Properties

Label 27.8.e.a.4.13
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 4.13
Character \(\chi\) = 27.4
Dual form 27.8.e.a.7.13

$q$-expansion

\(f(q)\) \(=\) \(q+(6.42719 + 2.33931i) q^{2} +(21.8338 - 41.3556i) q^{3} +(-62.2172 - 52.2064i) q^{4} +(40.2664 - 228.362i) q^{5} +(237.073 - 214.725i) q^{6} +(-1346.32 + 1129.70i) q^{7} +(-715.495 - 1239.27i) q^{8} +(-1233.57 - 1805.90i) q^{9} +O(q^{10})\) \(q+(6.42719 + 2.33931i) q^{2} +(21.8338 - 41.3556i) q^{3} +(-62.2172 - 52.2064i) q^{4} +(40.2664 - 228.362i) q^{5} +(237.073 - 214.725i) q^{6} +(-1346.32 + 1129.70i) q^{7} +(-715.495 - 1239.27i) q^{8} +(-1233.57 - 1805.90i) q^{9} +(793.009 - 1373.53i) q^{10} +(151.682 + 860.231i) q^{11} +(-3517.47 + 1433.17i) q^{12} +(8115.59 - 2953.83i) q^{13} +(-11295.8 + 4111.34i) q^{14} +(-8564.88 - 6651.25i) q^{15} +(105.666 + 599.260i) q^{16} +(19068.2 - 33027.1i) q^{17} +(-3703.85 - 14492.6i) q^{18} +(-14542.6 - 25188.5i) q^{19} +(-14427.2 + 12105.9i) q^{20} +(17324.1 + 80343.7i) q^{21} +(-1037.46 + 5883.70i) q^{22} +(-228.761 - 191.954i) q^{23} +(-66872.8 + 2531.68i) q^{24} +(22885.6 + 8329.68i) q^{25} +59070.4 q^{26} +(-101618. + 11585.5i) q^{27} +142742. q^{28} +(125276. + 45596.8i) q^{29} +(-39488.9 - 62784.8i) q^{30} +(-57472.9 - 48225.5i) q^{31} +(-32529.3 + 184483. i) q^{32} +(38887.2 + 12509.2i) q^{33} +(199815. - 167665. i) q^{34} +(203769. + 352939. i) q^{35} +(-17530.2 + 176758. i) q^{36} +(-19233.6 + 33313.5i) q^{37} +(-34544.4 - 195911. i) q^{38} +(55036.5 - 400118. i) q^{39} +(-311813. + 113491. i) q^{40} +(134487. - 48949.4i) q^{41} +(-76603.5 + 556911. i) q^{42} +(-81314.8 - 461159. i) q^{43} +(35472.4 - 61439.9i) q^{44} +(-462070. + 208984. i) q^{45} +(-1021.26 - 1768.87i) q^{46} +(-778592. + 653317. i) q^{47} +(27089.8 + 8714.25i) q^{48} +(393360. - 2.23086e6i) q^{49} +(127605. + 107073. i) q^{50} +(-949524. - 1.50968e6i) q^{51} +(-659138. - 239907. i) q^{52} +619176. q^{53} +(-680218. - 163253. i) q^{54} +202552. q^{55} +(2.36330e6 + 860169. i) q^{56} +(-1.35921e6 + 51457.0i) q^{57} +(698510. + 586120. i) q^{58} +(-148125. + 840057. i) q^{59} +(185645. + 860965. i) q^{60} +(-1.41982e6 + 1.19137e6i) q^{61} +(-256575. - 444401. i) q^{62} +(3.70091e6 + 1.03776e6i) q^{63} +(-601689. + 1.04216e6i) q^{64} +(-347758. - 1.97223e6i) q^{65} +(220672. + 171368. i) q^{66} +(3.11025e6 - 1.13204e6i) q^{67} +(-2.91060e6 + 1.05937e6i) q^{68} +(-12933.1 + 5269.49i) q^{69} +(484032. + 2.74508e6i) q^{70} +(1.32352e6 - 2.29241e6i) q^{71} +(-1.35539e6 + 2.82084e6i) q^{72} +(-307203. - 532092. i) q^{73} +(-201548. + 169119. i) q^{74} +(844158. - 764579. i) q^{75} +(-410203. + 2.32638e6i) q^{76} +(-1.17602e6 - 986795. i) q^{77} +(1.28973e6 - 2.44289e6i) q^{78} +(5.78037e6 + 2.10388e6i) q^{79} +141103. q^{80} +(-1.73957e6 + 4.45541e6i) q^{81} +978884. q^{82} +(-4.69511e6 - 1.70888e6i) q^{83} +(3.11660e6 - 5.90319e6i) q^{84} +(-6.77433e6 - 5.68434e6i) q^{85} +(556167. - 3.15418e6i) q^{86} +(4.62094e6 - 4.18532e6i) q^{87} +(957533. - 803466. i) q^{88} +(1.66391e6 + 2.88197e6i) q^{89} +(-3.45869e6 + 262255. i) q^{90} +(-7.58927e6 + 1.31450e7i) q^{91} +(4211.68 + 23885.6i) q^{92} +(-3.24924e6 + 1.32388e6i) q^{93} +(-6.53247e6 + 2.37763e6i) q^{94} +(-6.33768e6 + 2.30673e6i) q^{95} +(6.91915e6 + 5.37322e6i) q^{96} +(55624.9 + 315465. i) q^{97} +(7.74686e6 - 1.34180e7i) q^{98} +(1.36638e6 - 1.33508e6i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.42719 + 2.33931i 0.568089 + 0.206768i 0.610065 0.792351i \(-0.291143\pi\)
−0.0419763 + 0.999119i \(0.513365\pi\)
\(3\) 21.8338 41.3556i 0.466879 0.884321i
\(4\) −62.2172 52.2064i −0.486072 0.407863i
\(5\) 40.2664 228.362i 0.144061 0.817013i −0.824054 0.566511i \(-0.808293\pi\)
0.968116 0.250503i \(-0.0805959\pi\)
\(6\) 237.073 214.725i 0.448078 0.405838i
\(7\) −1346.32 + 1129.70i −1.48357 + 1.24486i −0.581292 + 0.813695i \(0.697452\pi\)
−0.902274 + 0.431164i \(0.858103\pi\)
\(8\) −715.495 1239.27i −0.494073 0.855760i
\(9\) −1233.57 1805.90i −0.564047 0.825743i
\(10\) 793.009 1373.53i 0.250772 0.434349i
\(11\) 151.682 + 860.231i 0.0343605 + 0.194868i 0.997156 0.0753622i \(-0.0240113\pi\)
−0.962796 + 0.270230i \(0.912900\pi\)
\(12\) −3517.47 + 1433.17i −0.587619 + 0.239421i
\(13\) 8115.59 2953.83i 1.02451 0.372893i 0.225525 0.974237i \(-0.427590\pi\)
0.798990 + 0.601344i \(0.205368\pi\)
\(14\) −11295.8 + 4111.34i −1.10019 + 0.400438i
\(15\) −8564.88 6651.25i −0.655243 0.508843i
\(16\) 105.666 + 599.260i 0.00644932 + 0.0365759i
\(17\) 19068.2 33027.1i 0.941322 1.63042i 0.178370 0.983963i \(-0.442918\pi\)
0.762952 0.646455i \(-0.223749\pi\)
\(18\) −3703.85 14492.6i −0.149692 0.585722i
\(19\) −14542.6 25188.5i −0.486412 0.842490i 0.513466 0.858110i \(-0.328361\pi\)
−0.999878 + 0.0156197i \(0.995028\pi\)
\(20\) −14427.2 + 12105.9i −0.403254 + 0.338370i
\(21\) 17324.1 + 80343.7i 0.408209 + 1.89315i
\(22\) −1037.46 + 5883.70i −0.0207726 + 0.117807i
\(23\) −228.761 191.954i −0.00392045 0.00328964i 0.640825 0.767687i \(-0.278592\pi\)
−0.644746 + 0.764397i \(0.723037\pi\)
\(24\) −66872.8 + 2531.68i −0.987439 + 0.0373826i
\(25\) 22885.6 + 8329.68i 0.292936 + 0.106620i
\(26\) 59070.4 0.659118
\(27\) −101618. + 11585.5i −0.993563 + 0.113277i
\(28\) 142742. 1.22885
\(29\) 125276. + 45596.8i 0.953841 + 0.347170i 0.771617 0.636087i \(-0.219448\pi\)
0.182224 + 0.983257i \(0.441670\pi\)
\(30\) −39488.9 62784.8i −0.267024 0.424551i
\(31\) −57472.9 48225.5i −0.346495 0.290744i 0.452886 0.891569i \(-0.350395\pi\)
−0.799381 + 0.600825i \(0.794839\pi\)
\(32\) −32529.3 + 184483.i −0.175489 + 0.995246i
\(33\) 38887.2 + 12509.2i 0.188368 + 0.0605942i
\(34\) 199815. 167665.i 0.871872 0.731588i
\(35\) 203769. + 352939.i 0.803342 + 1.39143i
\(36\) −17530.2 + 176758.i −0.0626222 + 0.631424i
\(37\) −19233.6 + 33313.5i −0.0624243 + 0.108122i −0.895549 0.444964i \(-0.853217\pi\)
0.833124 + 0.553086i \(0.186550\pi\)
\(38\) −34544.4 195911.i −0.102126 0.579184i
\(39\) 55036.5 400118.i 0.148568 1.08010i
\(40\) −311813. + 113491.i −0.770344 + 0.280382i
\(41\) 134487. 48949.4i 0.304746 0.110918i −0.185121 0.982716i \(-0.559268\pi\)
0.489867 + 0.871797i \(0.337045\pi\)
\(42\) −76603.5 + 556911.i −0.159542 + 1.15988i
\(43\) −81314.8 461159.i −0.155966 0.884527i −0.957897 0.287111i \(-0.907305\pi\)
0.801931 0.597416i \(-0.203806\pi\)
\(44\) 35472.4 61439.9i 0.0627778 0.108734i
\(45\) −462070. + 208984.i −0.755900 + 0.341876i
\(46\) −1021.26 1768.87i −0.00154697 0.00267943i
\(47\) −778592. + 653317.i −1.09387 + 0.917870i −0.996998 0.0774264i \(-0.975330\pi\)
−0.0968768 + 0.995296i \(0.530885\pi\)
\(48\) 27089.8 + 8714.25i 0.0353559 + 0.0113733i
\(49\) 393360. 2.23086e6i 0.477644 2.70885i
\(50\) 127605. + 107073.i 0.144368 + 0.121139i
\(51\) −949524. 1.50968e6i −1.00233 1.59364i
\(52\) −659138. 239907.i −0.650077 0.236609i
\(53\) 619176. 0.571280 0.285640 0.958337i \(-0.407794\pi\)
0.285640 + 0.958337i \(0.407794\pi\)
\(54\) −680218. 163253.i −0.587854 0.141085i
\(55\) 202552. 0.164160
\(56\) 2.36330e6 + 860169.i 1.79829 + 0.654524i
\(57\) −1.35921e6 + 51457.0i −0.972127 + 0.0368029i
\(58\) 698510. + 586120.i 0.470083 + 0.394447i
\(59\) −148125. + 840057.i −0.0938956 + 0.532509i 0.901185 + 0.433436i \(0.142699\pi\)
−0.995080 + 0.0990730i \(0.968412\pi\)
\(60\) 185645. + 860965.i 0.110957 + 0.514584i
\(61\) −1.41982e6 + 1.19137e6i −0.800899 + 0.672034i −0.948417 0.317025i \(-0.897316\pi\)
0.147518 + 0.989059i \(0.452872\pi\)
\(62\) −256575. 444401.i −0.136724 0.236812i
\(63\) 3.70091e6 + 1.03776e6i 1.86473 + 0.522884i
\(64\) −601689. + 1.04216e6i −0.286908 + 0.496939i
\(65\) −347758. 1.97223e6i −0.157065 0.890762i
\(66\) 220672. + 171368.i 0.0944810 + 0.0733713i
\(67\) 3.11025e6 1.13204e6i 1.26338 0.459833i 0.378478 0.925610i \(-0.376447\pi\)
0.884902 + 0.465777i \(0.154225\pi\)
\(68\) −2.91060e6 + 1.05937e6i −1.12254 + 0.408570i
\(69\) −12933.1 + 5269.49i −0.00473948 + 0.00193107i
\(70\) 484032. + 2.74508e6i 0.168667 + 0.956560i
\(71\) 1.32352e6 2.29241e6i 0.438861 0.760130i −0.558741 0.829343i \(-0.688715\pi\)
0.997602 + 0.0692122i \(0.0220486\pi\)
\(72\) −1.35539e6 + 2.82084e6i −0.427957 + 0.890666i
\(73\) −307203. 532092.i −0.0924264 0.160087i 0.816105 0.577903i \(-0.196129\pi\)
−0.908532 + 0.417816i \(0.862796\pi\)
\(74\) −201548. + 169119.i −0.0578187 + 0.0485156i
\(75\) 844158. 764579.i 0.231052 0.209271i
\(76\) −410203. + 2.32638e6i −0.107189 + 0.607900i
\(77\) −1.17602e6 986795.i −0.293559 0.246325i
\(78\) 1.28973e6 2.44289e6i 0.307729 0.582872i
\(79\) 5.78037e6 + 2.10388e6i 1.31905 + 0.480094i 0.903153 0.429318i \(-0.141246\pi\)
0.415895 + 0.909413i \(0.363468\pi\)
\(80\) 141103. 0.0308121
\(81\) −1.73957e6 + 4.45541e6i −0.363702 + 0.931516i
\(82\) 978884. 0.196057
\(83\) −4.69511e6 1.70888e6i −0.901307 0.328049i −0.150530 0.988605i \(-0.548098\pi\)
−0.750776 + 0.660557i \(0.770320\pi\)
\(84\) 3.11660e6 5.90319e6i 0.573725 1.08670i
\(85\) −6.77433e6 5.68434e6i −1.19646 1.00395i
\(86\) 556167. 3.15418e6i 0.0942889 0.534739i
\(87\) 4.62094e6 4.18532e6i 0.752338 0.681415i
\(88\) 957533. 803466.i 0.149784 0.125683i
\(89\) 1.66391e6 + 2.88197e6i 0.250187 + 0.433336i 0.963577 0.267431i \(-0.0861747\pi\)
−0.713390 + 0.700767i \(0.752841\pi\)
\(90\) −3.45869e6 + 262255.i −0.500107 + 0.0379206i
\(91\) −7.58927e6 + 1.31450e7i −1.05574 + 1.82859i
\(92\) 4211.68 + 23885.6i 0.000563895 + 0.00319801i
\(93\) −3.24924e6 + 1.32388e6i −0.418882 + 0.170670i
\(94\) −6.53247e6 + 2.37763e6i −0.811204 + 0.295254i
\(95\) −6.33768e6 + 2.30673e6i −0.758399 + 0.276035i
\(96\) 6.91915e6 + 5.37322e6i 0.798185 + 0.619848i
\(97\) 55624.9 + 315465.i 0.00618826 + 0.0350954i 0.987746 0.156073i \(-0.0498835\pi\)
−0.981557 + 0.191168i \(0.938772\pi\)
\(98\) 7.74686e6 1.34180e7i 0.831447 1.44011i
\(99\) 1.36638e6 1.33508e6i 0.141530 0.138288i
\(100\) −989016. 1.71303e6i −0.0989016 0.171303i
\(101\) 652314. 547356.i 0.0629987 0.0528622i −0.610745 0.791828i \(-0.709130\pi\)
0.673743 + 0.738965i \(0.264685\pi\)
\(102\) −2.57116e6 1.19243e7i −0.239899 1.11258i
\(103\) 1.18511e6 6.72112e6i 0.106864 0.606054i −0.883596 0.468250i \(-0.844885\pi\)
0.990460 0.137804i \(-0.0440043\pi\)
\(104\) −9.46726e6 7.94398e6i −0.825292 0.692503i
\(105\) 1.90450e7 721010.i 1.60553 0.0607825i
\(106\) 3.97957e6 + 1.44844e6i 0.324538 + 0.118122i
\(107\) −7.63468e6 −0.602487 −0.301243 0.953547i \(-0.597402\pi\)
−0.301243 + 0.953547i \(0.597402\pi\)
\(108\) 6.92720e6 + 4.58428e6i 0.529145 + 0.350177i
\(109\) −5.21603e6 −0.385787 −0.192894 0.981220i \(-0.561787\pi\)
−0.192894 + 0.981220i \(0.561787\pi\)
\(110\) 1.30184e6 + 473831.i 0.0932574 + 0.0339429i
\(111\) 957758. + 1.52278e6i 0.0664700 + 0.105683i
\(112\) −819245. 687428.i −0.0550999 0.0462343i
\(113\) −1.08747e6 + 6.16735e6i −0.0708994 + 0.402091i 0.928618 + 0.371036i \(0.120998\pi\)
−0.999518 + 0.0310541i \(0.990114\pi\)
\(114\) −8.85625e6 2.84888e6i −0.559865 0.180097i
\(115\) −53046.4 + 44511.2i −0.00325247 + 0.00272915i
\(116\) −5.41389e6 9.37714e6i −0.322038 0.557786i
\(117\) −1.53455e7 1.10122e7i −0.885788 0.635656i
\(118\) −2.91718e6 + 5.05270e6i −0.163447 + 0.283098i
\(119\) 1.16387e7 + 6.60065e7i 0.633128 + 3.59065i
\(120\) −2.11459e6 + 1.53732e7i −0.111710 + 0.812136i
\(121\) 1.75950e7 6.40404e6i 0.902900 0.328629i
\(122\) −1.19124e7 + 4.33576e6i −0.593937 + 0.216175i
\(123\) 912037. 6.63055e6i 0.0441921 0.321279i
\(124\) 1.05812e6 + 6.00091e6i 0.0498379 + 0.282645i
\(125\) 1.18817e7 2.05797e7i 0.544119 0.942442i
\(126\) 2.13588e7 + 1.53275e7i 0.951220 + 0.682611i
\(127\) 2.94667e6 + 5.10378e6i 0.127649 + 0.221095i 0.922765 0.385362i \(-0.125923\pi\)
−0.795116 + 0.606457i \(0.792590\pi\)
\(128\) 1.20632e7 1.01222e7i 0.508424 0.426619i
\(129\) −2.08469e7 6.70603e6i −0.855023 0.275043i
\(130\) 2.37855e6 1.34894e7i 0.0949535 0.538508i
\(131\) −1.16634e7 9.78673e6i −0.453288 0.380354i 0.387366 0.921926i \(-0.373385\pi\)
−0.840654 + 0.541572i \(0.817829\pi\)
\(132\) −1.76639e6 2.80845e6i −0.0668464 0.106281i
\(133\) 4.80345e7 + 1.74831e7i 1.77041 + 0.644375i
\(134\) 2.26384e7 0.812791
\(135\) −1.44609e6 + 2.36721e7i −0.0505858 + 0.828073i
\(136\) −5.45728e7 −1.86033
\(137\) 3.69521e7 + 1.34495e7i 1.22777 + 0.446872i 0.872833 0.488018i \(-0.162280\pi\)
0.354937 + 0.934890i \(0.384502\pi\)
\(138\) −95450.4 + 3613.58i −0.00309173 + 0.000117047i
\(139\) −1.01709e7 8.53442e6i −0.321224 0.269539i 0.467888 0.883788i \(-0.345015\pi\)
−0.789113 + 0.614248i \(0.789459\pi\)
\(140\) 5.74772e6 3.25969e7i 0.177030 1.00399i
\(141\) 1.00187e7 + 4.64635e7i 0.300984 + 1.39587i
\(142\) 1.38692e7 1.16376e7i 0.406483 0.341079i
\(143\) 3.77197e6 + 6.53324e6i 0.107868 + 0.186832i
\(144\) 951857. 930051.i 0.0265646 0.0259560i
\(145\) 1.54570e7 2.67723e7i 0.421054 0.729287i
\(146\) −729729. 4.13850e6i −0.0194056 0.110055i
\(147\) −8.36698e7 6.49757e7i −2.17249 1.68710i
\(148\) 2.93584e6 1.06856e6i 0.0744417 0.0270946i
\(149\) −8.35580e6 + 3.04126e6i −0.206936 + 0.0753186i −0.443409 0.896320i \(-0.646231\pi\)
0.236472 + 0.971638i \(0.424009\pi\)
\(150\) 7.21416e6 2.93935e6i 0.174528 0.0711103i
\(151\) −6.45338e6 3.65989e7i −0.152534 0.865066i −0.961005 0.276530i \(-0.910816\pi\)
0.808471 0.588536i \(-0.200296\pi\)
\(152\) −2.08103e7 + 3.60445e7i −0.480646 + 0.832504i
\(153\) −8.31656e7 + 6.30602e6i −1.87726 + 0.142343i
\(154\) −5.25007e6 9.09339e6i −0.115836 0.200633i
\(155\) −1.33271e7 + 1.11828e7i −0.287458 + 0.241206i
\(156\) −2.43130e7 + 2.20210e7i −0.512746 + 0.464409i
\(157\) 8.45786e6 4.79669e7i 0.174426 0.989220i −0.764378 0.644768i \(-0.776954\pi\)
0.938804 0.344451i \(-0.111935\pi\)
\(158\) 3.22299e7 + 2.70441e7i 0.650069 + 0.545473i
\(159\) 1.35190e7 2.56064e7i 0.266719 0.505194i
\(160\) 4.08190e7 + 1.48569e7i 0.787848 + 0.286753i
\(161\) 524837. 0.00991138
\(162\) −2.16031e7 + 2.45664e7i −0.399222 + 0.453982i
\(163\) 541760. 0.00979830 0.00489915 0.999988i \(-0.498441\pi\)
0.00489915 + 0.999988i \(0.498441\pi\)
\(164\) −1.09229e7 3.97561e6i −0.193368 0.0703802i
\(165\) 4.42247e6 8.37665e6i 0.0766428 0.145170i
\(166\) −2.61788e7 2.19666e7i −0.444193 0.372722i
\(167\) −5.15397e6 + 2.92296e7i −0.0856316 + 0.485641i 0.911587 + 0.411107i \(0.134858\pi\)
−0.997219 + 0.0745336i \(0.976253\pi\)
\(168\) 8.71725e7 7.89547e7i 1.41839 1.28468i
\(169\) 9.06950e6 7.61021e6i 0.144537 0.121281i
\(170\) −3.02425e7 5.23816e7i −0.472114 0.817725i
\(171\) −2.75486e7 + 5.73343e7i −0.421321 + 0.876855i
\(172\) −1.90163e7 + 3.29372e7i −0.284955 + 0.493557i
\(173\) −7.63065e6 4.32756e7i −0.112047 0.635450i −0.988170 0.153362i \(-0.950990\pi\)
0.876123 0.482088i \(-0.160121\pi\)
\(174\) 3.94904e7 1.60901e7i 0.568290 0.231545i
\(175\) −4.02215e7 + 1.46394e7i −0.567316 + 0.206486i
\(176\) −499474. + 181794.i −0.00690588 + 0.00251353i
\(177\) 3.15069e7 + 2.44674e7i 0.427071 + 0.331651i
\(178\) 3.95244e6 + 2.24154e7i 0.0525285 + 0.297904i
\(179\) 2.65386e7 4.59661e7i 0.345853 0.599035i −0.639655 0.768662i \(-0.720923\pi\)
0.985508 + 0.169627i \(0.0542562\pi\)
\(180\) 3.96590e7 + 1.11207e7i 0.506861 + 0.142127i
\(181\) 1.25234e7 + 2.16912e7i 0.156981 + 0.271899i 0.933779 0.357851i \(-0.116491\pi\)
−0.776798 + 0.629750i \(0.783157\pi\)
\(182\) −7.95279e7 + 6.67318e7i −0.977844 + 0.820509i
\(183\) 1.82697e7 + 8.47294e7i 0.220371 + 1.02201i
\(184\) −74205.4 + 420840.i −0.000878159 + 0.00498029i
\(185\) 6.83308e6 + 5.73363e6i 0.0793442 + 0.0665777i
\(186\) −2.39805e7 + 907856.i −0.273251 + 0.0103448i
\(187\) 3.13032e7 + 1.13934e7i 0.350061 + 0.127412i
\(188\) 8.25492e7 0.906067
\(189\) 1.23722e8 1.30395e8i 1.33300 1.40490i
\(190\) −4.61296e7 −0.487913
\(191\) 1.09493e8 + 3.98524e7i 1.13703 + 0.413845i 0.840839 0.541285i \(-0.182062\pi\)
0.296189 + 0.955129i \(0.404284\pi\)
\(192\) 2.99618e7 + 4.76374e7i 0.305502 + 0.485729i
\(193\) 8.10352e7 + 6.79966e7i 0.811377 + 0.680826i 0.950936 0.309387i \(-0.100124\pi\)
−0.139559 + 0.990214i \(0.544568\pi\)
\(194\) −380457. + 2.15768e6i −0.00374110 + 0.0212168i
\(195\) −8.91558e7 2.86796e7i −0.861050 0.276982i
\(196\) −1.40939e8 + 1.18262e8i −1.33701 + 1.12188i
\(197\) 5.46162e7 + 9.45980e7i 0.508967 + 0.881557i 0.999946 + 0.0103855i \(0.00330587\pi\)
−0.490979 + 0.871171i \(0.663361\pi\)
\(198\) 1.19051e7 5.38443e6i 0.108995 0.0492959i
\(199\) 4.75070e6 8.22845e6i 0.0427338 0.0740171i −0.843867 0.536552i \(-0.819727\pi\)
0.886601 + 0.462535i \(0.153060\pi\)
\(200\) −6.05178e6 3.43213e7i −0.0534907 0.303361i
\(201\) 2.10924e7 1.53343e8i 0.183206 1.33192i
\(202\) 5.47298e6 1.99200e6i 0.0467191 0.0170043i
\(203\) −2.20173e8 + 8.01365e7i −1.84726 + 0.672349i
\(204\) −1.97385e7 + 1.43500e8i −0.162782 + 1.18344i
\(205\) −5.76286e6 3.26828e7i −0.0467197 0.264960i
\(206\) 2.33397e7 4.04256e7i 0.186020 0.322197i
\(207\) −64455.4 + 649909.i −0.000505083 + 0.00509279i
\(208\) 2.62765e6 + 4.55123e6i 0.0202463 + 0.0350677i
\(209\) 1.94621e7 1.63306e7i 0.147461 0.123735i
\(210\) 1.24093e8 + 3.99181e7i 0.924654 + 0.297442i
\(211\) 7.40168e6 4.19770e7i 0.0542427 0.307626i −0.945601 0.325330i \(-0.894525\pi\)
0.999843 + 0.0177042i \(0.00563571\pi\)
\(212\) −3.85234e7 3.23250e7i −0.277683 0.233004i
\(213\) −6.59064e7 1.04787e8i −0.467304 0.742984i
\(214\) −4.90696e7 1.78599e7i −0.342266 0.124575i
\(215\) −1.08585e8 −0.745139
\(216\) 8.70644e7 + 1.17643e8i 0.587831 + 0.794285i
\(217\) 1.31857e8 0.875983
\(218\) −3.35245e7 1.22019e7i −0.219161 0.0797682i
\(219\) −2.87124e7 + 1.08700e6i −0.184720 + 0.00699317i
\(220\) −1.26022e7 1.05745e7i −0.0797935 0.0669547i
\(221\) 5.71932e7 3.24358e8i 0.356427 2.02140i
\(222\) 2.59346e6 + 1.20277e7i 0.0159090 + 0.0737812i
\(223\) −9.43968e7 + 7.92083e7i −0.570020 + 0.478304i −0.881653 0.471899i \(-0.843569\pi\)
0.311632 + 0.950203i \(0.399124\pi\)
\(224\) −1.64615e8 2.85122e8i −0.978592 1.69497i
\(225\) −1.31885e7 5.16043e7i −0.0771890 0.302028i
\(226\) −2.14167e7 + 3.70948e7i −0.123416 + 0.213764i
\(227\) −4.12954e7 2.34198e8i −0.234321 1.32890i −0.844039 0.536281i \(-0.819829\pi\)
0.609719 0.792618i \(-0.291282\pi\)
\(228\) 8.72524e7 + 6.77578e7i 0.487535 + 0.378606i
\(229\) 4.65531e6 1.69439e6i 0.0256168 0.00932374i −0.329180 0.944267i \(-0.606772\pi\)
0.354797 + 0.934943i \(0.384550\pi\)
\(230\) −445065. + 161990.i −0.00241199 + 0.000877893i
\(231\) −6.64864e7 + 2.70894e7i −0.354888 + 0.144596i
\(232\) −3.31276e7 1.87876e8i −0.174173 0.987786i
\(233\) −1.37051e8 + 2.37379e8i −0.709800 + 1.22941i 0.255131 + 0.966907i \(0.417881\pi\)
−0.964931 + 0.262504i \(0.915452\pi\)
\(234\) −7.28675e7 1.06675e8i −0.371774 0.544262i
\(235\) 1.17842e8 + 2.04108e8i 0.592327 + 1.02594i
\(236\) 5.30723e7 4.45329e7i 0.262831 0.220541i
\(237\) 2.13215e8 1.93115e8i 1.04039 0.942316i
\(238\) −7.96052e7 + 4.51463e8i −0.382756 + 2.17072i
\(239\) 2.31026e8 + 1.93854e8i 1.09463 + 0.918504i 0.997052 0.0767240i \(-0.0244460\pi\)
0.0975780 + 0.995228i \(0.468890\pi\)
\(240\) 3.08081e6 5.83540e6i 0.0143855 0.0272478i
\(241\) −6.68885e7 2.43454e7i −0.307817 0.112036i 0.183493 0.983021i \(-0.441259\pi\)
−0.491310 + 0.870985i \(0.663482\pi\)
\(242\) 1.28067e8 0.580877
\(243\) 1.46275e8 + 1.69220e8i 0.653954 + 0.756534i
\(244\) 1.50534e8 0.663392
\(245\) −4.93604e8 1.79657e8i −2.14436 0.780482i
\(246\) 2.13727e7 4.04823e7i 0.0915350 0.173377i
\(247\) −1.92424e8 1.61463e8i −0.812495 0.681764i
\(248\) −1.86430e7 + 1.05730e8i −0.0776130 + 0.440165i
\(249\) −1.73184e8 + 1.56858e8i −0.710902 + 0.643885i
\(250\) 1.24508e8 1.04475e8i 0.503974 0.422885i
\(251\) 2.16889e8 + 3.75663e8i 0.865725 + 1.49948i 0.866326 + 0.499479i \(0.166475\pi\)
−0.000601059 1.00000i \(0.500191\pi\)
\(252\) −1.76083e8 2.57778e8i −0.693130 1.01471i
\(253\) 130425. 225904.i 0.000506338 0.000877003i
\(254\) 6.99951e6 + 3.96962e7i 0.0268009 + 0.151995i
\(255\) −3.82988e8 + 1.56046e8i −1.44642 + 0.589334i
\(256\) 2.45954e8 8.95201e7i 0.916251 0.333488i
\(257\) 3.41044e8 1.24130e8i 1.25327 0.456153i 0.371764 0.928327i \(-0.378753\pi\)
0.881505 + 0.472174i \(0.156531\pi\)
\(258\) −1.18300e8 9.18683e7i −0.428859 0.333040i
\(259\) −1.17397e7 6.65790e7i −0.0419862 0.238116i
\(260\) −8.13268e7 + 1.40862e8i −0.286964 + 0.497035i
\(261\) −7.21939e7 2.82483e8i −0.251338 0.983447i
\(262\) −5.20686e7 9.01854e7i −0.178863 0.309800i
\(263\) 2.22663e8 1.86836e8i 0.754749 0.633310i −0.182005 0.983298i \(-0.558259\pi\)
0.936754 + 0.349988i \(0.113814\pi\)
\(264\) −1.23212e7 5.71421e7i −0.0412136 0.191136i
\(265\) 2.49320e7 1.41396e8i 0.0822994 0.466743i
\(266\) 2.67829e8 + 2.24735e8i 0.872512 + 0.732125i
\(267\) 1.55515e8 5.88751e6i 0.500015 0.0189296i
\(268\) −2.52611e8 9.19430e7i −0.801643 0.291774i
\(269\) −1.57246e8 −0.492546 −0.246273 0.969201i \(-0.579206\pi\)
−0.246273 + 0.969201i \(0.579206\pi\)
\(270\) −6.46707e7 + 1.48762e8i −0.199956 + 0.459960i
\(271\) 3.03389e8 0.925992 0.462996 0.886360i \(-0.346774\pi\)
0.462996 + 0.886360i \(0.346774\pi\)
\(272\) 2.18067e7 + 7.93698e6i 0.0657049 + 0.0239146i
\(273\) 3.77917e8 + 6.00864e8i 1.12416 + 1.78734i
\(274\) 2.06036e8 + 1.72885e8i 0.605085 + 0.507726i
\(275\) −3.69411e6 + 2.09504e7i −0.0107114 + 0.0607473i
\(276\) 1.07976e6 + 347338.i 0.00309134 + 0.000994420i
\(277\) −2.43332e8 + 2.04180e8i −0.687893 + 0.577210i −0.918301 0.395884i \(-0.870438\pi\)
0.230408 + 0.973094i \(0.425994\pi\)
\(278\) −4.54059e7 7.86453e7i −0.126752 0.219541i
\(279\) −1.61934e7 + 1.63280e8i −0.0446400 + 0.450109i
\(280\) 2.91591e8 5.05051e8i 0.793819 1.37494i
\(281\) 5.22797e7 + 2.96493e8i 0.140560 + 0.797155i 0.970826 + 0.239787i \(0.0770775\pi\)
−0.830266 + 0.557368i \(0.811811\pi\)
\(282\) −4.43005e7 + 3.22067e8i −0.117635 + 0.855213i
\(283\) −2.78863e8 + 1.01498e8i −0.731372 + 0.266198i −0.680745 0.732520i \(-0.738344\pi\)
−0.0506263 + 0.998718i \(0.516122\pi\)
\(284\) −2.02025e8 + 7.35309e7i −0.523347 + 0.190483i
\(285\) −4.29795e7 + 3.12463e8i −0.109978 + 0.799543i
\(286\) 8.95991e6 + 5.08142e7i 0.0226476 + 0.128441i
\(287\) −1.25765e8 + 2.17832e8i −0.314033 + 0.543920i
\(288\) 3.73284e8 1.68828e8i 0.920801 0.416457i
\(289\) −5.22023e8 9.04170e8i −1.27218 2.20347i
\(290\) 1.61974e8 1.35912e8i 0.389989 0.327240i
\(291\) 1.42607e7 + 4.58739e6i 0.0339247 + 0.0109129i
\(292\) −8.66529e6 + 4.91433e7i −0.0203677 + 0.115511i
\(293\) 5.70689e8 + 4.78865e8i 1.32545 + 1.11218i 0.985119 + 0.171876i \(0.0549829\pi\)
0.340329 + 0.940306i \(0.389462\pi\)
\(294\) −3.85764e8 6.13341e8i −0.885332 1.40762i
\(295\) 1.85873e8 + 6.76521e7i 0.421540 + 0.153428i
\(296\) 5.50460e7 0.123369
\(297\) −2.53797e7 8.56573e7i −0.0562133 0.189722i
\(298\) −6.08188e7 −0.133132
\(299\) −2.42353e6 882094.i −0.00524324 0.00190838i
\(300\) −9.24372e7 + 3.49950e6i −0.197662 + 0.00748310i
\(301\) 6.30448e8 + 5.29008e8i 1.33250 + 1.11810i
\(302\) 4.41391e7 2.50325e8i 0.0922144 0.522974i
\(303\) −8.39376e6 3.89277e7i −0.0173343 0.0803913i
\(304\) 1.35578e7 1.13764e7i 0.0276778 0.0232245i
\(305\) 2.14892e8 + 3.72204e8i 0.433682 + 0.751159i
\(306\) −5.49273e8 1.54020e8i −1.09588 0.307292i
\(307\) −2.27858e7 + 3.94661e7i −0.0449448 + 0.0778466i −0.887623 0.460571i \(-0.847645\pi\)
0.842678 + 0.538418i \(0.180978\pi\)
\(308\) 2.16514e7 + 1.22791e8i 0.0422239 + 0.239464i
\(309\) −2.52080e8 1.95759e8i −0.486054 0.377456i
\(310\) −1.11816e8 + 4.06976e7i −0.213175 + 0.0775895i
\(311\) −6.18389e8 + 2.25075e8i −1.16574 + 0.424294i −0.851144 0.524933i \(-0.824090\pi\)
−0.314593 + 0.949227i \(0.601868\pi\)
\(312\) −5.35234e8 + 2.18077e8i −0.997707 + 0.406508i
\(313\) −1.20177e8 6.81557e8i −0.221521 1.25631i −0.869225 0.494417i \(-0.835381\pi\)
0.647703 0.761893i \(-0.275730\pi\)
\(314\) 1.66570e8 2.88507e8i 0.303628 0.525899i
\(315\) 3.86008e8 8.03361e8i 0.695839 1.44818i
\(316\) −2.49802e8 4.32670e8i −0.445340 0.771351i
\(317\) 1.90716e7 1.60029e7i 0.0336263 0.0282158i −0.625820 0.779968i \(-0.715235\pi\)
0.659446 + 0.751752i \(0.270791\pi\)
\(318\) 1.46790e8 1.32952e8i 0.255978 0.231847i
\(319\) −2.02217e7 + 1.14683e8i −0.0348778 + 0.197802i
\(320\) 2.13761e8 + 1.79367e8i 0.364673 + 0.305997i
\(321\) −1.66694e8 + 3.15737e8i −0.281289 + 0.532792i
\(322\) 3.37323e6 + 1.22776e6i 0.00563055 + 0.00204935i
\(323\) −1.10920e9 −1.83148
\(324\) 3.40833e8 1.86386e8i 0.556716 0.304443i
\(325\) 2.10335e8 0.339875
\(326\) 3.48200e6 + 1.26734e6i 0.00556631 + 0.00202597i
\(327\) −1.13886e8 + 2.15712e8i −0.180116 + 0.341160i
\(328\) −1.56887e8 1.31643e8i −0.245486 0.205987i
\(329\) 3.10186e8 1.75915e9i 0.480216 2.72344i
\(330\) 4.80197e7 4.34928e7i 0.0735564 0.0666222i
\(331\) 5.19612e8 4.36006e8i 0.787556 0.660838i −0.157583 0.987506i \(-0.550370\pi\)
0.945139 + 0.326668i \(0.105926\pi\)
\(332\) 2.02902e8 + 3.51437e8i 0.304301 + 0.527065i
\(333\) 8.38868e7 6.36071e6i 0.124491 0.00943954i
\(334\) −1.01503e8 + 1.75808e8i −0.149061 + 0.258182i
\(335\) −1.33276e8 7.55848e8i −0.193685 1.09844i
\(336\) −4.63162e7 + 1.88712e7i −0.0666109 + 0.0271401i
\(337\) −9.21543e8 + 3.35414e8i −1.31163 + 0.477394i −0.900767 0.434303i \(-0.856995\pi\)
−0.410863 + 0.911697i \(0.634772\pi\)
\(338\) 7.60940e7 2.76960e7i 0.107187 0.0390129i
\(339\) 2.31311e8 + 1.79630e8i 0.322476 + 0.250426i
\(340\) 1.24721e8 + 7.07327e8i 0.172093 + 0.975987i
\(341\) 3.27674e7 5.67549e7i 0.0447509 0.0775109i
\(342\) −3.11183e8 + 3.04054e8i −0.420653 + 0.411016i
\(343\) 1.26692e9 + 2.19437e9i 1.69519 + 2.93616i
\(344\) −5.13322e8 + 4.30728e8i −0.679884 + 0.570491i
\(345\) 682583. + 3.16561e6i 0.000894930 + 0.00415041i
\(346\) 5.21912e7 2.95991e8i 0.0677378 0.384160i
\(347\) 3.46905e8 + 2.91088e8i 0.445716 + 0.374000i 0.837843 0.545911i \(-0.183816\pi\)
−0.392127 + 0.919911i \(0.628261\pi\)
\(348\) −5.06003e8 + 1.91563e7i −0.643614 + 0.0243660i
\(349\) −1.13530e9 4.13216e8i −1.42963 0.520342i −0.492802 0.870141i \(-0.664027\pi\)
−0.936824 + 0.349800i \(0.886250\pi\)
\(350\) −2.92757e8 −0.364981
\(351\) −7.90465e8 + 3.94184e8i −0.975681 + 0.486546i
\(352\) −1.63632e8 −0.199972
\(353\) 5.74160e8 + 2.08977e8i 0.694738 + 0.252864i 0.665163 0.746698i \(-0.268362\pi\)
0.0295757 + 0.999563i \(0.490584\pi\)
\(354\) 1.45264e8 + 2.30961e8i 0.174039 + 0.276712i
\(355\) −4.70206e8 3.94550e8i −0.557813 0.468061i
\(356\) 4.69338e7 2.66175e8i 0.0551329 0.312674i
\(357\) 2.98386e9 + 9.59846e8i 3.47088 + 1.11651i
\(358\) 2.78097e8 2.33351e8i 0.320336 0.268794i
\(359\) −6.07751e8 1.05266e9i −0.693258 1.20076i −0.970764 0.240035i \(-0.922841\pi\)
0.277506 0.960724i \(-0.410492\pi\)
\(360\) 5.89597e8 + 4.23105e8i 0.666034 + 0.477957i
\(361\) 2.39619e7 4.15032e7i 0.0268068 0.0464308i
\(362\) 2.97480e7 + 1.68709e8i 0.0329593 + 0.186921i
\(363\) 1.19322e8 8.67475e8i 0.130932 0.951883i
\(364\) 1.15844e9 4.21637e8i 1.25898 0.458230i
\(365\) −1.33880e8 + 4.87282e7i −0.144108 + 0.0524512i
\(366\) −8.07850e7 + 5.87311e8i −0.0861285 + 0.626159i
\(367\) 6.27892e7 + 3.56095e8i 0.0663062 + 0.376041i 0.999846 + 0.0175664i \(0.00559186\pi\)
−0.933540 + 0.358474i \(0.883297\pi\)
\(368\) 90857.9 157371.i 9.50376e−5 0.000164610i
\(369\) −2.54297e8 1.82488e8i −0.263481 0.189078i
\(370\) 3.05048e7 + 5.28358e7i 0.0313085 + 0.0542279i
\(371\) −8.33612e8 + 6.99484e8i −0.847530 + 0.711163i
\(372\) 2.71274e8 + 8.72633e7i 0.273217 + 0.0878883i
\(373\) −1.96697e8 + 1.11552e9i −0.196253 + 1.11301i 0.714369 + 0.699769i \(0.246714\pi\)
−0.910623 + 0.413239i \(0.864397\pi\)
\(374\) 1.74539e8 + 1.46456e8i 0.172521 + 0.144762i
\(375\) −5.91664e8 9.40709e8i −0.579383 0.921183i
\(376\) 1.36672e9 + 4.97444e8i 1.32593 + 0.482599i
\(377\) 1.15138e9 1.10668
\(378\) 1.10022e9 5.48651e8i 1.04775 0.522486i
\(379\) −1.18739e9 −1.12035 −0.560177 0.828373i \(-0.689267\pi\)
−0.560177 + 0.828373i \(0.689267\pi\)
\(380\) 5.14739e8 + 1.87350e8i 0.481221 + 0.175150i
\(381\) 2.75407e8 1.04264e7i 0.255116 0.00965821i
\(382\) 6.10509e8 + 5.12278e8i 0.560364 + 0.470201i
\(383\) 5.21945e7 2.96010e8i 0.0474710 0.269222i −0.951829 0.306629i \(-0.900799\pi\)
0.999300 + 0.0374075i \(0.0119100\pi\)
\(384\) −1.55225e8 7.19885e8i −0.139895 0.648790i
\(385\) −2.72701e8 + 2.28823e8i −0.243542 + 0.204356i
\(386\) 3.61764e8 + 6.26593e8i 0.320162 + 0.554537i
\(387\) −7.32499e8 + 7.15719e8i −0.642419 + 0.627703i
\(388\) 1.30085e7 2.25313e7i 0.0113062 0.0195828i
\(389\) −2.22016e8 1.25912e9i −0.191232 1.08453i −0.917683 0.397314i \(-0.869942\pi\)
0.726450 0.687219i \(-0.241169\pi\)
\(390\) −5.05931e8 3.92892e8i −0.431882 0.335388i
\(391\) −1.07017e7 + 3.89511e6i −0.00905390 + 0.00329535i
\(392\) −3.04609e9 + 1.10868e9i −2.55412 + 0.929623i
\(393\) −6.59392e8 + 2.68664e8i −0.547986 + 0.223273i
\(394\) 1.29735e8 + 7.35764e8i 0.106861 + 0.606041i
\(395\) 7.13202e8 1.23530e9i 0.582267 1.00852i
\(396\) −1.54712e8 + 1.17310e7i −0.125196 + 0.00949299i
\(397\) −3.12755e8 5.41708e8i −0.250864 0.434509i 0.712900 0.701266i \(-0.247381\pi\)
−0.963764 + 0.266757i \(0.914048\pi\)
\(398\) 4.97825e7 4.17725e7i 0.0395809 0.0332123i
\(399\) 1.77180e9 1.60477e9i 1.39640 1.26476i
\(400\) −2.57342e6 + 1.45946e7i −0.00201048 + 0.0114020i
\(401\) −5.47262e8 4.59207e8i −0.423828 0.355634i 0.405789 0.913967i \(-0.366997\pi\)
−0.829617 + 0.558333i \(0.811441\pi\)
\(402\) 4.94282e8 9.36225e8i 0.379475 0.718768i
\(403\) −6.08876e8 2.21613e8i −0.463405 0.168666i
\(404\) −6.91607e7 −0.0521824
\(405\) 9.47401e8 + 5.76656e8i 0.708665 + 0.431344i
\(406\) −1.60256e9 −1.18843
\(407\) −3.15747e7 1.14922e7i −0.0232145 0.00844937i
\(408\) −1.19153e9 + 2.25689e9i −0.868549 + 1.64513i
\(409\) −1.96514e9 1.64895e9i −1.42024 1.19173i −0.951210 0.308545i \(-0.900158\pi\)
−0.469033 0.883180i \(-0.655398\pi\)
\(410\) 3.94161e7 2.23540e8i 0.0282443 0.160181i
\(411\) 1.36302e9 1.23452e9i 0.968399 0.877108i
\(412\) −4.24620e8 + 3.56299e8i −0.299130 + 0.251000i
\(413\) −7.49589e8 1.29833e9i −0.523598 0.906898i
\(414\) −1.93460e6 + 4.02631e6i −0.00133996 + 0.00278873i
\(415\) −5.79299e8 + 1.00338e9i −0.397864 + 0.689120i
\(416\) 2.80937e8 + 1.59327e9i 0.191329 + 1.08508i
\(417\) −5.75016e8 + 2.34286e8i −0.388332 + 0.158223i
\(418\) 1.63289e8 5.94323e7i 0.109355 0.0398021i
\(419\) −1.53830e9 + 5.59897e8i −1.02163 + 0.371843i −0.797888 0.602806i \(-0.794049\pi\)
−0.223741 + 0.974649i \(0.571827\pi\)
\(420\) −1.22257e9 9.49415e8i −0.805196 0.625293i
\(421\) 5.21978e8 + 2.96028e9i 0.340930 + 1.93351i 0.358167 + 0.933657i \(0.383402\pi\)
−0.0172377 + 0.999851i \(0.505487\pi\)
\(422\) 1.45769e8 2.52480e8i 0.0944217 0.163543i
\(423\) 2.14027e9 + 6.00147e8i 1.37492 + 0.385537i
\(424\) −4.43017e8 7.67328e8i −0.282254 0.488878i
\(425\) 7.11492e8 5.97013e8i 0.449582 0.377244i
\(426\) −1.78464e8 8.27662e8i −0.111845 0.518704i
\(427\) 5.65645e8 3.20793e9i 0.351598 1.99401i
\(428\) 4.75009e8 + 3.98580e8i 0.292852 + 0.245732i
\(429\) 3.52542e8 1.33466e7i 0.215581 0.00816150i
\(430\) −6.97900e8 2.54015e8i −0.423305 0.154071i
\(431\) 2.66741e9 1.60480 0.802399 0.596789i \(-0.203557\pi\)
0.802399 + 0.596789i \(0.203557\pi\)
\(432\) −1.76802e7 5.96712e7i −0.0105510 0.0356099i
\(433\) 1.30539e9 0.772736 0.386368 0.922345i \(-0.373729\pi\)
0.386368 + 0.922345i \(0.373729\pi\)
\(434\) 8.47473e8 + 3.08455e8i 0.497636 + 0.181125i
\(435\) −7.69701e8 1.22378e9i −0.448342 0.712836i
\(436\) 3.24527e8 + 2.72311e8i 0.187520 + 0.157348i
\(437\) −1.50824e6 + 8.55366e6i −0.000864542 + 0.00490306i
\(438\) −1.87083e8 6.01808e7i −0.106384 0.0342214i
\(439\) 2.22118e9 1.86379e9i 1.25302 1.05141i 0.256632 0.966509i \(-0.417387\pi\)
0.996389 0.0849009i \(-0.0270574\pi\)
\(440\) −1.44925e8 2.51017e8i −0.0811070 0.140481i
\(441\) −4.51394e9 + 2.04155e9i −2.50623 + 1.13351i
\(442\) 1.12637e9 1.95092e9i 0.620442 1.07464i
\(443\) 9.64813e7 + 5.47173e8i 0.0527267 + 0.299028i 0.999755 0.0221214i \(-0.00704204\pi\)
−0.947029 + 0.321149i \(0.895931\pi\)
\(444\) 1.99096e7 1.44744e8i 0.0107950 0.0784802i
\(445\) 7.25133e8 2.63927e8i 0.390083 0.141979i
\(446\) −7.91999e8 + 2.88264e8i −0.422720 + 0.153857i
\(447\) −5.66656e7 + 4.11962e8i −0.0300084 + 0.218163i
\(448\) −3.67255e8 2.08281e9i −0.192972 1.09440i
\(449\) −1.12552e9 + 1.94945e9i −0.586800 + 1.01637i 0.407849 + 0.913050i \(0.366279\pi\)
−0.994648 + 0.103317i \(0.967054\pi\)
\(450\) 3.59536e7 3.62523e8i 0.0185994 0.187539i
\(451\) 6.25070e7 + 1.08265e8i 0.0320857 + 0.0555740i
\(452\) 3.89635e8 3.26942e8i 0.198460 0.166528i
\(453\) −1.65447e9 5.32210e8i −0.836211 0.268992i
\(454\) 2.82447e8 1.60184e9i 0.141658 0.803383i
\(455\) 2.69623e9 + 2.26240e9i 1.34189 + 1.12598i
\(456\) 1.03627e9 + 1.64761e9i 0.511797 + 0.813725i
\(457\) 2.34264e9 + 8.52651e8i 1.14815 + 0.417892i 0.844850 0.535003i \(-0.179689\pi\)
0.303300 + 0.952895i \(0.401912\pi\)
\(458\) 3.38843e7 0.0164804
\(459\) −1.55503e9 + 3.57705e9i −0.750575 + 1.72655i
\(460\) 5.62417e6 0.00269405
\(461\) −2.78797e9 1.01474e9i −1.32536 0.482393i −0.420191 0.907436i \(-0.638037\pi\)
−0.905173 + 0.425043i \(0.860259\pi\)
\(462\) −4.90691e8 + 1.85767e7i −0.231506 + 0.00876437i
\(463\) 5.60744e8 + 4.70520e8i 0.262562 + 0.220315i 0.764559 0.644554i \(-0.222957\pi\)
−0.501997 + 0.864869i \(0.667401\pi\)
\(464\) −1.40870e7 + 7.98911e7i −0.00654642 + 0.0371266i
\(465\) 1.71489e8 + 7.95312e8i 0.0790952 + 0.366819i
\(466\) −1.43616e9 + 1.20508e9i −0.657432 + 0.551651i
\(467\) 1.44420e9 + 2.50142e9i 0.656172 + 1.13652i 0.981599 + 0.190955i \(0.0611586\pi\)
−0.325427 + 0.945567i \(0.605508\pi\)
\(468\) 3.79847e8 + 1.48628e9i 0.171296 + 0.670255i
\(469\) −2.90855e9 + 5.03775e9i −1.30188 + 2.25492i
\(470\) 2.79920e8 + 1.58751e9i 0.124363 + 0.705299i
\(471\) −1.79903e9 1.39708e9i −0.793352 0.616095i
\(472\) 1.14704e9 4.17489e8i 0.502091 0.182746i
\(473\) 3.84369e8 1.39899e8i 0.167007 0.0607856i
\(474\) 1.82213e9 7.42412e8i 0.785877 0.320200i
\(475\) −1.23004e8 6.97589e8i −0.0526612 0.298657i
\(476\) 2.72184e9 4.71436e9i 1.15675 2.00354i
\(477\) −7.63798e8 1.11817e9i −0.322229 0.471730i
\(478\) 1.03136e9 + 1.78637e9i 0.431931 + 0.748126i
\(479\) 6.85005e8 5.74788e8i 0.284787 0.238964i −0.489192 0.872176i \(-0.662708\pi\)
0.773979 + 0.633212i \(0.218264\pi\)
\(480\) 1.50565e9 1.36371e9i 0.621412 0.562832i
\(481\) −5.76891e7 + 3.27171e8i −0.0236367 + 0.134050i
\(482\) −3.72954e8 3.12946e8i −0.151702 0.127293i
\(483\) 1.14592e7 2.17050e7i 0.00462742 0.00876484i
\(484\) −1.42904e9 5.20129e8i −0.572910 0.208522i
\(485\) 7.42800e7 0.0295649
\(486\) 5.44279e8 + 1.42979e9i 0.215077 + 0.564995i
\(487\) 3.52797e8 0.138412 0.0692059 0.997602i \(-0.477953\pi\)
0.0692059 + 0.997602i \(0.477953\pi\)
\(488\) 2.49230e9 + 9.07123e8i 0.970803 + 0.353343i
\(489\) 1.18287e7 2.24048e7i 0.00457462 0.00866484i
\(490\) −2.75221e9 2.30938e9i −1.05681 0.886767i
\(491\) 7.79941e8 4.42327e9i 0.297356 1.68639i −0.360114 0.932908i \(-0.617262\pi\)
0.657470 0.753481i \(-0.271627\pi\)
\(492\) −4.02902e8 + 3.64920e8i −0.152518 + 0.138140i
\(493\) 3.89472e9 3.26806e9i 1.46390 1.22836i
\(494\) −8.59037e8 1.48789e9i −0.320603 0.555300i
\(495\) −2.49862e8 3.65788e8i −0.0925939 0.135554i
\(496\) 2.28267e7 3.95370e7i 0.00839956 0.0145485i
\(497\) 8.07844e8 + 4.58151e9i 0.295176 + 1.67402i
\(498\) −1.48003e9 + 6.03025e8i −0.536990 + 0.218793i
\(499\) −9.11644e6 + 3.31811e6i −0.00328453 + 0.00119547i −0.343662 0.939093i \(-0.611667\pi\)
0.340377 + 0.940289i \(0.389445\pi\)
\(500\) −1.81364e9 + 6.60112e8i −0.648868 + 0.236169i
\(501\) 1.09628e9 + 8.51339e8i 0.389483 + 0.302462i
\(502\) 5.15197e8 + 2.92183e9i 0.181765 + 1.03084i
\(503\) −2.39048e9 + 4.14042e9i −0.837522 + 1.45063i 0.0544380 + 0.998517i \(0.482663\pi\)
−0.891960 + 0.452114i \(0.850670\pi\)
\(504\) −1.36191e9 5.32895e9i −0.473852 1.85411i
\(505\) −9.87291e7 1.71004e8i −0.0341134 0.0590862i
\(506\) 1.36673e6 1.14682e6i 0.000468981 0.000393522i
\(507\) −1.16703e8 5.41234e8i −0.0397700 0.184441i
\(508\) 8.31167e7 4.71378e8i 0.0281297 0.159532i
\(509\) 3.73271e8 + 3.13212e8i 0.125462 + 0.105275i 0.703360 0.710834i \(-0.251682\pi\)
−0.577898 + 0.816109i \(0.696127\pi\)
\(510\) −2.82658e9 + 1.07009e8i −0.943552 + 0.0357211i
\(511\) 1.01470e9 + 3.69321e8i 0.336407 + 0.122442i
\(512\) −2.25448e8 −0.0742338
\(513\) 1.76960e9 + 2.39111e9i 0.578716 + 0.781968i
\(514\) 2.48233e9 0.806286
\(515\) −1.48713e9 5.41271e8i −0.479759 0.174618i
\(516\) 9.46939e8 + 1.50557e9i 0.303423 + 0.482423i
\(517\) −6.80101e8 5.70673e8i −0.216450 0.181623i
\(518\) 8.02955e7 4.55379e8i 0.0253827 0.143952i
\(519\) −1.95629e9 6.29300e8i −0.614254 0.197593i
\(520\) −2.19532e9 + 1.84209e9i −0.684677 + 0.574512i
\(521\) −8.73666e8 1.51323e9i −0.270653 0.468785i 0.698376 0.715731i \(-0.253906\pi\)
−0.969029 + 0.246946i \(0.920573\pi\)
\(522\) 1.96811e8 1.98446e9i 0.0605623 0.610654i
\(523\) 1.74434e9 3.02129e9i 0.533183 0.923500i −0.466066 0.884750i \(-0.654329\pi\)
0.999249 0.0387498i \(-0.0123375\pi\)
\(524\) 2.14732e8 + 1.21781e9i 0.0651985 + 0.369759i
\(525\) −2.72765e8 + 1.98302e9i −0.0822682 + 0.598094i
\(526\) 1.86817e9 6.79956e8i 0.559713 0.203719i
\(527\) −2.68865e9 + 9.78588e8i −0.800197 + 0.291248i
\(528\) −3.38723e6 + 2.46253e7i −0.00100144 + 0.00728053i
\(529\) −5.91226e8 3.35301e9i −0.173644 0.984782i
\(530\) 4.91012e8 8.50458e8i 0.143261 0.248135i
\(531\) 1.69978e9 7.68772e8i 0.492677 0.222826i
\(532\) −2.07584e9 3.59546e9i −0.597728 1.03530i
\(533\) 9.46855e8 7.94506e8i 0.270856 0.227275i
\(534\) 1.01330e9 + 3.25957e8i 0.287967 + 0.0926331i
\(535\) −3.07421e8 + 1.74347e9i −0.0867952 + 0.492240i
\(536\) −3.62828e9 3.04449e9i −1.01771 0.853959i
\(537\) −1.32152e9 2.10113e9i −0.368268 0.585522i
\(538\) −1.01065e9 3.67847e8i −0.279810 0.101842i
\(539\) 1.97872e9 0.544281
\(540\) 1.32581e9 1.39732e9i 0.362329 0.381871i
\(541\) −4.86477e9 −1.32091 −0.660453 0.750867i \(-0.729636\pi\)
−0.660453 + 0.750867i \(0.729636\pi\)
\(542\) 1.94994e9 + 7.09720e8i 0.526046 + 0.191465i
\(543\) 1.17048e9 4.43123e7i 0.313737 0.0118775i
\(544\) 5.47265e9 + 4.59210e9i 1.45748 + 1.22297i
\(545\) −2.10031e8 + 1.19114e9i −0.0555771 + 0.315193i
\(546\) 1.02334e9 + 4.74593e9i 0.269058 + 1.24781i
\(547\) −8.87953e8 + 7.45081e8i −0.231971 + 0.194647i −0.751363 0.659889i \(-0.770603\pi\)
0.519391 + 0.854536i \(0.326159\pi\)
\(548\) −1.59691e9 2.76593e9i −0.414523 0.717974i
\(549\) 3.90293e9 + 1.09441e9i 1.00667 + 0.282277i
\(550\) −7.27521e7 + 1.26010e8i −0.0186456 + 0.0322951i
\(551\) −6.73326e8 3.81862e9i −0.171473 0.972469i
\(552\) 1.57839e7 + 1.22573e7i 0.00399418 + 0.00310177i
\(553\) −1.01590e10 + 3.69758e9i −2.55454 + 0.929778i
\(554\) −2.04158e9 + 7.43076e8i −0.510133 + 0.185673i
\(555\) 3.86310e8 1.57399e8i 0.0959202 0.0390820i
\(556\) 1.87255e8 + 1.06198e9i 0.0462031 + 0.262031i
\(557\) 1.94696e8 3.37223e8i 0.0477379 0.0826845i −0.841169 0.540772i \(-0.818132\pi\)
0.888907 + 0.458088i \(0.151465\pi\)
\(558\) −4.86040e8 + 1.01155e9i −0.118427 + 0.246472i
\(559\) −2.02210e9 3.50239e9i −0.489623 0.848052i
\(560\) −1.89971e8 + 1.59404e8i −0.0457118 + 0.0383567i
\(561\) 1.15465e9 1.04580e9i 0.276109 0.250080i
\(562\) −3.57577e8 + 2.02792e9i −0.0849751 + 0.481918i
\(563\) 4.31316e9 + 3.61917e9i 1.01863 + 0.854731i 0.989455 0.144843i \(-0.0462678\pi\)
0.0291742 + 0.999574i \(0.490712\pi\)
\(564\) 1.80236e9 3.41387e9i 0.423024 0.801254i
\(565\) 1.36460e9 + 4.96674e8i 0.318299 + 0.115852i
\(566\) −2.02974e9 −0.470525
\(567\) −2.69125e9 7.96362e9i −0.620031 1.83472i
\(568\) −3.78790e9 −0.867319
\(569\) −5.83075e8 2.12222e8i −0.132688 0.0482945i 0.274823 0.961495i \(-0.411381\pi\)
−0.407511 + 0.913200i \(0.633603\pi\)
\(570\) −1.00718e9 + 1.90772e9i −0.227797 + 0.431472i
\(571\) 2.35721e9 + 1.97793e9i 0.529873 + 0.444616i 0.868058 0.496464i \(-0.165368\pi\)
−0.338185 + 0.941080i \(0.609813\pi\)
\(572\) 1.06396e8 6.03401e8i 0.0237705 0.134809i
\(573\) 4.03878e9 3.65804e9i 0.896827 0.812283i
\(574\) −1.31790e9 + 1.10585e9i −0.290863 + 0.244063i
\(575\) −3.63643e6 6.29849e6i −0.000797697 0.00138165i
\(576\) 2.62426e9 1.98984e8i 0.572173 0.0433850i
\(577\) −1.62416e8 + 2.81313e8i −0.0351976 + 0.0609641i −0.883088 0.469208i \(-0.844539\pi\)
0.847890 + 0.530172i \(0.177873\pi\)
\(578\) −1.24001e9 7.03245e9i −0.267102 1.51481i
\(579\) 4.58134e9 1.86663e9i 0.980885 0.399654i
\(580\) −2.35938e9 + 8.58745e8i −0.502112 + 0.182754i
\(581\) 8.25167e9 3.00336e9i 1.74552 0.635318i
\(582\) 8.09252e7 + 6.28443e7i 0.0170158 + 0.0132140i
\(583\) 9.39178e7 + 5.32634e8i 0.0196294 + 0.111324i
\(584\) −4.39605e8 + 7.61418e8i −0.0913308 + 0.158190i
\(585\) −3.13267e9 + 3.06091e9i −0.646948 + 0.632127i
\(586\) 2.54772e9 + 4.41277e9i 0.523009 + 0.905878i
\(587\) −7.37813e9 + 6.19098e9i −1.50561 + 1.26336i −0.633818 + 0.773482i \(0.718513\pi\)
−0.871792 + 0.489875i \(0.837042\pi\)
\(588\) 1.81356e9 + 8.41071e9i 0.367883 + 1.70613i
\(589\) −3.78923e8 + 2.14898e9i −0.0764095 + 0.433340i
\(590\) 1.03638e9 + 8.69627e8i 0.207748 + 0.174321i
\(591\) 5.10464e9 1.93252e8i 1.01721 0.0385095i
\(592\) −2.19958e7 8.00581e6i −0.00435726 0.00158591i
\(593\) −7.62103e9 −1.50080 −0.750399 0.660985i \(-0.770139\pi\)
−0.750399 + 0.660985i \(0.770139\pi\)
\(594\) 3.72583e7 6.09907e8i 0.00729408 0.119402i
\(595\) 1.55420e10 3.02481
\(596\) 6.78648e8 + 2.47008e8i 0.131306 + 0.0477913i
\(597\) −2.36567e8 3.76126e8i −0.0455033 0.0723474i
\(598\) −1.35130e7 1.13388e7i −0.00258404 0.00216826i
\(599\) 1.94347e8 1.10219e9i 0.0369473 0.209539i −0.960745 0.277432i \(-0.910517\pi\)
0.997693 + 0.0678933i \(0.0216278\pi\)
\(600\) −1.55151e9 4.99090e8i −0.293242 0.0943300i
\(601\) −6.41882e8 + 5.38603e8i −0.120613 + 0.101206i −0.701099 0.713064i \(-0.747307\pi\)
0.580486 + 0.814270i \(0.302863\pi\)
\(602\) 2.81450e9 + 4.87485e9i 0.525791 + 0.910696i
\(603\) −5.88107e9 4.22035e9i −1.09231 0.783859i
\(604\) −1.50919e9 + 2.61399e9i −0.278686 + 0.482698i
\(605\) −7.53955e8 4.27589e9i −0.138421 0.785024i
\(606\) 3.71155e7 2.69831e8i 0.00677487 0.0492536i
\(607\) 7.61343e9 2.77106e9i 1.38172 0.502905i 0.459020 0.888426i \(-0.348201\pi\)
0.922699 + 0.385521i \(0.125978\pi\)
\(608\) 5.11990e9 1.86349e9i 0.923845 0.336252i
\(609\) −1.49312e9 + 1.08551e10i −0.267877 + 1.94748i
\(610\) 5.10454e8 + 2.89493e9i 0.0910547 + 0.516397i
\(611\) −4.38895e9 + 7.60188e9i −0.778424 + 1.34827i
\(612\) 5.50354e9 + 3.94943e9i 0.970538 + 0.696474i
\(613\) 1.64606e9 + 2.85106e9i 0.288625 + 0.499913i 0.973482 0.228765i \(-0.0734686\pi\)
−0.684857 + 0.728678i \(0.740135\pi\)
\(614\) −2.38772e8 + 2.00353e8i −0.0416288 + 0.0349307i
\(615\) −1.47744e9 4.75263e8i −0.256123 0.0823894i
\(616\) −3.81475e8 + 2.16345e9i −0.0657557 + 0.372919i
\(617\) 7.68141e8 + 6.44547e8i 0.131657 + 0.110473i 0.706238 0.707974i \(-0.250391\pi\)
−0.574582 + 0.818447i \(0.694835\pi\)
\(618\) −1.16223e9 1.84787e9i −0.198076 0.314929i
\(619\) 2.94274e9 + 1.07107e9i 0.498694 + 0.181510i 0.579106 0.815252i \(-0.303402\pi\)
−0.0804127 + 0.996762i \(0.525624\pi\)
\(620\) 1.41299e9 0.238104
\(621\) 2.54701e7 + 1.68556e7i 0.00426785 + 0.00282438i
\(622\) −4.50103e9 −0.749973
\(623\) −5.49592e9 2.00035e9i −0.910610 0.331435i
\(624\) 2.45590e8 9.29760e6i 0.0404637 0.00153188i
\(625\) −2.76366e9 2.31898e9i −0.452798 0.379942i
\(626\) 8.21971e8 4.66163e9i 0.133920 0.759499i
\(627\) −2.50432e8 1.16143e9i −0.0405745 0.188172i
\(628\) −3.03041e9 + 2.54281e9i −0.488250 + 0.409690i
\(629\) 7.33499e8 + 1.27046e9i 0.117523 + 0.203555i
\(630\) 4.36025e9 4.26037e9i 0.694736 0.678821i
\(631\) 1.34851e9 2.33568e9i 0.213674 0.370094i −0.739188 0.673499i \(-0.764790\pi\)
0.952861 + 0.303406i \(0.0981238\pi\)
\(632\) −1.52854e9 8.66877e9i −0.240861 1.36599i
\(633\) −1.57438e9 1.22262e9i −0.246715 0.191592i
\(634\) 1.60012e8 5.82398e7i 0.0249368 0.00907627i
\(635\) 1.28416e9 4.67397e8i 0.199027 0.0724399i
\(636\) −2.17793e9 + 8.87382e8i −0.335695 + 0.136776i
\(637\) −3.39723e9 1.92666e10i −0.520759 2.95337i
\(638\) −3.98247e8 + 6.89784e8i −0.0607127 + 0.105158i
\(639\) −5.77252e9 + 4.37701e8i −0.875210 + 0.0663628i
\(640\) −1.82579e9 3.16235e9i −0.275309 0.476849i
\(641\) 6.79995e9 5.70584e9i 1.01977 0.855690i 0.0301723 0.999545i \(-0.490394\pi\)
0.989599 + 0.143855i \(0.0459499\pi\)
\(642\) −1.80998e9 + 1.63935e9i −0.269961 + 0.244512i
\(643\) −1.93274e9 + 1.09611e10i −0.286705 + 1.62599i 0.412425 + 0.910991i \(0.364682\pi\)
−0.699131 + 0.714994i \(0.746429\pi\)
\(644\) −3.26539e7 2.73999e7i −0.00481765 0.00404248i
\(645\) −2.37083e9 + 4.49062e9i −0.347890 + 0.658942i
\(646\) −7.12907e9 2.59477e9i −1.04044 0.378691i
\(647\) −6.11342e9 −0.887400 −0.443700 0.896175i \(-0.646334\pi\)
−0.443700 + 0.896175i \(0.646334\pi\)
\(648\) 6.76612e9 1.03202e9i 0.976849 0.148996i
\(649\) −7.45111e8 −0.106995
\(650\) 1.35186e9 + 4.92037e8i 0.193079 + 0.0702751i
\(651\) 2.87895e9 5.45304e9i 0.408978 0.774650i
\(652\) −3.37068e7 2.82834e7i −0.00476268 0.00399636i
\(653\) −1.52658e9 + 8.65764e9i −0.214547 + 1.21676i 0.667144 + 0.744929i \(0.267516\pi\)
−0.881691 + 0.471827i \(0.843595\pi\)
\(654\) −1.23658e9 + 1.12001e9i −0.172863 + 0.156567i
\(655\) −2.70456e9 + 2.26940e9i −0.376056 + 0.315548i
\(656\) 4.35441e7 + 7.54206e7i 0.00602235 + 0.0104310i
\(657\) −5.81947e8 + 1.21115e9i −0.0800580 + 0.166617i
\(658\) 6.10882e9 1.05808e10i 0.835924 1.44786i
\(659\) −2.67733e8 1.51839e9i −0.0364421 0.206673i 0.961150 0.276026i \(-0.0890177\pi\)
−0.997592 + 0.0693528i \(0.977907\pi\)
\(660\) −7.12469e8 + 2.90290e8i −0.0964634 + 0.0393033i
\(661\) 6.68658e9 2.43372e9i 0.900532 0.327767i 0.150066 0.988676i \(-0.452051\pi\)
0.750466 + 0.660909i \(0.229829\pi\)
\(662\) 4.35960e9 1.58676e9i 0.584042 0.212574i
\(663\) −1.21653e10 9.44723e9i −1.62116 1.25895i
\(664\) 1.24156e9 + 7.04122e9i 0.164581 + 0.933382i
\(665\) 5.92666e9 1.02653e10i 0.781510 1.35362i
\(666\) 5.54036e8 + 1.55355e8i 0.0726739 + 0.0203782i
\(667\) −1.99059e7 3.44780e7i −0.00259742 0.00449886i
\(668\) 1.84664e9 1.54951e9i 0.239698 0.201131i
\(669\) 1.21467e9 + 5.63325e9i 0.156843 + 0.727391i
\(670\) 9.11567e8 5.16975e9i 0.117092 0.664061i
\(671\) −1.24021e9 1.04066e9i −0.158477 0.132978i
\(672\) −1.53856e10 + 5.82469e8i −1.95578 + 0.0740423i
\(673\) −6.01698e9 2.19000e9i −0.760897 0.276944i −0.0677136 0.997705i \(-0.521570\pi\)
−0.693184 + 0.720761i \(0.743793\pi\)
\(674\) −6.70758e9 −0.843832
\(675\) −2.42208e9 5.81302e8i −0.303128 0.0727509i
\(676\) −9.61581e8 −0.119722
\(677\) 6.85515e9 + 2.49507e9i 0.849096 + 0.309046i 0.729672 0.683798i \(-0.239673\pi\)
0.119424 + 0.992843i \(0.461895\pi\)
\(678\) 1.06647e9 + 1.69562e9i 0.131415 + 0.208942i
\(679\) −4.31270e8 3.61878e8i −0.0528695 0.0443627i
\(680\) −2.19745e9 + 1.24624e10i −0.268002 + 1.51991i
\(681\) −1.05870e10 3.40563e9i −1.28457 0.413221i
\(682\) 3.43370e8 2.88121e8i 0.0414492 0.0347800i
\(683\) 7.93816e9 + 1.37493e10i 0.953339 + 1.65123i 0.738125 + 0.674664i \(0.235711\pi\)
0.215214 + 0.976567i \(0.430955\pi\)
\(684\) 4.70721e9 2.12897e9i 0.562429 0.254374i
\(685\) 4.55928e9 7.89690e9i 0.541975 0.938728i
\(686\) 3.00943e9 + 1.70673e10i 0.355918 + 2.01851i
\(687\) 3.15703e7 2.29518e8i 0.00371476 0.0270065i
\(688\) 2.67762e8 9.74574e7i 0.0313465 0.0114092i
\(689\) 5.02498e9 1.82894e9i 0.585284 0.213026i
\(690\) −3.01824e6 + 2.19428e7i −0.000349770 + 0.00254284i
\(691\) −8.71009e8 4.93974e9i −0.100427 0.569549i −0.992949 0.118545i \(-0.962177\pi\)
0.892522 0.451004i \(-0.148934\pi\)
\(692\) −1.78451e9 + 3.09085e9i −0.204714 + 0.354574i
\(693\) −3.31352e8 + 3.34105e9i −0.0378201 + 0.381344i
\(694\) 1.54868e9 + 2.68240e9i 0.175875 + 0.304625i
\(695\) −2.35848e9 + 1.97900e9i −0.266493 + 0.223614i
\(696\) −8.49302e9 2.73203e9i −0.954838 0.307152i
\(697\) 9.47775e8 5.37510e9i 0.106021 0.601273i
\(698\) −6.33017e9 5.31164e9i −0.704566 0.591201i
\(699\) 6.82461e9 + 1.08507e10i 0.755802 + 1.20168i
\(700\) 3.26674e9 + 1.18900e9i 0.359974 + 0.131020i
\(701\) 7.59069e9 0.832277 0.416139 0.909301i \(-0.363383\pi\)
0.416139 + 0.909301i \(0.363383\pi\)
\(702\) −6.00259e9 + 6.84357e8i −0.654875 + 0.0746626i
\(703\) 1.11882e9 0.121456
\(704\) −9.87760e8 3.59515e8i −0.106696 0.0388341i
\(705\) 1.10139e10 4.16967e8i 1.18381 0.0448167i
\(706\) 3.20138e9 + 2.68627e9i 0.342389 + 0.287299i
\(707\) −2.59877e8 + 1.47384e9i −0.0276567 + 0.156849i
\(708\) −6.82917e8 3.16716e9i −0.0723189 0.335393i
\(709\) −6.81971e9 + 5.72242e9i −0.718628 + 0.603000i −0.927005 0.375048i \(-0.877626\pi\)
0.208377 + 0.978048i \(0.433182\pi\)
\(710\) −2.09913e9 3.63580e9i −0.220108 0.381238i
\(711\) −3.33110e9 1.30340e10i −0.347571 1.35999i
\(712\) 2.38103e9 4.12407e9i 0.247221 0.428199i
\(713\) 3.89052e6 + 2.20643e7i 0.000401971 + 0.00227969i
\(714\) 1.69325e10 + 1.31493e10i 1.74091 + 1.35194i
\(715\) 1.64383e9 5.98304e8i 0.168184 0.0612140i
\(716\) −4.05088e9 + 1.47440e9i −0.412434 + 0.150114i
\(717\) 1.30611e10 5.32165e9i 1.32331 0.539174i
\(718\) −1.44365e9 8.18734e9i −0.145555 0.825481i
\(719\) −1.24267e9 + 2.15237e9i −0.124683 + 0.215957i −0.921609 0.388120i \(-0.873125\pi\)
0.796926 + 0.604077i \(0.206458\pi\)
\(720\) −1.74061e8 2.54818e8i −0.0173795 0.0254429i
\(721\) 5.99730e9 + 1.03876e10i 0.595912 + 1.03215i
\(722\) 2.51096e8 2.10695e8i 0.0248291 0.0208340i
\(723\) −2.46725e9 + 2.23466e9i −0.242789 + 0.219901i
\(724\) 3.53247e8 2.00337e9i 0.0345935 0.196189i
\(725\) 2.48722e9 + 2.08702e9i 0.242399 + 0.203397i
\(726\) 2.79619e9 5.29630e9i 0.271200 0.513682i
\(727\) 2.08124e9 + 7.57509e8i 0.200887 + 0.0731168i 0.440504 0.897751i \(-0.354800\pi\)
−0.239617 + 0.970867i \(0.577022\pi\)
\(728\) 2.17203e10 2.08644
\(729\) 1.01919e10 2.35457e9i 0.974337 0.225095i
\(730\) −9.74461e8 −0.0927116
\(731\) −1.67813e10 6.10788e9i −1.58896 0.578335i
\(732\) 3.28673e9 6.22543e9i 0.309724 0.586652i
\(733\) −6.72300e9 5.64127e9i −0.630521 0.529070i 0.270570 0.962700i \(-0.412788\pi\)
−0.901091 + 0.433631i \(0.857232\pi\)
\(734\) −4.29458e8 + 2.43558e9i −0.0400852 + 0.227335i
\(735\) −1.82071e10 + 1.64907e10i −1.69135 + 1.53191i
\(736\) 4.28536e7 3.59584e7i 0.00396200 0.00332451i
\(737\) 1.44559e9 + 2.50383e9i 0.133017 + 0.230392i
\(738\) −1.20752e9 1.76776e9i −0.110585 0.161893i
\(739\) −7.70837e9 + 1.33513e10i −0.702598 + 1.21694i 0.264954 + 0.964261i \(0.414643\pi\)
−0.967551 + 0.252674i \(0.918690\pi\)
\(740\) −1.25802e8 7.13461e8i −0.0114124 0.0647231i
\(741\) −1.08788e10 + 4.43247e9i −0.982236 + 0.400205i
\(742\) −6.99409e9 + 2.54564e9i −0.628518 + 0.228762i
\(743\) 5.62543e9 2.04749e9i 0.503147 0.183131i −0.0779619 0.996956i \(-0.524841\pi\)
0.581109 + 0.813826i \(0.302619\pi\)
\(744\) 3.96546e9 + 3.07947e9i 0.353011 + 0.274139i
\(745\) 3.58051e8 + 2.03061e9i 0.0317248 + 0.179920i
\(746\) −3.87377e9 + 6.70956e9i −0.341623 + 0.591709i
\(747\) 2.70569e9 + 1.05869e10i 0.237496 + 0.929282i
\(748\) −1.35279e9 2.34310e9i −0.118188 0.204708i
\(749\) 1.02788e10 8.62490e9i 0.893829 0.750011i
\(750\) −1.60213e9 7.43020e9i −0.138671 0.643111i
\(751\) 5.33595e8 3.02617e9i 0.0459697 0.260707i −0.953158 0.302474i \(-0.902187\pi\)
0.999127 + 0.0417666i \(0.0132986\pi\)
\(752\) −4.73777e8 3.97546e8i −0.0406267 0.0340898i
\(753\) 2.02713e10 7.67433e8i 1.73021 0.0655025i
\(754\) 7.40012e9 + 2.69342e9i 0.628694 + 0.228826i
\(755\) −8.61767e9 −0.728745