133	−	183.407i	0.133641	−	0.385309i
$477$	−285.047	−	256.633i	−0.597584	−	0.538015i
$478$	−304.164	−	51.2509i	−0.636327	−	0.107220i
$479$	621.273	+	358.692i	1.29702	+	0.748836i	0.979889	−	0.199545i	$-0.0639464\pi$
$479$	621.273	+	358.692i	1.29702	+	0.748836i	0.317133	+	0.948381i	$0.397280\pi$
$480$	756.685	+	117.417i	1.57643	+	0.244619i
$481$	205.504	+	355.943i	0.427243	+	0.740006i
$482$	119.615	−	44.5690i	0.248163	−	0.0924667i
$483$	−124.244	−	47.6895i	−0.257235	−	0.0987361i
$484$	−352.383	+	304.935i	−0.728064	+	0.630030i
$485$	152.220			0.313855
$486$	281.824	+	395.943i	0.579886	+	0.814698i
$487$	668.869			1.37345			0.686724	−	0.726919i	$-0.259048\pi$
$487$	668.869			1.37345			0.686724	+	0.726919i	$0.259048\pi$
$488$	−338.872	+	206.093i	−0.694409	+	0.422322i
$489$	−356.939	−	137.006i	−0.729937	−	0.280176i
$490$	1175.33	−	437.935i	2.39864	−	0.893745i
$491$	−87.6907	−	151.885i	−0.178596	−	0.309337i	0.762804	−	0.646630i	$-0.223822\pi$
$491$	−87.6907	−	151.885i	−0.178596	−	0.309337i	−0.941400	+	0.337293i	$0.890489\pi$
$492$	634.226	−	229.244i	1.28908	−	0.465944i
$493$	−3.81227	−	2.20101i	−0.00773279	−	0.00446453i
$494$	25.9945	−	154.272i	0.0526204	−	0.312292i
$495$	113.166	+	101.885i	0.228618	+	0.205829i
$496$	−105.242	−	82.9880i	−0.212181	−	0.167314i
$497$	−307.898	−	177.765i	−0.619512	−	0.357676i
$498$	−4.93811	+	502.541i	−0.00991589	+	1.00912i
$499$	455.645	−	263.067i	0.913116	−	0.527188i	0.0316835	−	0.999498i	$-0.489913\pi$
$499$	455.645	−	263.067i	0.913116	−	0.527188i	0.881432	+	0.472310i	$0.156580\pi$
$500$	81.9833	+	426.885i	0.163967	+	0.853770i
$501$	−8.11644	−	51.2372i	−0.0162005	−	0.102270i
$502$	153.585	+	126.896i	0.305947	+	0.252781i
$503$		−	94.2248i		−	0.187326i	−0.995604	−	0.0936629i	$-0.970142\pi$
$503$		−	94.2248i		−	0.187326i	0.995604	−	0.0936629i	$-0.0298576\pi$
$504$	−150.884	+	799.270i	−0.299373	+	1.58585i
$505$	−845.881			−1.67501
$506$	10.6105	−	12.8422i	0.0209694	−	0.0253798i
$507$	−227.364	−	280.757i	−0.448449	−	0.553761i
$508$	−8.53734	−	44.4538i	−0.0168058	−	0.0875074i
$509$	321.839	+	557.442i	0.632297	+	1.09517i	0.987081	+	0.160223i	$0.0512212\pi$
$509$	321.839	+	557.442i	0.632297	+	1.09517i	−0.354784	+	0.934948i	$0.615445\pi$
$510$	−104.544	+	177.035i	−0.204988	+	0.347127i
$511$	482.788	−	836.213i	0.944790	−	1.63642i
$512$	−510.802	+	35.0091i	−0.997660	+	0.0683772i
$513$	−137.594	−	269.996i	−0.268215	−	0.526308i
$514$	−588.233	−	99.1157i	−1.14442	−	0.192832i
$515$	−243.513	+	421.778i	−0.472842	+	0.818986i
$516$	−528.170	−	445.192i	−1.02359	−	0.862775i
$517$	95.1011	−	54.9066i	0.183948	−	0.106202i
$518$	465.216	+	1248.55i	0.898100	+	2.41033i
$519$	462.967	+	571.688i	0.892036	+	1.10152i
$520$	379.986	−	231.098i	0.730743	−	0.444420i
$521$		−	124.089i		−	0.238174i	−0.992884	−	0.119087i	$-0.962003\pi$
$521$		−	124.089i		−	0.238174i	0.992884	−	0.119087i	$-0.0379967\pi$
$522$	17.1538	+	6.77839i	0.0328617	+	0.0129854i
$523$			570.827i			1.09145i	0.837965	+	0.545724i	$0.183745\pi$
$523$			570.827i			1.09145i	−0.837965	+	0.545724i	$0.816255\pi$
$524$	204.842	−	177.260i	0.390920	−	0.338283i
$525$	−1292.89	+	204.805i	−2.46265	+	0.390106i
$526$	−21.3165	−	57.2093i	−0.0405256	−	0.108763i
$527$	31.1642	−	17.9926i	0.0591351	−	0.0341417i
$528$	−88.8279	−	49.7584i	−0.168235	−	0.0942393i
$529$	−256.790	+	444.774i	−0.485426	+	0.840782i
$530$	−112.963	+	670.415i	−0.213138	+	1.26493i
$531$	95.9714	−	451.616i	0.180737	−	0.850502i
$532$	166.195	−	479.167i	0.312397	−	0.900689i
$533$	195.842	−	339.208i	0.367433	−	0.636413i
$534$	−309.704	−	548.807i	−0.579970	−	1.02773i
$535$	−27.9787	−	48.4605i	−0.0522966	−	0.0905804i
$536$	−17.9491	−	786.753i	−0.0334871	−	1.46782i
$537$	−264.327	+	688.644i	−0.492229	+	1.28239i
$538$	336.258	+	277.824i	0.625014	+	0.516402i
$539$	−166.771			−0.309409
$540$	324.444	−	798.027i	0.600823	−	1.47783i
$541$			380.160i			0.702699i	0.936244	+	0.351350i	$0.114277\pi$
$541$			380.160i			0.702699i	−0.936244	+	0.351350i	$0.885723\pi$
$542$	529.569	+	437.543i	0.977064	+	0.807275i
$543$	−150.423	−	57.7378i	−0.277022	−	0.106331i
$544$	42.0737	−	130.873i	0.0773414	−	0.240576i
$545$	263.467	−	152.113i	0.483425	−	0.279106i
$546$	232.177	+	411.425i	0.425232	+	0.753526i
$547$	610.683	+	352.578i	1.11642	+	0.644567i	0.940485	−	0.339835i	$-0.110371\pi$
$547$	610.683	+	352.578i	1.11642	+	0.644567i	0.175937	+	0.984401i	$0.443704\pi$
$548$	18.8040	−	54.2149i	0.0343139	−	0.0989322i
$549$	137.903	+	424.354i	0.251190	+	0.772958i
$550$	27.2253	−	161.577i	0.0495005	−	0.293776i
$551$	−9.95988	−	5.75034i	−0.0180760	−	0.0104362i
$552$	−88.7310	−	31.7558i	−0.160745	−	0.0575286i
$553$	74.7493	+	129.470i	0.135170	+	0.234122i
$554$	89.0707	+	239.049i	0.160777	+	0.431496i
$555$	−220.786	−	1393.77i	−0.397812	−	2.51130i
$556$	−552.536	−	638.511i	−0.993770	−	1.14840i
$557$	450.847			0.809420			0.404710	−	0.914445i	$-0.367372\pi$
$557$	450.847			0.809420			0.404710	+	0.914445i	$0.367372\pi$
$558$	−118.101	+	93.7349i	−0.211651	+	0.167984i
$559$	−401.198			−0.717707
$560$	1339.20	−	534.084i	2.39142	−	0.953722i
$561$	21.2444	−	17.2042i	0.0378688	−	0.0306670i
$562$	−271.131	−	727.663i	−0.482439	−	1.29477i
$563$	50.2105	+	86.9671i	0.0891838	+	0.154471i	0.907166	−	0.420772i	$-0.138241\pi$
$563$	50.2105	+	86.9671i	0.0891838	+	0.154471i	−0.817983	+	0.575243i	$0.804907\pi$
$564$	−475.015	−	400.388i	−0.842226	−	0.709907i
$565$	−963.561	−	556.312i	−1.70542	−	0.984624i
$566$	−491.851	−	82.8756i	−0.868994	−	0.146423i
$567$	835.985	+	372.109i	1.47440	+	0.656276i
$568$	−220.852	−	120.878i	−0.388824	−	0.212814i
$569$	−149.043	−	86.0498i	−0.261938	−	0.151230i	0.363280	−	0.931680i	$-0.381657\pi$
$569$	−149.043	−	86.0498i	−0.261938	−	0.151230i	−0.625218	+	0.780450i	$0.714990\pi$
$570$	−273.130	+	462.519i	−0.479175	+	0.811436i
$571$	−406.657	+	234.784i	−0.712184	+	0.411180i	−0.811869	−	0.583839i	$-0.801550\pi$
$571$	−406.657	+	234.784i	−0.712184	+	0.411180i	0.0996851	+	0.995019i	$0.468216\pi$
$572$	−58.0730	+	11.1529i	−0.101526	+	0.0194981i
$573$	−561.425	+	454.656i	−0.979800	+	0.793465i
$574$	808.767	−	978.871i	1.40900	−	1.70535i
$575$		−	151.667i		−	0.263770i
$576$	−93.9111	+	568.293i	−0.163040	+	0.986619i
$577$	402.048			0.696791			0.348395	−	0.937348i	$-0.386727\pi$
$577$	402.048			0.696791			0.348395	+	0.937348i	$0.386727\pi$
$578$	−417.131	−	344.644i	−0.721681	−	0.596270i
$579$	740.171	−	117.250i	1.27836	−	0.202504i
$580$	−6.16616	−	32.1071i	−0.0106313	−	0.0553570i
$581$	473.125	+	819.476i	0.814329	+	1.41046i
$582$	−1.12507	+	114.496i	−0.00193311	+	0.196728i
$583$	45.1984	−	78.2859i	0.0775273	−	0.134281i
$584$	328.291	−	599.808i	0.562142	−	1.02707i
$585$	−154.635	−	475.840i	−0.264333	−	0.813402i
$586$	−37.2477	+	221.058i	−0.0635626	+	0.377232i
$587$	−159.999	+	277.126i	−0.272570	+	0.472105i	−0.969519	−	0.245015i	$-0.921207\pi$
$587$	−159.999	+	277.126i	−0.272570	+	0.472105i	0.696949	+	0.717121i	$0.254540\pi$
$588$	320.717	+	887.295i	0.545438	+	1.50900i
$589$	81.4192	−	47.0074i	0.138233	−	0.0798088i
$590$	−766.882	+	285.744i	−1.29980	+	0.484312i
$591$	352.318	−	917.885i	0.596139	−	1.55311i
$592$	349.523	+	876.416i	0.590410	+	1.48043i
$593$		−	700.450i		−	1.18120i	−0.806965	−	0.590599i	$-0.798892\pi$
$593$		−	700.450i		−	1.18120i	0.806965	−	0.590599i	$-0.201108\pi$
$594$	−77.4721	+	84.3677i	−0.130424	+	0.142033i
$595$			387.109i			0.650603i
$596$	−554.151	+	479.535i	−0.929784	+	0.804589i
$597$	246.457	−	642.088i	0.412825	−	1.07552i
$598$	−51.2912	+	19.1114i	−0.0857713	+	0.0319588i
$599$	−461.232	+	266.292i	−0.770003	+	0.444561i	−0.832876	−	0.553460i	$-0.813307\pi$
$599$	−461.232	+	266.292i	−0.770003	+	0.444561i	0.0628729	+	0.998022i	$0.479974\pi$
$600$	−912.014	+	165.878i	−1.52002	+	0.276463i
$601$	−440.321	+	762.658i	−0.732647	+	1.26898i	0.223101	+	0.974795i	$0.428382\pi$
$601$	−440.321	+	762.658i	−0.732647	+	1.26898i	−0.955748	+	0.294187i	$0.904951\pi$
$602$	−1282.53	−	216.102i	−2.13044	−	0.358974i
$603$	−865.989	−	184.028i	−1.43613	−	0.305188i
$604$	596.844	+	207.011i	0.988153	+	0.342733i
$605$	464.632	−	804.766i	0.767987	−	1.33019i
$606$	6.25200	−	636.252i	0.0103168	−	1.04992i
$607$	−180.816	−	313.182i	−0.297884	−	0.515951i	0.677767	−	0.735276i	$-0.262948\pi$
$607$	−180.816	−	313.182i	−0.297884	−	0.515951i	−0.975652	+	0.219326i	$0.929614\pi$
$608$	109.921	−	341.918i	0.180791	−	0.562365i
$609$	34.3004	−	5.43349i	0.0563225	−	0.00892199i
$610$	503.765	−	609.719i	0.825844	−	0.999540i
$611$	−360.822			−0.590543
$612$	−132.389	−	79.9438i	−0.216321	−	0.130627i
$613$			237.930i			0.388140i	0.980988	+	0.194070i	$0.0621689\pi$
$613$			237.930i			0.388140i	−0.980988	+	0.194070i	$0.937831\pi$
$614$	541.439	−	655.317i	0.881823	−	1.06729i
$615$	−1045.09	+	846.337i	−1.69933	+	1.37616i
$616$	−191.652	+	4.37237i	−0.311123	+	0.00709800i
$617$	182.219	−	105.204i	0.295331	−	0.170510i	−0.345012	−	0.938598i	$-0.612125\pi$
$617$	182.219	−	105.204i	0.295331	−	0.170510i	0.640344	+	0.768089i	$0.278792\pi$
$618$	−315.451	−	186.283i	−0.510439	−	0.301428i
$619$	117.749	+	67.9823i	0.190224	+	0.109826i	0.592088	−	0.805874i	$-0.298304\pi$
$619$	117.749	+	67.9823i	0.190224	+	0.109826i	−0.401863	+	0.915700i	$0.631637\pi$
$620$	252.505	+	87.5796i	0.407267	+	0.141257i
$621$	−57.7377	+	88.9222i	−0.0929754	+	0.143192i
$622$	585.777	+	98.7020i	0.941764	+	0.158685i
$623$	−1027.54	−	593.248i	−1.64934	−	0.952244i
$624$	171.018	+	287.525i	0.274068	+	0.460777i
$625$	49.3927	+	85.5507i	0.0790284	+	0.136881i
$626$	379.216	−	141.298i	0.605776	−	0.225715i
$627$	55.5028	−	44.9475i	0.0885212	−	0.0716865i
$628$	−416.519	−	481.330i	−0.663246	−	0.766448i
$629$	−253.337			−0.402762
$630$	−238.020	−	1604.43i	−0.377809	−	2.54671i
$631$	368.187			0.583498			0.291749	−	0.956495i	$-0.405763\pi$
$631$	368.187			0.583498			0.291749	+	0.956495i	$0.405763\pi$
$632$	55.0110	+	90.4526i	0.0870428	+	0.143121i
$633$	73.4630	+	463.755i	0.116055	+	0.732631i
$634$	80.2951	−	29.9183i	0.126648	−	0.0471898i
$635$	45.1330	+	78.1726i	0.0710756	+	0.123106i
$636$	−503.436	−	89.9235i	−0.791565	−	0.141389i
$637$	474.559	+	273.986i	0.744990	+	0.430120i
$638$	−0.722287	+	4.28663i	−0.00113211	+	0.00671886i
$639$	−189.514	+	210.497i	−0.296579	+	0.329416i
$640$	939.479	−	399.743i	1.46794	−	0.624599i
$641$	212.362	+	122.607i	0.331297	+	0.191275i	0.656417	−	0.754398i	$-0.272071\pi$
$641$	212.362	+	122.607i	0.331297	+	0.191275i	−0.325120	+	0.945673i	$0.605405\pi$
$642$	36.6576	−	20.6867i	0.0570991	−	0.0322223i
$643$	1052.52	−	607.675i	1.63690	−	0.945062i	0.655002	−	0.755627i	$-0.272668\pi$
$643$	1052.52	−	607.675i	1.63690	−	0.945062i	0.981893	−	0.189435i	$-0.0606656\pi$
$644$	−174.259	+	33.4664i	−0.270588	+	0.0519665i
$645$	1285.99	+	493.611i	1.99379	+	0.765288i
$646$	74.3396	+	61.4212i	0.115077	+	0.0950792i
$647$			887.961i			1.37243i	0.727399	+	0.686214i	$0.240729\pi$
$647$			887.961i			1.37243i	−0.727399	+	0.686214i	$0.759271\pi$
$648$	597.859	+	249.938i	0.922622	+	0.385706i
$649$	108.815			0.167666
$650$	−342.924	+	415.049i	−0.527575	+	0.638537i
$651$	−101.731	+	265.039i	−0.156270	+	0.407125i
$652$	−500.625	+	96.1449i	−0.767829	+	0.147462i
$653$	−467.477	−	809.694i	−0.715891	−	1.23996i	−0.962615	−	0.270874i	$-0.912687\pi$
$653$	−467.477	−	809.694i	−0.715891	−	1.23996i	0.246723	−	0.969086i	$-0.420646\pi$
$654$	112.468	+	199.298i	0.171970	+	0.304737i
$655$	−270.093	+	467.815i	−0.412356	+	0.714221i
$656$	556.769	−	706.070i	0.848733	−	1.07633i
$657$	−571.684	−	514.697i	−0.870143	−	0.783405i
$658$	−1153.45	−	194.354i	−1.75297	−	0.295371i
$659$	−449.326	+	778.255i	−0.681830	+	1.18096i	0.292592	+	0.956237i	$0.405482\pi$
$659$	−449.326	+	778.255i	−0.681830	+	1.18096i	−0.974422	+	0.224727i	$0.927851\pi$
$660$	199.868	+	35.7003i	0.302830	+	0.0540913i
$661$	169.415	−	97.8116i	0.256301	−	0.147975i	−0.366345	−	0.930479i	$-0.619391\pi$
$661$	169.415	−	97.8116i	0.256301	−	0.147975i	0.622646	+	0.782504i	$0.286058\pi$
$662$	−149.164	−	400.327i	−0.225323	−	0.604724i
$663$	−88.7168	+	14.0535i	−0.133811	+	0.0211969i
$664$	348.192	+	572.519i	0.524386	+	0.862228i
$665$			1011.36i			1.52084i
$666$	1049.99	−	155.768i	1.57657	−	0.233887i
$667$			4.02374i			0.00603259i
$668$	−45.2610	−	52.3037i	−0.0677560	−	0.0782989i
$669$	454.828	+	561.638i	0.679862	+	0.839519i
$670$	547.924	+	1470.52i	0.817797	+	2.19481i
$671$	−91.0725	+	52.5807i	−0.135726	+	0.0783617i
$672$	391.827	+	1011.26i	0.583077	+	1.50485i
$673$	417.087	−	722.416i	0.619743	−	1.07343i	−0.369789	−	0.929116i	$-0.620570\pi$
$673$	417.087	−	722.416i	0.619743	−	1.07343i	0.989532	−	0.144311i	$-0.0460967\pi$
$674$	74.0324	−	439.368i	0.109840	−	0.651882i
$675$	−54.5038	+	1041.42i	−0.0807463	+	1.54285i
$676$	−455.101	−	157.848i	−0.673227	−	0.233504i
$677$	61.6931	−	106.856i	0.0911272	−	0.157837i	−0.816859	−	0.576838i	$-0.804286\pi$
$677$	61.6931	−	106.856i	0.0911272	−	0.157837i	0.907986	+	0.419001i	$0.137620\pi$
$678$	425.567	−	720.656i	0.627680	−	1.06292i
$679$	107.794	+	186.705i	0.158754	+	0.274970i
$680$	6.25245	+	274.060i	0.00919477	+	0.403029i
$681$	168.242	+	207.752i	0.247052	+	0.305069i
$682$	−27.3950	−	22.6344i	−0.0401686	−	0.0331883i
$683$	799.370			1.17038			0.585191	−	0.810896i	$-0.301020\pi$
$683$	799.370			1.17038			0.585191	+	0.810896i	$0.301020\pi$
$684$	−345.877	−	208.860i	−0.505668	−	0.305351i
$685$			114.429i			0.167050i
$686$	515.977	+	426.313i	0.752153	+	0.621448i
$687$	78.3881	+	494.846i	0.114102	+	0.720300i
$688$	−911.475	−	132.278i	−1.32482	−	0.192265i
$689$	−257.230	+	148.512i	−0.373338	+	0.215547i
$690$	187.921	+	1.84657i	0.272350	+	0.00267619i
$691$	−581.995	−	336.015i	−0.842250	−	0.486273i	0.0157784	−	0.999876i	$-0.494977\pi$
$691$	−581.995	−	336.015i	−0.842250	−	0.486273i	−0.858028	+	0.513602i	$0.828311\pi$
$692$	926.695	+	321.417i	1.33915	+	0.464476i
$693$	−44.8290	+	210.954i	−0.0646883	+	0.304406i
$694$	−48.0841	+	285.370i	−0.0692854	+	0.411196i
$695$	1458.22	+	841.905i	2.09816	+	1.21137i
$696$	24.1957	−	4.40073i	0.0347640	−	0.00632289i
$697$	120.713	+	209.081i	0.173190	+	0.299973i
$698$	−154.343	−	414.227i	−0.221122	−	0.593448i
$699$	382.532	+	146.830i	0.547256	+	0.210057i
$700$	−1319.80	+	1142.09i	−1.88543	+	1.63156i
$701$	−345.561			−0.492954			−0.246477	−	0.969149i	$-0.579273\pi$
$701$	−345.561			−0.492954			−0.246477	+	0.969149i	$0.579273\pi$
$702$	359.059	−	112.796i	0.511479	−	0.160678i
$703$	−661.866			−0.941488
$704$	−135.612	+	6.19097i	−0.192631	+	0.00879400i
$705$	1156.57	+	443.934i	1.64052	+	0.629693i
$706$	483.959	+	1298.85i	0.685494	+	1.83973i
$707$	−599.009	−	1037.51i	−0.847255	−	1.46749i
$708$	−209.262	−	578.943i	−0.295568	−	0.817716i
$709$	−1200.93	−	693.354i	−1.69383	−	0.977933i	−0.951374	−	0.308037i	$-0.900328\pi$
$709$	−1200.93	−	693.354i	−1.69383	−	0.977933i	−0.742455	−	0.669896i	$-0.766339\pi$
$710$	495.076	+	83.4191i	0.697290	+	0.117492i
$711$	113.270	−	36.8096i	0.159311	−	0.0517716i
$712$	−737.042	−	403.403i	−1.03517	−	0.566577i
$713$	−28.4861	−	16.4465i	−0.0399524	−	0.0230665i
$714$	−291.174	−	2.86116i	−0.407807	−	0.00400723i
$715$	102.122	−	58.9603i	0.142828	−	0.0824619i
$716$	185.493	+	965.857i	0.259068	+	1.34896i
$717$	72.3897	+	456.980i	0.100962	+	0.637350i
$718$	366.564	−	443.661i	0.510535	−	0.617913i
$719$		−	226.454i		−	0.314956i	−0.987522	−	0.157478i	$-0.949664\pi$
$719$		−	226.454i		−	0.314956i	0.987522	−	0.157478i	$-0.0503364\pi$
$720$	−194.424	−	1132.04i	−0.270033	−	1.57227i
$721$	−689.775			−0.956692
$722$	−362.378	−	299.406i	−0.501909	−	0.414689i
$723$	−120.501	−	148.799i	−0.166668	−	0.205808i
$724$	−210.975	+	40.5178i	−0.291402	+	0.0559638i
$725$	19.7889	+	34.2754i	0.0272951	+	0.0472765i
$726$	601.892	+	355.433i	0.829053	+	0.489578i
$727$	−348.940	+	604.381i	−0.479972	+	0.831336i	−0.999736	−	0.0229740i	$-0.992687\pi$
$727$	−348.940	+	604.381i	−0.479972	+	0.831336i	0.519764	+	0.854310i	$0.326020\pi$
$728$	552.540	+	302.420i	0.758984	+	0.415412i
$729$	428.411	−	589.835i	0.587669	−	0.809101i
$730$	−226.556	+	1344.57i	−0.310351	+	1.84187i
$731$	123.646	−	214.160i	0.169146	−	0.292969i
$732$	454.893	+	383.427i	0.621439	+	0.523807i
$733$	−174.486	+	100.740i	−0.238044	+	0.137435i	−0.614278	−	0.789090i	$-0.710552\pi$
$733$	−174.486	+	100.740i	−0.238044	+	0.137435i	0.376233	+	0.926525i	$0.377219\pi$
$734$	1231.02	−	458.683i	1.67714	−	0.624909i
$735$	−1184.04	−	1462.10i	−1.61094	−	1.98925i
$736$	−122.829	+	26.5076i	−0.166887	+	0.0360158i
$737$		−	208.656i		−	0.283116i
$738$	−628.871	−	792.346i	−0.852128	−	1.07364i
$739$		−	914.779i		−	1.23786i	−0.785446	−	0.618930i	$-0.787566\pi$
$739$		−	914.779i		−	1.23786i	0.785446	−	0.618930i	$-0.212434\pi$
$740$	−1231.20	−	1422.78i	−1.66379	−	1.92268i
$741$	−231.780	+	36.7161i	−0.312794	+	0.0495494i
$742$	−902.292	+	336.198i	−1.21603	+	0.453098i
$743$	−727.202	+	419.850i	−0.978738	+	0.565074i	−0.901889	−	0.431968i	$-0.857819\pi$
$743$	−727.202	+	419.850i	−0.978738	+	0.565074i	−0.0768489	+	0.997043i	$0.524486\pi$
$744$	−67.7416	+	189.281i	−0.0910505	+	0.254410i
$745$	730.673	−	1265.56i	0.980769	−	1.69874i
$746$	730.785	+	123.136i	0.979605	+	0.165061i
$747$	716.940	−	232.986i	0.959760	−	0.311896i
$748$	11.9441	−	34.4367i	0.0159681	−	0.0460384i
$749$	39.6261	−	68.6344i	0.0529054	−	0.0916348i
$750$	567.850	−	320.451i	0.757133	−	0.427267i
$751$	−92.3794	−	160.006i	−0.123008	−	0.213057i	0.797944	−	0.602731i	$-0.205921\pi$
$751$	−92.3794	−	160.006i	−0.123008	−	0.213057i	−0.920953	+	0.389674i	$0.872588\pi$
$752$	−819.744	−	118.966i	−1.09009	−	0.158199i
$753$	107.088	−	278.993i	0.142215	−	0.370509i
$754$	9.09777	−	11.0112i	0.0120660	−	0.0146038i
$755$	−1259.73			−1.66852
$756$	1208.57	−	167.174i	1.59864	−	0.221130i
$757$		−	549.800i		−	0.726288i	−0.931733	−	0.363144i	$-0.881703\pi$
$757$		−	549.800i		−	0.726288i	0.931733	−	0.363144i	$-0.118297\pi$
$758$	−768.960	+	930.691i	−1.01446	+	1.22782i
$759$	−23.3283	−	8.95424i	−0.0307355	−	0.0117974i
$760$	16.3351	+	716.005i	0.0214935	+	0.942112i
$761$	−454.835	+	262.599i	−0.597680	+	0.345071i	−0.768128	−	0.640296i	$-0.778812\pi$
$761$	−454.835	+	262.599i	−0.597680	+	0.345071i	0.170448	+	0.985367i	$0.445478\pi$
$762$	−59.1332	+	33.3702i	−0.0776026	+	0.0437929i
$763$	373.147	+	215.437i	0.489053	+	0.282355i
$764$	−315.647	+	910.059i	−0.413151	+	1.19118i
$765$	301.661	+	64.1050i	0.394329	+	0.0837974i
$766$	−649.740	−	109.480i	−0.848225	−	0.142924i
$767$	−309.640	−	178.771i	−0.403703	−	0.233078i
$768$	293.734	+	709.609i	0.382466	+	0.923970i
$769$	70.7173	+	122.486i	0.0919601	+	0.159280i	0.908336	−	0.418242i	$-0.137353\pi$
$769$	70.7173	+	122.486i	0.0919601	+	0.159280i	−0.816376	+	0.577521i	$0.804020\pi$
$770$	358.217	−	133.473i	0.465216	−	0.173342i
$771$	139.997	+	883.767i	0.181578	+	1.14626i
$772$	755.577	−	653.839i	0.978727	−	0.846942i
$773$	−746.557			−0.965792			−0.482896	−	0.875678i	$-0.660415\pi$
$773$	−746.557			−0.965792			−0.482896	+	0.875678i	$0.660415\pi$
$774$	−380.787	+	963.644i	−0.491973	+	1.24502i
$775$	−323.538			−0.417468
$776$	79.3300	+	130.439i	0.102229	+	0.168092i
$777$	1553.18	−	1257.80i	1.99894	−	1.61879i
$778$	1118.09	−	416.606i	1.43713	−	0.535483i
$779$	315.374	+	546.244i	0.404845	+	0.701211i
$780$	−510.085	−	429.947i	−0.653955	−	0.551215i
$781$	−57.8112	−	33.3773i	−0.0740220	−	0.0427366i
$782$	5.60579	−	33.2693i	0.00716853	−	0.0425439i
$783$	1.44598	−	27.6290i	0.00184672	−	0.0352860i
$784$	987.805	+	778.931i	1.25996	+	0.993534i
$785$	1099.25	+	634.654i	1.40032	+	0.808477i
$786$	−349.883	−	206.615i	−0.445144	−	0.262869i
$787$	−515.762	+	297.776i	−0.655352	+	0.378368i	−0.790504	−	0.612457i	$-0.790181\pi$
$787$	−515.762	+	297.776i	−0.655352	+	0.378368i	0.135151	+	0.990825i	$0.456848\pi$
$788$	−247.241	−	1287.38i	−0.313758	−	1.63373i
$789$	−71.1676	+	57.6332i	−0.0901998	+	0.0730459i
$790$	−162.748	−	134.467i	−0.206010	−	0.170211i
$791$		−	1575.81i		−	1.99217i
$792$	−28.3301	+	150.072i	−0.0357704	+	0.189485i
$793$	345.537			0.435734
$794$	990.218	−	1198.49i	1.24713	−	1.50943i
$795$	1007.24	−	159.556i	1.26697	−	0.200699i
$796$	−172.952	−	900.560i	−0.217277	−	1.13136i
$797$	−329.698	−	571.054i	−0.413674	−	0.716504i	0.581614	−	0.813465i	$-0.302421\pi$
$797$	−329.698	−	571.054i	−0.413674	−	0.716504i	−0.995288	+	0.0969605i	$0.969088\pi$
$798$	−760.718	−	7.47504i	−0.953281	−	0.00936722i
$799$	111.202	−	192.607i	0.139176	−	0.241060i
$800$	−915.927	+	829.877i	−1.14491	+	1.03735i
$801$	−632.458	+	702.484i	−0.789586	+	0.877008i
$802$	987.643	+	166.415i	1.23147	+	0.207500i
$803$	90.6488	−	157.008i	0.112888	−	0.195527i
$804$	−1110.14	+	401.267i	−1.38077	+	0.499088i
$805$	306.437	−	176.921i	0.380667	−	0.219778i
$806$	40.7684	+	109.415i	0.0505812	+	0.135750i
$807$	234.456	−	610.824i	0.290528	−	0.756907i
$808$	−440.835	−	724.850i	−0.545588	−	0.897091i
$809$		−	1442.15i		−	1.78263i	−0.453382	−	0.891317i	$-0.649783\pi$
$809$		−	1442.15i		−	1.78263i	0.453382	−	0.891317i	$-0.350217\pi$
$810$	−1289.70	−	80.2115i	−1.59222	−	0.0990265i
$811$			907.692i			1.11923i	0.828754	+	0.559613i	$0.189050\pi$
$811$			907.692i			1.11923i	−0.828754	+	0.559613i	$0.810950\pi$
$812$	35.0143	−	30.2997i	0.0431211	−	0.0373148i
$813$	369.243	−	961.980i	0.454173	−	1.18325i
$814$	87.3495	+	234.429i	0.107309	+	0.287997i
$815$	880.356	−	508.274i	1.08019	−	0.623649i
$816$	−206.188	+	2.67734i	−0.252681	+	0.00328105i
$817$	323.035	−	559.513i	0.395391	−	0.684838i
$818$	−139.606	+	828.537i	−0.170668	+	1.01288i
$819$	474.137	−	526.633i	0.578921	−	0.643019i
$820$	−587.574	+	1694.07i	−0.716554	+	2.06593i
$821$	−775.205	+	1342.69i	−0.944221	+	1.63544i	−0.186917	+	0.982376i	$0.559850\pi$
$821$	−775.205	+	1342.69i	−0.944221	+	1.63544i	−0.757304	+	0.653063i	$0.773484\pi$
$822$	−86.0708	−	0.845757i	−0.104709	−	0.00102890i
$823$	332.778	+	576.389i	0.404348	+	0.700351i	0.994245	−	0.107127i	$-0.0341652\pi$
$823$	332.778	+	576.389i	0.404348	+	0.700351i	−0.589898	+	0.807478i	$0.700832\pi$
$824$	−488.337	+	11.1410i	−0.592642	+	0.0135206i
$825$	−242.755	+	38.4545i	−0.294248	+	0.0466115i
$826$	−893.545	−	738.269i	−1.08177	−	0.893788i
$827$	−911.934			−1.10270			−0.551351	−	0.834274i	$-0.685887\pi$
$827$	−911.934			−1.10270			−0.551351	+	0.834274i	$0.685887\pi$
$828$	−2.77789	+	141.336i	−0.00335494	+	0.170696i
$829$		−	463.817i		−	0.559489i	−0.960074	−	0.279745i	$-0.909750\pi$
$829$		−	463.817i		−	0.559489i	0.960074	−	0.279745i	$-0.0902498\pi$
$830$	−1030.11	−	851.105i	−1.24110	−	1.02543i
$831$	297.373	−	240.820i	0.357850	−	0.289795i
$832$	396.064	+	205.179i	0.476039	+	0.246609i
$833$	−292.509	+	168.880i	−0.351151	+	0.202737i
$834$	−644.039	+	1090.62i	−0.772229	+	1.30769i
$835$	119.450	+	68.9647i	0.143054	+	0.0825924i
$836$	31.2050	−	89.9689i	0.0373266	−	0.107618i
$837$	189.689	+	123.166i	0.226630	+	0.147152i
$838$	69.0580	−	409.846i	0.0824082	−	0.489076i
$839$	54.8140	+	31.6469i	0.0653326	+	0.0377198i	0.532310	−	0.846549i	$-0.321324\pi$
$839$	54.8140	+	31.6469i	0.0653326	+	0.0377198i	−0.466978	+	0.884269i	$0.654657\pi$
$840$	−1399.02	−	1649.18i	−1.66550	−	1.96331i
$841$	419.975	+	727.418i	0.499376	+	0.864944i
$842$	−66.3284	−	178.013i	−0.0787748	−	0.211417i
$843$	−905.204	+	733.055i	−1.07379	+	0.869579i
$844$	409.664	+	473.408i	0.485383	+	0.560910i
$845$	960.563			1.13676
$846$	−342.465	+	866.663i	−0.404805	+	1.02442i
$847$	1316.11			1.55385
$848$	−633.362	+	252.590i	−0.746889	+	0.297866i
$849$	117.058	+	738.962i	0.137878	+	0.870391i
$850$	−115.868	−	310.968i	−0.136315	−	0.365844i
$851$	115.783	+	200.543i	0.136056	+	0.235655i
$852$	−66.4051	+	371.768i	−0.0779402	+	0.436348i
$853$	396.697	+	229.033i	0.465061	+	0.268503i	0.714170	−	0.699972i	$-0.246804\pi$
$853$	396.697	+	229.033i	0.465061	+	0.268503i	−0.249109	+	0.968475i	$0.580138\pi$
$854$	1104.59	+	186.121i	1.29343	+	0.217940i
$855$	788.117	+	167.480i	0.921774	+	0.195883i
$856$	26.9454	−	49.2308i	0.0314782	−	0.0575127i
$857$	−1107.08	−	639.171i	−1.29181	−	0.745824i	−0.312831	−	0.949809i	$-0.601277\pi$
$857$	−1107.08	−	639.171i	−1.29181	−	0.745824i	−0.978974	+	0.203984i	$0.934611\pi$
$858$	43.5937	+	77.2497i	0.0508085	+	0.0900346i
$859$	363.697	−	209.981i	0.423396	−	0.244448i	−0.273133	−	0.961976i	$-0.588060\pi$
$859$	363.697	−	209.981i	0.423396	−	0.244448i	0.696529	+	0.717528i	$0.254727\pi$
$860$	1803.67	−	346.394i	2.09729	−	0.402784i
$861$	−1778.15	−	682.520i	−2.06522	−	0.792706i
$862$	−305.281	+	369.489i	−0.354154	+	0.428642i
$863$			918.683i			1.06452i	0.846580	+	0.532261i	$0.178658\pi$
$863$			918.683i			1.06452i	−0.846580	+	0.532261i	$0.821342\pi$
$864$	852.928	−	137.874i	0.987186	−	0.159577i
$865$	−1955.94			−2.26120
$866$	−64.6300	−	53.3989i	−0.0746305	−	0.0616615i
$867$	−290.846	+	757.733i	−0.335462	+	0.873972i
$868$	71.3907	+	371.730i	0.0822473	+	0.428260i
$869$	14.0350	+	24.3093i	0.0161508	+	0.0279739i
$870$	−42.7094	+	24.1019i	−0.0490912	+	0.0277033i
$871$	−342.799	+	593.745i	−0.393570	+	0.681682i
$872$	267.655	+	146.495i	0.306944	+	0.167999i
$873$	163.343	−	53.0822i	0.187106	−	0.0608043i
$874$	14.6456	−	86.9189i	0.0167570	−	0.0994496i
$875$	613.834	−	1063.19i	0.701524	−	1.21508i
$876$	−1009.68	−	180.348i	−1.15260	−	0.205877i
$877$	1104.62	−	637.754i	1.25955	−	0.727200i	0.286561	−	0.958062i	$-0.407488\pi$
$877$	1104.62	−	637.754i	1.25955	−	0.727200i	0.972986	+	0.230862i	$0.0741547\pi$
$878$	995.107	−	370.782i	1.13338	−	0.422303i
$879$	332.120	−	52.6107i	0.377838	−	0.0598529i
$880$	251.449	−	100.280i	0.285738	−	0.113955i
$881$			211.510i			0.240079i	0.992769	+	0.120039i	$0.0383021\pi$
$881$			211.510i			0.240079i	−0.992769	+	0.120039i	$0.961698\pi$
$882$	1108.51	−	879.802i	1.25681	−	0.997508i
$883$		−	613.635i		−	0.694943i	−0.937690	−	0.347472i	$-0.887040\pi$
$883$		−	613.635i		−	0.694943i	0.937690	−	0.347472i	$-0.112960\pi$
$884$	−90.5633	+	78.3690i	−0.102447	+	0.0886527i
$885$	772.565	+	953.991i	0.872954	+	1.07796i
$886$	549.381	−	204.702i	0.620069	−	0.231041i
$887$	−978.062	+	564.684i	−1.10266	+	0.636623i	−0.936919	−	0.349546i	$-0.886336\pi$
$887$	−978.062	+	564.684i	−1.10266	+	0.636623i	−0.165744	+	0.986169i	$0.553003\pi$
$888$	1079.28	−	915.567i	1.21541	−	1.03104i
$889$	−63.9217	+	110.716i	−0.0719029	+	0.124540i
$890$	1652.20	+	278.392i	1.85641	+	0.312800i
$891$	156.966	+	69.8676i	0.176168	+	0.0784148i
$892$	910.404	+	315.767i	1.02063	+	0.353999i
$893$	290.525	−	503.203i	0.325335	−	0.563498i
$894$	946.526	+	558.949i	1.05875	+	0.625222i
$895$	−980.615	−	1698.47i	−1.09566	−	1.89774i
$896$	1155.60	+	869.240i	1.28973	+	0.970133i
$897$	51.6713	+	63.8056i	0.0576045	+	0.0711322i
$898$	341.751	−	413.629i	0.380569	−	0.460612i
$899$	8.58345			0.00954778
$900$	671.435	+	1217.61i	0.746039	+	1.35290i
$901$		−	183.080i		−	0.203196i
$902$	151.855	−	183.794i	0.168354	−	0.203763i
$903$	305.235	+	1926.88i	0.338024	+	2.13387i
$904$	−25.4519	−	1115.62i	−0.0281547	−	1.23409i
$905$	371.003	−	214.199i	0.409948	−	0.236684i
$906$	9.31082	−	947.542i	0.0102768	−	1.04585i
$907$	−515.588	−	297.675i	−0.568454	−	0.328197i	0.188078	−	0.982154i	$-0.439774\pi$
$907$	−515.588	−	297.675i	−0.568454	−	0.328197i	−0.756532	+	0.653957i	$0.773108\pi$
$908$	336.762	+	116.803i	0.370883	+	0.128638i
$909$	−907.697	+	294.977i	−0.998566	+	0.324507i
$910$	−1238.61	−	208.703i	−1.36111	−	0.229344i
$911$	−316.089	−	182.494i	−0.346969	−	0.200323i	0.316381	−	0.948632i	$-0.397532\pi$
$911$	−316.089	−	182.494i	−0.346969	−	0.200323i	−0.663349	+	0.748310i	$0.730866\pi$
$912$	−538.683	+	6.99478i	−0.590661	+	0.00766971i
$913$	88.8345	+	153.866i	0.0972995	+	0.168528i
$914$	−1397.88	+	520.858i	−1.52941	+	0.569866i
$915$	−1107.58	−	425.128i	−1.21047	−	0.464621i
$916$	437.128	+	505.146i	0.477214	+	0.551469i
$917$	−765.064			−0.834312
$918$	−50.4479	+	226.429i	−0.0549541	+	0.246654i
$919$	317.896			0.345915			0.172957	−	0.984929i	$-0.444668\pi$
$919$	317.896			0.345915			0.172957	+	0.984929i	$0.444668\pi$
$920$	214.089	−	130.204i	0.232706	−	0.141526i
$921$	−1190.41	−	456.921i	−1.29251	−	0.496114i
$922$	−1242.71	+	463.038i	−1.34784	+	0.502211i
$923$	109.670	+	189.955i	0.118819	+	0.205801i
$924$	97.7478	+	270.429i	0.105788	+	0.292672i
$925$	1972.56	+	1138.86i	2.13249	+	1.23120i
$926$	−94.6038	+	561.455i	−0.102164	+	0.606323i
$927$	−114.226	+	537.519i	−0.123221	+	0.579848i
$928$	24.2995	−	22.0166i	0.0261849	−	0.0237248i
$929$	1405.17	+	811.273i	1.51256	+	0.873276i	0.999892	+	0.0146874i	$0.00467530\pi$
$929$	1405.17	+	811.273i	1.51256	+	0.873276i	0.512666	+	0.858588i	$0.328658\pi$
$930$	3.93911	−	400.874i	0.00423560	−	0.431047i
$931$	−764.205	+	441.214i	−0.820844	+	0.473914i
$932$	536.520	−	103.039i	0.575665	−	0.110556i
$933$	−139.412	−	880.078i	−0.149424	−	0.943278i
$934$	−269.516	−	222.681i	−0.288562	−	0.238417i
$935$			72.6840i			0.0777369i
$936$	327.166	−	380.496i	0.349537	−	0.406513i
$937$	−935.489			−0.998387			−0.499194	−	0.866490i	$-0.666370\pi$
$937$	−935.489			−0.998387			−0.499194	+	0.866490i	$0.666370\pi$
$938$	−1415.66	+	1713.40i	−1.50923	+	1.82666i
$939$	−382.026	−	471.740i	−0.406843	−	0.502385i
$940$	1622.15	−	311.533i	1.72569	−	0.331418i
$941$	344.673	+	596.990i	0.366283	+	0.634421i	0.988981	−	0.148041i	$-0.0472968\pi$
$941$	344.673	+	596.990i	0.366283	+	0.634421i	−0.622698	+	0.782462i	$0.713963\pi$
$942$	−485.497	+	822.142i	−0.515389	+	0.872762i
$943$	110.340	−	191.114i	0.117009	−	0.202666i
$944$	−644.524	−	508.237i	−0.682758	−	0.538387i
$945$	−2167.72	+	1104.71i	−2.29389	+	1.16900i
$946$	−240.809	−	40.5757i	−0.254555	−	0.0428918i
$947$	571.731	−	990.266i	0.603728	−	1.04569i	−0.388523	−	0.921439i	$-0.627015\pi$
$947$	571.731	−	990.266i	0.603728	−	1.04569i	0.992251	−	0.124249i	$-0.0396521\pi$
$948$	102.345	−	121.421i	0.107959	−	0.128082i
$949$	−515.894	+	297.851i	−0.543618	+	0.313858i
$950$	−302.715	−	812.430i	−0.318648	−	0.855189i
$951$	−80.8900	−	99.8860i	−0.0850579	−	0.105033i
$952$	−331.720	+	201.744i	−0.348446	+	0.211916i
$953$			1635.29i			1.71594i	0.513697	+	0.857972i	$0.328276\pi$
$953$			1635.29i			1.71594i	−0.513697	+	0.857972i	$0.671724\pi$
$954$	112.569	+	758.801i	0.117997	+	0.795389i
$955$		−	1920.82i		−	2.01133i
$956$	403.678	+	466.491i	0.422258	+	0.487962i
$957$	6.44028	−	1.02020i	0.00672966	−	0.00106604i
$958$	−500.957	−	1344.47i	−0.522920	−	1.40342i
$959$	−140.353	+	81.0327i	−0.146353	+	0.0844971i
$960$	−1017.10	−	1144.97i	−1.05947	−	1.19268i
$961$	445.416	−	771.484i	0.463493	−	0.802793i
$962$	136.582	−	810.589i	0.141977	−	0.842608i
$963$	−46.9225	−	42.2452i	−0.0487254	−	0.0438683i
$964$	−241.200	−	83.6584i	−0.250207	−	0.0867825i
$965$	−996.261	+	1725.58i	−1.03240	+	1.78816i
$966$	130.811	+	231.802i	0.135415	+	0.239961i
$967$	−524.608	−	908.647i	−0.542510	−	0.939656i	−0.998759	−	0.0498033i	$-0.984141\pi$
$967$	−524.608	−	908.647i	−0.542510	−	0.939656i	0.456249	−	0.889852i	$-0.349193\pi$
$968$	931.763	−	21.2574i	0.962566	−	0.0219601i
$969$	51.8334	−	135.040i	0.0534917	−	0.139361i
$970$	−234.695	−	193.911i	−0.241954	−	0.199908i
$971$	1469.41			1.51329			0.756646	−	0.653824i	$-0.226836\pi$
$971$	1469.41			1.51329			0.756646	+	0.653824i	$0.226836\pi$
$972$	69.8655	−	969.486i	0.0718780	−	0.997413i
$973$			2384.77i			2.45095i
$974$	−1031.27	−	852.065i	−1.05880	−	0.874810i
$975$	753.950	+	289.394i	0.773283	+	0.296814i
$976$	785.019	+	113.926i	0.804322	+	0.116728i
$977$	−517.184	+	298.596i	−0.529359	+	0.305626i	−0.740756	−	0.671775i	$-0.765532\pi$
$977$	−517.184	+	298.596i	−0.529359	+	0.305626i	0.211396	+	0.977400i	$0.432199\pi$
$978$	375.805	+	665.940i	0.384258	+	0.680920i
$979$	−192.931	−	111.389i	−0.197070	−	0.113778i
$980$	−2370.03	−	822.028i	−2.41840	−	0.838804i
$981$	229.676	−	255.105i	0.234124	−	0.260046i
$982$	−58.2811	+	345.887i	−0.0593494	+	0.352227i
$983$	1503.96	+	868.311i	1.52997	+	0.883328i	0.999362	+	0.0357088i	$0.0113689\pi$
$983$	1503.96	+	868.311i	1.52997	+	0.883328i	0.530606	+	0.847619i	$0.321964\pi$
$984$	−1269.89	−	454.480i	−1.29054	−	0.461870i
$985$	1307.05	+	2263.88i	1.32695	+	2.29835i
$986$	3.07398	+	8.24997i	0.00311763	+	0.00836711i
$987$	274.516	+	1732.96i	0.278132	+	1.75579i
$988$	−236.605	+	204.746i	−0.239478	+	0.207233i
$989$	−226.040			−0.228554
$990$	−44.6909	−	301.250i	−0.0451423	−	0.304293i
$991$	506.650			0.511251			0.255626	−	0.966776i	$-0.417719\pi$
$991$	506.650			0.511251			0.255626	+	0.966776i	$0.417719\pi$
$992$	56.5462	+	262.019i	0.0570022	+	0.264132i
$993$	−498.002	+	403.294i	−0.501513	+	0.406137i
$994$	248.270	+	666.308i	0.249768	+	0.670330i
$995$	914.319	+	1583.65i	0.918914	+	1.59161i
$996$	647.795	−	768.536i	0.650396	−	0.771623i
$997$	420.474	+	242.761i	0.421739	+	0.243491i	0.695821	−	0.718215i	$-0.255041\pi$
$997$	420.474	+	242.761i	0.421739	+	0.243491i	−0.274082	+	0.961706i	$0.588374\pi$
$998$	−1037.64	−	174.840i	−1.03972	−	0.175190i
$999$	−722.958	−	1418.63i	−0.723682	−	1.42005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.3.j.a.29.6	yes	44
3.2	odd	2		216.3.j.a.197.17		44
4.3	odd	2		288.3.n.a.209.14		44
8.3	odd	2		288.3.n.a.209.9		44
8.5	even	2	inner	72.3.j.a.29.4	yes	44
9.2	odd	6		648.3.h.a.485.25		44
9.4	even	3		216.3.j.a.125.19		44
9.5	odd	6	inner	72.3.j.a.5.4	✓	44
9.7	even	3		648.3.h.a.485.20		44
12.11	even	2		864.3.n.a.305.21		44
24.5	odd	2		216.3.j.a.197.19		44
24.11	even	2		864.3.n.a.305.2		44
36.7	odd	6		2592.3.h.a.1457.42		44
36.11	even	6		2592.3.h.a.1457.4		44
36.23	even	6		288.3.n.a.113.9		44
36.31	odd	6		864.3.n.a.17.2		44
72.5	odd	6	inner	72.3.j.a.5.6	yes	44
72.11	even	6		2592.3.h.a.1457.41		44
72.13	even	6		216.3.j.a.125.17		44
72.29	odd	6		648.3.h.a.485.19		44
72.43	odd	6		2592.3.h.a.1457.3		44
72.59	even	6		288.3.n.a.113.14		44
72.61	even	6		648.3.h.a.485.26		44
72.67	odd	6		864.3.n.a.17.21		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.j.a.5.4	✓	44	9.5	odd	6	inner
72.3.j.a.5.6	yes	44	72.5	odd	6	inner
72.3.j.a.29.4	yes	44	8.5	even	2	inner
72.3.j.a.29.6	yes	44	1.1	even	1	trivial
216.3.j.a.125.17		44	72.13	even	6
216.3.j.a.125.19		44	9.4	even	3
216.3.j.a.197.17		44	3.2	odd	2
216.3.j.a.197.19		44	24.5	odd	2
288.3.n.a.113.9		44	36.23	even	6
288.3.n.a.113.14		44	72.59	even	6
288.3.n.a.209.9		44	8.3	odd	2
288.3.n.a.209.14		44	4.3	odd	2
648.3.h.a.485.19		44	72.29	odd	6
648.3.h.a.485.20		44	9.7	even	3
648.3.h.a.485.25		44	9.2	odd	6
648.3.h.a.485.26		44	72.61	even	6
864.3.n.a.17.2		44	36.31	odd	6
864.3.n.a.17.21		44	72.67	odd	6
864.3.n.a.305.2		44	24.11	even	2
864.3.n.a.305.21		44	12.11	even	2
2592.3.h.a.1457.3		44	72.43	odd	6
2592.3.h.a.1457.4		44	36.11	even	6
2592.3.h.a.1457.41		44	72.11	even	6
2592.3.h.a.1457.42		44	36.7	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	72.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.54182 - 1.27389i) q^{2} +(-1.07504 + 2.80077i) q^{3} +(0.754413 + 3.92821i) q^{4} +(-3.98823 - 6.90782i) q^{5} +(5.22538 - 2.94880i) q^{6} +(5.64852 - 9.78353i) q^{7} +(3.84094 - 7.01763i) q^{8} +(-6.68859 - 6.02186i) q^{9} +O(q^{10})\)	\(q+(-1.54182 - 1.27389i) q^{2} +(-1.07504 + 2.80077i) q^{3} +(0.754413 + 3.92821i) q^{4} +(-3.98823 - 6.90782i) q^{5} +(5.22538 - 2.94880i) q^{6} +(5.64852 - 9.78353i) q^{7} +(3.84094 - 7.01763i) q^{8} +(-6.68859 - 6.02186i) q^{9} +(-2.65067 + 15.7312i) q^{10} +(1.06057 - 1.83697i) q^{11} +(-11.8130 - 2.11004i) q^{12} +(-6.03586 + 3.48480i) q^{13} +(-21.1721 + 7.88884i) q^{14} +(23.6347 - 3.74395i) q^{15} +(-14.8617 + 5.92699i) q^{16} -4.29594i q^{17} +(2.64142 + 17.8051i) q^{18} -11.2235i q^{19} +(24.1266 - 20.8780i) q^{20} +(21.3290 + 26.3378i) q^{21} +(-3.97530 + 1.48122i) q^{22} +(-3.40068 + 1.96338i) q^{23} +(15.5256 + 18.3018i) q^{24} +(-19.3120 + 33.4494i) q^{25} +(13.7455 + 2.31608i) q^{26} +(24.0563 - 12.2595i) q^{27} +(42.6931 + 14.8078i) q^{28} +(0.512348 - 0.887412i) q^{29} +(-41.2098 - 24.3355i) q^{30} +(4.18829 + 7.25434i) q^{31} +(30.4644 + 9.79383i) q^{32} +(4.00476 + 4.94522i) q^{33} +(-5.47255 + 6.62356i) q^{34} -90.1105 q^{35} +(18.6092 - 30.8172i) q^{36} -58.9714i q^{37} +(-14.2975 + 17.3046i) q^{38} +(-3.27135 - 20.6513i) q^{39} +(-63.7951 + 1.45543i) q^{40} +(-48.6696 + 28.0994i) q^{41} +(0.666016 - 67.7790i) q^{42} +(49.8518 + 28.7820i) q^{43} +(8.01611 + 2.78033i) q^{44} +(-14.9222 + 70.2202i) q^{45} +(7.74436 + 1.30491i) q^{46} +(44.8348 + 25.8854i) q^{47} +(-0.623225 - 47.9960i) q^{48} +(-39.3116 - 68.0897i) q^{49} +(72.3864 - 26.9715i) q^{50} +(12.0319 + 4.61829i) q^{51} +(-18.2426 - 21.0812i) q^{52} +42.6170 q^{53} +(-52.7077 - 11.7432i) q^{54} -16.9193 q^{55} +(-46.9616 - 77.2172i) q^{56} +(31.4344 + 12.0657i) q^{57} +(-1.92041 + 0.715555i) q^{58} +(25.6501 + 44.4272i) q^{59} +(32.5374 + 90.0177i) q^{60} +(-42.9355 - 24.7888i) q^{61} +(2.78363 - 16.5203i) q^{62} +(-96.6956 + 31.4234i) q^{63} +(-34.4944 - 53.9086i) q^{64} +(48.1448 + 27.7964i) q^{65} +(0.125052 - 12.7263i) q^{66} +(85.1906 - 49.1848i) q^{67} +(16.8754 - 3.24091i) q^{68} +(-1.84312 - 11.6352i) q^{69} +(138.934 + 114.791i) q^{70} -31.4710i q^{71} +(-67.9497 + 23.8085i) q^{72} +85.4715 q^{73} +(-75.1230 + 90.9232i) q^{74} +(-72.9228 - 90.0478i) q^{75} +(44.0883 - 8.46716i) q^{76} +(-11.9813 - 20.7523i) q^{77} +(-21.2637 + 36.0080i) q^{78} +(-6.61671 + 11.4605i) q^{79} +(100.215 + 79.0239i) q^{80} +(8.47451 + 80.5555i) q^{81} +(110.835 + 18.6755i) q^{82} +(-41.8804 + 72.5390i) q^{83} +(-87.3698 + 103.655i) q^{84} +(-29.6756 + 17.1332i) q^{85} +(-40.1975 - 107.882i) q^{86} +(1.93464 + 2.38897i) q^{87} +(-8.81756 - 14.4984i) q^{88} -105.027i q^{89} +(112.460 - 89.2575i) q^{90} +78.7360i q^{91} +(-10.2781 - 11.8774i) q^{92} +(-24.8203 + 3.93176i) q^{93} +(-36.1520 - 97.0251i) q^{94} +(-77.5300 + 44.7620i) q^{95} +(-60.1806 + 74.7950i) q^{96} +(-9.54179 + 16.5269i) q^{97} +(-26.1273 + 155.061i) q^{98} +(-18.1557 + 5.90010i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) \) 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9	\( 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9} + 4 q^{10} + 14 q^{12} - 48 q^{14} + 14 q^{15} - q^{16} - 38 q^{18} - 66 q^{20} + 7 q^{22} - 6 q^{23} - 47 q^{24} - 72 q^{25} + 28 q^{28} + 16 q^{30} - 2 q^{31} - 93 q^{32} + 30 q^{33} + 9 q^{34} - 105 q^{36} + 99 q^{38} - 118 q^{39} - 56 q^{40} + 66 q^{41} + 236 q^{42} + 72 q^{46} - 6 q^{47} + 117 q^{48} - 72 q^{49} + 189 q^{50} - 42 q^{52} + 139 q^{54} + 92 q^{55} + 270 q^{56} - 8 q^{57} - 38 q^{58} + 456 q^{60} - 226 q^{63} + 2 q^{64} - 6 q^{65} - 258 q^{66} + 387 q^{68} - 4 q^{70} + 259 q^{72} - 8 q^{73} - 432 q^{74} - 63 q^{76} - 620 q^{78} - 2 q^{79} - 44 q^{81} + 186 q^{82} - 232 q^{84} - 615 q^{86} + 174 q^{87} - 77 q^{88} - 554 q^{90} - 624 q^{92} - 186 q^{94} + 144 q^{95} - 794 q^{96} - 2 q^{97}+O(q^{100}) \) 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9 + 4 * q^10 + 14 * q^12 - 48 * q^14 + 14 * q^15 - q^16 - 38 * q^18 - 66 * q^20 + 7 * q^22 - 6 * q^23 - 47 * q^24 - 72 * q^25 + 28 * q^28 + 16 * q^30 - 2 * q^31 - 93 * q^32 + 30 * q^33 + 9 * q^34 - 105 * q^36 + 99 * q^38 - 118 * q^39 - 56 * q^40 + 66 * q^41 + 236 * q^42 + 72 * q^46 - 6 * q^47 + 117 * q^48 - 72 * q^49 + 189 * q^50 - 42 * q^52 + 139 * q^54 + 92 * q^55 + 270 * q^56 - 8 * q^57 - 38 * q^58 + 456 * q^60 - 226 * q^63 + 2 * q^64 - 6 * q^65 - 258 * q^66 + 387 * q^68 - 4 * q^70 + 259 * q^72 - 8 * q^73 - 432 * q^74 - 63 * q^76 - 620 * q^78 - 2 * q^79 - 44 * q^81 + 186 * q^82 - 232 * q^84 - 615 * q^86 + 174 * q^87 - 77 * q^88 - 554 * q^90 - 624 * q^92 - 186 * q^94 + 144 * q^95 - 794 * q^96 - 2 * q^97

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