LMFDB - Embedded newform 43.4.c.a.36.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,4,Mod(6,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("43.6");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	43.c (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:	$2.53708213025$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 60 x^{18} - 25 x^{17} + 2336 x^{16} - 645 x^{15} + 52478 x^{14} - 2415 x^{13} + \cdots + 589824 $ x^20 - x^19 + 60x^18 - 25x^17 + 2336x^16 - 645x^15 + 52478x^14 - 2415x^13 + 850704x^12 - 4147x^11 + 8670544x^10 + 873865x^9 + 62344097x^8 + 3655316x^7 + 215661012x^6 + 43840208x^5 + 507687824x^4 - 3907840x^3 + 17517568x^2 + 245760x + 589824
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			36.8
Root			$-1.79682 - 3.11219i$ of defining polynomial
Character	$\chi$	$=$	43.36
Dual form			43.4.c.a.6.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.59365 q^{2} +(0.838961 + 1.45312i) q^{3} +4.91431 q^{4} +(4.86091 + 8.41934i) q^{5} +(3.01493 + 5.22201i) q^{6} +(7.88013 - 13.6488i) q^{7} -11.0889 q^{8} +(12.0923 - 20.9445i) q^{9} +O(q^{10})$	\(q+3.59365 q^{2} +(0.838961 + 1.45312i) q^{3} +4.91431 q^{4} +(4.86091 + 8.41934i) q^{5} +(3.01493 + 5.22201i) q^{6} +(7.88013 - 13.6488i) q^{7} -11.0889 q^{8} +(12.0923 - 20.9445i) q^{9} +(17.4684 + 30.2561i) q^{10} -59.3441 q^{11} +(4.12292 + 7.14110i) q^{12} +(-6.63817 + 11.4977i) q^{13} +(28.3184 - 49.0489i) q^{14} +(-8.15622 + 14.1270i) q^{15} -79.1640 q^{16} +(14.5119 - 25.1354i) q^{17} +(43.4554 - 75.2670i) q^{18} +(51.8454 + 89.7988i) q^{19} +(23.8880 + 41.3752i) q^{20} +26.4445 q^{21} -213.262 q^{22} +(-4.27121 - 7.39796i) q^{23} +(-9.30314 - 16.1135i) q^{24} +(15.2432 - 26.4020i) q^{25} +(-23.8553 + 41.3185i) q^{26} +85.8837 q^{27} +(38.7254 - 67.0744i) q^{28} +(-19.7412 + 34.1928i) q^{29} +(-29.3106 + 50.7674i) q^{30} +(-60.4027 - 104.621i) q^{31} -195.777 q^{32} +(-49.7874 - 86.2343i) q^{33} +(52.1508 - 90.3278i) q^{34} +153.218 q^{35} +(59.4253 - 102.928i) q^{36} +(164.024 + 284.097i) q^{37} +(186.314 + 322.705i) q^{38} -22.2767 q^{39} +(-53.9020 - 93.3610i) q^{40} +274.703 q^{41} +95.0322 q^{42} +(250.612 + 129.231i) q^{43} -291.635 q^{44} +235.118 q^{45} +(-15.3492 - 26.5857i) q^{46} -161.032 q^{47} +(-66.4155 - 115.035i) q^{48} +(47.3071 + 81.9383i) q^{49} +(54.7787 - 94.8794i) q^{50} +48.6998 q^{51} +(-32.6220 + 56.5030i) q^{52} +(-85.6364 - 148.327i) q^{53} +308.636 q^{54} +(-288.466 - 499.638i) q^{55} +(-87.3818 + 151.350i) q^{56} +(-86.9925 + 150.675i) q^{57} +(-70.9430 + 122.877i) q^{58} -789.671 q^{59} +(-40.0822 + 69.4244i) q^{60} +(-260.473 + 451.152i) q^{61} +(-217.066 - 375.969i) q^{62} +(-190.578 - 330.090i) q^{63} -70.2402 q^{64} -129.070 q^{65} +(-178.918 - 309.896i) q^{66} +(-222.349 - 385.120i) q^{67} +(71.3161 - 123.523i) q^{68} +(7.16677 - 12.4132i) q^{69} +550.613 q^{70} +(-428.064 + 741.429i) q^{71} +(-134.090 + 232.251i) q^{72} +(484.899 - 839.870i) q^{73} +(589.443 + 1020.95i) q^{74} +51.1538 q^{75} +(254.784 + 441.299i) q^{76} +(-467.639 + 809.975i) q^{77} -80.0545 q^{78} +(493.227 - 854.294i) q^{79} +(-384.809 - 666.509i) q^{80} +(-254.439 - 440.701i) q^{81} +987.186 q^{82} +(-60.8330 - 105.366i) q^{83} +129.956 q^{84} +282.164 q^{85} +(900.611 + 464.411i) q^{86} -66.2484 q^{87} +658.060 q^{88} +(345.715 + 598.796i) q^{89} +844.931 q^{90} +(104.619 + 181.206i) q^{91} +(-20.9901 - 36.3559i) q^{92} +(101.351 - 175.545i) q^{93} -578.693 q^{94} +(-504.031 + 873.007i) q^{95} +(-164.249 - 284.488i) q^{96} -503.922 q^{97} +(170.005 + 294.458i) q^{98} +(-717.606 + 1242.93i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 5 q^{3} + 78 q^{4} - 19 q^{5} + 15 q^{6} - 51 q^{7} - 72 q^{8} - 117 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 - 5 * q^3 + 78 * q^4 - 19 * q^5 + 15 * q^6 - 51 * q^7 - 72 * q^8 - 117 * q^9	\( 20 q - 2 q^{2} - 5 q^{3} + 78 q^{4} - 19 q^{5} + 15 q^{6} - 51 q^{7} - 72 q^{8} - 117 q^{9} + 27 q^{10} + 54 q^{11} - 72 q^{12} - 15 q^{13} + 96 q^{14} + 65 q^{15} + 134 q^{16} - 82 q^{17} + 247 q^{18} + 78 q^{19} - 495 q^{20} - 18 q^{21} + 380 q^{22} - 61 q^{23} + 202 q^{24} - 151 q^{25} - 21 q^{26} - 194 q^{27} - 794 q^{28} - 53 q^{29} + 627 q^{30} + 253 q^{31} - 798 q^{32} - 424 q^{33} - 231 q^{34} + 710 q^{35} - 1092 q^{36} - 129 q^{37} - 854 q^{38} + 1382 q^{39} + 1345 q^{40} + 782 q^{41} + 62 q^{42} + 1025 q^{43} + 754 q^{44} + 1888 q^{45} - 40 q^{46} - 668 q^{47} - 2401 q^{48} - 115 q^{49} + 424 q^{50} + 1590 q^{51} - 564 q^{52} + 773 q^{53} + 364 q^{54} - 1242 q^{55} - 923 q^{56} - 765 q^{57} + 1328 q^{58} - 2966 q^{59} - 1075 q^{60} + 437 q^{61} + 1509 q^{62} - 2222 q^{63} - 1476 q^{64} - 2126 q^{65} + 1483 q^{66} - 642 q^{67} - 1052 q^{68} - 3503 q^{69} - 170 q^{70} - 1545 q^{71} + 3834 q^{72} + 1292 q^{73} - 2232 q^{74} + 164 q^{75} - 252 q^{76} + 1448 q^{77} + 5644 q^{78} - 1405 q^{79} - 3157 q^{80} + 974 q^{81} + 6608 q^{82} + 543 q^{83} + 7304 q^{84} + 1946 q^{85} + 2776 q^{86} + 2818 q^{87} - 5372 q^{88} - 2196 q^{89} - 1484 q^{90} - 3513 q^{91} + 2629 q^{92} - 983 q^{93} + 9878 q^{94} - 149 q^{95} + 3540 q^{96} - 850 q^{97} - 213 q^{98} - 3181 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 - 5 * q^3 + 78 * q^4 - 19 * q^5 + 15 * q^6 - 51 * q^7 - 72 * q^8 - 117 * q^9 + 27 * q^10 + 54 * q^11 - 72 * q^12 - 15 * q^13 + 96 * q^14 + 65 * q^15 + 134 * q^16 - 82 * q^17 + 247 * q^18 + 78 * q^19 - 495 * q^20 - 18 * q^21 + 380 * q^22 - 61 * q^23 + 202 * q^24 - 151 * q^25 - 21 * q^26 - 194 * q^27 - 794 * q^28 - 53 * q^29 + 627 * q^30 + 253 * q^31 - 798 * q^32 - 424 * q^33 - 231 * q^34 + 710 * q^35 - 1092 * q^36 - 129 * q^37 - 854 * q^38 + 1382 * q^39 + 1345 * q^40 + 782 * q^41 + 62 * q^42 + 1025 * q^43 + 754 * q^44 + 1888 * q^45 - 40 * q^46 - 668 * q^47 - 2401 * q^48 - 115 * q^49 + 424 * q^50 + 1590 * q^51 - 564 * q^52 + 773 * q^53 + 364 * q^54 - 1242 * q^55 - 923 * q^56 - 765 * q^57 + 1328 * q^58 - 2966 * q^59 - 1075 * q^60 + 437 * q^61 + 1509 * q^62 - 2222 * q^63 - 1476 * q^64 - 2126 * q^65 + 1483 * q^66 - 642 * q^67 - 1052 * q^68 - 3503 * q^69 - 170 * q^70 - 1545 * q^71 + 3834 * q^72 + 1292 * q^73 - 2232 * q^74 + 164 * q^75 - 252 * q^76 + 1448 * q^77 + 5644 * q^78 - 1405 * q^79 - 3157 * q^80 + 974 * q^81 + 6608 * q^82 + 543 * q^83 + 7304 * q^84 + 1946 * q^85 + 2776 * q^86 + 2818 * q^87 - 5372 * q^88 - 2196 * q^89 - 1484 * q^90 - 3513 * q^91 + 2629 * q^92 - 983 * q^93 + 9878 * q^94 - 149 * q^95 + 3540 * q^96 - 850 * q^97 - 213 * q^98 - 3181 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

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

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 $

$2$	3.59365			1.27055			0.635273	−	0.772287i	$-0.280887\pi$
$2$	3.59365			1.27055			0.635273	+	0.772287i	$0.280887\pi$
$3$	0.838961	+	1.45312i	0.161458	+	0.279654i	0.935392	−	0.353613i	$-0.115047\pi$
$3$	0.838961	+	1.45312i	0.161458	+	0.279654i	−0.773934	+	0.633267i	$0.781714\pi$
$4$	4.91431			0.614289
$5$	4.86091	+	8.41934i	0.434773	+	0.753048i	0.997277	−	0.0737460i	$-0.0234954\pi$
$5$	4.86091	+	8.41934i	0.434773	+	0.753048i	−0.562504	+	0.826794i	$0.690162\pi$
$6$	3.01493	+	5.22201i	0.205140	+	0.355313i
$7$	7.88013	−	13.6488i	0.425487	−	0.736965i	−0.570979	−	0.820965i	$-0.693436\pi$
$7$	7.88013	−	13.6488i	0.425487	−	0.736965i	0.996466	+	0.0839997i	$0.0267695\pi$
$8$	−11.0889			−0.490064
$9$	12.0923	−	20.9445i	0.447863	−	0.775721i
$10$	17.4684	+	30.2561i	0.552399	+	0.956783i
$11$	−59.3441			−1.62663			−0.813315	−	0.581824i	$-0.802339\pi$
$11$	−59.3441			−1.62663			−0.813315	+	0.581824i	$0.802339\pi$
$12$	4.12292	+	7.14110i	0.0991819	+	0.171788i
$13$	−6.63817	+	11.4977i	−0.141623	+	0.245298i	−0.928108	−	0.372311i	$-0.878565\pi$
$13$	−6.63817	+	11.4977i	−0.141623	+	0.245298i	0.786485	+	0.617609i	$0.211899\pi$
$14$	28.3184	−	49.0489i	0.540601	−	0.936349i
$15$	−8.15622	+	14.1270i	−0.140395	+	0.243172i
$16$	−79.1640			−1.23694
$17$	14.5119	−	25.1354i	0.207039	−	0.358602i	−0.743742	−	0.668467i	$-0.766951\pi$
$17$	14.5119	−	25.1354i	0.207039	−	0.358602i	0.950780	+	0.309866i	$0.100284\pi$
$18$	43.4554	−	75.2670i	0.569030	−	0.985589i
$19$	51.8454	+	89.7988i	0.626007	+	1.08428i	0.988345	+	0.152230i	$0.0486454\pi$
$19$	51.8454	+	89.7988i	0.626007	+	1.08428i	−0.362338	+	0.932047i	$0.618021\pi$
$20$	23.8880	+	41.3752i	0.267076	+	0.462589i
$21$	26.4445			0.274793
$22$	−213.262			−2.06671
$23$	−4.27121	−	7.39796i	−0.0387222	−	0.0670688i	0.846015	−	0.533159i	$-0.178995\pi$
$23$	−4.27121	−	7.39796i	−0.0387222	−	0.0670688i	−0.884737	+	0.466091i	$0.845662\pi$
$24$	−9.30314	−	16.1135i	−0.0791248	−	0.137048i
$25$	15.2432	−	26.4020i	0.121946	−	0.211216i
$26$	−23.8553	+	41.3185i	−0.179939	+	0.311663i
$27$	85.8837			0.612160
$28$	38.7254	−	67.0744i	0.261372	−	0.452709i
$29$	−19.7412	+	34.1928i	−0.126409	+	0.218946i	−0.922283	−	0.386516i	$-0.873678\pi$
$29$	−19.7412	+	34.1928i	−0.126409	+	0.218946i	0.795874	+	0.605462i	$0.207012\pi$
$30$	−29.3106	+	50.7674i	−0.178379	+	0.308961i
$31$	−60.4027	−	104.621i	−0.349956	−	0.606142i	0.636285	−	0.771454i	$-0.280470\pi$
$31$	−60.4027	−	104.621i	−0.349956	−	0.606142i	−0.986241	+	0.165312i	$0.947137\pi$
$32$	−195.777			−1.08152
$33$	−49.7874	−	86.2343i	−0.262632	−	0.454893i
$34$	52.1508	−	90.3278i	0.263052	−	0.455620i
$35$	153.218			0.739960
$36$	59.4253	−	102.928i	0.275117	−	0.476517i
$37$	164.024	+	284.097i	0.728792	+	1.26231i	0.957394	+	0.288785i	$0.0932513\pi$
$37$	164.024	+	284.097i	0.728792	+	1.26231i	−0.228602	+	0.973520i	$0.573415\pi$
$38$	186.314	+	322.705i	0.795372	+	1.37762i
$39$	−22.2767			−0.0914647
$40$	−53.9020	−	93.3610i	−0.213066	−	0.369042i
$41$	274.703			1.04638			0.523188	−	0.852217i	$-0.324743\pi$
$41$	274.703			1.04638			0.523188	+	0.852217i	$0.324743\pi$
$42$	95.0322			0.349138
$43$	250.612	+	129.231i	0.888790	+	0.458315i
$43$	250.612	+	129.231i	0.888790	+	0.458315i
$44$	−291.635			−0.999220
$45$	235.118			0.778874
$46$	−15.3492	−	26.5857i	−0.0491983	−	0.0852140i
$47$	−161.032			−0.499765			−0.249882	−	0.968276i	$-0.580392\pi$
$47$	−161.032			−0.499765			−0.249882	+	0.968276i	$0.580392\pi$
$48$	−66.4155	−	115.035i	−0.199714	−	0.345914i
$49$	47.3071	+	81.9383i	0.137922	+	0.238887i
$50$	54.7787	−	94.8794i	0.154937	−	0.268360i
$51$	48.6998			0.133712
$52$	−32.6220	+	56.5030i	−0.0869974	+	0.150684i
$53$	−85.6364	−	148.327i	−0.221945	−	0.384419i	0.733454	−	0.679739i	$-0.237907\pi$
$53$	−85.6364	−	148.327i	−0.221945	−	0.384419i	−0.955398	+	0.295320i	$0.904574\pi$
$54$	308.636			0.777778
$55$	−288.466	−	499.638i	−0.707214	−	1.22493i
$56$	−87.3818	+	151.350i	−0.208516	+	0.361160i
$57$	−86.9925	+	150.675i	−0.202148	+	0.350131i
$58$	−70.9430	+	122.877i	−0.160608	+	0.278181i
$59$	−789.671			−1.74248			−0.871240	−	0.490856i	$-0.836684\pi$
$59$	−789.671			−1.74248			−0.871240	+	0.490856i	$0.836684\pi$
$60$	−40.0822	+	69.4244i	−0.0862432	+	0.149378i
$61$	−260.473	+	451.152i	−0.546723	+	0.946953i	0.451773	+	0.892133i	$0.350792\pi$
$61$	−260.473	+	451.152i	−0.546723	+	0.946953i	−0.998496	+	0.0548196i	$0.982542\pi$
$62$	−217.066	−	375.969i	−0.444636	−	0.770131i
$63$	−190.578	−	330.090i	−0.381119	−	0.660118i
$64$	−70.2402			−0.137188
$65$	−129.070			−0.246295
$66$	−178.918	−	309.896i	−0.333687	−	0.577963i
$67$	−222.349	−	385.120i	−0.405437	−	0.702238i	0.588935	−	0.808180i	$-0.299547\pi$
$67$	−222.349	−	385.120i	−0.405437	−	0.702238i	−0.994372	+	0.105942i	$0.966214\pi$
$68$	71.3161	−	123.523i	0.127182	−	0.220285i
$69$	7.16677	−	12.4132i	0.0125040	−	0.0216576i
$70$	550.613			0.940154
$71$	−428.064	+	741.429i	−0.715519	+	1.23932i	0.247240	+	0.968954i	$0.420477\pi$
$71$	−428.064	+	741.429i	−0.715519	+	1.23932i	−0.962759	+	0.270361i	$0.912857\pi$
$72$	−134.090	+	232.251i	−0.219481	+	0.380153i
$73$	484.899	−	839.870i	0.777441	−	1.34657i	−0.155971	−	0.987762i	$-0.549851\pi$
$73$	484.899	−	839.870i	0.777441	−	1.34657i	0.933412	−	0.358806i	$-0.116816\pi$
$74$	589.443	+	1020.95i	0.925964	+	1.60382i
$75$	51.1538			0.0787564
$76$	254.784	+	441.299i	0.384549	+	0.666059i
$77$	−467.639	+	809.975i	−0.692110	+	1.19877i
$78$	−80.0545			−0.116210
$79$	493.227	−	854.294i	0.702435	−	1.21665i	−0.265174	−	0.964201i	$-0.585429\pi$
$79$	493.227	−	854.294i	0.702435	−	1.21665i	0.967609	−	0.252453i	$-0.0812373\pi$
$80$	−384.809	−	666.509i	−0.537787	−	0.931474i
$81$	−254.439	−	440.701i	−0.349024	−	0.604528i
$82$	987.186			1.32947
$83$	−60.8330	−	105.366i	−0.0804493	−	0.139342i	0.822994	−	0.568050i	$-0.192302\pi$
$83$	−60.8330	−	105.366i	−0.0804493	−	0.139342i	−0.903443	+	0.428708i	$0.858969\pi$
$84$	129.956			0.168802
$85$	282.164			0.360059
$86$	900.611	+	464.411i	1.12925	+	0.582311i
$87$	−66.2484			−0.0816388
$88$	658.060			0.797152
$89$	345.715	+	598.796i	0.411750	+	0.713171i	0.995081	−	0.0990628i	$-0.0315845\pi$
$89$	345.715	+	598.796i	0.411750	+	0.713171i	−0.583332	+	0.812234i	$0.698251\pi$
$90$	844.931			0.989595
$91$	104.619	+	181.206i	0.120517	+	0.208742i
$92$	−20.9901	−	36.3559i	−0.0237866	−	0.0411996i
$93$	101.351	−	175.545i	0.113007	−	0.195733i
$94$	−578.693			−0.634974
$95$	−504.031	+	873.007i	−0.544342	+	0.942828i
$96$	−164.249	−	284.488i	−0.174621	−	0.302452i
$97$	−503.922			−0.527479			−0.263740	−	0.964594i	$-0.584956\pi$
$97$	−503.922			−0.527479			−0.263740	+	0.964594i	$0.584956\pi$
$98$	170.005	+	294.458i	0.175236	+	0.303517i
$99$	−717.606	+	1242.93i	−0.728506	+	1.26181i
$100$	74.9098	−	129.748i	0.0749098	−	0.129748i
$101$	729.445	−	1263.44i	0.718638	−	1.24472i	−0.242901	−	0.970051i	$-0.578099\pi$
$101$	729.445	−	1263.44i	0.718638	−	1.24472i	0.961539	−	0.274667i	$-0.0885675\pi$
$102$	175.010			0.169888
$103$	456.087	−	789.966i	0.436307	−	0.755705i	−0.561095	−	0.827752i	$-0.689620\pi$
$103$	456.087	−	789.966i	0.436307	−	0.755705i	0.997401	+	0.0720463i	$0.0229529\pi$
$104$	73.6099	−	127.496i	0.0694043	−	0.120212i
$105$	128.544	+	222.645i	0.119473	+	0.206933i
$106$	−307.747	−	533.034i	−0.281991	−	0.488423i
$107$	−1848.70			−1.67029			−0.835145	−	0.550030i	$-0.814616\pi$
$107$	−1848.70			−1.67029			−0.835145	+	0.550030i	$0.814616\pi$
$108$	422.059			0.376043
$109$	−283.829	−	491.606i	−0.249412	−	0.431994i	0.713951	−	0.700196i	$-0.246904\pi$
$109$	−283.829	−	491.606i	−0.249412	−	0.431994i	−0.963363	+	0.268202i	$0.913571\pi$
$110$	−1036.65	−	1795.52i	−0.898548	−	1.55633i
$111$	−275.219	+	476.693i	−0.235339	+	0.407619i
$112$	−623.823	+	1080.49i	−0.526301	+	0.911580i
$113$	566.990			0.472017			0.236009	−	0.971751i	$-0.424161\pi$
$113$	566.990			0.472017			0.236009	+	0.971751i	$0.424161\pi$
$114$	−312.620	+	541.474i	−0.256838	+	0.444857i
$115$	41.5239	−	71.9216i	0.0336707	−	0.0583193i
$116$	−97.0144	+	168.034i	−0.0776514	+	0.134496i
$117$	160.541	+	278.066i	0.126855	+	0.219720i
$118$	−2837.80			−2.21390
$119$	−228.712	−	396.140i	−0.176185	−	0.305161i
$120$	90.4434	−	156.653i	0.0688026	−	0.119170i
$121$	2190.72			1.64592
$122$	−936.048	+	1621.28i	−0.694637	+	1.20315i
$123$	230.465	+	399.177i	0.168946	+	0.292623i
$124$	−296.837	−	514.138i	−0.214974	−	0.372346i
$125$	1511.61			1.08162
$126$	−684.869	−	1186.23i	−0.484230	−	0.838711i
$127$	1597.46			1.11616			0.558079	−	0.829788i	$-0.311539\pi$
$127$	1597.46			1.11616			0.558079	+	0.829788i	$0.311539\pi$
$128$	1313.79			0.907220
$129$	22.4649	+	472.590i	0.0153328	+	0.322552i
$130$	−463.833			−0.312929
$131$	−921.062			−0.614302			−0.307151	−	0.951661i	$-0.599376\pi$
$131$	−921.062			−0.614302			−0.307151	+	0.951661i	$0.599376\pi$
$132$	−244.671	−	423.782i	−0.161332	−	0.279436i
$133$	1634.19			1.06543
$134$	−799.046	−	1383.99i	−0.515127	−	0.892226i
$135$	417.473	+	723.084i	0.266151	+	0.460986i
$136$	−160.921	+	278.723i	−0.101462	+	0.175738i
$137$	39.3329			0.0245287			0.0122644	−	0.999925i	$-0.496096\pi$
$137$	39.3329			0.0245287			0.0122644	+	0.999925i	$0.496096\pi$
$138$	25.7548	−	44.6087i	0.0158869	−	0.0275170i
$139$	−1389.77	−	2407.16i	−0.848051	−	1.46887i	−0.882945	−	0.469477i	$-0.844442\pi$
$139$	−1389.77	−	2407.16i	−0.848051	−	1.46887i	0.0348932	−	0.999391i	$-0.488891\pi$
$140$	752.962			0.454549
$141$	−135.100	−	233.999i	−0.0806911	−	0.139761i
$142$	−1538.31	+	2664.43i	−0.909101	+	1.57461i
$143$	393.936	−	682.318i	0.230368	−	0.399009i
$144$	−957.274	+	1658.05i	−0.553978	+	0.959518i
$145$	−383.841			−0.219836
$146$	1742.56	−	3018.20i	0.987775	−	1.71088i
$147$	−79.3776	+	137.486i	−0.0445371	+	0.0771406i
$148$	806.063	+	1396.14i	0.447689	+	0.775420i
$149$	1619.76	+	2805.50i	0.890574	+	1.54252i	0.839189	+	0.543841i	$0.183030\pi$
$149$	1619.76	+	2805.50i	0.890574	+	1.54252i	0.0513855	+	0.998679i	$0.483636\pi$
$150$	183.829			0.100064
$151$	−1497.13			−0.806853			−0.403427	−	0.915012i	$-0.632181\pi$
$151$	−1497.13			−0.806853			−0.403427	+	0.915012i	$0.632181\pi$
$152$	−574.907	−	995.768i	−0.306784	−	0.531365i
$153$	−350.965	−	607.889i	−0.185450	−	0.321208i
$154$	−1680.53	+	2910.77i	−0.879357	+	1.52309i
$155$	587.223	−	1017.10i	0.304303	−	0.527068i
$156$	−109.474			−0.0561857
$157$	−1043.04	+	1806.60i	−0.530214	+	0.918358i	0.469164	+	0.883111i	$0.344555\pi$
$157$	−1043.04	+	1806.60i	−0.530214	+	0.918358i	−0.999379	+	0.0352470i	$0.988778\pi$
$158$	1772.48	−	3070.03i	0.892477	−	1.54581i
$159$	143.691	−	248.881i	0.0716695	−	0.124135i
$160$	−951.652	−	1648.31i	−0.470217	−	0.814439i
$161$	−134.631			−0.0659031
$162$	−914.363	−	1583.72i	−0.443452	−	0.768081i
$163$	−980.210	+	1697.77i	−0.471018	+	0.815828i	−0.999450	−	0.0331480i	$-0.989447\pi$
$163$	−980.210	+	1697.77i	−0.471018	+	0.815828i	0.528432	+	0.848976i	$0.322780\pi$
$164$	1349.98			0.642777
$165$	484.024	−	838.354i	0.228371	−	0.395550i
$166$	−218.612	−	378.648i	−0.102215	−	0.177041i
$167$	926.384	+	1604.54i	0.429256	+	0.743493i	0.996807	−	0.0798449i	$-0.0254425\pi$
$167$	926.384	+	1604.54i	0.429256	+	0.743493i	−0.567551	+	0.823338i	$0.692109\pi$
$168$	−293.240			−0.134666
$169$	1010.37	+	1750.01i	0.459886	+	0.796546i
$170$	1014.00			0.457472
$171$	2507.72			1.12146
$172$	1231.58	+	635.082i	0.545974	+	0.281538i
$173$	−2223.10			−0.976990			−0.488495	−	0.872567i	$-0.662454\pi$
$173$	−2223.10			−0.976990			−0.488495	+	0.872567i	$0.662454\pi$
$174$	−238.073			−0.103726
$175$	−240.237	−	416.102i	−0.103772	−	0.179739i
$176$	4697.92			2.01204
$177$	−662.503	−	1147.49i	−0.281338	−	0.487291i
$178$	1242.38	+	2151.86i	0.523147	+	0.906117i
$179$	1549.79	−	2684.31i	0.647132	−	1.12087i	−0.336673	−	0.941622i	$-0.609302\pi$
$179$	1549.79	−	2684.31i	0.647132	−	1.12087i	0.983805	−	0.179244i	$-0.0573651\pi$
$180$	1155.44			0.478453
$181$	1554.54	−	2692.53i	0.638385	−	1.10572i	−0.347402	−	0.937716i	$-0.612936\pi$
$181$	1554.54	−	2692.53i	0.638385	−	1.10572i	0.985787	−	0.167999i	$-0.0537306\pi$
$182$	375.965	+	651.191i	0.153123	+	0.265217i
$183$	−874.106			−0.353092
$184$	47.3630	+	82.0351i	0.0189763	+	0.0328680i
$185$	−1594.61	+	2761.94i	−0.633718	+	1.09763i
$186$	364.220	−	630.847i	0.143580	−	0.248688i
$187$	−861.197	+	1491.64i	−0.336775	+	0.583312i
$188$	−791.362			−0.307000
$189$	676.775	−	1172.21i	0.260466	−	0.451141i
$190$	−1811.31	+	3137.28i	−0.691612	+	1.19791i
$191$	−800.922	−	1387.24i	−0.303417	−	0.525534i	0.673490	−	0.739196i	$-0.264794\pi$
$191$	−800.922	−	1387.24i	−0.303417	−	0.525534i	−0.976908	+	0.213662i	$0.931461\pi$
$192$	−58.9288	−	102.068i	−0.0221501	−	0.0383651i
$193$	−4058.62			−1.51371			−0.756854	−	0.653584i	$-0.773265\pi$
$193$	−4058.62			−1.51371			−0.756854	+	0.653584i	$0.773265\pi$
$194$	−1810.92			−0.670187
$195$	−108.285	−	187.555i	−0.0397663	−	0.0688773i
$196$	232.482	+	402.670i	0.0847237	+	0.146746i
$197$	−132.619	+	229.703i	−0.0479631	+	0.0830745i	−0.889010	−	0.457887i	$-0.848606\pi$
$197$	−132.619	+	229.703i	−0.0479631	+	0.0830745i	0.841047	+	0.540962i	$0.181940\pi$
$198$	−2578.82	+	4466.65i	−0.925601	+	1.60319i
$199$	1471.71			0.524256			0.262128	−	0.965033i	$-0.415576\pi$
$199$	1471.71			0.524256			0.262128	+	0.965033i	$0.415576\pi$
$200$	−169.030	+	292.768i	−0.0597611	+	0.103509i
$201$	373.085	−	646.202i	0.130922	−	0.226764i
$202$	2621.37	−	4540.34i	0.913063	−	1.58147i
$203$	311.126	+	538.887i	0.107570	+	0.186317i
$204$	239.326			0.0821380
$205$	1335.31	+	2312.82i	0.454936	+	0.787972i
$206$	1639.02	−	2838.86i	0.554348	−	0.960159i
$207$	−206.595			−0.0693688
$208$	525.505	−	910.201i	0.175179	−	0.303419i
$209$	−3076.72	−	5329.03i	−1.01828	−	1.76372i
$210$	461.943	+	800.108i	0.151796	+	0.262918i
$211$	1340.69			0.437425			0.218712	−	0.975789i	$-0.429814\pi$
$211$	1340.69			0.437425			0.218712	+	0.975789i	$0.429814\pi$
$212$	−420.844	−	728.923i	−0.136338	−	0.236145i
$213$	−1436.52			−0.462106
$214$	−6643.59			−2.12218
$215$	130.161	+	2738.17i	0.0412879	+	0.868564i
$216$	−952.355			−0.299998
$217$	−1903.92			−0.595607
$218$	−1019.98	−	1766.66i	−0.316889	−	0.548868i
$219$	1627.25			0.502097
$220$	−1417.61	−	2455.38i	−0.434434	−	0.752461i
$221$	192.665	+	333.706i	0.0586429	+	0.101572i
$222$	−989.040	+	1713.07i	−0.299009	+	0.517899i
$223$	−423.340			−0.127125			−0.0635626	−	0.997978i	$-0.520246\pi$
$223$	−423.340			−0.127125			−0.0635626	+	0.997978i	$0.520246\pi$
$224$	−1542.75	+	2672.11i	−0.460174	+	0.797045i
$225$	−368.650	−	638.521i	−0.109230	−	0.189191i
$226$	2037.56			0.599720
$227$	191.013	+	330.844i	0.0558501	+	0.0967353i	0.892599	−	0.450852i	$-0.148880\pi$
$227$	191.013	+	330.844i	0.0558501	+	0.0967353i	−0.836749	+	0.547587i	$0.815546\pi$
$228$	−427.508	+	740.466i	−0.124177	+	0.215081i
$229$	2161.10	−	3743.14i	0.623624	−	1.08015i	−0.365182	−	0.930936i	$-0.618993\pi$
$229$	2161.10	−	3743.14i	0.623624	−	1.08015i	0.988805	−	0.149212i	$-0.0476735\pi$
$230$	149.222	−	258.461i	0.0427802	−	0.0740974i
$231$	−1569.32			−0.446987
$232$	218.908	−	379.160i	0.0619483	−	0.107298i
$233$	−2883.86	+	4994.98i	−0.810848	+	1.40443i	0.101423	+	0.994843i	$0.467661\pi$
$233$	−2883.86	+	4994.98i	−0.810848	+	1.40443i	−0.912271	+	0.409587i	$0.865673\pi$
$234$	576.929	+	999.271i	0.161175	+	0.279164i
$235$	−782.762	−	1355.78i	−0.217284	−	0.376347i
$236$	−3880.69			−1.07039
$237$	1655.19			0.453655
$238$	−821.910	−	1423.59i	−0.223851	−	0.387721i
$239$	−515.985	−	893.712i	−0.139650	−	0.241880i	0.787714	−	0.616041i	$-0.211264\pi$
$239$	−515.985	−	893.712i	−0.139650	−	0.241880i	−0.927364	+	0.374160i	$0.877931\pi$
$240$	645.679	−	1118.35i	0.173660	−	0.300788i
$241$	−143.097	+	247.851i	−0.0382477	+	0.0662469i	−0.884516	−	0.466511i	$-0.845511\pi$
$241$	−143.097	+	247.851i	−0.0382477	+	0.0662469i	0.846268	+	0.532758i	$0.178844\pi$
$242$	7872.69			2.09122
$243$	1586.36	−	2747.65i	0.418786	−	0.725358i
$244$	−1280.04	+	2217.10i	−0.335846	+	0.581702i
$245$	−459.911	+	796.589i	−0.119929	+	0.207723i
$246$	828.211	+	1434.50i	0.214654	+	0.371791i
$247$	−1376.63			−0.354628
$248$	669.798	+	1160.12i	0.171501	+	0.297048i
$249$	102.073	−	176.796i	0.0259784	−	0.0449959i
$250$	5432.19			1.37425
$251$	−890.273	+	1542.00i	−0.223879	+	0.387769i	−0.955982	−	0.293424i	$-0.905205\pi$
$251$	−890.273	+	1542.00i	−0.223879	+	0.387769i	0.732104	+	0.681193i	$0.238539\pi$
$252$	−936.558	−	1622.17i	−0.234117	−	0.405503i
$253$	253.471	+	439.025i	0.0629866	+	0.109096i
$254$	5740.72			1.41813
$255$	236.725	+	410.020i	0.0581345	+	0.100692i
$256$	5283.24			1.28985
$257$	−2160.66			−0.524428			−0.262214	−	0.965010i	$-0.584453\pi$
$257$	−2160.66			−0.524428			−0.262214	+	0.965010i	$0.584453\pi$
$258$	80.7311	+	1698.32i	0.0194810	+	0.409817i
$259$	5170.11			1.24037
$260$	−634.291			−0.151296
$261$	477.433	+	826.938i	0.113227	+	0.196116i
$262$	−3309.97			−0.780500
$263$	2139.98	+	3706.56i	0.501738	+	0.869035i	0.999998	+	0.00200789i	$0.000639133\pi$
$263$	2139.98	+	3706.56i	0.501738	+	0.869035i	−0.498260	+	0.867028i	$0.666028\pi$
$264$	552.087	+	956.242i	0.128707	+	0.222927i
$265$	832.541	−	1442.00i	0.192991	−	0.334270i
$266$	5872.71			1.35368
$267$	−580.083	+	1004.73i	−0.132961	+	0.230295i
$268$	−1092.69	−	1892.60i	−0.249056	−	0.431377i
$269$	7428.76			1.68379			0.841895	−	0.539641i	$-0.181440\pi$
$269$	7428.76			1.68379			0.841895	+	0.539641i	$0.181440\pi$
$270$	1500.25	+	2598.51i	0.338157	+	0.585705i
$271$	1404.80	−	2433.18i	0.314891	−	0.545407i	−0.664523	−	0.747268i	$-0.731365\pi$
$271$	1404.80	−	2433.18i	0.314891	−	0.545407i	0.979414	+	0.201860i	$0.0646987\pi$
$272$	−1148.82	+	1989.82i	−0.256094	+	0.443568i
$273$	−175.543	+	304.050i	−0.0389170	+	0.0674063i
$274$	141.349			0.0311649
$275$	−904.593	+	1566.80i	−0.198360	+	0.343570i
$276$	35.2197	−	61.0023i	0.00768108	−	0.0133040i
$277$	1793.60	+	3106.61i	0.389051	+	0.673855i	0.992322	−	0.123680i	$-0.0394698\pi$
$277$	1793.60	+	3106.61i	0.389051	+	0.673855i	−0.603271	+	0.797536i	$0.706136\pi$
$278$	−4994.36	−	8650.49i	−1.07749	−	1.86627i
$279$	−2921.63			−0.626929
$280$	−1699.02			−0.362628
$281$	−3549.96	−	6148.70i	−0.753639	−	1.30534i	−0.946048	−	0.324026i	$-0.894963\pi$
$281$	−3549.96	−	6148.70i	−0.753639	−	1.30534i	0.192409	−	0.981315i	$-0.438370\pi$
$282$	−485.501	−	840.912i	−0.102522	−	0.177573i
$283$	−3169.55	+	5489.83i	−0.665761	+	1.15313i	0.313317	+	0.949649i	$0.398560\pi$
$283$	−3169.55	+	5489.83i	−0.665761	+	1.15313i	−0.979078	+	0.203484i	$0.934774\pi$
$284$	−2103.64	+	3643.61i	−0.439535	+	0.761298i
$285$	−1691.45			−0.351554
$286$	1415.67	−	2452.01i	0.292693	−	0.506959i
$287$	2164.70	−	3749.36i	0.445219	−	0.771143i
$288$	−2367.39	+	4100.44i	−0.484374	+	0.838960i
$289$	2035.31	+	3525.26i	0.414270	+	0.717537i
$290$	−1379.39			−0.279312
$291$	−422.771	−	732.260i	−0.0851658	−	0.147512i
$292$	2382.95	−	4127.38i	0.477573	−	0.827181i
$293$	−6570.41			−1.31006			−0.655030	−	0.755603i	$-0.727344\pi$
$293$	−6570.41			−1.31006			−0.655030	+	0.755603i	$0.727344\pi$
$294$	−285.255	+	494.077i	−0.0565865	+	0.0980107i
$295$	−3838.52	−	6648.50i	−0.757583	−	1.31217i
$296$	−1818.84	−	3150.32i	−0.357155	−	0.618610i
$297$	−5096.69			−0.995758
$298$	5820.83	+	10082.0i	1.13152	+	1.95984i
$299$	113.412			0.0219358
$300$	251.385			0.0483792
$301$	3738.70	−	2402.19i	0.715931	−	0.460000i
$302$	−5380.16			−1.02514
$303$	2447.90			0.464120
$304$	−4104.29	−	7108.84i	−0.774332	−	1.34118i
$305$	−5064.53			−0.950801
$306$	−1261.24	−	2184.54i	−0.235623	−	0.408110i
$307$	1964.00	+	3401.75i	0.365118	+	0.632404i	0.988795	−	0.149279i	$-0.0476951\pi$
$307$	1964.00	+	3401.75i	0.365118	+	0.632404i	−0.623677	+	0.781682i	$0.714362\pi$
$308$	−2298.12	+	3980.47i	−0.425155	+	0.736390i
$309$	1530.56			0.281781
$310$	2110.27	−	3655.10i	0.386631	−	0.669664i
$311$	4500.78	+	7795.59i	0.820630	+	1.42137i	0.905214	+	0.424957i	$0.139711\pi$
$311$	4500.78	+	7795.59i	0.820630	+	1.42137i	−0.0845832	+	0.996416i	$0.526956\pi$
$312$	247.023			0.0448236
$313$	−3635.23	−	6296.40i	−0.656470	−	1.13704i	−0.981523	−	0.191344i	$-0.938715\pi$
$313$	−3635.23	−	6296.40i	−0.656470	−	1.13704i	0.325053	−	0.945696i	$-0.394618\pi$
$314$	−3748.32	+	6492.28i	−0.673662	+	1.16682i
$315$	1852.76	−	3209.07i	0.331401	−	0.574003i
$316$	2423.87	−	4198.27i	0.431498	−	0.747377i
$317$	−8921.65			−1.58072			−0.790362	−	0.612640i	$-0.790108\pi$
$317$	−8921.65			−1.58072			−0.790362	+	0.612640i	$0.790108\pi$
$318$	516.376	−	894.389i	0.0910595	−	0.157720i
$319$	1171.52	−	2029.14i	0.205620	−	0.356144i
$320$	−341.431	−	591.376i	−0.0596456	−	0.103309i
$321$	−1550.99	−	2686.40i	−0.269682	−	0.467103i
$322$	−483.816			−0.0837330
$323$	3009.50			0.518431
$324$	−1250.39	−	2165.74i	−0.214402	−	0.371355i
$325$	202.374	+	350.522i	0.0345406	+	0.0598260i
$326$	−3522.53	+	6101.20i	−0.598451	+	1.03655i
$327$	476.243	−	824.877i	0.0805391	−	0.139498i
$328$	−3046.15			−0.512791
$329$	−1268.95	+	2197.89i	−0.212643	+	0.368309i
$330$	1739.41	−	3012.75i	0.290156	−	0.502565i
$331$	−1885.72	+	3266.16i	−0.313137	+	0.542370i	−0.979040	−	0.203669i	$-0.934713\pi$
$331$	−1885.72	+	3266.16i	−0.313137	+	0.542370i	0.665903	+	0.746039i	$0.268047\pi$
$332$	−298.952	−	517.801i	−0.0494191	−	0.0855964i
$333$	7933.68			1.30559
$334$	3329.10	+	5766.17i	0.545390	+	0.944643i
$335$	2161.64	−	3744.07i	0.352546	−	0.610628i
$336$	−2093.45			−0.339902
$337$	−3071.75	+	5320.42i	−0.496525	+	0.860006i	−0.999992	−	0.00400842i	$-0.998724\pi$
$337$	−3071.75	+	5320.42i	−0.496525	+	0.860006i	0.503467	+	0.864014i	$0.332057\pi$
$338$	3630.91	+	6288.92i	0.584307	+	1.01205i
$339$	475.683	+	823.906i	0.0762110	+	0.132001i
$340$	1386.64			0.221180
$341$	3584.54	+	6208.61i	0.569249	+	0.985968i
$342$	9011.85			1.42487
$343$	6896.91			1.08571
$344$	−2779.01	−	1433.03i	−0.435564	−	0.224604i
$345$	139.348			0.0217456
$346$	−7989.04			−1.24131
$347$	−2053.49	−	3556.76i	−0.317687	−	0.550250i	0.662318	−	0.749223i	$-0.269573\pi$
$347$	−2053.49	−	3556.76i	−0.317687	−	0.550250i	−0.980005	+	0.198973i	$0.936239\pi$
$348$	−325.565			−0.0501498
$349$	−4710.12	−	8158.17i	−0.722427	−	1.25128i	−0.960024	−	0.279917i	$-0.909693\pi$
$349$	−4710.12	−	8158.17i	−0.722427	−	1.25128i	0.237597	−	0.971364i	$-0.423640\pi$
$350$	−863.326	−	1495.32i	−0.131848	−	0.228367i
$351$	−570.111	+	987.461i	−0.0866959	+	0.150162i
$352$	11618.2			1.75924
$353$	2927.00	−	5069.71i	0.441327	−	0.764401i	−0.556461	−	0.830874i	$-0.687841\pi$
$353$	2927.00	−	5069.71i	0.441327	−	0.764401i	0.997788	+	0.0664729i	$0.0211746\pi$
$354$	−2380.80	−	4123.67i	−0.357453	−	0.619126i
$355$	−8323.12			−1.24435
$356$	1698.95	+	2942.67i	0.252933	+	0.438093i
$357$	383.760	−	664.693i	0.0568929	−	0.0985414i
$358$	5569.40	−	9646.48i	0.822211	−	1.42411i
$359$	−3429.95	+	5940.85i	−0.504251	+	0.873388i	0.495737	+	0.868473i	$0.334898\pi$
$359$	−3429.95	+	5940.85i	−0.504251	+	0.873388i	−0.999988	+	0.00491522i	$0.998435\pi$
$360$	−2607.20			−0.381698
$361$	−1946.38	+	3371.23i	−0.283771	+	0.491505i
$362$	5586.45	−	9676.02i	0.811098	−	1.40486i
$363$	1837.93	+	3183.39i	0.265748	+	0.460288i
$364$	514.132	+	890.502i	0.0740325	+	0.128228i
$365$	9428.20			1.35204
$366$	−3141.23			−0.448619
$367$	5751.19	+	9961.35i	0.818010	+	1.41683i	0.907146	+	0.420815i	$0.138256\pi$
$367$	5751.19	+	9961.35i	0.818010	+	1.41683i	−0.0891366	+	0.996019i	$0.528411\pi$
$368$	338.127	+	585.652i	0.0478969	+	0.0829599i
$369$	3321.79	−	5753.51i	0.468633	−	0.811695i
$370$	−5730.45	+	9925.44i	−0.805168	+	1.39459i
$371$	−2699.30			−0.377738
$372$	498.070	−	862.683i	0.0694186	−	0.120237i
$373$	2898.78	−	5020.83i	0.402394	−	0.696968i	−0.591620	−	0.806217i	$-0.701511\pi$
$373$	2898.78	−	5020.83i	0.402394	−	0.696968i	0.994014	+	0.109249i	$0.0348447\pi$
$374$	−3094.84	+	5360.42i	−0.427889	+	0.741125i
$375$	1268.18	+	2196.55i	0.174636	+	0.302479i
$376$	1785.67			0.244917
$377$	−262.091	−	453.955i	−0.0358047	−	0.0620156i
$378$	2432.09	−	4212.51i	0.330935	−	0.573196i
$379$	−890.341			−0.120670			−0.0603348	−	0.998178i	$-0.519217\pi$
$379$	−890.341			−0.120670			−0.0603348	+	0.998178i	$0.519217\pi$
$380$	−2476.96	+	4290.23i	−0.334383	+	0.579168i
$381$	1340.21	+	2321.31i	0.180213	+	0.312138i
$382$	−2878.23	−	4985.24i	−0.385506	−	0.667715i
$383$	5037.61			0.672088			0.336044	−	0.941846i	$-0.390911\pi$
$383$	5037.61			0.672088			0.336044	+	0.941846i	$0.390911\pi$
$384$	1102.22	+	1909.11i	0.146478	+	0.253707i
$385$	−9092.60			−1.20364
$386$	−14585.2			−1.92324
$387$	5737.15	−	3686.23i	0.753580	−	0.484190i
$388$	−2476.43			−0.324025
$389$	−1793.17			−0.233721			−0.116860	−	0.993148i	$-0.537283\pi$
$389$	−1793.17			−0.233721			−0.116860	+	0.993148i	$0.537283\pi$
$390$	−389.138	−	674.006i	−0.0505250	−	0.0875118i
$391$	−247.934			−0.0320680
$392$	−524.583	−	908.605i	−0.0675904	−	0.117070i
$393$	−772.736	−	1338.42i	−0.0991841	−	0.171792i
$394$	−476.587	+	825.473i	−0.0609393	+	0.105550i
$395$	9590.12			1.22160
$396$	−3526.54	+	6108.14i	−0.447513	+	0.775116i
$397$	5570.10	+	9647.69i	0.704169	+	1.21966i	0.966990	+	0.254812i	$0.0820137\pi$
$397$	5570.10	+	9647.69i	0.704169	+	1.21966i	−0.262821	+	0.964845i	$0.584653\pi$
$398$	5288.82			0.666091
$399$	1371.02	+	2374.68i	0.172023	+	0.297952i
$400$	−1206.71	+	2090.09i	−0.150839	+	0.261261i
$401$	−3862.98	+	6690.88i	−0.481068	+	0.833234i	−0.999764	−	0.0217248i	$-0.993084\pi$
$401$	−3862.98	+	6690.88i	−0.481068	+	0.833234i	0.518696	+	0.854959i	$0.326418\pi$
$402$	1340.74	−	2322.22i	0.166343	−	0.288114i
$403$	1603.85			0.198247
$404$	3584.72	−	6208.91i	0.441451	−	0.764616i
$405$	2473.60	−	4284.41i	0.303492	−	0.525664i
$406$	1118.08	+	1936.57i	0.136673	+	0.236725i
$407$	−9733.83	−	16859.5i	−1.18547	−	2.05330i
$408$	−540.026			−0.0655276
$409$	−458.669			−0.0554516			−0.0277258	−	0.999616i	$-0.508827\pi$
$409$	−458.669			−0.0554516			−0.0277258	+	0.999616i	$0.508827\pi$
$410$	4798.62	+	8311.45i	0.578017	+	1.00115i
$411$	32.9988	+	57.1555i	0.00396036	+	0.00685955i
$412$	2241.35	−	3882.14i	0.268018	−	0.464221i
$413$	−6222.71	+	10778.0i	−0.741403	+	1.28415i
$414$	−742.430			−0.0881363
$415$	591.407	−	1024.35i	0.0699543	−	0.121164i
$416$	1299.60	−	2250.97i	0.153168	−	0.265296i
$417$	2331.93	−	4039.03i	0.273850	−	0.474321i
$418$	−11056.6	−	19150.7i	−1.29377	−	2.24088i
$419$	10880.7			1.26864			0.634318	−	0.773072i	$-0.281281\pi$
$419$	10880.7			1.26864			0.634318	+	0.773072i	$0.281281\pi$
$420$	631.706	+	1094.15i	0.0733907	+	0.127116i
$421$	3593.73	−	6224.52i	0.416028	−	0.720581i	−0.579508	−	0.814967i	$-0.696755\pi$
$421$	3593.73	−	6224.52i	0.416028	−	0.720581i	0.995536	+	0.0943853i	$0.0300885\pi$
$422$	4817.95			0.555768
$423$	−1947.25	+	3372.73i	−0.223826	+	0.387678i
$424$	949.612	+	1644.78i	0.108767	+	0.188390i
$425$	−442.416	−	766.287i	−0.0504949	−	0.0874597i
$426$	−5162.34			−0.587127
$427$	4105.12	+	7110.27i	0.465247	+	0.805832i
$428$	−9085.11			−1.02604
$429$	1321.99			0.148779
$430$	467.752	+	9840.01i	0.0524582	+	1.10355i
$431$	5058.52			0.565337			0.282668	−	0.959218i	$-0.408780\pi$
$431$	5058.52			0.565337			0.282668	+	0.959218i	$0.408780\pi$
$432$	−6798.90			−0.757205
$433$	1223.61	+	2119.35i	0.135803	+	0.235218i	0.925904	−	0.377759i	$-0.123305\pi$
$433$	1223.61	+	2119.35i	0.135803	+	0.235218i	−0.790101	+	0.612977i	$0.789972\pi$
$434$	−6842.03			−0.756747
$435$	−322.027	−	557.768i	−0.0354943	−	0.0614780i
$436$	−1394.82	−	2415.90i	−0.153211	−	0.265369i
$437$	442.885	−	767.100i	0.0484807	−	0.0839711i
$438$	5847.75			0.637937
$439$	1333.56	−	2309.79i	0.144983	−	0.251117i	−0.784384	−	0.620276i	$-0.787021\pi$
$439$	1333.56	−	2309.79i	0.144983	−	0.251117i	0.929366	+	0.369158i	$0.120354\pi$
$440$	3198.77	+	5540.43i	0.346580	+	0.600294i
$441$	2288.20			0.247080
$442$	692.371	+	1199.22i	0.0745085	+	0.129052i
$443$	4635.15	−	8028.31i	0.497116	−	0.861030i	−0.502878	−	0.864357i	$-0.667726\pi$
$443$	4635.15	−	8028.31i	0.497116	−	0.861030i	0.999994	+	0.00332696i	$0.00105901\pi$
$444$	−1352.51	+	2342.62i	−0.144566	+	0.250396i
$445$	−3360.98	+	5821.38i	−0.358035	+	0.620135i
$446$	−1521.33			−0.161518
$447$	−2717.82	+	4707.41i	−0.287581	+	0.498105i
$448$	−553.502	+	958.694i	−0.0583717	+	0.101103i
$449$	−449.574	−	778.686i	−0.0472533	−	0.0818451i	0.841431	−	0.540364i	$-0.181713\pi$
$449$	−449.574	−	778.686i	−0.0472533	−	0.0818451i	−0.888685	+	0.458519i	$0.848380\pi$
$450$	−1324.80	−	2294.62i	−0.138781	−	0.240376i
$451$	−16302.0			−1.70207
$452$	2786.36			0.289955
$453$	−1256.03	−	2175.52i	−0.130273	−	0.225639i
$454$	686.434	+	1188.94i	0.0709602	+	0.122907i
$455$	−1017.09	+	1761.65i	−0.104795	+	0.181511i
$456$	964.650	−	1670.82i	0.0990655	−	0.171586i
$457$	−7051.87			−0.721822			−0.360911	−	0.932600i	$-0.617534\pi$
$457$	−7051.87			−0.721822			−0.360911	+	0.932600i	$0.617534\pi$
$458$	7766.25	−	13451.5i	0.792343	−	1.37238i
$459$	1246.34	−	2158.72i	0.126741	−	0.219522i
$460$	204.062	−	353.445i	0.0206835	−	0.0358249i
$461$	6265.45	+	10852.1i	0.632996	+	1.09638i	0.986936	+	0.161113i	$0.0515083\pi$
$461$	6265.45	+	10852.1i	0.632996	+	1.09638i	−0.353940	+	0.935268i	$0.615158\pi$
$462$	−5639.60			−0.567918
$463$	−1917.49	−	3321.18i	−0.192469	−	0.333366i	0.753599	−	0.657335i	$-0.228316\pi$
$463$	−1917.49	−	3321.18i	−0.192469	−	0.333366i	−0.946068	+	0.323969i	$0.894983\pi$
$464$	1562.79	−	2706.84i	0.156360	−	0.270823i
$465$	1970.63			0.196529
$466$	−10363.6	+	17950.2i	−1.03022	+	1.78439i
$467$	−9541.54	−	16526.4i	−0.945460	−	1.63759i	−0.754827	−	0.655924i	$-0.772279\pi$
$467$	−9541.54	−	16526.4i	−0.945460	−	1.63759i	−0.190634	−	0.981661i	$-0.561054\pi$
$468$	788.950	+	1366.50i	0.0779257	+	0.134971i
$469$	−7008.57			−0.690033
$470$	−2812.97	−	4872.21i	−0.276070	−	0.478166i
$471$	−3500.28			−0.342430
$472$	8756.57			0.853927
$473$	−14872.3	−	7669.10i	−1.44573	−	0.745509i
$474$	5948.18			0.576390
$475$	3161.15			0.305355
$476$	−1123.96	−	1946.76i	−0.108228	−	0.187457i
$477$	−4142.16			−0.397603
$478$	−1854.27	−	3211.69i	−0.177432	−	0.307320i
$479$	3935.52	+	6816.53i	0.375404	+	0.650220i	0.990387	−	0.138321i	$-0.0441705\pi$
$479$	3935.52	+	6816.53i	0.375404	+	0.650220i	−0.614983	+	0.788540i	$0.710837\pi$
$480$	1596.80	−	2765.73i	0.151841	−	0.262996i
$481$	−4355.27			−0.412855
$482$	−514.241	+	890.691i	−0.0485955	+	0.0841698i
$483$	−112.950	−	195.635i	−0.0106406	−	0.0184301i
$484$	10765.9			1.01107
$485$	−2449.52	−	4242.69i	−0.229334	−	0.397217i
$486$	5700.82	−	9874.10i	0.532087	−	0.921602i
$487$	−7864.60	+	13621.9i	−0.731785	+	1.26749i	0.224335	+	0.974512i	$0.427979\pi$
$487$	−7864.60	+	13621.9i	−0.731785	+	1.26749i	−0.956120	+	0.292976i	$0.905354\pi$
$488$	2888.35	−	5002.77i	0.267929	−	0.464067i
$489$	−3289.43			−0.304199
$490$	−1652.76	+	2862.66i	−0.152375	+	0.263922i
$491$	−4365.54	+	7561.34i	−0.401251	+	0.694987i	−0.993877	−	0.110491i	$-0.964758\pi$
$491$	−4365.54	+	7561.34i	−0.401251	+	0.694987i	0.592626	+	0.805477i	$0.298091\pi$
$492$	1132.58	+	1961.68i	0.103782	+	0.179755i
$493$	572.966	+	992.406i	0.0523430	+	0.0906607i
$494$	−4947.14			−0.450571
$495$	−13952.9			−1.26694
$496$	4781.72	+	8282.18i	0.432874	+	0.749760i
$497$	6746.40	+	11685.1i	0.608888	+	1.05463i
$498$	366.815	−	635.342i	0.0330068	−	0.0571694i
$499$	8584.11	−	14868.1i	0.770095	−	1.33384i	−0.167415	−	0.985887i	$-0.553542\pi$
$499$	8584.11	−	14868.1i	0.770095	−	1.33384i	0.937510	−	0.347958i	$-0.113125\pi$
$500$	7428.52			0.664427
$501$	−1554.40	+	2692.30i	−0.138614	+	0.240086i
$502$	−3199.33	+	5541.40i	−0.284448	+	0.492679i
$503$	1854.60	−	3212.27i	0.164399	−	0.284747i	−0.772043	−	0.635571i	$-0.780765\pi$
$503$	1854.60	−	3212.27i	0.164399	−	0.284747i	0.936442	+	0.350823i	$0.114098\pi$
$504$	2113.29	+	3660.33i	0.186773	+	0.323500i
$505$	14183.0			1.24978
$506$	910.887	+	1577.70i	0.0800274	+	0.138612i
$507$	−1695.32	+	2936.38i	−0.148505	+	0.257218i
$508$	7850.43			0.685643
$509$	8147.65	−	14112.1i	0.709505	−	1.22890i	−0.255535	−	0.966800i	$-0.582252\pi$
$509$	8147.65	−	14112.1i	0.709505	−	1.22890i	0.965041	−	0.262100i	$-0.0844150\pi$
$510$	850.706	+	1473.47i	0.0738626	+	0.127934i
$511$	−7642.14	−	13236.6i	−0.661582	−	1.14589i
$512$	8475.74			0.731599
$513$	4452.67	+	7712.26i	0.383217	+	0.663751i
$514$	−7764.64			−0.666310
$515$	8867.99			0.758777
$516$	110.400	+	2322.45i	0.00941874	+	0.198140i
$517$	9556.30			0.812932
$518$	18579.6			1.57594
$519$	−1865.10	−	3230.44i	−0.157743	−	0.273219i
$520$	1431.24			0.120700
$521$	−159.735	−	276.670i	−0.0134321	−	0.0232651i	0.859231	−	0.511587i	$-0.170942\pi$
$521$	−159.735	−	276.670i	−0.0134321	−	0.0232651i	−0.872663	+	0.488322i	$0.837609\pi$
$522$	1715.73	+	2971.72i	0.143861	+	0.249174i
$523$	−3257.83	+	5642.72i	−0.272380	+	0.471776i	−0.969471	−	0.245207i	$-0.921144\pi$
$523$	−3257.83	+	5642.72i	−0.272380	+	0.471776i	0.697091	+	0.716983i	$0.254477\pi$
$524$	−4526.39			−0.377359
$525$	403.098	−	698.187i	0.0335098	−	0.0580407i
$526$	7690.35	+	13320.1i	0.637481	+	1.10415i
$527$	−3506.24			−0.289818
$528$	3941.37	+	6826.65i	0.324860	+	0.562674i
$529$	6047.01	−	10473.7i	0.497001	−	0.860831i
$530$	2991.86	−	5182.05i	0.245204	−	0.424706i
$531$	−9548.93	+	16539.2i	−0.780392	+	1.35168i
$532$	8030.93			0.654483
$533$	−1823.53	+	3158.44i	−0.148191	+	0.256674i
$534$	−2084.61	+	3610.66i	−0.168933	+	0.292600i
$535$	−8986.38	−	15564.9i	−0.726196	−	1.25781i
$536$	2465.61	+	4270.56i	0.198690	+	0.344142i
$537$	5200.85			0.417939
$538$	26696.4			2.13933
$539$	−2807.40	−	4862.56i	−0.224347	−	0.388581i
$540$	2051.59	+	3553.46i	0.163493	+	0.283179i
$541$	−1677.17	+	2904.95i	−0.133285	+	0.230857i	−0.924941	−	0.380111i	$-0.875886\pi$
$541$	−1677.17	+	2904.95i	−0.133285	+	0.230857i	0.791656	+	0.610967i	$0.209219\pi$
$542$	5048.36	−	8744.01i	0.400084	−	0.692966i
$543$	5216.78			0.412290
$544$	−2841.10	+	4920.92i	−0.223917	+	0.387836i
$545$	2759.33	−	4779.30i	0.216875	−	0.375638i
$546$	−630.840	+	1092.65i	−0.0494459	+	0.0856428i
$547$	1183.04	+	2049.08i	0.0924737	+	0.160169i	0.908551	−	0.417773i	$-0.137189\pi$
$547$	1183.04	+	2049.08i	0.0924737	+	0.160169i	−0.816078	+	0.577942i	$0.803856\pi$
$548$	193.294			0.0150677
$549$	6299.42	+	10910.9i	0.489714	+	0.848209i
$550$	−3250.79	+	5630.53i	−0.252026	+	0.436521i
$551$	−4093.96			−0.316531
$552$	−79.4714	+	137.649i	−0.00612777	+	0.0106136i
$553$	−7773.39	−	13463.9i	−0.597754	−	1.03534i
$554$	6445.57	+	11164.1i	0.494307	+	0.856165i
$555$	−5351.25			−0.409276
$556$	−6829.78	−	11829.5i	−0.520949	−	0.902309i
$557$	9324.53			0.709323			0.354662	−	0.934995i	$-0.384596\pi$
$557$	9324.53			0.709323			0.354662	+	0.934995i	$0.384596\pi$
$558$	−10499.3			−0.796543
$559$	−3149.46	+	2023.59i	−0.238297	+	0.153110i
$560$	−12129.4			−0.915285
$561$	−2890.04			−0.217500
$562$	−12757.3	−	22096.3i	−0.957534	−	1.65850i
$563$	−16835.6			−1.26028			−0.630138	−	0.776483i	$-0.717002\pi$
$563$	−16835.6			−1.26028			−0.630138	+	0.776483i	$0.717002\pi$
$564$	−663.922	−	1149.95i	−0.0495676	−	0.0858537i
$565$	2756.09	+	4773.68i	0.205220	+	0.355452i
$566$	−11390.3	+	19728.5i	−0.845881	+	1.46511i
$567$	−8020.04			−0.594021
$568$	4746.75	−	8221.62i	0.350650	−	0.607344i
$569$	−6464.59	−	11197.0i	−0.476292	−	0.824961i	0.523339	−	0.852124i	$-0.324686\pi$
$569$	−6464.59	−	11197.0i	−0.476292	−	0.824961i	−0.999631	+	0.0271631i	$0.991353\pi$
$570$	−6078.47			−0.446665
$571$	6784.84	+	11751.7i	0.497262	+	0.861284i	0.999995	−	0.00315814i	$-0.00100527\pi$
$571$	6784.84	+	11751.7i	0.497262	+	0.861284i	−0.502733	+	0.864442i	$0.667672\pi$
$572$	1935.93	−	3353.12i	0.141512	−	0.245107i
$573$	1343.88	−	2327.68i	0.0979784	−	0.169703i
$574$	7779.16	−	13473.9i	0.565672	−	0.979773i
$575$	−260.428			−0.0188880
$576$	−849.365	+	1471.14i	−0.0614413	+	0.106420i
$577$	573.138	−	992.703i	0.0413519	−	0.0716235i	−0.844609	−	0.535384i	$-0.820167\pi$
$577$	573.138	−	992.703i	0.0413519	−	0.0716235i	0.885961	+	0.463761i	$0.153500\pi$
$578$	7314.18	+	12668.5i	0.526349	+	0.911664i
$579$	−3405.02	−	5897.67i	−0.244400	−	0.423314i
$580$	−1886.31			−0.135043
$581$	−1917.49			−0.136921
$582$	−1519.29	−	2631.49i	−0.108207	−	0.187420i
$583$	5082.02	+	8802.31i	0.361022	+	0.625308i
$584$	−5376.99	+	9313.23i	−0.380996	+	0.659904i
$585$	−1560.75	+	2703.30i	−0.110306	+	0.191056i
$586$	−23611.7			−1.66449
$587$	−1519.64	+	2632.09i	−0.106852	+	0.185073i	−0.914493	−	0.404601i	$-0.867410\pi$
$587$	−1519.64	+	2632.09i	−0.106852	+	0.185073i	0.807641	+	0.589674i	$0.200744\pi$
$588$	−390.086	+	675.649i	−0.0273587	+	0.0473866i
$589$	6263.20	−	10848.2i	0.438150	−	0.758899i
$590$	−13794.3	−	23892.4i	−0.962545	−	1.66718i
$591$	−445.050			−0.0309761
$592$	−12984.8	−	22490.3i	−0.901471	−	1.56139i
$593$	−6783.84	+	11750.0i	−0.469779	+	0.813681i	−0.999403	−	0.0345515i	$-0.989000\pi$
$593$	−6783.84	+	11750.0i	−0.469779	+	0.813681i	0.529624	+	0.848233i	$0.322333\pi$
$594$	−18315.7			−1.26516
$595$	2223.49	−	3851.20i	0.153200	−	0.265351i
$596$	7959.98	+	13787.1i	0.547070	+	0.947552i
$597$	1234.71	+	2138.58i	0.0846454	+	0.146610i
$598$	407.564			0.0278704
$599$	−2884.16	−	4995.51i	−0.196734	−	0.340753i	0.750734	−	0.660605i	$-0.229700\pi$
$599$	−2884.16	−	4995.51i	−0.196734	−	0.340753i	−0.947467	+	0.319852i	$0.896367\pi$
$600$	−567.238			−0.0385957
$601$	−19533.9			−1.32580			−0.662899	−	0.748708i	$-0.730674\pi$
$601$	−19533.9			−1.32580			−0.662899	+	0.748708i	$0.730674\pi$
$602$	13435.6	−	8632.63i	0.909624	−	0.584451i
$603$	−10754.9			−0.726321
$604$	−7357.37			−0.495641
$605$	10648.9	+	18444.4i	0.715602	+	1.23946i
$606$	8796.90			0.589686
$607$	8398.46	+	14546.6i	0.561587	+	0.972696i	0.997358	+	0.0726392i	$0.0231422\pi$
$607$	8398.46	+	14546.6i	0.561587	+	0.972696i	−0.435772	+	0.900057i	$0.643525\pi$
$608$	−10150.1	−	17580.5i	−0.677042	−	1.17267i
$609$	−522.046	+	904.210i	−0.0347362	+	0.0601649i
$610$	−18200.2			−1.20804
$611$	1068.96	−	1851.49i	0.0707781	−	0.122591i
$612$	−1724.75	−	2987.35i	−0.113920	−	0.197315i
$613$	15649.8			1.03114			0.515571	−	0.856847i	$-0.327580\pi$
$613$	15649.8			1.03114			0.515571	+	0.856847i	$0.327580\pi$
$614$	7057.92	+	12224.7i	0.463900	+	0.803498i
$615$	−2240.54	+	3880.73i	−0.146906	+	0.254449i
$616$	5185.60	−	8981.72i	0.339178	−	0.587474i
$617$	8473.97	−	14677.3i	0.552916	−	0.957678i	−0.445147	−	0.895458i	$-0.646848\pi$
$617$	8473.97	−	14677.3i	0.552916	−	0.957678i	0.998062	−	0.0622205i	$-0.0198182\pi$
$618$	5500.28			0.358016
$619$	8509.79	−	14739.4i	0.552564	−	0.957069i	−0.445524	−	0.895270i	$-0.646983\pi$
$619$	8509.79	−	14739.4i	0.552564	−	0.957069i	0.998089	−	0.0617996i	$-0.0196840\pi$
$620$	2885.80	−	4998.35i	0.186930	−	0.323772i
$621$	−366.828	−	635.365i	−0.0237042	−	0.0410568i
$622$	16174.2	+	28014.6i	1.04265	+	1.80592i
$623$	10897.1			0.700777
$624$	1763.51			0.113136
$625$	5442.39	+	9426.50i	0.348313	+	0.603296i
$626$	−13063.7	−	22627.0i	−0.834076	−	1.44466i
$627$	5162.49	−	8941.70i	0.328820	−	0.569533i
$628$	−5125.82	+	8878.18i	−0.325705	+	0.564137i
$629$	9521.19			0.603553
$630$	6658.17	−	11532.3i	0.421060	−	0.729297i
$631$	−4884.23	+	8459.73i	−0.308143	+	0.533719i	−0.977956	−	0.208811i	$-0.933041\pi$
$631$	−4884.23	+	8459.73i	−0.308143	+	0.533719i	0.669814	+	0.742529i	$0.266374\pi$
$632$	−5469.34	+	9473.17i	−0.344238	+	0.596238i
$633$	1124.78	+	1948.18i	0.0706257	+	0.122327i
$634$	−32061.3			−2.00838
$635$	7765.12	+	13449.6i	0.485275	+	0.840520i
$636$	706.143	−	1223.08i	0.0440258	−	0.0762549i
$637$	−1256.13			−0.0781314
$638$	4210.05	−	7292.01i	0.261250	−	0.452498i
$639$	10352.6	+	17931.1i	0.640909	+	1.11009i
$640$	6386.23	+	11061.3i	0.394434	+	0.683180i
$641$	−8665.73			−0.533971			−0.266986	−	0.963700i	$-0.586028\pi$
$641$	−8665.73			−0.533971			−0.266986	+	0.963700i	$0.586028\pi$
$642$	−5573.72	−	9653.96i	−0.342643	−	0.593476i
$643$	−5238.06			−0.321258			−0.160629	−	0.987015i	$-0.551352\pi$
$643$	−5238.06			−0.321258			−0.160629	+	0.987015i	$0.551352\pi$
$644$	−661.618			−0.0404835
$645$	−3869.69	+	2486.35i	−0.236231	+	0.151783i
$646$	10815.1			0.658691
$647$	5383.03			0.327092			0.163546	−	0.986536i	$-0.447707\pi$
$647$	5383.03			0.327092			0.163546	+	0.986536i	$0.447707\pi$
$648$	2821.44	+	4886.88i	0.171044	+	0.296257i
$649$	46862.3			2.83437
$650$	727.260	+	1259.65i	0.0438854	+	0.0760117i
$651$	−1597.32	−	2766.64i	−0.0961656	−	0.166564i
$652$	−4817.06	+	8343.39i	−0.289341	+	0.501154i
$653$	−4398.79			−0.263611			−0.131805	−	0.991276i	$-0.542077\pi$
$653$	−4398.79			−0.263611			−0.131805	+	0.991276i	$0.542077\pi$
$654$	1711.45	−	2964.32i	0.102329	−	0.177238i
$655$	−4477.20	−	7754.73i	−0.267082	−	0.462599i
$656$	−21746.6			−1.29430
$657$	−11727.1	−	20311.9i	−0.696373	−	1.20615i
$658$	−4560.17	+	7898.45i	−0.270173	+	0.467954i
$659$	3702.71	−	6413.29i	0.218873	−	0.379099i	−0.735591	−	0.677426i	$-0.763095\pi$
$659$	3702.71	−	6413.29i	0.218873	−	0.379099i	0.954464	+	0.298327i	$0.0964286\pi$
$660$	2378.64	−	4119.93i	0.140286	−	0.242982i
$661$	11093.5			0.652778			0.326389	−	0.945236i	$-0.394168\pi$
$661$	11093.5			0.652778			0.326389	+	0.945236i	$0.394168\pi$
$662$	−6776.61	+	11737.4i	−0.397855	+	0.689106i
$663$	−323.277	+	559.933i	−0.0189367	+	0.0327994i
$664$	674.570	+	1168.39i	0.0394253	+	0.0682866i
$665$	7943.66	+	13758.8i	0.463221	+	0.802322i
$666$	28510.9			1.65882
$667$	337.276			0.0195793
$668$	4552.54	+	7885.23i	0.263687	+	0.456719i
$669$	−355.165	−	615.164i	−0.0205254	−	0.0355510i
$670$	7768.17	−	13454.9i	0.447926	−	0.775831i
$671$	15457.5	−	26773.2i	0.889316	−	1.54034i
$672$	−5177.21			−0.297195
$673$	−8857.32	+	15341.3i	−0.507317	+	0.878699i	0.492647	+	0.870229i	$0.336029\pi$
$673$	−8857.32	+	15341.3i	−0.507317	+	0.878699i	−0.999964	+	0.00847000i	$0.997304\pi$
$674$	−11038.8	+	19119.7i	−0.630858	+	1.09268i
$675$	1309.14	−	2267.50i	0.0746502	−	0.129298i
$676$	4965.27	+	8600.10i	0.282503	+	0.489309i
$677$	15654.0			0.888671			0.444336	−	0.895860i	$-0.353440\pi$
$677$	15654.0			0.888671			0.444336	+	0.895860i	$0.353440\pi$
$678$	1709.44	+	2960.83i	0.0968296	+	0.167714i
$679$	−3970.97	+	6877.92i	−0.224436	+	0.388734i
$680$	−3128.89			−0.176452
$681$	−320.505	+	555.131i	−0.0180349	+	0.0312374i
$682$	12881.6	+	22311.6i	0.723257	+	1.25272i
$683$	−2154.62	−	3731.91i	−0.120709	−	0.209074i	0.799339	−	0.600881i	$-0.205183\pi$
$683$	−2154.62	−	3731.91i	−0.120709	−	0.209074i	−0.920047	+	0.391807i	$0.871850\pi$
$684$	12323.7			0.688901
$685$	191.194	+	331.157i	0.0106644	+	0.0184713i
$686$	24785.1			1.37944
$687$	7252.33			0.402756
$688$	−19839.4	−	10230.5i	−1.09938	−	0.566908i
$689$	2273.88			0.125730
$690$	500.767			0.0276288
$691$	5864.53	+	10157.7i	0.322862	+	0.559213i	0.981077	−	0.193617i	$-0.0620218\pi$
$691$	5864.53	+	10157.7i	0.322862	+	0.559213i	−0.658216	+	0.752829i	$0.728688\pi$
$692$	−10925.0			−0.600154
$693$	11309.7	+	19588.9i	0.619940	+	1.07377i
$694$	−7379.53	−	12781.7i	−0.403636	−	0.699118i
$695$	13511.1	−	23402.0i	0.737419	−	1.27725i
$696$	734.621			0.0400082
$697$	3986.47	−	6904.77i	0.216640	−	0.375232i
$698$	−16926.5	−	29317.6i	−0.917877	−	1.58981i
$699$	−9677.77			−0.523672
$700$	−1180.60	−	2044.85i	−0.0637463	−	0.110412i
$701$	−2682.43	+	4646.11i	−0.144528	+	0.250330i	−0.929197	−	0.369585i	$-0.879500\pi$
$701$	−2682.43	+	4646.11i	−0.144528	+	0.250330i	0.784669	+	0.619915i	$0.212833\pi$
$702$	−2048.78	+	3548.59i	−0.110151	+	0.190788i
$703$	−17007.7	+	29458.2i	−0.912459	+	1.58042i
$704$	4168.34			0.223154
$705$	1313.41	−	2274.90i	0.0701646	−	0.121529i
$706$	10518.6	−	18218.8i	0.560726	−	0.971207i
$707$	−11496.2	−	19912.1i	−0.611542	−	1.05922i
$708$	−3255.75	−	5639.12i	−0.172823	−	0.299338i
$709$	−11576.1			−0.613185			−0.306593	−	0.951841i	$-0.599189\pi$
$709$	−11576.1			−0.613185			−0.306593	+	0.951841i	$0.599189\pi$
$710$	−29910.4			−1.58101
$711$	−11928.5	−	20660.7i	−0.629189	−	1.08979i
$712$	−3833.59	−	6639.98i	−0.201784	−	0.349500i
$713$	−515.986	+	893.713i	−0.0271021	+	0.0469423i
$714$	1379.10	−	2388.67i	0.0722851	−	0.125201i
$715$	7659.55			0.400631
$716$	7616.14	−	13191.5i	0.397526	−	0.688535i
$717$	865.782	−	1499.58i	0.0450952	−	0.0781071i
$718$	−12326.0	+	21349.3i	−0.640674	+	1.10968i
$719$	7232.10	+	12526.4i	0.375121	+	0.649728i	0.990345	−	0.138624i	$-0.0442679\pi$
$719$	7232.10	+	12526.4i	0.375121	+	0.649728i	−0.615224	+	0.788352i	$0.710935\pi$
$720$	−18612.9			−0.963418
$721$	−7188.05	−	12450.1i	−0.371286	−	0.643086i
$722$	−6994.61	+	12115.0i	−0.360544	+	0.624480i
$723$	−480.212			−0.0247016
$724$	7639.47	−	13231.9i	0.392153	−	0.679229i
$725$	601.838	+	1042.41i	0.0308299	+	0.0533990i
$726$	6604.88	+	11440.0i	0.337645	+	0.584818i
$727$	−6297.55			−0.321270			−0.160635	−	0.987014i	$-0.551354\pi$
$727$	−6297.55			−0.321270			−0.160635	+	0.987014i	$0.551354\pi$
$728$	−1160.11	−	2009.37i	−0.0590613	−	0.102297i
$729$	−8416.12			−0.427583
$730$	33881.6			1.71783
$731$	6885.14	−	4423.84i	0.348367	−	0.223832i
$732$	−4295.63			−0.216900
$733$	−11396.4			−0.574262			−0.287131	−	0.957891i	$-0.592701\pi$
$733$	−11396.4			−0.574262			−0.287131	+	0.957891i	$0.592701\pi$
$734$	20667.8	+	35797.6i	1.03932	+	1.80015i
$735$	−1543.39			−0.0774541
$736$	836.204	+	1448.35i	0.0418789	+	0.0725364i
$737$	13195.1	+	22854.6i	0.659496	+	1.14228i
$738$	11937.3	−	20676.1i	0.595420	−	1.03130i
$739$	−36847.7			−1.83419			−0.917093	−	0.398673i	$-0.869471\pi$
$739$	−36847.7			−1.83419			−0.917093	+	0.398673i	$0.869471\pi$
$740$	−7836.39	+	13573.0i	−0.389286	+	0.674263i
$741$	−1154.94	−	2000.42i	−0.0572576	−	0.0991730i
$742$	−9700.35			−0.479934
$743$	−9811.44	−	16993.9i	−0.484451	−	0.839093i	0.515390	−	0.856956i	$-0.327647\pi$
$743$	−9811.44	−	16993.9i	−0.484451	−	0.839093i	−0.999840	+	0.0178628i	$0.994314\pi$
$744$	−1123.87	+	1946.60i	−0.0553804	+	0.0959217i
$745$	−15747.0	+	27274.5i	−0.774394	+	1.34129i
$746$	10417.2	−	18043.1i	0.511261	−	0.885530i
$747$	−2942.44			−0.144121
$748$	−4232.19	+	7330.37i	−0.206877	+	0.358322i
$749$	−14568.0	+	25232.6i	−0.710687	+	1.23095i
$750$	4557.40	+	7893.65i	0.221884	+	0.384314i
$751$	7138.38	+	12364.0i	0.346849	+	0.600759i	0.985688	−	0.168581i	$-0.0539184\pi$
$751$	7138.38	+	12364.0i	0.346849	+	0.600759i	−0.638839	+	0.769340i	$0.720585\pi$
$752$	12748.0			0.618178
$753$	−2987.62			−0.144588
$754$	−941.863	−	1631.35i	−0.0454916	−	0.0787937i
$755$	−7277.41	−	12604.9i	−0.350798	−	0.607599i
$756$	3325.88	−	5760.60i	0.160002	−	0.277131i
$757$	9784.51	−	16947.3i	0.469781	−	0.813684i	−0.529622	−	0.848234i	$-0.677666\pi$
$757$	9784.51	−	16947.3i	0.469781	−	0.813684i	0.999403	+	0.0345495i	$0.0109996\pi$
$758$	−3199.57			−0.153316
$759$	−425.305	+	736.650i	−0.0203394	+	0.0352289i
$760$	5589.14	−	9680.67i	0.266762	−	0.462046i
$761$	5399.16	−	9351.62i	0.257187	−	0.445461i	−0.708300	−	0.705911i	$-0.750538\pi$
$761$	5399.16	−	9351.62i	0.257187	−	0.445461i	0.965487	+	0.260450i	$0.0838710\pi$
$762$	4816.24	+	8341.98i	0.228969	+	0.396585i
$763$	−8946.43			−0.424486
$764$	−3935.98	−	6817.32i	−0.186386	−	0.322830i
$765$	3412.01	−	5909.78i	0.161257	−	0.279305i
$766$	18103.4			0.853919
$767$	5241.97	−	9079.36i	0.246775	−	0.427427i
$768$	4432.43	+	7677.20i	0.208257	+	0.360712i
$769$	−9140.84	−	15832.4i	−0.428644	−	0.742433i	0.568109	−	0.822953i	$-0.307675\pi$
$769$	−9140.84	−	15832.4i	−0.428644	−	0.742433i	−0.996753	+	0.0805204i	$0.974342\pi$
$770$	−32675.6			−1.52928
$771$	−1812.71	−	3139.70i	−0.0846731	−	0.146658i
$772$	−19945.3			−0.929854
$773$	12712.7			0.591517			0.295759	−	0.955263i	$-0.404428\pi$
$773$	12712.7			0.591517			0.295759	+	0.955263i	$0.404428\pi$
$774$	20617.3	−	13247.0i	0.957459	−	0.615186i
$775$	−3682.92			−0.170702
$776$	5587.93			0.258499
$777$	4337.52	+	7512.80i	0.200267	+	0.346873i
$778$	−6444.03			−0.296953
$779$	14242.1	+	24668.0i	0.655039	+	1.13456i
$780$	−532.145	−	921.702i	−0.0244280	−	0.0423106i
$781$	25403.1	−	43999.4i	1.16388	−	2.01591i
$782$	−890.988			−0.0407438
$783$	−1695.45	+	2936.60i	−0.0773824	+	0.134030i
$784$	−3745.02	−	6486.57i	−0.170600	−	0.295489i
$785$	−20280.5			−0.922090
$786$	−2776.94	−	4809.80i	−0.126018	−	0.218270i
$787$	−4211.67	+	7294.83i	−0.190762	+	0.330410i	−0.945503	−	0.325613i	$-0.894429\pi$
$787$	−4211.67	+	7294.83i	−0.190762	+	0.330410i	0.754741	+	0.656023i	$0.227763\pi$
$788$	−651.732	+	1128.83i	−0.0294632	+	0.0510317i
$789$	−3590.73	+	6219.32i	−0.162019	+	0.280626i
$790$	34463.5			1.55210
$791$	4467.95	−	7738.72i	0.200837	−	0.347860i
$792$	7957.45	−	13782.7i	0.357015	−	0.618368i
$793$	−3458.13	−	5989.65i	−0.154857	−	0.268220i
$794$	20017.0	+	34670.4i	0.894680	+	1.54963i
$795$	2793.88			0.124640
$796$	7232.45			0.322044
$797$	−21068.9	−	36492.4i	−0.936384	−	1.62186i	−0.772148	−	0.635443i	$-0.780818\pi$
$797$	−21068.9	−	36492.4i	−0.936384	−	1.62186i	−0.164236	−	0.986421i	$-0.552516\pi$
$798$	4926.98	+	8533.78i	0.218563	+	0.378562i
$799$	−2336.89	+	4047.60i	−0.103471	+	0.179216i
$800$	−2984.26	+	5168.89i	−0.131887	+	0.228435i
$801$	16721.9			0.737629
$802$	−13882.2	+	24044.7i	−0.611219	+	1.05866i
$803$	−28775.9	+	49841.4i	−1.26461	+	2.19037i
$804$	1833.46	−	3175.64i	0.0804241	−	0.139299i
$805$	−654.428	−	1133.50i	−0.0286529	−	0.0496282i
$806$	5763.69			0.251882
$807$	6232.44	+	10794.9i	0.271862	+	0.470878i
$808$	−8088.73	+	14010.1i	−0.352179	+	0.609991i
$809$	−16017.9			−0.696116			−0.348058	−	0.937473i	$-0.613159\pi$
$809$	−16017.9			−0.696116			−0.348058	+	0.937473i	$0.613159\pi$
$810$	8889.27	−	15396.7i	0.385601	−	0.667881i
$811$	−2781.13	−	4817.06i	−0.120418	−	0.208570i	0.799515	−	0.600647i	$-0.205090\pi$
$811$	−2781.13	−	4817.06i	−0.120418	−	0.208570i	−0.919932	+	0.392077i	$0.871757\pi$
$812$	1528.97	+	2648.26i	0.0660793	+	0.114453i
$813$	4714.29			0.203367
$814$	−34980.0	−	60587.1i	−1.50620	−	2.60882i
$815$	−19058.8			−0.819143
$816$	−3855.27			−0.165394
$817$	1388.27	+	29204.7i	0.0594484	+	1.25060i
$818$	−1648.30			−0.0704539
$819$	5060.35			0.215901
$820$	6562.11	+	11365.9i	0.279462	+	0.484042i
$821$	−18940.2			−0.805136			−0.402568	−	0.915390i	$-0.631882\pi$
$821$	−18940.2			−0.805136			−0.402568	+	0.915390i	$0.631882\pi$
$822$	118.586	+	205.397i	0.00503183	+	0.00871538i
$823$	−17812.5	−	30852.2i	−0.754441	−	1.30673i	−0.945652	−	0.325181i	$-0.894575\pi$
$823$	−17812.5	−	30852.2i	−0.754441	−	1.30673i	0.191211	−	0.981549i	$-0.438758\pi$
$824$	−5057.50	+	8759.84i	−0.213818	+	0.370344i
$825$	−3035.67			−0.128107
$826$	−22362.2	+	38732.5i	−0.941987	+	1.63157i
$827$	1540.17	+	2667.65i	0.0647604	+	0.112168i	0.896588	−	0.442866i	$-0.146038\pi$
$827$	1540.17	+	2667.65i	0.0647604	+	0.112168i	−0.831827	+	0.555035i	$0.812705\pi$
$828$	−1015.27			−0.0426125
$829$	−11753.2	−	20357.1i	−0.492407	−	0.852874i	0.507555	−	0.861619i	$-0.330549\pi$
$829$	−11753.2	−	20357.1i	−0.492407	−	0.852874i	−0.999962	+	0.00874569i	$0.997216\pi$
$830$	2125.31	−	3681.14i	0.0888802	−	0.153945i
$831$	−3009.52	+	5212.65i	−0.125631	+	0.217599i
$832$	466.267	−	807.597i	0.0194290	−	0.0336519i
$833$	2746.07			0.114220
$834$	8380.15	−	14514.8i	0.347939	−	0.602648i
$835$	−9006.13	+	15599.1i	−0.373257	+	0.646501i
$836$	−15119.9	−	26188.5i	−0.625519	−	1.08343i
$837$	−5187.61	−	8985.20i	−0.214229	−	0.371056i
$838$	39101.5			1.61186
$839$	30629.1			1.26035			0.630175	−	0.776453i	$-0.282983\pi$
$839$	30629.1			1.26035			0.630175	+	0.776453i	$0.282983\pi$
$840$	−1425.41	−	2468.89i	−0.0585492	−	0.101410i
$841$	11415.1	+	19771.5i	0.468042	+	0.810672i
$842$	12914.6	−	22368.8i	0.528583	−	0.915532i
$843$	5956.55	−	10317.0i	0.243362	−	0.421516i
$844$	6588.54			0.268705
$845$	−9822.62	+	17013.3i	−0.399892	+	0.692633i
$846$	−6997.72	+	12120.4i	−0.284381	+	0.492563i
$847$	17263.2	−	29900.7i	0.700318	−	1.21299i
$848$	6779.32	+	11742.1i	0.274532	+	0.475503i
$849$	−10636.5			−0.429970
$850$	−1589.89	−	2753.77i	−0.0641561	−	0.111122i
$851$	1401.16	−	2426.88i	0.0564408	−	0.0977584i
$852$	−7059.49			−0.283866
$853$	21240.4	−	36789.5i	0.852590	−	1.47673i	−0.0262732	−	0.999655i	$-0.508364\pi$
$853$	21240.4	−	36789.5i	0.852590	−	1.47673i	0.878863	−	0.477074i	$-0.158303\pi$
$854$	14752.4	+	25551.8i	0.591118	+	1.02385i
$855$	12189.8	+	21113.3i	0.487581	+	0.844514i
$856$	20500.1			0.818549
$857$	−16782.4	−	29067.9i	−0.668932	−	1.15862i	−0.978203	−	0.207650i	$-0.933418\pi$
$857$	−16782.4	−	29067.9i	−0.668932	−	1.15862i	0.309271	−	0.950974i	$-0.399915\pi$
$858$	4750.76			0.189031
$859$	32104.2			1.27518			0.637591	−	0.770375i	$-0.279931\pi$
$859$	32104.2			1.27518			0.637591	+	0.770375i	$0.279931\pi$
$860$	639.651	+	13456.2i	0.0253627	+	0.533549i
$861$	7264.38			0.287537
$862$	18178.5			0.718287
$863$	6971.78	+	12075.5i	0.274997	+	0.476308i	0.970134	−	0.242568i	$-0.0779899\pi$
$863$	6971.78	+	12075.5i	0.274997	+	0.476308i	−0.695138	+	0.718877i	$0.744657\pi$
$864$	−16814.0			−0.662066
$865$	−10806.3	−	18717.0i	−0.424768	−	0.735720i
$866$	4397.21	+	7616.20i	0.172544	+	0.298856i
$867$	−3415.09	+	5915.11i	−0.133774	+	0.231704i
$868$	−9356.47			−0.365875
$869$	−29270.1	+	50697.3i	−1.14260	+	1.97904i
$870$	−1157.25	−	2004.42i	−0.0450972	−	0.0781106i
$871$	5903.97			0.229677
$872$	3147.35	+	5451.36i	0.122228	+	0.211705i
$873$	−6093.57	+	10554.4i	−0.236238	+	0.409177i
$874$	1591.57	−	2756.69i	0.0615970	−	0.106689i
$875$	11911.7	−	20631.6i	0.460215	−	0.797116i
$876$	7996.80			0.308432
$877$	−12502.9	+	21655.7i	−0.481408	+	0.833822i	−0.999772	−	0.0213372i	$-0.993208\pi$
$877$	−12502.9	+	21655.7i	−0.481408	+	0.833822i	0.518365	+	0.855160i	$0.326541\pi$
$878$	4792.35	−	8300.59i	0.184207	−	0.319056i
$879$	−5512.32	−	9547.61i	−0.211520	−	0.366363i
$880$	22836.1	+	39553.4i	0.874780	+	1.51516i
$881$	8808.35			0.336845			0.168423	−	0.985715i	$-0.446133\pi$
$881$	8808.35			0.336845			0.168423	+	0.985715i	$0.446133\pi$
$882$	8223.00			0.313926
$883$	17956.0	+	31100.6i	0.684333	+	1.18530i	0.973646	+	0.228065i	$0.0732400\pi$
$883$	17956.0	+	31100.6i	0.684333	+	1.18530i	−0.289313	+	0.957235i	$0.593427\pi$
$884$	946.817	+	1639.94i	0.0360237	+	0.0623948i
$885$	6440.73	−	11155.7i	0.244636	−	0.423722i
$886$	16657.1	−	28850.9i	0.631609	−	1.09398i
$887$	−7344.85			−0.278034			−0.139017	−	0.990290i	$-0.544394\pi$
$887$	−7344.85			−0.278034			−0.139017	+	0.990290i	$0.544394\pi$
$888$	3051.87	−	5285.99i	0.115331	−	0.199759i
$889$	12588.2	−	21803.4i	0.474910	−	0.822569i
$890$	−12078.2	+	20920.0i	−0.454900	+	0.787910i
$891$	15099.4	+	26153.0i	0.567733	+	0.983342i
$892$	−2080.42			−0.0780916
$893$	−8348.77	−	14460.5i	−0.312856	−	0.541883i
$894$	−9766.90	+	16916.8i	−0.365385	+	0.632865i
$895$	30133.5			1.12542
$896$	10352.9	−	17931.7i	0.386010	−	0.668589i
$897$	95.1485	+	164.802i	0.00354171	+	0.00613442i
$898$	−1615.61	−	2798.32i	−0.0600375	−	0.103988i
$899$	4769.69			0.176950
$900$	−1811.66	−	3137.89i	−0.0670986	−	0.116218i
$901$	−4971.00			−0.183805
$902$	−58583.7			−2.16255
$903$	6627.30	+	3417.45i	0.244234	+	0.125942i
$904$	−6287.29			−0.231319
$905$	30225.8			1.11021
$906$	−4513.75	−	7818.04i	−0.165518	−	0.286685i
$907$	31143.4			1.14013			0.570065	−	0.821600i	$-0.306918\pi$
$907$	31143.4			1.14013			0.570065	+	0.821600i	$0.306918\pi$
$908$	938.697	+	1625.87i	0.0343081	+	0.0594234i
$909$	−17641.3	−	30555.6i	−0.643702	−	1.11492i
$910$	−3655.06	+	6330.75i	−0.133147	+	0.230618i
$911$	4255.28			0.154757			0.0773785	−	0.997002i	$-0.475345\pi$
$911$	4255.28			0.154757			0.0773785	+	0.997002i	$0.475345\pi$
$912$	6886.68	−	11928.1i	0.250045	−	0.433090i
$913$	3610.08	+	6252.84i	0.130861	+	0.226658i
$914$	−25341.9			−0.917109
$915$	−4248.95	−	7359.39i	−0.153515	−	0.265895i
$916$	10620.3	−	18395.0i	0.383085	−	0.663523i
$917$	−7258.09	+	12571.4i	−0.261378	+	0.452719i
$918$	4478.90	−	7757.69i	0.161030	−	0.278913i
$919$	−7736.57			−0.277700			−0.138850	−	0.990313i	$-0.544341\pi$
$919$	−7736.57			−0.277700			−0.138850	+	0.990313i	$0.544341\pi$
$920$	−460.454	+	797.530i	−0.0165008	+	0.0285802i
$921$	−3295.44	+	5707.87i	−0.117903	+	0.204213i
$922$	22515.8	+	38998.6i	0.804251	+	1.39300i
$923$	−5683.13	−	9843.46i	−0.202668	−	0.351031i
$924$	−7712.15			−0.274579
$925$	10001.0			0.355492
$926$	−6890.77	−	11935.2i	−0.244541	−	0.423557i
$927$	−11030.3	−	19105.0i	−0.390811	−	0.676904i
$928$	3864.87	−	6694.15i	0.136714	−	0.236795i
$929$	−8885.62	+	15390.3i	−0.313808	+	0.543531i	−0.979183	−	0.202978i	$-0.934938\pi$
$929$	−8885.62	+	15390.3i	−0.313808	+	0.543531i	0.665375	+	0.746509i	$0.268271\pi$
$930$	7081.75			0.249699
$931$	−4905.31	+	8496.24i	−0.172680	+	0.299090i
$932$	−14172.2	+	24546.9i	−0.498095	+	0.862726i
$933$	−7551.96	+	13080.4i	−0.264995	+	0.458985i
$934$	−34289.0	−	59390.2i	−1.20125	−	2.08063i
$935$	−16744.8			−0.585683
$936$	−1780.22	−	3083.44i	−0.0621672	−	0.107677i
$937$	−19191.0	+	33239.8i	−0.669096	+	1.15891i	0.309061	+	0.951042i	$0.399985\pi$
$937$	−19191.0	+	33239.8i	−0.669096	+	1.15891i	−0.978157	+	0.207866i	$0.933348\pi$
$938$	−25186.3			−0.876720
$939$	6099.63	−	10564.9i	0.211985	−	0.367169i
$940$	−3846.73	−	6662.74i	−0.133475	−	0.231186i
$941$	5673.08	+	9826.06i	0.196532	+	0.340404i	0.947402	−	0.320047i	$-0.103699\pi$
$941$	5673.08	+	9826.06i	0.196532	+	0.340404i	−0.750869	+	0.660451i	$0.770365\pi$
$942$	−12578.8			−0.435073
$943$	−1173.32	−	2032.24i	−0.0405179	−	0.0701791i
$944$	62513.5			2.15534
$945$	13159.0			0.452975
$946$	−53446.0	−	27560.1i	−1.83687	−	0.947204i
$947$	12147.2			0.416823			0.208411	−	0.978041i	$-0.433171\pi$
$947$	12147.2			0.416823			0.208411	+	0.978041i	$0.433171\pi$
$948$	8134.13			0.278675
$949$	6437.69	+	11150.4i	0.220207	+	0.381409i
$950$	11360.1			0.387968
$951$	−7484.92	−	12964.3i	−0.255221	−	0.442055i
$952$	2536.16	+	4392.75i	0.0863417	+	0.149548i
$953$	407.173	−	705.244i	0.0138401	−	0.0239718i	−0.859022	−	0.511938i	$-0.828928\pi$
$953$	407.173	−	705.244i	0.0138401	−	0.0239718i	0.872863	+	0.487966i	$0.162261\pi$
$954$	−14885.5			−0.505173
$955$	7786.41	−	13486.5i	0.263835	−	0.456976i
$956$	−2535.71	−	4391.98i	−0.0857853	−	0.148584i
$957$	3931.45			0.132796
$958$	14142.9	+	24496.2i	0.476969	+	0.826134i
$959$	309.948	−	536.846i	0.0104367	−	0.0180768i
$960$	572.895	−	992.283i	0.0192605	−	0.0333602i
$961$	7598.53	−	13161.0i	0.255061	−	0.441779i
$962$	−15651.3			−0.524551
$963$	−22355.1	+	38720.1i	−0.748060	+	1.29568i
$964$	−703.223	+	1218.02i	−0.0234951	+	0.0406948i
$965$	−19728.5	−	34170.8i	−0.658119	−	1.13989i
$966$	−405.903	−	703.045i	−0.0135194	−	0.0234162i
$967$	−23156.8			−0.770086			−0.385043	−	0.922899i	$-0.625813\pi$
$967$	−23156.8			−0.770086			−0.385043	+	0.922899i	$0.625813\pi$
$968$	−24292.7			−0.806607
$969$	2524.86	+	4373.18i	0.0837049	+	0.144981i
$970$	−8802.70	−	15246.7i	−0.291379	−	0.504683i
$971$	19167.2	−	33198.6i	0.633475	−	1.09721i	−0.353361	−	0.935487i	$-0.614961\pi$
$971$	19167.2	−	33198.6i	0.633475	−	1.09721i	0.986836	−	0.161724i	$-0.0517055\pi$
$972$	7795.86	−	13502.8i	0.257255	−	0.445580i
$973$	−43806.4			−1.44334
$974$	−28262.6	+	48952.3i	−0.929767	+	1.61040i
$975$	−339.568	+	588.148i	−0.0111537	+	0.0193188i
$976$	20620.1	−	35715.0i	0.676263	−	1.17132i
$977$	10478.8	+	18149.9i	0.343139	+	0.594335i	0.985014	−	0.172475i	$-0.0551763\pi$
$977$	10478.8	+	18149.9i	0.343139	+	0.594335i	−0.641875	+	0.766810i	$0.721843\pi$
$978$	−11821.1			−0.386499
$979$	−20516.1	−	35535.0i	−0.669764	−	1.16007i
$980$	−2260.14	+	3914.69i	−0.0736711	+	0.127602i
$981$	−13728.6			−0.446809
$982$	−15688.2	+	27172.8i	−0.509808	+	0.883013i
$983$	−3777.28	−	6542.43i	−0.122560	−	0.212280i	0.798217	−	0.602371i	$-0.205777\pi$
$983$	−3777.28	−	6542.43i	−0.122560	−	0.212280i	−0.920776	+	0.390091i	$0.872444\pi$
$984$	−2555.60	−	4426.43i	−0.0827943	−	0.143404i
$985$	−2578.60			−0.0834122
$986$	2059.04	+	3566.36i	0.0665042	+	0.115189i
$987$	−4258.41			−0.137332
$988$	−6765.21			−0.217844
$989$	−114.371	−	2405.99i	−0.00367722	−	0.0773570i
$990$	−50141.7			−1.60970
$991$	968.239			0.0310364			0.0155182	−	0.999880i	$-0.495060\pi$
$991$	968.239			0.0310364			0.0155182	+	0.999880i	$0.495060\pi$
$992$	11825.4	+	20482.3i	0.378486	+	0.655557i
$993$	−6328.17			−0.202234
$994$	24244.2	+	41992.2i	0.773621	+	1.33995i
$995$	7153.85	+	12390.8i	0.227932	+	0.394790i
$996$	501.619	−	868.829i	0.0159582	−	0.0276405i
$997$	−48984.2			−1.55601			−0.778006	−	0.628257i	$-0.783769\pi$
$997$	−48984.2			−1.55601			−0.778006	+	0.628257i	$0.783769\pi$
$998$	30848.3	−	53430.8i	0.978442	−	1.69471i
$999$	14087.0	+	24399.3i	0.446138	+	0.772733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.4.c.a.36.8	yes	20
43.6	even	3	inner	43.4.c.a.6.8	✓	20
43.7	odd	6		1849.4.a.f.1.3		10
43.36	even	3		1849.4.a.d.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.c.a.6.8	✓	20	43.6	even	3	inner
43.4.c.a.36.8	yes	20	1.1	even	1	trivial
1849.4.a.d.1.8		10	43.36	even	3
1849.4.a.f.1.3		10	43.7	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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	43.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+3.59365 q^{2} +(0.838961 + 1.45312i) q^{3} +4.91431 q^{4} +(4.86091 + 8.41934i) q^{5} +(3.01493 + 5.22201i) q^{6} +(7.88013 - 13.6488i) q^{7} -11.0889 q^{8} +(12.0923 - 20.9445i) q^{9} +O(q^{10})\)	\(q+3.59365 q^{2} +(0.838961 + 1.45312i) q^{3} +4.91431 q^{4} +(4.86091 + 8.41934i) q^{5} +(3.01493 + 5.22201i) q^{6} +(7.88013 - 13.6488i) q^{7} -11.0889 q^{8} +(12.0923 - 20.9445i) q^{9} +(17.4684 + 30.2561i) q^{10} -59.3441 q^{11} +(4.12292 + 7.14110i) q^{12} +(-6.63817 + 11.4977i) q^{13} +(28.3184 - 49.0489i) q^{14} +(-8.15622 + 14.1270i) q^{15} -79.1640 q^{16} +(14.5119 - 25.1354i) q^{17} +(43.4554 - 75.2670i) q^{18} +(51.8454 + 89.7988i) q^{19} +(23.8880 + 41.3752i) q^{20} +26.4445 q^{21} -213.262 q^{22} +(-4.27121 - 7.39796i) q^{23} +(-9.30314 - 16.1135i) q^{24} +(15.2432 - 26.4020i) q^{25} +(-23.8553 + 41.3185i) q^{26} +85.8837 q^{27} +(38.7254 - 67.0744i) q^{28} +(-19.7412 + 34.1928i) q^{29} +(-29.3106 + 50.7674i) q^{30} +(-60.4027 - 104.621i) q^{31} -195.777 q^{32} +(-49.7874 - 86.2343i) q^{33} +(52.1508 - 90.3278i) q^{34} +153.218 q^{35} +(59.4253 - 102.928i) q^{36} +(164.024 + 284.097i) q^{37} +(186.314 + 322.705i) q^{38} -22.2767 q^{39} +(-53.9020 - 93.3610i) q^{40} +274.703 q^{41} +95.0322 q^{42} +(250.612 + 129.231i) q^{43} -291.635 q^{44} +235.118 q^{45} +(-15.3492 - 26.5857i) q^{46} -161.032 q^{47} +(-66.4155 - 115.035i) q^{48} +(47.3071 + 81.9383i) q^{49} +(54.7787 - 94.8794i) q^{50} +48.6998 q^{51} +(-32.6220 + 56.5030i) q^{52} +(-85.6364 - 148.327i) q^{53} +308.636 q^{54} +(-288.466 - 499.638i) q^{55} +(-87.3818 + 151.350i) q^{56} +(-86.9925 + 150.675i) q^{57} +(-70.9430 + 122.877i) q^{58} -789.671 q^{59} +(-40.0822 + 69.4244i) q^{60} +(-260.473 + 451.152i) q^{61} +(-217.066 - 375.969i) q^{62} +(-190.578 - 330.090i) q^{63} -70.2402 q^{64} -129.070 q^{65} +(-178.918 - 309.896i) q^{66} +(-222.349 - 385.120i) q^{67} +(71.3161 - 123.523i) q^{68} +(7.16677 - 12.4132i) q^{69} +550.613 q^{70} +(-428.064 + 741.429i) q^{71} +(-134.090 + 232.251i) q^{72} +(484.899 - 839.870i) q^{73} +(589.443 + 1020.95i) q^{74} +51.1538 q^{75} +(254.784 + 441.299i) q^{76} +(-467.639 + 809.975i) q^{77} -80.0545 q^{78} +(493.227 - 854.294i) q^{79} +(-384.809 - 666.509i) q^{80} +(-254.439 - 440.701i) q^{81} +987.186 q^{82} +(-60.8330 - 105.366i) q^{83} +129.956 q^{84} +282.164 q^{85} +(900.611 + 464.411i) q^{86} -66.2484 q^{87} +658.060 q^{88} +(345.715 + 598.796i) q^{89} +844.931 q^{90} +(104.619 + 181.206i) q^{91} +(-20.9901 - 36.3559i) q^{92} +(101.351 - 175.545i) q^{93} -578.693 q^{94} +(-504.031 + 873.007i) q^{95} +(-164.249 - 284.488i) q^{96} -503.922 q^{97} +(170.005 + 294.458i) q^{98} +(-717.606 + 1242.93i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 5 q^{3} + 78 q^{4} - 19 q^{5} + 15 q^{6} - 51 q^{7} - 72 q^{8} - 117 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 - 5 * q^3 + 78 * q^4 - 19 * q^5 + 15 * q^6 - 51 * q^7 - 72 * q^8 - 117 * q^9	\( 20 q - 2 q^{2} - 5 q^{3} + 78 q^{4} - 19 q^{5} + 15 q^{6} - 51 q^{7} - 72 q^{8} - 117 q^{9} + 27 q^{10} + 54 q^{11} - 72 q^{12} - 15 q^{13} + 96 q^{14} + 65 q^{15} + 134 q^{16} - 82 q^{17} + 247 q^{18} + 78 q^{19} - 495 q^{20} - 18 q^{21} + 380 q^{22} - 61 q^{23} + 202 q^{24} - 151 q^{25} - 21 q^{26} - 194 q^{27} - 794 q^{28} - 53 q^{29} + 627 q^{30} + 253 q^{31} - 798 q^{32} - 424 q^{33} - 231 q^{34} + 710 q^{35} - 1092 q^{36} - 129 q^{37} - 854 q^{38} + 1382 q^{39} + 1345 q^{40} + 782 q^{41} + 62 q^{42} + 1025 q^{43} + 754 q^{44} + 1888 q^{45} - 40 q^{46} - 668 q^{47} - 2401 q^{48} - 115 q^{49} + 424 q^{50} + 1590 q^{51} - 564 q^{52} + 773 q^{53} + 364 q^{54} - 1242 q^{55} - 923 q^{56} - 765 q^{57} + 1328 q^{58} - 2966 q^{59} - 1075 q^{60} + 437 q^{61} + 1509 q^{62} - 2222 q^{63} - 1476 q^{64} - 2126 q^{65} + 1483 q^{66} - 642 q^{67} - 1052 q^{68} - 3503 q^{69} - 170 q^{70} - 1545 q^{71} + 3834 q^{72} + 1292 q^{73} - 2232 q^{74} + 164 q^{75} - 252 q^{76} + 1448 q^{77} + 5644 q^{78} - 1405 q^{79} - 3157 q^{80} + 974 q^{81} + 6608 q^{82} + 543 q^{83} + 7304 q^{84} + 1946 q^{85} + 2776 q^{86} + 2818 q^{87} - 5372 q^{88} - 2196 q^{89} - 1484 q^{90} - 3513 q^{91} + 2629 q^{92} - 983 q^{93} + 9878 q^{94} - 149 q^{95} + 3540 q^{96} - 850 q^{97} - 213 q^{98} - 3181 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 - 5 * q^3 + 78 * q^4 - 19 * q^5 + 15 * q^6 - 51 * q^7 - 72 * q^8 - 117 * q^9 + 27 * q^10 + 54 * q^11 - 72 * q^12 - 15 * q^13 + 96 * q^14 + 65 * q^15 + 134 * q^16 - 82 * q^17 + 247 * q^18 + 78 * q^19 - 495 * q^20 - 18 * q^21 + 380 * q^22 - 61 * q^23 + 202 * q^24 - 151 * q^25 - 21 * q^26 - 194 * q^27 - 794 * q^28 - 53 * q^29 + 627 * q^30 + 253 * q^31 - 798 * q^32 - 424 * q^33 - 231 * q^34 + 710 * q^35 - 1092 * q^36 - 129 * q^37 - 854 * q^38 + 1382 * q^39 + 1345 * q^40 + 782 * q^41 + 62 * q^42 + 1025 * q^43 + 754 * q^44 + 1888 * q^45 - 40 * q^46 - 668 * q^47 - 2401 * q^48 - 115 * q^49 + 424 * q^50 + 1590 * q^51 - 564 * q^52 + 773 * q^53 + 364 * q^54 - 1242 * q^55 - 923 * q^56 - 765 * q^57 + 1328 * q^58 - 2966 * q^59 - 1075 * q^60 + 437 * q^61 + 1509 * q^62 - 2222 * q^63 - 1476 * q^64 - 2126 * q^65 + 1483 * q^66 - 642 * q^67 - 1052 * q^68 - 3503 * q^69 - 170 * q^70 - 1545 * q^71 + 3834 * q^72 + 1292 * q^73 - 2232 * q^74 + 164 * q^75 - 252 * q^76 + 1448 * q^77 + 5644 * q^78 - 1405 * q^79 - 3157 * q^80 + 974 * q^81 + 6608 * q^82 + 543 * q^83 + 7304 * q^84 + 1946 * q^85 + 2776 * q^86 + 2818 * q^87 - 5372 * q^88 - 2196 * q^89 - 1484 * q^90 - 3513 * q^91 + 2629 * q^92 - 983 * q^93 + 9878 * q^94 - 149 * q^95 + 3540 * q^96 - 850 * q^97 - 213 * q^98 - 3181 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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