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Properties

Label 74.8.f.b.9.6
Level $74$
Weight $8$
Character 74.9
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 9.6
Character \(\chi\) \(=\) 74.9
Dual form 74.8.f.b.33.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.38919 - 7.87846i) q^{2} +(-0.307798 + 1.74561i) q^{3} +(-60.1403 + 21.8893i) q^{4} +(323.926 + 271.806i) q^{5} +14.1803 q^{6} +(-1225.86 - 1028.62i) q^{7} +(256.000 + 443.405i) q^{8} +(2052.16 + 746.923i) q^{9} +O(q^{10})\) \(q+(-1.38919 - 7.87846i) q^{2} +(-0.307798 + 1.74561i) q^{3} +(-60.1403 + 21.8893i) q^{4} +(323.926 + 271.806i) q^{5} +14.1803 q^{6} +(-1225.86 - 1028.62i) q^{7} +(256.000 + 443.405i) q^{8} +(2052.16 + 746.923i) q^{9} +(1691.42 - 2929.63i) q^{10} +(1378.80 + 2388.15i) q^{11} +(-19.6991 - 111.719i) q^{12} +(-4830.22 + 1758.06i) q^{13} +(-6400.99 + 11086.8i) q^{14} +(-574.171 + 481.787i) q^{15} +(3137.72 - 2632.86i) q^{16} +(-28782.7 - 10476.0i) q^{17} +(3033.78 - 17205.4i) q^{18} +(-2616.33 + 14837.9i) q^{19} +(-25430.6 - 9256.00i) q^{20} +(2172.89 - 1823.27i) q^{21} +(16899.6 - 14180.4i) q^{22} +(-41351.0 + 71622.0i) q^{23} +(-852.808 + 310.397i) q^{24} +(17483.1 + 99151.8i) q^{25} +(20560.9 + 35612.4i) q^{26} +(-3873.76 + 6709.54i) q^{27} +(96239.5 + 35028.3i) q^{28} +(103251. + 178836. i) q^{29} +(4593.37 + 3854.29i) q^{30} +152063. q^{31} +(-25101.7 - 21062.9i) q^{32} +(-4593.18 + 1671.78i) q^{33} +(-42550.6 + 241316. i) q^{34} +(-117503. - 666393. i) q^{35} -139767. q^{36} +(69103.4 + 300261. i) q^{37} +120535. q^{38} +(-1582.15 - 8972.81i) q^{39} +(-37595.1 + 213213. i) q^{40} +(-701076. + 255171. i) q^{41} +(-17383.1 - 14586.1i) q^{42} +715146. q^{43} +(-135197. - 113443. i) q^{44} +(461728. + 799736. i) q^{45} +(621715. + 226286. i) q^{46} +(168002. - 290989. i) q^{47} +(3630.16 + 6287.62i) q^{48} +(301671. + 1.71086e6i) q^{49} +(756877. - 275481. i) q^{50} +(27146.3 - 47018.8i) q^{51} +(252008. - 211460. i) q^{52} +(-599937. + 503407. i) q^{53} +(58242.3 + 21198.4i) q^{54} +(-202485. + 1.14835e6i) q^{55} +(142275. - 806880. i) q^{56} +(-25095.9 - 9134.17i) q^{57} +(1.26552e6 - 1.06189e6i) q^{58} +(-852325. + 715186. i) q^{59} +(23984.9 - 41543.0i) q^{60} +(-1.85646e6 + 675695. i) q^{61} +(-211244. - 1.19803e6i) q^{62} +(-1.74736e6 - 3.02651e6i) q^{63} +(-131072. + 227023. i) q^{64} +(-2.04248e6 - 743403. i) q^{65} +(19551.8 + 33864.8i) q^{66} +(-2.17735e6 - 1.82701e6i) q^{67} +1.96031e6 q^{68} +(-112296. - 94227.8i) q^{69} +(-5.08692e6 + 1.85149e6i) q^{70} +(198265. - 1.12442e6i) q^{71} +(194162. + 1.10115e6i) q^{72} +3.63800e6 q^{73} +(2.26960e6 - 961547. i) q^{74} -178462. q^{75} +(-167445. - 949627. i) q^{76} +(766283. - 4.34581e6i) q^{77} +(-68494.0 + 24929.8i) q^{78} +(1.13999e6 + 956563. i) q^{79} +1.73201e6 q^{80} +(3.64818e6 + 3.06119e6i) q^{81} +(2.98428e6 + 5.16892e6i) q^{82} +(-5.19859e6 - 1.89213e6i) q^{83} +(-90768.1 + 157215. i) q^{84} +(-6.47600e6 - 1.12168e7i) q^{85} +(-993471. - 5.63425e6i) q^{86} +(-343958. + 125190. i) q^{87} +(-705946. + 1.22273e6i) q^{88} +(-7.92054e6 + 6.64612e6i) q^{89} +(5.65926e6 - 4.74869e6i) q^{90} +(7.72955e6 + 2.81333e6i) q^{91} +(919107. - 5.21251e6i) q^{92} +(-46804.8 + 265443. i) q^{93} +(-2.52593e6 - 919363. i) q^{94} +(-4.88053e6 + 4.09525e6i) q^{95} +(44493.8 - 37334.7i) q^{96} +(887696. - 1.53753e6i) q^{97} +(1.30599e7 - 4.75340e6i) q^{98} +(1.04575e6 + 5.93072e6i) 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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.38919 − 7.87846i −0.122788 − 0.696364i
\(3\) −0.307798 + 1.74561i −0.00658175 + 0.0373270i −0.987922 − 0.154954i \(-0.950477\pi\)
0.981340 + 0.192280i \(0.0615883\pi\)
\(4\) −60.1403 + 21.8893i −0.469846 + 0.171010i
\(5\) 323.926 + 271.806i 1.15891 + 0.972443i 0.999890 − 0.0148323i \(-0.00472144\pi\)
0.159022 + 0.987275i \(0.449166\pi\)
\(6\) 14.1803 0.0268013
\(7\) −1225.86 − 1028.62i −1.35082 − 1.13347i −0.978701 − 0.205290i \(-0.934186\pi\)
−0.372121 − 0.928184i \(-0.621369\pi\)
\(8\) 256.000 + 443.405i 0.176777 + 0.306186i
\(9\) 2052.16 + 746.923i 0.938343 + 0.341529i
\(10\) 1691.42 − 2929.63i 0.534874 − 0.926429i
\(11\) 1378.80 + 2388.15i 0.312340 + 0.540988i 0.978868 − 0.204491i \(-0.0655539\pi\)
−0.666529 + 0.745479i \(0.732221\pi\)
\(12\) −19.6991 − 111.719i −0.00329088 − 0.0186635i
\(13\) −4830.22 + 1758.06i −0.609769 + 0.221938i −0.628402 − 0.777889i \(-0.716291\pi\)
0.0186332 + 0.999826i \(0.494069\pi\)
\(14\) −6400.99 + 11086.8i −0.623447 + 1.07984i
\(15\) −574.171 + 481.787i −0.0439260 + 0.0368583i
\(16\) 3137.72 − 2632.86i 0.191511 − 0.160697i
\(17\) −28782.7 − 10476.0i −1.42089 − 0.517161i −0.486582 − 0.873635i \(-0.661757\pi\)
−0.934305 + 0.356474i \(0.883979\pi\)
\(18\) 3033.78 − 17205.4i 0.122611 − 0.695364i
\(19\) −2616.33 + 14837.9i −0.0875093 + 0.496290i 0.909278 + 0.416190i \(0.136635\pi\)
−0.996787 + 0.0800997i \(0.974476\pi\)
\(20\) −25430.6 − 9256.00i −0.710808 − 0.258713i
\(21\) 2172.89 − 1823.27i 0.0512000 − 0.0429619i
\(22\) 16899.6 − 14180.4i 0.338373 − 0.283929i
\(23\) −41351.0 + 71622.0i −0.708661 + 1.22744i 0.256693 + 0.966493i \(0.417367\pi\)
−0.965354 + 0.260943i \(0.915966\pi\)
\(24\) −852.808 + 310.397i −0.0125925 + 0.00458330i
\(25\) 17483.1 + 99151.8i 0.223784 + 1.26914i
\(26\) 20560.9 + 35612.4i 0.229422 + 0.397370i
\(27\) −3873.76 + 6709.54i −0.0378756 + 0.0656024i
\(28\) 96239.5 + 35028.3i 0.828514 + 0.301555i
\(29\) 103251. + 178836.i 0.786141 + 1.36164i 0.928315 + 0.371794i \(0.121257\pi\)
−0.142174 + 0.989842i \(0.545409\pi\)
\(30\) 4593.37 + 3854.29i 0.0310604 + 0.0260628i
\(31\) 152063. 0.916767 0.458383 − 0.888755i \(-0.348429\pi\)
0.458383 + 0.888755i \(0.348429\pi\)
\(32\) −25101.7 − 21062.9i −0.135419 − 0.113630i
\(33\) −4593.18 + 1671.78i −0.0222492 + 0.00809804i
\(34\) −42550.6 + 241316.i −0.185665 + 1.05296i
\(35\) −117503. − 666393.i −0.463245 − 2.62719i
\(36\) −139767. −0.499282
\(37\) 69103.4 + 300261.i 0.224281 + 0.974524i
\(38\) 120535. 0.356344
\(39\) −1582.15 − 8972.81i −0.00427092 − 0.0242216i
\(40\) −37595.1 + 213213.i −0.0928799 + 0.526748i
\(41\) −701076. + 255171.i −1.58863 + 0.578213i −0.977057 − 0.212978i \(-0.931684\pi\)
−0.611569 + 0.791191i \(0.709461\pi\)
\(42\) −17383.1 − 14586.1i −0.0362038 − 0.0303786i
\(43\) 715146. 1.37169 0.685844 − 0.727749i \(-0.259433\pi\)
0.685844 + 0.727749i \(0.259433\pi\)
\(44\) −135197. − 113443.i −0.239266 − 0.200768i
\(45\) 461728. + 799736.i 0.755339 + 1.30829i
\(46\) 621715. + 226286.i 0.941758 + 0.342772i
\(47\) 168002. − 290989.i 0.236033 − 0.408821i −0.723539 − 0.690283i \(-0.757486\pi\)
0.959572 + 0.281462i \(0.0908193\pi\)
\(48\) 3630.16 + 6287.62i 0.00473785 + 0.00820620i
\(49\) 301671. + 1.71086e6i 0.366308 + 2.07744i
\(50\) 756877. − 275481.i 0.856308 − 0.311671i
\(51\) 27146.3 − 47018.8i 0.0286560 − 0.0496336i
\(52\) 252008. − 211460.i 0.248544 − 0.208553i
\(53\) −599937. + 503407.i −0.553528 + 0.464465i −0.876134 − 0.482068i \(-0.839886\pi\)
0.322605 + 0.946534i \(0.395441\pi\)
\(54\) 58242.3 + 21198.4i 0.0503338 + 0.0183200i
\(55\) −202485. + 1.14835e6i −0.164106 + 0.930690i
\(56\) 142275. − 806880.i 0.108260 − 0.613975i
\(57\) −25095.9 − 9134.17i −0.0179490 − 0.00653292i
\(58\) 1.26552e6 − 1.06189e6i 0.851666 − 0.714633i
\(59\) −852325. + 715186.i −0.540286 + 0.453353i −0.871636 − 0.490154i \(-0.836940\pi\)
0.331350 + 0.943508i \(0.392496\pi\)
\(60\) 23984.9 − 41543.0i 0.0143353 − 0.0248295i
\(61\) −1.85646e6 + 675695.i −1.04720 + 0.381150i −0.807606 − 0.589723i \(-0.799237\pi\)
−0.239595 + 0.970873i \(0.577015\pi\)
\(62\) −211244. − 1.19803e6i −0.112568 − 0.638404i
\(63\) −1.74736e6 − 3.02651e6i −0.880420 − 1.52493i
\(64\) −131072. + 227023.i −0.0625000 + 0.108253i
\(65\) −2.04248e6 − 743403.i −0.922490 − 0.335759i
\(66\) 19551.8 + 33864.8i 0.00837112 + 0.0144992i
\(67\) −2.17735e6 − 1.82701e6i −0.884435 − 0.742129i 0.0826513 − 0.996579i \(-0.473661\pi\)
−0.967086 + 0.254450i \(0.918106\pi\)
\(68\) 1.96031e6 0.756039
\(69\) −112296. − 94227.8i −0.0411523 − 0.0345308i
\(70\) −5.08692e6 + 1.85149e6i −1.77260 + 0.645175i
\(71\) 198265. − 1.12442e6i 0.0657420 − 0.372841i −0.934131 − 0.356929i \(-0.883824\pi\)
0.999873 − 0.0159121i \(-0.00506518\pi\)
\(72\) 194162. + 1.10115e6i 0.0613057 + 0.347682i
\(73\) 3.63800e6 1.09454 0.547271 − 0.836955i \(-0.315667\pi\)
0.547271 + 0.836955i \(0.315667\pi\)
\(74\) 2.26960e6 − 961547.i 0.651085 − 0.275841i
\(75\) −178462. −0.0488462
\(76\) −167445. − 949627.i −0.0437547 − 0.248145i
\(77\) 766283. − 4.34581e6i 0.191281 − 1.08481i
\(78\) −68494.0 + 24929.8i −0.0163426 + 0.00594823i
\(79\) 1.13999e6 + 956563.i 0.260139 + 0.218282i 0.763524 − 0.645780i \(-0.223468\pi\)
−0.503385 + 0.864062i \(0.667912\pi\)
\(80\) 1.73201e6 0.378213
\(81\) 3.64818e6 + 3.06119e6i 0.762744 + 0.640019i
\(82\) 2.98428e6 + 5.16892e6i 0.597711 + 1.03527i
\(83\) −5.19859e6 − 1.89213e6i −0.997959 − 0.363227i −0.209162 − 0.977881i \(-0.567074\pi\)
−0.788797 + 0.614654i \(0.789296\pi\)
\(84\) −90768.1 + 157215.i −0.0167092 + 0.0289412i
\(85\) −6.47600e6 − 1.12168e7i −1.14377 − 1.98108i
\(86\) −993471. − 5.63425e6i −0.168427 − 0.955194i
\(87\) −343958. + 125190.i −0.0559999 + 0.0203823i
\(88\) −705946. + 1.22273e6i −0.110429 + 0.191268i
\(89\) −7.92054e6 + 6.64612e6i −1.19094 + 0.999317i −0.191097 + 0.981571i \(0.561205\pi\)
−0.999843 + 0.0177459i \(0.994351\pi\)
\(90\) 5.65926e6 − 4.74869e6i 0.818297 − 0.686633i
\(91\) 7.72955e6 + 2.81333e6i 1.07525 + 0.391359i
\(92\) 919107. − 5.21251e6i 0.123058 − 0.697895i
\(93\) −46804.8 + 265443.i −0.00603393 + 0.0342201i
\(94\) −2.52593e6 − 919363.i −0.313670 − 0.114167i
\(95\) −4.88053e6 + 4.09525e6i −0.584029 + 0.490059i
\(96\) 44493.8 − 37334.7i 0.00513275 − 0.00430689i
\(97\) 887696. − 1.53753e6i 0.0987559 − 0.171050i −0.812414 − 0.583081i \(-0.801847\pi\)
0.911170 + 0.412031i \(0.135180\pi\)
\(98\) 1.30599e7 − 4.75340e6i 1.40168 − 0.510168i
\(99\) 1.04575e6 + 5.93072e6i 0.108319 + 0.614305i
\(100\) −3.22181e6 − 5.58033e6i −0.322181 − 0.558033i
\(101\) 182716. − 316474.i 0.0176463 − 0.0305642i −0.857067 − 0.515204i \(-0.827716\pi\)
0.874714 + 0.484640i \(0.161049\pi\)
\(102\) −408147. − 148553.i −0.0380817 − 0.0138606i
\(103\) −3.27687e6 − 5.67571e6i −0.295481 − 0.511788i 0.679616 − 0.733568i \(-0.262147\pi\)
−0.975097 + 0.221780i \(0.928813\pi\)
\(104\) −2.01607e6 − 1.69168e6i −0.175747 − 0.147469i
\(105\) 1.19943e6 0.101114
\(106\) 4.79949e6 + 4.02725e6i 0.391404 + 0.328427i
\(107\) 1.16238e7 − 4.23072e6i 0.917287 − 0.333865i 0.160128 − 0.987096i \(-0.448809\pi\)
0.757159 + 0.653231i \(0.226587\pi\)
\(108\) 86101.9 − 488308.i 0.00657702 − 0.0373002i
\(109\) −865998. − 4.91132e6i −0.0640507 − 0.363250i −0.999940 − 0.0109553i \(-0.996513\pi\)
0.935889 − 0.352294i \(-0.114598\pi\)
\(110\) 9.32853e6 0.668250
\(111\) −545408. + 28207.8i −0.0378522 + 0.00195767i
\(112\) −6.55462e6 −0.440843
\(113\) −471533. − 2.67420e6i −0.0307424 − 0.174349i 0.965571 − 0.260141i \(-0.0837690\pi\)
−0.996313 + 0.0857921i \(0.972658\pi\)
\(114\) −37100.3 + 210406.i −0.00234537 + 0.0133012i
\(115\) −3.28619e7 + 1.19608e7i −2.01489 + 0.733359i
\(116\) −1.01241e7 − 8.49515e6i −0.602219 − 0.505322i
\(117\) −1.12255e7 −0.647970
\(118\) 6.81860e6 + 5.72149e6i 0.382040 + 0.320569i
\(119\) 2.45077e7 + 4.24486e7i 1.33318 + 2.30913i
\(120\) −360614. − 131253.i −0.0190506 − 0.00693385i
\(121\) 5.94140e6 − 1.02908e7i 0.304888 − 0.528081i
\(122\) 7.90239e6 + 1.36873e7i 0.394003 + 0.682433i
\(123\) −229639. − 1.30235e6i −0.0111270 − 0.0631043i
\(124\) −9.14515e6 + 3.32856e6i −0.430740 + 0.156776i
\(125\) −4.76905e6 + 8.26023e6i −0.218397 + 0.378275i
\(126\) −2.14169e7 + 1.79709e7i −0.953803 + 0.800336i
\(127\) 2.98914e7 − 2.50819e7i 1.29489 − 1.08654i 0.303889 − 0.952707i \(-0.401715\pi\)
0.991003 − 0.133837i \(-0.0427298\pi\)
\(128\) 1.97068e6 + 717268.i 0.0830579 + 0.0302306i
\(129\) −220121. + 1.24837e6i −0.00902811 + 0.0512010i
\(130\) −3.01949e6 + 1.71244e7i −0.120540 + 0.683616i
\(131\) −6.33468e6 − 2.30564e6i −0.246193 − 0.0896068i 0.215977 − 0.976399i \(-0.430707\pi\)
−0.462169 + 0.886792i \(0.652929\pi\)
\(132\) 239641. − 201083.i 0.00906886 − 0.00760967i
\(133\) 1.84698e7 − 1.54980e7i 0.680742 − 0.571210i
\(134\) −1.13693e7 + 1.96922e7i −0.408194 + 0.707013i
\(135\) −3.07850e6 + 1.12048e6i −0.107689 + 0.0391956i
\(136\) −2.72324e6 − 1.54442e7i −0.0928323 − 0.526478i
\(137\) 2.49460e7 + 4.32078e7i 0.828857 + 1.43562i 0.898936 + 0.438081i \(0.144342\pi\)
−0.0700787 + 0.997541i \(0.522325\pi\)
\(138\) −586370. + 1.01562e6i −0.0189930 + 0.0328969i
\(139\) −4.82003e6 − 1.75435e6i −0.152229 − 0.0554069i 0.264782 − 0.964308i \(-0.414700\pi\)
−0.417011 + 0.908901i \(0.636922\pi\)
\(140\) 2.16535e7 + 3.75050e7i 0.666931 + 1.15516i
\(141\) 456242. + 382832.i 0.0137065 + 0.0115012i
\(142\) −9.13412e6 −0.267706
\(143\) −1.08584e7 − 9.11130e6i −0.310521 − 0.260558i
\(144\) 8.40563e6 − 3.05940e6i 0.234586 − 0.0853822i
\(145\) −1.51630e7 + 8.59937e7i −0.413045 + 2.34249i
\(146\) −5.05385e6 − 2.86618e7i −0.134396 − 0.762200i
\(147\) −3.07935e6 −0.0799554
\(148\) −1.07284e7 − 1.65452e7i −0.272031 − 0.419522i
\(149\) −2.81242e7 −0.696511 −0.348256 − 0.937400i \(-0.613226\pi\)
−0.348256 + 0.937400i \(0.613226\pi\)
\(150\) 247916. + 1.40600e6i 0.00599771 + 0.0340147i
\(151\) 1.03614e7 − 5.87624e7i 0.244906 − 1.38893i −0.575806 − 0.817586i \(-0.695312\pi\)
0.820712 − 0.571342i \(-0.193577\pi\)
\(152\) −7.24899e6 + 2.63842e6i −0.167427 + 0.0609384i
\(153\) −5.12417e7 − 4.29969e7i −1.15665 − 0.970548i
\(154\) −3.53028e7 −0.778909
\(155\) 4.92573e7 + 4.13318e7i 1.06245 + 0.891503i
\(156\) 291559. + 504995.i 0.00614881 + 0.0106500i
\(157\) 590111. + 214783.i 0.0121698 + 0.00442946i 0.348098 − 0.937458i \(-0.386828\pi\)
−0.335928 + 0.941888i \(0.609050\pi\)
\(158\) 5.95259e6 − 1.03102e7i 0.120062 − 0.207954i
\(159\) −694092. − 1.20220e6i −0.0136939 − 0.0237185i
\(160\) −2.40609e6 − 1.36456e7i −0.0464400 − 0.263374i
\(161\) 1.24362e8 − 4.52642e7i 2.34854 − 0.854800i
\(162\) 1.90495e7 − 3.29946e7i 0.352030 − 0.609734i
\(163\) 1.88547e7 − 1.58210e7i 0.341008 − 0.286139i −0.456160 − 0.889898i \(-0.650775\pi\)
0.797167 + 0.603759i \(0.206331\pi\)
\(164\) 3.65774e7 − 3.06921e7i 0.647530 − 0.543342i
\(165\) −1.94225e6 − 706920.i −0.0336597 − 0.0122511i
\(166\) −7.68529e6 + 4.35855e7i −0.130401 + 0.739543i
\(167\) −1.13418e7 + 6.43225e7i −0.188440 + 1.06870i 0.733014 + 0.680213i \(0.238113\pi\)
−0.921455 + 0.388486i \(0.872998\pi\)
\(168\) 1.36471e6 + 496712.i 0.0222053 + 0.00808206i
\(169\) −2.78279e7 + 2.33504e7i −0.443483 + 0.372126i
\(170\) −7.93744e7 + 6.66031e7i −1.23911 + 1.03974i
\(171\) −1.64519e7 + 2.84955e7i −0.251611 + 0.435803i
\(172\) −4.30091e7 + 1.56540e7i −0.644482 + 0.234572i
\(173\) −1.07426e7 − 6.09245e7i −0.157743 − 0.894604i −0.956235 − 0.292599i \(-0.905480\pi\)
0.798492 − 0.602005i \(-0.205631\pi\)
\(174\) 1.46413e6 + 2.53594e6i 0.0210696 + 0.0364937i
\(175\) 8.05576e7 − 1.39530e8i 1.13625 − 1.96804i
\(176\) 1.06140e7 + 3.86316e6i 0.146752 + 0.0534132i
\(177\) −986091. − 1.70796e6i −0.0133663 − 0.0231511i
\(178\) 6.33643e7 + 5.31690e7i 0.842122 + 0.706624i
\(179\) 7.44043e7 0.969644 0.484822 − 0.874613i \(-0.338884\pi\)
0.484822 + 0.874613i \(0.338884\pi\)
\(180\) −4.52741e7 − 3.79895e7i −0.578624 − 0.485523i
\(181\) 8.89298e7 − 3.23678e7i 1.11474 − 0.405731i 0.282008 − 0.959412i \(-0.408999\pi\)
0.832729 + 0.553681i \(0.186777\pi\)
\(182\) 1.14269e7 − 6.48052e7i 0.140501 − 0.796820i
\(183\) −608085. − 3.44862e6i −0.00733476 − 0.0415975i
\(184\) −4.23434e7 −0.501099
\(185\) −5.92283e7 + 1.16045e8i −0.687747 + 1.34749i
\(186\) 2.15631e6 0.0245706
\(187\) −1.46672e7 − 8.31818e7i −0.164022 − 0.930213i
\(188\) −3.73418e6 + 2.11776e7i −0.0409867 + 0.232447i
\(189\) 1.16503e7 − 4.24035e6i 0.125522 − 0.0456862i
\(190\) 3.90443e7 + 3.27620e7i 0.412971 + 0.346524i
\(191\) −1.02597e8 −1.06541 −0.532705 − 0.846301i \(-0.678824\pi\)
−0.532705 + 0.846301i \(0.678824\pi\)
\(192\) −355950. − 298678.i −0.00362940 − 0.00304543i
\(193\) 7.45496e7 + 1.29124e8i 0.746440 + 1.29287i 0.949519 + 0.313709i \(0.101572\pi\)
−0.203080 + 0.979162i \(0.565095\pi\)
\(194\) −1.33466e7 − 4.85776e6i −0.131239 − 0.0477672i
\(195\) 1.92636e6 − 3.33656e6i 0.0186045 − 0.0322239i
\(196\) −5.55921e7 − 9.62883e7i −0.527371 − 0.913434i
\(197\) −2.80903e7 − 1.59308e8i −0.261773 − 1.48459i −0.778070 − 0.628178i \(-0.783801\pi\)
0.516297 − 0.856410i \(-0.327310\pi\)
\(198\) 4.52722e7 − 1.64777e7i 0.414480 − 0.150858i
\(199\) −563738. + 976423.i −0.00507098 + 0.00878319i −0.868550 − 0.495602i \(-0.834947\pi\)
0.863479 + 0.504385i \(0.168281\pi\)
\(200\) −3.94887e7 + 3.31350e7i −0.349034 + 0.292875i
\(201\) 3.85943e6 − 3.23845e6i 0.0335226 − 0.0281288i
\(202\) −2.74715e6 − 999883.i −0.0234506 − 0.00853531i
\(203\) 5.73827e7 − 3.25433e8i 0.481443 − 2.73040i
\(204\) −603380. + 3.42194e6i −0.00497606 + 0.0282206i
\(205\) −2.96454e8 − 1.07900e8i −2.40336 − 0.874750i
\(206\) −4.01637e7 + 3.37013e7i −0.320109 + 0.268604i
\(207\) −1.38355e8 + 1.16093e8i −1.08417 + 0.909728i
\(208\) −1.05272e7 + 1.82336e7i −0.0811128 + 0.140492i
\(209\) −3.90426e7 + 1.42104e7i −0.295820 + 0.107670i
\(210\) −1.66623e6 − 9.44966e6i −0.0124156 − 0.0704123i
\(211\) −4.44538e7 − 7.69963e7i −0.325777 − 0.564262i 0.655892 − 0.754854i \(-0.272293\pi\)
−0.981669 + 0.190592i \(0.938959\pi\)
\(212\) 2.50612e7 − 4.34072e7i 0.180645 − 0.312886i
\(213\) 1.90177e6 + 692188.i 0.0134843 + 0.00490790i
\(214\) −4.94792e7 − 8.57005e7i −0.345123 − 0.597771i
\(215\) 2.31654e8 + 1.94381e8i 1.58967 + 1.33389i
\(216\) −3.96673e6 −0.0267821
\(217\) −1.86409e8 − 1.56415e8i −1.23839 − 1.03913i
\(218\) −3.74906e7 + 1.36455e7i −0.245089 + 0.0892052i
\(219\) −1.11977e6 + 6.35053e6i −0.00720401 + 0.0408559i
\(220\) −1.29591e7 − 7.34945e7i −0.0820529 − 0.465345i
\(221\) 1.57444e8 0.981191
\(222\) 979908. + 4.25779e6i 0.00601104 + 0.0261185i
\(223\) 8.72567e7 0.526904 0.263452 − 0.964672i \(-0.415139\pi\)
0.263452 + 0.964672i \(0.415139\pi\)
\(224\) 9.10558e6 + 5.16403e7i 0.0541302 + 0.306988i
\(225\) −3.81807e7 + 2.16534e8i −0.223463 + 1.26732i
\(226\) −2.04135e7 + 7.42991e6i −0.117635 + 0.0428158i
\(227\) −1.11772e8 − 9.37878e7i −0.634224 − 0.532177i 0.268014 − 0.963415i \(-0.413632\pi\)
−0.902238 + 0.431238i \(0.858077\pi\)
\(228\) 1.70922e6 0.00955048
\(229\) 1.70535e8 + 1.43096e8i 0.938403 + 0.787413i 0.977307 − 0.211830i \(-0.0679422\pi\)
−0.0389039 + 0.999243i \(0.512387\pi\)
\(230\) 1.39884e8 + 2.42286e8i 0.758088 + 1.31305i
\(231\) 7.35022e6 + 2.67526e6i 0.0392336 + 0.0142799i
\(232\) −5.28644e7 + 9.15638e7i −0.277943 + 0.481411i
\(233\) −396056. − 685989.i −0.00205121 − 0.00355280i 0.864998 − 0.501775i \(-0.167320\pi\)
−0.867049 + 0.498223i \(0.833986\pi\)
\(234\) 1.55943e7 + 8.84397e7i 0.0795629 + 0.451223i
\(235\) 1.33513e8 − 4.85946e7i 0.671097 − 0.244259i
\(236\) 3.56042e7 − 6.16683e7i 0.176323 − 0.305401i
\(237\) −2.02067e6 + 1.69555e6i −0.00985999 + 0.00827352i
\(238\) 3.00384e8 − 2.52052e8i 1.44430 − 1.21191i
\(239\) 2.17449e8 + 7.91451e7i 1.03030 + 0.375000i 0.801197 − 0.598401i \(-0.204197\pi\)
0.229108 + 0.973401i \(0.426419\pi\)
\(240\) −533111. + 3.02342e6i −0.00248930 + 0.0141175i
\(241\) −8.76721e6 + 4.97213e7i −0.0403461 + 0.228814i −0.998313 − 0.0580653i \(-0.981507\pi\)
0.957967 + 0.286880i \(0.0926179\pi\)
\(242\) −8.93294e7 − 3.25133e7i −0.405173 − 0.147471i
\(243\) −1.94463e7 + 1.63173e7i −0.0869389 + 0.0729504i
\(244\) 9.68574e7 − 8.12730e7i 0.426843 − 0.358164i
\(245\) −3.67303e8 + 6.36187e8i −1.59567 + 2.76378i
\(246\) −9.94148e6 + 3.61840e6i −0.0425773 + 0.0154969i
\(247\) −1.34485e7 − 7.62701e7i −0.0567850 − 0.322044i
\(248\) 3.89282e7 + 6.74257e7i 0.162063 + 0.280701i
\(249\) 4.90304e6 − 8.49232e6i 0.0201265 − 0.0348601i
\(250\) 7.17030e7 + 2.60978e7i 0.290233 + 0.105636i
\(251\) −1.09640e8 − 1.89901e8i −0.437633 − 0.758002i 0.559874 − 0.828578i \(-0.310850\pi\)
−0.997506 + 0.0705760i \(0.977516\pi\)
\(252\) 1.71335e8 + 1.43767e8i 0.674441 + 0.565923i
\(253\) −2.28059e8 −0.885371
\(254\) −2.39132e8 − 2.00655e8i −0.915627 − 0.768303i
\(255\) 2.15734e7 − 7.85207e6i 0.0814756 − 0.0296547i
\(256\) 2.91333e6 − 1.65223e7i 0.0108530 − 0.0615505i
\(257\) 4.06401e7 + 2.30481e8i 0.149344 + 0.846973i 0.963776 + 0.266714i \(0.0859378\pi\)
−0.814432 + 0.580260i \(0.802951\pi\)
\(258\) 1.01410e7 0.0367631
\(259\) 2.24143e8 − 4.39159e8i 0.801634 − 1.57063i
\(260\) 1.39108e8 0.490847
\(261\) 7.83101e7 + 4.44119e8i 0.272632 + 1.54617i
\(262\) −9.36481e6 + 5.31105e7i −0.0321695 + 0.182442i
\(263\) −5.01416e8 + 1.82500e8i −1.69962 + 0.618612i −0.995783 − 0.0917448i \(-0.970756\pi\)
−0.703841 + 0.710357i \(0.748533\pi\)
\(264\) −1.91713e6 − 1.60866e6i −0.00641265 − 0.00538085i
\(265\) −3.31164e8 −1.09316
\(266\) −1.47759e8 − 1.23984e8i −0.481357 − 0.403907i
\(267\) −9.16361e6 − 1.58718e7i −0.0294630 − 0.0510314i
\(268\) 1.70938e8 + 6.22165e7i 0.542460 + 0.197439i
\(269\) 2.68543e8 − 4.65130e8i 0.841165 − 1.45694i −0.0477462 − 0.998860i \(-0.515204\pi\)
0.888911 − 0.458080i \(-0.151463\pi\)
\(270\) 1.31043e7 + 2.26973e7i 0.0405173 + 0.0701781i
\(271\) 6.73031e7 + 3.81695e8i 0.205420 + 1.16499i 0.896777 + 0.442482i \(0.145902\pi\)
−0.691357 + 0.722513i \(0.742987\pi\)
\(272\) −1.17894e8 + 4.29098e7i −0.355222 + 0.129290i
\(273\) −7.29011e6 + 1.26268e7i −0.0216853 + 0.0375600i
\(274\) 3.05756e8 − 2.56560e8i 0.897942 − 0.753463i
\(275\) −2.12684e8 + 1.78463e8i −0.616695 + 0.517469i
\(276\) 8.81611e6 + 3.20880e6i 0.0252404 + 0.00918674i
\(277\) −4.65553e7 + 2.64028e8i −0.131610 + 0.746399i 0.845550 + 0.533896i \(0.179273\pi\)
−0.977160 + 0.212503i \(0.931838\pi\)
\(278\) −7.12565e6 + 4.04115e7i −0.0198915 + 0.112810i
\(279\) 3.12058e8 + 1.13580e8i 0.860241 + 0.313102i
\(280\) 2.65401e8 − 2.22698e8i 0.722520 − 0.606266i
\(281\) 3.33578e8 − 2.79905e8i 0.896862 − 0.752557i −0.0727126 − 0.997353i \(-0.523166\pi\)
0.969574 + 0.244796i \(0.0787211\pi\)
\(282\) 2.38232e6 − 4.12631e6i 0.00632600 − 0.0109569i
\(283\) −2.19481e8 + 7.98847e7i −0.575632 + 0.209513i −0.613399 − 0.789774i \(-0.710198\pi\)
0.0377661 + 0.999287i \(0.487976\pi\)
\(284\) 1.26890e7 + 7.19628e7i 0.0328710 + 0.186421i
\(285\) −5.64649e6 − 9.78002e6i −0.0144485 − 0.0250255i
\(286\) −5.66987e7 + 9.82050e7i −0.143315 + 0.248229i
\(287\) 1.12190e9 + 4.08337e8i 2.80134 + 1.01960i
\(288\) −3.57803e7 − 6.19734e7i −0.0882614 − 0.152873i
\(289\) 4.04357e8 + 3.39296e8i 0.985422 + 0.826867i
\(290\) 6.98562e8 1.68195
\(291\) 2.41070e6 + 2.02282e6i 0.00573480 + 0.00481207i
\(292\) −2.18790e8 + 7.96332e7i −0.514267 + 0.187178i
\(293\) −5.70744e7 + 3.23685e8i −0.132558 + 0.751772i 0.843972 + 0.536388i \(0.180211\pi\)
−0.976529 + 0.215384i \(0.930900\pi\)
\(294\) 4.27778e6 + 2.42605e7i 0.00981755 + 0.0556781i
\(295\) −4.70482e8 −1.06700
\(296\) −1.15447e8 + 1.07508e8i −0.258738 + 0.240945i
\(297\) −2.13646e7 −0.0473202
\(298\) 3.90697e7 + 2.21575e8i 0.0855231 + 0.485025i
\(299\) 7.38188e7 − 4.18647e8i 0.159705 − 0.905731i
\(300\) 1.07327e7 − 3.90640e6i 0.0229502 − 0.00835319i
\(301\) −8.76670e8 − 7.35614e8i −1.85291 − 1.55477i
\(302\) −4.77351e8 −0.997272
\(303\) 496200. + 416361.i 0.00102473 + 0.000859847i
\(304\) 3.08569e7 + 5.34456e7i 0.0629933 + 0.109108i
\(305\) −7.85012e8 − 2.85721e8i −1.58426 − 0.576624i
\(306\) −2.67565e8 + 4.63436e8i −0.533832 + 0.924624i
\(307\) −5.43022e7 − 9.40542e7i −0.107111 − 0.185521i 0.807488 − 0.589884i \(-0.200827\pi\)
−0.914599 + 0.404363i \(0.867493\pi\)
\(308\) 4.90421e7 + 2.78132e8i 0.0956405 + 0.542404i
\(309\) 1.09162e7 − 3.97317e6i 0.0210483 − 0.00766095i
\(310\) 2.57203e8 − 4.45489e8i 0.490355 − 0.849319i
\(311\) −3.04416e8 + 2.55435e8i −0.573860 + 0.481526i −0.882924 − 0.469516i \(-0.844429\pi\)
0.309064 + 0.951041i \(0.399984\pi\)
\(312\) 3.57356e6 − 2.99857e6i 0.00666131 − 0.00558950i
\(313\) −1.62118e7 − 5.90061e6i −0.0298831 − 0.0108766i 0.327035 − 0.945012i \(-0.393950\pi\)
−0.356918 + 0.934136i \(0.616173\pi\)
\(314\) 872385. − 4.94754e6i 0.00159021 − 0.00901853i
\(315\) 2.56610e8 − 1.45531e9i 0.462580 − 2.62342i
\(316\) −8.94977e7 − 3.25745e7i −0.159554 − 0.0580728i
\(317\) −1.74026e8 + 1.46025e8i −0.306836 + 0.257466i −0.783183 − 0.621792i \(-0.786405\pi\)
0.476347 + 0.879257i \(0.341961\pi\)
\(318\) −8.50729e6 + 7.13846e6i −0.0148353 + 0.0124483i
\(319\) −2.84725e8 + 4.93157e8i −0.491086 + 0.850586i
\(320\) −1.04164e8 + 3.79126e7i −0.177702 + 0.0646782i
\(321\) 3.80740e6 + 2.15928e7i 0.00642482 + 0.0364370i
\(322\) −5.29375e8 − 9.16904e8i −0.883624 − 1.53048i
\(323\) 2.30747e8 − 3.99666e8i 0.381003 − 0.659916i
\(324\) −2.86410e8 − 1.04245e8i −0.467822 − 0.170273i
\(325\) −2.58762e8 − 4.48189e8i −0.418128 − 0.724218i
\(326\) −1.50838e8 − 1.26568e8i −0.241129 − 0.202331i
\(327\) 8.83979e6 0.0139806
\(328\) −2.92620e8 − 2.45537e8i −0.457873 − 0.384201i
\(329\) −5.05264e8 + 1.83901e8i −0.782227 + 0.284707i
\(330\) −2.87130e6 + 1.62840e7i −0.00439825 + 0.0249437i
\(331\) 1.76328e8 + 1.00001e9i 0.267254 + 1.51567i 0.762539 + 0.646943i \(0.223953\pi\)
−0.495285 + 0.868731i \(0.664936\pi\)
\(332\) 3.54063e8 0.531003
\(333\) −8.24610e7 + 6.67797e8i −0.122375 + 0.991036i
\(334\) 5.22518e8 0.767342
\(335\) −2.08706e8 − 1.18363e9i −0.303304 − 1.72012i
\(336\) 2.01750e6 − 1.14418e7i 0.00290152 − 0.0164553i
\(337\) 4.26909e8 − 1.55382e8i 0.607618 − 0.221155i −0.0198426 − 0.999803i \(-0.506317\pi\)
0.627461 + 0.778648i \(0.284094\pi\)
\(338\) 2.22623e8 + 1.86803e8i 0.313590 + 0.263133i
\(339\) 4.81324e6 0.00671025
\(340\) 6.34995e8 + 5.32824e8i 0.876182 + 0.735204i
\(341\) 2.09665e8 + 3.63151e8i 0.286343 + 0.495960i
\(342\) 2.47356e8 + 9.00301e7i 0.334372 + 0.121702i
\(343\) 7.31081e8 − 1.26627e9i 0.978219 − 1.69432i
\(344\) 1.83077e8 + 3.17099e8i 0.242482 + 0.419992i
\(345\) −1.07640e7 − 6.10456e7i −0.0141126 − 0.0800364i
\(346\) −4.65068e8 + 1.69271e8i −0.603602 + 0.219693i
\(347\) −4.10525e8 + 7.11051e8i −0.527457 + 0.913582i 0.472031 + 0.881582i \(0.343521\pi\)
−0.999488 + 0.0319999i \(0.989812\pi\)
\(348\) 1.79454e7 − 1.50580e7i 0.0228258 − 0.0191531i
\(349\) 7.19557e8 − 6.03780e8i 0.906100 − 0.760308i −0.0652733 − 0.997867i \(-0.520792\pi\)
0.971373 + 0.237559i \(0.0763475\pi\)
\(350\) −1.21119e9 − 4.40837e8i −1.50999 − 0.549592i
\(351\) 6.91534e6 − 3.92189e7i 0.00853570 − 0.0484083i
\(352\) 1.56910e7 − 8.89883e7i 0.0191758 − 0.108751i
\(353\) −8.39658e8 − 3.05610e8i −1.01599 − 0.369791i −0.220262 − 0.975441i \(-0.570691\pi\)
−0.795732 + 0.605649i \(0.792913\pi\)
\(354\) −1.20862e7 + 1.01416e7i −0.0144804 + 0.0121505i
\(355\) 3.69847e8 − 3.10339e8i 0.438756 − 0.368160i
\(356\) 3.30865e8 − 5.73075e8i 0.388665 − 0.673188i
\(357\) −8.16421e7 + 2.97153e7i −0.0949676 + 0.0345654i
\(358\) −1.03361e8 − 5.86191e8i −0.119060 − 0.675225i
\(359\) 6.65197e8 + 1.15215e9i 0.758786 + 1.31426i 0.943470 + 0.331458i \(0.107541\pi\)
−0.184684 + 0.982798i \(0.559126\pi\)
\(360\) −2.36405e8 + 4.09465e8i −0.267053 + 0.462549i
\(361\) 6.26646e8 + 2.28080e8i 0.701047 + 0.255160i
\(362\) −3.78549e8 − 6.55666e8i −0.419413 − 0.726444i
\(363\) 1.61350e7 + 1.35389e7i 0.0177050 + 0.0148562i
\(364\) −5.26440e8 −0.572129
\(365\) 1.17844e9 + 9.88830e8i 1.26848 + 1.06438i
\(366\) −2.63251e7 + 9.58156e6i −0.0280664 + 0.0102153i
\(367\) 2.65396e8 − 1.50513e9i 0.280261 − 1.58944i −0.441476 − 0.897273i \(-0.645545\pi\)
0.721738 − 0.692167i \(-0.243344\pi\)
\(368\) 5.88228e7 + 3.33601e8i 0.0615288 + 0.348947i
\(369\) −1.62931e9 −1.68815
\(370\) 9.96535e8 + 3.05420e8i 1.02279 + 0.313467i
\(371\) 1.25325e9 1.27418
\(372\) −2.99551e6 − 1.69884e7i −0.00301697 − 0.0171101i
\(373\) 1.08421e8 − 6.14883e8i 0.108176 − 0.613496i −0.881728 − 0.471758i \(-0.843620\pi\)
0.989904 − 0.141738i \(-0.0452692\pi\)
\(374\) −6.34969e8 + 2.31110e8i −0.627627 + 0.228438i
\(375\) −1.29512e7 − 1.08674e7i −0.0126824 − 0.0106418i
\(376\) 1.72034e8 0.166901
\(377\) −8.13127e8 − 6.82295e8i −0.781563 − 0.655809i
\(378\) −4.95918e7 − 8.58955e7i −0.0472268 − 0.0817992i
\(379\) −1.50015e9 − 5.46011e8i −1.41546 − 0.515186i −0.482735 − 0.875767i \(-0.660356\pi\)
−0.932728 + 0.360580i \(0.882579\pi\)
\(380\) 2.03875e8 − 3.53121e8i 0.190599 − 0.330127i
\(381\) 3.45827e7 + 5.98989e7i 0.0320347 + 0.0554858i
\(382\) 1.42526e8 + 8.08304e8i 0.130819 + 0.741913i
\(383\) −3.37501e8 + 1.22840e8i −0.306959 + 0.111724i −0.490907 − 0.871212i \(-0.663334\pi\)
0.183948 + 0.982936i \(0.441112\pi\)
\(384\) −1.85864e6 + 3.21926e6i −0.00167508 + 0.00290133i
\(385\) 1.42944e9 − 1.19944e9i 1.27659 − 1.07119i
\(386\) 9.13733e8 − 7.66713e8i 0.808656 − 0.678543i
\(387\) 1.46759e9 + 5.34160e8i 1.28711 + 0.468471i
\(388\) −1.97308e7 + 1.11899e8i −0.0171488 + 0.0972556i
\(389\) −2.38322e8 + 1.35159e9i −0.205277 + 1.16418i 0.691726 + 0.722160i \(0.256850\pi\)
−0.897003 + 0.442024i \(0.854261\pi\)
\(390\) −2.89630e7 − 1.05417e7i −0.0247240 − 0.00899879i
\(391\) 1.94051e9 − 1.62828e9i 1.64171 − 1.37756i
\(392\) −6.81376e8 + 5.71742e8i −0.571328 + 0.479401i
\(393\) 5.97454e6 − 1.03482e7i 0.00496513 − 0.00859986i
\(394\) −1.21608e9 + 4.42617e8i −1.00167 + 0.364579i
\(395\) 1.09272e8 + 6.19711e8i 0.0892109 + 0.505940i
\(396\) −1.92711e8 − 3.33785e8i −0.155945 − 0.270106i
\(397\) −3.92426e8 + 6.79702e8i −0.314768 + 0.545195i −0.979388 − 0.201987i \(-0.935260\pi\)
0.664620 + 0.747182i \(0.268594\pi\)
\(398\) 8.47585e6 + 3.08496e6i 0.00673895 + 0.00245278i
\(399\) 2.13685e7 + 3.70114e7i 0.0168411 + 0.0291696i
\(400\) 3.15910e8 + 2.65080e8i 0.246805 + 0.207094i
\(401\) −7.22934e8 −0.559878 −0.279939 − 0.960018i \(-0.590314\pi\)
−0.279939 + 0.960018i \(0.590314\pi\)
\(402\) −3.08754e7 − 2.59076e7i −0.0237040 − 0.0198900i
\(403\) −7.34500e8 + 2.67336e8i −0.559016 + 0.203465i
\(404\) −4.06123e6 + 2.30324e7i −0.00306424 + 0.0173782i
\(405\) 3.49691e8 + 1.98320e9i 0.261572 + 1.48345i
\(406\) −2.64363e9 −1.96047
\(407\) −6.21789e8 + 5.79030e8i −0.457154 + 0.425716i
\(408\) 2.77978e7 0.0202628
\(409\) 1.75607e8 + 9.95914e8i 0.126914 + 0.719764i 0.980153 + 0.198244i \(0.0635238\pi\)
−0.853239 + 0.521520i \(0.825365\pi\)
\(410\) −4.38259e8 + 2.48549e9i −0.314042 + 1.78102i
\(411\) −8.31023e7 + 3.02468e7i −0.0590428 + 0.0214898i
\(412\) 3.21310e8 + 2.69611e8i 0.226352 + 0.189931i
\(413\) 1.78049e9 1.24369
\(414\) 1.10684e9 + 9.28748e8i 0.766625 + 0.643275i
\(415\) −1.16967e9 − 2.02592e9i −0.803329 − 1.39141i
\(416\) 1.58277e8 + 5.76080e7i 0.107793 + 0.0392334i
\(417\) 4.54600e6 − 7.87391e6i 0.00307011 − 0.00531758i
\(418\) 1.66193e8 + 2.87855e8i 0.111300 + 0.192778i
\(419\) 1.32743e8 + 7.52824e8i 0.0881583 + 0.499971i 0.996630 + 0.0820248i \(0.0261387\pi\)
−0.908472 + 0.417946i \(0.862750\pi\)
\(420\) −7.21341e7 + 2.62547e7i −0.0475081 + 0.0172915i
\(421\) −4.95426e7 + 8.58103e7i −0.0323587 + 0.0560470i −0.881751 − 0.471715i \(-0.843635\pi\)
0.849393 + 0.527762i \(0.176969\pi\)
\(422\) −5.44858e8 + 4.57190e8i −0.352931 + 0.296144i
\(423\) 5.62113e8 − 4.71669e8i 0.361104 − 0.303002i
\(424\) −3.76797e8 − 1.37143e8i −0.240064 − 0.0873761i
\(425\) 5.35506e8 − 3.03701e9i 0.338379 − 1.91904i
\(426\) 2.81147e6 − 1.59446e7i 0.00176197 − 0.00999264i
\(427\) 2.97079e9 + 1.08128e9i 1.84661 + 0.672110i
\(428\) −6.06452e8 + 5.08874e8i −0.373890 + 0.313731i
\(429\) 1.92470e7 − 1.61501e7i 0.0117696 − 0.00987587i
\(430\) 1.20961e9 − 2.09511e9i 0.733680 − 1.27077i
\(431\) −8.73147e8 + 3.17799e8i −0.525311 + 0.191198i −0.591044 − 0.806640i \(-0.701284\pi\)
0.0657323 + 0.997837i \(0.479062\pi\)
\(432\) 5.51052e6 + 3.12517e7i 0.00328851 + 0.0186501i
\(433\) 3.04796e8 + 5.27922e8i 0.180427 + 0.312509i 0.942026 − 0.335540i \(-0.108919\pi\)
−0.761599 + 0.648049i \(0.775585\pi\)
\(434\) −9.73357e8 + 1.68590e9i −0.571555 + 0.989963i
\(435\) −1.45444e8 − 5.29374e7i −0.0847196 − 0.0308354i
\(436\) 1.59587e8 + 2.76412e8i 0.0922133 + 0.159718i
\(437\) −9.54534e8 − 8.00949e8i −0.547150 − 0.459113i
\(438\) 5.15879e7 0.0293352
\(439\) 7.79187e8 + 6.53815e8i 0.439558 + 0.368833i 0.835544 − 0.549424i \(-0.185153\pi\)
−0.395986 + 0.918256i \(0.629597\pi\)
\(440\) −5.61021e8 + 2.04195e8i −0.313975 + 0.114277i
\(441\) −6.58806e8 + 3.73627e9i −0.365782 + 2.07445i
\(442\) −2.18719e8 − 1.24042e9i −0.120478 − 0.683266i
\(443\) −1.25280e9 −0.684652 −0.342326 − 0.939581i \(-0.611215\pi\)
−0.342326 + 0.939581i \(0.611215\pi\)
\(444\) 3.21836e7 − 1.36350e7i 0.0174499 − 0.00739291i
\(445\) −4.37212e9 −2.35197
\(446\) −1.21216e8 − 6.87449e8i −0.0646974 − 0.366917i
\(447\) 8.65657e6 − 4.90939e7i 0.00458426 − 0.0259986i
\(448\) 3.94197e8 − 1.43476e8i 0.207129 − 0.0753887i
\(449\) 1.72482e9 + 1.44730e9i 0.899253 + 0.754563i 0.970044 − 0.242929i \(-0.0781081\pi\)
−0.0707915 + 0.997491i \(0.522552\pi\)
\(450\) 1.75899e9 0.909955
\(451\) −1.57603e9 − 1.32245e9i −0.808997 − 0.678829i
\(452\) 8.68945e7 + 1.50506e8i 0.0442596 + 0.0766599i
\(453\) 9.93869e7 + 3.61739e7i 0.0502326 + 0.0182832i
\(454\) −5.83632e8 + 1.01088e9i −0.292714 + 0.506996i
\(455\) 1.73912e9 + 3.01225e9i 0.865546 + 1.49917i
\(456\) −2.37442e6 − 1.34660e7i −0.00117268 − 0.00665062i
\(457\) 1.79259e9 − 6.52449e8i 0.878565 − 0.319772i 0.136935 − 0.990580i \(-0.456275\pi\)
0.741631 + 0.670809i \(0.234053\pi\)
\(458\) 8.90470e8 − 1.54234e9i 0.433102 − 0.750155i
\(459\) 1.81786e8 − 1.52537e8i 0.0877439 − 0.0736259i
\(460\) 1.71451e9 − 1.43865e9i 0.821275 − 0.689132i
\(461\) −1.10184e9 − 4.01037e8i −0.523800 − 0.190648i 0.0665677 − 0.997782i \(-0.478795\pi\)
−0.590368 + 0.807134i \(0.701017\pi\)
\(462\) 1.08661e7 − 6.16249e7i 0.00512658 − 0.0290743i
\(463\) 2.02207e8 − 1.14677e9i 0.0946809 − 0.536962i −0.900164 − 0.435552i \(-0.856553\pi\)
0.994845 − 0.101410i \(-0.0323355\pi\)
\(464\) 7.94821e8 + 2.89291e8i 0.369365 + 0.134438i
\(465\) −8.73104e7 + 7.32621e7i −0.0402699 + 0.0337905i
\(466\) −4.85434e6 + 4.07328e6i −0.00222218 + 0.00186463i
\(467\) −2.68835e8 + 4.65636e8i −0.122145 + 0.211562i −0.920613 − 0.390475i \(-0.872311\pi\)
0.798468 + 0.602037i \(0.205644\pi\)
\(468\) 6.75105e8 − 2.45718e8i 0.304446 − 0.110809i
\(469\) 7.89826e8 + 4.47932e9i 0.353530 + 2.00497i
\(470\) −5.68325e8 − 9.84368e8i −0.252496 − 0.437336i
\(471\) −556562. + 963994.i −0.000245437 + 0.000425110i
\(472\) −5.35312e8 − 1.94838e8i −0.234321 − 0.0852857i
\(473\) 9.86044e8 + 1.70788e9i 0.428433 + 0.742067i
\(474\) 1.61654e7 + 1.35644e7i 0.00697207 + 0.00585026i
\(475\) −1.51695e9 −0.649446
\(476\) −2.40307e9 − 2.01642e9i −1.02127 − 0.856950i
\(477\) −1.60717e9 + 5.84962e8i −0.678028 + 0.246782i
\(478\) 3.21464e8 − 1.82311e9i 0.134628 − 0.763513i
\(479\) −4.75291e8 − 2.69551e9i −0.197599 − 1.12064i −0.908668 − 0.417519i \(-0.862900\pi\)
0.711069 − 0.703122i \(-0.248211\pi\)
\(480\) 2.45605e7 0.0101366
\(481\) −8.61660e8 − 1.32884e9i −0.353044 − 0.544458i
\(482\) 4.03907e8 0.164292
\(483\) 4.07351e7 + 2.31020e8i 0.0164496 + 0.0932901i
\(484\) −1.32059e8 + 7.48946e8i −0.0529432 + 0.300256i
\(485\) 7.05459e8 − 2.56766e8i 0.280786 − 0.102198i
\(486\) 1.55570e8 + 1.30539e8i 0.0614751 + 0.0515837i
\(487\) −1.15168e9 −0.451835 −0.225917 − 0.974146i \(-0.572538\pi\)
−0.225917 + 0.974146i \(0.572538\pi\)
\(488\) −7.74859e8 − 6.50184e8i −0.301824 − 0.253260i
\(489\) 2.18139e7 + 3.77827e7i 0.00843629 + 0.0146121i
\(490\) 5.52243e9 + 2.01000e9i 2.12053 + 0.771809i
\(491\) 1.28475e9 − 2.22525e9i 0.489815 − 0.848384i −0.510116 − 0.860105i \(-0.670398\pi\)
0.999931 + 0.0117211i \(0.00373102\pi\)
\(492\) 4.23180e7 + 7.32969e7i 0.0160194 + 0.0277465i
\(493\) −1.09834e9 − 6.22902e9i −0.412833 − 2.34129i
\(494\) −5.82209e8 + 2.11907e8i −0.217287 + 0.0790861i
\(495\) −1.27326e9 + 2.20535e9i −0.471845 + 0.817260i
\(496\) 4.77132e8 − 4.00361e8i 0.175571 − 0.147322i
\(497\) −1.39965e9 + 1.17444e9i −0.511412 + 0.429126i
\(498\) −7.37177e7 − 2.68310e7i −0.0267466 − 0.00973497i
\(499\) −3.27145e8 + 1.85533e9i −0.117866 + 0.668451i 0.867425 + 0.497567i \(0.165773\pi\)
−0.985291 + 0.170883i \(0.945338\pi\)
\(500\) 1.06001e8 − 6.01164e8i 0.0379242 − 0.215079i
\(501\) −1.08791e8 − 3.95967e7i −0.0386510 − 0.0140678i
\(502\) −1.34382e9 + 1.12760e9i −0.474109 + 0.397825i
\(503\) 3.43037e9 − 2.87842e9i 1.20186 − 1.00848i 0.202282 − 0.979327i \(-0.435164\pi\)
0.999575 − 0.0291502i \(-0.00928011\pi\)
\(504\) 8.94647e8 − 1.54957e9i 0.311275 − 0.539145i
\(505\) 1.45206e8 − 5.28507e7i 0.0501724 − 0.0182613i
\(506\) 3.16816e8 + 1.79675e9i 0.108713 + 0.616541i
\(507\) −3.21953e7 − 5.57638e7i −0.0109714 − 0.0190031i
\(508\) −1.24866e9 + 2.16274e9i −0.422591 + 0.731948i
\(509\) 2.01387e9 + 7.32989e8i 0.676892 + 0.246369i 0.657513 − 0.753444i \(-0.271609\pi\)
0.0193797 + 0.999812i \(0.493831\pi\)
\(510\) −9.18316e7 − 1.59057e8i −0.0306547 − 0.0530955i
\(511\) −4.45968e9 − 3.74212e9i −1.47853 − 1.24064i
\(512\) −1.34218e8 −0.0441942
\(513\) −8.94207e7 − 7.50329e7i −0.0292434 − 0.0245381i
\(514\) 1.75938e9 − 6.40362e8i 0.571464 − 0.207996i
\(515\) 4.81229e8 − 2.72918e9i 0.155248 − 0.880456i
\(516\) −1.40877e7 − 7.98954e7i −0.00451405 − 0.0256005i
\(517\) 9.26567e8 0.294890
\(518\) −3.77128e9 − 1.15583e9i −1.19216 − 0.365376i
\(519\) 1.09657e8 0.0344311
\(520\) −1.93247e8 − 1.09596e9i −0.0602700 − 0.341808i
\(521\) 3.82043e8 − 2.16667e9i 0.118353 − 0.671214i −0.866682 − 0.498861i \(-0.833752\pi\)
0.985035 − 0.172353i \(-0.0551371\pi\)
\(522\) 3.39019e9 − 1.23393e9i 1.04322 − 0.379702i
\(523\) 4.08449e9 + 3.42730e9i 1.24848 + 1.04760i 0.996812 + 0.0797881i \(0.0254244\pi\)
0.251671 + 0.967813i \(0.419020\pi\)
\(524\) 4.31439e8 0.130996
\(525\) 2.18769e8 + 1.83569e8i 0.0659825 + 0.0553659i
\(526\) 2.13438e9 + 3.69686e9i 0.639473 + 1.10760i
\(527\) −4.37679e9 − 1.59302e9i −1.30262 − 0.474116i
\(528\) −1.00105e7 + 1.73388e7i −0.00295964 + 0.00512624i
\(529\) −1.71739e9 − 2.97461e9i −0.504400 − 0.873646i
\(530\) 4.60048e8 + 2.60906e9i 0.134226 + 0.761235i
\(531\) −2.28329e9 + 8.31051e8i −0.661806 + 0.240878i
\(532\) −7.71541e8 + 1.33635e9i −0.222161 + 0.384795i
\(533\) 2.93775e9 − 2.46506e9i 0.840368 − 0.705152i
\(534\) −1.12316e8 + 9.42441e7i −0.0319188 + 0.0267830i
\(535\) 4.91519e9 + 1.78898e9i 1.38772 + 0.505089i
\(536\) 2.52705e8 − 1.43316e9i 0.0708822 − 0.401993i
\(537\) −2.29015e7 + 1.29881e8i −0.00638196 + 0.0361939i
\(538\) −4.03757e9 − 1.46955e9i −1.11785 − 0.406863i
\(539\) −3.66985e9 + 3.07937e9i −1.00946 + 0.847035i
\(540\) 1.60616e8 − 1.34773e8i 0.0438945 − 0.0368318i
\(541\) 1.89522e9 − 3.28262e9i 0.514600 − 0.891314i −0.485256 − 0.874372i \(-0.661274\pi\)
0.999856 − 0.0169418i \(-0.00539298\pi\)
\(542\) 2.91367e9 − 1.06049e9i 0.786038 − 0.286094i
\(543\) 2.91291e7 + 1.65200e8i 0.00780779 + 0.0442802i
\(544\) 5.01840e8 + 8.69212e8i 0.133650 + 0.231489i
\(545\) 1.05441e9 − 1.82629e9i 0.279010 − 0.483260i
\(546\) 1.09607e8 + 3.98939e7i 0.0288181 + 0.0104889i
\(547\) 2.59996e9 + 4.50327e9i 0.679221 + 1.17645i 0.975216 + 0.221256i \(0.0710157\pi\)
−0.295994 + 0.955190i \(0.595651\pi\)
\(548\) −2.44605e9 − 2.05248e9i −0.634941 − 0.532779i
\(549\) −4.31443e9 −1.11281
\(550\) 1.70147e9 + 1.42770e9i 0.436069 + 0.365906i
\(551\) −2.92369e9 + 1.06414e9i −0.744561 + 0.270998i
\(552\) 1.30332e7 − 7.39151e7i 0.00329811 − 0.0187045i
\(553\) −4.13527e8 − 2.34523e9i −0.103984 − 0.589722i
\(554\) 2.14481e9 0.535926
\(555\) −1.84339e8 − 1.39108e8i −0.0457711 − 0.0345403i
\(556\) 3.28280e8 0.0809995
\(557\) −8.54853e8 − 4.84811e9i −0.209603 − 1.18872i −0.890030 − 0.455903i \(-0.849316\pi\)
0.680426 − 0.732817i \(-0.261795\pi\)
\(558\) 4.61328e8 − 2.61632e9i 0.112406 − 0.637487i
\(559\) −3.45431e9 + 1.25727e9i −0.836413 + 0.304429i
\(560\) −2.12321e9 − 1.78158e9i −0.510899 − 0.428695i
\(561\) 1.49717e8 0.0358016
\(562\) −2.66863e9 − 2.23924e9i −0.634177 − 0.532138i
\(563\) 2.22270e9 + 3.84983e9i 0.524930 + 0.909205i 0.999579 + 0.0290299i \(0.00924179\pi\)
−0.474649 + 0.880175i \(0.657425\pi\)
\(564\) −3.58184e7 − 1.30368e7i −0.00840678 − 0.00305982i
\(565\) 5.74121e8 − 9.94407e8i 0.133916 − 0.231950i
\(566\) 9.34269e8 + 1.61820e9i 0.216578 + 0.375124i
\(567\) −1.32337e9 − 7.50519e9i −0.304887 − 1.72910i
\(568\) 5.49329e8 − 1.99939e8i 0.125781 − 0.0457804i
\(569\) −2.64655e9 + 4.58397e9i −0.602265 + 1.04315i 0.390212 + 0.920725i \(0.372402\pi\)
−0.992477 + 0.122429i \(0.960932\pi\)
\(570\) −6.92075e7 + 5.80720e7i −0.0156528 + 0.0131342i
\(571\) −5.79573e9 + 4.86319e9i −1.30281 + 1.09319i −0.313159 + 0.949701i \(0.601387\pi\)
−0.989652 + 0.143488i \(0.954168\pi\)
\(572\) 8.52469e8 + 3.10273e8i 0.190455 + 0.0693200i
\(573\) 3.15791e7 − 1.79094e8i 0.00701226 − 0.0397685i
\(574\) 1.65854e9 − 9.40607e9i 0.366046 − 2.07595i
\(575\) −7.82440e9 − 2.84785e9i −1.71638 − 0.624711i
\(576\) −4.38549e8 + 3.67986e8i −0.0956180 + 0.0802330i
\(577\) −1.88163e9 + 1.57888e9i −0.407774 + 0.342163i −0.823489 − 0.567332i \(-0.807976\pi\)
0.415715 + 0.909495i \(0.363531\pi\)
\(578\) 2.11140e9 − 3.65705e9i 0.454803 − 0.787742i
\(579\) −2.48346e8 + 9.03905e7i −0.0531718 + 0.0193530i
\(580\) −9.70432e8 − 5.50359e9i −0.206522 − 1.17125i
\(581\) 4.42647e9 + 7.66687e9i 0.936356 + 1.62182i
\(582\) 1.25878e7 − 2.18027e7i 0.00264679 − 0.00458437i
\(583\) −2.02941e9 − 7.38643e8i −0.424159 − 0.154381i
\(584\) 9.31328e8 + 1.61311e9i 0.193490 + 0.335134i
\(585\) −3.63623e9 − 3.05116e9i −0.750941 − 0.630114i
\(586\) 2.62943e9 0.539783
\(587\) 1.83239e8 + 1.53755e8i 0.0373924 + 0.0313760i 0.661292 − 0.750128i \(-0.270008\pi\)
−0.623900 + 0.781504i \(0.714453\pi\)
\(588\) 1.85193e8 − 6.74047e7i 0.0375668 − 0.0136732i
\(589\) −3.97848e8 + 2.25631e9i −0.0802257 + 0.454982i
\(590\) 6.53587e8 + 3.70667e9i 0.131015 + 0.743023i
\(591\) 2.86736e8 0.0571381
\(592\) 1.00737e9 + 7.60195e8i 0.199555 + 0.150591i
\(593\) 3.35375e9 0.660449 0.330225 − 0.943902i \(-0.392876\pi\)
0.330225 + 0.943902i \(0.392876\pi\)
\(594\) 2.96793e7 + 1.68320e8i 0.00581034 + 0.0329521i
\(595\) −3.59910e9 + 2.04115e10i −0.700463 + 3.97252i
\(596\) 1.69140e9 − 6.15618e8i 0.327253 − 0.119110i
\(597\) −1.53094e6 − 1.28461e6i −0.000294474 − 0.000247093i
\(598\) −3.40085e9 −0.650329
\(599\) 3.90887e9 + 3.27993e9i 0.743118 + 0.623550i 0.933673 − 0.358127i \(-0.116584\pi\)
−0.190555 + 0.981676i \(0.561029\pi\)
\(600\) −4.56862e7 − 7.91308e7i −0.00863487 − 0.0149560i
\(601\) 1.18864e8 + 4.32631e7i 0.0223353 + 0.00812937i 0.353164 − 0.935562i \(-0.385106\pi\)
−0.330828 + 0.943691i \(0.607328\pi\)
\(602\) −4.57765e9 + 7.92872e9i −0.855174 + 1.48121i
\(603\) −3.10362e9 − 5.37562e9i −0.576444 − 0.998431i
\(604\) 6.63129e8 + 3.76079e9i 0.122453 + 0.694464i
\(605\) 4.72168e9 − 1.71855e9i 0.866867 − 0.315514i
\(606\) 2.59097e6 − 4.48770e6i 0.000472943 − 0.000819161i
\(607\) 2.40181e9 − 2.01536e9i 0.435892 − 0.365757i −0.398278 − 0.917265i \(-0.630392\pi\)
0.834169 + 0.551508i \(0.185947\pi\)
\(608\) 3.78204e8 − 3.17350e8i 0.0682438 − 0.0572633i
\(609\) 5.50418e8 + 2.00336e8i 0.0987488 + 0.0359416i
\(610\) −1.16051e9 + 6.58160e9i −0.207012 + 1.17402i
\(611\) −2.99914e8 + 1.70090e9i −0.0531927 + 0.301671i
\(612\) 4.02286e9 + 1.46420e9i 0.709423 + 0.258209i
\(613\) 2.24814e9 − 1.88642e9i 0.394196 − 0.330770i −0.424049 − 0.905639i \(-0.639392\pi\)
0.818245 + 0.574869i \(0.194947\pi\)
\(614\) −6.65567e8 + 5.58477e8i −0.116039 + 0.0973679i
\(615\) 2.79600e8 − 4.84281e8i 0.0484701 − 0.0839527i
\(616\) 2.12312e9 − 7.72753e8i 0.365967 − 0.133201i
\(617\) 7.33278e8 + 4.15863e9i 0.125681 + 0.712774i 0.980901 + 0.194508i \(0.0623111\pi\)
−0.855220 + 0.518266i \(0.826578\pi\)
\(618\) −4.64671e7 − 8.04834e7i −0.00791928 − 0.0137166i
\(619\) 1.90253e9 − 3.29528e9i 0.322415 − 0.558439i −0.658571 − 0.752519i \(-0.728839\pi\)
0.980986 + 0.194080i \(0.0621721\pi\)
\(620\) −3.86707e9 − 1.40750e9i −0.651645 − 0.237179i
\(621\) −3.20367e8 − 5.54892e8i −0.0536819 − 0.0929797i
\(622\) 2.43533e9 + 2.04348e9i 0.405780 + 0.340490i
\(623\) 1.65458e10 2.74145
\(624\) −2.85885e7 − 2.39886e7i −0.00471026 − 0.00395238i
\(625\) 3.60138e9 − 1.31079e9i 0.590049 − 0.214760i
\(626\) −2.39666e7 + 1.35921e8i −0.00390477 + 0.0221451i
\(627\) −1.27885e7 − 7.25271e7i −0.00207197 − 0.0117507i
\(628\) −4.01909e7 −0.00647544
\(629\) 1.15656e9 − 9.36624e9i 0.185307 − 1.50068i
\(630\) −1.18221e10 −1.88366
\(631\) 6.51554e8 + 3.69515e9i 0.103240 + 0.585503i 0.991909 + 0.126953i \(0.0405198\pi\)
−0.888669 + 0.458550i \(0.848369\pi\)
\(632\) −1.32308e8 + 7.50356e8i −0.0208486 + 0.118238i
\(633\) 1.48088e8 − 5.38997e7i 0.0232064 − 0.00844643i
\(634\) 1.39221e9 + 1.16820e9i 0.216966 + 0.182056i
\(635\) 1.65000e10 2.55727
\(636\) 6.80583e7 + 5.71077e7i 0.0104901 + 0.00880227i
\(637\) −4.46492e9 − 7.73347e9i −0.684425 − 1.18546i
\(638\) 4.28086e9 + 1.55810e9i 0.652617 + 0.237533i
\(639\) 1.24673e9 − 2.15939e9i 0.189025 − 0.327400i
\(640\) 4.43396e8 + 7.67984e8i 0.0668593 + 0.115804i
\(641\) 1.09518e9 + 6.21108e9i 0.164242 + 0.931460i 0.949843 + 0.312727i \(0.101243\pi\)
−0.785601 + 0.618733i \(0.787646\pi\)
\(642\) 1.64829e8 − 5.99929e7i 0.0245845 − 0.00894803i
\(643\) −3.43978e9 + 5.95787e9i −0.510260 + 0.883797i 0.489669 + 0.871908i \(0.337118\pi\)
−0.999929 + 0.0118886i \(0.996216\pi\)
\(644\) −6.48839e9 + 5.44441e9i −0.957275 + 0.803249i
\(645\) −4.10616e8 + 3.44548e8i −0.0602528 + 0.0505581i
\(646\) −3.46931e9 − 1.26272e9i −0.506324 − 0.184287i
\(647\) −1.73843e9 + 9.85915e9i −0.252344 + 1.43112i 0.550455 + 0.834865i \(0.314454\pi\)
−0.802799 + 0.596250i \(0.796657\pi\)
\(648\) −4.23412e8 + 2.40129e9i −0.0611294 + 0.346682i
\(649\) −2.88316e9 − 1.04938e9i −0.414012 − 0.150688i
\(650\) −3.17157e9 + 2.66126e9i −0.452979 + 0.380094i
\(651\) 3.30417e8 − 2.77252e8i 0.0469384 − 0.0393860i
\(652\) −7.87620e8 + 1.36420e9i −0.111288 + 0.192757i
\(653\) 1.09737e10 − 3.99409e9i 1.54225 − 0.561334i 0.575668 − 0.817683i \(-0.304742\pi\)
0.966584 + 0.256349i \(0.0825198\pi\)
\(654\) −1.22801e7 − 6.96440e7i −0.00171664 − 0.00973557i
\(655\) −1.42528e9 − 2.46866e9i −0.198178 − 0.343255i
\(656\) −1.52795e9 + 2.64649e9i −0.211323 + 0.366022i
\(657\) 7.46574e9 + 2.71731e9i 1.02706 + 0.373818i
\(658\) 2.15076e9 + 3.72523e9i 0.294308 + 0.509756i
\(659\) −2.11063e9 − 1.77103e9i −0.287285 − 0.241061i 0.487744 − 0.872987i \(-0.337820\pi\)
−0.775029 + 0.631926i \(0.782265\pi\)
\(660\) 1.32281e8 0.0179100
\(661\) −7.41745e9 − 6.22398e9i −0.998963 − 0.838230i −0.0121229 − 0.999927i \(-0.503859\pi\)
−0.986841 + 0.161697i \(0.948303\pi\)
\(662\) 7.63357e9 − 2.77839e9i 1.02265 − 0.372212i
\(663\) −4.84610e7 + 2.74836e8i −0.00645795 + 0.0366249i
\(664\) −4.91859e8 − 2.78947e9i −0.0652007 − 0.369771i
\(665\) 1.01953e10 1.34439
\(666\) 5.37577e9 − 2.78028e8i 0.705148 − 0.0364694i
\(667\) −1.70781e10 −2.22843
\(668\) −7.25875e8 − 4.11664e9i −0.0942202 − 0.534350i
\(669\) −2.68574e7 + 1.52316e8i −0.00346795 + 0.0196677i
\(670\) −9.03527e9 + 3.28857e9i −1.16059 + 0.422421i
\(671\) −4.17334e9 − 3.50185e9i −0.533280 − 0.447475i
\(672\) −9.29465e7 −0.0118152
\(673\) −5.55250e9 − 4.65910e9i −0.702160 − 0.589182i 0.220227 − 0.975449i \(-0.429320\pi\)
−0.922387 + 0.386266i \(0.873765\pi\)
\(674\) −1.81723e9 − 3.14753e9i −0.228612 − 0.395968i
\(675\) −7.32989e8 − 2.66786e8i −0.0917348 − 0.0333888i
\(676\) 1.16245e9 − 2.01343e9i 0.144731 − 0.250682i
\(677\) −1.33697e9 − 2.31570e9i −0.165600 − 0.286828i 0.771268 − 0.636511i \(-0.219623\pi\)
−0.936868 + 0.349682i \(0.886289\pi\)
\(678\) −6.68649e6 − 3.79210e7i −0.000823937 − 0.00467278i
\(679\) −2.66973e9 + 9.71703e8i −0.327283 + 0.119121i
\(680\) 3.31571e9 − 5.74298e9i 0.404385 − 0.700416i
\(681\) 1.98120e8 − 1.66243e8i 0.0240389 − 0.0201710i
\(682\) 2.56981e9 − 2.15632e9i 0.310209 − 0.260297i
\(683\) −2.80945e9 − 1.02256e9i −0.337403 − 0.122805i 0.167762 − 0.985828i \(-0.446346\pi\)
−0.505165 + 0.863023i \(0.668568\pi\)
\(684\) 3.65676e8 − 2.07385e9i 0.0436918 − 0.247789i
\(685\) −3.66348e9 + 2.07766e10i −0.435488 + 2.46978i
\(686\) −1.09919e10 − 4.00071e9i −1.29998 − 0.473154i
\(687\) −3.02280e8 + 2.53643e8i −0.0355681 + 0.0298452i
\(688\) 2.24393e9 − 1.88288e9i 0.262693 − 0.220426i
\(689\) 2.01281e9 − 3.48629e9i 0.234442 − 0.406065i
\(690\) −4.65992e8 + 1.69607e8i −0.0540016 + 0.0196550i
\(691\) −1.00897e9 − 5.72214e9i −0.116333 − 0.659759i −0.986081 − 0.166263i \(-0.946830\pi\)
0.869748 − 0.493496i \(-0.164281\pi\)
\(692\) 1.97966e9 + 3.42887e9i 0.227101 + 0.393351i
\(693\) 4.81852e9 − 8.34592e9i 0.549980 − 0.952594i
\(694\) 6.17228e9 + 2.24653e9i 0.700951 + 0.255125i
\(695\) −1.08449e9 − 1.87839e9i −0.122540 − 0.212246i
\(696\) −1.43563e8 − 1.20464e8i −0.0161403 − 0.0135433i
\(697\) 2.28520e10 2.55629
\(698\) −5.75645e9 − 4.83024e9i −0.640709 − 0.537619i
\(699\) 1.31937e6 − 480213.i 0.000146116 − 5.31819e-5i
\(700\) −1.79055e9 + 1.01547e10i −0.197308 + 1.11899i
\(701\) −1.16979e8 − 6.63422e8i −0.0128261 − 0.0727406i 0.977723 − 0.209900i \(-0.0673138\pi\)
−0.990549 + 0.137159i \(0.956203\pi\)
\(702\) −3.18591e8 −0.0347579
\(703\) −4.63605e9 + 2.39771e8i −0.503273 + 0.0260287i
\(704\) −7.22889e8 −0.0780849
\(705\) 4.37323e7 + 2.48018e8i 0.00470046 + 0.0266577i
\(706\) −1.24130e9 + 7.03976e9i −0.132758 + 0.752907i
\(707\) −5.49516e8 + 2.00008e8i −0.0584807 + 0.0212852i
\(708\) 9.66899e7 + 8.11325e7i 0.0102392 + 0.00859168i
\(709\) 1.72117e10 1.81368 0.906841 − 0.421474i \(-0.138487\pi\)
0.906841 + 0.421474i \(0.138487\pi\)
\(710\) −2.95878e9 − 2.48271e9i −0.310247 − 0.260328i
\(711\) 1.62495e9 + 2.81450e9i 0.169550 + 0.293669i
\(712\) −4.97458e9 − 1.81060e9i −0.516507 − 0.187993i
\(713\) −6.28797e9 + 1.08911e10i −0.649677 + 1.12527i
\(714\) 3.47527e8 + 6.01934e8i 0.0357309 + 0.0618878i
\(715\) −1.04082e9 − 5.90277e9i −0.106489 − 0.603927i
\(716\) −4.47470e9 + 1.62866e9i −0.455584 + 0.165819i
\(717\) −2.05087e8 + 3.55221e8i −0.0207788 + 0.0359900i
\(718\) 8.15312e9 − 6.84128e9i 0.822031 − 0.689766i
\(719\) 1.27004e10 − 1.06569e10i 1.27428 − 1.06925i 0.280277 − 0.959919i \(-0.409574\pi\)
0.994005 − 0.109330i \(-0.0348707\pi\)
\(720\) 3.55436e9 + 1.29368e9i 0.354893 + 0.129171i
\(721\) −1.82116e9 + 1.03283e10i −0.180956 + 1.02625i
\(722\) 9.26396e8 − 5.25385e9i 0.0916044 − 0.519514i
\(723\) −8.40955e7 − 3.06083e7i −0.00827539 − 0.00301200i
\(724\) −4.63976e9 + 3.89322e9i −0.454371 + 0.381263i
\(725\) −1.59267e10 + 1.33641e10i −1.55219 + 1.30244i
\(726\) 8.42509e7 − 1.45927e8i 0.00817140 − 0.0141533i
\(727\) −3.97987e9 + 1.44855e9i −0.384147 + 0.139818i −0.526873 − 0.849944i \(-0.676636\pi\)
0.142725 + 0.989762i \(0.454413\pi\)
\(728\) 7.31322e8 + 4.14753e9i 0.0702504 + 0.398410i
\(729\) 5.18515e9 + 8.98094e9i 0.495695 + 0.858569i
\(730\) 6.15338e9 − 1.06580e10i 0.585442 − 1.01402i
\(731\) −2.05838e10 − 7.49190e9i −1.94901 − 0.709383i
\(732\) 1.12058e8 + 1.94091e8i 0.0105598 + 0.0182901i
\(733\) 2.60178e9 + 2.18315e9i 0.244010 + 0.204748i 0.756588 − 0.653892i \(-0.226865\pi\)
−0.512578 + 0.858641i \(0.671309\pi\)
\(734\) −1.22268e10 −1.14124
\(735\) −9.97480e8 − 8.36985e8i −0.0926613 − 0.0777521i
\(736\) 2.54655e9 − 9.26867e8i 0.235439 − 0.0856929i
\(737\) 1.36105e9 − 7.71892e9i 0.125239 − 0.710265i
\(738\) 2.26341e9 + 1.28365e10i 0.207284 + 1.17557i
\(739\) 1.80722e10 1.64724 0.823619 − 0.567144i \(-0.191952\pi\)
0.823619 + 0.567144i \(0.191952\pi\)
\(740\) 1.02187e9 − 8.27545e9i 0.0927010 − 0.750724i
\(741\) 1.37277e8 0.0123947
\(742\) −1.74100e9 − 9.87371e9i −0.156454 − 0.887292i
\(743\) 1.03502e9 − 5.86991e9i 0.0925740 − 0.525013i −0.902890 − 0.429872i \(-0.858559\pi\)
0.995464 − 0.0951412i \(-0.0303303\pi\)
\(744\) −1.29681e8 + 4.72000e7i −0.0115444 + 0.00420181i
\(745\) −9.11015e9 − 7.64432e9i −0.807195 − 0.677317i
\(746\) −4.99495e9 −0.440499
\(747\) −9.25505e9 − 7.76591e9i −0.812375 − 0.681663i
\(748\) 2.70288e9 + 4.68152e9i 0.236141 + 0.409008i
\(749\) −1.86010e10 − 6.77020e9i −1.61752 − 0.588729i
\(750\) −6.76266e7 + 1.17133e8i −0.00585333 + 0.0101383i
\(751\) −2.25280e9 − 3.90196e9i −0.194081 − 0.336157i 0.752518 − 0.658571i \(-0.228839\pi\)
−0.946599 + 0.322414i \(0.895506\pi\)
\(752\) −2.38988e8 − 1.35537e9i −0.0204933 − 0.116224i
\(753\) 3.65241e8 − 1.32937e8i 0.0311743 − 0.0113465i
\(754\) −4.24585e9 + 7.35403e9i −0.360716 + 0.624778i
\(755\) 1.93283e10 − 1.62184e10i 1.63448 − 1.37149i
\(756\) −6.07832e8 + 5.10032e8i −0.0511632 + 0.0429310i
\(757\) −1.46415e10 − 5.32907e9i −1.22673 − 0.446495i −0.354256 − 0.935149i \(-0.615266\pi\)