Properties

Label 27.8.e.a.4.15
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 4.15
Character \(\chi\) = 27.4
Dual form 27.8.e.a.7.15

$q$-expansion

\(f(q)\) \(=\) \(q+(9.90100 + 3.60367i) q^{2} +(7.82827 - 46.1055i) q^{3} +(-13.0104 - 10.9170i) q^{4} +(-29.9915 + 170.090i) q^{5} +(243.657 - 428.280i) q^{6} +(1223.81 - 1026.90i) q^{7} +(-763.805 - 1322.95i) q^{8} +(-2064.44 - 721.852i) q^{9} +O(q^{10})\) \(q+(9.90100 + 3.60367i) q^{2} +(7.82827 - 46.1055i) q^{3} +(-13.0104 - 10.9170i) q^{4} +(-29.9915 + 170.090i) q^{5} +(243.657 - 428.280i) q^{6} +(1223.81 - 1026.90i) q^{7} +(-763.805 - 1322.95i) q^{8} +(-2064.44 - 721.852i) q^{9} +(-909.893 + 1575.98i) q^{10} +(-790.523 - 4483.28i) q^{11} +(-605.184 + 514.390i) q^{12} +(1003.12 - 365.107i) q^{13} +(15817.6 - 5757.13i) q^{14} +(7607.30 + 2714.28i) q^{15} +(-2417.46 - 13710.1i) q^{16} +(-3552.17 + 6152.54i) q^{17} +(-17838.7 - 14586.6i) q^{18} +(28765.8 + 49823.9i) q^{19} +(2247.08 - 1885.52i) q^{20} +(-37765.5 - 64463.4i) q^{21} +(8329.28 - 47237.7i) q^{22} +(8840.13 + 7417.75i) q^{23} +(-66974.6 + 24859.2i) q^{24} +(45382.4 + 16517.8i) q^{25} +11247.6 q^{26} +(-49442.3 + 89531.0i) q^{27} -27133.0 q^{28} +(-8067.50 - 2936.33i) q^{29} +(65538.5 + 54288.3i) q^{30} +(107804. + 90458.6i) q^{31} +(-8482.76 + 48108.1i) q^{32} +(-212892. + 1351.17i) q^{33} +(-57341.7 + 48115.4i) q^{34} +(137962. + 238957. i) q^{35} +(18978.7 + 31929.1i) q^{36} +(162390. - 281268. i) q^{37} +(105262. + 596968. i) q^{38} +(-8980.72 - 49107.6i) q^{39} +(247928. - 90238.5i) q^{40} +(-792033. + 288276. i) q^{41} +(-141611. - 774346. i) q^{42} +(-80915.8 - 458896. i) q^{43} +(-38659.0 + 66959.4i) q^{44} +(184695. - 329491. i) q^{45} +(60795.0 + 105300. i) q^{46} +(559987. - 469885. i) q^{47} +(-651036. + 4131.95i) q^{48} +(300186. - 1.70244e6i) q^{49} +(389806. + 327086. i) q^{50} +(255859. + 211938. i) q^{51} +(-17036.9 - 6200.93i) q^{52} +1.20980e6 q^{53} +(-812168. + 708273. i) q^{54} +786269. q^{55} +(-2.29329e6 - 834691. i) q^{56} +(2.52234e6 - 936229. i) q^{57} +(-69294.7 - 58145.2i) q^{58} +(-303839. + 1.72316e6i) q^{59} +(-69342.2 - 118363. i) q^{60} +(41666.2 - 34962.1i) q^{61} +(741387. + 1.28412e6i) q^{62} +(-3.26776e6 + 1.23656e6i) q^{63} +(-1.14834e6 + 1.98898e6i) q^{64} +(32015.9 + 181571. i) q^{65} +(-2.11271e6 - 753815. i) q^{66} +(555568. - 202210. i) q^{67} +(113383. - 41267.9i) q^{68} +(411202. - 349511. i) q^{69} +(504838. + 2.86308e6i) q^{70} +(725420. - 1.25646e6i) q^{71} +(621853. + 3.28250e6i) q^{72} +(2.04720e6 + 3.54585e6i) q^{73} +(2.62142e6 - 2.19963e6i) q^{74} +(1.11683e6 - 1.96307e6i) q^{75} +(169673. - 962266. i) q^{76} +(-5.57133e6 - 4.67490e6i) q^{77} +(88049.5 - 518578. i) q^{78} +(-873499. - 317928. i) q^{79} +2.40446e6 q^{80} +(3.74083e6 + 2.98044e6i) q^{81} -8.88077e6 q^{82} +(4.23441e6 + 1.54120e6i) q^{83} +(-212404. + 1.25098e6i) q^{84} +(-939950. - 788712. i) q^{85} +(852563. - 4.83512e6i) q^{86} +(-198535. + 348970. i) q^{87} +(-5.32734e6 + 4.47017e6i) q^{88} +(-2.08301e6 - 3.60787e6i) q^{89} +(3.01604e6 - 2.59670e6i) q^{90} +(852706. - 1.47693e6i) q^{91} +(-34033.9 - 193016. i) q^{92} +(5.01456e6 - 4.26224e6i) q^{93} +(7.23774e6 - 2.63432e6i) q^{94} +(-9.33727e6 + 3.39849e6i) q^{95} +(2.15164e6 + 767705. i) q^{96} +(-68508.1 - 388529. i) q^{97} +(9.10717e6 - 1.57741e7i) q^{98} +(-1.60428e6 + 9.82608e6i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 9.90100 + 3.60367i 0.875133 + 0.318522i 0.740244 0.672339i \(-0.234710\pi\)
0.134889 + 0.990861i \(0.456932\pi\)
\(3\) 7.82827 46.1055i 0.167394 0.985890i
\(4\) −13.0104 10.9170i −0.101644 0.0852893i
\(5\) −29.9915 + 170.090i −0.107301 + 0.608532i 0.882976 + 0.469419i \(0.155536\pi\)
−0.990276 + 0.139114i \(0.955575\pi\)
\(6\) 243.657 428.280i 0.460520 0.809466i
\(7\) 1223.81 1026.90i 1.34857 1.13158i 0.369230 0.929338i \(-0.379621\pi\)
0.979335 0.202243i \(-0.0648230\pi\)
\(8\) −763.805 1322.95i −0.527434 0.913542i
\(9\) −2064.44 721.852i −0.943958 0.330065i
\(10\) −909.893 + 1575.98i −0.287733 + 0.498369i
\(11\) −790.523 4483.28i −0.179077 1.01560i −0.933332 0.359015i \(-0.883113\pi\)
0.754255 0.656582i \(-0.227998\pi\)
\(12\) −605.184 + 514.390i −0.101100 + 0.0859326i
\(13\) 1003.12 365.107i 0.126635 0.0460912i −0.277926 0.960603i \(-0.589647\pi\)
0.404560 + 0.914511i \(0.367425\pi\)
\(14\) 15817.6 5757.13i 1.54061 0.560735i
\(15\) 7607.30 + 2714.28i 0.581984 + 0.207652i
\(16\) −2417.46 13710.1i −0.147550 0.836799i
\(17\) −3552.17 + 6152.54i −0.175357 + 0.303727i −0.940285 0.340389i \(-0.889441\pi\)
0.764928 + 0.644116i \(0.222775\pi\)
\(18\) −17838.7 14586.6i −0.720955 0.589522i
\(19\) 28765.8 + 49823.9i 0.962142 + 1.66648i 0.717105 + 0.696965i \(0.245467\pi\)
0.245037 + 0.969514i \(0.421200\pi\)
\(20\) 2247.08 1885.52i 0.0628077 0.0527019i
\(21\) −37765.5 64463.4i −0.889872 1.51896i
\(22\) 8329.28 47237.7i 0.166774 0.945821i
\(23\) 8840.13 + 7417.75i 0.151500 + 0.127123i 0.715387 0.698728i \(-0.246250\pi\)
−0.563887 + 0.825852i \(0.690695\pi\)
\(24\) −66974.6 + 24859.2i −0.988941 + 0.367070i
\(25\) 45382.4 + 16517.8i 0.580894 + 0.211428i
\(26\) 11247.6 0.125503
\(27\) −49442.3 + 89531.0i −0.483421 + 0.875388i
\(28\) −27133.0 −0.233585
\(29\) −8067.50 2936.33i −0.0614251 0.0223569i 0.311125 0.950369i \(-0.399294\pi\)
−0.372550 + 0.928012i \(0.621516\pi\)
\(30\) 65538.5 + 54288.3i 0.443172 + 0.367098i
\(31\) 107804. + 90458.6i 0.649935 + 0.545361i 0.907051 0.421020i \(-0.138328\pi\)
−0.257116 + 0.966381i \(0.582772\pi\)
\(32\) −8482.76 + 48108.1i −0.0457628 + 0.259533i
\(33\) −212892. + 1351.17i −1.03124 + 0.00654502i
\(34\) −57341.7 + 48115.4i −0.250204 + 0.209946i
\(35\) 137962. + 238957.i 0.543902 + 0.942065i
\(36\) 18978.7 + 31929.1i 0.0677965 + 0.114059i
\(37\) 162390. 281268.i 0.527053 0.912882i −0.472450 0.881357i \(-0.656630\pi\)
0.999503 0.0315247i \(-0.0100363\pi\)
\(38\) 105262. + 596968.i 0.311191 + 1.76485i
\(39\) −8980.72 49107.6i −0.0242429 0.132563i
\(40\) 247928. 90238.5i 0.612514 0.222937i
\(41\) −792033. + 288276.i −1.79473 + 0.653229i −0.795874 + 0.605462i \(0.792988\pi\)
−0.998858 + 0.0477676i \(0.984789\pi\)
\(42\) −141611. 774346.i −0.294934 1.61273i
\(43\) −80915.8 458896.i −0.155201 0.880187i −0.958602 0.284749i \(-0.908090\pi\)
0.803401 0.595438i \(-0.203021\pi\)
\(44\) −38659.0 + 66959.4i −0.0684174 + 0.118502i
\(45\) 184695. 329491.i 0.302143 0.539013i
\(46\) 60795.0 + 105300.i 0.0920906 + 0.159506i
\(47\) 559987. 469885.i 0.786748 0.660160i −0.158191 0.987409i \(-0.550566\pi\)
0.944938 + 0.327249i \(0.106122\pi\)
\(48\) −651036. + 4131.95i −0.849691 + 0.00539276i
\(49\) 300186. 1.70244e6i 0.364506 2.06721i
\(50\) 389806. + 327086.i 0.441015 + 0.370056i
\(51\) 255859. + 211938.i 0.270087 + 0.223725i
\(52\) −17036.9 6200.93i −0.0168027 0.00611568i
\(53\) 1.20980e6 1.11622 0.558109 0.829768i \(-0.311527\pi\)
0.558109 + 0.829768i \(0.311527\pi\)
\(54\) −812168. + 708273.i −0.701888 + 0.612100i
\(55\) 786269. 0.637238
\(56\) −2.29329e6 834691.i −1.74503 0.635137i
\(57\) 2.52234e6 936229.i 1.80402 0.669607i
\(58\) −69294.7 58145.2i −0.0466339 0.0391305i
\(59\) −303839. + 1.72316e6i −0.192602 + 1.09230i 0.723190 + 0.690649i \(0.242675\pi\)
−0.915792 + 0.401652i \(0.868436\pi\)
\(60\) −69342.2 118363.i −0.0414446 0.0707435i
\(61\) 41666.2 34962.1i 0.0235033 0.0197216i −0.630960 0.775815i \(-0.717339\pi\)
0.654464 + 0.756093i \(0.272894\pi\)
\(62\) 741387. + 1.28412e6i 0.395070 + 0.684282i
\(63\) −3.26776e6 + 1.23656e6i −1.64648 + 0.623051i
\(64\) −1.14834e6 + 1.98898e6i −0.547570 + 0.948418i
\(65\) 32015.9 + 181571.i 0.0144600 + 0.0820068i
\(66\) −2.11271e6 753815.i −0.904559 0.322746i
\(67\) 555568. 202210.i 0.225671 0.0821375i −0.226710 0.973962i \(-0.572797\pi\)
0.452381 + 0.891825i \(0.350575\pi\)
\(68\) 113383. 41267.9i 0.0437286 0.0159159i
\(69\) 411202. 349511.i 0.150690 0.128082i
\(70\) 504838. + 2.86308e6i 0.175917 + 0.997677i
\(71\) 725420. 1.25646e6i 0.240539 0.416626i −0.720329 0.693633i \(-0.756009\pi\)
0.960868 + 0.277007i \(0.0893425\pi\)
\(72\) 621853. + 3.28250e6i 0.196347 + 1.03643i
\(73\) 2.04720e6 + 3.54585e6i 0.615928 + 1.06682i 0.990221 + 0.139508i \(0.0445520\pi\)
−0.374293 + 0.927310i \(0.622115\pi\)
\(74\) 2.62142e6 2.19963e6i 0.752014 0.631015i
\(75\) 1.11683e6 1.96307e6i 0.305684 0.537306i
\(76\) 169673. 962266.i 0.0443370 0.251448i
\(77\) −5.57133e6 4.67490e6i −1.39073 1.16696i
\(78\) 88049.5 518578.i 0.0210085 0.123732i
\(79\) −873499. 317928.i −0.199328 0.0725494i 0.240427 0.970667i \(-0.422712\pi\)
−0.439755 + 0.898118i \(0.644935\pi\)
\(80\) 2.40446e6 0.525051
\(81\) 3.74083e6 + 2.98044e6i 0.782114 + 0.623135i
\(82\) −8.88077e6 −1.77870
\(83\) 4.23441e6 + 1.54120e6i 0.812867 + 0.295859i 0.714808 0.699321i \(-0.246514\pi\)
0.0980596 + 0.995181i \(0.468736\pi\)
\(84\) −212404. + 1.25098e6i −0.0391008 + 0.230289i
\(85\) −939950. 788712.i −0.166012 0.139300i
\(86\) 852563. 4.83512e6i 0.144538 0.819715i
\(87\) −198535. + 348970.i −0.0323237 + 0.0568160i
\(88\) −5.32734e6 + 4.47017e6i −0.833338 + 0.699254i
\(89\) −2.08301e6 3.60787e6i −0.313203 0.542483i 0.665851 0.746085i \(-0.268069\pi\)
−0.979054 + 0.203602i \(0.934735\pi\)
\(90\) 3.01604e6 2.59670e6i 0.436102 0.375469i
\(91\) 852706. 1.47693e6i 0.118619 0.205454i
\(92\) −34033.9 193016.i −0.00455674 0.0258426i
\(93\) 5.01456e6 4.26224e6i 0.646461 0.549474i
\(94\) 7.23774e6 2.63432e6i 0.898784 0.327131i
\(95\) −9.33727e6 + 3.39849e6i −1.11734 + 0.406680i
\(96\) 2.15164e6 + 767705.i 0.248211 + 0.0885615i
\(97\) −68508.1 388529.i −0.00762151 0.0432237i 0.980760 0.195218i \(-0.0625415\pi\)
−0.988381 + 0.151994i \(0.951430\pi\)
\(98\) 9.10717e6 1.57741e7i 0.977444 1.69298i
\(99\) −1.60428e6 + 9.82608e6i −0.166172 + 1.01779i
\(100\) −410117. 710344.i −0.0410117 0.0710344i
\(101\) −1.44489e7 + 1.21240e7i −1.39543 + 1.17091i −0.432351 + 0.901706i \(0.642316\pi\)
−0.963084 + 0.269203i \(0.913240\pi\)
\(102\) 1.76950e6 + 3.02043e6i 0.165101 + 0.281818i
\(103\) 814958. 4.62186e6i 0.0734861 0.416760i −0.925766 0.378097i \(-0.876579\pi\)
0.999252 0.0386638i \(-0.0123102\pi\)
\(104\) −1.24921e6 1.04821e6i −0.108898 0.0913759i
\(105\) 1.20972e7 4.49018e6i 1.01982 0.378531i
\(106\) 1.19783e7 + 4.35973e6i 0.976839 + 0.355540i
\(107\) 4.22414e6 0.333346 0.166673 0.986012i \(-0.446698\pi\)
0.166673 + 0.986012i \(0.446698\pi\)
\(108\) 1.62068e6 625072.i 0.123798 0.0477471i
\(109\) −1.65129e7 −1.22132 −0.610661 0.791893i \(-0.709096\pi\)
−0.610661 + 0.791893i \(0.709096\pi\)
\(110\) 7.78485e6 + 2.83345e6i 0.557668 + 0.202975i
\(111\) −1.16968e7 9.68893e6i −0.811776 0.672427i
\(112\) −1.70375e7 1.42961e7i −1.14589 0.961513i
\(113\) 1.35059e6 7.65956e6i 0.0880537 0.499378i −0.908602 0.417663i \(-0.862849\pi\)
0.996656 0.0817146i \(-0.0260396\pi\)
\(114\) 2.83475e7 179914.i 1.79204 0.0113736i
\(115\) −1.52681e6 + 1.28115e6i −0.0936146 + 0.0785520i
\(116\) 72905.4 + 126276.i 0.00433667 + 0.00751134i
\(117\) −2.33444e6 + 29633.3i −0.134751 + 0.00171052i
\(118\) −9.21799e6 + 1.59660e7i −0.516475 + 0.894561i
\(119\) 1.97086e6 + 1.11773e7i 0.107211 + 0.608026i
\(120\) −2.21964e6 1.21373e7i −0.117260 0.641190i
\(121\) −1.16289e6 + 423256.i −0.0596745 + 0.0217197i
\(122\) 538529. 196008.i 0.0268503 0.00977271i
\(123\) 7.09089e6 + 3.87738e7i 0.343584 + 1.87876i
\(124\) −415039. 2.35380e6i −0.0195485 0.110865i
\(125\) −1.09172e7 + 1.89092e7i −0.499951 + 0.865941i
\(126\) −3.68102e7 + 467268.i −1.63935 + 0.0208098i
\(127\) −9.35270e6 1.61993e7i −0.405157 0.701753i 0.589182 0.808000i \(-0.299450\pi\)
−0.994340 + 0.106247i \(0.966117\pi\)
\(128\) −1.37473e7 + 1.15354e7i −0.579407 + 0.486180i
\(129\) −2.17911e7 + 138302.i −0.893747 + 0.00567237i
\(130\) −337333. + 1.91311e6i −0.0134666 + 0.0763727i
\(131\) −6.59189e6 5.53126e6i −0.256189 0.214968i 0.505643 0.862743i \(-0.331255\pi\)
−0.761832 + 0.647775i \(0.775700\pi\)
\(132\) 2.78456e6 + 2.30657e6i 0.105378 + 0.0872887i
\(133\) 8.63682e7 + 3.14355e7i 3.18327 + 1.15861i
\(134\) 6.22938e6 0.223655
\(135\) −1.37455e7 1.10948e7i −0.480830 0.388107i
\(136\) 1.08527e7 0.369956
\(137\) 3.41536e7 + 1.24309e7i 1.13479 + 0.413029i 0.840028 0.542543i \(-0.182538\pi\)
0.294759 + 0.955572i \(0.404761\pi\)
\(138\) 5.33083e6 1.97867e6i 0.172670 0.0640909i
\(139\) 1.28789e7 + 1.08067e7i 0.406749 + 0.341303i 0.823095 0.567903i \(-0.192245\pi\)
−0.416347 + 0.909206i \(0.636690\pi\)
\(140\) 813758. 4.61505e6i 0.0250638 0.142144i
\(141\) −1.72806e7 2.94969e7i −0.519147 0.886154i
\(142\) 1.17103e7 9.82608e6i 0.343208 0.287986i
\(143\) −2.42987e6 4.20865e6i −0.0694874 0.120356i
\(144\) −4.90598e6 + 3.00487e7i −0.136917 + 0.838604i
\(145\) 741396. 1.28414e6i 0.0201959 0.0349802i
\(146\) 7.49123e6 + 4.24849e7i 0.199213 + 1.12979i
\(147\) −7.61419e7 2.71674e7i −1.97703 0.705403i
\(148\) −5.18338e6 + 1.88659e6i −0.131431 + 0.0478368i
\(149\) −1.56118e7 + 5.68223e6i −0.386635 + 0.140724i −0.528022 0.849231i \(-0.677066\pi\)
0.141387 + 0.989954i \(0.454844\pi\)
\(150\) 1.81320e7 1.54117e7i 0.438658 0.372847i
\(151\) 2.03732e6 + 1.15542e7i 0.0481549 + 0.273100i 0.999372 0.0354208i \(-0.0112771\pi\)
−0.951218 + 0.308521i \(0.900166\pi\)
\(152\) 4.39430e7 7.61115e7i 1.01493 1.75791i
\(153\) 1.17745e7 1.01374e7i 0.265779 0.228826i
\(154\) −3.83150e7 6.63634e7i −0.845368 1.46422i
\(155\) −1.86193e7 + 1.56234e7i −0.401608 + 0.336989i
\(156\) −419266. + 736953.i −0.00884207 + 0.0155419i
\(157\) 1.27748e7 7.24496e7i 0.263455 1.49413i −0.509945 0.860207i \(-0.670334\pi\)
0.773400 0.633919i \(-0.218555\pi\)
\(158\) −7.50281e6 6.29560e6i −0.151330 0.126981i
\(159\) 9.47066e6 5.57786e7i 0.186849 1.10047i
\(160\) −7.92830e6 2.88566e6i −0.153024 0.0556962i
\(161\) 1.84360e7 0.348157
\(162\) 2.62974e7 + 4.29900e7i 0.485971 + 0.794447i
\(163\) −6.76637e6 −0.122377 −0.0611884 0.998126i \(-0.519489\pi\)
−0.0611884 + 0.998126i \(0.519489\pi\)
\(164\) 1.34518e7 + 4.89605e6i 0.238137 + 0.0866747i
\(165\) 6.15512e6 3.62513e7i 0.106670 0.628247i
\(166\) 3.63709e7 + 3.05188e7i 0.617129 + 0.517833i
\(167\) 7.48420e6 4.24450e7i 0.124348 0.705211i −0.857346 0.514741i \(-0.827888\pi\)
0.981693 0.190469i \(-0.0610009\pi\)
\(168\) −5.64364e7 + 9.91993e7i −0.918283 + 1.61408i
\(169\) −4.71952e7 + 3.96015e7i −0.752133 + 0.631114i
\(170\) −6.46419e6 1.11963e7i −0.100912 0.174785i
\(171\) −2.34197e7 1.23623e8i −0.358175 1.89066i
\(172\) −3.95703e6 + 6.85378e6i −0.0592953 + 0.102702i
\(173\) 1.65870e7 + 9.40694e7i 0.243560 + 1.38130i 0.823813 + 0.566861i \(0.191842\pi\)
−0.580253 + 0.814436i \(0.697046\pi\)
\(174\) −3.22327e6 + 2.73969e6i −0.0463846 + 0.0394257i
\(175\) 7.25017e7 2.63885e7i 1.02262 0.372204i
\(176\) −5.95552e7 + 2.16763e7i −0.823427 + 0.299703i
\(177\) 7.70685e7 + 2.74980e7i 1.04465 + 0.372730i
\(178\) −7.62226e6 4.32280e7i −0.101301 0.574507i
\(179\) −5.17733e7 + 8.96740e7i −0.674715 + 1.16864i 0.301837 + 0.953359i \(0.402400\pi\)
−0.976552 + 0.215281i \(0.930933\pi\)
\(180\) −6.00002e6 + 2.27048e6i −0.0766829 + 0.0290178i
\(181\) 5.81140e7 + 1.00656e8i 0.728460 + 1.26173i 0.957534 + 0.288321i \(0.0930970\pi\)
−0.229074 + 0.973409i \(0.573570\pi\)
\(182\) 1.37650e7 1.15502e7i 0.169249 0.142017i
\(183\) −1.28577e6 2.19473e6i −0.0155090 0.0264730i
\(184\) 3.06117e6 1.73608e7i 0.0362264 0.205450i
\(185\) 4.29706e7 + 3.60566e7i 0.498965 + 0.418681i
\(186\) 6.50088e7 2.41296e7i 0.740759 0.274951i
\(187\) 3.03916e7 + 1.10616e7i 0.339866 + 0.123701i
\(188\) −1.24154e7 −0.136273
\(189\) 3.14314e7 + 1.60342e8i 0.338647 + 1.72755i
\(190\) −1.04695e8 −1.10736
\(191\) −1.30673e8 4.75609e7i −1.35696 0.493894i −0.441848 0.897090i \(-0.645677\pi\)
−0.915113 + 0.403196i \(0.867899\pi\)
\(192\) 8.27133e7 + 6.85149e7i 0.843376 + 0.698603i
\(193\) −7.78121e7 6.52921e7i −0.779106 0.653748i 0.163917 0.986474i \(-0.447587\pi\)
−0.943023 + 0.332726i \(0.892031\pi\)
\(194\) 721831. 4.09370e6i 0.00709789 0.0402541i
\(195\) 8.62206e6 54721.9i 0.0832703 0.000528494i
\(196\) −2.24911e7 + 1.88723e7i −0.213361 + 0.179031i
\(197\) 1.40093e6 + 2.42649e6i 0.0130553 + 0.0226124i 0.872479 0.488651i \(-0.162511\pi\)
−0.859424 + 0.511264i \(0.829178\pi\)
\(198\) −5.12939e7 + 9.15067e7i −0.469610 + 0.837770i
\(199\) −4.95791e7 + 8.58736e7i −0.445978 + 0.772456i −0.998120 0.0612940i \(-0.980477\pi\)
0.552142 + 0.833750i \(0.313811\pi\)
\(200\) −1.28110e7 7.26550e7i −0.113235 0.642186i
\(201\) −4.97387e6 2.71977e7i −0.0432025 0.236236i
\(202\) −1.86749e8 + 6.79712e7i −1.59415 + 0.580223i
\(203\) −1.28884e7 + 4.69101e6i −0.108134 + 0.0393577i
\(204\) −1.01509e6 5.55062e6i −0.00837140 0.0457758i
\(205\) −2.52787e7 1.43363e8i −0.204935 1.16225i
\(206\) 2.47245e7 4.28242e7i 0.197058 0.341314i
\(207\) −1.28954e7 2.16947e7i −0.101050 0.170004i
\(208\) −7.43066e6 1.28703e7i −0.0572540 0.0991669i
\(209\) 2.00634e8 1.68352e8i 1.52017 1.27558i
\(210\) 1.35956e8 862874.i 1.01305 0.00642954i
\(211\) −1.59342e7 + 9.03674e7i −0.116773 + 0.662252i 0.869084 + 0.494664i \(0.164709\pi\)
−0.985857 + 0.167588i \(0.946402\pi\)
\(212\) −1.57400e7 1.32075e7i −0.113457 0.0952014i
\(213\) −5.22512e7 4.32818e7i −0.370482 0.306886i
\(214\) 4.18232e7 + 1.52224e7i 0.291722 + 0.106178i
\(215\) 8.04804e7 0.552275
\(216\) 1.56209e8 2.97458e6i 1.05468 0.0200834i
\(217\) 2.24824e8 1.49360
\(218\) −1.63494e8 5.95069e7i −1.06882 0.389018i
\(219\) 1.79509e8 6.66292e7i 1.15487 0.428658i
\(220\) −1.02297e7 8.58372e6i −0.0647713 0.0543496i
\(221\) −1.31693e6 + 7.46867e6i −0.00820709 + 0.0465447i
\(222\) −8.08941e7 1.38081e8i −0.496228 0.847032i
\(223\) −2.26700e8 + 1.90224e8i −1.36894 + 1.14868i −0.395830 + 0.918324i \(0.629543\pi\)
−0.973108 + 0.230351i \(0.926012\pi\)
\(224\) 3.90210e7 + 6.75863e7i 0.231969 + 0.401782i
\(225\) −8.17656e7 6.68594e7i −0.478555 0.391312i
\(226\) 4.09746e7 7.09702e7i 0.236122 0.408975i
\(227\) −4.70983e7 2.67107e8i −0.267248 1.51564i −0.762557 0.646921i \(-0.776056\pi\)
0.495309 0.868717i \(-0.335055\pi\)
\(228\) −4.30375e7 1.53558e7i −0.240478 0.0858024i
\(229\) 1.89940e8 6.91326e7i 1.04518 0.380416i 0.238341 0.971181i \(-0.423396\pi\)
0.806844 + 0.590765i \(0.201174\pi\)
\(230\) −1.97338e7 + 7.18252e6i −0.106946 + 0.0389251i
\(231\) −2.59153e8 + 2.20273e8i −1.38329 + 1.17576i
\(232\) 2.27738e6 + 1.29157e7i 0.0119737 + 0.0679062i
\(233\) 1.98574e7 3.43940e7i 0.102844 0.178130i −0.810012 0.586414i \(-0.800539\pi\)
0.912855 + 0.408284i \(0.133873\pi\)
\(234\) −2.32200e7 8.11913e6i −0.118470 0.0414242i
\(235\) 6.31279e7 + 1.09341e8i 0.317310 + 0.549597i
\(236\) 2.27648e7 1.91019e7i 0.112738 0.0945988i
\(237\) −2.14962e7 + 3.77843e7i −0.104892 + 0.184371i
\(238\) −2.07658e7 + 1.17769e8i −0.0998456 + 0.566252i
\(239\) 1.72682e7 + 1.44898e7i 0.0818193 + 0.0686545i 0.682780 0.730624i \(-0.260771\pi\)
−0.600961 + 0.799279i \(0.705215\pi\)
\(240\) 1.88227e7 1.10859e8i 0.0878907 0.517643i
\(241\) −1.01199e8 3.68335e7i −0.465712 0.169505i 0.0984969 0.995137i \(-0.468597\pi\)
−0.564209 + 0.825632i \(0.690819\pi\)
\(242\) −1.30390e7 −0.0591413
\(243\) 1.66699e8 1.49141e8i 0.745264 0.666769i
\(244\) −923776. −0.00407101
\(245\) 2.80565e8 + 1.02117e8i 1.21885 + 0.443627i
\(246\) −6.95210e7 + 4.09452e8i −0.297744 + 1.75360i
\(247\) 4.70467e7 + 3.94768e7i 0.198650 + 0.166688i
\(248\) 3.73306e7 2.11712e8i 0.155412 0.881385i
\(249\) 1.04206e8 1.83165e8i 0.427754 0.751872i
\(250\) −1.76234e8 + 1.47878e8i −0.713345 + 0.598568i
\(251\) −4.55818e7 7.89499e7i −0.181942 0.315133i 0.760600 0.649221i \(-0.224905\pi\)
−0.942542 + 0.334088i \(0.891572\pi\)
\(252\) 5.60144e7 + 1.95860e7i 0.220494 + 0.0770983i
\(253\) 2.62675e7 4.54967e7i 0.101976 0.176627i
\(254\) −3.42239e7 1.94094e8i −0.131042 0.743179i
\(255\) −4.37222e7 + 3.71626e7i −0.165124 + 0.140351i
\(256\) 9.85633e7 3.58741e7i 0.367177 0.133641i
\(257\) −3.31261e8 + 1.20569e8i −1.21732 + 0.443068i −0.869237 0.494396i \(-0.835389\pi\)
−0.348082 + 0.937464i \(0.613167\pi\)
\(258\) −2.16252e8 7.71585e7i −0.783954 0.279714i
\(259\) −9.00993e7 5.10979e8i −0.322235 1.82748i
\(260\) 1.56568e6 2.71183e6i 0.00552453 0.00956877i
\(261\) 1.45352e7 + 1.18854e7i 0.0506035 + 0.0413783i
\(262\) −4.53335e7 7.85199e7i −0.155727 0.269728i
\(263\) −3.94273e8 + 3.30834e8i −1.33645 + 1.12141i −0.353923 + 0.935274i \(0.615153\pi\)
−0.982524 + 0.186138i \(0.940403\pi\)
\(264\) 1.64396e8 + 2.80614e8i 0.549891 + 0.938631i
\(265\) −3.62838e7 + 2.05775e8i −0.119771 + 0.679255i
\(266\) 7.41848e8 + 6.22485e8i 2.41674 + 2.02788i
\(267\) −1.82649e8 + 6.77947e7i −0.587257 + 0.217975i
\(268\) −9.43570e6 3.43431e6i −0.0299435 0.0108985i
\(269\) −2.27462e8 −0.712484 −0.356242 0.934394i \(-0.615942\pi\)
−0.356242 + 0.934394i \(0.615942\pi\)
\(270\) −9.61120e7 1.59384e8i −0.297170 0.492800i
\(271\) 2.54368e8 0.776372 0.388186 0.921581i \(-0.373102\pi\)
0.388186 + 0.921581i \(0.373102\pi\)
\(272\) 9.29392e7 + 3.38271e7i 0.280032 + 0.101923i
\(273\) −6.14194e7 5.08763e7i −0.182699 0.151337i
\(274\) 2.93358e8 + 2.46156e8i 0.861530 + 0.722910i
\(275\) 3.81782e7 2.16519e8i 0.110701 0.627816i
\(276\) −9.16552e6 + 58171.1i −0.0262407 + 0.000166543i
\(277\) 2.44507e8 2.05165e8i 0.691212 0.579996i −0.228046 0.973650i \(-0.573234\pi\)
0.919259 + 0.393654i \(0.128789\pi\)
\(278\) 8.85701e7 + 1.53408e8i 0.247247 + 0.428244i
\(279\) −1.57257e8 2.64565e8i −0.433507 0.729319i
\(280\) 2.10752e8 3.65033e8i 0.573744 0.993754i
\(281\) −2.54207e7 1.44168e8i −0.0683463 0.387611i −0.999723 0.0235530i \(-0.992502\pi\)
0.931376 0.364058i \(-0.118609\pi\)
\(282\) −6.47978e7 3.54322e8i −0.172063 0.940862i
\(283\) −3.14891e8 + 1.14611e8i −0.825862 + 0.300589i −0.720159 0.693809i \(-0.755931\pi\)
−0.105703 + 0.994398i \(0.533709\pi\)
\(284\) −2.31549e7 + 8.42768e6i −0.0599830 + 0.0218320i
\(285\) 8.35944e7 + 4.57104e8i 0.213905 + 1.16966i
\(286\) −8.89151e6 5.04262e7i −0.0224747 0.127460i
\(287\) −6.73269e8 + 1.16614e9i −1.68113 + 2.91181i
\(288\) 5.22391e7 9.31928e7i 0.128861 0.229884i
\(289\) 1.79934e8 + 3.11654e8i 0.438500 + 0.759504i
\(290\) 1.19682e7 1.00425e7i 0.0288160 0.0241795i
\(291\) −1.84496e7 + 117095.i −0.0438897 + 0.000278556i
\(292\) 1.20753e7 6.84823e7i 0.0283829 0.160967i
\(293\) 4.67810e8 + 3.92539e8i 1.08651 + 0.911689i 0.996445 0.0842472i \(-0.0268485\pi\)
0.0900636 + 0.995936i \(0.471293\pi\)
\(294\) −6.55978e8 5.43374e8i −1.50548 1.24705i
\(295\) −2.83979e8 1.03360e8i −0.644034 0.234409i
\(296\) −4.96138e8 −1.11194
\(297\) 4.40478e8 + 1.50887e8i 0.975610 + 0.334199i
\(298\) −1.75049e8 −0.383180
\(299\) 1.15760e7 + 4.21332e6i 0.0250443 + 0.00911539i
\(300\) −3.59613e7 + 1.33479e7i −0.0768973 + 0.0285423i
\(301\) −5.70267e8 4.78511e8i −1.20530 1.01137i
\(302\) −2.14661e7 + 1.21740e8i −0.0448465 + 0.254337i
\(303\) 4.45876e8 + 7.61083e8i 0.920799 + 1.57175i
\(304\) 6.13550e8 5.14830e8i 1.25254 1.05101i
\(305\) 4.69707e6 + 8.13557e6i 0.00947933 + 0.0164187i
\(306\) 1.53111e8 5.79390e7i 0.305478 0.115597i
\(307\) 2.76433e8 4.78796e8i 0.545263 0.944423i −0.453328 0.891344i \(-0.649763\pi\)
0.998590 0.0530789i \(-0.0169035\pi\)
\(308\) 2.14493e7 + 1.21645e8i 0.0418297 + 0.237228i
\(309\) −2.06713e8 7.37552e7i −0.398579 0.142213i
\(310\) −2.40651e8 + 8.75899e7i −0.458799 + 0.166989i
\(311\) 5.06358e8 1.84299e8i 0.954544 0.347426i 0.182651 0.983178i \(-0.441532\pi\)
0.771893 + 0.635752i \(0.219310\pi\)
\(312\) −5.81074e7 + 4.93897e7i −0.108315 + 0.0920652i
\(313\) 6.38469e7 + 3.62094e8i 0.117689 + 0.667446i 0.985384 + 0.170349i \(0.0544895\pi\)
−0.867695 + 0.497097i \(0.834399\pi\)
\(314\) 3.87568e8 6.71287e8i 0.706470 1.22364i
\(315\) −1.12322e8 5.92899e8i −0.202477 1.06879i
\(316\) 7.89376e6 + 1.36724e7i 0.0140727 + 0.0243747i
\(317\) 4.46029e8 3.74263e8i 0.786422 0.659886i −0.158435 0.987369i \(-0.550645\pi\)
0.944857 + 0.327483i \(0.106200\pi\)
\(318\) 2.94776e8 5.18134e8i 0.514041 0.903540i
\(319\) −6.78683e6 + 3.84900e7i −0.0117058 + 0.0663867i
\(320\) −3.03865e8 2.54973e8i −0.518389 0.434980i
\(321\) 3.30677e7 1.94756e8i 0.0558002 0.328642i
\(322\) 1.82534e8 + 6.64371e7i 0.304684 + 0.110896i
\(323\) −4.08724e8 −0.674872
\(324\) −1.61322e7 7.96154e7i −0.0263503 0.130044i
\(325\) 5.15549e7 0.0833063
\(326\) −6.69938e7 2.43837e7i −0.107096 0.0389797i
\(327\) −1.29267e8 + 7.61334e8i −0.204442 + 1.20409i
\(328\) 9.86334e8 + 8.27633e8i 1.54335 + 1.29503i
\(329\) 2.02794e8 1.15010e9i 0.313957 1.78054i
\(330\) 1.91580e8 3.36743e8i 0.293461 0.515822i
\(331\) 3.73033e7 3.13012e7i 0.0565391 0.0474420i −0.614080 0.789244i \(-0.710473\pi\)
0.670619 + 0.741802i \(0.266028\pi\)
\(332\) −3.82661e7 6.62788e7i −0.0573893 0.0994011i
\(333\) −5.38279e8 + 4.63439e8i −0.798826 + 0.687761i
\(334\) 2.27059e8 3.93277e8i 0.333446 0.577545i
\(335\) 1.77316e7 + 1.00561e8i 0.0257687 + 0.146141i
\(336\) −7.92504e8 + 6.73607e8i −1.13976 + 0.968766i
\(337\) −4.31611e8 + 1.57093e8i −0.614310 + 0.223591i −0.630388 0.776280i \(-0.717104\pi\)
0.0160781 + 0.999871i \(0.494882\pi\)
\(338\) −6.09990e8 + 2.22018e8i −0.859240 + 0.312738i
\(339\) −3.42575e8 1.22231e8i −0.477592 0.170404i
\(340\) 3.61875e6 + 2.05229e7i 0.00499323 + 0.0283180i
\(341\) 3.20329e8 5.54826e8i 0.437478 0.757734i
\(342\) 2.13617e8 1.30839e9i 0.288765 1.76866i
\(343\) −7.23030e8 1.25232e9i −0.967446 1.67567i
\(344\) −5.45293e8 + 4.57555e8i −0.722229 + 0.606022i
\(345\) 4.71157e7 + 8.04237e7i 0.0617730 + 0.105443i
\(346\) −1.74767e8 + 9.91155e8i −0.226827 + 1.28640i
\(347\) 5.93836e8 + 4.98288e8i 0.762981 + 0.640217i 0.938901 0.344188i \(-0.111846\pi\)
−0.175920 + 0.984404i \(0.556290\pi\)
\(348\) 6.39274e6 2.37282e6i 0.00813129 0.00301813i
\(349\) 3.37732e7 + 1.22924e7i 0.0425288 + 0.0154792i 0.363197 0.931712i \(-0.381685\pi\)
−0.320668 + 0.947192i \(0.603907\pi\)
\(350\) 8.12935e8 1.01349
\(351\) −1.69083e7 + 1.07862e8i −0.0208702 + 0.133136i
\(352\) 2.22388e8 0.271776
\(353\) −6.35785e8 2.31407e8i −0.769306 0.280004i −0.0725997 0.997361i \(-0.523130\pi\)
−0.696706 + 0.717357i \(0.745352\pi\)
\(354\) 6.63961e8 + 5.49986e8i 0.795483 + 0.658932i
\(355\) 1.91956e8 + 1.61070e8i 0.227720 + 0.191080i
\(356\) −1.22865e7 + 6.96801e7i −0.0144329 + 0.0818529i
\(357\) 5.30763e8 3.36861e6i 0.617393 0.00391843i
\(358\) −8.35763e8 + 7.01288e8i −0.962703 + 0.807804i
\(359\) −2.25184e8 3.90030e8i −0.256866 0.444905i 0.708535 0.705676i \(-0.249357\pi\)
−0.965401 + 0.260771i \(0.916023\pi\)
\(360\) −5.76971e8 + 7.32405e6i −0.651771 + 0.00827356i
\(361\) −1.20801e9 + 2.09233e9i −1.35143 + 2.34075i
\(362\) 2.12654e8 + 1.20602e9i 0.235610 + 1.33621i
\(363\) 1.04111e7 + 5.69288e7i 0.0114241 + 0.0624682i
\(364\) −2.72177e7 + 9.90645e6i −0.0295799 + 0.0107662i
\(365\) −6.64512e8 + 2.41863e8i −0.715283 + 0.260342i
\(366\) −4.82132e6 2.63635e7i −0.00514023 0.0281074i
\(367\) 2.54577e8 + 1.44378e9i 0.268836 + 1.52465i 0.757885 + 0.652389i \(0.226233\pi\)
−0.489048 + 0.872257i \(0.662656\pi\)
\(368\) 8.03275e7 1.39131e8i 0.0840228 0.145532i
\(369\) 1.84320e9 2.33975e7i 1.90976 0.0242425i
\(370\) 2.95516e8 + 5.11848e8i 0.303301 + 0.525333i
\(371\) 1.48057e9 1.24235e9i 1.50529 1.26309i
\(372\) −1.11772e8 + 709389.i −0.112573 + 0.000714471i
\(373\) 1.80892e8 1.02589e9i 0.180484 1.02358i −0.751137 0.660146i \(-0.770494\pi\)
0.931621 0.363430i \(-0.118394\pi\)
\(374\) 2.61045e8 + 2.19042e8i 0.258026 + 0.216510i
\(375\) 7.86356e8 + 6.51371e8i 0.770034 + 0.637851i
\(376\) −1.04936e9 3.81934e8i −1.01804 0.370536i
\(377\) −9.16476e6 −0.00880900
\(378\) −2.66616e8 + 1.70081e9i −0.253902 + 1.61970i
\(379\) 1.91996e7 0.0181157 0.00905783 0.999959i \(-0.497117\pi\)
0.00905783 + 0.999959i \(0.497117\pi\)
\(380\) 1.58583e8 + 5.77195e7i 0.148257 + 0.0539610i
\(381\) −8.20095e8 + 3.04398e8i −0.759673 + 0.281971i
\(382\) −1.12239e9 9.41801e8i −1.03021 0.864445i
\(383\) 3.24353e8 1.83950e9i 0.295000 1.67303i −0.372201 0.928152i \(-0.621397\pi\)
0.667201 0.744878i \(-0.267492\pi\)
\(384\) 4.24227e8 + 7.24130e8i 0.382331 + 0.652615i
\(385\) 9.62247e8 8.07421e8i 0.859358 0.721087i
\(386\) −5.35126e8 9.26866e8i −0.473588 0.820278i
\(387\) −1.64210e8 + 1.00577e9i −0.144016 + 0.882086i
\(388\) −3.35026e6 + 5.80282e6i −0.00291184 + 0.00504346i
\(389\) −1.21739e8 6.90419e8i −0.104860 0.594688i −0.991276 0.131800i \(-0.957924\pi\)
0.886417 0.462888i \(-0.153187\pi\)
\(390\) 8.55642e7 + 3.05292e7i 0.0730409 + 0.0260609i
\(391\) −7.70397e7 + 2.80401e7i −0.0651772 + 0.0237226i
\(392\) −2.48153e9 + 9.03202e8i −2.08074 + 0.757327i
\(393\) −3.06624e8 + 2.60622e8i −0.254820 + 0.216590i
\(394\) 5.12638e6 + 2.90732e7i 0.00422254 + 0.0239472i
\(395\) 8.02738e7 1.39038e8i 0.0655367 0.113513i
\(396\) 1.28144e8 1.10327e8i 0.103697 0.0892791i
\(397\) 2.60613e8 + 4.51394e8i 0.209040 + 0.362067i 0.951412 0.307920i \(-0.0996329\pi\)
−0.742373 + 0.669987i \(0.766300\pi\)
\(398\) −8.00343e8 + 6.71567e8i −0.636334 + 0.533948i
\(399\) 2.12546e9 3.73596e9i 1.67513 2.94441i
\(400\) 1.16751e8 6.62129e8i 0.0912118 0.517288i
\(401\) 5.01464e8 + 4.20778e8i 0.388360 + 0.325872i 0.815974 0.578089i \(-0.196201\pi\)
−0.427614 + 0.903961i \(0.640646\pi\)
\(402\) 4.87652e7 2.87209e8i 0.0374385 0.220499i
\(403\) 1.41168e8 + 5.13809e7i 0.107441 + 0.0391052i
\(404\) 3.20344e8 0.241703
\(405\) −6.19135e8 + 5.46890e8i −0.463119 + 0.409079i
\(406\) −1.44513e8 −0.107168
\(407\) −1.38938e9 5.05692e8i −1.02150 0.371797i
\(408\) 8.49576e7 5.00368e8i 0.0619286 0.364736i
\(409\) −1.11904e9 9.38989e8i −0.808752 0.678623i 0.141558 0.989930i \(-0.454789\pi\)
−0.950310 + 0.311307i \(0.899233\pi\)
\(410\) 2.66347e8 1.51053e9i 0.190855 1.08239i
\(411\) 8.40496e8 1.47736e9i 0.597158 1.04964i
\(412\) −6.10599e7 + 5.12353e7i −0.0430146 + 0.0360935i
\(413\) 1.39767e9 + 2.42083e9i 0.976291 + 1.69099i
\(414\) −4.94963e7 2.61270e8i −0.0342825 0.180963i
\(415\) −3.89139e8 + 6.74008e8i −0.267261 + 0.462910i
\(416\) 9.05535e6 + 5.13554e7i 0.00616707 + 0.0349752i
\(417\) 5.99066e8 5.09190e8i 0.404574 0.343877i
\(418\) 2.59316e9 9.43834e8i 1.73665 0.632089i
\(419\) −8.89592e7 + 3.23785e7i −0.0590802 + 0.0215034i −0.371391 0.928476i \(-0.621119\pi\)
0.312311 + 0.949980i \(0.398897\pi\)
\(420\) −2.06409e8 7.36466e7i −0.135943 0.0485043i
\(421\) −1.37002e8 7.76979e8i −0.0894831 0.507484i −0.996299 0.0859566i \(-0.972605\pi\)
0.906816 0.421527i \(-0.138506\pi\)
\(422\) −4.83418e8 + 8.37305e8i −0.313134 + 0.542363i
\(423\) −1.49524e9 + 5.65819e8i −0.960552 + 0.363485i
\(424\) −9.24054e8 1.60051e9i −0.588731 1.01971i
\(425\) −2.62833e8 + 2.20543e8i −0.166080 + 0.139358i
\(426\) −3.61365e8 6.16829e8i −0.226471 0.386573i
\(427\) 1.50890e7 8.55741e7i 0.00937916 0.0531918i
\(428\) −5.49577e7 4.61150e7i −0.0338825 0.0284308i
\(429\) −2.13064e8 + 7.90837e7i −0.130289 + 0.0483600i
\(430\) 7.96836e8 + 2.90025e8i 0.483314 + 0.175912i
\(431\) 9.88388e8 0.594644 0.297322 0.954777i \(-0.403907\pi\)
0.297322 + 0.954777i \(0.403907\pi\)
\(432\) 1.34701e9 + 4.61422e8i 0.803852 + 0.275363i
\(433\) −2.37029e9 −1.40312 −0.701558 0.712613i \(-0.747512\pi\)
−0.701558 + 0.712613i \(0.747512\pi\)
\(434\) 2.22599e9 + 8.10192e8i 1.30710 + 0.475745i
\(435\) −5.34019e7 4.42350e7i −0.0311060 0.0257664i
\(436\) 2.14839e8 + 1.80271e8i 0.124140 + 0.104166i
\(437\) −1.15287e8 + 6.53827e8i −0.0660841 + 0.374781i
\(438\) 2.01743e9 1.28041e7i 1.14720 0.00728097i
\(439\) 1.31291e9 1.10166e9i 0.740643 0.621473i −0.192367 0.981323i \(-0.561616\pi\)
0.933010 + 0.359850i \(0.117172\pi\)
\(440\) −6.00557e8 1.04019e9i −0.336101 0.582144i
\(441\) −1.84863e9 + 3.29789e9i −1.02639 + 1.83105i
\(442\) −3.99535e7 + 6.92015e7i −0.0220078 + 0.0381187i
\(443\) 1.44113e8 + 8.17304e8i 0.0787571 + 0.446654i 0.998530 + 0.0542025i \(0.0172616\pi\)
−0.919773 + 0.392451i \(0.871627\pi\)
\(444\) 4.64056e7 + 2.53751e8i 0.0251611 + 0.137584i
\(445\) 6.76135e8 2.46093e8i 0.363725 0.132385i
\(446\) −2.93005e9 + 1.06645e9i −1.56388 + 0.569206i
\(447\) 1.39769e8 + 7.64272e8i 0.0740174 + 0.404736i
\(448\) 6.37134e8 + 3.61337e9i 0.334779 + 1.89862i
\(449\) 1.45499e9 2.52012e9i 0.758575 1.31389i −0.185002 0.982738i \(-0.559229\pi\)
0.943577 0.331153i \(-0.107437\pi\)
\(450\) −5.68622e8 9.56631e8i −0.294157 0.494881i
\(451\) 1.91854e9 + 3.32301e9i 0.984813 + 1.70575i
\(452\) −1.01191e8 + 8.49095e7i −0.0515417 + 0.0432486i
\(453\) 5.48663e8 3.48221e6i 0.277307 0.00176000i
\(454\) 4.96247e8 2.81436e9i 0.248887 1.41151i
\(455\) 2.25637e8 + 1.89332e8i 0.112298 + 0.0942289i
\(456\) −3.16516e9 2.62183e9i −1.56322 1.29488i
\(457\) −2.93606e9 1.06864e9i −1.43899 0.523750i −0.499497 0.866316i \(-0.666482\pi\)
−0.939494 + 0.342566i \(0.888704\pi\)
\(458\) 2.12973e9 1.03585
\(459\) −3.75216e8 6.22225e8i −0.181108 0.300333i
\(460\) 3.38508e7 0.0162150
\(461\) 1.70814e9 + 6.21714e8i 0.812029 + 0.295554i 0.714462 0.699675i \(-0.246672\pi\)
0.0975672 + 0.995229i \(0.468894\pi\)
\(462\) −3.35966e9 + 1.24702e9i −1.58507 + 0.588337i
\(463\) −4.11511e6 3.45298e6i −0.00192685 0.00161682i 0.641824 0.766852i \(-0.278178\pi\)
−0.643751 + 0.765235i \(0.722623\pi\)
\(464\) −2.07545e7 + 1.17705e8i −0.00964495 + 0.0546992i
\(465\) 5.74570e8 + 9.80757e8i 0.265007 + 0.452352i
\(466\) 3.20553e8 2.68976e8i 0.146740 0.123130i
\(467\) 3.75574e8 + 6.50514e8i 0.170642 + 0.295561i 0.938645 0.344886i \(-0.112082\pi\)
−0.768002 + 0.640447i \(0.778749\pi\)
\(468\) 3.06955e7 + 2.50996e7i 0.0138425 + 0.0113189i
\(469\) 4.72262e8 8.17981e8i 0.211387 0.366133i
\(470\) 2.31001e8 + 1.31007e9i 0.102629 + 0.582040i
\(471\) −3.24032e9 1.15614e9i −1.42894 0.509846i
\(472\) 2.51172e9 9.14192e8i 1.09945 0.400166i
\(473\) −1.99339e9 + 7.25536e8i −0.866122 + 0.315242i
\(474\) −3.48996e8 + 2.96637e8i −0.150521 + 0.127939i
\(475\) 4.82479e8 + 2.73627e9i 0.206562 + 1.17147i
\(476\) 9.63811e7 1.66937e8i 0.0409607 0.0709460i
\(477\) −2.49756e9 8.73299e8i −1.05366 0.368425i
\(478\) 1.18756e8 + 2.05692e8i 0.0497347 + 0.0861431i
\(479\) −3.11557e9 + 2.61427e9i −1.29528 + 1.08687i −0.304337 + 0.952564i \(0.598435\pi\)
−0.990940 + 0.134303i \(0.957121\pi\)
\(480\) −1.95110e8 + 3.42948e8i −0.0805258 + 0.141542i
\(481\) 6.02044e7 3.41436e8i 0.0246672 0.139895i
\(482\) −8.69237e8 7.29377e8i −0.353569 0.296679i
\(483\) 1.44322e8 8.50000e8i 0.0582796 0.343245i
\(484\) 1.97503e7 + 7.18853e6i 0.00791800 + 0.00288192i
\(485\) 6.81395e7 0.0271208
\(486\) 2.18794e9 8.75918e8i 0.864586 0.346128i
\(487\) 2.35490e9 0.923892 0.461946 0.886908i \(-0.347151\pi\)
0.461946 + 0.886908i \(0.347151\pi\)
\(488\) −7.80780e7 2.84181e7i −0.0304130 0.0110694i
\(489\) −5.29689e7 + 3.11967e8i −0.0204852 + 0.120650i
\(490\) 2.40987e9 + 2.02213e9i 0.925355 + 0.776465i
\(491\) −2.39034e8 + 1.35563e9i −0.0911329 + 0.516840i 0.904731 + 0.425983i \(0.140072\pi\)
−0.995864 + 0.0908570i \(0.971039\pi\)
\(492\) 3.31039e8 5.81874e8i 0.125315 0.220268i
\(493\) 4.67230e7 3.92052e7i 0.0175617 0.0147360i
\(494\) 3.23547e8 + 5.60401e8i 0.120752 + 0.209148i
\(495\) −1.62320e9 5.67570e8i −0.601526 0.210330i
\(496\) 9.79584e8 1.69669e9i 0.360459 0.624333i
\(497\) −4.02486e8 2.28261e9i −0.147063 0.834036i
\(498\) 1.69181e9 1.43799e9i 0.613830 0.521739i
\(499\) −1.95770e9 + 7.12543e8i −0.705332 + 0.256720i −0.669686 0.742645i \(-0.733571\pi\)
−0.0356461 + 0.999364i \(0.511349\pi\)
\(500\) 3.48470e8 1.26833e8i 0.124672 0.0453770i
\(501\) −1.89836e9 6.77333e8i −0.674445 0.240641i
\(502\) −1.66795e8 9.45944e8i −0.0588466 0.333736i
\(503\) 2.70727e8 4.68913e8i 0.0948513 0.164287i −0.814695 0.579889i \(-0.803096\pi\)
0.909547 + 0.415602i \(0.136429\pi\)
\(504\) 4.13184e9 + 3.37859e9i 1.43759 + 1.17551i
\(505\) −1.62884e9 2.82123e9i −0.562805 0.974806i
\(506\) 4.24029e8 3.55803e8i 0.145502 0.122091i
\(507\) 1.45639e9 + 2.48597e9i 0.496306 + 0.847165i
\(508\) −5.51663e7 + 3.12864e8i −0.0186703 + 0.105884i
\(509\) 3.29587e9 + 2.76556e9i 1.10779 + 0.929546i 0.997924 0.0644002i \(-0.0205134\pi\)
0.109866 + 0.993946i \(0.464958\pi\)
\(510\) −5.66815e8 + 2.10387e8i −0.189211 + 0.0702301i
\(511\) 6.14663e9 + 2.23719e9i 2.03781 + 0.741702i
\(512\) 3.40223e9 1.12026
\(513\) −5.88303e9 + 1.12026e8i −1.92394 + 0.0366360i
\(514\) −3.71430e9 −1.20644
\(515\) 7.61690e8 + 2.77233e8i 0.245727 + 0.0894373i
\(516\) 2.85021e8 + 2.36094e8i 0.0913276 + 0.0756505i
\(517\) −2.54931e9 2.13912e9i −0.811344 0.680798i
\(518\) 9.49324e8 5.38388e9i 0.300096 1.70193i
\(519\) 4.46697e9 2.83506e7i 1.40258 0.00890179i
\(520\) 2.15756e8 1.81040e8i 0.0672900 0.0564630i
\(521\) −1.12397e9 1.94678e9i −0.348196 0.603093i 0.637733 0.770257i \(-0.279872\pi\)
−0.985929 + 0.167164i \(0.946539\pi\)
\(522\) 1.01082e8 + 1.70058e8i 0.0311049 + 0.0523298i
\(523\) −2.17922e9 + 3.77453e9i −0.666110 + 1.15374i 0.312873 + 0.949795i \(0.398709\pi\)
−0.978983 + 0.203941i \(0.934625\pi\)
\(524\) 2.53783e7 + 1.43928e8i 0.00770555 + 0.0437004i
\(525\) −6.49091e8 3.54931e9i −0.195771 1.07050i
\(526\) −5.09591e9 + 1.85476e9i −1.52676 + 0.555696i
\(527\) −9.39489e8 + 3.41946e8i −0.279611 + 0.101770i
\(528\) 5.33183e8 + 2.91551e9i 0.157637 + 0.861977i
\(529\) −5.68117e8 3.22195e9i −0.166856 0.946290i
\(530\) −1.10079e9 + 1.90663e9i −0.321173 + 0.556289i
\(531\) 1.87112e9 3.33802e9i 0.542339 0.967516i
\(532\) −7.80504e8 1.35187e9i −0.224742 0.389264i
\(533\) −6.89255e8 + 5.78353e8i −0.197167 + 0.165443i
\(534\) −2.05272e9 + 1.30280e7i −0.583358 + 0.00370241i
\(535\) −1.26688e8 + 7.18483e8i −0.0357682 + 0.202852i
\(536\) −6.91860e8 5.80539e8i −0.194062 0.162838i
\(537\) 3.72917e9 + 3.08903e9i 1.03921 + 0.860819i
\(538\) −2.25210e9 8.19696e8i −0.623518 0.226942i
\(539\) −7.86981e9 −2.16473
\(540\) 5.77120e7 + 2.94408e8i 0.0157720 + 0.0804584i
\(541\) 1.75471e9 0.476447 0.238223 0.971210i \(-0.423435\pi\)
0.238223 + 0.971210i \(0.423435\pi\)
\(542\) 2.51850e9 + 9.16658e8i 0.679429 + 0.247292i
\(543\) 5.09575e9 1.89141e9i 1.36587 0.506975i
\(544\) −2.65855e8 2.23079e8i −0.0708025 0.0594103i
\(545\) 4.95245e8 2.80867e9i 0.131049 0.743213i
\(546\) −4.24772e8 7.25061e8i −0.111682 0.190634i
\(547\) 5.15682e9 4.32709e9i 1.34718 1.13042i 0.367466 0.930037i \(-0.380226\pi\)
0.979717 0.200384i \(-0.0642189\pi\)
\(548\) −3.08644e8 5.34586e8i −0.0801171 0.138767i
\(549\) −1.11255e8 + 4.21002e7i −0.0286956 + 0.0108588i
\(550\) 1.15827e9 2.00618e9i 0.296851 0.514162i
\(551\) −8.57689e7 4.86420e8i −0.0218424 0.123874i
\(552\) −7.76464e8 2.77042e8i −0.196487 0.0701065i
\(553\) −1.39548e9 + 5.07913e8i −0.350902 + 0.127718i
\(554\) 3.16021e9 1.15022e9i 0.789644 0.287407i
\(555\) 1.99879e9 1.69892e9i 0.496298 0.421840i
\(556\) −4.95828e7 2.81198e8i −0.0122340 0.0693826i
\(557\) −2.70436e9 + 4.68408e9i −0.663087 + 1.14850i 0.316713 + 0.948521i \(0.397421\pi\)
−0.979800 + 0.199979i \(0.935912\pi\)
\(558\) −6.03602e8 3.18616e9i −0.147072 0.776332i
\(559\) −2.48715e8 4.30786e8i −0.0602226 0.104309i
\(560\) 2.94260e9 2.46914e9i 0.708066 0.594138i
\(561\) 7.47916e8 1.31463e9i 0.178847 0.314364i
\(562\) 2.67843e8 1.51901e9i 0.0636506 0.360981i
\(563\) 7.76378e8 + 6.51458e8i 0.183355 + 0.153853i 0.729846 0.683612i \(-0.239592\pi\)
−0.546490 + 0.837466i \(0.684036\pi\)
\(564\) −9.71911e7 + 5.72418e8i −0.0228113 + 0.134350i
\(565\) 1.26231e9 + 4.59442e8i 0.294439 + 0.107167i
\(566\) −3.53075e9 −0.818483
\(567\) 7.63869e9 1.93962e8i 1.75986 0.0446864i
\(568\) −2.21632e9 −0.507473
\(569\) −7.16557e9 2.60806e9i −1.63064 0.593504i −0.645273 0.763952i \(-0.723256\pi\)
−0.985367 + 0.170447i \(0.945479\pi\)
\(570\) −8.19582e8 + 4.82703e9i −0.185366 + 1.09174i
\(571\) 3.21905e9 + 2.70110e9i 0.723605 + 0.607176i 0.928380 0.371633i \(-0.121202\pi\)
−0.204775 + 0.978809i \(0.565646\pi\)
\(572\) −1.43324e7 + 8.12831e7i −0.00320209 + 0.0181599i
\(573\) −3.21576e9 + 5.65240e9i −0.714073 + 1.25514i
\(574\) −1.08684e10 + 9.11967e9i −2.39869 + 2.01274i
\(575\) 2.78661e8 + 4.82655e8i 0.0611278 + 0.105876i
\(576\) 3.80642e9 3.27719e9i 0.829923 0.714534i
\(577\) 1.85846e9 3.21895e9i 0.402753 0.697588i −0.591304 0.806448i \(-0.701387\pi\)
0.994057 + 0.108860i \(0.0347202\pi\)
\(578\) 6.58423e8 + 3.73411e9i 0.141827 + 0.804339i
\(579\) −3.61946e9 + 3.07644e9i −0.774941 + 0.658679i
\(580\) −2.36648e7 + 8.61328e6i −0.00503622 + 0.00183304i
\(581\) 6.76479e9 2.46218e9i 1.43099 0.520839i
\(582\) −1.83092e8 6.53270e7i −0.0384980 0.0137361i
\(583\) −9.56377e8 5.42388e9i −0.199889 1.13363i
\(584\) 3.12732e9 5.41668e9i 0.649722 1.12535i
\(585\) 6.49728e7 3.97953e8i 0.0134179 0.0821838i
\(586\) 3.21721e9 + 5.57236e9i 0.660446 + 1.14393i
\(587\) −3.20709e8 + 2.69107e8i −0.0654452 + 0.0549151i −0.674924 0.737888i \(-0.735823\pi\)
0.609478 + 0.792803i \(0.291379\pi\)
\(588\) 6.94050e8 + 1.18470e9i 0.140789 + 0.240319i
\(589\) −1.40592e9 + 7.97334e9i −0.283502 + 1.60782i
\(590\) −2.43920e9 2.04673e9i −0.488951 0.410279i
\(591\) 1.22841e8 4.55956e7i 0.0244787 0.00908587i
\(592\) −4.24879e9 1.54643e9i −0.841665 0.306341i
\(593\) 7.64763e8 0.150604 0.0753018 0.997161i \(-0.476008\pi\)
0.0753018 + 0.997161i \(0.476008\pi\)
\(594\) 3.81742e9 + 3.08127e9i 0.747338 + 0.603222i
\(595\) −1.96025e9 −0.381507
\(596\) 2.65149e8 + 9.65063e7i 0.0513012 + 0.0186721i
\(597\) 3.57113e9 + 2.95811e9i 0.686903 + 0.568990i
\(598\) 9.94306e7 + 8.34322e7i 0.0190137 + 0.0159544i
\(599\) −7.59798e8 + 4.30903e9i −0.144446 + 0.819191i 0.823365 + 0.567512i \(0.192094\pi\)
−0.967811 + 0.251679i \(0.919017\pi\)
\(600\) −3.45008e9 + 2.18968e7i −0.652079 + 0.00413857i
\(601\) −1.71423e9 + 1.43841e9i −0.322113 + 0.270285i −0.789477 0.613780i \(-0.789648\pi\)
0.467364 + 0.884065i \(0.345204\pi\)
\(602\) −3.92182e9 6.79279e9i −0.732655 1.26900i
\(603\) −1.29290e9 + 1.64121e7i −0.240135 + 0.00304826i
\(604\) 9.96315e7 1.72567e8i 0.0183979 0.0318660i
\(605\) −3.71150e7 2.10489e8i −0.00681405 0.0386444i
\(606\) 1.67192e9 + 9.14227e9i 0.305184 + 1.66878i
\(607\) −2.21321e9 + 8.05541e8i −0.401663 + 0.146193i −0.534949 0.844884i \(-0.679669\pi\)
0.133286 + 0.991078i \(0.457447\pi\)
\(608\) −2.64095e9 + 9.61226e8i −0.476537 + 0.173445i
\(609\) 1.15387e8 + 6.30950e8i 0.0207013 + 0.113197i
\(610\) 1.71878e7 + 9.74769e7i 0.00306596 + 0.0173879i
\(611\) 3.90177e8 6.75807e8i 0.0692019 0.119861i
\(612\) −2.63860e8 + 3.34944e6i −0.0465312 + 0.000590666i
\(613\) −1.08351e9 1.87669e9i −0.189985 0.329064i 0.755260 0.655426i \(-0.227511\pi\)
−0.945245 + 0.326361i \(0.894177\pi\)
\(614\) 4.46239e9 3.74439e9i 0.777997 0.652817i
\(615\) −6.80770e9 + 4.32066e7i −1.18015 + 0.00749010i
\(616\) −1.92925e9 + 1.09413e10i −0.332549 + 1.88598i
\(617\) 5.60186e9 + 4.70052e9i 0.960140 + 0.805653i 0.980976 0.194130i \(-0.0621883\pi\)
−0.0208360 + 0.999783i \(0.506633\pi\)
\(618\) −1.78088e9 1.47518e9i −0.303511 0.251411i
\(619\) 6.01479e9 + 2.18921e9i 1.01930 + 0.370996i 0.796999 0.603981i \(-0.206420\pi\)
0.222305 + 0.974977i \(0.428642\pi\)
\(620\) 4.12806e8 0.0695625
\(621\) −1.10120e9 + 4.24715e8i −0.184520 + 0.0711668i
\(622\) 5.67760e9 0.946015
\(623\) −6.25414e9 2.27632e9i −1.03624 0.377160i
\(624\) −6.51560e8 + 2.41843e8i −0.107352 + 0.0398462i
\(625\) 1.47319e6 + 1.23615e6i 0.000241368 + 0.000202531i
\(626\) −6.72718e8 + 3.81517e9i −0.109603 + 0.621590i
\(627\) −6.19134e9 1.05682e10i −1.00311 1.71225i
\(628\) −9.57139e8 + 8.03135e8i −0.154211 + 0.129399i
\(629\) 1.15368e9 + 1.99823e9i 0.184844 + 0.320160i
\(630\) 1.02451e9 6.27506e9i 0.163240 0.999829i
\(631\) −1.13589e9 + 1.96742e9i −0.179984 + 0.311742i −0.941875 0.335964i \(-0.890938\pi\)
0.761891 + 0.647706i \(0.224271\pi\)
\(632\) 2.46581e8 + 1.39843e9i 0.0388553 + 0.220359i
\(633\) 4.04170e9 + 1.44207e9i 0.633360 + 0.225982i
\(634\) 5.76485e9 2.09823e9i 0.898412 0.326995i
\(635\) 3.03585e9 1.10496e9i 0.470513 0.171253i
\(636\) −7.32153e8 + 6.22311e8i −0.112850 + 0.0959196i
\(637\) −3.20449e8 1.81736e9i −0.0491214 0.278581i
\(638\) −2.05902e8 + 3.56632e8i −0.0313897 + 0.0543686i
\(639\) −2.40457e9 + 2.07024e9i −0.364572 + 0.313884i
\(640\) −1.54975e9 2.68425e9i −0.233686 0.404755i
\(641\) 7.02158e9 5.89180e9i 1.05301 0.883578i 0.0596008 0.998222i \(-0.481017\pi\)
0.993407 + 0.114644i \(0.0365728\pi\)
\(642\) 1.02924e9 1.80911e9i 0.153512 0.269832i
\(643\) 1.05520e9 5.98431e9i 0.156529 0.887720i −0.800846 0.598871i \(-0.795616\pi\)
0.957375 0.288849i \(-0.0932725\pi\)
\(644\) −2.39859e8 2.01266e8i −0.0353880 0.0296941i
\(645\) 6.30022e8 3.71059e9i 0.0924479 0.544483i
\(646\) −4.04678e9 1.47291e9i −0.590603 0.214962i
\(647\) −1.57673e9 −0.228872 −0.114436 0.993431i \(-0.536506\pi\)
−0.114436 + 0.993431i \(0.536506\pi\)
\(648\) 1.08570e9 7.22540e9i 0.156747 1.04316i
\(649\) 7.96557e9 1.14383
\(650\) 5.10444e8 + 1.85787e8i 0.0729040 + 0.0265349i
\(651\) 1.75998e9 1.03656e10i 0.250020 1.47253i
\(652\) 8.80332e7 + 7.38686e7i 0.0124388 + 0.0104374i
\(653\) 1.13152e9 6.41719e9i 0.159026 0.901880i −0.795987 0.605314i \(-0.793048\pi\)
0.955012 0.296566i \(-0.0958413\pi\)
\(654\) −4.02347e9 + 7.07213e9i −0.562443 + 0.988617i
\(655\) 1.13851e9 9.55325e8i 0.158304 0.132833i
\(656\) 5.86701e9 + 1.01620e10i 0.811435 + 1.40545i
\(657\) −1.66673e9 8.79796e9i −0.229291 1.21033i
\(658\) 6.15245e9 1.06564e10i 0.841894 1.45820i
\(659\) −1.22575e9 6.95158e9i −0.166841 0.946204i −0.947146 0.320804i \(-0.896047\pi\)
0.780304 0.625400i \(-0.215064\pi\)
\(660\) −4.75838e8 + 4.04449e8i −0.0644251 + 0.0547596i
\(661\) 1.37375e9 5.00005e8i 0.185014 0.0673394i −0.247852 0.968798i \(-0.579725\pi\)
0.432866 + 0.901458i \(0.357502\pi\)
\(662\) 4.82139e8 1.75484e8i 0.0645905 0.0235090i
\(663\) 3.34038e8 + 1.19184e8i 0.0445141 + 0.0158826i
\(664\) −1.19534e9 6.77909e9i −0.158454 0.898634i
\(665\) −7.93716e9 + 1.37476e10i −1.04662 + 1.81280i
\(666\) −6.99957e9 + 2.64873e9i −0.918146 + 0.347438i
\(667\) −4.95368e7 8.58002e7i −0.00646379 0.0111956i
\(668\) −5.60745e8 + 4.70521e8i −0.0727861 + 0.0610748i
\(669\) 6.99569e9 + 1.19412e10i 0.903315 + 1.54190i
\(670\) −1.86828e8 + 1.05955e9i −0.0239983 + 0.136101i
\(671\) −1.89683e8 1.59163e8i −0.0242381 0.0203382i
\(672\) 3.42157e9 1.27000e9i 0.434943 0.161440i
\(673\) 7.13390e8 + 2.59653e8i 0.0902141 + 0.0328353i 0.386733 0.922192i \(-0.373604\pi\)
−0.296519 + 0.955027i \(0.595826\pi\)
\(674\) −4.83949e9 −0.608821
\(675\) −3.72267e9 + 3.24645e9i −0.465898 + 0.406299i
\(676\) 1.04636e9 0.130277
\(677\) −3.17391e9 1.15521e9i −0.393128 0.143087i 0.137890 0.990448i \(-0.455968\pi\)
−0.531018 + 0.847361i \(0.678190\pi\)
\(678\) −2.95136e9 2.44473e9i −0.363678 0.301250i
\(679\) −4.82822e8 4.05136e8i −0.0591893 0.0496657i
\(680\) −3.25487e8 + 1.84593e9i −0.0396965 + 0.225130i
\(681\) −1.26838e10 + 8.05008e7i −1.53899 + 0.00976754i
\(682\) 5.17098e9 4.33897e9i 0.624206 0.523771i
\(683\) 1.76956e9 + 3.06497e9i 0.212517 + 0.368090i 0.952501 0.304534i \(-0.0985007\pi\)
−0.739985 + 0.672624i \(0.765167\pi\)
\(684\) −1.04489e9 + 1.86406e9i −0.124846 + 0.222722i
\(685\) −3.13868e9 + 5.43636e9i −0.373105 + 0.646236i
\(686\) −2.64575e9 1.50048e10i −0.312907 1.77458i
\(687\) −1.70049e9 9.29849e9i −0.200090 1.09412i
\(688\) −6.09591e9 + 2.21873e9i −0.713639 + 0.259744i
\(689\) 1.21358e9 4.41707e8i 0.141352 0.0514479i
\(690\) 1.76672e8 + 9.66064e8i 0.0204737 + 0.111953i
\(691\) −1.21514e9 6.89142e9i −0.140105 0.794576i −0.971168 0.238397i \(-0.923378\pi\)
0.831063 0.556179i \(-0.187733\pi\)
\(692\) 8.11155e8 1.40496e9i 0.0930535 0.161173i
\(693\) 8.12707e9 + 1.36727e10i 0.927615 + 1.56059i
\(694\) 4.08391e9 + 7.07353e9i 0.463786 + 0.803301i
\(695\) −2.22436e9 + 1.86646e9i −0.251338 + 0.210898i
\(696\) 6.13312e8 3.89253e6i 0.0689523 0.000437622i
\(697\) 1.03980e9 5.89702e9i 0.116315 0.659657i
\(698\) 2.90090e8 + 2.43414e8i 0.0322878 + 0.0270927i
\(699\) −1.43031e9 1.18478e9i −0.158401 0.131210i
\(700\) −1.23136e9 4.48179e8i −0.135688 0.0493865i
\(701\) 9.45606e9 1.03680 0.518402 0.855137i \(-0.326527\pi\)
0.518402 + 0.855137i \(0.326527\pi\)
\(702\) −5.56109e8 + 1.00701e9i −0.0606709 + 0.109864i
\(703\) 1.86852e10 2.02840
\(704\) 9.82492e9 + 3.57598e9i 1.06127 + 0.386270i
\(705\) 5.53539e9 2.05460e9i 0.594958 0.220833i
\(706\) −5.46099e9 4.58232e9i −0.584057 0.490082i
\(707\) −5.23253e9 + 2.96751e10i −0.556857 + 3.15809i
\(708\) −7.02496e8 1.19912e9i −0.0743922 0.126983i
\(709\) −6.18182e9 + 5.18716e9i −0.651410 + 0.546598i −0.907498 0.420056i \(-0.862011\pi\)
0.256089 + 0.966653i \(0.417566\pi\)
\(710\) 1.32011e9 + 2.28650e9i 0.138422 + 0.239754i
\(711\) 1.57379e9 + 1.28688e9i 0.164211 + 0.134275i
\(712\) −3.18202e9 + 5.51143e9i −0.330387 + 0.572248i
\(713\) 2.82005e8 + 1.59933e9i 0.0291369 + 0.165244i
\(714\) 5.26722e9 + 1.87934e9i 0.541549 + 0.193224i
\(715\) 7.88724e8 2.87072e8i 0.0806964 0.0293711i
\(716\) 1.65257e9 6.01485e8i 0.168253 0.0612391i
\(717\) 8.03239e8 6.82731e8i 0.0813819 0.0691724i
\(718\) −8.24006e8 4.67317e9i −0.0830796 0.471168i
\(719\) −3.29460e9 + 5.70641e9i −0.330561 + 0.572548i −0.982622 0.185618i \(-0.940571\pi\)
0.652061 + 0.758166i \(0.273905\pi\)
\(720\) −4.96385e9 1.73566e9i −0.495627 0.173301i
\(721\) −3.74884e9 6.49317e9i −0.372497 0.645184i
\(722\) −1.95006e10 + 1.63629e10i −1.92827 + 1.61801i
\(723\) −2.49044e9 + 4.37750e9i −0.245071 + 0.430767i
\(724\) 3.42782e8 1.94401e9i 0.0335686 0.190377i
\(725\) −3.17620e8 2.66515e8i −0.0309546 0.0259740i
\(726\) −1.02073e8 + 6.01170e8i −0.00989993 + 0.0583068i
\(727\) 7.33398e8 + 2.66935e8i 0.0707895 + 0.0257653i 0.377172 0.926143i \(-0.376896\pi\)
−0.306383 + 0.951908i \(0.599119\pi\)
\(728\) −2.60521e9 −0.250255
\(729\) −5.57126e9 8.85325e9i −0.532608 0.846362i
\(730\) −7.45092e9 −0.708892
\(731\) 3.11080e9 + 1.13224e9i 0.294552 + 0.107208i
\(732\) −7.23156e6 + 4.25912e7i −0.000681465 + 0.00401357i
\(733\) 5.44084e8 + 4.56541e8i 0.0510273 + 0.0428170i 0.667945 0.744211i \(-0.267174\pi\)
−0.616917 + 0.787028i \(0.711619\pi\)
\(734\) −2.68233e9 + 1.52122e10i −0.250366 + 1.41990i
\(735\) 6.90451e9 1.21362e10i 0.641397 1.12740i
\(736\) −4.31843e8 + 3.62359e8i −0.0399258 + 0.0335017i
\(737\) −1.34575e9 2.33091e9i −0.123831 0.214482i
\(738\) 1.83338e10 + 6.41060e9i 1.67902 + 0.587086i
\(739\) −7.87867e9 + 1.36463e10i −0.718121 + 1.24382i 0.243623 + 0.969870i \(0.421664\pi\)
−0.961744 + 0.273951i \(0.911669\pi\)
\(740\) −1.65434e8 9.38222e8i −0.0150077 0.0851127i
\(741\) 2.18839e9 1.86008e9i 0.197589 0.167945i
\(742\) 1.91362e10 6.96499e9i 1.71965 0.625903i
\(743\) 6.00089e9 2.18415e9i 0.536729 0.195353i −0.0594115 0.998234i \(-0.518922\pi\)
0.596140 + 0.802880i \(0.296700\pi\)
\(744\) −9.46888e9 3.37849e9i −0.842933 0.300758i
\(745\) −4.98270e8 2.82583e9i −0.0441487 0.250380i
\(746\) 5.48798e9 9.50546e9i 0.483979 0.838277i
\(747\) −7.62915e9 6.23833e9i −0.669660 0.547578i
\(748\) −2.74647e8 4.75702e8i −0.0239949 0.0415604i
\(749\) 5.16956e9 4.33777e9i 0.449538 0.377208i
\(750\) 5.43838e9 + 9.28299e9i 0.470712 + 0.803477i
\(751\) 5.92256e8 3.35885e9i 0.0510234 0.289368i −0.948610 0.316448i \(-0.897510\pi\)
0.999633 + 0.0270798i \(0.00862083\pi\)
\(752\) −7.79592e9 6.54155e9i −0.668505 0.560943i
\(753\) −3.99685e9 + 1.48353e9i −0.341142 + 0.126623i
\(754\) −9.07403e7 3.30268e7i −0.00770904 0.00280586i
\(755\) −2.02636e9 −0.171357