Properties

Label 177.11.c.a.58.8
Level $177$
Weight $11$
Character 177.58
Analytic conductor $112.458$
Analytic rank $0$
Dimension $100$
CM no
Inner twists $2$

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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 58.8
Character \(\chi\) \(=\) 177.58
Dual form 177.11.c.a.58.93

$q$-expansion

\(f(q)\) \(=\) \(q-55.7243i q^{2} +140.296 q^{3} -2081.20 q^{4} +5222.72 q^{5} -7817.90i q^{6} -1720.05 q^{7} +58911.7i q^{8} +19683.0 q^{9} +O(q^{10})\) \(q-55.7243i q^{2} +140.296 q^{3} -2081.20 q^{4} +5222.72 q^{5} -7817.90i q^{6} -1720.05 q^{7} +58911.7i q^{8} +19683.0 q^{9} -291033. i q^{10} +156119. i q^{11} -291984. q^{12} -373465. i q^{13} +95848.7i q^{14} +732728. q^{15} +1.15167e6 q^{16} -2.44429e6 q^{17} -1.09682e6i q^{18} +3.77809e6 q^{19} -1.08695e7 q^{20} -241317. q^{21} +8.69961e6 q^{22} +663159. i q^{23} +8.26508e6i q^{24} +1.75112e7 q^{25} -2.08111e7 q^{26} +2.76145e6 q^{27} +3.57977e6 q^{28} -2.35255e7 q^{29} -4.08308e7i q^{30} -7.44544e6i q^{31} -3.85018e6i q^{32} +2.19028e7i q^{33} +1.36207e8i q^{34} -8.98335e6 q^{35} -4.09642e7 q^{36} -1.27092e8i q^{37} -2.10531e8i q^{38} -5.23956e7i q^{39} +3.07679e8i q^{40} +1.98147e8 q^{41} +1.34472e7i q^{42} -2.76092e8i q^{43} -3.24914e8i q^{44} +1.02799e8 q^{45} +3.69541e7 q^{46} +7.61948e7i q^{47} +1.61574e8 q^{48} -2.79517e8 q^{49} -9.75801e8i q^{50} -3.42925e8 q^{51} +7.77254e8i q^{52} +4.15878e8 q^{53} -1.53880e8i q^{54} +8.15365e8i q^{55} -1.01331e8i q^{56} +5.30051e8 q^{57} +1.31094e9i q^{58} +(-6.79736e8 - 2.21531e8i) q^{59} -1.52495e9 q^{60} -4.25701e8i q^{61} -4.14892e8 q^{62} -3.38558e7 q^{63} +9.64756e8 q^{64} -1.95050e9i q^{65} +1.22052e9 q^{66} -2.68719e9i q^{67} +5.08706e9 q^{68} +9.30386e7i q^{69} +5.00591e8i q^{70} -1.83271e9 q^{71} +1.15956e9i q^{72} -1.40158e9i q^{73} -7.08209e9 q^{74} +2.45676e9 q^{75} -7.86295e9 q^{76} -2.68532e8i q^{77} -2.91971e9 q^{78} +9.59163e8 q^{79} +6.01483e9 q^{80} +3.87420e8 q^{81} -1.10416e10i q^{82} -6.82834e9i q^{83} +5.02228e8 q^{84} -1.27659e10 q^{85} -1.53850e10 q^{86} -3.30054e9 q^{87} -9.19721e9 q^{88} -6.05894e9i q^{89} -5.72840e9i q^{90} +6.42378e8i q^{91} -1.38017e9i q^{92} -1.04457e9i q^{93} +4.24590e9 q^{94} +1.97319e10 q^{95} -5.40166e8i q^{96} -2.41662e9i q^{97} +1.55759e10i q^{98} +3.07288e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + O(q^{10}) \) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + 620136q^{12} + 662904q^{15} + 27925160q^{16} - 2053136q^{17} - 5169828q^{19} - 1076324q^{20} - 1829224q^{22} + 215378180q^{25} - 22082700q^{26} - 102921320q^{28} - 112503588q^{29} - 76491392q^{35} - 1007769600q^{36} + 473464516q^{41} + 1215405588q^{46} - 1676272320q^{48} + 1975297276q^{49} + 733970808q^{51} + 3267506728q^{53} + 591502824q^{57} + 508142200q^{59} + 1264196808q^{60} - 6538206968q^{62} + 362009736q^{63} - 10324137972q^{64} - 2764346616q^{66} + 9997685952q^{68} + 14908523204q^{71} + 4863508712q^{74} + 1890481680q^{75} + 2044437240q^{76} - 758396196q^{78} - 3599839500q^{79} - 23217941144q^{80} + 38742048900q^{81} - 13094894808q^{84} + 23360564412q^{85} + 12186923752q^{86} + 7965322272q^{87} + 32415437996q^{88} - 22098322280q^{94} + 7834510028q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 55.7243i 1.74138i −0.491828 0.870692i \(-0.663671\pi\)
0.491828 0.870692i \(-0.336329\pi\)
\(3\) 140.296 0.577350
\(4\) −2081.20 −2.03242
\(5\) 5222.72 1.67127 0.835636 0.549284i \(-0.185099\pi\)
0.835636 + 0.549284i \(0.185099\pi\)
\(6\) 7817.90i 1.00539i
\(7\) −1720.05 −0.102341 −0.0511707 0.998690i \(-0.516295\pi\)
−0.0511707 + 0.998690i \(0.516295\pi\)
\(8\) 58911.7i 1.79784i
\(9\) 19683.0 0.333333
\(10\) 291033.i 2.91033i
\(11\) 156119.i 0.969374i 0.874688 + 0.484687i \(0.161067\pi\)
−0.874688 + 0.484687i \(0.838933\pi\)
\(12\) −291984. −1.17342
\(13\) 373465.i 1.00585i −0.864330 0.502924i \(-0.832257\pi\)
0.864330 0.502924i \(-0.167743\pi\)
\(14\) 95848.7i 0.178216i
\(15\) 732728. 0.964909
\(16\) 1.15167e6 1.09831
\(17\) −2.44429e6 −1.72151 −0.860753 0.509023i \(-0.830007\pi\)
−0.860753 + 0.509023i \(0.830007\pi\)
\(18\) 1.09682e6i 0.580462i
\(19\) 3.77809e6 1.52582 0.762912 0.646503i \(-0.223769\pi\)
0.762912 + 0.646503i \(0.223769\pi\)
\(20\) −1.08695e7 −3.39673
\(21\) −241317. −0.0590868
\(22\) 8.69961e6 1.68805
\(23\) 663159.i 0.103033i 0.998672 + 0.0515167i \(0.0164055\pi\)
−0.998672 + 0.0515167i \(0.983594\pi\)
\(24\) 8.26508e6i 1.03798i
\(25\) 1.75112e7 1.79315
\(26\) −2.08111e7 −1.75157
\(27\) 2.76145e6 0.192450
\(28\) 3.57977e6 0.208001
\(29\) −2.35255e7 −1.14696 −0.573481 0.819219i \(-0.694407\pi\)
−0.573481 + 0.819219i \(0.694407\pi\)
\(30\) 4.08308e7i 1.68028i
\(31\) 7.44544e6i 0.260065i −0.991510 0.130033i \(-0.958492\pi\)
0.991510 0.130033i \(-0.0415082\pi\)
\(32\) 3.85018e6i 0.114744i
\(33\) 2.19028e7i 0.559668i
\(34\) 1.36207e8i 2.99780i
\(35\) −8.98335e6 −0.171040
\(36\) −4.09642e7 −0.677474
\(37\) 1.27092e8i 1.83277i −0.400297 0.916385i \(-0.631093\pi\)
0.400297 0.916385i \(-0.368907\pi\)
\(38\) 2.10531e8i 2.65704i
\(39\) 5.23956e7i 0.580727i
\(40\) 3.07679e8i 3.00468i
\(41\) 1.98147e8 1.71029 0.855143 0.518392i \(-0.173469\pi\)
0.855143 + 0.518392i \(0.173469\pi\)
\(42\) 1.34472e7i 0.102893i
\(43\) 2.76092e8i 1.87807i −0.343825 0.939034i \(-0.611723\pi\)
0.343825 0.939034i \(-0.388277\pi\)
\(44\) 3.24914e8i 1.97018i
\(45\) 1.02799e8 0.557091
\(46\) 3.69541e7 0.179421
\(47\) 7.61948e7i 0.332228i 0.986107 + 0.166114i \(0.0531219\pi\)
−0.986107 + 0.166114i \(0.946878\pi\)
\(48\) 1.61574e8 0.634112
\(49\) −2.79517e8 −0.989526
\(50\) 9.75801e8i 3.12256i
\(51\) −3.42925e8 −0.993912
\(52\) 7.77254e8i 2.04431i
\(53\) 4.15878e8 0.994459 0.497230 0.867619i \(-0.334351\pi\)
0.497230 + 0.867619i \(0.334351\pi\)
\(54\) 1.53880e8i 0.335130i
\(55\) 8.15365e8i 1.62009i
\(56\) 1.01331e8i 0.183994i
\(57\) 5.30051e8 0.880934
\(58\) 1.31094e9i 1.99730i
\(59\) −6.79736e8 2.21531e8i −0.950780 0.309866i
\(60\) −1.52495e9 −1.96110
\(61\) 4.25701e8i 0.504029i −0.967724 0.252014i \(-0.918907\pi\)
0.967724 0.252014i \(-0.0810930\pi\)
\(62\) −4.14892e8 −0.452873
\(63\) −3.38558e7 −0.0341138
\(64\) 9.64756e8 0.898499
\(65\) 1.95050e9i 1.68105i
\(66\) 1.22052e9 0.974598
\(67\) 2.68719e9i 1.99032i −0.0982514 0.995162i \(-0.531325\pi\)
0.0982514 0.995162i \(-0.468675\pi\)
\(68\) 5.08706e9 3.49883
\(69\) 9.30386e7i 0.0594864i
\(70\) 5.00591e8i 0.297847i
\(71\) −1.83271e9 −1.01578 −0.507892 0.861421i \(-0.669575\pi\)
−0.507892 + 0.861421i \(0.669575\pi\)
\(72\) 1.15956e9i 0.599281i
\(73\) 1.40158e9i 0.676088i −0.941130 0.338044i \(-0.890235\pi\)
0.941130 0.338044i \(-0.109765\pi\)
\(74\) −7.08209e9 −3.19156
\(75\) 2.45676e9 1.03528
\(76\) −7.86295e9 −3.10111
\(77\) 2.68532e8i 0.0992071i
\(78\) −2.91971e9 −1.01127
\(79\) 9.59163e8 0.311714 0.155857 0.987780i \(-0.450186\pi\)
0.155857 + 0.987780i \(0.450186\pi\)
\(80\) 6.01483e9 1.83558
\(81\) 3.87420e8 0.111111
\(82\) 1.10416e10i 2.97827i
\(83\) 6.82834e9i 1.73350i −0.498740 0.866752i \(-0.666204\pi\)
0.498740 0.866752i \(-0.333796\pi\)
\(84\) 5.02228e8 0.120089
\(85\) −1.27659e10 −2.87710
\(86\) −1.53850e10 −3.27044
\(87\) −3.30054e9 −0.662199
\(88\) −9.19721e9 −1.74278
\(89\) 6.05894e9i 1.08504i −0.840042 0.542521i \(-0.817470\pi\)
0.840042 0.542521i \(-0.182530\pi\)
\(90\) 5.72840e9i 0.970109i
\(91\) 6.42378e8i 0.102940i
\(92\) 1.38017e9i 0.209407i
\(93\) 1.04457e9i 0.150149i
\(94\) 4.24590e9 0.578536
\(95\) 1.97319e10 2.55007
\(96\) 5.40166e8i 0.0662477i
\(97\) 2.41662e9i 0.281416i −0.990051 0.140708i \(-0.955062\pi\)
0.990051 0.140708i \(-0.0449379\pi\)
\(98\) 1.55759e10i 1.72315i
\(99\) 3.07288e9i 0.323125i
\(100\) −3.64443e10 −3.64443
\(101\) 2.10540e9i 0.200322i −0.994971 0.100161i \(-0.968064\pi\)
0.994971 0.100161i \(-0.0319357\pi\)
\(102\) 1.91092e10i 1.73078i
\(103\) 6.30277e9i 0.543682i −0.962342 0.271841i \(-0.912367\pi\)
0.962342 0.271841i \(-0.0876325\pi\)
\(104\) 2.20014e10 1.80836
\(105\) −1.26033e9 −0.0987501
\(106\) 2.31745e10i 1.73174i
\(107\) −8.77485e9 −0.625634 −0.312817 0.949813i \(-0.601273\pi\)
−0.312817 + 0.949813i \(0.601273\pi\)
\(108\) −5.74712e9 −0.391140
\(109\) 2.32371e10i 1.51025i 0.655580 + 0.755126i \(0.272424\pi\)
−0.655580 + 0.755126i \(0.727576\pi\)
\(110\) 4.54356e10 2.82120
\(111\) 1.78305e10i 1.05815i
\(112\) −1.98092e9 −0.112403
\(113\) 2.29984e10i 1.24826i 0.781321 + 0.624130i \(0.214546\pi\)
−0.781321 + 0.624130i \(0.785454\pi\)
\(114\) 2.95367e10i 1.53405i
\(115\) 3.46350e9i 0.172197i
\(116\) 4.89613e10 2.33111
\(117\) 7.35090e9i 0.335283i
\(118\) −1.23446e10 + 3.78778e10i −0.539596 + 1.65567i
\(119\) 4.20431e9 0.176181
\(120\) 4.31662e10i 1.73475i
\(121\) 1.56438e9 0.0603137
\(122\) −2.37219e10 −0.877708
\(123\) 2.77993e10 0.987435
\(124\) 1.54954e10i 0.528562i
\(125\) 4.04531e10 1.32557
\(126\) 1.88659e9i 0.0594052i
\(127\) 5.51974e10 1.67070 0.835352 0.549715i \(-0.185264\pi\)
0.835352 + 0.549715i \(0.185264\pi\)
\(128\) 5.77030e10i 1.67938i
\(129\) 3.87346e10i 1.08430i
\(130\) −1.08690e11 −2.92735
\(131\) 1.92759e10i 0.499642i −0.968292 0.249821i \(-0.919628\pi\)
0.968292 0.249821i \(-0.0803717\pi\)
\(132\) 4.55842e10i 1.13748i
\(133\) −6.49851e9 −0.156155
\(134\) −1.49742e11 −3.46592
\(135\) 1.44223e10 0.321636
\(136\) 1.43997e11i 3.09500i
\(137\) 6.47447e10 1.34153 0.670766 0.741669i \(-0.265965\pi\)
0.670766 + 0.741669i \(0.265965\pi\)
\(138\) 5.18451e9 0.103589
\(139\) −6.56303e9 −0.126482 −0.0632412 0.997998i \(-0.520144\pi\)
−0.0632412 + 0.997998i \(0.520144\pi\)
\(140\) 1.86961e10 0.347626
\(141\) 1.06898e10i 0.191812i
\(142\) 1.02126e11i 1.76887i
\(143\) 5.83048e10 0.975044
\(144\) 2.26682e10 0.366104
\(145\) −1.22867e11 −1.91688
\(146\) −7.81020e10 −1.17733
\(147\) −3.92151e10 −0.571303
\(148\) 2.64503e11i 3.72496i
\(149\) 1.37453e11i 1.87165i 0.352470 + 0.935823i \(0.385342\pi\)
−0.352470 + 0.935823i \(0.614658\pi\)
\(150\) 1.36901e11i 1.80281i
\(151\) 5.46762e10i 0.696488i −0.937404 0.348244i \(-0.886778\pi\)
0.937404 0.348244i \(-0.113222\pi\)
\(152\) 2.22574e11i 2.74319i
\(153\) −4.81110e10 −0.573835
\(154\) −1.49638e10 −0.172758
\(155\) 3.88855e10i 0.434639i
\(156\) 1.09046e11i 1.18028i
\(157\) 1.31912e11i 1.38289i 0.722430 + 0.691444i \(0.243025\pi\)
−0.722430 + 0.691444i \(0.756975\pi\)
\(158\) 5.34487e10i 0.542815i
\(159\) 5.83461e10 0.574151
\(160\) 2.01084e10i 0.191769i
\(161\) 1.14067e9i 0.0105446i
\(162\) 2.15887e10i 0.193487i
\(163\) 1.10590e11 0.961117 0.480559 0.876963i \(-0.340434\pi\)
0.480559 + 0.876963i \(0.340434\pi\)
\(164\) −4.12384e11 −3.47602
\(165\) 1.14393e11i 0.935358i
\(166\) −3.80505e11 −3.01870
\(167\) −2.01487e10 −0.155119 −0.0775593 0.996988i \(-0.524713\pi\)
−0.0775593 + 0.996988i \(0.524713\pi\)
\(168\) 1.42164e10i 0.106229i
\(169\) −1.61725e9 −0.0117312
\(170\) 7.11369e11i 5.01015i
\(171\) 7.43641e10 0.508608
\(172\) 5.74602e11i 3.81702i
\(173\) 1.50573e10i 0.0971664i −0.998819 0.0485832i \(-0.984529\pi\)
0.998819 0.0485832i \(-0.0154706\pi\)
\(174\) 1.83920e11i 1.15314i
\(175\) −3.01202e10 −0.183513
\(176\) 1.79796e11i 1.06468i
\(177\) −9.53643e10 3.10799e10i −0.548933 0.178901i
\(178\) −3.37630e11 −1.88948
\(179\) 2.90889e10i 0.158293i 0.996863 + 0.0791465i \(0.0252195\pi\)
−0.996863 + 0.0791465i \(0.974781\pi\)
\(180\) −2.13945e11 −1.13224
\(181\) −6.19928e10 −0.319116 −0.159558 0.987189i \(-0.551007\pi\)
−0.159558 + 0.987189i \(0.551007\pi\)
\(182\) 3.57961e10 0.179258
\(183\) 5.97241e10i 0.291001i
\(184\) −3.90678e10 −0.185238
\(185\) 6.63764e11i 3.06306i
\(186\) −5.82077e10 −0.261467
\(187\) 3.81600e11i 1.66878i
\(188\) 1.58576e11i 0.675227i
\(189\) −4.74983e9 −0.0196956
\(190\) 1.09955e12i 4.44064i
\(191\) 2.04257e11i 0.803544i 0.915740 + 0.401772i \(0.131605\pi\)
−0.915740 + 0.401772i \(0.868395\pi\)
\(192\) 1.35352e11 0.518749
\(193\) −2.63238e11 −0.983019 −0.491509 0.870872i \(-0.663555\pi\)
−0.491509 + 0.870872i \(0.663555\pi\)
\(194\) −1.34664e11 −0.490054
\(195\) 2.73648e11i 0.970553i
\(196\) 5.81730e11 2.01113
\(197\) −2.56402e11 −0.864151 −0.432075 0.901837i \(-0.642219\pi\)
−0.432075 + 0.901837i \(0.642219\pi\)
\(198\) 1.71234e11 0.562684
\(199\) 2.58652e11 0.828801 0.414400 0.910095i \(-0.363991\pi\)
0.414400 + 0.910095i \(0.363991\pi\)
\(200\) 1.03162e12i 3.22380i
\(201\) 3.77002e11i 1.14911i
\(202\) −1.17322e11 −0.348837
\(203\) 4.04651e10 0.117382
\(204\) 7.13695e11 2.02005
\(205\) 1.03487e12 2.85835
\(206\) −3.51217e11 −0.946760
\(207\) 1.30530e10i 0.0343445i
\(208\) 4.30106e11i 1.10474i
\(209\) 5.89830e11i 1.47909i
\(210\) 7.02310e10i 0.171962i
\(211\) 1.27868e11i 0.305738i 0.988246 + 0.152869i \(0.0488513\pi\)
−0.988246 + 0.152869i \(0.951149\pi\)
\(212\) −8.65526e11 −2.02116
\(213\) −2.57122e11 −0.586464
\(214\) 4.88972e11i 1.08947i
\(215\) 1.44195e12i 3.13876i
\(216\) 1.62682e11i 0.345995i
\(217\) 1.28065e10i 0.0266154i
\(218\) 1.29487e12 2.62993
\(219\) 1.96636e11i 0.390340i
\(220\) 1.69694e12i 3.29270i
\(221\) 9.12857e11i 1.73157i
\(222\) −9.93590e11 −1.84265
\(223\) −1.70666e11 −0.309473 −0.154736 0.987956i \(-0.549453\pi\)
−0.154736 + 0.987956i \(0.549453\pi\)
\(224\) 6.62251e9i 0.0117431i
\(225\) 3.44673e11 0.597716
\(226\) 1.28157e12 2.17370
\(227\) 3.84574e11i 0.638044i 0.947747 + 0.319022i \(0.103354\pi\)
−0.947747 + 0.319022i \(0.896646\pi\)
\(228\) −1.10314e12 −1.79043
\(229\) 2.41904e11i 0.384118i 0.981383 + 0.192059i \(0.0615166\pi\)
−0.981383 + 0.192059i \(0.938483\pi\)
\(230\) 1.93001e11 0.299861
\(231\) 3.76740e10i 0.0572772i
\(232\) 1.38593e12i 2.06206i
\(233\) 9.44883e11i 1.37594i 0.725741 + 0.687968i \(0.241497\pi\)
−0.725741 + 0.687968i \(0.758503\pi\)
\(234\) −4.09624e11 −0.583856
\(235\) 3.97944e11i 0.555243i
\(236\) 1.41467e12 + 4.61049e11i 1.93239 + 0.629778i
\(237\) 1.34567e11 0.179968
\(238\) 2.34282e11i 0.306799i
\(239\) −2.49110e11 −0.319449 −0.159724 0.987162i \(-0.551061\pi\)
−0.159724 + 0.987162i \(0.551061\pi\)
\(240\) 8.43857e11 1.05977
\(241\) 5.43565e11 0.668600 0.334300 0.942467i \(-0.391500\pi\)
0.334300 + 0.942467i \(0.391500\pi\)
\(242\) 8.71742e10i 0.105029i
\(243\) 5.43536e10 0.0641500
\(244\) 8.85968e11i 1.02440i
\(245\) −1.45984e12 −1.65377
\(246\) 1.54910e12i 1.71950i
\(247\) 1.41098e12i 1.53475i
\(248\) 4.38623e11 0.467556
\(249\) 9.57990e11i 1.00084i
\(250\) 2.25422e12i 2.30832i
\(251\) −6.46190e11 −0.648621 −0.324311 0.945951i \(-0.605132\pi\)
−0.324311 + 0.945951i \(0.605132\pi\)
\(252\) 7.04606e10 0.0693336
\(253\) −1.03531e11 −0.0998780
\(254\) 3.07584e12i 2.90934i
\(255\) −1.79100e12 −1.66110
\(256\) −2.22755e12 −2.02594
\(257\) 2.24160e10 0.0199937 0.00999684 0.999950i \(-0.496818\pi\)
0.00999684 + 0.999950i \(0.496818\pi\)
\(258\) −2.15846e12 −1.88819
\(259\) 2.18604e11i 0.187568i
\(260\) 4.05938e12i 3.41659i
\(261\) −4.63052e11 −0.382321
\(262\) −1.07414e12 −0.870068
\(263\) −3.89260e11 −0.309358 −0.154679 0.987965i \(-0.549434\pi\)
−0.154679 + 0.987965i \(0.549434\pi\)
\(264\) −1.29033e12 −1.00620
\(265\) 2.17202e12 1.66201
\(266\) 3.62125e11i 0.271926i
\(267\) 8.50045e11i 0.626449i
\(268\) 5.59257e12i 4.04517i
\(269\) 1.69602e12i 1.20412i −0.798451 0.602060i \(-0.794347\pi\)
0.798451 0.602060i \(-0.205653\pi\)
\(270\) 8.03672e11i 0.560093i
\(271\) −3.51440e11 −0.240439 −0.120219 0.992747i \(-0.538360\pi\)
−0.120219 + 0.992747i \(0.538360\pi\)
\(272\) −2.81501e12 −1.89075
\(273\) 9.01232e10i 0.0594324i
\(274\) 3.60785e12i 2.33612i
\(275\) 2.73383e12i 1.73823i
\(276\) 1.93632e11i 0.120901i
\(277\) −1.87563e12 −1.15013 −0.575066 0.818107i \(-0.695024\pi\)
−0.575066 + 0.818107i \(0.695024\pi\)
\(278\) 3.65720e11i 0.220255i
\(279\) 1.46549e11i 0.0866883i
\(280\) 5.29224e11i 0.307503i
\(281\) −2.28568e12 −1.30462 −0.652309 0.757953i \(-0.726200\pi\)
−0.652309 + 0.757953i \(0.726200\pi\)
\(282\) 5.95683e11 0.334018
\(283\) 7.69699e11i 0.424022i 0.977267 + 0.212011i \(0.0680013\pi\)
−0.977267 + 0.212011i \(0.931999\pi\)
\(284\) 3.81423e12 2.06450
\(285\) 2.76831e12 1.47228
\(286\) 3.24899e12i 1.69793i
\(287\) −3.40824e11 −0.175033
\(288\) 7.57832e10i 0.0382481i
\(289\) 3.95857e12 1.96358
\(290\) 6.84669e12i 3.33803i
\(291\) 3.39042e11i 0.162476i
\(292\) 2.91696e12i 1.37410i
\(293\) 3.00405e12 1.39114 0.695568 0.718460i \(-0.255153\pi\)
0.695568 + 0.718460i \(0.255153\pi\)
\(294\) 2.18523e12i 0.994859i
\(295\) −3.55007e12 1.15699e12i −1.58901 0.517870i
\(296\) 7.48718e12 3.29503
\(297\) 4.31114e11i 0.186556i
\(298\) 7.65949e12 3.25926
\(299\) 2.47666e11 0.103636
\(300\) −5.11300e12 −2.10411
\(301\) 4.74892e11i 0.192204i
\(302\) −3.04679e12 −1.21285
\(303\) 2.95380e11i 0.115656i
\(304\) 4.35109e12 1.67583
\(305\) 2.22332e12i 0.842369i
\(306\) 2.68095e12i 0.999268i
\(307\) −4.49649e12 −1.64885 −0.824427 0.565969i \(-0.808502\pi\)
−0.824427 + 0.565969i \(0.808502\pi\)
\(308\) 5.58869e11i 0.201631i
\(309\) 8.84254e11i 0.313895i
\(310\) −2.16687e12 −0.756874
\(311\) 4.13606e12 1.42162 0.710812 0.703382i \(-0.248328\pi\)
0.710812 + 0.703382i \(0.248328\pi\)
\(312\) 3.08671e12 1.04406
\(313\) 3.01952e12i 1.00512i −0.864543 0.502558i \(-0.832392\pi\)
0.864543 0.502558i \(-0.167608\pi\)
\(314\) 7.35072e12 2.40814
\(315\) −1.76819e11 −0.0570134
\(316\) −1.99621e12 −0.633535
\(317\) 2.83910e12 0.886920 0.443460 0.896294i \(-0.353751\pi\)
0.443460 + 0.896294i \(0.353751\pi\)
\(318\) 3.25130e12i 0.999818i
\(319\) 3.67277e12i 1.11184i
\(320\) 5.03866e12 1.50164
\(321\) −1.23108e12 −0.361210
\(322\) −6.35629e10 −0.0183622
\(323\) −9.23476e12 −2.62671
\(324\) −8.06299e11 −0.225825
\(325\) 6.53982e12i 1.80364i
\(326\) 6.16253e12i 1.67368i
\(327\) 3.26008e12i 0.871945i
\(328\) 1.16732e13i 3.07482i
\(329\) 1.31059e11i 0.0340006i
\(330\) 6.37444e12 1.62882
\(331\) −1.65363e12 −0.416197 −0.208099 0.978108i \(-0.566728\pi\)
−0.208099 + 0.978108i \(0.566728\pi\)
\(332\) 1.42111e13i 3.52321i
\(333\) 2.50154e12i 0.610924i
\(334\) 1.12277e12i 0.270121i
\(335\) 1.40344e13i 3.32637i
\(336\) −2.77916e11 −0.0648958
\(337\) 4.16379e11i 0.0957941i 0.998852 + 0.0478971i \(0.0152519\pi\)
−0.998852 + 0.0478971i \(0.984748\pi\)
\(338\) 9.01202e10i 0.0204286i
\(339\) 3.22658e12i 0.720683i
\(340\) 2.65683e13 5.84749
\(341\) 1.16237e12 0.252100
\(342\) 4.14389e12i 0.885682i
\(343\) 9.66655e11 0.203611
\(344\) 1.62650e13 3.37647
\(345\) 4.85915e11i 0.0994179i
\(346\) −8.39056e11 −0.169204
\(347\) 2.70846e12i 0.538363i 0.963089 + 0.269182i \(0.0867532\pi\)
−0.963089 + 0.269182i \(0.913247\pi\)
\(348\) 6.86907e12 1.34587
\(349\) 6.00981e12i 1.16074i −0.814354 0.580368i \(-0.802909\pi\)
0.814354 0.580368i \(-0.197091\pi\)
\(350\) 1.67843e12i 0.319567i
\(351\) 1.03130e12i 0.193576i
\(352\) 6.01086e11 0.111230
\(353\) 2.58702e12i 0.471983i −0.971755 0.235991i \(-0.924166\pi\)
0.971755 0.235991i \(-0.0758337\pi\)
\(354\) −1.73191e12 + 5.31411e12i −0.311536 + 0.955904i
\(355\) −9.57173e12 −1.69765
\(356\) 1.26099e13i 2.20526i
\(357\) 5.89848e11 0.101718
\(358\) 1.62096e12 0.275649
\(359\) 5.40023e12 0.905608 0.452804 0.891610i \(-0.350424\pi\)
0.452804 + 0.891610i \(0.350424\pi\)
\(360\) 6.05605e12i 1.00156i
\(361\) 8.14289e12 1.32814
\(362\) 3.45451e12i 0.555704i
\(363\) 2.19477e11 0.0348221
\(364\) 1.33692e12i 0.209217i
\(365\) 7.32006e12i 1.12993i
\(366\) −3.32809e12 −0.506745
\(367\) 9.21297e12i 1.38379i 0.721999 + 0.691894i \(0.243223\pi\)
−0.721999 + 0.691894i \(0.756777\pi\)
\(368\) 7.63737e11i 0.113163i
\(369\) 3.90013e12 0.570096
\(370\) −3.69878e13 −5.33396
\(371\) −7.15332e11 −0.101774
\(372\) 2.17395e12i 0.305165i
\(373\) 4.62903e12 0.641130 0.320565 0.947227i \(-0.396127\pi\)
0.320565 + 0.947227i \(0.396127\pi\)
\(374\) −2.12644e13 −2.90599
\(375\) 5.67542e12 0.765317
\(376\) −4.48876e12 −0.597293
\(377\) 8.78594e12i 1.15367i
\(378\) 2.64681e11i 0.0342976i
\(379\) 2.95507e12 0.377895 0.188948 0.981987i \(-0.439492\pi\)
0.188948 + 0.981987i \(0.439492\pi\)
\(380\) −4.10660e13 −5.18281
\(381\) 7.74398e12 0.964582
\(382\) 1.13821e13 1.39928
\(383\) −7.92491e12 −0.961613 −0.480807 0.876827i \(-0.659656\pi\)
−0.480807 + 0.876827i \(0.659656\pi\)
\(384\) 8.09550e12i 0.969589i
\(385\) 1.40247e12i 0.165802i
\(386\) 1.46688e13i 1.71181i
\(387\) 5.43431e12i 0.626022i
\(388\) 5.02946e12i 0.571956i
\(389\) −2.90100e12 −0.325687 −0.162843 0.986652i \(-0.552067\pi\)
−0.162843 + 0.986652i \(0.552067\pi\)
\(390\) −1.52488e13 −1.69011
\(391\) 1.62095e12i 0.177373i
\(392\) 1.64668e13i 1.77901i
\(393\) 2.70434e12i 0.288468i
\(394\) 1.42878e13i 1.50482i
\(395\) 5.00944e12 0.520959
\(396\) 6.39528e12i 0.656725i
\(397\) 4.31574e11i 0.0437625i 0.999761 + 0.0218813i \(0.00696558\pi\)
−0.999761 + 0.0218813i \(0.993034\pi\)
\(398\) 1.44132e13i 1.44326i
\(399\) −9.11715e11 −0.0901560
\(400\) 2.01671e13 1.96944
\(401\) 5.58971e12i 0.539097i 0.962987 + 0.269549i \(0.0868745\pi\)
−0.962987 + 0.269549i \(0.913126\pi\)
\(402\) −2.10082e13 −2.00105
\(403\) −2.78061e12 −0.261586
\(404\) 4.38176e12i 0.407138i
\(405\) 2.02339e12 0.185697
\(406\) 2.25489e12i 0.204407i
\(407\) 1.98414e13 1.77664
\(408\) 2.02023e13i 1.78690i
\(409\) 9.07152e12i 0.792617i −0.918117 0.396309i \(-0.870291\pi\)
0.918117 0.396309i \(-0.129709\pi\)
\(410\) 5.76674e13i 4.97749i
\(411\) 9.08343e12 0.774534
\(412\) 1.31173e13i 1.10499i
\(413\) 1.16918e12 + 3.81044e11i 0.0973042 + 0.0317121i
\(414\) 7.27367e11 0.0598070
\(415\) 3.56625e13i 2.89716i
\(416\) −1.43791e12 −0.115416
\(417\) −9.20767e11 −0.0730247
\(418\) 3.28679e13 2.57567
\(419\) 3.41397e12i 0.264356i 0.991226 + 0.132178i \(0.0421971\pi\)
−0.991226 + 0.132178i \(0.957803\pi\)
\(420\) 2.62300e12 0.200702
\(421\) 1.45397e13i 1.09938i 0.835370 + 0.549688i \(0.185253\pi\)
−0.835370 + 0.549688i \(0.814747\pi\)
\(422\) 7.12536e12 0.532408
\(423\) 1.49974e12i 0.110743i
\(424\) 2.45001e13i 1.78788i
\(425\) −4.28026e13 −3.08692
\(426\) 1.43279e13i 1.02126i
\(427\) 7.32227e11i 0.0515830i
\(428\) 1.82622e13 1.27155
\(429\) 8.17994e12 0.562942
\(430\) −8.03517e13 −5.46579
\(431\) 2.52408e13i 1.69713i 0.529087 + 0.848567i \(0.322534\pi\)
−0.529087 + 0.848567i \(0.677466\pi\)
\(432\) 3.18026e12 0.211371
\(433\) −1.04198e13 −0.684575 −0.342288 0.939595i \(-0.611202\pi\)
−0.342288 + 0.939595i \(0.611202\pi\)
\(434\) 7.13636e11 0.0463477
\(435\) −1.72378e13 −1.10671
\(436\) 4.83610e13i 3.06947i
\(437\) 2.50547e12i 0.157211i
\(438\) −1.09574e13 −0.679731
\(439\) 1.64315e13 1.00775 0.503877 0.863776i \(-0.331907\pi\)
0.503877 + 0.863776i \(0.331907\pi\)
\(440\) −4.80345e13 −2.91266
\(441\) −5.50173e12 −0.329842
\(442\) 5.08683e13 3.01534
\(443\) 1.13010e13i 0.662366i −0.943566 0.331183i \(-0.892552\pi\)
0.943566 0.331183i \(-0.107448\pi\)
\(444\) 3.71087e13i 2.15061i
\(445\) 3.16442e13i 1.81340i
\(446\) 9.51025e12i 0.538911i
\(447\) 1.92842e13i 1.08060i
\(448\) −1.65943e12 −0.0919536
\(449\) −1.43868e13 −0.788377 −0.394188 0.919030i \(-0.628974\pi\)
−0.394188 + 0.919030i \(0.628974\pi\)
\(450\) 1.92067e13i 1.04085i
\(451\) 3.09345e13i 1.65791i
\(452\) 4.78642e13i 2.53699i
\(453\) 7.67086e12i 0.402117i
\(454\) 2.14301e13 1.11108
\(455\) 3.35496e12i 0.172041i
\(456\) 3.12262e13i 1.58378i
\(457\) 4.60275e12i 0.230907i −0.993313 0.115453i \(-0.963168\pi\)
0.993313 0.115453i \(-0.0368321\pi\)
\(458\) 1.34799e13 0.668898
\(459\) −6.74979e12 −0.331304
\(460\) 7.20822e12i 0.349977i
\(461\) −2.70669e13 −1.29997 −0.649985 0.759947i \(-0.725225\pi\)
−0.649985 + 0.759947i \(0.725225\pi\)
\(462\) −2.09936e12 −0.0997417
\(463\) 2.33076e13i 1.09545i −0.836658 0.547725i \(-0.815494\pi\)
0.836658 0.547725i \(-0.184506\pi\)
\(464\) −2.70935e13 −1.25972
\(465\) 5.45548e12i 0.250939i
\(466\) 5.26530e13 2.39603
\(467\) 6.90086e12i 0.310684i 0.987861 + 0.155342i \(0.0496479\pi\)
−0.987861 + 0.155342i \(0.950352\pi\)
\(468\) 1.52987e13i 0.681436i
\(469\) 4.62210e12i 0.203692i
\(470\) 2.21752e13 0.966891
\(471\) 1.85068e13i 0.798411i
\(472\) 1.30507e13 4.00444e13i 0.557090 1.70935i
\(473\) 4.31031e13 1.82055
\(474\) 7.49864e12i 0.313394i
\(475\) 6.61590e13 2.73603
\(476\) −8.75000e12 −0.358075
\(477\) 8.18573e12 0.331486
\(478\) 1.38815e13i 0.556283i
\(479\) −1.84032e13 −0.729821 −0.364910 0.931043i \(-0.618900\pi\)
−0.364910 + 0.931043i \(0.618900\pi\)
\(480\) 2.82114e12i 0.110718i
\(481\) −4.74642e13 −1.84349
\(482\) 3.02898e13i 1.16429i
\(483\) 1.60031e11i 0.00608792i
\(484\) −3.25579e12 −0.122583
\(485\) 1.26213e13i 0.470323i
\(486\) 3.02882e12i 0.111710i
\(487\) 1.54655e13 0.564570 0.282285 0.959331i \(-0.408908\pi\)
0.282285 + 0.959331i \(0.408908\pi\)
\(488\) 2.50787e13 0.906164
\(489\) 1.55153e13 0.554901
\(490\) 8.13485e13i 2.87985i
\(491\) −4.63227e13 −1.62325 −0.811627 0.584176i \(-0.801418\pi\)
−0.811627 + 0.584176i \(0.801418\pi\)
\(492\) −5.78559e13 −2.00688
\(493\) 5.75032e13 1.97450
\(494\) −7.86260e13 −2.67258
\(495\) 1.60488e13i 0.540029i
\(496\) 8.57465e12i 0.285633i
\(497\) 3.15235e12 0.103957
\(498\) −5.33833e13 −1.74285
\(499\) 2.36443e13 0.764230 0.382115 0.924115i \(-0.375196\pi\)
0.382115 + 0.924115i \(0.375196\pi\)
\(500\) −8.41910e13 −2.69411
\(501\) −2.82678e12 −0.0895577
\(502\) 3.60085e13i 1.12950i
\(503\) 6.88373e12i 0.213788i 0.994270 + 0.106894i \(0.0340906\pi\)
−0.994270 + 0.106894i \(0.965909\pi\)
\(504\) 1.99450e12i 0.0613312i
\(505\) 1.09959e13i 0.334792i
\(506\) 5.76922e12i 0.173926i
\(507\) −2.26894e11 −0.00677304
\(508\) −1.14877e14 −3.39558
\(509\) 5.07411e13i 1.48515i −0.669761 0.742576i \(-0.733604\pi\)
0.669761 0.742576i \(-0.266396\pi\)
\(510\) 9.98023e13i 2.89261i
\(511\) 2.41079e12i 0.0691918i
\(512\) 6.50407e13i 1.84857i
\(513\) 1.04330e13 0.293645
\(514\) 1.24912e12i 0.0348167i
\(515\) 3.29176e13i 0.908641i
\(516\) 8.06144e13i 2.20376i
\(517\) −1.18954e13 −0.322053
\(518\) 1.21816e13 0.326629
\(519\) 2.11248e12i 0.0560990i
\(520\) 1.14907e14 3.02226
\(521\) 6.99867e13 1.82317 0.911584 0.411114i \(-0.134860\pi\)
0.911584 + 0.411114i \(0.134860\pi\)
\(522\) 2.58033e13i 0.665767i
\(523\) −3.24794e13 −0.830041 −0.415020 0.909812i \(-0.636226\pi\)
−0.415020 + 0.909812i \(0.636226\pi\)
\(524\) 4.01170e13i 1.01548i
\(525\) −4.22575e12 −0.105951
\(526\) 2.16912e13i 0.538711i
\(527\) 1.81988e13i 0.447704i
\(528\) 2.52247e13i 0.614691i
\(529\) 4.09867e13 0.989384
\(530\) 1.21034e14i 2.89420i
\(531\) −1.33792e13 4.36039e12i −0.316927 0.103289i
\(532\) 1.35247e13 0.317372
\(533\) 7.40010e13i 1.72029i
\(534\) −4.73682e13 −1.09089
\(535\) −4.58286e13 −1.04561
\(536\) 1.58307e14 3.57829
\(537\) 4.08105e12i 0.0913905i
\(538\) −9.45095e13 −2.09683
\(539\) 4.36378e13i 0.959221i
\(540\) −3.00156e13 −0.653701
\(541\) 7.29508e13i 1.57414i 0.616863 + 0.787071i \(0.288403\pi\)
−0.616863 + 0.787071i \(0.711597\pi\)
\(542\) 1.95837e13i 0.418696i
\(543\) −8.69735e12 −0.184242
\(544\) 9.41098e12i 0.197533i
\(545\) 1.21361e14i 2.52404i
\(546\) 5.02205e12 0.103495
\(547\) 2.29146e13 0.467925 0.233963 0.972246i \(-0.424831\pi\)
0.233963 + 0.972246i \(0.424831\pi\)
\(548\) −1.34747e14 −2.72656
\(549\) 8.37907e12i 0.168010i
\(550\) 1.52341e14 3.02693
\(551\) −8.88814e13 −1.75006
\(552\) −5.48106e12 −0.106947
\(553\) −1.64981e12 −0.0319013
\(554\) 1.04518e14i 2.00282i
\(555\) 9.31235e13i 1.76846i
\(556\) 1.36590e13 0.257065
\(557\) 5.73127e13 1.06899 0.534496 0.845171i \(-0.320501\pi\)
0.534496 + 0.845171i \(0.320501\pi\)
\(558\) −8.16632e12 −0.150958
\(559\) −1.03110e14 −1.88905
\(560\) −1.03458e13 −0.187856
\(561\) 5.35370e13i 0.963473i
\(562\) 1.27368e14i 2.27184i
\(563\) 6.59116e13i 1.16525i 0.812740 + 0.582626i \(0.197975\pi\)
−0.812740 + 0.582626i \(0.802025\pi\)
\(564\) 2.22477e13i 0.389842i
\(565\) 1.20114e14i 2.08618i
\(566\) 4.28910e13 0.738386
\(567\) −6.66383e11 −0.0113713
\(568\) 1.07968e14i 1.82622i
\(569\) 4.32147e12i 0.0724553i 0.999344 + 0.0362277i \(0.0115341\pi\)
−0.999344 + 0.0362277i \(0.988466\pi\)
\(570\) 1.54262e14i 2.56381i
\(571\) 7.89692e13i 1.30100i 0.759507 + 0.650500i \(0.225440\pi\)
−0.759507 + 0.650500i \(0.774560\pi\)
\(572\) −1.21344e14 −1.98170
\(573\) 2.86564e13i 0.463926i
\(574\) 1.89922e13i 0.304800i
\(575\) 1.16127e13i 0.184754i
\(576\) 1.89893e13 0.299500
\(577\) 7.96949e13 1.24610 0.623048 0.782183i \(-0.285894\pi\)
0.623048 + 0.782183i \(0.285894\pi\)
\(578\) 2.20589e14i 3.41936i
\(579\) −3.69313e13 −0.567546
\(580\) 2.55711e14 3.89592
\(581\) 1.17451e13i 0.177409i
\(582\) −1.88929e13 −0.282933
\(583\) 6.49264e13i 0.964003i
\(584\) 8.25694e13 1.21550
\(585\) 3.83917e13i 0.560349i
\(586\) 1.67399e14i 2.42250i
\(587\) 1.79859e13i 0.258073i 0.991640 + 0.129037i \(0.0411884\pi\)
−0.991640 + 0.129037i \(0.958812\pi\)
\(588\) 8.16144e13 1.16113
\(589\) 2.81295e13i 0.396813i
\(590\) −6.44727e13 + 1.97825e14i −0.901811 + 2.76708i
\(591\) −3.59721e13 −0.498918
\(592\) 1.46367e14i 2.01296i
\(593\) 8.00372e13 1.09149 0.545743 0.837952i \(-0.316247\pi\)
0.545743 + 0.837952i \(0.316247\pi\)
\(594\) 2.40235e13 0.324866
\(595\) 2.19579e13 0.294447
\(596\) 2.86068e14i 3.80397i
\(597\) 3.62878e13 0.478508
\(598\) 1.38010e13i 0.180470i
\(599\) −5.91243e13 −0.766712 −0.383356 0.923601i \(-0.625232\pi\)
−0.383356 + 0.923601i \(0.625232\pi\)
\(600\) 1.44732e14i 1.86126i
\(601\) 1.69409e12i 0.0216055i −0.999942 0.0108027i \(-0.996561\pi\)
0.999942 0.0108027i \(-0.00343869\pi\)
\(602\) 2.64630e13 0.334701
\(603\) 5.28919e13i 0.663441i
\(604\) 1.13792e14i 1.41556i
\(605\) 8.17034e12 0.100801
\(606\) −1.64598e13 −0.201401
\(607\) 4.87581e13 0.591702 0.295851 0.955234i \(-0.404397\pi\)
0.295851 + 0.955234i \(0.404397\pi\)
\(608\) 1.45463e13i 0.175080i
\(609\) 5.67709e12 0.0677703
\(610\) −1.23893e14 −1.46689
\(611\) 2.84560e13 0.334171
\(612\) 1.00129e14 1.16628
\(613\) 8.38466e13i 0.968686i −0.874878 0.484343i \(-0.839059\pi\)
0.874878 0.484343i \(-0.160941\pi\)
\(614\) 2.50564e14i 2.87129i
\(615\) 1.45188e14 1.65027
\(616\) 1.58197e13 0.178359
\(617\) 1.48956e14 1.66584 0.832920 0.553394i \(-0.186668\pi\)
0.832920 + 0.553394i \(0.186668\pi\)
\(618\) −4.92744e13 −0.546612
\(619\) −3.66420e13 −0.403205 −0.201603 0.979467i \(-0.564615\pi\)
−0.201603 + 0.979467i \(0.564615\pi\)
\(620\) 8.09284e13i 0.883370i
\(621\) 1.83128e12i 0.0198288i
\(622\) 2.30479e14i 2.47560i
\(623\) 1.04217e13i 0.111045i
\(624\) 6.03422e13i 0.637820i
\(625\) 4.02675e13 0.422235
\(626\) −1.68261e14 −1.75029
\(627\) 8.27509e13i 0.853955i
\(628\) 2.74536e14i 2.81061i
\(629\) 3.10649e14i 3.15513i
\(630\) 9.85314e12i 0.0992823i
\(631\) −6.94420e13 −0.694185 −0.347093 0.937831i \(-0.612831\pi\)
−0.347093 + 0.937831i \(0.612831\pi\)
\(632\) 5.65059e13i 0.560413i
\(633\) 1.79394e13i 0.176518i
\(634\) 1.58207e14i 1.54447i
\(635\) 2.88281e14 2.79220
\(636\) −1.21430e14 −1.16692
\(637\) 1.04390e14i 0.995314i
\(638\) −2.04663e14 −1.93613
\(639\) −3.60732e13 −0.338595
\(640\) 3.01367e14i 2.80670i
\(641\) 1.49366e13 0.138026 0.0690129 0.997616i \(-0.478015\pi\)
0.0690129 + 0.997616i \(0.478015\pi\)
\(642\) 6.86009e13i 0.629006i
\(643\) 7.23613e13 0.658342 0.329171 0.944270i \(-0.393231\pi\)
0.329171 + 0.944270i \(0.393231\pi\)
\(644\) 2.37396e12i 0.0214310i
\(645\) 2.02300e14i 1.81216i
\(646\) 5.14600e14i 4.57412i
\(647\) 1.15539e14 1.01908 0.509540 0.860447i \(-0.329816\pi\)
0.509540 + 0.860447i \(0.329816\pi\)
\(648\) 2.28236e13i 0.199760i
\(649\) 3.45851e13 1.06119e14i 0.300376 0.921662i
\(650\) −3.64427e14 −3.14083
\(651\) 1.79671e12i 0.0153664i
\(652\) −2.30159e14 −1.95339
\(653\) 2.07895e14 1.75097 0.875483 0.483249i \(-0.160543\pi\)
0.875483 + 0.483249i \(0.160543\pi\)
\(654\) 1.81665e14 1.51839
\(655\) 1.00673e14i 0.835037i
\(656\) 2.28199e14 1.87843
\(657\) 2.75873e13i 0.225363i
\(658\) −7.30317e12 −0.0592082
\(659\) 1.49164e14i 1.20015i −0.799942 0.600077i \(-0.795136\pi\)
0.799942 0.600077i \(-0.204864\pi\)
\(660\) 2.38074e14i 1.90104i
\(661\) −6.57803e12 −0.0521301 −0.0260651 0.999660i \(-0.508298\pi\)
−0.0260651 + 0.999660i \(0.508298\pi\)
\(662\) 9.21476e13i 0.724760i
\(663\) 1.28070e14i 0.999725i
\(664\) 4.02269e14 3.11657
\(665\) −3.39399e13 −0.260977
\(666\) −1.39397e14 −1.06385
\(667\) 1.56011e13i 0.118175i
\(668\) 4.19334e13 0.315266
\(669\) −2.39438e13 −0.178674
\(670\) −7.82059e14 −5.79249
\(671\) 6.64598e13 0.488592
\(672\) 9.29113e11i 0.00677988i
\(673\) 5.75405e13i 0.416772i 0.978047 + 0.208386i \(0.0668210\pi\)
−0.978047 + 0.208386i \(0.933179\pi\)
\(674\) 2.32024e13 0.166814
\(675\) 4.83563e13 0.345092
\(676\) 3.36582e12 0.0238428
\(677\) 2.05121e13 0.144234 0.0721168 0.997396i \(-0.477025\pi\)
0.0721168 + 0.997396i \(0.477025\pi\)
\(678\) 1.79799e14 1.25499
\(679\) 4.15670e12i 0.0288005i
\(680\) 7.52059e14i 5.17258i
\(681\) 5.39542e13i 0.368375i
\(682\) 6.47724e13i 0.439004i
\(683\) 1.82717e14i 1.22935i −0.788781 0.614675i \(-0.789287\pi\)
0.788781 0.614675i \(-0.210713\pi\)
\(684\) −1.54767e14 −1.03370
\(685\) 3.38144e14 2.24207
\(686\) 5.38662e13i 0.354565i
\(687\) 3.39381e13i 0.221771i
\(688\) 3.17965e14i 2.06271i
\(689\) 1.55316e14i 1.00028i
\(690\) 2.70773e13 0.173125
\(691\) 1.23818e14i 0.785949i 0.919549 + 0.392975i \(0.128554\pi\)
−0.919549 + 0.392975i \(0.871446\pi\)
\(692\) 3.13372e13i 0.197483i
\(693\) 5.28552e12i 0.0330690i
\(694\) 1.50927e14 0.937498
\(695\) −3.42769e13 −0.211386
\(696\) 1.94440e14i 1.19053i
\(697\) −4.84330e14 −2.94427
\(698\) −3.34892e14 −2.02129
\(699\) 1.32563e14i 0.794397i
\(700\) 6.26861e13 0.372976
\(701\) 1.43487e14i 0.847661i −0.905742 0.423830i \(-0.860685\pi\)
0.905742 0.423830i \(-0.139315\pi\)
\(702\) −5.74686e13 −0.337090
\(703\) 4.80163e14i 2.79648i
\(704\) 1.50616e14i 0.870982i
\(705\) 5.58300e13i 0.320570i
\(706\) −1.44160e14 −0.821903
\(707\) 3.62140e12i 0.0205012i
\(708\) 1.98472e14 + 6.46834e13i 1.11566 + 0.363602i
\(709\) 2.43610e14 1.35977 0.679884 0.733320i \(-0.262030\pi\)
0.679884 + 0.733320i \(0.262030\pi\)
\(710\) 5.33378e14i 2.95627i
\(711\) 1.88792e13 0.103905
\(712\) 3.56942e14 1.95073
\(713\) 4.93751e12 0.0267954
\(714\) 3.28689e13i 0.177131i
\(715\) 3.04510e14 1.62956
\(716\) 6.05397e13i 0.321718i
\(717\) −3.49491e13 −0.184434
\(718\) 3.00924e14i 1.57701i
\(719\) 2.74112e14i 1.42654i 0.700890 + 0.713269i \(0.252786\pi\)
−0.700890 + 0.713269i \(0.747214\pi\)
\(720\) 1.18390e14 0.611860
\(721\) 1.08411e13i 0.0556412i
\(722\) 4.53757e14i 2.31280i
\(723\) 7.62601e13 0.386017
\(724\) 1.29019e14 0.648578
\(725\) −4.11960e14 −2.05667
\(726\) 1.22302e13i 0.0606388i
\(727\) −2.40038e14 −1.18198 −0.590988 0.806680i \(-0.701262\pi\)
−0.590988 + 0.806680i \(0.701262\pi\)
\(728\) −3.78436e13 −0.185070
\(729\) 7.62560e12 0.0370370
\(730\) −4.07905e14 −1.96764
\(731\) 6.74849e14i 3.23310i
\(732\) 1.24298e14i 0.591436i
\(733\) 4.34418e13 0.205300 0.102650 0.994718i \(-0.467268\pi\)
0.102650 + 0.994718i \(0.467268\pi\)
\(734\) 5.13387e14 2.40971
\(735\) −2.04810e14 −0.954803
\(736\) 2.55328e12 0.0118225
\(737\) 4.19520e14 1.92937
\(738\) 2.17332e14i 0.992756i
\(739\) 4.22495e13i 0.191690i −0.995396 0.0958449i \(-0.969445\pi\)
0.995396 0.0958449i \(-0.0305553\pi\)
\(740\) 1.38143e15i 6.22542i
\(741\) 1.97955e14i 0.886087i
\(742\) 3.98614e13i 0.177228i
\(743\) −5.23748e13 −0.231301 −0.115651 0.993290i \(-0.536895\pi\)
−0.115651 + 0.993290i \(0.536895\pi\)
\(744\) 6.15372e13 0.269943
\(745\) 7.17881e14i 3.12803i
\(746\) 2.57950e14i 1.11645i
\(747\) 1.34402e14i 0.577835i
\(748\) 7.94185e14i 3.39167i
\(749\) 1.50932e13 0.0640283
\(750\) 3.16259e14i 1.33271i
\(751\) 2.62155e13i 0.109738i −0.998494 0.0548692i \(-0.982526\pi\)
0.998494 0.0548692i \(-0.0174742\pi\)
\(752\) 8.77509e13i 0.364890i
\(753\) −9.06579e13 −0.374482
\(754\) 4.89590e14 2.00898
\(755\) 2.85559e14i 1.16402i
\(756\) 9.88535e12 0.0400298
\(757\) 1.63745e14 0.658701 0.329350 0.944208i \(-0.393170\pi\)
0.329350 + 0.944208i \(0.393170\pi\)
\(758\) 1.64669e14i 0.658061i
\(759\) −1.45251e13 −0.0576646
\(760\) 1.16244e15i 4.58461i
\(761\) −2.09496e14 −0.820830 −0.410415 0.911899i \(-0.634616\pi\)
−0.410415 + 0.911899i \(0.634616\pi\)
\(762\) 4.31528e14i 1.67971i
\(763\) 3.99690e13i 0.154561i
\(764\) 4.25099e14i 1.63314i
\(765\) −2.51271e14 −0.959035
\(766\) 4.41610e14i 1.67454i
\(767\) −8.27338e13 + 2.53857e14i −0.311678 + 0.956341i
\(768\) −3.12516e14 −1.16968
\(769\) 2.72988e14i 1.01511i −0.861620 0.507553i \(-0.830550\pi\)
0.861620 0.507553i \(-0.169450\pi\)
\(770\) −7.81516e13 −0.288725
\(771\) 3.14488e12 0.0115434
\(772\) 5.47850e14 1.99791
\(773\) 9.16881e13i 0.332212i −0.986108 0.166106i \(-0.946881\pi\)
0.986108 0.166106i \(-0.0531194\pi\)
\(774\) −3.02823e14 −1.09015
\(775\) 1.30379e14i 0.466335i
\(776\) 1.42367e14 0.505942
\(777\) 3.06693e13i 0.108293i
\(778\) 1.61656e14i 0.567146i
\(779\) 7.48618e14 2.60959