Properties

Label 177.9.c.a.58.14
Level $177$
Weight $9$
Character 177.58
Analytic conductor $72.106$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(72.1060139808\)
Analytic rank: \(0\)
Dimension: \(80\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.14
Character \(\chi\) \(=\) 177.58
Dual form 177.9.c.a.58.67

$q$-expansion

\(f(q)\) \(=\) \(q-23.2103i q^{2} -46.7654 q^{3} -282.716 q^{4} +684.951 q^{5} +1085.44i q^{6} -2372.31 q^{7} +620.092i q^{8} +2187.00 q^{9} +O(q^{10})\) \(q-23.2103i q^{2} -46.7654 q^{3} -282.716 q^{4} +684.951 q^{5} +1085.44i q^{6} -2372.31 q^{7} +620.092i q^{8} +2187.00 q^{9} -15897.9i q^{10} +9748.41i q^{11} +13221.3 q^{12} -23347.2i q^{13} +55062.0i q^{14} -32032.0 q^{15} -57982.9 q^{16} +154078. q^{17} -50760.8i q^{18} +71059.1 q^{19} -193647. q^{20} +110942. q^{21} +226263. q^{22} +291010. i q^{23} -28998.8i q^{24} +78532.4 q^{25} -541894. q^{26} -102276. q^{27} +670692. q^{28} +820057. q^{29} +743471. i q^{30} -1.57709e6i q^{31} +1.50454e6i q^{32} -455888. i q^{33} -3.57619e6i q^{34} -1.62492e6 q^{35} -618301. q^{36} -1.45000e6i q^{37} -1.64930e6i q^{38} +1.09184e6i q^{39} +424732. i q^{40} +2.20221e6 q^{41} -2.57500e6i q^{42} -68355.0i q^{43} -2.75603e6i q^{44} +1.49799e6 q^{45} +6.75441e6 q^{46} -6.23313e6i q^{47} +2.71159e6 q^{48} -136932. q^{49} -1.82276e6i q^{50} -7.20551e6 q^{51} +6.60063e6i q^{52} +866154. q^{53} +2.37385e6i q^{54} +6.67718e6i q^{55} -1.47105e6i q^{56} -3.32311e6 q^{57} -1.90337e7i q^{58} +(-1.19635e7 - 1.92498e6i) q^{59} +9.05596e6 q^{60} -7.27564e6i q^{61} -3.66047e7 q^{62} -5.18825e6 q^{63} +2.00772e7 q^{64} -1.59917e7i q^{65} -1.05813e7 q^{66} -2.21972e7i q^{67} -4.35603e7 q^{68} -1.36092e7i q^{69} +3.77148e7i q^{70} -1.10994e7 q^{71} +1.35614e6i q^{72} +1.47868e7i q^{73} -3.36550e7 q^{74} -3.67260e6 q^{75} -2.00896e7 q^{76} -2.31263e7i q^{77} +2.53419e7 q^{78} -3.63921e7 q^{79} -3.97154e7 q^{80} +4.78297e6 q^{81} -5.11139e7i q^{82} -1.21628e7i q^{83} -3.13651e7 q^{84} +1.05536e8 q^{85} -1.58654e6 q^{86} -3.83503e7 q^{87} -6.04491e6 q^{88} +8.33425e7i q^{89} -3.47687e7i q^{90} +5.53868e7i q^{91} -8.22732e7i q^{92} +7.37533e7i q^{93} -1.44673e8 q^{94} +4.86720e7 q^{95} -7.03604e7i q^{96} +5.82423e7i q^{97} +3.17822e6i q^{98} +2.13198e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} + O(q^{10}) \) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} - 22680q^{12} - 59616q^{15} + 1199848q^{16} - 10608q^{17} - 27516q^{19} - 146436q^{20} - 974696q^{22} + 5718040q^{25} - 797484q^{26} - 3133000q^{28} + 1725924q^{29} + 4318800q^{35} - 22394880q^{36} - 732180q^{41} + 22752084q^{46} + 8703936q^{48} + 55899176q^{49} - 10373832q^{51} - 39265944q^{53} - 11408040q^{57} - 33575112q^{59} - 18034488q^{60} + 13038600q^{62} + 349920q^{63} - 241654260q^{64} - 35711928q^{66} + 36772608q^{68} - 235272660q^{71} - 63050712q^{74} + 74363184q^{75} + 9454680q^{76} - 10865988q^{78} + 17252580q^{79} + 318203976q^{80} + 382637520q^{81} - 20743128q^{84} - 27245820q^{85} + 105666984q^{86} + 29437992q^{87} + 82079788q^{88} + 121215992q^{94} - 690837276q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 23.2103i 1.45064i −0.688411 0.725321i \(-0.741691\pi\)
0.688411 0.725321i \(-0.258309\pi\)
\(3\) −46.7654 −0.577350
\(4\) −282.716 −1.10436
\(5\) 684.951 1.09592 0.547961 0.836504i \(-0.315404\pi\)
0.547961 + 0.836504i \(0.315404\pi\)
\(6\) 1085.44i 0.837528i
\(7\) −2372.31 −0.988052 −0.494026 0.869447i \(-0.664475\pi\)
−0.494026 + 0.869447i \(0.664475\pi\)
\(8\) 620.092i 0.151390i
\(9\) 2187.00 0.333333
\(10\) 15897.9i 1.58979i
\(11\) 9748.41i 0.665830i 0.942957 + 0.332915i \(0.108032\pi\)
−0.942957 + 0.332915i \(0.891968\pi\)
\(12\) 13221.3 0.637603
\(13\) 23347.2i 0.817450i −0.912658 0.408725i \(-0.865974\pi\)
0.912658 0.408725i \(-0.134026\pi\)
\(14\) 55062.0i 1.43331i
\(15\) −32032.0 −0.632730
\(16\) −57982.9 −0.884748
\(17\) 154078. 1.84478 0.922390 0.386260i \(-0.126233\pi\)
0.922390 + 0.386260i \(0.126233\pi\)
\(18\) 50760.8i 0.483547i
\(19\) 71059.1 0.545262 0.272631 0.962119i \(-0.412106\pi\)
0.272631 + 0.962119i \(0.412106\pi\)
\(20\) −193647. −1.21029
\(21\) 110942. 0.570452
\(22\) 226263. 0.965880
\(23\) 291010.i 1.03991i 0.854193 + 0.519955i \(0.174051\pi\)
−0.854193 + 0.519955i \(0.825949\pi\)
\(24\) 28998.8i 0.0874048i
\(25\) 78532.4 0.201043
\(26\) −541894. −1.18583
\(27\) −102276. −0.192450
\(28\) 670692. 1.09117
\(29\) 820057. 1.15945 0.579725 0.814812i \(-0.303160\pi\)
0.579725 + 0.814812i \(0.303160\pi\)
\(30\) 743471.i 0.917865i
\(31\) 1.57709e6i 1.70770i −0.520523 0.853848i \(-0.674263\pi\)
0.520523 0.853848i \(-0.325737\pi\)
\(32\) 1.50454e6i 1.43484i
\(33\) 455888.i 0.384417i
\(34\) 3.57619e6i 2.67611i
\(35\) −1.62492e6 −1.08283
\(36\) −618301. −0.368120
\(37\) 1.45000e6i 0.773681i −0.922147 0.386841i \(-0.873566\pi\)
0.922147 0.386841i \(-0.126434\pi\)
\(38\) 1.64930e6i 0.790980i
\(39\) 1.09184e6i 0.471955i
\(40\) 424732.i 0.165911i
\(41\) 2.20221e6 0.779333 0.389667 0.920956i \(-0.372590\pi\)
0.389667 + 0.920956i \(0.372590\pi\)
\(42\) 2.57500e6i 0.827522i
\(43\) 68355.0i 0.0199939i −0.999950 0.00999693i \(-0.996818\pi\)
0.999950 0.00999693i \(-0.00318218\pi\)
\(44\) 2.75603e6i 0.735316i
\(45\) 1.49799e6 0.365307
\(46\) 6.75441e6 1.50854
\(47\) 6.23313e6i 1.27737i −0.769470 0.638683i \(-0.779480\pi\)
0.769470 0.638683i \(-0.220520\pi\)
\(48\) 2.71159e6 0.510810
\(49\) −136932. −0.0237530
\(50\) 1.82276e6i 0.291641i
\(51\) −7.20551e6 −1.06508
\(52\) 6.60063e6i 0.902759i
\(53\) 866154. 0.109772 0.0548860 0.998493i \(-0.482520\pi\)
0.0548860 + 0.998493i \(0.482520\pi\)
\(54\) 2.37385e6i 0.279176i
\(55\) 6.67718e6i 0.729697i
\(56\) 1.47105e6i 0.149581i
\(57\) −3.32311e6 −0.314807
\(58\) 1.90337e7i 1.68195i
\(59\) −1.19635e7 1.92498e6i −0.987301 0.158861i
\(60\) 9.05596e6 0.698762
\(61\) 7.27564e6i 0.525475i −0.964867 0.262738i \(-0.915375\pi\)
0.964867 0.262738i \(-0.0846253\pi\)
\(62\) −3.66047e7 −2.47725
\(63\) −5.18825e6 −0.329351
\(64\) 2.00772e7 1.19669
\(65\) 1.59917e7i 0.895861i
\(66\) −1.05813e7 −0.557651
\(67\) 2.21972e7i 1.10154i −0.834658 0.550768i \(-0.814335\pi\)
0.834658 0.550768i \(-0.185665\pi\)
\(68\) −4.35603e7 −2.03730
\(69\) 1.36092e7i 0.600393i
\(70\) 3.77148e7i 1.57079i
\(71\) −1.10994e7 −0.436781 −0.218391 0.975861i \(-0.570081\pi\)
−0.218391 + 0.975861i \(0.570081\pi\)
\(72\) 1.35614e6i 0.0504632i
\(73\) 1.47868e7i 0.520695i 0.965515 + 0.260348i \(0.0838372\pi\)
−0.965515 + 0.260348i \(0.916163\pi\)
\(74\) −3.36550e7 −1.12233
\(75\) −3.67260e6 −0.116072
\(76\) −2.00896e7 −0.602166
\(77\) 2.31263e7i 0.657874i
\(78\) 2.53419e7 0.684637
\(79\) −3.63921e7 −0.934327 −0.467163 0.884171i \(-0.654724\pi\)
−0.467163 + 0.884171i \(0.654724\pi\)
\(80\) −3.97154e7 −0.969614
\(81\) 4.78297e6 0.111111
\(82\) 5.11139e7i 1.13053i
\(83\) 1.21628e7i 0.256284i −0.991756 0.128142i \(-0.959099\pi\)
0.991756 0.128142i \(-0.0409013\pi\)
\(84\) −3.13651e7 −0.629985
\(85\) 1.05536e8 2.02173
\(86\) −1.58654e6 −0.0290039
\(87\) −3.83503e7 −0.669409
\(88\) −6.04491e6 −0.100800
\(89\) 8.33425e7i 1.32833i 0.747585 + 0.664166i \(0.231213\pi\)
−0.747585 + 0.664166i \(0.768787\pi\)
\(90\) 3.47687e7i 0.529930i
\(91\) 5.53868e7i 0.807683i
\(92\) 8.22732e7i 1.14844i
\(93\) 7.37533e7i 0.985938i
\(94\) −1.44673e8 −1.85300
\(95\) 4.86720e7 0.597564
\(96\) 7.03604e7i 0.828407i
\(97\) 5.82423e7i 0.657888i 0.944349 + 0.328944i \(0.106693\pi\)
−0.944349 + 0.328944i \(0.893307\pi\)
\(98\) 3.17822e6i 0.0344571i
\(99\) 2.13198e7i 0.221943i
\(100\) −2.22024e7 −0.222024
\(101\) 1.47379e8i 1.41628i 0.706072 + 0.708140i \(0.250466\pi\)
−0.706072 + 0.708140i \(0.749534\pi\)
\(102\) 1.67242e8i 1.54505i
\(103\) 1.43420e8i 1.27426i −0.770754 0.637132i \(-0.780120\pi\)
0.770754 0.637132i \(-0.219880\pi\)
\(104\) 1.44774e7 0.123753
\(105\) 7.59899e7 0.625171
\(106\) 2.01037e7i 0.159240i
\(107\) 1.63576e8 1.24791 0.623956 0.781459i \(-0.285524\pi\)
0.623956 + 0.781459i \(0.285524\pi\)
\(108\) 2.89151e7 0.212534
\(109\) 4.50277e6i 0.0318988i −0.999873 0.0159494i \(-0.994923\pi\)
0.999873 0.0159494i \(-0.00507706\pi\)
\(110\) 1.54979e8 1.05853
\(111\) 6.78099e7i 0.446685i
\(112\) 1.37554e8 0.874178
\(113\) 1.52783e8i 0.937049i −0.883450 0.468525i \(-0.844786\pi\)
0.883450 0.468525i \(-0.155214\pi\)
\(114\) 7.71302e7i 0.456673i
\(115\) 1.99327e8i 1.13966i
\(116\) −2.31843e8 −1.28045
\(117\) 5.10603e7i 0.272483i
\(118\) −4.46793e7 + 2.77676e8i −0.230451 + 1.43222i
\(119\) −3.65521e8 −1.82274
\(120\) 1.98628e7i 0.0957888i
\(121\) 1.19327e8 0.556671
\(122\) −1.68870e8 −0.762276
\(123\) −1.02987e8 −0.449948
\(124\) 4.45870e8i 1.88591i
\(125\) −2.13768e8 −0.875594
\(126\) 1.20421e8i 0.477770i
\(127\) −3.50645e8 −1.34788 −0.673942 0.738785i \(-0.735400\pi\)
−0.673942 + 0.738785i \(0.735400\pi\)
\(128\) 8.08341e7i 0.301130i
\(129\) 3.19665e6i 0.0115435i
\(130\) −3.71171e8 −1.29957
\(131\) 1.17842e8i 0.400143i −0.979781 0.200071i \(-0.935883\pi\)
0.979781 0.200071i \(-0.0641174\pi\)
\(132\) 1.28887e8i 0.424535i
\(133\) −1.68574e8 −0.538748
\(134\) −5.15202e8 −1.59793
\(135\) −7.00539e7 −0.210910
\(136\) 9.55424e7i 0.279281i
\(137\) 2.80381e7 0.0795915 0.0397958 0.999208i \(-0.487329\pi\)
0.0397958 + 0.999208i \(0.487329\pi\)
\(138\) −3.15872e8 −0.870954
\(139\) −3.55113e8 −0.951279 −0.475639 0.879640i \(-0.657783\pi\)
−0.475639 + 0.879640i \(0.657783\pi\)
\(140\) 4.59391e8 1.19583
\(141\) 2.91495e8i 0.737487i
\(142\) 2.57619e8i 0.633613i
\(143\) 2.27598e8 0.544282
\(144\) −1.26809e8 −0.294916
\(145\) 5.61699e8 1.27067
\(146\) 3.43206e8 0.755342
\(147\) 6.40365e6 0.0137138
\(148\) 4.09940e8i 0.854423i
\(149\) 8.61218e7i 0.174730i 0.996176 + 0.0873651i \(0.0278447\pi\)
−0.996176 + 0.0873651i \(0.972155\pi\)
\(150\) 8.52420e7i 0.168379i
\(151\) 1.01980e9i 1.96159i −0.195051 0.980793i \(-0.562487\pi\)
0.195051 0.980793i \(-0.437513\pi\)
\(152\) 4.40632e7i 0.0825471i
\(153\) 3.36968e8 0.614926
\(154\) −5.36767e8 −0.954340
\(155\) 1.08023e9i 1.87150i
\(156\) 3.08681e8i 0.521208i
\(157\) 2.35092e8i 0.386936i −0.981107 0.193468i \(-0.938026\pi\)
0.981107 0.193468i \(-0.0619735\pi\)
\(158\) 8.44670e8i 1.35537i
\(159\) −4.05060e7 −0.0633769
\(160\) 1.03054e9i 1.57247i
\(161\) 6.90366e8i 1.02749i
\(162\) 1.11014e8i 0.161182i
\(163\) −1.10007e9 −1.55837 −0.779183 0.626796i \(-0.784366\pi\)
−0.779183 + 0.626796i \(0.784366\pi\)
\(164\) −6.22601e8 −0.860665
\(165\) 3.12261e8i 0.421291i
\(166\) −2.82302e8 −0.371776
\(167\) 1.00055e9 1.28639 0.643197 0.765700i \(-0.277607\pi\)
0.643197 + 0.765700i \(0.277607\pi\)
\(168\) 6.87943e7i 0.0863605i
\(169\) 2.70640e8 0.331776
\(170\) 2.44951e9i 2.93281i
\(171\) 1.55406e8 0.181754
\(172\) 1.93251e7i 0.0220804i
\(173\) 7.61863e8i 0.850535i −0.905068 0.425268i \(-0.860180\pi\)
0.905068 0.425268i \(-0.139820\pi\)
\(174\) 8.90120e8i 0.971072i
\(175\) −1.86304e8 −0.198641
\(176\) 5.65241e8i 0.589092i
\(177\) 5.59477e8 + 9.00225e7i 0.570018 + 0.0917187i
\(178\) 1.93440e9 1.92693
\(179\) 1.40082e9i 1.36449i −0.731125 0.682243i \(-0.761004\pi\)
0.731125 0.682243i \(-0.238996\pi\)
\(180\) −4.23505e8 −0.403431
\(181\) −1.44369e9 −1.34512 −0.672559 0.740044i \(-0.734805\pi\)
−0.672559 + 0.740044i \(0.734805\pi\)
\(182\) 1.28554e9 1.17166
\(183\) 3.40248e8i 0.303383i
\(184\) −1.80453e8 −0.157432
\(185\) 9.93181e8i 0.847894i
\(186\) 1.71183e9 1.43024
\(187\) 1.50201e9i 1.22831i
\(188\) 1.76221e9i 1.41067i
\(189\) 2.42630e8 0.190151
\(190\) 1.12969e9i 0.866852i
\(191\) 7.40160e8i 0.556150i −0.960559 0.278075i \(-0.910304\pi\)
0.960559 0.278075i \(-0.0896964\pi\)
\(192\) −9.38917e8 −0.690911
\(193\) −1.17043e9 −0.843560 −0.421780 0.906698i \(-0.638594\pi\)
−0.421780 + 0.906698i \(0.638594\pi\)
\(194\) 1.35182e9 0.954359
\(195\) 7.47856e8i 0.517225i
\(196\) 3.87128e7 0.0262319
\(197\) −1.17225e7 −0.00778318 −0.00389159 0.999992i \(-0.501239\pi\)
−0.00389159 + 0.999992i \(0.501239\pi\)
\(198\) 4.94838e8 0.321960
\(199\) −2.61087e9 −1.66484 −0.832420 0.554146i \(-0.813045\pi\)
−0.832420 + 0.554146i \(0.813045\pi\)
\(200\) 4.86973e7i 0.0304358i
\(201\) 1.03806e9i 0.635972i
\(202\) 3.42070e9 2.05451
\(203\) −1.94543e9 −1.14560
\(204\) 2.03711e9 1.17624
\(205\) 1.50841e9 0.854088
\(206\) −3.32881e9 −1.84850
\(207\) 6.36438e8i 0.346637i
\(208\) 1.35374e9i 0.723237i
\(209\) 6.92714e8i 0.363052i
\(210\) 1.76374e9i 0.906898i
\(211\) 1.45351e9i 0.733310i −0.930357 0.366655i \(-0.880503\pi\)
0.930357 0.366655i \(-0.119497\pi\)
\(212\) −2.44876e8 −0.121228
\(213\) 5.19065e8 0.252176
\(214\) 3.79664e9i 1.81027i
\(215\) 4.68198e7i 0.0219117i
\(216\) 6.34204e7i 0.0291349i
\(217\) 3.74136e9i 1.68729i
\(218\) −1.04511e8 −0.0462737
\(219\) 6.91512e8i 0.300624i
\(220\) 1.88775e9i 0.805848i
\(221\) 3.59728e9i 1.50801i
\(222\) 1.57389e9 0.647980
\(223\) −1.00430e9 −0.406110 −0.203055 0.979167i \(-0.565087\pi\)
−0.203055 + 0.979167i \(0.565087\pi\)
\(224\) 3.56924e9i 1.41770i
\(225\) 1.71750e8 0.0670143
\(226\) −3.54614e9 −1.35932
\(227\) 3.49000e9i 1.31438i 0.753724 + 0.657191i \(0.228255\pi\)
−0.753724 + 0.657191i \(0.771745\pi\)
\(228\) 9.39496e8 0.347661
\(229\) 1.94905e9i 0.708730i −0.935107 0.354365i \(-0.884697\pi\)
0.935107 0.354365i \(-0.115303\pi\)
\(230\) 4.62644e9 1.65324
\(231\) 1.08151e9i 0.379824i
\(232\) 5.08511e8i 0.175529i
\(233\) 2.50740e9i 0.850747i −0.905018 0.425374i \(-0.860143\pi\)
0.905018 0.425374i \(-0.139857\pi\)
\(234\) −1.18512e9 −0.395276
\(235\) 4.26939e9i 1.39989i
\(236\) 3.38227e9 + 5.44224e8i 1.09034 + 0.175440i
\(237\) 1.70189e9 0.539434
\(238\) 8.48383e9i 2.64414i
\(239\) 7.71077e8 0.236323 0.118162 0.992994i \(-0.462300\pi\)
0.118162 + 0.992994i \(0.462300\pi\)
\(240\) 1.85731e9 0.559807
\(241\) 1.97237e9 0.584681 0.292341 0.956314i \(-0.405566\pi\)
0.292341 + 0.956314i \(0.405566\pi\)
\(242\) 2.76962e9i 0.807530i
\(243\) −2.23677e8 −0.0641500
\(244\) 2.05694e9i 0.580314i
\(245\) −9.37913e7 −0.0260315
\(246\) 2.39036e9i 0.652714i
\(247\) 1.65903e9i 0.445725i
\(248\) 9.77942e8 0.258527
\(249\) 5.68798e8i 0.147966i
\(250\) 4.96161e9i 1.27017i
\(251\) 4.98630e9 1.25627 0.628136 0.778104i \(-0.283818\pi\)
0.628136 + 0.778104i \(0.283818\pi\)
\(252\) 1.46680e9 0.363722
\(253\) −2.83688e9 −0.692403
\(254\) 8.13855e9i 1.95530i
\(255\) −4.93542e9 −1.16725
\(256\) 3.26358e9 0.759861
\(257\) 1.39633e9 0.320079 0.160039 0.987111i \(-0.448838\pi\)
0.160039 + 0.987111i \(0.448838\pi\)
\(258\) 7.41951e7 0.0167454
\(259\) 3.43986e9i 0.764437i
\(260\) 4.52111e9i 0.989353i
\(261\) 1.79346e9 0.386483
\(262\) −2.73514e9 −0.580464
\(263\) 8.93441e9 1.86742 0.933712 0.358025i \(-0.116550\pi\)
0.933712 + 0.358025i \(0.116550\pi\)
\(264\) 2.82693e8 0.0581967
\(265\) 5.93273e8 0.120302
\(266\) 3.91266e9i 0.781530i
\(267\) 3.89754e9i 0.766913i
\(268\) 6.27551e9i 1.21649i
\(269\) 2.31516e9i 0.442153i −0.975257 0.221076i \(-0.929043\pi\)
0.975257 0.221076i \(-0.0709570\pi\)
\(270\) 1.62597e9i 0.305955i
\(271\) 5.44804e9 1.01010 0.505049 0.863091i \(-0.331475\pi\)
0.505049 + 0.863091i \(0.331475\pi\)
\(272\) −8.93387e9 −1.63217
\(273\) 2.59019e9i 0.466316i
\(274\) 6.50773e8i 0.115459i
\(275\) 7.65567e8i 0.133860i
\(276\) 3.84753e9i 0.663050i
\(277\) 8.14080e9 1.38276 0.691382 0.722489i \(-0.257002\pi\)
0.691382 + 0.722489i \(0.257002\pi\)
\(278\) 8.24228e9i 1.37996i
\(279\) 3.44910e9i 0.569232i
\(280\) 1.00760e9i 0.163929i
\(281\) −4.43224e8 −0.0710883 −0.0355441 0.999368i \(-0.511316\pi\)
−0.0355441 + 0.999368i \(0.511316\pi\)
\(282\) 6.76567e9 1.06983
\(283\) 1.33751e9i 0.208521i 0.994550 + 0.104261i \(0.0332476\pi\)
−0.994550 + 0.104261i \(0.966752\pi\)
\(284\) 3.13797e9 0.482364
\(285\) −2.27616e9 −0.345004
\(286\) 5.28261e9i 0.789559i
\(287\) −5.22433e9 −0.770022
\(288\) 3.29043e9i 0.478281i
\(289\) 1.67642e10 2.40321
\(290\) 1.30372e10i 1.84328i
\(291\) 2.72372e9i 0.379832i
\(292\) 4.18048e9i 0.575035i
\(293\) 9.25231e9 1.25539 0.627696 0.778458i \(-0.283998\pi\)
0.627696 + 0.778458i \(0.283998\pi\)
\(294\) 1.48630e8i 0.0198938i
\(295\) −8.19439e9 1.31852e9i −1.08200 0.174100i
\(296\) 8.99135e8 0.117127
\(297\) 9.97027e8i 0.128139i
\(298\) 1.99891e9 0.253471
\(299\) 6.79426e9 0.850075
\(300\) 1.03830e9 0.128186
\(301\) 1.62160e8i 0.0197550i
\(302\) −2.36698e10 −2.84556
\(303\) 6.89222e9i 0.817690i
\(304\) −4.12021e9 −0.482420
\(305\) 4.98346e9i 0.575879i
\(306\) 7.82112e9i 0.892038i
\(307\) −1.28673e10 −1.44856 −0.724278 0.689508i \(-0.757827\pi\)
−0.724278 + 0.689508i \(0.757827\pi\)
\(308\) 6.53818e9i 0.726530i
\(309\) 6.70707e9i 0.735697i
\(310\) −2.50724e10 −2.71487
\(311\) −6.82362e9 −0.729413 −0.364707 0.931123i \(-0.618831\pi\)
−0.364707 + 0.931123i \(0.618831\pi\)
\(312\) −6.77041e8 −0.0714491
\(313\) 8.37173e8i 0.0872244i −0.999049 0.0436122i \(-0.986113\pi\)
0.999049 0.0436122i \(-0.0138866\pi\)
\(314\) −5.45654e9 −0.561305
\(315\) −3.55369e9 −0.360942
\(316\) 1.02886e10 1.03183
\(317\) 1.23020e10 1.21825 0.609126 0.793074i \(-0.291520\pi\)
0.609126 + 0.793074i \(0.291520\pi\)
\(318\) 9.40156e8i 0.0919372i
\(319\) 7.99425e9i 0.771996i
\(320\) 1.37519e10 1.31148
\(321\) −7.64969e9 −0.720483
\(322\) −1.60236e10 −1.49051
\(323\) 1.09486e10 1.00589
\(324\) −1.35222e9 −0.122707
\(325\) 1.83351e9i 0.164343i
\(326\) 2.55329e10i 2.26063i
\(327\) 2.10574e8i 0.0184168i
\(328\) 1.36557e9i 0.117983i
\(329\) 1.47869e10i 1.26210i
\(330\) −7.24766e9 −0.611142
\(331\) −1.41369e10 −1.17772 −0.588858 0.808236i \(-0.700422\pi\)
−0.588858 + 0.808236i \(0.700422\pi\)
\(332\) 3.43863e9i 0.283030i
\(333\) 3.17116e9i 0.257894i
\(334\) 2.32231e10i 1.86610i
\(335\) 1.52040e10i 1.20720i
\(336\) −6.43274e9 −0.504707
\(337\) 1.60557e10i 1.24483i −0.782687 0.622416i \(-0.786151\pi\)
0.782687 0.622416i \(-0.213849\pi\)
\(338\) 6.28162e9i 0.481288i
\(339\) 7.14497e9i 0.541006i
\(340\) −2.98367e10 −2.23272
\(341\) 1.53741e10 1.13703
\(342\) 3.60702e9i 0.263660i
\(343\) 1.40008e10 1.01152
\(344\) 4.23864e7 0.00302686
\(345\) 9.32161e9i 0.657983i
\(346\) −1.76830e10 −1.23382
\(347\) 2.47209e10i 1.70508i 0.522658 + 0.852542i \(0.324940\pi\)
−0.522658 + 0.852542i \(0.675060\pi\)
\(348\) 1.08422e10 0.739269
\(349\) 1.81322e10i 1.22222i −0.791546 0.611109i \(-0.790724\pi\)
0.791546 0.611109i \(-0.209276\pi\)
\(350\) 4.32415e9i 0.288157i
\(351\) 2.38785e9i 0.157318i
\(352\) −1.46669e10 −0.955361
\(353\) 2.46460e10i 1.58726i −0.608402 0.793629i \(-0.708189\pi\)
0.608402 0.793629i \(-0.291811\pi\)
\(354\) 2.08945e9 1.29856e10i 0.133051 0.826892i
\(355\) −7.60251e9 −0.478678
\(356\) 2.35623e10i 1.46696i
\(357\) 1.70937e10 1.05236
\(358\) −3.25133e10 −1.97938
\(359\) −2.27075e10 −1.36707 −0.683536 0.729917i \(-0.739559\pi\)
−0.683536 + 0.729917i \(0.739559\pi\)
\(360\) 9.28890e8i 0.0553037i
\(361\) −1.19342e10 −0.702689
\(362\) 3.35085e10i 1.95128i
\(363\) −5.58039e9 −0.321394
\(364\) 1.56588e10i 0.891973i
\(365\) 1.01283e10i 0.570641i
\(366\) 7.89725e9 0.440100
\(367\) 1.30860e10i 0.721343i 0.932693 + 0.360672i \(0.117452\pi\)
−0.932693 + 0.360672i \(0.882548\pi\)
\(368\) 1.68736e10i 0.920059i
\(369\) 4.81623e9 0.259778
\(370\) −2.30520e10 −1.22999
\(371\) −2.05479e9 −0.108461
\(372\) 2.08513e10i 1.08883i
\(373\) 1.77480e10 0.916883 0.458442 0.888725i \(-0.348408\pi\)
0.458442 + 0.888725i \(0.348408\pi\)
\(374\) 3.48621e10 1.78184
\(375\) 9.99694e9 0.505524
\(376\) 3.86512e9 0.193380
\(377\) 1.91460e10i 0.947792i
\(378\) 5.63151e9i 0.275841i
\(379\) 1.19452e10 0.578946 0.289473 0.957186i \(-0.406520\pi\)
0.289473 + 0.957186i \(0.406520\pi\)
\(380\) −1.37604e10 −0.659927
\(381\) 1.63980e10 0.778201
\(382\) −1.71793e10 −0.806774
\(383\) 2.82331e8 0.0131209 0.00656045 0.999978i \(-0.497912\pi\)
0.00656045 + 0.999978i \(0.497912\pi\)
\(384\) 3.78024e9i 0.173858i
\(385\) 1.58404e10i 0.720978i
\(386\) 2.71660e10i 1.22370i
\(387\) 1.49492e8i 0.00666462i
\(388\) 1.64661e10i 0.726545i
\(389\) −6.39640e9 −0.279343 −0.139671 0.990198i \(-0.544605\pi\)
−0.139671 + 0.990198i \(0.544605\pi\)
\(390\) 1.73579e10 0.750308
\(391\) 4.48381e10i 1.91841i
\(392\) 8.49101e7i 0.00359596i
\(393\) 5.51093e9i 0.231023i
\(394\) 2.72083e8i 0.0112906i
\(395\) −2.49268e10 −1.02395
\(396\) 6.02745e9i 0.245105i
\(397\) 5.53926e9i 0.222992i −0.993765 0.111496i \(-0.964436\pi\)
0.993765 0.111496i \(-0.0355642\pi\)
\(398\) 6.05989e10i 2.41508i
\(399\) 7.88345e9 0.311046
\(400\) −4.55354e9 −0.177873
\(401\) 4.19487e10i 1.62234i 0.584813 + 0.811168i \(0.301168\pi\)
−0.584813 + 0.811168i \(0.698832\pi\)
\(402\) 2.40936e10 0.922567
\(403\) −3.68207e10 −1.39596
\(404\) 4.16664e10i 1.56408i
\(405\) 3.27610e9 0.121769
\(406\) 4.51540e10i 1.66185i
\(407\) 1.41352e10 0.515140
\(408\) 4.46808e9i 0.161243i
\(409\) 1.16259e9i 0.0415462i 0.999784 + 0.0207731i \(0.00661276\pi\)
−0.999784 + 0.0207731i \(0.993387\pi\)
\(410\) 3.50105e10i 1.23898i
\(411\) −1.31121e9 −0.0459522
\(412\) 4.05471e10i 1.40725i
\(413\) 2.83811e10 + 4.56666e9i 0.975505 + 0.156963i
\(414\) 1.47719e10 0.502846
\(415\) 8.33093e9i 0.280867i
\(416\) 3.51268e10 1.17291
\(417\) 1.66070e10 0.549221
\(418\) 1.60781e10 0.526658
\(419\) 4.46299e10i 1.44800i −0.689798 0.724002i \(-0.742301\pi\)
0.689798 0.724002i \(-0.257699\pi\)
\(420\) −2.14836e10 −0.690414
\(421\) 4.03763e10i 1.28528i −0.766167 0.642641i \(-0.777839\pi\)
0.766167 0.642641i \(-0.222161\pi\)
\(422\) −3.37363e10 −1.06377
\(423\) 1.36319e10i 0.425788i
\(424\) 5.37095e8i 0.0166184i
\(425\) 1.21001e10 0.370880
\(426\) 1.20476e10i 0.365817i
\(427\) 1.72601e10i 0.519197i
\(428\) −4.62456e10 −1.37815
\(429\) −1.06437e10 −0.314242
\(430\) −1.08670e9 −0.0317860
\(431\) 1.43649e10i 0.416288i −0.978098 0.208144i \(-0.933258\pi\)
0.978098 0.208144i \(-0.0667423\pi\)
\(432\) 5.93025e9 0.170270
\(433\) 4.76686e9 0.135607 0.0678034 0.997699i \(-0.478401\pi\)
0.0678034 + 0.997699i \(0.478401\pi\)
\(434\) 8.68379e10 2.44766
\(435\) −2.62680e10 −0.733619
\(436\) 1.27301e9i 0.0352277i
\(437\) 2.06789e10i 0.567024i
\(438\) −1.60502e10 −0.436097
\(439\) −1.66181e9 −0.0447428 −0.0223714 0.999750i \(-0.507122\pi\)
−0.0223714 + 0.999750i \(0.507122\pi\)
\(440\) −4.14047e9 −0.110469
\(441\) −2.99469e8 −0.00791768
\(442\) −8.34939e10 −2.18759
\(443\) 6.40780e9i 0.166377i 0.996534 + 0.0831887i \(0.0265104\pi\)
−0.996534 + 0.0831887i \(0.973490\pi\)
\(444\) 1.91710e10i 0.493301i
\(445\) 5.70855e10i 1.45575i
\(446\) 2.33101e10i 0.589121i
\(447\) 4.02752e9i 0.100880i
\(448\) −4.76294e10 −1.18240
\(449\) −5.48463e9 −0.134947 −0.0674733 0.997721i \(-0.521494\pi\)
−0.0674733 + 0.997721i \(0.521494\pi\)
\(450\) 3.98637e9i 0.0972138i
\(451\) 2.14680e10i 0.518903i
\(452\) 4.31944e10i 1.03484i
\(453\) 4.76913e10i 1.13252i
\(454\) 8.10037e10 1.90670
\(455\) 3.79372e10i 0.885157i
\(456\) 2.06063e9i 0.0476586i
\(457\) 4.57556e10i 1.04901i 0.851407 + 0.524505i \(0.175750\pi\)
−0.851407 + 0.524505i \(0.824250\pi\)
\(458\) −4.52379e10 −1.02811
\(459\) −1.57584e10 −0.355028
\(460\) 5.63531e10i 1.25860i
\(461\) −4.61834e10 −1.02255 −0.511273 0.859419i \(-0.670826\pi\)
−0.511273 + 0.859419i \(0.670826\pi\)
\(462\) 2.51021e10 0.550988
\(463\) 6.84846e10i 1.49028i −0.666906 0.745142i \(-0.732382\pi\)
0.666906 0.745142i \(-0.267618\pi\)
\(464\) −4.75493e10 −1.02582
\(465\) 5.05174e10i 1.08051i
\(466\) −5.81975e10 −1.23413
\(467\) 4.07709e10i 0.857200i 0.903494 + 0.428600i \(0.140993\pi\)
−0.903494 + 0.428600i \(0.859007\pi\)
\(468\) 1.44356e10i 0.300920i
\(469\) 5.26587e10i 1.08837i
\(470\) −9.90936e10 −2.03074
\(471\) 1.09942e10i 0.223397i
\(472\) 1.19367e9 7.41846e9i 0.0240500 0.149467i
\(473\) 6.66353e8 0.0133125
\(474\) 3.95013e10i 0.782525i
\(475\) 5.58045e9 0.109621
\(476\) 1.03339e11 2.01296
\(477\) 1.89428e9 0.0365907
\(478\) 1.78969e10i 0.342820i
\(479\) 3.48252e10 0.661534 0.330767 0.943712i \(-0.392693\pi\)
0.330767 + 0.943712i \(0.392693\pi\)
\(480\) 4.81934e10i 0.907868i
\(481\) −3.38535e10 −0.632446
\(482\) 4.57791e10i 0.848163i
\(483\) 3.22852e10i 0.593219i
\(484\) −3.37358e10 −0.614765
\(485\) 3.98931e10i 0.720993i
\(486\) 5.19161e9i 0.0930587i
\(487\) 5.02901e10 0.894060 0.447030 0.894519i \(-0.352482\pi\)
0.447030 + 0.894519i \(0.352482\pi\)
\(488\) 4.51157e9 0.0795515
\(489\) 5.14452e10 0.899724
\(490\) 2.17692e9i 0.0377623i
\(491\) 5.72661e10 0.985308 0.492654 0.870225i \(-0.336027\pi\)
0.492654 + 0.870225i \(0.336027\pi\)
\(492\) 2.91161e10 0.496905
\(493\) 1.26353e11 2.13893
\(494\) −3.85065e10 −0.646587
\(495\) 1.46030e10i 0.243232i
\(496\) 9.14443e10i 1.51088i
\(497\) 2.63311e10 0.431563
\(498\) 1.32020e10 0.214645
\(499\) 6.34009e10 1.02257 0.511285 0.859411i \(-0.329170\pi\)
0.511285 + 0.859411i \(0.329170\pi\)
\(500\) 6.04357e10 0.966971
\(501\) −4.67912e10 −0.742700
\(502\) 1.15733e11i 1.82240i
\(503\) 7.08382e10i 1.10661i 0.832978 + 0.553307i \(0.186634\pi\)
−0.832978 + 0.553307i \(0.813366\pi\)
\(504\) 3.21719e9i 0.0498603i
\(505\) 1.00947e11i 1.55213i
\(506\) 6.58448e10i 1.00443i
\(507\) −1.26566e10 −0.191551
\(508\) 9.91330e10 1.48855
\(509\) 8.20459e10i 1.22232i −0.791506 0.611161i \(-0.790703\pi\)
0.791506 0.611161i \(-0.209297\pi\)
\(510\) 1.14552e11i 1.69326i
\(511\) 3.50790e10i 0.514474i
\(512\) 9.64420e10i 1.40342i
\(513\) −7.26763e9 −0.104936
\(514\) 3.24093e10i 0.464320i
\(515\) 9.82354e10i 1.39649i
\(516\) 9.03745e8i 0.0127481i
\(517\) 6.07632e10 0.850508
\(518\) 7.98401e10 1.10892
\(519\) 3.56288e10i 0.491057i
\(520\) 9.91631e9 0.135624
\(521\) −4.24014e10 −0.575478 −0.287739 0.957709i \(-0.592904\pi\)
−0.287739 + 0.957709i \(0.592904\pi\)
\(522\) 4.16268e10i 0.560649i
\(523\) −5.41738e10 −0.724074 −0.362037 0.932164i \(-0.617919\pi\)
−0.362037 + 0.932164i \(0.617919\pi\)
\(524\) 3.33159e10i 0.441902i
\(525\) 8.71255e9 0.114685
\(526\) 2.07370e11i 2.70896i
\(527\) 2.42995e11i 3.15032i
\(528\) 2.64337e10i 0.340112i
\(529\) −6.37561e9 −0.0814140
\(530\) 1.37700e10i 0.174514i
\(531\) −2.61641e10 4.20994e9i −0.329100 0.0529538i
\(532\) 4.76588e10 0.594972
\(533\) 5.14154e10i 0.637066i
\(534\) −9.04630e10 −1.11252
\(535\) 1.12041e11 1.36761
\(536\) 1.37643e10 0.166761
\(537\) 6.55097e10i 0.787787i
\(538\) −5.37355e10 −0.641405
\(539\) 1.33486e9i 0.0158155i
\(540\) 1.98054e10 0.232921
\(541\) 4.29112e10i 0.500936i −0.968125 0.250468i \(-0.919416\pi\)
0.968125 0.250468i \(-0.0805844\pi\)
\(542\) 1.26450e11i 1.46529i
\(543\) 6.75148e10 0.776604
\(544\) 2.31816e11i 2.64697i
\(545\) 3.08418e9i 0.0349585i
\(546\) −6.01189e10 −0.676457
\(547\) 1.38075e11 1.54229 0.771145 0.636659i \(-0.219684\pi\)
0.771145 + 0.636659i \(0.219684\pi\)
\(548\) −7.92684e9 −0.0878978
\(549\) 1.59118e10i 0.175158i
\(550\) 1.77690e10 0.194183
\(551\) 5.82725e10 0.632204
\(552\) 8.43894e9 0.0908932
\(553\) 8.63335e10 0.923163
\(554\) 1.88950e11i 2.00589i
\(555\) 4.64465e10i 0.489532i
\(556\) 1.00396e11 1.05055
\(557\) 1.25469e11 1.30351 0.651757 0.758428i \(-0.274032\pi\)
0.651757 + 0.758428i \(0.274032\pi\)
\(558\) −8.00545e10 −0.825751
\(559\) −1.59590e9 −0.0163440
\(560\) 9.42174e10 0.958030
\(561\) 7.02422e10i 0.709164i
\(562\) 1.02873e10i 0.103124i
\(563\) 4.51344e10i 0.449236i 0.974447 + 0.224618i \(0.0721134\pi\)
−0.974447 + 0.224618i \(0.927887\pi\)
\(564\) 8.24103e10i 0.814452i
\(565\) 1.04649e11i 1.02693i
\(566\) 3.10439e10 0.302489
\(567\) −1.13467e10 −0.109784
\(568\) 6.88262e9i 0.0661242i
\(569\) 1.85314e11i 1.76790i −0.467579 0.883951i \(-0.654874\pi\)
0.467579 0.883951i \(-0.345126\pi\)
\(570\) 5.28304e10i 0.500477i
\(571\) 1.48590e11i 1.39780i 0.715220 + 0.698899i \(0.246326\pi\)
−0.715220 + 0.698899i \(0.753674\pi\)
\(572\) −6.43457e10 −0.601084
\(573\) 3.46138e10i 0.321093i
\(574\) 1.21258e11i 1.11703i
\(575\) 2.28537e10i 0.209067i
\(576\) 4.39088e10 0.398898
\(577\) −1.06355e11 −0.959519 −0.479760 0.877400i \(-0.659276\pi\)
−0.479760 + 0.877400i \(0.659276\pi\)
\(578\) 3.89102e11i 3.48620i
\(579\) 5.47355e10 0.487029
\(580\) −1.58801e11 −1.40327
\(581\) 2.88540e10i 0.253222i
\(582\) −6.32184e10 −0.551000
\(583\) 8.44363e9i 0.0730895i
\(584\) −9.16920e9 −0.0788279
\(585\) 3.49738e10i 0.298620i
\(586\) 2.14748e11i 1.82112i
\(587\) 1.42209e11i 1.19777i 0.800833 + 0.598887i \(0.204390\pi\)
−0.800833 + 0.598887i \(0.795610\pi\)
\(588\) −1.81042e9 −0.0151450
\(589\) 1.12067e11i 0.931142i
\(590\) −3.06031e10 + 1.90194e11i −0.252556 + 1.56960i
\(591\) 5.48209e8 0.00449362
\(592\) 8.40754e10i 0.684513i
\(593\) −1.71645e11 −1.38808 −0.694038 0.719938i \(-0.744170\pi\)
−0.694038 + 0.719938i \(0.744170\pi\)
\(594\) −2.31413e10 −0.185884
\(595\) −2.50364e11 −1.99758
\(596\) 2.43480e10i 0.192965i
\(597\) 1.22098e11 0.961195
\(598\) 1.57696e11i 1.23315i
\(599\) −3.93918e10 −0.305984 −0.152992 0.988227i \(-0.548891\pi\)
−0.152992 + 0.988227i \(0.548891\pi\)
\(600\) 2.27735e9i 0.0175721i
\(601\) 1.02104e11i 0.782606i 0.920262 + 0.391303i \(0.127975\pi\)
−0.920262 + 0.391303i \(0.872025\pi\)
\(602\) 3.76377e9 0.0286574
\(603\) 4.85452e10i 0.367179i
\(604\) 2.88314e11i 2.16630i
\(605\) 8.17333e10 0.610067
\(606\) −1.59970e11 −1.18617
\(607\) 1.71502e11 1.26332 0.631662 0.775244i \(-0.282373\pi\)
0.631662 + 0.775244i \(0.282373\pi\)
\(608\) 1.06911e11i 0.782365i
\(609\) 9.09789e10 0.661411
\(610\) −1.15667e11 −0.835394
\(611\) −1.45526e11 −1.04418
\(612\) −9.52664e10 −0.679101
\(613\) 1.49268e11i 1.05712i 0.848896 + 0.528560i \(0.177268\pi\)
−0.848896 + 0.528560i \(0.822732\pi\)
\(614\) 2.98654e11i 2.10134i
\(615\) −7.05411e10 −0.493108
\(616\) 1.43404e10 0.0995954
\(617\) −1.42930e11 −0.986238 −0.493119 0.869962i \(-0.664143\pi\)
−0.493119 + 0.869962i \(0.664143\pi\)
\(618\) 1.55673e11 1.06723
\(619\) 1.45330e11 0.989906 0.494953 0.868920i \(-0.335185\pi\)
0.494953 + 0.868920i \(0.335185\pi\)
\(620\) 3.05399e11i 2.06681i
\(621\) 2.97633e10i 0.200131i
\(622\) 1.58378e11i 1.05812i
\(623\) 1.97715e11i 1.31246i
\(624\) 6.33080e10i 0.417561i
\(625\) −1.77097e11 −1.16062
\(626\) −1.94310e10 −0.126531
\(627\) 3.23950e10i 0.209608i
\(628\) 6.64643e10i 0.427317i
\(629\) 2.23413e11i 1.42727i
\(630\) 8.24822e10i 0.523598i
\(631\) 1.41515e10 0.0892660 0.0446330 0.999003i \(-0.485788\pi\)
0.0446330 + 0.999003i \(0.485788\pi\)
\(632\) 2.25664e10i 0.141447i
\(633\) 6.79738e10i 0.423377i
\(634\) 2.85532e11i 1.76725i
\(635\) −2.40174e11 −1.47717
\(636\) 1.14517e10 0.0699910
\(637\) 3.19697e9i 0.0194169i
\(638\) 1.85549e11 1.11989
\(639\) −2.42743e10 −0.145594
\(640\) 5.53674e10i 0.330015i
\(641\) 2.61465e11 1.54875 0.774375 0.632727i \(-0.218064\pi\)
0.774375 + 0.632727i \(0.218064\pi\)
\(642\) 1.77551e11i 1.04516i
\(643\) 2.87732e10 0.168323 0.0841617 0.996452i \(-0.473179\pi\)
0.0841617 + 0.996452i \(0.473179\pi\)
\(644\) 1.95178e11i 1.13471i
\(645\) 2.18955e9i 0.0126507i
\(646\) 2.54121e11i 1.45918i
\(647\) −9.55469e10 −0.545255 −0.272628 0.962120i \(-0.587893\pi\)
−0.272628 + 0.962120i \(0.587893\pi\)
\(648\) 2.96588e9i 0.0168211i
\(649\) 1.87655e10 1.16625e11i 0.105775 0.657374i
\(650\) −4.25563e10 −0.238402
\(651\) 1.74966e11i 0.974158i
\(652\) 3.11008e11 1.72100
\(653\) −2.11634e11 −1.16394 −0.581972 0.813208i \(-0.697719\pi\)
−0.581972 + 0.813208i \(0.697719\pi\)
\(654\) 4.88747e9 0.0267161
\(655\) 8.07160e10i 0.438525i
\(656\) −1.27690e11 −0.689514
\(657\) 3.23388e10i 0.173565i
\(658\) 3.43209e11 1.83086
\(659\) 2.41201e11i 1.27890i −0.768832 0.639451i \(-0.779162\pi\)
0.768832 0.639451i \(-0.220838\pi\)
\(660\) 8.82812e10i 0.465257i
\(661\) −1.17302e11 −0.614468 −0.307234 0.951634i \(-0.599403\pi\)
−0.307234 + 0.951634i \(0.599403\pi\)
\(662\) 3.28120e11i 1.70844i
\(663\) 1.68228e11i 0.870653i
\(664\) 7.54206e9 0.0387988
\(665\) −1.15465e11 −0.590425
\(666\) −7.36034e10 −0.374111
\(667\) 2.38644e11i 1.20572i
\(668\) −2.82873e11 −1.42064
\(669\) 4.69665e10 0.234468
\(670\) −3.52888e11 −1.75121
\(671\) 7.09260e10 0.349877
\(672\) 1.66917e11i 0.818509i
\(673\) 2.43490e11i 1.18692i 0.804864 + 0.593459i \(0.202238\pi\)
−0.804864 + 0.593459i \(0.797762\pi\)
\(674\) −3.72658e11 −1.80580
\(675\) −8.03197e9 −0.0386908
\(676\) −7.65142e10 −0.366400
\(677\) 3.07432e11 1.46350 0.731752 0.681571i \(-0.238703\pi\)
0.731752 + 0.681571i \(0.238703\pi\)
\(678\) 1.65837e11 0.784805
\(679\) 1.38169e11i 0.650027i
\(680\) 6.54418e10i 0.306069i
\(681\) 1.63211e11i 0.758859i
\(682\) 3.56838e11i 1.64943i
\(683\) 3.50090e11i 1.60878i 0.594101 + 0.804390i \(0.297508\pi\)
−0.594101 + 0.804390i \(0.702492\pi\)
\(684\) −4.39359e10 −0.200722
\(685\) 1.92047e10 0.0872261
\(686\) 3.24961e11i 1.46735i
\(687\) 9.11480e10i 0.409185i
\(688\) 3.96342e9i 0.0176895i
\(689\) 2.02223e10i 0.0897331i
\(690\) −2.16357e11 −0.954497
\(691\) 2.89905e11i 1.27158i 0.771862 + 0.635790i \(0.219325\pi\)
−0.771862 + 0.635790i \(0.780675\pi\)
\(692\) 2.15391e11i 0.939298i
\(693\) 5.05772e10i 0.219291i
\(694\) 5.73778e11 2.47347
\(695\) −2.43235e11 −1.04253
\(696\) 2.37807e10i 0.101342i
\(697\) 3.39312e11 1.43770
\(698\) −4.20853e11 −1.77300
\(699\) 1.17260e11i 0.491179i
\(700\) 5.26710e10 0.219371
\(701\) 2.81948e11i 1.16761i −0.811895 0.583804i \(-0.801564\pi\)
0.811895 0.583804i \(-0.198436\pi\)
\(702\) 5.54227e10 0.228212
\(703\) 1.03036e11i 0.421859i
\(704\) 1.95721e11i 0.796794i
\(705\) 1.99660e11i 0.808228i
\(706\) −5.72040e11 −2.30254
\(707\) 3.49628e11i 1.39936i
\(708\) −1.58173e11 2.54508e10i −0.629506 0.101291i
\(709\) −3.58537e11 −1.41889 −0.709446 0.704760i \(-0.751055\pi\)
−0.709446 + 0.704760i \(0.751055\pi\)
\(710\) 1.76456e11i 0.694390i
\(711\) −7.95895e10 −0.311442
\(712\) −5.16800e10 −0.201096
\(713\) 4.58949e11 1.77585
\(714\) 3.96750e11i 1.52659i
\(715\) 1.55893e11 0.596491
\(716\) 3.96034e11i 1.50689i
\(717\) −3.60597e10 −0.136441
\(718\) 5.27047e11i 1.98313i
\(719\) 4.59130e11i 1.71799i 0.511985 + 0.858995i \(0.328910\pi\)
−0.511985 + 0.858995i \(0.671090\pi\)
\(720\) −8.68576e10 −0.323205
\(721\) 3.40236e11i 1.25904i
\(722\) 2.76995e11i 1.01935i
\(723\) −9.22384e10 −0.337566
\(724\) 4.08155e11 1.48549
\(725\) 6.44011e10 0.233099
\(726\) 1.29522e11i 0.466228i
\(727\) −1.26631e11 −0.453319 −0.226660 0.973974i \(-0.572780\pi\)
−0.226660 + 0.973974i \(0.572780\pi\)
\(728\) −3.43449e10 −0.122275
\(729\) 1.04604e10 0.0370370
\(730\) 2.35079e11 0.827795
\(731\) 1.05320e10i 0.0368843i
\(732\) 9.61937e10i 0.335044i
\(733\) 3.82085e11 1.32356 0.661781 0.749697i \(-0.269801\pi\)
0.661781 + 0.749697i \(0.269801\pi\)
\(734\) 3.03729e11 1.04641
\(735\) 4.38619e9 0.0150293
\(736\) −4.37836e11 −1.49211
\(737\) 2.16387e11 0.733435
\(738\) 1.11786e11i 0.376844i
\(739\) 2.11704e11i 0.709826i −0.934899 0.354913i \(-0.884511\pi\)
0.934899 0.354913i \(-0.115489\pi\)
\(740\) 2.80788e11i 0.936380i
\(741\) 7.75852e10i 0.257339i
\(742\) 4.76922e10i 0.157337i
\(743\) −1.54847e11 −0.508099 −0.254049 0.967191i \(-0.581763\pi\)
−0.254049 + 0.967191i \(0.581763\pi\)
\(744\) −4.57338e10 −0.149261
\(745\) 5.89892e10i 0.191490i
\(746\) 4.11936e11i 1.33007i
\(747\) 2.66001e10i 0.0854280i
\(748\) 4.24644e11i 1.35650i
\(749\) −3.88053e11 −1.23300
\(750\) 2.32032e11i 0.733334i
\(751\) 2.66071e11i 0.836446i −0.908344 0.418223i \(-0.862653\pi\)
0.908344 0.418223i \(-0.137347\pi\)
\(752\) 3.61415e11i 1.13015i
\(753\) −2.33186e11 −0.725309
\(754\) −4.44384e11 −1.37491
\(755\) 6.98513e11i 2.14974i
\(756\) −6.85956e10 −0.209995
\(757\) −7.24705e10 −0.220688 −0.110344 0.993893i \(-0.535195\pi\)
−0.110344 + 0.993893i \(0.535195\pi\)
\(758\) 2.77252e11i 0.839843i
\(759\) 1.32668e11 0.399759
\(760\) 3.01811e10i 0.0904651i
\(761\) −4.38033e11 −1.30607 −0.653037 0.757326i \(-0.726505\pi\)
−0.653037 + 0.757326i \(0.726505\pi\)
\(762\) 3.80603e11i 1.12889i
\(763\) 1.06820e10i 0.0315176i
\(764\) 2.09255e11i 0.614190i
\(765\) 2.30807e11 0.673911
\(766\) 6.55298e9i 0.0190337i
\(767\) −4.49429e10 + 2.79314e11i −0.129861 + 0.807069i
\(768\) −1.52622e11 −0.438706
\(769\) 3.09691e11i 0.885570i −0.896628 0.442785i \(-0.853990\pi\)
0.896628 0.442785i \(-0.146010\pi\)
\(770\) −3.67659e11 −1.04588
\(771\) −6.53001e10 −0.184798
\(772\) 3.30899e11 0.931594
\(773\) 1.94542e11i 0.544873i −0.962174 0.272437i \(-0.912170\pi\)
0.962174 0.272437i \(-0.0878295\pi\)
\(774\) −3.46976e9 −0.00966798
\(775\) 1.23853e11i 0.343320i
\(776\) −3.61156e10 −0.0995974
\(777\) 1.60866e11i 0.441348i
\(778\) 1.48462e11i 0.405226i
\(779\) 1.56487e11 0.424941
\(780\) 2.11431e11i 0.571203i
\(781\) 1.08201e11i 0.290822i
\(782\) 1.04070e12 2.78292