Properties

Label 8.14.b.b.5.9
Level 8
Weight 14
Character 8.5
Analytic conductor 8.578
Analytic rank 0
Dimension 10
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 14 \)
Character orbit: \([\chi]\) = 8.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(8.57847431615\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{48}\cdot 3^{4} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.9
Root \(37.4606 - 15.6556i\)
Character \(\chi\) = 8.5
Dual form 8.14.b.b.5.10

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+(84.9212 - 31.3112i) q^{2}\) \(-1415.71i q^{3}\) \(+(6231.21 - 5317.98i) q^{4}\) \(-2384.10i q^{5}\) \(+(-44327.5 - 120223. i) q^{6}\) \(-317448. q^{7}\) \(+(362649. - 646716. i) q^{8}\) \(-409898. q^{9}\) \(+O(q^{10})\) \(q\)\(+(84.9212 - 31.3112i) q^{2}\) \(-1415.71i q^{3}\) \(+(6231.21 - 5317.98i) q^{4}\) \(-2384.10i q^{5}\) \(+(-44327.5 - 120223. i) q^{6}\) \(-317448. q^{7}\) \(+(362649. - 646716. i) q^{8}\) \(-409898. q^{9}\) \(+(-74649.0 - 202460. i) q^{10}\) \(+1.40906e6i q^{11}\) \(+(-7.52869e6 - 8.82156e6i) q^{12}\) \(-2.51242e7i q^{13}\) \(+(-2.69581e7 + 9.93969e6i) q^{14}\) \(-3.37518e6 q^{15}\) \(+(1.05471e7 - 6.62749e7i) q^{16}\) \(+1.11400e8 q^{17}\) \(+(-3.48090e7 + 1.28344e7i) q^{18}\) \(+3.64846e8i q^{19}\) \(+(-1.26786e7 - 1.48558e7i) q^{20}\) \(+4.49413e8i q^{21}\) \(+(4.41194e7 + 1.19659e8i) q^{22}\) \(+7.49063e8 q^{23}\) \(+(-9.15559e8 - 5.13405e8i) q^{24}\) \(+1.21502e9 q^{25}\) \(+(-7.86670e8 - 2.13358e9i) q^{26}\) \(-1.67680e9i q^{27}\) \(+(-1.97809e9 + 1.68818e9i) q^{28}\) \(+2.83628e9i q^{29}\) \(+(-2.86624e8 + 1.05681e8i) q^{30}\) \(-2.93414e9 q^{31}\) \(+(-1.17947e9 - 5.95838e9i) q^{32}\) \(+1.99481e9 q^{33}\) \(+(9.46024e9 - 3.48808e9i) q^{34}\) \(+7.56826e8i q^{35}\) \(+(-2.55416e9 + 2.17983e9i) q^{36}\) \(-8.46017e9i q^{37}\) \(+(1.14238e10 + 3.09832e10i) q^{38}\) \(-3.55684e10 q^{39}\) \(+(-1.54183e9 - 8.64591e8i) q^{40}\) \(+3.90644e10 q^{41}\) \(+(1.40717e10 + 3.81647e10i) q^{42}\) \(-2.17473e10i q^{43}\) \(+(7.49334e9 + 8.78014e9i) q^{44}\) \(+9.77236e8i q^{45}\) \(+(6.36113e10 - 2.34541e10i) q^{46}\) \(-1.15068e11 q^{47}\) \(+(-9.38257e10 - 1.49316e10i) q^{48}\) \(+3.88420e9 q^{49}\) \(+(1.03181e11 - 3.80438e10i) q^{50}\) \(-1.57710e11i q^{51}\) \(+(-1.33610e11 - 1.56554e11i) q^{52}\) \(+1.71179e11i q^{53}\) \(+(-5.25026e10 - 1.42396e11i) q^{54}\) \(+3.35933e9 q^{55}\) \(+(-1.15122e11 + 2.05299e11i) q^{56}\) \(+5.16515e11 q^{57}\) \(+(8.88074e10 + 2.40860e11i) q^{58}\) \(+2.45442e11i q^{59}\) \(+(-2.10314e10 + 1.79491e10i) q^{60}\) \(+2.71473e11i q^{61}\) \(+(-2.49170e11 + 9.18715e10i) q^{62}\) \(+1.30121e11 q^{63}\) \(+(-2.86727e11 - 4.69062e11i) q^{64}\) \(-5.98985e10 q^{65}\) \(+(1.69402e11 - 6.24600e10i) q^{66}\) \(+6.82198e11i q^{67}\) \(+(6.94158e11 - 5.92424e11i) q^{68}\) \(-1.06045e12i q^{69}\) \(+(2.36972e10 + 6.42706e10i) q^{70}\) \(-2.90719e11 q^{71}\) \(+(-1.48649e11 + 2.65088e11i) q^{72}\) \(-1.48745e12 q^{73}\) \(+(-2.64899e11 - 7.18448e11i) q^{74}\) \(-1.72011e12i q^{75}\) \(+(1.94024e12 + 2.27344e12i) q^{76}\) \(-4.47303e11i q^{77}\) \(+(-3.02051e12 + 1.11369e12i) q^{78}\) \(+1.58653e12 q^{79}\) \(+(-1.58006e11 - 2.51454e10i) q^{80}\) \(-3.02736e12 q^{81}\) \(+(3.31740e12 - 1.22316e12i) q^{82}\) \(-7.79952e11i q^{83}\) \(+(2.38997e12 + 2.80039e12i) q^{84}\) \(-2.65589e11i q^{85}\) \(+(-6.80935e11 - 1.84681e12i) q^{86}\) \(+4.01533e12 q^{87}\) \(+(9.11260e11 + 5.10994e11i) q^{88}\) \(-4.10498e12 q^{89}\) \(+(3.05985e10 + 8.29881e10i) q^{90}\) \(+7.97562e12i q^{91}\) \(+(4.66757e12 - 3.98350e12i) q^{92}\) \(+4.15387e12i q^{93}\) \(+(-9.77175e12 + 3.60294e12i) q^{94}\) \(+8.69829e11 q^{95}\) \(+(-8.43531e12 + 1.66979e12i) q^{96}\) \(+1.11567e13 q^{97}\) \(+(3.29851e11 - 1.21619e11i) q^{98}\) \(-5.77570e11i q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(10q \) \(\mathstrut +\mathstrut 110q^{2} \) \(\mathstrut -\mathstrut 4716q^{4} \) \(\mathstrut -\mathstrut 267668q^{6} \) \(\mathstrut +\mathstrut 586960q^{7} \) \(\mathstrut -\mathstrut 270712q^{8} \) \(\mathstrut +\mathstrut 2014054q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(10q \) \(\mathstrut +\mathstrut 110q^{2} \) \(\mathstrut -\mathstrut 4716q^{4} \) \(\mathstrut -\mathstrut 267668q^{6} \) \(\mathstrut +\mathstrut 586960q^{7} \) \(\mathstrut -\mathstrut 270712q^{8} \) \(\mathstrut +\mathstrut 2014054q^{9} \) \(\mathstrut -\mathstrut 4542088q^{10} \) \(\mathstrut +\mathstrut 27987880q^{12} \) \(\mathstrut +\mathstrut 1408688q^{14} \) \(\mathstrut -\mathstrut 145914416q^{15} \) \(\mathstrut +\mathstrut 56624912q^{16} \) \(\mathstrut +\mathstrut 217326004q^{17} \) \(\mathstrut -\mathstrut 147615262q^{18} \) \(\mathstrut +\mathstrut 21655184q^{20} \) \(\mathstrut -\mathstrut 177987876q^{22} \) \(\mathstrut -\mathstrut 78679952q^{23} \) \(\mathstrut +\mathstrut 320199056q^{24} \) \(\mathstrut -\mathstrut 3076402574q^{25} \) \(\mathstrut +\mathstrut 3734872040q^{26} \) \(\mathstrut -\mathstrut 1653812448q^{28} \) \(\mathstrut +\mathstrut 6338232752q^{30} \) \(\mathstrut +\mathstrut 648233792q^{31} \) \(\mathstrut -\mathstrut 11298380000q^{32} \) \(\mathstrut +\mathstrut 15484079688q^{33} \) \(\mathstrut -\mathstrut 6096822724q^{34} \) \(\mathstrut +\mathstrut 4004708940q^{36} \) \(\mathstrut -\mathstrut 18764968628q^{38} \) \(\mathstrut -\mathstrut 63497510288q^{39} \) \(\mathstrut +\mathstrut 7466802592q^{40} \) \(\mathstrut +\mathstrut 59324640356q^{41} \) \(\mathstrut +\mathstrut 53897620960q^{42} \) \(\mathstrut +\mathstrut 13325704392q^{44} \) \(\mathstrut -\mathstrut 55046867440q^{46} \) \(\mathstrut -\mathstrut 10176534816q^{47} \) \(\mathstrut -\mathstrut 301841943264q^{48} \) \(\mathstrut +\mathstrut 182708552058q^{49} \) \(\mathstrut +\mathstrut 326454435302q^{50} \) \(\mathstrut -\mathstrut 53296499536q^{52} \) \(\mathstrut +\mathstrut 35449773752q^{54} \) \(\mathstrut -\mathstrut 123010753008q^{55} \) \(\mathstrut -\mathstrut 462152447680q^{56} \) \(\mathstrut -\mathstrut 511372324504q^{57} \) \(\mathstrut +\mathstrut 766482705096q^{58} \) \(\mathstrut +\mathstrut 1813082440992q^{60} \) \(\mathstrut -\mathstrut 1665308528960q^{62} \) \(\mathstrut -\mathstrut 898991123792q^{63} \) \(\mathstrut -\mathstrut 2180548996032q^{64} \) \(\mathstrut +\mathstrut 1577231990240q^{65} \) \(\mathstrut +\mathstrut 2269525079448q^{66} \) \(\mathstrut +\mathstrut 2338280915304q^{68} \) \(\mathstrut -\mathstrut 6070110714688q^{70} \) \(\mathstrut +\mathstrut 726361179984q^{71} \) \(\mathstrut -\mathstrut 3600753685960q^{72} \) \(\mathstrut -\mathstrut 633240365532q^{73} \) \(\mathstrut +\mathstrut 7528513982264q^{74} \) \(\mathstrut +\mathstrut 10338420845032q^{76} \) \(\mathstrut -\mathstrut 8252024440816q^{78} \) \(\mathstrut +\mathstrut 5445103565344q^{79} \) \(\mathstrut -\mathstrut 15406871881920q^{80} \) \(\mathstrut -\mathstrut 9674575380574q^{81} \) \(\mathstrut +\mathstrut 12273334206796q^{82} \) \(\mathstrut +\mathstrut 20362643366464q^{84} \) \(\mathstrut -\mathstrut 26794541719396q^{86} \) \(\mathstrut +\mathstrut 7632221772720q^{87} \) \(\mathstrut -\mathstrut 27677491769136q^{88} \) \(\mathstrut +\mathstrut 5506344808004q^{89} \) \(\mathstrut +\mathstrut 31454099524040q^{90} \) \(\mathstrut +\mathstrut 33971694298464q^{92} \) \(\mathstrut -\mathstrut 45356008560096q^{94} \) \(\mathstrut -\mathstrut 14214732035504q^{95} \) \(\mathstrut -\mathstrut 35398666935232q^{96} \) \(\mathstrut +\mathstrut 1361133320788q^{97} \) \(\mathstrut +\mathstrut 54325451514942q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 84.9212 31.3112i 0.938255 0.345944i
\(3\) 1415.71i 1.12120i −0.828085 0.560602i \(-0.810570\pi\)
0.828085 0.560602i \(-0.189430\pi\)
\(4\) 6231.21 5317.98i 0.760646 0.649167i
\(5\) 2384.10i 0.0682368i −0.999418 0.0341184i \(-0.989138\pi\)
0.999418 0.0341184i \(-0.0108623\pi\)
\(6\) −44327.5 120223.i −0.387873 1.05198i
\(7\) −317448. −1.01985 −0.509924 0.860220i \(-0.670326\pi\)
−0.509924 + 0.860220i \(0.670326\pi\)
\(8\) 362649. 646716.i 0.489105 0.872225i
\(9\) −409898. −0.257098
\(10\) −74649.0 202460.i −0.0236061 0.0640236i
\(11\) 1.40906e6i 0.239815i 0.992785 + 0.119908i \(0.0382598\pi\)
−0.992785 + 0.119908i \(0.961740\pi\)
\(12\) −7.52869e6 8.82156e6i −0.727849 0.852839i
\(13\) 2.51242e7i 1.44364i −0.692079 0.721822i \(-0.743305\pi\)
0.692079 0.721822i \(-0.256695\pi\)
\(14\) −2.69581e7 + 9.93969e6i −0.956877 + 0.352810i
\(15\) −3.37518e6 −0.0765074
\(16\) 1.05471e7 6.62749e7i 0.157164 0.987572i
\(17\) 1.11400e8 1.11936 0.559678 0.828710i \(-0.310925\pi\)
0.559678 + 0.828710i \(0.310925\pi\)
\(18\) −3.48090e7 + 1.28344e7i −0.241224 + 0.0889416i
\(19\) 3.64846e8i 1.77915i 0.456792 + 0.889573i \(0.348998\pi\)
−0.456792 + 0.889573i \(0.651002\pi\)
\(20\) −1.26786e7 1.48558e7i −0.0442971 0.0519041i
\(21\) 4.49413e8i 1.14346i
\(22\) 4.41194e7 + 1.19659e8i 0.0829625 + 0.225008i
\(23\) 7.49063e8 1.05509 0.527543 0.849528i \(-0.323113\pi\)
0.527543 + 0.849528i \(0.323113\pi\)
\(24\) −9.15559e8 5.13405e8i −0.977942 0.548386i
\(25\) 1.21502e9 0.995344
\(26\) −7.86670e8 2.13358e9i −0.499420 1.35451i
\(27\) 1.67680e9i 0.832944i
\(28\) −1.97809e9 + 1.68818e9i −0.775743 + 0.662051i
\(29\) 2.83628e9i 0.885446i 0.896659 + 0.442723i \(0.145987\pi\)
−0.896659 + 0.442723i \(0.854013\pi\)
\(30\) −2.86624e8 + 1.05681e8i −0.0717835 + 0.0264672i
\(31\) −2.93414e9 −0.593786 −0.296893 0.954911i \(-0.595950\pi\)
−0.296893 + 0.954911i \(0.595950\pi\)
\(32\) −1.17947e9 5.95838e9i −0.194184 0.980965i
\(33\) 1.99481e9 0.268882
\(34\) 9.46024e9 3.48808e9i 1.05024 0.387234i
\(35\) 7.56826e8i 0.0695912i
\(36\) −2.55416e9 + 2.17983e9i −0.195561 + 0.166900i
\(37\) 8.46017e9i 0.542086i −0.962567 0.271043i \(-0.912631\pi\)
0.962567 0.271043i \(-0.0873685\pi\)
\(38\) 1.14238e10 + 3.09832e10i 0.615485 + 1.66929i
\(39\) −3.55684e10 −1.61862
\(40\) −1.54183e9 8.64591e8i −0.0595179 0.0333750i
\(41\) 3.90644e10 1.28436 0.642180 0.766554i \(-0.278030\pi\)
0.642180 + 0.766554i \(0.278030\pi\)
\(42\) 1.40717e10 + 3.81647e10i 0.395572 + 1.07285i
\(43\) 2.17473e10i 0.524639i −0.964981 0.262319i \(-0.915513\pi\)
0.964981 0.262319i \(-0.0844874\pi\)
\(44\) 7.49334e9 + 8.78014e9i 0.155680 + 0.182414i
\(45\) 9.77236e8i 0.0175436i
\(46\) 6.36113e10 2.34541e10i 0.989940 0.365000i
\(47\) −1.15068e11 −1.55711 −0.778557 0.627574i \(-0.784048\pi\)
−0.778557 + 0.627574i \(0.784048\pi\)
\(48\) −9.38257e10 1.49316e10i −1.10727 0.176213i
\(49\) 3.88420e9 0.0400892
\(50\) 1.03181e11 3.80438e10i 0.933887 0.344333i
\(51\) 1.57710e11i 1.25503i
\(52\) −1.33610e11 1.56554e11i −0.937166 1.09810i
\(53\) 1.71179e11i 1.06086i 0.847729 + 0.530430i \(0.177970\pi\)
−0.847729 + 0.530430i \(0.822030\pi\)
\(54\) −5.25026e10 1.42396e11i −0.288152 0.781514i
\(55\) 3.35933e9 0.0163642
\(56\) −1.15122e11 + 2.05299e11i −0.498812 + 0.889537i
\(57\) 5.16515e11 1.99479
\(58\) 8.88074e10 + 2.40860e11i 0.306314 + 0.830774i
\(59\) 2.45442e11i 0.757549i 0.925489 + 0.378774i \(0.123654\pi\)
−0.925489 + 0.378774i \(0.876346\pi\)
\(60\) −2.10314e10 + 1.79491e10i −0.0581950 + 0.0496661i
\(61\) 2.71473e11i 0.674657i 0.941387 + 0.337328i \(0.109523\pi\)
−0.941387 + 0.337328i \(0.890477\pi\)
\(62\) −2.49170e11 + 9.18715e10i −0.557122 + 0.205416i
\(63\) 1.30121e11 0.262201
\(64\) −2.86727e11 4.69062e11i −0.521553 0.853219i
\(65\) −5.98985e10 −0.0985097
\(66\) 1.69402e11 6.24600e10i 0.252280 0.0930179i
\(67\) 6.82198e11i 0.921350i 0.887569 + 0.460675i \(0.152393\pi\)
−0.887569 + 0.460675i \(0.847607\pi\)
\(68\) 6.94158e11 5.92424e11i 0.851433 0.726649i
\(69\) 1.06045e12i 1.18297i
\(70\) 2.36972e10 + 6.42706e10i 0.0240746 + 0.0652943i
\(71\) −2.90719e11 −0.269336 −0.134668 0.990891i \(-0.542997\pi\)
−0.134668 + 0.990891i \(0.542997\pi\)
\(72\) −1.48649e11 + 2.65088e11i −0.125748 + 0.224248i
\(73\) −1.48745e12 −1.15039 −0.575194 0.818017i \(-0.695073\pi\)
−0.575194 + 0.818017i \(0.695073\pi\)
\(74\) −2.64899e11 7.18448e11i −0.187531 0.508615i
\(75\) 1.72011e12i 1.11598i
\(76\) 1.94024e12 + 2.27344e12i 1.15496 + 1.35330i
\(77\) 4.47303e11i 0.244575i
\(78\) −3.02051e12 + 1.11369e12i −1.51868 + 0.559951i
\(79\) 1.58653e12 0.734296 0.367148 0.930162i \(-0.380334\pi\)
0.367148 + 0.930162i \(0.380334\pi\)
\(80\) −1.58006e11 2.51454e10i −0.0673888 0.0107244i
\(81\) −3.02736e12 −1.19100
\(82\) 3.31740e12 1.22316e12i 1.20506 0.444316i
\(83\) 7.79952e11i 0.261855i −0.991392 0.130927i \(-0.958205\pi\)
0.991392 0.130927i \(-0.0417955\pi\)
\(84\) 2.38997e12 + 2.80039e12i 0.742295 + 0.869766i
\(85\) 2.65589e11i 0.0763812i
\(86\) −6.80935e11 1.84681e12i −0.181495 0.492245i
\(87\) 4.01533e12 0.992765
\(88\) 9.11260e11 + 5.10994e11i 0.209173 + 0.117295i
\(89\) −4.10498e12 −0.875540 −0.437770 0.899087i \(-0.644232\pi\)
−0.437770 + 0.899087i \(0.644232\pi\)
\(90\) 3.05985e10 + 8.29881e10i 0.00606909 + 0.0164604i
\(91\) 7.97562e12i 1.47230i
\(92\) 4.66757e12 3.98350e12i 0.802546 0.684927i
\(93\) 4.15387e12i 0.665755i
\(94\) −9.77175e12 + 3.60294e12i −1.46097 + 0.538673i
\(95\) 8.69829e11 0.121403
\(96\) −8.43531e12 + 1.66979e12i −1.09986 + 0.217720i
\(97\) 1.11567e13 1.35994 0.679971 0.733239i \(-0.261992\pi\)
0.679971 + 0.733239i \(0.261992\pi\)
\(98\) 3.29851e11 1.21619e11i 0.0376139 0.0138686i
\(99\) 5.77570e11i 0.0616561i
\(100\) 7.57104e12 6.46144e12i 0.757104 0.646144i
\(101\) 1.76850e13i 1.65774i −0.559444 0.828868i \(-0.688985\pi\)
0.559444 0.828868i \(-0.311015\pi\)
\(102\) −4.93809e12 1.33929e13i −0.434168 1.17753i
\(103\) 1.25010e11 0.0103158 0.00515790 0.999987i \(-0.498358\pi\)
0.00515790 + 0.999987i \(0.498358\pi\)
\(104\) −1.62482e13 9.11127e12i −1.25918 0.706094i
\(105\) 1.07144e12 0.0780259
\(106\) 5.35984e12 + 1.45368e13i 0.366998 + 0.995358i
\(107\) 5.03372e12i 0.324261i −0.986769 0.162130i \(-0.948164\pi\)
0.986769 0.162130i \(-0.0518365\pi\)
\(108\) −8.91716e12 1.04485e13i −0.540720 0.633576i
\(109\) 3.05175e13i 1.74291i 0.490472 + 0.871457i \(0.336825\pi\)
−0.490472 + 0.871457i \(0.663175\pi\)
\(110\) 2.85278e11 1.05185e11i 0.0153538 0.00566110i
\(111\) −1.19771e13 −0.607789
\(112\) −3.34816e12 + 2.10388e13i −0.160284 + 1.00717i
\(113\) 5.08544e12 0.229783 0.114892 0.993378i \(-0.463348\pi\)
0.114892 + 0.993378i \(0.463348\pi\)
\(114\) 4.38631e13 1.61727e13i 1.87162 0.690084i
\(115\) 1.78584e12i 0.0719957i
\(116\) 1.50833e13 + 1.76735e13i 0.574802 + 0.673511i
\(117\) 1.02984e13i 0.371159i
\(118\) 7.68509e12 + 2.08432e13i 0.262069 + 0.710774i
\(119\) −3.53638e13 −1.14157
\(120\) −1.22401e12 + 2.18278e12i −0.0374201 + 0.0667317i
\(121\) 3.25373e13 0.942489
\(122\) 8.50016e12 + 2.30538e13i 0.233393 + 0.633000i
\(123\) 5.53037e13i 1.44003i
\(124\) −1.82832e13 + 1.56037e13i −0.451661 + 0.385466i
\(125\) 5.80700e12i 0.136156i
\(126\) 1.10501e13 4.07426e12i 0.246012 0.0907069i
\(127\) −2.64256e13 −0.558858 −0.279429 0.960166i \(-0.590145\pi\)
−0.279429 + 0.960166i \(0.590145\pi\)
\(128\) −3.90361e13 3.08555e13i −0.784515 0.620109i
\(129\) −3.07878e13 −0.588227
\(130\) −5.08665e12 + 1.87550e12i −0.0924272 + 0.0340788i
\(131\) 7.50964e12i 0.129824i 0.997891 + 0.0649121i \(0.0206767\pi\)
−0.997891 + 0.0649121i \(0.979323\pi\)
\(132\) 1.24301e13 1.06084e13i 0.204524 0.174549i
\(133\) 1.15820e14i 1.81446i
\(134\) 2.13605e13 + 5.79331e13i 0.318735 + 0.864461i
\(135\) −3.99764e12 −0.0568375
\(136\) 4.03992e13 7.20443e13i 0.547482 0.976330i
\(137\) 2.25954e13 0.291969 0.145985 0.989287i \(-0.453365\pi\)
0.145985 + 0.989287i \(0.453365\pi\)
\(138\) −3.32041e13 9.00549e13i −0.409240 1.10992i
\(139\) 1.14864e14i 1.35079i 0.737458 + 0.675393i \(0.236026\pi\)
−0.737458 + 0.675393i \(0.763974\pi\)
\(140\) 4.02478e12 + 4.71595e12i 0.0451763 + 0.0529342i
\(141\) 1.62903e14i 1.74584i
\(142\) −2.46882e13 + 9.10278e12i −0.252706 + 0.0931750i
\(143\) 3.54014e13 0.346208
\(144\) −4.32325e12 + 2.71659e13i −0.0404067 + 0.253903i
\(145\) 6.76196e12 0.0604200
\(146\) −1.26316e14 + 4.65740e13i −1.07936 + 0.397969i
\(147\) 5.49888e12i 0.0449482i
\(148\) −4.49910e13 5.27171e13i −0.351904 0.412335i
\(149\) 6.70523e13i 0.501999i −0.967987 0.251000i \(-0.919241\pi\)
0.967987 0.251000i \(-0.0807593\pi\)
\(150\) −5.38588e13 1.46074e14i −0.386067 1.04708i
\(151\) 2.60422e14 1.78784 0.893918 0.448231i \(-0.147946\pi\)
0.893918 + 0.448231i \(0.147946\pi\)
\(152\) 2.35952e14 + 1.32311e14i 1.55182 + 0.870189i
\(153\) −4.56627e13 −0.287785
\(154\) −1.40056e13 3.79855e13i −0.0846091 0.229474i
\(155\) 6.99527e12i 0.0405180i
\(156\) −2.21634e14 + 1.89152e14i −1.23120 + 1.05075i
\(157\) 8.89796e13i 0.474179i 0.971488 + 0.237090i \(0.0761935\pi\)
−0.971488 + 0.237090i \(0.923806\pi\)
\(158\) 1.34730e14 4.96761e13i 0.688958 0.254025i
\(159\) 2.42340e14 1.18944
\(160\) −1.42054e13 + 2.81198e12i −0.0669379 + 0.0132505i
\(161\) −2.37789e14 −1.07603
\(162\) −2.57087e14 + 9.47904e13i −1.11746 + 0.412019i
\(163\) 1.43591e13i 0.0599664i 0.999550 + 0.0299832i \(0.00954538\pi\)
−0.999550 + 0.0299832i \(0.990455\pi\)
\(164\) 2.43419e14 2.07744e14i 0.976943 0.833764i
\(165\) 4.75582e12i 0.0183476i
\(166\) −2.44213e13 6.62345e13i −0.0905870 0.245687i
\(167\) −3.16007e14 −1.12730 −0.563650 0.826014i \(-0.690603\pi\)
−0.563650 + 0.826014i \(0.690603\pi\)
\(168\) 2.90642e14 + 1.62979e14i 0.997352 + 0.559270i
\(169\) −3.28350e14 −1.08411
\(170\) −8.31592e12 2.25541e13i −0.0264236 0.0716651i
\(171\) 1.49550e14i 0.457416i
\(172\) −1.15652e14 1.35512e14i −0.340578 0.399064i
\(173\) 5.70549e14i 1.61805i −0.587771 0.809027i \(-0.699994\pi\)
0.587771 0.809027i \(-0.300006\pi\)
\(174\) 3.40987e14 1.25725e14i 0.931467 0.343441i
\(175\) −3.85705e14 −1.01510
\(176\) 9.33851e13 + 1.48615e13i 0.236835 + 0.0376904i
\(177\) 3.47473e14 0.849367
\(178\) −3.48600e14 + 1.28532e14i −0.821480 + 0.302888i
\(179\) 3.77361e13i 0.0857456i 0.999081 + 0.0428728i \(0.0136510\pi\)
−0.999081 + 0.0428728i \(0.986349\pi\)
\(180\) 5.19692e12 + 6.08937e12i 0.0113887 + 0.0133445i
\(181\) 1.46717e14i 0.310148i −0.987903 0.155074i \(-0.950438\pi\)
0.987903 0.155074i \(-0.0495616\pi\)
\(182\) 2.49727e14 + 6.77299e14i 0.509332 + 1.38139i
\(183\) 3.84326e14 0.756428
\(184\) 2.71647e14 4.84431e14i 0.516047 0.920272i
\(185\) −2.01699e13 −0.0369902
\(186\) 1.30063e14 + 3.52752e14i 0.230314 + 0.624648i
\(187\) 1.56969e14i 0.268438i
\(188\) −7.17016e14 + 6.11931e14i −1.18441 + 1.01083i
\(189\) 5.32296e14i 0.849476i
\(190\) 7.38669e13 2.72354e13i 0.113907 0.0419987i
\(191\) −5.17437e14 −0.771153 −0.385576 0.922676i \(-0.625997\pi\)
−0.385576 + 0.922676i \(0.625997\pi\)
\(192\) −6.64054e14 + 4.05921e14i −0.956633 + 0.584767i
\(193\) 8.13631e14 1.13320 0.566598 0.823995i \(-0.308259\pi\)
0.566598 + 0.823995i \(0.308259\pi\)
\(194\) 9.47443e14 3.49331e14i 1.27597 0.470464i
\(195\) 8.47986e13i 0.110449i
\(196\) 2.42033e13 2.06561e13i 0.0304937 0.0260246i
\(197\) 1.27500e15i 1.55410i 0.629439 + 0.777050i \(0.283285\pi\)
−0.629439 + 0.777050i \(0.716715\pi\)
\(198\) −1.80844e13 4.90479e13i −0.0213295 0.0578491i
\(199\) −1.93695e14 −0.221092 −0.110546 0.993871i \(-0.535260\pi\)
−0.110546 + 0.993871i \(0.535260\pi\)
\(200\) 4.40626e14 7.85772e14i 0.486827 0.868164i
\(201\) 9.65792e14 1.03302
\(202\) −5.53739e14 1.50183e15i −0.573484 1.55538i
\(203\) 9.00371e14i 0.903020i
\(204\) −8.38697e14 9.82723e14i −0.814721 0.954630i
\(205\) 9.31334e13i 0.0876406i
\(206\) 1.06160e13 3.91422e12i 0.00967886 0.00356869i
\(207\) −3.07040e14 −0.271261
\(208\) −1.66510e15 2.64988e14i −1.42570 0.226890i
\(209\) −5.14090e14 −0.426666
\(210\) 9.09882e13 3.35482e13i 0.0732082 0.0269926i
\(211\) 7.41305e14i 0.578310i −0.957282 0.289155i \(-0.906626\pi\)
0.957282 0.289155i \(-0.0933743\pi\)
\(212\) 9.10328e14 + 1.06666e15i 0.688676 + 0.806939i
\(213\) 4.11572e14i 0.301980i
\(214\) −1.57612e14 4.27469e14i −0.112176 0.304239i
\(215\) −5.18477e13 −0.0357997
\(216\) −1.08441e15 6.08089e14i −0.726515 0.407397i
\(217\) 9.31436e14 0.605571
\(218\) 9.55540e14 + 2.59158e15i 0.602950 + 1.63530i
\(219\) 2.10579e15i 1.28982i
\(220\) 2.09327e13 1.78648e13i 0.0124474 0.0106231i
\(221\) 2.79884e15i 1.61595i
\(222\) −1.01711e15 + 3.75018e14i −0.570261 + 0.210261i
\(223\) 7.76195e14 0.422658 0.211329 0.977415i \(-0.432221\pi\)
0.211329 + 0.977415i \(0.432221\pi\)
\(224\) 3.74422e14 + 1.89148e15i 0.198038 + 1.00043i
\(225\) −4.98034e14 −0.255901
\(226\) 4.31862e14 1.59231e14i 0.215595 0.0794921i
\(227\) 2.58078e14i 0.125194i −0.998039 0.0625968i \(-0.980062\pi\)
0.998039 0.0625968i \(-0.0199382\pi\)
\(228\) 3.21851e15 2.74681e15i 1.51733 1.29495i
\(229\) 1.51272e15i 0.693151i 0.938022 + 0.346575i \(0.112656\pi\)
−0.938022 + 0.346575i \(0.887344\pi\)
\(230\) −5.59169e13 1.51656e14i −0.0249064 0.0675503i
\(231\) −6.33249e14 −0.274218
\(232\) 1.83427e15 + 1.02857e15i 0.772308 + 0.433076i
\(233\) −2.03207e15 −0.832002 −0.416001 0.909364i \(-0.636569\pi\)
−0.416001 + 0.909364i \(0.636569\pi\)
\(234\) 3.22454e14 + 8.74548e14i 0.128400 + 0.348242i
\(235\) 2.74334e14i 0.106252i
\(236\) 1.30525e15 + 1.52940e15i 0.491776 + 0.576227i
\(237\) 2.24605e15i 0.823296i
\(238\) −3.00313e15 + 1.10728e15i −1.07109 + 0.394920i
\(239\) −2.38480e15 −0.827687 −0.413844 0.910348i \(-0.635814\pi\)
−0.413844 + 0.910348i \(0.635814\pi\)
\(240\) −3.55984e13 + 2.23689e14i −0.0120242 + 0.0755566i
\(241\) −3.98380e15 −1.30975 −0.654873 0.755739i \(-0.727278\pi\)
−0.654873 + 0.755739i \(0.727278\pi\)
\(242\) 2.76310e15 1.01878e15i 0.884295 0.326048i
\(243\) 1.61249e15i 0.502409i
\(244\) 1.44369e15 + 1.69161e15i 0.437965 + 0.513175i
\(245\) 9.26031e12i 0.00273556i
\(246\) −1.73163e15 4.69646e15i −0.498169 1.35111i
\(247\) 9.16647e15 2.56846
\(248\) −1.06406e15 + 1.89755e15i −0.290423 + 0.517915i
\(249\) −1.10418e15 −0.293593
\(250\) −1.81824e14 4.93137e14i −0.0471023 0.127749i
\(251\) 6.79110e15i 1.71420i −0.515151 0.857099i \(-0.672264\pi\)
0.515151 0.857099i \(-0.327736\pi\)
\(252\) 8.10813e14 6.91982e14i 0.199442 0.170212i
\(253\) 1.05547e15i 0.253025i
\(254\) −2.24410e15 + 8.27420e14i −0.524351 + 0.193333i
\(255\) −3.75995e14 −0.0856390
\(256\) −4.28112e15 1.39802e15i −0.950599 0.310423i
\(257\) −7.36721e14 −0.159492 −0.0797458 0.996815i \(-0.525411\pi\)
−0.0797458 + 0.996815i \(0.525411\pi\)
\(258\) −2.61453e15 + 9.64003e14i −0.551907 + 0.203493i
\(259\) 2.68567e15i 0.552845i
\(260\) −3.73240e14 + 3.18539e14i −0.0749310 + 0.0639492i
\(261\) 1.16258e15i 0.227647i
\(262\) 2.35136e14 + 6.37728e14i 0.0449119 + 0.121808i
\(263\) 4.33694e14 0.0808110 0.0404055 0.999183i \(-0.487135\pi\)
0.0404055 + 0.999183i \(0.487135\pi\)
\(264\) 7.23417e14 1.29008e15i 0.131511 0.234525i
\(265\) 4.08108e14 0.0723898
\(266\) −3.62646e15 9.83555e15i −0.627700 1.70243i
\(267\) 5.81144e15i 0.981660i
\(268\) 3.62791e15 + 4.25092e15i 0.598110 + 0.700821i
\(269\) 3.36599e15i 0.541655i 0.962628 + 0.270827i \(0.0872973\pi\)
−0.962628 + 0.270827i \(0.912703\pi\)
\(270\) −3.39485e14 + 1.25171e14i −0.0533280 + 0.0196626i
\(271\) −8.64352e14 −0.132553 −0.0662766 0.997801i \(-0.521112\pi\)
−0.0662766 + 0.997801i \(0.521112\pi\)
\(272\) 1.17495e15 7.38303e15i 0.175923 1.10544i
\(273\) 1.12911e16 1.65075
\(274\) 1.91883e15 7.07491e14i 0.273942 0.101005i
\(275\) 1.71203e15i 0.238698i
\(276\) −5.63946e15 6.60791e15i −0.767943 0.899818i
\(277\) 4.29153e15i 0.570813i 0.958407 + 0.285407i \(0.0921286\pi\)
−0.958407 + 0.285407i \(0.907871\pi\)
\(278\) 3.59653e15 + 9.75436e15i 0.467296 + 1.26738i
\(279\) 1.20270e15 0.152661
\(280\) 4.89452e14 + 2.74463e14i 0.0606991 + 0.0340374i
\(281\) −1.75304e14 −0.0212422 −0.0106211 0.999944i \(-0.503381\pi\)
−0.0106211 + 0.999944i \(0.503381\pi\)
\(282\) 5.10070e15 + 1.38339e16i 0.603963 + 1.63805i
\(283\) 1.04579e16i 1.21013i 0.796177 + 0.605064i \(0.206853\pi\)
−0.796177 + 0.605064i \(0.793147\pi\)
\(284\) −1.81153e15 + 1.54604e15i −0.204869 + 0.174844i
\(285\) 1.23142e15i 0.136118i
\(286\) 3.00633e15 1.10846e15i 0.324831 0.119768i
\(287\) −1.24009e16 −1.30985
\(288\) 4.83464e14 + 2.44233e15i 0.0499244 + 0.252205i
\(289\) 2.50543e15 0.252956
\(290\) 5.74234e14 2.11725e14i 0.0566894 0.0209019i
\(291\) 1.57946e16i 1.52477i
\(292\) −9.26862e15 + 7.91023e15i −0.875038 + 0.746794i
\(293\) 1.28392e16i 1.18549i −0.805390 0.592745i \(-0.798044\pi\)
0.805390 0.592745i \(-0.201956\pi\)
\(294\) −1.72177e14 4.66972e14i −0.0155495 0.0421729i
\(295\) 5.85157e14 0.0516927
\(296\) −5.47133e15 3.06808e15i −0.472821 0.265137i
\(297\) 2.36270e15 0.199753
\(298\) −2.09949e15 5.69416e15i −0.173664 0.471004i
\(299\) 1.88196e16i 1.52317i
\(300\) −9.14750e15 1.07184e16i −0.724460 0.848868i
\(301\) 6.90364e15i 0.535052i
\(302\) 2.21153e16 8.15414e15i 1.67745 0.618490i
\(303\) −2.50367e16 −1.85866
\(304\) 2.41802e16 + 3.84808e15i 1.75704 + 0.279619i
\(305\) 6.47218e14 0.0460364
\(306\) −3.87773e15 + 1.42976e15i −0.270015 + 0.0995572i
\(307\) 8.53937e15i 0.582139i −0.956702 0.291069i \(-0.905989\pi\)
0.956702 0.291069i \(-0.0940110\pi\)
\(308\) −2.37874e15 2.78724e15i −0.158770 0.186035i
\(309\) 1.76977e14i 0.0115661i
\(310\) 2.19031e14 + 5.94046e14i 0.0140170 + 0.0380163i
\(311\) 3.52686e15 0.221027 0.110513 0.993875i \(-0.464750\pi\)
0.110513 + 0.993875i \(0.464750\pi\)
\(312\) −1.28989e16 + 2.30027e16i −0.791675 + 1.41180i
\(313\) −1.00518e16 −0.604234 −0.302117 0.953271i \(-0.597693\pi\)
−0.302117 + 0.953271i \(0.597693\pi\)
\(314\) 2.78606e15 + 7.55625e15i 0.164039 + 0.444901i
\(315\) 3.10222e14i 0.0178918i
\(316\) 9.88599e15 8.43711e15i 0.558540 0.476681i
\(317\) 3.13051e16i 1.73273i 0.499414 + 0.866363i \(0.333549\pi\)
−0.499414 + 0.866363i \(0.666451\pi\)
\(318\) 2.05798e16 7.58795e15i 1.11600 0.411480i
\(319\) −3.99648e15 −0.212343
\(320\) −1.11829e15 + 6.83584e14i −0.0582209 + 0.0355891i
\(321\) −7.12626e15 −0.363562
\(322\) −2.01933e16 + 7.44546e15i −1.00959 + 0.372245i
\(323\) 4.06440e16i 1.99150i
\(324\) −1.88641e16 + 1.60994e16i −0.905928 + 0.773157i
\(325\) 3.05264e16i 1.43692i
\(326\) 4.49602e14 + 1.21939e15i 0.0207450 + 0.0562638i
\(327\) 4.32037e16 1.95416
\(328\) 1.41667e16 2.52636e16i 0.628186 1.12025i
\(329\) 3.65282e16 1.58802
\(330\) −1.48911e14 4.03870e14i −0.00634724 0.0172148i
\(331\) 4.89913e15i 0.204756i −0.994746 0.102378i \(-0.967355\pi\)
0.994746 0.102378i \(-0.0326452\pi\)
\(332\) −4.14777e15 4.86005e15i −0.169987 0.199179i
\(333\) 3.46781e15i 0.139369i
\(334\) −2.68357e16 + 9.89457e15i −1.05770 + 0.389982i
\(335\) 1.62643e15 0.0628700
\(336\) 2.97848e16 + 4.74001e15i 1.12925 + 0.179711i
\(337\) −2.53208e16 −0.941636 −0.470818 0.882230i \(-0.656041\pi\)
−0.470818 + 0.882230i \(0.656041\pi\)
\(338\) −2.78838e16 + 1.02810e16i −1.01717 + 0.375041i
\(339\) 7.19948e15i 0.257634i
\(340\) −1.41239e15 1.65494e15i −0.0495842 0.0580991i
\(341\) 4.13437e15i 0.142399i
\(342\) −4.68259e15 1.26999e16i −0.158240 0.429173i
\(343\) 2.95242e16 0.978963
\(344\) −1.40643e16 7.88664e15i −0.457603 0.256603i
\(345\) −2.52822e15 −0.0807218
\(346\) −1.78646e16 4.84517e16i −0.559756 1.51815i
\(347\) 5.14894e16i 1.58335i 0.610943 + 0.791674i \(0.290790\pi\)
−0.610943 + 0.791674i \(0.709210\pi\)
\(348\) 2.50204e16 2.13534e16i 0.755143 0.644470i
\(349\) 3.91636e16i 1.16016i −0.814560 0.580079i \(-0.803022\pi\)
0.814560 0.580079i \(-0.196978\pi\)
\(350\) −3.27546e16 + 1.20769e16i −0.952422 + 0.351167i
\(351\) −4.21282e16 −1.20248
\(352\) 8.39571e15 1.66195e15i 0.235250 0.0465683i
\(353\) 1.84699e15 0.0508077 0.0254038 0.999677i \(-0.491913\pi\)
0.0254038 + 0.999677i \(0.491913\pi\)
\(354\) 2.95079e16 1.08798e16i 0.796923 0.293833i
\(355\) 6.93102e14i 0.0183786i
\(356\) −2.55790e16 + 2.18302e16i −0.665976 + 0.568372i
\(357\) 5.00647e16i 1.27994i
\(358\) 1.18156e15 + 3.20459e15i 0.0296631 + 0.0804512i
\(359\) 6.56490e16 1.61850 0.809252 0.587461i \(-0.199872\pi\)
0.809252 + 0.587461i \(0.199872\pi\)
\(360\) 6.31994e14 + 3.54394e14i 0.0153019 + 0.00858065i
\(361\) −9.10600e16 −2.16536
\(362\) −4.59389e15 1.24594e16i −0.107294 0.290998i
\(363\) 4.60632e16i 1.05672i
\(364\) 4.24142e16 + 4.96978e16i 0.955767 + 1.11990i
\(365\) 3.54623e15i 0.0784988i
\(366\) 3.26374e16 1.20337e16i 0.709723 0.261682i
\(367\) 6.75272e15 0.144261 0.0721305 0.997395i \(-0.477020\pi\)
0.0721305 + 0.997395i \(0.477020\pi\)
\(368\) 7.90047e15 4.96441e16i 0.165822 1.04197i
\(369\) −1.60124e16 −0.330207
\(370\) −1.71285e15 + 6.31544e14i −0.0347063 + 0.0127965i
\(371\) 5.43406e16i 1.08192i
\(372\) 2.20902e16 + 2.58837e16i 0.432186 + 0.506404i
\(373\) 6.35460e16i 1.22175i −0.791729 0.610873i \(-0.790819\pi\)
0.791729 0.610873i \(-0.209181\pi\)
\(374\) 4.91491e15 + 1.33300e16i 0.0928645 + 0.251864i
\(375\) −8.22099e15 −0.152659
\(376\) −4.17295e16 + 7.44166e16i −0.761592 + 1.35815i
\(377\) 7.12592e16 1.27827
\(378\) 1.66668e16 + 4.52032e16i 0.293871 + 0.797025i
\(379\) 1.76761e16i 0.306360i 0.988198 + 0.153180i \(0.0489515\pi\)
−0.988198 + 0.153180i \(0.951048\pi\)
\(380\) 5.42009e15 4.62573e15i 0.0923449 0.0788110i
\(381\) 3.74109e16i 0.626594i
\(382\) −4.39413e16 + 1.62016e16i −0.723538 + 0.266775i
\(383\) −1.13626e17 −1.83944 −0.919718 0.392580i \(-0.871583\pi\)
−0.919718 + 0.392580i \(0.871583\pi\)
\(384\) −4.36823e16 + 5.52636e16i −0.695269 + 0.879602i
\(385\) −1.06641e15 −0.0166890
\(386\) 6.90945e16 2.54758e16i 1.06323 0.392022i
\(387\) 8.91417e15i 0.134884i
\(388\) 6.95199e16 5.93312e16i 1.03444 0.882830i
\(389\) 5.13314e16i 0.751122i 0.926798 + 0.375561i \(0.122550\pi\)
−0.926798 + 0.375561i \(0.877450\pi\)
\(390\) 2.65515e15 + 7.20120e15i 0.0382093 + 0.103630i
\(391\) 8.34458e16 1.18102
\(392\) 1.40860e15 2.51197e15i 0.0196078 0.0349668i
\(393\) 1.06314e16 0.145560
\(394\) 3.99218e16 + 1.08274e17i 0.537631 + 1.45814i
\(395\) 3.78243e15i 0.0501061i
\(396\) −3.07150e15 3.59896e15i −0.0400251 0.0468984i
\(397\) 6.00314e16i 0.769556i −0.923009 0.384778i \(-0.874278\pi\)
0.923009 0.384778i \(-0.125722\pi\)
\(398\) −1.64488e16 + 6.06484e15i −0.207441 + 0.0764855i
\(399\) −1.63967e17 −2.03438
\(400\) 1.28150e16 8.05252e16i 0.156433 0.982974i
\(401\) 1.01141e17 1.21475 0.607376 0.794415i \(-0.292222\pi\)
0.607376 + 0.794415i \(0.292222\pi\)
\(402\) 8.20162e16 3.02401e16i 0.969237 0.357367i
\(403\) 7.37178e16i 0.857215i
\(404\) −9.40483e16 1.10199e17i −1.07615 1.26095i
\(405\) 7.21752e15i 0.0812700i
\(406\) −2.81917e16 7.64605e16i −0.312394 0.847263i
\(407\) 1.19209e16 0.130000
\(408\) −1.01993e17 5.71934e16i −1.09466 0.613839i
\(409\) −7.36411e16 −0.777891 −0.388945 0.921261i \(-0.627161\pi\)
−0.388945 + 0.921261i \(0.627161\pi\)
\(410\) −2.91612e15 7.90899e15i −0.0303187 0.0822292i
\(411\) 3.19885e16i 0.327357i
\(412\) 7.78964e14 6.64801e14i 0.00784667 0.00669668i
\(413\) 7.79151e16i 0.772585i
\(414\) −2.60742e16 + 9.61379e15i −0.254512 + 0.0938410i
\(415\) −1.85948e15 −0.0178681
\(416\) −1.49700e17 + 2.96333e16i −1.41616 + 0.280333i
\(417\) 1.62613e17 1.51451
\(418\) −4.36571e16 + 1.60968e16i −0.400322 + 0.147602i
\(419\) 2.79559e16i 0.252396i −0.992005 0.126198i \(-0.959723\pi\)
0.992005 0.126198i \(-0.0402775\pi\)
\(420\) 6.67639e15 5.69791e15i 0.0593501 0.0506518i
\(421\) 1.82667e17i 1.59892i 0.600718 + 0.799461i \(0.294882\pi\)
−0.600718 + 0.799461i \(0.705118\pi\)
\(422\) −2.32112e16 6.29525e16i −0.200063 0.542602i
\(423\) 4.71663e16 0.400331
\(424\) 1.10704e17 + 6.20781e16i 0.925309 + 0.518872i
\(425\) 1.35353e17 1.11414
\(426\) 1.28868e16 + 3.49512e16i 0.104468 + 0.283335i
\(427\) 8.61786e16i 0.688047i
\(428\) −2.67692e16 3.13661e16i −0.210499 0.246647i
\(429\) 5.01180e16i 0.388169i
\(430\) −4.40296e15 + 1.62341e15i −0.0335892 + 0.0123847i
\(431\) −3.02335e16 −0.227189 −0.113594 0.993527i \(-0.536236\pi\)
−0.113594 + 0.993527i \(0.536236\pi\)
\(432\) −1.11129e17 1.76854e16i −0.822593 0.130909i
\(433\) −8.25641e16 −0.602033 −0.301016 0.953619i \(-0.597326\pi\)
−0.301016 + 0.953619i \(0.597326\pi\)
\(434\) 7.90987e16 2.91644e16i 0.568180 0.209493i
\(435\) 9.57294e15i 0.0677431i
\(436\) 1.62291e17 + 1.90161e17i 1.13144 + 1.32574i
\(437\) 2.73293e17i 1.87715i
\(438\) 6.59350e16 + 1.78826e17i 0.446205 + 1.21018i
\(439\) 1.89165e17 1.26131 0.630653 0.776065i \(-0.282787\pi\)
0.630653 + 0.776065i \(0.282787\pi\)
\(440\) 1.21826e15 2.17253e15i 0.00800382 0.0142733i
\(441\) −1.59213e15 −0.0103069
\(442\) −8.76352e16 2.37681e17i −0.559028 1.51617i
\(443\) 1.83331e17i 1.15242i 0.817301 + 0.576210i \(0.195469\pi\)
−0.817301 + 0.576210i \(0.804531\pi\)
\(444\) −7.46319e16 + 6.36940e16i −0.462312 + 0.394556i
\(445\) 9.78667e15i 0.0597441i
\(446\) 6.59154e16 2.43036e16i 0.396561 0.146216i
\(447\) −9.49263e16 −0.562844
\(448\) 9.10208e16 + 1.48903e17i 0.531904 + 0.870153i
\(449\) −3.31235e17 −1.90781 −0.953904 0.300111i \(-0.902976\pi\)
−0.953904 + 0.300111i \(0.902976\pi\)
\(450\) −4.22936e16 + 1.55941e16i −0.240101 + 0.0885275i
\(451\) 5.50441e16i 0.308009i
\(452\) 3.16884e16 2.70442e16i 0.174784 0.149168i
\(453\) 3.68681e17i 2.00453i
\(454\) −8.08073e15 2.19163e16i −0.0433100 0.117464i
\(455\) 1.90147e16 0.100465
\(456\) 1.87314e17 3.34038e17i 0.975660 1.73990i
\(457\) −1.50721e17 −0.773961 −0.386980 0.922088i \(-0.626482\pi\)
−0.386980 + 0.922088i \(0.626482\pi\)
\(458\) 4.73651e16 + 1.28462e17i 0.239791 + 0.650352i
\(459\) 1.86795e17i 0.932361i
\(460\) −9.49705e15 1.11279e16i −0.0467372 0.0547632i
\(461\) 1.21235e17i 0.588261i −0.955765 0.294131i \(-0.904970\pi\)
0.955765 0.294131i \(-0.0950301\pi\)
\(462\) −5.37762e16 + 1.98278e16i −0.257287 + 0.0948641i
\(463\) −8.74764e15 −0.0412681 −0.0206340 0.999787i \(-0.506568\pi\)
−0.0206340 + 0.999787i \(0.506568\pi\)
\(464\) 1.87974e17 + 2.99146e16i 0.874442 + 0.139161i
\(465\) 9.90324e15 0.0454290
\(466\) −1.72565e17 + 6.36265e16i −0.780630 + 0.287826i
\(467\) 2.95016e17i 1.31609i −0.752978 0.658045i \(-0.771383\pi\)
0.752978 0.658045i \(-0.228617\pi\)
\(468\) 5.47664e16 + 6.41712e16i 0.240944 + 0.282320i
\(469\) 2.16562e17i 0.939636i
\(470\) 8.58975e15 + 2.32968e16i 0.0367574 + 0.0996919i
\(471\) 1.25969e17 0.531652
\(472\) 1.58731e17 + 8.90094e16i 0.660753 + 0.370521i
\(473\) 3.06432e16 0.125816
\(474\) −7.03268e16 1.90738e17i −0.284814 0.772462i
\(475\) 4.43295e17i 1.77086i
\(476\) −2.20359e17 + 1.88064e17i −0.868332 + 0.741071i
\(477\) 7.01661e16i 0.272746i
\(478\) −2.02520e17 + 7.46712e16i −0.776582 + 0.286333i
\(479\) −2.73322e17 −1.03394 −0.516969 0.856004i \(-0.672940\pi\)
−0.516969 + 0.856004i \(0.672940\pi\)
\(480\) 3.98093e15 + 2.01106e16i 0.0148565 + 0.0750511i
\(481\) −2.12555e17 −0.782579
\(482\) −3.38309e17 + 1.24738e17i −1.22888 + 0.453098i
\(483\) 3.36639e17i 1.20645i
\(484\) 2.02747e17 1.73032e17i 0.716900 0.611833i
\(485\) 2.65987e16i 0.0927982i
\(486\) 5.04892e16 + 1.36935e17i 0.173805 + 0.471387i
\(487\) 5.51673e17 1.87389 0.936943 0.349482i \(-0.113642\pi\)
0.936943 + 0.349482i \(0.113642\pi\)
\(488\) 1.75566e17 + 9.84496e16i 0.588453 + 0.329978i
\(489\) 2.03283e16 0.0672346
\(490\) −2.89952e14 7.86397e14i −0.000946349 0.00256665i
\(491\) 4.05694e17i 1.30668i −0.757065 0.653340i \(-0.773367\pi\)
0.757065 0.653340i \(-0.226633\pi\)
\(492\) −2.94104e17 3.44609e17i −0.934819 1.09535i
\(493\) 3.15962e17i 0.991128i
\(494\) 7.78428e17 2.87014e17i 2.40987 0.888541i
\(495\) −1.37698e15 −0.00420721
\(496\) −3.09467e16 + 1.94460e17i −0.0933220 + 0.586406i
\(497\) 9.22882e16 0.274682
\(498\) −9.37685e16 + 3.45733e16i −0.275465 + 0.101567i
\(499\) 4.14431e16i 0.120171i −0.998193 0.0600853i \(-0.980863\pi\)
0.998193 0.0600853i \(-0.0191373\pi\)
\(500\) −3.08815e16 3.61846e16i −0.0883879 0.103566i
\(501\) 4.47373e17i 1.26393i
\(502\) −2.12638e17 5.76709e17i −0.593016 1.60836i
\(503\) −2.67191e16 −0.0735579 −0.0367789 0.999323i \(-0.511710\pi\)
−0.0367789 + 0.999323i \(0.511710\pi\)
\(504\) 4.71884e16 8.41515e16i 0.128244 0.228698i
\(505\) −4.21627e16 −0.113119
\(506\) 3.30482e16 + 8.96321e16i 0.0875325 + 0.237402i
\(507\) 4.64846e17i 1.21551i
\(508\) −1.64664e17 + 1.40531e17i −0.425093 + 0.362792i
\(509\) 2.27992e17i 0.581104i 0.956859 + 0.290552i \(0.0938389\pi\)
−0.956859 + 0.290552i \(0.906161\pi\)
\(510\) −3.19300e16 + 1.17729e16i −0.0803512 + 0.0296263i
\(511\) 4.72188e17 1.17322
\(512\) −4.07331e17 + 1.53257e16i −0.999293 + 0.0375980i
\(513\) 6.11773e17 1.48193
\(514\) −6.25632e16 + 2.30676e16i −0.149644 + 0.0551751i
\(515\) 2.98036e14i 0.000703918i
\(516\) −1.91845e17 + 1.63729e17i −0.447433 + 0.381858i
\(517\) 1.62138e17i 0.373419i
\(518\) 8.40915e16 + 2.28070e17i 0.191253 + 0.518710i
\(519\) −8.07729e17 −1.81417
\(520\) −2.17221e16 + 3.87373e16i −0.0481816 + 0.0859226i
\(521\) 2.69956e17 0.591355 0.295678 0.955288i \(-0.404455\pi\)
0.295678 + 0.955288i \(0.404455\pi\)
\(522\) −3.64020e16 9.87281e16i −0.0787529 0.213591i
\(523\) 8.10541e17i 1.73187i −0.500161 0.865933i \(-0.666726\pi\)
0.500161 0.865933i \(-0.333274\pi\)
\(524\) 3.99361e16 + 4.67942e16i 0.0842776 + 0.0987503i
\(525\) 5.46045e17i 1.13813i
\(526\) 3.68298e16 1.35795e16i 0.0758214 0.0279561i
\(527\) −3.26864e17 −0.664657
\(528\) 2.10395e16 1.32206e17i 0.0422586 0.265540i
\(529\) 5.70597e16 0.113205
\(530\) 3.46570e16 1.27784e16i 0.0679201 0.0250428i
\(531\) 1.00606e17i 0.194765i
\(532\) −6.15927e17 7.21698e17i −1.17789 1.38016i
\(533\) 9.81462e17i 1.85416i
\(534\) 1.81964e17 + 4.93515e17i 0.339599 + 0.921047i
\(535\) −1.20009e16 −0.0221265
\(536\) 4.41188e17 + 2.47399e17i 0.803624 + 0.450637i
\(537\) 5.34231e16 0.0961383
\(538\) 1.05393e17 + 2.85844e17i 0.187382 + 0.508210i
\(539\) 5.47307e15i 0.00961399i
\(540\) −2.49102e16 + 2.12594e16i −0.0432332 + 0.0368970i
\(541\) 3.09047e17i 0.529959i −0.964254 0.264980i \(-0.914635\pi\)
0.964254 0.264980i \(-0.0853653\pi\)
\(542\) −7.34018e16 + 2.70639e16i −0.124369 + 0.0458559i
\(543\) −2.07708e17 −0.347739
\(544\) −1.31394e17 6.63765e17i −0.217361 1.09805i
\(545\) 7.27565e16 0.118931
\(546\) 9.58856e17 3.53539e17i 1.54882 0.571065i
\(547\) 4.33397e17i 0.691780i 0.938275 + 0.345890i \(0.112423\pi\)
−0.938275 + 0.345890i \(0.887577\pi\)
\(548\) 1.40797e17 1.20162e17i 0.222085 0.189537i
\(549\) 1.11276e17i 0.173453i
\(550\) 5.36059e16 + 1.45388e17i 0.0825762 + 0.223960i
\(551\) −1.03481e18 −1.57534
\(552\) −6.85812e17 3.84573e17i −1.03181 0.578594i
\(553\) −5.03640e17 −0.748871
\(554\) 1.34373e17 + 3.64442e17i 0.197469 + 0.535568i
\(555\) 2.85546e16i 0.0414736i
\(556\) 6.10843e17 + 7.15740e17i 0.876886 + 1.02747i
\(557\) 3.35954e17i 0.476674i 0.971183 + 0.238337i \(0.0766022\pi\)
−0.971183 + 0.238337i \(0.923398\pi\)
\(558\) 1.02134e17 3.76580e16i 0.143235 0.0528122i
\(559\) −5.46383e17 −0.757392
\(560\) 5.01586e16 + 7.98235e15i 0.0687263 + 0.0109373i
\(561\) 2.22222e17 0.300974
\(562\) −1.48870e16 + 5.48898e15i −0.0199306 + 0.00734861i
\(563\) 4.77847e17i 0.632389i −0.948694 0.316195i \(-0.897595\pi\)
0.948694 0.316195i \(-0.102405\pi\)
\(564\) 8.66314e17 + 1.01508e18i 1.13334 + 1.32797i
\(565\) 1.21242e16i 0.0156797i
\(566\) 3.27449e17 + 8.88095e17i 0.418636 + 1.13541i
\(567\) 9.61029e17 1.21464
\(568\) −1.05429e17 + 1.88013e17i −0.131733 + 0.234921i
\(569\) −3.86358e16 −0.0477265 −0.0238633 0.999715i \(-0.507597\pi\)
−0.0238633 + 0.999715i \(0.507597\pi\)
\(570\) −3.85573e16 1.04574e17i −0.0470891 0.127713i
\(571\) 8.78096e17i 1.06025i 0.847920 + 0.530124i \(0.177855\pi\)
−0.847920 + 0.530124i \(0.822145\pi\)
\(572\) 2.20594e17 1.88264e17i 0.263341 0.224747i
\(573\) 7.32538e17i 0.864619i
\(574\) −1.05310e18 + 3.88288e17i −1.22897 + 0.453135i
\(575\) 9.10126e17 1.05017
\(576\) 1.17529e17 + 1.92268e17i 0.134090 + 0.219361i
\(577\) 3.37219e17 0.380425 0.190213 0.981743i \(-0.439082\pi\)
0.190213 + 0.981743i \(0.439082\pi\)
\(578\) 2.12764e17 7.84480e16i 0.237338 0.0875087i
\(579\) 1.15186e18i 1.27054i
\(580\) 4.21352e16 3.59599e16i 0.0459582 0.0392227i
\(581\) 2.47594e17i 0.267052i
\(582\) −4.94550e17 1.34130e18i −0.527486 1.43063i
\(583\) −2.41202e17 −0.254410
\(584\) −5.39423e17 + 9.61958e17i −0.562660 + 1.00340i
\(585\) 2.45523e16 0.0253267
\(586\) −4.02011e17 1.09032e18i −0.410113 1.11229i
\(587\) 5.59350e16i 0.0564334i 0.999602 + 0.0282167i \(0.00898284\pi\)
−0.999602 + 0.0282167i \(0.991017\pi\)
\(588\) −2.92429e16 3.42647e16i −0.0291789 0.0341896i
\(589\) 1.07051e18i 1.05643i
\(590\) 4.96922e16 1.83220e16i 0.0485010 0.0178828i
\(591\) 1.80502e18 1.74246
\(592\) −5.60697e17 8.92305e16i −0.535349 0.0851966i
\(593\) −1.85096e18 −1.74800 −0.874000 0.485927i \(-0.838482\pi\)
−0.874000 + 0.485927i \(0.838482\pi\)
\(594\) 2.00644e17 7.39792e16i 0.187419 0.0691031i
\(595\) 8.43106e16i 0.0778972i
\(596\) −3.56583e17 4.17817e17i −0.325881 0.381844i
\(597\) 2.74215e17i 0.247890i
\(598\) −5.89265e17 1.59818e18i −0.526930 1.42912i
\(599\) −5.05656e17 −0.447281 −0.223641 0.974672i \(-0.571794\pi\)
−0.223641 + 0.974672i \(0.571794\pi\)
\(600\) −1.11242e18 6.23796e17i −0.973389 0.545833i
\(601\) 1.45684e16 0.0126103 0.00630517 0.999980i \(-0.497993\pi\)
0.00630517 + 0.999980i \(0.497993\pi\)
\(602\) 2.16161e17 + 5.86265e17i 0.185098 + 0.502015i
\(603\) 2.79632e17i 0.236878i
\(604\) 1.62274e18 1.38492e18i 1.35991 1.16060i
\(605\) 7.75720e16i 0.0643124i
\(606\) −2.12615e18 + 7.83931e17i −1.74390 + 0.642992i
\(607\) 1.20617e18 0.978772 0.489386 0.872067i \(-0.337221\pi\)
0.489386 + 0.872067i \(0.337221\pi\)
\(608\) 2.17390e18 4.30327e17i 1.74528 0.345482i
\(609\) −1.27466e18 −1.01247
\(610\) 5.49625e16 2.02652e16i 0.0431939 0.0159260i
\(611\) 2.89100e18i 2.24792i
\(612\) −2.84534e17 + 2.42833e17i −0.218902 + 0.186820i
\(613\) 1.01082e18i 0.769450i 0.923031 + 0.384725i \(0.125704\pi\)
−0.923031 + 0.384725i \(0.874296\pi\)
\(614\) −2.67378e17 7.25173e17i −0.201387 0.546195i
\(615\) −1.31849e17 −0.0982630
\(616\) −2.89278e17 1.62214e17i −0.213324 0.119623i
\(617\) 1.35500e18 0.988751 0.494376 0.869248i \(-0.335397\pi\)
0.494376 + 0.869248i \(0.335397\pi\)
\(618\) −5.54138e15 1.50291e16i −0.00400123 0.0108520i
\(619\) 3.64418e17i 0.260382i −0.991489 0.130191i \(-0.958441\pi\)
0.991489 0.130191i \(-0.0415590\pi\)
\(620\) 3.72007e16 + 4.35890e16i 0.0263030 + 0.0308199i
\(621\) 1.25603e18i 0.878827i
\(622\) 2.99505e17 1.10430e17i 0.207380 0.0764629i
\(623\) 1.30312e18 0.892918
\(624\) −3.75145e17 + 2.35729e18i −0.254390 + 1.59850i
\(625\) 1.46933e18 0.986053
\(626\) −8.53610e17 + 3.14734e17i −0.566926 + 0.209031i
\(627\) 7.27800e17i 0.478380i
\(628\) 4.73191e17 + 5.54451e17i 0.307822 + 0.360683i
\(629\) 9.42465e17i 0.606787i
\(630\) −9.71343e15 2.63444e16i −0.00618955 0.0167871i
\(631\) −2.16455e18 −1.36514 −0.682571 0.730819i \(-0.739138\pi\)
−0.682571 + 0.730819i \(0.739138\pi\)
\(632\) 5.75353e17 1.02603e18i 0.359148 0.640472i
\(633\) −1.04947e18 −0.648404
\(634\) 9.80202e17 + 2.65847e18i 0.599426 + 1.62574i
\(635\) 6.30013e16i 0.0381347i
\(636\) 1.51007e18 1.28876e18i 0.904744 0.772146i
\(637\) 9.75874e16i 0.0578745i
\(638\) −3.39386e17 + 1.25135e17i −0.199232 + 0.0734588i
\(639\) 1.19165e17 0.0692458
\(640\) −7.35626e16 + 9.30658e16i −0.0423143 + 0.0535328i
\(641\) −6.48038e17 −0.368997 −0.184499 0.982833i \(-0.559066\pi\)
−0.184499 + 0.982833i \(0.559066\pi\)
\(642\) −6.05170e17 + 2.23132e17i −0.341114 + 0.125772i
\(643\) 1.13754e18i 0.634738i −0.948302 0.317369i \(-0.897201\pi\)
0.948302 0.317369i \(-0.102799\pi\)
\(644\) −1.48171e18 + 1.26455e18i −0.818475 + 0.698521i
\(645\) 7.34010e16i 0.0401387i
\(646\) 1.27261e18 + 3.45153e18i 0.688946 + 1.86853i
\(647\) 4.00139e17 0.214453 0.107227 0.994235i \(-0.465803\pi\)
0.107227 + 0.994235i \(0.465803\pi\)
\(648\) −1.09787e18 + 1.95784e18i −0.582523 + 1.03882i
\(649\) −3.45842e17 −0.181672
\(650\) −9.55819e17 2.59234e18i −0.497094 1.34820i
\(651\) 1.31864e18i 0.678968i
\(652\) 7.63614e16 + 8.94747e16i 0.0389282 + 0.0456132i
\(653\) 5.15814e17i 0.260350i −0.991491 0.130175i \(-0.958446\pi\)
0.991491 0.130175i \(-0.0415539\pi\)
\(654\) 3.66891e18 1.35276e18i 1.83350 0.676030i
\(655\) 1.79037e16 0.00885880
\(656\) 4.12018e17 2.58899e18i 0.201856 1.26840i
\(657\) 6.09703e17 0.295763
\(658\) 3.10202e18 1.14374e18i 1.48997 0.549365i
\(659\) 2.76356e18i 1.31436i −0.753734 0.657180i \(-0.771749\pi\)
0.753734 0.657180i \(-0.228251\pi\)
\(660\) −2.52913e16 2.96345e16i −0.0119107 0.0139560i
\(661\) 2.27112e18i 1.05909i 0.848283 + 0.529543i \(0.177636\pi\)
−0.848283 + 0.529543i \(0.822364\pi\)
\(662\) −1.53398e17 4.16040e17i −0.0708341 0.192114i
\(663\) −3.96233e18 −1.81181
\(664\) −5.04408e17 2.82849e17i −0.228396 0.128074i
\(665\) −2.76125e17 −0.123813
\(666\) 1.08581e17 + 2.94490e17i 0.0482140 + 0.130764i
\(667\) 2.12455e18i 0.934221i
\(668\) −1.96911e18 + 1.68052e18i −0.857476 + 0.731806i
\(669\) 1.09886e18i 0.473886i
\(670\) 1.38118e17 5.09254e16i 0.0589881 0.0217495i
\(671\) −3.82521e17 −0.161793
\(672\) 2.67777e18 5.30071e17i 1.12169 0.222041i
\(673\) 3.76617e17 0.156243 0.0781217 0.996944i \(-0.475108\pi\)
0.0781217 + 0.996944i \(0.475108\pi\)
\(674\) −2.15027e18 + 7.92826e17i −0.883495 + 0.325753i
\(675\) 2.03734e18i 0.829066i
\(676\) −2.04602e18 + 1.74616e18i −0.824623 + 0.703768i
\(677\) 2.97834e18i 1.18891i 0.804130 + 0.594453i \(0.202631\pi\)
−0.804130 + 0.594453i \(0.797369\pi\)
\(678\) −2.25425e17 6.11389e17i −0.0891269 0.241727i
\(679\) −3.54168e18 −1.38693
\(680\) −1.71760e17 9.63156e16i −0.0666216 0.0373584i
\(681\) −3.65362e17 −0.140368
\(682\) −1.29452e17 3.51096e17i −0.0492619 0.133606i
\(683\) 1.79679e18i 0.677270i −0.940918 0.338635i \(-0.890035\pi\)
0.940918 0.338635i \(-0.109965\pi\)
\(684\) −7.95302e17 9.31877e17i −0.296939 0.347932i
\(685\) 5.38697e16i 0.0199231i
\(686\) 2.50723e18 9.24439e17i 0.918517 0.338666i
\(687\) 2.14156e18 0.777163
\(688\) −1.44130e18 2.29372e17i −0.518119 0.0824546i
\(689\) 4.30074e18 1.53151
\(690\) −2.14700e17 + 7.91618e16i −0.0757377 + 0.0279252i
\(691\) 8.70716e17i 0.304277i −0.988359 0.152139i \(-0.951384\pi\)
0.988359 0.152139i \(-0.0486160\pi\)
\(692\) −3.03417e18 3.55521e18i −1.05039 1.23077i
\(693\) 1.83348e17i 0.0628798i
\(694\) 1.61220e18 + 4.37254e18i 0.547750 + 1.48559i
\(695\) 2.73846e17 0.0921734
\(696\) 1.45616e18 2.59678e18i 0.485566 0.865915i
\(697\) 4.35179e18 1.43765
\(698\) −1.22626e18 3.32582e18i −0.401349 1.08852i
\(699\) 2.87681e18i 0.932844i
\(700\) −2.40341e18 + 2.05117e18i −0.772131 + 0.658969i
\(701\) 3.25269e18i 1.03532i −0.855586 0.517661i \(-0.826803\pi\)
0.855586 0.517661i \(-0.173197\pi\)
\(702\) −3.57757e18 + 1.31909e18i −1.12823 + 0.415989i
\(703\) 3.08666e18 0.964450
\(704\) 6.60936e17 4.04015e17i 0.204615 0.125076i
\(705\) 3.88376e17 0.119131
\(706\) 1.56849e17 5.78316e16i 0.0476706 0.0175766i
\(707\) 5.61406e18i 1.69064i
\(708\) 2.16518e18 1.84786e18i 0.646068 0.551381i
\(709\) 6.65027e17i 0.196625i −0.995156 0.0983125i \(-0.968656\pi\)
0.995156 0.0983125i \(-0.0313445\pi\)
\(710\) 2.17019e16 + 5.88590e16i 0.00635797 + 0.0172438i
\(711\) −6.50314e17 −0.188786
\(712\) −1.48867e18 + 2.65476e18i −0.428231 + 0.763668i
\(713\) −2.19786e18 −0.626494
\(714\) 1.56759e18 + 4.25155e18i 0.442785 + 1.20091i
\(715\) 8.44004e16i 0.0236241i
\(716\) 2.00679e17 + 2.35141e17i 0.0556632 + 0.0652220i
\(717\) 3.37618e18i 0.928006i
\(718\) 5.57499e18 2.05555e18i 1.51857 0.559911i
\(719\) 3.90552e18 1.05424 0.527122 0.849790i \(-0.323271\pi\)
0.527122 + 0.849790i \(0.323271\pi\)
\(720\) 6.47662e16 + 1.03070e16i 0.0173256 + 0.00275723i
\(721\) −3.96842e16 −0.0105205
\(722\) −7.73292e18 + 2.85120e18i −2.03166 + 0.749094i
\(723\) 5.63989e18i 1.46849i
\(724\) −7.80237e17 9.14224e17i −0.201338 0.235913i
\(725\) 3.44613e18i 0.881323i
\(726\) −1.44230e18 3.91174e18i −0.365566 0.991475i
\(727\) −5.10127e18 −1.28146 −0.640730 0.767766i \(-0.721368\pi\)
−0.640730 + 0.767766i \(0.721368\pi\)
\(728\) 5.15796e18 + 2.89235e18i 1.28417 + 0.720108i
\(729\) −2.54377e18 −0.627696
\(730\) 1.11037e17 + 3.01150e17i 0.0271562 + 0.0736519i
\(731\) 2.42265e18i 0.587257i
\(732\) 2.39482e18 2.04384e18i 0.575374 0.491048i
\(733\) 3.11289e18i 0.741289i 0.928775 + 0.370645i \(0.120863\pi\)
−0.928775 + 0.370645i \(0.879137\pi\)
\(734\) 5.73449e17 2.11436e17i 0.135354 0.0499062i
\(735\) −1.31099e16 −0.00306712
\(736\) −8.83501e17 4.46321e18i −0.204881 1.03500i
\(737\) −9.61257e17 −0.220953
\(738\) −1.35979e18 + 5.01369e17i −0.309818 + 0.114233i
\(739\) 7.69864e18i 1.73870i −0.494195 0.869351i \(-0.664537\pi\)
0.494195 0.869351i \(-0.335463\pi\)
\(740\) −1.25683e17 + 1.07263e17i −0.0281365 + 0.0240128i
\(741\) 1.29770e19i 2.87976i
\(742\) −1.70147e18 4.61466e18i −0.374282 1.01511i
\(743\) 6.25892e18 1.36481 0.682405 0.730974i \(-0.260934\pi\)
0.682405 + 0.730974i \(0.260934\pi\)
\(744\) 2.68638e18 + 1.50640e18i 0.580688 + 0.325624i
\(745\) −1.59859e17 −0.0342548
\(746\) −1.98970e18 5.39640e18i −0.422655 1.14631i
\(747\) 3.19701e17i 0.0673225i
\(748\) 8.34759e17 + 9.78109e17i 0.174261 + 0.204186i
\(749\) 1.59794e18i 0.330696i
\(750\) −6.98136e17 + 2.57410e17i −0.143233 + 0.0528113i
\(751\) −2.41477e18 −0.491153 −0.245577 0.969377i \(-0.578977\pi\)
−0.245577 + 0.969377i \(0.578977\pi\)
\(752\) −1.21364e18 + 7.62615e18i −0.244723 + 1.53776i
\(753\) −9.61420e18 −1.92197
\(754\) 6.05141e18 2.23121e18i 1.19934 0.442209i
\(755\) 6.20871e17i 0.121996i
\(756\) 2.83074e18 + 3.31685e18i 0.551452 + 0.646151i
\(757\) 3.19891e18i 0.617844i −0.951087 0.308922i \(-0.900032\pi\)
0.951087 0.308922i \(-0.0999682\pi\)
\(758\) 5.53462e17 + 1.50108e18i 0.105983 + 0.287444i
\(759\) 1.49424e18 0.283693
\(760\) 3.15443e17 5.62532e17i 0.0593789 0.105891i
\(761\) −5.76395e18 −1.07577 −0.537886 0.843018i \(-0.680777\pi\)
−0.537886 + 0.843018i \(0.680777\pi\)
\(762\) 1.17138e18 + 3.17698e18i 0.216766 + 0.587905i
\(763\) 9.68770e18i 1.77751i
\(764\) −3.22426e18 + 2.75172e18i −0.586574 + 0.500607i
\(765\) 1.08864e17i 0.0196375i
\(766\) −9.64923e18 + 3.55776e18i −1.72586 + 0.636341i
\(767\) 6.16653e18 1.09363
\(768\) −1.97918e18 + 6.06080e18i −0.348047 + 1.06582i
\(769\) −2.49093e18 −0.434351