Properties

Label 6.19.b.a.5.1
Level 6
Weight 19
Character 6.5
Analytic conductor 12.323
Analytic rank 0
Dimension 6
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 19 \)
Character orbit: \([\chi]\) = 6.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(12.3231682626\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{31}\cdot 3^{14} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.1
Root \(27.6459 - 55.6125i\)
Character \(\chi\) = 6.5
Dual form 6.19.b.a.5.4

$q$-expansion

\(f(q)\) \(=\) \(q-362.039i q^{2} +(-19019.3 - 5068.08i) q^{3} -131072. q^{4} -2.98937e6i q^{5} +(-1.83484e6 + 6.88573e6i) q^{6} -4.92752e7 q^{7} +4.74531e7i q^{8} +(3.36050e8 + 1.92783e8i) q^{9} +O(q^{10})\) \(q-362.039i q^{2} +(-19019.3 - 5068.08i) q^{3} -131072. q^{4} -2.98937e6i q^{5} +(-1.83484e6 + 6.88573e6i) q^{6} -4.92752e7 q^{7} +4.74531e7i q^{8} +(3.36050e8 + 1.92783e8i) q^{9} -1.08227e9 q^{10} +5.85405e8i q^{11} +(2.49290e9 + 6.64284e8i) q^{12} +1.21786e10 q^{13} +1.78395e10i q^{14} +(-1.51504e10 + 5.68558e10i) q^{15} +1.71799e10 q^{16} +1.49631e11i q^{17} +(6.97949e10 - 1.21663e11i) q^{18} -3.13905e11 q^{19} +3.91823e11i q^{20} +(9.37182e11 + 2.49731e11i) q^{21} +2.11939e11 q^{22} -2.41974e12i q^{23} +(2.40496e11 - 9.02527e11i) q^{24} -5.12163e12 q^{25} -4.40912e12i q^{26} +(-5.41440e12 - 5.36973e12i) q^{27} +6.45860e12 q^{28} +1.39605e13i q^{29} +(2.05840e13 + 5.48502e12i) q^{30} -2.16303e13 q^{31} -6.21978e12i q^{32} +(2.96688e12 - 1.11340e13i) q^{33} +5.41723e13 q^{34} +1.47302e14i q^{35} +(-4.40467e13 - 2.52685e13i) q^{36} +2.89041e13 q^{37} +1.13646e14i q^{38} +(-2.31628e14 - 6.17220e13i) q^{39} +1.41855e14 q^{40} -2.60395e14i q^{41} +(9.04123e13 - 3.39296e14i) q^{42} -9.12102e13 q^{43} -7.67302e13i q^{44} +(5.76300e14 - 1.00458e15i) q^{45} -8.76040e14 q^{46} +1.34983e15i q^{47} +(-3.26750e14 - 8.70690e13i) q^{48} +7.99636e14 q^{49} +1.85423e15i q^{50} +(7.58344e14 - 2.84589e15i) q^{51} -1.59627e15 q^{52} +4.92446e15i q^{53} +(-1.94405e15 + 1.96022e15i) q^{54} +1.74999e15 q^{55} -2.33826e15i q^{56} +(5.97026e15 + 1.59090e15i) q^{57} +5.05424e15 q^{58} +1.63011e15i q^{59} +(1.98579e15 - 7.45220e15i) q^{60} -1.27764e16 q^{61} +7.83100e15i q^{62} +(-1.65589e16 - 9.49943e15i) q^{63} -2.25180e15 q^{64} -3.64063e16i q^{65} +(-4.03094e15 - 1.07413e15i) q^{66} +1.62992e16 q^{67} -1.96125e16i q^{68} +(-1.22635e16 + 4.60219e16i) q^{69} +5.33290e16 q^{70} +3.19301e16i q^{71} +(-9.14816e15 + 1.59466e16i) q^{72} -6.00948e16 q^{73} -1.04644e16i q^{74} +(9.74100e16 + 2.59568e16i) q^{75} +4.11442e16 q^{76} -2.88460e16i q^{77} +(-2.23458e16 + 8.38585e16i) q^{78} -1.80165e17 q^{79} -5.13570e16i q^{80} +(7.57640e16 + 1.29569e17i) q^{81} -9.42729e16 q^{82} -8.49190e16i q^{83} +(-1.22838e17 - 3.27327e16i) q^{84} +4.47303e17 q^{85} +3.30216e16i q^{86} +(7.07530e16 - 2.65519e17i) q^{87} -2.77793e16 q^{88} -5.84125e17i q^{89} +(-3.63695e17 - 2.08643e17i) q^{90} -6.00102e17 q^{91} +3.17160e17i q^{92} +(4.11393e17 + 1.09624e17i) q^{93} +4.88692e17 q^{94} +9.38378e17i q^{95} +(-3.15223e16 + 1.18296e17i) q^{96} -1.70517e17 q^{97} -2.89499e17i q^{98} +(-1.12856e17 + 1.96725e17i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 6258q^{3} - 786432q^{4} - 15753216q^{6} + 28233804q^{7} + 695971638q^{9} + O(q^{10}) \) \( 6q - 6258q^{3} - 786432q^{4} - 15753216q^{6} + 28233804q^{7} + 695971638q^{9} - 434257920q^{10} + 820248576q^{12} + 29566196220q^{13} + 119627095680q^{15} + 103079215104q^{16} + 315939373056q^{18} - 438814047012q^{19} + 2876527406172q^{21} - 2844452929536q^{22} + 2064805527552q^{24} - 25696048717290q^{25} + 11197265522814q^{27} - 3700661157888q^{28} + 13072787619840q^{30} + 21775814927148q^{31} - 962560003968q^{33} + 99067611119616q^{34} - 91222394535936q^{36} + 638446564817436q^{37} - 736541155104180q^{39} + 56919054090240q^{40} - 203954622480384q^{42} - 1688313718883652q^{43} + 390590504075520q^{45} + 1979247919104q^{46} - 107511621353472q^{48} - 895767896448270q^{49} + 9636273526722048q^{51} - 3875300470947840q^{52} + 2993011804200960q^{54} - 1259959207783680q^{55} + 4023767318253996q^{57} + 21251172660756480q^{58} - 15679762684968960q^{60} - 16279597277700036q^{61} - 32525159214131028q^{63} - 13510798882111488q^{64} - 60047751762690048q^{66} + 11153724314613276q^{67} + 3612037794746112q^{69} + 161904998736691200q^{70} - 41410805505196032q^{72} - 78910243347781140q^{73} + 348225828845090910q^{75} + 57516234769956864q^{76} - 168903906208235520q^{78} - 476518976428926228q^{79} + 630680446106425062q^{81} + 396536393269149696q^{82} - 377032200181776384q^{84} - 967978669078932480q^{85} + 419256510981966720q^{87} + 372828134380142592q^{88} - 2046848246643179520q^{90} - 1032060167365562760q^{91} + 764294136047005116q^{93} + 2566175766871080960q^{94} - 270638190107295744q^{96} + 834695417243310348q^{97} + 761688154713814272q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 362.039i 0.707107i
\(3\) −19019.3 5068.08i −0.966282 0.257485i
\(4\) −131072. −0.500000
\(5\) 2.98937e6i 1.53056i −0.643699 0.765278i \(-0.722601\pi\)
0.643699 0.765278i \(-0.277399\pi\)
\(6\) −1.83484e6 + 6.88573e6i −0.182070 + 0.683265i
\(7\) −4.92752e7 −1.22109 −0.610543 0.791983i \(-0.709049\pi\)
−0.610543 + 0.791983i \(0.709049\pi\)
\(8\) 4.74531e7i 0.353553i
\(9\) 3.36050e8 + 1.92783e8i 0.867403 + 0.497607i
\(10\) −1.08227e9 −1.08227
\(11\) 5.85405e8i 0.248269i 0.992265 + 0.124134i \(0.0396154\pi\)
−0.992265 + 0.124134i \(0.960385\pi\)
\(12\) 2.49290e9 + 6.64284e8i 0.483141 + 0.128743i
\(13\) 1.21786e10 1.14844 0.574218 0.818703i \(-0.305306\pi\)
0.574218 + 0.818703i \(0.305306\pi\)
\(14\) 1.78395e10i 0.863439i
\(15\) −1.51504e10 + 5.68558e10i −0.394096 + 1.47895i
\(16\) 1.71799e10 0.250000
\(17\) 1.49631e11i 1.26178i 0.775874 + 0.630888i \(0.217309\pi\)
−0.775874 + 0.630888i \(0.782691\pi\)
\(18\) 6.97949e10 1.21663e11i 0.351861 0.613346i
\(19\) −3.13905e11 −0.972783 −0.486391 0.873741i \(-0.661687\pi\)
−0.486391 + 0.873741i \(0.661687\pi\)
\(20\) 3.91823e11i 0.765278i
\(21\) 9.37182e11 + 2.49731e11i 1.17991 + 0.314412i
\(22\) 2.11939e11 0.175553
\(23\) 2.41974e12i 1.34344i −0.740805 0.671721i \(-0.765556\pi\)
0.740805 0.671721i \(-0.234444\pi\)
\(24\) 2.40496e11 9.02527e11i 0.0910348 0.341632i
\(25\) −5.12163e12 −1.34260
\(26\) 4.40912e12i 0.812066i
\(27\) −5.41440e12 5.36973e12i −0.710029 0.704172i
\(28\) 6.45860e12 0.610543
\(29\) 1.39605e13i 0.962319i 0.876633 + 0.481159i \(0.159784\pi\)
−0.876633 + 0.481159i \(0.840216\pi\)
\(30\) 2.05840e13 + 5.48502e12i 1.04578 + 0.278668i
\(31\) −2.16303e13 −0.818101 −0.409050 0.912512i \(-0.634140\pi\)
−0.409050 + 0.912512i \(0.634140\pi\)
\(32\) 6.21978e12i 0.176777i
\(33\) 2.96688e12 1.11340e13i 0.0639256 0.239898i
\(34\) 5.41723e13 0.892210
\(35\) 1.47302e14i 1.86894i
\(36\) −4.40467e13 2.52685e13i −0.433701 0.248803i
\(37\) 2.89041e13 0.222404 0.111202 0.993798i \(-0.464530\pi\)
0.111202 + 0.993798i \(0.464530\pi\)
\(38\) 1.13646e14i 0.687861i
\(39\) −2.31628e14 6.17220e13i −1.10971 0.295705i
\(40\) 1.41855e14 0.541134
\(41\) 2.60395e14i 0.795384i −0.917519 0.397692i \(-0.869811\pi\)
0.917519 0.397692i \(-0.130189\pi\)
\(42\) 9.04123e13 3.39296e14i 0.222323 0.834325i
\(43\) −9.12102e13 −0.181479 −0.0907397 0.995875i \(-0.528923\pi\)
−0.0907397 + 0.995875i \(0.528923\pi\)
\(44\) 7.67302e13i 0.124134i
\(45\) 5.76300e14 1.00458e15i 0.761616 1.32761i
\(46\) −8.76040e14 −0.949956
\(47\) 1.34983e15i 1.20615i 0.797686 + 0.603073i \(0.206057\pi\)
−0.797686 + 0.603073i \(0.793943\pi\)
\(48\) −3.26750e14 8.70690e13i −0.241571 0.0643713i
\(49\) 7.99636e14 0.491052
\(50\) 1.85423e15i 0.949365i
\(51\) 7.58344e14 2.84589e15i 0.324889 1.21923i
\(52\) −1.59627e15 −0.574218
\(53\) 4.92446e15i 1.49237i 0.665740 + 0.746183i \(0.268116\pi\)
−0.665740 + 0.746183i \(0.731884\pi\)
\(54\) −1.94405e15 + 1.96022e15i −0.497925 + 0.502067i
\(55\) 1.74999e15 0.379989
\(56\) 2.33826e15i 0.431719i
\(57\) 5.97026e15 + 1.59090e15i 0.939983 + 0.250477i
\(58\) 5.05424e15 0.680462
\(59\) 1.63011e15i 0.188170i 0.995564 + 0.0940848i \(0.0299925\pi\)
−0.995564 + 0.0940848i \(0.970008\pi\)
\(60\) 1.98579e15 7.45220e15i 0.197048 0.739475i
\(61\) −1.27764e16 −1.09255 −0.546275 0.837606i \(-0.683955\pi\)
−0.546275 + 0.837606i \(0.683955\pi\)
\(62\) 7.83100e15i 0.578485i
\(63\) −1.65589e16 9.49943e15i −1.05917 0.607621i
\(64\) −2.25180e15 −0.125000
\(65\) 3.64063e16i 1.75775i
\(66\) −4.03094e15 1.07413e15i −0.169633 0.0452022i
\(67\) 1.62992e16 0.599091 0.299545 0.954082i \(-0.403165\pi\)
0.299545 + 0.954082i \(0.403165\pi\)
\(68\) 1.96125e16i 0.630888i
\(69\) −1.22635e16 + 4.60219e16i −0.345916 + 1.29814i
\(70\) 5.33290e16 1.32154
\(71\) 3.19301e16i 0.696425i 0.937416 + 0.348213i \(0.113211\pi\)
−0.937416 + 0.348213i \(0.886789\pi\)
\(72\) −9.14816e15 + 1.59466e16i −0.175931 + 0.306673i
\(73\) −6.00948e16 −1.02078 −0.510389 0.859944i \(-0.670499\pi\)
−0.510389 + 0.859944i \(0.670499\pi\)
\(74\) 1.04644e16i 0.157264i
\(75\) 9.74100e16 + 2.59568e16i 1.29733 + 0.345701i
\(76\) 4.11442e16 0.486391
\(77\) 2.88460e16i 0.303158i
\(78\) −2.23458e16 + 8.38585e16i −0.209095 + 0.784685i
\(79\) −1.80165e17 −1.50323 −0.751616 0.659600i \(-0.770726\pi\)
−0.751616 + 0.659600i \(0.770726\pi\)
\(80\) 5.13570e16i 0.382639i
\(81\) 7.57640e16 + 1.29569e17i 0.504775 + 0.863251i
\(82\) −9.42729e16 −0.562422
\(83\) 8.49190e16i 0.454257i −0.973865 0.227129i \(-0.927066\pi\)
0.973865 0.227129i \(-0.0729338\pi\)
\(84\) −1.22838e17 3.27327e16i −0.589957 0.157206i
\(85\) 4.47303e17 1.93122
\(86\) 3.30216e16i 0.128325i
\(87\) 7.07530e16 2.65519e17i 0.247783 0.929872i
\(88\) −2.77793e16 −0.0877763
\(89\) 5.84125e17i 1.66723i −0.552345 0.833616i \(-0.686267\pi\)
0.552345 0.833616i \(-0.313733\pi\)
\(90\) −3.63695e17 2.08643e17i −0.938761 0.538544i
\(91\) −6.00102e17 −1.40234
\(92\) 3.17160e17i 0.671721i
\(93\) 4.11393e17 + 1.09624e17i 0.790516 + 0.210649i
\(94\) 4.88692e17 0.852874
\(95\) 9.38378e17i 1.48890i
\(96\) −3.15223e16 + 1.18296e17i −0.0455174 + 0.170816i
\(97\) −1.70517e17 −0.224296 −0.112148 0.993692i \(-0.535773\pi\)
−0.112148 + 0.993692i \(0.535773\pi\)
\(98\) 2.89499e17i 0.347226i
\(99\) −1.12856e17 + 1.96725e17i −0.123540 + 0.215349i
\(100\) 6.71302e17 0.671302
\(101\) 1.55698e18i 1.42361i 0.702375 + 0.711807i \(0.252123\pi\)
−0.702375 + 0.711807i \(0.747877\pi\)
\(102\) −1.03032e18 2.74550e17i −0.862127 0.229731i
\(103\) −3.33880e17 −0.255891 −0.127945 0.991781i \(-0.540838\pi\)
−0.127945 + 0.991781i \(0.540838\pi\)
\(104\) 5.77912e17i 0.406033i
\(105\) 7.46538e17 2.80158e18i 0.481225 1.80593i
\(106\) 1.78284e18 1.05526
\(107\) 8.24602e17i 0.448529i 0.974528 + 0.224265i \(0.0719980\pi\)
−0.974528 + 0.224265i \(0.928002\pi\)
\(108\) 7.09676e17 + 7.03822e17i 0.355015 + 0.352086i
\(109\) −1.02433e18 −0.471630 −0.235815 0.971798i \(-0.575776\pi\)
−0.235815 + 0.971798i \(0.575776\pi\)
\(110\) 6.33564e17i 0.268693i
\(111\) −5.49736e17 1.46488e17i −0.214905 0.0572659i
\(112\) −8.46542e17 −0.305272
\(113\) 7.20059e17i 0.239697i −0.992792 0.119848i \(-0.961759\pi\)
0.992792 0.119848i \(-0.0382409\pi\)
\(114\) 5.75966e17 2.16147e18i 0.177114 0.664668i
\(115\) −7.23350e18 −2.05621
\(116\) 1.82983e18i 0.481159i
\(117\) 4.09261e18 + 2.34782e18i 0.996156 + 0.571469i
\(118\) 5.90164e17 0.133056
\(119\) 7.37312e18i 1.54074i
\(120\) −2.69799e18 7.18932e17i −0.522888 0.139334i
\(121\) 5.21722e18 0.938363
\(122\) 4.62557e18i 0.772550i
\(123\) −1.31970e18 + 4.95253e18i −0.204800 + 0.768566i
\(124\) 2.83512e18 0.409050
\(125\) 3.90690e18i 0.524375i
\(126\) −3.43916e18 + 5.99497e18i −0.429653 + 0.748949i
\(127\) 1.18563e19 1.37948 0.689741 0.724056i \(-0.257724\pi\)
0.689741 + 0.724056i \(0.257724\pi\)
\(128\) 8.15239e17i 0.0883883i
\(129\) 1.73476e18 + 4.62261e17i 0.175360 + 0.0467283i
\(130\) −1.31805e19 −1.24291
\(131\) 8.83199e17i 0.0777350i 0.999244 + 0.0388675i \(0.0123750\pi\)
−0.999244 + 0.0388675i \(0.987625\pi\)
\(132\) −3.88875e17 + 1.45936e18i −0.0319628 + 0.119949i
\(133\) 1.54677e19 1.18785
\(134\) 5.90094e18i 0.423621i
\(135\) −1.60521e19 + 1.61856e19i −1.07778 + 1.08674i
\(136\) −7.10047e18 −0.446105
\(137\) 1.83132e19i 1.07716i −0.842575 0.538579i \(-0.818961\pi\)
0.842575 0.538579i \(-0.181039\pi\)
\(138\) 1.66617e19 + 4.43984e18i 0.917926 + 0.244600i
\(139\) −3.64973e19 −1.88420 −0.942102 0.335327i \(-0.891153\pi\)
−0.942102 + 0.335327i \(0.891153\pi\)
\(140\) 1.93072e19i 0.934471i
\(141\) 6.84107e18 2.56729e19i 0.310565 1.16548i
\(142\) 1.15599e19 0.492447
\(143\) 7.12940e18i 0.285121i
\(144\) 5.77329e18 + 3.31199e18i 0.216851 + 0.124402i
\(145\) 4.17331e19 1.47288
\(146\) 2.17567e19i 0.721799i
\(147\) −1.52085e19 4.05262e18i −0.474495 0.126439i
\(148\) −3.78851e18 −0.111202
\(149\) 2.58816e19i 0.715015i −0.933910 0.357507i \(-0.883627\pi\)
0.933910 0.357507i \(-0.116373\pi\)
\(150\) 9.39738e18 3.52662e19i 0.244447 0.917354i
\(151\) −4.24973e19 −1.04128 −0.520642 0.853775i \(-0.674307\pi\)
−0.520642 + 0.853775i \(0.674307\pi\)
\(152\) 1.48958e19i 0.343931i
\(153\) −2.88464e19 + 5.02835e19i −0.627868 + 1.09447i
\(154\) −1.04434e19 −0.214365
\(155\) 6.46609e19i 1.25215i
\(156\) 3.03600e19 + 8.09003e18i 0.554856 + 0.147853i
\(157\) 6.25624e18 0.107949 0.0539743 0.998542i \(-0.482811\pi\)
0.0539743 + 0.998542i \(0.482811\pi\)
\(158\) 6.52266e19i 1.06295i
\(159\) 2.49576e19 9.36599e19i 0.384262 1.44205i
\(160\) −1.85932e19 −0.270567
\(161\) 1.19233e20i 1.64046i
\(162\) 4.69091e19 2.74295e19i 0.610411 0.356930i
\(163\) 6.37578e19 0.784955 0.392478 0.919762i \(-0.371618\pi\)
0.392478 + 0.919762i \(0.371618\pi\)
\(164\) 3.41304e19i 0.397692i
\(165\) −3.32837e19 8.86910e18i −0.367177 0.0978417i
\(166\) −3.07439e19 −0.321208
\(167\) 7.24036e18i 0.0716658i −0.999358 0.0358329i \(-0.988592\pi\)
0.999358 0.0358329i \(-0.0114084\pi\)
\(168\) −1.18505e19 + 4.44722e19i −0.111161 + 0.417163i
\(169\) 3.58624e19 0.318903
\(170\) 1.61941e20i 1.36558i
\(171\) −1.05488e20 6.05156e19i −0.843794 0.484063i
\(172\) 1.19551e19 0.0907397
\(173\) 1.82274e20i 1.31314i −0.754267 0.656568i \(-0.772008\pi\)
0.754267 0.656568i \(-0.227992\pi\)
\(174\) −9.61283e19 2.56153e19i −0.657518 0.175209i
\(175\) 2.52370e20 1.63944
\(176\) 1.00572e19i 0.0620672i
\(177\) 8.26154e18 3.10036e19i 0.0484509 0.181825i
\(178\) −2.11476e20 −1.17891
\(179\) 1.02672e19i 0.0544221i 0.999630 + 0.0272111i \(0.00866262\pi\)
−0.999630 + 0.0272111i \(0.991337\pi\)
\(180\) −7.55368e19 + 1.31672e20i −0.380808 + 0.663805i
\(181\) −2.72470e20 −1.30681 −0.653403 0.757010i \(-0.726659\pi\)
−0.653403 + 0.757010i \(0.726659\pi\)
\(182\) 2.17260e20i 0.991603i
\(183\) 2.42999e20 + 6.47521e19i 1.05571 + 0.281316i
\(184\) 1.14824e20 0.474978
\(185\) 8.64049e19i 0.340403i
\(186\) 3.96881e19 1.48940e20i 0.148951 0.558979i
\(187\) −8.75949e19 −0.313259
\(188\) 1.76925e20i 0.603073i
\(189\) 2.66796e20 + 2.64595e20i 0.867007 + 0.859855i
\(190\) 3.39729e20 1.05281
\(191\) 1.79319e20i 0.530062i −0.964240 0.265031i \(-0.914618\pi\)
0.964240 0.265031i \(-0.0853822\pi\)
\(192\) 4.28277e19 + 1.14123e19i 0.120785 + 0.0321857i
\(193\) −3.54201e20 −0.953309 −0.476654 0.879091i \(-0.658151\pi\)
−0.476654 + 0.879091i \(0.658151\pi\)
\(194\) 6.17336e19i 0.158601i
\(195\) −1.84510e20 + 6.92423e20i −0.452593 + 1.69848i
\(196\) −1.04810e20 −0.245526
\(197\) 4.40628e20i 0.985997i 0.870030 + 0.492999i \(0.164099\pi\)
−0.870030 + 0.492999i \(0.835901\pi\)
\(198\) 7.12221e19 + 4.08583e19i 0.152275 + 0.0873561i
\(199\) 2.86891e20 0.586191 0.293096 0.956083i \(-0.405315\pi\)
0.293096 + 0.956083i \(0.405315\pi\)
\(200\) 2.43037e20i 0.474682i
\(201\) −3.10000e20 8.26056e19i −0.578891 0.154257i
\(202\) 5.63689e20 1.00665
\(203\) 6.87907e20i 1.17507i
\(204\) −9.93976e19 + 3.73016e20i −0.162444 + 0.609616i
\(205\) −7.78415e20 −1.21738
\(206\) 1.20877e20i 0.180942i
\(207\) 4.66485e20 8.13153e20i 0.668505 1.16530i
\(208\) 2.09226e20 0.287109
\(209\) 1.83761e20i 0.241512i
\(210\) −1.01428e21 2.70276e20i −1.27698 0.340278i
\(211\) −7.22932e20 −0.872078 −0.436039 0.899928i \(-0.643619\pi\)
−0.436039 + 0.899928i \(0.643619\pi\)
\(212\) 6.45458e20i 0.746183i
\(213\) 1.61824e20 6.07288e20i 0.179319 0.672943i
\(214\) 2.98538e20 0.317158
\(215\) 2.72661e20i 0.277764i
\(216\) 2.54811e20 2.56930e20i 0.248962 0.251033i
\(217\) 1.06584e21 0.998972
\(218\) 3.70847e20i 0.333493i
\(219\) 1.14296e21 + 3.04566e20i 0.986360 + 0.262835i
\(220\) −2.29375e20 −0.189995
\(221\) 1.82230e21i 1.44907i
\(222\) −5.30344e19 + 1.99026e20i −0.0404931 + 0.151961i
\(223\) 8.51613e20 0.624451 0.312226 0.950008i \(-0.398926\pi\)
0.312226 + 0.950008i \(0.398926\pi\)
\(224\) 3.06481e20i 0.215860i
\(225\) −1.72112e21 9.87363e20i −1.16458 0.668089i
\(226\) −2.60689e20 −0.169491
\(227\) 3.23696e20i 0.202257i 0.994873 + 0.101129i \(0.0322454\pi\)
−0.994873 + 0.101129i \(0.967755\pi\)
\(228\) −7.82534e20 2.08522e20i −0.469991 0.125239i
\(229\) −1.50827e21 −0.870880 −0.435440 0.900218i \(-0.643407\pi\)
−0.435440 + 0.900218i \(0.643407\pi\)
\(230\) 2.61881e21i 1.45396i
\(231\) −1.46194e20 + 5.48631e20i −0.0780586 + 0.292936i
\(232\) −6.62469e20 −0.340231
\(233\) 5.01578e20i 0.247820i −0.992293 0.123910i \(-0.960457\pi\)
0.992293 0.123910i \(-0.0395433\pi\)
\(234\) 8.50003e20 1.48168e21i 0.404090 0.704388i
\(235\) 4.03515e21 1.84607
\(236\) 2.13662e20i 0.0940848i
\(237\) 3.42662e21 + 9.13090e20i 1.45255 + 0.387060i
\(238\) −2.66935e21 −1.08947
\(239\) 1.43956e21i 0.565781i 0.959152 + 0.282891i \(0.0912933\pi\)
−0.959152 + 0.282891i \(0.908707\pi\)
\(240\) −2.60281e20 + 9.76775e20i −0.0985240 + 0.369737i
\(241\) −2.26560e21 −0.826094 −0.413047 0.910710i \(-0.635535\pi\)
−0.413047 + 0.910710i \(0.635535\pi\)
\(242\) 1.88883e21i 0.663523i
\(243\) −7.84313e20 2.84830e21i −0.265481 0.964116i
\(244\) 1.67463e21 0.546275
\(245\) 2.39041e21i 0.751583i
\(246\) 1.79301e21 + 4.77783e20i 0.543458 + 0.144815i
\(247\) −3.82292e21 −1.11718
\(248\) 1.02642e21i 0.289242i
\(249\) −4.30376e20 + 1.61510e21i −0.116965 + 0.438941i
\(250\) 1.41445e21 0.370789
\(251\) 3.32950e21i 0.842006i −0.907059 0.421003i \(-0.861678\pi\)
0.907059 0.421003i \(-0.138322\pi\)
\(252\) 2.17041e21 + 1.24511e21i 0.529587 + 0.303811i
\(253\) 1.41653e21 0.333534
\(254\) 4.29244e21i 0.975441i
\(255\) −8.50741e21 2.26697e21i −1.86610 0.497260i
\(256\) 2.95148e20 0.0625000
\(257\) 5.49052e20i 0.112258i 0.998424 + 0.0561288i \(0.0178757\pi\)
−0.998424 + 0.0561288i \(0.982124\pi\)
\(258\) 1.67356e20 6.28049e20i 0.0330419 0.123998i
\(259\) −1.42426e21 −0.271575
\(260\) 4.77184e21i 0.878873i
\(261\) −2.69135e21 + 4.69142e21i −0.478856 + 0.834718i
\(262\) 3.19752e20 0.0549670
\(263\) 7.16927e21i 1.19089i 0.803394 + 0.595447i \(0.203025\pi\)
−0.803394 + 0.595447i \(0.796975\pi\)
\(264\) 5.28344e20 + 1.40788e20i 0.0848167 + 0.0226011i
\(265\) 1.47210e22 2.28415
\(266\) 5.59992e21i 0.839938i
\(267\) −2.96039e21 + 1.11097e22i −0.429288 + 1.61102i
\(268\) −2.13637e21 −0.299545
\(269\) 1.07660e22i 1.45977i −0.683571 0.729884i \(-0.739574\pi\)
0.683571 0.729884i \(-0.260426\pi\)
\(270\) 5.85983e21 + 5.81149e21i 0.768441 + 0.762102i
\(271\) −1.13119e21 −0.143487 −0.0717435 0.997423i \(-0.522856\pi\)
−0.0717435 + 0.997423i \(0.522856\pi\)
\(272\) 2.57065e21i 0.315444i
\(273\) 1.14135e22 + 3.04137e21i 1.35505 + 0.361082i
\(274\) −6.63009e21 −0.761665
\(275\) 2.99823e21i 0.333327i
\(276\) 1.60740e21 6.03218e21i 0.172958 0.649072i
\(277\) −3.46171e21 −0.360556 −0.180278 0.983616i \(-0.557700\pi\)
−0.180278 + 0.983616i \(0.557700\pi\)
\(278\) 1.32134e22i 1.33233i
\(279\) −7.26884e21 4.16995e21i −0.709623 0.407093i
\(280\) −6.98994e21 −0.660771
\(281\) 3.67928e21i 0.336826i −0.985717 0.168413i \(-0.946136\pi\)
0.985717 0.168413i \(-0.0538642\pi\)
\(282\) −9.29460e21 2.47673e21i −0.824117 0.219602i
\(283\) 2.56879e21 0.220623 0.110311 0.993897i \(-0.464815\pi\)
0.110311 + 0.993897i \(0.464815\pi\)
\(284\) 4.18514e21i 0.348213i
\(285\) 4.75578e21 1.78473e22i 0.383370 1.43870i
\(286\) 2.58112e21 0.201611
\(287\) 1.28310e22i 0.971233i
\(288\) 1.19907e21 2.09015e21i 0.0879653 0.153337i
\(289\) −8.32643e21 −0.592077
\(290\) 1.51090e22i 1.04149i
\(291\) 3.24311e21 + 8.64192e20i 0.216733 + 0.0577528i
\(292\) 7.87675e21 0.510389
\(293\) 9.92864e21i 0.623852i 0.950106 + 0.311926i \(0.100974\pi\)
−0.950106 + 0.311926i \(0.899026\pi\)
\(294\) −1.46721e21 + 5.50608e21i −0.0894057 + 0.335519i
\(295\) 4.87301e21 0.288004
\(296\) 1.37159e21i 0.0786319i
\(297\) 3.14347e21 3.16961e21i 0.174824 0.176278i
\(298\) −9.37014e21 −0.505592
\(299\) 2.94690e22i 1.54285i
\(300\) −1.27677e22 3.40221e21i −0.648667 0.172850i
\(301\) 4.49440e21 0.221602
\(302\) 1.53857e22i 0.736298i
\(303\) 7.89093e21 2.96128e22i 0.366559 1.37561i
\(304\) −5.39285e21 −0.243196
\(305\) 3.81935e22i 1.67221i
\(306\) 1.82046e22 + 1.04435e22i 0.773905 + 0.443970i
\(307\) −6.75725e21 −0.278949 −0.139474 0.990226i \(-0.544541\pi\)
−0.139474 + 0.990226i \(0.544541\pi\)
\(308\) 3.78090e21i 0.151579i
\(309\) 6.35017e21 + 1.69213e21i 0.247263 + 0.0658881i
\(310\) 2.34097e22 0.885403
\(311\) 3.33646e22i 1.22587i 0.790135 + 0.612933i \(0.210010\pi\)
−0.790135 + 0.612933i \(0.789990\pi\)
\(312\) 2.92890e21 1.09915e22i 0.104548 0.392343i
\(313\) −1.44873e22 −0.502444 −0.251222 0.967929i \(-0.580832\pi\)
−0.251222 + 0.967929i \(0.580832\pi\)
\(314\) 2.26500e21i 0.0763311i
\(315\) −2.83973e22 + 4.95007e22i −0.929998 + 1.62113i
\(316\) 2.36146e22 0.751616
\(317\) 2.47089e22i 0.764400i 0.924080 + 0.382200i \(0.124833\pi\)
−0.924080 + 0.382200i \(0.875167\pi\)
\(318\) −3.39085e22 9.03560e21i −1.01968 0.271715i
\(319\) −8.17254e21 −0.238914
\(320\) 6.73146e21i 0.191320i
\(321\) 4.17915e21 1.56834e22i 0.115490 0.433406i
\(322\) 4.31671e22 1.15998
\(323\) 4.69700e22i 1.22743i
\(324\) −9.93054e21 1.69829e22i −0.252387 0.431626i
\(325\) −6.23742e22 −1.54189
\(326\) 2.30828e22i 0.555047i
\(327\) 1.94821e22 + 5.19139e21i 0.455728 + 0.121438i
\(328\) 1.23565e22 0.281211
\(329\) 6.65134e22i 1.47281i
\(330\) −3.21096e21 + 1.20500e22i −0.0691845 + 0.259633i
\(331\) 7.51986e22 1.57673 0.788366 0.615206i \(-0.210927\pi\)
0.788366 + 0.615206i \(0.210927\pi\)
\(332\) 1.11305e22i 0.227129i
\(333\) 9.71320e21 + 5.57222e21i 0.192914 + 0.110670i
\(334\) −2.62129e21 −0.0506754
\(335\) 4.87243e22i 0.916943i
\(336\) 1.61007e22 + 4.29035e21i 0.294979 + 0.0786029i
\(337\) −8.71788e22 −1.55504 −0.777521 0.628857i \(-0.783523\pi\)
−0.777521 + 0.628857i \(0.783523\pi\)
\(338\) 1.29836e22i 0.225499i
\(339\) −3.64932e21 + 1.36951e22i −0.0617184 + 0.231615i
\(340\) −5.86289e22 −0.965609
\(341\) 1.26625e22i 0.203109i
\(342\) −2.19090e22 + 3.81906e22i −0.342284 + 0.596653i
\(343\) 4.08382e22 0.621469
\(344\) 4.32821e21i 0.0641626i
\(345\) 1.37576e23 + 3.66600e22i 1.98688 + 0.529445i
\(346\) −6.59902e22 −0.928527
\(347\) 1.05432e23i 1.44547i 0.691126 + 0.722734i \(0.257115\pi\)
−0.691126 + 0.722734i \(0.742885\pi\)
\(348\) −9.27373e21 + 3.48022e22i −0.123891 + 0.464936i
\(349\) −2.03959e22 −0.265530 −0.132765 0.991148i \(-0.542386\pi\)
−0.132765 + 0.991148i \(0.542386\pi\)
\(350\) 9.13675e22i 1.15926i
\(351\) −6.59397e22 6.53957e22i −0.815423 0.808696i
\(352\) 3.64109e21 0.0438881
\(353\) 1.27972e23i 1.50364i −0.659368 0.751821i \(-0.729176\pi\)
0.659368 0.751821i \(-0.270824\pi\)
\(354\) −1.12245e22 2.99100e21i −0.128570 0.0342600i
\(355\) 9.54507e22 1.06592
\(356\) 7.65625e22i 0.833616i
\(357\) −3.73676e22 + 1.40232e23i −0.396717 + 1.48879i
\(358\) 3.71713e21 0.0384822
\(359\) 8.56995e22i 0.865224i 0.901580 + 0.432612i \(0.142408\pi\)
−0.901580 + 0.432612i \(0.857592\pi\)
\(360\) 4.76703e22 + 2.73472e22i 0.469381 + 0.269272i
\(361\) −5.59102e21 −0.0536941
\(362\) 9.86446e22i 0.924052i
\(363\) −9.92280e22 2.64413e22i −0.906723 0.241615i
\(364\) 7.86566e22 0.701169
\(365\) 1.79646e23i 1.56236i
\(366\) 2.34428e22 8.79752e22i 0.198920 0.746501i
\(367\) 2.32847e23 1.92786 0.963930 0.266156i \(-0.0857537\pi\)
0.963930 + 0.266156i \(0.0857537\pi\)
\(368\) 4.15709e22i 0.335860i
\(369\) 5.01997e22 8.75055e22i 0.395789 0.689919i
\(370\) −3.12819e22 −0.240701
\(371\) 2.42654e23i 1.82231i
\(372\) −5.39222e22 1.43686e22i −0.395258 0.105324i
\(373\) −1.73285e23 −1.23989 −0.619944 0.784646i \(-0.712845\pi\)
−0.619944 + 0.784646i \(0.712845\pi\)
\(374\) 3.17127e22i 0.221508i
\(375\) 1.98005e22 7.43066e22i 0.135019 0.506695i
\(376\) −6.40539e22 −0.426437
\(377\) 1.70019e23i 1.10516i
\(378\) 9.57936e22 9.65904e22i 0.608009 0.613067i
\(379\) −1.45667e23 −0.902837 −0.451419 0.892312i \(-0.649082\pi\)
−0.451419 + 0.892312i \(0.649082\pi\)
\(380\) 1.22995e23i 0.744450i
\(381\) −2.25499e23 6.00888e22i −1.33297 0.355196i
\(382\) −6.49205e22 −0.374811
\(383\) 2.92179e22i 0.164763i −0.996601 0.0823816i \(-0.973747\pi\)
0.996601 0.0823816i \(-0.0262526\pi\)
\(384\) 4.13170e21 1.55053e22i 0.0227587 0.0854081i
\(385\) −8.62312e22 −0.464000
\(386\) 1.28234e23i 0.674091i
\(387\) −3.06511e22 1.75838e22i −0.157416 0.0903054i
\(388\) 2.23499e22 0.112148
\(389\) 3.53662e23i 1.73397i −0.498333 0.866986i \(-0.666054\pi\)
0.498333 0.866986i \(-0.333946\pi\)
\(390\) 2.50684e23 + 6.67997e22i 1.20101 + 0.320032i
\(391\) 3.62069e23 1.69512
\(392\) 3.79452e22i 0.173613i
\(393\) 4.47612e21 1.67978e22i 0.0200156 0.0751140i
\(394\) 1.59524e23 0.697205
\(395\) 5.38579e23i 2.30078i
\(396\) 1.47923e22 2.57851e22i 0.0617701 0.107675i
\(397\) 4.85574e22 0.198217 0.0991086 0.995077i \(-0.468401\pi\)
0.0991086 + 0.995077i \(0.468401\pi\)
\(398\) 1.03866e23i 0.414500i
\(399\) −2.94186e23 7.83918e22i −1.14780 0.305854i
\(400\) −8.79889e22 −0.335651
\(401\) 3.96506e23i 1.47894i 0.673190 + 0.739469i \(0.264923\pi\)
−0.673190 + 0.739469i \(0.735077\pi\)
\(402\) −2.99064e22 + 1.12232e23i −0.109076 + 0.409338i
\(403\) −2.63426e23 −0.939536
\(404\) 2.04077e23i 0.711807i
\(405\) 3.87331e23 2.26487e23i 1.32125 0.772587i
\(406\) −2.49049e23 −0.830903
\(407\) 1.69206e22i 0.0552161i
\(408\) 1.35046e23 + 3.59858e22i 0.431063 + 0.114865i
\(409\) 3.36745e23 1.05146 0.525728 0.850653i \(-0.323793\pi\)
0.525728 + 0.850653i \(0.323793\pi\)
\(410\) 2.81816e23i 0.860818i
\(411\) −9.28128e22 + 3.48305e23i −0.277352 + 1.04084i
\(412\) 4.37623e22 0.127945
\(413\) 8.03242e22i 0.229771i
\(414\) −2.94393e23 1.68886e23i −0.823995 0.472705i
\(415\) −2.53854e23 −0.695266
\(416\) 7.57480e22i 0.203017i
\(417\) 6.94155e23 + 1.84971e23i 1.82067 + 0.485155i
\(418\) −6.65288e22 −0.170774
\(419\) 5.91207e23i 1.48530i −0.669681 0.742648i \(-0.733569\pi\)
0.669681 0.742648i \(-0.266431\pi\)
\(420\) −9.78502e22 + 3.67209e23i −0.240613 + 0.902963i
\(421\) −4.25919e23 −1.02515 −0.512576 0.858642i \(-0.671309\pi\)
−0.512576 + 0.858642i \(0.671309\pi\)
\(422\) 2.61729e23i 0.616652i
\(423\) −2.60225e23 + 4.53611e23i −0.600186 + 1.04621i
\(424\) −2.33681e23 −0.527631
\(425\) 7.66356e23i 1.69406i
\(426\) −2.19862e23 5.85866e22i −0.475843 0.126798i
\(427\) 6.29562e23 1.33410
\(428\) 1.08082e23i 0.224265i
\(429\) 3.61324e22 1.35596e23i 0.0734143 0.275507i
\(430\) 9.87138e22 0.196409
\(431\) 7.33628e23i 1.42949i −0.699386 0.714744i \(-0.746543\pi\)
0.699386 0.714744i \(-0.253457\pi\)
\(432\) −9.30187e22 9.22513e22i −0.177507 0.176043i
\(433\) 1.04893e24 1.96045 0.980223 0.197896i \(-0.0634107\pi\)
0.980223 + 0.197896i \(0.0634107\pi\)
\(434\) 3.85874e23i 0.706380i
\(435\) −7.93735e23 2.11507e23i −1.42322 0.379246i
\(436\) 1.34261e23 0.235815
\(437\) 7.59569e23i 1.30688i
\(438\) 1.10265e23 4.13797e23i 0.185853 0.697462i
\(439\) −3.99418e23 −0.659549 −0.329774 0.944060i \(-0.606973\pi\)
−0.329774 + 0.944060i \(0.606973\pi\)
\(440\) 8.30426e22i 0.134347i
\(441\) 2.68717e23 + 1.54156e23i 0.425940 + 0.244351i
\(442\) 6.59742e23 1.02465
\(443\) 8.28371e22i 0.126064i −0.998012 0.0630320i \(-0.979923\pi\)
0.998012 0.0630320i \(-0.0200770\pi\)
\(444\) 7.20550e22 + 1.92005e22i 0.107453 + 0.0286329i
\(445\) −1.74617e24 −2.55179
\(446\) 3.08317e23i 0.441554i
\(447\) −1.31170e23 + 4.92251e23i −0.184106 + 0.690906i
\(448\) 1.10958e23 0.152636
\(449\) 1.61666e23i 0.217973i −0.994043 0.108986i \(-0.965240\pi\)
0.994043 0.108986i \(-0.0347605\pi\)
\(450\) −3.57464e23 + 6.23112e23i −0.472410 + 0.823481i
\(451\) 1.52436e23 0.197469
\(452\) 9.43796e22i 0.119848i
\(453\) 8.08270e23 + 2.15380e23i 1.00617 + 0.268115i
\(454\) 1.17190e23 0.143018
\(455\) 1.79393e24i 2.14636i
\(456\) −7.54930e22 + 2.83308e23i −0.0885571 + 0.332334i
\(457\) 5.79280e22 0.0666259 0.0333129 0.999445i \(-0.489394\pi\)
0.0333129 + 0.999445i \(0.489394\pi\)
\(458\) 5.46050e23i 0.615805i
\(459\) 8.03480e23 8.10163e23i 0.888507 0.895898i
\(460\) 9.48110e23 1.02811
\(461\) 1.63337e23i 0.173691i −0.996222 0.0868454i \(-0.972321\pi\)
0.996222 0.0868454i \(-0.0276786\pi\)
\(462\) 1.98626e23 + 5.29278e22i 0.207137 + 0.0551958i
\(463\) −1.28649e24 −1.31576 −0.657880 0.753122i \(-0.728547\pi\)
−0.657880 + 0.753122i \(0.728547\pi\)
\(464\) 2.39840e23i 0.240580i
\(465\) 3.27707e23 1.22981e24i 0.322410 1.20993i
\(466\) −1.81591e23 −0.175235
\(467\) 1.31844e24i 1.24798i 0.781433 + 0.623989i \(0.214489\pi\)
−0.781433 + 0.623989i \(0.785511\pi\)
\(468\) −5.36426e23 3.07734e23i −0.498078 0.285735i
\(469\) −8.03146e23 −0.731542
\(470\) 1.46088e24i 1.30537i
\(471\) −1.18990e23 3.17072e22i −0.104309 0.0277952i
\(472\) −7.73539e22 −0.0665280
\(473\) 5.33949e22i 0.0450557i
\(474\) 3.30574e23 1.24057e24i 0.273693 1.02711i
\(475\) 1.60770e24 1.30606
\(476\) 9.66409e23i 0.770368i
\(477\) −9.49352e23 + 1.65486e24i −0.742612 + 1.29448i
\(478\) 5.21176e23 0.400068
\(479\) 2.24990e24i 1.69490i −0.530874 0.847451i \(-0.678136\pi\)
0.530874 0.847451i \(-0.321864\pi\)
\(480\) 3.53630e23 + 9.42319e22i 0.261444 + 0.0696670i
\(481\) 3.52011e23 0.255417
\(482\) 8.20234e23i 0.584136i
\(483\) 6.04285e23 2.26774e24i 0.422394 1.58515i
\(484\) −6.83831e23 −0.469181
\(485\) 5.09737e23i 0.343297i
\(486\) −1.03120e24 + 2.83951e23i −0.681733 + 0.187723i
\(487\) 3.43498e23 0.222927 0.111464 0.993769i \(-0.464446\pi\)
0.111464 + 0.993769i \(0.464446\pi\)
\(488\) 6.06282e23i 0.386275i
\(489\) −1.21263e24 3.23130e23i −0.758488 0.202114i
\(490\) −8.65420e23 −0.531450
\(491\) 7.44341e23i 0.448785i 0.974499 + 0.224393i \(0.0720398\pi\)
−0.974499 + 0.224393i \(0.927960\pi\)
\(492\) 1.72976e23 6.49138e23i 0.102400 0.384283i
\(493\) −2.08893e24 −1.21423
\(494\) 1.38404e24i 0.789964i
\(495\) 5.88084e23 + 3.37369e23i 0.329604 + 0.189085i
\(496\) −3.71605e23 −0.204525
\(497\) 1.57336e24i 0.850396i
\(498\) 5.84729e23 + 1.55813e23i 0.310378 + 0.0827064i
\(499\) 1.18713e24 0.618863 0.309432 0.950922i \(-0.399861\pi\)
0.309432 + 0.950922i \(0.399861\pi\)
\(500\) 5.12085e23i 0.262188i
\(501\) −3.66947e22 + 1.37707e23i −0.0184529 + 0.0692494i
\(502\) −1.20541e24 −0.595388
\(503\) 3.10476e23i 0.150631i −0.997160 0.0753157i \(-0.976004\pi\)
0.997160 0.0753157i \(-0.0239965\pi\)
\(504\) 4.50778e23 7.85773e23i 0.214826 0.374474i
\(505\) 4.65440e24 2.17892
\(506\) 5.12838e23i 0.235844i
\(507\) −6.82079e23 1.81754e23i −0.308151 0.0821129i
\(508\) −1.55403e24 −0.689741
\(509\) 3.15226e24i 1.37456i 0.726394 + 0.687278i \(0.241195\pi\)
−0.726394 + 0.687278i \(0.758805\pi\)
\(510\) −8.20730e23 + 3.08001e24i −0.351616 + 1.31953i
\(511\) 2.96119e24 1.24646
\(512\) 1.06855e23i 0.0441942i
\(513\) 1.69961e24 + 1.68559e24i 0.690704 + 0.685006i
\(514\) 1.98778e23 0.0793781
\(515\) 9.98089e23i 0.391656i
\(516\) −2.27378e23 6.05894e22i −0.0876801 0.0233641i
\(517\) −7.90200e23 −0.299448
\(518\) 5.15635e23i 0.192033i
\(519\) −9.23779e23 + 3.46673e24i −0.338113 + 1.26886i
\(520\) 1.72759e24 0.621457
\(521\) 2.05204e24i 0.725515i −0.931884 0.362757i \(-0.881835\pi\)
0.931884 0.362757i \(-0.118165\pi\)
\(522\) 1.69848e24 + 9.74372e23i 0.590235 + 0.338603i
\(523\) −4.10015e24 −1.40050 −0.700252 0.713895i \(-0.746929\pi\)
−0.700252 + 0.713895i \(0.746929\pi\)
\(524\) 1.15763e23i 0.0388675i
\(525\) −4.79990e24 1.27903e24i −1.58416 0.422131i
\(526\) 2.59555e24 0.842089
\(527\) 3.23656e24i 1.03226i
\(528\) 5.09706e22 1.91281e23i 0.0159814 0.0599744i
\(529\) −2.61100e24 −0.804834
\(530\) 5.32958e24i 1.61514i
\(531\) −3.14258e23 + 5.47798e23i −0.0936345 + 0.163219i
\(532\) −2.02739e24 −0.593926
\(533\) 3.17124e24i 0.913447i
\(534\) 4.02213e24 + 1.07178e24i 1.13916 + 0.303552i
\(535\) 2.46504e24 0.686499
\(536\) 7.73447e23i 0.211811i
\(537\) 5.20351e22 1.95276e23i 0.0140129 0.0525871i
\(538\) −3.89771e24 −1.03221
\(539\) 4.68111e23i 0.121913i
\(540\) 2.10398e24 2.12148e24i 0.538888 0.543370i
\(541\) −5.58057e24 −1.40573 −0.702867 0.711322i \(-0.748097\pi\)
−0.702867 + 0.711322i \(0.748097\pi\)
\(542\) 4.09535e23i 0.101461i
\(543\) 5.18220e24 + 1.38090e24i 1.26274 + 0.336483i
\(544\) 9.30673e23 0.223052
\(545\) 3.06210e24i 0.721856i
\(546\) 1.10109e24 4.13215e24i 0.255323 0.958169i
\(547\) 3.61075e23 0.0823591 0.0411795 0.999152i \(-0.486888\pi\)
0.0411795 + 0.999152i \(0.486888\pi\)
\(548\) 2.40035e24i 0.538579i
\(549\) −4.29352e24 2.46308e24i −0.947681 0.543660i
\(550\) −1.08547e24 −0.235698
\(551\) 4.38227e24i 0.936127i
\(552\) −2.18388e24 5.81939e23i −0.458963 0.122300i
\(553\) 8.87767e24 1.83558
\(554\) 1.25327e24i 0.254952i
\(555\) −4.37907e23 + 1.64336e24i −0.0876487 + 0.328925i
\(556\) 4.78378e24 0.942102
\(557\) 1.15019e24i 0.222880i 0.993771 + 0.111440i \(0.0355463\pi\)
−0.993771 + 0.111440i \(0.964454\pi\)
\(558\) −1.50968e24 + 2.63160e24i −0.287858 + 0.501779i
\(559\) −1.11081e24 −0.208417
\(560\) 2.53063e24i 0.467236i
\(561\) 1.66600e24 + 4.43938e23i 0.302697 + 0.0806597i
\(562\) −1.33204e24 −0.238172
\(563\) 3.27424e24i 0.576149i −0.957608 0.288075i \(-0.906985\pi\)
0.957608 0.288075i \(-0.0930151\pi\)
\(564\) −8.96673e23 + 3.36500e24i −0.155282 + 0.582739i
\(565\) −2.15252e24 −0.366870
\(566\) 9.30000e23i 0.156004i
\(567\) −3.73329e24 6.38456e24i −0.616374 1.05410i
\(568\) −1.51518e24 −0.246224
\(569\) 1.03001e25i 1.64752i 0.566936 + 0.823762i \(0.308129\pi\)
−0.566936 + 0.823762i \(0.691871\pi\)
\(570\) −6.46142e24 1.72177e24i −1.01731 0.271083i
\(571\) 8.56464e23 0.132735 0.0663673 0.997795i \(-0.478859\pi\)
0.0663673 + 0.997795i \(0.478859\pi\)
\(572\) 9.34465e23i 0.142560i
\(573\) −9.08805e23 + 3.41053e24i −0.136483 + 0.512190i
\(574\) 4.64532e24 0.686766
\(575\) 1.23930e25i 1.80371i
\(576\) −7.56716e23 4.34109e23i −0.108425 0.0622009i
\(577\) 5.51272e24 0.777650 0.388825 0.921312i \(-0.372881\pi\)
0.388825 + 0.921312i \(0.372881\pi\)
\(578\) 3.01449e24i 0.418662i
\(579\) 6.73666e24 + 1.79512e24i 0.921165 + 0.245463i
\(580\) −5.47004e24 −0.736442
\(581\) 4.18440e24i 0.554687i
\(582\) 3.12871e23 1.17413e24i 0.0408374 0.153253i
\(583\) −2.88280e24 −0.370508
\(584\) 2.85169e24i 0.360900i
\(585\) 7.01851e24 1.22343e25i 0.874666 1.52467i
\(586\) 3.59455e24 0.441130
\(587\) 3.57180e23i 0.0431662i 0.999767 + 0.0215831i \(0.00687065\pi\)
−0.999767 + 0.0215831i \(0.993129\pi\)
\(588\) 1.99341e24 + 5.31185e23i 0.237248 + 0.0632194i
\(589\) 6.78985e24 0.795834
\(590\) 1.76422e24i 0.203650i
\(591\) 2.23314e24 8.38044e24i 0.253880 0.952752i
\(592\) 4.96568e23 0.0556011
\(593\) 1.13918e25i 1.25632i −0.778084 0.628160i \(-0.783808\pi\)
0.778084 0.628160i \(-0.216192\pi\)
\(594\) −1.14752e24 1.13806e24i −0.124647 0.123619i
\(595\) −2.20410e25 −2.35819
\(596\) 3.39235e24i 0.357507i
\(597\) −5.45648e24 1.45399e24i −0.566426 0.150936i
\(598\) −1.06689e25 −1.09096
\(599\) 7.81570e24i 0.787275i −0.919266 0.393638i \(-0.871217\pi\)
0.919266 0.393638i \(-0.128783\pi\)
\(600\) −1.23173e24 + 4.62241e24i −0.122224 + 0.458677i
\(601\) 1.73207e25 1.69315 0.846576 0.532267i \(-0.178660\pi\)
0.846576 + 0.532267i \(0.178660\pi\)
\(602\) 1.62715e24i 0.156696i
\(603\) 5.47733e24 + 3.14221e24i 0.519653 + 0.298112i
\(604\) 5.57021e24 0.520642
\(605\) 1.55962e25i 1.43622i
\(606\) −1.07210e25 2.85682e24i −0.972705 0.259197i
\(607\) −1.95831e25 −1.75058 −0.875291 0.483597i \(-0.839330\pi\)
−0.875291 + 0.483597i \(0.839330\pi\)
\(608\) 1.95242e24i 0.171965i
\(609\) −3.48637e24 + 1.30835e25i −0.302564 + 1.13545i
\(610\) 1.38275e25 1.18243
\(611\) 1.64391e25i 1.38518i
\(612\) 3.78095e24 6.59076e24i 0.313934 0.547234i
\(613\) 5.56489e24 0.455315 0.227658 0.973741i \(-0.426893\pi\)
0.227658 + 0.973741i \(0.426893\pi\)
\(614\) 2.44638e24i 0.197247i
\(615\) 1.48049e25 + 3.94507e24i 1.17633 + 0.313458i
\(616\) 1.36883e24 0.107182
\(617\) 1.88574e25i 1.45518i −0.686014 0.727589i \(-0.740641\pi\)
0.686014 0.727589i \(-0.259359\pi\)
\(618\) 6.12616e23 2.29901e24i 0.0465899 0.174841i
\(619\) −1.74654e25 −1.30907 −0.654536 0.756031i \(-0.727136\pi\)
−0.654536 + 0.756031i \(0.727136\pi\)
\(620\) 8.47523e24i 0.626075i
\(621\) −1.29934e25 + 1.31014e25i −0.946014 + 0.953883i
\(622\) 1.20793e25 0.866818
\(623\) 2.87829e25i 2.03583i
\(624\) −3.97935e24 1.06038e24i −0.277428 0.0739263i
\(625\) −7.85830e24 −0.540018
\(626\) 5.24496e24i 0.355282i
\(627\) −9.31318e23 + 3.49502e24i −0.0621857 + 0.233368i
\(628\) −8.20018e23 −0.0539743
\(629\) 4.32495e24i 0.280624i
\(630\) 1.79212e25 + 1.02809e25i 1.14631 + 0.657608i
\(631\) −4.13411e24 −0.260686 −0.130343 0.991469i \(-0.541608\pi\)
−0.130343 + 0.991469i \(0.541608\pi\)
\(632\) 8.54939e24i 0.531473i
\(633\) 1.37497e25 + 3.66388e24i 0.842674 + 0.224547i
\(634\) 8.94559e24 0.540512
\(635\) 3.54429e25i 2.11138i
\(636\) −3.27124e24 + 1.22762e25i −0.192131 + 0.721024i
\(637\) 9.73843e24 0.563942
\(638\) 2.95878e24i 0.168938i
\(639\) −6.15558e24 + 1.07301e25i −0.346546 + 0.604081i
\(640\) 2.43705e24 0.135283
\(641\) 1.36929e25i 0.749501i 0.927126 + 0.374750i \(0.122272\pi\)
−0.927126 + 0.374750i \(0.877728\pi\)
\(642\) −5.67799e24 1.51301e24i −0.306464 0.0816635i
\(643\) 2.29390e25 1.22089 0.610444 0.792059i \(-0.290991\pi\)
0.610444 + 0.792059i \(0.290991\pi\)
\(644\) 1.56282e25i 0.820229i
\(645\) 1.38187e24 5.18583e24i 0.0715202 0.268399i
\(646\) −1.70050e25 −0.867926
\(647\) 2.73672e25i 1.37750i −0.724999 0.688749i \(-0.758160\pi\)
0.724999 0.688749i \(-0.241840\pi\)
\(648\) −6.14847e24 + 3.59524e24i −0.305205 + 0.178465i
\(649\) −9.54275e23 −0.0467166
\(650\) 2.25819e25i 1.09028i
\(651\) −2.02715e25 5.40175e24i −0.965289 0.257220i
\(652\) −8.35686e24 −0.392478
\(653\) 4.03759e25i 1.87026i 0.354299 + 0.935132i \(0.384720\pi\)
−0.354299 + 0.935132i \(0.615280\pi\)
\(654\) 1.87948e24 7.05326e24i 0.0858695 0.322248i
\(655\) 2.64021e24 0.118978
\(656\) 4.47354e24i 0.198846i
\(657\) −2.01948e25 1.15853e25i −0.885426 0.507946i
\(658\) −2.40804e25 −1.04143
\(659\) 1.20317e25i 0.513286i 0.966506 + 0.256643i \(0.0826164\pi\)
−0.966506 + 0.256643i \(0.917384\pi\)
\(660\) 4.36256e24 + 1.16249e24i 0.183589 + 0.0489208i
\(661\) 2.12057e25 0.880318 0.440159 0.897920i \(-0.354922\pi\)
0.440159 + 0.897920i \(0.354922\pi\)
\(662\) 2.72248e25i 1.11492i
\(663\) 9.23555e24 3.46589e25i 0.373113 1.40021i
\(664\) 4.02967e24 0.160604
\(665\) 4.62388e25i 1.81807i
\(666\) 2.01736e24 3.51655e24i 0.0782555 0.136411i
\(667\) 3.37808e25 1.29282
\(668\) 9.49009e23i 0.0358329i
\(669\) −1.61971e25 4.31604e24i −0.603396 0.160787i
\(670\) −1.76401e25 −0.648376
\(671\) 7.47939e24i 0.271246i
\(672\) 1.55327e24 5.82906e24i 0.0555807 0.208581i
\(673\) −2.12038e25 −0.748650 −0.374325 0.927298i \(-0.622126\pi\)
−0.374325 + 0.927298i \(0.622126\pi\)
\(674\) 3.15621e25i 1.09958i
\(675\) 2.77305e25 + 2.75018e25i 0.953288 + 0.945424i
\(676\) −4.70056e24 −0.159452
\(677\) 7.94323e24i 0.265888i 0.991124 + 0.132944i \(0.0424431\pi\)
−0.991124 + 0.132944i \(0.957557\pi\)
\(678\) 4.95814e24 + 1.32120e24i 0.163776 + 0.0436415i
\(679\) 8.40224e24 0.273884
\(680\) 2.12259e25i 0.682789i
\(681\) 1.64052e24 6.15648e24i 0.0520783 0.195438i
\(682\) −4.58430e24 −0.143620
\(683\) 2.16897e25i 0.670607i −0.942110 0.335303i \(-0.891161\pi\)
0.942110 0.335303i \(-0.108839\pi\)
\(684\) 1.38265e25 + 7.93190e24i 0.421897 + 0.242032i
\(685\) −5.47449e25 −1.64865
\(686\) 1.47850e25i 0.439445i
\(687\) 2.86862e25 + 7.64401e24i 0.841516 + 0.224239i
\(688\) −1.56698e24 −0.0453698
\(689\) 5.99729e25i 1.71389i
\(690\) 1.32723e25 4.98080e25i 0.374374 1.40494i
\(691\) 1.13295e25 0.315435 0.157717 0.987484i \(-0.449586\pi\)
0.157717 + 0.987484i \(0.449586\pi\)
\(692\) 2.38910e25i 0.656568i
\(693\) 5.56101e24 9.69367e24i 0.150853 0.262960i
\(694\) 3.81706e25 1.02210
\(695\) 1.09104e26i 2.88388i
\(696\) 1.25997e25 + 3.35745e24i 0.328759 + 0.0876045i
\(697\) 3.89632e25 1.00360
\(698\) 7.38410e24i 0.187758i
\(699\) −2.54204e24 + 9.53969e24i −0.0638099 + 0.239464i
\(700\) −3.30786e25 −0.819718
\(701\) 1.73460e25i 0.424364i −0.977230 0.212182i \(-0.931943\pi\)
0.977230 0.212182i \(-0.0680569\pi\)
\(702\) −2.36758e25 + 2.38727e25i −0.571834 + 0.576591i
\(703\) −9.07313e24 −0.216351
\(704\) 1.31821e24i 0.0310336i
\(705\) −7.67459e25 2.04505e25i −1.78383 0.475337i
\(706\) −4.63310e25 −1.06323
\(707\) 7.67208e25i 1.73836i
\(708\) −1.08286e24 + 4.06371e24i −0.0242254 + 0.0909124i
\(709\) 8.17517e24 0.180585 0.0902923 0.995915i \(-0.471220\pi\)
0.0902923 + 0.995915i \(0.471220\pi\)
\(710\) 3.45569e25i 0.753718i
\(711\) −6.05443e25 3.47327e25i −1.30391 0.748019i
\(712\) 2.77186e25 0.589455
\(713\) 5.23397e25i 1.09907i
\(714\) 5.07693e25 + 1.35285e25i 1.05273 + 0.280521i
\(715\) 2.13124e25 0.436393
\(716\) 1.34574e24i 0.0272111i
\(717\) 7.29580e24 2.73795e25i 0.145680 0.546704i
\(718\) 3.10265e25 0.611806
\(719\) 1.53732e25i 0.299368i −0.988734 0.149684i \(-0.952174\pi\)
0.988734 0.149684i \(-0.0478256\pi\)
\(720\) 9.90075e24 1.72585e25i 0.190404 0.331902i
\(721\) 1.64520e25 0.312465
\(722\) 2.02417e24i 0.0379675i
\(723\) 4.30901e25 + 1.14822e25i 0.798240 + 0.212707i
\(724\) 3.57132e25 0.653403
\(725\) 7.15005e25i 1.29201i
\(726\) −9.57277e24 + 3.59244e25i −0.170847 + 0.641150i
\(727\) −6.79047e25 −1.19699 −0.598495 0.801127i \(-0.704234\pi\)
−0.598495 + 0.801127i \(0.704234\pi\)
\(728\) 2.84767e25i 0.495802i
\(729\) 4.81680e23 + 5.81477e25i 0.00828344 + 0.999966i
\(730\) 6.50387e25 1.10475
\(731\) 1.36479e25i 0.228986i
\(732\) −3.18504e25 8.48718e24i −0.527856 0.140658i
\(733\) −2.21096e25 −0.361947 −0.180974 0.983488i \(-0.557925\pi\)
−0.180974 + 0.983488i \(0.557925\pi\)
\(734\) 8.42995e25i 1.36320i
\(735\) −1.21148e25 + 4.54640e25i −0.193522 + 0.726242i
\(736\) −1.50503e25 −0.237489
\(737\) 9.54162e24i 0.148736i
\(738\) −3.16804e25 1.81742e25i −0.487846 0.279865i
\(739\) −3.66121e25 −0.556960 −0.278480 0.960442i \(-0.589831\pi\)
−0.278480 + 0.960442i \(0.589831\pi\)
\(740\) 1.13253e25i 0.170201i
\(741\) 7.27093e25 + 1.93749e25i 1.07951 + 0.287657i
\(742\) −8.78501e25 −1.28857
\(743\) 9.48611e25i 1.37464i −0.726355 0.687320i \(-0.758787\pi\)
0.726355 0.687320i \(-0.241213\pi\)
\(744\) −5.20200e24 + 1.95219e25i −0.0744756 + 0.279490i
\(745\) −7.73697e25 −1.09437
\(746\) 6.27360e25i 0.876733i
\(747\) 1.63709e25 2.85370e25i 0.226041 0.394024i
\(748\) 1.14812e25 0.156630
\(749\) 4.06325e25i 0.547693i
\(750\) −2.69019e25 7.16854e24i −0.358287 0.0954728i
\(751\) 1.23146e26 1.62054 0.810269 0.586058i \(-0.199321\pi\)
0.810269 + 0.586058i \(0.199321\pi\)
\(752\) 2.31900e25i 0.301536i
\(753\) −1.68742e25 + 6.33248e25i −0.216804 + 0.813615i
\(754\) 6.15535e25 0.781467
\(755\) 1.27040e26i 1.59374i
\(756\) −3.49695e25 3.46810e25i −0.433504 0.429927i
\(757\) 5.73956e25 0.703098 0.351549 0.936170i \(-0.385655\pi\)
0.351549 + 0.936170i \(0.385655\pi\)
\(758\) 5.27372e25i 0.638402i
\(759\) −2.69414e25 7.17908e24i −0.322288 0.0858802i
\(760\) −4.45290e25 −0.526405
\(761\) 2.63148e25i 0.307424i −0.988116 0.153712i \(-0.950877\pi\)
0.988116 0.153712i \(-0.0491228\pi\)
\(762\) −2.17545e25 + 8.16394e25i −0.251162 + 0.942552i
\(763\) 5.04741e25 0.575901
\(764\) 2.35037e25i 0.265031i
\(765\) 1.50316e26 + 8.62325e25i 1.67514 + 0.960988i
\(766\) −1.05780e25 −0.116505
\(767\) 1.98524e25i 0.216101i
\(768\) −5.61352e24 1.49583e24i −0.0603926 0.0160928i
\(769\) −1.31028e26 −1.39325 −0.696624 0.717436i \(-0.745316\pi\)
−0.696624 + 0.717436i \(0.745316\pi\)
\(770\) 3.12190e25i 0.328098i
\(771\) 2.78264e24 1.04426e25i 0.0289047 0.108472i
\(772\)