Properties

Label 16.12.e.a.5.6
Level 16
Weight 12
Character 16.5
Analytic conductor 12.293
Analytic rank 0
Dimension 42
CM No

Related objects

Downloads

Learn more about

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 5.6
Character \(\chi\) = 16.5
Dual form 16.12.e.a.13.6

$q$-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 \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −31.4901 + 32.5019i −0.695840 + 0.718196i
\(3\) 219.312 219.312i 0.521069 0.521069i −0.396825 0.917894i \(-0.629888\pi\)
0.917894 + 0.396825i \(0.129888\pi\)
\(4\) −64.7420 2046.98i −0.0316123 0.999500i
\(5\) −4575.66 4575.66i −0.654815 0.654815i 0.299333 0.954149i \(-0.403236\pi\)
−0.954149 + 0.299333i \(0.903236\pi\)
\(6\) 221.882 + 14034.2i 0.0116491 + 0.736811i
\(7\) 2778.29i 0.0624796i 0.999512 + 0.0312398i \(0.00994555\pi\)
−0.999512 + 0.0312398i \(0.990054\pi\)
\(8\) 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 0.723126 0.690716i \(-0.242704\pi\)
−0.690716 + 0.723126i \(0.742704\pi\)
\(12\) −463125. 434728.i −0.537281 0.504336i
\(13\) −1.16637e6 + 1.16637e6i −0.871263 + 0.871263i −0.992610 0.121347i \(-0.961278\pi\)
0.121347 + 0.992610i \(0.461278\pi\)
\(14\) −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 −0.628060 0.778165i \(-0.716151\pi\)
0.778165 + 0.628060i \(0.216151\pi\)
\(20\) −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 \(0.186427\pi\)
−0.833337 + 0.552765i \(0.813573\pi\)
\(24\) 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 −0.902897 0.429856i \(-0.858564\pi\)
0.429856 + 0.902897i \(0.358564\pi\)
\(30\) 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 0.849708 0.527253i \(-0.176778\pi\)
−0.527253 + 0.849708i \(0.676778\pi\)
\(38\) 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 \(0.219399\pi\)
−0.771716 + 0.635967i \(0.780601\pi\)
\(42\) −3.89911e7 + 616453.i −0.0460356 + 0.000727828i
\(43\) −1.75831e8 1.75831e8i −0.182397 0.182397i 0.610002 0.792400i \(-0.291169\pi\)
−0.792400 + 0.610002i \(0.791169\pi\)
\(44\) 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 0.264392 0.964415i \(-0.414829\pi\)
−0.964415 + 0.264392i \(0.914829\pi\)
\(54\) −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 0.681751 0.731584i \(-0.261219\pi\)
−0.731584 + 0.681751i \(0.761219\pi\)
\(60\) 1.29937e8 + 4.10827e9i 0.0215725 + 0.682067i
\(61\) 7.10089e9 7.10089e9i 1.07646 1.07646i 0.0796382 0.996824i \(-0.474624\pi\)
0.996824 0.0796382i \(-0.0253765\pi\)
\(62\) 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 −0.364818 0.931079i \(-0.618869\pi\)
0.931079 + 0.364818i \(0.118869\pi\)
\(68\) 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 \(-0.967942\pi\)
0.994933 0.100542i \(-0.0320576\pi\)
\(72\) −5.04776e9 + 5.55079e9i −0.307447 + 0.338085i
\(73\) 3.14465e10i 1.77540i −0.460420 0.887701i \(-0.652301\pi\)
0.460420 0.887701i \(-0.347699\pi\)
\(74\) −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 −0.369276 + 0.929320i \(0.620394\pi\)
−0.929320 + 0.369276i \(0.879606\pi\)
\(84\) 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 \(-0.964547\pi\)
0.993804 0.111150i \(-0.0354534\pi\)
\(90\) 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 0.726973 0.686666i \(-0.240926\pi\)
−0.686666 + 0.726973i \(0.740926\pi\)
\(102\) −1.69506e9 1.07214e11i −0.0152014 0.961502i
\(103\) 8.38400e10i 0.712601i −0.934371 0.356301i \(-0.884038\pi\)
0.934371 0.356301i \(-0.115962\pi\)
\(104\) −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 0.999332 0.0365502i \(-0.0116369\pi\)
−0.0365502 + 0.999332i \(0.511637\pi\)
\(108\) 1.12203e11 1.19532e11i 0.734805 0.782804i
\(109\) −1.03674e11 + 1.03674e11i −0.645393 + 0.645393i −0.951876 0.306483i \(-0.900848\pi\)
0.306483 + 0.951876i \(0.400848\pi\)
\(110\) 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 0.531407 0.847117i \(-0.321663\pi\)
0.847117 0.531407i \(-0.178337\pi\)
\(132\) −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 \(-0.893345\pi\)
0.944389 0.328832i \(-0.106655\pi\)
\(138\) −4.78918e11 + 7.57175e9i −0.814566 + 0.0128784i
\(139\) 4.19881e11 + 4.19881e11i 0.686348 + 0.686348i 0.961423 0.275075i \(-0.0887025\pi\)
−0.275075 + 0.961423i \(0.588703\pi\)
\(140\) −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 0.930320 0.366749i \(-0.119529\pi\)
−0.366749 + 0.930320i \(0.619529\pi\)
\(150\) 9.76050e10 1.54314e9i 0.104947 0.00165922i
\(151\) 8.08446e11i 0.838065i −0.907971 0.419033i \(-0.862369\pi\)
0.907971 0.419033i \(-0.137631\pi\)
\(152\) 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 −0.943154 0.332357i \(-0.892156\pi\)
0.332357 + 0.943154i \(0.392156\pi\)
\(158\) 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 −0.944314 0.329047i \(-0.893273\pi\)
0.329047 + 0.944314i \(0.393273\pi\)
\(164\) 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 \(0.230789\pi\)
−0.748469 + 0.663170i \(0.769211\pi\)
\(168\) 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 −0.857385 0.514675i \(-0.827913\pi\)
0.514675 + 0.857385i \(0.327913\pi\)
\(174\) −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 −0.145044 + 0.989425i \(0.546332\pi\)
−0.989425 + 0.145044i \(0.953668\pi\)
\(180\) −7.82195e11 7.34233e11i −0.308543 0.289624i
\(181\) 8.65718e11 + 8.65718e11i 0.331241 + 0.331241i 0.853058 0.521817i \(-0.174745\pi\)
−0.521817 + 0.853058i \(0.674745\pi\)
\(182\) 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 0.921290 0.388876i \(-0.127136\pi\)
−0.388876 + 0.921290i \(0.627136\pi\)
\(198\) −1.41786e9 8.96805e10i −0.000331111 0.0209430i
\(199\) 1.69752e12i 0.385588i 0.981239 + 0.192794i \(0.0617548\pi\)
−0.981239 + 0.192794i \(0.938245\pi\)
\(200\) 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 −0.600802 0.799398i \(-0.705152\pi\)
0.799398 + 0.600802i \(0.205152\pi\)
\(212\) −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 −0.575243 0.817983i \(-0.695092\pi\)
0.817983 + 0.575243i \(0.195092\pi\)
\(228\) −1.45461e12 + 4.60066e10i −0.156353 + 0.00494514i
\(229\) −6.95781e12 6.95781e12i −0.730092 0.730092i 0.240546 0.970638i \(-0.422673\pi\)
−0.970638 + 0.240546i \(0.922673\pi\)
\(230\) 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 \(0.276033\pi\)
−0.646977 + 0.762510i \(0.723967\pi\)
\(234\) 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 −0.941397 0.337302i \(-0.890486\pi\)
−0.337302 0.941397i \(-0.609514\pi\)
\(252\) 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 \(0.114474\pi\)
−0.936027 + 0.351928i \(0.885526\pi\)
\(264\) 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 −0.293475 0.955967i \(-0.594812\pi\)
0.955967 + 0.293475i \(0.0948116\pi\)
\(270\) 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 0.988693 + 0.149951i \(0.0479117\pi\)
0.149951 + 0.988693i \(0.452088\pi\)
\(278\) −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 \(-0.832715\pi\)
0.865052 0.501682i \(-0.167285\pi\)
\(282\) −5.18814e11 3.28154e13i −0.0173237 1.09574i
\(283\) 7.63667e12 + 7.63667e12i 0.250080 + 0.250080i 0.821003 0.570923i \(-0.193415\pi\)
−0.570923 + 0.821003i \(0.693415\pi\)
\(284\) −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 0.403620 0.914927i \(-0.367752\pi\)
−0.914927 + 0.403620i \(0.867752\pi\)
\(294\) 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 −0.786366 0.617761i \(-0.788040\pi\)
0.617761 + 0.786366i \(0.288040\pi\)
\(308\) 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 \(-0.928296\pi\)
0.974735 0.223365i \(-0.0717041\pi\)
\(312\) −3.19009e13 + 3.50800e13i −0.610876 + 0.671752i
\(313\) 1.16826e13i 0.219809i 0.993942 + 0.109904i \(0.0350544\pi\)
−0.993942 + 0.109904i \(0.964946\pi\)
\(314\) −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 −0.166150 0.986100i \(-0.553134\pi\)
0.986100 + 0.166150i \(0.0531337\pi\)
\(318\) 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 0.857790 0.514000i \(-0.171837\pi\)
−0.514000 + 0.857790i \(0.671837\pi\)
\(332\) 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 0.971169 0.238393i \(-0.0766207\pi\)
−0.238393 + 0.971169i \(0.576621\pi\)
\(348\) 4.69129e13 1.48377e12i 0.492727 0.0155840i
\(349\) 5.60520e13 5.60520e13i 0.579497 0.579497i −0.355268 0.934765i \(-0.615610\pi\)
0.934765 + 0.355268i \(0.115610\pi\)
\(350\) −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 \(-0.944286\pi\)
0.984721 0.174139i \(-0.0557141\pi\)
\(360\) 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 0.973155 + 0.230152i \(0.0739224\pi\)
0.230152 + 0.973155i \(0.426078\pi\)
\(374\) 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 0.933874 0.357603i \(-0.116406\pi\)
−0.357603 + 0.933874i \(0.616406\pi\)
\(380\) 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 0.611165 0.791503i \(-0.290701\pi\)
−0.791503 + 0.611165i \(0.790701\pi\)
\(390\) 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 −0.899244 0.437448i \(-0.855883\pi\)
0.437448 + 0.899244i \(0.355883\pi\)
\(398\) −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 \(-0.822572\pi\)
0.848631 0.528986i \(-0.177428\pi\)
\(410\) 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 −0.662213 0.749316i \(-0.730382\pi\)
0.749316 + 0.662213i \(0.230382\pi\)
\(420\) −1.14140e13 + 3.61002e11i −0.0426153 + 0.00134784i
\(421\) −2.71463e13 2.71463e13i −0.100036 0.100036i 0.655317 0.755354i \(-0.272535\pi\)
−0.755354 + 0.655317i \(0.772535\pi\)
\(422\) 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 \(-0.931552\pi\)
0.976969 0.213382i \(-0.0684479\pi\)
\(440\) 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 0.932940 0.360031i \(-0.117234\pi\)
−0.360031 + 0.932940i \(0.617234\pi\)
\(444\) −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 \(0.216891\pi\)
−0.776701 + 0.629869i \(0.783109\pi\)
\(458\) 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 −0.812294 0.583248i \(-0.801782\pi\)
0.583248 + 0.812294i \(0.301782\pi\)
\(462\) −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 −0.974042 0.226367i \(-0.927315\pi\)
0.226367 + 0.974042i \(0.427315\pi\)
\(468\) −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 \(0.273632\pi\)
−0.652710 + 0.757608i \(0.726368\pi\)
\(488\) 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 0.839087 0.543998i \(-0.183090\pi\)
−0.543998 + 0.839087i \(0.683090\pi\)
\(492\) 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 −0.625580 0.780160i \(-0.715138\pi\)
0.780160 + 0.625580i \(0.215138\pi\)
\(500\) 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 \(0.0256423\pi\)
−0.996757 + 0.0804706i \(0.974358\pi\)
\(504\) −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 0.0986346 0.995124i \(-0.468552\pi\)
0.995124 0.0986346i \(-0.0314475\pi\)
\(510\) −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 \(-0.947615\pi\)
0.986488 0.163831i \(-0.0523852\pi\)
\(522\) 2.70669e14 4.27930e12i 0.305669 0.00483265i
\(523\) −1.16485e15 1.16485e15i −1.30169 1.30169i −0.927249 0.374446i \(-0.877833\pi\)
−0.374446 0.927249i \(-0.622167\pi\)
\(524\) −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 −0.357172 0.934039i \(-0.616259\pi\)
0.934039 + 0.357172i \(0.116259\pi\)
\(542\) −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 −0.944974 0.327145i \(-0.893913\pi\)
0.327145 + 0.944974i \(0.393913\pi\)
\(548\) −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 −0.280825 0.959759i \(-0.590608\pi\)
0.959759 + 0.280825i \(0.0906081\pi\)
\(558\) 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 −0.969424 0.245390i \(-0.921084\pi\)
0.245390 + 0.969424i \(0.421084\pi\)
\(564\) 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 \(-0.841190\pi\)
0.878102 0.478474i \(-0.158810\pi\)
\(570\) −3.28964e12 2.08072e14i −0.00229001 0.144844i
\(571\) −1.36626e15 1.36626e15i −0.941966 0.941966i 0.0564400 0.998406i \(-0.482025\pi\)
−0.998406 + 0.0564400i \(0.982025\pi\)
\(572\) 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 0.975024 0.222099i \(-0.0712910\pi\)
−0.222099 + 0.975024i \(0.571291\pi\)
\(588\) −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 \(0.163869\pi\)
−0.870386 + 0.492370i \(0.836131\pi\)
\(600\) −9.47792e12 1.99695e14i −0.00497601 0.104842i
\(601\) 2.26696e15i 1.17932i 0.807650 + 0.589662i \(0.200739\pi\)
−0.807650 + 0.589662i \(0.799261\pi\)
\(602\) 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 0.697137 0.716938i \(-0.254457\pi\)
−0.716938 + 0.697137i \(0.754457\pi\)
\(614\) −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 \(-0.838453\pi\)
0.873955 0.486007i \(-0.161547\pi\)
\(618\) 1.17663e15 1.86026e13i 0.525053 0.00830114i
\(619\) 1.84800e15 + 1.84800e15i 0.817339 + 0.817339i 0.985722 0.168382i \(-0.0538543\pi\)
−0.168382 + 0.985722i \(0.553854\pi\)
\(620\) 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 \(-0.882873\pi\)
0.933061 0.359718i \(-0.117127\pi\)
\(632\) −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 −0.396538 0.918018i \(-0.629789\pi\)
0.918018 + 0.396538i \(0.129789\pi\)
\(644\) 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 \(0.286143\pi\)
−0.622436 + 0.782670i \(0.713857\pi\)
\(648\) 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 −0.322641 0.946521i \(-0.604571\pi\)
0.946521 + 0.322641i \(0.104571\pi\)
\(654\) −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 −0.968691 0.248270i \(-0.920138\pi\)
0.248270 + 0.968691i \(0.420138\pi\)
\(660\) −6.88728e13 + 7.33718e13i −0.0214070 + 0.0228054i
\(661\) −9.03518e13 9.03518e13i −0.0278502 0.0278502i 0.693045 0.720895i \(-0.256269\pi\)
−0.720895 + 0.693045i \(0.756269\pi\)
\(662\) −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 0.628655 0.777685i \(-0.283606\pi\)
−0.777685 + 0.628655i \(0.783606\pi\)
\(678\) −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 0.511287 0.859410i \(-0.329169\pi\)
−0.859410 + 0.511287i \(0.829169\pi\)
\(684\) 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 −0.560586 0.828096i \(-0.689424\pi\)
0.828096 + 0.560586i \(0.189424\pi\)
\(692\) 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 −0.680348 0.732889i \(-0.738171\pi\)
0.732889 + 0.680348i \(0.238171\pi\)
\(702\) 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 0.942184 + 0.335097i \(0.108769\pi\)
0.335097 + 0.942184i \(0.391231\pi\)
\(710\) −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 \(0.0150581\pi\)
−0.998881 + 0.0472888i \(0.984942\pi\)
\(728\) −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 −0.867850 0.496827i \(-0.834499\pi\)
0.496827 + 0.867850i \(0.334499\pi\)
\(734\) 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 −0.750858 0.660464i \(-0.770360\pi\)
0.660464 + 0.750858i \(0.270360\pi\)
\(740\) −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 \(0.451369\pi\)
−0.152185 + 0.988352i \(0.548631\pi\)
\(744\) −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 0.584644 0.811290i \(-0.301234\pi\)
−0.811290 + 0.584644i \(0.801234\pi\)
\(758\) −5.61394e15 + 8.87570e13i −0.814868 + 0.0128832i
\(759\) 2.59127e14i 0.0373407i
\(760\) −1.01661e15 9.24484e14i −0.145439 0.132259i
\(761\) 7.65104e14i