LMFDB - Embedded newform 27.4.e.a.13.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [27,4,Mod(4,27)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("27.4"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(27, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	27.e (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.59305157015$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			13.7
Character	$\chi$	$=$	27.13
Dual form			27.4.e.a.25.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.640527 + 3.63261i) q^{2} +(5.12390 - 0.863506i) q^{3} +(-5.26804 + 1.91741i) q^{4} +(-1.23763 - 1.03850i) q^{5} +(6.41878 + 18.0600i) q^{6} +(-31.9169 - 11.6168i) q^{7} +(4.41508 + 7.64714i) q^{8} +(25.5087 - 8.84904i) q^{9} +(2.97972 - 5.16102i) q^{10} +(18.8740 - 15.8372i) q^{11} +(-25.3372 + 14.3736i) q^{12} +(5.35351 - 30.3613i) q^{13} +(21.7557 - 123.382i) q^{14} +(-7.23826 - 4.25245i) q^{15} +(-59.3074 + 49.7648i) q^{16} +(-18.2417 + 31.5955i) q^{17} +(48.4841 + 86.9951i) q^{18} +(36.5170 + 63.2494i) q^{19} +(8.51112 + 3.09779i) q^{20} +(-173.570 - 31.9629i) q^{21} +(69.6196 + 58.4178i) q^{22} +(-62.9523 + 22.9128i) q^{23} +(29.2258 + 35.3707i) q^{24} +(-21.2528 - 120.530i) q^{25} +113.720 q^{26} +(123.063 - 67.3685i) q^{27} +190.413 q^{28} +(41.0688 + 232.913i) q^{29} +(10.8112 - 29.0176i) q^{30} +(-152.414 + 55.4740i) q^{31} +(-164.650 - 138.158i) q^{32} +(83.0331 - 97.4460i) q^{33} +(-126.458 - 46.0271i) q^{34} +(27.4374 + 47.5229i) q^{35} +(-117.414 + 95.5277i) q^{36} +(93.1046 - 161.262i) q^{37} +(-206.370 + 173.165i) q^{38} +(1.21372 - 160.191i) q^{39} +(2.47729 - 14.0494i) q^{40} +(-37.9265 + 215.092i) q^{41} +(4.93231 - 650.986i) q^{42} +(156.989 - 131.730i) q^{43} +(-69.0627 + 119.620i) q^{44} +(-40.7601 - 15.5389i) q^{45} +(-123.556 - 214.005i) q^{46} +(-450.185 - 163.854i) q^{47} +(-260.913 + 306.202i) q^{48} +(620.985 + 521.068i) q^{49} +(424.227 - 154.406i) q^{50} +(-66.1855 + 177.644i) q^{51} +(30.0125 + 170.209i) q^{52} +736.254 q^{53} +(323.549 + 403.888i) q^{54} -39.8060 q^{55} +(-52.0803 - 295.362i) q^{56} +(241.726 + 292.551i) q^{57} +(-819.775 + 298.374i) q^{58} +(39.2313 + 32.9190i) q^{59} +(46.2851 + 8.52338i) q^{60} +(108.686 + 39.5585i) q^{61} +(-299.141 - 518.127i) q^{62} +(-916.956 - 13.8958i) q^{63} +(86.7288 - 150.219i) q^{64} +(-38.1558 + 32.0165i) q^{65} +(407.168 + 239.210i) q^{66} +(20.2242 - 114.697i) q^{67} +(35.5163 - 201.423i) q^{68} +(-302.776 + 171.763i) q^{69} +(-155.058 + 130.109i) q^{70} +(118.488 - 205.227i) q^{71} +(180.293 + 156.000i) q^{72} +(-23.0477 - 39.9198i) q^{73} +(645.437 + 234.920i) q^{74} +(-212.976 - 599.234i) q^{75} +(-313.648 - 263.182i) q^{76} +(-786.377 + 286.218i) q^{77} +(582.689 - 98.1977i) q^{78} +(-130.778 - 741.681i) q^{79} +125.081 q^{80} +(572.389 - 451.455i) q^{81} -805.637 q^{82} +(-59.3213 - 336.428i) q^{83} +(975.660 - 164.423i) q^{84} +(55.3883 - 20.1597i) q^{85} +(579.078 + 485.904i) q^{86} +(411.554 + 1157.96i) q^{87} +(204.439 + 74.4099i) q^{88} +(-455.636 - 789.185i) q^{89} +(30.3387 - 158.019i) q^{90} +(-523.568 + 906.847i) q^{91} +(287.702 - 241.411i) q^{92} +(-733.050 + 415.854i) q^{93} +(306.862 - 1740.30i) q^{94} +(20.4896 - 116.202i) q^{95} +(-962.950 - 565.730i) q^{96} +(-37.6866 + 31.6228i) q^{97} +(-1495.08 + 2589.55i) q^{98} +(341.308 - 571.003i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9} - 3 q^{10} + 57 q^{11} + 147 q^{12} - 6 q^{13} + 51 q^{14} - 36 q^{15} + 18 q^{16} - 207 q^{17} - 639 q^{18} - 3 q^{19}+ \cdots - 1242 q^{99}+O(q^{100}) $ 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9 - 3 * q^10 + 57 * q^11 + 147 * q^12 - 6 * q^13 + 51 * q^14 - 36 * q^15 + 18 * q^16 - 207 * q^17 - 639 * q^18 - 3 * q^19 - 597 * q^20 - 138 * q^21 - 60 * q^22 + 402 * q^23 + 1170 * q^24 - 222 * q^25 + 1914 * q^26 + 1125 * q^27 - 12 * q^28 + 480 * q^29 + 459 * q^30 - 60 * q^31 - 648 * q^32 - 639 * q^33 + 288 * q^34 - 1257 * q^35 - 2088 * q^36 - 3 * q^37 - 1524 * q^38 - 768 * q^39 + 561 * q^40 - 1731 * q^41 - 3078 * q^42 + 507 * q^43 - 2211 * q^44 - 360 * q^45 - 3 * q^46 + 984 * q^47 + 2289 * q^48 - 600 * q^49 + 4359 * q^50 + 2655 * q^51 - 1431 * q^52 + 2736 * q^53 + 5454 * q^54 - 12 * q^55 + 5907 * q^56 + 3426 * q^57 - 897 * q^58 + 2238 * q^59 + 1314 * q^60 + 48 * q^61 - 2118 * q^62 - 2610 * q^63 - 195 * q^64 - 6990 * q^65 - 11115 * q^66 - 681 * q^67 - 11169 * q^68 - 6138 * q^69 - 33 * q^70 - 3105 * q^71 - 36 * q^72 - 219 * q^73 + 3543 * q^74 + 2604 * q^75 + 3426 * q^76 + 4722 * q^77 + 6066 * q^78 + 2802 * q^79 + 9870 * q^80 + 3438 * q^81 - 12 * q^82 + 3468 * q^83 + 7674 * q^84 + 2529 * q^85 + 3624 * q^86 + 2880 * q^87 + 2850 * q^88 - 5202 * q^89 - 12510 * q^90 + 267 * q^91 - 18453 * q^92 - 11802 * q^93 - 1653 * q^94 - 10113 * q^95 - 14094 * q^96 - 3381 * q^97 - 4392 * q^98 - 1242 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.640527	+	3.63261i	0.226461	+	1.28432i	0.859873	+	0.510507i	$0.170542\pi$
$2$	0.640527	+	3.63261i	0.226461	+	1.28432i	−0.633413	+	0.773814i	$0.718346\pi$
$3$	5.12390	−	0.863506i	0.986095	−	0.166182i
$3$	5.12390	−	0.863506i	0.986095	−	0.166182i
$4$	−5.26804	+	1.91741i	−0.658504	+	0.239676i
$5$	−1.23763	−	1.03850i	−0.110697	−	0.0928860i	0.585759	−	0.810485i	$-0.300797\pi$
$5$	−1.23763	−	1.03850i	−0.110697	−	0.0928860i	−0.696456	+	0.717599i	$0.745241\pi$
$6$	6.41878	+	18.0600i	0.436742	+	1.22883i
$7$	−31.9169	−	11.6168i	−1.72335	−	0.627248i	−0.725228	−	0.688508i	$-0.758266\pi$
$7$	−31.9169	−	11.6168i	−1.72335	−	0.627248i	−0.998122	+	0.0612602i	$0.980488\pi$
$8$	4.41508	+	7.64714i	0.195121	+	0.337959i
$9$	25.5087	−	8.84904i	0.944767	−	0.327742i
$10$	2.97972	−	5.16102i	0.0942269	−	0.163206i
$11$	18.8740	−	15.8372i	0.517339	−	0.434099i	−0.346364	−	0.938100i	$-0.612584\pi$
$11$	18.8740	−	15.8372i	0.517339	−	0.434099i	0.863703	+	0.504001i	$0.168139\pi$
$12$	−25.3372	+	14.3736i	−0.609518	+	0.345775i
$13$	5.35351	−	30.3613i	0.114215	−	0.647746i	−0.872921	−	0.487862i	$-0.837777\pi$
$13$	5.35351	−	30.3613i	0.114215	−	0.647746i	0.987136	−	0.159884i	$-0.0511121\pi$
$14$	21.7557	−	123.382i	0.415317	−	2.35538i
$15$	−7.23826	−	4.25245i	−0.124594	−	0.0731986i
$16$	−59.3074	+	49.7648i	−0.926679	+	0.777576i
$17$	−18.2417	+	31.5955i	−0.260250	+	0.450766i	−0.966308	−	0.257387i	$-0.917138\pi$
$17$	−18.2417	+	31.5955i	−0.260250	+	0.450766i	0.706058	+	0.708154i	$0.250472\pi$
$18$	48.4841	+	86.9951i	0.634879	+	1.13916i
$19$	36.5170	+	63.2494i	0.440925	+	0.763705i	0.997758	−	0.0669192i	$-0.0213170\pi$
$19$	36.5170	+	63.2494i	0.440925	+	0.763705i	−0.556833	+	0.830625i	$0.687984\pi$
$20$	8.51112	+	3.09779i	0.0951572	+	0.0346344i
$21$	−173.570	−	31.9629i	−1.80362	−	0.332137i
$22$	69.6196	+	58.4178i	0.674680	+	0.566124i
$23$	−62.9523	+	22.9128i	−0.570716	+	0.207724i	−0.611227	−	0.791455i	$-0.709324\pi$
$23$	−62.9523	+	22.9128i	−0.570716	+	0.207724i	0.0405108	+	0.999179i	$0.487101\pi$
$24$	29.2258	+	35.3707i	0.248570	+	0.300834i
$25$	−21.2528	−	120.530i	−0.170022	−	0.964243i
$26$	113.720			0.857780
$27$	123.063	−	67.3685i	0.877166	−	0.480188i
$28$	190.413			1.28517
$29$	41.0688	+	232.913i	0.262975	+	1.49141i	0.774739	+	0.632281i	$0.217881\pi$
$29$	41.0688	+	232.913i	0.262975	+	1.49141i	−0.511764	+	0.859126i	$0.671008\pi$
$30$	10.8112	−	29.0176i	0.0657949	−	0.176595i
$31$	−152.414	+	55.4740i	−0.883042	+	0.321401i	−0.743437	−	0.668806i	$-0.766806\pi$
$31$	−152.414	+	55.4740i	−0.883042	+	0.321401i	−0.139605	+	0.990207i	$0.544583\pi$
$32$	−164.650	−	138.158i	−0.909571	−	0.763221i
$33$	83.0331	−	97.4460i	0.438006	−	0.514035i
$34$	−126.458	−	46.0271i	−0.637865	−	0.232164i
$35$	27.4374	+	47.5229i	0.132508	+	0.229510i
$36$	−117.414	+	95.5277i	−0.543581	+	0.442258i
$37$	93.1046	−	161.262i	0.413684	−	0.716521i	−0.581605	−	0.813471i	$-0.697575\pi$
$37$	93.1046	−	161.262i	0.413684	−	0.716521i	0.995289	+	0.0969496i	$0.0309086\pi$
$38$	−206.370	+	173.165i	−0.880991	+	0.739239i
$39$	1.21372	−	160.191i	0.00498333	−	0.657720i
$40$	2.47729	−	14.0494i	0.00979234	−	0.0555351i
$41$	−37.9265	+	215.092i	−0.144466	+	0.819309i	0.823328	+	0.567566i	$0.192115\pi$
$41$	−37.9265	+	215.092i	−0.144466	+	0.819309i	−0.967794	+	0.251743i	$0.918996\pi$
$42$	4.93231	−	650.986i	0.0181208	−	2.39165i
$43$	156.989	−	131.730i	0.556759	−	0.467176i	−0.320463	−	0.947261i	$-0.603839\pi$
$43$	156.989	−	131.730i	0.556759	−	0.467176i	0.877222	+	0.480085i	$0.159394\pi$
$44$	−69.0627	+	119.620i	−0.236627	+	0.409850i
$45$	−40.7601	−	15.5389i	−0.135026	−	0.0514755i
$46$	−123.556	−	214.005i	−0.396029	−	0.685942i
$47$	−450.185	−	163.854i	−1.39715	−	0.508522i	−0.469821	−	0.882762i	$-0.655682\pi$
$47$	−450.185	−	163.854i	−1.39715	−	0.508522i	−0.927332	+	0.374239i	$0.877904\pi$
$48$	−260.913	+	306.202i	−0.784574	+	0.920761i
$49$	620.985	+	521.068i	1.81045	+	1.51915i
$50$	424.227	−	154.406i	1.19990	−	0.436726i
$51$	−66.1855	+	177.644i	−0.181722	+	0.487747i
$52$	30.0125	+	170.209i	0.0800381	+	0.453919i
$53$	736.254			1.90816			0.954078	−	0.299559i	$-0.0968396\pi$
$53$	736.254			1.90816			0.954078	+	0.299559i	$0.0968396\pi$
$54$	323.549	+	403.888i	0.815359	+	1.01782i
$55$	−39.8060			−0.0975898
$56$	−52.0803	−	295.362i	−0.124277	−	0.704811i
$57$	241.726	+	292.551i	0.561708	+	0.679812i
$58$	−819.775	+	298.374i	−1.85589	+	0.675490i
$59$	39.2313	+	32.9190i	0.0865675	+	0.0726387i	0.685044	−	0.728501i	$-0.259783\pi$
$59$	39.2313	+	32.9190i	0.0865675	+	0.0726387i	−0.598477	+	0.801140i	$0.704227\pi$
$60$	46.2851	+	8.52338i	0.0995896	+	0.0183394i
$61$	108.686	+	39.5585i	0.228128	+	0.0830319i	0.453555	−	0.891228i	$-0.350155\pi$
$61$	108.686	+	39.5585i	0.228128	+	0.0830319i	−0.225427	+	0.974260i	$0.572378\pi$
$62$	−299.141	−	518.127i	−0.612756	−	1.06133i
$63$	−916.956	−	13.8958i	−1.83374	−	0.0277889i
$64$	86.7288	−	150.219i	0.169392	−	0.293396i
$65$	−38.1558	+	32.0165i	−0.0728099	+	0.0610947i
$66$	407.168	+	239.210i	0.759378	+	0.446132i
$67$	20.2242	−	114.697i	0.0368773	−	0.209142i	−0.960801	−	0.277237i	$-0.910581\pi$
$67$	20.2242	−	114.697i	0.0368773	−	0.209142i	0.997679	+	0.0680957i	$0.0216923\pi$
$68$	35.5163	−	201.423i	0.0633380	−	0.359207i
$69$	−302.776	+	171.763i	−0.528260	+	0.299678i
$70$	−155.058	+	130.109i	−0.264757	+	0.222157i
$71$	118.488	−	205.227i	0.198055	−	0.343042i	−0.749843	−	0.661616i	$-0.769871\pi$
$71$	118.488	−	205.227i	0.198055	−	0.343042i	0.947898	+	0.318575i	$0.103204\pi$
$72$	180.293	+	156.000i	0.295107	+	0.255343i
$73$	−23.0477	−	39.9198i	−0.0369524	−	0.0640035i	0.846958	−	0.531660i	$-0.178432\pi$
$73$	−23.0477	−	39.9198i	−0.0369524	−	0.0640035i	−0.883910	+	0.467657i	$0.845098\pi$
$74$	645.437	+	234.920i	1.01393	+	0.369039i
$75$	−212.976	−	599.234i	−0.327898	−	0.922581i
$76$	−313.648	−	263.182i	−0.473393	−	0.397224i
$77$	−786.377	+	286.218i	−1.16384	+	0.423605i
$78$	582.689	−	98.1977i	0.845853	−	0.142547i
$79$	−130.778	−	741.681i	−0.186250	−	1.05627i	−0.924339	−	0.381572i	$-0.875383\pi$
$79$	−130.778	−	741.681i	−0.186250	−	1.05627i	0.738090	−	0.674703i	$-0.235728\pi$
$80$	125.081			0.174807
$81$	572.389	−	451.455i	0.785170	−	0.619280i
$82$	−805.637			−1.08497
$83$	−59.3213	−	336.428i	−0.0784501	−	0.444913i	−0.998579	−	0.0532963i	$-0.983027\pi$
$83$	−59.3213	−	336.428i	−0.0784501	−	0.444913i	0.920129	−	0.391616i	$-0.128084\pi$
$84$	975.660	−	164.423i	1.26730	−	0.213572i
$85$	55.3883	−	20.1597i	0.0706789	−	0.0257250i
$86$	579.078	+	485.904i	0.726088	+	0.609260i
$87$	411.554	+	1157.96i	0.507163	+	1.42697i
$88$	204.439	+	74.4099i	0.247651	+	0.0901377i
$89$	−455.636	−	789.185i	−0.542667	−	0.939926i	−0.998750	−	0.0499890i	$-0.984081\pi$
$89$	−455.636	−	789.185i	−0.542667	−	0.939926i	0.456083	−	0.889937i	$-0.349252\pi$
$90$	30.3387	−	158.019i	0.0355331	−	0.185074i
$91$	−523.568	+	906.847i	−0.603131	+	1.04465i
$92$	287.702	−	241.411i	0.326033	−	0.273574i
$93$	−733.050	+	415.854i	−0.817352	+	0.463678i
$94$	306.862	−	1740.30i	0.336706	−	1.90955i
$95$	20.4896	−	116.202i	0.0221283	−	0.125496i
$96$	−962.950	−	565.730i	−1.02376	−	0.601454i
$97$	−37.6866	+	31.6228i	−0.0394484	+	0.0331011i	−0.662299	−	0.749240i	$-0.730419\pi$
$97$	−37.6866	+	31.6228i	−0.0394484	+	0.0331011i	0.622850	+	0.782341i	$0.285975\pi$
$98$	−1495.08	+	2589.55i	−1.54108	+	2.66923i
$99$	341.308	−	571.003i	0.346493	−	0.579677i
$100$	343.066	+	594.208i	0.343066	+	0.594208i
$101$	1019.98	+	371.243i	1.00487	+	0.365743i	0.791461	−	0.611220i	$-0.209321\pi$
$101$	1019.98	+	371.243i	1.00487	+	0.365743i	0.213410	+	0.976963i	$0.431543\pi$
$102$	−687.704	−	126.641i	−0.667577	−	0.122934i
$103$	−436.880	−	366.586i	−0.417933	−	0.350687i	0.409443	−	0.912336i	$-0.365723\pi$
$103$	−436.880	−	366.586i	−0.417933	−	0.350687i	−0.827376	+	0.561648i	$0.810167\pi$
$104$	255.813	−	93.1084i	0.241198	−	0.0877887i
$105$	181.623	+	219.810i	0.168805	+	0.204298i
$106$	471.591	+	2674.52i	0.432122	+	2.45068i
$107$	−360.258			−0.325490			−0.162745	−	0.986668i	$-0.552035\pi$
$107$	−360.258			−0.325490			−0.162745	+	0.986668i	$0.552035\pi$
$108$	−519.127	+	590.862i	−0.462528	+	0.526442i
$109$	895.448			0.786866			0.393433	−	0.919353i	$-0.371287\pi$
$109$	895.448			0.786866			0.393433	+	0.919353i	$0.371287\pi$
$110$	−25.4968	−	144.600i	−0.0221002	−	0.125337i
$111$	337.808	−	906.686i	0.288859	−	0.775305i
$112$	2471.02	−	899.377i	2.08472	−	0.758778i
$113$	−41.0845	−	34.4740i	−0.0342027	−	0.0286995i	0.625526	−	0.780203i	$-0.284884\pi$
$113$	−41.0845	−	34.4740i	−0.0342027	−	0.0286995i	−0.659729	+	0.751504i	$0.729329\pi$
$114$	−907.891	+	1065.48i	−0.745893	+	0.875365i
$115$	101.707	+	37.0182i	0.0824713	+	0.0300171i
$116$	−662.941	−	1148.25i	−0.530625	−	0.919069i
$117$	−132.107	−	821.851i	−0.104387	−	0.649403i
$118$	−94.4530	+	163.597i	−0.0736874	+	0.127630i
$119$	949.255	−	796.520i	0.731244	−	0.613587i
$120$	0.561635	−	74.1269i	0.000427250	−	0.0563902i
$121$	−125.713	+	712.956i	−0.0944504	+	0.535655i
$122$	−74.0842	+	420.153i	−0.0549776	+	0.311794i
$123$	−8.59845	+	1134.86i	−0.00630322	+	0.831924i
$124$	696.554	−	584.478i	0.504455	−	0.423288i
$125$	−199.843	+	346.139i	−0.142996	+	0.247677i
$126$	−536.858	−	3339.85i	−0.379580	−	2.36141i
$127$	432.376	+	748.897i	0.302104	+	0.523259i	0.976612	−	0.215008i	$-0.0689778\pi$
$127$	432.376	+	748.897i	0.302104	+	0.523259i	−0.674509	+	0.738267i	$0.735644\pi$
$128$	−1014.55	−	369.265i	−0.700579	−	0.254990i
$129$	690.648	−	810.530i	0.471381	−	0.553203i
$130$	−140.743	−	118.098i	−0.0949539	−	0.0796757i
$131$	−522.721	+	190.255i	−0.348629	+	0.126891i	−0.510398	−	0.859938i	$-0.670502\pi$
$131$	−522.721	+	190.255i	−0.348629	+	0.126891i	0.161770	+	0.986829i	$0.448280\pi$
$132$	−250.578	+	672.557i	−0.165227	+	0.443474i
$133$	−430.755	−	2442.93i	−0.280836	−	1.59270i
$134$	429.604			0.276956
$135$	−222.269	−	44.4230i	−0.141703	−	0.0283209i
$136$	−322.153			−0.203121
$137$	150.903	+	855.811i	0.0941057	+	0.533700i	0.995018	+	0.0996981i	$0.0317877\pi$
$137$	150.903	+	855.811i	0.0941057	+	0.533700i	−0.900912	+	0.434002i	$0.857101\pi$
$138$	−817.882	−	989.849i	−0.504513	−	0.610591i
$139$	−871.640	+	317.251i	−0.531882	+	0.193589i	−0.593978	−	0.804481i	$-0.702444\pi$
$139$	−871.640	+	317.251i	−0.531882	+	0.193589i	0.0620966	+	0.998070i	$0.480221\pi$
$140$	−235.662	−	197.744i	−0.142265	−	0.119374i
$141$	−2448.19	−	450.834i	−1.46223	−	0.269270i
$142$	821.404	+	298.967i	0.485427	+	0.176681i
$143$	−379.795	−	657.824i	−0.222098	−	0.384685i
$144$	−1072.49	+	1794.25i	−0.620651	+	1.03834i
$145$	191.051	−	330.910i	0.109420	−	0.189521i
$146$	130.250	−	109.293i	0.0738328	−	0.0619531i
$147$	3631.81	+	2133.68i	2.03773	+	1.19716i
$148$	−181.273	+	1028.05i	−0.100680	+	0.570983i
$149$	−291.432	+	1652.79i	−0.160235	+	0.908739i	0.793607	+	0.608431i	$0.208201\pi$
$149$	−291.432	+	1652.79i	−0.160235	+	0.908739i	−0.953842	+	0.300309i	$0.902910\pi$
$150$	2040.37	−	1157.48i	1.11063	−	0.630054i
$151$	−1885.95	+	1582.50i	−1.01640	+	0.852861i	−0.989171	−	0.146768i	$-0.953113\pi$
$151$	−1885.95	+	1582.50i	−1.01640	+	0.852861i	−0.0272292	+	0.999629i	$0.508668\pi$
$152$	−322.451	+	558.502i	−0.172067	+	0.298030i
$153$	−185.732	+	967.381i	−0.0981406	+	0.511164i
$154$	−1543.41	−	2673.27i	−0.807609	−	1.39882i
$155$	246.242	+	89.6247i	0.127604	+	0.0464440i
$156$	300.758	+	846.219i	0.154358	+	0.434306i
$157$	−2134.05	−	1790.68i	−1.08481	−	0.910265i	−0.0884998	−	0.996076i	$-0.528207\pi$
$157$	−2134.05	−	1790.68i	−1.08481	−	0.910265i	−0.996311	+	0.0858116i	$0.972652\pi$
$158$	2610.47	−	950.134i	1.31442	−	0.478409i
$159$	3772.49	−	635.760i	1.88162	−	0.317101i
$160$	60.2998	+	341.977i	0.0297945	+	0.168973i
$161$	2275.42			1.11384
$162$	2006.59	+	1790.10i	0.973165	+	0.868168i
$163$	−2058.86			−0.989337			−0.494669	−	0.869082i	$-0.664711\pi$
$163$	−2058.86			−0.989337			−0.494669	+	0.869082i	$0.664711\pi$
$164$	−212.621	−	1205.83i	−0.101237	−	0.574144i
$165$	−203.962	+	34.3727i	−0.0962328	+	0.0162176i
$166$	1184.11	−	430.982i	0.553645	−	0.201510i
$167$	−285.177	−	239.292i	−0.132142	−	0.110880i	0.574321	−	0.818630i	$-0.305266\pi$
$167$	−285.177	−	239.292i	−0.132142	−	0.110880i	−0.706463	+	0.707750i	$0.749710\pi$
$168$	−521.901	−	1468.43i	−0.239676	−	0.674358i
$169$	1171.36	+	426.339i	0.533162	+	0.194055i
$170$	108.710	+	188.291i	0.0490451	+	0.0849487i
$171$	1491.20	+	1290.27i	0.666870	+	0.577014i
$172$	−574.445	+	994.968i	−0.254657	+	0.441079i
$173$	−1311.38	+	1100.38i	−0.576316	+	0.483586i	−0.883735	−	0.467988i	$-0.844979\pi$
$173$	−1311.38	+	1100.38i	−0.576316	+	0.483586i	0.307419	+	0.951574i	$0.400535\pi$
$174$	−3942.80	+	2236.72i	−1.71783	+	0.974513i
$175$	−721.855	+	4093.85i	−0.311812	+	1.76837i
$176$	−331.235	+	1878.53i	−0.141862	+	0.804541i
$177$	229.443	+	134.797i	0.0974350	+	0.0572428i
$178$	2574.95	−	2160.64i	1.08427	−	0.909815i
$179$	1512.45	−	2619.64i	0.631540	−	1.09386i	−0.355697	−	0.934601i	$-0.615757\pi$
$179$	1512.45	−	2619.64i	0.631540	−	1.09386i	0.987237	−	0.159258i	$-0.0509100\pi$
$180$	244.520	+	3.70551i	0.101253	+	0.00153440i
$181$	33.5721	+	58.1486i	0.0137867	+	0.0238793i	0.872836	−	0.488013i	$-0.162278\pi$
$181$	33.5721	+	58.1486i	0.0137867	+	0.0238793i	−0.859050	+	0.511892i	$0.828945\pi$
$182$	−3629.58	−	1321.06i	−1.47826	−	0.538041i
$183$	591.056	+	108.843i	0.238755	+	0.0439666i
$184$	−453.157	−	380.244i	−0.181561	−	0.152347i
$185$	−282.699	+	102.894i	−0.112348	+	0.0408915i
$186$	−1980.17	−	2396.52i	−0.780609	−	0.944739i
$187$	156.090	+	885.230i	0.0610397	+	0.346173i
$188$	2685.76			1.04191
$189$	−4710.39	+	720.597i	−1.81286	+	0.277332i
$190$	435.242			0.166188
$191$	175.616	+	995.967i	0.0665294	+	0.377307i	0.999834	+	0.0182213i	$0.00580035\pi$
$191$	175.616	+	995.967i	0.0665294	+	0.377307i	−0.933305	+	0.359086i	$0.883089\pi$
$192$	314.675	−	844.596i	0.118280	−	0.317466i
$193$	−188.381	+	68.5652i	−0.0702590	+	0.0255722i	−0.376911	−	0.926250i	$-0.623014\pi$
$193$	−188.381	+	68.5652i	−0.0702590	+	0.0255722i	0.306652	+	0.951822i	$0.400791\pi$
$194$	−139.013	−	116.645i	−0.0514460	−	0.0431683i
$195$	−167.860	+	196.997i	−0.0616446	+	0.0723449i
$196$	−4270.47	−	1554.32i	−1.55629	−	0.566445i
$197$	−1376.86	−	2384.79i	−0.497954	−	0.862482i	0.502043	−	0.864843i	$-0.332582\pi$
$197$	−1376.86	−	2384.79i	−0.497954	−	0.862482i	−0.999997	+	0.00236077i	$0.999249\pi$
$198$	2292.85	+	874.096i	0.822958	+	0.313734i
$199$	2395.21	−	4148.63i	0.853227	−	1.47783i	−0.0250538	−	0.999686i	$-0.507976\pi$
$199$	2395.21	−	4148.63i	0.853227	−	1.47783i	0.878280	−	0.478146i	$-0.158691\pi$
$200$	827.880	−	694.674i	0.292700	−	0.245604i
$201$	4.58511	−	605.161i	0.00160900	−	0.212362i
$202$	−695.254	+	3942.98i	−0.242168	+	1.37340i
$203$	1394.91	−	7910.94i	0.482284	−	2.73517i
$204$	8.05203	−	1062.74i	0.00276350	−	0.364738i
$205$	270.311	−	226.818i	0.0920944	−	0.0772763i
$206$	1051.83	−	1821.82i	0.355750	−	0.616177i
$207$	−1403.08	+	1141.54i	−0.471114	+	0.383298i
$208$	1193.42	+	2067.07i	0.397831	+	0.689064i
$209$	1690.92	+	615.443i	0.559632	+	0.203689i
$210$	−682.151	+	800.559i	−0.224157	+	0.263066i
$211$	751.352	+	630.459i	0.245143	+	0.205699i	0.757077	−	0.653325i	$-0.226627\pi$
$211$	751.352	+	630.459i	0.245143	+	0.205699i	−0.511934	+	0.859024i	$0.671071\pi$
$212$	−3878.61	+	1411.70i	−1.25653	+	0.457339i
$213$	429.905	−	1153.88i	0.138294	−	0.371185i
$214$	−230.755	−	1308.68i	−0.0737107	−	0.418034i
$215$	−331.096			−0.105026
$216$	1058.51	+	643.642i	0.333437	+	0.202751i
$217$	5509.00			1.72339
$218$	573.559	+	3252.81i	0.178194	+	1.01059i
$219$	−152.565	−	184.643i	−0.0470748	−	0.0569727i
$220$	209.699	−	76.3243i	0.0642633	−	0.0233899i
$221$	861.622	+	722.987i	0.262258	+	0.220060i
$222$	3510.01	+	646.368i	1.06116	+	0.195412i
$223$	−437.380	−	159.193i	−0.131341	−	0.0478044i	0.275513	−	0.961297i	$-0.411152\pi$
$223$	−437.380	−	159.193i	−0.131341	−	0.0478044i	−0.406855	+	0.913493i	$0.633374\pi$
$224$	3650.16	+	6322.27i	1.08878	+	1.88582i
$225$	−1608.71	−	2886.51i	−0.476655	−	0.855262i
$226$	98.9147	−	171.325i	0.0291138	−	0.0504265i
$227$	−3603.52	+	3023.71i	−1.05363	+	0.884100i	−0.993471	−	0.114089i	$-0.963605\pi$
$227$	−3603.52	+	3023.71i	−1.05363	+	0.884100i	−0.0601584	+	0.998189i	$0.519161\pi$
$228$	−1834.36	−	1077.68i	−0.532822	−	0.313031i
$229$	272.294	−	1544.26i	0.0785752	−	0.445622i	−0.919984	−	0.391956i	$-0.871798\pi$
$229$	272.294	−	1544.26i	0.0785752	−	0.445622i	0.998559	−	0.0536655i	$-0.0170905\pi$
$230$	−69.3268	+	393.172i	−0.0198751	+	0.112717i
$231$	−3782.17	+	2145.59i	−1.07727	+	0.611124i
$232$	−1599.79	+	1342.39i	−0.452723	+	0.379879i
$233$	−2879.03	+	4986.62i	−0.809491	+	1.40208i	0.103727	+	0.994606i	$0.466923\pi$
$233$	−2879.03	+	4986.62i	−0.809491	+	1.40208i	−0.913217	+	0.407473i	$0.866410\pi$
$234$	2900.84	−	1006.31i	0.810402	−	0.281131i
$235$	387.002	+	670.307i	0.107426	+	0.186068i
$236$	−269.791	−	98.1959i	−0.0744148	−	0.0270848i
$237$	−1310.54	−	3687.37i	−0.359193	−	1.01064i
$238$	3501.47	+	2938.08i	0.953641	+	0.800200i
$239$	−3026.69	+	1101.62i	−0.819164	+	0.298151i	−0.717404	−	0.696658i	$-0.754670\pi$
$239$	−3026.69	+	1101.62i	−0.819164	+	0.298151i	−0.101760	+	0.994809i	$0.532447\pi$
$240$	640.905	−	108.009i	0.172376	−	0.0290497i
$241$	−472.252	−	2678.27i	−0.126226	−	0.715862i	−0.980572	−	0.196158i	$-0.937153\pi$
$241$	−472.252	−	2678.27i	−0.126226	−	0.715862i	0.854346	−	0.519704i	$-0.173958\pi$
$242$	−2670.42			−0.709342
$243$	2543.03	−	2807.47i	0.671339	−	0.741150i
$244$	−648.412			−0.170124
$245$	−227.423	−	1289.78i	−0.0593043	−	0.336331i
$246$	−4128.00	+	695.672i	−1.06989	+	0.180303i
$247$	2115.83	−	770.098i	0.545048	−	0.198381i
$248$	−1097.14	−	920.607i	−0.280920	−	0.235720i
$249$	−594.464	−	1672.60i	−0.151296	−	0.425689i
$250$	−1385.39	−	504.241i	−0.350480	−	0.127564i
$251$	2711.14	+	4695.84i	0.681777	+	1.18087i	0.974438	+	0.224656i	$0.0721258\pi$
$251$	2711.14	+	4695.84i	0.681777	+	1.18087i	−0.292661	+	0.956216i	$0.594541\pi$
$252$	4857.20	−	1684.98i	1.21419	−	0.421204i
$253$	−825.290	+	1429.44i	−0.205081	+	0.355211i
$254$	−2443.50	+	2050.34i	−0.603618	+	0.506496i
$255$	266.396	−	151.124i	0.0654210	−	0.0371128i
$256$	932.515	−	5288.55i	0.227665	−	1.29115i
$257$	183.660	−	1041.59i	0.0445774	−	0.252811i	−0.954373	−	0.298617i	$-0.903475\pi$
$257$	183.660	−	1041.59i	0.0445774	−	0.252811i	0.998950	+	0.0458063i	$0.0145857\pi$
$258$	3386.72	+	1989.69i	0.817240	+	0.480126i
$259$	−4844.96	+	4065.40i	−1.16236	+	0.975335i
$260$	139.617	−	241.824i	0.0333027	−	0.0576819i
$261$	3108.67	+	5577.88i	0.737248	+	1.32284i
$262$	−1025.94	−	1776.98i	−0.241919	−	0.419016i
$263$	4969.14	+	1808.62i	1.16506	+	0.424046i	0.850902	−	0.525325i	$-0.176056\pi$
$263$	4969.14	+	1808.62i	1.16506	+	0.424046i	0.314156	+	0.949371i	$0.398278\pi$
$264$	1111.78	+	204.734i	0.259187	+	0.0477292i
$265$	−911.212	−	764.597i	−0.211228	−	0.177241i
$266$	8598.32	−	3129.53i	1.98194	−	0.721368i
$267$	−3016.10	−	3650.26i	−0.691320	−	0.836675i
$268$	113.379	+	643.007i	0.0258424	+	0.146559i
$269$	−7352.28			−1.66646			−0.833228	−	0.552930i	$-0.813510\pi$
$269$	−7352.28			−1.66646			−0.833228	+	0.552930i	$0.813510\pi$
$270$	19.0022	−	835.870i	0.00428311	−	0.188405i
$271$	3845.21			0.861917			0.430959	−	0.902372i	$-0.358175\pi$
$271$	3845.21			0.861917			0.430959	+	0.902372i	$0.358175\pi$
$272$	−490.478	−	2781.64i	−0.109337	−	0.620080i
$273$	−1899.64	+	5098.70i	−0.421142	+	1.13036i
$274$	−3012.17	+	1096.34i	−0.664131	+	0.241724i
$275$	−2309.99	−	1938.31i	−0.506536	−	0.425034i
$276$	1265.70	−	1485.40i	0.276036	−	0.323951i
$277$	3573.52	+	1300.65i	0.775133	+	0.282125i	0.699142	−	0.714983i	$-0.253566\pi$
$277$	3573.52	+	1300.65i	0.775133	+	0.282125i	0.0759911	+	0.997108i	$0.475788\pi$
$278$	−1710.76	−	2963.12i	−0.369081	−	0.639267i
$279$	−3396.98	+	2763.79i	−0.728932	+	0.593059i
$280$	−242.276	+	419.635i	−0.0517099	+	0.0895642i
$281$	4191.24	−	3516.87i	0.889781	−	0.746615i	−0.0783853	−	0.996923i	$-0.524976\pi$
$281$	4191.24	−	3516.87i	0.889781	−	0.746615i	0.968166	+	0.250308i	$0.0805320\pi$
$282$	69.5698	−	9182.09i	0.0146908	−	1.93896i
$283$	1071.49	−	6076.70i	0.225064	−	1.27640i	−0.637498	−	0.770452i	$-0.720030\pi$
$283$	1071.49	−	6076.70i	0.225064	−	1.27640i	0.862562	−	0.505951i	$-0.168858\pi$
$284$	−230.694	+	1308.33i	−0.0482014	+	0.273363i
$285$	4.64528	−	613.102i	0.000965482	−	0.127428i
$286$	2146.35	−	1801.00i	0.443763	−	0.372362i
$287$	3709.17	−	6424.47i	0.762876	−	1.32134i
$288$	−5422.57	−	2067.23i	−1.10947	−	0.422961i
$289$	1790.98	+	3102.08i	0.364540	+	0.631401i
$290$	1324.44	+	482.057i	0.268186	+	0.0976116i
$291$	−165.796	+	194.575i	−0.0333991	+	0.0391965i
$292$	197.959	+	166.107i	0.0396734	+	0.0332900i
$293$	−1483.01	+	539.771i	−0.295694	+	0.107624i	−0.485607	−	0.874177i	$-0.661402\pi$
$293$	−1483.01	+	539.771i	−0.295694	+	0.107624i	0.189913	+	0.981801i	$0.439179\pi$
$294$	−5424.54	+	14559.6i	−1.07607	+	2.88821i
$295$	−14.3677	−	81.4832i	−0.00283566	−	0.0160818i
$296$	1644.26			0.322873
$297$	1255.76	−	3220.49i	0.245343	−	0.629197i
$298$	−6190.63			−1.20340
$299$	358.645	+	2033.98i	0.0693678	+	0.393404i
$300$	2270.94	+	2748.42i	0.437043	+	0.528935i
$301$	−6540.88	+	2380.69i	−1.25253	+	0.455882i
$302$	−6956.61	−	5837.29i	−1.32552	−	1.11225i
$303$	5546.85	+	1021.45i	1.05168	+	0.193666i
$304$	−5313.33	−	1933.89i	−1.00243	−	0.364856i
$305$	−93.4321	−	161.829i	−0.0175407	−	0.0303813i
$306$	−3633.08	−	55.0566i	−0.678724	−	0.0102855i
$307$	−2688.23	+	4656.16i	−0.499758	+	0.865606i	−1.00000		0.000279643i	$-0.999911\pi$
$307$	−2688.23	+	4656.16i	−0.499758	+	0.865606i	0.500242	+	0.865886i	$0.333244\pi$
$308$	3593.87	−	3015.61i	0.664869	−	0.557891i
$309$	−2555.08	−	1501.10i	−0.470399	−	0.276358i
$310$	−167.847	+	951.907i	−0.0307518	+	0.174402i
$311$	−1068.47	+	6059.59i	−0.194814	+	1.10485i	0.717868	+	0.696179i	$0.245118\pi$
$311$	−1068.47	+	6059.59i	−0.194814	+	1.10485i	−0.912683	+	0.408669i	$0.865993\pi$
$312$	1230.36	−	697.974i	0.223255	−	0.126651i
$313$	5626.07	−	4720.84i	1.01599	−	0.852516i	0.0268706	−	0.999639i	$-0.491446\pi$
$313$	5626.07	−	4720.84i	1.01599	−	0.852516i	0.989118	+	0.147123i	$0.0470014\pi$
$314$	5137.91	−	8899.13i	0.923405	−	1.59939i
$315$	1120.42	+	969.454i	0.200409	+	0.173405i
$316$	2111.05	+	3656.45i	0.375810	+	0.650922i
$317$	−964.065	−	350.891i	−0.170812	−	0.0621703i	0.255199	−	0.966889i	$-0.417859\pi$
$317$	−964.065	−	350.891i	−0.170812	−	0.0621703i	−0.426010	+	0.904718i	$0.640081\pi$
$318$	4725.85	+	13296.8i	0.833373	+	2.34480i
$319$	4463.81	+	3745.59i	0.783466	+	0.657406i
$320$	−263.340	+	95.8479i	−0.0460036	+	0.0167439i
$321$	−1845.93	+	311.085i	−0.320964	+	0.0540906i
$322$	1457.47	+	8265.70i	0.252240	+	1.43053i
$323$	−2664.53			−0.459004
$324$	−2149.74	+	3475.79i	−0.368611	+	0.595985i
$325$	−3773.23			−0.644004
$326$	−1318.75	−	7479.02i	−0.224046	−	1.27063i
$327$	4588.19	−	773.225i	0.775925	−	0.130763i
$328$	−1812.28	+	659.618i	−0.305081	+	0.111041i
$329$	12465.0	+	10459.4i	2.08882	+	1.75272i
$330$	−255.506	−	718.897i	−0.0426216	−	0.119921i
$331$	5414.80	+	1970.83i	0.899167	+	0.327270i	0.749919	−	0.661530i	$-0.230092\pi$
$331$	5414.80	+	1970.83i	0.899167	+	0.327270i	0.149248	+	0.988800i	$0.452315\pi$
$332$	957.576	+	1658.57i	0.158295	+	0.274174i
$333$	947.966	−	4937.47i	0.156001	−	0.812528i
$334$	686.591	−	1189.21i	0.112481	−	0.194822i
$335$	−144.143	+	120.950i	−0.0235085	+	0.0197260i
$336$	11884.6	−	6742.06i	1.92964	−	1.09467i
$337$	557.882	−	3163.91i	0.0901774	−	0.511422i	−0.905941	−	0.423403i	$-0.860835\pi$
$337$	557.882	−	3163.91i	0.0901774	−	0.511422i	0.996119	−	0.0880185i	$-0.0280535\pi$
$338$	−798.438	+	4528.17i	−0.128489	+	0.728698i
$339$	−240.281	−	141.164i	−0.0384964	−	0.0226165i
$340$	−253.133	+	212.404i	−0.0403767	+	0.0338801i
$341$	−1998.11	+	3460.82i	−0.317312	+	0.549601i
$342$	−3731.89	+	6243.40i	−0.590051	+	0.987147i
$343$	−7941.72	−	13755.5i	−1.25018	−	2.16538i
$344$	1700.47	+	618.922i	0.266522	+	0.0970059i
$345$	553.101	+	101.853i	0.0863129	+	0.0158945i
$346$	−4837.23	−	4058.92i	−0.751593	−	0.630661i
$347$	3383.81	−	1231.60i	0.523494	−	0.190536i	−0.0667373	−	0.997771i	$-0.521259\pi$
$347$	3383.81	−	1231.60i	0.523494	−	0.190536i	0.590231	+	0.807235i	$0.299037\pi$
$348$	−4388.36	−	5311.05i	−0.675979	−	0.818110i
$349$	−321.225	−	1821.76i	−0.0492686	−	0.279416i	0.950213	−	0.311600i	$-0.100865\pi$
$349$	−321.225	−	1821.76i	−0.0492686	−	0.279416i	−0.999482	+	0.0321837i	$0.989754\pi$
$350$	−15333.7			−2.34177
$351$	−1386.58	−	4097.01i	−0.210855	−	0.623026i
$352$	−5295.63			−0.801870
$353$	540.224	+	3063.76i	0.0814538	+	0.461948i	0.998066	+	0.0621691i	$0.0198018\pi$
$353$	540.224	+	3063.76i	0.0814538	+	0.461948i	−0.916612	+	0.399778i	$0.869087\pi$
$354$	−342.701	+	919.818i	−0.0514529	+	0.138101i
$355$	−359.772	+	130.946i	−0.0537879	+	0.0195772i
$356$	3913.50	+	3283.81i	0.582626	+	0.488881i
$357$	4176.09	−	4900.98i	0.619110	−	0.726575i
$358$	10484.9	+	3816.18i	1.54788	+	0.563384i
$359$	3228.43	+	5591.80i	0.474624	+	0.822072i	0.999578	−	0.0290584i	$-0.00925087\pi$
$359$	3228.43	+	5591.80i	0.474624	+	0.822072i	−0.524954	+	0.851131i	$0.675918\pi$
$360$	−61.1312	−	380.304i	−0.00894972	−	0.0556771i
$361$	762.511	−	1320.71i	0.111169	−	0.192551i
$362$	−189.727	+	159.200i	−0.0275465	+	0.0231143i
$363$	−28.5010	+	3761.67i	−0.00412097	+	0.543902i
$364$	1019.38	−	5781.20i	0.146786	−	0.832464i
$365$	−12.9320	+	73.3410i	−0.00185450	+	0.0105174i
$366$	−16.7959	+	2216.79i	−0.00239873	+	0.316594i
$367$	−3998.61	+	3355.23i	−0.568735	+	0.477226i	−0.881226	−	0.472695i	$-0.843281\pi$
$367$	−3998.61	+	3355.23i	−0.568735	+	0.477226i	0.312491	+	0.949921i	$0.398837\pi$
$368$	2593.29	−	4491.71i	0.367350	−	0.636268i
$369$	935.899	+	5822.32i	0.132035	+	0.821404i
$370$	−554.851	−	961.030i	−0.0779603	−	0.135031i
$371$	−23498.9	−	8552.91i	−3.28842	−	1.19689i
$372$	3064.37	−	3596.29i	0.427098	−	0.501233i
$373$	4441.26	+	3726.66i	0.616515	+	0.517317i	0.896706	−	0.442627i	$-0.145953\pi$
$373$	4441.26	+	3726.66i	0.616515	+	0.517317i	−0.280191	+	0.959944i	$0.590398\pi$
$374$	−3115.72	+	1134.03i	−0.430775	+	0.156789i
$375$	−725.084	+	1946.15i	−0.0998485	+	0.267996i
$376$	−734.588	−	4166.06i	−0.100754	−	0.571404i
$377$	7291.39			0.996089
$378$	−5634.78	−	16649.5i	−0.766725	−	2.26549i
$379$	−12786.6			−1.73299			−0.866495	−	0.499185i	$-0.833633\pi$
$379$	−12786.6			−1.73299			−0.866495	+	0.499185i	$0.833633\pi$
$380$	114.867	+	651.445i	0.0155068	+	0.0879432i
$381$	2862.13	+	3463.91i	0.384859	+	0.465779i
$382$	−3505.47	+	1275.89i	−0.469517	+	0.170890i
$383$	2864.04	+	2403.21i	0.382103	+	0.320623i	0.813527	−	0.581527i	$-0.197544\pi$
$383$	2864.04	+	2403.21i	0.382103	+	0.320623i	−0.431424	+	0.902149i	$0.641989\pi$
$384$	−5517.30	−	1016.01i	−0.733212	−	0.135021i
$385$	1270.48	+	462.418i	0.168181	+	0.0612130i
$386$	−369.734	−	640.398i	−0.0487538	−	0.0844441i
$387$	2838.91	−	4749.46i	0.372894	−	0.623846i
$388$	137.900	−	238.851i	0.0180434	−	0.0312521i
$389$	4350.72	−	3650.69i	0.567070	−	0.475828i	−0.313602	−	0.949554i	$-0.601536\pi$
$389$	4350.72	−	3650.69i	0.567070	−	0.475828i	0.880672	+	0.473726i	$0.157091\pi$
$390$	−823.133	−	483.588i	−0.106874	−	0.0627883i
$391$	424.415	−	2406.98i	0.0548941	−	0.311320i
$392$	−1242.98	+	7049.31i	−0.160154	+	0.908276i
$393$	−2514.09	+	1426.22i	−0.322694	+	0.183062i
$394$	7781.08	−	6529.10i	0.994937	−	0.834851i
$395$	−608.378	+	1053.74i	−0.0774958	+	0.134227i
$396$	−703.177	+	3662.49i	−0.0892323	+	0.464766i
$397$	3935.17	+	6815.91i	0.497482	+	0.861664i	0.999996	−	0.00290500i	$-0.000924692\pi$
$397$	3935.17	+	6815.91i	0.497482	+	0.861664i	−0.502514	+	0.864569i	$0.667591\pi$
$398$	16604.5	+	6043.56i	2.09123	+	0.761147i
$399$	−4316.64	−	12145.4i	−0.541609	−	1.52389i
$400$	7258.62	+	6090.71i	0.907328	+	0.761339i
$401$	−11786.5	+	4289.92i	−1.46780	+	0.534236i	−0.947502	−	0.319749i	$-0.896401\pi$
$401$	−11786.5	+	4289.92i	−1.46780	+	0.534236i	−0.520298	+	0.853985i	$0.674179\pi$
$402$	2201.25	−	370.966i	0.273105	−	0.0460251i
$403$	868.314	+	4924.46i	0.107330	+	0.608696i
$404$	−6085.12			−0.749371
$405$	−1177.24	−	35.6886i	−0.144439	−	0.00437872i
$406$	29630.8			3.62205
$407$	−796.676	−	4518.17i	−0.0970265	−	0.550264i
$408$	−1650.68	+	278.181i	−0.200296	+	0.0337550i
$409$	7535.89	−	2742.84i	0.911065	−	0.331601i	0.156387	−	0.987696i	$-0.450015\pi$
$409$	7535.89	−	2742.84i	0.911065	−	0.331601i	0.754678	+	0.656095i	$0.227793\pi$
$410$	997.083	+	836.652i	0.120103	+	0.100779i
$411$	1512.21	+	4254.78i	0.181488	+	0.510640i
$412$	3004.39	+	1093.51i	0.359262	+	0.130761i
$413$	−869.728	−	1506.41i	−0.103624	−	0.179481i
$414$	−5045.49	−	4365.64i	−0.598967	−	0.518260i
$415$	−275.961	+	477.979i	−0.0326419	+	0.0565375i
$416$	−5076.10	+	4259.35i	−0.598260	+	0.502000i
$417$	−4192.25	+	2378.23i	−0.492315	+	0.279286i
$418$	−1152.59	+	6536.64i	−0.134868	+	0.764875i
$419$	2688.55	−	15247.5i	0.313471	−	1.77778i	−0.267199	−	0.963641i	$-0.586098\pi$
$419$	2688.55	−	15247.5i	0.313471	−	1.77778i	0.580670	−	0.814139i	$-0.302791\pi$
$420$	−1378.26	−	809.724i	−0.160124	−	0.0940726i
$421$	−2941.20	+	2467.96i	−0.340488	+	0.285703i	−0.796957	−	0.604036i	$-0.793558\pi$
$421$	−2941.20	+	2467.96i	−0.340488	+	0.285703i	0.456469	+	0.889739i	$0.349114\pi$
$422$	−1808.95	+	3133.19i	−0.208669	+	0.361425i
$423$	−12933.6	−	195.998i	−1.48665	−	0.0225290i
$424$	3250.62	+	5630.24i	0.372321	+	0.644878i
$425$	4195.90	+	1527.18i	0.478897	+	0.174304i
$426$	4466.95	+	822.588i	0.508039	+	0.0935552i
$427$	−3009.38	−	2525.17i	−0.341063	−	0.286186i
$428$	1897.85	−	690.762i	0.214337	−	0.0780122i
$429$	−2514.07	−	3042.67i	−0.282938	−	0.342428i
$430$	−212.076	−	1202.74i	−0.0237842	−	0.134887i
$431$	−4322.86			−0.483121			−0.241560	−	0.970386i	$-0.577659\pi$
$431$	−4322.86			−0.483121			−0.241560	+	0.970386i	$0.577659\pi$
$432$	−3945.96	+	10119.7i	−0.439468	+	1.12704i
$433$	−8167.34			−0.906460			−0.453230	−	0.891394i	$-0.649728\pi$
$433$	−8167.34			−0.906460			−0.453230	+	0.891394i	$0.649728\pi$
$434$	3528.66	+	20012.1i	0.390280	+	2.21339i
$435$	693.184	−	1860.52i	0.0764037	−	0.205070i
$436$	−4717.25	+	1716.94i	−0.518155	+	0.188593i
$437$	−3748.05	−	3144.99i	−0.410283	−	0.344268i
$438$	573.014	−	672.478i	0.0625107	−	0.0733613i
$439$	−6964.64	−	2534.92i	−0.757185	−	0.275593i	−0.0655591	−	0.997849i	$-0.520883\pi$
$439$	−6964.64	−	2534.92i	−0.757185	−	0.275593i	−0.691626	+	0.722256i	$0.743105\pi$
$440$	−175.747	−	304.402i	−0.0190418	−	0.0329813i
$441$	20451.5	+	7796.66i	2.20834	+	0.841881i
$442$	−2074.44	+	3593.03i	−0.223237	+	0.386658i
$443$	5428.84	−	4555.34i	0.582239	−	0.488556i	−0.303443	−	0.952850i	$-0.598136\pi$
$443$	5428.84	−	4555.34i	0.582239	−	0.488556i	0.885682	+	0.464293i	$0.153692\pi$
$444$	−41.0972	+	5424.17i	−0.00439276	+	0.579774i
$445$	−255.656	+	1449.90i	−0.0272343	+	0.154453i
$446$	298.134	−	1690.80i	0.0316525	−	0.179510i
$447$	−66.0717	+	8720.41i	−0.00699124	+	0.922732i
$448$	−4513.17	+	3787.00i	−0.475954	+	0.399373i
$449$	5632.70	−	9756.13i	0.592035	−	1.02543i	−0.401923	−	0.915673i	$-0.631658\pi$
$449$	5632.70	−	9756.13i	0.592035	−	1.02543i	0.993958	−	0.109761i	$-0.0350085\pi$
$450$	9455.14	−	7692.70i	0.990488	−	0.805861i
$451$	2690.62	+	4660.29i	0.280923	+	0.486573i
$452$	282.535	+	102.834i	0.0294012	+	0.0107012i
$453$	−8296.92	+	9737.10i	−0.860537	+	1.00991i
$454$	−13292.1	−	11153.4i	−1.37407	−	1.15298i
$455$	1589.74	−	578.619i	0.163799	−	0.0596178i
$456$	−1169.94	+	3140.15i	−0.120148	+	0.322480i
$457$	349.551	+	1982.40i	0.0357797	+	0.202917i	0.997457	−	0.0712659i	$-0.0227039\pi$
$457$	349.551	+	1982.40i	0.0357797	+	0.202917i	−0.961678	+	0.274182i	$0.911593\pi$
$458$	5784.10			0.590116
$459$	−116.331	+	5117.14i	−0.0118297	+	0.520366i
$460$	−606.774			−0.0615021
$461$	−2310.16	−	13101.6i	−0.233395	−	1.32365i	−0.845968	−	0.533233i	$-0.820977\pi$
$461$	−2310.16	−	13101.6i	−0.233395	−	1.32365i	0.612574	−	0.790414i	$-0.290134\pi$
$462$	−10216.7	−	12364.8i	−1.02884	−	1.24516i
$463$	16771.8	−	6104.42i	1.68348	−	0.612735i	0.689697	−	0.724098i	$-0.257744\pi$
$463$	16771.8	−	6104.42i	1.68348	−	0.612735i	0.993780	+	0.111363i	$0.0355217\pi$
$464$	−14026.6	−	11769.7i	−1.40338	−	1.17757i
$465$	1339.11	+	246.597i	0.133548	+	0.0245928i
$466$	−19958.5	−	7264.31i	−1.98404	−	0.722131i
$467$	5090.74	+	8817.42i	0.504435	+	0.873708i	0.999987	+	0.00512926i	$0.00163270\pi$
$467$	5090.74	+	8817.42i	0.504435	+	0.873708i	−0.495551	+	0.868579i	$0.665034\pi$
$468$	2271.77	+	4076.24i	0.224386	+	0.402616i
$469$	−1977.91	+	3425.84i	−0.194736	+	0.337293i
$470$	−2187.08	+	1835.18i	−0.214643	+	0.180107i
$471$	−12480.9	−	7332.49i	−1.22100	−	0.717332i
$472$	−78.5267	+	445.347i	−0.00765781	+	0.0434296i
$473$	876.792	−	4972.53i	0.0852324	−	0.483377i
$474$	12555.3	−	7122.55i	1.21664	−	0.690189i
$475$	6847.38	−	5745.64i	0.661431	−	0.555006i
$476$	−3473.46	+	6016.20i	−0.334466	+	0.579311i
$477$	18780.9	−	6515.14i	1.80276	−	0.625383i
$478$	−5940.44	−	10289.2i	−0.568430	−	0.984550i
$479$	2896.89	+	1054.38i	0.276330	+	0.100576i	0.476468	−	0.879192i	$-0.341917\pi$
$479$	2896.89	+	1054.38i	0.276330	+	0.100576i	−0.200138	+	0.979768i	$0.564139\pi$
$480$	604.269	+	1700.19i	0.0574604	+	0.161672i
$481$	−4397.68	−	3690.09i	−0.416875	−	0.349800i
$482$	9426.63	−	3431.01i	0.890812	−	0.324229i
$483$	11659.0	−	1964.84i	1.09835	−	0.185100i
$484$	−704.766	−	3996.92i	−0.0661876	−	0.375369i
$485$	79.4823			0.00744146
$486$	11827.3	+	7439.57i	1.10391	+	0.694374i
$487$	1482.64			0.137956			0.0689782	−	0.997618i	$-0.478026\pi$
$487$	1482.64			0.137956			0.0689782	+	0.997618i	$0.478026\pi$
$488$	177.348	+	1005.79i	0.0164512	+	0.0932993i
$489$	−10549.4	+	1777.83i	−0.975581	+	0.164410i
$490$	4539.60	−	1652.28i	0.418527	−	0.152331i
$491$	6066.55	+	5090.44i	0.557596	+	0.467878i	0.877503	−	0.479570i	$-0.159207\pi$
$491$	6066.55	+	5090.44i	0.557596	+	0.467878i	−0.319908	+	0.947449i	$0.603652\pi$
$492$	−2130.69	−	5994.96i	−0.195242	−	0.549337i
$493$	−8108.15	−	2951.13i	−0.740716	−	0.269598i
$494$	4152.71	+	7192.70i	0.378217	+	0.655091i
$495$	−1015.40	+	352.245i	−0.0921996	+	0.0319843i
$496$	6278.61	−	10874.9i	0.568383	−	0.984468i
$497$	−6165.84	+	5173.76i	−0.556491	+	0.466951i
$498$	5695.13	−	3230.80i	0.512459	−	0.290714i
$499$	−1417.01	+	8036.24i	−0.127122	+	0.720945i	0.852903	+	0.522070i	$0.174840\pi$
$499$	−1417.01	+	8036.24i	−0.127122	+	0.720945i	−0.980025	+	0.198875i	$0.936271\pi$
$500$	389.092	−	2206.65i	0.0348015	−	0.197369i
$501$	−1667.85	−	979.856i	−0.148731	−	0.0873788i
$502$	−15321.6	+	12856.3i	−1.36222	+	1.14304i
$503$	−8812.36	+	15263.5i	−0.781161	+	1.35301i	0.150105	+	0.988670i	$0.452039\pi$
$503$	−8812.36	+	15263.5i	−0.781161	+	1.35301i	−0.931266	+	0.364340i	$0.881295\pi$
$504$	−3942.17	−	7073.45i	−0.348409	−	0.625151i
$505$	−876.827	−	1518.71i	−0.0772640	−	0.133825i
$506$	−5721.23	−	2082.36i	−0.502648	−	0.182949i
$507$	6370.07	+	1173.05i	0.557997	+	0.102755i
$508$	−3713.71	−	3116.18i	−0.324349	−	0.272161i
$509$	8361.44	−	3043.31i	0.728122	−	0.265015i	0.0487523	−	0.998811i	$-0.484476\pi$
$509$	8361.44	−	3043.31i	0.728122	−	0.265015i	0.679370	+	0.733796i	$0.262253\pi$
$510$	719.610	+	870.914i	0.0624801	+	0.0756171i
$511$	271.871	+	1541.86i	0.0235359	+	0.133479i
$512$	11171.3			0.964269
$513$	8754.91	+	5323.55i	0.753487	+	0.458169i
$514$	3901.32			0.334786
$515$	159.999	+	907.397i	0.0136901	+	0.0776402i
$516$	−2084.24	+	5594.16i	−0.177817	+	0.477265i
$517$	−11091.8	+	4037.08i	−0.943551	+	0.343425i
$518$	−17871.3	−	14995.8i	−1.51587	−	1.27197i
$519$	−5769.21	+	6770.63i	−0.487939	+	0.572635i
$520$	−413.296	−	150.427i	−0.0348542	−	0.0126859i
$521$	−9964.97	−	17259.8i	−0.837953	−	1.45138i	−0.891604	−	0.452817i	$-0.850419\pi$
$521$	−9964.97	−	17259.8i	−0.837953	−	1.45138i	0.0536508	−	0.998560i	$-0.482914\pi$
$522$	−18271.1	+	14865.4i	−1.53200	+	1.24643i
$523$	894.732	−	1549.72i	0.0748067	−	0.129569i	−0.826195	−	0.563384i	$-0.809499\pi$
$523$	894.732	−	1549.72i	0.0748067	−	0.129569i	0.901002	+	0.433815i	$0.142833\pi$
$524$	2388.92	−	2004.54i	0.199161	−	0.167116i
$525$	−163.655	+	21599.8i	−0.0136047	+	1.79560i
$526$	−3387.14	+	19209.4i	−0.280772	+	1.59234i
$527$	1027.55	−	5827.52i	0.0849350	−	0.481690i
$528$	−75.0955	+	9911.40i	−0.00618960	+	0.816929i
$529$	−5882.46	+	4935.97i	−0.483477	+	0.405685i
$530$	2193.83	−	3799.82i	0.179800	−	0.311422i
$531$	1292.04	+	492.561i	0.105593	+	0.0402549i
$532$	6953.34	+	12043.5i	0.566664	+	0.981491i
$533$	6327.42	+	2302.99i	0.514204	+	0.187155i
$534$	11328.1	−	13294.4i	0.918003	−	1.07735i
$535$	445.867	+	374.127i	0.0360309	+	0.0302335i
$536$	966.397	−	351.740i	0.0778768	−	0.0283448i
$537$	5487.56	−	14728.8i	0.440979	−	1.18360i
$538$	−4709.34	−	26708.0i	−0.377386	−	2.14027i
$539$	19972.7			1.59608
$540$	1256.10	−	192.158i	0.100100	−	0.0153133i
$541$	9074.21			0.721129			0.360564	−	0.932734i	$-0.382584\pi$
$541$	9074.21			0.721129			0.360564	+	0.932734i	$0.382584\pi$
$542$	2462.96	+	13968.1i	0.195190	+	1.10698i
$543$	222.232	+	268.958i	0.0175633	+	0.0212561i
$544$	7368.65	−	2681.97i	0.580750	−	0.211376i
$545$	−1108.24	−	929.921i	−0.0871039	−	0.0730888i
$546$	−19738.4	−	3634.81i	−1.54711	−	0.284900i
$547$	7530.92	+	2741.03i	0.588664	+	0.214256i	0.619142	−	0.785279i	$-0.287481\pi$
$547$	7530.92	+	2741.03i	0.588664	+	0.214256i	−0.0304779	+	0.999535i	$0.509703\pi$
$548$	−2435.90	−	4219.10i	−0.189884	−	0.328889i
$549$	3122.50	+	47.3190i	0.242741	+	0.00367856i
$550$	5561.51	−	9632.82i	0.431170	−	0.746809i
$551$	−13231.9	+	11102.9i	−1.02304	+	0.858435i
$552$	−2650.27	−	1557.03i	−0.204353	−	0.120057i
$553$	−4441.92	+	25191.4i	−0.341573	+	1.93715i
$554$	−2435.83	+	13814.3i	−0.186802	+	1.05941i
$555$	−1359.67	+	771.332i	−0.103991	+	0.0589932i
$556$	3983.53	−	3342.58i	0.303848	−	0.254959i
$557$	3679.68	−	6373.39i	0.279915	−	0.484828i	−0.691448	−	0.722426i	$-0.743027\pi$
$557$	3679.68	−	6373.39i	0.279915	−	0.484828i	0.971363	+	0.237598i	$0.0763602\pi$
$558$	−12215.6	−	10569.6i	−0.926753	−	0.801879i
$559$	−3159.03	−	5471.61i	−0.239021	−	0.413997i
$560$	−3992.21	−	1453.05i	−0.301253	−	0.109647i
$561$	1564.19	+	4401.05i	0.117719	+	0.331216i
$562$	15460.0	+	12972.5i	1.16039	+	0.973686i
$563$	−1774.18	+	645.750i	−0.132812	+	0.0483395i	−0.407571	−	0.913174i	$-0.633624\pi$
$563$	−1774.18	+	645.750i	−0.132812	+	0.0483395i	0.274759	+	0.961513i	$0.411402\pi$
$564$	13761.6	−	2319.17i	1.02742	−	0.173147i
$565$	15.0464	+	85.3322i	0.00112036	+	0.00635390i
$566$	22760.6			1.69028
$567$	−23513.3	+	7759.72i	−1.74157	+	0.574740i
$568$	2092.53			0.154579
$569$	−4311.69	−	24452.8i	−0.317672	−	1.80161i	−0.556829	−	0.830627i	$-0.687982\pi$
$569$	−4311.69	−	24452.8i	−0.317672	−	1.80161i	0.239156	−	0.970981i	$-0.423129\pi$
$570$	2230.14	−	375.834i	0.163877	−	0.0276175i
$571$	13261.5	−	4826.79i	0.971939	−	0.353757i	0.193238	−	0.981152i	$-0.438101\pi$
$571$	13261.5	−	4826.79i	0.971939	−	0.353757i	0.778701	+	0.627395i	$0.215879\pi$
$572$	3262.09	+	2737.22i	0.238453	+	0.200085i
$573$	1759.86	+	4951.59i	0.128306	+	0.361005i
$574$	25713.4	+	9358.92i	1.86979	+	0.680547i
$575$	4099.60	+	7100.71i	0.297330	+	0.514992i
$576$	883.049	−	4599.35i	0.0638780	−	0.332708i
$577$	−4690.34	+	8123.90i	−0.338408	+	0.586140i	−0.984133	−	0.177430i	$-0.943222\pi$
$577$	−4690.34	+	8123.90i	−0.338408	+	0.586140i	0.645726	+	0.763570i	$0.276555\pi$
$578$	−10121.5	+	8492.91i	−0.728368	+	0.611174i
$579$	−906.041	+	513.990i	−0.0650324	+	0.0368924i
$580$	−371.974	+	2109.57i	−0.0266300	+	0.151026i
$581$	−2014.86	+	11426.9i	−0.143874	+	0.815948i
$582$	−813.011	−	477.641i	−0.0579044	−	0.0340187i
$583$	13896.1	−	11660.2i	0.987164	−	0.828329i
$584$	203.515	−	352.498i	0.0144204	−	0.0249768i
$585$	−689.990	+	1154.34i	−0.0487651	+	0.0815832i
$586$	−2910.69	−	5041.46i	−0.205187	−	0.355394i
$587$	−3439.46	−	1251.86i	−0.241843	−	0.0880236i	0.218255	−	0.975892i	$-0.429963\pi$
$587$	−3439.46	−	1251.86i	−0.241843	−	0.0880236i	−0.460098	+	0.887868i	$0.652186\pi$
$588$	−23223.6	−	4276.62i	−1.62879	−	0.299940i
$589$	−9074.39	−	7614.32i	−0.634811	−	0.532670i
$590$	286.794	−	104.384i	0.0200120	−	0.00728379i
$591$	−9114.15	−	11030.5i	−0.634359	−	0.767738i
$592$	2503.38	+	14197.4i	0.173798	+	0.985656i
$593$	−21034.0			−1.45660			−0.728299	−	0.685260i	$-0.759689\pi$
$593$	−21034.0			−1.45660			−0.728299	+	0.685260i	$0.759689\pi$
$594$	12503.1	+	2498.89i	0.863652	+	0.172611i
$595$	−2002.01			−0.137940
$596$	−1633.81	−	9265.77i	−0.112287	−	0.636814i
$597$	8690.46	−	23325.4i	0.595774	−	1.59907i
$598$	−7158.92	+	2605.63i	−0.489549	+	0.178181i
$599$	13783.5	+	11565.7i	0.940199	+	0.788921i	0.977620	−	0.210379i	$-0.0674698\pi$
$599$	13783.5	+	11565.7i	0.940199	+	0.788921i	−0.0374208	+	0.999300i	$0.511914\pi$
$600$	3642.12	−	4274.32i	0.247815	−	0.290831i
$601$	−18472.2	−	6723.33i	−1.25374	−	0.456324i	−0.372075	−	0.928203i	$-0.621354\pi$
$601$	−18472.2	−	6723.33i	−1.25374	−	0.456324i	−0.881663	+	0.471879i	$0.843576\pi$
$602$	−12837.7	−	22235.6i	−0.869147	−	1.50541i
$603$	−499.066	−	3104.74i	−0.0337041	−	0.209676i
$604$	6900.95	−	11952.8i	0.464894	−	0.805220i
$605$	895.990	−	751.825i	0.0602102	−	0.0505224i
$606$	−157.624	+	20803.8i	−0.0105661	+	1.39455i
$607$	3505.49	−	19880.6i	0.234404	−	1.32937i	−0.609461	−	0.792816i	$-0.708614\pi$
$607$	3505.49	−	19880.6i	0.234404	−	1.32937i	0.843865	−	0.536555i	$-0.180275\pi$
$608$	2725.86	−	15459.1i	0.181823	−	1.03117i
$609$	316.246	−	41739.4i	0.0210426	−	2.77728i
$610$	528.016	−	443.058i	0.0350471	−	0.0294080i
$611$	−7384.88	+	12791.0i	−0.488970	+	0.846920i
$612$	−876.424	−	5452.32i	−0.0578878	−	0.360126i
$613$	−2360.70	−	4088.85i	−0.155543	−	0.269408i	0.777714	−	0.628619i	$-0.216379\pi$
$613$	−2360.70	−	4088.85i	−0.155543	−	0.269408i	−0.933257	+	0.359210i	$0.883046\pi$
$614$	−18635.9	−	6782.91i	−1.22489	−	0.445824i
$615$	1189.19	−	1395.61i	0.0779719	−	0.0915062i
$616$	−5660.67	−	4749.86i	−0.370251	−	0.310678i
$617$	−25172.0	+	9161.84i	−1.64244	+	0.597799i	−0.987463	−	0.157851i	$-0.949543\pi$
$617$	−25172.0	+	9161.84i	−1.64244	+	0.597799i	−0.654976	+	0.755650i	$0.727321\pi$
$618$	3816.32	−	10243.1i	0.248406	−	0.666728i
$619$	4631.21	+	26264.9i	0.300717	+	1.70545i	0.643010	+	0.765858i	$0.277686\pi$
$619$	4631.21	+	26264.9i	0.300717	+	1.70545i	−0.342293	+	0.939593i	$0.611203\pi$
$620$	−1469.06			−0.0951593
$621$	−6203.50	+	7060.72i	−0.400866	+	0.456259i
$622$	−22696.5			−1.46310
$623$	5374.69	+	30481.4i	0.345638	+	1.96021i
$624$	7899.90	+	9560.92i	0.506809	+	0.613370i
$625$	−13769.3	+	5011.62i	−0.881235	+	0.320743i
$626$	20752.6	+	17413.5i	1.32499	+	1.11179i
$627$	9195.52	+	1693.35i	0.585700	+	0.107856i
$628$	14675.7	+	5341.51i	0.932522	+	0.339410i
$629$	3396.76	+	5883.37i	0.215323	+	0.372950i
$630$	−2803.99	+	4691.03i	−0.177323	+	0.296659i
$631$	8435.45	−	14610.6i	0.532187	−	0.921775i	−0.467107	−	0.884201i	$-0.654704\pi$
$631$	8435.45	−	14610.6i	0.532187	−	0.921775i	0.999294	−	0.0375740i	$-0.0119630\pi$
$632$	5094.34	−	4274.66i	0.320636	−	0.269046i
$633$	4394.26	+	2581.61i	0.275918	+	0.162101i
$634$	657.140	−	3726.83i	0.0411646	−	0.233456i
$635$	242.605	−	1375.88i	0.0151614	−	0.0859845i
$636$	−18654.6	+	10582.6i	−1.16306	+	0.659792i
$637$	19144.7	−	16064.3i	1.19080	−	0.999203i
$638$	−10747.1	+	18614.4i	−0.666897	+	1.15510i
$639$	1206.41	−	6283.58i	0.0746868	−	0.389005i
$640$	872.156	+	1510.62i	0.0538671	+	0.0933006i
$641$	13203.2	+	4805.57i	0.813564	+	0.296113i	0.715095	−	0.699027i	$-0.246383\pi$
$641$	13203.2	+	4805.57i	0.813564	+	0.296113i	0.0984690	+	0.995140i	$0.468605\pi$
$642$	−2312.42	−	6506.27i	−0.142155	−	0.399972i
$643$	3488.66	+	2927.33i	0.213965	+	0.179538i	0.743471	−	0.668768i	$-0.233178\pi$
$643$	3488.66	+	2927.33i	0.213965	+	0.179538i	−0.529506	+	0.848306i	$0.677623\pi$
$644$	−11987.0	+	4362.90i	−0.733467	+	0.266960i
$645$	−1696.50	+	285.903i	−0.103565	+	0.0174534i
$646$	−1706.70	−	9679.18i	−0.103946	−	0.589508i
$647$	23937.2			1.45451			0.727257	−	0.686366i	$-0.240795\pi$
$647$	23937.2			1.45451			0.727257	+	0.686366i	$0.240795\pi$
$648$	5979.48	+	2383.93i	0.362494	+	0.144521i
$649$	1261.80			0.0763171
$650$	−2416.86	−	13706.7i	−0.145842	−	0.827108i
$651$	28227.6	−	4757.06i	1.69943	−	0.286396i
$652$	10846.1	−	3947.67i	0.651483	−	0.237120i
$653$	9215.63	+	7732.83i	0.552275	+	0.463414i	0.875711	−	0.482836i	$-0.160393\pi$
$653$	9215.63	+	7732.83i	0.552275	+	0.463414i	−0.323436	+	0.946250i	$0.604838\pi$
$654$	5747.68	+	16171.8i	0.343658	+	0.966924i
$655$	844.516	+	307.379i	0.0503786	+	0.0183363i
$656$	−8454.68	−	14643.9i	−0.503201	−	0.871570i
$657$	−941.168	−	814.352i	−0.0558881	−	0.0483575i
$658$	−30010.8	+	51980.2i	−1.77803	+	3.07963i
$659$	−2768.22	+	2322.81i	−0.163633	+	0.137305i	−0.720928	−	0.693010i	$-0.756284\pi$
$659$	−2768.22	+	2322.81i	−0.163633	+	0.137305i	0.557294	+	0.830315i	$0.311840\pi$
$660$	1008.57	−	572.155i	0.0594827	−	0.0337441i
$661$	3903.14	−	22135.8i	0.229674	−	1.30254i	−0.623872	−	0.781527i	$-0.714441\pi$
$661$	3903.14	−	22135.8i	0.229674	−	1.30254i	0.853546	−	0.521018i	$-0.174448\pi$
$662$	−3690.91	+	20932.2i	−0.216694	+	1.22893i
$663$	5039.17	+	2960.50i	0.295181	+	0.173418i
$664$	2310.80	−	1938.99i	0.135055	−	0.113325i
$665$	−2003.86	+	3470.79i	−0.116852	+	0.202393i
$666$	18543.1	+	281.006i	1.07887	+	0.0163495i
$667$	−7922.05	−	13721.4i	−0.459885	−	0.796544i
$668$	1961.14	+	713.798i	0.113591	+	0.0413438i
$669$	−2378.56	−	438.011i	−0.137459	−	0.0253131i
$670$	−531.692	−	446.143i	−0.0306583	−	0.0257254i
$671$	2677.84	−	974.654i	0.154064	−	0.0560747i
$672$	24162.4	+	29242.7i	1.38703	+	1.67867i
$673$	816.402	+	4630.05i	0.0467608	+	0.265193i	0.999221	−	0.0394703i	$-0.0125670\pi$
$673$	816.402	+	4630.05i	0.0467608	+	0.265193i	−0.952460	+	0.304664i	$0.901456\pi$
$674$	11850.6			0.677251
$675$	−10735.4	−	13401.1i	−0.612156	−	0.764158i
$676$	−6988.22			−0.397600
$677$	1514.97	+	8591.82i	0.0860045	+	0.487756i	0.997135	+	0.0756384i	$0.0240995\pi$
$677$	1514.97	+	8591.82i	0.0860045	+	0.487756i	−0.911131	+	0.412117i	$0.864789\pi$
$678$	358.889	−	963.268i	0.0203290	−	0.0545635i
$679$	1570.19	−	571.504i	0.0887460	−	0.0323009i
$680$	398.708	+	334.555i	0.0224849	+	0.0188671i
$681$	−15853.1	+	18604.8i	−0.892057	+	1.04690i
$682$	−13851.7	−	5041.59i	−0.777723	−	0.283068i
$683$	−12790.4	−	22153.6i	−0.716559	−	1.24112i	−0.962355	−	0.271795i	$-0.912383\pi$
$683$	−12790.4	−	22153.6i	−0.716559	−	1.24112i	0.245796	−	0.969322i	$-0.420951\pi$
$684$	−10329.7	−	3937.95i	−0.577434	−	0.220133i
$685$	701.995	−	1215.89i	0.0391560	−	0.0678202i
$686$	44881.3	−	37659.9i	2.49793	−	2.09601i
$687$	61.7329	−	8147.75i	0.00342832	−	0.452483i
$688$	−2755.12	+	15625.1i	−0.152672	+	0.865844i
$689$	3941.54	−	22353.6i	0.217940	−	1.23600i
$690$	−15.7173	+	2074.44i	−0.000867173	+	0.114453i
$691$	−25192.3	+	21138.8i	−1.38692	+	1.16376i	−0.420346	+	0.907364i	$0.638091\pi$
$691$	−25192.3	+	21138.8i	−1.38692	+	1.16376i	−0.966571	+	0.256398i	$0.917464\pi$
$692$	4798.53	−	8311.30i	0.263602	−	0.456573i
$693$	−17526.7	+	14259.7i	−0.960729	+	0.781649i
$694$	6641.36	+	11503.2i	0.363260	+	0.629185i
$695$	1408.24	+	512.556i	0.0768596	+	0.0279746i
$696$	−7038.03	+	8259.69i	−0.383299	+	0.449831i
$697$	−6104.08	−	5121.93i	−0.331720	−	0.278346i
$698$	6411.97	−	2333.77i	0.347703	−	0.126554i
$699$	−10445.9	+	28037.0i	−0.565235	+	1.51711i
$700$	−4046.81	−	22950.6i	−0.218507	−	1.23922i
$701$	−27261.0			−1.46881			−0.734404	−	0.678713i	$-0.762538\pi$
$701$	−27261.0			−1.46881			−0.734404	+	0.678713i	$0.762538\pi$
$702$	13994.7	−	7661.13i	0.752415	−	0.411896i
$703$	13599.6			0.729615
$704$	−742.120	−	4208.77i	−0.0397297	−	0.225318i
$705$	2561.77	+	3100.41i	0.136854	+	0.165628i
$706$	−10783.4	+	3924.84i	−0.574843	+	0.209226i
$707$	−28242.0	−	23697.8i	−1.50233	−	1.26061i
$708$	−1467.17	−	270.180i	−0.0778811	−	0.0143418i
$709$	15803.5	+	5752.02i	0.837115	+	0.304685i	0.724776	−	0.688985i	$-0.241943\pi$
$709$	15803.5	+	5752.02i	0.837115	+	0.304685i	0.112339	+	0.993670i	$0.464166\pi$
$710$	−706.120	−	1223.04i	−0.0373243	−	0.0646475i
$711$	−9899.16	−	17762.1i	−0.522148	−	0.936891i
$712$	4023.34	−	6968.63i	0.211771	−	0.366798i
$713$	8323.73	−	6984.44i	0.437204	−	0.366857i
$714$	20478.2	+	12030.9i	1.07336	+	0.630595i
$715$	−213.102	+	1208.56i	−0.0111462	+	0.0632134i
$716$	−2944.72	+	16700.3i	−0.153700	+	0.871676i
$717$	−14557.2	+	8258.17i	−0.758226	+	0.430135i
$718$	−18244.9	+	15309.3i	−0.948321	+	0.795736i
$719$	−8119.01	+	14062.5i	−0.421124	+	0.729408i	−0.996050	−	0.0887976i	$-0.971698\pi$
$719$	−8119.01	+	14062.5i	−0.421124	+	0.729408i	0.574926	+	0.818206i	$0.305031\pi$
$720$	3190.67	−	1106.85i	0.165152	−	0.0572915i
$721$	9685.30	+	16775.4i	0.500277	+	0.866504i
$722$	5286.03	+	1923.96i	0.272473	+	0.0991721i
$723$	−4732.48	−	13315.4i	−0.243434	−	0.684932i
$724$	−288.353	−	241.957i	−0.0148019	−	0.0124203i
$725$	27200.2	−	9900.08i	1.39337	−	0.507144i
$726$	−13682.9	+	2305.92i	−0.699479	+	0.117880i
$727$	946.455	+	5367.62i	0.0482835	+	0.273829i	0.999386	−	0.0350472i	$-0.0111582\pi$
$727$	946.455	+	5367.62i	0.0482835	+	0.273829i	−0.951102	+	0.308876i	$0.900047\pi$
$728$	−9246.38			−0.470733
$729$	10606.0	−	16581.1i	0.538839	−	0.842409i
$730$	−274.702			−0.0139277
$731$	1298.32	+	7363.11i	0.0656907	+	0.372551i
$732$	−3322.40	+	559.908i	−0.167759	+	0.0282716i
$733$	−9511.13	+	3461.77i	−0.479266	+	0.174438i	−0.570345	−	0.821405i	$-0.693190\pi$
$733$	−9511.13	+	3461.77i	−0.479266	+	0.174438i	0.0910795	+	0.995844i	$0.470968\pi$
$734$	−14749.5	−	12376.3i	−0.741707	−	0.622366i
$735$	−2279.03	−	6412.33i	−0.114372	−	0.321799i
$736$	13530.7	+	4924.76i	0.677646	+	0.246643i
$737$	−1434.77	−	2485.09i	−0.0717101	−	0.124206i
$738$	−20550.8	+	7129.11i	−1.02505	+	0.355591i
$739$	458.883	−	794.808i	0.0228421	−	0.0395636i	−0.854378	−	0.519651i	$-0.826062\pi$
$739$	458.883	−	794.808i	0.0228421	−	0.0395636i	0.877220	+	0.480088i	$0.159395\pi$
$740$	1291.98	−	1084.10i	0.0641813	−	0.0538545i
$741$	10176.3	−	5772.93i	0.504502	−	0.286200i
$742$	16017.7	−	90840.8i	0.792490	−	4.49444i
$743$	2387.92	−	13542.6i	0.117906	−	0.668680i	−0.867364	−	0.497674i	$-0.834187\pi$
$743$	2387.92	−	13542.6i	0.117906	−	0.668680i	0.985270	−	0.171005i	$-0.0547015\pi$
$744$	−6416.57	−	3769.71i	−0.316186	−	0.185759i
$745$	2077.11	−	1742.90i	0.102147	−	0.0857113i
$746$	−10692.8	+	18520.4i	−0.524785	+	0.908955i
$747$	−4490.27	−	8056.90i	−0.219934	−	0.394627i
$748$	−2519.63	−	4364.14i	−0.123164	−	0.213327i
$749$	11498.3	+	4185.04i	0.560934	+	0.204163i
$750$	−7534.03	−	1387.39i	−0.366805	−	0.0675470i
$751$	17179.0	+	14414.9i	0.834713	+	0.700407i	0.956368	−	0.292165i	$-0.0943758\pi$
$751$	17179.0	+	14414.9i	0.834713	+	0.700407i	−0.121655	+	0.992572i	$0.538820\pi$
$752$	34853.5	−	12685.6i	1.69013	−	0.615156i
$753$	17946.5	+	21719.9i	0.868536	+	1.05115i
$754$	4670.33	+	26486.8i	0.225575	+	1.27930i
$755$	3977.53			0.191732
$756$	23432.8	−	12827.9i	1.12731	−	0.617123i
$757$	5900.33			0.283291			0.141645	−	0.989917i	$-0.454761\pi$
$757$	5900.33			0.283291			0.141645	+	0.989917i	$0.454761\pi$
$758$	−8190.16	−	46448.7i	−0.392454	−	2.22572i
$759$	−2994.37	+	8036.97i	−0.143200	+	0.384353i
$760$	979.079	−	356.356i	0.0467302	−	0.0170084i
$761$	8512.89	+	7143.17i	0.405509	+	0.340262i	0.822618	−	0.568594i	$-0.192512\pi$
$761$	8512.89	+	7143.17i	0.405509	+	0.340262i	−0.417110	+	0.908856i	$0.636957\pi$
$762$	−10749.8	+	12615.7i	−0.511054	+	0.599763i
$763$	−28579.9	−	10402.2i	−1.35605	−	0.493560i
$764$	−2834.83	−	4910.06i	−0.134241	−	0.232513i
$765$	1234.49	−	1004.38i	0.0583439	−	0.0474686i
$766$	−6895.44	+	11943.3i	−0.325251	+	0.563352i
$767$	1209.49	−	1014.88i	0.0569388	−	0.0477773i
$768$	211.414	−	27903.3i	0.00993326	−	1.31103i
$769$	1394.16	−	7906.68i	0.0653767	−	0.370770i	−0.934513	−	0.355929i	$-0.884165\pi$
$769$	1394.16	−	7906.68i	0.0653767	−	0.370770i	0.999890	−	0.0148412i	$-0.00472428\pi$
$770$	−866.005	+	4911.36i	−0.0405307	+	0.229861i
$771$	41.6382	−	5495.58i	0.00194496	−	0.256704i
$772$	860.932	−	722.408i	0.0401368	−	0.0336788i
$773$	661.004	−	1144.89i	0.0307564	−	0.0532716i	−0.850238	−	0.526399i	$-0.823542\pi$
$773$	661.004	−	1144.89i	0.0307564	−	0.0532716i	0.880994	+	0.473128i	$0.156875\pi$
$774$	19071.3	+	7270.50i	0.885664	+	0.337639i
$775$	9925.52	+	17191.5i	0.460045	+	0.796822i
$776$	−408.213	−	148.577i	−0.0188840	−	0.00687322i
$777$	−21314.6	+	25014.4i	−0.984113	+	1.15494i
$778$	16048.3	+	13466.1i	0.739535	+	0.620544i
$779$	−14989.4	+	5455.69i	−0.689410	+	0.250925i
$780$	506.569	−	1359.64i	0.0232539	−	0.0624142i
$781$	−1013.87	−	5749.97i	−0.0464524	−	0.263444i
$782$	9015.45			0.412266
$783$	20745.0	+	25896.2i	0.946829	+	1.18193i
$784$	−62759.9			−2.85896
$785$	781.552	+	4432.40i	0.0355347	+	0.201528i
$786$	−6791.24	−	8219.16i	−0.308188	−	0.372987i
$787$	−10920.8	+	3974.85i	−0.494644	+	0.180036i	−0.577284	−	0.816544i	$-0.695887\pi$
$787$	−10920.8	+	3974.85i	−0.494644	+	0.180036i	0.0826393	+	0.996580i	$0.473665\pi$
$788$	11825.9	+	9923.14i	0.534621	+	0.448600i
$789$	27023.1	+	4976.30i	1.21933	+	0.224539i
$790$	−4217.52	−	1535.05i	−0.189940	−	0.0691324i
$791$	910.812	+	1577.57i	0.0409415	+	0.0709128i
$792$	5873.44	+	89.0075i	0.263515	+	0.00399336i
$793$	1782.90	−	3088.07i	0.0798394	−	0.138286i
$794$	−22239.0	+	18660.7i	−0.993994	+	0.834060i
$795$	−5329.19	−	3130.88i	−0.237745	−	0.139674i
$796$	−4663.45	+	26447.7i	−0.207653	+	1.17766i
$797$	−5708.00	+	32371.7i	−0.253686	+	1.43872i	0.545737	+	0.837956i	$0.316250\pi$
$797$	−5708.00	+	32371.7i	−0.253686	+	1.43872i	−0.799423	+	0.600768i	$0.794861\pi$
$798$	41354.6	−	23460.1i	1.83451	−	1.04070i
$799$	13389.2	−	11234.8i	0.592834	−	0.497447i
$800$	−13152.9	+	22781.6i	−0.581283	+	1.00681i
$801$	−18606.2	−	16099.2i	−0.820747	−	0.710157i
$802$	−23133.2	−	40067.8i	−1.01853	−	1.76414i
$803$	−1067.22	−	388.436i	−0.0469008	−	0.0170705i
$804$	1136.19	+	3196.80i	0.0498385	+	0.140227i
$805$	−2816.13	−	2363.01i	−0.123299	−	0.103460i
$806$	−17332.4	+	6308.49i	−0.757456	+	0.275691i
$807$	−37672.4	+	6348.74i	−1.64328	+	0.276935i
$808$	1664.35	+	9439.00i	0.0724649	+	0.410969i
$809$	−19325.6			−0.839865			−0.419932	−	0.907555i	$-0.637946\pi$
$809$	−19325.6			−0.839865			−0.419932	+	0.907555i	$0.637946\pi$
$810$	−624.413	−	4299.32i	−0.0270860	−	0.186497i
$811$	20360.2			0.881556			0.440778	−	0.897616i	$-0.354703\pi$
$811$	20360.2			0.881556			0.440778	+	0.897616i	$0.354703\pi$
$812$	7820.05	+	44349.7i	0.337968	+	1.91671i
$813$	19702.5	−	3320.36i	0.849932	−	0.143235i
$814$	15902.5	−	5788.03i	0.684744	−	0.249226i
$815$	2548.11	+	2138.12i	0.109517	+	0.0918956i
$816$	−4915.12	−	13829.3i	−0.210862	−	0.593288i
$817$	14064.6	+	5119.09i	0.602274	+	0.219210i
$818$	14790.6	+	25618.1i	0.632202	+	1.09501i
$819$	−5330.83	+	27765.6i	−0.227441	+	1.18462i
$820$	−989.106	+	1713.18i	−0.0421233	+	0.0729596i
$821$	15151.1	−	12713.3i	0.644064	−	0.540434i	−0.261200	−	0.965285i	$-0.584118\pi$
$821$	15151.1	−	12713.3i	0.644064	−	0.540434i	0.905263	+	0.424851i	$0.139674\pi$
$822$	−14487.4	+	8218.56i	−0.614726	+	0.348729i
$823$	4602.09	−	26099.8i	0.194920	−	1.10544i	−0.717613	−	0.696442i	$-0.754765\pi$
$823$	4602.09	−	26099.8i	0.194920	−	1.10544i	0.912533	−	0.409003i	$-0.134123\pi$
$824$	874.474	−	4959.39i	0.0369706	−	0.209671i
$825$	−13509.9	−	7937.02i	−0.570126	−	0.334947i
$826$	4915.13	−	4124.28i	0.207045	−	0.173731i
$827$	9829.63	−	17025.4i	0.413313	−	0.715879i	−0.581937	−	0.813234i	$-0.697705\pi$
$827$	9829.63	−	17025.4i	0.413313	−	0.715879i	0.995250	+	0.0973550i	$0.0310382\pi$
$828$	5202.66	−	8703.96i	0.218363	−	0.365318i
$829$	23296.2	+	40350.2i	0.976007	+	1.69049i	0.676571	+	0.736378i	$0.263465\pi$
$829$	23296.2	+	40350.2i	0.976007	+	1.69049i	0.299436	+	0.954116i	$0.403201\pi$
$830$	−1913.07	−	696.301i	−0.0800044	−	0.0291192i
$831$	19433.5	+	3578.67i	0.811239	+	0.149389i
$832$	−4096.53	−	3437.39i	−0.170699	−	0.143233i
$833$	−27791.2	+	10115.2i	−1.15595	+	0.420732i
$834$	−11324.4	−	13705.5i	−0.470183	−	0.569043i
$835$	104.440	+	592.311i	0.00432852	+	0.0245482i
$836$	−10087.9			−0.417340
$837$	−15019.3	+	17094.7i	−0.620241	+	0.705948i
$838$	57110.4			2.35423
$839$	5314.48	+	30139.9i	0.218684	+	1.24022i	0.874397	+	0.485211i	$0.161257\pi$
$839$	5314.48	+	30139.9i	0.218684	+	1.24022i	−0.655713	+	0.755010i	$0.727632\pi$
$840$	−879.043	+	2359.37i	−0.0361070	+	0.0969121i
$841$	−29643.5	+	10789.4i	−1.21545	+	0.442386i
$842$	−10849.1	−	9103.45i	−0.444042	−	0.372596i
$843$	18438.7	−	21639.2i	0.753335	−	0.884099i
$844$	−5166.99	−	1880.63i	−0.210729	−	0.0766991i
$845$	−1006.96	−	1744.10i	−0.0409946	−	0.0710047i
$846$	−7572.33	−	47108.2i	−0.307733	−	1.91444i
$847$	12294.7	−	21295.0i	0.498760	−	0.863877i
$848$	−43665.3	+	36639.6i	−1.76825	+	1.48374i
$849$	242.921	−	32061.6i	0.00981980	−	1.29606i
$850$	−2860.07	+	16220.3i	−0.115411	+	0.654530i
$851$	−2166.19	+	12285.1i	−0.0872576	+	0.494862i
$852$	−52.3016	+	6902.97i	−0.00210308	+	0.277573i
$853$	27195.3	−	22819.6i	1.09162	−	0.915977i	0.0947855	−	0.995498i	$-0.469783\pi$
$853$	27195.3	−	22819.6i	1.09162	−	0.915977i	0.996833	+	0.0795209i	$0.0253390\pi$
$854$	7245.37	−	12549.3i	0.290318	−	0.502845i
$855$	−505.616	−	3145.49i	−0.0202242	−	0.125817i
$856$	−1590.57	−	2754.94i	−0.0635099	−	0.110002i
$857$	4997.32	+	1818.88i	0.199189	+	0.0724990i	0.439688	−	0.898150i	$-0.355089\pi$
$857$	4997.32	+	1818.88i	0.199189	+	0.0724990i	−0.240499	+	0.970649i	$0.577311\pi$
$858$	9442.50	−	11081.5i	0.375713	−	0.440929i
$859$	18040.0	+	15137.3i	0.716549	+	0.601256i	0.926428	−	0.376471i	$-0.122863\pi$
$859$	18040.0	+	15137.3i	0.716549	+	0.601256i	−0.209879	+	0.977727i	$0.567307\pi$
$860$	1744.22	−	634.846i	0.0691599	−	0.0251722i
$861$	13457.9	−	36121.3i	0.532686	−	1.42974i
$862$	−2768.91	−	15703.3i	−0.109408	−	0.620482i
$863$	41574.3			1.63987			0.819934	−	0.572459i	$-0.194010\pi$
$863$	41574.3			1.63987			0.819934	+	0.572459i	$0.194010\pi$
$864$	−29569.8	−	5909.86i	−1.16433	−	0.232706i
$865$	2765.75			0.108715
$866$	−5231.40	−	29668.7i	−0.205277	−	1.16419i
$867$	11855.5	+	14348.2i	0.464398	+	0.562042i
$868$	−29021.6	+	10563.0i	−1.13486	+	0.413055i
$869$	−14214.5	−	11927.3i	−0.554882	−	0.465601i
$870$	7202.56	+	1326.35i	0.280678	+	0.0516867i
$871$	−3374.08	−	1228.07i	−0.131259	−	0.0477743i
$872$	3953.48	+	6847.62i	0.153534	+	0.265929i
$873$	−681.505	+	1140.15i	−0.0264209	+	0.0442018i
$874$	9023.79	−	15629.7i	0.349238	−	0.604898i
$875$	10399.4	−	8726.13i	0.401787	−	0.337140i
$876$	1157.75	+	680.177i	0.0446540	+	0.0262341i
$877$	−7829.92	+	44405.7i	−0.301480	+	1.70978i	0.338149	+	0.941093i	$0.390199\pi$
$877$	−7829.92	+	44405.7i	−0.301480	+	1.70978i	−0.639629	+	0.768684i	$0.720912\pi$
$878$	4747.34	−	26923.5i	0.182477	−	1.03488i
$879$	−7132.70	+	4046.32i	−0.273697	+	0.155266i
$880$	2360.79	−	1980.94i	0.0904343	−	0.0758834i
$881$	24958.3	−	43229.1i	0.954446	−	1.65315i	0.218815	−	0.975766i	$-0.429781\pi$
$881$	24958.3	−	43229.1i	0.954446	−	1.65315i	0.735631	−	0.677382i	$-0.236886\pi$
$882$	−15222.5	+	79286.2i	−0.581143	+	3.02688i
$883$	−17926.2	−	31049.0i	−0.683197	−	1.18333i	−0.974000	−	0.226549i	$-0.927256\pi$
$883$	−17926.2	−	31049.0i	−0.683197	−	1.18333i	0.290803	−	0.956783i	$-0.406078\pi$
$884$	−5925.32	−	2156.64i	−0.225441	−	0.0820539i
$885$	−143.980	−	405.105i	−0.00546873	−	0.0153870i
$886$	20025.1	+	16803.0i	0.759318	+	0.637143i
$887$	−8119.60	+	2955.29i	−0.307361	+	0.111870i	−0.491096	−	0.871105i	$-0.663404\pi$
$887$	−8119.60	+	2955.29i	−0.307361	+	0.111870i	0.183734	+	0.982976i	$0.441181\pi$
$888$	8425.01	−	1419.83i	0.318384	−	0.0536557i
$889$	−5100.31	−	28925.3i	−0.192417	−	1.09125i
$890$	−5430.67			−0.204535
$891$	3653.50	−	17585.8i	0.137370	−	0.661220i
$892$	2609.37			0.0979465
$893$	−6075.76	−	34457.4i	−0.227679	−	1.29123i
$894$	−31720.2	+	5345.64i	−1.18667	+	0.199983i
$895$	−4592.34	+	1671.47i	−0.171514	+	0.0624259i
$896$	28091.5	+	23571.6i	1.04740	+	0.878874i
$897$	3594.01	+	10112.2i	0.133780	+	0.376407i
$898$	39048.1	+	14212.3i	1.45106	+	0.528143i
$899$	−19180.1	−	33220.8i	−0.711558	−	1.23245i
$900$	14009.4	+	12121.7i	0.518865	+	0.448951i
$901$	−13430.5	+	23262.3i	−0.496598	+	0.860132i
$902$	−15205.6	+	12759.0i	−0.561299	+	0.470985i
$903$	−31459.1	+	17846.5i	−1.15935	+	0.657690i
$904$	82.2361	−	466.384i	0.00302559	−	0.0171590i
$905$	18.8372	−	106.831i	0.000691900	−	0.00392396i
$906$	−40685.5	−	23902.6i	−1.49193	−	0.876502i
$907$	−17043.7	+	14301.3i	−0.623953	+	0.523559i	−0.899043	−	0.437860i	$-0.855737\pi$
$907$	−17043.7	+	14301.3i	−0.623953	+	0.523559i	0.275090	+	0.961418i	$0.411292\pi$
$908$	13185.8	−	22838.4i	0.481922	−	0.834713i
$909$	29303.5	+	444.072i	1.06924	+	0.0162035i
$910$	3120.17	+	5404.30i	0.113662	+	0.196869i
$911$	−29787.0	−	10841.6i	−1.08330	−	0.394289i	−0.262165	−	0.965023i	$-0.584436\pi$
$911$	−29787.0	−	10841.6i	−1.08330	−	0.394289i	−0.821135	+	0.570734i	$0.806659\pi$
$912$	−28894.9	−	5320.98i	−1.04913	−	0.193197i
$913$	−6447.70	−	5410.26i	−0.233721	−	0.196116i
$914$	−6977.40	+	2539.56i	−0.252507	+	0.0919052i
$915$	−618.477	−	748.517i	−0.0223456	−	0.0270440i
$916$	1526.52	+	8657.30i	0.0550628	+	0.312277i
$917$	18893.8			0.680401
$918$	−18663.1	+	2855.09i	−0.670996	+	0.102649i
$919$	−47605.4			−1.70877			−0.854384	−	0.519642i	$-0.826065\pi$
$919$	−47605.4			−1.70877			−0.854384	+	0.519642i	$0.826065\pi$
$920$	165.960	+	941.204i	0.00594731	+	0.0337289i
$921$	−9753.62	+	26179.0i	−0.348961	+	0.936620i
$922$	46113.2	−	16783.8i	1.64713	−	0.599507i
$923$	−5596.63	−	4696.13i	−0.199583	−	0.167470i
$924$	15810.6	−	18555.0i	0.562913	−	0.660623i
$925$	−21415.7	−	7794.67i	−0.761236	−	0.277067i
$926$	32917.7	+	57015.2i	1.16819	+	2.02336i
$927$	−14388.2	−	5485.17i	−0.509784	−	0.194344i
$928$	25416.7	−	44023.0i	0.899078	−	1.55725i
$929$	−33532.8	+	28137.3i	−1.18426	+	0.993709i	−0.184315	+	0.982867i	$0.559007\pi$
$929$	−33532.8	+	28137.3i	−1.18426	+	0.993709i	−0.999941	+	0.0108420i	$0.996549\pi$
$930$	−38.0532	+	5022.41i	−0.00134174	+	0.177088i
$931$	−10280.7	+	58304.8i	−0.361908	+	2.05248i
$932$	5605.43	−	31790.0i	0.197008	−	1.11729i
$933$	−242.237	+	31971.3i	−0.00849997	+	1.12186i
$934$	−28769.5	+	24140.5i	−1.00789	+	0.845718i
$935$	726.127	−	1257.69i	0.0253977	−	0.0439902i
$936$	5701.55	−	4638.78i	0.199103	−	0.161991i
$937$	−14470.7	−	25064.0i	−0.504522	−	0.873857i	−0.999986	−	0.00522921i	$-0.998335\pi$
$937$	−14470.7	−	25064.0i	−0.504522	−	0.873857i	0.495465	−	0.868628i	$-0.334998\pi$
$938$	−13711.6	−	4990.62i	−0.477293	−	0.173720i
$939$	24751.0	−	29047.2i	0.860189	−	1.00950i
$940$	−3323.99	−	2789.16i	−0.115337	−	0.0967791i
$941$	40949.4	−	14904.4i	1.41861	−	0.516332i	0.484965	−	0.874533i	$-0.338832\pi$
$941$	40949.4	−	14904.4i	1.41861	−	0.516332i	0.933644	+	0.358202i	$0.116610\pi$
$942$	18641.7	−	50034.9i	0.644777	−	1.73060i
$943$	−2540.79	−	14409.5i	−0.0877406	−	0.497602i
$944$	−3964.92			−0.136702
$945$	6578.07	+	3999.89i	0.226439	+	0.137690i
$946$	18624.9			0.640113
$947$	−671.678	−	3809.28i	−0.0230482	−	0.130713i	0.971113	−	0.238622i	$-0.0766956\pi$
$947$	−671.678	−	3809.28i	−0.0230482	−	0.130713i	−0.994161	+	0.107909i	$0.965584\pi$
$948$	13974.2	+	16912.4i	0.478756	+	0.579418i
$949$	−1335.40	+	486.046i	−0.0456786	+	0.0166256i
$950$	25257.6	+	21193.6i	0.862594	+	0.723803i
$951$	−5242.77	−	965.454i	−0.178768	−	0.0329201i
$952$	10282.1	+	3742.39i	0.350048	+	0.127407i
$953$	15695.5	+	27185.4i	0.533502	+	0.924053i	0.999234	+	0.0391271i	$0.0124577\pi$
$953$	15695.5	+	27185.4i	0.533502	+	0.924053i	−0.465732	+	0.884926i	$0.654209\pi$
$954$	35696.6	+	64050.5i	1.21145	+	2.17370i
$955$	816.961	−	1415.02i	0.0276819	−	0.0479465i
$956$	13832.4	−	11606.8i	0.467963	−	0.392668i
$957$	26106.5	+	15337.5i	0.881821	+	0.518067i
$958$	−1974.62	+	11198.6i	−0.0665940	+	0.377673i
$959$	5125.44	−	29067.8i	0.172585	−	0.978779i
$960$	−1266.56	+	718.511i	−0.0425814	+	0.0241561i
$961$	−2668.67	+	2239.28i	−0.0895798	+	0.0751664i
$962$	10587.8	−	18338.7i	0.354850	−	0.614618i
$963$	−9189.72	+	3187.94i	−0.307512	+	0.106677i
$964$	7623.18	+	13203.7i	0.254695	+	0.441145i
$965$	304.352	+	110.775i	0.0101528	+	0.00369531i
$966$	14605.4	+	41094.1i	0.486460	+	1.36872i
$967$	−19725.0	−	16551.3i	−0.655960	−	0.550416i	0.252913	−	0.967489i	$-0.418612\pi$
$967$	−19725.0	−	16551.3i	−0.655960	−	0.550416i	−0.908873	+	0.417073i	$0.863056\pi$
$968$	−6007.11	+	2186.41i	−0.199459	+	0.0725970i
$969$	−13652.8	+	2300.83i	−0.452621	+	0.0762781i
$970$	50.9106	+	288.728i	0.00168520	+	0.00955722i
$971$	−28752.1			−0.950258			−0.475129	−	0.879916i	$-0.657599\pi$
$971$	−28752.1			−0.950258			−0.475129	+	0.879916i	$0.657599\pi$
$972$	−8013.70	+	19665.9i	−0.264444	+	0.648955i
$973$	31505.5			1.03805
$974$	949.670	+	5385.85i	0.0312417	+	0.177180i
$975$	−19333.7	+	3258.21i	−0.635049	+	0.107022i
$976$	−8414.52	+	3062.63i	−0.275965	+	0.100443i
$977$	−3165.04	−	2655.78i	−0.103642	−	0.0869663i	0.589494	−	0.807773i	$-0.299327\pi$
$977$	−3165.04	−	2655.78i	−0.103642	−	0.0869663i	−0.693136	+	0.720806i	$0.743772\pi$
$978$	−13215.3	−	37183.0i	−0.432086	−	1.21573i
$979$	−21098.2	−	7679.10i	−0.688764	−	0.250690i
$980$	3671.11	+	6358.55i	0.119663	+	0.207262i
$981$	22841.7	−	7923.86i	0.743405	−	0.257889i
$982$	−14605.8	+	25298.0i	−0.474633	+	0.822088i
$983$	5353.10	−	4491.78i	0.173690	−	0.145743i	−0.551799	−	0.833977i	$-0.686058\pi$
$983$	5353.10	−	4491.78i	0.173690	−	0.145743i	0.725489	+	0.688234i	$0.241614\pi$
$984$	−8716.38	+	4944.73i	−0.282386	+	0.160195i
$985$	−772.550	+	4381.35i	−0.0249904	+	0.141727i
$986$	5526.80	−	31344.0i	0.178508	−	1.01237i
$987$	72901.4	+	42829.4i	2.35104	+	1.38123i
$988$	−9669.66	+	8113.81i	−0.311369	+	0.261270i
$989$	−6864.55	+	11889.7i	−0.220708	+	0.382277i
$990$	−1929.96	−	3462.93i	−0.0619577	−	0.111171i
$991$	−11482.3	−	19888.0i	−0.368060	−	0.637499i	0.621202	−	0.783651i	$-0.286645\pi$
$991$	−11482.3	−	19888.0i	−0.368060	−	0.637499i	−0.989262	+	0.146151i	$0.953311\pi$
$992$	32759.1	+	11923.3i	1.04849	+	0.381619i
$993$	29446.7	+	5422.60i	0.941050	+	0.173294i
$994$	−22743.6	−	19084.2i	−0.725738	−	0.608967i
$995$	−7272.73	+	2647.06i	−0.231720	+	0.0843391i
$996$	6338.71	+	7671.48i	0.201656	+	0.244056i
$997$	308.481	+	1749.48i	0.00979910	+	0.0555735i	0.989315	−	0.145792i	$-0.0465731\pi$
$997$	308.481	+	1749.48i	0.00979910	+	0.0555735i	−0.979516	+	0.201366i	$0.935462\pi$
$998$	−30100.1			−0.954713
$999$	593.746	−	26117.7i	0.0188041	−	0.827154i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.4.e.a.13.7	✓	48
3.2	odd	2		81.4.e.a.10.2		48
9.2	odd	6		243.4.e.b.109.2		48
9.4	even	3		243.4.e.d.190.2		48
9.5	odd	6		243.4.e.a.190.7		48
9.7	even	3		243.4.e.c.109.7		48
27.2	odd	18		81.4.e.a.73.2		48
27.5	odd	18		729.4.a.c.1.5		24
27.7	even	9		243.4.e.c.136.7		48
27.11	odd	18		243.4.e.a.55.7		48
27.16	even	9		243.4.e.d.55.2		48
27.20	odd	18		243.4.e.b.136.2		48
27.22	even	9		729.4.a.d.1.20		24
27.25	even	9	inner	27.4.e.a.25.7	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.13.7	✓	48	1.1	even	1	trivial
27.4.e.a.25.7	yes	48	27.25	even	9	inner
81.4.e.a.10.2		48	3.2	odd	2
81.4.e.a.73.2		48	27.2	odd	18
243.4.e.a.55.7		48	27.11	odd	18
243.4.e.a.190.7		48	9.5	odd	6
243.4.e.b.109.2		48	9.2	odd	6
243.4.e.b.136.2		48	27.20	odd	18
243.4.e.c.109.7		48	9.7	even	3
243.4.e.c.136.7		48	27.7	even	9
243.4.e.d.55.2		48	27.16	even	9
243.4.e.d.190.2		48	9.4	even	3
729.4.a.c.1.5		24	27.5	odd	18
729.4.a.d.1.20		24	27.22	even	9

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.640527 + 3.63261i) q^{2} +(5.12390 - 0.863506i) q^{3} +(-5.26804 + 1.91741i) q^{4} +(-1.23763 - 1.03850i) q^{5} +(6.41878 + 18.0600i) q^{6} +(-31.9169 - 11.6168i) q^{7} +(4.41508 + 7.64714i) q^{8} +(25.5087 - 8.84904i) q^{9} +(2.97972 - 5.16102i) q^{10} +(18.8740 - 15.8372i) q^{11} +(-25.3372 + 14.3736i) q^{12} +(5.35351 - 30.3613i) q^{13} +(21.7557 - 123.382i) q^{14} +(-7.23826 - 4.25245i) q^{15} +(-59.3074 + 49.7648i) q^{16} +(-18.2417 + 31.5955i) q^{17} +(48.4841 + 86.9951i) q^{18} +(36.5170 + 63.2494i) q^{19} +(8.51112 + 3.09779i) q^{20} +(-173.570 - 31.9629i) q^{21} +(69.6196 + 58.4178i) q^{22} +(-62.9523 + 22.9128i) q^{23} +(29.2258 + 35.3707i) q^{24} +(-21.2528 - 120.530i) q^{25} +113.720 q^{26} +(123.063 - 67.3685i) q^{27} +190.413 q^{28} +(41.0688 + 232.913i) q^{29} +(10.8112 - 29.0176i) q^{30} +(-152.414 + 55.4740i) q^{31} +(-164.650 - 138.158i) q^{32} +(83.0331 - 97.4460i) q^{33} +(-126.458 - 46.0271i) q^{34} +(27.4374 + 47.5229i) q^{35} +(-117.414 + 95.5277i) q^{36} +(93.1046 - 161.262i) q^{37} +(-206.370 + 173.165i) q^{38} +(1.21372 - 160.191i) q^{39} +(2.47729 - 14.0494i) q^{40} +(-37.9265 + 215.092i) q^{41} +(4.93231 - 650.986i) q^{42} +(156.989 - 131.730i) q^{43} +(-69.0627 + 119.620i) q^{44} +(-40.7601 - 15.5389i) q^{45} +(-123.556 - 214.005i) q^{46} +(-450.185 - 163.854i) q^{47} +(-260.913 + 306.202i) q^{48} +(620.985 + 521.068i) q^{49} +(424.227 - 154.406i) q^{50} +(-66.1855 + 177.644i) q^{51} +(30.0125 + 170.209i) q^{52} +736.254 q^{53} +(323.549 + 403.888i) q^{54} -39.8060 q^{55} +(-52.0803 - 295.362i) q^{56} +(241.726 + 292.551i) q^{57} +(-819.775 + 298.374i) q^{58} +(39.2313 + 32.9190i) q^{59} +(46.2851 + 8.52338i) q^{60} +(108.686 + 39.5585i) q^{61} +(-299.141 - 518.127i) q^{62} +(-916.956 - 13.8958i) q^{63} +(86.7288 - 150.219i) q^{64} +(-38.1558 + 32.0165i) q^{65} +(407.168 + 239.210i) q^{66} +(20.2242 - 114.697i) q^{67} +(35.5163 - 201.423i) q^{68} +(-302.776 + 171.763i) q^{69} +(-155.058 + 130.109i) q^{70} +(118.488 - 205.227i) q^{71} +(180.293 + 156.000i) q^{72} +(-23.0477 - 39.9198i) q^{73} +(645.437 + 234.920i) q^{74} +(-212.976 - 599.234i) q^{75} +(-313.648 - 263.182i) q^{76} +(-786.377 + 286.218i) q^{77} +(582.689 - 98.1977i) q^{78} +(-130.778 - 741.681i) q^{79} +125.081 q^{80} +(572.389 - 451.455i) q^{81} -805.637 q^{82} +(-59.3213 - 336.428i) q^{83} +(975.660 - 164.423i) q^{84} +(55.3883 - 20.1597i) q^{85} +(579.078 + 485.904i) q^{86} +(411.554 + 1157.96i) q^{87} +(204.439 + 74.4099i) q^{88} +(-455.636 - 789.185i) q^{89} +(30.3387 - 158.019i) q^{90} +(-523.568 + 906.847i) q^{91} +(287.702 - 241.411i) q^{92} +(-733.050 + 415.854i) q^{93} +(306.862 - 1740.30i) q^{94} +(20.4896 - 116.202i) q^{95} +(-962.950 - 565.730i) q^{96} +(-37.6866 + 31.6228i) q^{97} +(-1495.08 + 2589.55i) q^{98} +(341.308 - 571.003i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9} - 3 q^{10} + 57 q^{11} + 147 q^{12} - 6 q^{13} + 51 q^{14} - 36 q^{15} + 18 q^{16} - 207 q^{17} - 639 q^{18} - 3 q^{19}+ \cdots - 1242 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9 - 3 * q^10 + 57 * q^11 + 147 * q^12 - 6 * q^13 + 51 * q^14 - 36 * q^15 + 18 * q^16 - 207 * q^17 - 639 * q^18 - 3 * q^19 - 597 * q^20 - 138 * q^21 - 60 * q^22 + 402 * q^23 + 1170 * q^24 - 222 * q^25 + 1914 * q^26 + 1125 * q^27 - 12 * q^28 + 480 * q^29 + 459 * q^30 - 60 * q^31 - 648 * q^32 - 639 * q^33 + 288 * q^34 - 1257 * q^35 - 2088 * q^36 - 3 * q^37 - 1524 * q^38 - 768 * q^39 + 561 * q^40 - 1731 * q^41 - 3078 * q^42 + 507 * q^43 - 2211 * q^44 - 360 * q^45 - 3 * q^46 + 984 * q^47 + 2289 * q^48 - 600 * q^49 + 4359 * q^50 + 2655 * q^51 - 1431 * q^52 + 2736 * q^53 + 5454 * q^54 - 12 * q^55 + 5907 * q^56 + 3426 * q^57 - 897 * q^58 + 2238 * q^59 + 1314 * q^60 + 48 * q^61 - 2118 * q^62 - 2610 * q^63 - 195 * q^64 - 6990 * q^65 - 11115 * q^66 - 681 * q^67 - 11169 * q^68 - 6138 * q^69 - 33 * q^70 - 3105 * q^71 - 36 * q^72 - 219 * q^73 + 3543 * q^74 + 2604 * q^75 + 3426 * q^76 + 4722 * q^77 + 6066 * q^78 + 2802 * q^79 + 9870 * q^80 + 3438 * q^81 - 12 * q^82 + 3468 * q^83 + 7674 * q^84 + 2529 * q^85 + 3624 * q^86 + 2880 * q^87 + 2850 * q^88 - 5202 * q^89 - 12510 * q^90 + 267 * q^91 - 18453 * q^92 - 11802 * q^93 - 1653 * q^94 - 10113 * q^95 - 14094 * q^96 - 3381 * q^97 - 4392 * q^98 - 1242 * q^99

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