Properties

Label 16.12.e.a.13.18
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 13.18
Character \(\chi\) = 16.13
Dual form 16.12.e.a.5.18

$q$-expansion

\(f(q)\) \(=\) \(q+(40.4837 - 20.2255i) q^{2} +(-522.679 - 522.679i) q^{3} +(1229.86 - 1637.61i) q^{4} +(-3202.37 + 3202.37i) q^{5} +(-31731.4 - 10588.5i) q^{6} -31977.4i q^{7} +(16667.6 - 91170.9i) q^{8} +369239. i q^{9} +O(q^{10})\) \(q+(40.4837 - 20.2255i) q^{2} +(-522.679 - 522.679i) q^{3} +(1229.86 - 1637.61i) q^{4} +(-3202.37 + 3202.37i) q^{5} +(-31731.4 - 10588.5i) q^{6} -31977.4i q^{7} +(16667.6 - 91170.9i) q^{8} +369239. i q^{9} +(-64874.2 + 194414. i) q^{10} +(-406679. + 406679. i) q^{11} +(-1.49876e6 + 213123. i) q^{12} +(1.12564e6 + 1.12564e6i) q^{13} +(-646759. - 1.29456e6i) q^{14} +3.34763e6 q^{15} +(-1.16921e6 - 4.02804e6i) q^{16} -5.55545e6 q^{17} +(7.46806e6 + 1.49482e7i) q^{18} +(-7.81054e6 - 7.81054e6i) q^{19} +(1.30577e6 + 9.18269e6i) q^{20} +(-1.67139e7 + 1.67139e7i) q^{21} +(-8.23856e6 + 2.46892e7i) q^{22} -3.53021e7i q^{23} +(-5.63649e7 + 3.89413e7i) q^{24} +2.83177e7i q^{25} +(6.83367e7 + 2.28034e7i) q^{26} +(1.00402e8 - 1.00402e8i) q^{27} +(-5.23664e7 - 3.93275e7i) q^{28} +(-1.32950e8 - 1.32950e8i) q^{29} +(1.35524e8 - 6.77075e7i) q^{30} +7.64393e7 q^{31} +(-1.28803e8 - 1.39422e8i) q^{32} +4.25125e8 q^{33} +(-2.24905e8 + 1.12362e8i) q^{34} +(1.02403e8 + 1.02403e8i) q^{35} +(6.04669e8 + 4.54111e8i) q^{36} +(-6.43077e7 + 6.43077e7i) q^{37} +(-4.74171e8 - 1.58227e8i) q^{38} -1.17670e9i q^{39} +(2.38587e8 + 3.45339e8i) q^{40} -1.19596e9i q^{41} +(-3.38592e8 + 1.01469e9i) q^{42} +(-1.26260e9 + 1.26260e9i) q^{43} +(1.65824e8 + 1.16614e9i) q^{44} +(-1.18244e9 - 1.18244e9i) q^{45} +(-7.14004e8 - 1.42916e9i) q^{46} +5.29010e8 q^{47} +(-1.49425e9 + 2.71649e9i) q^{48} +9.54775e8 q^{49} +(5.72741e8 + 1.14641e9i) q^{50} +(2.90372e9 + 2.90372e9i) q^{51} +(3.22773e9 - 4.58982e8i) q^{52} +(-3.02648e9 + 3.02648e9i) q^{53} +(2.03397e9 - 6.09535e9i) q^{54} -2.60468e9i q^{55} +(-2.91540e9 - 5.32986e8i) q^{56} +8.16480e9i q^{57} +(-8.07126e9 - 2.69331e9i) q^{58} +(2.78580e9 - 2.78580e9i) q^{59} +(4.11710e9 - 5.48210e9i) q^{60} +(-3.36803e9 - 3.36803e9i) q^{61} +(3.09454e9 - 1.54602e9i) q^{62} +1.18073e10 q^{63} +(-8.03432e9 - 3.03920e9i) q^{64} -7.20944e9 q^{65} +(1.72106e10 - 8.59838e9i) q^{66} +(-1.24856e9 - 1.24856e9i) q^{67} +(-6.83240e9 + 9.09765e9i) q^{68} +(-1.84517e10 + 1.84517e10i) q^{69} +(6.21683e9 + 2.07450e9i) q^{70} -1.89319e9i q^{71} +(3.36638e10 + 6.15433e9i) q^{72} -7.84989e9i q^{73} +(-1.30275e9 + 3.90407e9i) q^{74} +(1.48011e10 - 1.48011e10i) q^{75} +(-2.23964e10 + 3.18476e9i) q^{76} +(1.30045e10 + 1.30045e10i) q^{77} +(-2.37993e10 - 4.76370e10i) q^{78} +1.00349e10 q^{79} +(1.66436e10 + 9.15504e9i) q^{80} -3.95468e10 q^{81} +(-2.41889e10 - 4.84167e10i) q^{82} +(-4.69132e9 - 4.69132e9i) q^{83} +(6.81512e9 + 4.79265e10i) q^{84} +(1.77906e10 - 1.77906e10i) q^{85} +(-2.55779e10 + 7.66512e10i) q^{86} +1.38980e11i q^{87} +(3.02989e10 + 4.38556e10i) q^{88} -2.92005e10i q^{89} +(-7.17851e10 - 2.39541e10i) q^{90} +(3.59950e10 - 3.59950e10i) q^{91} +(-5.78110e10 - 4.34165e10i) q^{92} +(-3.99532e10 - 3.99532e10i) q^{93} +(2.14163e10 - 1.06995e10i) q^{94} +5.00245e10 q^{95} +(-5.55014e9 + 1.40196e11i) q^{96} +1.08863e10 q^{97} +(3.86528e10 - 1.93108e10i) q^{98} +(-1.50162e11 - 1.50162e11i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 40.4837 20.2255i 0.894571 0.446925i
\(3\) −522.679 522.679i −1.24185 1.24185i −0.959234 0.282612i \(-0.908799\pi\)
−0.282612 0.959234i \(-0.591201\pi\)
\(4\) 1229.86 1637.61i 0.600516 0.799613i
\(5\) −3202.37 + 3202.37i −0.458287 + 0.458287i −0.898093 0.439806i \(-0.855047\pi\)
0.439806 + 0.898093i \(0.355047\pi\)
\(6\) −31731.4 10588.5i −1.66593 0.555908i
\(7\) 31977.4i 0.719123i −0.933121 0.359562i \(-0.882926\pi\)
0.933121 0.359562i \(-0.117074\pi\)
\(8\) 16667.6 91170.9i 0.179837 0.983696i
\(9\) 369239.i 2.08437i
\(10\) −64874.2 + 194414.i −0.205150 + 0.614790i
\(11\) −406679. + 406679.i −0.761364 + 0.761364i −0.976569 0.215205i \(-0.930958\pi\)
0.215205 + 0.976569i \(0.430958\pi\)
\(12\) −1.49876e6 + 213123.i −1.73874 + 0.247249i
\(13\) 1.12564e6 + 1.12564e6i 0.840835 + 0.840835i 0.988968 0.148132i \(-0.0473262\pi\)
−0.148132 + 0.988968i \(0.547326\pi\)
\(14\) −646759. 1.29456e6i −0.321394 0.643307i
\(15\) 3.34763e6 1.13824
\(16\) −1.16921e6 4.02804e6i −0.278762 0.960360i
\(17\) −5.55545e6 −0.948965 −0.474483 0.880265i \(-0.657365\pi\)
−0.474483 + 0.880265i \(0.657365\pi\)
\(18\) 7.46806e6 + 1.49482e7i 0.931556 + 1.86461i
\(19\) −7.81054e6 7.81054e6i −0.723662 0.723662i 0.245687 0.969349i \(-0.420986\pi\)
−0.969349 + 0.245687i \(0.920986\pi\)
\(20\) 1.30577e6 + 9.18269e6i 0.0912437 + 0.641660i
\(21\) −1.67139e7 + 1.67139e7i −0.893041 + 0.893041i
\(22\) −8.23856e6 + 2.46892e7i −0.340821 + 1.02137i
\(23\) 3.53021e7i 1.14366i −0.820371 0.571831i \(-0.806233\pi\)
0.820371 0.571831i \(-0.193767\pi\)
\(24\) −5.63649e7 + 3.89413e7i −1.44493 + 0.998271i
\(25\) 2.83177e7i 0.579947i
\(26\) 6.83367e7 + 2.28034e7i 1.12798 + 0.376396i
\(27\) 1.00402e8 1.00402e8i 1.34662 1.34662i
\(28\) −5.23664e7 3.93275e7i −0.575021 0.431845i
\(29\) −1.32950e8 1.32950e8i −1.20364 1.20364i −0.973050 0.230594i \(-0.925933\pi\)
−0.230594 0.973050i \(-0.574067\pi\)
\(30\) 1.35524e8 6.77075e7i 1.01824 0.508710i
\(31\) 7.64393e7 0.479543 0.239771 0.970829i \(-0.422928\pi\)
0.239771 + 0.970829i \(0.422928\pi\)
\(32\) −1.28803e8 1.39422e8i −0.678582 0.734525i
\(33\) 4.25125e8 1.89099
\(34\) −2.24905e8 + 1.12362e8i −0.848917 + 0.424117i
\(35\) 1.02403e8 + 1.02403e8i 0.329565 + 0.329565i
\(36\) 6.04669e8 + 4.54111e8i 1.66669 + 1.25169i
\(37\) −6.43077e7 + 6.43077e7i −0.152459 + 0.152459i −0.779215 0.626756i \(-0.784382\pi\)
0.626756 + 0.779215i \(0.284382\pi\)
\(38\) −4.74171e8 1.58227e8i −0.970791 0.323945i
\(39\) 1.17670e9i 2.08838i
\(40\) 2.38587e8 + 3.45339e8i 0.368398 + 0.533232i
\(41\) 1.19596e9i 1.61215i −0.591817 0.806073i \(-0.701589\pi\)
0.591817 0.806073i \(-0.298411\pi\)
\(42\) −3.38592e8 + 1.01469e9i −0.399766 + 1.19801i
\(43\) −1.26260e9 + 1.26260e9i −1.30975 + 1.30975i −0.388154 + 0.921594i \(0.626887\pi\)
−0.921594 + 0.388154i \(0.873113\pi\)
\(44\) 1.65824e8 + 1.16614e9i 0.151586 + 1.06601i
\(45\) −1.18244e9 1.18244e9i −0.955237 0.955237i
\(46\) −7.14004e8 1.42916e9i −0.511132 1.02309i
\(47\) 5.29010e8 0.336454 0.168227 0.985748i \(-0.446196\pi\)
0.168227 + 0.985748i \(0.446196\pi\)
\(48\) −1.49425e9 + 2.71649e9i −0.846440 + 1.53880i
\(49\) 9.54775e8 0.482862
\(50\) 5.72741e8 + 1.14641e9i 0.259193 + 0.518804i
\(51\) 2.90372e9 + 2.90372e9i 1.17847 + 1.17847i
\(52\) 3.22773e9 4.58982e8i 1.17728 0.167408i
\(53\) −3.02648e9 + 3.02648e9i −0.994079 + 0.994079i −0.999983 0.00590367i \(-0.998121\pi\)
0.00590367 + 0.999983i \(0.498121\pi\)
\(54\) 2.03397e9 6.09535e9i 0.602807 1.80648i
\(55\) 2.60468e9i 0.697845i
\(56\) −2.91540e9 5.32986e8i −0.707399 0.129325i
\(57\) 8.16480e9i 1.79736i
\(58\) −8.07126e9 2.69331e9i −1.61468 0.538806i
\(59\) 2.78580e9 2.78580e9i 0.507299 0.507299i −0.406398 0.913696i \(-0.633215\pi\)
0.913696 + 0.406398i \(0.133215\pi\)
\(60\) 4.11710e9 5.48210e9i 0.683533 0.910154i
\(61\) −3.36803e9 3.36803e9i −0.510577 0.510577i 0.404126 0.914703i \(-0.367576\pi\)
−0.914703 + 0.404126i \(0.867576\pi\)
\(62\) 3.09454e9 1.54602e9i 0.428985 0.214320i
\(63\) 1.18073e10 1.49892
\(64\) −8.03432e9 3.03920e9i −0.935318 0.353809i
\(65\) −7.20944e9 −0.770687
\(66\) 1.72106e10 8.59838e9i 1.69163 0.845133i
\(67\) −1.24856e9 1.24856e9i −0.112979 0.112979i 0.648357 0.761336i \(-0.275456\pi\)
−0.761336 + 0.648357i \(0.775456\pi\)
\(68\) −6.83240e9 + 9.09765e9i −0.569868 + 0.758805i
\(69\) −1.84517e10 + 1.84517e10i −1.42025 + 1.42025i
\(70\) 6.21683e9 + 2.07450e9i 0.442110 + 0.147528i
\(71\) 1.89319e9i 0.124530i −0.998060 0.0622649i \(-0.980168\pi\)
0.998060 0.0622649i \(-0.0198324\pi\)
\(72\) 3.36638e10 + 6.15433e9i 2.05038 + 0.374845i
\(73\) 7.84989e9i 0.443188i −0.975139 0.221594i \(-0.928874\pi\)
0.975139 0.221594i \(-0.0711259\pi\)
\(74\) −1.30275e9 + 3.90407e9i −0.0682477 + 0.204523i
\(75\) 1.48011e10 1.48011e10i 0.720205 0.720205i
\(76\) −2.23964e10 + 3.18476e9i −1.01322 + 0.144079i
\(77\) 1.30045e10 + 1.30045e10i 0.547514 + 0.547514i
\(78\) −2.37993e10 4.76370e10i −0.933348 1.86820i
\(79\) 1.00349e10 0.366914 0.183457 0.983028i \(-0.441271\pi\)
0.183457 + 0.983028i \(0.441271\pi\)
\(80\) 1.66436e10 + 9.15504e9i 0.567873 + 0.312367i
\(81\) −3.95468e10 −1.26021
\(82\) −2.41889e10 4.84167e10i −0.720509 1.44218i
\(83\) −4.69132e9 4.69132e9i −0.130727 0.130727i 0.638716 0.769443i \(-0.279466\pi\)
−0.769443 + 0.638716i \(0.779466\pi\)
\(84\) 6.81512e9 + 4.79265e10i 0.177802 + 1.25037i
\(85\) 1.77906e10 1.77906e10i 0.434898 0.434898i
\(86\) −2.55779e10 + 7.66512e10i −0.586304 + 1.75702i
\(87\) 1.38980e11i 2.98948i
\(88\) 3.02989e10 + 4.38556e10i 0.612030 + 0.885872i
\(89\) 2.92005e10i 0.554301i −0.960826 0.277151i \(-0.910610\pi\)
0.960826 0.277151i \(-0.0893901\pi\)
\(90\) −7.17851e10 2.39541e10i −1.28145 0.427608i
\(91\) 3.59950e10 3.59950e10i 0.604664 0.604664i
\(92\) −5.78110e10 4.34165e10i −0.914487 0.686787i
\(93\) −3.99532e10 3.99532e10i −0.595518 0.595518i
\(94\) 2.14163e10 1.06995e10i 0.300982 0.150370i
\(95\) 5.00245e10 0.663289
\(96\) −5.55014e9 + 1.40196e11i −0.0694724 + 1.75486i
\(97\) 1.08863e10 0.128717 0.0643585 0.997927i \(-0.479500\pi\)
0.0643585 + 0.997927i \(0.479500\pi\)
\(98\) 3.86528e10 1.93108e10i 0.431954 0.215803i
\(99\) −1.50162e11 1.50162e11i −1.58696 1.58696i
\(100\) 4.63733e10 + 3.48267e10i 0.463733 + 0.348267i
\(101\) 3.95900e10 3.95900e10i 0.374816 0.374816i −0.494412 0.869228i \(-0.664616\pi\)
0.869228 + 0.494412i \(0.164616\pi\)
\(102\) 1.76282e11 + 5.88239e10i 1.58091 + 0.527537i
\(103\) 1.94460e11i 1.65282i −0.563070 0.826409i \(-0.690380\pi\)
0.563070 0.826409i \(-0.309620\pi\)
\(104\) 1.21387e11 8.38638e10i 0.978340 0.675914i
\(105\) 1.07048e11i 0.818537i
\(106\) −6.13109e10 + 1.83735e11i −0.444995 + 1.33355i
\(107\) 8.90449e10 8.90449e10i 0.613760 0.613760i −0.330164 0.943924i \(-0.607104\pi\)
0.943924 + 0.330164i \(0.107104\pi\)
\(108\) −4.09393e10 2.87900e11i −0.268108 1.88543i
\(109\) 1.44452e11 + 1.44452e11i 0.899247 + 0.899247i 0.995370 0.0961226i \(-0.0306441\pi\)
−0.0961226 + 0.995370i \(0.530644\pi\)
\(110\) −5.26810e10 1.05447e11i −0.311885 0.624272i
\(111\) 6.72245e10 0.378661
\(112\) −1.28806e11 + 3.73884e10i −0.690617 + 0.200464i
\(113\) 1.40215e11 0.715920 0.357960 0.933737i \(-0.383472\pi\)
0.357960 + 0.933737i \(0.383472\pi\)
\(114\) 1.65137e11 + 3.30541e11i 0.803283 + 1.60786i
\(115\) 1.13051e11 + 1.13051e11i 0.524125 + 0.524125i
\(116\) −3.81228e11 + 5.42104e10i −1.68526 + 0.239643i
\(117\) −4.15630e11 + 4.15630e11i −1.75261 + 1.75261i
\(118\) 5.64351e10 1.69124e11i 0.227090 0.680540i
\(119\) 1.77649e11i 0.682423i
\(120\) 5.57969e10 3.05206e11i 0.204698 1.11969i
\(121\) 4.54641e10i 0.159349i
\(122\) −2.04470e11 6.82300e10i −0.684938 0.228558i
\(123\) −6.25101e11 + 6.25101e11i −2.00204 + 2.00204i
\(124\) 9.40093e10 1.25178e11i 0.287973 0.383449i
\(125\) −2.47050e11 2.47050e11i −0.724068 0.724068i
\(126\) 4.78003e11 2.38809e11i 1.34089 0.669903i
\(127\) 6.12201e10 0.164427 0.0822135 0.996615i \(-0.473801\pi\)
0.0822135 + 0.996615i \(0.473801\pi\)
\(128\) −3.86728e11 + 3.94604e10i −0.994835 + 0.101509i
\(129\) 1.31986e12 3.25301
\(130\) −2.91865e11 + 1.45815e11i −0.689434 + 0.344440i
\(131\) −4.24135e11 4.24135e11i −0.960533 0.960533i 0.0387173 0.999250i \(-0.487673\pi\)
−0.999250 + 0.0387173i \(0.987673\pi\)
\(132\) 5.22842e11 6.96188e11i 1.13557 1.51206i
\(133\) −2.49760e11 + 2.49760e11i −0.520403 + 0.520403i
\(134\) −7.57993e10 2.52936e10i −0.151561 0.0505747i
\(135\) 6.43052e11i 1.23427i
\(136\) −9.25960e10 + 5.06495e11i −0.170659 + 0.933494i
\(137\) 4.97152e10i 0.0880087i −0.999031 0.0440044i \(-0.985988\pi\)
0.999031 0.0440044i \(-0.0140115\pi\)
\(138\) −3.73797e11 + 1.12019e12i −0.635770 + 1.90526i
\(139\) 2.29908e10 2.29908e10i 0.0375814 0.0375814i −0.688066 0.725648i \(-0.741540\pi\)
0.725648 + 0.688066i \(0.241540\pi\)
\(140\) 2.93638e11 4.17552e10i 0.461433 0.0656155i
\(141\) −2.76502e11 2.76502e11i −0.417825 0.417825i
\(142\) −3.82908e10 7.66433e10i −0.0556555 0.111401i
\(143\) −9.15548e11 −1.28036
\(144\) 1.48731e12 4.31719e11i 2.00174 0.581042i
\(145\) 8.51509e11 1.10323
\(146\) −1.58768e11 3.17792e11i −0.198072 0.396463i
\(147\) −4.99041e11 4.99041e11i −0.599640 0.599640i
\(148\) 2.62216e10 + 1.84400e11i 0.0303542 + 0.213462i
\(149\) 3.55846e11 3.55846e11i 0.396952 0.396952i −0.480204 0.877157i \(-0.659438\pi\)
0.877157 + 0.480204i \(0.159438\pi\)
\(150\) 2.99842e11 8.98561e11i 0.322397 0.966153i
\(151\) 9.76411e11i 1.01218i 0.862479 + 0.506092i \(0.168910\pi\)
−0.862479 + 0.506092i \(0.831090\pi\)
\(152\) −8.42276e11 + 5.81910e11i −0.842005 + 0.581723i
\(153\) 2.05129e12i 1.97799i
\(154\) 7.89494e11 + 2.63448e11i 0.734489 + 0.245093i
\(155\) −2.44787e11 + 2.44787e11i −0.219768 + 0.219768i
\(156\) −1.92697e12 1.44717e12i −1.66989 1.25410i
\(157\) 1.03183e12 + 1.03183e12i 0.863301 + 0.863301i 0.991720 0.128419i \(-0.0409903\pi\)
−0.128419 + 0.991720i \(0.540990\pi\)
\(158\) 4.06250e11 2.02961e11i 0.328231 0.163983i
\(159\) 3.16376e12 2.46899
\(160\) 8.58958e11 + 3.40049e10i 0.647608 + 0.0256378i
\(161\) −1.12887e12 −0.822434
\(162\) −1.60100e12 + 7.99856e11i −1.12735 + 0.563221i
\(163\) −9.81653e11 9.81653e11i −0.668230 0.668230i 0.289076 0.957306i \(-0.406652\pi\)
−0.957306 + 0.289076i \(0.906652\pi\)
\(164\) −1.95851e12 1.47085e12i −1.28909 0.968118i
\(165\) −1.36141e12 + 1.36141e12i −0.866617 + 0.866617i
\(166\) −2.84806e11 9.50375e10i −0.175370 0.0585195i
\(167\) 1.29195e12i 0.769669i −0.922986 0.384835i \(-0.874258\pi\)
0.922986 0.384835i \(-0.125742\pi\)
\(168\) 1.24524e12 + 1.80240e12i 0.717880 + 1.03908i
\(169\) 7.41968e11i 0.414008i
\(170\) 3.60405e11 1.08006e12i 0.194680 0.583414i
\(171\) 2.88395e12 2.88395e12i 1.50838 1.50838i
\(172\) 5.14826e11 + 3.62045e12i 0.260768 + 1.83382i
\(173\) 4.67645e11 + 4.67645e11i 0.229437 + 0.229437i 0.812457 0.583021i \(-0.198129\pi\)
−0.583021 + 0.812457i \(0.698129\pi\)
\(174\) 2.81094e12 + 5.62642e12i 1.33608 + 2.67430i
\(175\) 9.05526e11 0.417053
\(176\) 2.11362e12 + 1.16263e12i 0.943423 + 0.518944i
\(177\) −2.91216e12 −1.25997
\(178\) −5.90596e11 1.18215e12i −0.247731 0.495862i
\(179\) −2.41512e12 2.41512e12i −0.982308 0.982308i 0.0175385 0.999846i \(-0.494417\pi\)
−0.999846 + 0.0175385i \(0.994417\pi\)
\(180\) −3.39061e12 + 4.82143e11i −1.33745 + 0.190185i
\(181\) −2.56410e11 + 2.56410e11i −0.0981076 + 0.0981076i −0.754457 0.656349i \(-0.772100\pi\)
0.656349 + 0.754457i \(0.272100\pi\)
\(182\) 7.29192e11 2.18523e12i 0.270676 0.811155i
\(183\) 3.52079e12i 1.26812i
\(184\) −3.21853e12 5.88402e11i −1.12502 0.205672i
\(185\) 4.11874e11i 0.139740i
\(186\) −2.42553e12 8.09377e11i −0.798886 0.266581i
\(187\) 2.25929e12 2.25929e12i 0.722507 0.722507i
\(188\) 6.50607e11 8.66312e11i 0.202046 0.269033i
\(189\) −3.21060e12 3.21060e12i −0.968383 0.968383i
\(190\) 2.02518e12 1.01177e12i 0.593360 0.296441i
\(191\) −3.93101e12 −1.11897 −0.559487 0.828839i \(-0.689002\pi\)
−0.559487 + 0.828839i \(0.689002\pi\)
\(192\) 2.61084e12 + 5.78789e12i 0.722144 + 1.60090i
\(193\) −2.53145e11 −0.0680463 −0.0340231 0.999421i \(-0.510832\pi\)
−0.0340231 + 0.999421i \(0.510832\pi\)
\(194\) 4.40718e11 2.20181e11i 0.115147 0.0575269i
\(195\) 3.76822e12 + 3.76822e12i 0.957075 + 0.957075i
\(196\) 1.17424e12 1.56355e12i 0.289966 0.386102i
\(197\) −1.37479e12 + 1.37479e12i −0.330119 + 0.330119i −0.852632 0.522512i \(-0.824995\pi\)
0.522512 + 0.852632i \(0.324995\pi\)
\(198\) −9.11620e12 3.04200e12i −2.12890 0.710396i
\(199\) 3.74912e12i 0.851604i 0.904816 + 0.425802i \(0.140008\pi\)
−0.904816 + 0.425802i \(0.859992\pi\)
\(200\) 2.58175e12 + 4.71988e11i 0.570492 + 0.104296i
\(201\) 1.30519e12i 0.280606i
\(202\) 8.02020e11 2.40348e12i 0.167785 0.502814i
\(203\) −4.25138e12 + 4.25138e12i −0.865569 + 0.865569i
\(204\) 8.32630e12 1.18400e12i 1.65001 0.234630i
\(205\) 3.82990e12 + 3.82990e12i 0.738825 + 0.738825i
\(206\) −3.93305e12 7.87245e12i −0.738686 1.47856i
\(207\) 1.30349e13 2.38381
\(208\) 3.21801e12 5.85024e12i 0.573112 1.04190i
\(209\) 6.35276e12 1.10194
\(210\) −2.16511e12 4.33371e12i −0.365825 0.732240i
\(211\) 2.83472e11 + 2.83472e11i 0.0466613 + 0.0466613i 0.730052 0.683391i \(-0.239496\pi\)
−0.683391 + 0.730052i \(0.739496\pi\)
\(212\) 1.23405e12 + 8.67833e12i 0.197919 + 1.39184i
\(213\) −9.89530e11 + 9.89530e11i −0.154647 + 0.154647i
\(214\) 1.80388e12 5.40584e12i 0.274747 0.823356i
\(215\) 8.08661e12i 1.20048i
\(216\) −7.48031e12 1.08272e13i −1.08249 1.56683i
\(217\) 2.44433e12i 0.344850i
\(218\) 8.76959e12 + 2.92634e12i 1.20634 + 0.402544i
\(219\) −4.10297e12 + 4.10297e12i −0.550371 + 0.550371i
\(220\) −4.26544e12 3.20338e12i −0.558006 0.419067i
\(221\) −6.25343e12 6.25343e12i −0.797923 0.797923i
\(222\) 2.72149e12 1.35965e12i 0.338740 0.169233i
\(223\) −1.20742e13 −1.46617 −0.733083 0.680139i \(-0.761919\pi\)
−0.733083 + 0.680139i \(0.761919\pi\)
\(224\) −4.45835e12 + 4.11879e12i −0.528214 + 0.487984i
\(225\) −1.04560e13 −1.20882
\(226\) 5.67644e12 2.83593e12i 0.640441 0.319963i
\(227\) 9.65173e12 + 9.65173e12i 1.06283 + 1.06283i 0.997889 + 0.0649391i \(0.0206853\pi\)
0.0649391 + 0.997889i \(0.479315\pi\)
\(228\) 1.33707e13 + 1.00415e13i 1.43719 + 1.07934i
\(229\) 6.95530e11 6.95530e11i 0.0729829 0.0729829i −0.669673 0.742656i \(-0.733566\pi\)
0.742656 + 0.669673i \(0.233566\pi\)
\(230\) 6.86321e12 + 2.29020e12i 0.703112 + 0.234622i
\(231\) 1.35944e13i 1.35986i
\(232\) −1.43371e13 + 9.90518e12i −1.40048 + 0.967561i
\(233\) 1.65081e13i 1.57485i 0.616408 + 0.787427i \(0.288587\pi\)
−0.616408 + 0.787427i \(0.711413\pi\)
\(234\) −8.41989e12 + 2.52326e13i −0.784548 + 2.35112i
\(235\) −1.69409e12 + 1.69409e12i −0.154192 + 0.154192i
\(236\) −1.13592e12 7.98818e12i −0.101002 0.710284i
\(237\) −5.24503e12 5.24503e12i −0.455651 0.455651i
\(238\) 3.59304e12 + 7.19187e12i 0.304992 + 0.610476i
\(239\) −9.73064e12 −0.807147 −0.403574 0.914947i \(-0.632232\pi\)
−0.403574 + 0.914947i \(0.632232\pi\)
\(240\) −3.91409e12 1.34844e13i −0.317299 1.09312i
\(241\) 1.62613e13 1.28843 0.644217 0.764843i \(-0.277184\pi\)
0.644217 + 0.764843i \(0.277184\pi\)
\(242\) −9.19536e11 1.84056e12i −0.0712171 0.142549i
\(243\) 2.88430e12 + 2.88430e12i 0.218376 + 0.218376i
\(244\) −9.65769e12 + 1.37332e12i −0.714874 + 0.101655i
\(245\) −3.05755e12 + 3.05755e12i −0.221289 + 0.221289i
\(246\) −1.26634e13 + 3.79494e13i −0.896204 + 2.68573i
\(247\) 1.75837e13i 1.21696i
\(248\) 1.27406e12 6.96903e12i 0.0862393 0.471724i
\(249\) 4.90411e12i 0.324686i
\(250\) −1.49982e13 5.00477e12i −0.971335 0.324126i
\(251\) 8.99971e12 8.99971e12i 0.570195 0.570195i −0.361988 0.932183i \(-0.617902\pi\)
0.932183 + 0.361988i \(0.117902\pi\)
\(252\) 1.45213e13 1.93357e13i 0.900122 1.19855i
\(253\) 1.43566e13 + 1.43566e13i 0.870743 + 0.870743i
\(254\) 2.47841e12 1.23821e12i 0.147092 0.0734866i
\(255\) −1.85976e13 −1.08015
\(256\) −1.48581e13 + 9.41928e12i −0.844583 + 0.535424i
\(257\) −1.01028e13 −0.562097 −0.281049 0.959694i \(-0.590682\pi\)
−0.281049 + 0.959694i \(0.590682\pi\)
\(258\) 5.34330e13 2.66950e13i 2.91005 1.45385i
\(259\) 2.05639e12 + 2.05639e12i 0.109637 + 0.109637i
\(260\) −8.86657e12 + 1.18062e13i −0.462809 + 0.616251i
\(261\) 4.90902e13 4.90902e13i 2.50883 2.50883i
\(262\) −2.57489e13 8.59219e12i −1.28855 0.429979i
\(263\) 7.04166e12i 0.345079i 0.985003 + 0.172539i \(0.0551972\pi\)
−0.985003 + 0.172539i \(0.944803\pi\)
\(264\) 7.08581e12 3.87590e13i 0.340070 1.86016i
\(265\) 1.93839e13i 0.911146i
\(266\) −5.05968e12 + 1.51628e13i −0.232956 + 0.698118i
\(267\) −1.52625e13 + 1.52625e13i −0.688357 + 0.688357i
\(268\) −3.58021e12 + 5.09104e11i −0.158186 + 0.0224939i
\(269\) 1.91908e13 + 1.91908e13i 0.830724 + 0.830724i 0.987616 0.156892i \(-0.0501475\pi\)
−0.156892 + 0.987616i \(0.550148\pi\)
\(270\) 1.30061e13 + 2.60331e13i 0.551627 + 1.10414i
\(271\) 9.16522e12 0.380901 0.190450 0.981697i \(-0.439005\pi\)
0.190450 + 0.981697i \(0.439005\pi\)
\(272\) 6.49551e12 + 2.23776e13i 0.264536 + 0.911348i
\(273\) −3.76276e13 −1.50180
\(274\) −1.00552e12 2.01265e12i −0.0393333 0.0787301i
\(275\) −1.15162e13 1.15162e13i −0.441550 0.441550i
\(276\) 7.52370e12 + 5.29095e13i 0.282769 + 1.98854i
\(277\) 2.10664e13 2.10664e13i 0.776159 0.776159i −0.203016 0.979175i \(-0.565074\pi\)
0.979175 + 0.203016i \(0.0650744\pi\)
\(278\) 4.65751e11 1.39575e12i 0.0168232 0.0504153i
\(279\) 2.82244e13i 0.999542i
\(280\) 1.10430e13 7.62939e12i 0.383459 0.264924i
\(281\) 2.26509e13i 0.771259i −0.922654 0.385629i \(-0.873984\pi\)
0.922654 0.385629i \(-0.126016\pi\)
\(282\) −1.67862e13 5.60143e12i −0.560510 0.187037i
\(283\) −3.00585e12 + 3.00585e12i −0.0984334 + 0.0984334i −0.754609 0.656175i \(-0.772173\pi\)
0.656175 + 0.754609i \(0.272173\pi\)
\(284\) −3.10030e12 2.32835e12i −0.0995756 0.0747821i
\(285\) −2.61468e13 2.61468e13i −0.823704 0.823704i
\(286\) −3.70648e13 + 1.85174e13i −1.14538 + 0.572226i
\(287\) −3.82435e13 −1.15933
\(288\) 5.14800e13 4.75592e13i 1.53102 1.41441i
\(289\) −3.40887e12 −0.0994653
\(290\) 3.44722e13 1.72222e13i 0.986916 0.493060i
\(291\) −5.69004e12 5.69004e12i −0.159847 0.159847i
\(292\) −1.28550e13 9.65423e12i −0.354379 0.266141i
\(293\) 2.78428e13 2.78428e13i 0.753252 0.753252i −0.221832 0.975085i \(-0.571204\pi\)
0.975085 + 0.221832i \(0.0712038\pi\)
\(294\) −3.02964e13 1.01096e13i −0.804415 0.268426i
\(295\) 1.78424e13i 0.464976i
\(296\) 4.79113e12 + 6.93484e12i 0.122556 + 0.177391i
\(297\) 8.16631e13i 2.05053i
\(298\) 7.20879e12 2.16032e13i 0.177694 0.532510i
\(299\) 3.97375e13 3.97375e13i 0.961631 0.961631i
\(300\) −6.03516e12 4.24415e13i −0.143391 1.00838i
\(301\) 4.03745e13 + 4.03745e13i 0.941871 + 0.941871i
\(302\) 1.97484e13 + 3.95287e13i 0.452371 + 0.905471i
\(303\) −4.13857e13 −0.930928
\(304\) −2.23290e13 + 4.05933e13i −0.493247 + 0.896706i
\(305\) 2.15714e13 0.467981
\(306\) −4.14884e13 8.30437e13i −0.884014 1.76945i
\(307\) 4.42585e13 + 4.42585e13i 0.926265 + 0.926265i 0.997462 0.0711968i \(-0.0226818\pi\)
−0.0711968 + 0.997462i \(0.522682\pi\)
\(308\) 3.72900e13 5.30262e12i 0.766591 0.109009i
\(309\) −1.01640e14 + 1.01640e14i −2.05255 + 2.05255i
\(310\) −4.95893e12 + 1.48608e13i −0.0983782 + 0.294818i
\(311\) 2.67481e13i 0.521328i 0.965430 + 0.260664i \(0.0839414\pi\)
−0.965430 + 0.260664i \(0.916059\pi\)
\(312\) −1.07280e14 1.96127e13i −2.05433 0.375567i
\(313\) 3.29514e13i 0.619984i 0.950739 + 0.309992i \(0.100326\pi\)
−0.950739 + 0.309992i \(0.899674\pi\)
\(314\) 6.26419e13 + 2.09031e13i 1.15812 + 0.386453i
\(315\) −3.78114e13 + 3.78114e13i −0.686933 + 0.686933i
\(316\) 1.23415e13 1.64332e13i 0.220338 0.293389i
\(317\) −2.04590e13 2.04590e13i −0.358970 0.358970i 0.504463 0.863433i \(-0.331690\pi\)
−0.863433 + 0.504463i \(0.831690\pi\)
\(318\) 1.28080e14 6.39886e13i 2.20868 1.10345i
\(319\) 1.08136e14 1.83282
\(320\) 3.54615e13 1.59962e13i 0.590790 0.266497i
\(321\) −9.30837e13 −1.52439
\(322\) −4.57008e13 + 2.28320e13i −0.735726 + 0.367567i
\(323\) 4.33910e13 + 4.33910e13i 0.686730 + 0.686730i
\(324\) −4.86369e13 + 6.47622e13i −0.756778 + 1.00768i
\(325\) −3.18755e13 + 3.18755e13i −0.487640 + 0.487640i
\(326\) −5.95954e13 1.98865e13i −0.896429 0.299131i
\(327\) 1.51004e14i 2.23345i
\(328\) −1.09036e14 1.99337e13i −1.58586 0.289923i
\(329\) 1.69164e13i 0.241952i
\(330\) −2.75796e13 + 8.26501e13i −0.387938 + 1.16256i
\(331\) 4.62084e13 4.62084e13i 0.639245 0.639245i −0.311124 0.950369i \(-0.600706\pi\)
0.950369 + 0.311124i \(0.100706\pi\)
\(332\) −1.34522e13 + 1.91289e12i −0.183035 + 0.0260275i
\(333\) −2.37449e13 2.37449e13i −0.317780 0.317780i
\(334\) −2.61303e13 5.23028e13i −0.343985 0.688524i
\(335\) 7.99673e12 0.103554
\(336\) 8.68663e13 + 4.77821e13i 1.10659 + 0.608695i
\(337\) 1.26706e14 1.58793 0.793967 0.607961i \(-0.208012\pi\)
0.793967 + 0.607961i \(0.208012\pi\)
\(338\) 1.50067e13 + 3.00376e13i 0.185031 + 0.370359i
\(339\) −7.32876e13 7.32876e13i −0.889063 0.889063i
\(340\) −7.25416e12 5.10140e13i −0.0865871 0.608913i
\(341\) −3.10863e13 + 3.10863e13i −0.365106 + 0.365106i
\(342\) 5.84236e13 1.75083e14i 0.675219 2.02348i
\(343\) 9.37609e13i 1.06636i
\(344\) 9.40675e13 + 1.36156e14i 1.05285 + 1.52394i
\(345\) 1.18178e14i 1.30177i
\(346\) 2.83904e13 + 9.47363e12i 0.307789 + 0.102706i
\(347\) −5.70643e13 + 5.70643e13i −0.608909 + 0.608909i −0.942661 0.333752i \(-0.891685\pi\)
0.333752 + 0.942661i \(0.391685\pi\)
\(348\) 2.27594e14 + 1.70925e14i 2.39043 + 1.79523i
\(349\) −1.09506e14 1.09506e14i −1.13213 1.13213i −0.989822 0.142310i \(-0.954547\pi\)
−0.142310 0.989822i \(-0.545453\pi\)
\(350\) 3.66590e13 1.83147e13i 0.373084 0.186392i
\(351\) 2.26034e14 2.26456
\(352\) 1.09082e14 + 4.31838e12i 1.07589 + 0.0425928i
\(353\) −1.29109e14 −1.25371 −0.626854 0.779136i \(-0.715658\pi\)
−0.626854 + 0.779136i \(0.715658\pi\)
\(354\) −1.17895e14 + 5.88999e13i −1.12714 + 0.563115i
\(355\) 6.06270e12 + 6.06270e12i 0.0570703 + 0.0570703i
\(356\) −4.78190e13 3.59125e13i −0.443227 0.332866i
\(357\) 9.28532e13 9.28532e13i 0.847465 0.847465i
\(358\) −1.46620e14 4.89259e13i −1.31776 0.439726i
\(359\) 8.35761e13i 0.739712i 0.929089 + 0.369856i \(0.120593\pi\)
−0.929089 + 0.369856i \(0.879407\pi\)
\(360\) −1.27513e14 + 8.80958e13i −1.11145 + 0.767876i
\(361\) 5.51866e12i 0.0473744i
\(362\) −5.19439e12 + 1.55664e13i −0.0439175 + 0.131611i
\(363\) −2.37631e13 + 2.37631e13i −0.197887 + 0.197887i
\(364\) −1.46770e13 1.03214e14i −0.120387 0.846608i
\(365\) 2.51383e13 + 2.51383e13i 0.203107 + 0.203107i
\(366\) 7.12099e13 + 1.42535e14i 0.566754 + 1.13442i
\(367\) −1.22093e14 −0.957253 −0.478626 0.878019i \(-0.658865\pi\)
−0.478626 + 0.878019i \(0.658865\pi\)
\(368\) −1.42198e14 + 4.12757e13i −1.09833 + 0.318810i
\(369\) 4.41594e14 3.36030
\(370\) −8.33038e12 1.66742e13i −0.0624533 0.125007i
\(371\) 9.67789e13 + 9.67789e13i 0.714865 + 0.714865i
\(372\) −1.14564e14 + 1.62910e13i −0.833802 + 0.118566i
\(373\) −1.68544e14 + 1.68544e14i −1.20869 + 1.20869i −0.237242 + 0.971451i \(0.576244\pi\)
−0.971451 + 0.237242i \(0.923756\pi\)
\(374\) 4.57689e13 1.37159e14i 0.323428 0.969241i
\(375\) 2.58255e14i 1.79836i
\(376\) 8.81733e12 4.82303e13i 0.0605068 0.330969i
\(377\) 2.99307e14i 2.02413i
\(378\) −1.94913e14 6.50409e13i −1.29908 0.433493i
\(379\) 1.60222e14 1.60222e14i 1.05247 1.05247i 0.0539201 0.998545i \(-0.482828\pi\)
0.998545 0.0539201i \(-0.0171716\pi\)
\(380\) 6.15229e13 8.19205e13i 0.398316 0.530375i
\(381\) −3.19984e13 3.19984e13i −0.204193 0.204193i
\(382\) −1.59142e14 + 7.95067e13i −1.00100 + 0.500098i
\(383\) −1.77441e14 −1.10017 −0.550086 0.835108i \(-0.685405\pi\)
−0.550086 + 0.835108i \(0.685405\pi\)
\(384\) 2.22760e14 + 1.81509e14i 1.36149 + 1.10937i
\(385\) −8.32907e13 −0.501837
\(386\) −1.02482e13 + 5.12000e12i −0.0608723 + 0.0304116i
\(387\) −4.66200e14 4.66200e14i −2.72999 2.72999i
\(388\) 1.33886e13 1.78275e13i 0.0772966 0.102924i
\(389\) −1.26265e14 + 1.26265e14i −0.718718 + 0.718718i −0.968343 0.249624i \(-0.919693\pi\)
0.249624 + 0.968343i \(0.419693\pi\)
\(390\) 2.28766e14 + 7.63371e13i 1.28391 + 0.428431i
\(391\) 1.96119e14i 1.08530i
\(392\) 1.59138e13 8.70477e13i 0.0868362 0.474989i
\(393\) 4.43373e14i 2.38567i
\(394\) −2.78506e13 + 8.34622e13i −0.147777 + 0.442854i
\(395\) −3.21355e13 + 3.21355e13i −0.168152 + 0.168152i
\(396\) −4.30584e14 + 6.12288e13i −2.22195 + 0.315960i
\(397\) 2.09722e14 + 2.09722e14i 1.06733 + 1.06733i 0.997564 + 0.0697623i \(0.0222241\pi\)
0.0697623 + 0.997564i \(0.477776\pi\)
\(398\) 7.58279e13 + 1.51778e14i 0.380603 + 0.761820i
\(399\) 2.61089e14 1.29252
\(400\) 1.14065e14 3.31095e13i 0.556958 0.161667i
\(401\) −2.06836e14 −0.996168 −0.498084 0.867129i \(-0.665963\pi\)
−0.498084 + 0.867129i \(0.665963\pi\)
\(402\) 2.63982e13 + 5.28391e13i 0.125410 + 0.251022i
\(403\) 8.60431e13 + 8.60431e13i 0.403216 + 0.403216i
\(404\) −1.61429e13 1.13523e14i −0.0746250 0.524791i
\(405\) 1.26644e14 1.26644e14i 0.577539 0.577539i
\(406\) −8.61250e13 + 2.58098e14i −0.387468 + 1.16116i
\(407\) 5.23052e13i 0.232154i
\(408\) 3.13132e14 2.16336e14i 1.37119 0.947324i
\(409\) 3.48873e14i 1.50726i −0.657297 0.753632i \(-0.728300\pi\)
0.657297 0.753632i \(-0.271700\pi\)
\(410\) 2.32510e14 + 7.75867e13i 0.991131 + 0.330732i
\(411\) −2.59851e13 + 2.59851e13i −0.109293 + 0.109293i
\(412\) −3.18449e14 2.39158e14i −1.32162 0.992543i
\(413\) −8.90825e13 8.90825e13i −0.364810 0.364810i
\(414\) 5.27702e14 2.63638e14i 2.13249 1.06538i
\(415\) 3.00467e13 0.119821
\(416\) 1.19528e13 3.01925e14i 0.0470387 1.18819i
\(417\) −2.40336e13 −0.0933406
\(418\) 2.57183e14 1.28488e14i 0.985764 0.492485i
\(419\) −2.52229e12 2.52229e12i −0.00954155 0.00954155i 0.702320 0.711861i \(-0.252148\pi\)
−0.711861 + 0.702320i \(0.752148\pi\)
\(420\) −1.75303e14 1.31654e14i −0.654513 0.491544i
\(421\) 1.37467e14 1.37467e14i 0.506580 0.506580i −0.406895 0.913475i \(-0.633388\pi\)
0.913475 + 0.406895i \(0.133388\pi\)
\(422\) 1.72094e13 + 5.74262e12i 0.0625960 + 0.0208878i
\(423\) 1.95331e14i 0.701294i
\(424\) 2.25483e14 + 3.26371e14i 0.799100 + 1.15664i
\(425\) 1.57318e14i 0.550349i
\(426\) −2.00460e13 + 6.00736e13i −0.0692270 + 0.207458i
\(427\) −1.07701e14 + 1.07701e14i −0.367168 + 0.367168i
\(428\) −3.63082e13 2.55333e14i −0.122198 0.859342i
\(429\) 4.78538e14 + 4.78538e14i 1.59001 + 1.59001i
\(430\) −1.63556e14 3.27376e14i −0.536525 1.07392i
\(431\) −1.08957e13 −0.0352882 −0.0176441 0.999844i \(-0.505617\pi\)
−0.0176441 + 0.999844i \(0.505617\pi\)
\(432\) −5.21817e14 2.87033e14i −1.66862 0.917850i
\(433\) 9.41215e13 0.297170 0.148585 0.988900i \(-0.452528\pi\)
0.148585 + 0.988900i \(0.452528\pi\)
\(434\) −4.94378e13 9.89553e13i −0.154122 0.308493i
\(435\) −4.45066e14 4.45066e14i −1.37004 1.37004i
\(436\) 4.14212e14 5.89007e13i 1.25906 0.179038i
\(437\) −2.75728e14 + 2.75728e14i −0.827625 + 0.827625i
\(438\) −8.31186e13 + 2.49088e14i −0.246371 + 0.738321i
\(439\) 1.73610e14i 0.508182i 0.967180 + 0.254091i \(0.0817763\pi\)
−0.967180 + 0.254091i \(0.918224\pi\)
\(440\) −2.37471e14 4.34137e13i −0.686468 0.125498i
\(441\) 3.52540e14i 1.00646i
\(442\) −3.79641e14 1.26683e14i −1.07041 0.357187i
\(443\) 1.24084e14 1.24084e14i 0.345537 0.345537i −0.512907 0.858444i \(-0.671431\pi\)
0.858444 + 0.512907i \(0.171431\pi\)
\(444\) 8.26764e13 1.10087e14i 0.227392 0.302783i
\(445\) 9.35111e13 + 9.35111e13i 0.254029 + 0.254029i
\(446\) −4.88810e14 + 2.44208e14i −1.31159 + 0.655267i
\(447\) −3.71987e14 −0.985907
\(448\) −9.71856e13 + 2.56916e14i −0.254433 + 0.672609i
\(449\) 3.76031e14 0.972452 0.486226 0.873833i \(-0.338373\pi\)
0.486226 + 0.873833i \(0.338373\pi\)
\(450\) −4.23298e14 + 2.11478e14i −1.08138 + 0.540253i
\(451\) 4.86371e14 + 4.86371e14i 1.22743 + 1.22743i
\(452\) 1.72445e14 2.29618e14i 0.429921 0.572459i
\(453\) 5.10349e14 5.10349e14i 1.25698 1.25698i
\(454\) 5.85949e14 + 1.95526e14i 1.42578 + 0.475771i
\(455\) 2.30539e14i 0.554219i
\(456\) 7.44392e14 + 1.36088e14i 1.76805 + 0.323230i
\(457\) 1.37694e14i 0.323130i 0.986862 + 0.161565i \(0.0516542\pi\)
−0.986862 + 0.161565i \(0.948346\pi\)
\(458\) 1.40902e13 4.22251e13i 0.0326705 0.0979063i
\(459\) −5.57781e14 + 5.57781e14i −1.27789 + 1.27789i
\(460\) 3.24169e14 4.60966e13i 0.733842 0.104352i
\(461\) −6.11026e14 6.11026e14i −1.36680 1.36680i −0.864961 0.501839i \(-0.832657\pi\)
−0.501839 0.864961i \(-0.667343\pi\)
\(462\) −2.74954e14 5.50350e14i −0.607755 1.21649i
\(463\) −4.91890e14 −1.07442 −0.537209 0.843449i \(-0.680521\pi\)
−0.537209 + 0.843449i \(0.680521\pi\)
\(464\) −3.80080e14 + 6.90973e14i −0.820401 + 1.49146i
\(465\) 2.55890e14 0.545836
\(466\) 3.33885e14 + 6.68309e14i 0.703842 + 1.40882i
\(467\) 1.36385e14 + 1.36385e14i 0.284134 + 0.284134i 0.834755 0.550621i \(-0.185609\pi\)
−0.550621 + 0.834755i \(0.685609\pi\)
\(468\) 1.69474e14 + 1.19180e15i 0.348940 + 2.45388i
\(469\) −3.99257e13 + 3.99257e13i −0.0812461 + 0.0812461i
\(470\) −3.43191e13 + 1.02847e14i −0.0690236 + 0.206849i
\(471\) 1.07864e15i 2.14417i
\(472\) −2.07551e14 3.00416e14i −0.407797 0.590259i
\(473\) 1.02694e15i 1.99439i
\(474\) −3.18422e14 1.06255e14i −0.611254 0.203970i
\(475\) 2.21177e14 2.21177e14i 0.419686 0.419686i
\(476\) 2.90919e14 + 2.18482e14i 0.545674 + 0.409806i
\(477\) −1.11750e15 1.11750e15i −2.07202 2.07202i
\(478\) −3.93932e14 + 1.96807e14i −0.722051 + 0.360735i
\(479\) 3.59543e14 0.651487 0.325744 0.945458i \(-0.394385\pi\)
0.325744 + 0.945458i \(0.394385\pi\)
\(480\) −4.31185e14 4.66733e14i −0.772391 0.836068i
\(481\) −1.44774e14 −0.256386
\(482\) 6.58318e14 3.28894e14i 1.15260 0.575833i
\(483\) 5.90036e14 + 5.90036e14i 1.02134 + 1.02134i
\(484\) −7.44524e13 5.59143e13i −0.127418 0.0956916i
\(485\) −3.48620e13 + 3.48620e13i −0.0589893 + 0.0589893i
\(486\) 1.75103e14 + 5.84305e13i 0.292951 + 0.0977553i
\(487\) 8.67572e14i 1.43515i −0.696483 0.717573i \(-0.745253\pi\)
0.696483 0.717573i \(-0.254747\pi\)
\(488\) −3.63203e14 + 2.50929e14i −0.594074 + 0.410433i
\(489\) 1.02618e15i 1.65968i
\(490\) −6.19402e13 + 1.85621e14i −0.0990591 + 0.296858i
\(491\) −4.96939e13 + 4.96939e13i −0.0785877 + 0.0785877i −0.745308 0.666720i \(-0.767698\pi\)
0.666720 + 0.745308i \(0.267698\pi\)
\(492\) 2.54886e14 + 1.79245e15i 0.398601 + 2.80311i
\(493\) 7.38595e14 + 7.38595e14i 1.14222 + 1.14222i
\(494\) −3.55640e14 7.11853e14i −0.543891 1.08866i
\(495\) 9.61749e14 1.45456
\(496\) −8.93738e13 3.07901e14i −0.133678 0.460534i
\(497\) −6.05392e13 −0.0895523
\(498\) 9.91882e13 + 1.98536e14i 0.145110 + 0.290455i
\(499\) −2.77104e14 2.77104e14i −0.400950 0.400950i 0.477618 0.878568i \(-0.341500\pi\)
−0.878568 + 0.477618i \(0.841500\pi\)
\(500\) −7.08407e14 + 1.00735e14i −1.01379 + 0.144160i
\(501\) −6.75273e14 + 6.75273e14i −0.955811 + 0.955811i
\(502\) 1.82317e14 5.46365e14i 0.255245 0.764914i
\(503\) 5.28828e14i 0.732303i −0.930555 0.366151i \(-0.880675\pi\)
0.930555 0.366151i \(-0.119325\pi\)
\(504\) 1.96799e14 1.07648e15i 0.269560 1.47448i
\(505\) 2.53564e14i 0.343546i
\(506\) 8.71580e14 + 2.90839e14i 1.16810 + 0.389784i
\(507\) 3.87811e14 3.87811e14i 0.514134 0.514134i
\(508\) 7.52918e13 1.00254e14i 0.0987410 0.131478i
\(509\) 7.87171e14 + 7.87171e14i 1.02122 + 1.02122i 0.999770 + 0.0214544i \(0.00682967\pi\)
0.0214544 + 0.999770i \(0.493170\pi\)
\(510\) −7.52898e14 + 3.76146e14i −0.966274 + 0.482748i
\(511\) −2.51019e14 −0.318707
\(512\) −4.10999e14 + 6.81839e14i −0.516245 + 0.856441i
\(513\) −1.56839e15 −1.94899
\(514\) −4.09000e14 + 2.04335e14i −0.502836 + 0.251216i
\(515\) 6.22733e14 + 6.22733e14i 0.757464 + 0.757464i
\(516\) 1.62324e15 2.16142e15i 1.95349 2.60115i
\(517\) −2.15137e14 + 2.15137e14i −0.256164 + 0.256164i
\(518\) 1.24842e14 + 4.16586e13i 0.147077 + 0.0490785i
\(519\) 4.88857e14i 0.569851i
\(520\) −1.20164e14 + 6.57291e14i −0.138598 + 0.758122i
\(521\) 7.63542e13i 0.0871416i −0.999050 0.0435708i \(-0.986127\pi\)
0.999050 0.0435708i \(-0.0138734\pi\)
\(522\) 9.94476e14 2.98023e15i 1.12307 3.36559i
\(523\) 1.04168e15 1.04168e15i 1.16406 1.16406i 0.180486 0.983578i \(-0.442233\pi\)
0.983578 0.180486i \(-0.0577671\pi\)
\(524\) −1.21619e15 + 1.72942e14i −1.34487 + 0.191240i
\(525\) −4.73299e14 4.73299e14i −0.517916 0.517916i
\(526\) 1.42421e14 + 2.85072e14i 0.154225 + 0.308698i
\(527\) −4.24655e14 −0.455069
\(528\) −4.97062e14 1.71242e15i −0.527137 1.81603i
\(529\) −2.93430e14 −0.307963
\(530\) −3.92049e14 7.84730e14i −0.407214 0.815085i
\(531\) 1.02863e15 + 1.02863e15i 1.05740 + 1.05740i
\(532\) 1.01840e14 + 7.16179e14i 0.103611 + 0.728630i
\(533\) 1.34622e15 1.34622e15i 1.35555 1.35555i
\(534\) −3.09190e14 + 9.26574e14i −0.308140 + 0.923429i
\(535\) 5.70310e14i 0.562555i
\(536\) −1.34643e14 + 9.30220e13i −0.131455 + 0.0908195i
\(537\) 2.52467e15i 2.43975i
\(538\) 1.16506e15 + 3.88771e14i 1.11441 + 0.371870i
\(539\) −3.88287e14 + 3.88287e14i −0.367633 + 0.367633i
\(540\) 1.05307e15 + 7.90862e14i 0.986939 + 0.741199i
\(541\) −9.36152e14 9.36152e14i −0.868483 0.868483i 0.123822 0.992304i \(-0.460485\pi\)
−0.992304 + 0.123822i \(0.960485\pi\)
\(542\) 3.71042e14 1.85372e14i 0.340743 0.170234i
\(543\) 2.68040e14 0.243669
\(544\) 7.15561e14 + 7.74552e14i 0.643951 + 0.697038i
\(545\) −9.25181e14 −0.824226
\(546\) −1.52330e15 + 7.61039e14i −1.34347 + 0.671193i
\(547\) −1.07576e15 1.07576e15i −0.939260 0.939260i 0.0589980 0.998258i \(-0.481209\pi\)
−0.998258 + 0.0589980i \(0.981209\pi\)
\(548\) −8.14139e13 6.11425e13i −0.0703729 0.0528506i
\(549\) 1.24361e15 1.24361e15i 1.06423 1.06423i
\(550\) −6.99141e14 2.33297e14i −0.592338 0.197658i
\(551\) 2.07682e15i 1.74206i
\(552\) 1.37471e15 + 1.98980e15i 1.14168 + 1.65251i
\(553\) 3.20890e14i 0.263856i
\(554\) 4.26765e14 1.27892e15i 0.347445 1.04122i
\(555\) −2.15278e14 + 2.15278e14i −0.173535 + 0.173535i
\(556\) −9.37454e12 6.59253e13i −0.00748236 0.0526188i
\(557\) 1.11930e15 + 1.11930e15i 0.884589 + 0.884589i 0.993997 0.109408i \(-0.0348956\pi\)
−0.109408 + 0.993997i \(0.534896\pi\)
\(558\) 5.70853e14 + 1.14263e15i 0.446721 + 0.894162i
\(559\) −2.84246e15 −2.20257
\(560\) 2.92754e14 5.32217e14i 0.224631 0.408371i
\(561\) −2.36176e15 −1.79449
\(562\) −4.58126e14 9.16991e14i −0.344695 0.689946i
\(563\) 3.91419e14 + 3.91419e14i 0.291639 + 0.291639i 0.837728 0.546088i \(-0.183884\pi\)
−0.546088 + 0.837728i \(0.683884\pi\)
\(564\) −7.92861e14 + 1.12744e14i −0.585008 + 0.0831878i
\(565\) −4.49022e14 + 4.49022e14i −0.328096 + 0.328096i
\(566\) −6.08930e13 + 1.82483e14i −0.0440633 + 0.132048i
\(567\) 1.26460e15i 0.906249i
\(568\) −1.72604e14 3.15549e13i −0.122499 0.0223950i
\(569\) 7.99582e14i 0.562012i −0.959706 0.281006i \(-0.909332\pi\)
0.959706 0.281006i \(-0.0906680\pi\)
\(570\) −1.58735e15 5.29685e14i −1.10500 0.368728i
\(571\) −1.15369e15 + 1.15369e15i −0.795410 + 0.795410i −0.982368 0.186958i \(-0.940137\pi\)
0.186958 + 0.982368i \(0.440137\pi\)
\(572\) −1.12599e15 + 1.49931e15i −0.768878 + 1.02379i
\(573\) 2.05465e15 + 2.05465e15i 1.38959 + 1.38959i
\(574\) −1.54824e15 + 7.73496e14i −1.03710 + 0.518135i
\(575\) 9.99676e14 0.663263
\(576\) 1.12219e15 2.96658e15i 0.737468 1.94954i
\(577\) 2.33224e14 0.151812 0.0759061 0.997115i \(-0.475815\pi\)
0.0759061 + 0.997115i \(0.475815\pi\)
\(578\) −1.38003e14 + 6.89461e13i −0.0889788 + 0.0444536i
\(579\) 1.32314e14 + 1.32314e14i 0.0845030 + 0.0845030i
\(580\) 1.04723e15 1.39444e15i 0.662505 0.882155i
\(581\) −1.50016e14 + 1.50016e14i −0.0940089 + 0.0940089i
\(582\) −3.45438e14 1.15270e14i −0.214434 0.0715548i
\(583\) 2.46161e15i 1.51371i
\(584\) −7.15681e14 1.30839e14i −0.435962 0.0797014i
\(585\) 2.66201e15i 1.60639i
\(586\) 5.64043e14 1.69031e15i 0.337190 1.01049i
\(587\) −1.75624e14 + 1.75624e14i −0.104010 + 0.104010i −0.757197 0.653187i \(-0.773432\pi\)
0.653187 + 0.757197i \(0.273432\pi\)
\(588\) −1.43098e15 + 2.03485e14i −0.839573 + 0.119387i
\(589\) −5.97032e14 5.97032e14i −0.347027 0.347027i
\(590\) 3.60871e14 + 7.22324e14i 0.207810 + 0.415955i
\(591\) 1.43714e15 0.819915
\(592\) 3.34223e14 + 1.83845e14i 0.188915 + 0.103916i
\(593\) 2.53949e15 1.42215 0.711074 0.703117i \(-0.248209\pi\)
0.711074 + 0.703117i \(0.248209\pi\)
\(594\) 1.65168e15 + 3.30602e15i 0.916433 + 1.83434i
\(595\) −5.68898e14 5.68898e14i −0.312745 0.312745i
\(596\) −1.45097e14 1.02038e15i −0.0790322 0.555784i
\(597\) 1.95959e15 1.95959e15i 1.05756 1.05756i
\(598\) 8.05007e14 2.41243e15i 0.430470 1.29003i
\(599\) 1.72237e15i 0.912597i 0.889827 + 0.456298i \(0.150825\pi\)
−0.889827 + 0.456298i \(0.849175\pi\)
\(600\) −1.10273e15 1.59612e15i −0.578944 0.837982i
\(601\) 5.93900e14i 0.308961i 0.987996 + 0.154481i \(0.0493704\pi\)
−0.987996 + 0.154481i \(0.950630\pi\)
\(602\) 2.45110e15 + 8.17912e14i 1.26352 + 0.421625i
\(603\) 4.61018e14 4.61018e14i 0.235490 0.235490i
\(604\) 1.59898e15 + 1.20085e15i 0.809356 + 0.607832i
\(605\) 1.45593e14 + 1.45593e14i 0.0730275 + 0.0730275i
\(606\) −1.67545e15 + 8.37048e14i −0.832781 + 0.416055i
\(607\) −1.61954e15 −0.797727 −0.398863 0.917010i \(-0.630595\pi\)
−0.398863 + 0.917010i \(0.630595\pi\)
\(608\) −8.29373e13 + 2.09498e15i −0.0404837 + 1.02261i
\(609\) 4.44421e15 2.14981
\(610\) 8.73288e14 4.36292e14i 0.418643 0.209153i
\(611\) 5.95475e14 + 5.95475e14i 0.282903 + 0.282903i
\(612\) −3.35921e15 2.52279e15i −1.58163 1.18781i
\(613\) −1.79505e15 + 1.79505e15i −0.837613 + 0.837613i −0.988544 0.150931i \(-0.951773\pi\)
0.150931 + 0.988544i \(0.451773\pi\)
\(614\) 2.68690e15 + 8.96595e14i 1.24258 + 0.414639i
\(615\) 4.00362e15i 1.83501i
\(616\) 1.40239e15 9.68880e14i 0.637051 0.440125i
\(617\) 1.35402e14i 0.0609617i 0.999535 + 0.0304809i \(0.00970386\pi\)
−0.999535 + 0.0304809i \(0.990296\pi\)
\(618\) −2.05904e15 + 6.17048e15i −0.918814 + 2.75348i
\(619\) 1.58928e15 1.58928e15i 0.702913 0.702913i −0.262122 0.965035i \(-0.584422\pi\)
0.965035 + 0.262122i \(0.0844222\pi\)
\(620\) 9.98124e13 + 7.01918e14i 0.0437553 + 0.307703i
\(621\) −3.54442e15 3.54442e15i −1.54007 1.54007i
\(622\) 5.40995e14 + 1.08286e15i 0.232995 + 0.466365i
\(623\) −9.33756e14 −0.398611
\(624\) −4.73978e15 + 1.37581e15i −2.00559 + 0.582160i
\(625\) 1.99592e14 0.0837148
\(626\) 6.66460e14 + 1.33400e15i 0.277087 + 0.554620i
\(627\) −3.32045e15 3.32045e15i −1.36844 1.36844i
\(628\) 2.95875e15 4.20733e14i 1.20873 0.171881i
\(629\) 3.57258e14 3.57258e14i 0.144678 0.144678i
\(630\) −7.65988e14 + 2.29550e15i −0.307503 + 0.921518i
\(631\) 1.72429e14i 0.0686197i −0.999411 0.0343098i \(-0.989077\pi\)
0.999411 0.0343098i \(-0.0109233\pi\)
\(632\) 1.67258e14 9.14891e14i 0.0659846 0.360932i
\(633\) 2.96330e14i 0.115892i
\(634\) −1.24205e15 4.14461e14i −0.481557 0.160691i
\(635\) −1.96050e14 + 1.96050e14i −0.0753547 + 0.0753547i
\(636\) 3.89096e15 5.18099e15i 1.48266 1.97423i
\(637\) 1.07473e15 + 1.07473e15i 0.406007 + 0.406007i
\(638\) 4.37773e15 2.18710e15i 1.63959 0.819134i
\(639\) 6.99039e14 0.259566
\(640\) 1.11208e15 1.36482e15i 0.409399 0.502440i
\(641\) 1.45391e15 0.530664 0.265332 0.964157i \(-0.414518\pi\)
0.265332 + 0.964157i \(0.414518\pi\)
\(642\) −3.76837e15 + 1.88267e15i −1.36368 + 0.681289i
\(643\) −2.75731e15 2.75731e15i −0.989293 0.989293i 0.0106503 0.999943i \(-0.496610\pi\)
−0.999943 + 0.0106503i \(0.996610\pi\)
\(644\) −1.38835e15 + 1.84864e15i −0.493885 + 0.657629i
\(645\) −4.22670e15 + 4.22670e15i −1.49081 + 1.49081i
\(646\) 2.63424e15 + 8.79022e14i 0.921246 + 0.307412i
\(647\) 2.17754e14i 0.0755079i −0.999287 0.0377539i \(-0.987980\pi\)
0.999287 0.0377539i \(-0.0120203\pi\)
\(648\) −6.59151e14 + 3.60552e15i −0.226633 + 1.23967i
\(649\) 2.26585e15i 0.772478i
\(650\) −6.45739e14 + 1.93514e15i −0.218290 + 0.654167i
\(651\) −1.27760e15 + 1.27760e15i −0.428251 + 0.428251i
\(652\) −2.81485e15 + 4.00271e14i −0.935608 + 0.133043i
\(653\) −3.81537e15 3.81537e15i −1.25752 1.25752i −0.952274 0.305244i \(-0.901262\pi\)
−0.305244 0.952274i \(-0.598738\pi\)
\(654\) −3.05414e15 6.11321e15i −0.998187 1.99798i
\(655\) 2.71648e15 0.880399
\(656\) −4.81736e15 + 1.39833e15i −1.54824 + 0.449405i
\(657\) 2.89849e15 0.923765
\(658\) −3.42142e14 6.84836e14i −0.108135 0.216443i
\(659\) 3.81617e15 + 3.81617e15i 1.19607 + 1.19607i 0.975333 + 0.220740i \(0.0708471\pi\)
0.220740 + 0.975333i \(0.429153\pi\)
\(660\) 5.55117e14 + 3.90379e15i 0.172541 + 1.21338i
\(661\) −2.97433e14 + 2.97433e14i −0.0916813 + 0.0916813i −0.751460 0.659779i \(-0.770650\pi\)
0.659779 + 0.751460i \(0.270650\pi\)
\(662\) 9.36097e14 2.80528e15i 0.286155 0.857545i
\(663\) 6.53707e15i 1.98180i
\(664\) −5.05905e14 + 3.49519e14i −0.152105 + 0.105086i
\(665\) 1.59965e15i 0.476987i
\(666\) −1.44153e15 4.81028e14i −0.426301 0.142253i
\(667\) −4.69340e15 + 4.69340e15i −1.37656 + 1.37656i
\(668\) −2.11570e15 1.58891e15i −0.615438 0.462198i
\(669\) 6.31095e15 + 6.31095e15i 1.82075 + 1.82075i
\(670\) 3.23737e14 1.61738e14i 0.0926363 0.0462808i
\(671\) 2.73941e15 0.777470
\(672\) 4.48309e15 + 1.77479e14i 1.26196 + 0.0499592i
\(673\) 2.17839e15 0.608209 0.304105 0.952639i \(-0.401643\pi\)
0.304105 + 0.952639i \(0.401643\pi\)
\(674\) 5.12952e15 2.56269e15i 1.42052 0.709688i
\(675\) 2.84317e15 + 2.84317e15i 0.780965 + 0.780965i
\(676\) 1.21505e15 + 9.12514e14i 0.331046 + 0.248618i
\(677\) 7.96688e14 7.96688e14i 0.215303 0.215303i −0.591213 0.806516i \(-0.701351\pi\)
0.806516 + 0.591213i \(0.201351\pi\)
\(678\) −4.44923e15 1.48467e15i −1.19267 0.397985i
\(679\) 3.48115e14i 0.0925634i
\(680\) −1.32546e15 1.91851e15i −0.349597 0.506018i
\(681\) 1.00895e16i 2.63974i
\(682\) −6.29750e14 + 1.88722e15i −0.163438 + 0.489789i
\(683\) −4.41139e15 + 4.41139e15i −1.13569 + 1.13569i −0.146481 + 0.989214i \(0.546795\pi\)
−0.989214 + 0.146481i \(0.953205\pi\)
\(684\) −1.17594e15 8.26963e15i −0.300314 2.11192i
\(685\) 1.59207e14 + 1.59207e14i 0.0403332 + 0.0403332i
\(686\) −1.89636e15 3.79579e15i −0.476583 0.953935i
\(687\) −7.27078e14 −0.181267
\(688\) 6.56204e15 + 3.60955e15i 1.62294 + 0.892722i
\(689\) −6.81346e15 −1.67171
\(690\) −2.39022e15 4.78429e15i −0.581792 1.16452i
\(691\) −2.75302e15 2.75302e15i −0.664784 0.664784i 0.291720 0.956504i \(-0.405773\pi\)
−0.956504 + 0.291720i \(0.905773\pi\)
\(692\) 1.34096e15 1.90683e14i 0.321241 0.0456803i
\(693\) −4.80178e15 + 4.80178e15i −1.14122 + 1.14122i
\(694\) −1.15602e15 + 3.46433e15i −0.272575 + 0.816849i
\(695\) 1.47250e14i 0.0344461i
\(696\) 1.26709e16 + 2.31646e15i 2.94074 + 0.537618i
\(697\) 6.64408e15i 1.52987i
\(698\) −6.64801e15 2.21838e15i −1.51875 0.506794i
\(699\) 8.62844e15 8.62844e15i 1.95573 1.95573i
\(700\) 1.11367e15 1.48290e15i 0.250447 0.333481i
\(701\) −3.57573e15 3.57573e15i −0.797840 0.797840i 0.184915 0.982755i \(-0.440799\pi\)
−0.982755 + 0.184915i \(0.940799\pi\)
\(702\) 9.15068e15 4.57166e15i 2.02581 1.01209i
\(703\) 1.00455e15 0.220658
\(704\) 4.50337e15 2.03141e15i 0.981494 0.442739i
\(705\) 1.77093e15 0.382967
\(706\) −5.22682e15 + 2.61130e15i −1.12153 + 0.560314i
\(707\) −1.26598e15 1.26598e15i −0.269539 0.269539i
\(708\) −3.58153e15 + 4.76897e15i −0.756634 + 1.00749i
\(709\) 7.05716e14 7.05716e14i 0.147937 0.147937i −0.629259 0.777196i \(-0.716642\pi\)
0.777196 + 0.629259i \(0.216642\pi\)
\(710\) 3.68062e14 + 1.22819e14i 0.0765596 + 0.0255473i
\(711\) 3.70528e15i 0.764783i
\(712\) −2.66224e15 4.86703e14i −0.545264 0.0996836i
\(713\) 2.69847e15i 0.548435i
\(714\) 1.88103e15 5.63704e15i 0.379364 1.13687i
\(715\) 2.93193e15 2.93193e15i 0.586773 0.586773i
\(716\) −6.92528e15 + 9.84771e14i −1.37536 + 0.195575i
\(717\) 5.08600e15 + 5.08600e15i 1.00235 + 1.00235i
\(718\) 1.69037e15 + 3.38347e15i 0.330596 + 0.661725i
\(719\) −4.16359e13 −0.00808089 −0.00404045 0.999992i \(-0.501286\pi\)
−0.00404045 + 0.999992i \(0.501286\pi\)
\(720\) −3.38040e15 + 6.14545e15i −0.651087 + 1.18366i
\(721\) −6.21831e15 −1.18858
\(722\) 1.11618e14 + 2.23415e14i 0.0211728 + 0.0423798i
\(723\) −8.49944e15 8.49944e15i −1.60004 1.60004i
\(724\) 1.04552e14 + 7.35246e14i 0.0195330 + 0.137363i
\(725\) 3.76483e15 3.76483e15i 0.698050 0.698050i
\(726\) −4.81397e14 + 1.44264e15i −0.0885833 + 0.265465i
\(727\) 2.63729e15i 0.481635i 0.970570 + 0.240818i \(0.0774156\pi\)
−0.970570 + 0.240818i \(0.922584\pi\)
\(728\) −2.68174e15 3.88164e15i −0.486065 0.703547i
\(729\) 3.99048e15i 0.717834i
\(730\) 1.52613e15 + 5.09255e14i 0.272467 + 0.0909200i
\(731\) 7.01429e15 7.01429e15i 1.24291 1.24291i
\(732\) 5.76568e15 + 4.33007e15i 1.01400 + 0.761524i
\(733\) −4.82418e15 4.82418e15i −0.842076 0.842076i 0.147053 0.989129i \(-0.453021\pi\)
−0.989129 + 0.147053i \(0.953021\pi\)
\(734\) −4.94276e15 + 2.46939e15i −0.856331 + 0.427820i
\(735\) 3.19623e15 0.549614
\(736\) −4.92189e15 + 4.54703e15i −0.840048 + 0.776069i
\(737\) 1.01553e15 0.172037
\(738\) 1.78773e16 8.93147e15i 3.00603 1.50180i
\(739\) 4.71087e15 + 4.71087e15i 0.786243 + 0.786243i 0.980876 0.194633i \(-0.0623517\pi\)
−0.194633 + 0.980876i \(0.562352\pi\)
\(740\) −6.74489e14 5.06546e14i −0.111738 0.0839160i
\(741\) −9.19062e15 + 9.19062e15i −1.51128 + 1.51128i
\(742\) 5.87537e15 + 1.96056e15i 0.958990 + 0.320007i
\(743\) 9.62498e15i 1.55941i 0.626145 + 0.779707i \(0.284632\pi\)
−0.626145 + 0.779707i \(0.715368\pi\)
\(744\) −4.30849e15 + 2.97664e15i −0.692905 + 0.478713i
\(745\) 2.27911e15i 0.363836i
\(746\) −3.41440e15 + 1.02322e16i −0.541066 + 1.62146i
\(747\) 1.73222e15 1.73222e15i 0.272483 0.272483i
\(748\) −9.21228e14 6.47842e15i −0.143849 1.01160i
\(749\) −2.84742e15 2.84742e15i −0.441369 0.441369i
\(750\) 5.22335e15 + 1.04551e16i 0.803734 + 1.60876i
\(751\) 9.84069e15 1.50316 0.751581 0.659641i \(-0.229292\pi\)
0.751581 + 0.659641i \(0.229292\pi\)
\(752\) −6.18526e14 2.13088e15i −0.0937907 0.323117i
\(753\) −9.40792e15 −1.41619
\(754\) −6.05364e15 1.21170e16i −0.904636 1.81073i
\(755\) −3.12684e15 3.12684e15i −0.463870 0.463870i
\(756\) −9.20629e15 + 1.30913e15i −1.35586 + 0.192803i
\(757\) 7.22313e15 7.22313e15i 1.05608 1.05608i 0.0577528 0.998331i \(-0.481606\pi\)
0.998331 0.0577528i \(-0.0183935\pi\)
\(758\) 3.24581e15 9.72698e15i 0.471132 1.41188i
\(759\) 1.50078e16i 2.16266i
\(760\) 8.33789e14 4.56078e15i 0.119284 0.652476i
\(761\)