Properties

Label 16.12.e.a.13.6
Level 16
Weight 12
Character 16.13
Analytic conductor 12.293
Analytic rank 0
Dimension 42
CM no
Inner twists 2

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(12.2934908890\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(21\) over \(\Q(i)\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 13.6
Character \(\chi\) = 16.13
Dual form 16.12.e.a.5.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-31.4901 - 32.5019i) q^{2} +(219.312 + 219.312i) q^{3} +(-64.7420 + 2046.98i) q^{4} +(-4575.66 + 4575.66i) q^{5} +(221.882 - 14034.2i) q^{6} -2778.29i q^{7} +(68569.3 - 62355.3i) q^{8} -80951.6i q^{9} +O(q^{10})\) \(q+(-31.4901 - 32.5019i) q^{2} +(219.312 + 219.312i) q^{3} +(-64.7420 + 2046.98i) q^{4} +(-4575.66 + 4575.66i) q^{5} +(221.882 - 14034.2i) q^{6} -2778.29i q^{7} +(68569.3 - 62355.3i) q^{8} -80951.6i q^{9} +(292806. + 4629.29i) q^{10} +(17312.0 - 17312.0i) q^{11} +(-463125. + 434728. i) q^{12} +(-1.16637e6 - 1.16637e6i) q^{13} +(-90299.6 + 87488.7i) q^{14} -2.00699e6 q^{15} +(-4.18592e6 - 265051. i) q^{16} -7.63947e6 q^{17} +(-2.63108e6 + 2.54918e6i) q^{18} +(1.62010e6 + 1.62010e6i) q^{19} +(-9.07003e6 - 9.66251e6i) q^{20} +(609312. - 609312. i) q^{21} +(-1.10783e6 - 17514.9i) q^{22} -3.41251e7i q^{23} +(2.87133e7 + 1.36279e6i) q^{24} +6.95479e6i q^{25} +(-1.18004e6 + 7.46386e7i) q^{26} +(5.66041e7 - 5.66041e7i) q^{27} +(5.68709e6 + 179872. i) q^{28} +(-5.22501e7 - 5.22501e7i) q^{29} +(6.32005e7 + 6.52310e7i) q^{30} -1.70466e8 q^{31} +(1.23201e8 + 1.44397e8i) q^{32} +7.59345e6 q^{33} +(2.40568e8 + 2.48297e8i) q^{34} +(1.27125e7 + 1.27125e7i) q^{35} +(1.65706e8 + 5.24097e6i) q^{36} +(1.36013e8 - 1.36013e8i) q^{37} +(1.63909e6 - 1.03673e8i) q^{38} -5.11599e8i q^{39} +(-2.84329e7 + 5.99067e8i) q^{40} -9.43574e8i q^{41} +(-3.89911e7 - 616453. i) q^{42} +(-1.75831e8 + 1.75831e8i) q^{43} +(3.43164e7 + 3.65580e7i) q^{44} +(3.70407e8 + 3.70407e8i) q^{45} +(-1.10913e9 + 1.07460e9i) q^{46} -2.33824e9 q^{47} +(-8.59894e8 - 9.76151e8i) q^{48} +1.96961e9 q^{49} +(2.26044e8 - 2.19007e8i) q^{50} +(-1.67543e9 - 1.67543e9i) q^{51} +(2.46305e9 - 2.31203e9i) q^{52} +(-2.13123e9 + 2.13123e9i) q^{53} +(-3.62221e9 - 5.72675e7i) q^{54} +1.58428e8i q^{55} +(-1.73241e8 - 1.90505e8i) q^{56} +7.10614e8i q^{57} +(-5.28625e7 + 3.34359e9i) q^{58} +(-2.73656e8 + 2.73656e8i) q^{59} +(1.29937e8 - 4.10827e9i) q^{60} +(7.10089e9 + 7.10089e9i) q^{61} +(5.36800e9 + 5.54046e9i) q^{62} -2.24907e8 q^{63} +(8.13557e8 - 8.55132e9i) q^{64} +1.06739e10 q^{65} +(-2.39119e8 - 2.46801e8i) q^{66} +(6.25789e9 + 6.25789e9i) q^{67} +(4.94594e8 - 1.56378e10i) q^{68} +(7.48403e9 - 7.48403e9i) q^{69} +(1.28615e7 - 8.13499e8i) q^{70} +3.05701e9i q^{71} +(-5.04776e9 - 5.55079e9i) q^{72} +3.14465e10i q^{73} +(-8.70371e9 - 1.37607e8i) q^{74} +(-1.52527e9 + 1.52527e9i) q^{75} +(-3.42119e9 + 3.21142e9i) q^{76} +(-4.80977e7 - 4.80977e7i) q^{77} +(-1.66279e10 + 1.61103e10i) q^{78} -4.76542e10 q^{79} +(2.03661e10 - 1.79406e10i) q^{80} +1.04876e10 q^{81} +(-3.06679e10 + 2.97133e10i) q^{82} +(-4.66019e10 - 4.66019e10i) q^{83} +(1.20780e9 + 1.28670e9i) q^{84} +(3.49556e10 - 3.49556e10i) q^{85} +(1.12518e10 + 1.77892e8i) q^{86} -2.29182e10i q^{87} +(1.07576e8 - 2.26657e9i) q^{88} +1.17108e10i q^{89} +(3.74748e8 - 2.37031e10i) q^{90} +(-3.24052e9 + 3.24052e9i) q^{91} +(6.98532e10 + 2.20932e9i) q^{92} +(-3.73852e10 - 3.73852e10i) q^{93} +(7.36315e10 + 7.59972e10i) q^{94} -1.48261e10 q^{95} +(-4.64856e9 + 5.86873e10i) q^{96} +3.59417e10 q^{97} +(-6.20232e10 - 6.40159e10i) q^{98} +(-1.40143e9 - 1.40143e9i) 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 \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −31.4901 32.5019i −0.695840 0.718196i
\(3\) 219.312 + 219.312i 0.521069 + 0.521069i 0.917894 0.396825i \(-0.129888\pi\)
−0.396825 + 0.917894i \(0.629888\pi\)
\(4\) −64.7420 + 2046.98i −0.0316123 + 0.999500i
\(5\) −4575.66 + 4575.66i −0.654815 + 0.654815i −0.954149 0.299333i \(-0.903236\pi\)
0.299333 + 0.954149i \(0.403236\pi\)
\(6\) 221.882 14034.2i 0.0116491 0.736811i
\(7\) 2778.29i 0.0624796i −0.999512 0.0312398i \(-0.990054\pi\)
0.999512 0.0312398i \(-0.00994555\pi\)
\(8\) 68569.3 62355.3i 0.739835 0.672789i
\(9\) 80951.6i 0.456974i
\(10\) 292806. + 4629.29i 0.925933 + 0.0146391i
\(11\) 17312.0 17312.0i 0.0324106 0.0324106i −0.690716 0.723126i \(-0.742704\pi\)
0.723126 + 0.690716i \(0.242704\pi\)
\(12\) −463125. + 434728.i −0.537281 + 0.504336i
\(13\) −1.16637e6 1.16637e6i −0.871263 0.871263i 0.121347 0.992610i \(-0.461278\pi\)
−0.992610 + 0.121347i \(0.961278\pi\)
\(14\) −90299.6 + 87488.7i −0.0448726 + 0.0434758i
\(15\) −2.00699e6 −0.682408
\(16\) −4.18592e6 265051.i −0.998001 0.0631930i
\(17\) −7.63947e6 −1.30495 −0.652475 0.757810i \(-0.726269\pi\)
−0.652475 + 0.757810i \(0.726269\pi\)
\(18\) −2.63108e6 + 2.54918e6i −0.328197 + 0.317981i
\(19\) 1.62010e6 + 1.62010e6i 0.150106 + 0.150106i 0.778165 0.628060i \(-0.216151\pi\)
−0.628060 + 0.778165i \(0.716151\pi\)
\(20\) −9.07003e6 9.66251e6i −0.633788 0.675188i
\(21\) 609312. 609312.i 0.0325562 0.0325562i
\(22\) −1.10783e6 17514.9i −0.0458298 0.000724574i
\(23\) 3.41251e7i 1.10553i −0.833337 0.552765i \(-0.813573\pi\)
0.833337 0.552765i \(-0.186427\pi\)
\(24\) 2.87133e7 + 1.36279e6i 0.736074 + 0.0349355i
\(25\) 6.95479e6i 0.142434i
\(26\) −1.18004e6 + 7.46386e7i −0.0194780 + 1.23200i
\(27\) 5.66041e7 5.66041e7i 0.759184 0.759184i
\(28\) 5.68709e6 + 179872.i 0.0624484 + 0.00197512i
\(29\) −5.22501e7 5.22501e7i −0.473041 0.473041i 0.429856 0.902897i \(-0.358564\pi\)
−0.902897 + 0.429856i \(0.858564\pi\)
\(30\) 6.32005e7 + 6.52310e7i 0.474847 + 0.490103i
\(31\) −1.70466e8 −1.06942 −0.534710 0.845035i \(-0.679579\pi\)
−0.534710 + 0.845035i \(0.679579\pi\)
\(32\) 1.23201e8 + 1.44397e8i 0.649065 + 0.760733i
\(33\) 7.59345e6 0.0337763
\(34\) 2.40568e8 + 2.48297e8i 0.908037 + 0.937211i
\(35\) 1.27125e7 + 1.27125e7i 0.0409126 + 0.0409126i
\(36\) 1.65706e8 + 5.24097e6i 0.456746 + 0.0144460i
\(37\) 1.36013e8 1.36013e8i 0.322455 0.322455i −0.527253 0.849708i \(-0.676778\pi\)
0.849708 + 0.527253i \(0.176778\pi\)
\(38\) 1.63909e6 1.03673e8i 0.00335577 0.212255i
\(39\) 5.11599e8i 0.907976i
\(40\) −2.84329e7 + 5.99067e8i −0.0439027 + 0.925007i
\(41\) 9.43574e8i 1.27193i −0.771716 0.635967i \(-0.780601\pi\)
0.771716 0.635967i \(-0.219399\pi\)
\(42\) −3.89911e7 616453.i −0.0460356 0.000727828i
\(43\) −1.75831e8 + 1.75831e8i −0.182397 + 0.182397i −0.792400 0.610002i \(-0.791169\pi\)
0.610002 + 0.792400i \(0.291169\pi\)
\(44\) 3.43164e7 + 3.65580e7i 0.0313698 + 0.0334190i
\(45\) 3.70407e8 + 3.70407e8i 0.299233 + 0.299233i
\(46\) −1.10913e9 + 1.07460e9i −0.793987 + 0.769272i
\(47\) −2.33824e9 −1.48714 −0.743569 0.668660i \(-0.766868\pi\)
−0.743569 + 0.668660i \(0.766868\pi\)
\(48\) −8.59894e8 9.76151e8i −0.487100 0.552956i
\(49\) 1.96961e9 0.996096
\(50\) 2.26044e8 2.19007e8i 0.102296 0.0991114i
\(51\) −1.67543e9 1.67543e9i −0.679969 0.679969i
\(52\) 2.46305e9 2.31203e9i 0.898370 0.843285i
\(53\) −2.13123e9 + 2.13123e9i −0.700023 + 0.700023i −0.964415 0.264392i \(-0.914829\pi\)
0.264392 + 0.964415i \(0.414829\pi\)
\(54\) −3.62221e9 5.72675e7i −1.07351 0.0169724i
\(55\) 1.58428e8i 0.0424459i
\(56\) −1.73241e8 1.90505e8i −0.0420356 0.0462246i
\(57\) 7.10614e8i 0.156431i
\(58\) −5.28625e7 + 3.34359e9i −0.0105753 + 0.668897i
\(59\) −2.73656e8 + 2.73656e8i −0.0498333 + 0.0498333i −0.731584 0.681751i \(-0.761219\pi\)
0.681751 + 0.731584i \(0.261219\pi\)
\(60\) 1.29937e8 4.10827e9i 0.0215725 0.682067i
\(61\) 7.10089e9 + 7.10089e9i 1.07646 + 1.07646i 0.996824 + 0.0796382i \(0.0253765\pi\)
0.0796382 + 0.996824i \(0.474624\pi\)
\(62\) 5.36800e9 + 5.54046e9i 0.744146 + 0.768054i
\(63\) −2.24907e8 −0.0285515
\(64\) 8.13557e8 8.55132e9i 0.0947106 0.995505i
\(65\) 1.06739e10 1.14103
\(66\) −2.39119e8 2.46801e8i −0.0235029 0.0242580i
\(67\) 6.25789e9 + 6.25789e9i 0.566261 + 0.566261i 0.931079 0.364818i \(-0.118869\pi\)
−0.364818 + 0.931079i \(0.618869\pi\)
\(68\) 4.94594e8 1.56378e10i 0.0412525 1.30430i
\(69\) 7.48403e9 7.48403e9i 0.576057 0.576057i
\(70\) 1.28615e7 8.13499e8i 0.000914645 0.0578519i
\(71\) 3.05701e9i 0.201083i 0.994933 + 0.100542i \(0.0320576\pi\)
−0.994933 + 0.100542i \(0.967942\pi\)
\(72\) −5.04776e9 5.55079e9i −0.307447 0.338085i
\(73\) 3.14465e10i 1.77540i 0.460420 + 0.887701i \(0.347699\pi\)
−0.460420 + 0.887701i \(0.652301\pi\)
\(74\) −8.70371e9 1.37607e8i −0.455964 0.00720883i
\(75\) −1.52527e9 + 1.52527e9i −0.0742180 + 0.0742180i
\(76\) −3.42119e9 + 3.21142e9i −0.154776 + 0.145285i
\(77\) −4.80977e7 4.80977e7i −0.00202500 0.00202500i
\(78\) −1.66279e10 + 1.61103e10i −0.652105 + 0.631806i
\(79\) −4.76542e10 −1.74242 −0.871209 0.490912i \(-0.836664\pi\)
−0.871209 + 0.490912i \(0.836664\pi\)
\(80\) 2.03661e10 1.79406e10i 0.694886 0.612127i
\(81\) 1.04876e10 0.334201
\(82\) −3.06679e10 + 2.97133e10i −0.913498 + 0.885063i
\(83\) −4.66019e10 4.66019e10i −1.29860 1.29860i −0.929320 0.369276i \(-0.879606\pi\)
−0.369276 0.929320i \(-0.620394\pi\)
\(84\) 1.20780e9 + 1.28670e9i 0.0315107 + 0.0335691i
\(85\) 3.49556e10 3.49556e10i 0.854501 0.854501i
\(86\) 1.12518e10 + 1.77892e8i 0.257917 + 0.00407769i
\(87\) 2.29182e10i 0.492974i
\(88\) 1.07576e8 2.26657e9i 0.00217300 0.0457840i
\(89\) 1.17108e10i 0.222300i 0.993804 + 0.111150i \(0.0354534\pi\)
−0.993804 + 0.111150i \(0.964547\pi\)
\(90\) 3.74748e8 2.37031e10i 0.00668968 0.423127i
\(91\) −3.24052e9 + 3.24052e9i −0.0544361 + 0.0544361i
\(92\) 6.98532e10 + 2.20932e9i 1.10498 + 0.0349483i
\(93\) −3.73852e10 3.73852e10i −0.557242 0.557242i
\(94\) 7.36315e10 + 7.59972e10i 1.03481 + 1.06806i
\(95\) −1.48261e10 −0.196583
\(96\) −4.64856e9 + 5.86873e10i −0.0581871 + 0.734602i
\(97\) 3.59417e10 0.424966 0.212483 0.977165i \(-0.431845\pi\)
0.212483 + 0.977165i \(0.431845\pi\)
\(98\) −6.20232e10 6.40159e10i −0.693124 0.715393i
\(99\) −1.40143e9 1.40143e9i −0.0148108 0.0148108i
\(100\) −1.42363e10 4.50267e8i −0.142363 0.00450267i
\(101\) 4.25749e9 4.25749e9i 0.0403075 0.0403075i −0.686666 0.726973i \(-0.740926\pi\)
0.726973 + 0.686666i \(0.240926\pi\)
\(102\) −1.69506e9 + 1.07214e11i −0.0152014 + 0.961502i
\(103\) 8.38400e10i 0.712601i 0.934371 + 0.356301i \(0.115962\pi\)
−0.934371 + 0.356301i \(0.884038\pi\)
\(104\) −1.52707e11 7.24777e9i −1.23077 0.0584146i
\(105\) 5.57601e9i 0.0426366i
\(106\) 1.36381e11 + 2.15621e9i 0.989859 + 0.0156498i
\(107\) 1.39681e11 1.39681e11i 0.962782 0.962782i −0.0365502 0.999332i \(-0.511637\pi\)
0.999332 + 0.0365502i \(0.0116369\pi\)
\(108\) 1.12203e11 + 1.19532e11i 0.734805 + 0.782804i
\(109\) −1.03674e11 1.03674e11i −0.645393 0.645393i 0.306483 0.951876i \(-0.400848\pi\)
−0.951876 + 0.306483i \(0.900848\pi\)
\(110\) 5.14919e9 4.98891e9i 0.0304845 0.0295356i
\(111\) 5.96583e10 0.336043
\(112\) −7.36387e8 + 1.16297e10i −0.00394827 + 0.0623547i
\(113\) −4.37338e10 −0.223298 −0.111649 0.993748i \(-0.535613\pi\)
−0.111649 + 0.993748i \(0.535613\pi\)
\(114\) 2.30963e10 2.23773e10i 0.112348 0.108851i
\(115\) 1.56145e11 + 1.56145e11i 0.723917 + 0.723917i
\(116\) 1.10338e11 1.03572e11i 0.487758 0.457850i
\(117\) −9.44197e10 + 9.44197e10i −0.398144 + 0.398144i
\(118\) 1.75118e10 + 2.76864e8i 0.0704661 + 0.00111408i
\(119\) 2.12246e10i 0.0815328i
\(120\) −1.37618e11 + 1.25147e11i −0.504869 + 0.459116i
\(121\) 2.84712e11i 0.997899i
\(122\) 7.18411e9 4.54400e11i 0.0240655 1.52216i
\(123\) 2.06937e11 2.06937e11i 0.662765 0.662765i
\(124\) 1.10363e10 3.48940e11i 0.0338068 1.06889i
\(125\) −2.55244e11 2.55244e11i −0.748083 0.748083i
\(126\) 7.08235e9 + 7.30989e9i 0.0198673 + 0.0205056i
\(127\) −6.00265e11 −1.61221 −0.806107 0.591770i \(-0.798430\pi\)
−0.806107 + 0.591770i \(0.798430\pi\)
\(128\) −3.03553e11 + 2.42840e11i −0.780871 + 0.624692i
\(129\) −7.71236e10 −0.190083
\(130\) −3.36121e11 3.46920e11i −0.793976 0.819485i
\(131\) 6.08704e11 + 6.08704e11i 1.37852 + 1.37852i 0.847117 + 0.531407i \(0.178337\pi\)
0.531407 + 0.847117i \(0.321663\pi\)
\(132\) −4.91615e8 + 1.55436e10i −0.00106775 + 0.0337594i
\(133\) 4.50111e9 4.50111e9i 0.00937854 0.00937854i
\(134\) 6.33124e9 4.00455e11i 0.0126594 0.800714i
\(135\) 5.18002e11i 0.994251i
\(136\) −5.23833e11 + 4.76362e11i −0.965447 + 0.877956i
\(137\) 3.71507e11i 0.657663i 0.944389 + 0.328832i \(0.106655\pi\)
−0.944389 + 0.328832i \(0.893345\pi\)
\(138\) −4.78918e11 7.57175e9i −0.814566 0.0128784i
\(139\) 4.19881e11 4.19881e11i 0.686348 0.686348i −0.275075 0.961423i \(-0.588703\pi\)
0.961423 + 0.275075i \(0.0887025\pi\)
\(140\) −2.68452e10 + 2.51992e10i −0.0421855 + 0.0395988i
\(141\) −5.12804e11 5.12804e11i −0.774901 0.774901i
\(142\) 9.93585e10 9.62657e10i 0.144417 0.139922i
\(143\) −4.03845e10 −0.0564763
\(144\) −2.14563e10 + 3.38857e11i −0.0288776 + 0.456061i
\(145\) 4.78158e11 0.619509
\(146\) 1.02207e12 9.90255e11i 1.27509 1.23540i
\(147\) 4.31958e11 + 4.31958e11i 0.519035 + 0.519035i
\(148\) 2.69609e11 + 2.87220e11i 0.312101 + 0.332488i
\(149\) 5.05211e11 5.05211e11i 0.563571 0.563571i −0.366749 0.930320i \(-0.619529\pi\)
0.930320 + 0.366749i \(0.119529\pi\)
\(150\) 9.76050e10 + 1.54314e9i 0.104947 + 0.00165922i
\(151\) 8.08446e11i 0.838065i 0.907971 + 0.419033i \(0.137631\pi\)
−0.907971 + 0.419033i \(0.862369\pi\)
\(152\) 2.12111e11 + 1.00672e10i 0.212043 + 0.0100640i
\(153\) 6.18427e11i 0.596328i
\(154\) −4.86614e7 + 3.07787e9i −4.52711e−5 + 0.00286343i
\(155\) 7.79995e11 7.79995e11i 0.700273 0.700273i
\(156\) 1.04723e12 + 3.31220e10i 0.907522 + 0.0287032i
\(157\) −7.30037e11 7.30037e11i −0.610797 0.610797i 0.332357 0.943154i \(-0.392156\pi\)
−0.943154 + 0.332357i \(0.892156\pi\)
\(158\) 1.50064e12 + 1.54885e12i 1.21245 + 1.25140i
\(159\) −9.34807e11 −0.729521
\(160\) −1.22443e12 9.69862e10i −0.923157 0.0731223i
\(161\) −9.48093e10 −0.0690730
\(162\) −3.30255e11 3.40866e11i −0.232550 0.240022i
\(163\) −9.03848e11 9.03848e11i −0.615267 0.615267i 0.329047 0.944314i \(-0.393273\pi\)
−0.944314 + 0.329047i \(0.893273\pi\)
\(164\) 1.93147e12 + 6.10888e10i 1.27130 + 0.0402088i
\(165\) −3.47450e10 + 3.47450e10i −0.0221173 + 0.0221173i
\(166\) −4.71481e10 + 2.98215e12i −0.0290315 + 1.83626i
\(167\) 2.22636e12i 1.32634i −0.748469 0.663170i \(-0.769211\pi\)
0.748469 0.663170i \(-0.230789\pi\)
\(168\) 3.78623e9 7.97739e10i 0.00218276 0.0459896i
\(169\) 9.28692e11i 0.518197i
\(170\) −2.23688e12 3.53653e10i −1.20830 0.0191033i
\(171\) 1.31150e11 1.31150e11i 0.0685944 0.0685944i
\(172\) −3.48538e11 3.71305e11i −0.176540 0.188072i
\(173\) −6.98524e11 6.98524e11i −0.342711 0.342711i 0.514675 0.857385i \(-0.327913\pi\)
−0.857385 + 0.514675i \(0.827913\pi\)
\(174\) −7.44883e11 + 7.21696e11i −0.354052 + 0.343031i
\(175\) 1.93224e10 0.00889922
\(176\) −7.70552e10 + 6.78780e10i −0.0343939 + 0.0302977i
\(177\) −1.20032e11 −0.0519332
\(178\) 3.80621e11 3.68773e11i 0.159655 0.154685i
\(179\) −2.78923e12 2.78923e12i −1.13447 1.13447i −0.989425 0.145044i \(-0.953668\pi\)
−0.145044 0.989425i \(-0.546332\pi\)
\(180\) −7.82195e11 + 7.34233e11i −0.308543 + 0.289624i
\(181\) 8.65718e11 8.65718e11i 0.331241 0.331241i −0.521817 0.853058i \(-0.674745\pi\)
0.853058 + 0.521817i \(0.174745\pi\)
\(182\) 2.07367e11 + 3.27850e9i 0.0769747 + 0.00121698i
\(183\) 3.11462e12i 1.12182i
\(184\) −2.12788e12 2.33993e12i −0.743788 0.817909i
\(185\) 1.24469e12i 0.422297i
\(186\) −3.78234e10 + 2.39236e12i −0.0124577 + 0.787961i
\(187\) −1.32254e11 + 1.32254e11i −0.0422942 + 0.0422942i
\(188\) 1.51382e11 4.78632e12i 0.0470118 1.48639i
\(189\) −1.57263e11 1.57263e11i −0.0474335 0.0474335i
\(190\) 4.66874e11 + 4.81874e11i 0.136790 + 0.141185i
\(191\) −3.97152e12 −1.13051 −0.565254 0.824917i \(-0.691222\pi\)
−0.565254 + 0.824917i \(0.691222\pi\)
\(192\) 2.05383e12 1.69698e12i 0.568078 0.469376i
\(193\) 5.02696e12 1.35126 0.675632 0.737239i \(-0.263871\pi\)
0.675632 + 0.737239i \(0.263871\pi\)
\(194\) −1.13181e12 1.16817e12i −0.295708 0.305209i
\(195\) 2.34090e12 + 2.34090e12i 0.594557 + 0.594557i
\(196\) −1.27516e11 + 4.03174e12i −0.0314889 + 0.995598i
\(197\) 2.21725e12 2.21725e12i 0.532415 0.532415i −0.388876 0.921290i \(-0.627136\pi\)
0.921290 + 0.388876i \(0.127136\pi\)
\(198\) −1.41786e9 + 8.96805e10i −0.000331111 + 0.0209430i
\(199\) 1.69752e12i 0.385588i −0.981239 0.192794i \(-0.938245\pi\)
0.981239 0.192794i \(-0.0617548\pi\)
\(200\) 4.33668e11 + 4.76885e11i 0.0958280 + 0.105378i
\(201\) 2.74486e12i 0.590122i
\(202\) −2.72445e11 4.30739e9i −0.0569963 0.000901117i
\(203\) −1.45166e11 + 1.45166e11i −0.0295554 + 0.0295554i
\(204\) 3.53803e12 3.32109e12i 0.701125 0.658134i
\(205\) 4.31747e12 + 4.31747e12i 0.832882 + 0.832882i
\(206\) 2.72496e12 2.64013e12i 0.511788 0.495857i
\(207\) −2.76248e12 −0.505198
\(208\) 4.57320e12 + 5.19149e12i 0.814464 + 0.924579i
\(209\) 5.60943e10 0.00973003
\(210\) 1.81231e11 1.75589e11i 0.0306214 0.0296682i
\(211\) 1.20649e12 + 1.20649e12i 0.198596 + 0.198596i 0.799398 0.600802i \(-0.205152\pi\)
−0.600802 + 0.799398i \(0.705152\pi\)
\(212\) −4.22459e12 4.50055e12i −0.677544 0.721803i
\(213\) −6.70439e11 + 6.70439e11i −0.104778 + 0.104778i
\(214\) −8.93849e12 1.41318e11i −1.36141 0.0215240i
\(215\) 1.60908e12i 0.238873i
\(216\) 3.51734e11 7.41087e12i 0.0509002 1.07244i
\(217\) 4.73604e11i 0.0668170i
\(218\) −1.04889e11 + 6.63430e12i −0.0144284 + 0.912609i
\(219\) −6.89660e12 + 6.89660e12i −0.925108 + 0.925108i
\(220\) −3.24297e11 1.02569e10i −0.0424247 0.00134181i
\(221\) 8.91047e12 + 8.91047e12i 1.13695 + 1.13695i
\(222\) −1.87865e12 1.93901e12i −0.233832 0.241345i
\(223\) 3.81312e12 0.463025 0.231512 0.972832i \(-0.425633\pi\)
0.231512 + 0.972832i \(0.425633\pi\)
\(224\) 4.01176e11 3.42287e11i 0.0475303 0.0405533i
\(225\) 5.63001e11 0.0650887
\(226\) 1.37718e12 + 1.42143e12i 0.155380 + 0.160372i
\(227\) 2.20437e12 + 2.20437e12i 0.242740 + 0.242740i 0.817983 0.575243i \(-0.195092\pi\)
−0.575243 + 0.817983i \(0.695092\pi\)
\(228\) −1.45461e12 4.60066e10i −0.156353 0.00494514i
\(229\) −6.95781e12 + 6.95781e12i −0.730092 + 0.730092i −0.970638 0.240546i \(-0.922673\pi\)
0.240546 + 0.970638i \(0.422673\pi\)
\(230\) 1.57975e11 9.99201e12i 0.0161839 1.02365i
\(231\) 2.10968e10i 0.00211033i
\(232\) −6.84083e12 3.24679e11i −0.668228 0.0317154i
\(233\) 1.59857e13i 1.52502i −0.646977 0.762510i \(-0.723967\pi\)
0.646977 0.762510i \(-0.276033\pi\)
\(234\) 6.04211e12 + 9.55264e10i 0.562991 + 0.00890094i
\(235\) 1.06990e13 1.06990e13i 0.973800 0.973800i
\(236\) −5.42451e11 5.77885e11i −0.0482330 0.0513837i
\(237\) −1.04511e13 1.04511e13i −0.907920 0.907920i
\(238\) 6.89841e11 6.68367e11i 0.0585565 0.0567338i
\(239\) 1.48081e13 1.22831 0.614157 0.789184i \(-0.289496\pi\)
0.614157 + 0.789184i \(0.289496\pi\)
\(240\) 8.40112e12 + 5.31955e11i 0.681044 + 0.0431234i
\(241\) −1.00810e13 −0.798750 −0.399375 0.916788i \(-0.630773\pi\)
−0.399375 + 0.916788i \(0.630773\pi\)
\(242\) 9.25368e12 8.96563e12i 0.716688 0.694379i
\(243\) −7.72719e12 7.72719e12i −0.585042 0.585042i
\(244\) −1.49951e13 + 1.40756e13i −1.10995 + 1.04189i
\(245\) −9.01226e12 + 9.01226e12i −0.652259 + 0.652259i
\(246\) −1.32423e13 2.09362e11i −0.937175 0.0148168i
\(247\) 3.77928e12i 0.261563i
\(248\) −1.16887e13 + 1.06295e13i −0.791194 + 0.719494i
\(249\) 2.04407e13i 1.35332i
\(250\) −2.58235e11 + 1.63336e13i −0.0167242 + 1.05782i
\(251\) −2.01824e13 + 2.01824e13i −1.27870 + 1.27870i −0.337302 + 0.941397i \(0.609514\pi\)
−0.941397 + 0.337302i \(0.890486\pi\)
\(252\) 1.45609e10 4.60379e11i 0.000902580 0.0285373i
\(253\) −5.90772e11 5.90772e11i −0.0358309 0.0358309i
\(254\) 1.89024e13 + 1.95097e13i 1.12184 + 1.15789i
\(255\) 1.53324e13 0.890509
\(256\) 1.74517e13 + 2.21896e12i 0.992013 + 0.126133i
\(257\) −2.83439e13 −1.57699 −0.788493 0.615044i \(-0.789138\pi\)
−0.788493 + 0.615044i \(0.789138\pi\)
\(258\) 2.42863e12 + 2.50666e12i 0.132268 + 0.136517i
\(259\) −3.77882e11 3.77882e11i −0.0201469 0.0201469i
\(260\) −6.91047e11 + 2.18491e13i −0.0360707 + 1.14046i
\(261\) −4.22973e12 + 4.22973e12i −0.216167 + 0.216167i
\(262\) 6.15838e11 3.89522e13i 0.0308184 1.94928i
\(263\) 1.43628e13i 0.703855i −0.936027 0.351928i \(-0.885526\pi\)
0.936027 0.351928i \(-0.114474\pi\)
\(264\) 5.20677e11 4.73492e11i 0.0249889 0.0227243i
\(265\) 1.95035e13i 0.916772i
\(266\) −2.88035e11 4.55386e9i −0.0132616 0.000209667i
\(267\) −2.56831e12 + 2.56831e12i −0.115834 + 0.115834i
\(268\) −1.32149e13 + 1.24046e13i −0.583879 + 0.548077i
\(269\) 1.53045e13 + 1.53045e13i 0.662492 + 0.662492i 0.955967 0.293475i \(-0.0948116\pi\)
−0.293475 + 0.955967i \(0.594812\pi\)
\(270\) 1.68360e13 1.63120e13i 0.714067 0.691840i
\(271\) 3.43046e13 1.42568 0.712838 0.701329i \(-0.247410\pi\)
0.712838 + 0.701329i \(0.247410\pi\)
\(272\) 3.19782e13 + 2.02485e12i 1.30234 + 0.0824637i
\(273\) −1.42137e12 −0.0567300
\(274\) 1.20747e13 1.16988e13i 0.472331 0.457628i
\(275\) 1.20401e11 + 1.20401e11i 0.00461637 + 0.00461637i
\(276\) 1.48351e13 + 1.58042e13i 0.557559 + 0.593980i
\(277\) 3.09049e13 3.09049e13i 1.13864 1.13864i 0.149951 0.988693i \(-0.452088\pi\)
0.988693 0.149951i \(-0.0479117\pi\)
\(278\) −2.68690e13 4.24802e11i −0.970522 0.0153441i
\(279\) 1.37995e13i 0.488697i
\(280\) 1.66438e12 + 7.89947e10i 0.0577941 + 0.00274302i
\(281\) 2.94675e13i 1.00336i 0.865052 + 0.501682i \(0.167285\pi\)
−0.865052 + 0.501682i \(0.832715\pi\)
\(282\) −5.18814e11 + 3.28154e13i −0.0173237 + 1.09574i
\(283\) 7.63667e12 7.63667e12i 0.250080 0.250080i −0.570923 0.821003i \(-0.693415\pi\)
0.821003 + 0.570923i \(0.193415\pi\)
\(284\) −6.25763e12 1.97917e11i −0.200983 0.00635671i
\(285\) −3.25153e12 3.25153e12i −0.102433 0.102433i
\(286\) 1.27171e12 + 1.31257e12i 0.0392985 + 0.0405611i
\(287\) −2.62152e12 −0.0794699
\(288\) 1.16891e13 9.97328e12i 0.347635 0.296606i
\(289\) 2.40896e13 0.702896
\(290\) −1.50573e13 1.55410e13i −0.431079 0.444929i
\(291\) 7.88244e12 + 7.88244e12i 0.221437 + 0.221437i
\(292\) −6.43703e13 2.03591e12i −1.77452 0.0561246i
\(293\) −1.88996e13 + 1.88996e13i −0.511307 + 0.511307i −0.914927 0.403620i \(-0.867752\pi\)
0.403620 + 0.914927i \(0.367752\pi\)
\(294\) 4.37021e11 2.76419e13i 0.0116036 0.733935i
\(295\) 2.50432e12i 0.0652632i
\(296\) 8.45173e11 1.78074e13i 0.0216193 0.455508i
\(297\) 1.95986e12i 0.0492112i
\(298\) −3.23295e13 5.11133e11i −0.796910 0.0125992i
\(299\) −3.98025e13 + 3.98025e13i −0.963206 + 0.963206i
\(300\) −3.02344e12 3.22094e12i −0.0718347 0.0765271i
\(301\) 4.88509e11 + 4.88509e11i 0.0113961 + 0.0113961i
\(302\) 2.62760e13 2.54581e13i 0.601896 0.583160i
\(303\) 1.86744e12 0.0420060
\(304\) −6.35220e12 7.21102e12i −0.140320 0.159291i
\(305\) −6.49825e13 −1.40977
\(306\) 2.01000e13 1.94743e13i 0.428281 0.414949i
\(307\) −8.05621e12 8.05621e12i −0.168605 0.168605i 0.617761 0.786366i \(-0.288040\pi\)
−0.786366 + 0.617761i \(0.788040\pi\)
\(308\) 1.01569e11 9.53409e10i 0.00208800 0.00195997i
\(309\) −1.83871e13 + 1.83871e13i −0.371315 + 0.371315i
\(310\) −4.99134e13 7.89136e11i −0.990212 0.0156553i
\(311\) 2.29206e13i 0.446729i 0.974735 + 0.223365i \(0.0717041\pi\)
−0.974735 + 0.223365i \(0.928296\pi\)
\(312\) −3.19009e13 3.50800e13i −0.610876 0.671752i
\(313\) 1.16826e13i 0.219809i −0.993942 0.109904i \(-0.964946\pi\)
0.993942 0.109904i \(-0.0350544\pi\)
\(314\) −7.38593e11 + 4.67165e13i −0.0136550 + 0.863690i
\(315\) 1.02910e12 1.02910e12i 0.0186960 0.0186960i
\(316\) 3.08523e12 9.75471e13i 0.0550819 1.74155i
\(317\) 4.67319e13 + 4.67319e13i 0.819950 + 0.819950i 0.986100 0.166150i \(-0.0531337\pi\)
−0.166150 + 0.986100i \(0.553134\pi\)
\(318\) 2.94372e13 + 3.03830e13i 0.507630 + 0.523939i
\(319\) −1.80911e12 −0.0306631
\(320\) 3.54054e13 + 4.28505e13i 0.589854 + 0.713890i
\(321\) 6.12676e13 1.00335
\(322\) 2.98556e12 + 3.08148e12i 0.0480638 + 0.0496080i
\(323\) −1.23767e13 1.23767e13i −0.195880 0.195880i
\(324\) −6.78987e11 + 2.14678e13i −0.0105649 + 0.334034i
\(325\) 8.11188e12 8.11188e12i 0.124097 0.124097i
\(326\) −9.14441e11 + 5.78390e13i −0.0137549 + 0.870010i
\(327\) 4.54739e13i 0.672588i
\(328\) −5.88369e13 6.47002e13i −0.855743 0.941021i
\(329\) 6.49631e12i 0.0929157i
\(330\) 2.22341e12 + 3.51523e10i 0.0312746 + 0.000494455i
\(331\) 2.48513e13 2.48513e13i 0.343791 0.343791i −0.514000 0.857790i \(-0.671837\pi\)
0.857790 + 0.514000i \(0.171837\pi\)
\(332\) 9.84101e13 9.23759e13i 1.33900 1.25690i
\(333\) −1.10104e13 1.10104e13i −0.147354 0.147354i
\(334\) −7.23608e13 + 7.01084e13i −0.952572 + 0.922920i
\(335\) −5.72680e13 −0.741593
\(336\) −2.71203e12 + 2.38903e12i −0.0345484 + 0.0304338i
\(337\) 1.14158e14 1.43068 0.715342 0.698775i \(-0.246271\pi\)
0.715342 + 0.698775i \(0.246271\pi\)
\(338\) 3.01842e13 2.92447e13i 0.372167 0.360583i
\(339\) −9.59133e12 9.59133e12i −0.116354 0.116354i
\(340\) 6.92902e13 + 7.38164e13i 0.827062 + 0.881087i
\(341\) −2.95111e12 + 2.95111e12i −0.0346606 + 0.0346606i
\(342\) −8.39253e12 1.32687e11i −0.0969949 0.00153350i
\(343\) 1.09657e13i 0.124715i
\(344\) −1.09260e12 + 2.30206e13i −0.0122290 + 0.257659i
\(345\) 6.84888e13i 0.754422i
\(346\) −7.06710e11 + 4.46999e13i −0.00766166 + 0.484605i
\(347\) 6.86725e13 6.86725e13i 0.732776 0.732776i −0.238393 0.971169i \(-0.576621\pi\)
0.971169 + 0.238393i \(0.0766207\pi\)
\(348\) 4.69129e13 + 1.48377e12i 0.492727 + 0.0155840i
\(349\) 5.60520e13 + 5.60520e13i 0.579497 + 0.579497i 0.934765 0.355268i \(-0.115610\pi\)
−0.355268 + 0.934765i \(0.615610\pi\)
\(350\) −6.08465e11 6.28014e11i −0.00619244 0.00639139i
\(351\) −1.32043e14 −1.32290
\(352\) 4.63264e12 + 3.66947e11i 0.0456924 + 0.00361925i
\(353\) 5.46239e13 0.530423 0.265211 0.964190i \(-0.414558\pi\)
0.265211 + 0.964190i \(0.414558\pi\)
\(354\) 3.77983e12 + 3.90127e12i 0.0361372 + 0.0372982i
\(355\) −1.39878e13 1.39878e13i −0.131672 0.131672i
\(356\) −2.39716e13 7.58178e11i −0.222189 0.00702742i
\(357\) −4.65482e12 + 4.65482e12i −0.0424842 + 0.0424842i
\(358\) −2.82192e12 + 1.78488e14i −0.0253623 + 1.60418i
\(359\) 3.93500e13i 0.348278i 0.984721 + 0.174139i \(0.0557141\pi\)
−0.984721 + 0.174139i \(0.944286\pi\)
\(360\) 4.84954e13 + 2.30169e12i 0.422704 + 0.0200624i
\(361\) 1.11241e14i 0.954937i
\(362\) −5.53990e13 8.75864e11i −0.468387 0.00740525i
\(363\) −6.24408e13 + 6.24408e13i −0.519974 + 0.519974i
\(364\) −6.42347e12 6.84307e12i −0.0526881 0.0561298i
\(365\) −1.43889e14 1.43889e14i −1.16256 1.16256i
\(366\) 1.01231e14 9.80798e13i 0.805689 0.780609i
\(367\) −1.36804e14 −1.07260 −0.536299 0.844028i \(-0.680178\pi\)
−0.536299 + 0.844028i \(0.680178\pi\)
\(368\) −9.04487e12 + 1.42845e14i −0.0698617 + 1.10332i
\(369\) −7.63838e13 −0.581241
\(370\) 4.04549e13 3.91956e13i 0.303292 0.293851i
\(371\) 5.92116e12 + 5.92116e12i 0.0437372 + 0.0437372i
\(372\) 7.89471e13 7.41063e13i 0.574579 0.539348i
\(373\) 1.67793e14 1.67793e14i 1.20331 1.20331i 0.230152 0.973155i \(-0.426078\pi\)
0.973155 0.230152i \(-0.0739224\pi\)
\(374\) 8.46322e12 + 1.33804e11i 0.0598056 + 0.000945533i
\(375\) 1.11956e14i 0.779606i
\(376\) −1.60332e14 + 1.45802e14i −1.10024 + 1.00053i
\(377\) 1.21886e14i 0.824285i
\(378\) −1.59106e11 + 1.00635e13i −0.00106043 + 0.0670727i
\(379\) 8.77288e13 8.77288e13i 0.576271 0.576271i −0.357603 0.933874i \(-0.616406\pi\)
0.933874 + 0.357603i \(0.116406\pi\)
\(380\) 9.59868e11 3.03486e13i 0.00621444 0.196485i
\(381\) −1.31645e14 1.31645e14i −0.840075 0.840075i
\(382\) 1.25064e14 + 1.29082e14i 0.786652 + 0.811926i
\(383\) −6.00616e13 −0.372395 −0.186197 0.982512i \(-0.559616\pi\)
−0.186197 + 0.982512i \(0.559616\pi\)
\(384\) −1.19831e14 1.33150e13i −0.732396 0.0813805i
\(385\) 4.40157e11 0.00265200
\(386\) −1.58300e14 1.63386e14i −0.940264 0.970473i
\(387\) 1.42338e13 + 1.42338e13i 0.0833508 + 0.0833508i
\(388\) −2.32694e12 + 7.35718e13i −0.0134341 + 0.424753i
\(389\) −3.16819e13 + 3.16819e13i −0.180339 + 0.180339i −0.791503 0.611165i \(-0.790701\pi\)
0.611165 + 0.791503i \(0.290701\pi\)
\(390\) 2.36834e12 1.49799e14i 0.0132919 0.840725i
\(391\) 2.60697e14i 1.44266i
\(392\) 1.35055e14 1.22816e14i 0.736947 0.670162i
\(393\) 2.66992e14i 1.43661i
\(394\) −1.41886e14 2.24323e12i −0.752854 0.0119027i
\(395\) 2.18050e14 2.18050e14i 1.14096 1.14096i
\(396\) 2.95943e12 2.77797e12i 0.0152716 0.0143352i
\(397\) −9.07399e13 9.07399e13i −0.461796 0.461796i 0.437448 0.899244i \(-0.355883\pi\)
−0.899244 + 0.437448i \(0.855883\pi\)
\(398\) −5.51726e13 + 5.34551e13i −0.276928 + 0.268307i
\(399\) 1.97429e12 0.00977373
\(400\) 1.84337e12 2.91122e13i 0.00900084 0.142149i
\(401\) −1.18853e14 −0.572424 −0.286212 0.958166i \(-0.592396\pi\)
−0.286212 + 0.958166i \(0.592396\pi\)
\(402\) 8.92131e13 8.64361e13i 0.423824 0.410631i
\(403\) 1.98827e14 + 1.98827e14i 0.931746 + 0.931746i
\(404\) 8.43934e12 + 8.99061e12i 0.0390131 + 0.0415616i
\(405\) −4.79876e13 + 4.79876e13i −0.218840 + 0.218840i
\(406\) 9.28946e12 + 1.46867e11i 0.0417924 + 0.000660742i
\(407\) 4.70929e12i 0.0209019i
\(408\) −2.19355e14 1.04110e13i −0.960541 0.0455891i
\(409\) 2.44879e14i 1.05797i 0.848631 + 0.528986i \(0.177428\pi\)
−0.848631 + 0.528986i \(0.822572\pi\)
\(410\) 4.36807e12 2.76284e14i 0.0186200 1.17773i
\(411\) −8.14758e13 + 8.14758e13i −0.342688 + 0.342688i
\(412\) −1.71619e14 5.42797e12i −0.712245 0.0225270i
\(413\) 7.60297e11 + 7.60297e11i 0.00311356 + 0.00311356i
\(414\) 8.69908e13 + 8.97856e13i 0.351537 + 0.362831i
\(415\) 4.26469e14 1.70068
\(416\) 2.47226e13 3.12118e14i 0.0972927 1.22830i
\(417\) 1.84170e14 0.715270
\(418\) −1.76642e12 1.82317e12i −0.00677055 0.00698807i
\(419\) 2.30256e13 + 2.30256e13i 0.0871033 + 0.0871033i 0.749316 0.662213i \(-0.230382\pi\)
−0.662213 + 0.749316i \(0.730382\pi\)
\(420\) −1.14140e13 3.61002e11i −0.0426153 0.00134784i
\(421\) −2.71463e13 + 2.71463e13i −0.100036 + 0.100036i −0.755354 0.655317i \(-0.772535\pi\)
0.655317 + 0.755354i \(0.272535\pi\)
\(422\) 1.22063e12 7.72057e13i 0.00443982 0.280822i
\(423\) 1.89284e14i 0.679583i
\(424\) −1.32433e13 + 2.79030e14i −0.0469337 + 0.988869i
\(425\) 5.31309e13i 0.185869i
\(426\) 4.29027e13 + 6.78296e11i 0.148160 + 0.00234243i
\(427\) 1.97283e13 1.97283e13i 0.0672569 0.0672569i
\(428\) 2.76881e14 + 2.94968e14i 0.931865 + 0.992736i
\(429\) −8.85680e12 8.85680e12i −0.0294281 0.0294281i
\(430\) −5.22982e13 + 5.06703e13i −0.171558 + 0.166218i
\(431\) 4.22363e13 0.136792 0.0683961 0.997658i \(-0.478212\pi\)
0.0683961 + 0.997658i \(0.478212\pi\)
\(432\) −2.51943e14 + 2.21937e14i −0.805642 + 0.709692i
\(433\) −3.22774e14 −1.01909 −0.509547 0.860443i \(-0.670187\pi\)
−0.509547 + 0.860443i \(0.670187\pi\)
\(434\) 1.53930e13 1.49139e13i 0.0479877 0.0464939i
\(435\) 1.04866e14 + 1.04866e14i 0.322807 + 0.322807i
\(436\) 2.18930e14 2.05506e14i 0.665472 0.624668i
\(437\) 5.52860e13 5.52860e13i 0.165946 0.165946i
\(438\) 4.41327e14 + 6.97743e12i 1.30814 + 0.0206818i
\(439\) 1.45795e14i 0.426764i 0.976969 + 0.213382i \(0.0684479\pi\)
−0.976969 + 0.213382i \(0.931552\pi\)
\(440\) 9.87880e12 + 1.08633e13i 0.0285571 + 0.0314030i
\(441\) 1.59443e14i 0.455190i
\(442\) 9.01490e12 5.70199e14i 0.0254178 1.60770i
\(443\) 2.05734e14 2.05734e14i 0.572909 0.572909i −0.360031 0.932940i \(-0.617234\pi\)
0.932940 + 0.360031i \(0.117234\pi\)
\(444\) −3.86240e12 + 1.22119e14i −0.0106231 + 0.335875i
\(445\) −5.35844e13 5.35844e13i −0.145566 0.145566i
\(446\) −1.20076e14 1.23934e14i −0.322191 0.332543i
\(447\) 2.21598e14 0.587319
\(448\) −2.37580e13 2.26030e12i −0.0621987 0.00591748i
\(449\) 1.85617e13 0.0480024 0.0240012 0.999712i \(-0.492359\pi\)
0.0240012 + 0.999712i \(0.492359\pi\)
\(450\) −1.77290e13 1.82986e13i −0.0452913 0.0467464i
\(451\) −1.63351e13 1.63351e13i −0.0412241 0.0412241i
\(452\) 2.83141e12 8.95220e13i 0.00705897 0.223187i
\(453\) −1.77302e14 + 1.77302e14i −0.436690 + 0.436690i
\(454\) 2.23020e12 1.41062e14i 0.00542671 0.343243i
\(455\) 2.96551e13i 0.0712912i
\(456\) 4.43106e13 + 4.87263e13i 0.105245 + 0.115733i
\(457\) 5.36809e14i 1.25974i −0.776701 0.629869i \(-0.783109\pi\)
0.776701 0.629869i \(-0.216891\pi\)
\(458\) 4.45244e14 + 7.03936e12i 1.03238 + 0.0163220i
\(459\) −4.32425e14 + 4.32425e14i −0.990698 + 0.990698i
\(460\) −3.29734e14 + 3.09515e14i −0.746440 + 0.700671i
\(461\) −1.02395e14 1.02395e14i −0.229046 0.229046i 0.583248 0.812294i \(-0.301782\pi\)
−0.812294 + 0.583248i \(0.801782\pi\)
\(462\) −6.85685e11 + 6.64341e11i −0.00151563 + 0.00146845i
\(463\) −6.64099e14 −1.45057 −0.725283 0.688451i \(-0.758291\pi\)
−0.725283 + 0.688451i \(0.758291\pi\)
\(464\) 2.04866e14 + 2.32564e14i 0.442202 + 0.501988i
\(465\) 3.42124e14 0.729781
\(466\) −5.19567e14 + 5.03393e14i −1.09526 + 1.06117i
\(467\) −3.58885e14 3.58885e14i −0.747675 0.747675i 0.226367 0.974042i \(-0.427315\pi\)
−0.974042 + 0.226367i \(0.927315\pi\)
\(468\) −1.87162e14 1.99388e14i −0.385359 0.410532i
\(469\) 1.73862e13 1.73862e13i 0.0353798 0.0353798i
\(470\) −6.84650e14 1.08244e13i −1.37699 0.0217703i
\(471\) 3.20212e14i 0.636535i
\(472\) −1.70048e12 + 3.58284e13i −0.00334112 + 0.0703957i
\(473\) 6.08796e12i 0.0118232i
\(474\) −1.05736e13 + 6.68789e14i −0.0202975 + 1.28383i
\(475\) −1.12675e13 + 1.12675e13i −0.0213802 + 0.0213802i
\(476\) −4.34464e13 1.37413e12i −0.0814920 0.00257744i
\(477\) 1.72526e14 + 1.72526e14i 0.319892 + 0.319892i
\(478\) −4.66308e14 4.81289e14i −0.854711 0.882171i
\(479\) −1.53948e14 −0.278951 −0.139475 0.990226i \(-0.544542\pi\)
−0.139475 + 0.990226i \(0.544542\pi\)
\(480\) −2.47263e14 2.89803e14i −0.442927 0.519130i
\(481\) −3.17283e14 −0.561886
\(482\) 3.17453e14 + 3.27652e14i 0.555803 + 0.573660i
\(483\) −2.07928e13 2.07928e13i −0.0359918 0.0359918i
\(484\) −5.82799e14 1.84328e13i −0.997400 0.0315459i
\(485\) −1.64457e14 + 1.64457e14i −0.278274 + 0.278274i
\(486\) −7.81776e12 + 4.94479e14i −0.0130792 + 0.827271i
\(487\) 9.15975e14i 1.51522i −0.652710 0.757608i \(-0.726368\pi\)
0.652710 0.757608i \(-0.273632\pi\)
\(488\) 9.29681e14 + 4.41245e13i 1.52064 + 0.0721723i
\(489\) 3.96449e14i 0.641193i
\(490\) 5.76712e14 + 9.11788e12i 0.922318 + 0.0145819i
\(491\) 1.86596e14 1.86596e14i 0.295089 0.295089i −0.543998 0.839087i \(-0.683090\pi\)
0.839087 + 0.543998i \(0.183090\pi\)
\(492\) 4.10198e14 + 4.36993e14i 0.641483 + 0.683386i
\(493\) 3.99163e14 + 3.99163e14i 0.617295 + 0.617295i
\(494\) −1.22834e14 + 1.19010e14i −0.187854 + 0.182006i
\(495\) 1.28250e13 0.0193967
\(496\) 7.13557e14 + 4.51821e13i 1.06728 + 0.0675799i
\(497\) 8.49326e12 0.0125636
\(498\) −6.64361e14 + 6.43681e14i −0.971947 + 0.941692i
\(499\) 1.06833e14 + 1.06833e14i 0.154580 + 0.154580i 0.780160 0.625580i \(-0.215138\pi\)
−0.625580 + 0.780160i \(0.715138\pi\)
\(500\) 5.39003e14 5.05953e14i 0.771358 0.724061i
\(501\) 4.88267e14 4.88267e14i 0.691114 0.691114i
\(502\) 1.29151e15 + 2.04190e13i 1.80813 + 0.0285867i
\(503\) 1.16223e14i 0.160941i −0.996757 0.0804706i \(-0.974358\pi\)
0.996757 0.0804706i \(-0.0256423\pi\)
\(504\) −1.54217e13 + 1.40241e13i −0.0211234 + 0.0192092i
\(505\) 3.89616e13i 0.0527879i
\(506\) −5.97696e11 + 3.78047e13i −0.000801037 + 0.0506662i
\(507\) −2.03673e14 + 2.03673e14i −0.270017 + 0.270017i
\(508\) 3.88624e13 1.22873e15i 0.0509658 1.61141i
\(509\) 8.43081e14 + 8.43081e14i 1.09376 + 1.09376i 0.995124 + 0.0986346i \(0.0314475\pi\)
0.0986346 + 0.995124i \(0.468552\pi\)
\(510\) −4.82818e14 4.98330e14i −0.619652 0.639560i
\(511\) 8.73675e13 0.110926
\(512\) −4.77436e14 6.37088e14i −0.599694 0.800229i
\(513\) 1.83409e14 0.227916
\(514\) 8.92554e14 + 9.21230e14i 1.09733 + 1.13259i
\(515\) −3.83624e14 3.83624e14i −0.466622 0.466622i
\(516\) 4.99314e12 1.57870e14i 0.00600897 0.189988i
\(517\) −4.04796e13 + 4.04796e13i −0.0481990 + 0.0481990i
\(518\) −3.82311e11 + 2.41814e13i −0.000450405 + 0.0284884i
\(519\) 3.06389e14i 0.357152i
\(520\) 7.31899e14 6.65572e14i 0.844175 0.767674i
\(521\) 2.87101e14i 0.327662i 0.986488 + 0.163831i \(0.0523852\pi\)
−0.986488 + 0.163831i \(0.947615\pi\)
\(522\) 2.70669e14 + 4.27930e12i 0.305669 + 0.00483265i
\(523\) −1.16485e15 + 1.16485e15i −1.30169 + 1.30169i −0.374446 + 0.927249i \(0.622167\pi\)
−0.927249 + 0.374446i \(0.877833\pi\)
\(524\) −1.28541e15 + 1.20659e15i −1.42141 + 1.33426i
\(525\) 4.23764e12 + 4.23764e12i 0.00463711 + 0.00463711i
\(526\) −4.66819e14 + 4.52287e14i −0.505506 + 0.489771i
\(527\) 1.30227e15 1.39554
\(528\) −3.17856e13 2.01265e12i −0.0337088 0.00213443i
\(529\) −2.11709e14 −0.222195
\(530\) −6.33901e14 + 6.14169e14i −0.658422 + 0.637927i
\(531\) 2.21529e13 + 2.21529e13i 0.0227725 + 0.0227725i
\(532\) 8.92225e12 + 9.50507e12i 0.00907737 + 0.00967033i
\(533\) −1.10056e15 + 1.10056e15i −1.10819 + 1.10819i
\(534\) 1.64351e14 + 2.59841e12i 0.163793 + 0.00258959i
\(535\) 1.27827e15i 1.26089i
\(536\) 8.19312e14 + 3.88862e13i 0.799914 + 0.0379655i
\(537\) 1.22342e15i 1.18227i
\(538\) 1.54838e13 9.79364e14i 0.0148107 0.936789i
\(539\) 3.40978e13 3.40978e13i 0.0322841 0.0322841i
\(540\) −1.06034e15 3.35365e13i −0.993754 0.0314306i
\(541\) 6.21814e14 + 6.21814e14i 0.576866 + 0.576866i 0.934039 0.357172i \(-0.116259\pi\)
−0.357172 + 0.934039i \(0.616259\pi\)
\(542\) −1.08026e15 1.11496e15i −0.992043 1.02392i
\(543\) 3.79725e14 0.345199
\(544\) −9.41187e14 1.10311e15i −0.846997 0.992719i
\(545\) 9.48754e14 0.845226
\(546\) 4.47591e13 + 4.61972e13i 0.0394750 + 0.0407433i
\(547\) −7.07617e14 7.07617e14i −0.617829 0.617829i 0.327145 0.944974i \(-0.393913\pi\)
−0.944974 + 0.327145i \(0.893913\pi\)
\(548\) −7.60465e14 2.40521e13i −0.657334 0.0207902i
\(549\) 5.74828e14 5.74828e14i 0.491915 0.491915i
\(550\) 1.21812e11 7.70471e12i 0.000103204 0.00652772i
\(551\) 1.69301e14i 0.142012i
\(552\) 4.65053e13 9.79844e14i 0.0386222 0.813752i
\(553\) 1.32397e14i 0.108866i
\(554\) −1.97766e15 3.12671e13i −1.61009 0.0254556i
\(555\) −2.72976e14 + 2.72976e14i −0.220046 + 0.220046i
\(556\) 8.32302e14 + 8.86670e14i 0.664308 + 0.707702i
\(557\) 8.59075e14 + 8.59075e14i 0.678934 + 0.678934i 0.959759 0.280825i \(-0.0906081\pi\)
−0.280825 + 0.959759i \(0.590608\pi\)
\(558\) 4.48509e14 4.34548e14i 0.350981 0.340055i
\(559\) 4.10169e14 0.317832
\(560\) −4.98441e13 5.65830e13i −0.0382454 0.0434162i
\(561\) −5.80099e13 −0.0440764
\(562\) 9.57749e14 9.27936e14i 0.720613 0.698182i
\(563\) −9.71752e14 9.71752e14i −0.724034 0.724034i 0.245390 0.969424i \(-0.421084\pi\)
−0.969424 + 0.245390i \(0.921084\pi\)
\(564\) 1.08290e15 1.01650e15i 0.799010 0.750018i
\(565\) 2.00111e14 2.00111e14i 0.146219 0.146219i
\(566\) −4.88686e14 7.72617e12i −0.353622 0.00559080i
\(567\) 2.91375e13i 0.0208807i
\(568\) 1.90621e14 + 2.09617e14i 0.135287 + 0.148768i
\(569\) 1.36146e15i 0.956949i 0.878102 + 0.478474i \(0.158810\pi\)
−0.878102 + 0.478474i \(0.841190\pi\)
\(570\) −3.28964e12 + 2.08072e14i −0.00229001 + 0.144844i
\(571\) −1.36626e15 + 1.36626e15i −0.941966 + 0.941966i −0.998406 0.0564400i \(-0.982025\pi\)
0.0564400 + 0.998406i \(0.482025\pi\)
\(572\) 2.61457e12 8.26661e13i 0.00178535 0.0564481i
\(573\) −8.71002e14 8.71002e14i −0.589072 0.589072i
\(574\) 8.25520e13 + 8.52043e13i 0.0552984 + 0.0570750i
\(575\) 2.37333e14 0.157465
\(576\) −6.92243e14 6.58587e13i −0.454920 0.0432803i
\(577\) −1.37482e15 −0.894911 −0.447456 0.894306i \(-0.647670\pi\)
−0.447456 + 0.894306i \(0.647670\pi\)
\(578\) −7.58584e14 7.82956e14i −0.489103 0.504817i
\(579\) 1.10247e15 + 1.10247e15i 0.704102 + 0.704102i
\(580\) −3.09569e13 + 9.78778e14i −0.0195841 + 0.619199i
\(581\) −1.29474e14 + 1.29474e14i −0.0811357 + 0.0811357i
\(582\) 7.97483e12 5.04413e14i 0.00495045 0.313119i
\(583\) 7.37915e13i 0.0453763i
\(584\) 1.96086e15 + 2.15627e15i 1.19447 + 1.31350i
\(585\) 8.64065e14i 0.521422i
\(586\) 1.20943e15 + 1.91211e13i 0.723007 + 0.0114308i
\(587\) 1.27134e15 1.27134e15i 0.752925 0.752925i −0.222099 0.975024i \(-0.571291\pi\)
0.975024 + 0.222099i \(0.0712910\pi\)
\(588\) −9.12175e14 + 8.56243e14i −0.535184 + 0.502368i
\(589\) −2.76172e14 2.76172e14i −0.160526 0.160526i
\(590\) −8.13950e13 + 7.88613e13i −0.0468718 + 0.0454128i
\(591\) 9.72538e14 0.554850
\(592\) −6.05388e14 + 5.33288e14i −0.342188 + 0.301434i
\(593\) −1.66805e15 −0.934131 −0.467066 0.884223i \(-0.654689\pi\)
−0.467066 + 0.884223i \(0.654689\pi\)
\(594\) −6.36990e13 + 6.17162e13i −0.0353433 + 0.0342432i
\(595\) −9.71168e13 9.71168e13i −0.0533889 0.0533889i
\(596\) 1.00145e15 + 1.06686e15i 0.545473 + 0.581105i
\(597\) 3.72286e14 3.72286e14i 0.200918 0.200918i
\(598\) 2.54704e15 + 4.02690e13i 1.36201 + 0.0215335i
\(599\) 1.85853e15i 0.984741i −0.870386 0.492370i \(-0.836131\pi\)
0.870386 0.492370i \(-0.163869\pi\)
\(600\) −9.47792e12 + 1.99695e14i −0.00497601 + 0.104842i
\(601\) 2.26696e15i 1.17932i −0.807650 0.589662i \(-0.799261\pi\)
0.807650 0.589662i \(-0.200739\pi\)
\(602\) 4.94234e11 3.12607e13i 0.000254772 0.0161145i
\(603\) 5.06586e14 5.06586e14i 0.258767 0.258767i
\(604\) −1.65487e15 5.23404e13i −0.837647 0.0264932i
\(605\) −1.30275e15 1.30275e15i −0.653440 0.653440i
\(606\) −5.88058e13 6.06951e13i −0.0292295 0.0301685i
\(607\) −1.39375e15 −0.686508 −0.343254 0.939243i \(-0.611529\pi\)
−0.343254 + 0.939243i \(0.611529\pi\)
\(608\) −3.43398e13 + 4.33534e14i −0.0167621 + 0.211619i
\(609\) −6.36733e13 −0.0308008
\(610\) 2.04631e15 + 2.11205e15i 0.980973 + 1.01249i
\(611\) 2.72726e15 + 2.72726e15i 1.29569 + 1.29569i
\(612\) −1.26591e15 4.00382e13i −0.596030 0.0188513i
\(613\) −4.24343e13 + 4.24343e13i −0.0198009 + 0.0198009i −0.716938 0.697137i \(-0.754457\pi\)
0.697137 + 0.716938i \(0.254457\pi\)
\(614\) −8.15063e12 + 5.15533e14i −0.00376934 + 0.238413i
\(615\) 1.89375e15i 0.867978i
\(616\) −6.29717e12 2.98876e11i −0.00286056 0.000135768i
\(617\) 2.15894e15i 0.972013i 0.873955 + 0.486007i \(0.161547\pi\)
−0.873955 + 0.486007i \(0.838453\pi\)
\(618\) 1.17663e15 + 1.86026e13i 0.525053 + 0.00830114i
\(619\) 1.84800e15 1.84800e15i 0.817339 0.817339i −0.168382 0.985722i \(-0.553854\pi\)
0.985722 + 0.168382i \(0.0538543\pi\)
\(620\) 1.54613e15 + 1.64713e15i 0.677786 + 0.722060i
\(621\) −1.93162e15 1.93162e15i −0.839300 0.839300i
\(622\) 7.44963e14 7.21774e14i 0.320839 0.310852i
\(623\) 3.25359e13 0.0138892
\(624\) −1.35600e14 + 2.14151e15i −0.0573777 + 0.906161i
\(625\) 1.99623e15 0.837278
\(626\) −3.79705e14 + 3.67886e14i −0.157866 + 0.152952i
\(627\) 1.23021e13 + 1.23021e13i 0.00507002 + 0.00507002i
\(628\) 1.54163e15 1.44711e15i 0.629801 0.591183i
\(629\) −1.03906e15 + 1.03906e15i −0.420788 + 0.420788i
\(630\) −6.58540e13 1.04116e12i −0.0264368 0.000417969i
\(631\) 1.80781e15i 0.719435i 0.933061 + 0.359718i \(0.117127\pi\)
−0.933061 + 0.359718i \(0.882873\pi\)
\(632\) −3.26762e15 + 2.97150e15i −1.28910 + 1.17228i
\(633\) 5.29195e14i 0.206964i
\(634\) 4.72796e13 2.99047e15i 0.0183309 1.15944i
\(635\) 2.74661e15 2.74661e15i 1.05570 1.05570i
\(636\) 6.05213e13 1.91353e15i 0.0230618 0.729156i
\(637\) −2.29730e15 2.29730e15i −0.867861 0.867861i
\(638\) 5.69691e13 + 5.87994e13i 0.0213366 + 0.0220221i
\(639\) 2.47470e14 0.0918898
\(640\) 2.77801e14 2.50011e15i 0.102269 0.920384i
\(641\) −3.37793e15 −1.23291 −0.616456 0.787389i \(-0.711432\pi\)
−0.616456 + 0.787389i \(0.711432\pi\)
\(642\) −1.92933e15 1.99131e15i −0.698173 0.720604i
\(643\) 1.45344e15 + 1.45344e15i 0.521480 + 0.521480i 0.918018 0.396538i \(-0.129789\pi\)
−0.396538 + 0.918018i \(0.629789\pi\)
\(644\) 6.13814e12 1.94072e14i 0.00218356 0.0690385i
\(645\) 3.52891e14 3.52891e14i 0.124469 0.124469i
\(646\) −1.25218e13 + 7.92010e14i −0.00437912 + 0.276982i
\(647\) 4.51422e15i 1.56534i −0.622436 0.782670i \(-0.713857\pi\)
0.622436 0.782670i \(-0.286143\pi\)
\(648\) 7.19126e14 6.53956e14i 0.247253 0.224847i
\(649\) 9.47507e12i 0.00323025i
\(650\) −5.19095e14 8.20695e12i −0.175478 0.00277433i
\(651\) −1.03867e14 + 1.03867e14i −0.0348163 + 0.0348163i
\(652\) 1.90867e15 1.79164e15i 0.634409 0.595509i
\(653\) 1.89288e15 + 1.89288e15i 0.623880 + 0.623880i 0.946521 0.322641i \(-0.104571\pi\)
−0.322641 + 0.946521i \(0.604571\pi\)
\(654\) −1.47799e15 + 1.43198e15i −0.483050 + 0.468014i
\(655\) −5.57045e15 −1.80536
\(656\) −2.50095e14 + 3.94972e15i −0.0803773 + 1.26939i
\(657\) 2.54565e15 0.811313
\(658\) 2.11142e14 2.04570e14i 0.0667317 0.0646545i
\(659\) −2.29856e15 2.29856e15i −0.720420 0.720420i 0.248270 0.968691i \(-0.420138\pi\)
−0.968691 + 0.248270i \(0.920138\pi\)
\(660\) −6.88728e13 7.33718e13i −0.0214070 0.0228054i
\(661\) −9.03518e13 + 9.03518e13i −0.0278502 + 0.0278502i −0.720895 0.693045i \(-0.756269\pi\)
0.693045 + 0.720895i \(0.256269\pi\)
\(662\) −1.59028e15 2.51425e13i −0.486133 0.00768581i
\(663\) 3.90834e15i 1.18486i
\(664\) −6.10133e15 2.89581e14i −1.83443 0.0870655i
\(665\) 4.11911e13i 0.0122824i
\(666\) −1.11395e13 + 7.04579e14i −0.00329425 + 0.208363i
\(667\) −1.78304e15 + 1.78304e15i −0.522960 + 0.522960i
\(668\) 4.55730e15 + 1.44139e14i 1.32568 + 0.0419286i
\(669\) 8.36263e14 + 8.36263e14i 0.241268 + 0.241268i
\(670\) 1.80338e15 + 1.86132e15i 0.516030 + 0.532609i
\(671\) 2.45861e14 0.0697776
\(672\) 1.63050e14 + 1.29150e13i 0.0458976 + 0.00363550i
\(673\) 5.82094e14 0.162521 0.0812606 0.996693i \(-0.474105\pi\)
0.0812606 + 0.996693i \(0.474105\pi\)
\(674\) −3.59486e15 3.71036e15i −0.995527 1.02751i
\(675\) 3.93670e14 + 3.93670e14i 0.108134 + 0.108134i
\(676\) −1.90101e15 6.01254e13i −0.517938 0.0163814i
\(677\) −5.51457e14 + 5.51457e14i −0.149030 + 0.149030i −0.777685 0.628655i \(-0.783606\pi\)
0.628655 + 0.777685i \(0.283606\pi\)
\(678\) −9.70375e12 + 6.13769e14i −0.00260121 + 0.164529i
\(679\) 9.98564e13i 0.0265517i
\(680\) 2.17212e14 4.57655e15i 0.0572908 1.20709i
\(681\) 9.66887e14i 0.252969i
\(682\) 1.88847e14 + 2.98569e12i 0.0490113 + 0.000774874i
\(683\) −1.35222e15 + 1.35222e15i −0.348123 + 0.348123i −0.859410 0.511287i \(-0.829169\pi\)
0.511287 + 0.859410i \(0.329169\pi\)
\(684\) 2.59969e14 + 2.76951e14i 0.0663916 + 0.0707285i
\(685\) −1.69989e15 1.69989e15i −0.430648 0.430648i
\(686\) −3.56406e14 + 3.45312e14i −0.0895701 + 0.0867819i
\(687\) −3.05186e15 −0.760856
\(688\) 7.82618e14 6.89410e14i 0.193559 0.170507i
\(689\) 4.97161e15 1.21981
\(690\) 2.22601e15 2.15672e15i 0.541823 0.524957i
\(691\) 1.10782e15 + 1.10782e15i 0.267510 + 0.267510i 0.828096 0.560586i \(-0.189424\pi\)
−0.560586 + 0.828096i \(0.689424\pi\)
\(692\) 1.47509e15 1.38464e15i 0.353373 0.331705i
\(693\) −3.89358e12 + 3.89358e12i −0.000925373 + 0.000925373i
\(694\) −4.39449e15 6.94774e13i −1.03617 0.0163820i
\(695\) 3.84246e15i 0.898863i
\(696\) −1.42907e15 1.57148e15i −0.331667 0.364719i
\(697\) 7.20840e15i 1.65981i
\(698\) 5.67089e13 3.58688e15i 0.0129553 0.819430i
\(699\) 3.50587e15 3.50587e15i 0.794641 0.794641i
\(700\) −1.25097e12 + 3.95525e13i −0.000281325 + 0.00889477i
\(701\) 2.35478e14 + 2.35478e14i 0.0525413 + 0.0525413i 0.732889 0.680348i \(-0.238171\pi\)
−0.680348 + 0.732889i \(0.738171\pi\)
\(702\) 4.15805e15 + 4.29164e15i 0.920526 + 0.950100i
\(703\) 4.40708e14 0.0968047
\(704\) −1.33956e14 1.62125e14i −0.0291953 0.0353345i
\(705\) 4.69284e15 1.01483
\(706\) −1.72012e15 1.77538e15i −0.369089 0.380948i
\(707\) −1.18285e13 1.18285e13i −0.00251840 0.00251840i
\(708\) 7.77113e12 2.45703e14i 0.00164173 0.0519072i
\(709\) 6.09313e15 6.09313e15i 1.27728 1.27728i 0.335097 0.942184i \(-0.391231\pi\)
0.942184 0.335097i \(-0.108769\pi\)
\(710\) −1.41518e13 + 8.95110e14i −0.00294368 + 0.186190i
\(711\) 3.85768e15i 0.796240i
\(712\) 7.30228e14 + 8.02998e14i 0.149561 + 0.164465i
\(713\) 5.81716e15i 1.18228i
\(714\) 2.97871e14 + 4.70937e12i 0.0600742 + 0.000949780i
\(715\) 1.84786e14 1.84786e14i 0.0369815 0.0369815i
\(716\) 5.89007e15 5.52891e15i 1.16976 1.09804i
\(717\) 3.24758e15 + 3.24758e15i 0.640037 + 0.640037i
\(718\) 1.27895e15 1.23914e15i 0.250132 0.242346i
\(719\) 2.52319e15 0.489713 0.244856 0.969559i \(-0.421259\pi\)
0.244856 + 0.969559i \(0.421259\pi\)
\(720\) −1.45232e15 1.64867e15i −0.279726 0.317545i
\(721\) 2.32932e14 0.0445230
\(722\) −3.61553e15 + 3.50299e15i −0.685832 + 0.664483i
\(723\) −2.21089e15 2.21089e15i −0.416204 0.416204i
\(724\) 1.71606e15 + 1.82815e15i 0.320604 + 0.341547i
\(725\) 3.63389e14 3.63389e14i 0.0673771 0.0673771i
\(726\) 3.99571e15 + 6.31726e13i 0.735263 + 0.0116246i
\(727\) 5.17879e14i 0.0945777i −0.998881 0.0472888i \(-0.984942\pi\)
0.998881 0.0472888i \(-0.0150581\pi\)
\(728\) −2.01364e13 + 4.24264e14i −0.00364972 + 0.0768978i
\(729\) 5.24717e15i 0.943896i
\(730\) −1.45575e14 + 9.20772e15i −0.0259903 + 1.64390i
\(731\) 1.34325e15 1.34325e15i 0.238019 0.238019i
\(732\) −6.37555e15 2.01647e14i −1.12126 0.0354634i
\(733\) −2.12556e15 2.12556e15i −0.371023 0.371023i 0.496827 0.867850i \(-0.334499\pi\)
−0.867850 + 0.496827i \(0.834499\pi\)
\(734\) 4.30799e15 + 4.44640e15i 0.746356 + 0.770336i
\(735\) −3.95299e15 −0.679744
\(736\) 4.92755e15 4.20423e15i 0.841013 0.717560i
\(737\) 2.16673e14 0.0367057
\(738\) 2.40534e15 + 2.48261e15i 0.404451 + 0.417445i
\(739\) −5.41609e14 5.41609e14i −0.0903945 0.0903945i 0.660464 0.750858i \(-0.270360\pi\)
−0.750858 + 0.660464i \(0.770360\pi\)
\(740\) −2.54786e15 8.05840e13i −0.422086 0.0133498i
\(741\) 8.28842e14 8.28842e14i 0.136292 0.136292i
\(742\) 5.99056e12 3.78907e14i 0.000977791 0.0618460i
\(743\) 1.22006e16i 1.97670i −0.152185 0.988352i \(-0.548631\pi\)
0.152185 0.988352i \(-0.451369\pi\)
\(744\) −4.89465e15 2.32309e14i −0.787173 0.0373608i
\(745\) 4.62335e15i 0.738070i
\(746\) −1.07374e16 1.69760e14i −1.70152 0.0269012i
\(747\) −3.77250e15 + 3.77250e15i −0.593424 + 0.593424i
\(748\) −2.62159e14 2.79284e14i −0.0409361 0.0436101i
\(749\) −3.88075e14 3.88075e14i −0.0601542 0.0601542i
\(750\) −3.63878e15 + 3.52551e15i −0.559910 + 0.542481i
\(751\) −4.45402e15 −0.680351 −0.340175 0.940362i \(-0.610486\pi\)
−0.340175 + 0.940362i \(0.610486\pi\)
\(752\) 9.78769e15 + 6.19752e14i 1.48417 + 0.0939767i
\(753\) −8.85250e15 −1.33258
\(754\) 3.96153e15 3.83822e15i 0.591999 0.573571i
\(755\) −3.69918e15 3.69918e15i −0.548778 0.548778i
\(756\) 3.32094e14 3.11731e14i 0.0489093 0.0459103i
\(757\) −1.55016e15 + 1.55016e15i −0.226646 + 0.226646i −0.811290 0.584644i \(-0.801234\pi\)
0.584644 + 0.811290i \(0.301234\pi\)
\(758\) −5.61394e15 8.87570e13i −0.814868 0.0128832i
\(759\) 2.59127e14i 0.0373407i
\(760\) −1.01661e15 + 9.24484e14i −0.145439 + 0.132259i