Properties

Label 37.8.f.a.7.7
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 7.7
Character \(\chi\) \(=\) 37.7
Dual form 37.8.f.a.16.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-12.0215 + 4.37547i) q^{2} +(-68.2052 - 24.8247i) q^{3} +(27.3180 - 22.9225i) q^{4} +(75.7434 + 429.562i) q^{5} +928.548 q^{6} +(226.548 + 1284.82i) q^{7} +(590.646 - 1023.03i) q^{8} +(2360.34 + 1980.56i) q^{9} +O(q^{10})\) \(q+(-12.0215 + 4.37547i) q^{2} +(-68.2052 - 24.8247i) q^{3} +(27.3180 - 22.9225i) q^{4} +(75.7434 + 429.562i) q^{5} +928.548 q^{6} +(226.548 + 1284.82i) q^{7} +(590.646 - 1023.03i) q^{8} +(2360.34 + 1980.56i) q^{9} +(-2790.09 - 4832.57i) q^{10} +(-3990.89 + 6912.42i) q^{11} +(-2432.27 + 885.274i) q^{12} +(-4135.39 + 3470.00i) q^{13} +(-8345.11 - 14454.2i) q^{14} +(5497.64 - 31178.7i) q^{15} +(-3416.86 + 19378.0i) q^{16} +(902.800 + 757.539i) q^{17} +(-37040.7 - 13481.7i) q^{18} +(4840.41 + 1761.76i) q^{19} +(11915.8 + 9998.54i) q^{20} +(16443.4 - 93255.0i) q^{21} +(17731.4 - 100560. i) q^{22} +(33977.6 + 58851.0i) q^{23} +(-65681.5 + 55113.3i) q^{24} +(-105373. + 38352.7i) q^{25} +(34530.7 - 59808.9i) q^{26} +(-32451.9 - 56208.4i) q^{27} +(35640.0 + 29905.5i) q^{28} +(11624.6 - 20134.3i) q^{29} +(70331.4 + 398869. i) q^{30} -170615. q^{31} +(-17455.3 - 98994.2i) q^{32} +(443798. - 372390. i) q^{33} +(-14167.6 - 5156.58i) q^{34} +(-534749. + 194633. i) q^{35} +109879. q^{36} +(-79930.3 + 297562. i) q^{37} -65897.5 q^{38} +(368197. - 134013. i) q^{39} +(484193. + 176232. i) q^{40} +(402111. - 337411. i) q^{41} +(210360. + 1.19301e6i) q^{42} +303369. q^{43} +(49427.0 + 280314. i) q^{44} +(-671995. + 1.16393e6i) q^{45} +(-665963. - 558809. i) q^{46} +(2730.33 + 4729.07i) q^{47} +(714099. - 1.23686e6i) q^{48} +(-825550. + 300475. i) q^{49} +(1.09893e6 - 922114. i) q^{50} +(-42770.0 - 74079.7i) q^{51} +(-33429.3 + 189587. i) q^{52} +(345971. - 1.96210e6i) q^{53} +(636058. + 533716. i) q^{54} +(-3.27160e6 - 1.19076e6i) q^{55} +(1.44821e6 + 527107. i) q^{56} +(-286406. - 240323. i) q^{57} +(-51647.5 + 292908. i) q^{58} +(-32426.6 + 183901. i) q^{59} +(-564509. - 977758. i) q^{60} +(-759736. + 637494. i) q^{61} +(2.05104e6 - 746518. i) q^{62} +(-2.00993e6 + 3.48130e6i) q^{63} +(-616337. - 1.06753e6i) q^{64} +(-1.80381e6 - 1.51358e6i) q^{65} +(-3.70573e6 + 6.41851e6i) q^{66} +(660415. + 3.74540e6i) q^{67} +42027.3 q^{68} +(-856495. - 4.85743e6i) q^{69} +(5.57687e6 - 4.67955e6i) q^{70} +(-81185.6 - 29549.1i) q^{71} +(3.42030e6 - 1.24489e6i) q^{72} +5.50694e6 q^{73} +(-341090. - 3.92687e6i) q^{74} +8.13910e6 q^{75} +(172614. - 62826.4i) q^{76} +(-9.78531e6 - 3.56156e6i) q^{77} +(-3.83991e6 + 3.22206e6i) q^{78} +(260635. + 1.47813e6i) q^{79} -8.58285e6 q^{80} +(-352111. - 1.99692e6i) q^{81} +(-3.35764e6 + 5.81560e6i) q^{82} +(3.51188e6 + 2.94681e6i) q^{83} +(-1.68844e6 - 2.92446e6i) q^{84} +(-257029. + 445187. i) q^{85} +(-3.64695e6 + 1.32738e6i) q^{86} +(-1.29268e6 + 1.08469e6i) q^{87} +(4.71441e6 + 8.16559e6i) q^{88} +(1.77929e6 - 1.00909e7i) q^{89} +(2.98565e6 - 1.69325e7i) q^{90} +(-5.39518e6 - 4.52709e6i) q^{91} +(2.27721e6 + 828837. i) q^{92} +(1.16368e7 + 4.23545e6i) q^{93} +(-53514.5 - 44904.0i) q^{94} +(-390159. + 2.21270e6i) q^{95} +(-1.26695e6 + 7.18524e6i) q^{96} +(8.51427e6 + 1.47471e7i) q^{97} +(8.60962e6 - 7.22433e6i) q^{98} +(-2.31103e7 + 8.41148e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 132q + 15q^{2} + 33q^{3} - 279q^{4} + 576q^{5} - 12q^{6} - 597q^{7} - 3750q^{8} - 3243q^{9} + O(q^{10}) \) \( 132q + 15q^{2} + 33q^{3} - 279q^{4} + 576q^{5} - 12q^{6} - 597q^{7} - 3750q^{8} - 3243q^{9} - 6003q^{10} - 15975q^{11} - 4635q^{12} - 15981q^{13} - 13491q^{14} + 38493q^{15} - 74151q^{16} + 37698q^{17} - 20100q^{18} - 66102q^{19} - 176184q^{20} - 142530q^{21} + 132783q^{22} + 140631q^{23} - 38793q^{24} - 544092q^{25} - 423147q^{26} + 130557q^{27} + 603813q^{28} + 22890q^{29} - 319860q^{30} - 1288044q^{31} - 217866q^{32} + 112344q^{33} + 812019q^{34} + 1479252q^{35} + 8118132q^{36} - 1664550q^{37} + 305010q^{38} - 1580340q^{39} - 4681425q^{40} - 2956593q^{41} - 3553029q^{42} - 1023528q^{43} + 6409524q^{44} + 1803336q^{45} + 10219434q^{46} - 2607204q^{47} - 2984043q^{48} - 6819531q^{49} + 5724015q^{50} - 1675833q^{51} + 11768451q^{52} + 2280177q^{53} - 7803897q^{54} - 3542196q^{55} + 12168843q^{56} - 85203q^{57} - 12425487q^{58} - 7014600q^{59} + 2356788q^{60} + 10840332q^{61} + 6334368q^{62} - 3331359q^{63} - 26175624q^{64} - 573195q^{65} - 36720249q^{66} + 6642918q^{67} - 25277742q^{68} - 1236438q^{69} - 27401982q^{70} + 20311041q^{71} + 40093005q^{72} + 38643780q^{73} - 9531q^{74} + 16639446q^{75} + 5787405q^{76} - 316971q^{77} + 9363381q^{78} + 17712534q^{79} - 74410128q^{80} - 10355109q^{81} - 16702371q^{82} - 31021176q^{83} - 61626192q^{84} + 23576445q^{85} + 18579072q^{86} + 104996631q^{87} + 57279702q^{88} - 13471320q^{89} + 56306910q^{90} - 2335911q^{91} - 178133436q^{92} + 24366258q^{93} + 77086020q^{94} - 26254407q^{95} + 152523921q^{96} + 14408415q^{97} - 521205q^{98} + 58375668q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −12.0215 + 4.37547i −1.06256 + 0.386740i −0.813390 0.581719i \(-0.802380\pi\)
−0.249171 + 0.968460i \(0.580158\pi\)
\(3\) −68.2052 24.8247i −1.45845 0.530834i −0.513515 0.858080i \(-0.671657\pi\)
−0.944939 + 0.327246i \(0.893879\pi\)
\(4\) 27.3180 22.9225i 0.213422 0.179082i
\(5\) 75.7434 + 429.562i 0.270988 + 1.53685i 0.751424 + 0.659819i \(0.229367\pi\)
−0.480436 + 0.877030i \(0.659522\pi\)
\(6\) 928.548 1.75499
\(7\) 226.548 + 1284.82i 0.249641 + 1.41579i 0.809462 + 0.587172i \(0.199759\pi\)
−0.559821 + 0.828614i \(0.689130\pi\)
\(8\) 590.646 1023.03i 0.407861 0.706437i
\(9\) 2360.34 + 1980.56i 1.07926 + 0.905607i
\(10\) −2790.09 4832.57i −0.882302 1.52819i
\(11\) −3990.89 + 6912.42i −0.904055 + 1.56587i −0.0818752 + 0.996643i \(0.526091\pi\)
−0.822180 + 0.569227i \(0.807242\pi\)
\(12\) −2432.27 + 885.274i −0.406328 + 0.147891i
\(13\) −4135.39 + 3470.00i −0.522053 + 0.438055i −0.865347 0.501174i \(-0.832902\pi\)
0.343294 + 0.939228i \(0.388457\pi\)
\(14\) −8345.11 14454.2i −0.812800 1.40781i
\(15\) 5497.64 31178.7i 0.420588 2.38527i
\(16\) −3416.86 + 19378.0i −0.208549 + 1.18274i
\(17\) 902.800 + 757.539i 0.0445677 + 0.0373967i 0.664799 0.747022i \(-0.268517\pi\)
−0.620232 + 0.784419i \(0.712961\pi\)
\(18\) −37040.7 13481.7i −1.49701 0.544868i
\(19\) 4840.41 + 1761.76i 0.161899 + 0.0589264i 0.421698 0.906736i \(-0.361434\pi\)
−0.259799 + 0.965663i \(0.583656\pi\)
\(20\) 11915.8 + 9998.54i 0.333057 + 0.279468i
\(21\) 16443.4 93255.0i 0.387457 2.19738i
\(22\) 17731.4 100560.i 0.355028 2.01347i
\(23\) 33977.6 + 58851.0i 0.582299 + 1.00857i 0.995206 + 0.0977980i \(0.0311799\pi\)
−0.412908 + 0.910773i \(0.635487\pi\)
\(24\) −65681.5 + 55113.3i −0.969848 + 0.813799i
\(25\) −105373. + 38352.7i −1.34878 + 0.490915i
\(26\) 34530.7 59808.9i 0.385299 0.667358i
\(27\) −32451.9 56208.4i −0.317298 0.549576i
\(28\) 35640.0 + 29905.5i 0.306821 + 0.257453i
\(29\) 11624.6 20134.3i 0.0885082 0.153301i −0.818373 0.574688i \(-0.805123\pi\)
0.906881 + 0.421387i \(0.138457\pi\)
\(30\) 70331.4 + 398869.i 0.475581 + 2.69716i
\(31\) −170615. −1.02861 −0.514304 0.857608i \(-0.671950\pi\)
−0.514304 + 0.857608i \(0.671950\pi\)
\(32\) −17455.3 98994.2i −0.0941680 0.534054i
\(33\) 443798. 372390.i 2.14974 1.80385i
\(34\) −14167.6 5156.58i −0.0618187 0.0225002i
\(35\) −534749. + 194633.i −2.10820 + 0.767322i
\(36\) 109879. 0.392515
\(37\) −79930.3 + 297562.i −0.259421 + 0.965764i
\(38\) −65897.5 −0.194817
\(39\) 368197. 134013.i 0.993925 0.361759i
\(40\) 484193. + 176232.i 1.19621 + 0.435386i
\(41\) 402111. 337411.i 0.911175 0.764567i −0.0611668 0.998128i \(-0.519482\pi\)
0.972342 + 0.233561i \(0.0750377\pi\)
\(42\) 210360. + 1.19301e6i 0.438118 + 2.48469i
\(43\) 303369. 0.581878 0.290939 0.956742i \(-0.406032\pi\)
0.290939 + 0.956742i \(0.406032\pi\)
\(44\) 49427.0 + 280314.i 0.0874741 + 0.496090i
\(45\) −671995. + 1.16393e6i −1.09931 + 1.90407i
\(46\) −665963. 558809.i −1.00878 0.846469i
\(47\) 2730.33 + 4729.07i 0.00383595 + 0.00664405i 0.867937 0.496674i \(-0.165446\pi\)
−0.864101 + 0.503318i \(0.832112\pi\)
\(48\) 714099. 1.23686e6i 0.931996 1.61426i
\(49\) −825550. + 300475.i −1.00244 + 0.364857i
\(50\) 1.09893e6 922114.i 1.24330 1.04325i
\(51\) −42770.0 74079.7i −0.0451485 0.0781995i
\(52\) −33429.3 + 189587.i −0.0329697 + 0.186981i
\(53\) 345971. 1.96210e6i 0.319208 1.81032i −0.228381 0.973572i \(-0.573343\pi\)
0.547589 0.836747i \(-0.315546\pi\)
\(54\) 636058. + 533716.i 0.549691 + 0.461246i
\(55\) −3.27160e6 1.19076e6i −2.65149 0.965065i
\(56\) 1.44821e6 + 527107.i 1.10198 + 0.401089i
\(57\) −286406. 240323.i −0.204842 0.171883i
\(58\) −51647.5 + 292908.i −0.0347577 + 0.197121i
\(59\) −32426.6 + 183901.i −0.0205551 + 0.116574i −0.993359 0.115057i \(-0.963295\pi\)
0.972804 + 0.231631i \(0.0744061\pi\)
\(60\) −564509. 977758.i −0.337397 0.584389i
\(61\) −759736. + 637494.i −0.428557 + 0.359602i −0.831407 0.555664i \(-0.812464\pi\)
0.402850 + 0.915266i \(0.368020\pi\)
\(62\) 2.05104e6 746518.i 1.09296 0.397804i
\(63\) −2.00993e6 + 3.48130e6i −1.01272 + 1.75408i
\(64\) −616337. 1.06753e6i −0.293892 0.509036i
\(65\) −1.80381e6 1.51358e6i −0.814694 0.683609i
\(66\) −3.70573e6 + 6.41851e6i −1.58661 + 2.74809i
\(67\) 660415. + 3.74540e6i 0.268259 + 1.52137i 0.759590 + 0.650402i \(0.225399\pi\)
−0.491331 + 0.870973i \(0.663489\pi\)
\(68\) 42027.3 0.0162088
\(69\) −856495. 4.85743e6i −0.313872 1.78006i
\(70\) 5.57687e6 4.67955e6i 1.94333 1.63065i
\(71\) −81185.6 29549.1i −0.0269200 0.00979807i 0.328525 0.944495i \(-0.393448\pi\)
−0.355445 + 0.934697i \(0.615671\pi\)
\(72\) 3.42030e6 1.24489e6i 1.07994 0.393067i
\(73\) 5.50694e6 1.65684 0.828420 0.560108i \(-0.189240\pi\)
0.828420 + 0.560108i \(0.189240\pi\)
\(74\) −341090. 3.92687e6i −0.0978494 1.12651i
\(75\) 8.13910e6 2.22773
\(76\) 172614. 62826.4i 0.0451054 0.0164170i
\(77\) −9.78531e6 3.56156e6i −2.44263 0.889043i
\(78\) −3.83991e6 + 3.22206e6i −0.916198 + 0.768782i
\(79\) 260635. + 1.47813e6i 0.0594755 + 0.337302i 0.999997 0.00243180i \(-0.000774066\pi\)
−0.940522 + 0.339734i \(0.889663\pi\)
\(80\) −8.58285e6 −1.87420
\(81\) −352111. 1.99692e6i −0.0736176 0.417506i
\(82\) −3.35764e6 + 5.81560e6i −0.672490 + 1.16479i
\(83\) 3.51188e6 + 2.94681e6i 0.674165 + 0.565691i 0.914295 0.405049i \(-0.132746\pi\)
−0.240130 + 0.970741i \(0.577190\pi\)
\(84\) −1.68844e6 2.92446e6i −0.310819 0.538354i
\(85\) −257029. + 445187.i −0.0453958 + 0.0786279i
\(86\) −3.64695e6 + 1.32738e6i −0.618280 + 0.225035i
\(87\) −1.29268e6 + 1.08469e6i −0.210462 + 0.176599i
\(88\) 4.71441e6 + 8.16559e6i 0.737459 + 1.27732i
\(89\) 1.77929e6 1.00909e7i 0.267536 1.51727i −0.494179 0.869360i \(-0.664531\pi\)
0.761715 0.647912i \(-0.224358\pi\)
\(90\) 2.98565e6 1.69325e7i 0.431708 2.44834i
\(91\) −5.39518e6 4.52709e6i −0.750518 0.629759i
\(92\) 2.27721e6 + 828837.i 0.304892 + 0.110972i
\(93\) 1.16368e7 + 4.23545e6i 1.50018 + 0.546020i
\(94\) −53514.5 44904.0i −0.00664545 0.00557619i
\(95\) −390159. + 2.21270e6i −0.0466883 + 0.264783i
\(96\) −1.26695e6 + 7.18524e6i −0.146154 + 0.828880i
\(97\) 8.51427e6 + 1.47471e7i 0.947210 + 1.64062i 0.751264 + 0.660001i \(0.229444\pi\)
0.195946 + 0.980615i \(0.437222\pi\)
\(98\) 8.60962e6 7.22433e6i 0.924044 0.775365i
\(99\) −2.31103e7 + 8.41148e6i −2.39377 + 0.871263i
\(100\) −1.99944e6 + 3.46314e6i −0.199944 + 0.346314i
\(101\) −431643. 747628.i −0.0416869 0.0722039i 0.844429 0.535667i \(-0.179940\pi\)
−0.886116 + 0.463463i \(0.846607\pi\)
\(102\) 838292. + 703411.i 0.0782159 + 0.0656309i
\(103\) 1.63701e6 2.83538e6i 0.147612 0.255671i −0.782733 0.622358i \(-0.786175\pi\)
0.930344 + 0.366687i \(0.119508\pi\)
\(104\) 1.10736e6 + 6.28017e6i 0.0965325 + 0.547463i
\(105\) 4.13043e7 3.48203
\(106\) 4.42601e6 + 2.51011e7i 0.360945 + 2.04702i
\(107\) −1.27598e7 + 1.07067e7i −1.00693 + 0.844915i −0.987929 0.154904i \(-0.950493\pi\)
−0.0190013 + 0.999819i \(0.506049\pi\)
\(108\) −2.17496e6 791619.i −0.166137 0.0604690i
\(109\) −1.11076e7 + 4.04284e6i −0.821539 + 0.299016i −0.718381 0.695649i \(-0.755117\pi\)
−0.103157 + 0.994665i \(0.532895\pi\)
\(110\) 4.45397e7 3.19060
\(111\) 1.28385e7 1.83110e7i 0.891014 1.27081i
\(112\) −2.56712e7 −1.72657
\(113\) 8.88096e6 3.23241e6i 0.579009 0.210742i −0.0358793 0.999356i \(-0.511423\pi\)
0.614889 + 0.788614i \(0.289201\pi\)
\(114\) 4.49455e6 + 1.63588e6i 0.284131 + 0.103415i
\(115\) −2.27066e7 + 1.90531e7i −1.39223 + 1.16822i
\(116\) −143970. 816493.i −0.00856383 0.0485679i
\(117\) −1.66335e7 −0.960137
\(118\) −414834. 2.35264e6i −0.0232427 0.131816i
\(119\) −768770. + 1.33155e6i −0.0418198 + 0.0724341i
\(120\) −2.86495e7 2.40398e7i −1.51350 1.26998i
\(121\) −2.21108e7 3.82970e7i −1.13463 1.96524i
\(122\) 6.34383e6 1.09878e7i 0.316295 0.547838i
\(123\) −3.58021e7 + 1.30309e7i −1.73477 + 0.631403i
\(124\) −4.66084e6 + 3.91091e6i −0.219527 + 0.184205i
\(125\) −7.41759e6 1.28476e7i −0.339686 0.588354i
\(126\) 8.93004e6 5.06448e7i 0.397701 2.25547i
\(127\) −1.83716e6 + 1.04191e7i −0.0795856 + 0.451353i 0.918809 + 0.394704i \(0.129153\pi\)
−0.998394 + 0.0566490i \(0.981958\pi\)
\(128\) 2.19367e7 + 1.84071e7i 0.924563 + 0.775800i
\(129\) −2.06913e7 7.53103e6i −0.848642 0.308880i
\(130\) 2.83071e7 + 1.03029e7i 1.13004 + 0.411301i
\(131\) 5.56875e6 + 4.67273e6i 0.216425 + 0.181602i 0.744555 0.667562i \(-0.232662\pi\)
−0.528129 + 0.849164i \(0.677106\pi\)
\(132\) 3.58753e6 2.03459e7i 0.135765 0.769960i
\(133\) −1.16696e6 + 6.61815e6i −0.0430105 + 0.243925i
\(134\) −2.43270e7 4.21357e7i −0.873419 1.51281i
\(135\) 2.16870e7 1.81975e7i 0.758631 0.636567i
\(136\) 1.30822e6 476153.i 0.0445959 0.0162316i
\(137\) 1.22161e7 2.11589e7i 0.405891 0.703025i −0.588533 0.808473i \(-0.700294\pi\)
0.994425 + 0.105448i \(0.0336278\pi\)
\(138\) 3.15499e7 + 5.46460e7i 1.02193 + 1.77003i
\(139\) −1.56237e7 1.31099e7i −0.493438 0.414044i 0.361818 0.932249i \(-0.382156\pi\)
−0.855257 + 0.518205i \(0.826601\pi\)
\(140\) −1.01468e7 + 1.75747e7i −0.312522 + 0.541304i
\(141\) −68825.1 390326.i −0.00206766 0.0117263i
\(142\) 1.10526e6 0.0323934
\(143\) −7.48225e6 4.24339e7i −0.213972 1.21349i
\(144\) −4.64442e7 + 3.89713e7i −1.29617 + 1.08762i
\(145\) 9.52943e6 + 3.46843e6i 0.259585 + 0.0944811i
\(146\) −6.62017e7 + 2.40954e7i −1.76049 + 0.640766i
\(147\) 6.37660e7 1.65569
\(148\) 4.63733e6 + 9.96098e6i 0.117585 + 0.252573i
\(149\) 4.51903e7 1.11916 0.559582 0.828775i \(-0.310962\pi\)
0.559582 + 0.828775i \(0.310962\pi\)
\(150\) −9.78441e7 + 3.56123e7i −2.36709 + 0.861551i
\(151\) 3.17802e7 + 1.15670e7i 0.751168 + 0.273403i 0.689097 0.724669i \(-0.258007\pi\)
0.0620711 + 0.998072i \(0.480229\pi\)
\(152\) 4.66131e6 3.91130e6i 0.107660 0.0903376i
\(153\) 630563. + 3.57610e6i 0.0142334 + 0.0807216i
\(154\) 1.33218e8 2.93927
\(155\) −1.29229e7 7.32896e7i −0.278740 1.58082i
\(156\) 6.98648e6 1.21009e7i 0.147340 0.255201i
\(157\) 4.63414e6 + 3.88851e6i 0.0955698 + 0.0801926i 0.689321 0.724456i \(-0.257909\pi\)
−0.593751 + 0.804649i \(0.702354\pi\)
\(158\) −9.60075e6 1.66290e7i −0.193645 0.335402i
\(159\) −7.23054e7 + 1.25237e8i −1.42653 + 2.47082i
\(160\) 4.12020e7 1.49963e7i 0.795241 0.289444i
\(161\) −6.79151e7 + 5.69876e7i −1.28255 + 1.07619i
\(162\) 1.29704e7 + 2.24653e7i 0.239690 + 0.415155i
\(163\) 4.65363e6 2.63921e7i 0.0841658 0.477328i −0.913368 0.407136i \(-0.866528\pi\)
0.997533 0.0701922i \(-0.0223613\pi\)
\(164\) 3.25054e6 1.84348e7i 0.0575443 0.326350i
\(165\) 1.93580e8 + 1.62433e8i 3.35479 + 2.81501i
\(166\) −5.51117e7 2.00590e7i −0.935116 0.340354i
\(167\) 7.78650e6 + 2.83405e6i 0.129370 + 0.0470869i 0.405894 0.913920i \(-0.366960\pi\)
−0.276524 + 0.961007i \(0.589182\pi\)
\(168\) −8.56904e7 7.19028e7i −1.39428 1.16994i
\(169\) −5.83565e6 + 3.30956e7i −0.0930005 + 0.527432i
\(170\) 1.14197e6 6.47644e6i 0.0178272 0.101103i
\(171\) 7.93574e6 + 1.37451e7i 0.121367 + 0.210214i
\(172\) 8.28742e6 6.95397e6i 0.124185 0.104204i
\(173\) 1.08126e8 3.93547e7i 1.58770 0.577877i 0.610843 0.791751i \(-0.290831\pi\)
0.976861 + 0.213874i \(0.0686083\pi\)
\(174\) 1.07940e7 1.86957e7i 0.155331 0.269041i
\(175\) −7.31483e7 1.26696e8i −1.03174 1.78703i
\(176\) −1.20312e8 1.00954e8i −1.66347 1.39582i
\(177\) 6.77693e6 1.17380e7i 0.0918600 0.159106i
\(178\) 2.27625e7 + 1.29093e8i 0.302517 + 1.71566i
\(179\) 5.80179e7 0.756095 0.378047 0.925786i \(-0.376596\pi\)
0.378047 + 0.925786i \(0.376596\pi\)
\(180\) 8.32263e6 + 4.72000e7i 0.106367 + 0.603237i
\(181\) −1.00841e8 + 8.46160e7i −1.26405 + 1.06066i −0.268811 + 0.963193i \(0.586631\pi\)
−0.995238 + 0.0974700i \(0.968925\pi\)
\(182\) 8.46662e7 + 3.08160e7i 1.04102 + 0.378901i
\(183\) 6.76435e7 2.46202e7i 0.815919 0.296970i
\(184\) 8.02751e7 0.949989
\(185\) −1.33876e8 1.17967e7i −1.55453 0.136981i
\(186\) −1.58424e8 −1.80520
\(187\) −8.83940e6 + 3.21728e6i −0.0988501 + 0.0359785i
\(188\) 182989. + 66602.6i 0.00200850 + 0.000731036i
\(189\) 6.48655e7 5.44286e7i 0.698871 0.586423i
\(190\) −4.99130e6 2.83071e7i −0.0527930 0.299404i
\(191\) 6.79519e7 0.705643 0.352821 0.935691i \(-0.385222\pi\)
0.352821 + 0.935691i \(0.385222\pi\)
\(192\) 1.55364e7 + 8.81112e7i 0.158415 + 0.898414i
\(193\) 1.61597e7 2.79895e7i 0.161802 0.280249i −0.773713 0.633536i \(-0.781603\pi\)
0.935515 + 0.353287i \(0.114936\pi\)
\(194\) −1.66880e8 1.40029e8i −1.64096 1.37693i
\(195\) 8.54552e7 + 1.48013e8i 0.825311 + 1.42948i
\(196\) −1.56647e7 + 2.71320e7i −0.148602 + 0.257387i
\(197\) 4.47788e7 1.62982e7i 0.417293 0.151882i −0.124836 0.992177i \(-0.539841\pi\)
0.542129 + 0.840295i \(0.317618\pi\)
\(198\) 2.41017e8 2.02237e8i 2.20658 1.85154i
\(199\) −3.65140e7 6.32441e7i −0.328453 0.568898i 0.653752 0.756709i \(-0.273194\pi\)
−0.982205 + 0.187811i \(0.939861\pi\)
\(200\) −2.30024e7 + 1.30453e8i −0.203314 + 1.15305i
\(201\) 4.79345e7 2.71850e8i 0.416353 2.36126i
\(202\) 8.46022e6 + 7.09897e6i 0.0722190 + 0.0605990i
\(203\) 2.85024e7 + 1.03740e7i 0.239136 + 0.0870385i
\(204\) −2.86648e6 1.04331e6i −0.0236398 0.00860418i
\(205\) 1.75396e8 + 1.47175e8i 1.42194 + 1.19315i
\(206\) −7.27318e6 + 4.12482e7i −0.0579681 + 0.328753i
\(207\) −3.63592e7 + 2.06203e8i −0.284917 + 1.61584i
\(208\) −5.31116e7 9.19920e7i −0.409230 0.708807i
\(209\) −3.14956e7 + 2.64279e7i −0.238637 + 0.200240i
\(210\) −4.96540e8 + 1.80726e8i −3.69987 + 1.34664i
\(211\) 5.38095e7 9.32008e7i 0.394339 0.683016i −0.598677 0.800990i \(-0.704307\pi\)
0.993017 + 0.117974i \(0.0376401\pi\)
\(212\) −3.55250e7 6.15310e7i −0.256070 0.443526i
\(213\) 4.80373e6 + 4.03081e6i 0.0340604 + 0.0285801i
\(214\) 1.06545e8 1.84541e8i 0.743162 1.28719i
\(215\) 2.29782e7 + 1.30316e8i 0.157682 + 0.894258i
\(216\) −7.66704e7 −0.517654
\(217\) −3.86523e7 2.19208e8i −0.256783 1.45629i
\(218\) 1.15841e8 9.72020e7i 0.757293 0.635444i
\(219\) −3.75602e8 1.36708e8i −2.41642 0.879507i
\(220\) −1.16669e8 + 4.24639e7i −0.738712 + 0.268869i
\(221\) −6.36209e6 −0.0396485
\(222\) −7.42191e7 + 2.76300e8i −0.455282 + 1.69491i
\(223\) −9.99635e7 −0.603635 −0.301817 0.953366i \(-0.597593\pi\)
−0.301817 + 0.953366i \(0.597593\pi\)
\(224\) 1.23235e8 4.48538e7i 0.732597 0.266644i
\(225\) −3.24677e8 1.18173e8i −1.90026 0.691638i
\(226\) −9.26192e7 + 7.77167e7i −0.533730 + 0.447852i
\(227\) −2.59901e7 1.47397e8i −0.147475 0.836371i −0.965347 0.260971i \(-0.915957\pi\)
0.817872 0.575400i \(-0.195154\pi\)
\(228\) −1.33328e7 −0.0744989
\(229\) 1.44138e7 + 8.17445e7i 0.0793146 + 0.449816i 0.998439 + 0.0558487i \(0.0177865\pi\)
−0.919125 + 0.393967i \(0.871102\pi\)
\(230\) 1.89601e8 3.28399e8i 1.02753 1.77973i
\(231\) 5.78994e8 + 4.85834e8i 3.09052 + 2.59326i
\(232\) −1.37320e7 2.37845e7i −0.0721982 0.125051i
\(233\) −3.50398e7 + 6.06907e7i −0.181475 + 0.314323i −0.942383 0.334536i \(-0.891420\pi\)
0.760908 + 0.648859i \(0.224754\pi\)
\(234\) 1.99959e8 7.27793e7i 1.02020 0.371323i
\(235\) −1.82463e6 + 1.53104e6i −0.00917141 + 0.00769573i
\(236\) 3.32963e6 + 5.76709e6i 0.0164894 + 0.0285604i
\(237\) 1.89175e7 1.07287e8i 0.0923092 0.523512i
\(238\) 3.41562e6 1.93709e7i 0.0164229 0.0931390i
\(239\) −2.45545e8 2.06037e8i −1.16343 0.976231i −0.163481 0.986547i \(-0.552272\pi\)
−0.999947 + 0.0103151i \(0.996717\pi\)
\(240\) 5.85395e8 + 2.13066e8i 2.73344 + 0.994891i
\(241\) 6.28572e7 + 2.28782e7i 0.289265 + 0.105284i 0.482577 0.875853i \(-0.339701\pi\)
−0.193312 + 0.981137i \(0.561923\pi\)
\(242\) 4.33372e8 + 3.63642e8i 1.96565 + 1.64938i
\(243\) −5.02055e7 + 2.84730e8i −0.224455 + 1.27295i
\(244\) −6.14148e6 + 3.48301e7i −0.0270650 + 0.153493i
\(245\) −1.91603e8 3.31866e8i −0.832378 1.44172i
\(246\) 3.73379e8 3.13302e8i 1.59910 1.34181i
\(247\) −2.61303e7 + 9.51065e6i −0.110333 + 0.0401579i
\(248\) −1.00773e8 + 1.74544e8i −0.419530 + 0.726647i
\(249\) −1.66375e8 2.88169e8i −0.682950 1.18290i
\(250\) 1.45385e8 + 1.21992e8i 0.588477 + 0.493791i
\(251\) −1.08336e8 + 1.87644e8i −0.432429 + 0.748989i −0.997082 0.0763393i \(-0.975677\pi\)
0.564653 + 0.825329i \(0.309010\pi\)
\(252\) 2.48929e7 + 1.41174e8i 0.0979880 + 0.555718i
\(253\) −5.42404e8 −2.10572
\(254\) −2.35028e7 1.33291e8i −0.0899917 0.510368i
\(255\) 2.85823e7 2.39834e7i 0.107946 0.0905775i
\(256\) −1.95985e8 7.13326e7i −0.730100 0.265735i
\(257\) −3.83260e8 + 1.39495e8i −1.40840 + 0.512617i −0.930661 0.365883i \(-0.880767\pi\)
−0.477743 + 0.878500i \(0.658545\pi\)
\(258\) 2.81693e8 1.02119
\(259\) −4.00420e8 3.52837e7i −1.43208 0.126190i
\(260\) −8.39714e7 −0.296295
\(261\) 6.73152e7 2.45007e7i 0.234354 0.0852977i
\(262\) −8.73901e7 3.18074e7i −0.300198 0.109263i
\(263\) 1.69480e8 1.42210e8i 0.574477 0.482043i −0.308651 0.951175i \(-0.599878\pi\)
0.883128 + 0.469132i \(0.155433\pi\)
\(264\) −1.18839e8 6.73969e8i −0.397507 2.25438i
\(265\) 8.69048e8 2.86869
\(266\) −1.49289e7 8.46661e7i −0.0486343 0.275819i
\(267\) −3.71859e8 + 6.44079e8i −1.19561 + 2.07086i
\(268\) 1.03895e8 + 8.71783e7i 0.329703 + 0.276654i
\(269\) 1.60680e8 + 2.78306e8i 0.503303 + 0.871746i 0.999993 + 0.00381799i \(0.00121531\pi\)
−0.496690 + 0.867928i \(0.665451\pi\)
\(270\) −1.81087e8 + 3.13652e8i −0.559905 + 0.969784i
\(271\) 7.39582e7 2.69186e7i 0.225732 0.0821599i −0.226678 0.973970i \(-0.572786\pi\)
0.452410 + 0.891810i \(0.350564\pi\)
\(272\) −1.77643e7 + 1.49060e7i −0.0535250 + 0.0449128i
\(273\) 2.55596e8 + 4.42704e8i 0.760298 + 1.31688i
\(274\) −5.42756e7 + 3.07812e8i −0.159396 + 0.903980i
\(275\) 1.55423e8 8.81446e8i 0.450661 2.55583i
\(276\) −1.34742e8 1.13062e8i −0.385764 0.323694i
\(277\) 2.32958e8 + 8.47896e7i 0.658563 + 0.239697i 0.649616 0.760263i \(-0.274930\pi\)
0.00894737 + 0.999960i \(0.497152\pi\)
\(278\) 2.45182e8 + 8.92391e7i 0.684435 + 0.249114i
\(279\) −4.02709e8 3.37913e8i −1.11014 0.931515i
\(280\) −1.16733e8 + 6.62023e8i −0.317789 + 1.80227i
\(281\) −4.79146e7 + 2.71737e8i −0.128824 + 0.730595i 0.850139 + 0.526558i \(0.176518\pi\)
−0.978963 + 0.204037i \(0.934594\pi\)
\(282\) 2.53524e6 + 4.39117e6i 0.00673205 + 0.0116603i
\(283\) −4.48681e7 + 3.76488e7i −0.117675 + 0.0987413i −0.699726 0.714411i \(-0.746695\pi\)
0.582051 + 0.813152i \(0.302250\pi\)
\(284\) −2.89517e6 + 1.05375e6i −0.00749996 + 0.00272976i
\(285\) 8.15403e7 1.41232e8i 0.208649 0.361390i
\(286\) 2.75616e8 + 4.77381e8i 0.696664 + 1.20666i
\(287\) 5.24608e8 + 4.40198e8i 1.30993 + 1.09916i
\(288\) 1.54864e8 2.68232e8i 0.382011 0.661662i
\(289\) −7.10134e7 4.02737e8i −0.173060 0.981474i
\(290\) −1.29734e8 −0.312364
\(291\) −2.14624e8 1.21720e9i −0.510568 2.89558i
\(292\) 1.50438e8 1.26233e8i 0.353605 0.296710i
\(293\) 4.99744e8 + 1.81892e8i 1.16068 + 0.422452i 0.849339 0.527848i \(-0.177001\pi\)
0.311338 + 0.950299i \(0.399223\pi\)
\(294\) −7.66562e8 + 2.79006e8i −1.75927 + 0.640321i
\(295\) −8.14528e7 −0.184726
\(296\) 2.57204e8 + 2.57525e8i 0.576443 + 0.577163i
\(297\) 5.18048e8 1.14742
\(298\) −5.43255e8 + 1.97729e8i −1.18918 + 0.432826i
\(299\) −3.44724e8 1.25469e8i −0.745800 0.271449i
\(300\) 2.22343e8 1.86568e8i 0.475445 0.398945i
\(301\) 6.87275e7 + 3.89773e8i 0.145261 + 0.823814i
\(302\) −4.32657e8 −0.903898
\(303\) 1.08807e7 + 6.17075e7i 0.0224702 + 0.127435i
\(304\) −5.06784e7 + 8.77776e7i −0.103458 + 0.179195i
\(305\) −3.31388e8 2.78068e8i −0.668787 0.561179i
\(306\) −2.32274e7 4.02311e7i −0.0463421 0.0802670i
\(307\) 2.14798e8 3.72040e8i 0.423687 0.733847i −0.572610 0.819828i \(-0.694069\pi\)
0.996297 + 0.0859808i \(0.0274024\pi\)
\(308\) −3.48955e8 + 1.27009e8i −0.680521 + 0.247689i
\(309\) −1.82040e8 + 1.52750e8i −0.351004 + 0.294527i
\(310\) 4.76029e8 + 8.24506e8i 0.907544 + 1.57191i
\(311\) −8.48104e7 + 4.80983e8i −0.159878 + 0.906711i 0.794312 + 0.607509i \(0.207831\pi\)
−0.954190 + 0.299201i \(0.903280\pi\)
\(312\) 8.03751e7 4.55830e8i 0.149824 0.849693i
\(313\) 1.40790e8 + 1.18137e8i 0.259517 + 0.217760i 0.763257 0.646095i \(-0.223599\pi\)
−0.503741 + 0.863855i \(0.668043\pi\)
\(314\) −7.27234e7 2.64691e7i −0.132562 0.0482487i
\(315\) −1.64767e9 5.99704e8i −2.97019 1.08106i
\(316\) 4.10025e7 + 3.44052e7i 0.0730981 + 0.0613366i
\(317\) −1.30265e8 + 7.38767e8i −0.229678 + 1.30257i 0.623860 + 0.781536i \(0.285564\pi\)
−0.853538 + 0.521031i \(0.825548\pi\)
\(318\) 3.21250e8 1.82190e9i 0.560207 3.17709i
\(319\) 9.27846e7 + 1.60708e8i 0.160033 + 0.277185i
\(320\) 4.11886e8 3.45613e8i 0.702671 0.589611i
\(321\) 1.13607e9 4.13497e8i 1.91707 0.697757i
\(322\) 5.67094e8 9.82236e8i 0.946585 1.63953i
\(323\) 3.03531e6 + 5.25732e6i 0.00501181 + 0.00868071i
\(324\) −5.53933e7 4.64805e7i −0.0904795 0.0759213i
\(325\) 3.02675e8 5.24249e8i 0.489086 0.847122i
\(326\) 5.95340e7 + 3.37634e8i 0.0951707 + 0.539740i
\(327\) 8.57959e8 1.35690
\(328\) −1.07676e8 6.10661e8i −0.168485 0.955525i
\(329\) −5.45743e6 + 4.57933e6i −0.00844895 + 0.00708951i
\(330\) −3.03784e9 1.10568e9i −4.65335 1.69368i
\(331\) −1.03833e9 + 3.77921e8i −1.57376 + 0.572800i −0.973834 0.227258i \(-0.927024\pi\)
−0.599922 + 0.800059i \(0.704802\pi\)
\(332\) 1.63486e8 0.245186
\(333\) −7.78003e8 + 5.44041e8i −1.15459 + 0.807378i
\(334\) −1.06006e8 −0.155674
\(335\) −1.55886e9 + 5.67379e8i −2.26543 + 0.824548i
\(336\) 1.75091e9 + 6.37278e8i 2.51812 + 0.916520i
\(337\) −1.60789e8 + 1.34918e8i −0.228851 + 0.192029i −0.750002 0.661436i \(-0.769947\pi\)
0.521151 + 0.853465i \(0.325503\pi\)
\(338\) −7.46555e7 4.23392e8i −0.105161 0.596396i
\(339\) −6.85971e8 −0.956328
\(340\) 3.18329e6 + 1.80534e7i 0.00439239 + 0.0249105i
\(341\) 6.80903e8 1.17936e9i 0.929919 1.61067i
\(342\) −1.55541e8 1.30514e8i −0.210258 0.176427i
\(343\) −3.58700e7 6.21287e7i −0.0479957 0.0831310i
\(344\) 1.79184e8 3.10355e8i 0.237325 0.411060i
\(345\) 2.02169e9 7.35836e8i 2.65063 0.964749i
\(346\) −1.12764e9 + 9.46205e8i −1.46354 + 1.22806i
\(347\) 1.44718e8 + 2.50659e8i 0.185939 + 0.322056i 0.943892 0.330253i \(-0.107134\pi\)
−0.757954 + 0.652308i \(0.773801\pi\)
\(348\) −1.04497e7 + 5.92630e7i −0.0132915 + 0.0753801i
\(349\) −3.07275e7 + 1.74264e8i −0.0386935 + 0.219442i −0.998023 0.0628462i \(-0.979982\pi\)
0.959330 + 0.282288i \(0.0910933\pi\)
\(350\) 1.43371e9 + 1.20302e9i 1.78740 + 1.49981i
\(351\) 3.29245e8 + 1.19835e8i 0.406391 + 0.147914i
\(352\) 7.53952e8 + 2.74416e8i 0.921391 + 0.335359i
\(353\) −5.73794e8 4.81471e8i −0.694296 0.582584i 0.225848 0.974162i \(-0.427485\pi\)
−0.920145 + 0.391579i \(0.871929\pi\)
\(354\) −3.01097e7 + 1.70760e8i −0.0360740 + 0.204586i
\(355\) 6.54392e6 3.71124e7i 0.00776317 0.0440271i
\(356\) −1.82701e8 3.16448e8i −0.214618 0.371730i
\(357\) 8.54894e7 7.17341e7i 0.0994428 0.0834424i
\(358\) −6.97462e8 + 2.53855e8i −0.803396 + 0.292412i
\(359\) −5.41796e8 + 9.38419e8i −0.618024 + 1.07045i 0.371822 + 0.928304i \(0.378733\pi\)
−0.989846 + 0.142145i \(0.954600\pi\)
\(360\) 7.93823e8 + 1.37494e9i 0.896736 + 1.55319i
\(361\) −6.64420e8 5.57514e8i −0.743305 0.623707i
\(362\) 8.42030e8 1.45844e9i 0.932927 1.61588i
\(363\) 5.57360e8 + 3.16094e9i 0.611593 + 3.46852i
\(364\) −2.51157e8 −0.272955
\(365\) 4.17115e8 + 2.36557e9i 0.448983 + 2.54631i
\(366\) −7.05451e8 + 5.91943e8i −0.752113 + 0.631097i
\(367\) 1.10301e8 + 4.01461e7i 0.116479 + 0.0423948i 0.399602 0.916689i \(-0.369148\pi\)
−0.283123 + 0.959084i \(0.591371\pi\)
\(368\) −1.25651e9 + 4.57332e8i −1.31431 + 0.478370i
\(369\) 1.61738e9 1.67579
\(370\) 1.66100e9 4.43954e8i 1.70476 0.455651i
\(371\) 2.59931e9 2.64271
\(372\) 4.14980e8 1.51041e8i 0.417953 0.152122i
\(373\) −8.29253e8 3.01823e8i −0.827382 0.301142i −0.106598 0.994302i \(-0.533996\pi\)
−0.720784 + 0.693160i \(0.756218\pi\)
\(374\) 9.21857e7 7.73530e7i 0.0911198 0.0764586i
\(375\) 1.86980e8 + 1.06041e9i 0.183099 + 1.03840i
\(376\) 6.45064e6 0.00625814
\(377\) 2.17941e7 + 1.23601e8i 0.0209481 + 0.118803i
\(378\) −5.41629e8 + 9.38130e8i −0.515800 + 0.893391i
\(379\) 4.85302e8 + 4.07217e8i 0.457905 + 0.384228i 0.842359 0.538916i \(-0.181166\pi\)
−0.384455 + 0.923144i \(0.625610\pi\)
\(380\) 4.00622e7 + 6.93898e7i 0.0374535 + 0.0648714i
\(381\) 3.83954e8 6.65028e8i 0.355665 0.616030i
\(382\) −8.16883e8 + 2.97321e8i −0.749788 + 0.272900i
\(383\) −2.78870e8 + 2.34000e8i −0.253634 + 0.212824i −0.760735 0.649062i \(-0.775161\pi\)
0.507101 + 0.861886i \(0.330717\pi\)
\(384\) −1.03925e9 1.80003e9i −0.936612 1.62226i
\(385\) 7.88740e8 4.47317e9i 0.704403 3.99487i
\(386\) −7.17972e7 + 4.07182e8i −0.0635407 + 0.360357i
\(387\) 7.16055e8 + 6.00841e8i 0.627997 + 0.526952i
\(388\) 5.70634e8 + 2.07694e8i 0.495960 + 0.180515i
\(389\) −5.78320e8 2.10491e8i −0.498132 0.181305i 0.0807216 0.996737i \(-0.474278\pi\)
−0.578854 + 0.815431i \(0.696500\pi\)
\(390\) −1.67492e9 1.40543e9i −1.42978 1.19973i
\(391\) −1.39069e7 + 7.88700e7i −0.0117655 + 0.0667257i
\(392\) −1.80213e8 + 1.02204e9i −0.151107 + 0.856969i
\(393\) −2.63818e8 4.56947e8i −0.219246 0.379745i
\(394\) −4.66996e8 + 3.91856e8i −0.384660 + 0.322768i
\(395\) −6.15210e8 + 2.23918e8i −0.502265 + 0.182810i
\(396\) −4.38515e8 + 7.59531e8i −0.354856 + 0.614628i
\(397\) −8.08234e8 1.39990e9i −0.648292 1.12287i −0.983531 0.180741i \(-0.942150\pi\)
0.335239 0.942133i \(-0.391183\pi\)
\(398\) 7.15676e8 + 6.00523e8i 0.569017 + 0.477462i
\(399\) 2.43886e8 4.22423e8i 0.192213 0.332922i
\(400\) −3.83153e8 2.17297e9i −0.299338 1.69763i
\(401\) −2.90741e7 −0.0225165 −0.0112583 0.999937i \(-0.503584\pi\)
−0.0112583 + 0.999937i \(0.503584\pi\)
\(402\) 6.13226e8 + 3.47778e9i 0.470793 + 2.67000i
\(403\) 7.05557e8 5.92033e8i 0.536988 0.450587i
\(404\) −2.89291e7 1.05293e7i −0.0218273 0.00794449i
\(405\) 8.31132e8 3.02507e8i 0.621695 0.226278i
\(406\) −3.88033e8 −0.287758
\(407\) −1.73788e9 1.74005e9i −1.27773 1.27932i
\(408\) −1.01048e8 −0.0736573
\(409\) 2.13927e9 7.78629e8i 1.54608 0.562729i 0.578590 0.815619i \(-0.303603\pi\)
0.967495 + 0.252890i \(0.0813810\pi\)
\(410\) −2.75248e9 1.00182e9i −1.97234 0.717872i
\(411\) −1.35846e9 + 1.13988e9i −0.965164 + 0.809868i
\(412\) −2.02743e7 1.14981e8i −0.0142825 0.0810003i
\(413\) −2.43624e8 −0.170175
\(414\) −4.65144e8 2.63796e9i −0.322171 1.82712i
\(415\) −9.99839e8 + 1.73177e9i −0.686692 + 1.18938i
\(416\) 4.15695e8 + 3.48809e8i 0.283105 + 0.237554i
\(417\) 7.40171e8 + 1.28201e9i 0.499869 + 0.865798i
\(418\) 2.62989e8 4.55511e8i 0.176125 0.305058i
\(419\) 8.24049e7 2.99929e7i 0.0547273 0.0199191i −0.314511 0.949254i \(-0.601841\pi\)
0.369239 + 0.929335i \(0.379618\pi\)
\(420\) 1.12835e9 9.46798e8i 0.743141 0.623569i
\(421\) −1.02345e8 1.77266e8i −0.0668463 0.115781i 0.830665 0.556772i \(-0.187960\pi\)
−0.897512 + 0.440991i \(0.854627\pi\)
\(422\) −2.39074e8 + 1.35585e9i −0.154860 + 0.878253i
\(423\) −2.92170e6 + 1.65698e7i −0.00187692 + 0.0106445i
\(424\) −1.80294e9 1.51284e9i −1.14868 0.963860i
\(425\) −1.24185e8 4.51995e7i −0.0784705 0.0285609i
\(426\) −7.53847e7 2.74378e7i −0.0472443 0.0171955i
\(427\) −9.91178e8 8.31697e8i −0.616104 0.516973i
\(428\) −1.03146e8 + 5.84971e8i −0.0635917 + 0.360646i
\(429\) −5.43080e8 + 3.07996e9i −0.332096 + 1.88341i
\(430\) −8.46425e8 1.46605e9i −0.513392 0.889221i
\(431\) 2.15203e9 1.80577e9i 1.29472 1.08640i 0.303694 0.952770i \(-0.401780\pi\)
0.991031 0.133634i \(-0.0426646\pi\)
\(432\) 1.20009e9 4.36796e8i 0.716176 0.260667i
\(433\) 6.62495e8 1.14747e9i 0.392170 0.679259i −0.600565 0.799576i \(-0.705058\pi\)
0.992736 + 0.120317i \(0.0383910\pi\)
\(434\) 1.42380e9 + 2.46609e9i 0.836053 + 1.44809i
\(435\) −5.63854e8 4.73130e8i −0.328439 0.275593i
\(436\) −2.10765e8 + 3.65056e8i −0.121786 + 0.210939i
\(437\) 6.07840e7 + 3.44723e8i 0.0348421 + 0.197599i
\(438\) 5.11346e9 2.90774
\(439\) 2.94107e7 + 1.66796e8i 0.0165913 + 0.0940937i 0.991979 0.126403i \(-0.0403433\pi\)
−0.975388 + 0.220497i \(0.929232\pi\)
\(440\) −3.15055e9 + 2.64362e9i −1.76320 + 1.47950i
\(441\) −2.54369e9 9.25828e8i −1.41231 0.514038i
\(442\) 7.64818e7 2.78371e7i 0.0421289 0.0153337i
\(443\) −1.70301e9 −0.930686 −0.465343 0.885131i \(-0.654069\pi\)
−0.465343 + 0.885131i \(0.654069\pi\)
\(444\) −6.90116e7 7.94511e8i −0.0374181 0.430784i
\(445\) 4.46943e9 2.40432
\(446\) 1.20171e9 4.37387e8i 0.641398 0.233450i
\(447\) −3.08221e9 1.12183e9i −1.63225 0.594090i
\(448\) 1.23195e9 1.03372e9i 0.647319 0.543165i
\(449\) −5.44275e8 3.08674e9i −0.283763 1.60930i −0.709670 0.704534i \(-0.751156\pi\)
0.425907 0.904767i \(-0.359955\pi\)
\(450\) 4.42016e9 2.28662
\(451\) 7.27547e8 + 4.12613e9i 0.373459 + 2.11799i
\(452\) 1.68515e8 2.91877e8i 0.0858330 0.148667i
\(453\) −1.88043e9 1.57786e9i −0.950413 0.797492i
\(454\) 9.57372e8 + 1.65822e9i 0.480159 + 0.831660i
\(455\) 1.53602e9 2.66046e9i 0.764463 1.32409i
\(456\) −4.15022e8 + 1.51056e8i −0.204972 + 0.0746036i
\(457\) −7.57163e8 + 6.35335e8i −0.371093 + 0.311384i −0.809194 0.587542i \(-0.800096\pi\)
0.438101 + 0.898926i \(0.355651\pi\)
\(458\) −5.30946e8 9.19625e8i −0.258238 0.447282i
\(459\) 1.32824e7 7.53285e7i 0.00641111 0.0363592i
\(460\) −1.83553e8 + 1.04098e9i −0.0879245 + 0.498645i
\(461\) 1.54622e9 + 1.29743e9i 0.735052 + 0.616782i 0.931504 0.363732i \(-0.118498\pi\)
−0.196452 + 0.980513i \(0.562942\pi\)
\(462\) −9.08613e9 3.30708e9i −4.28679 1.56026i
\(463\) −4.13555e8 1.50522e8i −0.193642 0.0704800i 0.243379 0.969931i \(-0.421744\pi\)
−0.437021 + 0.899451i \(0.643966\pi\)
\(464\) 3.50443e8 + 2.94057e8i 0.162856 + 0.136653i
\(465\) −9.37978e8 + 5.31954e9i −0.432621 + 2.45351i
\(466\) 1.55681e8 8.82908e8i 0.0712662 0.404171i
\(467\) 1.69822e9 + 2.94141e9i 0.771588 + 1.33643i 0.936692 + 0.350153i \(0.113871\pi\)
−0.165104 + 0.986276i \(0.552796\pi\)
\(468\) −4.54393e8 + 3.81281e8i −0.204914 + 0.171943i
\(469\) −4.66253e9 + 1.69702e9i −2.08697 + 0.759596i
\(470\) 1.52357e7 2.63890e7i 0.00676893 0.0117241i
\(471\) −2.19542e8 3.80257e8i −0.0968152 0.167689i
\(472\) 1.68983e8 + 1.41794e8i 0.0739684 + 0.0620668i
\(473\) −1.21071e9 + 2.09701e9i −0.526050 + 0.911144i
\(474\) 2.42012e8 + 1.37252e9i 0.104379 + 0.591962i
\(475\) −5.77618e8 −0.247294
\(476\) 9.52119e6 + 5.39973e7i 0.00404638 + 0.0229482i
\(477\) 4.70267e9 3.94601e9i 1.98395 1.66473i
\(478\) 3.85333e9 + 1.40250e9i 1.61376 + 0.587360i
\(479\) 1.90177e9 6.92189e8i 0.790651 0.287773i 0.0850442 0.996377i \(-0.472897\pi\)
0.705607 + 0.708604i \(0.250675\pi\)
\(480\) −3.18247e9 −1.31347
\(481\) −7.01998e8 1.50789e9i −0.287626 0.617821i
\(482\) −8.55741e8 −0.348079
\(483\) 6.04686e9 2.20088e9i 2.44183 0.888752i
\(484\) −1.48188e9 5.39362e8i −0.594094 0.216233i
\(485\) −5.68992e9 + 4.77441e9i −2.26470 + 1.90031i
\(486\) −6.42279e8 3.64255e9i −0.253803 1.43939i
\(487\) 3.04423e9 1.19434 0.597168 0.802116i \(-0.296293\pi\)
0.597168 + 0.802116i \(0.296293\pi\)
\(488\) 2.03440e8 + 1.15377e9i 0.0792441 + 0.449416i
\(489\) −9.72576e8 + 1.68455e9i −0.376134 + 0.651483i
\(490\) 3.75542e9 + 3.15117e9i 1.44202 + 1.21000i
\(491\) −8.39515e8 1.45408e9i −0.320069 0.554375i 0.660433 0.750885i \(-0.270373\pi\)
−0.980502 + 0.196510i \(0.937039\pi\)
\(492\) −6.79340e8 + 1.17665e9i −0.257164 + 0.445420i
\(493\) 2.57472e7 9.37121e6i 0.00967755 0.00352234i
\(494\) 2.72512e8 2.28665e8i 0.101705 0.0853404i
\(495\) −5.36371e9 9.29022e9i −1.98768 3.44277i
\(496\) 5.82966e8 3.30616e9i 0.214515 1.21657i
\(497\) 1.95728e7 1.11003e8i 0.00715164 0.0405589i
\(498\) 3.26095e9 + 2.73626e9i 1.18315 + 0.992783i
\(499\) −1.13146e9 4.11816e8i −0.407648 0.148372i 0.130053 0.991507i \(-0.458485\pi\)
−0.537702 + 0.843135i \(0.680707\pi\)
\(500\) −4.97133e8 1.80942e8i −0.177860 0.0647357i
\(501\) −4.60725e8 3.86594e8i −0.163685 0.137348i
\(502\) 4.81333e8 2.72978e9i 0.169818 0.963084i
\(503\) 8.87660e7 5.03417e8i 0.0310999 0.176376i −0.965301 0.261139i \(-0.915902\pi\)
0.996401 + 0.0847625i \(0.0270132\pi\)
\(504\) 2.37431e9 + 4.11243e9i 0.826097 + 1.43084i
\(505\) 2.88459e8 2.42046e8i 0.0996698 0.0836329i
\(506\) 6.52050e9 2.37327e9i 2.23746 0.814367i
\(507\) 1.21961e9 2.11242e9i 0.415616 0.719868i
\(508\) 1.88643e8 + 3.26740e8i 0.0638438 + 0.110581i
\(509\) 9.15496e8 + 7.68193e8i 0.307712 + 0.258201i 0.783546 0.621334i \(-0.213409\pi\)
−0.475834 + 0.879535i \(0.657854\pi\)
\(510\) −2.38664e8 + 4.13378e8i −0.0796692 + 0.137991i
\(511\) 1.24758e9 + 7.07540e9i 0.413615 + 2.34573i
\(512\) −9.97307e8 −0.328386
\(513\) −5.80546e7 3.29244e8i −0.0189857 0.107673i
\(514\) 3.99700e9 3.35388e9i 1.29826 1.08937i
\(515\) 1.34197e9 + 4.88436e8i 0.432929 + 0.157573i
\(516\) −7.37875e8 + 2.68565e8i −0.236433 + 0.0860547i
\(517\) −4.35857e7 −0.0138716
\(518\) 4.96803e9 1.32786e9i 1.57047 0.419758i
\(519\) −8.35174e9 −2.62235
\(520\) −2.61385e9 + 9.51363e8i −0.815209 + 0.296712i
\(521\) 5.01892e9 + 1.82674e9i 1.55481 + 0.565905i 0.969540 0.244932i \(-0.0787656\pi\)
0.585272 + 0.810837i \(0.300988\pi\)
\(522\) −7.02028e8 + 5.89071e8i −0.216027 + 0.181268i
\(523\) 4.25837e8 + 2.41504e9i 0.130163 + 0.738191i 0.978107 + 0.208104i \(0.0667294\pi\)
−0.847944 + 0.530086i \(0.822160\pi\)
\(524\) 2.59238e8 0.0787115
\(525\) 1.84389e9 + 1.04572e10i 0.556132 + 3.15398i
\(526\) −1.41516e9 + 2.45113e9i −0.423990 + 0.734373i
\(527\) −1.54031e8 1.29247e8i −0.0458427 0.0384666i
\(528\) 5.69977e9 + 9.87230e9i 1.68515 + 2.91877i
\(529\) −6.06548e8 + 1.05057e9i −0.178144 + 0.308554i
\(530\) −1.04473e10 + 3.80249e9i −3.04815 + 1.10944i
\(531\) −4.40764e8 + 3.69845e8i −0.127754 + 0.107199i
\(532\) 1.19826e8 + 2.07544e8i 0.0345032 + 0.0597612i
\(533\) −4.92067e8 + 2.79065e9i −0.140760 + 0.798289i
\(534\) 1.65216e9 9.36985e9i 0.469523 2.66280i
\(535\) −5.56567e9 4.67015e9i −1.57137 1.31854i
\(536\) 4.22172e9 + 1.53658e9i 1.18417 + 0.431002i
\(537\) −3.95712e9 1.44027e9i −1.10273 0.401361i
\(538\) −3.14934e9 2.64261e9i −0.871929 0.731635i
\(539\) 1.21766e9 6.90571e9i 0.334939 1.89954i
\(540\) 1.75311e8 9.94239e8i 0.0479106 0.271714i
\(541\) −1.39372e9 2.41399e9i −0.378429 0.655459i 0.612405 0.790545i \(-0.290202\pi\)
−0.990834 + 0.135086i \(0.956869\pi\)
\(542\) −7.71307e8 + 6.47204e8i −0.208080 + 0.174600i
\(543\) 8.97847e9 3.26790e9i 2.40659 0.875929i
\(544\) 5.92333e7 1.02595e8i 0.0157750 0.0273231i
\(545\) −2.57798e9 4.46519e9i −0.682169 1.18155i
\(546\) −5.00968e9 4.20362e9i −1.31715 1.10522i
\(547\) 2.06861e8 3.58293e8i 0.0540409 0.0936015i −0.837739 0.546070i \(-0.816123\pi\)
0.891780 + 0.452469i \(0.149457\pi\)
\(548\) −1.51296e8 8.58040e8i −0.0392730 0.222728i
\(549\) −3.05583e9 −0.788182
\(550\) 1.98832e9 + 1.12763e10i 0.509586 + 2.89001i
\(551\) 9.17396e7 7.69786e7i 0.0233629 0.0196038i
\(552\) −5.47518e9 1.99280e9i −1.38552 0.504286i
\(553\) −1.84008e9 + 6.69736e8i −0.462700 + 0.168409i
\(554\) −3.17149e9 −0.792464
\(555\) 8.83816e9 + 4.12801e9i 2.19450 + 1.02498i
\(556\) −7.27319e8 −0.179458
\(557\) −4.64458e8 + 1.69049e8i −0.113882 + 0.0414495i −0.398332 0.917241i \(-0.630411\pi\)
0.284451 + 0.958691i \(0.408189\pi\)
\(558\) 6.31969e9 + 2.30018e9i 1.53984 + 0.560456i
\(559\) −1.25455e9 + 1.05269e9i −0.303771 + 0.254894i
\(560\) −1.94442e9 1.10274e10i −0.467878 2.65347i
\(561\) 6.82760e8 0.163267
\(562\) −6.12971e8 3.47633e9i −0.145668 0.826122i
\(563\) 1.80452e9 3.12552e9i 0.426169 0.738146i −0.570360 0.821395i \(-0.693196\pi\)
0.996529 + 0.0832489i \(0.0265296\pi\)
\(564\) −1.08274e7 9.08528e6i −0.00254125 0.00213236i
\(565\) 2.06119e9 + 3.57009e9i 0.480783 + 0.832741i
\(566\) 3.74651e8 6.48914e8i 0.0868499 0.150428i
\(567\) 2.48590e9 9.04795e8i 0.572722 0.208454i
\(568\) −7.81816e7 + 6.56022e7i −0.0179013 + 0.0150210i
\(569\) −3.92341e8 6.79555e8i −0.0892835 0.154644i 0.817925 0.575325i \(-0.195124\pi\)
−0.907208 + 0.420681i \(0.861791\pi\)
\(570\) −3.62281e8 + 2.05460e9i −0.0819376 + 0.464691i
\(571\) −9.23006e8 + 5.23462e9i −0.207481 + 1.17668i 0.686007 + 0.727595i \(0.259362\pi\)
−0.893488 + 0.449087i \(0.851749\pi\)
\(572\) −1.17709e9 9.87697e8i −0.262981 0.220667i
\(573\) −4.63467e9 1.68688e9i −1.02915 0.374579i
\(574\) −8.23264e9 2.99644e9i −1.81697 0.661323i
\(575\) −5.83743e9 4.89819e9i −1.28051 1.07448i
\(576\) 6.59537e8 3.74042e9i 0.143801 0.815534i
\(577\) 8.38179e8 4.75355e9i 0.181644 1.03016i −0.748547 0.663081i \(-0.769248\pi\)
0.930192 0.367074i \(-0.119641\pi\)
\(578\) 2.61585e9 + 4.53078e9i 0.563463 + 0.975946i
\(579\) −1.79701e9 + 1.50787e9i −0.384747 + 0.322841i
\(580\) 3.39830e8 1.23688e8i 0.0723208 0.0263226i
\(581\) −2.99051e9 + 5.17971e9i −0.632599 + 1.09569i
\(582\) 7.90590e9 + 1.36934e10i 1.66234 + 2.87927i
\(583\) 1.21821e10 + 1.02220e10i 2.54614 + 2.13647i
\(584\) 3.25265e9 5.63376e9i 0.675761 1.17045i
\(585\) −1.25988e9 7.14512e9i −0.260185 1.47558i
\(586\) −6.80354e9 −1.39667
\(587\) −1.66039e9 9.41657e9i −0.338827 1.92158i −0.385575 0.922677i \(-0.625997\pi\)
0.0467479 0.998907i \(-0.485114\pi\)
\(588\) 1.74196e9 1.46167e9i 0.353359 0.296504i
\(589\) −8.25844e8 3.00583e8i −0.166531 0.0606122i
\(590\) 9.79185e8 3.56394e8i 0.196283 0.0714412i
\(591\) −3.45874e9 −0.689227
\(592\) −5.49303e9 2.56561e9i −1.08814 0.508236i
\(593\) −2.12165e9 −0.417813 −0.208906 0.977936i \(-0.566990\pi\)
−0.208906 + 0.977936i \(0.566990\pi\)
\(594\) −6.22771e9 + 2.26670e9i −1.21920 + 0.443753i
\(595\) −6.30213e8 2.29379e8i −0.122653 0.0446420i
\(596\) 1.23451e9 1.03588e9i 0.238854 0.200422i
\(597\) 9.20431e8 + 5.22002e9i 0.177044 + 1.00407i
\(598\) 4.69308e9 0.897438
\(599\) 7.48439e8 + 4.24461e9i 0.142286 + 0.806945i 0.969506 + 0.245067i \(0.0788099\pi\)
−0.827220 + 0.561878i \(0.810079\pi\)
\(600\) 4.80733e9 8.32654e9i 0.908603 1.57375i
\(601\) −2.18075e9 1.82987e9i −0.409775 0.343842i 0.414482 0.910057i \(-0.363963\pi\)
−0.824258 + 0.566215i \(0.808407\pi\)
\(602\) −2.53165e9 4.38494e9i −0.472950 0.819174i
\(603\) −5.85919e9 + 1.01484e10i −1.08825 + 1.88490i
\(604\) 1.13332e9 4.12493e8i 0.209277 0.0761706i
\(605\) 1.47762e10 1.23987e10i 2.71281 2.27632i
\(606\) −4.00801e8 6.94208e8i −0.0731602 0.126717i
\(607\) 6.31063e8 3.57894e9i 0.114528 0.649522i −0.872454 0.488695i \(-0.837473\pi\)
0.986983 0.160826i \(-0.0514159\pi\)
\(608\) 8.99134e7 5.09924e8i 0.0162242 0.0920118i
\(609\) −1.68648e9 1.41512e9i −0.302566 0.253883i
\(610\) 5.20046e9 + 1.89281e9i 0.927657 + 0.337640i
\(611\) −2.77009e7 1.00823e7i −0.00491303 0.00178819i
\(612\) 9.91989e7 + 8.32377e7i 0.0174935 + 0.0146788i
\(613\) −1.76915e9 + 1.00334e10i −0.310209 + 1.75928i 0.287705 + 0.957719i \(0.407108\pi\)
−0.597913 + 0.801561i \(0.704003\pi\)
\(614\) −9.54338e8 + 5.41232e9i −0.166385 + 0.943614i
\(615\) −8.30936e9 1.43922e10i −1.44047 2.49497i
\(616\) −9.42324e9 + 7.90704e9i −1.62431 + 1.36295i
\(617\) −1.26301e9 + 4.59697e8i −0.216475 + 0.0787905i −0.447981 0.894043i \(-0.647857\pi\)
0.231506 + 0.972833i \(0.425635\pi\)
\(618\) 1.52004e9 2.63279e9i 0.259057 0.448700i
\(619\) 3.05237e9 + 5.28686e9i 0.517273 + 0.895944i 0.999799 + 0.0200616i \(0.00638625\pi\)
−0.482525 + 0.875882i \(0.660280\pi\)
\(620\) −2.03301e9 1.70590e9i −0.342585 0.287463i
\(621\) 2.20528e9 3.81966e9i 0.369524 0.640035i
\(622\) −1.08498e9 6.15323e9i −0.180782 1.02527i
\(623\) 1.33680e10 2.21492
\(624\) 1.33882e9 + 7.59280e9i 0.220584 + 1.25100i
\(625\) −1.75399e9 + 1.47177e9i −0.287374 + 0.241135i
\(626\) −2.20940e9 8.04157e8i −0.359969 0.131018i
\(627\) 2.80423e9 1.02065e9i 0.454335 0.165365i
\(628\) 2.15730e8 0.0347577
\(629\) −2.97576e8 + 2.08088e8i −0.0476782 + 0.0333404i
\(630\) 2.24315e10 3.57409
\(631\) 6.79134e9 2.47184e9i 1.07610 0.391668i 0.257645 0.966240i \(-0.417053\pi\)
0.818455 + 0.574571i \(0.194831\pi\)
\(632\) 1.66612e9 + 6.06418e8i 0.262540 + 0.0955569i
\(633\) −5.98376e9 + 5.02097e9i −0.937694 + 0.786819i
\(634\) −1.66648e9 9.45105e9i −0.259709 1.47288i
\(635\) −4.61479e9 −0.715228
\(636\) 8.95499e8 + 5.07863e9i 0.138027 + 0.782792i
\(637\) 2.37132e9 4.10724e9i 0.363498 0.629597i
\(638\) −1.81858e9 1.52597e9i −0.277243 0.232634i
\(639\) −1.33102e8 2.30539e8i −0.0201805 0.0349536i
\(640\) −6.24543e9 + 1.08174e10i −0.941743 + 1.63115i
\(641\) −1.00247e10 + 3.64869e9i −1.50338 + 0.547184i −0.956932 0.290311i \(-0.906241\pi\)
−0.546444 + 0.837495i \(0.684019\pi\)
\(642\) −1.18481e10 + 9.94170e9i −1.76715 + 1.48282i
\(643\) 1.28979e9 + 2.23399e9i 0.191329 + 0.331392i 0.945691 0.325067i \(-0.105387\pi\)
−0.754362 + 0.656459i \(0.772053\pi\)
\(644\) −5.49006e8 + 3.11357e9i −0.0809984 + 0.459365i
\(645\) 1.66781e9 9.45864e9i 0.244731 1.38794i
\(646\) −5.94922e7 4.99199e7i −0.00868253 0.00728551i
\(647\) 3.20864e9 + 1.16785e9i 0.465753 + 0.169520i 0.564228 0.825619i \(-0.309174\pi\)
−0.0984743 + 0.995140i \(0.531396\pi\)
\(648\) −2.25088e9 8.19254e8i −0.324968 0.118279i
\(649\) −1.14179e9 9.58073e8i −0.163956 0.137576i
\(650\) −1.34478e9 + 7.62660e9i −0.192067 + 1.08927i
\(651\) −2.80548e9 + 1.59107e10i −0.398541 + 2.26024i
\(652\) −4.77844e8 8.27650e8i −0.0675180 0.116945i
\(653\) −6.73281e9 + 5.64950e9i −0.946238 + 0.793988i −0.978660 0.205487i \(-0.934122\pi\)
0.0324222 + 0.999474i \(0.489678\pi\)
\(654\) −1.03139e10 + 3.75397e9i −1.44179 + 0.524770i
\(655\) −1.58543e9 + 2.74605e9i −0.220447 + 0.381825i
\(656\) 5.16438e9 + 8.94497e9i 0.714258 + 1.23713i
\(657\) 1.29983e10 + 1.09068e10i 1.78816 + 1.50045i
\(658\) 4.55698e7 7.89292e7i 0.00623572 0.0108006i
\(659\) −1.09233e9 6.19489e9i −0.148680 0.843207i −0.964338 0.264673i \(-0.914736\pi\)
0.815658 0.578534i \(-0.196375\pi\)
\(660\) 9.01156e9 1.22010
\(661\) −4.48653e8 2.54444e9i −0.0604235 0.342679i −1.00000 0.000339492i \(-0.999892\pi\)
0.939576 0.342339i \(-0.111219\pi\)
\(662\) 1.08287e10 9.08636e9i 1.45069 1.21727i
\(663\) 4.33927e8 + 1.57937e8i 0.0578255 + 0.0210468i
\(664\) 5.08896e9 1.85223e9i 0.674591 0.245531i
\(665\) −2.93130e9 −0.386531
\(666\) 6.97232e9 9.94431e9i 0.914572 1.30441i
\(667\) 1.57990e9 0.206153
\(668\) 2.77675e8 1.01065e8i 0.0360428 0.0131185i
\(669\) 6.81802e9 + 2.48156e9i 0.880374 + 0.320430i
\(670\) 1.62573e10 1.36415e10i 2.08827 1.75226i
\(671\) −1.37461e9 7.79578e9i −0.175651 0.996164i
\(672\) −9.51873e9 −1.21000
\(673\) −1.81653e9 1.03020e10i −0.229715 1.30278i −0.853463 0.521153i \(-0.825502\pi\)
0.623748 0.781625i \(-0.285609\pi\)
\(674\) 1.34260e9 2.32545e9i 0.168903 0.292548i
\(675\) 5.57531e9 + 4.67824e9i 0.697759 + 0.585490i
\(676\) 5.99215e8 + 1.03787e9i 0.0746053 + 0.129220i
\(677\) 7.90303e8 1.36884e9i 0.0978889 0.169548i −0.812922 0.582373i \(-0.802124\pi\)
0.910811 + 0.412824i \(0.135458\pi\)
\(678\) 8.24640e9 3.00144e9i 1.01616 0.369850i
\(679\) −1.70185e10 + 1.42802e10i −2.08630 + 1.75061i
\(680\) 3.03627e8 + 5.25897e8i 0.0370304 + 0.0641385i
\(681\) −1.88643e9 + 1.06985e10i −0.228889 + 1.29809i
\(682\) −3.02523e9 + 1.71569e10i −0.365185 + 2.07107i
\(683\) −1.01200e10 8.49167e9i −1.21537 1.01981i −0.999054 0.0434894i \(-0.986153\pi\)
−0.216313 0.976324i \(-0.569403\pi\)
\(684\) 5.31860e8 + 1.93581e8i 0.0635479 + 0.0231295i
\(685\) 1.00143e10 + 3.64492e9i 1.19043 + 0.433283i
\(686\) 7.03053e8 + 5.89932e8i 0.0831484 + 0.0697698i
\(687\) 1.04619e9 5.93322e9i 0.123101 0.698139i
\(688\) −1.03657e9 + 5.87867e9i −0.121350 + 0.688208i
\(689\) 5.37776e9 + 9.31456e9i 0.626375 + 1.08491i
\(690\) −2.10842e10 + 1.76917e10i −2.44334 + 2.05021i
\(691\) 1.08552e10 3.95095e9i 1.25159 0.455542i 0.370653 0.928772i \(-0.379134\pi\)
0.880939 + 0.473229i \(0.156912\pi\)
\(692\) 2.05168e9 3.55361e9i 0.235363 0.407661i
\(693\) −1.60428e10 2.77869e10i −1.83111 3.17157i
\(694\) −2.83648e9 2.38009e9i −0.322123 0.270293i
\(695\) 4.44811e9 7.70435e9i 0.502607 0.870541i
\(696\) 3.46151e8 + 1.96312e9i 0.0389165 + 0.220706i
\(697\) 6.18627e8 0.0692013
\(698\) −3.93097e8 2.22936e9i −0.0437528 0.248134i
\(699\) 3.89652e9 3.26957e9i 0.431526 0.362093i
\(700\) −4.90246e9 1.78435e9i −0.540220 0.196624i
\(701\) −1.08316e10 + 3.94237e9i −1.18762 + 0.432260i −0.858889 0.512162i \(-0.828845\pi\)
−0.328735 + 0.944422i \(0.606622\pi\)
\(702\) −4.48235e9 −0.489019
\(703\) −9.11129e8 + 1.29950e9i −0.0989091 + 0.141070i
\(704\) 9.83892e9 1.06278
\(705\) 1.62456e8 5.91293e7i 0.0174612 0.00635537i
\(706\) 9.00452e9 + 3.27738e9i 0.963040 + 0.350518i
\(707\) 8.62776e8 7.23955e8i 0.0918185 0.0770449i
\(708\) −8.39320e7 4.76002e8i −0.00888814 0.0504072i
\(709\) 1.11960e10 1.17978 0.589889 0.807484i \(-0.299171\pi\)
0.589889 + 0.807484i \(0.299171\pi\)
\(710\) 8.37165e7 + 4.74780e8i 0.00877822 + 0.0497838i
\(711\) −2.31235e9 + 4.00511e9i −0.241274 + 0.417898i
\(712\) −9.27232e9 7.78040e9i −0.962739 0.807834i
\(713\) −5.79708e9 1.00408e10i −0.598957 1.03742i
\(714\) −7.13840e8 + 1.23641e9i −0.0733934 + 0.127121i
\(715\) 1.76613e10 6.42818e9i 1.80697 0.657684i
\(716\) 1.58493e9 1.32991e9i 0.161367 0.135403i
\(717\) 1.16327e10 + 2.01484e10i 1.17859 + 2.04138i
\(718\) 2.40718e9 1.36518e10i 0.242702 1.37643i
\(719\) −4.30019e8 + 2.43876e9i −0.0431456 + 0.244691i −0.998751 0.0499575i \(-0.984091\pi\)
0.955606 + 0.294648i \(0.0952025\pi\)
\(720\) −2.02585e10 1.69989e10i −2.02275 1.69729i
\(721\) 4.01381e9 + 1.46091e9i 0.398826 + 0.145161i
\(722\) 1.04267e10 + 3.79501e9i 1.03102 + 0.375260i
\(723\) −3.71925e9 3.12082e9i −0.365991 0.307103i
\(724\) −8.15172e8 + 4.62307e9i −0.0798297 + 0.452737i
\(725\) −4.52711e8 + 2.56745e9i −0.0441203 + 0.250219i
\(726\) −2.05309e10 3.55606e10i −1.99127 3.44898i
\(727\) 7.33950e9 6.15857e9i 0.708428 0.594442i −0.215729 0.976453i \(-0.569213\pi\)
0.924158 + 0.382011i \(0.124768\pi\)
\(728\) −7.81799e9 + 2.84552e9i −0.750992 + 0.273339i
\(729\) 8.27527e9 1.43332e10i 0.791108 1.37024i
\(730\) −1.53648e10 2.66127e10i −1.46183 2.53197i
\(731\) 2.73881e8 + 2.29814e8i 0.0259329 + 0.0217603i
\(732\) 1.28353e9 2.22313e9i 0.120953 0.209496i
\(733\) 1.45483e9 + 8.25076e9i 0.136442 + 0.773803i 0.973844 + 0.227216i \(0.0729622\pi\)
−0.837402 + 0.546587i \(0.815927\pi\)
\(734\) −1.50164e9 −0.140161
\(735\) 4.82985e9 + 2.73915e10i 0.448671 + 2.54454i
\(736\) 5.23282e9 4.39085e9i 0.483797 0.405954i
\(737\) −2.85254e10 1.03824e10i −2.62480 0.955348i
\(738\) −1.94434e10 + 7.07680e9i −1.78063 + 0.648097i
\(739\) −1.35358e10 −1.23376 −0.616878 0.787059i \(-0.711603\pi\)
−0.616878 + 0.787059i \(0.711603\pi\)
\(740\) −3.92762e9 + 2.74650e9i −0.356302 + 0.249154i
\(741\) 2.01832e9 0.182233
\(742\) −3.12476e10 + 1.13732e10i −2.80804 + 1.02204i
\(743\) −6.47304e9 2.35599e9i −0.578959 0.210724i 0.0359076 0.999355i \(-0.488568\pi\)
−0.614866 + 0.788631i \(0.710790\pi\)
\(744\) 1.12062e10 9.40313e9i 0.997594 0.837081i
\(745\) 3.42287e9 + 1.94121e10i 0.303280 + 1.71999i
\(746\) 1.12895e10 0.995607
\(747\) 2.45288e9 + 1.39110e10i 0.215305 + 1.22106i
\(748\) −1.67726e8 + 2.90510e8i −0.0146536 + 0.0253809i
\(749\) −1.66469e10 1.39684e10i −1.44759 1.21467i
\(750\) −6.88759e9 1.19296e10i −0.596146 1.03256i
\(751\) −5.11147e8 + 8.85332e8i −0.0440358 + 0.0762723i −0.887203 0.461379i \(-0.847355\pi\)
0.843167 + 0.537651i \(0.180688\pi\)
\(752\) −1.00969e8 + 3.67497e7i −0.00865815 + 0.00315131i
\(753\) 1.20473e10 1.01089e10i 1.02827 0.862819i
\(754\) −8.02808e8 1.39050e9i −0.0682043 0.118133i
\(755\) −2.56163e9 + 1.45277e10i −0.216621 + 1.22852i
\(756\) 5.24353e8 2.97376e9i 0.0441365 0.250310i
\(757\) −1.37456e9 1.15339e9i −0.115167 0.0966367i 0.583385 0.812195i \(-0.301728\pi\)
−0.698553 + 0.715559i \(0.746172\pi\)
\(758\) −7.61583e9 2.77193e9i −0.635148 0.231175i
\(759\) 3.69947e10 + 1.34650e10i 3.07110 + 1.11779i
\(760\) 2.03321e9 + 1.70607e9i 0.168010 + 0.140977i
\(761\) 8.02093e8 4.54889e9i 0.0659748 0.374162i −0.933887 0.357567i \(-0.883606\pi\)
0.999862 0.0165948i \(-0.00528253\pi\)
\(762\) −1.70589e9 + 9.67460e9i −0.139672 + 0.792120i
\(763\) −7.71071e9 1.33553e10i −0.628432 1.08848i
\(764\) 1.85631e9 1.55763e9i 0.150599