LMFDB - Embedded newform 39.4.e.c.16.1

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			16.1
Root			$2.66520 + 4.61626i$ of defining polynomial
Character	$\chi$	$=$	39.16
Dual form			39.4.e.c.22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.66520 - 4.61626i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-10.2065 + 17.6783i) q^{4} -16.4131 q^{5} +(7.99559 - 13.8488i) q^{6} +(-4.83984 + 8.38285i) q^{7} +66.1667 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-2.66520 - 4.61626i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-10.2065 + 17.6783i) q^{4} -16.4131 q^{5} +(7.99559 - 13.8488i) q^{6} +(-4.83984 + 8.38285i) q^{7} +66.1667 q^{8} +(-4.50000 + 7.79423i) q^{9} +(43.7441 + 75.7670i) q^{10} +(-13.7941 - 23.8921i) q^{11} -61.2393 q^{12} +(-37.3033 - 28.3807i) q^{13} +51.5965 q^{14} +(-24.6196 - 42.6425i) q^{15} +(-94.6948 - 164.016i) q^{16} +(-53.9641 + 93.4685i) q^{17} +47.9735 q^{18} +(1.12362 - 1.94616i) q^{19} +(167.521 - 290.155i) q^{20} -29.0391 q^{21} +(-73.5279 + 127.354i) q^{22} +(-20.9045 - 36.2077i) q^{23} +(99.2500 + 171.906i) q^{24} +144.390 q^{25} +(-31.5919 + 247.842i) q^{26} -27.0000 q^{27} +(-98.7961 - 171.120i) q^{28} +(-30.8106 - 53.3656i) q^{29} +(-131.232 + 227.301i) q^{30} +191.932 q^{31} +(-240.094 + 415.855i) q^{32} +(41.3822 - 71.6762i) q^{33} +575.300 q^{34} +(79.4368 - 137.589i) q^{35} +(-91.8589 - 159.104i) q^{36} +(-49.2118 - 85.2373i) q^{37} -11.9786 q^{38} +(17.7803 - 139.488i) q^{39} -1086.00 q^{40} +(15.3726 + 26.6261i) q^{41} +(77.3948 + 134.052i) q^{42} +(-119.163 + 206.396i) q^{43} +563.160 q^{44} +(73.8589 - 127.927i) q^{45} +(-111.429 + 193.001i) q^{46} -511.482 q^{47} +(284.084 - 492.048i) q^{48} +(124.652 + 215.903i) q^{49} +(-384.826 - 666.539i) q^{50} -323.785 q^{51} +(882.459 - 369.788i) q^{52} +492.825 q^{53} +(71.9603 + 124.639i) q^{54} +(226.404 + 392.142i) q^{55} +(-320.236 + 554.665i) q^{56} +6.74170 q^{57} +(-164.233 + 284.460i) q^{58} +(-242.089 + 419.311i) q^{59} +1005.13 q^{60} +(222.011 - 384.534i) q^{61} +(-511.536 - 886.007i) q^{62} +(-43.5586 - 75.4457i) q^{63} +1044.47 q^{64} +(612.262 + 465.815i) q^{65} -441.167 q^{66} +(-95.0568 - 164.643i) q^{67} +(-1101.57 - 1907.98i) q^{68} +(62.7135 - 108.623i) q^{69} -846.858 q^{70} +(-242.392 + 419.836i) q^{71} +(-297.750 + 515.718i) q^{72} -957.780 q^{73} +(-262.318 + 454.348i) q^{74} +(216.584 + 375.135i) q^{75} +(22.9365 + 39.7271i) q^{76} +267.045 q^{77} +(-691.300 + 289.684i) q^{78} -375.216 q^{79} +(1554.23 + 2692.01i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(81.9421 - 141.928i) q^{82} -715.765 q^{83} +(296.388 - 513.360i) q^{84} +(885.717 - 1534.11i) q^{85} +1270.37 q^{86} +(92.4319 - 160.097i) q^{87} +(-912.708 - 1580.86i) q^{88} +(519.076 + 899.066i) q^{89} -787.394 q^{90} +(418.453 - 175.350i) q^{91} +853.451 q^{92} +(287.898 + 498.654i) q^{93} +(1363.20 + 2361.13i) q^{94} +(-18.4420 + 31.9425i) q^{95} -1440.56 q^{96} +(-32.7818 + 56.7797i) q^{97} +(664.443 - 1150.85i) q^{98} +248.293 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 $

$2$	−2.66520	−	4.61626i	−0.942289	−	1.63209i	−0.761090	−	0.648647i	$-0.775335\pi$
$2$	−2.66520	−	4.61626i	−0.942289	−	1.63209i	−0.181199	−	0.983446i	$-0.557998\pi$
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$	−10.2065	+	17.6783i	−1.27582	+	2.20978i
$5$	−16.4131			−1.46803			−0.734016	−	0.679132i	$-0.762356\pi$
$5$	−16.4131			−1.46803			−0.734016	+	0.679132i	$0.762356\pi$
$6$	7.99559	−	13.8488i	0.544031	−	0.942289i
$7$	−4.83984	+	8.38285i	−0.261327	+	0.452631i	−0.966595	−	0.256309i	$-0.917493\pi$
$7$	−4.83984	+	8.38285i	−0.261327	+	0.452631i	0.705268	+	0.708941i	$0.250827\pi$
$8$	66.1667			2.92418
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	43.7441	+	75.7670i	1.38331	+	2.39596i
$11$	−13.7941	−	23.8921i	−0.378098	−	0.654884i	0.612688	−	0.790325i	$-0.290088\pi$
$11$	−13.7941	−	23.8921i	−0.378098	−	0.654884i	−0.990785	+	0.135441i	$0.956755\pi$
$12$	−61.2393			−1.47319
$13$	−37.3033	−	28.3807i	−0.795852	−	0.605491i
$13$	−37.3033	−	28.3807i	−0.795852	−	0.605491i
$14$	51.5965			0.984982
$15$	−24.6196	−	42.6425i	−0.423784	−	0.734016i
$16$	−94.6948	−	164.016i	−1.47961	−	2.56275i
$17$	−53.9641	+	93.4685i	−0.769895	+	1.33350i	0.167725	+	0.985834i	$0.446358\pi$
$17$	−53.9641	+	93.4685i	−0.769895	+	1.33350i	−0.937619	+	0.347663i	$0.886975\pi$
$18$	47.9735			0.628193
$19$	1.12362	−	1.94616i	0.0135671	−	0.0234989i	−0.859162	−	0.511703i	$-0.829015\pi$
$19$	1.12362	−	1.94616i	0.0135671	−	0.0234989i	0.872729	+	0.488205i	$0.162348\pi$
$20$	167.521	−	290.155i	1.87294	−	3.24403i
$21$	−29.0391			−0.301754
$22$	−73.5279	+	127.354i	−0.712554	+	1.23418i
$23$	−20.9045	−	36.2077i	−0.189517	−	0.328253i	0.755572	−	0.655065i	$-0.227359\pi$
$23$	−20.9045	−	36.2077i	−0.189517	−	0.328253i	−0.945089	+	0.326812i	$0.894026\pi$
$24$	99.2500	+	171.906i	0.844138	+	1.46209i
$25$	144.390			1.15512
$26$	−31.5919	+	247.842i	−0.238296	+	1.86945i
$27$	−27.0000			−0.192450
$28$	−98.7961	−	171.120i	−0.666811	−	1.15495i
$29$	−30.8106	−	53.3656i	−0.197289	−	0.341715i	0.750359	−	0.661030i	$-0.229881\pi$
$29$	−30.8106	−	53.3656i	−0.197289	−	0.341715i	−0.947649	+	0.319315i	$0.896547\pi$
$30$	−131.232	+	227.301i	−0.798655	+	1.38331i
$31$	191.932			1.11200			0.556000	−	0.831182i	$-0.312335\pi$
$31$	191.932			1.11200			0.556000	+	0.831182i	$0.312335\pi$
$32$	−240.094	+	415.855i	−1.32634	+	2.29729i
$33$	41.3822	−	71.6762i	0.218295	−	0.378098i
$34$	575.300			2.90185
$35$	79.4368	−	137.589i	0.383636	−	0.664477i
$36$	−91.8589	−	159.104i	−0.425273	−	0.736594i
$37$	−49.2118	−	85.2373i	−0.218659	−	0.378728i	0.735740	−	0.677265i	$-0.236835\pi$
$37$	−49.2118	−	85.2373i	−0.218659	−	0.378728i	−0.954398	+	0.298537i	$0.903501\pi$
$38$	−11.9786			−0.0511366
$39$	17.7803	−	139.488i	0.0730031	−	0.572716i
$40$	−1086.00			−4.29279
$41$	15.3726	+	26.6261i	0.0585561	+	0.101422i	0.893817	−	0.448431i	$-0.148017\pi$
$41$	15.3726	+	26.6261i	0.0585561	+	0.101422i	−0.835261	+	0.549853i	$0.814684\pi$
$42$	77.3948	+	134.052i	0.284340	+	0.492491i
$43$	−119.163	+	206.396i	−0.422608	+	0.731978i	−0.996194	−	0.0871672i	$-0.972219\pi$
$43$	−119.163	+	206.396i	−0.422608	+	0.731978i	0.573586	+	0.819145i	$0.305552\pi$
$44$	563.160			1.92953
$45$	73.8589	−	127.927i	0.244672	−	0.423784i
$46$	−111.429	+	193.001i	−0.357160	+	0.618618i
$47$	−511.482			−1.58739			−0.793695	−	0.608316i	$-0.791845\pi$
$47$	−511.482			−1.58739			−0.793695	+	0.608316i	$0.791845\pi$
$48$	284.084	−	492.048i	0.854251	−	1.47961i
$49$	124.652	+	215.903i	0.363416	+	0.629456i
$50$	−384.826	−	666.539i	−1.08845	−	1.88526i
$51$	−323.785			−0.888998
$52$	882.459	−	369.788i	2.35337	−	0.986162i
$53$	492.825			1.27726			0.638630	−	0.769514i	$-0.279502\pi$
$53$	492.825			1.27726			0.638630	+	0.769514i	$0.279502\pi$
$54$	71.9603	+	124.639i	0.181344	+	0.314096i
$55$	226.404	+	392.142i	0.555059	+	0.961390i
$56$	−320.236	+	554.665i	−0.764167	+	1.32358i
$57$	6.74170			0.0156660
$58$	−164.233	+	284.460i	−0.371807	+	0.643989i
$59$	−242.089	+	419.311i	−0.534192	+	0.925248i	0.465010	+	0.885306i	$0.346051\pi$
$59$	−242.089	+	419.311i	−0.534192	+	0.925248i	−0.999202	+	0.0399427i	$0.987282\pi$
$60$	1005.13			2.16269
$61$	222.011	−	384.534i	0.465993	−	0.807123i	−0.533253	−	0.845956i	$-0.679031\pi$
$61$	222.011	−	384.534i	0.465993	−	0.807123i	0.999246	+	0.0388329i	$0.0123640\pi$
$62$	−511.536	−	886.007i	−1.04783	−	1.81489i
$63$	−43.5586	−	75.4457i	−0.0871090	−	0.150877i
$64$	1044.47			2.03998
$65$	612.262	+	465.815i	1.16834	+	0.888880i
$66$	−441.167			−0.822787
$67$	−95.0568	−	164.643i	−0.173329	−	0.300215i	0.766253	−	0.642539i	$-0.222119\pi$
$67$	−95.0568	−	164.643i	−0.173329	−	0.300215i	−0.939582	+	0.342325i	$0.888786\pi$
$68$	−1101.57	−	1907.98i	−1.96449	−	3.40260i
$69$	62.7135	−	108.623i	0.109418	−	0.189517i
$70$	−846.858			−1.44598
$71$	−242.392	+	419.836i	−0.405164	+	0.701765i	−0.994341	−	0.106239i	$-0.966119\pi$
$71$	−242.392	+	419.836i	−0.405164	+	0.701765i	0.589176	+	0.808005i	$0.299452\pi$
$72$	−297.750	+	515.718i	−0.487363	+	0.844138i
$73$	−957.780			−1.53561			−0.767806	−	0.640683i	$-0.778651\pi$
$73$	−957.780			−1.53561			−0.767806	+	0.640683i	$0.778651\pi$
$74$	−262.318	+	454.348i	−0.412079	+	0.713742i
$75$	216.584	+	375.135i	0.333453	+	0.577558i
$76$	22.9365	+	39.7271i	0.0346183	+	0.0599607i
$77$	267.045			0.395228
$78$	−691.300	+	289.684i	−1.00352	+	0.420517i
$79$	−375.216			−0.534368			−0.267184	−	0.963646i	$-0.586093\pi$
$79$	−375.216			−0.534368			−0.267184	+	0.963646i	$0.586093\pi$
$80$	1554.23	+	2692.01i	2.17211	+	3.76220i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	81.9421	−	141.928i	0.110354	−	0.191138i
$83$	−715.765			−0.946571			−0.473286	−	0.880909i	$-0.656932\pi$
$83$	−715.765			−0.946571			−0.473286	+	0.880909i	$0.656932\pi$
$84$	296.388	−	513.360i	0.384984	−	0.666811i
$85$	885.717	−	1534.11i	1.13023	−	1.95762i
$86$	1270.37			1.59288
$87$	92.4319	−	160.097i	0.113905	−	0.197289i
$88$	−912.708	−	1580.86i	−1.10563	−	1.91500i
$89$	519.076	+	899.066i	0.618224	+	1.07080i	0.989810	+	0.142397i	$0.0454810\pi$
$89$	519.076	+	899.066i	0.618224	+	1.07080i	−0.371585	+	0.928399i	$0.621186\pi$
$90$	−787.394			−0.922207
$91$	418.453	−	175.350i	0.482042	−	0.201996i
$92$	853.451			0.967157
$93$	287.898	+	498.654i	0.321007	+	0.556000i
$94$	1363.20	+	2361.13i	1.49578	+	2.59077i
$95$	−18.4420	+	31.9425i	−0.0199169	+	0.0344972i
$96$	−1440.56			−1.53153
$97$	−32.7818	+	56.7797i	−0.0343143	+	0.0594341i	−0.882673	−	0.469989i	$-0.844258\pi$
$97$	−32.7818	+	56.7797i	−0.0343143	+	0.0594341i	0.848358	+	0.529423i	$0.177591\pi$
$98$	664.443	−	1150.85i	0.684887	−	1.18626i
$99$	248.293			0.252065
$100$	−1473.72	+	2552.56i	−1.47372	+	2.55256i
$101$	−265.899	−	460.551i	−0.261960	−	0.453728i	0.704803	−	0.709403i	$-0.251035\pi$
$101$	−265.899	−	460.551i	−0.261960	−	0.453728i	−0.966763	+	0.255676i	$0.917702\pi$
$102$	862.949	+	1494.67i	0.837693	+	1.45093i
$103$	−735.984			−0.704064			−0.352032	−	0.935988i	$-0.614509\pi$
$103$	−735.984			−0.704064			−0.352032	+	0.935988i	$0.614509\pi$
$104$	−2468.23	−	1877.86i	−2.32721	−	1.77057i
$105$	476.621			0.442985
$106$	−1313.48	−	2275.01i	−1.20355	−	2.08461i
$107$	391.632	+	678.327i	0.353837	+	0.612863i	0.986918	−	0.161222i	$-0.0515435\pi$
$107$	391.632	+	678.327i	0.353837	+	0.612863i	−0.633081	+	0.774085i	$0.718210\pi$
$108$	275.577	−	477.313i	0.245531	−	0.425273i
$109$	−532.339			−0.467788			−0.233894	−	0.972262i	$-0.575147\pi$
$109$	−532.339			−0.467788			−0.233894	+	0.972262i	$0.575147\pi$
$110$	1206.82	−	2090.27i	1.04605	−	1.81182i
$111$	147.635	−	255.712i	0.126243	−	0.218659i
$112$	1833.23			1.54664
$113$	90.2946	−	156.395i	0.0751699	−	0.130198i	−0.825990	−	0.563684i	$-0.809383\pi$
$113$	90.2946	−	156.395i	0.0751699	−	0.130198i	0.901160	+	0.433486i	$0.142717\pi$
$114$	−17.9679	−	31.1214i	−0.0147619	−	0.0255683i
$115$	343.107	+	594.280i	0.278217	+	0.481886i
$116$	1257.88			1.00682
$117$	389.070	−	163.037i	0.307432	−	0.128827i
$118$	2580.86			2.01346
$119$	−522.355	−	904.746i	−0.402389	−	0.696957i
$120$	−1629.00	−	2821.51i	−1.23922	−	2.14639i
$121$	284.947	−	493.542i	0.214085	−	0.370805i
$122$	−2366.81			−1.75640
$123$	−46.1178	+	79.8784i	−0.0338074	+	0.0585561i
$124$	−1958.96	+	3393.02i	−1.41871	+	2.45728i
$125$	−318.242			−0.227716
$126$	−232.184	+	402.155i	−0.164164	+	0.284340i
$127$	−715.817	−	1239.83i	−0.500146	−	0.866278i	−1.00000		0.000168331i	$-0.999946\pi$
$127$	−715.817	−	1239.83i	−0.500146	−	0.866278i	0.499854	−	0.866110i	$-0.333387\pi$
$128$	−862.972	−	1494.71i	−0.595912	−	1.03215i
$129$	−714.976			−0.487986
$130$	518.521	−	4067.85i	0.349825	−	2.74441i
$131$	2067.32			1.37880			0.689400	−	0.724381i	$-0.257874\pi$
$131$	2067.32			1.37880			0.689400	+	0.724381i	$0.257874\pi$
$132$	844.740	+	1463.13i	0.557009	+	0.964767i
$133$	10.8762	+	18.8382i	0.00709090	+	0.0122818i
$134$	−506.690	+	877.613i	−0.326652	+	0.565778i
$135$	443.153			0.282523
$136$	−3570.62	+	6184.50i	−2.25131	+	3.89939i
$137$	193.756	−	335.595i	0.120830	−	0.209283i	−0.799265	−	0.600978i	$-0.794778\pi$
$137$	193.756	−	335.595i	0.120830	−	0.209283i	0.920095	+	0.391695i	$0.128111\pi$
$138$	−668.575			−0.412412
$139$	−376.284	+	651.743i	−0.229611	+	0.397699i	−0.957693	−	0.287792i	$-0.907079\pi$
$139$	−376.284	+	651.743i	−0.229611	+	0.397699i	0.728082	+	0.685491i	$0.240412\pi$
$140$	1621.55	+	2808.61i	0.978900	+	1.69550i
$141$	−767.223	−	1328.87i	−0.458240	−	0.793695i
$142$	2584.09			1.52713
$143$	−163.508	+	1282.74i	−0.0956171	+	0.750126i
$144$	1704.51			0.986404
$145$	505.698	+	875.894i	0.289627	+	0.501649i
$146$	2552.67	+	4421.36i	1.44699	+	2.50626i
$147$	−373.956	+	647.710i	−0.209819	+	0.363416i
$148$	2009.13			1.11587
$149$	1318.36	−	2283.47i	0.724862	−	1.25550i	−0.234169	−	0.972196i	$-0.575237\pi$
$149$	1318.36	−	2283.47i	0.724862	−	1.25550i	0.959031	−	0.283301i	$-0.0914296\pi$
$150$	1154.48	−	1999.62i	0.628419	−	1.08845i
$151$	−3332.42			−1.79595			−0.897975	−	0.440046i	$-0.854962\pi$
$151$	−3332.42			−1.79595			−0.897975	+	0.440046i	$0.854962\pi$
$152$	74.3459	−	128.771i	0.0396727	−	0.0687151i
$153$	−485.677	−	841.217i	−0.256632	−	0.444499i
$154$	−711.727	−	1232.75i	−0.372419	−	0.645049i
$155$	−3150.20			−1.63245
$156$	2284.43	+	1738.01i	1.17244	+	0.892003i
$157$	−1625.26			−0.826179			−0.413089	−	0.910690i	$-0.635550\pi$
$157$	−1625.26			−0.826179			−0.413089	+	0.910690i	$0.635550\pi$
$158$	1000.02	+	1732.09i	0.503529	+	0.872138i
$159$	739.238	+	1280.40i	0.368713	+	0.638630i
$160$	3940.68	−	6825.46i	1.94711	−	3.37250i
$161$	404.698			0.198104
$162$	−215.881	+	373.917i	−0.104699	+	0.181344i
$163$	917.683	−	1589.47i	0.440972	−	0.763786i	−0.556790	−	0.830653i	$-0.687967\pi$
$163$	917.683	−	1589.47i	0.440972	−	0.763786i	0.997762	+	0.0668673i	$0.0213004\pi$
$164$	−627.605			−0.298828
$165$	−679.211	+	1176.43i	−0.320463	+	0.555059i
$166$	1907.65	+	3304.15i	0.891944	+	1.54489i
$167$	−972.498	−	1684.42i	−0.450624	−	0.780503i	0.547801	−	0.836609i	$-0.315465\pi$
$167$	−972.498	−	1684.42i	−0.450624	−	0.780503i	−0.998425	+	0.0561052i	$0.982132\pi$
$168$	−1921.42			−0.882384
$169$	586.072	+	2117.39i	0.266760	+	0.963763i
$170$	−9442.44			−4.26001
$171$	10.1125	+	17.5154i	0.00452237	+	0.00783298i
$172$	−2432.48	−	4213.18i	−1.07834	−	1.86774i
$173$	−1265.81	+	2192.45i	−0.556289	+	0.963522i	0.441512	+	0.897255i	$0.354442\pi$
$173$	−1265.81	+	2192.45i	−0.556289	+	0.963522i	−0.997802	+	0.0662666i	$0.978891\pi$
$174$	−985.397			−0.429326
$175$	−698.823	+	1210.40i	−0.301863	+	0.522842i
$176$	−2612.46	+	4524.90i	−1.11887	+	1.93794i
$177$	−1452.54			−0.616832
$178$	2766.88	−	4792.38i	1.16509	−	2.01800i
$179$	−2131.51	−	3691.88i	−0.890035	−	1.54159i	−0.839831	−	0.542847i	$-0.817346\pi$
$179$	−2131.51	−	3691.88i	−0.890035	−	1.54159i	−0.0502037	−	0.998739i	$-0.515987\pi$
$180$	1507.69	+	2611.39i	0.624314	+	1.08134i
$181$	3944.61			1.61989			0.809946	−	0.586504i	$-0.199496\pi$
$181$	3944.61			1.61989			0.809946	+	0.586504i	$0.199496\pi$
$182$	−1924.72	−	1464.35i	−0.783900	−	0.596398i
$183$	1332.06			0.538082
$184$	−1383.18	−	2395.74i	−0.554182	−	0.959871i
$185$	807.717	+	1399.01i	0.320998	+	0.555984i
$186$	1534.61	−	2658.02i	0.604962	−	1.04783i
$187$	2977.54			1.16438
$188$	5220.46	−	9042.11i	2.02522	−	3.50779i
$189$	130.676	−	226.337i	0.0502924	−	0.0871090i
$190$	196.606			0.0750701
$191$	107.054	−	185.424i	0.0405559	−	0.0702449i	−0.845035	−	0.534711i	$-0.820420\pi$
$191$	107.054	−	185.424i	0.0405559	−	0.0702449i	0.885591	+	0.464466i	$0.153754\pi$
$192$	1566.71	+	2713.62i	0.588893	+	1.01999i
$193$	603.593	+	1045.45i	0.225117	+	0.389914i	0.956355	−	0.292209i	$-0.0943902\pi$
$193$	603.593	+	1045.45i	0.225117	+	0.389914i	−0.731238	+	0.682123i	$0.761057\pi$
$194$	349.480			0.129336
$195$	−291.829	+	2289.43i	−0.107171	+	0.840765i
$196$	−5089.06			−1.85461
$197$	463.816	+	803.352i	0.167744	+	0.290541i	0.937626	−	0.347645i	$-0.113019\pi$
$197$	463.816	+	803.352i	0.167744	+	0.290541i	−0.769883	+	0.638186i	$0.779685\pi$
$198$	−661.751	−	1146.19i	−0.237518	−	0.411394i
$199$	−239.476	+	414.784i	−0.0853064	+	0.147755i	−0.905522	−	0.424300i	$-0.860520\pi$
$199$	−239.476	+	414.784i	−0.0853064	+	0.147755i	0.820215	+	0.572055i	$0.193854\pi$
$200$	9553.77			3.37777
$201$	285.170	−	493.930i	0.100072	−	0.173329i
$202$	−1417.35	+	2454.92i	−0.493684	+	0.855086i
$203$	596.474			0.206228
$204$	3304.72	−	5723.95i	1.13420	−	1.96449i
$205$	−252.312	−	437.017i	−0.0859621	−	0.148891i
$206$	1961.54	+	3397.49i	0.663432	+	1.14910i
$207$	376.281			0.126345
$208$	−1122.46	+	8805.85i	−0.374178	+	2.93546i
$209$	−61.9970			−0.0205188
$210$	−1270.29	−	2200.20i	−0.417420	−	0.722992i
$211$	725.477	+	1256.56i	0.236701	+	0.409978i	0.959766	−	0.280802i	$-0.0906005\pi$
$211$	725.477	+	1256.56i	0.236701	+	0.409978i	−0.723065	+	0.690780i	$0.757267\pi$
$212$	−5030.04	+	8712.29i	−1.62955	+	2.82246i
$213$	−1454.35			−0.467843
$214$	2087.55	−	3615.75i	0.666833	−	1.15499i
$215$	1955.83	−	3387.59i	0.620402	−	1.07457i
$216$	−1786.50			−0.562759
$217$	−928.920	+	1608.94i	−0.290595	+	0.503326i
$218$	1418.79	+	2457.41i	0.440791	+	0.763473i
$219$	−1436.67	−	2488.38i	−0.443293	−	0.767806i
$220$	−9243.19			−2.83262
$221$	4665.74	−	1955.15i	1.42014	−	0.595101i
$222$	−1573.91			−0.475828
$223$	1029.89	+	1783.83i	0.309268	+	0.535668i	0.978202	−	0.207654i	$-0.0665827\pi$
$223$	1029.89	+	1783.83i	0.309268	+	0.535668i	−0.668935	+	0.743321i	$0.733249\pi$
$224$	−2324.03	−	4025.34i	−0.693218	−	1.20069i
$225$	−649.753	+	1125.41i	−0.192519	+	0.333453i
$226$	−962.612			−0.283327
$227$	−2241.23	+	3881.93i	−0.655311	+	1.13503i	0.326504	+	0.945196i	$0.394129\pi$
$227$	−2241.23	+	3881.93i	−0.655311	+	1.13503i	−0.981816	+	0.189837i	$0.939204\pi$
$228$	−68.8094	+	119.181i	−0.0199869	+	0.0346183i
$229$	−1630.39			−0.470477			−0.235239	−	0.971938i	$-0.575587\pi$
$229$	−1630.39			−0.470477			−0.235239	+	0.971938i	$0.575587\pi$
$230$	1828.90	−	3167.74i	0.524321	−	0.908151i
$231$	400.567	+	693.803i	0.114093	+	0.197614i
$232$	−2038.64	−	3531.02i	−0.576910	−	0.999237i
$233$	−1903.69			−0.535258			−0.267629	−	0.963522i	$-0.586240\pi$
$233$	−1903.69			−0.535258			−0.267629	+	0.963522i	$0.586240\pi$
$234$	−1789.57	−	1361.52i	−0.499948	−	0.380365i
$235$	8395.00			2.33034
$236$	−4941.79	−	8559.44i	−1.36306	−	2.36090i
$237$	−562.824	−	974.839i	−0.154259	−	0.267184i
$238$	−2784.36	+	4822.65i	−0.758333	+	1.31347i
$239$	3763.79			1.01866			0.509328	−	0.860572i	$-0.329894\pi$
$239$	3763.79			1.01866			0.509328	+	0.860572i	$0.329894\pi$
$240$	−4662.70	+	8076.04i	−1.25407	+	2.17211i
$241$	1807.37	−	3130.46i	0.483083	−	0.836724i	−0.516728	−	0.856149i	$-0.672850\pi$
$241$	1807.37	−	3130.46i	0.483083	−	0.836724i	0.999811	+	0.0194250i	$0.00618357\pi$
$242$	−3037.75			−0.806918
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	4531.92	+	7849.52i	1.18904	+	2.05948i
$245$	−2045.92	−	3543.64i	−0.533507	−	0.924061i
$246$	491.652			0.127425
$247$	−97.1479	+	40.7092i	−0.0250258	+	0.0104869i
$248$	12699.5			3.25169
$249$	−1073.65	−	1859.61i	−0.273252	−	0.473286i
$250$	848.178	+	1469.09i	0.214574	+	0.371653i
$251$	2864.88	−	4962.12i	0.720438	−	1.24783i	−0.240387	−	0.970677i	$-0.577274\pi$
$251$	2864.88	−	4962.12i	0.720438	−	1.24783i	0.960824	−	0.277158i	$-0.0893924\pi$
$252$	1778.33			0.444541
$253$	−576.717	+	998.903i	−0.143312	+	0.248223i
$254$	−3815.59	+	6608.79i	−0.942564	+	1.63257i
$255$	5314.30			1.30508
$256$	−422.095	+	731.091i	−0.103051	+	0.178489i
$257$	2762.89	+	4785.47i	0.670602	+	1.16152i	0.977734	+	0.209849i	$0.0672974\pi$
$257$	2762.89	+	4785.47i	0.670602	+	1.16152i	−0.307132	+	0.951667i	$0.599369\pi$
$258$	1905.55	+	3300.51i	0.459824	+	0.796438i
$259$	952.709			0.228565
$260$	−14483.9	+	6069.37i	−3.45482	+	1.44772i
$261$	554.591			0.131526
$262$	−5509.82	−	9543.28i	−1.29923	−	2.25033i
$263$	−2611.60	−	4523.43i	−0.612313	−	1.06056i	−0.990850	−	0.134971i	$-0.956906\pi$
$263$	−2611.60	−	4523.43i	−0.612313	−	1.06056i	0.378536	−	0.925586i	$-0.376427\pi$
$264$	2738.12	−	4742.57i	0.638333	−	1.10563i
$265$	−8088.78			−1.87506
$266$	57.9747	−	100.415i	0.0133634	−	0.0231460i
$267$	−1557.23	+	2697.20i	−0.356932	+	0.618224i
$268$	3880.81			0.884545
$269$	−3601.94	+	6238.75i	−0.816410	+	1.41406i	0.0919010	+	0.995768i	$0.470706\pi$
$269$	−3601.94	+	6238.75i	−0.816410	+	1.41406i	−0.908311	+	0.418295i	$0.862628\pi$
$270$	−1181.09	−	2045.71i	−0.266218	−	0.461103i
$271$	4288.84	+	7428.49i	0.961360	+	1.66512i	0.719091	+	0.694916i	$0.244558\pi$
$271$	4288.84	+	7428.49i	0.961360	+	1.66512i	0.242269	+	0.970209i	$0.422108\pi$
$272$	20440.5			4.55656
$273$	1083.25	+	824.148i	0.240152	+	0.182710i
$274$	−2065.59			−0.455427
$275$	−1991.72	−	3449.76i	−0.436747	−	0.756467i
$276$	1280.18	+	2217.33i	0.279194	+	0.483578i
$277$	−3584.60	+	6208.70i	−0.777536	+	1.34673i	0.155822	+	0.987785i	$0.450197\pi$
$277$	−3584.60	+	6208.70i	−0.777536	+	1.34673i	−0.933358	+	0.358947i	$0.883136\pi$
$278$	4011.48			0.865442
$279$	−863.694	+	1495.96i	−0.185333	+	0.321007i
$280$	5256.06	−	9103.77i	1.12182	−	1.94305i
$281$	849.157			0.180272			0.0901360	−	0.995929i	$-0.471270\pi$
$281$	849.157			0.180272			0.0901360	+	0.995929i	$0.471270\pi$
$282$	−4089.60	+	7083.40i	−0.863589	+	1.49578i
$283$	−557.686	−	965.941i	−0.117141	−	0.202895i	0.801492	−	0.598005i	$-0.204040\pi$
$283$	−557.686	−	965.941i	−0.117141	−	0.202895i	−0.918634	+	0.395110i	$0.870706\pi$
$284$	−4947.97	−	8570.14i	−1.03383	−	1.79065i
$285$	−110.652			−0.0229981
$286$	6357.23	−	2663.95i	1.31437	−	0.550779i
$287$	−297.604			−0.0612091
$288$	−2160.84	−	3742.69i	−0.442114	−	0.765765i
$289$	−3367.75	−	5833.11i	−0.685476	−	1.18728i
$290$	2695.57	−	4668.86i	0.545825	−	0.945396i
$291$	−196.691			−0.0396227
$292$	9775.62	−	16931.9i	1.95916	−	3.39337i
$293$	931.764	−	1613.86i	0.185782	−	0.321784i	−0.758058	−	0.652188i	$-0.773851\pi$
$293$	931.764	−	1613.86i	0.185782	−	0.321784i	0.943840	+	0.330403i	$0.107185\pi$
$294$	3986.66			0.790839
$295$	3973.43	−	6882.19i	0.784211	−	1.35829i
$296$	−3256.18	−	5639.87i	−0.639397	−	1.10747i
$297$	372.440	+	645.085i	0.0727649	+	0.126033i
$298$	−14054.8			−2.73212
$299$	−247.792	+	1943.95i	−0.0479269	+	0.375992i
$300$	−8842.31			−1.70170
$301$	−1153.46	−	1997.85i	−0.220878	−	0.382571i
$302$	8881.55	+	15383.3i	1.69230	+	2.93116i
$303$	797.697	−	1381.65i	0.151243	−	0.261960i
$304$	−425.602			−0.0802959
$305$	−3643.88	+	6311.39i	−0.684092	+	1.18488i
$306$	−2588.85	+	4484.02i	−0.483642	+	0.837693i
$307$	−6387.50			−1.18747			−0.593736	−	0.804660i	$-0.702348\pi$
$307$	−6387.50			−1.18747			−0.593736	+	0.804660i	$0.702348\pi$
$308$	−2725.60	+	4720.89i	−0.504239	+	0.873368i
$309$	−1103.98	−	1912.14i	−0.203246	−	0.352032i
$310$	8395.89	+	14542.1i	1.53824	+	2.66431i
$311$	−3492.59			−0.636806			−0.318403	−	0.947955i	$-0.603147\pi$
$311$	−3492.59			−0.636806			−0.318403	+	0.947955i	$0.603147\pi$
$312$	1176.46	−	9229.44i	0.213474	−	1.67473i
$313$	−5912.01			−1.06762			−0.533812	−	0.845603i	$-0.679241\pi$
$313$	−5912.01			−1.06762			−0.533812	+	0.845603i	$0.679241\pi$
$314$	4331.64	+	7502.63i	0.778499	+	1.34840i
$315$	714.931	+	1238.30i	0.127879	+	0.221492i
$316$	3829.66	−	6633.16i	0.681756	−	1.18084i
$317$	−1677.54			−0.297224			−0.148612	−	0.988896i	$-0.547481\pi$
$317$	−1677.54			−0.297224			−0.148612	+	0.988896i	$0.547481\pi$
$318$	3940.43	−	6825.02i	0.694869	−	1.20355i
$319$	−850.009	+	1472.26i	−0.149189	+	0.258403i
$320$	−17143.0			−2.99476
$321$	−1174.90	+	2034.98i	−0.204288	+	0.353837i
$322$	−1078.60	−	1868.19i	−0.186671	−	0.323323i
$323$	121.270	+	210.045i	0.0208905	+	0.0361834i
$324$	1653.46			0.283515
$325$	−5386.21	−	4097.88i	−0.919301	−	0.699413i
$326$	−9783.22			−1.66209
$327$	−798.509	−	1383.06i	−0.135039	−	0.233894i
$328$	1017.15	+	1761.76i	0.171228	+	0.296576i
$329$	2475.49	−	4287.68i	0.414828	−	0.718503i
$330$	7240.92			1.20788
$331$	−1005.15	+	1740.98i	−0.166913	+	0.289102i	−0.937333	−	0.348435i	$-0.886713\pi$
$331$	−1005.15	+	1740.98i	−0.166913	+	0.289102i	0.770420	+	0.637537i	$0.220047\pi$
$332$	7305.49	−	12653.5i	1.20765	−	2.09172i
$333$	885.812			0.145772
$334$	−5183.80	+	8978.60i	−0.849236	+	1.47092i
$335$	1560.18	+	2702.30i	0.254452	+	0.440724i
$336$	2749.85	+	4762.87i	0.446477	+	0.773322i
$337$	7139.24			1.15400			0.577002	−	0.816743i	$-0.304222\pi$
$337$	7139.24			1.15400			0.577002	+	0.816743i	$0.304222\pi$
$338$	8212.40	−	8348.71i	1.32159	−	1.34352i
$339$	541.768			0.0867988
$340$	18080.2	+	31315.9i	2.88394	+	4.99512i
$341$	−2647.53	−	4585.65i	−0.420444	−	0.728231i
$342$	53.9038	−	93.3642i	0.00852276	−	0.0147619i
$343$	−5733.31			−0.902536
$344$	−7884.60	+	13656.5i	−1.23578	+	2.14044i
$345$	−1029.32	+	1782.84i	−0.160629	+	0.278217i
$346$	13494.6			2.09674
$347$	−0.569949	+	0.987181i	−8.81743e−5	+	0.000152722i	−0.866069	−	0.499924i	$-0.833361\pi$
$347$	−0.569949	+	0.987181i	−8.81743e−5	+	0.000152722i	0.865981	+	0.500076i	$0.166695\pi$
$348$	1886.82	+	3268.07i	0.290644	+	0.503411i
$349$	−6099.55	−	10564.7i	−0.935535	−	1.62039i	−0.773678	−	0.633579i	$-0.781585\pi$
$349$	−6099.55	−	10564.7i	−0.935535	−	1.62039i	−0.161857	−	0.986814i	$-0.551748\pi$
$350$	7450.00			1.13777
$351$	1007.19	+	766.279i	0.153162	+	0.116527i
$352$	13247.5			2.00595
$353$	5446.15	+	9433.01i	0.821160	+	1.42229i	0.904819	+	0.425796i	$0.140006\pi$
$353$	5446.15	+	9433.01i	0.821160	+	1.42229i	−0.0836595	+	0.996494i	$0.526661\pi$
$354$	3871.29	+	6705.28i	0.581234	+	1.00673i
$355$	3978.41	−	6890.80i	0.594794	−	1.03021i
$356$	−21191.9			−3.15497
$357$	1567.07	−	2714.24i	0.232319	−	0.402389i
$358$	−11361.8	+	19679.2i	−1.67734	+	2.90524i
$359$	−3525.78			−0.518339			−0.259169	−	0.965832i	$-0.583449\pi$
$359$	−3525.78			−0.518339			−0.259169	+	0.965832i	$0.583449\pi$
$360$	4887.00	−	8464.53i	0.715465	−	1.23922i
$361$	3426.97	+	5935.69i	0.499632	+	0.865388i
$362$	−10513.2	−	18209.3i	−1.52641	−	2.64382i
$363$	1709.68			0.247204
$364$	−1171.08	+	9187.24i	−0.168630	+	1.32292i
$365$	15720.1			2.25433
$366$	−3550.21	−	6149.15i	−0.507029	−	0.878200i
$367$	−1191.88	−	2064.39i	−0.169525	−	0.293625i	0.768728	−	0.639576i	$-0.220890\pi$
$367$	−1191.88	−	2064.39i	−0.169525	−	0.293625i	−0.938253	+	0.345950i	$0.887557\pi$
$368$	−3959.09	+	6857.35i	−0.560821	+	0.971370i
$369$	−276.707			−0.0390374
$370$	4305.45	−	7457.26i	0.604945	−	1.04780i
$371$	−2385.20	+	4131.28i	−0.333782	+	0.578128i
$372$	−11753.8			−1.63818
$373$	6641.10	−	11502.7i	0.921885	−	1.59675i	0.125390	−	0.992108i	$-0.459982\pi$
$373$	6641.10	−	11502.7i	0.921885	−	1.59675i	0.796495	−	0.604645i	$-0.206685\pi$
$374$	−7935.73	−	13745.1i	−1.09718	−	1.90038i
$375$	−477.363	−	826.818i	−0.0657358	−	0.113858i
$376$	−33843.1			−4.64181
$377$	−365.214	+	2865.14i	−0.0498925	+	0.391412i
$378$	−1393.11			−0.189560
$379$	2218.36	+	3842.32i	0.300659	+	0.520756i	0.976285	−	0.216488i	$-0.0694601\pi$
$379$	2218.36	+	3842.32i	0.300659	+	0.520756i	−0.675627	+	0.737244i	$0.736127\pi$
$380$	−376.458	−	652.045i	−0.0508208	−	0.0880242i
$381$	2147.45	−	3719.50i	0.288759	−	0.500146i
$382$	−1141.28			−0.152862
$383$	405.206	−	701.838i	0.0540602	−	0.0936351i	−0.837729	−	0.546086i	$-0.816117\pi$
$383$	405.206	−	701.838i	0.0540602	−	0.0936351i	0.891789	+	0.452451i	$0.149450\pi$
$384$	2588.92	−	4484.14i	0.344050	−	0.595912i
$385$	−4383.03			−0.580207
$386$	3217.39	−	5572.68i	0.424251	−	0.734824i
$387$	−1072.46	−	1857.56i	−0.140869	−	0.243993i
$388$	−669.177	−	1159.05i	−0.0875576	−	0.151654i
$389$	3463.79			0.451469			0.225734	−	0.974189i	$-0.427522\pi$
$389$	3463.79			0.451469			0.225734	+	0.974189i	$0.427522\pi$
$390$	11346.4	−	4754.62i	1.47319	−	0.617332i
$391$	4512.37			0.583633
$392$	8247.80	+	14285.6i	1.06270	+	1.84064i
$393$	3100.98	+	5371.06i	0.398025	+	0.689400i
$394$	2472.32	−	4282.18i	0.316126	−	0.547546i
$395$	6158.45			0.784469
$396$	−2534.22	+	4389.40i	−0.321589	+	0.557009i
$397$	−212.703	+	368.412i	−0.0268898	+	0.0465745i	−0.879157	−	0.476532i	$-0.841894\pi$
$397$	−212.703	+	368.412i	−0.0268898	+	0.0465745i	0.852267	+	0.523106i	$0.175227\pi$
$398$	2553.00			0.321533
$399$	−32.6287	+	56.5146i	−0.00409394	+	0.00709090i
$400$	−13672.9	−	23682.2i	−1.70912	−	2.96028i
$401$	593.424	+	1027.84i	0.0739007	+	0.128000i	0.900608	−	0.434633i	$-0.143122\pi$
$401$	593.424	+	1027.84i	0.0739007	+	0.128000i	−0.826707	+	0.562633i	$0.809789\pi$
$402$	−3040.14			−0.377185
$403$	−7159.70	−	5447.16i	−0.884987	−	0.673306i
$404$	10855.6			1.33685
$405$	664.730	+	1151.35i	0.0815573	+	0.141261i
$406$	−1589.72	−	2753.48i	−0.194327	−	0.336583i
$407$	−1357.66	+	2351.54i	−0.165349	+	0.286392i
$408$	−21423.7			−2.59959
$409$	−4003.71	+	6934.63i	−0.484036	+	0.838375i	−0.999832	−	0.0183369i	$-0.994163\pi$
$409$	−4003.71	+	6934.63i	−0.484036	+	0.838375i	0.515796	+	0.856711i	$0.327496\pi$
$410$	−1344.92	+	2329.47i	−0.162002	+	0.280596i
$411$	1162.54			0.139522
$412$	7511.85	−	13010.9i	0.898258	−	1.55583i
$413$	−2343.35	−	4058.80i	−0.279198	−	0.483585i
$414$	−1002.86	−	1737.01i	−0.119053	−	0.206206i
$415$	11747.9			1.38960
$416$	20758.5	−	8698.72i	2.44656	−	1.02522i
$417$	−2257.70			−0.265132
$418$	165.234	+	286.194i	0.0193346	+	0.0334885i
$419$	−3416.23	−	5917.08i	−0.398314	−	0.689901i	0.595204	−	0.803575i	$-0.297071\pi$
$419$	−3416.23	−	5917.08i	−0.398314	−	0.689901i	−0.993518	+	0.113674i	$0.963738\pi$
$420$	−4864.65	+	8425.82i	−0.565168	+	0.978900i
$421$	10739.6			1.24326			0.621632	−	0.783309i	$-0.286470\pi$
$421$	10739.6			1.24326			0.621632	+	0.783309i	$0.286470\pi$
$422$	3867.08	−	6697.98i	0.446082	−	0.772636i
$423$	2301.67	−	3986.61i	0.264565	−	0.458240i
$424$	32608.6			3.73494
$425$	−7791.85	+	13495.9i	−0.889318	+	1.54034i
$426$	3876.14	+	6713.67i	0.440844	+	0.763564i
$427$	2148.99	+	3722.16i	0.243553	+	0.421846i
$428$	−15988.9			−1.80573
$429$	−3577.91	+	1499.30i	−0.402665	+	0.168734i
$430$	−20850.7			−2.33839
$431$	−2607.22	−	4515.84i	−0.291382	−	0.504688i	0.682755	−	0.730647i	$-0.260782\pi$
$431$	−2607.22	−	4515.84i	−0.291382	−	0.504688i	−0.974137	+	0.225959i	$0.927448\pi$
$432$	2556.76	+	4428.44i	0.284750	+	0.493202i
$433$	−4321.12	+	7484.40i	−0.479584	+	0.830664i	−0.999726	−	0.0234161i	$-0.992546\pi$
$433$	−4321.12	+	7484.40i	−0.479584	+	0.830664i	0.520142	+	0.854080i	$0.325879\pi$
$434$	9903.02			1.09530
$435$	−1517.09	+	2627.68i	−0.167216	+	0.289627i
$436$	5433.34	−	9410.83i	0.596812	−	1.03371i
$437$	−93.9545			−0.0102848
$438$	−7658.01	+	13264.1i	−0.835420	+	1.44699i
$439$	6513.12	+	11281.1i	0.708097	+	1.22646i	0.965562	+	0.260172i	$0.0837793\pi$
$439$	6513.12	+	11281.1i	0.708097	+	1.22646i	−0.257466	+	0.966287i	$0.582887\pi$
$440$	14980.4	+	25946.8i	1.62309	+	2.81128i
$441$	−2243.73			−0.242278
$442$	−21460.6	−	16327.4i	−2.30945	−	1.75705i
$443$	−11533.0			−1.23690			−0.618450	−	0.785824i	$-0.712239\pi$
$443$	−11533.0			−1.23690			−0.618450	+	0.785824i	$0.712239\pi$
$444$	3013.69	+	5219.87i	0.322125	+	0.557937i
$445$	−8519.64	−	14756.5i	−0.907573	−	1.57196i
$446$	5489.74	−	9508.50i	0.582840	−	1.00951i
$447$	7910.17			0.836998
$448$	−5055.08	+	8755.65i	−0.533103	+	0.923361i
$449$	−4941.37	+	8558.71i	−0.519372	+	0.899578i	0.480375	+	0.877063i	$0.340501\pi$
$449$	−4941.37	+	8558.71i	−0.519372	+	0.899578i	−0.999747	+	0.0225149i	$0.992833\pi$
$450$	6926.88			0.725636
$451$	424.102	−	734.566i	0.0442798	−	0.0766949i
$452$	1843.19	+	3192.50i	0.191806	+	0.332218i
$453$	−4998.63	−	8657.88i	−0.518446	−	0.897975i
$454$	23893.3			2.46997
$455$	−6868.11	+	2878.04i	−0.707653	+	0.296537i
$456$	446.075			0.0458101
$457$	7814.04	+	13534.3i	0.799836	+	1.38536i	0.919722	+	0.392569i	$0.128414\pi$
$457$	7814.04	+	13534.3i	0.799836	+	1.38536i	−0.119886	+	0.992788i	$0.538253\pi$
$458$	4345.31	+	7526.31i	0.443326	+	0.767863i
$459$	1457.03	−	2523.65i	0.148166	−	0.256632i
$460$	−14007.8			−1.41982
$461$	3873.73	−	6709.50i	0.391361	−	0.677858i	−0.601268	−	0.799047i	$-0.705338\pi$
$461$	3873.73	−	6709.50i	0.391361	−	0.677858i	0.992629	+	0.121190i	$0.0386709\pi$
$462$	2135.18	−	3698.24i	0.215016	−	0.372419i
$463$	−333.422			−0.0334675			−0.0167337	−	0.999860i	$-0.505327\pi$
$463$	−333.422			−0.0334675			−0.0167337	+	0.999860i	$0.505327\pi$
$464$	−5835.21	+	10106.9i	−0.583821	+	1.01121i
$465$	−4725.29	−	8184.45i	−0.471248	−	0.816225i
$466$	5073.71	+	8787.93i	0.504368	+	0.873590i
$467$	8198.33			0.812363			0.406182	−	0.913792i	$-0.366860\pi$
$467$	8198.33			0.812363			0.406182	+	0.913792i	$0.366860\pi$
$468$	−1088.85	+	8542.13i	−0.107547	+	0.843719i
$469$	1840.24			0.181182
$470$	−22374.3	−	38753.5i	−2.19585	−	3.80333i
$471$	−2437.89	−	4222.56i	−0.238497	−	0.413089i
$472$	−16018.2	+	27744.4i	−1.56208	+	2.70559i
$473$	6574.96			0.639148
$474$	−3000.07	+	5196.28i	−0.290713	+	0.503529i
$475$	162.238	−	281.005i	0.0156716	−	0.0271440i
$476$	21325.8			2.05350
$477$	−2217.71	+	3841.19i	−0.212877	+	0.368713i
$478$	−10031.2	−	17374.6i	−0.959870	−	1.66254i
$479$	3217.94	+	5573.64i	0.306955	+	0.531662i	0.977695	−	0.210031i	$-0.0673565\pi$
$479$	3217.94	+	5573.64i	0.306955	+	0.531662i	−0.670740	+	0.741693i	$0.734023\pi$
$480$	23644.1			2.24833
$481$	−583.332	+	4576.30i	−0.0552966	+	0.433807i
$482$	−19268.0			−1.82082
$483$	607.047	+	1051.44i	0.0571876	+	0.0990518i
$484$	5816.64	+	10074.7i	0.546266	+	0.946160i
$485$	538.050	−	931.931i	0.0503745	−	0.0872511i
$486$	−1295.29			−0.120896
$487$	−4047.69	+	7010.80i	−0.376629	+	0.652340i	−0.990569	−	0.137012i	$-0.956250\pi$
$487$	−4047.69	+	7010.80i	−0.376629	+	0.652340i	0.613941	+	0.789352i	$0.289583\pi$
$488$	14689.7	−	25443.3i	1.36265	−	2.36017i
$489$	5506.10			0.509191
$490$	−10905.6	+	18889.0i	−1.00544	+	1.74147i
$491$	−2558.23	−	4430.99i	−0.235135	−	0.407266i	0.724177	−	0.689614i	$-0.242220\pi$
$491$	−2558.23	−	4430.99i	−0.235135	−	0.407266i	−0.959312	+	0.282348i	$0.908887\pi$
$492$	−941.408	−	1630.57i	−0.0862641	−	0.149414i
$493$	6650.67			0.607568
$494$	446.842	+	339.962i	0.0406971	+	0.0309628i
$495$	−4075.26			−0.370039
$496$	−18175.0	−	31479.9i	−1.64532	−	2.84978i
$497$	−2346.28	−	4063.88i	−0.211761	−	0.366780i
$498$	−5722.96	+	9912.46i	−0.514964	+	0.891944i
$499$	−18050.7			−1.61936			−0.809682	−	0.586870i	$-0.800360\pi$
$499$	−18050.7			−1.61936			−0.809682	+	0.586870i	$0.800360\pi$
$500$	3248.15	−	5625.97i	0.290524	−	0.503202i
$501$	2917.50	−	5053.25i	0.260168	−	0.450624i
$502$	−30541.9			−2.71544
$503$	−5265.53	+	9120.16i	−0.466756	+	0.808445i	−0.999279	−	0.0379705i	$-0.987911\pi$
$503$	−5265.53	+	9120.16i	−0.466756	+	0.808445i	0.532523	+	0.846416i	$0.321244\pi$
$504$	−2882.13	−	4991.99i	−0.254722	−	0.441192i
$505$	4364.22	+	7559.06i	0.384565	+	0.666087i
$506$	6148.25			0.540165
$507$	−4622.02	+	4698.74i	−0.404874	+	0.411595i
$508$	29224.1			2.55238
$509$	981.654	+	1700.27i	0.0854834	+	0.148062i	0.905597	−	0.424139i	$-0.139423\pi$
$509$	981.654	+	1700.27i	0.0854834	+	0.148062i	−0.820114	+	0.572201i	$0.806090\pi$
$510$	−14163.7	−	24532.2i	−1.22976	−	2.13001i
$511$	4635.50	−	8028.93i	0.401297	−	0.695066i
$512$	−9307.69			−0.803409
$513$	−30.3376	+	52.5463i	−0.00261099	+	0.00452237i
$514$	14727.3	−	25508.5i	1.26380	−	2.18897i
$515$	12079.8			1.03359
$516$	7297.44	−	12639.5i	0.622581	−	1.07834i
$517$	7055.43	+	12220.4i	0.600188	+	1.03956i
$518$	−2539.16	−	4397.95i	−0.215375	−	0.373040i
$519$	−7594.89			−0.642348
$520$	40511.4	+	30821.4i	3.41642	+	2.59925i
$521$	−7044.93			−0.592407			−0.296203	−	0.955125i	$-0.595721\pi$
$521$	−7044.93			−0.592407			−0.296203	+	0.955125i	$0.595721\pi$
$522$	−1478.10	−	2560.14i	−0.123936	−	0.214663i
$523$	1606.65	+	2782.79i	0.134328	+	0.232664i	0.925341	−	0.379137i	$-0.123779\pi$
$523$	1606.65	+	2782.79i	0.134328	+	0.232664i	−0.791012	+	0.611800i	$0.790446\pi$
$524$	−21100.2	+	36546.6i	−1.75910	+	3.04685i
$525$	−4192.94			−0.348561
$526$	−13920.9	+	24111.7i	−1.15395	+	1.99870i
$527$	−10357.4	+	17939.6i	−0.856123	+	1.48285i
$528$	−15674.7			−1.29196
$529$	5209.50	−	9023.13i	0.428167	−	0.741606i
$530$	21558.2	+	37339.9i	1.76685	+	3.06027i
$531$	−2178.80	−	3773.80i	−0.178064	−	0.308416i
$532$	−444.036			−0.0361868
$533$	182.219	−	1429.53i	0.0148082	−	0.116172i
$534$	16601.3			1.34533
$535$	−6427.90	−	11133.4i	−0.519443	−	0.899702i
$536$	−6289.59	−	10893.9i	−0.506845	−	0.877882i
$537$	6394.52	−	11075.6i	0.513862	−	0.890035i
$538$	38399.5			3.07718
$539$	3438.92	−	5956.38i	0.274814	−	0.475991i
$540$	−4523.07	+	7834.18i	−0.360448	+	0.624314i
$541$	11251.4			0.894150			0.447075	−	0.894497i	$-0.352466\pi$
$541$	11251.4			0.894150			0.447075	+	0.894497i	$0.352466\pi$
$542$	22861.2	−	39596.8i	1.81176	−	3.13806i
$543$	5916.91	+	10248.4i	0.467623	+	0.809946i
$544$	−25912.9	−	44882.4i	−2.04229	−	3.53735i
$545$	8737.33			0.686727
$546$	917.399	−	7197.09i	0.0719067	−	0.564115i
$547$	1533.54			0.119871			0.0599353	−	0.998202i	$-0.480911\pi$
$547$	1533.54			0.119871			0.0599353	+	0.998202i	$0.480911\pi$
$548$	3955.16	+	6850.53i	0.308314	+	0.534015i
$549$	1998.10	+	3460.80i	0.155331	+	0.269041i
$550$	−10616.7	+	18388.6i	−0.823083	+	1.42562i
$551$	−138.477			−0.0107066
$552$	4149.54	−	7187.22i	0.319957	−	0.554182i
$553$	1815.98	−	3145.38i	0.139645	−	0.241872i
$554$	38214.6			2.93066
$555$	−2423.15	+	4197.02i	−0.185328	+	0.320998i
$556$	−7681.12	−	13304.1i	−0.585885	−	1.01478i
$557$	−8422.84	−	14588.8i	−0.640731	−	1.10978i	−0.985270	−	0.171006i	$-0.945298\pi$
$557$	−8422.84	−	14588.8i	−0.640731	−	1.10978i	0.344539	−	0.938772i	$-0.388035\pi$
$558$	9207.65			0.698550
$559$	10302.8	−	4317.33i	0.779540	−	0.326661i
$560$	−30089.0			−2.27052
$561$	4466.31	+	7735.88i	0.336128	+	0.582191i
$562$	−2263.17	−	3919.92i	−0.169868	−	0.294221i
$563$	10410.0	−	18030.7i	0.779273	−	1.34974i	−0.153089	−	0.988212i	$-0.548922\pi$
$563$	10410.0	−	18030.7i	0.779273	−	1.34974i	0.932361	−	0.361528i	$-0.117745\pi$
$564$	31322.8			2.33852
$565$	−1482.01	+	2566.92i	−0.110352	+	0.191135i
$566$	−2972.69	+	5148.84i	−0.220762	+	0.382371i
$567$	784.054			0.0580726
$568$	−16038.3	+	27779.1i	−1.18477	+	2.05209i
$569$	−11818.3	−	20469.9i	−0.870735	−	1.50816i	−0.861237	−	0.508203i	$-0.830310\pi$
$569$	−11818.3	−	20469.9i	−0.870735	−	1.50816i	−0.00949803	−	0.999955i	$-0.503023\pi$
$570$	294.909	+	510.798i	0.0216709	+	0.0375351i
$571$	−26955.1			−1.97554			−0.987771	−	0.155913i	$-0.950168\pi$
$571$	−26955.1			−1.97554			−0.987771	+	0.155913i	$0.950168\pi$
$572$	−21007.7	−	15982.9i	−1.53562	−	1.16832i
$573$	642.326			0.0468300
$574$	793.173	+	1373.82i	0.0576767	+	0.0998989i
$575$	−3018.39	−	5228.01i	−0.218914	−	0.379170i
$576$	−4700.12	+	8140.85i	−0.339997	+	0.588893i
$577$	23499.8			1.69551			0.847755	−	0.530388i	$-0.177954\pi$
$577$	23499.8			1.69551			0.847755	+	0.530388i	$0.177954\pi$
$578$	−17951.4	+	31092.8i	−1.29183	+	2.23752i
$579$	−1810.78	+	3136.36i	−0.129971	+	0.225117i
$580$	−20645.7			−1.47805
$581$	3464.19	−	6000.15i	0.247365	−	0.428448i
$582$	524.219	+	907.975i	0.0373361	+	0.0646680i
$583$	−6798.07	−	11774.6i	−0.482929	−	0.836457i
$584$	−63373.1			−4.49040
$585$	−6385.85	+	2675.95i	−0.451320	+	0.189123i
$586$	−9933.33			−0.700243
$587$	−2318.75	−	4016.19i	−0.163041	−	0.282395i	0.772917	−	0.634507i	$-0.218797\pi$
$587$	−2318.75	−	4016.19i	−0.163041	−	0.282395i	−0.935958	+	0.352112i	$0.885464\pi$
$588$	−7633.59	−	13221.8i	−0.535381	−	0.927307i
$589$	215.658	−	373.530i	0.0150866	−	0.0261308i
$590$	−42359.9			−2.95582
$591$	−1391.45	+	2410.06i	−0.0968468	+	0.167744i
$592$	−9320.20	+	16143.1i	−0.647057	+	1.12074i
$593$	12633.5			0.874869			0.437434	−	0.899250i	$-0.355887\pi$
$593$	12633.5			0.874869			0.437434	+	0.899250i	$0.355887\pi$
$594$	1985.25	−	3438.56i	0.137131	−	0.237518i
$595$	8573.47	+	14849.7i	0.590719	+	1.02316i
$596$	26911.8	+	46612.7i	1.84958	+	3.20357i
$597$	−1436.85			−0.0985033
$598$	9634.18	−	4037.14i	0.658814	−	0.276072i
$599$	−18757.1			−1.27946			−0.639730	−	0.768600i	$-0.720954\pi$
$599$	−18757.1			−1.27946			−0.639730	+	0.768600i	$0.720954\pi$
$600$	14330.7	+	24821.4i	0.975078	+	1.68888i
$601$	1816.49	+	3146.25i	0.123288	+	0.213541i	0.921062	−	0.389415i	$-0.127323\pi$
$601$	1816.49	+	3146.25i	0.123288	+	0.213541i	−0.797774	+	0.602956i	$0.793989\pi$
$602$	−6148.38	+	10649.3i	−0.416261	+	0.720986i
$603$	1711.02			0.115553
$604$	34012.5	−	58911.4i	2.29131	−	3.96866i
$605$	−4676.85	+	8100.55i	−0.314283	+	0.544354i
$606$	−8504.08			−0.570057
$607$	6349.99	−	10998.5i	0.424610	−	0.735445i	−0.571774	−	0.820411i	$-0.693745\pi$
$607$	6349.99	−	10998.5i	0.424610	−	0.735445i	0.996384	+	0.0849656i	$0.0270781\pi$
$608$	539.546	+	934.522i	0.0359893	+	0.0623353i
$609$	894.712	+	1549.69i	0.0595329	+	0.103114i
$610$	38846.6			2.57845
$611$	19080.0	+	14516.2i	1.26333	+	0.961151i
$612$	19828.3			1.30966
$613$	−10820.1	−	18740.9i	−0.712918	−	1.23481i	−0.963757	−	0.266781i	$-0.914040\pi$
$613$	−10820.1	−	18740.9i	−0.712918	−	1.23481i	0.250839	−	0.968029i	$-0.419293\pi$
$614$	17023.9	+	29486.3i	1.11894	+	1.93806i
$615$	756.936	−	1311.05i	0.0496303	−	0.0859621i
$616$	17669.5			1.15572
$617$	8270.85	−	14325.5i	0.539663	−	0.934723i	−0.459259	−	0.888302i	$-0.651885\pi$
$617$	8270.85	−	14325.5i	0.539663	−	0.934723i	0.998922	−	0.0464208i	$-0.0147815\pi$
$618$	−5884.62	+	10192.5i	−0.383033	+	0.663432i
$619$	−21138.9			−1.37261			−0.686303	−	0.727316i	$-0.740767\pi$
$619$	−21138.9			−1.37261			−0.686303	+	0.727316i	$0.740767\pi$
$620$	32152.6	−	55690.0i	2.08271	−	3.60736i
$621$	564.421	+	977.607i	0.0364726	+	0.0631723i
$622$	9308.44	+	16122.7i	0.600055	+	1.03933i
$623$	−10049.0			−0.646235
$624$	−24562.0	+	10292.5i	−1.57575	+	0.660305i
$625$	−12825.4			−0.820823
$626$	15756.7	+	27291.3i	1.00601	+	1.74246i
$627$	−92.9955	−	161.073i	−0.00592326	−	0.0102594i
$628$	16588.3	−	28731.8i	1.05405	−	1.82568i
$629$	10622.7			0.673377
$630$	3810.86	−	6600.61i	0.240997	−	0.417420i
$631$	−2744.90	+	4754.31i	−0.173174	+	0.299946i	−0.939528	−	0.342473i	$-0.888736\pi$
$631$	−2744.90	+	4754.31i	−0.173174	+	0.299946i	0.766354	+	0.642419i	$0.222069\pi$
$632$	−24826.8			−1.56259
$633$	−2176.43	+	3769.69i	−0.136659	+	0.236701i
$634$	4470.97	+	7743.94i	0.280071	+	0.485097i
$635$	11748.8	+	20349.5i	0.734230	+	1.27172i
$636$	−30180.3			−1.88164
$637$	1477.56	−	11591.6i	0.0919044	−	0.720999i
$638$	9061.76			0.562318
$639$	−2181.53	−	3778.52i	−0.135055	−	0.233922i
$640$	14164.0	+	24532.8i	0.874817	+	1.51523i
$641$	−2148.52	+	3721.35i	−0.132389	+	0.229305i	−0.924597	−	0.380946i	$-0.875598\pi$
$641$	−2148.52	+	3721.35i	−0.132389	+	0.229305i	0.792208	+	0.610251i	$0.208932\pi$
$642$	12525.3			0.769993
$643$	−12848.5	+	22254.2i	−0.788016	+	1.36488i	0.139164	+	0.990269i	$0.455558\pi$
$643$	−12848.5	+	22254.2i	−0.788016	+	1.36488i	−0.927181	+	0.374615i	$0.877775\pi$
$644$	−4130.57	+	7154.35i	−0.252744	+	0.437766i
$645$	11735.0			0.716378
$646$	646.416	−	1119.62i	0.0393698	−	0.0681905i
$647$	−1087.49	−	1883.59i	−0.0660798	−	0.114454i	0.831093	−	0.556134i	$-0.187716\pi$
$647$	−1087.49	−	1883.59i	−0.0660798	−	0.114454i	−0.897172	+	0.441680i	$0.854383\pi$
$648$	−2679.75	−	4641.46i	−0.162454	−	0.281379i
$649$	13357.6			0.807907
$650$	−4561.54	+	35785.7i	−0.275259	+	2.15943i
$651$	−5573.52			−0.335551
$652$	18732.7	+	32446.1i	1.12520	+	1.94890i
$653$	7727.27	+	13384.0i	0.463080	+	0.802078i	0.999113	−	0.0421191i	$-0.0134109\pi$
$653$	7727.27	+	13384.0i	0.463080	+	0.802078i	−0.536032	+	0.844197i	$0.680078\pi$
$654$	−4256.37	+	7372.24i	−0.254491	+	0.440791i
$655$	−33931.1			−2.02412
$656$	2911.41	−	5042.71i	0.173280	−	0.300129i
$657$	4310.01	−	7465.15i	0.255935	−	0.443293i
$658$	−26390.7			−1.56355
$659$	1574.39	−	2726.92i	0.0930643	−	0.161192i	−0.815735	−	0.578426i	$-0.803667\pi$
$659$	1574.39	−	2726.92i	0.0930643	−	0.161192i	0.908799	+	0.417234i	$0.137000\pi$
$660$	−13864.8	−	24014.5i	−0.817706	−	1.41631i
$661$	1049.85	+	1818.39i	0.0617767	+	0.107000i	0.895260	−	0.445545i	$-0.146990\pi$
$661$	1049.85	+	1818.39i	0.0617767	+	0.107000i	−0.833483	+	0.552545i	$0.813657\pi$
$662$	10715.7			0.629122
$663$	12078.2	+	9189.23i	0.707511	+	0.538281i
$664$	−47359.8			−2.76795
$665$	−178.513	−	309.193i	−0.0104097	−	0.0180301i
$666$	−2360.86	−	4089.14i	−0.137360	−	0.237914i
$667$	−1288.16	+	2231.16i	−0.0747794	+	0.129522i
$668$	39703.4			2.29966
$669$	−3089.68	+	5351.48i	−0.178556	+	0.309268i
$670$	8316.35	−	14404.3i	0.479535	−	0.830580i
$671$	−12249.7			−0.704763
$672$	6972.09	−	12076.0i	0.400230	−	0.693218i
$673$	−15485.4	−	26821.5i	−0.886950	−	1.53624i	−0.843462	−	0.537189i	$-0.819486\pi$
$673$	−15485.4	−	26821.5i	−0.886950	−	1.53624i	−0.0434884	−	0.999054i	$-0.513847\pi$
$674$	−19027.5	−	32956.6i	−1.08741	−	1.88344i
$675$	−3898.52			−0.222302
$676$	−43413.5	−	11250.5i	−2.47004	−	0.640104i
$677$	14640.6			0.831141			0.415570	−	0.909561i	$-0.363582\pi$
$677$	14640.6			0.831141			0.415570	+	0.909561i	$0.363582\pi$
$678$	−1443.92	−	2500.94i	−0.0817895	−	0.141664i
$679$	−317.317	−	549.610i	−0.0179345	−	0.0310635i
$680$	58605.0	−	101507.i	3.30500	−	5.72442i
$681$	−13447.4			−0.756688
$682$	−14112.4	+	24443.3i	−0.792360	+	1.37241i
$683$	3342.92	−	5790.10i	0.187281	−	0.324381i	−0.757062	−	0.653343i	$-0.773366\pi$
$683$	3342.92	−	5790.10i	0.187281	−	0.324381i	0.944343	+	0.328963i	$0.106699\pi$
$684$	−412.856			−0.0230789
$685$	−3180.13	+	5508.15i	−0.177382	+	0.307235i
$686$	15280.4	+	26466.4i	0.850450	+	1.47302i
$687$	−2445.59	−	4235.88i	−0.135815	−	0.235239i
$688$	45136.3			2.50117
$689$	−18384.0	−	13986.7i	−1.01651	−	0.773370i
$690$	10973.4			0.605434
$691$	15097.0	+	26148.8i	0.831141	+	1.43958i	0.897134	+	0.441758i	$0.145645\pi$
$691$	15097.0	+	26148.8i	0.831141	+	1.43958i	−0.0659934	+	0.997820i	$0.521022\pi$
$692$	−25839.2	−	44754.8i	−1.41945	−	2.45856i
$693$	−1201.70	+	2081.41i	−0.0658714	+	0.114093i
$694$	6.07611			0.000332343
$695$	6175.98	−	10697.1i	0.337077	−	0.583834i
$696$	6115.91	−	10593.1i	0.333079	−	0.576910i
$697$	−3318.28			−0.180328
$698$	−32513.0	+	56314.2i	−1.76309	+	3.05376i
$699$	−2855.54	−	4945.94i	−0.154516	−	0.267629i
$700$	−14265.1	−	24707.9i	−0.770245	−	1.33410i
$701$	−30300.9			−1.63260			−0.816298	−	0.577631i	$-0.803977\pi$
$701$	−30300.9			−1.63260			−0.816298	+	0.577631i	$0.803977\pi$
$702$	852.982	−	6691.73i	0.0458600	−	0.359776i
$703$	−221.181			−0.0118663
$704$	−14407.5	−	24954.6i	−0.771313	−	1.33595i
$705$	12592.5	+	21810.9i	0.672711	+	1.16517i
$706$	29030.1	−	50281.7i	1.54754	−	2.68042i
$707$	5147.64			0.273829
$708$	14825.4	−	25678.3i	0.786966	−	1.36306i
$709$	−13061.6	+	22623.4i	−0.691875	+	1.19836i	0.279348	+	0.960190i	$0.409882\pi$
$709$	−13061.6	+	22623.4i	−0.691875	+	1.19836i	−0.971223	+	0.238173i	$0.923452\pi$
$710$	−42412.9			−2.24187
$711$	1688.47	−	2924.52i	0.0890613	−	0.154259i
$712$	34345.5	+	59488.2i	1.80780	+	3.13120i
$713$	−4012.24	−	6949.41i	−0.210743	−	0.365017i
$714$	−16706.2			−0.875647
$715$	2683.68	−	21053.7i	0.140369	−	1.10121i
$716$	87021.3			4.54209
$717$	5645.68	+	9778.60i	0.294061	+	0.509328i
$718$	9396.90	+	16275.9i	0.488425	+	0.845977i
$719$	−9662.83	+	16736.5i	−0.501200	+	0.868104i	0.498799	+	0.866718i	$0.333775\pi$
$719$	−9662.83	+	16736.5i	−0.501200	+	0.868104i	−0.999999	+	0.00138631i	$0.999559\pi$
$720$	−27976.2			−1.44807
$721$	3562.05	−	6169.64i	0.183991	−	0.318682i
$722$	18267.1	−	31639.6i	0.941595	−	1.63089i
$723$	10844.2			0.557816
$724$	−40260.8	+	69733.8i	−2.06669	+	3.57961i
$725$	−4448.73	−	7705.43i	−0.227892	−	0.394721i
$726$	−4556.63	−	7892.32i	−0.232937	−	0.403459i
$727$	26065.8			1.32975			0.664875	−	0.746954i	$-0.268485\pi$
$727$	26065.8			1.32975			0.664875	+	0.746954i	$0.268485\pi$
$728$	27687.7	−	11602.3i	1.40958	−	0.590674i
$729$	729.000			0.0370370
$730$	−41897.2	−	72568.1i	−2.12423	−	3.67927i
$731$	−12861.0	−	22275.9i	−0.650727	−	1.12709i
$732$	−13595.8	+	23548.6i	−0.686495	+	1.18904i
$733$	1055.45			0.0531843			0.0265921	−	0.999646i	$-0.491534\pi$
$733$	1055.45			0.0531843			0.0265921	+	0.999646i	$0.491534\pi$
$734$	−6353.18	+	11004.0i	−0.319482	+	0.553359i
$735$	6137.77	−	10630.9i	0.308020	−	0.533507i
$736$	20076.2			1.00546
$737$	−2622.44	+	4542.21i	−0.131070	+	0.227021i
$738$	737.479	+	1277.35i	0.0367845	+	0.0637126i
$739$	−4705.20	−	8149.64i	−0.234213	−	0.405669i	0.724831	−	0.688927i	$-0.241918\pi$
$739$	−4705.20	−	8149.64i	−0.234213	−	0.405669i	−0.959044	+	0.283258i	$0.908585\pi$
$740$	−32976.0			−1.63814
$741$	−251.487	−	191.334i	−0.0124678	−	0.00948560i
$742$	25428.1			1.25808
$743$	3761.85	+	6515.72i	0.185746	+	0.321721i	0.943827	−	0.330439i	$-0.107197\pi$
$743$	3761.85	+	6515.72i	0.185746	+	0.321721i	−0.758082	+	0.652159i	$0.773863\pi$
$744$	19049.2	+	32994.3i	0.938682	+	1.62584i
$745$	−21638.4	+	37478.8i	−1.06412	+	1.84311i
$746$	−70799.4			−3.47473
$747$	3220.94	−	5578.84i	0.157762	−	0.273252i
$748$	−30390.4	+	52637.7i	−1.48554	+	2.57303i
$749$	−7581.76			−0.369868
$750$	−2544.53	+	4407.26i	−0.123884	+	0.214574i
$751$	6492.03	+	11244.5i	0.315443	+	0.546363i	0.979532	−	0.201291i	$-0.0645136\pi$
$751$	6492.03	+	11244.5i	0.315443	+	0.546363i	−0.664089	+	0.747654i	$0.731180\pi$
$752$	48434.7	+	83891.3i	2.34871	+	4.06809i
$753$	17189.3			0.831890
$754$	14199.6	−	5950.24i	0.685833	−	0.287394i
$755$	54695.3			2.63651
$756$	2667.50	+	4620.24i	0.128328	+	0.222270i
$757$	13967.3	+	24192.1i	0.670609	+	1.16153i	0.977732	+	0.209859i	$0.0673004\pi$
$757$	13967.3	+	24192.1i	0.670609	+	1.16153i	−0.307123	+	0.951670i	$0.599366\pi$
$758$	11824.7	−	20481.1i	0.566615	−	0.981406i
$759$	−3460.30			−0.165482
$760$	−1220.25	+	2113.53i	−0.0582408	+	0.100876i
$761$	7759.63	−	13440.1i	0.369627	−	0.640214i	−0.619880	−	0.784697i	$-0.712819\pi$
$761$	7759.63	−	13440.1i	0.369627	−	0.640214i	0.989507	+	0.144483i	$0.0461520\pi$
$762$	−22893.5			−1.08838
$763$	2576.44	−	4462.52i	0.122246	−	0.211735i
$764$	2185.31	+	3785.07i	0.103484	+	0.179240i
$765$	7971.46	+	13807.0i	0.376743	+	0.652539i
$766$	−4319.82			−0.203761
$767$	20931.1	−	8771.02i	0.985368	−	0.412912i
$768$	−2532.57			−0.118993
$769$	−6442.59	−	11158.9i	−0.302114	−	0.523277i	0.674501	−	0.738274i	$-0.264359\pi$
$769$	−6442.59	−	11158.9i	−0.302114	−	0.523277i	−0.976615	+	0.214997i	$0.931026\pi$
$770$	11681.6	+	20233.2i	0.546723	+	0.946952i
$771$	−8288.68	+	14356.4i	−0.387172	+	0.670602i
$772$	−24642.4			−1.14883
$773$	−2946.02	+	5102.66i	−0.137078	+	0.237425i	−0.926389	−	0.376567i	$-0.877104\pi$
$773$	−2946.02	+	5102.66i	−0.137078	+	0.237425i	0.789312	+	0.613993i	$0.210438\pi$
$774$	−5716.66	+	9901.54i	−0.265479	+	0.459824i
$775$	27713.0			1.28449
$776$	−2169.06	+	3756.92i	−0.100341	+	0.173796i
$777$	1429.06	+	2475.21i	0.0659812	+	0.114283i
$778$	−9231.69	−	15989.8i	−0.425414	−	0.736839i
$779$	69.0916			0.00317775
$780$	−37494.5	−	28526.2i	−1.72118	−	1.30949i
$781$	13374.3			0.612766
$782$	−12026.4	−	20830.2i	−0.549951	−	0.952542i
$783$	831.887	+	1440.87i	0.0379684	+	0.0657631i
$784$	23607.8	−	40889.8i	1.07543	−	1.86269i
$785$	26675.6			1.21286
$786$	16529.5	−	28629.9i	0.750109	−	1.29923i
$787$	10510.2	−	18204.2i	0.476045	−	0.824535i	−0.523578	−	0.851978i	$-0.675403\pi$
$787$	10510.2	−	18204.2i	0.476045	−	0.824535i	0.999623	+	0.0274430i	$0.00873649\pi$
$788$	−18935.8			−0.856042
$789$	7834.81	−	13570.3i	0.353519	−	0.612313i
$790$	−16413.5	−	28429.0i	−0.739197	−	1.28033i
$791$	874.023	+	1513.85i	0.0392879	+	0.0680486i
$792$	16428.7			0.737084
$793$	−19195.1	+	8043.56i	−0.859567	+	0.360196i
$794$	2267.58			0.101352
$795$	−12133.2	−	21015.3i	−0.541282	−	0.937528i
$796$	−4888.44	−	8467.02i	−0.217671	−	0.377017i
$797$	−15677.8	+	27154.7i	−0.696782	+	1.20686i	0.272794	+	0.962073i	$0.412052\pi$
$797$	−15677.8	+	27154.7i	−0.696782	+	1.20686i	−0.969576	+	0.244790i	$0.921281\pi$
$798$	347.848			0.0154307
$799$	27601.7	−	47807.5i	1.22212	−	2.11678i
$800$	−34667.0	+	60045.0i	−1.53208	+	2.65364i
$801$	−9343.37			−0.412150
$802$	3163.18	−	5478.80i	0.139272	−	0.241226i
$803$	13211.7	+	22883.3i	0.580611	+	1.00565i
$804$	5821.21	+	10082.6i	0.255346	+	0.442272i
$805$	−6642.34			−0.290822
$806$	−6063.50	+	47568.7i	−0.264985	+	2.07883i
$807$	−21611.7			−0.942709
$808$	−17593.6	−	30473.1i	−0.766018	−	1.32678i
$809$	9066.27	+	15703.2i	0.394009	+	0.682443i	0.992974	−	0.118332i	$-0.0377546\pi$
$809$	9066.27	+	15703.2i	0.394009	+	0.682443i	−0.598965	+	0.800775i	$0.704421\pi$
$810$	3543.27	−	6137.13i	0.153701	−	0.266218i
$811$	−24755.3			−1.07186			−0.535928	−	0.844263i	$-0.680038\pi$
$811$	−24755.3			−1.07186			−0.535928	+	0.844263i	$0.680038\pi$
$812$	−6087.94	+	10544.6i	−0.263110	+	0.455719i
$813$	−12866.5	+	22285.5i	−0.555042	+	0.961360i
$814$	14473.8			0.623225
$815$	−15062.0	+	26088.2i	−0.647361	+	1.12126i
$816$	30660.7	+	53105.9i	1.31537	+	2.27828i
$817$	267.786	+	463.819i	0.0114671	+	0.0198617i
$818$	42682.7			1.82441
$819$	−516.322	+	4050.60i	−0.0220290	+	0.172820i
$820$	10300.9			0.438688
$821$	−2041.32	−	3535.67i	−0.0867755	−	0.150300i	0.819371	−	0.573264i	$-0.194323\pi$
$821$	−2041.32	−	3535.67i	−0.0867755	−	0.150300i	−0.906146	+	0.422964i	$0.860990\pi$
$822$	−3098.39	−	5366.56i	−0.131470	−	0.227713i
$823$	17163.5	−	29728.1i	0.726954	−	1.25912i	−0.231211	−	0.972904i	$-0.574269\pi$
$823$	17163.5	−	29728.1i	0.726954	−	1.25912i	0.958165	−	0.286217i	$-0.0923978\pi$
$824$	−48697.6			−2.05881
$825$	5975.16	−	10349.3i	0.252156	−	0.436747i
$826$	−12491.0	+	21635.0i	−0.526170	+	0.911353i
$827$	3228.87			0.135767			0.0678833	−	0.997693i	$-0.478375\pi$
$827$	3228.87			0.135767			0.0678833	+	0.997693i	$0.478375\pi$
$828$	−3840.53	+	6651.99i	−0.161193	+	0.279194i
$829$	5226.19	+	9052.03i	0.218954	+	0.379240i	0.954489	−	0.298248i	$-0.0964021\pi$
$829$	5226.19	+	9052.03i	0.218954	+	0.379240i	−0.735534	+	0.677487i	$0.763069\pi$
$830$	−31310.5	−	54231.4i	−1.30940	−	2.26795i
$831$	−21507.6			−0.897821
$832$	−38962.2	−	29642.8i	−1.62352	−	1.23519i
$833$	−26906.9			−1.11917
$834$	6017.23	+	10422.1i	0.249832	+	0.432721i
$835$	15961.7	+	27646.5i	0.661530	+	1.14580i
$836$	632.775	−	1096.00i	0.0261782	−	0.0453420i
$837$	−5182.16			−0.214004
$838$	−18209.8	+	31540.4i	−0.750655	+	1.30017i
$839$	14144.5	−	24499.0i	0.582028	−	1.00810i	−0.413211	−	0.910635i	$-0.635593\pi$
$839$	14144.5	−	24499.0i	0.582028	−	1.00810i	0.995239	−	0.0974668i	$-0.0310740\pi$
$840$	31536.4			1.29537
$841$	10295.9	−	17833.0i	0.422154	−	0.731192i
$842$	−28623.0	−	49576.6i	−1.17151	−	2.02912i
$843$	1273.73	+	2206.17i	0.0520400	+	0.0901360i
$844$	−29618.5			−1.20795
$845$	−9619.26	−	34752.9i	−0.391613	−	1.41483i
$846$	−24537.6			−0.997187
$847$	2758.19	+	4777.33i	0.111892	+	0.193803i
$848$	−46668.0	−	80831.3i	−1.88984	−	3.27330i
$849$	1673.06	−	2897.82i	0.0676316	−	0.117141i
$850$	83067.2			3.35198
$851$	−2057.50	+	3563.69i	−0.0828790	+	0.143551i
$852$	14843.9	−	25710.4i	0.596883	−	1.03383i
$853$	−26631.8			−1.06900			−0.534498	−	0.845170i	$-0.679499\pi$
$853$	−26631.8			−1.06900			−0.534498	+	0.845170i	$0.679499\pi$
$854$	11455.0	−	19840.6i	0.458994	−	0.795002i
$855$	−165.978	−	287.482i	−0.00663898	−	0.0114991i
$856$	25913.0	+	44882.6i	1.03468	+	1.79212i
$857$	11796.7			0.470209			0.235104	−	0.971970i	$-0.424457\pi$
$857$	11796.7			0.470209			0.235104	+	0.971970i	$0.424457\pi$
$858$	16457.0	+	12520.6i	0.654817	+	0.498190i
$859$	−22672.8			−0.900567			−0.450283	−	0.892886i	$-0.648677\pi$
$859$	−22672.8			−0.900567			−0.450283	+	0.892886i	$0.648677\pi$
$860$	39924.5	+	69151.2i	1.58304	+	2.74190i
$861$	−446.406	−	773.198i	−0.0176695	−	0.0306046i
$862$	−13897.5	+	24071.2i	−0.549132	+	0.951124i
$863$	21421.1			0.844940			0.422470	−	0.906377i	$-0.361163\pi$
$863$	21421.1			0.844940			0.422470	+	0.906377i	$0.361163\pi$
$864$	6482.53	−	11228.1i	0.255255	−	0.442114i
$865$	20775.9	−	35985.0i	0.816650	−	1.41448i
$866$	46066.6			1.80763
$867$	10103.2	−	17499.3i	0.395760	−	0.685476i
$868$	−18962.1	−	32843.4i	−0.741494	−	1.28431i
$869$	5175.76	+	8964.67i	0.202043	+	0.349949i
$870$	16173.4			0.630264
$871$	−1126.76	+	8839.52i	−0.0438332	+	0.343875i
$872$	−35223.1			−1.36790
$873$	−295.036	−	511.017i	−0.0114381	−	0.0198114i
$874$	250.407	+	433.718i	0.00969125	+	0.0167857i
$875$	1540.24	−	2667.78i	0.0595082	−	0.103071i
$876$	58653.7			2.26224
$877$	2577.60	−	4464.53i	0.0992466	−	0.171900i	−0.812126	−	0.583482i	$-0.801690\pi$
$877$	2577.60	−	4464.53i	0.0992466	−	0.171900i	0.911373	+	0.411581i	$0.135023\pi$
$878$	34717.5	−	60132.5i	1.33446	−	2.31136i
$879$	5590.58			0.214523
$880$	42878.5	−	74267.7i	1.64254	−	2.84496i
$881$	−11846.1	−	20518.0i	−0.453013	−	0.784642i	0.545558	−	0.838073i	$-0.316318\pi$
$881$	−11846.1	−	20518.0i	−0.453013	−	0.784642i	−0.998572	+	0.0534309i	$0.982984\pi$
$882$	5979.99	+	10357.6i	0.228296	+	0.395420i
$883$	−14591.5			−0.556108			−0.278054	−	0.960565i	$-0.589689\pi$
$883$	−14591.5			−0.556108			−0.278054	+	0.960565i	$0.589689\pi$
$884$	−13057.5	+	102437.i	−0.496800	+	3.89745i
$885$	23840.6			0.905529
$886$	30737.6	+	53239.1i	1.16552	+	2.01874i
$887$	4861.13	+	8419.72i	0.184014	+	0.318722i	0.943244	−	0.332101i	$-0.107757\pi$
$887$	4861.13	+	8419.72i	0.184014	+	0.318722i	−0.759230	+	0.650823i	$0.774424\pi$
$888$	9768.54	−	16919.6i	0.369156	−	0.639397i
$889$	13857.8			0.522806
$890$	−45413.1	+	78657.7i	−1.71039	+	2.96249i
$891$	−1117.32	+	1935.26i	−0.0420108	+	0.0727649i
$892$	−42046.6			−1.57828
$893$	−574.709	+	995.426i	−0.0215363	+	0.0373020i
$894$	−21082.2	−	36515.4i	−0.788694	−	1.36606i
$895$	34984.6	+	60595.1i	1.30660	+	2.26310i
$896$	16706.6			0.622911
$897$	−5422.22	+	2272.14i	−0.201831	+	0.0845760i
$898$	52678.9			1.95759
$899$	−5913.55	−	10242.6i	−0.219386	−	0.379987i
$900$	−13263.5	−	22973.0i	−0.491239	−	0.850852i
$901$	−26594.9	+	46063.7i	−0.983355	+	1.70322i
$902$	−4521.26			−0.166898
$903$	3460.37	−	5993.54i	0.127524	−	0.220878i
$904$	5974.49	−	10348.1i	0.219810	−	0.380723i
$905$	−64743.2			−2.37805
$906$	−26644.7	+	46149.9i	−0.977053	+	1.69230i
$907$	−5899.50	−	10218.2i	−0.215975	−	0.374080i	0.737599	−	0.675239i	$-0.235960\pi$
$907$	−5899.50	−	10218.2i	−0.215975	−	0.374080i	−0.953574	+	0.301159i	$0.902626\pi$
$908$	−45750.4	−	79242.1i	−1.67212	−	2.89619i
$909$	4786.18			0.174640
$910$	31590.6	+	24034.4i	1.15079	+	0.875531i
$911$	−43012.4			−1.56429			−0.782143	−	0.623099i	$-0.785873\pi$
$911$	−43012.4			−1.56429			−0.782143	+	0.623099i	$0.785873\pi$
$912$	−638.403	−	1105.75i	−0.0231794	−	0.0401480i
$913$	9873.32	+	17101.1i	0.357896	+	0.619895i
$914$	41651.9	−	72143.2i	1.50735	−	2.61081i
$915$	−21863.3			−0.789921
$916$	16640.7	−	28822.5i	0.600244	−	1.03965i
$917$	−10005.5	+	17330.1i	−0.360317	+	0.624088i
$918$	−15533.1			−0.558462
$919$	2475.70	−	4288.04i	0.0888639	−	0.153917i	−0.818167	−	0.574980i	$-0.805010\pi$
$919$	2475.70	−	4288.04i	0.0888639	−	0.153917i	0.907031	+	0.421063i	$0.138343\pi$
$920$	22702.3	+	39321.5i	0.813556	+	1.40912i
$921$	−9581.25	−	16595.2i	−0.342793	−	0.593736i
$922$	−41297.0			−1.47510
$923$	20957.3	−	8782.00i	0.747364	−	0.313178i
$924$	−16353.6			−0.582245
$925$	−7105.67	−	12307.4i	−0.252576	−	0.437475i
$926$	888.635	+	1539.16i	0.0315360	+	0.0546220i
$927$	3311.93	−	5736.43i	0.117344	−	0.203246i
$928$	29589.8			1.04669
$929$	4467.43	−	7737.82i	0.157774	−	0.273272i	−0.776292	−	0.630374i	$-0.782902\pi$
$929$	4467.43	−	7737.82i	0.157774	−	0.273272i	0.934065	+	0.357102i	$0.116235\pi$
$930$	−25187.7	+	43626.3i	−0.888104	+	1.53824i
$931$	560.243			0.0197221
$932$	19430.1	−	33654.0i	0.682891	−	1.18280i
$933$	−5238.89	−	9074.02i	−0.183830	−	0.318403i
$934$	−21850.2	−	37845.6i	−0.765481	−	1.32585i
$935$	−48870.6			−1.70935
$936$	25743.5	−	10787.6i	0.898987	−	0.376715i
$937$	−13182.8			−0.459620			−0.229810	−	0.973235i	$-0.573811\pi$
$937$	−13182.8			−0.459620			−0.229810	+	0.973235i	$0.573811\pi$
$938$	−4904.60	−	8495.02i	−0.170726	−	0.295706i
$939$	−8868.01	−	15359.8i	−0.308197	−	0.533812i
$940$	−85684.0	+	148409.i	−2.97309	+	5.14954i
$941$	−21693.7			−0.751536			−0.375768	−	0.926714i	$-0.622621\pi$
$941$	−21693.7			−0.751536			−0.375768	+	0.926714i	$0.622621\pi$
$942$	−12994.9	+	22507.9i	−0.449467	+	0.778499i
$943$	642.714	−	1113.21i	0.0221947	−	0.0384424i
$944$	91698.4			3.16158
$945$	−2144.79	+	3714.89i	−0.0738308	+	0.127879i
$946$	−17523.6	−	30351.7i	−0.602262	−	1.04315i
$947$	24895.0	+	43119.4i	0.854254	+	1.47961i	0.877335	+	0.479878i	$0.159319\pi$
$947$	24895.0	+	43119.4i	0.854254	+	1.47961i	−0.0230813	+	0.999734i	$0.507348\pi$
$948$	22977.9			0.787224
$949$	35728.3	+	27182.4i	1.22212	+	0.929799i
$950$	−1729.59			−0.0590687
$951$	−2516.31	−	4358.37i	−0.0858011	−	0.148612i
$952$	−34562.5	−	59864.0i	−1.17666	−	2.03803i
$953$	−2108.96	+	3652.83i	−0.0716853	+	0.124162i	−0.899640	−	0.436632i	$-0.856171\pi$
$953$	−2108.96	+	3652.83i	−0.0716853	+	0.124162i	0.827955	+	0.560795i	$0.189504\pi$
$954$	23642.6			0.802365
$955$	−1757.09	+	3043.37i	−0.0595374	+	0.103122i
$956$	−38415.2	+	66537.2i	−1.29962	+	2.25101i
$957$	−5100.05			−0.172269
$958$	17152.9	−	29709.7i	0.578481	−	1.00196i
$959$	1875.50	+	3248.45i	0.0631522	+	0.109383i
$960$	−25714.5	−	44538.8i	−0.864513	−	1.49738i
$961$	7046.87			0.236544
$962$	22680.1	−	9503.92i	0.760119	−	0.318523i
$963$	−7049.38			−0.235891
$964$	36894.0	+	63902.3i	1.23265	+	2.13502i
$965$	−9906.83	−	17159.1i	−0.330479	−	0.572406i
$966$	3235.80	−	5604.57i	0.107774	−	0.186671i
$967$	−40927.9			−1.36107			−0.680534	−	0.732717i	$-0.738252\pi$
$967$	−40927.9			−1.36107			−0.680534	+	0.732717i	$0.738252\pi$
$968$	18854.0	−	32656.0i	0.626022	−	1.08430i
$969$	−363.809	+	630.136i	−0.0120611	+	0.0208905i
$970$	−5736.04			−0.189869
$971$	8557.42	−	14821.9i	0.282822	−	0.489863i	−0.689256	−	0.724518i	$-0.742063\pi$
$971$	8557.42	−	14821.9i	0.282822	−	0.489863i	0.972079	+	0.234655i	$0.0753959\pi$
$972$	2480.19	+	4295.82i	0.0818438	+	0.141758i
$973$	−3642.31	−	6308.67i	−0.120007	−	0.207859i
$974$	43151.5			1.41957
$975$	2567.28	−	20140.6i	0.0843270	−	0.661554i
$976$	−84093.0			−2.75794
$977$	59.2348	+	102.598i	0.00193970	+	0.00335966i	0.866994	−	0.498319i	$-0.166049\pi$
$977$	59.2348	+	102.598i	0.00193970	+	0.00335966i	−0.865054	+	0.501679i	$0.832716\pi$
$978$	−14674.8	−	25417.6i	−0.479805	−	0.831047i
$979$	14320.4	−	24803.6i	0.467498	−	0.809731i
$980$	83527.2			2.72263
$981$	2395.53	−	4149.17i	0.0779646	−	0.135039i
$982$	−13636.4	+	23618.9i	−0.443131	+	0.767525i
$983$	26002.8			0.843705			0.421852	−	0.906665i	$-0.361380\pi$
$983$	26002.8			0.843705			0.421852	+	0.906665i	$0.361380\pi$
$984$	−3051.46	+	5285.29i	−0.0988588	+	0.171228i
$985$	−7612.65	−	13185.5i	−0.246253	−	0.426523i
$986$	−17725.3	−	30701.2i	−0.572505	−	0.991608i
$987$	14853.0			0.479002
$988$	271.878	−	2132.91i	0.00875463	−	0.0686810i
$989$	9964.14			0.320365
$990$	10861.4	+	18812.5i	0.348684	+	0.603939i
$991$	8031.00	+	13910.1i	0.257430	+	0.445882i	0.965553	−	0.260208i	$-0.0837910\pi$
$991$	8031.00	+	13910.1i	0.257430	+	0.445882i	−0.708123	+	0.706089i	$0.750458\pi$
$992$	−46081.7	+	79815.8i	−1.47489	+	2.55459i
$993$	−6030.93			−0.192735
$994$	−12506.6	+	21662.1i	−0.399080	+	0.691226i
$995$	3930.53	−	6807.88i	0.125232	−	0.216909i
$996$	43832.9			1.39448
$997$	−680.772	+	1179.13i	−0.0216251	+	0.0374558i	−0.876635	−	0.481155i	$-0.840217\pi$
$997$	−680.772	+	1179.13i	−0.0216251	+	0.0374558i	0.855010	+	0.518611i	$0.173551\pi$
$998$	48108.8	+	83326.8i	1.52591	+	2.64295i
$999$	1328.72	+	2301.41i	0.0420809	+	0.0728862i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.4.e.c.16.1	✓	8
3.2	odd	2		117.4.g.e.55.4		8
4.3	odd	2		624.4.q.i.289.1		8
13.2	odd	12		507.4.b.h.337.1		8
13.3	even	3		507.4.a.m.1.4		4
13.9	even	3	inner	39.4.e.c.22.1	yes	8
13.10	even	6		507.4.a.i.1.1		4
13.11	odd	12		507.4.b.h.337.8		8
39.23	odd	6		1521.4.a.bb.1.4		4
39.29	odd	6		1521.4.a.v.1.1		4
39.35	odd	6		117.4.g.e.100.4		8
52.35	odd	6		624.4.q.i.529.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.e.c.16.1	✓	8	1.1	even	1	trivial
39.4.e.c.22.1	yes	8	13.9	even	3	inner
117.4.g.e.55.4		8	3.2	odd	2
117.4.g.e.100.4		8	39.35	odd	6
507.4.a.i.1.1		4	13.10	even	6
507.4.a.m.1.4		4	13.3	even	3
507.4.b.h.337.1		8	13.2	odd	12
507.4.b.h.337.8		8	13.11	odd	12
624.4.q.i.289.1		8	4.3	odd	2
624.4.q.i.529.1		8	52.35	odd	6
1521.4.a.v.1.1		4	39.29	odd	6
1521.4.a.bb.1.4		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)

\(f(q)\)	\(=\)	\(q+(-2.66520 - 4.61626i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-10.2065 + 17.6783i) q^{4} -16.4131 q^{5} +(7.99559 - 13.8488i) q^{6} +(-4.83984 + 8.38285i) q^{7} +66.1667 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-2.66520 - 4.61626i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-10.2065 + 17.6783i) q^{4} -16.4131 q^{5} +(7.99559 - 13.8488i) q^{6} +(-4.83984 + 8.38285i) q^{7} +66.1667 q^{8} +(-4.50000 + 7.79423i) q^{9} +(43.7441 + 75.7670i) q^{10} +(-13.7941 - 23.8921i) q^{11} -61.2393 q^{12} +(-37.3033 - 28.3807i) q^{13} +51.5965 q^{14} +(-24.6196 - 42.6425i) q^{15} +(-94.6948 - 164.016i) q^{16} +(-53.9641 + 93.4685i) q^{17} +47.9735 q^{18} +(1.12362 - 1.94616i) q^{19} +(167.521 - 290.155i) q^{20} -29.0391 q^{21} +(-73.5279 + 127.354i) q^{22} +(-20.9045 - 36.2077i) q^{23} +(99.2500 + 171.906i) q^{24} +144.390 q^{25} +(-31.5919 + 247.842i) q^{26} -27.0000 q^{27} +(-98.7961 - 171.120i) q^{28} +(-30.8106 - 53.3656i) q^{29} +(-131.232 + 227.301i) q^{30} +191.932 q^{31} +(-240.094 + 415.855i) q^{32} +(41.3822 - 71.6762i) q^{33} +575.300 q^{34} +(79.4368 - 137.589i) q^{35} +(-91.8589 - 159.104i) q^{36} +(-49.2118 - 85.2373i) q^{37} -11.9786 q^{38} +(17.7803 - 139.488i) q^{39} -1086.00 q^{40} +(15.3726 + 26.6261i) q^{41} +(77.3948 + 134.052i) q^{42} +(-119.163 + 206.396i) q^{43} +563.160 q^{44} +(73.8589 - 127.927i) q^{45} +(-111.429 + 193.001i) q^{46} -511.482 q^{47} +(284.084 - 492.048i) q^{48} +(124.652 + 215.903i) q^{49} +(-384.826 - 666.539i) q^{50} -323.785 q^{51} +(882.459 - 369.788i) q^{52} +492.825 q^{53} +(71.9603 + 124.639i) q^{54} +(226.404 + 392.142i) q^{55} +(-320.236 + 554.665i) q^{56} +6.74170 q^{57} +(-164.233 + 284.460i) q^{58} +(-242.089 + 419.311i) q^{59} +1005.13 q^{60} +(222.011 - 384.534i) q^{61} +(-511.536 - 886.007i) q^{62} +(-43.5586 - 75.4457i) q^{63} +1044.47 q^{64} +(612.262 + 465.815i) q^{65} -441.167 q^{66} +(-95.0568 - 164.643i) q^{67} +(-1101.57 - 1907.98i) q^{68} +(62.7135 - 108.623i) q^{69} -846.858 q^{70} +(-242.392 + 419.836i) q^{71} +(-297.750 + 515.718i) q^{72} -957.780 q^{73} +(-262.318 + 454.348i) q^{74} +(216.584 + 375.135i) q^{75} +(22.9365 + 39.7271i) q^{76} +267.045 q^{77} +(-691.300 + 289.684i) q^{78} -375.216 q^{79} +(1554.23 + 2692.01i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(81.9421 - 141.928i) q^{82} -715.765 q^{83} +(296.388 - 513.360i) q^{84} +(885.717 - 1534.11i) q^{85} +1270.37 q^{86} +(92.4319 - 160.097i) q^{87} +(-912.708 - 1580.86i) q^{88} +(519.076 + 899.066i) q^{89} -787.394 q^{90} +(418.453 - 175.350i) q^{91} +853.451 q^{92} +(287.898 + 498.654i) q^{93} +(1363.20 + 2361.13i) q^{94} +(-18.4420 + 31.9425i) q^{95} -1440.56 q^{96} +(-32.7818 + 56.7797i) q^{97} +(664.443 - 1150.85i) q^{98} +248.293 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

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