Properties

Label 16.12.e.a.13.8
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 13.8
Character \(\chi\) = 16.13
Dual form 16.12.e.a.5.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-26.9679 - 36.3419i) q^{2} +(-199.508 - 199.508i) q^{3} +(-593.467 + 1960.13i) q^{4} +(8937.54 - 8937.54i) q^{5} +(-1870.19 + 12630.8i) q^{6} -55653.3i q^{7} +(87239.3 - 31292.8i) q^{8} -97540.0i q^{9} +O(q^{10})\) \(q+(-26.9679 - 36.3419i) q^{2} +(-199.508 - 199.508i) q^{3} +(-593.467 + 1960.13i) q^{4} +(8937.54 - 8937.54i) q^{5} +(-1870.19 + 12630.8i) q^{6} -55653.3i q^{7} +(87239.3 - 31292.8i) q^{8} -97540.0i q^{9} +(-565834. - 83780.7i) q^{10} +(-146129. + 146129. i) q^{11} +(509463. - 272660. i) q^{12} +(1.33136e6 + 1.33136e6i) q^{13} +(-2.02255e6 + 1.50085e6i) q^{14} -3.56623e6 q^{15} +(-3.48990e6 - 2.32654e6i) q^{16} -2.92311e6 q^{17} +(-3.54479e6 + 2.63045e6i) q^{18} +(-1.11550e7 - 1.11550e7i) q^{19} +(1.22146e7 + 2.28229e7i) q^{20} +(-1.11033e7 + 1.11033e7i) q^{21} +(9.25139e6 + 1.36981e6i) q^{22} +2.12560e7i q^{23} +(-2.36481e7 - 1.11618e7i) q^{24} -1.10931e8i q^{25} +(1.24802e7 - 8.42879e7i) q^{26} +(-5.48023e7 + 5.48023e7i) q^{27} +(1.09088e8 + 3.30284e7i) q^{28} +(-1.31742e7 - 1.31742e7i) q^{29} +(9.61736e7 + 1.29603e8i) q^{30} +1.84262e8 q^{31} +(9.56423e6 + 1.89571e8i) q^{32} +5.83078e7 q^{33} +(7.88301e7 + 1.06231e8i) q^{34} +(-4.97404e8 - 4.97404e8i) q^{35} +(1.91191e8 + 5.78867e7i) q^{36} +(6.58484e7 - 6.58484e7i) q^{37} +(-1.04567e8 + 7.06223e8i) q^{38} -5.31233e8i q^{39} +(5.00025e8 - 1.05939e9i) q^{40} +7.48317e8i q^{41} +(7.02947e8 + 1.04082e8i) q^{42} +(-3.10180e8 + 3.10180e8i) q^{43} +(-1.99709e8 - 3.73154e8i) q^{44} +(-8.71768e8 - 8.71768e8i) q^{45} +(7.72484e8 - 5.73230e8i) q^{46} -1.85656e9 q^{47} +(2.32099e8 + 1.16043e9i) q^{48} -1.11996e9 q^{49} +(-4.03145e9 + 2.99158e9i) q^{50} +(5.83185e8 + 5.83185e8i) q^{51} +(-3.39974e9 + 1.81951e9i) q^{52} +(3.45179e9 - 3.45179e9i) q^{53} +(3.46952e9 + 5.13718e8i) q^{54} +2.61207e9i q^{55} +(-1.74155e9 - 4.85516e9i) q^{56} +4.45104e9i q^{57} +(-1.23495e8 + 8.34058e8i) q^{58} +(8.57741e8 - 8.57741e8i) q^{59} +(2.11644e9 - 6.99026e9i) q^{60} +(6.80487e9 + 6.80487e9i) q^{61} +(-4.96916e9 - 6.69644e9i) q^{62} -5.42842e9 q^{63} +(6.63146e9 - 5.45992e9i) q^{64} +2.37981e10 q^{65} +(-1.57244e9 - 2.11902e9i) q^{66} +(-5.85461e9 - 5.85461e9i) q^{67} +(1.73477e9 - 5.72967e9i) q^{68} +(4.24075e9 - 4.24075e9i) q^{69} +(-4.66267e9 + 3.14905e10i) q^{70} +1.15906e8i q^{71} +(-3.05230e9 - 8.50932e9i) q^{72} -1.23316e9i q^{73} +(-4.16885e9 - 6.17264e8i) q^{74} +(-2.21317e10 + 2.21317e10i) q^{75} +(2.84854e10 - 1.52452e10i) q^{76} +(8.13256e9 + 8.13256e9i) q^{77} +(-1.93060e10 + 1.43262e10i) q^{78} -1.66808e9 q^{79} +(-5.19847e10 + 1.03976e10i) q^{80} +4.58810e9 q^{81} +(2.71953e10 - 2.01805e10i) q^{82} +(-1.21868e10 - 1.21868e10i) q^{83} +(-1.51744e10 - 2.83533e10i) q^{84} +(-2.61254e10 + 2.61254e10i) q^{85} +(1.96374e10 + 2.90763e9i) q^{86} +5.25674e9i q^{87} +(-8.17540e9 + 1.73210e10i) q^{88} -3.35444e10i q^{89} +(-8.17197e9 + 5.51914e10i) q^{90} +(7.40944e10 - 7.40944e10i) q^{91} +(-4.16645e10 - 1.26147e10i) q^{92} +(-3.67618e10 - 3.67618e10i) q^{93} +(5.00674e10 + 6.74708e10i) q^{94} -1.99397e11 q^{95} +(3.59129e10 - 3.97292e10i) q^{96} +2.49231e10 q^{97} +(3.02030e10 + 4.07016e10i) q^{98} +(1.42534e10 + 1.42534e10i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −26.9679 36.3419i −0.595912 0.803050i
\(3\) −199.508 199.508i −0.474017 0.474017i 0.429195 0.903212i \(-0.358797\pi\)
−0.903212 + 0.429195i \(0.858797\pi\)
\(4\) −593.467 + 1960.13i −0.289779 + 0.957094i
\(5\) 8937.54 8937.54i 1.27904 1.27904i 0.337830 0.941207i \(-0.390307\pi\)
0.941207 0.337830i \(-0.109693\pi\)
\(6\) −1870.19 + 12630.8i −0.0981871 + 0.663131i
\(7\) 55653.3i 1.25156i −0.780000 0.625780i \(-0.784781\pi\)
0.780000 0.625780i \(-0.215219\pi\)
\(8\) 87239.3 31292.8i 0.941277 0.337636i
\(9\) 97540.0i 0.550616i
\(10\) −565834. 83780.7i −1.78932 0.264938i
\(11\) −146129. + 146129.i −0.273575 + 0.273575i −0.830538 0.556963i \(-0.811967\pi\)
0.556963 + 0.830538i \(0.311967\pi\)
\(12\) 509463. 272660.i 0.591039 0.316319i
\(13\) 1.33136e6 + 1.33136e6i 0.994502 + 0.994502i 0.999985 0.00548268i \(-0.00174520\pi\)
−0.00548268 + 0.999985i \(0.501745\pi\)
\(14\) −2.02255e6 + 1.50085e6i −1.00507 + 0.745819i
\(15\) −3.56623e6 −1.21257
\(16\) −3.48990e6 2.32654e6i −0.832057 0.554691i
\(17\) −2.92311e6 −0.499317 −0.249659 0.968334i \(-0.580318\pi\)
−0.249659 + 0.968334i \(0.580318\pi\)
\(18\) −3.54479e6 + 2.63045e6i −0.442172 + 0.328119i
\(19\) −1.11550e7 1.11550e7i −1.03354 1.03354i −0.999418 0.0341197i \(-0.989137\pi\)
−0.0341197 0.999418i \(-0.510863\pi\)
\(20\) 1.22146e7 + 2.28229e7i 0.853521 + 1.59480i
\(21\) −1.11033e7 + 1.11033e7i −0.593261 + 0.593261i
\(22\) 9.25139e6 + 1.36981e6i 0.382721 + 0.0566679i
\(23\) 2.12560e7i 0.688619i 0.938856 + 0.344309i \(0.111887\pi\)
−0.938856 + 0.344309i \(0.888113\pi\)
\(24\) −2.36481e7 1.11618e7i −0.606226 0.286136i
\(25\) 1.10931e8i 2.27187i
\(26\) 1.24802e7 8.42879e7i 0.206000 1.39127i
\(27\) −5.48023e7 + 5.48023e7i −0.735018 + 0.735018i
\(28\) 1.09088e8 + 3.30284e7i 1.19786 + 0.362676i
\(29\) −1.31742e7 1.31742e7i −0.119271 0.119271i 0.644952 0.764223i \(-0.276877\pi\)
−0.764223 + 0.644952i \(0.776877\pi\)
\(30\) 9.61736e7 + 1.29603e8i 0.722585 + 0.973755i
\(31\) 1.84262e8 1.15597 0.577986 0.816047i \(-0.303839\pi\)
0.577986 + 0.816047i \(0.303839\pi\)
\(32\) 9.56423e6 + 1.89571e8i 0.0503878 + 0.998730i
\(33\) 5.83078e7 0.259358
\(34\) 7.88301e7 + 1.06231e8i 0.297549 + 0.400977i
\(35\) −4.97404e8 4.97404e8i −1.60079 1.60079i
\(36\) 1.91191e8 + 5.78867e7i 0.526991 + 0.159557i
\(37\) 6.58484e7 6.58484e7i 0.156112 0.156112i −0.624729 0.780841i \(-0.714791\pi\)
0.780841 + 0.624729i \(0.214791\pi\)
\(38\) −1.04567e8 + 7.06223e8i −0.214085 + 1.44588i
\(39\) 5.31233e8i 0.942822i
\(40\) 5.00025e8 1.05939e9i 0.772078 1.63578i
\(41\) 7.48317e8i 1.00873i 0.863491 + 0.504364i \(0.168273\pi\)
−0.863491 + 0.504364i \(0.831727\pi\)
\(42\) 7.02947e8 + 1.04082e8i 0.829949 + 0.122887i
\(43\) −3.10180e8 + 3.10180e8i −0.321764 + 0.321764i −0.849443 0.527680i \(-0.823062\pi\)
0.527680 + 0.849443i \(0.323062\pi\)
\(44\) −1.99709e8 3.73154e8i −0.182561 0.341113i
\(45\) −8.71768e8 8.71768e8i −0.704258 0.704258i
\(46\) 7.72484e8 5.73230e8i 0.552995 0.410356i
\(47\) −1.85656e9 −1.18078 −0.590392 0.807117i \(-0.701027\pi\)
−0.590392 + 0.807117i \(0.701027\pi\)
\(48\) 2.32099e8 + 1.16043e9i 0.131476 + 0.657342i
\(49\) −1.11996e9 −0.566403
\(50\) −4.03145e9 + 2.99158e9i −1.82443 + 1.35384i
\(51\) 5.83185e8 + 5.83185e8i 0.236685 + 0.236685i
\(52\) −3.39974e9 + 1.81951e9i −1.24002 + 0.663646i
\(53\) 3.45179e9 3.45179e9i 1.13378 1.13378i 0.144232 0.989544i \(-0.453929\pi\)
0.989544 0.144232i \(-0.0460710\pi\)
\(54\) 3.46952e9 + 5.13718e8i 1.02826 + 0.152251i
\(55\) 2.61207e9i 0.699825i
\(56\) −1.74155e9 4.85516e9i −0.422572 1.17806i
\(57\) 4.45104e9i 0.979828i
\(58\) −1.23495e8 + 8.34058e8i −0.0247057 + 0.166856i
\(59\) 8.57741e8 8.57741e8i 0.156196 0.156196i −0.624683 0.780879i \(-0.714772\pi\)
0.780879 + 0.624683i \(0.214772\pi\)
\(60\) 2.11644e9 6.99026e9i 0.351377 1.16054i
\(61\) 6.80487e9 + 6.80487e9i 1.03159 + 1.03159i 0.999485 + 0.0321015i \(0.0102200\pi\)
0.0321015 + 0.999485i \(0.489780\pi\)
\(62\) −4.96916e9 6.69644e9i −0.688857 0.928303i
\(63\) −5.42842e9 −0.689129
\(64\) 6.63146e9 5.45992e9i 0.772003 0.635619i
\(65\) 2.37981e10 2.54401
\(66\) −1.57244e9 2.11902e9i −0.154555 0.208278i
\(67\) −5.85461e9 5.85461e9i −0.529769 0.529769i 0.390735 0.920503i \(-0.372221\pi\)
−0.920503 + 0.390735i \(0.872221\pi\)
\(68\) 1.73477e9 5.72967e9i 0.144691 0.477893i
\(69\) 4.24075e9 4.24075e9i 0.326417 0.326417i
\(70\) −4.66267e9 + 3.14905e10i −0.331586 + 2.23945i
\(71\) 1.15906e8i 0.00762402i 0.999993 + 0.00381201i \(0.00121340\pi\)
−0.999993 + 0.00381201i \(0.998787\pi\)
\(72\) −3.05230e9 8.50932e9i −0.185908 0.518282i
\(73\) 1.23316e9i 0.0696213i −0.999394 0.0348106i \(-0.988917\pi\)
0.999394 0.0348106i \(-0.0110828\pi\)
\(74\) −4.16885e9 6.17264e8i −0.218394 0.0323368i
\(75\) −2.21317e10 + 2.21317e10i −1.07691 + 1.07691i
\(76\) 2.84854e10 1.52452e10i 1.28869 0.689695i
\(77\) 8.13256e9 + 8.13256e9i 0.342396 + 0.342396i
\(78\) −1.93060e10 + 1.43262e10i −0.757133 + 0.561838i
\(79\) −1.66808e9 −0.0609914 −0.0304957 0.999535i \(-0.509709\pi\)
−0.0304957 + 0.999535i \(0.509709\pi\)
\(80\) −5.19847e10 + 1.03976e10i −1.77370 + 0.354761i
\(81\) 4.58810e9 0.146206
\(82\) 2.71953e10 2.01805e10i 0.810059 0.601113i
\(83\) −1.21868e10 1.21868e10i −0.339593 0.339593i 0.516621 0.856214i \(-0.327190\pi\)
−0.856214 + 0.516621i \(0.827190\pi\)
\(84\) −1.51744e10 2.83533e10i −0.395892 0.739720i
\(85\) −2.61254e10 + 2.61254e10i −0.638645 + 0.638645i
\(86\) 1.96374e10 + 2.90763e9i 0.450135 + 0.0666497i
\(87\) 5.25674e9i 0.113073i
\(88\) −8.17540e9 + 1.73210e10i −0.165141 + 0.349879i
\(89\) 3.35444e10i 0.636759i −0.947963 0.318379i \(-0.896861\pi\)
0.947963 0.318379i \(-0.103139\pi\)
\(90\) −8.17197e9 + 5.51914e10i −0.145879 + 0.985231i
\(91\) 7.40944e10 7.40944e10i 1.24468 1.24468i
\(92\) −4.16645e10 1.26147e10i −0.659073 0.199547i
\(93\) −3.67618e10 3.67618e10i −0.547950 0.547950i
\(94\) 5.00674e10 + 6.74708e10i 0.703643 + 0.948228i
\(95\) −1.99397e11 −2.64387
\(96\) 3.59129e10 3.97292e10i 0.449530 0.497299i
\(97\) 2.49231e10 0.294685 0.147342 0.989086i \(-0.452928\pi\)
0.147342 + 0.989086i \(0.452928\pi\)
\(98\) 3.02030e10 + 4.07016e10i 0.337526 + 0.454850i
\(99\) 1.42534e10 + 1.42534e10i 0.150635 + 0.150635i
\(100\) 2.17440e11 + 6.58340e10i 2.17440 + 0.658340i
\(101\) 7.39401e10 7.39401e10i 0.700023 0.700023i −0.264392 0.964415i \(-0.585171\pi\)
0.964415 + 0.264392i \(0.0851713\pi\)
\(102\) 5.46678e9 3.69213e10i 0.0490265 0.331113i
\(103\) 1.55937e10i 0.132539i −0.997802 0.0662694i \(-0.978890\pi\)
0.997802 0.0662694i \(-0.0211097\pi\)
\(104\) 1.57808e11 + 7.44847e10i 1.27188 + 0.600322i
\(105\) 1.98472e11i 1.51760i
\(106\) −2.18532e11 3.23571e10i −1.58611 0.234848i
\(107\) 6.52098e10 6.52098e10i 0.449471 0.449471i −0.445707 0.895179i \(-0.647048\pi\)
0.895179 + 0.445707i \(0.147048\pi\)
\(108\) −7.48962e10 1.39943e11i −0.490489 0.916474i
\(109\) −1.02657e11 1.02657e11i −0.639061 0.639061i 0.311263 0.950324i \(-0.399248\pi\)
−0.950324 + 0.311263i \(0.899248\pi\)
\(110\) 9.49275e10 7.04419e10i 0.561995 0.417034i
\(111\) −2.62746e10 −0.147999
\(112\) −1.29480e11 + 1.94224e11i −0.694229 + 1.04137i
\(113\) −2.05501e10 −0.104926 −0.0524630 0.998623i \(-0.516707\pi\)
−0.0524630 + 0.998623i \(0.516707\pi\)
\(114\) 1.61759e11 1.20035e11i 0.786851 0.583891i
\(115\) 1.89977e11 + 1.89977e11i 0.880769 + 0.880769i
\(116\) 3.36417e10 1.80047e10i 0.148716 0.0795916i
\(117\) 1.29860e11 1.29860e11i 0.547589 0.547589i
\(118\) −5.43034e10 8.04048e9i −0.218512 0.0323542i
\(119\) 1.62681e11i 0.624925i
\(120\) −3.11115e11 + 1.11597e11i −1.14136 + 0.409408i
\(121\) 2.42604e11i 0.850313i
\(122\) 6.37889e10 4.30815e11i 0.213681 1.44315i
\(123\) 1.49295e11 1.49295e11i 0.478154 0.478154i
\(124\) −1.09354e11 + 3.61178e11i −0.334976 + 1.10637i
\(125\) −5.55050e11 5.55050e11i −1.62677 1.62677i
\(126\) 1.46393e11 + 1.97279e11i 0.410660 + 0.553405i
\(127\) 6.09498e11 1.63701 0.818506 0.574498i \(-0.194803\pi\)
0.818506 + 0.574498i \(0.194803\pi\)
\(128\) −3.77260e11 9.37572e10i −0.970479 0.241185i
\(129\) 1.23767e11 0.305043
\(130\) −6.41785e11 8.64868e11i −1.51601 2.04297i
\(131\) −9.65459e10 9.65459e10i −0.218646 0.218646i 0.589282 0.807928i \(-0.299411\pi\)
−0.807928 + 0.589282i \(0.799411\pi\)
\(132\) −3.46038e10 + 1.14291e11i −0.0751565 + 0.248230i
\(133\) −6.20815e11 + 6.20815e11i −1.29353 + 1.29353i
\(134\) −5.48812e10 + 3.70654e11i −0.109735 + 0.741126i
\(135\) 9.79596e11i 1.88023i
\(136\) −2.55010e11 + 9.14723e10i −0.469995 + 0.168588i
\(137\) 4.17036e11i 0.738262i 0.929377 + 0.369131i \(0.120345\pi\)
−0.929377 + 0.369131i \(0.879655\pi\)
\(138\) −2.68481e11 3.97529e10i −0.456645 0.0676135i
\(139\) 4.11704e11 4.11704e11i 0.672982 0.672982i −0.285420 0.958403i \(-0.592133\pi\)
0.958403 + 0.285420i \(0.0921331\pi\)
\(140\) 1.27017e12 6.79783e11i 1.99598 1.06823i
\(141\) 3.70399e11 + 3.70399e11i 0.559711 + 0.559711i
\(142\) 4.21224e9 3.12573e9i 0.00612247 0.00454324i
\(143\) −3.89099e11 −0.544142
\(144\) −2.26931e11 + 3.40405e11i −0.305422 + 0.458144i
\(145\) −2.35491e11 −0.305105
\(146\) −4.48152e10 + 3.32556e10i −0.0559094 + 0.0414881i
\(147\) 2.23442e11 + 2.23442e11i 0.268484 + 0.268484i
\(148\) 8.99924e10 + 1.68150e11i 0.104176 + 0.194651i
\(149\) 5.89614e11 5.89614e11i 0.657724 0.657724i −0.297117 0.954841i \(-0.596025\pi\)
0.954841 + 0.297117i \(0.0960253\pi\)
\(150\) 1.40115e12 + 2.07463e11i 1.50655 + 0.223069i
\(151\) 1.16918e12i 1.21201i −0.795459 0.606007i \(-0.792770\pi\)
0.795459 0.606007i \(-0.207230\pi\)
\(152\) −1.32223e12 6.24086e11i −1.32180 0.623885i
\(153\) 2.85120e11i 0.274932i
\(154\) 7.62347e10 5.14870e11i 0.0709233 0.478998i
\(155\) 1.64685e12 1.64685e12i 1.47853 1.47853i
\(156\) 1.04128e12 + 3.15269e11i 0.902369 + 0.273210i
\(157\) −1.50102e12 1.50102e12i −1.25585 1.25585i −0.953057 0.302791i \(-0.902081\pi\)
−0.302791 0.953057i \(-0.597919\pi\)
\(158\) 4.49846e10 + 6.06212e10i 0.0363455 + 0.0489791i
\(159\) −1.37732e12 −1.07486
\(160\) 1.77978e12 + 1.60882e12i 1.34186 + 1.21296i
\(161\) 1.18297e12 0.861848
\(162\) −1.23731e11 1.66740e11i −0.0871258 0.117411i
\(163\) 1.05489e12 + 1.05489e12i 0.718085 + 0.718085i 0.968213 0.250128i \(-0.0804727\pi\)
−0.250128 + 0.968213i \(0.580473\pi\)
\(164\) −1.46680e12 4.44101e11i −0.965448 0.292308i
\(165\) 5.21129e11 5.21129e11i 0.331729 0.331729i
\(166\) −1.14239e11 + 7.71540e11i −0.0703427 + 0.475077i
\(167\) 2.19763e12i 1.30923i 0.755965 + 0.654613i \(0.227168\pi\)
−0.755965 + 0.654613i \(0.772832\pi\)
\(168\) −6.21190e11 + 1.31610e12i −0.358116 + 0.758729i
\(169\) 1.75286e12i 0.978070i
\(170\) 1.65400e12 + 2.44900e11i 0.893440 + 0.132288i
\(171\) −1.08806e12 + 1.08806e12i −0.569082 + 0.569082i
\(172\) −4.23911e11 7.92074e11i −0.214718 0.401198i
\(173\) −2.08631e12 2.08631e12i −1.02359 1.02359i −0.999715 0.0238746i \(-0.992400\pi\)
−0.0238746 0.999715i \(-0.507600\pi\)
\(174\) 1.91040e11 1.41763e11i 0.0908036 0.0673817i
\(175\) −6.17369e12 −2.84339
\(176\) 8.49950e11 1.70000e11i 0.379379 0.0758804i
\(177\) −3.42253e11 −0.148079
\(178\) −1.21907e12 + 9.04621e11i −0.511349 + 0.379452i
\(179\) −7.81494e11 7.81494e11i −0.317859 0.317859i 0.530086 0.847944i \(-0.322160\pi\)
−0.847944 + 0.530086i \(0.822160\pi\)
\(180\) 2.22614e12 1.19141e12i 0.878120 0.469962i
\(181\) 1.08737e12 1.08737e12i 0.416052 0.416052i −0.467789 0.883840i \(-0.654949\pi\)
0.883840 + 0.467789i \(0.154949\pi\)
\(182\) −4.69090e12 6.94562e11i −1.74126 0.257821i
\(183\) 2.71525e12i 0.977978i
\(184\) 6.65160e11 + 1.85436e12i 0.232503 + 0.648181i
\(185\) 1.17705e12i 0.399346i
\(186\) −3.44606e11 + 2.32738e12i −0.113502 + 0.766561i
\(187\) 4.27151e11 4.27151e11i 0.136601 0.136601i
\(188\) 1.10181e12 3.63909e12i 0.342166 1.13012i
\(189\) 3.04993e12 + 3.04993e12i 0.919919 + 0.919919i
\(190\) 5.37732e12 + 7.24648e12i 1.57551 + 2.12316i
\(191\) 2.35610e12 0.670672 0.335336 0.942099i \(-0.391150\pi\)
0.335336 + 0.942099i \(0.391150\pi\)
\(192\) −2.41233e12 2.33731e11i −0.667236 0.0646487i
\(193\) 5.05945e12 1.36000 0.679999 0.733213i \(-0.261980\pi\)
0.679999 + 0.733213i \(0.261980\pi\)
\(194\) −6.72124e11 9.05754e11i −0.175606 0.236647i
\(195\) −4.74792e12 4.74792e12i −1.20590 1.20590i
\(196\) 6.64661e11 2.19527e12i 0.164131 0.542101i
\(197\) −2.28419e12 + 2.28419e12i −0.548490 + 0.548490i −0.926004 0.377514i \(-0.876779\pi\)
0.377514 + 0.926004i \(0.376779\pi\)
\(198\) 1.33612e11 9.02380e11i 0.0312023 0.210732i
\(199\) 1.32865e12i 0.301799i 0.988549 + 0.150899i \(0.0482170\pi\)
−0.988549 + 0.150899i \(0.951783\pi\)
\(200\) −3.47135e12 9.67757e12i −0.767067 2.13846i
\(201\) 2.33608e12i 0.502239i
\(202\) −4.68113e12 6.93116e11i −0.979306 0.145002i
\(203\) −7.33190e11 + 7.33190e11i −0.149275 + 0.149275i
\(204\) −1.48922e12 + 7.97016e11i −0.295116 + 0.157943i
\(205\) 6.68812e12 + 6.68812e12i 1.29020 + 1.29020i
\(206\) −5.66703e11 + 4.20528e11i −0.106435 + 0.0789814i
\(207\) 2.07331e12 0.379165
\(208\) −1.54884e12 7.74375e12i −0.275841 1.37912i
\(209\) 3.26015e12 0.565500
\(210\) 7.21286e12 5.35238e12i 1.21871 0.904358i
\(211\) 7.82026e12 + 7.82026e12i 1.28726 + 1.28726i 0.936442 + 0.350823i \(0.114098\pi\)
0.350823 + 0.936442i \(0.385902\pi\)
\(212\) 4.71743e12 + 8.81447e12i 0.756585 + 1.41367i
\(213\) 2.31242e10 2.31242e10i 0.00361392 0.00361392i
\(214\) −4.12842e12 6.11278e11i −0.628793 0.0931028i
\(215\) 5.54449e12i 0.823096i
\(216\) −3.06600e12 + 6.49583e12i −0.443686 + 0.940024i
\(217\) 1.02548e13i 1.44677i
\(218\) −9.62307e11 + 6.49919e12i −0.132374 + 0.894022i
\(219\) −2.46025e11 + 2.46025e11i −0.0330017 + 0.0330017i
\(220\) −5.11999e12 1.55018e12i −0.669798 0.202794i
\(221\) −3.89170e12 3.89170e12i −0.496572 0.496572i
\(222\) 7.08570e11 + 9.54868e11i 0.0881945 + 0.118851i
\(223\) 1.45466e13 1.76638 0.883190 0.469015i \(-0.155391\pi\)
0.883190 + 0.469015i \(0.155391\pi\)
\(224\) 1.05503e13 5.32281e11i 1.24997 0.0630633i
\(225\) −1.08202e13 −1.25093
\(226\) 5.54193e11 + 7.46830e11i 0.0625266 + 0.0842608i
\(227\) −1.14517e13 1.14517e13i −1.26104 1.26104i −0.950591 0.310446i \(-0.899522\pi\)
−0.310446 0.950591i \(-0.600478\pi\)
\(228\) −8.72461e12 2.64155e12i −0.937787 0.283933i
\(229\) 8.19588e12 8.19588e12i 0.860004 0.860004i −0.131335 0.991338i \(-0.541926\pi\)
0.991338 + 0.131335i \(0.0419262\pi\)
\(230\) 1.78084e12 1.20274e13i 0.182441 1.23216i
\(231\) 3.24502e12i 0.324603i
\(232\) −1.56157e12 7.37053e11i −0.152538 0.0719970i
\(233\) 1.19894e13i 1.14378i 0.820332 + 0.571888i \(0.193789\pi\)
−0.820332 + 0.571888i \(0.806211\pi\)
\(234\) −8.22144e12 1.21731e12i −0.766056 0.113427i
\(235\) −1.65931e13 + 1.65931e13i −1.51027 + 1.51027i
\(236\) 1.17224e12 + 2.19032e12i 0.104232 + 0.194757i
\(237\) 3.32796e11 + 3.32796e11i 0.0289109 + 0.0289109i
\(238\) 5.91213e12 4.38716e12i 0.501846 0.372400i
\(239\) −1.05045e13 −0.871339 −0.435669 0.900107i \(-0.643488\pi\)
−0.435669 + 0.900107i \(0.643488\pi\)
\(240\) 1.24458e13 + 8.29697e12i 1.00893 + 0.672602i
\(241\) −4.17569e12 −0.330853 −0.165426 0.986222i \(-0.552900\pi\)
−0.165426 + 0.986222i \(0.552900\pi\)
\(242\) 8.81670e12 6.54253e12i 0.682844 0.506712i
\(243\) 8.79270e12 + 8.79270e12i 0.665714 + 0.665714i
\(244\) −1.73769e13 + 9.29995e12i −1.28626 + 0.688393i
\(245\) −1.00097e13 + 1.00097e13i −0.724450 + 0.724450i
\(246\) −9.45185e12 1.39950e12i −0.668920 0.0990441i
\(247\) 2.97027e13i 2.05571i
\(248\) 1.60749e13 5.76608e12i 1.08809 0.390298i
\(249\) 4.86271e12i 0.321945i
\(250\) −5.20305e12 + 3.51401e13i −0.336967 + 2.27579i
\(251\) 1.23422e13 1.23422e13i 0.781962 0.781962i −0.198199 0.980162i \(-0.563509\pi\)
0.980162 + 0.198199i \(0.0635093\pi\)
\(252\) 3.22159e12 1.06404e13i 0.199695 0.659561i
\(253\) −3.10612e12 3.10612e12i −0.188389 0.188389i
\(254\) −1.64369e13 2.21503e13i −0.975514 1.31460i
\(255\) 1.04245e13 0.605457
\(256\) 6.76659e12 + 1.62388e13i 0.384636 + 0.923068i
\(257\) −1.61488e13 −0.898477 −0.449238 0.893412i \(-0.648305\pi\)
−0.449238 + 0.893412i \(0.648305\pi\)
\(258\) −3.33773e12 4.49792e12i −0.181779 0.244965i
\(259\) −3.66468e12 3.66468e12i −0.195383 0.195383i
\(260\) −1.41234e13 + 4.66473e13i −0.737200 + 2.43486i
\(261\) −1.28501e12 + 1.28501e12i −0.0656728 + 0.0656728i
\(262\) −9.05023e11 + 6.11230e12i −0.0452900 + 0.305878i
\(263\) 2.33354e13i 1.14356i 0.820407 + 0.571780i \(0.193747\pi\)
−0.820407 + 0.571780i \(0.806253\pi\)
\(264\) 5.08673e12 1.82461e12i 0.244128 0.0875688i
\(265\) 6.17011e13i 2.90028i
\(266\) 3.93036e13 + 5.81953e12i 1.80960 + 0.267941i
\(267\) −6.69238e12 + 6.69238e12i −0.301834 + 0.301834i
\(268\) 1.49503e13 8.00126e12i 0.660554 0.353523i
\(269\) 2.23132e12 + 2.23132e12i 0.0965881 + 0.0965881i 0.753750 0.657162i \(-0.228243\pi\)
−0.657162 + 0.753750i \(0.728243\pi\)
\(270\) 3.56004e13 2.64176e13i 1.50992 1.12045i
\(271\) 3.01445e13 1.25279 0.626393 0.779508i \(-0.284531\pi\)
0.626393 + 0.779508i \(0.284531\pi\)
\(272\) 1.02014e13 + 6.80074e12i 0.415460 + 0.276967i
\(273\) −2.95649e13 −1.18000
\(274\) 1.51559e13 1.12466e13i 0.592861 0.439939i
\(275\) 1.62103e13 + 1.62103e13i 0.621528 + 0.621528i
\(276\) 5.79567e12 + 1.08292e13i 0.217823 + 0.407000i
\(277\) −1.38774e13 + 1.38774e13i −0.511292 + 0.511292i −0.914922 0.403630i \(-0.867748\pi\)
0.403630 + 0.914922i \(0.367748\pi\)
\(278\) −2.60649e13 3.85932e12i −0.941477 0.139401i
\(279\) 1.79729e13i 0.636497i
\(280\) −5.89583e13 2.78280e13i −2.04727 0.966302i
\(281\) 1.23343e13i 0.419981i −0.977703 0.209990i \(-0.932657\pi\)
0.977703 0.209990i \(-0.0673433\pi\)
\(282\) 3.47212e12 2.34498e13i 0.115938 0.783015i
\(283\) 5.76116e12 5.76116e12i 0.188662 0.188662i −0.606455 0.795118i \(-0.707409\pi\)
0.795118 + 0.606455i \(0.207409\pi\)
\(284\) −2.27190e11 6.87862e10i −0.00729690 0.00220928i
\(285\) 3.97814e13 + 3.97814e13i 1.25324 + 1.25324i
\(286\) 1.04932e13 + 1.41406e13i 0.324260 + 0.436973i
\(287\) 4.16463e13 1.26248
\(288\) 1.84908e13 9.32895e11i 0.549917 0.0277443i
\(289\) −2.57273e13 −0.750683
\(290\) 6.35068e12 + 8.55818e12i 0.181816 + 0.245015i
\(291\) −4.97237e12 4.97237e12i −0.139686 0.139686i
\(292\) 2.41714e12 + 7.31837e11i 0.0666341 + 0.0201748i
\(293\) −3.65192e13 + 3.65192e13i −0.987982 + 0.987982i −0.999929 0.0119465i \(-0.996197\pi\)
0.0119465 + 0.999929i \(0.496197\pi\)
\(294\) 2.09455e12 1.41461e13i 0.0556135 0.375600i
\(295\) 1.53322e13i 0.399561i
\(296\) 3.68399e12 7.80515e12i 0.0942354 0.199653i
\(297\) 1.60164e13i 0.402165i
\(298\) −3.73283e13 5.52705e12i −0.920130 0.136240i
\(299\) −2.82993e13 + 2.82993e13i −0.684833 + 0.684833i
\(300\) −3.02465e13 5.65154e13i −0.718635 1.34276i
\(301\) 1.72625e13 + 1.72625e13i 0.402707 + 0.402707i
\(302\) −4.24902e13 + 3.15303e13i −0.973308 + 0.722253i
\(303\) −2.95033e13 −0.663646
\(304\) 1.29773e13 + 6.48826e13i 0.286668 + 1.43326i
\(305\) 1.21638e14 2.63887
\(306\) 1.03618e13 7.68909e12i 0.220784 0.163835i
\(307\) −3.86138e13 3.86138e13i −0.808131 0.808131i 0.176220 0.984351i \(-0.443613\pi\)
−0.984351 + 0.176220i \(0.943613\pi\)
\(308\) −2.07673e13 + 1.11144e13i −0.426924 + 0.228486i
\(309\) −3.11106e12 + 3.11106e12i −0.0628256 + 0.0628256i
\(310\) −1.04262e14 1.54376e13i −2.06841 0.306261i
\(311\) 2.21250e13i 0.431221i 0.976479 + 0.215611i \(0.0691742\pi\)
−0.976479 + 0.215611i \(0.930826\pi\)
\(312\) −1.66238e13 4.63444e13i −0.318331 0.887456i
\(313\) 4.91648e13i 0.925039i 0.886609 + 0.462520i \(0.153055\pi\)
−0.886609 + 0.462520i \(0.846945\pi\)
\(314\) −1.40705e13 + 9.50290e13i −0.260134 + 1.75688i
\(315\) −4.85168e13 + 4.85168e13i −0.881422 + 0.881422i
\(316\) 9.89951e11 3.26965e12i 0.0176740 0.0583744i
\(317\) −2.50121e13 2.50121e13i −0.438858 0.438858i 0.452770 0.891627i \(-0.350436\pi\)
−0.891627 + 0.452770i \(0.850436\pi\)
\(318\) 3.71434e13 + 5.00544e13i 0.640520 + 0.863164i
\(319\) 3.85027e12 0.0652594
\(320\) 1.04707e13 1.08067e14i 0.174441 1.80040i
\(321\) −2.60198e13 −0.426114
\(322\) −3.19021e13 4.29913e13i −0.513585 0.692107i
\(323\) 3.26074e13 + 3.26074e13i 0.516063 + 0.516063i
\(324\) −2.72288e12 + 8.99325e12i −0.0423674 + 0.139933i
\(325\) 1.47689e14 1.47689e14i 2.25938 2.25938i
\(326\) 9.88856e12 6.67849e13i 0.148743 1.00457i
\(327\) 4.09618e13i 0.605852i
\(328\) 2.34169e13 + 6.52826e13i 0.340583 + 0.949493i
\(329\) 1.03324e14i 1.47782i
\(330\) −3.29925e13 4.88507e12i −0.464076 0.0687138i
\(331\) 6.15855e13 6.15855e13i 0.851970 0.851970i −0.138405 0.990376i \(-0.544198\pi\)
0.990376 + 0.138405i \(0.0441977\pi\)
\(332\) 3.11200e13 1.66552e13i 0.423429 0.226615i
\(333\) −6.42285e12 6.42285e12i −0.0859577 0.0859577i
\(334\) 7.98661e13 5.92655e13i 1.05137 0.780182i
\(335\) −1.04652e14 −1.35519
\(336\) 6.45816e13 1.29171e13i 0.822703 0.164550i
\(337\) −1.50805e11 −0.00188996 −0.000944980 1.00000i \(-0.500301\pi\)
−0.000944980 1.00000i \(0.500301\pi\)
\(338\) 6.37022e13 4.72709e13i 0.785439 0.582843i
\(339\) 4.09992e12 + 4.09992e12i 0.0497367 + 0.0497367i
\(340\) −3.57046e13 6.67138e13i −0.426177 0.796309i
\(341\) −2.69261e13 + 2.69261e13i −0.316245 + 0.316245i
\(342\) 6.88850e13 + 1.01995e13i 0.796124 + 0.117879i
\(343\) 4.77151e13i 0.542673i
\(344\) −1.73535e13 + 3.67663e13i −0.194230 + 0.411508i
\(345\) 7.58038e13i 0.834999i
\(346\) −1.95571e13 + 1.32084e14i −0.212025 + 1.43196i
\(347\) 1.74401e13 1.74401e13i 0.186096 0.186096i −0.607910 0.794006i \(-0.707992\pi\)
0.794006 + 0.607910i \(0.207992\pi\)
\(348\) −1.03039e13 3.11970e12i −0.108222 0.0327662i
\(349\) −3.25744e13 3.25744e13i −0.336773 0.336773i 0.518378 0.855151i \(-0.326536\pi\)
−0.855151 + 0.518378i \(0.826536\pi\)
\(350\) 1.66491e14 + 2.24364e14i 1.69441 + 2.28338i
\(351\) −1.45923e14 −1.46195
\(352\) −2.90995e13 2.63043e13i −0.287012 0.259443i
\(353\) −1.61148e12 −0.0156481 −0.00782407 0.999969i \(-0.502491\pi\)
−0.00782407 + 0.999969i \(0.502491\pi\)
\(354\) 9.22983e12 + 1.24381e13i 0.0882421 + 0.118915i
\(355\) 1.03591e12 + 1.03591e12i 0.00975141 + 0.00975141i
\(356\) 6.57513e13 + 1.99075e13i 0.609438 + 0.184519i
\(357\) 3.24562e13 3.24562e13i 0.296225 0.296225i
\(358\) −7.32574e12 + 4.94762e13i −0.0658407 + 0.444672i
\(359\) 5.33566e13i 0.472246i −0.971723 0.236123i \(-0.924123\pi\)
0.971723 0.236123i \(-0.0758769\pi\)
\(360\) −1.03332e14 4.87724e13i −0.900685 0.425119i
\(361\) 1.32379e14i 1.13640i
\(362\) −6.88415e13 1.01931e13i −0.582040 0.0861803i
\(363\) 4.84015e13 4.84015e13i 0.403063 0.403063i
\(364\) 1.01262e14 + 1.89207e14i 0.830593 + 1.55196i
\(365\) −1.10214e13 1.10214e13i −0.0890482 0.0890482i
\(366\) −9.86774e13 + 7.32246e13i −0.785366 + 0.582789i
\(367\) 9.63988e13 0.755802 0.377901 0.925846i \(-0.376646\pi\)
0.377901 + 0.925846i \(0.376646\pi\)
\(368\) 4.94530e13 7.41814e13i 0.381971 0.572970i
\(369\) 7.29908e13 0.555422
\(370\) −4.27761e13 + 3.17424e13i −0.320695 + 0.237975i
\(371\) −1.92104e14 1.92104e14i −1.41899 1.41899i
\(372\) 9.38748e13 5.02410e13i 0.683224 0.365655i
\(373\) −6.67716e13 + 6.67716e13i −0.478843 + 0.478843i −0.904761 0.425919i \(-0.859951\pi\)
0.425919 + 0.904761i \(0.359951\pi\)
\(374\) −2.70428e13 4.00412e12i −0.191099 0.0282952i
\(375\) 2.21474e14i 1.54224i
\(376\) −1.61965e14 + 5.80969e13i −1.11144 + 0.398676i
\(377\) 3.50792e13i 0.237231i
\(378\) 2.85901e13 1.93090e14i 0.190551 1.28693i
\(379\) 3.97407e13 3.97407e13i 0.261048 0.261048i −0.564432 0.825480i \(-0.690905\pi\)
0.825480 + 0.564432i \(0.190905\pi\)
\(380\) 1.18336e14 3.90844e14i 0.766136 2.53043i
\(381\) −1.21600e14 1.21600e14i −0.775971 0.775971i
\(382\) −6.35391e13 8.56252e13i −0.399662 0.538584i
\(383\) −1.57401e14 −0.975918 −0.487959 0.872866i \(-0.662259\pi\)
−0.487959 + 0.872866i \(0.662259\pi\)
\(384\) 5.65612e13 + 9.39718e13i 0.345698 + 0.574349i
\(385\) 1.45370e14 0.875873
\(386\) −1.36443e14 1.83870e14i −0.810438 1.09215i
\(387\) 3.02549e13 + 3.02549e13i 0.177168 + 0.177168i
\(388\) −1.47910e13 + 4.88525e13i −0.0853934 + 0.282041i
\(389\) −1.16568e14 + 1.16568e14i −0.663525 + 0.663525i −0.956209 0.292684i \(-0.905452\pi\)
0.292684 + 0.956209i \(0.405452\pi\)
\(390\) −4.45070e13 + 3.00590e14i −0.249789 + 1.68701i
\(391\) 6.21337e13i 0.343839i
\(392\) −9.77048e13 + 3.50468e13i −0.533142 + 0.191238i
\(393\) 3.85234e13i 0.207284i
\(394\) 1.44612e14 + 2.14121e13i 0.767317 + 0.113613i
\(395\) −1.49086e13 + 1.49086e13i −0.0780102 + 0.0780102i
\(396\) −3.63974e13 + 1.94796e13i −0.187822 + 0.100521i
\(397\) −6.93873e13 6.93873e13i −0.353128 0.353128i 0.508144 0.861272i \(-0.330332\pi\)
−0.861272 + 0.508144i \(0.830332\pi\)
\(398\) 4.82855e13 3.58308e13i 0.242360 0.179845i
\(399\) 2.47715e14 1.22631
\(400\) −2.58086e14 + 3.87139e14i −1.26019 + 1.89033i
\(401\) −1.22810e14 −0.591482 −0.295741 0.955268i \(-0.595566\pi\)
−0.295741 + 0.955268i \(0.595566\pi\)
\(402\) 8.48977e13 6.29992e13i 0.403323 0.299290i
\(403\) 2.45319e14 + 2.45319e14i 1.14962 + 1.14962i
\(404\) 1.01051e14 + 1.88813e14i 0.467136 + 0.872840i
\(405\) 4.10063e13 4.10063e13i 0.187003 0.187003i
\(406\) 4.64181e13 + 6.87293e12i 0.208831 + 0.0309207i
\(407\) 1.92447e13i 0.0854166i
\(408\) 6.91261e13 + 3.26272e13i 0.302699 + 0.142872i
\(409\) 7.71261e13i 0.333214i −0.986023 0.166607i \(-0.946719\pi\)
0.986023 0.166607i \(-0.0532811\pi\)
\(410\) 6.26945e13 4.23423e14i 0.267250 1.80494i
\(411\) 8.32021e13 8.32021e13i 0.349948 0.349948i
\(412\) 3.05656e13 + 9.25431e12i 0.126852 + 0.0384069i
\(413\) −4.77361e13 4.77361e13i −0.195489 0.195489i
\(414\) −5.59128e13 7.53481e13i −0.225949 0.304488i
\(415\) −2.17839e14 −0.868704
\(416\) −2.39654e14 + 2.65120e14i −0.943128 + 1.04335i
\(417\) −1.64277e14 −0.638010
\(418\) −8.79193e13 1.18480e14i −0.336988 0.454125i
\(419\) 3.70961e14 + 3.70961e14i 1.40330 + 1.40330i 0.789314 + 0.613989i \(0.210436\pi\)
0.613989 + 0.789314i \(0.289564\pi\)
\(420\) −3.89031e14 1.17787e14i −1.45249 0.439770i
\(421\) 1.97013e13 1.97013e13i 0.0726011 0.0726011i −0.669874 0.742475i \(-0.733652\pi\)
0.742475 + 0.669874i \(0.233652\pi\)
\(422\) 7.33073e13 4.95099e14i 0.266642 1.80083i
\(423\) 1.81089e14i 0.650159i
\(424\) 1.93116e14 4.09148e14i 0.684392 1.45000i
\(425\) 3.24265e14i 1.13438i
\(426\) −1.46398e12 2.16766e11i −0.00505573 0.000748581i
\(427\) 3.78713e14 3.78713e14i 1.29109 1.29109i
\(428\) 8.91197e13 + 1.66519e14i 0.299939 + 0.560433i
\(429\) 7.76285e13 + 7.76285e13i 0.257932 + 0.257932i
\(430\) 2.01497e14 1.49523e14i 0.660987 0.490492i
\(431\) 8.37088e13 0.271110 0.135555 0.990770i \(-0.456718\pi\)
0.135555 + 0.990770i \(0.456718\pi\)
\(432\) 3.18754e14 6.37546e13i 1.01928 0.203869i
\(433\) 3.95547e14 1.24886 0.624431 0.781080i \(-0.285331\pi\)
0.624431 + 0.781080i \(0.285331\pi\)
\(434\) −3.72679e14 + 2.76550e14i −1.16183 + 0.862146i
\(435\) 4.69823e13 + 4.69823e13i 0.144625 + 0.144625i
\(436\) 2.62144e14 1.40297e14i 0.796828 0.426455i
\(437\) 2.37112e14 2.37112e14i 0.711713 0.711713i
\(438\) 1.55758e13 + 2.30624e12i 0.0461681 + 0.00683591i
\(439\) 4.95762e14i 1.45117i 0.688132 + 0.725586i \(0.258431\pi\)
−0.688132 + 0.725586i \(0.741569\pi\)
\(440\) 8.17389e13 + 2.27875e14i 0.236286 + 0.658729i
\(441\) 1.09241e14i 0.311871i
\(442\) −3.64809e13 + 2.46383e14i −0.102859 + 0.694685i
\(443\) 9.47829e13 9.47829e13i 0.263943 0.263943i −0.562711 0.826654i \(-0.690242\pi\)
0.826654 + 0.562711i \(0.190242\pi\)
\(444\) 1.55931e13 5.15015e13i 0.0428870 0.141649i
\(445\) −2.99805e14 2.99805e14i −0.814438 0.814438i
\(446\) −3.92290e14 5.28650e14i −1.05261 1.41849i
\(447\) −2.35266e14 −0.623544
\(448\) −3.03863e14 3.69063e14i −0.795515 0.966209i
\(449\) −3.01226e14 −0.779001 −0.389500 0.921026i \(-0.627352\pi\)
−0.389500 + 0.921026i \(0.627352\pi\)
\(450\) 2.91799e14 + 3.93228e14i 0.745444 + 1.00456i
\(451\) −1.09351e14 1.09351e14i −0.275963 0.275963i
\(452\) 1.21958e13 4.02808e13i 0.0304053 0.100424i
\(453\) −2.33261e14 + 2.33261e14i −0.574515 + 0.574515i
\(454\) −1.07348e14 + 7.25005e14i −0.261209 + 1.76414i
\(455\) 1.32444e15i 3.18398i
\(456\) 1.39286e14 + 3.88306e14i 0.330826 + 0.922289i
\(457\) 1.00211e14i 0.235166i −0.993063 0.117583i \(-0.962485\pi\)
0.993063 0.117583i \(-0.0375146\pi\)
\(458\) −5.18879e14 7.68283e13i −1.20311 0.178140i
\(459\) 1.60193e14 1.60193e14i 0.367007 0.367007i
\(460\) −4.85123e14 + 2.59634e14i −1.09821 + 0.587751i
\(461\) 3.90890e14 + 3.90890e14i 0.874377 + 0.874377i 0.992946 0.118568i \(-0.0378305\pi\)
−0.118568 + 0.992946i \(0.537831\pi\)
\(462\) −1.17930e14 + 8.75114e13i −0.260672 + 0.193434i
\(463\) −7.10495e13 −0.155191 −0.0775953 0.996985i \(-0.524724\pi\)
−0.0775953 + 0.996985i \(0.524724\pi\)
\(464\) 1.53263e13 + 7.66272e13i 0.0330818 + 0.165399i
\(465\) −6.57121e14 −1.40170
\(466\) 4.35718e14 3.23329e14i 0.918509 0.681589i
\(467\) −4.92262e14 4.92262e14i −1.02554 1.02554i −0.999665 0.0258775i \(-0.991762\pi\)
−0.0258775 0.999665i \(-0.508238\pi\)
\(468\) 1.77475e14 + 3.31611e14i 0.365414 + 0.682774i
\(469\) −3.25828e14 + 3.25828e14i −0.663037 + 0.663037i
\(470\) 1.05050e15 + 1.55544e14i 2.11280 + 0.312834i
\(471\) 5.98930e14i 1.19059i
\(472\) 4.79876e13 1.01670e14i 0.0942863 0.199761i
\(473\) 9.06525e13i 0.176053i
\(474\) 3.11963e12 2.10692e13i 0.00598856 0.0404453i
\(475\) −1.23744e15 + 1.23744e15i −2.34807 + 2.34807i
\(476\) −3.18875e14 9.65457e13i −0.598112 0.181090i
\(477\) −3.36688e14 3.36688e14i −0.624275 0.624275i
\(478\) 2.83284e14 + 3.81753e14i 0.519241 + 0.699728i
\(479\) 1.05196e15 1.90614 0.953069 0.302752i \(-0.0979053\pi\)
0.953069 + 0.302752i \(0.0979053\pi\)
\(480\) −3.41082e13 6.76055e14i −0.0610987 1.21103i
\(481\) 1.75335e14 0.310507
\(482\) 1.12610e14 + 1.51752e14i 0.197159 + 0.265691i
\(483\) −2.36012e14 2.36012e14i −0.408530 0.408530i
\(484\) −4.75536e14 1.43978e14i −0.813830 0.246403i
\(485\) 2.22752e14 2.22752e14i 0.376913 0.376913i
\(486\) 8.24229e13 5.56664e14i 0.137895 0.931308i
\(487\) 1.75551e14i 0.290398i 0.989403 + 0.145199i \(0.0463822\pi\)
−0.989403 + 0.145199i \(0.953618\pi\)
\(488\) 8.06595e14 + 3.80709e14i 1.31931 + 0.622707i
\(489\) 4.20919e14i 0.680769i
\(490\) 6.33713e14 + 9.38313e13i 1.01348 + 0.150062i
\(491\) −3.90969e14 + 3.90969e14i −0.618293 + 0.618293i −0.945093 0.326800i \(-0.894030\pi\)
0.326800 + 0.945093i \(0.394030\pi\)
\(492\) 2.04036e14 + 3.81240e14i 0.319080 + 0.596197i
\(493\) 3.85098e13 + 3.85098e13i 0.0595543 + 0.0595543i
\(494\) −1.07945e15 + 8.01018e14i −1.65084 + 1.22502i
\(495\) 2.54781e14 0.385335
\(496\) −6.43057e14 4.28694e14i −0.961834 0.641207i
\(497\) 6.45054e12 0.00954192
\(498\) 1.76720e14 1.31137e14i 0.258538 0.191851i
\(499\) −4.65711e14 4.65711e14i −0.673851 0.673851i 0.284751 0.958602i \(-0.408089\pi\)
−0.958602 + 0.284751i \(0.908089\pi\)
\(500\) 1.41737e15 7.58565e14i 2.02838 1.08557i
\(501\) 4.38445e14 4.38445e14i 0.620595 0.620595i
\(502\) −7.81380e14 1.15696e14i −1.09394 0.161974i
\(503\) 1.00596e15i 1.39302i −0.717546 0.696511i \(-0.754735\pi\)
0.717546 0.696511i \(-0.245265\pi\)
\(504\) −4.73572e14 + 1.69870e14i −0.648661 + 0.232675i
\(505\) 1.32169e15i 1.79071i
\(506\) −2.91168e13 + 1.96648e14i −0.0390226 + 0.263549i
\(507\) 3.49709e14 3.49709e14i 0.463621 0.463621i
\(508\) −3.61717e14 + 1.19469e15i −0.474371 + 1.56677i
\(509\) 9.28220e14 + 9.28220e14i 1.20421 + 1.20421i 0.972873 + 0.231339i \(0.0743105\pi\)
0.231339 + 0.972873i \(0.425690\pi\)
\(510\) −2.81126e14 3.78845e14i −0.360799 0.486212i
\(511\) −6.86292e13 −0.0871352
\(512\) 4.07668e14 6.83837e14i 0.512061 0.858949i
\(513\) 1.22264e15 1.51934
\(514\) 4.35498e14 + 5.86876e14i 0.535413 + 0.721522i
\(515\) −1.39369e14 1.39369e14i −0.169522 0.169522i
\(516\) −7.34515e13 + 2.42599e14i −0.0883950 + 0.291955i
\(517\) 2.71297e14 2.71297e14i 0.323033 0.323033i
\(518\) −3.43528e13 + 2.32010e14i −0.0404714 + 0.273334i
\(519\) 8.32473e14i 0.970397i
\(520\) 2.07613e15 7.44709e14i 2.39462 0.858951i
\(521\) 3.89954e14i 0.445047i 0.974927 + 0.222523i \(0.0714294\pi\)
−0.974927 + 0.222523i \(0.928571\pi\)
\(522\) 8.13540e13 + 1.20457e13i 0.0918737 + 0.0136034i
\(523\) −8.43298e14 + 8.43298e14i −0.942370 + 0.942370i −0.998428 0.0560573i \(-0.982147\pi\)
0.0560573 + 0.998428i \(0.482147\pi\)
\(524\) 2.46539e14 1.31946e14i 0.272624 0.145906i
\(525\) 1.23170e15 + 1.23170e15i 1.34781 + 1.34781i
\(526\) 8.48053e14 6.29307e14i 0.918336 0.681461i
\(527\) −5.38619e14 −0.577196
\(528\) −2.03488e14 1.35656e14i −0.215801 0.143864i
\(529\) 5.00991e14 0.525804
\(530\) −2.24233e15 + 1.66395e15i −2.32907 + 1.72831i
\(531\) −8.36641e13 8.36641e13i −0.0860041 0.0860041i
\(532\) −8.48443e14 1.58531e15i −0.863195 1.61287i
\(533\) −9.96276e14 + 9.96276e14i −1.00318 + 1.00318i
\(534\) 4.23693e14 + 6.27345e13i 0.422255 + 0.0625215i
\(535\) 1.16563e15i 1.14978i
\(536\) −6.93959e14 3.27545e14i −0.677528 0.319790i
\(537\) 3.11829e14i 0.301341i
\(538\) 2.09164e13 1.41264e14i 0.0200071 0.135123i
\(539\) 1.63659e14 1.63659e14i 0.154954 0.154954i
\(540\) −1.92013e15 5.81358e14i −1.79956 0.544851i
\(541\) 7.75321e14 + 7.75321e14i 0.719277 + 0.719277i 0.968457 0.249180i \(-0.0801610\pi\)
−0.249180 + 0.968457i \(0.580161\pi\)
\(542\) −8.12933e14 1.09551e15i −0.746549 1.00605i
\(543\) −4.33880e14 −0.394431
\(544\) −2.79573e13 5.54138e14i −0.0251595 0.498683i
\(545\) −1.83500e15 −1.63477
\(546\) 7.97302e14 + 1.07444e15i 0.703175 + 0.947597i
\(547\) 1.27728e15 + 1.27728e15i 1.11521 + 1.11521i 0.992435 + 0.122774i \(0.0391790\pi\)
0.122774 + 0.992435i \(0.460821\pi\)
\(548\) −8.17444e14 2.47497e14i −0.706585 0.213932i
\(549\) 6.63747e14 6.63747e14i 0.568008 0.568008i
\(550\) 1.51955e14 1.02627e15i 0.128742 0.869493i
\(551\) 2.93918e14i 0.246543i
\(552\) 2.37255e14 5.02665e14i 0.197038 0.417459i
\(553\) 9.28343e13i 0.0763344i
\(554\) 8.78574e14 + 1.30087e14i 0.715278 + 0.105908i
\(555\) −2.34830e14 + 2.34830e14i −0.189297 + 0.189297i
\(556\) 5.62660e14 + 1.05133e15i 0.449091 + 0.839123i
\(557\) −6.89209e14 6.89209e14i −0.544687 0.544687i 0.380212 0.924899i \(-0.375851\pi\)
−0.924899 + 0.380212i \(0.875851\pi\)
\(558\) −6.53171e14 + 4.84692e14i −0.511139 + 0.379296i
\(559\) −8.25920e14 −0.639990
\(560\) 5.78658e14 + 2.89312e15i 0.444005 + 2.21989i
\(561\) −1.70440e14 −0.129502
\(562\) −4.48251e14 + 3.32630e14i −0.337266 + 0.250271i
\(563\) 7.63745e14 + 7.63745e14i 0.569052 + 0.569052i 0.931863 0.362811i \(-0.118183\pi\)
−0.362811 + 0.931863i \(0.618183\pi\)
\(564\) −9.45848e14 + 5.06209e14i −0.697889 + 0.373504i
\(565\) −1.83668e14 + 1.83668e14i −0.134204 + 0.134204i
\(566\) −3.64738e14 5.40052e13i −0.263931 0.0390792i
\(567\) 2.55343e14i 0.182985i
\(568\) 3.62701e12 + 1.01115e13i 0.00257415 + 0.00717631i
\(569\) 1.49261e14i 0.104913i −0.998623 0.0524563i \(-0.983295\pi\)
0.998623 0.0524563i \(-0.0167050\pi\)
\(570\) 3.72911e14 2.51855e15i 0.259594 1.75323i
\(571\) 1.12561e15 1.12561e15i 0.776052 0.776052i −0.203105 0.979157i \(-0.565103\pi\)
0.979157 + 0.203105i \(0.0651032\pi\)
\(572\) 2.30917e14 7.62684e14i 0.157681 0.520795i
\(573\) −4.70061e14 4.70061e14i −0.317910 0.317910i
\(574\) −1.12311e15 1.51351e15i −0.752329 1.01384i
\(575\) 2.35796e15 1.56445
\(576\) −5.32561e14 6.46832e14i −0.349982 0.425077i
\(577\) −1.10552e15 −0.719615 −0.359807 0.933027i \(-0.617158\pi\)
−0.359807 + 0.933027i \(0.617158\pi\)
\(578\) 6.93811e14 + 9.34979e14i 0.447340 + 0.602836i
\(579\) −1.00940e15 1.00940e15i −0.644662 0.644662i
\(580\) 1.39756e14 4.61592e14i 0.0884130 0.292014i
\(581\) −6.78233e14 + 6.78233e14i −0.425021 + 0.425021i
\(582\) −4.66110e13 + 3.14799e14i −0.0289343 + 0.195415i
\(583\) 1.00881e15i 0.620345i
\(584\) −3.85889e13 1.07580e14i −0.0235067 0.0655329i
\(585\) 2.32127e15i 1.40077i
\(586\) 2.31202e15 + 3.42331e14i 1.38215 + 0.204649i
\(587\) −5.74857e14 + 5.74857e14i −0.340448 + 0.340448i −0.856536 0.516088i \(-0.827388\pi\)
0.516088 + 0.856536i \(0.327388\pi\)
\(588\) −5.70580e14 + 3.05369e14i −0.334766 + 0.179164i
\(589\) −2.05545e15 2.05545e15i −1.19474 1.19474i
\(590\) −5.57201e14 + 4.13477e14i −0.320868 + 0.238103i
\(591\) 9.11431e14 0.519987
\(592\) −3.83003e14 + 7.66052e13i −0.216488 + 0.0433001i
\(593\) 1.70041e15 0.952252 0.476126 0.879377i \(-0.342041\pi\)
0.476126 + 0.879377i \(0.342041\pi\)
\(594\) −5.82066e14 + 4.31928e14i −0.322959 + 0.239655i
\(595\) 1.45397e15 + 1.45397e15i 0.799303 + 0.799303i
\(596\) 8.05803e14 + 1.50564e15i 0.438909 + 0.820097i
\(597\) 2.65076e14 2.65076e14i 0.143058 0.143058i
\(598\) 1.79162e15 + 2.65278e14i 0.958055 + 0.141855i
\(599\) 9.06284e14i 0.480194i −0.970749 0.240097i \(-0.922821\pi\)
0.970749 0.240097i \(-0.0771792\pi\)
\(600\) −1.23819e15 + 2.62332e15i −0.650064 + 1.37727i
\(601\) 3.33138e15i 1.73306i 0.499124 + 0.866531i \(0.333655\pi\)
−0.499124 + 0.866531i \(0.666345\pi\)
\(602\) 1.61819e14 1.09289e15i 0.0834161 0.563371i
\(603\) −5.71058e14 + 5.71058e14i −0.291699 + 0.291699i
\(604\) 2.29174e15 + 6.93869e14i 1.16001 + 0.351216i
\(605\) 2.16829e15 + 2.16829e15i 1.08758 + 1.08758i
\(606\) 7.95642e14 + 1.07221e15i 0.395474 + 0.532941i
\(607\) 1.62819e15 0.801986 0.400993 0.916081i \(-0.368665\pi\)
0.400993 + 0.916081i \(0.368665\pi\)
\(608\) 2.00799e15 2.22137e15i 0.980147 1.08430i
\(609\) 2.92555e14 0.141518
\(610\) −3.28031e15 4.42054e15i −1.57254 2.11915i
\(611\) −2.47174e15 2.47174e15i −1.17429 1.17429i
\(612\) −5.58872e14 1.69209e14i −0.263136 0.0796694i
\(613\) −1.39720e15 + 1.39720e15i −0.651968 + 0.651968i −0.953467 0.301499i \(-0.902513\pi\)
0.301499 + 0.953467i \(0.402513\pi\)
\(614\) −3.61966e14 + 2.44463e15i −0.167395 + 1.13054i
\(615\) 2.66867e15i 1.22315i
\(616\) 9.63969e14 + 4.54988e14i 0.437894 + 0.206684i
\(617\) 1.42742e15i 0.642661i −0.946967 0.321331i \(-0.895870\pi\)
0.946967 0.321331i \(-0.104130\pi\)
\(618\) 1.96961e14 + 2.91631e13i 0.0878907 + 0.0130136i
\(619\) −5.96980e14 + 5.96980e14i −0.264035 + 0.264035i −0.826691 0.562656i \(-0.809780\pi\)
0.562656 + 0.826691i \(0.309780\pi\)
\(620\) 2.25069e15 + 4.20539e15i 0.986646 + 1.84354i
\(621\) −1.16488e15 1.16488e15i −0.506147 0.506147i
\(622\) 8.04063e14 5.96663e14i 0.346292 0.256970i
\(623\) −1.86686e15 −0.796942
\(624\) −1.23594e15 + 1.85395e15i −0.522974 + 0.784481i
\(625\) −4.50500e15 −1.88953
\(626\) 1.78674e15 1.32587e15i 0.742853 0.551242i
\(627\) −6.50426e14 6.50426e14i −0.268057 0.268057i
\(628\) 3.83299e15 2.05138e15i 1.56588 0.838046i
\(629\) −1.92482e14 + 1.92482e14i −0.0779493 + 0.0779493i
\(630\) 3.07159e15 + 4.54797e14i 1.23308 + 0.182576i
\(631\) 3.18386e15i 1.26704i 0.773724 + 0.633522i \(0.218392\pi\)
−0.773724 + 0.633522i \(0.781608\pi\)
\(632\) −1.45522e14 + 5.21989e13i −0.0574097 + 0.0205929i
\(633\) 3.12041e15i 1.22037i
\(634\) −2.34463e14 + 1.58351e15i −0.0909043 + 0.613945i
\(635\) 5.44742e15 5.44742e15i 2.09380 2.09380i
\(636\) 8.17394e14 2.69972e15i 0.311471 1.02874i
\(637\) −1.49107e15 1.49107e15i −0.563289 0.563289i
\(638\) −1.03834e14 1.39926e14i −0.0388888 0.0524065i
\(639\) 1.13054e13 0.00419791
\(640\) −4.20974e15 + 2.53382e15i −1.54976 + 0.932795i
\(641\) 3.07527e15 1.12244 0.561222 0.827665i \(-0.310331\pi\)
0.561222 + 0.827665i \(0.310331\pi\)
\(642\) 7.01698e14 + 9.45608e14i 0.253926 + 0.342191i
\(643\) −2.71246e14 2.71246e14i −0.0973203 0.0973203i 0.656770 0.754091i \(-0.271922\pi\)
−0.754091 + 0.656770i \(0.771922\pi\)
\(644\) −7.02052e14 + 2.31877e15i −0.249745 + 0.824869i
\(645\) 1.10617e15 1.10617e15i 0.390161 0.390161i
\(646\) 3.05662e14 2.06437e15i 0.106896 0.721952i
\(647\) 4.50034e15i 1.56053i 0.625451 + 0.780264i \(0.284915\pi\)
−0.625451 + 0.780264i \(0.715085\pi\)
\(648\) 4.00262e14 1.43574e14i 0.137620 0.0493644i
\(649\) 2.50682e14i 0.0854627i
\(650\) −9.35016e15 1.38444e15i −3.16079 0.468005i
\(651\) −2.04592e15 + 2.04592e15i −0.685792 + 0.685792i
\(652\) −2.69376e15 + 1.44168e15i −0.895360 + 0.479189i
\(653\) −2.95719e15 2.95719e15i −0.974668 0.974668i 0.0250186 0.999687i \(-0.492035\pi\)
−0.999687 + 0.0250186i \(0.992035\pi\)
\(654\) 1.48863e15 1.10465e15i 0.486529 0.361034i
\(655\) −1.72577e15 −0.559313
\(656\) 1.74099e15 2.61155e15i 0.559532 0.839319i
\(657\) −1.20282e14 −0.0383346
\(658\) 3.75498e15 2.78642e15i 1.18676 0.880651i
\(659\) 2.05647e15 + 2.05647e15i 0.644545 + 0.644545i 0.951669 0.307124i \(-0.0993668\pi\)
−0.307124 + 0.951669i \(0.599367\pi\)
\(660\) 7.12206e14 + 1.33075e15i 0.221368 + 0.413624i
\(661\) 2.94861e15 2.94861e15i 0.908887 0.908887i −0.0872957 0.996182i \(-0.527823\pi\)
0.996182 + 0.0872957i \(0.0278225\pi\)
\(662\) −3.89896e15 5.77303e14i −1.19187 0.176476i
\(663\) 1.55285e15i 0.470767i
\(664\) −1.44452e15 6.81806e14i −0.434310 0.204992i
\(665\) 1.10971e16i 3.30896i
\(666\) −6.02079e13 + 4.06629e14i −0.0178051 + 0.120251i
\(667\) 2.80032e14 2.80032e14i 0.0821326 0.0821326i
\(668\) −4.30764e15 1.30422e15i −1.25305 0.379386i
\(669\) −2.90216e15 2.90216e15i −0.837294 0.837294i
\(670\) 2.82223e15 + 3.80324e15i 0.807572 + 1.08828i
\(671\) −1.98878e15 −0.564432
\(672\) −2.21106e15 1.99867e15i −0.622400 0.562614i
\(673\) −3.67663e15 −1.02652 −0.513259 0.858234i \(-0.671562\pi\)
−0.513259 + 0.858234i \(0.671562\pi\)
\(674\) 4.06690e12 + 5.48056e12i 0.00112625 + 0.00151773i
\(675\) 6.07929e15 + 6.07929e15i 1.66987 + 1.66987i
\(676\) −3.43583e15 1.04026e15i −0.936104 0.283424i
\(677\) −1.77059e15 + 1.77059e15i −0.478499 + 0.478499i −0.904651 0.426152i \(-0.859869\pi\)
0.426152 + 0.904651i \(0.359869\pi\)
\(678\) 3.84327e13 2.59565e14i 0.0103024 0.0695797i
\(679\) 1.38705e15i 0.368816i
\(680\) −1.46163e15 + 3.09670e15i −0.385512 + 0.816772i
\(681\) 4.56942e15i 1.19551i
\(682\) 1.70468e15 + 2.52405e14i 0.442415 + 0.0655065i
\(683\) 2.83214e15 2.83214e15i 0.729124 0.729124i −0.241321 0.970445i \(-0.577581\pi\)
0.970445 + 0.241321i \(0.0775807\pi\)
\(684\) −1.48701e15 2.77847e15i −0.379757 0.709573i
\(685\) 3.72728e15 + 3.72728e15i 0.944264 + 0.944264i
\(686\) −1.73406e15 + 1.28678e15i −0.435793 + 0.323385i
\(687\) −3.27029e15 −0.815312
\(688\) 1.80414e15 3.60850e14i 0.446205 0.0892463i
\(689\) 9.19112e15 2.25508
\(690\) −2.75485e15 + 2.04427e15i −0.670546 + 0.497586i
\(691\) −2.15938e15 2.15938e15i −0.521435 0.521435i 0.396570 0.918005i \(-0.370200\pi\)
−0.918005 + 0.396570i \(0.870200\pi\)
\(692\) 5.32760e15 2.85128e15i 1.27629 0.683057i
\(693\) 7.93250e14 7.93250e14i 0.188529 0.188529i
\(694\) −1.10413e15 1.63484e14i −0.260341 0.0385477i
\(695\) 7.35925e15i 1.72154i
\(696\) 1.64498e14 + 4.58594e14i 0.0381777 + 0.106433i
\(697\) 2.18741e15i 0.503675i
\(698\) −3.05353e14 + 2.06228e15i −0.0697586 + 0.471132i
\(699\) 2.39199e15 2.39199e15i 0.542169 0.542169i
\(700\) 3.66388e15 1.21012e16i 0.823953 2.72139i
\(701\) −2.82397e14 2.82397e14i −0.0630102 0.0630102i 0.674900 0.737910i \(-0.264187\pi\)
−0.737910 + 0.674900i \(0.764187\pi\)
\(702\) 3.93523e15 + 5.30311e15i 0.871196 + 1.17402i
\(703\) −1.46908e15 −0.322695
\(704\) −1.71195e14 + 1.76690e15i −0.0373115 + 0.385090i
\(705\) 6.62091e15 1.43178
\(706\) 4.34581e13 + 5.85641e13i 0.00932491 + 0.0125662i
\(707\) −4.11501e15 4.11501e15i −0.876121 0.876121i
\(708\) 2.03116e14 6.70859e14i 0.0429102 0.141726i
\(709\) 5.08406e15 5.08406e15i 1.06575 1.06575i 0.0680718 0.997680i \(-0.478315\pi\)
0.997680 0.0680718i \(-0.0216847\pi\)
\(710\) 9.71067e12 6.55834e13i 0.00201989 0.0136418i
\(711\) 1.62705e14i 0.0335828i
\(712\) −1.04970e15 2.92639e15i −0.214993 0.599366i
\(713\) 3.91668e15i 0.796024i
\(714\) −2.05479e15 3.04244e14i −0.414408 0.0613596i
\(715\) −3.47759e15 + 3.47759e15i −0.695978 + 0.695978i
\(716\) 1.99562e15 1.06804e15i 0.396329 0.212112i
\(717\) 2.09573e15 + 2.09573e15i 0.413029 + 0.413029i
\(718\) −1.93908e15 + 1.43891e15i −0.379237 + 0.281417i
\(719\) −5.28231e15 −1.02522 −0.512608 0.858623i \(-0.671321\pi\)
−0.512608 + 0.858623i \(0.671321\pi\)
\(720\) 1.01418e15 + 5.07059e15i 0.195337 + 0.976629i
\(721\) −8.67838e14 −0.165880
\(722\) 4.81092e15 3.56999e15i 0.912586 0.677194i
\(723\) 8.33084e14 + 8.33084e14i 0.156830 + 0.156830i
\(724\) 1.48607e15 + 2.77671e15i 0.277637 + 0.518763i
\(725\) −1.46144e15 + 1.46144e15i −0.270970 + 0.270970i
\(726\) −3.06429e15 4.53717e14i −0.563870 0.0834898i
\(727\) 1.04603e16i 1.91032i 0.296087 + 0.955161i \(0.404318\pi\)
−0.296087 + 0.955161i \(0.595682\pi\)
\(728\) 4.14532e15 8.78256e15i 0.751339 1.59184i
\(729\) 4.32120e15i 0.777325i
\(730\) −1.03315e14 + 6.97761e14i −0.0184453 + 0.124575i
\(731\) 9.06691e14 9.06691e14i 0.160662 0.160662i
\(732\) 5.32224e15 + 1.61141e15i 0.936017 + 0.283397i
\(733\) 2.63519e15 + 2.63519e15i 0.459982 + 0.459982i 0.898649 0.438668i \(-0.144549\pi\)
−0.438668 + 0.898649i \(0.644549\pi\)
\(734\) −2.59967e15 3.50331e15i −0.450391 0.606947i
\(735\) 3.99404e15 0.686803
\(736\) −4.02953e15 + 2.03297e14i −0.687744 + 0.0346980i
\(737\) 1.71105e15 0.289863
\(738\) −1.96841e15 2.65262e15i −0.330983 0.446032i
\(739\) 1.96675e15 + 1.96675e15i 0.328250 + 0.328250i 0.851921 0.523671i \(-0.175438\pi\)
−0.523671 + 0.851921i \(0.675438\pi\)
\(740\) 2.30716e15 + 6.98538e14i 0.382211 + 0.115722i
\(741\) −5.92592e15 + 5.92592e15i −0.974442 + 0.974442i
\(742\) −1.80078e15 + 1.21620e16i −0.293927 + 1.98511i
\(743\) 3.54440e15i 0.574255i 0.957892 + 0.287127i \(0.0927003\pi\)
−0.957892 + 0.287127i \(0.907300\pi\)
\(744\) −4.35746e15 2.05670e15i −0.700780 0.330765i
\(745\) 1.05394e16i 1.68251i
\(746\) 4.22729e15 + 6.25918e14i 0.669883 + 0.0991868i
\(747\) −1.18870e15 + 1.18870e15i −0.186985 + 0.186985i
\(748\) 5.83771e14 + 1.09077e15i 0.0911557 + 0.170324i
\(749\) −3.62914e15 3.62914e15i −0.562541 0.562541i
\(750\) 8.04878e15 5.97268e15i 1.23849 0.919036i
\(751\) −7.22921e15 −1.10426 −0.552130 0.833758i \(-0.686185\pi\)
−0.552130 + 0.833758i \(0.686185\pi\)
\(752\) 6.47920e15 + 4.31936e15i 0.982479 + 0.654970i
\(753\) −4.92473e15 −0.741327
\(754\) −1.27484e15 + 9.46012e14i −0.190509 + 0.141369i
\(755\) −1.04496e16 1.04496e16i −1.55021 1.55021i
\(756\) −7.78828e15 + 4.16822e15i −1.14702 + 0.613876i
\(757\) 1.87506e15 1.87506e15i 0.274150 0.274150i −0.556618 0.830768i \(-0.687901\pi\)
0.830768 + 0.556618i \(0.187901\pi\)
\(758\) −2.51598e15 3.72530e14i −0.365196 0.0540730i
\(759\) 1.23939e15i 0.178599i
\(760\) −1.73953e16 + 6.23970e15i −2.48861 + 0.892665i
\(761\)