Properties

Label 177.3.c.a.58.12
Level $177$
Weight $3$
Character 177.58
Analytic conductor $4.823$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(4.82290067918\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \(x^{20} + 60 x^{18} + 1522 x^{16} + 21286 x^{14} + 179593 x^{12} + 941588 x^{10} + 3057025 x^{8} + 5962230 x^{6} + 6517782 x^{4} + 3428244 x^{2} + 570861\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{7}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.12
Root \(1.08628i\) of defining polynomial
Character \(\chi\) \(=\) 177.58
Dual form 177.3.c.a.58.9

$q$-expansion

\(f(q)\) \(=\) \(q+1.08628i q^{2} +1.73205 q^{3} +2.82000 q^{4} +3.33671 q^{5} +1.88149i q^{6} -1.22637 q^{7} +7.40842i q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+1.08628i q^{2} +1.73205 q^{3} +2.82000 q^{4} +3.33671 q^{5} +1.88149i q^{6} -1.22637 q^{7} +7.40842i q^{8} +3.00000 q^{9} +3.62460i q^{10} -1.21764i q^{11} +4.88438 q^{12} -12.6555i q^{13} -1.33218i q^{14} +5.77936 q^{15} +3.23240 q^{16} -0.815320 q^{17} +3.25883i q^{18} -7.74812 q^{19} +9.40954 q^{20} -2.12414 q^{21} +1.32270 q^{22} +33.8014i q^{23} +12.8318i q^{24} -13.8663 q^{25} +13.7474 q^{26} +5.19615 q^{27} -3.45837 q^{28} +7.53415 q^{29} +6.27799i q^{30} -7.71953i q^{31} +33.1450i q^{32} -2.10902i q^{33} -0.885664i q^{34} -4.09206 q^{35} +8.46000 q^{36} -16.7957i q^{37} -8.41661i q^{38} -21.9199i q^{39} +24.7198i q^{40} -19.0497 q^{41} -2.30741i q^{42} -48.9576i q^{43} -3.43375i q^{44} +10.0101 q^{45} -36.7177 q^{46} +4.79310i q^{47} +5.59868 q^{48} -47.4960 q^{49} -15.0627i q^{50} -1.41218 q^{51} -35.6884i q^{52} -48.7328 q^{53} +5.64447i q^{54} -4.06292i q^{55} -9.08548i q^{56} -13.4201 q^{57} +8.18418i q^{58} +(43.5656 - 39.7874i) q^{59} +16.2978 q^{60} -87.6284i q^{61} +8.38556 q^{62} -3.67912 q^{63} -23.0750 q^{64} -42.2277i q^{65} +2.29098 q^{66} +42.6674i q^{67} -2.29920 q^{68} +58.5457i q^{69} -4.44511i q^{70} -20.2245 q^{71} +22.2252i q^{72} -45.6107i q^{73} +18.2448 q^{74} -24.0172 q^{75} -21.8497 q^{76} +1.49328i q^{77} +23.8111 q^{78} -62.5528 q^{79} +10.7856 q^{80} +9.00000 q^{81} -20.6933i q^{82} -22.8390i q^{83} -5.99008 q^{84} -2.72049 q^{85} +53.1815 q^{86} +13.0495 q^{87} +9.02079 q^{88} -55.8982i q^{89} +10.8738i q^{90} +15.5203i q^{91} +95.3199i q^{92} -13.3706i q^{93} -5.20664 q^{94} -25.8533 q^{95} +57.4087i q^{96} +123.320i q^{97} -51.5939i q^{98} -3.65292i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 40q^{4} - 8q^{7} + 60q^{9} + O(q^{10}) \) \( 20q - 40q^{4} - 8q^{7} + 60q^{9} - 24q^{12} + 24q^{15} - 8q^{16} + 16q^{17} - 60q^{19} - 164q^{20} + 40q^{22} + 100q^{25} - 156q^{26} + 200q^{28} - 60q^{29} - 32q^{35} - 120q^{36} + 28q^{41} + 180q^{46} - 96q^{48} + 284q^{49} - 24q^{51} - 8q^{53} + 24q^{57} - 152q^{59} - 72q^{60} - 8q^{62} - 24q^{63} + 204q^{64} - 120q^{66} + 384q^{68} + 92q^{71} + 104q^{74} + 240q^{75} + 120q^{76} - 468q^{78} - 420q^{79} + 376q^{80} + 180q^{81} + 168q^{84} - 348q^{85} + 232q^{86} + 144q^{87} - 212q^{88} + 152q^{94} + 788q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.08628i 0.543139i 0.962419 + 0.271570i \(0.0875427\pi\)
−0.962419 + 0.271570i \(0.912457\pi\)
\(3\) 1.73205 0.577350
\(4\) 2.82000 0.705000
\(5\) 3.33671 0.667343 0.333671 0.942689i \(-0.391712\pi\)
0.333671 + 0.942689i \(0.391712\pi\)
\(6\) 1.88149i 0.313581i
\(7\) −1.22637 −0.175196 −0.0875981 0.996156i \(-0.527919\pi\)
−0.0875981 + 0.996156i \(0.527919\pi\)
\(8\) 7.40842i 0.926052i
\(9\) 3.00000 0.333333
\(10\) 3.62460i 0.362460i
\(11\) 1.21764i 0.110695i −0.998467 0.0553473i \(-0.982373\pi\)
0.998467 0.0553473i \(-0.0176266\pi\)
\(12\) 4.88438 0.407032
\(13\) 12.6555i 0.973497i −0.873542 0.486749i \(-0.838183\pi\)
0.873542 0.486749i \(-0.161817\pi\)
\(14\) 1.33218i 0.0951559i
\(15\) 5.77936 0.385291
\(16\) 3.23240 0.202025
\(17\) −0.815320 −0.0479600 −0.0239800 0.999712i \(-0.507634\pi\)
−0.0239800 + 0.999712i \(0.507634\pi\)
\(18\) 3.25883i 0.181046i
\(19\) −7.74812 −0.407796 −0.203898 0.978992i \(-0.565361\pi\)
−0.203898 + 0.978992i \(0.565361\pi\)
\(20\) 9.40954 0.470477
\(21\) −2.12414 −0.101150
\(22\) 1.32270 0.0601226
\(23\) 33.8014i 1.46963i 0.678270 + 0.734813i \(0.262730\pi\)
−0.678270 + 0.734813i \(0.737270\pi\)
\(24\) 12.8318i 0.534656i
\(25\) −13.8663 −0.554653
\(26\) 13.7474 0.528744
\(27\) 5.19615 0.192450
\(28\) −3.45837 −0.123513
\(29\) 7.53415 0.259798 0.129899 0.991527i \(-0.458535\pi\)
0.129899 + 0.991527i \(0.458535\pi\)
\(30\) 6.27799i 0.209266i
\(31\) 7.71953i 0.249017i −0.992219 0.124509i \(-0.960265\pi\)
0.992219 0.124509i \(-0.0397354\pi\)
\(32\) 33.1450i 1.03578i
\(33\) 2.10902i 0.0639096i
\(34\) 0.885664i 0.0260489i
\(35\) −4.09206 −0.116916
\(36\) 8.46000 0.235000
\(37\) 16.7957i 0.453937i −0.973902 0.226969i \(-0.927119\pi\)
0.973902 0.226969i \(-0.0728815\pi\)
\(38\) 8.41661i 0.221490i
\(39\) 21.9199i 0.562049i
\(40\) 24.7198i 0.617994i
\(41\) −19.0497 −0.464627 −0.232314 0.972641i \(-0.574630\pi\)
−0.232314 + 0.972641i \(0.574630\pi\)
\(42\) 2.30741i 0.0549383i
\(43\) 48.9576i 1.13855i −0.822148 0.569274i \(-0.807224\pi\)
0.822148 0.569274i \(-0.192776\pi\)
\(44\) 3.43375i 0.0780397i
\(45\) 10.0101 0.222448
\(46\) −36.7177 −0.798211
\(47\) 4.79310i 0.101981i 0.998699 + 0.0509904i \(0.0162378\pi\)
−0.998699 + 0.0509904i \(0.983762\pi\)
\(48\) 5.59868 0.116639
\(49\) −47.4960 −0.969306
\(50\) 15.0627i 0.301254i
\(51\) −1.41218 −0.0276897
\(52\) 35.6884i 0.686316i
\(53\) −48.7328 −0.919488 −0.459744 0.888052i \(-0.652059\pi\)
−0.459744 + 0.888052i \(0.652059\pi\)
\(54\) 5.64447i 0.104527i
\(55\) 4.06292i 0.0738713i
\(56\) 9.08548i 0.162241i
\(57\) −13.4201 −0.235441
\(58\) 8.18418i 0.141107i
\(59\) 43.5656 39.7874i 0.738400 0.674363i
\(60\) 16.2978 0.271630
\(61\) 87.6284i 1.43653i −0.695769 0.718265i \(-0.744936\pi\)
0.695769 0.718265i \(-0.255064\pi\)
\(62\) 8.38556 0.135251
\(63\) −3.67912 −0.0583987
\(64\) −23.0750 −0.360547
\(65\) 42.2277i 0.649657i
\(66\) 2.29098 0.0347118
\(67\) 42.6674i 0.636826i 0.947952 + 0.318413i \(0.103150\pi\)
−0.947952 + 0.318413i \(0.896850\pi\)
\(68\) −2.29920 −0.0338118
\(69\) 58.5457i 0.848489i
\(70\) 4.44511i 0.0635016i
\(71\) −20.2245 −0.284852 −0.142426 0.989805i \(-0.545490\pi\)
−0.142426 + 0.989805i \(0.545490\pi\)
\(72\) 22.2252i 0.308684i
\(73\) 45.6107i 0.624804i −0.949950 0.312402i \(-0.898866\pi\)
0.949950 0.312402i \(-0.101134\pi\)
\(74\) 18.2448 0.246551
\(75\) −24.0172 −0.320229
\(76\) −21.8497 −0.287496
\(77\) 1.49328i 0.0193933i
\(78\) 23.8111 0.305271
\(79\) −62.5528 −0.791808 −0.395904 0.918292i \(-0.629569\pi\)
−0.395904 + 0.918292i \(0.629569\pi\)
\(80\) 10.7856 0.134820
\(81\) 9.00000 0.111111
\(82\) 20.6933i 0.252357i
\(83\) 22.8390i 0.275169i −0.990490 0.137584i \(-0.956066\pi\)
0.990490 0.137584i \(-0.0439338\pi\)
\(84\) −5.99008 −0.0713105
\(85\) −2.72049 −0.0320058
\(86\) 53.1815 0.618390
\(87\) 13.0495 0.149995
\(88\) 9.02079 0.102509
\(89\) 55.8982i 0.628070i −0.949411 0.314035i \(-0.898319\pi\)
0.949411 0.314035i \(-0.101681\pi\)
\(90\) 10.8738i 0.120820i
\(91\) 15.5203i 0.170553i
\(92\) 95.3199i 1.03609i
\(93\) 13.3706i 0.143770i
\(94\) −5.20664 −0.0553897
\(95\) −25.8533 −0.272140
\(96\) 57.4087i 0.598008i
\(97\) 123.320i 1.27134i 0.771962 + 0.635669i \(0.219276\pi\)
−0.771962 + 0.635669i \(0.780724\pi\)
\(98\) 51.5939i 0.526468i
\(99\) 3.65292i 0.0368982i
\(100\) −39.1031 −0.391031
\(101\) 39.0946i 0.387075i 0.981093 + 0.193538i \(0.0619962\pi\)
−0.981093 + 0.193538i \(0.938004\pi\)
\(102\) 1.53401i 0.0150394i
\(103\) 56.8713i 0.552149i 0.961136 + 0.276074i \(0.0890336\pi\)
−0.961136 + 0.276074i \(0.910966\pi\)
\(104\) 93.7570 0.901509
\(105\) −7.08765 −0.0675015
\(106\) 52.9374i 0.499410i
\(107\) 34.8029 0.325261 0.162630 0.986687i \(-0.448002\pi\)
0.162630 + 0.986687i \(0.448002\pi\)
\(108\) 14.6532 0.135677
\(109\) 9.83542i 0.0902332i −0.998982 0.0451166i \(-0.985634\pi\)
0.998982 0.0451166i \(-0.0143659\pi\)
\(110\) 4.41346 0.0401224
\(111\) 29.0910i 0.262081i
\(112\) −3.96413 −0.0353940
\(113\) 145.812i 1.29037i 0.764025 + 0.645186i \(0.223220\pi\)
−0.764025 + 0.645186i \(0.776780\pi\)
\(114\) 14.5780i 0.127877i
\(115\) 112.786i 0.980744i
\(116\) 21.2463 0.183158
\(117\) 37.9664i 0.324499i
\(118\) 43.2202 + 47.3244i 0.366273 + 0.401054i
\(119\) 0.999886 0.00840241
\(120\) 42.8159i 0.356799i
\(121\) 119.517 0.987747
\(122\) 95.1888 0.780236
\(123\) −32.9951 −0.268253
\(124\) 21.7691i 0.175557i
\(125\) −129.686 −1.03749
\(126\) 3.99655i 0.0317186i
\(127\) 145.827 1.14825 0.574123 0.818769i \(-0.305343\pi\)
0.574123 + 0.818769i \(0.305343\pi\)
\(128\) 107.514i 0.839952i
\(129\) 84.7970i 0.657341i
\(130\) 45.8710 0.352854
\(131\) 30.5967i 0.233562i 0.993158 + 0.116781i \(0.0372576\pi\)
−0.993158 + 0.116781i \(0.962742\pi\)
\(132\) 5.94742i 0.0450562i
\(133\) 9.50208 0.0714442
\(134\) −46.3486 −0.345885
\(135\) 17.3381 0.128430
\(136\) 6.04023i 0.0444134i
\(137\) −39.4511 −0.287964 −0.143982 0.989580i \(-0.545991\pi\)
−0.143982 + 0.989580i \(0.545991\pi\)
\(138\) −63.5969 −0.460847
\(139\) 93.5556 0.673062 0.336531 0.941672i \(-0.390746\pi\)
0.336531 + 0.941672i \(0.390746\pi\)
\(140\) −11.5396 −0.0824257
\(141\) 8.30189i 0.0588786i
\(142\) 21.9694i 0.154714i
\(143\) −15.4098 −0.107761
\(144\) 9.69720 0.0673417
\(145\) 25.1393 0.173375
\(146\) 49.5459 0.339356
\(147\) −82.2655 −0.559629
\(148\) 47.3638i 0.320026i
\(149\) 133.435i 0.895536i −0.894150 0.447768i \(-0.852219\pi\)
0.894150 0.447768i \(-0.147781\pi\)
\(150\) 26.0894i 0.173929i
\(151\) 95.5402i 0.632717i 0.948640 + 0.316358i \(0.102460\pi\)
−0.948640 + 0.316358i \(0.897540\pi\)
\(152\) 57.4013i 0.377640i
\(153\) −2.44596 −0.0159867
\(154\) −1.62212 −0.0105332
\(155\) 25.7579i 0.166180i
\(156\) 61.8142i 0.396245i
\(157\) 245.077i 1.56100i 0.625157 + 0.780499i \(0.285035\pi\)
−0.625157 + 0.780499i \(0.714965\pi\)
\(158\) 67.9498i 0.430062i
\(159\) −84.4078 −0.530866
\(160\) 110.595i 0.691220i
\(161\) 41.4531i 0.257473i
\(162\) 9.77650i 0.0603488i
\(163\) 204.601 1.25522 0.627611 0.778527i \(-0.284033\pi\)
0.627611 + 0.778527i \(0.284033\pi\)
\(164\) −53.7202 −0.327562
\(165\) 7.03718i 0.0426496i
\(166\) 24.8095 0.149455
\(167\) −100.875 −0.604043 −0.302022 0.953301i \(-0.597661\pi\)
−0.302022 + 0.953301i \(0.597661\pi\)
\(168\) 15.7365i 0.0936698i
\(169\) 8.83915 0.0523027
\(170\) 2.95521i 0.0173836i
\(171\) −23.2443 −0.135932
\(172\) 138.060i 0.802677i
\(173\) 192.449i 1.11242i −0.831041 0.556212i \(-0.812254\pi\)
0.831041 0.556212i \(-0.187746\pi\)
\(174\) 14.1754i 0.0814679i
\(175\) 17.0053 0.0971732
\(176\) 3.93590i 0.0223631i
\(177\) 75.4579 68.9138i 0.426316 0.389343i
\(178\) 60.7210 0.341129
\(179\) 66.4049i 0.370977i −0.982646 0.185488i \(-0.940613\pi\)
0.982646 0.185488i \(-0.0593867\pi\)
\(180\) 28.2286 0.156826
\(181\) 100.811 0.556968 0.278484 0.960441i \(-0.410168\pi\)
0.278484 + 0.960441i \(0.410168\pi\)
\(182\) −16.8594 −0.0926340
\(183\) 151.777i 0.829381i
\(184\) −250.415 −1.36095
\(185\) 56.0424i 0.302932i
\(186\) 14.5242 0.0780872
\(187\) 0.992766i 0.00530891i
\(188\) 13.5165i 0.0718965i
\(189\) −6.37242 −0.0337165
\(190\) 28.0838i 0.147810i
\(191\) 285.899i 1.49686i 0.663216 + 0.748428i \(0.269191\pi\)
−0.663216 + 0.748428i \(0.730809\pi\)
\(192\) −39.9671 −0.208162
\(193\) 11.7169 0.0607093 0.0303546 0.999539i \(-0.490336\pi\)
0.0303546 + 0.999539i \(0.490336\pi\)
\(194\) −133.960 −0.690513
\(195\) 73.1405i 0.375079i
\(196\) −133.939 −0.683361
\(197\) −269.535 −1.36820 −0.684099 0.729389i \(-0.739805\pi\)
−0.684099 + 0.729389i \(0.739805\pi\)
\(198\) 3.96809 0.0200409
\(199\) 164.357 0.825912 0.412956 0.910751i \(-0.364496\pi\)
0.412956 + 0.910751i \(0.364496\pi\)
\(200\) 102.728i 0.513638i
\(201\) 73.9021i 0.367672i
\(202\) −42.4676 −0.210236
\(203\) −9.23968 −0.0455157
\(204\) −3.98233 −0.0195212
\(205\) −63.5635 −0.310066
\(206\) −61.7781 −0.299894
\(207\) 101.404i 0.489875i
\(208\) 40.9075i 0.196671i
\(209\) 9.43442i 0.0451408i
\(210\) 7.69916i 0.0366627i
\(211\) 155.167i 0.735391i 0.929946 + 0.367695i \(0.119853\pi\)
−0.929946 + 0.367695i \(0.880147\pi\)
\(212\) −137.427 −0.648239
\(213\) −35.0298 −0.164459
\(214\) 37.8056i 0.176662i
\(215\) 163.357i 0.759802i
\(216\) 38.4953i 0.178219i
\(217\) 9.46703i 0.0436269i
\(218\) 10.6840 0.0490092
\(219\) 79.0001i 0.360731i
\(220\) 11.4574i 0.0520792i
\(221\) 10.3183i 0.0466889i
\(222\) 31.6009 0.142346
\(223\) 212.798 0.954251 0.477126 0.878835i \(-0.341679\pi\)
0.477126 + 0.878835i \(0.341679\pi\)
\(224\) 40.6481i 0.181465i
\(225\) −41.5990 −0.184884
\(226\) −158.392 −0.700852
\(227\) 272.876i 1.20210i 0.799213 + 0.601048i \(0.205250\pi\)
−0.799213 + 0.601048i \(0.794750\pi\)
\(228\) −37.8448 −0.165986
\(229\) 350.552i 1.53080i −0.643557 0.765398i \(-0.722542\pi\)
0.643557 0.765398i \(-0.277458\pi\)
\(230\) −122.517 −0.532681
\(231\) 2.58644i 0.0111967i
\(232\) 55.8161i 0.240587i
\(233\) 1.64412i 0.00705630i 0.999994 + 0.00352815i \(0.00112305\pi\)
−0.999994 + 0.00352815i \(0.998877\pi\)
\(234\) 41.2421 0.176248
\(235\) 15.9932i 0.0680562i
\(236\) 122.855 112.200i 0.520572 0.475426i
\(237\) −108.345 −0.457151
\(238\) 1.08615i 0.00456368i
\(239\) −74.5410 −0.311887 −0.155943 0.987766i \(-0.549842\pi\)
−0.155943 + 0.987766i \(0.549842\pi\)
\(240\) 18.6812 0.0778384
\(241\) −56.4597 −0.234272 −0.117136 0.993116i \(-0.537371\pi\)
−0.117136 + 0.993116i \(0.537371\pi\)
\(242\) 129.829i 0.536484i
\(243\) 15.5885 0.0641500
\(244\) 247.112i 1.01275i
\(245\) −158.481 −0.646860
\(246\) 35.8418i 0.145698i
\(247\) 98.0560i 0.396988i
\(248\) 57.1895 0.230603
\(249\) 39.5583i 0.158869i
\(250\) 140.875i 0.563500i
\(251\) −21.6224 −0.0861451 −0.0430726 0.999072i \(-0.513715\pi\)
−0.0430726 + 0.999072i \(0.513715\pi\)
\(252\) −10.3751 −0.0411711
\(253\) 41.1580 0.162680
\(254\) 158.409i 0.623657i
\(255\) −4.71203 −0.0184785
\(256\) −209.090 −0.816758
\(257\) 70.0007 0.272376 0.136188 0.990683i \(-0.456515\pi\)
0.136188 + 0.990683i \(0.456515\pi\)
\(258\) 92.1131 0.357028
\(259\) 20.5978i 0.0795281i
\(260\) 119.082i 0.458008i
\(261\) 22.6025 0.0865994
\(262\) −33.2365 −0.126857
\(263\) 450.103 1.71142 0.855709 0.517457i \(-0.173121\pi\)
0.855709 + 0.517457i \(0.173121\pi\)
\(264\) 15.6245 0.0591836
\(265\) −162.608 −0.613614
\(266\) 10.3219i 0.0388042i
\(267\) 96.8186i 0.362617i
\(268\) 120.322i 0.448963i
\(269\) 167.392i 0.622275i −0.950365 0.311137i \(-0.899290\pi\)
0.950365 0.311137i \(-0.100710\pi\)
\(270\) 18.8340i 0.0697555i
\(271\) 136.135 0.502342 0.251171 0.967943i \(-0.419184\pi\)
0.251171 + 0.967943i \(0.419184\pi\)
\(272\) −2.63544 −0.00968912
\(273\) 26.8820i 0.0984689i
\(274\) 42.8549i 0.156405i
\(275\) 16.8842i 0.0613971i
\(276\) 165.099i 0.598185i
\(277\) −195.176 −0.704606 −0.352303 0.935886i \(-0.614601\pi\)
−0.352303 + 0.935886i \(0.614601\pi\)
\(278\) 101.627i 0.365566i
\(279\) 23.1586i 0.0830057i
\(280\) 30.3157i 0.108270i
\(281\) 475.581 1.69246 0.846229 0.532820i \(-0.178868\pi\)
0.846229 + 0.532820i \(0.178868\pi\)
\(282\) −9.01816 −0.0319793
\(283\) 444.223i 1.56969i 0.619691 + 0.784846i \(0.287258\pi\)
−0.619691 + 0.784846i \(0.712742\pi\)
\(284\) −57.0330 −0.200821
\(285\) −44.7791 −0.157120
\(286\) 16.7393i 0.0585292i
\(287\) 23.3621 0.0814009
\(288\) 99.4349i 0.345260i
\(289\) −288.335 −0.997700
\(290\) 27.3083i 0.0941665i
\(291\) 213.596i 0.734007i
\(292\) 128.622i 0.440487i
\(293\) −56.4950 −0.192816 −0.0964079 0.995342i \(-0.530735\pi\)
−0.0964079 + 0.995342i \(0.530735\pi\)
\(294\) 89.3632i 0.303956i
\(295\) 145.366 132.759i 0.492766 0.450031i
\(296\) 124.429 0.420369
\(297\) 6.32705i 0.0213032i
\(298\) 144.947 0.486401
\(299\) 427.772 1.43068
\(300\) −67.7285 −0.225762
\(301\) 60.0403i 0.199469i
\(302\) −103.783 −0.343653
\(303\) 67.7138i 0.223478i
\(304\) −25.0450 −0.0823849
\(305\) 292.391i 0.958659i
\(306\) 2.65699i 0.00868298i
\(307\) 279.533 0.910530 0.455265 0.890356i \(-0.349545\pi\)
0.455265 + 0.890356i \(0.349545\pi\)
\(308\) 4.21106i 0.0136723i
\(309\) 98.5040i 0.318783i
\(310\) 27.9802 0.0902588
\(311\) 210.784 0.677762 0.338881 0.940829i \(-0.389952\pi\)
0.338881 + 0.940829i \(0.389952\pi\)
\(312\) 162.392 0.520487
\(313\) 372.662i 1.19061i 0.803499 + 0.595306i \(0.202969\pi\)
−0.803499 + 0.595306i \(0.797031\pi\)
\(314\) −266.221 −0.847839
\(315\) −12.2762 −0.0389720
\(316\) −176.399 −0.558225
\(317\) 299.104 0.943544 0.471772 0.881720i \(-0.343614\pi\)
0.471772 + 0.881720i \(0.343614\pi\)
\(318\) 91.6903i 0.288334i
\(319\) 9.17389i 0.0287583i
\(320\) −76.9948 −0.240609
\(321\) 60.2804 0.187789
\(322\) 45.0296 0.139844
\(323\) 6.31719 0.0195579
\(324\) 25.3800 0.0783333
\(325\) 175.485i 0.539954i
\(326\) 222.254i 0.681760i
\(327\) 17.0354i 0.0520962i
\(328\) 141.128i 0.430269i
\(329\) 5.87813i 0.0178666i
\(330\) 7.64434 0.0231647
\(331\) 268.182 0.810217 0.405109 0.914269i \(-0.367234\pi\)
0.405109 + 0.914269i \(0.367234\pi\)
\(332\) 64.4060i 0.193994i
\(333\) 50.3870i 0.151312i
\(334\) 109.579i 0.328079i
\(335\) 142.369i 0.424982i
\(336\) −6.86608 −0.0204347
\(337\) 372.241i 1.10457i −0.833655 0.552286i \(-0.813756\pi\)
0.833655 0.552286i \(-0.186244\pi\)
\(338\) 9.60178i 0.0284076i
\(339\) 252.554i 0.744997i
\(340\) −7.67178 −0.0225641
\(341\) −9.39962 −0.0275649
\(342\) 25.2498i 0.0738299i
\(343\) 118.340 0.345015
\(344\) 362.698 1.05436
\(345\) 195.350i 0.566233i
\(346\) 209.053 0.604201
\(347\) 162.680i 0.468820i 0.972138 + 0.234410i \(0.0753158\pi\)
−0.972138 + 0.234410i \(0.924684\pi\)
\(348\) 36.7997 0.105746
\(349\) 474.478i 1.35954i −0.733427 0.679768i \(-0.762080\pi\)
0.733427 0.679768i \(-0.237920\pi\)
\(350\) 18.4725i 0.0527785i
\(351\) 65.7597i 0.187350i
\(352\) 40.3586 0.114655
\(353\) 553.231i 1.56723i 0.621248 + 0.783614i \(0.286626\pi\)
−0.621248 + 0.783614i \(0.713374\pi\)
\(354\) 74.8595 + 81.9682i 0.211468 + 0.231549i
\(355\) −67.4833 −0.190094
\(356\) 157.633i 0.442790i
\(357\) 1.73185 0.00485113
\(358\) 72.1342 0.201492
\(359\) −347.072 −0.966775 −0.483387 0.875407i \(-0.660594\pi\)
−0.483387 + 0.875407i \(0.660594\pi\)
\(360\) 74.1593i 0.205998i
\(361\) −300.967 −0.833703
\(362\) 109.509i 0.302511i
\(363\) 207.010 0.570276
\(364\) 43.7673i 0.120240i
\(365\) 152.190i 0.416959i
\(366\) 164.872 0.450469
\(367\) 617.839i 1.68349i 0.539879 + 0.841743i \(0.318470\pi\)
−0.539879 + 0.841743i \(0.681530\pi\)
\(368\) 109.260i 0.296901i
\(369\) −57.1491 −0.154876
\(370\) 60.8776 0.164534
\(371\) 59.7647 0.161091
\(372\) 37.7052i 0.101358i
\(373\) −427.265 −1.14548 −0.572741 0.819736i \(-0.694120\pi\)
−0.572741 + 0.819736i \(0.694120\pi\)
\(374\) −1.07842 −0.00288348
\(375\) −224.623 −0.598993
\(376\) −35.5093 −0.0944395
\(377\) 95.3482i 0.252913i
\(378\) 6.92222i 0.0183128i
\(379\) −400.731 −1.05734 −0.528668 0.848828i \(-0.677308\pi\)
−0.528668 + 0.848828i \(0.677308\pi\)
\(380\) −72.9062 −0.191858
\(381\) 252.580 0.662940
\(382\) −310.566 −0.813001
\(383\) −18.1585 −0.0474111 −0.0237056 0.999719i \(-0.507546\pi\)
−0.0237056 + 0.999719i \(0.507546\pi\)
\(384\) 186.220i 0.484947i
\(385\) 4.98266i 0.0129420i
\(386\) 12.7278i 0.0329736i
\(387\) 146.873i 0.379516i
\(388\) 347.762i 0.896293i
\(389\) −308.582 −0.793269 −0.396635 0.917977i \(-0.629822\pi\)
−0.396635 + 0.917977i \(0.629822\pi\)
\(390\) 79.4509 0.203720
\(391\) 27.5589i 0.0704832i
\(392\) 351.870i 0.897628i
\(393\) 52.9950i 0.134847i
\(394\) 292.790i 0.743122i
\(395\) −208.721 −0.528407
\(396\) 10.3012i 0.0260132i
\(397\) 193.629i 0.487730i −0.969809 0.243865i \(-0.921585\pi\)
0.969809 0.243865i \(-0.0784154\pi\)
\(398\) 178.537i 0.448585i
\(399\) 16.4581 0.0412484
\(400\) −44.8216 −0.112054
\(401\) 148.241i 0.369678i 0.982769 + 0.184839i \(0.0591763\pi\)
−0.982769 + 0.184839i \(0.940824\pi\)
\(402\) −80.2782 −0.199697
\(403\) −97.6943 −0.242418
\(404\) 110.247i 0.272888i
\(405\) 30.0304 0.0741492
\(406\) 10.0369i 0.0247213i
\(407\) −20.4511 −0.0502484
\(408\) 10.4620i 0.0256421i
\(409\) 486.132i 1.18859i −0.804249 0.594293i \(-0.797432\pi\)
0.804249 0.594293i \(-0.202568\pi\)
\(410\) 69.0476i 0.168409i
\(411\) −68.3314 −0.166256
\(412\) 160.377i 0.389265i
\(413\) −53.4277 + 48.7942i −0.129365 + 0.118146i
\(414\) −110.153 −0.266070
\(415\) 76.2073i 0.183632i
\(416\) 419.465 1.00833
\(417\) 162.043 0.388592
\(418\) −10.2484 −0.0245177
\(419\) 393.978i 0.940281i −0.882592 0.470140i \(-0.844203\pi\)
0.882592 0.470140i \(-0.155797\pi\)
\(420\) −19.9872 −0.0475885
\(421\) 545.228i 1.29508i −0.762032 0.647539i \(-0.775798\pi\)
0.762032 0.647539i \(-0.224202\pi\)
\(422\) −168.555 −0.399420
\(423\) 14.3793i 0.0339936i
\(424\) 361.033i 0.851493i
\(425\) 11.3055 0.0266012
\(426\) 38.0521i 0.0893243i
\(427\) 107.465i 0.251675i
\(428\) 98.1441 0.229309
\(429\) −26.6906 −0.0622158
\(430\) 177.452 0.412678
\(431\) 645.842i 1.49847i −0.662302 0.749237i \(-0.730420\pi\)
0.662302 0.749237i \(-0.269580\pi\)
\(432\) 16.7960 0.0388797
\(433\) −440.441 −1.01719 −0.508593 0.861007i \(-0.669834\pi\)
−0.508593 + 0.861007i \(0.669834\pi\)
\(434\) −10.2838 −0.0236954
\(435\) 43.5426 0.100098
\(436\) 27.7359i 0.0636144i
\(437\) 261.897i 0.599307i
\(438\) 85.8160 0.195927
\(439\) −817.423 −1.86201 −0.931006 0.365003i \(-0.881068\pi\)
−0.931006 + 0.365003i \(0.881068\pi\)
\(440\) 30.0998 0.0684086
\(441\) −142.488 −0.323102
\(442\) −11.2085 −0.0253586
\(443\) 522.987i 1.18056i 0.807200 + 0.590278i \(0.200982\pi\)
−0.807200 + 0.590278i \(0.799018\pi\)
\(444\) 82.0365i 0.184767i
\(445\) 186.517i 0.419138i
\(446\) 231.158i 0.518291i
\(447\) 231.116i 0.517038i
\(448\) 28.2986 0.0631665
\(449\) −721.573 −1.60707 −0.803533 0.595260i \(-0.797049\pi\)
−0.803533 + 0.595260i \(0.797049\pi\)
\(450\) 45.1881i 0.100418i
\(451\) 23.1957i 0.0514317i
\(452\) 411.190i 0.909713i
\(453\) 165.481i 0.365299i
\(454\) −296.419 −0.652905
\(455\) 51.7869i 0.113817i
\(456\) 99.4219i 0.218031i
\(457\) 899.045i 1.96728i −0.180157 0.983638i \(-0.557660\pi\)
0.180157 0.983638i \(-0.442340\pi\)
\(458\) 380.797 0.831435
\(459\) −4.23653 −0.00922990
\(460\) 318.055i 0.691425i
\(461\) 126.539 0.274489 0.137245 0.990537i \(-0.456175\pi\)
0.137245 + 0.990537i \(0.456175\pi\)
\(462\) −2.80959 −0.00608137
\(463\) 169.302i 0.365663i −0.983144 0.182831i \(-0.941474\pi\)
0.983144 0.182831i \(-0.0585263\pi\)
\(464\) 24.3534 0.0524858
\(465\) 44.6139i 0.0959440i
\(466\) −1.78597 −0.00383255
\(467\) 98.8969i 0.211771i −0.994378 0.105885i \(-0.966232\pi\)
0.994378 0.105885i \(-0.0337676\pi\)
\(468\) 107.065i 0.228772i
\(469\) 52.3261i 0.111570i
\(470\) −17.3731 −0.0369640
\(471\) 424.485i 0.901243i
\(472\) 294.762 + 322.752i 0.624495 + 0.683797i
\(473\) −59.6127 −0.126031
\(474\) 117.692i 0.248296i
\(475\) 107.438 0.226185
\(476\) 2.81968 0.00592370
\(477\) −146.199 −0.306496
\(478\) 80.9722i 0.169398i
\(479\) −91.0329 −0.190048 −0.0950240 0.995475i \(-0.530293\pi\)
−0.0950240 + 0.995475i \(0.530293\pi\)
\(480\) 191.557i 0.399076i
\(481\) −212.557 −0.441907
\(482\) 61.3309i 0.127242i
\(483\) 71.7989i 0.148652i
\(484\) 337.039 0.696361
\(485\) 411.483i 0.848419i
\(486\) 16.9334i 0.0348424i
\(487\) −72.6279 −0.149133 −0.0745667 0.997216i \(-0.523757\pi\)
−0.0745667 + 0.997216i \(0.523757\pi\)
\(488\) 649.187 1.33030
\(489\) 354.380 0.724703
\(490\) 172.154i 0.351335i
\(491\) −269.921 −0.549736 −0.274868 0.961482i \(-0.588634\pi\)
−0.274868 + 0.961482i \(0.588634\pi\)
\(492\) −93.0461 −0.189118
\(493\) −6.14274 −0.0124599
\(494\) −106.516 −0.215620
\(495\) 12.1888i 0.0246238i
\(496\) 24.9526i 0.0503077i
\(497\) 24.8028 0.0499050
\(498\) 42.9713 0.0862878
\(499\) 219.786 0.440452 0.220226 0.975449i \(-0.429320\pi\)
0.220226 + 0.975449i \(0.429320\pi\)
\(500\) −365.714 −0.731428
\(501\) −174.721 −0.348745
\(502\) 23.4880i 0.0467888i
\(503\) 800.462i 1.59138i −0.605707 0.795688i \(-0.707110\pi\)
0.605707 0.795688i \(-0.292890\pi\)
\(504\) 27.2565i 0.0540803i
\(505\) 130.448i 0.258312i
\(506\) 44.7090i 0.0883577i
\(507\) 15.3099 0.0301970
\(508\) 411.233 0.809513
\(509\) 12.6193i 0.0247924i −0.999923 0.0123962i \(-0.996054\pi\)
0.999923 0.0123962i \(-0.00394593\pi\)
\(510\) 5.11857i 0.0100364i
\(511\) 55.9358i 0.109463i
\(512\) 202.926i 0.396339i
\(513\) −40.2604 −0.0784803
\(514\) 76.0403i 0.147938i
\(515\) 189.763i 0.368473i
\(516\) 239.128i 0.463426i
\(517\) 5.83627 0.0112887
\(518\) −22.3749 −0.0431948
\(519\) 333.332i 0.642258i
\(520\) 312.840 0.601616
\(521\) 629.736 1.20871 0.604353 0.796717i \(-0.293432\pi\)
0.604353 + 0.796717i \(0.293432\pi\)
\(522\) 24.5525i 0.0470355i
\(523\) 852.513 1.63004 0.815022 0.579430i \(-0.196725\pi\)
0.815022 + 0.579430i \(0.196725\pi\)
\(524\) 86.2826i 0.164661i
\(525\) 29.4541 0.0561030
\(526\) 488.937i 0.929538i
\(527\) 6.29389i 0.0119429i
\(528\) 6.81718i 0.0129113i
\(529\) −613.534 −1.15980
\(530\) 176.637i 0.333277i
\(531\) 130.697 119.362i 0.246133 0.224788i
\(532\) 26.7959 0.0503682
\(533\) 241.083i 0.452313i
\(534\) 105.172 0.196951
\(535\) 116.127 0.217060
\(536\) −316.098 −0.589734
\(537\) 115.017i 0.214184i
\(538\) 181.834 0.337982
\(539\) 57.8331i 0.107297i
\(540\) 48.8934 0.0905433
\(541\) 463.558i 0.856855i 0.903576 + 0.428427i \(0.140932\pi\)
−0.903576 + 0.428427i \(0.859068\pi\)
\(542\) 147.880i 0.272842i
\(543\) 174.610 0.321566
\(544\) 27.0237i 0.0496760i
\(545\) 32.8180i 0.0602165i
\(546\) −29.2013 −0.0534823
\(547\) 306.278 0.559922 0.279961 0.960011i \(-0.409678\pi\)
0.279961 + 0.960011i \(0.409678\pi\)
\(548\) −111.252 −0.203015
\(549\) 262.885i 0.478844i
\(550\) −18.3409 −0.0333472
\(551\) −58.3755 −0.105945
\(552\) −433.731 −0.785745
\(553\) 76.7131 0.138722
\(554\) 212.015i 0.382699i
\(555\) 97.0682i 0.174898i
\(556\) 263.827 0.474508
\(557\) −994.672 −1.78577 −0.892883 0.450288i \(-0.851321\pi\)
−0.892883 + 0.450288i \(0.851321\pi\)
\(558\) 25.1567 0.0450836
\(559\) −619.581 −1.10837
\(560\) −13.2272 −0.0236199
\(561\) 1.71952i 0.00306510i
\(562\) 516.613i 0.919240i
\(563\) 206.256i 0.366352i 0.983080 + 0.183176i \(0.0586378\pi\)
−0.983080 + 0.183176i \(0.941362\pi\)
\(564\) 23.4113i 0.0415094i
\(565\) 486.533i 0.861121i
\(566\) −482.550 −0.852561
\(567\) −11.0374 −0.0194662
\(568\) 149.831i 0.263788i
\(569\) 588.448i 1.03418i 0.855931 + 0.517089i \(0.172985\pi\)
−0.855931 + 0.517089i \(0.827015\pi\)
\(570\) 48.6426i 0.0853379i
\(571\) 139.611i 0.244503i 0.992499 + 0.122251i \(0.0390114\pi\)
−0.992499 + 0.122251i \(0.960989\pi\)
\(572\) −43.4557 −0.0759714
\(573\) 495.192i 0.864210i
\(574\) 25.3777i 0.0442120i
\(575\) 468.701i 0.815133i
\(576\) −69.2251 −0.120182
\(577\) 947.400 1.64194 0.820971 0.570970i \(-0.193433\pi\)
0.820971 + 0.570970i \(0.193433\pi\)
\(578\) 313.212i 0.541890i
\(579\) 20.2942 0.0350505
\(580\) 70.8929 0.122229
\(581\) 28.0092i 0.0482085i
\(582\) −232.025 −0.398668
\(583\) 59.3391i 0.101782i
\(584\) 337.903 0.578601
\(585\) 126.683i 0.216552i
\(586\) 61.3693i 0.104726i
\(587\) 672.802i 1.14617i −0.819496 0.573085i \(-0.805746\pi\)
0.819496 0.573085i \(-0.194254\pi\)
\(588\) −231.989 −0.394539
\(589\) 59.8118i 0.101548i
\(590\) 144.213 + 157.908i 0.244429 + 0.267641i
\(591\) −466.849 −0.789930
\(592\) 54.2903i 0.0917067i
\(593\) 235.268 0.396742 0.198371 0.980127i \(-0.436435\pi\)
0.198371 + 0.980127i \(0.436435\pi\)
\(594\) 6.87293 0.0115706
\(595\) 3.33634 0.00560729
\(596\) 376.287i 0.631353i
\(597\) 284.674 0.476841
\(598\) 464.680i 0.777056i
\(599\) −938.758 −1.56721 −0.783604 0.621260i \(-0.786621\pi\)
−0.783604 + 0.621260i \(0.786621\pi\)
\(600\) 177.929i 0.296549i
\(601\) 396.943i 0.660470i 0.943899 + 0.330235i \(0.107128\pi\)
−0.943899 + 0.330235i \(0.892872\pi\)
\(602\) −65.2204 −0.108340
\(603\) 128.002i 0.212275i
\(604\) 269.423i 0.446065i
\(605\) 398.795 0.659166
\(606\) −73.5561 −0.121380
\(607\) 794.727 1.30927 0.654635 0.755945i \(-0.272822\pi\)
0.654635 + 0.755945i \(0.272822\pi\)
\(608\) 256.811i 0.422386i
\(609\) −16.0036 −0.0262785
\(610\) 317.618 0.520685
\(611\) 60.6589 0.0992780
\(612\) −6.89761 −0.0112706
\(613\) 14.2456i 0.0232392i −0.999932 0.0116196i \(-0.996301\pi\)
0.999932 0.0116196i \(-0.00369872\pi\)
\(614\) 303.650i 0.494544i
\(615\) −110.095 −0.179017
\(616\) −11.0629 −0.0179592
\(617\) 739.753 1.19895 0.599476 0.800393i \(-0.295376\pi\)
0.599476 + 0.800393i \(0.295376\pi\)
\(618\) −107.003 −0.173144
\(619\) 202.230 0.326705 0.163352 0.986568i \(-0.447769\pi\)
0.163352 + 0.986568i \(0.447769\pi\)
\(620\) 72.6372i 0.117157i
\(621\) 175.637i 0.282830i
\(622\) 228.970i 0.368119i
\(623\) 68.5521i 0.110036i
\(624\) 70.8539i 0.113548i
\(625\) −86.0664 −0.137706
\(626\) −404.814 −0.646668
\(627\) 16.3409i 0.0260620i
\(628\) 691.116i 1.10050i
\(629\) 13.6938i 0.0217708i
\(630\) 13.3353i 0.0211672i
\(631\) −504.848 −0.800076 −0.400038 0.916499i \(-0.631003\pi\)
−0.400038 + 0.916499i \(0.631003\pi\)
\(632\) 463.417i 0.733255i
\(633\) 268.758i 0.424578i
\(634\) 324.910i 0.512476i
\(635\) 486.584 0.766274
\(636\) −238.030 −0.374261
\(637\) 601.084i 0.943617i
\(638\) 9.96539 0.0156197
\(639\) −60.6734 −0.0949506
\(640\) 358.743i 0.560536i
\(641\) 757.354 1.18152 0.590760 0.806847i \(-0.298828\pi\)
0.590760 + 0.806847i \(0.298828\pi\)
\(642\) 65.4812i 0.101996i
\(643\) 390.062 0.606628 0.303314 0.952891i \(-0.401907\pi\)
0.303314 + 0.952891i \(0.401907\pi\)
\(644\) 116.898i 0.181518i
\(645\) 282.943i 0.438672i
\(646\) 6.86223i 0.0106226i
\(647\) −992.824 −1.53450 −0.767252 0.641346i \(-0.778376\pi\)
−0.767252 + 0.641346i \(0.778376\pi\)
\(648\) 66.6757i 0.102895i
\(649\) −48.4467 53.0473i −0.0746483 0.0817369i
\(650\) −190.625 −0.293270
\(651\) 16.3974i 0.0251880i
\(652\) 576.976 0.884932
\(653\) 1166.56 1.78646 0.893228 0.449604i \(-0.148435\pi\)
0.893228 + 0.449604i \(0.148435\pi\)
\(654\) 18.5052 0.0282955
\(655\) 102.092i 0.155866i
\(656\) −61.5763 −0.0938663
\(657\) 136.832i 0.208268i
\(658\) 6.38528 0.00970407
\(659\) 689.431i 1.04618i 0.852278 + 0.523089i \(0.175220\pi\)
−0.852278 + 0.523089i \(0.824780\pi\)
\(660\) 19.8449i 0.0300680i
\(661\) 1035.80 1.56703 0.783513 0.621376i \(-0.213426\pi\)
0.783513 + 0.621376i \(0.213426\pi\)
\(662\) 291.320i 0.440061i
\(663\) 17.8717i 0.0269559i
\(664\) 169.201 0.254821
\(665\) 31.7057 0.0476778
\(666\) 54.7343 0.0821836
\(667\) 254.665i 0.381806i
\(668\) −284.468 −0.425851
\(669\) 368.577 0.550937
\(670\) −154.652 −0.230824
\(671\) −106.700 −0.159016
\(672\) 70.4046i 0.104769i
\(673\) 504.708i 0.749937i −0.927037 0.374969i \(-0.877653\pi\)
0.927037 0.374969i \(-0.122347\pi\)
\(674\) 404.357 0.599936
\(675\) −72.0516 −0.106743
\(676\) 24.9264 0.0368734
\(677\) 184.647 0.272743 0.136372 0.990658i \(-0.456456\pi\)
0.136372 + 0.990658i \(0.456456\pi\)
\(678\) −274.344 −0.404637
\(679\) 151.236i 0.222734i
\(680\) 20.1545i 0.0296390i
\(681\) 472.635i 0.694030i
\(682\) 10.2106i 0.0149715i
\(683\) 150.545i 0.220417i 0.993908 + 0.110209i \(0.0351519\pi\)
−0.993908 + 0.110209i \(0.964848\pi\)
\(684\) −65.5491 −0.0958320
\(685\) −131.637 −0.192171
\(686\) 128.550i 0.187391i
\(687\) 607.175i 0.883806i
\(688\) 158.251i 0.230015i
\(689\) 616.737i 0.895119i
\(690\) −212.205 −0.307543
\(691\) 8.87982i 0.0128507i 0.999979 + 0.00642534i \(0.00204526\pi\)
−0.999979 + 0.00642534i \(0.997955\pi\)
\(692\) 542.707i 0.784259i
\(693\) 4.47985i 0.00646442i
\(694\) −176.716 −0.254634
\(695\) 312.168 0.449163
\(696\) 96.6764i 0.138903i
\(697\) 15.5316 0.0222835
\(698\) 515.415 0.738417
\(699\) 2.84770i 0.00407396i
\(700\) 47.9550 0.0685071
\(701\) 672.703i 0.959633i −0.877369 0.479817i \(-0.840703\pi\)
0.877369 0.479817i \(-0.159297\pi\)
\(702\) 71.4334 0.101757
\(703\) 130.135i 0.185114i
\(704\) 28.0971i 0.0399106i
\(705\) 27.7010i 0.0392922i
\(706\) −600.963 −0.851223
\(707\) 47.9446i 0.0678141i
\(708\) 212.791 194.337i 0.300553 0.274487i
\(709\) −885.467 −1.24890 −0.624448 0.781067i \(-0.714676\pi\)
−0.624448 + 0.781067i \(0.714676\pi\)
\(710\) 73.3057i 0.103247i
\(711\) −187.658 −0.263936
\(712\) 414.117 0.581626
\(713\) 260.931 0.365962
\(714\) 1.88128i 0.00263484i
\(715\) −51.4181 −0.0719135
\(716\) 187.262i 0.261539i
\(717\) −129.109 −0.180068
\(718\) 377.017i 0.525093i
\(719\) 900.012i 1.25175i −0.779922 0.625877i \(-0.784741\pi\)
0.779922 0.625877i \(-0.215259\pi\)
\(720\) 32.3568 0.0449400
\(721\) 69.7455i 0.0967344i
\(722\) 326.934i 0.452816i
\(723\) −97.7910 −0.135257
\(724\) 284.288 0.392662
\(725\) −104.471 −0.144098
\(726\) 224.871i 0.309739i
\(727\) −702.800 −0.966713 −0.483357 0.875424i \(-0.660583\pi\)
−0.483357 + 0.875424i \(0.660583\pi\)
\(728\) −114.981 −0.157941
\(729\) 27.0000 0.0370370
\(730\) 165.321 0.226467
\(731\) 39.9161i 0.0546048i
\(732\) 428.011i 0.584714i
\(733\) −389.940 −0.531978 −0.265989 0.963976i \(-0.585698\pi\)
−0.265989 + 0.963976i \(0.585698\pi\)
\(734\) −671.145 −0.914366
\(735\) −274.497 −0.373465
\(736\) −1120.35 −1.52221
\(737\) 51.9535 0.0704933
\(738\) 62.0799i 0.0841191i
\(739\) 1203.79i 1.62894i −0.580206 0.814470i \(-0.697028\pi\)
0.580206 0.814470i \(-0.302972\pi\)
\(740\) 158.039i 0.213567i
\(741\) 169.838i 0.229201i
\(742\) 64.9210i 0.0874947i
\(743\) −1379.37 −1.85649 −0.928247 0.371965i \(-0.878684\pi\)
−0.928247 + 0.371965i \(0.878684\pi\)
\(744\) 99.0551 0.133139
\(745\) 445.234i 0.597630i
\(746\) 464.128i 0.622156i
\(747\) 68.5170i 0.0917229i
\(748\) 2.79960i 0.00374278i
\(749\) −42.6813 −0.0569844
\(750\) 244.003i 0.325337i
\(751\) 855.872i 1.13964i −0.821769 0.569821i \(-0.807012\pi\)
0.821769 0.569821i \(-0.192988\pi\)
\(752\) 15.4932i 0.0206027i
\(753\) −37.4511 −0.0497359
\(754\) 103.575 0.137367
\(755\) 318.791i 0.422239i
\(756\) −17.9702 −0.0237702
\(757\) −126.963 −0.167719 −0.0838593 0.996478i \(-0.526725\pi\)
−0.0838593 + 0.996478i \(0.526725\pi\)
\(758\) 435.305i 0.574281i
\(759\) 71.2877 0.0939231
\(760\) 191.532i 0.252015i
\(761\) 615.423 0.808703 0.404351 0.914604i \(-0.367497\pi\)
0.404351 + 0.914604i \(0.367497\pi\)
\(762\) 274.372i 0.360069i
\(763\) 12.0619i 0.0158085i
\(764\) 806.236i 1.05528i
\(765\) −8.16147 −0.0106686
\(766\) 19.7251i 0.0257508i
\(767\) −503.528 551.343i −0.656490 0.718831i
\(768\) −362.155 −0.471556
\(769\) 986.655i 1.28304i −0.767108 0.641518i \(-0.778305\pi\)
0.767108 0.641518i \(-0.221695\pi\)
\(770\) −5.41255 −0.00702929
\(771\) 121.245 0.157257
\(772\) 33.0416 0.0428000
\(773\) 6.18406i 0.00800008i 0.999992 + 0.00400004i \(0.00127326\pi\)
−0.999992 + 0.00400004i \(0.998727\pi\)
\(774\) 159.545 0.206130
\(775\) 107.042i 0.138118i
\(776\) −913.604 −1.17733
\(777\) 35.6764i 0.0459155i
\(778\) 335.206i 0.430856i
\(779\) 147.599 0.189473
\(780\) 206.256i 0.264431i
\(781\) 24.6262i 0.0315316i
\(782\) 29.9367 0.0382822
\(783\) 39.1486 0.0499982
\(784\) −153.526 −0.195824
\(785\) 817.751i 1.04172i
\(786\) −57.5673 −0.0732408
\(787\) 545.010 0.692516 0.346258 0.938139i \(-0.387452\pi\)
0.346258 + 0.938139i \(0.387452\pi\)
\(788\) −760.089 −0.964580
\(789\) 779.601 0.988088
\(790\) 226.729i 0.286999i
\(791\) 178.820i