Properties

Label 16.12.e.a.5.7
Level 16
Weight 12
Character 16.5
Analytic conductor 12.293
Analytic rank 0
Dimension 42
CM No

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Newspace parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 16.e (of order \(4\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(12.293490889\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(21\) over \(\Q(i)\)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 5.7
Character \(\chi\) = 16.5
Dual form 16.12.e.a.13.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-30.9382 - 33.0277i) q^{2} +(585.540 - 585.540i) q^{3} +(-133.660 + 2043.63i) q^{4} +(-6859.07 - 6859.07i) q^{5} +(-37454.6 - 1223.52i) q^{6} +19914.8i q^{7} +(71631.8 - 58811.8i) q^{8} -508568. i q^{9} +O(q^{10})\) \(q+(-30.9382 - 33.0277i) q^{2} +(585.540 - 585.540i) q^{3} +(-133.660 + 2043.63i) q^{4} +(-6859.07 - 6859.07i) q^{5} +(-37454.6 - 1223.52i) q^{6} +19914.8i q^{7} +(71631.8 - 58811.8i) q^{8} -508568. i q^{9} +(-14332.4 + 438747. i) q^{10} +(-96496.9 - 96496.9i) q^{11} +(1.11837e6 + 1.27489e6i) q^{12} +(-674561. + 674561. i) q^{13} +(657740. - 616127. i) q^{14} -8.03253e6 q^{15} +(-4.15857e6 - 546304. i) q^{16} +3.70861e6 q^{17} +(-1.67968e7 + 1.57342e7i) q^{18} +(-2.61985e6 + 2.61985e6i) q^{19} +(1.49342e7 - 1.31007e7i) q^{20} +(1.16609e7 + 1.16609e7i) q^{21} +(-201635. + 6.17251e6i) q^{22} +2.97611e7i q^{23} +(7.50660e6 - 7.63799e7i) q^{24} +4.52657e7i q^{25} +(4.31489e7 + 1.40953e6i) q^{26} +(-1.94060e8 - 1.94060e8i) q^{27} +(-4.06985e7 - 2.66181e6i) q^{28} +(4.14366e7 - 4.14366e7i) q^{29} +(2.48512e8 + 2.65296e8i) q^{30} +6.07925e7 q^{31} +(1.10615e8 + 1.54250e8i) q^{32} -1.13006e8 q^{33} +(-1.14738e8 - 1.22487e8i) q^{34} +(1.36597e8 - 1.36597e8i) q^{35} +(1.03933e9 + 6.79752e7i) q^{36} +(-4.37984e8 - 4.37984e8i) q^{37} +(1.67581e8 + 5.47432e6i) q^{38} +7.89965e8i q^{39} +(-8.94722e8 - 8.79330e7i) q^{40} -1.20680e9i q^{41} +(2.43661e7 - 7.45900e8i) q^{42} +(-1.45559e8 - 1.45559e8i) q^{43} +(2.10102e8 - 1.84306e8i) q^{44} +(-3.48830e9 + 3.48830e9i) q^{45} +(9.82941e8 - 9.20754e8i) q^{46} +1.52664e9 q^{47} +(-2.75490e9 + 2.11513e9i) q^{48} +1.58073e9 q^{49} +(1.49502e9 - 1.40044e9i) q^{50} +(2.17154e9 - 2.17154e9i) q^{51} +(-1.28839e9 - 1.46872e9i) q^{52} +(-2.52787e9 - 2.52787e9i) q^{53} +(-4.05499e8 + 1.24132e10i) q^{54} +1.32376e9i q^{55} +(1.17122e9 + 1.42653e9i) q^{56} +3.06806e9i q^{57} +(-2.65053e9 - 8.65839e7i) q^{58} +(-4.54873e9 - 4.54873e9i) q^{59} +(1.07363e9 - 1.64155e10i) q^{60} +(9.96512e7 - 9.96512e7i) q^{61} +(-1.88081e9 - 2.00784e9i) q^{62} +1.01280e10 q^{63} +(1.67228e9 - 8.42558e9i) q^{64} +9.25373e9 q^{65} +(3.49619e9 + 3.73232e9i) q^{66} +(7.32144e9 - 7.32144e9i) q^{67} +(-4.95693e8 + 7.57904e9i) q^{68} +(1.74263e10 + 1.74263e10i) q^{69} +(-8.73755e9 - 2.85426e8i) q^{70} -1.31476e9i q^{71} +(-2.99098e10 - 3.64296e10i) q^{72} +2.59505e9i q^{73} +(-9.15190e8 + 2.80160e10i) q^{74} +(2.65049e10 + 2.65049e10i) q^{75} +(-5.00385e9 - 5.70419e9i) q^{76} +(1.92171e9 - 1.92171e9i) q^{77} +(2.60907e10 - 2.44401e10i) q^{78} -4.08802e9 q^{79} +(2.47768e10 + 3.22711e10i) q^{80} -1.37169e11 q^{81} +(-3.98579e10 + 3.73363e10i) q^{82} +(3.03277e10 - 3.03277e10i) q^{83} +(-2.53892e10 + 2.22720e10i) q^{84} +(-2.54376e10 - 2.54376e10i) q^{85} +(-3.04154e8 + 9.31083e9i) q^{86} -4.85256e10i q^{87} +(-1.25874e10 - 1.23709e9i) q^{88} +5.68675e10i q^{89} +(2.23132e11 + 7.28899e9i) q^{90} +(-1.34337e10 - 1.34337e10i) q^{91} +(-6.08208e10 - 3.97787e9i) q^{92} +(3.55964e10 - 3.55964e10i) q^{93} +(-4.72314e10 - 5.04214e10i) q^{94} +3.59395e10 q^{95} +(1.55089e11 + 2.55497e10i) q^{96} -5.73135e10 q^{97} +(-4.89048e10 - 5.22078e10i) q^{98} +(-4.90752e10 + 4.90752e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42q - 2q^{2} - 2q^{3} + 3080q^{4} - 2q^{5} + 30352q^{6} + 74836q^{8} + O(q^{10}) \) \( 42q - 2q^{2} - 2q^{3} + 3080q^{4} - 2q^{5} + 30352q^{6} + 74836q^{8} - 988948q^{10} - 540846q^{11} + 2300260q^{12} - 2q^{13} - 1829956q^{14} - 6075004q^{15} - 3721448q^{16} - 4q^{17} - 32219106q^{18} - 11291290q^{19} + 68655164q^{20} + 354292q^{21} - 85011388q^{22} - 66180944q^{24} + 305685384q^{26} - 66463304q^{27} - 322075880q^{28} + 77673206q^{29} + 290643636q^{30} + 343549808q^{31} + 404698568q^{32} - 4q^{33} - 882461836q^{34} - 434731684q^{35} + 1854387628q^{36} - 522762058q^{37} - 1276252832q^{38} - 483241016q^{40} + 2372079160q^{42} + 3824193658q^{43} - 2657283740q^{44} + 97301954q^{45} - 1032658964q^{46} - 4586900144q^{47} - 1058870552q^{48} - 8474257474q^{49} + 6515930886q^{50} + 7074245796q^{51} - 13915491564q^{52} - 2100608058q^{53} + 4385621536q^{54} + 12910845976q^{56} - 21491153128q^{58} + 955824746q^{59} + 25615752768q^{60} + 2150827022q^{61} - 15814519760q^{62} + 27758037828q^{63} + 9674332160q^{64} - 1884965292q^{65} + 10932459412q^{66} - 3186519018q^{67} + 13817664656q^{68} - 16193060732q^{69} - 27206453120q^{70} - 20773133628q^{72} + 14141420908q^{74} + 28890034486q^{75} - 11786004940q^{76} - 22711870540q^{77} + 37031200508q^{78} + 48011833792q^{79} - 8952586328q^{80} - 90656394430q^{81} - 81555388352q^{82} + 55713221118q^{83} + 61178517160q^{84} - 84575506252q^{85} + 10047297860q^{86} - 162855622152q^{88} + 160133627736q^{90} - 147369662716q^{91} - 169766721928q^{92} - 69689773328q^{93} + 160320530128q^{94} + 375702304500q^{95} + 230764310192q^{96} - 4q^{97} - 108887063494q^{98} - 286271331106q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −30.9382 33.0277i −0.683643 0.729816i
\(3\) 585.540 585.540i 1.39120 1.39120i 0.568557 0.822644i \(-0.307502\pi\)
0.822644 0.568557i \(-0.192498\pi\)
\(4\) −133.660 + 2043.63i −0.0652637 + 0.997868i
\(5\) −6859.07 6859.07i −0.981591 0.981591i 0.0182428 0.999834i \(-0.494193\pi\)
−0.999834 + 0.0182428i \(0.994193\pi\)
\(6\) −37454.6 1223.52i −1.96641 0.0642359i
\(7\) 19914.8i 0.447854i 0.974606 + 0.223927i \(0.0718877\pi\)
−0.974606 + 0.223927i \(0.928112\pi\)
\(8\) 71631.8 58811.8i 0.772877 0.634555i
\(9\) 508568.i 2.87088i
\(10\) −14332.4 + 438747.i −0.0453230 + 1.38744i
\(11\) −96496.9 96496.9i −0.180656 0.180656i 0.610985 0.791642i \(-0.290773\pi\)
−0.791642 + 0.610985i \(0.790773\pi\)
\(12\) 1.11837e6 + 1.27489e6i 1.29744 + 1.47903i
\(13\) −674561. + 674561.i −0.503887 + 0.503887i −0.912643 0.408757i \(-0.865962\pi\)
0.408757 + 0.912643i \(0.365962\pi\)
\(14\) 657740. 616127.i 0.326851 0.306172i
\(15\) −8.03253e6 −2.73118
\(16\) −4.15857e6 546304.i −0.991481 0.130249i
\(17\) 3.70861e6 0.633494 0.316747 0.948510i \(-0.397409\pi\)
0.316747 + 0.948510i \(0.397409\pi\)
\(18\) −1.67968e7 + 1.57342e7i −2.09521 + 1.96266i
\(19\) −2.61985e6 + 2.61985e6i −0.242735 + 0.242735i −0.817981 0.575246i \(-0.804906\pi\)
0.575246 + 0.817981i \(0.304906\pi\)
\(20\) 1.49342e7 1.31007e7i 1.04356 0.915436i
\(21\) 1.16609e7 + 1.16609e7i 0.623055 + 0.623055i
\(22\) −201635. + 6.17251e6i −0.00834145 + 0.255351i
\(23\) 2.97611e7i 0.964153i 0.876129 + 0.482077i \(0.160117\pi\)
−0.876129 + 0.482077i \(0.839883\pi\)
\(24\) 7.50660e6 7.63799e7i 0.192434 1.95802i
\(25\) 4.52657e7i 0.927041i
\(26\) 4.31489e7 + 1.40953e6i 0.712223 + 0.0232660i
\(27\) −1.94060e8 1.94060e8i −2.60277 2.60277i
\(28\) −4.06985e7 2.66181e6i −0.446899 0.0292286i
\(29\) 4.14366e7 4.14366e7i 0.375142 0.375142i −0.494204 0.869346i \(-0.664541\pi\)
0.869346 + 0.494204i \(0.164541\pi\)
\(30\) 2.48512e8 + 2.65296e8i 1.86715 + 1.99326i
\(31\) 6.07925e7 0.381382 0.190691 0.981650i \(-0.438927\pi\)
0.190691 + 0.981650i \(0.438927\pi\)
\(32\) 1.10615e8 + 1.54250e8i 0.582762 + 0.812643i
\(33\) −1.13006e8 −0.502659
\(34\) −1.14738e8 1.22487e8i −0.433084 0.462334i
\(35\) 1.36597e8 1.36597e8i 0.439609 0.439609i
\(36\) 1.03933e9 + 6.79752e7i 2.86476 + 0.187364i
\(37\) −4.37984e8 4.37984e8i −1.03836 1.03836i −0.999234 0.0391281i \(-0.987542\pi\)
−0.0391281 0.999234i \(-0.512458\pi\)
\(38\) 1.67581e8 + 5.47432e6i 0.343096 + 0.0112078i
\(39\) 7.89965e8i 1.40201i
\(40\) −8.94722e8 8.79330e7i −1.38152 0.135776i
\(41\) 1.20680e9i 1.62677i −0.581729 0.813383i \(-0.697624\pi\)
0.581729 0.813383i \(-0.302376\pi\)
\(42\) 2.43661e7 7.45900e8i 0.0287683 0.880663i
\(43\) −1.45559e8 1.45559e8i −0.150995 0.150995i 0.627567 0.778562i \(-0.284051\pi\)
−0.778562 + 0.627567i \(0.784051\pi\)
\(44\) 2.10102e8 1.84306e8i 0.192062 0.168481i
\(45\) −3.48830e9 + 3.48830e9i −2.81803 + 2.81803i
\(46\) 9.82941e8 9.20754e8i 0.703655 0.659137i
\(47\) 1.52664e9 0.970953 0.485476 0.874250i \(-0.338646\pi\)
0.485476 + 0.874250i \(0.338646\pi\)
\(48\) −2.75490e9 + 2.11513e9i −1.56055 + 1.19815i
\(49\) 1.58073e9 0.799427
\(50\) 1.49502e9 1.40044e9i 0.676570 0.633765i
\(51\) 2.17154e9 2.17154e9i 0.881317 0.881317i
\(52\) −1.28839e9 1.46872e9i −0.469927 0.535698i
\(53\) −2.52787e9 2.52787e9i −0.830306 0.830306i 0.157252 0.987558i \(-0.449736\pi\)
−0.987558 + 0.157252i \(0.949736\pi\)
\(54\) −4.05499e8 + 1.24132e10i −0.120178 + 3.67891i
\(55\) 1.32376e9i 0.354661i
\(56\) 1.17122e9 + 1.42653e9i 0.284188 + 0.346136i
\(57\) 3.06806e9i 0.675386i
\(58\) −2.65053e9 8.65839e7i −0.530247 0.0173214i
\(59\) −4.54873e9 4.54873e9i −0.828332 0.828332i 0.158954 0.987286i \(-0.449188\pi\)
−0.987286 + 0.158954i \(0.949188\pi\)
\(60\) 1.07363e9 1.64155e10i 0.178247 2.72536i
\(61\) 9.96512e7 9.96512e7i 0.0151067 0.0151067i −0.699513 0.714620i \(-0.746600\pi\)
0.714620 + 0.699513i \(0.246600\pi\)
\(62\) −1.88081e9 2.00784e9i −0.260729 0.278339i
\(63\) 1.01280e10 1.28573
\(64\) 1.67228e9 8.42558e9i 0.194679 0.980867i
\(65\) 9.25373e9 0.989221
\(66\) 3.49619e9 + 3.73232e9i 0.343639 + 0.366849i
\(67\) 7.32144e9 7.32144e9i 0.662498 0.662498i −0.293470 0.955968i \(-0.594810\pi\)
0.955968 + 0.293470i \(0.0948101\pi\)
\(68\) −4.95693e8 + 7.57904e9i −0.0413441 + 0.632143i
\(69\) 1.74263e10 + 1.74263e10i 1.34133 + 1.34133i
\(70\) −8.73755e9 2.85426e8i −0.621370 0.0202981i
\(71\) 1.31476e9i 0.0864822i −0.999065 0.0432411i \(-0.986232\pi\)
0.999065 0.0432411i \(-0.0137684\pi\)
\(72\) −2.99098e10 3.64296e10i −1.82173 2.21884i
\(73\) 2.59505e9i 0.146511i 0.997313 + 0.0732556i \(0.0233389\pi\)
−0.997313 + 0.0732556i \(0.976661\pi\)
\(74\) −9.15190e8 + 2.80160e10i −0.0479443 + 1.46768i
\(75\) 2.65049e10 + 2.65049e10i 1.28970 + 1.28970i
\(76\) −5.00385e9 5.70419e9i −0.226375 0.258059i
\(77\) 1.92171e9 1.92171e9i 0.0809077 0.0809077i
\(78\) 2.60907e10 2.44401e10i 1.02321 0.958478i
\(79\) −4.08802e9 −0.149473 −0.0747367 0.997203i \(-0.523812\pi\)
−0.0747367 + 0.997203i \(0.523812\pi\)
\(80\) 2.47768e10 + 3.22711e10i 0.845378 + 1.10108i
\(81\) −1.37169e11 −4.37107
\(82\) −3.98579e10 + 3.73363e10i −1.18724 + 1.11213i
\(83\) 3.03277e10 3.03277e10i 0.845103 0.845103i −0.144415 0.989517i \(-0.546130\pi\)
0.989517 + 0.144415i \(0.0461299\pi\)
\(84\) −2.53892e10 + 2.22720e10i −0.662389 + 0.581064i
\(85\) −2.54376e10 2.54376e10i −0.621832 0.621832i
\(86\) −3.04154e8 + 9.31083e9i −0.00697191 + 0.213426i
\(87\) 4.85256e10i 1.04379i
\(88\) −1.25874e10 1.23709e9i −0.254262 0.0249888i
\(89\) 5.68675e10i 1.07949i 0.841828 + 0.539746i \(0.181480\pi\)
−0.841828 + 0.539746i \(0.818520\pi\)
\(90\) 2.23132e11 + 7.28899e9i 3.98317 + 0.130117i
\(91\) −1.34337e10 1.34337e10i −0.225668 0.225668i
\(92\) −6.08208e10 3.97787e9i −0.962098 0.0629242i
\(93\) 3.55964e10 3.55964e10i 0.530579 0.530579i
\(94\) −4.72314e10 5.04214e10i −0.663785 0.708617i
\(95\) 3.59395e10 0.476532
\(96\) 1.55089e11 + 2.55497e10i 1.94129 + 0.319811i
\(97\) −5.73135e10 −0.677661 −0.338830 0.940847i \(-0.610031\pi\)
−0.338830 + 0.940847i \(0.610031\pi\)
\(98\) −4.89048e10 5.22078e10i −0.546523 0.583435i
\(99\) −4.90752e10 + 4.90752e10i −0.518643 + 0.518643i
\(100\) −9.25064e10 6.05021e9i −0.925064 0.0605021i
\(101\) 3.62044e10 + 3.62044e10i 0.342763 + 0.342763i 0.857405 0.514642i \(-0.172075\pi\)
−0.514642 + 0.857405i \(0.672075\pi\)
\(102\) −1.38905e11 4.53755e9i −1.24571 0.0406930i
\(103\) 9.12485e10i 0.775570i 0.921750 + 0.387785i \(0.126760\pi\)
−0.921750 + 0.387785i \(0.873240\pi\)
\(104\) −8.64784e9 + 8.79921e10i −0.0696987 + 0.709186i
\(105\) 1.59966e11i 1.22317i
\(106\) −5.28212e9 + 1.61698e11i −0.0383377 + 1.17360i
\(107\) 7.80580e10 + 7.80580e10i 0.538030 + 0.538030i 0.922950 0.384920i \(-0.125771\pi\)
−0.384920 + 0.922950i \(0.625771\pi\)
\(108\) 4.22526e11 3.70650e11i 2.76709 2.42735i
\(109\) 3.50084e9 3.50084e9i 0.0217935 0.0217935i −0.696126 0.717920i \(-0.745095\pi\)
0.717920 + 0.696126i \(0.245095\pi\)
\(110\) 4.37207e10 4.09547e10i 0.258838 0.242462i
\(111\) −5.12915e11 −2.88914
\(112\) 1.08795e10 8.28171e10i 0.0583326 0.444039i
\(113\) 3.13967e11 1.60307 0.801534 0.597949i \(-0.204018\pi\)
0.801534 + 0.597949i \(0.204018\pi\)
\(114\) 1.01331e11 9.49201e10i 0.492907 0.461723i
\(115\) 2.04134e11 2.04134e11i 0.946404 0.946404i
\(116\) 7.91428e10 + 9.02197e10i 0.349859 + 0.398825i
\(117\) 3.43060e11 + 3.43060e11i 1.44660 + 1.44660i
\(118\) −9.50482e9 + 2.90964e11i −0.0382466 + 1.17081i
\(119\) 7.38562e10i 0.283713i
\(120\) −5.75384e11 + 4.72407e11i −2.11087 + 1.73308i
\(121\) 2.66688e11i 0.934727i
\(122\) −6.37427e9 2.08226e8i −0.0213526 0.000697519i
\(123\) −7.06631e11 7.06631e11i −2.26316 2.26316i
\(124\) −8.12552e9 + 1.24238e11i −0.0248904 + 0.380569i
\(125\) −2.44352e10 + 2.44352e10i −0.0716160 + 0.0716160i
\(126\) −3.13342e11 3.34505e11i −0.878984 0.938350i
\(127\) 6.20048e11 1.66535 0.832673 0.553765i \(-0.186809\pi\)
0.832673 + 0.553765i \(0.186809\pi\)
\(128\) −3.30015e11 + 2.05440e11i −0.848944 + 0.528483i
\(129\) −1.70462e11 −0.420130
\(130\) −2.86293e11 3.05629e11i −0.676274 0.721949i
\(131\) 1.33237e9 1.33237e9i 0.00301739 0.00301739i −0.705596 0.708614i \(-0.749321\pi\)
0.708614 + 0.705596i \(0.249321\pi\)
\(132\) 1.51043e10 2.30942e11i 0.0328054 0.501587i
\(133\) −5.21738e10 5.21738e10i −0.108710 0.108710i
\(134\) −4.68322e11 1.52985e10i −0.936415 0.0305895i
\(135\) 2.66215e12i 5.10971i
\(136\) 2.65654e11 2.18110e11i 0.489613 0.401987i
\(137\) 2.80780e11i 0.497054i 0.968625 + 0.248527i \(0.0799464\pi\)
−0.968625 + 0.248527i \(0.920054\pi\)
\(138\) 3.64132e10 1.11469e12i 0.0619333 1.89592i
\(139\) 1.98123e11 + 1.98123e11i 0.323857 + 0.323857i 0.850245 0.526388i \(-0.176454\pi\)
−0.526388 + 0.850245i \(0.676454\pi\)
\(140\) 2.60897e11 + 2.97412e11i 0.409982 + 0.467363i
\(141\) 8.93909e11 8.93909e11i 1.35079 1.35079i
\(142\) −4.34236e10 + 4.06764e10i −0.0631161 + 0.0591230i
\(143\) 1.30186e11 0.182061
\(144\) −2.77833e11 + 2.11492e12i −0.373929 + 2.84642i
\(145\) −5.68434e11 −0.736471
\(146\) 8.57087e10 8.02862e10i 0.106926 0.100161i
\(147\) 9.25580e11 9.25580e11i 1.11216 1.11216i
\(148\) 9.53620e11 8.36538e11i 1.10392 0.968381i
\(149\) 6.80120e11 + 6.80120e11i 0.758685 + 0.758685i 0.976083 0.217398i \(-0.0697571\pi\)
−0.217398 + 0.976083i \(0.569757\pi\)
\(150\) 5.53833e10 1.69541e12i 0.0595493 1.82294i
\(151\) 1.24483e12i 1.29044i −0.763996 0.645221i \(-0.776765\pi\)
0.763996 0.645221i \(-0.223235\pi\)
\(152\) −3.35864e10 + 3.41743e11i −0.0335756 + 0.341633i
\(153\) 1.88608e12i 1.81868i
\(154\) −1.22924e11 4.01552e9i −0.114360 0.00373575i
\(155\) −4.16980e11 4.16980e11i −0.374361 0.374361i
\(156\) −1.61440e12 1.05587e11i −1.39903 0.0915006i
\(157\) −5.32516e11 + 5.32516e11i −0.445538 + 0.445538i −0.893868 0.448330i \(-0.852019\pi\)
0.448330 + 0.893868i \(0.352019\pi\)
\(158\) 1.26476e11 + 1.35018e11i 0.102187 + 0.109088i
\(159\) −2.96035e12 −2.31025
\(160\) 2.99291e11 1.81673e12i 0.225650 1.36972i
\(161\) −5.92686e11 −0.431800
\(162\) 4.24375e12 + 4.53037e12i 2.98825 + 3.19008i
\(163\) −2.47550e9 + 2.47550e9i −0.00168512 + 0.00168512i −0.707949 0.706264i \(-0.750379\pi\)
0.706264 + 0.707949i \(0.250379\pi\)
\(164\) 2.46626e12 + 1.61301e11i 1.62330 + 0.106169i
\(165\) 7.75114e11 + 7.75114e11i 0.493405 + 0.493405i
\(166\) −1.93994e12 6.33712e10i −1.19452 0.0390209i
\(167\) 1.98829e12i 1.18451i −0.805751 0.592254i \(-0.798238\pi\)
0.805751 0.592254i \(-0.201762\pi\)
\(168\) 1.52109e12 + 1.49492e11i 0.876908 + 0.0861823i
\(169\) 8.82095e11i 0.492197i
\(170\) −5.31533e10 + 1.62714e12i −0.0287118 + 0.878934i
\(171\) 1.33237e12 + 1.33237e12i 0.696862 + 0.696862i
\(172\) 3.16925e11 2.78014e11i 0.160528 0.140819i
\(173\) 2.52033e11 2.52033e11i 0.123653 0.123653i −0.642572 0.766225i \(-0.722133\pi\)
0.766225 + 0.642572i \(0.222133\pi\)
\(174\) −1.60269e12 + 1.50129e12i −0.761778 + 0.713583i
\(175\) −9.01456e11 −0.415179
\(176\) 3.48573e11 + 4.54006e11i 0.155587 + 0.202648i
\(177\) −5.32693e12 −2.30475
\(178\) 1.87820e12 1.75938e12i 0.787830 0.737987i
\(179\) −1.45805e12 + 1.45805e12i −0.593037 + 0.593037i −0.938451 0.345414i \(-0.887739\pi\)
0.345414 + 0.938451i \(0.387739\pi\)
\(180\) −6.66257e12 7.59506e12i −2.62811 2.99594i
\(181\) 1.35746e12 + 1.35746e12i 0.519392 + 0.519392i 0.917387 0.397996i \(-0.130294\pi\)
−0.397996 + 0.917387i \(0.630294\pi\)
\(182\) −2.80705e10 + 8.59301e11i −0.0104197 + 0.318972i
\(183\) 1.16700e11i 0.0420328i
\(184\) 1.75030e12 + 2.13184e12i 0.611809 + 0.745172i
\(185\) 6.00833e12i 2.03849i
\(186\) −2.27696e12 7.43806e10i −0.749953 0.0244984i
\(187\) −3.57869e11 3.57869e11i −0.114445 0.114445i
\(188\) −2.04051e11 + 3.11989e12i −0.0633679 + 0.968883i
\(189\) 3.86467e12 3.86467e12i 1.16566 1.16566i
\(190\) −1.11190e12 1.18700e12i −0.325778 0.347781i
\(191\) 2.60506e12 0.741539 0.370770 0.928725i \(-0.379094\pi\)
0.370770 + 0.928725i \(0.379094\pi\)
\(192\) −3.95433e12 5.91271e12i −1.09375 1.63542i
\(193\) −2.54172e12 −0.683222 −0.341611 0.939841i \(-0.610973\pi\)
−0.341611 + 0.939841i \(0.610973\pi\)
\(194\) 1.77317e12 + 1.89293e12i 0.463278 + 0.494568i
\(195\) 5.41843e12 5.41843e12i 1.37620 1.37620i
\(196\) −2.11280e11 + 3.23043e12i −0.0521735 + 0.797723i
\(197\) −2.85642e12 2.85642e12i −0.685896 0.685896i 0.275426 0.961322i \(-0.411181\pi\)
−0.961322 + 0.275426i \(0.911181\pi\)
\(198\) 3.13914e12 + 1.02545e11i 0.733081 + 0.0239473i
\(199\) 3.66476e12i 0.832442i 0.909263 + 0.416221i \(0.136646\pi\)
−0.909263 + 0.416221i \(0.863354\pi\)
\(200\) 2.66215e12 + 3.24246e12i 0.588259 + 0.716489i
\(201\) 8.57399e12i 1.84334i
\(202\) 7.56510e10 2.31585e12i 0.0158264 0.484482i
\(203\) 8.25201e11 + 8.25201e11i 0.168009 + 0.168009i
\(204\) 4.14759e12 + 4.72808e12i 0.821920 + 0.936956i
\(205\) −8.27755e12 + 8.27755e12i −1.59682 + 1.59682i
\(206\) 3.01373e12 2.82306e12i 0.566024 0.530213i
\(207\) 1.51355e13 2.76797
\(208\) 3.17373e12 2.43670e12i 0.565225 0.433963i
\(209\) 5.05615e11 0.0877032
\(210\) −5.28331e12 + 4.94906e12i −0.892689 + 0.836212i
\(211\) 1.86773e12 1.86773e12i 0.307441 0.307441i −0.536475 0.843916i \(-0.680245\pi\)
0.843916 + 0.536475i \(0.180245\pi\)
\(212\) 5.50393e12 4.82817e12i 0.882725 0.774347i
\(213\) −7.69847e11 7.69847e11i −0.120314 0.120314i
\(214\) 1.63106e11 4.99305e12i 0.0248425 0.760484i
\(215\) 1.99680e12i 0.296431i
\(216\) −2.53139e13 2.48784e12i −3.66322 0.360021i
\(217\) 1.21067e12i 0.170804i
\(218\) −2.23934e11 7.31518e9i −0.0308042 0.00100627i
\(219\) 1.51951e12 + 1.51951e12i 0.203826 + 0.203826i
\(220\) −2.70528e12 1.76934e11i −0.353905 0.0231465i
\(221\) −2.50168e12 + 2.50168e12i −0.319209 + 0.319209i
\(222\) 1.58686e13 + 1.69404e13i 1.97514 + 2.10854i
\(223\) −1.26372e13 −1.53453 −0.767263 0.641332i \(-0.778382\pi\)
−0.767263 + 0.641332i \(0.778382\pi\)
\(224\) −3.07185e12 + 2.20288e12i −0.363945 + 0.260992i
\(225\) 2.30207e13 2.66142
\(226\) −9.71355e12 1.03696e13i −1.09593 1.16995i
\(227\) 6.38980e12 6.38980e12i 0.703632 0.703632i −0.261557 0.965188i \(-0.584236\pi\)
0.965188 + 0.261557i \(0.0842358\pi\)
\(228\) −6.26999e12 4.10077e11i −0.673946 0.0440781i
\(229\) 1.21476e12 + 1.21476e12i 0.127466 + 0.127466i 0.767962 0.640496i \(-0.221271\pi\)
−0.640496 + 0.767962i \(0.721271\pi\)
\(230\) −1.30576e13 4.26548e11i −1.33770 0.0436983i
\(231\) 2.25048e12i 0.225118i
\(232\) 5.31216e11 5.40514e12i 0.0518904 0.527987i
\(233\) 1.65378e13i 1.57769i 0.614595 + 0.788843i \(0.289319\pi\)
−0.614595 + 0.788843i \(0.710681\pi\)
\(234\) 7.16841e11 2.19441e13i 0.0667938 2.04471i
\(235\) −1.04713e13 1.04713e13i −0.953078 0.953078i
\(236\) 9.90393e12 8.68796e12i 0.880626 0.772506i
\(237\) −2.39370e12 + 2.39370e12i −0.207948 + 0.207948i
\(238\) 2.43930e12 2.28498e12i 0.207058 0.193958i
\(239\) 9.34650e12 0.775283 0.387642 0.921810i \(-0.373290\pi\)
0.387642 + 0.921810i \(0.373290\pi\)
\(240\) 3.34039e13 + 4.38820e12i 2.70791 + 0.355734i
\(241\) 1.11589e13 0.884150 0.442075 0.896978i \(-0.354243\pi\)
0.442075 + 0.896978i \(0.354243\pi\)
\(242\) −8.80811e12 + 8.25085e12i −0.682179 + 0.639020i
\(243\) −4.59407e13 + 4.59407e13i −3.47827 + 3.47827i
\(244\) 1.90331e11 + 2.16970e11i 0.0140885 + 0.0160604i
\(245\) −1.08423e13 1.08423e13i −0.784710 0.784710i
\(246\) −1.47654e12 + 4.52003e13i −0.104497 + 3.19888i
\(247\) 3.53450e12i 0.244622i
\(248\) 4.35467e12 3.57531e12i 0.294762 0.242008i
\(249\) 3.55161e13i 2.35142i
\(250\) 1.56302e12 + 5.10585e10i 0.101226 + 0.00330673i
\(251\) −8.13313e12 8.13313e12i −0.515291 0.515291i 0.400852 0.916143i \(-0.368714\pi\)
−0.916143 + 0.400852i \(0.868714\pi\)
\(252\) −1.35371e12 + 2.06980e13i −0.0839118 + 1.28299i
\(253\) 2.87185e12 2.87185e12i 0.174180 0.174180i
\(254\) −1.91831e13 2.04788e13i −1.13850 1.21540i
\(255\) −2.97895e13 −1.73019
\(256\) 1.69953e13 + 4.54369e12i 0.966070 + 0.258279i
\(257\) 1.40965e13 0.784294 0.392147 0.919903i \(-0.371732\pi\)
0.392147 + 0.919903i \(0.371732\pi\)
\(258\) 5.27377e12 + 5.62996e12i 0.287219 + 0.306617i
\(259\) 8.72236e12 8.72236e12i 0.465035 0.465035i
\(260\) −1.23685e12 + 1.89112e13i −0.0645602 + 0.987112i
\(261\) −2.10733e13 2.10733e13i −1.07699 1.07699i
\(262\) −8.52261e10 2.78405e9i −0.00426496 0.000139322i
\(263\) 3.74224e13i 1.83390i −0.399003 0.916950i \(-0.630644\pi\)
0.399003 0.916950i \(-0.369356\pi\)
\(264\) −8.09479e12 + 6.64606e12i −0.388494 + 0.318965i
\(265\) 3.46778e13i 1.63004i
\(266\) −1.09020e11 + 3.33734e12i −0.00501945 + 0.153657i
\(267\) 3.32982e13 + 3.32982e13i 1.50179 + 1.50179i
\(268\) 1.39837e13 + 1.59409e13i 0.617849 + 0.704323i
\(269\) 6.31416e12 6.31416e12i 0.273324 0.273324i −0.557113 0.830437i \(-0.688091\pi\)
0.830437 + 0.557113i \(0.188091\pi\)
\(270\) 8.79246e13 8.23619e13i 3.72915 3.49322i
\(271\) −3.31124e12 −0.137613 −0.0688064 0.997630i \(-0.521919\pi\)
−0.0688064 + 0.997630i \(0.521919\pi\)
\(272\) −1.54225e13 2.02603e12i −0.628097 0.0825120i
\(273\) −1.57320e13 −0.627898
\(274\) 9.27353e12 8.68682e12i 0.362758 0.339807i
\(275\) 4.36799e12 4.36799e12i 0.167476 0.167476i
\(276\) −3.79422e13 + 3.32838e13i −1.42601 + 1.25093i
\(277\) 3.06698e13 + 3.06698e13i 1.12998 + 1.12998i 0.990179 + 0.139803i \(0.0446469\pi\)
0.139803 + 0.990179i \(0.455353\pi\)
\(278\) 4.13988e11 1.26731e13i 0.0149535 0.457759i
\(279\) 3.09171e13i 1.09490i
\(280\) 1.75117e12 1.78182e13i 0.0608077 0.618720i
\(281\) 1.12496e13i 0.383046i −0.981488 0.191523i \(-0.938657\pi\)
0.981488 0.191523i \(-0.0613427\pi\)
\(282\) −5.71796e13 1.86787e12i −1.90929 0.0623700i
\(283\) 3.47187e13 + 3.47187e13i 1.13694 + 1.13694i 0.988995 + 0.147946i \(0.0472662\pi\)
0.147946 + 0.988995i \(0.452734\pi\)
\(284\) 2.68689e12 + 1.75731e11i 0.0862978 + 0.00564414i
\(285\) 2.10440e13 2.10440e13i 0.662952 0.662952i
\(286\) −4.02772e12 4.29975e12i −0.124465 0.132871i
\(287\) 2.40332e13 0.728553
\(288\) 7.84465e13 5.62555e13i 2.33300 1.67304i
\(289\) −2.05181e13 −0.598686
\(290\) 1.75863e13 + 1.87741e13i 0.503483 + 0.537489i
\(291\) −3.35594e13 + 3.35594e13i −0.942763 + 0.942763i
\(292\) −5.30334e12 3.46855e11i −0.146199 0.00956185i
\(293\) −4.28304e13 4.28304e13i −1.15873 1.15873i −0.984750 0.173975i \(-0.944339\pi\)
−0.173975 0.984750i \(-0.555661\pi\)
\(294\) −5.92055e13 1.93405e12i −1.57200 0.0513519i
\(295\) 6.24002e13i 1.62617i
\(296\) −5.71322e13 5.61494e12i −1.46143 0.143628i
\(297\) 3.74524e13i 0.940414i
\(298\) 1.42115e12 4.35045e13i 0.0350307 1.07237i
\(299\) −2.00757e13 2.00757e13i −0.485824 0.485824i
\(300\) −5.77089e13 + 5.06236e13i −1.37112 + 1.20278i
\(301\) 2.89878e12 2.89878e12i 0.0676238 0.0676238i
\(302\) −4.11140e13 + 3.85129e13i −0.941785 + 0.882202i
\(303\) 4.23983e13 0.953705
\(304\) 1.23261e13 9.46361e12i 0.272283 0.209051i
\(305\) −1.36703e12 −0.0296571
\(306\) −6.22929e13 + 5.83519e13i −1.32731 + 1.24333i
\(307\) 5.00993e11 5.00993e11i 0.0104851 0.0104851i −0.701845 0.712330i \(-0.747640\pi\)
0.712330 + 0.701845i \(0.247640\pi\)
\(308\) 3.67042e12 + 4.18414e12i 0.0754549 + 0.0860155i
\(309\) 5.34297e13 + 5.34297e13i 1.07897 + 1.07897i
\(310\) −8.71301e11 + 2.66725e13i −0.0172854 + 0.529145i
\(311\) 6.71357e13i 1.30849i −0.756282 0.654246i \(-0.772986\pi\)
0.756282 0.654246i \(-0.227014\pi\)
\(312\) 4.64593e13 + 5.65866e13i 0.889656 + 1.08359i
\(313\) 1.16967e13i 0.220075i 0.993927 + 0.110037i \(0.0350971\pi\)
−0.993927 + 0.110037i \(0.964903\pi\)
\(314\) 3.40629e13 + 1.11272e12i 0.629750 + 0.0205718i
\(315\) −6.94688e13 6.94688e13i −1.26207 1.26207i
\(316\) 5.46405e11 8.35442e12i 0.00975519 0.149155i
\(317\) 5.42552e13 5.42552e13i 0.951952 0.951952i −0.0469451 0.998897i \(-0.514949\pi\)
0.998897 + 0.0469451i \(0.0149486\pi\)
\(318\) 9.15876e13 + 9.77734e13i 1.57938 + 1.68605i
\(319\) −7.99701e12 −0.135543
\(320\) −6.92620e13 + 4.63214e13i −1.15391 + 0.771715i
\(321\) 9.14122e13 1.49702
\(322\) 1.83366e13 + 1.95751e13i 0.295197 + 0.315134i
\(323\) −9.71601e12 + 9.71601e12i −0.153771 + 0.153771i
\(324\) 1.83340e13 2.80323e14i 0.285272 4.36175i
\(325\) −3.05345e13 3.05345e13i −0.467123 0.467123i
\(326\) 1.58348e11 + 5.17270e9i 0.00238186 + 7.78073e-5i
\(327\) 4.09976e12i 0.0606381i
\(328\) −7.09742e13 8.64454e13i −1.03227 1.25729i
\(329\) 3.04027e13i 0.434845i
\(330\) 1.61964e12 4.95808e13i 0.0227820 0.697408i
\(331\) 9.47342e13 + 9.47342e13i 1.31055 + 1.31055i 0.921011 + 0.389537i \(0.127365\pi\)
0.389537 + 0.921011i \(0.372635\pi\)
\(332\) 5.79250e13 + 6.60322e13i 0.788146 + 0.898455i
\(333\) −2.22745e14 + 2.22745e14i −2.98101 + 2.98101i
\(334\) −6.56685e13 + 6.15139e13i −0.864474 + 0.809781i
\(335\) −1.00437e14 −1.30060
\(336\) −4.21223e13 5.48631e13i −0.536595 0.698899i
\(337\) −2.48393e13 −0.311298 −0.155649 0.987812i \(-0.549747\pi\)
−0.155649 + 0.987812i \(0.549747\pi\)
\(338\) 2.91336e13 2.72904e13i 0.359213 0.336487i
\(339\) 1.83840e14 1.83840e14i 2.23019 2.23019i
\(340\) 5.53852e13 4.85852e13i 0.661089 0.579923i
\(341\) −5.86628e12 5.86628e12i −0.0688992 0.0688992i
\(342\) 2.78406e12 8.52264e13i 0.0321762 0.984987i
\(343\) 7.08579e13i 0.805880i
\(344\) −1.89873e13 1.86606e12i −0.212516 0.0208860i
\(345\) 2.39057e14i 2.63328i
\(346\) −1.61215e13 5.26637e11i −0.174778 0.00570943i
\(347\) −4.05821e13 4.05821e13i −0.433035 0.433035i 0.456625 0.889659i \(-0.349058\pi\)
−0.889659 + 0.456625i \(0.849058\pi\)
\(348\) 9.91686e13 + 6.48593e12i 1.04157 + 0.0681219i
\(349\) −5.40864e13 + 5.40864e13i −0.559175 + 0.559175i −0.929073 0.369897i \(-0.879393\pi\)
0.369897 + 0.929073i \(0.379393\pi\)
\(350\) 2.78894e13 + 2.97730e13i 0.283834 + 0.303004i
\(351\) 2.61811e14 2.62300
\(352\) 4.21058e12 2.55587e13i 0.0415296 0.252089i
\(353\) 1.19115e14 1.15666 0.578328 0.815805i \(-0.303706\pi\)
0.578328 + 0.815805i \(0.303706\pi\)
\(354\) 1.64806e14 + 1.75936e14i 1.57563 + 1.68205i
\(355\) −9.01806e12 + 9.01806e12i −0.0848901 + 0.0848901i
\(356\) −1.16216e14 7.60091e12i −1.07719 0.0704516i
\(357\) 4.32458e13 + 4.32458e13i 0.394701 + 0.394701i
\(358\) 9.32657e13 + 3.04668e12i 0.838234 + 0.0273823i
\(359\) 1.67025e14i 1.47830i 0.673541 + 0.739150i \(0.264772\pi\)
−0.673541 + 0.739150i \(0.735228\pi\)
\(360\) −4.47199e13 + 4.55027e14i −0.389796 + 3.96619i
\(361\) 1.02763e14i 0.882160i
\(362\) 2.83648e12 8.68312e13i 0.0239819 0.734139i
\(363\) −1.56157e14 1.56157e14i −1.30039 1.30039i
\(364\) 2.92492e13 2.56581e13i 0.239914 0.210459i
\(365\) 1.77997e13 1.77997e13i 0.143814 0.143814i
\(366\) −3.85432e12 + 3.61047e12i −0.0306762 + 0.0287354i
\(367\) −1.32967e14 −1.04251 −0.521255 0.853401i \(-0.674536\pi\)
−0.521255 + 0.853401i \(0.674536\pi\)
\(368\) 1.62586e13 1.23764e14i 0.125580 0.955940i
\(369\) −6.13741e14 −4.67025
\(370\) 1.98441e14 1.85887e14i 1.48773 1.39360i
\(371\) 5.03421e13 5.03421e13i 0.371856 0.371856i
\(372\) 6.79883e13 + 7.75039e13i 0.494821 + 0.564076i
\(373\) −1.58936e14 1.58936e14i −1.13979 1.13979i −0.988488 0.151297i \(-0.951655\pi\)
−0.151297 0.988488i \(-0.548345\pi\)
\(374\) −7.47787e11 + 2.28914e13i −0.00528426 + 0.161763i
\(375\) 2.86156e13i 0.199265i
\(376\) 1.09356e14 8.97844e13i 0.750427 0.616123i
\(377\) 5.59030e13i 0.378058i
\(378\) −2.47207e14 8.07542e12i −1.64761 0.0538220i
\(379\) 2.82445e12 + 2.82445e12i 0.0185532 + 0.0185532i 0.716323 0.697769i \(-0.245824\pi\)
−0.697769 + 0.716323i \(0.745824\pi\)
\(380\) −4.80368e12 + 7.34472e13i −0.0311003 + 0.475516i
\(381\) 3.63063e14 3.63063e14i 2.31683 2.31683i
\(382\) −8.05958e13 8.60392e13i −0.506948 0.541188i
\(383\) −5.92249e13 −0.367207 −0.183604 0.983000i \(-0.558776\pi\)
−0.183604 + 0.983000i \(0.558776\pi\)
\(384\) −7.29434e13 + 3.13531e14i −0.445825 + 1.91628i
\(385\) −2.63624e13 −0.158836
\(386\) 7.86360e13 + 8.39471e13i 0.467080 + 0.498627i
\(387\) −7.40268e13 + 7.40268e13i −0.433489 + 0.433489i
\(388\) 7.66052e12 1.17128e14i 0.0442266 0.676216i
\(389\) 2.33475e13 + 2.33475e13i 0.132898 + 0.132898i 0.770427 0.637529i \(-0.220043\pi\)
−0.637529 + 0.770427i \(0.720043\pi\)
\(390\) −3.46595e14 1.13221e13i −1.94521 0.0635435i
\(391\) 1.10372e14i 0.610785i
\(392\) 1.13230e14 9.29655e13i 0.617859 0.507281i
\(393\) 1.56031e12i 0.00839560i
\(394\) −5.96864e12 + 1.82714e14i −0.0316699 + 0.969486i
\(395\) 2.80400e13 + 2.80400e13i 0.146722 + 0.146722i
\(396\) −9.37323e13 1.06851e14i −0.483689 0.551386i
\(397\) 2.18990e13 2.18990e13i 0.111449 0.111449i −0.649183 0.760632i \(-0.724889\pi\)
0.760632 + 0.649183i \(0.224889\pi\)
\(398\) 1.21039e14 1.13381e14i 0.607530 0.569094i
\(399\) −6.10997e13 −0.302474
\(400\) 2.47288e13 1.88241e14i 0.120746 0.919144i
\(401\) 7.84224e13 0.377699 0.188850 0.982006i \(-0.439524\pi\)
0.188850 + 0.982006i \(0.439524\pi\)
\(402\) −2.83179e14 + 2.65264e14i −1.34530 + 1.26018i
\(403\) −4.10082e13 + 4.10082e13i −0.192173 + 0.192173i
\(404\) −7.88277e13 + 6.91495e13i −0.364403 + 0.319663i
\(405\) 9.40851e14 + 9.40851e14i 4.29060 + 4.29060i
\(406\) 1.72430e12 5.27847e13i 0.00775746 0.237473i
\(407\) 8.45282e13i 0.375174i
\(408\) 2.78391e13 2.83264e14i 0.121906 1.24039i
\(409\) 5.44125e13i 0.235083i −0.993068 0.117541i \(-0.962499\pi\)
0.993068 0.117541i \(-0.0375013\pi\)
\(410\) 5.29481e14 + 1.72964e13i 2.25704 + 0.0737299i
\(411\) 1.64408e14 + 1.64408e14i 0.691502 + 0.691502i
\(412\) −1.86478e14 1.21963e13i −0.773916 0.0506165i
\(413\) 9.05871e13 9.05871e13i 0.370972 0.370972i
\(414\) −4.68266e14 4.99892e14i −1.89230 2.02011i
\(415\) −4.16039e14 −1.65909
\(416\) −1.78668e14 2.94341e13i −0.703126 0.115834i
\(417\) 2.32018e14 0.901100
\(418\) −1.56428e13 1.66993e13i −0.0599577 0.0640072i
\(419\) 2.47223e14 2.47223e14i 0.935214 0.935214i −0.0628113 0.998025i \(-0.520007\pi\)
0.998025 + 0.0628113i \(0.0200066\pi\)
\(420\) 3.26912e14 + 2.13811e13i 1.22056 + 0.0798285i
\(421\) −3.01416e14 3.01416e14i −1.11074 1.11074i −0.993050 0.117695i \(-0.962449\pi\)
−0.117695 0.993050i \(-0.537551\pi\)
\(422\) −1.19471e14 3.90272e12i −0.434555 0.0141955i
\(423\) 7.76399e14i 2.78749i
\(424\) −3.29745e14 3.24072e13i −1.16860 0.114850i
\(425\) 1.67873e14i 0.587274i
\(426\) −1.60863e12 + 4.92439e13i −0.00555526 + 0.170059i
\(427\) 1.98453e12 + 1.98453e12i 0.00676557 + 0.00676557i
\(428\) −1.69955e14 + 1.49089e14i −0.571997 + 0.501769i
\(429\) 7.62292e13 7.62292e13i 0.253283 0.253283i
\(430\) 6.59499e13 6.17775e13i 0.216340 0.202653i
\(431\) −4.56713e14 −1.47917 −0.739586 0.673062i \(-0.764979\pi\)
−0.739586 + 0.673062i \(0.764979\pi\)
\(432\) 7.00998e14 + 9.13030e14i 2.24159 + 2.91961i
\(433\) 1.87325e14 0.591443 0.295721 0.955274i \(-0.404440\pi\)
0.295721 + 0.955274i \(0.404440\pi\)
\(434\) 3.99856e13 3.74559e13i 0.124655 0.116769i
\(435\) −3.32841e14 + 3.32841e14i −1.02458 + 1.02458i
\(436\) 6.68650e12 + 7.62235e12i 0.0203247 + 0.0231693i
\(437\) −7.79697e13 7.79697e13i −0.234033 0.234033i
\(438\) 3.17509e12 9.71967e13i 0.00941128 0.288100i
\(439\) 6.17945e14i 1.80882i 0.426667 + 0.904409i \(0.359688\pi\)
−0.426667 + 0.904409i \(0.640312\pi\)
\(440\) 7.78526e13 + 9.48231e13i 0.225052 + 0.274110i
\(441\) 8.03907e14i 2.29506i
\(442\) 1.60022e14 + 5.22740e12i 0.451189 + 0.0147388i
\(443\) 3.84254e14 + 3.84254e14i 1.07004 + 1.07004i 0.997355 + 0.0726803i \(0.0231553\pi\)
0.0726803 + 0.997355i \(0.476845\pi\)
\(444\) 6.85562e13 1.04821e15i 0.188556 2.88298i
\(445\) 3.90058e14 3.90058e14i 1.05962 1.05962i
\(446\) 3.90972e14 + 4.17378e14i 1.04907 + 1.11992i
\(447\) 7.96476e14 2.11097
\(448\) 1.67794e14 + 3.33031e13i 0.439285 + 0.0871878i
\(449\) 3.39135e12 0.00877037 0.00438518 0.999990i \(-0.498604\pi\)
0.00438518 + 0.999990i \(0.498604\pi\)
\(450\) −7.12217e14 7.60320e14i −1.81946 1.94235i
\(451\) −1.16453e14 + 1.16453e14i −0.293886 + 0.293886i
\(452\) −4.19648e13 + 6.41633e14i −0.104622 + 1.59965i
\(453\) −7.28901e14 7.28901e14i −1.79526 1.79526i
\(454\) −4.08729e14 1.33518e13i −0.994555 0.0324888i
\(455\) 1.84286e14i 0.443026i
\(456\) 1.80438e14 + 2.19770e14i 0.428570 + 0.521990i
\(457\) 6.33305e14i 1.48619i 0.669187 + 0.743094i \(0.266643\pi\)
−0.669187 + 0.743094i \(0.733357\pi\)
\(458\) 2.53830e12 7.77030e13i 0.00588549 0.180168i
\(459\) −7.19694e14 7.19694e14i −1.64884 1.64884i
\(460\) 3.89890e14 + 4.44459e14i 0.882620 + 1.00615i
\(461\) −4.96950e14 + 4.96950e14i −1.11162 + 1.11162i −0.118692 + 0.992931i \(0.537870\pi\)
−0.992931 + 0.118692i \(0.962130\pi\)
\(462\) −7.43283e13 + 6.96258e13i −0.164295 + 0.153900i
\(463\) 6.46594e14 1.41233 0.706165 0.708047i \(-0.250424\pi\)
0.706165 + 0.708047i \(0.250424\pi\)
\(464\) −1.94954e14 + 1.49680e14i −0.420808 + 0.323084i
\(465\) −4.88317e14 −1.04162
\(466\) 5.46206e14 5.11650e14i 1.15142 1.07857i
\(467\) 2.80275e14 2.80275e14i 0.583904 0.583904i −0.352070 0.935974i \(-0.614522\pi\)
0.935974 + 0.352070i \(0.114522\pi\)
\(468\) −7.46942e14 + 6.55236e14i −1.53792 + 1.34910i
\(469\) 1.45805e14 + 1.45805e14i 0.296702 + 0.296702i
\(470\) −2.18804e13 + 6.69808e14i −0.0440065 + 1.34714i
\(471\) 6.23619e14i 1.23967i
\(472\) −5.93353e14 5.83146e13i −1.16582 0.114577i
\(473\) 2.80920e13i 0.0545566i
\(474\) 1.53115e14 + 5.00176e12i 0.293926 + 0.00960157i
\(475\) −1.18589e14 1.18589e14i −0.225025 0.225025i
\(476\) −1.50935e14 9.87162e12i −0.283108 0.0185161i
\(477\) −1.28560e15 + 1.28560e15i −2.38371 + 2.38371i
\(478\) −2.89163e14 3.08693e14i −0.530017 0.565814i
\(479\) −7.99937e14 −1.44947 −0.724737 0.689025i \(-0.758039\pi\)
−0.724737 + 0.689025i \(0.758039\pi\)
\(480\) −8.88522e14 1.23902e15i −1.59163 2.21947i
\(481\) 5.90894e14 1.04643
\(482\) −3.45234e14 3.68551e14i −0.604443 0.645267i
\(483\) −3.47042e14 + 3.47042e14i −0.600720 + 0.600720i
\(484\) 5.45013e14 + 3.56456e13i 0.932734 + 0.0610037i
\(485\) 3.93118e14 + 3.93118e14i 0.665186 + 0.665186i
\(486\) 2.93864e15 + 9.59955e13i 4.91639 + 0.160602i
\(487\) 5.92515e14i 0.980145i −0.871682 0.490072i \(-0.836970\pi\)
0.871682 0.490072i \(-0.163030\pi\)
\(488\) 1.27752e12 1.29988e13i 0.00208958 0.0212616i
\(489\) 2.89902e12i 0.00468869i
\(490\) −2.26556e13 + 6.93539e14i −0.0362324 + 1.10916i
\(491\) −3.01153e14 3.01153e14i −0.476254 0.476254i 0.427677 0.903932i \(-0.359332\pi\)
−0.903932 + 0.427677i \(0.859332\pi\)
\(492\) 1.53854e15 1.34965e15i 2.40603 2.11063i
\(493\) 1.53672e14 1.53672e14i 0.237650 0.237650i
\(494\) −1.16736e14 + 1.09351e14i −0.178529 + 0.167234i
\(495\) 6.73221e14 1.01819
\(496\) −2.52810e14 3.32112e13i −0.378133 0.0496747i
\(497\) 2.61832e13 0.0387314
\(498\) −1.17302e15 + 1.09880e15i −1.71610 + 1.60753i
\(499\) 4.74558e14 4.74558e14i 0.686651 0.686651i −0.274839 0.961490i \(-0.588625\pi\)
0.961490 + 0.274839i \(0.0886245\pi\)
\(500\) −4.66705e13 5.32025e13i −0.0667894 0.0761373i
\(501\) −1.16422e15 1.16422e15i −1.64789 1.64789i
\(502\) −1.69946e13 + 5.20243e14i −0.0237925 + 0.728343i
\(503\) 8.88794e14i 1.23077i −0.788226 0.615385i \(-0.789000\pi\)
0.788226 0.615385i \(-0.211000\pi\)
\(504\) 7.25488e14 5.95647e14i 0.993715 0.815870i
\(505\) 4.96658e14i 0.672907i
\(506\) −1.83701e14 6.00089e12i −0.246197 0.00804244i
\(507\) 5.16502e14 + 5.16502e14i 0.684744 + 0.684744i
\(508\) −8.28756e13 + 1.26715e15i −0.108687 + 1.66180i
\(509\) 6.54049e14 6.54049e14i 0.848521 0.848521i −0.141428 0.989949i \(-0.545169\pi\)
0.989949 + 0.141428i \(0.0451694\pi\)
\(510\) 9.21633e14 + 9.83880e14i 1.18283 + 1.26272i
\(511\) −5.16799e13 −0.0656156
\(512\) −3.75735e14 7.01889e14i −0.471951 0.881625i
\(513\) 1.01682e15 1.26357
\(514\) −4.36120e14 4.65575e14i −0.536177 0.572391i
\(515\) 6.25880e14 6.25880e14i 0.761292 0.761292i
\(516\) 2.27839e13 3.48361e14i 0.0274192 0.419234i
\(517\) −1.47316e14 1.47316e14i −0.175409 0.175409i
\(518\) −5.57933e14 1.82258e13i −0.657308 0.0214720i
\(519\) 2.95151e14i 0.344052i
\(520\) 6.62861e14 5.44228e14i 0.764546 0.627715i
\(521\) 6.02759e14i 0.687918i 0.938985 + 0.343959i \(0.111768\pi\)
−0.938985 + 0.343959i \(0.888232\pi\)
\(522\) −4.40338e13 + 1.34797e15i −0.0497277 + 1.52228i
\(523\) −1.41456e14 1.41456e14i −0.158075 0.158075i 0.623638 0.781713i \(-0.285654\pi\)
−0.781713 + 0.623638i \(0.785654\pi\)
\(524\) 2.54479e12 + 2.90096e12i 0.00281403 + 0.00320789i
\(525\) −5.27839e14 + 5.27839e14i −0.577597 + 0.577597i
\(526\) −1.23598e15 + 1.15778e15i −1.33841 + 1.25373i
\(527\) 2.25456e14 0.241603
\(528\) 4.69942e14 + 6.17354e13i 0.498377 + 0.0654708i
\(529\) 6.70861e13 0.0704087
\(530\) 1.14533e15 1.07287e15i 1.18963 1.11437i
\(531\) −2.31334e15 + 2.31334e15i −2.37804 + 2.37804i
\(532\) 1.13598e14 9.96506e13i 0.115573 0.101383i
\(533\) 8.14062e14 + 8.14062e14i 0.819705 + 0.819705i
\(534\) 6.95783e13 2.12995e15i 0.0693421 2.12272i
\(535\) 1.07081e15i 1.05625i
\(536\) 9.38605e13 9.55034e14i 0.0916382 0.932422i
\(537\) 1.70750e15i 1.65007i
\(538\) −4.03891e14 1.31938e13i −0.386333 0.0126202i
\(539\) −1.52535e14 1.52535e14i −0.144422 0.144422i
\(540\) −5.44045e15 3.55823e14i −5.09882 0.333478i
\(541\) 3.03750e14 3.03750e14i 0.281794 0.281794i −0.552030 0.833824i \(-0.686147\pi\)
0.833824 + 0.552030i \(0.186147\pi\)
\(542\) 1.02444e14 + 1.09363e14i 0.0940781 + 0.100432i
\(543\) 1.58970e15 1.44516
\(544\) 4.10230e14 + 5.72053e14i 0.369176 + 0.514804i
\(545\) −4.80250e13 −0.0427845
\(546\) 4.86719e14 + 5.19592e14i 0.429258 + 0.458250i
\(547\) 3.85320e14 3.85320e14i 0.336427 0.336427i −0.518594 0.855021i \(-0.673544\pi\)
0.855021 + 0.518594i \(0.173544\pi\)
\(548\) −5.73812e14 3.75291e13i −0.495994 0.0324395i
\(549\) −5.06794e13 5.06794e13i −0.0433694 0.0433694i
\(550\) −2.79403e14 9.12715e12i −0.236720 0.00773286i
\(551\) 2.17116e14i 0.182120i
\(552\) 2.27315e15 + 2.23405e14i 1.88783 + 0.185536i
\(553\) 8.14121e13i 0.0669423i
\(554\) 6.40860e13 1.96182e15i 0.0521747 1.59718i
\(555\) 3.51812e15 + 3.51812e15i 2.83595 + 2.83595i
\(556\) −4.31372e14 + 3.78410e14i −0.344303 + 0.302030i
\(557\) −7.16583e14 + 7.16583e14i −0.566321 + 0.566321i −0.931096 0.364775i \(-0.881146\pi\)
0.364775 + 0.931096i \(0.381146\pi\)
\(558\) −1.02112e15 + 9.56518e14i −0.799078 + 0.748523i
\(559\) 1.96377e14 0.152169
\(560\) −6.42672e14 + 4.93425e14i −0.493123 + 0.378606i
\(561\) −4.19094e14 −0.318431
\(562\) −3.71547e14 + 3.48041e14i −0.279553 + 0.261867i
\(563\) 8.55321e14 8.55321e14i 0.637284 0.637284i −0.312600 0.949885i \(-0.601200\pi\)
0.949885 + 0.312600i \(0.101200\pi\)
\(564\) 1.70734e15 + 1.94630e15i 1.25975 + 1.43607i
\(565\) −2.15352e15 2.15352e15i −1.57356 1.57356i
\(566\) 7.25465e13 2.22081e15i 0.0524960 1.60702i
\(567\) 2.73169e15i 1.95760i
\(568\) −7.73236e13 9.41788e13i −0.0548777 0.0668401i
\(569\) 1.81588e15i 1.27635i 0.769891 + 0.638175i \(0.220311\pi\)
−0.769891 + 0.638175i \(0.779689\pi\)
\(570\) −1.34610e15 4.39726e13i −0.937056 0.0306105i
\(571\) 1.13410e15 + 1.13410e15i 0.781901 + 0.781901i 0.980151 0.198251i \(-0.0635260\pi\)
−0.198251 + 0.980151i \(0.563526\pi\)
\(572\) −1.74007e13 + 2.66053e14i −0.0118820 + 0.181673i
\(573\) 1.52537e15 1.52537e15i 1.03163 1.03163i
\(574\) −7.43543e14 7.93762e14i −0.498071 0.531710i
\(575\) −1.34716e15 −0.893809
\(576\) −4.28498e15 8.50468e14i −2.81595 0.558900i
\(577\) −2.48933e15 −1.62038 −0.810188 0.586170i \(-0.800635\pi\)
−0.810188 + 0.586170i \(0.800635\pi\)
\(578\) 6.34792e14 + 6.77666e14i 0.409288 + 0.436931i
\(579\) −1.48828e15 + 1.48828e15i −0.950499 + 0.950499i
\(580\) 7.59768e13 1.16167e15i 0.0480648 0.734901i
\(581\) 6.03969e14 + 6.03969e14i 0.378483 + 0.378483i
\(582\) 2.14665e15 + 7.01240e13i 1.33256 + 0.0435302i
\(583\) 4.87864e14i 0.300000i
\(584\) 1.52620e14 + 1.85888e14i 0.0929694 + 0.113235i
\(585\) 4.70615e15i 2.83993i
\(586\) −8.94964e13 + 2.73969e15i −0.0535018 + 1.63781i
\(587\) −1.17168e15 1.17168e15i −0.693903 0.693903i 0.269185 0.963088i \(-0.413246\pi\)
−0.963088 + 0.269185i \(0.913246\pi\)
\(588\) 1.76783e15 + 2.01526e15i 1.03721 + 1.18238i
\(589\) −1.59267e14 + 1.59267e14i −0.0925747 + 0.0925747i
\(590\) 2.06094e15 1.93055e15i 1.18680 1.11172i
\(591\) −3.34510e15 −1.90844
\(592\) 1.58212e15 + 2.06066e15i 0.894271 + 1.16476i
\(593\) 2.16626e15 1.21314 0.606569 0.795031i \(-0.292545\pi\)
0.606569 + 0.795031i \(0.292545\pi\)
\(594\) 1.23697e15 1.15871e15i 0.686330 0.642908i
\(595\) 5.06585e14 5.06585e14i 0.278490 0.278490i
\(596\) −1.48082e15 + 1.29901e15i −0.806582 + 0.707553i
\(597\) 2.14587e15 + 2.14587e15i 1.15809 + 1.15809i
\(598\) −4.19492e13 + 1.28416e15i −0.0224319 + 0.686692i
\(599\) 2.29916e15i 1.21821i −0.793089 0.609105i \(-0.791529\pi\)
0.793089 0.609105i \(-0.208471\pi\)
\(600\) 3.45739e15 + 3.39791e14i 1.81517 + 0.178394i
\(601\) 7.60944e14i 0.395861i −0.980216 0.197931i \(-0.936578\pi\)
0.980216 0.197931i \(-0.0634221\pi\)
\(602\) −1.85423e14 6.05715e12i −0.0955836 0.00312240i
\(603\) −3.72345e15 3.72345e15i −1.90195 1.90195i
\(604\) 2.54399e15 + 1.66385e14i 1.28769 + 0.0842189i
\(605\) −1.82924e15 + 1.82924e15i −0.917519 + 0.917519i
\(606\) −1.31173e15 1.40032e15i −0.651994 0.696030i
\(607\) 1.83671e15 0.904694 0.452347 0.891842i \(-0.350587\pi\)
0.452347 + 0.891842i \(0.350587\pi\)
\(608\) −6.93908e14 1.14316e14i −0.338713 0.0558002i
\(609\) 9.66377e14 0.467467
\(610\) 4.22934e13 + 4.51499e13i 0.0202749 + 0.0216442i
\(611\) −1.02981e15 + 1.02981e15i −0.489250 + 0.489250i
\(612\) 3.85446e15 + 2.52093e14i 1.81481 + 0.118694i
\(613\) 8.30874e14 + 8.30874e14i 0.387706 + 0.387706i 0.873868 0.486162i \(-0.161604\pi\)
−0.486162 + 0.873868i \(0.661604\pi\)
\(614\) −3.20465e13 1.04685e12i −0.0148202 0.000484127i
\(615\) 9.69367e15i 4.44299i
\(616\) 2.46363e13 2.50675e14i 0.0111913 0.113872i
\(617\) 2.95927e15i 1.33234i 0.745799 + 0.666171i \(0.232068\pi\)
−0.745799 + 0.666171i \(0.767932\pi\)
\(618\) 1.11644e14 3.41768e15i 0.0498194 1.52509i
\(619\) −1.00184e15 1.00184e15i −0.443100 0.443100i 0.449953 0.893052i \(-0.351441\pi\)
−0.893052 + 0.449953i \(0.851441\pi\)
\(620\) 9.07888e14 7.96421e14i 0.397995 0.349131i
\(621\) 5.77545e15 5.77545e15i 2.50947 2.50947i
\(622\) −2.21734e15 + 2.07705e15i −0.954959 + 0.894542i
\(623\) −1.13250e15 −0.483454
\(624\) 4.31561e14 3.28513e15i 0.182611 1.39007i
\(625\) 2.54544e15 1.06764
\(626\) 3.86316e14 3.61875e14i 0.160614 0.150453i
\(627\) 2.96058e14 2.96058e14i 0.122013 0.122013i
\(628\) −1.01709e15 1.15944e15i −0.415510 0.473665i
\(629\) −1.62431e15 1.62431e15i −0.657796 0.657796i
\(630\) −1.45159e14 + 4.44363e15i −0.0582733 + 1.78388i
\(631\) 2.54047e15i 1.01100i 0.862825 + 0.505502i \(0.168693\pi\)
−0.862825 + 0.505502i \(0.831307\pi\)
\(632\) −2.92832e14 + 2.40424e14i −0.115525 + 0.0948492i
\(633\) 2.18727e15i 0.855423i
\(634\) −3.47048e15 1.13369e14i −1.34555 0.0439545i
\(635\) −4.25295e15 4.25295e15i −1.63469 1.63469i
\(636\) 3.95680e14 6.04986e15i 0.150775 2.30532i
\(637\) −1.06630e15 + 1.06630e15i −0.402820 + 0.402820i
\(638\) 2.47413e14 + 2.64123e14i 0.0926634 + 0.0989218i
\(639\) −6.68646e14 −0.248280
\(640\) 3.67273e15 + 8.54466e14i 1.35207 + 0.314561i
\(641\) −2.18928e15 −0.799064 −0.399532 0.916719i \(-0.630827\pi\)
−0.399532 + 0.916719i \(0.630827\pi\)
\(642\) −2.82812e15 3.01914e15i −1.02342 1.09255i
\(643\) 1.65718e15 1.65718e15i 0.594577 0.594577i −0.344287 0.938864i \(-0.611879\pi\)
0.938864 + 0.344287i \(0.111879\pi\)
\(644\) 7.92184e13 1.21123e15i 0.0281808 0.430879i
\(645\) 1.16921e15 + 1.16921e15i 0.412395 + 0.412395i
\(646\) 6.21493e14 + 2.03021e13i 0.217349 + 0.00710006i
\(647\) 1.95252e15i 0.677051i −0.940957 0.338526i \(-0.890072\pi\)
0.940957 0.338526i \(-0.109928\pi\)
\(648\) −9.82565e15 + 8.06715e15i −3.37830 + 2.77369i
\(649\) 8.77877e14i 0.299287i
\(650\) −6.38033e13 + 1.95316e15i −0.0215685 + 0.660260i
\(651\) 7.08895e14 + 7.08895e14i 0.237622 + 0.237622i
\(652\) −4.72815e12 5.38990e12i −0.00157155 0.00179151i
\(653\) −1.59179e15 + 1.59179e15i −0.524642 + 0.524642i −0.918970 0.394328i \(-0.870978\pi\)
0.394328 + 0.918970i \(0.370978\pi\)
\(654\) −1.35406e14 + 1.26839e14i −0.0442547 + 0.0414549i
\(655\) −1.82776e13 −0.00592369
\(656\) −6.59281e14 + 5.01858e15i −0.211885 + 1.61291i
\(657\) 1.31976e15 0.420616
\(658\) 1.00413e15 9.40603e14i 0.317357 0.297279i
\(659\) −1.25231e15 + 1.25231e15i −0.392502 + 0.392502i −0.875578 0.483077i \(-0.839519\pi\)
0.483077 + 0.875578i \(0.339519\pi\)
\(660\) −1.68765e15 + 1.48045e15i −0.524555 + 0.460152i
\(661\) −1.31167e15 1.31167e15i −0.404311 0.404311i 0.475438 0.879749i \(-0.342290\pi\)
−0.879749 + 0.475438i \(0.842290\pi\)
\(662\) 1.97952e14 6.05976e15i 0.0605119 1.85241i
\(663\) 2.92967e15i 0.888168i
\(664\) 3.88799e14 3.95605e15i 0.116896 1.18943i
\(665\) 7.15728e14i 0.213417i
\(666\) 1.42481e16 + 4.65436e14i 4.21354 + 0.137642i
\(667\) 1.23320e15 + 1.23320e15i 0.361694 + 0.361694i
\(668\) 4.06333e15 + 2.65754e14i 1.18198 + 0.0773054i
\(669\) −7.39959e15 + 7.39959e15i −2.13483 + 2.13483i
\(670\) 3.10732e15 + 3.31719e15i 0.889150 + 0.949202i
\(671\) −1.92320e13 −0.00545823
\(672\) −5.08816e14 + 3.08857e15i −0.143229 + 0.869414i
\(673\) −4.42717e15 −1.23607 −0.618035 0.786151i \(-0.712071\pi\)
−0.618035 + 0.786151i \(0.712071\pi\)
\(674\) 7.68484e14 + 8.20387e14i 0.212816 + 0.227190i
\(675\) 8.78426e15 8.78426e15i 2.41287 2.41287i
\(676\) −1.80268e15 1.17901e14i −0.491147 0.0321226i
\(677\) 4.02631e15 + 4.02631e15i 1.08810 + 1.08810i 0.995724 + 0.0923785i \(0.0294470\pi\)
0.0923785 + 0.995724i \(0.470553\pi\)
\(678\) −1.17595e16 3.84143e14i −3.15228 0.102975i
\(679\) 1.14139e15i 0.303493i
\(680\) −3.31818e15 3.26109e14i −0.875186 0.0860131i
\(681\) 7.48297e15i 1.95779i
\(682\) −1.22579e13 + 3.75242e14i −0.00318128 + 0.0973862i
\(683\) 1.78162e15 + 1.78162e15i 0.458671 + 0.458671i 0.898219 0.439548i \(-0.144861\pi\)
−0.439548 + 0.898219i \(0.644861\pi\)
\(684\) −2.90097e15 + 2.54480e15i −0.740856 + 0.649897i
\(685\) 1.92589e15 1.92589e15i 0.487903 0.487903i
\(686\) 2.34027e15 2.19221e15i 0.588145 0.550935i
\(687\) 1.42258e15 0.354662
\(688\) 5.25799e14 + 6.84839e14i 0.130042 + 0.169376i
\(689\) 3.41041e15 0.836760
\(690\) −7.89550e15 + 7.39598e15i −1.92181 + 1.80022i
\(691\) −2.83219e15 + 2.83219e15i −0.683902 + 0.683902i −0.960877 0.276975i \(-0.910668\pi\)
0.276975 + 0.960877i \(0.410668\pi\)
\(692\) 4.81377e14 + 5.48751e14i 0.115319 + 0.131459i
\(693\) −9.77322e14 9.77322e14i −0.232276 0.232276i
\(694\) −8.47985e13 + 2.59587e15i −0.0199945 + 0.612077i
\(695\) 2.71788e15i 0.635790i
\(696\) −2.85388e15 3.47597e15i −0.662345 0.806725i
\(697\) 4.47556e15i 1.03055i
\(698\) 3.45968e15 + 1.13016e14i 0.790372 + 0.0258188i
\(699\) 9.68356e15 + 9.68356e15i 2.19488 + 2.19488i
\(700\) 1.20489e14 1.84225e15i 0.0270961 0.414294i
\(701\) 2.66761e15 2.66761e15i 0.595214 0.595214i −0.343821 0.939035i \(-0.611721\pi\)
0.939035 + 0.343821i \(0.111721\pi\)
\(702\) −8.09995e15 8.64702e15i −1.79320 1.91431i
\(703\) 2.29491e15 0.504093
\(704\) −9.74412e14 + 6.51673e14i −0.212370 + 0.142030i
\(705\) −1.22628e16 −2.65185
\(706\) −3.68519e15 3.93408e15i −0.790740 0.844146i
\(707\) −7.21004e14 + 7.21004e14i −0.153508 + 0.153508i
\(708\) 7.11998e14 1.08863e16i 0.150417 2.29984i
\(709\) 2.91989e15 + 2.91989e15i 0.612085 + 0.612085i 0.943489 0.331404i \(-0.107522\pi\)
−0.331404 + 0.943489i \(0.607522\pi\)
\(710\) 5.76848e14 + 1.88437e13i 0.119989 + 0.00391963i
\(711\) 2.07904e15i 0.429120i
\(712\) 3.34448e15 + 4.07352e15i 0.684997 + 0.834314i
\(713\) 1.80925e15i 0.367711i
\(714\) 9.03643e13 2.76625e15i 0.0182245 0.557894i
\(715\) −8.92956e14 8.92956e14i −0.178709 0.178709i
\(716\) −2.78484e15 3.17461e15i −0.553069 0.630477i
\(717\) 5.47275e15 5.47275e15i 1.07857 1.07857i
\(718\) 5.51646e15 5.16745e15i 1.07889 1.01063i
\(719\) 7.46765e15 1.44935 0.724677 0.689088i \(-0.241989\pi\)
0.724677 + 0.689088i \(0.241989\pi\)
\(720\) 1.64120e16 1.26007e16i 3.16107 2.42698i
\(721\) −1.81719e15 −0.347342
\(722\) 3.39403e15 3.17930e15i 0.643815 0.603083i
\(723\) 6.53396e15 6.53396e15i 1.23003 1.23003i
\(724\) −2.95559e15 + 2.59271e15i −0.552182 + 0.484387i
\(725\) 1.87566e15 + 1.87566e15i 0.347772 + 0.347772i
\(726\) −3.26298e14 + 9.98871e15i −0.0600430 + 1.83805i
\(727\) 8.34141e13i 0.0152335i −0.999971 0.00761676i \(-0.997575\pi\)
0.999971 0.00761676i \(-0.00242451\pi\)
\(728\) −1.75234e15 1.72220e14i −0.317612 0.0312148i
\(729\) 2.95012e16i 5.30687i
\(730\) −1.13857e15 3.71933e13i −0.203275 0.00664032i
\(731\) −5.39823e14 5.39823e14i −0.0956546 0.0956546i
\(732\) 2.38491e14 + 1.55981e13i 0.0419432 + 0.00274321i
\(733\) 7.73562e15 7.73562e15i 1.35028 1.35028i 0.464933 0.885346i \(-0.346079\pi\)
0.885346 0.464933i \(-0.153921\pi\)
\(734\) 4.11375e15 + 4.39159e15i 0.712705 + 0.760841i
\(735\) −1.26972e16 −2.18338
\(736\) −4.59065e15 + 3.29204e15i −0.783512 + 0.561872i
\(737\) −1.41299e15 −0.239369
\(738\) 1.89880e16 + 2.02705e16i 3.19278 + 3.40842i
\(739\) −2.34299e15 + 2.34299e15i −0.391044 + 0.391044i −0.875060 0.484015i \(-0.839178\pi\)
0.484015 + 0.875060i \(0.339178\pi\)
\(740\) −1.22788e16 8.03074e14i −2.03415 0.133040i
\(741\) −2.06959e15 2.06959e15i −0.340318 0.340318i
\(742\) −3.22018e15 1.05192e14i −0.525603 0.0171697i
\(743\) 7.38859e15i 1.19708i −0.801093 0.598540i \(-0.795748\pi\)
0.801093 0.598540i \(-0.204252\pi\)
\(744\) 4.56345e14 4.64333e15i 0.0733909 0.746755i
\(745\) 9.32999e15i 1.48944i
\(746\) −3.32104e14 + 1.01665e16i −0.0526273 + 1.61104i
\(747\) −1.54237e16 1.54237e16i −2.42619 2.42619i
\(748\) 7.79187e14 6.83521e14i 0.121670 0.106732i
\(749\) −1.55451e15 + 1.55451e15i −0.240959 + 0.240959i
\(750\) 9.45106e14 8.85313e14i 0.145427 0.136226i
\(751\) 2.74146e14 0.0418758 0.0209379 0.999781i \(-0.493335\pi\)
0.0209379 + 0.999781i \(0.493335\pi\)
\(752\) −6.34864e15 8.34009e14i −0.962682 0.126466i
\(753\) −9.52455e15 −1.43375
\(754\) 1.84635e15 1.72954e15i 0.275913 0.258457i
\(755\) −8.53841e15 + 8.53841e15i −1.26669 + 1.26669i
\(756\) 7.38141e15 + 8.41451e15i 1.08710 + 1.23925i
\(757\) 1.20145e15 + 1.20145e15i 0.175662 + 0.175662i 0.789462 0.613800i \(-0.210360\pi\)
−0.613800 + 0.789462i \(0.710360\pi\)
\(758\) 5.90184e12 1.80669e14i 0.000856656 0.0262242i
\(759\) 3.36317e15i 0.484640i
\(760\) 2.57441e15 2.11367e15i 0.368301 0.302386i
\(761\) 5.15297e15i 0.731883i −0.930638 0.