LMFDB - Embedded newform 54.3.f.a.5.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,3,Mod(5,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("54.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$N$	$=$	$54 = 2 \cdot 3^{3}$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	54.f (of order $18$ , degree $6$ , 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:	$1.47139342755$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			5.4
Character	$\chi$	$=$	54.5
Dual form			54.3.f.a.11.4

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.909039 + 1.08335i) q^{2} +(-2.95590 + 0.512490i) q^{3} +(-0.347296 + 1.96962i) q^{4} +(2.71293 + 7.45370i) q^{5} +(-3.24224 - 2.73640i) q^{6} +(0.0787775 + 0.446769i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(8.47471 - 3.02974i) q^{9} +(-5.60882 + 9.71475i) q^{10} +(4.82381 - 13.2533i) q^{11} +(0.0171659 - 5.99998i) q^{12} +(-9.80599 - 8.22820i) q^{13} +(-0.412396 + 0.491475i) q^{14} +(-11.8391 - 20.6421i) q^{15} +(-3.75877 - 1.36808i) q^{16} +(28.5583 + 16.4882i) q^{17} +(10.9861 + 6.42693i) q^{18} +(0.202792 + 0.351246i) q^{19} +(-15.6231 + 2.75478i) q^{20} +(-0.461823 - 1.28023i) q^{21} +(18.7430 - 6.82189i) q^{22} +(14.2603 + 2.51448i) q^{23} +(6.51568 - 5.43561i) q^{24} +(-29.0466 + 24.3730i) q^{25} -18.1031i q^{26} +(-23.4977 + 13.2988i) q^{27} -0.907323 q^{28} +(-16.8547 - 20.0866i) q^{29} +(11.6004 - 31.5903i) q^{30} +(4.33881 - 24.6066i) q^{31} +(-1.93476 - 5.31570i) q^{32} +(-7.46652 + 41.6476i) q^{33} +(8.09818 + 45.9270i) q^{34} +(-3.11637 + 1.79924i) q^{35} +(3.02419 + 17.7441i) q^{36} +(3.84477 - 6.65933i) q^{37} +(-0.196177 + 0.538991i) q^{38} +(33.2024 + 19.2963i) q^{39} +(-17.1864 - 14.4211i) q^{40} +(-15.9304 + 18.9851i) q^{41} +(0.967127 - 1.66410i) q^{42} +(-16.8662 - 6.13880i) q^{43} +(24.4286 + 14.1039i) q^{44} +(45.5740 + 54.9485i) q^{45} +(10.2391 + 17.7347i) q^{46} +(-46.7491 + 8.24313i) q^{47} +(11.8117 + 2.11758i) q^{48} +(45.8515 - 16.6886i) q^{49} +(-52.8090 - 9.31165i) q^{50} +(-92.8656 - 34.1015i) q^{51} +(19.6120 - 16.4564i) q^{52} -0.261457i q^{53} +(-35.7676 - 13.3671i) q^{54} +111.873 q^{55} +(-0.824792 - 0.982949i) q^{56} +(-0.779443 - 0.934320i) q^{57} +(6.43929 - 36.5190i) q^{58} +(18.8461 + 51.7793i) q^{59} +(44.7686 - 16.1495i) q^{60} +(-18.1761 - 103.082i) q^{61} +(30.6018 - 17.6679i) q^{62} +(2.02121 + 3.54757i) q^{63} +(4.00000 - 6.92820i) q^{64} +(34.7276 - 95.4134i) q^{65} +(-51.9063 + 29.7704i) q^{66} +(-49.4929 - 41.5295i) q^{67} +(-42.3935 + 50.5226i) q^{68} +(-43.4407 - 0.124283i) q^{69} +(-4.78210 - 1.74054i) q^{70} +(-94.6180 - 54.6277i) q^{71} +(-16.4740 + 19.4064i) q^{72} +(31.4705 + 54.5085i) q^{73} +(10.7094 - 1.88836i) q^{74} +(73.3680 - 86.9302i) q^{75} +(-0.762248 + 0.277436i) q^{76} +(6.30118 + 1.11107i) q^{77} +(9.27764 + 53.5109i) q^{78} +(-14.7532 + 12.3794i) q^{79} -31.7283i q^{80} +(62.6414 - 51.3523i) q^{81} -35.0489 q^{82} +(36.7220 + 43.7636i) q^{83} +(2.68196 - 0.464994i) q^{84} +(-45.4212 + 257.596i) q^{85} +(-8.68158 - 23.8524i) q^{86} +(60.1149 + 50.7362i) q^{87} +(6.92713 + 39.2857i) q^{88} +(89.7902 - 51.8404i) q^{89} +(-18.0999 + 99.3230i) q^{90} +(2.90362 - 5.02921i) q^{91} +(-9.90511 + 27.2141i) q^{92} +(-0.214455 + 74.9584i) q^{93} +(-51.4269 - 43.1523i) q^{94} +(-2.06792 + 2.46445i) q^{95} +(8.44320 + 14.7212i) q^{96} +(-52.8231 - 19.2260i) q^{97} +(59.7604 + 34.5027i) q^{98} +(0.726312 - 126.933i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$36 q + 18 q^{5} + 12 q^{6} - 12 q^{9} - 18 q^{11} - 12 q^{12} - 36 q^{14} - 18 q^{15} - 48 q^{18} - 72 q^{20} - 228 q^{21} + 36 q^{22} - 180 q^{23} + 18 q^{25} + 54 q^{27} + 144 q^{29} + 144 q^{30} - 90 q^{31}+ \cdots + 126 q^{99}+O(q^{100})$ 36 * q + 18 * q^5 + 12 * q^6 - 12 * q^9 - 18 * q^11 - 12 * q^12 - 36 * q^14 - 18 * q^15 - 48 * q^18 - 72 * q^20 - 228 * q^21 + 36 * q^22 - 180 * q^23 + 18 * q^25 + 54 * q^27 + 144 * q^29 + 144 * q^30 - 90 * q^31 + 324 * q^33 - 72 * q^34 + 486 * q^35 + 168 * q^36 + 180 * q^38 + 102 * q^39 - 90 * q^41 + 48 * q^42 + 90 * q^43 - 378 * q^45 - 378 * q^47 - 24 * q^48 + 72 * q^49 - 54 * q^51 - 36 * q^54 - 72 * q^56 + 72 * q^57 + 252 * q^59 + 36 * q^60 - 144 * q^61 + 318 * q^63 + 144 * q^64 + 18 * q^65 - 432 * q^66 - 594 * q^67 - 180 * q^68 - 522 * q^69 - 360 * q^70 - 648 * q^71 - 192 * q^72 + 126 * q^73 - 504 * q^74 - 438 * q^75 - 72 * q^76 - 342 * q^77 - 288 * q^78 - 72 * q^79 + 324 * q^81 + 594 * q^83 + 216 * q^84 + 360 * q^85 + 540 * q^86 + 1062 * q^87 + 144 * q^88 + 648 * q^89 + 720 * q^90 - 198 * q^91 + 396 * q^92 + 462 * q^93 + 504 * q^94 + 252 * q^95 + 96 * q^96 + 702 * q^97 + 648 * q^98 + 126 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$ .

$n$	$29$
$\chi(n)$	$e\left(\frac{5}{18}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.909039	+	1.08335i	0.454519	+	0.541675i
$2$	0.909039	+	1.08335i	0.454519	+	0.541675i
$3$	−2.95590	+	0.512490i	−0.985301	+	0.170830i
$3$	−2.95590	+	0.512490i	−0.985301	+	0.170830i
$4$	−0.347296	+	1.96962i	−0.0868241	+	0.492404i
$5$	2.71293	+	7.45370i	0.542585	+	1.49074i	0.843521	+	0.537096i	$0.180479\pi$
$5$	2.71293	+	7.45370i	0.542585	+	1.49074i	−0.300936	+	0.953644i	$0.597299\pi$
$6$	−3.24224	−	2.73640i	−0.540373	−	0.456067i
$7$	0.0787775	+	0.446769i	0.0112539	+	0.0638242i	0.989918	−	0.141645i	$-0.0452391\pi$
$7$	0.0787775	+	0.446769i	0.0112539	+	0.0638242i	−0.978664	+	0.205469i	$0.934128\pi$
$8$	−2.44949	+	1.41421i	−0.306186	+	0.176777i
$9$	8.47471	−	3.02974i	0.941634	−	0.336638i
$10$	−5.60882	+	9.71475i	−0.560882	+	0.971475i
$11$	4.82381	−	13.2533i	0.438528	−	1.20485i	−0.501922	−	0.864913i	$-0.667373\pi$
$11$	4.82381	−	13.2533i	0.438528	−	1.20485i	0.940450	−	0.339933i	$-0.110404\pi$
$12$	0.0171659	−	5.99998i	0.00143049	−	0.499998i
$13$	−9.80599	−	8.22820i	−0.754307	−	0.632939i	0.182331	−	0.983237i	$-0.441636\pi$
$13$	−9.80599	−	8.22820i	−0.754307	−	0.632939i	−0.936638	+	0.350299i	$0.886080\pi$
$14$	−0.412396	+	0.491475i	−0.0294569	+	0.0351053i
$15$	−11.8391	−	20.6421i	−0.789273	−	1.37614i
$16$	−3.75877	−	1.36808i	−0.234923	−	0.0855050i
$17$	28.5583	+	16.4882i	1.67990	+	0.969891i	0.961720	+	0.274036i	$0.0883586\pi$
$17$	28.5583	+	16.4882i	1.67990	+	0.969891i	0.718182	+	0.695856i	$0.244975\pi$
$18$	10.9861	+	6.42693i	0.610339	+	0.357052i
$19$	0.202792	+	0.351246i	0.0106733	+	0.0184866i	0.871313	−	0.490728i	$-0.163269\pi$
$19$	0.202792	+	0.351246i	0.0106733	+	0.0184866i	−0.860639	+	0.509215i	$0.829936\pi$
$20$	−15.6231	+	2.75478i	−0.781156	+	0.137739i
$21$	−0.461823	−	1.28023i	−0.0219916	−	0.0609635i
$22$	18.7430	−	6.82189i	0.851955	−	0.310086i
$23$	14.2603	+	2.51448i	0.620013	+	0.109325i	0.474827	−	0.880079i	$-0.342511\pi$
$23$	14.2603	+	2.51448i	0.620013	+	0.109325i	0.145187	+	0.989404i	$0.453622\pi$
$24$	6.51568	−	5.43561i	0.271487	−	0.226484i
$25$	−29.0466	+	24.3730i	−1.16186	+	0.974920i
$26$		−	18.1031i		−	0.696272i
$27$	−23.4977	+	13.2988i	−0.870285	+	0.492549i
$28$	−0.907323			−0.0324044
$29$	−16.8547	−	20.0866i	−0.581195	−	0.692642i	0.392693	−	0.919670i	$-0.371544\pi$
$29$	−16.8547	−	20.0866i	−0.581195	−	0.692642i	−0.973888	+	0.227028i	$0.927099\pi$
$30$	11.6004	−	31.5903i	0.386680	−	1.05301i
$31$	4.33881	−	24.6066i	0.139962	−	0.793762i	−0.831314	−	0.555804i	$-0.812411\pi$
$31$	4.33881	−	24.6066i	0.139962	−	0.793762i	0.971275	−	0.237959i	$-0.0764783\pi$
$32$	−1.93476	−	5.31570i	−0.0604612	−	0.166116i
$33$	−7.46652	+	41.6476i	−0.226258	+	1.26205i
$34$	8.09818	+	45.9270i	0.238182	+	1.35080i
$35$	−3.11637	+	1.79924i	−0.0890391	+	0.0514068i
$36$	3.02419	+	17.7441i	0.0840052	+	0.492893i
$37$	3.84477	−	6.65933i	0.103913	−	0.179982i	−0.809381	−	0.587284i	$-0.800197\pi$
$37$	3.84477	−	6.65933i	0.103913	−	0.179982i	0.913293	+	0.407302i	$0.133530\pi$
$38$	−0.196177	+	0.538991i	−0.00516254	+	0.0141840i
$39$	33.2024	+	19.2963i	0.851344	+	0.494777i
$40$	−17.1864	−	14.4211i	−0.429660	−	0.360528i
$41$	−15.9304	+	18.9851i	−0.388547	+	0.463052i	−0.924492	−	0.381200i	$-0.875511\pi$
$41$	−15.9304	+	18.9851i	−0.388547	+	0.463052i	0.535946	+	0.844253i	$0.319955\pi$
$42$	0.967127	−	1.66410i	0.0230268	−	0.0396214i
$43$	−16.8662	−	6.13880i	−0.392238	−	0.142763i	0.138369	−	0.990381i	$-0.455814\pi$
$43$	−16.8662	−	6.13880i	−0.392238	−	0.142763i	−0.530607	+	0.847618i	$0.678036\pi$
$44$	24.4286	+	14.1039i	0.555196	+	0.320543i
$45$	45.5740	+	54.9485i	1.01276	+	1.22108i
$46$	10.2391	+	17.7347i	0.222589	+	0.385536i
$47$	−46.7491	+	8.24313i	−0.994662	+	0.175386i	−0.647210	−	0.762312i	$-0.724064\pi$
$47$	−46.7491	+	8.24313i	−0.994662	+	0.175386i	−0.347452	+	0.937698i	$0.612953\pi$
$48$	11.8117	+	2.11758i	0.246077	+	0.0441162i
$49$	45.8515	−	16.6886i	0.935746	−	0.340584i
$50$	−52.8090	−	9.31165i	−1.05618	−	0.186233i
$51$	−92.8656	−	34.1015i	−1.82089	−	0.668657i
$52$	19.6120	−	16.4564i	0.377153	−	0.316469i
$53$		−	0.261457i		−	0.00493315i	−0.999997	−	0.00246657i	$-0.999215\pi$
$53$		−	0.261457i		−	0.00493315i	0.999997	−	0.00246657i	$-0.000785136\pi$
$54$	−35.7676	−	13.3671i	−0.662363	−	0.247539i
$55$	111.873			2.03405
$56$	−0.824792	−	0.982949i	−0.0147284	−	0.0175527i
$57$	−0.779443	−	0.934320i	−0.0136744	−	0.0163916i
$58$	6.43929	−	36.5190i	0.111022	−	0.629638i
$59$	18.8461	+	51.7793i	0.319426	+	0.877615i	0.990658	+	0.136368i	$0.0435430\pi$
$59$	18.8461	+	51.7793i	0.319426	+	0.877615i	−0.671232	+	0.741247i	$0.734235\pi$
$60$	44.7686	−	16.1495i	0.746143	−	0.269159i
$61$	−18.1761	−	103.082i	−0.297969	−	1.68987i	−0.654885	−	0.755729i	$-0.727283\pi$
$61$	−18.1761	−	103.082i	−0.297969	−	1.68987i	0.356916	−	0.934137i	$-0.383828\pi$
$62$	30.6018	−	17.6679i	0.493577	−	0.284967i
$63$	2.02121	+	3.54757i	0.0320827	+	0.0563106i
$64$	4.00000	−	6.92820i	0.0625000	−	0.108253i
$65$	34.7276	−	95.4134i	0.534271	−	1.46790i
$66$	−51.9063	+	29.7704i	−0.786459	+	0.451067i
$67$	−49.4929	−	41.5295i	−0.738700	−	0.619843i	0.193788	−	0.981043i	$-0.437923\pi$
$67$	−49.4929	−	41.5295i	−0.738700	−	0.619843i	−0.932488	+	0.361200i	$0.882367\pi$
$68$	−42.3935	+	50.5226i	−0.623434	+	0.742980i
$69$	−43.4407	−	0.124283i	−0.629576	−	0.00180121i
$70$	−4.78210	−	1.74054i	−0.0683158	−	0.0248649i
$71$	−94.6180	−	54.6277i	−1.33265	−	0.769405i	−0.346943	−	0.937886i	$-0.612780\pi$
$71$	−94.6180	−	54.6277i	−1.33265	−	0.769405i	−0.985705	+	0.168481i	$0.946114\pi$
$72$	−16.4740	+	19.4064i	−0.228806	+	0.269533i
$73$	31.4705	+	54.5085i	0.431103	+	0.746692i	0.996969	−	0.0778057i	$-0.0247914\pi$
$73$	31.4705	+	54.5085i	0.431103	+	0.746692i	−0.565866	+	0.824497i	$0.691458\pi$
$74$	10.7094	−	1.88836i	0.144722	−	0.0255184i
$75$	73.3680	−	86.9302i	0.978240	−	1.15907i
$76$	−0.762248	+	0.277436i	−0.0100296	+	0.00365047i
$77$	6.30118	+	1.11107i	0.0818335	+	0.0144295i
$78$	9.27764	+	53.5109i	0.118944	+	0.686037i
$79$	−14.7532	+	12.3794i	−0.186750	+	0.156702i	−0.731369	−	0.681981i	$-0.761118\pi$
$79$	−14.7532	+	12.3794i	−0.186750	+	0.156702i	0.544620	+	0.838683i	$0.316674\pi$
$80$		−	31.7283i		−	0.396603i
$81$	62.6414	−	51.3523i	0.773350	−	0.633979i
$82$	−35.0489			−0.427426
$83$	36.7220	+	43.7636i	0.442434	+	0.527273i	0.940467	−	0.339886i	$-0.110388\pi$
$83$	36.7220	+	43.7636i	0.442434	+	0.527273i	−0.498033	+	0.867158i	$0.665944\pi$
$84$	2.68196	−	0.464994i	0.0319281	−	0.00553564i
$85$	−45.4212	+	257.596i	−0.534367	+	3.03055i
$86$	−8.68158	−	23.8524i	−0.100949	−	0.277354i
$87$	60.1149	+	50.7362i	0.690976	+	0.583175i
$88$	6.92713	+	39.2857i	0.0787174	+	0.446429i
$89$	89.7902	−	51.8404i	1.00888	−	0.582476i	0.0980154	−	0.995185i	$-0.468751\pi$
$89$	89.7902	−	51.8404i	1.00888	−	0.582476i	0.910863	+	0.412709i	$0.135417\pi$
$90$	−18.0999	+	99.3230i	−0.201110	+	1.10359i
$91$	2.90362	−	5.02921i	0.0319079	−	0.0552661i
$92$	−9.90511	+	27.2141i	−0.107664	+	0.295805i
$93$	−0.214455	+	74.9584i	−0.00230597	+	0.806004i
$94$	−51.4269	−	43.1523i	−0.547095	−	0.459067i
$95$	−2.06792	+	2.46445i	−0.0217676	+	0.0259416i
$96$	8.44320	+	14.7212i	0.0879500	+	0.153345i
$97$	−52.8231	−	19.2260i	−0.544568	−	0.198207i	0.0550633	−	0.998483i	$-0.482464\pi$
$97$	−52.8231	−	19.2260i	−0.544568	−	0.198207i	−0.599631	+	0.800276i	$0.704686\pi$
$98$	59.7604	+	34.5027i	0.609800	+	0.352068i
$99$	0.726312	−	126.933i	0.00733649	−	1.28215i
$100$	−37.9176	−	65.6753i	−0.379176	−	0.656753i
$101$	−44.2921	+	7.80990i	−0.438536	+	0.0773258i	−0.388557	−	0.921425i	$-0.627026\pi$
$101$	−44.2921	+	7.80990i	−0.438536	+	0.0773258i	−0.0499788	+	0.998750i	$0.515915\pi$
$102$	−47.4746	−	131.606i	−0.465437	−	1.29025i
$103$	85.6429	−	31.1715i	0.831485	−	0.302636i	0.109017	−	0.994040i	$-0.465230\pi$
$103$	85.6429	−	31.1715i	0.831485	−	0.302636i	0.722468	+	0.691404i	$0.243008\pi$
$104$	35.6561	+	6.28713i	0.342847	+	0.0604532i
$105$	8.28959	−	6.91547i	0.0789485	−	0.0658617i
$106$	0.283249	−	0.237674i	0.00267216	−	0.00224221i
$107$			206.049i			1.92569i	0.270046	+	0.962847i	$0.412961\pi$
$107$			206.049i			1.92569i	−0.270046	+	0.962847i	$0.587039\pi$
$108$	−18.0329	−	50.9000i	−0.166971	−	0.471297i
$109$	−140.161			−1.28588			−0.642942	−	0.765915i	$-0.722286\pi$
$109$	−140.161			−1.28588			−0.642942	+	0.765915i	$0.722286\pi$
$110$	101.697	+	121.197i	0.924516	+	1.10180i
$111$	−7.95191	+	21.6547i	−0.0716388	+	0.195088i
$112$	0.315110	−	1.78708i	0.00281348	−	0.0159561i
$113$	−24.9375	−	68.5153i	−0.220686	−	0.606330i	0.779102	−	0.626897i	$-0.215675\pi$
$113$	−24.9375	−	68.5153i	−0.220686	−	0.606330i	−0.999788	+	0.0205666i	$0.993453\pi$
$114$	0.303651	−	1.69374i	0.00266361	−	0.0148574i
$115$	19.9450	+	113.114i	0.173435	+	0.983597i
$116$	45.4165	−	26.2212i	0.391521	−	0.226045i
$117$	−108.032	−	40.0220i	−0.923352	−	0.342069i
$118$	−38.9633	+	67.4864i	−0.330197	+	0.571918i
$119$	−5.11665	+	14.0579i	−0.0429971	+	0.118133i
$120$	58.1920	+	33.8195i	0.484933	+	0.281829i
$121$	−59.6896	−	50.0855i	−0.493302	−	0.413930i
$122$	95.1509	−	113.396i	0.779925	−	0.929479i
$123$	37.3591	−	64.2824i	0.303732	−	0.522621i
$124$	46.9588	+	17.0916i	0.378700	+	0.137835i
$125$	−88.7360	−	51.2318i	−0.709888	−	0.409854i
$126$	−2.00590	+	5.41456i	−0.0159198	+	0.0429727i
$127$	−5.49347	−	9.51497i	−0.0432557	−	0.0749210i	0.843587	−	0.536993i	$-0.180440\pi$
$127$	−5.49347	−	9.51497i	−0.0432557	−	0.0749210i	−0.886843	+	0.462072i	$0.847106\pi$
$128$	11.1418	−	1.96460i	0.0870455	−	0.0153485i
$129$	53.0010	+	9.50193i	0.410860	+	0.0736584i
$130$	134.935	−	49.1123i	1.03796	−	0.377787i
$131$	36.9106	+	6.50833i	0.281760	+	0.0496819i	0.312742	−	0.949838i	$-0.398752\pi$
$131$	36.9106	+	6.50833i	0.281760	+	0.0496819i	−0.0309820	+	0.999520i	$0.509863\pi$
$132$	−79.4367	−	29.1702i	−0.601793	−	0.220987i
$133$	−0.140951	+	0.118272i	−0.00105978	+	0.000889260i
$134$		−	91.3701i		−	0.681866i
$135$	−162.873	−	139.066i	−1.20647	−	1.03012i
$136$	−93.2711			−0.685817
$137$	−27.2090	−	32.4264i	−0.198606	−	0.236689i	0.657545	−	0.753415i	$-0.271595\pi$
$137$	−27.2090	−	32.4264i	−0.198606	−	0.236689i	−0.856151	+	0.516726i	$0.827150\pi$
$138$	−39.3547	−	47.1745i	−0.285179	−	0.341844i
$139$	−28.2955	+	160.472i	−0.203565	+	1.15447i	0.696117	+	0.717928i	$0.254909\pi$
$139$	−28.2955	+	160.472i	−0.203565	+	1.15447i	−0.899682	+	0.436545i	$0.856202\pi$
$140$	−2.46150	−	6.76292i	−0.0175821	−	0.0483066i
$141$	133.961	−	48.3243i	0.950079	−	0.342726i
$142$	−26.8305	−	152.163i	−0.188947	−	1.07157i
$143$	−156.353	+	90.2705i	−1.09338	+	0.631262i
$144$	−35.9994	−	0.205990i	−0.249996	−	0.00143048i
$145$	103.994	−	180.123i	0.717201	−	1.24223i
$146$	−30.4439	+	83.6439i	−0.208520	+	0.572903i
$147$	−126.980	+	72.8283i	−0.863809	+	0.495431i
$148$	11.7810	+	9.88547i	0.0796017	+	0.0667937i
$149$	115.419	−	137.551i	0.774624	−	0.923161i	−0.224054	−	0.974577i	$-0.571929\pi$
$149$	115.419	−	137.551i	0.774624	−	0.923161i	0.998677	+	0.0514163i	$0.0163735\pi$
$150$	160.870	+	0.460248i	1.07247	+	0.00306832i
$151$	151.225	+	55.0415i	1.00149	+	0.364514i	0.790160	−	0.612901i	$-0.209997\pi$
$151$	151.225	+	55.0415i	1.00149	+	0.364514i	0.211333	+	0.977414i	$0.432220\pi$
$152$	−0.993473	−	0.573582i	−0.00653601	−	0.00377357i
$153$	291.978	+	53.2080i	1.90835	+	0.347765i
$154$	4.52434	+	7.83639i	0.0293788	+	0.0508856i
$155$	195.181	−	34.4157i	1.25923	−	0.222037i
$156$	−49.5373	+	58.6945i	−0.317547	+	0.376246i
$157$	−72.6336	+	26.4365i	−0.462635	+	0.168385i	−0.562813	−	0.826584i	$-0.690281\pi$
$157$	−72.6336	+	26.4365i	−0.462635	+	0.168385i	0.100178	+	0.994969i	$0.468059\pi$
$158$	−26.8225	−	4.72954i	−0.169763	−	0.0299338i
$159$	0.133994	+	0.772841i	0.000842730	+	0.00486063i
$160$	34.3728	−	28.8422i	0.214830	−	0.180264i
$161$			6.56915i			0.0408022i
$162$	112.576	+	21.1813i	0.694913	+	0.130749i
$163$	−2.14092			−0.0131345			−0.00656723	−	0.999978i	$-0.502090\pi$
$163$	−2.14092			−0.0131345			−0.00656723	+	0.999978i	$0.502090\pi$
$164$	−31.8608	−	37.9703i	−0.194273	−	0.231526i
$165$	−330.685	+	57.3337i	−2.00415	+	0.347477i
$166$	−14.0296	+	79.5657i	−0.0845155	+	0.479311i
$167$	30.6994	+	84.3460i	0.183829	+	0.505066i	0.997038	−	0.0769052i	$-0.0245039\pi$
$167$	30.6994	+	84.3460i	0.183829	+	0.505066i	−0.813209	+	0.581971i	$0.802282\pi$
$168$	2.94176	+	2.48280i	0.0175105	+	0.0147786i
$169$	−0.892424	−	5.06119i	−0.00528061	−	0.0299479i
$170$	−320.357	+	184.958i	−1.88445	+	1.08799i
$171$	2.78279	+	2.36230i	0.0162736	+	0.0138146i
$172$	17.9487	−	31.0880i	0.104353	−	0.180744i
$173$	−62.3682	+	171.355i	−0.360510	+	0.990492i	0.618340	+	0.785911i	$0.287805\pi$
$173$	−62.3682	+	171.355i	−0.360510	+	0.990492i	−0.978850	+	0.204581i	$0.934417\pi$
$174$	−0.318275	+	111.247i	−0.00182917	+	0.639349i
$175$	−13.1773	−	11.0571i	−0.0752990	−	0.0631834i
$176$	−36.2632	+	43.2168i	−0.206041	+	0.245550i
$177$	−82.2436	−	143.396i	−0.464653	−	0.810147i
$178$	137.784	+	50.1493i	0.774068	+	0.281738i
$179$	−104.032	−	60.0628i	−0.581183	−	0.335546i	0.180420	−	0.983590i	$-0.442254\pi$
$179$	−104.032	−	60.0628i	−0.581183	−	0.335546i	−0.761604	+	0.648043i	$0.775588\pi$
$180$	−124.055	+	70.6799i	−0.689195	+	0.392666i
$181$	−79.9928	−	138.552i	−0.441949	−	0.765478i	0.555885	−	0.831259i	$-0.312380\pi$
$181$	−79.9928	−	138.552i	−0.441949	−	0.765478i	−0.997834	+	0.0657809i	$0.979046\pi$
$182$	8.08790	−	1.42612i	0.0444390	−	0.00783580i
$183$	106.555	+	295.385i	0.582268	+	1.61412i
$184$	−38.4865	+	14.0079i	−0.209166	+	0.0761301i
$185$	60.0672	+	10.5915i	0.324688	+	0.0572512i
$186$	−81.4012	+	67.9078i	−0.437641	+	0.365096i
$187$	356.282	−	298.956i	1.90525	−	1.59870i
$188$		−	94.9406i		−	0.505003i
$189$	−7.79259	−	9.45040i	−0.0412307	−	0.0500021i
$190$	−4.54969			−0.0239457
$191$	−82.0805	−	97.8197i	−0.429741	−	0.512145i	0.507107	−	0.861883i	$-0.330715\pi$
$191$	−82.0805	−	97.8197i	−0.429741	−	0.512145i	−0.936847	+	0.349738i	$0.886271\pi$
$192$	−8.27297	+	22.5290i	−0.0430884	+	0.117339i
$193$	17.3129	−	98.1865i	0.0897043	−	0.508738i	−0.906538	−	0.422125i	$-0.861284\pi$
$193$	17.3129	−	98.1865i	0.0897043	−	0.508738i	0.996242	−	0.0866135i	$-0.0276045\pi$
$194$	−27.1897	−	74.7032i	−0.140153	−	0.385068i
$195$	−53.7531	+	299.830i	−0.275657	+	1.53759i
$196$	16.9460	+	96.1058i	0.0864594	+	0.490336i
$197$	−32.9869	+	19.0450i	−0.167446	+	0.0966751i	−0.581381	−	0.813631i	$-0.697487\pi$
$197$	−32.9869	+	19.0450i	−0.167446	+	0.0966751i	0.413935	+	0.910306i	$0.364154\pi$
$198$	138.173	−	114.600i	0.697843	−	0.578788i
$199$	−192.718	+	333.797i	−0.968430	+	1.67737i	−0.268329	+	0.963327i	$0.586471\pi$
$199$	−192.718	+	333.797i	−0.968430	+	1.67737i	−0.700102	+	0.714043i	$0.746862\pi$
$200$	36.6807	−	100.779i	0.183404	−	0.503897i
$201$	167.580	+	97.3925i	0.833730	+	0.484540i
$202$	−48.7241	−	40.8844i	−0.241209	−	0.202398i
$203$	7.64631	−	9.11252i	0.0376666	−	0.0448893i
$204$	99.4187	−	171.066i	0.487347	−	0.838560i
$205$	−184.728	−	67.2354i	−0.901110	−	0.327977i
$206$	111.622	+	64.4452i	0.541856	+	0.312841i
$207$	128.470	−	21.8956i	0.620629	−	0.105776i
$208$	25.6016	+	44.3433i	0.123085	+	0.213189i
$209$	5.63340	−	0.993320i	0.0269541	−	0.00475273i
$210$	15.0274	+	2.69410i	0.0715592	+	0.0128290i
$211$	320.622	−	116.697i	1.51953	−	0.553065i	0.558502	−	0.829503i	$-0.311376\pi$
$211$	320.622	−	116.697i	1.51953	−	0.553065i	0.961032	+	0.276439i	$0.0891542\pi$
$212$	0.514970	+	0.0908030i	0.00242910	+	0.000428316i
$213$	307.678	+	112.983i	1.44450	+	0.530439i
$214$	−223.224	+	187.307i	−1.04310	+	0.875266i
$215$		−	142.370i		−	0.662186i
$216$	38.7500	−	65.8061i	0.179398	−	0.304658i
$217$	11.3353			0.0522364
$218$	−127.412	−	151.844i	−0.584459	−	0.696532i
$219$	−120.959	−	144.993i	−0.552323	−	0.662070i
$220$	−38.8530	+	220.346i	−0.176605	+	1.00157i
$221$	−144.375	−	396.666i	−0.653279	−	1.79487i
$222$	−30.6883	+	11.0703i	−0.138235	+	0.0498661i
$223$	−10.1542	−	57.5872i	−0.0455344	−	0.258238i	0.953539	−	0.301268i	$-0.0974100\pi$
$223$	−10.1542	−	57.5872i	−0.0455344	−	0.258238i	−0.999074	+	0.0430300i	$0.986299\pi$
$224$	2.22248	−	1.28315i	0.00992178	−	0.00572834i
$225$	−172.318	+	294.558i	−0.765856	+	1.30914i
$226$	51.5569	−	89.2992i	0.228128	−	0.395129i
$227$	14.3644	−	39.4658i	0.0632792	−	0.173858i	−0.904024	−	0.427483i	$-0.859400\pi$
$227$	14.3644	−	39.4658i	0.0632792	−	0.173858i	0.967303	+	0.253624i	$0.0816227\pi$
$228$	2.11095	−	1.21072i	0.00925854	−	0.00531016i
$229$	68.1857	+	57.2146i	0.297754	+	0.249845i	0.779409	−	0.626516i	$-0.215520\pi$
$229$	68.1857	+	57.2146i	0.297754	+	0.249845i	−0.481655	+	0.876361i	$0.659964\pi$
$230$	−104.411	+	124.432i	−0.453961	+	0.541009i
$231$	−19.1951	−	0.0549169i	−0.0830956	−	0.000237735i
$232$	69.6921	+	25.3658i	0.300397	+	0.109336i
$233$	121.622	+	70.2184i	0.521982	+	0.301367i	0.737745	−	0.675079i	$-0.235891\pi$
$233$	121.622	+	70.2184i	0.521982	+	0.301367i	−0.215763	+	0.976446i	$0.569224\pi$
$234$	−54.8476	−	153.418i	−0.234391	−	0.655634i
$235$	−188.269	−	326.091i	−0.801143	−	1.38762i
$236$	−108.530	+	19.1369i	−0.459875	+	0.0810884i
$237$	37.2648	−	44.1533i	0.157235	−	0.186301i
$238$	−19.8808	+	7.23604i	−0.0835330	+	0.0304035i
$239$	−28.6122	−	5.04510i	−0.119716	−	0.0211092i	0.113469	−	0.993542i	$-0.463804\pi$
$239$	−28.6122	−	5.04510i	−0.119716	−	0.0211092i	−0.233185	+	0.972432i	$0.574915\pi$
$240$	16.2604	+	93.7856i	0.0677517	+	0.390773i
$241$	−113.719	+	95.4212i	−0.471861	+	0.395938i	−0.847473	−	0.530839i	$-0.821877\pi$
$241$	−113.719	+	95.4212i	−0.471861	+	0.395938i	0.375612	+	0.926777i	$0.377433\pi$
$242$		−	110.194i		−	0.455349i
$243$	−158.844	+	183.895i	−0.653680	+	0.756771i
$244$	209.344			0.857967
$245$	248.784	+	296.489i	1.01544	+	1.21016i
$246$	103.601	−	17.9622i	0.421143	−	0.0730172i
$247$	0.901547	−	5.11293i	0.00364999	−	0.0207001i
$248$	24.1712	+	66.4097i	0.0974643	+	0.267781i
$249$	−130.975	−	110.541i	−0.526005	−	0.443941i
$250$	−25.1625	−	142.704i	−0.100650	−	0.570816i
$251$	270.246	−	156.027i	1.07668	−	0.621621i	0.146680	−	0.989184i	$-0.453141\pi$
$251$	270.246	−	156.027i	1.07668	−	0.621621i	0.929999	+	0.367563i	$0.119808\pi$
$252$	−7.68930	+	2.74895i	−0.0305131	+	0.0109085i
$253$	102.114	−	176.867i	0.403613	−	0.699078i
$254$	5.31427	−	14.6008i	0.0209223	−	0.0574836i
$255$	2.24504	−	784.707i	0.00880407	−	3.07728i
$256$	12.2567	+	10.2846i	0.0478778	+	0.0401742i
$257$	−33.8555	+	40.3474i	−0.131733	+	0.156994i	−0.827879	−	0.560907i	$-0.810452\pi$
$257$	−33.8555	+	40.3474i	−0.131733	+	0.156994i	0.696145	+	0.717901i	$0.254897\pi$
$258$	37.8860	+	66.0563i	0.146845	+	0.256032i
$259$	3.27807	+	1.19312i	0.0126566	+	0.00460664i
$260$	175.867	+	101.537i	0.676411	+	0.390526i
$261$	−203.696	−	119.163i	−0.780443	−	0.456563i
$262$	26.5024	+	45.9034i	0.101154	+	0.175204i
$263$	−15.7913	+	2.78443i	−0.0600429	+	0.0105872i	−0.203589	−	0.979056i	$-0.565261\pi$
$263$	−15.7913	+	2.78443i	−0.0600429	+	0.0105872i	0.143546	+	0.989644i	$0.454149\pi$
$264$	−40.6095	−	112.575i	−0.153824	−	0.426419i
$265$	1.94882	−	0.709313i	0.00735404	−	0.00267665i
$266$	−0.256259	−	0.0451854i	−0.000963380	−	0.000169870i
$267$	−238.843	+	199.252i	−0.894544	+	0.746261i
$268$	98.9858	−	83.0590i	0.369350	−	0.309922i
$269$			233.865i			0.869388i	0.900578	+	0.434694i	$0.143143\pi$
$269$			233.865i			0.869388i	−0.900578	+	0.434694i	$0.856857\pi$
$270$	2.59954	−	302.865i	0.00962791	−	1.12172i
$271$	−229.874			−0.848243			−0.424122	−	0.905605i	$-0.639417\pi$
$271$	−229.874			−0.848243			−0.424122	+	0.905605i	$0.639417\pi$
$272$	−84.7870	−	101.045i	−0.311717	−	0.371490i
$273$	−6.00539	+	16.3539i	−0.0219978	+	0.0599045i
$274$	10.3951	−	58.9537i	0.0379384	−	0.215159i
$275$	182.907	+	502.534i	0.665118	+	1.82740i
$276$	15.3316	−	85.5183i	0.0555492	−	0.309849i
$277$	45.6767	+	259.046i	0.164898	+	0.935183i	0.949170	+	0.314765i	$0.101926\pi$
$277$	45.6767	+	259.046i	0.164898	+	0.935183i	−0.784272	+	0.620418i	$0.786963\pi$
$278$	−199.569	+	115.221i	−0.717874	+	0.414465i
$279$	−37.7815	−	221.680i	−0.135418	−	0.794550i
$280$	5.08901	−	8.81442i	0.0181750	−	0.0314801i
$281$	−168.471	+	462.870i	−0.599540	+	1.64722i	0.152653	+	0.988280i	$0.451218\pi$
$281$	−168.471	+	462.870i	−0.599540	+	1.64722i	−0.752193	+	0.658943i	$0.771004\pi$
$282$	174.128	+	101.198i	0.617476	+	0.358859i
$283$	−375.336	−	314.944i	−1.32628	−	1.11288i	−0.984933	−	0.172938i	$-0.944674\pi$
$283$	−375.336	−	314.944i	−1.32628	−	1.11288i	−0.341343	−	0.939939i	$-0.610882\pi$
$284$	140.456	−	167.389i	0.494564	−	0.589398i
$285$	4.84957	−	8.34447i	0.0170160	−	0.0292789i
$286$	−239.926	−	87.3258i	−0.838901	−	0.305335i
$287$	−9.73694	−	5.62162i	−0.0339266	−	0.0195875i
$288$	−32.5017	−	39.1872i	−0.112853	−	0.136067i
$289$	399.218	+	691.467i	1.38138	+	2.39262i
$290$	289.671	−	51.0768i	0.998866	−	0.176127i
$291$	165.993	+	29.7590i	0.570423	+	0.102265i
$292$	−118.290	+	43.0542i	−0.405104	+	0.147446i
$293$	−149.954	−	26.4409i	−0.511788	−	0.0902420i	−0.0882105	−	0.996102i	$-0.528115\pi$
$293$	−149.954	−	26.4409i	−0.511788	−	0.0902420i	−0.423578	+	0.905860i	$0.639226\pi$
$294$	−194.328	−	71.3600i	−0.660980	−	0.242721i
$295$	−334.819	+	280.947i	−1.13498	+	0.952362i
$296$			21.7493i			0.0734773i
$297$	62.9048	+	375.573i	0.211801	+	1.26456i
$298$	253.936			0.852135
$299$	−119.147	−	141.994i	−0.398484	−	0.474895i
$300$	145.739	+	174.697i	0.485796	+	0.582324i
$301$	1.41395	−	8.01892i	0.00469751	−	0.0266409i
$302$	77.8405	+	213.865i	0.257750	+	0.708162i
$303$	126.921	−	45.7846i	0.418880	−	0.151104i
$304$	−0.281716	−	1.59769i	−0.000926696	−	0.00525555i
$305$	719.030	−	415.132i	2.35748	−	1.36109i
$306$	207.777	+	364.683i	0.679009	+	1.19177i
$307$	−152.701	+	264.487i	−0.497399	+	0.861520i	−0.999995	−	0.00300104i	$-0.999045\pi$
$307$	−152.701	+	264.487i	−0.497399	+	0.861520i	0.502597	+	0.864521i	$0.332378\pi$
$308$	−4.37675	+	12.0250i	−0.0142102	+	0.0390423i
$309$	−237.177	+	136.031i	−0.767563	+	0.440230i
$310$	214.712	+	180.165i	0.692619	+	0.581176i
$311$	−227.448	+	271.062i	−0.731344	+	0.871582i	−0.995680	−	0.0928489i	$-0.970403\pi$
$311$	−227.448	+	271.062i	−0.731344	+	0.871582i	0.264336	+	0.964431i	$0.414847\pi$
$312$	−108.618	−	0.310755i	−0.348135	−	0.000996009i
$313$	−109.151	−	39.7277i	−0.348725	−	0.126926i	0.161718	−	0.986837i	$-0.448297\pi$
$313$	−109.151	−	39.7277i	−0.348725	−	0.126926i	−0.510443	+	0.859911i	$0.670519\pi$
$314$	−94.6668	−	54.6559i	−0.301487	−	0.174063i
$315$	−20.9591	+	24.6898i	−0.0665368	+	0.0783803i
$316$	−19.2590	−	33.3575i	−0.0609462	−	0.105562i
$317$	223.759	−	39.4548i	0.705866	−	0.124463i	0.190819	−	0.981625i	$-0.438886\pi$
$317$	223.759	−	39.4548i	0.705866	−	0.124463i	0.515047	+	0.857162i	$0.327775\pi$
$318$	−0.715452	+	0.847705i	−0.00224985	+	0.00266574i
$319$	−347.518	+	126.486i	−1.08940	+	0.396508i
$320$	62.4925	+	11.0191i	0.195289	+	0.0344347i
$321$	−105.598	−	609.062i	−0.328966	−	1.89739i
$322$	−7.11670	+	5.97162i	−0.0221015	+	0.0185454i
$323$			13.3747i			0.0414076i
$324$	79.3892	+	141.214i	0.245028	+	0.435845i
$325$	485.376			1.49347
$326$	−1.94618	−	2.31936i	−0.00596987	−	0.00711461i
$327$	414.303	−	71.8313i	1.26698	−	0.219668i
$328$	12.1724	−	69.0329i	0.0371109	−	0.210466i
$329$	−7.36556	−	20.2367i	−0.0223877	−	0.0615097i
$330$	−362.718	−	306.129i	−1.09915	−	0.927664i
$331$	−16.3581	−	92.7715i	−0.0494203	−	0.280276i	0.950076	−	0.312019i	$-0.101005\pi$
$331$	−16.3581	−	92.7715i	−0.0494203	−	0.280276i	−0.999496	+	0.0317429i	$0.989894\pi$
$332$	−98.9509	+	57.1293i	−0.298045	+	0.172076i
$333$	12.4072	−	68.0845i	0.0372590	−	0.204458i
$334$	−63.4693	+	109.932i	−0.190028	+	0.329138i
$335$	175.278	−	481.572i	0.523217	−	1.43753i
$336$	−0.0155750	+	5.44392i	−4.63541e−5	+	0.0162021i
$337$	55.5042	+	46.5735i	0.164701	+	0.138200i	0.721413	−	0.692505i	$-0.243493\pi$
$337$	55.5042	+	46.5735i	0.164701	+	0.138200i	−0.556712	+	0.830705i	$0.687937\pi$
$338$	4.67179	−	5.56762i	0.0138219	−	0.0164723i
$339$	108.826	+	189.744i	0.321021	+	0.559718i
$340$	−491.591	−	178.925i	−1.44586	−	0.526249i
$341$	−305.190	−	176.201i	−0.894984	−	0.516719i
$342$	−0.0295380	+	5.16216i	−8.63684e−5	+	0.0150940i
$343$	22.1827	+	38.4216i	0.0646727	+	0.112016i
$344$	49.9952	−	8.81551i	0.145335	−	0.0256265i
$345$	−116.925	−	324.131i	−0.338913	−	0.939511i
$346$	−242.333	+	88.2019i	−0.700384	+	0.254919i
$347$	−407.086	−	71.7802i	−1.17316	−	0.206859i	−0.447094	−	0.894487i	$-0.647541\pi$
$347$	−407.086	−	71.7802i	−1.17316	−	0.206859i	−0.726063	+	0.687628i	$0.758652\pi$
$348$	−120.808	+	100.783i	−0.347151	+	0.289606i
$349$	−53.8823	+	45.2127i	−0.154391	+	0.129549i	−0.716711	−	0.697370i	$-0.754353\pi$
$349$	−53.8823	+	45.2127i	−0.154391	+	0.129549i	0.562320	+	0.826920i	$0.309909\pi$
$350$		−	24.3270i		−	0.0695057i
$351$	339.843	+	62.9357i	0.968215	+	0.179304i
$352$	−79.7835			−0.226658
$353$	−318.904	−	380.055i	−0.903411	−	1.07664i	−0.996714	−	0.0810052i	$-0.974187\pi$
$353$	−318.904	−	380.055i	−0.903411	−	1.07664i	0.0933029	−	0.995638i	$-0.470257\pi$
$354$	80.5855	−	219.451i	0.227643	−	0.619919i
$355$	150.487	−	853.456i	0.423908	−	2.40410i
$356$	70.9218	+	194.856i	0.199219	+	0.547349i
$357$	7.91979	−	44.1759i	0.0221843	−	0.123742i
$358$	−29.4999	−	167.302i	−0.0824020	−	0.467325i
$359$	251.693	−	145.315i	0.701094	−	0.404777i	−0.106661	−	0.994295i	$-0.534016\pi$
$359$	251.693	−	145.315i	0.701094	−	0.404777i	0.807755	+	0.589519i	$0.200683\pi$
$360$	−189.342	−	70.1444i	−0.525950	−	0.194845i
$361$	180.418	−	312.493i	0.499772	−	0.865631i
$362$	77.3834	−	212.609i	0.213766	−	0.587318i
$363$	202.105	+	117.457i	0.556762	+	0.323574i
$364$	8.89720	+	7.46564i	0.0244429	+	0.0205100i
$365$	−320.913	+	382.449i	−0.879213	+	1.04781i
$366$	−223.142	+	383.953i	−0.609678	+	1.04905i
$367$	536.255	+	195.181i	1.46119	+	0.531828i	0.945692	−	0.325065i	$-0.105386\pi$
$367$	536.255	+	195.181i	1.46119	+	0.531828i	0.515495	+	0.856893i	$0.327608\pi$
$368$	−50.1612	−	28.9606i	−0.136308	−	0.0786973i
$369$	−77.4857	+	209.159i	−0.209988	+	0.566825i
$370$	43.1292	+	74.7019i	0.116565	+	0.201897i
$371$	0.116811	−	0.0205969i	0.000314854	−	5.55173e-5i
$372$	−147.565	−	26.4552i	−0.396679	−	0.0711161i
$373$	18.7449	−	6.82259i	0.0502545	−	0.0182911i	−0.316771	−	0.948502i	$-0.602599\pi$
$373$	18.7449	−	6.82259i	0.0502545	−	0.0182911i	0.367025	+	0.930211i	$0.380376\pi$
$374$	647.749	+	114.216i	1.73195	+	0.305389i
$375$	288.551	+	105.960i	0.769469	+	0.282559i
$376$	102.854	−	86.3047i	0.273548	−	0.229534i
$377$			335.653i			0.890325i
$378$	3.15433	−	17.0329i	0.00834479	−	0.0450606i
$379$	−37.0647			−0.0977961			−0.0488981	−	0.998804i	$-0.515571\pi$
$379$	−37.0647			−0.0977961			−0.0488981	+	0.998804i	$0.515571\pi$
$380$	−4.13585	−	4.92891i	−0.0108838	−	0.0129708i
$381$	21.1145	+	25.3100i	0.0554186	+	0.0664304i
$382$	31.3587	−	177.844i	0.0820908	−	0.465560i
$383$	−139.086	−	382.135i	−0.363148	−	0.997740i	−0.977910	−	0.209028i	$-0.932970\pi$
$383$	−139.086	−	382.135i	−0.363148	−	0.997740i	0.614762	−	0.788713i	$-0.289252\pi$
$384$	−31.9273	+	11.5173i	−0.0831440	+	0.0299928i
$385$	8.81306	+	49.9814i	0.0228911	+	0.129822i
$386$	122.109	−	70.4994i	0.316343	−	0.182641i
$387$	−161.535	−	0.924309i	−0.417404	−	0.00238840i
$388$	56.2132	−	97.3641i	0.144879	−	0.250938i
$389$	−53.2715	+	146.362i	−0.136945	+	0.376253i	−0.989141	−	0.146970i	$-0.953048\pi$
$389$	−53.2715	+	146.362i	−0.136945	+	0.376253i	0.852196	+	0.523222i	$0.175270\pi$
$390$	−373.685	+	214.324i	−0.958166	+	0.549549i
$391$	365.791	+	306.935i	0.935528	+	0.785001i
$392$	−88.7116	+	105.722i	−0.226305	+	0.269700i
$393$	−112.440	−	0.321688i	−0.286106	−	0.000818545i
$394$	−50.6188	−	18.4237i	−0.128474	−	0.0467607i
$395$	−132.297	−	76.3818i	−0.334929	−	0.193372i
$396$	249.756	+	45.5138i	0.630698	+	0.114934i
$397$	−203.720	−	352.853i	−0.513147	−	0.888797i	−0.999884	−	0.0152485i	$-0.995146\pi$
$397$	−203.720	−	352.853i	−0.513147	−	0.888797i	0.486736	−	0.873549i	$-0.338187\pi$
$398$	−536.807	+	94.6535i	−1.34876	+	0.237823i
$399$	0.356023	−	0.421835i	0.000892288	−	0.00105723i
$400$	142.524	−	51.8744i	0.356309	−	0.129686i
$401$	−57.1810	−	10.0826i	−0.142596	−	0.0251435i	0.101894	−	0.994795i	$-0.467510\pi$
$401$	−57.1810	−	10.0826i	−0.142596	−	0.0251435i	−0.244491	+	0.969652i	$0.578621\pi$
$402$	46.8262	+	270.081i	0.116483	+	0.671843i
$403$	−245.015	+	205.592i	−0.607977	+	0.510153i
$404$		−	89.9509i		−	0.222651i
$405$	552.706	+	327.595i	1.36471	+	0.808877i
$406$	16.8229			0.0414356
$407$	−69.7117	−	83.0792i	−0.171282	−	0.204126i
$408$	275.700	−	47.8005i	0.675736	−	0.117158i
$409$	50.2599	−	285.038i	0.122885	−	0.696915i	−0.859657	−	0.510872i	$-0.829323\pi$
$409$	50.2599	−	285.038i	0.122885	−	0.696915i	0.982542	−	0.186043i	$-0.0595664\pi$
$410$	−95.0851	−	261.244i	−0.231915	−	0.637181i
$411$	97.0452	+	81.9049i	0.236120	+	0.199282i
$412$	31.6524	+	179.509i	0.0768261	+	0.435702i
$413$	−21.6488	+	12.4989i	−0.0524183	+	0.0302637i
$414$	140.505	+	119.274i	0.339384	+	0.288102i
$415$	−226.577	+	392.443i	−0.545968	+	0.945645i
$416$	−24.7665	+	68.0453i	−0.0595348	+	0.163570i
$417$	1.39857	−	488.840i	0.00335387	−	1.17228i
$418$	6.19709	+	5.19998i	0.0148256	+	0.0124401i
$419$	432.059	−	514.908i	1.03117	−	1.22890i	0.0581156	−	0.998310i	$-0.481491\pi$
$419$	432.059	−	514.908i	1.03117	−	1.22890i	0.973052	−	0.230587i	$-0.0740648\pi$
$420$	10.7419	+	18.7290i	0.0255759	+	0.0445929i
$421$	211.095	+	76.8324i	0.501414	+	0.182500i	0.580330	−	0.814381i	$-0.302924\pi$
$421$	211.095	+	76.8324i	0.501414	+	0.182500i	−0.0789157	+	0.996881i	$0.525146\pi$
$422$	417.881	+	241.264i	0.990239	+	0.571715i
$423$	−371.210	+	211.496i	−0.877566	+	0.499990i
$424$	0.369756	+	0.640436i	0.000872066	+	0.00151046i
$425$	−1231.39	+	217.127i	−2.89738	+	0.510887i
$426$	157.290	+	436.029i	0.369226	+	1.02354i
$427$	44.6219	−	16.2411i	0.104501	−	0.0380353i
$428$	−405.838	−	71.5602i	−0.948220	−	0.167197i
$429$	415.902	−	346.960i	0.969468	−	0.808765i
$430$	154.237	−	129.420i	0.358690	−	0.300976i
$431$			189.283i			0.439171i	0.975593	+	0.219585i	$0.0704705\pi$
$431$			189.283i			0.439171i	−0.975593	+	0.219585i	$0.929530\pi$
$432$	106.516	−	17.8404i	0.246565	−	0.0412973i
$433$	−364.876			−0.842669			−0.421334	−	0.906905i	$-0.638438\pi$
$433$	−364.876			−0.842669			−0.421334	+	0.906905i	$0.638438\pi$
$434$	10.3042	+	12.2801i	0.0237425	+	0.0282952i
$435$	−215.085	+	585.722i	−0.494449	+	1.34649i
$436$	48.6775	−	276.064i	0.111646	−	0.633174i
$437$	2.00868	+	5.51879i	0.00459651	+	0.0126288i
$438$	47.1225	−	262.845i	0.107586	−	0.600104i
$439$	73.6423	+	417.646i	0.167750	+	0.951358i	0.946183	+	0.323631i	$0.104904\pi$
$439$	73.6423	+	417.646i	0.167750	+	0.951358i	−0.778433	+	0.627727i	$0.783985\pi$
$440$	−274.031	+	158.212i	−0.622798	+	0.359573i
$441$	338.016	−	280.349i	0.766477	−	0.635712i
$442$	298.486	−	516.994i	0.675308	−	1.16967i
$443$	61.4880	−	168.937i	0.138799	−	0.381348i	−0.850745	−	0.525579i	$-0.823849\pi$
$443$	61.4880	−	168.937i	0.138799	−	0.381348i	0.989544	+	0.144231i	$0.0460710\pi$
$444$	−39.8898	−	23.1828i	−0.0898419	−	0.0522135i
$445$	629.997	+	528.630i	1.41572	+	1.18793i
$446$	53.1565	−	63.3495i	0.119185	−	0.142039i
$447$	−270.674	+	465.738i	−0.605534	+	1.04192i
$448$	3.41042	+	1.24129i	0.00761254	+	0.00277074i
$449$	558.134	+	322.239i	1.24306	+	0.717681i	0.969716	−	0.244236i	$-0.0785372\pi$
$449$	558.134	+	322.239i	1.24306	+	0.717681i	0.273343	+	0.961917i	$0.411871\pi$
$450$	−475.753	+	81.0839i	−1.05723	+	0.180187i
$451$	174.770	+	302.711i	0.387518	+	0.671200i
$452$	143.610	−	25.3222i	0.317720	−	0.0560226i
$453$	−475.216	−	85.1959i	−1.04904	−	0.188070i
$454$	55.8131	−	20.3143i	0.122936	−	0.0447452i
$455$	45.3636	+	7.99882i	0.0997001	+	0.0175798i
$456$	3.23056	+	1.18631i	0.00708457	+	0.00260155i
$457$	198.907	−	166.903i	0.435246	−	0.365215i	−0.398681	−	0.917090i	$-0.630532\pi$
$457$	198.907	−	166.903i	0.435246	−	0.365215i	0.833927	+	0.551875i	$0.186088\pi$
$458$			125.879i			0.274846i
$459$	−890.327	−	7.64182i	−1.93971	−	0.0166488i
$460$	−229.717			−0.499385
$461$	313.010	+	373.031i	0.678981	+	0.809178i	0.989976	−	0.141234i	$-0.0451069\pi$
$461$	313.010	+	373.031i	0.678981	+	0.809178i	−0.310996	+	0.950411i	$0.600662\pi$
$462$	−17.3896	−	20.8449i	−0.0376398	−	0.0451189i
$463$	104.106	−	590.412i	0.224850	−	1.27519i	−0.638121	−	0.769936i	$-0.720288\pi$
$463$	104.106	−	590.412i	0.224850	−	1.27519i	0.862972	−	0.505252i	$-0.168601\pi$
$464$	35.8727	+	98.5595i	0.0773119	+	0.212413i
$465$	−559.299	+	201.758i	−1.20279	+	0.433888i
$466$	34.4879	+	195.590i	0.0740083	+	0.419722i
$467$	−551.534	+	318.428i	−1.18102	+	0.681860i	−0.956249	−	0.292553i	$-0.905495\pi$
$467$	−551.534	+	318.428i	−1.18102	+	0.681860i	−0.224766	+	0.974413i	$0.572162\pi$
$468$	116.347	−	198.882i	0.248605	−	0.424962i
$469$	14.6552	−	25.3835i	0.0312477	−	0.0541226i
$470$	182.127	−	500.390i	0.387505	−	1.06466i
$471$	201.149	−	115.368i	0.427069	−	0.244942i
$472$	−119.390	−	100.180i	−0.252946	−	0.212247i
$473$	−162.719	+	193.921i	−0.344015	+	0.409981i
$474$	81.7086	+	0.233767i	0.172381	+	0.000493180i
$475$	−14.4513	−	5.25985i	−0.0304238	−	0.0110734i
$476$	−25.9116	−	14.9601i	−0.0544362	−	0.0314288i
$477$	−0.792146	−	2.21577i	−0.00166068	−	0.00464522i
$478$	−20.5440	−	35.5832i	−0.0429790	−	0.0744419i
$479$	393.091	−	69.3125i	0.820649	−	0.144703i	0.252467	−	0.967605i	$-0.418758\pi$
$479$	393.091	−	69.3125i	0.820649	−	0.144703i	0.568182	+	0.822903i	$0.307647\pi$
$480$	−86.8213	+	102.870i	−0.180878	+	0.214314i
$481$	−92.4960	+	33.6658i	−0.192299	+	0.0699913i
$482$	−206.749	−	36.4555i	−0.428940	−	0.0756337i
$483$	−3.36663	−	19.4178i	−0.00697024	−	0.0402024i
$484$	119.379	−	100.171i	0.246651	−	0.206965i
$485$		−	445.886i		−	0.919354i
$486$	−343.619	−	4.91577i	−0.707034	−	0.0101147i
$487$	−379.619			−0.779505			−0.389753	−	0.920920i	$-0.627440\pi$
$487$	−379.619			−0.779505			−0.389753	+	0.920920i	$0.627440\pi$
$488$	190.302	+	226.793i	0.389963	+	0.464740i
$489$	6.32834	−	1.09720i	0.0129414	−	0.00224376i
$490$	−95.0473	+	539.040i	−0.193974	+	1.10008i
$491$	204.694	+	562.393i	0.416893	+	1.14540i	0.953453	+	0.301541i	$0.0975010\pi$
$491$	204.694	+	562.393i	0.416893	+	1.14540i	−0.536561	+	0.843862i	$0.680277\pi$
$492$	113.637	+	95.9080i	0.230969	+	0.194935i
$493$	−150.150	−	851.542i	−0.304564	−	1.72727i
$494$	6.35863	−	3.67116i	0.0128717	−	0.00743149i
$495$	948.089	−	338.945i	1.91533	−	0.684738i
$496$	−49.9725	+	86.5549i	−0.100751	+	0.174506i
$497$	16.9522	−	46.5759i	0.0341091	−	0.0937141i
$498$	0.693442	−	242.378i	0.00139245	−	0.486703i
$499$	−35.4771	−	29.7688i	−0.0710964	−	0.0596569i	0.606547	−	0.795048i	$-0.292554\pi$
$499$	−35.4771	−	29.7688i	−0.0710964	−	0.0596569i	−0.677643	+	0.735391i	$0.736999\pi$
$500$	131.725	−	156.983i	0.263449	−	0.313966i
$501$	−133.971	−	233.585i	−0.267407	−	0.466238i
$502$	414.696	+	150.937i	0.826088	+	0.300672i
$503$	−728.991	−	420.883i	−1.44929	−	0.836745i	−0.450847	−	0.892601i	$-0.648878\pi$
$503$	−728.991	−	420.883i	−1.44929	−	0.836745i	−0.998439	+	0.0558562i	$0.982211\pi$
$504$	−9.96795	−	5.83130i	−0.0197777	−	0.0115700i
$505$	−178.374	−	308.953i	−0.353216	−	0.611788i
$506$	284.434	−	50.1535i	0.562123	−	0.0991175i
$507$	5.23172	+	14.5030i	0.0103190	+	0.0286055i
$508$	20.6487	−	7.51551i	0.0406470	−	0.0147943i
$509$	503.035	+	88.6986i	0.988281	+	0.174261i	0.644347	−	0.764733i	$-0.277129\pi$
$509$	503.035	+	88.6986i	0.988281	+	0.174261i	0.343934	+	0.938994i	$0.388240\pi$
$510$	852.154	−	710.897i	1.67089	−	1.39392i
$511$	−21.8736	+	18.3541i	−0.0428054	+	0.0359180i
$512$			22.6274i			0.0441942i
$513$	−9.43630	−	5.55658i	−0.0183943	−	0.0108315i
$514$	−74.4863			−0.144915
$515$	464.686	+	553.791i	0.902303	+	1.07532i
$516$	−37.1222	+	101.092i	−0.0719423	+	0.195914i
$517$	−116.260	+	659.343i	−0.224874	+	1.27533i
$518$	1.68732	+	4.63589i	0.00325738	+	0.00894959i
$519$	96.5364	−	538.472i	0.186005	−	1.03752i
$520$	49.8699	+	282.827i	0.0959037	+	0.543897i
$521$	−496.828	+	286.844i	−0.953604	+	0.550563i	−0.894199	−	0.447670i	$-0.852254\pi$
$521$	−496.828	+	286.844i	−0.953604	+	0.550563i	−0.0594053	+	0.998234i	$0.518920\pi$
$522$	−56.0720	−	328.997i	−0.107418	−	0.630263i
$523$	257.403	−	445.835i	0.492166	−	0.852457i	−0.507793	−	0.861479i	$-0.669539\pi$
$523$	257.403	−	445.835i	0.492166	−	0.852457i	0.999959	+	0.00902213i	$0.00287187\pi$
$524$	−25.6378	+	70.4394i	−0.0489272	+	0.134426i
$525$	44.6175	+	25.9304i	0.0849858	+	0.0493913i
$526$	−17.3714	−	14.5763i	−0.0330255	−	0.0277117i
$527$	529.627	−	631.185i	1.00499	−	1.19769i
$528$	85.0422	−	146.329i	0.161065	−	0.277138i
$529$	−300.064	−	109.214i	−0.567228	−	0.206454i
$530$	2.53999	+	1.46646i	0.00479243	+	0.00276691i
$531$	316.593	+	381.716i	0.596221	+	0.718862i
$532$	−0.183998	−	0.318694i	−0.000345861	−	0.000599048i
$533$	312.427	−	55.0893i	0.586167	−	0.103357i
$534$	−432.977	−	77.6235i	−0.810819	−	0.145362i
$535$	−1535.83	+	558.997i	−2.87071	+	1.04485i
$536$	179.964	+	31.7325i	0.335754	+	0.0592024i
$537$	338.289	+	124.224i	0.629962	+	0.231331i
$538$	−253.358	+	212.593i	−0.470926	+	0.395154i
$539$		−	688.187i		−	1.27678i
$540$	330.472	−	272.500i	0.611985	−	0.504629i
$541$	104.119			0.192457			0.0962284	−	0.995359i	$-0.469322\pi$
$541$	104.119			0.192457			0.0962284	+	0.995359i	$0.469322\pi$
$542$	−208.964	−	249.034i	−0.385543	−	0.459472i
$543$	307.457	+	368.549i	0.566219	+	0.678728i
$544$	32.3927	−	183.708i	0.0595454	−	0.337699i
$545$	−380.247	−	1044.72i	−0.697702	−	1.91692i
$546$	−23.1762	+	8.36043i	−0.0424472	+	0.0153121i
$547$	−34.7198	−	196.906i	−0.0634732	−	0.359974i	−0.999957	−	0.00926380i	$-0.997051\pi$
$547$	−34.7198	−	196.906i	−0.0634732	−	0.359974i	0.936484	−	0.350711i	$-0.114060\pi$
$548$	73.3171	−	42.3296i	0.133790	−	0.0772439i
$549$	−466.348	−	818.519i	−0.849450	−	1.49093i
$550$	−378.150	+	654.976i	−0.687546	+	1.19087i
$551$	3.63735	−	9.99353i	0.00660136	−	0.0181371i
$552$	106.583	−	61.1300i	0.193086	−	0.110743i
$553$	−6.69298	−	5.61608i	−0.0121030	−	0.0101557i
$554$	−239.115	+	284.966i	−0.431616	+	0.514380i
$555$	−182.981	−	0.523506i	−0.329695	−	0.000943254i
$556$	−306.241	−	111.463i	−0.550793	−	0.200472i
$557$	289.044	+	166.880i	0.518930	+	0.299604i	0.736497	−	0.676441i	$-0.236479\pi$
$557$	289.044	+	166.880i	0.518930	+	0.299604i	−0.217567	+	0.976045i	$0.569812\pi$
$558$	205.812	−	242.446i	0.368838	−	0.434491i
$559$	114.879	+	198.976i	0.205508	+	0.355950i
$560$	14.1752	−	2.49947i	0.0253129	−	0.00446334i
$561$	−899.923	+	1066.28i	−1.60414	+	1.90067i
$562$	−654.597	+	238.254i	−1.16476	+	0.423939i
$563$	989.177	+	174.419i	1.75697	+	0.309802i	0.956969	−	0.290190i	$-0.0937187\pi$
$563$	989.177	+	174.419i	1.75697	+	0.309802i	0.800006	+	0.599992i	$0.204830\pi$
$564$	48.6561	+	280.635i	0.0862696	+	0.497580i
$565$	443.039	−	371.754i	0.784140	−	0.657971i
$566$		−	692.917i		−	1.22423i
$567$	27.8774	+	23.9408i	0.0491664	+	0.0422237i
$568$	309.021			0.544051
$569$	441.594	+	526.272i	0.776089	+	0.924906i	0.998750	−	0.0499895i	$-0.0159188\pi$
$569$	441.594	+	526.272i	0.776089	+	0.924906i	−0.222661	+	0.974896i	$0.571474\pi$
$570$	13.4484	−	2.33167i	0.0235937	−	0.00409065i
$571$	−67.2813	+	381.571i	−0.117831	+	0.668251i	0.867479	+	0.497474i	$0.165739\pi$
$571$	−67.2813	+	381.571i	−0.117831	+	0.668251i	−0.985310	+	0.170777i	$0.945372\pi$
$572$	−123.497	−	339.306i	−0.215904	−	0.593192i
$573$	292.753	+	247.080i	0.510914	+	0.431204i
$574$	−2.76107	−	15.6588i	−0.00481022	−	0.0272801i
$575$	−475.499	+	274.529i	−0.826954	+	0.477442i
$576$	12.9082	−	70.8335i	0.0224100	−	0.122975i
$577$	−279.632	+	484.337i	−0.484631	+	0.839406i	−0.999844	−	0.0176564i	$-0.994379\pi$
$577$	−279.632	+	484.337i	−0.484631	+	0.839406i	0.515213	+	0.857062i	$0.327713\pi$
$578$	−386.196	+	1061.06i	−0.668158	+	1.83575i
$579$	−0.855729	+	299.102i	−0.00147794	+	0.516584i
$580$	318.656	+	267.385i	0.549408	+	0.461008i
$581$	−16.6594	+	19.8539i	−0.0286736	+	0.0341719i
$582$	118.655	+	206.881i	0.203874	+	0.355465i
$583$	−3.46517	−	1.26122i	−0.00594368	−	0.00216332i
$584$	−154.173	−	89.0120i	−0.263995	−	0.152418i
$585$	5.22888	−	913.817i	0.00893826	−	1.56208i
$586$	−107.669	−	186.488i	−0.183736	−	0.318240i
$587$	499.131	−	88.0103i	0.850309	−	0.149932i	0.268522	−	0.963274i	$-0.413465\pi$
$587$	499.131	−	88.0103i	0.850309	−	0.149932i	0.581787	+	0.813341i	$0.302354\pi$
$588$	−99.3441	−	275.395i	−0.168953	−	0.468358i
$589$	9.52286	−	3.46604i	0.0161678	−	0.00588461i
$590$	−608.728	−	107.335i	−1.03174	−	0.181924i
$591$	87.7456	−	73.2005i	0.148470	−	0.123859i
$592$	−23.5621	+	19.7709i	−0.0398008	+	0.0333969i
$593$			598.516i			1.00930i	0.863324	+	0.504651i	$0.168379\pi$
$593$			598.516i			1.00930i	−0.863324	+	0.504651i	$0.831621\pi$
$594$	−349.694	+	409.558i	−0.588711	+	0.689492i
$595$	−118.664			−0.199436
$596$	230.838	+	275.102i	0.387312	+	0.461580i
$597$	398.587	−	1085.44i	0.667650	−	1.81815i
$598$	45.5198	−	258.155i	0.0761200	−	0.431698i
$599$	264.288	+	726.125i	0.441215	+	1.21223i	0.938694	+	0.344753i	$0.112037\pi$
$599$	264.288	+	726.125i	0.441215	+	1.21223i	−0.497478	+	0.867477i	$0.665741\pi$
$600$	−56.7762	+	316.693i	−0.0946269	+	0.527821i
$601$	−22.6179	−	128.272i	−0.0376337	−	0.213431i	0.960192	−	0.279341i	$-0.0901161\pi$
$601$	−22.6179	−	128.272i	−0.0376337	−	0.213431i	−0.997826	+	0.0659100i	$0.979005\pi$
$602$	9.97263	−	5.75770i	0.0165658	−	0.00956429i
$603$	−545.262	−	202.000i	−0.904248	−	0.334991i
$604$	−160.931	+	278.740i	−0.266442	+	0.461490i
$605$	211.389	−	580.786i	0.349403	−	0.959978i
$606$	164.977	+	95.8797i	0.272239	+	0.158217i
$607$	485.221	+	407.149i	0.799376	+	0.670756i	0.948047	−	0.318131i	$-0.103055\pi$
$607$	485.221	+	407.149i	0.799376	+	0.670756i	−0.148671	+	0.988887i	$0.547500\pi$
$608$	1.47477	−	1.75756i	0.00242560	−	0.00289072i
$609$	−17.9317	+	30.8544i	−0.0294445	+	0.0506640i
$610$	1103.36	+	401.590i	1.80879	+	0.658345i
$611$	526.247	+	303.829i	0.861288	+	0.497265i
$612$	−206.202	+	556.606i	−0.336932	+	0.909487i
$613$	−388.396	−	672.722i	−0.633599	−	1.09743i	−0.986810	−	0.161883i	$-0.948243\pi$
$613$	−388.396	−	672.722i	−0.633599	−	1.09743i	0.353211	−	0.935544i	$-0.385090\pi$
$614$	−425.343	+	74.9995i	−0.692741	+	0.122149i
$615$	580.494	+	104.070i	0.943893	+	0.169220i
$616$	−17.0060	+	6.18966i	−0.0276071	+	0.0100482i
$617$	−360.546	−	63.5740i	−0.584353	−	0.103037i	−0.126347	−	0.991986i	$-0.540325\pi$
$617$	−360.546	−	63.5740i	−0.584353	−	0.103037i	−0.458006	+	0.888949i	$0.651436\pi$
$618$	−362.972	−	133.288i	−0.587334	−	0.215677i
$619$	341.806	−	286.809i	0.552190	−	0.463343i	−0.323492	−	0.946231i	$-0.604857\pi$
$619$	341.806	−	286.809i	0.552190	−	0.463343i	0.875682	+	0.482888i	$0.160412\pi$
$620$			396.385i			0.639330i
$621$	−368.524	+	130.561i	−0.593436	+	0.210243i
$622$	−500.414			−0.804524
$623$	30.2342	+	36.0317i	0.0485299	+	0.0578357i
$624$	−98.4014	−	117.954i	−0.157694	−	0.189029i
$625$	−23.4761	+	133.140i	−0.0375618	+	0.213024i
$626$	−56.1835	−	154.363i	−0.0897500	−	0.246586i
$627$	−16.1427	+	5.82322i	−0.0257459	+	0.00928743i
$628$	−26.8443	−	152.242i	−0.0427457	−	0.242423i
$629$	219.600	−	126.786i	0.349126	−	0.201568i
$630$	−45.8003	−	0.262071i	−0.0726989	−	0.000415985i
$631$	444.799	−	770.415i	0.704911	−	1.22094i	−0.261812	−	0.965119i	$-0.584320\pi$
$631$	444.799	−	770.415i	0.704911	−	1.22094i	0.966723	−	0.255824i	$-0.0823466\pi$
$632$	18.6307	−	51.1875i	0.0294790	−	0.0809929i
$633$	−887.920	+	509.259i	−1.40272	+	0.804517i
$634$	246.150	+	206.544i	0.388248	+	0.325779i
$635$	56.0184	−	66.7601i	0.0882179	−	0.105134i
$636$	−1.56873	−	0.00448813i	−0.00246656	−	7.05681e-6i
$637$	−586.937	−	213.628i	−0.921408	−	0.335365i
$638$	−452.936	−	261.503i	−0.709931	−	0.409879i
$639$	−967.368	−	176.286i	−1.51388	−	0.275878i
$640$	44.8705	+	77.7180i	0.0701102	+	0.121434i
$641$	460.754	−	81.2433i	0.718805	−	0.126745i	0.197731	−	0.980256i	$-0.436643\pi$
$641$	460.754	−	81.2433i	0.718805	−	0.126745i	0.521074	+	0.853512i	$0.325532\pi$
$642$	563.834	−	668.061i	0.878246	−	1.04059i
$643$	367.369	−	133.711i	0.571336	−	0.207949i	−0.0401649	−	0.999193i	$-0.512788\pi$
$643$	367.369	−	133.711i	0.571336	−	0.207949i	0.611501	+	0.791244i	$0.290566\pi$
$644$	−12.9387	−	2.28144i	−0.0200912	−	0.00354261i
$645$	72.9632	+	420.832i	0.113121	+	0.652452i
$646$	−14.4894	+	12.1581i	−0.0224295	+	0.0188206i
$647$			343.874i			0.531490i	0.964043	+	0.265745i	$0.0856180\pi$
$647$			343.874i			0.531490i	−0.964043	+	0.265745i	$0.914382\pi$
$648$	−80.8162	+	214.375i	−0.124716	+	0.330826i
$649$	777.157			1.19747
$650$	441.226	+	525.833i	0.678809	+	0.808974i
$651$	−33.5060	+	5.80922i	−0.0514685	+	0.00892354i
$652$	0.743533	−	4.21678i	0.00114039	−	0.00646746i
$653$	40.4063	+	111.015i	0.0618779	+	0.170008i	0.966779	−	0.255614i	$-0.0822776\pi$
$653$	40.4063	+	111.015i	0.0618779	+	0.170008i	−0.904901	+	0.425622i	$0.860055\pi$
$654$	454.436	+	383.538i	0.694857	+	0.586450i
$655$	51.6245	+	292.777i	0.0788161	+	0.446988i
$656$	85.8520	−	49.5667i	0.130872	−	0.0755590i
$657$	431.850	+	366.596i	0.657306	+	0.557985i
$658$	15.2279	−	26.3754i	0.0231426	−	0.0400842i
$659$	−236.242	+	649.069i	−0.358485	+	0.984930i	0.621070	+	0.783755i	$0.286698\pi$
$659$	−236.242	+	649.069i	−0.358485	+	0.984930i	−0.979555	+	0.201175i	$0.935524\pi$
$660$	1.92039	−	671.234i	0.00290969	−	1.01702i
$661$	767.161	+	643.724i	1.16061	+	0.973864i	0.999914	−	0.0131403i	$-0.00418282\pi$
$661$	767.161	+	643.724i	1.16061	+	0.973864i	0.160692	+	0.987005i	$0.448627\pi$
$662$	85.6338	−	102.054i	0.129356	−	0.154161i
$663$	630.045	+	1098.52i	0.950294	+	1.65689i
$664$	−151.841	−	55.2657i	−0.228677	−	0.0832315i
$665$	−1.26395	−	0.729741i	−0.00190068	−	0.00109736i
$666$	85.0380	−	48.4501i	0.127685	−	0.0727479i
$667$	−189.845	−	328.822i	−0.284626	−	0.492986i
$668$	−176.791	+	31.1730i	−0.264657	+	0.0466662i
$669$	59.5276	+	165.018i	0.0889799	+	0.246664i
$670$	681.045	−	247.880i	1.01649	−	0.369971i
$671$	−1453.85	−	256.353i	−2.16669	−	0.382047i
$672$	−5.91183	+	4.93186i	−0.00879736	+	0.00733908i
$673$	−122.061	+	102.421i	−0.181368	+	0.152186i	−0.728952	−	0.684565i	$-0.759992\pi$
$673$	−122.061	+	102.421i	−0.181368	+	0.152186i	0.547584	+	0.836751i	$0.315548\pi$
$674$			102.468i			0.152029i
$675$	358.396	−	958.994i	0.530957	−	1.42073i
$676$	10.2785			0.0152049
$677$	−657.379	−	783.434i	−0.971018	−	1.15721i	−0.987543	−	0.157351i	$-0.949705\pi$
$677$	−657.379	−	783.434i	−0.971018	−	1.15721i	0.0165244	−	0.999863i	$-0.494740\pi$
$678$	−106.632	+	290.382i	−0.157275	+	0.428292i
$679$	4.42833	−	25.1143i	0.00652185	−	0.0369872i
$680$	−253.038	−	695.215i	−0.372114	−	1.02237i
$681$	−22.2339	+	124.019i	−0.0326489	+	0.182113i
$682$	−86.5415	−	490.801i	−0.126894	−	0.719650i
$683$	376.428	−	217.331i	0.551139	−	0.318200i	−0.198442	−	0.980113i	$-0.563588\pi$
$683$	376.428	−	217.331i	0.551139	−	0.318200i	0.749581	+	0.661912i	$0.230255\pi$
$684$	−5.61927	+	4.66060i	−0.00821531	+	0.00681374i
$685$	167.881	−	290.778i	0.245081	−	0.424493i
$686$	−21.4591	+	58.9584i	−0.0312815	+	0.0859452i
$687$	−230.872	−	134.176i	−0.336058	−	0.195307i
$688$	54.9979	+	46.1487i	0.0799388	+	0.0670766i
$689$	−2.15132	+	2.56384i	−0.00312238	+	0.00372111i
$690$	244.858	−	421.319i	0.354867	−	0.610607i
$691$	−576.062	−	209.669i	−0.833664	−	0.303429i	−0.110302	−	0.993898i	$-0.535182\pi$
$691$	−576.062	−	209.669i	−0.833664	−	0.303429i	−0.723362	+	0.690469i	$0.757404\pi$
$692$	−315.843	−	182.352i	−0.456421	−	0.263515i
$693$	56.7669	−	9.67495i	0.0819147	−	0.0139610i
$694$	−292.294	−	506.267i	−0.421172	−	0.729492i
$695$	−1272.87	+	224.442i	−1.83147	+	0.322938i
$696$	−219.003	−	39.2624i	−0.314659	−	0.0564116i
$697$	−767.976	+	279.520i	−1.10183	+	0.401034i
$698$	−97.9623	−	17.2734i	−0.140347	−	0.0247470i
$699$	−395.489	−	145.229i	−0.565792	−	0.207766i
$700$	26.3547	−	22.1142i	0.0376495	−	0.0315917i
$701$		−	644.120i		−	0.918859i	−0.888214	−	0.459430i	$-0.848054\pi$
$701$		−	644.120i		−	0.918859i	0.888214	−	0.459430i	$-0.151946\pi$
$702$	240.749	+	425.381i	0.342948	+	0.605955i
$703$	3.11875			0.00443634
$704$	−72.5264	−	86.4335i	−0.103020	−	0.122775i
$705$	723.622	+	867.407i	1.02641	+	1.23036i
$706$	121.837	−	690.970i	0.172573	−	0.978710i
$707$	−6.97845	−	19.1731i	−0.00987051	−	0.0271190i
$708$	310.998	−	112.187i	0.439263	−	0.158457i
$709$	54.3773	+	308.389i	0.0766958	+	0.434963i	0.998842	+	0.0481207i	$0.0153232\pi$
$709$	54.3773	+	308.389i	0.0766958	+	0.434963i	−0.922146	+	0.386843i	$0.873566\pi$
$710$	1061.39	−	612.794i	1.49492	−	0.863090i
$711$	−87.5229	+	149.611i	−0.123098	+	0.210423i
$712$	−146.627	+	253.965i	−0.205936	+	0.356692i
$713$	123.746	−	339.988i	0.173556	−	0.476842i
$714$	55.0574	−	31.5777i	0.0771112	−	0.0442265i
$715$	−1097.02	−	920.512i	−1.53430	−	1.28743i
$716$	154.431	−	184.043i	0.215685	−	0.257043i
$717$	87.1604	+	0.249365i	0.121563	+	0.000347789i
$718$	386.226	+	140.575i	0.537919	+	0.195786i
$719$	−1134.61	−	655.066i	−1.57804	−	0.911079i	−0.995133	−	0.0985362i	$-0.968584\pi$
$719$	−1134.61	−	655.066i	−1.57804	−	0.911079i	−0.582902	−	0.812543i	$-0.698083\pi$
$720$	−96.1283	−	268.888i	−0.133512	−	0.373455i
$721$	20.6732	+	35.8070i	0.0286730	+	0.0496630i
$722$	502.546	−	88.6124i	0.696047	−	0.122732i
$723$	287.238	−	340.335i	0.397287	−	0.470726i
$724$	300.675	−	109.437i	0.415296	−	0.151156i
$725$	979.141	+	172.649i	1.35054	+	0.238137i
$726$	56.4735	+	325.724i	0.0777872	+	0.448655i
$727$	965.609	−	810.242i	1.32821	−	1.11450i	0.343718	−	0.939073i	$-0.388314\pi$
$727$	965.609	−	810.242i	1.32821	−	1.11450i	0.984492	−	0.175428i	$-0.0561308\pi$
$728$			16.4253i			0.0225623i
$729$	375.283	−	624.983i	0.514792	−	0.857315i
$730$	−706.049			−0.967190
$731$	−380.454	−	453.407i	−0.520456	−	0.620256i
$732$	−618.800	+	107.287i	−0.845355	+	0.146566i
$733$	36.7966	−	208.684i	0.0502000	−	0.284698i	−0.949365	−	0.314174i	$-0.898273\pi$
$733$	36.7966	−	208.684i	0.0502000	−	0.284698i	0.999566	+	0.0294754i	$0.00938366\pi$
$734$	276.028	+	758.380i	0.376059	+	1.03321i
$735$	−887.327	−	748.893i	−1.20725	−	1.01890i
$736$	−14.2240	−	80.6685i	−0.0193261	−	0.109604i
$737$	−789.147	+	455.614i	−1.07076	+	0.618201i
$738$	−297.029	+	106.189i	−0.402479	+	0.143888i
$739$	26.2115	−	45.3996i	0.0354688	−	0.0614338i	−0.847746	−	0.530402i	$-0.822041\pi$
$739$	26.2115	−	45.3996i	0.0354688	−	0.0614338i	0.883215	+	0.468968i	$0.155374\pi$
$740$	−41.7223	+	114.631i	−0.0563814	+	0.154907i
$741$	−0.0445609	+	15.5753i	−6.01361e−5	+	0.0210194i
$742$	0.128499	+	0.107824i	0.000173180	+	0.000145315i
$743$	−12.7448	+	15.1886i	−0.0171531	+	0.0204423i	−0.774553	−	0.632509i	$-0.782025\pi$
$743$	−12.7448	+	15.1886i	−0.0171531	+	0.0204423i	0.757400	+	0.652952i	$0.226469\pi$
$744$	−105.482	−	183.913i	−0.141777	−	0.247195i
$745$	1338.39	+	487.133i	1.79649	+	0.653870i
$746$	24.4311	+	14.1053i	0.0327495	+	0.0189079i
$747$	443.801	+	259.626i	0.594111	+	0.347558i
$748$	465.094	+	805.566i	0.621783	+	1.07696i
$749$	−92.0566	+	16.2321i	−0.122906	+	0.0216716i
$750$	147.512	+	408.923i	0.196683	+	0.545231i
$751$	1260.89	−	458.927i	1.67895	−	0.611088i	0.685785	−	0.727804i	$-0.259459\pi$
$751$	1260.89	−	458.927i	1.67895	−	0.611088i	0.993165	+	0.116716i	$0.0372368\pi$
$752$	186.996	+	32.9725i	0.248665	+	0.0438464i
$753$	−718.860	+	599.699i	−0.954661	+	0.796412i
$754$	−363.629	+	305.121i	−0.482267	+	0.404670i
$755$			1276.51i			1.69075i
$756$	21.3200	−	12.0663i	0.0282011	−	0.0159607i
$757$	1369.68			1.80935			0.904675	−	0.426102i	$-0.140114\pi$
$757$	1369.68			1.80935			0.904675	+	0.426102i	$0.140114\pi$
$758$	−33.6933	−	40.1541i	−0.0444503	−	0.0529738i
$759$	−211.197	+	575.133i	−0.278257	+	0.757752i
$760$	1.58009	−	8.96114i	0.00207907	−	0.0117910i
$761$	−18.9789	−	52.1440i	−0.0249394	−	0.0685204i	0.926598	−	0.376053i	$-0.122719\pi$
$761$	−18.9789	−	52.1440i	−0.0249394	−	0.0685204i	−0.951538	+	0.307533i	$0.900497\pi$
$762$	−8.22567	+	45.8821i	−0.0107948	+	0.0602128i
$763$	−11.0416	−	62.6198i	−0.0144712	−	0.0820705i
$764$	221.174	−	127.695i	0.289494	−	0.167140i
$765$	395.518	+	2320.67i	0.517018	+	3.03355i
$766$	287.551	−	498.054i	0.375393	−	0.650200i
$767$	241.246	−	662.817i	0.314531	−	0.864168i
$768$	−41.5004	−	24.1188i	−0.0540370	−	0.0314047i
$769$	−859.169	−	720.928i	−1.11725	−	0.937488i	−0.118792	−	0.992919i	$-0.537902\pi$
$769$	−859.169	−	720.928i	−1.11725	−	0.937488i	−0.998463	+	0.0554311i	$0.982347\pi$
$770$	−46.1359	+	54.9826i	−0.0599168	+	0.0714060i
$771$	79.3958	−	136.613i	0.102978	−	0.177190i
$772$	187.377	+	68.1996i	0.242716	+	0.0883415i
$773$	−126.972	−	73.3074i	−0.164259	−	0.0948349i	0.415617	−	0.909540i	$-0.363566\pi$
$773$	−126.972	−	73.3074i	−0.164259	−	0.0948349i	−0.579876	+	0.814705i	$0.696899\pi$
$774$	−145.841	−	175.840i	−0.188425	−	0.227183i
$775$	473.709	+	820.489i	0.611238	+	1.05870i
$776$	156.579	−	27.6092i	0.201778	−	0.0355788i
$777$	−10.3011	−	1.84677i	−0.0132575	−	0.00237679i
$778$	−206.988	+	75.3373i	−0.266051	+	0.0968346i
$779$	−9.89901	−	1.74546i	−0.0127073	−	0.00224065i
$780$	−571.882	−	210.003i	−0.733182	−	0.269234i
$781$	−1180.42	+	990.488i	−1.51142	+	1.26823i
$782$			675.296i			0.863550i
$783$	663.174	+	247.842i	0.846965	+	0.316529i
$784$	−195.177			−0.248950
$785$	−394.099	−	469.669i	−0.502037	−	0.598305i
$786$	−101.863	−	122.104i	−0.129597	−	0.155348i
$787$	−249.810	+	1416.74i	−0.317420	+	1.80018i	0.240896	+	0.970551i	$0.422559\pi$
$787$	−249.810	+	1416.74i	−0.317420	+	1.80018i	−0.558317	+	0.829628i	$0.688553\pi$
$788$	−26.0551	−	71.5857i	−0.0330648	−	0.0908448i
$789$	45.2505	−	16.3234i	0.0573517	−	0.0206887i
$790$	−37.5150	−	212.758i	−0.0474873	−	0.269314i
$791$	28.6460	−	16.5388i	0.0362150	−	0.0209087i
$792$	177.731	+	311.948i	0.224408	+	0.393873i
$793$	−669.943	+	1160.38i	−0.844821	+	1.46327i
$794$	197.074	−	541.456i	0.248204	−	0.681935i
$795$	−5.39701	+	3.09541i	−0.00678869	+	0.00389360i
$796$	−590.521	−	495.506i	−0.741861	−	0.622495i
$797$	−866.974	+	1033.22i	−1.08780	+	1.29639i	−0.135646	+	0.990757i	$0.543311\pi$
$797$	−866.974	+	1033.22i	−1.08780	+	1.29639i	−0.952151	+	0.305629i	$0.901133\pi$
$798$	0.780633	+	0.00223338i	0.000978237	+	2.79873e-6i
$799$	−1470.99	−	535.396i	−1.84104	−	0.670083i
$800$	185.758	+	107.247i	0.232197	+	0.134059i
$801$	603.883	−	711.373i	0.753911	−	0.888106i
$802$	−41.0568	−	71.1125i	−0.0511931	−	0.0886690i
$803$	874.225	−	154.149i	1.08870	−	0.191967i
$804$	−250.026	+	296.243i	−0.310977	+	0.368462i
$805$	−48.9645	+	17.8216i	−0.0608255	+	0.0221387i
$806$	−445.456	−	78.5459i	−0.552675	−	0.0974515i
$807$	−119.854	−	691.283i	−0.148518	−	0.856609i
$808$	97.4483	−	81.7688i	0.120604	−	0.101199i
$809$		−	596.082i		−	0.736813i	−0.929665	−	0.368407i	$-0.879903\pi$
$809$		−	596.082i		−	0.736813i	0.929665	−	0.368407i	$-0.120097\pi$
$810$	147.531	+	896.571i	0.182137	+	1.10688i
$811$	−304.801			−0.375833			−0.187917	−	0.982185i	$-0.560173\pi$
$811$	−304.801			−0.375833			−0.187917	+	0.982185i	$0.560173\pi$
$812$	15.2926	+	18.2250i	0.0188333	+	0.0224446i
$813$	679.485	−	117.808i	0.835775	−	0.144905i
$814$	26.6332	−	151.044i	0.0327189	−	0.185558i
$815$	−5.80815	−	15.9578i	−0.00712656	−	0.0195801i
$816$	302.407	+	255.227i	0.370597	+	0.312779i
$817$	−1.26410	−	7.16909i	−0.00154725	−	0.00877490i
$818$	354.485	−	204.662i	0.433355	−	0.250198i
$819$	9.37011	−	51.4183i	0.0114409	−	0.0627818i
$820$	196.583	−	340.492i	0.239735	−	0.415234i
$821$	−226.613	+	622.615i	−0.276021	+	0.758362i	0.721782	+	0.692120i	$0.243323\pi$
$821$	−226.613	+	622.615i	−0.276021	+	0.758362i	−0.997804	+	0.0662419i	$0.978899\pi$
$822$	−0.513801	+	179.589i	−0.000625062	+	0.218478i
$823$	837.373	+	702.639i	1.01746	+	0.853753i	0.989307	−	0.145850i	$-0.0465918\pi$
$823$	837.373	+	702.639i	1.01746	+	0.853753i	0.0281569	+	0.999604i	$0.491036\pi$
$824$	−165.698	+	197.472i	−0.201090	+	0.239650i
$825$	−798.200	−	1391.70i	−0.967515	−	1.68691i
$826$	−33.2203	−	12.0912i	−0.0402182	−	0.0146382i
$827$	876.396	+	505.987i	1.05973	+	0.611835i	0.925357	−	0.379096i	$-0.123765\pi$
$827$	876.396	+	505.987i	1.05973	+	0.611835i	0.134372	+	0.990931i	$0.457098\pi$
$828$	−1.49139	+	260.641i	−0.00180120	+	0.314784i
$829$	482.406	+	835.551i	0.581913	+	1.00790i	0.995253	+	0.0973256i	$0.0310288\pi$
$829$	482.406	+	835.551i	0.581913	+	1.00790i	−0.413340	+	0.910577i	$0.635638\pi$
$830$	−631.120	+	111.283i	−0.760385	+	0.134076i
$831$	−267.774	−	742.305i	−0.322231	−	0.893267i
$832$	−96.2306	+	35.0251i	−0.115662	+	0.0420975i
$833$	1584.61	+	279.409i	1.90229	+	0.335425i
$834$	530.856	−	442.860i	0.636519	−	0.531007i
$835$	−545.405	+	457.649i	−0.653179	+	0.548083i
$836$			11.4406i			0.0136849i
$837$	225.287	+	635.900i	0.269160	+	0.759737i
$838$	950.584			1.13435
$839$	−641.845	−	764.921i	−0.765012	−	0.911705i	0.233142	−	0.972443i	$-0.425099\pi$
$839$	−641.845	−	764.921i	−0.765012	−	0.911705i	−0.998154	+	0.0607373i	$0.980655\pi$
$840$	−10.5253	+	28.6626i	−0.0125301	+	0.0341222i
$841$	26.6461	−	151.117i	0.0316838	−	0.179688i
$842$	108.657	+	298.534i	0.129047	+	0.354553i
$843$	260.767	−	1454.54i	0.309332	−	1.72543i
$844$	118.497	+	672.029i	0.140399	+	0.796243i
$845$	35.3035	−	20.3825i	0.0417793	−	0.0241213i
$846$	−566.569	−	209.893i	−0.669703	−	0.248101i
$847$	17.6745	−	30.6131i	0.0208671	−	0.0361430i
$848$	−0.357694	+	0.982756i	−0.000421809	+	0.00115891i
$849$	1270.86	+	738.588i	1.49689	+	0.869951i
$850$	−1354.60	−	1136.65i	−1.59365	−	1.33723i
$851$	71.5723	−	85.2965i	0.0841037	−	0.100231i
$852$	−329.389	+	566.768i	−0.386607	+	0.665221i
$853$	−1055.33	−	384.107i	−1.23719	−	0.450301i	−0.361138	−	0.932513i	$-0.617612\pi$
$853$	−1055.33	−	384.107i	−1.23719	−	0.450301i	−0.876055	+	0.482211i	$0.839834\pi$
$854$	58.1578	+	33.5774i	0.0681005	+	0.0393178i
$855$	−10.0584	+	27.1508i	−0.0117642	+	0.0317553i
$856$	−291.398	−	504.716i	−0.340418	−	0.589621i
$857$	385.076	−	67.8994i	0.449331	−	0.0792291i	0.0555962	−	0.998453i	$-0.482294\pi$
$857$	385.076	−	67.8994i	0.449331	−	0.0792291i	0.393735	+	0.919224i	$0.371183\pi$
$858$	753.950	+	135.167i	0.878730	+	0.157537i
$859$	1362.58	−	495.937i	1.58624	−	0.577343i	0.609688	−	0.792642i	$-0.291295\pi$
$859$	1362.58	−	495.937i	1.58624	−	0.577343i	0.976548	+	0.215299i	$0.0690726\pi$
$860$	280.414	+	49.4446i	0.326063	+	0.0574937i
$861$	31.6625	+	11.6269i	0.0367741	+	0.0135039i
$862$	−205.059	+	172.065i	−0.237888	+	0.199612i
$863$		−	953.368i		−	1.10471i	−0.833608	−	0.552357i	$-0.813729\pi$
$863$		−	953.368i		−	1.10471i	0.833608	−	0.552357i	$-0.186271\pi$
$864$	116.155	+	99.1768i	0.134439	+	0.114788i
$865$	−1446.43			−1.67217
$866$	−331.686	−	395.288i	−0.383009	−	0.456453i
$867$	−1534.42	−	1839.31i	−1.76980	−	2.12147i
$868$	−3.93671	+	22.3262i	−0.00453538	+	0.0257214i
$869$	92.9017	+	255.245i	0.106906	+	0.293723i
$870$	−830.063	+	299.432i	−0.954095	+	0.344174i
$871$	143.614	+	814.475i	0.164884	+	0.935104i
$872$	343.324	−	198.218i	0.393720	−	0.227314i
$873$	−505.910	−	2.89483i	−0.579508	−	0.00331596i
$874$	−4.15282	+	7.19290i	−0.00475151	+	0.00822986i
$875$	15.8984	−	43.6805i	0.0181696	−	0.0499205i
$876$	327.590	−	187.886i	0.373961	−	0.214482i
$877$	−949.180	−	796.456i	−1.08230	−	0.908160i	−0.0861931	−	0.996278i	$-0.527470\pi$
$877$	−949.180	−	796.456i	−1.08230	−	0.908160i	−0.996110	+	0.0881183i	$0.971915\pi$
$878$	−385.513	+	459.437i	−0.439081	+	0.523277i
$879$	456.800	+	1.30690i	0.519681	+	0.00148680i
$880$	−420.504	−	153.051i	−0.477846	−	0.173922i
$881$	−43.1058	−	24.8871i	−0.0489282	−	0.0282487i	0.475336	−	0.879804i	$-0.342326\pi$
$881$	−43.1058	−	24.8871i	−0.0489282	−	0.0282487i	−0.524265	+	0.851555i	$0.675660\pi$
$882$	610.986	+	111.342i	0.692728	+	0.126238i
$883$	214.961	+	372.324i	0.243444	+	0.421658i	0.961693	−	0.274128i	$-0.0883893\pi$
$883$	214.961	+	372.324i	0.243444	+	0.421658i	−0.718249	+	0.695787i	$0.755056\pi$
$884$	831.421	−	146.602i	0.940521	−	0.165839i
$885$	845.711	−	1002.04i	0.955605	−	1.13225i
$886$	238.913	−	86.9572i	0.269653	−	0.0981458i
$887$	−611.223	−	107.775i	−0.689091	−	0.121505i	−0.181871	−	0.983322i	$-0.558215\pi$
$887$	−611.223	−	107.775i	−0.689091	−	0.121505i	−0.507219	+	0.861817i	$0.669327\pi$
$888$	−11.1463	−	64.2887i	−0.0125521	−	0.0723972i
$889$	3.81824	−	3.20388i	0.00429498	−	0.00360391i
$890$			1163.05i			1.30680i
$891$	−378.418	−	1077.92i	−0.424711	−	1.20979i
$892$	116.951			0.131111
$893$	−12.3757	−	14.7488i	−0.0138586	−	0.0165160i
$894$	−750.610	+	130.140i	−0.839609	+	0.145570i
$895$	165.460	−	938.368i	0.184871	−	1.04846i
$896$	1.75545	+	4.82306i	0.00195921	+	0.00538288i
$897$	424.957	+	358.658i	0.473753	+	0.399841i
$898$	158.268	+	897.582i	0.176245	+	0.999534i
$899$	−567.393	+	327.585i	−0.631138	+	0.364388i
$900$	−520.320	−	441.698i	−0.578133	−	0.490776i
$901$	4.31094	−	7.46677i	0.00478462	−	0.00828720i
$902$	−169.069	+	464.514i	−0.187438	+	0.514982i
$903$	−0.0698876	+	24.4278i	−7.73949e−5	+	0.0270518i
$904$	157.980	+	132.561i	0.174756	+	0.146638i
$905$	815.708	−	972.123i	0.901334	−	1.07417i
$906$	−339.692	−	592.271i	−0.374937	−	0.653721i
$907$	1623.70	+	590.977i	1.79018	+	0.651573i	0.999211	+	0.0397211i	$0.0126470\pi$
$907$	1623.70	+	590.977i	1.79018	+	0.651573i	0.790972	+	0.611852i	$0.209575\pi$
$908$	72.7438	+	41.9987i	0.0801143	+	0.0462540i
$909$	−351.701	+	200.380i	−0.386910	+	0.220440i
$910$	32.5717	+	56.4159i	0.0357931	+	0.0619955i
$911$	−633.504	+	111.704i	−0.695394	+	0.122617i	−0.510162	−	0.860078i	$-0.670415\pi$
$911$	−633.504	+	111.704i	−0.695394	+	0.122617i	−0.185231	+	0.982695i	$0.559303\pi$
$912$	1.65152	+	4.57823i	0.00181088	+	0.00501999i
$913$	757.153	−	275.581i	0.829302	−	0.301841i
$914$	361.629	+	63.7649i	0.395655	+	0.0697647i
$915$	−1912.63	+	1595.59i	−2.09031	+	1.74381i
$916$	−136.371	+	114.429i	−0.148877	+	0.124923i
$917$			17.0032i			0.0185422i
$918$	−801.064	−	971.483i	−0.872618	−	1.05826i
$919$	436.696			0.475186			0.237593	−	0.971365i	$-0.423642\pi$
$919$	436.696			0.475186			0.237593	+	0.971365i	$0.423642\pi$
$920$	−208.822	−	248.864i	−0.226980	−	0.270505i
$921$	315.824	−	860.054i	0.342914	−	0.933827i
$922$	−119.585	+	678.199i	−0.129702	+	0.735574i
$923$	478.335	+	1314.22i	0.518240	+	1.42385i
$924$	6.77455	−	37.7879i	0.00733176	−	0.0408959i
$925$	50.6304	+	287.139i	0.0547356	+	0.310421i
$926$	734.259	−	423.925i	0.792937	−	0.457802i
$927$	631.357	−	523.645i	0.681076	−	0.564881i
$928$	−74.1648	+	128.457i	−0.0799189	+	0.138424i
$929$	−537.202	+	1475.95i	−0.578258	+	1.58875i	0.212856	+	0.977084i	$0.431723\pi$
$929$	−537.202	+	1475.95i	−0.578258	+	1.58875i	−0.791115	+	0.611668i	$0.790499\pi$
$930$	−727.000	−	422.511i	−0.781720	−	0.454313i
$931$	15.1601	+	12.7209i	0.0162837	+	0.0136636i
$932$	−180.542	+	215.162i	−0.193715	+	0.230860i
$933$	533.397	−	917.797i	0.571701	−	0.983705i
$934$	−846.336	−	308.041i	−0.906141	−	0.329808i
$935$	3194.90	+	1844.58i	3.41700	+	1.97281i
$936$	321.223	−	54.7471i	0.343187	−	0.0584905i
$937$	−492.267	−	852.632i	−0.525366	−	0.909960i	−0.999564	−	0.0295416i	$-0.990595\pi$
$937$	−492.267	−	852.632i	−0.525366	−	0.909960i	0.474198	−	0.880418i	$-0.342738\pi$
$938$	40.8214	−	7.19791i	0.0435196	−	0.00767368i
$939$	343.000	+	61.4925i	0.365282	+	0.0654872i
$940$	707.659	−	257.567i	0.752828	−	0.274007i
$941$	−202.540	−	35.7132i	−0.215239	−	0.0379524i	0.0649887	−	0.997886i	$-0.479299\pi$
$941$	−202.540	−	35.7132i	−0.215239	−	0.0379524i	−0.280228	+	0.959934i	$0.590410\pi$
$942$	307.836	+	113.042i	0.326790	+	0.120002i
$943$	−274.910	+	230.677i	−0.291527	+	0.244621i
$944$		−	220.410i		−	0.233485i
$945$	49.2998	−	83.7219i	0.0521691	−	0.0885946i
$946$	−358.002			−0.378438
$947$	−401.343	−	478.302i	−0.423804	−	0.505070i	0.511320	−	0.859391i	$-0.329157\pi$
$947$	−401.343	−	478.302i	−0.423804	−	0.505070i	−0.935124	+	0.354320i	$0.884712\pi$
$948$	74.0231	+	88.7316i	0.0780834	+	0.0935987i
$949$	139.908	−	793.455i	0.147426	−	0.836096i
$950$	−7.43856	−	20.4373i	−0.00783006	−	0.0215129i
$951$	−641.191	+	231.299i	−0.674228	+	0.243217i
$952$	−7.34766	−	41.6707i	−0.00771813	−	0.0437717i
$953$	593.317	−	342.552i	0.622578	−	0.359445i	−0.155294	−	0.987868i	$-0.549633\pi$
$953$	593.317	−	342.552i	0.622578	−	0.359445i	0.777872	+	0.628423i	$0.216299\pi$
$954$	1.68036	−	2.87239i	0.00176139	−	0.00301090i
$955$	506.441	−	877.181i	0.530304	−	0.918514i
$956$	19.8738	−	54.6029i	0.0207885	−	0.0571160i
$957$	962.405	−	551.980i	1.00565	−	0.576781i
$958$	432.425	+	362.847i	0.451383	+	0.378755i
$959$	12.3437	−	14.7106i	0.0128714	−	0.0153395i
$960$	−190.369	−	0.544643i	−0.198301	−	0.000567336i
$961$	316.383	+	115.154i	0.329223	+	0.119827i
$962$	−120.554	−	69.6021i	−0.125316	−	0.0723515i
$963$	624.276	+	1746.21i	0.648261	+	1.81330i
$964$	−148.449	−	257.121i	−0.153993	−	0.266723i
$965$	778.822	−	137.327i	0.807069	−	0.142308i
$966$	17.9759	−	21.2987i	0.0186086	−	0.0220484i
$967$	−665.140	+	242.091i	−0.687839	+	0.250353i	−0.662210	−	0.749319i	$-0.730381\pi$
$967$	−665.140	+	242.091i	−0.687839	+	0.250353i	−0.0256294	+	0.999672i	$0.508159\pi$
$968$	217.041	+	38.2701i	0.224215	+	0.0395352i
$969$	−6.85438	−	39.5342i	−0.00707366	−	0.0407989i
$970$	483.051	−	405.328i	0.497991	−	0.417864i
$971$		−	1276.82i		−	1.31496i	−0.753473	−	0.657479i	$-0.771623\pi$
$971$		−	1276.82i		−	1.31496i	0.753473	−	0.657479i	$-0.228377\pi$
$972$	−307.037	−	376.728i	−0.315882	−	0.387580i
$973$	−73.9230			−0.0759743
$974$	−345.089	−	411.261i	−0.354300	−	0.422239i
$975$	−1434.73	+	248.751i	−1.47151	+	0.255129i
$976$	−72.7044	+	412.327i	−0.0744922	+	0.422466i
$977$	−552.252	−	1517.30i	−0.565252	−	1.55302i	−0.811829	−	0.583895i	$-0.801528\pi$
$977$	−552.252	−	1517.30i	−0.565252	−	1.55302i	0.246577	−	0.969123i	$-0.420694\pi$
$978$	6.94136	+	5.85842i	0.00709750	+	0.00599020i
$979$	−253.926	−	1440.08i	−0.259373	−	1.47098i
$980$	−670.371	+	387.039i	−0.684052	+	0.394937i
$981$	−1187.83	+	424.652i	−1.21083	+	0.432877i
$982$	−423.193	+	732.993i	−0.430951	+	0.746428i
$983$	−308.388	+	847.290i	−0.313721	+	0.861943i	0.678176	+	0.734900i	$0.262771\pi$
$983$	−308.388	+	847.290i	−0.313721	+	0.861943i	−0.991897	+	0.127043i	$0.959451\pi$
$984$	−0.601645	+	210.293i	−0.000611428	+	0.213712i
$985$	−231.447	−	194.207i	−0.234971	−	0.197164i
$986$	786.026	−	936.750i	0.797187	−	0.950050i
$987$	32.1430	+	56.0429i	0.0325663	+	0.0567811i
$988$	9.75740	+	3.55140i	0.00987591	+	0.00359454i
$989$	−225.082	−	129.951i	−0.227585	−	0.131396i
$990$	1229.05	+	718.999i	1.24146	+	0.726261i
$991$	442.929	+	767.176i	0.446952	+	0.774143i	0.998186	−	0.0602077i	$-0.0191763\pi$
$991$	442.929	+	767.176i	0.446952	+	0.774143i	−0.551234	+	0.834350i	$0.685843\pi$
$992$	−139.196	+	24.5440i	−0.140319	+	0.0247420i
$993$	95.8974	+	265.840i	0.0965734	+	0.267714i
$994$	65.8683	−	23.9741i	0.0662658	−	0.0241188i
$995$	−3010.85	−	530.894i	−3.02598	−	0.533562i
$996$	263.211	−	219.580i	0.264268	−	0.220462i
$997$	−962.201	+	807.383i	−0.965097	+	0.809812i	−0.981775	−	0.190049i	$-0.939135\pi$
$997$	−962.201	+	807.383i	−0.965097	+	0.809812i	0.0166779	+	0.999861i	$0.494691\pi$
$998$		−	65.4951i		−	0.0656264i
$999$	−1.78195	+	207.610i	−0.00178373	+	0.207818i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.3.f.a.5.4	✓	36
3.2	odd	2		162.3.f.a.125.1		36
4.3	odd	2		432.3.bc.c.113.6		36
27.4	even	9		1458.3.b.c.1457.20		36
27.11	odd	18	inner	54.3.f.a.11.4	yes	36
27.16	even	9		162.3.f.a.35.1		36
27.23	odd	18		1458.3.b.c.1457.17		36
108.11	even	18		432.3.bc.c.65.6		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.3.f.a.5.4	✓	36	1.1	even	1	trivial
54.3.f.a.11.4	yes	36	27.11	odd	18	inner
162.3.f.a.35.1		36	27.16	even	9
162.3.f.a.125.1		36	3.2	odd	2
432.3.bc.c.65.6		36	108.11	even	18
432.3.bc.c.113.6		36	4.3	odd	2
1458.3.b.c.1457.17		36	27.23	odd	18
1458.3.b.c.1457.20		36	27.4	even	9

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	54.3.f.a.5.4

Level	$54$
Weight	$3$
Character	54.5
Analytic conductor	$1.471$
Analytic rank	$0$
Dimension	$36$
Inner twists	$2$