Properties

Label 13.7.f.a.2.6
Level 13
Weight 7
Character 13.2
Analytic conductor 2.991
Analytic rank 0
Dimension 24
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 13 \)
Weight: \( k \) = \( 7 \)
Character orbit: \([\chi]\) = 13.f (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.99070308706\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{12})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 2.6
Character \(\chi\) = 13.2
Dual form 13.7.f.a.7.6

$q$-expansion

\(f(q)\) \(=\) \(q+(12.5088 + 3.35172i) q^{2} +(-1.31220 - 2.27280i) q^{3} +(89.8106 + 51.8522i) q^{4} +(24.9454 - 24.9454i) q^{5} +(-8.79628 - 32.8282i) q^{6} +(-400.516 + 107.318i) q^{7} +(363.576 + 363.576i) q^{8} +(361.056 - 625.368i) q^{9} +O(q^{10})\) \(q+(12.5088 + 3.35172i) q^{2} +(-1.31220 - 2.27280i) q^{3} +(89.8106 + 51.8522i) q^{4} +(24.9454 - 24.9454i) q^{5} +(-8.79628 - 32.8282i) q^{6} +(-400.516 + 107.318i) q^{7} +(363.576 + 363.576i) q^{8} +(361.056 - 625.368i) q^{9} +(395.648 - 228.427i) q^{10} +(-169.267 + 631.712i) q^{11} -272.162i q^{12} +(-1807.65 - 1248.68i) q^{13} -5369.68 q^{14} +(-89.4294 - 23.9625i) q^{15} +(10.7557 + 18.6295i) q^{16} +(4044.24 + 2334.94i) q^{17} +(6612.44 - 6612.44i) q^{18} +(2588.98 + 9662.21i) q^{19} +(3533.84 - 946.889i) q^{20} +(769.471 + 769.471i) q^{21} +(-4234.65 + 7334.63i) q^{22} +(13824.2 - 7981.38i) q^{23} +(349.251 - 1303.42i) q^{24} +14380.5i q^{25} +(-18426.3 - 21678.3i) q^{26} -3808.31 q^{27} +(-41535.3 - 11129.3i) q^{28} +(6616.02 + 11459.3i) q^{29} +(-1038.34 - 599.486i) q^{30} +(-6057.12 + 6057.12i) q^{31} +(-8444.89 - 31516.8i) q^{32} +(1657.87 - 444.225i) q^{33} +(42762.5 + 42762.5i) q^{34} +(-7313.95 + 12668.1i) q^{35} +(64853.3 - 37443.1i) q^{36} +(21020.2 - 78448.4i) q^{37} +129540. i q^{38} +(-466.005 + 5746.96i) q^{39} +18139.1 q^{40} +(-114237. - 30609.7i) q^{41} +(7046.11 + 12204.2i) q^{42} +(-38616.8 - 22295.4i) q^{43} +(-47957.6 + 47957.6i) q^{44} +(-6593.36 - 24606.8i) q^{45} +(199675. - 53502.8i) q^{46} +(34061.0 + 34061.0i) q^{47} +(28.2274 - 48.8913i) q^{48} +(47009.1 - 27140.7i) q^{49} +(-48199.3 + 179882. i) q^{50} -12255.7i q^{51} +(-97599.2 - 205876. i) q^{52} -14637.4 q^{53} +(-47637.4 - 12764.4i) q^{54} +(11535.9 + 19980.8i) q^{55} +(-184636. - 106600. i) q^{56} +(18563.0 - 18563.0i) q^{57} +(44350.1 + 165517. i) q^{58} +(-101893. + 27302.2i) q^{59} +(-6789.20 - 6789.20i) q^{60} +(107360. - 185953. i) q^{61} +(-96069.2 + 55465.6i) q^{62} +(-77495.7 + 289218. i) q^{63} -423919. i q^{64} +(-76241.5 + 13943.7i) q^{65} +22226.9 q^{66} +(470454. + 126058. i) q^{67} +(242144. + 419405. i) q^{68} +(-36280.2 - 20946.4i) q^{69} +(-133949. + 133949. i) q^{70} +(4932.21 + 18407.2i) q^{71} +(358640. - 96097.3i) q^{72} +(158416. + 158416. i) q^{73} +(525875. - 910842. i) q^{74} +(32683.9 - 18870.1i) q^{75} +(-268489. + 1.00201e6i) q^{76} -271176. i q^{77} +(-25091.4 + 70325.6i) q^{78} -280091. q^{79} +(733.027 + 196.414i) q^{80} +(-258213. - 447238. i) q^{81} +(-1.32637e6 - 765781. i) q^{82} +(-662356. + 662356. i) q^{83} +(29207.9 + 109005. i) q^{84} +(159131. - 42639.1i) q^{85} +(-408322. - 408322. i) q^{86} +(17363.1 - 30073.8i) q^{87} +(-291217. + 168134. i) q^{88} +(-4803.85 + 17928.2i) q^{89} -329900. i q^{90} +(858000. + 306124. i) q^{91} +1.65541e6 q^{92} +(21714.8 + 5818.47i) q^{93} +(311899. + 540225. i) q^{94} +(305611. + 176445. i) q^{95} +(-60549.9 + 60549.9i) q^{96} +(-295344. - 1.10224e6i) q^{97} +(678996. - 181936. i) q^{98} +(333938. + 333938. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 12q^{2} - 2q^{3} - 6q^{4} - 114q^{5} + 634q^{6} + 316q^{7} - 1398q^{8} - 1946q^{9} + O(q^{10}) \) \( 24q - 12q^{2} - 2q^{3} - 6q^{4} - 114q^{5} + 634q^{6} + 316q^{7} - 1398q^{8} - 1946q^{9} + 4674q^{10} + 228q^{11} - 1552q^{13} - 14616q^{14} + 7486q^{15} - 2138q^{16} + 20898q^{17} - 5630q^{18} - 14036q^{19} - 14634q^{20} - 314q^{21} + 37852q^{22} + 29634q^{23} + 47154q^{24} + 510q^{26} - 107060q^{27} - 40572q^{28} + 1026q^{29} - 247734q^{30} - 118116q^{31} + 180876q^{32} + 306046q^{33} + 101898q^{34} + 104862q^{35} + 105066q^{36} - 31470q^{37} + 28510q^{39} - 275328q^{40} - 357216q^{41} - 25636q^{42} - 480486q^{43} - 797712q^{44} + 464248q^{45} + 1012050q^{46} + 140028q^{47} + 676102q^{48} + 854562q^{49} + 756714q^{50} - 771704q^{52} - 1397076q^{53} - 1271048q^{54} - 205490q^{55} - 1461108q^{56} - 1483394q^{57} + 1133806q^{58} + 1568052q^{59} + 886808q^{60} + 768676q^{61} + 3741966q^{62} + 1336264q^{63} - 946968q^{65} - 5076928q^{66} - 1489892q^{67} - 569052q^{68} - 1475766q^{69} - 2626556q^{70} + 2136948q^{71} + 4787052q^{72} + 326326q^{73} + 2159718q^{74} + 3466008q^{75} + 1522158q^{76} - 1573544q^{78} - 1734344q^{79} - 5214300q^{80} - 773072q^{81} - 3540426q^{82} - 3642132q^{83} + 2952364q^{84} + 3509916q^{85} - 132324q^{86} + 531698q^{87} + 4478052q^{88} + 632754q^{89} - 2946788q^{91} - 1656060q^{92} - 295514q^{93} + 1552210q^{94} - 2753718q^{95} - 3979208q^{96} + 2258214q^{97} + 4984308q^{98} + 4336480q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 12.5088 + 3.35172i 1.56360 + 0.418966i 0.933801 0.357792i \(-0.116470\pi\)
0.629800 + 0.776758i \(0.283137\pi\)
\(3\) −1.31220 2.27280i −0.0486001 0.0841778i 0.840702 0.541498i \(-0.182143\pi\)
−0.889302 + 0.457320i \(0.848809\pi\)
\(4\) 89.8106 + 51.8522i 1.40329 + 0.810190i
\(5\) 24.9454 24.9454i 0.199563 0.199563i −0.600249 0.799813i \(-0.704932\pi\)
0.799813 + 0.600249i \(0.204932\pi\)
\(6\) −8.79628 32.8282i −0.0407235 0.151982i
\(7\) −400.516 + 107.318i −1.16769 + 0.312880i −0.790032 0.613066i \(-0.789936\pi\)
−0.377654 + 0.925947i \(0.623269\pi\)
\(8\) 363.576 + 363.576i 0.710109 + 0.710109i
\(9\) 361.056 625.368i 0.495276 0.857843i
\(10\) 395.648 228.427i 0.395648 0.228427i
\(11\) −169.267 + 631.712i −0.127173 + 0.474615i −0.999908 0.0135791i \(-0.995677\pi\)
0.872735 + 0.488194i \(0.162344\pi\)
\(12\) 272.162i 0.157501i
\(13\) −1807.65 1248.68i −0.822781 0.568358i
\(14\) −5369.68 −1.95688
\(15\) −89.4294 23.9625i −0.0264976 0.00710001i
\(16\) 10.7557 + 18.6295i 0.00262591 + 0.00454822i
\(17\) 4044.24 + 2334.94i 0.823171 + 0.475258i 0.851509 0.524340i \(-0.175688\pi\)
−0.0283376 + 0.999598i \(0.509021\pi\)
\(18\) 6612.44 6612.44i 1.13382 1.13382i
\(19\) 2588.98 + 9662.21i 0.377458 + 1.40869i 0.849721 + 0.527233i \(0.176771\pi\)
−0.472263 + 0.881458i \(0.656563\pi\)
\(20\) 3533.84 946.889i 0.441730 0.118361i
\(21\) 769.471 + 769.471i 0.0830872 + 0.0830872i
\(22\) −4234.65 + 7334.63i −0.397695 + 0.688827i
\(23\) 13824.2 7981.38i 1.13620 0.655986i 0.190714 0.981646i \(-0.438920\pi\)
0.945487 + 0.325660i \(0.105586\pi\)
\(24\) 349.251 1303.42i 0.0252641 0.0942868i
\(25\) 14380.5i 0.920349i
\(26\) −18426.3 21678.3i −1.04838 1.23340i
\(27\) −3808.31 −0.193482
\(28\) −41535.3 11129.3i −1.89210 0.506985i
\(29\) 6616.02 + 11459.3i 0.271271 + 0.469854i 0.969187 0.246324i \(-0.0792229\pi\)
−0.697917 + 0.716179i \(0.745890\pi\)
\(30\) −1038.34 599.486i −0.0384570 0.0222032i
\(31\) −6057.12 + 6057.12i −0.203321 + 0.203321i −0.801421 0.598100i \(-0.795922\pi\)
0.598100 + 0.801421i \(0.295922\pi\)
\(32\) −8444.89 31516.8i −0.257718 0.961815i
\(33\) 1657.87 444.225i 0.0461327 0.0123612i
\(34\) 42762.5 + 42762.5i 1.08799 + 1.08799i
\(35\) −7313.95 + 12668.1i −0.170588 + 0.295467i
\(36\) 64853.3 37443.1i 1.39003 0.802536i
\(37\) 21020.2 78448.4i 0.414984 1.54874i −0.369884 0.929078i \(-0.620603\pi\)
0.784868 0.619663i \(-0.212731\pi\)
\(38\) 129540.i 2.36077i
\(39\) −466.005 + 5746.96i −0.00785591 + 0.0968822i
\(40\) 18139.1 0.283424
\(41\) −114237. 30609.7i −1.65750 0.444127i −0.695804 0.718232i \(-0.744952\pi\)
−0.961700 + 0.274105i \(0.911618\pi\)
\(42\) 7046.11 + 12204.2i 0.0951046 + 0.164726i
\(43\) −38616.8 22295.4i −0.485703 0.280421i 0.237087 0.971488i \(-0.423807\pi\)
−0.722790 + 0.691068i \(0.757141\pi\)
\(44\) −47957.6 + 47957.6i −0.562988 + 0.562988i
\(45\) −6593.36 24606.8i −0.0723551 0.270033i
\(46\) 199675. 53502.8i 2.05140 0.549671i
\(47\) 34061.0 + 34061.0i 0.328068 + 0.328068i 0.851851 0.523784i \(-0.175480\pi\)
−0.523784 + 0.851851i \(0.675480\pi\)
\(48\) 28.2274 48.8913i 0.000255239 0.000442087i
\(49\) 47009.1 27140.7i 0.399571 0.230692i
\(50\) −48199.3 + 179882.i −0.385595 + 1.43906i
\(51\) 12255.7i 0.0923904i
\(52\) −97599.2 205876.i −0.694123 1.46418i
\(53\) −14637.4 −0.0983186 −0.0491593 0.998791i \(-0.515654\pi\)
−0.0491593 + 0.998791i \(0.515654\pi\)
\(54\) −47637.4 12764.4i −0.302529 0.0810623i
\(55\) 11535.9 + 19980.8i 0.0693367 + 0.120095i
\(56\) −184636. 106600.i −1.05136 0.607005i
\(57\) 18563.0 18563.0i 0.100236 0.100236i
\(58\) 44350.1 + 165517.i 0.227306 + 0.848318i
\(59\) −101893. + 27302.2i −0.496124 + 0.132936i −0.498200 0.867062i \(-0.666006\pi\)
0.00207678 + 0.999998i \(0.499339\pi\)
\(60\) −6789.20 6789.20i −0.0314315 0.0314315i
\(61\) 107360. 185953.i 0.472991 0.819245i −0.526531 0.850156i \(-0.676508\pi\)
0.999522 + 0.0309113i \(0.00984093\pi\)
\(62\) −96069.2 + 55465.6i −0.403097 + 0.232728i
\(63\) −77495.7 + 289218.i −0.309924 + 1.15665i
\(64\) 423919.i 1.61712i
\(65\) −76241.5 + 13943.7i −0.277620 + 0.0507735i
\(66\) 22226.9 0.0773120
\(67\) 470454. + 126058.i 1.56420 + 0.419126i 0.933990 0.357299i \(-0.116302\pi\)
0.630210 + 0.776425i \(0.282969\pi\)
\(68\) 242144. + 419405.i 0.770099 + 1.33385i
\(69\) −36280.2 20946.4i −0.110439 0.0637620i
\(70\) −133949. + 133949.i −0.390522 + 0.390522i
\(71\) 4932.21 + 18407.2i 0.0137805 + 0.0514297i 0.972474 0.233012i \(-0.0748583\pi\)
−0.958693 + 0.284442i \(0.908192\pi\)
\(72\) 358640. 96097.3i 0.960862 0.257462i
\(73\) 158416. + 158416.i 0.407222 + 0.407222i 0.880769 0.473547i \(-0.157027\pi\)
−0.473547 + 0.880769i \(0.657027\pi\)
\(74\) 525875. 910842.i 1.29774 2.24775i
\(75\) 32683.9 18870.1i 0.0774730 0.0447290i
\(76\) −268489. + 1.00201e6i −0.611625 + 2.28262i
\(77\) 271176.i 0.593991i
\(78\) −25091.4 + 70325.6i −0.0528738 + 0.148194i
\(79\) −280091. −0.568091 −0.284046 0.958811i \(-0.591677\pi\)
−0.284046 + 0.958811i \(0.591677\pi\)
\(80\) 733.027 + 196.414i 0.00143169 + 0.000383621i
\(81\) −258213. 447238.i −0.485873 0.841556i
\(82\) −1.32637e6 765781.i −2.40560 1.38887i
\(83\) −662356. + 662356.i −1.15840 + 1.15840i −0.173576 + 0.984820i \(0.555532\pi\)
−0.984820 + 0.173576i \(0.944468\pi\)
\(84\) 29207.9 + 109005.i 0.0492791 + 0.183912i
\(85\) 159131. 42639.1i 0.259119 0.0694307i
\(86\) −408322. 408322.i −0.641959 0.641959i
\(87\) 17363.1 30073.8i 0.0263675 0.0456699i
\(88\) −291217. + 168134.i −0.427335 + 0.246722i
\(89\) −4803.85 + 17928.2i −0.00681427 + 0.0254312i −0.969249 0.246081i \(-0.920857\pi\)
0.962435 + 0.271512i \(0.0875237\pi\)
\(90\) 329900.i 0.452538i
\(91\) 858000. + 306124.i 1.13858 + 0.406232i
\(92\) 1.65541e6 2.12589
\(93\) 21714.8 + 5818.47i 0.0269965 + 0.00723369i
\(94\) 311899. + 540225.i 0.375518 + 0.650416i
\(95\) 305611. + 176445.i 0.356450 + 0.205796i
\(96\) −60549.9 + 60549.9i −0.0684384 + 0.0684384i
\(97\) −295344. 1.10224e6i −0.323603 1.20770i −0.915709 0.401843i \(-0.868370\pi\)
0.592106 0.805860i \(-0.298297\pi\)
\(98\) 678996. 181936.i 0.721421 0.193304i
\(99\) 333938. + 333938.i 0.344160 + 0.344160i
\(100\) −745658. + 1.29152e6i −0.745658 + 1.29152i
\(101\) −197622. + 114097.i −0.191810 + 0.110742i −0.592830 0.805328i \(-0.701989\pi\)
0.401019 + 0.916070i \(0.368656\pi\)
\(102\) 41077.6 153304.i 0.0387084 0.144462i
\(103\) 844428.i 0.772772i 0.922337 + 0.386386i \(0.126277\pi\)
−0.922337 + 0.386386i \(0.873723\pi\)
\(104\) −203227. 1.11121e6i −0.180668 0.987861i
\(105\) 38389.6 0.0331623
\(106\) −183096. 49060.4i −0.153731 0.0411921i
\(107\) 183259. + 317414.i 0.149594 + 0.259104i 0.931077 0.364822i \(-0.118870\pi\)
−0.781484 + 0.623926i \(0.785537\pi\)
\(108\) −342026. 197469.i −0.271511 0.156757i
\(109\) −239407. + 239407.i −0.184866 + 0.184866i −0.793473 0.608606i \(-0.791729\pi\)
0.608606 + 0.793473i \(0.291729\pi\)
\(110\) 77330.3 + 288601.i 0.0580994 + 0.216830i
\(111\) −205880. + 55165.5i −0.150538 + 0.0403365i
\(112\) −6307.13 6307.13i −0.00448929 0.00448929i
\(113\) 1.14875e6 1.98970e6i 0.796145 1.37896i −0.125965 0.992035i \(-0.540203\pi\)
0.922110 0.386928i \(-0.126464\pi\)
\(114\) 294419. 169983.i 0.198725 0.114734i
\(115\) 145751. 543948.i 0.0958333 0.357655i
\(116\) 1.37222e6i 0.879123i
\(117\) −1.43355e6 + 679602.i −0.895066 + 0.424323i
\(118\) −1.36607e6 −0.831435
\(119\) −1.87037e6 501163.i −1.10990 0.297398i
\(120\) −23802.2 41226.6i −0.0137744 0.0238580i
\(121\) 1.16381e6 + 671925.i 0.656939 + 0.379284i
\(122\) 1.96621e6 1.96621e6i 1.08280 1.08280i
\(123\) 80332.1 + 299804.i 0.0431692 + 0.161110i
\(124\) −858069. + 229919.i −0.450046 + 0.120590i
\(125\) 748499. + 748499.i 0.383231 + 0.383231i
\(126\) −1.93876e6 + 3.35803e6i −0.969196 + 1.67870i
\(127\) 2.93309e6 1.69342e6i 1.43191 0.826712i 0.434641 0.900604i \(-0.356875\pi\)
0.997266 + 0.0738916i \(0.0235419\pi\)
\(128\) 880386. 3.28565e6i 0.419801 1.56672i
\(129\) 117024.i 0.0545139i
\(130\) −1.00043e6 81121.8i −0.455360 0.0369239i
\(131\) −4.30851e6 −1.91652 −0.958259 0.285900i \(-0.907707\pi\)
−0.958259 + 0.285900i \(0.907707\pi\)
\(132\) 171928. + 46068.0i 0.0747524 + 0.0200299i
\(133\) −2.07386e6 3.59203e6i −0.881504 1.52681i
\(134\) 5.46230e6 + 3.15366e6i 2.27019 + 1.31069i
\(135\) −94999.8 + 94999.8i −0.0386119 + 0.0386119i
\(136\) 621459. + 2.31932e6i 0.247056 + 0.922027i
\(137\) −2.56532e6 + 687375.i −0.997654 + 0.267321i −0.720462 0.693494i \(-0.756070\pi\)
−0.277192 + 0.960815i \(0.589404\pi\)
\(138\) −383615. 383615.i −0.145968 0.145968i
\(139\) 63545.5 110064.i 0.0236614 0.0409827i −0.853952 0.520351i \(-0.825801\pi\)
0.877614 + 0.479369i \(0.159134\pi\)
\(140\) −1.31374e6 + 758489.i −0.478769 + 0.276417i
\(141\) 32718.9 122109.i 0.0116719 0.0435601i
\(142\) 246784.i 0.0861890i
\(143\) 1.09478e6 930555.i 0.374387 0.318225i
\(144\) 15533.7 0.00520221
\(145\) 450896. + 120817.i 0.147901 + 0.0396301i
\(146\) 1.45063e6 + 2.51256e6i 0.466120 + 0.807344i
\(147\) −123371. 71228.2i −0.0388383 0.0224233i
\(148\) 5.95555e6 5.95555e6i 1.83712 1.83712i
\(149\) 720669. + 2.68957e6i 0.217860 + 0.813064i 0.985140 + 0.171752i \(0.0549428\pi\)
−0.767280 + 0.641312i \(0.778391\pi\)
\(150\) 472084. 126495.i 0.139877 0.0374799i
\(151\) 2.69616e6 + 2.69616e6i 0.783097 + 0.783097i 0.980352 0.197255i \(-0.0632027\pi\)
−0.197255 + 0.980352i \(0.563203\pi\)
\(152\) −2.57166e6 + 4.45424e6i −0.732288 + 1.26836i
\(153\) 2.92040e6 1.68609e6i 0.815394 0.470768i
\(154\) 908909. 3.39209e6i 0.248862 0.928765i
\(155\) 302195.i 0.0811507i
\(156\) −339844. + 491974.i −0.0895171 + 0.129589i
\(157\) 4.22843e6 1.09265 0.546325 0.837574i \(-0.316027\pi\)
0.546325 + 0.837574i \(0.316027\pi\)
\(158\) −3.50361e6 938789.i −0.888268 0.238011i
\(159\) 19207.2 + 33267.8i 0.00477829 + 0.00827624i
\(160\) −996860. 575538.i −0.243374 0.140512i
\(161\) −4.68025e6 + 4.68025e6i −1.12148 + 1.12148i
\(162\) −1.73092e6 6.45987e6i −0.407128 1.51942i
\(163\) −4.39530e6 + 1.17772e6i −1.01491 + 0.271943i −0.727678 0.685919i \(-0.759400\pi\)
−0.287228 + 0.957862i \(0.592734\pi\)
\(164\) −8.67250e6 8.67250e6i −1.96613 1.96613i
\(165\) 30274.9 52437.6i 0.00673954 0.0116732i
\(166\) −1.05053e7 + 6.06525e6i −2.29660 + 1.32594i
\(167\) 817591. 3.05129e6i 0.175544 0.655140i −0.820914 0.571052i \(-0.806536\pi\)
0.996458 0.0840883i \(-0.0267978\pi\)
\(168\) 559522.i 0.118002i
\(169\) 1.70839e6 + 4.51436e6i 0.353938 + 0.935269i
\(170\) 2.13346e6 0.434248
\(171\) 6.97720e6 + 1.86954e6i 1.39538 + 0.373891i
\(172\) −2.31213e6 4.00473e6i −0.454388 0.787023i
\(173\) 3.36007e6 + 1.93994e6i 0.648948 + 0.374671i 0.788053 0.615607i \(-0.211089\pi\)
−0.139105 + 0.990278i \(0.544422\pi\)
\(174\) 317991. 317991.i 0.0603625 0.0603625i
\(175\) −1.54328e6 5.75960e6i −0.287959 1.07468i
\(176\) −13589.1 + 3641.18i −0.00249260 + 0.000667889i
\(177\) 195757. + 195757.i 0.0353019 + 0.0353019i
\(178\) −120181. + 208159.i −0.0213096 + 0.0369093i
\(179\) 877019. 506347.i 0.152915 0.0882854i −0.421590 0.906786i \(-0.638528\pi\)
0.574505 + 0.818501i \(0.305195\pi\)
\(180\) 683760. 2.55183e6i 0.117243 0.437556i
\(181\) 3.85774e6i 0.650574i 0.945615 + 0.325287i \(0.105461\pi\)
−0.945615 + 0.325287i \(0.894539\pi\)
\(182\) 9.70651e6 + 6.70503e6i 1.61009 + 1.11221i
\(183\) −563512. −0.0919496
\(184\) 7.92797e6 + 2.12429e6i 1.27265 + 0.341005i
\(185\) −1.43257e6 2.48129e6i −0.226256 0.391888i
\(186\) 252125. + 145564.i 0.0391811 + 0.0226212i
\(187\) −2.15957e6 + 2.15957e6i −0.330249 + 0.330249i
\(188\) 1.29290e6 + 4.82517e6i 0.194577 + 0.726171i
\(189\) 1.52529e6 408700.i 0.225926 0.0605368i
\(190\) 3.23144e6 + 3.23144e6i 0.471124 + 0.471124i
\(191\) 2.86422e6 4.96098e6i 0.411061 0.711979i −0.583945 0.811793i \(-0.698492\pi\)
0.995006 + 0.0998143i \(0.0318249\pi\)
\(192\) −963483. + 556267.i −0.136126 + 0.0785923i
\(193\) −1.95867e6 + 7.30986e6i −0.272452 + 1.01680i 0.685078 + 0.728470i \(0.259768\pi\)
−0.957530 + 0.288334i \(0.906899\pi\)
\(194\) 1.47776e7i 2.02394i
\(195\) 131736. + 154985.i 0.0177664 + 0.0209019i
\(196\) 5.62922e6 0.747618
\(197\) −173531. 46497.5i −0.0226975 0.00608178i 0.247452 0.968900i \(-0.420407\pi\)
−0.270150 + 0.962818i \(0.587073\pi\)
\(198\) 3.05790e6 + 5.29643e6i 0.393937 + 0.682319i
\(199\) −7.25547e6 4.18895e6i −0.920675 0.531552i −0.0368244 0.999322i \(-0.511724\pi\)
−0.883850 + 0.467770i \(0.845058\pi\)
\(200\) −5.22839e6 + 5.22839e6i −0.653548 + 0.653548i
\(201\) −330826. 1.23466e6i −0.0407391 0.152041i
\(202\) −2.85444e6 + 764845.i −0.346312 + 0.0927939i
\(203\) −3.87961e6 3.87961e6i −0.463767 0.463767i
\(204\) 635483. 1.10069e6i 0.0748538 0.129651i
\(205\) −3.61326e6 + 2.08611e6i −0.419409 + 0.242146i
\(206\) −2.83029e6 + 1.05628e7i −0.323765 + 1.20831i
\(207\) 1.15269e7i 1.29958i
\(208\) 3819.71 47106.1i 0.000424463 0.00523465i
\(209\) −6.54197e6 −0.716588
\(210\) 480208. + 128671.i 0.0518527 + 0.0138939i
\(211\) −4.52220e6 7.83268e6i −0.481396 0.833802i 0.518376 0.855153i \(-0.326537\pi\)
−0.999772 + 0.0213508i \(0.993203\pi\)
\(212\) −1.31459e6 758979.i −0.137969 0.0796567i
\(213\) 35364.0 35364.0i 0.00365950 0.00365950i
\(214\) 1.22847e6 + 4.58470e6i 0.125349 + 0.467810i
\(215\) −1.51948e6 + 407143.i −0.152890 + 0.0409668i
\(216\) −1.38461e6 1.38461e6i −0.137393 0.137393i
\(217\) 1.77594e6 3.07602e6i 0.173800 0.301030i
\(218\) −3.79713e6 + 2.19227e6i −0.366510 + 0.211605i
\(219\) 152174. 567922.i 0.0144880 0.0540700i
\(220\) 2.39265e6i 0.224704i
\(221\) −4.39497e6 9.27074e6i −0.407173 0.858890i
\(222\) −2.76022e6 −0.252281
\(223\) 9.34354e6 + 2.50359e6i 0.842553 + 0.225761i 0.654182 0.756337i \(-0.273013\pi\)
0.188370 + 0.982098i \(0.439680\pi\)
\(224\) 6.76463e6 + 1.17167e7i 0.601867 + 1.04246i
\(225\) 8.99307e6 + 5.19215e6i 0.789515 + 0.455827i
\(226\) 2.10385e7 2.10385e7i 1.82259 1.82259i
\(227\) 2.93077e6 + 1.09378e7i 0.250556 + 0.935087i 0.970509 + 0.241065i \(0.0774965\pi\)
−0.719953 + 0.694023i \(0.755837\pi\)
\(228\) 2.62969e6 704623.i 0.221871 0.0594501i
\(229\) −1.76098e6 1.76098e6i −0.146639 0.146639i 0.629976 0.776615i \(-0.283065\pi\)
−0.776615 + 0.629976i \(0.783065\pi\)
\(230\) 3.64633e6 6.31563e6i 0.299690 0.519079i
\(231\) −616330. + 355838.i −0.0500009 + 0.0288680i
\(232\) −1.76089e6 + 6.57174e6i −0.141016 + 0.526280i
\(233\) 6.96111e6i 0.550314i 0.961399 + 0.275157i \(0.0887299\pi\)
−0.961399 + 0.275157i \(0.911270\pi\)
\(234\) −2.02098e7 + 3.69614e6i −1.57730 + 0.288470i
\(235\) 1.69933e6 0.130941
\(236\) −1.05668e7 2.83136e6i −0.803909 0.215407i
\(237\) 367536. + 636592.i 0.0276093 + 0.0478207i
\(238\) −2.17163e7 1.25379e7i −1.61085 0.930024i
\(239\) −8.08660e6 + 8.08660e6i −0.592341 + 0.592341i −0.938263 0.345922i \(-0.887566\pi\)
0.345922 + 0.938263i \(0.387566\pi\)
\(240\) −515.470 1923.76i −3.72881e−5 0.000139161i
\(241\) −2.82455e6 + 756837.i −0.201790 + 0.0540694i −0.358298 0.933607i \(-0.616643\pi\)
0.156508 + 0.987677i \(0.449976\pi\)
\(242\) 1.23057e7 + 1.23057e7i 0.868284 + 0.868284i
\(243\) −2.06578e6 + 3.57804e6i −0.143968 + 0.249360i
\(244\) 1.92841e7 1.11337e7i 1.32749 0.766425i
\(245\) 495625. 1.84970e6i 0.0337020 0.125777i
\(246\) 4.01944e6i 0.269998i
\(247\) 7.38506e6 2.06987e7i 0.490076 1.37358i
\(248\) −4.40445e6 −0.288760
\(249\) 2.37455e6 + 636258.i 0.153809 + 0.0412131i
\(250\) 6.85406e6 + 1.18716e7i 0.438660 + 0.759782i
\(251\) 5.83721e6 + 3.37012e6i 0.369134 + 0.213120i 0.673080 0.739569i \(-0.264971\pi\)
−0.303946 + 0.952689i \(0.598304\pi\)
\(252\) −2.19565e7 + 2.19565e7i −1.37202 + 1.37202i
\(253\) 2.70197e6 + 1.00839e7i 0.166847 + 0.622681i
\(254\) 4.23654e7 1.13518e7i 2.58530 0.692728i
\(255\) −305723. 305723.i −0.0184377 0.0184377i
\(256\) 8.45976e6 1.46527e7i 0.504241 0.873371i
\(257\) 2.33937e7 1.35064e7i 1.37816 0.795682i 0.386224 0.922405i \(-0.373779\pi\)
0.991938 + 0.126723i \(0.0404460\pi\)
\(258\) −392233. + 1.46383e6i −0.0228394 + 0.0852379i
\(259\) 3.36757e7i 1.93828i
\(260\) −7.57031e6 2.70100e6i −0.430718 0.153675i
\(261\) 9.55502e6 0.537415
\(262\) −5.38943e7 1.44409e7i −2.99667 0.802956i
\(263\) −5.21923e6 9.03997e6i −0.286906 0.496935i 0.686164 0.727447i \(-0.259293\pi\)
−0.973070 + 0.230512i \(0.925960\pi\)
\(264\) 764271. + 441252.i 0.0415370 + 0.0239814i
\(265\) −365135. + 365135.i −0.0196208 + 0.0196208i
\(266\) −1.39020e7 5.18830e7i −0.738640 2.75664i
\(267\) 47050.9 12607.2i 0.00247192 0.000662348i
\(268\) 3.57153e7 + 3.57153e7i 1.85546 + 1.85546i
\(269\) −1.53380e7 + 2.65662e7i −0.787973 + 1.36481i 0.139233 + 0.990260i \(0.455536\pi\)
−0.927207 + 0.374550i \(0.877797\pi\)
\(270\) −1.50675e6 + 869921.i −0.0765507 + 0.0441966i
\(271\) 2.31549e6 8.64151e6i 0.116341 0.434192i −0.883042 0.469293i \(-0.844509\pi\)
0.999384 + 0.0351012i \(0.0111754\pi\)
\(272\) 100456.i 0.00499195i
\(273\) −430109. 2.35176e6i −0.0211393 0.115586i
\(274\) −3.43930e7 −1.67193
\(275\) −9.08431e6 2.43413e6i −0.436811 0.117043i
\(276\) −2.17223e6 3.76241e6i −0.103319 0.178953i
\(277\) −1.90907e7 1.10220e7i −0.898218 0.518587i −0.0215966 0.999767i \(-0.506875\pi\)
−0.876622 + 0.481180i \(0.840208\pi\)
\(278\) 1.16378e6 1.16378e6i 0.0541673 0.0541673i
\(279\) 1.60097e6 + 5.97489e6i 0.0737174 + 0.275117i
\(280\) −7.26501e6 + 1.94665e6i −0.330950 + 0.0886777i
\(281\) −1.70282e7 1.70282e7i −0.767449 0.767449i 0.210208 0.977657i \(-0.432586\pi\)
−0.977657 + 0.210208i \(0.932586\pi\)
\(282\) 818549. 1.41777e6i 0.0365004 0.0632205i
\(283\) −8.32872e6 + 4.80859e6i −0.367467 + 0.212157i −0.672351 0.740232i \(-0.734716\pi\)
0.304884 + 0.952389i \(0.401382\pi\)
\(284\) −511491. + 1.90891e6i −0.0223297 + 0.0833356i
\(285\) 926125.i 0.0400069i
\(286\) 1.68134e7 7.97072e6i 0.718716 0.340721i
\(287\) 4.90387e7 2.07440
\(288\) −2.27587e7 6.09816e6i −0.952728 0.255283i
\(289\) −1.16486e6 2.01760e6i −0.0482594 0.0835877i
\(290\) 5.23522e6 + 3.02256e6i 0.214655 + 0.123931i
\(291\) −2.11762e6 + 2.11762e6i −0.0859347 + 0.0859347i
\(292\) 6.01323e6 + 2.24417e7i 0.241523 + 0.901377i
\(293\) 1.15240e6 308784.i 0.0458141 0.0122758i −0.235839 0.971792i \(-0.575784\pi\)
0.281653 + 0.959516i \(0.409117\pi\)
\(294\) −1.30449e6 1.30449e6i −0.0513331 0.0513331i
\(295\) −1.86071e6 + 3.22284e6i −0.0724790 + 0.125537i
\(296\) 3.61644e7 2.08795e7i 1.39446 0.805091i
\(297\) 644620. 2.40575e6i 0.0246056 0.0918295i
\(298\) 3.60588e7i 1.36258i
\(299\) −3.49555e7 2.83444e6i −1.30768 0.106036i
\(300\) 3.91381e6 0.144956
\(301\) 1.78593e7 + 4.78540e6i 0.654886 + 0.175476i
\(302\) 2.46890e7 + 4.27626e7i 0.896361 + 1.55254i
\(303\) 518641. + 299437.i 0.0186440 + 0.0107641i
\(304\) −152156. + 152156.i −0.00541586 + 0.00541586i
\(305\) −1.96053e6 7.31682e6i −0.0690995 0.257883i
\(306\) 4.21820e7 1.13026e7i 1.47219 0.394471i
\(307\) 4.80186e6 + 4.80186e6i 0.165956 + 0.165956i 0.785199 0.619243i \(-0.212560\pi\)
−0.619243 + 0.785199i \(0.712560\pi\)
\(308\) 1.40611e7 2.43545e7i 0.481246 0.833542i
\(309\) 1.91922e6 1.10806e6i 0.0650502 0.0375568i
\(310\) −1.01287e6 + 3.78010e6i −0.0339994 + 0.126887i
\(311\) 6.99673e6i 0.232602i −0.993214 0.116301i \(-0.962896\pi\)
0.993214 0.116301i \(-0.0371038\pi\)
\(312\) −2.25888e6 + 1.92003e6i −0.0743755 + 0.0632184i
\(313\) 4.60593e6 0.150205 0.0751025 0.997176i \(-0.476072\pi\)
0.0751025 + 0.997176i \(0.476072\pi\)
\(314\) 5.28927e7 + 1.41726e7i 1.70847 + 0.457782i
\(315\) 5.28150e6 + 9.14782e6i 0.168976 + 0.292675i
\(316\) −2.51552e7 1.45233e7i −0.797197 0.460262i
\(317\) 1.11600e7 1.11600e7i 0.350337 0.350337i −0.509898 0.860235i \(-0.670317\pi\)
0.860235 + 0.509898i \(0.170317\pi\)
\(318\) 128754. + 480518.i 0.00400388 + 0.0149427i
\(319\) −8.35884e6 + 2.23974e6i −0.257498 + 0.0689964i
\(320\) −1.05748e7 1.05748e7i −0.322718 0.322718i
\(321\) 480946. 833022.i 0.0145405 0.0251850i
\(322\) −7.42313e7 + 4.28575e7i −2.22341 + 1.28369i
\(323\) −1.20903e7 + 4.51214e7i −0.358780 + 1.33898i
\(324\) 5.35556e7i 1.57460i
\(325\) 1.79566e7 2.59948e7i 0.523088 0.757246i
\(326\) −5.89273e7 −1.70084
\(327\) 858277. + 229975.i 0.0245462 + 0.00657713i
\(328\) −3.04048e7 5.26627e7i −0.861630 1.49239i
\(329\) −1.72973e7 9.98661e6i −0.485726 0.280434i
\(330\) 554459. 554459.i 0.0154286 0.0154286i
\(331\) 1.63243e7 + 6.09232e7i 0.450144 + 1.67996i 0.701986 + 0.712191i \(0.252297\pi\)
−0.251842 + 0.967768i \(0.581036\pi\)
\(332\) −9.38312e7 + 2.51420e7i −2.56409 + 0.687045i
\(333\) −4.14696e7 4.14696e7i −1.12305 1.12305i
\(334\) 2.04542e7 3.54277e7i 0.548962 0.950831i
\(335\) 1.48802e7 8.59110e6i 0.395799 0.228515i
\(336\) −6058.62 + 22611.1i −0.000159719 + 0.000596079i
\(337\) 4.12078e7i 1.07669i −0.842725 0.538344i \(-0.819050\pi\)
0.842725 0.538344i \(-0.180950\pi\)
\(338\) 6.23903e6 + 6.21954e7i 0.161572 + 1.61068i
\(339\) −6.02959e6 −0.154771
\(340\) 1.65026e7 + 4.42186e6i 0.419871 + 0.112504i
\(341\) −2.80109e6 4.85163e6i −0.0706422 0.122356i
\(342\) 8.10103e7 + 4.67713e7i 2.02517 + 1.16923i
\(343\) 1.85793e7 1.85793e7i 0.460411 0.460411i
\(344\) −5.93406e6 2.21462e7i −0.145773 0.544031i
\(345\) −1.42754e6 + 382508.i −0.0347641 + 0.00931502i
\(346\) 3.55283e7 + 3.55283e7i 0.857722 + 0.857722i
\(347\) −2.18829e7 + 3.79023e7i −0.523741 + 0.907146i 0.475877 + 0.879512i \(0.342131\pi\)
−0.999618 + 0.0276341i \(0.991203\pi\)
\(348\) 3.11878e6 1.80063e6i 0.0740026 0.0427254i
\(349\) 7.45551e6 2.78243e7i 0.175389 0.654559i −0.821097 0.570789i \(-0.806637\pi\)
0.996485 0.0837696i \(-0.0266960\pi\)
\(350\) 7.72184e7i 1.80101i
\(351\) 6.88409e6 + 4.75537e6i 0.159193 + 0.109967i
\(352\) 2.13390e7 0.489267
\(353\) 6.61158e7 + 1.77157e7i 1.50308 + 0.402748i 0.914129 0.405423i \(-0.132876\pi\)
0.588947 + 0.808172i \(0.299543\pi\)
\(354\) 1.79257e6 + 3.10482e6i 0.0404078 + 0.0699884i
\(355\) 582212. + 336141.i 0.0130136 + 0.00751339i
\(356\) −1.36105e6 + 1.36105e6i −0.0301665 + 0.0301665i
\(357\) 1.31525e6 + 4.90860e6i 0.0289071 + 0.107883i
\(358\) 1.26676e7 3.39427e6i 0.276086 0.0739771i
\(359\) −2.63511e7 2.63511e7i −0.569529 0.569529i 0.362467 0.931997i \(-0.381934\pi\)
−0.931997 + 0.362467i \(0.881934\pi\)
\(360\) 6.54924e6 1.13436e7i 0.140373 0.243133i
\(361\) −4.59126e7 + 2.65076e7i −0.975911 + 0.563442i
\(362\) −1.29301e7 + 4.82557e7i −0.272568 + 1.01724i
\(363\) 3.52680e6i 0.0737329i
\(364\) 6.11842e7 + 7.19823e7i 1.26863 + 1.49253i
\(365\) 7.90351e6 0.162533
\(366\) −7.04887e6 1.88874e6i −0.143773 0.0385237i
\(367\) −2.68381e7 4.64849e7i −0.542942 0.940403i −0.998733 0.0503164i \(-0.983977\pi\)
0.455791 0.890087i \(-0.349356\pi\)
\(368\) 297378. + 171691.i 0.00596713 + 0.00344513i
\(369\) −6.03882e7 + 6.03882e7i −1.20191 + 1.20191i
\(370\) −9.60317e6 3.58395e7i −0.189587 0.707549i
\(371\) 5.86251e6 1.57085e6i 0.114805 0.0307620i
\(372\) 1.64852e6 + 1.64852e6i 0.0320233 + 0.0320233i
\(373\) 2.29187e7 3.96963e7i 0.441634 0.764933i −0.556177 0.831064i \(-0.687732\pi\)
0.997811 + 0.0661312i \(0.0210656\pi\)
\(374\) −3.42519e7 + 1.97753e7i −0.654742 + 0.378015i
\(375\) 719007. 2.68337e6i 0.0136345 0.0508847i
\(376\) 2.47675e7i 0.465928i
\(377\) 2.34956e6 2.89757e7i 0.0438492 0.540766i
\(378\) 2.04494e7 0.378621
\(379\) 2.24848e7 + 6.02479e6i 0.413021 + 0.110669i 0.459345 0.888258i \(-0.348084\pi\)
−0.0463244 + 0.998926i \(0.514751\pi\)
\(380\) 1.82981e7 + 3.16932e7i 0.333468 + 0.577584i
\(381\) −7.69763e6 4.44423e6i −0.139182 0.0803566i
\(382\) 5.24558e7 5.24558e7i 0.941031 0.941031i
\(383\) −1.88742e7 7.04396e7i −0.335949 1.25378i −0.902837 0.429983i \(-0.858520\pi\)
0.566888 0.823795i \(-0.308147\pi\)
\(384\) −8.62287e6 + 2.31049e6i −0.152285 + 0.0408047i
\(385\) −6.76461e6 6.76461e6i −0.118539 0.118539i
\(386\) −4.90013e7 + 8.48727e7i −0.852011 + 1.47573i
\(387\) −2.78857e7 + 1.60998e7i −0.481114 + 0.277771i
\(388\) 3.06284e7 1.14307e8i 0.524360 1.95694i
\(389\) 1.07448e8i 1.82537i 0.408666 + 0.912684i \(0.365994\pi\)
−0.408666 + 0.912684i \(0.634006\pi\)
\(390\) 1.12839e6 + 2.38022e6i 0.0190224 + 0.0401257i
\(391\) 7.45443e7 1.24705
\(392\) 2.69591e7 + 7.22366e6i 0.447556 + 0.119922i
\(393\) 5.65364e6 + 9.79238e6i 0.0931430 + 0.161328i
\(394\) −2.01482e6 1.16326e6i −0.0329418 0.0190189i
\(395\) −6.98699e6 + 6.98699e6i −0.113370 + 0.113370i
\(396\) 1.26757e7 + 4.73065e7i 0.204121 + 0.761791i
\(397\) −4.47372e7 + 1.19873e7i −0.714986 + 0.191580i −0.597933 0.801546i \(-0.704011\pi\)
−0.117052 + 0.993126i \(0.537345\pi\)
\(398\) −7.67170e7 7.67170e7i −1.21687 1.21687i
\(399\) −5.44265e6 + 9.42694e6i −0.0856823 + 0.148406i
\(400\) −267901. + 154672.i −0.00418595 + 0.00241676i
\(401\) 1.44648e7 5.39833e7i 0.224325 0.837194i −0.758348 0.651850i \(-0.773993\pi\)
0.982674 0.185344i \(-0.0593400\pi\)
\(402\) 1.65530e7i 0.254799i
\(403\) 1.85126e7 3.38574e6i 0.282847 0.0517295i
\(404\) −2.36648e7 −0.358887
\(405\) −1.75978e7 4.71530e6i −0.264906 0.0709814i
\(406\) −3.55259e7 6.15327e7i −0.530844 0.919449i
\(407\) 4.59988e7 + 2.65574e7i 0.682281 + 0.393915i
\(408\) 4.45587e6 4.45587e6i 0.0656072 0.0656072i
\(409\) 1.01992e7 + 3.80638e7i 0.149072 + 0.556343i 0.999540 + 0.0303171i \(0.00965171\pi\)
−0.850469 + 0.526026i \(0.823682\pi\)
\(410\) −5.21896e7 + 1.39842e7i −0.757238 + 0.202901i
\(411\) 4.92849e6 + 4.92849e6i 0.0709885 + 0.0709885i
\(412\) −4.37854e7 + 7.58386e7i −0.626092 + 1.08442i
\(413\) 3.78799e7 2.18700e7i 0.537723 0.310455i
\(414\) 3.86350e7 1.44188e8i 0.544478 2.03202i
\(415\) 3.30455e7i 0.462347i
\(416\) −2.40890e7 + 6.75163e7i −0.334610 + 0.937840i
\(417\) −333538. −0.00459978
\(418\) −8.18322e7 2.19269e7i −1.12046 0.300226i
\(419\) 1.16420e7 + 2.01646e7i 0.158266 + 0.274124i 0.934243 0.356636i \(-0.116076\pi\)
−0.775978 + 0.630760i \(0.782743\pi\)
\(420\) 3.44779e6 + 1.99058e6i 0.0465364 + 0.0268678i
\(421\) 3.75681e7 3.75681e7i 0.503469 0.503469i −0.409045 0.912514i \(-0.634138\pi\)
0.912514 + 0.409045i \(0.134138\pi\)
\(422\) −3.03143e7 1.13135e8i −0.403376 1.50542i
\(423\) 3.35986e7 9.00270e6i 0.443915 0.118947i
\(424\) −5.32180e6 5.32180e6i −0.0698169 0.0698169i
\(425\) −3.35775e7 + 5.81580e7i −0.437403 + 0.757605i
\(426\) 560891. 323831.i 0.00725521 0.00418880i
\(427\) −2.30433e7 + 8.59988e7i −0.295979 + 1.10461i
\(428\) 3.80095e7i 0.484798i
\(429\) −3.55154e6 1.26715e6i −0.0449827 0.0160493i
\(430\) −2.03715e7 −0.256223
\(431\) −8.54875e7 2.29063e7i −1.06775 0.286104i −0.318183 0.948029i \(-0.603073\pi\)
−0.749570 + 0.661926i \(0.769739\pi\)
\(432\) −40961.2 70946.8i −0.000508067 0.000879998i
\(433\) 5.45440e7 + 3.14910e7i 0.671867 + 0.387903i 0.796784 0.604265i \(-0.206533\pi\)
−0.124917 + 0.992167i \(0.539866\pi\)
\(434\) 3.25248e7 3.25248e7i 0.397874 0.397874i
\(435\) −317073. 1.18333e6i −0.00385205 0.0143760i
\(436\) −3.39151e7 + 9.08753e6i −0.409198 + 0.109644i
\(437\) 1.12908e8 + 1.12908e8i 1.35295 + 1.35295i
\(438\) 3.80704e6 6.59399e6i 0.0453070 0.0784740i
\(439\) 4.53364e7 2.61750e7i 0.535862 0.309380i −0.207538 0.978227i \(-0.566545\pi\)
0.743400 + 0.668847i \(0.233212\pi\)
\(440\) −3.07035e6 + 1.14587e7i −0.0360437 + 0.134517i
\(441\) 3.91973e7i 0.457025i
\(442\) −2.39029e7 1.30697e8i −0.276811 1.51355i
\(443\) −1.06292e8 −1.22261 −0.611306 0.791395i \(-0.709355\pi\)
−0.611306 + 0.791395i \(0.709355\pi\)
\(444\) −2.13507e7 5.72090e6i −0.243929 0.0653605i
\(445\) 327393. + 567061.i 0.00371526 + 0.00643501i
\(446\) 1.08485e8 + 6.26340e7i 1.22283 + 0.706001i
\(447\) 5.16720e6 5.16720e6i 0.0578539 0.0578539i
\(448\) 4.54941e7 + 1.69786e8i 0.505966 + 1.88829i
\(449\) 8.62989e7 2.31237e7i 0.953380 0.255457i 0.251584 0.967835i \(-0.419048\pi\)
0.701796 + 0.712378i \(0.252382\pi\)
\(450\) 9.50899e7 + 9.50899e7i 1.04351 + 1.04351i
\(451\) 3.86730e7 6.69836e7i 0.421578 0.730195i
\(452\) 2.06341e8 1.19131e8i 2.23444 1.29006i
\(453\) 2.58993e6 9.66576e6i 0.0278608 0.103978i
\(454\) 1.46642e8i 1.56708i
\(455\) 2.90396e7 1.37668e7i 0.308287 0.146150i
\(456\) 1.34981e7 0.142357
\(457\) −2.83776e7 7.60377e6i −0.297323 0.0796673i 0.107074 0.994251i \(-0.465852\pi\)
−0.404397 + 0.914584i \(0.632518\pi\)
\(458\) −1.61255e7 2.79301e7i −0.167848 0.290721i
\(459\) −1.54017e7 8.89218e6i −0.159269 0.0919539i
\(460\) 4.12948e7 4.12948e7i 0.424251 0.424251i
\(461\) 1.04941e7 + 3.91645e7i 0.107113 + 0.399751i 0.998576 0.0533418i \(-0.0169873\pi\)
−0.891463 + 0.453093i \(0.850321\pi\)
\(462\) −8.90223e6 + 2.38535e6i −0.0902761 + 0.0241894i
\(463\) −7.77336e6 7.77336e6i −0.0783188 0.0783188i 0.666862 0.745181i \(-0.267637\pi\)
−0.745181 + 0.666862i \(0.767637\pi\)
\(464\) −142320. + 246506.i −0.00142467 + 0.00246759i
\(465\) 686829. 396541.i 0.00683109 0.00394393i
\(466\) −2.33317e7 + 8.70752e7i −0.230563 + 0.860472i
\(467\) 1.44943e8i 1.42314i −0.702615 0.711570i \(-0.747984\pi\)
0.702615 0.711570i \(-0.252016\pi\)
\(468\) −1.63987e8 1.32972e7i −1.59982 0.129725i
\(469\) −2.01953e8 −1.95763
\(470\) 2.12566e7 + 5.69569e6i 0.204739 + 0.0548596i
\(471\) −5.54856e6 9.61039e6i −0.0531028 0.0919768i
\(472\) −4.69724e7 2.71195e7i −0.446701 0.257903i
\(473\) 2.06208e7 2.06208e7i 0.194860 0.194860i
\(474\) 2.46376e6 + 9.19488e6i 0.0231347 + 0.0863398i
\(475\) −1.38947e8 + 3.72307e7i −1.29649 + 0.347393i
\(476\) −1.41992e8 1.41992e8i −1.31657 1.31657i
\(477\) −5.28491e6 + 9.15374e6i −0.0486948 + 0.0843419i
\(478\) −1.28258e8 + 7.40496e7i −1.17436 + 0.678015i
\(479\) 3.29660e7 1.23031e8i 0.299958 1.11946i −0.637242 0.770664i \(-0.719925\pi\)
0.937200 0.348793i \(-0.113408\pi\)
\(480\) 3.02089e6i 0.0273156i
\(481\) −1.35954e8 + 1.15560e8i −1.22168 + 1.03842i
\(482\) −3.78685e7 −0.338172
\(483\) 1.67787e7 + 4.49585e6i 0.148908 + 0.0398997i
\(484\) 6.96815e7 + 1.20692e8i 0.614584 + 1.06449i
\(485\) −3.48633e7 2.01283e7i −0.305593 0.176434i
\(486\) −3.78331e7 + 3.78331e7i −0.329582 + 0.329582i
\(487\) −3.76889e7 1.40657e8i −0.326307 1.21779i −0.912992 0.407978i \(-0.866234\pi\)
0.586685 0.809815i \(-0.300433\pi\)
\(488\) 1.06642e8 2.85745e7i 0.917628 0.245878i
\(489\) 8.44424e6 + 8.44424e6i 0.0722161 + 0.0722161i
\(490\) 1.23994e7 2.14763e7i 0.105393 0.182546i
\(491\) 9.25186e7 5.34156e7i 0.781600 0.451257i −0.0553972 0.998464i \(-0.517643\pi\)
0.836997 + 0.547208i \(0.184309\pi\)
\(492\) −8.33079e6 + 3.10909e7i −0.0699505 + 0.261059i
\(493\) 6.17921e7i 0.515694i
\(494\) 1.61755e8 2.34164e8i 1.34176 1.94240i
\(495\) 1.66604e7 0.137363
\(496\) −177990. 47692.3i −0.00145865 0.000390844i
\(497\) −3.95086e6 6.84309e6i −0.0321827 0.0557420i
\(498\) 2.75702e7 + 1.59177e7i 0.223230 + 0.128882i
\(499\) −5.23268e7 + 5.23268e7i −0.421136 + 0.421136i −0.885595 0.464459i \(-0.846249\pi\)
0.464459 + 0.885595i \(0.346249\pi\)
\(500\) 2.84118e7 + 1.06034e8i 0.227295 + 0.848275i
\(501\) −8.00782e6 + 2.14569e6i −0.0636797 + 0.0170629i
\(502\) 6.17209e7 + 6.17209e7i 0.487889 + 0.487889i
\(503\) 5.19728e7 9.00196e7i 0.408388 0.707348i −0.586322 0.810078i \(-0.699425\pi\)
0.994709 + 0.102730i \(0.0327579\pi\)
\(504\) −1.33328e8 + 7.69771e7i −1.04143 + 0.601270i
\(505\) −2.08357e6 + 7.77598e6i −0.0161783 + 0.0603783i
\(506\) 1.35194e8i 1.04353i
\(507\) 8.01850e6 9.80659e6i 0.0615275 0.0752479i
\(508\) 3.51231e8 2.67918
\(509\) −6.66679e6 1.78636e6i −0.0505549 0.0135462i 0.233453 0.972368i \(-0.424998\pi\)
−0.284008 + 0.958822i \(0.591664\pi\)
\(510\) −2.79953e6 4.84893e6i −0.0211045 0.0365540i
\(511\) −8.04491e7 4.64473e7i −0.602919 0.348095i
\(512\) 996858. 996858.i 0.00742717 0.00742717i
\(513\) −9.85964e6 3.67967e7i −0.0730313 0.272556i
\(514\) 3.37897e8 9.05393e7i 2.48826 0.666727i
\(515\) 2.10646e7 + 2.10646e7i 0.154217 + 0.154217i
\(516\) −6.06796e6 + 1.05100e7i −0.0441666 + 0.0764988i
\(517\) −2.72821e7 + 1.57513e7i −0.197427 + 0.113985i
\(518\) −1.12872e8 + 4.21243e8i −0.812074 + 3.03070i
\(519\) 1.01824e7i 0.0728361i
\(520\) −3.27892e7 2.26500e7i −0.233196 0.161086i
\(521\) 1.25619e8 0.888264 0.444132 0.895961i \(-0.353512\pi\)
0.444132 + 0.895961i \(0.353512\pi\)
\(522\) 1.19522e8 + 3.20258e7i 0.840303 + 0.225158i
\(523\) 1.38607e7 + 2.40074e7i 0.0968903 + 0.167819i 0.910396 0.413738i \(-0.135777\pi\)
−0.813506 + 0.581557i \(0.802444\pi\)
\(524\) −3.86950e8 2.23406e8i −2.68943 1.55274i
\(525\) −1.10653e7 + 1.10653e7i −0.0764693 + 0.0764693i
\(526\) −3.49868e7 1.30573e8i −0.240407 0.897212i
\(527\) −3.86395e7 + 1.03534e7i −0.263997 + 0.0707379i
\(528\) 26107.3 + 26107.3i 0.000177362 + 0.000177362i
\(529\) 5.33870e7 9.24689e7i 0.360635 0.624639i
\(530\) −5.79124e6 + 3.34358e6i −0.0388995 + 0.0224586i
\(531\) −1.97153e7 + 7.35785e7i −0.131680 + 0.491436i
\(532\) 4.30136e8i 2.85674i
\(533\) 1.68278e8 + 1.97977e8i 1.11134 + 1.30747i
\(534\) 630806. 0.00414259
\(535\) 1.24895e7 + 3.34655e6i 0.0815612 + 0.0218542i
\(536\) 1.25214e8 + 2.16877e8i 0.813128 + 1.40838i
\(537\) −2.30165e6 1.32886e6i −0.0148634 0.00858136i
\(538\) −2.80902e8 + 2.80902e8i −1.80388 + 1.80388i
\(539\) 9.18805e6 + 3.42903e7i 0.0586755 + 0.218980i
\(540\) −1.34579e7 + 3.60604e6i −0.0854668 + 0.0229007i
\(541\) 8.17036e7 + 8.17036e7i 0.516000 + 0.516000i 0.916359 0.400359i \(-0.131114\pi\)
−0.400359 + 0.916359i \(0.631114\pi\)
\(542\) 5.79280e7 1.00334e8i 0.363823 0.630160i
\(543\) 8.76787e6 5.06213e6i 0.0547639 0.0316180i
\(544\) 3.94367e7 1.47180e8i 0.244965 0.914221i
\(545\) 1.19442e7i 0.0737852i
\(546\) 2.50230e6 3.08593e7i 0.0153731 0.189587i
\(547\) 3.62271e7 0.221346 0.110673 0.993857i \(-0.464699\pi\)
0.110673 + 0.993857i \(0.464699\pi\)
\(548\) −2.66035e8 7.12838e7i −1.61658 0.433161i
\(549\) −7.75260e7 1.34279e8i −0.468522 0.811505i
\(550\) −1.05475e8 6.08962e7i −0.633961 0.366018i
\(551\) −9.35932e7 + 9.35932e7i −0.559487 + 0.559487i
\(552\) −5.57500e6 2.08062e7i −0.0331458 0.123702i
\(553\) 1.12181e8 3.00588e7i 0.663352 0.177745i
\(554\) −2.01859e8 2.01859e8i −1.18719 1.18719i
\(555\) −3.75965e6 + 6.51190e6i −0.0219922 + 0.0380915i
\(556\) 1.14141e7 6.58994e6i 0.0664076 0.0383404i
\(557\) −4.42041e7 + 1.64972e8i −0.255798 + 0.954652i 0.711847 + 0.702335i \(0.247859\pi\)
−0.967645 + 0.252317i \(0.918808\pi\)
\(558\) 8.01048e7i 0.461058i
\(559\) 4.19657e7 + 8.85224e7i 0.240248 + 0.506778i
\(560\) −314668. −0.00179180
\(561\) 7.74206e6 + 2.07448e6i 0.0438498 + 0.0117495i
\(562\) −1.55928e8 2.70076e8i −0.878449 1.52152i
\(563\) 1.47839e8 + 8.53549e7i 0.828445 + 0.478303i 0.853320 0.521388i \(-0.174585\pi\)
−0.0248749 + 0.999691i \(0.507919\pi\)
\(564\) 9.27011e6 9.27011e6i 0.0516711 0.0516711i
\(565\) −2.09778e7 7.82901e7i −0.116309 0.434072i
\(566\) −1.20299e8 + 3.22341e7i −0.663459 + 0.177773i
\(567\) 1.51415e8 + 1.51415e8i 0.830653 + 0.830653i
\(568\) −4.89920e6 + 8.48566e6i −0.0267350 + 0.0463064i
\(569\) −1.04701e8 + 6.04490e7i −0.568347 + 0.328135i −0.756489 0.654007i \(-0.773087\pi\)
0.188142 + 0.982142i \(0.439753\pi\)
\(570\) 3.10412e6 1.15847e7i 0.0167615 0.0625548i
\(571\) 1.76317e8i 0.947080i −0.880772 0.473540i \(-0.842976\pi\)
0.880772 0.473540i \(-0.157024\pi\)
\(572\) 1.46574e8 2.68068e7i 0.783195 0.143237i
\(573\) −1.50338e7 −0.0799105
\(574\) 6.13415e8 + 1.64364e8i 3.24354 + 0.869103i
\(575\) 1.14776e8 + 1.98798e8i 0.603736 + 1.04570i
\(576\) −2.65105e8 1.53059e8i −1.38724 0.800922i
\(577\) −5.78495e7 + 5.78495e7i −0.301142 + 0.301142i −0.841461 0.540318i \(-0.818304\pi\)
0.540318 + 0.841461i \(0.318304\pi\)
\(578\) −7.80861e6 2.91421e7i −0.0404380 0.150917i
\(579\) 1.91840e7 5.14035e6i 0.0988335 0.0264824i
\(580\) 3.42306e7 + 3.42306e7i 0.175441 + 0.175441i
\(581\) 1.94202e8 3.36367e8i 0.990204 1.71508i
\(582\) −3.35865e7 + 1.93912e7i −0.170371 + 0.0983639i
\(583\) 2.47762e6 9.24661e6i 0.0125034 0.0466634i
\(584\) 1.15193e8i 0.578343i
\(585\) −1.88076e7 + 5.27134e7i −0.0939430 + 0.263302i
\(586\) 1.54501e7 0.0767781
\(587\) −1.68309e8 4.50984e7i −0.832135 0.222970i −0.182490 0.983208i \(-0.558416\pi\)
−0.649645 + 0.760238i \(0.725082\pi\)
\(588\) −7.38668e6 1.27941e7i −0.0363343 0.0629329i
\(589\) −7.42070e7 4.28434e7i −0.363161 0.209671i
\(590\) −3.40773e7 + 3.40773e7i −0.165924 + 0.165924i
\(591\) 122028. + 455415.i 0.000591150 + 0.00220620i
\(592\) 1.68754e6 452175.i 0.00813372 0.00217942i
\(593\) −2.18905e8 2.18905e8i −1.04977 1.04977i −0.998695 0.0510709i \(-0.983737\pi\)
−0.0510709 0.998695i \(-0.516263\pi\)
\(594\) 1.61269e7 2.79325e7i 0.0769468 0.133276i
\(595\) −5.91588e7 + 3.41553e7i −0.280846 + 0.162147i
\(596\) −7.47365e7 + 2.78920e8i −0.353016 + 1.31747i
\(597\) 2.19870e7i 0.103334i
\(598\) −4.27751e8 1.52617e8i −2.00026 0.713671i
\(599\) −3.89795e8 −1.81366 −0.906829 0.421499i \(-0.861504\pi\)
−0.906829 + 0.421499i \(0.861504\pi\)
\(600\) 1.87438e7 + 5.02238e6i 0.0867768 + 0.0232518i
\(601\) 1.20190e8 + 2.08175e8i 0.553662 + 0.958971i 0.998006 + 0.0631150i \(0.0201035\pi\)
−0.444344 + 0.895856i \(0.646563\pi\)
\(602\) 2.07360e8 + 1.19719e8i 0.950462 + 0.548750i
\(603\) 2.48693e8 2.48693e8i 1.13426 1.13426i
\(604\) 1.02342e8 + 3.81946e8i 0.464455 + 1.73337i
\(605\) 4.57931e7 1.22702e7i 0.206792 0.0554098i
\(606\) 5.48395e6 + 5.48395e6i 0.0246420 + 0.0246420i
\(607\) −7.71816e7 + 1.33682e8i −0.345102 + 0.597735i −0.985372 0.170415i \(-0.945489\pi\)
0.640270 + 0.768150i \(0.278822\pi\)
\(608\) 2.82658e8 1.63193e8i 1.25762 0.726089i
\(609\) −3.72675e6 + 1.39084e7i −0.0164998 + 0.0615780i
\(610\) 9.80958e7i 0.432176i
\(611\) −1.90390e7 1.04102e8i −0.0834680 0.456388i
\(612\) 3.49710e8 1.52565
\(613\) −1.48913e8 3.99012e7i −0.646475 0.173222i −0.0793403 0.996848i \(-0.525281\pi\)
−0.567135 + 0.823625i \(0.691948\pi\)
\(614\) 4.39710e7 + 7.61600e7i 0.189960 + 0.329020i
\(615\) 9.48265e6 + 5.47481e6i 0.0407666 + 0.0235366i
\(616\) 9.85932e7 9.85932e7i 0.421798 0.421798i
\(617\) 6.25487e6 + 2.33435e7i 0.0266295 + 0.0993825i 0.977962 0.208785i \(-0.0669509\pi\)
−0.951332 + 0.308168i \(0.900284\pi\)
\(618\) 2.77210e7 7.42783e6i 0.117448 0.0314700i
\(619\) 2.54367e8 + 2.54367e8i 1.07248 + 1.07248i 0.997159 + 0.0753200i \(0.0239978\pi\)
0.0753200 + 0.997159i \(0.476002\pi\)
\(620\) −1.56695e7 + 2.71403e7i −0.0657475 + 0.113878i
\(621\) −5.26466e7 + 3.03956e7i −0.219834 + 0.126922i
\(622\) 2.34511e7 8.75208e7i 0.0974524 0.363697i
\(623\) 7.69608e6i 0.0318277i
\(624\) −112075. + 53131.3i −0.000461270 + 0.000218674i
\(625\) −1.87351e8 −0.767391
\(626\) 5.76147e7 + 1.54378e7i 0.234861 + 0.0629308i
\(627\) 8.58439e6 + 1.48686e7i 0.0348262 + 0.0603208i
\(628\) 3.79758e8 + 2.19254e8i 1.53330 + 0.885253i
\(629\) 2.68183e8 2.68183e8i 1.07765 1.07765i
\(630\) 3.54043e7 + 1.32130e8i 0.141590 + 0.528423i
\(631\) 5.46658e7 1.46477e7i 0.217584 0.0583015i −0.148380 0.988930i \(-0.547406\pi\)
0.365964 + 0.930629i \(0.380739\pi\)
\(632\) −1.01834e8 1.01834e8i −0.403407 0.403407i
\(633\) −1.18681e7 + 2.05561e7i −0.0467917 + 0.0810457i
\(634\) 1.77003e8 1.02193e8i 0.694566 0.401008i
\(635\) 3.09241e7 1.15410e8i 0.120775 0.450738i
\(636\) 3.98374e6i 0.0154853i
\(637\) −1.18866e8 9.63853e6i −0.459875 0.0372900i
\(638\) −1.12066e8 −0.431531
\(639\) 1.32921e7 + 3.56161e6i 0.0509438 + 0.0136503i
\(640\) −6.00002e7 1.03923e8i −0.228883 0.396437i
\(641\) 1.29789e8 + 7.49340e7i 0.492794 + 0.284515i 0.725733 0.687977i \(-0.241501\pi\)
−0.232939 + 0.972491i \(0.574834\pi\)
\(642\) 8.80812e6 8.80812e6i 0.0332873 0.0332873i
\(643\) −7.50428e7 2.80064e8i −0.282277 1.05347i −0.950806 0.309787i \(-0.899742\pi\)
0.668528 0.743687i \(-0.266925\pi\)
\(644\) −6.63018e8 + 1.77655e8i −2.48238 + 0.665151i
\(645\) 2.91922e6 + 2.91922e6i 0.0108790 + 0.0108790i
\(646\) −3.02469e8 + 5.23892e8i −1.12198 + 1.94332i
\(647\) −3.12630e8 + 1.80497e8i −1.15430 + 0.666435i −0.949931 0.312459i \(-0.898847\pi\)
−0.204368 + 0.978894i \(0.565514\pi\)
\(648\) 6.87249e7 2.56485e8i 0.252574 0.942620i
\(649\) 6.89887e7i 0.252373i
\(650\) 3.11743e8 2.64979e8i 1.13516 0.964875i
\(651\) −9.32156e6 −0.0337867
\(652\) −4.55812e8 1.22134e8i −1.64453 0.440651i
\(653\) −1.36881e8 2.37084e8i −0.491589 0.851457i 0.508364 0.861142i \(-0.330250\pi\)
−0.999953 + 0.00968495i \(0.996917\pi\)
\(654\) 9.96521e6 + 5.75341e6i 0.0356248 + 0.0205680i
\(655\) −1.07478e8 + 1.07478e8i −0.382467 + 0.382467i
\(656\) −658459. 2.45740e6i −0.00233248 0.00870492i
\(657\) 1.56265e8 4.18712e7i 0.551019 0.147645i
\(658\) −1.82897e8 1.82897e8i −0.641989 0.641989i
\(659\) −1.69995e8 + 2.94439e8i −0.593990 + 1.02882i 0.399698 + 0.916647i \(0.369115\pi\)
−0.993689 + 0.112174i \(0.964218\pi\)
\(660\) 5.43801e6 3.13964e6i 0.0189151 0.0109206i
\(661\) 6.71663e7 2.50668e8i 0.232566 0.867950i −0.746664 0.665201i \(-0.768346\pi\)
0.979231 0.202749i \(-0.0649875\pi\)
\(662\) 8.16791e8i 2.81538i
\(663\) −1.53034e7 + 2.21540e7i −0.0525108 + 0.0760171i
\(664\) −4.81633e8 −1.64518
\(665\) −1.41338e8 3.78714e7i −0.480611 0.128779i
\(666\) −3.79741e8 6.57730e8i −1.28548 2.22651i
\(667\) 1.82922e8 + 1.05610e8i 0.616436 + 0.355899i
\(668\) 2.31644e8 2.31644e8i 0.777127 0.777127i
\(669\) −6.57045e6 2.45212e7i −0.0219440 0.0818963i
\(670\) 2.14929e8 5.75900e7i 0.714612 0.191480i
\(671\) 9.92963e7 + 9.92963e7i 0.328674 + 0.328674i
\(672\) 1.77531e7 3.07493e7i 0.0585015 0.101328i
\(673\) 3.56842e8 2.06023e8i 1.17066 0.675881i 0.216825 0.976210i \(-0.430430\pi\)
0.953836 + 0.300329i \(0.0970965\pi\)
\(674\) 1.38117e8 5.15461e8i 0.451096 1.68351i
\(675\) 5.47652e7i 0.178071i
\(676\) −8.06479e7 + 4.94021e8i −0.261068 + 1.59921i
\(677\) 7.49337e7 0.241497 0.120748 0.992683i \(-0.461471\pi\)
0.120748 + 0.992683i \(0.461471\pi\)
\(678\) −7.54230e7 2.02095e7i −0.242000 0.0648436i
\(679\) 2.36580e8 + 4.09768e8i 0.755733 + 1.30897i
\(680\) 7.33589e7 + 4.23538e7i 0.233306 + 0.134699i
\(681\) 2.10137e7 2.10137e7i 0.0665366 0.0665366i
\(682\) −1.87770e7 7.00766e7i −0.0591933 0.220912i
\(683\) −1.53175e8 + 4.10431e7i −0.480756 + 0.128818i −0.491055 0.871129i \(-0.663389\pi\)
0.0102984 + 0.999947i \(0.496722\pi\)
\(684\) 5.29687e8 + 5.29687e8i 1.65520 + 1.65520i
\(685\) −4.68461e7 + 8.11399e7i −0.145748 + 0.252443i
\(686\) 2.94677e8 1.70132e8i 0.912796 0.527003i
\(687\) −1.69160e6 + 6.31313e6i −0.00521707 + 0.0194704i
\(688\) 959215.i 0.00294544i
\(689\) 2.64593e7 + 1.82774e7i 0.0808947 + 0.0558802i
\(690\) −1.91389e7 −0.0582599
\(691\) −1.22148e8 3.27294e7i −0.370212 0.0991981i 0.0689160 0.997622i \(-0.478046\pi\)
−0.439128 + 0.898424i \(0.644713\pi\)
\(692\) 2.01180e8 + 3.48454e8i 0.607109 + 1.05154i
\(693\) −1.69585e8 9.79100e7i −0.509551 0.294189i
\(694\) −4.00767e8 + 4.00767e8i −1.19898 + 1.19898i
\(695\) −1.16042e6 4.33076e6i −0.00345670 0.0129006i
\(696\) 1.72469e7 4.62130e6i 0.0511545 0.0137068i
\(697\) −3.90529e8 3.90529e8i −1.15333 1.15333i
\(698\) 1.86519e8 3.23061e8i 0.548475 0.949987i
\(699\) 1.58212e7 9.13439e6i 0.0463243 0.0267453i
\(700\) 1.60045e8 5.97296e8i 0.466603 1.74139i
\(701\) 4.53196e8i 1.31562i 0.753182 + 0.657812i \(0.228518\pi\)
−0.753182 + 0.657812i \(0.771482\pi\)
\(702\) 7.01730e7 + 8.25575e7i 0.202843 + 0.238641i
\(703\) 8.12406e8 2.33834
\(704\) 2.67795e8 + 7.17554e7i 0.767510 + 0.205654i
\(705\) −2.22987e6 3.86224e6i −0.00636372 0.0110223i
\(706\) 7.67651e8 + 4.43204e8i 2.18147 + 1.25947i
\(707\) 6.69062e7 6.69062e7i 0.189325 0.189325i
\(708\) 7.43064e6 + 2.77315e7i 0.0209376 + 0.0781401i
\(709\) 1.76984e8 4.74227e7i 0.496587 0.133060i −0.00182856 0.999998i \(-0.500582\pi\)
0.498416 + 0.866938i \(0.333915\pi\)
\(710\) 6.15613e6 + 6.15613e6i 0.0172002 + 0.0172002i
\(711\) −1.01129e8 + 1.75160e8i −0.281362 + 0.487333i
\(712\) −8.26483e6 + 4.77170e6i −0.0228978 + 0.0132201i
\(713\) −3.53904e7 + 1.32079e8i −0.0976376 + 0.364389i
\(714\) 6.58091e7i 0.180797i
\(715\) 4.09676e6 5.05229e7i 0.0112079 0.138220i
\(716\) 1.05021e8 0.286112
\(717\) 2.89905e7 + 7.76797e6i 0.0786498 + 0.0210742i
\(718\) −2.41300e8 4.17943e8i −0.651903 1.12913i
\(719\) −4.25042e8 2.45398e8i −1.14352 0.660213i −0.196223 0.980559i \(-0.562868\pi\)
−0.947301 + 0.320346i \(0.896201\pi\)
\(720\) 387495. 387495.i 0.00103817 0.00103817i
\(721\) −9.06224e7 3.38207e8i −0.241785 0.902354i
\(722\) −6.63158e8 + 1.77693e8i −1.76200 + 0.472126i
\(723\) 5.42653e6 + 5.42653e6i 0.0143584 + 0.0143584i
\(724\) −2.00032e8 + 3.46466e8i −0.527089 + 0.912945i
\(725\) −1.64790e8 + 9.51413e7i −0.432430 + 0.249664i
\(726\) 1.18209e7 4.41161e7i 0.0308916 0.115289i
\(727\) 5.71482e7i 0.148730i −0.997231 0.0743651i \(-0.976307\pi\)
0.997231 0.0743651i \(-0.0236930\pi\)
\(728\) 2.00649e8 + 4.23247e8i 0.520046 + 1.09698i
\(729\) −3.65631e8 −0.943758
\(730\) 9.88635e7 + 2.64904e7i 0.254137 + 0.0680958i
\(731\) −1.04117e8 1.80336e8i −0.266544 0.461668i
\(732\) −5.06094e7 2.92193e7i −0.129032 0.0744967i
\(733\) 2.08775e8 2.08775e8i 0.530112 0.530112i −0.390494 0.920606i \(-0.627696\pi\)
0.920606 + 0.390494i \(0.127696\pi\)
\(734\) −1.79908e8 6.71425e8i −0.454948 1.69789i
\(735\) −4.85436e6 + 1.30072e6i −0.0122256 + 0.00327584i
\(736\) −3.68291e8 3.68291e8i −0.923756 0.923756i
\(737\) −1.59264e8 + 2.75854e8i −0.397847 + 0.689091i
\(738\) −9.57789e8 + 5.52980e8i −2.38287 + 1.37575i
\(739\) 5.73400e7 2.13996e8i 0.142077 0.530239i −0.857791 0.513999i \(-0.828164\pi\)
0.999868 0.0162405i \(-0.00516974\pi\)
\(740\) 2.97128e8i 0.733243i
\(741\) −5.67348e7 + 1.03761e7i −0.139442 + 0.0255024i
\(742\) 7.85980e7 0.192398
\(743\) −1.76192e8 4.72106e7i −0.429557 0.115099i 0.0375612 0.999294i \(-0.488041\pi\)
−0.467118 + 0.884195i \(0.654708\pi\)
\(744\) 5.77953e6 + 1.00104e7i 0.0140337 + 0.0243072i
\(745\) 8.50700e7 + 4.91152e7i 0.205735 + 0.118781i
\(746\) 4.19736e8 4.19736e8i 1.01102 1.01102i
\(747\) 1.75068e8 + 6.53364e8i 0.419997 + 1.56745i
\(748\) −3.05930e8 + 8.19738e7i −0.731001 + 0.195871i
\(749\) −1.07462e8 1.07462e8i −0.255747 0.255747i
\(750\) 1.79878e7 3.11559e7i 0.0426378 0.0738509i
\(751\) −3.85818e8 + 2.22752e8i −0.910882 + 0.525898i −0.880715 0.473647i \(-0.842937\pi\)
−0.0301672 + 0.999545i \(0.509604\pi\)
\(752\) −268188. + 1.00089e6i −0.000630645 + 0.00235360i
\(753\) 1.76891e7i 0.0414306i
\(754\) 1.26509e8 3.54576e8i 0.295125 0.827171i
\(755\) 1.34514e8 0.312555
\(756\) 1.58179e8 + 4.23840e7i 0.366086 + 0.0980926i
\(757\) 2.61550e8 + 4.53018e8i 0.602930 + 1.04431i 0.992375 + 0.123255i \(0.0393334\pi\)
−0.389445 + 0.921050i \(0.627333\pi\)
\(758\) 2.61065e8 + 1.50726e8i 0.599433 + 0.346083i
\(759\) 1.93731e7 1.93731e7i 0.0443072 0.0443072i
\(760\) 4.69618e7 + 1.75264e8i 0.106980 + 0.399256i
\(761\) 3.46101e8 9.27376e7i 0.785325 0.210427i 0.156194 0.987726i \(-0.450078\pi\)
0.629131 + 0.777299i \(0.283411\pi\)
\(762\) −8.13923e7 8.13923e7i −0.183958 0.183958i
\(763\) 7.01938e7 1.21579e8i 0.158025 0.273707i