Properties

Label 230.3.d.a.91.8
Level $230$
Weight $3$
Character 230.91
Analytic conductor $6.267$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 230.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.26704608029\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \( x^{16} + 78x^{14} + 2165x^{12} + 28310x^{10} + 184804x^{8} + 569634x^{6} + 696037x^{4} + 285578x^{2} + 529 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 91.8
Root \(-3.47734i\) of defining polynomial
Character \(\chi\) \(=\) 230.91
Dual form 230.3.d.a.91.7

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} +4.76369 q^{3} +2.00000 q^{4} +2.23607i q^{5} -6.73687 q^{6} -7.05858i q^{7} -2.82843 q^{8} +13.6927 q^{9} +O(q^{10})\) \(q-1.41421 q^{2} +4.76369 q^{3} +2.00000 q^{4} +2.23607i q^{5} -6.73687 q^{6} -7.05858i q^{7} -2.82843 q^{8} +13.6927 q^{9} -3.16228i q^{10} -10.4520i q^{11} +9.52738 q^{12} +19.0223 q^{13} +9.98235i q^{14} +10.6519i q^{15} +4.00000 q^{16} -12.8329i q^{17} -19.3645 q^{18} +22.7880i q^{19} +4.47214i q^{20} -33.6249i q^{21} +14.7813i q^{22} +(-6.14050 + 22.1652i) q^{23} -13.4737 q^{24} -5.00000 q^{25} -26.9016 q^{26} +22.3548 q^{27} -14.1172i q^{28} -8.61694 q^{29} -15.0641i q^{30} +22.2032 q^{31} -5.65685 q^{32} -49.7900i q^{33} +18.1485i q^{34} +15.7835 q^{35} +27.3855 q^{36} +29.8603i q^{37} -32.2271i q^{38} +90.6164 q^{39} -6.32456i q^{40} -18.7911 q^{41} +47.5528i q^{42} -10.0531i q^{43} -20.9039i q^{44} +30.6179i q^{45} +(8.68398 - 31.3463i) q^{46} +20.6079 q^{47} +19.0548 q^{48} -0.823620 q^{49} +7.07107 q^{50} -61.1320i q^{51} +38.0446 q^{52} -17.3941i q^{53} -31.6144 q^{54} +23.3713 q^{55} +19.9647i q^{56} +108.555i q^{57} +12.1862 q^{58} -103.279 q^{59} +21.3039i q^{60} -74.6163i q^{61} -31.4001 q^{62} -96.6514i q^{63} +8.00000 q^{64} +42.5352i q^{65} +70.4136i q^{66} +101.145i q^{67} -25.6658i q^{68} +(-29.2514 + 105.588i) q^{69} -22.3212 q^{70} -69.4218 q^{71} -38.7289 q^{72} -122.376 q^{73} -42.2289i q^{74} -23.8184 q^{75} +45.5761i q^{76} -73.7761 q^{77} -128.151 q^{78} -140.900i q^{79} +8.94427i q^{80} -16.7435 q^{81} +26.5747 q^{82} +126.423i q^{83} -67.2498i q^{84} +28.6953 q^{85} +14.2173i q^{86} -41.0484 q^{87} +29.5626i q^{88} -11.9403i q^{89} -43.3002i q^{90} -134.271i q^{91} +(-12.2810 + 44.3303i) q^{92} +105.769 q^{93} -29.1440 q^{94} -50.9556 q^{95} -26.9475 q^{96} -57.0325i q^{97} +1.16477 q^{98} -143.116i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9} + 24 q^{13} + 64 q^{16} - 32 q^{18} + 4 q^{23} - 16 q^{24} - 80 q^{25} + 96 q^{26} - 96 q^{27} - 108 q^{29} - 116 q^{31} + 60 q^{35} + 128 q^{36} + 248 q^{39} - 156 q^{41} - 124 q^{46} - 128 q^{47} - 28 q^{49} + 48 q^{52} + 224 q^{54} + 160 q^{58} + 204 q^{59} + 64 q^{62} + 128 q^{64} - 268 q^{69} - 120 q^{70} + 236 q^{71} - 64 q^{72} - 112 q^{73} - 936 q^{77} - 432 q^{78} - 136 q^{81} - 64 q^{82} + 60 q^{85} - 152 q^{87} + 8 q^{92} + 856 q^{93} - 216 q^{94} - 160 q^{95} - 32 q^{96} + 256 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 −0.707107
\(3\) 4.76369 1.58790 0.793948 0.607985i \(-0.208022\pi\)
0.793948 + 0.607985i \(0.208022\pi\)
\(4\) 2.00000 0.500000
\(5\) 2.23607i 0.447214i
\(6\) −6.73687 −1.12281
\(7\) 7.05858i 1.00837i −0.863596 0.504185i \(-0.831793\pi\)
0.863596 0.504185i \(-0.168207\pi\)
\(8\) −2.82843 −0.353553
\(9\) 13.6927 1.52142
\(10\) 3.16228i 0.316228i
\(11\) 10.4520i 0.950179i −0.879937 0.475090i \(-0.842416\pi\)
0.879937 0.475090i \(-0.157584\pi\)
\(12\) 9.52738 0.793948
\(13\) 19.0223 1.46326 0.731628 0.681704i \(-0.238761\pi\)
0.731628 + 0.681704i \(0.238761\pi\)
\(14\) 9.98235i 0.713025i
\(15\) 10.6519i 0.710129i
\(16\) 4.00000 0.250000
\(17\) 12.8329i 0.754877i −0.926035 0.377439i \(-0.876805\pi\)
0.926035 0.377439i \(-0.123195\pi\)
\(18\) −19.3645 −1.07580
\(19\) 22.7880i 1.19937i 0.800236 + 0.599685i \(0.204707\pi\)
−0.800236 + 0.599685i \(0.795293\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 33.6249i 1.60119i
\(22\) 14.7813i 0.671878i
\(23\) −6.14050 + 22.1652i −0.266978 + 0.963703i
\(24\) −13.4737 −0.561406
\(25\) −5.00000 −0.200000
\(26\) −26.9016 −1.03468
\(27\) 22.3548 0.827954
\(28\) 14.1172i 0.504185i
\(29\) −8.61694 −0.297136 −0.148568 0.988902i \(-0.547466\pi\)
−0.148568 + 0.988902i \(0.547466\pi\)
\(30\) 15.0641i 0.502137i
\(31\) 22.2032 0.716233 0.358116 0.933677i \(-0.383419\pi\)
0.358116 + 0.933677i \(0.383419\pi\)
\(32\) −5.65685 −0.176777
\(33\) 49.7900i 1.50879i
\(34\) 18.1485i 0.533779i
\(35\) 15.7835 0.450956
\(36\) 27.3855 0.760708
\(37\) 29.8603i 0.807036i 0.914972 + 0.403518i \(0.132213\pi\)
−0.914972 + 0.403518i \(0.867787\pi\)
\(38\) 32.2271i 0.848083i
\(39\) 90.6164 2.32350
\(40\) 6.32456i 0.158114i
\(41\) −18.7911 −0.458320 −0.229160 0.973389i \(-0.573598\pi\)
−0.229160 + 0.973389i \(0.573598\pi\)
\(42\) 47.5528i 1.13221i
\(43\) 10.0531i 0.233794i −0.993144 0.116897i \(-0.962705\pi\)
0.993144 0.116897i \(-0.0372948\pi\)
\(44\) 20.9039i 0.475090i
\(45\) 30.6179i 0.680398i
\(46\) 8.68398 31.3463i 0.188782 0.681441i
\(47\) 20.6079 0.438466 0.219233 0.975673i \(-0.429645\pi\)
0.219233 + 0.975673i \(0.429645\pi\)
\(48\) 19.0548 0.396974
\(49\) −0.823620 −0.0168086
\(50\) 7.07107 0.141421
\(51\) 61.1320i 1.19867i
\(52\) 38.0446 0.731628
\(53\) 17.3941i 0.328191i −0.986444 0.164096i \(-0.947529\pi\)
0.986444 0.164096i \(-0.0524706\pi\)
\(54\) −31.6144 −0.585452
\(55\) 23.3713 0.424933
\(56\) 19.9647i 0.356512i
\(57\) 108.555i 1.90448i
\(58\) 12.1862 0.210107
\(59\) −103.279 −1.75048 −0.875242 0.483686i \(-0.839298\pi\)
−0.875242 + 0.483686i \(0.839298\pi\)
\(60\) 21.3039i 0.355064i
\(61\) 74.6163i 1.22322i −0.791160 0.611609i \(-0.790523\pi\)
0.791160 0.611609i \(-0.209477\pi\)
\(62\) −31.4001 −0.506453
\(63\) 96.6514i 1.53415i
\(64\) 8.00000 0.125000
\(65\) 42.5352i 0.654388i
\(66\) 70.4136i 1.06687i
\(67\) 101.145i 1.50963i 0.655937 + 0.754816i \(0.272274\pi\)
−0.655937 + 0.754816i \(0.727726\pi\)
\(68\) 25.6658i 0.377439i
\(69\) −29.2514 + 105.588i −0.423934 + 1.53026i
\(70\) −22.3212 −0.318874
\(71\) −69.4218 −0.977772 −0.488886 0.872348i \(-0.662597\pi\)
−0.488886 + 0.872348i \(0.662597\pi\)
\(72\) −38.7289 −0.537902
\(73\) −122.376 −1.67638 −0.838189 0.545380i \(-0.816385\pi\)
−0.838189 + 0.545380i \(0.816385\pi\)
\(74\) 42.2289i 0.570661i
\(75\) −23.8184 −0.317579
\(76\) 45.5761i 0.599685i
\(77\) −73.7761 −0.958132
\(78\) −128.151 −1.64296
\(79\) 140.900i 1.78355i −0.452482 0.891774i \(-0.649461\pi\)
0.452482 0.891774i \(-0.350539\pi\)
\(80\) 8.94427i 0.111803i
\(81\) −16.7435 −0.206710
\(82\) 26.5747 0.324082
\(83\) 126.423i 1.52317i 0.648064 + 0.761586i \(0.275579\pi\)
−0.648064 + 0.761586i \(0.724421\pi\)
\(84\) 67.2498i 0.800593i
\(85\) 28.6953 0.337591
\(86\) 14.2173i 0.165317i
\(87\) −41.0484 −0.471821
\(88\) 29.5626i 0.335939i
\(89\) 11.9403i 0.134161i −0.997748 0.0670805i \(-0.978632\pi\)
0.997748 0.0670805i \(-0.0213684\pi\)
\(90\) 43.3002i 0.481114i
\(91\) 134.271i 1.47550i
\(92\) −12.2810 + 44.3303i −0.133489 + 0.481851i
\(93\) 105.769 1.13730
\(94\) −29.1440 −0.310042
\(95\) −50.9556 −0.536374
\(96\) −26.9475 −0.280703
\(97\) 57.0325i 0.587964i −0.955811 0.293982i \(-0.905019\pi\)
0.955811 0.293982i \(-0.0949805\pi\)
\(98\) 1.16477 0.0118855
\(99\) 143.116i 1.44562i
\(100\) −10.0000 −0.100000
\(101\) −28.7667 −0.284819 −0.142410 0.989808i \(-0.545485\pi\)
−0.142410 + 0.989808i \(0.545485\pi\)
\(102\) 86.4538i 0.847586i
\(103\) 165.265i 1.60452i 0.596976 + 0.802259i \(0.296369\pi\)
−0.596976 + 0.802259i \(0.703631\pi\)
\(104\) −53.8032 −0.517339
\(105\) 75.1876 0.716072
\(106\) 24.5990i 0.232066i
\(107\) 194.859i 1.82112i 0.413381 + 0.910558i \(0.364348\pi\)
−0.413381 + 0.910558i \(0.635652\pi\)
\(108\) 44.7095 0.413977
\(109\) 62.2801i 0.571377i −0.958323 0.285688i \(-0.907778\pi\)
0.958323 0.285688i \(-0.0922222\pi\)
\(110\) −33.0520 −0.300473
\(111\) 142.245i 1.28149i
\(112\) 28.2343i 0.252092i
\(113\) 47.4389i 0.419813i 0.977721 + 0.209907i \(0.0673160\pi\)
−0.977721 + 0.209907i \(0.932684\pi\)
\(114\) 153.520i 1.34667i
\(115\) −49.5628 13.7306i −0.430981 0.119396i
\(116\) −17.2339 −0.148568
\(117\) 260.468 2.22622
\(118\) 146.058 1.23778
\(119\) −90.5822 −0.761195
\(120\) 30.1282i 0.251069i
\(121\) 11.7563 0.0971591
\(122\) 105.523i 0.864946i
\(123\) −89.5152 −0.727766
\(124\) 44.4064 0.358116
\(125\) 11.1803i 0.0894427i
\(126\) 136.686i 1.08481i
\(127\) 194.450 1.53110 0.765552 0.643374i \(-0.222466\pi\)
0.765552 + 0.643374i \(0.222466\pi\)
\(128\) −11.3137 −0.0883883
\(129\) 47.8901i 0.371241i
\(130\) 60.1539i 0.462722i
\(131\) −77.9594 −0.595110 −0.297555 0.954705i \(-0.596171\pi\)
−0.297555 + 0.954705i \(0.596171\pi\)
\(132\) 99.5799i 0.754393i
\(133\) 160.851 1.20941
\(134\) 143.041i 1.06747i
\(135\) 49.9868i 0.370272i
\(136\) 36.2970i 0.266889i
\(137\) 231.913i 1.69279i −0.532553 0.846397i \(-0.678767\pi\)
0.532553 0.846397i \(-0.321233\pi\)
\(138\) 41.3678 149.324i 0.299766 1.08206i
\(139\) 49.7145 0.357658 0.178829 0.983880i \(-0.442769\pi\)
0.178829 + 0.983880i \(0.442769\pi\)
\(140\) 31.5670 0.225478
\(141\) 98.1696 0.696238
\(142\) 98.1773 0.691389
\(143\) 198.821i 1.39036i
\(144\) 54.7710 0.380354
\(145\) 19.2681i 0.132883i
\(146\) 173.065 1.18538
\(147\) −3.92347 −0.0266903
\(148\) 59.7207i 0.403518i
\(149\) 179.442i 1.20431i 0.798379 + 0.602156i \(0.205691\pi\)
−0.798379 + 0.602156i \(0.794309\pi\)
\(150\) 33.6844 0.224562
\(151\) −33.4205 −0.221327 −0.110664 0.993858i \(-0.535298\pi\)
−0.110664 + 0.993858i \(0.535298\pi\)
\(152\) 64.4543i 0.424041i
\(153\) 175.718i 1.14848i
\(154\) 104.335 0.677501
\(155\) 49.6479i 0.320309i
\(156\) 181.233 1.16175
\(157\) 18.9433i 0.120658i 0.998179 + 0.0603291i \(0.0192150\pi\)
−0.998179 + 0.0603291i \(0.980785\pi\)
\(158\) 199.263i 1.26116i
\(159\) 82.8603i 0.521134i
\(160\) 12.6491i 0.0790569i
\(161\) 156.455 + 43.3432i 0.971768 + 0.269213i
\(162\) 23.6789 0.146166
\(163\) −322.188 −1.97661 −0.988307 0.152478i \(-0.951275\pi\)
−0.988307 + 0.152478i \(0.951275\pi\)
\(164\) −37.5823 −0.229160
\(165\) 111.334 0.674750
\(166\) 178.790i 1.07705i
\(167\) −49.4087 −0.295861 −0.147930 0.988998i \(-0.547261\pi\)
−0.147930 + 0.988998i \(0.547261\pi\)
\(168\) 95.1056i 0.566105i
\(169\) 192.849 1.14112
\(170\) −40.5812 −0.238713
\(171\) 312.031i 1.82474i
\(172\) 20.1063i 0.116897i
\(173\) 218.540 1.26324 0.631619 0.775279i \(-0.282391\pi\)
0.631619 + 0.775279i \(0.282391\pi\)
\(174\) 58.0513 0.333628
\(175\) 35.2929i 0.201674i
\(176\) 41.8079i 0.237545i
\(177\) −491.987 −2.77959
\(178\) 16.8862i 0.0948662i
\(179\) −299.137 −1.67116 −0.835579 0.549370i \(-0.814868\pi\)
−0.835579 + 0.549370i \(0.814868\pi\)
\(180\) 61.2358i 0.340199i
\(181\) 43.0432i 0.237808i 0.992906 + 0.118904i \(0.0379380\pi\)
−0.992906 + 0.118904i \(0.962062\pi\)
\(182\) 189.887i 1.04334i
\(183\) 355.449i 1.94234i
\(184\) 17.3680 62.6925i 0.0943910 0.340720i
\(185\) −66.7698 −0.360918
\(186\) −149.580 −0.804195
\(187\) −134.129 −0.717269
\(188\) 41.2158 0.219233
\(189\) 157.793i 0.834884i
\(190\) 72.0621 0.379274
\(191\) 312.014i 1.63358i −0.576933 0.816792i \(-0.695751\pi\)
0.576933 0.816792i \(-0.304249\pi\)
\(192\) 38.1095 0.198487
\(193\) 92.5081 0.479317 0.239658 0.970857i \(-0.422965\pi\)
0.239658 + 0.970857i \(0.422965\pi\)
\(194\) 80.6561i 0.415753i
\(195\) 202.624i 1.03910i
\(196\) −1.64724 −0.00840428
\(197\) 49.6153 0.251855 0.125927 0.992039i \(-0.459809\pi\)
0.125927 + 0.992039i \(0.459809\pi\)
\(198\) 202.397i 1.02221i
\(199\) 169.572i 0.852122i 0.904694 + 0.426061i \(0.140099\pi\)
−0.904694 + 0.426061i \(0.859901\pi\)
\(200\) 14.1421 0.0707107
\(201\) 481.825i 2.39714i
\(202\) 40.6823 0.201397
\(203\) 60.8234i 0.299623i
\(204\) 122.264i 0.599334i
\(205\) 42.0183i 0.204967i
\(206\) 233.721i 1.13457i
\(207\) −84.0802 + 303.502i −0.406185 + 1.46619i
\(208\) 76.0893 0.365814
\(209\) 238.180 1.13962
\(210\) −106.331 −0.506340
\(211\) 185.271 0.878061 0.439030 0.898472i \(-0.355322\pi\)
0.439030 + 0.898472i \(0.355322\pi\)
\(212\) 34.7883i 0.164096i
\(213\) −330.704 −1.55260
\(214\) 275.573i 1.28772i
\(215\) 22.4795 0.104556
\(216\) −63.2288 −0.292726
\(217\) 156.723i 0.722227i
\(218\) 88.0773i 0.404024i
\(219\) −582.959 −2.66191
\(220\) 46.7426 0.212467
\(221\) 244.112i 1.10458i
\(222\) 201.165i 0.906151i
\(223\) −6.88625 −0.0308800 −0.0154400 0.999881i \(-0.504915\pi\)
−0.0154400 + 0.999881i \(0.504915\pi\)
\(224\) 39.9294i 0.178256i
\(225\) −68.4637 −0.304283
\(226\) 67.0887i 0.296853i
\(227\) 168.723i 0.743274i 0.928378 + 0.371637i \(0.121203\pi\)
−0.928378 + 0.371637i \(0.878797\pi\)
\(228\) 217.110i 0.952238i
\(229\) 112.037i 0.489246i 0.969618 + 0.244623i \(0.0786642\pi\)
−0.969618 + 0.244623i \(0.921336\pi\)
\(230\) 70.0924 + 19.4180i 0.304750 + 0.0844259i
\(231\) −351.447 −1.52141
\(232\) 24.3724 0.105053
\(233\) −46.2974 −0.198701 −0.0993507 0.995052i \(-0.531677\pi\)
−0.0993507 + 0.995052i \(0.531677\pi\)
\(234\) −368.357 −1.57417
\(235\) 46.0806i 0.196088i
\(236\) −206.557 −0.875242
\(237\) 671.205i 2.83209i
\(238\) 128.103 0.538246
\(239\) 386.253 1.61612 0.808062 0.589098i \(-0.200517\pi\)
0.808062 + 0.589098i \(0.200517\pi\)
\(240\) 42.6077i 0.177532i
\(241\) 107.193i 0.444784i 0.974957 + 0.222392i \(0.0713866\pi\)
−0.974957 + 0.222392i \(0.928613\pi\)
\(242\) −16.6259 −0.0687019
\(243\) −280.954 −1.15619
\(244\) 149.233i 0.611609i
\(245\) 1.84167i 0.00751702i
\(246\) 126.594 0.514608
\(247\) 433.481i 1.75498i
\(248\) −62.8002 −0.253226
\(249\) 602.241i 2.41864i
\(250\) 15.8114i 0.0632456i
\(251\) 217.402i 0.866145i −0.901359 0.433073i \(-0.857429\pi\)
0.901359 0.433073i \(-0.142571\pi\)
\(252\) 193.303i 0.767074i
\(253\) 231.670 + 64.1803i 0.915690 + 0.253677i
\(254\) −274.994 −1.08265
\(255\) 136.695 0.536060
\(256\) 16.0000 0.0625000
\(257\) 277.660 1.08039 0.540195 0.841540i \(-0.318350\pi\)
0.540195 + 0.841540i \(0.318350\pi\)
\(258\) 67.7268i 0.262507i
\(259\) 210.772 0.813791
\(260\) 85.0704i 0.327194i
\(261\) −117.990 −0.452067
\(262\) 110.251 0.420807
\(263\) 146.744i 0.557962i −0.960297 0.278981i \(-0.910003\pi\)
0.960297 0.278981i \(-0.0899966\pi\)
\(264\) 140.827i 0.533437i
\(265\) 38.8945 0.146772
\(266\) −227.478 −0.855180
\(267\) 56.8801i 0.213034i
\(268\) 202.291i 0.754816i
\(269\) 450.903 1.67622 0.838110 0.545502i \(-0.183661\pi\)
0.838110 + 0.545502i \(0.183661\pi\)
\(270\) 70.6920i 0.261822i
\(271\) 482.964 1.78216 0.891078 0.453851i \(-0.149950\pi\)
0.891078 + 0.453851i \(0.149950\pi\)
\(272\) 51.3317i 0.188719i
\(273\) 639.624i 2.34294i
\(274\) 327.974i 1.19699i
\(275\) 52.2599i 0.190036i
\(276\) −58.5029 + 211.176i −0.211967 + 0.765130i
\(277\) 339.496 1.22562 0.612809 0.790231i \(-0.290040\pi\)
0.612809 + 0.790231i \(0.290040\pi\)
\(278\) −70.3069 −0.252903
\(279\) 304.023 1.08969
\(280\) −44.6424 −0.159437
\(281\) 306.804i 1.09183i −0.837841 0.545914i \(-0.816182\pi\)
0.837841 0.545914i \(-0.183818\pi\)
\(282\) −138.833 −0.492315
\(283\) 440.226i 1.55557i −0.628531 0.777784i \(-0.716344\pi\)
0.628531 0.777784i \(-0.283656\pi\)
\(284\) −138.844 −0.488886
\(285\) −242.737 −0.851707
\(286\) 281.175i 0.983130i
\(287\) 132.639i 0.462156i
\(288\) −77.4578 −0.268951
\(289\) 124.316 0.430160
\(290\) 27.2492i 0.0939626i
\(291\) 271.685i 0.933625i
\(292\) −244.751 −0.838189
\(293\) 105.316i 0.359439i −0.983718 0.179719i \(-0.942481\pi\)
0.983718 0.179719i \(-0.0575190\pi\)
\(294\) 5.54862 0.0188729
\(295\) 230.938i 0.782840i
\(296\) 84.4578i 0.285330i
\(297\) 233.651i 0.786705i
\(298\) 253.770i 0.851577i
\(299\) −116.807 + 421.633i −0.390657 + 1.41014i
\(300\) −47.6369 −0.158790
\(301\) −70.9610 −0.235751
\(302\) 47.2637 0.156502
\(303\) −137.036 −0.452263
\(304\) 91.1521i 0.299842i
\(305\) 166.847 0.547040
\(306\) 248.503i 0.812100i
\(307\) −364.046 −1.18582 −0.592909 0.805270i \(-0.702021\pi\)
−0.592909 + 0.805270i \(0.702021\pi\)
\(308\) −147.552 −0.479066
\(309\) 787.273i 2.54781i
\(310\) 70.2127i 0.226493i
\(311\) −444.626 −1.42967 −0.714833 0.699295i \(-0.753497\pi\)
−0.714833 + 0.699295i \(0.753497\pi\)
\(312\) −256.302 −0.821481
\(313\) 78.3010i 0.250163i 0.992146 + 0.125081i \(0.0399192\pi\)
−0.992146 + 0.125081i \(0.960081\pi\)
\(314\) 26.7899i 0.0853182i
\(315\) 216.119 0.686092
\(316\) 281.800i 0.891774i
\(317\) −100.802 −0.317986 −0.158993 0.987280i \(-0.550825\pi\)
−0.158993 + 0.987280i \(0.550825\pi\)
\(318\) 117.182i 0.368497i
\(319\) 90.0641i 0.282332i
\(320\) 17.8885i 0.0559017i
\(321\) 928.250i 2.89174i
\(322\) −221.260 61.2966i −0.687144 0.190362i
\(323\) 292.437 0.905377
\(324\) −33.4870 −0.103355
\(325\) −95.1116 −0.292651
\(326\) 455.643 1.39768
\(327\) 296.683i 0.907287i
\(328\) 53.1494 0.162041
\(329\) 145.463i 0.442135i
\(330\) −157.450 −0.477120
\(331\) −454.682 −1.37366 −0.686831 0.726817i \(-0.740999\pi\)
−0.686831 + 0.726817i \(0.740999\pi\)
\(332\) 252.847i 0.761586i
\(333\) 408.870i 1.22784i
\(334\) 69.8745 0.209205
\(335\) −226.168 −0.675128
\(336\) 134.500i 0.400297i
\(337\) 656.763i 1.94885i −0.224708 0.974426i \(-0.572143\pi\)
0.224708 0.974426i \(-0.427857\pi\)
\(338\) −272.729 −0.806891
\(339\) 225.984i 0.666620i
\(340\) 57.3905 0.168796
\(341\) 232.067i 0.680549i
\(342\) 441.278i 1.29029i
\(343\) 340.057i 0.991420i
\(344\) 28.4346i 0.0826587i
\(345\) −236.102 65.4082i −0.684353 0.189589i
\(346\) −309.062 −0.893244
\(347\) 605.936 1.74621 0.873107 0.487528i \(-0.162101\pi\)
0.873107 + 0.487528i \(0.162101\pi\)
\(348\) −82.0969 −0.235911
\(349\) −433.209 −1.24129 −0.620643 0.784093i \(-0.713129\pi\)
−0.620643 + 0.784093i \(0.713129\pi\)
\(350\) 49.9117i 0.142605i
\(351\) 425.239 1.21151
\(352\) 59.1253i 0.167970i
\(353\) 64.7160 0.183331 0.0916657 0.995790i \(-0.470781\pi\)
0.0916657 + 0.995790i \(0.470781\pi\)
\(354\) 695.774 1.96546
\(355\) 155.232i 0.437273i
\(356\) 23.8807i 0.0670805i
\(357\) −431.506 −1.20870
\(358\) 423.044 1.18169
\(359\) 258.799i 0.720889i 0.932781 + 0.360445i \(0.117375\pi\)
−0.932781 + 0.360445i \(0.882625\pi\)
\(360\) 86.6005i 0.240557i
\(361\) −158.294 −0.438488
\(362\) 60.8723i 0.168155i
\(363\) 56.0031 0.154279
\(364\) 268.541i 0.737751i
\(365\) 273.640i 0.749699i
\(366\) 502.681i 1.37344i
\(367\) 208.595i 0.568378i 0.958768 + 0.284189i \(0.0917243\pi\)
−0.958768 + 0.284189i \(0.908276\pi\)
\(368\) −24.5620 + 88.6606i −0.0667445 + 0.240926i
\(369\) −257.302 −0.697296
\(370\) 94.4267 0.255207
\(371\) −122.778 −0.330938
\(372\) 211.538 0.568652
\(373\) 429.843i 1.15240i 0.817310 + 0.576198i \(0.195464\pi\)
−0.817310 + 0.576198i \(0.804536\pi\)
\(374\) 189.687 0.507186
\(375\) 53.2597i 0.142026i
\(376\) −58.2879 −0.155021
\(377\) −163.914 −0.434786
\(378\) 223.153i 0.590352i
\(379\) 34.7433i 0.0916710i −0.998949 0.0458355i \(-0.985405\pi\)
0.998949 0.0458355i \(-0.0145950\pi\)
\(380\) −101.911 −0.268187
\(381\) 926.301 2.43124
\(382\) 441.255i 1.15512i
\(383\) 287.953i 0.751835i 0.926653 + 0.375918i \(0.122672\pi\)
−0.926653 + 0.375918i \(0.877328\pi\)
\(384\) −53.8950 −0.140352
\(385\) 164.968i 0.428490i
\(386\) −130.826 −0.338928
\(387\) 137.655i 0.355698i
\(388\) 114.065i 0.293982i
\(389\) 35.8847i 0.0922485i 0.998936 + 0.0461242i \(0.0146870\pi\)
−0.998936 + 0.0461242i \(0.985313\pi\)
\(390\) 286.554i 0.734755i
\(391\) 284.444 + 78.8005i 0.727477 + 0.201536i
\(392\) 2.32955 0.00594273
\(393\) −371.375 −0.944974
\(394\) −70.1667 −0.178088
\(395\) 315.063 0.797627
\(396\) 286.232i 0.722809i
\(397\) 366.185 0.922379 0.461190 0.887302i \(-0.347423\pi\)
0.461190 + 0.887302i \(0.347423\pi\)
\(398\) 239.811i 0.602541i
\(399\) 766.245 1.92041
\(400\) −20.0000 −0.0500000
\(401\) 204.806i 0.510738i 0.966844 + 0.255369i \(0.0821969\pi\)
−0.966844 + 0.255369i \(0.917803\pi\)
\(402\) 681.403i 1.69503i
\(403\) 422.357 1.04803
\(404\) −57.5334 −0.142410
\(405\) 37.4396i 0.0924435i
\(406\) 86.0173i 0.211865i
\(407\) 312.100 0.766829
\(408\) 172.908i 0.423793i
\(409\) −602.537 −1.47320 −0.736598 0.676331i \(-0.763569\pi\)
−0.736598 + 0.676331i \(0.763569\pi\)
\(410\) 59.4228i 0.144934i
\(411\) 1104.76i 2.68798i
\(412\) 330.531i 0.802259i
\(413\) 729.000i 1.76513i
\(414\) 118.907 429.216i 0.287216 1.03675i
\(415\) −282.691 −0.681183
\(416\) −107.606 −0.258669
\(417\) 236.824 0.567924
\(418\) −336.837 −0.805831
\(419\) 232.219i 0.554221i 0.960838 + 0.277111i \(0.0893769\pi\)
−0.960838 + 0.277111i \(0.910623\pi\)
\(420\) 150.375 0.358036
\(421\) 164.906i 0.391702i −0.980634 0.195851i \(-0.937253\pi\)
0.980634 0.195851i \(-0.0627468\pi\)
\(422\) −262.012 −0.620883
\(423\) 282.179 0.667089
\(424\) 49.1981i 0.116033i
\(425\) 64.1646i 0.150975i
\(426\) 467.686 1.09785
\(427\) −526.685 −1.23346
\(428\) 389.719i 0.910558i
\(429\) 947.121i 2.20774i
\(430\) −31.7908 −0.0739322
\(431\) 410.913i 0.953394i −0.879068 0.476697i \(-0.841834\pi\)
0.879068 0.476697i \(-0.158166\pi\)
\(432\) 89.4191 0.206989
\(433\) 653.473i 1.50918i 0.656199 + 0.754588i \(0.272163\pi\)
−0.656199 + 0.754588i \(0.727837\pi\)
\(434\) 221.640i 0.510692i
\(435\) 91.7871i 0.211005i
\(436\) 124.560i 0.285688i
\(437\) −505.100 139.930i −1.15584 0.320206i
\(438\) 824.429 1.88226
\(439\) −433.746 −0.988031 −0.494016 0.869453i \(-0.664471\pi\)
−0.494016 + 0.869453i \(0.664471\pi\)
\(440\) −66.1041 −0.150237
\(441\) −11.2776 −0.0255728
\(442\) 345.226i 0.781055i
\(443\) 127.713 0.288291 0.144146 0.989556i \(-0.453957\pi\)
0.144146 + 0.989556i \(0.453957\pi\)
\(444\) 284.491i 0.640745i
\(445\) 26.6994 0.0599987
\(446\) 9.73863 0.0218355
\(447\) 854.808i 1.91232i
\(448\) 56.4687i 0.126046i
\(449\) 647.900 1.44298 0.721492 0.692422i \(-0.243457\pi\)
0.721492 + 0.692422i \(0.243457\pi\)
\(450\) 96.8223 0.215161
\(451\) 196.404i 0.435487i
\(452\) 94.8778i 0.209907i
\(453\) −159.205 −0.351445
\(454\) 238.611i 0.525574i
\(455\) 300.238 0.659864
\(456\) 307.040i 0.673334i
\(457\) 504.529i 1.10400i −0.833844 0.552001i \(-0.813865\pi\)
0.833844 0.552001i \(-0.186135\pi\)
\(458\) 158.445i 0.345949i
\(459\) 286.877i 0.625004i
\(460\) −99.1256 27.4611i −0.215490 0.0596981i
\(461\) −106.745 −0.231551 −0.115776 0.993275i \(-0.536935\pi\)
−0.115776 + 0.993275i \(0.536935\pi\)
\(462\) 497.021 1.07580
\(463\) 90.1407 0.194688 0.0973442 0.995251i \(-0.468965\pi\)
0.0973442 + 0.995251i \(0.468965\pi\)
\(464\) −34.4678 −0.0742840
\(465\) 236.507i 0.508617i
\(466\) 65.4744 0.140503
\(467\) 715.930i 1.53304i −0.642219 0.766521i \(-0.721986\pi\)
0.642219 0.766521i \(-0.278014\pi\)
\(468\) 520.935 1.11311
\(469\) 713.943 1.52227
\(470\) 65.1679i 0.138655i
\(471\) 90.2402i 0.191593i
\(472\) 292.116 0.618889
\(473\) −105.075 −0.222146
\(474\) 949.227i 2.00259i
\(475\) 113.940i 0.239874i
\(476\) −181.164 −0.380598
\(477\) 238.174i 0.499316i
\(478\) −546.245 −1.14277
\(479\) 596.758i 1.24584i −0.782285 0.622921i \(-0.785946\pi\)
0.782285 0.622921i \(-0.214054\pi\)
\(480\) 60.2564i 0.125534i
\(481\) 568.013i 1.18090i
\(482\) 151.594i 0.314510i
\(483\) 745.301 + 206.474i 1.54307 + 0.427482i
\(484\) 23.5125 0.0485796
\(485\) 127.528 0.262945
\(486\) 397.329 0.817549
\(487\) −74.0657 −0.152086 −0.0760428 0.997105i \(-0.524229\pi\)
−0.0760428 + 0.997105i \(0.524229\pi\)
\(488\) 211.047i 0.432473i
\(489\) −1534.80 −3.13866
\(490\) 2.60451i 0.00531534i
\(491\) 299.500 0.609980 0.304990 0.952356i \(-0.401347\pi\)
0.304990 + 0.952356i \(0.401347\pi\)
\(492\) −179.030 −0.363883
\(493\) 110.581i 0.224301i
\(494\) 613.035i 1.24096i
\(495\) 320.017 0.646500
\(496\) 88.8128 0.179058
\(497\) 490.020i 0.985955i
\(498\) 851.698i 1.71024i
\(499\) −298.145 −0.597484 −0.298742 0.954334i \(-0.596567\pi\)
−0.298742 + 0.954334i \(0.596567\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) −235.368 −0.469796
\(502\) 307.453i 0.612457i
\(503\) 125.936i 0.250371i 0.992133 + 0.125185i \(0.0399525\pi\)
−0.992133 + 0.125185i \(0.960047\pi\)
\(504\) 273.371i 0.542404i
\(505\) 64.3244i 0.127375i
\(506\) −327.630 90.7647i −0.647491 0.179377i
\(507\) 918.671 1.81197
\(508\) 388.901 0.765552
\(509\) 143.424 0.281777 0.140888 0.990025i \(-0.455004\pi\)
0.140888 + 0.990025i \(0.455004\pi\)
\(510\) −193.316 −0.379052
\(511\) 863.798i 1.69041i
\(512\) −22.6274 −0.0441942
\(513\) 509.421i 0.993023i
\(514\) −392.671 −0.763951
\(515\) −369.545 −0.717563
\(516\) 95.7801i 0.185620i
\(517\) 215.393i 0.416621i
\(518\) −298.076 −0.575437
\(519\) 1041.06 2.00589
\(520\) 120.308i 0.231361i
\(521\) 149.956i 0.287824i −0.989591 0.143912i \(-0.954032\pi\)
0.989591 0.143912i \(-0.0459682\pi\)
\(522\) 166.862 0.319660
\(523\) 308.927i 0.590683i 0.955392 + 0.295342i \(0.0954335\pi\)
−0.955392 + 0.295342i \(0.904567\pi\)
\(524\) −155.919 −0.297555
\(525\) 168.125i 0.320237i
\(526\) 207.527i 0.394538i
\(527\) 284.932i 0.540668i
\(528\) 199.160i 0.377197i
\(529\) −453.589 272.210i −0.857445 0.514575i
\(530\) −55.0051 −0.103783
\(531\) −1414.17 −2.66321
\(532\) 321.702 0.604704
\(533\) −357.451 −0.670640
\(534\) 80.4405i 0.150638i
\(535\) −435.719 −0.814428
\(536\) 286.082i 0.533735i
\(537\) −1425.00 −2.65363
\(538\) −637.673 −1.18527
\(539\) 8.60845i 0.0159712i
\(540\) 99.9735i 0.185136i
\(541\) −365.240 −0.675120 −0.337560 0.941304i \(-0.609602\pi\)
−0.337560 + 0.941304i \(0.609602\pi\)
\(542\) −683.014 −1.26017
\(543\) 205.044i 0.377614i
\(544\) 72.5939i 0.133445i
\(545\) 139.262 0.255528
\(546\) 904.565i 1.65671i
\(547\) 788.355 1.44123 0.720617 0.693334i \(-0.243859\pi\)
0.720617 + 0.693334i \(0.243859\pi\)
\(548\) 463.825i 0.846397i
\(549\) 1021.70i 1.86102i
\(550\) 73.9066i 0.134376i
\(551\) 196.363i 0.356376i
\(552\) 82.7355 298.648i 0.149883 0.541029i
\(553\) −994.556 −1.79847
\(554\) −480.120 −0.866642
\(555\) −318.070 −0.573100
\(556\) 99.4290 0.178829
\(557\) 316.183i 0.567654i 0.958876 + 0.283827i \(0.0916041\pi\)
−0.958876 + 0.283827i \(0.908396\pi\)
\(558\) −429.953 −0.770525
\(559\) 191.234i 0.342100i
\(560\) 63.1339 0.112739
\(561\) −638.950 −1.13895
\(562\) 433.886i 0.772039i
\(563\) 849.606i 1.50907i 0.656260 + 0.754535i \(0.272137\pi\)
−0.656260 + 0.754535i \(0.727863\pi\)
\(564\) 196.339 0.348119
\(565\) −106.077 −0.187746
\(566\) 622.573i 1.09995i
\(567\) 118.185i 0.208440i
\(568\) 196.355 0.345695
\(569\) 251.184i 0.441448i 0.975336 + 0.220724i \(0.0708420\pi\)
−0.975336 + 0.220724i \(0.929158\pi\)
\(570\) 343.281 0.602248
\(571\) 731.800i 1.28161i −0.767704 0.640805i \(-0.778601\pi\)
0.767704 0.640805i \(-0.221399\pi\)
\(572\) 397.642i 0.695178i
\(573\) 1486.34i 2.59396i
\(574\) 187.580i 0.326794i
\(575\) 30.7025 110.826i 0.0533956 0.192741i
\(576\) 109.542 0.190177
\(577\) −232.889 −0.403620 −0.201810 0.979425i \(-0.564682\pi\)
−0.201810 + 0.979425i \(0.564682\pi\)
\(578\) −175.810 −0.304169
\(579\) 440.680 0.761105
\(580\) 38.5361i 0.0664416i
\(581\) 892.369 1.53592
\(582\) 384.221i 0.660173i
\(583\) −181.803 −0.311841
\(584\) 346.130 0.592689
\(585\) 582.423i 0.995596i
\(586\) 148.939i 0.254162i
\(587\) −257.843 −0.439255 −0.219628 0.975584i \(-0.570484\pi\)
−0.219628 + 0.975584i \(0.570484\pi\)
\(588\) −7.84694 −0.0133451
\(589\) 505.967i 0.859028i
\(590\) 326.595i 0.553551i
\(591\) 236.352 0.399919
\(592\) 119.441i 0.201759i
\(593\) 86.9783 0.146675 0.0733375 0.997307i \(-0.476635\pi\)
0.0733375 + 0.997307i \(0.476635\pi\)
\(594\) 330.433i 0.556284i
\(595\) 202.548i 0.340417i
\(596\) 358.885i 0.602156i
\(597\) 807.790i 1.35308i
\(598\) 165.189 596.279i 0.276236 0.997122i
\(599\) −382.075 −0.637854 −0.318927 0.947779i \(-0.603323\pi\)
−0.318927 + 0.947779i \(0.603323\pi\)
\(600\) 67.3687 0.112281
\(601\) −109.548 −0.182277 −0.0911384 0.995838i \(-0.529051\pi\)
−0.0911384 + 0.995838i \(0.529051\pi\)
\(602\) 100.354 0.166701
\(603\) 1384.96i 2.29678i
\(604\) −66.8409 −0.110664
\(605\) 26.2878i 0.0434509i
\(606\) 193.798 0.319798
\(607\) −936.232 −1.54239 −0.771196 0.636597i \(-0.780341\pi\)
−0.771196 + 0.636597i \(0.780341\pi\)
\(608\) 128.909i 0.212021i
\(609\) 289.744i 0.475770i
\(610\) −235.957 −0.386815
\(611\) 392.010 0.641587
\(612\) 351.436i 0.574241i
\(613\) 85.4745i 0.139436i −0.997567 0.0697182i \(-0.977790\pi\)
0.997567 0.0697182i \(-0.0222100\pi\)
\(614\) 514.839 0.838500
\(615\) 200.162i 0.325467i
\(616\) 208.670 0.338751
\(617\) 476.428i 0.772169i −0.922463 0.386085i \(-0.873827\pi\)
0.922463 0.386085i \(-0.126173\pi\)
\(618\) 1113.37i 1.80157i
\(619\) 207.565i 0.335323i −0.985845 0.167662i \(-0.946378\pi\)
0.985845 0.167662i \(-0.0536216\pi\)
\(620\) 99.2958i 0.160154i
\(621\) −137.269 + 495.497i −0.221046 + 0.797902i
\(622\) 628.796 1.01093
\(623\) −84.2819 −0.135284
\(624\) 362.466 0.580875
\(625\) 25.0000 0.0400000
\(626\) 110.734i 0.176892i
\(627\) 1134.61 1.80959
\(628\) 37.8867i 0.0603291i
\(629\) 383.195 0.609214
\(630\) −305.638 −0.485140
\(631\) 406.573i 0.644331i 0.946683 + 0.322166i \(0.104411\pi\)
−0.946683 + 0.322166i \(0.895589\pi\)
\(632\) 398.526i 0.630579i
\(633\) 882.573 1.39427
\(634\) 142.555 0.224850
\(635\) 434.804i 0.684731i
\(636\) 165.721i 0.260567i
\(637\) −15.6672 −0.0245952
\(638\) 127.370i 0.199639i
\(639\) −950.575 −1.48760
\(640\) 25.2982i 0.0395285i
\(641\) 356.666i 0.556421i −0.960520 0.278210i \(-0.910259\pi\)
0.960520 0.278210i \(-0.0897412\pi\)
\(642\) 1312.74i 2.04477i
\(643\) 311.622i 0.484637i −0.970197 0.242318i \(-0.922092\pi\)
0.970197 0.242318i \(-0.0779079\pi\)
\(644\) 312.909 + 86.6865i 0.485884 + 0.134606i
\(645\) 107.085 0.166024
\(646\) −413.568 −0.640198
\(647\) −512.625 −0.792310 −0.396155 0.918184i \(-0.629656\pi\)
−0.396155 + 0.918184i \(0.629656\pi\)
\(648\) 47.3578 0.0730830
\(649\) 1079.46i 1.66327i
\(650\) 134.508 0.206936
\(651\) 746.581i 1.14682i
\(652\) −644.376 −0.988307
\(653\) 1018.05 1.55903 0.779515 0.626384i \(-0.215466\pi\)
0.779515 + 0.626384i \(0.215466\pi\)
\(654\) 419.573i 0.641549i
\(655\) 174.323i 0.266141i
\(656\) −75.1646 −0.114580
\(657\) −1675.66 −2.55047
\(658\) 205.715i 0.312637i
\(659\) 396.548i 0.601742i 0.953665 + 0.300871i \(0.0972773\pi\)
−0.953665 + 0.300871i \(0.902723\pi\)
\(660\) 222.667 0.337375
\(661\) 71.0934i 0.107554i −0.998553 0.0537772i \(-0.982874\pi\)
0.998553 0.0537772i \(-0.0171261\pi\)
\(662\) 643.017 0.971325
\(663\) 1162.87i 1.75396i
\(664\) 357.579i 0.538523i
\(665\) 359.674i 0.540864i
\(666\) 578.230i 0.868212i
\(667\) 52.9123 190.996i 0.0793288 0.286351i
\(668\) −98.8174 −0.147930
\(669\) −32.8040 −0.0490343
\(670\) 319.850 0.477387
\(671\) −779.888 −1.16228
\(672\) 190.211i 0.283052i
\(673\) −889.230 −1.32129 −0.660646 0.750697i \(-0.729718\pi\)
−0.660646 + 0.750697i \(0.729718\pi\)
\(674\) 928.804i 1.37805i
\(675\) −111.774 −0.165591
\(676\) 385.697 0.570558
\(677\) 1106.29i 1.63411i −0.576561 0.817054i \(-0.695606\pi\)
0.576561 0.817054i \(-0.304394\pi\)
\(678\) 319.590i 0.471372i
\(679\) −402.569 −0.592884
\(680\) −81.1625 −0.119357
\(681\) 803.746i 1.18024i
\(682\) 328.193i 0.481221i
\(683\) 769.950 1.12731 0.563653 0.826012i \(-0.309396\pi\)
0.563653 + 0.826012i \(0.309396\pi\)
\(684\) 624.061i 0.912370i
\(685\) 518.573 0.757040
\(686\) 480.913i 0.701040i
\(687\) 533.711i 0.776872i
\(688\) 40.2126i 0.0584485i
\(689\) 330.877i 0.480228i
\(690\) 333.898 + 92.5011i 0.483911 + 0.134060i
\(691\) −314.516 −0.455160 −0.227580 0.973759i \(-0.573081\pi\)
−0.227580 + 0.973759i \(0.573081\pi\)
\(692\) 437.080 0.631619
\(693\) −1010.20 −1.45772
\(694\) −856.923 −1.23476
\(695\) 111.165i 0.159950i
\(696\) 116.103 0.166814
\(697\) 241.145i 0.345976i
\(698\) 612.650 0.877722
\(699\) −220.547 −0.315517
\(700\) 70.5858i 0.100837i
\(701\) 853.482i 1.21752i −0.793354 0.608760i \(-0.791667\pi\)
0.793354 0.608760i \(-0.208333\pi\)
\(702\) −601.379 −0.856666
\(703\) −680.458 −0.967935
\(704\) 83.6158i 0.118772i
\(705\) 219.514i 0.311367i
\(706\) −91.5222 −0.129635
\(707\) 203.052i 0.287203i
\(708\) −983.974 −1.38979
\(709\) 1121.84i 1.58229i −0.611631 0.791143i \(-0.709486\pi\)
0.611631 0.791143i \(-0.290514\pi\)
\(710\) 219.531i 0.309199i
\(711\) 1929.31i 2.71352i
\(712\) 33.7724i 0.0474331i
\(713\) −136.339 + 492.138i −0.191218 + 0.690235i
\(714\) 610.241 0.854680
\(715\) 444.577 0.621786
\(716\) −598.275 −0.835579
\(717\) 1839.99 2.56624
\(718\) 365.997i 0.509746i
\(719\) −1026.36 −1.42748 −0.713739 0.700411i \(-0.753000\pi\)
−0.713739 + 0.700411i \(0.753000\pi\)
\(720\) 122.472i 0.170099i
\(721\) 1166.54 1.61795
\(722\) 223.862 0.310058
\(723\) 510.635i 0.706272i
\(724\) 86.0864i 0.118904i
\(725\) 43.0847 0.0594272
\(726\) −79.2004 −0.109091
\(727\) 86.2743i 0.118672i −0.998238 0.0593358i \(-0.981102\pi\)
0.998238 0.0593358i \(-0.0188983\pi\)
\(728\) 379.775i 0.521669i
\(729\) −1187.68 −1.62920
\(730\) 386.985i 0.530117i
\(731\) −129.011 −0.176486
\(732\) 710.898i 0.971172i
\(733\) 224.013i 0.305611i −0.988256 0.152806i \(-0.951169\pi\)
0.988256 0.152806i \(-0.0488308\pi\)
\(734\) 294.998i 0.401904i
\(735\) 8.77315i 0.0119363i
\(736\) 34.7359 125.385i 0.0471955 0.170360i
\(737\) 1057.17 1.43442
\(738\) 363.880 0.493063
\(739\) 865.320 1.17093 0.585467 0.810696i \(-0.300911\pi\)
0.585467 + 0.810696i \(0.300911\pi\)
\(740\) −133.540 −0.180459
\(741\) 2064.97i 2.78673i
\(742\) 173.634 0.234009
\(743\) 1204.15i 1.62066i −0.585975 0.810329i \(-0.699288\pi\)
0.585975 0.810329i \(-0.300712\pi\)
\(744\) −299.160 −0.402097
\(745\) −401.245 −0.538584
\(746\) 607.890i 0.814867i
\(747\) 1731.08i 2.31738i
\(748\) −268.259 −0.358635
\(749\) 1375.43 1.83636
\(750\) 75.3206i 0.100427i
\(751\) 1410.90i 1.87870i 0.342967 + 0.939348i \(0.388568\pi\)
−0.342967 + 0.939348i \(0.611432\pi\)
\(752\) 82.4316 0.109616
\(753\) 1035.64i 1.37535i
\(754\) 231.810 0.307440
\(755\) 74.7304i 0.0989807i
\(756\) 315.586i 0.417442i
\(757\) 1113.96i 1.47155i 0.677226 + 0.735775i \(0.263182\pi\)
−0.677226 + 0.735775i \(0.736818\pi\)
\(758\) 49.1345i 0.0648212i
\(759\) 1103.60 + 305.735i 1.45402 + 0.402813i
\(760\) 144.124 0.189637
\(761\) 308.718 0.405674 0.202837 0.979212i \(-0.434984\pi\)
0.202837 + 0.979212i \(0.434984\pi\)
\(762\) −1309.99 −1.71914
\(763\) −439.609 −0.576159
\(764\) 624.029i 0.816792i
\(765\) 392.917 0.513617
\(766\) 407.227i 0.531628i
\(767\) −1964.60 −2.56140
\(768\) 76.2190 0.0992435
\(769\) 630.246i 0.819566i −0.912183 0.409783i \(-0.865604\pi\)
0.912183 0.409783i \(-0.134396\pi\)
\(770\) 233.301i 0.302988i
\(771\) 1322.69 1.71555
\(772\) 185.016 0.239658
\(773\) 408.103i 0.527947i −0.964530 0.263974i \(-0.914967\pi\)
0.964530 0.263974i \(-0.0850332\pi\)
\(774\) 194.674i 0.251516i
\(775\) −111.016 −0.143247
\(776\) 161.312i 0.207877i
\(777\) 1004.05 1.29222
\(778\) 50.7486i 0.0652295i
\(779\) 428.213i 0.549696i
\(780\) 405.249i 0.519550i
\(781\) 725.595i 0.929059i
\(782\) −402.264 111.441i −0.514404 0.142507i
\(783\) −192.630 −0.246015
\(784\) −3.29448 −0.00420214
\(785\) −42.3586 −0.0539600
\(786\) 525.203 0.668197
\(787\) 220.127i 0.279703i 0.990172 + 0.139852i \(0.0446626\pi\)
−0.990