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Properties

Label 74.8.f.b.53.8
Level $74$
Weight $8$
Character 74.53
Analytic conductor $23.116$
Analytic rank $0$
Dimension $66$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [74,8,Mod(7,74)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(74, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("74.7");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 74.f (of order \(9\), degree \(6\), 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: \(23.1164918858\)
Analytic rank: \(0\)
Dimension: \(66\)
Relative dimension: \(11\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 53.8
Character \(\chi\) \(=\) 74.53
Dual form 74.8.f.b.7.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(7.51754 + 2.73616i) q^{2} +(28.9563 - 10.5392i) q^{3} +(49.0268 + 41.1384i) q^{4} +(-48.7600 + 276.532i) q^{5} +246.517 q^{6} +(-219.425 + 1244.42i) q^{7} +(256.000 + 443.405i) q^{8} +(-947.948 + 795.422i) q^{9} +O(q^{10})\) \(q+(7.51754 + 2.73616i) q^{2} +(28.9563 - 10.5392i) q^{3} +(49.0268 + 41.1384i) q^{4} +(-48.7600 + 276.532i) q^{5} +246.517 q^{6} +(-219.425 + 1244.42i) q^{7} +(256.000 + 443.405i) q^{8} +(-947.948 + 795.422i) q^{9} +(-1123.19 + 1945.43i) q^{10} +(-3015.94 - 5223.76i) q^{11} +(1853.20 + 674.511i) q^{12} +(-7240.19 - 6075.24i) q^{13} +(-5054.47 + 8754.60i) q^{14} +(1502.52 + 8521.23i) q^{15} +(711.263 + 4033.77i) q^{16} +(-210.162 + 176.347i) q^{17} +(-9302.64 + 3385.88i) q^{18} +(-18746.1 + 6823.04i) q^{19} +(-13766.6 + 11551.6i) q^{20} +(6761.50 + 38346.4i) q^{21} +(-8379.40 - 47521.9i) q^{22} +(-5092.72 + 8820.85i) q^{23} +(12086.0 + 10141.3i) q^{24} +(-678.898 - 247.099i) q^{25} +(-37805.6 - 65481.2i) q^{26} +(-52761.7 + 91386.0i) q^{27} +(-61951.2 + 51983.2i) q^{28} +(62198.9 + 107732. i) q^{29} +(-12020.2 + 68169.9i) q^{30} +252964. q^{31} +(-5690.10 + 32270.2i) q^{32} +(-142385. - 119475. i) q^{33} +(-2062.42 + 750.659i) q^{34} +(-333423. - 121356. i) q^{35} -79197.3 q^{36} +(62581.8 + 301688. i) q^{37} -159594. q^{38} +(-273678. - 99610.5i) q^{39} +(-135098. + 49171.7i) q^{40} +(27192.6 + 22817.3i) q^{41} +(-54092.0 + 306771. i) q^{42} +191047. q^{43} +(67035.2 - 380175. i) q^{44} +(-173738. - 300923. i) q^{45} +(-62420.0 + 52376.6i) q^{46} +(-311979. + 540363. i) q^{47} +(63108.4 + 109307. i) q^{48} +(-726558. - 264446. i) q^{49} +(-4427.54 - 3715.15i) q^{50} +(-4226.96 + 7321.31i) q^{51} +(-105038. - 595700. i) q^{52} +(69783.4 + 395761. i) q^{53} +(-646685. + 542633. i) q^{54} +(1.59159e6 - 579293. i) q^{55} +(-607955. + 221278. i) q^{56} +(-470909. + 395140. i) q^{57} +(172812. + 980064. i) q^{58} +(-55562.0 - 315108. i) q^{59} +(-276886. + 479581. i) q^{60} +(1.57280e6 + 1.31974e6i) q^{61} +(1.90167e6 + 692150. i) q^{62} +(-781837. - 1.35418e6i) q^{63} +(-131072. + 227023. i) q^{64} +(2.03303e6 - 1.70592e6i) q^{65} +(-743481. - 1.28775e6i) q^{66} +(-354280. + 2.00922e6i) q^{67} -17558.2 q^{68} +(-54501.3 + 309092. i) q^{69} +(-2.17447e6 - 1.82460e6i) q^{70} +(-1.13493e6 + 413080. i) q^{71} +(-595369. - 216697. i) q^{72} +78153.9 q^{73} +(-355004. + 2.43918e6i) q^{74} -22262.6 q^{75} +(-1.19975e6 - 436675. i) q^{76} +(7.16233e6 - 2.60687e6i) q^{77} +(-1.78483e6 - 1.49765e6i) q^{78} +(540661. - 3.06624e6i) q^{79} -1.15015e6 q^{80} +(-94698.6 + 537063. i) q^{81} +(141989. + 245933. i) q^{82} +(6.99293e6 - 5.86777e6i) q^{83} +(-1.24601e6 + 2.15816e6i) q^{84} +(-38518.1 - 66715.3i) q^{85} +(1.43621e6 + 522736. i) q^{86} +(2.93646e6 + 2.46398e6i) q^{87} +(1.54416e6 - 2.67457e6i) q^{88} +(1.44464e6 + 8.19298e6i) q^{89} +(-482708. - 2.73757e6i) q^{90} +(9.14884e6 - 7.67679e6i) q^{91} +(-612555. + 222952. i) q^{92} +(7.32490e6 - 2.66605e6i) q^{93} +(-3.82383e6 + 3.20858e6i) q^{94} +(-972726. - 5.51660e6i) q^{95} +(175339. + 994394. i) q^{96} +(-5.47272e6 + 9.47903e6i) q^{97} +(-4.73837e6 - 3.97596e6i) q^{98} +(7.01405e6 + 2.55290e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 66 q - 39 q^{3} + 459 q^{5} - 918 q^{7} + 16896 q^{8} + 3237 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 66 q - 39 q^{3} + 459 q^{5} - 918 q^{7} + 16896 q^{8} + 3237 q^{9} + 4704 q^{10} + 4539 q^{11} - 2496 q^{12} - 10542 q^{13} + 6744 q^{14} - 39894 q^{15} - 78822 q^{17} + 51792 q^{18} + 79461 q^{19} + 29376 q^{20} - 5835 q^{21} + 18168 q^{22} - 199479 q^{23} + 19968 q^{24} + 356301 q^{25} + 186744 q^{26} - 91689 q^{27} - 91584 q^{28} - 38526 q^{29} + 319152 q^{30} + 1917246 q^{31} - 902847 q^{33} - 205776 q^{34} - 1574793 q^{35} + 3079296 q^{36} - 396513 q^{37} - 692880 q^{38} + 2514306 q^{39} + 470016 q^{40} + 2989350 q^{41} + 46680 q^{42} + 6006348 q^{43} - 145344 q^{44} + 1083726 q^{45} - 588744 q^{46} - 894135 q^{47} + 7973742 q^{49} + 2012400 q^{50} - 524880 q^{51} - 2262720 q^{52} + 1457844 q^{53} + 1452312 q^{54} + 2415690 q^{55} - 1202688 q^{56} + 2734338 q^{57} - 3423360 q^{58} + 3099522 q^{59} - 3102912 q^{60} - 10968396 q^{61} - 3067320 q^{62} - 10727970 q^{63} - 8650752 q^{64} - 13497300 q^{65} - 4598712 q^{66} - 1978119 q^{67} + 5026176 q^{68} - 7251108 q^{69} + 435744 q^{70} - 19555002 q^{71} + 3314688 q^{72} - 31332840 q^{73} + 7607472 q^{74} + 44758074 q^{75} + 5085504 q^{76} + 1982007 q^{77} - 22512264 q^{78} + 10522902 q^{79} + 4816896 q^{80} - 7548876 q^{81} - 7150320 q^{82} + 19771926 q^{83} + 3556224 q^{84} - 6684072 q^{85} + 22982496 q^{86} - 67769667 q^{87} - 2323968 q^{88} - 42018963 q^{89} - 25158672 q^{90} + 4847565 q^{91} - 1096704 q^{92} - 14558475 q^{93} + 3175680 q^{94} + 4508415 q^{95} - 2555904 q^{96} - 39286662 q^{97} + 71630904 q^{98} + 66155463 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.51754 + 2.73616i 0.664463 + 0.241845i
\(3\) 28.9563 − 10.5392i 0.619182 − 0.225364i −0.0133338 − 0.999911i \(-0.504244\pi\)
0.632516 + 0.774547i \(0.282022\pi\)
\(4\) 49.0268 + 41.1384i 0.383022 + 0.321394i
\(5\) −48.7600 + 276.532i −0.174449 + 0.989351i 0.764328 + 0.644827i \(0.223071\pi\)
−0.938778 + 0.344524i \(0.888040\pi\)
\(6\) 246.517 0.465927
\(7\) −219.425 + 1244.42i −0.241793 + 1.37127i 0.586033 + 0.810287i \(0.300689\pi\)
−0.827825 + 0.560986i \(0.810422\pi\)
\(8\) 256.000 + 443.405i 0.176777 + 0.306186i
\(9\) −947.948 + 795.422i −0.433447 + 0.363705i
\(10\) −1123.19 + 1945.43i −0.355184 + 0.615197i
\(11\) −3015.94 − 5223.76i −0.683201 − 1.18334i −0.973999 − 0.226554i \(-0.927254\pi\)
0.290798 − 0.956784i \(-0.406079\pi\)
\(12\) 1853.20 + 674.511i 0.309591 + 0.112682i
\(13\) −7240.19 − 6075.24i −0.914005 − 0.766941i 0.0588720 − 0.998266i \(-0.481250\pi\)
−0.972877 + 0.231325i \(0.925694\pi\)
\(14\) −5054.47 + 8754.60i −0.492298 + 0.852684i
\(15\) 1502.52 + 8521.23i 0.114948 + 0.651903i
\(16\) 711.263 + 4033.77i 0.0434120 + 0.246202i
\(17\) −210.162 + 176.347i −0.0103749 + 0.00870557i −0.647960 − 0.761674i \(-0.724378\pi\)
0.637585 + 0.770380i \(0.279933\pi\)
\(18\) −9302.64 + 3385.88i −0.375969 + 0.136842i
\(19\) −18746.1 + 6823.04i −0.627010 + 0.228213i −0.635929 − 0.771747i \(-0.719383\pi\)
0.00891943 + 0.999960i \(0.497161\pi\)
\(20\) −13766.6 + 11551.6i −0.384789 + 0.322876i
\(21\) 6761.50 + 38346.4i 0.159322 + 0.903560i
\(22\) −8379.40 − 47521.9i −0.167777 − 0.951513i
\(23\) −5092.72 + 8820.85i −0.0872775 + 0.151169i −0.906359 − 0.422508i \(-0.861150\pi\)
0.819082 + 0.573677i \(0.194483\pi\)
\(24\) 12086.0 + 10141.3i 0.178460 + 0.149746i
\(25\) −678.898 − 247.099i −0.00868990 − 0.00316286i
\(26\) −37805.6 − 65481.2i −0.421842 − 0.730651i
\(27\) −52761.7 + 91386.0i −0.515877 + 0.893524i
\(28\) −61951.2 + 51983.2i −0.533331 + 0.447518i
\(29\) 62198.9 + 107732.i 0.473576 + 0.820258i 0.999542 − 0.0302474i \(-0.00962953\pi\)
−0.525966 + 0.850505i \(0.676296\pi\)
\(30\) −12020.2 + 68169.9i −0.0812806 + 0.460965i
\(31\) 252964. 1.52508 0.762540 − 0.646941i \(-0.223952\pi\)
0.762540 + 0.646941i \(0.223952\pi\)
\(32\) −5690.10 + 32270.2i −0.0306970 + 0.174091i
\(33\) −142385. − 119475.i −0.689707 − 0.578733i
\(34\) −2062.42 + 750.659i −0.00899913 + 0.00327542i
\(35\) −333423. − 121356.i −1.31449 − 0.478435i
\(36\) −79197.3 −0.282912
\(37\) 62581.8 + 301688.i 0.203115 + 0.979155i
\(38\) −159594. −0.471817
\(39\) −273678. − 99610.5i −0.738776 − 0.268893i
\(40\) −135098. + 49171.7i −0.333764 + 0.121480i
\(41\) 27192.6 + 22817.3i 0.0616178 + 0.0517035i 0.673076 − 0.739573i \(-0.264972\pi\)
−0.611459 + 0.791276i \(0.709417\pi\)
\(42\) −54092.0 + 306771.i −0.112658 + 0.638913i
\(43\) 191047. 0.366439 0.183219 − 0.983072i \(-0.441348\pi\)
0.183219 + 0.983072i \(0.441348\pi\)
\(44\) 67035.2 − 380175.i 0.118637 − 0.672821i
\(45\) −173738. − 300923.i −0.284217 − 0.492279i
\(46\) −62420.0 + 52376.6i −0.0945521 + 0.0793386i
\(47\) −311979. + 540363.i −0.438311 + 0.759177i −0.997559 − 0.0698229i \(-0.977757\pi\)
0.559248 + 0.829000i \(0.311090\pi\)
\(48\) 63108.4 + 109307.i 0.0823650 + 0.142660i
\(49\) −726558. − 264446.i −0.882235 − 0.321107i
\(50\) −4427.54 − 3715.15i −0.00500919 − 0.00420321i
\(51\) −4226.96 + 7321.31i −0.00446203 + 0.00772846i
\(52\) −105038. − 595700.i −0.103594 − 0.587511i
\(53\) 69783.4 + 395761.i 0.0643852 + 0.365147i 0.999929 + 0.0119354i \(0.00379926\pi\)
−0.935544 + 0.353211i \(0.885090\pi\)
\(54\) −646685. + 542633.i −0.558875 + 0.468952i
\(55\) 1.59159e6 − 579293.i 1.28992 − 0.469493i
\(56\) −607955. + 221278.i −0.462608 + 0.168376i
\(57\) −470909. + 395140.i −0.336803 + 0.282611i
\(58\) 172812. + 980064.i 0.116299 + 0.659563i
\(59\) −55562.0 − 315108.i −0.0352205 − 0.199746i 0.962120 − 0.272626i \(-0.0878921\pi\)
−0.997341 + 0.0728801i \(0.976781\pi\)
\(60\) −276886. + 479581.i −0.165490 + 0.286637i
\(61\) 1.57280e6 + 1.31974e6i 0.887196 + 0.744446i 0.967646 − 0.252313i \(-0.0811912\pi\)
−0.0804497 + 0.996759i \(0.525636\pi\)
\(62\) 1.90167e6 + 692150.i 1.01336 + 0.368833i
\(63\) −781837. − 1.35418e6i −0.393935 − 0.682315i
\(64\) −131072. + 227023.i −0.0625000 + 0.108253i
\(65\) 2.03303e6 − 1.70592e6i 0.918221 − 0.770479i
\(66\) −743481. − 1.28775e6i −0.318322 − 0.551349i
\(67\) −354280. + 2.00922e6i −0.143908 + 0.816142i 0.824330 + 0.566110i \(0.191552\pi\)
−0.968238 + 0.250032i \(0.919559\pi\)
\(68\) −17558.2 −0.00677173
\(69\) −54501.3 + 309092.i −0.0199726 + 0.113270i
\(70\) −2.17447e6 − 1.82460e6i −0.757723 − 0.635805i
\(71\) −1.13493e6 + 413080.i −0.376326 + 0.136971i −0.523256 − 0.852175i \(-0.675283\pi\)
0.146930 + 0.989147i \(0.453061\pi\)
\(72\) −595369. − 216697.i −0.187985 − 0.0684208i
\(73\) 78153.9 0.0235137 0.0117568 − 0.999931i \(-0.496258\pi\)
0.0117568 + 0.999931i \(0.496258\pi\)
\(74\) −355004. + 2.43918e6i −0.101841 + 0.699735i
\(75\) −22262.6 −0.00609343
\(76\) −1.19975e6 − 436675.i −0.313505 − 0.114106i
\(77\) 7.16233e6 − 2.60687e6i 1.78787 − 0.650733i
\(78\) −1.78483e6 − 1.49765e6i −0.425859 − 0.357338i
\(79\) 540661. − 3.06624e6i 0.123376 − 0.699699i −0.858883 − 0.512171i \(-0.828841\pi\)
0.982259 − 0.187528i \(-0.0600475\pi\)
\(80\) −1.15015e6 −0.251153
\(81\) −94698.6 + 537063.i −0.0197991 + 0.112286i
\(82\) 141989. + 245933.i 0.0284386 + 0.0492570i
\(83\) 6.99293e6 − 5.86777e6i 1.34241 − 1.12642i 0.361413 − 0.932406i \(-0.382294\pi\)
0.980999 − 0.194012i \(-0.0621502\pi\)
\(84\) −1.24601e6 + 2.15816e6i −0.229375 + 0.397289i
\(85\) −38518.1 − 66715.3i −0.00680297 − 0.0117831i
\(86\) 1.43621e6 + 522736.i 0.243485 + 0.0886213i
\(87\) 2.93646e6 + 2.46398e6i 0.478087 + 0.401162i
\(88\) 1.54416e6 − 2.67457e6i 0.241548 − 0.418373i
\(89\) 1.44464e6 + 8.19298e6i 0.217218 + 1.23190i 0.877016 + 0.480461i \(0.159531\pi\)
−0.659798 + 0.751443i \(0.729358\pi\)
\(90\) −482708. − 2.73757e6i −0.0697968 − 0.395837i
\(91\) 9.14884e6 − 7.67679e6i 1.27269 − 1.06791i
\(92\) −612555. + 222952.i −0.0820140 + 0.0298507i
\(93\) 7.32490e6 − 2.66605e6i 0.944303 − 0.343698i
\(94\) −3.82383e6 + 3.20858e6i −0.474845 + 0.398442i
\(95\) −972726. − 5.51660e6i −0.116401 − 0.660144i
\(96\) 175339. + 994394.i 0.0202268 + 0.114712i
\(97\) −5.47272e6 + 9.47903e6i −0.608839 + 1.05454i 0.382593 + 0.923917i \(0.375031\pi\)
−0.991432 + 0.130623i \(0.958302\pi\)
\(98\) −4.73837e6 − 3.97596e6i −0.508554 − 0.426728i
\(99\) 7.01405e6 + 2.55290e6i 0.726517 + 0.264430i
\(100\) −23119.0 − 40043.3i −0.00231190 − 0.00400433i
\(101\) 4.26280e6 − 7.38338e6i 0.411689 − 0.713067i −0.583385 − 0.812196i \(-0.698272\pi\)
0.995075 + 0.0991286i \(0.0316055\pi\)
\(102\) −51808.6 + 43472.6i −0.00483394 + 0.00405616i
\(103\) −1.05318e7 − 1.82416e7i −0.949668 − 1.64487i −0.746124 − 0.665807i \(-0.768087\pi\)
−0.203544 − 0.979066i \(-0.565246\pi\)
\(104\) 840304. − 4.76560e6i 0.0732520 − 0.415433i
\(105\) −1.09337e7 −0.921731
\(106\) −558267. + 3.16609e6i −0.0455272 + 0.258198i
\(107\) −2.09415e6 − 1.75720e6i −0.165259 − 0.138669i 0.556408 − 0.830909i \(-0.312179\pi\)
−0.721667 + 0.692241i \(0.756624\pi\)
\(108\) −6.34621e6 + 2.30983e6i −0.484765 + 0.176440i
\(109\) 9.61004e6 + 3.49777e6i 0.710775 + 0.258701i 0.672005 − 0.740547i \(-0.265434\pi\)
0.0387709 + 0.999248i \(0.487656\pi\)
\(110\) 1.35499e7 0.970649
\(111\) 4.99169e6 + 8.07619e6i 0.346432 + 0.560501i
\(112\) −5.17578e6 −0.348107
\(113\) −1.06194e7 − 3.86515e6i −0.692350 − 0.251995i −0.0282091 − 0.999602i \(-0.508980\pi\)
−0.664141 + 0.747607i \(0.731203\pi\)
\(114\) −4.62125e6 + 1.68200e6i −0.292141 + 0.106331i
\(115\) −2.19092e6 − 1.83840e6i −0.134334 − 0.112719i
\(116\) −1.38249e6 + 7.84051e6i −0.0822356 + 0.466381i
\(117\) 1.16957e7 0.675112
\(118\) 444496. − 2.52086e6i 0.0249047 − 0.141241i
\(119\) −173335. − 300225.i −0.00942915 − 0.0163318i
\(120\) −3.39371e6 + 2.84766e6i −0.179284 + 0.150437i
\(121\) −8.44819e6 + 1.46327e7i −0.433526 + 0.750889i
\(122\) 8.21259e6 + 1.42246e7i 0.409469 + 0.709220i
\(123\) 1.02787e6 + 374115.i 0.0498048 + 0.0181275i
\(124\) 1.24020e7 + 1.04065e7i 0.584140 + 0.490152i
\(125\) −1.08672e7 + 1.88226e7i −0.497661 + 0.861975i
\(126\) −2.17223e6 − 1.23193e7i −0.0967407 − 0.548644i
\(127\) 5.52363e6 + 3.13260e7i 0.239283 + 1.35704i 0.833404 + 0.552664i \(0.186389\pi\)
−0.594121 + 0.804375i \(0.702500\pi\)
\(128\) −1.60651e6 + 1.34802e6i −0.0677094 + 0.0568149i
\(129\) 5.53202e6 − 2.01349e6i 0.226892 − 0.0825821i
\(130\) 1.99511e7 − 7.26159e6i 0.796460 − 0.289888i
\(131\) −3.41187e7 + 2.86290e7i −1.32600 + 1.11265i −0.341004 + 0.940062i \(0.610767\pi\)
−0.984995 + 0.172583i \(0.944789\pi\)
\(132\) −2.06567e6 − 1.17150e7i −0.0781720 − 0.443335i
\(133\) −4.37736e6 − 2.48252e7i −0.161336 − 0.914982i
\(134\) −8.16086e6 + 1.41350e7i −0.293001 + 0.507493i
\(135\) −2.26985e7 − 1.90463e7i −0.794015 − 0.666258i
\(136\) −131995. − 48042.2i −0.00449956 − 0.00163771i
\(137\) −2.51914e7 − 4.36328e7i −0.837009 − 1.44974i −0.892384 − 0.451277i \(-0.850969\pi\)
0.0553750 − 0.998466i \(-0.482365\pi\)
\(138\) −1.25544e6 + 2.17449e6i −0.0406649 + 0.0704337i
\(139\) −1.32628e7 + 1.11288e7i −0.418874 + 0.351477i −0.827735 − 0.561120i \(-0.810371\pi\)
0.408860 + 0.912597i \(0.365926\pi\)
\(140\) −1.13543e7 − 1.96662e7i −0.349713 − 0.605720i
\(141\) −3.33874e6 + 1.89349e7i −0.100303 + 0.568849i
\(142\) −9.66212e6 −0.283180
\(143\) −9.89963e6 + 5.61436e7i −0.283102 + 1.60555i
\(144\) −3.88279e6 − 3.25805e6i −0.108362 − 0.0909262i
\(145\) −3.28241e7 + 1.19470e7i −0.894138 + 0.325440i
\(146\) 587525. + 213842.i 0.0156240 + 0.00568666i
\(147\) −2.38255e7 −0.618630
\(148\) −9.34276e6 + 1.73653e7i −0.236897 + 0.440318i
\(149\) 7.97514e6 0.197509 0.0987544 − 0.995112i \(-0.468514\pi\)
0.0987544 + 0.995112i \(0.468514\pi\)
\(150\) −167360. − 60914.1i −0.00404886 − 0.00147366i
\(151\) −3.39321e7 + 1.23503e7i −0.802031 + 0.291916i −0.710328 − 0.703871i \(-0.751453\pi\)
−0.0917034 + 0.995786i \(0.529231\pi\)
\(152\) −7.82438e6 − 6.56544e6i −0.180716 − 0.151639i
\(153\) 58952.4 − 334336.i 0.00133070 − 0.00754680i
\(154\) 6.09759e7 1.34535
\(155\) −1.23345e7 + 6.99526e7i −0.266049 + 1.50884i
\(156\) −9.31973e6 − 1.61422e7i −0.196547 − 0.340430i
\(157\) 4.10060e7 − 3.44082e7i 0.845666 − 0.709598i −0.113164 − 0.993576i \(-0.536099\pi\)
0.958831 + 0.283978i \(0.0916542\pi\)
\(158\) 1.24542e7 − 2.15712e7i 0.251197 − 0.435086i
\(159\) 6.19168e6 + 1.07243e7i 0.122157 + 0.211582i
\(160\) −8.64629e6 − 3.14699e6i −0.166882 − 0.0607401i
\(161\) −9.85938e6 − 8.27300e6i −0.186191 − 0.156233i
\(162\) −2.18139e6 + 3.77828e6i −0.0403117 + 0.0698219i
\(163\) −1.25411e7 − 7.11240e7i −0.226818 − 1.28635i −0.859178 − 0.511676i \(-0.829025\pi\)
0.632360 − 0.774675i \(-0.282086\pi\)
\(164\) 394499. + 2.23732e6i 0.00698381 + 0.0396072i
\(165\) 3.99814e7 − 3.35483e7i 0.692889 − 0.581403i
\(166\) 6.86248e7 − 2.49774e7i 1.16440 − 0.423808i
\(167\) 7.04735e7 − 2.56503e7i 1.17090 − 0.426171i 0.317918 − 0.948118i \(-0.397016\pi\)
0.852978 + 0.521947i \(0.174794\pi\)
\(168\) −1.52720e7 + 1.28148e7i −0.248493 + 0.208511i
\(169\) 4.61565e6 + 2.61766e7i 0.0735579 + 0.417167i
\(170\) −107018. − 606927.i −0.00167064 − 0.00947469i
\(171\) 1.23432e7 − 2.13790e7i 0.188773 − 0.326965i
\(172\) 9.36645e6 + 7.85939e6i 0.140354 + 0.117771i
\(173\) 4.01559e7 + 1.46156e7i 0.589642 + 0.214612i 0.619572 − 0.784940i \(-0.287306\pi\)
−0.0299301 + 0.999552i \(0.509528\pi\)
\(174\) 1.53331e7 + 2.65577e7i 0.220652 + 0.382180i
\(175\) 456462. − 790616.i 0.00643831 − 0.0111515i
\(176\) 1.89263e7 − 1.58811e7i 0.261681 − 0.219576i
\(177\) −4.92986e6 − 8.53877e6i −0.0668234 − 0.115741i
\(178\) −1.15571e7 + 6.55438e7i −0.153596 + 0.871087i
\(179\) 9.43845e7 1.23003 0.615014 − 0.788516i \(-0.289150\pi\)
0.615014 + 0.788516i \(0.289150\pi\)
\(180\) 3.86166e6 − 2.19006e7i 0.0493538 − 0.279899i
\(181\) −1.10111e8 − 9.23940e7i −1.38024 − 1.15816i −0.969123 − 0.246579i \(-0.920693\pi\)
−0.411119 − 0.911581i \(-0.634862\pi\)
\(182\) 8.97817e7 − 3.26779e7i 1.10392 − 0.401794i
\(183\) 5.94515e7 + 2.16386e7i 0.717107 + 0.261006i
\(184\) −5.21494e6 −0.0617145
\(185\) −8.64777e7 + 2.59558e6i −1.00416 + 0.0301393i
\(186\) 6.23600e7 0.710576
\(187\) 1.55503e6 + 565985.i 0.0173898 + 0.00632936i
\(188\) −3.75250e7 + 1.36580e7i −0.411878 + 0.149911i
\(189\) −1.02145e8 − 8.57102e7i −1.10053 − 0.923455i
\(190\) 7.78180e6 − 4.41328e7i 0.0823081 − 0.466793i
\(191\) 1.30241e8 1.35248 0.676239 − 0.736683i \(-0.263609\pi\)
0.676239 + 0.736683i \(0.263609\pi\)
\(192\) −1.40271e6 + 7.95515e6i −0.0143025 + 0.0811137i
\(193\) 8.23621e6 + 1.42655e7i 0.0824664 + 0.142836i 0.904309 − 0.426879i \(-0.140387\pi\)
−0.821842 + 0.569715i \(0.807054\pi\)
\(194\) −6.70776e7 + 5.62848e7i −0.659586 + 0.553458i
\(195\) 4.08900e7 − 7.08236e7i 0.394908 − 0.684001i
\(196\) −2.47420e7 − 4.28544e7i −0.234714 − 0.406536i
\(197\) −6.35417e7 − 2.31273e7i −0.592143 − 0.215523i 0.0285286 − 0.999593i \(-0.490918\pi\)
−0.620672 + 0.784070i \(0.713140\pi\)
\(198\) 4.57432e7 + 3.83831e7i 0.418792 + 0.351408i
\(199\) 7.94225e7 − 1.37564e8i 0.714427 − 1.23742i −0.248754 − 0.968567i \(-0.580021\pi\)
0.963180 − 0.268856i \(-0.0866457\pi\)
\(200\) −64233.1 − 364284.i −0.000567746 − 0.00321985i
\(201\) 1.09170e7 + 6.19134e7i 0.0948238 + 0.537773i
\(202\) 5.22479e7 − 4.38412e7i 0.446004 − 0.374242i
\(203\) −1.47712e8 + 5.37626e7i −1.23931 + 0.451070i
\(204\) −508421. + 185050.i −0.00419294 + 0.00152610i
\(205\) −7.63561e6 + 6.40704e6i −0.0619021 + 0.0519420i
\(206\) −2.92612e7 − 1.65949e8i −0.233215 − 1.32263i
\(207\) −2.18867e6 − 1.24126e7i −0.0171508 − 0.0972669i
\(208\) 1.93565e7 − 3.35264e7i 0.149144 − 0.258324i
\(209\) 9.21792e7 + 7.73475e7i 0.698427 + 0.586049i
\(210\) −8.21945e7 − 2.99163e7i −0.612456 − 0.222916i
\(211\) 9.79992e7 + 1.69740e8i 0.718181 + 1.24393i 0.961720 + 0.274035i \(0.0883585\pi\)
−0.243538 + 0.969891i \(0.578308\pi\)
\(212\) −1.28597e7 + 2.22737e7i −0.0926950 + 0.160552i
\(213\) −2.85098e7 + 2.39225e7i −0.202146 + 0.169621i
\(214\) −1.09349e7 − 1.89398e7i −0.0762722 − 0.132107i
\(215\) −9.31548e6 + 5.28307e7i −0.0639250 + 0.362537i
\(216\) −5.40280e7 −0.364780
\(217\) −5.55066e7 + 3.14794e8i −0.368753 + 2.09130i
\(218\) 6.26734e7 + 5.25892e7i 0.409718 + 0.343795i
\(219\) 2.26305e6 − 823682.i 0.0145593 − 0.00529914i
\(220\) 1.01862e8 + 3.70747e7i 0.644960 + 0.234746i
\(221\) 2.59297e6 0.0161594
\(222\) 1.54275e7 + 7.43712e7i 0.0946368 + 0.456215i
\(223\) 3.40302e7 0.205493 0.102747 − 0.994708i \(-0.467237\pi\)
0.102747 + 0.994708i \(0.467237\pi\)
\(224\) −3.89091e7 − 1.41618e7i −0.231304 − 0.0841878i
\(225\) 840108. − 305774.i 0.00491696 − 0.00178963i
\(226\) −6.92562e7 − 5.81128e7i −0.399098 − 0.334883i
\(227\) −8.96457e6 + 5.08406e7i −0.0508673 + 0.288483i −0.999621 − 0.0275340i \(-0.991235\pi\)
0.948754 + 0.316017i \(0.102346\pi\)
\(228\) −3.93426e7 −0.219832
\(229\) −3.48965e7 + 1.97908e8i −0.192025 + 1.08903i 0.724568 + 0.689204i \(0.242039\pi\)
−0.916593 + 0.399823i \(0.869072\pi\)
\(230\) −1.14402e7 − 1.98150e7i −0.0619992 − 0.107386i
\(231\) 1.79920e8 − 1.50971e8i 0.960368 − 0.805844i
\(232\) −3.18458e7 + 5.51586e7i −0.167434 + 0.290005i
\(233\) −1.77837e8 − 3.08023e8i −0.921037 − 1.59528i −0.797813 − 0.602904i \(-0.794010\pi\)
−0.123224 − 0.992379i \(-0.539323\pi\)
\(234\) 8.79230e7 + 3.20013e7i 0.448587 + 0.163272i
\(235\) −1.34216e8 − 1.12620e8i −0.674630 − 0.566082i
\(236\) 1.02390e7 − 1.77345e7i 0.0507067 − 0.0878266i
\(237\) −1.66603e7 − 9.44851e7i −0.0812948 − 0.461046i
\(238\) −481589. − 2.73123e6i −0.00231557 − 0.0131322i
\(239\) 1.18722e8 − 9.96192e7i 0.562519 − 0.472009i −0.316635 − 0.948547i \(-0.602553\pi\)
0.879154 + 0.476538i \(0.158109\pi\)
\(240\) −3.33040e7 + 1.21217e7i −0.155510 + 0.0566009i
\(241\) −3.17337e8 + 1.15501e8i −1.46037 + 0.531530i −0.945466 − 0.325721i \(-0.894393\pi\)
−0.514899 + 0.857251i \(0.672171\pi\)
\(242\) −1.03547e8 + 8.68863e7i −0.469661 + 0.394092i
\(243\) −3.71564e7 − 2.10724e8i −0.166116 − 0.942091i
\(244\) 2.28176e7 + 1.29405e8i 0.100556 + 0.570279i
\(245\) 1.08555e8 − 1.88022e8i 0.471593 − 0.816823i
\(246\) 6.70343e6 + 5.62485e6i 0.0287094 + 0.0240901i
\(247\) 1.77177e8 + 6.44873e7i 0.748116 + 0.272292i
\(248\) 6.47588e7 + 1.12166e8i 0.269599 + 0.466959i
\(249\) 1.40648e8 − 2.43609e8i 0.577344 − 0.999990i
\(250\) −1.33197e8 + 1.11765e8i −0.539142 + 0.452394i
\(251\) 1.31200e8 + 2.27245e8i 0.523692 + 0.907061i 0.999620 + 0.0275768i \(0.00877907\pi\)
−0.475928 + 0.879484i \(0.657888\pi\)
\(252\) 1.73779e7 − 9.85548e7i 0.0684060 − 0.387950i
\(253\) 6.14373e7 0.238512
\(254\) −4.41890e7 + 2.50608e8i −0.169198 + 0.959572i
\(255\) −1.81847e6 − 1.52588e6i −0.00686776 − 0.00576274i
\(256\) −1.57654e7 + 5.73815e6i −0.0587308 + 0.0213763i
\(257\) 4.43312e7 + 1.61352e7i 0.162908 + 0.0592938i 0.422187 − 0.906509i \(-0.361263\pi\)
−0.259279 + 0.965803i \(0.583485\pi\)
\(258\) 4.70965e7 0.170734
\(259\) −3.89158e8 + 1.16803e7i −1.39180 + 0.0417741i
\(260\) 1.69852e8 0.599326
\(261\) −1.44654e8 − 5.26496e7i −0.503602 − 0.183296i
\(262\) −3.34822e8 + 1.21865e8i −1.15016 + 0.418626i
\(263\) 3.49310e8 + 2.93106e8i 1.18404 + 0.993526i 0.999944 + 0.0106179i \(0.00337985\pi\)
0.184095 + 0.982908i \(0.441065\pi\)
\(264\) 1.65253e7 − 9.37198e7i 0.0552759 − 0.313485i
\(265\) −1.12843e8 −0.372490
\(266\) 3.50189e7 − 1.98602e8i 0.114082 − 0.646990i
\(267\) 1.28179e8 + 2.22013e8i 0.412124 + 0.713820i
\(268\) −1.00025e8 + 8.39312e7i −0.317423 + 0.266349i
\(269\) 3.90046e7 − 6.75579e7i 0.122175 − 0.211613i −0.798450 − 0.602061i \(-0.794346\pi\)
0.920625 + 0.390448i \(0.127680\pi\)
\(270\) −1.18523e8 − 2.05288e8i −0.366463 − 0.634732i
\(271\) −3.42798e7 − 1.24768e7i −0.104627 − 0.0380812i 0.289176 − 0.957276i \(-0.406619\pi\)
−0.393803 + 0.919195i \(0.628841\pi\)
\(272\) −860825. − 722318.i −0.00259372 − 0.00217639i
\(273\) 1.84009e8 − 3.18713e8i 0.547356 − 0.948048i
\(274\) −6.99910e7 − 3.96939e8i −0.205549 − 1.16573i
\(275\) 756731. + 4.29164e6i 0.00219421 + 0.0124440i
\(276\) −1.53876e7 + 1.29117e7i −0.0440544 + 0.0369660i
\(277\) −3.29629e8 + 1.19975e8i −0.931849 + 0.339165i −0.762942 − 0.646467i \(-0.776246\pi\)
−0.168907 + 0.985632i \(0.554024\pi\)
\(278\) −1.30154e8 + 4.73722e7i −0.363329 + 0.132241i
\(279\) −2.39797e8 + 2.01213e8i −0.661041 + 0.554679i
\(280\) −3.15464e7 − 1.78909e8i −0.0858809 − 0.487055i
\(281\) −5.50474e7 − 3.12189e8i −0.148001 − 0.839355i −0.964909 − 0.262586i \(-0.915425\pi\)
0.816908 − 0.576769i \(-0.195687\pi\)
\(282\) −7.69081e7 + 1.33209e8i −0.204221 + 0.353721i
\(283\) 3.83620e8 + 3.21895e8i 1.00612 + 0.844232i 0.987820 − 0.155600i \(-0.0497312\pi\)
0.0182967 + 0.999833i \(0.494176\pi\)
\(284\) −7.26354e7 − 2.64371e7i −0.188163 − 0.0684857i
\(285\) −8.63072e7 − 1.49489e8i −0.220846 − 0.382517i
\(286\) −2.28039e8 + 3.94975e8i −0.576405 + 0.998362i
\(287\) −3.43610e7 + 2.88323e7i −0.0857984 + 0.0719934i
\(288\) −2.02745e7 − 3.51165e7i −0.0500123 − 0.0866238i
\(289\) −7.12415e7 + 4.04031e8i −0.173616 + 0.984627i
\(290\) −2.79445e8 −0.672827
\(291\) −5.85680e7 + 3.32156e8i −0.139327 + 0.790163i
\(292\) 3.83164e6 + 3.21513e6i 0.00900626 + 0.00755715i
\(293\) 3.19442e8 − 1.16267e8i 0.741918 − 0.270036i 0.0567169 − 0.998390i \(-0.481937\pi\)
0.685201 + 0.728354i \(0.259715\pi\)
\(294\) −1.79109e8 − 6.51904e7i −0.411057 − 0.149613i
\(295\) 8.98466e7 0.203763
\(296\) −1.17749e8 + 1.04981e8i −0.263898 + 0.235283i
\(297\) 6.36505e8 1.40979
\(298\) 5.99535e7 + 2.18213e7i 0.131237 + 0.0477665i
\(299\) 9.04610e7 − 3.29251e7i 0.195710 − 0.0712325i
\(300\) −1.09147e6 − 915848.i −0.00233392 − 0.00195839i
\(301\) −4.19206e7 + 2.37743e8i −0.0886022 + 0.502488i
\(302\) −2.88878e8 −0.603518
\(303\) 4.56196e7 − 2.58722e8i 0.0942112 − 0.534299i
\(304\) −4.08560e7 − 7.07647e7i −0.0834063 − 0.144464i
\(305\) −4.41639e8 + 3.70580e8i −0.891289 + 0.747880i
\(306\) 1.35797e6 − 2.35208e6i 0.00270936 − 0.00469274i
\(307\) 4.28156e8 + 7.41588e8i 0.844536 + 1.46278i 0.886024 + 0.463640i \(0.153457\pi\)
−0.0414883 + 0.999139i \(0.513210\pi\)
\(308\) 4.58389e8 + 1.66840e8i 0.893936 + 0.325366i
\(309\) −4.97214e8 − 4.17212e8i −0.958713 − 0.804455i
\(310\) −2.84127e8 + 4.92123e8i −0.541685 + 0.938226i
\(311\) 3.51165e7 + 1.99156e8i 0.0661988 + 0.375432i 0.999851 + 0.0172517i \(0.00549167\pi\)
−0.933652 + 0.358181i \(0.883397\pi\)
\(312\) −2.58937e7 − 1.46850e8i −0.0482672 − 0.273737i
\(313\) −1.43606e8 + 1.20499e8i −0.264707 + 0.222116i −0.765475 − 0.643466i \(-0.777496\pi\)
0.500767 + 0.865582i \(0.333051\pi\)
\(314\) 4.02411e8 − 1.46466e8i 0.733527 − 0.266982i
\(315\) 4.12597e8 − 1.50173e8i 0.743770 − 0.270710i
\(316\) 1.52647e8 − 1.28086e8i 0.272135 − 0.228348i
\(317\) −1.51722e8 − 8.60459e8i −0.267511 − 1.51713i −0.761789 − 0.647826i \(-0.775678\pi\)
0.494278 − 0.869304i \(-0.335433\pi\)
\(318\) 1.72028e7 + 9.75619e7i 0.0299988 + 0.170132i
\(319\) 3.75176e8 − 6.49824e8i 0.647095 − 1.12080i
\(320\) −5.63881e7 − 4.73153e7i −0.0961973 − 0.0807191i
\(321\) −7.91585e7 − 2.88113e7i −0.133576 − 0.0486178i
\(322\) −5.14820e7 − 8.91694e7i −0.0859330 − 0.148840i
\(323\) 2.73651e6 − 4.73978e6i 0.00451844 − 0.00782616i
\(324\) −2.67367e7 + 2.24347e7i −0.0436717 + 0.0366449i
\(325\) 3.41417e6 + 5.91352e6i 0.00551688 + 0.00955551i
\(326\) 1.00329e8 − 5.68992e8i 0.160385 − 0.909587i
\(327\) 3.15135e8 0.498402
\(328\) −3.15599e6 + 1.78985e7i −0.00493830 + 0.0280065i
\(329\) −6.03983e8 − 5.06802e8i −0.935060 − 0.784608i
\(330\) 3.92355e8 − 1.42806e8i 0.601009 − 0.218749i
\(331\) 6.14600e8 + 2.23696e8i 0.931525 + 0.339047i 0.762814 − 0.646618i \(-0.223817\pi\)
0.168711 + 0.985666i \(0.446040\pi\)
\(332\) 5.84232e8 0.876198
\(333\) −2.99293e8 − 2.36205e8i −0.444163 − 0.350537i
\(334\) 5.99971e8 0.881084
\(335\) −5.38339e8 − 1.95939e8i −0.782346 − 0.284751i
\(336\) −1.49871e8 + 5.45487e7i −0.215542 + 0.0784508i
\(337\) 6.09311e8 + 5.11273e8i 0.867230 + 0.727692i 0.963513 − 0.267662i \(-0.0862509\pi\)
−0.0962830 + 0.995354i \(0.530695\pi\)
\(338\) −3.69252e7 + 2.09413e8i −0.0520133 + 0.294982i
\(339\) −3.48235e8 −0.485482
\(340\) 856140. − 4.85541e6i 0.00118132 − 0.00669962i
\(341\) −7.62924e8 − 1.32142e9i −1.04194 − 1.80469i
\(342\) 1.51287e8 − 1.26945e8i 0.204507 − 0.171602i
\(343\) −3.18151e7 + 5.51054e7i −0.0425701 + 0.0737335i
\(344\) 4.89081e7 + 8.47114e7i 0.0647778 + 0.112199i
\(345\) −8.28164e7 − 3.01427e7i −0.108580 − 0.0395199i
\(346\) 2.61883e8 + 2.19746e8i 0.339892 + 0.285204i
\(347\) 1.13558e8 − 1.96689e8i 0.145904 − 0.252713i −0.783806 − 0.621006i \(-0.786724\pi\)
0.929710 + 0.368293i \(0.120058\pi\)
\(348\) 4.26010e7 + 2.41603e8i 0.0541867 + 0.307308i
\(349\) 2.46197e8 + 1.39625e9i 0.310022 + 1.75822i 0.598868 + 0.800848i \(0.295618\pi\)
−0.288845 + 0.957376i \(0.593271\pi\)
\(350\) 5.59472e6 − 4.69453e6i 0.00697494 − 0.00585267i
\(351\) 9.37197e8 − 3.41112e8i 1.15679 − 0.421039i
\(352\) 1.85733e8 − 6.76012e7i 0.226981 − 0.0826142i
\(353\) 1.16151e9 − 9.74626e8i 1.40544 − 1.17931i 0.446820 − 0.894624i \(-0.352556\pi\)
0.958622 − 0.284682i \(-0.0918882\pi\)
\(354\) −1.36970e7 − 7.76795e7i −0.0164102 − 0.0930668i
\(355\) −5.88907e7 − 3.33986e8i −0.0698630 − 0.396213i
\(356\) −2.66220e8 + 4.61106e8i −0.312727 + 0.541659i
\(357\) −8.18329e6 − 6.86659e6i −0.00951895 − 0.00798735i
\(358\) 7.09539e8 + 2.58251e8i 0.817308 + 0.297476i
\(359\) −6.16609e6 − 1.06800e7i −0.00703363 − 0.0121826i 0.862487 − 0.506079i \(-0.168906\pi\)
−0.869521 + 0.493896i \(0.835572\pi\)
\(360\) 8.89537e7 − 1.54072e8i 0.100486 − 0.174047i
\(361\) −3.79881e8 + 3.18758e8i −0.424984 + 0.356604i
\(362\) −5.74958e8 − 9.95857e8i −0.637025 − 1.10336i
\(363\) −9.04110e7 + 5.12746e8i −0.0992083 + 0.562638i
\(364\) 7.64349e8 0.830686
\(365\) −3.81079e6 + 2.16121e7i −0.00410194 + 0.0232633i
\(366\) 3.87723e8 + 3.25338e8i 0.413369 + 0.346857i
\(367\) −7.97989e8 + 2.90444e8i −0.842686 + 0.306713i −0.727055 − 0.686580i \(-0.759111\pi\)
−0.115631 + 0.993292i \(0.536889\pi\)
\(368\) −3.92035e7 − 1.42689e7i −0.0410070 − 0.0149253i
\(369\) −4.39265e7 −0.0455129
\(370\) −6.57202e8 − 2.17105e8i −0.674517 − 0.222825i
\(371\) −5.07806e8 −0.516284
\(372\) 4.68794e8 + 1.70627e8i 0.472152 + 0.171849i
\(373\) 7.91725e8 − 2.88164e8i 0.789939 − 0.287514i 0.0846281 − 0.996413i \(-0.473030\pi\)
0.705311 + 0.708898i \(0.250808\pi\)
\(374\) 1.01414e7 + 8.50964e6i 0.0100241 + 0.00841125i
\(375\) −1.16299e8 + 6.59565e8i −0.113885 + 0.645875i
\(376\) −3.19466e8 −0.309933
\(377\) 2.04164e8 − 1.15787e9i 0.196239 − 1.11292i
\(378\) −5.33365e8 − 9.23816e8i −0.507930 − 0.879760i
\(379\) 4.78995e8 − 4.01924e8i 0.451953 − 0.379234i −0.388207 − 0.921572i \(-0.626905\pi\)
0.840160 + 0.542338i \(0.182461\pi\)
\(380\) 1.79254e8 − 3.10478e8i 0.167582 − 0.290261i
\(381\) 4.90096e8 + 8.48871e8i 0.453987 + 0.786329i
\(382\) 9.79090e8 + 3.56360e8i 0.898671 + 0.327090i
\(383\) −9.83787e8 − 8.25496e8i −0.894758 − 0.750791i 0.0744008 − 0.997228i \(-0.476296\pi\)
−0.969159 + 0.246437i \(0.920740\pi\)
\(384\) −3.23115e7 + 5.59652e7i −0.0291204 + 0.0504381i
\(385\) 3.71649e8 + 2.10772e9i 0.331910 + 1.88235i
\(386\) 2.28833e7 + 1.29777e8i 0.0202517 + 0.114853i
\(387\) −1.81103e8 + 1.51963e8i −0.158832 + 0.133276i
\(388\) −6.58263e8 + 2.39588e8i −0.572121 + 0.208235i
\(389\) −1.85907e9 + 6.76648e8i −1.60130 + 0.582826i −0.979693 − 0.200502i \(-0.935743\pi\)
−0.621608 + 0.783328i \(0.713520\pi\)
\(390\) 5.01177e8 − 4.20537e8i 0.427824 − 0.358987i
\(391\) −485233. − 2.75190e6i −0.000410518 − 0.00232816i
\(392\) −6.87424e7 − 3.89858e8i −0.0576400 − 0.326892i
\(393\) −6.86224e8 + 1.18857e9i −0.570285 + 0.987763i
\(394\) −4.14397e8 − 3.47720e8i −0.341334 − 0.286413i
\(395\) 8.21550e8 + 2.99020e8i 0.670725 + 0.244124i
\(396\) 2.38854e8 + 4.13708e8i 0.193286 + 0.334781i
\(397\) 8.44715e7 − 1.46309e8i 0.0677553 − 0.117356i −0.830158 − 0.557529i \(-0.811750\pi\)
0.897913 + 0.440173i \(0.145083\pi\)
\(398\) 9.73458e8 − 8.16828e8i 0.773974 − 0.649442i
\(399\) −3.88391e8 − 6.72713e8i −0.306101 − 0.530182i
\(400\) 513865. − 2.91427e6i 0.000401457 − 0.00227678i
\(401\) −1.34697e9 −1.04316 −0.521582 − 0.853201i \(-0.674658\pi\)
−0.521582 + 0.853201i \(0.674658\pi\)
\(402\) −8.73361e7 + 4.95307e8i −0.0670506 + 0.380263i
\(403\) −1.83151e9 − 1.53682e9i −1.39393 − 1.16965i
\(404\) 5.12732e8 − 1.86619e8i 0.386862 − 0.140806i
\(405\) −1.43897e8 − 5.23744e7i −0.107637 − 0.0391766i
\(406\) −1.25753e9 −0.932562
\(407\) 1.38720e9 − 1.23678e9i 1.01990 − 0.909313i
\(408\) −4.32841e6 −0.00315513
\(409\) −1.92594e9 − 7.00986e8i −1.39191 − 0.506615i −0.466145 − 0.884708i \(-0.654357\pi\)
−0.925767 + 0.378094i \(0.876580\pi\)
\(410\) −7.49317e7 + 2.72729e7i −0.0536936 + 0.0195429i
\(411\) −1.18931e9 − 9.97946e8i −0.844981 − 0.709023i
\(412\) 2.34090e8 − 1.32759e9i 0.164908 − 0.935240i
\(413\) 4.04318e8 0.282422
\(414\) 1.75094e7 − 9.93005e7i 0.0121274 − 0.0687781i
\(415\) 1.28165e9 + 2.21988e9i 0.880240 + 1.52462i
\(416\) 2.37247e8 − 1.99074e8i 0.161575 − 0.135577i
\(417\) −2.66753e8 + 4.62029e8i −0.180149 + 0.312028i
\(418\) 4.81325e8 + 8.33680e8i 0.322346 + 0.558319i
\(419\) 2.27987e9 + 8.29804e8i 1.51412 + 0.551095i 0.959672 − 0.281123i \(-0.0907068\pi\)
0.554449 + 0.832218i \(0.312929\pi\)
\(420\) −5.36044e8 − 4.49795e8i −0.353044 − 0.296239i
\(421\) −2.81362e8 + 4.87334e8i −0.183772 + 0.318302i −0.943162 − 0.332334i \(-0.892164\pi\)
0.759390 + 0.650635i \(0.225497\pi\)
\(422\) 2.72278e8 + 1.54417e9i 0.176368 + 1.00023i
\(423\) −1.34077e8 − 7.60391e8i −0.0861320 − 0.488479i
\(424\) −1.57618e8 + 1.32257e8i −0.100421 + 0.0842633i
\(425\) 186254. − 67790.9i 0.000117691 − 4.28361e-5i
\(426\) −2.79779e8 + 1.01831e8i −0.175340 + 0.0638187i
\(427\) −1.98742e9 + 1.66764e9i −1.23536 + 1.03659i
\(428\) −3.03812e7 − 1.72300e8i −0.0187306 − 0.106226i
\(429\) 3.05054e8 + 1.73004e9i 0.186542 + 1.05793i
\(430\) −2.14583e8 + 3.71668e8i −0.130153 + 0.225432i
\(431\) −5.74221e8 − 4.81829e8i −0.345469 − 0.289883i 0.453499 − 0.891257i \(-0.350176\pi\)
−0.798967 + 0.601374i \(0.794620\pi\)
\(432\) −4.06158e8 − 1.47829e8i −0.242383 − 0.0882201i
\(433\) −4.00814e8 − 6.94231e8i −0.237266 − 0.410957i 0.722663 − 0.691201i \(-0.242918\pi\)
−0.959929 + 0.280244i \(0.909585\pi\)
\(434\) −1.27860e9 + 2.21460e9i −0.750794 + 1.30041i
\(435\) −8.24552e8 + 6.91881e8i −0.480292 + 0.403013i
\(436\) 3.27257e8 + 5.66826e8i 0.189098 + 0.327527i
\(437\) 3.52839e7 − 2.00105e8i 0.0202251 − 0.114702i
\(438\) 1.92663e7 0.0109557
\(439\) −1.39188e8 + 7.89377e8i −0.0785195 + 0.445306i 0.920048 + 0.391805i \(0.128149\pi\)
−0.998568 + 0.0535011i \(0.982962\pi\)
\(440\) 6.64309e8 + 5.57422e8i 0.371780 + 0.311960i
\(441\) 8.99085e8 − 3.27240e8i 0.499190 − 0.181690i
\(442\) 1.94927e7 + 7.09478e6i 0.0107373 + 0.00390806i
\(443\) 2.59087e9 1.41590 0.707950 − 0.706263i \(-0.249620\pi\)
0.707950 + 0.706263i \(0.249620\pi\)
\(444\) −8.75147e7 + 6.01300e8i −0.0474505 + 0.326025i
\(445\) −2.33606e9 −1.25668
\(446\) 2.55824e8 + 9.31122e7i 0.136543 + 0.0496975i
\(447\) 2.30931e8 − 8.40519e7i 0.122294 − 0.0445114i
\(448\) −2.53752e8 − 2.12923e8i −0.133333 − 0.111879i
\(449\) −1.97213e8 + 1.11845e9i −0.102819 + 0.583116i 0.889250 + 0.457421i \(0.151227\pi\)
−0.992069 + 0.125694i \(0.959884\pi\)
\(450\) 7.15219e6 0.00369995
\(451\) 3.71808e7 − 2.10863e8i 0.0190854 − 0.108239i
\(452\) −3.61630e8 − 6.26362e8i −0.184196 − 0.319037i
\(453\) −8.52385e8 + 7.15236e8i −0.430817 + 0.361498i
\(454\) −2.06500e8 + 3.57668e8i −0.103568 + 0.179384i
\(455\) 1.67678e9 + 2.90427e9i 0.834518 + 1.44543i
\(456\) −2.95760e8 − 1.07648e8i −0.146070 − 0.0531653i
\(457\) 6.93019e8 + 5.81512e8i 0.339655 + 0.285005i 0.796620 − 0.604480i \(-0.206619\pi\)
−0.456965 + 0.889485i \(0.651064\pi\)
\(458\) −8.03843e8 + 1.39230e9i −0.390969 + 0.677177i
\(459\) −5.02713e6 − 2.85103e7i −0.00242647 − 0.0137612i
\(460\) −3.17851e7 − 1.80262e8i −0.0152255 − 0.0863480i
\(461\) 1.46795e9 − 1.23175e9i 0.697842 − 0.585559i −0.223317 − 0.974746i \(-0.571688\pi\)
0.921159 + 0.389187i \(0.127244\pi\)
\(462\) 1.76564e9 − 6.42639e8i 0.833018 − 0.303194i
\(463\) −3.75193e9 + 1.36559e9i −1.75680 + 0.639422i −0.999900 − 0.0141118i \(-0.995508\pi\)
−0.756897 + 0.653534i \(0.773286\pi\)
\(464\) −3.90325e8 + 3.27522e8i −0.181390 + 0.152204i
\(465\) 3.80084e8 + 2.15557e9i 0.175305 + 0.994205i
\(466\) −4.94098e8 − 2.80217e9i −0.226184 − 1.28275i
\(467\) 1.91003e9 − 3.30827e9i 0.867822 − 1.50311i 0.00360524 − 0.999994i \(-0.498852\pi\)
0.864217 − 0.503119i \(-0.167814\pi\)
\(468\) 5.73404e8 + 4.81143e8i 0.258583 + 0.216977i
\(469\) −2.42258e9 − 8.81746e8i −1.08436 − 0.394674i
\(470\) −7.00824e8 − 1.21386e9i −0.311363 − 0.539296i
\(471\) 8.24748e8 − 1.42850e9i 0.363704 − 0.629954i
\(472\) 1.25496e8 − 1.05304e8i 0.0549332 − 0.0460944i
\(473\) −5.76187e8 − 9.97986e8i −0.250351 − 0.433621i
\(474\) 1.33282e8 − 7.55880e8i 0.0574841 − 0.326009i
\(475\) 1.44127e7 0.00617046
\(476\) 3.85272e6 − 2.18498e7i 0.00163735 − 0.00928590i
\(477\) −3.80948e8 − 3.19654e8i −0.160713 − 0.134854i
\(478\) 1.16507e9 − 4.24050e8i 0.487926 − 0.177591i
\(479\) 7.22235e8 + 2.62872e8i 0.300265 + 0.109287i 0.487759 − 0.872978i \(-0.337814\pi\)
−0.187495 + 0.982266i \(0.560037\pi\)
\(480\) −2.83531e8 −0.117019
\(481\) 1.37972e9 − 2.56448e9i 0.565306 − 1.05073i
\(482\) −2.70163e9 −1.09891
\(483\) −3.72682e8 − 1.35645e8i −0.150495 − 0.0547759i
\(484\) −1.01615e9 + 3.69850e8i −0.407381 + 0.148275i
\(485\) −2.35441e9 − 1.97558e9i −0.937098 − 0.786319i
\(486\) 2.97251e8 − 1.68579e9i 0.117462 − 0.666159i
\(487\) 5.32812e8 0.209037 0.104518 − 0.994523i \(-0.466670\pi\)
0.104518 + 0.994523i \(0.466670\pi\)
\(488\) −1.82541e8 + 1.03524e9i −0.0711035 + 0.403248i
\(489\) −1.11274e9 − 1.92731e9i −0.430339 − 0.745369i
\(490\) 1.33052e9 − 1.11644e9i 0.510900 − 0.428696i
\(491\) 3.62757e7 − 6.28313e7i 0.0138302 − 0.0239547i −0.859027 − 0.511930i \(-0.828931\pi\)
0.872858 + 0.487975i \(0.162264\pi\)
\(492\) 3.50028e7 + 6.06267e7i 0.0132503 + 0.0229502i
\(493\) −3.20700e7 − 1.16725e7i −0.0120541 − 0.00438734i
\(494\) 1.15549e9 + 9.69572e8i 0.431243 + 0.361856i
\(495\) −1.04797e9 + 1.81513e9i −0.388355 + 0.672650i
\(496\) 1.79924e8 + 1.02040e9i 0.0662069 + 0.375478i
\(497\) −2.65014e8 − 1.50297e9i −0.0968325 − 0.549164i
\(498\) 1.72388e9 − 1.44651e9i 0.625466 − 0.524828i
\(499\) −1.21840e8 + 4.43463e7i −0.0438975 + 0.0159774i −0.363876 − 0.931448i \(-0.618547\pi\)
0.319978 + 0.947425i \(0.396324\pi\)
\(500\) −1.30712e9 + 4.75752e8i −0.467649 + 0.170210i
\(501\) 1.77032e9 − 1.48547e9i 0.628954 − 0.527755i
\(502\) 3.64522e8 + 2.06731e9i 0.128606 + 0.729361i
\(503\) 2.43861e8 + 1.38301e9i 0.0854387 + 0.484547i 0.997261 + 0.0739621i \(0.0235644\pi\)
−0.911822 + 0.410585i \(0.865324\pi\)
\(504\) 4.00300e8 − 6.93341e8i 0.139277 − 0.241235i
\(505\) 1.83389e9 + 1.53881e9i 0.633655 + 0.531699i
\(506\) 4.61858e8 + 1.68102e8i 0.158482 + 0.0576829i
\(507\) 4.09534e8 + 7.09333e8i 0.139560 + 0.241725i
\(508\) −1.01790e9 + 1.76305e9i −0.344494 + 0.596680i
\(509\) 3.15496e9 − 2.64732e9i 1.06043 − 0.889804i 0.0662764 − 0.997801i \(-0.478888\pi\)
0.994151 + 0.107997i \(0.0344436\pi\)
\(510\) −9.49537e6 − 1.64465e7i −0.00316969 − 0.00549006i
\(511\) −1.71489e7 + 9.72564e7i −0.00568543 + 0.0322437i
\(512\) −1.34218e8 −0.0441942
\(513\) 3.65549e8 − 2.07313e9i 0.119546 − 0.677978i
\(514\) 2.89113e8 + 2.42594e8i 0.0939067 + 0.0787971i
\(515\) 5.55791e9 − 2.02291e9i 1.79303 − 0.652608i
\(516\) 3.54050e8 + 1.28864e8i 0.113446 + 0.0412911i
\(517\) 3.76364e9 1.19782
\(518\) −2.95747e9 − 9.76992e8i −0.934903 − 0.308842i
\(519\) 1.31680e9 0.413462
\(520\) 1.27687e9 + 4.64742e8i 0.398230 + 0.144944i
\(521\) 4.07778e9 − 1.48419e9i 1.26326 − 0.459788i 0.378396 − 0.925644i \(-0.376476\pi\)
0.884861 + 0.465856i \(0.154253\pi\)
\(522\) −9.43381e8 − 7.91591e8i −0.290296 − 0.243587i
\(523\) −7.89448e7 + 4.47718e8i −0.0241306 + 0.136851i −0.994493 − 0.104803i \(-0.966579\pi\)
0.970362 + 0.241654i \(0.0776899\pi\)
\(524\) −2.85048e9 −0.865484
\(525\) 4.88497e6 − 2.77041e7i 0.00147335 − 0.00835576i
\(526\) 1.82397e9 + 3.15920e9i 0.546471 + 0.946515i
\(527\) −5.31635e7 + 4.46095e7i −0.0158226 + 0.0132767i
\(528\) 3.80662e8 − 6.59326e8i 0.112544 − 0.194931i
\(529\) 1.65054e9 + 2.85882e9i 0.484765 + 0.839638i
\(530\) −8.48304e8 − 3.08757e8i −0.247506 − 0.0900848i
\(531\) 3.03314e8 + 2.54510e8i 0.0879146 + 0.0737691i
\(532\) 8.06663e8 − 1.39718e9i 0.232274 − 0.402311i
\(533\) −5.82589e7 − 3.30403e8i −0.0166655 − 0.0945145i
\(534\) 3.56129e8 + 2.01971e9i 0.101208 + 0.573977i
\(535\) 5.88034e8 − 4.93419e8i 0.166021 − 0.139308i
\(536\) −9.81594e8 + 3.57271e8i −0.275331 + 0.100212i
\(537\) 2.73302e9 − 9.94739e8i 0.761611 − 0.277204i
\(538\) 4.78068e8 − 4.01146e8i 0.132358 − 0.111062i
\(539\) 8.09856e8 + 4.59292e9i 0.222765 + 1.26336i
\(540\) −3.29301e8 − 1.86756e9i −0.0899943 − 0.510383i
\(541\) 2.96386e9 − 5.13355e9i 0.804761 − 1.39389i −0.111691 − 0.993743i \(-0.535627\pi\)
0.916452 − 0.400144i \(-0.131040\pi\)
\(542\) −2.23561e8 − 1.87590e8i −0.0603113 − 0.0506072i
\(543\) −4.16217e9 − 1.51490e9i −1.11563 − 0.406056i
\(544\) −4.49491e6 − 7.78541e6i −0.00119708 − 0.00207341i
\(545\) −1.43583e9 + 2.48693e9i −0.379940 + 0.658076i
\(546\) 2.25535e9 − 1.89246e9i 0.592978 − 0.497568i
\(547\) 3.34236e8 + 5.78914e8i 0.0873168 + 0.151237i 0.906376 − 0.422472i \(-0.138837\pi\)
−0.819059 + 0.573709i \(0.805504\pi\)
\(548\) 5.59928e8 − 3.17551e9i 0.145345 − 0.824293i
\(549\) −2.54068e9 −0.655311
\(550\) −6.05385e6 + 3.43331e7i −0.00155154 + 0.00879921i
\(551\) −1.90105e9 − 1.59517e9i −0.484130 − 0.406234i
\(552\) −1.51005e8 + 5.49615e7i −0.0382125 + 0.0139082i
\(553\) 3.69706e9 + 1.34562e9i 0.929647 + 0.338364i
\(554\) −2.80627e9 −0.701205
\(555\) −2.47672e9 + 9.86567e8i −0.614966 + 0.244963i
\(556\) −1.10806e9 −0.273401
\(557\) −1.12888e9 − 4.10879e8i −0.276793 − 0.100744i 0.199894 − 0.979818i \(-0.435940\pi\)
−0.476687 + 0.879073i \(0.658162\pi\)
\(558\) −2.35323e9 + 8.56507e8i −0.573384 + 0.208695i
\(559\) −1.38322e9 − 1.16066e9i −0.334927 − 0.281037i
\(560\) 2.52371e8 − 1.43127e9i 0.0607270 − 0.344400i
\(561\) 5.09930e7 0.0121938
\(562\) 4.40379e8 − 2.49751e9i 0.104652 − 0.593514i
\(563\) −1.37420e9 − 2.38019e9i −0.324543 − 0.562125i 0.656877 − 0.753998i \(-0.271877\pi\)
−0.981420 + 0.191873i \(0.938544\pi\)
\(564\) −9.42641e8 + 7.90970e8i −0.221243 + 0.185645i
\(565\) 1.58664e9 − 2.74814e9i 0.370091 − 0.641017i
\(566\) 2.00312e9 + 3.46951e9i 0.464354 + 0.804285i
\(567\) −6.47553e8 − 2.35690e8i −0.149188 − 0.0543001i
\(568\) −4.73703e8 − 3.97484e8i −0.108464 − 0.0910125i
\(569\) −1.98035e9 + 3.43007e9i −0.450661 + 0.780568i −0.998427 − 0.0560637i \(-0.982145\pi\)
0.547766 + 0.836631i \(0.315478\pi\)
\(570\) −2.39794e8 − 1.35994e9i −0.0542345 − 0.307579i
\(571\) −3.80045e8 − 2.15534e9i −0.0854296 − 0.484495i −0.997263 − 0.0739351i \(-0.976444\pi\)
0.911833 − 0.410560i \(-0.134667\pi\)
\(572\) −2.79501e9 + 2.34529e9i −0.624448 + 0.523974i
\(573\) 3.77129e9 − 1.37264e9i 0.837430 − 0.304800i
\(574\) −3.37200e8 + 1.22731e8i −0.0744211 + 0.0270871i
\(575\) 5.63706e6 − 4.73005e6i 0.00123656 − 0.00103760i
\(576\) −5.63301e7 − 3.19464e8i −0.0122818 − 0.0696535i
\(577\) 5.89405e8 + 3.34268e9i 0.127732 + 0.724402i 0.979648 + 0.200724i \(0.0643294\pi\)
−0.851916 + 0.523678i \(0.824559\pi\)
\(578\) −1.64105e9 + 2.84239e9i −0.353489 + 0.612260i
\(579\) 3.88838e8 + 3.26274e8i 0.0832518 + 0.0698566i
\(580\) −2.10074e9 − 7.64607e8i −0.447069 − 0.162720i
\(581\) 5.76755e9 + 9.98969e9i 1.22004 + 2.11317i
\(582\) −1.34912e9 + 2.33674e9i −0.283674 + 0.491338i
\(583\) 1.85690e9 − 1.55812e9i 0.388104 − 0.325658i
\(584\) 2.00074e7 + 3.46538e7i 0.00415667 + 0.00719957i
\(585\) −5.70283e8 + 3.23424e9i −0.117773 + 0.667923i
\(586\) 2.71955e9 0.558284
\(587\) 4.33341e7 − 2.45760e8i 0.00884294 − 0.0501508i −0.980067 − 0.198667i \(-0.936339\pi\)
0.988910 + 0.148516i \(0.0474498\pi\)
\(588\) −1.16809e9 − 9.80143e8i −0.236949 − 0.198824i
\(589\) −4.74210e9 + 1.72598e9i −0.956241 + 0.348043i
\(590\) 6.75425e8 + 2.45835e8i 0.135393 + 0.0492789i
\(591\) −2.08367e9 −0.415216
\(592\) −1.17243e9 + 4.67020e8i −0.232252 + 0.0925144i
\(593\) 5.89087e8 0.116008 0.0580040 − 0.998316i \(-0.481526\pi\)
0.0580040 + 0.998316i \(0.481526\pi\)
\(594\) 4.78495e9 + 1.74158e9i 0.936752 + 0.340950i
\(595\) 9.14737e7 − 3.32937e7i 0.0178027 − 0.00647967i
\(596\) 3.90996e8 + 3.28085e8i 0.0756503 + 0.0634781i
\(597\) 8.49964e8 − 4.82039e9i 0.163490 − 0.927197i
\(598\) 7.70133e8 0.147269
\(599\) −1.22496e9 + 6.94708e9i −0.232877 + 1.32071i 0.614161 + 0.789181i \(0.289494\pi\)
−0.847038 + 0.531532i \(0.821617\pi\)
\(600\) −5.69923e6 − 9.87135e6i −0.00107718 − 0.00186572i
\(601\) −5.24729e9 + 4.40300e9i −0.985994 + 0.827347i −0.984983 − 0.172653i \(-0.944766\pi\)
−0.00101083 + 0.999999i \(0.500322\pi\)
\(602\) −9.65644e8 + 1.67254e9i −0.180397 + 0.312457i
\(603\) −1.26234e9 − 2.18644e9i −0.234458 − 0.406094i
\(604\) −2.17165e9 − 7.90418e8i −0.401016 − 0.145958i
\(605\) −3.63448e9 − 3.04969e9i −0.667264 − 0.559901i
\(606\) 1.05085e9 − 1.82013e9i 0.191817 − 0.332237i
\(607\) −1.19296e9 − 6.76559e9i −0.216503 − 1.22785i −0.878279 − 0.478148i \(-0.841308\pi\)
0.661776 − 0.749701i \(-0.269803\pi\)
\(608\) −1.13513e8 − 6.43765e8i −0.0204825 − 0.116162i
\(609\) −3.71056e9 + 3.11353e9i −0.665701 + 0.558589i
\(610\) −4.33401e9 + 1.57745e9i −0.773099 + 0.281385i
\(611\) 5.54162e9 − 2.01699e9i 0.982863 − 0.357733i
\(612\) 1.66443e7 − 1.39662e7i 0.00293518 − 0.00246291i
\(613\) −2.82525e8 − 1.60228e9i −0.0495387 − 0.280948i 0.949968 − 0.312347i \(-0.101115\pi\)
−0.999507 + 0.0313985i \(0.990004\pi\)
\(614\) 1.18958e9 + 6.74643e9i 0.207397 + 1.17621i
\(615\) −1.53574e8 + 2.65998e8i −0.0266228 + 0.0461121i
\(616\) 2.98946e9 + 2.50845e9i 0.515300 + 0.432388i
\(617\) −5.41653e9 − 1.97146e9i −0.928375 − 0.337901i −0.166810 − 0.985989i \(-0.553347\pi\)
−0.761565 + 0.648088i \(0.775569\pi\)
\(618\) −2.59627e9 − 4.49686e9i −0.442476 − 0.766390i
\(619\) 2.22635e9 − 3.85616e9i 0.377291 − 0.653488i −0.613376 − 0.789791i \(-0.710189\pi\)
0.990667 + 0.136303i \(0.0435222\pi\)
\(620\) −3.48246e9 + 2.92213e9i −0.586835 + 0.492413i
\(621\) −5.37401e8 − 9.30806e8i −0.0900488 − 0.155969i
\(622\) −2.80932e8 + 1.59325e9i −0.0468097 + 0.265471i
\(623\) −1.05125e10 −1.74180
\(624\) 2.07149e8 − 1.17480e9i 0.0341301 − 0.193561i
\(625\) −4.71840e9 − 3.95921e9i −0.773063 − 0.648677i
\(626\) −1.40927e9 + 5.12931e8i −0.229606 + 0.0835697i
\(627\) 3.48435e9 + 1.26820e9i 0.564528 + 0.205471i
\(628\) 3.42589e9 0.551970
\(629\) −6.63541e7 − 5.23672e7i −0.0106314 − 0.00839039i
\(630\) 3.51261e9 0.559678
\(631\) 5.02868e9 + 1.83029e9i 0.796803 + 0.290013i 0.708161 − 0.706051i \(-0.249525\pi\)
0.0886420 + 0.996064i \(0.471747\pi\)
\(632\) 1.49799e9 − 5.45226e8i 0.236048 − 0.0859145i
\(633\) 4.62662e9 + 3.88219e9i 0.725021 + 0.608365i
\(634\) 1.21378e9 − 6.88367e9i 0.189159 − 1.07277i
\(635\) −8.93198e9 −1.38433
\(636\) −1.37622e8 + 7.80495e8i −0.0212124 + 0.120301i
\(637\) 3.65385e9 + 6.32866e9i 0.560097 + 0.970116i
\(638\) 4.59843e9 − 3.85854e9i 0.701031 − 0.588235i
\(639\) 7.47279e8 − 1.29433e9i 0.113300 − 0.196241i
\(640\) −2.94438e8 − 5.09981e8i −0.0443980 − 0.0768997i
\(641\) −2.30914e9 − 8.40460e8i −0.346296 − 0.126042i 0.163016 − 0.986623i \(-0.447878\pi\)
−0.509312 + 0.860582i \(0.670100\pi\)
\(642\) −5.16244e8 − 4.33181e8i −0.0769986 − 0.0646095i
\(643\) −3.89772e9 + 6.75104e9i −0.578192 + 1.00146i 0.417495 + 0.908679i \(0.362908\pi\)
−0.995687 + 0.0927781i \(0.970425\pi\)
\(644\) −1.43036e8 − 8.11198e8i −0.0211030 − 0.119681i
\(645\) 2.87053e8 + 1.62796e9i 0.0421215 + 0.238883i
\(646\) 3.35406e7 − 2.81439e7i 0.00489505 − 0.00410744i
\(647\) −6.82726e9 + 2.48492e9i −0.991018 + 0.360701i −0.786114 − 0.618081i \(-0.787910\pi\)
−0.204904 + 0.978782i \(0.565688\pi\)
\(648\) −2.62379e8 + 9.54982e7i −0.0378806 + 0.0137874i
\(649\) −1.47848e9 + 1.24059e9i −0.212304 + 0.178144i
\(650\) 9.48583e6 + 5.37968e7i 0.00135481 + 0.00768351i
\(651\) 1.71042e9 + 9.70026e9i 0.242979 + 1.37800i
\(652\) 2.31108e9 − 4.00290e9i 0.326549 − 0.565599i
\(653\) 6.34689e9 + 5.32567e9i 0.892000 + 0.748477i 0.968610 − 0.248584i \(-0.0799653\pi\)
−0.0766105 + 0.997061i \(0.524410\pi\)
\(654\) 2.36904e9 + 8.62260e8i 0.331169 + 0.120536i
\(655\) −6.25320e9 − 1.08309e10i −0.869477 − 1.50598i
\(656\) −7.26986e7 + 1.25918e8i −0.0100545 + 0.0174150i
\(657\) −7.40858e7 + 6.21654e7i −0.0101919 + 0.00855204i
\(658\) −3.15378e9 − 5.46250e9i −0.431559 − 0.747482i
\(659\) 1.10221e9 − 6.25092e9i 0.150025 − 0.850834i −0.813169 − 0.582027i \(-0.802260\pi\)
0.963194 − 0.268806i \(-0.0866292\pi\)
\(660\) 3.34029e9 0.452251
\(661\) −1.12817e9 + 6.39818e9i −0.151939 + 0.861690i 0.809592 + 0.586993i \(0.199689\pi\)
−0.961531 + 0.274697i \(0.911423\pi\)
\(662\) 4.00821e9 + 3.36329e9i 0.536967 + 0.450569i
\(663\) 7.50827e7 − 2.73279e7i 0.0100056 − 0.00364174i
\(664\) 4.39199e9 + 1.59855e9i 0.582201 + 0.211904i
\(665\) 7.07841e9 0.933384
\(666\) −1.60366e9 − 2.59460e9i −0.210354 − 0.340338i
\(667\) −1.26705e9 −0.165330
\(668\) 4.51030e9 + 1.64162e9i 0.585448 + 0.213086i
\(669\) 9.85390e8 − 3.58652e8i 0.127238 − 0.0463108i
\(670\) −3.51086e9 − 2.94596e9i −0.450975 − 0.378413i
\(671\) 2.15052e9 − 1.21962e10i 0.274798 − 1.55846i
\(672\) −1.27592e9 −0.162192
\(673\) −1.62704e9 + 9.22741e9i −0.205753 + 1.16688i 0.690498 + 0.723335i \(0.257392\pi\)
−0.896251 + 0.443548i \(0.853720\pi\)
\(674\) 3.18160e9 + 5.51068e9i 0.400254 + 0.693260i
\(675\) 5.84012e7 − 4.90044e7i 0.00730901 − 0.00613299i
\(676\) −8.50574e8 + 1.47324e9i −0.105901 + 0.183425i
\(677\) −9.50969e8 − 1.64713e9i −0.117789 − 0.204017i 0.801102 − 0.598528i \(-0.204247\pi\)
−0.918891 + 0.394511i \(0.870914\pi\)
\(678\) −2.61787e9 − 9.52826e8i −0.322585 − 0.117411i
\(679\) −1.05951e10 − 8.89030e9i −1.29885 − 1.08986i
\(680\) 1.97213e7 − 3.41582e7i 0.00240521 − 0.00416595i
\(681\) 2.76240e8 + 1.56663e9i 0.0335175 + 0.190087i
\(682\) −2.11969e9 − 1.20213e10i −0.255874 − 1.45113i
\(683\) −8.29666e9 + 6.96172e9i −0.996393 + 0.836073i −0.986481 − 0.163878i \(-0.947600\pi\)
−0.00991226 + 0.999951i \(0.503155\pi\)
\(684\) 1.48464e9 − 5.40366e8i 0.177389 − 0.0645642i
\(685\) 1.32942e10 − 4.83869e9i 1.58032 − 0.575189i
\(686\) −3.89949e8 + 3.27206e8i −0.0461183 + 0.0386978i
\(687\) 1.07532e9 + 6.09845e9i 0.126529 + 0.717581i
\(688\) 1.35885e8 + 7.70642e8i 0.0159079 + 0.0902180i
\(689\) 1.89910e9 − 3.28934e9i 0.221198 − 0.383126i
\(690\) −5.40101e8 − 4.53198e8i −0.0625897 − 0.0525190i
\(691\) 7.92565e9 + 2.88470e9i 0.913822 + 0.332604i 0.755778 − 0.654828i \(-0.227259\pi\)
0.158044 + 0.987432i \(0.449481\pi\)
\(692\) 1.36746e9 + 2.36851e9i 0.156871 + 0.271708i
\(693\) −4.71595e9 + 8.16826e9i −0.538273 + 0.932316i
\(694\) 1.39185e9 − 1.16790e9i 0.158065 − 0.132632i
\(695\) −2.43078e9 − 4.21023e9i −0.274662 − 0.475729i
\(696\) −3.40808e8 + 1.93282e9i −0.0383158 + 0.217300i
\(697\) −9.73861e6 −0.00108939
\(698\) −1.96957e9 + 1.11700e10i −0.219219 + 1.24325i
\(699\) −8.39584e9 − 7.04494e9i −0.929809 − 0.780203i
\(700\) 5.49036e7 − 1.99833e7i 0.00605003 − 0.00220203i
\(701\) −7.89636e8 − 2.87404e8i −0.0865793 − 0.0315123i 0.298367 − 0.954451i \(-0.403558\pi\)
−0.384947 + 0.922939i \(0.625780\pi\)
\(702\) 7.97875e9 0.870473
\(703\) −3.23159e9 − 5.22848e9i −0.350811 − 0.567586i
\(704\) 1.58122e9 0.170800
\(705\) −5.07332e9 − 1.84654e9i −0.545293 − 0.198471i
\(706\) 1.13985e10 − 4.14870e9i 1.21907 − 0.443706i
\(707\) 8.25267e9 + 6.92481e9i 0.878267 + 0.736953i
\(708\) 1.09576e8 − 6.21436e8i 0.0116038 − 0.0658082i
\(709\) −1.05130e10 −1.10781 −0.553905 − 0.832580i \(-0.686863\pi\)
−0.553905 + 0.832580i \(0.686863\pi\)
\(710\) 4.71126e8 − 2.67189e9i 0.0494006 − 0.280165i
\(711\) 1.92644e9 + 3.33669e9i 0.201007 + 0.348154i
\(712\) −3.26298e9 + 2.73796e9i −0.338793 + 0.284281i
\(713\) −1.28827e9 + 2.23136e9i −0.133105 + 0.230545i
\(714\) −4.27301e7 − 7.40107e7i −0.00439329 − 0.00760941i
\(715\) −1.50428e10 − 5.47513e9i −1.53907 − 0.560174i
\(716\) 4.62737e9 + 3.88283e9i 0.471128 + 0.395323i
\(717\) 2.38783e9 − 4.13584e9i 0.241928 − 0.419031i
\(718\) −1.71317e7 − 9.71586e7i −0.00172729 − 0.00979593i
\(719\) −5.60537e8 − 3.17896e9i −0.0562410 − 0.318959i 0.943688 − 0.330835i \(-0.107331\pi\)
−0.999929 + 0.0118768i \(0.996219\pi\)
\(720\) 1.09028e9 − 9.14854e8i 0.108862 − 0.0913457i
\(721\) 2.50111e10 − 9.10331e9i 2.48519 − 0.904536i
\(722\) −3.72795e9 + 1.35686e9i −0.368629 + 0.134170i
\(723\) −7.97162e9 + 6.68898e9i −0.784445 + 0.658227i
\(724\) −1.59745e9 − 9.05957e9i −0.156438 − 0.887203i
\(725\) −1.56064e7 − 8.85081e7i −0.00152096 − 0.00862582i
\(726\) −2.08262e9 + 3.60721e9i −0.201991 + 0.349859i
\(727\) 2.42877e9 + 2.03798e9i 0.234432 + 0.196711i 0.752434 − 0.658668i \(-0.228880\pi\)
−0.518002 + 0.855379i \(0.673324\pi\)
\(728\) 5.74603e9 + 2.09138e9i 0.551960 + 0.200897i
\(729\) −3.89312e9 − 6.74308e9i −0.372179 − 0.644632i
\(730\) −8.77818e7 + 1.52043e8i −0.00835169 + 0.0144656i
\(731\) −4.01510e7 + 3.36907e7i −0.00380176 + 0.00319006i
\(732\) 2.02454e9 + 3.50661e9i 0.190782 + 0.330445i
\(733\) −2.42140e9 + 1.37324e10i −0.227092 + 1.28790i 0.631553 + 0.775333i \(0.282418\pi\)
−0.858645 + 0.512571i \(0.828693\pi\)
\(734\) −6.79362e9 −0.634110
\(735\) 1.16173e9 − 6.58851e9i 0.107920 − 0.612043i
\(736\) −2.55672e8 − 2.14534e8i −0.0236380 − 0.0198347i
\(737\) 1.15642e10 − 4.20901e9i 1.06409 − 0.387297i
\(738\) −3.30219e8 − 1.20190e8i −0.0302416 − 0.0110070i
\(739\) 1.92596e9 0.175546 0.0877732 − 0.996140i \(-0.472025\pi\)
0.0877732 + 0.996140i \(0.472025\pi\)
\(740\) −4.34651e9 − 3.43030e9i −0.394303 − 0.311187i
\(741\) 5.81005e9 0.524585
\(742\) −3.81745e9 − 1.38944e9i −0.343052 − 0.124861i
\(743\) 1.63191e9 − 5.93967e8i 0.145961 − 0.0531253i −0.268007 − 0.963417i \(-0.586365\pi\)
0.413967 + 0.910292i \(0.364143\pi\)
\(744\) 3.05731e9 + 2.56539e9i 0.272166 + 0.228375i
\(745\) −3.88868e8 + 2.20538e9i −0.0344553 + 0.195406i
\(746\) 6.74029e9 0.594419
\(747\) −1.96158e9 + 1.11247e10i −0.172180 + 0.976484i
\(748\) 5.29546e7 + 9.17200e7i 0.00462645 + 0.00801325i
\(749\) 2.64621e9 − 2.22043e9i 0.230111 − 0.193086i
\(750\) −2.67896e9 + 4.64009e9i −0.231874 + 0.401617i
\(751\) 1.51763e9 + 2.62861e9i 0.130745 + 0.226457i 0.923964 − 0.382479i \(-0.124930\pi\)
−0.793219 + 0.608937i \(0.791596\pi\)
\(752\) −2.40160e9 − 8.74111e8i −0.205939 − 0.0749556i
\(753\) 6.19406e9 + 5.19743e9i 0.528680 + 0.443615i
\(754\) 4.70293e9 − 8.14572e9i 0.399548 − 0.692038i
\(755\) −1.76071e9 − 9.98551e9i −0.148893 − 0.844415i
\(756\) −1.48189e9 − 8.40420e9i −0.124735 − 0.707408i
\(757\) 1.20432e10 − 1.01054e10i 1.00903 −