Properties

Label 37.8.f.a.7.19
Level $37$
Weight $8$
Character 37.7
Analytic conductor $11.558$
Analytic rank $0$
Dimension $132$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 37 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 37.f (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.5582459429\)
Analytic rank: \(0\)
Dimension: \(132\)
Relative dimension: \(22\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 7.19
Character \(\chi\) \(=\) 37.7
Dual form 37.8.f.a.16.19

$q$-expansion

\(f(q)\) \(=\) \(q+(15.5384 - 5.65552i) q^{2} +(-16.3965 - 5.96785i) q^{3} +(111.404 - 93.4791i) q^{4} +(86.0271 + 487.884i) q^{5} -288.528 q^{6} +(270.212 + 1532.45i) q^{7} +(144.088 - 249.568i) q^{8} +(-1442.11 - 1210.07i) q^{9} +O(q^{10})\) \(q+(15.5384 - 5.65552i) q^{2} +(-16.3965 - 5.96785i) q^{3} +(111.404 - 93.4791i) q^{4} +(86.0271 + 487.884i) q^{5} -288.528 q^{6} +(270.212 + 1532.45i) q^{7} +(144.088 - 249.568i) q^{8} +(-1442.11 - 1210.07i) q^{9} +(4095.96 + 7094.42i) q^{10} +(2185.34 - 3785.12i) q^{11} +(-2384.51 + 867.890i) q^{12} +(6485.52 - 5442.00i) q^{13} +(12865.5 + 22283.7i) q^{14} +(1501.07 - 8513.00i) q^{15} +(-2404.95 + 13639.1i) q^{16} +(13390.7 + 11236.1i) q^{17} +(-29251.7 - 10646.7i) q^{18} +(-22692.7 - 8259.47i) q^{19} +(55190.7 + 46310.5i) q^{20} +(4714.89 - 26739.4i) q^{21} +(12549.9 - 71174.1i) q^{22} +(-7086.11 - 12273.5i) q^{23} +(-3851.93 + 3232.15i) q^{24} +(-157217. + 57222.1i) q^{25} +(69997.4 - 121239. i) q^{26} +(35504.3 + 61495.3i) q^{27} +(173355. + 145462. i) q^{28} +(-5320.03 + 9214.56i) q^{29} +(-24821.2 - 140768. i) q^{30} +228116. q^{31} +(46172.7 + 261858. i) q^{32} +(-58421.1 + 49021.1i) q^{33} +(271617. + 98860.4i) q^{34} +(-724412. + 263664. i) q^{35} -273773. q^{36} +(119121. - 284151. i) q^{37} -399320. q^{38} +(-138817. + 50525.3i) q^{39} +(134156. + 48828.7i) q^{40} +(513959. - 431263. i) q^{41} +(-77963.7 - 442154. i) q^{42} +428169. q^{43} +(-110374. - 625961. i) q^{44} +(466314. - 807680. i) q^{45} +(-179520. - 150635. i) q^{46} +(-523273. - 906336. i) q^{47} +(120829. - 209282. i) q^{48} +(-1.50151e6 + 546505. i) q^{49} +(-2.11928e6 + 1.77828e6i) q^{50} +(-152506. - 264147. i) q^{51} +(213800. - 1.21252e6i) q^{52} +(-110974. + 629363. i) q^{53} +(899470. + 754745. i) q^{54} +(2.03470e6 + 740570. i) q^{55} +(421385. + 153372. i) q^{56} +(322790. + 270853. i) q^{57} +(-30551.7 + 173267. i) q^{58} +(-112414. + 637532. i) q^{59} +(-628562. - 1.08870e6i) q^{60} +(-1.35694e6 + 1.13861e6i) q^{61} +(3.54457e6 - 1.29012e6i) q^{62} +(1.46470e6 - 2.53693e6i) q^{63} +(1.31202e6 + 2.27249e6i) q^{64} +(3.21299e6 + 2.69602e6i) q^{65} +(-630531. + 1.09211e6i) q^{66} +(-385777. - 2.18785e6i) q^{67} +2.54212e6 q^{68} +(42941.2 + 243532. i) q^{69} +(-9.76506e6 + 8.19386e6i) q^{70} +(316182. + 115081. i) q^{71} +(-509786. + 185547. i) q^{72} +3.23137e6 q^{73} +(243932. - 5.08896e6i) q^{74} +2.91930e6 q^{75} +(-3.30014e6 + 1.20115e6i) q^{76} +(6.39101e6 + 2.32614e6i) q^{77} +(-1.87125e6 + 1.57017e6i) q^{78} +(79877.6 + 453008. i) q^{79} -6.86121e6 q^{80} +(499776. + 2.83437e6i) q^{81} +(5.54710e6 - 9.60786e6i) q^{82} +(-5.85176e6 - 4.91021e6i) q^{83} +(-1.97432e6 - 3.41962e6i) q^{84} +(-4.32996e6 + 7.49972e6i) q^{85} +(6.65307e6 - 2.42152e6i) q^{86} +(142221. - 119338. i) q^{87} +(-629764. - 1.09078e6i) q^{88} +(756150. - 4.28834e6i) q^{89} +(2.67794e6 - 1.51873e7i) q^{90} +(1.00921e7 + 8.46824e6i) q^{91} +(-1.93674e6 - 704914. i) q^{92} +(-3.74032e6 - 1.36136e6i) q^{93} +(-1.32566e7 - 1.11236e7i) q^{94} +(2.07747e6 - 1.17819e7i) q^{95} +(805659. - 4.56912e6i) q^{96} +(2.17665e6 + 3.77008e6i) q^{97} +(-2.02403e7 + 1.69837e7i) q^{98} +(-7.73177e6 + 2.81413e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 132 q + 15 q^{2} + 33 q^{3} - 279 q^{4} + 576 q^{5} - 12 q^{6} - 597 q^{7} - 3750 q^{8} - 3243 q^{9} + O(q^{10}) \) \( 132 q + 15 q^{2} + 33 q^{3} - 279 q^{4} + 576 q^{5} - 12 q^{6} - 597 q^{7} - 3750 q^{8} - 3243 q^{9} - 6003 q^{10} - 15975 q^{11} - 4635 q^{12} - 15981 q^{13} - 13491 q^{14} + 38493 q^{15} - 74151 q^{16} + 37698 q^{17} - 20100 q^{18} - 66102 q^{19} - 176184 q^{20} - 142530 q^{21} + 132783 q^{22} + 140631 q^{23} - 38793 q^{24} - 544092 q^{25} - 423147 q^{26} + 130557 q^{27} + 603813 q^{28} + 22890 q^{29} - 319860 q^{30} - 1288044 q^{31} - 217866 q^{32} + 112344 q^{33} + 812019 q^{34} + 1479252 q^{35} + 8118132 q^{36} - 1664550 q^{37} + 305010 q^{38} - 1580340 q^{39} - 4681425 q^{40} - 2956593 q^{41} - 3553029 q^{42} - 1023528 q^{43} + 6409524 q^{44} + 1803336 q^{45} + 10219434 q^{46} - 2607204 q^{47} - 2984043 q^{48} - 6819531 q^{49} + 5724015 q^{50} - 1675833 q^{51} + 11768451 q^{52} + 2280177 q^{53} - 7803897 q^{54} - 3542196 q^{55} + 12168843 q^{56} - 85203 q^{57} - 12425487 q^{58} - 7014600 q^{59} + 2356788 q^{60} + 10840332 q^{61} + 6334368 q^{62} - 3331359 q^{63} - 26175624 q^{64} - 573195 q^{65} - 36720249 q^{66} + 6642918 q^{67} - 25277742 q^{68} - 1236438 q^{69} - 27401982 q^{70} + 20311041 q^{71} + 40093005 q^{72} + 38643780 q^{73} - 9531 q^{74} + 16639446 q^{75} + 5787405 q^{76} - 316971 q^{77} + 9363381 q^{78} + 17712534 q^{79} - 74410128 q^{80} - 10355109 q^{81} - 16702371 q^{82} - 31021176 q^{83} - 61626192 q^{84} + 23576445 q^{85} + 18579072 q^{86} + 104996631 q^{87} + 57279702 q^{88} - 13471320 q^{89} + 56306910 q^{90} - 2335911 q^{91} - 178133436 q^{92} + 24366258 q^{93} + 77086020 q^{94} - 26254407 q^{95} + 152523921 q^{96} + 14408415 q^{97} - 521205 q^{98} + 58375668 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 15.5384 5.65552i 1.37342 0.499882i 0.453240 0.891388i \(-0.350268\pi\)
0.920176 + 0.391506i \(0.128046\pi\)
\(3\) −16.3965 5.96785i −0.350613 0.127613i 0.160709 0.987002i \(-0.448622\pi\)
−0.511322 + 0.859389i \(0.670844\pi\)
\(4\) 111.404 93.4791i 0.870344 0.730305i
\(5\) 86.0271 + 487.884i 0.307780 + 1.74551i 0.610123 + 0.792307i \(0.291120\pi\)
−0.302343 + 0.953199i \(0.597769\pi\)
\(6\) −288.528 −0.545328
\(7\) 270.212 + 1532.45i 0.297757 + 1.68866i 0.655781 + 0.754951i \(0.272339\pi\)
−0.358024 + 0.933712i \(0.616550\pi\)
\(8\) 144.088 249.568i 0.0994978 0.172335i
\(9\) −1442.11 1210.07i −0.659400 0.553302i
\(10\) 4095.96 + 7094.42i 1.29526 + 2.24345i
\(11\) 2185.34 3785.12i 0.495045 0.857443i −0.504939 0.863155i \(-0.668485\pi\)
0.999984 + 0.00571200i \(0.00181820\pi\)
\(12\) −2384.51 + 867.890i −0.398350 + 0.144987i
\(13\) 6485.52 5442.00i 0.818734 0.687000i −0.133941 0.990989i \(-0.542763\pi\)
0.952675 + 0.303990i \(0.0983189\pi\)
\(14\) 12865.5 + 22283.7i 1.25308 + 2.17039i
\(15\) 1501.07 8513.00i 0.114837 0.651273i
\(16\) −2404.95 + 13639.1i −0.146786 + 0.832467i
\(17\) 13390.7 + 11236.1i 0.661047 + 0.554684i 0.910400 0.413729i \(-0.135774\pi\)
−0.249354 + 0.968412i \(0.580218\pi\)
\(18\) −29251.7 10646.7i −1.18222 0.430292i
\(19\) −22692.7 8259.47i −0.759012 0.276258i −0.0666190 0.997778i \(-0.521221\pi\)
−0.692393 + 0.721521i \(0.743443\pi\)
\(20\) 55190.7 + 46310.5i 1.54263 + 1.29442i
\(21\) 4714.89 26739.4i 0.111097 0.630064i
\(22\) 12549.9 71174.1i 0.251282 1.42509i
\(23\) −7086.11 12273.5i −0.121440 0.210340i 0.798896 0.601469i \(-0.205418\pi\)
−0.920336 + 0.391130i \(0.872084\pi\)
\(24\) −3851.93 + 3232.15i −0.0568773 + 0.0477258i
\(25\) −157217. + 57222.1i −2.01237 + 0.732443i
\(26\) 69997.4 121239.i 0.781043 1.35281i
\(27\) 35504.3 + 61495.3i 0.347143 + 0.601269i
\(28\) 173355. + 145462.i 1.49239 + 1.25226i
\(29\) −5320.03 + 9214.56i −0.0405062 + 0.0701587i −0.885568 0.464510i \(-0.846230\pi\)
0.845062 + 0.534669i \(0.179564\pi\)
\(30\) −24821.2 140768.i −0.167841 0.951874i
\(31\) 228116. 1.37528 0.687639 0.726053i \(-0.258647\pi\)
0.687639 + 0.726053i \(0.258647\pi\)
\(32\) 46172.7 + 261858.i 0.249092 + 1.41267i
\(33\) −58421.1 + 49021.1i −0.282990 + 0.237457i
\(34\) 271617. + 98860.4i 1.18517 + 0.431366i
\(35\) −724412. + 263664.i −2.85593 + 1.03947i
\(36\) −273773. −0.977984
\(37\) 119121. 284151.i 0.386619 0.922239i
\(38\) −399320. −1.18054
\(39\) −138817. + 50525.3i −0.374728 + 0.136390i
\(40\) 134156. + 48828.7i 0.331436 + 0.120633i
\(41\) 513959. 431263.i 1.16462 0.977235i 0.164664 0.986350i \(-0.447346\pi\)
0.999958 + 0.00911506i \(0.00290145\pi\)
\(42\) −77963.7 442154.i −0.162375 0.920876i
\(43\) 428169. 0.821250 0.410625 0.911804i \(-0.365311\pi\)
0.410625 + 0.911804i \(0.365311\pi\)
\(44\) −110374. 625961.i −0.195336 1.10780i
\(45\) 466314. 807680.i 0.762843 1.32128i
\(46\) −179520. 150635.i −0.271932 0.228178i
\(47\) −523273. 906336.i −0.735167 1.27335i −0.954650 0.297730i \(-0.903770\pi\)
0.219483 0.975616i \(-0.429563\pi\)
\(48\) 120829. 209282.i 0.157698 0.273142i
\(49\) −1.50151e6 + 546505.i −1.82323 + 0.663602i
\(50\) −2.11928e6 + 1.77828e6i −2.39769 + 2.01190i
\(51\) −152506. 264147.i −0.160987 0.278837i
\(52\) 213800. 1.21252e6i 0.210861 1.19585i
\(53\) −110974. + 629363.i −0.102389 + 0.580679i 0.889842 + 0.456269i \(0.150815\pi\)
−0.992231 + 0.124409i \(0.960296\pi\)
\(54\) 899470. + 754745.i 0.777335 + 0.652262i
\(55\) 2.03470e6 + 740570.i 1.64904 + 0.600201i
\(56\) 421385. + 153372.i 0.320642 + 0.116704i
\(57\) 322790. + 270853.i 0.230865 + 0.193719i
\(58\) −30551.7 + 173267.i −0.0205607 + 0.116605i
\(59\) −112414. + 637532.i −0.0712589 + 0.404129i 0.928225 + 0.372018i \(0.121334\pi\)
−0.999484 + 0.0321109i \(0.989777\pi\)
\(60\) −628562. 1.08870e6i −0.375680 0.650698i
\(61\) −1.35694e6 + 1.13861e6i −0.765431 + 0.642273i −0.939534 0.342455i \(-0.888742\pi\)
0.174103 + 0.984727i \(0.444297\pi\)
\(62\) 3.54457e6 1.29012e6i 1.88883 0.687477i
\(63\) 1.46470e6 2.53693e6i 0.738001 1.27825i
\(64\) 1.31202e6 + 2.27249e6i 0.625622 + 1.08361i
\(65\) 3.21299e6 + 2.69602e6i 1.45115 + 1.21766i
\(66\) −630531. + 1.09211e6i −0.269962 + 0.467588i
\(67\) −385777. 2.18785e6i −0.156702 0.888702i −0.957213 0.289384i \(-0.906550\pi\)
0.800511 0.599318i \(-0.204561\pi\)
\(68\) 2.54212e6 0.980426
\(69\) 42941.2 + 243532.i 0.0157363 + 0.0892450i
\(70\) −9.76506e6 + 8.19386e6i −3.40276 + 2.85526i
\(71\) 316182. + 115081.i 0.104841 + 0.0381592i 0.393908 0.919150i \(-0.371123\pi\)
−0.289067 + 0.957309i \(0.593345\pi\)
\(72\) −509786. + 185547.i −0.160962 + 0.0585855i
\(73\) 3.23137e6 0.972203 0.486101 0.873902i \(-0.338419\pi\)
0.486101 + 0.873902i \(0.338419\pi\)
\(74\) 243932. 5.08896e6i 0.0699774 1.45988i
\(75\) 2.91930e6 0.799032
\(76\) −3.30014e6 + 1.20115e6i −0.862354 + 0.313871i
\(77\) 6.39101e6 + 2.32614e6i 1.59534 + 0.580655i
\(78\) −1.87125e6 + 1.57017e6i −0.446479 + 0.374640i
\(79\) 79877.6 + 453008.i 0.0182276 + 0.103374i 0.992564 0.121722i \(-0.0388416\pi\)
−0.974337 + 0.225096i \(0.927730\pi\)
\(80\) −6.86121e6 −1.49825
\(81\) 499776. + 2.83437e6i 0.104491 + 0.592596i
\(82\) 5.54710e6 9.60786e6i 1.11101 1.92432i
\(83\) −5.85176e6 4.91021e6i −1.12334 0.942598i −0.124576 0.992210i \(-0.539757\pi\)
−0.998769 + 0.0496125i \(0.984201\pi\)
\(84\) −1.97432e6 3.41962e6i −0.363446 0.629507i
\(85\) −4.32996e6 + 7.49972e6i −0.764748 + 1.32458i
\(86\) 6.65307e6 2.42152e6i 1.12792 0.410528i
\(87\) 142221. 119338.i 0.0231551 0.0194294i
\(88\) −629764. 1.09078e6i −0.0985118 0.170627i
\(89\) 756150. 4.28834e6i 0.113695 0.644799i −0.873692 0.486479i \(-0.838281\pi\)
0.987388 0.158320i \(-0.0506078\pi\)
\(90\) 2.67794e6 1.51873e7i 0.387214 2.19600i
\(91\) 1.00921e7 + 8.46824e6i 1.40389 + 1.17801i
\(92\) −1.93674e6 704914.i −0.259306 0.0943798i
\(93\) −3.74032e6 1.36136e6i −0.482190 0.175503i
\(94\) −1.32566e7 1.11236e7i −1.64621 1.38134i
\(95\) 2.07747e6 1.17819e7i 0.248601 1.40989i
\(96\) 805659. 4.56912e6i 0.0929398 0.527088i
\(97\) 2.17665e6 + 3.77008e6i 0.242152 + 0.419420i 0.961327 0.275409i \(-0.0888133\pi\)
−0.719175 + 0.694829i \(0.755480\pi\)
\(98\) −2.02403e7 + 1.69837e7i −2.17233 + 1.82280i
\(99\) −7.73177e6 + 2.81413e6i −0.800858 + 0.291489i
\(100\) −1.21655e7 + 2.10712e7i −1.21655 + 2.10712i
\(101\) 1.91685e6 + 3.32008e6i 0.185124 + 0.320644i 0.943618 0.331035i \(-0.107398\pi\)
−0.758494 + 0.651680i \(0.774065\pi\)
\(102\) −3.86359e6 3.24193e6i −0.360487 0.302485i
\(103\) 4.25945e6 7.37759e6i 0.384082 0.665249i −0.607560 0.794274i \(-0.707851\pi\)
0.991641 + 0.129025i \(0.0411847\pi\)
\(104\) −423662. 2.40271e6i −0.0369320 0.209452i
\(105\) 1.34514e7 1.13397
\(106\) 1.83502e6 + 1.04069e7i 0.149648 + 0.848696i
\(107\) 1.08356e7 9.09211e6i 0.855082 0.717499i −0.105821 0.994385i \(-0.533747\pi\)
0.960903 + 0.276886i \(0.0893025\pi\)
\(108\) 9.70385e6 + 3.53191e6i 0.741243 + 0.269791i
\(109\) −4.85108e6 + 1.76565e6i −0.358794 + 0.130590i −0.515127 0.857114i \(-0.672255\pi\)
0.156332 + 0.987704i \(0.450033\pi\)
\(110\) 3.58043e7 2.56484
\(111\) −3.64895e6 + 3.94820e6i −0.253243 + 0.274011i
\(112\) −2.15511e7 −1.44946
\(113\) 7.09452e6 2.58219e6i 0.462539 0.168350i −0.100231 0.994964i \(-0.531958\pi\)
0.562770 + 0.826614i \(0.309736\pi\)
\(114\) 6.54747e6 + 2.38308e6i 0.413911 + 0.150651i
\(115\) 5.37845e6 4.51305e6i 0.329772 0.276712i
\(116\) 268696. + 1.52385e6i 0.0159830 + 0.0906440i
\(117\) −1.59380e7 −0.919992
\(118\) 1.85884e6 + 1.05420e7i 0.104149 + 0.590658i
\(119\) −1.36005e7 + 2.35567e7i −0.739843 + 1.28145i
\(120\) −1.90829e6 1.60124e6i −0.100811 0.0845907i
\(121\) 192157. + 332825.i 0.00986069 + 0.0170792i
\(122\) −1.46453e7 + 2.53664e7i −0.730194 + 1.26473i
\(123\) −1.10009e7 + 4.00399e6i −0.533039 + 0.194010i
\(124\) 2.54131e7 2.13241e7i 1.19696 1.00437i
\(125\) −2.20907e7 3.82622e7i −1.01163 1.75220i
\(126\) 8.41143e6 4.77036e7i 0.374605 2.12449i
\(127\) 2.69309e6 1.52733e7i 0.116664 0.661635i −0.869249 0.494375i \(-0.835397\pi\)
0.985913 0.167260i \(-0.0534919\pi\)
\(128\) 7.16668e6 + 6.01356e6i 0.302053 + 0.253453i
\(129\) −7.02048e6 2.55525e6i −0.287941 0.104802i
\(130\) 6.51722e7 + 2.37208e7i 2.60172 + 0.946949i
\(131\) 2.96254e7 + 2.48586e7i 1.15137 + 0.966113i 0.999751 0.0223267i \(-0.00710740\pi\)
0.151617 + 0.988439i \(0.451552\pi\)
\(132\) −1.92589e6 + 1.09223e7i −0.0728826 + 0.413338i
\(133\) 6.52537e6 3.70072e7i 0.240505 1.36397i
\(134\) −1.83678e7 3.18140e7i −0.659463 1.14222i
\(135\) −2.69482e7 + 2.26123e7i −0.942675 + 0.790999i
\(136\) 4.73362e6 1.72290e6i 0.161364 0.0587318i
\(137\) −2.21247e7 + 3.83211e7i −0.735114 + 1.27326i 0.219559 + 0.975599i \(0.429538\pi\)
−0.954673 + 0.297656i \(0.903795\pi\)
\(138\) 2.04454e6 + 3.54124e6i 0.0662245 + 0.114704i
\(139\) 2.41965e6 + 2.03033e6i 0.0764190 + 0.0641232i 0.680197 0.733029i \(-0.261894\pi\)
−0.603778 + 0.797153i \(0.706339\pi\)
\(140\) −5.60553e7 + 9.70906e7i −1.72651 + 2.99040i
\(141\) 3.17099e6 + 1.79836e7i 0.0952638 + 0.540268i
\(142\) 5.56381e6 0.163066
\(143\) −6.42555e6 3.64411e7i −0.183753 1.04211i
\(144\) 1.99725e7 1.67590e7i 0.557397 0.467712i
\(145\) −4.95330e6 1.80285e6i −0.134929 0.0491103i
\(146\) 5.02104e7 1.82751e7i 1.33524 0.485987i
\(147\) 2.78810e7 0.723932
\(148\) −1.32916e7 4.27909e7i −0.337025 1.08502i
\(149\) −6.28499e7 −1.55651 −0.778256 0.627947i \(-0.783895\pi\)
−0.778256 + 0.627947i \(0.783895\pi\)
\(150\) 4.53613e7 1.65102e7i 1.09740 0.399422i
\(151\) −1.41838e6 516249.i −0.0335254 0.0122022i 0.325203 0.945644i \(-0.394567\pi\)
−0.358728 + 0.933442i \(0.616790\pi\)
\(152\) −5.33105e6 + 4.47328e6i −0.123129 + 0.103317i
\(153\) −5.71430e6 3.24074e7i −0.128986 0.731517i
\(154\) 1.12462e8 2.48132
\(155\) 1.96242e7 + 1.11294e8i 0.423283 + 2.40055i
\(156\) −1.07417e7 + 1.86052e7i −0.226536 + 0.392372i
\(157\) −3.37635e7 2.83309e7i −0.696303 0.584267i 0.224416 0.974493i \(-0.427952\pi\)
−0.920719 + 0.390226i \(0.872397\pi\)
\(158\) 3.80317e6 + 6.58729e6i 0.0767090 + 0.132864i
\(159\) 5.57553e6 9.65710e6i 0.110001 0.190527i
\(160\) −1.23784e8 + 4.50538e7i −2.38916 + 0.869584i
\(161\) 1.68938e7 1.41756e7i 0.319033 0.267701i
\(162\) 2.37956e7 + 4.12151e7i 0.439738 + 0.761648i
\(163\) −969048. + 5.49574e6i −0.0175262 + 0.0993962i −0.992316 0.123729i \(-0.960515\pi\)
0.974790 + 0.223125i \(0.0716258\pi\)
\(164\) 1.69431e7 9.60889e7i 0.299943 1.70106i
\(165\) −2.89424e7 2.42855e7i −0.501580 0.420876i
\(166\) −1.18697e8 4.32021e7i −2.01401 0.733038i
\(167\) 5.28872e7 + 1.92494e7i 0.878704 + 0.319822i 0.741687 0.670746i \(-0.234026\pi\)
0.137018 + 0.990569i \(0.456248\pi\)
\(168\) −5.99395e6 5.02952e6i −0.0975284 0.0818360i
\(169\) 1.55046e6 8.79309e6i 0.0247091 0.140132i
\(170\) −2.48660e7 + 1.41022e8i −0.388181 + 2.20148i
\(171\) 2.27308e7 + 3.93708e7i 0.347638 + 0.602127i
\(172\) 4.76997e7 4.00248e7i 0.714770 0.599763i
\(173\) −7.88885e7 + 2.87131e7i −1.15838 + 0.421617i −0.848520 0.529164i \(-0.822506\pi\)
−0.309864 + 0.950781i \(0.600284\pi\)
\(174\) 1.53498e6 2.65866e6i 0.0220892 0.0382595i
\(175\) −1.30172e8 2.25464e8i −1.83605 3.18013i
\(176\) 4.63702e7 + 3.89092e7i 0.641127 + 0.537970i
\(177\) 5.64790e6 9.78245e6i 0.0765562 0.132599i
\(178\) −1.25034e7 7.09105e7i −0.166173 0.942411i
\(179\) 2.36493e7 0.308200 0.154100 0.988055i \(-0.450752\pi\)
0.154100 + 0.988055i \(0.450752\pi\)
\(180\) −2.35519e7 1.33569e8i −0.301004 1.70708i
\(181\) −5.85318e7 + 4.91141e7i −0.733698 + 0.615646i −0.931137 0.364670i \(-0.881182\pi\)
0.197439 + 0.980315i \(0.436738\pi\)
\(182\) 2.04707e8 + 7.45072e7i 2.51700 + 0.916112i
\(183\) 2.90441e7 1.05712e7i 0.350332 0.127510i
\(184\) −4.08410e6 −0.0483319
\(185\) 1.48881e8 + 3.36726e7i 1.72877 + 0.390999i
\(186\) −6.58178e7 −0.749977
\(187\) 7.17934e7 2.61306e7i 0.802858 0.292216i
\(188\) −1.43018e8 5.20543e7i −1.56978 0.571353i
\(189\) −8.46448e7 + 7.10254e7i −0.911977 + 0.765239i
\(190\) −3.43524e7 1.94822e8i −0.363345 2.06063i
\(191\) −5.43901e7 −0.564811 −0.282405 0.959295i \(-0.591132\pi\)
−0.282405 + 0.959295i \(0.591132\pi\)
\(192\) −7.95076e6 4.50910e7i −0.0810689 0.459765i
\(193\) 3.98899e7 6.90913e7i 0.399404 0.691788i −0.594249 0.804281i \(-0.702551\pi\)
0.993652 + 0.112494i \(0.0358838\pi\)
\(194\) 5.51435e7 + 4.62709e7i 0.542236 + 0.454990i
\(195\) −3.65925e7 6.33800e7i −0.353403 0.612113i
\(196\) −1.16187e8 + 2.01243e8i −1.10221 + 1.90908i
\(197\) −2.42547e7 + 8.82798e6i −0.226029 + 0.0822677i −0.452552 0.891738i \(-0.649486\pi\)
0.226523 + 0.974006i \(0.427264\pi\)
\(198\) −1.04224e8 + 8.74544e7i −0.954201 + 0.800670i
\(199\) −2.02495e7 3.50731e7i −0.182149 0.315492i 0.760463 0.649381i \(-0.224972\pi\)
−0.942612 + 0.333890i \(0.891639\pi\)
\(200\) −8.37223e6 + 4.74813e7i −0.0740007 + 0.419679i
\(201\) −6.73136e6 + 3.81754e7i −0.0584678 + 0.331587i
\(202\) 4.85616e7 + 4.07480e7i 0.414537 + 0.347838i
\(203\) −1.55584e7 5.66279e6i −0.130535 0.0475110i
\(204\) −4.16820e7 1.51710e7i −0.343750 0.125115i
\(205\) 2.54621e8 + 2.13652e8i 2.06422 + 1.73208i
\(206\) 2.44611e7 1.38726e8i 0.194958 1.10566i
\(207\) −4.63289e6 + 2.62744e7i −0.0363041 + 0.205891i
\(208\) 5.86268e7 + 1.01545e8i 0.451726 + 0.782412i
\(209\) −8.08544e7 + 6.78449e7i −0.612620 + 0.514050i
\(210\) 2.09013e8 7.60744e7i 1.55742 0.566854i
\(211\) 9.79102e7 1.69585e8i 0.717529 1.24280i −0.244447 0.969663i \(-0.578607\pi\)
0.961976 0.273134i \(-0.0880601\pi\)
\(212\) 4.64694e7 + 8.04873e7i 0.334959 + 0.580165i
\(213\) −4.49750e6 3.77385e6i −0.0318891 0.0267582i
\(214\) 1.16947e8 2.02558e8i 0.815718 1.41286i
\(215\) 3.68341e7 + 2.08897e8i 0.252764 + 1.43350i
\(216\) 2.04630e7 0.138160
\(217\) 6.16398e7 + 3.49577e8i 0.409498 + 2.32238i
\(218\) −6.53924e7 + 5.48708e7i −0.427494 + 0.358710i
\(219\) −5.29833e7 1.92843e7i −0.340867 0.124065i
\(220\) 2.95901e8 1.07699e8i 1.87356 0.681920i
\(221\) 1.47993e8 0.922289
\(222\) −3.43698e7 + 8.19855e7i −0.210834 + 0.502923i
\(223\) −2.46654e8 −1.48944 −0.744718 0.667379i \(-0.767416\pi\)
−0.744718 + 0.667379i \(0.767416\pi\)
\(224\) −3.88808e8 + 1.41515e8i −2.31136 + 0.841266i
\(225\) 2.95966e8 + 1.07723e8i 1.73222 + 0.630477i
\(226\) 9.56339e7 8.02464e7i 0.551103 0.462430i
\(227\) 3.20230e7 + 1.81612e8i 0.181707 + 1.03051i 0.930114 + 0.367272i \(0.119708\pi\)
−0.748407 + 0.663240i \(0.769181\pi\)
\(228\) 6.12792e7 0.342406
\(229\) −3.30625e7 1.87507e8i −0.181933 1.03179i −0.929833 0.367982i \(-0.880049\pi\)
0.747900 0.663812i \(-0.231062\pi\)
\(230\) 5.80489e7 1.00544e8i 0.314591 0.544888i
\(231\) −9.09084e7 7.62812e7i −0.485246 0.407170i
\(232\) 1.53311e6 + 2.65542e6i 0.00806055 + 0.0139613i
\(233\) −1.13584e8 + 1.96734e8i −0.588265 + 1.01891i 0.406194 + 0.913787i \(0.366856\pi\)
−0.994460 + 0.105119i \(0.966478\pi\)
\(234\) −2.47652e8 + 9.01379e7i −1.26353 + 0.459888i
\(235\) 3.97171e8 3.33266e8i 1.99636 1.67515i
\(236\) 4.70725e7 + 8.15320e7i 0.233118 + 0.403772i
\(237\) 1.39377e6 7.90447e6i 0.00680099 0.0385703i
\(238\) −7.81044e7 + 4.42952e8i −0.375540 + 2.12979i
\(239\) −6.57459e7 5.51673e7i −0.311513 0.261390i 0.473604 0.880738i \(-0.342953\pi\)
−0.785117 + 0.619348i \(0.787397\pi\)
\(240\) 1.12500e8 + 4.09467e7i 0.525307 + 0.191196i
\(241\) −2.49442e8 9.07895e7i −1.14792 0.417807i −0.303150 0.952943i \(-0.598038\pi\)
−0.844766 + 0.535136i \(0.820260\pi\)
\(242\) 4.86812e6 + 4.08484e6i 0.0220804 + 0.0185277i
\(243\) 3.56874e7 2.02393e8i 0.159548 0.904844i
\(244\) −4.47325e7 + 2.53691e8i −0.197133 + 1.11800i
\(245\) −3.95801e8 6.85548e8i −1.71948 2.97822i
\(246\) −1.48291e8 + 1.24431e8i −0.635102 + 0.532914i
\(247\) −1.92122e8 + 6.99266e7i −0.811218 + 0.295259i
\(248\) 3.28689e7 5.69305e7i 0.136837 0.237009i
\(249\) 6.66451e7 + 1.15433e8i 0.273571 + 0.473840i
\(250\) −5.59647e8 4.69599e8i −2.26529 1.90080i
\(251\) 1.24400e8 2.15467e8i 0.496548 0.860047i −0.503444 0.864028i \(-0.667934\pi\)
0.999992 + 0.00398101i \(0.00126720\pi\)
\(252\) −7.39768e7 4.19543e8i −0.291202 1.65149i
\(253\) −6.19423e7 −0.240472
\(254\) −4.45319e7 2.52553e8i −0.170511 0.967018i
\(255\) 1.15754e8 9.71288e7i 0.437163 0.366824i
\(256\) −1.70254e8 6.19673e7i −0.634244 0.230846i
\(257\) −1.82221e8 + 6.63229e7i −0.669625 + 0.243724i −0.654386 0.756160i \(-0.727073\pi\)
−0.0152386 + 0.999884i \(0.504851\pi\)
\(258\) −1.23538e8 −0.447851
\(259\) 4.67636e8 + 1.05766e8i 1.67247 + 0.378266i
\(260\) 6.09962e8 2.15227
\(261\) 1.88223e7 6.85077e6i 0.0655287 0.0238505i
\(262\) 6.00920e8 + 2.18717e8i 2.06425 + 0.751325i
\(263\) 3.39830e8 2.85151e8i 1.15191 0.966564i 0.152143 0.988358i \(-0.451383\pi\)
0.999762 + 0.0217948i \(0.00693806\pi\)
\(264\) 3.81631e6 + 2.16434e7i 0.0127653 + 0.0723955i
\(265\) −3.16603e8 −1.04509
\(266\) −1.07901e8 6.11938e8i −0.351512 1.99353i
\(267\) −3.79904e7 + 6.58014e7i −0.122148 + 0.211566i
\(268\) −2.47495e8 2.07673e8i −0.785408 0.659036i
\(269\) −2.85662e7 4.94782e7i −0.0894788 0.154982i 0.817812 0.575485i \(-0.195187\pi\)
−0.907291 + 0.420503i \(0.861853\pi\)
\(270\) −2.90849e8 + 5.03765e8i −0.899279 + 1.55760i
\(271\) 4.46856e7 1.62642e7i 0.136388 0.0496410i −0.272925 0.962035i \(-0.587991\pi\)
0.409312 + 0.912394i \(0.365769\pi\)
\(272\) −1.85455e8 + 1.55615e8i −0.558789 + 0.468880i
\(273\) −1.14937e8 1.99078e8i −0.341895 0.592179i
\(274\) −1.27057e8 + 7.20575e8i −0.373140 + 2.11618i
\(275\) −1.26979e8 + 7.20133e8i −0.368186 + 2.08809i
\(276\) 2.75489e7 + 2.31163e7i 0.0788720 + 0.0661815i
\(277\) 1.03178e8 + 3.75536e7i 0.291680 + 0.106163i 0.483716 0.875225i \(-0.339287\pi\)
−0.192036 + 0.981388i \(0.561509\pi\)
\(278\) 4.90802e7 + 1.78637e7i 0.137009 + 0.0498673i
\(279\) −3.28968e8 2.76037e8i −0.906858 0.760944i
\(280\) −3.85770e7 + 2.18781e8i −0.105021 + 0.595602i
\(281\) −7.45208e7 + 4.22628e8i −0.200357 + 1.13628i 0.704223 + 0.709979i \(0.251296\pi\)
−0.904580 + 0.426304i \(0.859815\pi\)
\(282\) 1.50979e8 + 2.61503e8i 0.400907 + 0.694392i
\(283\) −4.28659e7 + 3.59687e7i −0.112424 + 0.0943349i −0.697267 0.716812i \(-0.745601\pi\)
0.584843 + 0.811147i \(0.301156\pi\)
\(284\) 4.59816e7 1.67359e7i 0.119116 0.0433546i
\(285\) −1.04376e8 + 1.80785e8i −0.267082 + 0.462599i
\(286\) −3.05936e8 5.29897e8i −0.773303 1.33940i
\(287\) 7.99767e8 + 6.71084e8i 1.99699 + 1.67568i
\(288\) 2.50281e8 4.33500e8i 0.617383 1.06934i
\(289\) −1.81944e7 1.03185e8i −0.0443399 0.251464i
\(290\) −8.71626e7 −0.209864
\(291\) −1.31903e7 7.48061e7i −0.0313784 0.177956i
\(292\) 3.59988e8 3.02066e8i 0.846151 0.710005i
\(293\) 4.69358e8 + 1.70832e8i 1.09010 + 0.396765i 0.823659 0.567085i \(-0.191929\pi\)
0.266444 + 0.963850i \(0.414151\pi\)
\(294\) 4.33227e8 1.57682e8i 0.994260 0.361881i
\(295\) −3.20712e8 −0.727342
\(296\) −5.37511e7 7.06717e7i −0.120467 0.158389i
\(297\) 3.10356e8 0.687405
\(298\) −9.76588e8 + 3.55449e8i −2.13774 + 0.778073i
\(299\) −1.12749e8 4.10374e7i −0.243930 0.0887833i
\(300\) 3.25222e8 2.72893e8i 0.695432 0.583537i
\(301\) 1.15696e8 + 6.56147e8i 0.244533 + 1.38681i
\(302\) −2.49591e7 −0.0521440
\(303\) −1.16159e7 6.58772e7i −0.0239886 0.136046i
\(304\) 1.67227e8 2.89645e8i 0.341388 0.591302i
\(305\) −6.72242e8 5.64078e8i −1.35668 1.13839i
\(306\) −2.72072e8 4.71243e8i −0.542824 0.940199i
\(307\) 2.37985e8 4.12202e8i 0.469424 0.813066i −0.529965 0.848020i \(-0.677795\pi\)
0.999389 + 0.0349532i \(0.0111282\pi\)
\(308\) 9.29430e8 3.38285e8i 1.81255 0.659713i
\(309\) −1.13869e8 + 9.55471e7i −0.219558 + 0.184231i
\(310\) 9.34356e8 + 1.61835e9i 1.78134 + 3.08537i
\(311\) −3.91542e7 + 2.22055e8i −0.0738104 + 0.418599i 0.925405 + 0.378981i \(0.123725\pi\)
−0.999215 + 0.0396185i \(0.987386\pi\)
\(312\) −7.39240e6 + 4.19244e7i −0.0137799 + 0.0781494i
\(313\) −6.76389e8 5.67558e8i −1.24678 1.04618i −0.996962 0.0778844i \(-0.975183\pi\)
−0.249822 0.968292i \(-0.580372\pi\)
\(314\) −6.84857e8 2.49268e8i −1.24838 0.454373i
\(315\) 1.36373e9 + 4.96358e8i 2.45834 + 0.894764i
\(316\) 5.12455e7 + 4.30001e7i 0.0913589 + 0.0766592i
\(317\) 7.55019e7 4.28193e8i 0.133122 0.754974i −0.843027 0.537872i \(-0.819228\pi\)
0.976149 0.217102i \(-0.0696604\pi\)
\(318\) 3.20190e7 1.81589e8i 0.0558358 0.316660i
\(319\) 2.32522e7 + 4.02739e7i 0.0401047 + 0.0694635i
\(320\) −9.95843e8 + 8.35612e8i −1.69889 + 1.42554i
\(321\) −2.31926e8 + 8.44141e7i −0.391365 + 0.142445i
\(322\) 1.82332e8 3.15809e8i 0.304346 0.527144i
\(323\) −2.11067e8 3.65578e8i −0.348506 0.603631i
\(324\) 3.20631e8 + 2.69041e8i 0.523719 + 0.439452i
\(325\) −7.08228e8 + 1.22669e9i −1.14441 + 1.98217i
\(326\) 1.60238e7 + 9.08757e7i 0.0256156 + 0.145273i
\(327\) 9.00780e7 0.142463
\(328\) −3.35740e7 1.90408e8i −0.0525346 0.297938i
\(329\) 1.24752e9 1.04679e9i 1.93135 1.62060i
\(330\) −5.87067e8 2.13675e8i −0.899267 0.327306i
\(331\) 3.61690e8 1.31645e8i 0.548200 0.199529i −0.0530465 0.998592i \(-0.516893\pi\)
0.601247 + 0.799064i \(0.294671\pi\)
\(332\) −1.11091e9 −1.66608
\(333\) −5.15629e8 + 2.65632e8i −0.765214 + 0.394208i
\(334\) 9.30649e8 1.36670
\(335\) 1.03423e9 3.76429e8i 1.50300 0.547049i
\(336\) 3.53364e8 + 1.28614e8i 0.508200 + 0.184970i
\(337\) −7.31672e8 + 6.13945e8i −1.04139 + 0.873826i −0.992162 0.124962i \(-0.960119\pi\)
−0.0492240 + 0.998788i \(0.515675\pi\)
\(338\) −2.56379e7 1.45399e8i −0.0361138 0.204812i
\(339\) −1.31736e8 −0.183656
\(340\) 2.18691e8 + 1.24026e9i 0.301755 + 1.71134i
\(341\) 4.98512e8 8.63447e8i 0.680824 1.17922i
\(342\) 5.75863e8 + 4.83207e8i 0.778445 + 0.653193i
\(343\) −6.02464e8 1.04350e9i −0.806124 1.39625i
\(344\) 6.16940e7 1.06857e8i 0.0817125 0.141530i
\(345\) −1.15121e8 + 4.19007e7i −0.150934 + 0.0549356i
\(346\) −1.06342e9 + 8.92312e8i −1.38018 + 1.15811i
\(347\) 3.96333e8 + 6.86469e8i 0.509222 + 0.881998i 0.999943 + 0.0106813i \(0.00340002\pi\)
−0.490721 + 0.871317i \(0.663267\pi\)
\(348\) 4.68843e6 2.65894e7i 0.00596348 0.0338206i
\(349\) 7.22851e7 4.09949e8i 0.0910248 0.516227i −0.904868 0.425691i \(-0.860031\pi\)
0.995893 0.0905359i \(-0.0288580\pi\)
\(350\) −3.29778e9 2.76717e9i −4.11135 3.44983i
\(351\) 5.64921e8 + 2.05615e8i 0.697289 + 0.253793i
\(352\) 1.09207e9 + 3.97480e8i 1.33460 + 0.485754i
\(353\) 7.32139e8 + 6.14338e8i 0.885895 + 0.743354i 0.967382 0.253320i \(-0.0815226\pi\)
−0.0814874 + 0.996674i \(0.525967\pi\)
\(354\) 3.24346e7 1.83946e8i 0.0388595 0.220383i
\(355\) −2.89459e7 + 1.64160e8i −0.0343390 + 0.194746i
\(356\) −3.16632e8 5.48423e8i −0.371946 0.644229i
\(357\) 3.63584e8 3.05083e8i 0.422927 0.354878i
\(358\) 3.67472e8 1.33749e8i 0.423286 0.154064i
\(359\) 5.24901e7 9.09155e7i 0.0598751 0.103707i −0.834534 0.550956i \(-0.814263\pi\)
0.894409 + 0.447250i \(0.147596\pi\)
\(360\) −1.34381e8 2.32754e8i −0.151802 0.262929i
\(361\) −2.38006e8 1.99711e8i −0.266264 0.223422i
\(362\) −6.31727e8 + 1.09418e9i −0.699922 + 1.21230i
\(363\) −1.16445e6 6.60395e6i −0.00127776 0.00724654i
\(364\) 1.91590e9 2.08218
\(365\) 2.77985e8 + 1.57653e9i 0.299224 + 1.69699i
\(366\) 3.91515e8 3.28520e8i 0.417411 0.350250i
\(367\) −1.37818e9 5.01616e8i −1.45537 0.529712i −0.511287 0.859410i \(-0.670831\pi\)
−0.944087 + 0.329698i \(0.893053\pi\)
\(368\) 1.84442e8 6.71313e7i 0.192927 0.0702195i
\(369\) −1.26304e9 −1.30866
\(370\) 2.50381e9 3.18778e8i 2.56977 0.327176i
\(371\) −9.94454e8 −1.01106
\(372\) −5.43945e8 + 1.97980e8i −0.547841 + 0.199398i
\(373\) −7.44749e8 2.71066e8i −0.743068 0.270455i −0.0573824 0.998352i \(-0.518275\pi\)
−0.685686 + 0.727898i \(0.740498\pi\)
\(374\) 9.67773e8 8.12058e8i 0.956584 0.802669i
\(375\) 1.33868e8 + 7.59201e8i 0.131089 + 0.743442i
\(376\) −3.01590e8 −0.292590
\(377\) 1.56425e7 + 8.87128e7i 0.0150352 + 0.0852690i
\(378\) −9.13560e8 + 1.58233e9i −0.869993 + 1.50687i
\(379\) −1.36788e8 1.14779e8i −0.129066 0.108299i 0.575970 0.817471i \(-0.304625\pi\)
−0.705036 + 0.709172i \(0.749069\pi\)
\(380\) −8.69926e8 1.50676e9i −0.813279 1.40864i
\(381\) −1.35306e8 + 2.34356e8i −0.125337 + 0.217090i
\(382\) −8.45136e8 + 3.07604e8i −0.775720 + 0.282339i
\(383\) 1.30368e9 1.09392e9i 1.18571 0.994925i 0.185782 0.982591i \(-0.440518\pi\)
0.999924 0.0123343i \(-0.00392622\pi\)
\(384\) −8.16207e7 1.41371e8i −0.0735599 0.127409i
\(385\) −5.85085e8 + 3.31818e9i −0.522524 + 2.96338i
\(386\) 2.29078e8 1.29917e9i 0.202735 1.14977i
\(387\) −6.17465e8 5.18115e8i −0.541532 0.454399i
\(388\) 5.94911e8 + 2.16530e8i 0.517060 + 0.188194i
\(389\) 1.05959e9 + 3.85661e8i 0.912675 + 0.332187i 0.755321 0.655356i \(-0.227481\pi\)
0.157355 + 0.987542i \(0.449703\pi\)
\(390\) −9.27037e8 7.77876e8i −0.791354 0.664025i
\(391\) 4.30187e7 2.43971e8i 0.0363948 0.206405i
\(392\) −7.99597e7 + 4.53474e8i −0.0670455 + 0.380234i
\(393\) −3.37401e8 5.84395e8i −0.280396 0.485660i
\(394\) −3.26952e8 + 2.74346e8i −0.269307 + 0.225975i
\(395\) −2.14144e8 + 7.79420e7i −0.174830 + 0.0636329i
\(396\) −5.98287e8 + 1.03626e9i −0.484146 + 0.838566i
\(397\) −6.48891e8 1.12391e9i −0.520481 0.901500i −0.999716 0.0238132i \(-0.992419\pi\)
0.479235 0.877686i \(-0.340914\pi\)
\(398\) −5.13001e8 4.30459e8i −0.407876 0.342248i
\(399\) −3.27847e8 + 5.67848e8i −0.258384 + 0.447535i
\(400\) −4.02363e8 2.28191e9i −0.314346 1.78275i
\(401\) −3.14070e8 −0.243232 −0.121616 0.992577i \(-0.538808\pi\)
−0.121616 + 0.992577i \(0.538808\pi\)
\(402\) 1.11307e8 + 6.31255e8i 0.0854541 + 0.484634i
\(403\) 1.47945e9 1.24141e9i 1.12599 0.944815i
\(404\) 5.23902e8 + 1.90685e8i 0.395290 + 0.143874i
\(405\) −1.33985e9 + 4.87665e8i −1.00222 + 0.364778i
\(406\) −2.73779e8 −0.203029
\(407\) −8.15227e8 1.07186e9i −0.599374 0.788054i
\(408\) −8.78970e7 −0.0640713
\(409\) 5.36976e8 1.95443e8i 0.388082 0.141250i −0.140608 0.990065i \(-0.544906\pi\)
0.528690 + 0.848815i \(0.322683\pi\)
\(410\) 5.16472e9 + 1.87980e9i 3.70087 + 1.34700i
\(411\) 5.91462e8 4.96296e8i 0.420224 0.352610i
\(412\) −2.15130e8 1.22006e9i −0.151552 0.859492i
\(413\) −1.00736e9 −0.703656
\(414\) 7.66078e7 + 4.34465e8i 0.0530606 + 0.300921i
\(415\) 1.89220e9 3.27739e9i 1.29957 2.25092i
\(416\) 1.72448e9 + 1.44701e9i 1.17445 + 0.985477i
\(417\) −2.75572e7 4.77305e7i −0.0186106 0.0322344i
\(418\) −8.72651e8 + 1.51148e9i −0.584418 + 1.01224i
\(419\) −9.38575e8 + 3.41613e8i −0.623333 + 0.226875i −0.634327 0.773065i \(-0.718723\pi\)
0.0109941 + 0.999940i \(0.496500\pi\)
\(420\) 1.49853e9 1.25742e9i 0.986948 0.828148i
\(421\) −7.93356e7 1.37413e8i −0.0518180 0.0897515i 0.838953 0.544204i \(-0.183168\pi\)
−0.890771 + 0.454453i \(0.849835\pi\)
\(422\) 5.62276e8 3.18882e9i 0.364213 2.06556i
\(423\) −3.42115e8 + 1.94023e9i −0.219776 + 1.24641i
\(424\) 1.41079e8 + 1.18379e8i 0.0898839 + 0.0754215i
\(425\) −2.74819e9 1.00026e9i −1.73655 0.632051i
\(426\) −9.12272e7 3.32040e7i −0.0571730 0.0208093i
\(427\) −2.11152e9 1.77178e9i −1.31249 1.10131i
\(428\) 3.57202e8 2.02579e9i 0.220222 1.24894i
\(429\) −1.12118e8 + 6.35854e8i −0.0685608 + 0.388828i
\(430\) 1.75376e9 + 3.03761e9i 1.06373 + 1.84243i
\(431\) −9.66475e8 + 8.10969e8i −0.581460 + 0.487903i −0.885426 0.464780i \(-0.846134\pi\)
0.303966 + 0.952683i \(0.401689\pi\)
\(432\) −9.24129e8 + 3.36356e8i −0.551493 + 0.200727i
\(433\) −1.30079e9 + 2.25304e9i −0.770016 + 1.33371i 0.167537 + 0.985866i \(0.446419\pi\)
−0.937553 + 0.347841i \(0.886915\pi\)
\(434\) 2.93482e9 + 5.08326e9i 1.72333 + 2.98489i
\(435\) 7.04578e7 + 5.91211e7i 0.0410409 + 0.0344374i
\(436\) −3.75378e8 + 6.50174e8i −0.216903 + 0.375688i
\(437\) 5.94304e7 + 3.37046e8i 0.0340662 + 0.193199i
\(438\) −9.32340e8 −0.530170
\(439\) −2.00212e8 1.13546e9i −0.112944 0.640539i −0.987748 0.156060i \(-0.950121\pi\)
0.874803 0.484478i \(-0.160991\pi\)
\(440\) 4.77999e8 4.01088e8i 0.267511 0.224469i
\(441\) 2.82665e9 + 1.02882e9i 1.56941 + 0.571219i
\(442\) 2.29957e9 8.36976e8i 1.26669 0.461036i
\(443\) −1.04546e9 −0.571340 −0.285670 0.958328i \(-0.592216\pi\)
−0.285670 + 0.958328i \(0.592216\pi\)
\(444\) −3.74335e7 + 7.80945e8i −0.0202965 + 0.423429i
\(445\) 2.15726e9 1.16049
\(446\) −3.83262e9 + 1.39496e9i −2.04562 + 0.744543i
\(447\) 1.03052e9 + 3.75079e8i 0.545733 + 0.198630i
\(448\) −3.12796e9 + 2.62467e9i −1.64357 + 1.37912i
\(449\) 4.98091e8 + 2.82482e9i 0.259685 + 1.47275i 0.783755 + 0.621071i \(0.213302\pi\)
−0.524070 + 0.851675i \(0.675587\pi\)
\(450\) 5.20808e9 2.69422
\(451\) −5.09207e8 2.88786e9i −0.261382 1.48237i
\(452\) 5.48977e8 9.50855e8i 0.279621 0.484317i
\(453\) 2.01756e7 + 1.69294e7i 0.0101973 + 0.00855652i
\(454\) 1.52470e9 + 2.64085e9i 0.764694 + 1.32449i
\(455\) −3.26333e9 + 5.65225e9i −1.62413 + 2.81307i
\(456\) 1.14107e8 4.15314e7i 0.0563552 0.0205116i
\(457\) 1.54936e9 1.30007e9i 0.759357 0.637176i −0.178603 0.983921i \(-0.557158\pi\)
0.937959 + 0.346745i \(0.112713\pi\)
\(458\) −1.57419e9 2.72658e9i −0.765645 1.32614i
\(459\) −2.15542e8 + 1.22240e9i −0.104037 + 0.590021i
\(460\) 1.77305e8 1.00554e9i 0.0849312 0.481669i
\(461\) −3.94056e8 3.30653e8i −0.187329 0.157188i 0.544300 0.838891i \(-0.316795\pi\)
−0.731629 + 0.681703i \(0.761240\pi\)
\(462\) −1.84398e9 6.71155e8i −0.869982 0.316648i
\(463\) −8.02838e8 2.92209e8i −0.375919 0.136823i 0.147149 0.989114i \(-0.452990\pi\)
−0.523068 + 0.852291i \(0.675213\pi\)
\(464\) −1.12884e8 9.47212e7i −0.0524591 0.0440184i
\(465\) 3.42419e8 1.94195e9i 0.157933 0.895681i
\(466\) −6.52289e8 + 3.69932e9i −0.298600 + 1.69344i
\(467\) −6.59217e8 1.14180e9i −0.299516 0.518776i 0.676510 0.736434i \(-0.263492\pi\)
−0.976025 + 0.217658i \(0.930158\pi\)
\(468\) −1.77556e9 + 1.48987e9i −0.800709 + 0.671875i
\(469\) 3.24853e9 1.18237e9i 1.45406 0.529234i
\(470\) 4.28662e9 7.42464e9i 1.90446 3.29862i
\(471\) 3.84529e8 + 6.66024e8i 0.169573 + 0.293709i
\(472\) 1.42910e8 + 1.19916e8i 0.0625556 + 0.0524904i
\(473\) 9.35694e8 1.62067e9i 0.406556 0.704175i
\(474\) −2.30469e7 1.30705e8i −0.00994004 0.0563728i
\(475\) 4.04029e9 1.72976
\(476\) 6.86912e8 + 3.89567e9i 0.291929 + 1.65561i
\(477\) 9.21611e8 7.73324e8i 0.388806 0.326247i
\(478\) −1.33359e9 4.85386e8i −0.558501 0.203278i
\(479\) 3.30550e9 1.20310e9i 1.37424 0.500182i 0.453813 0.891097i \(-0.350063\pi\)
0.920427 + 0.390915i \(0.127841\pi\)
\(480\) 2.29851e9 0.948640
\(481\) −7.73787e8 2.49113e9i −0.317040 1.02068i
\(482\) −4.38940e9 −1.78542
\(483\) −3.61597e8 + 1.31611e8i −0.146019 + 0.0531466i
\(484\) 5.25192e7 + 1.91154e7i 0.0210552 + 0.00766347i
\(485\) −1.65211e9 + 1.38628e9i −0.657570 + 0.551767i
\(486\) −5.90114e8 3.34670e9i −0.233189 1.32248i
\(487\) 3.15410e8 0.123744 0.0618721 0.998084i \(-0.480293\pi\)
0.0618721 + 0.998084i \(0.480293\pi\)
\(488\) 8.86411e7 + 5.02709e8i 0.0345276 + 0.195815i
\(489\) 4.86868e7 8.43280e7i 0.0188291 0.0326130i
\(490\) −1.00273e10 8.41387e9i −3.85031 3.23080i
\(491\) −1.27624e8 2.21051e8i −0.0486572 0.0842767i 0.840671 0.541546i \(-0.182161\pi\)
−0.889328 + 0.457269i \(0.848828\pi\)
\(492\) −8.51251e8 + 1.47441e9i −0.322240 + 0.558137i
\(493\) −1.74775e8 + 6.36129e7i −0.0656924 + 0.0239101i
\(494\) −2.58980e9 + 2.17310e9i −0.966544 + 0.811027i
\(495\) −2.03811e9 3.53011e9i −0.755283 1.30819i
\(496\) −5.48608e8 + 3.11131e9i −0.201872 + 1.14487i
\(497\) −9.09193e7 + 5.15629e8i −0.0332207 + 0.188404i
\(498\) 1.68839e9 + 1.41673e9i 0.612591 + 0.514025i
\(499\) 9.50644e8 + 3.46006e8i 0.342504 + 0.124661i 0.507545 0.861625i \(-0.330553\pi\)
−0.165040 + 0.986287i \(0.552775\pi\)
\(500\) −6.03770e9 2.19754e9i −2.16011 0.786217i
\(501\) −7.52289e8 6.31246e8i −0.267272 0.224268i
\(502\) 7.14399e8 4.05156e9i 0.252045 1.42942i
\(503\) −5.81837e8 + 3.29976e9i −0.203851 + 1.15610i 0.695386 + 0.718636i \(0.255233\pi\)
−0.899237 + 0.437461i \(0.855878\pi\)
\(504\) −4.22092e8 7.31085e8i −0.146859 0.254367i
\(505\) −1.45491e9 + 1.22082e9i −0.502709 + 0.421823i
\(506\) −9.62485e8 + 3.50316e8i −0.330269 + 0.120208i
\(507\) −7.78980e7 + 1.34923e8i −0.0265460 + 0.0459790i
\(508\) −1.12771e9 1.95325e9i −0.381658 0.661050i
\(509\) −1.10740e9 9.29215e8i −0.372212 0.312323i 0.437424 0.899256i \(-0.355891\pi\)
−0.809636 + 0.586932i \(0.800335\pi\)
\(510\) 1.24931e9 2.16388e9i 0.417038 0.722332i
\(511\) 8.73156e8 + 4.95191e9i 0.289480 + 1.64172i
\(512\) −4.19343e9 −1.38078
\(513\) −2.97771e8 1.68874e9i −0.0973803 0.552271i
\(514\) −2.45633e9 + 2.06111e9i −0.797840 + 0.669467i
\(515\) 3.96584e9 + 1.44345e9i 1.27941 + 0.465667i
\(516\) −1.02097e9 + 3.71603e8i −0.327145 + 0.119071i
\(517\) −4.57412e9 −1.45576
\(518\) 7.86448e9 1.00128e9i 2.48609 0.316522i
\(519\) 1.46485e9 0.459948
\(520\) 1.13579e9 4.13396e8i 0.354232 0.128930i
\(521\) 4.13585e9 + 1.50533e9i 1.28125 + 0.466335i 0.890844 0.454309i \(-0.150114\pi\)
0.390402 + 0.920645i \(0.372336\pi\)
\(522\) 2.53725e8 2.12900e8i 0.0780758 0.0655133i
\(523\) −5.62056e8 3.18758e9i −0.171800 0.974327i −0.941773 0.336250i \(-0.890841\pi\)
0.769973 0.638077i \(-0.220270\pi\)
\(524\) 5.62415e9 1.70764
\(525\) 7.88830e8 + 4.47368e9i 0.237917 + 1.34930i
\(526\) 3.66775e9 6.35272e9i 1.09888 1.90331i
\(527\) 3.05464e9 + 2.56314e9i 0.909122 + 0.762844i
\(528\) −5.28106e8 9.14706e8i −0.156136 0.270435i
\(529\) 1.60199e9 2.77472e9i 0.470505 0.814938i
\(530\) −4.91951e9 + 1.79056e9i −1.43535 + 0.522423i
\(531\) 9.33573e8 7.83361e8i 0.270594 0.227055i
\(532\) −2.73245e9 4.73274e9i −0.786794 1.36277i
\(533\) 9.86361e8 5.59393e9i 0.282157 1.60019i
\(534\) −2.18170e8 + 1.23731e9i −0.0620014 + 0.351627i
\(535\) 5.36804e9 + 4.50432e9i 1.51558 + 1.27172i
\(536\) −6.01604e8 2.18966e8i −0.168746 0.0614186i
\(537\) −3.87766e8 1.41135e8i −0.108059 0.0393301i
\(538\) −7.23700e8 6.07256e8i −0.200364 0.168126i
\(539\) −1.21272e9 + 6.87770e9i −0.333581 + 1.89183i
\(540\) −8.88369e8 + 5.03819e9i −0.242781 + 1.37688i
\(541\) −2.64227e9 4.57655e9i −0.717442 1.24265i −0.962010 0.273014i \(-0.911980\pi\)
0.244568 0.969632i \(-0.421354\pi\)
\(542\) 6.02361e8 5.05441e8i 0.162502 0.136355i
\(543\) 1.25282e9 4.55991e8i 0.335808 0.122224i
\(544\) −2.32399e9 + 4.02527e9i −0.618925 + 1.07201i
\(545\) −1.27875e9 2.21487e9i −0.338376 0.586084i
\(546\) −2.91184e9 2.44332e9i −0.765583 0.642401i
\(547\) −1.26598e9 + 2.19274e9i −0.330727 + 0.572837i −0.982655 0.185445i \(-0.940627\pi\)
0.651927 + 0.758281i \(0.273961\pi\)
\(548\) 1.11744e9 + 6.33731e9i 0.290063 + 1.64503i
\(549\) 3.33465e9 0.860096
\(550\) 2.09968e9 + 1.19079e10i 0.538125 + 3.05186i
\(551\) 1.96833e8 1.65163e8i 0.0501265 0.0420612i
\(552\) 6.69651e7 + 2.43733e7i 0.0169458 + 0.00616776i
\(553\) −6.72629e8 + 2.44817e8i −0.169137 + 0.0615607i
\(554\) 1.81560e9 0.453667
\(555\) −2.24017e9 1.44061e9i −0.556232 0.357702i
\(556\) 4.59353e8 0.113340
\(557\) 7.20226e9 2.62141e9i 1.76594 0.642749i 0.765938 0.642914i \(-0.222275\pi\)
1.00000 0.000165500i \(5.26802e-5\pi\)
\(558\) −6.67278e9 2.42869e9i −1.62588 0.591770i
\(559\) 2.77690e9 2.33009e9i 0.672385 0.564198i
\(560\) −1.85398e9 1.05145e10i −0.446116 2.53005i
\(561\) −1.33311e9 −0.318783
\(562\) 1.23225e9 + 6.98843e9i 0.292834 + 1.66074i
\(563\) −3.58222e9 + 6.20458e9i −0.846004 + 1.46532i 0.0387427 + 0.999249i \(0.487665\pi\)
−0.884747 + 0.466072i \(0.845669\pi\)
\(564\) 2.03435e9 + 1.70702e9i 0.477473 + 0.400647i
\(565\) 1.87013e9 + 3.23916e9i 0.436217 + 0.755550i
\(566\) −4.62646e8 + 8.01326e8i −0.107248 + 0.185760i
\(567\) −4.20848e9 + 1.53176e9i −0.969582 + 0.352899i
\(568\) 7.42786e7 6.23271e7i 0.0170077 0.0142711i
\(569\) 3.70840e9 + 6.42314e9i 0.843905 + 1.46169i 0.886569 + 0.462597i \(0.153082\pi\)
−0.0426639 + 0.999089i \(0.513584\pi\)
\(570\) −5.99409e8 + 3.39941e9i −0.135569 + 0.768851i
\(571\) −1.96727e8 + 1.11570e9i −0.0442220 + 0.250796i −0.998903 0.0468369i \(-0.985086\pi\)
0.954681 + 0.297632i \(0.0961970\pi\)
\(572\) −4.12231e9 3.45903e9i −0.920989 0.772802i
\(573\) 8.91809e8 + 3.24592e8i 0.198030 + 0.0720770i
\(574\) 1.62225e10 + 5.90449e9i 3.58035 + 1.30314i
\(575\) 1.81637e9 + 1.52411e9i 0.398443 + 0.334334i
\(576\) 8.57800e8 4.86483e9i 0.187028 1.06069i
\(577\) −4.29051e8 + 2.43327e9i −0.0929809 + 0.527321i 0.902367 + 0.430969i \(0.141828\pi\)
−0.995347 + 0.0963513i \(0.969283\pi\)
\(578\) −8.66279e8 1.50044e9i −0.186599 0.323200i
\(579\) −1.06638e9 + 8.94801e8i −0.228317 + 0.191581i
\(580\) −7.20347e8 + 2.62185e8i −0.153301 + 0.0557968i
\(581\) 5.94343e9 1.02943e10i 1.25725 2.17761i
\(582\) −6.28025e8 1.08777e9i −0.132052 0.228722i
\(583\) 2.13970e9 + 1.79542e9i 0.447212 + 0.375255i
\(584\) 4.65603e8 8.06447e8i 0.0967320 0.167545i
\(585\) −1.37110e9 7.77591e9i −0.283155 1.60585i
\(586\) 8.25923e9 1.69550
\(587\) −6.86269e8 3.89202e9i −0.140043 0.794222i −0.971215 0.238206i \(-0.923441\pi\)
0.831172 0.556016i \(-0.187671\pi\)
\(588\) 3.10606e9 2.60629e9i 0.630070 0.528691i
\(589\) −5.17657e9 1.88412e9i −1.04385 0.379931i
\(590\) −4.98336e9 + 1.81380e9i −0.998943 + 0.363585i
\(591\) 4.50376e8 0.0897469
\(592\) 3.58910e9 + 2.30808e9i 0.710984 + 0.457220i
\(593\) −4.85300e9 −0.955694 −0.477847 0.878443i \(-0.658583\pi\)
−0.477847 + 0.878443i \(0.658583\pi\)
\(594\) 4.82245e9 1.75523e9i 0.944093 0.343622i
\(595\) −1.26629e10 4.60894e9i −2.46448 0.896998i
\(596\) −7.00173e9 + 5.87515e9i −1.35470 + 1.13673i
\(597\) 1.22710e8 + 6.95923e8i 0.0236031 + 0.133860i
\(598\) −1.98404e9 −0.379398
\(599\) −3.00613e8 1.70486e9i −0.0571496 0.324111i 0.942808 0.333337i \(-0.108175\pi\)
−0.999957 + 0.00922524i \(0.997063\pi\)
\(600\) 4.20637e8 7.28564e8i 0.0795019 0.137701i
\(601\) 7.72286e9 + 6.48025e9i 1.45117 + 1.21767i 0.931723 + 0.363169i \(0.118305\pi\)
0.519443 + 0.854505i \(0.326139\pi\)
\(602\) 5.50859e9 + 9.54116e9i 1.02909 + 1.78243i
\(603\) −2.09113e9 + 3.62194e9i −0.388391 + 0.672714i
\(604\) −2.06272e8 + 7.50768e7i −0.0380900 + 0.0138636i
\(605\) −1.45849e8 + 1.22382e8i −0.0267769 + 0.0224685i
\(606\) −5.53064e8 9.57934e8i −0.100953 0.174856i
\(607\) 1.32006e9 7.48641e9i 0.239570 1.35867i −0.593204 0.805052i \(-0.702137\pi\)
0.832773 0.553614i \(-0.186752\pi\)
\(608\) 1.11503e9 6.32363e9i 0.201198 1.14105i
\(609\) 2.21309e8 + 1.85700e8i 0.0397044 + 0.0333159i
\(610\) −1.36357e10 4.96300e9i −2.43234 0.885299i
\(611\) −8.32597e9 3.03041e9i −1.47669 0.537473i
\(612\) −3.66601e9 3.07615e9i −0.646493 0.542472i
\(613\) −1.30810e9 + 7.41859e9i −0.229366 + 1.30080i 0.624795 + 0.780789i \(0.285183\pi\)
−0.854161 + 0.520009i \(0.825928\pi\)
\(614\) 1.36669e9 7.75090e9i 0.238277 1.35134i
\(615\) −2.89985e9 5.02269e9i −0.502705 0.870710i
\(616\) 1.50140e9 1.25982e9i 0.258800 0.217159i
\(617\) −3.77753e9 + 1.37491e9i −0.647455 + 0.235654i −0.644811 0.764342i \(-0.723064\pi\)
−0.00264389 + 0.999997i \(0.500842\pi\)
\(618\) −1.22897e9 + 2.12864e9i −0.209451 + 0.362779i
\(619\) −4.49962e9 7.79357e9i −0.762533 1.32075i −0.941541 0.336898i \(-0.890622\pi\)
0.179008 0.983848i \(-0.442711\pi\)
\(620\) 1.25899e10 + 1.05642e10i 2.12154 + 1.78018i
\(621\) 5.03175e8 8.71525e8i 0.0843138 0.146036i
\(622\) 6.47441e8 + 3.67182e9i 0.107878 + 0.611807i
\(623\) 6.77599e9 1.12270
\(624\) −3.55273e8 2.01486e9i −0.0585351 0.331969i
\(625\) 6.75427e9 5.66751e9i 1.10662 0.928565i
\(626\) −1.37199e10 4.99362e9i −2.23532 0.813589i
\(627\) 1.73062e9 6.29894e8i 0.280392 0.102054i
\(628\) −6.40973e9 −1.03272
\(629\) 4.78788e9 2.46652e9i 0.767125 0.395192i
\(630\) 2.39974e10 3.82360
\(631\) −8.75975e9 + 3.18829e9i −1.38800 + 0.505190i −0.924593 0.380956i \(-0.875595\pi\)
−0.463406 + 0.886146i \(0.653373\pi\)
\(632\) 1.24566e8 + 4.53383e7i 0.0196286 + 0.00714423i
\(633\) −2.61745e9 + 2.19630e9i −0.410171 + 0.344174i
\(634\) −1.24847e9 7.08044e9i −0.194566 1.10344i
\(635\) 7.68325e9 1.19080
\(636\) −2.81600e8 1.59703e9i −0.0434044 0.246158i
\(637\) −6.76399e9 + 1.17156e10i −1.03685 + 1.79587i
\(638\) 5.89072e8 + 4.94290e8i 0.0898040 + 0.0753545i
\(639\) −3.16712e8 5.48562e8i −0.0480189 0.0831712i
\(640\) −2.31739e9 + 4.01384e9i −0.349437 + 0.605243i
\(641\) −7.98403e7 + 2.90595e7i −0.0119734 + 0.00435798i −0.348000 0.937495i \(-0.613139\pi\)
0.336026 + 0.941853i \(0.390917\pi\)
\(642\) −3.12636e9 + 2.62332e9i −0.466300 + 0.391273i
\(643\) −3.29542e8 5.70783e8i −0.0488846 0.0846705i 0.840548 0.541737i \(-0.182233\pi\)
−0.889432 + 0.457067i \(0.848900\pi\)
\(644\) 5.56916e8 3.15843e9i 0.0821654 0.465983i
\(645\) 6.42712e8 3.64500e9i 0.0943099 0.534858i
\(646\) −5.34718e9 4.48682e9i −0.780389 0.654824i
\(647\) −7.10194e9 2.58489e9i −1.03089 0.375213i −0.229470 0.973316i \(-0.573699\pi\)
−0.801419 + 0.598103i \(0.795921\pi\)
\(648\) 7.79380e8 + 2.83671e8i 0.112522 + 0.0409546i
\(649\) 2.16747e9 + 1.81873e9i 0.311241 + 0.261163i
\(650\) −4.06719e9 + 2.30662e10i −0.580895 + 3.29442i
\(651\) 1.07554e9 6.09970e9i 0.152790 0.866513i
\(652\) 4.05781e8 + 7.02833e8i 0.0573357 + 0.0993084i
\(653\) −4.49883e9 + 3.77497e9i −0.632271 + 0.530539i −0.901634 0.432500i \(-0.857631\pi\)
0.269363 + 0.963039i \(0.413187\pi\)
\(654\) 1.39967e9 5.09438e8i 0.195661 0.0712146i
\(655\) −9.57954e9 + 1.65923e10i −1.33199 + 2.30707i
\(656\) 4.64601e9 + 8.04713e9i 0.642565 + 1.11296i
\(657\) −4.65999e9 3.91019e9i −0.641071 0.537922i
\(658\) 1.34643e10 2.33209e10i 1.84244 3.19120i
\(659\) 6.40659e8 + 3.63336e9i 0.0872023 + 0.494549i 0.996860 + 0.0791894i \(0.0252332\pi\)
−0.909657 + 0.415360i \(0.863656\pi\)
\(660\) −5.49449e9 −0.743915
\(661\) −3.70938e8 2.10369e9i −0.0499570 0.283320i 0.949587 0.313502i \(-0.101502\pi\)
−0.999544 + 0.0301822i \(0.990391\pi\)
\(662\) 4.87558e9 4.09110e9i 0.653166 0.548071i
\(663\) −2.42657e9 8.83198e8i −0.323366 0.117696i
\(664\) −2.06860e9 + 7.52909e8i −0.274213 + 0.0998054i
\(665\) 1.86166e10 2.45485
\(666\) −6.50978e9 + 7.04365e9i −0.853899 + 0.923928i
\(667\) 1.50793e8 0.0196762
\(668\) 7.69126e9 2.79939e9i 0.998343 0.363367i
\(669\) 4.04428e9 + 1.47200e9i 0.522215 + 0.190071i
\(670\) 1.39414e10 1.16982e10i 1.79079 1.50265i
\(671\) 1.34439e9 + 7.62443e9i 0.171790 + 0.974268i
\(672\) 7.21964e9 0.917748
\(673\) 2.02664e9 + 1.14937e10i 0.256286 + 1.45347i 0.792751 + 0.609546i \(0.208648\pi\)
−0.536465 + 0.843923i \(0.680241\pi\)
\(674\) −7.89684e9 + 1.36777e10i −0.993445 + 1.72070i
\(675\) −9.10076e9 7.63644e9i −1.13898 0.955714i
\(676\) −6.49243e8 1.12452e9i −0.0808339 0.140008i
\(677\) 2.96482e9 5.13523e9i 0.367230 0.636062i −0.621901 0.783096i \(-0.713639\pi\)
0.989131 + 0.147034i \(0.0469727\pi\)
\(678\) −2.04696e9 + 7.45034e8i −0.252236 + 0.0918062i
\(679\) −5.18929e9 + 4.35433e9i −0.636156 + 0.533799i
\(680\) 1.24779e9 + 2.16124e9i 0.152181 + 0.263586i
\(681\) 5.58764e8 3.16891e9i 0.0677975 0.384499i
\(682\) 2.86284e9 1.62360e10i 0.345582 1.95989i
\(683\) −7.77973e9 6.52797e9i −0.934313 0.783981i 0.0422740 0.999106i \(-0.486540\pi\)
−0.976587 + 0.215125i \(0.930984\pi\)
\(684\) 6.21265e9 + 2.26122e9i 0.742302 + 0.270176i
\(685\) −2.05995e10 7.49762e9i −2.44873 0.891264i
\(686\) −1.52629e10 1.28071e10i −1.80510 1.51466i
\(687\) −5.76902e8 + 3.27177e9i −0.0678818 + 0.384977i
\(688\) −1.02972e9 + 5.83985e9i −0.120548 + 0.683663i
\(689\) 2.70527e9 + 4.68566e9i 0.315096 + 0.545763i
\(690\) −1.55183e9 + 1.30214e9i −0.179834 + 0.150899i
\(691\) 1.07605e10 3.91649e9i 1.24068 0.451569i 0.363434 0.931620i \(-0.381604\pi\)
0.877241 + 0.480051i \(0.159382\pi\)
\(692\) −6.10443e9 + 1.05732e10i −0.700283 + 1.21293i
\(693\) −6.40174e9 1.10881e10i −0.730687 1.26559i
\(694\) 1.00407e10 + 8.42517e9i 1.14027 + 0.956799i
\(695\) −7.82410e8 + 1.35517e9i −0.0884072 + 0.153126i
\(696\) −9.29050e6 5.26890e7i −0.00104450 0.00592363i
\(697\) 1.17280e10 1.31193
\(698\) −1.19528e9 6.77878e9i −0.133038 0.754497i
\(699\) 3.03647e9 2.54790e9i 0.336278 0.282171i
\(700\) −3.55778e10 1.29493e10i −3.92046 1.42693i
\(701\) −7.49490e9 + 2.72792e9i −0.821775 + 0.299102i −0.718479 0.695549i \(-0.755161\pi\)
−0.103296 + 0.994651i \(0.532939\pi\)
\(702\) 9.94084e9 1.08453
\(703\) −5.05012e9 + 5.46428e9i −0.548224 + 0.593184i
\(704\) 1.14689e10 1.23884
\(705\) −8.50111e9 + 3.09415e9i −0.913721 + 0.332567i
\(706\) 1.48507e10 + 5.40521e9i 1.58829 + 0.578091i
\(707\) −4.56990e9 + 3.83460e9i −0.486338 + 0.408086i
\(708\) −2.85255e8 1.61776e9i −0.0302077 0.171316i
\(709\) −5.93032e9 −0.624908 −0.312454 0.949933i \(-0.601151\pi\)
−0.312454 + 0.949933i \(0.601151\pi\)
\(710\) 4.78639e8 + 2.71449e9i 0.0501884 + 0.284633i
\(711\) 4.32981e8 7.49945e8i 0.0451778 0.0782502i
\(712\) −9.61281e8 8.06611e8i −0.0998092 0.0837498i
\(713\) −1.61646e9 2.79978e9i −0.167013 0.289275i
\(714\) 3.92411e9 6.79676e9i 0.403457 0.698809i
\(715\) 1.72262e10 6.26984e9i 1.76246 0.641483i
\(716\) 2.63462e9 2.21071e9i 0.268240 0.225080i
\(717\) 7.48774e8 + 1.29691e9i 0.0758636 + 0.131400i
\(718\) 3.01438e8 1.70954e9i 0.0303923 0.172363i
\(719\) 1.59361e9 9.03782e9i 0.159894 0.906802i −0.794281 0.607551i \(-0.792152\pi\)
0.954174 0.299251i \(-0.0967368\pi\)
\(720\) 9.89460e9 + 8.30256e9i 0.987949 + 0.828988i
\(721\) 1.24567e10 + 4.53388e9i 1.23774 + 0.450502i
\(722\) −4.82770e9 1.75714e9i −0.477376 0.173751i
\(723\) 3.54817e9 + 2.97727e9i 0.349156 + 0.292977i
\(724\) −1.92955e9 + 1.09430e10i −0.188960 + 1.07165i
\(725\) 3.09120e8 1.75310e9i 0.0301261 0.170854i
\(726\) −5.54426e7 9.60293e7i −0.00537731 0.00931378i
\(727\) 1.58500e10 1.32998e10i 1.52989 1.28373i 0.730516 0.682896i \(-0.239280\pi\)
0.799374 0.600834i \(-0.205165\pi\)
\(728\) 3.56755e9 1.29848e9i 0.342697 0.124731i
\(729\) 1.35419e9 2.34553e9i 0.129460 0.224231i
\(730\) 1.32356e10 + 2.29247e10i 1.25925 + 2.18109i
\(731\) 5.73348e9 + 4.81096e9i 0.542884 + 0.455534i
\(732\) 2.24745e9 3.89269e9i 0.211788 0.366827i
\(733\) 1.42476e8 + 8.08020e8i 0.0133622 + 0.0757807i 0.990760 0.135629i \(-0.0433056\pi\)
−0.977397 + 0.211410i \(0.932194\pi\)
\(734\) −2.42516e10 −2.26363
\(735\) 2.39852e9 + 1.36027e10i 0.222812 + 1.26363i
\(736\) 2.88673e9 2.42226e9i 0.266891 0.223948i
\(737\) −9.12434e9 3.32099e9i −0.839586 0.305584i
\(738\) −1.96257e10 + 7.14318e9i −1.79733 + 0.654175i
\(739\) −1.56662e10 −1.42794 −0.713968 0.700179i \(-0.753104\pi\)
−0.713968 + 0.700179i \(0.753104\pi\)
\(740\) 1.97336e10 1.01659e10i 1.79017 0.922225i
\(741\) 3.56744e9 0.322102
\(742\) −1.54522e10 + 5.62416e9i −1.38860 + 0.505410i
\(743\) 5.36546e9 + 1.95287e9i 0.479895 + 0.174667i 0.570629 0.821208i \(-0.306699\pi\)
−0.0907348 + 0.995875i \(0.528922\pi\)
\(744\) −8.78688e8 + 7.37307e8i −0.0782221 + 0.0656361i
\(745\) −5.40679e9 3.06634e10i −0.479063 2.71690i
\(746\) −1.31052e10 −1.15574
\(747\) 2.49716e9 + 1.41621e10i 0.219192 + 1.24310i
\(748\) 5.55540e9 9.62223e9i 0.485355 0.840660i
\(749\) 1.68611e10 + 1.41481e10i 1.46622 + 1.23031i
\(750\) 6.37377e9 + 1.10397e10i 0.551673 + 0.955526i
\(751\) −2.69590e9 + 4.66943e9i −0.232254 + 0.402276i −0.958471 0.285190i \(-0.907943\pi\)
0.726217 + 0.687466i \(0.241277\pi\)
\(752\) 1.36201e10 4.95731e9i 1.16793 0.425092i
\(753\) −3.32560e9 + 2.79051e9i −0.283849 + 0.238178i
\(754\) 7.44776e8 + 1.28999e9i 0.0632741 + 0.109594i
\(755\) 1.29850e8 7.36417e8i 0.0109807 0.0622744i
\(756\) −2.79038e9 + 1.58250e10i −0.234875 + 1.33204i
\(757\) 1.71158e10 + 1.43619e10i 1.43404 + 1.20330i 0.943274 + 0.332014i \(0.107728\pi\)
0.490768 + 0.871290i \(0.336716\pi\)
\(758\) −2.77461e9 1.00988e9i −0.231398 0.0842221i
\(759\) 1.01564e9 + 3.69662e8i 0.0843127 + 0.0306873i
\(760\) −2.64106e9 2.21611e9i −0.218238 0.183123i
\(761\) −9.71711e8 + 5.51085e9i −0.0799265 + 0.453286i 0.918410 + 0.395630i \(0.129474\pi\)
−0.998337 + 0.0576558i \(0.981637\pi\)
\(762\) −7.77030e8 + 4.40676e9i −0.0636202 + 0.360808i
\(763\) −4.01659e9 6.95693e9i −0.327357 0.566998i
\(764\) −6.05927e9 + 5.08433e9i −0.491579