LMFDB - Embedded newform 190.4.e.d.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [190,4,Mod(11,190)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(190, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("190.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 190 = 2 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	190.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.2103629011$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 35x^{6} + 307x^{5} + 1306x^{4} + 5584x^{3} + 49561x^{2} + 188916x + 348537 $ x^8 - 3x^7 + 35x^6 + 307x^5 + 1306x^4 + 5584x^3 + 49561x^2 + 188916*x + 348537
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.1
Root			$-3.30180 + 2.02322i$ of defining polynomial
Character	$\chi$	$=$	190.11
Dual form			190.4.e.d.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(-3.30180 + 5.71889i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(2.50000 - 4.33013i) q^{5} +(6.60360 + 11.4378i) q^{6} -3.99135 q^{7} -8.00000 q^{8} +(-8.30378 - 14.3826i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(-3.30180 + 5.71889i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(2.50000 - 4.33013i) q^{5} +(6.60360 + 11.4378i) q^{6} -3.99135 q^{7} -8.00000 q^{8} +(-8.30378 - 14.3826i) q^{9} +(-5.00000 - 8.66025i) q^{10} -17.5478 q^{11} +26.4144 q^{12} +(-16.1707 - 28.0084i) q^{13} +(-3.99135 + 6.91323i) q^{14} +(16.5090 + 28.5944i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(37.9685 - 65.7634i) q^{17} -33.2151 q^{18} +(-11.4274 - 82.0269i) q^{19} -20.0000 q^{20} +(13.1787 - 22.8261i) q^{21} +(-17.5478 + 30.3937i) q^{22} +(-41.4559 - 71.8038i) q^{23} +(26.4144 - 45.7511i) q^{24} +(-12.5000 - 21.6506i) q^{25} -64.6827 q^{26} -68.6275 q^{27} +(7.98271 + 13.8265i) q^{28} +(-143.135 - 247.916i) q^{29} +66.0360 q^{30} -192.152 q^{31} +(16.0000 + 27.7128i) q^{32} +(57.9394 - 100.354i) q^{33} +(-75.9371 - 131.527i) q^{34} +(-9.97839 + 17.2831i) q^{35} +(-33.2151 + 57.5303i) q^{36} +327.538 q^{37} +(-153.502 - 62.2341i) q^{38} +213.569 q^{39} +(-20.0000 + 34.6410i) q^{40} +(6.74998 - 11.6913i) q^{41} +(-26.3573 - 45.6522i) q^{42} +(22.6461 - 39.2242i) q^{43} +(35.0956 + 60.7874i) q^{44} -83.0378 q^{45} -165.824 q^{46} +(283.331 + 490.744i) q^{47} +(-52.8288 - 91.5022i) q^{48} -327.069 q^{49} -50.0000 q^{50} +(250.729 + 434.275i) q^{51} +(-64.6827 + 112.034i) q^{52} +(-77.1559 - 133.638i) q^{53} +(-68.6275 + 118.866i) q^{54} +(-43.8695 + 75.9843i) q^{55} +31.9308 q^{56} +(506.834 + 205.485i) q^{57} -572.539 q^{58} +(-95.1709 + 164.841i) q^{59} +(66.0360 - 114.378i) q^{60} +(76.9613 + 133.301i) q^{61} +(-192.152 + 332.818i) q^{62} +(33.1433 + 57.4060i) q^{63} +64.0000 q^{64} -161.707 q^{65} +(-115.879 - 200.708i) q^{66} +(-67.5615 - 117.020i) q^{67} -303.748 q^{68} +547.517 q^{69} +(19.9568 + 34.5661i) q^{70} +(-33.6555 + 58.2931i) q^{71} +(66.4303 + 115.061i) q^{72} +(-116.745 + 202.208i) q^{73} +(327.538 - 567.312i) q^{74} +165.090 q^{75} +(-261.295 + 203.639i) q^{76} +70.0396 q^{77} +(213.569 - 369.913i) q^{78} +(-369.439 + 639.887i) q^{79} +(40.0000 + 69.2820i) q^{80} +(450.797 - 780.802i) q^{81} +(-13.5000 - 23.3826i) q^{82} +986.821 q^{83} -105.429 q^{84} +(-189.843 - 328.817i) q^{85} +(-45.2923 - 78.4485i) q^{86} +1890.41 q^{87} +140.383 q^{88} +(-127.042 - 220.042i) q^{89} +(-83.0378 + 143.826i) q^{90} +(64.5429 + 111.792i) q^{91} +(-165.824 + 287.215i) q^{92} +(634.449 - 1098.90i) q^{93} +1133.32 q^{94} +(-383.755 - 155.585i) q^{95} -211.315 q^{96} +(435.454 - 754.228i) q^{97} +(-327.069 + 566.500i) q^{98} +(145.713 + 252.383i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 3 q^{3} - 16 q^{4} + 20 q^{5} - 6 q^{6} - 82 q^{7} - 64 q^{8} - 73 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 3 * q^3 - 16 * q^4 + 20 * q^5 - 6 * q^6 - 82 * q^7 - 64 * q^8 - 73 * q^9	\( 8 q + 8 q^{2} + 3 q^{3} - 16 q^{4} + 20 q^{5} - 6 q^{6} - 82 q^{7} - 64 q^{8} - 73 q^{9} - 40 q^{10} + 20 q^{11} - 24 q^{12} - 11 q^{13} - 82 q^{14} - 15 q^{15} - 64 q^{16} - 81 q^{17} - 292 q^{18} + 219 q^{19} - 160 q^{20} + 84 q^{21} + 20 q^{22} + 75 q^{23} - 24 q^{24} - 100 q^{25} - 44 q^{26} - 828 q^{27} + 164 q^{28} - 28 q^{29} - 60 q^{30} - 370 q^{31} + 128 q^{32} - 367 q^{33} + 162 q^{34} - 205 q^{35} - 292 q^{36} + 678 q^{37} - 198 q^{38} + 766 q^{39} - 160 q^{40} - 5 q^{41} - 168 q^{42} + 349 q^{43} - 40 q^{44} - 730 q^{45} + 300 q^{46} - 132 q^{47} + 48 q^{48} - 90 q^{49} - 400 q^{50} + 8 q^{51} - 44 q^{52} + 4 q^{53} - 828 q^{54} + 50 q^{55} + 656 q^{56} - 731 q^{57} - 112 q^{58} + 1368 q^{59} - 60 q^{60} + 1197 q^{61} - 370 q^{62} - 784 q^{63} + 512 q^{64} - 110 q^{65} + 734 q^{66} - 1816 q^{67} + 648 q^{68} + 2942 q^{69} + 410 q^{70} + 137 q^{71} + 584 q^{72} - 1592 q^{73} + 678 q^{74} - 150 q^{75} - 1272 q^{76} - 958 q^{77} + 766 q^{78} + 398 q^{79} + 320 q^{80} + 596 q^{81} + 10 q^{82} + 3222 q^{83} - 672 q^{84} + 405 q^{85} - 698 q^{86} + 4672 q^{87} - 160 q^{88} - 495 q^{89} - 730 q^{90} + 1894 q^{91} + 300 q^{92} - 462 q^{93} - 528 q^{94} - 495 q^{95} + 192 q^{96} + 2087 q^{97} - 90 q^{98} + 944 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 3 * q^3 - 16 * q^4 + 20 * q^5 - 6 * q^6 - 82 * q^7 - 64 * q^8 - 73 * q^9 - 40 * q^10 + 20 * q^11 - 24 * q^12 - 11 * q^13 - 82 * q^14 - 15 * q^15 - 64 * q^16 - 81 * q^17 - 292 * q^18 + 219 * q^19 - 160 * q^20 + 84 * q^21 + 20 * q^22 + 75 * q^23 - 24 * q^24 - 100 * q^25 - 44 * q^26 - 828 * q^27 + 164 * q^28 - 28 * q^29 - 60 * q^30 - 370 * q^31 + 128 * q^32 - 367 * q^33 + 162 * q^34 - 205 * q^35 - 292 * q^36 + 678 * q^37 - 198 * q^38 + 766 * q^39 - 160 * q^40 - 5 * q^41 - 168 * q^42 + 349 * q^43 - 40 * q^44 - 730 * q^45 + 300 * q^46 - 132 * q^47 + 48 * q^48 - 90 * q^49 - 400 * q^50 + 8 * q^51 - 44 * q^52 + 4 * q^53 - 828 * q^54 + 50 * q^55 + 656 * q^56 - 731 * q^57 - 112 * q^58 + 1368 * q^59 - 60 * q^60 + 1197 * q^61 - 370 * q^62 - 784 * q^63 + 512 * q^64 - 110 * q^65 + 734 * q^66 - 1816 * q^67 + 648 * q^68 + 2942 * q^69 + 410 * q^70 + 137 * q^71 + 584 * q^72 - 1592 * q^73 + 678 * q^74 - 150 * q^75 - 1272 * q^76 - 958 * q^77 + 766 * q^78 + 398 * q^79 + 320 * q^80 + 596 * q^81 + 10 * q^82 + 3222 * q^83 - 672 * q^84 + 405 * q^85 - 698 * q^86 + 4672 * q^87 - 160 * q^88 - 495 * q^89 - 730 * q^90 + 1894 * q^91 + 300 * q^92 - 462 * q^93 - 528 * q^94 - 495 * q^95 + 192 * q^96 + 2087 * q^97 - 90 * q^98 + 944 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/190\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−3.30180	+	5.71889i	−0.635432	+	1.10060i	0.350992	+	0.936379i	$0.385845\pi$
$3$	−3.30180	+	5.71889i	−0.635432	+	1.10060i	−0.986423	+	0.164222i	$0.947489\pi$
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$6$	6.60360	+	11.4378i	0.449318	+	0.778242i
$7$	−3.99135			−0.215513			−0.107756	−	0.994177i	$-0.534367\pi$
$7$	−3.99135			−0.215513			−0.107756	+	0.994177i	$0.534367\pi$
$8$	−8.00000			−0.353553
$9$	−8.30378	−	14.3826i	−0.307547	−	0.532688i
$10$	−5.00000	−	8.66025i	−0.158114	−	0.273861i
$11$	−17.5478			−0.480988			−0.240494	−	0.970651i	$-0.577309\pi$
$11$	−17.5478			−0.480988			−0.240494	+	0.970651i	$0.577309\pi$
$12$	26.4144			0.635432
$13$	−16.1707	−	28.0084i	−0.344995	−	0.597549i	0.640358	−	0.768077i	$-0.278786\pi$
$13$	−16.1707	−	28.0084i	−0.344995	−	0.597549i	−0.985353	+	0.170528i	$0.945453\pi$
$14$	−3.99135	+	6.91323i	−0.0761953	+	0.131974i
$15$	16.5090	+	28.5944i	0.284174	+	0.492203i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	37.9685	−	65.7634i	0.541689	−	0.938234i	−0.457118	−	0.889406i	$-0.651118\pi$
$17$	37.9685	−	65.7634i	0.541689	−	0.938234i	0.998807	−	0.0488275i	$-0.0155485\pi$
$18$	−33.2151			−0.434938
$19$	−11.4274	−	82.0269i	−0.137980	−	0.990435i
$19$	−11.4274	−	82.0269i	−0.137980	−	0.990435i
$20$	−20.0000			−0.223607
$21$	13.1787	−	22.8261i	0.136944	−	0.237194i
$22$	−17.5478	+	30.3937i	−0.170055	+	0.294544i
$23$	−41.4559	−	71.8038i	−0.375833	−	0.650962i	0.614618	−	0.788825i	$-0.289310\pi$
$23$	−41.4559	−	71.8038i	−0.375833	−	0.650962i	−0.990451	+	0.137863i	$0.955977\pi$
$24$	26.4144	−	45.7511i	0.224659	−	0.389121i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	−64.6827			−0.487897
$27$	−68.6275			−0.489162
$28$	7.98271	+	13.8265i	0.0538782	+	0.0933198i
$29$	−143.135	−	247.916i	−0.916532	−	1.58748i	−0.804642	−	0.593760i	$-0.797643\pi$
$29$	−143.135	−	247.916i	−0.916532	−	1.58748i	−0.111890	−	0.993721i	$-0.535690\pi$
$30$	66.0360			0.401882
$31$	−192.152			−1.11328			−0.556638	−	0.830755i	$-0.687909\pi$
$31$	−192.152			−1.11328			−0.556638	+	0.830755i	$0.687909\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$	57.9394	−	100.354i	0.305635	−	0.529375i
$34$	−75.9371	−	131.527i	−0.383032	−	0.663431i
$35$	−9.97839	+	17.2831i	−0.0481901	+	0.0834678i
$36$	−33.2151	+	57.5303i	−0.153774	+	0.266344i
$37$	327.538			1.45532			0.727661	−	0.685937i	$-0.240608\pi$
$37$	327.538			1.45532			0.727661	+	0.685937i	$0.240608\pi$
$38$	−153.502	−	62.2341i	−0.655298	−	0.265677i
$39$	213.569			0.876884
$40$	−20.0000	+	34.6410i	−0.0790569	+	0.136931i
$41$	6.74998	−	11.6913i	0.0257114	−	0.0445335i	−0.852883	−	0.522101i	$-0.825148\pi$
$41$	6.74998	−	11.6913i	0.0257114	−	0.0445335i	0.878595	+	0.477568i	$0.158482\pi$
$42$	−26.3573	−	45.6522i	−0.0968339	−	0.167721i
$43$	22.6461	−	39.2242i	0.0803140	−	0.139108i	−0.823071	−	0.567939i	$-0.807741\pi$
$43$	22.6461	−	39.2242i	0.0803140	−	0.139108i	0.903385	+	0.428831i	$0.141074\pi$
$44$	35.0956	+	60.7874i	0.120247	+	0.208274i
$45$	−83.0378			−0.275079
$46$	−165.824			−0.531508
$47$	283.331	+	490.744i	0.879320	+	1.52303i	0.852088	+	0.523399i	$0.175336\pi$
$47$	283.331	+	490.744i	0.879320	+	1.52303i	0.0272325	+	0.999629i	$0.491331\pi$
$48$	−52.8288	−	91.5022i	−0.158858	−	0.275150i
$49$	−327.069			−0.953554
$50$	−50.0000			−0.141421
$51$	250.729	+	434.275i	0.688414	+	1.19237i
$52$	−64.6827	+	112.034i	−0.172498	+	0.298774i
$53$	−77.1559	−	133.638i	−0.199966	−	0.346350i	0.748551	−	0.663077i	$-0.230750\pi$
$53$	−77.1559	−	133.638i	−0.199966	−	0.346350i	−0.948517	+	0.316726i	$0.897416\pi$
$54$	−68.6275	+	118.866i	−0.172945	+	0.299549i
$55$	−43.8695	+	75.9843i	−0.107552	+	0.186286i
$56$	31.9308			0.0761953
$57$	506.834	+	205.485i	1.17775	+	0.477493i
$58$	−572.539			−1.29617
$59$	−95.1709	+	164.841i	−0.210003	+	0.363736i	−0.951715	−	0.306982i	$-0.900681\pi$
$59$	−95.1709	+	164.841i	−0.210003	+	0.363736i	0.741712	+	0.670718i	$0.234014\pi$
$60$	66.0360	−	114.378i	0.142087	−	0.246102i
$61$	76.9613	+	133.301i	0.161539	+	0.279794i	0.935421	−	0.353536i	$-0.115021\pi$
$61$	76.9613	+	133.301i	0.161539	+	0.279794i	−0.773882	+	0.633330i	$0.781688\pi$
$62$	−192.152	+	332.818i	−0.393603	+	0.681740i
$63$	33.1433	+	57.4060i	0.0662805	+	0.114801i
$64$	64.0000			0.125000
$65$	−161.707			−0.308573
$66$	−115.879	−	200.708i	−0.216117	−	0.374325i
$67$	−67.5615	−	117.020i	−0.123193	−	0.213377i	0.797832	−	0.602880i	$-0.205980\pi$
$67$	−67.5615	−	117.020i	−0.123193	−	0.213377i	−0.921025	+	0.389503i	$0.872647\pi$
$68$	−303.748			−0.541689
$69$	547.517			0.955265
$70$	19.9568	+	34.5661i	0.0340756	+	0.0590206i
$71$	−33.6555	+	58.2931i	−0.0562560	+	0.0974383i	−0.892782	−	0.450489i	$-0.851250\pi$
$71$	−33.6555	+	58.2931i	−0.0562560	+	0.0974383i	0.836526	+	0.547927i	$0.184583\pi$
$72$	66.4303	+	115.061i	0.108734	+	0.188334i
$73$	−116.745	+	202.208i	−0.187177	+	0.324200i	−0.944308	−	0.329063i	$-0.893267\pi$
$73$	−116.745	+	202.208i	−0.187177	+	0.324200i	0.757131	+	0.653263i	$0.226600\pi$
$74$	327.538	−	567.312i	0.514534	−	0.891199i
$75$	165.090			0.254173
$76$	−261.295	+	203.639i	−0.394376	+	0.307356i
$77$	70.0396			0.103659
$78$	213.569	−	369.913i	0.310025	−	0.536979i
$79$	−369.439	+	639.887i	−0.526141	+	0.911302i	0.473396	+	0.880850i	$0.343028\pi$
$79$	−369.439	+	639.887i	−0.526141	+	0.911302i	−0.999536	+	0.0304523i	$0.990305\pi$
$80$	40.0000	+	69.2820i	0.0559017	+	0.0968246i
$81$	450.797	−	780.802i	0.618377	−	1.07106i
$82$	−13.5000	−	23.3826i	−0.0181807	−	0.0314900i
$83$	986.821			1.30503			0.652516	−	0.757775i	$-0.273713\pi$
$83$	986.821			1.30503			0.652516	+	0.757775i	$0.273713\pi$
$84$	−105.429			−0.136944
$85$	−189.843	−	328.817i	−0.242251	−	0.419591i
$86$	−45.2923	−	78.4485i	−0.0567906	−	0.0983642i
$87$	1890.41			2.32958
$88$	140.383			0.170055
$89$	−127.042	−	220.042i	−0.151308	−	0.262073i	0.780401	−	0.625280i	$-0.215015\pi$
$89$	−127.042	−	220.042i	−0.151308	−	0.262073i	−0.931708	+	0.363207i	$0.881682\pi$
$90$	−83.0378	+	143.826i	−0.0972551	+	0.168451i
$91$	64.5429	+	111.792i	0.0743509	+	0.128780i
$92$	−165.824	+	287.215i	−0.187916	+	0.325481i
$93$	634.449	−	1098.90i	0.707412	−	1.22527i
$94$	1133.32			1.24355
$95$	−383.755	−	155.585i	−0.414447	−	0.168029i
$96$	−211.315			−0.224659
$97$	435.454	−	754.228i	0.455811	−	0.789487i	−0.542924	−	0.839782i	$-0.682683\pi$
$97$	435.454	−	754.228i	0.455811	−	0.789487i	0.998734	+	0.0502947i	$0.0160160\pi$
$98$	−327.069	+	566.500i	−0.337132	+	0.583930i
$99$	145.713	+	252.383i	0.147927	+	0.256216i
$100$	−50.0000	+	86.6025i	−0.0500000	+	0.0866025i
$101$	82.8479	+	143.497i	0.0816205	+	0.141371i	0.903946	−	0.427646i	$-0.140657\pi$
$101$	82.8479	+	143.497i	0.0816205	+	0.141371i	−0.822326	+	0.569017i	$0.807324\pi$
$102$	1002.92			0.973564
$103$	−874.897			−0.836953			−0.418477	−	0.908228i	$-0.637436\pi$
$103$	−874.897			−0.836953			−0.418477	+	0.908228i	$0.637436\pi$
$104$	129.365	+	224.067i	0.121974	+	0.211265i
$105$	−65.8933	−	114.131i	−0.0612431	−	0.106076i
$106$	−308.623			−0.282794
$107$	−475.798			−0.429879			−0.214940	−	0.976627i	$-0.568956\pi$
$107$	−475.798			−0.429879			−0.214940	+	0.976627i	$0.568956\pi$
$108$	137.255	+	237.733i	0.122290	+	0.211813i
$109$	−117.562	+	203.623i	−0.103306	+	0.178932i	−0.913045	−	0.407859i	$-0.866276\pi$
$109$	−117.562	+	203.623i	−0.103306	+	0.178932i	0.809739	+	0.586791i	$0.199609\pi$
$110$	87.7391	+	151.969i	0.0760508	+	0.131724i
$111$	−1081.46	+	1873.15i	−0.924758	+	1.60173i
$112$	31.9308	−	55.3058i	0.0269391	−	0.0466599i
$113$	322.387			0.268386			0.134193	−	0.990955i	$-0.457156\pi$
$113$	322.387			0.268386			0.134193	+	0.990955i	$0.457156\pi$
$114$	862.744	−	672.377i	0.708801	−	0.552402i
$115$	−414.559			−0.336155
$116$	−572.539	+	991.666i	−0.458266	+	0.793740i
$117$	−268.555	+	465.152i	−0.212205	+	0.367549i
$118$	190.342	+	329.682i	0.148495	+	0.257200i
$119$	−151.546	+	262.485i	−0.116741	+	0.202201i
$120$	−132.072	−	228.755i	−0.100471	−	0.174020i
$121$	−1023.07			−0.768651
$122$	307.845			0.228451
$123$	44.5742	+	77.2047i	0.0326757	+	0.0565961i
$124$	384.305	+	665.635i	0.278319	+	0.482063i
$125$	−125.000			−0.0894427
$126$	132.573			0.0937347
$127$	−737.884	−	1278.05i	−0.515564	−	0.892982i	−0.999837	−	0.0180656i	$-0.994249\pi$
$127$	−737.884	−	1278.05i	−0.515564	−	0.892982i	0.484273	−	0.874917i	$-0.339084\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$	149.546	+	259.021i	0.102068	+	0.176787i
$130$	−161.707	+	280.084i	−0.109097	+	0.188962i
$131$	30.7369	−	53.2379i	0.0205000	−	0.0355070i	−0.855593	−	0.517648i	$-0.826808\pi$
$131$	30.7369	−	53.2379i	0.0205000	−	0.0355070i	0.876093	+	0.482141i	$0.160141\pi$
$132$	−463.515			−0.305635
$133$	45.6107	+	327.399i	0.0297365	+	0.213452i
$134$	−270.246			−0.174222
$135$	−171.569	+	297.166i	−0.109380	+	0.189452i
$136$	−303.748	+	526.107i	−0.191516	+	0.331716i
$137$	−235.154	−	407.298i	−0.146646	−	0.253999i	0.783340	−	0.621594i	$-0.213515\pi$
$137$	−235.154	−	407.298i	−0.146646	−	0.253999i	−0.929986	+	0.367595i	$0.880181\pi$
$138$	547.517	−	948.327i	0.337737	−	0.584978i
$139$	721.445	+	1249.58i	0.440232	+	0.762503i	0.997706	−	0.0676905i	$-0.0215630\pi$
$139$	721.445	+	1249.58i	0.440232	+	0.762503i	−0.557475	+	0.830194i	$0.688230\pi$
$140$	79.8271			0.0481901
$141$	−3742.01			−2.23499
$142$	67.3111	+	116.586i	0.0397790	+	0.0688993i
$143$	283.760	+	491.487i	0.165938	+	0.287414i
$144$	265.721			0.153774
$145$	−1431.35			−0.819771
$146$	233.489	+	404.415i	0.132354	+	0.229244i
$147$	1079.92	−	1870.47i	0.605919	−	1.04948i
$148$	−655.076	−	1134.62i	−0.363830	−	0.630173i
$149$	−1626.39	+	2816.99i	−0.894222	+	1.54884i	−0.0594581	+	0.998231i	$0.518937\pi$
$149$	−1626.39	+	2816.99i	−0.894222	+	1.54884i	−0.834764	+	0.550608i	$0.814396\pi$
$150$	165.090	−	285.944i	0.0898636	−	0.155648i
$151$	−491.188			−0.264718			−0.132359	−	0.991202i	$-0.542255\pi$
$151$	−491.188			−0.264718			−0.132359	+	0.991202i	$0.542255\pi$
$152$	91.4190	+	656.215i	0.0487833	+	0.350172i
$153$	−1261.13			−0.666381
$154$	70.0396	−	121.312i	0.0366490	−	0.0634780i
$155$	−480.381	+	832.044i	−0.248936	+	0.431170i
$156$	−427.139	−	739.826i	−0.219221	−	0.379702i
$157$	1802.38	−	3121.81i	0.916213	−	1.58693i	0.111099	−	0.993809i	$-0.464563\pi$
$157$	1802.38	−	3121.81i	0.916213	−	1.58693i	0.805115	−	0.593119i	$-0.202104\pi$
$158$	738.878	+	1279.77i	0.372038	+	0.644388i
$159$	1019.01			0.508258
$160$	160.000			0.0790569
$161$	165.465	+	286.594i	0.0809968	+	0.140291i
$162$	−901.593	−	1561.60i	−0.437258	−	0.757354i
$163$	3170.53			1.52353			0.761763	−	0.647856i	$-0.224334\pi$
$163$	3170.53			1.52353			0.761763	+	0.647856i	$0.224334\pi$
$164$	−53.9998			−0.0257114
$165$	−289.697	−	501.770i	−0.136684	−	0.236744i
$166$	986.821	−	1709.22i	0.461399	−	0.799166i
$167$	−850.768	−	1473.57i	−0.394218	−	0.682805i	0.598783	−	0.800911i	$-0.295651\pi$
$167$	−850.768	−	1473.57i	−0.394218	−	0.682805i	−0.993001	+	0.118106i	$0.962318\pi$
$168$	−105.429	+	182.609i	−0.0484169	+	0.0838606i
$169$	575.519	−	996.828i	0.261957	−	0.453722i
$170$	−759.371			−0.342594
$171$	−1084.87	+	845.489i	−0.485157	+	0.378106i
$172$	−181.169			−0.0803140
$173$	−1033.82	+	1790.63i	−0.454334	+	0.786930i	−0.998650	−	0.0519508i	$-0.983456\pi$
$173$	−1033.82	+	1790.63i	−0.454334	+	0.786930i	0.544316	+	0.838881i	$0.316789\pi$
$174$	1890.41	−	3274.28i	0.823629	−	1.42657i
$175$	49.8919	+	86.4154i	0.0215513	+	0.0373279i
$176$	140.383	−	243.150i	0.0601235	−	0.104137i
$177$	−628.471	−	1088.54i	−0.266886	−	0.462259i
$178$	−508.166			−0.213981
$179$	1692.79			0.706843			0.353422	−	0.935464i	$-0.385018\pi$
$179$	1692.79			0.706843			0.353422	+	0.935464i	$0.385018\pi$
$180$	166.076	+	287.651i	0.0687697	+	0.119113i
$181$	−2263.65	−	3920.75i	−0.929589	−	1.61010i	−0.784010	−	0.620749i	$-0.786829\pi$
$181$	−2263.65	−	3920.75i	−0.929589	−	1.61010i	−0.145579	−	0.989347i	$-0.546505\pi$
$182$	258.171			0.105148
$183$	−1016.44			−0.410588
$184$	331.647	+	574.430i	0.132877	+	0.230150i
$185$	818.844	−	1418.28i	0.325420	−	0.563643i
$186$	−1268.90	−	2197.80i	−0.500216	−	0.866399i
$187$	−666.265	+	1154.00i	−0.260546	+	0.451279i
$188$	1133.32	−	1962.97i	0.439660	−	0.761514i
$189$	273.917			0.105421
$190$	−653.237	+	509.099i	−0.249425	+	0.194389i
$191$	−188.251			−0.0713159			−0.0356580	−	0.999364i	$-0.511353\pi$
$191$	−188.251			−0.0713159			−0.0356580	+	0.999364i	$0.511353\pi$
$192$	−211.315	+	366.009i	−0.0794290	+	0.137575i
$193$	−659.905	+	1142.99i	−0.246119	+	0.426291i	−0.962446	−	0.271474i	$-0.912489\pi$
$193$	−659.905	+	1142.99i	−0.246119	+	0.426291i	0.716327	+	0.697765i	$0.245822\pi$
$194$	−870.908	−	1508.46i	−0.322307	−	0.558252i
$195$	533.923	−	924.782i	0.196077	−	0.339616i
$196$	654.138	+	1133.00i	0.238389	+	0.412901i
$197$	947.378			0.342629			0.171314	−	0.985216i	$-0.445199\pi$
$197$	947.378			0.342629			0.171314	+	0.985216i	$0.445199\pi$
$198$	582.853			0.209200
$199$	−2713.96	−	4700.72i	−0.966772	−	1.67450i	−0.704777	−	0.709429i	$-0.748953\pi$
$199$	−2713.96	−	4700.72i	−0.966772	−	1.67450i	−0.261995	−	0.965069i	$-0.584380\pi$
$200$	100.000	+	173.205i	0.0353553	+	0.0612372i
$201$	892.299			0.313124
$202$	331.391			0.115429
$203$	571.301	+	989.523i	0.197525	+	0.342123i
$204$	1002.92	−	1737.10i	0.344207	−	0.596184i
$205$	−33.7499	−	58.4565i	−0.0114985	−	0.0199160i
$206$	−874.897	+	1515.37i	−0.295908	+	0.512527i
$207$	−688.482	+	1192.49i	−0.231173	+	0.400403i
$208$	517.461			0.172498
$209$	200.526	+	1439.39i	0.0663667	+	0.476387i
$210$	−263.573			−0.0866109
$211$	−448.372	+	776.603i	−0.146290	+	0.253382i	−0.929853	−	0.367930i	$-0.880067\pi$
$211$	−448.372	+	776.603i	−0.146290	+	0.253382i	0.783563	+	0.621312i	$0.213400\pi$
$212$	−308.623	+	534.551i	−0.0999828	+	0.173175i
$213$	−222.248	−	384.945i	−0.0714938	−	0.123831i
$214$	−475.798	+	824.106i	−0.151985	+	0.263246i
$215$	−113.231	−	196.121i	−0.0359175	−	0.0622110i
$216$	549.020			0.172945
$217$	766.948			0.239926
$218$	235.124	+	407.246i	0.0730486	+	0.126524i
$219$	−770.935	−	1335.30i	−0.237877	−	0.412014i
$220$	350.956			0.107552
$221$	−2455.91			−0.747521
$222$	2162.93	+	3746.30i	0.653902	+	1.13259i
$223$	−249.878	+	432.802i	−0.0750362	+	0.129967i	−0.901102	−	0.433607i	$-0.857241\pi$
$223$	−249.878	+	432.802i	−0.0750362	+	0.129967i	0.826066	+	0.563574i	$0.190574\pi$
$224$	−63.8617	−	110.612i	−0.0190488	−	0.0329935i
$225$	−207.595	+	359.564i	−0.0615095	+	0.106538i
$226$	322.387	−	558.391i	0.0948888	−	0.164352i
$227$	4162.48			1.21706			0.608532	−	0.793529i	$-0.291759\pi$
$227$	4162.48			1.21706			0.608532	+	0.793529i	$0.291759\pi$
$228$	−301.847	−	2166.69i	−0.0876769	−	0.629354i
$229$	960.673			0.277219			0.138609	−	0.990347i	$-0.455737\pi$
$229$	960.673			0.277219			0.138609	+	0.990347i	$0.455737\pi$
$230$	−414.559	+	718.038i	−0.118849	+	0.205852i
$231$	−231.257	+	400.548i	−0.0658683	+	0.114087i
$232$	1145.08	+	1983.33i	0.324043	+	0.561259i
$233$	−941.368	+	1630.50i	−0.264683	+	0.458444i	−0.967480	−	0.252946i	$-0.918601\pi$
$233$	−941.368	+	1630.50i	−0.264683	+	0.458444i	0.702798	+	0.711390i	$0.251934\pi$
$234$	537.111	+	930.303i	0.150051	+	0.259897i
$235$	2833.31			0.786488
$236$	761.367			0.210003
$237$	−2439.63	−	4225.56i	−0.668653	−	1.15814i
$238$	303.092	+	524.970i	0.0825484	+	0.142978i
$239$	3026.29			0.819055			0.409527	−	0.912298i	$-0.365694\pi$
$239$	3026.29			0.819055			0.409527	+	0.912298i	$0.365694\pi$
$240$	−528.288			−0.142087
$241$	−2079.57	−	3601.93i	−0.555839	−	0.962741i	−0.997838	−	0.0657255i	$-0.979064\pi$
$241$	−2079.57	−	3601.93i	−0.555839	−	0.962741i	0.441999	−	0.897016i	$-0.354270\pi$
$242$	−1023.07	+	1772.02i	−0.271759	+	0.470701i
$243$	2050.41	+	3551.41i	0.541291	+	0.937544i
$244$	307.845	−	533.204i	0.0807695	−	0.139897i
$245$	−817.673	+	1416.25i	−0.213221	+	0.369310i
$246$	178.297			0.0462105
$247$	−2112.66	+	1646.49i	−0.544231	+	0.424145i
$248$	1537.22			0.393603
$249$	−3258.29	+	5643.52i	−0.829260	+	1.43632i
$250$	−125.000	+	216.506i	−0.0316228	+	0.0547723i
$251$	470.181	+	814.378i	0.118237	+	0.204793i	0.919069	−	0.394096i	$-0.128942\pi$
$251$	470.181	+	814.378i	0.118237	+	0.204793i	−0.800832	+	0.598889i	$0.795609\pi$
$252$	132.573	−	229.624i	0.0331402	−	0.0574006i
$253$	727.461	+	1260.00i	0.180771	+	0.313105i
$254$	−2951.53			−0.729117
$255$	2507.29			0.615736
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	2590.30	+	4486.54i	0.628711	+	1.08896i	0.987811	+	0.155660i	$0.0497504\pi$
$257$	2590.30	+	4486.54i	0.628711	+	1.08896i	−0.359100	+	0.933299i	$0.616916\pi$
$258$	598.184			0.144346
$259$	−1307.32			−0.313640
$260$	323.413	+	560.168i	0.0771432	+	0.133616i
$261$	−2377.12	+	4117.29i	−0.563754	+	0.976451i
$262$	−61.4738	−	106.476i	−0.0144957	−	0.0251072i
$263$	−3376.66	+	5848.54i	−0.791687	+	1.37124i	0.133235	+	0.991084i	$0.457463\pi$
$263$	−3376.66	+	5848.54i	−0.791687	+	1.37124i	−0.924922	+	0.380157i	$0.875870\pi$
$264$	−463.515	+	802.832i	−0.108058	+	0.187162i
$265$	−771.559			−0.178855
$266$	612.682	+	248.398i	0.141225	+	0.0572567i
$267$	1677.86			0.384583
$268$	−270.246	+	468.080i	−0.0615967	+	0.106689i
$269$	635.478	−	1100.68i	0.144036	−	0.249478i	−0.784977	−	0.619525i	$-0.787325\pi$
$269$	635.478	−	1100.68i	0.144036	−	0.249478i	0.929013	+	0.370047i	$0.120658\pi$
$270$	343.138	+	594.332i	0.0773433	+	0.133963i
$271$	1017.64	−	1762.60i	0.228107	−	0.395093i	−0.729140	−	0.684365i	$-0.760080\pi$
$271$	1017.64	−	1762.60i	0.228107	−	0.395093i	0.957247	+	0.289271i	$0.0934130\pi$
$272$	607.496	+	1052.21i	0.135422	+	0.234558i
$273$	−852.431			−0.188980
$274$	−940.616			−0.207389
$275$	219.348	+	379.921i	0.0480988	+	0.0833095i
$276$	−1095.03	−	1896.65i	−0.238816	−	0.413642i
$277$	5042.20			1.09370			0.546852	−	0.837229i	$-0.315826\pi$
$277$	5042.20			1.09370			0.546852	+	0.837229i	$0.315826\pi$
$278$	2885.78			0.622581
$279$	1595.59	+	2763.65i	0.342386	+	0.593029i
$280$	79.8271	−	138.265i	0.0170378	−	0.0295103i
$281$	−595.279	−	1031.05i	−0.126375	−	0.218888i	0.795895	−	0.605435i	$-0.207001\pi$
$281$	−595.279	−	1031.05i	−0.126375	−	0.218888i	−0.922270	+	0.386547i	$0.873668\pi$
$282$	−3742.01	+	6481.35i	−0.790189	+	1.36865i
$283$	3785.31	−	6556.34i	0.795099	−	1.37715i	−0.127677	−	0.991816i	$-0.540752\pi$
$283$	3785.31	−	6556.34i	0.795099	−	1.37715i	0.922776	−	0.385336i	$-0.125915\pi$
$284$	269.244			0.0562560
$285$	2156.86	−	1680.94i	0.448285	−	0.349370i
$286$	1135.04			0.234672
$287$	−26.9416	+	46.6641i	−0.00554115	+	0.00959755i
$288$	265.721	−	460.242i	0.0543672	−	0.0941668i
$289$	−426.718	−	739.098i	−0.0868550	−	0.150437i
$290$	−1431.35	+	2479.16i	−0.289833	+	0.502005i
$291$	2875.56	+	4980.62i	0.579273	+	1.00333i
$292$	933.957			0.187177
$293$	−2965.59			−0.591302			−0.295651	−	0.955296i	$-0.595536\pi$
$293$	−2965.59			−0.591302			−0.295651	+	0.955296i	$0.595536\pi$
$294$	−2159.83	−	3740.94i	−0.428449	−	0.742096i
$295$	475.854	+	824.204i	0.0939163	+	0.162668i
$296$	−2620.30			−0.514534
$297$	1204.26			0.235281
$298$	3252.78	+	5633.98i	0.632311	+	1.09519i
$299$	−1340.74	+	2322.23i	−0.259321	+	0.449157i
$300$	−330.180	−	571.889i	−0.0635432	−	0.110060i
$301$	−90.3887	+	156.558i	−0.0173087	+	0.0299796i
$302$	−491.188	+	850.763i	−0.0935918	+	0.162106i
$303$	−1094.19			−0.207457
$304$	1228.02	+	497.873i	0.231683	+	0.0939308i
$305$	769.613			0.144485
$306$	−1261.13	+	2184.34i	−0.235601	+	0.408073i
$307$	4036.26	−	6991.02i	0.750364	−	1.29967i	−0.197282	−	0.980347i	$-0.563211\pi$
$307$	4036.26	−	6991.02i	0.750364	−	1.29967i	0.947646	−	0.319322i	$-0.103455\pi$
$308$	−140.079	−	242.624i	−0.0259148	−	0.0448857i
$309$	2888.74	−	5003.44i	0.531827	−	0.921151i
$310$	960.762	+	1664.09i	0.176025	+	0.304883i
$311$	6715.16			1.22438			0.612190	−	0.790711i	$-0.290289\pi$
$311$	6715.16			1.22438			0.612190	+	0.790711i	$0.290289\pi$
$312$	−1708.55			−0.310025
$313$	−2981.64	−	5164.35i	−0.538442	−	0.932608i	−0.998988	−	0.0449726i	$-0.985680\pi$
$313$	−2981.64	−	5164.35i	−0.538442	−	0.932608i	0.460547	−	0.887635i	$-0.347653\pi$
$314$	−3604.76	−	6243.62i	−0.647861	−	1.12213i
$315$	331.433			0.0592830
$316$	2955.51			0.526141
$317$	1410.15	+	2442.45i	0.249848	+	0.432749i	0.963483	−	0.267768i	$-0.0862861\pi$
$317$	1410.15	+	2442.45i	0.249848	+	0.432749i	−0.713636	+	0.700517i	$0.752953\pi$
$318$	1019.01	−	1764.98i	0.179696	−	0.311243i
$319$	2511.70	+	4350.39i	0.440841	+	0.763559i
$320$	160.000	−	277.128i	0.0279508	−	0.0484123i
$321$	1570.99	−	2721.03i	0.273159	−	0.473125i
$322$	661.861			0.114547
$323$	−5828.25	−	2362.94i	−1.00400	−	0.407051i
$324$	−3606.37			−0.618377
$325$	−404.267	+	700.210i	−0.0689990	+	0.119510i
$326$	3170.53	−	5491.51i	0.538648	−	0.932965i
$327$	−776.332	−	1344.65i	−0.131288	−	0.227398i
$328$	−53.9998	+	93.5304i	−0.00909037	+	0.0157450i
$329$	−1130.87	−	1958.73i	−0.189505	−	0.328232i
$330$	−1158.79			−0.193301
$331$	6465.65			1.07367			0.536834	−	0.843688i	$-0.319620\pi$
$331$	6465.65			1.07367			0.536834	+	0.843688i	$0.319620\pi$
$332$	−1973.64	−	3418.45i	−0.326258	−	0.565096i
$333$	−2719.80	−	4710.84i	−0.447580	−	0.775232i
$334$	−3403.07			−0.557508
$335$	−675.615			−0.110188
$336$	210.859	+	365.218i	0.0342359	+	0.0592984i
$337$	−1193.01	+	2066.35i	−0.192841	+	0.334010i	−0.946191	−	0.323610i	$-0.895103\pi$
$337$	−1193.01	+	2066.35i	−0.192841	+	0.334010i	0.753350	+	0.657620i	$0.228437\pi$
$338$	−1151.04	−	1993.66i	−0.185231	−	0.320830i
$339$	−1064.46	+	1843.69i	−0.170541	+	0.295386i
$340$	−759.371	+	1315.27i	−0.121125	+	0.209795i
$341$	3371.85			0.535473
$342$	379.562	+	2724.53i	0.0600127	+	0.430778i
$343$	2674.48			0.421016
$344$	−181.169	+	313.794i	−0.0283953	+	0.0491821i
$345$	1368.79	−	2370.82i	0.213604	−	0.369973i
$346$	2067.64	+	3581.25i	0.321263	+	0.556443i
$347$	−1375.50	+	2382.43i	−0.212797	+	0.368575i	−0.952589	−	0.304261i	$-0.901591\pi$
$347$	−1375.50	+	2382.43i	−0.212797	+	0.368575i	0.739792	+	0.672836i	$0.234924\pi$
$348$	−3780.82	−	6548.57i	−0.582394	−	1.00874i
$349$	8581.95			1.31628			0.658139	−	0.752896i	$-0.271344\pi$
$349$	8581.95			1.31628			0.658139	+	0.752896i	$0.271344\pi$
$350$	199.568			0.0304781
$351$	1109.75	+	1922.15i	0.168758	+	0.292298i
$352$	−280.765	−	486.299i	−0.0425137	−	0.0736359i
$353$	10210.4			1.53950			0.769752	−	0.638344i	$-0.220380\pi$
$353$	10210.4			1.53950			0.769752	+	0.638344i	$0.220380\pi$
$354$	−2513.88			−0.377433
$355$	168.278	+	291.466i	0.0251585	+	0.0435757i
$356$	−508.166	+	880.170i	−0.0756538	+	0.131036i
$357$	−1000.75	−	1733.35i	−0.148362	−	0.256971i
$358$	1692.79	−	2932.00i	0.249907	−	0.432851i
$359$	−4569.55	+	7914.69i	−0.671787	+	1.16357i	0.305609	+	0.952157i	$0.401140\pi$
$359$	−4569.55	+	7914.69i	−0.671787	+	1.16357i	−0.977397	+	0.211413i	$0.932194\pi$
$360$	664.303			0.0972551
$361$	−6597.83	+	1874.71i	−0.961923	+	0.273320i
$362$	−9054.59			−1.31464
$363$	3377.99	−	5850.85i	0.488425	−	0.845977i
$364$	258.171	−	447.166i	0.0371754	−	0.0643898i
$365$	583.723	+	1011.04i	0.0837081	+	0.144987i
$366$	−1016.44	+	1760.53i	−0.145165	+	0.251433i
$367$	−6605.15	−	11440.4i	−0.939471	−	1.62721i	−0.766461	−	0.642291i	$-0.777984\pi$
$367$	−6605.15	−	11440.4i	−0.939471	−	1.62721i	−0.173010	−	0.984920i	$-0.555349\pi$
$368$	1326.59			0.187916
$369$	−224.201			−0.0316300
$370$	−1637.69	−	2836.56i	−0.230106	−	0.398556i
$371$	307.956	+	533.396i	0.0430951	+	0.0746430i
$372$	−5075.59			−0.707412
$373$	−9533.85			−1.32344			−0.661721	−	0.749750i	$-0.730174\pi$
$373$	−9533.85			−1.32344			−0.661721	+	0.749750i	$0.730174\pi$
$374$	1332.53	+	2308.01i	0.184234	+	0.319102i
$375$	412.725	−	714.861i	0.0568348	−	0.0984407i
$376$	−2266.65	−	3925.95i	−0.310887	−	0.538472i
$377$	−4629.17	+	8017.95i	−0.632398	+	1.09535i
$378$	273.917	−	474.438i	0.0372718	−	0.0645567i
$379$	−3046.43			−0.412888			−0.206444	−	0.978458i	$-0.566189\pi$
$379$	−3046.43			−0.412888			−0.206444	+	0.978458i	$0.566189\pi$
$380$	228.548	+	1640.54i	0.0308533	+	0.221468i
$381$	9745.38			1.31042
$382$	−188.251	+	326.060i	−0.0252140	+	0.0436719i
$383$	−6805.22	+	11787.0i	−0.907912	+	1.57255i	−0.0909518	+	0.995855i	$0.528991\pi$
$383$	−6805.22	+	11787.0i	−0.907912	+	1.57255i	−0.816960	+	0.576694i	$0.804342\pi$
$384$	422.631	+	732.018i	0.0561648	+	0.0972803i
$385$	175.099	−	303.280i	0.0231789	−	0.0401470i
$386$	1319.81	+	2285.98i	0.174032	+	0.301433i
$387$	−752.194			−0.0988015
$388$	−3483.63			−0.455811
$389$	−7431.19	−	12871.2i	−0.968576	−	1.67762i	−0.699683	−	0.714453i	$-0.746675\pi$
$389$	−7431.19	−	12871.2i	−0.968576	−	1.67762i	−0.268893	−	0.963170i	$-0.586658\pi$
$390$	−1067.85	−	1849.56i	−0.138647	−	0.240144i
$391$	−6296.08			−0.814339
$392$	2616.55			0.337132
$393$	202.974	+	351.562i	0.0260527	+	0.0451245i
$394$	947.378	−	1640.91i	0.121138	−	0.209817i
$395$	1847.19	+	3199.43i	0.235297	+	0.407547i
$396$	582.853	−	1009.53i	0.0739633	−	0.128108i
$397$	3388.58	−	5869.18i	0.428382	−	0.741980i	−0.568347	−	0.822789i	$-0.692417\pi$
$397$	3388.58	−	5869.18i	0.428382	−	0.741980i	0.996730	+	0.0808090i	$0.0257504\pi$
$398$	−10855.8			−1.36722
$399$	−2022.95	−	820.162i	−0.253820	−	0.102906i
$400$	400.000			0.0500000
$401$	2606.50	−	4514.58i	0.324594	−	0.562213i	−0.656836	−	0.754033i	$-0.728106\pi$
$401$	2606.50	−	4514.58i	0.324594	−	0.562213i	0.981430	+	0.191820i	$0.0614390\pi$
$402$	892.299	−	1545.51i	0.110706	−	0.191749i
$403$	3107.23	+	5381.88i	0.384075	+	0.665238i
$404$	331.391	−	573.987i	0.0408102	−	0.0706854i
$405$	−2253.98	−	3904.01i	−0.276546	−	0.478992i
$406$	2285.20			0.279342
$407$	−5747.57			−0.699992
$408$	−2005.83	−	3474.20i	−0.243391	−	0.421565i
$409$	5180.88	+	8973.55i	0.626352	+	1.08487i	0.988278	+	0.152667i	$0.0487862\pi$
$409$	5180.88	+	8973.55i	0.626352	+	1.08487i	−0.361925	+	0.932207i	$0.617880\pi$
$410$	−135.000			−0.0162613
$411$	3105.73			0.372735
$412$	1749.79	+	3030.73i	0.209238	+	0.362411i
$413$	379.861	−	657.938i	0.0452584	−	0.0783899i
$414$	1376.96	+	2384.97i	0.163464	+	0.283128i
$415$	2467.05	−	4273.06i	0.291814	−	0.505437i
$416$	517.461	−	896.269i	0.0609871	−	0.105633i
$417$	−9528.27			−1.11895
$418$	2693.63	+	1092.07i	0.315191	+	0.127787i
$419$	7010.59			0.817398			0.408699	−	0.912669i	$-0.365983\pi$
$419$	7010.59			0.817398			0.408699	+	0.912669i	$0.365983\pi$
$420$	−263.573	+	456.522i	−0.0306216	+	0.0530381i
$421$	5962.29	−	10327.0i	0.690224	−	1.19550i	−0.281540	−	0.959549i	$-0.590845\pi$
$421$	5962.29	−	10327.0i	0.690224	−	1.19550i	0.971764	−	0.235954i	$-0.0758214\pi$
$422$	896.744	+	1553.21i	0.103443	+	0.179168i
$423$	4705.44	−	8150.06i	0.540866	−	0.936807i
$424$	617.247	+	1069.10i	0.0706985	+	0.122453i
$425$	−1898.43			−0.216676
$426$	−888.991			−0.101107
$427$	−307.180	−	532.051i	−0.0348138	−	0.0602992i
$428$	951.595	+	1648.21i	0.107470	+	0.186143i
$429$	−3747.67			−0.421770
$430$	−452.923			−0.0507950
$431$	3912.08	+	6775.92i	0.437212	+	0.757273i	0.997473	−	0.0710427i	$-0.0226327\pi$
$431$	3912.08	+	6775.92i	0.437212	+	0.757273i	−0.560261	+	0.828316i	$0.689299\pi$
$432$	549.020	−	950.931i	0.0611452	−	0.105907i
$433$	5227.61	+	9054.49i	0.580191	+	1.00492i	0.995456	+	0.0952205i	$0.0303556\pi$
$433$	5227.61	+	9054.49i	0.580191	+	1.00492i	−0.415265	+	0.909701i	$0.636311\pi$
$434$	766.948	−	1328.39i	0.0848265	−	0.146924i
$435$	4726.02	−	8185.71i	0.520909	−	0.902241i
$436$	940.495			0.103306
$437$	−5416.11	+	4221.03i	−0.592878	+	0.462058i
$438$	−3083.74			−0.336408
$439$	−4142.15	+	7174.41i	−0.450328	+	0.779991i	−0.998406	−	0.0564364i	$-0.982026\pi$
$439$	−4142.15	+	7174.41i	−0.450328	+	0.779991i	0.548078	+	0.836427i	$0.315360\pi$
$440$	350.956	−	607.874i	0.0380254	−	0.0658620i
$441$	2715.91	+	4704.09i	0.293263	+	0.507947i
$442$	−2455.91	+	4253.75i	−0.264289	+	0.457761i
$443$	−1916.77	−	3319.94i	−0.205572	−	0.356061i	0.744743	−	0.667352i	$-0.232572\pi$
$443$	−1916.77	−	3319.94i	−0.205572	−	0.356061i	−0.950315	+	0.311290i	$0.899239\pi$
$444$	8651.72			0.924758
$445$	−1270.42			−0.135334
$446$	499.756	+	865.603i	0.0530586	+	0.0919002i
$447$	−10740.0	−	18602.3i	−1.13643	−	1.96836i
$448$	−255.447			−0.0269391
$449$	−5353.68			−0.562708			−0.281354	−	0.959604i	$-0.590784\pi$
$449$	−5353.68			−0.562708			−0.281354	+	0.959604i	$0.590784\pi$
$450$	415.189	+	719.129i	0.0434938	+	0.0753334i
$451$	−118.447	+	205.157i	−0.0123669	+	0.0214201i
$452$	−644.774	−	1116.78i	−0.0670965	−	0.116215i
$453$	1621.81	−	2809.05i	0.168210	−	0.291348i
$454$	4162.48	−	7209.63i	0.430297	−	0.745297i
$455$	645.429			0.0665015
$456$	−4054.67	−	1643.88i	−0.416398	−	0.168819i
$457$	14247.0			1.45831			0.729153	−	0.684350i	$-0.239914\pi$
$457$	14247.0			1.45831			0.729153	+	0.684350i	$0.239914\pi$
$458$	960.673	−	1663.93i	0.0980116	−	0.169761i
$459$	−2605.69	+	4513.18i	−0.264974	+	0.458948i
$460$	829.118	+	1436.08i	0.0840388	+	0.145559i
$461$	8780.47	−	15208.2i	0.887088	−	1.53648i	0.0437857	−	0.999041i	$-0.486058\pi$
$461$	8780.47	−	15208.2i	0.887088	−	1.53648i	0.843302	−	0.537440i	$-0.180609\pi$
$462$	462.513	+	801.097i	0.0465759	+	0.0806718i
$463$	−9839.90			−0.987687			−0.493844	−	0.869551i	$-0.664408\pi$
$463$	−9839.90			−0.987687			−0.493844	+	0.869551i	$0.664408\pi$
$464$	4580.31			0.458266
$465$	−3172.24	−	5494.49i	−0.316364	−	0.547959i
$466$	1882.74	+	3261.00i	0.187159	+	0.324169i
$467$	−12809.4			−1.26927			−0.634635	−	0.772812i	$-0.718850\pi$
$467$	−12809.4			−1.26927			−0.634635	+	0.772812i	$0.718850\pi$
$468$	2148.44			0.212205
$469$	269.662	+	467.068i	0.0265498	+	0.0459855i
$470$	2833.31	−	4907.44i	0.278066	−	0.481624i
$471$	11902.2	+	20615.2i	1.16438	+	2.01677i
$472$	761.367	−	1318.73i	0.0742474	−	0.128600i
$473$	−397.390	+	688.300i	−0.0386301	+	0.0669092i
$474$	−9758.51			−0.945618
$475$	−1633.09	+	1272.75i	−0.157750	+	0.122942i
$476$	1212.37			0.116741
$477$	−1281.37	+	2219.40i	−0.122998	+	0.213038i
$478$	3026.29	−	5241.68i	0.289580	−	0.501567i
$479$	−5783.71	−	10017.7i	−0.551700	−	0.955573i	−0.998152	−	0.0607653i	$-0.980646\pi$
$479$	−5783.71	−	10017.7i	−0.551700	−	0.955573i	0.446452	−	0.894808i	$-0.352687\pi$
$480$	−528.288	+	915.022i	−0.0502353	+	0.0870101i
$481$	−5296.50	−	9173.81i	−0.502079	−	0.869626i
$482$	−8318.30			−0.786075
$483$	−2185.33			−0.205872
$484$	2046.15	+	3544.03i	0.192163	+	0.332836i
$485$	−2177.27	−	3771.14i	−0.203845	−	0.353069i
$486$	8201.64			0.765502
$487$	−482.254			−0.0448727			−0.0224363	−	0.999748i	$-0.507142\pi$
$487$	−482.254			−0.0448727			−0.0224363	+	0.999748i	$0.507142\pi$
$488$	−615.690	−	1066.41i	−0.0571127	−	0.0989221i
$489$	−10468.4	+	18131.9i	−0.968097	+	1.67679i
$490$	1635.35	+	2832.50i	0.150770	+	0.261142i
$491$	2753.96	−	4769.99i	0.253125	−	0.438425i	−0.711260	−	0.702929i	$-0.751875\pi$
$491$	2753.96	−	4769.99i	0.253125	−	0.438425i	0.964384	+	0.264504i	$0.0852083\pi$
$492$	178.297	−	308.819i	0.0163379	−	0.0282980i
$493$	−21738.4			−1.98590
$494$	739.153	+	5305.72i	0.0673200	+	0.483230i
$495$	1457.13			0.132310
$496$	1537.22	−	2662.54i	0.139160	−	0.241032i
$497$	134.331	−	232.668i	0.0121239	−	0.0209992i
$498$	6516.58	+	11287.0i	0.586375	+	1.01563i
$499$	−2469.39	+	4277.11i	−0.221533	+	0.383707i	−0.955274	−	0.295723i	$-0.904439\pi$
$499$	−2469.39	+	4277.11i	−0.221533	+	0.383707i	0.733741	+	0.679430i	$0.237773\pi$
$500$	250.000	+	433.013i	0.0223607	+	0.0387298i
$501$	11236.3			1.00199
$502$	1880.73			0.167213
$503$	1344.29	+	2328.37i	0.119163	+	0.206396i	0.919436	−	0.393239i	$-0.128646\pi$
$503$	1344.29	+	2328.37i	0.119163	+	0.206396i	−0.800273	+	0.599635i	$0.795312\pi$
$504$	−265.147	−	459.248i	−0.0234337	−	0.0405883i
$505$	828.479			0.0730036
$506$	2909.84			0.255649
$507$	3800.50	+	6582.66i	0.332911	+	0.576620i
$508$	−2951.53	+	5112.21i	−0.257782	+	0.446491i
$509$	8890.38	+	15398.6i	0.774183	+	1.34092i	0.935252	+	0.353982i	$0.115172\pi$
$509$	8890.38	+	15398.6i	0.774183	+	1.34092i	−0.161069	+	0.986943i	$0.551494\pi$
$510$	2507.29	−	4342.75i	0.217695	−	0.377060i
$511$	465.969	−	807.082i	0.0403391	−	0.0698693i
$512$	−512.000			−0.0441942
$513$	784.232	+	5629.30i	0.0674946	+	0.484483i
$514$	10361.2			0.889131
$515$	−2187.24	+	3788.42i	−0.187148	+	0.324151i
$516$	598.184	−	1036.09i	0.0510341	−	0.0883936i
$517$	−4971.84	−	8611.48i	−0.422942	−	0.732558i
$518$	−1307.32	+	2264.34i	−0.110889	+	0.192065i
$519$	−6826.93	−	11824.6i	−0.577397	−	1.00008i
$520$	1293.65			0.109097
$521$	−4614.07			−0.387996			−0.193998	−	0.981002i	$-0.562146\pi$
$521$	−4614.07			−0.387996			−0.193998	+	0.981002i	$0.562146\pi$
$522$	4754.24	+	8234.58i	0.398635	+	0.690455i
$523$	−3751.49	−	6497.76i	−0.313654	−	0.543264i	0.665497	−	0.746401i	$-0.268220\pi$
$523$	−3751.49	−	6497.76i	−0.313654	−	0.543264i	−0.979150	+	0.203136i	$0.934887\pi$
$524$	−245.895			−0.0205000
$525$	−658.933			−0.0547775
$526$	6753.31	+	11697.1i	0.559807	+	0.969614i
$527$	−7295.74	+	12636.6i	−0.603050	+	1.04451i
$528$	927.030	+	1605.66i	0.0764087	+	0.132344i
$529$	2646.31	−	4583.55i	0.217499	−	0.376720i
$530$	−771.559	+	1336.38i	−0.0632346	+	0.109526i
$531$	3161.11			0.258344
$532$	1042.92	−	812.797i	0.0849931	−	0.0662392i
$533$	−436.606			−0.0354813
$534$	1677.86	−	2906.15i	0.135971	−	0.235508i
$535$	−1189.49	+	2060.26i	−0.0961240	+	0.166492i
$536$	540.492	+	936.160i	0.0435554	+	0.0754402i
$537$	−5589.25	+	9680.87i	−0.449151	+	0.777952i
$538$	−1270.96	−	2201.36i	−0.101849	−	0.176408i
$539$	5739.35			0.458648
$540$	1372.55			0.109380
$541$	7528.91	+	13040.5i	0.598324	+	1.03633i	0.993069	+	0.117536i	$0.0374996\pi$
$541$	7528.91	+	13040.5i	0.598324	+	1.03633i	−0.394745	+	0.918791i	$0.629167\pi$
$542$	−2035.27	−	3525.20i	−0.161296	−	0.279373i
$543$	29896.5			2.36276
$544$	2429.99			0.191516
$545$	587.809	+	1018.12i	0.0462000	+	0.0800207i
$546$	−852.431	+	1476.45i	−0.0668144	+	0.115726i
$547$	−69.9220	−	121.108i	−0.00546553	−	0.00946658i	0.863280	−	0.504726i	$-0.168406\pi$
$547$	−69.9220	−	121.108i	−0.00546553	−	0.00946658i	−0.868745	+	0.495259i	$0.835073\pi$
$548$	−940.616	+	1629.19i	−0.0733232	+	0.126999i
$549$	1278.14	−	2213.80i	0.0993619	−	0.172100i
$550$	877.391			0.0680219
$551$	−18700.2	+	14573.9i	−1.44583	+	1.12681i
$552$	−4380.13			−0.337737
$553$	1474.56	−	2554.01i	0.113390	−	0.196397i
$554$	5042.20	−	8733.34i	0.386683	−	0.669755i
$555$	5407.32	+	9365.76i	0.413564	+	0.716314i
$556$	2885.78	−	4998.32i	0.220116	−	0.381252i
$557$	−88.7628	−	153.742i	−0.00675224	−	0.0116952i	0.862630	−	0.505836i	$-0.168816\pi$
$557$	−88.7628	−	153.742i	−0.00675224	−	0.0116952i	−0.869382	+	0.494141i	$0.835483\pi$
$558$	6382.37			0.484206
$559$	−1464.81			−0.110832
$560$	−159.654	−	276.529i	−0.0120475	−	0.0208669i
$561$	−4399.75	−	7620.59i	−0.331119	−	0.573514i
$562$	−2381.12			−0.178721
$563$	21292.5			1.59391			0.796957	−	0.604036i	$-0.206442\pi$
$563$	21292.5			1.59391			0.796957	+	0.604036i	$0.206442\pi$
$564$	7484.02	+	12962.7i	0.558748	+	0.967780i
$565$	805.967	−	1395.98i	0.0600129	−	0.103945i
$566$	−7570.61	−	13112.7i	−0.562220	−	0.973794i
$567$	−1799.29	+	3116.46i	−0.133268	+	0.230827i
$568$	269.244	−	466.345i	0.0198895	−	0.0344496i
$569$	3481.62			0.256515			0.128257	−	0.991741i	$-0.459062\pi$
$569$	3481.62			0.256515			0.128257	+	0.991741i	$0.459062\pi$
$570$	−754.619	−	5416.73i	−0.0554517	−	0.398038i
$571$	−12064.1			−0.884178			−0.442089	−	0.896971i	$-0.645762\pi$
$571$	−12064.1			−0.884178			−0.442089	+	0.896971i	$0.645762\pi$
$572$	1135.04	−	1965.95i	0.0829692	−	0.143707i
$573$	621.566	−	1076.58i	0.0453164	−	0.0784903i
$574$	53.8831	+	93.3283i	0.00391818	+	0.00678649i
$575$	−1036.40	+	1795.09i	−0.0751666	+	0.130192i
$576$	−531.442	−	920.485i	−0.0384434	−	0.0665860i
$577$	−6537.93			−0.471711			−0.235856	−	0.971788i	$-0.575789\pi$
$577$	−6537.93			−0.471711			−0.235856	+	0.971788i	$0.575789\pi$
$578$	−1706.87			−0.122831
$579$	−4357.75	−	7547.84i	−0.312784	−	0.541757i
$580$	2862.69	+	4958.33i	0.204943	+	0.354971i
$581$	−3938.75			−0.281251
$582$	11502.3			0.819216
$583$	1353.92	+	2345.05i	0.0961810	+	0.166590i
$584$	933.957	−	1617.66i	0.0661771	−	0.114622i
$585$	1342.78	+	2325.76i	0.0949008	+	0.164373i
$586$	−2965.59	+	5136.55i	−0.209057	+	0.362097i
$587$	3000.18	−	5196.47i	0.210955	−	0.365385i	−0.741058	−	0.671441i	$-0.765676\pi$
$587$	3000.18	−	5196.47i	0.210955	−	0.365385i	0.952014	+	0.306055i	$0.0990092\pi$
$588$	−8639.34			−0.605919
$589$	2195.80	+	15761.7i	0.153610	+	1.10263i
$590$	1903.42			0.132818
$591$	−3128.05	+	5417.95i	−0.217717	+	0.377098i
$592$	−2620.30	+	4538.50i	−0.181915	+	0.315086i
$593$	5612.12	+	9720.48i	0.388638	+	0.673141i	0.992267	−	0.124125i	$-0.0396124\pi$
$593$	5612.12	+	9720.48i	0.388638	+	0.673141i	−0.603629	+	0.797266i	$0.706279\pi$
$594$	1204.26	−	2085.84i	0.0831844	−	0.144080i
$595$	757.729	+	1312.43i	0.0522082	+	0.0904272i
$596$	13011.1			0.894222
$597$	35843.8			2.45727
$598$	2681.48	+	4644.46i	0.183368	+	0.317602i
$599$	−8401.93	−	14552.6i	−0.573111	−	0.992658i	−0.996244	−	0.0865902i	$-0.972403\pi$
$599$	−8401.93	−	14552.6i	−0.573111	−	0.992658i	0.423133	−	0.906068i	$-0.360930\pi$
$600$	−1320.72			−0.0898636
$601$	25720.1			1.74567			0.872833	−	0.488019i	$-0.162280\pi$
$601$	25720.1			1.74567			0.872833	+	0.488019i	$0.162280\pi$
$602$	180.777	+	313.116i	0.0122391	+	0.0211987i
$603$	−1122.03	+	1943.42i	−0.0757756	+	0.131247i
$604$	982.377	+	1701.53i	0.0661794	+	0.114626i
$605$	−2557.69	+	4430.04i	−0.171876	+	0.297697i
$606$	−1094.19	+	1895.19i	−0.0733472	+	0.127041i
$607$	−13262.7			−0.886850			−0.443425	−	0.896311i	$-0.646237\pi$
$607$	−13262.7			−0.886850			−0.443425	+	0.896311i	$0.646237\pi$
$608$	2090.36	−	1629.12i	0.139433	−	0.108667i
$609$	−7545.29			−0.502054
$610$	769.613	−	1333.01i	0.0510831	−	0.0884786i
$611$	9163.30	−	15871.3i	0.606722	−	1.05087i
$612$	2522.26	+	4368.68i	0.166595	+	0.288551i
$613$	−7972.60	+	13809.0i	−0.525302	+	0.909850i	0.474263	+	0.880383i	$0.342714\pi$
$613$	−7972.60	+	13809.0i	−0.525302	+	0.909850i	−0.999566	+	0.0294674i	$0.990619\pi$
$614$	−8072.53	−	13982.0i	−0.530588	−	0.919005i
$615$	445.742			0.0292261
$616$	−560.316			−0.0366490
$617$	−367.945	−	637.299i	−0.0240080	−	0.0415830i	0.853772	−	0.520647i	$-0.174309\pi$
$617$	−367.945	−	637.299i	−0.0240080	−	0.0415830i	−0.877780	+	0.479064i	$0.840976\pi$
$618$	−5777.47	−	10006.9i	−0.376058	−	0.651352i
$619$	−18208.1			−1.18230			−0.591152	−	0.806560i	$-0.701327\pi$
$619$	−18208.1			−1.18230			−0.591152	+	0.806560i	$0.701327\pi$
$620$	3843.05			0.248936
$621$	2845.02	+	4927.71i	0.183843	+	0.318426i
$622$	6715.16	−	11631.0i	0.432883	−	0.749776i
$623$	507.068	+	878.268i	0.0326088	+	0.0564800i
$624$	−1708.55	+	2959.30i	−0.109610	+	0.189851i
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−11926.6			−0.761471
$627$	−8893.82	−	3605.81i	−0.566483	−	0.229668i
$628$	−14419.0			−0.916213
$629$	12436.1	−	21540.0i	0.788332	−	1.36543i
$630$	331.433	−	574.060i	0.0209597	−	0.0363033i
$631$	−14426.1	−	24986.7i	−0.910130	−	1.57639i	−0.813879	−	0.581035i	$-0.802648\pi$
$631$	−14426.1	−	24986.7i	−0.910130	−	1.57639i	−0.0962513	−	0.995357i	$-0.530685\pi$
$632$	2955.51	−	5119.09i	0.186019	−	0.322194i
$633$	−2960.87	−	5128.38i	−0.185915	−	0.322014i
$634$	5640.59			0.353338
$635$	−7378.84			−0.461134
$636$	−2038.03	−	3529.97i	−0.127064	−	0.220082i
$637$	5288.93	+	9160.69i	0.328971	+	0.569795i
$638$	10046.8			0.623443
$639$	1117.87			0.0692056
$640$	−320.000	−	554.256i	−0.0197642	−	0.0342327i
$641$	−14646.8	+	25369.0i	−0.902519	+	1.56321i	−0.0783046	+	0.996929i	$0.524951\pi$
$641$	−14646.8	+	25369.0i	−0.902519	+	1.56321i	−0.824214	+	0.566278i	$0.808383\pi$
$642$	−3141.98	−	5442.07i	−0.193153	−	0.334550i
$643$	4757.25	−	8239.80i	0.291769	−	0.505359i	−0.682459	−	0.730924i	$-0.739089\pi$
$643$	4757.25	−	8239.80i	0.291769	−	0.505359i	0.974228	+	0.225565i	$0.0724227\pi$
$644$	661.861	−	1146.38i	0.0404984	−	0.0701453i
$645$	1495.46			0.0912926
$646$	−9920.98	+	7731.89i	−0.604235	+	0.470909i
$647$	31911.7			1.93907			0.969534	−	0.244957i	$-0.0787739\pi$
$647$	31911.7			1.93907			0.969534	+	0.244957i	$0.0787739\pi$
$648$	−3606.37	+	6246.42i	−0.218629	+	0.378677i
$649$	1670.04	−	2892.60i	0.101009	−	0.174953i
$650$	808.533	+	1400.42i	0.0487897	+	0.0845062i
$651$	−2532.31	+	4386.09i	−0.152456	+	0.264062i
$652$	−6341.05	−	10983.0i	−0.380881	−	0.659706i
$653$	17136.1			1.02693			0.513466	−	0.858110i	$-0.328361\pi$
$653$	17136.1			1.02693			0.513466	+	0.858110i	$0.328361\pi$
$654$	−3105.33			−0.185670
$655$	−153.685	−	266.189i	−0.00916786	−	0.0158792i
$656$	108.000	+	187.061i	0.00642786	+	0.0111334i
$657$	3877.69			0.230263
$658$	−4523.50			−0.268000
$659$	−6340.25	−	10981.6i	−0.374782	−	0.649141i	0.615513	−	0.788127i	$-0.288949\pi$
$659$	−6340.25	−	10981.6i	−0.374782	−	0.649141i	−0.990294	+	0.138986i	$0.955616\pi$
$660$	−1158.79	+	2007.08i	−0.0683421	+	0.118372i
$661$	−5817.11	−	10075.5i	−0.342299	−	0.592879i	0.642560	−	0.766235i	$-0.277872\pi$
$661$	−5817.11	−	10075.5i	−0.342299	−	0.592879i	−0.984859	+	0.173356i	$0.944539\pi$
$662$	6465.65	−	11198.8i	0.379599	−	0.657485i
$663$	8108.91	−	14045.0i	0.474999	−	0.822722i
$664$	−7894.57			−0.461399
$665$	1531.70	+	620.996i	0.0893187	+	0.0362123i
$666$	−10879.2			−0.632974
$667$	−11867.6	+	20555.2i	−0.688926	+	1.19325i
$668$	−3403.07	+	5894.29i	−0.197109	+	0.341403i
$669$	−1650.10	−	2858.05i	−0.0953608	−	0.165170i
$670$	−675.615	+	1170.20i	−0.0389572	+	0.0674758i
$671$	−1350.50	−	2339.14i	−0.0776983	−	0.134577i
$672$	843.434			0.0484169
$673$	−30000.5			−1.71833			−0.859163	−	0.511702i	$-0.829015\pi$
$673$	−30000.5			−1.71833			−0.859163	+	0.511702i	$0.829015\pi$
$674$	2386.02	+	4132.71i	0.136359	+	0.236181i
$675$	857.844	+	1485.83i	0.0489162	+	0.0847253i
$676$	−4604.15			−0.261957
$677$	22267.7			1.26413			0.632065	−	0.774916i	$-0.282208\pi$
$677$	22267.7			1.26413			0.632065	+	0.774916i	$0.282208\pi$
$678$	2128.92	+	3687.39i	0.120591	+	0.208869i
$679$	−1738.05	+	3010.39i	−0.0982331	+	0.170145i
$680$	1518.74	+	2630.54i	0.0856486	+	0.148348i
$681$	−13743.7	+	23804.8i	−0.773362	+	1.33950i
$682$	3371.85	−	5840.22i	0.189318	−	0.327909i
$683$	−28218.3			−1.58088			−0.790440	−	0.612539i	$-0.790148\pi$
$683$	−28218.3			−1.58088			−0.790440	+	0.612539i	$0.790148\pi$
$684$	5098.59	+	2067.11i	0.285014	+	0.115553i
$685$	−2351.54			−0.131164
$686$	2674.48	−	4632.34i	0.148852	−	0.257819i
$687$	−3171.95	+	5493.98i	−0.176154	+	0.305107i
$688$	362.338	+	627.588i	0.0200785	+	0.0347770i
$689$	−2495.32	+	4322.03i	−0.137974	+	0.238978i
$690$	−2737.58	−	4741.64i	−0.151041	−	0.261610i
$691$	−12894.5			−0.709883			−0.354942	−	0.934889i	$-0.615499\pi$
$691$	−12894.5			−0.709883			−0.354942	+	0.934889i	$0.615499\pi$
$692$	8270.55			0.454334
$693$	−581.593	−	1007.35i	−0.0318801	−	0.0552179i
$694$	2750.99	+	4764.86i	0.150470	+	0.260622i
$695$	7214.45			0.393755
$696$	−15123.3			−0.823629
$697$	−512.573	−	887.803i	−0.0278552	−	0.0482467i
$698$	8581.95	−	14864.4i	0.465375	−	0.806053i
$699$	−6216.42	−	10767.2i	−0.336376	−	0.582620i
$700$	199.568	−	345.661i	0.0107756	−	0.0186640i
$701$	14133.1	−	24479.3i	0.761484	−	1.31893i	−0.180602	−	0.983556i	$-0.557805\pi$
$701$	14133.1	−	24479.3i	0.761484	−	1.31893i	0.942086	−	0.335372i	$-0.108862\pi$
$702$	4439.01			0.238660
$703$	−3742.90	−	26866.9i	−0.200805	−	1.44140i
$704$	−1123.06			−0.0601235
$705$	−9355.02	+	16203.4i	−0.499760	+	0.865609i
$706$	10210.4	−	17684.9i	0.544297	−	0.942749i
$707$	−330.675	−	572.746i	−0.0175903	−	0.0304672i
$708$	−2513.88	+	4354.17i	−0.133443	+	0.231130i
$709$	7091.33	+	12282.5i	0.375628	+	0.650607i	0.990421	−	0.138082i	$-0.0440936\pi$
$709$	7091.33	+	12282.5i	0.375628	+	0.650607i	−0.614793	+	0.788689i	$0.710760\pi$
$710$	673.111			0.0355794
$711$	12271.0			0.647253
$712$	1016.33	+	1760.34i	0.0534953	+	0.0926566i
$713$	7965.85	+	13797.3i	0.418406	+	0.724701i
$714$	−4002.99			−0.209816
$715$	2837.60			0.148420
$716$	−3385.58	−	5863.99i	−0.176711	−	0.306072i
$717$	−9992.19	+	17307.0i	−0.520454	+	0.901452i
$718$	9139.10	+	15829.4i	0.475025	+	0.822768i
$719$	16000.6	−	27713.9i	0.829934	−	1.43749i	−0.0681552	−	0.997675i	$-0.521711\pi$
$719$	16000.6	−	27713.9i	0.829934	−	1.43749i	0.898089	−	0.439813i	$-0.144955\pi$
$720$	664.303	−	1150.61i	0.0343849	−	0.0595563i
$721$	3492.02			0.180374
$722$	−3350.75	+	13302.5i	−0.172717	+	0.685689i
$723$	27465.4			1.41279
$724$	−9054.59	+	15683.0i	−0.464794	+	0.805048i
$725$	−3578.37	+	6197.91i	−0.183306	+	0.317496i
$726$	−6755.97	−	11701.7i	−0.345369	−	0.598196i
$727$	1533.88	−	2656.76i	0.0782509	−	0.135535i	−0.824244	−	0.566234i	$-0.808400\pi$
$727$	1533.88	−	2656.76i	0.0782509	−	0.135535i	0.902495	+	0.430700i	$0.141733\pi$
$728$	−516.343	−	894.332i	−0.0262870	−	0.0455304i
$729$	−2737.17			−0.139062
$730$	2334.89			0.118381
$731$	−1719.68	−	2978.57i	−0.0870105	−	0.150707i
$732$	2032.89	+	3521.06i	0.102647	+	0.177790i
$733$	5382.20			0.271209			0.135604	−	0.990763i	$-0.456702\pi$
$733$	5382.20			0.271209			0.135604	+	0.990763i	$0.456702\pi$
$734$	−26420.6			−1.32861
$735$	−5399.59	−	9352.36i	−0.270975	−	0.469343i
$736$	1326.59	−	2297.72i	0.0664385	−	0.115075i
$737$	1185.56	+	2053.45i	0.0592545	+	0.102632i
$738$	−224.201	+	388.328i	−0.0111829	+	0.0193693i
$739$	−5203.22	+	9012.24i	−0.259003	+	0.448607i	−0.965975	−	0.258635i	$-0.916727\pi$
$739$	−5203.22	+	9012.24i	−0.259003	+	0.448607i	0.706972	+	0.707242i	$0.250061\pi$
$740$	−6550.76			−0.325420
$741$	−2440.54	−	17518.4i	−0.120992	−	0.868496i
$742$	1231.83			0.0609457
$743$	4459.51	−	7724.10i	0.220193	−	0.381386i	−0.734673	−	0.678421i	$-0.762665\pi$
$743$	4459.51	−	7724.10i	0.220193	−	0.381386i	0.954867	+	0.297035i	$0.0959979\pi$
$744$	−5075.59	+	8791.18i	−0.250108	+	0.433199i
$745$	8131.95	+	14085.0i	0.399908	+	0.692662i
$746$	−9533.85	+	16513.1i	−0.467907	+	0.810439i
$747$	−8194.35	−	14193.0i	−0.401360	−	0.695175i
$748$	5330.12			0.260546
$749$	1899.08			0.0926446
$750$	−825.450	−	1429.72i	−0.0401882	−	0.0696081i
$751$	−19182.6	−	33225.2i	−0.932067	−	1.61439i	−0.779783	−	0.626050i	$-0.784670\pi$
$751$	−19182.6	−	33225.2i	−0.932067	−	1.61439i	−0.152284	−	0.988337i	$-0.548663\pi$
$752$	−9066.59			−0.439660
$753$	−6209.78			−0.300527
$754$	9258.33	+	16035.9i	0.447173	+	0.774527i
$755$	−1227.97	+	2126.91i	−0.0591926	+	0.102525i
$756$	−547.834	−	948.875i	−0.0263552	−	0.0456485i
$757$	−13522.4	+	23421.5i	−0.649249	+	1.12453i	0.334054	+	0.942554i	$0.391583\pi$
$757$	−13522.4	+	23421.5i	−0.649249	+	1.12453i	−0.983303	+	0.181978i	$0.941750\pi$
$758$	−3046.43	+	5276.57i	−0.145978	+	0.252841i
$759$	−9607.72			−0.459471
$760$	3070.04	+	1244.68i	0.146529	+	0.0594071i
$761$	9062.57			0.431692			0.215846	−	0.976427i	$-0.430749\pi$
$761$	9062.57			0.431692			0.215846	+	0.976427i	$0.430749\pi$
$762$	9745.38	−	16879.5i	0.463304	−	0.802467i
$763$	469.231	−	812.732i	0.0222638	−	0.0385621i
$764$	376.501	+	652.119i	0.0178290	+	0.0308807i
$765$	−3152.82	+	5460.85i	−0.149007	+	0.258088i
$766$	13610.4	+	23574.0i	0.641991	+	1.11196i
$767$	6155.90			0.289800
$768$	1690.52			0.0794290
$769$	−1140.32	−	1975.10i	−0.0534735	−	0.0926188i	0.838050	−	0.545594i	$-0.183696\pi$
$769$	−1140.32	−	1975.10i	−0.0534735	−	0.0926188i	−0.891523	+	0.452975i	$0.850363\pi$
$770$	−350.198	−	606.560i	−0.0163899	−	0.0283882i
$771$	−34210.7			−1.59801
$772$	5279.24			0.246119
$773$	−13382.9	−	23179.8i	−0.622702	−	1.07855i	−0.988980	−	0.148047i	$-0.952701\pi$
$773$	−13382.9	−	23179.8i	−0.622702	−	1.07855i	0.366278	−	0.930505i	$-0.380632\pi$
$774$	−752.194	+	1302.84i	−0.0349316	+	0.0605033i
$775$	2401.90	+	4160.22i	0.111328	+	0.192825i
$776$	−3483.63	+	6033.83i	−0.161153	+	0.279126i
$777$	4316.51	−	7476.41i	0.199297	−	0.345193i
$778$	−29724.8			−1.36977
$779$	−1036.14	−	420.079i	−0.0476552	−	0.0193208i
$780$	−4271.39			−0.196077
$781$	590.581	−	1022.92i	0.0270585	−	0.0468666i
$782$	−6296.08	+	10905.1i	−0.287912	+	0.498679i
$783$	9822.98	+	17013.9i	0.448333	+	0.776535i
$784$	2616.55	−	4532.00i	0.119194	−	0.206451i
$785$	−9011.90	−	15609.1i	−0.409743	−	0.709696i
$786$	811.897			0.0368440
$787$	2103.81			0.0952893			0.0476447	−	0.998864i	$-0.484828\pi$
$787$	2103.81			0.0952893			0.0476447	+	0.998864i	$0.484828\pi$
$788$	−1894.76	−	3281.81i	−0.0856572	−	0.148363i
$789$	−22298.1	−	38621.4i	−1.00613	−	1.74266i
$790$	7388.78			0.332761
$791$	−1286.76			−0.0578406
$792$	−1165.71	−	2019.06i	−0.0522999	−	0.0905862i
$793$	2489.03	−	4311.13i	0.111460	−	0.193055i
$794$	−6777.15	−	11738.4i	−0.302912	−	0.524659i
$795$	2547.53	−	4412.46i	0.113650	−	0.196847i
$796$	−10855.8	+	18802.9i	−0.483386	+	0.837249i
$797$	20448.1			0.908792			0.454396	−	0.890800i	$-0.349855\pi$
$797$	20448.1			0.908792			0.454396	+	0.890800i	$0.349855\pi$
$798$	−3443.52	+	2683.69i	−0.152756	+	0.119050i
$799$	43030.6			1.90527
$800$	400.000	−	692.820i	0.0176777	−	0.0306186i
$801$	−2109.85	+	3654.37i	−0.0930686	+	0.161200i
$802$	−5212.99	−	9029.17i	−0.229523	−	0.397545i
$803$	2048.61	−	3548.30i	0.0900299	−	0.155936i
$804$	−1784.60	−	3091.01i	−0.0782810	−	0.135587i
$805$	1654.65			0.0724458
$806$	12428.9			0.543164
$807$	4196.45	+	7268.46i	0.183051	+	0.317053i
$808$	−662.783	−	1147.97i	−0.0288572	−	0.0499821i
$809$	15086.6			0.655644			0.327822	−	0.944739i	$-0.393685\pi$
$809$	15086.6			0.655644			0.327822	+	0.944739i	$0.393685\pi$
$810$	−9015.93			−0.391096
$811$	−19021.2	−	32945.8i	−0.823583	−	1.42649i	−0.902997	−	0.429646i	$-0.858638\pi$
$811$	−19021.2	−	32945.8i	−0.823583	−	1.42649i	0.0794140	−	0.996842i	$-0.474695\pi$
$812$	2285.20	−	3958.09i	0.0987623	−	0.171061i
$813$	6720.07	+	11639.5i	0.289893	+	0.502110i
$814$	−5747.57	+	9955.09i	−0.247484	+	0.428656i
$815$	7926.31	−	13728.8i	0.340671	−	0.590059i
$816$	−8023.33			−0.344207
$817$	−3476.23	−	1409.36i	−0.148859	−	0.0603517i
$818$	20723.5			0.885796
$819$	1071.90	−	1856.58i	0.0457329	−	0.0792116i
$820$	−135.000	+	233.826i	−0.00574925	+	0.00995800i
$821$	−10001.9	−	17323.8i	−0.425175	−	0.736424i	0.571262	−	0.820768i	$-0.306454\pi$
$821$	−10001.9	−	17323.8i	−0.425175	−	0.736424i	−0.996437	+	0.0843435i	$0.973121\pi$
$822$	3105.73	−	5379.27i	0.131782	−	0.228253i
$823$	17994.7	+	31167.7i	0.762157	+	1.32009i	0.941737	+	0.336351i	$0.109193\pi$
$823$	17994.7	+	31167.7i	0.762157	+	1.32009i	−0.179580	+	0.983743i	$0.557474\pi$
$824$	6999.18			0.295908
$825$	−2896.97			−0.122254
$826$	−759.721	−	1315.88i	−0.0320025	−	0.0554300i
$827$	−1011.43	−	1751.86i	−0.0425284	−	0.0736614i	0.843978	−	0.536378i	$-0.180208\pi$
$827$	−1011.43	−	1751.86i	−0.0425284	−	0.0736614i	−0.886506	+	0.462717i	$0.846875\pi$
$828$	5507.86			0.231173
$829$	17546.2			0.735107			0.367554	−	0.930002i	$-0.380195\pi$
$829$	17546.2			0.735107			0.367554	+	0.930002i	$0.380195\pi$
$830$	−4934.11	−	8546.12i	−0.206344	−	0.357398i
$831$	−16648.3	+	28835.8i	−0.694975	+	1.20373i
$832$	−1034.92	−	1792.54i	−0.0431244	−	0.0746936i
$833$	−12418.3	+	21509.2i	−0.516530	+	0.894657i
$834$	−9528.27	+	16503.5i	−0.395608	+	0.685213i
$835$	−8507.68			−0.352599
$836$	4585.15	−	3573.43i	0.189690	−	0.147834i
$837$	13186.9			0.544573
$838$	7010.59	−	12142.7i	0.288994	−	0.500552i
$839$	15482.2	−	26816.0i	0.637075	−	1.10345i	−0.348997	−	0.937124i	$-0.613478\pi$
$839$	15482.2	−	26816.0i	0.637075	−	1.10345i	0.986072	−	0.166322i	$-0.0531891\pi$
$840$	527.146	+	913.044i	0.0216527	+	0.0375036i
$841$	−28780.6	+	49849.4i	−1.18006	+	2.04393i
$842$	−11924.6	−	20654.0i	−0.488062	−	0.845348i
$843$	7861.98			0.321211
$844$	3586.98			0.146290
$845$	−2877.60	−	4984.14i	−0.117151	−	0.202911i
$846$	−9410.87	−	16300.1i	−0.382450	−	0.662422i
$847$	4083.45			0.165654
$848$	2468.99			0.0999828
$849$	24996.7	+	43295.5i	1.01046	+	1.75017i
$850$	−1898.43	+	3288.17i	−0.0766065	+	0.132686i
$851$	−13578.4	−	23518.4i	−0.546958	−	0.947358i
$852$	−888.991	+	1539.78i	−0.0357469	+	0.0619154i
$853$	10529.5	−	18237.6i	0.422652	−	0.732055i	−0.573546	−	0.819173i	$-0.694433\pi$
$853$	10529.5	−	18237.6i	0.422652	−	0.732055i	0.996198	+	0.0871187i	$0.0277659\pi$
$854$	−1228.72			−0.0492341
$855$	948.905	+	6811.34i	0.0379554	+	0.272448i
$856$	3806.38			0.151985
$857$	3517.52	−	6092.52i	0.140206	−	0.242843i	−0.787368	−	0.616483i	$-0.788557\pi$
$857$	3517.52	−	6092.52i	0.140206	−	0.242843i	0.927574	+	0.373640i	$0.121890\pi$
$858$	−3747.67	+	6491.16i	−0.149118	+	0.258280i
$859$	10250.3	+	17754.1i	0.407144	+	0.705194i	0.994568	−	0.104085i	$-0.0331913\pi$
$859$	10250.3	+	17754.1i	0.407144	+	0.705194i	−0.587424	+	0.809279i	$0.699858\pi$
$860$	−452.923	+	784.485i	−0.0179588	+	0.0311055i
$861$	−177.911	−	308.151i	−0.00704205	−	0.0121972i
$862$	15648.3			0.618311
$863$	11388.0			0.449192			0.224596	−	0.974452i	$-0.427894\pi$
$863$	11388.0			0.449192			0.224596	+	0.974452i	$0.427894\pi$
$864$	−1098.04	−	1901.86i	−0.0432362	−	0.0748873i
$865$	5169.09	+	8953.13i	0.203184	+	0.351926i
$866$	20910.4			0.820515
$867$	5635.76			0.220762
$868$	−1533.90	−	2656.79i	−0.0599814	−	0.103891i
$869$	6482.84	−	11228.6i	0.253067	−	0.438325i
$870$	−9452.04	−	16371.4i	−0.368338	−	0.637981i
$871$	−2185.03	+	3784.58i	−0.0850022	+	0.147228i
$872$	940.495	−	1628.98i	0.0365243	−	0.0632619i
$873$	−14463.7			−0.560734
$874$	1894.93	+	13602.0i	0.0733375	+	0.526424i
$875$	498.919			0.0192761
$876$	−3083.74	+	5341.20i	−0.118938	+	0.206007i
$877$	12353.5	−	21396.9i	0.475653	−	0.823855i	−0.523958	−	0.851744i	$-0.675545\pi$
$877$	12353.5	−	21396.9i	0.475653	−	0.823855i	0.999611	+	0.0278893i	$0.00887859\pi$
$878$	8284.29	+	14348.8i	0.318430	+	0.551537i
$879$	9791.78	−	16959.9i	0.375732	−	0.650787i
$880$	−701.913	−	1215.75i	−0.0268880	−	0.0465714i
$881$	47631.3			1.82150			0.910748	−	0.412962i	$-0.135506\pi$
$881$	47631.3			1.82150			0.910748	+	0.412962i	$0.135506\pi$
$882$	10863.6			0.414737
$883$	−21105.8	−	36556.3i	−0.804378	−	1.39322i	−0.916710	−	0.399554i	$-0.869165\pi$
$883$	−21105.8	−	36556.3i	−0.804378	−	1.39322i	0.112331	−	0.993671i	$-0.464168\pi$
$884$	4911.81	+	8507.51i	0.186880	+	0.323686i
$885$	−6284.71			−0.238710
$886$	−7667.07			−0.290723
$887$	−6565.47	−	11371.7i	−0.248531	−	0.430468i	0.714587	−	0.699546i	$-0.246614\pi$
$887$	−6565.47	−	11371.7i	−0.248531	−	0.430468i	−0.963118	+	0.269078i	$0.913281\pi$
$888$	8651.72	−	14985.2i	0.326951	−	0.566296i
$889$	2945.16	+	5101.16i	0.111111	+	0.192449i
$890$	−1270.42	+	2200.42i	−0.0478477	+	0.0828746i
$891$	−7910.49	+	13701.4i	−0.297432	+	0.515167i
$892$	1999.03			0.0750362
$893$	37016.5	−	28848.7i	1.38713	−	1.08106i
$894$	−42960.2			−1.60716
$895$	4231.97	−	7329.99i	0.158055	−	0.273759i
$896$	−255.447	+	442.447i	−0.00952441	+	0.0164968i
$897$	−8853.71	−	15335.1i	−0.329562	−	0.570818i
$898$	−5353.68	+	9272.85i	−0.198947	+	0.344587i
$899$	27503.7	+	47637.7i	1.02035	+	1.76731i
$900$	1660.76			0.0615095
$901$	−11718.0			−0.433277
$902$	236.895	+	410.314i	0.00874471	+	0.0151463i
$903$	−596.891	−	1033.85i	−0.0219970	−	0.0380999i
$904$	−2579.10			−0.0948888
$905$	−22636.5			−0.831450
$906$	−3243.61	−	5618.10i	−0.118942	−	0.206014i
$907$	17413.1	−	30160.4i	0.637479	−	1.10415i	−0.348505	−	0.937307i	$-0.613311\pi$
$907$	17413.1	−	30160.4i	0.637479	−	1.10415i	0.985984	−	0.166839i	$-0.0533560\pi$
$908$	−8324.96	−	14419.3i	−0.304266	−	0.527004i
$909$	1375.90	−	2383.13i	0.0502044	−	0.0869565i
$910$	645.429	−	1117.92i	0.0235118	−	0.0407237i
$911$	9739.87			0.354222			0.177111	−	0.984191i	$-0.443325\pi$
$911$	9739.87			0.354222			0.177111	+	0.984191i	$0.443325\pi$
$912$	−6901.95	+	5379.02i	−0.250599	+	0.195304i
$913$	−17316.6			−0.627705
$914$	14247.0	−	24676.5i	0.515589	−	0.893027i
$915$	−2541.11	+	4401.33i	−0.0918104	+	0.159020i
$916$	−1921.35	−	3327.87i	−0.0693046	−	0.120039i
$917$	−122.682	+	212.491i	−0.00441801	+	0.00765221i
$918$	5211.37	+	9026.36i	0.187365	+	0.324525i
$919$	24584.8			0.882457			0.441229	−	0.897395i	$-0.354543\pi$
$919$	24584.8			0.882457			0.441229	+	0.897395i	$0.354543\pi$
$920$	3316.47			0.118849
$921$	26653.9	+	46165.9i	0.953611	+	1.65170i
$922$	−17560.9	−	30416.5i	−0.627266	−	1.08646i
$923$	2176.93			0.0776322
$924$	1850.05			0.0658683
$925$	−4094.22	−	7091.40i	−0.145532	−	0.252069i
$926$	−9839.90	+	17043.2i	−0.349200	+	0.604832i
$927$	7264.96	+	12583.3i	0.257403	+	0.445835i
$928$	4580.31	−	7933.33i	0.162022	−	0.280630i
$929$	21168.0	−	36664.0i	0.747577	−	1.29484i	−0.201404	−	0.979508i	$-0.564551\pi$
$929$	21168.0	−	36664.0i	0.747577	−	1.29484i	0.948981	−	0.315333i	$-0.102116\pi$
$930$	−12689.0			−0.447406
$931$	3737.54	+	26828.5i	0.131571	+	0.944433i
$932$	7530.95			0.264683
$933$	−22172.1	+	38403.3i	−0.778010	+	1.34755i
$934$	−12809.4	+	22186.6i	−0.448755	+	0.777266i
$935$	3331.32	+	5770.02i	0.116520	+	0.201818i
$936$	2148.44	−	3721.21i	0.0750257	−	0.129948i
$937$	22391.7	+	38783.6i	0.780688	+	1.35219i	0.931541	+	0.363636i	$0.118465\pi$
$937$	22391.7	+	38783.6i	0.780688	+	1.35219i	−0.150853	+	0.988556i	$0.548202\pi$
$938$	1078.65			0.0375470
$939$	39379.1			1.36857
$940$	−5666.62	−	9814.87i	−0.196622	−	0.340559i
$941$	14734.7	+	25521.2i	0.510453	+	0.884130i	0.999927	+	0.0121124i	$0.00385560\pi$
$941$	14734.7	+	25521.2i	0.510453	+	0.884130i	−0.489474	+	0.872018i	$0.662811\pi$
$942$	47608.8			1.64669
$943$	−1119.31			−0.0386528
$944$	−1522.73	−	2637.45i	−0.0525008	−	0.0909341i
$945$	684.792	−	1186.09i	0.0235728	−	0.0408293i
$946$	794.780	+	1376.60i	0.0273156	+	0.0473120i
$947$	−22273.1	+	38578.2i	−0.764287	+	1.32378i	0.176335	+	0.984330i	$0.443576\pi$
$947$	−22273.1	+	38578.2i	−0.764287	+	1.32378i	−0.940623	+	0.339454i	$0.889758\pi$
$948$	−9758.51	+	16902.2i	−0.334327	+	0.579071i
$949$	7551.35			0.258301
$950$	571.369	+	4101.35i	0.0195133	+	0.140069i
$951$	−18624.1			−0.635045
$952$	1212.37	−	2099.88i	0.0412742	−	0.0714890i
$953$	−28746.8	+	49790.9i	−0.977124	+	1.69243i	−0.304384	+	0.952549i	$0.598451\pi$
$953$	−28746.8	+	49790.9i	−0.977124	+	1.69243i	−0.672740	+	0.739879i	$0.734883\pi$
$954$	2562.74	+	4438.80i	0.0869726	+	0.150641i
$955$	−470.627	+	815.149i	−0.0159467	+	0.0276205i
$956$	−6052.57	−	10483.4i	−0.204764	−	0.354661i
$957$	−33172.5			−1.12050
$958$	−23134.8			−0.780222
$959$	938.583	+	1625.67i	0.0316042	+	0.0547401i
$960$	1056.58	+	1830.04i	0.0355217	+	0.0615254i
$961$	7131.53			0.239386
$962$	−21186.0			−0.710046
$963$	3950.92	+	6843.19i	0.132208	+	0.228992i
$964$	−8318.30	+	14407.7i	−0.277919	+	0.481371i
$965$	3299.52	+	5714.94i	0.110068	+	0.190643i
$966$	−2185.33	+	3785.11i	−0.0727867	+	0.126070i
$967$	−15760.8	+	27298.5i	−0.524129	+	0.907818i	0.475477	+	0.879728i	$0.342276\pi$
$967$	−15760.8	+	27298.5i	−0.524129	+	0.907818i	−0.999605	+	0.0280893i	$0.991058\pi$
$968$	8184.59			0.271759
$969$	32757.1	−	25529.2i	1.08597	−	0.846352i
$970$	−8709.08			−0.288280
$971$	−17868.7	+	30949.6i	−0.590562	+	1.02288i	0.403595	+	0.914938i	$0.367760\pi$
$971$	−17868.7	+	30949.6i	−0.590562	+	1.02288i	−0.994157	+	0.107945i	$0.965573\pi$
$972$	8201.64	−	14205.7i	0.270646	−	0.468772i
$973$	−2879.54	−	4987.52i	−0.0948756	−	0.164329i
$974$	−482.254	+	835.288i	−0.0158649	+	0.0274788i
$975$	−2669.62	−	4623.91i	−0.0876884	−	0.151881i
$976$	−2462.76			−0.0807695
$977$	15296.9			0.500912			0.250456	−	0.968128i	$-0.419419\pi$
$977$	15296.9			0.500912			0.250456	+	0.968128i	$0.419419\pi$
$978$	20936.9	+	36263.8i	0.684548	+	1.18567i
$979$	2229.30	+	3861.27i	0.0727771	+	0.126054i
$980$	6541.38			0.213221
$981$	3904.83			0.127086
$982$	−5507.91	−	9539.98i	−0.178986	−	0.310013i
$983$	13465.0	−	23322.1i	0.436894	−	0.756723i	−0.560554	−	0.828118i	$-0.689412\pi$
$983$	13465.0	−	23322.1i	0.436894	−	0.756723i	0.997448	+	0.0713949i	$0.0227450\pi$
$984$	−356.593	−	617.638i	−0.0115526	−	0.0200097i
$985$	2368.45	−	4102.27i	0.0766142	−	0.132700i
$986$	−21738.4	+	37652.1i	−0.702123	+	1.21611i
$987$	14935.7			0.481670
$988$	9928.93	+	4025.47i	0.319718	+	0.129623i
$989$	−3755.26			−0.120739
$990$	1457.13	−	2523.83i	0.0467785	−	0.0810227i
$991$	−6836.34	+	11840.9i	−0.219136	+	0.379554i	−0.954544	−	0.298070i	$-0.903657\pi$
$991$	−6836.34	+	11840.9i	−0.219136	+	0.379554i	0.735408	+	0.677624i	$0.236990\pi$
$992$	−3074.44	−	5325.08i	−0.0984007	−	0.170435i
$993$	−21348.3	+	36976.3i	−0.682243	+	1.18168i
$994$	−268.662	−	465.337i	−0.00857289	−	0.0148487i
$995$	−27139.6			−0.864707
$996$	26066.3			0.829260
$997$	−3589.03	−	6216.39i	−0.114008	−	0.197467i	0.803375	−	0.595474i	$-0.203036\pi$
$997$	−3589.03	−	6216.39i	−0.114008	−	0.197467i	−0.917383	+	0.398006i	$0.869702\pi$
$998$	4938.78	+	8554.22i	0.156648	+	0.271322i
$999$	−22478.1			−0.711888

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	190.4.e.d.11.1	✓	8
19.7	even	3	inner	190.4.e.d.121.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.4.e.d.11.1	✓	8	1.1	even	1	trivial
190.4.e.d.121.1	yes	8	19.7	even	3	inner

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:	\( N \)	\(=\)	\( 190 = 2 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	190.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-3.30180 + 5.71889i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(2.50000 - 4.33013i) q^{5} +(6.60360 + 11.4378i) q^{6} -3.99135 q^{7} -8.00000 q^{8} +(-8.30378 - 14.3826i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(-3.30180 + 5.71889i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(2.50000 - 4.33013i) q^{5} +(6.60360 + 11.4378i) q^{6} -3.99135 q^{7} -8.00000 q^{8} +(-8.30378 - 14.3826i) q^{9} +(-5.00000 - 8.66025i) q^{10} -17.5478 q^{11} +26.4144 q^{12} +(-16.1707 - 28.0084i) q^{13} +(-3.99135 + 6.91323i) q^{14} +(16.5090 + 28.5944i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(37.9685 - 65.7634i) q^{17} -33.2151 q^{18} +(-11.4274 - 82.0269i) q^{19} -20.0000 q^{20} +(13.1787 - 22.8261i) q^{21} +(-17.5478 + 30.3937i) q^{22} +(-41.4559 - 71.8038i) q^{23} +(26.4144 - 45.7511i) q^{24} +(-12.5000 - 21.6506i) q^{25} -64.6827 q^{26} -68.6275 q^{27} +(7.98271 + 13.8265i) q^{28} +(-143.135 - 247.916i) q^{29} +66.0360 q^{30} -192.152 q^{31} +(16.0000 + 27.7128i) q^{32} +(57.9394 - 100.354i) q^{33} +(-75.9371 - 131.527i) q^{34} +(-9.97839 + 17.2831i) q^{35} +(-33.2151 + 57.5303i) q^{36} +327.538 q^{37} +(-153.502 - 62.2341i) q^{38} +213.569 q^{39} +(-20.0000 + 34.6410i) q^{40} +(6.74998 - 11.6913i) q^{41} +(-26.3573 - 45.6522i) q^{42} +(22.6461 - 39.2242i) q^{43} +(35.0956 + 60.7874i) q^{44} -83.0378 q^{45} -165.824 q^{46} +(283.331 + 490.744i) q^{47} +(-52.8288 - 91.5022i) q^{48} -327.069 q^{49} -50.0000 q^{50} +(250.729 + 434.275i) q^{51} +(-64.6827 + 112.034i) q^{52} +(-77.1559 - 133.638i) q^{53} +(-68.6275 + 118.866i) q^{54} +(-43.8695 + 75.9843i) q^{55} +31.9308 q^{56} +(506.834 + 205.485i) q^{57} -572.539 q^{58} +(-95.1709 + 164.841i) q^{59} +(66.0360 - 114.378i) q^{60} +(76.9613 + 133.301i) q^{61} +(-192.152 + 332.818i) q^{62} +(33.1433 + 57.4060i) q^{63} +64.0000 q^{64} -161.707 q^{65} +(-115.879 - 200.708i) q^{66} +(-67.5615 - 117.020i) q^{67} -303.748 q^{68} +547.517 q^{69} +(19.9568 + 34.5661i) q^{70} +(-33.6555 + 58.2931i) q^{71} +(66.4303 + 115.061i) q^{72} +(-116.745 + 202.208i) q^{73} +(327.538 - 567.312i) q^{74} +165.090 q^{75} +(-261.295 + 203.639i) q^{76} +70.0396 q^{77} +(213.569 - 369.913i) q^{78} +(-369.439 + 639.887i) q^{79} +(40.0000 + 69.2820i) q^{80} +(450.797 - 780.802i) q^{81} +(-13.5000 - 23.3826i) q^{82} +986.821 q^{83} -105.429 q^{84} +(-189.843 - 328.817i) q^{85} +(-45.2923 - 78.4485i) q^{86} +1890.41 q^{87} +140.383 q^{88} +(-127.042 - 220.042i) q^{89} +(-83.0378 + 143.826i) q^{90} +(64.5429 + 111.792i) q^{91} +(-165.824 + 287.215i) q^{92} +(634.449 - 1098.90i) q^{93} +1133.32 q^{94} +(-383.755 - 155.585i) q^{95} -211.315 q^{96} +(435.454 - 754.228i) q^{97} +(-327.069 + 566.500i) q^{98} +(145.713 + 252.383i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 3 q^{3} - 16 q^{4} + 20 q^{5} - 6 q^{6} - 82 q^{7} - 64 q^{8} - 73 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 3 * q^3 - 16 * q^4 + 20 * q^5 - 6 * q^6 - 82 * q^7 - 64 * q^8 - 73 * q^9	\( 8 q + 8 q^{2} + 3 q^{3} - 16 q^{4} + 20 q^{5} - 6 q^{6} - 82 q^{7} - 64 q^{8} - 73 q^{9} - 40 q^{10} + 20 q^{11} - 24 q^{12} - 11 q^{13} - 82 q^{14} - 15 q^{15} - 64 q^{16} - 81 q^{17} - 292 q^{18} + 219 q^{19} - 160 q^{20} + 84 q^{21} + 20 q^{22} + 75 q^{23} - 24 q^{24} - 100 q^{25} - 44 q^{26} - 828 q^{27} + 164 q^{28} - 28 q^{29} - 60 q^{30} - 370 q^{31} + 128 q^{32} - 367 q^{33} + 162 q^{34} - 205 q^{35} - 292 q^{36} + 678 q^{37} - 198 q^{38} + 766 q^{39} - 160 q^{40} - 5 q^{41} - 168 q^{42} + 349 q^{43} - 40 q^{44} - 730 q^{45} + 300 q^{46} - 132 q^{47} + 48 q^{48} - 90 q^{49} - 400 q^{50} + 8 q^{51} - 44 q^{52} + 4 q^{53} - 828 q^{54} + 50 q^{55} + 656 q^{56} - 731 q^{57} - 112 q^{58} + 1368 q^{59} - 60 q^{60} + 1197 q^{61} - 370 q^{62} - 784 q^{63} + 512 q^{64} - 110 q^{65} + 734 q^{66} - 1816 q^{67} + 648 q^{68} + 2942 q^{69} + 410 q^{70} + 137 q^{71} + 584 q^{72} - 1592 q^{73} + 678 q^{74} - 150 q^{75} - 1272 q^{76} - 958 q^{77} + 766 q^{78} + 398 q^{79} + 320 q^{80} + 596 q^{81} + 10 q^{82} + 3222 q^{83} - 672 q^{84} + 405 q^{85} - 698 q^{86} + 4672 q^{87} - 160 q^{88} - 495 q^{89} - 730 q^{90} + 1894 q^{91} + 300 q^{92} - 462 q^{93} - 528 q^{94} - 495 q^{95} + 192 q^{96} + 2087 q^{97} - 90 q^{98} + 944 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 3 * q^3 - 16 * q^4 + 20 * q^5 - 6 * q^6 - 82 * q^7 - 64 * q^8 - 73 * q^9 - 40 * q^10 + 20 * q^11 - 24 * q^12 - 11 * q^13 - 82 * q^14 - 15 * q^15 - 64 * q^16 - 81 * q^17 - 292 * q^18 + 219 * q^19 - 160 * q^20 + 84 * q^21 + 20 * q^22 + 75 * q^23 - 24 * q^24 - 100 * q^25 - 44 * q^26 - 828 * q^27 + 164 * q^28 - 28 * q^29 - 60 * q^30 - 370 * q^31 + 128 * q^32 - 367 * q^33 + 162 * q^34 - 205 * q^35 - 292 * q^36 + 678 * q^37 - 198 * q^38 + 766 * q^39 - 160 * q^40 - 5 * q^41 - 168 * q^42 + 349 * q^43 - 40 * q^44 - 730 * q^45 + 300 * q^46 - 132 * q^47 + 48 * q^48 - 90 * q^49 - 400 * q^50 + 8 * q^51 - 44 * q^52 + 4 * q^53 - 828 * q^54 + 50 * q^55 + 656 * q^56 - 731 * q^57 - 112 * q^58 + 1368 * q^59 - 60 * q^60 + 1197 * q^61 - 370 * q^62 - 784 * q^63 + 512 * q^64 - 110 * q^65 + 734 * q^66 - 1816 * q^67 + 648 * q^68 + 2942 * q^69 + 410 * q^70 + 137 * q^71 + 584 * q^72 - 1592 * q^73 + 678 * q^74 - 150 * q^75 - 1272 * q^76 - 958 * q^77 + 766 * q^78 + 398 * q^79 + 320 * q^80 + 596 * q^81 + 10 * q^82 + 3222 * q^83 - 672 * q^84 + 405 * q^85 - 698 * q^86 + 4672 * q^87 - 160 * q^88 - 495 * q^89 - 730 * q^90 + 1894 * q^91 + 300 * q^92 - 462 * q^93 - 528 * q^94 - 495 * q^95 + 192 * q^96 + 2087 * q^97 - 90 * q^98 + 944 * q^99

Introduction

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Modular forms

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