Properties

Label 16.12.e.a.13.14
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 13.14
Character \(\chi\) = 16.13
Dual form 16.12.e.a.5.14

$q$-expansion

\(f(q)\) \(=\) \(q+(25.1148 + 37.6464i) q^{2} +(367.824 + 367.824i) q^{3} +(-786.499 + 1890.96i) q^{4} +(-502.344 + 502.344i) q^{5} +(-4609.43 + 23085.1i) q^{6} +33063.2i q^{7} +(-90940.4 + 17882.1i) q^{8} +93442.1i q^{9} +O(q^{10})\) \(q+(25.1148 + 37.6464i) q^{2} +(367.824 + 367.824i) q^{3} +(-786.499 + 1890.96i) q^{4} +(-502.344 + 502.344i) q^{5} +(-4609.43 + 23085.1i) q^{6} +33063.2i q^{7} +(-90940.4 + 17882.1i) q^{8} +93442.1i q^{9} +(-31527.7 - 6295.18i) q^{10} +(335681. - 335681. i) q^{11} +(-984833. + 406247. i) q^{12} +(568061. + 568061. i) q^{13} +(-1.24471e6 + 830373. i) q^{14} -369548. q^{15} +(-2.95714e6 - 2.97447e6i) q^{16} -6.78457e6 q^{17} +(-3.51776e6 + 2.34678e6i) q^{18} +(1.33879e6 + 1.33879e6i) q^{19} +(-554819. - 1.34500e6i) q^{20} +(-1.21614e7 + 1.21614e7i) q^{21} +(2.10677e7 + 4.20662e6i) q^{22} -1.07133e6i q^{23} +(-4.00276e7 - 2.68726e7i) q^{24} +4.83234e7i q^{25} +(-7.11873e6 + 3.56522e7i) q^{26} +(3.07887e7 - 3.07887e7i) q^{27} +(-6.25211e7 - 2.60041e7i) q^{28} +(5.01359e7 + 5.01359e7i) q^{29} +(-9.28112e6 - 1.39122e7i) q^{30} +2.95969e8 q^{31} +(3.77101e7 - 1.86029e8i) q^{32} +2.46943e8 q^{33} +(-1.70393e8 - 2.55414e8i) q^{34} +(-1.66091e7 - 1.66091e7i) q^{35} +(-1.76695e8 - 7.34921e7i) q^{36} +(5.11883e8 - 5.11883e8i) q^{37} +(-1.67772e7 + 8.40240e7i) q^{38} +4.17893e8i q^{39} +(3.67004e7 - 5.46664e7i) q^{40} +9.31803e8i q^{41} +(-7.63265e8 - 1.52402e8i) q^{42} +(-1.27362e9 + 1.27362e9i) q^{43} +(3.70746e8 + 8.98771e8i) q^{44} +(-4.69401e7 - 4.69401e7i) q^{45} +(4.03318e7 - 2.69063e7i) q^{46} -1.80739e7 q^{47} +(6.37366e6 - 2.18179e9i) q^{48} +8.84154e8 q^{49} +(-1.81920e9 + 1.21363e9i) q^{50} +(-2.49553e9 - 2.49553e9i) q^{51} +(-1.52096e9 + 6.27401e8i) q^{52} +(2.29607e9 - 2.29607e9i) q^{53} +(1.93233e9 + 3.85832e8i) q^{54} +3.37255e8i q^{55} +(-5.91240e8 - 3.00678e9i) q^{56} +9.84878e8i q^{57} +(-6.28284e8 + 3.14658e9i) q^{58} +(-4.81453e8 + 4.81453e8i) q^{59} +(2.90649e8 - 6.98801e8i) q^{60} +(1.30887e9 + 1.30887e9i) q^{61} +(7.43318e9 + 1.11422e10i) q^{62} -3.08949e9 q^{63} +(7.95039e9 - 3.25242e9i) q^{64} -5.70724e8 q^{65} +(6.20191e9 + 9.29651e9i) q^{66} +(-9.42251e9 - 9.42251e9i) q^{67} +(5.33606e9 - 1.28293e10i) q^{68} +(3.94062e8 - 3.94062e8i) q^{69} +(2.08139e8 - 1.04240e9i) q^{70} -1.74203e10i q^{71} +(-1.67094e9 - 8.49767e9i) q^{72} -8.91310e9i q^{73} +(3.21263e10 + 6.41472e9i) q^{74} +(-1.77745e10 + 1.77745e10i) q^{75} +(-3.58455e9 + 1.47864e9i) q^{76} +(1.10987e10 + 1.10987e10i) q^{77} +(-1.57322e10 + 1.04953e10i) q^{78} -4.07466e10 q^{79} +(2.97971e9 + 8.70463e6i) q^{80} +3.92026e10 q^{81} +(-3.50790e10 + 2.34020e10i) q^{82} +(1.16461e10 + 1.16461e10i) q^{83} +(-1.34318e10 - 3.25617e10i) q^{84} +(3.40819e9 - 3.40819e9i) q^{85} +(-7.99336e10 - 1.59605e10i) q^{86} +3.68824e10i q^{87} +(-2.45243e10 + 3.65297e10i) q^{88} -7.96706e10i q^{89} +(5.88235e8 - 2.94601e9i) q^{90} +(-1.87819e10 + 1.87819e10i) q^{91} +(2.02585e9 + 8.42602e8i) q^{92} +(1.08864e11 + 1.08864e11i) q^{93} +(-4.53922e8 - 6.80417e8i) q^{94} -1.34507e9 q^{95} +(8.22966e10 - 5.45552e10i) q^{96} -1.03397e10 q^{97} +(2.22053e10 + 3.32852e10i) q^{98} +(3.13667e10 + 3.13667e10i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 25.1148 + 37.6464i 0.554963 + 0.831875i
\(3\) 367.824 + 367.824i 0.873923 + 0.873923i 0.992897 0.118974i \(-0.0379606\pi\)
−0.118974 + 0.992897i \(0.537961\pi\)
\(4\) −786.499 + 1890.96i −0.384032 + 0.923320i
\(5\) −502.344 + 502.344i −0.0718896 + 0.0718896i −0.742137 0.670248i \(-0.766188\pi\)
0.670248 + 0.742137i \(0.266188\pi\)
\(6\) −4609.43 + 23085.1i −0.242000 + 1.21199i
\(7\) 33063.2i 0.743542i 0.928325 + 0.371771i \(0.121249\pi\)
−0.928325 + 0.371771i \(0.878751\pi\)
\(8\) −90940.4 + 17882.1i −0.981210 + 0.192941i
\(9\) 93442.1i 0.527483i
\(10\) −31527.7 6295.18i −0.0996993 0.0199071i
\(11\) 335681. 335681.i 0.628444 0.628444i −0.319232 0.947677i \(-0.603425\pi\)
0.947677 + 0.319232i \(0.103425\pi\)
\(12\) −984833. + 406247.i −1.14253 + 0.471295i
\(13\) 568061. + 568061.i 0.424333 + 0.424333i 0.886692 0.462360i \(-0.152997\pi\)
−0.462360 + 0.886692i \(0.652997\pi\)
\(14\) −1.24471e6 + 830373.i −0.618534 + 0.412638i
\(15\) −369548. −0.125652
\(16\) −2.95714e6 2.97447e6i −0.705038 0.709169i
\(17\) −6.78457e6 −1.15892 −0.579460 0.815001i \(-0.696736\pi\)
−0.579460 + 0.815001i \(0.696736\pi\)
\(18\) −3.51776e6 + 2.34678e6i −0.438800 + 0.292734i
\(19\) 1.33879e6 + 1.33879e6i 0.124042 + 0.124042i 0.766402 0.642361i \(-0.222045\pi\)
−0.642361 + 0.766402i \(0.722045\pi\)
\(20\) −554819. 1.34500e6i −0.0387691 0.0939850i
\(21\) −1.21614e7 + 1.21614e7i −0.649798 + 0.649798i
\(22\) 2.10677e7 + 4.20662e6i 0.871550 + 0.174024i
\(23\) 1.07133e6i 0.0347074i −0.999849 0.0173537i \(-0.994476\pi\)
0.999849 0.0173537i \(-0.00552412\pi\)
\(24\) −4.00276e7 2.68726e7i −1.02612 0.688887i
\(25\) 4.83234e7i 0.989664i
\(26\) −7.11873e6 + 3.56522e7i −0.117503 + 0.588481i
\(27\) 3.07887e7 3.07887e7i 0.412943 0.412943i
\(28\) −6.25211e7 2.60041e7i −0.686526 0.285544i
\(29\) 5.01359e7 + 5.01359e7i 0.453899 + 0.453899i 0.896647 0.442747i \(-0.145996\pi\)
−0.442747 + 0.896647i \(0.645996\pi\)
\(30\) −9.28112e6 1.39122e7i −0.0697322 0.104527i
\(31\) 2.95969e8 1.85676 0.928382 0.371628i \(-0.121200\pi\)
0.928382 + 0.371628i \(0.121200\pi\)
\(32\) 3.77101e7 1.86029e8i 0.198670 0.980066i
\(33\) 2.46943e8 1.09842
\(34\) −1.70393e8 2.55414e8i −0.643157 0.964076i
\(35\) −1.66091e7 1.66091e7i −0.0534529 0.0534529i
\(36\) −1.76695e8 7.34921e7i −0.487036 0.202571i
\(37\) 5.11883e8 5.11883e8i 1.21356 1.21356i 0.243711 0.969848i \(-0.421635\pi\)
0.969848 0.243711i \(-0.0783649\pi\)
\(38\) −1.67772e7 + 8.40240e7i −0.0343487 + 0.172026i
\(39\) 4.17893e8i 0.741669i
\(40\) 3.67004e7 5.46664e7i 0.0566684 0.0844093i
\(41\) 9.31803e8i 1.25607i 0.778186 + 0.628034i \(0.216140\pi\)
−0.778186 + 0.628034i \(0.783860\pi\)
\(42\) −7.63265e8 1.52402e8i −0.901165 0.179937i
\(43\) −1.27362e9 + 1.27362e9i −1.32118 + 1.32118i −0.408358 + 0.912822i \(0.633899\pi\)
−0.912822 + 0.408358i \(0.866101\pi\)
\(44\) 3.70746e8 + 8.98771e8i 0.338912 + 0.821598i
\(45\) −4.69401e7 4.69401e7i −0.0379206 0.0379206i
\(46\) 4.03318e7 2.69063e7i 0.0288722 0.0192613i
\(47\) −1.80739e7 −0.0114951 −0.00574756 0.999983i \(-0.501830\pi\)
−0.00574756 + 0.999983i \(0.501830\pi\)
\(48\) 6.37366e6 2.18179e9i 0.00361046 1.23591i
\(49\) 8.84154e8 0.447146
\(50\) −1.81920e9 + 1.21363e9i −0.823277 + 0.549227i
\(51\) −2.49553e9 2.49553e9i −1.01281 1.01281i
\(52\) −1.52096e9 + 6.27401e8i −0.554752 + 0.228837i
\(53\) 2.29607e9 2.29607e9i 0.754168 0.754168i −0.221086 0.975254i \(-0.570960\pi\)
0.975254 + 0.221086i \(0.0709602\pi\)
\(54\) 1.93233e9 + 3.85832e8i 0.572685 + 0.114349i
\(55\) 3.37255e8i 0.0903572i
\(56\) −5.91240e8 3.00678e9i −0.143460 0.729571i
\(57\) 9.84878e8i 0.216806i
\(58\) −6.28284e8 + 3.14658e9i −0.125690 + 0.629485i
\(59\) −4.81453e8 + 4.81453e8i −0.0876734 + 0.0876734i −0.749583 0.661910i \(-0.769746\pi\)
0.661910 + 0.749583i \(0.269746\pi\)
\(60\) 2.90649e8 6.98801e8i 0.0482545 0.116017i
\(61\) 1.30887e9 + 1.30887e9i 0.198419 + 0.198419i 0.799322 0.600903i \(-0.205192\pi\)
−0.600903 + 0.799322i \(0.705192\pi\)
\(62\) 7.43318e9 + 1.11422e10i 1.03043 + 1.54460i
\(63\) −3.08949e9 −0.392206
\(64\) 7.95039e9 3.25242e9i 0.925548 0.378631i
\(65\) −5.70724e8 −0.0610103
\(66\) 6.20191e9 + 9.29651e9i 0.609585 + 0.913752i
\(67\) −9.42251e9 9.42251e9i −0.852619 0.852619i 0.137836 0.990455i \(-0.455985\pi\)
−0.990455 + 0.137836i \(0.955985\pi\)
\(68\) 5.33606e9 1.28293e10i 0.445063 1.07005i
\(69\) 3.94062e8 3.94062e8i 0.0303316 0.0303316i
\(70\) 2.08139e8 1.04240e9i 0.0148018 0.0741305i
\(71\) 1.74203e10i 1.14587i −0.819601 0.572934i \(-0.805805\pi\)
0.819601 0.572934i \(-0.194195\pi\)
\(72\) −1.67094e9 8.49767e9i −0.101773 0.517572i
\(73\) 8.91310e9i 0.503215i −0.967829 0.251607i \(-0.919041\pi\)
0.967829 0.251607i \(-0.0809591\pi\)
\(74\) 3.21263e10 + 6.41472e9i 1.68301 + 0.336049i
\(75\) −1.77745e10 + 1.77745e10i −0.864890 + 0.864890i
\(76\) −3.58455e9 + 1.47864e9i −0.162166 + 0.0668941i
\(77\) 1.10987e10 + 1.10987e10i 0.467274 + 0.467274i
\(78\) −1.57322e10 + 1.04953e10i −0.616976 + 0.411599i
\(79\) −4.07466e10 −1.48985 −0.744924 0.667149i \(-0.767514\pi\)
−0.744924 + 0.667149i \(0.767514\pi\)
\(80\) 2.97971e9 + 8.70463e6i 0.101667 + 0.000296999i
\(81\) 3.92026e10 1.24924
\(82\) −3.50790e10 + 2.34020e10i −1.04489 + 0.697071i
\(83\) 1.16461e10 + 1.16461e10i 0.324527 + 0.324527i 0.850501 0.525974i \(-0.176299\pi\)
−0.525974 + 0.850501i \(0.676299\pi\)
\(84\) −1.34318e10 3.25617e10i −0.350428 0.849515i
\(85\) 3.40819e9 3.40819e9i 0.0833143 0.0833143i
\(86\) −7.99336e10 1.59605e10i −1.83226 0.365851i
\(87\) 3.68824e10i 0.793346i
\(88\) −2.45243e10 + 3.65297e10i −0.495383 + 0.737889i
\(89\) 7.96706e10i 1.51235i −0.654368 0.756176i \(-0.727065\pi\)
0.654368 0.756176i \(-0.272935\pi\)
\(90\) 5.88235e8 2.94601e9i 0.0105007 0.0525897i
\(91\) −1.87819e10 + 1.87819e10i −0.315509 + 0.315509i
\(92\) 2.02585e9 + 8.42602e8i 0.0320460 + 0.0133288i
\(93\) 1.08864e11 + 1.08864e11i 1.62267 + 1.62267i
\(94\) −4.53922e8 6.80417e8i −0.00637937 0.00956251i
\(95\) −1.34507e9 −0.0178346
\(96\) 8.22966e10 5.45552e10i 1.03013 0.682880i
\(97\) −1.03397e10 −0.122254 −0.0611269 0.998130i \(-0.519469\pi\)
−0.0611269 + 0.998130i \(0.519469\pi\)
\(98\) 2.22053e10 + 3.32852e10i 0.248149 + 0.371970i
\(99\) 3.13667e10 + 3.13667e10i 0.331494 + 0.331494i
\(100\) −9.13776e10 3.80063e10i −0.913776 0.380063i
\(101\) −3.36018e10 + 3.36018e10i −0.318123 + 0.318123i −0.848046 0.529923i \(-0.822221\pi\)
0.529923 + 0.848046i \(0.322221\pi\)
\(102\) 3.12730e10 1.56622e11i 0.280459 1.40460i
\(103\) 9.27041e10i 0.787942i −0.919123 0.393971i \(-0.871101\pi\)
0.919123 0.393971i \(-0.128899\pi\)
\(104\) −6.18179e10 4.15016e10i −0.498231 0.334489i
\(105\) 1.22184e10i 0.0934275i
\(106\) 1.44104e11 + 2.87735e10i 1.04591 + 0.208838i
\(107\) 2.88146e10 2.88146e10i 0.198610 0.198610i −0.600794 0.799404i \(-0.705149\pi\)
0.799404 + 0.600794i \(0.205149\pi\)
\(108\) 3.40049e10 + 8.24354e10i 0.222695 + 0.539862i
\(109\) −2.21468e10 2.21468e10i −0.137868 0.137868i 0.634804 0.772673i \(-0.281081\pi\)
−0.772673 + 0.634804i \(0.781081\pi\)
\(110\) −1.26964e10 + 8.47006e9i −0.0751659 + 0.0501449i
\(111\) 3.76565e11 2.12111
\(112\) 9.83455e10 9.77725e10i 0.527297 0.524225i
\(113\) −1.71538e11 −0.875849 −0.437924 0.899012i \(-0.644286\pi\)
−0.437924 + 0.899012i \(0.644286\pi\)
\(114\) −3.70771e10 + 2.47350e10i −0.180355 + 0.120319i
\(115\) 5.38178e8 + 5.38178e8i 0.00249510 + 0.00249510i
\(116\) −1.34237e11 + 5.53731e10i −0.593406 + 0.244782i
\(117\) −5.30808e10 + 5.30808e10i −0.223829 + 0.223829i
\(118\) −3.02165e10 6.03339e9i −0.121589 0.0242778i
\(119\) 2.24319e11i 0.861705i
\(120\) 3.36069e10 6.60832e9i 0.123291 0.0242434i
\(121\) 5.99484e10i 0.210116i
\(122\) −1.64023e10 + 8.21462e10i −0.0549446 + 0.275175i
\(123\) −3.42740e11 + 3.42740e11i −1.09771 + 1.09771i
\(124\) −2.32779e11 + 5.59665e11i −0.713057 + 1.71439i
\(125\) −4.88035e10 4.88035e10i −0.143036 0.143036i
\(126\) −7.75918e10 1.16308e11i −0.217660 0.326266i
\(127\) 5.54635e11 1.48966 0.744830 0.667254i \(-0.232531\pi\)
0.744830 + 0.667254i \(0.232531\pi\)
\(128\) 3.22114e11 + 2.17620e11i 0.828619 + 0.559814i
\(129\) −9.36933e11 −2.30922
\(130\) −1.43336e10 2.14857e10i −0.0338584 0.0507529i
\(131\) −4.50085e11 4.50085e11i −1.01930 1.01930i −0.999810 0.0194915i \(-0.993795\pi\)
−0.0194915 0.999810i \(-0.506205\pi\)
\(132\) −1.94220e11 + 4.66959e11i −0.421830 + 1.01420i
\(133\) −4.42646e10 + 4.42646e10i −0.0922301 + 0.0922301i
\(134\) 1.18079e11 5.91367e11i 0.236101 1.18244i
\(135\) 3.09330e10i 0.0593727i
\(136\) 6.16992e11 1.21323e11i 1.13714 0.223603i
\(137\) 7.75745e11i 1.37327i −0.727002 0.686635i \(-0.759087\pi\)
0.727002 0.686635i \(-0.240913\pi\)
\(138\) 2.47318e10 + 4.93824e9i 0.0420650 + 0.00839918i
\(139\) −3.80649e11 + 3.80649e11i −0.622219 + 0.622219i −0.946098 0.323880i \(-0.895013\pi\)
0.323880 + 0.946098i \(0.395013\pi\)
\(140\) 4.44701e10 1.83441e10i 0.0698818 0.0288265i
\(141\) −6.64802e9 6.64802e9i −0.0100459 0.0100459i
\(142\) 6.55811e11 4.37507e11i 0.953220 0.635915i
\(143\) 3.81374e11 0.533339
\(144\) 2.77941e11 2.76322e11i 0.374075 0.371896i
\(145\) −5.03709e10 −0.0652613
\(146\) 3.35546e11 2.23850e11i 0.418612 0.279265i
\(147\) 3.25213e11 + 3.25213e11i 0.390771 + 0.390771i
\(148\) 5.65354e11 + 1.37054e12i 0.654457 + 1.58655i
\(149\) −1.21482e11 + 1.21482e11i −0.135515 + 0.135515i −0.771610 0.636095i \(-0.780549\pi\)
0.636095 + 0.771610i \(0.280549\pi\)
\(150\) −1.11555e12 2.22744e11i −1.19946 0.239499i
\(151\) 4.18981e11i 0.434331i −0.976135 0.217166i \(-0.930319\pi\)
0.976135 0.217166i \(-0.0696812\pi\)
\(152\) −1.45691e11 9.78097e10i −0.145644 0.0977783i
\(153\) 6.33965e11i 0.611311i
\(154\) −1.39084e11 + 6.96565e11i −0.129394 + 0.648034i
\(155\) −1.48678e11 + 1.48678e11i −0.133482 + 0.133482i
\(156\) −7.90219e11 3.28672e11i −0.684797 0.284825i
\(157\) 1.64950e12 + 1.64950e12i 1.38008 + 1.38008i 0.844456 + 0.535626i \(0.179924\pi\)
0.535626 + 0.844456i \(0.320076\pi\)
\(158\) −1.02334e12 1.53396e12i −0.826810 1.23937i
\(159\) 1.68910e12 1.31817
\(160\) 7.45070e10 + 1.12394e11i 0.0561743 + 0.0847389i
\(161\) 3.54217e10 0.0258064
\(162\) 9.84564e11 + 1.47584e12i 0.693284 + 1.03922i
\(163\) 1.07698e12 + 1.07698e12i 0.733121 + 0.733121i 0.971237 0.238116i \(-0.0765299\pi\)
−0.238116 + 0.971237i \(0.576530\pi\)
\(164\) −1.76200e12 7.32862e11i −1.15975 0.482371i
\(165\) −1.24050e11 + 1.24050e11i −0.0789653 + 0.0789653i
\(166\) −1.45944e11 + 7.30922e11i −0.0898655 + 0.450066i
\(167\) 1.59845e12i 0.952268i −0.879373 0.476134i \(-0.842038\pi\)
0.879373 0.476134i \(-0.157962\pi\)
\(168\) 8.88493e11 1.32344e12i 0.512216 0.762961i
\(169\) 1.14677e12i 0.639883i
\(170\) 2.13902e11 + 4.27101e10i 0.115543 + 0.0230708i
\(171\) −1.25099e11 + 1.25099e11i −0.0654299 + 0.0654299i
\(172\) −1.40666e12 3.41005e12i −0.712495 1.72725i
\(173\) 1.45486e12 + 1.45486e12i 0.713785 + 0.713785i 0.967325 0.253540i \(-0.0815949\pi\)
−0.253540 + 0.967325i \(0.581595\pi\)
\(174\) −1.38849e12 + 9.26291e11i −0.659965 + 0.440278i
\(175\) −1.59773e12 −0.735856
\(176\) −1.99113e12 5.81668e9i −0.888751 0.00259631i
\(177\) −3.54180e11 −0.153240
\(178\) 2.99931e12 2.00091e12i 1.25809 0.839299i
\(179\) −1.30891e12 1.30891e12i −0.532376 0.532376i 0.388903 0.921279i \(-0.372854\pi\)
−0.921279 + 0.388903i \(0.872854\pi\)
\(180\) 1.25680e11 5.18434e10i 0.0495756 0.0204501i
\(181\) −2.38152e12 + 2.38152e12i −0.911219 + 0.911219i −0.996368 0.0851488i \(-0.972863\pi\)
0.0851488 + 0.996368i \(0.472863\pi\)
\(182\) −1.17877e12 2.35368e11i −0.437560 0.0873683i
\(183\) 9.62869e11i 0.346806i
\(184\) 1.91577e10 + 9.74275e10i 0.00669647 + 0.0340552i
\(185\) 5.14282e11i 0.174485i
\(186\) −1.36425e12 + 6.83245e12i −0.449337 + 2.25038i
\(187\) −2.27745e12 + 2.27745e12i −0.728316 + 0.728316i
\(188\) 1.42151e10 3.41770e10i 0.00441450 0.0106137i
\(189\) 1.01797e12 + 1.01797e12i 0.307040 + 0.307040i
\(190\) −3.37810e10 5.06369e10i −0.00989755 0.0148362i
\(191\) −3.52280e12 −1.00278 −0.501388 0.865223i \(-0.667177\pi\)
−0.501388 + 0.865223i \(0.667177\pi\)
\(192\) 4.12066e12 + 1.72803e12i 1.13975 + 0.477963i
\(193\) 4.01739e12 1.07989 0.539944 0.841701i \(-0.318445\pi\)
0.539944 + 0.841701i \(0.318445\pi\)
\(194\) −2.59678e11 3.89251e11i −0.0678463 0.101700i
\(195\) −2.09926e11 2.09926e11i −0.0533183 0.0533183i
\(196\) −6.95386e11 + 1.67190e12i −0.171719 + 0.412859i
\(197\) 3.98851e12 3.98851e12i 0.957737 0.957737i −0.0414057 0.999142i \(-0.513184\pi\)
0.999142 + 0.0414057i \(0.0131836\pi\)
\(198\) −3.93076e11 + 1.96861e12i −0.0917947 + 0.459728i
\(199\) 1.41250e11i 0.0320846i −0.999871 0.0160423i \(-0.994893\pi\)
0.999871 0.0160423i \(-0.00510665\pi\)
\(200\) −8.64126e11 4.39455e12i −0.190947 0.971068i
\(201\) 6.93165e12i 1.49025i
\(202\) −2.10889e12 4.21086e11i −0.441186 0.0880923i
\(203\) −1.65765e12 + 1.65765e12i −0.337493 + 0.337493i
\(204\) 6.68167e12 2.75621e12i 1.32409 0.546194i
\(205\) −4.68086e11 4.68086e11i −0.0902982 0.0902982i
\(206\) 3.48997e12 2.32824e12i 0.655469 0.437278i
\(207\) 1.00108e11 0.0183076
\(208\) 9.84338e9 3.36952e12i 0.00175306 0.600095i
\(209\) 8.98812e11 0.155907
\(210\) 4.59980e11 3.06863e11i 0.0777200 0.0518488i
\(211\) −3.64182e12 3.64182e12i −0.599466 0.599466i 0.340704 0.940170i \(-0.389334\pi\)
−0.940170 + 0.340704i \(0.889334\pi\)
\(212\) 2.53592e12 + 6.14763e12i 0.406713 + 0.985963i
\(213\) 6.40761e12 6.40761e12i 1.00140 1.00140i
\(214\) 1.80843e12 + 3.61093e11i 0.275440 + 0.0549976i
\(215\) 1.27959e12i 0.189958i
\(216\) −2.24937e12 + 3.35050e12i −0.325510 + 0.484858i
\(217\) 9.78567e12i 1.38058i
\(218\) 2.77535e11 1.38996e12i 0.0381775 0.191201i
\(219\) 3.27845e12 3.27845e12i 0.439771 0.439771i
\(220\) −6.37734e11 2.65250e11i −0.0834286 0.0347001i
\(221\) −3.85405e12 3.85405e12i −0.491768 0.491768i
\(222\) 9.45735e12 + 1.41763e13i 1.17714 + 1.76450i
\(223\) −5.31451e12 −0.645337 −0.322668 0.946512i \(-0.604580\pi\)
−0.322668 + 0.946512i \(0.604580\pi\)
\(224\) 6.15070e12 + 1.24682e12i 0.728720 + 0.147720i
\(225\) −4.51544e12 −0.522031
\(226\) −4.30814e12 6.45779e12i −0.486064 0.728597i
\(227\) −4.88964e12 4.88964e12i −0.538437 0.538437i 0.384633 0.923070i \(-0.374328\pi\)
−0.923070 + 0.384633i \(0.874328\pi\)
\(228\) −1.86236e12 7.74605e11i −0.200181 0.0832605i
\(229\) −7.07133e12 + 7.07133e12i −0.742003 + 0.742003i −0.972963 0.230960i \(-0.925813\pi\)
0.230960 + 0.972963i \(0.425813\pi\)
\(230\) −6.74424e9 + 3.37766e10i −0.000690924 + 0.00346030i
\(231\) 8.16472e12i 0.816724i
\(232\) −5.45592e12 3.66284e12i −0.532947 0.357795i
\(233\) 1.54810e13i 1.47687i 0.674324 + 0.738435i \(0.264435\pi\)
−0.674324 + 0.738435i \(0.735565\pi\)
\(234\) −3.33141e12 6.65189e11i −0.310414 0.0619809i
\(235\) 9.07932e9 9.07932e9i 0.000826380 0.000826380i
\(236\) −5.31746e11 1.28907e12i −0.0472811 0.114620i
\(237\) −1.49876e13 1.49876e13i −1.30201 1.30201i
\(238\) 8.44481e12 5.63373e12i 0.716831 0.478214i
\(239\) 1.47869e13 1.22656 0.613280 0.789866i \(-0.289850\pi\)
0.613280 + 0.789866i \(0.289850\pi\)
\(240\) 1.09281e12 + 1.09921e12i 0.0885895 + 0.0891086i
\(241\) −3.70990e12 −0.293946 −0.146973 0.989140i \(-0.546953\pi\)
−0.146973 + 0.989140i \(0.546953\pi\)
\(242\) −2.25684e12 + 1.50559e12i −0.174790 + 0.116606i
\(243\) 8.96555e12 + 8.96555e12i 0.678801 + 0.678801i
\(244\) −3.50445e12 + 1.44560e12i −0.259403 + 0.107005i
\(245\) −4.44149e11 + 4.44149e11i −0.0321452 + 0.0321452i
\(246\) −2.15107e13 4.29508e12i −1.52234 0.303968i
\(247\) 1.52103e12i 0.105270i
\(248\) −2.69155e13 + 5.29255e12i −1.82188 + 0.358246i
\(249\) 8.56743e12i 0.567223i
\(250\) 6.11587e11 3.06296e12i 0.0396085 0.198368i
\(251\) 1.64619e13 1.64619e13i 1.04297 1.04297i 0.0439391 0.999034i \(-0.486009\pi\)
0.999034 0.0439391i \(-0.0139908\pi\)
\(252\) 2.42988e12 5.84210e12i 0.150620 0.362131i
\(253\) −3.59626e11 3.59626e11i −0.0218116 0.0218116i
\(254\) 1.39295e13 + 2.08800e13i 0.826706 + 1.23921i
\(255\) 2.50723e12 0.145621
\(256\) −1.02783e11 + 1.75919e13i −0.00584255 + 0.999983i
\(257\) 2.20187e13 1.22506 0.612532 0.790446i \(-0.290151\pi\)
0.612532 + 0.790446i \(0.290151\pi\)
\(258\) −2.35308e13 3.52721e13i −1.28153 1.92098i
\(259\) 1.69245e13 + 1.69245e13i 0.902331 + 0.902331i
\(260\) 4.48874e11 1.07922e12i 0.0234299 0.0563320i
\(261\) −4.68480e12 + 4.68480e12i −0.239424 + 0.239424i
\(262\) 5.64030e12 2.82479e13i 0.282257 1.41361i
\(263\) 4.64085e12i 0.227426i 0.993514 + 0.113713i \(0.0362745\pi\)
−0.993514 + 0.113713i \(0.963726\pi\)
\(264\) −2.24571e13 + 4.41587e12i −1.07779 + 0.211931i
\(265\) 2.30684e12i 0.108434i
\(266\) −2.77810e12 5.54708e11i −0.127908 0.0255397i
\(267\) 2.93047e13 2.93047e13i 1.32168 1.32168i
\(268\) 2.52284e13 1.04068e13i 1.11467 0.459807i
\(269\) −3.23177e12 3.23177e12i −0.139895 0.139895i 0.633691 0.773586i \(-0.281539\pi\)
−0.773586 + 0.633691i \(0.781539\pi\)
\(270\) −1.16452e12 + 7.76875e11i −0.0493906 + 0.0329496i
\(271\) −3.04462e13 −1.26533 −0.632663 0.774427i \(-0.718038\pi\)
−0.632663 + 0.774427i \(0.718038\pi\)
\(272\) 2.00630e13 + 2.01805e13i 0.817083 + 0.821870i
\(273\) −1.38169e13 −0.551461
\(274\) 2.92040e13 1.94826e13i 1.14239 0.762114i
\(275\) 1.62212e13 + 1.62212e13i 0.621949 + 0.621949i
\(276\) 4.35226e11 + 1.05508e12i 0.0163574 + 0.0396540i
\(277\) 1.12987e13 1.12987e13i 0.416282 0.416282i −0.467638 0.883920i \(-0.654895\pi\)
0.883920 + 0.467638i \(0.154895\pi\)
\(278\) −2.38899e13 4.77014e12i −0.862916 0.172300i
\(279\) 2.76559e13i 0.979412i
\(280\) 1.80744e12 + 1.21343e12i 0.0627618 + 0.0421353i
\(281\) 2.01696e13i 0.686772i −0.939194 0.343386i \(-0.888426\pi\)
0.939194 0.343386i \(-0.111574\pi\)
\(282\) 8.33104e10 4.17237e11i 0.00278182 0.0139320i
\(283\) −2.67176e12 + 2.67176e12i −0.0874929 + 0.0874929i −0.749499 0.662006i \(-0.769705\pi\)
0.662006 + 0.749499i \(0.269705\pi\)
\(284\) 3.29411e13 + 1.37010e13i 1.05800 + 0.440051i
\(285\) −4.94748e11 4.94748e11i −0.0155861 0.0155861i
\(286\) 9.57813e12 + 1.43574e13i 0.295983 + 0.443672i
\(287\) −3.08084e13 −0.933938
\(288\) 1.73829e13 + 3.52371e12i 0.516969 + 0.104795i
\(289\) 1.17585e13 0.343095
\(290\) −1.26505e12 1.89628e12i −0.0362176 0.0542893i
\(291\) −3.80318e12 3.80318e12i −0.106840 0.106840i
\(292\) 1.68543e13 + 7.01014e12i 0.464628 + 0.193251i
\(293\) −3.85320e13 + 3.85320e13i −1.04244 + 1.04244i −0.0433791 + 0.999059i \(0.513812\pi\)
−0.999059 + 0.0433791i \(0.986188\pi\)
\(294\) −4.07545e12 + 2.04107e13i −0.108209 + 0.541936i
\(295\) 4.83710e11i 0.0126056i
\(296\) −3.73973e13 + 5.57044e13i −0.956611 + 1.42490i
\(297\) 2.06703e13i 0.519024i
\(298\) −7.62436e12 1.52237e12i −0.187938 0.0375258i
\(299\) 6.08583e11 6.08583e11i 0.0147275 0.0147275i
\(300\) −1.96312e13 4.75905e13i −0.466424 1.13072i
\(301\) −4.21098e13 4.21098e13i −0.982352 0.982352i
\(302\) 1.57731e13 1.05226e13i 0.361309 0.241038i
\(303\) −2.47191e13 −0.556031
\(304\) 2.31986e10 7.94119e12i 0.000512456 0.175421i
\(305\) −1.31501e12 −0.0285285
\(306\) 2.38665e13 1.59219e13i 0.508534 0.339255i
\(307\) −3.24055e13 3.24055e13i −0.678199 0.678199i 0.281393 0.959593i \(-0.409203\pi\)
−0.959593 + 0.281393i \(0.909203\pi\)
\(308\) −2.97162e13 + 1.22580e13i −0.610892 + 0.251995i
\(309\) 3.40988e13 3.40988e13i 0.688601 0.688601i
\(310\) −9.33121e12 1.86318e12i −0.185118 0.0369628i
\(311\) 5.32038e13i 1.03696i −0.855091 0.518478i \(-0.826499\pi\)
0.855091 0.518478i \(-0.173501\pi\)
\(312\) −7.47282e12 3.80034e13i −0.143098 0.727733i
\(313\) 7.41435e13i 1.39502i 0.716577 + 0.697508i \(0.245708\pi\)
−0.716577 + 0.697508i \(0.754292\pi\)
\(314\) −2.06709e13 + 1.03525e14i −0.382161 + 1.91395i
\(315\) 1.55199e12 1.55199e12i 0.0281955 0.0281955i
\(316\) 3.20471e13 7.70501e13i 0.572150 1.37561i
\(317\) 6.45432e12 + 6.45432e12i 0.113246 + 0.113246i 0.761459 0.648213i \(-0.224483\pi\)
−0.648213 + 0.761459i \(0.724483\pi\)
\(318\) 4.24214e13 + 6.35885e13i 0.731535 + 1.09655i
\(319\) 3.36593e13 0.570501
\(320\) −2.36000e12 + 5.62767e12i −0.0393176 + 0.0937569i
\(321\) 2.11974e13 0.347140
\(322\) 8.89607e11 + 1.33350e12i 0.0143216 + 0.0214677i
\(323\) −9.08312e12 9.08312e12i −0.143754 0.143754i
\(324\) −3.08328e13 + 7.41305e13i −0.479751 + 1.15345i
\(325\) −2.74507e13 + 2.74507e13i −0.419947 + 0.419947i
\(326\) −1.34963e13 + 6.75924e13i −0.203010 + 1.01672i
\(327\) 1.62922e13i 0.240973i
\(328\) −1.66626e13 8.47386e13i −0.242347 1.23247i
\(329\) 5.97580e11i 0.00854710i
\(330\) −7.78554e12 1.55455e12i −0.109512 0.0218665i
\(331\) −5.80148e13 + 5.80148e13i −0.802574 + 0.802574i −0.983497 0.180923i \(-0.942091\pi\)
0.180923 + 0.983497i \(0.442091\pi\)
\(332\) −3.11819e13 + 1.28626e13i −0.424271 + 0.175013i
\(333\) 4.78314e13 + 4.78314e13i 0.640132 + 0.640132i
\(334\) 6.01759e13 4.01447e13i 0.792168 0.528473i
\(335\) 9.46668e12 0.122589
\(336\) 7.21369e13 + 2.10733e11i 0.918949 + 0.00268453i
\(337\) −7.30225e13 −0.915150 −0.457575 0.889171i \(-0.651282\pi\)
−0.457575 + 0.889171i \(0.651282\pi\)
\(338\) 4.31719e13 2.88009e13i 0.532303 0.355111i
\(339\) −6.30958e13 6.30958e13i −0.765425 0.765425i
\(340\) 3.76421e12 + 9.12528e12i 0.0449303 + 0.108921i
\(341\) 9.93510e13 9.93510e13i 1.16687 1.16687i
\(342\) −7.85138e12 1.56770e12i −0.0907407 0.0181184i
\(343\) 9.46096e13i 1.07601i
\(344\) 9.30482e13 1.38598e14i 1.04145 1.55127i
\(345\) 3.95910e11i 0.00436105i
\(346\) −1.82317e13 + 9.13086e13i −0.197656 + 0.989904i
\(347\) −4.07174e13 + 4.07174e13i −0.434478 + 0.434478i −0.890149 0.455670i \(-0.849400\pi\)
0.455670 + 0.890149i \(0.349400\pi\)
\(348\) −6.97430e13 2.90079e13i −0.732512 0.304671i
\(349\) 7.50423e13 + 7.50423e13i 0.775829 + 0.775829i 0.979119 0.203290i \(-0.0651633\pi\)
−0.203290 + 0.979119i \(0.565163\pi\)
\(350\) −4.01265e13 6.01486e13i −0.408373 0.612140i
\(351\) 3.49797e13 0.350451
\(352\) −4.97878e13 7.51049e13i −0.491064 0.740770i
\(353\) 1.92000e14 1.86441 0.932205 0.361931i \(-0.117882\pi\)
0.932205 + 0.361931i \(0.117882\pi\)
\(354\) −8.89514e12 1.33336e13i −0.0850423 0.127476i
\(355\) 8.75099e12 + 8.75099e12i 0.0823761 + 0.0823761i
\(356\) 1.50654e14 + 6.26608e13i 1.39638 + 0.580792i
\(357\) 8.25101e13 8.25101e13i 0.753064 0.753064i
\(358\) 1.64028e13 8.21487e13i 0.147421 0.738319i
\(359\) 6.04811e13i 0.535304i −0.963516 0.267652i \(-0.913752\pi\)
0.963516 0.267652i \(-0.0862477\pi\)
\(360\) 5.10814e12 + 3.42936e12i 0.0445245 + 0.0298916i
\(361\) 1.12906e14i 0.969227i
\(362\) −1.49467e14 2.98444e13i −1.26371 0.252328i
\(363\) −2.20505e13 + 2.20505e13i −0.183625 + 0.183625i
\(364\) −2.07439e13 5.02877e13i −0.170150 0.412481i
\(365\) 4.47744e12 + 4.47744e12i 0.0361759 + 0.0361759i
\(366\) −3.62485e13 + 2.41822e13i −0.288499 + 0.192464i
\(367\) 7.73489e13 0.606444 0.303222 0.952920i \(-0.401938\pi\)
0.303222 + 0.952920i \(0.401938\pi\)
\(368\) −3.18665e12 + 3.16809e12i −0.0246134 + 0.0244700i
\(369\) −8.70696e13 −0.662555
\(370\) −1.93609e13 + 1.29161e13i −0.145149 + 0.0968325i
\(371\) 7.59154e13 + 7.59154e13i 0.560755 + 0.560755i
\(372\) −2.91480e14 + 1.20236e14i −2.12140 + 0.875084i
\(373\) −7.33207e13 + 7.33207e13i −0.525809 + 0.525809i −0.919320 0.393511i \(-0.871260\pi\)
0.393511 + 0.919320i \(0.371260\pi\)
\(374\) −1.42935e14 2.85401e13i −1.01006 0.201680i
\(375\) 3.59022e13i 0.250005i
\(376\) 1.64365e12 3.23200e11i 0.0112791 0.00221788i
\(377\) 5.69605e13i 0.385209i
\(378\) −1.27568e13 + 6.38890e13i −0.0850233 + 0.425815i
\(379\) −1.92106e14 + 1.92106e14i −1.26190 + 1.26190i −0.311734 + 0.950169i \(0.600910\pi\)
−0.950169 + 0.311734i \(0.899090\pi\)
\(380\) 1.05789e12 2.54346e12i 0.00684907 0.0164671i
\(381\) 2.04008e14 + 2.04008e14i 1.30185 + 1.30185i
\(382\) −8.84741e13 1.32620e14i −0.556503 0.834184i
\(383\) 1.28679e14 0.797836 0.398918 0.916987i \(-0.369386\pi\)
0.398918 + 0.916987i \(0.369386\pi\)
\(384\) 3.84355e13 + 1.98527e14i 0.234915 + 1.21338i
\(385\) −1.11507e13 −0.0671844
\(386\) 1.00896e14 + 1.51240e14i 0.599298 + 0.898333i
\(387\) −1.19009e14 1.19009e14i −0.696900 0.696900i
\(388\) 8.13214e12 1.95519e13i 0.0469494 0.112879i
\(389\) −2.00352e14 + 2.00352e14i −1.14044 + 1.14044i −0.152068 + 0.988370i \(0.548593\pi\)
−0.988370 + 0.152068i \(0.951407\pi\)
\(390\) 2.63071e12 1.31752e13i 0.0147645 0.0739438i
\(391\) 7.26854e12i 0.0402230i
\(392\) −8.04053e13 + 1.58106e13i −0.438744 + 0.0862728i
\(393\) 3.31104e14i 1.78158i
\(394\) 2.50323e14 + 4.99825e13i 1.32823 + 0.265209i
\(395\) 2.04688e13 2.04688e13i 0.107105 0.107105i
\(396\) −8.39830e13 + 3.46433e13i −0.433379 + 0.178770i
\(397\) −1.54966e14 1.54966e14i −0.788657 0.788657i 0.192617 0.981274i \(-0.438303\pi\)
−0.981274 + 0.192617i \(0.938303\pi\)
\(398\) 5.31756e12 3.54746e12i 0.0266904 0.0178058i
\(399\) −3.25632e13 −0.161204
\(400\) 1.43737e14 1.42899e14i 0.701839 0.697751i
\(401\) −3.58680e14 −1.72748 −0.863740 0.503938i \(-0.831884\pi\)
−0.863740 + 0.503938i \(0.831884\pi\)
\(402\) 2.60951e14 1.74087e14i 1.23970 0.827032i
\(403\) 1.68128e14 + 1.68128e14i 0.787886 + 0.787886i
\(404\) −3.71119e13 8.99675e13i −0.171560 0.415899i
\(405\) −1.96932e13 + 1.96932e13i −0.0898077 + 0.0898077i
\(406\) −1.04036e14 2.07730e13i −0.468048 0.0934560i
\(407\) 3.43658e14i 1.52531i
\(408\) 2.71570e14 + 1.82319e14i 1.18919 + 0.798365i
\(409\) 4.56728e13i 0.197324i 0.995121 + 0.0986618i \(0.0314562\pi\)
−0.995121 + 0.0986618i \(0.968544\pi\)
\(410\) 5.86587e12 2.93776e13i 0.0250047 0.125229i
\(411\) 2.85338e14 2.85338e14i 1.20013 1.20013i
\(412\) 1.75300e14 + 7.29116e13i 0.727522 + 0.302595i
\(413\) −1.59184e13 1.59184e13i −0.0651888 0.0651888i
\(414\) 2.51418e12 + 3.76869e12i 0.0101600 + 0.0152296i
\(415\) −1.17007e13 −0.0466602
\(416\) 1.27097e14 8.42541e13i 0.500177 0.331572i
\(417\) −2.80024e14 −1.08754
\(418\) 2.25734e13 + 3.38370e13i 0.0865224 + 0.129695i
\(419\) 2.11630e13 + 2.11630e13i 0.0800572 + 0.0800572i 0.746001 0.665944i \(-0.231971\pi\)
−0.665944 + 0.746001i \(0.731971\pi\)
\(420\) 2.31046e13 + 9.60979e12i 0.0862634 + 0.0358792i
\(421\) −1.92706e14 + 1.92706e14i −0.710138 + 0.710138i −0.966564 0.256426i \(-0.917455\pi\)
0.256426 + 0.966564i \(0.417455\pi\)
\(422\) 4.56379e13 2.28565e14i 0.166000 0.831362i
\(423\) 1.68886e12i 0.00606349i
\(424\) −1.67747e14 + 2.49864e14i −0.594488 + 0.885508i
\(425\) 3.27854e14i 1.14694i
\(426\) 4.02149e14 + 8.02977e13i 1.38878 + 0.277300i
\(427\) −4.32754e13 + 4.32754e13i −0.147533 + 0.147533i
\(428\) 3.18245e13 + 7.71498e13i 0.107108 + 0.259653i
\(429\) 1.40279e14 + 1.40279e14i 0.466097 + 0.466097i
\(430\) 4.81718e13 3.21365e13i 0.158022 0.105420i
\(431\) 3.15533e14 1.02193 0.510964 0.859602i \(-0.329289\pi\)
0.510964 + 0.859602i \(0.329289\pi\)
\(432\) −1.82627e14 5.33507e11i −0.583987 0.00170600i
\(433\) 9.43423e13 0.297867 0.148934 0.988847i \(-0.452416\pi\)
0.148934 + 0.988847i \(0.452416\pi\)
\(434\) −3.68395e14 + 2.45765e14i −1.14847 + 0.766171i
\(435\) −1.85276e13 1.85276e13i −0.0570334 0.0570334i
\(436\) 5.92970e13 2.44602e13i 0.180243 0.0743507i
\(437\) 1.43429e12 1.43429e12i 0.00430516 0.00430516i
\(438\) 2.05759e14 + 4.10843e13i 0.609891 + 0.121778i
\(439\) 4.26118e12i 0.0124731i −0.999981 0.00623655i \(-0.998015\pi\)
0.999981 0.00623655i \(-0.00198517\pi\)
\(440\) −6.03083e12 3.06701e13i −0.0174336 0.0886595i
\(441\) 8.26172e13i 0.235862i
\(442\) 4.82975e13 2.41885e14i 0.136177 0.682002i
\(443\) 1.07675e13 1.07675e13i 0.0299843 0.0299843i −0.691956 0.721940i \(-0.743251\pi\)
0.721940 + 0.691956i \(0.243251\pi\)
\(444\) −2.96168e14 + 7.12070e14i −0.814577 + 1.95847i
\(445\) 4.00220e13 + 4.00220e13i 0.108722 + 0.108722i
\(446\) −1.33473e14 2.00072e14i −0.358138 0.536840i
\(447\) −8.93681e13 −0.236860
\(448\) 1.07535e14 + 2.62865e14i 0.281528 + 0.688183i
\(449\) 1.49573e14 0.386811 0.193405 0.981119i \(-0.438047\pi\)
0.193405 + 0.981119i \(0.438047\pi\)
\(450\) −1.13404e14 1.69990e14i −0.289708 0.434265i
\(451\) 3.12788e14 + 3.12788e14i 0.789368 + 0.789368i
\(452\) 1.34914e14 3.24371e14i 0.336354 0.808688i
\(453\) 1.54111e14 1.54111e14i 0.379572 0.379572i
\(454\) 6.12752e13 3.06880e14i 0.149100 0.746725i
\(455\) 1.88700e13i 0.0453637i
\(456\) −1.76117e13 8.95653e13i −0.0418307 0.212732i
\(457\) 5.73073e13i 0.134484i −0.997737 0.0672420i \(-0.978580\pi\)
0.997737 0.0672420i \(-0.0214200\pi\)
\(458\) −4.43804e14 8.86152e13i −1.02904 0.205470i
\(459\) −2.08888e14 + 2.08888e14i −0.478568 + 0.478568i
\(460\) −1.44095e12 + 5.94396e11i −0.00326197 + 0.00134557i
\(461\) −5.04689e14 5.04689e14i −1.12893 1.12893i −0.990351 0.138583i \(-0.955745\pi\)
−0.138583 0.990351i \(-0.544255\pi\)
\(462\) −3.07372e14 + 2.05055e14i −0.679412 + 0.453251i
\(463\) −1.04606e14 −0.228487 −0.114243 0.993453i \(-0.536444\pi\)
−0.114243 + 0.993453i \(0.536444\pi\)
\(464\) 8.68755e11 2.97387e14i 0.00187520 0.641908i
\(465\) −1.09375e14 −0.233306
\(466\) −5.82805e14 + 3.88802e14i −1.22857 + 0.819608i
\(467\) −5.83143e14 5.83143e14i −1.21488 1.21488i −0.969404 0.245472i \(-0.921057\pi\)
−0.245472 0.969404i \(-0.578943\pi\)
\(468\) −5.86256e13 1.42122e14i −0.120708 0.292623i
\(469\) 3.11538e14 3.11538e14i 0.633958 0.633958i
\(470\) 5.69828e11 + 1.13779e11i 0.00114606 + 0.000228835i
\(471\) 1.21345e15i 2.41217i
\(472\) 3.51741e13 5.23930e13i 0.0691103 0.102942i
\(473\) 8.55057e14i 1.66058i
\(474\) 1.87819e14 9.40637e14i 0.360543 1.80568i
\(475\) −6.46949e13 + 6.46949e13i −0.122760 + 0.122760i
\(476\) 4.24179e14 + 1.76427e14i 0.795629 + 0.330923i
\(477\) 2.14550e14 + 2.14550e14i 0.397811 + 0.397811i
\(478\) 3.71369e14 + 5.56673e14i 0.680695 + 1.02034i
\(479\) −9.29337e12 −0.0168394 −0.00841972 0.999965i \(-0.502680\pi\)
−0.00841972 + 0.999965i \(0.502680\pi\)
\(480\) −1.39357e13 + 6.87467e13i −0.0249633 + 0.123147i
\(481\) 5.81561e14 1.02991
\(482\) −9.31731e13 1.39664e14i −0.163129 0.244527i
\(483\) 1.30289e13 + 1.30289e13i 0.0225528 + 0.0225528i
\(484\) −1.13360e14 4.71494e13i −0.194004 0.0806912i
\(485\) 5.19407e12 5.19407e12i 0.00878878 0.00878878i
\(486\) −1.12353e14 + 5.62688e14i −0.187968 + 0.941386i
\(487\) 2.67485e14i 0.442477i −0.975220 0.221238i \(-0.928990\pi\)
0.975220 0.221238i \(-0.0710099\pi\)
\(488\) −1.42435e14 9.56239e13i −0.232974 0.156407i
\(489\) 7.92278e14i 1.28138i
\(490\) −2.78753e13 5.56591e12i −0.0445801 0.00890139i
\(491\) 3.39834e13 3.39834e13i 0.0537425 0.0537425i −0.679725 0.733467i \(-0.737901\pi\)
0.733467 + 0.679725i \(0.237901\pi\)
\(492\) −3.78542e14 9.17670e14i −0.591979 1.43509i
\(493\) −3.40150e14 3.40150e14i −0.526033 0.526033i
\(494\) −5.72612e13 + 3.82003e13i −0.0875714 + 0.0584209i
\(495\) −3.15138e13 −0.0476619
\(496\) −8.75222e14 8.80351e14i −1.30909 1.31676i
\(497\) 5.75970e14 0.852001
\(498\) −3.22533e14 + 2.15169e14i −0.471859 + 0.314788i
\(499\) 1.03300e14 + 1.03300e14i 0.149468 + 0.149468i 0.777880 0.628412i \(-0.216295\pi\)
−0.628412 + 0.777880i \(0.716295\pi\)
\(500\) 1.30669e14 5.39015e13i 0.186999 0.0771376i
\(501\) 5.87949e14 5.87949e14i 0.832209 0.832209i
\(502\) 1.03316e15 + 2.06294e14i 1.44644 + 0.288812i
\(503\) 1.03966e15i 1.43969i −0.694136 0.719843i \(-0.744214\pi\)
0.694136 0.719843i \(-0.255786\pi\)
\(504\) 2.80960e14 5.52467e13i 0.384836 0.0756726i
\(505\) 3.37594e13i 0.0457395i
\(506\) 4.50670e12 2.25705e13i 0.00603991 0.0302492i
\(507\) 4.21811e14 4.21811e14i 0.559209 0.559209i
\(508\) −4.36220e14 + 1.04879e15i −0.572078 + 1.37543i
\(509\) 5.30191e14 + 5.30191e14i 0.687835 + 0.687835i 0.961753 0.273918i \(-0.0883196\pi\)
−0.273918 + 0.961753i \(0.588320\pi\)
\(510\) 6.29684e13 + 9.43880e13i 0.0808140 + 0.121138i
\(511\) 2.94695e14 0.374161
\(512\) −6.64852e14 + 4.37946e14i −0.835103 + 0.550093i
\(513\) 8.24391e13 0.102444
\(514\) 5.52993e14 + 8.28923e14i 0.679865 + 1.01910i
\(515\) 4.65693e13 + 4.65693e13i 0.0566448 + 0.0566448i
\(516\) 7.36897e14 1.77170e15i 0.886815 2.13215i
\(517\) −6.06706e12 + 6.06706e12i −0.00722405 + 0.00722405i
\(518\) −2.12091e14 + 1.06220e15i −0.249867 + 1.25139i
\(519\) 1.07026e15i 1.24759i
\(520\) 5.19019e13 1.02058e13i 0.0598639 0.0117714i
\(521\) 7.25048e14i 0.827484i 0.910394 + 0.413742i \(0.135778\pi\)
−0.910394 + 0.413742i \(0.864222\pi\)
\(522\) −2.94023e14 5.87081e13i −0.332043 0.0662996i
\(523\) 6.35477e14 6.35477e14i 0.710134 0.710134i −0.256429 0.966563i \(-0.582546\pi\)
0.966563 + 0.256429i \(0.0825459\pi\)
\(524\) 1.20508e15 4.97101e14i 1.33259 0.549696i
\(525\) −5.87682e14 5.87682e14i −0.643082 0.643082i
\(526\) −1.74711e14 + 1.16554e14i −0.189190 + 0.126213i
\(527\) −2.00802e15 −2.15184
\(528\) −7.30246e14 7.34525e14i −0.774431 0.778969i
\(529\) 9.51662e14 0.998795
\(530\) −8.68440e13 + 5.79356e13i −0.0902033 + 0.0601767i
\(531\) −4.49880e13 4.49880e13i −0.0462463 0.0462463i
\(532\) −4.88885e13 1.18517e14i −0.0497385 0.120577i
\(533\) −5.29321e14 + 5.29321e14i −0.532991 + 0.532991i
\(534\) 1.83920e15 + 3.67236e14i 1.83295 + 0.365989i
\(535\) 2.89497e13i 0.0285560i
\(536\) 1.02538e15 + 6.88392e14i 1.00110 + 0.672094i
\(537\) 9.62898e14i 0.930511i
\(538\) 4.04993e13 2.02830e14i 0.0387387 0.194012i
\(539\) 2.96793e14 2.96793e14i 0.281006 0.281006i
\(540\) −5.84931e13 2.43288e13i −0.0548199 0.0228010i
\(541\) −1.14149e15 1.14149e15i −1.05898 1.05898i −0.998148 0.0608311i \(-0.980625\pi\)
−0.0608311 0.998148i \(-0.519375\pi\)
\(542\) −7.64650e14 1.14619e15i −0.702209 1.05259i
\(543\) −1.75196e15 −1.59267
\(544\) −2.55847e14 + 1.26213e15i −0.230243 + 1.13582i
\(545\) 2.22506e13 0.0198226
\(546\) −3.47007e14 5.20155e14i −0.306041 0.458747i
\(547\) −7.92097e14 7.92097e14i −0.691589 0.691589i 0.270993 0.962581i \(-0.412648\pi\)
−0.962581 + 0.270993i \(0.912648\pi\)
\(548\) 1.46690e15 + 6.10122e14i 1.26797 + 0.527380i
\(549\) −1.22304e14 + 1.22304e14i −0.104663 + 0.104663i
\(550\) −2.03279e14 + 1.01806e15i −0.172225 + 0.862542i
\(551\) 1.34243e14i 0.112605i
\(552\) −2.87895e13 + 4.28829e13i −0.0239094 + 0.0356138i
\(553\) 1.34721e15i 1.10776i
\(554\) 7.09116e14 + 1.41590e14i 0.577316 + 0.115274i
\(555\) −1.89165e14 + 1.89165e14i −0.152486 + 0.152486i
\(556\) −4.20411e14 1.01917e15i −0.335554 0.813459i
\(557\) 1.32985e15 + 1.32985e15i 1.05099 + 1.05099i 0.998628 + 0.0523642i \(0.0166757\pi\)
0.0523642 + 0.998628i \(0.483324\pi\)
\(558\) −1.04115e15 + 6.94572e14i −0.814748 + 0.543537i
\(559\) −1.44698e15 −1.12124
\(560\) −2.87803e11 + 9.85187e13i −0.000220831 + 0.0755935i
\(561\) −1.67540e15 −1.27299
\(562\) 7.59312e14 5.06555e14i 0.571309 0.381133i
\(563\) 6.09588e14 + 6.09588e14i 0.454193 + 0.454193i 0.896743 0.442551i \(-0.145926\pi\)
−0.442551 + 0.896743i \(0.645926\pi\)
\(564\) 1.77998e13 7.34247e12i 0.0131335 0.00541760i
\(565\) 8.61711e13 8.61711e13i 0.0629644 0.0629644i
\(566\) −1.67683e14 3.34815e13i −0.121338 0.0242279i
\(567\) 1.29616e15i 0.928865i
\(568\) 3.11512e14 + 1.58421e15i 0.221085 + 1.12434i
\(569\) 1.37610e15i 0.967234i 0.875280 + 0.483617i \(0.160677\pi\)
−0.875280 + 0.483617i \(0.839323\pi\)
\(570\) 6.19999e12 3.10509e13i 0.00431598 0.0216154i
\(571\) −4.57011e14 + 4.57011e14i −0.315085 + 0.315085i −0.846876 0.531790i \(-0.821519\pi\)
0.531790 + 0.846876i \(0.321519\pi\)
\(572\) −2.99950e14 + 7.21163e14i −0.204820 + 0.492442i
\(573\) −1.29577e15 1.29577e15i −0.876349 0.876349i
\(574\) −7.73744e14 1.15982e15i −0.518301 0.776920i
\(575\) 5.17705e13 0.0343486
\(576\) 3.03913e14 + 7.42901e14i 0.199722 + 0.488211i
\(577\) 1.10753e15 0.720921 0.360460 0.932775i \(-0.382620\pi\)
0.360460 + 0.932775i \(0.382620\pi\)
\(578\) 2.95312e14 + 4.42665e14i 0.190405 + 0.285412i
\(579\) 1.47769e15 + 1.47769e15i 0.943740 + 0.943740i
\(580\) 3.96166e13 9.52493e13i 0.0250625 0.0602570i
\(581\) −3.85057e14 + 3.85057e14i −0.241299 + 0.241299i
\(582\) 4.76600e13 2.38692e14i 0.0295854 0.148170i
\(583\) 1.54149e15i 0.947905i
\(584\) 1.59385e14 + 8.10561e14i 0.0970907 + 0.493759i
\(585\) 5.33297e13i 0.0321819i
\(586\) −2.41831e15 4.82869e14i −1.44569 0.288664i
\(587\) 7.20142e14 7.20142e14i 0.426490 0.426490i −0.460941 0.887431i \(-0.652488\pi\)
0.887431 + 0.460941i \(0.152488\pi\)
\(588\) −8.70744e14 + 3.59185e14i −0.510876 + 0.210738i
\(589\) 3.96240e14 + 3.96240e14i 0.230316 + 0.230316i
\(590\) 1.82099e13 1.21483e13i 0.0104863 0.00699565i
\(591\) 2.93414e15 1.67398
\(592\) −3.03629e15 8.86991e12i −1.71622 0.00501360i
\(593\) 1.05889e15 0.592996 0.296498 0.955034i \(-0.404181\pi\)
0.296498 + 0.955034i \(0.404181\pi\)
\(594\) 7.78163e14 5.19130e14i 0.431763 0.288039i
\(595\) 1.12686e14 + 1.12686e14i 0.0619476 + 0.0619476i
\(596\) −1.34172e14 3.25263e14i −0.0730816 0.177166i
\(597\) 5.19552e13 5.19552e13i 0.0280395 0.0280395i
\(598\) 3.81953e13 + 7.62653e12i 0.0204246 + 0.00407822i
\(599\) 8.03403e14i 0.425682i −0.977087 0.212841i \(-0.931728\pi\)
0.977087 0.212841i \(-0.0682717\pi\)
\(600\) 1.29858e15 1.93427e15i 0.681766 1.01551i
\(601\) 1.38624e15i 0.721155i −0.932729 0.360578i \(-0.882580\pi\)
0.932729 0.360578i \(-0.117420\pi\)
\(602\) 5.27704e14 2.64286e15i 0.272025 1.36236i
\(603\) 8.80459e14 8.80459e14i 0.449742 0.449742i
\(604\) 7.92276e14 + 3.29528e14i 0.401027 + 0.166797i
\(605\) −3.01147e13 3.01147e13i −0.0151051 0.0151051i
\(606\) −6.20815e14 9.30586e14i −0.308576 0.462548i
\(607\) 3.18636e15 1.56948 0.784742 0.619823i \(-0.212796\pi\)
0.784742 + 0.619823i \(0.212796\pi\)
\(608\) 2.99540e14 1.98568e14i 0.146213 0.0969257i
\(609\) −1.21945e15 −0.589886
\(610\) −3.30261e13 4.95053e13i −0.0158323 0.0237322i
\(611\) −1.02671e13 1.02671e13i −0.00487776 0.00487776i
\(612\) 1.19880e15 + 4.98612e14i 0.564435 + 0.234763i
\(613\) 1.13972e15 1.13972e15i 0.531820 0.531820i −0.389294 0.921114i \(-0.627281\pi\)
0.921114 + 0.389294i \(0.127281\pi\)
\(614\) 4.06093e14 2.03380e15i 0.187802 0.940552i
\(615\) 3.44346e14i 0.157827i
\(616\) −1.20779e15 8.10850e14i −0.548651 0.368338i
\(617\) 4.02609e15i 1.81265i 0.422578 + 0.906326i \(0.361125\pi\)
−0.422578 + 0.906326i \(0.638875\pi\)
\(618\) 2.14008e15 + 4.27313e14i 0.954977 + 0.190682i
\(619\) 1.12455e14 1.12455e14i 0.0497370 0.0497370i −0.681801 0.731538i \(-0.738803\pi\)
0.731538 + 0.681801i \(0.238803\pi\)
\(620\) −1.64209e14 3.98079e14i −0.0719851 0.174508i
\(621\) −3.29849e13 3.29849e13i −0.0143322 0.0143322i
\(622\) 2.00293e15 1.33620e15i 0.862618 0.575472i
\(623\) 2.63416e15 1.12450
\(624\) 1.24301e15 1.23577e15i 0.525969 0.522905i
\(625\) −2.31051e15 −0.969098
\(626\) −2.79124e15 + 1.86210e15i −1.16048 + 0.774182i
\(627\) 3.30605e14 + 3.30605e14i 0.136250 + 0.136250i
\(628\) −4.41647e15 + 1.82181e15i −1.80425 + 0.744260i
\(629\) −3.47290e15 + 3.47290e15i −1.40642 + 1.40642i
\(630\) 9.74045e13 + 1.94489e13i 0.0391026 + 0.00780769i
\(631\) 3.54561e15i 1.41101i 0.708706 + 0.705504i \(0.249279\pi\)
−0.708706 + 0.705504i \(0.750721\pi\)
\(632\) 3.70551e15 7.28636e14i 1.46185 0.287453i
\(633\) 2.67910e15i 1.04777i
\(634\) −8.08830e13 + 4.05080e14i −0.0313593 + 0.157054i
\(635\) −2.78618e14 + 2.78618e14i −0.107091 + 0.107091i
\(636\) −1.32848e15 + 3.19402e15i −0.506220 + 1.21709i
\(637\) 5.02253e14 + 5.02253e14i 0.189739 + 0.189739i
\(638\) 8.45345e14 + 1.26715e15i 0.316607 + 0.474586i
\(639\) 1.62779e15 0.604427
\(640\) −2.71132e14 + 5.24920e13i −0.0998139 + 0.0193243i
\(641\) −3.99466e15 −1.45801 −0.729005 0.684509i \(-0.760017\pi\)
−0.729005 + 0.684509i \(0.760017\pi\)
\(642\) 5.32367e14 + 7.98005e14i 0.192650 + 0.288777i
\(643\) −7.20860e14 7.20860e14i −0.258637 0.258637i 0.565863 0.824500i \(-0.308543\pi\)
−0.824500 + 0.565863i \(0.808543\pi\)
\(644\) −2.78591e13 + 6.69809e13i −0.00991048 + 0.0238275i
\(645\) 4.70663e14 4.70663e14i 0.166009 0.166009i
\(646\) 1.13826e14 5.70067e14i 0.0398073 0.199364i
\(647\) 2.38050e15i 0.825458i −0.910854 0.412729i \(-0.864576\pi\)
0.910854 0.412729i \(-0.135424\pi\)
\(648\) −3.56510e15 + 7.01027e14i −1.22577 + 0.241030i
\(649\) 3.23229e14i 0.110196i
\(650\) −1.72283e15 3.44001e14i −0.582398 0.116288i
\(651\) −3.59940e15 + 3.59940e15i −1.20652 + 1.20652i
\(652\) −2.88356e15 + 1.18948e15i −0.958447 + 0.395362i
\(653\) 3.05366e15 + 3.05366e15i 1.00646 + 1.00646i 0.999979 + 0.00648374i \(0.00206385\pi\)
0.00648374 + 0.999979i \(0.497936\pi\)
\(654\) 6.13343e14 4.09175e14i 0.200459 0.133731i
\(655\) 4.52195e14 0.146554
\(656\) 2.77162e15 2.75548e15i 0.890764 0.885575i
\(657\) 8.32859e14 0.265437
\(658\) 2.24967e13 1.50081e13i 0.00711012 0.00474332i
\(659\) −3.38786e15 3.38786e15i −1.06183 1.06183i −0.997958 0.0638750i \(-0.979654\pi\)
−0.0638750 0.997958i \(-0.520346\pi\)
\(660\) −1.37009e14 3.32139e14i −0.0425850 0.103235i
\(661\) 2.17225e15 2.17225e15i 0.669580 0.669580i −0.288039 0.957619i \(-0.593003\pi\)
0.957619 + 0.288039i \(0.0930032\pi\)
\(662\) −3.64108e15 7.27020e14i −1.11304 0.222243i
\(663\) 2.83523e15i 0.859534i
\(664\) −1.26736e15 8.50844e14i −0.381044 0.255815i
\(665\) 4.44722e13i 0.0132608i
\(666\) −5.99405e14 + 3.00195e15i −0.177260 + 0.887760i
\(667\) 5.37122e13 5.37122e13i 0.0157536 0.0157536i
\(668\) 3.02261e15 + 1.25718e15i 0.879248 + 0.365702i
\(669\) −1.95480e15 1.95480e15i −0.563975 0.563975i
\(670\) 2.37753e14 + 3.56386e14i 0.0680323 + 0.101979i
\(671\) 8.78726e14 0.249390
\(672\) 1.80377e15 + 2.72099e15i 0.507750 + 0.765941i
\(673\) −2.38223e14 −0.0665121 −0.0332561 0.999447i \(-0.510588\pi\)
−0.0332561 + 0.999447i \(0.510588\pi\)
\(674\) −1.83394e15 2.74903e15i −0.507874 0.761291i
\(675\) 1.48781e15 + 1.48781e15i 0.408675 + 0.408675i
\(676\) 2.16850e15 + 9.01936e14i 0.590817 + 0.245736i
\(677\) 1.90659e15 1.90659e15i 0.515252 0.515252i −0.400879 0.916131i \(-0.631295\pi\)
0.916131 + 0.400879i \(0.131295\pi\)
\(678\) 7.90693e14 3.95997e15i 0.211955 1.06152i
\(679\) 3.41862e14i 0.0909007i
\(680\) −2.48996e14 + 3.70888e14i −0.0656741 + 0.0978236i
\(681\) 3.59706e15i 0.941106i
\(682\) 6.23538e15 + 1.24503e15i 1.61826 + 0.323121i
\(683\) −2.55329e15 + 2.55329e15i −0.657334 + 0.657334i −0.954748 0.297415i \(-0.903876\pi\)
0.297415 + 0.954748i \(0.403876\pi\)
\(684\) −1.38167e14 3.34948e14i −0.0352855 0.0855400i
\(685\) 3.89691e14 + 3.89691e14i 0.0987239 + 0.0987239i
\(686\) −3.56171e15 + 2.37610e15i −0.895109 + 0.597147i
\(687\) −5.20201e15 −1.29691
\(688\) 7.55460e15 + 2.20692e13i 1.86842 + 0.00545822i
\(689\) 2.60862e15 0.640037
\(690\) −1.49046e13 + 9.94317e12i −0.00362785 + 0.00242022i
\(691\) −4.73213e14 4.73213e14i −0.114269 0.114269i 0.647660 0.761929i \(-0.275748\pi\)
−0.761929 + 0.647660i \(0.775748\pi\)
\(692\) −3.89532e15 + 1.60683e15i −0.933168 + 0.384935i
\(693\) −1.03708e15 + 1.03708e15i −0.246479 + 0.246479i
\(694\) −2.55547e15 5.10255e14i −0.602551 0.120312i
\(695\) 3.82433e14i 0.0894621i
\(696\) −6.59535e14 3.35410e15i −0.153069 0.778440i
\(697\) 6.32188e15i 1.45568i
\(698\) −9.40401e14 + 4.70974e15i −0.214837 + 1.07595i
\(699\) −5.69430e15 + 5.69430e15i −1.29067 + 1.29067i
\(700\) 1.25661e15 3.02123e15i 0.282593 0.679430i
\(701\) 4.29380e14 + 4.29380e14i 0.0958061 + 0.0958061i 0.753385 0.657579i \(-0.228420\pi\)
−0.657579 + 0.753385i \(0.728420\pi\)
\(702\) 8.78507e14 + 1.31686e15i 0.194487 + 0.291531i
\(703\) 1.37061e15 0.301064
\(704\) 1.57702e15 3.76057e15i 0.343706 0.819604i
\(705\) 6.67918e12 0.00144439
\(706\) 4.82204e15 + 7.22812e15i 1.03468 + 1.55096i
\(707\) −1.11098e15 1.11098e15i −0.236538 0.236538i
\(708\) 2.78562e14 6.69740e14i 0.0588490 0.141489i
\(709\) −1.83229e14 + 1.83229e14i −0.0384097 + 0.0384097i −0.726051 0.687641i \(-0.758646\pi\)
0.687641 + 0.726051i \(0.258646\pi\)
\(710\) −1.09664e14 + 5.49222e14i −0.0228109 + 0.114242i
\(711\) 3.80744e15i 0.785870i
\(712\) 1.42468e15 + 7.24528e15i 0.291795 + 1.48394i
\(713\) 3.17081e14i 0.0644433i
\(714\) 5.17843e15 + 1.03398e15i 1.04438 + 0.208533i
\(715\) −1.91581e14 + 1.91581e14i −0.0383415 + 0.0383415i
\(716\) 3.50455e15 1.44564e15i 0.696003 0.287104i
\(717\) 5.43898e15 + 5.43898e15i 1.07192 + 1.07192i
\(718\) 2.27689e15 1.51897e15i 0.445306 0.297074i
\(719\) −4.63852e15 −0.900265 −0.450133 0.892962i \(-0.648623\pi\)
−0.450133 + 0.892962i \(0.648623\pi\)
\(720\) −8.13379e11 + 2.78431e14i −0.000156662 + 0.0536276i
\(721\) 3.06509e15 0.585867
\(722\) 4.25048e15 2.83559e15i 0.806276 0.537885i
\(723\) −1.36459e15 1.36459e15i −0.256887 0.256887i
\(724\) −2.63030e15 6.37643e15i −0.491409 1.19128i
\(725\) −2.42274e15 + 2.42274e15i −0.449208 + 0.449208i
\(726\) −1.38391e15 2.76328e14i −0.254658 0.0508480i
\(727\) 3.43021e15i 0.626442i 0.949680 + 0.313221i \(0.101408\pi\)
−0.949680 + 0.313221i \(0.898592\pi\)
\(728\) 1.37217e15 2.04389e15i 0.248706 0.370455i
\(729\) 3.49140e14i 0.0628055i
\(730\) −5.61096e13 + 2.81009e14i −0.0100176 + 0.0501701i
\(731\) 8.64094e15 8.64094e15i 1.53114 1.53114i
\(732\) −1.82074e15 7.57295e14i −0.320212 0.133185i
\(733\) 4.05712e15 + 4.05712e15i 0.708184 + 0.708184i 0.966153 0.257969i \(-0.0830534\pi\)
−0.257969 + 0.966153i \(0.583053\pi\)
\(734\) 1.94260e15 + 2.91191e15i 0.336554 + 0.504486i
\(735\) −3.26738e14 −0.0561848
\(736\) −1.99299e14 4.04001e13i −0.0340155 0.00689533i
\(737\) −6.32591e15 −1.07165
\(738\) −2.18673e15 3.27786e15i −0.367693 0.551163i
\(739\) 1.67030e15 + 1.67030e15i 0.278772 + 0.278772i 0.832619 0.553846i \(-0.186841\pi\)
−0.553846 + 0.832619i \(0.686841\pi\)
\(740\) −9.72487e14 4.04482e14i −0.161105 0.0670078i
\(741\) −5.59471e14 + 5.59471e14i −0.0919978 + 0.0919978i
\(742\) −9.51343e14 + 4.76454e15i −0.155280 + 0.777677i
\(743\) 4.61265e15i 0.747330i −0.927564 0.373665i \(-0.878101\pi\)
0.927564 0.373665i \(-0.121899\pi\)
\(744\) −1.18469e16 7.95345e15i −1.90526 1.27910i
\(745\) 1.22052e14i 0.0194843i
\(746\) −4.60169e15 9.18827e14i −0.729212 0.145603i
\(747\) −1.08824e15 + 1.08824e15i −0.171183 + 0.171183i
\(748\) −2.51535e15 6.09778e15i −0.392772 0.952166i
\(749\) 9.52701e14 + 9.52701e14i 0.147675 + 0.147675i
\(750\) 1.35159e15 9.01675e14i 0.207973 0.138744i
\(751\) −6.38439e14 −0.0975214 −0.0487607 0.998810i \(-0.515527\pi\)
−0.0487607 + 0.998810i \(0.515527\pi\)
\(752\) 5.34471e13 + 5.37603e13i 0.00810450 + 0.00815199i
\(753\) 1.21101e16 1.82296
\(754\) −2.14436e15 + 1.43055e15i −0.320446 + 0.213777i
\(755\) 2.10473e14 + 2.10473e14i 0.0312239 + 0.0312239i
\(756\) −2.72557e15 + 1.12431e15i −0.401410 + 0.165583i
\(757\) −3.03835e15 + 3.03835e15i −0.444232 + 0.444232i −0.893432 0.449199i \(-0.851709\pi\)
0.449199 + 0.893432i \(0.351709\pi\)
\(758\) −1.20568e16 2.40740e15i −1.75006 0.349437i
\(759\) 2.64558e14i 0.0381234i
\(760\) 1.22321e14 2.40527e13i 0.0174995 0.00344103i