Properties

Label 177.3.c.a.58.18
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 58.18
Root \(3.07256i\) of defining polynomial
Character \(\chi\) \(=\) 177.58
Dual form 177.3.c.a.58.3

$q$-expansion

\(f(q)\) \(=\) \(q+3.07256i q^{2} +1.73205 q^{3} -5.44061 q^{4} -6.03179 q^{5} +5.32183i q^{6} -9.30133 q^{7} -4.42637i q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+3.07256i q^{2} +1.73205 q^{3} -5.44061 q^{4} -6.03179 q^{5} +5.32183i q^{6} -9.30133 q^{7} -4.42637i q^{8} +3.00000 q^{9} -18.5330i q^{10} -12.6629i q^{11} -9.42342 q^{12} +16.7819i q^{13} -28.5789i q^{14} -10.4474 q^{15} -8.16217 q^{16} +14.0828 q^{17} +9.21767i q^{18} -37.4075 q^{19} +32.8166 q^{20} -16.1104 q^{21} +38.9074 q^{22} +27.8025i q^{23} -7.66670i q^{24} +11.3824 q^{25} -51.5635 q^{26} +5.19615 q^{27} +50.6050 q^{28} +39.1159 q^{29} -32.1001i q^{30} +0.257147i q^{31} -42.7842i q^{32} -21.9327i q^{33} +43.2703i q^{34} +56.1036 q^{35} -16.3218 q^{36} +54.7014i q^{37} -114.937i q^{38} +29.0672i q^{39} +26.6989i q^{40} -11.3202 q^{41} -49.5001i q^{42} +7.36421i q^{43} +68.8937i q^{44} -18.0954 q^{45} -85.4249 q^{46} +28.7287i q^{47} -14.1373 q^{48} +37.5148 q^{49} +34.9732i q^{50} +24.3922 q^{51} -91.3041i q^{52} -47.3053 q^{53} +15.9655i q^{54} +76.3796i q^{55} +41.1711i q^{56} -64.7917 q^{57} +120.186i q^{58} +(-28.6844 + 51.5578i) q^{59} +56.8401 q^{60} -84.0505i q^{61} -0.790099 q^{62} -27.9040 q^{63} +98.8084 q^{64} -101.225i q^{65} +67.3895 q^{66} -81.5123i q^{67} -76.6193 q^{68} +48.1554i q^{69} +172.382i q^{70} -6.96917 q^{71} -13.2791i q^{72} +131.681i q^{73} -168.073 q^{74} +19.7150 q^{75} +203.520 q^{76} +117.781i q^{77} -89.3106 q^{78} +51.9880 q^{79} +49.2325 q^{80} +9.00000 q^{81} -34.7820i q^{82} +16.5553i q^{83} +87.6504 q^{84} -84.9447 q^{85} -22.6270 q^{86} +67.7508 q^{87} -56.0505 q^{88} +69.2544i q^{89} -55.5990i q^{90} -156.094i q^{91} -151.263i q^{92} +0.445392i q^{93} -88.2705 q^{94} +225.634 q^{95} -74.1045i q^{96} -110.495i q^{97} +115.266i q^{98} -37.9886i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 40q^{4} - 8q^{7} + 60q^{9} + O(q^{10}) \) \( 20q - 40q^{4} - 8q^{7} + 60q^{9} - 24q^{12} + 24q^{15} - 8q^{16} + 16q^{17} - 60q^{19} - 164q^{20} + 40q^{22} + 100q^{25} - 156q^{26} + 200q^{28} - 60q^{29} - 32q^{35} - 120q^{36} + 28q^{41} + 180q^{46} - 96q^{48} + 284q^{49} - 24q^{51} - 8q^{53} + 24q^{57} - 152q^{59} - 72q^{60} - 8q^{62} - 24q^{63} + 204q^{64} - 120q^{66} + 384q^{68} + 92q^{71} + 104q^{74} + 240q^{75} + 120q^{76} - 468q^{78} - 420q^{79} + 376q^{80} + 180q^{81} + 168q^{84} - 348q^{85} + 232q^{86} + 144q^{87} - 212q^{88} + 152q^{94} + 788q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.07256i 1.53628i 0.640282 + 0.768140i \(0.278817\pi\)
−0.640282 + 0.768140i \(0.721183\pi\)
\(3\) 1.73205 0.577350
\(4\) −5.44061 −1.36015
\(5\) −6.03179 −1.20636 −0.603179 0.797606i \(-0.706099\pi\)
−0.603179 + 0.797606i \(0.706099\pi\)
\(6\) 5.32183i 0.886971i
\(7\) −9.30133 −1.32876 −0.664381 0.747394i \(-0.731305\pi\)
−0.664381 + 0.747394i \(0.731305\pi\)
\(8\) 4.42637i 0.553296i
\(9\) 3.00000 0.333333
\(10\) 18.5330i 1.85330i
\(11\) 12.6629i 1.15117i −0.817742 0.575584i \(-0.804775\pi\)
0.817742 0.575584i \(-0.195225\pi\)
\(12\) −9.42342 −0.785285
\(13\) 16.7819i 1.29092i 0.763795 + 0.645459i \(0.223334\pi\)
−0.763795 + 0.645459i \(0.776666\pi\)
\(14\) 28.5789i 2.04135i
\(15\) −10.4474 −0.696491
\(16\) −8.16217 −0.510136
\(17\) 14.0828 0.828402 0.414201 0.910185i \(-0.364061\pi\)
0.414201 + 0.910185i \(0.364061\pi\)
\(18\) 9.21767i 0.512093i
\(19\) −37.4075 −1.96882 −0.984408 0.175902i \(-0.943716\pi\)
−0.984408 + 0.175902i \(0.943716\pi\)
\(20\) 32.8166 1.64083
\(21\) −16.1104 −0.767161
\(22\) 38.9074 1.76852
\(23\) 27.8025i 1.20881i 0.796679 + 0.604403i \(0.206588\pi\)
−0.796679 + 0.604403i \(0.793412\pi\)
\(24\) 7.66670i 0.319446i
\(25\) 11.3824 0.455298
\(26\) −51.5635 −1.98321
\(27\) 5.19615 0.192450
\(28\) 50.6050 1.80732
\(29\) 39.1159 1.34882 0.674412 0.738355i \(-0.264397\pi\)
0.674412 + 0.738355i \(0.264397\pi\)
\(30\) 32.1001i 1.07000i
\(31\) 0.257147i 0.00829506i 0.999991 + 0.00414753i \(0.00132020\pi\)
−0.999991 + 0.00414753i \(0.998680\pi\)
\(32\) 42.7842i 1.33701i
\(33\) 21.9327i 0.664627i
\(34\) 43.2703i 1.27266i
\(35\) 56.1036 1.60296
\(36\) −16.3218 −0.453385
\(37\) 54.7014i 1.47842i 0.673477 + 0.739208i \(0.264800\pi\)
−0.673477 + 0.739208i \(0.735200\pi\)
\(38\) 114.937i 3.02465i
\(39\) 29.0672i 0.745312i
\(40\) 26.6989i 0.667473i
\(41\) −11.3202 −0.276102 −0.138051 0.990425i \(-0.544084\pi\)
−0.138051 + 0.990425i \(0.544084\pi\)
\(42\) 49.5001i 1.17857i
\(43\) 7.36421i 0.171261i 0.996327 + 0.0856303i \(0.0272904\pi\)
−0.996327 + 0.0856303i \(0.972710\pi\)
\(44\) 68.8937i 1.56577i
\(45\) −18.0954 −0.402119
\(46\) −85.4249 −1.85706
\(47\) 28.7287i 0.611248i 0.952152 + 0.305624i \(0.0988651\pi\)
−0.952152 + 0.305624i \(0.901135\pi\)
\(48\) −14.1373 −0.294527
\(49\) 37.5148 0.765608
\(50\) 34.9732i 0.699464i
\(51\) 24.3922 0.478278
\(52\) 91.3041i 1.75585i
\(53\) −47.3053 −0.892552 −0.446276 0.894895i \(-0.647250\pi\)
−0.446276 + 0.894895i \(0.647250\pi\)
\(54\) 15.9655i 0.295657i
\(55\) 76.3796i 1.38872i
\(56\) 41.1711i 0.735199i
\(57\) −64.7917 −1.13670
\(58\) 120.186i 2.07217i
\(59\) −28.6844 + 51.5578i −0.486176 + 0.873861i
\(60\) 56.8401 0.947334
\(61\) 84.0505i 1.37788i −0.724820 0.688938i \(-0.758077\pi\)
0.724820 0.688938i \(-0.241923\pi\)
\(62\) −0.790099 −0.0127435
\(63\) −27.9040 −0.442921
\(64\) 98.8084 1.54388
\(65\) 101.225i 1.55731i
\(66\) 67.3895 1.02105
\(67\) 81.5123i 1.21660i −0.793707 0.608300i \(-0.791852\pi\)
0.793707 0.608300i \(-0.208148\pi\)
\(68\) −76.6193 −1.12675
\(69\) 48.1554i 0.697905i
\(70\) 172.382i 2.46260i
\(71\) −6.96917 −0.0981573 −0.0490787 0.998795i \(-0.515628\pi\)
−0.0490787 + 0.998795i \(0.515628\pi\)
\(72\) 13.2791i 0.184432i
\(73\) 131.681i 1.80385i 0.431896 + 0.901923i \(0.357845\pi\)
−0.431896 + 0.901923i \(0.642155\pi\)
\(74\) −168.073 −2.27126
\(75\) 19.7150 0.262866
\(76\) 203.520 2.67789
\(77\) 117.781i 1.52963i
\(78\) −89.3106 −1.14501
\(79\) 51.9880 0.658076 0.329038 0.944317i \(-0.393276\pi\)
0.329038 + 0.944317i \(0.393276\pi\)
\(80\) 49.2325 0.615406
\(81\) 9.00000 0.111111
\(82\) 34.7820i 0.424170i
\(83\) 16.5553i 0.199461i 0.995014 + 0.0997305i \(0.0317981\pi\)
−0.995014 + 0.0997305i \(0.968202\pi\)
\(84\) 87.6504 1.04346
\(85\) −84.9447 −0.999349
\(86\) −22.6270 −0.263104
\(87\) 67.7508 0.778744
\(88\) −56.0505 −0.636937
\(89\) 69.2544i 0.778139i 0.921208 + 0.389070i \(0.127203\pi\)
−0.921208 + 0.389070i \(0.872797\pi\)
\(90\) 55.5990i 0.617767i
\(91\) 156.094i 1.71532i
\(92\) 151.263i 1.64416i
\(93\) 0.445392i 0.00478916i
\(94\) −88.2705 −0.939048
\(95\) 225.634 2.37509
\(96\) 74.1045i 0.771922i
\(97\) 110.495i 1.13912i −0.821949 0.569560i \(-0.807113\pi\)
0.821949 0.569560i \(-0.192887\pi\)
\(98\) 115.266i 1.17619i
\(99\) 37.9886i 0.383723i
\(100\) −61.9275 −0.619275
\(101\) 159.617i 1.58037i −0.612868 0.790186i \(-0.709984\pi\)
0.612868 0.790186i \(-0.290016\pi\)
\(102\) 74.9464i 0.734769i
\(103\) 26.7475i 0.259684i −0.991535 0.129842i \(-0.958553\pi\)
0.991535 0.129842i \(-0.0414470\pi\)
\(104\) 74.2831 0.714260
\(105\) 97.1744 0.925470
\(106\) 145.348i 1.37121i
\(107\) −35.3863 −0.330713 −0.165356 0.986234i \(-0.552877\pi\)
−0.165356 + 0.986234i \(0.552877\pi\)
\(108\) −28.2703 −0.261762
\(109\) 68.2150i 0.625826i 0.949782 + 0.312913i \(0.101305\pi\)
−0.949782 + 0.312913i \(0.898695\pi\)
\(110\) −234.681 −2.13346
\(111\) 94.7456i 0.853564i
\(112\) 75.9191 0.677849
\(113\) 120.908i 1.06998i −0.844858 0.534990i \(-0.820315\pi\)
0.844858 0.534990i \(-0.179685\pi\)
\(114\) 199.076i 1.74628i
\(115\) 167.699i 1.45825i
\(116\) −212.815 −1.83461
\(117\) 50.3458i 0.430306i
\(118\) −158.414 88.1345i −1.34249 0.746902i
\(119\) −130.989 −1.10075
\(120\) 46.2439i 0.385366i
\(121\) −39.3479 −0.325189
\(122\) 258.250 2.11680
\(123\) −19.6072 −0.159408
\(124\) 1.39904i 0.0112826i
\(125\) 82.1382 0.657105
\(126\) 85.7367i 0.680450i
\(127\) −158.088 −1.24479 −0.622393 0.782705i \(-0.713839\pi\)
−0.622393 + 0.782705i \(0.713839\pi\)
\(128\) 132.458i 1.03482i
\(129\) 12.7552i 0.0988774i
\(130\) 311.020 2.39246
\(131\) 130.513i 0.996282i 0.867096 + 0.498141i \(0.165984\pi\)
−0.867096 + 0.498141i \(0.834016\pi\)
\(132\) 119.327i 0.903995i
\(133\) 347.939 2.61609
\(134\) 250.451 1.86904
\(135\) −31.3421 −0.232164
\(136\) 62.3359i 0.458352i
\(137\) 208.921 1.52497 0.762487 0.647004i \(-0.223978\pi\)
0.762487 + 0.647004i \(0.223978\pi\)
\(138\) −147.960 −1.07218
\(139\) −73.8315 −0.531162 −0.265581 0.964089i \(-0.585564\pi\)
−0.265581 + 0.964089i \(0.585564\pi\)
\(140\) −305.238 −2.18027
\(141\) 49.7595i 0.352904i
\(142\) 21.4132i 0.150797i
\(143\) 212.507 1.48606
\(144\) −24.4865 −0.170045
\(145\) −235.939 −1.62716
\(146\) −404.597 −2.77121
\(147\) 64.9775 0.442024
\(148\) 297.609i 2.01087i
\(149\) 66.3172i 0.445082i 0.974923 + 0.222541i \(0.0714351\pi\)
−0.974923 + 0.222541i \(0.928565\pi\)
\(150\) 60.5754i 0.403836i
\(151\) 103.185i 0.683347i 0.939819 + 0.341673i \(0.110994\pi\)
−0.939819 + 0.341673i \(0.889006\pi\)
\(152\) 165.579i 1.08934i
\(153\) 42.2485 0.276134
\(154\) −361.890 −2.34994
\(155\) 1.55106i 0.0100068i
\(156\) 158.143i 1.01374i
\(157\) 251.051i 1.59905i 0.600630 + 0.799527i \(0.294916\pi\)
−0.600630 + 0.799527i \(0.705084\pi\)
\(158\) 159.736i 1.01099i
\(159\) −81.9351 −0.515315
\(160\) 258.065i 1.61291i
\(161\) 258.601i 1.60622i
\(162\) 27.6530i 0.170698i
\(163\) −96.4209 −0.591539 −0.295770 0.955259i \(-0.595576\pi\)
−0.295770 + 0.955259i \(0.595576\pi\)
\(164\) 61.5888 0.375542
\(165\) 132.293i 0.801778i
\(166\) −50.8670 −0.306428
\(167\) 78.3907 0.469405 0.234703 0.972067i \(-0.424588\pi\)
0.234703 + 0.972067i \(0.424588\pi\)
\(168\) 71.3105i 0.424467i
\(169\) −112.633 −0.666470
\(170\) 260.997i 1.53528i
\(171\) −112.222 −0.656272
\(172\) 40.0658i 0.232941i
\(173\) 52.2561i 0.302058i 0.988529 + 0.151029i \(0.0482587\pi\)
−0.988529 + 0.151029i \(0.951741\pi\)
\(174\) 208.168i 1.19637i
\(175\) −105.872 −0.604982
\(176\) 103.356i 0.587252i
\(177\) −49.6828 + 89.3007i −0.280694 + 0.504524i
\(178\) −212.788 −1.19544
\(179\) 117.505i 0.656453i −0.944599 0.328226i \(-0.893549\pi\)
0.944599 0.328226i \(-0.106451\pi\)
\(180\) 98.4499 0.546944
\(181\) 160.180 0.884972 0.442486 0.896776i \(-0.354097\pi\)
0.442486 + 0.896776i \(0.354097\pi\)
\(182\) 479.609 2.63521
\(183\) 145.580i 0.795517i
\(184\) 123.064 0.668828
\(185\) 329.947i 1.78350i
\(186\) −1.36849 −0.00735748
\(187\) 178.329i 0.953630i
\(188\) 156.302i 0.831391i
\(189\) −48.3311 −0.255720
\(190\) 693.274i 3.64881i
\(191\) 14.2938i 0.0748369i −0.999300 0.0374184i \(-0.988087\pi\)
0.999300 0.0374184i \(-0.0119134\pi\)
\(192\) 171.141 0.891360
\(193\) 71.9463 0.372779 0.186389 0.982476i \(-0.440321\pi\)
0.186389 + 0.982476i \(0.440321\pi\)
\(194\) 339.501 1.75001
\(195\) 175.327i 0.899113i
\(196\) −204.103 −1.04134
\(197\) −44.5489 −0.226137 −0.113068 0.993587i \(-0.536068\pi\)
−0.113068 + 0.993587i \(0.536068\pi\)
\(198\) 116.722 0.589505
\(199\) −125.217 −0.629233 −0.314617 0.949219i \(-0.601876\pi\)
−0.314617 + 0.949219i \(0.601876\pi\)
\(200\) 50.3829i 0.251915i
\(201\) 141.183i 0.702405i
\(202\) 490.434 2.42789
\(203\) −363.830 −1.79227
\(204\) −132.708 −0.650532
\(205\) 68.2810 0.333078
\(206\) 82.1831 0.398947
\(207\) 83.4076i 0.402935i
\(208\) 136.977i 0.658544i
\(209\) 473.686i 2.26644i
\(210\) 298.574i 1.42178i
\(211\) 106.781i 0.506071i −0.967457 0.253035i \(-0.918571\pi\)
0.967457 0.253035i \(-0.0814289\pi\)
\(212\) 257.370 1.21401
\(213\) −12.0710 −0.0566711
\(214\) 108.726i 0.508067i
\(215\) 44.4193i 0.206602i
\(216\) 23.0001i 0.106482i
\(217\) 2.39181i 0.0110222i
\(218\) −209.595 −0.961443
\(219\) 228.078i 1.04145i
\(220\) 415.552i 1.88887i
\(221\) 236.337i 1.06940i
\(222\) −291.111 −1.31131
\(223\) −37.6647 −0.168900 −0.0844501 0.996428i \(-0.526913\pi\)
−0.0844501 + 0.996428i \(0.526913\pi\)
\(224\) 397.950i 1.77656i
\(225\) 34.1473 0.151766
\(226\) 371.496 1.64379
\(227\) 189.636i 0.835399i −0.908585 0.417699i \(-0.862837\pi\)
0.908585 0.417699i \(-0.137163\pi\)
\(228\) 352.507 1.54608
\(229\) 206.938i 0.903658i 0.892104 + 0.451829i \(0.149228\pi\)
−0.892104 + 0.451829i \(0.850772\pi\)
\(230\) 515.265 2.24028
\(231\) 204.003i 0.883131i
\(232\) 173.142i 0.746300i
\(233\) 213.272i 0.915330i 0.889125 + 0.457665i \(0.151314\pi\)
−0.889125 + 0.457665i \(0.848686\pi\)
\(234\) −154.690 −0.661070
\(235\) 173.285i 0.737384i
\(236\) 156.061 280.506i 0.661274 1.18858i
\(237\) 90.0458 0.379940
\(238\) 402.472i 1.69106i
\(239\) −142.148 −0.594760 −0.297380 0.954759i \(-0.596113\pi\)
−0.297380 + 0.954759i \(0.596113\pi\)
\(240\) 85.2732 0.355305
\(241\) −391.267 −1.62351 −0.811756 0.583996i \(-0.801488\pi\)
−0.811756 + 0.583996i \(0.801488\pi\)
\(242\) 120.899i 0.499581i
\(243\) 15.5885 0.0641500
\(244\) 457.286i 1.87412i
\(245\) −226.281 −0.923596
\(246\) 60.2441i 0.244895i
\(247\) 627.770i 2.54158i
\(248\) 1.13823 0.00458963
\(249\) 28.6745i 0.115159i
\(250\) 252.374i 1.00950i
\(251\) 135.007 0.537877 0.268938 0.963157i \(-0.413327\pi\)
0.268938 + 0.963157i \(0.413327\pi\)
\(252\) 151.815 0.602440
\(253\) 352.060 1.39154
\(254\) 485.734i 1.91234i
\(255\) −147.128 −0.576974
\(256\) −11.7500 −0.0458983
\(257\) −133.333 −0.518807 −0.259403 0.965769i \(-0.583526\pi\)
−0.259403 + 0.965769i \(0.583526\pi\)
\(258\) −39.1910 −0.151903
\(259\) 508.796i 1.96446i
\(260\) 550.727i 2.11818i
\(261\) 117.348 0.449608
\(262\) −401.009 −1.53057
\(263\) 272.345 1.03553 0.517765 0.855523i \(-0.326764\pi\)
0.517765 + 0.855523i \(0.326764\pi\)
\(264\) −97.0823 −0.367736
\(265\) 285.335 1.07674
\(266\) 1069.06i 4.01904i
\(267\) 119.952i 0.449259i
\(268\) 443.477i 1.65476i
\(269\) 275.151i 1.02287i 0.859323 + 0.511434i \(0.170886\pi\)
−0.859323 + 0.511434i \(0.829114\pi\)
\(270\) 96.3004i 0.356668i
\(271\) −142.359 −0.525308 −0.262654 0.964890i \(-0.584598\pi\)
−0.262654 + 0.964890i \(0.584598\pi\)
\(272\) −114.947 −0.422598
\(273\) 270.363i 0.990342i
\(274\) 641.923i 2.34278i
\(275\) 144.134i 0.524124i
\(276\) 261.995i 0.949257i
\(277\) −282.049 −1.01823 −0.509114 0.860699i \(-0.670027\pi\)
−0.509114 + 0.860699i \(0.670027\pi\)
\(278\) 226.852i 0.816013i
\(279\) 0.771441i 0.00276502i
\(280\) 248.336i 0.886913i
\(281\) −273.179 −0.972168 −0.486084 0.873912i \(-0.661575\pi\)
−0.486084 + 0.873912i \(0.661575\pi\)
\(282\) −152.889 −0.542159
\(283\) 240.930i 0.851343i 0.904878 + 0.425671i \(0.139962\pi\)
−0.904878 + 0.425671i \(0.860038\pi\)
\(284\) 37.9166 0.133509
\(285\) 390.810 1.37126
\(286\) 652.941i 2.28301i
\(287\) 105.293 0.366874
\(288\) 128.353i 0.445669i
\(289\) −90.6737 −0.313750
\(290\) 724.936i 2.49978i
\(291\) 191.382i 0.657672i
\(292\) 716.424i 2.45351i
\(293\) −321.271 −1.09649 −0.548245 0.836318i \(-0.684704\pi\)
−0.548245 + 0.836318i \(0.684704\pi\)
\(294\) 199.647i 0.679072i
\(295\) 173.018 310.986i 0.586502 1.05419i
\(296\) 242.129 0.818002
\(297\) 65.7981i 0.221542i
\(298\) −203.763 −0.683770
\(299\) −466.581 −1.56047
\(300\) −107.262 −0.357539
\(301\) 68.4969i 0.227565i
\(302\) −317.043 −1.04981
\(303\) 276.466i 0.912428i
\(304\) 305.326 1.00436
\(305\) 506.974i 1.66221i
\(306\) 129.811i 0.424219i
\(307\) −569.638 −1.85550 −0.927750 0.373203i \(-0.878259\pi\)
−0.927750 + 0.373203i \(0.878259\pi\)
\(308\) 640.803i 2.08053i
\(309\) 46.3280i 0.149929i
\(310\) 4.76571 0.0153733
\(311\) −357.447 −1.14935 −0.574673 0.818383i \(-0.694871\pi\)
−0.574673 + 0.818383i \(0.694871\pi\)
\(312\) 128.662 0.412378
\(313\) 540.979i 1.72837i 0.503176 + 0.864184i \(0.332165\pi\)
−0.503176 + 0.864184i \(0.667835\pi\)
\(314\) −771.370 −2.45659
\(315\) 168.311 0.534320
\(316\) −282.847 −0.895084
\(317\) 431.328 1.36066 0.680328 0.732908i \(-0.261837\pi\)
0.680328 + 0.732908i \(0.261837\pi\)
\(318\) 251.750i 0.791668i
\(319\) 495.319i 1.55272i
\(320\) −595.991 −1.86247
\(321\) −61.2908 −0.190937
\(322\) 794.566 2.46760
\(323\) −526.804 −1.63097
\(324\) −48.9655 −0.151128
\(325\) 191.019i 0.587752i
\(326\) 296.259i 0.908770i
\(327\) 118.152i 0.361321i
\(328\) 50.1074i 0.152766i
\(329\) 267.215i 0.812203i
\(330\) −406.479 −1.23176
\(331\) 241.399 0.729301 0.364650 0.931145i \(-0.381189\pi\)
0.364650 + 0.931145i \(0.381189\pi\)
\(332\) 90.0708i 0.271297i
\(333\) 164.104i 0.492805i
\(334\) 240.860i 0.721138i
\(335\) 491.664i 1.46766i
\(336\) 131.496 0.391356
\(337\) 122.088i 0.362278i −0.983457 0.181139i \(-0.942022\pi\)
0.983457 0.181139i \(-0.0579784\pi\)
\(338\) 346.073i 1.02388i
\(339\) 209.419i 0.617754i
\(340\) 462.151 1.35927
\(341\) 3.25621 0.00954901
\(342\) 344.810i 1.00822i
\(343\) 106.828 0.311452
\(344\) 32.5967 0.0947579
\(345\) 290.463i 0.841922i
\(346\) −160.560 −0.464046
\(347\) 403.930i 1.16406i −0.813166 0.582032i \(-0.802258\pi\)
0.813166 0.582032i \(-0.197742\pi\)
\(348\) −368.606 −1.05921
\(349\) 449.445i 1.28781i 0.765106 + 0.643904i \(0.222686\pi\)
−0.765106 + 0.643904i \(0.777314\pi\)
\(350\) 325.298i 0.929422i
\(351\) 87.2015i 0.248437i
\(352\) −541.771 −1.53912
\(353\) 213.176i 0.603899i 0.953324 + 0.301950i \(0.0976374\pi\)
−0.953324 + 0.301950i \(0.902363\pi\)
\(354\) −274.382 152.653i −0.775089 0.431224i
\(355\) 42.0365 0.118413
\(356\) 376.786i 1.05839i
\(357\) −226.880 −0.635518
\(358\) 361.041 1.00849
\(359\) 405.372 1.12917 0.564585 0.825375i \(-0.309036\pi\)
0.564585 + 0.825375i \(0.309036\pi\)
\(360\) 80.0968i 0.222491i
\(361\) 1038.32 2.87623
\(362\) 492.162i 1.35956i
\(363\) −68.1525 −0.187748
\(364\) 849.249i 2.33310i
\(365\) 794.270i 2.17608i
\(366\) 447.302 1.22214
\(367\) 541.192i 1.47464i 0.675546 + 0.737318i \(0.263908\pi\)
−0.675546 + 0.737318i \(0.736092\pi\)
\(368\) 226.929i 0.616655i
\(369\) −33.9606 −0.0920341
\(370\) 1013.78 2.73995
\(371\) 440.002 1.18599
\(372\) 2.42320i 0.00651399i
\(373\) −107.068 −0.287046 −0.143523 0.989647i \(-0.545843\pi\)
−0.143523 + 0.989647i \(0.545843\pi\)
\(374\) 547.926 1.46504
\(375\) 142.268 0.379380
\(376\) 127.164 0.338201
\(377\) 656.441i 1.74122i
\(378\) 148.500i 0.392858i
\(379\) −204.702 −0.540112 −0.270056 0.962845i \(-0.587042\pi\)
−0.270056 + 0.962845i \(0.587042\pi\)
\(380\) −1227.59 −3.23049
\(381\) −273.816 −0.718678
\(382\) 43.9187 0.114970
\(383\) −4.98048 −0.0130039 −0.00650193 0.999979i \(-0.502070\pi\)
−0.00650193 + 0.999979i \(0.502070\pi\)
\(384\) 229.423i 0.597456i
\(385\) 710.432i 1.84528i
\(386\) 221.059i 0.572692i
\(387\) 22.0926i 0.0570869i
\(388\) 601.159i 1.54938i
\(389\) 138.904 0.357079 0.178539 0.983933i \(-0.442863\pi\)
0.178539 + 0.983933i \(0.442863\pi\)
\(390\) 538.702 1.38129
\(391\) 391.539i 1.00138i
\(392\) 166.054i 0.423608i
\(393\) 226.055i 0.575204i
\(394\) 136.879i 0.347409i
\(395\) −313.580 −0.793874
\(396\) 206.681i 0.521922i
\(397\) 266.530i 0.671359i −0.941976 0.335679i \(-0.891034\pi\)
0.941976 0.335679i \(-0.108966\pi\)
\(398\) 384.738i 0.966678i
\(399\) 602.649 1.51040
\(400\) −92.9055 −0.232264
\(401\) 515.725i 1.28610i 0.765825 + 0.643049i \(0.222331\pi\)
−0.765825 + 0.643049i \(0.777669\pi\)
\(402\) 433.794 1.07909
\(403\) −4.31542 −0.0107082
\(404\) 868.417i 2.14955i
\(405\) −54.2861 −0.134040
\(406\) 1117.89i 2.75342i
\(407\) 692.676 1.70191
\(408\) 107.969i 0.264630i
\(409\) 53.2453i 0.130184i 0.997879 + 0.0650920i \(0.0207341\pi\)
−0.997879 + 0.0650920i \(0.979266\pi\)
\(410\) 209.797i 0.511701i
\(411\) 361.862 0.880444
\(412\) 145.523i 0.353210i
\(413\) 266.803 479.556i 0.646012 1.16115i
\(414\) −256.275 −0.619021
\(415\) 99.8578i 0.240621i
\(416\) 718.002 1.72597
\(417\) −127.880 −0.306667
\(418\) −1455.43 −3.48188
\(419\) 275.166i 0.656721i −0.944553 0.328360i \(-0.893504\pi\)
0.944553 0.328360i \(-0.106496\pi\)
\(420\) −528.688 −1.25878
\(421\) 508.314i 1.20740i −0.797213 0.603699i \(-0.793693\pi\)
0.797213 0.603699i \(-0.206307\pi\)
\(422\) 328.091 0.777466
\(423\) 86.1860i 0.203749i
\(424\) 209.391i 0.493846i
\(425\) 160.297 0.377170
\(426\) 37.0887i 0.0870627i
\(427\) 781.781i 1.83087i
\(428\) 192.523 0.449820
\(429\) 368.073 0.857980
\(430\) 136.481 0.317398
\(431\) 331.069i 0.768141i 0.923304 + 0.384070i \(0.125478\pi\)
−0.923304 + 0.384070i \(0.874522\pi\)
\(432\) −42.4119 −0.0981757
\(433\) 216.406 0.499783 0.249891 0.968274i \(-0.419605\pi\)
0.249891 + 0.968274i \(0.419605\pi\)
\(434\) 7.34897 0.0169331
\(435\) −408.658 −0.939444
\(436\) 371.132i 0.851219i
\(437\) 1040.02i 2.37992i
\(438\) −700.782 −1.59996
\(439\) 594.843 1.35500 0.677498 0.735525i \(-0.263064\pi\)
0.677498 + 0.735525i \(0.263064\pi\)
\(440\) 338.085 0.768374
\(441\) 112.544 0.255203
\(442\) −726.160 −1.64290
\(443\) 101.223i 0.228495i −0.993452 0.114247i \(-0.963554\pi\)
0.993452 0.114247i \(-0.0364456\pi\)
\(444\) 515.474i 1.16098i
\(445\) 417.728i 0.938714i
\(446\) 115.727i 0.259478i
\(447\) 114.865i 0.256968i
\(448\) −919.049 −2.05145
\(449\) 612.041 1.36312 0.681561 0.731762i \(-0.261302\pi\)
0.681561 + 0.731762i \(0.261302\pi\)
\(450\) 104.920i 0.233155i
\(451\) 143.346i 0.317840i
\(452\) 657.813i 1.45534i
\(453\) 178.722i 0.394530i
\(454\) 582.666 1.28341
\(455\) 941.528i 2.06929i
\(456\) 286.792i 0.628930i
\(457\) 406.851i 0.890264i −0.895465 0.445132i \(-0.853157\pi\)
0.895465 0.445132i \(-0.146843\pi\)
\(458\) −635.828 −1.38827
\(459\) 73.1766 0.159426
\(460\) 912.385i 1.98345i
\(461\) −852.748 −1.84978 −0.924889 0.380236i \(-0.875843\pi\)
−0.924889 + 0.380236i \(0.875843\pi\)
\(462\) −626.812 −1.35674
\(463\) 727.640i 1.57158i 0.618495 + 0.785788i \(0.287743\pi\)
−0.618495 + 0.785788i \(0.712257\pi\)
\(464\) −319.271 −0.688084
\(465\) 2.68651i 0.00577743i
\(466\) −655.290 −1.40620
\(467\) 24.1720i 0.0517602i −0.999665 0.0258801i \(-0.991761\pi\)
0.999665 0.0258801i \(-0.00823880\pi\)
\(468\) 273.912i 0.585282i
\(469\) 758.173i 1.61657i
\(470\) 532.429 1.13283
\(471\) 434.834i 0.923214i
\(472\) 228.214 + 126.968i 0.483504 + 0.268999i
\(473\) 93.2519 0.197150
\(474\) 276.671i 0.583694i
\(475\) −425.789 −0.896397
\(476\) 712.661 1.49719
\(477\) −141.916 −0.297517
\(478\) 436.757i 0.913717i
\(479\) −540.528 −1.12845 −0.564225 0.825621i \(-0.690825\pi\)
−0.564225 + 0.825621i \(0.690825\pi\)
\(480\) 446.982i 0.931213i
\(481\) −917.996 −1.90851
\(482\) 1202.19i 2.49417i
\(483\) 447.909i 0.927349i
\(484\) 214.077 0.442307
\(485\) 666.481i 1.37419i
\(486\) 47.8964i 0.0985524i
\(487\) −564.800 −1.15975 −0.579877 0.814704i \(-0.696899\pi\)
−0.579877 + 0.814704i \(0.696899\pi\)
\(488\) −372.038 −0.762374
\(489\) −167.006 −0.341525
\(490\) 695.262i 1.41890i
\(491\) 8.09712 0.0164911 0.00824554 0.999966i \(-0.497375\pi\)
0.00824554 + 0.999966i \(0.497375\pi\)
\(492\) 106.675 0.216819
\(493\) 550.863 1.11737
\(494\) 1928.86 3.90458
\(495\) 229.139i 0.462907i
\(496\) 2.09888i 0.00423161i
\(497\) 64.8226 0.130428
\(498\) −88.1042 −0.176916
\(499\) 719.073 1.44103 0.720514 0.693440i \(-0.243906\pi\)
0.720514 + 0.693440i \(0.243906\pi\)
\(500\) −446.882 −0.893764
\(501\) 135.777 0.271011
\(502\) 414.817i 0.826329i
\(503\) 524.427i 1.04260i −0.853374 0.521299i \(-0.825448\pi\)
0.853374 0.521299i \(-0.174552\pi\)
\(504\) 123.513i 0.245066i
\(505\) 962.778i 1.90649i
\(506\) 1081.72i 2.13779i
\(507\) −195.087 −0.384787
\(508\) 860.095 1.69310
\(509\) 749.520i 1.47253i 0.676691 + 0.736267i \(0.263413\pi\)
−0.676691 + 0.736267i \(0.736587\pi\)
\(510\) 452.061i 0.886394i
\(511\) 1224.81i 2.39688i
\(512\) 493.728i 0.964312i
\(513\) −194.375 −0.378899
\(514\) 409.674i 0.797032i
\(515\) 161.335i 0.313272i
\(516\) 69.3960i 0.134488i
\(517\) 363.787 0.703650
\(518\) 1563.31 3.01796
\(519\) 90.5102i 0.174393i
\(520\) −448.060 −0.861653
\(521\) −191.543 −0.367646 −0.183823 0.982959i \(-0.558847\pi\)
−0.183823 + 0.982959i \(0.558847\pi\)
\(522\) 360.558i 0.690724i
\(523\) 985.876 1.88504 0.942520 0.334149i \(-0.108449\pi\)
0.942520 + 0.334149i \(0.108449\pi\)
\(524\) 710.071i 1.35510i
\(525\) −183.375 −0.349287
\(526\) 836.795i 1.59086i
\(527\) 3.62136i 0.00687165i
\(528\) 179.019i 0.339050i
\(529\) −243.981 −0.461212
\(530\) 876.709i 1.65417i
\(531\) −86.0532 + 154.673i −0.162059 + 0.291287i
\(532\) −1893.00 −3.55828
\(533\) 189.975i 0.356426i
\(534\) −368.560 −0.690187
\(535\) 213.443 0.398958
\(536\) −360.804 −0.673141
\(537\) 203.525i 0.379003i
\(538\) −845.419 −1.57141
\(539\) 475.044i 0.881343i
\(540\) 170.520 0.315778
\(541\) 239.083i 0.441928i −0.975282 0.220964i \(-0.929080\pi\)
0.975282 0.220964i \(-0.0709204\pi\)
\(542\) 437.405i 0.807020i
\(543\) 277.440 0.510939
\(544\) 602.523i 1.10758i
\(545\) 411.458i 0.754969i
\(546\) 830.707 1.52144
\(547\) 106.125 0.194013 0.0970065 0.995284i \(-0.469073\pi\)
0.0970065 + 0.995284i \(0.469073\pi\)
\(548\) −1136.66 −2.07420
\(549\) 252.151i 0.459292i
\(550\) 442.861 0.805201
\(551\) −1463.23 −2.65559
\(552\) 213.154 0.386148
\(553\) −483.557 −0.874426
\(554\) 866.613i 1.56428i
\(555\) 571.485i 1.02970i
\(556\) 401.689 0.722462
\(557\) 8.64276 0.0155166 0.00775831 0.999970i \(-0.497530\pi\)
0.00775831 + 0.999970i \(0.497530\pi\)
\(558\) −2.37030 −0.00424784
\(559\) −123.586 −0.221084
\(560\) −457.928 −0.817728
\(561\) 308.875i 0.550579i
\(562\) 839.359i 1.49352i
\(563\) 327.402i 0.581530i −0.956794 0.290765i \(-0.906090\pi\)
0.956794 0.290765i \(-0.0939099\pi\)
\(564\) 270.722i 0.480004i
\(565\) 729.290i 1.29078i
\(566\) −740.272 −1.30790
\(567\) −83.7120 −0.147640
\(568\) 30.8481i 0.0543101i
\(569\) 616.454i 1.08340i −0.840572 0.541700i \(-0.817781\pi\)
0.840572 0.541700i \(-0.182219\pi\)
\(570\) 1200.79i 2.10664i
\(571\) 518.165i 0.907470i 0.891137 + 0.453735i \(0.149909\pi\)
−0.891137 + 0.453735i \(0.850091\pi\)
\(572\) −1156.17 −2.02128
\(573\) 24.7577i 0.0432071i
\(574\) 323.519i 0.563621i
\(575\) 316.461i 0.550367i
\(576\) 296.425 0.514627
\(577\) 787.940 1.36558 0.682790 0.730614i \(-0.260766\pi\)
0.682790 + 0.730614i \(0.260766\pi\)
\(578\) 278.600i 0.482007i
\(579\) 124.615 0.215224
\(580\) 1283.65 2.21319
\(581\) 153.986i 0.265036i
\(582\) 588.034 1.01037
\(583\) 599.020i 1.02748i
\(584\) 582.868 0.998062
\(585\) 303.675i 0.519103i
\(586\) 987.125i 1.68451i
\(587\) 782.879i 1.33370i −0.745194 0.666848i \(-0.767643\pi\)
0.745194 0.666848i \(-0.232357\pi\)
\(588\) −353.517 −0.601220
\(589\) 9.61922i 0.0163314i
\(590\) 955.521 + 531.608i 1.61953 + 0.901031i
\(591\) −77.1610 −0.130560
\(592\) 446.482i 0.754193i
\(593\) 1037.25 1.74916 0.874580 0.484881i \(-0.161137\pi\)
0.874580 + 0.484881i \(0.161137\pi\)
\(594\) 202.169 0.340351
\(595\) 790.098 1.32790
\(596\) 360.806i 0.605380i
\(597\) −216.883 −0.363288
\(598\) 1433.60i 2.39732i
\(599\) 673.671 1.12466 0.562330 0.826913i \(-0.309905\pi\)
0.562330 + 0.826913i \(0.309905\pi\)
\(600\) 87.2658i 0.145443i
\(601\) 962.944i 1.60224i 0.598506 + 0.801118i \(0.295761\pi\)
−0.598506 + 0.801118i \(0.704239\pi\)
\(602\) 210.461 0.349603
\(603\) 244.537i 0.405534i
\(604\) 561.392i 0.929457i
\(605\) 237.338 0.392294
\(606\) 849.457 1.40174
\(607\) −790.355 −1.30207 −0.651034 0.759049i \(-0.725664\pi\)
−0.651034 + 0.759049i \(0.725664\pi\)
\(608\) 1600.45i 2.63232i
\(609\) −630.172 −1.03477
\(610\) −1557.71 −2.55362
\(611\) −482.123 −0.789071
\(612\) −229.858 −0.375585
\(613\) 953.011i 1.55467i −0.629088 0.777334i \(-0.716572\pi\)
0.629088 0.777334i \(-0.283428\pi\)
\(614\) 1750.25i 2.85056i
\(615\) 118.266 0.192303
\(616\) 521.344 0.846338
\(617\) 419.167 0.679364 0.339682 0.940540i \(-0.389681\pi\)
0.339682 + 0.940540i \(0.389681\pi\)
\(618\) 142.345 0.230332
\(619\) −209.634 −0.338666 −0.169333 0.985559i \(-0.554161\pi\)
−0.169333 + 0.985559i \(0.554161\pi\)
\(620\) 8.43869i 0.0136108i
\(621\) 144.466i 0.232635i
\(622\) 1098.28i 1.76572i
\(623\) 644.158i 1.03396i
\(624\) 237.251i 0.380210i
\(625\) −780.001 −1.24800
\(626\) −1662.19 −2.65526
\(627\) 820.448i 1.30853i
\(628\) 1365.87i 2.17496i
\(629\) 770.351i 1.22472i
\(630\) 517.145i 0.820865i
\(631\) −612.575 −0.970800 −0.485400 0.874292i \(-0.661326\pi\)
−0.485400 + 0.874292i \(0.661326\pi\)
\(632\) 230.118i 0.364111i
\(633\) 184.950i 0.292180i
\(634\) 1325.28i 2.09035i
\(635\) 953.552 1.50166
\(636\) 445.777 0.700908
\(637\) 629.571i 0.988337i
\(638\) 1521.90 2.38542
\(639\) −20.9075 −0.0327191
\(640\) 798.955i 1.24837i
\(641\) 198.748 0.310060 0.155030 0.987910i \(-0.450453\pi\)
0.155030 + 0.987910i \(0.450453\pi\)
\(642\) 188.320i 0.293333i
\(643\) −157.384 −0.244766 −0.122383 0.992483i \(-0.539054\pi\)
−0.122383 + 0.992483i \(0.539054\pi\)
\(644\) 1406.95i 2.18470i
\(645\) 76.9365i 0.119281i
\(646\) 1618.63i 2.50563i
\(647\) 1214.33 1.87686 0.938430 0.345470i \(-0.112280\pi\)
0.938430 + 0.345470i \(0.112280\pi\)
\(648\) 39.8373i 0.0614774i
\(649\) 652.869 + 363.226i 1.00596 + 0.559671i
\(650\) −586.918 −0.902951
\(651\) 4.14273i 0.00636365i
\(652\) 524.589 0.804584
\(653\) −404.646 −0.619673 −0.309836 0.950790i \(-0.600274\pi\)
−0.309836 + 0.950790i \(0.600274\pi\)
\(654\) −363.028 −0.555089
\(655\) 787.226i 1.20187i
\(656\) 92.3974 0.140850
\(657\) 395.042i 0.601282i
\(658\) 821.033 1.24777
\(659\) 1245.68i 1.89025i 0.326703 + 0.945127i \(0.394062\pi\)
−0.326703 + 0.945127i \(0.605938\pi\)
\(660\) 719.757i 1.09054i
\(661\) 96.3638 0.145785 0.0728924 0.997340i \(-0.476777\pi\)
0.0728924 + 0.997340i \(0.476777\pi\)
\(662\) 741.711i 1.12041i
\(663\) 409.348i 0.617418i
\(664\) 73.2797 0.110361
\(665\) −2098.70 −3.15593
\(666\) −504.220 −0.757087
\(667\) 1087.52i 1.63047i
\(668\) −426.493 −0.638463
\(669\) −65.2372 −0.0975146
\(670\) −1510.67 −2.25473
\(671\) −1064.32 −1.58617
\(672\) 689.270i 1.02570i
\(673\) 786.566i 1.16875i 0.811485 + 0.584373i \(0.198660\pi\)
−0.811485 + 0.584373i \(0.801340\pi\)
\(674\) 375.122 0.556561
\(675\) 59.1449 0.0876221
\(676\) 612.795 0.906502
\(677\) −797.643 −1.17820 −0.589101 0.808059i \(-0.700518\pi\)
−0.589101 + 0.808059i \(0.700518\pi\)
\(678\) 643.451 0.949042
\(679\) 1027.75i 1.51362i
\(680\) 375.997i 0.552936i
\(681\) 328.458i 0.482318i
\(682\) 10.0049i 0.0146700i
\(683\) 743.492i 1.08857i −0.838901 0.544284i \(-0.816801\pi\)
0.838901 0.544284i \(-0.183199\pi\)
\(684\) 610.559 0.892630
\(685\) −1260.17 −1.83966
\(686\) 328.235i 0.478477i
\(687\) 358.427i 0.521727i
\(688\) 60.1079i 0.0873662i
\(689\) 793.874i 1.15221i
\(690\) 892.465 1.29343
\(691\) 652.050i 0.943632i −0.881697 0.471816i \(-0.843599\pi\)
0.881697 0.471816i \(-0.156401\pi\)
\(692\) 284.305i 0.410845i
\(693\) 353.344i 0.509876i
\(694\) 1241.10 1.78833
\(695\) 445.336 0.640771
\(696\) 299.890i 0.430877i
\(697\) −159.420 −0.228724
\(698\) −1380.95 −1.97843
\(699\) 369.398i 0.528466i
\(700\) 576.008 0.822869
\(701\) 24.8059i 0.0353864i 0.999843 + 0.0176932i \(0.00563221\pi\)
−0.999843 + 0.0176932i \(0.994368\pi\)
\(702\) −267.932 −0.381669
\(703\) 2046.24i 2.91073i
\(704\) 1251.20i 1.77727i
\(705\) 300.139i 0.425729i
\(706\) −654.997 −0.927758
\(707\) 1484.66i 2.09994i
\(708\) 270.305 485.851i 0.381787 0.686230i
\(709\) 521.844 0.736028 0.368014 0.929820i \(-0.380038\pi\)
0.368014 + 0.929820i \(0.380038\pi\)
\(710\) 129.160i 0.181915i
\(711\) 155.964 0.219359
\(712\) 306.546 0.430542
\(713\) −7.14934 −0.0100271
\(714\) 697.102i 0.976333i
\(715\) −1281.80 −1.79272
\(716\) 639.299i 0.892876i
\(717\) −246.207 −0.343385
\(718\) 1245.53i 1.73472i
\(719\) 997.450i 1.38727i 0.720325 + 0.693637i \(0.243993\pi\)
−0.720325 + 0.693637i \(0.756007\pi\)
\(720\) 147.697 0.205135
\(721\) 248.787i 0.345058i
\(722\) 3190.30i 4.41870i
\(723\) −677.693 −0.937335
\(724\) −871.477 −1.20370
\(725\) 445.235 0.614117
\(726\) 209.403i 0.288433i
\(727\) −570.949 −0.785349 −0.392675 0.919677i \(-0.628450\pi\)
−0.392675 + 0.919677i \(0.628450\pi\)
\(728\) −690.932 −0.949082
\(729\) 27.0000 0.0370370
\(730\) 2440.44 3.34307
\(731\) 103.709i 0.141873i
\(732\) 792.043i 1.08203i
\(733\) −337.572 −0.460535 −0.230268 0.973127i \(-0.573960\pi\)
−0.230268 + 0.973127i \(0.573960\pi\)
\(734\) −1662.84 −2.26545
\(735\) −391.930 −0.533239
\(736\) 1189.51 1.61618
\(737\) −1032.18 −1.40051
\(738\) 104.346i 0.141390i
\(739\) 1041.04i 1.40872i −0.709843 0.704360i \(-0.751234\pi\)
0.709843 0.704360i \(-0.248766\pi\)
\(740\) 1795.12i 2.42583i
\(741\) 1087.33i 1.46738i
\(742\) 1351.93i 1.82201i
\(743\) 955.497 1.28600 0.643000 0.765867i \(-0.277690\pi\)
0.643000 + 0.765867i \(0.277690\pi\)
\(744\) 1.97147 0.00264982
\(745\) 400.011i 0.536928i
\(746\) 328.974i 0.440983i
\(747\) 49.6658i 0.0664870i
\(748\) 970.219i 1.29708i
\(749\) 329.140 0.439439
\(750\) 437.125i 0.582834i
\(751\) 450.913i 0.600416i −0.953874 0.300208i \(-0.902944\pi\)
0.953874 0.300208i \(-0.0970561\pi\)
\(752\) 234.488i 0.311820i
\(753\) 233.839 0.310543
\(754\) −2016.95 −2.67500
\(755\) 622.392i 0.824360i
\(756\) 262.951 0.347819
\(757\) 410.015 0.541632 0.270816 0.962631i \(-0.412707\pi\)
0.270816 + 0.962631i \(0.412707\pi\)
\(758\) 628.960i 0.829763i
\(759\) 609.785 0.803406
\(760\) 998.740i 1.31413i
\(761\) 1469.25 1.93068 0.965339 0.260998i \(-0.0840517\pi\)
0.965339 + 0.260998i \(0.0840517\pi\)
\(762\) 841.316i 1.10409i
\(763\) 634.490i 0.831573i
\(764\) 77.7673i 0.101790i
\(765\) −254.834 −0.333116
\(766\) 15.3028i 0.0199776i
\(767\) −865.240 481.380i −1.12808 0.627614i
\(768\) −20.3515 −0.0264994
\(769\) 469.742i 0.610848i −0.952216 0.305424i \(-0.901202\pi\)
0.952216 0.305424i \(-0.0987982\pi\)
\(770\) 2182.84 2.83486
\(771\) −230.940 −0.299533
\(772\) −391.432 −0.507037
\(773\) 373.454i 0.483122i −0.970386 0.241561i \(-0.922341\pi\)
0.970386 0.241561i \(-0.0776595\pi\)
\(774\) −67.8809 −0.0877014
\(775\) 2.92696i 0.00377672i
\(776\) −489.091 −0.630271
\(777\) 881.260i 1.13418i
\(778\) 426.789i 0.548572i
\(779\) 423.460 0.543594
\(780\) 953.886i 1.22293i
\(781\) 88.2496i 0.112996i
\(782\) −1203.03 −1.53840
\(783\) 203.252 0.259581
\(784\) −306.202 −0.390564
\(785\) 1514.29i 1.92903i
\(786\) −694.567 −0.883674
\(787\) −97.7362 −0.124188 −0.0620942 0.998070i \(-0.519778\pi\)
−0.0620942 + 0.998070i \(0.519778\pi\)
\(788\) 242.374 0.307581
\(789\) 471.715 0.597864
\(790\) 963.494i 1.21961i
\(791\) 1124.60i 1.42175i