LMFDB - Embedded newform 39.4.j.c.4.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [39,4,Mod(4,39)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(39, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("39.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 39 = 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	39.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.30107449022$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 70x^{8} + 1645x^{6} + 14700x^{4} + 44100x^{2} + 27648 $ x^10 + 70x^8 + 1645x^6 + 14700x^4 + 44100x^2 + 27648
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.2
Root			$-2.04224i$ of defining polynomial
Character	$\chi$	$=$	39.4
Dual form			39.4.j.c.10.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.76863 - 1.02112i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-1.91462 - 3.31622i) q^{4} +12.0825i q^{5} +(5.30590 - 3.06336i) q^{6} +(-25.7533 + 14.8686i) q^{7} +24.1582i q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.76863 - 1.02112i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-1.91462 - 3.31622i) q^{4} +12.0825i q^{5} +(5.30590 - 3.06336i) q^{6} +(-25.7533 + 14.8686i) q^{7} +24.1582i q^{8} +(-4.50000 - 7.79423i) q^{9} +(12.3377 - 21.3694i) q^{10} +(24.3038 + 14.0318i) q^{11} +11.4877 q^{12} +(-40.9717 - 22.7667i) q^{13} +60.7308 q^{14} +(-31.3911 - 18.1237i) q^{15} +(9.35146 - 16.1972i) q^{16} +(-25.3278 - 43.8690i) q^{17} +18.3802i q^{18} +(91.0612 - 52.5742i) q^{19} +(40.0681 - 23.1333i) q^{20} -89.2119i q^{21} +(-28.6563 - 49.6342i) q^{22} +(-80.2961 + 139.077i) q^{23} +(-62.7648 - 36.2373i) q^{24} -20.9857 q^{25} +(49.2164 + 82.1030i) q^{26} +27.0000 q^{27} +(98.6155 + 56.9357i) q^{28} +(-70.0525 + 121.334i) q^{29} +(37.0130 + 64.1083i) q^{30} +223.593i q^{31} +(134.294 - 77.5348i) q^{32} +(-72.9113 + 42.0954i) q^{33} +103.451i q^{34} +(-179.650 - 311.163i) q^{35} +(-17.2316 + 29.8460i) q^{36} +(-197.759 - 114.176i) q^{37} -214.739 q^{38} +(120.607 - 72.2975i) q^{39} -291.890 q^{40} +(256.259 + 147.951i) q^{41} +(-91.0962 + 157.783i) q^{42} +(96.0517 + 166.366i) q^{43} -107.462i q^{44} +(94.1734 - 54.3710i) q^{45} +(284.029 - 163.984i) q^{46} -36.9300i q^{47} +(28.0544 + 48.5916i) q^{48} +(270.653 - 468.785i) q^{49} +(37.1160 + 21.4289i) q^{50} +151.967 q^{51} +(2.94589 + 179.461i) q^{52} +149.102 q^{53} +(-47.7531 - 27.5703i) q^{54} +(-169.538 + 293.649i) q^{55} +(-359.200 - 622.152i) q^{56} +315.445i q^{57} +(247.794 - 143.064i) q^{58} +(-380.070 + 219.433i) q^{59} +138.800i q^{60} +(-143.073 - 247.809i) q^{61} +(228.316 - 395.454i) q^{62} +(231.779 + 133.818i) q^{63} -466.313 q^{64} +(275.077 - 495.038i) q^{65} +171.938 q^{66} +(465.166 + 268.564i) q^{67} +(-96.9863 + 167.985i) q^{68} +(-240.888 - 417.231i) q^{69} +733.777i q^{70} +(88.9656 - 51.3643i) q^{71} +(188.294 - 108.712i) q^{72} +75.5209i q^{73} +(233.175 + 403.871i) q^{74} +(31.4786 - 54.5225i) q^{75} +(-348.696 - 201.319i) q^{76} -834.535 q^{77} +(-287.134 + 4.71337i) q^{78} +17.5526 q^{79} +(195.702 + 112.989i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-302.152 - 523.342i) q^{82} +1463.08i q^{83} +(-295.847 + 170.807i) q^{84} +(530.045 - 306.022i) q^{85} -392.322i q^{86} +(-210.157 - 364.003i) q^{87} +(-338.983 + 587.135i) q^{88} +(-290.036 - 167.453i) q^{89} -222.078 q^{90} +(1393.66 - 22.8773i) q^{91} +614.946 q^{92} +(-580.912 - 335.390i) q^{93} +(-37.7100 + 65.3156i) q^{94} +(635.225 + 1100.24i) q^{95} +465.209i q^{96} +(-648.442 + 374.378i) q^{97} +(-957.374 + 552.740i) q^{98} -252.572i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 15 q^{3} + 30 q^{4} + 30 q^{7} - 45 q^{9}+O(q^{10}) $ 10 * q - 15 * q^3 + 30 * q^4 + 30 * q^7 - 45 * q^9	\( 10 q - 15 q^{3} + 30 q^{4} + 30 q^{7} - 45 q^{9} + 40 q^{10} + 60 q^{11} - 180 q^{12} + 25 q^{13} - 60 q^{14} + 45 q^{15} - 250 q^{16} + 105 q^{17} + 180 q^{19} + 510 q^{20} - 290 q^{22} - 60 q^{23} - 960 q^{25} - 30 q^{26} + 270 q^{27} + 150 q^{28} - 495 q^{29} + 120 q^{30} + 1440 q^{32} - 180 q^{33} + 60 q^{35} + 270 q^{36} - 405 q^{37} - 1380 q^{38} + 345 q^{39} + 2000 q^{40} + 1065 q^{41} + 90 q^{42} - 370 q^{43} - 135 q^{45} - 390 q^{46} - 750 q^{48} + 775 q^{49} - 4320 q^{50} - 630 q^{51} + 2940 q^{52} + 330 q^{53} - 260 q^{55} - 2670 q^{56} + 2040 q^{58} + 780 q^{59} - 1375 q^{61} - 780 q^{62} - 270 q^{63} - 3140 q^{64} + 1605 q^{65} + 1740 q^{66} + 1590 q^{67} - 600 q^{68} - 180 q^{69} + 1620 q^{71} + 2190 q^{74} + 1440 q^{75} - 5190 q^{76} - 4320 q^{77} + 2340 q^{78} + 1100 q^{79} + 8430 q^{80} - 405 q^{81} - 2390 q^{82} - 450 q^{84} + 525 q^{85} - 1485 q^{87} + 3170 q^{88} + 2040 q^{89} - 720 q^{90} + 4770 q^{91} - 1740 q^{92} - 990 q^{93} - 3230 q^{94} - 1380 q^{95} - 3750 q^{97} + 180 q^{98}+O(q^{100}) \) 10 * q - 15 * q^3 + 30 * q^4 + 30 * q^7 - 45 * q^9 + 40 * q^10 + 60 * q^11 - 180 * q^12 + 25 * q^13 - 60 * q^14 + 45 * q^15 - 250 * q^16 + 105 * q^17 + 180 * q^19 + 510 * q^20 - 290 * q^22 - 60 * q^23 - 960 * q^25 - 30 * q^26 + 270 * q^27 + 150 * q^28 - 495 * q^29 + 120 * q^30 + 1440 * q^32 - 180 * q^33 + 60 * q^35 + 270 * q^36 - 405 * q^37 - 1380 * q^38 + 345 * q^39 + 2000 * q^40 + 1065 * q^41 + 90 * q^42 - 370 * q^43 - 135 * q^45 - 390 * q^46 - 750 * q^48 + 775 * q^49 - 4320 * q^50 - 630 * q^51 + 2940 * q^52 + 330 * q^53 - 260 * q^55 - 2670 * q^56 + 2040 * q^58 + 780 * q^59 - 1375 * q^61 - 780 * q^62 - 270 * q^63 - 3140 * q^64 + 1605 * q^65 + 1740 * q^66 + 1590 * q^67 - 600 * q^68 - 180 * q^69 + 1620 * q^71 + 2190 * q^74 + 1440 * q^75 - 5190 * q^76 - 4320 * q^77 + 2340 * q^78 + 1100 * q^79 + 8430 * q^80 - 405 * q^81 - 2390 * q^82 - 450 * q^84 + 525 * q^85 - 1485 * q^87 + 3170 * q^88 + 2040 * q^89 - 720 * q^90 + 4770 * q^91 - 1740 * q^92 - 990 * q^93 - 3230 * q^94 - 1380 * q^95 - 3750 * q^97 + 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$.

$n$	$14$	$28$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.76863	−	1.02112i	−0.625307	−	0.361021i	0.153626	−	0.988129i	$-0.450905\pi$
$2$	−1.76863	−	1.02112i	−0.625307	−	0.361021i	−0.778932	+	0.627108i	$0.784238\pi$
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$4$	−1.91462	−	3.31622i	−0.239328	−	0.414528i
$5$			12.0825i			1.08069i	0.841444	+	0.540344i	$0.181706\pi$
$5$			12.0825i			1.08069i	−0.841444	+	0.540344i	$0.818294\pi$
$6$	5.30590	−	3.06336i	0.361021	−	0.208436i
$7$	−25.7533	+	14.8686i	−1.39055	+	0.802832i	−0.993375	−	0.114914i	$-0.963341\pi$
$7$	−25.7533	+	14.8686i	−1.39055	+	0.802832i	−0.397170	+	0.917745i	$0.630008\pi$
$8$			24.1582i			1.06765i
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	12.3377	−	21.3694i	0.390151	−	0.675761i
$11$	24.3038	+	14.0318i	0.666169	+	0.384613i	0.794624	−	0.607102i	$-0.207668\pi$
$11$	24.3038	+	14.0318i	0.666169	+	0.384613i	−0.128454	+	0.991715i	$0.541002\pi$
$12$	11.4877			0.276352
$13$	−40.9717	−	22.7667i	−0.874115	−	0.485719i
$13$	−40.9717	−	22.7667i	−0.874115	−	0.485719i
$14$	60.7308			1.15936
$15$	−31.3911	−	18.1237i	−0.540344	−	0.311968i
$16$	9.35146	−	16.1972i	0.146117	−	0.253081i
$17$	−25.3278	−	43.8690i	−0.361347	−	0.625871i	0.626836	−	0.779151i	$-0.284350\pi$
$17$	−25.3278	−	43.8690i	−0.361347	−	0.625871i	−0.988183	+	0.153280i	$0.951016\pi$
$18$			18.3802i			0.240681i
$19$	91.0612	−	52.5742i	1.09952	−	0.634808i	0.163425	−	0.986556i	$-0.447746\pi$
$19$	91.0612	−	52.5742i	1.09952	−	0.634808i	0.936095	+	0.351748i	$0.114413\pi$
$20$	40.0681	−	23.1333i	0.447975	−	0.258639i
$21$		−	89.2119i		−	0.927030i
$22$	−28.6563	−	49.6342i	−0.277707	−	0.481002i
$23$	−80.2961	+	139.077i	−0.727951	+	1.26085i	0.229796	+	0.973239i	$0.426194\pi$
$23$	−80.2961	+	139.077i	−0.727951	+	1.26085i	−0.957748	+	0.287610i	$0.907139\pi$
$24$	−62.7648	−	36.2373i	−0.533826	−	0.308204i
$25$	−20.9857			−0.167886
$26$	49.2164	+	82.1030i	0.371235	+	0.619297i
$27$	27.0000			0.192450
$28$	98.6155	+	56.9357i	0.665592	+	0.384280i
$29$	−70.0525	+	121.334i	−0.448566	+	0.776939i	−0.998293	−	0.0584051i	$-0.981398\pi$
$29$	−70.0525	+	121.334i	−0.448566	+	0.776939i	0.549727	+	0.835344i	$0.314732\pi$
$30$	37.0130	+	64.1083i	0.225254	+	0.390151i
$31$			223.593i			1.29544i	0.761880	+	0.647718i	$0.224276\pi$
$31$			223.593i			1.29544i	−0.761880	+	0.647718i	$0.775724\pi$
$32$	134.294	−	77.5348i	0.741878	−	0.428323i
$33$	−72.9113	+	42.0954i	−0.384613	+	0.222056i
$34$			103.451i			0.521815i
$35$	−179.650	−	311.163i	−0.867610	−	1.50274i
$36$	−17.2316	+	29.8460i	−0.0797759	+	0.138176i
$37$	−197.759	−	114.176i	−0.878684	−	0.507308i	−0.00845956	−	0.999964i	$-0.502693\pi$
$37$	−197.759	−	114.176i	−0.878684	−	0.507308i	−0.870224	+	0.492656i	$0.836026\pi$
$38$	−214.739			−0.916716
$39$	120.607	−	72.2975i	0.495195	−	0.296843i
$40$	−291.890			−1.15380
$41$	256.259	+	147.951i	0.976119	+	0.563563i	0.901096	−	0.433619i	$-0.142764\pi$
$41$	256.259	+	147.951i	0.976119	+	0.563563i	0.0750227	+	0.997182i	$0.476097\pi$
$42$	−91.0962	+	157.783i	−0.334677	+	0.579678i
$43$	96.0517	+	166.366i	0.340645	+	0.590015i	0.984553	−	0.175088i	$-0.0560211\pi$
$43$	96.0517	+	166.366i	0.340645	+	0.590015i	−0.643907	+	0.765103i	$0.722688\pi$
$44$		−	107.462i		−	0.368194i
$45$	94.1734	−	54.3710i	0.311968	−	0.180115i
$46$	284.029	−	163.984i	0.910386	−	0.525611i
$47$		−	36.9300i		−	0.114613i	−0.998357	−	0.0573063i	$-0.981749\pi$
$47$		−	36.9300i		−	0.114613i	0.998357	−	0.0573063i	$-0.0182512\pi$
$48$	28.0544	+	48.5916i	0.0843605	+	0.146117i
$49$	270.653	−	468.785i	0.789077	−	1.36672i
$50$	37.1160	+	21.4289i	0.104980	+	0.0606102i
$51$	151.967			0.417247
$52$	2.94589	+	179.461i	0.00785618	+	0.478591i
$53$	149.102			0.386429			0.193214	−	0.981157i	$-0.438109\pi$
$53$	149.102			0.386429			0.193214	+	0.981157i	$0.438109\pi$
$54$	−47.7531	−	27.5703i	−0.120340	−	0.0694785i
$55$	−169.538	+	293.649i	−0.415647	+	0.719921i
$56$	−359.200	−	622.152i	−0.857144	−	1.48462i
$57$			315.445i			0.733013i
$58$	247.794	−	143.064i	0.560983	−	0.323884i
$59$	−380.070	+	219.433i	−0.838659	+	0.484200i	−0.856808	−	0.515635i	$-0.827556\pi$
$59$	−380.070	+	219.433i	−0.838659	+	0.484200i	0.0181492	+	0.999835i	$0.494223\pi$
$60$			138.800i			0.298650i
$61$	−143.073	−	247.809i	−0.300305	−	0.520143i	0.675900	−	0.736993i	$-0.263755\pi$
$61$	−143.073	−	247.809i	−0.300305	−	0.520143i	−0.976205	+	0.216850i	$0.930422\pi$
$62$	228.316	−	395.454i	0.467679	−	0.810044i
$63$	231.779	+	133.818i	0.463515	+	0.267611i
$64$	−466.313			−0.910768
$65$	275.077	−	495.038i	0.524910	−	0.944645i
$66$	171.938			0.320668
$67$	465.166	+	268.564i	0.848195	+	0.489706i	0.860042	−	0.510224i	$-0.170438\pi$
$67$	465.166	+	268.564i	0.848195	+	0.489706i	−0.0118462	+	0.999930i	$0.503771\pi$
$68$	−96.9863	+	167.985i	−0.172961	+	0.299576i
$69$	−240.888	−	417.231i	−0.420283	−	0.727951i
$70$			733.777i			1.25290i
$71$	88.9656	−	51.3643i	0.148708	−	0.0858567i	−0.423800	−	0.905756i	$-0.639304\pi$
$71$	88.9656	−	51.3643i	0.148708	−	0.0858567i	0.572508	+	0.819899i	$0.305971\pi$
$72$	188.294	−	108.712i	0.308204	−	0.177942i
$73$			75.5209i			0.121083i	0.998166	+	0.0605414i	$0.0192827\pi$
$73$			75.5209i			0.121083i	−0.998166	+	0.0605414i	$0.980717\pi$
$74$	233.175	+	403.871i	0.366298	+	0.634446i
$75$	31.4786	−	54.5225i	0.0484644	−	0.0839428i
$76$	−348.696	−	201.319i	−0.526291	−	0.303854i
$77$	−834.535			−1.23512
$78$	−287.134	+	4.71337i	−0.416815	+	0.00684211i
$79$	17.5526			0.0249978			0.0124989	−	0.999922i	$-0.496021\pi$
$79$	17.5526			0.0249978			0.0124989	+	0.999922i	$0.496021\pi$
$80$	195.702	+	112.989i	0.273502	+	0.157906i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	−302.152	−	523.342i	−0.406916	−	0.704799i
$83$			1463.08i			1.93487i	0.253122	+	0.967434i	$0.418543\pi$
$83$			1463.08i			1.93487i	−0.253122	+	0.967434i	$0.581457\pi$
$84$	−295.847	+	170.807i	−0.384280	+	0.221864i
$85$	530.045	−	306.022i	0.676371	−	0.390503i
$86$		−	392.322i		−	0.491920i
$87$	−210.157	−	364.003i	−0.258980	−	0.448566i
$88$	−338.983	+	587.135i	−0.410633	+	0.711236i
$89$	−290.036	−	167.453i	−0.345436	−	0.199438i	0.317237	−	0.948346i	$-0.397245\pi$
$89$	−290.036	−	167.453i	−0.345436	−	0.199438i	−0.662673	+	0.748909i	$0.730578\pi$
$90$	−222.078			−0.260101
$91$	1393.66	−	22.8773i	1.60545	−	0.0263538i
$92$	614.946			0.696876
$93$	−580.912	−	335.390i	−0.647718	−	0.373960i
$94$	−37.7100	+	65.3156i	−0.0413776	+	0.0716680i
$95$	635.225	+	1100.24i	0.686029	+	1.18824i
$96$			465.209i			0.494585i
$97$	−648.442	+	374.378i	−0.678756	+	0.391880i	−0.799386	−	0.600818i	$-0.794842\pi$
$97$	−648.442	+	374.378i	−0.678756	+	0.391880i	0.120630	+	0.992697i	$0.461508\pi$
$98$	−957.374	+	552.740i	−0.986830	+	0.569747i
$99$		−	252.572i		−	0.256409i
$100$	40.1797	+	69.5933i	0.0401797	+	0.0695933i
$101$	−392.001	+	678.966i	−0.386194	+	0.668907i	−0.991934	−	0.126755i	$-0.959544\pi$
$101$	−392.001	+	678.966i	−0.386194	+	0.668907i	0.605740	+	0.795662i	$0.292877\pi$
$102$	−268.774	−	155.176i	−0.260907	−	0.150635i
$103$	−396.040			−0.378864			−0.189432	−	0.981894i	$-0.560665\pi$
$103$	−396.040			−0.378864			−0.189432	+	0.981894i	$0.560665\pi$
$104$	550.002	−	989.801i	0.518578	−	0.933250i
$105$	1077.90			1.00183
$106$	−263.707	−	152.251i	−0.241636	−	0.139509i
$107$	718.296	−	1244.12i	0.648974	−	1.12406i	−0.334394	−	0.942433i	$-0.608532\pi$
$107$	718.296	−	1244.12i	0.648974	−	1.12406i	0.983368	−	0.181623i	$-0.0581351\pi$
$108$	−51.6948	−	89.5380i	−0.0460587	−	0.0797759i
$109$		−	1977.92i		−	1.73807i	−0.494746	−	0.869037i	$-0.664739\pi$
$109$		−	1977.92i		−	1.73807i	0.494746	−	0.869037i	$-0.335261\pi$
$110$	599.703	−	346.239i	0.519813	−	0.300114i
$111$	593.276	−	342.528i	0.507308	−	0.292895i
$112$			556.175i			0.469228i
$113$	−61.2026	−	106.006i	−0.0509509	−	0.0882496i	0.839425	−	0.543475i	$-0.182892\pi$
$113$	−61.2026	−	106.006i	−0.0509509	−	0.0882496i	−0.890376	+	0.455226i	$0.849559\pi$
$114$	322.108	−	557.907i	0.264633	−	0.458358i
$115$	−1680.39	−	970.173i	−1.36258	−	0.786688i
$116$	536.496			0.429417
$117$	6.92382	+	421.793i	0.00547100	+	0.333288i
$118$	896.273			0.699225
$119$	1304.55	+	753.180i	1.00494	+	0.580201i
$120$	437.835	−	758.353i	0.333073	−	0.576899i
$121$	−271.718	−	470.629i	−0.204146	−	0.353591i
$122$			584.379i			0.433665i
$123$	−768.776	+	443.853i	−0.563563	+	0.325373i
$124$	741.484	−	428.096i	0.536994	−	0.310034i
$125$			1256.75i			0.899256i
$126$	−273.289	−	473.350i	−0.193226	−	0.334677i
$127$	1154.80	−	2000.18i	0.806868	−	1.39754i	−0.108154	−	0.994134i	$-0.534494\pi$
$127$	1154.80	−	2000.18i	0.806868	−	1.39754i	0.915022	−	0.403403i	$-0.132173\pi$
$128$	−249.616	−	144.116i	−0.172369	−	0.0995170i
$129$	−576.310			−0.393343
$130$	−992.006	+	594.654i	−0.669266	+	0.401190i
$131$	−1444.26			−0.963250			−0.481625	−	0.876377i	$-0.659953\pi$
$131$	−1444.26			−0.963250			−0.481625	+	0.876377i	$0.659953\pi$
$132$	279.195	+	161.193i	0.184097	+	0.106289i
$133$	−1563.41	+	2707.91i	−1.01929	+	1.76546i
$134$	−548.472	−	949.982i	−0.353588	−	0.612433i
$135$			326.226i			0.207978i
$136$	1059.80	−	611.874i	0.668212	−	0.385792i
$137$	637.324	−	367.959i	0.397447	−	0.229466i	−0.287935	−	0.957650i	$-0.592969\pi$
$137$	637.324	−	367.959i	0.397447	−	0.229466i	0.685382	+	0.728184i	$0.259635\pi$
$138$			983.904i			0.606924i
$139$	752.571	+	1303.49i	0.459225	+	0.795400i	0.998920	−	0.0464599i	$-0.0147940\pi$
$139$	752.571	+	1303.49i	0.459225	+	0.795400i	−0.539696	+	0.841860i	$0.681461\pi$
$140$	−687.923	+	1191.52i	−0.415286	+	0.719297i
$141$	95.9469	+	55.3950i	0.0573063	+	0.0330858i
$142$	−209.797			−0.123984
$143$	−676.309	−	1128.22i	−0.395495	−	0.659767i
$144$	−168.326			−0.0974111
$145$	−1466.02	−	846.406i	−0.839629	−	0.484760i
$146$	77.1160	−	133.569i	0.0437134	−	0.0757139i
$147$	811.960	+	1406.36i	0.455574	+	0.789077i
$148$			874.415i			0.485652i
$149$	370.523	−	213.921i	0.203721	−	0.117618i	−0.394669	−	0.918823i	$-0.629141\pi$
$149$	370.523	−	213.921i	0.203721	−	0.117618i	0.598390	+	0.801205i	$0.295807\pi$
$150$	−111.348	+	64.2868i	−0.0606102	+	0.0349933i
$151$			1601.83i			0.863278i	0.902046	+	0.431639i	$0.142065\pi$
$151$			1601.83i			0.863278i	−0.902046	+	0.431639i	$0.857935\pi$
$152$	1270.10	+	2199.87i	0.677753	+	1.17390i
$153$	−227.950	+	394.821i	−0.120449	+	0.208624i
$154$	1475.99	+	852.161i	0.772327	+	0.445903i
$155$	−2701.55			−1.39996
$156$	−470.672	−	261.538i	−0.241563	−	0.134229i
$157$	−730.346			−0.371261			−0.185631	−	0.982620i	$-0.559433\pi$
$157$	−730.346			−0.371261			−0.185631	+	0.982620i	$0.559433\pi$
$158$	−31.0442	−	17.9234i	−0.0156313	−	0.00902473i
$159$	−223.653	+	387.378i	−0.111552	+	0.193214i
$160$	936.811	+	1622.60i	0.462884	+	0.801738i
$161$		−	4775.58i		−	2.33769i
$162$	143.259	−	82.7108i	0.0694785	−	0.0401134i
$163$	−1644.03	+	949.180i	−0.790001	+	0.456107i	−0.839963	−	0.542644i	$-0.817423\pi$
$163$	−1644.03	+	949.180i	−0.790001	+	0.456107i	0.0499619	+	0.998751i	$0.484090\pi$
$164$		−	1133.08i		−	0.539505i
$165$	−508.615	−	880.948i	−0.239974	−	0.415647i
$166$	1493.98	−	2587.66i	0.698528	−	1.20989i
$167$	1236.25	+	713.751i	0.572839	+	0.330729i	0.758282	−	0.651926i	$-0.226039\pi$
$167$	1236.25	+	713.751i	0.572839	+	0.330729i	−0.185444	+	0.982655i	$0.559372\pi$
$168$	2155.20			0.989745
$169$	1160.36	+	1865.58i	0.528155	+	0.849148i
$170$	−1249.94			−0.563919
$171$	−819.551	−	473.168i	−0.366507	−	0.211603i
$172$	367.806	−	637.058i	0.163052	−	0.282414i
$173$	−1022.20	−	1770.50i	−0.449227	−	0.778084i	0.549109	−	0.835751i	$-0.314967\pi$
$173$	−1022.20	−	1770.50i	−0.449227	−	0.778084i	−0.998336	+	0.0576667i	$0.981634\pi$
$174$			858.385i			0.373988i
$175$	540.450	−	312.029i	0.233453	−	0.134784i
$176$	454.552	−	262.436i	0.194677	−	0.112397i
$177$		−	1316.60i		−	0.559106i
$178$	341.979	+	592.325i	0.144002	+	0.249419i
$179$	−1944.86	+	3368.59i	−0.812098	+	1.40660i	0.0992948	+	0.995058i	$0.468341\pi$
$179$	−1944.86	+	3368.59i	−0.812098	+	1.40660i	−0.911393	+	0.411537i	$0.864992\pi$
$180$	−360.613	−	208.200i	−0.149325	−	0.0862129i
$181$	2477.02			1.01721			0.508606	−	0.861000i	$-0.330161\pi$
$181$	2477.02			1.01721			0.508606	+	0.861000i	$0.330161\pi$
$182$	−2488.24	−	1382.64i	−1.01341	−	0.563121i
$183$	858.437			0.346762
$184$	−3359.84	−	1939.81i	−1.34615	−	0.777198i
$185$	1379.53	−	2389.41i	0.548242	−	0.949583i
$186$	684.947	+	1186.36i	0.270015	+	0.467679i
$187$		−	1421.58i		−	0.555914i
$188$	−122.468	+	70.7070i	−0.0475101	+	0.0274300i
$189$	−695.338	+	401.454i	−0.267611	+	0.154505i
$190$		−	2594.57i		−	0.990683i
$191$	−1138.40	−	1971.78i	−0.431267	−	0.746977i	0.565715	−	0.824601i	$-0.308600\pi$
$191$	−1138.40	−	1971.78i	−0.431267	−	0.746977i	−0.996983	+	0.0776235i	$0.975267\pi$
$192$	699.470	−	1211.52i	0.262916	−	0.455384i
$193$	3396.92	+	1961.21i	1.26692	+	0.731456i	0.974404	−	0.224805i	$-0.0721744\pi$
$193$	3396.92	+	1961.21i	1.26692	+	0.731456i	0.292515	+	0.956261i	$0.405508\pi$
$194$	1529.14			0.565907
$195$	873.531	+	1457.23i	0.320794	+	0.535151i
$196$	−2072.80			−0.755392
$197$	4384.88	+	2531.61i	1.58584	+	0.915584i	0.993982	+	0.109539i	$0.0349375\pi$
$197$	4384.88	+	2531.61i	1.58584	+	0.915584i	0.591855	+	0.806045i	$0.298396\pi$
$198$	−257.907	+	446.708i	−0.0925689	+	0.160334i
$199$	1635.03	+	2831.95i	0.582433	+	1.00880i	0.995190	+	0.0979624i	$0.0312325\pi$
$199$	1635.03	+	2831.95i	0.582433	+	1.00880i	−0.412757	+	0.910841i	$0.635434\pi$
$200$		−	506.977i		−	0.179243i
$201$	−1395.50	+	805.691i	−0.489706	+	0.282732i
$202$	1386.61	−	800.561i	0.482979	−	0.278848i
$203$		−	4166.34i		−	1.44049i
$204$	−290.959	−	503.956i	−0.0998588	−	0.172961i
$205$	−1787.61	+	3096.23i	−0.609035	+	1.05488i
$206$	700.450	+	404.405i	0.236906	+	0.136778i
$207$	1445.33			0.485301
$208$	−751.902	+	450.725i	−0.250649	+	0.150251i
$209$	2950.84			0.976622
$210$	−1906.41	−	1100.67i	−0.626451	−	0.361682i
$211$	1406.09	−	2435.42i	0.458764	−	0.794602i	−0.540132	−	0.841580i	$-0.681626\pi$
$211$	1406.09	−	2435.42i	0.458764	−	0.794602i	0.998896	+	0.0469781i	$0.0149591\pi$
$212$	−285.474	−	494.455i	−0.0924831	−	0.160185i
$213$			308.186i			0.0991388i
$214$	−2540.80	+	1466.93i	−0.811616	+	0.468587i
$215$	−2010.12	+	1160.54i	−0.637622	+	0.368131i
$216$			652.271i			0.205470i
$217$	−3324.53	−	5758.25i	−1.04002	−	1.80136i
$218$	−2019.69	+	3498.21i	−0.627481	+	1.08683i
$219$	−196.209	−	113.281i	−0.0605414	−	0.0349536i
$220$	1298.41			0.397903
$221$	38.9700	+	2374.02i	0.0118616	+	0.722596i
$222$	−1399.05			−0.422964
$223$	794.783	+	458.868i	0.238666	+	0.137794i	0.614564	−	0.788867i	$-0.289332\pi$
$223$	794.783	+	458.868i	0.238666	+	0.137794i	−0.375897	+	0.926661i	$0.622665\pi$
$224$	−2305.68	+	3993.55i	−0.687743	+	1.19121i
$225$	94.4357	+	163.567i	0.0279809	+	0.0484644i
$226$			249.981i			0.0735774i
$227$	−1157.35	+	668.194i	−0.338396	+	0.195373i	−0.659562	−	0.751650i	$-0.729258\pi$
$227$	−1157.35	+	668.194i	−0.338396	+	0.195373i	0.321167	+	0.947023i	$0.395925\pi$
$228$	1046.09	−	603.958i	0.303854	−	0.175430i
$229$		−	164.820i		−	0.0475617i	−0.999717	−	0.0237808i	$-0.992430\pi$
$229$		−	164.820i		−	0.0475617i	0.999717	−	0.0237808i	$-0.00757039\pi$
$230$	1981.33	+	3431.76i	0.568022	+	0.983843i
$231$	1251.80	−	2168.19i	0.356548	−	0.617559i
$232$	−2931.22	−	1692.34i	−0.829500	−	0.478912i
$233$	4243.42			1.19312			0.596558	−	0.802570i	$-0.296535\pi$
$233$	4243.42			1.19312			0.596558	+	0.802570i	$0.296535\pi$
$234$	418.456	−	753.067i	0.116903	−	0.210383i
$235$	446.205			0.123860
$236$	1455.38	+	840.264i	0.401429	+	0.231765i
$237$	−26.3289	+	45.6031i	−0.00721624	+	0.0124989i
$238$	−1538.18	−	2664.20i	−0.418929	−	0.725607i
$239$		−	2491.07i		−	0.674200i	−0.941469	−	0.337100i	$-0.890554\pi$
$239$		−	2491.07i		−	0.674200i	0.941469	−	0.337100i	$-0.109446\pi$
$240$	−587.106	+	338.966i	−0.157906	+	0.0911673i
$241$	−2526.54	+	1458.70i	−0.675306	+	0.389888i	−0.798084	−	0.602546i	$-0.794153\pi$
$241$	−2526.54	+	1458.70i	−0.675306	+	0.389888i	0.122778	+	0.992434i	$0.460820\pi$
$242$			1109.83i			0.294803i
$243$	−121.500	−	210.444i	−0.0320750	−	0.0555556i
$244$	−547.861	+	948.922i	−0.143743	+	0.248969i
$245$	5664.08	+	3270.16i	1.47700	+	0.852746i
$246$	1812.91			0.469866
$247$	−4927.87	+	80.8921i	−1.26944	+	0.0208382i
$248$	−5401.60			−1.38307
$249$	−3801.20	−	2194.62i	−0.967434	−	0.558549i
$250$	1283.29	−	2222.73i	0.324650	−	0.562310i
$251$	−656.939	−	1137.85i	−0.165202	−	0.286138i	0.771525	−	0.636199i	$-0.219494\pi$
$251$	−656.939	−	1137.85i	−0.165202	−	0.286138i	−0.936727	+	0.350061i	$0.886161\pi$
$252$		−	1024.84i		−	0.256187i
$253$	−3902.99	+	2253.39i	−0.969878	+	0.559959i
$254$	−4084.85	+	2358.39i	−1.00908	+	0.582593i
$255$			1836.13i			0.450914i
$256$	2159.57	+	3740.49i	0.527239	+	0.913205i
$257$	−493.791	+	855.271i	−0.119851	+	0.207589i	−0.919709	−	0.392601i	$-0.871575\pi$
$257$	−493.791	+	855.271i	−0.119851	+	0.207589i	0.799857	+	0.600190i	$0.204909\pi$
$258$	1019.28	+	588.483i	0.245960	+	0.142005i
$259$	6790.57			1.62913
$260$	−2168.33	+	35.5936i	−0.517207	+	0.00849007i
$261$	1260.94			0.299044
$262$	2554.37	+	1474.77i	0.602326	+	0.347753i
$263$	3493.23	−	6050.44i	0.819017	−	1.41858i	−0.0873899	−	0.996174i	$-0.527853\pi$
$263$	3493.23	−	6050.44i	0.819017	−	1.41858i	0.906407	−	0.422405i	$-0.138814\pi$
$264$	−1016.95	−	1761.41i	−0.237079	−	0.410633i
$265$			1801.52i			0.417609i
$266$	5530.22	−	3192.87i	1.27473	−	0.735968i
$267$	870.109	−	502.358i	0.199438	−	0.115145i
$268$		−	2056.79i		−	0.468801i
$269$	2952.17	+	5113.31i	0.669134	+	1.15897i	0.978147	+	0.207916i	$0.0666681\pi$
$269$	2952.17	+	5113.31i	0.669134	+	1.15897i	−0.309013	+	0.951058i	$0.599999\pi$
$270$	333.117	−	576.975i	0.0750846	−	0.130050i
$271$	−1845.97	−	1065.77i	−0.413781	−	0.238897i	0.278632	−	0.960398i	$-0.410119\pi$
$271$	−1845.97	−	1065.77i	−0.413781	−	0.238897i	−0.692413	+	0.721501i	$0.743452\pi$
$272$	−947.408			−0.211195
$273$	−2031.06	+	3655.16i	−0.450276	+	0.810331i
$274$	−1502.92			−0.331368
$275$	−510.032	−	294.467i	−0.111840	−	0.0645710i
$276$	−922.420	+	1597.68i	−0.201171	+	0.348438i
$277$	2016.21	+	3492.17i	0.437336	+	0.757489i	0.997483	−	0.0709046i	$-0.0225886\pi$
$277$	2016.21	+	3492.17i	0.437336	+	0.757489i	−0.560147	+	0.828393i	$0.689255\pi$
$278$		−	3073.86i		−	0.663159i
$279$	1742.74	−	1006.17i	0.373960	−	0.215906i
$280$	7517.12	−	4340.01i	1.60441	−	0.926305i
$281$			2298.29i			0.487916i	0.969786	+	0.243958i	$0.0784459\pi$
$281$			2298.29i			0.487916i	−0.969786	+	0.243958i	$0.921554\pi$
$282$	−113.130	−	195.947i	−0.0238893	−	0.0413776i
$283$	3328.40	−	5764.96i	0.699127	−	1.21092i	−0.269643	−	0.962960i	$-0.586906\pi$
$283$	3328.40	−	5764.96i	0.699127	−	1.21092i	0.968770	−	0.247963i	$-0.0797611\pi$
$284$	−340.671	−	196.687i	−0.0711800	−	0.0410958i
$285$	−3811.35			−0.792158
$286$	44.0914	+	2686.01i	0.00911601	+	0.555339i
$287$	−8799.33			−1.80978
$288$	−1208.65	−	697.813i	−0.247293	−	0.142774i
$289$	1173.51	−	2032.57i	0.238857	−	0.413713i
$290$	1728.57	+	2993.96i	0.350017	+	0.606247i
$291$		−	2246.27i		−	0.452504i
$292$	250.444	−	144.594i	0.0501922	−	0.0289785i
$293$	−6466.60	+	3733.49i	−1.28936	+	0.744413i	−0.978540	−	0.206055i	$-0.933937\pi$
$293$	−6466.60	+	3733.49i	−1.28936	+	0.744413i	−0.310821	+	0.950468i	$0.600604\pi$
$294$		−	3316.44i		−	0.657887i
$295$	−2651.29	−	4592.18i	−0.523269	−	0.906328i
$296$	2758.28	−	4777.49i	0.541628	−	0.938128i
$297$	656.202	+	378.858i	0.128204	+	0.0740188i
$298$	−873.759			−0.169851
$299$	6456.18	−	3870.14i	1.24873	−	0.748548i
$300$	−241.078			−0.0463955
$301$	−4947.29	−	2856.32i	−0.947365	−	0.546962i
$302$	1635.66	−	2833.05i	0.311662	−	0.539814i
$303$	−1176.00	−	2036.90i	−0.222969	−	0.386194i
$304$		−	1966.58i		−	0.371024i
$305$	2994.14	−	1728.67i	0.562112	−	0.324536i
$306$	806.321	−	465.529i	0.150635	−	0.0869691i
$307$			3965.99i			0.737299i	0.929568	+	0.368650i	$0.120180\pi$
$307$			3965.99i			0.737299i	−0.929568	+	0.368650i	$0.879820\pi$
$308$	1597.82	+	2767.50i	0.295598	+	0.511991i
$309$	594.060	−	1028.94i	0.109369	−	0.189432i
$310$	4778.06	+	2758.61i	0.875405	+	0.505415i
$311$	−7372.29			−1.34419			−0.672097	−	0.740463i	$-0.734606\pi$
$311$	−7372.29			−1.34419			−0.672097	+	0.740463i	$0.734606\pi$
$312$	1746.58	+	2913.65i	0.316925	+	0.528695i
$313$	8249.55			1.48975			0.744875	−	0.667204i	$-0.232509\pi$
$313$	8249.55			1.48975			0.744875	+	0.667204i	$0.232509\pi$
$314$	1291.72	+	745.772i	0.232152	+	0.134033i
$315$	−1616.85	+	2800.46i	−0.289203	+	0.500915i
$316$	−33.6067	−	58.2084i	−0.00598267	−	0.0103623i
$317$		−	5575.26i		−	0.987817i	−0.869514	−	0.493909i	$-0.835568\pi$
$317$		−	5575.26i		−	0.987817i	0.869514	−	0.493909i	$-0.164432\pi$
$318$	791.120	−	456.753i	0.139509	−	0.0805455i
$319$	−3405.08	+	1965.92i	−0.597642	+	0.345049i
$320$		−	5634.21i		−	0.984256i
$321$	2154.89	+	3732.37i	0.374686	+	0.648974i
$322$	−4876.44	+	8446.25i	−0.843955	+	1.46177i
$323$	−4612.76	−	2663.18i	−0.794615	−	0.458771i
$324$	310.169			0.0531840
$325$	859.819	+	477.775i	0.146751	+	0.0815452i
$326$	3876.91			0.658657
$327$	5138.78	+	2966.88i	0.869037	+	0.501739i
$328$	−3574.23	+	6190.74i	−0.601688	+	1.04215i
$329$	549.099	+	951.068i	0.0920146	+	0.159374i
$330$			2077.43i			0.346542i
$331$	−3600.38	+	2078.68i	−0.597870	+	0.345180i	−0.768203	−	0.640206i	$-0.778849\pi$
$331$	−3600.38	+	2078.68i	−0.597870	+	0.345180i	0.170333	+	0.985387i	$0.445516\pi$
$332$	4851.91	−	2801.25i	0.802057	−	0.463068i
$333$			2055.17i			0.338206i
$334$	−1457.65	−	2524.73i	−0.238800	−	0.413614i
$335$	−3244.91	+	5620.35i	−0.529219	+	0.916634i
$336$	−1444.98	−	834.262i	−0.234614	−	0.135454i
$337$	−3225.18			−0.521326			−0.260663	−	0.965430i	$-0.583941\pi$
$337$	−3225.18			−0.521326			−0.260663	+	0.965430i	$0.583941\pi$
$338$	−147.264	−	4484.39i	−0.0236986	−	0.721653i
$339$	367.215			0.0588330
$340$	−2029.67	−	1171.83i	−0.323749	−	0.186916i
$341$	−3137.41	+	5434.15i	−0.498241	+	0.862979i
$342$	966.324	+	1673.72i	0.152786	+	0.264633i
$343$			5897.11i			0.928321i
$344$	−4019.11	+	2320.44i	−0.629930	+	0.363690i
$345$	5041.17	−	2910.52i	0.786688	−	0.454195i
$346$			4175.15i			0.648721i
$347$	−1645.25	−	2849.65i	−0.254529	−	0.440856i	0.710239	−	0.703961i	$-0.248587\pi$
$347$	−1645.25	−	2849.65i	−0.254529	−	0.440856i	−0.964767	+	0.263104i	$0.915254\pi$
$348$	−804.744	+	1393.86i	−0.123962	+	0.214709i
$349$	−3889.77	−	2245.76i	−0.596604	−	0.344449i	0.171101	−	0.985254i	$-0.445268\pi$
$349$	−3889.77	−	2245.76i	−0.596604	−	0.344449i	−0.767704	+	0.640804i	$0.778601\pi$
$350$	−1274.48			−0.194639
$351$	−1106.24	−	614.700i	−0.168224	−	0.0934766i
$352$	4351.81			0.658955
$353$	−5107.71	−	2948.94i	−0.770130	−	0.444635i	0.0627907	−	0.998027i	$-0.480000\pi$
$353$	−5107.71	−	2948.94i	−0.770130	−	0.444635i	−0.832921	+	0.553392i	$0.813333\pi$
$354$	−1344.41	+	2328.58i	−0.201849	+	0.349613i
$355$	620.607	+	1074.92i	0.0927843	+	0.160707i
$356$			1282.43i			0.190924i
$357$	−3913.64	+	2259.54i	−0.580201	+	0.334979i
$358$	6879.49	−	3971.87i	1.01562	−	0.586369i
$359$			9277.20i			1.36388i	0.731410	+	0.681938i	$0.238863\pi$
$359$			9277.20i			1.36388i	−0.731410	+	0.681938i	$0.761137\pi$
$360$	1313.51	+	2275.06i	0.192300	+	0.333073i
$361$	2098.59	−	3634.87i	0.305962	−	0.529942i
$362$	−4380.94	−	2529.33i	−0.636069	−	0.367234i
$363$	1630.31			0.235727
$364$	−2744.21	−	4577.90i	−0.395152	−	0.659195i
$365$	−912.477			−0.130853
$366$	−1518.26	−	876.568i	−0.216833	−	0.125188i
$367$	3287.18	−	5693.56i	0.467546	−	0.809814i	−0.531766	−	0.846891i	$-0.678471\pi$
$367$	3287.18	−	5693.56i	0.467546	−	0.809814i	0.999312	+	0.0370774i	$0.0118048\pi$
$368$	1501.77	+	2601.14i	0.212732	+	0.368462i
$369$		−	2663.12i		−	0.375708i
$370$	−4879.75	+	2817.33i	−0.685638	+	0.395853i
$371$	−3839.86	+	2216.94i	−0.537347	+	0.310237i
$372$			2568.58i			0.357996i
$373$	2672.77	+	4629.38i	0.371021	+	0.642628i	0.989723	−	0.142998i	$-0.0456743\pi$
$373$	2672.77	+	4629.38i	0.371021	+	0.642628i	−0.618702	+	0.785626i	$0.712341\pi$
$374$	−1451.60	+	2514.25i	−0.200697	+	0.347617i
$375$	−3265.13	−	1885.12i	−0.449628	−	0.259593i
$376$	892.162			0.122366
$377$	5632.55	−	3376.41i	0.769472	−	0.461258i
$378$	1639.73			0.223118
$379$	899.378	+	519.256i	0.121894	+	0.0703757i	0.559707	−	0.828690i	$-0.310914\pi$
$379$	899.378	+	519.256i	0.121894	+	0.0703757i	−0.437813	+	0.899066i	$0.644247\pi$
$380$	2432.43	−	4213.10i	0.328372	−	0.568756i
$381$	3464.41	+	6000.54i	0.465846	+	0.806868i
$382$			4649.80i			0.622786i
$383$	5844.97	−	3374.59i	0.779801	−	0.450219i	−0.0565585	−	0.998399i	$-0.518013\pi$
$383$	5844.97	−	3374.59i	0.779801	−	0.450219i	0.836360	+	0.548181i	$0.184679\pi$
$384$	748.849	−	432.348i	0.0995170	−	0.0574562i
$385$		−	10083.2i		−	1.33478i
$386$	−4005.27	−	6937.33i	−0.528142	−	0.914769i
$387$	864.465	−	1497.30i	0.113548	−	0.196672i
$388$	2483.04	+	1433.59i	0.324890	+	0.187575i
$389$	1246.11			0.162417			0.0812083	−	0.996697i	$-0.474122\pi$
$389$	1246.11			0.162417			0.0812083	+	0.996697i	$0.474122\pi$
$390$	−56.9491	−	3469.29i	−0.00739418	−	0.450447i
$391$	8134.89			1.05217
$392$	11325.0	+	6538.50i	1.45918	+	0.842459i
$393$	2166.39	−	3752.30i	0.278066	−	0.481625i
$394$	−5170.17	−	8954.99i	−0.661090	−	1.14504i
$395$			212.079i			0.0270148i
$396$	−837.586	+	483.580i	−0.106289	+	0.0613657i
$397$	−7236.24	+	4177.85i	−0.914802	+	0.528161i	−0.881973	−	0.471300i	$-0.843785\pi$
$397$	−7236.24	+	4177.85i	−0.914802	+	0.528161i	−0.0328293	+	0.999461i	$0.510452\pi$
$398$		−	6678.25i		−	0.841082i
$399$	−4690.24	−	8123.74i	−0.588486	−	1.01929i
$400$	−196.247	+	339.910i	−0.0245309	+	0.0424887i
$401$	2843.73	+	1641.83i	0.354137	+	0.204461i	0.666506	−	0.745500i	$-0.267789\pi$
$401$	2843.73	+	1641.83i	0.354137	+	0.204461i	−0.312369	+	0.949961i	$0.601122\pi$
$402$	3290.83			0.408288
$403$	5090.47	−	9160.98i	0.629217	−	1.13236i
$404$	3002.14			0.369708
$405$	−847.561	−	489.339i	−0.103989	−	0.0600382i
$406$	−4254.34	+	7368.74i	−0.520048	+	0.900749i
$407$	−3204.18	−	5549.81i	−0.390235	−	0.675906i
$408$			3671.24i			0.445474i
$409$	9464.72	−	5464.46i	1.14426	−	0.660636i	0.196775	−	0.980449i	$-0.436953\pi$
$409$	9464.72	−	5464.46i	1.14426	−	0.660636i	0.947481	+	0.319813i	$0.103620\pi$
$410$	6323.26	−	3650.74i	0.761667	−	0.439749i
$411$			2207.75i			0.264965i
$412$	758.267	+	1313.36i	0.0906726	+	0.157050i
$413$	6525.36	−	11302.3i	0.777462	−	1.34660i
$414$	−2556.26	−	1475.86i	−0.303462	−	0.175204i
$415$	−17677.6			−2.09099
$416$	−7267.47	+	119.297i	−0.856531	+	0.0140601i
$417$	−4515.43			−0.530267
$418$	−5218.96	−	3013.17i	−0.610688	−	0.352581i
$419$	−3651.47	+	6324.53i	−0.425742	+	0.737407i	−0.996489	−	0.0837185i	$-0.973320\pi$
$419$	−3651.47	+	6324.53i	−0.425742	+	0.737407i	0.570747	+	0.821126i	$0.306654\pi$
$420$	−2063.77	−	3574.55i	−0.239766	−	0.415286i
$421$			7580.99i			0.877612i	0.898582	+	0.438806i	$0.144599\pi$
$421$			7580.99i			0.877612i	−0.898582	+	0.438806i	$0.855401\pi$
$422$	−4973.71	+	2871.57i	−0.573736	+	0.331247i
$423$	−287.841	+	166.185i	−0.0330858	+	0.0191021i
$424$			3602.03i			0.412571i
$425$	531.521	+	920.622i	0.0606649	+	0.105075i
$426$	314.695	−	545.068i	0.0357912	−	0.0619921i
$427$	7369.18	+	4254.60i	0.835175	+	0.482188i
$428$	−5501.06			−0.621270
$429$	3945.67	−	64.7690i	0.444053	−	0.00728923i
$430$	4740.21			0.531612
$431$	8709.40	+	5028.37i	0.973357	+	0.561968i	0.900258	−	0.435357i	$-0.143378\pi$
$431$	8709.40	+	5028.37i	0.973357	+	0.561968i	0.0730993	+	0.997325i	$0.476711\pi$
$432$	252.490	−	437.325i	0.0281202	−	0.0487055i
$433$	1366.69	+	2367.18i	0.151683	+	0.262723i	0.931846	−	0.362853i	$-0.118197\pi$
$433$	1366.69	+	2367.18i	0.151683	+	0.262723i	−0.780163	+	0.625576i	$0.784864\pi$
$434$			13579.0i			1.50187i
$435$	4398.05	−	2539.22i	0.484760	−	0.279876i
$436$	−6559.22	+	3786.97i	−0.720481	+	0.415970i
$437$			16886.0i			1.84844i
$438$	231.348	+	400.706i	0.0252380	+	0.0437134i
$439$	3372.12	−	5840.68i	0.366611	−	0.634989i	−0.622422	−	0.782682i	$-0.713851\pi$
$439$	3372.12	−	5840.68i	0.366611	−	0.634989i	0.989033	+	0.147692i	$0.0471846\pi$
$440$	−7094.03	−	4095.74i	−0.768624	−	0.443765i
$441$	−4871.76			−0.526051
$442$	2355.24	−	4238.56i	0.253455	−	0.456126i
$443$	8655.69			0.928317			0.464158	−	0.885752i	$-0.346357\pi$
$443$	8655.69			0.928317			0.464158	+	0.885752i	$0.346357\pi$
$444$	−2271.80	−	1311.62i	−0.242826	−	0.140196i
$445$	2023.24	−	3504.35i	0.215530	−	0.373308i
$446$	−937.120	−	1623.14i	−0.0994931	−	0.172327i
$447$			1283.53i			0.135814i
$448$	12009.1	−	6933.45i	1.26646	−	0.731193i
$449$	5648.62	−	3261.23i	0.593708	−	0.342777i	−0.172854	−	0.984947i	$-0.555299\pi$
$449$	5648.62	−	3261.23i	0.593708	−	0.342777i	0.766562	+	0.642170i	$0.221966\pi$
$450$		−	385.721i		−	0.0404068i
$451$	4152.03	+	7191.53i	0.433507	+	0.750856i
$452$	−234.360	+	405.923i	−0.0243879	+	0.0422411i
$453$	−4161.67	−	2402.74i	−0.431639	−	0.249207i
$454$	2729.23			0.282135
$455$	276.414	+	16838.9i	0.0284802	+	1.73499i
$456$	−7620.59			−0.782602
$457$	−1343.40	−	775.613i	−0.137509	−	0.0793909i	0.429667	−	0.902987i	$-0.358631\pi$
$457$	−1343.40	−	775.613i	−0.137509	−	0.0793909i	−0.567176	+	0.823596i	$0.691964\pi$
$458$	−168.301	+	291.507i	−0.0171708	+	0.0297406i
$459$	−683.850	−	1184.46i	−0.0695412	−	0.120449i
$460$			7430.06i			0.753105i
$461$	−6725.77	+	3883.12i	−0.679501	+	0.392310i	−0.799667	−	0.600444i	$-0.794991\pi$
$461$	−6725.77	+	3883.12i	−0.679501	+	0.392310i	0.120166	+	0.992754i	$0.461657\pi$
$462$	−4427.96	+	2556.48i	−0.445903	+	0.257442i
$463$		−	2004.52i		−	0.201205i	−0.994927	−	0.100603i	$-0.967923\pi$
$463$		−	2004.52i		−	0.201205i	0.994927	−	0.100603i	$-0.0320771\pi$
$464$	1310.19	+	2269.31i	0.131086	+	0.227048i
$465$	4052.33	−	7018.84i	0.404134	−	0.699980i
$466$	−7505.06	−	4333.05i	−0.746063	−	0.430739i
$467$	−18674.3			−1.85042			−0.925209	−	0.379458i	$-0.876111\pi$
$467$	−18674.3			−1.85042			−0.925209	+	0.379458i	$0.876111\pi$
$468$	1385.50	−	830.535i	0.136848	−	0.0820331i
$469$	−15972.7			−1.57261
$470$	−789.173	−	455.629i	−0.0774507	−	0.0447162i
$471$	1095.52	−	1897.50i	0.107174	−	0.185631i
$472$	−5301.11	−	9181.80i	−0.516957	−	0.895395i
$473$			5391.11i			0.524067i
$474$	93.1326	−	53.7701i	0.00902473	−	0.00521043i
$475$	−1910.98	+	1103.31i	−0.184594	+	0.106575i
$476$		−	5768.22i		−	0.555433i
$477$	−670.959	−	1162.13i	−0.0644048	−	0.111552i
$478$	−2543.68	+	4405.79i	−0.243400	+	0.421581i
$479$	8065.31	+	4656.51i	0.769340	+	0.444178i	0.832639	−	0.553816i	$-0.186829\pi$
$479$	8065.31	+	4656.51i	0.769340	+	0.444178i	−0.0632994	+	0.997995i	$0.520162\pi$
$480$	−5620.86			−0.534492
$481$	5503.09	+	9180.28i	0.521662	+	0.870239i
$482$	5958.03			0.563031
$483$	12407.3	+	7163.36i	1.16884	+	0.674833i
$484$	−1040.47	+	1802.15i	−0.0977155	+	0.169248i
$485$	−4523.41	−	7834.77i	−0.423500	−	0.733523i
$486$			496.265i			0.0463190i
$487$	3062.96	−	1768.40i	0.285002	−	0.164546i	−0.350684	−	0.936494i	$-0.614051\pi$
$487$	3062.96	−	1768.40i	0.285002	−	0.164546i	0.635686	+	0.771948i	$0.280717\pi$
$488$	5986.62	−	3456.38i	0.555331	−	0.320621i
$489$		−	5695.08i		−	0.526667i
$490$	−6678.46	−	11567.4i	−0.615718	−	1.06646i
$491$	−1680.89	+	2911.39i	−0.154496	+	0.267595i	−0.932875	−	0.360199i	$-0.882709\pi$
$491$	−1680.89	+	2911.39i	−0.154496	+	0.267595i	0.778379	+	0.627794i	$0.216042\pi$
$492$	2943.83	+	1699.62i	0.269752	+	0.155742i
$493$	7097.10			0.648351
$494$	8798.20	+	4888.88i	0.801315	+	0.445266i
$495$	3051.69			0.277098
$496$	3621.58	+	2090.92i	0.327851	+	0.189285i
$497$	−1527.44	+	2645.60i	−0.137857	+	0.238775i
$498$	4481.95	+	7762.97i	0.403295	+	0.698528i
$499$		−	4027.43i		−	0.361308i	−0.983547	−	0.180654i	$-0.942179\pi$
$499$		−	4027.43i		−	0.361308i	0.983547	−	0.180654i	$-0.0578214\pi$
$500$	4167.66	−	2406.20i	0.372767	−	0.215217i
$501$	−3708.76	+	2141.25i	−0.330729	+	0.190946i
$502$			2683.26i			0.238565i
$503$	−883.336	−	1529.98i	−0.0783022	−	0.135623i	0.824215	−	0.566277i	$-0.191617\pi$
$503$	−883.336	−	1529.98i	−0.0783022	−	0.135623i	−0.902518	+	0.430653i	$0.858283\pi$
$504$	−3232.80	+	5599.37i	−0.285715	+	0.494872i
$505$	−8203.57	−	4736.33i	−0.722880	−	0.417355i
$506$	9203.96			0.808628
$507$	−6587.45	+	216.327i	−0.577039	+	0.0189496i
$508$	−8844.05			−0.772424
$509$	−5903.06	−	3408.13i	−0.514044	−	0.296784i	0.220450	−	0.975398i	$-0.429247\pi$
$509$	−5903.06	−	3408.13i	−0.514044	−	0.296784i	−0.734495	+	0.678615i	$0.762581\pi$
$510$	1874.91	−	3247.44i	0.162789	−	0.281959i
$511$	−1122.89	−	1944.91i	−0.0972091	−	0.168371i
$512$		−	6514.89i		−	0.562344i
$513$	2458.65	−	1419.50i	0.211603	−	0.122169i
$514$	1746.67	−	1008.44i	0.149888	−	0.0865378i
$515$		−	4785.13i		−	0.409433i
$516$	1103.42	+	1911.17i	0.0941380	+	0.163052i
$517$	518.194	−	897.538i	0.0440815	−	0.0763514i
$518$	−12010.0	−	6933.99i	−1.01871	−	0.588151i
$519$	6133.19			0.518723
$520$	11959.2	+	6645.37i	1.00855	+	0.560421i
$521$	−5442.27			−0.457640			−0.228820	−	0.973469i	$-0.573487\pi$
$521$	−5442.27			−0.457640			−0.228820	+	0.973469i	$0.573487\pi$
$522$	−2230.15	−	1287.58i	−0.186994	−	0.107961i
$523$	−10364.3	+	17951.4i	−0.866535	+	1.50088i	−0.00101984	+	0.999999i	$0.500325\pi$
$523$	−10364.3	+	17951.4i	−0.866535	+	1.50088i	−0.865515	+	0.500883i	$0.833009\pi$
$524$	2765.22	+	4789.49i	0.230532	+	0.399294i
$525$			1872.17i			0.155635i
$526$	−12356.5	+	7134.01i	−1.02427	+	0.591365i
$527$	9808.81	−	5663.12i	0.810775	−	0.468101i
$528$			1574.61i			0.129785i
$529$	−6811.41	−	11797.7i	−0.559827	−	0.969648i
$530$	1839.57	−	3186.22i	0.150765	−	0.261133i
$531$	3420.63	+	1974.90i	0.279553	+	0.161400i
$532$	11973.4			0.975775
$533$	−7130.99	−	11896.0i	−0.579508	−	0.966738i
$534$	−2051.87			−0.166279
$535$	15032.1	+	8678.77i	1.21475	+	0.701339i
$536$	−6488.01	+	11237.6i	−0.522835	+	0.905577i
$537$	−5834.58	−	10105.8i	−0.468865	−	0.812098i
$538$		−	12058.1i		−	0.966285i
$539$	13155.8	−	7595.50i	1.05132	−	0.606979i
$540$	1081.84	−	624.600i	0.0862129	−	0.0497750i
$541$		−	8577.44i		−	0.681651i	−0.940127	−	0.340825i	$-0.889294\pi$
$541$		−	8577.44i		−	0.681651i	0.940127	−	0.340825i	$-0.110706\pi$
$542$	2176.56	+	3769.92i	0.172493	+	0.298767i
$543$	−3715.53	+	6435.48i	−0.293644	+	0.508606i
$544$	−6802.75	−	3927.57i	−0.536150	−	0.309546i
$545$	23898.1			1.87832
$546$	7324.56	−	4390.68i	0.574107	−	0.344146i
$547$	8723.99			0.681921			0.340961	−	0.940078i	$-0.389248\pi$
$547$	8723.99			0.681921			0.340961	+	0.940078i	$0.389248\pi$
$548$	−2440.47	−	1409.01i	−0.190240	−	0.109835i
$549$	−1287.65	+	2230.28i	−0.100102	+	0.173381i
$550$	601.373	+	1041.61i	0.0466230	+	0.0807533i
$551$			14731.8i			1.13901i
$552$	10079.5	−	5819.42i	0.777198	−	0.448716i
$553$	−452.037	+	260.984i	−0.0347606	+	0.0200690i
$554$		−	8235.17i		−	0.631550i
$555$	4138.58	+	7168.22i	0.316528	+	0.548242i
$556$	2881.78	−	4991.39i	0.219810	−	0.380723i
$557$	−835.720	−	482.503i	−0.0635738	−	0.0367043i	0.467876	−	0.883794i	$-0.345019\pi$
$557$	−835.720	−	482.503i	−0.0635738	−	0.0367043i	−0.531450	+	0.847090i	$0.678353\pi$
$558$	−4109.68			−0.311786
$559$	−147.788	−	9003.09i	−0.0111820	−	0.681199i
$560$	−6719.95			−0.507089
$561$	3693.36	+	2132.37i	0.277957	+	0.160479i
$562$	2346.83	−	4064.83i	0.176148	−	0.305097i
$563$	−7302.60	−	12648.5i	−0.546657	−	0.946837i	−0.998501	−	0.0547402i	$-0.982567\pi$
$563$	−7302.60	−	12648.5i	−0.546657	−	0.946837i	0.451844	−	0.892097i	$-0.350766\pi$
$564$		−	424.242i		−	0.0316734i
$565$	1280.81	−	739.477i	0.0953702	−	0.0550620i
$566$	−11773.4	+	6797.40i	−0.874337	+	0.504799i
$567$		−	2408.72i		−	0.178407i
$568$	1240.87	+	2149.25i	0.0916650	+	0.158768i
$569$	3901.24	−	6757.15i	0.287432	−	0.497846i	−0.685764	−	0.727824i	$-0.740532\pi$
$569$	3901.24	−	6757.15i	0.287432	−	0.497846i	0.973196	+	0.229977i	$0.0738653\pi$
$570$	6740.89	+	3891.85i	0.495342	+	0.285986i
$571$	−11988.2			−0.878618			−0.439309	−	0.898336i	$-0.644777\pi$
$571$	−11988.2			−0.878618			−0.439309	+	0.898336i	$0.644777\pi$
$572$	−2446.56	+	4402.91i	−0.178839	+	0.321844i
$573$	6830.43			0.497985
$574$	15562.8	+	8985.18i	1.13167	+	0.653370i
$575$	1685.07	−	2918.63i	0.122213	−	0.211678i
$576$	2098.41	+	3634.55i	0.151795	+	0.262916i
$577$			5576.90i			0.402374i	0.979553	+	0.201187i	$0.0644798\pi$
$577$			5576.90i			0.402374i	−0.979553	+	0.201187i	$0.935520\pi$
$578$	−4151.01	+	2396.58i	−0.298718	+	0.172465i
$579$	−10190.8	+	5883.63i	−0.731456	+	0.422306i
$580$			6482.19i			0.464066i
$581$	−21754.1	−	37679.1i	−1.55337	−	2.69052i
$582$	−2293.71	+	3972.83i	−0.163363	+	0.282954i
$583$	3623.74	+	2092.17i	0.257427	+	0.148626i
$584$	−1824.45			−0.129274
$585$	−5096.29	+	83.6567i	−0.360181	+	0.00591245i
$586$	15249.4			1.07499
$587$	−23169.7	−	13377.0i	−1.62916	−	0.940593i	−0.984345	−	0.176251i	$-0.943603\pi$
$587$	−23169.7	−	13377.0i	−1.62916	−	0.940593i	−0.644810	−	0.764343i	$-0.723064\pi$
$588$	3109.19	−	5385.28i	0.218063	−	0.377696i
$589$	11755.2	+	20360.6i	0.822353	+	1.42436i
$590$			10829.2i			0.755644i
$591$	−13154.6	+	7594.84i	−0.915584	+	0.528612i
$592$	−3698.66	+	2135.42i	−0.256781	+	0.148252i
$593$			3589.40i			0.248565i	0.992247	+	0.124283i	$0.0396629\pi$
$593$			3589.40i			0.248565i	−0.992247	+	0.124283i	$0.960337\pi$
$594$	−773.721	−	1340.12i	−0.0534447	−	0.0925689i
$595$	−9100.26	+	15762.1i	−0.627016	+	1.08602i
$596$	−1418.82	−	819.158i	−0.0975122	−	0.0562987i
$597$	−9810.18			−0.672536
$598$	−15370.5	+	252.310i	−1.05108	+	0.0172537i
$599$	−7462.78			−0.509050			−0.254525	−	0.967066i	$-0.581919\pi$
$599$	−7462.78			−0.509050			−0.254525	+	0.967066i	$0.581919\pi$
$600$	1317.16	+	760.465i	0.0896216	+	0.0517431i
$601$	8255.52	−	14299.0i	0.560316	−	0.970495i	−0.437153	−	0.899387i	$-0.644013\pi$
$601$	8255.52	−	14299.0i	0.560316	−	0.970495i	0.997469	−	0.0711081i	$-0.0226535\pi$
$602$	5833.30	+	10103.6i	0.394929	+	0.684037i
$603$		−	4834.15i		−	0.326471i
$604$	5312.02	−	3066.90i	0.357853	−	0.206606i
$605$	5686.35	−	3283.02i	0.382121	−	0.220618i
$606$			4803.37i			0.321986i
$607$	5976.78	+	10352.1i	0.399654	+	0.692222i	0.993683	−	0.112222i	$-0.0357968\pi$
$607$	5976.78	+	10352.1i	0.399654	+	0.692222i	−0.594029	+	0.804444i	$0.702464\pi$
$608$	8152.66	−	14120.8i	0.543806	−	0.941900i
$609$	10824.5	+	6249.51i	0.720246	+	0.415834i
$610$	−7060.73			−0.468657
$611$	−840.773	+	1513.08i	−0.0556695	+	0.100185i
$612$	1745.75			0.115307
$613$	3962.63	+	2287.82i	0.261091	+	0.150741i	0.624832	−	0.780759i	$-0.285167\pi$
$613$	3962.63	+	2287.82i	0.261091	+	0.150741i	−0.363741	+	0.931500i	$0.618501\pi$
$614$	4049.76	−	7014.38i	0.266181	−	0.461038i
$615$	−5362.83	−	9288.70i	−0.351627	−	0.609035i
$616$		−	20160.9i		−	1.31868i
$617$	−16654.6	+	9615.51i	−1.08669	+	0.627400i	−0.932693	−	0.360671i	$-0.882548\pi$
$617$	−16654.6	+	9615.51i	−1.08669	+	0.627400i	−0.153996	+	0.988071i	$0.549214\pi$
$618$	−2101.35	+	1213.21i	−0.136778	+	0.0789687i
$619$			11715.6i			0.760727i	0.924837	+	0.380363i	$0.124201\pi$
$619$			11715.6i			0.760727i	−0.924837	+	0.380363i	$0.875799\pi$
$620$	5172.45	+	8958.95i	0.335050	+	0.580323i
$621$	−2167.99	+	3755.07i	−0.140094	+	0.242650i
$622$	13038.9	+	7528.00i	0.840533	+	0.485282i
$623$	9959.17			0.640459
$624$	−43.1652	−	2629.59i	−0.00276922	−	0.168698i
$625$	−17807.8			−1.13970
$626$	−14590.4	−	8423.79i	−0.931551	−	0.537831i
$627$	−4426.26	+	7666.51i	−0.281926	+	0.488311i
$628$	1398.34	+	2421.99i	0.0888531	+	0.153898i
$629$			11567.3i			0.733256i
$630$	5719.22	−	3302.00i	0.361682	−	0.208817i
$631$	7603.78	−	4390.04i	0.479717	−	0.276965i	−0.240581	−	0.970629i	$-0.577338\pi$
$631$	7603.78	−	4390.04i	0.479717	−	0.276965i	0.720299	+	0.693664i	$0.244005\pi$
$632$			424.040i			0.0266889i
$633$	4218.27	+	7306.25i	0.264867	+	0.458764i
$634$	−5693.02	+	9860.60i	−0.356623	+	0.617689i
$635$	24167.1	+	13952.9i	1.51030	+	0.871973i
$636$	1712.84			0.106790
$637$	−21761.8	+	13045.0i	−1.35359	+	0.811403i
$638$	8029.78			0.498279
$639$	−800.691	−	462.279i	−0.0495694	−	0.0286189i
$640$	1741.28	−	3015.98i	0.107547	−	0.186277i
$641$	12495.9	+	21643.5i	0.769980	+	1.33364i	0.937573	+	0.347789i	$0.113067\pi$
$641$	12495.9	+	21643.5i	0.769980	+	1.33364i	−0.167593	+	0.985856i	$0.553599\pi$
$642$		−	8801.60i		−	0.541077i
$643$	−2038.50	+	1176.93i	−0.125024	+	0.0721827i	−0.561208	−	0.827675i	$-0.689663\pi$
$643$	−2038.50	+	1176.93i	−0.125024	+	0.0721827i	0.436184	+	0.899858i	$0.356330\pi$
$644$	−15836.9	+	9143.42i	−0.969038	+	0.559474i
$645$		−	6963.24i		−	0.425081i
$646$	5438.85	+	9420.37i	0.331252	+	0.573745i
$647$	−2955.40	+	5118.90i	−0.179581	+	0.311043i	−0.941737	−	0.336350i	$-0.890807\pi$
$647$	−2955.40	+	5118.90i	−0.179581	+	0.311043i	0.762156	+	0.647393i	$0.224141\pi$
$648$	−1694.65	−	978.407i	−0.102735	−	0.0593140i
$649$	−12316.2			−0.744918
$650$	−1032.84	−	1722.99i	−0.0623251	−	0.103971i
$651$	19947.2			1.20091
$652$	6295.38	+	3634.64i	0.378138	+	0.218318i
$653$	−2962.17	+	5130.63i	−0.177517	+	0.307469i	−0.941029	−	0.338325i	$-0.890140\pi$
$653$	−2962.17	+	5130.63i	−0.177517	+	0.307469i	0.763512	+	0.645793i	$0.223473\pi$
$654$	−6059.08	−	10494.6i	−0.362277	−	0.627481i
$655$		−	17450.2i		−	1.04097i
$656$	4792.79	−	2767.12i	0.285254	−	0.164692i
$657$	588.627	−	339.844i	0.0349536	−	0.0201805i
$658$		−	2242.79i		−	0.132877i
$659$	6419.77	+	11119.4i	0.379482	+	0.657282i	0.990987	−	0.133958i	$-0.0427688\pi$
$659$	6419.77	+	11119.4i	0.379482	+	0.657282i	−0.611505	+	0.791241i	$0.709436\pi$
$660$	−1947.61	+	3373.36i	−0.114865	+	0.198952i
$661$	8890.18	+	5132.75i	0.523129	+	0.302028i	0.738214	−	0.674567i	$-0.235670\pi$
$661$	8890.18	+	5132.75i	0.523129	+	0.302028i	−0.215085	+	0.976595i	$0.569003\pi$
$662$	8490.35			0.498469
$663$	−6226.33	−	3459.78i	−0.364722	−	0.202665i
$664$	−35345.4			−2.06577
$665$	−32718.2	−	18889.9i	−1.90791	−	1.10153i
$666$	2098.57	−	3634.84i	0.122099	−	0.211482i
$667$	−11249.9	−	19485.4i	−0.653069	−	1.13115i
$668$		−	5466.25i		−	0.316610i
$669$	−2384.35	+	1376.60i	−0.137794	+	0.0795555i
$670$	11478.1	−	6626.89i	0.661848	−	0.382118i
$671$		−	8030.27i		−	0.462004i
$672$	−6917.03	−	11980.6i	−0.397069	−	0.687743i
$673$	4931.41	−	8541.45i	0.282454	−	0.489225i	−0.689534	−	0.724253i	$-0.742185\pi$
$673$	4931.41	−	8541.45i	0.282454	−	0.489225i	0.971989	+	0.235028i	$0.0755181\pi$
$674$	5704.17	+	3293.30i	0.325989	+	0.188210i
$675$	−566.614			−0.0323096
$676$	3965.03	−	7419.88i	0.225593	−	0.422160i
$677$	32615.5			1.85158			0.925788	−	0.378043i	$-0.123403\pi$
$677$	32615.5			1.85158			0.925788	+	0.378043i	$0.123403\pi$
$678$	−649.470	−	374.971i	−0.0367887	−	0.0212400i
$679$	11133.0	−	19282.9i	0.629227	−	1.08985i
$680$	7392.93	+	12804.9i	0.416921	+	0.722128i
$681$		−	4009.17i		−	0.225597i
$682$	11097.9	−	6407.35i	0.623107	−	0.359751i
$683$	18729.9	−	10813.7i	1.04931	−	0.605820i	0.126854	−	0.991921i	$-0.459512\pi$
$683$	18729.9	−	10813.7i	1.04931	−	0.605820i	0.922456	+	0.386102i	$0.126179\pi$
$684$			3623.75i			0.202570i
$685$	4445.85	+	7700.44i	0.247981	+	0.429516i
$686$	6021.66	−	10429.8i	0.335143	−	0.580485i
$687$	428.215	+	247.230i	0.0237808	+	0.0137299i
$688$	3592.90			0.199096
$689$	−6108.95	−	3394.56i	−0.337783	−	0.187696i
$690$	−11888.0			−0.655895
$691$	−12326.3	−	7116.57i	−0.678601	−	0.391790i	0.120727	−	0.992686i	$-0.461477\pi$
$691$	−12326.3	−	7116.57i	−0.678601	−	0.391790i	−0.799328	+	0.600896i	$0.794811\pi$
$692$	−3914.25	+	6779.67i	−0.215025	+	0.372434i
$693$	3755.41	+	6504.56i	0.205853	+	0.356548i
$694$			6719.98i			0.367561i
$695$	−15749.4	+	9092.90i	−0.859579	+	0.496278i
$696$	8793.66	−	5077.02i	0.478912	−	0.276500i
$697$		−	14989.1i		−	0.814566i
$698$	4586.39	+	7943.86i	0.248707	+	0.430773i
$699$	−6365.13	+	11024.7i	−0.344423	+	0.596558i
$700$	−2069.52	−	1194.84i	−0.111743	−	0.0645151i
$701$	28747.0			1.54887			0.774437	−	0.632651i	$-0.218033\pi$
$701$	28747.0			1.54887			0.774437	+	0.632651i	$0.218033\pi$
$702$	1328.84	+	2216.78i	0.0714443	+	0.119184i
$703$	−24010.8			−1.28817
$704$	−11333.2	−	6543.21i	−0.606726	−	0.350293i
$705$	−669.307	+	1159.27i	−0.0357554	+	0.0619302i
$706$	6022.45	+	10431.2i	0.321045	+	0.556066i
$707$		−	23314.1i		−	1.24019i
$708$	−4366.14	+	2520.79i	−0.231765	+	0.133810i
$709$	1575.00	−	909.324i	0.0834276	−	0.0481670i	−0.457706	−	0.889104i	$-0.651329\pi$
$709$	1575.00	−	909.324i	0.0834276	−	0.0481670i	0.541133	+	0.840937i	$0.317995\pi$
$710$		−	2534.86i		−	0.133988i
$711$	−78.9868	−	136.809i	−0.00416630	−	0.00721624i
$712$	4045.35	−	7006.75i	0.212930	−	0.368805i
$713$	−31096.6	−	17953.6i	−1.63335	−	0.943014i
$714$	9229.06			0.483738
$715$	13631.7	−	8171.47i	0.713002	−	0.427407i
$716$	14894.7			0.777431
$717$	6471.98	+	3736.60i	0.337100	+	0.194625i
$718$	9473.15	−	16408.0i	0.492388	−	0.852841i
$719$	13070.9	+	22639.5i	0.677973	+	1.17428i	0.975590	+	0.219599i	$0.0704748\pi$
$719$	13070.9	+	22639.5i	0.677973	+	1.17428i	−0.297617	+	0.954685i	$0.596192\pi$
$720$		−	2033.80i		−	0.105271i
$721$	10199.3	−	5888.58i	0.526827	−	0.304164i
$722$	−7423.29	+	4285.84i	−0.382640	+	0.220917i
$723$		−	8752.19i		−	0.450204i
$724$	−4742.55	−	8214.34i	−0.243447	−	0.421662i
$725$	1470.10	−	2546.29i	0.0753078	−	0.130437i
$726$	−2883.42	−	1664.74i	−0.147402	−	0.0851024i
$727$	1340.10			0.0683652			0.0341826	−	0.999416i	$-0.489117\pi$
$727$	1340.10			0.0683652			0.0341826	+	0.999416i	$0.489117\pi$
$728$	552.674	+	33668.4i	0.0281366	+	1.71406i
$729$	729.000			0.0370370
$730$	1613.84	+	931.750i	0.0818231	+	0.0472406i
$731$	4865.56	−	8427.39i	0.246182	−	0.426400i
$732$	−1643.58	−	2846.77i	−0.0829898	−	0.143743i
$733$		−	32517.1i		−	1.63854i	−0.573409	−	0.819269i	$-0.694380\pi$
$733$		−	32517.1i		−	1.63854i	0.573409	−	0.819269i	$-0.305620\pi$
$734$	−11627.6	+	6713.22i	−0.584719	+	0.337588i
$735$	−16992.2	+	9810.47i	−0.852746	+	0.492333i
$736$			24903.0i			1.24719i
$737$	7536.86	+	13054.2i	0.376694	+	0.652454i
$738$	−2719.37	+	4710.08i	−0.135639	+	0.234933i
$739$	−19200.2	−	11085.3i	−0.955741	−	0.551797i	−0.0608813	−	0.998145i	$-0.519391\pi$
$739$	−19200.2	−	11085.3i	−0.955741	−	0.551797i	−0.894860	+	0.446348i	$0.852724\pi$
$740$	−10565.1			−0.524838
$741$	7181.64	−	12924.3i	0.356038	−	0.640738i
$742$	9055.07			0.448008
$743$	26316.6	+	15193.9i	1.29941	+	0.750216i	0.980303	−	0.197502i	$-0.0632828\pi$
$743$	26316.6	+	15193.9i	1.29941	+	0.750216i	0.319110	+	0.947718i	$0.396616\pi$
$744$	8102.40	−	14033.8i	0.399259	−	0.691536i
$745$	2584.70	+	4476.83i	0.127109	+	0.220159i
$746$		−	10916.9i		−	0.535786i
$747$	11403.6	−	6583.87i	0.558549	−	0.322478i
$748$	−4714.27	+	2721.78i	−0.230442	+	0.133046i
$749$			42720.3i			2.08407i
$750$	3849.88	+	6668.18i	0.187437	+	0.324650i
$751$	−8449.17	+	14634.4i	−0.410539	+	0.711074i	−0.994949	−	0.100385i	$-0.967993\pi$
$751$	−8449.17	+	14634.4i	−0.410539	+	0.711074i	0.584410	+	0.811459i	$0.301326\pi$
$752$	−598.163	−	345.350i	−0.0290063	−	0.0167468i
$753$	3941.63			0.190758
$754$	−13409.6	+	220.122i	−0.647680	+	0.0106318i
$755$	−19354.0			−0.932934
$756$	2662.62	+	1537.26i	0.128093	+	0.0739547i
$757$	−16462.9	+	28514.6i	−0.790428	+	1.36906i	0.135275	+	0.990808i	$0.456808\pi$
$757$	−16462.9	+	28514.6i	−0.790428	+	1.36906i	−0.925702	+	0.378253i	$0.876525\pi$
$758$	−1060.45	−	1836.75i	−0.0508142	−	0.0880128i
$759$		−	13520.4i		−	0.646585i
$760$	−26579.9	+	15345.9i	−1.26862	+	0.732440i
$761$	14542.3	−	8396.01i	0.692718	−	0.399941i	−0.111911	−	0.993718i	$-0.535697\pi$
$761$	14542.3	−	8396.01i	0.692718	−	0.399941i	0.804630	+	0.593777i	$0.202364\pi$
$762$		−	14150.3i		−	0.672720i
$763$	29409.0	+	50937.8i	1.39538	+	2.41687i
$764$	−4359.23	+	7550.41i	−0.206429	+	0.357545i
$765$	−4770.41	−	2754.20i	−0.225457	−	0.130168i
$766$	−13783.5			−0.650153
$767$	20567.9	−	337.626i	0.968270	−	0.0158944i
$768$	−12957.4			−0.608804
$769$	1335.04	+	770.783i	0.0626042	+	0.0361445i	0.530975	−	0.847387i	$-0.321826\pi$
$769$	1335.04	+	770.783i	0.0626042	+	0.0361445i	−0.468371	+	0.883532i	$0.655159\pi$
$770$	−10296.2	+	17833.5i	−0.481882	+	0.834645i
$771$	−1481.37	−	2565.81i	−0.0691963	−	0.119851i
$772$		−	15019.9i		−	0.700231i
$773$	−32970.6	+	19035.6i	−1.53411	+	0.885721i	−0.534948	+	0.844885i	$0.679669\pi$
$773$	−32970.6	+	19035.6i	−1.53411	+	0.885721i	−0.999166	+	0.0408357i	$0.986998\pi$
$774$	−3057.85	+	1765.45i	−0.142005	+	0.0819867i
$775$		−	4692.26i		−	0.217485i
$776$	−9044.30	−	15665.2i	−0.418391	−	0.724674i
$777$	−10185.9	+	17642.4i	−0.470290	+	0.814566i
$778$	−2203.91	−	1272.43i	−0.101560	−	0.0586358i
$779$	31113.6			1.43102
$780$	3160.02	−	5686.87i	0.145060	−	0.261055i
$781$	2882.93			0.132086
$782$	−14387.6	−	8306.71i	−0.657930	−	0.379856i
$783$	−1891.42	+	3276.03i	−0.0863266	+	0.149522i
$784$	−5062.01	−	8767.66i	−0.230595	−	0.399401i
$785$		−	8824.38i		−	0.401217i
$786$	−7663.11	+	4424.30i	−0.347753	+	0.200775i
$787$	−17363.6	+	10024.9i	−0.786463	+	0.454065i	−0.838716	−	0.544569i	$-0.816693\pi$
$787$	−17363.6	+	10024.9i	−0.786463	+	0.454065i	0.0522528	+	0.998634i	$0.483360\pi$
$788$		−	19388.3i		−	0.876498i
$789$	10479.7	+	18151.3i	0.472860	+	0.819017i
$790$	216.558	−	375.090i	0.00975291	−	0.0168925i
$791$	3152.33	+	1820.00i	0.141699	+	0.0818100i
$792$	6101.69			0.273755
$793$	220.136	+	13410.5i	0.00985781	+	0.600529i
$794$	17064.4			0.762709
$795$	−4680.48	−	2702.28i	−0.208804	−	0.120553i
$796$	6260.93	−	10844.2i	0.278785	−	0.482869i
$797$	−11200.9	−	19400.6i	−0.497813	−	0.862238i	0.502183	−	0.864761i	$-0.332530\pi$
$797$	−11200.9	−	19400.6i	−0.497813	−	0.862238i	−0.999997	+	0.00252302i	$0.999197\pi$
$798$			19157.2i			0.849823i
$799$	−1620.08	+	935.355i	−0.0717327	+	0.0414149i
$800$	−2818.26	+	1627.12i	−0.124551	+	0.0719093i
$801$			3014.15i			0.132958i
$802$	−3353.01	−	5807.59i	−0.147630	−	0.255702i
$803$	−1059.69	+	1835.44i	−0.0465700	+	0.0806617i
$804$	5343.70	+	3085.19i	0.234400	+	0.135331i
$805$	57700.7			2.52631
$806$	−18357.7	+	11004.4i	−0.802259	+	0.480911i
$807$	−17713.0			−0.772649
$808$	−16402.6	−	9470.04i	−0.714159	−	0.412320i
$809$	20983.2	−	36343.9i	0.911903	−	1.57946i	0.100530	−	0.994934i	$-0.467946\pi$
$809$	20983.2	−	36343.9i	0.911903	−	1.57946i	0.811373	−	0.584528i	$-0.198720\pi$
$810$	999.350	+	1730.92i	0.0433501	+	0.0750846i
$811$		−	13029.1i		−	0.564133i	−0.959395	−	0.282067i	$-0.908980\pi$
$811$		−	13029.1i		−	0.564133i	0.959395	−	0.282067i	$-0.0910199\pi$
$812$	−13816.5	+	7976.97i	−0.597124	+	0.344750i
$813$	5537.91	−	3197.31i	0.238897	−	0.137927i
$814$			13087.4i			0.563532i
$815$	−11468.4	−	19863.9i	−0.492909	−	0.853744i
$816$	1421.11	−	2461.44i	0.0609667	−	0.105597i
$817$	17493.2	+	10099.7i	0.749092	+	0.432489i
$818$	−22319.5			−0.954014
$819$	−6449.80	−	10759.6i	−0.275182	−	0.459060i
$820$	13690.4			0.583036
$821$	−7706.01	−	4449.07i	−0.327578	−	0.189127i	0.327187	−	0.944960i	$-0.393899\pi$
$821$	−7706.01	−	4449.07i	−0.327578	−	0.189127i	−0.654765	+	0.755832i	$0.727233\pi$
$822$	2254.39	−	3904.71i	0.0956578	−	0.165684i
$823$	11361.8	+	19679.2i	0.481224	+	0.833504i	0.999768	−	0.0215466i	$-0.00685902\pi$
$823$	11361.8	+	19679.2i	0.481224	+	0.833504i	−0.518544	+	0.855051i	$0.673526\pi$
$824$		−	9567.61i		−	0.404494i
$825$	1530.09	−	883.401i	0.0645710	−	0.0372801i
$826$	−23081.9	+	13326.4i	−0.972304	+	0.561360i
$827$		−	19073.3i		−	0.801989i	−0.916081	−	0.400994i	$-0.868665\pi$
$827$		−	19073.3i		−	0.801989i	0.916081	−	0.400994i	$-0.131335\pi$
$828$	−2767.26	−	4793.03i	−0.116146	−	0.201171i
$829$	21251.9	−	36809.4i	0.890361	−	1.54215i	0.0509178	−	0.998703i	$-0.483785\pi$
$829$	21251.9	−	36809.4i	0.890361	−	1.54215i	0.839443	−	0.543448i	$-0.182881\pi$
$830$	31265.2	+	18051.0i	1.30751	+	0.754891i
$831$	−12097.2			−0.504992
$832$	19105.6	+	10616.4i	0.796116	+	0.442377i
$833$	−27420.2			−1.14052
$834$	7986.13	+	4610.80i	0.331579	+	0.191437i
$835$	−8623.86	+	14937.0i	−0.357414	+	0.619060i
$836$	−5649.74	−	9785.65i	−0.233733	−	0.404837i
$837$			6037.01i			0.249307i
$838$	12916.2	−	7457.19i	0.532439	−	0.307404i
$839$	16824.5	−	9713.62i	0.692307	−	0.399704i	−0.112168	−	0.993689i	$-0.535780\pi$
$839$	16824.5	−	9713.62i	0.692307	−	0.399704i	0.804476	+	0.593985i	$0.202446\pi$
$840$			26040.1i			1.06960i
$841$	2379.80	+	4121.94i	0.0975768	+	0.169008i
$842$	7741.11	−	13408.0i	0.316836	−	0.548777i
$843$	−5971.13	−	3447.43i	−0.243958	−	0.140849i
$844$	−10768.5			−0.439180
$845$	−22540.8	+	14020.0i	−0.917664	+	0.570770i
$846$	678.780			0.0275850
$847$	13995.2	+	8080.15i	0.567747	+	0.327789i
$848$	1394.32	−	2415.03i	0.0564637	−	0.0977979i
$849$	9985.20	+	17294.9i	0.403641	+	0.699127i
$850$		−	2170.99i		−	0.0876052i
$851$	31758.5	−	18335.8i	1.27928	−	0.738592i
$852$	1022.01	−	590.060i	0.0410958	−	0.0237267i
$853$		−	26851.8i		−	1.07783i	−0.842361	−	0.538914i	$-0.818835\pi$
$853$		−	26851.8i		−	1.07783i	0.842361	−	0.538914i	$-0.181165\pi$
$854$	−8688.92	−	15049.7i	−0.348160	−	0.603031i
$855$	5717.03	−	9902.18i	0.228676	−	0.396079i
$856$	30055.8	+	17352.7i	1.20010	+	0.692878i
$857$	−41539.4			−1.65573			−0.827864	−	0.560929i	$-0.810444\pi$
$857$	−41539.4			−1.65573			−0.827864	+	0.560929i	$0.810444\pi$
$858$	−7044.58	−	3914.46i	−0.280301	−	0.155754i
$859$	−11936.2			−0.474107			−0.237054	−	0.971497i	$-0.576182\pi$
$859$	−11936.2			−0.474107			−0.237054	+	0.971497i	$0.576182\pi$
$860$	7697.22	+	4443.99i	0.305201	+	0.176208i
$861$	13199.0	−	22861.3i	0.522439	−	0.904892i
$862$	−10269.2	−	17786.7i	−0.405765	−	0.702805i
$863$			41128.6i			1.62229i	0.584848	+	0.811143i	$0.301154\pi$
$863$			41128.6i			1.62229i	−0.584848	+	0.811143i	$0.698846\pi$
$864$	3625.94	−	2093.44i	0.142774	−	0.0824309i
$865$	21392.0	−	12350.7i	0.840866	−	0.485474i
$866$		−	5582.22i		−	0.219043i
$867$	3520.52	+	6097.72i	0.137904	+	0.238857i
$868$	−12730.4	+	22049.7i	−0.497810	+	0.862232i
$869$	426.595	+	246.295i	0.0166528	+	0.00961448i
$870$	−10371.4			−0.404165
$871$	−12944.3	−	21593.8i	−0.503561	−	0.840044i
$872$	47782.9			1.85566
$873$	5835.98	+	3369.40i	0.226252	+	0.130627i
$874$	17242.7	−	29865.2i	0.667325	−	1.15584i
$875$	−18686.1	−	32365.4i	−0.721951	−	1.25046i
$876$			867.564i			0.0334615i
$877$	−5548.50	+	3203.43i	−0.213637	+	0.123343i	−0.603001	−	0.797741i	$-0.706028\pi$
$877$	−5548.50	+	3203.43i	−0.213637	+	0.123343i	0.389364	+	0.921084i	$0.372695\pi$
$878$	−11928.1	+	6886.68i	−0.458489	+	0.264709i
$879$		−	22401.0i		−	0.859574i
$880$	3170.87	+	5492.10i	0.121466	+	0.210385i
$881$	−1469.04	+	2544.45i	−0.0561783	+	0.0973037i	−0.892747	−	0.450559i	$-0.851225\pi$
$881$	−1469.04	+	2544.45i	−0.0561783	+	0.0973037i	0.836569	+	0.547862i	$0.184558\pi$
$882$	8616.36	+	4974.66i	0.328943	+	0.189916i
$883$	−3022.06			−0.115176			−0.0575881	−	0.998340i	$-0.518341\pi$
$883$	−3022.06			−0.115176			−0.0575881	+	0.998340i	$0.518341\pi$
$884$	7798.16	−	4674.58i	0.296697	−	0.177854i
$885$	15907.8			0.604219
$886$	−15308.8	−	8838.51i	−0.580483	−	0.335142i
$887$	5030.22	−	8712.59i	0.190415	−	0.329809i	−0.754973	−	0.655756i	$-0.772350\pi$
$887$	5030.22	−	8712.59i	0.190415	−	0.329809i	0.945388	+	0.325948i	$0.105683\pi$
$888$	8274.85	+	14332.5i	0.312709	+	0.541628i
$889$			68681.5i			2.59112i
$890$	−7156.74	+	4131.94i	−0.269544	+	0.155621i
$891$	−1968.61	+	1136.57i	−0.0740188	+	0.0427348i
$892$		−	3514.24i		−	0.131912i
$893$	−1941.57	−	3362.89i	−0.0727570	−	0.126019i
$894$	1310.64	−	2270.09i	0.0490317	−	0.0849254i
$895$	−40700.9	−	23498.7i	−1.52009	−	0.877624i
$896$	8571.24			0.319582
$897$	370.637	+	22578.9i	0.0137962	+	0.840453i
$898$	−13320.5			−0.494999
$899$	−27129.5	−	15663.2i	−1.00647	−	0.581088i
$900$	361.617	−	626.339i	0.0133932	−	0.0231978i
$901$	−3776.42	−	6540.95i	−0.139635	−	0.241854i
$902$		−	16958.9i		−	0.626020i
$903$	14841.9	−	8568.96i	0.546962	−	0.315788i
$904$	2560.91	−	1478.54i	0.0942197	−	0.0543978i
$905$			29928.4i			1.09929i
$906$	4906.99	+	8499.15i	0.179938	+	0.311662i
$907$	−21579.3	+	37376.5i	−0.789999	+	1.36832i	0.135967	+	0.990713i	$0.456586\pi$
$907$	−21579.3	+	37376.5i	−0.789999	+	1.36832i	−0.925967	+	0.377606i	$0.876748\pi$
$908$	4431.76	+	2558.68i	0.161975	+	0.0935163i
$909$	7056.02			0.257462
$910$	16705.7	−	30064.1i	0.608558	−	1.09518i
$911$	−32665.9			−1.18800			−0.594001	−	0.804464i	$-0.702453\pi$
$911$	−32665.9			−1.18800			−0.594001	+	0.804464i	$0.702453\pi$
$912$	5109.33	+	2949.87i	0.185512	+	0.107105i
$913$	−20529.7	+	35558.4i	−0.744176	+	1.28895i
$914$	1583.99	+	2743.55i	0.0573235	+	0.0992873i
$915$			10372.0i			0.374741i
$916$	−546.581	+	315.568i	−0.0197156	+	0.0113828i
$917$	37194.4	−	21474.2i	1.33944	−	0.773327i
$918$			2793.18i			0.100423i
$919$	−9494.97	−	16445.8i	−0.340816	−	0.590311i	0.643768	−	0.765221i	$-0.277370\pi$
$919$	−9494.97	−	16445.8i	−0.340816	−	0.590311i	−0.984585	+	0.174909i	$0.944037\pi$
$920$	23437.6	−	40595.2i	0.839909	−	1.45476i
$921$	−10303.9	−	5948.98i	−0.368650	−	0.212840i
$922$	15860.6			0.566529
$923$	−4814.47	+	79.0305i	−0.171690	+	0.00281833i
$924$	−9586.91			−0.341327
$925$	4150.10	+	2396.06i	0.147518	+	0.0851698i
$926$	−2046.86	+	3545.27i	−0.0726393	+	0.125815i
$927$	1782.18	+	3086.83i	0.0631440	+	0.109369i
$928$			21726.0i			0.768525i
$929$	−4846.98	+	2798.40i	−0.171178	+	0.0988295i	−0.583141	−	0.812371i	$-0.698177\pi$
$929$	−4846.98	+	2798.40i	−0.171178	+	0.0988295i	0.411963	+	0.911200i	$0.364843\pi$
$930$	−14334.2	+	8275.84i	−0.505415	+	0.291802i
$931$		−	56917.6i		−	2.00365i
$932$	−8124.55	−	14072.1i	−0.285546	−	0.494579i
$933$	11058.4	−	19153.8i	0.388035	−	0.672097i
$934$	33028.1	+	19068.8i	1.15708	+	0.668040i
$935$	17176.1			0.600770
$936$	−10189.7	+	167.267i	−0.355836	+	0.00584112i
$937$	40294.4			1.40487			0.702433	−	0.711750i	$-0.252097\pi$
$937$	40294.4			1.40487			0.702433	+	0.711750i	$0.252097\pi$
$938$	28249.9	+	16310.1i	0.983360	+	0.567743i
$939$	−12374.3	+	21432.9i	−0.430054	+	0.744875i
$940$	−854.314	−	1479.72i	−0.0296432	−	0.0513436i
$941$			43648.8i			1.51213i	0.654499	+	0.756063i	$0.272880\pi$
$941$			43648.8i			1.51213i	−0.654499	+	0.756063i	$0.727120\pi$
$942$	−3875.15	+	2237.32i	−0.134033	+	0.0773840i
$943$	−41153.1	+	23759.8i	−1.42113	+	0.820492i
$944$			8208.10i			0.282999i
$945$	−4850.54	−	8401.39i	−0.166972	−	0.289203i
$946$	5504.98	−	9534.90i	0.189199	−	0.327702i
$947$	−9081.62	−	5243.28i	−0.311629	−	0.179919i	0.336026	−	0.941853i	$-0.390917\pi$
$947$	−9081.62	−	5243.28i	−0.311629	−	0.179919i	−0.647655	+	0.761933i	$0.724250\pi$
$948$	201.640			0.00690819
$949$	1719.36	−	3094.22i	0.0588122	−	0.105840i
$950$	4506.44			0.153903
$951$	14485.0	+	8362.90i	0.493909	+	0.285158i
$952$	−18195.5	+	31515.5i	−0.619452	+	1.07292i
$953$	16529.4	+	28629.7i	0.561846	+	0.973145i	0.997335	+	0.0729517i	$0.0232419\pi$
$953$	16529.4	+	28629.7i	0.561846	+	0.973145i	−0.435490	+	0.900194i	$0.643425\pi$
$954$			2740.52i			0.0930059i
$955$	23823.9	−	13754.7i	0.807249	−	0.466065i
$956$	−8260.93	+	4769.45i	−0.279475	+	0.161355i
$957$		−	11795.5i		−	0.398428i
$958$	−9509.73	−	16471.3i	−0.320715	−	0.555495i
$959$	−10942.1	+	18952.3i	−0.368445	+	0.638166i
$960$	14638.1	+	8451.31i	0.492128	+	0.284130i
$961$	−20202.8			−0.678152
$962$	−358.769	−	21855.9i	−0.0120241	−	0.732497i
$963$	−12929.3			−0.432650
$964$	9674.74	+	5585.71i	0.323239	+	0.186622i
$965$	−23696.2	+	41043.1i	−0.790476	+	1.36914i
$966$	−14629.3	−	25338.7i	−0.487258	−	0.843955i
$967$		−	53634.9i		−	1.78364i	−0.452389	−	0.891821i	$-0.649428\pi$
$967$		−	53634.9i		−	1.78364i	0.452389	−	0.891821i	$-0.350572\pi$
$968$	11369.5	−	6564.21i	0.377511	−	0.217956i
$969$	13838.3	−	7989.53i	0.458771	−	0.264872i
$970$			18475.8i			0.611569i
$971$	2043.40	+	3539.27i	0.0675344	+	0.116973i	0.897815	−	0.440372i	$-0.145153\pi$
$971$	2043.40	+	3539.27i	0.0675344	+	0.116973i	−0.830281	+	0.557345i	$0.811820\pi$
$972$	−465.253	+	805.842i	−0.0153529	+	0.0265920i
$973$	−38762.3	−	22379.4i	−1.27715	−	0.737360i
$974$	−7223.00			−0.237618
$975$	−2531.02	+	1517.21i	−0.0831361	+	0.0498356i
$976$	−5351.76			−0.175518
$977$	−12454.3	−	7190.48i	−0.407827	−	0.235459i	0.282028	−	0.959406i	$-0.408993\pi$
$977$	−12454.3	−	7190.48i	−0.407827	−	0.235459i	−0.689856	+	0.723947i	$0.742326\pi$
$978$	−5815.37	+	10072.5i	−0.190138	+	0.329329i
$979$	−4699.32	−	8139.46i	−0.153413	−	0.265718i
$980$		−	25044.5i		−	0.816343i
$981$	−15416.3	+	8900.63i	−0.501739	+	0.289679i
$982$	5945.76	−	3432.79i	0.193215	−	0.111553i
$983$			12916.5i			0.419099i	0.977798	+	0.209549i	$0.0671997\pi$
$983$			12916.5i			0.419099i	−0.977798	+	0.209549i	$0.932800\pi$
$984$	−10722.7	−	18572.2i	−0.347385	−	0.601688i
$985$	−30588.1	+	52980.1i	−0.989460	+	1.71379i
$986$	−12552.2	−	7247.00i	−0.405418	−	0.234068i
$987$	−3294.59			−0.106249
$988$	9703.27	+	16187.0i	0.312451	+	0.521233i
$989$	−30850.3			−0.991893
$990$	−5397.33	−	3116.15i	−0.173271	−	0.100038i
$991$	2919.49	−	5056.71i	0.0935829	−	0.162090i	−0.815433	−	0.578851i	$-0.803501\pi$
$991$	2919.49	−	5056.71i	0.0935829	−	0.162090i	0.909016	+	0.416761i	$0.136835\pi$
$992$	17336.2	+	30027.2i	0.554865	+	0.961055i
$993$		−	12472.1i		−	0.398580i
$994$	5402.95	−	3119.40i	0.172406	−	0.0995385i
$995$	−34217.0	+	19755.2i	−1.09020	+	0.629428i
$996$			16807.5i			0.534705i
$997$	−22145.1	−	38356.4i	−0.703452	−	1.21841i	−0.967247	−	0.253835i	$-0.918308\pi$
$997$	−22145.1	−	38356.4i	−0.703452	−	1.21841i	0.263796	−	0.964579i	$-0.415026\pi$
$998$	−4112.50	+	7123.05i	−0.130440	+	0.225928i
$999$	−5339.48	−	3082.75i	−0.169103	−	0.0976315i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.4.j.c.4.2	✓	10
3.2	odd	2		117.4.q.e.82.4		10
4.3	odd	2		624.4.bv.h.433.4		10
13.4	even	6		507.4.b.i.337.4		10
13.6	odd	12		507.4.a.r.1.7		10
13.7	odd	12		507.4.a.r.1.4		10
13.9	even	3		507.4.b.i.337.7		10
13.10	even	6	inner	39.4.j.c.10.2	yes	10
39.20	even	12		1521.4.a.bk.1.7		10
39.23	odd	6		117.4.q.e.10.4		10
39.32	even	12		1521.4.a.bk.1.4		10
52.23	odd	6		624.4.bv.h.49.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.j.c.4.2	✓	10	1.1	even	1	trivial
39.4.j.c.10.2	yes	10	13.10	even	6	inner
117.4.q.e.10.4		10	39.23	odd	6
117.4.q.e.82.4		10	3.2	odd	2
507.4.a.r.1.4		10	13.7	odd	12
507.4.a.r.1.7		10	13.6	odd	12
507.4.b.i.337.4		10	13.4	even	6
507.4.b.i.337.7		10	13.9	even	3
624.4.bv.h.49.2		10	52.23	odd	6
624.4.bv.h.433.4		10	4.3	odd	2
1521.4.a.bk.1.4		10	39.32	even	12
1521.4.a.bk.1.7		10	39.20	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	39.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.76863 - 1.02112i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-1.91462 - 3.31622i) q^{4} +12.0825i q^{5} +(5.30590 - 3.06336i) q^{6} +(-25.7533 + 14.8686i) q^{7} +24.1582i q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.76863 - 1.02112i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-1.91462 - 3.31622i) q^{4} +12.0825i q^{5} +(5.30590 - 3.06336i) q^{6} +(-25.7533 + 14.8686i) q^{7} +24.1582i q^{8} +(-4.50000 - 7.79423i) q^{9} +(12.3377 - 21.3694i) q^{10} +(24.3038 + 14.0318i) q^{11} +11.4877 q^{12} +(-40.9717 - 22.7667i) q^{13} +60.7308 q^{14} +(-31.3911 - 18.1237i) q^{15} +(9.35146 - 16.1972i) q^{16} +(-25.3278 - 43.8690i) q^{17} +18.3802i q^{18} +(91.0612 - 52.5742i) q^{19} +(40.0681 - 23.1333i) q^{20} -89.2119i q^{21} +(-28.6563 - 49.6342i) q^{22} +(-80.2961 + 139.077i) q^{23} +(-62.7648 - 36.2373i) q^{24} -20.9857 q^{25} +(49.2164 + 82.1030i) q^{26} +27.0000 q^{27} +(98.6155 + 56.9357i) q^{28} +(-70.0525 + 121.334i) q^{29} +(37.0130 + 64.1083i) q^{30} +223.593i q^{31} +(134.294 - 77.5348i) q^{32} +(-72.9113 + 42.0954i) q^{33} +103.451i q^{34} +(-179.650 - 311.163i) q^{35} +(-17.2316 + 29.8460i) q^{36} +(-197.759 - 114.176i) q^{37} -214.739 q^{38} +(120.607 - 72.2975i) q^{39} -291.890 q^{40} +(256.259 + 147.951i) q^{41} +(-91.0962 + 157.783i) q^{42} +(96.0517 + 166.366i) q^{43} -107.462i q^{44} +(94.1734 - 54.3710i) q^{45} +(284.029 - 163.984i) q^{46} -36.9300i q^{47} +(28.0544 + 48.5916i) q^{48} +(270.653 - 468.785i) q^{49} +(37.1160 + 21.4289i) q^{50} +151.967 q^{51} +(2.94589 + 179.461i) q^{52} +149.102 q^{53} +(-47.7531 - 27.5703i) q^{54} +(-169.538 + 293.649i) q^{55} +(-359.200 - 622.152i) q^{56} +315.445i q^{57} +(247.794 - 143.064i) q^{58} +(-380.070 + 219.433i) q^{59} +138.800i q^{60} +(-143.073 - 247.809i) q^{61} +(228.316 - 395.454i) q^{62} +(231.779 + 133.818i) q^{63} -466.313 q^{64} +(275.077 - 495.038i) q^{65} +171.938 q^{66} +(465.166 + 268.564i) q^{67} +(-96.9863 + 167.985i) q^{68} +(-240.888 - 417.231i) q^{69} +733.777i q^{70} +(88.9656 - 51.3643i) q^{71} +(188.294 - 108.712i) q^{72} +75.5209i q^{73} +(233.175 + 403.871i) q^{74} +(31.4786 - 54.5225i) q^{75} +(-348.696 - 201.319i) q^{76} -834.535 q^{77} +(-287.134 + 4.71337i) q^{78} +17.5526 q^{79} +(195.702 + 112.989i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-302.152 - 523.342i) q^{82} +1463.08i q^{83} +(-295.847 + 170.807i) q^{84} +(530.045 - 306.022i) q^{85} -392.322i q^{86} +(-210.157 - 364.003i) q^{87} +(-338.983 + 587.135i) q^{88} +(-290.036 - 167.453i) q^{89} -222.078 q^{90} +(1393.66 - 22.8773i) q^{91} +614.946 q^{92} +(-580.912 - 335.390i) q^{93} +(-37.7100 + 65.3156i) q^{94} +(635.225 + 1100.24i) q^{95} +465.209i q^{96} +(-648.442 + 374.378i) q^{97} +(-957.374 + 552.740i) q^{98} -252.572i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 15 q^{3} + 30 q^{4} + 30 q^{7} - 45 q^{9}+O(q^{10}) \) 10 * q - 15 * q^3 + 30 * q^4 + 30 * q^7 - 45 * q^9	\( 10 q - 15 q^{3} + 30 q^{4} + 30 q^{7} - 45 q^{9} + 40 q^{10} + 60 q^{11} - 180 q^{12} + 25 q^{13} - 60 q^{14} + 45 q^{15} - 250 q^{16} + 105 q^{17} + 180 q^{19} + 510 q^{20} - 290 q^{22} - 60 q^{23} - 960 q^{25} - 30 q^{26} + 270 q^{27} + 150 q^{28} - 495 q^{29} + 120 q^{30} + 1440 q^{32} - 180 q^{33} + 60 q^{35} + 270 q^{36} - 405 q^{37} - 1380 q^{38} + 345 q^{39} + 2000 q^{40} + 1065 q^{41} + 90 q^{42} - 370 q^{43} - 135 q^{45} - 390 q^{46} - 750 q^{48} + 775 q^{49} - 4320 q^{50} - 630 q^{51} + 2940 q^{52} + 330 q^{53} - 260 q^{55} - 2670 q^{56} + 2040 q^{58} + 780 q^{59} - 1375 q^{61} - 780 q^{62} - 270 q^{63} - 3140 q^{64} + 1605 q^{65} + 1740 q^{66} + 1590 q^{67} - 600 q^{68} - 180 q^{69} + 1620 q^{71} + 2190 q^{74} + 1440 q^{75} - 5190 q^{76} - 4320 q^{77} + 2340 q^{78} + 1100 q^{79} + 8430 q^{80} - 405 q^{81} - 2390 q^{82} - 450 q^{84} + 525 q^{85} - 1485 q^{87} + 3170 q^{88} + 2040 q^{89} - 720 q^{90} + 4770 q^{91} - 1740 q^{92} - 990 q^{93} - 3230 q^{94} - 1380 q^{95} - 3750 q^{97} + 180 q^{98}+O(q^{100}) \) 10 * q - 15 * q^3 + 30 * q^4 + 30 * q^7 - 45 * q^9 + 40 * q^10 + 60 * q^11 - 180 * q^12 + 25 * q^13 - 60 * q^14 + 45 * q^15 - 250 * q^16 + 105 * q^17 + 180 * q^19 + 510 * q^20 - 290 * q^22 - 60 * q^23 - 960 * q^25 - 30 * q^26 + 270 * q^27 + 150 * q^28 - 495 * q^29 + 120 * q^30 + 1440 * q^32 - 180 * q^33 + 60 * q^35 + 270 * q^36 - 405 * q^37 - 1380 * q^38 + 345 * q^39 + 2000 * q^40 + 1065 * q^41 + 90 * q^42 - 370 * q^43 - 135 * q^45 - 390 * q^46 - 750 * q^48 + 775 * q^49 - 4320 * q^50 - 630 * q^51 + 2940 * q^52 + 330 * q^53 - 260 * q^55 - 2670 * q^56 + 2040 * q^58 + 780 * q^59 - 1375 * q^61 - 780 * q^62 - 270 * q^63 - 3140 * q^64 + 1605 * q^65 + 1740 * q^66 + 1590 * q^67 - 600 * q^68 - 180 * q^69 + 1620 * q^71 + 2190 * q^74 + 1440 * q^75 - 5190 * q^76 - 4320 * q^77 + 2340 * q^78 + 1100 * q^79 + 8430 * q^80 - 405 * q^81 - 2390 * q^82 - 450 * q^84 + 525 * q^85 - 1485 * q^87 + 3170 * q^88 + 2040 * q^89 - 720 * q^90 + 4770 * q^91 - 1740 * q^92 - 990 * q^93 - 3230 * q^94 - 1380 * q^95 - 3750 * q^97 + 180 * q^98

Introduction

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