Properties

Label 29.9.f.a.2.16
Level $29$
Weight $9$
Character 29.2
Analytic conductor $11.814$
Analytic rank $0$
Dimension $228$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 29.f (of order \(28\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.8139796918\)
Analytic rank: \(0\)
Dimension: \(228\)
Relative dimension: \(19\) over \(\Q(\zeta_{28})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label 2.16
Character \(\chi\) \(=\) 29.2
Dual form 29.9.f.a.15.16

$q$-expansion

\(f(q)\) \(=\) \(q+(19.6004 + 2.20843i) q^{2} +(-83.4552 - 52.4384i) q^{3} +(129.715 + 29.6067i) q^{4} +(14.4052 - 11.4877i) q^{5} +(-1519.95 - 1212.12i) q^{6} +(772.012 + 3382.40i) q^{7} +(-2289.00 - 800.955i) q^{8} +(1368.27 + 2841.25i) q^{9} +O(q^{10})\) \(q+(19.6004 + 2.20843i) q^{2} +(-83.4552 - 52.4384i) q^{3} +(129.715 + 29.6067i) q^{4} +(14.4052 - 11.4877i) q^{5} +(-1519.95 - 1212.12i) q^{6} +(772.012 + 3382.40i) q^{7} +(-2289.00 - 800.955i) q^{8} +(1368.27 + 2841.25i) q^{9} +(307.716 - 193.351i) q^{10} +(-19598.3 + 6857.75i) q^{11} +(-9272.90 - 9272.90i) q^{12} +(-21261.3 + 44149.6i) q^{13} +(7661.90 + 68001.3i) q^{14} +(-1804.58 + 203.328i) q^{15} +(-73784.4 - 35532.7i) q^{16} +(58343.9 - 58343.9i) q^{17} +(20544.0 + 58711.2i) q^{18} +(-14594.5 - 23227.1i) q^{19} +(2208.69 - 1063.65i) q^{20} +(112939. - 322762. i) q^{21} +(-399279. + 91132.9i) q^{22} +(228462. - 286483. i) q^{23} +(149028. + 186875. i) q^{24} +(-86846.7 + 380500. i) q^{25} +(-514231. + 818394. i) q^{26} +(-37602.9 + 333735. i) q^{27} +461607. i q^{28} +(-59396.6 - 704783. i) q^{29} -35819.5 q^{30} +(-1.06683e6 - 120203. i) q^{31} +(-842064. - 529104. i) q^{32} +(1.99519e6 + 455390. i) q^{33} +(1.27241e6 - 1.01471e6i) q^{34} +(49977.1 + 39855.4i) q^{35} +(93366.2 + 409064. i) q^{36} +(-652675. - 228381. i) q^{37} +(-234763. - 487490. i) q^{38} +(4.08950e6 - 2.56960e6i) q^{39} +(-42174.6 + 14757.5i) q^{40} +(826924. + 826924. i) q^{41} +(2.92645e6 - 6.07684e6i) q^{42} +(88820.7 + 788306. i) q^{43} +(-2.74524e6 + 309315. i) q^{44} +(52349.7 + 25210.3i) q^{45} +(5.11062e6 - 5.11062e6i) q^{46} +(-1.58392e6 - 4.52658e6i) q^{47} +(4.29441e6 + 6.83452e6i) q^{48} +(-5.65075e6 + 2.72126e6i) q^{49} +(-2.54254e6 + 7.26615e6i) q^{50} +(-7.92856e6 + 1.80964e6i) q^{51} +(-4.06505e6 + 5.09741e6i) q^{52} +(6.31622e6 + 7.92028e6i) q^{53} +(-1.47406e6 + 6.45828e6i) q^{54} +(-203537. + 323928. i) q^{55} +(942021. - 8.36067e6i) q^{56} +2.70373e6i q^{57} +(392269. - 1.39452e7i) q^{58} -1.26885e7 q^{59} +(-240102. - 27053.0i) q^{60} +(-5.41484e6 - 3.40237e6i) q^{61} +(-2.06449e7 - 4.71206e6i) q^{62} +(-8.55393e6 + 6.82153e6i) q^{63} +(1.05482e6 + 841189. i) q^{64} +(200906. + 880227. i) q^{65} +(3.81008e7 + 1.33320e7i) q^{66} +(8.93817e6 + 1.85603e7i) q^{67} +(9.29548e6 - 5.84074e6i) q^{68} +(-3.40891e7 + 1.19283e7i) q^{69} +(891552. + 891552. i) q^{70} +(-7.98729e6 + 1.65858e7i) q^{71} +(-856263. - 7.59954e6i) q^{72} +(1.56965e7 - 1.76857e6i) q^{73} +(-1.22883e7 - 5.91774e6i) q^{74} +(2.72006e7 - 2.72006e7i) q^{75} +(-1.20546e6 - 3.44501e6i) q^{76} +(-3.83258e7 - 6.09952e7i) q^{77} +(8.58305e7 - 4.13338e7i) q^{78} +(-2.06555e7 + 5.90300e7i) q^{79} +(-1.47107e6 + 335761. i) q^{80} +(3.35389e7 - 4.20565e7i) q^{81} +(1.43818e7 + 1.80342e7i) q^{82} +(-3.24788e6 + 1.42299e7i) q^{83} +(2.42059e7 - 3.85235e7i) q^{84} +(170214. - 1.51069e6i) q^{85} +1.56472e7i q^{86} +(-3.20007e7 + 6.19324e7i) q^{87} +5.03533e7 q^{88} +(-1.95390e7 - 2.20152e6i) q^{89} +(970399. + 609742. i) q^{90} +(-1.65746e8 - 3.78304e7i) q^{91} +(3.81169e7 - 3.03972e7i) q^{92} +(8.27295e7 + 6.59746e7i) q^{93} +(-2.10488e7 - 9.22207e7i) q^{94} +(-477063. - 166932. i) q^{95} +(4.25293e7 + 8.83129e7i) q^{96} +(1.31178e8 - 8.24246e7i) q^{97} +(-1.16766e8 + 4.08584e7i) q^{98} +(-4.63005e7 - 4.63005e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 228q - 6q^{2} - 12q^{3} - 14q^{4} - 14q^{5} - 14q^{6} - 10q^{7} + 3664q^{8} - 14q^{9} + O(q^{10}) \) \( 228q - 6q^{2} - 12q^{3} - 14q^{4} - 14q^{5} - 14q^{6} - 10q^{7} + 3664q^{8} - 14q^{9} - 15884q^{10} + 8376q^{11} - 5036q^{12} - 14q^{13} - 12742q^{14} + 35516q^{15} + 245898q^{16} - 76248q^{17} + 465008q^{18} + 164474q^{19} - 907274q^{20} - 628270q^{21} + 1214962q^{22} + 173408q^{23} + 1858618q^{24} + 43976q^{25} - 4604204q^{26} - 1727586q^{27} + 1079922q^{29} + 8909208q^{30} + 3657848q^{31} + 1160364q^{32} - 4279184q^{33} - 8655374q^{34} - 8269058q^{35} - 3366854q^{36} - 5622890q^{37} + 15536626q^{38} + 16110008q^{39} - 23544696q^{40} - 9561672q^{41} - 14q^{42} + 5181008q^{43} + 51041750q^{44} - 35245194q^{45} - 43159224q^{46} - 12806808q^{47} + 83954488q^{48} + 10429400q^{49} + 80809398q^{50} + 18760882q^{51} - 93050550q^{52} - 30960322q^{53} - 106220916q^{54} - 126174004q^{55} - 40136268q^{56} + 159368354q^{58} + 11188020q^{59} + 255893612q^{60} + 139657128q^{61} + 102501616q^{62} + 9797746q^{63} - 135941792q^{64} - 14207858q^{65} - 447597656q^{66} - 148930894q^{67} - 167094904q^{68} + 66986722q^{69} + 586255934q^{70} - 15272096q^{71} + 41230600q^{72} - 219415072q^{73} - 347464696q^{74} + 391507416q^{75} + 271512490q^{76} + 240416780q^{77} + 141747906q^{78} + 112667220q^{79} - 375642638q^{80} - 358099268q^{81} - 262154910q^{82} - 109463350q^{83} - 694921012q^{84} - 356627386q^{85} + 199703522q^{87} + 251202768q^{88} + 839849154q^{89} + 675826020q^{90} + 533256766q^{91} + 742339570q^{92} + 78998570q^{93} - 209116610q^{94} - 633414122q^{95} - 431412576q^{96} - 402046736q^{97} - 2192087384q^{98} - 1966368188q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{28}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 19.6004 + 2.20843i 1.22502 + 0.138027i 0.700677 0.713479i \(-0.252881\pi\)
0.524346 + 0.851506i \(0.324310\pi\)
\(3\) −83.4552 52.4384i −1.03031 0.647387i −0.0929226 0.995673i \(-0.529621\pi\)
−0.937388 + 0.348286i \(0.886764\pi\)
\(4\) 129.715 + 29.6067i 0.506701 + 0.115651i
\(5\) 14.4052 11.4877i 0.0230483 0.0183804i −0.611898 0.790937i \(-0.709594\pi\)
0.634946 + 0.772556i \(0.281022\pi\)
\(6\) −1519.95 1212.12i −1.17280 0.935275i
\(7\) 772.012 + 3382.40i 0.321538 + 1.40875i 0.834817 + 0.550527i \(0.185573\pi\)
−0.513280 + 0.858221i \(0.671570\pi\)
\(8\) −2289.00 800.955i −0.558838 0.195546i
\(9\) 1368.27 + 2841.25i 0.208546 + 0.433051i
\(10\) 307.716 193.351i 0.0307716 0.0193351i
\(11\) −19598.3 + 6857.75i −1.33859 + 0.468394i −0.902183 0.431354i \(-0.858036\pi\)
−0.436410 + 0.899748i \(0.643750\pi\)
\(12\) −9272.90 9272.90i −0.447188 0.447188i
\(13\) −21261.3 + 44149.6i −0.744418 + 1.54580i 0.0907927 + 0.995870i \(0.471060\pi\)
−0.835211 + 0.549930i \(0.814654\pi\)
\(14\) 7661.90 + 68001.3i 0.199446 + 1.77013i
\(15\) −1804.58 + 203.328i −0.0356461 + 0.00401635i
\(16\) −73784.4 35532.7i −1.12586 0.542186i
\(17\) 58343.9 58343.9i 0.698554 0.698554i −0.265544 0.964099i \(-0.585552\pi\)
0.964099 + 0.265544i \(0.0855517\pi\)
\(18\) 20544.0 + 58711.2i 0.195701 + 0.559283i
\(19\) −14594.5 23227.1i −0.111989 0.178230i 0.786027 0.618192i \(-0.212135\pi\)
−0.898016 + 0.439962i \(0.854992\pi\)
\(20\) 2208.69 1063.65i 0.0138043 0.00664780i
\(21\) 112939. 322762.i 0.580722 1.65961i
\(22\) −399279. + 91132.9i −1.70446 + 0.389031i
\(23\) 228462. 286483.i 0.816401 1.02373i −0.182776 0.983155i \(-0.558508\pi\)
0.999176 0.0405794i \(-0.0129204\pi\)
\(24\) 149028. + 186875.i 0.449183 + 0.563257i
\(25\) −86846.7 + 380500.i −0.222328 + 0.974081i
\(26\) −514231. + 818394.i −1.12529 + 1.79089i
\(27\) −37602.9 + 333735.i −0.0707565 + 0.627981i
\(28\) 461607.i 0.751000i
\(29\) −59396.6 704783.i −0.0839788 0.996468i
\(30\) −35819.5 −0.0442217
\(31\) −1.06683e6 120203.i −1.15518 0.130158i −0.486482 0.873691i \(-0.661720\pi\)
−0.668699 + 0.743533i \(0.733149\pi\)
\(32\) −842064. 529104.i −0.803055 0.504593i
\(33\) 1.99519e6 + 455390.i 1.68240 + 0.383997i
\(34\) 1.27241e6 1.01471e6i 0.952164 0.759325i
\(35\) 49977.1 + 39855.4i 0.0333042 + 0.0265592i
\(36\) 93366.2 + 409064.i 0.0555878 + 0.243546i
\(37\) −652675. 228381.i −0.348249 0.121858i 0.150486 0.988612i \(-0.451916\pi\)
−0.498735 + 0.866755i \(0.666202\pi\)
\(38\) −234763. 487490.i −0.112589 0.233793i
\(39\) 4.08950e6 2.56960e6i 1.76771 1.11073i
\(40\) −42174.6 + 14757.5i −0.0164744 + 0.00576466i
\(41\) 826924. + 826924.i 0.292638 + 0.292638i 0.838121 0.545484i \(-0.183654\pi\)
−0.545484 + 0.838121i \(0.683654\pi\)
\(42\) 2.92645e6 6.07684e6i 0.940468 1.95290i
\(43\) 88820.7 + 788306.i 0.0259801 + 0.230580i 0.999992 + 0.00408141i \(0.00129916\pi\)
−0.974012 + 0.226498i \(0.927272\pi\)
\(44\) −2.74524e6 + 309315.i −0.732437 + 0.0825258i
\(45\) 52349.7 + 25210.3i 0.0127663 + 0.00614792i
\(46\) 5.11062e6 5.11062e6i 1.14141 1.14141i
\(47\) −1.58392e6 4.52658e6i −0.324595 0.927639i −0.984360 0.176167i \(-0.943630\pi\)
0.659765 0.751472i \(-0.270656\pi\)
\(48\) 4.29441e6 + 6.83452e6i 0.808982 + 1.28749i
\(49\) −5.65075e6 + 2.72126e6i −0.980216 + 0.472047i
\(50\) −2.54254e6 + 7.26615e6i −0.406806 + 1.16258i
\(51\) −7.92856e6 + 1.80964e6i −1.17196 + 0.267493i
\(52\) −4.06505e6 + 5.09741e6i −0.555971 + 0.697166i
\(53\) 6.31622e6 + 7.92028e6i 0.800485 + 1.00378i 0.999716 + 0.0238244i \(0.00758426\pi\)
−0.199231 + 0.979953i \(0.563844\pi\)
\(54\) −1.47406e6 + 6.45828e6i −0.173357 + 0.759525i
\(55\) −203537. + 323928.i −0.0222430 + 0.0353995i
\(56\) 942021. 8.36067e6i 0.0957874 0.850137i
\(57\) 2.70373e6i 0.256132i
\(58\) 392269. 1.39452e7i 0.0346634 1.23229i
\(59\) −1.26885e7 −1.04713 −0.523566 0.851985i \(-0.675399\pi\)
−0.523566 + 0.851985i \(0.675399\pi\)
\(60\) −240102. 27053.0i −0.0185264 0.00208743i
\(61\) −5.41484e6 3.40237e6i −0.391080 0.245732i 0.322110 0.946702i \(-0.395608\pi\)
−0.713191 + 0.700970i \(0.752751\pi\)
\(62\) −2.06449e7 4.71206e6i −1.39716 0.318892i
\(63\) −8.55393e6 + 6.82153e6i −0.543005 + 0.433032i
\(64\) 1.05482e6 + 841189.i 0.0628721 + 0.0501388i
\(65\) 200906. + 880227.i 0.0112548 + 0.0493107i
\(66\) 3.81008e7 + 1.33320e7i 2.00797 + 0.702621i
\(67\) 8.93817e6 + 1.85603e7i 0.443557 + 0.921055i 0.996155 + 0.0876073i \(0.0279221\pi\)
−0.552598 + 0.833448i \(0.686364\pi\)
\(68\) 9.29548e6 5.84074e6i 0.434747 0.273169i
\(69\) −3.40891e7 + 1.19283e7i −1.50390 + 0.526237i
\(70\) 891552. + 891552.i 0.0371325 + 0.0371325i
\(71\) −7.98729e6 + 1.65858e7i −0.314316 + 0.652683i −0.996947 0.0780795i \(-0.975121\pi\)
0.682631 + 0.730763i \(0.260835\pi\)
\(72\) −856263. 7.59954e6i −0.0318623 0.282786i
\(73\) 1.56965e7 1.76857e6i 0.552729 0.0622776i 0.168817 0.985647i \(-0.446005\pi\)
0.383912 + 0.923370i \(0.374577\pi\)
\(74\) −1.22883e7 5.91774e6i −0.409793 0.197346i
\(75\) 2.72006e7 2.72006e7i 0.859674 0.859674i
\(76\) −1.20546e6 3.44501e6i −0.0361325 0.103261i
\(77\) −3.83258e7 6.09952e7i −1.09026 1.73513i
\(78\) 8.58305e7 4.13338e7i 2.31880 1.11667i
\(79\) −2.06555e7 + 5.90300e7i −0.530307 + 1.51553i 0.297614 + 0.954686i \(0.403809\pi\)
−0.827921 + 0.560844i \(0.810477\pi\)
\(80\) −1.47107e6 + 335761.i −0.0359147 + 0.00819730i
\(81\) 3.35389e7 4.20565e7i 0.779129 0.976997i
\(82\) 1.43818e7 + 1.80342e7i 0.318096 + 0.398879i
\(83\) −3.24788e6 + 1.42299e7i −0.0684365 + 0.299840i −0.997550 0.0699543i \(-0.977715\pi\)
0.929114 + 0.369794i \(0.120572\pi\)
\(84\) 2.42059e7 3.85235e7i 0.486188 0.773764i
\(85\) 170214. 1.51069e6i 0.00326077 0.0289402i
\(86\) 1.56472e7i 0.286051i
\(87\) −3.20007e7 + 6.19324e7i −0.558576 + 1.08104i
\(88\) 5.03533e7 0.839648
\(89\) −1.95390e7 2.20152e6i −0.311417 0.0350883i −0.0451271 0.998981i \(-0.514369\pi\)
−0.266290 + 0.963893i \(0.585798\pi\)
\(90\) 970399. + 609742.i 0.0147904 + 0.00929343i
\(91\) −1.65746e8 3.78304e7i −2.41700 0.551665i
\(92\) 3.81169e7 3.03972e7i 0.532067 0.424309i
\(93\) 8.27295e7 + 6.59746e7i 1.10593 + 0.881952i
\(94\) −2.10488e7 9.22207e7i −0.269597 1.18118i
\(95\) −477063. 166932.i −0.00585708 0.00204948i
\(96\) 4.25293e7 + 8.83129e7i 0.500729 + 1.03977i
\(97\) 1.31178e8 8.24246e7i 1.48175 0.931043i 0.483293 0.875459i \(-0.339441\pi\)
0.998454 0.0555844i \(-0.0177022\pi\)
\(98\) −1.16766e8 + 4.08584e7i −1.26594 + 0.442972i
\(99\) −4.63005e7 4.63005e7i −0.481997 0.481997i
\(100\) −2.25307e7 + 4.67855e7i −0.225307 + 0.467855i
\(101\) −1.34644e6 1.19499e7i −0.0129390 0.114837i 0.985582 0.169196i \(-0.0541170\pi\)
−0.998521 + 0.0543591i \(0.982688\pi\)
\(102\) −1.59399e8 + 1.79600e7i −1.47260 + 0.165922i
\(103\) 9.91204e7 + 4.77339e7i 0.880672 + 0.424109i 0.818870 0.573979i \(-0.194601\pi\)
0.0618023 + 0.998088i \(0.480315\pi\)
\(104\) 8.40290e7 8.40290e7i 0.718283 0.718283i
\(105\) −2.08090e6 5.94686e6i −0.0171196 0.0489250i
\(106\) 1.06309e8 + 1.69189e8i 0.842065 + 1.34014i
\(107\) −1.65564e8 + 7.97315e7i −1.26308 + 0.608268i −0.940988 0.338440i \(-0.890101\pi\)
−0.322093 + 0.946708i \(0.604387\pi\)
\(108\) −1.47585e7 + 4.21773e7i −0.108479 + 0.310016i
\(109\) 6.47953e6 1.47891e6i 0.0459026 0.0104770i −0.199508 0.979896i \(-0.563934\pi\)
0.245411 + 0.969419i \(0.421077\pi\)
\(110\) −4.70478e6 + 5.89960e6i −0.0321342 + 0.0402951i
\(111\) 4.24932e7 + 5.32848e7i 0.279916 + 0.351003i
\(112\) 6.32235e7 2.77000e8i 0.401797 1.76039i
\(113\) −4.29708e7 + 6.83876e7i −0.263548 + 0.419434i −0.952116 0.305738i \(-0.901097\pi\)
0.688568 + 0.725172i \(0.258240\pi\)
\(114\) −5.97100e6 + 5.29941e7i −0.0353531 + 0.313768i
\(115\) 6.75135e6i 0.0386011i
\(116\) 1.31616e7 9.31797e7i 0.0726906 0.514623i
\(117\) −1.54531e8 −0.824656
\(118\) −2.48699e8 2.80216e7i −1.28276 0.144532i
\(119\) 2.42385e8 + 1.52301e8i 1.20870 + 0.759475i
\(120\) 4.29355e6 + 979974.i 0.0207058 + 0.00472596i
\(121\) 1.69473e8 1.35151e8i 0.790606 0.630487i
\(122\) −9.86189e7 7.86459e7i −0.445165 0.355007i
\(123\) −2.56485e7 1.12374e8i −0.112058 0.490957i
\(124\) −1.34826e8 4.71777e7i −0.570278 0.199549i
\(125\) 6.24281e6 + 1.29633e7i 0.0255705 + 0.0530978i
\(126\) −1.82725e8 + 1.14814e8i −0.724963 + 0.455524i
\(127\) −3.49157e8 + 1.22175e8i −1.34217 + 0.469644i −0.903339 0.428928i \(-0.858891\pi\)
−0.438826 + 0.898572i \(0.644606\pi\)
\(128\) 1.98840e8 + 1.98840e8i 0.740737 + 0.740737i
\(129\) 3.39249e7 7.04458e7i 0.122507 0.254388i
\(130\) 1.99391e6 + 1.76965e7i 0.00698124 + 0.0619602i
\(131\) 2.57897e8 2.90580e7i 0.875712 0.0986691i 0.337347 0.941381i \(-0.390471\pi\)
0.538365 + 0.842711i \(0.319042\pi\)
\(132\) 2.45325e8 + 1.18142e8i 0.808064 + 0.389143i
\(133\) 6.72962e7 6.72962e7i 0.215072 0.215072i
\(134\) 1.34202e8 + 3.83528e8i 0.416237 + 1.18954i
\(135\) 3.29218e6 + 5.23948e6i 0.00991172 + 0.0157744i
\(136\) −1.80280e8 + 8.68183e7i −0.526978 + 0.253779i
\(137\) 1.36210e8 3.89266e8i 0.386658 1.10501i −0.571953 0.820286i \(-0.693814\pi\)
0.958611 0.284719i \(-0.0919002\pi\)
\(138\) −6.94501e8 + 1.58515e8i −1.91494 + 0.437074i
\(139\) −1.07903e8 + 1.35306e8i −0.289051 + 0.362458i −0.905062 0.425279i \(-0.860176\pi\)
0.616012 + 0.787737i \(0.288747\pi\)
\(140\) 5.30282e6 + 6.64953e6i 0.0138037 + 0.0173093i
\(141\) −1.05180e8 + 4.60825e8i −0.266108 + 1.16590i
\(142\) −1.93182e8 + 3.07448e8i −0.475132 + 0.756168i
\(143\) 1.13919e8 1.01106e9i 0.272429 2.41788i
\(144\) 2.58258e8i 0.600626i
\(145\) −8.95198e6 9.47018e6i −0.0202510 0.0214233i
\(146\) 3.11563e8 0.685701
\(147\) 6.14283e8 + 6.92131e7i 1.31552 + 0.148224i
\(148\) −7.79004e7 4.89481e7i −0.162365 0.102021i
\(149\) 7.74409e8 + 1.76754e8i 1.57118 + 0.358611i 0.917365 0.398046i \(-0.130312\pi\)
0.653812 + 0.756657i \(0.273169\pi\)
\(150\) 5.93213e8 4.73071e8i 1.17178 0.934462i
\(151\) 6.82842e7 + 5.44548e7i 0.131345 + 0.104744i 0.686959 0.726697i \(-0.258945\pi\)
−0.555614 + 0.831440i \(0.687517\pi\)
\(152\) 1.48030e7 + 6.48563e7i 0.0277317 + 0.121500i
\(153\) 2.45600e8 + 8.59392e7i 0.448191 + 0.156829i
\(154\) −6.16497e8 1.28017e9i −1.09609 2.27606i
\(155\) −1.67488e7 + 1.05240e7i −0.0290173 + 0.0182328i
\(156\) 6.06549e8 2.12241e8i 1.02416 0.358369i
\(157\) −6.71788e8 6.71788e8i −1.10569 1.10569i −0.993710 0.111980i \(-0.964281\pi\)
−0.111980 0.993710i \(-0.535719\pi\)
\(158\) −5.35219e8 + 1.11139e9i −0.858822 + 1.78336i
\(159\) −1.11794e8 9.92201e8i −0.174916 1.55243i
\(160\) −1.82083e7 + 2.05158e6i −0.0277836 + 0.00313046i
\(161\) 1.14538e9 + 5.51584e8i 1.70469 + 0.820934i
\(162\) 7.50254e8 7.50254e8i 1.08930 1.08930i
\(163\) 1.71099e8 + 4.88971e8i 0.242379 + 0.692681i 0.999235 + 0.0390989i \(0.0124487\pi\)
−0.756856 + 0.653582i \(0.773266\pi\)
\(164\) 8.27823e7 + 1.31747e8i 0.114436 + 0.182124i
\(165\) 3.39725e7 1.63603e7i 0.0458344 0.0220727i
\(166\) −9.50854e7 + 2.71738e8i −0.125222 + 0.357864i
\(167\) −4.83023e8 + 1.10247e8i −0.621014 + 0.141742i −0.521440 0.853288i \(-0.674605\pi\)
−0.0995738 + 0.995030i \(0.531748\pi\)
\(168\) −5.17036e8 + 6.48343e8i −0.649058 + 0.813894i
\(169\) −9.88543e8 1.23959e9i −1.21185 1.51961i
\(170\) 6.67253e6 2.92342e7i 0.00798904 0.0350023i
\(171\) 4.60246e7 7.32477e7i 0.0538276 0.0856662i
\(172\) −1.18177e7 + 1.04885e8i −0.0135027 + 0.119840i
\(173\) 6.13510e8i 0.684916i 0.939533 + 0.342458i \(0.111259\pi\)
−0.939533 + 0.342458i \(0.888741\pi\)
\(174\) −7.63999e8 + 1.14323e9i −0.833481 + 1.24720i
\(175\) −1.35405e9 −1.44372
\(176\) 1.68973e9 + 1.90386e8i 1.76102 + 0.198420i
\(177\) 1.05892e9 + 6.65363e8i 1.07887 + 0.677900i
\(178\) −3.78110e8 8.63010e7i −0.376650 0.0859678i
\(179\) −8.28687e8 + 6.60856e8i −0.807195 + 0.643716i −0.937589 0.347746i \(-0.886947\pi\)
0.130394 + 0.991462i \(0.458376\pi\)
\(180\) 6.04418e6 + 4.82007e6i 0.00575768 + 0.00459159i
\(181\) 1.89642e8 + 8.30877e8i 0.176694 + 0.774145i 0.983142 + 0.182841i \(0.0585295\pi\)
−0.806449 + 0.591304i \(0.798613\pi\)
\(182\) −3.16513e9 1.10753e9i −2.88474 1.00941i
\(183\) 2.73482e8 + 5.67890e8i 0.243851 + 0.506361i
\(184\) −7.52410e8 + 4.72771e8i −0.656422 + 0.412457i
\(185\) −1.20255e7 + 4.20790e6i −0.0102663 + 0.00359234i
\(186\) 1.47583e9 + 1.47583e9i 1.23306 + 1.23306i
\(187\) −7.43336e8 + 1.54355e9i −0.607881 + 1.26228i
\(188\) −7.14417e7 6.34063e8i −0.0571900 0.507576i
\(189\) −1.15786e9 + 1.30459e8i −0.907418 + 0.102241i
\(190\) −8.98195e6 4.32548e6i −0.00689218 0.00331910i
\(191\) −5.72516e8 + 5.72516e8i −0.430184 + 0.430184i −0.888691 0.458507i \(-0.848384\pi\)
0.458507 + 0.888691i \(0.348384\pi\)
\(192\) −4.39194e7 1.25515e8i −0.0323185 0.0923611i
\(193\) −6.99829e7 1.11377e8i −0.0504385 0.0802725i 0.820553 0.571570i \(-0.193666\pi\)
−0.870992 + 0.491298i \(0.836523\pi\)
\(194\) 2.75316e9 1.32585e9i 1.94368 0.936028i
\(195\) 2.93910e7 8.39947e7i 0.0203271 0.0580916i
\(196\) −8.13557e8 + 1.85689e8i −0.551269 + 0.125824i
\(197\) −1.31589e9 + 1.65007e9i −0.873684 + 1.09557i 0.121006 + 0.992652i \(0.461388\pi\)
−0.994690 + 0.102913i \(0.967184\pi\)
\(198\) −8.05255e8 1.00976e9i −0.523929 0.656986i
\(199\) 6.03545e8 2.64430e9i 0.384855 1.68616i −0.297165 0.954826i \(-0.596041\pi\)
0.682020 0.731334i \(-0.261102\pi\)
\(200\) 5.03556e8 8.01404e8i 0.314722 0.500878i
\(201\) 2.27335e8 2.01766e9i 0.139278 1.23613i
\(202\) 2.37197e8i 0.142463i
\(203\) 2.33800e9 7.45004e8i 1.37677 0.438707i
\(204\) −1.08204e9 −0.624771
\(205\) 2.14115e7 + 2.41249e6i 0.0121236 + 0.00136600i
\(206\) 1.83738e9 + 1.15450e9i 1.02030 + 0.641100i
\(207\) 1.12657e9 + 2.57132e8i 0.613587 + 0.140047i
\(208\) 3.13751e9 2.50208e9i 1.67622 1.33674i
\(209\) 4.45314e8 + 3.55126e8i 0.233389 + 0.186122i
\(210\) −2.76531e7 1.21156e8i −0.0142189 0.0622972i
\(211\) −1.53360e8 5.36629e7i −0.0773716 0.0270735i 0.291316 0.956627i \(-0.405907\pi\)
−0.368687 + 0.929553i \(0.620193\pi\)
\(212\) 5.84817e8 + 1.21439e9i 0.289519 + 0.601192i
\(213\) 1.53631e9 9.65329e8i 0.746382 0.468983i
\(214\) −3.42120e9 + 1.19713e9i −1.63126 + 0.570803i
\(215\) 1.03353e7 + 1.03353e7i 0.00483694 + 0.00483694i
\(216\) 3.53380e8 7.33801e8i 0.162340 0.337103i
\(217\) −4.17032e8 3.70126e9i −0.188075 1.66921i
\(218\) 1.30267e8 1.46776e7i 0.0576779 0.00649873i
\(219\) −1.40270e9 6.75503e8i −0.609800 0.293664i
\(220\) −3.59924e7 + 3.59924e7i −0.0153645 + 0.0153645i
\(221\) 1.33539e9 + 3.81633e9i 0.559809 + 1.59984i
\(222\) 7.15206e8 + 1.13824e9i 0.294455 + 0.468623i
\(223\) 8.60979e8 4.14626e8i 0.348155 0.167663i −0.251630 0.967823i \(-0.580967\pi\)
0.599786 + 0.800161i \(0.295252\pi\)
\(224\) 1.13956e9 3.25668e9i 0.452632 1.29355i
\(225\) −1.19993e9 + 2.73875e8i −0.468192 + 0.106862i
\(226\) −9.93273e8 + 1.24552e9i −0.380745 + 0.477440i
\(227\) 2.43452e8 + 3.05279e8i 0.0916873 + 0.114972i 0.825559 0.564316i \(-0.190860\pi\)
−0.733872 + 0.679288i \(0.762289\pi\)
\(228\) −8.00486e7 + 3.50716e8i −0.0296220 + 0.129782i
\(229\) −6.55957e8 + 1.04395e9i −0.238525 + 0.379610i −0.944439 0.328688i \(-0.893394\pi\)
0.705914 + 0.708298i \(0.250537\pi\)
\(230\) 1.49099e7 1.32329e8i 0.00532798 0.0472872i
\(231\) 7.10011e9i 2.49355i
\(232\) −4.28541e8 + 1.66082e9i −0.147924 + 0.573285i
\(233\) −1.43859e9 −0.488104 −0.244052 0.969762i \(-0.578477\pi\)
−0.244052 + 0.969762i \(0.578477\pi\)
\(234\) −3.02887e9 3.41272e8i −1.01022 0.113825i
\(235\) −7.48169e7 4.70105e7i −0.0245317 0.0154143i
\(236\) −1.64589e9 3.75664e8i −0.530583 0.121102i
\(237\) 4.81925e9 3.84322e9i 1.52752 1.21815i
\(238\) 4.41449e9 + 3.52044e9i 1.37585 + 1.09721i
\(239\) −8.03750e8 3.52146e9i −0.246337 1.07927i −0.935127 0.354312i \(-0.884715\pi\)
0.688790 0.724961i \(-0.258142\pi\)
\(240\) 1.40375e8 + 4.91193e7i 0.0423101 + 0.0148050i
\(241\) −2.22015e9 4.61019e9i −0.658134 1.36663i −0.916286 0.400525i \(-0.868828\pi\)
0.258152 0.966104i \(-0.416886\pi\)
\(242\) 3.62021e9 2.27473e9i 1.05553 0.663236i
\(243\) −2.92454e9 + 1.02334e9i −0.838748 + 0.293491i
\(244\) −6.01655e8 6.01655e8i −0.169742 0.169742i
\(245\) −5.01389e7 + 1.04115e8i −0.0139159 + 0.0288966i
\(246\) −2.54551e8 2.25921e9i −0.0695080 0.616901i
\(247\) 1.33576e9 1.50504e8i 0.358874 0.0404354i
\(248\) 2.34570e9 + 1.12963e9i 0.620107 + 0.298628i
\(249\) 1.01724e9 1.01724e9i 0.264623 0.264623i
\(250\) 9.37327e7 + 2.67873e8i 0.0239956 + 0.0685754i
\(251\) −3.67857e9 5.85441e9i −0.926796 1.47499i −0.879384 0.476112i \(-0.842046\pi\)
−0.0474118 0.998875i \(-0.515097\pi\)
\(252\) −1.31154e9 + 6.31604e8i −0.325222 + 0.156618i
\(253\) −2.51285e9 + 7.18132e9i −0.613317 + 1.75276i
\(254\) −7.11342e9 + 1.62359e9i −1.70901 + 0.390069i
\(255\) −9.34236e7 + 1.17149e8i −0.0220951 + 0.0277064i
\(256\) 3.24287e9 + 4.06643e9i 0.755039 + 0.946790i
\(257\) −1.21198e9 + 5.31005e9i −0.277821 + 1.21721i 0.622722 + 0.782443i \(0.286027\pi\)
−0.900542 + 0.434768i \(0.856830\pi\)
\(258\) 8.20515e8 1.30584e9i 0.185186 0.294722i
\(259\) 2.68604e8 2.38392e9i 0.0596916 0.529777i
\(260\) 1.20127e8i 0.0262874i
\(261\) 1.92119e9 1.13310e9i 0.414008 0.244177i
\(262\) 5.11905e9 1.08639
\(263\) −5.14766e9 5.80002e8i −1.07594 0.121229i −0.443831 0.896111i \(-0.646381\pi\)
−0.632106 + 0.774882i \(0.717809\pi\)
\(264\) −4.20224e9 2.64045e9i −0.865099 0.543578i
\(265\) 1.81972e8 + 4.15340e7i 0.0368996 + 0.00842210i
\(266\) 1.46765e9 1.17041e9i 0.293154 0.233782i
\(267\) 1.51519e9 + 1.20832e9i 0.298141 + 0.237759i
\(268\) 6.09909e8 + 2.67219e9i 0.118230 + 0.517997i
\(269\) 2.96328e9 + 1.03690e9i 0.565931 + 0.198028i 0.598054 0.801456i \(-0.295941\pi\)
−0.0321225 + 0.999484i \(0.510227\pi\)
\(270\) 5.29570e7 + 1.09966e8i 0.00996479 + 0.0206921i
\(271\) −7.52779e9 + 4.73002e9i −1.39569 + 0.876973i −0.999157 0.0410459i \(-0.986931\pi\)
−0.396537 + 0.918019i \(0.629788\pi\)
\(272\) −6.37799e9 + 2.23175e9i −1.16522 + 0.407728i
\(273\) 1.18486e10 + 1.18486e10i 2.13312 + 2.13312i
\(274\) 3.52943e9 7.32895e9i 0.626185 1.30029i
\(275\) −9.07326e8 8.05274e9i −0.158647 1.40803i
\(276\) −4.77504e9 + 5.38017e8i −0.822887 + 0.0927171i
\(277\) 3.84207e9 + 1.85025e9i 0.652599 + 0.314275i 0.730729 0.682668i \(-0.239180\pi\)
−0.0781294 + 0.996943i \(0.524895\pi\)
\(278\) −2.41375e9 + 2.41375e9i −0.404123 + 0.404123i
\(279\) −1.11819e9 3.19561e9i −0.184544 0.527396i
\(280\) −8.24752e7 1.31259e8i −0.0134181 0.0213548i
\(281\) 6.15662e9 2.96487e9i 0.987454 0.475533i 0.130792 0.991410i \(-0.458248\pi\)
0.856663 + 0.515877i \(0.172534\pi\)
\(282\) −3.07927e9 + 8.80005e9i −0.486913 + 1.39152i
\(283\) −6.48283e9 + 1.47966e9i −1.01069 + 0.230684i −0.695640 0.718391i \(-0.744879\pi\)
−0.315052 + 0.949074i \(0.602022\pi\)
\(284\) −1.52713e9 + 1.91496e9i −0.234748 + 0.294364i
\(285\) 3.10598e7 + 3.89477e7i 0.00470781 + 0.00590340i
\(286\) 4.46573e9 1.95656e10i 0.667464 2.92435i
\(287\) −2.15860e9 + 3.43539e9i −0.318159 + 0.506347i
\(288\) 3.51142e8 3.11647e9i 0.0510403 0.452995i
\(289\) 1.67727e8i 0.0240443i
\(290\) −1.54548e8 2.05389e8i −0.0218510 0.0290392i
\(291\) −1.52697e10 −2.12941
\(292\) 2.08844e9 + 2.35311e8i 0.287271 + 0.0323676i
\(293\) −8.71490e9 5.47594e9i −1.18248 0.742998i −0.210388 0.977618i \(-0.567473\pi\)
−0.972087 + 0.234620i \(0.924616\pi\)
\(294\) 1.18873e10 + 2.71320e9i 1.59109 + 0.363156i
\(295\) −1.82780e8 + 1.45762e8i −0.0241346 + 0.0192467i
\(296\) 1.31105e9 + 1.04553e9i 0.170786 + 0.136197i
\(297\) −1.55172e9 6.79852e9i −0.199428 0.873753i
\(298\) 1.47883e10 + 5.17467e9i 1.87523 + 0.656171i
\(299\) 7.79068e9 + 1.61775e10i 0.974745 + 2.02408i
\(300\) 4.33366e9 2.72302e9i 0.535020 0.336175i
\(301\) −2.59780e9 + 9.09009e8i −0.316475 + 0.110739i
\(302\) 1.21813e9 + 1.21813e9i 0.146443 + 0.146443i
\(303\) −5.14268e8 + 1.06789e9i −0.0610126 + 0.126694i
\(304\) 2.51528e8 + 2.23238e9i 0.0294505 + 0.261381i
\(305\) −1.17087e8 + 1.31926e7i −0.0135304 + 0.00152451i
\(306\) 4.62406e9 + 2.22683e9i 0.527397 + 0.253981i
\(307\) 1.18000e9 1.18000e9i 0.132840 0.132840i −0.637560 0.770400i \(-0.720056\pi\)
0.770400 + 0.637560i \(0.220056\pi\)
\(308\) −3.16559e9 9.04673e9i −0.351764 1.00528i
\(309\) −5.76903e9 9.18135e9i −0.632803 1.00710i
\(310\) −3.51524e8 + 1.69285e8i −0.0380634 + 0.0183304i
\(311\) −3.84503e9 + 1.09885e10i −0.411016 + 1.17462i 0.533401 + 0.845863i \(0.320914\pi\)
−0.944416 + 0.328752i \(0.893372\pi\)
\(312\) −1.14190e10 + 2.60631e9i −1.20506 + 0.275048i
\(313\) 8.71122e9 1.09235e10i 0.907615 1.13811i −0.0823218 0.996606i \(-0.526234\pi\)
0.989937 0.141508i \(-0.0451950\pi\)
\(314\) −1.16837e10 1.46509e10i −1.20188 1.50711i
\(315\) −4.48568e7 + 1.96531e8i −0.00455603 + 0.0199613i
\(316\) −4.42702e9 + 7.04557e9i −0.443980 + 0.706590i
\(317\) 4.27030e8 3.78999e9i 0.0422884 0.375320i −0.954688 0.297610i \(-0.903811\pi\)
0.996976 0.0777100i \(-0.0247608\pi\)
\(318\) 1.96944e10i 1.92590i
\(319\) 5.99730e9 + 1.34052e10i 0.579153 + 1.29453i
\(320\) 2.48582e7 0.00237066
\(321\) 1.79982e10 + 2.02791e9i 1.69515 + 0.190998i
\(322\) 2.12317e10 + 1.33407e10i 1.97497 + 1.24096i
\(323\) −2.20666e9 5.03656e8i −0.202733 0.0462726i
\(324\) 5.59567e9 4.46240e9i 0.507776 0.404938i
\(325\) −1.49525e10 1.19242e10i −1.34023 1.06880i
\(326\) 2.27373e9 + 9.96188e9i 0.201312 + 0.882004i
\(327\) −6.18302e8 2.16353e8i −0.0540766 0.0189222i
\(328\) −1.23050e9 2.55516e9i −0.106313 0.220761i
\(329\) 1.40879e10 8.85203e9i 1.20244 0.755544i
\(330\) 7.02003e8 2.45642e8i 0.0591948 0.0207131i
\(331\) 8.26203e9 + 8.26203e9i 0.688296 + 0.688296i 0.961855 0.273559i \(-0.0882010\pi\)
−0.273559 + 0.961855i \(0.588201\pi\)
\(332\) −8.42601e8 + 1.74968e9i −0.0693537 + 0.144014i
\(333\) −2.44151e8 2.16690e9i −0.0198555 0.176223i
\(334\) −9.71089e9 + 1.09415e9i −0.780321 + 0.0879210i
\(335\) 3.41972e8 + 1.64685e8i 0.0271526 + 0.0130760i
\(336\) −1.98018e10 + 1.98018e10i −1.55363 + 1.55363i
\(337\) 4.98559e9 + 1.42480e10i 0.386542 + 1.10467i 0.958673 + 0.284512i \(0.0918315\pi\)
−0.572130 + 0.820163i \(0.693883\pi\)
\(338\) −1.66382e10 2.64796e10i −1.27480 2.02883i
\(339\) 7.17227e9 3.45398e9i 0.543073 0.261530i
\(340\) 6.68061e7 1.90921e8i 0.00499920 0.0142869i
\(341\) 2.17325e10 4.96030e9i 1.60728 0.366851i
\(342\) 1.06386e9 1.33404e9i 0.0777643 0.0975133i
\(343\) −1.09684e9 1.37539e9i −0.0792438 0.0993686i
\(344\) 4.28087e8 1.87557e9i 0.0305702 0.133937i
\(345\) −3.54030e8 + 5.63435e8i −0.0249898 + 0.0397711i
\(346\) −1.35489e9 + 1.20250e10i −0.0945368 + 0.839037i
\(347\) 8.75402e9i 0.603795i −0.953340 0.301897i \(-0.902380\pi\)
0.953340 0.301897i \(-0.0976200\pi\)
\(348\) −5.98460e9 + 7.08616e9i −0.408054 + 0.483163i
\(349\) 1.30015e10 0.876381 0.438191 0.898882i \(-0.355620\pi\)
0.438191 + 0.898882i \(0.355620\pi\)
\(350\) −2.65399e10 2.99033e9i −1.76859 0.199272i
\(351\) −1.39348e10 8.75580e9i −0.918061 0.576856i
\(352\) 2.01315e10 + 4.59489e9i 1.31131 + 0.299298i
\(353\) 7.46871e9 5.95609e9i 0.481002 0.383586i −0.352757 0.935715i \(-0.614756\pi\)
0.833759 + 0.552129i \(0.186184\pi\)
\(354\) 1.92858e10 + 1.53799e10i 1.22807 + 0.979356i
\(355\) 7.54748e7 + 3.30677e8i 0.00475214 + 0.0208205i
\(356\) −2.46933e9 8.64056e8i −0.153737 0.0537950i
\(357\) −1.22419e10 2.54205e10i −0.753660 1.56499i
\(358\) −1.77020e10 + 1.11229e10i −1.07768 + 0.677152i
\(359\) 7.12634e9 2.49361e9i 0.429031 0.150124i −0.107121 0.994246i \(-0.534163\pi\)
0.536152 + 0.844122i \(0.319877\pi\)
\(360\) −9.96362e7 9.96362e7i −0.00593208 0.00593208i
\(361\) 7.04240e9 1.46237e10i 0.414660 0.861049i
\(362\) 1.88212e9 + 1.67043e10i 0.109601 + 0.972734i
\(363\) −2.12305e10 + 2.39210e9i −1.22274 + 0.137770i
\(364\) −2.03798e10 9.81437e9i −1.16090 0.559058i
\(365\) 2.05794e8 2.05794e8i 0.0115948 0.0115948i
\(366\) 4.10619e9 + 1.17348e10i 0.228831 + 0.653961i
\(367\) −1.26770e10 2.01753e10i −0.698799 1.11213i −0.987939 0.154846i \(-0.950512\pi\)
0.289140 0.957287i \(-0.406631\pi\)
\(368\) −2.70365e10 + 1.30201e10i −1.47421 + 0.709941i
\(369\) −1.21804e9 + 3.48095e9i −0.0656985 + 0.187756i
\(370\) −2.44996e8 + 5.59189e7i −0.0130723 + 0.00298367i
\(371\) −2.19134e10 + 2.74785e10i −1.15668 + 1.45043i
\(372\) 8.77801e9 + 1.10073e10i 0.458378 + 0.574788i
\(373\) −2.89546e9 + 1.26858e10i −0.149583 + 0.655366i 0.843418 + 0.537258i \(0.180540\pi\)
−0.993001 + 0.118108i \(0.962317\pi\)
\(374\) −1.79785e10 + 2.86126e10i −0.918896 + 1.46241i
\(375\) 1.58781e8 1.40922e9i 0.00802921 0.0712612i
\(376\) 1.16300e10i 0.581873i
\(377\) 3.23787e10 + 1.23623e10i 1.60285 + 0.611974i
\(378\) −2.29825e10 −1.12572
\(379\) 4.05246e9 + 4.56602e8i 0.196409 + 0.0221300i 0.209621 0.977783i \(-0.432777\pi\)
−0.0132118 + 0.999913i \(0.504206\pi\)
\(380\) −5.69402e7 3.57779e7i −0.00273077 0.00171585i
\(381\) 3.55456e10 + 8.11306e9i 1.68689 + 0.385021i
\(382\) −1.24859e10 + 9.95715e9i −0.586362 + 0.467608i
\(383\) 1.11495e10 + 8.89143e9i 0.518156 + 0.413216i 0.847340 0.531050i \(-0.178202\pi\)
−0.329185 + 0.944266i \(0.606774\pi\)
\(384\) −6.16739e9 2.70211e10i −0.283646 1.24273i
\(385\) −1.25279e9 4.38369e8i −0.0570210 0.0199525i
\(386\) −1.12572e9 2.33758e9i −0.0507086 0.105297i
\(387\) −2.11824e9 + 1.33098e9i −0.0944347 + 0.0593373i
\(388\) 1.94561e10 6.80800e9i 0.858479 0.300395i
\(389\) 2.49824e10 + 2.49824e10i 1.09103 + 1.09103i 0.995419 + 0.0956110i \(0.0304805\pi\)
0.0956110 + 0.995419i \(0.469520\pi\)
\(390\) 7.61571e8 1.58142e9i 0.0329194 0.0683578i
\(391\) −3.38514e9 3.00439e10i −0.144834 1.28543i
\(392\) 1.51142e10 1.70296e9i 0.640089 0.0721207i
\(393\) −2.30466e10 1.10987e10i −0.966133 0.465265i
\(394\) −2.94360e10 + 2.94360e10i −1.22150 + 1.22150i
\(395\) 3.80576e8 + 1.08762e9i 0.0156334 + 0.0446776i
\(396\) −4.63508e9 7.37669e9i −0.188485 0.299972i
\(397\) −4.21030e10 + 2.02758e10i −1.69493 + 0.816235i −0.700171 + 0.713975i \(0.746893\pi\)
−0.994758 + 0.102259i \(0.967393\pi\)
\(398\) 1.76694e10 5.04964e10i 0.704191 2.01246i
\(399\) −9.14511e9 + 2.08731e9i −0.360826 + 0.0823561i
\(400\) 1.99281e10 2.49891e10i 0.778442 0.976136i
\(401\) −3.05624e9 3.83240e9i −0.118198 0.148215i 0.719212 0.694790i \(-0.244503\pi\)
−0.837410 + 0.546575i \(0.815931\pi\)
\(402\) 8.91170e9 3.90447e10i 0.341237 1.49506i
\(403\) 2.79892e10 4.45446e10i 1.06113 1.68879i
\(404\) 1.79145e8 1.58996e9i 0.00672480 0.0596842i
\(405\) 9.91118e8i 0.0368388i
\(406\) 4.74710e10 9.43902e9i 1.74713 0.347394i
\(407\) 1.43575e10 0.523241
\(408\) 1.95979e10 + 2.20815e9i 0.707244 + 0.0796873i
\(409\) 1.65158e10 + 1.03776e10i 0.590210 + 0.370853i 0.793778 0.608207i \(-0.208111\pi\)
−0.203568 + 0.979061i \(0.565254\pi\)
\(410\) 4.14345e8 + 9.45714e7i 0.0146631 + 0.00334676i
\(411\) −3.17799e10 + 2.53436e10i −1.11374 + 0.888181i
\(412\) 1.14442e10 + 9.12645e9i 0.397189 + 0.316748i
\(413\) −9.79566e9 4.29176e10i −0.336692 1.47515i
\(414\) 2.15133e10 + 7.52782e9i 0.732327 + 0.256252i
\(415\) 1.16683e8 + 2.42295e8i 0.00393383 + 0.00816868i
\(416\) 4.12631e10 2.59273e10i 1.37781 0.865734i
\(417\) 1.61003e10 5.63373e9i 0.532463 0.186317i
\(418\) 7.94404e9 + 7.94404e9i 0.260217 + 0.260217i
\(419\) −8.74759e9 + 1.81646e10i −0.283813 + 0.589344i −0.993325 0.115350i \(-0.963201\pi\)
0.709512 + 0.704693i \(0.248915\pi\)
\(420\) −9.38575e7 8.33009e8i −0.00301628 0.0267702i
\(421\) −2.61118e10 + 2.94209e9i −0.831204 + 0.0936542i −0.517304 0.855802i \(-0.673064\pi\)
−0.313900 + 0.949456i \(0.601636\pi\)
\(422\) −2.88740e9 1.39050e9i −0.0910451 0.0438450i
\(423\) 1.06939e10 1.06939e10i 0.334022 0.334022i
\(424\) −8.11402e9 2.31885e10i −0.251057 0.717480i
\(425\) 1.71329e10 + 2.72669e10i 0.525140 + 0.835756i
\(426\) 3.22441e10 1.55280e10i 0.979067 0.471494i
\(427\) 7.32787e9 2.09418e10i 0.220428 0.629946i
\(428\) −2.38368e10 + 5.44060e9i −0.710352 + 0.162133i
\(429\) −6.25257e10 + 7.84047e10i −1.84599 + 2.31480i
\(430\) 1.79751e8 + 2.25401e8i 0.00525773 + 0.00659298i
\(431\) −7.80515e9 + 3.41966e10i −0.226189 + 0.991000i 0.726527 + 0.687138i \(0.241133\pi\)
−0.952716 + 0.303862i \(0.901724\pi\)
\(432\) 1.46330e10 2.32883e10i 0.420144 0.668656i
\(433\) 1.70270e8 1.51119e9i 0.00484382 0.0429901i −0.991058 0.133433i \(-0.957400\pi\)
0.995902 + 0.0904432i \(0.0288284\pi\)
\(434\) 7.34670e10i 2.07078i
\(435\) 2.50488e8 + 1.25976e9i 0.00699568 + 0.0351829i
\(436\) 8.84281e8 0.0244706
\(437\) −9.98845e9 1.12543e9i −0.273888 0.0308597i
\(438\) −2.60016e10 1.63379e10i −0.706485 0.443914i
\(439\) 1.51634e10 + 3.46095e9i 0.408262 + 0.0931831i 0.421720 0.906726i \(-0.361427\pi\)
−0.0134576 + 0.999909i \(0.504284\pi\)
\(440\) 7.25348e8 5.78446e8i 0.0193524 0.0154331i
\(441\) −1.54635e10 1.23318e10i −0.408841 0.326040i
\(442\) 1.77461e10 + 7.77506e10i 0.464957 + 2.03711i
\(443\) 4.52013e10 + 1.58166e10i 1.17364 + 0.410676i 0.845512 0.533956i \(-0.179295\pi\)
0.328132 + 0.944632i \(0.393581\pi\)
\(444\) 3.93444e9 + 8.16994e9i 0.101240 + 0.210226i
\(445\) −3.06753e8 + 1.92746e8i −0.00782256 + 0.00491524i
\(446\) 1.77912e10 6.22540e9i 0.449640 0.157336i
\(447\) −5.53598e10 5.53598e10i −1.38664 1.38664i
\(448\) −2.03091e9 + 4.21723e9i −0.0504172 + 0.104692i
\(449\) 2.68435e9 + 2.38243e10i 0.0660472 + 0.586185i 0.982529 + 0.186109i \(0.0595878\pi\)
−0.916482 + 0.400076i \(0.868984\pi\)
\(450\) −2.41238e10 + 2.71810e9i −0.588296 + 0.0662851i
\(451\) −2.18772e10 1.05355e10i −0.528792 0.254653i
\(452\) −7.59871e9 + 7.59871e9i −0.182048 + 0.182048i
\(453\) −2.84315e9 8.12525e9i −0.0675160 0.192950i
\(454\) 4.09755e9 + 6.52122e9i 0.0964497 + 0.153499i
\(455\) −2.82218e9 + 1.35909e9i −0.0658475 + 0.0317105i
\(456\) 2.16557e9 6.18884e9i 0.0500856 0.143136i
\(457\) −5.26064e10 + 1.20071e10i −1.20607 + 0.275279i −0.777883 0.628409i \(-0.783706\pi\)
−0.428192 + 0.903688i \(0.640849\pi\)
\(458\) −1.51625e10 + 1.90132e10i −0.344595 + 0.432108i
\(459\) 1.72775e10 + 2.16653e10i 0.389252 + 0.488106i
\(460\) 1.99885e8 8.75754e8i 0.00446426 0.0195592i
\(461\) 1.03613e10 1.64900e10i 0.229410 0.365104i −0.712106 0.702072i \(-0.752259\pi\)
0.941516 + 0.336968i \(0.109401\pi\)
\(462\) −1.56801e10 + 1.39165e11i −0.344176 + 3.05465i
\(463\) 6.79043e9i 0.147766i 0.997267 + 0.0738828i \(0.0235391\pi\)
−0.997267 + 0.0738828i \(0.976461\pi\)
\(464\) −2.06603e10 + 5.41125e10i −0.445722 + 1.16742i
\(465\) 1.94963e9 0.0417005
\(466\) −2.81968e10 3.17702e9i −0.597939 0.0673715i
\(467\) −3.39275e10 2.13181e10i −0.713321 0.448209i 0.125870 0.992047i \(-0.459828\pi\)
−0.839190 + 0.543838i \(0.816971\pi\)
\(468\) −2.00451e10 4.57516e9i −0.417854 0.0953725i
\(469\) −5.58780e10 + 4.45613e10i −1.15491 + 0.921014i
\(470\) −1.36262e9 1.08665e9i −0.0279243 0.0222689i
\(471\) 2.08367e10 + 9.12916e10i 0.423395 + 1.85501i
\(472\) 2.90439e10 + 1.01629e10i 0.585177 + 0.204762i
\(473\) −7.14674e9 1.48404e10i −0.142779 0.296483i
\(474\) 1.02946e11 6.46856e10i 2.03938 1.28143i
\(475\) 1.01054e10 3.53603e9i 0.198508 0.0694610i
\(476\) 2.69320e10 + 2.69320e10i 0.524614 + 0.524614i
\(477\) −1.38612e10 + 2.87831e10i −0.267748 + 0.555985i
\(478\) −7.97690e9 7.07969e10i −0.152800 1.35613i
\(479\) 1.14110e10 1.28571e9i 0.216761 0.0244231i −0.00291616 0.999996i \(-0.500928\pi\)
0.219677 + 0.975573i \(0.429500\pi\)
\(480\) 1.62716e9 + 7.83597e8i 0.0306524 + 0.0147614i
\(481\) 2.39597e10 2.39597e10i 0.447611 0.447611i
\(482\) −3.33345e10 9.52644e10i −0.617597 1.76499i
\(483\) −6.66634e10 1.06094e11i −1.22490 1.94941i
\(484\) 2.59847e10 1.25136e10i 0.473518 0.228034i
\(485\) 9.42769e8 2.69428e9i 0.0170388 0.0486940i
\(486\) −5.95819e10 + 1.35992e10i −1.06800 + 0.243763i
\(487\) 5.28930e10 6.63257e10i 0.940335 1.17914i −0.0433172 0.999061i \(-0.513793\pi\)
0.983652 0.180081i \(-0.0576360\pi\)
\(488\) 9.66941e9 + 1.21251e10i 0.170499 + 0.213798i
\(489\) 1.13618e10 4.97793e10i 0.198706 0.870590i
\(490\) −1.21267e9 + 1.92995e9i −0.0210358 + 0.0334783i
\(491\) −1.64424e9 + 1.45930e10i −0.0282904 + 0.251084i 0.971605 + 0.236610i \(0.0760362\pi\)
−0.999895 + 0.0144748i \(0.995392\pi\)
\(492\) 1.53360e10i 0.261728i
\(493\) −4.45852e10 3.76544e10i −0.754750 0.637423i
\(494\) 2.65138e10 0.445210
\(495\) −1.19885e9 1.35078e8i −0.0199685 0.00224991i
\(496\) 7.44445e10 + 4.67766e10i 1.23000 + 0.772862i
\(497\) −6.22661e10 1.42118e10i −1.02053 0.232930i
\(498\) 2.21849e10 1.76919e10i 0.360695 0.287644i
\(499\) 7.10253e10 + 5.66408e10i 1.14554 + 0.913538i 0.997154 0.0753909i \(-0.0240205\pi\)
0.148387 + 0.988929i \(0.452592\pi\)
\(500\) 4.25987e8 + 1.86637e9i 0.00681580 + 0.0298620i
\(501\) 4.60919e10 + 1.61282e10i 0.731600 + 0.255998i
\(502\) −5.91723e10 1.22872e11i −0.931758 1.93482i
\(503\) 6.62360e10 4.16188e10i 1.03472 0.650156i 0.0961912 0.995363i \(-0.469334\pi\)
0.938527 + 0.345207i \(0.112191\pi\)
\(504\) 2.50437e10 8.76316e9i 0.388129 0.135812i
\(505\) −1.56673e8 1.56673e8i −0.00240896 0.00240896i
\(506\) −6.51123e10 + 1.35207e11i −0.993255 + 2.06252i
\(507\) 1.74968e10 + 1.55288e11i 0.264805 + 2.35021i
\(508\) −4.89083e10 + 5.51064e9i −0.734391 + 0.0827460i
\(509\) −4.72569e10 2.27577e10i −0.704035 0.339046i 0.0473783 0.998877i \(-0.484913\pi\)
−0.751414 + 0.659831i \(0.770628\pi\)
\(510\) −2.08985e9 + 2.08985e9i −0.0308912 + 0.0308912i
\(511\) 1.80999e10 + 5.17266e10i 0.265456 + 0.758631i
\(512\) 1.62812e10 + 2.59113e10i 0.236922 + 0.377059i
\(513\) 8.30048e9 3.99730e9i 0.119849 0.0577161i
\(514\) −3.54822e10 + 1.01402e11i −0.508344 + 1.45276i
\(515\) 1.97620e9 4.51055e8i 0.0280933 0.00641211i
\(516\) 6.48625e9 8.13351e9i 0.0914945 0.114731i
\(517\) 6.20844e10 + 7.78514e10i 0.869001 + 1.08969i
\(518\) 1.05295e10 4.61326e10i 0.146247 0.640750i
\(519\) 3.21715e10 5.12006e10i 0.443406 0.705676i
\(520\) 2.45149e8 2.17575e9i 0.00335287 0.0297575i
\(521\) 6.29231e10i 0.854003i −0.904251 0.427001i \(-0.859570\pi\)
0.904251 0.427001i \(-0.140430\pi\)
\(522\) 4.01584e10 1.79663e10i 0.540872 0.241978i
\(523\) −7.87718e10 −1.05284 −0.526422 0.850224i \(-0.676467\pi\)
−0.526422 + 0.850224i \(0.676467\pi\)
\(524\) 3.43136e10 + 3.86621e9i 0.455135 + 0.0512814i
\(525\) 1.13003e11 + 7.10043e10i 1.48748 + 0.934647i
\(526\) −9.96151e10 2.27365e10i −1.30131 0.297016i
\(527\) −6.92564e10 + 5.52301e10i −0.897878 + 0.716034i
\(528\) −1.31033e11 1.04495e11i −1.68595 1.34450i
\(529\) −1.24515e10 5.45535e10i −0.159000 0.696626i
\(530\) 3.47500e9 + 1.21595e9i 0.0440404 + 0.0154104i
\(531\) −1.73613e10 3.60511e10i −0.218376 0.453462i
\(532\) 1.07218e10 6.73694e9i 0.133851 0.0841039i
\(533\) −5.40898e10 + 1.89269e10i −0.670204 + 0.234514i
\(534\) 2.70297e10 + 2.70297e10i 0.332412 + 0.332412i
\(535\) −1.46905e9 + 3.05050e9i −0.0179316 + 0.0372354i
\(536\) −5.59349e9 4.96436e10i −0.0677678 0.601456i
\(537\) 1.03812e11 1.16968e10i 1.24839 0.140660i
\(538\) 5.57914e10 + 2.68677e10i 0.665945 + 0.320702i
\(539\) 9.20836e10 9.20836e10i 1.09101 1.09101i
\(540\) 2.71923e8 + 7.77112e8i 0.00319795 + 0.00913921i
\(541\) 3.18443e10 + 5.06799e10i 0.371743 + 0.591626i 0.979242 0.202695i \(-0.0649699\pi\)
−0.607499 + 0.794321i \(0.707827\pi\)
\(542\) −1.57993e11 + 7.60856e10i −1.83080 + 0.881668i
\(543\) 2.77432e10 7.92855e10i 0.319122 0.912000i
\(544\) −7.99993e10 + 1.82593e10i −0.913463 + 0.208492i
\(545\) 7.63494e7 9.57391e7i 0.000865405 0.00108518i
\(546\) 2.06070e11 + 2.58403e11i 2.31869 + 2.90755i
\(547\) 2.92356e10 1.28089e11i 0.326559 1.43075i −0.499082 0.866555i \(-0.666329\pi\)
0.825642 0.564195i \(-0.190813\pi\)
\(548\) 2.91934e10 4.64611e10i 0.323715 0.515190i
\(549\) 2.25800e9 2.00403e10i 0.0248561 0.220604i
\(550\) 1.59840e11i 1.74677i
\(551\) −1.55032e10 + 1.16656e10i −0.168195 + 0.126561i
\(552\) 8.75838e10 0.943339
\(553\) −2.15610e11 2.42934e10i −2.30551 0.259769i
\(554\) 7.12199e10 + 4.47504e10i 0.756071 + 0.475071i
\(555\) 1.22424e9 + 2.79426e8i 0.0129032 + 0.00294506i
\(556\) −1.80026e10 + 1.43566e10i −0.188381 + 0.150229i
\(557\) −7.93380e10 6.32699e10i −0.824253 0.657320i 0.117706 0.993049i \(-0.462446\pi\)
−0.941959 + 0.335729i \(0.891017\pi\)
\(558\) −1.48597e10 6.51046e10i −0.153276 0.671544i
\(559\) −3.66918e10 1.28390e10i −0.375770 0.131488i
\(560\) −2.27136e9 4.71653e9i −0.0230959 0.0479591i
\(561\) 1.42977e11 8.98381e10i 1.44349 0.907004i
\(562\) 1.27220e11 4.45161e10i 1.27529 0.446243i
\(563\) −1.29459e10 1.29459e10i −0.128855 0.128855i 0.639738 0.768593i \(-0.279043\pi\)
−0.768593 + 0.639738i \(0.779043\pi\)
\(564\) −2.72870e10 + 5.66621e10i −0.269674 + 0.559985i
\(565\) 1.66618e8 + 1.47877e9i 0.00163504 + 0.0145113i
\(566\) −1.30333e11 + 1.46851e10i −1.26996 + 0.143090i
\(567\) 1.68145e11 + 8.09742e10i 1.62686 + 0.783455i
\(568\) 3.15674e10 3.15674e10i 0.303281 0.303281i
\(569\) 6.08983e10 + 1.74037e11i 0.580973 + 1.66033i 0.739648 + 0.672994i \(0.234992\pi\)
−0.158675 + 0.987331i \(0.550722\pi\)
\(570\) 5.22769e8 + 8.31983e8i 0.00495234 + 0.00788161i
\(571\) −3.85626e10 + 1.85708e10i −0.362762 + 0.174697i −0.606381 0.795174i \(-0.707379\pi\)
0.243620 + 0.969871i \(0.421665\pi\)
\(572\) 4.47114e10 1.27778e11i 0.417671 1.19363i
\(573\) 7.78012e10 1.77576e10i 0.721718 0.164727i
\(574\) −4.98961e10 + 6.25677e10i −0.459641 + 0.576372i
\(575\) 8.91656e10 + 1.11810e11i 0.815691 + 1.02284i
\(576\) −9.46749e8 + 4.14798e9i −0.00860092 + 0.0376831i
\(577\) 5.14848e10 8.19376e10i 0.464489 0.739230i −0.529547 0.848281i \(-0.677638\pi\)
0.994036 + 0.109050i \(0.0347809\pi\)
\(578\) −3.70414e8 + 3.28751e9i −0.00331876 + 0.0294548i
\(579\) 1.29648e10i 0.115359i
\(580\) −8.80829e8 1.49347e9i −0.00778358 0.0131973i
\(581\) −5.06387e10 −0.444404
\(582\) −2.99291e11 3.37221e10i −2.60857 0.293915i
\(583\) −1.78103e11 1.11909e11i −1.54169 0.968706i
\(584\) −3.73459e10 8.52395e9i −0.321064 0.0732807i
\(585\) −2.22605e9 + 1.77522e9i −0.0190069 + 0.0151575i
\(586\) −1.58722e11 1.26577e11i −1.34600 1.07340i
\(587\) 5.46155e9 + 2.39286e10i 0.0460006 + 0.201542i 0.992706 0.120558i \(-0.0384684\pi\)
−0.946706 + 0.322100i \(0.895611\pi\)
\(588\) 7.76328e10 + 2.71649e10i 0.649436 + 0.227247i
\(589\) 1.27780e10 + 2.65337e10i 0.106170 + 0.220464i
\(590\) −3.90445e9 + 2.45333e9i −0.0322220 + 0.0202464i
\(591\) 1.96345e11 6.87040e10i 1.60942 0.563161i
\(592\) 4.00422e10 + 4.00422e10i 0.326010 + 0.326010i
\(593\) −1.86465e10 + 3.87198e10i −0.150792 + 0.313123i −0.962658 0.270721i \(-0.912738\pi\)
0.811866 + 0.583844i \(0.198452\pi\)
\(594\) −1.54002e10 1.36680e11i −0.123703 1.09789i
\(595\) 5.24119e9 5.90540e8i 0.0418179 0.00471174i
\(596\) 9.52197e10 + 4.58554e10i 0.754644 + 0.363417i
\(597\) −1.89032e11 + 1.89032e11i −1.48812 + 1.48812i
\(598\) 1.16973e11 + 3.34290e11i 0.914707 + 2.61408i
\(599\) 7.15750e8 + 1.13911e9i 0.00555974 + 0.00884827i 0.849493 0.527601i \(-0.176908\pi\)
−0.843933 + 0.536449i \(0.819765\pi\)
\(600\) −8.40487e10 + 4.04757e10i −0.648524 + 0.312312i
\(601\) 1.88127e10 5.37637e10i 0.144196 0.412089i −0.849022 0.528358i \(-0.822808\pi\)
0.993218 + 0.116269i \(0.0370935\pi\)
\(602\) −5.29253e10 + 1.20798e10i −0.402974 + 0.0919762i
\(603\) −4.05046e10 + 5.07911e10i −0.306362 + 0.384166i
\(604\) 7.24529e9 + 9.08530e9i 0.0544387 + 0.0682640i
\(605\) 8.88719e8 3.89373e9i 0.00663350 0.0290633i
\(606\) −1.24382e10 + 1.97953e10i −0.0922290 + 0.146782i
\(607\) −2.63224e10 + 2.33617e11i −0.193897 + 1.72088i 0.400150 + 0.916449i \(0.368958\pi\)
−0.594047 + 0.804430i \(0.702471\pi\)
\(608\) 2.72807e10i 0.199637i
\(609\) −2.34185e11 6.04267e10i −1.70251 0.439299i
\(610\) −2.32409e9 −0.0167854
\(611\) 2.33523e11 + 2.63117e10i 1.67558 + 0.188792i
\(612\) 2.93138e10 + 1.84191e10i 0.208961 + 0.131299i
\(613\) −2.24833e11 5.13167e10i −1.59228 0.363426i −0.667702 0.744429i \(-0.732722\pi\)
−0.924574 + 0.381003i \(0.875579\pi\)
\(614\) 2.57344e10 2.05225e10i 0.181068 0.144397i
\(615\) −1.66039e9 1.32412e9i −0.0116067 0.00925605i
\(616\) 3.88734e10 + 1.70315e11i 0.269978 + 1.18285i
\(617\) 9.24276e10 + 3.23418e10i 0.637766 + 0.223164i 0.629743 0.776804i \(-0.283160\pi\)
0.00802324 + 0.999968i \(0.497446\pi\)
\(618\) −9.27986e10 1.92698e11i −0.636191 1.32106i
\(619\) 8.39391e10 5.27424e10i 0.571744 0.359250i −0.214920 0.976632i \(-0.568949\pi\)
0.786664 + 0.617381i \(0.211806\pi\)
\(620\) −2.48416e9 + 8.69244e8i −0.0168117 + 0.00588267i
\(621\) 8.70185e10 + 8.70185e10i 0.585120 + 0.585120i
\(622\) −9.96313e10 + 2.06886e11i −0.665632 + 1.38220i
\(623\) −7.63792e9 6.77884e10i −0.0507017 0.449990i
\(624\) −3.93046e11 + 4.42857e10i −2.59242 + 0.292095i
\(625\) −1.37119e11 6.60328e10i −0.898621 0.432753i
\(626\) 1.94867e11 1.94867e11i 1.26894 1.26894i
\(627\) −1.85415e10 5.29886e10i −0.119971 0.342857i
\(628\) −6.72519e10 1.07031e11i −0.432380 0.688129i
\(629\) −5.14043e10 + 2.47550e10i −0.328395 + 0.158147i
\(630\) −1.31323e9 + 3.75301e9i −0.00833643 + 0.0238241i
\(631\) −4.66540e10 + 1.06485e10i −0.294287 + 0.0671691i −0.367115 0.930175i \(-0.619655\pi\)
0.0728284 + 0.997344i \(0.476797\pi\)
\(632\) 9.45608e10 1.18576e11i 0.592711 0.743236i
\(633\) 9.98467e9 + 1.25204e10i 0.0621898 + 0.0779835i
\(634\) 1.67399e10 7.33422e10i 0.103608 0.453938i
\(635\) −3.62615e9 + 5.77098e9i −0.0223024 + 0.0354940i
\(636\) 1.48744e10 1.32014e11i 0.0909096 0.806845i
\(637\) 3.07336e11i 1.86662i
\(638\) 8.79447e10 + 2.75992e11i 0.530795 + 1.66577i
\(639\) −5.80531e10 −0.348195
\(640\) 5.14855e9 + 5.80102e8i 0.0306877 + 0.00345768i
\(641\) 7.25505e10 + 4.55865e10i 0.429743 + 0.270025i 0.729487 0.683994i \(-0.239759\pi\)
−0.299745 + 0.954019i \(0.596902\pi\)
\(642\) 3.48292e11 + 7.94955e10i 2.05024 + 0.467953i
\(643\) 1.62029e10 1.29214e10i 0.0947869 0.0755900i −0.574950 0.818189i \(-0.694978\pi\)
0.669737 + 0.742599i \(0.266407\pi\)
\(644\) 1.32242e11 + 1.05460e11i 0.768825 + 0.613117i
\(645\) −3.20569e8 1.40450e9i −0.00185218 0.00811492i
\(646\) −4.21391e10 1.47451e10i −0.241966 0.0846676i
\(647\) 1.79999e10 + 3.73772e10i 0.102720 + 0.213299i 0.945994 0.324184i \(-0.105090\pi\)
−0.843275 + 0.537483i \(0.819375\pi\)
\(648\) −1.10456e11 + 6.94041e10i −0.626454 + 0.393627i
\(649\) 2.48673e11 8.70145e10i 1.40168 0.490470i
\(650\) −2.66740e11 2.66740e11i −1.49429 1.49429i
\(651\) −1.59285e11 + 3.30758e11i −0.886849 + 1.84156i
\(652\) 7.71729e9 + 6.84928e10i 0.0427046 + 0.379014i
\(653\) 1.41636e11 1.59586e10i 0.778973 0.0877692i 0.286481 0.958086i \(-0.407515\pi\)
0.492492 + 0.870317i \(0.336086\pi\)
\(654\) −1.16411e10 5.60608e9i −0.0636333 0.0306442i
\(655\) 3.38124e9 3.38124e9i 0.0183701 0.0183701i
\(656\) −3.16312e10 9.03969e10i −0.170805 0.488133i
\(657\) 2.65021e10 + 4.21778e10i 0.142239 + 0.226372i
\(658\) 2.95678e11 1.42391e11i 1.57730 0.759589i
\(659\) 9.95535e10 2.84508e11i 0.527855 1.50852i −0.303527 0.952823i \(-0.598164\pi\)
0.831382 0.555701i \(-0.187550\pi\)
\(660\) 4.89113e9 1.11637e9i 0.0257771 0.00588345i
\(661\) −1.68321e11 + 2.11068e11i −0.881725 + 1.10565i 0.111991 + 0.993709i \(0.464277\pi\)
−0.993715 + 0.111938i \(0.964294\pi\)
\(662\) 1.43693e11 + 1.80185e11i 0.748174 + 0.938181i
\(663\) 8.86768e10 3.88518e11i 0.458940 2.01075i
\(664\) 1.88319e10 2.99708e10i 0.0968773 0.154179i
\(665\) 1.96332e8 1.74249e9i 0.00100393 0.00891014i
\(666\) 4.30112e10i 0.218617i
\(667\) −2.15478e11 1.44000e11i −1.08868 0.727545i
\(668\) −6.59195e10 −0.331061
\(669\) −9.35954e10 1.05457e10i −0.467251 0.0526465i
\(670\) 6.33907e9 + 3.98310e9i 0.0314577 + 0.0197662i
\(671\) 1.29454e11 + 2.95471e10i 0.638597 + 0.145756i
\(672\) −2.65877e11 + 2.12030e11i −1.30378 + 1.03973i
\(673\) 1.43797e11 + 1.14675e11i 0.700956 + 0.558994i 0.907812 0.419378i \(-0.137752\pi\)
−0.206856 + 0.978371i \(0.566323\pi\)
\(674\) 6.62537e10 + 2.90276e11i 0.321048 + 1.40660i
\(675\) −1.23721e11 4.32917e10i −0.595973 0.208540i
\(676\) −9.15290e10 1.90062e11i −0.438300 0.910140i
\(677\) 2.93543e11 1.84445e11i 1.39739 0.878037i 0.398160 0.917316i \(-0.369649\pi\)
0.999228 + 0.0392785i \(0.0125059\pi\)
\(678\) 1.48207e11 5.18599e10i 0.701374 0.245422i
\(679\) 3.80064e11 + 3.80064e11i 1.78804 + 1.78804i
\(680\) −1.59962e9 + 3.32164e9i −0.00748137 + 0.0155352i
\(681\) −4.30898e9 3.82433e10i −0.0200349 0.177814i
\(682\) 4.36919e11 4.92290e10i 2.01959 0.227553i
\(683\) −2.00326e11 9.64719e10i −0.920565 0.443321i −0.0872922 0.996183i \(-0.527821\pi\)
−0.833273 + 0.552862i \(0.813536\pi\)
\(684\) 8.13872e9 8.13872e9i 0.0371819 0.0371819i
\(685\) −2.50966e9 7.17219e9i −0.0113986 0.0325754i
\(686\) −1.84609e10 2.93804e10i −0.0833600 0.132667i
\(687\) 1.09486e11 5.27257e10i 0.491509 0.236698i
\(688\) 2.14570e10 6.13207e10i 0.0957670 0.273686i
\(689\) −4.83968e11 + 1.10463e11i −2.14753 + 0.490161i
\(690\) −8.18342e9 + 1.02617e10i −0.0361026 + 0.0452712i
\(691\) −1.48257e11 1.85908e11i −0.650283 0.815429i 0.341963 0.939713i \(-0.388908\pi\)
−0.992247 + 0.124284i \(0.960337\pi\)
\(692\) −1.81640e10 + 7.95817e10i −0.0792113 + 0.347048i
\(693\) 1.20862e11 1.92351e11i 0.524033 0.833993i
\(694\) 1.93326e10 1.71582e11i 0.0833399 0.739662i
\(695\) 3.18867e9i 0.0136669i
\(696\) 1.22855e11 1.16132e11i 0.523546 0.494898i
\(697\) 9.64920e10 0.408846
\(698\) 2.54835e11 + 2.87130e10i 1.07359 + 0.120964i
\(699\) 1.20058e11 + 7.54372e10i 0.502899 + 0.315992i
\(700\) −1.75642e11 4.00890e10i −0.731535 0.166968i
\(701\) −1.41866e11 + 1.13135e11i −0.587500 + 0.468516i −0.871559 0.490291i \(-0.836890\pi\)
0.284059 + 0.958807i \(0.408319\pi\)
\(702\) −2.53790e11 2.02391e11i −1.04502 0.833378i
\(703\) 4.22087e9 + 1.84928e10i 0.0172815 + 0.0757150i
\(704\) −2.64413e10 9.25223e9i −0.107645 0.0376665i
\(705\) 3.77870e9 + 7.84655e9i 0.0152963 + 0.0317630i
\(706\) 1.59543e11 1.00247e11i 0.642183 0.403510i
\(707\) 3.93801e10 1.37797e10i 0.157615 0.0551520i
\(708\) 1.17659e11 + 1.17659e11i 0.468266 + 0.468266i
\(709\) 1.43868e11 2.98746e11i 0.569351 1.18227i −0.395254 0.918572i \(-0.629343\pi\)
0.964605 0.263698i \(-0.0849423\pi\)
\(710\) 7.49057e8 + 6.64807e9i 0.00294769 + 0.0261615i
\(711\) −1.95981e11 + 2.20818e10i −0.766896 + 0.0864084i
\(712\) 4.29614e10 + 2.06891e10i 0.167170 + 0.0805049i
\(713\) −2.78168e11 + 2.78168e11i −1.07634 + 1.07634i
\(714\) −1.83806e11 5.25287e11i −0.707240 2.02118i
\(715\) −9.97380e9 1.58732e10i −0.0381625 0.0607352i
\(716\) −1.27059e11 + 6.11885e10i −0.483453 + 0.232819i
\(717\) −1.17583e11 + 3.36032e11i −0.444904 + 1.27146i
\(718\) 1.45186e11 3.31377e10i 0.546294 0.124688i
\(719\) −1.92271e11 + 2.41100e11i −0.719446 + 0.902157i −0.998306 0.0581746i \(-0.981472\pi\)
0.278860 + 0.960332i \(0.410043\pi\)
\(720\) −2.96680e9 3.72025e9i −0.0110397 0.0138434i
\(721\) −8.49332e10 + 3.72117e11i −0.314294 + 1.37701i
\(722\) 1.70329e11 2.71077e11i 0.626815 0.997571i
\(723\) −5.64678e10 + 5.01165e11i −0.206656 + 1.83412i
\(724\) 1.13392e11i 0.412695i
\(725\) 2.73328e11 + 3.86076e10i 0.989311 + 0.139740i
\(726\) −4.21408e11 −1.51690
\(727\) 3.26332e10 + 3.67687e9i 0.116821 + 0.0131626i 0.170181 0.985413i \(-0.445565\pi\)
−0.0533603 + 0.998575i \(0.516993\pi\)
\(728\) 3.49091e11 + 2.19349e11i 1.24284 + 0.780925i
\(729\) −4.63526e10 1.05797e10i −0.164121 0.0374596i
\(730\) 4.48812e9 3.57916e9i 0.0158042 0.0126034i
\(731\) 5.11750e10 + 4.08107e10i 0.179221 + 0.142924i
\(732\) 1.86614e10 + 8.17611e10i 0.0649981 + 0.284775i
\(733\) −3.25063e10 1.13744e10i −0.112603 0.0394016i 0.273389 0.961903i \(-0.411855\pi\)
−0.385993 + 0.922502i \(0.626141\pi\)
\(734\) −2.03918e11 4.23440e11i −0.702541 1.45884i
\(735\) 9.64395e9 6.05970e9i 0.0330450 0.0207635i
\(736\) −3.43959e11 + 1.20356e11i −1.17218 + 0.410165i
\(737\) −3.02455e11 3.02455e11i −1.02516 1.02516i
\(738\) −3.15614e10 + 6.55380e10i −0.106397 + 0.220937i
\(739\) 4.97673e10 + 4.41697e11i 0.166866 + 1.48097i 0.746112 + 0.665820i \(0.231918\pi\)
−0.579246 + 0.815152i \(0.696653\pi\)
\(740\) −1.68447e9 + 1.89794e8i −0.00561742 + 0.000632931i
\(741\) −1.19369e11 5.74849e10i −0.395929 0.190669i
\(742\) −4.90195e11 + 4.90195e11i −1.61716 + 1.61716i
\(743\) 6.83563e10 + 1.95351e11i 0.224297 + 0.641004i 0.999952 + 0.00984635i \(0.00313424\pi\)
−0.775654 + 0.631158i \(0.782580\pi\)
\(744\) −1.36525e11 2.17278e11i −0.445575 0.709128i
\(745\) 1.31860e10 6.35004e9i 0.0428043 0.0206135i
\(746\) −8.47678e10 + 2.42252e11i −0.273701 + 0.782191i
\(747\) −4.48747e10 + 1.02423e10i −0.144118 + 0.0328940i
\(748\) −1.42122e11 + 1.78215e11i −0.453998 + 0.569295i
\(749\) −3.97502e11 4.98451e11i −1.26302 1.58378i
\(750\) 6.22432e9 2.72705e10i 0.0196719 0.0861884i
\(751\) −6.67874e10 + 1.06292e11i −0.209959 + 0.334148i −0.935057 0.354498i \(-0.884652\pi\)
0.725098 + 0.688646i \(0.241795\pi\)
\(752\) −4.39731e10 + 3.90272e11i −0.137504 + 1.22038i
\(753\) 6.81479e11i 2.11969i
\(754\) 6.07333e11 + 3.13811e11i 1.87906 + 0.970919i
\(755\) 1.60921e9 0.00495250
\(756\) −1.54054e11 1.73578e10i −0.471614 0.0531381i
\(757\) −4.00528e11 2.51668e11i −1.21969 0.766382i −0.240761 0.970584i \(-0.577397\pi\)
−0.978929 + 0.204203i \(0.934540\pi\)
\(758\) 7.84212e10 + 1.78991e10i 0.237551 + 0.0542195i
\(759\) 5.86288e11 4.67549e11i 1.76662 1.40883i
\(760\) 9.58292e8 + 7.64212e8i 0.00287239 + 0.00229066i
\(761\) −6.67227e10 2.92331e11i −0.198946 0.871639i −0.971566 0.236770i \(-0.923911\pi\)
0.772620 0.634869i \(-0.218946\pi\)
\(762\) 6.78790e11 + 2.37519e11i