Properties

Label 27.8.e.a.4.4
Level 27
Weight 8
Character 27.4
Analytic conductor 8.434
Analytic rank 0
Dimension 120
CM No

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Newspace parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 27.e (of order \(9\) and degree \(6\))

Newform invariants

Self dual: No
Analytic conductor: \(8.43439568807\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(20\) over \(\Q(\zeta_{9})\)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 4.4
Character \(\chi\) = 27.4
Dual form 27.8.e.a.7.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-15.5171 - 5.64776i) q^{2} +(-4.90318 - 46.5076i) q^{3} +(110.829 + 92.9968i) q^{4} +(-48.1497 + 273.071i) q^{5} +(-186.581 + 749.355i) q^{6} +(-92.9707 + 78.0117i) q^{7} +(-137.696 - 238.496i) q^{8} +(-2138.92 + 456.070i) q^{9} +O(q^{10})\) \(q+(-15.5171 - 5.64776i) q^{2} +(-4.90318 - 46.5076i) q^{3} +(110.829 + 92.9968i) q^{4} +(-48.1497 + 273.071i) q^{5} +(-186.581 + 749.355i) q^{6} +(-92.9707 + 78.0117i) q^{7} +(-137.696 - 238.496i) q^{8} +(-2138.92 + 456.070i) q^{9} +(2289.38 - 3965.33i) q^{10} +(264.033 + 1497.40i) q^{11} +(3781.64 - 5610.38i) q^{12} +(13567.2 - 4938.04i) q^{13} +(1883.23 - 685.439i) q^{14} +(12936.0 + 900.415i) q^{15} +(-2426.07 - 13758.9i) q^{16} +(-3936.89 + 6818.89i) q^{17} +(35765.6 + 5003.21i) q^{18} +(-10039.8 - 17389.5i) q^{19} +(-30731.1 + 25786.4i) q^{20} +(4083.99 + 3941.34i) q^{21} +(4359.96 - 24726.5i) q^{22} +(9573.92 + 8033.47i) q^{23} +(-10416.7 + 7573.28i) q^{24} +(1164.27 + 423.758i) q^{25} -238412. q^{26} +(31698.2 + 97239.8i) q^{27} -17558.7 q^{28} +(58464.4 + 21279.3i) q^{29} +(-195643. - 87031.0i) q^{30} +(172864. + 145050. i) q^{31} +(-46182.7 + 261915. i) q^{32} +(68346.1 - 19621.6i) q^{33} +(99600.5 - 83574.7i) q^{34} +(-16826.2 - 29143.8i) q^{35} +(-279468. - 148367. i) q^{36} +(221531. - 383703. i) q^{37} +(57577.3 + 326537. i) q^{38} +(-296179. - 606765. i) q^{39} +(71756.2 - 26117.1i) q^{40} +(656063. - 238787. i) q^{41} +(-41111.9 - 84223.6i) q^{42} +(150928. + 855954. i) q^{43} +(-109991. + 190510. i) q^{44} +(-21551.2 - 606035. i) q^{45} +(-103188. - 178727. i) q^{46} +(-428043. + 359170. i) q^{47} +(-627999. + 180293. i) q^{48} +(-140449. + 796526. i) q^{49} +(-15672.7 - 13151.0i) q^{50} +(336434. + 149661. i) q^{51} +(1.96286e6 + 714423. i) q^{52} +973072. q^{53} +(57322.3 - 1.68790e6i) q^{54} -421610. q^{55} +(31407.1 + 11431.3i) q^{56} +(-759518. + 552193. i) q^{57} +(-787017. - 660386. i) q^{58} +(152194. - 863134. i) q^{59} +(1.34995e6 + 1.30279e6i) q^{60} +(1.55607e6 - 1.30570e6i) q^{61} +(-1.86314e6 - 3.22705e6i) q^{62} +(163278. - 209262. i) q^{63} +(1.30170e6 - 2.25461e6i) q^{64} +(695180. + 3.94256e6i) q^{65} +(-1.17135e6 - 81532.6i) q^{66} +(-3.74812e6 + 1.36420e6i) q^{67} +(-1.07046e6 + 389614. i) q^{68} +(326675. - 484650. i) q^{69} +(96496.3 + 547258. i) q^{70} +(-1.04660e6 + 1.81276e6i) q^{71} +(403290. + 447324. i) q^{72} +(-692089. - 1.19873e6i) q^{73} +(-5.60458e6 + 4.70280e6i) q^{74} +(13999.4 - 56225.0i) q^{75} +(504461. - 2.86094e6i) q^{76} +(-141362. - 118617. i) q^{77} +(1.16898e6 + 1.10880e7i) q^{78} +(1.91605e6 + 697385. i) q^{79} +3.87397e6 q^{80} +(4.36697e6 - 1.95099e6i) q^{81} -1.15288e7 q^{82} +(1.71393e6 + 623820. i) q^{83} +(86093.5 + 816614. i) q^{84} +(-1.67248e6 - 1.40338e6i) q^{85} +(2.49226e6 - 1.41343e7i) q^{86} +(702988. - 2.82338e6i) q^{87} +(320768. - 269157. i) q^{88} +(-3.31222e6 - 5.73693e6i) q^{89} +(-3.08833e6 + 9.52562e6i) q^{90} +(-876124. + 1.51749e6i) q^{91} +(313983. + 1.78069e6i) q^{92} +(5.89835e6 - 8.75069e6i) q^{93} +(8.67048e6 - 3.15580e6i) q^{94} +(5.23198e6 - 1.90429e6i) q^{95} +(1.24075e7 + 863630. i) q^{96} +(2.73025e6 + 1.54840e7i) q^{97} +(6.67795e6 - 1.15665e7i) q^{98} +(-1.24767e6 - 3.08241e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120q - 6q^{2} - 6q^{3} - 6q^{4} - 219q^{5} + 1386q^{6} - 6q^{7} - 4611q^{8} - 1728q^{9} + O(q^{10}) \) \( 120q - 6q^{2} - 6q^{3} - 6q^{4} - 219q^{5} + 1386q^{6} - 6q^{7} - 4611q^{8} - 1728q^{9} - 3q^{10} + 9399q^{11} - 10545q^{12} - 6q^{13} + 16647q^{14} + 11709q^{15} + 378q^{16} - 58959q^{17} - 156051q^{18} - 3q^{19} + 240243q^{20} - 516q^{21} + 105762q^{22} - 144084q^{23} - 150894q^{24} - 107997q^{25} + 443202q^{26} + 114363q^{27} - 12q^{28} + 107886q^{29} - 179901q^{30} + 297975q^{31} - 639576q^{32} - 31338q^{33} - 265806q^{34} - 450672q^{35} + 51264q^{36} - 3q^{37} - 145596q^{38} + 1919661q^{39} + 283521q^{40} + 227085q^{41} + 3792042q^{42} - 1080969q^{43} - 1205115q^{44} - 4430925q^{45} - 3q^{46} - 5184339q^{47} - 2424039q^{48} + 976008q^{49} + 2324559q^{50} + 2918034q^{51} - 3366135q^{52} + 5631750q^{53} + 11971422q^{54} - 12q^{55} + 5254923q^{56} - 284637q^{57} + 3884295q^{58} - 12534492q^{59} - 29390886q^{60} + 3865440q^{61} - 9923646q^{62} + 3292389q^{63} - 10223619q^{64} + 17158395q^{65} + 39100653q^{66} + 5567061q^{67} + 19858455q^{68} - 12682935q^{69} - 1020993q^{70} - 18563877q^{71} - 33138540q^{72} + 3770934q^{73} - 36278085q^{74} - 26317941q^{75} - 1156998q^{76} + 8471751q^{77} + 36593658q^{78} + 16415526q^{79} + 101080590q^{80} + 45736524q^{81} - 12q^{82} + 3147699q^{83} - 27588054q^{84} - 7672131q^{85} - 70854834q^{86} - 55384731q^{87} - 34323078q^{88} - 54647613q^{89} - 25256970q^{90} + 3315066q^{91} + 73858515q^{92} + 69808065q^{93} + 22126539q^{94} + 32541447q^{95} + 33014034q^{96} + 41250117q^{97} - 88493274q^{98} - 111262167q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −15.5171 5.64776i −1.37153 0.499196i −0.451930 0.892053i \(-0.649264\pi\)
−0.919600 + 0.392857i \(0.871487\pi\)
\(3\) −4.90318 46.5076i −0.104846 0.994488i
\(4\) 110.829 + 92.9968i 0.865853 + 0.726537i
\(5\) −48.1497 + 273.071i −0.172266 + 0.976968i 0.768987 + 0.639264i \(0.220761\pi\)
−0.941253 + 0.337703i \(0.890350\pi\)
\(6\) −186.581 + 749.355i −0.352645 + 1.41631i
\(7\) −92.9707 + 78.0117i −0.102448 + 0.0859640i −0.692573 0.721348i \(-0.743523\pi\)
0.590125 + 0.807312i \(0.299078\pi\)
\(8\) −137.696 238.496i −0.0950835 0.164689i
\(9\) −2138.92 + 456.070i −0.978014 + 0.208537i
\(10\) 2289.38 3965.33i 0.723966 1.25395i
\(11\) 264.033 + 1497.40i 0.0598113 + 0.339207i 0.999999 0.00145022i \(-0.000461619\pi\)
−0.940188 + 0.340657i \(0.889351\pi\)
\(12\) 3781.64 5610.38i 0.631751 0.937256i
\(13\) 13567.2 4938.04i 1.71272 0.623381i 0.715554 0.698557i \(-0.246174\pi\)
0.997170 + 0.0751768i \(0.0239521\pi\)
\(14\) 1883.23 685.439i 0.183423 0.0667606i
\(15\) 12936.0 + 900.415i 0.989644 + 0.0688848i
\(16\) −2426.07 13758.9i −0.148076 0.839778i
\(17\) −3936.89 + 6818.89i −0.194349 + 0.336622i −0.946687 0.322155i \(-0.895593\pi\)
0.752338 + 0.658777i \(0.228926\pi\)
\(18\) 35765.6 + 5003.21i 1.44548 + 0.202206i
\(19\) −10039.8 17389.5i −0.335806 0.581634i 0.647833 0.761782i \(-0.275675\pi\)
−0.983639 + 0.180149i \(0.942342\pi\)
\(20\) −30731.1 + 25786.4i −0.858960 + 0.720753i
\(21\) 4083.99 + 3941.34i 0.0962315 + 0.0928703i
\(22\) 4359.96 24726.5i 0.0872977 0.495090i
\(23\) 9573.92 + 8033.47i 0.164075 + 0.137675i 0.721128 0.692801i \(-0.243624\pi\)
−0.557053 + 0.830477i \(0.688068\pi\)
\(24\) −10416.7 + 7573.28i −0.153813 + 0.111827i
\(25\) 1164.27 + 423.758i 0.0149026 + 0.00542410i
\(26\) −238412. −2.66024
\(27\) 31698.2 + 97239.8i 0.309929 + 0.950760i
\(28\) −17558.7 −0.151161
\(29\) 58464.4 + 21279.3i 0.445142 + 0.162018i 0.554859 0.831944i \(-0.312772\pi\)
−0.109717 + 0.993963i \(0.534994\pi\)
\(30\) −195643. 87031.0i −1.32294 0.588504i
\(31\) 172864. + 145050.i 1.04217 + 0.874484i 0.992248 0.124270i \(-0.0396588\pi\)
0.0499205 + 0.998753i \(0.484103\pi\)
\(32\) −46182.7 + 261915.i −0.249146 + 1.41298i
\(33\) 68346.1 19621.6i 0.331066 0.0950463i
\(34\) 99600.5 83574.7i 0.434595 0.364669i
\(35\) −16826.2 29143.8i −0.0663358 0.114897i
\(36\) −279468. 148367.i −0.998327 0.530002i
\(37\) 221531. 383703.i 0.719000 1.24534i −0.242397 0.970177i \(-0.577934\pi\)
0.961396 0.275167i \(-0.0887332\pi\)
\(38\) 57577.3 + 326537.i 0.170219 + 0.965362i
\(39\) −296179. 606765.i −0.799518 1.63793i
\(40\) 71756.2 26117.1i 0.177276 0.0645231i
\(41\) 656063. 238787.i 1.48663 0.541088i 0.534067 0.845442i \(-0.320663\pi\)
0.952559 + 0.304354i \(0.0984407\pi\)
\(42\) −41111.9 84223.6i −0.0856239 0.175413i
\(43\) 150928. + 855954.i 0.289487 + 1.64176i 0.688801 + 0.724950i \(0.258137\pi\)
−0.399314 + 0.916814i \(0.630752\pi\)
\(44\) −109991. + 190510.i −0.194659 + 0.337159i
\(45\) −21551.2 606035.i −0.0352555 0.991412i
\(46\) −103188. 178727.i −0.156307 0.270731i
\(47\) −428043. + 359170.i −0.601374 + 0.504613i −0.891887 0.452258i \(-0.850618\pi\)
0.290513 + 0.956871i \(0.406174\pi\)
\(48\) −627999. + 180293.i −0.819624 + 0.235307i
\(49\) −140449. + 796526.i −0.170542 + 0.967194i
\(50\) −15672.7 13151.0i −0.0177317 0.0148786i
\(51\) 336434. + 149661.i 0.355143 + 0.157984i
\(52\) 1.96286e6 + 714423.i 1.93588 + 0.704602i
\(53\) 973072. 0.897799 0.448900 0.893582i \(-0.351816\pi\)
0.448900 + 0.893582i \(0.351816\pi\)
\(54\) 57322.3 1.68790e6i 0.0495388 1.45871i
\(55\) −421610. −0.341697
\(56\) 31407.1 + 11431.3i 0.0238985 + 0.00869833i
\(57\) −759518. + 552193.i −0.543220 + 0.394938i
\(58\) −787017. 660386.i −0.529647 0.444426i
\(59\) 152194. 863134.i 0.0964751 0.547137i −0.897810 0.440382i \(-0.854843\pi\)
0.994285 0.106755i \(-0.0340460\pi\)
\(60\) 1.34995e6 + 1.30279e6i 0.806840 + 0.778658i
\(61\) 1.55607e6 1.30570e6i 0.877757 0.736525i −0.0879598 0.996124i \(-0.528035\pi\)
0.965717 + 0.259599i \(0.0835902\pi\)
\(62\) −1.86314e6 3.22705e6i −0.992827 1.71963i
\(63\) 163278. 209262.i 0.0822689 0.105438i
\(64\) 1.30170e6 2.25461e6i 0.620698 1.07508i
\(65\) 695180. + 3.94256e6i 0.313979 + 1.78066i
\(66\) −1.17135e6 81532.6i −0.501514 0.0349082i
\(67\) −3.74812e6 + 1.36420e6i −1.52248 + 0.554137i −0.961766 0.273873i \(-0.911695\pi\)
−0.560713 + 0.828010i \(0.689473\pi\)
\(68\) −1.07046e6 + 389614.i −0.412846 + 0.150264i
\(69\) 326675. 484650.i 0.119714 0.177605i
\(70\) 96496.3 + 547258.i 0.0336254 + 0.190699i
\(71\) −1.04660e6 + 1.81276e6i −0.347036 + 0.601084i −0.985722 0.168384i \(-0.946145\pi\)
0.638685 + 0.769468i \(0.279479\pi\)
\(72\) 403290. + 447324.i 0.127337 + 0.141240i
\(73\) −692089. 1.19873e6i −0.208225 0.360655i 0.742931 0.669368i \(-0.233435\pi\)
−0.951155 + 0.308713i \(0.900102\pi\)
\(74\) −5.60458e6 + 4.70280e6i −1.60780 + 1.34911i
\(75\) 13999.4 56225.0i 0.00383172 0.0153892i
\(76\) 504461. 2.86094e6i 0.131820 0.747586i
\(77\) −141362. 118617.i −0.0352871 0.0296094i
\(78\) 1.16898e6 + 1.10880e7i 0.278917 + 2.64558i
\(79\) 1.91605e6 + 697385.i 0.437232 + 0.159139i 0.551252 0.834339i \(-0.314150\pi\)
−0.114020 + 0.993478i \(0.536373\pi\)
\(80\) 3.87397e6 0.845944
\(81\) 4.36697e6 1.95099e6i 0.913025 0.407904i
\(82\) −1.15288e7 −2.30906
\(83\) 1.71393e6 + 623820.i 0.329018 + 0.119753i 0.501247 0.865304i \(-0.332875\pi\)
−0.172229 + 0.985057i \(0.555097\pi\)
\(84\) 86093.5 + 816614.i 0.0158487 + 0.150328i
\(85\) −1.67248e6 1.40338e6i −0.295389 0.247861i
\(86\) 2.49226e6 1.41343e7i 0.422522 2.39624i
\(87\) 702988. 2.82338e6i 0.114454 0.459676i
\(88\) 320768. 269157.i 0.0501767 0.0421033i
\(89\) −3.31222e6 5.73693e6i −0.498028 0.862610i 0.501969 0.864885i \(-0.332609\pi\)
−0.999997 + 0.00227542i \(0.999276\pi\)
\(90\) −3.08833e6 + 9.52562e6i −0.446555 + 1.37735i
\(91\) −876124. + 1.51749e6i −0.121877 + 0.211097i
\(92\) 313983. + 1.78069e6i 0.0420387 + 0.238413i
\(93\) 5.89835e6 8.75069e6i 0.760396 1.12811i
\(94\) 8.67048e6 3.15580e6i 1.07670 0.391888i
\(95\) 5.23198e6 1.90429e6i 0.626085 0.227876i
\(96\) 1.24075e7 + 863630.i 1.43131 + 0.0996273i
\(97\) 2.73025e6 + 1.54840e7i 0.303739 + 1.72259i 0.629381 + 0.777097i \(0.283308\pi\)
−0.325642 + 0.945493i \(0.605580\pi\)
\(98\) 6.67795e6 1.15665e7i 0.716724 1.24140i
\(99\) −1.24767e6 3.08241e6i −0.129233 0.319276i
\(100\) 89626.5 + 155238.i 0.00896265 + 0.0155238i
\(101\) 9.71749e6 8.15394e6i 0.938489 0.787486i −0.0388327 0.999246i \(-0.512364\pi\)
0.977322 + 0.211760i \(0.0679195\pi\)
\(102\) −4.37522e6 4.22240e6i −0.408225 0.393966i
\(103\) −823874. + 4.67242e6i −0.0742900 + 0.421320i 0.924868 + 0.380289i \(0.124175\pi\)
−0.999158 + 0.0410311i \(0.986936\pi\)
\(104\) −3.04584e6 2.55576e6i −0.265516 0.222794i
\(105\) −1.27291e6 + 925444.i −0.107309 + 0.0780167i
\(106\) −1.50992e7 5.49568e6i −1.23136 0.448178i
\(107\) 1.21781e7 0.961029 0.480515 0.876987i \(-0.340450\pi\)
0.480515 + 0.876987i \(0.340450\pi\)
\(108\) −5.52989e6 + 1.37248e7i −0.422409 + 1.04839i
\(109\) −9.09360e6 −0.672578 −0.336289 0.941759i \(-0.609172\pi\)
−0.336289 + 0.941759i \(0.609172\pi\)
\(110\) 6.54216e6 + 2.38115e6i 0.468648 + 0.170574i
\(111\) −1.89313e7 8.42152e6i −1.31387 0.584467i
\(112\) 1.29891e6 + 1.08992e6i 0.0873607 + 0.0733043i
\(113\) −3.66560e6 + 2.07886e7i −0.238985 + 1.35535i 0.595072 + 0.803672i \(0.297123\pi\)
−0.834057 + 0.551678i \(0.813988\pi\)
\(114\) 1.49042e7 4.27885e6i 0.942194 0.270496i
\(115\) −2.65469e6 + 2.22755e6i −0.162769 + 0.136579i
\(116\) 4.50066e6 + 7.79537e6i 0.267715 + 0.463697i
\(117\) −2.67670e7 + 1.67497e7i −1.54507 + 0.966842i
\(118\) −7.23638e6 + 1.25338e7i −0.405447 + 0.702255i
\(119\) −165938. 941080.i −0.00902675 0.0511932i
\(120\) −1.56648e6 3.20915e6i −0.0827542 0.169534i
\(121\) 1.61394e7 5.87428e6i 0.828209 0.301443i
\(122\) −3.15199e7 + 1.14723e7i −1.57154 + 0.571994i
\(123\) −1.43222e7 2.93411e7i −0.693973 1.42170i
\(124\) 5.66919e6 + 3.21516e7i 0.267021 + 1.51435i
\(125\) −1.10032e7 + 1.90580e7i −0.503886 + 0.872756i
\(126\) −3.71546e6 + 2.32498e6i −0.165469 + 0.103543i
\(127\) −2.20656e6 3.82188e6i −0.0955879 0.165563i 0.814266 0.580492i \(-0.197140\pi\)
−0.909854 + 0.414929i \(0.863806\pi\)
\(128\) −6.85412e6 + 5.75129e6i −0.288880 + 0.242399i
\(129\) 3.90684e7 1.12162e7i 1.60236 0.460025i
\(130\) 1.14795e7 6.51033e7i 0.458269 2.59897i
\(131\) −3.46368e7 2.90637e7i −1.34613 1.12954i −0.980004 0.198975i \(-0.936239\pi\)
−0.366129 0.930564i \(-0.619317\pi\)
\(132\) 9.39949e6 + 4.18132e6i 0.355709 + 0.158236i
\(133\) 2.29000e6 + 833491.i 0.0844023 + 0.0307199i
\(134\) 6.58646e7 2.36475
\(135\) −2.80796e7 + 3.97379e6i −0.982252 + 0.139007i
\(136\) 2.16837e6 0.0739174
\(137\) −3.97795e7 1.44785e7i −1.32171 0.481064i −0.417706 0.908582i \(-0.637166\pi\)
−0.904007 + 0.427518i \(0.859388\pi\)
\(138\) −7.80623e6 + 5.67537e6i −0.252851 + 0.183831i
\(139\) 4.95527e6 + 4.15796e6i 0.156500 + 0.131319i 0.717675 0.696378i \(-0.245206\pi\)
−0.561175 + 0.827697i \(0.689651\pi\)
\(140\) 845447. 4.79477e6i 0.0260399 0.147679i
\(141\) 1.88029e7 + 1.81462e7i 0.564883 + 0.545153i
\(142\) 2.64781e7 2.22178e7i 0.776030 0.651166i
\(143\) 1.09764e7 + 1.90117e7i 0.313895 + 0.543683i
\(144\) 1.14642e7 + 2.83227e7i 0.319945 + 0.790436i
\(145\) −8.62580e6 + 1.49403e7i −0.234969 + 0.406979i
\(146\) 3.96905e6 + 2.25096e7i 0.105548 + 0.598595i
\(147\) 3.77332e7 + 2.62644e6i 0.979744 + 0.0681957i
\(148\) 6.02353e7 2.19239e7i 1.52734 0.555905i
\(149\) −5.57525e7 + 2.02922e7i −1.38074 + 0.502548i −0.922403 0.386230i \(-0.873777\pi\)
−0.458338 + 0.888778i \(0.651555\pi\)
\(150\) −534775. + 793383.i −0.0129375 + 0.0191939i
\(151\) 3.61969e6 + 2.05283e7i 0.0855564 + 0.485215i 0.997235 + 0.0743108i \(0.0236757\pi\)
−0.911679 + 0.410904i \(0.865213\pi\)
\(152\) −2.76488e6 + 4.78892e6i −0.0638593 + 0.110608i
\(153\) 5.31078e6 1.63805e7i 0.119878 0.369750i
\(154\) 1.52361e6 + 2.63897e6i 0.0336164 + 0.0582254i
\(155\) −4.79322e7 + 4.02199e7i −1.03387 + 0.867522i
\(156\) 2.36019e7 9.47909e7i 0.497749 1.99908i
\(157\) 2.37786e6 1.34855e7i 0.0490386 0.278112i −0.950422 0.310964i \(-0.899348\pi\)
0.999460 + 0.0328526i \(0.0104592\pi\)
\(158\) −2.57928e7 2.16428e7i −0.520235 0.436529i
\(159\) −4.77115e6 4.52553e7i −0.0941310 0.892851i
\(160\) −6.92976e7 2.52223e7i −1.33751 0.486815i
\(161\) −1.51680e6 −0.0286443
\(162\) −7.87814e7 + 5.61016e6i −1.45586 + 0.103675i
\(163\) 4.55609e7 0.824017 0.412008 0.911180i \(-0.364827\pi\)
0.412008 + 0.911180i \(0.364827\pi\)
\(164\) 9.49174e7 + 3.45471e7i 1.68032 + 0.611587i
\(165\) 2.06723e6 + 1.96081e7i 0.0358257 + 0.339814i
\(166\) −2.30720e7 1.93597e7i −0.391478 0.328489i
\(167\) 793110. 4.49795e6i 0.0131773 0.0747321i −0.977510 0.210889i \(-0.932364\pi\)
0.990687 + 0.136157i \(0.0434752\pi\)
\(168\) 377646. 1.51672e6i 0.00614472 0.0246787i
\(169\) 1.11616e8 9.36566e7i 1.77878 1.49257i
\(170\) 1.80261e7 + 3.12221e7i 0.281404 + 0.487406i
\(171\) 2.94052e7 + 3.26159e7i 0.449716 + 0.498818i
\(172\) −6.28738e7 + 1.08901e8i −0.942150 + 1.63185i
\(173\) 6.00575e6 + 3.40603e7i 0.0881873 + 0.500135i 0.996623 + 0.0821109i \(0.0261662\pi\)
−0.908436 + 0.418024i \(0.862723\pi\)
\(174\) −2.68541e7 + 3.98403e7i −0.386445 + 0.573324i
\(175\) −141301. + 51429.2i −0.00199302 + 0.000725399i
\(176\) 1.99621e7 7.26561e6i 0.276002 0.100456i
\(177\) −4.08885e7 2.84607e6i −0.554237 0.0385780i
\(178\) 1.89952e7 + 1.07727e8i 0.252449 + 1.43171i
\(179\) 6.43185e7 1.11403e8i 0.838205 1.45181i −0.0531893 0.998584i \(-0.516939\pi\)
0.891394 0.453229i \(-0.149728\pi\)
\(180\) 5.39708e7 6.91706e7i 0.689772 0.884032i
\(181\) 3.56974e6 + 6.18297e6i 0.0447468 + 0.0775037i 0.887531 0.460747i \(-0.152419\pi\)
−0.842785 + 0.538251i \(0.819085\pi\)
\(182\) 2.21653e7 1.85989e7i 0.272536 0.228685i
\(183\) −6.83545e7 6.59670e7i −0.824496 0.795697i
\(184\) 597663. 3.38951e6i 0.00707284 0.0401121i
\(185\) 9.41115e7 + 7.89689e7i 1.09280 + 0.916970i
\(186\) −1.40947e8 + 1.02473e8i −1.60606 + 1.16765i
\(187\) −1.12501e7 4.09470e6i −0.125809 0.0457906i
\(188\) −8.08413e7 −0.887321
\(189\) −1.05329e7 6.56762e6i −0.113483 0.0707606i
\(190\) −9.19401e7 −0.972450
\(191\) −1.07056e8 3.89651e7i −1.11171 0.404631i −0.280093 0.959973i \(-0.590365\pi\)
−0.831622 + 0.555342i \(0.812587\pi\)
\(192\) −1.11239e8 4.94841e7i −1.13423 0.504558i
\(193\) 5.07432e7 + 4.25786e7i 0.508075 + 0.426325i 0.860451 0.509533i \(-0.170182\pi\)
−0.352376 + 0.935858i \(0.614626\pi\)
\(194\) 4.50844e7 2.55686e8i 0.443323 2.51421i
\(195\) 1.79951e8 5.16623e7i 1.73793 0.498944i
\(196\) −8.96402e7 + 7.52171e7i −0.850367 + 0.713543i
\(197\) 46465.8 + 80481.2i 0.000433014 + 0.000750002i 0.866242 0.499625i \(-0.166529\pi\)
−0.865809 + 0.500375i \(0.833196\pi\)
\(198\) 1.95146e6 + 5.48765e7i 0.0178661 + 0.502410i
\(199\) 4.97863e7 8.62324e7i 0.447841 0.775684i −0.550404 0.834898i \(-0.685526\pi\)
0.998245 + 0.0592146i \(0.0188596\pi\)
\(200\) −59249.7 336022.i −0.000523698 0.00297004i
\(201\) 8.18235e7 + 1.67627e8i 0.710709 + 1.45599i
\(202\) −1.96839e8 + 7.16434e7i −1.68028 + 0.611570i
\(203\) −7.09552e6 + 2.58256e6i −0.0595316 + 0.0216677i
\(204\) 2.33687e7 + 4.78740e7i 0.192721 + 0.394816i
\(205\) 3.36166e7 + 1.90649e8i 0.272530 + 1.54560i
\(206\) 3.91728e7 6.78494e7i 0.312212 0.540767i
\(207\) −2.41417e7 1.28166e7i −0.189178 0.100433i
\(208\) −1.00857e8 1.74690e8i −0.777114 1.34600i
\(209\) 2.33883e7 1.96251e7i 0.177209 0.148696i
\(210\) 2.49785e7 7.17112e6i 0.186123 0.0534342i
\(211\) −3.76523e7 + 2.13537e8i −0.275933 + 1.56489i 0.460051 + 0.887892i \(0.347831\pi\)
−0.735984 + 0.676999i \(0.763280\pi\)
\(212\) 1.07845e8 + 9.04925e7i 0.777363 + 0.652285i
\(213\) 8.94387e7 + 3.97864e7i 0.634157 + 0.282102i
\(214\) −1.88969e8 6.87790e7i −1.31808 0.479742i
\(215\) −2.41003e8 −1.65382
\(216\) 1.88266e7 2.09494e7i 0.127111 0.141444i
\(217\) −2.73869e7 −0.181942
\(218\) 1.41106e8 + 5.13584e7i 0.922461 + 0.335749i
\(219\) −5.23568e7 + 3.80650e7i −0.336836 + 0.244890i
\(220\) −4.67267e7 3.92084e7i −0.295860 0.248256i
\(221\) −1.97404e7 + 1.11954e8i −0.123022 + 0.697694i
\(222\) 2.46196e8 + 2.37597e8i 1.51024 + 1.45749i
\(223\) 2.20203e8 1.84772e8i 1.32971 1.11576i 0.345560 0.938397i \(-0.387689\pi\)
0.984146 0.177359i \(-0.0567554\pi\)
\(224\) −1.61388e7 2.79532e7i −0.0959407 0.166174i
\(225\) −2.68353e6 375396.i −0.0157061 0.00219711i
\(226\) 1.74289e8 3.01877e8i 1.00436 1.73960i
\(227\) −2.12288e7 1.20394e8i −0.120458 0.683150i −0.983902 0.178706i \(-0.942809\pi\)
0.863445 0.504444i \(-0.168302\pi\)
\(228\) −1.35529e8 9.43357e6i −0.757286 0.0527113i
\(229\) 1.05065e7 3.82406e6i 0.0578142 0.0210426i −0.312951 0.949769i \(-0.601318\pi\)
0.370765 + 0.928727i \(0.379095\pi\)
\(230\) 5.37737e7 1.95720e7i 0.291422 0.106069i
\(231\) −4.82347e6 + 7.15603e6i −0.0257465 + 0.0381971i
\(232\) −2.97527e6 1.68736e7i −0.0156429 0.0887155i
\(233\) 2.92498e7 5.06621e7i 0.151488 0.262384i −0.780287 0.625422i \(-0.784927\pi\)
0.931775 + 0.363037i \(0.118260\pi\)
\(234\) 5.09943e8 1.08733e8i 2.60176 0.554759i
\(235\) −7.74688e7 1.34180e8i −0.389394 0.674450i
\(236\) 9.71362e7 8.15070e7i 0.481049 0.403648i
\(237\) 2.30390e7 9.25303e7i 0.112420 0.451507i
\(238\) −2.74012e6 + 1.55400e7i −0.0131750 + 0.0747191i
\(239\) 2.20228e8 + 1.84793e8i 1.04347 + 0.875575i 0.992392 0.123120i \(-0.0392901\pi\)
0.0510773 + 0.998695i \(0.483734\pi\)
\(240\) −1.89948e7 1.80169e8i −0.0886942 0.841282i
\(241\) 4.93808e7 + 1.79731e7i 0.227247 + 0.0827112i 0.453134 0.891442i \(-0.350306\pi\)
−0.225887 + 0.974153i \(0.572528\pi\)
\(242\) −2.83614e8 −1.28639
\(243\) −1.12148e8 1.93531e8i −0.501384 0.865225i
\(244\) 2.93883e8 1.29512
\(245\) −2.10745e8 7.67050e7i −0.915539 0.333229i
\(246\) 5.65278e7 + 5.36177e8i 0.242097 + 2.29633i
\(247\) −2.22082e8 1.86349e8i −0.937723 0.786843i
\(248\) 1.07912e7 6.12000e7i 0.0449251 0.254783i
\(249\) 2.06087e7 8.27695e7i 0.0845964 0.339760i
\(250\) 2.78372e8 2.33582e8i 1.12677 0.945473i
\(251\) −8.50969e7 1.47392e8i −0.339669 0.588323i 0.644702 0.764434i \(-0.276982\pi\)
−0.984370 + 0.176111i \(0.943648\pi\)
\(252\) 3.75566e7 8.00801e6i 0.147838 0.0315227i
\(253\) −9.50153e6 + 1.64571e7i −0.0368869 + 0.0638899i
\(254\) 1.26544e7 + 7.17665e7i 0.0484532 + 0.274792i
\(255\) −5.70672e7 + 8.46640e7i −0.215524 + 0.319748i
\(256\) −1.74300e8 + 6.34400e7i −0.649318 + 0.236332i
\(257\) 5.70098e7 2.07499e7i 0.209500 0.0762517i −0.235139 0.971962i \(-0.575554\pi\)
0.444638 + 0.895710i \(0.353332\pi\)
\(258\) −6.69574e8 4.66061e7i −2.42733 0.168956i
\(259\) 9.33743e6 + 5.29552e7i 0.0333948 + 0.189391i
\(260\) −2.89599e8 + 5.01601e8i −1.02186 + 1.76991i
\(261\) −1.34755e8 1.88508e7i −0.469142 0.0656278i
\(262\) 3.73317e8 + 6.46604e8i 1.28240 + 2.22118i
\(263\) −2.20466e8 + 1.84993e8i −0.747304 + 0.627062i −0.934788 0.355205i \(-0.884411\pi\)
0.187485 + 0.982268i \(0.439967\pi\)
\(264\) −1.40906e7 1.35984e7i −0.0471320 0.0454858i
\(265\) −4.68531e7 + 2.65717e8i −0.154660 + 0.877121i
\(266\) −3.08267e7 2.58667e7i −0.100425 0.0842666i
\(267\) −2.50571e8 + 1.82173e8i −0.805639 + 0.585725i
\(268\) −5.42268e8 1.97369e8i −1.72085 0.626336i
\(269\) 4.56332e8 1.42938 0.714691 0.699440i \(-0.246567\pi\)
0.714691 + 0.699440i \(0.246567\pi\)
\(270\) 4.58157e8 + 9.69251e7i 1.41658 + 0.299684i
\(271\) −4.32212e8 −1.31918 −0.659591 0.751625i \(-0.729270\pi\)
−0.659591 + 0.751625i \(0.729270\pi\)
\(272\) 1.03372e8 + 3.76242e7i 0.311466 + 0.113364i
\(273\) 7.48707e7 + 3.33059e7i 0.222712 + 0.0990723i
\(274\) 5.35490e8 + 4.49330e8i 1.57262 + 1.31959i
\(275\) −327133. + 1.85526e6i −0.000948548 + 0.00537948i
\(276\) 8.12760e7 2.33336e7i 0.232692 0.0668037i
\(277\) −8.72657e7 + 7.32246e7i −0.246697 + 0.207004i −0.757749 0.652547i \(-0.773701\pi\)
0.511051 + 0.859550i \(0.329256\pi\)
\(278\) −5.34082e7 9.25057e7i −0.149091 0.258233i
\(279\) −4.35894e8 2.31412e8i −1.20162 0.637927i
\(280\) −4.63379e6 + 8.02595e6i −0.0126149 + 0.0218496i
\(281\) −3.71976e7 2.10958e8i −0.100010 0.567184i −0.993097 0.117299i \(-0.962576\pi\)
0.893087 0.449884i \(-0.148535\pi\)
\(282\) −1.89282e8 3.87770e8i −0.502616 1.02968i
\(283\) −2.10936e8 + 7.67744e7i −0.553220 + 0.201356i −0.603477 0.797381i \(-0.706218\pi\)
0.0502563 + 0.998736i \(0.483996\pi\)
\(284\) −2.84574e8 + 1.03576e8i −0.737193 + 0.268316i
\(285\) −1.14217e8 2.33990e8i −0.292263 0.598743i
\(286\) −6.29485e7 3.56999e8i −0.159113 0.902372i
\(287\) −4.23664e7 + 7.33808e7i −0.105788 + 0.183230i
\(288\) −2.06707e7 5.81277e8i −0.0509896 1.43387i
\(289\) 1.74171e8 + 3.01673e8i 0.424457 + 0.735181i
\(290\) 2.18227e8 1.83114e8i 0.525430 0.440888i
\(291\) 7.06737e8 2.02898e8i 1.68125 0.482672i
\(292\) 3.47746e7 1.97217e8i 0.0817377 0.463558i
\(293\) 3.83216e8 + 3.21556e8i 0.890034 + 0.746827i 0.968217 0.250112i \(-0.0804675\pi\)
−0.0781832 + 0.996939i \(0.524912\pi\)
\(294\) −5.70676e8 2.53863e8i −1.30971 0.582617i
\(295\) 2.28369e8 + 8.31194e7i 0.517916 + 0.188506i
\(296\) −1.22015e8 −0.273460
\(297\) −1.37238e8 + 7.31396e7i −0.303967 + 0.161996i
\(298\) 9.79722e8 2.14460
\(299\) 1.69561e8 + 6.17150e7i 0.366839 + 0.133519i
\(300\) 6.78028e6 4.92947e6i 0.0144985 0.0105409i
\(301\) −8.08063e7 6.78046e7i −0.170790 0.143310i
\(302\) 5.97718e7 3.38983e8i 0.124874 0.708196i
\(303\) −4.26867e8 4.11957e8i −0.881543 0.850751i
\(304\) −2.14904e8 + 1.80325e8i −0.438719 + 0.368129i
\(305\) 2.81623e8 + 4.87786e8i 0.568354 + 0.984418i
\(306\) −1.74921e8 + 2.24184e8i −0.348994 + 0.447281i
\(307\) −4.85146e7 + 8.40298e7i −0.0956948 + 0.165748i −0.909898 0.414831i \(-0.863841\pi\)
0.814204 + 0.580579i \(0.197174\pi\)
\(308\) −4.63608e6 2.62925e7i −0.00904114 0.0512748i
\(309\) 2.21343e8 + 1.54067e7i 0.426787 + 0.0297067i
\(310\) 9.70921e8 3.53387e8i 1.85105 0.673727i
\(311\) −4.45007e8 + 1.61969e8i −0.838890 + 0.305331i −0.725502 0.688220i \(-0.758393\pi\)
−0.113388 + 0.993551i \(0.536170\pi\)
\(312\) −1.03928e8 + 1.54186e8i −0.193728 + 0.287412i
\(313\) −1.33337e8 7.56192e8i −0.245779 1.39388i −0.818675 0.574257i \(-0.805291\pi\)
0.572896 0.819628i \(-0.305820\pi\)
\(314\) −1.13060e8 + 1.95826e8i −0.206090 + 0.356958i
\(315\) 4.92815e7 + 5.46623e7i 0.0888376 + 0.0985374i
\(316\) 1.47500e8 + 2.55477e8i 0.262958 + 0.455457i
\(317\) 5.64249e8 4.73461e8i 0.994863 0.834789i 0.00859847 0.999963i \(-0.497263\pi\)
0.986264 + 0.165174i \(0.0528185\pi\)
\(318\) −1.81556e8 + 7.29176e8i −0.316604 + 1.27156i
\(319\) −1.64272e7 + 9.31633e7i −0.0283332 + 0.160686i
\(320\) 5.52990e8 + 4.64014e8i 0.943393 + 0.791601i
\(321\) −5.97115e7 5.66375e8i −0.100760 0.955733i
\(322\) 2.35363e7 + 8.56652e6i 0.0392865 + 0.0142991i
\(323\) 1.58103e8 0.261054
\(324\) 6.65424e8 + 1.89887e8i 1.08690 + 0.310161i
\(325\) 1.78883e7 0.0289053
\(326\) −7.06973e8 2.57317e8i −1.13016 0.411346i
\(327\) 4.45875e7 + 4.22922e8i 0.0705174 + 0.668871i
\(328\) −1.47287e8 1.23588e8i −0.230465 0.193383i
\(329\) 1.17759e7 6.67847e7i 0.0182310 0.103393i
\(330\) 7.86644e7 3.15936e8i 0.120498 0.483949i
\(331\) 1.61949e7 1.35892e7i 0.0245460 0.0205966i −0.630432 0.776244i \(-0.717122\pi\)
0.654978 + 0.755648i \(0.272678\pi\)
\(332\) 1.31940e8 + 2.28527e8i 0.197877 + 0.342732i
\(333\) −2.98841e8 + 9.21743e8i −0.443492 + 1.36790i
\(334\) −3.77101e7 + 6.53158e7i −0.0553790 + 0.0959192i
\(335\) −1.92053e8 1.08919e9i −0.279103 1.58287i
\(336\) 4.43206e7 6.57533e7i 0.0637409 0.0945649i
\(337\) −3.62692e8 + 1.32009e8i −0.516218 + 0.187888i −0.586974 0.809606i \(-0.699681\pi\)
0.0707564 + 0.997494i \(0.477459\pi\)
\(338\) −2.26090e9 + 8.22900e8i −3.18473 + 1.15915i
\(339\) 9.84803e8 + 6.85478e7i 1.37294 + 0.0955641i
\(340\) −5.48501e7 3.11070e8i −0.0756835 0.429222i
\(341\) −1.71557e8 + 2.97145e8i −0.234297 + 0.405815i
\(342\) −2.72077e8 6.72177e8i −0.367791 0.908641i
\(343\) −9.90552e7 1.71569e8i −0.132540 0.229567i
\(344\) 1.83359e8 1.53857e8i 0.242856 0.203780i
\(345\) 1.16614e8 + 1.12541e8i 0.152892 + 0.147552i
\(346\) 9.91727e7 5.62436e8i 0.128714 0.729973i
\(347\) 6.88717e8 + 5.77903e8i 0.884887 + 0.742509i 0.967178 0.254100i \(-0.0817792\pi\)
−0.0822908 + 0.996608i \(0.526224\pi\)
\(348\) 3.40477e8 2.47537e8i 0.433072 0.314857i
\(349\) −3.30577e8 1.20320e8i −0.416278 0.151513i 0.125386 0.992108i \(-0.459983\pi\)
−0.541664 + 0.840595i \(0.682205\pi\)
\(350\) 2.48304e6 0.00309560
\(351\) 9.10230e8 + 1.16274e9i 1.12351 + 1.43519i
\(352\) −4.04386e8 −0.494193
\(353\) 1.78596e7 + 6.50035e6i 0.0216102 + 0.00786548i 0.352803 0.935698i \(-0.385229\pi\)
−0.331192 + 0.943563i \(0.607451\pi\)
\(354\) 6.18397e8 + 2.75091e8i 0.740894 + 0.329584i
\(355\) −4.44618e8 3.73079e8i −0.527458 0.442589i
\(356\) 1.66425e8 9.43845e8i 0.195499 1.10873i
\(357\) −4.29538e7 + 1.23317e7i −0.0499646 + 0.0143444i
\(358\) −1.62721e9 + 1.36539e9i −1.87436 + 1.57278i
\(359\) −4.90435e8 8.49459e8i −0.559437 0.968973i −0.997543 0.0700503i \(-0.977684\pi\)
0.438106 0.898923i \(-0.355649\pi\)
\(360\) −1.41569e8 + 8.85883e7i −0.159923 + 0.100073i
\(361\) 2.45339e8 4.24940e8i 0.274468 0.475393i
\(362\) −2.04720e7 1.16103e8i −0.0226820 0.128636i
\(363\) −3.52333e8 7.21805e8i −0.386617 0.792039i
\(364\) −2.38222e8 + 8.67057e7i −0.258897 + 0.0942308i
\(365\) 3.60663e8 1.31271e8i 0.388219 0.141300i
\(366\) 6.88098e8 + 1.40967e9i 0.733612 + 1.50291i
\(367\) 3.66455e7 + 2.07827e8i 0.0386981 + 0.219468i 0.998024 0.0628330i \(-0.0200135\pi\)
−0.959326 + 0.282301i \(0.908902\pi\)
\(368\) 8.73049e7 1.51217e8i 0.0913212 0.158173i
\(369\) −1.29436e9 + 8.09957e8i −1.34111 + 0.839208i
\(370\) −1.01434e9 1.75689e9i −1.04106 1.80317i
\(371\) −9.04672e7 + 7.59110e7i −0.0919777 + 0.0771785i
\(372\) 1.46750e9 4.21305e8i 1.47801 0.424323i
\(373\) −8.89990e6 + 5.04739e7i −0.00887983 + 0.0503600i −0.988926 0.148411i \(-0.952584\pi\)
0.980046 + 0.198771i \(0.0636951\pi\)
\(374\) 1.51443e8 + 1.27076e8i 0.149692 + 0.125606i
\(375\) 9.40294e8 + 4.18286e8i 0.920776 + 0.409603i
\(376\) 1.44600e8 + 5.26302e7i 0.140285 + 0.0510596i
\(377\) 8.98275e8 0.863405
\(378\) 1.26347e8 + 1.61397e8i 0.120321 + 0.153700i
\(379\) −2.14876e8 −0.202746 −0.101373 0.994849i \(-0.532323\pi\)
−0.101373 + 0.994849i \(0.532323\pi\)
\(380\) 7.56949e8 + 2.75507e8i 0.707659 + 0.257567i
\(381\) −1.66927e8 + 1.21361e8i −0.154629 + 0.112420i
\(382\) 1.44113e9 + 1.20925e9i 1.32276 + 1.10993i
\(383\) 1.09761e8 6.22485e8i 0.0998280 0.566152i −0.893333 0.449396i \(-0.851639\pi\)
0.993161 0.116756i \(-0.0372497\pi\)
\(384\) 3.01086e8 + 2.90569e8i 0.271351 + 0.261873i
\(385\) 3.91974e7 3.28905e7i 0.0350062 0.0293737i
\(386\) −5.46913e8 9.47282e8i −0.484020 0.838347i
\(387\) −7.13197e8 1.76198e9i −0.625492 1.54530i
\(388\) −1.13737e9 + 1.96998e9i −0.988532 + 1.71219i
\(389\) 2.76831e7 + 1.56999e8i 0.0238447 + 0.135230i 0.994406 0.105623i \(-0.0336838\pi\)
−0.970562 + 0.240853i \(0.922573\pi\)
\(390\) −3.08409e9 2.14670e8i −2.63269 0.183250i
\(391\) −9.24708e7 + 3.36566e7i −0.0782323 + 0.0284742i
\(392\) 2.09307e8 7.61816e7i 0.175502 0.0638776i
\(393\) −1.18185e9 + 1.75338e9i −0.982177 + 1.45714i
\(394\) −266476. 1.51126e6i −0.000219494 0.00124481i
\(395\) −2.82693e8 + 4.89638e8i −0.230794 + 0.399747i
\(396\) 1.48376e8 4.57650e8i 0.120069 0.370339i
\(397\) 1.07644e7 + 1.86446e7i 0.00863426 + 0.0149550i 0.870310 0.492504i \(-0.163918\pi\)
−0.861676 + 0.507459i \(0.830585\pi\)
\(398\) −1.25956e9 + 1.05690e9i −1.00145 + 0.840313i
\(399\) 2.75354e7 1.10589e8i 0.0217013 0.0871579i
\(400\) 3.00586e6 1.70471e7i 0.00234833 0.0133180i
\(401\) −8.30358e8 6.96753e8i −0.643073 0.539602i 0.261887 0.965098i \(-0.415655\pi\)
−0.904960 + 0.425496i \(0.860100\pi\)
\(402\) −3.22946e8 3.06320e9i −0.247935 2.35172i
\(403\) 3.06154e9 + 1.11431e9i 2.33008 + 0.848081i
\(404\) 1.83527e9 1.38473
\(405\) 3.22491e8 + 1.28643e9i 0.241226 + 0.962263i
\(406\) 1.24687e8 0.0924659
\(407\) 6.33050e8 + 2.30411e8i 0.465434 + 0.169404i
\(408\) −1.06319e7 1.00846e8i −0.00774997 0.0735100i
\(409\) −1.53439e9 1.28751e9i −1.10893 0.930503i −0.110938 0.993827i \(-0.535385\pi\)
−0.997993 + 0.0633242i \(0.979830\pi\)
\(410\) 5.55108e8 3.14818e9i 0.397772 2.25588i
\(411\) −4.78317e8 + 1.92104e9i −0.339836 + 1.36487i
\(412\) −5.25830e8 + 4.41223e8i −0.370429 + 0.310827i
\(413\) 5.31850e7 + 9.21191e7i 0.0371504 + 0.0643465i
\(414\) 3.02224e8 + 3.35222e8i 0.209328 + 0.232183i
\(415\) −2.52872e8 + 4.37987e8i −0.173673 + 0.300811i
\(416\) 6.66779e8 + 3.78149e9i 0.454104 + 2.57535i
\(417\) 1.69080e8 2.50845e8i 0.114187 0.169406i
\(418\) −4.73756e8 + 1.72433e8i −0.317276 + 0.115479i
\(419\) 2.25477e9 8.20668e8i 1.49745 0.545028i 0.542052 0.840345i \(-0.317648\pi\)
0.955399 + 0.295318i \(0.0954255\pi\)
\(420\) −2.27139e8 1.58101e7i −0.149596 0.0104127i
\(421\) −2.27852e8 1.29221e9i −0.148822 0.844009i −0.964219 0.265107i \(-0.914593\pi\)
0.815397 0.578902i \(-0.196519\pi\)
\(422\) 1.79026e9 3.10082e9i 1.15964 2.00855i
\(423\) 7.51741e8 9.63454e8i 0.482922 0.618927i
\(424\) −1.33988e8 2.32073e8i −0.0853659 0.147858i
\(425\) −7.47314e6 + 6.27071e6i −0.00472217 + 0.00396237i
\(426\) −1.16312e9 1.12250e9i −0.728941 0.703480i
\(427\) −4.28092e7 + 2.42783e8i −0.0266097 + 0.150911i
\(428\) 1.34969e9 + 1.13252e9i 0.832111 + 0.698224i
\(429\) 8.30371e8 6.03705e8i 0.507775 0.369168i
\(430\) 3.73967e9 + 1.36113e9i 2.26826 + 0.825580i
\(431\) −2.40860e9 −1.44909 −0.724543 0.689230i \(-0.757949\pi\)
−0.724543 + 0.689230i \(0.757949\pi\)
\(432\) 1.26101e9 6.72044e8i 0.752534 0.401056i
\(433\) −1.72459e9 −1.02089 −0.510445 0.859911i \(-0.670519\pi\)
−0.510445 + 0.859911i \(0.670519\pi\)
\(434\) 4.24965e8 + 1.54674e8i 0.249539 + 0.0908248i
\(435\) 7.37133e8 + 3.27910e8i 0.429372 + 0.191004i
\(436\) −1.00784e9 8.45675e8i −0.582354 0.488653i
\(437\) 4.35776e7 2.47141e8i 0.0249792 0.141664i
\(438\) 1.02741e9 2.94960e8i 0.584229 0.167727i
\(439\) 3.09353e8 2.59578e8i 0.174513 0.146434i −0.551348 0.834276i \(-0.685886\pi\)
0.725861 + 0.687842i \(0.241442\pi\)
\(440\) 5.80539e7 + 1.00552e8i 0.0324898 + 0.0562740i
\(441\) −6.28630e7 1.76776e9i −0.0349028 0.981494i
\(442\) 9.38601e8 1.62570e9i 0.517015 0.895496i
\(443\) 1.31679e8 + 7.46786e8i 0.0719618 + 0.408116i 0.999416 + 0.0341783i \(0.0108814\pi\)
−0.927454 + 0.373937i \(0.878007\pi\)
\(444\) −1.31497e9 2.69390e9i −0.712977 1.46063i
\(445\) 1.72607e9 6.28238e8i 0.928535 0.337959i
\(446\) −4.46045e9 + 1.62347e9i −2.38071 + 0.866509i
\(447\) 1.21711e9 + 2.49342e9i 0.644544 + 1.32044i
\(448\) 5.48659e7 + 3.11160e8i 0.0288290 + 0.163497i
\(449\) 2.06257e8 3.57248e8i 0.107534 0.186255i −0.807237 0.590228i \(-0.799038\pi\)
0.914771 + 0.403973i \(0.132371\pi\)
\(450\) 3.95204e7 + 2.09810e7i 0.0204446 + 0.0108538i
\(451\) 5.30783e8 + 9.19343e8i 0.272458 + 0.471911i
\(452\) −2.33953e9 + 1.96310e9i −1.19164 + 0.999903i
\(453\) 9.36975e8 2.68997e8i 0.473570 0.135958i
\(454\) −3.50550e8 + 1.98807e9i −0.175814 + 0.997093i
\(455\) −3.72197e8 3.12311e8i −0.185239 0.155434i
\(456\) 2.36278e8 + 1.05107e8i 0.116693 + 0.0519105i
\(457\) 3.78038e8 + 1.37594e8i 0.185280 + 0.0674364i 0.432994 0.901397i \(-0.357457\pi\)
−0.247714 + 0.968833i \(0.579679\pi\)
\(458\) −1.84628e8 −0.0897983
\(459\) −7.87860e8 1.66675e8i −0.380281 0.0804501i
\(460\) −5.01372e8 −0.240164
\(461\) −1.60037e9 5.82486e8i −0.760793 0.276906i −0.0676527 0.997709i \(-0.521551\pi\)
−0.693140 + 0.720803i \(0.743773\pi\)
\(462\) 1.15262e8 8.37989e7i 0.0543799 0.0395359i
\(463\) 4.15841e7 + 3.48932e7i 0.0194713 + 0.0163383i 0.652471 0.757813i \(-0.273732\pi\)
−0.633000 + 0.774152i \(0.718177\pi\)
\(464\) 1.50942e8 8.56032e8i 0.0701449 0.397811i
\(465\) 2.10555e9 + 2.03201e9i 0.971138 + 0.937217i
\(466\) −7.39999e8 + 6.20933e8i −0.338751 + 0.284246i
\(467\) 8.87812e8 + 1.53774e9i 0.403378 + 0.698671i 0.994131 0.108181i \(-0.0345027\pi\)
−0.590753 + 0.806852i \(0.701169\pi\)
\(468\) −4.52423e9 6.32889e8i −2.04025 0.285409i
\(469\) 2.42041e8 4.19228e8i 0.108339 0.187649i
\(470\) 4.44275e8 + 2.51961e9i 0.197383 + 1.11941i
\(471\) −6.38839e8 4.44667e7i −0.281720 0.0196093i
\(472\) −2.26810e8 + 8.25522e7i −0.0992809 + 0.0361353i
\(473\) −1.24186e9 + 4.52000e8i −0.539583 + 0.196392i
\(474\) −8.80087e8 + 1.30568e9i −0.379578 + 0.563136i
\(475\) −4.32009e6 2.45005e7i −0.00184955 0.0104893i
\(476\) 6.91267e7 1.19731e8i 0.0293779 0.0508841i
\(477\) −2.08132e9 + 4.43789e8i −0.878061 + 0.187224i
\(478\) −2.37363e9 4.11125e9i −0.994066 1.72177i
\(479\) −1.36375e9 + 1.14432e9i −0.566971 + 0.475745i −0.880639 0.473788i \(-0.842886\pi\)
0.313668 + 0.949533i \(0.398442\pi\)
\(480\) −8.33249e8 + 3.34654e9i −0.343899 + 1.38118i
\(481\) 1.11081e9 6.29970e9i 0.455125 2.58114i
\(482\) −6.64739e8 5.57782e8i −0.270387 0.226882i
\(483\) 7.43714e6 + 7.05428e7i 0.00300325 + 0.0284864i
\(484\) 2.33501e9 + 8.49875e8i 0.936117 + 0.340719i
\(485\) −4.35969e9 −1.73524
\(486\) 6.47195e8 + 3.63643e9i 0.255746 + 1.43697i
\(487\) 3.39420e8 0.133164 0.0665818 0.997781i \(-0.478791\pi\)
0.0665818 + 0.997781i \(0.478791\pi\)
\(488\) −5.25667e8 1.91327e8i −0.204758 0.0745259i
\(489\) −2.23393e8 2.11893e9i −0.0863952 0.819475i
\(490\) 2.83694e9 + 2.38048e9i 1.08934 + 0.914067i
\(491\) −5.91211e7 + 3.35292e8i −0.0225402 + 0.127832i −0.994002 0.109366i \(-0.965118\pi\)
0.971461 + 0.237198i \(0.0762290\pi\)
\(492\) 1.14131e9 4.58377e9i 0.432040 1.73518i
\(493\) −3.75269e8 + 3.14888e8i −0.141052 + 0.118356i
\(494\) 2.39362e9 + 4.14586e9i 0.893326 + 1.54729i
\(495\) 9.01790e8 1.92284e8i 0.334185 0.0712566i
\(496\) 1.57635e9 2.73032e9i 0.580052 1.00468i
\(497\) −4.41135e7 2.50180e8i −0.0161185 0.0914125i
\(498\) −7.87249e8 + 1.16795e9i −0.285634 + 0.423761i
\(499\) −1.08810e9 + 3.96036e8i −0.392028 + 0.142687i −0.530511 0.847678i \(-0.678000\pi\)
0.138482 + 0.990365i \(0.455778\pi\)
\(500\) −2.99181e9 + 1.08893e9i −1.07038 + 0.389587i
\(501\) −2.13078e8 1.48314e7i −0.0757018 0.00526927i
\(502\) 4.88021e8 + 2.76770e9i 0.172177 + 0.976465i
\(503\) −2.50058e7 + 4.33113e7i −0.00876098 + 0.0151745i −0.870373 0.492394i \(-0.836122\pi\)
0.861612 + 0.507568i \(0.169455\pi\)
\(504\) −7.23907e7 1.01267e7i −0.0251870 0.00352338i
\(505\) 1.75871e9 + 3.04617e9i 0.607679 + 1.05253i
\(506\) 2.40382e8 2.01704e8i 0.0824850 0.0692131i
\(507\) −4.90302e9 4.73176e9i −1.67084 1.61248i
\(508\) 1.10871e8 6.28779e8i 0.0375227 0.212802i
\(509\) 3.83269e9 + 3.21601e9i 1.28822 + 1.08095i 0.992054 + 0.125813i \(0.0401538\pi\)
0.296170 + 0.955135i \(0.404291\pi\)
\(510\) 1.36368e9 9.91437e8i 0.455215 0.330955i
\(511\) 1.57859e8 + 5.74561e7i 0.0523356 + 0.0190486i
\(512\) 4.20819e9 1.38564
\(513\) 1.37271e9 1.52749e9i 0.448918 0.499536i
\(514\) −1.00182e9 −0.325400
\(515\) −1.23623e9 4.49952e8i −0.398818 0.145158i
\(516\) 5.37299e9 + 2.39015e9i 1.72164 + 0.765863i
\(517\) −6.50840e8 5.46120e8i −0.207137 0.173809i
\(518\) 1.54188e8 8.74446e8i 0.0487414 0.276426i
\(519\) 1.55462e9 4.46317e8i 0.488132 0.140139i
\(520\) 8.44561e8 7.08671e8i 0.263402 0.221021i
\(521\) 3.04302e8 + 5.27067e8i 0.0942699 + 0.163280i 0.909304 0.416133i \(-0.136615\pi\)
−0.815034 + 0.579414i \(0.803282\pi\)
\(522\) 1.98455e9 + 1.05358e9i 0.610681 + 0.324204i
\(523\) −1.22368e9 + 2.11947e9i −0.374034 + 0.647846i −0.990182 0.139784i \(-0.955359\pi\)
0.616148 + 0.787631i \(0.288692\pi\)
\(524\) −1.13594e9 6.44222e9i −0.344901 1.95603i
\(525\) 3.08467e6 + 6.31939e6i 0.000930361 + 0.00190598i
\(526\) 4.46579e9 1.62542e9i 1.33798 0.486984i
\(527\) −1.66962e9 + 6.07694e8i −0.496915 + 0.180862i
\(528\) −4.35784e8 8.92765e8i −0.128841 0.263948i
\(529\) −5.64118e8 3.19927e9i −0.165682 0.939630i
\(530\) 2.22773e9 3.85855e9i 0.649976 1.12579i
\(531\) 6.81198e7 + 1.91558e9i 0.0197443 + 0.555227i
\(532\) 1.76287e8 + 3.05337e8i 0.0507608 + 0.0879203i
\(533\) 7.72177e9 6.47933e9i 2.20888 1.85347i
\(534\) 4.91699e9 1.41163e9i 1.39735 0.401167i
\(535\) −5.86373e8 + 3.32549e9i −0.165552 + 0.938894i
\(536\) 8.41456e8 + 7.06065e8i 0.236023 + 0.198047i
\(537\) −5.49645e9 2.44507e9i −1.53169 0.681368i
\(538\) −7.08095e9 2.57726e9i −1.96044 0.713542i
\(539\) −1.22980e9 −0.338279
\(540\) −3.48159e9 2.17090e9i −0.951480 0.593283i
\(541\) −1.97224e9 −0.535512 −0.267756 0.963487i \(-0.586282\pi\)
−0.267756 + 0.963487i \(0.586282\pi\)
\(542\) 6.70668e9 + 2.44103e9i 1.80930 + 0.658530i
\(543\) 2.70052e8 1.96336e8i 0.0723850 0.0526261i
\(544\) −1.60415e9 1.34604e9i −0.427218 0.358478i
\(545\) 4.37854e8 2.48319e9i 0.115862 0.657087i
\(546\) −9.73672e8 9.39663e8i −0.255999 0.247057i
\(547\) −4.76256e9 + 3.99626e9i −1.24418 + 1.04399i −0.246998 + 0.969016i \(0.579444\pi\)
−0.997185 + 0.0749781i \(0.976111\pi\)
\(548\) −3.06227e9 5.30401e9i −0.794898 1.37680i
\(549\) −2.73281e9 + 3.50245e9i −0.704866 + 0.903377i
\(550\) 1.55542e7 2.69407e7i 0.00398638 0.00690461i
\(551\) −2.16937e8 1.23031e9i −0.0552462 0.313317i
\(552\) −1.60569e8 1.11765e7i −0.0406325 0.00282825i
\(553\) −2.32541e8 + 8.46379e7i −0.0584738 + 0.0212827i
\(554\) 1.76766e9 6.43377e8i 0.441688 0.160761i
\(555\) 3.21121e9 4.76410e9i 0.797339 1.18292i
\(556\) 1.62511e8 + 9.21648e8i 0.0400979 + 0.227407i
\(557\) −3.00714e9 + 5.20852e9i −0.737328 + 1.27709i 0.216367 + 0.976312i \(0.430579\pi\)
−0.953695 + 0.300777i \(0.902754\pi\)
\(558\) 5.45686e9 + 6.05267e9i 1.32961 + 1.47478i
\(559\) 6.27440e9 + 1.08676e10i 1.51926 + 2.63143i
\(560\) −3.60166e8 + 3.02215e8i −0.0866652 + 0.0727208i
\(561\) −1.35274e8 + 5.43292e8i −0.0323477 + 0.129916i
\(562\) −6.14242e8 + 3.48354e9i −0.145969 + 0.827834i
\(563\) −5.42971e8 4.55607e8i −0.128232 0.107600i 0.576416 0.817156i \(-0.304451\pi\)
−0.704648 + 0.709557i \(0.748895\pi\)
\(564\) 3.96380e8 + 3.75974e9i 0.0930324 + 0.882431i
\(565\) −5.50027e9 2.00194e9i −1.28296 0.466961i
\(566\) 3.70672e9 0.859274
\(567\) −2.53800e8 + 5.22060e8i −0.0584724 + 0.120276i
\(568\) 5.76447e8 0.131990
\(569\) −1.15365e9 4.19895e8i −0.262532 0.0955537i 0.207401 0.978256i \(-0.433500\pi\)
−0.469933 + 0.882702i \(0.655722\pi\)
\(570\) 4.50799e8 + 4.27591e9i 0.101958 + 0.967090i
\(571\) 3.33801e9 + 2.80092e9i 0.750344 + 0.629614i 0.935594 0.353078i \(-0.114865\pi\)
−0.185250 + 0.982692i \(0.559309\pi\)
\(572\) −5.51520e8 + 3.12783e9i −0.123218 + 0.698806i
\(573\) −1.28726e9 + 5.16996e9i −0.285842 + 1.14801i
\(574\) 1.07184e9 8.99381e8i 0.236559 0.198496i
\(575\) 7.74234e6 + 1.34101e7i 0.00169838 + 0.00294168i
\(576\) −1.75596e9 + 5.41608e9i −0.382857 + 1.18088i
\(577\) −2.65927e9 + 4.60600e9i −0.576299 + 0.998178i 0.419601 + 0.907709i \(0.362170\pi\)
−0.995899 + 0.0904696i \(0.971163\pi\)
\(578\) −9.98852e8 5.66477e9i −0.215156 1.22021i
\(579\) 1.73143e9 2.56872e9i 0.370706 0.549973i
\(580\) −2.34539e9 + 8.53653e8i −0.499135 + 0.181670i
\(581\) −2.08011e8 + 7.57097e7i −0.0440017 + 0.0160153i
\(582\) −1.21124e10 8.43092e8i −2.54683 0.177274i
\(583\) 2.56923e8 + 1.45708e9i 0.0536986 + 0.304540i
\(584\) −1.90595e8 + 3.30121e8i −0.0395974 + 0.0685847i
\(585\) −3.28502e9 8.11576e9i −0.678410 1.67604i
\(586\) −4.13032e9 7.15392e9i −0.847895 1.46860i
\(587\) −1.66926e9 + 1.40068e9i −0.340637 + 0.285828i −0.797017 0.603957i \(-0.793590\pi\)
0.456381 + 0.889785i \(0.349146\pi\)
\(588\) 3.93769e9 + 3.80015e9i 0.798768 + 0.770868i
\(589\) 7.86823e8 4.46229e9i 0.158662 0.899818i
\(590\) −3.07418e9 2.57954e9i −0.616236 0.517083i
\(591\) 3.51516e6 2.55563e6i 0.000700469 0.000509262i
\(592\) −5.81679e9 2.11714e9i −1.15228 0.419395i
\(593\) 8.21835e9 1.61843 0.809213 0.587515i \(-0.199894\pi\)
0.809213 + 0.587515i \(0.199894\pi\)
\(594\) 2.54261e9 3.59827e8i 0.497768 0.0704435i
\(595\) 2.64971e8 0.0515691
\(596\) −8.06611e9 2.93583e9i −1.56064 0.568026i
\(597\) −4.25458e9 1.89263e9i −0.818363 0.364045i
\(598\) −2.28254e9 1.91528e9i −0.436479 0.366250i
\(599\) 9.59029e8 5.43892e9i 0.182321 1.03400i −0.747027 0.664793i \(-0.768520\pi\)
0.929349 0.369203i \(-0.120369\pi\)
\(600\) −1.53371e7 + 4.40314e6i −0.00289876 + 0.000832210i
\(601\) 7.92901e9 6.65323e9i 1.48990 1.25018i 0.595151 0.803614i \(-0.297092\pi\)
0.894752 0.446564i \(-0.147352\pi\)
\(602\) 8.70935e8 + 1.50850e9i 0.162704 + 0.281812i
\(603\) 7.39474e9 4.62732e9i 1.37345 0.859447i
\(604\) −1.50790e9 + 2.61176e9i −0.278447 + 0.482285i
\(605\) 8.26983e8 + 4.69005e9i 0.151828 + 0.861061i
\(606\) 4.29710e9 + 8.80322e9i 0.784370 + 1.60689i
\(607\) 2.00478e9 7.29682e8i 0.363837 0.132426i −0.153631 0.988128i \(-0.549097\pi\)
0.517468 + 0.855702i \(0.326875\pi\)
\(608\) 5.01824e9 1.82649e9i 0.905500 0.329575i
\(609\) 1.54899e8 + 3.17333e8i 0.0277900 + 0.0569317i
\(610\) −1.61508e9 9.15955e9i −0.288097 1.63388i
\(611\) −4.03373e9 + 6.98662e9i −0.715422 + 1.23915i
\(612\) 2.11193e9 1.32156e9i 0.372434 0.233054i
\(613\) 1.68829e9 + 2.92421e9i 0.296030 + 0.512739i 0.975224 0.221220i \(-0.0710038\pi\)
−0.679194 + 0.733959i \(0.737670\pi\)
\(614\) 1.22739e9 1.02990e9i 0.213989 0.179558i
\(615\) 8.70180e9 2.49821e9i 1.50850 0.433078i
\(616\) −8.82470e6 + 5.00474e7i −0.00152113 + 0.00862678i
\(617\) −4.09951e8 3.43990e8i −0.0702642 0.0589587i 0.606979 0.794718i \(-0.292381\pi\)
−0.677243 + 0.735759i \(0.736826\pi\)
\(618\) −3.34758e9 1.48916e9i −0.570521 0.253794i
\(619\) −3.09300e9 1.12576e9i −0.524159 0.190778i 0.0663696 0.997795i \(-0.478858\pi\)
−0.590528 + 0.807017i \(0.701081\pi\)
\(620\) −9.05262e9 −1.52547
\(621\) −4.77697e8 + 1.18561e9i −0.0800445 + 0.198665i
\(622\) 7.81997e9 1.30298
\(623\) 7.55487e8 + 2.74975e8i 0.125175 + 0.0455601i
\(624\) −7.62987e9 + 5.54716e9i −1.25710 + 0.913954i
\(625\) −4.60024e9 3.86006e9i −0.753703 0.632432i
\(626\) −2.20179e9 + 1.24870e10i −0.358728 + 2.03445i
\(627\) −1.02739e9 9.91508e8i −0.166456 0.160642i
\(628\) 1.51765e9 1.27346e9i 0.244519 0.205175i
\(629\) 1.74429e9 + 3.02119e9i 0.279473 + 0.484062i
\(630\) −4.55986e8 1.12653e9i −0.0726540 0.179494i
\(631\) 4.50051e9 7.79511e9i 0.713114 1.23515i −0.250568 0.968099i \(-0.580617\pi\)
0.963682 0.267051i \(-0.0860492\pi\)
\(632\) −9.75082e7 5.52996e8i −0.0153650 0.0871390i
\(633\) 1.01157e10 + 7.04110e8i 1.58520 + 0.110339i
\(634\) −1.14295e10 + 4.16000e9i −1.78121 + 0.648307i
\(635\) 1.14989e9 4.18525e8i 0.178216 0.0648654i
\(636\) 3.67981e9 5.45931e9i 0.567186 0.841468i
\(637\) 2.02779e9 + 1.15001e10i 0.310838 + 1.76285i
\(638\) 7.81066e8 1.35285e9i 0.119074 0.206241i
\(639\) 1.41184e9 4.35466e9i 0.214058 0.660239i
\(640\) −1.24049e9 2.14858e9i −0.187052 0.323983i
\(641\) 1.22394e9 1.02701e9i 0.183552 0.154018i −0.546382 0.837536i \(-0.683995\pi\)
0.729934 + 0.683518i \(0.239551\pi\)
\(642\) −2.27220e9 + 9.12573e9i −0.338902 + 1.36112i
\(643\) 2.04990e8 1.16256e9i 0.0304085 0.172455i −0.965821 0.259209i \(-0.916538\pi\)
0.996230 + 0.0867537i \(0.0276493\pi\)
\(644\) −1.68106e8 1.41057e8i −0.0248017 0.0208111i
\(645\) 1.18168e9 + 1.12085e10i 0.173397 + 1.64470i
\(646\) −2.45330e9 8.92927e8i −0.358044 0.130317i
\(647\) −8.31587e9 −1.20710 −0.603549 0.797326i \(-0.706247\pi\)
−0.603549 + 0.797326i \(0.706247\pi\)
\(648\) −1.06662e9 7.72860e8i −0.153991 0.111581i
\(649\) 1.33264e9 0.191363
\(650\) −2.77575e8 1.01029e8i −0.0396445 0.0144294i
\(651\) 1.34283e8 + 1.27370e9i 0.0190760 + 0.180939i
\(652\) 5.04948e9 + 4.23702e9i 0.713478 + 0.598679i
\(653\) −1.39235e9 + 7.89638e9i −0.195682 + 1.10977i 0.715762 + 0.698344i \(0.246079\pi\)
−0.911444 + 0.411424i \(0.865032\pi\)
\(654\) 1.69669e9 6.81433e9i 0.237181 0.952579i
\(655\) 9.60420e9 8.05888e9i 1.33542 1.12055i
\(656\) −4.87711e9 8.44740e9i −0.674526 1.16831i
\(657\) 2.02703e9 + 2.24835e9i 0.278857 + 0.309304i
\(658\) −5.59912e8 + 9.69796e8i −0.0766177 + 0.132706i
\(659\) −1.20237e9 6.81897e9i −0.163658 0.928153i −0.950437 0.310918i \(-0.899364\pi\)
0.786778 0.617236i \(-0.211747\pi\)
\(660\) −1.59438e9 + 2.36540e9i −0.215868 + 0.320258i
\(661\) −5.01044e9 + 1.82365e9i −0.674794 + 0.245605i −0.656611 0.754230i \(-0.728010\pi\)
−0.0181832 + 0.999835i \(0.505788\pi\)
\(662\) −3.28047e8 + 1.19399e8i −0.0439473 + 0.0159955i
\(663\) 5.30348e9 + 3.69152e8i 0.706747 + 0.0491935i
\(664\) −8.72223e7 4.94662e8i −0.0115622 0.0655723i
\(665\) −3.37865e8 + 5.85199e8i −0.0445520 + 0.0771663i
\(666\) 9.84293e9 1.26150e10i 1.29111 1.65473i
\(667\) 3.88787e8 + 6.73399e8i 0.0507308 + 0.0878682i
\(668\) 5.06195e8 4.24748e8i 0.0657052 0.0551332i
\(669\) −9.67300e9 9.33513e9i −1.24902 1.20539i
\(670\) −3.17136e9 + 1.79857e10i −0.407365 + 2.31028i
\(671\) 2.36601e9 + 1.98532e9i 0.302334 + 0.253689i
\(672\) −1.22091e9 + 8.87636e8i −0.155199 + 0.112835i
\(673\) 4.44645e8 + 1.61838e8i 0.0562290 + 0.0204657i 0.369982 0.929039i \(-0.379364\pi\)
−0.313753 + 0.949505i \(0.601586\pi\)
\(674\) 6.37347e9 0.801801
\(675\) −4.30096e6 + 1.26645e8i −0.000538272 + 0.0158499i
\(676\) 2.10800e10 2.62457
\(677\) 4.75627e9 + 1.73114e9i 0.589123 + 0.214423i 0.619344 0.785120i \(-0.287399\pi\)
−0.0302206 + 0.999543i \(0.509621\pi\)
\(678\) −1.48941e10 6.62560e9i −1.83532 0.816434i
\(679\) −1.46177e9 1.22657e9i −0.179198 0.150365i
\(680\) −1.04406e8 + 5.92118e8i −0.0127334 + 0.0722149i
\(681\) −5.49517e9 + 1.57762e9i −0.666755 + 0.191420i
\(682\) 4.34026e9 3.64191e9i 0.523927 0.439627i
\(683\) −4.77386e9 8.26857e9i −0.573321 0.993020i −0.996222 0.0868446i \(-0.972322\pi\)
0.422901 0.906176i \(-0.361012\pi\)
\(684\) 2.25790e8 + 6.34938e9i 0.0269779 + 0.758639i
\(685\) 5.86904e9 1.01655e10i 0.697670 1.20840i
\(686\) 5.68070e8 + 3.22169e9i 0.0671843 + 0.381021i
\(687\) −2.29363e8 4.69883e8i −0.0269883 0.0552893i
\(688\) 1.14108e10 4.15321e9i 1.33585 0.486210i
\(689\) 1.32018e10 4.80507e9i 1.53768 0.559671i
\(690\) −1.17391e9 2.40492e9i −0.136039 0.278695i
\(691\) 1.72671e9 + 9.79265e9i 0.199088 + 1.12909i 0.906475 + 0.422259i \(0.138763\pi\)
−0.707387 + 0.706827i \(0.750126\pi\)
\(692\) −2.50189e9 + 4.33339e9i −0.287010 + 0.497115i
\(693\) 3.56460e8 + 1.89241e8i 0.0406860 + 0.0215998i
\(694\) −7.42304e9 1.28571e10i −0.842992 1.46010i
\(695\) −1.37401e9 + 1.15293e9i −0.155254 + 0.130274i
\(696\) −7.70162e8 + 2.21107e8i −0.0865864 + 0.0248582i
\(697\) −9.54581e8 + 5.41370e9i −0.106782 + 0.605591i
\(698\) 4.45005e9 + 3.73404e9i 0.495303 + 0.415609i
\(699\) −2.49959e9 1.11193e9i −0.276821 0.123143i
\(700\) −2.04430e7 7.44064e6i −0.00225269 0.000819912i
\(701\) −1.05940e10 −1.16157 −0.580785 0.814057i \(-0.697254\pi\)
−0.580785 + 0.814057i \(0.697254\pi\)
\(702\) −7.55724e9 2.31831e10i −0.824486 2.52925i
\(703\) −8.89655e9 −0.965779
\(704\) 3.71975e9 + 1.35388e9i 0.401799 + 0.146243i
\(705\) −5.86054e9 + 4.26080e9i −0.629906 + 0.457961i
\(706\) −2.40416e8 2.01733e8i −0.0257127 0.0215755i
\(707\) −2.67339e8 + 1.51616e9i −0.0284508 + 0.161353i
\(708\) −4.26697e9 4.11793e9i −0.451859 0.436076i
\(709\) −1.78576e9 + 1.49843e9i −0.188175 + 0.157897i −0.732008 0.681296i \(-0.761417\pi\)
0.543833 + 0.839193i \(0.316972\pi\)
\(710\) 4.79212e9 + 8.30019e9i 0.502485 + 0.870329i
\(711\) −4.41633e9 6.17795e8i −0.460806 0.0644616i
\(712\) −9.12156e8 + 1.57990e9i −0.0947085 + 0.164040i
\(713\) 4.89730e8 + 2.77739e9i 0.0505991 + 0.286962i
\(714\) 7.36164e8 + 5.12411e7i 0.0756887 + 0.00526836i
\(715\) −5.72006e9 + 2.08193e9i −0.585234 + 0.213008i
\(716\) 1.74885e10 6.36528e9i 1.78056 0.648071i
\(717\) 7.51447e9 1.11483e10i 0.761345 1.12952i
\(718\) 2.81259e9 + 1.59510e10i 0.283577 + 1.60824i
\(719\) −5.72000e9 + 9.90733e9i −0.573912 + 0.994044i 0.422247 + 0.906481i \(0.361241\pi\)
−0.996159 + 0.0875634i \(0.972092\pi\)
\(720\) −8.28611e9 + 1.76680e9i −0.827346 + 0.176411i
\(721\) −2.87908e8 4.98670e8i −0.0286075 0.0495496i
\(722\) −6.20691e9 + 5.20822e9i −0.613755 + 0.515002i
\(723\) 5.93765e8 2.38471e9i 0.0584293 0.234667i
\(724\) −1.79365e8 + 1.01723e9i −0.0175652 + 0.0996170i
\(725\) 5.90508e7 + 4.95495e7i 0.00575497 + 0.00482899i
\(726\) 1.39061e9 + 1.31902e10i 0.134874 + 1.27930i
\(727\) 9.56230e9 + 3.48039e9i 0.922979 + 0.335937i 0.759423 0.650597i \(-0.225481\pi\)
0.163556 + 0.986534i \(0.447703\pi\)
\(728\) 4.82554e8 0.0463539
\(729\) −8.45080e9 + 6.16466e9i −0.807888 + 0.589336i
\(730\) −6.33782e9 −0.602990
\(731\) −6.43084e9 2.34063e9i −0.608915 0.221627i
\(732\) −1.44096e9 1.36678e10i −0.135789 1.28798i
\(733\) 1.32309e10 + 1.11020e10i 1.24087 + 1.04121i 0.997456 + 0.0712891i \(0.0227113\pi\)
0.243412 + 0.969923i \(0.421733\pi\)
\(734\) 6.05125e8 3.43183e9i 0.0564818 0.320324i
\(735\) −2.53405e9 + 1.01774e10i −0.235401 + 0.945430i
\(736\) −2.54624e9 + 2.13654e9i −0.235411 + 0.197533i
\(737\) −3.03239e9 5.25225e9i −0.279029 0.483292i
\(738\) 2.46591e10 5.25794e9i 2.25830 0.481525i
\(739\) −3.69684e9 + 6.40312e9i −0.336958 + 0.583628i −0.983859 0.178946i \(-0.942731\pi\)
0.646901 + 0.762574i \(0.276065\pi\)
\(740\) 3.08645e9 + 1.75041e10i 0.279994 + 1.58792i
\(741\) −7.57775e9 + 1.12422e10i −0.684190 + 1.01505i
\(742\) 1.83252e9 6.66981e8i 0.164677 0.0599377i
\(743\) −1.08896e10 + 3.96350e9i −0.973984 + 0.354501i −0.779498 0.626404i \(-0.784526\pi\)
−0.194486 + 0.980905i \(0.562304\pi\)
\(744\) −2.89918e9 2.01799e8i −0.258089 0.0179644i
\(745\) −2.85675e9 1.62014e10i −0.253119 1.43551i
\(746\) 4.23165e8 7.32943e8i 0.0373185 0.0646375i
\(747\) −3.95046e9 5.52626e8i −0.346757 0.0485075i
\(748\) −8.66046e8 1.50004e9i −0.0756633 0.131053i
\(749\) −1.13221e9 + 9.50035e8i −0.0984555 + 0.0826140i
\(750\) −1.22282e10 1.18011e10i −1.05840 1.02143i
\(751\) 2.09449e9 1.18784e10i 0.180442 1.02334i −0.751230 0.660040i \(-0.770539\pi\)
0.931673 0.363299i \(-0.118350\pi\)
\(752\) 5.98026e9 + 5.01803e9i 0.512811 + 0.430300i
\(753\) −6.43761e9 + 4.68034e9i −0.549468 + 0.399480i
\(754\) −1.39386e10 5.07324e9i −1.18419 0.431008i
\(755\) −5.77997e9 −0.488777