LMFDB - Embedded newform 39.4.e.c.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [39,4,Mod(16,39)]

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, 2]))

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

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

chi := DirichletCharacter("39.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 39 = 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	39.e (of order $3$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 29x^{6} + 2x^{5} + 595x^{4} - 288x^{3} + 2526x^{2} + 1872x + 6084 $ x^8 - 2x^7 + 29x^6 + 2x^5 + 595x^4 - 288x^3 + 2526x^2 + 1872*x + 6084
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.2
Root			$1.18088 + 2.04535i$ of defining polynomial
Character	$\chi$	$=$	39.16
Dual form			39.4.e.c.22.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18088 - 2.04535i) q^{2} +(1.50000 + 2.59808i) q^{3} +(1.21104 - 2.09758i) q^{4} +6.42208 q^{5} +(3.54264 - 6.13604i) q^{6} +(14.7469 - 25.5424i) q^{7} -24.6145 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.18088 - 2.04535i) q^{2} +(1.50000 + 2.59808i) q^{3} +(1.21104 - 2.09758i) q^{4} +6.42208 q^{5} +(3.54264 - 6.13604i) q^{6} +(14.7469 - 25.5424i) q^{7} -24.6145 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-7.58371 - 13.1354i) q^{10} +(0.312358 + 0.541019i) q^{11} +7.26623 q^{12} +(44.3948 + 15.0368i) q^{13} -69.6575 q^{14} +(9.63312 + 16.6850i) q^{15} +(19.3785 + 33.5645i) q^{16} +(-43.8645 + 75.9756i) q^{17} +21.2559 q^{18} +(-41.4009 + 71.7085i) q^{19} +(7.77738 - 13.4708i) q^{20} +88.4815 q^{21} +(0.737715 - 1.27776i) q^{22} +(37.3989 + 64.7767i) q^{23} +(-36.9217 - 63.9503i) q^{24} -83.7569 q^{25} +(-21.6695 - 108.559i) q^{26} -27.0000 q^{27} +(-35.7182 - 61.8657i) q^{28} +(-113.165 - 196.007i) q^{29} +(22.7511 - 39.4061i) q^{30} +173.660 q^{31} +(-52.6906 + 91.2627i) q^{32} +(-0.937073 + 1.62306i) q^{33} +207.195 q^{34} +(94.7059 - 164.035i) q^{35} +(10.8993 + 18.8782i) q^{36} +(-56.0102 - 97.0124i) q^{37} +195.558 q^{38} +(27.5255 + 137.896i) q^{39} -158.076 q^{40} +(133.506 + 231.238i) q^{41} +(-104.486 - 180.975i) q^{42} +(-191.725 + 332.077i) q^{43} +1.51311 q^{44} +(-28.8993 + 50.0551i) q^{45} +(88.3272 - 152.987i) q^{46} +337.380 q^{47} +(-58.1354 + 100.693i) q^{48} +(-263.443 - 456.297i) q^{49} +(98.9070 + 171.312i) q^{50} -263.187 q^{51} +(85.3046 - 74.9115i) q^{52} -146.354 q^{53} +(31.8838 + 55.2244i) q^{54} +(2.00598 + 3.47447i) q^{55} +(-362.988 + 628.713i) q^{56} -248.406 q^{57} +(-267.268 + 462.922i) q^{58} +(264.587 - 458.277i) q^{59} +46.6643 q^{60} +(-101.636 + 176.038i) q^{61} +(-205.072 - 355.195i) q^{62} +(132.722 + 229.882i) q^{63} +558.941 q^{64} +(285.107 + 96.5673i) q^{65} +4.42629 q^{66} +(-60.7484 - 105.219i) q^{67} +(106.243 + 184.019i) q^{68} +(-112.197 + 194.330i) q^{69} -447.346 q^{70} +(330.657 - 572.715i) q^{71} +(110.765 - 191.851i) q^{72} +167.341 q^{73} +(-132.283 + 229.120i) q^{74} +(-125.635 - 217.607i) q^{75} +(100.276 + 173.684i) q^{76} +18.4253 q^{77} +(249.541 - 219.138i) q^{78} -101.399 q^{79} +(124.450 + 215.554i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(315.308 - 546.130i) q^{82} -506.985 q^{83} +(107.155 - 185.597i) q^{84} +(-281.702 + 487.921i) q^{85} +905.617 q^{86} +(339.494 - 588.020i) q^{87} +(-7.68852 - 13.3169i) q^{88} +(-701.166 - 1214.45i) q^{89} +136.507 q^{90} +(1038.76 - 912.204i) q^{91} +181.166 q^{92} +(260.490 + 451.183i) q^{93} +(-398.405 - 690.058i) q^{94} +(-265.880 + 460.518i) q^{95} -316.143 q^{96} +(-951.445 + 1647.95i) q^{97} +(-622.191 + 1077.67i) q^{98} -5.62244 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 12 q^{3} - 22 q^{4} - 12 q^{5} + 6 q^{6} + 14 q^{7} + 108 q^{8} - 36 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 12 * q^3 - 22 * q^4 - 12 * q^5 + 6 * q^6 + 14 * q^7 + 108 * q^8 - 36 * q^9	\( 8 q - 2 q^{2} + 12 q^{3} - 22 q^{4} - 12 q^{5} + 6 q^{6} + 14 q^{7} + 108 q^{8} - 36 q^{9} + 62 q^{10} - 40 q^{11} - 132 q^{12} - 60 q^{13} + 80 q^{14} - 18 q^{15} - 122 q^{16} - 98 q^{17} + 36 q^{18} - 124 q^{19} + 466 q^{20} + 84 q^{21} - 220 q^{22} - 104 q^{23} + 162 q^{24} - 116 q^{25} + 14 q^{26} - 216 q^{27} + 144 q^{28} - 194 q^{29} - 186 q^{30} + 52 q^{31} - 654 q^{32} + 120 q^{33} + 2124 q^{34} - 88 q^{35} - 198 q^{36} - 102 q^{37} + 664 q^{38} + 342 q^{39} - 1996 q^{40} + 1054 q^{41} + 120 q^{42} - 450 q^{43} - 88 q^{44} + 54 q^{45} + 172 q^{46} - 192 q^{47} + 366 q^{48} - 1070 q^{49} - 996 q^{50} - 588 q^{51} + 2280 q^{52} + 524 q^{53} + 54 q^{54} - 204 q^{55} - 2164 q^{56} - 744 q^{57} - 722 q^{58} - 308 q^{59} + 2796 q^{60} + 928 q^{61} - 2780 q^{62} + 126 q^{63} + 2052 q^{64} + 2346 q^{65} - 1320 q^{66} + 1134 q^{67} - 1786 q^{68} + 312 q^{69} - 4648 q^{70} - 1064 q^{71} - 486 q^{72} + 1904 q^{73} - 1158 q^{74} - 174 q^{75} + 1708 q^{76} + 5016 q^{77} + 480 q^{78} - 1492 q^{79} + 2922 q^{80} - 324 q^{81} - 1734 q^{82} - 808 q^{83} - 432 q^{84} + 1394 q^{85} + 6336 q^{86} + 582 q^{87} - 3060 q^{88} - 1620 q^{89} - 1116 q^{90} + 3278 q^{91} + 664 q^{92} + 78 q^{93} + 772 q^{94} - 2204 q^{95} - 3924 q^{96} - 2166 q^{97} + 1906 q^{98} + 720 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 12 * q^3 - 22 * q^4 - 12 * q^5 + 6 * q^6 + 14 * q^7 + 108 * q^8 - 36 * q^9 + 62 * q^10 - 40 * q^11 - 132 * q^12 - 60 * q^13 + 80 * q^14 - 18 * q^15 - 122 * q^16 - 98 * q^17 + 36 * q^18 - 124 * q^19 + 466 * q^20 + 84 * q^21 - 220 * q^22 - 104 * q^23 + 162 * q^24 - 116 * q^25 + 14 * q^26 - 216 * q^27 + 144 * q^28 - 194 * q^29 - 186 * q^30 + 52 * q^31 - 654 * q^32 + 120 * q^33 + 2124 * q^34 - 88 * q^35 - 198 * q^36 - 102 * q^37 + 664 * q^38 + 342 * q^39 - 1996 * q^40 + 1054 * q^41 + 120 * q^42 - 450 * q^43 - 88 * q^44 + 54 * q^45 + 172 * q^46 - 192 * q^47 + 366 * q^48 - 1070 * q^49 - 996 * q^50 - 588 * q^51 + 2280 * q^52 + 524 * q^53 + 54 * q^54 - 204 * q^55 - 2164 * q^56 - 744 * q^57 - 722 * q^58 - 308 * q^59 + 2796 * q^60 + 928 * q^61 - 2780 * q^62 + 126 * q^63 + 2052 * q^64 + 2346 * q^65 - 1320 * q^66 + 1134 * q^67 - 1786 * q^68 + 312 * q^69 - 4648 * q^70 - 1064 * q^71 - 486 * q^72 + 1904 * q^73 - 1158 * q^74 - 174 * q^75 + 1708 * q^76 + 5016 * q^77 + 480 * q^78 - 1492 * q^79 + 2922 * q^80 - 324 * q^81 - 1734 * q^82 - 808 * q^83 - 432 * q^84 + 1394 * q^85 + 6336 * q^86 + 582 * q^87 - 3060 * q^88 - 1620 * q^89 - 1116 * q^90 + 3278 * q^91 + 664 * q^92 + 78 * q^93 + 772 * q^94 - 2204 * q^95 - 3924 * q^96 - 2166 * q^97 + 1906 * q^98 + 720 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$14$	$28$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.18088	−	2.04535i	−0.417505	−	0.723139i	0.578183	−	0.815907i	$-0.303762\pi$
$2$	−1.18088	−	2.04535i	−0.417505	−	0.723139i	−0.995688	+	0.0927678i	$0.970429\pi$
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$	1.21104	−	2.09758i	0.151380	−	0.262198i
$5$	6.42208			0.574408			0.287204	−	0.957869i	$-0.407274\pi$
$5$	6.42208			0.574408			0.287204	+	0.957869i	$0.407274\pi$
$6$	3.54264	−	6.13604i	0.241046	−	0.417505i
$7$	14.7469	−	25.5424i	0.796259	−	1.37916i	−0.125778	−	0.992058i	$-0.540143\pi$
$7$	14.7469	−	25.5424i	0.796259	−	1.37916i	0.922037	−	0.387102i	$-0.126524\pi$
$8$	−24.6145			−1.08782
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	−7.58371	−	13.1354i	−0.239818	−	0.415377i
$11$	0.312358	+	0.541019i	0.00856176	+	0.0148294i	0.870275	−	0.492567i	$-0.163941\pi$
$11$	0.312358	+	0.541019i	0.00856176	+	0.0148294i	−0.861713	+	0.507396i	$0.830608\pi$
$12$	7.26623			0.174798
$13$	44.3948	+	15.0368i	0.947146	+	0.320804i
$13$	44.3948	+	15.0368i	0.947146	+	0.320804i
$14$	−69.6575			−1.32977
$15$	9.63312	+	16.6850i	0.165817	+	0.287204i
$16$	19.3785	+	33.5645i	0.302788	+	0.524445i
$17$	−43.8645	+	75.9756i	−0.625807	+	1.08393i	0.362577	+	0.931954i	$0.381897\pi$
$17$	−43.8645	+	75.9756i	−0.625807	+	1.08393i	−0.988384	+	0.151976i	$0.951437\pi$
$18$	21.2559			0.278336
$19$	−41.4009	+	71.7085i	−0.499896	+	0.865845i	−1.00000		0.000120110i	$-0.999962\pi$
$19$	−41.4009	+	71.7085i	−0.499896	+	0.865845i	0.500104	+	0.865965i	$0.333295\pi$
$20$	7.77738	−	13.4708i	0.0869538	−	0.150608i
$21$	88.4815			0.919441
$22$	0.737715	−	1.27776i	0.00714915	−	0.0123827i
$23$	37.3989	+	64.7767i	0.339052	+	0.587256i	0.984255	−	0.176756i	$-0.0565603\pi$
$23$	37.3989	+	64.7767i	0.339052	+	0.587256i	−0.645203	+	0.764012i	$0.723227\pi$
$24$	−36.9217	−	63.9503i	−0.314026	−	0.543908i
$25$	−83.7569			−0.670055
$26$	−21.6695	−	108.559i	−0.163452	−	0.818855i
$27$	−27.0000			−0.192450
$28$	−35.7182	−	61.8657i	−0.241075	−	0.417554i
$29$	−113.165	−	196.007i	−0.724625	−	1.25509i	−0.959128	−	0.282973i	$-0.908679\pi$
$29$	−113.165	−	196.007i	−0.724625	−	1.25509i	0.234503	−	0.972115i	$-0.424654\pi$
$30$	22.7511	−	39.4061i	0.138459	−	0.239818i
$31$	173.660			1.00614			0.503070	−	0.864246i	$-0.332204\pi$
$31$	173.660			1.00614			0.503070	+	0.864246i	$0.332204\pi$
$32$	−52.6906	+	91.2627i	−0.291077	+	0.504160i
$33$	−0.937073	+	1.62306i	−0.00494313	+	0.00856176i
$34$	207.195			1.04511
$35$	94.7059	−	164.035i	0.457378	−	0.792201i
$36$	10.8993	+	18.8782i	0.0504599	+	0.0873992i
$37$	−56.0102	−	97.0124i	−0.248865	−	0.431047i	0.714346	−	0.699793i	$-0.246724\pi$
$37$	−56.0102	−	97.0124i	−0.248865	−	0.431047i	−0.963211	+	0.268745i	$0.913391\pi$
$38$	195.558			0.834835
$39$	27.5255	+	137.896i	0.113015	+	0.566181i
$40$	−158.076			−0.624850
$41$	133.506	+	231.238i	0.508538	+	0.880814i	0.999951	+	0.00988706i	$0.00314720\pi$
$41$	133.506	+	231.238i	0.508538	+	0.880814i	−0.491413	+	0.870927i	$0.663519\pi$
$42$	−104.486	−	180.975i	−0.383871	−	0.664884i
$43$	−191.725	+	332.077i	−0.679948	+	1.17770i	0.295048	+	0.955483i	$0.404664\pi$
$43$	−191.725	+	332.077i	−0.679948	+	1.17770i	−0.974996	+	0.222222i	$0.928669\pi$
$44$	1.51311			0.00518431
$45$	−28.8993	+	50.0551i	−0.0957347	+	0.165817i
$46$	88.3272	−	152.987i	0.283112	−	0.490364i
$47$	337.380			1.04706			0.523530	−	0.852007i	$-0.324615\pi$
$47$	337.380			1.04706			0.523530	+	0.852007i	$0.324615\pi$
$48$	−58.1354	+	100.693i	−0.174815	+	0.302788i
$49$	−263.443	−	456.297i	−0.768057	−	1.33031i
$50$	98.9070	+	171.312i	0.279751	+	0.484543i
$51$	−263.187			−0.722619
$52$	85.3046	−	74.9115i	0.227493	−	0.199776i
$53$	−146.354			−0.379308			−0.189654	−	0.981851i	$-0.560737\pi$
$53$	−146.354			−0.379308			−0.189654	+	0.981851i	$0.560737\pi$
$54$	31.8838	+	55.2244i	0.0803488	+	0.139168i
$55$	2.00598	+	3.47447i	0.00491794	+	0.00851813i
$56$	−362.988	+	628.713i	−0.866183	+	1.50027i
$57$	−248.406			−0.577230
$58$	−267.268	+	462.922i	−0.605069	+	1.04801i
$59$	264.587	−	458.277i	0.583834	−	1.01123i	−0.411185	−	0.911552i	$-0.634885\pi$
$59$	264.587	−	458.277i	0.583834	−	1.01123i	0.995020	−	0.0996790i	$-0.0317816\pi$
$60$	46.6643			0.100406
$61$	−101.636	+	176.038i	−0.213330	+	0.369499i	−0.952755	−	0.303741i	$-0.901764\pi$
$61$	−101.636	+	176.038i	−0.213330	+	0.369499i	0.739425	+	0.673239i	$0.235098\pi$
$62$	−205.072	−	355.195i	−0.420068	−	0.727579i
$63$	132.722	+	229.882i	0.265420	+	0.459720i
$64$	558.941			1.09168
$65$	285.107	+	96.5673i	0.544048	+	0.184272i
$66$	4.42629			0.00825513
$67$	−60.7484	−	105.219i	−0.110770	−	0.191859i	0.805311	−	0.592853i	$-0.201998\pi$
$67$	−60.7484	−	105.219i	−0.110770	−	0.191859i	−0.916081	+	0.400993i	$0.868665\pi$
$68$	106.243	+	184.019i	0.189469	+	0.328170i
$69$	−112.197	+	194.330i	−0.195752	+	0.339052i
$70$	−447.346			−0.763829
$71$	330.657	−	572.715i	0.552701	−	0.957306i	−0.445378	−	0.895343i	$-0.646931\pi$
$71$	330.657	−	572.715i	0.552701	−	0.957306i	0.998078	−	0.0619630i	$-0.0197361\pi$
$72$	110.765	−	191.851i	0.181303	−	0.314026i
$73$	167.341			0.268299			0.134150	−	0.990961i	$-0.457170\pi$
$73$	167.341			0.268299			0.134150	+	0.990961i	$0.457170\pi$
$74$	−132.283	+	229.120i	−0.207805	+	0.359928i
$75$	−125.635	−	217.607i	−0.193428	−	0.335028i
$76$	100.276	+	173.684i	0.151348	+	0.262143i
$77$	18.4253			0.0272695
$78$	249.541	−	219.138i	0.362243	−	0.318109i
$79$	−101.399			−0.144408			−0.0722042	−	0.997390i	$-0.523003\pi$
$79$	−101.399			−0.144408			−0.0722042	+	0.997390i	$0.523003\pi$
$80$	124.450	+	215.554i	0.173924	+	0.301245i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	315.308	−	546.130i	0.424634	−	0.735487i
$83$	−506.985			−0.670468			−0.335234	−	0.942135i	$-0.608815\pi$
$83$	−506.985			−0.670468			−0.335234	+	0.942135i	$0.608815\pi$
$84$	107.155	−	185.597i	0.139185	−	0.241075i
$85$	−281.702	+	487.921i	−0.359468	+	0.622618i
$86$	905.617			1.13553
$87$	339.494	−	588.020i	0.418363	−	0.724625i
$88$	−7.68852	−	13.3169i	−0.00931362	−	0.0161317i
$89$	−701.166	−	1214.45i	−0.835095	−	1.44643i	−0.893953	−	0.448160i	$-0.852079\pi$
$89$	−701.166	−	1214.45i	−0.835095	−	1.44643i	0.0588586	−	0.998266i	$-0.481254\pi$
$90$	136.507			0.159879
$91$	1038.76	−	912.204i	1.19661	−	1.05082i
$92$	181.166			0.205303
$93$	260.490	+	451.183i	0.290447	+	0.503070i
$94$	−398.405	−	690.058i	−0.437153	−	0.757171i
$95$	−265.880	+	460.518i	−0.287144	+	0.497348i
$96$	−316.143			−0.336107
$97$	−951.445	+	1647.95i	−0.995924	+	1.72499i	−0.419849	+	0.907594i	$0.637917\pi$
$97$	−951.445	+	1647.95i	−0.995924	+	1.72499i	−0.576075	+	0.817397i	$0.695416\pi$
$98$	−622.191	+	1077.67i	−0.641334	+	1.11082i
$99$	−5.62244			−0.00570784
$100$	−101.433	+	175.687i	−0.101433	+	0.175687i
$101$	−916.546	−	1587.50i	−0.902968	−	1.56399i	−0.823622	−	0.567139i	$-0.808050\pi$
$101$	−916.546	−	1587.50i	−0.902968	−	1.56399i	−0.0793462	−	0.996847i	$-0.525283\pi$
$102$	310.793	+	538.309i	0.301697	+	0.522554i
$103$	1446.99			1.38423			0.692115	−	0.721787i	$-0.256679\pi$
$103$	1446.99			1.38423			0.692115	+	0.721787i	$0.256679\pi$
$104$	−1092.75	−	370.122i	−1.03032	−	0.348976i
$105$	568.235			0.528134
$106$	172.827	+	299.345i	0.158363	+	0.274292i
$107$	184.643	+	319.811i	0.166823	+	0.288947i	0.937301	−	0.348520i	$-0.113316\pi$
$107$	184.643	+	319.811i	0.166823	+	0.288947i	−0.770478	+	0.637467i	$0.779982\pi$
$108$	−32.6980	+	56.6347i	−0.0291331	+	0.0504599i
$109$	−815.694			−0.716782			−0.358391	−	0.933572i	$-0.616675\pi$
$109$	−815.694			−0.716782			−0.358391	+	0.933572i	$0.616675\pi$
$110$	4.73766	−	8.20587i	0.00410653	−	0.00711272i
$111$	168.030	−	291.037i	0.143682	−	0.248865i
$112$	1143.09			0.964392
$113$	−895.282	+	1550.67i	−0.745319	+	1.29093i	0.204726	+	0.978819i	$0.434370\pi$
$113$	−895.282	+	1550.67i	−0.745319	+	1.29093i	−0.950045	+	0.312112i	$0.898964\pi$
$114$	293.337	+	508.075i	0.240996	+	0.417418i
$115$	240.178	+	416.001i	0.194754	+	0.337324i
$116$	−548.187			−0.438775
$117$	−316.977	+	278.357i	−0.250466	+	0.219950i
$118$	−1249.78			−0.975014
$119$	1293.73	+	2240.81i	0.996608	+	1.72618i
$120$	−237.114	−	410.694i	−0.180379	−	0.312425i
$121$	665.305	−	1152.34i	0.499853	−	0.865771i
$122$	480.079			0.356265
$123$	−400.517	+	693.715i	−0.293605	+	0.508538i
$124$	210.309	−	364.266i	0.152309	−	0.263807i
$125$	−1340.65			−0.959293
$126$	313.459	−	542.926i	0.221628	−	0.383871i
$127$	22.6450	+	39.2223i	0.0158222	+	0.0274048i	0.873828	−	0.486235i	$-0.161630\pi$
$127$	22.6450	+	39.2223i	0.0158222	+	0.0274048i	−0.858006	+	0.513640i	$0.828297\pi$
$128$	−238.518	−	413.125i	−0.164705	−	0.285277i
$129$	−1150.35			−0.785137
$130$	−139.163	−	697.176i	−0.0938880	−	0.470357i
$131$	1051.82			0.701511			0.350756	−	0.936467i	$-0.385925\pi$
$131$	1051.82			0.701511			0.350756	+	0.936467i	$0.385925\pi$
$132$	2.26966	+	3.93117i	0.00149658	+	0.00259216i
$133$	1221.07	+	2114.96i	0.796093	+	1.37887i
$134$	−143.473	+	248.503i	−0.0924940	+	0.160204i
$135$	−173.396			−0.110545
$136$	1079.70	−	1870.10i	0.680763	−	1.17912i
$137$	771.471	−	1336.23i	0.481104	−	0.833296i	−0.518661	−	0.854980i	$-0.673569\pi$
$137$	771.471	−	1336.23i	0.481104	−	0.833296i	0.999765	+	0.0216836i	$0.00690265\pi$
$138$	529.963			0.326909
$139$	−18.9322	+	32.7915i	−0.0115526	+	0.0200097i	−0.871744	−	0.489962i	$-0.837011\pi$
$139$	−18.9322	+	32.7915i	−0.0115526	+	0.0200097i	0.860191	+	0.509971i	$0.170344\pi$
$140$	−229.385	−	397.306i	−0.138475	−	0.239847i
$141$	506.069	+	876.538i	0.302260	+	0.523530i
$142$	−1561.87			−0.923020
$143$	5.73186	+	28.7153i	0.00335190	+	0.0167923i
$144$	−348.812			−0.201859
$145$	−726.752	−	1258.77i	−0.416231	−	0.720933i
$146$	−197.610	−	342.271i	−0.112016	−	0.194018i
$147$	790.330	−	1368.89i	0.443438	−	0.768057i
$148$	−271.322			−0.150693
$149$	911.199	−	1578.24i	0.500995	−	0.867749i	−0.499004	−	0.866600i	$-0.666301\pi$
$149$	911.199	−	1578.24i	0.500995	−	0.867749i	0.999999	−	0.00114972i	$-0.000365968\pi$
$150$	−296.721	+	513.936i	−0.161514	+	0.279751i
$151$	−3239.36			−1.74580			−0.872900	−	0.487899i	$-0.837763\pi$
$151$	−3239.36			−1.74580			−0.872900	+	0.487899i	$0.837763\pi$
$152$	1019.06	−	1765.07i	0.543795	−	0.941881i
$153$	−394.781	−	683.781i	−0.208602	−	0.361310i
$154$	−21.7580	−	37.6860i	−0.0113851	−	0.0197197i
$155$	1115.26			0.577934
$156$	322.583	+	109.261i	0.165560	+	0.0560760i
$157$	830.565			0.422206			0.211103	−	0.977464i	$-0.432295\pi$
$157$	830.565			0.422206			0.211103	+	0.977464i	$0.432295\pi$
$158$	119.740	+	207.396i	0.0602912	+	0.104427i
$159$	−219.531	−	380.240i	−0.109497	−	0.189654i
$160$	−338.383	+	586.096i	−0.167197	+	0.289594i
$161$	2206.07			1.07989
$162$	−95.6514	+	165.673i	−0.0463894	+	0.0803488i
$163$	1039.95	−	1801.25i	0.499725	−	0.865550i	−0.500275	−	0.865867i	$-0.666768\pi$
$163$	1039.95	−	1801.25i	0.499725	−	0.865550i	1.00000		0.000317114i	$0.000100941\pi$
$164$	646.721			0.307930
$165$	−6.01795	+	10.4234i	−0.00283938	+	0.00491794i
$166$	598.689	+	1036.96i	0.279923	+	0.484842i
$167$	−42.9895	−	74.4600i	−0.0199199	−	0.0345023i	0.855894	−	0.517152i	$-0.173008\pi$
$167$	−42.9895	−	74.4600i	−0.0199199	−	0.0345023i	−0.875814	+	0.482650i	$0.839674\pi$
$168$	−2177.93			−1.00018
$169$	1744.79	+	1335.11i	0.794170	+	0.607696i
$170$	1330.62			0.600319
$171$	−372.608	−	645.377i	−0.166632	−	0.288615i
$172$	464.373	+	804.317i	0.205861	+	0.356562i
$173$	−1353.23	+	2343.87i	−0.594708	+	1.03006i	0.398880	+	0.917003i	$0.369399\pi$
$173$	−1353.23	+	2343.87i	−0.594708	+	1.03006i	−0.993588	+	0.113061i	$0.963935\pi$
$174$	−1603.61			−0.698673
$175$	−1235.16	+	2139.35i	−0.533538	+	0.924114i
$176$	−12.1060	+	20.9682i	−0.00518480	+	0.00898035i
$177$	1587.52			0.674154
$178$	−1655.99	+	2868.25i	−0.697312	+	1.20778i
$179$	2201.05	+	3812.33i	0.919074	+	1.59188i	0.800825	+	0.598899i	$0.204395\pi$
$179$	2201.05	+	3812.33i	0.919074	+	1.59188i	0.118250	+	0.992984i	$0.462272\pi$
$180$	69.9965	+	121.237i	0.0289846	+	0.0502028i
$181$	−1673.98			−0.687435			−0.343718	−	0.939073i	$-0.611686\pi$
$181$	−1673.98			−0.687435			−0.343718	+	0.939073i	$0.611686\pi$
$182$	−3092.43	−	1047.42i	−1.25948	−	0.426594i
$183$	−609.815			−0.246332
$184$	−920.553	−	1594.44i	−0.368826	−	0.638826i
$185$	−359.702	−	623.021i	−0.142950	−	0.247597i
$186$	615.217	−	1065.59i	0.242526	−	0.420068i
$187$	−54.8057			−0.0214320
$188$	408.580	−	707.681i	0.158504	−	0.274537i
$189$	−398.167	+	689.645i	−0.153240	+	0.265420i
$190$	1255.89			0.479536
$191$	145.059	−	251.249i	0.0549533	−	0.0951819i	−0.837240	−	0.546835i	$-0.815832\pi$
$191$	145.059	−	251.249i	0.0549533	−	0.0951819i	0.892193	+	0.451654i	$0.149166\pi$
$192$	838.411	+	1452.17i	0.315141	+	0.545840i
$193$	−519.750	−	900.233i	−0.193847	−	0.335752i	0.752675	−	0.658392i	$-0.228763\pi$
$193$	−519.750	−	900.233i	−0.193847	−	0.335752i	−0.946522	+	0.322640i	$0.895430\pi$
$194$	4494.18			1.66321
$195$	176.771	+	885.580i	0.0649170	+	0.325219i
$196$	−1276.16			−0.465073
$197$	−709.352	−	1228.63i	−0.256544	−	0.444348i	0.708769	−	0.705440i	$-0.249251\pi$
$197$	−709.352	−	1228.63i	−0.256544	−	0.444348i	−0.965314	+	0.261092i	$0.915917\pi$
$198$	6.63943	+	11.4998i	0.00238305	+	0.00412756i
$199$	1194.19	−	2068.40i	0.425398	−	0.736810i	−0.571060	−	0.820908i	$-0.693468\pi$
$199$	1194.19	−	2068.40i	0.425398	−	0.736810i	0.996457	+	0.0840980i	$0.0268009\pi$
$200$	2061.63			0.728897
$201$	182.245	−	315.658i	0.0639531	−	0.110770i
$202$	−2164.66	+	3749.31i	−0.753987	+	1.30594i
$203$	−6675.32			−2.30796
$204$	−318.730	+	552.057i	−0.109390	+	0.189469i
$205$	857.383	+	1485.03i	0.292108	+	0.505946i
$206$	−1708.72	−	2959.59i	−0.577922	−	1.00099i
$207$	−673.179			−0.226035
$208$	355.601	+	1781.48i	0.118541	+	0.593861i
$209$	−51.7276			−0.0171200
$210$	−671.018	−	1162.24i	−0.220498	−	0.381914i
$211$	−2170.72	−	3759.81i	−0.708241	−	1.22671i	−0.965509	−	0.260369i	$-0.916156\pi$
$211$	−2170.72	−	3759.81i	−0.708241	−	1.22671i	0.257268	−	0.966340i	$-0.417178\pi$
$212$	−177.241	+	306.990i	−0.0574195	+	0.0994536i
$213$	1983.94			0.638204
$214$	436.083	−	755.317i	0.139299	−	0.241273i
$215$	−1231.27	+	2132.63i	−0.390568	+	0.676483i
$216$	664.591			0.209350
$217$	2560.95	−	4435.70i	0.801147	−	1.38763i
$218$	963.237	+	1668.38i	0.299260	+	0.518333i
$219$	251.012	+	434.766i	0.0774513	+	0.134150i
$220$	9.71730			0.00297791
$221$	−3089.78	+	2713.34i	−0.940459	+	0.825878i
$222$	−793.696			−0.239952
$223$	−2307.69	−	3997.03i	−0.692978	−	1.20027i	−0.970858	−	0.239657i	$-0.922965\pi$
$223$	−2307.69	−	3997.03i	−0.692978	−	1.20027i	0.277880	−	0.960616i	$-0.410368\pi$
$224$	1554.05	+	2691.69i	0.463545	+	0.802884i
$225$	376.906	−	652.821i	0.111676	−	0.193428i
$226$	4228.89			1.24470
$227$	1081.72	−	1873.59i	0.316283	−	0.547817i	−0.663427	−	0.748241i	$-0.730899\pi$
$227$	1081.72	−	1873.59i	0.316283	−	0.547817i	0.979709	+	0.200424i	$0.0642319\pi$
$228$	−300.829	+	521.051i	−0.0873810	+	0.151348i
$229$	1859.48			0.536584			0.268292	−	0.963338i	$-0.413541\pi$
$229$	1859.48			0.536584			0.268292	+	0.963338i	$0.413541\pi$
$230$	567.244	−	982.496i	0.162622	−	0.281669i
$231$	27.6379	+	47.8702i	0.00787203	+	0.0136348i
$232$	2785.49	+	4824.60i	0.788259	+	1.36531i
$233$	2866.87			0.806073			0.403037	−	0.915184i	$-0.367955\pi$
$233$	2866.87			0.806073			0.403037	+	0.915184i	$0.367955\pi$
$234$	943.649	+	319.620i	0.263625	+	0.0892914i
$235$	2166.68			0.601440
$236$	−640.849	−	1109.98i	−0.176762	−	0.306160i
$237$	−152.098	−	263.442i	−0.0416871	−	0.0722042i
$238$	3055.49	−	5292.27i	0.832177	−	1.44137i
$239$	1893.55			0.512485			0.256242	−	0.966613i	$-0.417516\pi$
$239$	1893.55			0.512485			0.256242	+	0.966613i	$0.417516\pi$
$240$	−373.350	+	646.661i	−0.100415	+	0.173924i
$241$	906.788	−	1570.60i	0.242371	−	0.419798i	−0.719018	−	0.694991i	$-0.755408\pi$
$241$	906.788	−	1570.60i	0.242371	−	0.419798i	0.961389	+	0.275193i	$0.0887416\pi$
$242$	−3142.58			−0.834764
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	246.170	+	426.379i	0.0645878	+	0.111869i
$245$	−1691.85	−	2930.38i	−0.441178	−	0.764142i
$246$	1891.85			0.490325
$247$	−2916.25	+	2560.95i	−0.751241	+	0.659713i
$248$	−4274.56			−1.09449
$249$	−760.478	−	1317.19i	−0.193547	−	0.335234i
$250$	1583.15	+	2742.10i	0.400509	+	0.693703i
$251$	−2081.16	+	3604.67i	−0.523353	+	0.906474i	0.476278	+	0.879295i	$0.341986\pi$
$251$	−2081.16	+	3604.67i	−0.523353	+	0.906474i	−0.999631	+	0.0271788i	$0.991348\pi$
$252$	642.927			0.160717
$253$	−23.3636	+	40.4670i	−0.00580577	+	0.0100559i
$254$	53.4821	−	92.6337i	0.0132117	−	0.0228833i
$255$	−1690.21			−0.415078
$256$	1672.44	−	2896.75i	0.408310	−	0.707214i
$257$	−2992.65	−	5183.42i	−0.726368	−	1.25811i	−0.958409	−	0.285400i	$-0.907874\pi$
$257$	−2992.65	−	5183.42i	−0.726368	−	1.25811i	0.232041	−	0.972706i	$-0.425460\pi$
$258$	1358.43	+	2352.86i	0.327798	+	0.567763i
$259$	−3303.91			−0.792645
$260$	547.833	−	481.087i	0.130674	−	0.114753i
$261$	2036.96			0.483084
$262$	−1242.07	−	2151.34i	−0.292884	−	0.507290i
$263$	−287.309	−	497.634i	−0.0673621	−	0.116675i	0.830377	−	0.557202i	$-0.188125\pi$
$263$	−287.309	−	497.634i	−0.0673621	−	0.116675i	−0.897739	+	0.440527i	$0.854792\pi$
$264$	23.0656	−	39.9507i	0.00537722	−	0.00931362i
$265$	−939.899			−0.217877
$266$	2883.88	−	4995.03i	0.664745	−	1.15137i
$267$	2103.50	−	3643.36i	0.482142	−	0.835095i
$268$	−294.275			−0.0670734
$269$	−3174.30	+	5498.06i	−0.719482	+	1.24618i	0.241723	+	0.970345i	$0.422288\pi$
$269$	−3174.30	+	5498.06i	−0.719482	+	1.24618i	−0.961205	+	0.275835i	$0.911046\pi$
$270$	204.760	+	354.655i	0.0461530	+	0.0799393i
$271$	1639.19	+	2839.16i	0.367431	+	0.636408i	0.989163	−	0.146821i	$-0.0469042\pi$
$271$	1639.19	+	2839.16i	0.367431	+	0.636408i	−0.621732	+	0.783230i	$0.713571\pi$
$272$	−3400.11			−0.757948
$273$	3928.12	+	1330.48i	0.870844	+	0.294960i
$274$	−3644.06			−0.803452
$275$	−26.1621	−	45.3141i	−0.00573685	−	0.00993652i
$276$	271.749	+	470.683i	0.0592658	+	0.102651i
$277$	−1976.09	+	3422.68i	−0.428633	+	0.742415i	−0.996752	−	0.0805318i	$-0.974338\pi$
$277$	−1976.09	+	3422.68i	−0.428633	+	0.742415i	0.568119	+	0.822947i	$0.307671\pi$
$278$	89.4267			0.0192930
$279$	−781.471	+	1353.55i	−0.167690	+	0.290447i
$280$	−2331.14	+	4037.64i	−0.497543	+	0.861769i
$281$	−411.389			−0.0873360			−0.0436680	−	0.999046i	$-0.513904\pi$
$281$	−411.389			−0.0873360			−0.0436680	+	0.999046i	$0.513904\pi$
$282$	1195.22	−	2070.17i	0.252390	−	0.437153i
$283$	2936.39	+	5085.98i	0.616785	+	1.06830i	0.990068	+	0.140586i	$0.0448987\pi$
$283$	2936.39	+	5085.98i	0.616785	+	1.06830i	−0.373283	+	0.927717i	$0.621768\pi$
$284$	−800.877	−	1387.16i	−0.167335	−	0.289834i
$285$	−1595.28			−0.331566
$286$	51.9640	−	45.6330i	0.0107437	−	0.00943474i
$287$	7875.18			1.61971
$288$	−474.215	−	821.365i	−0.0970257	−	0.168053i
$289$	−1391.70	−	2410.49i	−0.283268	−	0.490635i
$290$	−1716.42	+	2972.92i	−0.347556	+	0.601985i
$291$	−5708.67			−1.14999
$292$	202.657	−	351.012i	0.0406151	−	0.0703474i
$293$	250.478	−	433.841i	0.0499423	−	0.0865026i	−0.839974	−	0.542627i	$-0.817430\pi$
$293$	250.478	−	433.841i	0.0499423	−	0.0865026i	0.889916	+	0.456125i	$0.150763\pi$
$294$	−3733.14			−0.740549
$295$	1699.20	−	2943.09i	0.335359	−	0.580859i
$296$	1378.66	+	2387.91i	0.270720	+	0.468900i
$297$	−8.43366	−	14.6075i	−0.00164771	−	0.00285392i
$298$	−4304.07			−0.836671
$299$	686.281	+	3438.11i	0.132738	+	0.664986i
$300$	−608.597			−0.117125
$301$	5654.70	+	9794.24i	1.08283	+	1.87552i
$302$	3825.31	+	6625.62i	0.728879	+	1.26246i
$303$	2749.64	−	4762.51i	0.521329	−	0.902968i
$304$	−3209.14			−0.605451
$305$	−652.713	+	1130.53i	−0.122539	+	0.212243i
$306$	−932.379	+	1614.93i	−0.174185	+	0.301697i
$307$	−5975.57			−1.11089			−0.555446	−	0.831553i	$-0.687452\pi$
$307$	−5975.57			−1.11089			−0.555446	+	0.831553i	$0.687452\pi$
$308$	22.3137	−	38.6485i	0.00412805	−	0.00715000i
$309$	2170.48	+	3759.38i	0.399593	+	0.692115i
$310$	−1316.99	−	2281.09i	−0.241290	−	0.417927i
$311$	44.4925			0.00811234			0.00405617	−	0.999992i	$-0.498709\pi$
$311$	44.4925			0.00811234			0.00405617	+	0.999992i	$0.498709\pi$
$312$	−677.525	−	3394.24i	−0.122940	−	0.615901i
$313$	9957.78			1.79823			0.899117	−	0.437709i	$-0.144210\pi$
$313$	9957.78			1.79823			0.899117	+	0.437709i	$0.144210\pi$
$314$	−980.798	−	1698.79i	−0.176273	−	0.305313i
$315$	852.353	+	1476.32i	0.152459	+	0.264067i
$316$	−122.798	+	212.692i	−0.0218605	+	0.0378636i
$317$	7752.29			1.37354			0.686770	−	0.726875i	$-0.259028\pi$
$317$	7752.29			1.37354			0.686770	+	0.726875i	$0.259028\pi$
$318$	−518.481	+	898.036i	−0.0914308	+	0.158363i
$319$	70.6956	−	122.448i	0.0124081	−	0.0214915i
$320$	3589.56			0.627070
$321$	−553.929	+	959.432i	−0.0963155	+	0.166823i
$322$	−2605.11	−	4512.18i	−0.450860	−	0.780913i
$323$	−3632.07	−	6290.92i	−0.625677	−	1.08370i
$324$	−196.188			−0.0336400
$325$	−3718.37	−	1259.43i	−0.634640	−	0.214956i
$326$	−4912.23			−0.834550
$327$	−1223.54	−	2119.23i	−0.206917	−	0.358391i
$328$	−3286.17	−	5691.81i	−0.553196	−	0.958163i
$329$	4975.31	−	8617.49i	0.833732	−	1.44407i
$330$	28.4260			0.00474181
$331$	669.427	−	1159.48i	0.111163	−	0.192540i	−0.805076	−	0.593171i	$-0.797876\pi$
$331$	669.427	−	1159.48i	0.111163	−	0.192540i	0.916240	+	0.400631i	$0.131209\pi$
$332$	−613.979	+	1063.44i	−0.101495	+	0.175795i
$333$	1008.18			0.165910
$334$	−101.531	+	175.857i	−0.0166333	+	0.0288097i
$335$	−390.131	−	675.726i	−0.0636272	−	0.110206i
$336$	1714.64	+	2969.84i	0.278396	+	0.482196i
$337$	3788.95			0.612454			0.306227	−	0.951958i	$-0.400933\pi$
$337$	3788.95			0.612454			0.306227	+	0.951958i	$0.400933\pi$
$338$	670.368	−	5145.31i	0.107879	−	0.828011i
$339$	−5371.69			−0.860621
$340$	682.303	+	1181.78i	0.108833	+	0.188504i
$341$	54.2441	+	93.9536i	0.00861432	+	0.0149204i
$342$	−880.012	+	1524.23i	−0.139139	+	0.240996i
$343$	−5423.53			−0.853770
$344$	4719.21	−	8173.91i	0.739659	−	1.28113i
$345$	−720.535	+	1248.00i	−0.112441	+	0.194754i
$346$	6392.03			0.993173
$347$	−3897.58	+	6750.80i	−0.602977	+	1.04439i	0.389391	+	0.921072i	$0.372685\pi$
$347$	−3897.58	+	6750.80i	−0.602977	+	1.04439i	−0.992368	+	0.123314i	$0.960648\pi$
$348$	−822.280	−	1424.23i	−0.126663	−	0.219387i
$349$	−67.2666	−	116.509i	−0.0103172	−	0.0178699i	0.860821	−	0.508908i	$-0.169951\pi$
$349$	−67.2666	−	116.509i	−0.0103172	−	0.0178699i	−0.871138	+	0.491038i	$0.836617\pi$
$350$	5834.29			0.891018
$351$	−1198.66	−	405.993i	−0.182278	−	0.0617387i
$352$	−65.8332			−0.00996853
$353$	1486.85	+	2575.31i	0.224185	+	0.388300i	0.956075	−	0.293124i	$-0.0946947\pi$
$353$	1486.85	+	2575.31i	0.224185	+	0.388300i	−0.731890	+	0.681423i	$0.761361\pi$
$354$	−1874.67	−	3247.03i	−0.281462	−	0.487507i
$355$	2123.50	−	3678.02i	0.317476	−	0.549884i
$356$	−3396.56			−0.505666
$357$	−3881.20	+	6722.44i	−0.575392	+	0.996608i
$358$	5198.36	−	9003.82i	0.767435	−	1.32924i
$359$	8671.60			1.27485			0.637423	−	0.770514i	$-0.280001\pi$
$359$	8671.60			1.27485			0.637423	+	0.770514i	$0.280001\pi$
$360$	711.342	−	1232.08i	0.104142	−	0.180379i
$361$	1.42682	+	2.47133i	0.000208022	+	0.000360304i
$362$	1976.77	+	3423.86i	0.287007	+	0.497111i
$363$	3991.83			0.577181
$364$	−655.440	−	3283.60i	−0.0943802	−	0.472823i
$365$	1074.68			0.154113
$366$	720.119	+	1247.28i	0.102845	+	0.178133i
$367$	−2257.16	−	3909.52i	−0.321043	−	0.556063i	0.659660	−	0.751564i	$-0.270700\pi$
$367$	−2257.16	−	3909.52i	−0.321043	−	0.556063i	−0.980704	+	0.195501i	$0.937367\pi$
$368$	−1449.46	+	2510.55i	−0.205322	+	0.355628i
$369$	−2403.10			−0.339025
$370$	−849.530	+	1471.43i	−0.119365	+	0.206746i
$371$	−2158.28	+	3738.24i	−0.302027	+	0.523126i
$372$	1261.86			0.175871
$373$	−3285.30	+	5690.31i	−0.456049	+	0.789901i	−0.998748	−	0.0500270i	$-0.984069\pi$
$373$	−3285.30	+	5690.31i	−0.456049	+	0.789901i	0.542699	+	0.839928i	$0.317403\pi$
$374$	64.7190	+	112.097i	0.00894797	+	0.0154983i
$375$	−2010.98	−	3483.12i	−0.276924	−	0.479647i
$376$	−8304.42			−1.13901
$377$	−2076.61	−	10403.3i	−0.283689	−	1.42121i
$378$	1880.75			0.255914
$379$	2745.19	+	4754.81i	0.372060	+	0.644427i	0.989882	−	0.141891i	$-0.0453181\pi$
$379$	2745.19	+	4754.81i	0.372060	+	0.644427i	−0.617822	+	0.786318i	$0.711985\pi$
$380$	643.982	+	1115.41i	0.0869357	+	0.150577i
$381$	−67.9350	+	117.667i	−0.00913495	+	0.0158222i
$382$	−685.188			−0.0917730
$383$	−5093.63	+	8822.42i	−0.679562	+	1.17704i	0.295551	+	0.955327i	$0.404497\pi$
$383$	−5093.63	+	8822.42i	−0.679562	+	1.17704i	−0.975113	+	0.221709i	$0.928836\pi$
$384$	715.554	−	1239.38i	0.0950923	−	0.164705i
$385$	118.328			0.0156638
$386$	−1227.53	+	2126.14i	−0.161864	+	0.280356i
$387$	−1725.52	−	2988.70i	−0.226649	−	0.392568i
$388$	2304.47	+	3991.47i	0.301526	+	0.522258i
$389$	4883.97			0.636573			0.318287	−	0.947995i	$-0.396893\pi$
$389$	4883.97			0.636573			0.318287	+	0.947995i	$0.396893\pi$
$390$	1602.57	−	1407.32i	0.208075	−	0.182724i
$391$	−6561.94			−0.848725
$392$	6484.52	+	11231.5i	0.835504	+	1.44714i
$393$	1577.73	+	2732.71i	0.202509	+	0.350756i
$394$	−1675.32	+	2901.74i	−0.214217	+	0.371035i
$395$	−651.192			−0.0829494
$396$	−6.80899	+	11.7935i	−0.000864052	+	0.00149658i
$397$	1057.52	−	1831.68i	0.133691	−	0.231560i	−0.791406	−	0.611291i	$-0.790650\pi$
$397$	1057.52	−	1831.68i	0.133691	−	0.231560i	0.925097	+	0.379732i	$0.123984\pi$
$398$	−5640.80			−0.710422
$399$	−3663.22	+	6344.88i	−0.459625	+	0.796093i
$400$	−1623.08	−	2811.26i	−0.202885	−	0.351407i
$401$	337.127	+	583.921i	0.0419834	+	0.0727173i	0.886254	−	0.463201i	$-0.153299\pi$
$401$	337.127	+	583.921i	0.0419834	+	0.0727173i	−0.844270	+	0.535918i	$0.819966\pi$
$402$	−860.839			−0.106803
$403$	7709.61	+	2611.29i	0.952960	+	0.322773i
$404$	−4439.89			−0.546765
$405$	−260.094	−	450.496i	−0.0319116	−	0.0552724i
$406$	7882.76	+	13653.3i	0.963583	+	1.66897i
$407$	34.9904	−	60.6051i	0.00426145	−	0.00738105i
$408$	6478.22			0.786077
$409$	−2336.67	+	4047.23i	−0.282496	+	0.489297i	−0.971999	−	0.234986i	$-0.924496\pi$
$409$	−2336.67	+	4047.23i	−0.282496	+	0.489297i	0.689503	+	0.724283i	$0.257829\pi$
$410$	2024.93	−	3507.29i	0.243913	−	0.422470i
$411$	4628.83			0.555531
$412$	1752.35	−	3035.17i	0.209544	−	0.362942i
$413$	−7803.67	−	13516.4i	−0.929767	−	1.61040i
$414$	794.945	+	1376.89i	0.0943706	+	0.163455i
$415$	−3255.90			−0.385122
$416$	−3711.48	+	3259.29i	−0.437429	+	0.384134i
$417$	−113.593			−0.0133398
$418$	61.0841	+	105.801i	0.00714766	+	0.0123801i
$419$	128.427	+	222.441i	0.0149739	+	0.0259355i	0.873415	−	0.486976i	$-0.161900\pi$
$419$	128.427	+	222.441i	0.0149739	+	0.0259355i	−0.858441	+	0.512912i	$0.828567\pi$
$420$	688.155	−	1191.92i	0.0799489	−	0.138475i
$421$	−8746.82			−1.01257			−0.506287	−	0.862365i	$-0.668982\pi$
$421$	−8746.82			−1.01257			−0.506287	+	0.862365i	$0.668982\pi$
$422$	−5126.74	+	8879.77i	−0.591388	+	1.02431i
$423$	−1518.21	+	2629.61i	−0.174510	+	0.302260i
$424$	3602.43			0.412617
$425$	3673.96	−	6363.48i	0.419325	−	0.726293i
$426$	−2342.80	−	4057.85i	−0.266453	−	0.461510i
$427$	2997.63	+	5192.05i	0.339732	+	0.588433i
$428$	894.439			0.101015
$429$	−66.0067	+	57.9647i	−0.00742851	+	0.00652346i
$430$	5815.95			0.652255
$431$	−4381.36	−	7588.74i	−0.489658	−	0.848113i	0.510271	−	0.860014i	$-0.329545\pi$
$431$	−4381.36	−	7588.74i	−0.489658	−	0.848113i	−0.999929	+	0.0119008i	$0.996212\pi$
$432$	−523.218	−	906.241i	−0.0582717	−	0.100929i
$433$	−3212.75	+	5564.64i	−0.356570	+	0.617597i	−0.987385	−	0.158336i	$-0.949387\pi$
$433$	−3212.75	+	5564.64i	−0.356570	+	0.617597i	0.630815	+	0.775933i	$0.282721\pi$
$434$	−12096.7			−1.33793
$435$	2180.26	−	3776.31i	0.240311	−	0.416231i
$436$	−987.836	+	1710.98i	−0.108506	+	0.187939i
$437$	−6193.39			−0.677963
$438$	592.831	−	1026.81i	0.0646725	−	0.112016i
$439$	−3410.14	−	5906.54i	−0.370745	−	0.642149i	0.618935	−	0.785442i	$-0.287564\pi$
$439$	−3410.14	−	5906.54i	−0.370745	−	0.642149i	−0.989680	+	0.143293i	$0.954231\pi$
$440$	−49.3763	−	85.5222i	−0.00534982	−	0.00926616i
$441$	4741.98			0.512038
$442$	9198.39	+	3115.55i	0.989870	+	0.335275i
$443$	5062.48			0.542948			0.271474	−	0.962446i	$-0.412489\pi$
$443$	5062.48			0.542948			0.271474	+	0.962446i	$0.412489\pi$
$444$	−406.983	−	704.915i	−0.0435012	−	0.0753463i
$445$	−4502.94	−	7799.32i	−0.479685	−	0.830839i
$446$	−5450.20	+	9440.03i	−0.578643	+	1.00224i
$447$	5467.19			0.578500
$448$	8242.65	−	14276.7i	0.869261	−	1.50560i
$449$	3295.41	−	5707.82i	0.346370	−	0.599930i	−0.639232	−	0.769014i	$-0.720748\pi$
$449$	3295.41	−	5707.82i	0.346370	−	0.599930i	0.985602	+	0.169084i	$0.0540809\pi$
$450$	−1780.33			−0.186501
$451$	−83.4029	+	144.458i	−0.00870796	+	0.0150826i
$452$	2168.44	+	3755.85i	0.225653	+	0.390842i
$453$	−4859.05	−	8416.12i	−0.503969	−	0.872900i
$454$	−5109.52			−0.528198
$455$	6671.01	−	5858.24i	0.687344	−	0.603601i
$456$	6114.37			0.627920
$457$	1127.37	+	1952.67i	0.115397	+	0.199873i	0.917938	−	0.396723i	$-0.129853\pi$
$457$	1127.37	+	1952.67i	0.115397	+	0.199873i	−0.802542	+	0.596596i	$0.796519\pi$
$458$	−2195.82	−	3803.28i	−0.224026	−	0.388025i
$459$	1184.34	−	2051.34i	0.120437	−	0.208602i
$460$	1163.46			0.117928
$461$	−3679.40	+	6372.90i	−0.371728	+	0.643852i	−0.989831	−	0.142245i	$-0.954568\pi$
$461$	−3679.40	+	6372.90i	−0.371728	+	0.643852i	0.618104	+	0.786097i	$0.287901\pi$
$462$	65.2741	−	113.058i	0.00657322	−	0.0113851i
$463$	11598.3			1.16419			0.582096	−	0.813120i	$-0.302233\pi$
$463$	11598.3			1.16419			0.582096	+	0.813120i	$0.302233\pi$
$464$	4385.91	−	7596.62i	0.438816	−	0.760052i
$465$	1672.89	+	2897.53i	0.166835	+	0.288967i
$466$	−3385.44	−	5863.75i	−0.336539	−	0.582903i
$467$	−302.150			−0.0299397			−0.0149698	−	0.999888i	$-0.504765\pi$
$467$	−302.150			−0.0299397			−0.0149698	+	0.999888i	$0.504765\pi$
$468$	200.006	+	1001.99i	0.0197549	+	0.0989675i
$469$	−3583.41			−0.352807
$470$	−2558.59	−	4431.61i	−0.251104	−	0.434925i
$471$	1245.85	+	2157.87i	0.121880	+	0.211103i
$472$	−6512.66	+	11280.3i	−0.635105	+	1.10003i
$473$	−239.547			−0.0232862
$474$	−359.220	+	622.188i	−0.0348091	+	0.0602912i
$475$	3467.61	−	6006.08i	0.334958	−	0.580164i
$476$	6267.05			0.603466
$477$	658.594	−	1140.72i	0.0632180	−	0.109497i
$478$	−2236.06	−	3872.97i	−0.213965	−	0.370598i
$479$	1573.07	+	2724.64i	0.150053	+	0.259900i	0.931247	−	0.364389i	$-0.118722\pi$
$479$	1573.07	+	2724.64i	0.150053	+	0.259900i	−0.781193	+	0.624289i	$0.785389\pi$
$480$	−2030.30			−0.193062
$481$	−1027.80	−	5149.06i	−0.0974300	−	0.488101i
$482$	−4283.24			−0.404764
$483$	3309.11	+	5731.54i	0.311738	+	0.539947i
$484$	−1611.42	−	2791.06i	−0.151335	−	0.262121i
$485$	−6110.25	+	10583.3i	−0.572067	+	0.990849i
$486$	−573.908			−0.0535659
$487$	−1534.08	+	2657.10i	−0.142743	+	0.247238i	−0.928529	−	0.371261i	$-0.878926\pi$
$487$	−1534.08	+	2657.10i	−0.142743	+	0.247238i	0.785786	+	0.618499i	$0.212259\pi$
$488$	2501.71	−	4333.09i	0.232064	−	0.401947i
$489$	6239.70			0.577033
$490$	−3995.76	+	6920.85i	−0.368388	+	0.638066i
$491$	50.2791	+	87.0859i	0.00462131	+	0.00800435i	0.868327	−	0.495992i	$-0.165196\pi$
$491$	50.2791	+	87.0859i	0.00462131	+	0.00800435i	−0.863706	+	0.503997i	$0.831862\pi$
$492$	970.082	+	1680.23i	0.0888916	+	0.153965i
$493$	19855.7			1.81390
$494$	8681.77	+	2940.57i	0.790711	+	0.267818i
$495$	−36.1077			−0.00327863
$496$	3365.27	+	5828.82i	0.304647	+	0.527665i
$497$	−9752.34	−	16891.6i	−0.880186	−	1.52453i
$498$	−1796.07	+	3110.88i	−0.161614	+	0.279923i
$499$	3616.55			0.324447			0.162223	−	0.986754i	$-0.448133\pi$
$499$	3616.55			0.324447			0.162223	+	0.986754i	$0.448133\pi$
$500$	−1623.58	+	2812.13i	−0.145218	+	0.251524i
$501$	128.968	−	223.380i	0.0115008	−	0.0199199i
$502$	9830.40			0.874009
$503$	2686.32	−	4652.84i	0.238125	−	0.412445i	−0.722051	−	0.691840i	$-0.756800\pi$
$503$	2686.32	−	4652.84i	0.238125	−	0.412445i	0.960176	+	0.279395i	$0.0901337\pi$
$504$	−3266.89	−	5658.42i	−0.288728	−	0.500091i
$505$	−5886.13	−	10195.1i	−0.518672	−	0.898366i
$506$	110.359			0.00969574
$507$	−851.527	+	6535.76i	−0.0745910	+	0.572512i
$508$	109.696			0.00958065
$509$	5657.37	+	9798.85i	0.492649	+	0.853293i	0.999964	−	0.00846746i	$-0.00269531\pi$
$509$	5657.37	+	9798.85i	0.492649	+	0.853293i	−0.507315	+	0.861761i	$0.669362\pi$
$510$	1995.94	+	3457.06i	0.173297	+	0.300159i
$511$	2467.77	−	4274.30i	0.213636	−	0.370028i
$512$	−11716.1			−1.01130
$513$	1117.82	−	1936.13i	0.0962050	−	0.166632i
$514$	−7067.93	+	12242.0i	−0.606524	+	1.05053i
$515$	9292.65			0.795113
$516$	−1393.12	+	2412.95i	−0.118854	+	0.205861i
$517$	105.383	+	182.529i	0.00896469	+	0.0155273i
$518$	3901.52	+	6757.64i	0.330933	+	0.573192i
$519$	−8119.40			−0.686709
$520$	−7017.75	−	2376.95i	−0.591824	−	0.200454i
$521$	−18470.9			−1.55321			−0.776606	−	0.629986i	$-0.783061\pi$
$521$	−18470.9			−1.55321			−0.776606	+	0.629986i	$0.783061\pi$
$522$	−2405.41	−	4166.29i	−0.201690	−	0.349337i
$523$	−5445.51	−	9431.90i	−0.455288	−	0.788582i	0.543417	−	0.839463i	$-0.317130\pi$
$523$	−5445.51	−	9431.90i	−0.455288	−	0.788582i	−0.998705	+	0.0508814i	$0.983797\pi$
$524$	1273.79	−	2206.28i	0.106195	−	0.183935i
$525$	−7410.94			−0.616076
$526$	−678.556	+	1175.29i	−0.0562480	+	0.0974243i
$527$	−7617.53	+	13193.9i	−0.629649	+	1.09058i
$528$	−72.6361			−0.00598690
$529$	3286.15	−	5691.78i	0.270087	−	0.467805i
$530$	1109.91	+	1922.42i	0.0909648	+	0.157556i
$531$	2381.28	+	4124.50i	0.194611	+	0.337077i
$532$	5915.06			0.482050
$533$	2449.87	+	12273.3i	0.199091	+	0.997400i
$534$	−9935.92			−0.805186
$535$	1185.79	+	2053.85i	0.0958247	+	0.165973i
$536$	1495.29	+	2589.92i	0.120497	+	0.208708i
$537$	−6603.15	+	11437.0i	−0.530628	+	0.919074i
$538$	14993.9			1.20155
$539$	164.577	−	285.056i	0.0131518	−	0.0227796i
$540$	−209.989	+	363.712i	−0.0167343	+	0.0289846i
$541$	−13416.3			−1.06620			−0.533099	−	0.846053i	$-0.678973\pi$
$541$	−13416.3			−1.06620			−0.533099	+	0.846053i	$0.678973\pi$
$542$	3871.38	−	6705.42i	0.306808	−	0.531407i
$543$	−2510.97	−	4349.12i	−0.198445	−	0.343718i
$544$	−4622.50	−	8006.40i	−0.364316	−	0.631014i
$545$	−5238.45			−0.411726
$546$	−1917.35	−	9605.50i	−0.150284	−	0.752889i
$547$	−17849.0			−1.39519			−0.697593	−	0.716495i	$-0.745745\pi$
$547$	−17849.0			−1.39519			−0.697593	+	0.716495i	$0.745745\pi$
$548$	−1868.56	−	3236.45i	−0.145659	−	0.252289i
$549$	−914.723	−	1584.35i	−0.0711100	−	0.123166i
$550$	−61.7887	+	107.021i	−0.00479033	+	0.00829709i
$551$	18740.5			1.44895
$552$	2761.66	−	4783.33i	0.212942	−	0.368826i
$553$	−1495.32	+	2589.97i	−0.114987	+	0.199163i
$554$	9334.09			0.715826
$555$	1079.10	−	1869.06i	0.0825323	−	0.142950i
$556$	45.8553	+	79.4237i	0.00349766	+	0.00605812i
$557$	10065.7	+	17434.3i	0.765703	+	1.32624i	0.939874	+	0.341521i	$0.110942\pi$
$557$	10065.7	+	17434.3i	0.765703	+	1.32624i	−0.174172	+	0.984715i	$0.555725\pi$
$558$	3691.30			0.280045
$559$	−13505.0	+	11859.6i	−1.02182	+	0.897328i
$560$	7341.02			0.553955
$561$	−82.2086	−	142.389i	−0.00618689	−	0.0107160i
$562$	485.801	+	841.433i	0.0364632	+	0.0631561i
$563$	11172.9	−	19352.0i	0.836380	−	1.44865i	−0.0565220	−	0.998401i	$-0.518001\pi$
$563$	11172.9	−	19352.0i	0.836380	−	1.44865i	0.892902	−	0.450251i	$-0.148666\pi$
$564$	2451.48			0.183025
$565$	−5749.57	+	9958.55i	−0.428117	+	0.741521i
$566$	6935.05	−	12011.9i	0.515021	−	0.892043i
$567$	−2389.00			−0.176946
$568$	−8138.94	+	14097.1i	−0.601237	+	1.04137i
$569$	4227.86	+	7322.87i	0.311496	+	0.539527i	0.978686	−	0.205360i	$-0.0658367\pi$
$569$	4227.86	+	7322.87i	0.311496	+	0.539527i	−0.667191	+	0.744887i	$0.732503\pi$
$570$	1883.84	+	3262.90i	0.138430	+	0.239768i
$571$	12813.0			0.939069			0.469534	−	0.882914i	$-0.344422\pi$
$571$	12813.0			0.939069			0.469534	+	0.882914i	$0.344422\pi$
$572$	67.1741	+	22.7523i	0.00491030	+	0.00166315i
$573$	870.352			0.0634546
$574$	−9299.65	−	16107.5i	−0.676237	−	1.17128i
$575$	−3132.41	−	5425.50i	−0.227184	−	0.393494i
$576$	−2515.23	+	4356.51i	−0.181947	+	0.315141i
$577$	1971.59			0.142251			0.0711253	−	0.997467i	$-0.477341\pi$
$577$	1971.59			0.142251			0.0711253	+	0.997467i	$0.477341\pi$
$578$	−3286.86	+	5693.01i	−0.236532	+	0.409685i
$579$	1559.25	−	2700.70i	0.111917	−	0.193847i
$580$	−3520.50			−0.252036
$581$	−7476.47	+	12949.6i	−0.533866	+	0.924683i
$582$	6741.26	+	11676.2i	0.480128	+	0.831606i
$583$	−45.7149	−	79.1805i	−0.00324754	−	0.00562491i
$584$	−4119.02			−0.291860
$585$	−2035.65	+	1787.63i	−0.143870	+	0.126341i
$586$	−1183.14			−0.0834046
$587$	−4292.85	−	7435.43i	−0.301848	−	0.522816i	0.674707	−	0.738086i	$-0.264270\pi$
$587$	−4292.85	−	7435.43i	−0.301848	−	0.522816i	−0.976555	+	0.215270i	$0.930937\pi$
$588$	−1914.24	−	3315.56i	−0.134255	−	0.232537i
$589$	−7189.70	+	12452.9i	−0.502965	+	0.871161i
$590$	−8026.19			−0.560056
$591$	2128.06	−	3685.90i	0.148116	−	0.256544i
$592$	2170.78	−	3759.90i	0.150707	−	0.261032i
$593$	−1746.73			−0.120961			−0.0604803	−	0.998169i	$-0.519263\pi$
$593$	−1746.73			−0.120961			−0.0604803	+	0.998169i	$0.519263\pi$
$594$	−19.9183	+	34.4995i	−0.00137585	+	0.00238305i
$595$	8308.46	+	14390.7i	0.572460	+	0.991530i
$596$	−2206.99	−	3822.63i	−0.151681	−	0.262720i
$597$	7165.16			0.491207
$598$	6221.70	−	5463.68i	0.425459	−	0.373623i
$599$	27531.1			1.87794			0.938972	−	0.343994i	$-0.111780\pi$
$599$	27531.1			1.87794			0.938972	+	0.343994i	$0.111780\pi$
$600$	3092.45	+	5356.28i	0.210414	+	0.364449i
$601$	8769.54	+	15189.3i	0.595203	+	1.03092i	0.993518	+	0.113673i	$0.0362616\pi$
$601$	8769.54	+	15189.3i	0.595203	+	1.03092i	−0.398315	+	0.917249i	$0.630405\pi$
$602$	13355.1	−	23131.7i	0.904173	−	1.56607i
$603$	1093.47			0.0738467
$604$	−3923.00	+	6794.83i	−0.264279	+	0.457744i
$605$	4272.64	−	7400.43i	0.287120	−	0.497306i
$606$	−12988.0			−0.870629
$607$	11345.5	−	19651.1i	0.758651	−	1.31402i	−0.184887	−	0.982760i	$-0.559192\pi$
$607$	11345.5	−	19651.1i	0.758651	−	1.31402i	0.943539	−	0.331263i	$-0.107475\pi$
$608$	−4362.88	−	7556.72i	−0.291016	−	0.504055i
$609$	−10013.0	−	17343.0i	−0.666250	−	1.15398i
$610$	3083.11			0.204642
$611$	14977.9	+	5073.10i	0.991719	+	0.335901i
$612$	−1912.38			−0.126313
$613$	−3607.65	−	6248.63i	−0.237702	−	0.411713i	0.722352	−	0.691525i	$-0.243061\pi$
$613$	−3607.65	−	6248.63i	−0.237702	−	0.411713i	−0.960055	+	0.279813i	$0.909728\pi$
$614$	7056.44	+	12222.1i	0.463802	+	0.803329i
$615$	−2572.15	+	4455.09i	−0.168649	+	0.292108i
$616$	−453.528			−0.0296642
$617$	8435.22	−	14610.2i	0.550387	−	0.953299i	−0.447859	−	0.894104i	$-0.647813\pi$
$617$	8435.22	−	14610.2i	0.550387	−	0.953299i	0.998246	−	0.0591947i	$-0.0188533\pi$
$618$	5126.15	−	8878.76i	0.333664	−	0.577922i
$619$	2244.53			0.145743			0.0728717	−	0.997341i	$-0.476784\pi$
$619$	2244.53			0.145743			0.0728717	+	0.997341i	$0.476784\pi$
$620$	1350.62	−	2339.35i	0.0874876	−	0.151533i
$621$	−1009.77	−	1748.97i	−0.0652506	−	0.113017i
$622$	−52.5403	−	91.0025i	−0.00338694	−	0.00586635i
$623$	−41360.1			−2.65981
$624$	−4095.01	+	3596.09i	−0.262711	+	0.230703i
$625$	1859.84			0.119030
$626$	−11759.0	−	20367.1i	−0.750771	−	1.30037i
$627$	−77.5914	−	134.392i	−0.00494211	−	0.00855998i
$628$	1005.85	−	1742.18i	0.0639134	−	0.110701i
$629$	9827.44			0.622966
$630$	2013.06	−	3486.71i	0.127305	−	0.220498i
$631$	1834.61	−	3177.63i	0.115744	−	0.200475i	−0.802333	−	0.596877i	$-0.796408\pi$
$631$	1834.61	−	3177.63i	0.115744	−	0.200475i	0.918077	+	0.396402i	$0.129741\pi$
$632$	2495.88			0.157090
$633$	6512.17	−	11279.4i	0.408903	−	0.708241i
$634$	−9154.54	−	15856.1i	−0.573459	−	0.993260i
$635$	145.428	+	251.889i	0.00908840	+	0.0157416i
$636$	−1063.44			−0.0663024
$637$	−4834.27	−	24218.6i	−0.300692	−	1.50640i
$638$	−333.933			−0.0207218
$639$	2975.91	+	5154.43i	0.184234	+	0.319102i
$640$	−1531.78	−	2653.12i	−0.0946077	−	0.163865i
$641$	−7339.30	+	12712.0i	−0.452239	+	0.783300i	−0.998525	−	0.0542983i	$-0.982708\pi$
$641$	−7339.30	+	12712.0i	−0.452239	+	0.783300i	0.546286	+	0.837599i	$0.316041\pi$
$642$	2616.50			0.160849
$643$	−2759.86	+	4780.22i	−0.169266	+	0.293178i	−0.938162	−	0.346196i	$-0.887473\pi$
$643$	−2759.86	+	4780.22i	−0.169266	+	0.293178i	0.768896	+	0.639374i	$0.220807\pi$
$644$	2671.64	−	4627.41i	0.163474	−	0.283145i
$645$	−7387.63			−0.450989
$646$	−8578.08	+	14857.7i	−0.522446	+	0.904902i
$647$	5663.43	+	9809.35i	0.344131	+	0.596052i	0.985195	−	0.171435i	$-0.0548404\pi$
$647$	5663.43	+	9809.35i	0.344131	+	0.596052i	−0.641065	+	0.767487i	$0.721507\pi$
$648$	996.886	+	1726.66i	0.0604342	+	0.104675i
$649$	330.582			0.0199946
$650$	1814.97	+	9092.59i	0.109522	+	0.548678i
$651$	15365.7			0.925085
$652$	−2518.84	−	4362.76i	−0.151297	−	0.262054i
$653$	−1951.44	−	3380.00i	−0.116946	−	0.202557i	0.801610	−	0.597848i	$-0.203977\pi$
$653$	−1951.44	−	3380.00i	−0.116946	−	0.202557i	−0.918556	+	0.395291i	$0.870644\pi$
$654$	−2889.71	+	5005.13i	−0.172778	+	0.299260i
$655$	6754.87			0.402954
$656$	−5174.26	+	8962.09i	−0.307959	+	0.533400i
$657$	−753.036	+	1304.30i	−0.0447165	+	0.0774513i
$658$	−23501.0			−1.39235
$659$	−4011.23	+	6947.66i	−0.237110	+	0.410687i	−0.959884	−	0.280398i	$-0.909534\pi$
$659$	−4011.23	+	6947.66i	−0.237110	+	0.410687i	0.722774	+	0.691085i	$0.242867\pi$
$660$	14.5760	+	25.2463i	0.000859649	+	0.00148896i
$661$	2584.38	+	4476.27i	0.152074	+	0.263399i	0.931990	−	0.362485i	$-0.118072\pi$
$661$	2584.38	+	4476.27i	0.152074	+	0.263399i	−0.779916	+	0.625884i	$0.784738\pi$
$662$	−3162.05			−0.185645
$663$	−11684.1	−	3957.49i	−0.684426	−	0.231819i
$664$	12479.2			0.729346
$665$	7841.82	+	13582.4i	0.457282	+	0.792036i
$666$	−1190.54	−	2062.08i	−0.0692682	−	0.119976i
$667$	8464.45	−	14660.9i	0.491372	−	0.851081i
$668$	−208.248			−0.0120619
$669$	6923.06	−	11991.1i	0.400091	−	0.692978i
$670$	−921.396	+	1595.91i	−0.0531293	+	0.0920227i
$671$	−126.987			−0.00730593
$672$	−4662.14	+	8075.07i	−0.267628	+	0.463545i
$673$	3327.05	+	5762.62i	0.190562	+	0.330063i	0.945437	−	0.325806i	$-0.105636\pi$
$673$	3327.05	+	5762.62i	0.190562	+	0.330063i	−0.754875	+	0.655869i	$0.772302\pi$
$674$	−4474.30	−	7749.71i	−0.255702	−	0.442890i
$675$	2261.44			0.128952
$676$	4913.51	−	2042.97i	0.279558	−	0.116236i
$677$	−20649.4			−1.17226			−0.586130	−	0.810217i	$-0.699349\pi$
$677$	−20649.4			−1.17226			−0.586130	+	0.810217i	$0.699349\pi$
$678$	6343.33	+	10987.0i	0.359313	+	0.622348i
$679$	28061.8	+	48604.4i	1.58603	+	2.74708i
$680$	6933.93	−	12009.9i	0.391036	−	0.677294i
$681$	6490.31			0.365212
$682$	128.112	−	221.896i	0.00719304	−	0.0124587i
$683$	−14237.8	+	24660.6i	−0.797649	+	1.38157i	0.123495	+	0.992345i	$0.460590\pi$
$683$	−14237.8	+	24660.6i	−0.797649	+	1.38157i	−0.921144	+	0.389223i	$0.872744\pi$
$684$	−1804.97			−0.100899
$685$	4954.45	−	8581.36i	0.276350	−	0.478652i
$686$	6404.54	+	11093.0i	0.356453	+	0.617394i
$687$	2789.22	+	4831.07i	0.154899	+	0.268292i
$688$	−14861.3			−0.823522
$689$	−6497.37	−	2200.70i	−0.359260	−	0.121683i
$690$	3403.47			0.187779
$691$	−5305.41	−	9189.24i	−0.292080	−	0.505897i	0.682221	−	0.731146i	$-0.261014\pi$
$691$	−5305.41	−	9189.24i	−0.292080	−	0.505897i	−0.974301	+	0.225248i	$0.927681\pi$
$692$	3277.64	+	5677.03i	0.180053	+	0.311862i
$693$	−82.9136	+	143.611i	−0.00454492	+	0.00787203i
$694$	18410.3			1.00698
$695$	−121.584	+	210.590i	−0.00663590	+	0.0114937i
$696$	−8356.46	+	14473.8i	−0.455102	+	0.788259i
$697$	−23424.6			−1.27299
$698$	−158.868	+	275.167i	−0.00861495	+	0.0149215i
$699$	4300.31	+	7448.36i	0.232693	+	0.403037i
$700$	2991.65	+	5181.68i	0.161534	+	0.279785i
$701$	−13518.9			−0.728390			−0.364195	−	0.931323i	$-0.618656\pi$
$701$	−13518.9			−0.728390			−0.364195	+	0.931323i	$0.618656\pi$
$702$	585.078	+	2931.10i	0.0314563	+	0.157589i
$703$	9275.49			0.497627
$704$	174.589	+	302.398i	0.00934671	+	0.0161890i
$705$	3250.02	+	5629.19i	0.173621	+	0.300720i
$706$	3511.60	−	6082.26i	0.187196	−	0.324234i
$707$	−54064.9			−2.87599
$708$	1922.55	−	3329.95i	0.102053	−	0.176762i
$709$	−7422.69	+	12856.5i	−0.393180	+	0.681008i	−0.992867	−	0.119226i	$-0.961959\pi$
$709$	−7422.69	+	12856.5i	−0.393180	+	0.681008i	0.599687	+	0.800235i	$0.295292\pi$
$710$	−10030.4			−0.530190
$711$	456.295	−	790.326i	0.0240681	−	0.0416871i
$712$	17258.8	+	29893.2i	0.908430	+	1.57345i
$713$	6494.70	+	11249.1i	0.341134	+	0.590861i
$714$	18333.0			0.960915
$715$	36.8104	+	184.412i	0.00192536	+	0.00964561i
$716$	10662.2			0.556517
$717$	2840.33	+	4919.60i	0.147942	+	0.256242i
$718$	−10240.1	−	17736.4i	−0.532254	−	0.921891i
$719$	17950.1	−	31090.4i	0.931049	−	1.61262i	0.149518	−	0.988759i	$-0.452228\pi$
$719$	17950.1	−	31090.4i	0.931049	−	1.61262i	0.781531	−	0.623866i	$-0.214439\pi$
$720$	−2240.10			−0.115949
$721$	21338.6	−	36959.5i	1.10221	−	1.90908i
$722$	3.36981	−	5.83669i	0.000173700	−	0.000300857i
$723$	5440.73			0.279866
$724$	−2027.25	+	3511.30i	−0.104064	+	0.180244i
$725$	9478.32	+	16416.9i	0.485539	+	0.840978i
$726$	−4713.88	−	8164.67i	−0.240976	−	0.417382i
$727$	12951.4			0.660715			0.330357	−	0.943856i	$-0.392831\pi$
$727$	12951.4			0.660715			0.330357	+	0.943856i	$0.392831\pi$
$728$	−25568.6	+	22453.4i	−1.30170	+	1.14310i
$729$	729.000			0.0370370
$730$	−1269.07	−	2198.09i	−0.0643429	−	0.111445i
$731$	−16819.9	−	29132.8i	−0.851032	−	1.47403i
$732$	−738.510	+	1279.14i	−0.0372898	+	0.0645878i
$733$	−1105.36			−0.0556989			−0.0278494	−	0.999612i	$-0.508866\pi$
$733$	−1105.36			−0.0556989			−0.0278494	+	0.999612i	$0.508866\pi$
$734$	−5330.88	+	9233.35i	−0.268074	+	0.464318i
$735$	5075.56	−	8791.13i	0.254714	−	0.441178i
$736$	−7882.27			−0.394761
$737$	37.9504	−	65.7321i	0.00189677	−	0.00328531i
$738$	2837.77	+	4915.17i	0.141545	+	0.245162i
$739$	−6819.03	−	11810.9i	−0.339434	−	0.587917i	0.644892	−	0.764274i	$-0.276902\pi$
$739$	−6819.03	−	11810.9i	−0.339434	−	0.587917i	−0.984326	+	0.176356i	$0.943569\pi$
$740$	−1742.45			−0.0865591
$741$	−11027.9	−	3735.22i	−0.546721	−	0.185178i
$742$	10194.7			0.504391
$743$	−5077.44	−	8794.38i	−0.250704	−	0.434232i	0.713016	−	0.701148i	$-0.247329\pi$
$743$	−5077.44	−	8794.38i	−0.250704	−	0.434232i	−0.963720	+	0.266916i	$0.913995\pi$
$744$	−6411.83	−	11105.6i	−0.315953	−	0.547247i
$745$	5851.79	−	10135.6i	0.287776	−	0.498442i
$746$	15518.2			0.761611
$747$	2281.43	−	3951.56i	0.111745	−	0.193547i
$748$	−66.3718	+	114.959i	−0.00324438	+	0.00561943i
$749$	10891.7			0.531338
$750$	−4749.46	+	8226.30i	−0.231234	+	0.400509i
$751$	−13289.7	−	23018.5i	−0.645738	−	1.11845i	−0.984131	−	0.177446i	$-0.943217\pi$
$751$	−13289.7	−	23018.5i	−0.645738	−	1.11845i	0.338393	−	0.941005i	$-0.390117\pi$
$752$	6537.90	+	11324.0i	0.317038	+	0.549126i
$753$	−12487.0			−0.604316
$754$	−18826.1	+	16532.4i	−0.909294	+	0.798510i
$755$	−20803.5			−1.00280
$756$	964.391	+	1670.37i	0.0463949	+	0.0803584i
$757$	6838.86	+	11845.3i	0.328352	+	0.568723i	0.982185	−	0.187916i	$-0.0601734\pi$
$757$	6838.86	+	11845.3i	0.328352	+	0.568723i	−0.653833	+	0.756639i	$0.726840\pi$
$758$	6483.48	−	11229.7i	0.310674	−	0.538103i
$759$	−140.182			−0.00670392
$760$	6544.49	−	11335.4i	0.312360	−	0.541024i
$761$	−8998.36	+	15585.6i	−0.428634	+	0.742415i	−0.996752	−	0.0805314i	$-0.974338\pi$
$761$	−8998.36	+	15585.6i	−0.428634	+	0.742415i	0.568118	+	0.822947i	$0.307672\pi$
$762$	320.893			0.0152555
$763$	−12029.0	+	20834.8i	−0.570744	+	0.988558i
$764$	−351.343	−	608.544i	−0.0166376	−	0.0288172i
$765$	−2535.31	−	4391.29i	−0.119823	−	0.207539i
$766$	24059.9			1.13488
$767$	18637.3	−	16366.6i	0.877383	−	0.770487i
$768$	10034.6			0.471476
$769$	−1497.52	−	2593.78i	−0.0702236	−	0.121631i	0.828776	−	0.559581i	$-0.189038\pi$
$769$	−1497.52	−	2593.78i	−0.0702236	−	0.121631i	−0.898999	+	0.437950i	$0.855705\pi$
$770$	−139.732	−	242.023i	−0.00653972	−	0.0113271i
$771$	8977.95	−	15550.3i	0.419369	−	0.726368i
$772$	−2517.75			−0.117378
$773$	13027.7	−	22564.7i	0.606177	−	1.04993i	−0.385688	−	0.922629i	$-0.626036\pi$
$773$	13027.7	−	22564.7i	0.606177	−	1.04993i	0.991864	−	0.127299i	$-0.0406309\pi$
$774$	−4075.28	+	7058.59i	−0.189254	+	0.327798i
$775$	−14545.3			−0.674169
$776$	23419.3	−	40563.5i	1.08338	−	1.87647i
$777$	−4955.86	−	8583.81i	−0.228817	−	0.396322i
$778$	−5767.39	−	9989.41i	−0.265772	−	0.460331i
$779$	−22109.0			−1.01686
$780$	2071.65	+	701.681i	0.0950987	+	0.0322105i
$781$	413.133			0.0189284
$782$	7748.87	+	13421.4i	0.354346	+	0.613746i
$783$	3055.44	+	5292.18i	0.139454	+	0.241542i
$784$	10210.3	−	17684.7i	0.465117	−	0.805607i
$785$	5333.95			0.242518
$786$	3726.22	−	6454.01i	0.169097	−	0.292884i
$787$	11496.0	−	19911.7i	0.520697	−	0.901874i	−0.479013	−	0.877808i	$-0.659005\pi$
$787$	11496.0	−	19911.7i	0.520697	−	0.901874i	0.999710	−	0.0240662i	$-0.00766123\pi$
$788$	−3436.21			−0.155343
$789$	861.927	−	1492.90i	0.0388915	−	0.0673621i
$790$	768.980	+	1331.91i	0.0346318	+	0.0599840i
$791$	26405.3	+	45735.4i	1.18693	+	2.05583i
$792$	138.393			0.00620908
$793$	−7159.15	+	6286.91i	−0.320591	+	0.281532i
$794$	−4995.22			−0.223267
$795$	−1409.85	−	2441.93i	−0.0628958	−	0.108939i
$796$	−2892.43	−	5009.84i	−0.128793	−	0.223077i
$797$	12913.1	−	22366.2i	0.573910	−	0.994042i	−0.422249	−	0.906480i	$-0.638759\pi$
$797$	12913.1	−	22366.2i	0.573910	−	0.994042i	0.996159	−	0.0875619i	$-0.0279076\pi$
$798$	17303.3			0.767582
$799$	−14799.0	+	25632.6i	−0.655258	+	1.13494i
$800$	4413.20	−	7643.89i	0.195038	−	0.337815i
$801$	12621.0			0.556730
$802$	796.214	−	1379.08i	0.0350565	−	0.0607196i
$803$	52.2704	+	90.5349i	0.00229711	+	0.00397872i
$804$	−441.412	−	764.548i	−0.0193624	−	0.0335367i
$805$	14167.6			0.620299
$806$	−3763.14	−	18852.4i	−0.164455	−	0.823882i
$807$	−19045.8			−0.830787
$808$	22560.3	+	39075.6i	0.982263	+	1.70133i
$809$	14247.9	+	24678.1i	0.619195	+	1.07248i	0.989633	+	0.143620i	$0.0458744\pi$
$809$	14247.9	+	24678.1i	0.619195	+	1.07248i	−0.370438	+	0.928857i	$0.620792\pi$
$810$	−614.281	+	1063.97i	−0.0266464	+	0.0461530i
$811$	6992.41			0.302758			0.151379	−	0.988476i	$-0.451629\pi$
$811$	6992.41			0.302758			0.151379	+	0.988476i	$0.451629\pi$
$812$	−8084.07	+	14002.0i	−0.349378	+	0.605141i
$813$	−4917.57	+	8517.48i	−0.212136	+	0.367431i
$814$	−165.278			−0.00711670
$815$	6678.64	−	11567.8i	0.287046	−	0.497179i
$816$	−5100.16	−	8833.74i	−0.218801	−	0.378974i
$817$	−15875.2	−	27496.6i	−0.679807	−	1.17746i
$818$	11037.3			0.471773
$819$	2435.50	+	12201.3i	0.103911	+	0.520570i
$820$	4153.29			0.176877
$821$	−15756.3	−	27290.8i	−0.669793	−	1.16012i	−0.977962	−	0.208784i	$-0.933049\pi$
$821$	−15756.3	−	27290.8i	−0.669793	−	1.16012i	0.308168	−	0.951332i	$-0.400284\pi$
$822$	−5466.10	−	9467.56i	−0.231937	−	0.401726i
$823$	−19579.8	+	33913.2i	−0.829293	+	1.43638i	0.0693001	+	0.997596i	$0.477923\pi$
$823$	−19579.8	+	33913.2i	−0.829293	+	1.43638i	−0.898593	+	0.438782i	$0.855410\pi$
$824$	−35616.8			−1.50579
$825$	78.4863	−	135.942i	0.00331217	−	0.00573685i
$826$	−18430.4	+	31922.4i	−0.776364	+	1.34470i
$827$	−36557.6			−1.53716			−0.768581	−	0.639752i	$-0.779037\pi$
$827$	−36557.6			−1.53716			−0.768581	+	0.639752i	$0.779037\pi$
$828$	−815.246	+	1412.05i	−0.0342171	+	0.0592658i
$829$	−7337.59	−	12709.1i	−0.307413	−	0.532454i	0.670383	−	0.742015i	$-0.266130\pi$
$829$	−7337.59	−	12709.1i	−0.307413	−	0.532454i	−0.977796	+	0.209561i	$0.932797\pi$
$830$	3844.83	+	6659.44i	0.160790	+	0.278497i
$831$	−11856.5			−0.494943
$832$	24814.0	+	8404.66i	1.03398	+	0.350215i
$833$	46223.3			1.92262
$834$	134.140	+	232.338i	0.00556942	+	0.00964651i
$835$	−276.082	−	478.188i	−0.0114422	−	0.0198184i
$836$	−62.6441	+	108.503i	−0.00259162	+	0.00448881i
$837$	−4688.83			−0.193632
$838$	303.313	−	525.354i	0.0125033	−	0.0216564i
$839$	4257.78	−	7374.69i	0.175202	−	0.303459i	−0.765029	−	0.643996i	$-0.777275\pi$
$839$	4257.78	−	7374.69i	0.175202	−	0.303459i	0.940231	+	0.340536i	$0.110609\pi$
$840$	−13986.8			−0.574513
$841$	−13417.9	+	23240.6i	−0.550164	+	0.952912i
$842$	10329.0	+	17890.3i	0.422755	+	0.732232i
$843$	−617.083	−	1068.82i	−0.0252117	−	0.0436680i
$844$	−10515.3			−0.428854
$845$	11205.2	+	8574.17i	0.456177	+	0.349066i
$846$	7171.29			0.291435
$847$	−19622.4	−	33987.0i	−0.796025	−	1.37876i
$848$	−2836.12	−	4912.31i	−0.114850	−	0.198926i
$849$	−8809.17	+	15257.9i	−0.356101	+	0.616785i
$850$	−17354.0			−0.700281
$851$	4189.43	−	7256.31i	0.168757	−	0.292295i
$852$	2402.63	−	4161.48i	0.0966112	−	0.167335i
$853$	9645.93			0.387187			0.193593	−	0.981082i	$-0.437986\pi$
$853$	9645.93			0.387187			0.193593	+	0.981082i	$0.437986\pi$
$854$	7079.69	−	12262.4i	0.283679	−	0.491347i
$855$	−2392.92	−	4144.66i	−0.0957148	−	0.165783i
$856$	−4544.89	−	7871.97i	−0.181473	−	0.314321i
$857$	36139.6			1.44050			0.720248	−	0.693717i	$-0.244028\pi$
$857$	36139.6			1.44050			0.720248	+	0.693717i	$0.244028\pi$
$858$	196.504	+	66.5571i	0.00781881	+	0.00264828i
$859$	−7108.04			−0.282332			−0.141166	−	0.989986i	$-0.545085\pi$
$859$	−7108.04			−0.282332			−0.141166	+	0.989986i	$0.545085\pi$
$860$	2982.24	+	5165.39i	0.118248	+	0.204812i
$861$	11812.8	+	20460.3i	0.467570	+	0.809856i
$862$	−10347.7	+	17922.8i	−0.408869	+	0.708182i
$863$	16225.8			0.640016			0.320008	−	0.947415i	$-0.396314\pi$
$863$	16225.8			0.640016			0.320008	+	0.947415i	$0.396314\pi$
$864$	1422.65	−	2464.09i	0.0560178	−	0.0970257i
$865$	−8690.57	+	15052.5i	−0.341605	+	0.591677i
$866$	15175.5			0.595478
$867$	4175.09	−	7231.47i	0.163545	−	0.283268i
$868$	−6202.83	−	10743.6i	−0.242555	−	0.420118i
$869$	−31.6727	−	54.8588i	−0.00123639	−	0.00214149i
$870$	−10298.5			−0.401324
$871$	−1114.75	−	5584.64i	−0.0433661	−	0.217254i
$872$	20077.9			0.779727
$873$	−8563.01	−	14831.6i	−0.331975	−	0.574997i
$874$	7313.66	+	12667.6i	0.283053	+	0.490262i
$875$	−19770.5	+	34243.5i	−0.763846	+	1.32302i
$876$	1215.94			0.0468982
$877$	15491.5	−	26832.0i	0.596477	−	1.03313i	−0.396860	−	0.917879i	$-0.629900\pi$
$877$	15491.5	−	26832.0i	0.596477	−	1.03313i	0.993337	−	0.115249i	$-0.0367667\pi$
$878$	−8053.94	+	13949.8i	−0.309576	+	0.536201i
$879$	1502.87			0.0576684
$880$	−77.7458	+	134.660i	−0.00297819	+	0.00515838i
$881$	3835.38	+	6643.07i	0.146671	+	0.254042i	0.929995	−	0.367572i	$-0.119811\pi$
$881$	3835.38	+	6643.07i	0.146671	+	0.254042i	−0.783324	+	0.621614i	$0.786477\pi$
$882$	−5599.72	−	9698.99i	−0.213778	−	0.370275i
$883$	−34340.6			−1.30878			−0.654390	−	0.756157i	$-0.727075\pi$
$883$	−34340.6			−1.30878			−0.654390	+	0.756157i	$0.727075\pi$
$884$	1949.60	+	9767.03i	0.0741766	+	0.371607i
$885$	10195.2			0.387239
$886$	−5978.19	−	10354.5i	−0.226683	−	0.392627i
$887$	9604.17	+	16634.9i	0.363559	+	0.629702i	0.988544	−	0.150935i	$-0.0482283\pi$
$887$	9604.17	+	16634.9i	0.363559	+	0.629702i	−0.624985	+	0.780637i	$0.714895\pi$
$888$	−4135.98	+	7163.73i	−0.156300	+	0.270720i
$889$	1335.78			0.0503943
$890$	−10634.9	+	18420.1i	−0.400541	+	0.693758i
$891$	25.3010	−	43.8226i	0.000951307	−	0.00164771i
$892$	−11178.8			−0.419611
$893$	−13967.8	+	24193.0i	−0.523422	+	0.906593i
$894$	−6456.11	−	11182.3i	−0.241526	−	0.418336i
$895$	14135.3	+	24483.1i	0.527924	+	0.914390i
$896$	−14069.6			−0.524591
$897$	−7903.04	+	6940.17i	−0.294175	+	0.258334i
$898$	−15566.0			−0.578444
$899$	−19652.2	−	34038.6i	−0.729074	−	1.26279i
$900$	−912.896	−	1581.18i	−0.0338110	−	0.0585623i
$901$	6419.77	−	11119.4i	0.237373	−	0.411143i
$902$	393.956			0.0145425
$903$	−16964.1	+	29382.7i	−0.625172	+	1.08283i
$904$	22036.9	−	38169.0i	0.810770	−	1.40430i
$905$	−10750.4			−0.394868
$906$	−11475.9	+	19876.9i	−0.420819	+	0.728879i
$907$	23240.5	+	40253.7i	0.850813	+	1.47365i	0.880475	+	0.474092i	$0.157224\pi$
$907$	23240.5	+	40253.7i	0.850813	+	1.47365i	−0.0296621	+	0.999560i	$0.509443\pi$
$908$	−2620.00	−	4537.98i	−0.0957576	−	0.165857i
$909$	16497.8			0.601979
$910$	−19859.8	−	6726.63i	−0.723457	−	0.245039i
$911$	−34109.3			−1.24050			−0.620248	−	0.784406i	$-0.712968\pi$
$911$	−34109.3			−1.24050			−0.620248	+	0.784406i	$0.712968\pi$
$912$	−4813.72	−	8337.60i	−0.174779	−	0.302725i
$913$	−158.361	−	274.289i	−0.00574039	−	0.00994264i
$914$	2662.59	−	4611.74i	0.0963573	−	0.166896i
$915$	−3916.28			−0.141495
$916$	2251.90	−	3900.41i	0.0812280	−	0.140691i
$917$	15511.1	−	26866.0i	0.558584	−	0.967497i
$918$	−5594.27			−0.201131
$919$	18766.8	−	32505.1i	0.673623	−	1.16675i	−0.303246	−	0.952912i	$-0.598070\pi$
$919$	18766.8	−	32505.1i	0.673623	−	1.16675i	0.976869	−	0.213837i	$-0.0685962\pi$
$920$	−5911.86	−	10239.6i	−0.211857	−	0.366947i
$921$	−8963.35	−	15525.0i	−0.320687	−	0.555446i
$922$	17379.7			0.620793
$923$	23291.2	−	20453.5i	0.830596	−	0.729399i
$924$	133.882			0.00476667
$925$	4691.24	+	8125.46i	0.166753	+	0.288825i
$926$	−13696.3	−	23722.6i	−0.486055	−	0.841872i
$927$	−6511.43	+	11278.1i	−0.230705	+	0.399593i
$928$	23850.8			0.843687
$929$	−2483.37	+	4301.33i	−0.0877038	+	0.151907i	−0.906540	−	0.422120i	$-0.861286\pi$
$929$	−2483.37	+	4301.33i	−0.0877038	+	0.151907i	0.818836	+	0.574027i	$0.194620\pi$
$930$	3950.97	−	6843.28i	0.139309	−	0.241290i
$931$	43627.2			1.53579
$932$	3471.89	−	6013.50i	0.122023	−	0.211351i
$933$	66.7387	+	115.595i	0.00234183	+	0.00405617i
$934$	356.803	+	618.001i	0.0124999	+	0.0216505i
$935$	−351.966			−0.0123107
$936$	7802.21	−	6851.62i	0.272461	−	0.239265i
$937$	−5096.90			−0.177704			−0.0888519	−	0.996045i	$-0.528320\pi$
$937$	−5096.90			−0.177704			−0.0888519	+	0.996045i	$0.528320\pi$
$938$	4231.58	+	7329.31i	0.147298	+	0.255128i
$939$	14936.7	+	25871.1i	0.519105	+	0.899117i
$940$	2623.93	−	4544.78i	0.0910459	−	0.157696i
$941$	54774.8			1.89756			0.948781	−	0.315933i	$-0.102318\pi$
$941$	54774.8			1.89756			0.948781	+	0.315933i	$0.102318\pi$
$942$	2942.39	−	5096.38i	0.101771	−	0.176273i
$943$	−9985.91	+	17296.1i	−0.344842	+	0.597284i
$944$	20509.1			0.707113
$945$	−2557.06	+	4428.96i	−0.0880223	+	0.152459i
$946$	282.877	+	489.957i	0.00972210	+	0.0168392i
$947$	6884.24	+	11923.9i	0.236228	+	0.409159i	0.959629	−	0.281269i	$-0.0907555\pi$
$947$	6884.24	+	11923.9i	0.236228	+	0.409159i	−0.723401	+	0.690428i	$0.757422\pi$
$948$	−736.788			−0.0252424
$949$	7429.08	+	2516.28i	0.254118	+	0.0860714i
$950$	−16379.4			−0.559386
$951$	11628.4	+	20141.0i	0.396507	+	0.686770i
$952$	−31844.6	−	55156.4i	−1.08413	−	1.87776i
$953$	−17933.3	+	31061.4i	−0.609566	+	1.05580i	0.381746	+	0.924267i	$0.375323\pi$
$953$	−17933.3	+	31061.4i	−0.609566	+	1.05580i	−0.991312	+	0.131532i	$0.958010\pi$
$954$	−3110.89			−0.105575
$955$	931.578	−	1613.54i	0.0315656	−	0.0546732i
$956$	2293.17	−	3971.88i	0.0775798	−	0.134372i
$957$	424.174			0.0143277
$958$	3715.23	−	6434.96i	0.125296	−	0.217019i
$959$	−22753.7	−	39410.5i	−0.766167	−	1.32704i
$960$	5384.34	+	9325.95i	0.181020	+	0.313535i
$961$	366.899			0.0123158
$962$	−9317.89	+	8182.64i	−0.312288	+	0.274240i
$963$	−3323.57			−0.111216
$964$	−2196.31	−	3804.12i	−0.0733801	−	0.127098i
$965$	−3337.87	−	5781.37i	−0.111347	−	0.192859i
$966$	7815.33	−	13536.5i	0.260304	−	0.450860i
$967$	−24476.5			−0.813972			−0.406986	−	0.913434i	$-0.633420\pi$
$967$	−24476.5			−0.813972			−0.406986	+	0.913434i	$0.633420\pi$
$968$	−16376.1	+	28364.3i	−0.543749	+	0.941800i
$969$	10896.2	−	18872.8i	0.361235	−	0.625677i
$970$	28861.9			0.955362
$971$	4488.03	−	7773.50i	0.148329	−	0.256914i	−0.782281	−	0.622926i	$-0.785944\pi$
$971$	4488.03	−	7773.50i	0.148329	−	0.256914i	0.930610	+	0.366012i	$0.119277\pi$
$972$	−294.282	−	509.712i	−0.00971102	−	0.0168200i
$973$	558.383	+	967.149i	0.0183977	+	0.0318657i
$974$	7246.26			0.238383
$975$	−2305.45	−	11549.8i	−0.0757266	−	0.379373i
$976$	−7878.18			−0.258376
$977$	21001.4	+	36375.5i	0.687711	+	1.19115i	0.972576	+	0.232583i	$0.0747178\pi$
$977$	21001.4	+	36375.5i	0.687711	+	1.19115i	−0.284865	+	0.958568i	$0.591949\pi$
$978$	−7368.35	−	12762.4i	−0.240914	−	0.417275i
$979$	438.029	−	758.688i	0.0142998	−	0.0247679i
$980$	−8195.60			−0.267142
$981$	3670.62	−	6357.70i	0.119464	−	0.206917i
$982$	118.747	−	205.676i	0.00385884	−	0.00668370i
$983$	43240.7			1.40301			0.701507	−	0.712662i	$-0.252511\pi$
$983$	43240.7			1.40301			0.701507	+	0.712662i	$0.252511\pi$
$984$	9858.50	−	17075.4i	0.319388	−	0.553196i
$985$	−4555.51	−	7890.38i	−0.147361	−	0.255237i
$986$	−23447.2	−	40611.7i	−0.757312	−	1.31170i
$987$	29851.9			0.962710
$988$	1840.10	+	9218.47i	0.0592524	+	0.296841i
$989$	−28681.2			−0.922152
$990$	42.6389	+	73.8528i	0.00136884	+	0.00237091i
$991$	−18958.3	−	32836.7i	−0.607698	−	1.05256i	−0.991619	−	0.129198i	$-0.958760\pi$
$991$	−18958.3	−	32836.7i	−0.607698	−	1.05256i	0.383921	−	0.923366i	$-0.374574\pi$
$992$	−9150.26	+	15848.7i	−0.292864	+	0.507255i
$993$	4016.56			0.128360
$994$	−23032.7	+	39893.8i	−0.734963	+	1.27299i
$995$	7669.20	−	13283.5i	0.244352	−	0.423230i
$996$	−3683.87			−0.117197
$997$	−3317.43	+	5745.96i	−0.105380	+	0.182524i	−0.913893	−	0.405954i	$-0.866939\pi$
$997$	−3317.43	+	5745.96i	−0.105380	+	0.182524i	0.808513	+	0.588478i	$0.200273\pi$
$998$	−4270.71	−	7397.09i	−0.135458	−	0.234620i
$999$	1512.27	+	2619.34i	0.0478941	+	0.0829551i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.4.e.c.16.2	✓	8
3.2	odd	2		117.4.g.e.55.3		8
4.3	odd	2		624.4.q.i.289.3		8
13.2	odd	12		507.4.b.h.337.3		8
13.3	even	3		507.4.a.m.1.3		4
13.9	even	3	inner	39.4.e.c.22.2	yes	8
13.10	even	6		507.4.a.i.1.2		4
13.11	odd	12		507.4.b.h.337.6		8
39.23	odd	6		1521.4.a.bb.1.3		4
39.29	odd	6		1521.4.a.v.1.2		4
39.35	odd	6		117.4.g.e.100.3		8
52.35	odd	6		624.4.q.i.529.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.e.c.16.2	✓	8	1.1	even	1	trivial
39.4.e.c.22.2	yes	8	13.9	even	3	inner
117.4.g.e.55.3		8	3.2	odd	2
117.4.g.e.100.3		8	39.35	odd	6
507.4.a.i.1.2		4	13.10	even	6
507.4.a.m.1.3		4	13.3	even	3
507.4.b.h.337.3		8	13.2	odd	12
507.4.b.h.337.6		8	13.11	odd	12
624.4.q.i.289.3		8	4.3	odd	2
624.4.q.i.529.3		8	52.35	odd	6
1521.4.a.v.1.2		4	39.29	odd	6
1521.4.a.bb.1.3		4	39.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.18088 - 2.04535i) q^{2} +(1.50000 + 2.59808i) q^{3} +(1.21104 - 2.09758i) q^{4} +6.42208 q^{5} +(3.54264 - 6.13604i) q^{6} +(14.7469 - 25.5424i) q^{7} -24.6145 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.18088 - 2.04535i) q^{2} +(1.50000 + 2.59808i) q^{3} +(1.21104 - 2.09758i) q^{4} +6.42208 q^{5} +(3.54264 - 6.13604i) q^{6} +(14.7469 - 25.5424i) q^{7} -24.6145 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-7.58371 - 13.1354i) q^{10} +(0.312358 + 0.541019i) q^{11} +7.26623 q^{12} +(44.3948 + 15.0368i) q^{13} -69.6575 q^{14} +(9.63312 + 16.6850i) q^{15} +(19.3785 + 33.5645i) q^{16} +(-43.8645 + 75.9756i) q^{17} +21.2559 q^{18} +(-41.4009 + 71.7085i) q^{19} +(7.77738 - 13.4708i) q^{20} +88.4815 q^{21} +(0.737715 - 1.27776i) q^{22} +(37.3989 + 64.7767i) q^{23} +(-36.9217 - 63.9503i) q^{24} -83.7569 q^{25} +(-21.6695 - 108.559i) q^{26} -27.0000 q^{27} +(-35.7182 - 61.8657i) q^{28} +(-113.165 - 196.007i) q^{29} +(22.7511 - 39.4061i) q^{30} +173.660 q^{31} +(-52.6906 + 91.2627i) q^{32} +(-0.937073 + 1.62306i) q^{33} +207.195 q^{34} +(94.7059 - 164.035i) q^{35} +(10.8993 + 18.8782i) q^{36} +(-56.0102 - 97.0124i) q^{37} +195.558 q^{38} +(27.5255 + 137.896i) q^{39} -158.076 q^{40} +(133.506 + 231.238i) q^{41} +(-104.486 - 180.975i) q^{42} +(-191.725 + 332.077i) q^{43} +1.51311 q^{44} +(-28.8993 + 50.0551i) q^{45} +(88.3272 - 152.987i) q^{46} +337.380 q^{47} +(-58.1354 + 100.693i) q^{48} +(-263.443 - 456.297i) q^{49} +(98.9070 + 171.312i) q^{50} -263.187 q^{51} +(85.3046 - 74.9115i) q^{52} -146.354 q^{53} +(31.8838 + 55.2244i) q^{54} +(2.00598 + 3.47447i) q^{55} +(-362.988 + 628.713i) q^{56} -248.406 q^{57} +(-267.268 + 462.922i) q^{58} +(264.587 - 458.277i) q^{59} +46.6643 q^{60} +(-101.636 + 176.038i) q^{61} +(-205.072 - 355.195i) q^{62} +(132.722 + 229.882i) q^{63} +558.941 q^{64} +(285.107 + 96.5673i) q^{65} +4.42629 q^{66} +(-60.7484 - 105.219i) q^{67} +(106.243 + 184.019i) q^{68} +(-112.197 + 194.330i) q^{69} -447.346 q^{70} +(330.657 - 572.715i) q^{71} +(110.765 - 191.851i) q^{72} +167.341 q^{73} +(-132.283 + 229.120i) q^{74} +(-125.635 - 217.607i) q^{75} +(100.276 + 173.684i) q^{76} +18.4253 q^{77} +(249.541 - 219.138i) q^{78} -101.399 q^{79} +(124.450 + 215.554i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(315.308 - 546.130i) q^{82} -506.985 q^{83} +(107.155 - 185.597i) q^{84} +(-281.702 + 487.921i) q^{85} +905.617 q^{86} +(339.494 - 588.020i) q^{87} +(-7.68852 - 13.3169i) q^{88} +(-701.166 - 1214.45i) q^{89} +136.507 q^{90} +(1038.76 - 912.204i) q^{91} +181.166 q^{92} +(260.490 + 451.183i) q^{93} +(-398.405 - 690.058i) q^{94} +(-265.880 + 460.518i) q^{95} -316.143 q^{96} +(-951.445 + 1647.95i) q^{97} +(-622.191 + 1077.67i) q^{98} -5.62244 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 12 q^{3} - 22 q^{4} - 12 q^{5} + 6 q^{6} + 14 q^{7} + 108 q^{8} - 36 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 12 * q^3 - 22 * q^4 - 12 * q^5 + 6 * q^6 + 14 * q^7 + 108 * q^8 - 36 * q^9	\( 8 q - 2 q^{2} + 12 q^{3} - 22 q^{4} - 12 q^{5} + 6 q^{6} + 14 q^{7} + 108 q^{8} - 36 q^{9} + 62 q^{10} - 40 q^{11} - 132 q^{12} - 60 q^{13} + 80 q^{14} - 18 q^{15} - 122 q^{16} - 98 q^{17} + 36 q^{18} - 124 q^{19} + 466 q^{20} + 84 q^{21} - 220 q^{22} - 104 q^{23} + 162 q^{24} - 116 q^{25} + 14 q^{26} - 216 q^{27} + 144 q^{28} - 194 q^{29} - 186 q^{30} + 52 q^{31} - 654 q^{32} + 120 q^{33} + 2124 q^{34} - 88 q^{35} - 198 q^{36} - 102 q^{37} + 664 q^{38} + 342 q^{39} - 1996 q^{40} + 1054 q^{41} + 120 q^{42} - 450 q^{43} - 88 q^{44} + 54 q^{45} + 172 q^{46} - 192 q^{47} + 366 q^{48} - 1070 q^{49} - 996 q^{50} - 588 q^{51} + 2280 q^{52} + 524 q^{53} + 54 q^{54} - 204 q^{55} - 2164 q^{56} - 744 q^{57} - 722 q^{58} - 308 q^{59} + 2796 q^{60} + 928 q^{61} - 2780 q^{62} + 126 q^{63} + 2052 q^{64} + 2346 q^{65} - 1320 q^{66} + 1134 q^{67} - 1786 q^{68} + 312 q^{69} - 4648 q^{70} - 1064 q^{71} - 486 q^{72} + 1904 q^{73} - 1158 q^{74} - 174 q^{75} + 1708 q^{76} + 5016 q^{77} + 480 q^{78} - 1492 q^{79} + 2922 q^{80} - 324 q^{81} - 1734 q^{82} - 808 q^{83} - 432 q^{84} + 1394 q^{85} + 6336 q^{86} + 582 q^{87} - 3060 q^{88} - 1620 q^{89} - 1116 q^{90} + 3278 q^{91} + 664 q^{92} + 78 q^{93} + 772 q^{94} - 2204 q^{95} - 3924 q^{96} - 2166 q^{97} + 1906 q^{98} + 720 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 12 * q^3 - 22 * q^4 - 12 * q^5 + 6 * q^6 + 14 * q^7 + 108 * q^8 - 36 * q^9 + 62 * q^10 - 40 * q^11 - 132 * q^12 - 60 * q^13 + 80 * q^14 - 18 * q^15 - 122 * q^16 - 98 * q^17 + 36 * q^18 - 124 * q^19 + 466 * q^20 + 84 * q^21 - 220 * q^22 - 104 * q^23 + 162 * q^24 - 116 * q^25 + 14 * q^26 - 216 * q^27 + 144 * q^28 - 194 * q^29 - 186 * q^30 + 52 * q^31 - 654 * q^32 + 120 * q^33 + 2124 * q^34 - 88 * q^35 - 198 * q^36 - 102 * q^37 + 664 * q^38 + 342 * q^39 - 1996 * q^40 + 1054 * q^41 + 120 * q^42 - 450 * q^43 - 88 * q^44 + 54 * q^45 + 172 * q^46 - 192 * q^47 + 366 * q^48 - 1070 * q^49 - 996 * q^50 - 588 * q^51 + 2280 * q^52 + 524 * q^53 + 54 * q^54 - 204 * q^55 - 2164 * q^56 - 744 * q^57 - 722 * q^58 - 308 * q^59 + 2796 * q^60 + 928 * q^61 - 2780 * q^62 + 126 * q^63 + 2052 * q^64 + 2346 * q^65 - 1320 * q^66 + 1134 * q^67 - 1786 * q^68 + 312 * q^69 - 4648 * q^70 - 1064 * q^71 - 486 * q^72 + 1904 * q^73 - 1158 * q^74 - 174 * q^75 + 1708 * q^76 + 5016 * q^77 + 480 * q^78 - 1492 * q^79 + 2922 * q^80 - 324 * q^81 - 1734 * q^82 - 808 * q^83 - 432 * q^84 + 1394 * q^85 + 6336 * q^86 + 582 * q^87 - 3060 * q^88 - 1620 * q^89 - 1116 * q^90 + 3278 * q^91 + 664 * q^92 + 78 * q^93 + 772 * q^94 - 2204 * q^95 - 3924 * q^96 - 2166 * q^97 + 1906 * q^98 + 720 * q^99

Introduction

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