Properties

Label 177.11.c.a.58.19
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 58.19
Character \(\chi\) \(=\) 177.58
Dual form 177.11.c.a.58.82

$q$-expansion

\(f(q)\) \(=\) \(q-45.0342i q^{2} +140.296 q^{3} -1004.08 q^{4} -5626.54 q^{5} -6318.12i q^{6} -22190.3 q^{7} -897.122i q^{8} +19683.0 q^{9} +O(q^{10})\) \(q-45.0342i q^{2} +140.296 q^{3} -1004.08 q^{4} -5626.54 q^{5} -6318.12i q^{6} -22190.3 q^{7} -897.122i q^{8} +19683.0 q^{9} +253387. i q^{10} -28695.6i q^{11} -140868. q^{12} +405198. i q^{13} +999323. i q^{14} -789382. q^{15} -1.06858e6 q^{16} +193238. q^{17} -886408. i q^{18} -1.39719e6 q^{19} +5.64949e6 q^{20} -3.11321e6 q^{21} -1.29228e6 q^{22} +9.59887e6i q^{23} -125863. i q^{24} +2.18923e7 q^{25} +1.82478e7 q^{26} +2.76145e6 q^{27} +2.22808e7 q^{28} -8.13874e6 q^{29} +3.55492e7i q^{30} +8.53152e6i q^{31} +4.72039e7i q^{32} -4.02588e6i q^{33} -8.70231e6i q^{34} +1.24855e8 q^{35} -1.97633e7 q^{36} -3.75479e7i q^{37} +6.29214e7i q^{38} +5.68477e7i q^{39} +5.04769e6i q^{40} -1.74499e8 q^{41} +1.40201e8i q^{42} -1.52269e8i q^{43} +2.88127e7i q^{44} -1.10747e8 q^{45} +4.32278e8 q^{46} +2.46599e8i q^{47} -1.49917e8 q^{48} +2.09935e8 q^{49} -9.85903e8i q^{50} +2.71105e7 q^{51} -4.06851e8i q^{52} -7.65345e8 q^{53} -1.24360e8i q^{54} +1.61457e8i q^{55} +1.99074e7i q^{56} -1.96020e8 q^{57} +3.66521e8i q^{58} +(-3.15700e8 + 6.41444e8i) q^{59} +7.92602e8 q^{60} +2.67620e8i q^{61} +3.84210e8 q^{62} -4.36772e8 q^{63} +1.03157e9 q^{64} -2.27986e9i q^{65} -1.81302e8 q^{66} -1.82349e9i q^{67} -1.94026e8 q^{68} +1.34668e9i q^{69} -5.62273e9i q^{70} +3.31693e9 q^{71} -1.76580e7i q^{72} -3.54365e9i q^{73} -1.69094e9 q^{74} +3.07141e9 q^{75} +1.40289e9 q^{76} +6.36764e8i q^{77} +2.56009e9 q^{78} -4.35656e9 q^{79} +6.01240e9 q^{80} +3.87420e8 q^{81} +7.85841e9i q^{82} -2.12713e9i q^{83} +3.12591e9 q^{84} -1.08726e9 q^{85} -6.85733e9 q^{86} -1.14183e9 q^{87} -2.57434e7 q^{88} -2.36898e9i q^{89} +4.98741e9i q^{90} -8.99147e9i q^{91} -9.63803e9i q^{92} +1.19694e9i q^{93} +1.11054e10 q^{94} +7.86135e9 q^{95} +6.62253e9i q^{96} -1.02166e9i q^{97} -9.45424e9i q^{98} -5.64815e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + O(q^{10}) \) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + 620136q^{12} + 662904q^{15} + 27925160q^{16} - 2053136q^{17} - 5169828q^{19} - 1076324q^{20} - 1829224q^{22} + 215378180q^{25} - 22082700q^{26} - 102921320q^{28} - 112503588q^{29} - 76491392q^{35} - 1007769600q^{36} + 473464516q^{41} + 1215405588q^{46} - 1676272320q^{48} + 1975297276q^{49} + 733970808q^{51} + 3267506728q^{53} + 591502824q^{57} + 508142200q^{59} + 1264196808q^{60} - 6538206968q^{62} + 362009736q^{63} - 10324137972q^{64} - 2764346616q^{66} + 9997685952q^{68} + 14908523204q^{71} + 4863508712q^{74} + 1890481680q^{75} + 2044437240q^{76} - 758396196q^{78} - 3599839500q^{79} - 23217941144q^{80} + 38742048900q^{81} - 13094894808q^{84} + 23360564412q^{85} + 12186923752q^{86} + 7965322272q^{87} + 32415437996q^{88} - 22098322280q^{94} + 7834510028q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 45.0342i 1.40732i −0.710537 0.703659i \(-0.751548\pi\)
0.710537 0.703659i \(-0.248452\pi\)
\(3\) 140.296 0.577350
\(4\) −1004.08 −0.980546
\(5\) −5626.54 −1.80049 −0.900246 0.435381i \(-0.856614\pi\)
−0.900246 + 0.435381i \(0.856614\pi\)
\(6\) 6318.12i 0.812516i
\(7\) −22190.3 −1.32030 −0.660151 0.751133i \(-0.729508\pi\)
−0.660151 + 0.751133i \(0.729508\pi\)
\(8\) 897.122i 0.0273780i
\(9\) 19683.0 0.333333
\(10\) 253387.i 2.53387i
\(11\) 28695.6i 0.178177i −0.996024 0.0890886i \(-0.971605\pi\)
0.996024 0.0890886i \(-0.0283954\pi\)
\(12\) −140868. −0.566118
\(13\) 405198.i 1.09132i 0.838008 + 0.545658i \(0.183720\pi\)
−0.838008 + 0.545658i \(0.816280\pi\)
\(14\) 999323.i 1.85809i
\(15\) −789382. −1.03951
\(16\) −1.06858e6 −1.01908
\(17\) 193238. 0.136097 0.0680484 0.997682i \(-0.478323\pi\)
0.0680484 + 0.997682i \(0.478323\pi\)
\(18\) 886408.i 0.469106i
\(19\) −1.39719e6 −0.564271 −0.282135 0.959375i \(-0.591043\pi\)
−0.282135 + 0.959375i \(0.591043\pi\)
\(20\) 5.64949e6 1.76547
\(21\) −3.11321e6 −0.762277
\(22\) −1.29228e6 −0.250752
\(23\) 9.59887e6i 1.49136i 0.666307 + 0.745678i \(0.267874\pi\)
−0.666307 + 0.745678i \(0.732126\pi\)
\(24\) 125863.i 0.0158067i
\(25\) 2.18923e7 2.24177
\(26\) 1.82478e7 1.53583
\(27\) 2.76145e6 0.192450
\(28\) 2.22808e7 1.29462
\(29\) −8.13874e6 −0.396796 −0.198398 0.980122i \(-0.563574\pi\)
−0.198398 + 0.980122i \(0.563574\pi\)
\(30\) 3.55492e7i 1.46293i
\(31\) 8.53152e6i 0.298001i 0.988837 + 0.149001i \(0.0476056\pi\)
−0.988837 + 0.149001i \(0.952394\pi\)
\(32\) 4.72039e7i 1.40679i
\(33\) 4.02588e6i 0.102871i
\(34\) 8.70231e6i 0.191531i
\(35\) 1.24855e8 2.37719
\(36\) −1.97633e7 −0.326849
\(37\) 3.75479e7i 0.541473i −0.962653 0.270737i \(-0.912733\pi\)
0.962653 0.270737i \(-0.0872673\pi\)
\(38\) 6.29214e7i 0.794109i
\(39\) 5.68477e7i 0.630071i
\(40\) 5.04769e6i 0.0492939i
\(41\) −1.74499e8 −1.50617 −0.753083 0.657925i \(-0.771434\pi\)
−0.753083 + 0.657925i \(0.771434\pi\)
\(42\) 1.40201e8i 1.07277i
\(43\) 1.52269e8i 1.03579i −0.855445 0.517893i \(-0.826716\pi\)
0.855445 0.517893i \(-0.173284\pi\)
\(44\) 2.88127e7i 0.174711i
\(45\) −1.10747e8 −0.600164
\(46\) 4.32278e8 2.09881
\(47\) 2.46599e8i 1.07523i 0.843190 + 0.537616i \(0.180675\pi\)
−0.843190 + 0.537616i \(0.819325\pi\)
\(48\) −1.49917e8 −0.588364
\(49\) 2.09935e8 0.743197
\(50\) 9.85903e8i 3.15489i
\(51\) 2.71105e7 0.0785755
\(52\) 4.06851e8i 1.07009i
\(53\) −7.65345e8 −1.83011 −0.915057 0.403325i \(-0.867854\pi\)
−0.915057 + 0.403325i \(0.867854\pi\)
\(54\) 1.24360e8i 0.270839i
\(55\) 1.61457e8i 0.320807i
\(56\) 1.99074e7i 0.0361472i
\(57\) −1.96020e8 −0.325782
\(58\) 3.66521e8i 0.558418i
\(59\) −3.15700e8 + 6.41444e8i −0.441585 + 0.897220i
\(60\) 7.92602e8 1.01929
\(61\) 2.67620e8i 0.316862i 0.987370 + 0.158431i \(0.0506435\pi\)
−0.987370 + 0.158431i \(0.949356\pi\)
\(62\) 3.84210e8 0.419383
\(63\) −4.36772e8 −0.440101
\(64\) 1.03157e9 0.960721
\(65\) 2.27986e9i 1.96491i
\(66\) −1.81302e8 −0.144772
\(67\) 1.82349e9i 1.35061i −0.737538 0.675306i \(-0.764012\pi\)
0.737538 0.675306i \(-0.235988\pi\)
\(68\) −1.94026e8 −0.133449
\(69\) 1.34668e9i 0.861034i
\(70\) 5.62273e9i 3.34547i
\(71\) 3.31693e9 1.83842 0.919210 0.393767i \(-0.128828\pi\)
0.919210 + 0.393767i \(0.128828\pi\)
\(72\) 1.76580e7i 0.00912599i
\(73\) 3.54365e9i 1.70937i −0.519145 0.854686i \(-0.673749\pi\)
0.519145 0.854686i \(-0.326251\pi\)
\(74\) −1.69094e9 −0.762026
\(75\) 3.07141e9 1.29429
\(76\) 1.40289e9 0.553294
\(77\) 6.36764e8i 0.235248i
\(78\) 2.56009e9 0.886711
\(79\) −4.35656e9 −1.41582 −0.707911 0.706302i \(-0.750362\pi\)
−0.707911 + 0.706302i \(0.750362\pi\)
\(80\) 6.01240e9 1.83484
\(81\) 3.87420e8 0.111111
\(82\) 7.85841e9i 2.11966i
\(83\) 2.12713e9i 0.540013i −0.962859 0.270006i \(-0.912974\pi\)
0.962859 0.270006i \(-0.0870258\pi\)
\(84\) 3.12591e9 0.747447
\(85\) −1.08726e9 −0.245041
\(86\) −6.85733e9 −1.45768
\(87\) −1.14183e9 −0.229090
\(88\) −2.57434e7 −0.00487813
\(89\) 2.36898e9i 0.424239i −0.977244 0.212119i \(-0.931963\pi\)
0.977244 0.212119i \(-0.0680366\pi\)
\(90\) 4.98741e9i 0.844622i
\(91\) 8.99147e9i 1.44087i
\(92\) 9.63803e9i 1.46234i
\(93\) 1.19694e9i 0.172051i
\(94\) 1.11054e10 1.51320
\(95\) 7.86135e9 1.01597
\(96\) 6.62253e9i 0.812208i
\(97\) 1.02166e9i 0.118973i −0.998229 0.0594867i \(-0.981054\pi\)
0.998229 0.0594867i \(-0.0189464\pi\)
\(98\) 9.45424e9i 1.04591i
\(99\) 5.64815e8i 0.0593924i
\(100\) −2.19816e10 −2.19816
\(101\) 1.13007e10i 1.07522i −0.843192 0.537612i \(-0.819326\pi\)
0.843192 0.537612i \(-0.180674\pi\)
\(102\) 1.22090e9i 0.110581i
\(103\) 3.37848e9i 0.291431i 0.989327 + 0.145715i \(0.0465484\pi\)
−0.989327 + 0.145715i \(0.953452\pi\)
\(104\) 3.63512e8 0.0298780
\(105\) 1.75166e10 1.37247
\(106\) 3.44667e10i 2.57555i
\(107\) 1.30900e10 0.933299 0.466650 0.884442i \(-0.345461\pi\)
0.466650 + 0.884442i \(0.345461\pi\)
\(108\) −2.77271e9 −0.188706
\(109\) 5.01716e9i 0.326081i 0.986619 + 0.163041i \(0.0521302\pi\)
−0.986619 + 0.163041i \(0.947870\pi\)
\(110\) 7.27108e9 0.451477
\(111\) 5.26783e9i 0.312620i
\(112\) 2.37121e10 1.34549
\(113\) 1.49437e10i 0.811085i 0.914076 + 0.405543i \(0.132917\pi\)
−0.914076 + 0.405543i \(0.867083\pi\)
\(114\) 8.82762e9i 0.458479i
\(115\) 5.40084e10i 2.68517i
\(116\) 8.17194e9 0.389076
\(117\) 7.97551e9i 0.363772i
\(118\) 2.88869e10 + 1.42173e10i 1.26267 + 0.621450i
\(119\) −4.28801e9 −0.179689
\(120\) 7.08171e8i 0.0284598i
\(121\) 2.51140e10 0.968253
\(122\) 1.20521e10 0.445926
\(123\) −2.44815e10 −0.869586
\(124\) 8.56632e9i 0.292204i
\(125\) −6.82313e10 −2.23580
\(126\) 1.96697e10i 0.619362i
\(127\) −2.45788e10 −0.743946 −0.371973 0.928244i \(-0.621319\pi\)
−0.371973 + 0.928244i \(0.621319\pi\)
\(128\) 1.88104e9i 0.0547456i
\(129\) 2.13628e10i 0.598012i
\(130\) −1.02672e11 −2.76525
\(131\) 6.06689e10i 1.57257i −0.617865 0.786284i \(-0.712002\pi\)
0.617865 0.786284i \(-0.287998\pi\)
\(132\) 4.04230e9i 0.100869i
\(133\) 3.10041e10 0.745008
\(134\) −8.21196e10 −1.90074
\(135\) −1.55374e10 −0.346505
\(136\) 1.73358e8i 0.00372605i
\(137\) 1.09680e10 0.227261 0.113631 0.993523i \(-0.463752\pi\)
0.113631 + 0.993523i \(0.463752\pi\)
\(138\) 6.06469e10 1.21175
\(139\) 8.72029e9 0.168057 0.0840286 0.996463i \(-0.473221\pi\)
0.0840286 + 0.996463i \(0.473221\pi\)
\(140\) −1.25364e11 −2.33095
\(141\) 3.45969e10i 0.620786i
\(142\) 1.49375e11i 2.58724i
\(143\) 1.16274e10 0.194447
\(144\) −2.10328e10 −0.339692
\(145\) 4.57929e10 0.714428
\(146\) −1.59586e11 −2.40563
\(147\) 2.94530e10 0.429085
\(148\) 3.77011e10i 0.530940i
\(149\) 8.70992e9i 0.118600i 0.998240 + 0.0592998i \(0.0188868\pi\)
−0.998240 + 0.0592998i \(0.981113\pi\)
\(150\) 1.38318e11i 1.82148i
\(151\) 1.24128e11i 1.58120i −0.612336 0.790598i \(-0.709770\pi\)
0.612336 0.790598i \(-0.290230\pi\)
\(152\) 1.25345e9i 0.0154486i
\(153\) 3.80350e9 0.0453656
\(154\) 2.86762e10 0.331068
\(155\) 4.80029e10i 0.536549i
\(156\) 5.70796e10i 0.617814i
\(157\) 1.13466e11i 1.18951i 0.803908 + 0.594754i \(0.202750\pi\)
−0.803908 + 0.594754i \(0.797250\pi\)
\(158\) 1.96194e11i 1.99251i
\(159\) −1.07375e11 −1.05662
\(160\) 2.65595e11i 2.53291i
\(161\) 2.13002e11i 1.96904i
\(162\) 1.74472e10i 0.156369i
\(163\) 2.83643e9 0.0246510 0.0123255 0.999924i \(-0.496077\pi\)
0.0123255 + 0.999924i \(0.496077\pi\)
\(164\) 1.75211e11 1.47687
\(165\) 2.26518e10i 0.185218i
\(166\) −9.57937e10 −0.759970
\(167\) −2.06017e10 −0.158607 −0.0793034 0.996851i \(-0.525270\pi\)
−0.0793034 + 0.996851i \(0.525270\pi\)
\(168\) 2.79293e9i 0.0208696i
\(169\) −2.63269e10 −0.190970
\(170\) 4.89639e10i 0.344851i
\(171\) −2.75009e10 −0.188090
\(172\) 1.52891e11i 1.01564i
\(173\) 1.10379e11i 0.712289i −0.934431 0.356144i \(-0.884091\pi\)
0.934431 0.356144i \(-0.115909\pi\)
\(174\) 5.14215e10i 0.322403i
\(175\) −4.85797e11 −2.95982
\(176\) 3.06635e10i 0.181576i
\(177\) −4.42914e10 + 8.99921e10i −0.254949 + 0.518010i
\(178\) −1.06685e11 −0.597039
\(179\) 2.16332e11i 1.17721i 0.808420 + 0.588607i \(0.200323\pi\)
−0.808420 + 0.588607i \(0.799677\pi\)
\(180\) 1.11199e11 0.588489
\(181\) −5.36385e9 −0.0276111 −0.0138055 0.999905i \(-0.504395\pi\)
−0.0138055 + 0.999905i \(0.504395\pi\)
\(182\) −4.04924e11 −2.02776
\(183\) 3.75461e10i 0.182940i
\(184\) 8.61136e9 0.0408303
\(185\) 2.11265e11i 0.974919i
\(186\) 5.39032e10 0.242131
\(187\) 5.54508e9i 0.0242493i
\(188\) 2.47605e11i 1.05432i
\(189\) −6.12774e10 −0.254092
\(190\) 3.54030e11i 1.42979i
\(191\) 3.93716e11i 1.54887i 0.632651 + 0.774437i \(0.281967\pi\)
−0.632651 + 0.774437i \(0.718033\pi\)
\(192\) 1.44725e11 0.554672
\(193\) −2.89861e10 −0.108244 −0.0541219 0.998534i \(-0.517236\pi\)
−0.0541219 + 0.998534i \(0.517236\pi\)
\(194\) −4.60098e10 −0.167433
\(195\) 3.19856e11i 1.13444i
\(196\) −2.10791e11 −0.728738
\(197\) −3.75059e11 −1.26406 −0.632031 0.774943i \(-0.717778\pi\)
−0.632031 + 0.774943i \(0.717778\pi\)
\(198\) −2.54360e10 −0.0835840
\(199\) 1.72084e11 0.551409 0.275705 0.961242i \(-0.411089\pi\)
0.275705 + 0.961242i \(0.411089\pi\)
\(200\) 1.96401e10i 0.0613752i
\(201\) 2.55829e11i 0.779776i
\(202\) −5.08919e11 −1.51318
\(203\) 1.80601e11 0.523890
\(204\) −2.72211e10 −0.0770469
\(205\) 9.81824e11 2.71184
\(206\) 1.52147e11 0.410136
\(207\) 1.88935e11i 0.497118i
\(208\) 4.32986e11i 1.11213i
\(209\) 4.00932e10i 0.100540i
\(210\) 7.88847e11i 1.93151i
\(211\) 2.78128e11i 0.665015i 0.943101 + 0.332508i \(0.107895\pi\)
−0.943101 + 0.332508i \(0.892105\pi\)
\(212\) 7.68467e11 1.79451
\(213\) 4.65353e11 1.06141
\(214\) 5.89498e11i 1.31345i
\(215\) 8.56750e11i 1.86493i
\(216\) 2.47736e9i 0.00526890i
\(217\) 1.89317e11i 0.393451i
\(218\) 2.25944e11 0.458900
\(219\) 4.97161e11i 0.986907i
\(220\) 1.62116e11i 0.314566i
\(221\) 7.82996e10i 0.148525i
\(222\) −2.37232e11 −0.439956
\(223\) 8.44345e11 1.53107 0.765536 0.643393i \(-0.222474\pi\)
0.765536 + 0.643393i \(0.222474\pi\)
\(224\) 1.04747e12i 1.85738i
\(225\) 4.30907e11 0.747258
\(226\) 6.72979e11 1.14146
\(227\) 4.73535e11i 0.785639i 0.919616 + 0.392819i \(0.128500\pi\)
−0.919616 + 0.392819i \(0.871500\pi\)
\(228\) 1.96820e11 0.319444
\(229\) 8.37316e11i 1.32957i 0.747034 + 0.664786i \(0.231477\pi\)
−0.747034 + 0.664786i \(0.768523\pi\)
\(230\) −2.43223e12 −3.77890
\(231\) 8.93356e10i 0.135820i
\(232\) 7.30144e9i 0.0108635i
\(233\) 4.53701e11i 0.660678i −0.943862 0.330339i \(-0.892837\pi\)
0.943862 0.330339i \(-0.107163\pi\)
\(234\) 3.59171e11 0.511943
\(235\) 1.38750e12i 1.93595i
\(236\) 3.16987e11 6.44061e11i 0.432994 0.879765i
\(237\) −6.11209e11 −0.817425
\(238\) 1.93107e11i 0.252879i
\(239\) −2.54511e11 −0.326375 −0.163187 0.986595i \(-0.552178\pi\)
−0.163187 + 0.986595i \(0.552178\pi\)
\(240\) 8.43516e11 1.05934
\(241\) 1.20698e12 1.48461 0.742307 0.670060i \(-0.233732\pi\)
0.742307 + 0.670060i \(0.233732\pi\)
\(242\) 1.13099e12i 1.36264i
\(243\) 5.43536e10 0.0641500
\(244\) 2.68712e11i 0.310698i
\(245\) −1.18121e12 −1.33812
\(246\) 1.10250e12i 1.22378i
\(247\) 5.66139e11i 0.615798i
\(248\) 7.65381e9 0.00815867
\(249\) 2.98428e11i 0.311777i
\(250\) 3.07274e12i 3.14649i
\(251\) −1.28580e12 −1.29064 −0.645319 0.763913i \(-0.723275\pi\)
−0.645319 + 0.763913i \(0.723275\pi\)
\(252\) 4.38554e11 0.431539
\(253\) 2.75445e11 0.265725
\(254\) 1.10689e12i 1.04697i
\(255\) −1.52538e11 −0.141475
\(256\) 1.14104e12 1.03777
\(257\) 1.40208e12 1.25057 0.625283 0.780398i \(-0.284984\pi\)
0.625283 + 0.780398i \(0.284984\pi\)
\(258\) −9.62057e11 −0.841593
\(259\) 8.33200e11i 0.714908i
\(260\) 2.28916e12i 1.92668i
\(261\) −1.60195e11 −0.132265
\(262\) −2.73217e12 −2.21310
\(263\) −3.94685e11 −0.313669 −0.156835 0.987625i \(-0.550129\pi\)
−0.156835 + 0.987625i \(0.550129\pi\)
\(264\) −3.61171e9 −0.00281639
\(265\) 4.30624e12 3.29511
\(266\) 1.39624e12i 1.04846i
\(267\) 3.32358e11i 0.244934i
\(268\) 1.83093e12i 1.32434i
\(269\) 8.99702e11i 0.638759i 0.947627 + 0.319380i \(0.103475\pi\)
−0.947627 + 0.319380i \(0.896525\pi\)
\(270\) 6.99714e11i 0.487643i
\(271\) 2.66302e12 1.82192 0.910958 0.412500i \(-0.135344\pi\)
0.910958 + 0.412500i \(0.135344\pi\)
\(272\) −2.06490e11 −0.138693
\(273\) 1.26147e12i 0.831884i
\(274\) 4.93936e11i 0.319829i
\(275\) 6.28213e11i 0.399433i
\(276\) 1.35218e12i 0.844284i
\(277\) 1.10030e12 0.674700 0.337350 0.941379i \(-0.390469\pi\)
0.337350 + 0.941379i \(0.390469\pi\)
\(278\) 3.92711e11i 0.236510i
\(279\) 1.67926e11i 0.0993337i
\(280\) 1.12010e11i 0.0650828i
\(281\) −1.67835e12 −0.957967 −0.478984 0.877824i \(-0.658995\pi\)
−0.478984 + 0.877824i \(0.658995\pi\)
\(282\) 1.55804e12 0.873644
\(283\) 1.13383e12i 0.624620i 0.949980 + 0.312310i \(0.101103\pi\)
−0.949980 + 0.312310i \(0.898897\pi\)
\(284\) −3.33046e12 −1.80266
\(285\) 1.10292e12 0.586568
\(286\) 5.23631e11i 0.273650i
\(287\) 3.87218e12 1.98859
\(288\) 9.29115e11i 0.468929i
\(289\) −1.97865e12 −0.981478
\(290\) 2.06225e12i 1.00543i
\(291\) 1.43336e11i 0.0686893i
\(292\) 3.55811e12i 1.67612i
\(293\) 8.14054e11 0.376977 0.188489 0.982075i \(-0.439641\pi\)
0.188489 + 0.982075i \(0.439641\pi\)
\(294\) 1.32639e12i 0.603859i
\(295\) 1.77630e12 3.60911e12i 0.795070 1.61544i
\(296\) −3.36850e10 −0.0148244
\(297\) 7.92414e10i 0.0342902i
\(298\) 3.92244e11 0.166907
\(299\) −3.88944e12 −1.62754
\(300\) −3.08394e12 −1.26911
\(301\) 3.37891e12i 1.36755i
\(302\) −5.59001e12 −2.22525
\(303\) 1.58545e12i 0.620781i
\(304\) 1.49301e12 0.575035
\(305\) 1.50578e12i 0.570507i
\(306\) 1.71288e11i 0.0638438i
\(307\) −2.37197e12 −0.869796 −0.434898 0.900480i \(-0.643216\pi\)
−0.434898 + 0.900480i \(0.643216\pi\)
\(308\) 6.39362e11i 0.230671i
\(309\) 4.73988e11i 0.168258i
\(310\) −2.16177e12 −0.755095
\(311\) 2.97835e11 0.102370 0.0511851 0.998689i \(-0.483700\pi\)
0.0511851 + 0.998689i \(0.483700\pi\)
\(312\) 5.09993e10 0.0172501
\(313\) 2.87994e12i 0.958652i 0.877637 + 0.479326i \(0.159119\pi\)
−0.877637 + 0.479326i \(0.840881\pi\)
\(314\) 5.10985e12 1.67402
\(315\) 2.45751e12 0.792398
\(316\) 4.37433e12 1.38828
\(317\) −1.12526e12 −0.351526 −0.175763 0.984432i \(-0.556239\pi\)
−0.175763 + 0.984432i \(0.556239\pi\)
\(318\) 4.83554e12i 1.48700i
\(319\) 2.33546e11i 0.0706999i
\(320\) −5.80415e12 −1.72977
\(321\) 1.83648e12 0.538841
\(322\) −9.59237e12 −2.77106
\(323\) −2.69990e11 −0.0767954
\(324\) −3.89001e11 −0.108950
\(325\) 8.87072e12i 2.44648i
\(326\) 1.27736e11i 0.0346918i
\(327\) 7.03889e11i 0.188263i
\(328\) 1.56547e11i 0.0412358i
\(329\) 5.47211e12i 1.41963i
\(330\) 1.02010e12 0.260660
\(331\) 4.32711e12 1.08907 0.544537 0.838737i \(-0.316705\pi\)
0.544537 + 0.838737i \(0.316705\pi\)
\(332\) 2.13581e12i 0.529508i
\(333\) 7.39055e11i 0.180491i
\(334\) 9.27783e11i 0.223210i
\(335\) 1.02600e13i 2.43177i
\(336\) 3.32671e12 0.776817
\(337\) 2.09082e12i 0.481023i 0.970646 + 0.240512i \(0.0773152\pi\)
−0.970646 + 0.240512i \(0.922685\pi\)
\(338\) 1.18561e12i 0.268756i
\(339\) 2.09655e12i 0.468280i
\(340\) 1.09170e12 0.240274
\(341\) 2.44817e11 0.0530970
\(342\) 1.23848e12i 0.264703i
\(343\) 1.60970e12 0.339058
\(344\) −1.36604e11 −0.0283578
\(345\) 7.57717e12i 1.55029i
\(346\) −4.97083e12 −1.00242
\(347\) 7.74052e12i 1.53859i −0.638895 0.769294i \(-0.720608\pi\)
0.638895 0.769294i \(-0.279392\pi\)
\(348\) 1.14649e12 0.224633
\(349\) 1.01012e13i 1.95095i −0.220099 0.975477i \(-0.570638\pi\)
0.220099 0.975477i \(-0.429362\pi\)
\(350\) 2.18775e13i 4.16541i
\(351\) 1.11893e12i 0.210024i
\(352\) 1.35454e12 0.250657
\(353\) 6.56754e12i 1.19820i 0.800675 + 0.599100i \(0.204475\pi\)
−0.800675 + 0.599100i \(0.795525\pi\)
\(354\) 4.05272e12 + 1.99463e12i 0.729005 + 0.358794i
\(355\) −1.86628e13 −3.31006
\(356\) 2.37864e12i 0.415986i
\(357\) −6.01591e11 −0.103743
\(358\) 9.74233e12 1.65671
\(359\) −1.83840e12 −0.308296 −0.154148 0.988048i \(-0.549263\pi\)
−0.154148 + 0.988048i \(0.549263\pi\)
\(360\) 9.93537e10i 0.0164313i
\(361\) −4.17892e12 −0.681598
\(362\) 2.41557e11i 0.0388576i
\(363\) 3.52339e12 0.559021
\(364\) 9.02815e12i 1.41284i
\(365\) 1.99385e13i 3.07771i
\(366\) 1.69086e12 0.257455
\(367\) 4.47888e12i 0.672728i −0.941732 0.336364i \(-0.890803\pi\)
0.941732 0.336364i \(-0.109197\pi\)
\(368\) 1.02571e13i 1.51980i
\(369\) −3.43466e12 −0.502056
\(370\) 9.51414e12 1.37202
\(371\) 1.69832e13 2.41630
\(372\) 1.20182e12i 0.168704i
\(373\) 2.05362e12 0.284430 0.142215 0.989836i \(-0.454578\pi\)
0.142215 + 0.989836i \(0.454578\pi\)
\(374\) −2.49718e11 −0.0341265
\(375\) −9.57259e12 −1.29084
\(376\) 2.21230e11 0.0294377
\(377\) 3.29780e12i 0.433029i
\(378\) 2.75958e12i 0.357589i
\(379\) 5.75685e12 0.736188 0.368094 0.929789i \(-0.380011\pi\)
0.368094 + 0.929789i \(0.380011\pi\)
\(380\) −7.89342e12 −0.996201
\(381\) −3.44831e12 −0.429517
\(382\) 1.77307e13 2.17976
\(383\) 1.33107e13 1.61513 0.807567 0.589776i \(-0.200784\pi\)
0.807567 + 0.589776i \(0.200784\pi\)
\(384\) 2.63903e11i 0.0316074i
\(385\) 3.58278e12i 0.423561i
\(386\) 1.30537e12i 0.152334i
\(387\) 2.99712e12i 0.345262i
\(388\) 1.02583e12i 0.116659i
\(389\) −9.51362e12 −1.06807 −0.534033 0.845464i \(-0.679324\pi\)
−0.534033 + 0.845464i \(0.679324\pi\)
\(390\) −1.44045e13 −1.59652
\(391\) 1.85487e12i 0.202969i
\(392\) 1.88337e11i 0.0203472i
\(393\) 8.51161e12i 0.907922i
\(394\) 1.68905e13i 1.77894i
\(395\) 2.45124e13 2.54918
\(396\) 5.67119e11i 0.0582369i
\(397\) 1.37121e13i 1.39043i −0.718799 0.695217i \(-0.755308\pi\)
0.718799 0.695217i \(-0.244692\pi\)
\(398\) 7.74964e12i 0.776008i
\(399\) 4.34975e12 0.430130
\(400\) −2.33937e13 −2.28454
\(401\) 5.09480e12i 0.491366i 0.969350 + 0.245683i \(0.0790122\pi\)
−0.969350 + 0.245683i \(0.920988\pi\)
\(402\) −1.15211e13 −1.09739
\(403\) −3.45695e12 −0.325213
\(404\) 1.13468e13i 1.05431i
\(405\) −2.17984e12 −0.200055
\(406\) 8.13323e12i 0.737280i
\(407\) −1.07746e12 −0.0964782
\(408\) 2.43214e10i 0.00215124i
\(409\) 1.87597e13i 1.63911i −0.572999 0.819556i \(-0.694220\pi\)
0.572999 0.819556i \(-0.305780\pi\)
\(410\) 4.42157e13i 3.81643i
\(411\) 1.53877e12 0.131209
\(412\) 3.39226e12i 0.285761i
\(413\) 7.00547e12 1.42338e13i 0.583025 1.18460i
\(414\) 8.50852e12 0.699604
\(415\) 1.19684e13i 0.972289i
\(416\) −1.91269e13 −1.53525
\(417\) 1.22342e12 0.0970279
\(418\) 1.80557e12 0.141492
\(419\) 5.45055e12i 0.422056i 0.977480 + 0.211028i \(0.0676811\pi\)
−0.977480 + 0.211028i \(0.932319\pi\)
\(420\) −1.75881e13 −1.34577
\(421\) 8.20035e11i 0.0620043i −0.999519 0.0310022i \(-0.990130\pi\)
0.999519 0.0310022i \(-0.00986987\pi\)
\(422\) 1.25253e13 0.935889
\(423\) 4.85381e12i 0.358411i
\(424\) 6.86608e11i 0.0501048i
\(425\) 4.23043e12 0.305098
\(426\) 2.09568e13i 1.49375i
\(427\) 5.93858e12i 0.418353i
\(428\) −1.31434e13 −0.915143
\(429\) 1.63128e12 0.112264
\(430\) 3.85830e13 2.62455
\(431\) 2.14838e13i 1.44452i −0.691620 0.722262i \(-0.743103\pi\)
0.691620 0.722262i \(-0.256897\pi\)
\(432\) −2.95082e12 −0.196121
\(433\) 5.73747e12 0.376948 0.188474 0.982078i \(-0.439646\pi\)
0.188474 + 0.982078i \(0.439646\pi\)
\(434\) −8.52574e12 −0.553711
\(435\) 6.42457e12 0.412475
\(436\) 5.03763e12i 0.319738i
\(437\) 1.34115e13i 0.841528i
\(438\) −2.23892e13 −1.38889
\(439\) 9.11837e12 0.559235 0.279618 0.960111i \(-0.409792\pi\)
0.279618 + 0.960111i \(0.409792\pi\)
\(440\) 1.44847e11 0.00878304
\(441\) 4.13214e12 0.247732
\(442\) 3.52616e12 0.209021
\(443\) 2.76185e13i 1.61876i −0.587288 0.809378i \(-0.699804\pi\)
0.587288 0.809378i \(-0.300196\pi\)
\(444\) 5.28931e12i 0.306538i
\(445\) 1.33291e13i 0.763839i
\(446\) 3.80244e13i 2.15471i
\(447\) 1.22197e12i 0.0684735i
\(448\) −2.28908e13 −1.26844
\(449\) 3.20562e13 1.75663 0.878314 0.478084i \(-0.158669\pi\)
0.878314 + 0.478084i \(0.158669\pi\)
\(450\) 1.94055e13i 1.05163i
\(451\) 5.00735e12i 0.268364i
\(452\) 1.50047e13i 0.795306i
\(453\) 1.74147e13i 0.912903i
\(454\) 2.13253e13 1.10564
\(455\) 5.05909e13i 2.59427i
\(456\) 1.75854e11i 0.00891925i
\(457\) 5.98878e12i 0.300440i −0.988653 0.150220i \(-0.952002\pi\)
0.988653 0.150220i \(-0.0479981\pi\)
\(458\) 3.77079e13 1.87113
\(459\) 5.33617e11 0.0261918
\(460\) 5.42287e13i 2.63294i
\(461\) 2.61854e13 1.25763 0.628817 0.777553i \(-0.283539\pi\)
0.628817 + 0.777553i \(0.283539\pi\)
\(462\) 4.02316e12 0.191142
\(463\) 3.74521e12i 0.176024i −0.996119 0.0880118i \(-0.971949\pi\)
0.996119 0.0880118i \(-0.0280513\pi\)
\(464\) 8.69688e12 0.404365
\(465\) 6.73462e12i 0.309777i
\(466\) −2.04320e13 −0.929784
\(467\) 3.53965e13i 1.59359i −0.604250 0.796794i \(-0.706527\pi\)
0.604250 0.796794i \(-0.293473\pi\)
\(468\) 8.00804e12i 0.356695i
\(469\) 4.04639e13i 1.78321i
\(470\) −6.24850e13 −2.72450
\(471\) 1.59188e13i 0.686762i
\(472\) 5.75453e11 + 2.83221e11i 0.0245641 + 0.0120897i
\(473\) −4.36946e12 −0.184553
\(474\) 2.75253e13i 1.15038i
\(475\) −3.05877e13 −1.26497
\(476\) 4.30550e12 0.176193
\(477\) −1.50643e13 −0.610038
\(478\) 1.14617e13i 0.459313i
\(479\) 1.25567e13 0.497964 0.248982 0.968508i \(-0.419904\pi\)
0.248982 + 0.968508i \(0.419904\pi\)
\(480\) 3.72619e13i 1.46238i
\(481\) 1.52143e13 0.590918
\(482\) 5.43552e13i 2.08932i
\(483\) 2.98833e13i 1.13682i
\(484\) −2.52164e13 −0.949417
\(485\) 5.74844e12i 0.214211i
\(486\) 2.44777e12i 0.0902795i
\(487\) −1.22247e13 −0.446265 −0.223133 0.974788i \(-0.571628\pi\)
−0.223133 + 0.974788i \(0.571628\pi\)
\(488\) 2.40088e11 0.00867504
\(489\) 3.97940e11 0.0142323
\(490\) 5.31946e13i 1.88316i
\(491\) −4.44368e13 −1.55717 −0.778583 0.627541i \(-0.784061\pi\)
−0.778583 + 0.627541i \(0.784061\pi\)
\(492\) 2.45814e13 0.852669
\(493\) −1.57271e12 −0.0540026
\(494\) −2.54956e13 −0.866624
\(495\) 3.17796e12i 0.106936i
\(496\) 9.11659e12i 0.303686i
\(497\) −7.36038e13 −2.42727
\(498\) −1.34395e13 −0.438769
\(499\) −9.54778e12 −0.308603 −0.154301 0.988024i \(-0.549313\pi\)
−0.154301 + 0.988024i \(0.549313\pi\)
\(500\) 6.85097e13 2.19231
\(501\) −2.89034e12 −0.0915716
\(502\) 5.79049e13i 1.81634i
\(503\) 4.02782e13i 1.25092i 0.780256 + 0.625461i \(0.215089\pi\)
−0.780256 + 0.625461i \(0.784911\pi\)
\(504\) 3.91838e11i 0.0120491i
\(505\) 6.35839e13i 1.93593i
\(506\) 1.24045e13i 0.373960i
\(507\) −3.69356e12 −0.110257
\(508\) 2.46790e13 0.729473
\(509\) 2.69555e13i 0.788966i 0.918903 + 0.394483i \(0.129076\pi\)
−0.918903 + 0.394483i \(0.870924\pi\)
\(510\) 6.86945e12i 0.199100i
\(511\) 7.86347e13i 2.25689i
\(512\) 4.94594e13i 1.40572i
\(513\) −3.85827e12 −0.108594
\(514\) 6.31415e13i 1.75994i
\(515\) 1.90092e13i 0.524719i
\(516\) 2.14499e13i 0.586378i
\(517\) 7.07631e12 0.191582
\(518\) 3.75225e13 1.00610
\(519\) 1.54858e13i 0.411240i
\(520\) −2.04531e12 −0.0537952
\(521\) 9.50332e12 0.247564 0.123782 0.992309i \(-0.460498\pi\)
0.123782 + 0.992309i \(0.460498\pi\)
\(522\) 7.21424e12i 0.186139i
\(523\) 2.38341e13 0.609103 0.304551 0.952496i \(-0.401493\pi\)
0.304551 + 0.952496i \(0.401493\pi\)
\(524\) 6.09163e13i 1.54198i
\(525\) −6.81555e13 −1.70885
\(526\) 1.77743e13i 0.441433i
\(527\) 1.64861e12i 0.0405570i
\(528\) 4.30197e12i 0.104833i
\(529\) −5.07118e13 −1.22414
\(530\) 1.93928e14i 4.63726i
\(531\) −6.21391e12 + 1.26255e13i −0.147195 + 0.299073i
\(532\) −3.11306e13 −0.730514
\(533\) 7.07065e13i 1.64370i
\(534\) −1.49675e13 −0.344701
\(535\) −7.36514e13 −1.68040
\(536\) −1.63590e12 −0.0369770
\(537\) 3.03505e13i 0.679664i
\(538\) 4.05174e13 0.898938
\(539\) 6.02420e12i 0.132421i
\(540\) 1.56008e13 0.339764
\(541\) 5.05282e13i 1.09030i −0.838337 0.545152i \(-0.816472\pi\)
0.838337 0.545152i \(-0.183528\pi\)
\(542\) 1.19927e14i 2.56402i
\(543\) −7.52527e11 −0.0159413
\(544\) 9.12159e12i 0.191459i
\(545\) 2.82293e13i 0.587107i
\(546\) −5.68092e13 −1.17073
\(547\) 7.08827e13 1.44745 0.723725 0.690089i \(-0.242429\pi\)
0.723725 + 0.690089i \(0.242429\pi\)
\(548\) −1.10128e13 −0.222840
\(549\) 5.26757e12i 0.105621i
\(550\) −2.82911e13 −0.562129
\(551\) 1.13714e13 0.223900
\(552\) 1.20814e12 0.0235734
\(553\) 9.66734e13 1.86931
\(554\) 4.95509e13i 0.949518i
\(555\) 2.96396e13i 0.562870i
\(556\) −8.75586e12 −0.164788
\(557\) 8.11846e12 0.151425 0.0757125 0.997130i \(-0.475877\pi\)
0.0757125 + 0.997130i \(0.475877\pi\)
\(558\) 7.56241e12 0.139794
\(559\) 6.16992e13 1.13037
\(560\) −1.33417e14 −2.42254
\(561\) 7.77953e11i 0.0140004i
\(562\) 7.55831e13i 1.34816i
\(563\) 8.26188e13i 1.46062i 0.683117 + 0.730309i \(0.260624\pi\)
−0.683117 + 0.730309i \(0.739376\pi\)
\(564\) 3.47380e13i 0.608709i
\(565\) 8.40814e13i 1.46035i
\(566\) 5.10612e13 0.879040
\(567\) −8.59698e12 −0.146700
\(568\) 2.97569e12i 0.0503322i
\(569\) 9.00309e13i 1.50949i 0.656018 + 0.754745i \(0.272239\pi\)
−0.656018 + 0.754745i \(0.727761\pi\)
\(570\) 4.96690e13i 0.825488i
\(571\) 6.91183e13i 1.13871i 0.822093 + 0.569354i \(0.192807\pi\)
−0.822093 + 0.569354i \(0.807193\pi\)
\(572\) −1.16748e13 −0.190665
\(573\) 5.52368e13i 0.894243i
\(574\) 1.74381e14i 2.79859i
\(575\) 2.10142e14i 3.34328i
\(576\) 2.03043e13 0.320240
\(577\) −3.78206e13 −0.591356 −0.295678 0.955288i \(-0.595546\pi\)
−0.295678 + 0.955288i \(0.595546\pi\)
\(578\) 8.91071e13i 1.38125i
\(579\) −4.06664e12 −0.0624946
\(580\) −4.59797e13 −0.700529
\(581\) 4.72017e13i 0.712980i
\(582\) −6.45500e12 −0.0966677
\(583\) 2.19620e13i 0.326084i
\(584\) −3.17909e12 −0.0467992
\(585\) 4.48745e13i 0.654969i
\(586\) 3.66603e13i 0.530527i
\(587\) 2.91118e13i 0.417713i 0.977946 + 0.208857i \(0.0669742\pi\)
−0.977946 + 0.208857i \(0.933026\pi\)
\(588\) −2.95732e13 −0.420737
\(589\) 1.19202e13i 0.168153i
\(590\) −1.62533e14 7.99941e13i −2.27344 1.11892i
\(591\) −5.26193e13 −0.729806
\(592\) 4.01229e13i 0.551802i
\(593\) −4.78928e13 −0.653126 −0.326563 0.945175i \(-0.605891\pi\)
−0.326563 + 0.945175i \(0.605891\pi\)
\(594\) −3.56857e12 −0.0482572
\(595\) 2.41267e13 0.323528
\(596\) 8.74545e12i 0.116292i
\(597\) 2.41427e13 0.318356
\(598\) 1.75158e14i 2.29047i
\(599\) 8.90386e13 1.15463 0.577317 0.816520i \(-0.304100\pi\)
0.577317 + 0.816520i \(0.304100\pi\)
\(600\) 2.75543e12i 0.0354350i
\(601\) 5.52898e13i 0.705135i −0.935786 0.352568i \(-0.885309\pi\)
0.935786 0.352568i \(-0.114691\pi\)
\(602\) 1.52166e14 1.92458
\(603\) 3.58918e13i 0.450204i
\(604\) 1.24634e14i 1.55043i
\(605\) −1.41305e14 −1.74333
\(606\) −7.13993e13 −0.873637
\(607\) 9.75041e13 1.18326 0.591629 0.806210i \(-0.298485\pi\)
0.591629 + 0.806210i \(0.298485\pi\)
\(608\) 6.59529e13i 0.793809i
\(609\) 2.53376e13 0.302468
\(610\) −6.78114e13 −0.802886
\(611\) −9.99215e13 −1.17342
\(612\) −3.81902e12 −0.0444830
\(613\) 1.20146e14i 1.38806i −0.719947 0.694029i \(-0.755834\pi\)
0.719947 0.694029i \(-0.244166\pi\)
\(614\) 1.06820e14i 1.22408i
\(615\) 1.37746e14 1.56568
\(616\) 5.71255e11 0.00644060
\(617\) 5.83950e13 0.653055 0.326527 0.945188i \(-0.394121\pi\)
0.326527 + 0.945188i \(0.394121\pi\)
\(618\) 2.13457e13 0.236792
\(619\) −9.32857e13 −1.02651 −0.513253 0.858237i \(-0.671560\pi\)
−0.513253 + 0.858237i \(0.671560\pi\)
\(620\) 4.81987e13i 0.526111i
\(621\) 2.65068e13i 0.287011i
\(622\) 1.34128e13i 0.144067i
\(623\) 5.25683e13i 0.560123i
\(624\) 6.07462e13i 0.642090i
\(625\) 1.70114e14 1.78378
\(626\) 1.29696e14 1.34913
\(627\) 5.62492e12i 0.0580469i
\(628\) 1.13929e14i 1.16637i
\(629\) 7.25568e12i 0.0736928i
\(630\) 1.10672e14i 1.11516i
\(631\) 1.09580e14 1.09543 0.547717 0.836664i \(-0.315497\pi\)
0.547717 + 0.836664i \(0.315497\pi\)
\(632\) 3.90837e12i 0.0387623i
\(633\) 3.90202e13i 0.383947i
\(634\) 5.06753e13i 0.494710i
\(635\) 1.38293e14 1.33947
\(636\) 1.07813e14 1.03606
\(637\) 8.50651e13i 0.811062i
\(638\) 1.05176e13 0.0994973
\(639\) 6.52872e13 0.612807
\(640\) 1.05838e13i 0.0985691i
\(641\) −5.54416e13 −0.512325 −0.256162 0.966634i \(-0.582458\pi\)
−0.256162 + 0.966634i \(0.582458\pi\)
\(642\) 8.27043e13i 0.758320i
\(643\) 8.60177e13 0.782588 0.391294 0.920266i \(-0.372028\pi\)
0.391294 + 0.920266i \(0.372028\pi\)
\(644\) 2.13871e14i 1.93073i
\(645\) 1.20199e14i 1.07672i
\(646\) 1.21588e13i 0.108076i
\(647\) −1.11602e14 −0.984353 −0.492177 0.870495i \(-0.663799\pi\)
−0.492177 + 0.870495i \(0.663799\pi\)
\(648\) 3.47563e11i 0.00304200i
\(649\) 1.84066e13 + 9.05919e12i 0.159864 + 0.0786803i
\(650\) 3.99486e14 3.44298
\(651\) 2.65604e13i 0.227159i
\(652\) −2.84800e12 −0.0241714
\(653\) 6.79967e13 0.572693 0.286347 0.958126i \(-0.407559\pi\)
0.286347 + 0.958126i \(0.407559\pi\)
\(654\) 3.16991e13 0.264946
\(655\) 3.41356e14i 2.83140i
\(656\) 1.86466e14 1.53490
\(657\) 6.97497e13i 0.569791i
\(658\) −2.46432e14 −1.99787
\(659\) 1.24712e14i 1.00341i 0.865038 + 0.501707i \(0.167294\pi\)
−0.865038 + 0.501707i \(0.832706\pi\)
\(660\) 2.27442e13i 0.181615i
\(661\) −1.82791e14 −1.44860 −0.724300 0.689485i \(-0.757837\pi\)
−0.724300 + 0.689485i \(0.757837\pi\)
\(662\) 1.94868e14i 1.53267i
\(663\) 1.09851e13i 0.0857507i
\(664\) −1.90830e12 −0.0147845
\(665\) −1.74446e14 −1.34138
\(666\) −3.32828e13 −0.254009
\(667\) 7.81227e13i 0.591763i
\(668\) 2.06858e13 0.155521
\(669\) 1.18458e14 0.883965
\(670\) 4.62049e14 3.42227
\(671\) 7.67953e12 0.0564575
\(672\) 1.46956e14i 1.07236i
\(673\) 2.27493e14i 1.64775i −0.566769 0.823877i \(-0.691807\pi\)
0.566769 0.823877i \(-0.308193\pi\)
\(674\) 9.41582e13 0.676953
\(675\) 6.04545e13 0.431430
\(676\) 2.64343e13 0.187255
\(677\) 6.74546e13 0.474317 0.237158 0.971471i \(-0.423784\pi\)
0.237158 + 0.971471i \(0.423784\pi\)
\(678\) 9.44163e13 0.659020
\(679\) 2.26711e13i 0.157081i
\(680\) 9.75405e11i 0.00670873i
\(681\) 6.64351e13i 0.453589i
\(682\) 1.10251e13i 0.0747244i
\(683\) 1.46199e14i 0.983651i 0.870694 + 0.491825i \(0.163670\pi\)
−0.870694 + 0.491825i \(0.836330\pi\)
\(684\) 2.76131e13 0.184431
\(685\) −6.17120e13 −0.409182
\(686\) 7.24915e13i 0.477163i
\(687\) 1.17472e14i 0.767629i
\(688\) 1.62712e14i 1.05554i
\(689\) 3.10116e14i 1.99723i
\(690\) −3.41232e14 −2.18175
\(691\) 1.79039e14i 1.13647i 0.822868 + 0.568233i \(0.192373\pi\)
−0.822868 + 0.568233i \(0.807627\pi\)
\(692\) 1.10829e14i 0.698432i
\(693\) 1.25334e13i 0.0784158i
\(694\) −3.48588e14 −2.16528
\(695\) −4.90651e13 −0.302586
\(696\) 1.02436e12i 0.00627203i
\(697\) −3.37198e13 −0.204984
\(698\) −4.54901e14 −2.74562
\(699\) 6.36524e13i 0.381442i
\(700\) 4.87779e14 2.90224
\(701\) 2.73394e14i 1.61510i −0.589801 0.807548i \(-0.700794\pi\)
0.589801 0.807548i \(-0.299206\pi\)
\(702\) 5.03903e13 0.295570
\(703\) 5.24616e13i 0.305538i
\(704\) 2.96014e13i 0.171178i
\(705\) 1.94661e14i 1.11772i
\(706\) 2.95764e14 1.68625
\(707\) 2.50766e14i 1.41962i
\(708\) 4.44721e13 9.03592e13i 0.249989 0.507933i
\(709\) −1.22783e14 −0.685341 −0.342670 0.939456i \(-0.611331\pi\)
−0.342670 + 0.939456i \(0.611331\pi\)
\(710\) 8.40466e14i 4.65831i
\(711\) −8.57502e13 −0.471940
\(712\) −2.12526e12 −0.0116148
\(713\) −8.18930e13 −0.444425
\(714\) 2.70922e13i 0.146000i
\(715\) −6.54220e13 −0.350101
\(716\) 2.17214e14i 1.15431i
\(717\) −3.57069e13 −0.188433
\(718\) 8.27910e13i 0.433871i
\(719\) 1.35503e14i 0.705188i −0.935776 0.352594i \(-0.885300\pi\)
0.935776 0.352594i \(-0.114700\pi\)
\(720\) 1.18342e14 0.611613
\(721\) 7.49696e13i 0.384777i
\(722\) 1.88195e14i 0.959226i
\(723\) 1.69334e14 0.857142
\(724\) 5.38573e12 0.0270739
\(725\) −1.78176e14 −0.889526
\(726\) 1.58673e14i 0.786721i
\(727\) −8.06261e13 −0.397012 −0.198506 0.980100i \(-0.563609\pi\)
−0.198506 + 0.980100i \(0.563609\pi\)
\(728\) −8.06644e12 −0.0394480
\(729\) 7.62560e12 0.0370370
\(730\) 8.97914e14 4.33132
\(731\) 2.94242e13i 0.140967i
\(732\) 3.76992e13i 0.179381i
\(733\) 1.43569e14 0.678487 0.339243 0.940699i \(-0.389829\pi\)
0.339243 + 0.940699i \(0.389829\pi\)
\(734\) −2.01703e14 −0.946743
\(735\) −1.65719e14 −0.772564
\(736\) −4.53104e14 −2.09802
\(737\) −5.23263e13 −0.240648
\(738\) 1.54677e14i 0.706552i
\(739\) 2.12888e14i 0.965893i 0.875650 + 0.482947i \(0.160434\pi\)
−0.875650 + 0.482947i \(0.839566\pi\)
\(740\) 2.12127e14i 0.955953i
\(741\) 7.94271e13i 0.355531i
\(742\) 7.64827e14i 3.40051i
\(743\) −4.45283e14 −1.96649 −0.983245 0.182288i \(-0.941650\pi\)
−0.983245 + 0.182288i \(0.941650\pi\)
\(744\) 1.07380e12 0.00471041
\(745\) 4.90067e13i 0.213538i
\(746\) 9.24831e13i 0.400284i
\(747\) 4.18684e13i 0.180004i
\(748\) 5.56770e12i 0.0237776i
\(749\) −2.90471e14 −1.23224
\(750\) 4.31094e14i 1.81663i
\(751\) 4.39685e12i 0.0184053i −0.999958 0.00920263i \(-0.997071\pi\)
0.999958 0.00920263i \(-0.00292933\pi\)
\(752\) 2.63511e14i 1.09574i
\(753\) −1.80393e14 −0.745150
\(754\) −1.48514e14 −0.609411
\(755\) 6.98412e14i 2.84693i
\(756\) 6.15274e13 0.249149
\(757\) −4.84573e12 −0.0194931 −0.00974653 0.999953i \(-0.503102\pi\)
−0.00974653 + 0.999953i \(0.503102\pi\)
\(758\) 2.59255e14i 1.03605i
\(759\) 3.86439e13 0.153417
\(760\) 7.05259e12i 0.0278151i
\(761\) 1.51033e13 0.0591762 0.0295881 0.999562i \(-0.490580\pi\)
0.0295881 + 0.999562i \(0.490580\pi\)
\(762\) 1.55292e14i 0.604468i
\(763\) 1.11332e14i 0.430526i
\(764\) 3.95322e14i 1.51874i
\(765\) −2.14006e13 −0.0816804
\(766\) 5.99439e14i 2.27301i
\(767\) −2.59912e14 1.27921e14i −0.979150 0.481908i
\(768\) 1.60083e14 0.599154
\(769\) 3.43597e14i 1.27767i 0.769346 + 0.638833i \(0.220582\pi\)
−0.769346 + 0.638833i \(0.779418\pi\)
\(770\) −1.61348e14 −0.596086
\(771\) 1.96706e14 0.722014
\(772\) 2.91043e13 0.106138
\(773\) 2.71018e14i 0.981975i 0.871167 + 0.490987i \(0.163364\pi\)
−0.871167 + 0.490987i \(0.836636\pi\)
\(774\) −1.34973e14 −0.485894
\(775\) 1.86775e14i 0.668051i
\(776\) −9.16558e11 −0.00325725
\(777\) 1.16895e14i 0.412752i
\(778\) 4.28438e14i 1.50311i
\(779\) 2.43808e14 0.849886