Properties

Label 16.12.e.a.13.16
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 13.16
Character \(\chi\) = 16.13
Dual form 16.12.e.a.5.16

$q$-expansion

\(f(q)\) \(=\) \(q+(30.2883 - 33.6246i) q^{2} +(-56.4628 - 56.4628i) q^{3} +(-213.234 - 2036.87i) q^{4} +(6260.45 - 6260.45i) q^{5} +(-3608.71 + 188.377i) q^{6} +32944.0i q^{7} +(-74947.5 - 54523.5i) q^{8} -170771. i q^{9} +O(q^{10})\) \(q+(30.2883 - 33.6246i) q^{2} +(-56.4628 - 56.4628i) q^{3} +(-213.234 - 2036.87i) q^{4} +(6260.45 - 6260.45i) q^{5} +(-3608.71 + 188.377i) q^{6} +32944.0i q^{7} +(-74947.5 - 54523.5i) q^{8} -170771. i q^{9} +(-20886.8 - 400124. i) q^{10} +(-151744. + 151744. i) q^{11} +(-102968. + 127047. i) q^{12} +(-1.05140e6 - 1.05140e6i) q^{13} +(1.10773e6 + 997818. i) q^{14} -706965. q^{15} +(-4.10337e6 + 868658. i) q^{16} -1.95797e6 q^{17} +(-5.74211e6 - 5.17237e6i) q^{18} +(5.25340e6 + 5.25340e6i) q^{19} +(-1.40867e7 - 1.14168e7i) q^{20} +(1.86011e6 - 1.86011e6i) q^{21} +(506267. + 9.69844e6i) q^{22} -4.62502e7i q^{23} +(1.15320e6 + 7.31029e6i) q^{24} -2.95583e7i q^{25} +(-6.71982e7 + 3.50780e6i) q^{26} +(-1.96444e7 + 1.96444e7i) q^{27} +(6.71026e7 - 7.02476e6i) q^{28} +(1.16274e8 + 1.16274e8i) q^{29} +(-2.14128e7 + 2.37714e7i) q^{30} +2.86231e8 q^{31} +(-9.50758e7 + 1.64284e8i) q^{32} +1.71358e7 q^{33} +(-5.93038e7 + 6.58362e7i) q^{34} +(2.06244e8 + 2.06244e8i) q^{35} +(-3.47838e8 + 3.64141e7i) q^{36} +(3.33901e8 - 3.33901e8i) q^{37} +(3.35760e8 - 1.75270e7i) q^{38} +1.18730e8i q^{39} +(-8.10546e8 + 1.27864e8i) q^{40} -1.31100e8i q^{41} +(-6.20590e6 - 1.18885e8i) q^{42} +(5.60465e8 - 5.60465e8i) q^{43} +(3.41441e8 + 2.76727e8i) q^{44} +(-1.06910e9 - 1.06910e9i) q^{45} +(-1.55515e9 - 1.40084e9i) q^{46} +1.10264e8 q^{47} +(2.80734e8 + 1.82641e8i) q^{48} +8.92021e8 q^{49} +(-9.93888e8 - 8.95272e8i) q^{50} +(1.10553e8 + 1.10553e8i) q^{51} +(-1.91737e9 + 2.36576e9i) q^{52} +(-2.81385e9 + 2.81385e9i) q^{53} +(6.55399e7 + 1.25553e9i) q^{54} +1.89998e9i q^{55} +(1.79622e9 - 2.46907e9i) q^{56} -5.93243e8i q^{57} +(7.43142e9 - 3.87926e8i) q^{58} +(-3.57157e8 + 3.57157e8i) q^{59} +(1.50749e8 + 1.43999e9i) q^{60} +(-6.15858e9 - 6.15858e9i) q^{61} +(8.66945e9 - 9.62440e9i) q^{62} +5.62587e9 q^{63} +(2.64432e9 + 8.17279e9i) q^{64} -1.31645e10 q^{65} +(5.19016e8 - 5.76186e8i) q^{66} +(8.27855e9 + 8.27855e9i) q^{67} +(4.17506e8 + 3.98814e9i) q^{68} +(-2.61142e9 + 2.61142e9i) q^{69} +(1.31817e10 - 6.88094e8i) q^{70} +1.51270e10i q^{71} +(-9.31102e9 + 1.27989e10i) q^{72} -1.11074e10i q^{73} +(-1.11400e9 - 2.13406e10i) q^{74} +(-1.66895e9 + 1.66895e9i) q^{75} +(9.58028e9 - 1.18207e10i) q^{76} +(-4.99907e9 - 4.99907e9i) q^{77} +(3.99226e9 + 3.59614e9i) q^{78} +1.68275e10 q^{79} +(-2.02507e10 + 3.11271e10i) q^{80} -2.80332e10 q^{81} +(-4.40818e9 - 3.97079e9i) q^{82} +(-1.04553e10 - 1.04553e10i) q^{83} +(-4.18544e9 - 3.39216e9i) q^{84} +(-1.22578e10 + 1.22578e10i) q^{85} +(-1.86989e9 - 3.58210e10i) q^{86} -1.31303e10i q^{87} +(1.96465e10 - 3.09923e9i) q^{88} -3.00687e10i q^{89} +(-6.83295e10 + 3.56686e9i) q^{90} +(3.46373e10 - 3.46373e10i) q^{91} +(-9.42056e10 + 9.86210e9i) q^{92} +(-1.61614e10 - 1.61614e10i) q^{93} +(3.33972e9 - 3.70759e9i) q^{94} +6.57772e10 q^{95} +(1.46442e10 - 3.90771e9i) q^{96} +1.53440e11 q^{97} +(2.70178e10 - 2.99939e10i) q^{98} +(2.59135e10 + 2.59135e10i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 30.2883 33.6246i 0.669284 0.743007i
\(3\) −56.4628 56.4628i −0.134151 0.134151i 0.636842 0.770994i \(-0.280240\pi\)
−0.770994 + 0.636842i \(0.780240\pi\)
\(4\) −213.234 2036.87i −0.104118 0.994565i
\(5\) 6260.45 6260.45i 0.895922 0.895922i −0.0991500 0.995072i \(-0.531612\pi\)
0.995072 + 0.0991500i \(0.0316124\pi\)
\(6\) −3608.71 + 188.377i −0.189461 + 0.00989002i
\(7\) 32944.0i 0.740861i 0.928860 + 0.370431i \(0.120790\pi\)
−0.928860 + 0.370431i \(0.879210\pi\)
\(8\) −74947.5 54523.5i −0.808653 0.588286i
\(9\) 170771.i 0.964007i
\(10\) −20886.8 400124.i −0.0660499 1.26530i
\(11\) −151744. + 151744.i −0.284088 + 0.284088i −0.834737 0.550649i \(-0.814380\pi\)
0.550649 + 0.834737i \(0.314380\pi\)
\(12\) −102968. + 127047.i −0.119455 + 0.147390i
\(13\) −1.05140e6 1.05140e6i −0.785380 0.785380i 0.195353 0.980733i \(-0.437415\pi\)
−0.980733 + 0.195353i \(0.937415\pi\)
\(14\) 1.10773e6 + 997818.i 0.550465 + 0.495846i
\(15\) −706965. −0.240379
\(16\) −4.10337e6 + 868658.i −0.978319 + 0.207104i
\(17\) −1.95797e6 −0.334455 −0.167228 0.985918i \(-0.553481\pi\)
−0.167228 + 0.985918i \(0.553481\pi\)
\(18\) −5.74211e6 5.17237e6i −0.716263 0.645194i
\(19\) 5.25340e6 + 5.25340e6i 0.486738 + 0.486738i 0.907275 0.420537i \(-0.138158\pi\)
−0.420537 + 0.907275i \(0.638158\pi\)
\(20\) −1.40867e7 1.14168e7i −0.984335 0.797771i
\(21\) 1.86011e6 1.86011e6i 0.0993876 0.0993876i
\(22\) 506267. + 9.69844e6i 0.0209438 + 0.401215i
\(23\) 4.62502e7i 1.49834i −0.662377 0.749170i \(-0.730452\pi\)
0.662377 0.749170i \(-0.269548\pi\)
\(24\) 1.15320e6 + 7.31029e6i 0.0295625 + 0.187401i
\(25\) 2.95583e7i 0.605354i
\(26\) −6.71982e7 + 3.50780e6i −1.10919 + 0.0579004i
\(27\) −1.96444e7 + 1.96444e7i −0.263474 + 0.263474i
\(28\) 6.71026e7 7.02476e6i 0.736834 0.0771369i
\(29\) 1.16274e8 + 1.16274e8i 1.05267 + 1.05267i 0.998533 + 0.0541405i \(0.0172419\pi\)
0.0541405 + 0.998533i \(0.482758\pi\)
\(30\) −2.14128e7 + 2.37714e7i −0.160882 + 0.178603i
\(31\) 2.86231e8 1.79567 0.897836 0.440331i \(-0.145139\pi\)
0.897836 + 0.440331i \(0.145139\pi\)
\(32\) −9.50758e7 + 1.64284e8i −0.500893 + 0.865509i
\(33\) 1.71358e7 0.0762217
\(34\) −5.93038e7 + 6.58362e7i −0.223845 + 0.248502i
\(35\) 2.06244e8 + 2.06244e8i 0.663754 + 0.663754i
\(36\) −3.47838e8 + 3.64141e7i −0.958767 + 0.100370i
\(37\) 3.33901e8 3.33901e8i 0.791606 0.791606i −0.190150 0.981755i \(-0.560897\pi\)
0.981755 + 0.190150i \(0.0608973\pi\)
\(38\) 3.35760e8 1.75270e7i 0.687416 0.0358837i
\(39\) 1.18730e8i 0.210720i
\(40\) −8.10546e8 + 1.27864e8i −1.25155 + 0.197432i
\(41\) 1.31100e8i 0.176722i −0.996089 0.0883610i \(-0.971837\pi\)
0.996089 0.0883610i \(-0.0281629\pi\)
\(42\) −6.20590e6 1.18885e8i −0.00732713 0.140364i
\(43\) 5.60465e8 5.60465e8i 0.581396 0.581396i −0.353891 0.935287i \(-0.615141\pi\)
0.935287 + 0.353891i \(0.115141\pi\)
\(44\) 3.41441e8 + 2.76727e8i 0.312123 + 0.252965i
\(45\) −1.06910e9 1.06910e9i −0.863675 0.863675i
\(46\) −1.55515e9 1.40084e9i −1.11328 1.00282i
\(47\) 1.10264e8 0.0701288 0.0350644 0.999385i \(-0.488836\pi\)
0.0350644 + 0.999385i \(0.488836\pi\)
\(48\) 2.80734e8 + 1.82641e8i 0.159026 + 0.103460i
\(49\) 8.92021e8 0.451125
\(50\) −9.93888e8 8.95272e8i −0.449782 0.405154i
\(51\) 1.10553e8 + 1.10553e8i 0.0448677 + 0.0448677i
\(52\) −1.91737e9 + 2.36576e9i −0.699340 + 0.862884i
\(53\) −2.81385e9 + 2.81385e9i −0.924238 + 0.924238i −0.997326 0.0730872i \(-0.976715\pi\)
0.0730872 + 0.997326i \(0.476715\pi\)
\(54\) 6.55399e7 + 1.25553e9i 0.0194241 + 0.372102i
\(55\) 1.89998e9i 0.509042i
\(56\) 1.79622e9 2.46907e9i 0.435838 0.599099i
\(57\) 5.93243e8i 0.130593i
\(58\) 7.43142e9 3.87926e8i 1.48668 0.0776060i
\(59\) −3.57157e8 + 3.57157e8i −0.0650389 + 0.0650389i −0.738878 0.673839i \(-0.764644\pi\)
0.673839 + 0.738878i \(0.264644\pi\)
\(60\) 1.50749e8 + 1.43999e9i 0.0250277 + 0.239072i
\(61\) −6.15858e9 6.15858e9i −0.933612 0.933612i 0.0643176 0.997929i \(-0.479513\pi\)
−0.997929 + 0.0643176i \(0.979513\pi\)
\(62\) 8.66945e9 9.62440e9i 1.20181 1.33420i
\(63\) 5.62587e9 0.714195
\(64\) 2.64432e9 + 8.17279e9i 0.307839 + 0.951438i
\(65\) −1.31645e10 −1.40728
\(66\) 5.19016e8 5.76186e8i 0.0510140 0.0566332i
\(67\) 8.27855e9 + 8.27855e9i 0.749106 + 0.749106i 0.974311 0.225206i \(-0.0723054\pi\)
−0.225206 + 0.974311i \(0.572305\pi\)
\(68\) 4.17506e8 + 3.98814e9i 0.0348228 + 0.332637i
\(69\) −2.61142e9 + 2.61142e9i −0.201005 + 0.201005i
\(70\) 1.31817e10 6.88094e8i 0.937414 0.0489338i
\(71\) 1.51270e10i 0.995020i 0.867458 + 0.497510i \(0.165752\pi\)
−0.867458 + 0.497510i \(0.834248\pi\)
\(72\) −9.31102e9 + 1.27989e10i −0.567112 + 0.779547i
\(73\) 1.11074e10i 0.627100i −0.949572 0.313550i \(-0.898482\pi\)
0.949572 0.313550i \(-0.101518\pi\)
\(74\) −1.11400e9 2.13406e10i −0.0583593 1.11798i
\(75\) −1.66895e9 + 1.66895e9i −0.0812092 + 0.0812092i
\(76\) 9.58028e9 1.18207e10i 0.433415 0.534771i
\(77\) −4.99907e9 4.99907e9i −0.210470 0.210470i
\(78\) 3.99226e9 + 3.59614e9i 0.156566 + 0.141031i
\(79\) 1.68275e10 0.615275 0.307638 0.951504i \(-0.400462\pi\)
0.307638 + 0.951504i \(0.400462\pi\)
\(80\) −2.02507e10 + 3.11271e10i −0.690949 + 1.06205i
\(81\) −2.80332e10 −0.893316
\(82\) −4.40818e9 3.97079e9i −0.131306 0.118277i
\(83\) −1.04553e10 1.04553e10i −0.291345 0.291345i 0.546267 0.837611i \(-0.316049\pi\)
−0.837611 + 0.546267i \(0.816049\pi\)
\(84\) −4.18544e9 3.39216e9i −0.109195 0.0884994i
\(85\) −1.22578e10 + 1.22578e10i −0.299646 + 0.299646i
\(86\) −1.86989e9 3.58210e10i −0.0428621 0.821100i
\(87\) 1.31303e10i 0.282436i
\(88\) 1.96465e10 3.09923e9i 0.396854 0.0626036i
\(89\) 3.00687e10i 0.570781i −0.958411 0.285391i \(-0.907877\pi\)
0.958411 0.285391i \(-0.0921233\pi\)
\(90\) −6.83295e10 + 3.56686e9i −1.21976 + 0.0636725i
\(91\) 3.46373e10 3.46373e10i 0.581858 0.581858i
\(92\) −9.42056e10 + 9.86210e9i −1.49020 + 0.156004i
\(93\) −1.61614e10 1.61614e10i −0.240892 0.240892i
\(94\) 3.33972e9 3.70759e9i 0.0469361 0.0521061i
\(95\) 6.57772e10 0.872159
\(96\) 1.46442e10 3.90771e9i 0.183305 0.0489137i
\(97\) 1.53440e11 1.81423 0.907117 0.420878i \(-0.138278\pi\)
0.907117 + 0.420878i \(0.138278\pi\)
\(98\) 2.70178e10 2.99939e10i 0.301931 0.335189i
\(99\) 2.59135e10 + 2.59135e10i 0.273863 + 0.273863i
\(100\) −6.02064e10 + 6.30282e9i −0.602064 + 0.0630282i
\(101\) −1.83207e10 + 1.83207e10i −0.173450 + 0.173450i −0.788493 0.615043i \(-0.789138\pi\)
0.615043 + 0.788493i \(0.289138\pi\)
\(102\) 7.06575e9 3.68838e8i 0.0633662 0.00330777i
\(103\) 2.26120e11i 1.92192i 0.276688 + 0.960960i \(0.410763\pi\)
−0.276688 + 0.960960i \(0.589237\pi\)
\(104\) 2.14738e10 + 1.36126e11i 0.173072 + 1.09713i
\(105\) 2.32902e10i 0.178087i
\(106\) 9.38789e9 + 1.79842e11i 0.0681374 + 1.30529i
\(107\) 8.60250e10 8.60250e10i 0.592945 0.592945i −0.345481 0.938426i \(-0.612284\pi\)
0.938426 + 0.345481i \(0.112284\pi\)
\(108\) 4.42020e10 + 3.58243e10i 0.289475 + 0.234610i
\(109\) −5.61060e10 5.61060e10i −0.349272 0.349272i 0.510567 0.859838i \(-0.329436\pi\)
−0.859838 + 0.510567i \(0.829436\pi\)
\(110\) 6.38860e10 + 5.75471e10i 0.378222 + 0.340694i
\(111\) −3.77060e10 −0.212390
\(112\) −2.86170e10 1.35181e11i −0.153435 0.724798i
\(113\) 2.67377e11 1.36519 0.682595 0.730797i \(-0.260851\pi\)
0.682595 + 0.730797i \(0.260851\pi\)
\(114\) −1.99476e10 1.79683e10i −0.0970317 0.0874040i
\(115\) −2.89547e11 2.89547e11i −1.34240 1.34240i
\(116\) 2.12041e11 2.61629e11i 0.937350 1.15655i
\(117\) −1.79549e11 + 1.79549e11i −0.757112 + 0.757112i
\(118\) 1.19159e9 + 2.28270e10i 0.00479485 + 0.0918539i
\(119\) 6.45034e10i 0.247785i
\(120\) 5.29852e10 + 3.85462e10i 0.194383 + 0.141411i
\(121\) 2.39259e11i 0.838588i
\(122\) −3.93613e11 + 2.05469e10i −1.31853 + 0.0688284i
\(123\) −7.40226e9 + 7.40226e9i −0.0237075 + 0.0237075i
\(124\) −6.10340e10 5.83014e11i −0.186962 1.78591i
\(125\) 1.20638e11 + 1.20638e11i 0.353572 + 0.353572i
\(126\) 1.70398e11 1.89168e11i 0.477999 0.530652i
\(127\) −3.39115e11 −0.910807 −0.455404 0.890285i \(-0.650505\pi\)
−0.455404 + 0.890285i \(0.650505\pi\)
\(128\) 3.54899e11 + 1.58626e11i 0.912957 + 0.408056i
\(129\) −6.32909e10 −0.155990
\(130\) −3.98730e11 + 4.42651e11i −0.941870 + 1.04562i
\(131\) −5.87379e11 5.87379e11i −1.33023 1.33023i −0.905162 0.425068i \(-0.860250\pi\)
−0.425068 0.905162i \(-0.639750\pi\)
\(132\) −3.65394e9 3.49034e10i −0.00793605 0.0758074i
\(133\) −1.73068e11 + 1.73068e11i −0.360605 + 0.360605i
\(134\) 5.29107e11 2.76198e10i 1.05795 0.0552261i
\(135\) 2.45966e11i 0.472105i
\(136\) 1.46745e11 + 1.06756e11i 0.270458 + 0.196755i
\(137\) 6.79735e11i 1.20331i −0.798757 0.601654i \(-0.794509\pi\)
0.798757 0.601654i \(-0.205491\pi\)
\(138\) 8.71250e9 + 1.66903e11i 0.0148186 + 0.283877i
\(139\) −7.49060e11 + 7.49060e11i −1.22443 + 1.22443i −0.258393 + 0.966040i \(0.583193\pi\)
−0.966040 + 0.258393i \(0.916807\pi\)
\(140\) 3.76114e11 4.64070e11i 0.591038 0.729255i
\(141\) −6.22582e9 6.22582e9i −0.00940788 0.00940788i
\(142\) 5.08640e11 + 4.58171e11i 0.739306 + 0.665951i
\(143\) 3.19089e11 0.446235
\(144\) 1.48341e11 + 7.00736e11i 0.199650 + 0.943106i
\(145\) 1.45586e12 1.88623
\(146\) −3.73482e11 3.36424e11i −0.465939 0.419708i
\(147\) −5.03660e10 5.03660e10i −0.0605191 0.0605191i
\(148\) −7.51313e11 6.08915e11i −0.869724 0.704883i
\(149\) −7.36973e11 + 7.36973e11i −0.822105 + 0.822105i −0.986410 0.164305i \(-0.947462\pi\)
0.164305 + 0.986410i \(0.447462\pi\)
\(150\) 5.56812e9 + 1.06667e11i 0.00598696 + 0.114691i
\(151\) 5.40219e11i 0.560011i 0.959998 + 0.280006i \(0.0903363\pi\)
−0.959998 + 0.280006i \(0.909664\pi\)
\(152\) −1.07295e11 6.80162e11i −0.107261 0.679944i
\(153\) 3.34365e11i 0.322417i
\(154\) −3.19505e11 + 1.66784e10i −0.297245 + 0.0155164i
\(155\) 1.79193e12 1.79193e12i 1.60878 1.60878i
\(156\) 2.41838e11 2.53173e10i 0.209575 0.0219397i
\(157\) −1.25630e11 1.25630e11i −0.105110 0.105110i 0.652596 0.757706i \(-0.273680\pi\)
−0.757706 + 0.652596i \(0.773680\pi\)
\(158\) 5.09676e11 5.65817e11i 0.411794 0.457154i
\(159\) 3.17756e11 0.247976
\(160\) 4.33277e11 + 1.62371e12i 0.326667 + 1.22419i
\(161\) 1.52367e12 1.11006
\(162\) −8.49079e11 + 9.42606e11i −0.597882 + 0.663740i
\(163\) −8.92563e11 8.92563e11i −0.607585 0.607585i 0.334729 0.942314i \(-0.391355\pi\)
−0.942314 + 0.334729i \(0.891355\pi\)
\(164\) −2.67033e11 + 2.79549e10i −0.175762 + 0.0183999i
\(165\) 1.07278e11 1.07278e11i 0.0682887 0.0682887i
\(166\) −6.68230e11 + 3.48822e10i −0.411464 + 0.0214787i
\(167\) 2.53237e12i 1.50864i 0.656506 + 0.754321i \(0.272034\pi\)
−0.656506 + 0.754321i \(0.727966\pi\)
\(168\) −2.40830e11 + 3.79909e10i −0.138838 + 0.0219017i
\(169\) 4.18729e11i 0.233645i
\(170\) 4.08958e10 + 7.83432e11i 0.0220907 + 0.423187i
\(171\) 8.97127e11 8.97127e11i 0.469219 0.469219i
\(172\) −1.26110e12 1.02208e12i −0.638770 0.517702i
\(173\) −1.51275e12 1.51275e12i −0.742188 0.742188i 0.230810 0.972999i \(-0.425862\pi\)
−0.972999 + 0.230810i \(0.925862\pi\)
\(174\) −4.41502e11 3.97695e11i −0.209851 0.189030i
\(175\) 9.73768e11 0.448483
\(176\) 4.90849e11 7.54477e11i 0.219093 0.336765i
\(177\) 4.03322e10 0.0174501
\(178\) −1.01105e12 9.10731e11i −0.424094 0.382015i
\(179\) −6.66463e8 6.66463e8i −0.000271072 0.000271072i 0.706971 0.707242i \(-0.250061\pi\)
−0.707242 + 0.706971i \(0.750061\pi\)
\(180\) −1.94965e12 + 2.40559e12i −0.769057 + 0.948905i
\(181\) −8.79540e11 + 8.79540e11i −0.336530 + 0.336530i −0.855060 0.518530i \(-0.826480\pi\)
0.518530 + 0.855060i \(0.326480\pi\)
\(182\) −1.15561e11 2.21378e12i −0.0428962 0.821752i
\(183\) 6.95461e11i 0.250491i
\(184\) −2.52172e12 + 3.46634e12i −0.881453 + 1.21164i
\(185\) 4.18075e12i 1.41843i
\(186\) −1.03292e12 + 5.39194e10i −0.340209 + 0.0177592i
\(187\) 2.97112e11 2.97112e11i 0.0950147 0.0950147i
\(188\) −2.35120e10 2.24594e11i −0.00730166 0.0697476i
\(189\) −6.47165e11 6.47165e11i −0.195198 0.195198i
\(190\) 1.99228e12 2.21174e12i 0.583722 0.648020i
\(191\) 5.27207e12 1.50071 0.750357 0.661033i \(-0.229882\pi\)
0.750357 + 0.661033i \(0.229882\pi\)
\(192\) 3.12153e11 6.10764e11i 0.0863398 0.168934i
\(193\) −4.42702e12 −1.19000 −0.595000 0.803726i \(-0.702848\pi\)
−0.595000 + 0.803726i \(0.702848\pi\)
\(194\) 4.64744e12 5.15936e12i 1.21424 1.34799i
\(195\) 7.43304e11 + 7.43304e11i 0.188789 + 0.188789i
\(196\) −1.90209e11 1.81693e12i −0.0469702 0.448673i
\(197\) −1.55303e12 + 1.55303e12i −0.372920 + 0.372920i −0.868540 0.495620i \(-0.834941\pi\)
0.495620 + 0.868540i \(0.334941\pi\)
\(198\) 1.65621e12 8.64556e10i 0.386774 0.0201899i
\(199\) 9.09713e11i 0.206639i 0.994648 + 0.103320i \(0.0329464\pi\)
−0.994648 + 0.103320i \(0.967054\pi\)
\(200\) −1.61162e12 + 2.21532e12i −0.356121 + 0.489521i
\(201\) 9.34861e11i 0.200987i
\(202\) 6.11235e10 + 1.17093e12i 0.0127872 + 0.244962i
\(203\) −3.83053e12 + 3.83053e12i −0.779885 + 0.779885i
\(204\) 2.01608e11 2.48755e11i 0.0399523 0.0492953i
\(205\) −8.20744e11 8.20744e11i −0.158329 0.158329i
\(206\) 7.60322e12 + 6.84881e12i 1.42800 + 1.28631i
\(207\) −7.89819e12 −1.44441
\(208\) 5.22759e12 + 3.40098e12i 0.931008 + 0.605697i
\(209\) −1.59435e12 −0.276553
\(210\) −7.83126e11 7.05422e11i −0.132320 0.119191i
\(211\) 7.96643e12 + 7.96643e12i 1.31132 + 1.31132i 0.920440 + 0.390884i \(0.127831\pi\)
0.390884 + 0.920440i \(0.372169\pi\)
\(212\) 6.33146e12 + 5.13144e12i 1.01544 + 0.822985i
\(213\) 8.54112e11 8.54112e11i 0.133483 0.133483i
\(214\) −2.87006e11 5.49812e12i −0.0437135 0.837410i
\(215\) 7.01753e12i 1.04177i
\(216\) 2.54338e12 4.01218e11i 0.368058 0.0580610i
\(217\) 9.42957e12i 1.33034i
\(218\) −3.58590e12 + 1.87187e11i −0.493273 + 0.0257493i
\(219\) −6.27155e11 + 6.27155e11i −0.0841263 + 0.0841263i
\(220\) 3.87000e12 4.05139e11i 0.506275 0.0530004i
\(221\) 2.05862e12 + 2.05862e12i 0.262675 + 0.262675i
\(222\) −1.14205e12 + 1.26785e12i −0.142149 + 0.157807i
\(223\) 6.00097e12 0.728693 0.364346 0.931263i \(-0.381292\pi\)
0.364346 + 0.931263i \(0.381292\pi\)
\(224\) −5.41218e12 3.13218e12i −0.641222 0.371092i
\(225\) −5.04770e12 −0.583566
\(226\) 8.09842e12 8.99047e12i 0.913700 1.01435i
\(227\) −9.49853e12 9.49853e12i −1.04596 1.04596i −0.998892 0.0470662i \(-0.985013\pi\)
−0.0470662 0.998892i \(-0.514987\pi\)
\(228\) −1.20836e12 + 1.26499e11i −0.129884 + 0.0135971i
\(229\) 3.57204e12 3.57204e12i 0.374819 0.374819i −0.494410 0.869229i \(-0.664616\pi\)
0.869229 + 0.494410i \(0.164616\pi\)
\(230\) −1.85058e13 + 9.66019e11i −1.89586 + 0.0989652i
\(231\) 5.64522e11i 0.0564697i
\(232\) −2.37478e12 1.50541e13i −0.231974 1.47052i
\(233\) 5.68541e12i 0.542380i −0.962526 0.271190i \(-0.912583\pi\)
0.962526 0.271190i \(-0.0874172\pi\)
\(234\) 5.99031e11 + 1.14755e13i 0.0558164 + 1.06926i
\(235\) 6.90303e11 6.90303e11i 0.0628299 0.0628299i
\(236\) 8.03640e11 + 6.51325e11i 0.0714572 + 0.0579137i
\(237\) −9.50126e11 9.50126e11i −0.0825401 0.0825401i
\(238\) −2.16891e12 1.95370e12i −0.184106 0.165838i
\(239\) −1.23973e13 −1.02834 −0.514171 0.857688i \(-0.671900\pi\)
−0.514171 + 0.857688i \(0.671900\pi\)
\(240\) 2.90094e12 6.14111e11i 0.235167 0.0497834i
\(241\) −2.15671e12 −0.170883 −0.0854414 0.996343i \(-0.527230\pi\)
−0.0854414 + 0.996343i \(0.527230\pi\)
\(242\) 8.04500e12 + 7.24675e12i 0.623076 + 0.561253i
\(243\) 5.06278e12 + 5.06278e12i 0.383314 + 0.383314i
\(244\) −1.12310e13 + 1.38574e13i −0.831332 + 1.02574i
\(245\) 5.58445e12 5.58445e12i 0.404173 0.404173i
\(246\) 2.46962e10 + 4.73101e11i 0.00174778 + 0.0334819i
\(247\) 1.10469e13i 0.764549i
\(248\) −2.14523e13 1.56063e13i −1.45207 1.05637i
\(249\) 1.18067e12i 0.0781687i
\(250\) 7.71031e12 4.02485e11i 0.499347 0.0260663i
\(251\) −2.78742e11 + 2.78742e11i −0.0176603 + 0.0176603i −0.715882 0.698222i \(-0.753975\pi\)
0.698222 + 0.715882i \(0.253975\pi\)
\(252\) −1.19962e12 1.14592e13i −0.0743605 0.710313i
\(253\) 7.01821e12 + 7.01821e12i 0.425661 + 0.425661i
\(254\) −1.02712e13 + 1.14026e13i −0.609589 + 0.676736i
\(255\) 1.38422e12 0.0803959
\(256\) 1.60831e13 7.12884e12i 0.914216 0.405228i
\(257\) 1.43940e13 0.800844 0.400422 0.916331i \(-0.368864\pi\)
0.400422 + 0.916331i \(0.368864\pi\)
\(258\) −1.91698e12 + 2.12813e12i −0.104402 + 0.115902i
\(259\) 1.10000e13 + 1.10000e13i 0.586470 + 0.586470i
\(260\) 2.80711e12 + 2.68143e13i 0.146523 + 1.39963i
\(261\) 1.98562e13 1.98562e13i 1.01478 1.01478i
\(262\) −3.75412e13 + 1.95968e12i −1.87867 + 0.0980682i
\(263\) 1.03878e13i 0.509057i −0.967065 0.254529i \(-0.918080\pi\)
0.967065 0.254529i \(-0.0819203\pi\)
\(264\) −1.28429e12 9.34305e11i −0.0616369 0.0448402i
\(265\) 3.52320e13i 1.65609i
\(266\) 5.77408e11 + 1.10613e13i 0.0265848 + 0.509280i
\(267\) −1.69776e12 + 1.69776e12i −0.0765711 + 0.0765711i
\(268\) 1.50971e13 1.86276e13i 0.667039 0.823029i
\(269\) 2.99941e13 + 2.99941e13i 1.29837 + 1.29837i 0.929468 + 0.368903i \(0.120266\pi\)
0.368903 + 0.929468i \(0.379734\pi\)
\(270\) 8.27051e12 + 7.44989e12i 0.350777 + 0.315973i
\(271\) −2.44910e13 −1.01783 −0.508915 0.860817i \(-0.669953\pi\)
−0.508915 + 0.860817i \(0.669953\pi\)
\(272\) 8.03429e12 1.70081e12i 0.327204 0.0692670i
\(273\) −3.91144e12 −0.156114
\(274\) −2.28558e13 2.05880e13i −0.894065 0.805354i
\(275\) 4.48531e12 + 4.48531e12i 0.171974 + 0.171974i
\(276\) 5.87596e12 + 4.76227e12i 0.220840 + 0.178984i
\(277\) 1.19102e13 1.19102e13i 0.438815 0.438815i −0.452798 0.891613i \(-0.649574\pi\)
0.891613 + 0.452798i \(0.149574\pi\)
\(278\) 2.49910e12 + 4.78746e13i 0.0902686 + 1.72925i
\(279\) 4.88799e13i 1.73104i
\(280\) −4.21233e12 2.67026e13i −0.146269 0.927224i
\(281\) 1.77505e13i 0.604403i −0.953244 0.302201i \(-0.902279\pi\)
0.953244 0.302201i \(-0.0977215\pi\)
\(282\) −3.97911e11 + 2.07713e10i −0.0132867 + 0.000693575i
\(283\) −6.56292e12 + 6.56292e12i −0.214917 + 0.214917i −0.806353 0.591435i \(-0.798562\pi\)
0.591435 + 0.806353i \(0.298562\pi\)
\(284\) 3.08117e13 3.22558e12i 0.989612 0.103599i
\(285\) −3.71397e12 3.71397e12i −0.117001 0.117001i
\(286\) 9.66466e12 1.07292e13i 0.298658 0.331555i
\(287\) 4.31895e12 0.130927
\(288\) 2.80550e13 + 1.62362e13i 0.834357 + 0.482865i
\(289\) −3.04382e13 −0.888140
\(290\) 4.40954e13 4.89526e13i 1.26242 1.40148i
\(291\) −8.66364e12 8.66364e12i −0.243382 0.243382i
\(292\) −2.26243e13 + 2.36847e12i −0.623691 + 0.0652923i
\(293\) −1.28607e13 + 1.28607e13i −0.347931 + 0.347931i −0.859338 0.511408i \(-0.829124\pi\)
0.511408 + 0.859338i \(0.329124\pi\)
\(294\) −3.21904e12 + 1.68037e11i −0.0854705 + 0.00446163i
\(295\) 4.47193e12i 0.116540i
\(296\) −4.32305e13 + 6.81961e12i −1.10582 + 0.174444i
\(297\) 5.96186e12i 0.149700i
\(298\) 2.45877e12 + 4.71021e13i 0.0606078 + 1.16105i
\(299\) −4.86275e13 + 4.86275e13i −1.17677 + 1.17677i
\(300\) 3.75530e12 + 3.04355e12i 0.0892231 + 0.0723125i
\(301\) 1.84640e13 + 1.84640e13i 0.430734 + 0.430734i
\(302\) 1.81647e13 + 1.63623e13i 0.416092 + 0.374806i
\(303\) 2.06887e12 0.0465371
\(304\) −2.61200e13 1.69932e13i −0.576991 0.375380i
\(305\) −7.71109e13 −1.67289
\(306\) 1.12429e13 + 1.01274e13i 0.239558 + 0.215789i
\(307\) 2.49037e13 + 2.49037e13i 0.521199 + 0.521199i 0.917933 0.396735i \(-0.129857\pi\)
−0.396735 + 0.917933i \(0.629857\pi\)
\(308\) −9.11647e12 + 1.12484e13i −0.187412 + 0.231240i
\(309\) 1.27674e13 1.27674e13i 0.257828 0.257828i
\(310\) −5.97844e12 1.14528e14i −0.118604 2.27207i
\(311\) 4.08332e13i 0.795851i 0.917418 + 0.397925i \(0.130270\pi\)
−0.917418 + 0.397925i \(0.869730\pi\)
\(312\) 6.47358e12 8.89853e12i 0.123964 0.170399i
\(313\) 1.00390e13i 0.188885i −0.995530 0.0944423i \(-0.969893\pi\)
0.995530 0.0944423i \(-0.0301068\pi\)
\(314\) −8.02940e12 + 4.19142e11i −0.148447 + 0.00774904i
\(315\) 3.52205e13 3.52205e13i 0.639863 0.639863i
\(316\) −3.58818e12 3.42753e13i −0.0640612 0.611931i
\(317\) −6.71251e13 6.71251e13i −1.17777 1.17777i −0.980312 0.197455i \(-0.936732\pi\)
−0.197455 0.980312i \(-0.563268\pi\)
\(318\) 9.62430e12 1.06844e13i 0.165966 0.184248i
\(319\) −3.52879e13 −0.598104
\(320\) 6.77200e13 + 3.46107e13i 1.12822 + 0.576615i
\(321\) −9.71443e12 −0.159089
\(322\) 4.61493e13 5.12327e13i 0.742947 0.824784i
\(323\) −1.02860e13 1.02860e13i −0.162792 0.162792i
\(324\) 5.97762e12 + 5.70999e13i 0.0930102 + 0.888461i
\(325\) −3.10776e13 + 3.10776e13i −0.475433 + 0.475433i
\(326\) −5.70463e13 + 2.97787e12i −0.858086 + 0.0447928i
\(327\) 6.33580e12i 0.0937106i
\(328\) −7.14802e12 + 9.82560e12i −0.103963 + 0.142907i
\(329\) 3.63254e12i 0.0519557i
\(330\) −3.57913e11 6.85646e12i −0.00503443 0.0964435i
\(331\) 3.21941e13 3.21941e13i 0.445371 0.445371i −0.448441 0.893812i \(-0.648021\pi\)
0.893812 + 0.448441i \(0.148021\pi\)
\(332\) −1.90667e13 + 2.35255e13i −0.259427 + 0.320096i
\(333\) −5.70207e13 5.70207e13i −0.763113 0.763113i
\(334\) 8.51500e13 + 7.67012e13i 1.12093 + 1.00971i
\(335\) 1.03655e14 1.34228
\(336\) −6.01691e12 + 9.24851e12i −0.0766492 + 0.117816i
\(337\) 1.17704e14 1.47512 0.737562 0.675279i \(-0.235977\pi\)
0.737562 + 0.675279i \(0.235977\pi\)
\(338\) 1.40796e13 + 1.26826e13i 0.173600 + 0.156375i
\(339\) −1.50969e13 1.50969e13i −0.183142 0.183142i
\(340\) 2.75813e13 + 2.23538e13i 0.329216 + 0.266819i
\(341\) −4.34339e13 + 4.34339e13i −0.510129 + 0.510129i
\(342\) −2.99310e12 5.73381e13i −0.0345921 0.662673i
\(343\) 9.45277e13i 1.07508i
\(344\) −7.25640e13 + 1.14470e13i −0.812175 + 0.128120i
\(345\) 3.26973e13i 0.360169i
\(346\) −9.66845e13 + 5.04701e12i −1.04819 + 0.0547162i
\(347\) 6.26543e13 6.26543e13i 0.668558 0.668558i −0.288824 0.957382i \(-0.593264\pi\)
0.957382 + 0.288824i \(0.0932644\pi\)
\(348\) −2.67447e13 + 2.79982e12i −0.280900 + 0.0294066i
\(349\) 4.36968e13 + 4.36968e13i 0.451762 + 0.451762i 0.895939 0.444177i \(-0.146504\pi\)
−0.444177 + 0.895939i \(0.646504\pi\)
\(350\) 2.94938e13 3.27426e13i 0.300163 0.333226i
\(351\) 4.13083e13 0.413855
\(352\) −1.05020e13 3.93565e13i −0.103583 0.388179i
\(353\) 1.05748e14 1.02686 0.513431 0.858131i \(-0.328374\pi\)
0.513431 + 0.858131i \(0.328374\pi\)
\(354\) 1.22160e12 1.35616e12i 0.0116791 0.0129656i
\(355\) 9.47017e13 + 9.47017e13i 0.891460 + 0.891460i
\(356\) −6.12460e13 + 6.41166e12i −0.567679 + 0.0594286i
\(357\) −3.64205e12 + 3.64205e12i −0.0332407 + 0.0332407i
\(358\) −4.25956e10 + 2.22353e9i −0.000382832 + 1.99842e-5i
\(359\) 2.59583e13i 0.229751i 0.993380 + 0.114875i \(0.0366469\pi\)
−0.993380 + 0.114875i \(0.963353\pi\)
\(360\) 2.18354e13 + 1.38418e14i 0.190325 + 1.20650i
\(361\) 6.12939e13i 0.526172i
\(362\) 2.93442e12 + 5.62140e13i 0.0248099 + 0.475278i
\(363\) 1.35092e13 1.35092e13i 0.112498 0.112498i
\(364\) −7.79376e13 6.31659e13i −0.639277 0.518114i
\(365\) −6.95373e13 6.95373e13i −0.561833 0.561833i
\(366\) 2.33846e13 + 2.10644e13i 0.186116 + 0.167650i
\(367\) 1.12895e14 0.885137 0.442568 0.896735i \(-0.354067\pi\)
0.442568 + 0.896735i \(0.354067\pi\)
\(368\) 4.01756e13 + 1.89782e14i 0.310313 + 1.46586i
\(369\) −2.23880e13 −0.170361
\(370\) −1.40576e14 1.26628e14i −1.05391 0.949335i
\(371\) −9.26995e13 9.26995e13i −0.684732 0.684732i
\(372\) −2.94725e13 + 3.63648e13i −0.214502 + 0.264664i
\(373\) −4.27445e13 + 4.27445e13i −0.306536 + 0.306536i −0.843564 0.537028i \(-0.819547\pi\)
0.537028 + 0.843564i \(0.319547\pi\)
\(374\) −9.91257e11 1.89893e13i −0.00700475 0.134188i
\(375\) 1.36231e13i 0.0948644i
\(376\) −8.26402e12 6.01198e12i −0.0567098 0.0412558i
\(377\) 2.44501e14i 1.65350i
\(378\) −4.13623e13 + 2.15914e12i −0.275676 + 0.0143905i
\(379\) −1.18007e14 + 1.18007e14i −0.775162 + 0.775162i −0.979004 0.203842i \(-0.934657\pi\)
0.203842 + 0.979004i \(0.434657\pi\)
\(380\) −1.40259e13 1.33980e14i −0.0908075 0.867419i
\(381\) 1.91474e13 + 1.91474e13i 0.122186 + 0.122186i
\(382\) 1.59682e14 1.77272e14i 1.00440 1.11504i
\(383\) −7.83589e13 −0.485842 −0.242921 0.970046i \(-0.578106\pi\)
−0.242921 + 0.970046i \(0.578106\pi\)
\(384\) −1.10821e13 2.89951e13i −0.0677332 0.177216i
\(385\) −6.25928e13 −0.377129
\(386\) −1.34087e14 + 1.48857e14i −0.796447 + 0.884177i
\(387\) −9.57112e13 9.57112e13i −0.560470 0.560470i
\(388\) −3.27185e13 3.12537e14i −0.188894 1.80437i
\(389\) 5.66527e13 5.66527e13i 0.322476 0.322476i −0.527240 0.849716i \(-0.676773\pi\)
0.849716 + 0.527240i \(0.176773\pi\)
\(390\) 4.75068e13 2.47989e12i 0.266625 0.0139180i
\(391\) 9.05567e13i 0.501128i
\(392\) −6.68548e13 4.86361e13i −0.364803 0.265390i
\(393\) 6.63302e13i 0.356904i
\(394\) 5.18139e12 + 9.92587e13i 0.0274927 + 0.526671i
\(395\) 1.05347e14 1.05347e14i 0.551239 0.551239i
\(396\) 4.72568e13 5.83081e13i 0.243860 0.300888i
\(397\) 1.13353e14 + 1.13353e14i 0.576881 + 0.576881i 0.934043 0.357161i \(-0.116255\pi\)
−0.357161 + 0.934043i \(0.616255\pi\)
\(398\) 3.05888e13 + 2.75537e13i 0.153534 + 0.138300i
\(399\) 1.95438e13 0.0967515
\(400\) 2.56761e13 + 1.21289e14i 0.125371 + 0.592229i
\(401\) 2.11807e14 1.02011 0.510054 0.860142i \(-0.329625\pi\)
0.510054 + 0.860142i \(0.329625\pi\)
\(402\) −3.14344e13 2.83154e13i −0.149335 0.134518i
\(403\) −3.00943e14 3.00943e14i −1.41029 1.41029i
\(404\) 4.12234e13 + 3.34102e13i 0.190566 + 0.154448i
\(405\) −1.75500e14 + 1.75500e14i −0.800342 + 0.800342i
\(406\) 1.27798e13 + 2.44821e14i 0.0574953 + 1.10142i
\(407\) 1.01335e14i 0.449771i
\(408\) −2.25793e12 1.43134e13i −0.00988735 0.0626774i
\(409\) 3.06014e14i 1.32210i 0.750343 + 0.661049i \(0.229888\pi\)
−0.750343 + 0.661049i \(0.770112\pi\)
\(410\) −5.24562e13 + 2.73826e12i −0.223607 + 0.0116725i
\(411\) −3.83797e13 + 3.83797e13i −0.161425 + 0.161425i
\(412\) 4.60578e14 4.82165e13i 1.91147 0.200106i
\(413\) −1.17662e13 1.17662e13i −0.0481848 0.0481848i
\(414\) −2.39223e14 + 2.65574e14i −0.966721 + 1.07321i
\(415\) −1.30910e14 −0.522045
\(416\) 2.72692e14 7.27660e13i 1.07315 0.286362i
\(417\) 8.45880e13 0.328519
\(418\) −4.82901e13 + 5.36094e13i −0.185093 + 0.205481i
\(419\) 4.57305e13 + 4.57305e13i 0.172993 + 0.172993i 0.788293 0.615300i \(-0.210965\pi\)
−0.615300 + 0.788293i \(0.710965\pi\)
\(420\) −4.74392e13 + 4.96626e12i −0.177119 + 0.0185421i
\(421\) −2.12318e14 + 2.12318e14i −0.782412 + 0.782412i −0.980237 0.197825i \(-0.936612\pi\)
0.197825 + 0.980237i \(0.436612\pi\)
\(422\) 5.09158e14 2.65785e13i 1.85197 0.0966744i
\(423\) 1.88299e13i 0.0676046i
\(424\) 3.64312e14 5.74702e13i 1.29110 0.203672i
\(425\) 5.78744e13i 0.202464i
\(426\) −2.84958e12 5.45889e13i −0.00984076 0.188517i
\(427\) 2.02888e14 2.02888e14i 0.691677 0.691677i
\(428\) −1.93565e14 1.56878e14i −0.651458 0.527986i
\(429\) −1.80166e13 1.80166e13i −0.0598630 0.0598630i
\(430\) −2.35962e14 2.12549e14i −0.774043 0.697241i
\(431\) −4.65703e14 −1.50829 −0.754143 0.656710i \(-0.771948\pi\)
−0.754143 + 0.656710i \(0.771948\pi\)
\(432\) 6.35440e13 9.76725e13i 0.203195 0.312329i
\(433\) 3.52107e14 1.11171 0.555855 0.831280i \(-0.312391\pi\)
0.555855 + 0.831280i \(0.312391\pi\)
\(434\) 3.17066e14 + 2.85606e14i 0.988454 + 0.890377i
\(435\) −8.22017e13 8.22017e13i −0.253040 0.253040i
\(436\) −1.02317e14 + 1.26244e14i −0.311008 + 0.383739i
\(437\) 2.42971e14 2.42971e14i 0.729300 0.729300i
\(438\) 2.09238e12 + 4.00833e13i 0.00620203 + 0.118811i
\(439\) 3.34946e14i 0.980438i 0.871599 + 0.490219i \(0.163083\pi\)
−0.871599 + 0.490219i \(0.836917\pi\)
\(440\) 1.03593e14 1.42398e14i 0.299462 0.411638i
\(441\) 1.52331e14i 0.434887i
\(442\) 1.31572e14 6.86819e12i 0.370973 0.0193651i
\(443\) −2.92942e14 + 2.92942e14i −0.815758 + 0.815758i −0.985490 0.169732i \(-0.945710\pi\)
0.169732 + 0.985490i \(0.445710\pi\)
\(444\) 8.04019e12 + 7.68022e13i 0.0221136 + 0.211236i
\(445\) −1.88244e14 1.88244e14i −0.511376 0.511376i
\(446\) 1.81759e14 2.01780e14i 0.487702 0.541424i
\(447\) 8.32231e13 0.220573
\(448\) −2.69244e14 + 8.71143e13i −0.704884 + 0.228066i
\(449\) 9.79517e13 0.253313 0.126656 0.991947i \(-0.459575\pi\)
0.126656 + 0.991947i \(0.459575\pi\)
\(450\) −1.52886e14 + 1.69727e14i −0.390571 + 0.433593i
\(451\) 1.98937e13 + 1.98937e13i 0.0502046 + 0.0502046i
\(452\) −5.70138e13 5.44613e14i −0.142141 1.35777i
\(453\) 3.05023e13 3.05023e13i 0.0751263 0.0751263i
\(454\) −6.07079e14 + 3.16901e13i −1.47720 + 0.0771109i
\(455\) 4.33691e14i 1.04260i
\(456\) −3.23457e13 + 4.44621e13i −0.0768262 + 0.105605i
\(457\) 2.00143e14i 0.469679i −0.972034 0.234840i \(-0.924544\pi\)
0.972034 0.234840i \(-0.0754565\pi\)
\(458\) −1.19174e13 2.28300e14i −0.0276327 0.529353i
\(459\) 3.84633e13 3.84633e13i 0.0881204 0.0881204i
\(460\) −5.28028e14 + 6.51511e14i −1.19533 + 1.47487i
\(461\) 1.05469e14 + 1.05469e14i 0.235923 + 0.235923i 0.815159 0.579237i \(-0.196649\pi\)
−0.579237 + 0.815159i \(0.696649\pi\)
\(462\) 1.89819e13 + 1.70984e13i 0.0419574 + 0.0377943i
\(463\) 4.68208e14 1.02269 0.511345 0.859376i \(-0.329148\pi\)
0.511345 + 0.859376i \(0.329148\pi\)
\(464\) −5.78117e14 3.76113e14i −1.24786 0.811838i
\(465\) −2.02355e14 −0.431641
\(466\) −1.91170e14 1.72201e14i −0.402992 0.363006i
\(467\) 2.01214e14 + 2.01214e14i 0.419193 + 0.419193i 0.884926 0.465732i \(-0.154209\pi\)
−0.465732 + 0.884926i \(0.654209\pi\)
\(468\) 4.04003e14 + 3.27431e14i 0.831826 + 0.674168i
\(469\) −2.72728e14 + 2.72728e14i −0.554983 + 0.554983i
\(470\) −2.30307e12 4.41193e13i −0.00463200 0.0887341i
\(471\) 1.41869e13i 0.0282015i
\(472\) 4.62415e13 7.29459e12i 0.0908554 0.0143324i
\(473\) 1.70095e14i 0.330335i
\(474\) −6.07254e13 + 3.16991e12i −0.116571 + 0.00608508i
\(475\) 1.55282e14 1.55282e14i 0.294649 0.294649i
\(476\) −1.31385e14 + 1.37543e13i −0.246438 + 0.0257988i
\(477\) 4.80524e14 + 4.80524e14i 0.890972 + 0.890972i
\(478\) −3.75493e14 + 4.16854e14i −0.688253 + 0.764065i
\(479\) −3.21690e13 −0.0582897 −0.0291449 0.999575i \(-0.509278\pi\)
−0.0291449 + 0.999575i \(0.509278\pi\)
\(480\) 6.72153e13 1.16143e14i 0.120404 0.208050i
\(481\) −7.02129e14 −1.24342
\(482\) −6.53232e13 + 7.25186e13i −0.114369 + 0.126967i
\(483\) −8.60304e13 8.60304e13i −0.148917 0.148917i
\(484\) 4.87339e14 5.10180e13i 0.834030 0.0873121i
\(485\) 9.60602e14 9.60602e14i 1.62541 1.62541i
\(486\) 3.23578e14 1.68910e13i 0.541351 0.0282590i
\(487\) 1.04866e15i 1.73470i −0.497699 0.867350i \(-0.665821\pi\)
0.497699 0.867350i \(-0.334179\pi\)
\(488\) 1.25783e14 + 7.97357e14i 0.205737 + 1.30420i
\(489\) 1.00793e14i 0.163017i
\(490\) −1.86315e13 3.56919e14i −0.0297967 0.570810i
\(491\) −1.74910e14 + 1.74910e14i −0.276609 + 0.276609i −0.831754 0.555145i \(-0.812663\pi\)
0.555145 + 0.831754i \(0.312663\pi\)
\(492\) 1.66559e13 + 1.34990e13i 0.0260471 + 0.0211103i
\(493\) −2.27662e14 2.27662e14i −0.352072 0.352072i
\(494\) −3.71447e14 3.34591e14i −0.568065 0.511701i
\(495\) 3.24461e14 0.490720
\(496\) −1.17451e15 + 2.48636e14i −1.75674 + 0.371891i
\(497\) −4.98343e14 −0.737171
\(498\) 3.96997e13 + 3.57606e13i 0.0580799 + 0.0523170i
\(499\) 7.23474e14 + 7.23474e14i 1.04681 + 1.04681i 0.998849 + 0.0479657i \(0.0152738\pi\)
0.0479657 + 0.998849i \(0.484726\pi\)
\(500\) 2.19999e14 2.71447e14i 0.314837 0.388464i
\(501\) 1.42985e14 1.42985e14i 0.202387 0.202387i
\(502\) 9.29971e11 + 1.78152e13i 0.00130196 + 0.0249414i
\(503\) 3.28578e14i 0.455004i 0.973778 + 0.227502i \(0.0730557\pi\)
−0.973778 + 0.227502i \(0.926944\pi\)
\(504\) −4.21645e14 3.06742e14i −0.577536 0.420151i
\(505\) 2.29391e14i 0.310795i
\(506\) 4.48555e14 2.34149e13i 0.601157 0.0313809i
\(507\) 2.36426e13 2.36426e13i 0.0313438 0.0313438i
\(508\) 7.23107e13 + 6.90733e14i 0.0948314 + 0.905857i
\(509\) −1.04845e14 1.04845e14i −0.136019 0.136019i 0.635819 0.771838i \(-0.280662\pi\)
−0.771838 + 0.635819i \(0.780662\pi\)
\(510\) 4.19257e13 4.65439e13i 0.0538077 0.0597347i
\(511\) 3.65922e14 0.464594
\(512\) 2.47424e14 7.56708e14i 0.310783 0.950481i
\(513\) −2.06400e14 −0.256486
\(514\) 4.35969e14 4.83992e14i 0.535992 0.595033i
\(515\) 1.41562e15 + 1.41562e15i 1.72189 + 1.72189i
\(516\) 1.34957e13 + 1.28915e14i 0.0162414 + 0.155143i
\(517\) −1.67320e13 + 1.67320e13i −0.0199227 + 0.0199227i
\(518\) 7.03045e14 3.66996e13i 0.828266 0.0432362i
\(519\) 1.70828e14i 0.199131i
\(520\) 9.86645e14 + 7.17774e14i 1.13800 + 0.827883i
\(521\) 5.46017e14i 0.623158i −0.950220 0.311579i \(-0.899142\pi\)
0.950220 0.311579i \(-0.100858\pi\)
\(522\) −6.62465e13 1.26907e15i −0.0748127 1.43317i
\(523\) −3.73217e14 + 3.73217e14i −0.417063 + 0.417063i −0.884190 0.467127i \(-0.845289\pi\)
0.467127 + 0.884190i \(0.345289\pi\)
\(524\) −1.07117e15 + 1.32166e15i −1.18450 + 1.46150i
\(525\) −5.49817e13 5.49817e13i −0.0601647 0.0601647i
\(526\) −3.49286e14 3.14629e14i −0.378233 0.340704i
\(527\) −5.60432e14 −0.600571
\(528\) −7.03146e13 + 1.48852e13i −0.0745691 + 0.0157858i
\(529\) −1.18627e15 −1.24503
\(530\) 1.18466e15 + 1.06712e15i 1.23049 + 1.10840i
\(531\) 6.09921e13 + 6.09921e13i 0.0626980 + 0.0626980i
\(532\) 3.89420e14 + 3.15613e14i 0.396191 + 0.321100i
\(533\) −1.37839e14 + 1.37839e14i −0.138794 + 0.138794i
\(534\) 5.66427e12 + 1.08509e14i 0.00564504 + 0.108141i
\(535\) 1.07711e15i 1.06246i
\(536\) −1.69081e14 1.07183e15i −0.165078 1.04645i
\(537\) 7.52607e10i 7.27294e-5i
\(538\) 1.91701e15 1.00070e14i 1.83368 0.0957195i
\(539\) −1.35359e14 + 1.35359e14i −0.128159 + 0.128159i
\(540\) 5.01000e14 5.24482e13i 0.469539 0.0491546i
\(541\) −4.09581e14 4.09581e14i −0.379974 0.379974i 0.491118 0.871093i \(-0.336588\pi\)
−0.871093 + 0.491118i \(0.836588\pi\)
\(542\) −7.41792e14 + 8.23501e14i −0.681218 + 0.756255i
\(543\) 9.93226e13 0.0902919
\(544\) 1.86156e14 3.21665e14i 0.167526 0.289474i
\(545\) −7.02497e14 −0.625841
\(546\) −1.18471e14 + 1.31521e14i −0.104485 + 0.115994i
\(547\) −1.12176e15 1.12176e15i −0.979419 0.979419i 0.0203735 0.999792i \(-0.493514\pi\)
−0.999792 + 0.0203735i \(0.993514\pi\)
\(548\) −1.38453e15 + 1.44942e14i −1.19677 + 0.125286i
\(549\) −1.05171e15 + 1.05171e15i −0.900008 + 0.900008i
\(550\) 2.86670e14 1.49644e13i 0.242877 0.0126784i
\(551\) 1.22167e15i 1.02475i
\(552\) 3.38103e14 5.33356e13i 0.280791 0.0442948i
\(553\) 5.54363e14i 0.455834i
\(554\) −3.97362e13 7.61218e14i −0.0323506 0.619734i
\(555\) −2.36057e14 + 2.36057e14i −0.190285 + 0.190285i
\(556\) 1.68546e15 + 1.36601e15i 1.34526 + 1.09029i
\(557\) −4.15223e13 4.15223e13i −0.0328154 0.0328154i 0.690509 0.723324i \(-0.257387\pi\)
−0.723324 + 0.690509i \(0.757387\pi\)
\(558\) −1.64357e15 1.48049e15i −1.28617 1.15856i
\(559\) −1.17855e15 −0.913234
\(560\) −1.02545e15 6.67140e14i −0.786829 0.511897i
\(561\) −3.35515e13 −0.0254927
\(562\) −5.96855e14 5.37634e14i −0.449075 0.404517i
\(563\) −3.90578e13 3.90578e13i −0.0291013 0.0291013i 0.692406 0.721508i \(-0.256551\pi\)
−0.721508 + 0.692406i \(0.756551\pi\)
\(564\) −1.13536e13 + 1.40087e13i −0.00837722 + 0.0103363i
\(565\) 1.67390e15 1.67390e15i 1.22311 1.22311i
\(566\) 2.18959e13 + 4.19455e14i 0.0158443 + 0.303526i
\(567\) 9.23525e14i 0.661823i
\(568\) 8.24776e14 1.13373e15i 0.585356 0.804625i
\(569\) 1.33180e14i 0.0936100i −0.998904 0.0468050i \(-0.985096\pi\)
0.998904 0.0468050i \(-0.0149039\pi\)
\(570\) −2.37371e14 + 1.23910e13i −0.165240 + 0.00862567i
\(571\) 1.12590e15 1.12590e15i 0.776252 0.776252i −0.202939 0.979191i \(-0.565049\pi\)
0.979191 + 0.202939i \(0.0650493\pi\)
\(572\) −6.80404e13 6.49942e14i −0.0464610 0.443809i
\(573\) −2.97676e14 2.97676e14i −0.201323 0.201323i
\(574\) 1.30814e14 1.45223e14i 0.0876270 0.0972793i
\(575\) −1.36708e15 −0.907027
\(576\) 1.39568e15 4.51573e14i 0.917193 0.296759i
\(577\) 1.08744e15 0.707846 0.353923 0.935275i \(-0.384848\pi\)
0.353923 + 0.935275i \(0.384848\pi\)
\(578\) −9.21923e14 + 1.02347e15i −0.594418 + 0.659894i
\(579\) 2.49962e14 + 2.49962e14i 0.159640 + 0.159640i
\(580\) −3.10437e14 2.96539e15i −0.196390 1.87598i
\(581\) 3.44439e14 3.44439e14i 0.215846 0.215846i
\(582\) −5.53719e14 + 2.89046e13i −0.343727 + 0.0179428i
\(583\) 8.53973e14i 0.525130i
\(584\) −6.05614e14 + 8.32471e14i −0.368914 + 0.507106i
\(585\) 2.24811e15i 1.35663i
\(586\) 4.29073e13 + 8.21966e14i 0.0256504 + 0.491379i
\(587\) −1.48568e15 + 1.48568e15i −0.879865 + 0.879865i −0.993520 0.113655i \(-0.963744\pi\)
0.113655 + 0.993520i \(0.463744\pi\)
\(588\) −9.18493e13 + 1.13329e14i −0.0538890 + 0.0664913i
\(589\) 1.50368e15 + 1.50368e15i 0.874022 + 0.874022i
\(590\) 1.50367e14 + 1.35447e14i 0.0865898 + 0.0779981i
\(591\) 1.75377e14 0.100055
\(592\) −1.08007e15 + 1.66017e15i −0.610498 + 0.938387i
\(593\) 8.96247e13 0.0501911 0.0250956 0.999685i \(-0.492011\pi\)
0.0250956 + 0.999685i \(0.492011\pi\)
\(594\) −2.00466e14 1.80575e14i −0.111228 0.100192i
\(595\) −4.03821e14 4.03821e14i −0.221996 0.221996i
\(596\) 1.65826e15 + 1.34397e15i 0.903232 + 0.732041i
\(597\) 5.13650e13 5.13650e13i 0.0277209 0.0277209i
\(598\) 1.62237e14 + 3.10793e15i 0.0867546 + 1.66194i
\(599\) 1.01799e15i 0.539382i 0.962947 + 0.269691i \(0.0869215\pi\)
−0.962947 + 0.269691i \(0.913078\pi\)
\(600\) 2.16080e14 3.40866e13i 0.113444 0.0178958i
\(601\) 1.26276e15i 0.656918i −0.944518 0.328459i \(-0.893471\pi\)
0.944518 0.328459i \(-0.106529\pi\)
\(602\) 1.18009e15 6.16015e13i 0.608321 0.0317549i
\(603\) 1.41374e15 1.41374e15i 0.722143 0.722143i
\(604\) 1.10036e15 1.15193e14i 0.556967 0.0583072i
\(605\) 1.49787e15 + 1.49787e15i 0.751310 + 0.751310i
\(606\) 6.26627e13 6.95652e13i 0.0311466 0.0345774i
\(607\) 1.97399e15 0.972315 0.486158 0.873871i \(-0.338398\pi\)
0.486158 + 0.873871i \(0.338398\pi\)
\(608\) −1.36252e15 + 3.63580e14i −0.665080 + 0.177472i
\(609\) 4.32565e14 0.209245
\(610\) −2.33556e15 + 2.59283e15i −1.11964 + 1.24297i
\(611\) −1.15932e14 1.15932e14i −0.0550778 0.0550778i
\(612\) 6.81058e14 7.12978e13i 0.320665 0.0335694i
\(613\) 5.25981e13 5.25981e13i 0.0245436 0.0245436i −0.694729 0.719272i \(-0.744475\pi\)
0.719272 + 0.694729i \(0.244475\pi\)
\(614\) 1.59167e15 8.30866e13i 0.736084 0.0384242i
\(615\) 9.26830e13i 0.0424802i
\(616\) 1.02101e14 + 6.47234e14i 0.0463806 + 0.294013i
\(617\) 1.26267e15i 0.568490i −0.958752 0.284245i \(-0.908257\pi\)
0.958752 0.284245i \(-0.0917429\pi\)
\(618\) −4.25960e13 8.16002e14i −0.0190078 0.364129i
\(619\) −3.09325e14 + 3.09325e14i −0.136810 + 0.136810i −0.772195 0.635386i \(-0.780841\pi\)
0.635386 + 0.772195i \(0.280841\pi\)
\(620\) −4.03203e15 3.26783e15i −1.76754 1.43254i
\(621\) 9.08559e14 + 9.08559e14i 0.394775 + 0.394775i
\(622\) 1.37300e15 + 1.23677e15i 0.591322 + 0.532650i
\(623\) 9.90582e14 0.422870
\(624\) −1.03136e14 4.87193e14i −0.0436410 0.206151i
\(625\) 2.95377e15 1.23890
\(626\) −3.37558e14 3.04065e14i −0.140343 0.126417i
\(627\) 9.00213e13 + 9.00213e13i 0.0371000 + 0.0371000i
\(628\) −2.29104e14 + 2.82681e14i −0.0935953 + 0.115483i
\(629\) −6.53770e14 + 6.53770e14i −0.264757 + 0.264757i
\(630\) −1.17506e14 2.25105e15i −0.0471725 0.903673i
\(631\) 3.14311e15i 1.25083i −0.780293 0.625414i \(-0.784930\pi\)
0.780293 0.625414i \(-0.215070\pi\)
\(632\) −1.26118e15 9.17491e14i −0.497544 0.361958i
\(633\) 8.99613e14i 0.351832i
\(634\) −4.29017e15 + 2.23950e14i −1.66335 + 0.0868282i
\(635\) −2.12301e15 + 2.12301e15i −0.816013 + 0.816013i
\(636\) −6.77562e13 6.47227e14i −0.0258187 0.246628i
\(637\) −9.37872e14 9.37872e14i −0.354305 0.354305i
\(638\) −1.06881e15 + 1.18654e15i −0.400302 + 0.444395i
\(639\) 2.58325e15 0.959206
\(640\) 3.21490e15 1.22876e15i 1.18353 0.452352i
\(641\) 4.51734e15 1.64878 0.824392 0.566019i \(-0.191517\pi\)
0.824392 + 0.566019i \(0.191517\pi\)
\(642\) −2.94234e14 + 3.26644e14i −0.106476 + 0.118204i
\(643\) −1.65387e15 1.65387e15i −0.593392 0.593392i 0.345154 0.938546i \(-0.387827\pi\)
−0.938546 + 0.345154i \(0.887827\pi\)
\(644\) −3.24897e14 3.10351e15i −0.115577 1.10403i
\(645\) −3.96229e14 + 3.96229e14i −0.139755 + 0.139755i
\(646\) −6.57410e14 + 3.43173e13i −0.229910 + 0.0120015i
\(647\) 3.33623e15i 1.15687i 0.815730 + 0.578433i \(0.196335\pi\)
−0.815730 + 0.578433i \(0.803665\pi\)
\(648\) 2.10102e15 + 1.52847e15i 0.722382 + 0.525525i
\(649\) 1.08393e14i 0.0369536i
\(650\) 1.03685e14 + 1.98627e15i 0.0350503 + 0.671450i
\(651\) 5.32420e14 5.32420e14i 0.178467 0.178467i
\(652\) −1.62771e15 + 2.00836e15i −0.541022 + 0.667543i
\(653\) −2.00196e15 2.00196e15i −0.659832 0.659832i 0.295508 0.955340i \(-0.404511\pi\)
−0.955340 + 0.295508i \(0.904511\pi\)
\(654\) 2.13039e14 + 1.91901e14i 0.0696276 + 0.0627190i
\(655\) −7.35452e15 −2.38356
\(656\) 1.13881e14 + 5.37951e14i 0.0365999 + 0.172891i
\(657\) −1.89682e15 −0.604528
\(658\) 1.22143e14 + 1.10024e14i 0.0386034 + 0.0347731i
\(659\) −4.02032e15 4.02032e15i −1.26006 1.26006i −0.951064 0.308994i \(-0.900008\pi\)
−0.308994 0.951064i \(-0.599992\pi\)
\(660\) −2.41387e14 1.95636e14i −0.0750277 0.0608075i
\(661\) −2.33815e15 + 2.33815e15i −0.720716 + 0.720716i −0.968751 0.248035i \(-0.920215\pi\)
0.248035 + 0.968751i \(0.420215\pi\)
\(662\) −1.07409e14 2.05762e15i −0.0328340 0.628994i
\(663\) 2.32471e14i 0.0704764i
\(664\) 2.13539e14 + 1.35366e15i 0.0642027 + 0.406991i
\(665\) 2.16696e15i 0.646149i
\(666\) −3.64436e15 + 1.90239e14i −1.07774 + 0.0562588i
\(667\) 5.37770e15 5.37770e15i 1.57726 1.57726i
\(668\) 5.15810e15 5.39986e14i 1.50044 0.157077i
\(669\) −3.38831e14 3.38831e14i −0.0977552 0.0977552i
\(670\) 3.13953e15 3.48536e15i 0.898367 0.997324i
\(671\) 1.86906e15 0.530456
\(672\) 1.28736e14 + 4.82438e14i 0.0362383 + 0.135803i
\(673\) −2.38810e15 −0.666761 −0.333380 0.942792i \(-0.608189\pi\)
−0.333380 + 0.942792i \(0.608189\pi\)
\(674\) 3.56507e15 3.95777e15i 0.987277 1.09603i
\(675\) 5.80656e14 + 5.80656e14i 0.159495 + 0.159495i
\(676\) 8.52897e14 8.92872e13i 0.232375 0.0243266i
\(677\) −2.44961e15 + 2.44961e15i −0.662001 + 0.662001i −0.955851 0.293851i \(-0.905063\pi\)
0.293851 + 0.955851i \(0.405063\pi\)
\(678\) −9.64887e14 + 5.03679e13i −0.258650 + 0.0135018i
\(679\) 5.05492e15i 1.34410i
\(680\) 1.58703e15 2.50354e14i 0.418587 0.0660320i
\(681\) 1.07263e15i 0.280634i
\(682\) 1.44909e14 + 2.77599e15i 0.0376081 + 0.720450i
\(683\) −1.97634e15 + 1.97634e15i −0.508801 + 0.508801i −0.914158 0.405358i \(-0.867147\pi\)
0.405358 + 0.914158i \(0.367147\pi\)
\(684\) −2.01863e15 1.63603e15i −0.515523 0.417815i
\(685\) −4.25545e15 4.25545e15i −1.07807 1.07807i
\(686\) 3.17846e15 + 2.86309e15i 0.798793 + 0.719535i
\(687\) −4.03375e14 −0.100565
\(688\) −1.81294e15 + 2.78665e15i −0.448381 + 0.689200i
\(689\) 5.91698e15 1.45176
\(690\) 1.09943e15 + 9.90346e14i 0.267608 + 0.241055i
\(691\) 7.91531e14 + 7.91531e14i 0.191134 + 0.191134i 0.796186 0.605052i \(-0.206848\pi\)
−0.605052 + 0.796186i \(0.706848\pi\)
\(692\) −2.75871e15 + 3.40385e15i −0.660879 + 0.815430i
\(693\) −8.53695e14 + 8.53695e14i −0.202894 + 0.202894i
\(694\) −2.09034e14 4.00442e15i −0.0492879 0.944198i
\(695\) 9.37890e15i 2.19399i
\(696\) −7.15910e14 + 9.84084e14i −0.166153 + 0.228392i
\(697\) 2.56690e14i 0.0591056i
\(698\) 2.79280e15 1.45786e14i 0.638020 0.0333052i
\(699\) −3.21014e14 + 3.21014e14i −0.0727611 + 0.0727611i
\(700\) −2.07640e14 1.98344e15i −0.0466952 0.446046i
\(701\) −1.40321e15 1.40321e15i −0.313092 0.313092i 0.533014 0.846106i \(-0.321059\pi\)
−0.846106 + 0.533014i \(0.821059\pi\)
\(702\) 1.25116e15 1.38898e15i 0.276987 0.307497i
\(703\) 3.50823e15 0.770609
\(704\) −1.64144e15 8.38916e14i −0.357746 0.182839i
\(705\) −7.79529e13 −0.0168575
\(706\) 3.20294e15 3.55575e15i 0.687263 0.762966i
\(707\) −6.03556e14 6.03556e14i −0.128502 0.128502i
\(708\) −8.60018e12 8.21514e13i −0.00181687 0.0173553i
\(709\) −2.29645e15 + 2.29645e15i −0.481397 + 0.481397i −0.905578 0.424181i \(-0.860562\pi\)
0.424181 + 0.905578i \(0.360562\pi\)
\(710\) 6.05267e15 3.15954e14i 1.25900 0.0657209i
\(711\) 2.87364e15i 0.593130i
\(712\) −1.63945e15 + 2.25357e15i −0.335783 + 0.461564i
\(713\) 1.32382e16i 2.69053i
\(714\) 1.21510e13 + 2.32774e14i 0.00245060 + 0.0469455i
\(715\) 1.99764e15 1.99764e15i 0.399792 0.399792i
\(716\) −1.21539e12 + 1.49961e12i −0.000241375 + 0.000297822i
\(717\) 6.99985e14 + 6.99985e14i 0.137954 + 0.137954i
\(718\) 8.72840e14 + 7.86234e14i 0.170706 + 0.153769i
\(719\) 6.67854e15 1.29620 0.648101 0.761555i \(-0.275564\pi\)
0.648101 + 0.761555i \(0.275564\pi\)
\(720\) 5.31560e15 + 3.45824e15i 1.02382 + 0.666079i
\(721\) −7.44931e15 −1.42388
\(722\) −2.06099e15 1.85649e15i −0.390949 0.352158i
\(723\) 1.21774e14 + 1.21774e14i 0.0229242 + 0.0229242i
\(724\) 1.97905e15 + 1.60396e15i 0.369739 + 0.299662i
\(725\) 3.43686e15 3.43686e15i 0.637241 0.637241i
\(726\) −4.50710e13 8.63415e14i −0.00829365 0.158880i
\(727\) 5.13449e15i 0.937687i 0.883281 + 0.468844i \(0.155329\pi\)
−0.883281 + 0.468844i \(0.844671\pi\)
\(728\) −4.48453e15 + 7.07434e14i −0.812820 + 0.128222i
\(729\) 4.39428e15i 0.790471i
\(730\) −4.44433e15 + 2.31998e14i −0.793471 + 0.0414198i
\(731\) −1.09738e15 + 1.09738e15i −0.194451 + 0.194451i
\(732\) 1.41656e15 1.48296e14i 0.249129 0.0260806i
\(733\) 2.05664e14 + 2.05664e14i 0.0358993 + 0.0358993i 0.724829 0.688929i \(-0.241919\pi\)
−0.688929 + 0.724829i \(0.741919\pi\)
\(734\) 3.41939e15 3.79605e15i 0.592408 0.657663i
\(735\) −6.30628e14 −0.108441
\(736\) 7.59819e15 + 4.39728e15i 1.29683 + 0.750509i
\(737\) −2.51245e15 −0.425624
\(738\) −6.78096e14 + 7.52790e14i −0.114020 + 0.126580i
\(739\) 3.42273e15 + 3.42273e15i 0.571252 + 0.571252i 0.932478 0.361226i \(-0.117642\pi\)
−0.361226 + 0.932478i \(0.617642\pi\)
\(740\) −8.51563e15 + 8.91475e14i −1.41073 + 0.147685i
\(741\) −6.23737e14 + 6.23737e14i −0.102565 + 0.102565i
\(742\) −5.92470e15 + 3.09274e14i −0.967041 + 0.0504803i
\(743\) 1.18217e16i 1.91533i −0.287891 0.957663i \(-0.592954\pi\)
0.287891 0.957663i \(-0.407046\pi\)
\(744\) 3.30080e14 + 2.09243e15i 0.0530846 + 0.336511i
\(745\) 9.22756e15i 1.47308i
\(746\) 1.42609e14 + 2.73193e15i 0.0225987 + 0.432918i
\(747\) −1.78546e15 + 1.78546e15i −0.280858 + 0.280858i
\(748\) −6.68532e14 5.41823e14i −0.104391 0.0846056i
\(749\) 2.83401e15 + 2.83401e15i 0.439289 + 0.439289i
\(750\) −4.58071e14 4.12620e14i −0.0704849 0.0634912i
\(751\) 1.82477e15 0.278734 0.139367 0.990241i \(-0.455493\pi\)
0.139367 + 0.990241i \(0.455493\pi\)
\(752\) −4.52454e14 + 9.57818e13i −0.0686083 + 0.0145240i
\(753\) 3.14771e13 0.00473830
\(754\) −8.22127e15 7.40554e15i −1.22856 1.10666i
\(755\) 3.38201e15 + 3.38201e15i 0.501726 + 0.501726i
\(756\) −1.18019e15 + 1.45619e15i −0.173813 + 0.214461i
\(757\) −3.85298e15 + 3.85298e15i −0.563339 + 0.563339i −0.930254 0.366916i \(-0.880414\pi\)
0.366916 + 0.930254i \(0.380414\pi\)
\(758\) 3.93708e14 + 7.54218e15i 0.0571471 + 1.09475i
\(759\) 7.92536e14i 0.114206i
\(760\) −4.92984e15 3.58640e15i −0.705274 0.513079i
\(761\)