Properties

Label 27.8.e.a.4.12
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 4.12
Character \(\chi\) = 27.4
Dual form 27.8.e.a.7.12

$q$-expansion

\(f(q)\) \(=\) \(q+(4.29826 + 1.56444i) q^{2} +(11.1293 + 45.4218i) q^{3} +(-82.0261 - 68.8281i) q^{4} +(-20.3422 + 115.366i) q^{5} +(-23.2230 + 212.646i) q^{6} +(-610.300 + 512.103i) q^{7} +(-537.635 - 931.211i) q^{8} +(-1939.28 + 1011.02i) q^{9} +O(q^{10})\) \(q+(4.29826 + 1.56444i) q^{2} +(11.1293 + 45.4218i) q^{3} +(-82.0261 - 68.8281i) q^{4} +(-20.3422 + 115.366i) q^{5} +(-23.2230 + 212.646i) q^{6} +(-610.300 + 512.103i) q^{7} +(-537.635 - 931.211i) q^{8} +(-1939.28 + 1011.02i) q^{9} +(-267.920 + 464.051i) q^{10} +(-574.721 - 3259.40i) q^{11} +(2213.40 - 4491.78i) q^{12} +(-6697.04 + 2437.52i) q^{13} +(-3424.38 + 1246.37i) q^{14} +(-5466.55 + 359.967i) q^{15} +(1525.94 + 8654.02i) q^{16} +(-11610.6 + 20110.2i) q^{17} +(-9917.20 + 1311.76i) q^{18} +(-4586.04 - 7943.25i) q^{19} +(9609.05 - 8062.95i) q^{20} +(-30052.8 - 22021.6i) q^{21} +(2628.84 - 14908.9i) q^{22} +(33136.2 + 27804.5i) q^{23} +(36313.8 - 34784.1i) q^{24} +(60517.9 + 22026.7i) q^{25} -32599.0 q^{26} +(-67505.3 - 76833.5i) q^{27} +85307.6 q^{28} +(10873.9 + 3957.76i) q^{29} +(-24059.8 - 7004.84i) q^{30} +(191932. + 161050. i) q^{31} +(-30879.8 + 175128. i) q^{32} +(141652. - 62379.7i) q^{33} +(-81366.8 + 68274.8i) q^{34} +(-46664.6 - 80825.5i) q^{35} +(228658. + 50546.4i) q^{36} +(168615. - 292051. i) q^{37} +(-7285.25 - 41316.7i) q^{38} +(-185250. - 277064. i) q^{39} +(118367. - 43082.2i) q^{40} +(-225331. + 82013.7i) q^{41} +(-94723.4 - 141670. i) q^{42} +(-14599.4 - 82797.6i) q^{43} +(-177196. + 306913. i) q^{44} +(-77189.1 - 244294. i) q^{45} +(98929.3 + 171351. i) q^{46} +(-867282. + 727736. i) q^{47} +(-376098. + 165624. i) q^{48} +(-32789.6 + 185959. i) q^{49} +(225662. + 189353. i) q^{50} +(-1.04266e6 - 303564. i) q^{51} +(717103. + 261004. i) q^{52} -1.76668e6 q^{53} +(-169954. - 435858. i) q^{54} +387717. q^{55} +(804995. + 292994. i) q^{56} +(309757. - 296709. i) q^{57} +(40547.0 + 34023.0i) q^{58} +(26452.5 - 150019. i) q^{59} +(473176. + 346725. i) q^{60} +(1.52266e6 - 1.27766e6i) q^{61} +(573021. + 992502. i) q^{62} +(665793. - 1.61014e6i) q^{63} +(155695. - 269671. i) q^{64} +(-144976. - 822199. i) q^{65} +(706445. - 46518.7i) q^{66} +(-3.19283e6 + 1.16209e6i) q^{67} +(2.33653e6 - 850426. i) q^{68} +(-894150. + 1.81455e6i) q^{69} +(-74130.1 - 420413. i) q^{70} +(1.63983e6 - 2.84026e6i) q^{71} +(1.98410e6 + 1.26232e6i) q^{72} +(1.48613e6 + 2.57405e6i) q^{73} +(1.18165e6 - 991520. i) q^{74} +(-326971. + 2.99397e6i) q^{75} +(-170544. + 967203. i) q^{76} +(2.01990e6 + 1.69490e6i) q^{77} +(-362803. - 1.48070e6i) q^{78} +(-3.46317e6 - 1.26049e6i) q^{79} -1.02942e6 q^{80} +(2.73863e6 - 3.92132e6i) q^{81} -1.09684e6 q^{82} +(-1.47926e6 - 538406. i) q^{83} +(949413. + 3.87482e6i) q^{84} +(-2.08386e6 - 1.74857e6i) q^{85} +(66779.5 - 378725. i) q^{86} +(-58750.2 + 537957. i) q^{87} +(-2.72620e6 + 2.28756e6i) q^{88} +(-224262. - 388434. i) q^{89} +(50404.2 - 1.17080e6i) q^{90} +(2.83894e6 - 4.91719e6i) q^{91} +(-804298. - 4.56140e6i) q^{92} +(-5.17913e6 + 1.05103e7i) q^{93} +(-4.86630e6 + 1.77119e6i) q^{94} +(1.00968e6 - 367492. i) q^{95} +(-8.29830e6 + 546435. i) q^{96} +(-1.73183e6 - 9.82167e6i) q^{97} +(-431860. + 748003. i) q^{98} +(4.40988e6 + 5.73983e6i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.29826 + 1.56444i 0.379916 + 0.138278i 0.524917 0.851153i \(-0.324096\pi\)
−0.145001 + 0.989431i \(0.546319\pi\)
\(3\) 11.1293 + 45.4218i 0.237981 + 0.971270i
\(4\) −82.0261 68.8281i −0.640829 0.537720i
\(5\) −20.3422 + 115.366i −0.0727786 + 0.412748i 0.926552 + 0.376166i \(0.122758\pi\)
−0.999331 + 0.0365813i \(0.988353\pi\)
\(6\) −23.2230 + 212.646i −0.0438924 + 0.401908i
\(7\) −610.300 + 512.103i −0.672512 + 0.564305i −0.913808 0.406147i \(-0.866872\pi\)
0.241295 + 0.970452i \(0.422428\pi\)
\(8\) −537.635 931.211i −0.371255 0.643033i
\(9\) −1939.28 + 1011.02i −0.886730 + 0.462288i
\(10\) −267.920 + 464.051i −0.0847237 + 0.146746i
\(11\) −574.721 3259.40i −0.130192 0.738353i −0.978088 0.208191i \(-0.933242\pi\)
0.847897 0.530162i \(-0.177869\pi\)
\(12\) 2213.40 4491.78i 0.369765 0.750385i
\(13\) −6697.04 + 2437.52i −0.845437 + 0.307714i −0.728179 0.685387i \(-0.759633\pi\)
−0.117259 + 0.993101i \(0.537411\pi\)
\(14\) −3424.38 + 1246.37i −0.333529 + 0.121395i
\(15\) −5466.55 + 359.967i −0.418209 + 0.0275387i
\(16\) 1525.94 + 8654.02i 0.0931358 + 0.528199i
\(17\) −11610.6 + 20110.2i −0.573172 + 0.992764i 0.423065 + 0.906099i \(0.360954\pi\)
−0.996238 + 0.0866645i \(0.972379\pi\)
\(18\) −9917.20 + 1311.76i −0.400807 + 0.0530154i
\(19\) −4586.04 7943.25i −0.153391 0.265681i 0.779081 0.626923i \(-0.215686\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(20\) 9609.05 8062.95i 0.268581 0.225366i
\(21\) −30052.8 22021.6i −0.708138 0.518897i
\(22\) 2628.84 14908.9i 0.0526362 0.298515i
\(23\) 33136.2 + 27804.5i 0.567878 + 0.476506i 0.880941 0.473226i \(-0.156911\pi\)
−0.313063 + 0.949732i \(0.601355\pi\)
\(24\) 36313.8 34784.1i 0.536207 0.513619i
\(25\) 60517.9 + 22026.7i 0.774629 + 0.281942i
\(26\) −32599.0 −0.363745
\(27\) −67505.3 76833.5i −0.660032 0.751238i
\(28\) 85307.6 0.734403
\(29\) 10873.9 + 3957.76i 0.0827925 + 0.0301340i 0.383084 0.923713i \(-0.374862\pi\)
−0.300292 + 0.953847i \(0.597084\pi\)
\(30\) −24059.8 7004.84i −0.162692 0.0473668i
\(31\) 191932. + 161050.i 1.15713 + 0.970948i 0.999862 0.0166083i \(-0.00528682\pi\)
0.157268 + 0.987556i \(0.449731\pi\)
\(32\) −30879.8 + 175128.i −0.166590 + 0.944780i
\(33\) 141652. 62379.7i 0.686156 0.302165i
\(34\) −81366.8 + 68274.8i −0.355035 + 0.297910i
\(35\) −46664.6 80825.5i −0.183971 0.318647i
\(36\) 228658. + 50546.4i 0.816824 + 0.180564i
\(37\) 168615. 292051.i 0.547257 0.947877i −0.451204 0.892421i \(-0.649005\pi\)
0.998461 0.0554563i \(-0.0176613\pi\)
\(38\) −7285.25 41316.7i −0.0215378 0.122147i
\(39\) −185250. 277064.i −0.500072 0.747917i
\(40\) 118367. 43082.2i 0.292430 0.106436i
\(41\) −225331. + 82013.7i −0.510596 + 0.185842i −0.584454 0.811427i \(-0.698691\pi\)
0.0738579 + 0.997269i \(0.476469\pi\)
\(42\) −94723.4 141670.i −0.197281 0.295057i
\(43\) −14599.4 82797.6i −0.0280025 0.158810i 0.967600 0.252488i \(-0.0812488\pi\)
−0.995603 + 0.0936778i \(0.970138\pi\)
\(44\) −177196. + 306913.i −0.313596 + 0.543165i
\(45\) −77189.1 244294.i −0.126274 0.399640i
\(46\) 98929.3 + 171351.i 0.149855 + 0.259557i
\(47\) −867282. + 727736.i −1.21848 + 1.02242i −0.219575 + 0.975596i \(0.570467\pi\)
−0.998903 + 0.0468293i \(0.985088\pi\)
\(48\) −376098. + 165624.i −0.490859 + 0.216162i
\(49\) −32789.6 + 185959.i −0.0398153 + 0.225804i
\(50\) 225662. + 189353.i 0.255307 + 0.214228i
\(51\) −1.04266e6 303564.i −1.10065 0.320446i
\(52\) 717103. + 261004.i 0.707245 + 0.257416i
\(53\) −1.76668e6 −1.63002 −0.815010 0.579447i \(-0.803269\pi\)
−0.815010 + 0.579447i \(0.803269\pi\)
\(54\) −169954. 435858.i −0.146877 0.376675i
\(55\) 387717. 0.314229
\(56\) 804995. + 292994.i 0.612541 + 0.222947i
\(57\) 309757. 296709.i 0.221544 0.212211i
\(58\) 40547.0 + 34023.0i 0.0272873 + 0.0228968i
\(59\) 26452.5 150019.i 0.0167681 0.0950967i −0.975275 0.220994i \(-0.929070\pi\)
0.992043 + 0.125897i \(0.0401810\pi\)
\(60\) 473176. + 346725.i 0.282809 + 0.207232i
\(61\) 1.52266e6 1.27766e6i 0.858911 0.720712i −0.102822 0.994700i \(-0.532787\pi\)
0.961733 + 0.273987i \(0.0883427\pi\)
\(62\) 573021. + 992502.i 0.305351 + 0.528884i
\(63\) 665793. 1.61014e6i 0.335465 0.811280i
\(64\) 155695. 269671.i 0.0742411 0.128589i
\(65\) −144976. 822199.i −0.0654785 0.371347i
\(66\) 706445. 46518.7i 0.302465 0.0199170i
\(67\) −3.19283e6 + 1.16209e6i −1.29692 + 0.472041i −0.895993 0.444069i \(-0.853535\pi\)
−0.400928 + 0.916109i \(0.631312\pi\)
\(68\) 2.33653e6 850426.i 0.901134 0.327986i
\(69\) −894150. + 1.81455e6i −0.327671 + 0.664962i
\(70\) −74130.1 420413.i −0.0258316 0.146498i
\(71\) 1.63983e6 2.84026e6i 0.543743 0.941790i −0.454942 0.890521i \(-0.650340\pi\)
0.998685 0.0512693i \(-0.0163267\pi\)
\(72\) 1.98410e6 + 1.26232e6i 0.626470 + 0.398570i
\(73\) 1.48613e6 + 2.57405e6i 0.447123 + 0.774440i 0.998197 0.0600162i \(-0.0191152\pi\)
−0.551074 + 0.834456i \(0.685782\pi\)
\(74\) 1.18165e6 991520.i 0.338982 0.284440i
\(75\) −326971. + 2.99397e6i −0.0894942 + 0.819470i
\(76\) −170544. + 967203.i −0.0445645 + 0.252738i
\(77\) 2.01990e6 + 1.69490e6i 0.504211 + 0.423084i
\(78\) −362803. 1.48070e6i −0.0865646 0.353295i
\(79\) −3.46317e6 1.26049e6i −0.790276 0.287637i −0.0848252 0.996396i \(-0.527033\pi\)
−0.705451 + 0.708759i \(0.749255\pi\)
\(80\) −1.02942e6 −0.224791
\(81\) 2.73863e6 3.92132e6i 0.572579 0.819850i
\(82\) −1.09684e6 −0.219681
\(83\) −1.47926e6 538406.i −0.283969 0.103356i 0.196109 0.980582i \(-0.437169\pi\)
−0.480078 + 0.877226i \(0.659392\pi\)
\(84\) 949413. + 3.87482e6i 0.174774 + 0.713304i
\(85\) −2.08386e6 1.74857e6i −0.368046 0.308828i
\(86\) 66779.5 378725.i 0.0113214 0.0642066i
\(87\) −58750.2 + 537957.i −0.00956516 + 0.0875851i
\(88\) −2.72620e6 + 2.28756e6i −0.426451 + 0.357835i
\(89\) −224262. 388434.i −0.0337203 0.0584052i 0.848673 0.528918i \(-0.177402\pi\)
−0.882393 + 0.470513i \(0.844069\pi\)
\(90\) 50404.2 1.17080e6i 0.00728816 0.169291i
\(91\) 2.83894e6 4.91719e6i 0.394923 0.684026i
\(92\) −804298. 4.56140e6i −0.107686 0.610718i
\(93\) −5.17913e6 + 1.05103e7i −0.667676 + 1.35495i
\(94\) −4.86630e6 + 1.77119e6i −0.604298 + 0.219947i
\(95\) 1.00968e6 367492.i 0.120823 0.0439759i
\(96\) −8.29830e6 + 546435.i −0.957282 + 0.0630361i
\(97\) −1.73183e6 9.82167e6i −0.192665 1.09266i −0.915705 0.401852i \(-0.868367\pi\)
0.723040 0.690807i \(-0.242744\pi\)
\(98\) −431860. + 748003.i −0.0463502 + 0.0802809i
\(99\) 4.40988e6 + 5.73983e6i 0.456777 + 0.594533i
\(100\) −3.44799e6 5.97209e6i −0.344799 0.597209i
\(101\) 1.23097e7 1.03291e7i 1.18884 0.997553i 0.188959 0.981985i \(-0.439489\pi\)
0.999879 0.0155682i \(-0.00495570\pi\)
\(102\) −4.00672e6 2.93597e6i −0.373842 0.273938i
\(103\) −3.23442e6 + 1.83433e7i −0.291653 + 1.65404i 0.388852 + 0.921300i \(0.372872\pi\)
−0.680505 + 0.732743i \(0.738240\pi\)
\(104\) 5.87042e6 + 4.92587e6i 0.511743 + 0.429404i
\(105\) 3.15189e6 3.01912e6i 0.265711 0.254518i
\(106\) −7.59366e6 2.76386e6i −0.619270 0.225396i
\(107\) −2.26605e7 −1.78824 −0.894122 0.447824i \(-0.852199\pi\)
−0.894122 + 0.447824i \(0.852199\pi\)
\(108\) 248899. + 1.09486e7i 0.0190126 + 0.836327i
\(109\) 1.28788e7 0.952537 0.476269 0.879300i \(-0.341989\pi\)
0.476269 + 0.879300i \(0.341989\pi\)
\(110\) 1.66651e6 + 606559.i 0.119380 + 0.0434509i
\(111\) 1.51420e7 + 4.40850e6i 1.05088 + 0.305957i
\(112\) −5.36302e6 4.50011e6i −0.360700 0.302663i
\(113\) −2.07028e6 + 1.17411e7i −0.134975 + 0.765482i 0.839902 + 0.542738i \(0.182613\pi\)
−0.974877 + 0.222744i \(0.928499\pi\)
\(114\) 1.79560e6 790735.i 0.113512 0.0499878i
\(115\) −3.88178e6 + 3.25720e6i −0.238006 + 0.199711i
\(116\) −619536. 1.07307e6i −0.0368522 0.0638299i
\(117\) 1.05230e7 1.14979e7i 0.607422 0.663695i
\(118\) 348396. 603439.i 0.0195203 0.0338101i
\(119\) −3.21252e6 1.82191e7i −0.174756 0.991090i
\(120\) 3.27421e6 + 4.89698e6i 0.172971 + 0.258699i
\(121\) 8.01854e6 2.91851e6i 0.411478 0.149766i
\(122\) 8.54361e6 3.10962e6i 0.425973 0.155041i
\(123\) −6.23298e6 9.32218e6i −0.302015 0.451699i
\(124\) −4.65868e6 2.64207e7i −0.219425 1.24442i
\(125\) −8.34824e6 + 1.44596e7i −0.382305 + 0.662171i
\(126\) 5.38071e6 5.87919e6i 0.239631 0.261831i
\(127\) 1.90968e7 + 3.30767e7i 0.827271 + 1.43288i 0.900171 + 0.435536i \(0.143441\pi\)
−0.0729000 + 0.997339i \(0.523225\pi\)
\(128\) 1.85280e7 1.55468e7i 0.780895 0.655249i
\(129\) 3.59833e6 1.58461e6i 0.147583 0.0649918i
\(130\) 663136. 3.76083e6i 0.0264728 0.150135i
\(131\) 3.09678e7 + 2.59851e7i 1.20354 + 1.00989i 0.999522 + 0.0309242i \(0.00984505\pi\)
0.204020 + 0.978967i \(0.434599\pi\)
\(132\) −1.59126e7 4.63285e6i −0.602189 0.175323i
\(133\) 6.86662e6 + 2.49924e6i 0.253083 + 0.0921145i
\(134\) −1.55416e7 −0.557994
\(135\) 1.02372e7 6.22489e6i 0.358108 0.217753i
\(136\) 2.49692e7 0.851173
\(137\) −2.38775e7 8.69068e6i −0.793352 0.288757i −0.0866235 0.996241i \(-0.527608\pi\)
−0.706729 + 0.707484i \(0.749830\pi\)
\(138\) −6.68204e6 + 6.40055e6i −0.216437 + 0.207320i
\(139\) 2.99687e7 + 2.51468e7i 0.946492 + 0.794201i 0.978703 0.205280i \(-0.0658106\pi\)
−0.0322117 + 0.999481i \(0.510255\pi\)
\(140\) −1.73535e6 + 9.84164e6i −0.0534488 + 0.303123i
\(141\) −4.27073e7 3.12943e7i −1.28303 0.940153i
\(142\) 1.14918e7 9.64277e6i 0.336806 0.282613i
\(143\) 1.17938e7 + 2.04275e7i 0.337270 + 0.584169i
\(144\) −1.17086e7 1.52398e7i −0.326767 0.425314i
\(145\) −677792. + 1.17397e6i −0.0184633 + 0.0319793i
\(146\) 2.36083e6 + 1.33889e7i 0.0627811 + 0.356049i
\(147\) −8.81152e6 + 580230.i −0.228792 + 0.0150657i
\(148\) −3.39322e7 + 1.23503e7i −0.860390 + 0.313156i
\(149\) −4.92490e7 + 1.79252e7i −1.21968 + 0.443927i −0.870051 0.492962i \(-0.835914\pi\)
−0.349628 + 0.936889i \(0.613692\pi\)
\(150\) −6.08929e6 + 1.23573e7i −0.147315 + 0.298955i
\(151\) −5.73375e6 3.25177e7i −0.135525 0.768600i −0.974493 0.224419i \(-0.927952\pi\)
0.838968 0.544181i \(-0.183160\pi\)
\(152\) −4.93123e6 + 8.54114e6i −0.113895 + 0.197271i
\(153\) 2.18433e6 5.07380e7i 0.0493059 1.14528i
\(154\) 6.03049e6 + 1.04451e7i 0.133055 + 0.230458i
\(155\) −2.24841e7 + 1.88664e7i −0.484971 + 0.406939i
\(156\) −3.87443e6 + 3.54769e7i −0.0817093 + 0.748186i
\(157\) −4.40457e6 + 2.49796e7i −0.0908353 + 0.515153i 0.905109 + 0.425180i \(0.139789\pi\)
−0.995944 + 0.0899728i \(0.971322\pi\)
\(158\) −1.29136e7 1.08358e7i −0.260465 0.218556i
\(159\) −1.96619e7 8.02459e7i −0.387915 1.58319i
\(160\) −1.95757e7 7.12499e6i −0.377832 0.137519i
\(161\) −3.44618e7 −0.650799
\(162\) 1.79060e7 1.25704e7i 0.330899 0.232299i
\(163\) 5.99313e7 1.08392 0.541960 0.840404i \(-0.317682\pi\)
0.541960 + 0.840404i \(0.317682\pi\)
\(164\) 2.41279e7 + 8.78183e6i 0.427135 + 0.155465i
\(165\) 4.31502e6 + 1.76108e7i 0.0747806 + 0.305201i
\(166\) −5.51593e6 4.62841e6i −0.0935924 0.0785333i
\(167\) 241906. 1.37192e6i 0.00401919 0.0227940i −0.982732 0.185034i \(-0.940761\pi\)
0.986751 + 0.162240i \(0.0518717\pi\)
\(168\) −4.34930e6 + 3.98251e7i −0.0707679 + 0.647999i
\(169\) −9.15928e6 + 7.68555e6i −0.145968 + 0.122482i
\(170\) −6.22145e6 1.07759e7i −0.0971226 0.168221i
\(171\) 1.69244e7 + 1.07676e7i 0.258838 + 0.164676i
\(172\) −4.50126e6 + 7.79642e6i −0.0674504 + 0.116828i
\(173\) −9.58750e6 5.43734e7i −0.140781 0.798409i −0.970658 0.240463i \(-0.922701\pi\)
0.829877 0.557946i \(-0.188410\pi\)
\(174\) −1.09412e6 + 2.22037e6i −0.0157451 + 0.0319523i
\(175\) −4.82140e7 + 1.75485e7i −0.680048 + 0.247517i
\(176\) 2.73299e7 9.94729e6i 0.377872 0.137534i
\(177\) 7.10855e6 468091.i 0.0963550 0.00634489i
\(178\) −356257. 2.02043e6i −0.00473471 0.0268519i
\(179\) −2.25872e7 + 3.91222e7i −0.294359 + 0.509845i −0.974836 0.222925i \(-0.928439\pi\)
0.680477 + 0.732770i \(0.261773\pi\)
\(180\) −1.04828e7 + 2.53513e7i −0.133975 + 0.324001i
\(181\) −1.61353e7 2.79472e7i −0.202256 0.350318i 0.746999 0.664825i \(-0.231494\pi\)
−0.949255 + 0.314507i \(0.898161\pi\)
\(182\) 1.98952e7 1.66940e7i 0.244623 0.205263i
\(183\) 7.49799e7 + 5.49424e7i 0.904411 + 0.662719i
\(184\) 8.07674e6 4.58055e7i 0.0955815 0.542070i
\(185\) 3.02628e7 + 2.53935e7i 0.351406 + 0.294864i
\(186\) −3.87039e7 + 3.70735e7i −0.441021 + 0.422443i
\(187\) 7.22203e7 + 2.62860e7i 0.807632 + 0.293954i
\(188\) 1.21228e8 1.33061
\(189\) 8.05451e7 + 1.23218e7i 0.867807 + 0.132757i
\(190\) 4.91476e6 0.0519834
\(191\) 2.31250e7 + 8.41681e6i 0.240140 + 0.0874039i 0.459287 0.888288i \(-0.348105\pi\)
−0.219146 + 0.975692i \(0.570327\pi\)
\(192\) 1.39817e7 + 4.07069e6i 0.142563 + 0.0415062i
\(193\) −3.30316e7 2.77168e7i −0.330734 0.277519i 0.462265 0.886742i \(-0.347037\pi\)
−0.792999 + 0.609223i \(0.791481\pi\)
\(194\) 7.92156e6 4.49254e7i 0.0778941 0.441760i
\(195\) 3.57323e7 1.57356e7i 0.345096 0.151971i
\(196\) 1.54888e7 1.29967e7i 0.146934 0.123292i
\(197\) −6.59068e7 1.14154e8i −0.614184 1.06380i −0.990527 0.137318i \(-0.956152\pi\)
0.376343 0.926480i \(-0.377181\pi\)
\(198\) 9.97519e6 + 3.15703e7i 0.0913257 + 0.289035i
\(199\) 1.06706e7 1.84820e7i 0.0959846 0.166250i −0.814035 0.580816i \(-0.802733\pi\)
0.910019 + 0.414566i \(0.136067\pi\)
\(200\) −1.20250e7 6.81973e7i −0.106287 0.602784i
\(201\) −8.83183e7 1.32091e8i −0.767122 1.14732i
\(202\) 6.90694e7 2.51392e7i 0.589598 0.214596i
\(203\) −8.66310e6 + 3.15311e6i −0.0726837 + 0.0264547i
\(204\) 6.46317e7 + 9.66645e7i 0.533016 + 0.797190i
\(205\) −4.87790e6 2.76640e7i −0.0395453 0.224272i
\(206\) −4.25993e7 + 7.37841e7i −0.339521 + 0.588068i
\(207\) −9.23713e7 2.04193e7i −0.723837 0.160009i
\(208\) −3.13136e7 5.42368e7i −0.241275 0.417900i
\(209\) −2.32546e7 + 1.95129e7i −0.176196 + 0.147846i
\(210\) 1.82709e7 8.04602e6i 0.136142 0.0599533i
\(211\) −1.78489e7 + 1.01226e8i −0.130804 + 0.741828i 0.846886 + 0.531775i \(0.178475\pi\)
−0.977690 + 0.210053i \(0.932636\pi\)
\(212\) 1.44914e8 + 1.21597e8i 1.04456 + 0.876494i
\(213\) 1.47260e8 + 4.28737e7i 1.04413 + 0.303992i
\(214\) −9.74008e7 3.54510e7i −0.679382 0.247275i
\(215\) 9.84905e6 0.0675865
\(216\) −3.52550e7 + 1.04170e8i −0.238030 + 0.703323i
\(217\) −1.99611e8 −1.32609
\(218\) 5.53563e7 + 2.01480e7i 0.361884 + 0.131715i
\(219\) −1.00379e8 + 9.61501e7i −0.645783 + 0.618580i
\(220\) −3.18029e7 2.66858e7i −0.201367 0.168967i
\(221\) 2.87378e7 1.62980e8i 0.179094 1.01569i
\(222\) 5.81875e7 + 4.26376e7i 0.356939 + 0.261552i
\(223\) −2.00056e8 + 1.67867e8i −1.20805 + 1.01368i −0.208688 + 0.977982i \(0.566919\pi\)
−0.999363 + 0.0356932i \(0.988636\pi\)
\(224\) −7.08376e7 1.22694e8i −0.421110 0.729384i
\(225\) −1.39630e8 + 1.84692e7i −0.817225 + 0.108096i
\(226\) −2.72668e7 + 4.72276e7i −0.157129 + 0.272155i
\(227\) 2.59174e7 + 1.46985e8i 0.147062 + 0.834030i 0.965688 + 0.259704i \(0.0836248\pi\)
−0.818626 + 0.574326i \(0.805264\pi\)
\(228\) −4.58301e7 + 3.01787e6i −0.256082 + 0.0168628i
\(229\) 3.66191e6 1.33282e6i 0.0201504 0.00733413i −0.331925 0.943306i \(-0.607698\pi\)
0.352076 + 0.935972i \(0.385476\pi\)
\(230\) −2.17806e7 + 7.92747e6i −0.118038 + 0.0429623i
\(231\) −5.45053e7 + 1.10611e8i −0.290935 + 0.590411i
\(232\) −2.16066e6 1.22537e7i −0.0113600 0.0644257i
\(233\) 1.47100e8 2.54785e8i 0.761845 1.31955i −0.180053 0.983657i \(-0.557627\pi\)
0.941898 0.335898i \(-0.109040\pi\)
\(234\) 6.32185e7 3.29584e7i 0.322544 0.168155i
\(235\) −6.63139e7 1.14859e8i −0.333324 0.577335i
\(236\) −1.24953e7 + 1.04848e7i −0.0618808 + 0.0519242i
\(237\) 1.87111e7 1.71332e8i 0.0913020 0.836023i
\(238\) 1.46944e7 8.33363e7i 0.0706535 0.400696i
\(239\) −1.30824e8 1.09775e8i −0.619864 0.520127i 0.277897 0.960611i \(-0.410363\pi\)
−0.897761 + 0.440483i \(0.854807\pi\)
\(240\) −1.14568e7 4.67583e7i −0.0534962 0.218333i
\(241\) 2.38989e8 + 8.69851e7i 1.09981 + 0.400299i 0.827248 0.561838i \(-0.189905\pi\)
0.272566 + 0.962137i \(0.412128\pi\)
\(242\) 3.90316e7 0.177036
\(243\) 2.08592e8 + 8.07519e7i 0.932558 + 0.361020i
\(244\) −2.12837e8 −0.937957
\(245\) −2.07864e7 7.56564e6i −0.0903023 0.0328673i
\(246\) −1.22070e7 4.98202e7i −0.0522801 0.213370i
\(247\) 5.00748e7 + 4.20177e7i 0.211436 + 0.177416i
\(248\) 4.67824e7 2.65316e8i 0.194761 1.10454i
\(249\) 7.99227e6 7.31826e7i 0.0328074 0.300407i
\(250\) −5.85040e7 + 4.90906e7i −0.236807 + 0.198705i
\(251\) 1.40351e8 + 2.43095e8i 0.560218 + 0.970325i 0.997477 + 0.0709900i \(0.0226158\pi\)
−0.437259 + 0.899335i \(0.644051\pi\)
\(252\) −1.65435e8 + 8.62481e7i −0.651217 + 0.339506i
\(253\) 7.15822e7 1.23984e8i 0.277897 0.481331i
\(254\) 3.03367e7 + 1.72048e8i 0.116158 + 0.658766i
\(255\) 5.62311e7 1.14113e8i 0.212367 0.430967i
\(256\) 6.65058e7 2.42061e7i 0.247753 0.0901748i
\(257\) −3.78086e8 + 1.37612e8i −1.38939 + 0.505698i −0.925012 0.379938i \(-0.875945\pi\)
−0.464381 + 0.885636i \(0.653723\pi\)
\(258\) 1.79456e7 1.18170e6i 0.0650562 0.00428389i
\(259\) 4.66538e7 + 2.64587e8i 0.166854 + 0.946279i
\(260\) −4.46986e7 + 7.74202e7i −0.157720 + 0.273179i
\(261\) −2.50888e7 + 3.31854e6i −0.0873451 + 0.0115533i
\(262\) 9.24556e7 + 1.60138e8i 0.317599 + 0.550097i
\(263\) −1.92393e8 + 1.61437e8i −0.652144 + 0.547214i −0.907721 0.419575i \(-0.862179\pi\)
0.255576 + 0.966789i \(0.417735\pi\)
\(264\) −1.34246e8 9.83702e7i −0.449042 0.329041i
\(265\) 3.59383e7 2.03816e8i 0.118631 0.672787i
\(266\) 2.56046e7 + 2.14848e7i 0.0834127 + 0.0699915i
\(267\) 1.51475e7 1.45094e7i 0.0487024 0.0466509i
\(268\) 3.41880e8 + 1.24434e8i 1.08493 + 0.394882i
\(269\) 4.35706e8 1.36477 0.682387 0.730991i \(-0.260942\pi\)
0.682387 + 0.730991i \(0.260942\pi\)
\(270\) 5.37406e7 1.07407e7i 0.166161 0.0332092i
\(271\) 1.96129e8 0.598618 0.299309 0.954156i \(-0.403244\pi\)
0.299309 + 0.954156i \(0.403244\pi\)
\(272\) −1.91751e8 6.97918e7i −0.577760 0.210287i
\(273\) 2.54943e8 + 7.42250e7i 0.758358 + 0.220791i
\(274\) −8.90354e7 7.47096e7i −0.261478 0.219406i
\(275\) 3.70130e7 2.09911e8i 0.107322 0.608656i
\(276\) 1.98236e8 8.72978e7i 0.567544 0.249932i
\(277\) 2.83115e8 2.37562e8i 0.800357 0.671579i −0.147928 0.988998i \(-0.547261\pi\)
0.948285 + 0.317419i \(0.102816\pi\)
\(278\) 8.94728e7 + 1.54971e8i 0.249767 + 0.432608i
\(279\) −5.35036e8 1.18273e8i −1.47492 0.326040i
\(280\) −5.01771e7 + 8.69093e7i −0.136600 + 0.236599i
\(281\) 1.09261e8 + 6.19648e8i 0.293759 + 1.66599i 0.672202 + 0.740368i \(0.265349\pi\)
−0.378443 + 0.925625i \(0.623540\pi\)
\(282\) −1.34609e8 2.01324e8i −0.357439 0.534593i
\(283\) 4.96744e8 1.80800e8i 1.30281 0.474183i 0.404898 0.914362i \(-0.367307\pi\)
0.897910 + 0.440179i \(0.145085\pi\)
\(284\) −3.29998e8 + 1.20110e8i −0.854865 + 0.311146i
\(285\) 2.79291e7 + 4.17713e7i 0.0714661 + 0.106886i
\(286\) 1.87353e7 + 1.06253e8i 0.0473565 + 0.268572i
\(287\) 9.55200e7 1.65445e8i 0.238511 0.413112i
\(288\) −1.17174e8 3.70842e8i −0.289040 0.914777i
\(289\) −6.44450e7 1.11622e8i −0.157053 0.272024i
\(290\) −4.74993e6 + 3.98566e6i −0.0114365 + 0.00959638i
\(291\) 4.26844e8 1.87971e8i 1.01542 0.447162i
\(292\) 5.52657e7 3.13427e8i 0.129902 0.736711i
\(293\) 6.84067e7 + 5.74001e7i 0.158877 + 0.133314i 0.718761 0.695257i \(-0.244710\pi\)
−0.559883 + 0.828571i \(0.689154\pi\)
\(294\) −3.87819e7 1.12911e7i −0.0890048 0.0259132i
\(295\) 1.67691e7 + 6.10346e6i 0.0380306 + 0.0138420i
\(296\) −3.62614e8 −0.812689
\(297\) −2.11635e8 + 2.64185e8i −0.468748 + 0.585141i
\(298\) −2.39728e8 −0.524761
\(299\) −2.89689e8 1.05438e8i −0.626733 0.228112i
\(300\) 2.32890e8 2.23079e8i 0.497996 0.477018i
\(301\) 5.13109e7 + 4.30549e7i 0.108449 + 0.0909998i
\(302\) 2.62268e7 1.48740e8i 0.0547925 0.310744i
\(303\) 6.06163e8 + 4.44173e8i 1.25181 + 0.917283i
\(304\) 6.17430e7 5.18085e7i 0.126046 0.105765i
\(305\) 1.16425e8 + 2.01654e8i 0.234962 + 0.406966i
\(306\) 8.87652e7 2.14668e8i 0.177100 0.428294i
\(307\) −2.11296e8 + 3.65975e8i −0.416779 + 0.721883i −0.995613 0.0935622i \(-0.970175\pi\)
0.578834 + 0.815445i \(0.303508\pi\)
\(308\) −4.90281e7 2.78052e8i −0.0956131 0.542249i
\(309\) −8.69182e8 + 5.72348e7i −1.67593 + 0.110358i
\(310\) −1.26158e8 + 4.59178e7i −0.240519 + 0.0875417i
\(311\) −8.02839e8 + 2.92209e8i −1.51345 + 0.550849i −0.959501 0.281704i \(-0.909100\pi\)
−0.553945 + 0.832553i \(0.686878\pi\)
\(312\) −1.58408e8 + 3.21466e8i −0.295281 + 0.599231i
\(313\) 4.34117e7 + 2.46200e8i 0.0800206 + 0.453819i 0.998320 + 0.0579338i \(0.0184512\pi\)
−0.918300 + 0.395886i \(0.870438\pi\)
\(314\) −5.80109e7 + 1.00478e8i −0.105744 + 0.183154i
\(315\) 1.72212e8 + 1.09564e8i 0.310440 + 0.197506i
\(316\) 1.97313e8 + 3.41756e8i 0.351764 + 0.609273i
\(317\) −2.41693e8 + 2.02804e8i −0.426144 + 0.357577i −0.830494 0.557027i \(-0.811942\pi\)
0.404351 + 0.914604i \(0.367498\pi\)
\(318\) 4.10277e7 3.75677e8i 0.0715454 0.655119i
\(319\) 6.65051e6 3.77169e7i 0.0114706 0.0650532i
\(320\) 2.79439e7 + 2.34477e7i 0.0476718 + 0.0400014i
\(321\) −2.52196e8 1.02928e9i −0.425569 1.73687i
\(322\) −1.48126e8 5.39133e7i −0.247249 0.0899913i
\(323\) 2.12988e8 0.351678
\(324\) −4.94536e8 + 1.33156e8i −0.807774 + 0.217497i
\(325\) −4.58981e8 −0.741657
\(326\) 2.57600e8 + 9.37588e7i 0.411799 + 0.149882i
\(327\) 1.43332e8 + 5.84977e8i 0.226686 + 0.925170i
\(328\) 1.97518e8 + 1.65737e8i 0.309064 + 0.259335i
\(329\) 1.56627e8 8.88275e8i 0.242482 1.37519i
\(330\) −9.00396e6 + 8.24464e7i −0.0137922 + 0.126291i
\(331\) −2.71975e8 + 2.28214e8i −0.412222 + 0.345895i −0.825195 0.564848i \(-0.808935\pi\)
0.412973 + 0.910743i \(0.364490\pi\)
\(332\) 8.42804e7 + 1.45978e8i 0.126399 + 0.218929i
\(333\) −3.17219e7 + 7.36842e8i −0.0470766 + 1.09350i
\(334\) 3.18605e6 5.51840e6i 0.00467886 0.00810402i
\(335\) −6.91175e7 3.91985e8i −0.100446 0.569656i
\(336\) 1.44716e8 2.93681e8i 0.208128 0.422366i
\(337\) 2.62363e8 9.54923e7i 0.373420 0.135914i −0.148491 0.988914i \(-0.547442\pi\)
0.521911 + 0.853000i \(0.325219\pi\)
\(338\) −5.13925e7 + 1.87053e7i −0.0723922 + 0.0263486i
\(339\) −5.56344e8 + 3.66347e7i −0.775611 + 0.0510733i
\(340\) 5.05805e7 + 2.86856e8i 0.0697922 + 0.395811i
\(341\) 4.14621e8 7.18144e8i 0.566253 0.980779i
\(342\) 5.59003e7 + 7.27590e7i 0.0755654 + 0.0983548i
\(343\) −4.03273e8 6.98489e8i −0.539597 0.934610i
\(344\) −6.92529e7 + 5.81100e7i −0.0917240 + 0.0769656i
\(345\) −1.91149e8 1.40067e8i −0.250614 0.183641i
\(346\) 4.38543e7 2.48710e8i 0.0569175 0.322795i
\(347\) 9.77265e8 + 8.20023e8i 1.25562 + 1.05359i 0.996134 + 0.0878471i \(0.0279987\pi\)
0.259489 + 0.965746i \(0.416446\pi\)
\(348\) 4.18456e7 4.00829e7i 0.0532259 0.0509837i
\(349\) −1.24283e9 4.52353e8i −1.56503 0.569625i −0.593149 0.805092i \(-0.702116\pi\)
−0.971882 + 0.235468i \(0.924338\pi\)
\(350\) −2.34690e8 −0.292587
\(351\) 6.39370e8 + 3.50011e8i 0.789182 + 0.432023i
\(352\) 5.88560e8 0.719270
\(353\) 1.03435e9 + 3.76471e8i 1.25157 + 0.455534i 0.880931 0.473244i \(-0.156917\pi\)
0.370637 + 0.928778i \(0.379139\pi\)
\(354\) 3.12867e7 + 9.10890e6i 0.0374842 + 0.0109133i
\(355\) 2.94313e8 + 2.46958e8i 0.349149 + 0.292971i
\(356\) −8.33978e6 + 4.72973e7i −0.00979670 + 0.0555598i
\(357\) 7.91792e8 3.48684e8i 0.921027 0.405596i
\(358\) −1.58290e8 + 1.32821e8i −0.182332 + 0.152995i
\(359\) −7.88452e7 1.36564e8i −0.0899383 0.155778i 0.817547 0.575863i \(-0.195334\pi\)
−0.907485 + 0.420085i \(0.862000\pi\)
\(360\) −1.85990e8 + 2.03221e8i −0.210102 + 0.229567i
\(361\) 4.04872e8 7.01260e8i 0.452942 0.784519i
\(362\) −2.56321e7 1.45367e8i −0.0283991 0.161059i
\(363\) 2.21805e8 + 3.31735e8i 0.243387 + 0.364014i
\(364\) −5.71309e8 + 2.07939e8i −0.620892 + 0.225986i
\(365\) −3.27191e8 + 1.19088e8i −0.352189 + 0.128186i
\(366\) 2.36329e8 + 3.53458e8i 0.251961 + 0.376837i
\(367\) −1.11722e8 6.33607e8i −0.117980 0.669097i −0.985232 0.171227i \(-0.945227\pi\)
0.867252 0.497870i \(-0.165884\pi\)
\(368\) −1.90057e8 + 3.29189e8i −0.198800 + 0.344332i
\(369\) 3.54061e8 3.86862e8i 0.366848 0.400834i
\(370\) 9.03509e7 + 1.56492e8i 0.0927313 + 0.160615i
\(371\) 1.07821e9 9.04723e8i 1.09621 0.919828i
\(372\) 1.14823e9 5.05649e8i 1.15645 0.509271i
\(373\) −8.14846e7 + 4.62122e8i −0.0813008 + 0.461080i 0.916793 + 0.399363i \(0.130769\pi\)
−0.998094 + 0.0617167i \(0.980342\pi\)
\(374\) 2.69298e8 + 2.25968e8i 0.266185 + 0.223356i
\(375\) −7.49689e8 2.18267e8i −0.734128 0.213737i
\(376\) 1.14396e9 + 4.16366e8i 1.10982 + 0.403941i
\(377\) −8.24699e7 −0.0792685
\(378\) 3.26927e8 + 1.78970e8i 0.311336 + 0.170435i
\(379\) 3.28473e7 0.0309929 0.0154965 0.999880i \(-0.495067\pi\)
0.0154965 + 0.999880i \(0.495067\pi\)
\(380\) −1.08114e8 3.93501e7i −0.101074 0.0367878i
\(381\) −1.28987e9 + 1.23553e9i −1.19483 + 1.14450i
\(382\) 8.62296e7 + 7.23553e7i 0.0791471 + 0.0664123i
\(383\) 2.69953e8 1.53098e9i 0.245523 1.39243i −0.573752 0.819029i \(-0.694513\pi\)
0.819275 0.573401i \(-0.194376\pi\)
\(384\) 9.12367e8 + 6.68548e8i 0.822262 + 0.602523i
\(385\) −2.36624e8 + 1.98551e8i −0.211323 + 0.177321i
\(386\) −9.86170e7 1.70810e8i −0.0872763 0.151167i
\(387\) 1.12023e8 + 1.45807e8i 0.0982467 + 0.127876i
\(388\) −5.33952e8 + 9.24832e8i −0.464078 + 0.803807i
\(389\) −1.28134e8 7.26683e8i −0.110367 0.625924i −0.988940 0.148315i \(-0.952615\pi\)
0.878573 0.477608i \(-0.158496\pi\)
\(390\) 1.78204e8 1.17346e7i 0.152122 0.0100171i
\(391\) −9.43888e8 + 3.43547e8i −0.798550 + 0.290648i
\(392\) 1.90796e8 6.94441e7i 0.159981 0.0582283i
\(393\) −8.35639e8 + 1.69581e9i −0.694456 + 1.40930i
\(394\) −1.04698e8 5.93770e8i −0.0862383 0.489082i
\(395\) 2.15867e8 3.73892e8i 0.176237 0.305251i
\(396\) 3.33363e7 7.74340e8i 0.0269764 0.626612i
\(397\) −3.84512e8 6.65995e8i −0.308421 0.534200i 0.669596 0.742725i \(-0.266467\pi\)
−0.978017 + 0.208525i \(0.933134\pi\)
\(398\) 7.47787e7 6.27468e7i 0.0594548 0.0498885i
\(399\) −3.70996e7 + 3.39709e8i −0.0292391 + 0.267733i
\(400\) −9.82730e7 + 5.57334e8i −0.0767758 + 0.435417i
\(401\) 1.32596e9 + 1.11262e9i 1.02690 + 0.861668i 0.990478 0.137669i \(-0.0439609\pi\)
0.0364177 + 0.999337i \(0.488405\pi\)
\(402\) −1.72967e8 7.05928e8i −0.132792 0.541962i
\(403\) −1.67794e9 6.10722e8i −1.27706 0.464810i
\(404\) −1.72065e9 −1.29825
\(405\) 3.96679e8 + 3.95714e8i 0.296720 + 0.295998i
\(406\) −4.21691e7 −0.0312718
\(407\) −1.04882e9 3.81738e8i −0.771116 0.280663i
\(408\) 2.77889e8 + 1.13414e9i 0.202563 + 0.826719i
\(409\) −1.70550e9 1.43108e9i −1.23259 1.03427i −0.998066 0.0621561i \(-0.980202\pi\)
−0.234524 0.972110i \(-0.575353\pi\)
\(410\) 2.23121e7 1.26538e8i 0.0159881 0.0906729i
\(411\) 1.29007e8 1.18128e9i 0.0916574 0.839278i
\(412\) 1.52784e9 1.28201e9i 1.07631 0.903132i
\(413\) 6.06814e7 + 1.05103e8i 0.0423868 + 0.0734160i
\(414\) −3.65091e8 2.32276e8i −0.252872 0.160881i
\(415\) 9.22054e7 1.59704e8i 0.0633269 0.109685i
\(416\) −2.20076e8 1.24811e9i −0.149881 0.850015i
\(417\) −8.08680e8 + 1.64110e9i −0.546136 + 1.10830i
\(418\) −1.30481e8 + 4.74912e7i −0.0873836 + 0.0318050i
\(419\) −1.55448e9 + 5.65784e8i −1.03237 + 0.375752i −0.801983 0.597347i \(-0.796222\pi\)
−0.230388 + 0.973099i \(0.573999\pi\)
\(420\) −4.66338e8 + 3.07079e7i −0.307134 + 0.0202245i
\(421\) 1.61452e7 + 9.15641e7i 0.0105452 + 0.0598051i 0.989626 0.143666i \(-0.0458890\pi\)
−0.979081 + 0.203471i \(0.934778\pi\)
\(422\) −2.35081e8 + 4.07172e8i −0.152273 + 0.263745i
\(423\) 9.46142e8 2.28813e9i 0.607806 1.46990i
\(424\) 9.49831e8 + 1.64516e9i 0.605154 + 1.04816i
\(425\) −1.14561e9 + 9.61284e8i −0.723897 + 0.607422i
\(426\) 5.65888e8 + 4.14661e8i 0.354647 + 0.259872i
\(427\) −2.74985e8 + 1.55952e9i −0.170927 + 0.969376i
\(428\) 1.85876e9 + 1.55968e9i 1.14596 + 0.961574i
\(429\) −7.96596e8 + 7.63039e8i −0.487122 + 0.466602i
\(430\) 4.23337e7 + 1.54082e7i 0.0256772 + 0.00934572i
\(431\) 3.77937e8 0.227378 0.113689 0.993516i \(-0.463733\pi\)
0.113689 + 0.993516i \(0.463733\pi\)
\(432\) 5.61909e8 7.01435e8i 0.335330 0.418595i
\(433\) 2.48961e9 1.47375 0.736875 0.676028i \(-0.236300\pi\)
0.736875 + 0.676028i \(0.236300\pi\)
\(434\) −8.57978e8 3.12278e8i −0.503805 0.183370i
\(435\) −6.08671e7 1.77211e7i −0.0354544 0.0103223i
\(436\) −1.05640e9 8.86422e8i −0.610414 0.512198i
\(437\) 6.88948e7 3.90722e8i 0.0394913 0.223966i
\(438\) −5.81874e8 + 2.56242e8i −0.330879 + 0.145711i
\(439\) 5.47868e8 4.59716e8i 0.309065 0.259336i −0.475040 0.879964i \(-0.657567\pi\)
0.784105 + 0.620628i \(0.213122\pi\)
\(440\) −2.08450e8 3.61047e8i −0.116659 0.202059i
\(441\) −1.24421e8 3.93777e8i −0.0690810 0.218633i
\(442\) 3.78495e8 6.55573e8i 0.208489 0.361113i
\(443\) 2.97053e8 + 1.68467e9i 0.162338 + 0.920666i 0.951767 + 0.306823i \(0.0992660\pi\)
−0.789428 + 0.613843i \(0.789623\pi\)
\(444\) −9.38614e8 1.40381e9i −0.508916 0.761146i
\(445\) 4.93742e7 1.79707e7i 0.0265607 0.00966732i
\(446\) −1.12251e9 + 4.08561e8i −0.599127 + 0.218064i
\(447\) −1.36230e9 2.03748e9i −0.721433 1.07899i
\(448\) 4.30788e7 + 2.44312e8i 0.0226355 + 0.128373i
\(449\) −1.33697e9 + 2.31569e9i −0.697040 + 1.20731i 0.272448 + 0.962171i \(0.412167\pi\)
−0.969488 + 0.245139i \(0.921166\pi\)
\(450\) −6.29062e8 1.39058e8i −0.325424 0.0719370i
\(451\) 3.96818e8 + 6.87309e8i 0.203692 + 0.352805i
\(452\) 9.77936e8 8.20586e8i 0.498111 0.417965i
\(453\) 1.41320e9 6.22336e8i 0.714266 0.314544i
\(454\) −1.18549e8 + 6.72324e8i −0.0594569 + 0.337197i
\(455\) 5.09529e8 + 4.27546e8i 0.253588 + 0.212786i
\(456\) −4.42835e8 1.28928e8i −0.218708 0.0636754i
\(457\) 5.18047e8 + 1.88554e8i 0.253900 + 0.0924120i 0.465835 0.884872i \(-0.345754\pi\)
−0.211935 + 0.977284i \(0.567976\pi\)
\(458\) 1.78249e7 0.00866959
\(459\) 2.32892e9 4.65462e8i 1.12411 0.224667i
\(460\) 5.42594e8 0.259910
\(461\) 2.51762e9 + 9.16338e8i 1.19684 + 0.435615i 0.862121 0.506702i \(-0.169136\pi\)
0.334721 + 0.942317i \(0.391358\pi\)
\(462\) −4.07321e8 + 3.90163e8i −0.192172 + 0.184077i
\(463\) 3.15363e9 + 2.64621e9i 1.47665 + 1.23906i 0.909675 + 0.415320i \(0.136330\pi\)
0.566974 + 0.823736i \(0.308114\pi\)
\(464\) −1.76577e7 + 1.00142e8i −0.00820581 + 0.0465375i
\(465\) −1.10718e9 8.11300e8i −0.510661 0.374193i
\(466\) 1.03087e9 8.65001e8i 0.471903 0.395973i
\(467\) −1.40928e9 2.44095e9i −0.640307 1.10904i −0.985364 0.170463i \(-0.945474\pi\)
0.345057 0.938582i \(-0.387860\pi\)
\(468\) −1.65454e9 + 2.18849e8i −0.746135 + 0.0986926i
\(469\) 1.35347e9 2.34428e9i 0.605821 1.04931i
\(470\) −1.05344e8 5.97438e8i −0.0468025 0.265430i
\(471\) −1.18364e9 + 7.79413e7i −0.521969 + 0.0343712i
\(472\) −1.53922e8 + 5.60229e7i −0.0673756 + 0.0245227i
\(473\) −2.61480e8 + 9.51710e7i −0.113612 + 0.0413514i
\(474\) 3.48463e8 7.07155e8i 0.150291 0.304993i
\(475\) −1.02574e8 5.81724e8i −0.0439145 0.249052i
\(476\) −9.90477e8 + 1.71556e9i −0.420940 + 0.729089i
\(477\) 3.42609e9 1.78616e9i 1.44539 0.753539i
\(478\) −3.90581e8 6.76507e8i −0.163574 0.283318i
\(479\) 8.35356e8 7.00947e8i 0.347294 0.291414i −0.452408 0.891811i \(-0.649435\pi\)
0.799702 + 0.600397i \(0.204991\pi\)
\(480\) 1.05766e8 9.68461e8i 0.0436516 0.399704i
\(481\) −4.17345e8 + 2.36688e9i −0.170996 + 0.969769i
\(482\) 8.91156e8 + 7.47768e8i 0.362484 + 0.304160i
\(483\) −3.83535e8 1.56532e9i −0.154878 0.632102i
\(484\) −8.58605e8 3.12507e8i −0.344219 0.125285i
\(485\) 1.16832e9 0.465014
\(486\) 7.70251e8 + 6.73422e8i 0.304373 + 0.266109i
\(487\) 1.70729e9 0.669818 0.334909 0.942250i \(-0.391294\pi\)
0.334909 + 0.942250i \(0.391294\pi\)
\(488\) −2.00841e9 7.31001e8i −0.782317 0.284740i
\(489\) 6.66993e8 + 2.72219e9i 0.257953 + 1.05278i
\(490\) −7.75095e7 6.50382e7i −0.0297624 0.0249737i
\(491\) 3.04291e8 1.72572e9i 0.116012 0.657939i −0.870232 0.492643i \(-0.836031\pi\)
0.986244 0.165296i \(-0.0528580\pi\)
\(492\) −1.30360e8 + 1.19367e9i −0.0493477 + 0.451861i
\(493\) −2.05844e8 + 1.72724e8i −0.0773703 + 0.0649214i
\(494\) 1.49500e8 + 2.58942e8i 0.0557953 + 0.0966402i
\(495\) −7.51891e8 + 3.91992e8i −0.278636 + 0.145264i
\(496\) −1.10086e9 + 1.90674e9i −0.405084 + 0.701625i
\(497\) 4.53720e8 + 2.57317e9i 0.165783 + 0.940202i
\(498\) 1.48842e8 3.02054e8i 0.0540038 0.109593i
\(499\) −1.05008e9 + 3.82199e8i −0.378330 + 0.137701i −0.524184 0.851605i \(-0.675629\pi\)
0.145853 + 0.989306i \(0.453407\pi\)
\(500\) 1.68000e9 6.11469e8i 0.601054 0.218766i
\(501\) 6.50071e7 4.28066e6i 0.0230956 0.00152082i
\(502\) 2.22957e8 + 1.26445e9i 0.0786609 + 0.446108i
\(503\) −6.14025e8 + 1.06352e9i −0.215129 + 0.372614i −0.953312 0.301986i \(-0.902350\pi\)
0.738184 + 0.674600i \(0.235684\pi\)
\(504\) −1.85733e9 + 2.45672e8i −0.646223 + 0.0854771i
\(505\) 9.41221e8 + 1.63024e9i 0.325216 + 0.563290i
\(506\) 5.01644e8 4.20929e8i 0.172135 0.144438i
\(507\) −4.51028e8 3.30496e8i −0.153701 0.112626i
\(508\) 7.10165e8 4.02755e9i 0.240346 1.36307i
\(509\) 1.44191e9 + 1.20991e9i 0.484647 + 0.406667i 0.852103 0.523374i \(-0.175327\pi\)
−0.367456 + 0.930041i \(0.619771\pi\)
\(510\) 4.20219e8 4.02517e8i 0.140275 0.134366i
\(511\) −2.22517e9 8.09894e8i −0.737716 0.268507i
\(512\) −2.77215e9 −0.912791
\(513\) −3.00726e8 + 8.88573e8i −0.0983467 + 0.290591i
\(514\) −1.84040e9 −0.597779
\(515\) −2.05041e9 7.46287e8i −0.661477 0.240758i
\(516\) −4.04223e8 1.17687e8i −0.129523 0.0377098i
\(517\) 2.87043e9 + 2.40858e9i 0.913546 + 0.766556i
\(518\) −2.13400e8 + 1.21025e9i −0.0674589 + 0.382579i
\(519\) 2.36304e9 1.04062e9i 0.741967 0.326743i
\(520\) −6.87697e8 + 5.77046e8i −0.214479 + 0.179970i
\(521\) −8.90502e8 1.54240e9i −0.275869 0.477819i 0.694485 0.719507i \(-0.255632\pi\)
−0.970354 + 0.241688i \(0.922299\pi\)
\(522\) −1.13030e8 2.49860e7i −0.0347814 0.00768864i
\(523\) 2.74805e8 4.75977e8i 0.0839980 0.145489i −0.820966 0.570977i \(-0.806564\pi\)
0.904964 + 0.425489i \(0.139898\pi\)
\(524\) −7.51666e8 4.26291e9i −0.228226 1.29434i
\(525\) −1.33367e9 1.99466e9i −0.402245 0.601606i
\(526\) −1.07951e9 + 3.92910e8i −0.323428 + 0.117718i
\(527\) −5.46722e9 + 1.98991e9i −1.62716 + 0.592237i
\(528\) 7.55987e8 + 1.13067e9i 0.223509 + 0.334285i
\(529\) −2.66329e8 1.51043e9i −0.0782210 0.443614i
\(530\) 4.73329e8 8.19830e8i 0.138101 0.239198i
\(531\) 1.00375e8 + 3.17673e8i 0.0290933 + 0.0920768i
\(532\) −3.91224e8 6.77620e8i −0.112651 0.195117i
\(533\) 1.30914e9 1.09850e9i 0.374491 0.314235i
\(534\) 8.78068e7 3.86678e7i 0.0249536 0.0109889i
\(535\) 4.60965e8 2.61427e9i 0.130146 0.738094i
\(536\) 2.79873e9 + 2.34841e9i 0.785027 + 0.658716i
\(537\) −2.02838e9 5.90549e8i −0.565249 0.164568i
\(538\) 1.87278e9 + 6.81635e8i 0.518499 + 0.188718i
\(539\) 6.24961e8 0.171906
\(540\) −1.26817e9 1.94005e8i −0.346576 0.0530193i
\(541\) −2.87142e9 −0.779661 −0.389830 0.920887i \(-0.627466\pi\)
−0.389830 + 0.920887i \(0.627466\pi\)
\(542\) 8.43014e8 + 3.06832e8i 0.227425 + 0.0827758i
\(543\) 1.08984e9 1.04393e9i 0.292120 0.279815i
\(544\) −3.16333e9 2.65435e9i −0.842459 0.706907i
\(545\) −2.61983e8 + 1.48578e9i −0.0693243 + 0.393158i
\(546\) 9.79691e8 + 7.17881e8i 0.257582 + 0.188746i
\(547\) −2.69308e9 + 2.25976e9i −0.703548 + 0.590347i −0.922781 0.385326i \(-0.874089\pi\)
0.219233 + 0.975673i \(0.429645\pi\)
\(548\) 1.36041e9 + 2.35630e9i 0.353133 + 0.611645i
\(549\) −1.66111e9 + 4.01719e9i −0.428445 + 1.03614i
\(550\) 4.87485e8 8.44349e8i 0.124937 0.216398i
\(551\) −1.84304e7 1.04524e8i −0.00469359 0.0266187i
\(552\) 2.17046e9 1.42922e8i 0.549242 0.0361671i
\(553\) 2.75907e9 1.00422e9i 0.693785 0.252517i
\(554\) 1.58855e9 5.78186e8i 0.396933 0.144472i
\(555\) −8.16616e8 + 1.65720e9i −0.202765 + 0.411482i
\(556\) −7.27416e8 4.12538e9i −0.179482 1.01789i
\(557\) 1.17687e9 2.03840e9i 0.288559 0.499799i −0.684907 0.728630i \(-0.740157\pi\)
0.973466 + 0.228832i \(0.0734905\pi\)
\(558\) −2.11469e9 1.34540e9i −0.515261 0.327817i
\(559\) 2.99594e8 + 5.18912e8i 0.0725424 + 0.125647i
\(560\) 6.28258e8 5.27171e8i 0.151175 0.126851i
\(561\) −3.90198e8 + 3.57292e9i −0.0933072 + 0.854384i
\(562\) −4.99770e8 + 2.83434e9i −0.118766 + 0.673557i
\(563\) −6.25891e9 5.25185e9i −1.47815 1.24032i −0.908129 0.418690i \(-0.862489\pi\)
−0.570024 0.821628i \(-0.693066\pi\)
\(564\) 1.34919e9 + 5.50641e9i 0.316662 + 1.29239i
\(565\) −1.31242e9 4.77681e8i −0.306128 0.111421i
\(566\) 2.41799e9 0.560527
\(567\) 3.36731e8 + 3.79564e9i 0.0775787 + 0.874468i
\(568\) −3.52651e9 −0.807470
\(569\) 1.26058e9 + 4.58815e8i 0.286866 + 0.104411i 0.481445 0.876476i \(-0.340112\pi\)
−0.194580 + 0.980887i \(0.562334\pi\)
\(570\) 5.46978e7 + 2.23237e8i 0.0123711 + 0.0504899i
\(571\) −2.09458e9 1.75756e9i −0.470836 0.395078i 0.376263 0.926513i \(-0.377209\pi\)
−0.847099 + 0.531434i \(0.821653\pi\)
\(572\) 4.38584e8 2.48733e9i 0.0979866 0.555709i
\(573\) −1.24942e8 + 1.14405e9i −0.0277438 + 0.254042i
\(574\) 6.69399e8 5.61692e8i 0.147738 0.123967i
\(575\) 1.39289e9 + 2.41255e9i 0.305547 + 0.529224i
\(576\) −2.92911e7 + 6.80379e8i −0.00638642 + 0.148345i
\(577\) −5.88464e7 + 1.01925e8i −0.0127528 + 0.0220885i −0.872331 0.488915i \(-0.837393\pi\)
0.859579 + 0.511004i \(0.170726\pi\)
\(578\) −1.02376e8 5.80600e8i −0.0220520 0.125063i
\(579\) 8.91328e8 1.80882e9i 0.190837 0.387276i
\(580\) 1.36399e8 4.96451e7i 0.0290277 0.0105652i
\(581\) 1.17851e9 4.28943e8i 0.249297 0.0907367i
\(582\) 2.12875e9 1.40176e8i 0.447605 0.0294744i
\(583\) 1.01535e9 + 5.75833e9i 0.212215 + 1.20353i
\(584\) 1.59799e9 2.76780e9i 0.331994 0.575030i
\(585\) 1.11241e9 + 1.44790e9i 0.229731 + 0.299015i
\(586\) 2.04231e8 + 3.53738e8i 0.0419257 + 0.0726174i
\(587\) −3.93845e9 + 3.30475e9i −0.803696 + 0.674381i −0.949094 0.314992i \(-0.897998\pi\)
0.145398 + 0.989373i \(0.453554\pi\)
\(588\) 7.62711e8 + 5.58886e8i 0.154718 + 0.113371i
\(589\) 3.99054e8 2.26315e9i 0.0804690 0.456362i
\(590\) 6.25295e7 + 5.24685e7i 0.0125344 + 0.0105176i
\(591\) 4.45158e9 4.26406e9i 0.887070 0.849703i
\(592\) 2.78471e9 + 1.01355e9i 0.551637 + 0.200779i
\(593\) 5.30223e9 1.04416 0.522080 0.852896i \(-0.325156\pi\)
0.522080 + 0.852896i \(0.325156\pi\)
\(594\) −1.32296e9 + 8.04446e8i −0.258997 + 0.157487i
\(595\) 2.16723e9 0.421789
\(596\) 5.27346e9 + 1.91938e9i 1.02031 + 0.371364i
\(597\) 9.58239e8 + 2.78985e8i 0.184316 + 0.0536625i
\(598\) −1.08020e9 9.06400e8i −0.206563 0.173327i
\(599\) 1.61768e9 9.17429e9i 0.307537 1.74413i −0.303778 0.952743i \(-0.598248\pi\)
0.611315 0.791387i \(-0.290641\pi\)
\(600\) 2.96381e9 1.30518e9i 0.560172 0.246685i
\(601\) −3.36439e9 + 2.82306e9i −0.632188 + 0.530468i −0.901608 0.432554i \(-0.857612\pi\)
0.269420 + 0.963023i \(0.413168\pi\)
\(602\) 1.53191e8 + 2.65334e8i 0.0286183 + 0.0495684i
\(603\) 5.01687e9 5.48165e9i 0.931800 1.01812i
\(604\) −1.76781e9 + 3.06194e9i −0.326443 + 0.565416i
\(605\) 1.73583e8 + 9.84439e8i 0.0318687 + 0.180736i
\(606\) 1.91056e9 + 2.85747e9i 0.348744 + 0.521589i
\(607\) 1.94529e9 7.08027e8i 0.353040 0.128496i −0.159412 0.987212i \(-0.550960\pi\)
0.512451 + 0.858716i \(0.328738\pi\)
\(608\) 1.53270e9 5.57858e8i 0.276564 0.100661i
\(609\) −2.39634e8 3.58402e8i −0.0429920 0.0642998i
\(610\) 1.84950e8 + 1.04890e9i 0.0329913 + 0.187103i
\(611\) 4.03435e9 6.98770e9i 0.715533 1.23934i
\(612\) −3.67137e9 + 4.01150e9i −0.647438 + 0.707419i
\(613\) −4.98110e9 8.62752e9i −0.873401 1.51277i −0.858457 0.512886i \(-0.828576\pi\)
−0.0149438 0.999888i \(-0.504757\pi\)
\(614\) −1.48075e9 + 1.24250e9i −0.258162 + 0.216623i
\(615\) 1.20226e9 5.29444e8i 0.208418 0.0917818i
\(616\) 4.92339e8 2.79219e9i 0.0848656 0.481297i
\(617\) −7.01038e9 5.88241e9i −1.20155 1.00822i −0.999584 0.0288327i \(-0.990821\pi\)
−0.201971 0.979392i \(-0.564735\pi\)
\(618\) −3.82551e9 1.11377e9i −0.651973 0.189817i
\(619\) 5.22019e9 + 1.89999e9i 0.884645 + 0.321984i 0.744083 0.668088i \(-0.232887\pi\)
0.140562 + 0.990072i \(0.455109\pi\)
\(620\) 3.14283e9 0.529602
\(621\) −1.00548e8 4.42292e9i −0.0168482 0.741120i
\(622\) −3.90795e9 −0.651153
\(623\) 3.35785e8 + 1.22216e8i 0.0556357 + 0.0202497i
\(624\) 2.11503e9 2.02594e9i 0.348475 0.333795i
\(625\) 2.35594e9 + 1.97687e9i 0.385997 + 0.323890i
\(626\) −1.98570e8 + 1.12615e9i −0.0323522 + 0.183478i
\(627\) −1.14512e9 8.39100e8i −0.185530 0.135949i
\(628\) 2.08059e9 1.74582e9i 0.335218 0.281281i
\(629\) 3.91547e9 + 6.78179e9i 0.627345 + 1.08659i
\(630\) 5.68806e8 + 7.40349e8i 0.0906301 + 0.117963i
\(631\) −4.43172e9 + 7.67597e9i −0.702215 + 1.21627i 0.265473 + 0.964118i \(0.414472\pi\)
−0.967687 + 0.252153i \(0.918861\pi\)
\(632\) 6.88138e8 + 3.90263e9i 0.108434 + 0.614960i
\(633\) −4.79651e9 + 3.15845e8i −0.751644 + 0.0494950i
\(634\) −1.35613e9 + 4.93592e8i −0.211344 + 0.0769228i
\(635\) −4.20441e9 + 1.53028e9i −0.651624 + 0.237172i
\(636\) −3.91038e9 + 7.93555e9i −0.602725 + 1.22314i
\(637\) −2.33686e8 1.32530e9i −0.0358216 0.203155i
\(638\) 8.75914e7 1.51713e8i 0.0133533 0.0231286i
\(639\) −3.08503e8 + 7.16596e9i −0.0467743 + 1.08648i
\(640\) 1.41668e9 + 2.45376e9i 0.213620 + 0.370001i
\(641\) −6.27972e9 + 5.26931e9i −0.941753 + 0.790225i −0.977890 0.209122i \(-0.932939\pi\)
0.0361365 + 0.999347i \(0.488495\pi\)
\(642\) 5.26245e8 4.81866e9i 0.0784902 0.718710i
\(643\) −8.39804e7 + 4.76277e8i −0.0124578 + 0.0706514i −0.990403 0.138211i \(-0.955865\pi\)
0.977945 + 0.208862i \(0.0669760\pi\)
\(644\) 2.82677e9 + 2.37194e9i 0.417051 + 0.349948i
\(645\) 1.09613e8 + 4.47361e8i 0.0160843 + 0.0656447i
\(646\) 9.15475e8 + 3.33206e8i 0.133608 + 0.0486294i
\(647\) −5.31938e9 −0.772140 −0.386070 0.922469i \(-0.626168\pi\)
−0.386070 + 0.922469i \(0.626168\pi\)
\(648\) −5.12396e9 4.42004e8i −0.739763 0.0638137i
\(649\) −5.04177e8 −0.0723980
\(650\) −1.97282e9 7.18048e8i −0.281767 0.102555i
\(651\) −2.22152e9 9.06667e9i −0.315586 1.28800i
\(652\) −4.91594e9 4.12496e9i −0.694608 0.582845i
\(653\) −1.19403e9 + 6.77166e9i −0.167810 + 0.951697i 0.778310 + 0.627880i \(0.216077\pi\)
−0.946120 + 0.323817i \(0.895034\pi\)
\(654\) −2.99084e8 + 2.73862e9i −0.0418091 + 0.382833i
\(655\) −3.62776e9 + 3.04405e9i −0.504422 + 0.423260i
\(656\) −1.05359e9 1.82487e9i −0.145716 0.252388i
\(657\) −5.48445e9 3.48929e9i −0.754492 0.480019i
\(658\) 2.06287e9 3.57300e9i 0.282281 0.488925i
\(659\) 1.37811e9 + 7.81563e9i 0.187579 + 1.06381i 0.922597 + 0.385765i \(0.126062\pi\)
−0.735018 + 0.678047i \(0.762826\pi\)
\(660\) 8.58174e8 1.74154e9i 0.116191 0.235792i
\(661\) 1.04813e10 3.81490e9i 1.41160 0.513781i 0.480002 0.877267i \(-0.340636\pi\)
0.931599 + 0.363487i \(0.118414\pi\)
\(662\) −1.52605e9 + 5.55435e8i −0.204439 + 0.0744099i
\(663\) 7.72269e9 5.08532e8i 1.02913 0.0677674i
\(664\) 2.93931e8 + 1.66697e9i 0.0389635 + 0.220973i
\(665\) −4.28011e8 + 7.41338e8i −0.0564390 + 0.0977553i
\(666\) −1.28909e9 + 3.11751e9i −0.169092 + 0.408929i
\(667\) 2.50274e8 + 4.33488e8i 0.0326570 + 0.0565635i
\(668\) −1.14269e8 + 9.58831e7i −0.0148324 + 0.0124458i
\(669\) −9.85132e9 7.21867e9i −1.27205 0.932108i
\(670\) 3.16151e8 1.79298e9i 0.0406100 0.230311i
\(671\) −5.03953e9 4.22866e9i −0.643963 0.540349i
\(672\) 4.78462e9 4.58307e9i 0.608212 0.582591i
\(673\) 9.62384e8 + 3.50279e8i 0.121701 + 0.0442957i 0.402153 0.915572i \(-0.368262\pi\)
−0.280452 + 0.959868i \(0.590484\pi\)
\(674\) 1.27710e9 0.160662
\(675\) −2.39289e9 6.13672e9i −0.299474 0.768021i
\(676\) 1.28028e9 0.159402
\(677\) −5.57370e9 2.02866e9i −0.690372 0.251275i −0.0270775 0.999633i \(-0.508620\pi\)
−0.663294 + 0.748359i \(0.730842\pi\)
\(678\) −2.44862e9 7.12900e8i −0.301729 0.0878465i
\(679\) 6.08664e9 + 5.10729e9i 0.746162 + 0.626104i
\(680\) −5.07929e8 + 2.88061e9i −0.0619472 + 0.351320i
\(681\) −6.38787e9 + 2.81305e9i −0.775070 + 0.341320i
\(682\) 2.90564e9 2.43812e9i 0.350749 0.294313i
\(683\) −4.02868e9 6.97788e9i −0.483827 0.838013i 0.516000 0.856588i \(-0.327420\pi\)
−0.999827 + 0.0185753i \(0.994087\pi\)
\(684\) −6.47134e8 2.04810e9i −0.0773210 0.244712i
\(685\) 1.48833e9 2.57787e9i 0.176923 0.306439i
\(686\) −6.40628e8 3.63318e9i −0.0757655 0.429687i
\(687\) 1.01294e8 + 1.51497e8i 0.0119188 + 0.0178261i
\(688\) 6.94253e8 2.52688e8i 0.0812753 0.0295818i
\(689\) 1.18315e10 4.30633e9i 1.37808 0.501580i
\(690\) −6.02482e8 9.01085e8i −0.0698188 0.104422i
\(691\) 1.57923e9 + 8.95628e9i 0.182085 + 1.03265i 0.929644 + 0.368458i \(0.120114\pi\)
−0.747560 + 0.664195i \(0.768775\pi\)
\(692\) −2.95599e9 + 5.11993e9i −0.339103 + 0.587344i
\(693\) −5.63073e9 1.24471e9i −0.642686 0.142070i
\(694\) 2.91766e9 + 5.05354e9i 0.331342 + 0.573902i
\(695\) −3.51072e9 + 2.94585e9i −0.396689 + 0.332861i
\(696\) 5.32538e8 2.34516e8i 0.0598713 0.0263657i
\(697\) 9.66922e8 5.48369e9i 0.108163 0.613420i
\(698\) −4.63433e9 3.88866e9i −0.515814 0.432819i
\(699\) 1.32099e10 + 3.84597e9i 1.46295 + 0.425928i
\(700\) 5.16263e9 + 1.87905e9i 0.568890 + 0.207059i
\(701\) −4.96286e9 −0.544151 −0.272075 0.962276i \(-0.587710\pi\)
−0.272075 + 0.962276i \(0.587710\pi\)
\(702\) 2.20060e9 + 2.50469e9i 0.240083 + 0.273259i
\(703\) −3.09311e9 −0.335777
\(704\) −9.68449e8 3.52487e8i −0.104610 0.0380749i
\(705\) 4.47908e9 4.29040e9i 0.481423 0.461143i
\(706\) 3.85692e9 + 3.23634e9i 0.412501 + 0.346129i
\(707\) −2.22307e9 + 1.26077e10i −0.236584 + 1.34173i
\(708\) −6.15304e8 4.50872e8i −0.0651589 0.0477460i
\(709\) 4.59856e9 3.85865e9i 0.484574 0.406606i −0.367503 0.930022i \(-0.619787\pi\)
0.852077 + 0.523416i \(0.175343\pi\)
\(710\) 8.78684e8 + 1.52193e9i 0.0921358 + 0.159584i
\(711\) 7.99043e9 1.05691e9i 0.833732 0.110279i
\(712\) −2.41143e8 + 4.17671e8i −0.0250377 + 0.0433665i
\(713\) 1.88197e9 + 1.06732e10i 0.194446 + 1.10276i
\(714\) 3.94882e9 2.60026e8i 0.405998 0.0267346i
\(715\) −2.59656e9 + 9.45070e8i −0.265661 + 0.0966925i
\(716\) 4.54545e9 1.65441e9i 0.462787 0.168441i
\(717\) 3.53018e9 7.16399e9i 0.357668 0.725835i
\(718\) −1.25251e8 7.10335e8i −0.0126284 0.0716189i
\(719\) 1.52622e9 2.64350e9i 0.153132 0.265233i −0.779245 0.626719i \(-0.784397\pi\)
0.932377 + 0.361486i \(0.117731\pi\)
\(720\) 1.99634e9 1.04077e9i 0.199329 0.103918i
\(721\) −7.41968e9 1.28513e10i −0.737245 1.27695i
\(722\) 2.83732e9 2.38080e9i 0.280562 0.235419i
\(723\) −1.29123e9 + 1.18234e10i −0.127063 + 1.16348i
\(724\) −6.00034e8 + 3.40296e9i −0.0587612 + 0.333251i
\(725\) 5.70886e8 + 4.79031e8i 0.0556374 + 0.0466853i
\(726\) 4.34394e8 + 1.77288e9i 0.0421313 + 0.171950i
\(727\) 8.56173e9 + 3.11622e9i 0.826402 + 0.300786i 0.720381 0.693578i \(-0.243967\pi\)
0.106020 + 0.994364i \(0.466189\pi\)
\(728\) −6.10526e9 −0.586468
\(729\) −1.34641e9 + 1.03733e10i −0.128716 + 0.991682i
\(730\) −1.59266e9 −0.151528
\(731\) 1.83459e9 + 6.67735e8i 0.173711 + 0.0632257i
\(732\) −2.36873e9 9.66744e9i −0.223216 0.911009i
\(733\) −3.36988e9 2.82767e9i −0.316047 0.265195i 0.470939 0.882166i \(-0.343915\pi\)
−0.786986 + 0.616971i \(0.788360\pi\)
\(734\) 5.11029e8 2.89819e9i 0.0476990 0.270515i
\(735\) 1.12307e8 1.02836e9i 0.0104328 0.0955297i
\(736\) −5.89259e9 + 4.94447e9i −0.544796 + 0.457138i
\(737\) 5.62272e9 + 9.73884e9i 0.517381 + 0.896130i
\(738\) 2.12707e9 1.10893e9i 0.194798 0.101556i
\(739\) 3.90587e9 6.76516e9i 0.356010 0.616627i −0.631280 0.775555i \(-0.717470\pi\)
0.987290 + 0.158928i \(0.0508037\pi\)
\(740\) −7.34555e8 4.16587e9i −0.0666367 0.377915i
\(741\) −1.35122e9 + 2.74211e9i −0.122001 + 0.247583i
\(742\) 6.04979e9 2.20194e9i 0.543659 0.197876i
\(743\) 1.13282e9 4.12311e8i 0.101321 0.0368777i −0.290862 0.956765i \(-0.593942\pi\)
0.392183 + 0.919887i \(0.371720\pi\)
\(744\) 1.25718e10 8.27840e8i 1.11916 0.0736955i
\(745\) −1.06613e9 6.04632e9i −0.0944633 0.535728i
\(746\) −1.07320e9 + 1.85884e9i −0.0946447 + 0.163929i
\(747\) 3.41303e9 4.51448e8i 0.299584 0.0396265i
\(748\) −4.11473e9 7.12693e9i −0.359489 0.622654i
\(749\) 1.38297e10 1.16045e10i 1.20262 1.00911i
\(750\) −2.88089e9 2.11101e9i −0.249352 0.182716i
\(751\) −1.82681e9 + 1.03604e10i −0.157382 + 0.892555i 0.799194 + 0.601073i \(0.205260\pi\)
−0.956576 + 0.291483i \(0.905851\pi\)
\(752\) −7.62126e9 6.39499e9i −0.653528 0.548375i
\(753\) −9.47979e9 + 9.08045e9i −0.809126 + 0.775042i
\(754\) −3.54477e8 1.29019e8i −0.0301154 0.0109611i
\(755\) 3.86809e9 0.327101