Properties

Label 16.12.e.a.13.10
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 13.10
Character \(\chi\) = 16.13
Dual form 16.12.e.a.5.10

$q$-expansion

\(f(q)\) \(=\) \(q+(-5.89788 + 44.8689i) q^{2} +(137.041 + 137.041i) q^{3} +(-1978.43 - 529.262i) q^{4} +(3899.66 - 3899.66i) q^{5} +(-6957.14 + 5340.63i) q^{6} -37938.5i q^{7} +(35416.0 - 85648.4i) q^{8} -139586. i q^{9} +O(q^{10})\) \(q+(-5.89788 + 44.8689i) q^{2} +(137.041 + 137.041i) q^{3} +(-1978.43 - 529.262i) q^{4} +(3899.66 - 3899.66i) q^{5} +(-6957.14 + 5340.63i) q^{6} -37938.5i q^{7} +(35416.0 - 85648.4i) q^{8} -139586. i q^{9} +(151974. + 197973. i) q^{10} +(-68184.4 + 68184.4i) q^{11} +(-198596. - 343657. i) q^{12} +(-109818. - 109818. i) q^{13} +(1.70226e6 + 223757. i) q^{14} +1.06883e6 q^{15} +(3.63407e6 + 2.09422e6i) q^{16} +8.85033e6 q^{17} +(6.26308e6 + 823264. i) q^{18} +(-712421. - 712421. i) q^{19} +(-9.77915e6 + 5.65126e6i) q^{20} +(5.19914e6 - 5.19914e6i) q^{21} +(-2.65721e6 - 3.46150e6i) q^{22} -2.69728e7i q^{23} +(1.65908e7 - 6.88392e6i) q^{24} +1.84134e7i q^{25} +(5.57512e6 - 4.27973e6i) q^{26} +(4.34056e7 - 4.34056e7i) q^{27} +(-2.00794e7 + 7.50587e7i) q^{28} +(-1.10441e8 - 1.10441e8i) q^{29} +(-6.30383e6 + 4.79572e7i) q^{30} -1.15699e8 q^{31} +(-1.15398e8 + 1.50705e8i) q^{32} -1.86882e7 q^{33} +(-5.21982e7 + 3.97104e8i) q^{34} +(-1.47947e8 - 1.47947e8i) q^{35} +(-7.38778e7 + 2.76162e8i) q^{36} +(3.15546e8 - 3.15546e8i) q^{37} +(3.61673e7 - 2.77637e7i) q^{38} -3.00993e7i q^{39} +(-1.95889e8 - 4.72110e8i) q^{40} -8.66621e8i q^{41} +(2.02616e8 + 2.63943e8i) q^{42} +(-3.13940e8 + 3.13940e8i) q^{43} +(1.70986e8 - 9.88107e7i) q^{44} +(-5.44339e8 - 5.44339e8i) q^{45} +(1.21024e9 + 1.59082e8i) q^{46} +1.93131e9 q^{47} +(2.11023e8 + 7.85012e8i) q^{48} +5.37998e8 q^{49} +(-8.26189e8 - 1.08600e8i) q^{50} +(1.21286e9 + 1.21286e9i) q^{51} +(1.59145e8 + 2.75390e8i) q^{52} +(8.24466e8 - 8.24466e8i) q^{53} +(1.69156e9 + 2.20356e9i) q^{54} +5.31792e8i q^{55} +(-3.24937e9 - 1.34363e9i) q^{56} -1.95262e8i q^{57} +(5.60671e9 - 4.30398e9i) q^{58} +(-7.47540e9 + 7.47540e9i) q^{59} +(-2.11460e9 - 5.65691e8i) q^{60} +(-6.44620e8 - 6.44620e8i) q^{61} +(6.82382e8 - 5.19130e9i) q^{62} -5.29570e9 q^{63} +(-6.08136e9 - 6.06664e9i) q^{64} -8.56508e8 q^{65} +(1.10221e8 - 8.38517e8i) q^{66} +(5.39064e9 + 5.39064e9i) q^{67} +(-1.75098e10 - 4.68415e9i) q^{68} +(3.69638e9 - 3.69638e9i) q^{69} +(7.51080e9 - 5.76565e9i) q^{70} +2.90073e10i q^{71} +(-1.19553e10 - 4.94358e9i) q^{72} -1.12038e10i q^{73} +(1.22971e10 + 1.60192e10i) q^{74} +(-2.52340e9 + 2.52340e9i) q^{75} +(1.03242e9 + 1.78653e9i) q^{76} +(2.58681e9 + 2.58681e9i) q^{77} +(1.35052e9 + 1.77522e8i) q^{78} -2.03542e7 q^{79} +(2.23384e10 - 6.00489e9i) q^{80} -1.28306e10 q^{81} +(3.88843e10 + 5.11123e9i) q^{82} +(2.10772e10 + 2.10772e10i) q^{83} +(-1.30378e10 + 7.53443e9i) q^{84} +(3.45133e10 - 3.45133e10i) q^{85} +(-1.22346e10 - 1.59377e10i) q^{86} -3.02699e10i q^{87} +(3.42507e9 + 8.25470e9i) q^{88} -7.01544e10i q^{89} +(2.76343e10 - 2.12134e10i) q^{90} +(-4.16634e9 + 4.16634e9i) q^{91} +(-1.42757e10 + 5.33637e10i) q^{92} +(-1.58556e10 - 1.58556e10i) q^{93} +(-1.13906e10 + 8.66558e10i) q^{94} -5.55640e9 q^{95} +(-3.64672e10 + 4.83845e9i) q^{96} -3.85844e10 q^{97} +(-3.17305e9 + 2.41393e10i) q^{98} +(9.51762e9 + 9.51762e9i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.89788 + 44.8689i −0.130326 + 0.991471i
\(3\) 137.041 + 137.041i 0.325600 + 0.325600i 0.850911 0.525310i \(-0.176051\pi\)
−0.525310 + 0.850911i \(0.676051\pi\)
\(4\) −1978.43 529.262i −0.966030 0.258429i
\(5\) 3899.66 3899.66i 0.558074 0.558074i −0.370685 0.928759i \(-0.620877\pi\)
0.928759 + 0.370685i \(0.120877\pi\)
\(6\) −6957.14 + 5340.63i −0.365257 + 0.280389i
\(7\) 37938.5i 0.853180i −0.904445 0.426590i \(-0.859715\pi\)
0.904445 0.426590i \(-0.140285\pi\)
\(8\) 35416.0 85648.4i 0.382124 0.924111i
\(9\) 139586.i 0.787969i
\(10\) 151974. + 197973.i 0.480583 + 0.626046i
\(11\) −68184.4 + 68184.4i −0.127651 + 0.127651i −0.768046 0.640395i \(-0.778771\pi\)
0.640395 + 0.768046i \(0.278771\pi\)
\(12\) −198596. 343657.i −0.230395 0.398684i
\(13\) −109818. 109818.i −0.0820325 0.0820325i 0.664900 0.746932i \(-0.268474\pi\)
−0.746932 + 0.664900i \(0.768474\pi\)
\(14\) 1.70226e6 + 223757.i 0.845904 + 0.111192i
\(15\) 1.06883e6 0.363418
\(16\) 3.63407e6 + 2.09422e6i 0.866429 + 0.499300i
\(17\) 8.85033e6 1.51179 0.755893 0.654695i \(-0.227203\pi\)
0.755893 + 0.654695i \(0.227203\pi\)
\(18\) 6.26308e6 + 823264.i 0.781249 + 0.102693i
\(19\) −712421. 712421.i −0.0660073 0.0660073i 0.673333 0.739340i \(-0.264862\pi\)
−0.739340 + 0.673333i \(0.764862\pi\)
\(20\) −9.77915e6 + 5.65126e6i −0.683339 + 0.394894i
\(21\) 5.19914e6 5.19914e6i 0.277796 0.277796i
\(22\) −2.65721e6 3.46150e6i −0.109926 0.143199i
\(23\) 2.69728e7i 0.873821i −0.899505 0.436910i \(-0.856073\pi\)
0.899505 0.436910i \(-0.143927\pi\)
\(24\) 1.65908e7 6.88392e6i 0.425310 0.176471i
\(25\) 1.84134e7i 0.377107i
\(26\) 5.57512e6 4.27973e6i 0.0920239 0.0706419i
\(27\) 4.34056e7 4.34056e7i 0.582163 0.582163i
\(28\) −2.00794e7 + 7.50587e7i −0.220486 + 0.824198i
\(29\) −1.10441e8 1.10441e8i −0.999862 0.999862i 0.000137853 1.00000i \(-0.499956\pi\)
−1.00000 0.000137853i \(0.999956\pi\)
\(30\) −6.30383e6 + 4.79572e7i −0.0473628 + 0.360318i
\(31\) −1.15699e8 −0.725842 −0.362921 0.931820i \(-0.618221\pi\)
−0.362921 + 0.931820i \(0.618221\pi\)
\(32\) −1.15398e8 + 1.50705e8i −0.607960 + 0.793968i
\(33\) −1.86882e7 −0.0831266
\(34\) −5.21982e7 + 3.97104e8i −0.197025 + 1.49889i
\(35\) −1.47947e8 1.47947e8i −0.476138 0.476138i
\(36\) −7.38778e7 + 2.76162e8i −0.203634 + 0.761202i
\(37\) 3.15546e8 3.15546e8i 0.748088 0.748088i −0.226032 0.974120i \(-0.572575\pi\)
0.974120 + 0.226032i \(0.0725754\pi\)
\(38\) 3.61673e7 2.77637e7i 0.0740468 0.0568419i
\(39\) 3.00993e7i 0.0534196i
\(40\) −1.95889e8 4.72110e8i −0.302469 0.728976i
\(41\) 8.66621e8i 1.16820i −0.811681 0.584101i \(-0.801447\pi\)
0.811681 0.584101i \(-0.198553\pi\)
\(42\) 2.02616e8 + 2.63943e8i 0.239222 + 0.311630i
\(43\) −3.13940e8 + 3.13940e8i −0.325665 + 0.325665i −0.850935 0.525271i \(-0.823964\pi\)
0.525271 + 0.850935i \(0.323964\pi\)
\(44\) 1.70986e8 9.88107e7i 0.156304 0.0903263i
\(45\) −5.44339e8 5.44339e8i −0.439745 0.439745i
\(46\) 1.21024e9 + 1.59082e8i 0.866368 + 0.113882i
\(47\) 1.93131e9 1.22833 0.614164 0.789179i \(-0.289493\pi\)
0.614164 + 0.789179i \(0.289493\pi\)
\(48\) 2.11023e8 + 7.85012e8i 0.119537 + 0.444682i
\(49\) 5.37998e8 0.272083
\(50\) −8.26189e8 1.08600e8i −0.373890 0.0491468i
\(51\) 1.21286e9 + 1.21286e9i 0.492238 + 0.492238i
\(52\) 1.59145e8 + 2.75390e8i 0.0580463 + 0.100446i
\(53\) 8.24466e8 8.24466e8i 0.270804 0.270804i −0.558620 0.829424i \(-0.688669\pi\)
0.829424 + 0.558620i \(0.188669\pi\)
\(54\) 1.69156e9 + 2.20356e9i 0.501327 + 0.653069i
\(55\) 5.31792e8i 0.142478i
\(56\) −3.24937e9 1.34363e9i −0.788434 0.326020i
\(57\) 1.95262e8i 0.0429840i
\(58\) 5.60671e9 4.30398e9i 1.12164 0.861026i
\(59\) −7.47540e9 + 7.47540e9i −1.36128 + 1.36128i −0.488998 + 0.872285i \(0.662637\pi\)
−0.872285 + 0.488998i \(0.837363\pi\)
\(60\) −2.11460e9 5.65691e8i −0.351073 0.0939177i
\(61\) −6.44620e8 6.44620e8i −0.0977215 0.0977215i 0.656556 0.754277i \(-0.272013\pi\)
−0.754277 + 0.656556i \(0.772013\pi\)
\(62\) 6.82382e8 5.19130e9i 0.0945961 0.719651i
\(63\) −5.29570e9 −0.672280
\(64\) −6.08136e9 6.06664e9i −0.707963 0.706250i
\(65\) −8.56508e8 −0.0915605
\(66\) 1.10221e8 8.38517e8i 0.0108336 0.0824176i
\(67\) 5.39064e9 + 5.39064e9i 0.487786 + 0.487786i 0.907607 0.419821i \(-0.137907\pi\)
−0.419821 + 0.907607i \(0.637907\pi\)
\(68\) −1.75098e10 4.68415e9i −1.46043 0.390689i
\(69\) 3.69638e9 3.69638e9i 0.284516 0.284516i
\(70\) 7.51080e9 5.76565e9i 0.534130 0.410024i
\(71\) 2.90073e10i 1.90804i 0.299747 + 0.954019i \(0.403098\pi\)
−0.299747 + 0.954019i \(0.596902\pi\)
\(72\) −1.19553e10 4.94358e9i −0.728171 0.301102i
\(73\) 1.12038e10i 0.632540i −0.948669 0.316270i \(-0.897569\pi\)
0.948669 0.316270i \(-0.102431\pi\)
\(74\) 1.22971e10 + 1.60192e10i 0.644212 + 0.839203i
\(75\) −2.52340e9 + 2.52340e9i −0.122786 + 0.122786i
\(76\) 1.03242e9 + 1.78653e9i 0.0467068 + 0.0808232i
\(77\) 2.58681e9 + 2.58681e9i 0.108910 + 0.108910i
\(78\) 1.35052e9 + 1.77522e8i 0.0529640 + 0.00696197i
\(79\) −2.03542e7 −0.000744226 −0.000372113 1.00000i \(-0.500118\pi\)
−0.000372113 1.00000i \(0.500118\pi\)
\(80\) 2.23384e10 6.00489e9i 0.762178 0.204885i
\(81\) −1.28306e10 −0.408864
\(82\) 3.88843e10 + 5.11123e9i 1.15824 + 0.152247i
\(83\) 2.10772e10 + 2.10772e10i 0.587330 + 0.587330i 0.936908 0.349577i \(-0.113675\pi\)
−0.349577 + 0.936908i \(0.613675\pi\)
\(84\) −1.30378e10 + 7.53443e9i −0.340149 + 0.196569i
\(85\) 3.45133e10 3.45133e10i 0.843689 0.843689i
\(86\) −1.22346e10 1.59377e10i −0.280445 0.365330i
\(87\) 3.02699e10i 0.651111i
\(88\) 3.42507e9 + 8.25470e9i 0.0691854 + 0.166743i
\(89\) 7.01544e10i 1.33171i −0.746081 0.665855i \(-0.768067\pi\)
0.746081 0.665855i \(-0.231933\pi\)
\(90\) 2.76343e10 2.12134e10i 0.493305 0.378684i
\(91\) −4.16634e9 + 4.16634e9i −0.0699886 + 0.0699886i
\(92\) −1.42757e10 + 5.33637e10i −0.225821 + 0.844137i
\(93\) −1.58556e10 1.58556e10i −0.236334 0.236334i
\(94\) −1.13906e10 + 8.66558e10i −0.160083 + 1.21785i
\(95\) −5.55640e9 −0.0736739
\(96\) −3.64672e10 + 4.83845e9i −0.456468 + 0.0605641i
\(97\) −3.85844e10 −0.456213 −0.228107 0.973636i \(-0.573253\pi\)
−0.228107 + 0.973636i \(0.573253\pi\)
\(98\) −3.17305e9 + 2.41393e10i −0.0354595 + 0.269763i
\(99\) 9.51762e9 + 9.51762e9i 0.100585 + 0.100585i
\(100\) 9.74553e9 3.64296e10i 0.0974553 0.364296i
\(101\) 7.64448e9 7.64448e9i 0.0723736 0.0723736i −0.669993 0.742367i \(-0.733703\pi\)
0.742367 + 0.669993i \(0.233703\pi\)
\(102\) −6.15730e10 + 4.72664e10i −0.552191 + 0.423888i
\(103\) 1.42256e11i 1.20911i −0.796562 0.604557i \(-0.793350\pi\)
0.796562 0.604557i \(-0.206650\pi\)
\(104\) −1.32951e10 + 5.51644e9i −0.107154 + 0.0444606i
\(105\) 4.05498e10i 0.310061i
\(106\) 3.21303e10 + 4.18555e10i 0.233202 + 0.303787i
\(107\) −1.42681e11 + 1.42681e11i −0.983455 + 0.983455i −0.999865 0.0164100i \(-0.994776\pi\)
0.0164100 + 0.999865i \(0.494776\pi\)
\(108\) −1.08848e11 + 6.29019e10i −0.712835 + 0.411939i
\(109\) 1.77386e11 + 1.77386e11i 1.10427 + 1.10427i 0.993890 + 0.110376i \(0.0352056\pi\)
0.110376 + 0.993890i \(0.464794\pi\)
\(110\) −2.38609e10 3.13645e9i −0.141263 0.0185686i
\(111\) 8.64856e10 0.487155
\(112\) 7.94515e10 1.37871e11i 0.425993 0.739220i
\(113\) −2.63766e11 −1.34675 −0.673376 0.739300i \(-0.735156\pi\)
−0.673376 + 0.739300i \(0.735156\pi\)
\(114\) 8.76119e9 + 1.15163e9i 0.0426174 + 0.00560193i
\(115\) −1.05185e11 1.05185e11i −0.487657 0.487657i
\(116\) 1.60047e11 + 2.76951e11i 0.707504 + 1.22429i
\(117\) −1.53291e10 + 1.53291e10i −0.0646391 + 0.0646391i
\(118\) −2.91324e11 3.79502e11i −1.17226 1.52708i
\(119\) 3.35768e11i 1.28983i
\(120\) 3.78536e10 9.15435e10i 0.138871 0.335839i
\(121\) 2.76013e11i 0.967410i
\(122\) 3.27253e10 2.51215e10i 0.109624 0.0841524i
\(123\) 1.18763e11 1.18763e11i 0.380367 0.380367i
\(124\) 2.28903e11 + 6.12354e10i 0.701185 + 0.187579i
\(125\) 2.62219e11 + 2.62219e11i 0.768528 + 0.768528i
\(126\) 3.12334e10 2.37612e11i 0.0876155 0.666546i
\(127\) 2.05563e11 0.552109 0.276055 0.961142i \(-0.410973\pi\)
0.276055 + 0.961142i \(0.410973\pi\)
\(128\) 3.08070e11 2.37083e11i 0.792492 0.609882i
\(129\) −8.60456e10 −0.212073
\(130\) 5.05158e9 3.84305e10i 0.0119327 0.0907796i
\(131\) 4.20410e11 + 4.20410e11i 0.952097 + 0.952097i 0.998904 0.0468069i \(-0.0149045\pi\)
−0.0468069 + 0.998904i \(0.514905\pi\)
\(132\) 3.69732e10 + 9.89095e9i 0.0803028 + 0.0214823i
\(133\) −2.70282e10 + 2.70282e10i −0.0563161 + 0.0563161i
\(134\) −2.73665e11 + 2.10079e11i −0.547197 + 0.420054i
\(135\) 3.38534e11i 0.649780i
\(136\) 3.13443e11 7.58017e11i 0.577690 1.39706i
\(137\) 8.28024e11i 1.46582i 0.680327 + 0.732909i \(0.261838\pi\)
−0.680327 + 0.732909i \(0.738162\pi\)
\(138\) 1.44052e11 + 1.87653e11i 0.245010 + 0.319170i
\(139\) −5.46403e11 + 5.46403e11i −0.893165 + 0.893165i −0.994820 0.101654i \(-0.967586\pi\)
0.101654 + 0.994820i \(0.467586\pi\)
\(140\) 2.14400e11 + 3.71006e11i 0.336916 + 0.583011i
\(141\) 2.64670e11 + 2.64670e11i 0.399944 + 0.399944i
\(142\) −1.30153e12 1.71082e11i −1.89176 0.248667i
\(143\) 1.49758e10 0.0209431
\(144\) 2.92324e11 5.07266e11i 0.393433 0.682719i
\(145\) −8.61363e11 −1.11599
\(146\) 5.02700e11 + 6.60784e10i 0.627145 + 0.0824364i
\(147\) 7.37279e10 + 7.37279e10i 0.0885904 + 0.0885904i
\(148\) −7.91291e11 + 4.57278e11i −0.916003 + 0.529348i
\(149\) 2.56398e11 2.56398e11i 0.286016 0.286016i −0.549486 0.835503i \(-0.685177\pi\)
0.835503 + 0.549486i \(0.185177\pi\)
\(150\) −9.83393e10 1.28105e11i −0.105737 0.137741i
\(151\) 1.65411e12i 1.71471i −0.514724 0.857356i \(-0.672106\pi\)
0.514724 0.857356i \(-0.327894\pi\)
\(152\) −8.62488e10 + 3.57866e10i −0.0862210 + 0.0357751i
\(153\) 1.23539e12i 1.19124i
\(154\) −1.31324e11 + 1.00811e11i −0.122175 + 0.0937870i
\(155\) −4.51189e11 + 4.51189e11i −0.405074 + 0.405074i
\(156\) −1.59304e10 + 5.95493e10i −0.0138052 + 0.0516050i
\(157\) 3.88138e11 + 3.88138e11i 0.324742 + 0.324742i 0.850583 0.525841i \(-0.176249\pi\)
−0.525841 + 0.850583i \(0.676249\pi\)
\(158\) 1.20047e8 9.13270e8i 9.69920e−5 0.000737879i
\(159\) 2.25972e11 0.176348
\(160\) 1.37684e11 + 1.03771e12i 0.103806 + 0.782379i
\(161\) −1.02331e12 −0.745527
\(162\) 7.56733e10 5.75694e11i 0.0532856 0.405377i
\(163\) −7.23237e11 7.23237e11i −0.492321 0.492321i 0.416716 0.909037i \(-0.363181\pi\)
−0.909037 + 0.416716i \(0.863181\pi\)
\(164\) −4.58670e11 + 1.71455e12i −0.301897 + 1.12852i
\(165\) −7.28775e10 + 7.28775e10i −0.0463908 + 0.0463908i
\(166\) −1.07002e12 + 8.21397e11i −0.658866 + 0.505777i
\(167\) 5.49609e11i 0.327426i −0.986508 0.163713i \(-0.947653\pi\)
0.986508 0.163713i \(-0.0523471\pi\)
\(168\) −2.61165e11 6.29431e11i −0.150562 0.362866i
\(169\) 1.76804e12i 0.986541i
\(170\) 1.34502e12 + 1.75213e12i 0.726539 + 0.946448i
\(171\) −9.94442e10 + 9.94442e10i −0.0520117 + 0.0520117i
\(172\) 7.87266e11 4.54952e11i 0.398763 0.230441i
\(173\) 1.95564e12 + 1.95564e12i 0.959477 + 0.959477i 0.999210 0.0397338i \(-0.0126510\pi\)
−0.0397338 + 0.999210i \(0.512651\pi\)
\(174\) 1.35817e12 + 1.78528e11i 0.645557 + 0.0848566i
\(175\) 6.98577e11 0.321740
\(176\) −3.90580e11 + 1.04994e11i −0.174337 + 0.0468645i
\(177\) −2.04888e12 −0.886468
\(178\) 3.14775e12 + 4.13762e11i 1.32035 + 0.173556i
\(179\) 2.41737e12 + 2.41737e12i 0.983220 + 0.983220i 0.999862 0.0166415i \(-0.00529739\pi\)
−0.0166415 + 0.999862i \(0.505297\pi\)
\(180\) 7.88839e11 + 1.36504e12i 0.311164 + 0.538450i
\(181\) 3.47137e12 3.47137e12i 1.32822 1.32822i 0.421289 0.906926i \(-0.361578\pi\)
0.906926 0.421289i \(-0.138422\pi\)
\(182\) −1.62366e11 2.11512e11i −0.0602703 0.0785130i
\(183\) 1.76679e11i 0.0636362i
\(184\) −2.31017e12 9.55266e11i −0.807508 0.333908i
\(185\) 2.46104e12i 0.834977i
\(186\) 8.04938e11 6.17909e11i 0.265119 0.203518i
\(187\) −6.03455e11 + 6.03455e11i −0.192982 + 0.192982i
\(188\) −3.82097e12 1.02217e12i −1.18660 0.317435i
\(189\) −1.64674e12 1.64674e12i −0.496690 0.496690i
\(190\) 3.27710e10 2.49309e11i 0.00960162 0.0730456i
\(191\) −1.42722e12 −0.406264 −0.203132 0.979151i \(-0.565112\pi\)
−0.203132 + 0.979151i \(0.565112\pi\)
\(192\) −2.01698e9 1.66478e12i −0.000557884 0.460468i
\(193\) 2.73266e12 0.734550 0.367275 0.930112i \(-0.380291\pi\)
0.367275 + 0.930112i \(0.380291\pi\)
\(194\) 2.27566e11 1.73124e12i 0.0594564 0.452322i
\(195\) −1.17377e11 1.17377e11i −0.0298121 0.0298121i
\(196\) −1.06439e12 2.84742e11i −0.262841 0.0703142i
\(197\) −6.90303e11 + 6.90303e11i −0.165758 + 0.165758i −0.785112 0.619354i \(-0.787395\pi\)
0.619354 + 0.785112i \(0.287395\pi\)
\(198\) −4.83178e11 + 3.70911e11i −0.112836 + 0.0866186i
\(199\) 6.35449e12i 1.44341i 0.692202 + 0.721704i \(0.256641\pi\)
−0.692202 + 0.721704i \(0.743359\pi\)
\(200\) 1.57708e12 + 6.52128e11i 0.348488 + 0.144101i
\(201\) 1.47748e12i 0.317646i
\(202\) 2.97913e11 + 3.88085e11i 0.0623242 + 0.0811885i
\(203\) −4.18995e12 + 4.18995e12i −0.853063 + 0.853063i
\(204\) −1.75764e12 3.04148e12i −0.348308 0.602725i
\(205\) −3.37953e12 3.37953e12i −0.651944 0.651944i
\(206\) 6.38288e12 + 8.39011e11i 1.19880 + 0.157579i
\(207\) −3.76503e12 −0.688544
\(208\) −1.69104e11 6.29070e11i −0.0301165 0.112034i
\(209\) 9.71520e10 0.0168518
\(210\) 1.81942e12 + 2.39158e11i 0.307417 + 0.0404090i
\(211\) 3.30209e12 + 3.30209e12i 0.543545 + 0.543545i 0.924566 0.381021i \(-0.124427\pi\)
−0.381021 + 0.924566i \(0.624427\pi\)
\(212\) −2.06751e12 + 1.19479e12i −0.331589 + 0.191621i
\(213\) −3.97520e12 + 3.97520e12i −0.621257 + 0.621257i
\(214\) −5.56041e12 7.24344e12i −0.846898 1.10324i
\(215\) 2.44852e12i 0.363490i
\(216\) −2.18037e12 5.25486e12i −0.315525 0.760442i
\(217\) 4.38946e12i 0.619274i
\(218\) −9.00531e12 + 6.91291e12i −1.23876 + 0.950934i
\(219\) 1.53538e12 1.53538e12i 0.205955 0.205955i
\(220\) 2.81458e11 1.05211e12i 0.0368204 0.137638i
\(221\) −9.71928e11 9.71928e11i −0.124016 0.124016i
\(222\) −5.10082e11 + 3.88051e12i −0.0634890 + 0.483000i
\(223\) 1.22014e13 1.48161 0.740806 0.671719i \(-0.234444\pi\)
0.740806 + 0.671719i \(0.234444\pi\)
\(224\) 5.71752e12 + 4.37804e12i 0.677398 + 0.518700i
\(225\) 2.57026e12 0.297148
\(226\) 1.55566e12 1.18349e13i 0.175517 1.33527i
\(227\) −4.44935e12 4.44935e12i −0.489953 0.489953i 0.418338 0.908291i \(-0.362613\pi\)
−0.908291 + 0.418338i \(0.862613\pi\)
\(228\) −1.03345e11 + 3.86313e11i −0.0111083 + 0.0415238i
\(229\) 2.35262e11 2.35262e11i 0.0246864 0.0246864i −0.694656 0.719342i \(-0.744443\pi\)
0.719342 + 0.694656i \(0.244443\pi\)
\(230\) 5.33988e12 4.09915e12i 0.547052 0.419943i
\(231\) 7.09001e11i 0.0709220i
\(232\) −1.33704e13 + 5.54770e12i −1.30605 + 0.541913i
\(233\) 1.95717e12i 0.186711i 0.995633 + 0.0933555i \(0.0297593\pi\)
−0.995633 + 0.0933555i \(0.970241\pi\)
\(234\) −5.97391e11 7.78210e11i −0.0556637 0.0725120i
\(235\) 7.53146e12 7.53146e12i 0.685498 0.685498i
\(236\) 1.87460e13 1.08331e13i 1.66684 0.963246i
\(237\) −2.78937e9 2.78937e9i −0.000242320 0.000242320i
\(238\) 1.50655e13 + 1.98032e12i 1.27883 + 0.168098i
\(239\) −1.55805e13 −1.29239 −0.646195 0.763172i \(-0.723641\pi\)
−0.646195 + 0.763172i \(0.723641\pi\)
\(240\) 3.88420e12 + 2.23836e12i 0.314876 + 0.181455i
\(241\) 1.49774e13 1.18670 0.593352 0.804943i \(-0.297804\pi\)
0.593352 + 0.804943i \(0.297804\pi\)
\(242\) −1.23844e13 1.62789e12i −0.959159 0.126079i
\(243\) −9.44749e12 9.44749e12i −0.715289 0.715289i
\(244\) 9.34163e11 + 1.61651e12i 0.0691478 + 0.119656i
\(245\) 2.09801e12 2.09801e12i 0.151843 0.151843i
\(246\) 4.62831e12 + 6.02921e12i 0.327551 + 0.426695i
\(247\) 1.56474e11i 0.0108295i
\(248\) −4.09761e12 + 9.90947e12i −0.277361 + 0.670759i
\(249\) 5.77688e12i 0.382470i
\(250\) −1.33120e13 + 1.02189e13i −0.862132 + 0.661814i
\(251\) 1.35422e13 1.35422e13i 0.857996 0.857996i −0.133106 0.991102i \(-0.542495\pi\)
0.991102 + 0.133106i \(0.0424951\pi\)
\(252\) 1.04772e13 + 2.80281e12i 0.649443 + 0.173737i
\(253\) 1.83912e12 + 1.83912e12i 0.111544 + 0.111544i
\(254\) −1.21239e12 + 9.22339e12i −0.0719542 + 0.547400i
\(255\) 9.45950e12 0.549411
\(256\) 8.82069e12 + 1.52211e13i 0.501398 + 0.865217i
\(257\) 1.84308e12 0.102545 0.0512723 0.998685i \(-0.483672\pi\)
0.0512723 + 0.998685i \(0.483672\pi\)
\(258\) 5.07487e11 3.86077e12i 0.0276386 0.210264i
\(259\) −1.19713e13 1.19713e13i −0.638254 0.638254i
\(260\) 1.69454e12 + 4.53318e11i 0.0884502 + 0.0236619i
\(261\) −1.54160e13 + 1.54160e13i −0.787860 + 0.787860i
\(262\) −2.13429e13 + 1.63838e13i −1.06806 + 0.819894i
\(263\) 1.20322e13i 0.589642i −0.955553 0.294821i \(-0.904740\pi\)
0.955553 0.294821i \(-0.0952600\pi\)
\(264\) −6.61859e11 + 1.60061e12i −0.0317646 + 0.0768182i
\(265\) 6.43028e12i 0.302258i
\(266\) −1.05331e12 1.37213e12i −0.0484964 0.0631753i
\(267\) 9.61405e12 9.61405e12i 0.433605 0.433605i
\(268\) −7.81195e12 1.35181e13i −0.345158 0.597274i
\(269\) −2.45811e13 2.45811e13i −1.06405 1.06405i −0.997803 0.0662507i \(-0.978896\pi\)
−0.0662507 0.997803i \(-0.521104\pi\)
\(270\) 1.51896e13 + 1.99663e12i 0.644238 + 0.0846832i
\(271\) −1.50612e12 −0.0625935 −0.0312967 0.999510i \(-0.509964\pi\)
−0.0312967 + 0.999510i \(0.509964\pi\)
\(272\) 3.21627e13 + 1.85345e13i 1.30986 + 0.754836i
\(273\) −1.14192e12 −0.0455766
\(274\) −3.71525e13 4.88359e12i −1.45332 0.191034i
\(275\) −1.25551e12 1.25551e12i −0.0481382 0.0481382i
\(276\) −9.26939e12 + 5.35668e12i −0.348379 + 0.201324i
\(277\) −2.54745e13 + 2.54745e13i −0.938570 + 0.938570i −0.998219 0.0596494i \(-0.981002\pi\)
0.0596494 + 0.998219i \(0.481002\pi\)
\(278\) −2.12939e13 2.77391e13i −0.769145 1.00195i
\(279\) 1.61501e13i 0.571941i
\(280\) −1.79111e13 + 7.43175e12i −0.621948 + 0.258061i
\(281\) 2.86124e13i 0.974249i 0.873332 + 0.487125i \(0.161954\pi\)
−0.873332 + 0.487125i \(0.838046\pi\)
\(282\) −1.34364e13 + 1.03144e13i −0.448656 + 0.344410i
\(283\) 2.53014e13 2.53014e13i 0.828550 0.828550i −0.158766 0.987316i \(-0.550752\pi\)
0.987316 + 0.158766i \(0.0507517\pi\)
\(284\) 1.53525e13 5.73890e13i 0.493092 1.84322i
\(285\) −7.61456e11 7.61456e11i −0.0239882 0.0239882i
\(286\) −8.83255e10 + 6.71947e11i −0.00272943 + 0.0207645i
\(287\) −3.28783e13 −0.996687
\(288\) 2.10364e13 + 1.61080e13i 0.625622 + 0.479054i
\(289\) 4.40565e13 1.28550
\(290\) 5.08021e12 3.86484e13i 0.145443 1.10648i
\(291\) −5.28766e12 5.28766e12i −0.148543 0.148543i
\(292\) −5.92973e12 + 2.21658e13i −0.163467 + 0.611053i
\(293\) 1.19988e13 1.19988e13i 0.324614 0.324614i −0.525920 0.850534i \(-0.676279\pi\)
0.850534 + 0.525920i \(0.176279\pi\)
\(294\) −3.74292e12 + 2.87325e12i −0.0993804 + 0.0762892i
\(295\) 5.83031e13i 1.51939i
\(296\) −1.58506e13 3.82013e13i −0.405454 0.977179i
\(297\) 5.91917e12i 0.148628i
\(298\) 9.99209e12 + 1.30165e13i 0.246301 + 0.320852i
\(299\) −2.96210e12 + 2.96210e12i −0.0716818 + 0.0716818i
\(300\) 6.32791e12 3.65683e12i 0.150346 0.0868835i
\(301\) 1.19104e13 + 1.19104e13i 0.277851 + 0.277851i
\(302\) 7.42180e13 + 9.75574e12i 1.70009 + 0.223472i
\(303\) 2.09522e12 0.0471297
\(304\) −1.09702e12 4.08095e12i −0.0242332 0.0901481i
\(305\) −5.02760e12 −0.109072
\(306\) 5.54304e13 + 7.28616e12i 1.18108 + 0.155250i
\(307\) 3.56171e13 + 3.56171e13i 0.745414 + 0.745414i 0.973614 0.228200i \(-0.0732841\pi\)
−0.228200 + 0.973614i \(0.573284\pi\)
\(308\) −3.74873e12 6.48694e12i −0.0770646 0.133355i
\(309\) 1.94950e13 1.94950e13i 0.393687 0.393687i
\(310\) −1.75833e13 2.29054e13i −0.348827 0.454410i
\(311\) 5.85014e12i 0.114021i −0.998374 0.0570104i \(-0.981843\pi\)
0.998374 0.0570104i \(-0.0181568\pi\)
\(312\) −2.57795e12 1.06599e12i −0.0493657 0.0204129i
\(313\) 7.17988e12i 0.135090i 0.997716 + 0.0675450i \(0.0215166\pi\)
−0.997716 + 0.0675450i \(0.978483\pi\)
\(314\) −1.97045e13 + 1.51261e13i −0.364294 + 0.279650i
\(315\) −2.06514e13 + 2.06514e13i −0.375182 + 0.375182i
\(316\) 4.02694e10 + 1.07727e10i 0.000718945 + 0.000192330i
\(317\) 1.76432e13 + 1.76432e13i 0.309564 + 0.309564i 0.844740 0.535176i \(-0.179755\pi\)
−0.535176 + 0.844740i \(0.679755\pi\)
\(318\) −1.33275e12 + 1.01391e13i −0.0229827 + 0.174844i
\(319\) 1.50607e13 0.255268
\(320\) −4.73731e13 + 5.73952e10i −0.789235 + 0.000956205i
\(321\) −3.91063e13 −0.640426
\(322\) 6.03534e12 4.59146e13i 0.0971615 0.739168i
\(323\) −6.30516e12 6.30516e12i −0.0997889 0.0997889i
\(324\) 2.53844e13 + 6.79075e12i 0.394975 + 0.105662i
\(325\) 2.02213e12 2.02213e12i 0.0309350 0.0309350i
\(326\) 3.67164e13 2.81852e13i 0.552285 0.423960i
\(327\) 4.86184e13i 0.719099i
\(328\) −7.42247e13 3.06922e13i −1.07955 0.446398i
\(329\) 7.32711e13i 1.04798i
\(330\) −2.84011e12 3.69975e12i −0.0399492 0.0520411i
\(331\) −3.82241e13 + 3.82241e13i −0.528790 + 0.528790i −0.920211 0.391422i \(-0.871983\pi\)
0.391422 + 0.920211i \(0.371983\pi\)
\(332\) −3.05443e13 5.28550e13i −0.415596 0.719162i
\(333\) −4.40459e13 4.40459e13i −0.589470 0.589470i
\(334\) 2.46603e13 + 3.24153e12i 0.324634 + 0.0426721i
\(335\) 4.20434e13 0.544441
\(336\) 2.97822e13 8.00589e12i 0.379394 0.101987i
\(337\) 2.67134e13 0.334784 0.167392 0.985890i \(-0.446465\pi\)
0.167392 + 0.985890i \(0.446465\pi\)
\(338\) 7.93300e13 + 1.04277e13i 0.978127 + 0.128572i
\(339\) −3.61469e13 3.61469e13i −0.438503 0.438503i
\(340\) −8.65487e13 + 5.00156e13i −1.03306 + 0.596995i
\(341\) 7.88890e12 7.88890e12i 0.0926547 0.0926547i
\(342\) −3.87544e12 5.04846e12i −0.0447896 0.0583466i
\(343\) 9.54276e13i 1.08532i
\(344\) 1.57700e13 + 3.80070e13i 0.176506 + 0.425395i
\(345\) 2.88293e13i 0.317562i
\(346\) −9.92813e13 + 7.62130e13i −1.07634 + 0.826249i
\(347\) −1.05470e14 + 1.05470e14i −1.12543 + 1.12543i −0.134515 + 0.990912i \(0.542948\pi\)
−0.990912 + 0.134515i \(0.957052\pi\)
\(348\) −1.60207e13 + 5.98868e13i −0.168266 + 0.628993i
\(349\) 2.45469e13 + 2.45469e13i 0.253780 + 0.253780i 0.822518 0.568738i \(-0.192568\pi\)
−0.568738 + 0.822518i \(0.692568\pi\)
\(350\) −4.12012e12 + 3.13444e13i −0.0419311 + 0.318996i
\(351\) −9.53345e12 −0.0955126
\(352\) −2.40736e12 1.81441e13i −0.0237441 0.178958i
\(353\) −5.54612e13 −0.538553 −0.269276 0.963063i \(-0.586785\pi\)
−0.269276 + 0.963063i \(0.586785\pi\)
\(354\) 1.20840e13 9.19308e13i 0.115530 0.878907i
\(355\) 1.13119e14 + 1.13119e14i 1.06483 + 1.06483i
\(356\) −3.71301e13 + 1.38796e14i −0.344152 + 1.28647i
\(357\) 4.60141e13 4.60141e13i 0.419968 0.419968i
\(358\) −1.22722e14 + 9.42071e13i −1.10297 + 0.846695i
\(359\) 1.17444e14i 1.03947i −0.854328 0.519734i \(-0.826031\pi\)
0.854328 0.519734i \(-0.173969\pi\)
\(360\) −6.59001e13 + 2.73435e13i −0.574410 + 0.238336i
\(361\) 1.15475e14i 0.991286i
\(362\) 1.35283e14 + 1.76230e14i 1.14379 + 1.48999i
\(363\) −3.78252e13 + 3.78252e13i −0.314989 + 0.314989i
\(364\) 1.04479e13 6.03772e12i 0.0856981 0.0495240i
\(365\) −4.36908e13 4.36908e13i −0.353004 0.353004i
\(366\) 7.92740e12 + 1.04203e12i 0.0630935 + 0.00829346i
\(367\) 6.53804e13 0.512607 0.256303 0.966596i \(-0.417495\pi\)
0.256303 + 0.966596i \(0.417495\pi\)
\(368\) 5.64868e13 9.80208e13i 0.436299 0.757104i
\(369\) −1.20969e14 −0.920507
\(370\) 1.10424e14 + 1.45149e13i 0.827856 + 0.108819i
\(371\) −3.12790e13 3.12790e13i −0.231045 0.231045i
\(372\) 2.29774e13 + 3.97610e13i 0.167230 + 0.289382i
\(373\) 1.53272e14 1.53272e14i 1.09917 1.09917i 0.104658 0.994508i \(-0.466625\pi\)
0.994508 0.104658i \(-0.0333747\pi\)
\(374\) −2.35172e13 3.06354e13i −0.166185 0.216486i
\(375\) 7.18697e13i 0.500465i
\(376\) 6.83992e13 1.65414e14i 0.469373 1.13511i
\(377\) 2.42568e13i 0.164042i
\(378\) 8.35997e13 6.41751e13i 0.557186 0.427722i
\(379\) 1.21627e14 1.21627e14i 0.798940 0.798940i −0.183988 0.982928i \(-0.558901\pi\)
0.982928 + 0.183988i \(0.0589009\pi\)
\(380\) 1.09929e13 + 2.94079e12i 0.0711712 + 0.0190395i
\(381\) 2.81707e13 + 2.81707e13i 0.179767 + 0.179767i
\(382\) 8.41760e12 6.40379e13i 0.0529468 0.402799i
\(383\) −9.93966e13 −0.616280 −0.308140 0.951341i \(-0.599707\pi\)
−0.308140 + 0.951341i \(0.599707\pi\)
\(384\) 7.47085e13 + 9.72816e12i 0.456613 + 0.0594578i
\(385\) 2.01754e13 0.121559
\(386\) −1.61169e13 + 1.22612e14i −0.0957309 + 0.728285i
\(387\) 4.38218e13 + 4.38218e13i 0.256614 + 0.256614i
\(388\) 7.63366e13 + 2.04213e13i 0.440716 + 0.117899i
\(389\) −5.20938e13 + 5.20938e13i −0.296526 + 0.296526i −0.839652 0.543125i \(-0.817241\pi\)
0.543125 + 0.839652i \(0.317241\pi\)
\(390\) 5.95885e12 4.57430e12i 0.0334431 0.0256726i
\(391\) 2.38718e14i 1.32103i
\(392\) 1.90537e13 4.60786e13i 0.103969 0.251435i
\(393\) 1.15227e14i 0.620006i
\(394\) −2.69018e13 3.50444e13i −0.142742 0.185947i
\(395\) −7.93745e10 + 7.93745e10i −0.000415333 + 0.000415333i
\(396\) −1.37926e13 2.38673e13i −0.0711743 0.123163i
\(397\) 2.43146e14 + 2.43146e14i 1.23743 + 1.23743i 0.961050 + 0.276376i \(0.0891335\pi\)
0.276376 + 0.961050i \(0.410866\pi\)
\(398\) −2.85119e14 3.74780e13i −1.43110 0.188113i
\(399\) −7.40795e12 −0.0366731
\(400\) −3.85617e13 + 6.69156e13i −0.188289 + 0.326736i
\(401\) −1.60446e14 −0.772744 −0.386372 0.922343i \(-0.626272\pi\)
−0.386372 + 0.922343i \(0.626272\pi\)
\(402\) −6.62929e13 8.71401e12i −0.314937 0.0413976i
\(403\) 1.27059e13 + 1.27059e13i 0.0595427 + 0.0595427i
\(404\) −1.91700e13 + 1.10781e13i −0.0886185 + 0.0512116i
\(405\) −5.00350e13 + 5.00350e13i −0.228177 + 0.228177i
\(406\) −1.63287e14 2.12710e14i −0.734611 0.956963i
\(407\) 4.30306e13i 0.190989i
\(408\) 1.46834e14 6.09250e13i 0.642978 0.266787i
\(409\) 8.28735e13i 0.358045i 0.983845 + 0.179022i \(0.0572935\pi\)
−0.983845 + 0.179022i \(0.942707\pi\)
\(410\) 1.71568e14 1.31704e14i 0.731348 0.561418i
\(411\) −1.13474e14 + 1.13474e14i −0.477270 + 0.477270i
\(412\) −7.52909e13 + 2.81444e14i −0.312470 + 1.16804i
\(413\) 2.83605e14 + 2.83605e14i 1.16142 + 1.16142i
\(414\) 2.22057e13 1.68933e14i 0.0897352 0.682671i
\(415\) 1.64388e14 0.655548
\(416\) 2.92230e13 3.87730e12i 0.115004 0.0152587i
\(417\) −1.49760e14 −0.581630
\(418\) −5.72991e11 + 4.35910e12i −0.00219623 + 0.0167081i
\(419\) −7.37301e11 7.37301e11i −0.00278912 0.00278912i 0.705711 0.708500i \(-0.250628\pi\)
−0.708500 + 0.705711i \(0.750628\pi\)
\(420\) −2.14615e13 + 8.02249e13i −0.0801288 + 0.299528i
\(421\) −2.94206e14 + 2.94206e14i −1.08418 + 1.08418i −0.0880630 + 0.996115i \(0.528068\pi\)
−0.996115 + 0.0880630i \(0.971932\pi\)
\(422\) −1.67637e14 + 1.28686e14i −0.609748 + 0.468071i
\(423\) 2.69585e14i 0.967884i
\(424\) −4.14149e13 9.98134e13i −0.146773 0.353734i
\(425\) 1.62965e14i 0.570105i
\(426\) −1.54918e14 2.01808e14i −0.534993 0.696925i
\(427\) −2.44559e13 + 2.44559e13i −0.0833740 + 0.0833740i
\(428\) 3.57799e14 2.06768e14i 1.20420 0.695894i
\(429\) 2.05230e12 + 2.05230e12i 0.00681909 + 0.00681909i
\(430\) −1.09862e14 1.44411e13i −0.360390 0.0473722i
\(431\) −1.13680e14 −0.368180 −0.184090 0.982909i \(-0.558934\pi\)
−0.184090 + 0.982909i \(0.558934\pi\)
\(432\) 2.48639e14 6.68380e13i 0.795077 0.213729i
\(433\) −3.36153e14 −1.06134 −0.530669 0.847579i \(-0.678059\pi\)
−0.530669 + 0.847579i \(0.678059\pi\)
\(434\) −1.96950e14 2.58885e13i −0.613992 0.0807075i
\(435\) −1.18042e14 1.18042e14i −0.363368 0.363368i
\(436\) −2.57062e14 4.44830e14i −0.781380 1.35213i
\(437\) −1.92160e13 + 1.92160e13i −0.0576785 + 0.0576785i
\(438\) 5.98352e13 + 7.79461e13i 0.177357 + 0.231040i
\(439\) 1.16264e14i 0.340323i −0.985416 0.170162i \(-0.945571\pi\)
0.985416 0.170162i \(-0.0544290\pi\)
\(440\) 4.55472e13 + 1.88339e13i 0.131665 + 0.0544442i
\(441\) 7.50971e13i 0.214393i
\(442\) 4.93416e13 3.78770e13i 0.139120 0.106796i
\(443\) −1.78673e14 + 1.78673e14i −0.497551 + 0.497551i −0.910675 0.413124i \(-0.864438\pi\)
0.413124 + 0.910675i \(0.364438\pi\)
\(444\) −1.71106e14 4.57736e13i −0.470607 0.125895i
\(445\) −2.73578e14 2.73578e14i −0.743193 0.743193i
\(446\) −7.19627e13 + 5.47465e14i −0.193093 + 1.46898i
\(447\) 7.02743e13 0.186254
\(448\) −2.30159e14 + 2.30717e14i −0.602558 + 0.604020i
\(449\) 7.06977e14 1.82831 0.914156 0.405363i \(-0.132855\pi\)
0.914156 + 0.405363i \(0.132855\pi\)
\(450\) −1.51591e13 + 1.15325e14i −0.0387262 + 0.294614i
\(451\) 5.90901e13 + 5.90901e13i 0.149123 + 0.149123i
\(452\) 5.21843e14 + 1.39602e14i 1.30100 + 0.348040i
\(453\) 2.26681e14 2.26681e14i 0.558311 0.558311i
\(454\) 2.25879e14 1.73396e14i 0.549628 0.421921i
\(455\) 3.24946e13i 0.0781176i
\(456\) −1.67239e13 6.91540e12i −0.0397220 0.0164252i
\(457\) 1.46033e13i 0.0342698i −0.999853 0.0171349i \(-0.994546\pi\)
0.999853 0.0171349i \(-0.00545448\pi\)
\(458\) 9.16841e12 + 1.19435e13i 0.0212586 + 0.0276931i
\(459\) 3.84154e14 3.84154e14i 0.880106 0.880106i
\(460\) 1.52430e14 + 2.63771e14i 0.345067 + 0.597116i
\(461\) 9.16736e13 + 9.16736e13i 0.205064 + 0.205064i 0.802166 0.597102i \(-0.203681\pi\)
−0.597102 + 0.802166i \(0.703681\pi\)
\(462\) −3.18121e13 4.18160e12i −0.0703171 0.00924298i
\(463\) 2.43203e14 0.531219 0.265610 0.964081i \(-0.414427\pi\)
0.265610 + 0.964081i \(0.414427\pi\)
\(464\) −1.70062e14 6.32636e14i −0.367078 1.36554i
\(465\) −1.23663e14 −0.263784
\(466\) −8.78158e13 1.15431e13i −0.185119 0.0243333i
\(467\) 7.14887e13 + 7.14887e13i 0.148934 + 0.148934i 0.777642 0.628708i \(-0.216416\pi\)
−0.628708 + 0.777642i \(0.716416\pi\)
\(468\) 3.84408e13 2.22145e13i 0.0791480 0.0457387i
\(469\) 2.04513e14 2.04513e14i 0.416169 0.416169i
\(470\) 2.93508e14 + 3.82348e14i 0.590313 + 0.768989i
\(471\) 1.06382e14i 0.211472i
\(472\) 3.75508e14 + 9.05004e14i 0.737798 + 1.77816i
\(473\) 4.28117e13i 0.0831431i
\(474\) 1.41607e11 1.08704e11i 0.000271834 0.000208673i
\(475\) 1.31181e13 1.31181e13i 0.0248918 0.0248918i
\(476\) −1.77710e14 + 6.64294e14i −0.333329 + 1.24601i
\(477\) −1.15084e14 1.15084e14i −0.213385 0.213385i
\(478\) 9.18921e13 6.99080e14i 0.168432 1.28137i
\(479\) −2.74810e14 −0.497951 −0.248975 0.968510i \(-0.580094\pi\)
−0.248975 + 0.968510i \(0.580094\pi\)
\(480\) −1.23341e14 + 1.61078e14i −0.220944 + 0.288542i
\(481\) −6.93054e13 −0.122735
\(482\) −8.83349e13 + 6.72019e14i −0.154658 + 1.17658i
\(483\) −1.40235e14 1.40235e14i −0.242744 0.242744i
\(484\) 1.46084e14 5.46073e14i 0.250007 0.934548i
\(485\) −1.50466e14 + 1.50466e14i −0.254601 + 0.254601i
\(486\) 4.79618e14 3.68178e14i 0.802410 0.615968i
\(487\) 4.74099e14i 0.784260i 0.919910 + 0.392130i \(0.128262\pi\)
−0.919910 + 0.392130i \(0.871738\pi\)
\(488\) −7.80405e13 + 3.23808e13i −0.127647 + 0.0529638i
\(489\) 1.98227e14i 0.320600i
\(490\) 8.17614e13 + 1.06509e14i 0.130759 + 0.170337i
\(491\) 3.34687e14 3.34687e14i 0.529287 0.529287i −0.391073 0.920360i \(-0.627896\pi\)
0.920360 + 0.391073i \(0.127896\pi\)
\(492\) −2.97821e14 + 1.72107e14i −0.465744 + 0.269148i
\(493\) −9.77437e14 9.77437e14i −1.51158 1.51158i
\(494\) −7.02080e12 9.22863e11i −0.0107371 0.00141136i
\(495\) 7.42310e13 0.112268
\(496\) −4.20460e14 2.42300e14i −0.628891 0.362413i
\(497\) 1.10049e15 1.62790
\(498\) −2.59202e14 3.40714e13i −0.379208 0.0498458i
\(499\) −3.00431e14 3.00431e14i −0.434702 0.434702i 0.455523 0.890224i \(-0.349452\pi\)
−0.890224 + 0.455523i \(0.849452\pi\)
\(500\) −3.80000e14 6.57565e14i −0.543811 0.941031i
\(501\) 7.53192e13 7.53192e13i 0.106610 0.106610i
\(502\) 5.27754e14 + 6.87495e14i 0.738859 + 0.962497i
\(503\) 7.90668e14i 1.09489i 0.836842 + 0.547444i \(0.184399\pi\)
−0.836842 + 0.547444i \(0.815601\pi\)
\(504\) −1.87552e14 + 4.53568e14i −0.256894 + 0.621261i
\(505\) 5.96217e13i 0.0807796i
\(506\) −9.33663e13 + 7.16724e13i −0.125130 + 0.0960560i
\(507\) 2.42295e14 2.42295e14i 0.321218 0.321218i
\(508\) −4.06692e14 1.08797e14i −0.533354 0.142681i
\(509\) −3.74275e14 3.74275e14i −0.485560 0.485560i 0.421342 0.906902i \(-0.361559\pi\)
−0.906902 + 0.421342i \(0.861559\pi\)
\(510\) −5.57910e13 + 4.24437e14i −0.0716025 + 0.544725i
\(511\) −4.25054e14 −0.539671
\(512\) −7.34975e14 + 3.06003e14i −0.923183 + 0.384362i
\(513\) −6.18461e13 −0.0768540
\(514\) −1.08703e13 + 8.26970e13i −0.0133642 + 0.101670i
\(515\) −5.54752e14 5.54752e14i −0.674775 0.674775i
\(516\) 1.70235e14 + 4.55407e13i 0.204869 + 0.0548058i
\(517\) −1.31685e14 + 1.31685e14i −0.156798 + 0.156798i
\(518\) 6.07745e14 4.66534e14i 0.715992 0.549629i
\(519\) 5.36006e14i 0.624811i
\(520\) −3.03340e13 + 7.33585e13i −0.0349874 + 0.0846121i
\(521\) 3.28240e14i 0.374614i −0.982301 0.187307i \(-0.940024\pi\)
0.982301 0.187307i \(-0.0599759\pi\)
\(522\) −6.00777e14 7.82621e14i −0.678462 0.883820i
\(523\) −7.89619e14 + 7.89619e14i −0.882385 + 0.882385i −0.993777 0.111392i \(-0.964469\pi\)
0.111392 + 0.993777i \(0.464469\pi\)
\(524\) −6.09245e14 1.05426e15i −0.673705 1.16580i
\(525\) 9.57339e13 + 9.57339e13i 0.104759 + 0.104759i
\(526\) 5.39871e14 + 7.09645e13i 0.584613 + 0.0768457i
\(527\) −1.02398e15 −1.09732
\(528\) −6.79141e13 3.91371e13i −0.0720233 0.0415051i
\(529\) 2.25279e14 0.236437
\(530\) 2.88519e14 + 3.79250e13i 0.299680 + 0.0393920i
\(531\) 1.04346e15 + 1.04346e15i 1.07265 + 1.07265i
\(532\) 6.77784e13 3.91684e13i 0.0689568 0.0398494i
\(533\) −9.51709e13 + 9.51709e13i −0.0958306 + 0.0958306i
\(534\) 3.74669e14 + 4.88074e14i 0.373397 + 0.486417i
\(535\) 1.11281e15i 1.09768i
\(536\) 6.52615e14 2.70785e14i 0.637163 0.264374i
\(537\) 6.62558e14i 0.640273i
\(538\) 1.24790e15 9.57949e14i 1.19365 0.916305i
\(539\) −3.66831e13 + 3.66831e13i −0.0347318 + 0.0347318i
\(540\) −1.79173e14 + 6.69766e14i −0.167922 + 0.627707i
\(541\) 3.87444e13 + 3.87444e13i 0.0359438 + 0.0359438i 0.724850 0.688906i \(-0.241909\pi\)
−0.688906 + 0.724850i \(0.741909\pi\)
\(542\) 8.88293e12 6.75780e13i 0.00815756 0.0620596i
\(543\) 9.51442e14 0.864934
\(544\) −1.02131e15 + 1.33379e15i −0.919106 + 1.20031i
\(545\) 1.38349e15 1.23252
\(546\) 6.73492e12 5.12367e13i 0.00593981 0.0451879i
\(547\) 7.46902e14 + 7.46902e14i 0.652129 + 0.652129i 0.953505 0.301377i \(-0.0974462\pi\)
−0.301377 + 0.953505i \(0.597446\pi\)
\(548\) 4.38242e14 1.63819e15i 0.378810 1.41602i
\(549\) −8.99802e13 + 8.99802e13i −0.0770015 + 0.0770015i
\(550\) 6.37381e13 4.89284e13i 0.0540013 0.0414540i
\(551\) 1.57361e14i 0.131996i
\(552\) −1.85678e14 4.47500e14i −0.154204 0.371645i
\(553\) 7.72208e11i 0.000634959i
\(554\) −9.92766e14 1.29326e15i −0.808245 1.05289i
\(555\) 3.37264e14 3.37264e14i 0.271869 0.271869i
\(556\) 1.37021e15 7.91830e14i 1.09364 0.632005i
\(557\) 3.84096e14 + 3.84096e14i 0.303554 + 0.303554i 0.842403 0.538849i \(-0.181141\pi\)
−0.538849 + 0.842403i \(0.681141\pi\)
\(558\) −7.24635e14 9.52512e13i −0.567063 0.0745388i
\(559\) 6.89528e13 0.0534302
\(560\) −2.27816e14 8.47484e14i −0.174804 0.650275i
\(561\) −1.65397e14 −0.125670
\(562\) −1.28381e15 1.68753e14i −0.965940 0.126970i
\(563\) −1.33405e15 1.33405e15i −0.993979 0.993979i 0.00600253 0.999982i \(-0.498089\pi\)
−0.999982 + 0.00600253i \(0.998089\pi\)
\(564\) −3.83550e14 6.63710e14i −0.283001 0.489715i
\(565\) −1.02860e15 + 1.02860e15i −0.751587 + 0.751587i
\(566\) 9.86019e14 + 1.28447e15i 0.713502 + 0.929465i
\(567\) 4.86773e14i 0.348835i
\(568\) 2.48443e15 + 1.02732e15i 1.76324 + 0.729106i
\(569\) 6.39918e14i 0.449787i −0.974383 0.224893i \(-0.927797\pi\)
0.974383 0.224893i \(-0.0722034\pi\)
\(570\) 3.86567e13 2.96747e13i 0.0269099 0.0206574i
\(571\) 1.74958e15 1.74958e15i 1.20625 1.20625i 0.234014 0.972233i \(-0.424814\pi\)
0.972233 0.234014i \(-0.0751860\pi\)
\(572\) −2.96286e13 7.92613e12i −0.0202317 0.00541231i
\(573\) −1.95589e14 1.95589e14i −0.132280 0.132280i
\(574\) 1.93912e14 1.47521e15i 0.129894 0.988187i
\(575\) 4.96661e14 0.329524
\(576\) −8.46820e14 + 8.48874e14i −0.556503 + 0.557853i
\(577\) −1.55990e15 −1.01538 −0.507690 0.861540i \(-0.669501\pi\)
−0.507690 + 0.861540i \(0.669501\pi\)
\(578\) −2.59840e14 + 1.97676e15i −0.167534 + 1.27454i
\(579\) 3.74488e14 + 3.74488e14i 0.239169 + 0.239169i
\(580\) 1.70415e15 + 4.55887e14i 1.07808 + 0.288405i
\(581\) 7.99636e14 7.99636e14i 0.501099 0.501099i
\(582\) 2.68437e14 2.06065e14i 0.166635 0.127917i
\(583\) 1.12432e14i 0.0691371i
\(584\) −9.59583e14 3.96792e14i −0.584537 0.241708i
\(585\) 1.19557e14i 0.0721468i
\(586\) 4.67606e14 + 6.09141e14i 0.279540 + 0.364151i
\(587\) −5.95871e14 + 5.95871e14i −0.352893 + 0.352893i −0.861185 0.508292i \(-0.830277\pi\)
0.508292 + 0.861185i \(0.330277\pi\)
\(588\) −1.06844e14 1.84887e14i −0.0626867 0.108475i
\(589\) 8.24267e13 + 8.24267e13i 0.0479109 + 0.0479109i
\(590\) −2.61599e15 3.43864e14i −1.50643 0.198016i
\(591\) −1.89200e14 −0.107942
\(592\) 1.80754e15 4.85893e14i 1.02169 0.274645i
\(593\) 4.06287e14 0.227526 0.113763 0.993508i \(-0.463709\pi\)
0.113763 + 0.993508i \(0.463709\pi\)
\(594\) −2.65586e14 3.49105e13i −0.147360 0.0193701i
\(595\) −1.30938e15 1.30938e15i −0.719819 0.719819i
\(596\) −6.42968e14 + 3.71564e14i −0.350215 + 0.202385i
\(597\) −8.70828e14 + 8.70828e14i −0.469974 + 0.469974i
\(598\) −1.15436e14 1.50376e14i −0.0617284 0.0804124i
\(599\) 2.58399e15i 1.36913i −0.728953 0.684563i \(-0.759993\pi\)
0.728953 0.684563i \(-0.240007\pi\)
\(600\) 1.26756e14 + 3.05493e14i 0.0665485 + 0.160387i
\(601\) 8.49105e14i 0.441725i 0.975305 + 0.220862i \(0.0708872\pi\)
−0.975305 + 0.220862i \(0.929113\pi\)
\(602\) −6.04653e14 + 4.64161e14i −0.311692 + 0.239270i
\(603\) 7.52460e14 7.52460e14i 0.384360 0.384360i
\(604\) −8.75458e14 + 3.27254e15i −0.443131 + 1.65646i
\(605\) 1.07636e15 + 1.07636e15i 0.539887 + 0.539887i
\(606\) −1.23573e13 + 9.40100e13i −0.00614223 + 0.0467277i
\(607\) −9.22193e14 −0.454238 −0.227119 0.973867i \(-0.572931\pi\)
−0.227119 + 0.973867i \(0.572931\pi\)
\(608\) 1.89578e14 2.51531e13i 0.0925374 0.0122778i
\(609\) −1.14839e15 −0.555515
\(610\) 2.96522e13 2.25583e14i 0.0142149 0.108141i
\(611\) −2.12093e14 2.12093e14i −0.100763 0.100763i
\(612\) −6.53843e14 + 2.44412e15i −0.307851 + 1.15078i
\(613\) −4.49009e14 + 4.49009e14i −0.209518 + 0.209518i −0.804063 0.594544i \(-0.797332\pi\)
0.594544 + 0.804063i \(0.297332\pi\)
\(614\) −1.80816e15 + 1.38803e15i −0.836203 + 0.641910i
\(615\) 9.26270e14i 0.424546i
\(616\) 3.13171e14 1.29942e14i 0.142262 0.0590277i
\(617\) 1.59922e15i 0.720014i 0.932950 + 0.360007i \(0.117226\pi\)
−0.932950 + 0.360007i \(0.882774\pi\)
\(618\) 7.59739e14 + 9.89698e14i 0.339022 + 0.441637i
\(619\) −9.83868e14 + 9.83868e14i −0.435149 + 0.435149i −0.890376 0.455226i \(-0.849558\pi\)
0.455226 + 0.890376i \(0.349558\pi\)
\(620\) 1.13144e15 6.53848e14i 0.495996 0.286631i
\(621\) −1.17077e15 1.17077e15i −0.508706 0.508706i
\(622\) 2.62489e14 + 3.45034e13i 0.113048 + 0.0148599i
\(623\) −2.66155e15 −1.13619
\(624\) 6.30344e13 1.09383e14i 0.0266724 0.0462843i
\(625\) 1.14604e15 0.480684
\(626\) −3.22153e14 4.23461e13i −0.133938 0.0176057i
\(627\) 1.33138e13 + 1.33138e13i 0.00548696 + 0.00548696i
\(628\) −5.62477e14 9.73331e14i −0.229788 0.397633i
\(629\) 2.79268e15 2.79268e15i 1.13095 1.13095i
\(630\) −8.04806e14 1.04841e15i −0.323086 0.420878i
\(631\) 3.81351e15i 1.51762i −0.651311 0.758811i \(-0.725780\pi\)
0.651311 0.758811i \(-0.274220\pi\)
\(632\) −7.20863e11 + 1.74330e12i −0.000284386 + 0.000687748i
\(633\) 9.05046e14i 0.353957i
\(634\) −8.95686e14 + 6.87571e14i −0.347268 + 0.266580i
\(635\) 8.01627e14 8.01627e14i 0.308118 0.308118i
\(636\) −4.47069e14 1.19598e14i −0.170357 0.0455734i
\(637\) −5.90820e13 5.90820e13i −0.0223197 0.0223197i
\(638\) −8.88261e13 + 6.75755e14i −0.0332680 + 0.253090i
\(639\) 4.04903e15 1.50347
\(640\) 2.76825e14 2.12591e15i 0.101910 0.782629i
\(641\) 8.09256e13 0.0295370 0.0147685 0.999891i \(-0.495299\pi\)
0.0147685 + 0.999891i \(0.495299\pi\)
\(642\) 2.30644e14 1.75466e15i 0.0834642 0.634964i
\(643\) −4.31419e14 4.31419e14i −0.154788 0.154788i 0.625464 0.780253i \(-0.284910\pi\)
−0.780253 + 0.625464i \(0.784910\pi\)
\(644\) 2.02454e15 + 5.41598e14i 0.720202 + 0.192666i
\(645\) −3.35549e14 + 3.35549e14i −0.118352 + 0.118352i
\(646\) 3.20093e14 2.45718e14i 0.111943 0.0859328i
\(647\) 2.56351e15i 0.888918i −0.895799 0.444459i \(-0.853396\pi\)
0.895799 0.444459i \(-0.146604\pi\)
\(648\) −4.54408e14 + 1.09892e15i −0.156237 + 0.377836i
\(649\) 1.01941e15i 0.347539i
\(650\) 7.88044e13 + 1.02657e14i 0.0266395 + 0.0347028i
\(651\) −6.01538e14 + 6.01538e14i −0.201636 + 0.201636i
\(652\) 1.04809e15 + 1.81366e15i 0.348367 + 0.602827i
\(653\) 1.70508e15 + 1.70508e15i 0.561983 + 0.561983i 0.929870 0.367887i \(-0.119919\pi\)
−0.367887 + 0.929870i \(0.619919\pi\)
\(654\) −2.18145e15 2.86746e14i −0.712965 0.0937172i
\(655\) 3.27892e15 1.06268
\(656\) 1.81489e15 3.14936e15i 0.583284 1.01216i
\(657\) −1.56389e15 −0.498422
\(658\) 3.28759e15 + 4.32144e14i 1.03905 + 0.136580i
\(659\) 3.27825e15 + 3.27825e15i 1.02748 + 1.02748i 0.999612 + 0.0278658i \(0.00887111\pi\)
0.0278658 + 0.999612i \(0.491129\pi\)
\(660\) 1.82754e14 1.05612e14i 0.0568037 0.0328262i
\(661\) −3.34786e15 + 3.34786e15i −1.03195 + 1.03195i −0.0324779 + 0.999472i \(0.510340\pi\)
−0.999472 + 0.0324779i \(0.989660\pi\)
\(662\) −1.48963e15 1.94051e15i −0.455365 0.593195i
\(663\) 2.66389e14i 0.0807591i
\(664\) 2.55169e15 1.05876e15i 0.767191 0.318326i
\(665\) 2.10801e14i 0.0628571i
\(666\) 2.23607e15 1.71651e15i 0.661266 0.507619i
\(667\) −2.97889e15 + 2.97889e15i −0.873700 + 0.873700i
\(668\) −2.90887e14 + 1.08736e15i −0.0846164 + 0.316304i
\(669\) 1.67210e15 + 1.67210e15i 0.482413 + 0.482413i
\(670\) −2.47967e14 + 1.88644e15i −0.0709548 + 0.539798i
\(671\) 8.79061e13 0.0249486
\(672\) 1.83564e14 + 1.38351e15i 0.0516721 + 0.389449i
\(673\) −6.35604e15 −1.77461 −0.887307 0.461180i \(-0.847426\pi\)
−0.887307 + 0.461180i \(0.847426\pi\)
\(674\) −1.57552e14 + 1.19860e15i −0.0436310 + 0.331928i
\(675\) 7.99244e14 + 7.99244e14i 0.219538 + 0.219538i
\(676\) −9.35757e14 + 3.49794e15i −0.254951 + 0.953029i
\(677\) 4.38761e15 4.38761e15i 1.18574 1.18574i 0.207509 0.978233i \(-0.433464\pi\)
0.978233 0.207509i \(-0.0665357\pi\)
\(678\) 1.83506e15 1.40868e15i 0.491911 0.377615i
\(679\) 1.46384e15i 0.389232i
\(680\) −1.73369e15 4.17833e15i −0.457269 1.10206i
\(681\) 1.21949e15i 0.319058i
\(682\) 3.07438e14 + 4.00494e14i 0.0797892 + 0.103940i
\(683\) −4.43219e15 + 4.43219e15i −1.14105 + 1.14105i −0.152790 + 0.988259i \(0.548826\pi\)
−0.988259 + 0.152790i \(0.951174\pi\)
\(684\) 2.49376e14 1.44111e14i 0.0636862 0.0368035i
\(685\) 3.22901e15 + 3.22901e15i 0.818035 + 0.818035i
\(686\) 4.28173e15 + 5.62821e14i 1.07606 + 0.141445i
\(687\) 6.44814e13 0.0160758
\(688\) −1.79834e15 + 4.83421e14i −0.444770 + 0.119561i
\(689\) −1.81083e14 −0.0444295
\(690\) 1.29354e15 + 1.70032e14i 0.314854 + 0.0413866i
\(691\) 2.89530e14 + 2.89530e14i 0.0699139 + 0.0699139i 0.741199 0.671285i \(-0.234257\pi\)
−0.671285 + 0.741199i \(0.734257\pi\)
\(692\) −2.83404e15 4.90413e15i −0.678927 1.17484i
\(693\) 3.61084e14 3.61084e14i 0.0858174 0.0858174i
\(694\) −4.11027e15 5.35437e15i −0.969156 1.26250i
\(695\) 4.26157e15i 0.996905i
\(696\) −2.59257e15 1.07204e15i −0.601699 0.248805i
\(697\) 7.66989e15i 1.76607i
\(698\) −1.24617e15 + 9.56618e14i −0.284690 + 0.218541i
\(699\) −2.68213e14 + 2.68213e14i −0.0607932 + 0.0607932i
\(700\) −1.38209e15 3.69731e14i −0.310811 0.0831469i
\(701\) 1.61287e15 + 1.61287e15i 0.359874 + 0.359874i 0.863766 0.503892i \(-0.168099\pi\)
−0.503892 + 0.863766i \(0.668099\pi\)
\(702\) 5.62271e13 4.27755e14i 0.0124478 0.0946980i
\(703\) −4.49603e14 −0.0987585
\(704\) 8.28304e14 1.00354e12i 0.180526 0.000218718i
\(705\) 2.06424e15 0.446396
\(706\) 3.27103e14 2.48848e15i 0.0701874 0.533960i
\(707\) −2.90020e14 2.90020e14i −0.0617477 0.0617477i
\(708\) 4.05356e15 + 1.08439e15i 0.856355 + 0.229089i
\(709\) 1.86537e14 1.86537e14i 0.0391030 0.0391030i −0.687285 0.726388i \(-0.741198\pi\)
0.726388 + 0.687285i \(0.241198\pi\)
\(710\) −5.74267e15 + 4.40835e15i −1.19452 + 0.916970i
\(711\) 2.84117e12i 0.000586427i
\(712\) −6.00861e15 2.48458e15i −1.23065 0.508878i
\(713\) 3.12074e15i 0.634256i
\(714\) 1.79322e15 + 2.33599e15i 0.361653 + 0.471119i
\(715\) 5.84005e13 5.84005e13i 0.0116878 0.0116878i
\(716\) −3.50317e15 6.06201e15i −0.695728 1.20391i
\(717\) −2.13518e15 2.13518e15i −0.420802 0.420802i
\(718\) 5.26957e15 + 6.92670e14i 1.03060 + 0.135470i
\(719\) −6.94242e15 −1.34742 −0.673709 0.738997i \(-0.735300\pi\)
−0.673709 + 0.738997i \(0.735300\pi\)
\(720\) −8.38201e14 3.11813e15i −0.161443 0.600573i
\(721\) −5.39699e15 −1.03159
\(722\) 5.18124e15 + 6.81059e14i 0.982832 + 0.129190i
\(723\) 2.05252e15 + 2.05252e15i 0.386391 + 0.386391i
\(724\) −8.70512e15 + 5.03059e15i −1.62635 + 0.939847i
\(725\) 2.03359e15 2.03359e15i 0.377055 0.377055i
\(726\) −1.47409e15 1.92026e15i −0.271251 0.353354i
\(727\) 4.03478e15i 0.736853i 0.929657 + 0.368426i \(0.120103\pi\)
−0.929657 + 0.368426i \(0.879897\pi\)
\(728\) 2.09285e14 + 5.04395e14i 0.0379329 + 0.0914215i
\(729\) 3.16490e14i 0.0569323i
\(730\) 2.21804e15 1.70268e15i 0.395999 0.303988i
\(731\) −2.77848e15 + 2.77848e15i −0.492335 + 0.492335i
\(732\) −9.35097e13 + 3.49547e14i −0.0164454 + 0.0614745i
\(733\) −5.85001e15 5.85001e15i −1.02114 1.02114i −0.999772 0.0213673i \(-0.993198\pi\)
−0.0213673 0.999772i \(-0.506802\pi\)
\(734\) −3.85606e14 + 2.93355e15i −0.0668060 + 0.508235i
\(735\) 5.75028e14 0.0988800
\(736\) 4.06493e15 + 3.11262e15i 0.693785 + 0.531248i
\(737\) −7.35116e14 −0.124533
\(738\) 7.13458e14 5.42772e15i 0.119966 0.912657i
\(739\) 6.33201e15 + 6.33201e15i 1.05681 + 1.05681i 0.998286 + 0.0585244i \(0.0186395\pi\)
0.0585244 + 0.998286i \(0.481360\pi\)
\(740\) −1.30254e15 + 4.86900e15i −0.215782 + 0.806613i
\(741\) −2.14434e13 + 2.14434e13i −0.00352608 + 0.00352608i
\(742\) 1.58793e15 1.21897e15i 0.259185 0.198963i
\(743\) 7.78552e15i 1.26139i −0.776031 0.630695i \(-0.782770\pi\)
0.776031 0.630695i \(-0.217230\pi\)
\(744\) −1.91955e15 + 7.96466e14i −0.308708 + 0.128090i
\(745\) 1.99973e15i 0.319236i
\(746\) 5.97315e15 + 7.78110e15i 0.946541 + 1.23304i
\(747\) 2.94208e15 2.94208e15i 0.462798 0.462798i
\(748\) 1.51328e15 8.74507e14i 0.236298 0.136554i
\(749\) 5.41309e15 + 5.41309e15i 0.839065 + 0.839065i
\(750\) −3.22471e15 4.23879e14i −0.496197 0.0652236i
\(751\) 2.79527e15 0.426976 0.213488 0.976946i \(-0.431518\pi\)
0.213488 + 0.976946i \(0.431518\pi\)
\(752\) 7.01852e15 + 4.04459e15i 1.06426 + 0.613304i
\(753\) 3.71169e15 0.558727
\(754\) −1.08838e15 1.43064e14i −0.162643 0.0213790i
\(755\) −6.45047e15 6.45047e15i −0.956936 0.956936i
\(756\) 2.38640e15 + 4.12952e15i 0.351459 + 0.608177i
\(757\) 2.93505e15 2.93505e15i 0.429130 0.429130i −0.459202 0.888332i \(-0.651865\pi\)
0.888332 + 0.459202i \(0.151865\pi\)
\(758\) 4.73992e15 + 6.17461e15i 0.688003 + 0.896249i
\(759\) 5.04072e14i 0.0726378i
\(760\) −1.96785e14 + 4.75897e14i −0.0281525 + 0.0680829i