LMFDB - Embedded newform 126.4.f.d.85.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,4,Mod(43,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("126.43");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	126.f (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:	$7.43424066072$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 3 x^{10} + 27 x^{9} + 159 x^{8} + 2001 x^{7} + 12876 x^{6} + 4140 x^{5} + \cdots + 256562019 $ x^12 - x^11 + 3x^10 + 27x^9 + 159x^8 + 2001x^7 + 12876x^6 + 4140x^5 + 332841x^4 + 2657720x^3 + 20571241x^2 + 107277462x + 256562019
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			85.6
Root			$5.63850 + 2.34186i$ of defining polynomial
Character	$\chi$	$=$	126.85
Dual form			126.4.f.d.43.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(4.34736 - 2.84613i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-1.45017 + 2.51177i) q^{5} +(-9.27700 - 4.68372i) q^{6} +(-3.50000 - 6.06218i) q^{7} +8.00000 q^{8} +(10.7991 - 24.7463i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(4.34736 - 2.84613i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-1.45017 + 2.51177i) q^{5} +(-9.27700 - 4.68372i) q^{6} +(-3.50000 - 6.06218i) q^{7} +8.00000 q^{8} +(10.7991 - 24.7463i) q^{9} +5.80068 q^{10} +(-32.7125 - 56.6596i) q^{11} +(1.16455 + 20.7520i) q^{12} +(19.6851 - 34.0956i) q^{13} +(-7.00000 + 12.1244i) q^{14} +(0.844398 + 15.0469i) q^{15} +(-8.00000 - 13.8564i) q^{16} +13.8868 q^{17} +(-53.6610 + 6.04167i) q^{18} -11.6969 q^{19} +(-5.80068 - 10.0471i) q^{20} +(-32.4695 - 16.3930i) q^{21} +(-65.4249 + 113.319i) q^{22} +(4.12692 - 7.14803i) q^{23} +(34.7789 - 22.7690i) q^{24} +(58.2940 + 100.968i) q^{25} -78.7403 q^{26} +(-23.4834 - 138.317i) q^{27} +28.0000 q^{28} +(-147.693 - 255.812i) q^{29} +(25.2177 - 16.5095i) q^{30} +(-124.362 + 215.402i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(-303.473 - 153.216i) q^{33} +(-13.8868 - 24.0526i) q^{34} +20.3024 q^{35} +(64.1254 + 86.9018i) q^{36} +289.301 q^{37} +(11.6969 + 20.2597i) q^{38} +(-11.4621 - 204.252i) q^{39} +(-11.6014 + 20.0941i) q^{40} +(110.621 - 191.601i) q^{41} +(4.07593 + 72.6319i) q^{42} +(64.9493 + 112.496i) q^{43} +261.700 q^{44} +(46.4964 + 63.0112i) q^{45} -16.5077 q^{46} +(259.239 + 449.015i) q^{47} +(-74.2160 - 37.4698i) q^{48} +(-24.5000 + 42.4352i) q^{49} +(116.588 - 201.936i) q^{50} +(60.3707 - 39.5235i) q^{51} +(78.7403 + 136.382i) q^{52} +264.820 q^{53} +(-216.088 + 178.991i) q^{54} +189.754 q^{55} +(-28.0000 - 48.4974i) q^{56} +(-50.8508 + 33.2910i) q^{57} +(-295.386 + 511.624i) q^{58} +(117.658 - 203.790i) q^{59} +(-53.8129 - 27.1688i) q^{60} +(207.228 + 358.929i) q^{61} +497.449 q^{62} +(-187.813 + 21.1459i) q^{63} +64.0000 q^{64} +(57.0934 + 98.8887i) q^{65} +(38.0953 + 678.847i) q^{66} +(-69.8848 + 121.044i) q^{67} +(-27.7735 + 48.1051i) q^{68} +(-2.40300 - 42.8208i) q^{69} +(-20.3024 - 35.1647i) q^{70} +145.858 q^{71} +(86.3929 - 197.970i) q^{72} +771.401 q^{73} +(-289.301 - 501.084i) q^{74} +(540.794 + 273.033i) q^{75} +(23.3939 - 40.5194i) q^{76} +(-228.987 + 396.617i) q^{77} +(-342.313 + 224.105i) q^{78} +(137.837 + 238.741i) q^{79} +46.4054 q^{80} +(-495.758 - 534.476i) q^{81} -442.483 q^{82} +(-545.558 - 944.934i) q^{83} +(121.726 - 79.6916i) q^{84} +(-20.1381 + 34.8803i) q^{85} +(129.899 - 224.991i) q^{86} +(-1370.15 - 691.754i) q^{87} +(-261.700 - 453.277i) q^{88} +852.941 q^{89} +(62.6422 - 143.545i) q^{90} -275.591 q^{91} +(16.5077 + 28.5921i) q^{92} +(72.4131 + 1290.38i) q^{93} +(518.477 - 898.029i) q^{94} +(16.9626 - 29.3800i) q^{95} +(9.31640 + 166.016i) q^{96} +(-758.377 - 1313.55i) q^{97} +98.0000 q^{98} +(-1755.38 + 197.638i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} - 7 q^{3} - 24 q^{4} - 9 q^{5} + 22 q^{6} - 42 q^{7} + 96 q^{8} + 11 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 - 7 * q^3 - 24 * q^4 - 9 * q^5 + 22 * q^6 - 42 * q^7 + 96 * q^8 + 11 * q^9	\( 12 q - 12 q^{2} - 7 q^{3} - 24 q^{4} - 9 q^{5} + 22 q^{6} - 42 q^{7} + 96 q^{8} + 11 q^{9} + 36 q^{10} - 39 q^{11} - 16 q^{12} - 21 q^{13} - 84 q^{14} - 45 q^{15} - 96 q^{16} + 174 q^{17} - 32 q^{18} + 192 q^{19} - 36 q^{20} + 77 q^{21} - 78 q^{22} - 168 q^{23} - 56 q^{24} - 309 q^{25} + 84 q^{26} + 83 q^{27} + 336 q^{28} - 117 q^{29} + 186 q^{30} - 129 q^{31} - 192 q^{32} - 693 q^{33} - 174 q^{34} + 126 q^{35} + 20 q^{36} + 942 q^{37} - 192 q^{38} + 814 q^{39} - 72 q^{40} - 255 q^{41} - 56 q^{42} - 942 q^{43} + 312 q^{44} + 537 q^{45} + 672 q^{46} - 81 q^{47} + 176 q^{48} - 294 q^{49} - 618 q^{50} - 1452 q^{51} - 84 q^{52} + 180 q^{53} - 200 q^{54} + 1392 q^{55} - 336 q^{56} + 2602 q^{57} - 234 q^{58} - 444 q^{59} - 192 q^{60} - 978 q^{61} + 516 q^{62} - 112 q^{63} + 768 q^{64} - 747 q^{65} + 1146 q^{66} - 663 q^{67} - 348 q^{68} - 2127 q^{69} - 126 q^{70} + 1014 q^{71} + 88 q^{72} + 288 q^{73} - 942 q^{74} + 5954 q^{75} - 384 q^{76} - 273 q^{77} + 32 q^{78} - 609 q^{79} + 288 q^{80} - 1477 q^{81} + 1020 q^{82} - 516 q^{83} - 196 q^{84} - 1563 q^{85} - 1884 q^{86} - 2379 q^{87} - 312 q^{88} + 756 q^{89} - 486 q^{90} + 294 q^{91} - 672 q^{92} + 5953 q^{93} - 162 q^{94} - 846 q^{95} - 128 q^{96} - 2292 q^{97} + 1176 q^{98} - 7638 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 7 * q^3 - 24 * q^4 - 9 * q^5 + 22 * q^6 - 42 * q^7 + 96 * q^8 + 11 * q^9 + 36 * q^10 - 39 * q^11 - 16 * q^12 - 21 * q^13 - 84 * q^14 - 45 * q^15 - 96 * q^16 + 174 * q^17 - 32 * q^18 + 192 * q^19 - 36 * q^20 + 77 * q^21 - 78 * q^22 - 168 * q^23 - 56 * q^24 - 309 * q^25 + 84 * q^26 + 83 * q^27 + 336 * q^28 - 117 * q^29 + 186 * q^30 - 129 * q^31 - 192 * q^32 - 693 * q^33 - 174 * q^34 + 126 * q^35 + 20 * q^36 + 942 * q^37 - 192 * q^38 + 814 * q^39 - 72 * q^40 - 255 * q^41 - 56 * q^42 - 942 * q^43 + 312 * q^44 + 537 * q^45 + 672 * q^46 - 81 * q^47 + 176 * q^48 - 294 * q^49 - 618 * q^50 - 1452 * q^51 - 84 * q^52 + 180 * q^53 - 200 * q^54 + 1392 * q^55 - 336 * q^56 + 2602 * q^57 - 234 * q^58 - 444 * q^59 - 192 * q^60 - 978 * q^61 + 516 * q^62 - 112 * q^63 + 768 * q^64 - 747 * q^65 + 1146 * q^66 - 663 * q^67 - 348 * q^68 - 2127 * q^69 - 126 * q^70 + 1014 * q^71 + 88 * q^72 + 288 * q^73 - 942 * q^74 + 5954 * q^75 - 384 * q^76 - 273 * q^77 + 32 * q^78 - 609 * q^79 + 288 * q^80 - 1477 * q^81 + 1020 * q^82 - 516 * q^83 - 196 * q^84 - 1563 * q^85 - 1884 * q^86 - 2379 * q^87 - 312 * q^88 + 756 * q^89 - 486 * q^90 + 294 * q^91 - 672 * q^92 + 5953 * q^93 - 162 * q^94 - 846 * q^95 - 128 * q^96 - 2292 * q^97 + 1176 * q^98 - 7638 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$3$	4.34736	−	2.84613i	0.836650	−	0.547737i
$3$	4.34736	−	2.84613i	0.836650	−	0.547737i
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	−1.45017	+	2.51177i	−0.129707	+	0.224659i	−0.923563	−	0.383447i	$-0.874737\pi$
$5$	−1.45017	+	2.51177i	−0.129707	+	0.224659i	0.793856	+	0.608106i	$0.208070\pi$
$6$	−9.27700	−	4.68372i	−0.631220	−	0.318687i
$7$	−3.50000	−	6.06218i	−0.188982	−	0.327327i
$7$	−3.50000	−	6.06218i	−0.188982	−	0.327327i
$8$	8.00000			0.353553
$9$	10.7991	−	24.7463i	0.399967	−	0.916529i
$10$	5.80068			0.183434
$11$	−32.7125	−	56.6596i	−0.896652	−	1.55305i	−0.831746	−	0.555156i	$-0.812659\pi$
$11$	−32.7125	−	56.6596i	−0.896652	−	1.55305i	−0.0649060	−	0.997891i	$-0.520675\pi$
$12$	1.16455	+	20.7520i	0.0280147	+	0.499215i
$13$	19.6851	−	34.0956i	0.419974	−	0.727416i	−0.575963	−	0.817476i	$-0.695373\pi$
$13$	19.6851	−	34.0956i	0.419974	−	0.727416i	0.995936	+	0.0900602i	$0.0287059\pi$
$14$	−7.00000	+	12.1244i	−0.133631	+	0.231455i
$15$	0.844398	+	15.0469i	0.0145348	+	0.259007i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	13.8868			0.198120			0.0990598	−	0.995081i	$-0.468416\pi$
$17$	13.8868			0.198120			0.0990598	+	0.995081i	$0.468416\pi$
$18$	−53.6610	+	6.04167i	−0.702667	+	0.0791131i
$19$	−11.6969			−0.141235			−0.0706174	−	0.997503i	$-0.522497\pi$
$19$	−11.6969			−0.141235			−0.0706174	+	0.997503i	$0.522497\pi$
$20$	−5.80068	−	10.0471i	−0.0648536	−	0.112330i
$21$	−32.4695	−	16.3930i	−0.337401	−	0.170345i
$22$	−65.4249	+	113.319i	−0.634029	+	1.09817i
$23$	4.12692	−	7.14803i	0.0374140	−	0.0648029i	−0.846712	−	0.532051i	$-0.821421\pi$
$23$	4.12692	−	7.14803i	0.0374140	−	0.0648029i	0.884126	+	0.467248i	$0.154755\pi$
$24$	34.7789	−	22.7690i	0.295801	−	0.193654i
$25$	58.2940	+	100.968i	0.466352	+	0.807746i
$26$	−78.7403			−0.593933
$27$	−23.4834	−	138.317i	−0.167385	−	0.985892i
$28$	28.0000			0.188982
$29$	−147.693	−	255.812i	−0.945721	−	1.63804i	−0.754301	−	0.656529i	$-0.772024\pi$
$29$	−147.693	−	255.812i	−0.945721	−	1.63804i	−0.191421	−	0.981508i	$-0.561310\pi$
$30$	25.2177	−	16.5095i	0.153470	−	0.100473i
$31$	−124.362	+	215.402i	−0.720520	+	1.24798i	0.240271	+	0.970706i	$0.422764\pi$
$31$	−124.362	+	215.402i	−0.720520	+	1.24798i	−0.960792	+	0.277272i	$0.910570\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$	−303.473	−	153.216i	−1.60085	−	0.808227i
$34$	−13.8868	−	24.0526i	−0.0700458	−	0.121323i
$35$	20.3024			0.0980494
$36$	64.1254	+	86.9018i	0.296877	+	0.402323i
$37$	289.301			1.28543			0.642713	−	0.766107i	$-0.277809\pi$
$37$	289.301			1.28543			0.642713	+	0.766107i	$0.277809\pi$
$38$	11.6969	+	20.2597i	0.0499341	+	0.0864883i
$39$	−11.4621	−	204.252i	−0.0470618	−	0.838628i
$40$	−11.6014	+	20.0941i	−0.0458584	+	0.0794291i
$41$	110.621	−	191.601i	0.421367	−	0.729830i	−0.574706	−	0.818360i	$-0.694884\pi$
$41$	110.621	−	191.601i	0.421367	−	0.729830i	0.996073	+	0.0885302i	$0.0282170\pi$
$42$	4.07593	+	72.6319i	0.0149745	+	0.266841i
$43$	64.9493	+	112.496i	0.230341	+	0.398963i	0.957909	−	0.287073i	$-0.0926824\pi$
$43$	64.9493	+	112.496i	0.230341	+	0.398963i	−0.727567	+	0.686036i	$0.759349\pi$
$44$	261.700			0.896652
$45$	46.4964	+	63.0112i	0.154028	+	0.208737i
$46$	−16.5077			−0.0529113
$47$	259.239	+	449.015i	0.804550	+	1.39352i	0.916594	+	0.399819i	$0.130927\pi$
$47$	259.239	+	449.015i	0.804550	+	1.39352i	−0.112044	+	0.993703i	$0.535740\pi$
$48$	−74.2160	−	37.4698i	−0.223170	−	0.112673i
$49$	−24.5000	+	42.4352i	−0.0714286	+	0.123718i
$50$	116.588	−	201.936i	0.329761	−	0.571162i
$51$	60.3707	−	39.5235i	0.165757	−	0.108518i
$52$	78.7403	+	136.382i	0.209987	+	0.363708i
$53$	264.820			0.686337			0.343168	−	0.939274i	$-0.388500\pi$
$53$	264.820			0.686337			0.343168	+	0.939274i	$0.388500\pi$
$54$	−216.088	+	178.991i	−0.544553	+	0.451067i
$55$	189.754			0.465209
$56$	−28.0000	−	48.4974i	−0.0668153	−	0.115728i
$57$	−50.8508	+	33.2910i	−0.118164	+	0.0773596i
$58$	−295.386	+	511.624i	−0.668726	+	1.15827i
$59$	117.658	−	203.790i	0.259624	−	0.449682i	−0.706517	−	0.707696i	$-0.749735\pi$
$59$	117.658	−	203.790i	0.259624	−	0.449682i	0.966141	+	0.258014i	$0.0830681\pi$
$60$	−53.8129	−	27.1688i	−0.115787	−	0.0584579i
$61$	207.228	+	358.929i	0.434964	+	0.753380i	0.997293	−	0.0735337i	$-0.0234277\pi$
$61$	207.228	+	358.929i	0.434964	+	0.753380i	−0.562328	+	0.826914i	$0.690094\pi$
$62$	497.449			1.01897
$63$	−187.813	+	21.1459i	−0.375591	+	0.0422877i
$64$	64.0000			0.125000
$65$	57.0934	+	98.8887i	0.108947	+	0.188702i
$66$	38.0953	+	678.847i	0.0710486	+	1.26607i
$67$	−69.8848	+	121.044i	−0.127430	+	0.220715i	−0.922680	−	0.385566i	$-0.874006\pi$
$67$	−69.8848	+	121.044i	−0.127430	+	0.220715i	0.795250	+	0.606281i	$0.207339\pi$
$68$	−27.7735	+	48.1051i	−0.0495299	+	0.0857883i
$69$	−2.40300	−	42.8208i	−0.00419257	−	0.0747104i
$70$	−20.3024	−	35.1647i	−0.0346657	−	0.0600427i
$71$	145.858			0.243805			0.121902	−	0.992542i	$-0.461101\pi$
$71$	145.858			0.243805			0.121902	+	0.992542i	$0.461101\pi$
$72$	86.3929	−	197.970i	0.141410	−	0.324042i
$73$	771.401			1.23679			0.618395	−	0.785867i	$-0.287783\pi$
$73$	771.401			1.23679			0.618395	+	0.785867i	$0.287783\pi$
$74$	−289.301	−	501.084i	−0.454467	−	0.787159i
$75$	540.794	+	273.033i	0.832606	+	0.420362i
$76$	23.3939	−	40.5194i	0.0353087	−	0.0611565i
$77$	−228.987	+	396.617i	−0.338903	+	0.586997i
$78$	−342.313	+	224.105i	−0.496914	+	0.325319i
$79$	137.837	+	238.741i	0.196303	+	0.340006i	0.947327	−	0.320269i	$-0.103773\pi$
$79$	137.837	+	238.741i	0.196303	+	0.340006i	−0.751024	+	0.660275i	$0.770440\pi$
$80$	46.4054			0.0648536
$81$	−495.758	−	534.476i	−0.680052	−	0.733164i
$82$	−442.483			−0.595903
$83$	−545.558	−	944.934i	−0.721479	−	1.24964i	−0.960407	−	0.278601i	$-0.910129\pi$
$83$	−545.558	−	944.934i	−0.721479	−	1.24964i	0.238928	−	0.971037i	$-0.423204\pi$
$84$	121.726	−	79.6916i	0.158112	−	0.103513i
$85$	−20.1381	+	34.8803i	−0.0256975	+	0.0445094i
$86$	129.899	−	224.991i	0.162876	−	0.282109i
$87$	−1370.15	−	691.754i	−1.68845	−	0.852457i
$88$	−261.700	−	453.277i	−0.317014	−	0.549085i
$89$	852.941			1.01586			0.507930	−	0.861398i	$-0.330411\pi$
$89$	852.941			1.01586			0.507930	+	0.861398i	$0.330411\pi$
$90$	62.6422	−	143.545i	0.0733674	−	0.168122i
$91$	−275.591			−0.317470
$92$	16.5077	+	28.5921i	0.0187070	+	0.0324015i
$93$	72.4131	+	1290.38i	0.0807407	+	1.43878i
$94$	518.477	−	898.029i	0.568903	−	0.985369i
$95$	16.9626	−	29.3800i	0.0183192	−	0.0317297i
$96$	9.31640	+	166.016i	0.00990470	+	0.176499i
$97$	−758.377	−	1313.55i	−0.793830	−	1.37495i	−0.923580	−	0.383407i	$-0.874751\pi$
$97$	−758.377	−	1313.55i	−0.793830	−	1.37495i	0.129750	−	0.991547i	$-0.458583\pi$
$98$	98.0000			0.101015
$99$	−1755.38	+	197.638i	−1.78205	+	0.200640i
$100$	−466.352			−0.466352
$101$	364.071	+	630.590i	0.358678	+	0.621248i	0.987740	−	0.156107i	$-0.0498943\pi$
$101$	364.071	+	630.590i	0.358678	+	0.621248i	−0.629062	+	0.777355i	$0.716561\pi$
$102$	−128.827	−	65.0417i	−0.125057	−	0.0631381i
$103$	18.5884	−	32.1960i	0.0177822	−	0.0307997i	−0.856997	−	0.515321i	$-0.827673\pi$
$103$	18.5884	−	32.1960i	0.0177822	−	0.0307997i	0.874780	+	0.484521i	$0.161006\pi$
$104$	157.481	−	272.764i	0.148483	−	0.257180i
$105$	88.2618	−	57.7831i	0.0820330	−	0.0537053i
$106$	−264.820	−	458.682i	−0.242657	−	0.420294i
$107$	−1213.30			−1.09621			−0.548103	−	0.836411i	$-0.684650\pi$
$107$	−1213.30			−1.09621			−0.548103	+	0.836411i	$0.684650\pi$
$108$	526.110	+	195.285i	0.468750	+	0.173993i
$109$	727.706			0.639464			0.319732	−	0.947508i	$-0.396407\pi$
$109$	727.706			0.639464			0.319732	+	0.947508i	$0.396407\pi$
$110$	−189.754	−	328.664i	−0.164476	−	0.284881i
$111$	1257.69	−	823.387i	1.07545	−	0.704076i
$112$	−56.0000	+	96.9948i	−0.0472456	+	0.0818317i
$113$	−881.264	+	1526.39i	−0.733649	+	1.27072i	0.221664	+	0.975123i	$0.428851\pi$
$113$	−881.264	+	1526.39i	−0.733649	+	1.27072i	−0.955313	+	0.295595i	$0.904482\pi$
$114$	108.513	+	54.7853i	0.0891503	+	0.0450097i
$115$	11.9695	+	20.7317i	0.00970572	+	0.0168108i
$116$	1181.54			0.945721
$117$	−631.157	−	855.335i	−0.498722	−	0.675861i
$118$	−470.633			−0.367164
$119$	−48.6036	−	84.1840i	−0.0374411	−	0.0648498i
$120$	6.75518	+	120.375i	0.00513884	+	0.0915727i
$121$	−1474.71	+	2554.27i	−1.10797	+	1.91906i
$122$	414.456	−	717.859i	0.307566	−	0.532720i
$123$	−64.4117	−	1147.80i	−0.0472180	−	0.841411i
$124$	−497.449	−	861.607i	−0.360260	−	0.623989i
$125$	−700.687			−0.501371
$126$	224.439	+	304.156i	0.158687	+	0.215051i
$127$	1643.70			1.14846			0.574232	−	0.818692i	$-0.305301\pi$
$127$	1643.70			1.14846			0.574232	+	0.818692i	$0.305301\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$	602.535	+	304.205i	0.411242	+	0.207626i
$130$	114.187	−	197.777i	0.0770373	−	0.133432i
$131$	−221.956	+	384.438i	−0.148033	+	0.256401i	−0.930500	−	0.366291i	$-0.880628\pi$
$131$	−221.956	+	384.438i	−0.148033	+	0.256401i	0.782467	+	0.622692i	$0.213961\pi$
$132$	1137.70	−	744.830i	0.750184	−	0.491130i
$133$	40.9393	+	70.9089i	0.0266909	+	0.0462300i
$134$	279.539			0.180213
$135$	381.475	+	141.598i	0.243201	+	0.0902726i
$136$	111.094			0.0700458
$137$	591.845	+	1025.11i	0.369085	+	0.639275i	0.989423	−	0.145060i	$-0.0463376\pi$
$137$	591.845	+	1025.11i	0.369085	+	0.639275i	−0.620337	+	0.784335i	$0.713004\pi$
$138$	−71.7648	+	46.9829i	−0.0442683	+	0.0289815i
$139$	268.477	−	465.017i	0.163827	−	0.283757i	−0.772411	−	0.635123i	$-0.780949\pi$
$139$	268.477	−	465.017i	0.163827	−	0.283757i	0.936238	+	0.351366i	$0.114283\pi$
$140$	−40.6047	+	70.3295i	−0.0245123	+	0.0424566i
$141$	2404.96	+	1214.20i	1.43641	+	0.725208i
$142$	−145.858	−	252.633i	−0.0861980	−	0.149299i
$143$	−2575.79			−1.50628
$144$	−429.288	+	48.3334i	−0.248430	+	0.0279707i
$145$	856.720			0.490667
$146$	−771.401	−	1336.11i	−0.437271	−	0.757376i
$147$	14.2657	+	254.212i	0.00800421	+	0.142633i
$148$	−578.601	+	1002.17i	−0.321356	+	0.556606i
$149$	−666.974	+	1155.23i	−0.366716	+	0.635170i	−0.989050	−	0.147581i	$-0.952851\pi$
$149$	−666.974	+	1155.23i	−0.366716	+	0.635170i	0.622334	+	0.782752i	$0.286185\pi$
$150$	−67.8863	−	1209.72i	−0.0369526	−	0.658485i
$151$	−759.060	−	1314.73i	−0.409082	−	0.708551i	0.585705	−	0.810524i	$-0.300818\pi$
$151$	−759.060	−	1314.73i	−0.409082	−	0.708551i	−0.994787	+	0.101973i	$0.967484\pi$
$152$	−93.5755			−0.0499341
$153$	149.965	−	343.646i	0.0792413	−	0.181582i
$154$	915.949			0.479281
$155$	−360.693	−	624.738i	−0.186913	−	0.323743i
$156$	730.474	+	368.798i	0.374902	+	0.189279i
$157$	1608.97	−	2786.82i	0.817898	−	1.41664i	−0.0893309	−	0.996002i	$-0.528473\pi$
$157$	1608.97	−	2786.82i	0.817898	−	1.41664i	0.907228	−	0.420638i	$-0.138194\pi$
$158$	275.675	−	477.483i	0.138807	−	0.240421i
$159$	1151.27	−	753.712i	0.574224	−	0.375932i
$160$	−46.4054	−	80.3766i	−0.0229292	−	0.0397145i
$161$	−57.7768			−0.0282823
$162$	−429.982	+	1393.15i	−0.208534	+	0.675658i
$163$	−3272.13			−1.57235			−0.786176	−	0.618003i	$-0.787942\pi$
$163$	−3272.13			−1.57235			−0.786176	+	0.618003i	$0.787942\pi$
$164$	442.483	+	766.403i	0.210684	+	0.364915i
$165$	824.931	−	540.065i	0.389217	−	0.254812i
$166$	−1091.12	+	1889.87i	−0.510163	+	0.883628i
$167$	296.399	−	513.378i	0.137341	−	0.237882i	−0.789148	−	0.614203i	$-0.789478\pi$
$167$	296.399	−	513.378i	0.137341	−	0.237882i	0.926489	+	0.376321i	$0.122811\pi$
$168$	−259.756	−	131.144i	−0.119289	−	0.0602262i
$169$	323.495	+	560.310i	0.147244	+	0.255034i
$170$	80.5526			0.0363418
$171$	−126.317	+	289.456i	−0.0564893	+	0.129446i
$172$	−519.595			−0.230341
$173$	1686.82	+	2921.66i	0.741311	+	1.28399i	0.951899	+	0.306413i	$0.0991288\pi$
$173$	1686.82	+	2921.66i	0.741311	+	1.28399i	−0.210588	+	0.977575i	$0.567538\pi$
$174$	171.996	+	3064.92i	0.0749367	+	1.33535i
$175$	408.058	−	706.777i	0.176265	−	0.305299i
$176$	−523.399	+	906.554i	−0.224163	+	0.388262i
$177$	−68.5095	−	1220.82i	−0.0290932	−	0.518432i
$178$	−852.941	−	1477.34i	−0.359161	−	0.622085i
$179$	597.839			0.249634			0.124817	−	0.992180i	$-0.460166\pi$
$179$	597.839			0.249634			0.124817	+	0.992180i	$0.460166\pi$
$180$	−311.270	+	35.0458i	−0.128893	+	0.0145120i
$181$	4639.73			1.90535			0.952675	−	0.303991i	$-0.0983192\pi$
$181$	4639.73			1.90535			0.952675	+	0.303991i	$0.0983192\pi$
$182$	275.591	+	477.338i	0.112243	+	0.194410i
$183$	1922.45	+	970.599i	0.776568	+	0.392070i
$184$	33.0153	−	57.1842i	0.0132278	−	0.0229113i
$185$	−419.535	+	726.656i	−0.166729	+	0.288783i
$186$	2162.59	−	1415.80i	0.852521	−	0.558128i
$187$	−454.270	−	786.818i	−0.177644	−	0.307689i
$188$	−2073.91			−0.804550
$189$	−756.309	+	626.469i	−0.291076	+	0.241106i
$190$	−67.8502			−0.0259072
$191$	−515.653	−	893.137i	−0.195347	−	0.338352i	0.751667	−	0.659543i	$-0.229250\pi$
$191$	−515.653	−	893.137i	−0.195347	−	0.338352i	−0.947014	+	0.321191i	$0.895917\pi$
$192$	278.231	−	182.152i	0.104581	−	0.0684672i
$193$	−1403.84	+	2431.52i	−0.523578	+	0.906863i	0.476046	+	0.879421i	$0.342070\pi$
$193$	−1403.84	+	2431.52i	−0.523578	+	0.906863i	−0.999623	+	0.0274426i	$0.991264\pi$
$194$	−1516.75	+	2627.09i	−0.561323	+	0.972239i
$195$	529.656	+	267.410i	0.194510	+	0.0982032i
$196$	−98.0000	−	169.741i	−0.0357143	−	0.0618590i
$197$	−3913.63			−1.41540			−0.707702	−	0.706511i	$-0.750268\pi$
$197$	−3913.63			−1.41540			−0.707702	+	0.706511i	$0.750268\pi$
$198$	2097.70	+	2842.77i	0.752915	+	1.02034i
$199$	822.179			0.292878			0.146439	−	0.989220i	$-0.453219\pi$
$199$	822.179			0.292878			0.146439	+	0.989220i	$0.453219\pi$
$200$	466.352	+	807.746i	0.164880	+	0.285581i
$201$	40.6922	+	725.123i	0.0142796	+	0.254459i
$202$	728.143	−	1261.18i	0.253624	−	0.439289i
$203$	−1033.85	+	1790.68i	−0.357449	+	0.619120i
$204$	16.1718	+	288.177i	0.00555026	+	0.0989042i
$205$	320.838	+	555.707i	0.109309	+	0.189328i
$206$	−74.3536			−0.0251479
$207$	−132.320	−	179.318i	−0.0444294	−	0.0602100i
$208$	−629.923			−0.209987
$209$	382.636	+	662.744i	0.126639	+	0.219344i
$210$	−188.345	−	95.0907i	−0.0618907	−	0.0312471i
$211$	−1446.79	+	2505.91i	−0.472043	+	0.817603i	−0.999488	−	0.0319861i	$-0.989817\pi$
$211$	−1446.79	+	2505.91i	−0.472043	+	0.817603i	0.527445	+	0.849589i	$0.323150\pi$
$212$	−529.640	+	917.364i	−0.171584	+	0.297192i
$213$	634.097	−	415.130i	0.203979	−	0.133541i
$214$	1213.30	+	2101.50i	0.387568	+	0.671287i
$215$	−376.750			−0.119508
$216$	−187.867	−	1106.53i	−0.0591795	−	0.348565i
$217$	1741.07			0.544662
$218$	−727.706	−	1260.42i	−0.226085	−	0.391590i
$219$	3353.56	−	2195.51i	1.03476	−	0.677436i
$220$	−379.509	+	657.329i	−0.116302	+	0.201441i
$221$	273.362	−	473.477i	0.0832050	−	0.144115i
$222$	−2683.84	−	1355.00i	−0.811386	−	0.409649i
$223$	−2291.37	−	3968.77i	−0.688078	−	1.19179i	−0.972459	−	0.233074i	$-0.925121\pi$
$223$	−2291.37	−	3968.77i	−0.688078	−	1.19179i	0.284381	−	0.958711i	$-0.408212\pi$
$224$	224.000			0.0668153
$225$	3128.11	−	352.193i	0.926848	−	0.104354i
$226$	3525.06			1.03754
$227$	−1296.50	−	2245.60i	−0.379082	−	0.656590i	0.611847	−	0.790976i	$-0.290427\pi$
$227$	−1296.50	−	2245.60i	−0.379082	−	0.656590i	−0.990929	+	0.134387i	$0.957094\pi$
$228$	−13.6217	−	242.734i	−0.00395666	−	0.0705065i
$229$	1539.79	−	2666.99i	0.444332	−	0.769605i	−0.553673	−	0.832734i	$-0.686774\pi$
$229$	1539.79	−	2666.99i	0.444332	−	0.769605i	0.998005	+	0.0631284i	$0.0201078\pi$
$230$	23.9389	−	41.4634i	0.00686298	−	0.0118870i
$231$	133.334	+	2375.97i	0.0379771	+	0.676741i
$232$	−1181.54	−	2046.50i	−0.334363	−	0.579134i
$233$	2940.24			0.826702			0.413351	−	0.910572i	$-0.364358\pi$
$233$	2940.24			0.826702			0.413351	+	0.910572i	$0.364358\pi$
$234$	−850.326	+	1948.53i	−0.237554	+	0.544357i
$235$	−1503.76			−0.417424
$236$	470.633	+	815.161i	0.129812	+	0.224841i
$237$	1278.72	+	645.592i	0.350471	+	0.176944i
$238$	−97.2073	+	168.368i	−0.0264748	+	0.0458558i
$239$	2949.31	−	5108.36i	0.798223	−	1.38256i	−0.122550	−	0.992462i	$-0.539107\pi$
$239$	2949.31	−	5108.36i	0.798223	−	1.38256i	0.920773	−	0.390100i	$-0.127560\pi$
$240$	201.741	−	132.076i	0.0542597	−	0.0355227i
$241$	−2287.02	−	3961.24i	−0.611287	−	1.05878i	−0.991024	−	0.133686i	$-0.957319\pi$
$241$	−2287.02	−	3961.24i	−0.611287	−	1.05878i	0.379737	−	0.925095i	$-0.376015\pi$
$242$	5898.84			1.56691
$243$	−3676.43	−	912.571i	−0.970547	−	0.240911i
$244$	−1657.82			−0.434964
$245$	−71.0583	−	123.077i	−0.0185296	−	0.0320942i
$246$	−1923.63	+	1259.36i	−0.498563	+	0.326399i
$247$	−230.255	+	398.814i	−0.0593149	+	0.102736i
$248$	−994.898	+	1723.21i	−0.254742	+	0.441227i
$249$	−5061.14	−	2555.24i	−1.28810	−	0.650329i
$250$	700.687	+	1213.63i	0.177261	+	0.307026i
$251$	−1514.83			−0.380938			−0.190469	−	0.981693i	$-0.561001\pi$
$251$	−1514.83			−0.380938			−0.190469	+	0.981693i	$0.561001\pi$
$252$	302.375	−	692.896i	0.0755867	−	0.173208i
$253$	−540.006			−0.134189
$254$	−1643.70	−	2846.98i	−0.406043	−	0.703288i
$255$	11.7259	+	208.953i	0.00287964	+	0.0513143i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	1960.66	−	3395.97i	0.475886	−	0.824259i	−0.523732	−	0.851883i	$-0.675461\pi$
$257$	1960.66	−	3395.97i	0.475886	−	0.824259i	0.999618	+	0.0276240i	$0.00879410\pi$
$258$	−75.6368	−	1347.83i	−0.0182517	−	0.325240i
$259$	−1012.55	−	1753.79i	−0.242923	−	0.420754i
$260$	−456.747			−0.108947
$261$	−7925.35	+	892.314i	−1.87957	+	0.211620i
$262$	887.822			0.209351
$263$	3250.21	+	5629.53i	0.762040	+	1.31989i	0.941797	+	0.336181i	$0.109135\pi$
$263$	3250.21	+	5629.53i	0.762040	+	1.31989i	−0.179757	+	0.983711i	$0.557531\pi$
$264$	−2427.79	−	1225.73i	−0.565985	−	0.285752i
$265$	−384.034	+	665.166i	−0.0890227	+	0.154192i
$266$	81.8786	−	141.818i	0.0188733	−	0.0326895i
$267$	3708.04	−	2427.58i	0.849920	−	0.556425i
$268$	−279.539	−	484.176i	−0.0637148	−	0.110357i
$269$	−2072.23			−0.469689			−0.234844	−	0.972033i	$-0.575458\pi$
$269$	−2072.23			−0.469689			−0.234844	+	0.972033i	$0.575458\pi$
$270$	−136.220	−	802.331i	−0.0307040	−	0.180846i
$271$	19.3588			0.00433934			0.00216967	−	0.999998i	$-0.499309\pi$
$271$	19.3588			0.00433934			0.00216967	+	0.999998i	$0.499309\pi$
$272$	−111.094	−	192.420i	−0.0247649	−	0.0428941i
$273$	−1198.09	+	784.367i	−0.265612	+	0.173890i
$274$	1183.69	−	2050.21i	0.260983	−	0.452035i
$275$	3813.88	−	6605.83i	0.836311	−	1.44853i
$276$	153.142	+	77.3173i	0.0333987	+	0.0168622i
$277$	−2167.02	−	3753.38i	−0.470048	−	0.814148i	0.529365	−	0.848394i	$-0.322430\pi$
$277$	−2167.02	−	3753.38i	−0.470048	−	0.814148i	−0.999413	+	0.0342464i	$0.989097\pi$
$278$	−1073.91			−0.231686
$279$	3987.39	+	5403.65i	0.855624	+	1.15953i
$280$	162.419			0.0346657
$281$	2680.38	+	4642.55i	0.569032	+	0.985593i	0.996662	+	0.0816387i	$0.0260154\pi$
$281$	2680.38	+	4642.55i	0.569032	+	0.985593i	−0.427630	+	0.903954i	$0.640651\pi$
$282$	−301.897	−	5379.71i	−0.0637506	−	1.13602i
$283$	−690.576	+	1196.11i	−0.145055	+	0.251242i	−0.929393	−	0.369091i	$-0.879669\pi$
$283$	−690.576	+	1196.11i	−0.145055	+	0.251242i	0.784339	+	0.620333i	$0.213002\pi$
$284$	−291.716	+	505.266i	−0.0609512	+	0.105571i
$285$	−9.87687	−	176.003i	−0.00205283	−	0.0365808i
$286$	2575.79	+	4461.40i	0.532551	+	0.922405i
$287$	−1548.69			−0.318524
$288$	513.004	+	695.215i	0.104962	+	0.142243i
$289$	−4720.16			−0.960749
$290$	−856.720	−	1483.88i	−0.173477	−	0.300471i
$291$	−7035.46	−	3552.03i	−1.41727	−	0.715545i
$292$	−1542.80	+	2672.21i	−0.309198	+	0.535546i
$293$	3808.28	−	6596.13i	0.759324	−	1.31519i	−0.183871	−	0.982950i	$-0.558863\pi$
$293$	3808.28	−	6596.13i	0.759324	−	1.31519i	0.943196	−	0.332238i	$-0.107804\pi$
$294$	426.042	−	278.920i	0.0845144	−	0.0553298i
$295$	341.249	+	591.061i	0.0673501	+	0.116654i
$296$	2314.41			0.454467
$297$	−7068.78	+	5855.24i	−1.38105	+	1.14396i
$298$	2667.90			0.518614
$299$	−162.477	−	281.419i	−0.0314258	−	0.0544310i
$300$	−2027.40	+	1327.30i	−0.390174	+	0.255439i
$301$	454.645	−	787.469i	0.0870609	−	0.150794i
$302$	−1518.12	+	2629.46i	−0.289265	+	0.501021i
$303$	3377.49	+	1705.21i	0.640369	+	0.323306i
$304$	93.5755	+	162.078i	0.0176544	+	0.0305782i
$305$	−1202.06			−0.225672
$306$	−745.176	+	83.8992i	−0.139212	+	0.0156739i
$307$	1394.89			0.259318			0.129659	−	0.991559i	$-0.458612\pi$
$307$	1394.89			0.259318			0.129659	+	0.991559i	$0.458612\pi$
$308$	−915.949	−	1586.47i	−0.169451	−	0.293498i
$309$	−10.8236	−	192.873i	−0.00199266	−	0.0355086i
$310$	−721.386	+	1249.48i	−0.132168	+	0.228921i
$311$	−1756.79	+	3042.85i	−0.320317	+	0.554805i	−0.980553	−	0.196253i	$-0.937123\pi$
$311$	−1756.79	+	3042.85i	−0.320317	+	0.554805i	0.660237	+	0.751058i	$0.270456\pi$
$312$	−91.6971	−	1634.02i	−0.0166389	−	0.296500i
$313$	3197.10	+	5537.54i	0.577351	+	1.00000i	0.995782	+	0.0917528i	$0.0292470\pi$
$313$	3197.10	+	5537.54i	0.577351	+	1.00000i	−0.418431	+	0.908249i	$0.637420\pi$
$314$	−6435.89			−1.15668
$315$	219.248	−	502.409i	0.0392165	−	0.0898651i
$316$	−1102.70			−0.196303
$317$	−1650.78	−	2859.24i	−0.292483	−	0.506595i	0.681913	−	0.731433i	$-0.261148\pi$
$317$	−1650.78	−	2859.24i	−0.292483	−	0.506595i	−0.974396	+	0.224838i	$0.927815\pi$
$318$	−2456.74	−	1240.34i	−0.433229	−	0.218727i
$319$	−9662.81	+	16736.5i	−1.69597	+	2.93750i
$320$	−92.8109	+	160.753i	−0.0162134	+	0.0280824i
$321$	−5274.65	+	3453.21i	−0.917141	+	0.600433i
$322$	57.7768	+	100.072i	0.00999930	+	0.0173193i
$323$	−162.433			−0.0279814
$324$	2843.00	−	648.404i	0.487482	−	0.111180i
$325$	4590.09			0.783423
$326$	3272.13	+	5667.50i	0.555910	+	0.962865i
$327$	3163.60	−	2071.14i	0.535008	−	0.350258i
$328$	884.966	−	1532.81i	0.148976	−	0.258034i
$329$	1814.67	−	3143.10i	0.304091	−	0.526702i
$330$	−1760.35	−	888.757i	−0.293649	−	0.148256i
$331$	666.004	+	1153.55i	0.110595	+	0.191556i	0.916010	−	0.401155i	$-0.131391\pi$
$331$	666.004	+	1153.55i	0.110595	+	0.191556i	−0.805415	+	0.592711i	$0.798058\pi$
$332$	4364.46			0.721479
$333$	3124.19	−	7159.12i	0.514128	−	1.17813i
$334$	−1185.59			−0.194230
$335$	−202.690	−	351.069i	−0.0330571	−	0.0572565i
$336$	32.6074	+	581.055i	0.00529429	+	0.0943427i
$337$	5638.25	−	9765.73i	0.911380	−	1.57856i	0.0992627	−	0.995061i	$-0.468352\pi$
$337$	5638.25	−	9765.73i	0.911380	−	1.57856i	0.812117	−	0.583495i	$-0.198315\pi$
$338$	646.990	−	1120.62i	0.104117	−	0.180336i
$339$	513.138	+	9143.98i	0.0822119	+	1.46499i
$340$	−80.5526	−	139.521i	−0.0128488	−	0.0222547i
$341$	16272.8			2.58422
$342$	627.669	−	70.6691i	0.0992411	−	0.0111735i
$343$	343.000			0.0539949
$344$	519.595	+	899.964i	0.0814380	+	0.141055i
$345$	111.041	+	56.0616i	0.0173282	+	0.00874857i
$346$	3373.65	−	5843.33i	0.524186	−	0.907917i
$347$	4229.45	−	7325.63i	0.654320	−	1.13332i	−0.327744	−	0.944767i	$-0.606288\pi$
$347$	4229.45	−	7325.63i	0.654320	−	1.13332i	0.982064	−	0.188549i	$-0.0603783\pi$
$348$	5136.60	−	3362.83i	0.791238	−	0.518007i
$349$	3360.96	+	5821.36i	0.515497	+	0.892866i	0.999838	+	0.0179874i	$0.00572586\pi$
$349$	3360.96	+	5821.36i	0.515497	+	0.892866i	−0.484342	+	0.874879i	$0.660941\pi$
$350$	−1632.23			−0.249276
$351$	−5178.26	−	1922.10i	−0.787450	−	0.292290i
$352$	2093.60			0.317014
$353$	854.724	+	1480.43i	0.128874	+	0.223216i	0.923240	−	0.384223i	$-0.125531\pi$
$353$	854.724	+	1480.43i	0.128874	+	0.223216i	−0.794367	+	0.607438i	$0.792197\pi$
$354$	−2046.01	+	1339.48i	−0.307187	+	0.201109i
$355$	−211.519	+	366.361i	−0.0316232	+	0.0547730i
$356$	−1705.88	+	2954.67i	−0.253965	+	0.439880i
$357$	−450.896	−	227.646i	−0.0668458	−	0.0337488i
$358$	−597.839	−	1035.49i	−0.0882591	−	0.152869i
$359$	2066.56			0.303814			0.151907	−	0.988395i	$-0.451459\pi$
$359$	2066.56			0.303814			0.151907	+	0.988395i	$0.451459\pi$
$360$	371.971	+	504.090i	0.0544572	+	0.0737996i
$361$	−6722.18			−0.980053
$362$	−4639.73	−	8036.25i	−0.673643	−	1.16678i
$363$	858.686	+	15301.5i	0.124158	+	2.21246i
$364$	551.182	−	954.676i	0.0793676	−	0.137469i
$365$	−1118.66	+	1937.58i	−0.160420	+	0.277856i
$366$	−241.327	−	4300.39i	−0.0344655	−	0.614166i
$367$	5938.04	+	10285.0i	0.844587	+	1.46287i	0.885980	+	0.463724i	$0.153487\pi$
$367$	5938.04	+	10285.0i	0.844587	+	1.46287i	−0.0413929	+	0.999143i	$0.513180\pi$
$368$	−132.061			−0.0187070
$369$	−3546.80	−	4806.57i	−0.500377	−	0.678104i
$370$	1678.14			0.235790
$371$	−926.870	−	1605.39i	−0.129705	−	0.224656i
$372$	−4614.83	−	2329.91i	−0.643194	−	0.324732i
$373$	−1399.87	+	2424.64i	−0.194323	+	0.336577i	−0.946678	−	0.322180i	$-0.895584\pi$
$373$	−1399.87	+	2424.64i	−0.194323	+	0.336577i	0.752355	+	0.658757i	$0.228918\pi$
$374$	−908.539	+	1573.64i	−0.125614	+	0.217569i
$375$	−3046.14	+	1994.25i	−0.419472	+	0.274620i
$376$	2073.91	+	3592.12i	0.284451	+	0.492684i
$377$	−11629.4			−1.58871
$378$	1841.39	+	683.496i	0.250557	+	0.0930033i
$379$	3922.24			0.531588			0.265794	−	0.964030i	$-0.414366\pi$
$379$	3922.24			0.531588			0.265794	+	0.964030i	$0.414366\pi$
$380$	67.8502	+	117.520i	0.00915958	+	0.0158649i
$381$	7145.77	−	4678.19i	0.960863	−	0.629057i
$382$	−1031.31	+	1786.27i	−0.138131	+	0.239251i
$383$	2495.30	−	4321.98i	0.332908	−	0.576613i	−0.650173	−	0.759786i	$-0.725304\pi$
$383$	2495.30	−	4321.98i	0.332908	−	0.576613i	0.983081	+	0.183173i	$0.0586369\pi$
$384$	−593.728	−	299.758i	−0.0789025	−	0.0398359i
$385$	−664.140	−	1150.32i	−0.0879162	−	0.152275i
$386$	5615.35			0.740451
$387$	3485.24	−	392.403i	0.457790	−	0.0515425i
$388$	6067.01			0.793830
$389$	5933.21	+	10276.6i	0.773331	+	1.33945i	0.935728	+	0.352724i	$0.114744\pi$
$389$	5933.21	+	10276.6i	0.773331	+	1.33945i	−0.162396	+	0.986726i	$0.551922\pi$
$390$	−66.4881	−	1184.80i	−0.00863271	−	0.153833i
$391$	57.3095	−	99.2629i	0.00741244	−	0.0128387i
$392$	−196.000	+	339.482i	−0.0252538	+	0.0437409i
$393$	129.239	+	2303.01i	0.0165884	+	0.295601i
$394$	3913.63	+	6778.61i	0.500421	+	0.866754i
$395$	−799.550			−0.101847
$396$	2826.12	−	6476.10i	0.358632	−	0.821808i
$397$	−10596.6			−1.33962			−0.669812	−	0.742531i	$-0.733625\pi$
$397$	−10596.6			−1.33962			−0.669812	+	0.742531i	$0.733625\pi$
$398$	−822.179	−	1424.06i	−0.103548	−	0.179350i
$399$	379.794	+	191.748i	0.0476528	+	0.0240587i
$400$	932.704	−	1615.49i	0.116588	−	0.201936i
$401$	−3928.67	+	6804.66i	−0.489248	+	0.847403i	−0.999923	−	0.0123707i	$-0.996062\pi$
$401$	−3928.67	+	6804.66i	−0.489248	+	0.847403i	0.510675	+	0.859774i	$0.329396\pi$
$402$	1215.26	−	795.604i	0.150775	−	0.0987093i
$403$	4896.16	+	8480.40i	0.605199	+	1.04824i
$404$	−2912.57			−0.358678
$405$	2061.41	−	470.148i	0.252920	−	0.0576836i
$406$	4135.41			0.505509
$407$	−9463.74	−	16391.7i	−1.15258	−	1.99633i
$408$	482.966	−	316.188i	0.0586039	−	0.0383667i
$409$	2323.97	−	4025.23i	0.280961	−	0.486638i	−0.690661	−	0.723179i	$-0.742680\pi$
$409$	2323.97	−	4025.23i	0.280961	−	0.486638i	0.971622	+	0.236540i	$0.0760136\pi$
$410$	641.675	−	1111.41i	0.0772929	−	0.133875i
$411$	5490.54	+	2772.04i	0.658950	+	0.332687i
$412$	74.3536	+	128.784i	0.00889111	+	0.0153999i
$413$	−1647.22			−0.196257
$414$	−178.268	+	408.503i	−0.0211628	+	0.0484948i
$415$	3164.61			0.374324
$416$	629.923	+	1091.06i	0.0742416	+	0.128590i
$417$	−156.328	−	2785.72i	−0.0183583	−	0.327139i
$418$	765.271	−	1325.49i	0.0895470	−	0.155100i
$419$	−3868.66	+	6700.72i	−0.451065	+	0.781268i	−0.998452	−	0.0556113i	$-0.982289\pi$
$419$	−3868.66	+	6700.72i	−0.451065	+	0.781268i	0.547387	+	0.836880i	$0.315623\pi$
$420$	23.6431	+	421.314i	0.00274683	+	0.0489477i
$421$	1085.58	+	1880.28i	0.125672	+	0.217670i	0.921995	−	0.387201i	$-0.126558\pi$
$421$	1085.58	+	1880.28i	0.125672	+	0.217670i	−0.796324	+	0.604871i	$0.793225\pi$
$422$	5787.16			0.667570
$423$	13911.0	−	1566.24i	1.59900	−	0.180031i
$424$	2118.56			0.242657
$425$	809.515	+	1402.12i	0.0923935	+	0.160030i
$426$	−1353.12	−	683.158i	−0.153894	−	0.0776974i
$427$	1450.60	−	2512.51i	0.164401	−	0.284751i
$428$	2426.60	−	4202.99i	0.274052	−	0.474671i
$429$	−11197.9	+	7331.02i	−1.26023	+	0.825047i
$430$	376.750	+	652.551i	0.0422524	+	0.0731832i
$431$	4714.95			0.526940			0.263470	−	0.964668i	$-0.415133\pi$
$431$	4714.95			0.526940			0.263470	+	0.964668i	$0.415133\pi$
$432$	−1728.71	+	1431.93i	−0.192529	+	0.159476i
$433$	−6862.68			−0.761661			−0.380830	−	0.924645i	$-0.624362\pi$
$433$	−6862.68			−0.761661			−0.380830	+	0.924645i	$0.624362\pi$
$434$	−1741.07	−	3015.62i	−0.192567	−	0.333536i
$435$	3724.47	−	2438.33i	0.410517	−	0.268757i
$436$	−1455.41	+	2520.85i	−0.159866	+	0.276896i
$437$	−48.2723	+	83.6101i	−0.00528416	+	0.00915243i
$438$	−7156.29	−	3613.03i	−0.780686	−	0.394149i
$439$	−250.010	−	433.030i	−0.0271807	−	0.0470784i	0.852115	−	0.523354i	$-0.175320\pi$
$439$	−250.010	−	433.030i	−0.0271807	−	0.0470784i	−0.879296	+	0.476276i	$0.841986\pi$
$440$	1518.04			0.164476
$441$	785.537	+	1064.55i	0.0848220	+	0.114950i
$442$	−1093.45			−0.117670
$443$	876.172	+	1517.57i	0.0939688	+	0.162759i	0.909178	−	0.416408i	$-0.136711\pi$
$443$	876.172	+	1517.57i	0.0939688	+	0.162759i	−0.815209	+	0.579167i	$0.803378\pi$
$444$	336.905	+	6003.56i	0.0360108	+	0.641703i
$445$	−1236.91	+	2142.39i	−0.131764	+	0.228222i
$446$	−4582.74	+	7937.53i	−0.486544	+	0.842720i
$447$	388.362	+	6920.51i	0.0410938	+	0.732280i
$448$	−224.000	−	387.979i	−0.0236228	−	0.0409159i
$449$	−11846.4			−1.24514			−0.622568	−	0.782565i	$-0.713911\pi$
$449$	−11846.4			−1.24514			−0.622568	+	0.782565i	$0.713911\pi$
$450$	−3738.13	−	5065.86i	−0.391594	−	0.530682i
$451$	−14474.7			−1.51128
$452$	−3525.06	−	6105.58i	−0.366825	−	0.635359i
$453$	−7041.79	−	3555.23i	−0.730358	−	0.368740i
$454$	−2593.00	+	4491.20i	−0.268052	+	0.464279i
$455$	399.654	−	692.221i	0.0411782	−	0.0713227i
$456$	−406.807	+	266.328i	−0.0417774	+	0.0273508i
$457$	−6403.59	−	11091.3i	−0.655464	−	1.13530i	−0.981777	−	0.190036i	$-0.939140\pi$
$457$	−6403.59	−	11091.3i	−0.655464	−	1.13530i	0.326313	−	0.945262i	$-0.394194\pi$
$458$	−6159.15			−0.628380
$459$	−326.109	−	1920.77i	−0.0331622	−	0.195324i
$460$	−95.7556			−0.00970572
$461$	5370.10	+	9301.29i	0.542539	+	0.939706i	0.998757	+	0.0498377i	$0.0158704\pi$
$461$	5370.10	+	9301.29i	0.542539	+	0.939706i	−0.456218	+	0.889868i	$0.650796\pi$
$462$	3981.96	−	2606.91i	0.400990	−	0.262520i
$463$	−1618.65	+	2803.59i	−0.162473	+	0.281412i	−0.935755	−	0.352650i	$-0.885281\pi$
$463$	−1618.65	+	2803.59i	−0.162473	+	0.281412i	0.773282	+	0.634063i	$0.218614\pi$
$464$	−2363.09	+	4092.99i	−0.236430	+	0.409509i
$465$	−3346.15	−	1689.39i	−0.333707	−	0.168480i
$466$	−2940.24	−	5092.64i	−0.292283	−	0.506249i
$467$	13705.1			1.35802			0.679009	−	0.734130i	$-0.262410\pi$
$467$	13705.1			1.35802			0.679009	+	0.734130i	$0.262410\pi$
$468$	4225.28	−	475.723i	0.417337	−	0.0469879i
$469$	978.388			0.0963278
$470$	1503.76	+	2604.59i	0.147581	+	0.255619i
$471$	−936.864	−	16694.7i	−0.0916527	−	1.63323i
$472$	941.266	−	1630.32i	0.0917909	−	0.158986i
$473$	4249.30	−	7360.01i	0.413072	−	0.715462i
$474$	−160.519	−	2860.40i	−0.0155546	−	0.277178i
$475$	−681.862	−	1181.02i	−0.0658652	−	0.114082i
$476$	388.829			0.0374411
$477$	2859.82	−	6553.32i	0.274512	−	0.629048i
$478$	−11797.3			−1.12886
$479$	−5330.20	−	9232.19i	−0.508441	−	0.880646i	−0.999952	−	0.00977450i	$-0.996889\pi$
$479$	−5330.20	−	9232.19i	−0.508441	−	0.880646i	0.491511	−	0.870871i	$-0.336445\pi$
$480$	−430.503	−	217.350i	−0.0409369	−	0.0206680i
$481$	5694.91	−	9863.87i	0.539845	−	0.935039i
$482$	−4574.05	+	7922.49i	−0.432245	+	0.748671i
$483$	−251.177	+	164.440i	−0.0236624	+	0.0154913i
$484$	−5898.84	−	10217.1i	−0.553985	−	0.959531i
$485$	4399.10			0.411862
$486$	2095.81	+	7280.33i	0.195613	+	0.679511i
$487$	−14014.9			−1.30406			−0.652030	−	0.758193i	$-0.726082\pi$
$487$	−14014.9			−1.30406			−0.652030	+	0.758193i	$0.726082\pi$
$488$	1657.82	+	2871.43i	0.153783	+	0.266360i
$489$	−14225.1	+	9312.91i	−1.31551	+	0.861236i
$490$	−142.117	+	246.153i	−0.0131024	+	0.0226940i
$491$	−511.254	+	885.517i	−0.0469910	+	0.0813907i	−0.888564	−	0.458752i	$-0.848297\pi$
$491$	−511.254	+	885.517i	−0.0469910	+	0.0813907i	0.841573	+	0.540143i	$0.181630\pi$
$492$	4104.91	+	2072.47i	0.376146	+	0.189907i
$493$	−2050.98	−	3552.40i	−0.187366	−	0.324527i
$494$	921.021			0.0838840
$495$	2049.18	−	4695.72i	0.186068	−	0.426377i
$496$	3979.59			0.360260
$497$	−510.502	−	884.216i	−0.0460748	−	0.0798038i
$498$	635.330	+	11321.4i	0.0571683	+	1.01872i
$499$	7620.97	−	13199.9i	0.683691	−	1.18419i	−0.290156	−	0.956979i	$-0.593707\pi$
$499$	7620.97	−	13199.9i	0.683691	−	1.18419i	0.973846	−	0.227207i	$-0.0729596\pi$
$500$	1401.37	−	2427.25i	0.125343	−	0.217100i
$501$	−172.586	−	3075.43i	−0.0153903	−	0.274251i
$502$	1514.83	+	2623.77i	0.134682	+	0.233276i
$503$	−11798.5			−1.04586			−0.522930	−	0.852375i	$-0.675161\pi$
$503$	−11798.5			−1.04586			−0.522930	+	0.852375i	$0.675161\pi$
$504$	−1502.51	+	169.167i	−0.132792	+	0.0149510i
$505$	−2111.86			−0.186092
$506$	540.006	+	935.318i	0.0474431	+	0.0821738i
$507$	3001.06	+	1515.16i	0.262884	+	0.132723i
$508$	−3287.40	+	5693.95i	−0.287116	+	0.497300i
$509$	−1784.24	+	3090.40i	−0.155374	+	0.269115i	−0.933195	−	0.359370i	$-0.882991\pi$
$509$	−1784.24	+	3090.40i	−0.155374	+	0.269115i	0.777821	+	0.628485i	$0.216325\pi$
$510$	350.191	−	229.263i	0.0304054	−	0.0199058i
$511$	−2699.90	−	4676.37i	−0.233731	−	0.404835i
$512$	512.000			0.0441942
$513$	274.684	+	1617.88i	0.0236406	+	0.139242i
$514$	−7842.65			−0.673005
$515$	53.9126	+	93.3794i	0.00461296	+	0.00798988i
$516$	−2258.87	+	1478.83i	−0.192715	+	0.126167i
$517$	16960.7	−	29376.7i	1.44280	−	2.49901i
$518$	−2025.10	+	3507.58i	−0.171772	+	0.297518i
$519$	15648.7	+	7900.61i	1.32351	+	0.668205i
$520$	456.747	+	791.110i	0.0385186	+	0.0667162i
$521$	−20499.0			−1.72376			−0.861878	−	0.507116i	$-0.830712\pi$
$521$	−20499.0			−1.72376			−0.861878	+	0.507116i	$0.830712\pi$
$522$	9470.88	+	12834.8i	0.794118	+	1.07618i
$523$	−14517.6			−1.21379			−0.606893	−	0.794783i	$-0.707584\pi$
$523$	−14517.6			−1.21379			−0.606893	+	0.794783i	$0.707584\pi$
$524$	−887.822	−	1537.75i	−0.0740166	−	0.128200i
$525$	−237.602	−	4234.00i	−0.0197520	−	0.351975i
$526$	6500.42	−	11259.1i	0.538844	−	0.933305i
$527$	−1726.99	+	2991.23i	−0.142749	+	0.247249i
$528$	304.762	+	5430.78i	0.0251195	+	0.447622i
$529$	6049.44	+	10477.9i	0.497200	+	0.861176i
$530$	1536.14			0.125897
$531$	−3772.45	−	5112.36i	−0.308305	−	0.417811i
$532$	−327.514			−0.0266909
$533$	−4355.16	−	7543.35i	−0.353926	−	0.613019i
$534$	−7912.73	−	3994.94i	−0.641231	−	0.323742i
$535$	1759.49	−	3047.53i	0.142186	−	0.246273i
$536$	−559.079	+	968.353i	−0.0450532	+	0.0780344i
$537$	2599.02	−	1701.52i	0.208857	−	0.136734i
$538$	2072.23	+	3589.21i	0.166060	+	0.287625i
$539$	3205.82			0.256186
$540$	−1253.46	+	1038.27i	−0.0998894	+	0.0827409i
$541$	18273.3			1.45218			0.726090	−	0.687600i	$-0.241336\pi$
$541$	18273.3			1.45218			0.726090	+	0.687600i	$0.241336\pi$
$542$	−19.3588	−	33.5304i	−0.00153419	−	0.00265729i
$543$	20170.6	−	13205.3i	1.59411	−	1.04363i
$544$	−222.188	+	384.841i	−0.0175115	+	0.0303307i
$545$	−1055.30	+	1827.83i	−0.0829430	+	0.143662i
$546$	2556.66	+	1290.79i	0.200394	+	0.101174i
$547$	4515.88	+	7821.74i	0.352989	+	0.611395i	0.986772	−	0.162116i	$-0.0518319\pi$
$547$	4515.88	+	7821.74i	0.352989	+	0.611395i	−0.633782	+	0.773511i	$0.718499\pi$
$548$	−4734.76			−0.369085
$549$	11120.1	−	1252.00i	0.864467	−	0.0973301i
$550$	−15255.5			−1.18272
$551$	1727.56	+	2992.22i	0.133569	+	0.231348i
$552$	−19.2240	−	342.566i	−0.00148230	−	0.0264141i
$553$	964.862	−	1671.19i	0.0741955	−	0.128510i
$554$	−4334.03	+	7506.77i	−0.332374	+	0.575689i
$555$	244.285	+	4353.09i	0.0186834	+	0.332934i
$556$	1073.91	+	1860.07i	0.0819135	+	0.141878i
$557$	18384.7			1.39854			0.699268	−	0.714859i	$-0.253509\pi$
$557$	18384.7			1.39854			0.699268	+	0.714859i	$0.253509\pi$
$558$	5372.01	−	12310.0i	0.407554	−	0.933915i
$559$	5114.13			0.386949
$560$	−162.419	−	281.318i	−0.0122562	−	0.0212283i
$561$	−4214.26	−	2127.67i	−0.317159	−	0.160126i
$562$	5360.76	−	9285.11i	0.402367	−	0.696919i
$563$	542.778	−	940.120i	0.0406312	−	0.0703753i	−0.844995	−	0.534775i	$-0.820396\pi$
$563$	542.778	−	940.120i	0.0406312	−	0.0703753i	0.885626	+	0.464399i	$0.153730\pi$
$564$	−9016.04	+	5902.61i	−0.673127	+	0.440682i
$565$	−2555.96	−	4427.06i	−0.190319	−	0.329642i
$566$	2762.30			0.205138
$567$	−1504.94	+	4876.04i	−0.111466	+	0.361154i
$568$	1166.86			0.0861980
$569$	6922.59	+	11990.3i	0.510035	+	0.883407i	0.999932	+	0.0116265i	$0.00370093\pi$
$569$	6922.59	+	11990.3i	0.510035	+	0.883407i	−0.489897	+	0.871780i	$0.662966\pi$
$570$	−294.969	+	193.110i	−0.0216753	+	0.0141904i
$571$	−3373.44	+	5842.96i	−0.247240	+	0.428232i	−0.962759	−	0.270361i	$-0.912857\pi$
$571$	−3373.44	+	5842.96i	−0.247240	+	0.428232i	0.715519	+	0.698593i	$0.246190\pi$
$572$	5151.58	−	8922.79i	0.376570	−	0.652239i
$573$	−4783.71	−	2415.18i	−0.348765	−	0.176083i
$574$	1548.69	+	2682.41i	0.112615	+	0.195055i
$575$	962.298			0.0697923
$576$	691.143	−	1583.76i	0.0499959	−	0.114566i
$577$	19670.9			1.41926			0.709629	−	0.704575i	$-0.248863\pi$
$577$	19670.9			1.41926			0.709629	+	0.704575i	$0.248863\pi$
$578$	4720.16	+	8175.55i	0.339676	+	0.588336i
$579$	817.420	+	14566.2i	0.0586715	+	1.04551i
$580$	−1713.44	+	2967.77i	−0.122667	+	0.212465i
$581$	−3818.91	+	6614.54i	−0.272693	+	0.472319i
$582$	883.168	+	15737.8i	0.0629012	+	1.12088i
$583$	−8662.91	−	15004.6i	−0.615405	−	1.06591i
$584$	6171.21			0.437271
$585$	3063.69	−	344.940i	0.216526	−	0.0243786i
$586$	−15233.1			−1.07385
$587$	9440.72	+	16351.8i	0.663816	+	1.14976i	0.979605	+	0.200934i	$0.0643976\pi$
$587$	9440.72	+	16351.8i	0.663816	+	1.14976i	−0.315789	+	0.948830i	$0.602269\pi$
$588$	−909.146	−	459.005i	−0.0637628	−	0.0321923i
$589$	1454.66	−	2519.54i	0.101763	−	0.176258i
$590$	682.498	−	1182.12i	0.0476237	−	0.0824867i
$591$	−17014.0	+	11138.7i	−1.18420	+	0.775270i
$592$	−2314.41	−	4008.67i	−0.160678	−	0.278303i
$593$	−14887.6			−1.03096			−0.515480	−	0.856902i	$-0.672386\pi$
$593$	−14887.6			−1.03096			−0.515480	+	0.856902i	$0.672386\pi$
$594$	17210.4	+	6388.24i	1.18880	+	0.441267i
$595$	281.934			0.0194255
$596$	−2667.90	−	4620.93i	−0.183358	−	0.317585i
$597$	3574.31	−	2340.03i	0.245036	−	0.160420i
$598$	−324.955	+	562.838i	−0.0222214	+	0.0384886i
$599$	−12822.5	+	22209.2i	−0.874647	+	1.51493i	−0.0175095	+	0.999847i	$0.505574\pi$
$599$	−12822.5	+	22209.2i	−0.874647	+	1.51493i	−0.857138	+	0.515087i	$0.827760\pi$
$600$	4326.35	+	2184.27i	0.294371	+	0.148620i
$601$	−11322.3	−	19610.8i	−0.768464	−	1.33102i	−0.938396	−	0.345562i	$-0.887688\pi$
$601$	−11322.3	−	19610.8i	−0.768464	−	1.33102i	0.169932	−	0.985456i	$-0.445645\pi$
$602$	−1818.58			−0.123123
$603$	2240.70	+	3036.56i	0.151324	+	0.205072i
$604$	6072.48			0.409082
$605$	−4277.16	−	7408.25i	−0.287423	−	0.497832i
$606$	−423.979	−	7555.20i	−0.0284208	−	0.506450i
$607$	855.111	−	1481.10i	0.0571794	−	0.0990376i	−0.836019	−	0.548701i	$-0.815123\pi$
$607$	855.111	−	1481.10i	0.0571794	−	0.0990376i	0.893198	+	0.449663i	$0.148456\pi$
$608$	187.151	−	324.155i	0.0124835	−	0.0216221i
$609$	601.986	+	10727.2i	0.0400553	+	0.713775i
$610$	1202.06	+	2082.03i	0.0797871	+	0.138195i
$611$	20412.5			1.35156
$612$	890.494	+	1206.78i	0.0588171	+	0.0797081i
$613$	8644.91			0.569600			0.284800	−	0.958587i	$-0.408073\pi$
$613$	8644.91			0.569600			0.284800	+	0.958587i	$0.408073\pi$
$614$	−1394.89	−	2416.02i	−0.0916829	−	0.158799i
$615$	2976.41	+	1502.72i	0.195155	+	0.0985290i
$616$	−1831.90	+	3172.94i	−0.119820	+	0.207535i
$617$	−10539.3	+	18254.6i	−0.687677	+	1.19109i	0.284910	+	0.958554i	$0.408036\pi$
$617$	−10539.3	+	18254.6i	−0.687677	+	1.19109i	−0.972587	+	0.232538i	$0.925297\pi$
$618$	−323.242	+	211.620i	−0.0210400	+	0.0137744i
$619$	1315.79	+	2279.01i	0.0854376	+	0.147982i	0.905578	−	0.424181i	$-0.139438\pi$
$619$	1315.79	+	2279.01i	0.0854376	+	0.147982i	−0.820140	+	0.572163i	$0.806105\pi$
$620$	2885.54			0.186913
$621$	−1085.61	−	402.961i	−0.0701512	−	0.0260391i
$622$	7027.17			0.452996
$623$	−2985.29	−	5170.68i	−0.191980	−	0.332518i
$624$	−2738.50	+	1792.84i	−0.175686	+	0.115018i
$625$	−6270.64	+	10861.1i	−0.401321	+	0.695108i
$626$	6394.20	−	11075.1i	0.408249	−	0.707108i
$627$	3549.71	+	1792.16i	0.226095	+	0.114150i
$628$	6435.89	+	11147.3i	0.408949	+	0.708320i
$629$	4017.45			0.254668
$630$	−1089.44	+	122.660i	−0.0688961	+	0.00775699i
$631$	11022.1			0.695378			0.347689	−	0.937610i	$-0.386966\pi$
$631$	11022.1			0.695378			0.347689	+	0.937610i	$0.386966\pi$
$632$	1102.70	+	1909.93i	0.0694035	+	0.120210i
$633$	842.430	+	15011.9i	0.0528967	+	0.942604i
$634$	−3301.56	+	5718.47i	−0.206817	+	0.358217i
$635$	−2383.65	+	4128.60i	−0.148964	+	0.258013i
$636$	308.396	+	5495.54i	0.0192275	+	0.342629i
$637$	964.569	+	1670.68i	0.0599963	+	0.103917i
$638$	38651.2			2.39846
$639$	1575.14	−	3609.44i	0.0975139	−	0.223454i
$640$	371.243			0.0229292
$641$	−1810.24	−	3135.44i	−0.111545	−	0.193202i	0.804848	−	0.593481i	$-0.202247\pi$
$641$	−1810.24	−	3135.44i	−0.111545	−	0.193202i	−0.916393	+	0.400279i	$0.868913\pi$
$642$	11255.8	+	5682.76i	0.691947	+	0.349347i
$643$	−2713.80	+	4700.43i	−0.166441	+	0.288285i	−0.937166	−	0.348883i	$-0.886561\pi$
$643$	−2713.80	+	4700.43i	−0.166441	+	0.288285i	0.770725	+	0.637168i	$0.219894\pi$
$644$	115.554	−	200.145i	0.00707058	−	0.0122466i
$645$	−1637.87	+	1072.28i	−0.0999861	+	0.0654588i
$646$	162.433	+	281.341i	0.00989292	+	0.0171350i
$647$	−25639.9			−1.55797			−0.778986	−	0.627041i	$-0.784266\pi$
$647$	−25639.9			−1.55797			−0.778986	+	0.627041i	$0.784266\pi$
$648$	−3966.07	−	4275.81i	−0.240435	−	0.259212i
$649$	−15395.6			−0.931169
$650$	−4590.09	−	7950.27i	−0.276982	−	0.479746i
$651$	7569.07	−	4955.31i	0.455692	−	0.298332i
$652$	6544.27	−	11335.0i	0.393088	−	0.680848i
$653$	−5218.91	+	9039.41i	−0.312759	+	0.541714i	−0.978959	−	0.204059i	$-0.934587\pi$
$653$	−5218.91	+	9039.41i	−0.312759	+	0.541714i	0.666200	+	0.745773i	$0.267920\pi$
$654$	−6750.93	−	3408.37i	−0.403642	−	0.203789i
$655$	−643.746	−	1115.00i	−0.0384019	−	0.0665141i
$656$	−3539.86			−0.210684
$657$	8330.45	−	19089.3i	0.494676	−	1.13355i
$658$	−7258.68			−0.430050
$659$	−3359.50	−	5818.82i	−0.198585	−	0.343959i	0.749485	−	0.662021i	$-0.230301\pi$
$659$	−3359.50	−	5818.82i	−0.198585	−	0.343959i	−0.948070	+	0.318062i	$0.896968\pi$
$660$	220.979	+	3937.78i	0.0130327	+	0.232239i
$661$	−5808.68	+	10060.9i	−0.341803	+	0.592019i	−0.984768	−	0.173876i	$-0.944371\pi$
$661$	−5808.68	+	10060.9i	−0.341803	+	0.592019i	0.642965	+	0.765896i	$0.277704\pi$
$662$	1332.01	−	2307.10i	0.0782023	−	0.135450i
$663$	−159.172	−	2836.40i	−0.00932386	−	0.166149i
$664$	−4364.46	−	7559.47i	−0.255081	−	0.441814i
$665$	−237.476			−0.0138480
$666$	−15524.2	+	1747.86i	−0.903226	+	0.101694i
$667$	−2438.07			−0.141533
$668$	1185.59	+	2053.51i	0.0686707	+	0.118941i
$669$	−21257.0	−	10732.1i	−1.22847	−	0.620222i
$670$	−405.379	+	702.138i	−0.0233749	+	0.0404865i
$671$	13557.9	−	23482.9i	0.780023	−	1.35104i
$672$	973.809	−	637.533i	0.0559010	−	0.0365973i
$673$	16630.2	+	28804.4i	0.952522	+	1.64982i	0.739939	+	0.672673i	$0.234854\pi$
$673$	16630.2	+	28804.4i	0.952522	+	1.64982i	0.212583	+	0.977143i	$0.431813\pi$
$674$	−22553.0			−1.28889
$675$	12596.7	−	10434.1i	0.718289	−	0.594977i
$676$	−2587.96			−0.147244
$677$	6363.46	+	11021.8i	0.361252	+	0.625707i	0.988167	−	0.153381i	$-0.0490161\pi$
$677$	6363.46	+	11021.8i	0.361252	+	0.625707i	−0.626915	+	0.779087i	$0.715683\pi$
$678$	15324.7	−	10032.8i	0.868055	−	0.568298i
$679$	−5308.64	+	9194.83i	−0.300040	+	0.519684i
$680$	−161.105	+	279.042i	−0.00908544	+	0.0157365i
$681$	−12027.6	−	6072.45i	−0.676798	−	0.341698i
$682$	−16272.8	−	28185.3i	−0.913661	−	1.58251i
$683$	−12156.0			−0.681020			−0.340510	−	0.940241i	$-0.610600\pi$
$683$	−12156.0			−0.681020			−0.340510	+	0.940241i	$0.610600\pi$
$684$	−750.072	−	1016.49i	−0.0419294	−	0.0568221i
$685$	−3433.10			−0.191492
$686$	−343.000	−	594.093i	−0.0190901	−	0.0330650i
$687$	−896.580	−	15976.8i	−0.0497913	−	0.887268i
$688$	1039.19	−	1799.93i	0.0575854	−	0.0997408i
$689$	5213.00	−	9029.19i	0.288243	−	0.499252i
$690$	−13.9390	−	248.390i	−0.000769058	−	0.0137044i
$691$	13998.4	+	24245.9i	0.770657	+	1.33482i	0.937204	+	0.348783i	$0.113405\pi$
$691$	13998.4	+	24245.9i	0.770657	+	1.33482i	−0.166547	+	0.986034i	$0.553262\pi$
$692$	−13494.6			−0.741311
$693$	7341.95	+	9949.70i	0.402450	+	0.545394i
$694$	−16917.8			−0.925348
$695$	778.676	+	1348.71i	0.0424991	+	0.0736105i
$696$	−10961.2	−	5534.03i	−0.596958	−	0.301389i
$697$	1536.16	−	2660.71i	0.0834811	−	0.144594i
$698$	6721.93	−	11642.7i	0.364511	−	0.631352i
$699$	12782.3	−	8368.30i	0.691660	−	0.452815i
$700$	1632.23	+	2827.11i	0.0881323	+	0.152650i
$701$	−11244.9			−0.605869			−0.302935	−	0.953011i	$-0.597966\pi$
$701$	−11244.9			−0.605869			−0.302935	+	0.953011i	$0.597966\pi$
$702$	1849.09	+	10891.1i	0.0994153	+	0.585553i
$703$	−3383.93			−0.181547
$704$	−2093.60	−	3626.22i	−0.112082	−	0.194131i
$705$	−6537.39	+	4279.89i	−0.349237	+	0.228639i
$706$	1709.45	−	2960.85i	0.0911274	−	0.157837i
$707$	2548.50	−	4414.13i	0.135567	−	0.234810i
$708$	4366.06	+	2204.32i	0.231761	+	0.117010i
$709$	4156.09	+	7198.56i	0.220148	+	0.381308i	0.954853	−	0.297079i	$-0.0960125\pi$
$709$	4156.09	+	7198.56i	0.220148	+	0.381308i	−0.734705	+	0.678387i	$0.762679\pi$
$710$	846.074			0.0447220
$711$	7396.48	−	832.768i	0.390140	−	0.0439258i
$712$	6823.53			0.359161
$713$	1026.47	+	1777.89i	0.0539150	+	0.0933836i
$714$	56.6014	+	1008.62i	0.00296674	+	0.0528665i
$715$	3735.33	−	6469.78i	0.195375	−	0.338400i
$716$	−1195.68	+	2070.97i	−0.0624086	+	0.108095i
$717$	−1717.31	−	30602.0i	−0.0894480	−	1.59394i
$718$	−2066.56	−	3579.39i	−0.107414	−	0.186047i
$719$	−2599.23			−0.134819			−0.0674096	−	0.997725i	$-0.521473\pi$
$719$	−2599.23			−0.134819			−0.0674096	+	0.997725i	$0.521473\pi$
$720$	501.138	−	1148.36i	0.0259393	−	0.0594402i
$721$	−260.237			−0.0134421
$722$	6722.18	+	11643.2i	0.346501	+	0.600157i
$723$	−21216.7	−	10711.8i	−1.09137	−	0.551004i
$724$	−9279.46	+	16072.5i	−0.476337	+	0.825041i
$725$	17219.2	−	29824.6i	0.882078	−	1.52780i
$726$	25644.4	−	16788.8i	1.31095	−	0.858254i
$727$	17879.9	+	30968.9i	0.912143	+	1.57988i	0.811030	+	0.585004i	$0.198907\pi$
$727$	17879.9	+	30968.9i	0.912143	+	1.57988i	0.101113	+	0.994875i	$0.467760\pi$
$728$	−2204.73			−0.112243
$729$	−18580.1	+	6496.31i	−0.943965	+	0.330046i
$730$	4474.65			0.226869
$731$	901.936	+	1562.20i	0.0456351	+	0.0790424i
$732$	−7207.16	+	4718.38i	−0.363913	+	0.238246i
$733$	−8201.83	+	14206.0i	−0.413290	+	0.715840i	−0.995247	−	0.0973799i	$-0.968954\pi$
$733$	−8201.83	+	14206.0i	−0.413290	+	0.715840i	0.581957	+	0.813219i	$0.302287\pi$
$734$	11876.1	−	20570.0i	0.597213	−	1.03440i
$735$	−659.208	−	332.818i	−0.0330820	−	0.0167023i
$736$	132.061	+	228.737i	0.00661392	+	0.0114556i
$737$	9144.42			0.457041
$738$	−4778.43	+	10949.8i	−0.238342	+	0.546163i
$739$	37710.3			1.87713			0.938563	−	0.345107i	$-0.112157\pi$
$739$	37710.3			1.87713			0.938563	+	0.345107i	$0.112157\pi$
$740$	−1678.14	−	2906.62i	−0.0833644	−	0.144391i
$741$	134.072	+	2389.12i	0.00664677	+	0.118444i
$742$	−1853.74	+	3210.77i	−0.0917156	+	0.158856i
$743$	−11788.5	+	20418.3i	−0.582070	+	1.00817i	0.413164	+	0.910657i	$0.364424\pi$
$743$	−11788.5	+	20418.3i	−0.582070	+	1.00817i	−0.995234	+	0.0975176i	$0.968910\pi$
$744$	579.304	+	10323.0i	0.0285461	+	0.508684i
$745$	−1934.45	−	3350.57i	−0.0951313	−	0.164772i
$746$	5599.48			0.274814
$747$	−29275.2	+	3296.08i	−1.43390	+	0.161442i
$748$	3634.16			0.177644
$749$	4246.55	+	7355.24i	0.207164	+	0.358818i
$750$	6500.28	+	3281.83i	0.316475	+	0.159780i
$751$	−10464.2	+	18124.5i	−0.508448	+	0.880658i	0.491504	+	0.870875i	$0.336447\pi$
$751$	−10464.2	+	18124.5i	−0.508448	+	0.880658i	−0.999952	+	0.00978251i	$0.996886\pi$
$752$	4147.82	−	7184.23i	0.201138	−	0.348380i
$753$	−6585.53	+	4311.41i	−0.318712	+	0.208654i
$754$	11629.4	+	20142.7i	0.561695	+	0.972884i
$755$	4403.06			0.212243
$756$	−657.536	−	3872.87i	−0.0316327	−	0.186316i
$757$	−726.989			−0.0349047			−0.0174523	−	0.999848i	$-0.505556\pi$
$757$	−726.989			−0.0349047			−0.0174523	+	0.999848i	$0.505556\pi$
$758$	−3922.24	−	6793.51i	−0.187945	−	0.325530i
$759$	−2347.60	+	1536.93i	−0.112270	+	0.0735005i
$760$	135.700	−	235.040i	0.00647680	−	0.0112182i
$761$	−4471.05	+	7744.08i	−0.212977	+	0.368887i	−0.952645	−	0.304085i	$-0.901649\pi$
$761$	−4471.05	+	7744.08i	−0.212977	+	0.368887i	0.739668	+	0.672972i	$0.234983\pi$
$762$	−15248.6	−	7698.65i	−0.724934	−	0.366001i
$763$	−2546.97	−	4411.48i	−0.120847	−	0.209314i
$764$	4125.22			0.195347
$765$	645.684	+	875.021i	0.0305160	+	0.0413548i
$766$	−9981.19			−0.470803
$767$	−4632.23	−	8023.25i	−0.218070	−	0.377709i
$768$	74.5312	+	1328.13i	0.00350184	+	0.0624018i
$769$	17450.1	−	30224.5i	0.818293	−	1.41733i	−0.0886459	−	0.996063i	$-0.528254\pi$
$769$	17450.1	−	30224.5i	0.818293	−	1.41733i	0.906939	−	0.421262i	$-0.138413\pi$
$770$	−1328.28	+	2300.65i	−0.0621661	+	0.107675i
$771$	−1141.64	−	20343.8i	−0.0533273	−	0.950277i
$772$	−5615.35	−	9726.08i	−0.261789	−	0.453432i
$773$	9031.51			0.420234			0.210117	−	0.977676i	$-0.432616\pi$
$773$	9031.51			0.420234			0.210117	+	0.977676i	$0.432616\pi$
$774$	−4164.91	−	5644.22i	−0.193417	−	0.262115i
$775$	−28998.3			−1.34406
$776$	−6067.01	−	10508.4i	−0.280661	−	0.486120i
$777$	−9393.45	−	4742.52i	−0.433704	−	0.218966i
$778$	11866.4	−	20553.3i	0.546828	−	0.947134i
$779$	−1293.92	+	2241.14i	−0.0595118	+	0.103077i
$780$	−1985.65	+	1299.96i	−0.0911507	+	0.0596744i
$781$	−4771.37	−	8264.25i	−0.218608	−	0.378640i
$782$	−229.238			−0.0104828
$783$	−31914.7	+	26435.8i	−1.45663	+	1.20656i
$784$	784.000			0.0357143
$785$	4666.56	+	8082.73i	0.212174	+	0.367497i
$786$	3859.68	−	2526.86i	0.175153	−	0.114669i
$787$	5044.79	−	8737.84i	0.228497	−	0.395769i	−0.728866	−	0.684657i	$-0.759952\pi$
$787$	5044.79	−	8737.84i	0.228497	−	0.395769i	0.957363	+	0.288888i	$0.0932854\pi$
$788$	7827.26	−	13557.2i	0.353851	−	0.612888i
$789$	30152.2	+	15223.1i	1.36052	+	0.686890i
$790$	799.550	+	1384.86i	0.0360085	+	0.0623686i
$791$	12337.7			0.554587
$792$	−14043.1	+	1581.10i	−0.630048	+	0.0709370i
$793$	16317.2			0.730694
$794$	10596.6	+	18353.9i	0.473628	+	0.820349i
$795$	223.613	+	3984.73i	0.00997579	+	0.177766i
$796$	−1644.36	+	2848.11i	−0.0732195	+	0.126820i
$797$	5139.21	−	8901.37i	0.228407	−	0.395612i	−0.728929	−	0.684589i	$-0.759982\pi$
$797$	5139.21	−	8901.37i	0.228407	−	0.395612i	0.957336	+	0.288977i	$0.0933151\pi$
$798$	−47.6759	−	849.571i	−0.00211492	−	0.0376873i
$799$	3599.98	+	6235.36i	0.159397	+	0.276084i
$800$	−3730.82			−0.164880
$801$	9211.01	−	21107.1i	0.406311	−	0.931066i
$802$	15714.7			0.691902
$803$	−25234.4	−	43707.3i	−1.10897	−	1.92079i
$804$	−2593.29	−	1309.29i	−0.113754	−	0.0574315i
$805$	83.7862	−	145.122i	0.00366842	−	0.00635388i
$806$	9792.33	−	16960.8i	0.427940	−	0.741214i
$807$	−9008.75	+	5897.84i	−0.392965	+	0.257266i
$808$	2912.57	+	5044.72i	0.126812	+	0.219644i
$809$	−20199.7			−0.877855			−0.438927	−	0.898523i	$-0.644641\pi$
$809$	−20199.7			−0.877855			−0.438927	+	0.898523i	$0.644641\pi$
$810$	−2875.73	−	3100.32i	−0.124744	−	0.134487i
$811$	−34950.3			−1.51328			−0.756640	−	0.653832i	$-0.773160\pi$
$811$	−34950.3			−1.51328			−0.756640	+	0.653832i	$0.773160\pi$
$812$	−4135.41	−	7162.73i	−0.178725	−	0.309560i
$813$	84.1596	−	55.0976i	0.00363051	−	0.00237682i
$814$	−18927.5	+	32783.3i	−0.814997	+	1.41162i
$815$	4745.15	−	8218.84i	0.203945	−	0.353243i
$816$	−1030.62	−	520.334i	−0.0442143	−	0.0223227i
$817$	−759.709	−	1315.85i	−0.0325322	−	0.0563475i
$818$	−9295.88			−0.397339
$819$	−2976.14	+	6819.86i	−0.126978	+	0.290971i
$820$	−2566.70			−0.109309
$821$	13336.1	+	23098.9i	0.566911	+	0.981919i	0.996869	+	0.0790701i	$0.0251951\pi$
$821$	13336.1	+	23098.9i	0.566911	+	0.981919i	−0.429958	+	0.902849i	$0.641472\pi$
$822$	−689.233	−	12281.9i	−0.0292454	−	0.521146i
$823$	−3813.26	+	6604.75i	−0.161509	+	0.279741i	−0.935410	−	0.353565i	$-0.884969\pi$
$823$	−3813.26	+	6604.75i	−0.161509	+	0.279741i	0.773901	+	0.633306i	$0.218303\pi$
$824$	148.707	−	257.568i	0.00628696	−	0.0108893i
$825$	−2220.73	−	39572.7i	−0.0937161	−	1.67000i
$826$	1647.22	+	2853.06i	0.0693874	+	0.120182i
$827$	−26226.5			−1.10276			−0.551381	−	0.834253i	$-0.685899\pi$
$827$	−26226.5			−1.10276			−0.551381	+	0.834253i	$0.685899\pi$
$828$	885.817	−	99.7339i	0.0371791	−	0.00418598i
$829$	36002.3			1.50834			0.754169	−	0.656680i	$-0.228040\pi$
$829$	36002.3			1.50834			0.754169	+	0.656680i	$0.228040\pi$
$830$	−3164.61	−	5481.26i	−0.132343	−	0.229226i
$831$	−20103.4	−	10149.7i	−0.839205	−	0.423694i
$832$	1259.85	−	2182.12i	0.0524967	−	0.0909270i
$833$	−340.225	+	589.288i	−0.0141514	+	0.0245109i
$834$	−4668.67	+	3056.48i	−0.193841	+	0.126903i
$835$	859.657	+	1488.97i	0.0356283	+	0.0617101i
$836$	−3061.09			−0.126639
$837$	32714.1	+	12143.0i	1.35097	+	0.501462i
$838$	15474.6			0.637903
$839$	−4297.00	−	7442.63i	−0.176816	−	0.306255i	0.763972	−	0.645249i	$-0.223247\pi$
$839$	−4297.00	−	7442.63i	−0.176816	−	0.306255i	−0.940788	+	0.338994i	$0.889913\pi$
$840$	706.094	−	462.265i	0.0290031	−	0.0189877i
$841$	−31432.0	+	54441.8i	−1.28878	+	2.23223i
$842$	2171.16	−	3760.55i	0.0888634	−	0.153916i
$843$	24865.9	+	12554.2i	1.01593	+	0.512916i
$844$	−5787.16	−	10023.7i	−0.236022	−	0.408802i
$845$	−1876.49			−0.0763944
$846$	−16623.8	−	22528.3i	−0.675577	−	0.915531i
$847$	20645.9			0.837547
$848$	−2118.56	−	3669.45i	−0.0857921	−	0.148596i
$849$	402.105	+	7165.40i	0.0162547	+	0.289654i
$850$	1619.03	−	2804.24i	0.0653321	−	0.113158i
$851$	1193.92	−	2067.93i	0.0480929	−	0.0832993i
$852$	169.859	+	3026.84i	0.00683012	+	0.121711i
$853$	−1721.51	−	2981.74i	−0.0691011	−	0.119687i	0.829405	−	0.558648i	$-0.188680\pi$
$853$	−1721.51	−	2981.74i	−0.0691011	−	0.119687i	−0.898506	+	0.438962i	$0.855346\pi$
$854$	−5802.38			−0.232498
$855$	−543.866	−	737.038i	−0.0217542	−	0.0294809i
$856$	−9706.40			−0.387568
$857$	−434.979	−	753.406i	−0.0173379	−	0.0300302i	0.857226	−	0.514940i	$-0.172186\pi$
$857$	−434.979	−	753.406i	−0.0173379	−	0.0300302i	−0.874564	+	0.484910i	$0.838852\pi$
$858$	23895.6	+	12064.3i	0.950795	+	0.480033i
$859$	24437.8	−	42327.6i	0.970673	−	1.68126i	0.277141	−	0.960829i	$-0.410613\pi$
$859$	24437.8	−	42327.6i	0.970673	−	1.68126i	0.693532	−	0.720426i	$-0.256054\pi$
$860$	753.501	−	1305.10i	0.0298769	−	0.0517483i
$861$	−6732.72	+	4407.77i	−0.266493	+	0.174467i
$862$	−4714.95	−	8166.53i	−0.186301	−	0.322683i
$863$	2645.88			0.104365			0.0521823	−	0.998638i	$-0.483382\pi$
$863$	2645.88			0.104365			0.0521823	+	0.998638i	$0.483382\pi$
$864$	4208.88	+	1562.28i	0.165728	+	0.0615159i
$865$	−9784.72			−0.384613
$866$	6862.68	+	11886.5i	0.269288	+	0.466420i
$867$	−20520.2	+	13434.2i	−0.803811	+	0.526238i
$868$	−3482.14	+	6031.25i	−0.136166	+	0.235846i
$869$	9018.00	−	15619.6i	0.352031	−	0.609735i
$870$	−7947.79	−	4012.64i	−0.309719	−	0.156369i
$871$	2751.38	+	4765.52i	0.107034	+	0.185389i
$872$	5821.65			0.226085
$873$	−40695.2	+	4581.87i	−1.57769	+	0.177632i
$874$	193.089			0.00747293
$875$	2452.41	+	4247.69i	0.0947502	+	0.164112i
$876$	898.335	+	16008.1i	0.0346483	+	0.617424i
$877$	3796.16	−	6575.13i	0.146165	−	0.253166i	−0.783642	−	0.621213i	$-0.786640\pi$
$877$	3796.16	−	6575.13i	0.146165	−	0.253166i	0.929807	+	0.368047i	$0.119973\pi$
$878$	−500.020	+	866.061i	−0.0192197	+	0.0332895i
$879$	−2217.47	−	39514.6i	−0.0850890	−	1.51626i
$880$	−1518.04	−	2629.31i	−0.0581511	−	0.100721i
$881$	23336.2			0.892413			0.446206	−	0.894930i	$-0.352775\pi$
$881$	23336.2			0.892413			0.446206	+	0.894930i	$0.352775\pi$
$882$	1058.31	−	2425.14i	0.0404028	−	0.0925835i
$883$	−36313.8			−1.38398			−0.691992	−	0.721905i	$-0.743267\pi$
$883$	−36313.8			−1.38398			−0.691992	+	0.721905i	$0.743267\pi$
$884$	1093.45	+	1893.91i	0.0416025	+	0.0720577i
$885$	3165.77	+	1598.32i	0.120244	+	0.0607083i
$886$	1752.34	−	3035.15i	0.0664460	−	0.115088i
$887$	−5517.46	+	9556.53i	−0.208859	+	0.361755i	−0.951356	−	0.308095i	$-0.900308\pi$
$887$	−5517.46	+	9556.53i	−0.208859	+	0.361755i	0.742496	+	0.669850i	$0.233642\pi$
$888$	10061.6	−	6587.09i	0.380230	−	0.248928i
$889$	−5752.96	−	9964.41i	−0.217039	−	0.375923i
$890$	4947.64			0.186343
$891$	−14065.8	+	45573.5i	−0.528867	+	1.71355i
$892$	18330.9			0.688078
$893$	−3032.30	−	5252.10i	−0.113631	−	0.196814i
$894$	11598.3	−	7593.17i	0.433899	−	0.284065i
$895$	−866.967	+	1501.63i	−0.0323794	+	0.0560827i
$896$	−448.000	+	775.959i	−0.0167038	+	0.0289319i
$897$	−1507.30	−	760.999i	−0.0561063	−	0.0283267i
$898$	11846.4	+	20518.6i	0.440222	+	0.762488i
$899$	73469.8			2.72564
$900$	−5036.19	+	11540.5i	−0.186526	+	0.427425i
$901$	3677.49			0.135977
$902$	14474.7	+	25070.9i	0.534318	+	0.925466i
$903$	−264.729	−	4717.39i	−0.00975595	−	0.173848i
$904$	−7050.11	+	12211.2i	−0.259384	+	0.449267i
$905$	−6728.39	+	11653.9i	−0.247137	+	0.428055i
$906$	883.963	+	15752.0i	0.0324147	+	0.577621i
$907$	−17128.1	−	29666.8i	−0.627045	−	1.08607i	−0.988142	−	0.153545i	$-0.950931\pi$
$907$	−17128.1	−	29666.8i	−0.627045	−	1.08607i	0.361097	−	0.932528i	$-0.382402\pi$
$908$	10372.0			0.379082
$909$	19536.4	−	2199.60i	0.712852	−	0.0802598i
$910$	−1598.62			−0.0582347
$911$	−7494.50	−	12980.9i	−0.272562	−	0.472091i	0.696955	−	0.717115i	$-0.254538\pi$
$911$	−7494.50	−	12980.9i	−0.272562	−	0.472091i	−0.969517	+	0.245024i	$0.921204\pi$
$912$	868.100	+	438.282i	0.0315194	+	0.0159133i
$913$	−35693.1	+	61822.2i	−1.29383	+	2.24098i
$914$	−12807.2	+	22182.7i	−0.463483	+	0.802776i
$915$	−5225.80	+	3421.22i	−0.188808	+	0.123609i
$916$	6159.15	+	10668.0i	0.222166	+	0.384803i
$917$	3107.38			0.111903
$918$	−3000.76	+	2485.61i	−0.107887	+	0.0893652i
$919$	25897.1			0.929561			0.464780	−	0.885426i	$-0.346133\pi$
$919$	25897.1			0.929561			0.464780	+	0.885426i	$0.346133\pi$
$920$	95.7556	+	165.854i	0.00343149	+	0.00594351i
$921$	6064.10	−	3970.04i	0.216959	−	0.142038i
$922$	10740.2	−	18602.6i	0.383633	−	0.664472i
$923$	2871.22	−	4973.10i	0.102392	−	0.177347i
$924$	−8497.25	−	4290.05i	−0.302532	−	0.152741i
$925$	16864.5	+	29210.2i	0.599461	+	1.03830i
$926$	6474.62			0.229772
$927$	−595.994	−	807.683i	−0.0211165	−	0.0286168i
$928$	9452.36			0.334363
$929$	24384.4	+	42235.0i	0.861168	+	1.49159i	0.870802	+	0.491633i	$0.163600\pi$
$929$	24384.4	+	42235.0i	0.861168	+	1.49159i	−0.00963402	+	0.999954i	$0.503067\pi$
$930$	420.045	+	7485.08i	0.0148106	+	0.263920i
$931$	286.575	−	496.363i	0.0100882	−	0.0174733i
$932$	−5880.48	+	10185.3i	−0.206675	+	0.357972i
$933$	1022.94	+	18228.4i	0.0358943	+	0.639627i
$934$	−13705.1	−	23737.8i	−0.480132	−	0.831612i
$935$	2635.07			0.0921669
$936$	−5049.26	−	6842.68i	−0.176325	−	0.238953i
$937$	30690.4			1.07002			0.535011	−	0.844845i	$-0.320307\pi$
$937$	30690.4			1.07002			0.535011	+	0.844845i	$0.320307\pi$
$938$	−978.388	−	1694.62i	−0.0340570	−	0.0589885i
$939$	29659.5	+	14974.3i	1.03078	+	0.520415i
$940$	3007.52	−	5209.18i	0.104356	−	0.180750i
$941$	−4042.95	+	7002.60i	−0.140060	+	0.242591i	−0.927519	−	0.373776i	$-0.878063\pi$
$941$	−4042.95	+	7002.60i	−0.140060	+	0.242591i	0.787459	+	0.616367i	$0.211396\pi$
$942$	−27979.1	+	18317.4i	−0.967738	+	0.633558i
$943$	−913.045	−	1581.44i	−0.0315301	−	0.0546116i
$944$	−3765.07			−0.129812
$945$	−476.769	−	2808.16i	−0.0164120	−	0.0966660i
$946$	−16997.2			−0.584173
$947$	−15361.7	−	26607.3i	−0.527127	−	0.913010i	−0.999500	−	0.0316119i	$-0.989936\pi$
$947$	−15361.7	−	26607.3i	−0.527127	−	0.913010i	0.472373	−	0.881399i	$-0.343397\pi$
$948$	−4793.83	+	3138.42i	−0.164237	+	0.107522i
$949$	15185.1	−	26301.4i	0.519419	−	0.899661i
$950$	−1363.72	+	2362.04i	−0.0465737	+	0.0806681i
$951$	−15314.3	−	7731.80i	−0.522187	−	0.263639i
$952$	−388.829	−	673.472i	−0.0132374	−	0.0229279i
$953$	17357.3			0.589988			0.294994	−	0.955499i	$-0.404682\pi$
$953$	17357.3			0.589988			0.294994	+	0.955499i	$0.404682\pi$
$954$	−14210.5	+	1599.96i	−0.482266	+	0.0542982i
$955$	2991.14			0.101352
$956$	11797.3	+	20433.4i	0.399111	+	0.691281i
$957$	5626.41	+	100261.i	0.190048	+	3.38660i
$958$	−10660.4	+	18464.4i	−0.359522	+	0.622711i
$959$	4142.91	−	7175.74i	0.139501	−	0.241623i
$960$	54.0415	+	963.004i	0.00181685	+	0.0323758i
$961$	−16036.4	−	27775.9i	−0.538298	−	0.932360i
$962$	−22779.6			−0.763456
$963$	−13102.6	+	30024.7i	−0.438447	+	1.00471i
$964$	18296.2			0.611287
$965$	−4071.61	−	7052.23i	−0.135824	−	0.235253i
$966$	535.995	+	270.611i	0.0178524	+	0.00901321i
$967$	−1569.05	+	2717.68i	−0.0521792	+	0.0903771i	−0.890935	−	0.454130i	$-0.849950\pi$
$967$	−1569.05	+	2717.68i	−0.0521792	+	0.0903771i	0.838756	+	0.544507i	$0.183283\pi$
$968$	−11797.7	+	20434.2i	−0.391727	+	0.678491i
$969$	−706.153	+	462.304i	−0.0234106	+	0.0153265i
$970$	−4399.10	−	7619.47i	−0.145615	−	0.252213i
$971$	31486.5			1.04063			0.520313	−	0.853975i	$-0.325815\pi$
$971$	31486.5			1.04063			0.520313	+	0.853975i	$0.325815\pi$
$972$	10514.1	−	10910.4i	0.346954	−	0.360031i
$973$	−3758.68			−0.123842
$974$	14014.9	+	24274.6i	0.461055	+	0.798570i
$975$	19954.8	−	13064.0i	0.655451	−	0.429110i
$976$	3315.65	−	5742.87i	0.108741	−	0.188345i
$977$	12956.9	−	22441.9i	0.424285	−	0.734883i	−0.572068	−	0.820206i	$-0.693859\pi$
$977$	12956.9	−	22441.9i	0.424285	−	0.734883i	0.996353	+	0.0853227i	$0.0271921\pi$
$978$	30355.6	+	15325.8i	0.992499	+	0.501088i
$979$	−27901.8	−	48327.3i	−0.910873	−	1.57768i
$980$	568.466			0.0185296
$981$	7858.58	−	18008.0i	0.255765	−	0.586088i
$982$	2045.01			0.0664552
$983$	−8185.26	−	14177.3i	−0.265584	−	0.460005i	0.702132	−	0.712047i	$-0.252232\pi$
$983$	−8185.26	−	14177.3i	−0.265584	−	0.460005i	−0.967717	+	0.252041i	$0.918898\pi$
$984$	−515.294	−	9182.39i	−0.0166941	−	0.297484i
$985$	5675.43	−	9830.13i	0.183588	−	0.317984i
$986$	−4101.96	+	7104.79i	−0.132488	+	0.229475i
$987$	−1056.64	−	18829.0i	−0.0340761	−	0.607227i
$988$	−921.021	−	1595.26i	−0.0296575	−	0.0513682i
$989$	1072.16			0.0344720
$990$	−10182.4	+	1146.43i	−0.326887	+	0.0368041i
$991$	37103.8			1.18935			0.594673	−	0.803967i	$-0.297281\pi$
$991$	37103.8			1.18935			0.594673	+	0.803967i	$0.297281\pi$
$992$	−3979.59	−	6892.86i	−0.127371	−	0.220613i
$993$	6178.51	+	3119.38i	0.197451	+	0.0996883i
$994$	−1021.00	+	1768.43i	−0.0325798	+	0.0564298i
$995$	−1192.30	+	2065.12i	−0.0379884	+	0.0657978i
$996$	18973.9	−	12421.8i	0.603626	−	0.395181i
$997$	3917.45	+	6785.23i	0.124440	+	0.215537i	0.921514	−	0.388345i	$-0.126953\pi$
$997$	3917.45	+	6785.23i	0.124440	+	0.215537i	−0.797074	+	0.603882i	$0.793620\pi$
$998$	−30483.9			−0.966885
$999$	−6793.77	−	40015.1i	−0.215161	−	1.26729i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.4.f.d.85.6	yes	12
3.2	odd	2		378.4.f.d.253.3		12
9.2	odd	6		378.4.f.d.127.3		12
9.4	even	3		1134.4.a.t.1.3		6
9.5	odd	6		1134.4.a.s.1.4		6
9.7	even	3	inner	126.4.f.d.43.6	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.4.f.d.43.6	✓	12	9.7	even	3	inner
126.4.f.d.85.6	yes	12	1.1	even	1	trivial
378.4.f.d.127.3		12	9.2	odd	6
378.4.f.d.253.3		12	3.2	odd	2
1134.4.a.s.1.4		6	9.5	odd	6
1134.4.a.t.1.3		6	9.4	even	3

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	126.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(4.34736 - 2.84613i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-1.45017 + 2.51177i) q^{5} +(-9.27700 - 4.68372i) q^{6} +(-3.50000 - 6.06218i) q^{7} +8.00000 q^{8} +(10.7991 - 24.7463i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(4.34736 - 2.84613i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-1.45017 + 2.51177i) q^{5} +(-9.27700 - 4.68372i) q^{6} +(-3.50000 - 6.06218i) q^{7} +8.00000 q^{8} +(10.7991 - 24.7463i) q^{9} +5.80068 q^{10} +(-32.7125 - 56.6596i) q^{11} +(1.16455 + 20.7520i) q^{12} +(19.6851 - 34.0956i) q^{13} +(-7.00000 + 12.1244i) q^{14} +(0.844398 + 15.0469i) q^{15} +(-8.00000 - 13.8564i) q^{16} +13.8868 q^{17} +(-53.6610 + 6.04167i) q^{18} -11.6969 q^{19} +(-5.80068 - 10.0471i) q^{20} +(-32.4695 - 16.3930i) q^{21} +(-65.4249 + 113.319i) q^{22} +(4.12692 - 7.14803i) q^{23} +(34.7789 - 22.7690i) q^{24} +(58.2940 + 100.968i) q^{25} -78.7403 q^{26} +(-23.4834 - 138.317i) q^{27} +28.0000 q^{28} +(-147.693 - 255.812i) q^{29} +(25.2177 - 16.5095i) q^{30} +(-124.362 + 215.402i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(-303.473 - 153.216i) q^{33} +(-13.8868 - 24.0526i) q^{34} +20.3024 q^{35} +(64.1254 + 86.9018i) q^{36} +289.301 q^{37} +(11.6969 + 20.2597i) q^{38} +(-11.4621 - 204.252i) q^{39} +(-11.6014 + 20.0941i) q^{40} +(110.621 - 191.601i) q^{41} +(4.07593 + 72.6319i) q^{42} +(64.9493 + 112.496i) q^{43} +261.700 q^{44} +(46.4964 + 63.0112i) q^{45} -16.5077 q^{46} +(259.239 + 449.015i) q^{47} +(-74.2160 - 37.4698i) q^{48} +(-24.5000 + 42.4352i) q^{49} +(116.588 - 201.936i) q^{50} +(60.3707 - 39.5235i) q^{51} +(78.7403 + 136.382i) q^{52} +264.820 q^{53} +(-216.088 + 178.991i) q^{54} +189.754 q^{55} +(-28.0000 - 48.4974i) q^{56} +(-50.8508 + 33.2910i) q^{57} +(-295.386 + 511.624i) q^{58} +(117.658 - 203.790i) q^{59} +(-53.8129 - 27.1688i) q^{60} +(207.228 + 358.929i) q^{61} +497.449 q^{62} +(-187.813 + 21.1459i) q^{63} +64.0000 q^{64} +(57.0934 + 98.8887i) q^{65} +(38.0953 + 678.847i) q^{66} +(-69.8848 + 121.044i) q^{67} +(-27.7735 + 48.1051i) q^{68} +(-2.40300 - 42.8208i) q^{69} +(-20.3024 - 35.1647i) q^{70} +145.858 q^{71} +(86.3929 - 197.970i) q^{72} +771.401 q^{73} +(-289.301 - 501.084i) q^{74} +(540.794 + 273.033i) q^{75} +(23.3939 - 40.5194i) q^{76} +(-228.987 + 396.617i) q^{77} +(-342.313 + 224.105i) q^{78} +(137.837 + 238.741i) q^{79} +46.4054 q^{80} +(-495.758 - 534.476i) q^{81} -442.483 q^{82} +(-545.558 - 944.934i) q^{83} +(121.726 - 79.6916i) q^{84} +(-20.1381 + 34.8803i) q^{85} +(129.899 - 224.991i) q^{86} +(-1370.15 - 691.754i) q^{87} +(-261.700 - 453.277i) q^{88} +852.941 q^{89} +(62.6422 - 143.545i) q^{90} -275.591 q^{91} +(16.5077 + 28.5921i) q^{92} +(72.4131 + 1290.38i) q^{93} +(518.477 - 898.029i) q^{94} +(16.9626 - 29.3800i) q^{95} +(9.31640 + 166.016i) q^{96} +(-758.377 - 1313.55i) q^{97} +98.0000 q^{98} +(-1755.38 + 197.638i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} - 7 q^{3} - 24 q^{4} - 9 q^{5} + 22 q^{6} - 42 q^{7} + 96 q^{8} + 11 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 - 7 * q^3 - 24 * q^4 - 9 * q^5 + 22 * q^6 - 42 * q^7 + 96 * q^8 + 11 * q^9	\( 12 q - 12 q^{2} - 7 q^{3} - 24 q^{4} - 9 q^{5} + 22 q^{6} - 42 q^{7} + 96 q^{8} + 11 q^{9} + 36 q^{10} - 39 q^{11} - 16 q^{12} - 21 q^{13} - 84 q^{14} - 45 q^{15} - 96 q^{16} + 174 q^{17} - 32 q^{18} + 192 q^{19} - 36 q^{20} + 77 q^{21} - 78 q^{22} - 168 q^{23} - 56 q^{24} - 309 q^{25} + 84 q^{26} + 83 q^{27} + 336 q^{28} - 117 q^{29} + 186 q^{30} - 129 q^{31} - 192 q^{32} - 693 q^{33} - 174 q^{34} + 126 q^{35} + 20 q^{36} + 942 q^{37} - 192 q^{38} + 814 q^{39} - 72 q^{40} - 255 q^{41} - 56 q^{42} - 942 q^{43} + 312 q^{44} + 537 q^{45} + 672 q^{46} - 81 q^{47} + 176 q^{48} - 294 q^{49} - 618 q^{50} - 1452 q^{51} - 84 q^{52} + 180 q^{53} - 200 q^{54} + 1392 q^{55} - 336 q^{56} + 2602 q^{57} - 234 q^{58} - 444 q^{59} - 192 q^{60} - 978 q^{61} + 516 q^{62} - 112 q^{63} + 768 q^{64} - 747 q^{65} + 1146 q^{66} - 663 q^{67} - 348 q^{68} - 2127 q^{69} - 126 q^{70} + 1014 q^{71} + 88 q^{72} + 288 q^{73} - 942 q^{74} + 5954 q^{75} - 384 q^{76} - 273 q^{77} + 32 q^{78} - 609 q^{79} + 288 q^{80} - 1477 q^{81} + 1020 q^{82} - 516 q^{83} - 196 q^{84} - 1563 q^{85} - 1884 q^{86} - 2379 q^{87} - 312 q^{88} + 756 q^{89} - 486 q^{90} + 294 q^{91} - 672 q^{92} + 5953 q^{93} - 162 q^{94} - 846 q^{95} - 128 q^{96} - 2292 q^{97} + 1176 q^{98} - 7638 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 7 * q^3 - 24 * q^4 - 9 * q^5 + 22 * q^6 - 42 * q^7 + 96 * q^8 + 11 * q^9 + 36 * q^10 - 39 * q^11 - 16 * q^12 - 21 * q^13 - 84 * q^14 - 45 * q^15 - 96 * q^16 + 174 * q^17 - 32 * q^18 + 192 * q^19 - 36 * q^20 + 77 * q^21 - 78 * q^22 - 168 * q^23 - 56 * q^24 - 309 * q^25 + 84 * q^26 + 83 * q^27 + 336 * q^28 - 117 * q^29 + 186 * q^30 - 129 * q^31 - 192 * q^32 - 693 * q^33 - 174 * q^34 + 126 * q^35 + 20 * q^36 + 942 * q^37 - 192 * q^38 + 814 * q^39 - 72 * q^40 - 255 * q^41 - 56 * q^42 - 942 * q^43 + 312 * q^44 + 537 * q^45 + 672 * q^46 - 81 * q^47 + 176 * q^48 - 294 * q^49 - 618 * q^50 - 1452 * q^51 - 84 * q^52 + 180 * q^53 - 200 * q^54 + 1392 * q^55 - 336 * q^56 + 2602 * q^57 - 234 * q^58 - 444 * q^59 - 192 * q^60 - 978 * q^61 + 516 * q^62 - 112 * q^63 + 768 * q^64 - 747 * q^65 + 1146 * q^66 - 663 * q^67 - 348 * q^68 - 2127 * q^69 - 126 * q^70 + 1014 * q^71 + 88 * q^72 + 288 * q^73 - 942 * q^74 + 5954 * q^75 - 384 * q^76 - 273 * q^77 + 32 * q^78 - 609 * q^79 + 288 * q^80 - 1477 * q^81 + 1020 * q^82 - 516 * q^83 - 196 * q^84 - 1563 * q^85 - 1884 * q^86 - 2379 * q^87 - 312 * q^88 + 756 * q^89 - 486 * q^90 + 294 * q^91 - 672 * q^92 + 5953 * q^93 - 162 * q^94 - 846 * q^95 - 128 * q^96 - 2292 * q^97 + 1176 * q^98 - 7638 * q^99

Introduction

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