Properties

Label 177.11.c.a.58.5
Level $177$
Weight $11$
Character 177.58
Analytic conductor $112.458$
Analytic rank $0$
Dimension $100$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(112.458233723\)
Analytic rank: \(0\)
Dimension: \(100\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.5
Character \(\chi\) \(=\) 177.58
Dual form 177.11.c.a.58.96

$q$-expansion

\(f(q)\) \(=\) \(q-58.9981i q^{2} -140.296 q^{3} -2456.77 q^{4} +878.334 q^{5} +8277.20i q^{6} -5578.77 q^{7} +84530.8i q^{8} +19683.0 q^{9} +O(q^{10})\) \(q-58.9981i q^{2} -140.296 q^{3} -2456.77 q^{4} +878.334 q^{5} +8277.20i q^{6} -5578.77 q^{7} +84530.8i q^{8} +19683.0 q^{9} -51820.0i q^{10} -8137.20i q^{11} +344676. q^{12} +545367. i q^{13} +329136. i q^{14} -123227. q^{15} +2.47142e6 q^{16} +193046. q^{17} -1.16126e6i q^{18} +3.36874e6 q^{19} -2.15787e6 q^{20} +782679. q^{21} -480079. q^{22} -5.01255e6i q^{23} -1.18593e7i q^{24} -8.99415e6 q^{25} +3.21756e7 q^{26} -2.76145e6 q^{27} +1.37058e7 q^{28} +1.17377e7 q^{29} +7.27014e6i q^{30} +3.31260e7i q^{31} -5.92495e7i q^{32} +1.14162e6i q^{33} -1.13893e7i q^{34} -4.90002e6 q^{35} -4.83567e7 q^{36} -6.48748e7i q^{37} -1.98749e8i q^{38} -7.65128e7i q^{39} +7.42463e7i q^{40} -4.00314e7 q^{41} -4.61766e7i q^{42} -2.00048e8i q^{43} +1.99913e7i q^{44} +1.72882e7 q^{45} -2.95731e8 q^{46} -1.47000e8i q^{47} -3.46731e8 q^{48} -2.51353e8 q^{49} +5.30638e8i q^{50} -2.70836e7 q^{51} -1.33984e9i q^{52} +4.79174e7 q^{53} +1.62920e8i q^{54} -7.14718e6i q^{55} -4.71578e8i q^{56} -4.72621e8 q^{57} -6.92502e8i q^{58} +(1.12376e8 + 7.06037e8i) q^{59} +3.02740e8 q^{60} -5.55854e8i q^{61} +1.95437e9 q^{62} -1.09807e8 q^{63} -9.64871e8 q^{64} +4.79014e8i q^{65} +6.73533e7 q^{66} -8.19852e8i q^{67} -4.74270e8 q^{68} +7.03241e8i q^{69} +2.89092e8i q^{70} +3.33641e8 q^{71} +1.66382e9i q^{72} +2.91990e9i q^{73} -3.82749e9 q^{74} +1.26184e9 q^{75} -8.27623e9 q^{76} +4.53956e7i q^{77} -4.51411e9 q^{78} -3.70815e9 q^{79} +2.17073e9 q^{80} +3.87420e8 q^{81} +2.36177e9i q^{82} +5.07449e9i q^{83} -1.92286e9 q^{84} +1.69559e8 q^{85} -1.18024e10 q^{86} -1.64675e9 q^{87} +6.87845e8 q^{88} -1.18443e9i q^{89} -1.01997e9i q^{90} -3.04247e9i q^{91} +1.23147e10i q^{92} -4.64745e9i q^{93} -8.67271e9 q^{94} +2.95888e9 q^{95} +8.31247e9i q^{96} -1.13463e9i q^{97} +1.48293e10i q^{98} -1.60165e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + O(q^{10}) \) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + 620136q^{12} + 662904q^{15} + 27925160q^{16} - 2053136q^{17} - 5169828q^{19} - 1076324q^{20} - 1829224q^{22} + 215378180q^{25} - 22082700q^{26} - 102921320q^{28} - 112503588q^{29} - 76491392q^{35} - 1007769600q^{36} + 473464516q^{41} + 1215405588q^{46} - 1676272320q^{48} + 1975297276q^{49} + 733970808q^{51} + 3267506728q^{53} + 591502824q^{57} + 508142200q^{59} + 1264196808q^{60} - 6538206968q^{62} + 362009736q^{63} - 10324137972q^{64} - 2764346616q^{66} + 9997685952q^{68} + 14908523204q^{71} + 4863508712q^{74} + 1890481680q^{75} + 2044437240q^{76} - 758396196q^{78} - 3599839500q^{79} - 23217941144q^{80} + 38742048900q^{81} - 13094894808q^{84} + 23360564412q^{85} + 12186923752q^{86} + 7965322272q^{87} + 32415437996q^{88} - 22098322280q^{94} + 7834510028q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 58.9981i 1.84369i −0.387559 0.921845i \(-0.626682\pi\)
0.387559 0.921845i \(-0.373318\pi\)
\(3\) −140.296 −0.577350
\(4\) −2456.77 −2.39919
\(5\) 878.334 0.281067 0.140533 0.990076i \(-0.455118\pi\)
0.140533 + 0.990076i \(0.455118\pi\)
\(6\) 8277.20i 1.06445i
\(7\) −5578.77 −0.331931 −0.165966 0.986132i \(-0.553074\pi\)
−0.165966 + 0.986132i \(0.553074\pi\)
\(8\) 84530.8i 2.57968i
\(9\) 19683.0 0.333333
\(10\) 51820.0i 0.518200i
\(11\) 8137.20i 0.0505256i −0.999681 0.0252628i \(-0.991958\pi\)
0.999681 0.0252628i \(-0.00804226\pi\)
\(12\) 344676. 1.38517
\(13\) 545367.i 1.46883i 0.678700 + 0.734416i \(0.262544\pi\)
−0.678700 + 0.734416i \(0.737456\pi\)
\(14\) 329136.i 0.611978i
\(15\) −123227. −0.162274
\(16\) 2.47142e6 2.35693
\(17\) 193046. 0.135962 0.0679808 0.997687i \(-0.478344\pi\)
0.0679808 + 0.997687i \(0.478344\pi\)
\(18\) 1.16126e6i 0.614563i
\(19\) 3.36874e6 1.36050 0.680251 0.732979i \(-0.261871\pi\)
0.680251 + 0.732979i \(0.261871\pi\)
\(20\) −2.15787e6 −0.674333
\(21\) 782679. 0.191640
\(22\) −480079. −0.0931536
\(23\) 5.01255e6i 0.778788i −0.921071 0.389394i \(-0.872684\pi\)
0.921071 0.389394i \(-0.127316\pi\)
\(24\) 1.18593e7i 1.48938i
\(25\) −8.99415e6 −0.921001
\(26\) 3.21756e7 2.70807
\(27\) −2.76145e6 −0.192450
\(28\) 1.37058e7 0.796366
\(29\) 1.17377e7 0.572260 0.286130 0.958191i \(-0.407631\pi\)
0.286130 + 0.958191i \(0.407631\pi\)
\(30\) 7.27014e6i 0.299183i
\(31\) 3.31260e7i 1.15707i 0.815657 + 0.578536i \(0.196376\pi\)
−0.815657 + 0.578536i \(0.803624\pi\)
\(32\) 5.92495e7i 1.76577i
\(33\) 1.14162e6i 0.0291710i
\(34\) 1.13893e7i 0.250671i
\(35\) −4.90002e6 −0.0932948
\(36\) −4.83567e7 −0.799731
\(37\) 6.48748e7i 0.935550i −0.883848 0.467775i \(-0.845056\pi\)
0.883848 0.467775i \(-0.154944\pi\)
\(38\) 1.98749e8i 2.50835i
\(39\) 7.65128e7i 0.848030i
\(40\) 7.42463e7i 0.725061i
\(41\) −4.00314e7 −0.345526 −0.172763 0.984963i \(-0.555270\pi\)
−0.172763 + 0.984963i \(0.555270\pi\)
\(42\) 4.61766e7i 0.353326i
\(43\) 2.00048e8i 1.36079i −0.732845 0.680396i \(-0.761808\pi\)
0.732845 0.680396i \(-0.238192\pi\)
\(44\) 1.99913e7i 0.121221i
\(45\) 1.72882e7 0.0936889
\(46\) −2.95731e8 −1.43584
\(47\) 1.47000e8i 0.640955i −0.947256 0.320478i \(-0.896157\pi\)
0.947256 0.320478i \(-0.103843\pi\)
\(48\) −3.46731e8 −1.36077
\(49\) −2.51353e8 −0.889822
\(50\) 5.30638e8i 1.69804i
\(51\) −2.70836e7 −0.0784974
\(52\) 1.33984e9i 3.52401i
\(53\) 4.79174e7 0.114581 0.0572907 0.998358i \(-0.481754\pi\)
0.0572907 + 0.998358i \(0.481754\pi\)
\(54\) 1.62920e8i 0.354818i
\(55\) 7.14718e6i 0.0142011i
\(56\) 4.71578e8i 0.856275i
\(57\) −4.72621e8 −0.785487
\(58\) 6.92502e8i 1.05507i
\(59\) 1.12376e8 + 7.06037e8i 0.157186 + 0.987569i
\(60\) 3.02740e8 0.389326
\(61\) 5.55854e8i 0.658130i −0.944307 0.329065i \(-0.893266\pi\)
0.944307 0.329065i \(-0.106734\pi\)
\(62\) 1.95437e9 2.13328
\(63\) −1.09807e8 −0.110644
\(64\) −9.64871e8 −0.898606
\(65\) 4.79014e8i 0.412840i
\(66\) 6.73533e7 0.0537823
\(67\) 8.19852e8i 0.607241i −0.952793 0.303621i \(-0.901804\pi\)
0.952793 0.303621i \(-0.0981955\pi\)
\(68\) −4.74270e8 −0.326198
\(69\) 7.03241e8i 0.449633i
\(70\) 2.89092e8i 0.172007i
\(71\) 3.33641e8 0.184922 0.0924609 0.995716i \(-0.470527\pi\)
0.0924609 + 0.995716i \(0.470527\pi\)
\(72\) 1.66382e9i 0.859892i
\(73\) 2.91990e9i 1.40849i 0.709958 + 0.704244i \(0.248714\pi\)
−0.709958 + 0.704244i \(0.751286\pi\)
\(74\) −3.82749e9 −1.72486
\(75\) 1.26184e9 0.531740
\(76\) −8.27623e9 −3.26411
\(77\) 4.53956e7i 0.0167710i
\(78\) −4.51411e9 −1.56350
\(79\) −3.70815e9 −1.20510 −0.602548 0.798083i \(-0.705848\pi\)
−0.602548 + 0.798083i \(0.705848\pi\)
\(80\) 2.17073e9 0.662455
\(81\) 3.87420e8 0.111111
\(82\) 2.36177e9i 0.637043i
\(83\) 5.07449e9i 1.28826i 0.764918 + 0.644128i \(0.222780\pi\)
−0.764918 + 0.644128i \(0.777220\pi\)
\(84\) −1.92286e9 −0.459782
\(85\) 1.69559e8 0.0382143
\(86\) −1.18024e10 −2.50888
\(87\) −1.64675e9 −0.330394
\(88\) 6.87845e8 0.130340
\(89\) 1.18443e9i 0.212110i −0.994360 0.106055i \(-0.966178\pi\)
0.994360 0.106055i \(-0.0338219\pi\)
\(90\) 1.01997e9i 0.172733i
\(91\) 3.04247e9i 0.487551i
\(92\) 1.23147e10i 1.86846i
\(93\) 4.64745e9i 0.668036i
\(94\) −8.67271e9 −1.18172
\(95\) 2.95888e9 0.382392
\(96\) 8.31247e9i 1.01947i
\(97\) 1.13463e9i 0.132128i −0.997815 0.0660640i \(-0.978956\pi\)
0.997815 0.0660640i \(-0.0210442\pi\)
\(98\) 1.48293e10i 1.64056i
\(99\) 1.60165e8i 0.0168419i
\(100\) 2.20966e10 2.20966
\(101\) 2.89566e9i 0.275512i −0.990466 0.137756i \(-0.956011\pi\)
0.990466 0.137756i \(-0.0439890\pi\)
\(102\) 1.59788e9i 0.144725i
\(103\) 1.48531e10i 1.28124i −0.767858 0.640621i \(-0.778677\pi\)
0.767858 0.640621i \(-0.221323\pi\)
\(104\) −4.61003e10 −3.78911
\(105\) 6.87454e8 0.0538638
\(106\) 2.82704e9i 0.211253i
\(107\) 1.76146e10 1.25590 0.627948 0.778256i \(-0.283895\pi\)
0.627948 + 0.778256i \(0.283895\pi\)
\(108\) 6.78425e9 0.461725
\(109\) 1.79260e10i 1.16506i −0.812808 0.582532i \(-0.802062\pi\)
0.812808 0.582532i \(-0.197938\pi\)
\(110\) −4.21670e8 −0.0261824
\(111\) 9.10168e9i 0.540140i
\(112\) −1.37875e10 −0.782338
\(113\) 1.41136e10i 0.766030i 0.923742 + 0.383015i \(0.125114\pi\)
−0.923742 + 0.383015i \(0.874886\pi\)
\(114\) 2.78837e10i 1.44819i
\(115\) 4.40269e9i 0.218891i
\(116\) −2.88369e10 −1.37296
\(117\) 1.07345e10i 0.489610i
\(118\) 4.16548e10 6.62996e9i 1.82077 0.289801i
\(119\) −1.07696e9 −0.0451299
\(120\) 1.04165e10i 0.418614i
\(121\) 2.58712e10 0.997447
\(122\) −3.27943e10 −1.21339
\(123\) 5.61624e9 0.199490
\(124\) 8.13830e10i 2.77604i
\(125\) −1.64773e10 −0.539930
\(126\) 6.47839e9i 0.203993i
\(127\) −1.92944e10 −0.584001 −0.292000 0.956418i \(-0.594321\pi\)
−0.292000 + 0.956418i \(0.594321\pi\)
\(128\) 3.74596e9i 0.109022i
\(129\) 2.80660e10i 0.785654i
\(130\) 2.82609e10 0.761148
\(131\) 3.30391e10i 0.856389i −0.903687 0.428195i \(-0.859150\pi\)
0.903687 0.428195i \(-0.140850\pi\)
\(132\) 2.80470e9i 0.0699868i
\(133\) −1.87934e10 −0.451593
\(134\) −4.83697e10 −1.11956
\(135\) −2.42547e9 −0.0540913
\(136\) 1.63183e10i 0.350737i
\(137\) −1.61857e10 −0.335373 −0.167687 0.985840i \(-0.553630\pi\)
−0.167687 + 0.985840i \(0.553630\pi\)
\(138\) 4.14899e10 0.828985
\(139\) 3.74958e10 0.722618 0.361309 0.932446i \(-0.382330\pi\)
0.361309 + 0.932446i \(0.382330\pi\)
\(140\) 1.20382e10 0.223832
\(141\) 2.06235e10i 0.370056i
\(142\) 1.96842e10i 0.340939i
\(143\) 4.43776e9 0.0742136
\(144\) 4.86450e10 0.785643
\(145\) 1.03096e10 0.160843
\(146\) 1.72268e11 2.59682
\(147\) 3.52638e10 0.513739
\(148\) 1.59383e11i 2.24456i
\(149\) 7.52577e10i 1.02475i 0.858761 + 0.512377i \(0.171235\pi\)
−0.858761 + 0.512377i \(0.828765\pi\)
\(150\) 7.44464e10i 0.980364i
\(151\) 2.90345e10i 0.369853i 0.982752 + 0.184926i \(0.0592047\pi\)
−0.982752 + 0.184926i \(0.940795\pi\)
\(152\) 2.84762e11i 3.50966i
\(153\) 3.79972e9 0.0453205
\(154\) 2.67825e9 0.0309206
\(155\) 2.90957e10i 0.325214i
\(156\) 1.87975e11i 2.03459i
\(157\) 6.67856e10i 0.700140i −0.936724 0.350070i \(-0.886158\pi\)
0.936724 0.350070i \(-0.113842\pi\)
\(158\) 2.18774e11i 2.22182i
\(159\) −6.72263e9 −0.0661536
\(160\) 5.20408e10i 0.496300i
\(161\) 2.79638e10i 0.258504i
\(162\) 2.28571e10i 0.204854i
\(163\) 7.80950e10 0.678711 0.339356 0.940658i \(-0.389791\pi\)
0.339356 + 0.940658i \(0.389791\pi\)
\(164\) 9.83479e10 0.828984
\(165\) 1.00272e9i 0.00819900i
\(166\) 2.99385e11 2.37514
\(167\) 5.27454e10 0.406071 0.203035 0.979171i \(-0.434919\pi\)
0.203035 + 0.979171i \(0.434919\pi\)
\(168\) 6.61605e10i 0.494370i
\(169\) −1.59566e11 −1.15747
\(170\) 1.00036e10i 0.0704553i
\(171\) 6.63069e10 0.453501
\(172\) 4.91472e11i 3.26480i
\(173\) 1.11742e11i 0.721085i −0.932743 0.360542i \(-0.882592\pi\)
0.932743 0.360542i \(-0.117408\pi\)
\(174\) 9.71553e10i 0.609145i
\(175\) 5.01763e10 0.305709
\(176\) 2.01105e10i 0.119085i
\(177\) −1.57659e10 9.90543e10i −0.0907511 0.570173i
\(178\) −6.98793e10 −0.391065
\(179\) 3.34656e11i 1.82110i −0.413403 0.910548i \(-0.635660\pi\)
0.413403 0.910548i \(-0.364340\pi\)
\(180\) −4.24733e10 −0.224778
\(181\) −3.32967e11 −1.71399 −0.856996 0.515324i \(-0.827672\pi\)
−0.856996 + 0.515324i \(0.827672\pi\)
\(182\) −1.79500e11 −0.898892
\(183\) 7.79842e10i 0.379972i
\(184\) 4.23715e11 2.00902
\(185\) 5.69817e10i 0.262952i
\(186\) −2.74190e11 −1.23165
\(187\) 1.57085e9i 0.00686954i
\(188\) 3.61145e11i 1.53777i
\(189\) 1.54055e10 0.0638802
\(190\) 1.74568e11i 0.705013i
\(191\) 4.09885e11i 1.61248i 0.591587 + 0.806241i \(0.298502\pi\)
−0.591587 + 0.806241i \(0.701498\pi\)
\(192\) 1.35368e11 0.518810
\(193\) −2.89215e11 −1.08002 −0.540012 0.841657i \(-0.681580\pi\)
−0.540012 + 0.841657i \(0.681580\pi\)
\(194\) −6.69409e10 −0.243603
\(195\) 6.72038e10i 0.238353i
\(196\) 6.17516e11 2.13485
\(197\) −3.80310e9 −0.0128176 −0.00640880 0.999979i \(-0.502040\pi\)
−0.00640880 + 0.999979i \(0.502040\pi\)
\(198\) −9.44940e9 −0.0310512
\(199\) −1.29787e11 −0.415879 −0.207939 0.978142i \(-0.566676\pi\)
−0.207939 + 0.978142i \(0.566676\pi\)
\(200\) 7.60283e11i 2.37589i
\(201\) 1.15022e11i 0.350591i
\(202\) −1.70838e11 −0.507959
\(203\) −6.54819e10 −0.189951
\(204\) 6.65382e10 0.188330
\(205\) −3.51609e10 −0.0971159
\(206\) −8.76304e11 −2.36221
\(207\) 9.86620e10i 0.259596i
\(208\) 1.34783e12i 3.46193i
\(209\) 2.74121e10i 0.0687403i
\(210\) 4.05584e10i 0.0993081i
\(211\) 6.14086e11i 1.46831i 0.678984 + 0.734153i \(0.262421\pi\)
−0.678984 + 0.734153i \(0.737579\pi\)
\(212\) −1.17722e11 −0.274903
\(213\) −4.68086e10 −0.106765
\(214\) 1.03923e12i 2.31548i
\(215\) 1.75709e11i 0.382474i
\(216\) 2.33428e11i 0.496459i
\(217\) 1.84802e11i 0.384068i
\(218\) −1.05760e12 −2.14802
\(219\) 4.09650e11i 0.813191i
\(220\) 1.75590e10i 0.0340711i
\(221\) 1.05281e11i 0.199705i
\(222\) 5.36981e11 0.995851
\(223\) −3.91815e11 −0.710487 −0.355244 0.934774i \(-0.615602\pi\)
−0.355244 + 0.934774i \(0.615602\pi\)
\(224\) 3.30539e11i 0.586115i
\(225\) −1.77032e11 −0.307000
\(226\) 8.32675e11 1.41232
\(227\) 8.46193e10i 0.140391i −0.997533 0.0701956i \(-0.977638\pi\)
0.997533 0.0701956i \(-0.0223624\pi\)
\(228\) 1.16112e12 1.88453
\(229\) 4.23162e11i 0.671938i −0.941873 0.335969i \(-0.890936\pi\)
0.941873 0.335969i \(-0.109064\pi\)
\(230\) −2.59750e11 −0.403568
\(231\) 6.36882e9i 0.00968276i
\(232\) 9.92198e11i 1.47624i
\(233\) 1.16336e11i 0.169408i −0.996406 0.0847038i \(-0.973006\pi\)
0.996406 0.0847038i \(-0.0269944\pi\)
\(234\) 6.33312e11 0.902690
\(235\) 1.29115e11i 0.180151i
\(236\) −2.76082e11 1.73457e12i −0.377118 2.36937i
\(237\) 5.20239e11 0.695762
\(238\) 6.35385e10i 0.0832055i
\(239\) −5.97628e11 −0.766376 −0.383188 0.923670i \(-0.625174\pi\)
−0.383188 + 0.923670i \(0.625174\pi\)
\(240\) −3.04545e11 −0.382468
\(241\) 8.42531e11 1.03634 0.518168 0.855279i \(-0.326614\pi\)
0.518168 + 0.855279i \(0.326614\pi\)
\(242\) 1.52635e12i 1.83898i
\(243\) −5.43536e10 −0.0641500
\(244\) 1.36561e12i 1.57898i
\(245\) −2.20771e11 −0.250099
\(246\) 3.31348e11i 0.367797i
\(247\) 1.83720e12i 1.99835i
\(248\) −2.80017e12 −2.98487
\(249\) 7.11931e11i 0.743775i
\(250\) 9.72132e11i 0.995463i
\(251\) −1.56342e12 −1.56930 −0.784651 0.619937i \(-0.787158\pi\)
−0.784651 + 0.619937i \(0.787158\pi\)
\(252\) 2.69770e11 0.265455
\(253\) −4.07881e10 −0.0393488
\(254\) 1.13833e12i 1.07672i
\(255\) −2.37884e10 −0.0220630
\(256\) −1.20903e12 −1.09961
\(257\) −1.50581e12 −1.34309 −0.671545 0.740963i \(-0.734369\pi\)
−0.671545 + 0.740963i \(0.734369\pi\)
\(258\) 1.65584e12 1.44850
\(259\) 3.61921e11i 0.310538i
\(260\) 1.17683e12i 0.990482i
\(261\) 2.31033e11 0.190753
\(262\) −1.94924e12 −1.57892
\(263\) −1.97250e12 −1.56761 −0.783806 0.621005i \(-0.786725\pi\)
−0.783806 + 0.621005i \(0.786725\pi\)
\(264\) −9.65019e10 −0.0752517
\(265\) 4.20875e10 0.0322050
\(266\) 1.10877e12i 0.832598i
\(267\) 1.66171e11i 0.122462i
\(268\) 2.01419e12i 1.45689i
\(269\) 1.72362e11i 0.122372i −0.998126 0.0611858i \(-0.980512\pi\)
0.998126 0.0611858i \(-0.0194882\pi\)
\(270\) 1.43098e11i 0.0997276i
\(271\) 6.13704e11 0.419868 0.209934 0.977716i \(-0.432675\pi\)
0.209934 + 0.977716i \(0.432675\pi\)
\(272\) 4.77098e11 0.320452
\(273\) 4.26847e11i 0.281488i
\(274\) 9.54924e11i 0.618324i
\(275\) 7.31873e10i 0.0465342i
\(276\) 1.72770e12i 1.07876i
\(277\) −1.33413e12 −0.818085 −0.409042 0.912515i \(-0.634137\pi\)
−0.409042 + 0.912515i \(0.634137\pi\)
\(278\) 2.21218e12i 1.33228i
\(279\) 6.52019e11i 0.385691i
\(280\) 4.14203e11i 0.240670i
\(281\) −6.02278e11 −0.343768 −0.171884 0.985117i \(-0.554985\pi\)
−0.171884 + 0.985117i \(0.554985\pi\)
\(282\) 1.21675e12 0.682268
\(283\) 4.75465e10i 0.0261931i −0.999914 0.0130965i \(-0.995831\pi\)
0.999914 0.0130965i \(-0.00416887\pi\)
\(284\) −8.19681e11 −0.443663
\(285\) −4.15119e11 −0.220774
\(286\) 2.61819e11i 0.136827i
\(287\) 2.23326e11 0.114691
\(288\) 1.16621e12i 0.588591i
\(289\) −1.97873e12 −0.981514
\(290\) 6.08248e11i 0.296545i
\(291\) 1.59184e11i 0.0762842i
\(292\) 7.17352e12i 3.37923i
\(293\) −2.20283e12 −1.02010 −0.510050 0.860145i \(-0.670373\pi\)
−0.510050 + 0.860145i \(0.670373\pi\)
\(294\) 2.08050e12i 0.947175i
\(295\) 9.87035e10 + 6.20136e11i 0.0441797 + 0.277573i
\(296\) 5.48392e12 2.41342
\(297\) 2.24705e10i 0.00972366i
\(298\) 4.44006e12 1.88933
\(299\) 2.73368e12 1.14391
\(300\) −3.10007e12 −1.27575
\(301\) 1.11602e12i 0.451689i
\(302\) 1.71298e12 0.681894
\(303\) 4.06250e11i 0.159067i
\(304\) 8.32557e12 3.20661
\(305\) 4.88226e11i 0.184979i
\(306\) 2.24176e11i 0.0835570i
\(307\) 3.22845e12 1.18387 0.591933 0.805987i \(-0.298365\pi\)
0.591933 + 0.805987i \(0.298365\pi\)
\(308\) 1.11527e11i 0.0402369i
\(309\) 2.08383e12i 0.739725i
\(310\) 1.71659e12 0.599595
\(311\) 8.05238e11 0.276772 0.138386 0.990378i \(-0.455809\pi\)
0.138386 + 0.990378i \(0.455809\pi\)
\(312\) 6.46769e12 2.18764
\(313\) 1.45199e12i 0.483330i −0.970360 0.241665i \(-0.922307\pi\)
0.970360 0.241665i \(-0.0776934\pi\)
\(314\) −3.94022e12 −1.29084
\(315\) −9.64471e10 −0.0310983
\(316\) 9.11007e12 2.89126
\(317\) 2.50893e12 0.783775 0.391888 0.920013i \(-0.371822\pi\)
0.391888 + 0.920013i \(0.371822\pi\)
\(318\) 3.96622e11i 0.121967i
\(319\) 9.55121e10i 0.0289138i
\(320\) −8.47478e11 −0.252568
\(321\) −2.47126e12 −0.725091
\(322\) 1.64981e12 0.476601
\(323\) 6.50322e11 0.184976
\(324\) −9.51804e11 −0.266577
\(325\) 4.90511e12i 1.35280i
\(326\) 4.60745e12i 1.25133i
\(327\) 2.51494e12i 0.672650i
\(328\) 3.38388e12i 0.891346i
\(329\) 8.20078e11i 0.212753i
\(330\) 5.91586e10 0.0151164
\(331\) −7.32593e12 −1.84384 −0.921919 0.387382i \(-0.873379\pi\)
−0.921919 + 0.387382i \(0.873379\pi\)
\(332\) 1.24669e13i 3.09077i
\(333\) 1.27693e12i 0.311850i
\(334\) 3.11187e12i 0.748669i
\(335\) 7.20103e11i 0.170675i
\(336\) 1.93433e12 0.451683
\(337\) 1.61710e12i 0.372038i −0.982546 0.186019i \(-0.940441\pi\)
0.982546 0.186019i \(-0.0595586\pi\)
\(338\) 9.41412e12i 2.13401i
\(339\) 1.98008e12i 0.442267i
\(340\) −4.16567e11 −0.0916834
\(341\) 2.69553e11 0.0584618
\(342\) 3.91198e12i 0.836115i
\(343\) 2.97810e12 0.627291
\(344\) 1.69102e13 3.51040
\(345\) 6.17680e11i 0.126377i
\(346\) −6.59257e12 −1.32946
\(347\) 5.66931e12i 1.12689i −0.826152 0.563447i \(-0.809475\pi\)
0.826152 0.563447i \(-0.190525\pi\)
\(348\) 4.04570e12 0.792679
\(349\) 2.94604e12i 0.568998i −0.958676 0.284499i \(-0.908173\pi\)
0.958676 0.284499i \(-0.0918273\pi\)
\(350\) 2.96030e12i 0.563633i
\(351\) 1.50600e12i 0.282677i
\(352\) −4.82125e11 −0.0892168
\(353\) 3.12828e12i 0.570732i −0.958419 0.285366i \(-0.907885\pi\)
0.958419 0.285366i \(-0.0921152\pi\)
\(354\) −5.84401e12 + 9.30157e11i −1.05122 + 0.167317i
\(355\) 2.93049e11 0.0519754
\(356\) 2.90988e12i 0.508892i
\(357\) 1.51093e11 0.0260557
\(358\) −1.97440e13 −3.35754
\(359\) −1.08107e13 −1.81293 −0.906465 0.422281i \(-0.861229\pi\)
−0.906465 + 0.422281i \(0.861229\pi\)
\(360\) 1.46139e12i 0.241687i
\(361\) 5.21734e12 0.850968
\(362\) 1.96444e13i 3.16007i
\(363\) −3.62963e12 −0.575876
\(364\) 7.47467e12i 1.16973i
\(365\) 2.56464e12i 0.395879i
\(366\) 4.60092e12 0.700550
\(367\) 1.20760e11i 0.0181381i 0.999959 + 0.00906904i \(0.00288680\pi\)
−0.999959 + 0.00906904i \(0.997113\pi\)
\(368\) 1.23881e13i 1.83555i
\(369\) −7.87937e11 −0.115175
\(370\) −3.36181e12 −0.484802
\(371\) −2.67320e11 −0.0380331
\(372\) 1.14177e13i 1.60275i
\(373\) −1.97848e12 −0.274024 −0.137012 0.990569i \(-0.543750\pi\)
−0.137012 + 0.990569i \(0.543750\pi\)
\(374\) −9.26774e10 −0.0126653
\(375\) 2.31171e12 0.311729
\(376\) 1.24260e13 1.65346
\(377\) 6.40135e12i 0.840553i
\(378\) 9.08893e11i 0.117775i
\(379\) −1.30205e12 −0.166506 −0.0832530 0.996528i \(-0.526531\pi\)
−0.0832530 + 0.996528i \(0.526531\pi\)
\(380\) −7.26929e12 −0.917432
\(381\) 2.70693e12 0.337173
\(382\) 2.41824e13 2.97292
\(383\) −9.48784e12 −1.15126 −0.575630 0.817710i \(-0.695243\pi\)
−0.575630 + 0.817710i \(0.695243\pi\)
\(384\) 5.25544e11i 0.0629438i
\(385\) 3.98724e10i 0.00471378i
\(386\) 1.70631e13i 1.99123i
\(387\) 3.93754e12i 0.453597i
\(388\) 2.78752e12i 0.317001i
\(389\) −4.80814e12 −0.539795 −0.269898 0.962889i \(-0.586990\pi\)
−0.269898 + 0.962889i \(0.586990\pi\)
\(390\) −3.96490e12 −0.439449
\(391\) 9.67652e11i 0.105885i
\(392\) 2.12470e13i 2.29545i
\(393\) 4.63525e12i 0.494437i
\(394\) 2.24376e11i 0.0236317i
\(395\) −3.25699e12 −0.338712
\(396\) 3.93488e11i 0.0404069i
\(397\) 7.74867e12i 0.785732i −0.919596 0.392866i \(-0.871484\pi\)
0.919596 0.392866i \(-0.128516\pi\)
\(398\) 7.65720e12i 0.766752i
\(399\) 2.63664e12 0.260727
\(400\) −2.22283e13 −2.17074
\(401\) 1.99175e11i 0.0192094i 0.999954 + 0.00960469i \(0.00305732\pi\)
−0.999954 + 0.00960469i \(0.996943\pi\)
\(402\) 6.78608e12 0.646381
\(403\) −1.80658e13 −1.69954
\(404\) 7.11398e12i 0.661006i
\(405\) 3.40284e11 0.0312296
\(406\) 3.86331e12i 0.350210i
\(407\) −5.27899e11 −0.0472693
\(408\) 2.28940e12i 0.202498i
\(409\) 3.39310e12i 0.296469i −0.988952 0.148235i \(-0.952641\pi\)
0.988952 0.148235i \(-0.0473591\pi\)
\(410\) 2.07442e12i 0.179052i
\(411\) 2.27079e12 0.193628
\(412\) 3.64907e13i 3.07394i
\(413\) −6.26918e11 3.93882e12i −0.0521748 0.327805i
\(414\) −5.82087e12 −0.478615
\(415\) 4.45710e12i 0.362086i
\(416\) 3.23127e13 2.59362
\(417\) −5.26052e12 −0.417204
\(418\) −1.61726e12 −0.126736
\(419\) 7.11612e12i 0.551028i 0.961297 + 0.275514i \(0.0888480\pi\)
−0.961297 + 0.275514i \(0.911152\pi\)
\(420\) −1.68892e12 −0.129230
\(421\) 1.08044e13i 0.816937i −0.912772 0.408469i \(-0.866063\pi\)
0.912772 0.408469i \(-0.133937\pi\)
\(422\) 3.62299e13 2.70710
\(423\) 2.89340e12i 0.213652i
\(424\) 4.05050e12i 0.295583i
\(425\) −1.73629e12 −0.125221
\(426\) 2.76162e12i 0.196841i
\(427\) 3.10098e12i 0.218454i
\(428\) −4.32750e13 −3.01313
\(429\) −6.22601e11 −0.0428473
\(430\) −1.03665e13 −0.705163
\(431\) 1.42715e13i 0.959586i −0.877382 0.479793i \(-0.840712\pi\)
0.877382 0.479793i \(-0.159288\pi\)
\(432\) −6.82470e12 −0.453591
\(433\) 2.64948e10 0.00174069 0.000870344 1.00000i \(-0.499723\pi\)
0.000870344 1.00000i \(0.499723\pi\)
\(434\) −1.09030e13 −0.708102
\(435\) −1.44640e12 −0.0928629
\(436\) 4.40400e13i 2.79521i
\(437\) 1.68860e13i 1.05954i
\(438\) −2.41686e13 −1.49927
\(439\) −1.87522e13 −1.15008 −0.575042 0.818124i \(-0.695014\pi\)
−0.575042 + 0.818124i \(0.695014\pi\)
\(440\) 6.04157e11 0.0366342
\(441\) −4.94737e12 −0.296607
\(442\) 6.21137e12 0.368193
\(443\) 1.85113e13i 1.08497i −0.840064 0.542487i \(-0.817483\pi\)
0.840064 0.542487i \(-0.182517\pi\)
\(444\) 2.23607e13i 1.29590i
\(445\) 1.04033e12i 0.0596170i
\(446\) 2.31163e13i 1.30992i
\(447\) 1.05584e13i 0.591642i
\(448\) 5.38279e12 0.298275
\(449\) −1.42119e13 −0.778788 −0.389394 0.921071i \(-0.627316\pi\)
−0.389394 + 0.921071i \(0.627316\pi\)
\(450\) 1.04445e13i 0.566014i
\(451\) 3.25743e11i 0.0174579i
\(452\) 3.46739e13i 1.83785i
\(453\) 4.07342e12i 0.213535i
\(454\) −4.99238e12 −0.258838
\(455\) 2.67231e12i 0.137034i
\(456\) 3.99510e13i 2.02630i
\(457\) 1.91190e13i 0.959146i −0.877502 0.479573i \(-0.840792\pi\)
0.877502 0.479573i \(-0.159208\pi\)
\(458\) −2.49658e13 −1.23885
\(459\) −5.33087e11 −0.0261658
\(460\) 1.08164e13i 0.525163i
\(461\) 2.60561e13 1.25143 0.625713 0.780053i \(-0.284808\pi\)
0.625713 + 0.780053i \(0.284808\pi\)
\(462\) −3.75748e11 −0.0178520
\(463\) 1.34310e13i 0.631253i 0.948884 + 0.315626i \(0.102215\pi\)
−0.948884 + 0.315626i \(0.897785\pi\)
\(464\) 2.90088e13 1.34878
\(465\) 4.08201e12i 0.187763i
\(466\) −6.86357e12 −0.312335
\(467\) 2.92825e12i 0.131833i 0.997825 + 0.0659164i \(0.0209971\pi\)
−0.997825 + 0.0659164i \(0.979003\pi\)
\(468\) 2.63721e13i 1.17467i
\(469\) 4.57376e12i 0.201562i
\(470\) −7.61753e12 −0.332143
\(471\) 9.36976e12i 0.404226i
\(472\) −5.96819e13 + 9.49922e12i −2.54761 + 0.405488i
\(473\) −1.62783e12 −0.0687549
\(474\) 3.06931e13i 1.28277i
\(475\) −3.02990e13 −1.25303
\(476\) 2.64584e12 0.108275
\(477\) 9.43159e11 0.0381938
\(478\) 3.52589e13i 1.41296i
\(479\) 1.37810e13 0.546515 0.273258 0.961941i \(-0.411899\pi\)
0.273258 + 0.961941i \(0.411899\pi\)
\(480\) 7.30112e12i 0.286539i
\(481\) 3.53805e13 1.37417
\(482\) 4.97077e13i 1.91068i
\(483\) 3.92322e12i 0.149247i
\(484\) −6.35597e13 −2.39307
\(485\) 9.96583e11i 0.0371368i
\(486\) 3.20676e12i 0.118273i
\(487\) −1.30167e13 −0.475178 −0.237589 0.971366i \(-0.576357\pi\)
−0.237589 + 0.971366i \(0.576357\pi\)
\(488\) 4.69868e13 1.69776
\(489\) −1.09564e13 −0.391854
\(490\) 1.30251e13i 0.461106i
\(491\) 4.71076e13 1.65076 0.825380 0.564578i \(-0.190961\pi\)
0.825380 + 0.564578i \(0.190961\pi\)
\(492\) −1.37978e13 −0.478614
\(493\) 2.26592e12 0.0778053
\(494\) 1.08391e14 3.68434
\(495\) 1.40678e11i 0.00473369i
\(496\) 8.18682e13i 2.72714i
\(497\) −1.86131e12 −0.0613813
\(498\) −4.20026e13 −1.37129
\(499\) −7.09676e12 −0.229381 −0.114691 0.993401i \(-0.536588\pi\)
−0.114691 + 0.993401i \(0.536588\pi\)
\(500\) 4.04811e13 1.29540
\(501\) −7.39997e12 −0.234445
\(502\) 9.22387e13i 2.89331i
\(503\) 3.49998e13i 1.08699i 0.839413 + 0.543495i \(0.182899\pi\)
−0.839413 + 0.543495i \(0.817101\pi\)
\(504\) 9.28206e12i 0.285425i
\(505\) 2.54336e12i 0.0774373i
\(506\) 2.40642e12i 0.0725469i
\(507\) 2.23866e13 0.668263
\(508\) 4.74020e13 1.40113
\(509\) 2.08317e13i 0.609728i −0.952396 0.304864i \(-0.901389\pi\)
0.952396 0.304864i \(-0.0986111\pi\)
\(510\) 1.40347e12i 0.0406774i
\(511\) 1.62894e13i 0.467521i
\(512\) 6.74947e13i 1.91831i
\(513\) −9.30260e12 −0.261829
\(514\) 8.88400e13i 2.47624i
\(515\) 1.30460e13i 0.360114i
\(516\) 6.89517e13i 1.88493i
\(517\) −1.19617e12 −0.0323847
\(518\) 2.13526e13 0.572536
\(519\) 1.56770e13i 0.416319i
\(520\) −4.04915e13 −1.06499
\(521\) 3.85247e13 1.00358 0.501789 0.864990i \(-0.332676\pi\)
0.501789 + 0.864990i \(0.332676\pi\)
\(522\) 1.36305e13i 0.351690i
\(523\) 4.12615e12 0.105448 0.0527238 0.998609i \(-0.483210\pi\)
0.0527238 + 0.998609i \(0.483210\pi\)
\(524\) 8.11695e13i 2.05464i
\(525\) −7.03954e12 −0.176501
\(526\) 1.16374e14i 2.89019i
\(527\) 6.39484e12i 0.157317i
\(528\) 2.82142e12i 0.0687540i
\(529\) 1.63009e13 0.393489
\(530\) 2.48308e12i 0.0593761i
\(531\) 2.21189e12 + 1.38969e13i 0.0523952 + 0.329190i
\(532\) 4.61711e13 1.08346
\(533\) 2.18318e13i 0.507520i
\(534\) 9.80380e12 0.225781
\(535\) 1.54715e13 0.352990
\(536\) 6.93027e13 1.56649
\(537\) 4.69509e13i 1.05141i
\(538\) −1.01690e13 −0.225615
\(539\) 2.04531e12i 0.0449588i
\(540\) 5.95884e12 0.129775
\(541\) 5.42521e13i 1.17066i −0.810796 0.585329i \(-0.800965\pi\)
0.810796 0.585329i \(-0.199035\pi\)
\(542\) 3.62073e13i 0.774105i
\(543\) 4.67140e13 0.989573
\(544\) 1.14379e13i 0.240077i
\(545\) 1.57450e13i 0.327461i
\(546\) 2.51832e13 0.518976
\(547\) −3.18411e13 −0.650207 −0.325104 0.945678i \(-0.605399\pi\)
−0.325104 + 0.945678i \(0.605399\pi\)
\(548\) 3.97645e13 0.804624
\(549\) 1.09409e13i 0.219377i
\(550\) 4.31791e12 0.0857946
\(551\) 3.95413e13 0.778561
\(552\) −5.94455e13 −1.15991
\(553\) 2.06869e13 0.400009
\(554\) 7.87109e13i 1.50829i
\(555\) 7.99431e12i 0.151815i
\(556\) −9.21187e13 −1.73370
\(557\) −1.04334e14 −1.94603 −0.973017 0.230734i \(-0.925887\pi\)
−0.973017 + 0.230734i \(0.925887\pi\)
\(558\) 3.84678e13 0.711094
\(559\) 1.09100e14 1.99877
\(560\) −1.21100e13 −0.219889
\(561\) 2.20385e11i 0.00396613i
\(562\) 3.55332e13i 0.633801i
\(563\) 5.93567e13i 1.04937i −0.851297 0.524684i \(-0.824184\pi\)
0.851297 0.524684i \(-0.175816\pi\)
\(564\) 5.06673e13i 0.887834i
\(565\) 1.23965e13i 0.215306i
\(566\) −2.80515e12 −0.0482919
\(567\) −2.16133e12 −0.0368812
\(568\) 2.82030e13i 0.477038i
\(569\) 3.20243e12i 0.0536931i 0.999640 + 0.0268465i \(0.00854654\pi\)
−0.999640 + 0.0268465i \(0.991453\pi\)
\(570\) 2.44912e13i 0.407039i
\(571\) 7.95421e13i 1.31044i −0.755439 0.655219i \(-0.772576\pi\)
0.755439 0.655219i \(-0.227424\pi\)
\(572\) −1.09026e13 −0.178053
\(573\) 5.75053e13i 0.930967i
\(574\) 1.31758e13i 0.211454i
\(575\) 4.50836e13i 0.717265i
\(576\) −1.89915e13 −0.299535
\(577\) 9.22842e13 1.44294 0.721470 0.692446i \(-0.243467\pi\)
0.721470 + 0.692446i \(0.243467\pi\)
\(578\) 1.16741e14i 1.80961i
\(579\) 4.05757e13 0.623553
\(580\) −2.53284e13 −0.385894
\(581\) 2.83094e13i 0.427612i
\(582\) 9.39155e12 0.140644
\(583\) 3.89914e11i 0.00578930i
\(584\) −2.46821e14 −3.63344
\(585\) 9.42843e12i 0.137613i
\(586\) 1.29963e14i 1.88075i
\(587\) 7.51498e13i 1.07830i 0.842211 + 0.539148i \(0.181253\pi\)
−0.842211 + 0.539148i \(0.818747\pi\)
\(588\) −8.66351e13 −1.23256
\(589\) 1.11593e14i 1.57420i
\(590\) 3.65868e13 5.82331e12i 0.511758 0.0814536i
\(591\) 5.33560e11 0.00740024
\(592\) 1.60333e14i 2.20503i
\(593\) −1.12517e14 −1.53442 −0.767211 0.641394i \(-0.778356\pi\)
−0.767211 + 0.641394i \(0.778356\pi\)
\(594\) 1.32571e12 0.0179274
\(595\) −9.45929e11 −0.0126845
\(596\) 1.84891e14i 2.45858i
\(597\) 1.82087e13 0.240108
\(598\) 1.61282e14i 2.10901i
\(599\) −9.96471e13 −1.29220 −0.646101 0.763252i \(-0.723602\pi\)
−0.646101 + 0.763252i \(0.723602\pi\)
\(600\) 1.06665e14i 1.37172i
\(601\) 3.86261e12i 0.0492616i 0.999697 + 0.0246308i \(0.00784102\pi\)
−0.999697 + 0.0246308i \(0.992159\pi\)
\(602\) 6.58431e13 0.832775
\(603\) 1.61371e13i 0.202414i
\(604\) 7.13311e13i 0.887348i
\(605\) 2.27236e13 0.280349
\(606\) 2.39680e13 0.293270
\(607\) 1.06519e14 1.29266 0.646331 0.763057i \(-0.276303\pi\)
0.646331 + 0.763057i \(0.276303\pi\)
\(608\) 1.99596e14i 2.40234i
\(609\) 9.18686e12 0.109668
\(610\) −2.88044e13 −0.341043
\(611\) 8.01688e13 0.941455
\(612\) −9.33506e12 −0.108733
\(613\) 9.28471e13i 1.07267i −0.844005 0.536335i \(-0.819808\pi\)
0.844005 0.536335i \(-0.180192\pi\)
\(614\) 1.90473e14i 2.18268i
\(615\) 4.93294e12 0.0560699
\(616\) −3.83732e12 −0.0432638
\(617\) 1.55222e14 1.73591 0.867953 0.496646i \(-0.165435\pi\)
0.867953 + 0.496646i \(0.165435\pi\)
\(618\) 1.22942e14 1.36382
\(619\) −9.06182e13 −0.997154 −0.498577 0.866845i \(-0.666144\pi\)
−0.498577 + 0.866845i \(0.666144\pi\)
\(620\) 7.14814e13i 0.780252i
\(621\) 1.38419e13i 0.149878i
\(622\) 4.75075e13i 0.510282i
\(623\) 6.60768e12i 0.0704058i
\(624\) 1.89095e14i 1.99875i
\(625\) 7.33609e13 0.769245
\(626\) −8.56649e13 −0.891110
\(627\) 3.84581e12i 0.0396872i
\(628\) 1.64077e14i 1.67977i
\(629\) 1.25238e13i 0.127199i
\(630\) 5.69019e12i 0.0573356i
\(631\) 1.77515e14 1.77455 0.887277 0.461238i \(-0.152595\pi\)
0.887277 + 0.461238i \(0.152595\pi\)
\(632\) 3.13453e14i 3.10876i
\(633\) 8.61538e13i 0.847727i
\(634\) 1.48022e14i 1.44504i
\(635\) −1.69470e13 −0.164143
\(636\) 1.65160e13 0.158715
\(637\) 1.37079e14i 1.30700i
\(638\) −5.63503e12 −0.0533080
\(639\) 6.56706e12 0.0616406
\(640\) 3.29021e12i 0.0306424i
\(641\) −2.06098e14 −1.90451 −0.952256 0.305300i \(-0.901243\pi\)
−0.952256 + 0.305300i \(0.901243\pi\)
\(642\) 1.45799e14i 1.33684i
\(643\) −1.15575e14 −1.05150 −0.525749 0.850640i \(-0.676215\pi\)
−0.525749 + 0.850640i \(0.676215\pi\)
\(644\) 6.87008e13i 0.620201i
\(645\) 2.46513e13i 0.220821i
\(646\) 3.83677e13i 0.341039i
\(647\) 8.52398e13 0.751833 0.375916 0.926654i \(-0.377328\pi\)
0.375916 + 0.926654i \(0.377328\pi\)
\(648\) 3.27490e13i 0.286631i
\(649\) 5.74517e12 9.14425e11i 0.0498976 0.00794190i
\(650\) −2.89392e14 −2.49414
\(651\) 2.59270e13i 0.221742i
\(652\) −1.91862e14 −1.62836
\(653\) −2.95306e13 −0.248718 −0.124359 0.992237i \(-0.539687\pi\)
−0.124359 + 0.992237i \(0.539687\pi\)
\(654\) 1.48377e14 1.24016
\(655\) 2.90193e13i 0.240703i
\(656\) −9.89343e13 −0.814381
\(657\) 5.74723e13i 0.469496i
\(658\) 4.83830e13 0.392250
\(659\) 2.36748e13i 0.190484i −0.995454 0.0952421i \(-0.969637\pi\)
0.995454 0.0952421i \(-0.0303625\pi\)
\(660\) 2.46346e12i 0.0196710i
\(661\) 1.92368e14 1.52450 0.762248 0.647285i \(-0.224096\pi\)
0.762248 + 0.647285i \(0.224096\pi\)
\(662\) 4.32216e14i 3.39947i
\(663\) 1.47705e13i 0.115300i
\(664\) −4.28951e14 −3.32328
\(665\) −1.65069e13 −0.126928
\(666\) −7.53364e13 −0.574955
\(667\) 5.88358e13i 0.445669i
\(668\) −1.29583e14 −0.974242
\(669\) 5.49701e13 0.410200
\(670\) −4.24847e13 −0.314672
\(671\) −4.52310e12 −0.0332524
\(672\) 4.63733e13i 0.338393i
\(673\) 4.95325e13i 0.358769i 0.983779 + 0.179385i \(0.0574106\pi\)
−0.983779 + 0.179385i \(0.942589\pi\)
\(674\) −9.54057e13 −0.685922
\(675\) 2.48369e13 0.177247
\(676\) 3.92019e14 2.77698
\(677\) 1.47697e14 1.03855 0.519277 0.854606i \(-0.326201\pi\)
0.519277 + 0.854606i \(0.326201\pi\)
\(678\) −1.16821e14 −0.815404
\(679\) 6.32983e12i 0.0438574i
\(680\) 1.43329e13i 0.0985805i
\(681\) 1.18718e13i 0.0810549i
\(682\) 1.59031e13i 0.107785i
\(683\) 1.28534e14i 0.864799i 0.901682 + 0.432400i \(0.142333\pi\)
−0.901682 + 0.432400i \(0.857667\pi\)
\(684\) −1.62901e14 −1.08804
\(685\) −1.42164e13 −0.0942622
\(686\) 1.75702e14i 1.15653i
\(687\) 5.93680e13i 0.387944i
\(688\) 4.94403e14i 3.20729i
\(689\) 2.61326e13i 0.168301i
\(690\) 3.64419e13 0.233000
\(691\) 3.89661e12i 0.0247341i 0.999924 + 0.0123671i \(0.00393666\pi\)
−0.999924 + 0.0123671i \(0.996063\pi\)
\(692\) 2.74525e14i 1.73002i
\(693\) 8.93521e11i 0.00559034i
\(694\) −3.34478e14 −2.07764
\(695\) 3.29338e13 0.203104
\(696\) 1.39201e14i 0.852310i
\(697\) −7.72789e12 −0.0469783
\(698\) −1.73810e14 −1.04906
\(699\) 1.63214e13i 0.0978075i
\(700\) −1.23272e14 −0.733455
\(701\) 1.98299e14i 1.17147i −0.810504 0.585733i \(-0.800807\pi\)
0.810504 0.585733i \(-0.199193\pi\)
\(702\) −8.88512e13 −0.521168
\(703\) 2.18546e14i 1.27282i
\(704\) 7.85135e12i 0.0454026i
\(705\) 1.81143e13i 0.104010i
\(706\) −1.84563e14 −1.05225
\(707\) 1.61542e13i 0.0914510i
\(708\) 3.87332e13 + 2.43354e14i 0.217729 + 1.36796i
\(709\) −2.33879e14 −1.30545 −0.652726 0.757594i \(-0.726375\pi\)
−0.652726 + 0.757594i \(0.726375\pi\)
\(710\) 1.72893e13i 0.0958265i
\(711\) −7.29875e13 −0.401699
\(712\) 1.00121e14 0.547175
\(713\) 1.66046e14 0.901114
\(714\) 8.91420e12i 0.0480387i
\(715\) 3.89784e12 0.0208590
\(716\) 8.22172e14i 4.36916i
\(717\) 8.38449e13 0.442467
\(718\) 6.37810e14i 3.34248i
\(719\) 3.09647e14i 1.61147i −0.592277 0.805735i \(-0.701771\pi\)
0.592277 0.805735i \(-0.298229\pi\)
\(720\) 4.27265e13 0.220818
\(721\) 8.28620e13i 0.425284i
\(722\) 3.07813e14i 1.56892i
\(723\) −1.18204e14 −0.598329
\(724\) 8.18025e14 4.11219
\(725\) −1.05571e14 −0.527052
\(726\) 2.14141e14i 1.06174i
\(727\) 1.40474e14 0.691712 0.345856 0.938288i \(-0.387589\pi\)
0.345856 + 0.938288i \(0.387589\pi\)
\(728\) 2.57183e14 1.25772
\(729\) 7.62560e12 0.0370370
\(730\) 1.51309e14 0.729879
\(731\) 3.86185e13i 0.185015i
\(732\) 1.91589e14i 0.911625i
\(733\) 7.94185e13 0.375320 0.187660 0.982234i \(-0.439910\pi\)
0.187660 + 0.982234i \(0.439910\pi\)
\(734\) 7.12458e12 0.0334410
\(735\) 3.09734e13 0.144395
\(736\) −2.96991e14 −1.37516
\(737\) −6.67130e12 −0.0306812
\(738\) 4.64868e13i 0.212348i
\(739\) 3.40946e13i 0.154690i 0.997004 + 0.0773451i \(0.0246443\pi\)
−0.997004 + 0.0773451i \(0.975356\pi\)
\(740\) 1.39991e14i 0.630873i
\(741\) 2.57752e14i 1.15375i
\(742\) 1.57714e13i 0.0701213i
\(743\) 4.85674e13 0.214487 0.107243 0.994233i \(-0.465798\pi\)
0.107243 + 0.994233i \(0.465798\pi\)
\(744\) 3.92852e14 1.72332
\(745\) 6.61014e13i 0.288024i
\(746\) 1.16727e14i 0.505215i
\(747\) 9.98812e13i 0.429419i
\(748\) 3.85923e12i 0.0164814i
\(749\) −9.82676e13 −0.416871
\(750\) 1.36386e14i 0.574731i
\(751\) 3.59154e14i 1.50342i 0.659494 + 0.751710i \(0.270771\pi\)
−0.659494 + 0.751710i \(0.729229\pi\)
\(752\) 3.63298e14i 1.51069i
\(753\) 2.19342e14 0.906037
\(754\) 3.77668e14 1.54972
\(755\) 2.55019e13i 0.103953i
\(756\) −3.78477e13 −0.153261
\(757\) −1.69304e12 −0.00681065 −0.00340532 0.999994i \(-0.501084\pi\)
−0.00340532 + 0.999994i \(0.501084\pi\)
\(758\) 7.68182e13i 0.306986i
\(759\) 5.72241e12 0.0227180
\(760\) 2.50116e14i 0.986448i
\(761\) −2.82739e14 −1.10780 −0.553902 0.832582i \(-0.686862\pi\)
−0.553902 + 0.832582i \(0.686862\pi\)
\(762\) 1.59704e14i 0.621643i
\(763\) 1.00005e14i 0.386721i
\(764\) 1.00699e15i 3.86866i
\(765\) 3.33743e12 0.0127381
\(766\) 5.59764e14i 2.12257i
\(767\) −3.85049e14 + 6.12860e13i −1.45057 + 0.230879i
\(768\) 1.69622e14 0.634859
\(769\) 2.52231e14i 0.937923i 0.883219 + 0.468962i \(0.155372\pi\)
−0.883219 + 0.468962i \(0.844628\pi\)
\(770\) 2.35240e12 0.00869075
\(771\) 2.11260e14 0.775434
\(772\) 7.10535e14 2.59119
\(773\) 3.63335e13i 0.131647i 0.997831 + 0.0658234i \(0.0209674\pi\)
−0.997831 + 0.0658234i \(0.979033\pi\)
\(774\) −2.32308e14 −0.836293
\(775\) 2.97940e14i 1.06566i
\(776\) 9.59111e13 0.340848
\(777\) 5.07761e13i 0.179289i
\(778\) 2.83671e14i 0.995215i
\(779\) −1.34855e14 −0.470089