Properties

Label 177.9.c.a.58.3
Level $177$
Weight $9$
Character 177.58
Analytic conductor $72.106$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 58.3
Character \(\chi\) \(=\) 177.58
Dual form 177.9.c.a.58.78

$q$-expansion

\(f(q)\) \(=\) \(q-29.8918i q^{2} +46.7654 q^{3} -637.520 q^{4} -247.630 q^{5} -1397.90i q^{6} +4057.23 q^{7} +11404.3i q^{8} +2187.00 q^{9} +O(q^{10})\) \(q-29.8918i q^{2} +46.7654 q^{3} -637.520 q^{4} -247.630 q^{5} -1397.90i q^{6} +4057.23 q^{7} +11404.3i q^{8} +2187.00 q^{9} +7402.10i q^{10} -21197.9i q^{11} -29813.9 q^{12} +21525.6i q^{13} -121278. i q^{14} -11580.5 q^{15} +177691. q^{16} -95116.6 q^{17} -65373.4i q^{18} -41670.2 q^{19} +157869. q^{20} +189738. q^{21} -633643. q^{22} +492438. i q^{23} +533328. i q^{24} -329304. q^{25} +643438. q^{26} +102276. q^{27} -2.58657e6 q^{28} -1.25263e6 q^{29} +346162. i q^{30} +1.66108e6i q^{31} -2.39199e6i q^{32} -991326. i q^{33} +2.84321e6i q^{34} -1.00469e6 q^{35} -1.39426e6 q^{36} -889974. i q^{37} +1.24560e6i q^{38} +1.00665e6i q^{39} -2.82405e6i q^{40} +1.19968e6 q^{41} -5.67161e6i q^{42} -2.01013e6i q^{43} +1.35141e7i q^{44} -541566. q^{45} +1.47199e7 q^{46} -2.76926e6i q^{47} +8.30977e6 q^{48} +1.06963e7 q^{49} +9.84351e6i q^{50} -4.44816e6 q^{51} -1.37230e7i q^{52} -8.79299e6 q^{53} -3.05721e6i q^{54} +5.24922e6i q^{55} +4.62700e7i q^{56} -1.94872e6 q^{57} +3.74433e7i q^{58} +(-1.17794e7 + 2.84185e6i) q^{59} +7.38280e6 q^{60} -1.24584e7i q^{61} +4.96526e7 q^{62} +8.87316e6 q^{63} -2.60121e7 q^{64} -5.33037e6i q^{65} -2.96325e7 q^{66} +2.43467e7i q^{67} +6.06387e7 q^{68} +2.30290e7i q^{69} +3.00320e7i q^{70} -4.11384e7 q^{71} +2.49413e7i q^{72} +2.32169e7i q^{73} -2.66029e7 q^{74} -1.54000e7 q^{75} +2.65656e7 q^{76} -8.60046e7i q^{77} +3.00906e7 q^{78} +2.79916e6 q^{79} -4.40015e7 q^{80} +4.78297e6 q^{81} -3.58607e7i q^{82} -2.03547e6i q^{83} -1.20962e8 q^{84} +2.35537e7 q^{85} -6.00863e7 q^{86} -5.85796e7 q^{87} +2.41747e8 q^{88} +2.00226e6i q^{89} +1.61884e7i q^{90} +8.73341e7i q^{91} -3.13939e8i q^{92} +7.76809e7i q^{93} -8.27781e7 q^{94} +1.03188e7 q^{95} -1.11862e8i q^{96} -3.90744e7i q^{97} -3.19732e8i q^{98} -4.63598e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} + O(q^{10}) \) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} - 22680q^{12} - 59616q^{15} + 1199848q^{16} - 10608q^{17} - 27516q^{19} - 146436q^{20} - 974696q^{22} + 5718040q^{25} - 797484q^{26} - 3133000q^{28} + 1725924q^{29} + 4318800q^{35} - 22394880q^{36} - 732180q^{41} + 22752084q^{46} + 8703936q^{48} + 55899176q^{49} - 10373832q^{51} - 39265944q^{53} - 11408040q^{57} - 33575112q^{59} - 18034488q^{60} + 13038600q^{62} + 349920q^{63} - 241654260q^{64} - 35711928q^{66} + 36772608q^{68} - 235272660q^{71} - 63050712q^{74} + 74363184q^{75} + 9454680q^{76} - 10865988q^{78} + 17252580q^{79} + 318203976q^{80} + 382637520q^{81} - 20743128q^{84} - 27245820q^{85} + 105666984q^{86} + 29437992q^{87} + 82079788q^{88} + 121215992q^{94} - 690837276q^{95} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 29.8918i 1.86824i −0.356962 0.934119i \(-0.616187\pi\)
0.356962 0.934119i \(-0.383813\pi\)
\(3\) 46.7654 0.577350
\(4\) −637.520 −2.49031
\(5\) −247.630 −0.396208 −0.198104 0.980181i \(-0.563478\pi\)
−0.198104 + 0.980181i \(0.563478\pi\)
\(6\) 1397.90i 1.07863i
\(7\) 4057.23 1.68981 0.844904 0.534918i \(-0.179657\pi\)
0.844904 + 0.534918i \(0.179657\pi\)
\(8\) 11404.3i 2.78426i
\(9\) 2187.00 0.333333
\(10\) 7402.10i 0.740210i
\(11\) 21197.9i 1.44784i −0.689882 0.723922i \(-0.742338\pi\)
0.689882 0.723922i \(-0.257662\pi\)
\(12\) −29813.9 −1.43778
\(13\) 21525.6i 0.753669i 0.926281 + 0.376835i \(0.122988\pi\)
−0.926281 + 0.376835i \(0.877012\pi\)
\(14\) 121278.i 3.15696i
\(15\) −11580.5 −0.228751
\(16\) 177691. 2.71135
\(17\) −95116.6 −1.13883 −0.569417 0.822049i \(-0.692831\pi\)
−0.569417 + 0.822049i \(0.692831\pi\)
\(18\) 65373.4i 0.622746i
\(19\) −41670.2 −0.319750 −0.159875 0.987137i \(-0.551109\pi\)
−0.159875 + 0.987137i \(0.551109\pi\)
\(20\) 157869. 0.986681
\(21\) 189738. 0.975611
\(22\) −633643. −2.70492
\(23\) 492438.i 1.75971i 0.475246 + 0.879853i \(0.342359\pi\)
−0.475246 + 0.879853i \(0.657641\pi\)
\(24\) 533328.i 1.60749i
\(25\) −329304. −0.843020
\(26\) 643438. 1.40803
\(27\) 102276. 0.192450
\(28\) −2.58657e6 −4.20815
\(29\) −1.25263e6 −1.77105 −0.885523 0.464595i \(-0.846200\pi\)
−0.885523 + 0.464595i \(0.846200\pi\)
\(30\) 346162.i 0.427361i
\(31\) 1.66108e6i 1.79864i 0.437296 + 0.899318i \(0.355936\pi\)
−0.437296 + 0.899318i \(0.644064\pi\)
\(32\) 2.39199e6i 2.28118i
\(33\) 991326.i 0.835913i
\(34\) 2.84321e6i 2.12761i
\(35\) −1.00469e6 −0.669515
\(36\) −1.39426e6 −0.830104
\(37\) 889974.i 0.474865i −0.971404 0.237433i \(-0.923694\pi\)
0.971404 0.237433i \(-0.0763059\pi\)
\(38\) 1.24560e6i 0.597370i
\(39\) 1.00665e6i 0.435131i
\(40\) 2.82405e6i 1.10314i
\(41\) 1.19968e6 0.424552 0.212276 0.977210i \(-0.431912\pi\)
0.212276 + 0.977210i \(0.431912\pi\)
\(42\) 5.67161e6i 1.82267i
\(43\) 2.01013e6i 0.587963i −0.955811 0.293981i \(-0.905020\pi\)
0.955811 0.293981i \(-0.0949803\pi\)
\(44\) 1.35141e7i 3.60558i
\(45\) −541566. −0.132069
\(46\) 1.47199e7 3.28755
\(47\) 2.76926e6i 0.567508i −0.958897 0.283754i \(-0.908420\pi\)
0.958897 0.283754i \(-0.0915799\pi\)
\(48\) 8.30977e6 1.56540
\(49\) 1.06963e7 1.85545
\(50\) 9.84351e6i 1.57496i
\(51\) −4.44816e6 −0.657506
\(52\) 1.37230e7i 1.87687i
\(53\) −8.79299e6 −1.11438 −0.557190 0.830385i \(-0.688120\pi\)
−0.557190 + 0.830385i \(0.688120\pi\)
\(54\) 3.05721e6i 0.359543i
\(55\) 5.24922e6i 0.573647i
\(56\) 4.62700e7i 4.70486i
\(57\) −1.94872e6 −0.184608
\(58\) 3.74433e7i 3.30874i
\(59\) −1.17794e7 + 2.84185e6i −0.972110 + 0.234527i
\(60\) 7.38280e6 0.569661
\(61\) 1.24584e7i 0.899793i −0.893081 0.449896i \(-0.851461\pi\)
0.893081 0.449896i \(-0.148539\pi\)
\(62\) 4.96526e7 3.36028
\(63\) 8.87316e6 0.563269
\(64\) −2.60121e7 −1.55044
\(65\) 5.33037e6i 0.298610i
\(66\) −2.96325e7 −1.56168
\(67\) 2.43467e7i 1.20820i 0.796907 + 0.604102i \(0.206468\pi\)
−0.796907 + 0.604102i \(0.793532\pi\)
\(68\) 6.06387e7 2.83605
\(69\) 2.30290e7i 1.01597i
\(70\) 3.00320e7i 1.25081i
\(71\) −4.11384e7 −1.61888 −0.809439 0.587205i \(-0.800228\pi\)
−0.809439 + 0.587205i \(0.800228\pi\)
\(72\) 2.49413e7i 0.928086i
\(73\) 2.32169e7i 0.817547i 0.912636 + 0.408773i \(0.134043\pi\)
−0.912636 + 0.408773i \(0.865957\pi\)
\(74\) −2.66029e7 −0.887161
\(75\) −1.54000e7 −0.486718
\(76\) 2.65656e7 0.796279
\(77\) 8.60046e7i 2.44658i
\(78\) 3.00906e7 0.812929
\(79\) 2.79916e6 0.0718652 0.0359326 0.999354i \(-0.488560\pi\)
0.0359326 + 0.999354i \(0.488560\pi\)
\(80\) −4.40015e7 −1.07426
\(81\) 4.78297e6 0.111111
\(82\) 3.58607e7i 0.793165i
\(83\) 2.03547e6i 0.0428896i −0.999770 0.0214448i \(-0.993173\pi\)
0.999770 0.0214448i \(-0.00682661\pi\)
\(84\) −1.20962e8 −2.42958
\(85\) 2.35537e7 0.451215
\(86\) −6.00863e7 −1.09845
\(87\) −5.85796e7 −1.02251
\(88\) 2.41747e8 4.03117
\(89\) 2.00226e6i 0.0319124i 0.999873 + 0.0159562i \(0.00507924\pi\)
−0.999873 + 0.0159562i \(0.994921\pi\)
\(90\) 1.61884e7i 0.246737i
\(91\) 8.73341e7i 1.27356i
\(92\) 3.13939e8i 4.38222i
\(93\) 7.76809e7i 1.03844i
\(94\) −8.27781e7 −1.06024
\(95\) 1.03188e7 0.126688
\(96\) 1.11862e8i 1.31704i
\(97\) 3.90744e7i 0.441373i −0.975345 0.220686i \(-0.929170\pi\)
0.975345 0.220686i \(-0.0708297\pi\)
\(98\) 3.19732e8i 3.46642i
\(99\) 4.63598e7i 0.482614i
\(100\) 2.09938e8 2.09938
\(101\) 1.41791e8i 1.36258i 0.732012 + 0.681291i \(0.238581\pi\)
−0.732012 + 0.681291i \(0.761419\pi\)
\(102\) 1.32964e8i 1.22838i
\(103\) 2.84725e7i 0.252975i 0.991968 + 0.126487i \(0.0403703\pi\)
−0.991968 + 0.126487i \(0.959630\pi\)
\(104\) −2.45484e8 −2.09841
\(105\) −4.69847e7 −0.386545
\(106\) 2.62838e8i 2.08193i
\(107\) 1.77416e8 1.35350 0.676748 0.736215i \(-0.263389\pi\)
0.676748 + 0.736215i \(0.263389\pi\)
\(108\) −6.52029e7 −0.479261
\(109\) 1.88778e8i 1.33735i 0.743555 + 0.668675i \(0.233138\pi\)
−0.743555 + 0.668675i \(0.766862\pi\)
\(110\) 1.56909e8 1.07171
\(111\) 4.16200e7i 0.274164i
\(112\) 7.20932e8 4.58165
\(113\) 1.94290e8i 1.19162i 0.803127 + 0.595808i \(0.203168\pi\)
−0.803127 + 0.595808i \(0.796832\pi\)
\(114\) 5.82508e7i 0.344892i
\(115\) 1.21942e8i 0.697209i
\(116\) 7.98575e8 4.41046
\(117\) 4.70764e7i 0.251223i
\(118\) 8.49479e7 + 3.52108e8i 0.438152 + 1.81613i
\(119\) −3.85910e8 −1.92441
\(120\) 1.32068e8i 0.636901i
\(121\) −2.34991e8 −1.09625
\(122\) −3.72404e8 −1.68103
\(123\) 5.61037e7 0.245115
\(124\) 1.05897e9i 4.47917i
\(125\) 1.78276e8 0.730218
\(126\) 2.65235e8i 1.05232i
\(127\) 1.85538e8 0.713210 0.356605 0.934255i \(-0.383934\pi\)
0.356605 + 0.934255i \(0.383934\pi\)
\(128\) 1.65199e8i 0.615413i
\(129\) 9.40043e7i 0.339460i
\(130\) −1.59334e8 −0.557874
\(131\) 5.84623e8i 1.98514i −0.121683 0.992569i \(-0.538829\pi\)
0.121683 0.992569i \(-0.461171\pi\)
\(132\) 6.31991e8i 2.08168i
\(133\) −1.69066e8 −0.540317
\(134\) 7.27766e8 2.25721
\(135\) −2.53266e7 −0.0762502
\(136\) 1.08474e9i 3.17081i
\(137\) −3.84843e8 −1.09245 −0.546224 0.837639i \(-0.683935\pi\)
−0.546224 + 0.837639i \(0.683935\pi\)
\(138\) 6.88379e8 1.89807
\(139\) 1.34828e8 0.361179 0.180589 0.983559i \(-0.442199\pi\)
0.180589 + 0.983559i \(0.442199\pi\)
\(140\) 6.40511e8 1.66730
\(141\) 1.29505e8i 0.327651i
\(142\) 1.22970e9i 3.02445i
\(143\) 4.56296e8 1.09120
\(144\) 3.88610e8 0.903782
\(145\) 3.10188e8 0.701702
\(146\) 6.93995e8 1.52737
\(147\) 5.00217e8 1.07125
\(148\) 5.67376e8i 1.18256i
\(149\) 4.99204e8i 1.01282i −0.862292 0.506411i \(-0.830972\pi\)
0.862292 0.506411i \(-0.169028\pi\)
\(150\) 4.60335e8i 0.909304i
\(151\) 6.49690e8i 1.24968i −0.780754 0.624839i \(-0.785165\pi\)
0.780754 0.624839i \(-0.214835\pi\)
\(152\) 4.75221e8i 0.890268i
\(153\) −2.08020e8 −0.379611
\(154\) −2.57083e9 −4.57079
\(155\) 4.11332e8i 0.712633i
\(156\) 6.41760e8i 1.08361i
\(157\) 3.80148e8i 0.625683i 0.949805 + 0.312842i \(0.101281\pi\)
−0.949805 + 0.312842i \(0.898719\pi\)
\(158\) 8.36718e7i 0.134261i
\(159\) −4.11207e8 −0.643387
\(160\) 5.92328e8i 0.903821i
\(161\) 1.99793e9i 2.97356i
\(162\) 1.42972e8i 0.207582i
\(163\) 4.70927e8 0.667119 0.333560 0.942729i \(-0.391750\pi\)
0.333560 + 0.942729i \(0.391750\pi\)
\(164\) −7.64823e8 −1.05727
\(165\) 2.45482e8i 0.331195i
\(166\) −6.08438e7 −0.0801280
\(167\) −1.19539e9 −1.53689 −0.768444 0.639917i \(-0.778969\pi\)
−0.768444 + 0.639917i \(0.778969\pi\)
\(168\) 2.16383e9i 2.71635i
\(169\) 3.52381e8 0.431982
\(170\) 7.04063e8i 0.842977i
\(171\) −9.11327e7 −0.106583
\(172\) 1.28150e9i 1.46421i
\(173\) 2.68426e8i 0.299668i −0.988711 0.149834i \(-0.952126\pi\)
0.988711 0.149834i \(-0.0478740\pi\)
\(174\) 1.75105e9i 1.91030i
\(175\) −1.33606e9 −1.42454
\(176\) 3.76667e9i 3.92560i
\(177\) −5.50868e8 + 1.32900e8i −0.561248 + 0.135404i
\(178\) 5.98511e7 0.0596200
\(179\) 5.25010e8i 0.511394i 0.966757 + 0.255697i \(0.0823049\pi\)
−0.966757 + 0.255697i \(0.917695\pi\)
\(180\) 3.45259e8 0.328894
\(181\) 1.34593e9 1.25403 0.627017 0.779006i \(-0.284276\pi\)
0.627017 + 0.779006i \(0.284276\pi\)
\(182\) 2.61057e9 2.37931
\(183\) 5.82621e8i 0.519496i
\(184\) −5.61592e9 −4.89948
\(185\) 2.20384e8i 0.188145i
\(186\) 2.32202e9 1.94006
\(187\) 2.01627e9i 1.64885i
\(188\) 1.76546e9i 1.41327i
\(189\) 4.14957e8 0.325204
\(190\) 3.08447e8i 0.236683i
\(191\) 3.31156e8i 0.248828i 0.992230 + 0.124414i \(0.0397051\pi\)
−0.992230 + 0.124414i \(0.960295\pi\)
\(192\) −1.21646e9 −0.895148
\(193\) −2.19184e9 −1.57972 −0.789859 0.613289i \(-0.789846\pi\)
−0.789859 + 0.613289i \(0.789846\pi\)
\(194\) −1.16801e9 −0.824590
\(195\) 2.49277e8i 0.172402i
\(196\) −6.81911e9 −4.62065
\(197\) 1.88008e9 1.24828 0.624139 0.781313i \(-0.285450\pi\)
0.624139 + 0.781313i \(0.285450\pi\)
\(198\) −1.38578e9 −0.901639
\(199\) −1.84676e9 −1.17760 −0.588799 0.808279i \(-0.700399\pi\)
−0.588799 + 0.808279i \(0.700399\pi\)
\(200\) 3.75550e9i 2.34718i
\(201\) 1.13858e9i 0.697557i
\(202\) 4.23839e9 2.54563
\(203\) −5.08220e9 −2.99273
\(204\) 2.83579e9 1.63740
\(205\) −2.97077e8 −0.168211
\(206\) 8.51096e8 0.472617
\(207\) 1.07696e9i 0.586568i
\(208\) 3.82489e9i 2.04346i
\(209\) 8.83320e8i 0.462949i
\(210\) 1.40446e9i 0.722157i
\(211\) 1.12595e9i 0.568056i 0.958816 + 0.284028i \(0.0916708\pi\)
−0.958816 + 0.284028i \(0.908329\pi\)
\(212\) 5.60571e9 2.77515
\(213\) −1.92385e9 −0.934659
\(214\) 5.30328e9i 2.52865i
\(215\) 4.97767e8i 0.232955i
\(216\) 1.16639e9i 0.535831i
\(217\) 6.73937e9i 3.03935i
\(218\) 5.64291e9 2.49849
\(219\) 1.08575e9i 0.472011i
\(220\) 3.34649e9i 1.42856i
\(221\) 2.04744e9i 0.858305i
\(222\) −1.24410e9 −0.512203
\(223\) 1.27587e9 0.515924 0.257962 0.966155i \(-0.416949\pi\)
0.257962 + 0.966155i \(0.416949\pi\)
\(224\) 9.70485e9i 3.85476i
\(225\) −7.20189e8 −0.281007
\(226\) 5.80767e9 2.22622
\(227\) 1.10307e9i 0.415433i 0.978189 + 0.207716i \(0.0666031\pi\)
−0.978189 + 0.207716i \(0.933397\pi\)
\(228\) 1.24235e9 0.459732
\(229\) 1.07539e8i 0.0391043i 0.999809 + 0.0195521i \(0.00622404\pi\)
−0.999809 + 0.0195521i \(0.993776\pi\)
\(230\) −3.64507e9 −1.30255
\(231\) 4.02204e9i 1.41253i
\(232\) 1.42854e10i 4.93105i
\(233\) 8.76987e8i 0.297557i 0.988871 + 0.148778i \(0.0475341\pi\)
−0.988871 + 0.148778i \(0.952466\pi\)
\(234\) 1.40720e9 0.469345
\(235\) 6.85751e8i 0.224851i
\(236\) 7.50961e9 1.81173e9i 2.42086 0.584045i
\(237\) 1.30904e8 0.0414914
\(238\) 1.15355e10i 3.59526i
\(239\) 1.11886e9 0.342913 0.171457 0.985192i \(-0.445153\pi\)
0.171457 + 0.985192i \(0.445153\pi\)
\(240\) −2.05775e9 −0.620222
\(241\) 3.82849e9 1.13490 0.567452 0.823407i \(-0.307929\pi\)
0.567452 + 0.823407i \(0.307929\pi\)
\(242\) 7.02431e9i 2.04806i
\(243\) 2.23677e8 0.0641500
\(244\) 7.94247e9i 2.24077i
\(245\) −2.64872e9 −0.735144
\(246\) 1.67704e9i 0.457934i
\(247\) 8.96974e8i 0.240986i
\(248\) −1.89435e10 −5.00787
\(249\) 9.51894e7i 0.0247623i
\(250\) 5.32899e9i 1.36422i
\(251\) −4.29677e9 −1.08255 −0.541275 0.840846i \(-0.682058\pi\)
−0.541275 + 0.840846i \(0.682058\pi\)
\(252\) −5.65682e9 −1.40272
\(253\) 1.04386e10 2.54778
\(254\) 5.54606e9i 1.33245i
\(255\) 1.10150e9 0.260509
\(256\) −1.72101e9 −0.400703
\(257\) 5.03295e9 1.15369 0.576847 0.816852i \(-0.304283\pi\)
0.576847 + 0.816852i \(0.304283\pi\)
\(258\) −2.80996e9 −0.634193
\(259\) 3.61083e9i 0.802431i
\(260\) 3.39822e9i 0.743631i
\(261\) −2.73950e9 −0.590349
\(262\) −1.74754e10 −3.70871
\(263\) 3.01837e8 0.0630884 0.0315442 0.999502i \(-0.489957\pi\)
0.0315442 + 0.999502i \(0.489957\pi\)
\(264\) 1.13054e10 2.32740
\(265\) 2.17741e9 0.441525
\(266\) 5.05368e9i 1.00944i
\(267\) 9.36364e7i 0.0184247i
\(268\) 1.55215e10i 3.00881i
\(269\) 4.48283e9i 0.856136i −0.903747 0.428068i \(-0.859194\pi\)
0.903747 0.428068i \(-0.140806\pi\)
\(270\) 7.57056e8i 0.142454i
\(271\) −2.34851e9 −0.435427 −0.217713 0.976013i \(-0.569860\pi\)
−0.217713 + 0.976013i \(0.569860\pi\)
\(272\) −1.69013e10 −3.08777
\(273\) 4.08421e9i 0.735288i
\(274\) 1.15036e10i 2.04095i
\(275\) 6.98056e9i 1.22056i
\(276\) 1.46815e10i 2.53007i
\(277\) −7.92826e9 −1.34666 −0.673331 0.739341i \(-0.735137\pi\)
−0.673331 + 0.739341i \(0.735137\pi\)
\(278\) 4.03026e9i 0.674768i
\(279\) 3.63278e9i 0.599545i
\(280\) 1.14578e10i 1.86410i
\(281\) −8.25964e9 −1.32476 −0.662378 0.749170i \(-0.730453\pi\)
−0.662378 + 0.749170i \(0.730453\pi\)
\(282\) −3.87115e9 −0.612130
\(283\) 4.43696e8i 0.0691736i 0.999402 + 0.0345868i \(0.0110115\pi\)
−0.999402 + 0.0345868i \(0.988988\pi\)
\(284\) 2.62265e10 4.03151
\(285\) 4.82562e8 0.0731431
\(286\) 1.36395e10i 2.03861i
\(287\) 4.86739e9 0.717412
\(288\) 5.23128e9i 0.760393i
\(289\) 2.07141e9 0.296944
\(290\) 9.27208e9i 1.31095i
\(291\) 1.82733e9i 0.254827i
\(292\) 1.48012e10i 2.03595i
\(293\) 3.14415e9 0.426612 0.213306 0.976985i \(-0.431577\pi\)
0.213306 + 0.976985i \(0.431577\pi\)
\(294\) 1.49524e10i 2.00134i
\(295\) 2.91693e9 7.03726e8i 0.385157 0.0929213i
\(296\) 1.01496e10 1.32215
\(297\) 2.16803e9i 0.278638i
\(298\) −1.49221e10 −1.89219
\(299\) −1.06000e10 −1.32624
\(300\) 9.81784e9 1.21208
\(301\) 8.15555e9i 0.993544i
\(302\) −1.94204e10 −2.33470
\(303\) 6.63091e9i 0.786688i
\(304\) −7.40441e9 −0.866954
\(305\) 3.08507e9i 0.356505i
\(306\) 6.21809e9i 0.709205i
\(307\) −3.18785e9 −0.358876 −0.179438 0.983769i \(-0.557428\pi\)
−0.179438 + 0.983769i \(0.557428\pi\)
\(308\) 5.48297e10i 6.09274i
\(309\) 1.33153e9i 0.146055i
\(310\) −1.22955e10 −1.33137
\(311\) −1.43538e10 −1.53435 −0.767176 0.641437i \(-0.778339\pi\)
−0.767176 + 0.641437i \(0.778339\pi\)
\(312\) −1.14802e10 −1.21152
\(313\) 6.81720e9i 0.710279i 0.934813 + 0.355140i \(0.115567\pi\)
−0.934813 + 0.355140i \(0.884433\pi\)
\(314\) 1.13633e10 1.16892
\(315\) −2.19726e9 −0.223172
\(316\) −1.78452e9 −0.178967
\(317\) 5.79535e9 0.573909 0.286954 0.957944i \(-0.407357\pi\)
0.286954 + 0.957944i \(0.407357\pi\)
\(318\) 1.22917e10i 1.20200i
\(319\) 2.65530e10i 2.56420i
\(320\) 6.44137e9 0.614297
\(321\) 8.29691e9 0.781441
\(322\) 5.97218e10 5.55533
\(323\) 3.96353e9 0.364143
\(324\) −3.04924e9 −0.276701
\(325\) 7.08846e9i 0.635358i
\(326\) 1.40769e10i 1.24634i
\(327\) 8.82826e9i 0.772119i
\(328\) 1.36816e10i 1.18206i
\(329\) 1.12355e10i 0.958979i
\(330\) 7.33790e9 0.618751
\(331\) −1.65954e10 −1.38253 −0.691266 0.722601i \(-0.742947\pi\)
−0.691266 + 0.722601i \(0.742947\pi\)
\(332\) 1.29765e9i 0.106809i
\(333\) 1.94637e9i 0.158288i
\(334\) 3.57322e10i 2.87127i
\(335\) 6.02896e9i 0.478700i
\(336\) 3.37147e10 2.64522
\(337\) 1.80474e10i 1.39925i 0.714512 + 0.699623i \(0.246649\pi\)
−0.714512 + 0.699623i \(0.753351\pi\)
\(338\) 1.05333e10i 0.807046i
\(339\) 9.08603e9i 0.687979i
\(340\) −1.50160e10 −1.12367
\(341\) 3.52113e10 2.60414
\(342\) 2.72412e9i 0.199123i
\(343\) 2.00082e10 1.44555
\(344\) 2.29241e10 1.63704
\(345\) 5.70267e9i 0.402534i
\(346\) −8.02375e9 −0.559852
\(347\) 2.10020e10i 1.44858i −0.689494 0.724292i \(-0.742167\pi\)
0.689494 0.724292i \(-0.257833\pi\)
\(348\) 3.73457e10 2.54638
\(349\) 4.85779e9i 0.327444i −0.986507 0.163722i \(-0.947650\pi\)
0.986507 0.163722i \(-0.0523500\pi\)
\(350\) 3.99374e10i 2.66138i
\(351\) 2.20154e9i 0.145044i
\(352\) −5.07051e10 −3.30279
\(353\) 1.90800e10i 1.22879i 0.788997 + 0.614397i \(0.210601\pi\)
−0.788997 + 0.614397i \(0.789399\pi\)
\(354\) 3.97262e9 + 1.64664e10i 0.252967 + 1.04854i
\(355\) 1.01871e10 0.641411
\(356\) 1.27648e9i 0.0794720i
\(357\) −1.80472e10 −1.11106
\(358\) 1.56935e10 0.955405
\(359\) −8.81861e9 −0.530912 −0.265456 0.964123i \(-0.585522\pi\)
−0.265456 + 0.964123i \(0.585522\pi\)
\(360\) 6.17620e9i 0.367715i
\(361\) −1.52472e10 −0.897760
\(362\) 4.02324e10i 2.34283i
\(363\) −1.09894e10 −0.632920
\(364\) 5.56772e10i 3.17155i
\(365\) 5.74919e9i 0.323918i
\(366\) −1.74156e10 −0.970541
\(367\) 1.46733e10i 0.808840i −0.914573 0.404420i \(-0.867473\pi\)
0.914573 0.404420i \(-0.132527\pi\)
\(368\) 8.75016e10i 4.77117i
\(369\) 2.62371e9 0.141517
\(370\) 6.58768e9 0.351500
\(371\) −3.56752e10 −1.88309
\(372\) 4.95232e10i 2.58605i
\(373\) 4.10565e9 0.212103 0.106051 0.994361i \(-0.466179\pi\)
0.106051 + 0.994361i \(0.466179\pi\)
\(374\) 6.02699e10 3.08045
\(375\) 8.33714e9 0.421592
\(376\) 3.15815e10 1.58009
\(377\) 2.69635e10i 1.33478i
\(378\) 1.24038e10i 0.607558i
\(379\) −3.96543e10 −1.92191 −0.960955 0.276704i \(-0.910758\pi\)
−0.960955 + 0.276704i \(0.910758\pi\)
\(380\) −6.57843e9 −0.315492
\(381\) 8.67674e9 0.411772
\(382\) 9.89885e9 0.464870
\(383\) 1.49720e10 0.695799 0.347899 0.937532i \(-0.386895\pi\)
0.347899 + 0.937532i \(0.386895\pi\)
\(384\) 7.72558e9i 0.355309i
\(385\) 2.12973e10i 0.969353i
\(386\) 6.55180e10i 2.95129i
\(387\) 4.39615e9i 0.195988i
\(388\) 2.49107e10i 1.09916i
\(389\) 3.75472e9 0.163975 0.0819877 0.996633i \(-0.473873\pi\)
0.0819877 + 0.996633i \(0.473873\pi\)
\(390\) −7.45133e9 −0.322089
\(391\) 4.68390e10i 2.00401i
\(392\) 1.21984e11i 5.16606i
\(393\) 2.73401e10i 1.14612i
\(394\) 5.61990e10i 2.33208i
\(395\) −6.93154e8 −0.0284735
\(396\) 2.95553e10i 1.20186i
\(397\) 5.89403e9i 0.237274i −0.992938 0.118637i \(-0.962148\pi\)
0.992938 0.118637i \(-0.0378525\pi\)
\(398\) 5.52029e10i 2.20003i
\(399\) −7.90641e9 −0.311952
\(400\) −5.85144e10 −2.28572
\(401\) 3.30329e10i 1.27752i 0.769404 + 0.638762i \(0.220553\pi\)
−0.769404 + 0.638762i \(0.779447\pi\)
\(402\) 3.40343e10 1.30320
\(403\) −3.57556e10 −1.35558
\(404\) 9.03946e10i 3.39326i
\(405\) −1.18441e9 −0.0440231
\(406\) 1.51916e11i 5.59113i
\(407\) −1.88656e10 −0.687530
\(408\) 5.07283e10i 1.83067i
\(409\) 3.04752e10i 1.08906i −0.838740 0.544532i \(-0.816707\pi\)
0.838740 0.544532i \(-0.183293\pi\)
\(410\) 8.88018e9i 0.314258i
\(411\) −1.79973e10 −0.630725
\(412\) 1.81518e10i 0.629987i
\(413\) −4.77917e10 + 1.15300e10i −1.64268 + 0.396305i
\(414\) 3.21923e10 1.09585
\(415\) 5.04043e8i 0.0169932i
\(416\) 5.14889e10 1.71926
\(417\) 6.30530e9 0.208527
\(418\) 2.64040e10 0.864898
\(419\) 1.81306e9i 0.0588241i −0.999567 0.0294121i \(-0.990637\pi\)
0.999567 0.0294121i \(-0.00936350\pi\)
\(420\) 2.99537e10 0.962617
\(421\) 3.79069e10i 1.20667i −0.797486 0.603337i \(-0.793837\pi\)
0.797486 0.603337i \(-0.206163\pi\)
\(422\) 3.36568e10 1.06126
\(423\) 6.05637e9i 0.189169i
\(424\) 1.00278e11i 3.10272i
\(425\) 3.13223e10 0.960060
\(426\) 5.75074e10i 1.74617i
\(427\) 5.05465e10i 1.52048i
\(428\) −1.13106e11 −3.37063
\(429\) 2.13388e10 0.630002
\(430\) 1.48792e10 0.435216
\(431\) 6.06752e10i 1.75834i −0.476510 0.879169i \(-0.658098\pi\)
0.476510 0.879169i \(-0.341902\pi\)
\(432\) 1.81735e10 0.521799
\(433\) −2.64222e10 −0.751653 −0.375826 0.926690i \(-0.622641\pi\)
−0.375826 + 0.926690i \(0.622641\pi\)
\(434\) 2.01452e11 5.67823
\(435\) 1.45061e10 0.405128
\(436\) 1.20350e11i 3.33042i
\(437\) 2.05200e10i 0.562667i
\(438\) 3.24549e10 0.881829
\(439\) −6.36143e10 −1.71276 −0.856380 0.516347i \(-0.827292\pi\)
−0.856380 + 0.516347i \(0.827292\pi\)
\(440\) −5.98639e10 −1.59718
\(441\) 2.33928e10 0.618484
\(442\) −6.12016e10 −1.60352
\(443\) 3.79235e10i 0.984677i 0.870404 + 0.492338i \(0.163858\pi\)
−0.870404 + 0.492338i \(0.836142\pi\)
\(444\) 2.65336e10i 0.682753i
\(445\) 4.95819e8i 0.0126440i
\(446\) 3.81380e10i 0.963869i
\(447\) 2.33455e10i 0.584753i
\(448\) −1.05537e11 −2.61995
\(449\) −1.87339e10 −0.460938 −0.230469 0.973080i \(-0.574026\pi\)
−0.230469 + 0.973080i \(0.574026\pi\)
\(450\) 2.15277e10i 0.524987i
\(451\) 2.54307e10i 0.614685i
\(452\) 1.23864e11i 2.96749i
\(453\) 3.03830e10i 0.721502i
\(454\) 3.29728e10 0.776127
\(455\) 2.16265e10i 0.504593i
\(456\) 2.22239e10i 0.513997i
\(457\) 1.55748e10i 0.357074i 0.983933 + 0.178537i \(0.0571364\pi\)
−0.983933 + 0.178537i \(0.942864\pi\)
\(458\) 3.21454e9 0.0730561
\(459\) −9.72813e9 −0.219169
\(460\) 7.77406e10i 1.73627i
\(461\) 1.36617e10 0.302484 0.151242 0.988497i \(-0.451673\pi\)
0.151242 + 0.988497i \(0.451673\pi\)
\(462\) −1.20226e11 −2.63895
\(463\) 2.90985e10i 0.633209i 0.948558 + 0.316604i \(0.102543\pi\)
−0.948558 + 0.316604i \(0.897457\pi\)
\(464\) −2.22580e11 −4.80192
\(465\) 1.92361e10i 0.411439i
\(466\) 2.62147e10 0.555906
\(467\) 9.71527e9i 0.204262i −0.994771 0.102131i \(-0.967434\pi\)
0.994771 0.102131i \(-0.0325661\pi\)
\(468\) 3.00121e10i 0.625624i
\(469\) 9.87800e10i 2.04163i
\(470\) 2.04983e10 0.420075
\(471\) 1.77778e10i 0.361238i
\(472\) −3.24093e10 1.34336e11i −0.652984 2.70661i
\(473\) −4.26104e10 −0.851278
\(474\) 3.91294e9i 0.0775158i
\(475\) 1.37222e10 0.269556
\(476\) 2.46025e11 4.79239
\(477\) −1.92303e10 −0.371460
\(478\) 3.34448e10i 0.640644i
\(479\) 5.28028e10 1.00303 0.501516 0.865148i \(-0.332776\pi\)
0.501516 + 0.865148i \(0.332776\pi\)
\(480\) 2.77004e10i 0.521821i
\(481\) 1.91572e10 0.357891
\(482\) 1.14440e11i 2.12027i
\(483\) 9.34341e10i 1.71679i
\(484\) 1.49811e11 2.73001
\(485\) 9.67599e9i 0.174875i
\(486\) 6.68612e9i 0.119848i
\(487\) 6.59238e10 1.17200 0.585998 0.810312i \(-0.300703\pi\)
0.585998 + 0.810312i \(0.300703\pi\)
\(488\) 1.42080e11 2.50526
\(489\) 2.20231e10 0.385162
\(490\) 7.91751e10i 1.37342i
\(491\) 1.08414e11 1.86535 0.932675 0.360719i \(-0.117469\pi\)
0.932675 + 0.360719i \(0.117469\pi\)
\(492\) −3.57672e10 −0.610414
\(493\) 1.19146e11 2.01693
\(494\) −2.68122e10 −0.450219
\(495\) 1.14801e10i 0.191216i
\(496\) 2.95158e11i 4.87672i
\(497\) −1.66908e11 −2.73559
\(498\) −2.84538e9 −0.0462619
\(499\) −2.38659e10 −0.384925 −0.192462 0.981304i \(-0.561647\pi\)
−0.192462 + 0.981304i \(0.561647\pi\)
\(500\) −1.13655e11 −1.81847
\(501\) −5.59027e10 −0.887323
\(502\) 1.28438e11i 2.02246i
\(503\) 1.22240e10i 0.190960i 0.995431 + 0.0954799i \(0.0304386\pi\)
−0.995431 + 0.0954799i \(0.969561\pi\)
\(504\) 1.01192e11i 1.56829i
\(505\) 3.51117e10i 0.539866i
\(506\) 3.12030e11i 4.75986i
\(507\) 1.64792e10 0.249405
\(508\) −1.18284e11 −1.77612
\(509\) 3.81044e10i 0.567680i −0.958872 0.283840i \(-0.908392\pi\)
0.958872 0.283840i \(-0.0916085\pi\)
\(510\) 3.29258e10i 0.486693i
\(511\) 9.41963e10i 1.38150i
\(512\) 9.37349e10i 1.36402i
\(513\) −4.26186e9 −0.0615360
\(514\) 1.50444e11i 2.15537i
\(515\) 7.05065e9i 0.100231i
\(516\) 5.99297e10i 0.845363i
\(517\) −5.87024e10 −0.821662
\(518\) −1.07934e11 −1.49913
\(519\) 1.25531e10i 0.173014i
\(520\) 6.07892e10 0.831406
\(521\) −1.64846e10 −0.223732 −0.111866 0.993723i \(-0.535683\pi\)
−0.111866 + 0.993723i \(0.535683\pi\)
\(522\) 8.18885e10i 1.10291i
\(523\) 8.28989e9 0.110801 0.0554003 0.998464i \(-0.482357\pi\)
0.0554003 + 0.998464i \(0.482357\pi\)
\(524\) 3.72709e11i 4.94362i
\(525\) −6.24815e10 −0.822459
\(526\) 9.02246e9i 0.117864i
\(527\) 1.57996e11i 2.04835i
\(528\) 1.76150e11i 2.26645i
\(529\) −1.64184e11 −2.09656
\(530\) 6.50866e10i 0.824875i
\(531\) −2.57616e10 + 6.21512e9i −0.324037 + 0.0781756i
\(532\) 1.07783e11 1.34556
\(533\) 2.58239e10i 0.319972i
\(534\) 2.79896e9 0.0344216
\(535\) −4.39334e10 −0.536265
\(536\) −2.77657e11 −3.36395
\(537\) 2.45523e10i 0.295253i
\(538\) −1.34000e11 −1.59947
\(539\) 2.26739e11i 2.68640i
\(540\) 1.61462e10 0.189887
\(541\) 9.07595e10i 1.05951i −0.848152 0.529753i \(-0.822285\pi\)
0.848152 0.529753i \(-0.177715\pi\)
\(542\) 7.02012e10i 0.813481i
\(543\) 6.29431e10 0.724017
\(544\) 2.27518e11i 2.59789i
\(545\) 4.67470e10i 0.529868i
\(546\) 1.22084e11 1.37369
\(547\) −3.63083e10 −0.405561 −0.202781 0.979224i \(-0.564998\pi\)
−0.202781 + 0.979224i \(0.564998\pi\)
\(548\) 2.45345e11 2.72054
\(549\) 2.72465e10i 0.299931i
\(550\) 2.08661e11 2.28030
\(551\) 5.21973e10 0.566293
\(552\) −2.62631e11 −2.82871
\(553\) 1.13568e10 0.121438
\(554\) 2.36990e11i 2.51589i
\(555\) 1.03063e10i 0.108626i
\(556\) −8.59558e10 −0.899448
\(557\) −1.36428e10 −0.141737 −0.0708684 0.997486i \(-0.522577\pi\)
−0.0708684 + 0.997486i \(0.522577\pi\)
\(558\) 1.08590e11 1.12009
\(559\) 4.32691e10 0.443129
\(560\) −1.78524e11 −1.81529
\(561\) 9.42916e10i 0.951966i
\(562\) 2.46895e11i 2.47496i
\(563\) 9.41472e9i 0.0937073i 0.998902 + 0.0468537i \(0.0149194\pi\)
−0.998902 + 0.0468537i \(0.985081\pi\)
\(564\) 8.25623e10i 0.815953i
\(565\) 4.81119e10i 0.472127i
\(566\) 1.32629e10 0.129233
\(567\) 1.94056e10 0.187756
\(568\) 4.69156e11i 4.50737i
\(569\) 1.09073e11i 1.04056i −0.853995 0.520281i \(-0.825827\pi\)
0.853995 0.520281i \(-0.174173\pi\)
\(570\) 1.44246e10i 0.136649i
\(571\) 1.44117e11i 1.35572i 0.735189 + 0.677862i \(0.237093\pi\)
−0.735189 + 0.677862i \(0.762907\pi\)
\(572\) −2.90898e11 −2.71742
\(573\) 1.54866e10i 0.143661i
\(574\) 1.45495e11i 1.34030i
\(575\) 1.62162e11i 1.48347i
\(576\) −5.68884e10 −0.516814
\(577\) 2.14805e11 1.93794 0.968972 0.247172i \(-0.0795013\pi\)
0.968972 + 0.247172i \(0.0795013\pi\)
\(578\) 6.19181e10i 0.554762i
\(579\) −1.02502e11 −0.912050
\(580\) −1.97751e11 −1.74746
\(581\) 8.25836e9i 0.0724752i
\(582\) −5.46222e10 −0.476077
\(583\) 1.86393e11i 1.61345i
\(584\) −2.64773e11 −2.27626
\(585\) 1.16575e10i 0.0995365i
\(586\) 9.39843e10i 0.797012i
\(587\) 1.59442e11i 1.34292i −0.741039 0.671461i \(-0.765667\pi\)
0.741039 0.671461i \(-0.234333\pi\)
\(588\) −3.18898e11 −2.66774
\(589\) 6.92175e10i 0.575115i
\(590\) −2.10356e10 8.71923e10i −0.173599 0.719565i
\(591\) 8.79227e10 0.720694
\(592\) 1.58140e11i 1.28752i
\(593\) 1.49251e11 1.20698 0.603488 0.797372i \(-0.293777\pi\)
0.603488 + 0.797372i \(0.293777\pi\)
\(594\) −6.48064e10 −0.520561
\(595\) 9.55628e10 0.762467
\(596\) 3.18253e11i 2.52224i
\(597\) −8.63642e10 −0.679887
\(598\) 3.16853e11i 2.47772i
\(599\) 9.04429e9 0.0702533 0.0351267 0.999383i \(-0.488817\pi\)
0.0351267 + 0.999383i \(0.488817\pi\)
\(600\) 1.75627e11i 1.35515i
\(601\) 3.45042e10i 0.264469i 0.991218 + 0.132234i \(0.0422152\pi\)
−0.991218 + 0.132234i \(0.957785\pi\)
\(602\) −2.43784e11 −1.85618
\(603\) 5.32462e10i 0.402735i
\(604\) 4.14190e11i 3.11209i
\(605\) 5.81908e10 0.434343
\(606\) 1.98210e11 1.46972
\(607\) −1.49775e11 −1.10328 −0.551639 0.834083i \(-0.685997\pi\)
−0.551639 + 0.834083i \(0.685997\pi\)
\(608\) 9.96747e10i 0.729408i
\(609\) −2.37671e11 −1.72785
\(610\) 9.22182e10 0.666036
\(611\) 5.96098e10 0.427713
\(612\) 1.32617e11 0.945351
\(613\) 7.52477e10i 0.532907i −0.963848 0.266453i \(-0.914148\pi\)
0.963848 0.266453i \(-0.0858518\pi\)
\(614\) 9.52906e10i 0.670465i
\(615\) −1.38929e10 −0.0971166
\(616\) 9.80825e11 6.81191
\(617\) −1.95339e11 −1.34787 −0.673934 0.738791i \(-0.735397\pi\)
−0.673934 + 0.738791i \(0.735397\pi\)
\(618\) 3.98018e10 0.272866
\(619\) −3.92472e10 −0.267329 −0.133664 0.991027i \(-0.542674\pi\)
−0.133664 + 0.991027i \(0.542674\pi\)
\(620\) 2.62233e11i 1.77468i
\(621\) 5.03645e10i 0.338655i
\(622\) 4.29060e11i 2.86653i
\(623\) 8.12362e9i 0.0539259i
\(624\) 1.78872e11i 1.17979i
\(625\) 8.44881e10 0.553701
\(626\) 2.03779e11 1.32697
\(627\) 4.13088e10i 0.267284i
\(628\) 2.42352e11i 1.55815i
\(629\) 8.46513e10i 0.540793i
\(630\) 6.56800e10i 0.416938i
\(631\) −1.90888e11 −1.20410 −0.602048 0.798460i \(-0.705648\pi\)
−0.602048 + 0.798460i \(0.705648\pi\)
\(632\) 3.19225e10i 0.200091i
\(633\) 5.26557e10i 0.327967i
\(634\) 1.73234e11i 1.07220i
\(635\) −4.59447e10 −0.282579
\(636\) 2.62153e11 1.60224
\(637\) 2.30244e11i 1.39840i
\(638\) 7.93718e11 4.79053
\(639\) −8.99697e10 −0.539626
\(640\) 4.09081e10i 0.243831i
\(641\) 1.74358e11 1.03278 0.516392 0.856352i \(-0.327275\pi\)
0.516392 + 0.856352i \(0.327275\pi\)
\(642\) 2.48010e11i 1.45992i
\(643\) −1.55791e10 −0.0911376 −0.0455688 0.998961i \(-0.514510\pi\)
−0.0455688 + 0.998961i \(0.514510\pi\)
\(644\) 1.27372e12i 7.40511i
\(645\) 2.32783e10i 0.134497i
\(646\) 1.18477e11i 0.680306i
\(647\) 8.29547e10 0.473395 0.236697 0.971583i \(-0.423935\pi\)
0.236697 + 0.971583i \(0.423935\pi\)
\(648\) 5.45465e10i 0.309362i
\(649\) 6.02411e10 + 2.49698e11i 0.339558 + 1.40746i
\(650\) −2.11887e11 −1.18700
\(651\) 3.15169e11i 1.75477i
\(652\) −3.00226e11 −1.66134
\(653\) −2.11139e10 −0.116122 −0.0580612 0.998313i \(-0.518492\pi\)
−0.0580612 + 0.998313i \(0.518492\pi\)
\(654\) 2.63893e11 1.44250
\(655\) 1.44770e11i 0.786527i
\(656\) 2.13173e11 1.15111
\(657\) 5.07753e10i 0.272516i
\(658\) −3.35850e11 −1.79160
\(659\) 2.40511e11i 1.27524i −0.770350 0.637622i \(-0.779918\pi\)
0.770350 0.637622i \(-0.220082\pi\)
\(660\) 1.56500e11i 0.824779i
\(661\) 4.97787e10 0.260758 0.130379 0.991464i \(-0.458381\pi\)
0.130379 + 0.991464i \(0.458381\pi\)
\(662\) 4.96066e11i 2.58290i
\(663\) 9.57492e10i 0.495542i
\(664\) 2.32131e10 0.119416
\(665\) 4.18657e10 0.214078
\(666\) −5.81806e10 −0.295720
\(667\) 6.16841e11i 3.11652i
\(668\) 7.62083e11 3.82733
\(669\) 5.96664e10 0.297869
\(670\) −1.80217e11 −0.894325
\(671\) −2.64091e11 −1.30276
\(672\) 4.53851e11i 2.22554i
\(673\) 3.50853e9i 0.0171027i 0.999963 + 0.00855136i \(0.00272201\pi\)
−0.999963 + 0.00855136i \(0.997278\pi\)
\(674\) 5.39468e11 2.61412
\(675\) −3.36799e10 −0.162239
\(676\) −2.24650e11 −1.07577
\(677\) −1.33644e11 −0.636200 −0.318100 0.948057i \(-0.603045\pi\)
−0.318100 + 0.948057i \(0.603045\pi\)
\(678\) 2.71598e11 1.28531
\(679\) 1.58534e11i 0.745835i
\(680\) 2.68614e11i 1.25630i
\(681\) 5.15856e10i 0.239850i
\(682\) 1.05253e12i 4.86516i
\(683\) 2.61051e11i 1.19962i 0.800144 + 0.599808i \(0.204756\pi\)
−0.800144 + 0.599808i \(0.795244\pi\)
\(684\) 5.80990e10 0.265426
\(685\) 9.52985e10 0.432836
\(686\) 5.98083e11i 2.70063i
\(687\) 5.02911e9i 0.0225769i
\(688\) 3.57181e11i 1.59417i
\(689\) 1.89274e11i 0.839873i
\(690\) −1.70463e11 −0.752029
\(691\) 1.53433e11i 0.672987i 0.941686 + 0.336493i \(0.109241\pi\)
−0.941686 + 0.336493i \(0.890759\pi\)
\(692\) 1.71127e11i 0.746268i
\(693\) 1.88092e11i 0.815526i
\(694\) −6.27789e11 −2.70630
\(695\) −3.33875e10 −0.143102
\(696\) 6.68061e11i 2.84695i
\(697\) −1.14110e11 −0.483495
\(698\) −1.45208e11 −0.611743
\(699\) 4.10126e10i 0.171794i
\(700\) 8.51768e11 3.54755
\(701\) 8.71726e10i 0.361001i −0.983575 0.180500i \(-0.942228\pi\)
0.983575 0.180500i \(-0.0577717\pi\)
\(702\) 6.58081e10 0.270976
\(703\) 3.70854e10i 0.151838i
\(704\) 5.51401e11i 2.24480i
\(705\) 3.20694e10i 0.129818i
\(706\) 5.70335e11 2.29568
\(707\) 5.75278e11i 2.30250i
\(708\) 3.51190e11 8.47264e10i 1.39768 0.337199i
\(709\) 3.33405e10 0.131943 0.0659717 0.997821i \(-0.478985\pi\)
0.0659717 + 0.997821i \(0.478985\pi\)
\(710\) 3.04511e11i 1.19831i
\(711\) 6.12175e9 0.0239551
\(712\) −2.28344e10 −0.0888525
\(713\) −8.17977e11 −3.16507
\(714\) 5.39464e11i 2.07572i
\(715\) −1.12992e11 −0.432340
\(716\) 3.34704e11i 1.27353i
\(717\) 5.23239e10 0.197981
\(718\) 2.63604e11i 0.991870i
\(719\) 9.49106e10i 0.355140i −0.984108 0.177570i \(-0.943176\pi\)
0.984108 0.177570i \(-0.0568236\pi\)
\(720\) −9.62313e10 −0.358085
\(721\) 1.15520e11i 0.427479i
\(722\) 4.55765e11i 1.67723i
\(723\) 1.79041e11 0.655237
\(724\) −8.58059e11 −3.12294
\(725\) 4.12496e11 1.49303
\(726\) 3.28494e11i 1.18245i
\(727\) −1.53628e11 −0.549963 −0.274981 0.961450i \(-0.588672\pi\)
−0.274981 + 0.961450i \(0.588672\pi\)
\(728\) −9.95987e11 −3.54591
\(729\) 1.04604e10 0.0370370
\(730\) −1.71854e11 −0.605156
\(731\) 1.91196e11i 0.669592i
\(732\) 3.71433e11i 1.29371i
\(733\) 4.52962e10 0.156908 0.0784541 0.996918i \(-0.475002\pi\)
0.0784541 + 0.996918i \(0.475002\pi\)
\(734\) −4.38611e11 −1.51111
\(735\) −1.23869e11 −0.424436
\(736\) 1.17791e12 4.01420
\(737\) 5.16098e11 1.74929
\(738\) 7.84274e10i 0.264388i
\(739\) 3.89715e11i 1.30668i 0.757065 + 0.653340i \(0.226633\pi\)
−0.757065 + 0.653340i \(0.773367\pi\)
\(740\) 1.40499e11i 0.468541i
\(741\) 4.19473e10i 0.139133i
\(742\) 1.06640e12i 3.51805i
\(743\) −2.21515e10 −0.0726854 −0.0363427 0.999339i \(-0.511571\pi\)
−0.0363427 + 0.999339i \(0.511571\pi\)
\(744\) −8.85899e11 −2.89129
\(745\) 1.23618e11i 0.401288i
\(746\) 1.22725e11i 0.396259i
\(747\) 4.45157e9i 0.0142965i
\(748\) 1.28541e12i 4.10616i
\(749\) 7.19816e11 2.28715
\(750\) 2.49212e11i 0.787634i
\(751\) 1.70755e10i 0.0536803i −0.999640 0.0268401i \(-0.991455\pi\)
0.999640 0.0268401i \(-0.00854450\pi\)
\(752\) 4.92071e11i 1.53871i
\(753\) −2.00940e11 −0.625010
\(754\) −8.05988e11 −2.49369
\(755\) 1.60882e11i 0.495132i
\(756\) −2.64543e11 −0.809859
\(757\) −3.31538e10 −0.100960 −0.0504800 0.998725i \(-0.516075\pi\)
−0.0504800 + 0.998725i \(0.516075\pi\)
\(758\) 1.18534e12i 3.59059i
\(759\) 4.88167e11 1.47096
\(760\) 1.17679e11i 0.352731i
\(761\) −5.71126e11 −1.70292 −0.851458 0.524423i \(-0.824281\pi\)
−0.851458 + 0.524423i \(0.824281\pi\)
\(762\) 2.59363e11i 0.769288i
\(763\) 7.65915e11i 2.25986i
\(764\) 2.11119e11i 0.619659i
\(765\) 5.15119e10 0.150405
\(766\) 4.47539e11i 1.29992i
\(767\) −6.11723e10 2.53558e11i −0.176756 0.732649i
\(768\) −8.04836e10 −0.231346
\(769\) 8.44024e10i 0.241351i −0.992692 0.120676i \(-0.961494\pi\)
0.992692 0.120676i \(-0.0385061\pi\)
\(770\) 6.36615e11 1.81098
\(771\) 2.35368e11 0.666085
\(772\) 1.39734e12 3.93399
\(773\) 2.74428e11i 0.768618i −0.923205 0.384309i \(-0.874440\pi\)
0.923205 0.384309i \(-0.125560\pi\)
\(774\) −1.31409e11 −0.366151
\(775\) 5.47000e11i 1.51628i
\(776\) 4.45617e11 1.22890
\(777\) 1.68862e11i 0.463284i
\(778\) 1.12235e11i 0.306345i
\(779\) −4.99911e10 −0.135751
\(780\) 1.58919e11i 0.429336i
\(781\) 8.72046e11i 2.34388i
\(782\) −1.40010e12 −3.74397