Properties

Label 230.3.d.a.91.10
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 91.10
Root \(-6.02373i\) of defining polynomial
Character \(\chi\) \(=\) 230.91
Dual form 230.3.d.a.91.9

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421 q^{2} -3.79379 q^{3} +2.00000 q^{4} +2.23607i q^{5} -5.36524 q^{6} -7.10180i q^{7} +2.82843 q^{8} +5.39287 q^{9} +O(q^{10})\) \(q+1.41421 q^{2} -3.79379 q^{3} +2.00000 q^{4} +2.23607i q^{5} -5.36524 q^{6} -7.10180i q^{7} +2.82843 q^{8} +5.39287 q^{9} +3.16228i q^{10} -11.2644i q^{11} -7.58759 q^{12} +20.0597 q^{13} -10.0435i q^{14} -8.48318i q^{15} +4.00000 q^{16} -1.63128i q^{17} +7.62667 q^{18} -29.4164i q^{19} +4.47214i q^{20} +26.9428i q^{21} -15.9302i q^{22} +(20.0280 - 11.3084i) q^{23} -10.7305 q^{24} -5.00000 q^{25} +28.3688 q^{26} +13.6847 q^{27} -14.2036i q^{28} -50.3233 q^{29} -11.9970i q^{30} +11.1316 q^{31} +5.65685 q^{32} +42.7347i q^{33} -2.30698i q^{34} +15.8801 q^{35} +10.7857 q^{36} -40.5429i q^{37} -41.6011i q^{38} -76.1025 q^{39} +6.32456i q^{40} -7.24039 q^{41} +38.1028i q^{42} +71.7020i q^{43} -22.5287i q^{44} +12.0588i q^{45} +(28.3239 - 15.9924i) q^{46} -6.40666 q^{47} -15.1752 q^{48} -1.43550 q^{49} -7.07107 q^{50} +6.18873i q^{51} +40.1195 q^{52} +20.4148i q^{53} +19.3531 q^{54} +25.1879 q^{55} -20.0869i q^{56} +111.600i q^{57} -71.1679 q^{58} -65.8889 q^{59} -16.9664i q^{60} +37.7281i q^{61} +15.7425 q^{62} -38.2991i q^{63} +8.00000 q^{64} +44.8549i q^{65} +60.4360i q^{66} +124.242i q^{67} -3.26256i q^{68} +(-75.9821 + 42.9016i) q^{69} +22.4578 q^{70} +43.5656 q^{71} +15.2533 q^{72} +48.1194 q^{73} -57.3363i q^{74} +18.9690 q^{75} -58.8328i q^{76} -79.9972 q^{77} -107.625 q^{78} -101.026i q^{79} +8.94427i q^{80} -100.453 q^{81} -10.2395 q^{82} -102.409i q^{83} +53.8855i q^{84} +3.64765 q^{85} +101.402i q^{86} +190.916 q^{87} -31.8604i q^{88} +9.63875i q^{89} +17.0538i q^{90} -142.460i q^{91} +(40.0560 - 22.6167i) q^{92} -42.2310 q^{93} -9.06039 q^{94} +65.7771 q^{95} -21.4609 q^{96} -143.631i q^{97} -2.03010 q^{98} -60.7473i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9}+O(q^{10}) \) 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
\(3\) −3.79379 −1.26460 −0.632299 0.774724i \(-0.717889\pi\)
−0.632299 + 0.774724i \(0.717889\pi\)
\(4\) 2.00000 0.500000
\(5\) 2.23607i 0.447214i
\(6\) −5.36524 −0.894206
\(7\) 7.10180i 1.01454i −0.861787 0.507271i \(-0.830654\pi\)
0.861787 0.507271i \(-0.169346\pi\)
\(8\) 2.82843 0.353553
\(9\) 5.39287 0.599208
\(10\) 3.16228i 0.316228i
\(11\) 11.2644i 1.02403i −0.858975 0.512017i \(-0.828899\pi\)
0.858975 0.512017i \(-0.171101\pi\)
\(12\) −7.58759 −0.632299
\(13\) 20.0597 1.54306 0.771528 0.636195i \(-0.219493\pi\)
0.771528 + 0.636195i \(0.219493\pi\)
\(14\) 10.0435i 0.717390i
\(15\) 8.48318i 0.565545i
\(16\) 4.00000 0.250000
\(17\) 1.63128i 0.0959575i −0.998848 0.0479788i \(-0.984722\pi\)
0.998848 0.0479788i \(-0.0152780\pi\)
\(18\) 7.62667 0.423704
\(19\) 29.4164i 1.54823i −0.633044 0.774116i \(-0.718195\pi\)
0.633044 0.774116i \(-0.281805\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 26.9428i 1.28299i
\(22\) 15.9302i 0.724101i
\(23\) 20.0280 11.3084i 0.870783 0.491668i
\(24\) −10.7305 −0.447103
\(25\) −5.00000 −0.200000
\(26\) 28.3688 1.09111
\(27\) 13.6847 0.506841
\(28\) 14.2036i 0.507271i
\(29\) −50.3233 −1.73529 −0.867644 0.497187i \(-0.834366\pi\)
−0.867644 + 0.497187i \(0.834366\pi\)
\(30\) 11.9970i 0.399901i
\(31\) 11.1316 0.359084 0.179542 0.983750i \(-0.442538\pi\)
0.179542 + 0.983750i \(0.442538\pi\)
\(32\) 5.65685 0.176777
\(33\) 42.7347i 1.29499i
\(34\) 2.30698i 0.0678522i
\(35\) 15.8801 0.453717
\(36\) 10.7857 0.299604
\(37\) 40.5429i 1.09575i −0.836559 0.547877i \(-0.815436\pi\)
0.836559 0.547877i \(-0.184564\pi\)
\(38\) 41.6011i 1.09477i
\(39\) −76.1025 −1.95135
\(40\) 6.32456i 0.158114i
\(41\) −7.24039 −0.176595 −0.0882975 0.996094i \(-0.528143\pi\)
−0.0882975 + 0.996094i \(0.528143\pi\)
\(42\) 38.1028i 0.907210i
\(43\) 71.7020i 1.66749i 0.552150 + 0.833745i \(0.313808\pi\)
−0.552150 + 0.833745i \(0.686192\pi\)
\(44\) 22.5287i 0.512017i
\(45\) 12.0588i 0.267974i
\(46\) 28.3239 15.9924i 0.615736 0.347662i
\(47\) −6.40666 −0.136312 −0.0681560 0.997675i \(-0.521712\pi\)
−0.0681560 + 0.997675i \(0.521712\pi\)
\(48\) −15.1752 −0.316150
\(49\) −1.43550 −0.0292959
\(50\) −7.07107 −0.141421
\(51\) 6.18873i 0.121348i
\(52\) 40.1195 0.771528
\(53\) 20.4148i 0.385184i 0.981279 + 0.192592i \(0.0616894\pi\)
−0.981279 + 0.192592i \(0.938311\pi\)
\(54\) 19.3531 0.358390
\(55\) 25.1879 0.457962
\(56\) 20.0869i 0.358695i
\(57\) 111.600i 1.95789i
\(58\) −71.1679 −1.22703
\(59\) −65.8889 −1.11676 −0.558381 0.829585i \(-0.688577\pi\)
−0.558381 + 0.829585i \(0.688577\pi\)
\(60\) 16.9664i 0.282773i
\(61\) 37.7281i 0.618493i 0.950982 + 0.309247i \(0.100077\pi\)
−0.950982 + 0.309247i \(0.899923\pi\)
\(62\) 15.7425 0.253911
\(63\) 38.2991i 0.607922i
\(64\) 8.00000 0.125000
\(65\) 44.8549i 0.690076i
\(66\) 60.4360i 0.915697i
\(67\) 124.242i 1.85437i 0.374609 + 0.927183i \(0.377777\pi\)
−0.374609 + 0.927183i \(0.622223\pi\)
\(68\) 3.26256i 0.0479788i
\(69\) −75.9821 + 42.9016i −1.10119 + 0.621763i
\(70\) 22.4578 0.320826
\(71\) 43.5656 0.613600 0.306800 0.951774i \(-0.400742\pi\)
0.306800 + 0.951774i \(0.400742\pi\)
\(72\) 15.2533 0.211852
\(73\) 48.1194 0.659169 0.329585 0.944126i \(-0.393091\pi\)
0.329585 + 0.944126i \(0.393091\pi\)
\(74\) 57.3363i 0.774815i
\(75\) 18.9690 0.252920
\(76\) 58.8328i 0.774116i
\(77\) −79.9972 −1.03893
\(78\) −107.625 −1.37981
\(79\) 101.026i 1.27882i −0.768868 0.639408i \(-0.779179\pi\)
0.768868 0.639408i \(-0.220821\pi\)
\(80\) 8.94427i 0.111803i
\(81\) −100.453 −1.24016
\(82\) −10.2395 −0.124871
\(83\) 102.409i 1.23384i −0.787025 0.616921i \(-0.788380\pi\)
0.787025 0.616921i \(-0.211620\pi\)
\(84\) 53.8855i 0.641494i
\(85\) 3.64765 0.0429135
\(86\) 101.402i 1.17909i
\(87\) 190.916 2.19444
\(88\) 31.8604i 0.362050i
\(89\) 9.63875i 0.108301i 0.998533 + 0.0541503i \(0.0172450\pi\)
−0.998533 + 0.0541503i \(0.982755\pi\)
\(90\) 17.0538i 0.189486i
\(91\) 142.460i 1.56550i
\(92\) 40.0560 22.6167i 0.435391 0.245834i
\(93\) −42.2310 −0.454097
\(94\) −9.06039 −0.0963871
\(95\) 65.7771 0.692390
\(96\) −21.4609 −0.223551
\(97\) 143.631i 1.48074i −0.672202 0.740368i \(-0.734651\pi\)
0.672202 0.740368i \(-0.265349\pi\)
\(98\) −2.03010 −0.0207154
\(99\) 60.7473i 0.613609i
\(100\) −10.0000 −0.100000
\(101\) 103.099 1.02078 0.510391 0.859943i \(-0.329501\pi\)
0.510391 + 0.859943i \(0.329501\pi\)
\(102\) 8.75219i 0.0858058i
\(103\) 98.8637i 0.959841i −0.877312 0.479921i \(-0.840665\pi\)
0.877312 0.479921i \(-0.159335\pi\)
\(104\) 56.7375 0.545553
\(105\) −60.2458 −0.573770
\(106\) 28.8708i 0.272366i
\(107\) 22.5494i 0.210742i −0.994433 0.105371i \(-0.966397\pi\)
0.994433 0.105371i \(-0.0336029\pi\)
\(108\) 27.3694 0.253420
\(109\) 30.2389i 0.277421i 0.990333 + 0.138711i \(0.0442958\pi\)
−0.990333 + 0.138711i \(0.955704\pi\)
\(110\) 35.6211 0.323828
\(111\) 153.811i 1.38569i
\(112\) 28.4072i 0.253636i
\(113\) 213.437i 1.88882i 0.328771 + 0.944410i \(0.393365\pi\)
−0.328771 + 0.944410i \(0.606635\pi\)
\(114\) 157.826i 1.38444i
\(115\) 25.2863 + 44.7840i 0.219881 + 0.389426i
\(116\) −100.647 −0.867644
\(117\) 108.180 0.924612
\(118\) −93.1810 −0.789670
\(119\) −11.5850 −0.0973530
\(120\) 23.9941i 0.199951i
\(121\) −5.88598 −0.0486445
\(122\) 53.3556i 0.437341i
\(123\) 27.4686 0.223322
\(124\) 22.2632 0.179542
\(125\) 11.1803i 0.0894427i
\(126\) 54.1631i 0.429866i
\(127\) −29.9509 −0.235834 −0.117917 0.993023i \(-0.537622\pi\)
−0.117917 + 0.993023i \(0.537622\pi\)
\(128\) 11.3137 0.0883883
\(129\) 272.023i 2.10870i
\(130\) 63.4345i 0.487957i
\(131\) −116.486 −0.889208 −0.444604 0.895727i \(-0.646656\pi\)
−0.444604 + 0.895727i \(0.646656\pi\)
\(132\) 85.4694i 0.647495i
\(133\) −208.909 −1.57075
\(134\) 175.705i 1.31123i
\(135\) 30.5999i 0.226666i
\(136\) 4.61395i 0.0339261i
\(137\) 94.8211i 0.692125i 0.938212 + 0.346062i \(0.112481\pi\)
−0.938212 + 0.346062i \(0.887519\pi\)
\(138\) −107.455 + 60.6720i −0.778659 + 0.439653i
\(139\) 89.2774 0.642284 0.321142 0.947031i \(-0.395933\pi\)
0.321142 + 0.947031i \(0.395933\pi\)
\(140\) 31.7602 0.226859
\(141\) 24.3056 0.172380
\(142\) 61.6111 0.433881
\(143\) 225.960i 1.58014i
\(144\) 21.5715 0.149802
\(145\) 112.526i 0.776044i
\(146\) 68.0510 0.466103
\(147\) 5.44599 0.0370476
\(148\) 81.0857i 0.547877i
\(149\) 182.441i 1.22443i 0.790690 + 0.612217i \(0.209722\pi\)
−0.790690 + 0.612217i \(0.790278\pi\)
\(150\) 26.8262 0.178841
\(151\) 29.7608 0.197092 0.0985458 0.995133i \(-0.468581\pi\)
0.0985458 + 0.995133i \(0.468581\pi\)
\(152\) 83.2022i 0.547383i
\(153\) 8.79728i 0.0574985i
\(154\) −113.133 −0.734631
\(155\) 24.8910i 0.160587i
\(156\) −152.205 −0.975673
\(157\) 64.1093i 0.408340i 0.978935 + 0.204170i \(0.0654495\pi\)
−0.978935 + 0.204170i \(0.934551\pi\)
\(158\) 142.873i 0.904260i
\(159\) 77.4494i 0.487103i
\(160\) 12.6491i 0.0790569i
\(161\) −80.3097 142.235i −0.498818 0.883446i
\(162\) −142.062 −0.876924
\(163\) −75.3328 −0.462164 −0.231082 0.972934i \(-0.574227\pi\)
−0.231082 + 0.972934i \(0.574227\pi\)
\(164\) −14.4808 −0.0882975
\(165\) −95.5577 −0.579137
\(166\) 144.828i 0.872458i
\(167\) 272.459 1.63149 0.815745 0.578412i \(-0.196327\pi\)
0.815745 + 0.578412i \(0.196327\pi\)
\(168\) 76.2056i 0.453605i
\(169\) 233.393 1.38102
\(170\) 5.15855 0.0303444
\(171\) 158.639i 0.927713i
\(172\) 143.404i 0.833745i
\(173\) 261.815 1.51338 0.756691 0.653773i \(-0.226815\pi\)
0.756691 + 0.653773i \(0.226815\pi\)
\(174\) 269.996 1.55170
\(175\) 35.5090i 0.202908i
\(176\) 45.0575i 0.256008i
\(177\) 249.969 1.41225
\(178\) 13.6312i 0.0765800i
\(179\) −184.406 −1.03020 −0.515101 0.857130i \(-0.672246\pi\)
−0.515101 + 0.857130i \(0.672246\pi\)
\(180\) 24.1177i 0.133987i
\(181\) 191.867i 1.06004i 0.847986 + 0.530019i \(0.177815\pi\)
−0.847986 + 0.530019i \(0.822185\pi\)
\(182\) 201.469i 1.10697i
\(183\) 143.133i 0.782145i
\(184\) 56.6477 31.9849i 0.307868 0.173831i
\(185\) 90.6566 0.490036
\(186\) −59.7237 −0.321095
\(187\) −18.3753 −0.0982637
\(188\) −12.8133 −0.0681560
\(189\) 97.1859i 0.514211i
\(190\) 93.0228 0.489594
\(191\) 32.6185i 0.170778i −0.996348 0.0853888i \(-0.972787\pi\)
0.996348 0.0853888i \(-0.0272132\pi\)
\(192\) −30.3504 −0.158075
\(193\) 316.748 1.64118 0.820592 0.571515i \(-0.193644\pi\)
0.820592 + 0.571515i \(0.193644\pi\)
\(194\) 203.125i 1.04704i
\(195\) 170.170i 0.872669i
\(196\) −2.87100 −0.0146480
\(197\) −194.946 −0.989573 −0.494787 0.869015i \(-0.664754\pi\)
−0.494787 + 0.869015i \(0.664754\pi\)
\(198\) 85.9097i 0.433887i
\(199\) 74.0815i 0.372269i −0.982524 0.186134i \(-0.940404\pi\)
0.982524 0.186134i \(-0.0595960\pi\)
\(200\) −14.1421 −0.0707107
\(201\) 471.350i 2.34503i
\(202\) 145.804 0.721802
\(203\) 357.386i 1.76052i
\(204\) 12.3775i 0.0606739i
\(205\) 16.1900i 0.0789757i
\(206\) 139.814i 0.678710i
\(207\) 108.008 60.9846i 0.521780 0.294612i
\(208\) 80.2390 0.385764
\(209\) −331.357 −1.58544
\(210\) −85.2005 −0.405716
\(211\) −4.75017 −0.0225126 −0.0112563 0.999937i \(-0.503583\pi\)
−0.0112563 + 0.999937i \(0.503583\pi\)
\(212\) 40.8295i 0.192592i
\(213\) −165.279 −0.775958
\(214\) 31.8896i 0.149017i
\(215\) −160.331 −0.745724
\(216\) 38.7062 0.179195
\(217\) 79.0544i 0.364306i
\(218\) 42.7643i 0.196167i
\(219\) −182.555 −0.833584
\(220\) 50.3758 0.228981
\(221\) 32.7230i 0.148068i
\(222\) 217.522i 0.979829i
\(223\) 211.977 0.950571 0.475286 0.879832i \(-0.342345\pi\)
0.475286 + 0.879832i \(0.342345\pi\)
\(224\) 40.1738i 0.179347i
\(225\) −26.9644 −0.119842
\(226\) 301.845i 1.33560i
\(227\) 389.941i 1.71780i 0.512141 + 0.858901i \(0.328852\pi\)
−0.512141 + 0.858901i \(0.671148\pi\)
\(228\) 223.200i 0.978945i
\(229\) 156.000i 0.681224i −0.940204 0.340612i \(-0.889366\pi\)
0.940204 0.340612i \(-0.110634\pi\)
\(230\) 35.7602 + 63.3341i 0.155479 + 0.275366i
\(231\) 303.493 1.31382
\(232\) −142.336 −0.613517
\(233\) −46.4968 −0.199557 −0.0997785 0.995010i \(-0.531813\pi\)
−0.0997785 + 0.995010i \(0.531813\pi\)
\(234\) 152.989 0.653800
\(235\) 14.3257i 0.0609606i
\(236\) −131.778 −0.558381
\(237\) 383.274i 1.61719i
\(238\) −16.3837 −0.0688389
\(239\) −454.735 −1.90266 −0.951328 0.308181i \(-0.900280\pi\)
−0.951328 + 0.308181i \(0.900280\pi\)
\(240\) 33.9327i 0.141386i
\(241\) 149.357i 0.619739i 0.950779 + 0.309870i \(0.100285\pi\)
−0.950779 + 0.309870i \(0.899715\pi\)
\(242\) −8.32404 −0.0343968
\(243\) 257.935 1.06146
\(244\) 75.4562i 0.309247i
\(245\) 3.20988i 0.0131015i
\(246\) 38.8464 0.157912
\(247\) 590.085i 2.38901i
\(248\) 31.4849 0.126955
\(249\) 388.518i 1.56031i
\(250\) 15.8114i 0.0632456i
\(251\) 364.513i 1.45224i 0.687567 + 0.726121i \(0.258679\pi\)
−0.687567 + 0.726121i \(0.741321\pi\)
\(252\) 76.5982i 0.303961i
\(253\) −127.382 225.603i −0.503485 0.891711i
\(254\) −42.3570 −0.166760
\(255\) −13.8384 −0.0542683
\(256\) 16.0000 0.0625000
\(257\) 59.7088 0.232330 0.116165 0.993230i \(-0.462940\pi\)
0.116165 + 0.993230i \(0.462940\pi\)
\(258\) 384.698i 1.49108i
\(259\) −287.927 −1.11169
\(260\) 89.7099i 0.345038i
\(261\) −271.387 −1.03980
\(262\) −164.736 −0.628765
\(263\) 282.085i 1.07257i 0.844038 + 0.536284i \(0.180172\pi\)
−0.844038 + 0.536284i \(0.819828\pi\)
\(264\) 120.872i 0.457848i
\(265\) −45.6488 −0.172260
\(266\) −295.442 −1.11069
\(267\) 36.5674i 0.136957i
\(268\) 248.485i 0.927183i
\(269\) 14.7823 0.0549529 0.0274764 0.999622i \(-0.491253\pi\)
0.0274764 + 0.999622i \(0.491253\pi\)
\(270\) 43.2748i 0.160277i
\(271\) −34.7150 −0.128100 −0.0640499 0.997947i \(-0.520402\pi\)
−0.0640499 + 0.997947i \(0.520402\pi\)
\(272\) 6.52511i 0.0239894i
\(273\) 540.465i 1.97972i
\(274\) 134.097i 0.489406i
\(275\) 56.3218i 0.204807i
\(276\) −151.964 + 85.8032i −0.550595 + 0.310881i
\(277\) −191.042 −0.689682 −0.344841 0.938661i \(-0.612067\pi\)
−0.344841 + 0.938661i \(0.612067\pi\)
\(278\) 126.257 0.454163
\(279\) 60.0314 0.215166
\(280\) 44.9157 0.160413
\(281\) 471.349i 1.67740i 0.544596 + 0.838698i \(0.316683\pi\)
−0.544596 + 0.838698i \(0.683317\pi\)
\(282\) 34.3733 0.121891
\(283\) 23.4603i 0.0828984i 0.999141 + 0.0414492i \(0.0131975\pi\)
−0.999141 + 0.0414492i \(0.986803\pi\)
\(284\) 87.1312 0.306800
\(285\) −249.545 −0.875595
\(286\) 319.556i 1.11733i
\(287\) 51.4198i 0.179163i
\(288\) 30.5067 0.105926
\(289\) 286.339 0.990792
\(290\) 159.136i 0.548746i
\(291\) 544.908i 1.87254i
\(292\) 96.2387 0.329585
\(293\) 289.288i 0.987331i 0.869652 + 0.493666i \(0.164343\pi\)
−0.869652 + 0.493666i \(0.835657\pi\)
\(294\) 7.70180 0.0261966
\(295\) 147.332i 0.499431i
\(296\) 114.673i 0.387407i
\(297\) 154.149i 0.519022i
\(298\) 258.010i 0.865805i
\(299\) 401.756 226.843i 1.34367 0.758672i
\(300\) 37.9379 0.126460
\(301\) 509.213 1.69174
\(302\) 42.0882 0.139365
\(303\) −391.136 −1.29088
\(304\) 117.666i 0.387058i
\(305\) −84.3625 −0.276599
\(306\) 12.4412i 0.0406576i
\(307\) −563.775 −1.83640 −0.918200 0.396117i \(-0.870358\pi\)
−0.918200 + 0.396117i \(0.870358\pi\)
\(308\) −159.994 −0.519463
\(309\) 375.068i 1.21381i
\(310\) 35.2012i 0.113552i
\(311\) 76.9428 0.247404 0.123702 0.992319i \(-0.460523\pi\)
0.123702 + 0.992319i \(0.460523\pi\)
\(312\) −215.250 −0.689905
\(313\) 436.773i 1.39544i −0.716370 0.697721i \(-0.754198\pi\)
0.716370 0.697721i \(-0.245802\pi\)
\(314\) 90.6643i 0.288740i
\(315\) 85.6394 0.271871
\(316\) 202.053i 0.639408i
\(317\) 95.6774 0.301822 0.150911 0.988547i \(-0.451779\pi\)
0.150911 + 0.988547i \(0.451779\pi\)
\(318\) 109.530i 0.344434i
\(319\) 566.860i 1.77699i
\(320\) 17.8885i 0.0559017i
\(321\) 85.5476i 0.266503i
\(322\) −113.575 201.150i −0.352718 0.624691i
\(323\) −47.9863 −0.148565
\(324\) −200.906 −0.620079
\(325\) −100.299 −0.308611
\(326\) −106.537 −0.326799
\(327\) 114.720i 0.350827i
\(328\) −20.4789 −0.0624357
\(329\) 45.4988i 0.138294i
\(330\) −135.139 −0.409512
\(331\) 515.137 1.55631 0.778153 0.628074i \(-0.216157\pi\)
0.778153 + 0.628074i \(0.216157\pi\)
\(332\) 204.818i 0.616921i
\(333\) 218.643i 0.656584i
\(334\) 385.315 1.15364
\(335\) −277.815 −0.829297
\(336\) 107.771i 0.320747i
\(337\) 251.793i 0.747161i −0.927598 0.373580i \(-0.878130\pi\)
0.927598 0.373580i \(-0.121870\pi\)
\(338\) 330.068 0.976532
\(339\) 809.734i 2.38860i
\(340\) 7.29530 0.0214568
\(341\) 125.391i 0.367714i
\(342\) 224.349i 0.655992i
\(343\) 337.793i 0.984820i
\(344\) 202.804i 0.589547i
\(345\) −95.9309 169.901i −0.278061 0.492467i
\(346\) 370.262 1.07012
\(347\) −167.899 −0.483858 −0.241929 0.970294i \(-0.577780\pi\)
−0.241929 + 0.970294i \(0.577780\pi\)
\(348\) 381.833 1.09722
\(349\) 131.699 0.377360 0.188680 0.982039i \(-0.439579\pi\)
0.188680 + 0.982039i \(0.439579\pi\)
\(350\) 50.2173i 0.143478i
\(351\) 274.511 0.782084
\(352\) 63.7209i 0.181025i
\(353\) 232.683 0.659159 0.329580 0.944128i \(-0.393093\pi\)
0.329580 + 0.944128i \(0.393093\pi\)
\(354\) 353.510 0.998615
\(355\) 97.4157i 0.274410i
\(356\) 19.2775i 0.0541503i
\(357\) 43.9511 0.123112
\(358\) −260.790 −0.728463
\(359\) 205.862i 0.573432i −0.958016 0.286716i \(-0.907436\pi\)
0.958016 0.286716i \(-0.0925636\pi\)
\(360\) 34.1075i 0.0947431i
\(361\) −504.325 −1.39702
\(362\) 271.341i 0.749560i
\(363\) 22.3302 0.0615157
\(364\) 284.920i 0.782748i
\(365\) 107.598i 0.294789i
\(366\) 202.420i 0.553060i
\(367\) 158.406i 0.431623i 0.976435 + 0.215811i \(0.0692396\pi\)
−0.976435 + 0.215811i \(0.930760\pi\)
\(368\) 80.1120 45.2335i 0.217696 0.122917i
\(369\) −39.0465 −0.105817
\(370\) 128.208 0.346508
\(371\) 144.981 0.390786
\(372\) −84.4621 −0.227049
\(373\) 67.1037i 0.179903i 0.995946 + 0.0899513i \(0.0286712\pi\)
−0.995946 + 0.0899513i \(0.971329\pi\)
\(374\) −25.9866 −0.0694829
\(375\) 42.4159i 0.113109i
\(376\) −18.1208 −0.0481936
\(377\) −1009.47 −2.67765
\(378\) 137.442i 0.363602i
\(379\) 10.5032i 0.0277128i −0.999904 0.0138564i \(-0.995589\pi\)
0.999904 0.0138564i \(-0.00441078\pi\)
\(380\) 131.554 0.346195
\(381\) 113.628 0.298235
\(382\) 46.1296i 0.120758i
\(383\) 360.978i 0.942501i 0.882000 + 0.471250i \(0.156197\pi\)
−0.882000 + 0.471250i \(0.843803\pi\)
\(384\) −42.9219 −0.111776
\(385\) 178.879i 0.464621i
\(386\) 447.950 1.16049
\(387\) 386.680i 0.999173i
\(388\) 287.263i 0.740368i
\(389\) 47.2280i 0.121409i −0.998156 0.0607044i \(-0.980665\pi\)
0.998156 0.0607044i \(-0.0193347\pi\)
\(390\) 240.657i 0.617070i
\(391\) −18.4471 32.6712i −0.0471793 0.0835582i
\(392\) −4.06021 −0.0103577
\(393\) 441.925 1.12449
\(394\) −275.695 −0.699734
\(395\) 225.902 0.571904
\(396\) 121.495i 0.306805i
\(397\) 4.85826 0.0122374 0.00611872 0.999981i \(-0.498052\pi\)
0.00611872 + 0.999981i \(0.498052\pi\)
\(398\) 104.767i 0.263234i
\(399\) 792.559 1.98636
\(400\) −20.0000 −0.0500000
\(401\) 297.502i 0.741900i −0.928653 0.370950i \(-0.879032\pi\)
0.928653 0.370950i \(-0.120968\pi\)
\(402\) 666.590i 1.65818i
\(403\) 223.297 0.554087
\(404\) 206.198 0.510391
\(405\) 224.619i 0.554615i
\(406\) 505.420i 1.24488i
\(407\) −456.690 −1.12209
\(408\) 17.5044i 0.0429029i
\(409\) 238.943 0.584213 0.292106 0.956386i \(-0.405644\pi\)
0.292106 + 0.956386i \(0.405644\pi\)
\(410\) 22.8961i 0.0558442i
\(411\) 359.732i 0.875259i
\(412\) 197.727i 0.479921i
\(413\) 467.930i 1.13300i
\(414\) 152.747 86.2452i 0.368954 0.208322i
\(415\) 228.993 0.551791
\(416\) 113.475 0.272776
\(417\) −338.700 −0.812231
\(418\) −468.610 −1.12108
\(419\) 197.316i 0.470920i 0.971884 + 0.235460i \(0.0756597\pi\)
−0.971884 + 0.235460i \(0.924340\pi\)
\(420\) −120.492 −0.286885
\(421\) 459.256i 1.09087i 0.838153 + 0.545435i \(0.183635\pi\)
−0.838153 + 0.545435i \(0.816365\pi\)
\(422\) −6.71775 −0.0159188
\(423\) −34.5503 −0.0816793
\(424\) 57.7417i 0.136183i
\(425\) 8.15639i 0.0191915i
\(426\) −233.740 −0.548685
\(427\) 267.937 0.627487
\(428\) 45.0987i 0.105371i
\(429\) 857.247i 1.99824i
\(430\) −226.742 −0.527306
\(431\) 475.283i 1.10275i −0.834259 0.551373i \(-0.814104\pi\)
0.834259 0.551373i \(-0.185896\pi\)
\(432\) 54.7388 0.126710
\(433\) 694.309i 1.60349i −0.597669 0.801743i \(-0.703906\pi\)
0.597669 0.801743i \(-0.296094\pi\)
\(434\) 111.800i 0.257603i
\(435\) 426.902i 0.981384i
\(436\) 60.4779i 0.138711i
\(437\) −332.651 589.152i −0.761216 1.34817i
\(438\) −258.172 −0.589433
\(439\) −692.132 −1.57661 −0.788305 0.615284i \(-0.789041\pi\)
−0.788305 + 0.615284i \(0.789041\pi\)
\(440\) 71.2421 0.161914
\(441\) −7.74147 −0.0175544
\(442\) 46.2773i 0.104700i
\(443\) −282.065 −0.636716 −0.318358 0.947971i \(-0.603131\pi\)
−0.318358 + 0.947971i \(0.603131\pi\)
\(444\) 307.623i 0.692844i
\(445\) −21.5529 −0.0484335
\(446\) 299.781 0.672155
\(447\) 692.142i 1.54842i
\(448\) 56.8144i 0.126818i
\(449\) −4.51574 −0.0100573 −0.00502866 0.999987i \(-0.501601\pi\)
−0.00502866 + 0.999987i \(0.501601\pi\)
\(450\) −38.1334 −0.0847408
\(451\) 81.5584i 0.180839i
\(452\) 426.873i 0.944410i
\(453\) −112.907 −0.249242
\(454\) 551.460i 1.21467i
\(455\) 318.551 0.700111
\(456\) 315.652i 0.692219i
\(457\) 399.040i 0.873174i 0.899662 + 0.436587i \(0.143813\pi\)
−0.899662 + 0.436587i \(0.856187\pi\)
\(458\) 220.618i 0.481698i
\(459\) 22.3235i 0.0486352i
\(460\) 50.5726 + 89.5679i 0.109940 + 0.194713i
\(461\) 44.2537 0.0959950 0.0479975 0.998847i \(-0.484716\pi\)
0.0479975 + 0.998847i \(0.484716\pi\)
\(462\) 429.204 0.929013
\(463\) −668.258 −1.44332 −0.721661 0.692247i \(-0.756621\pi\)
−0.721661 + 0.692247i \(0.756621\pi\)
\(464\) −201.293 −0.433822
\(465\) 94.4315i 0.203078i
\(466\) −65.7564 −0.141108
\(467\) 670.150i 1.43501i −0.696554 0.717505i \(-0.745284\pi\)
0.696554 0.717505i \(-0.254716\pi\)
\(468\) 216.359 0.462306
\(469\) 882.345 1.88133
\(470\) 20.2597i 0.0431056i
\(471\) 243.218i 0.516385i
\(472\) −186.362 −0.394835
\(473\) 807.678 1.70756
\(474\) 542.031i 1.14352i
\(475\) 147.082i 0.309646i
\(476\) −23.1700 −0.0486765
\(477\) 110.094i 0.230805i
\(478\) −643.092 −1.34538
\(479\) 310.492i 0.648209i −0.946021 0.324105i \(-0.894937\pi\)
0.946021 0.324105i \(-0.105063\pi\)
\(480\) 47.9881i 0.0999753i
\(481\) 813.279i 1.69081i
\(482\) 211.223i 0.438222i
\(483\) 304.679 + 539.609i 0.630804 + 1.11720i
\(484\) −11.7720 −0.0243222
\(485\) 321.169 0.662205
\(486\) 364.775 0.750566
\(487\) 829.644 1.70358 0.851790 0.523883i \(-0.175517\pi\)
0.851790 + 0.523883i \(0.175517\pi\)
\(488\) 106.711i 0.218670i
\(489\) 285.797 0.584452
\(490\) 4.53945i 0.00926419i
\(491\) −123.794 −0.252126 −0.126063 0.992022i \(-0.540234\pi\)
−0.126063 + 0.992022i \(0.540234\pi\)
\(492\) 54.9371 0.111661
\(493\) 82.0913i 0.166514i
\(494\) 834.507i 1.68928i
\(495\) 135.835 0.274414
\(496\) 44.5264 0.0897710
\(497\) 309.394i 0.622523i
\(498\) 549.448i 1.10331i
\(499\) 757.919 1.51887 0.759437 0.650580i \(-0.225474\pi\)
0.759437 + 0.650580i \(0.225474\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) −1033.65 −2.06318
\(502\) 515.499i 1.02689i
\(503\) 242.915i 0.482933i 0.970409 + 0.241467i \(0.0776284\pi\)
−0.970409 + 0.241467i \(0.922372\pi\)
\(504\) 108.326i 0.214933i
\(505\) 230.536i 0.456507i
\(506\) −180.145 319.050i −0.356017 0.630535i
\(507\) −885.445 −1.74644
\(508\) −59.9018 −0.117917
\(509\) 822.585 1.61608 0.808040 0.589127i \(-0.200528\pi\)
0.808040 + 0.589127i \(0.200528\pi\)
\(510\) −19.5705 −0.0383735
\(511\) 341.734i 0.668755i
\(512\) 22.6274 0.0441942
\(513\) 402.555i 0.784707i
\(514\) 84.4409 0.164282
\(515\) 221.066 0.429254
\(516\) 544.046i 1.05435i
\(517\) 72.1670i 0.139588i
\(518\) −407.191 −0.786082
\(519\) −993.273 −1.91382
\(520\) 126.869i 0.243979i
\(521\) 95.3538i 0.183021i 0.995804 + 0.0915103i \(0.0291694\pi\)
−0.995804 + 0.0915103i \(0.970831\pi\)
\(522\) −383.800 −0.735248
\(523\) 277.463i 0.530522i −0.964177 0.265261i \(-0.914542\pi\)
0.964177 0.265261i \(-0.0854581\pi\)
\(524\) −232.972 −0.444604
\(525\) 134.714i 0.256598i
\(526\) 398.929i 0.758420i
\(527\) 18.1588i 0.0344568i
\(528\) 170.939i 0.323748i
\(529\) 273.242 452.968i 0.516525 0.856272i
\(530\) −64.5571 −0.121806
\(531\) −355.331 −0.669173
\(532\) −417.819 −0.785373
\(533\) −145.240 −0.272496
\(534\) 51.7141i 0.0968430i
\(535\) 50.4219 0.0942465
\(536\) 351.411i 0.655617i
\(537\) 699.599 1.30279
\(538\) 20.9054 0.0388575
\(539\) 16.1700i 0.0300000i
\(540\) 61.1998i 0.113333i
\(541\) −666.108 −1.23125 −0.615627 0.788038i \(-0.711097\pi\)
−0.615627 + 0.788038i \(0.711097\pi\)
\(542\) −49.0945 −0.0905802
\(543\) 727.903i 1.34052i
\(544\) 9.22790i 0.0169631i
\(545\) −67.6163 −0.124067
\(546\) 764.332i 1.39988i
\(547\) 349.611 0.639143 0.319571 0.947562i \(-0.396461\pi\)
0.319571 + 0.947562i \(0.396461\pi\)
\(548\) 189.642i 0.346062i
\(549\) 203.463i 0.370606i
\(550\) 79.6511i 0.144820i
\(551\) 1480.33i 2.68663i
\(552\) −214.910 + 121.344i −0.389329 + 0.219826i
\(553\) −717.469 −1.29741
\(554\) −270.174 −0.487679
\(555\) −343.933 −0.619698
\(556\) 178.555 0.321142
\(557\) 8.96150i 0.0160889i 0.999968 + 0.00804443i \(0.00256065\pi\)
−0.999968 + 0.00804443i \(0.997439\pi\)
\(558\) 84.8972 0.152145
\(559\) 1438.32i 2.57303i
\(560\) 63.5204 0.113429
\(561\) 69.7122 0.124264
\(562\) 666.587i 1.18610i
\(563\) 732.683i 1.30139i −0.759339 0.650696i \(-0.774477\pi\)
0.759339 0.650696i \(-0.225523\pi\)
\(564\) 48.6111 0.0861900
\(565\) −477.259 −0.844706
\(566\) 33.1778i 0.0586181i
\(567\) 713.395i 1.25819i
\(568\) 123.222 0.216940
\(569\) 42.5363i 0.0747563i 0.999301 + 0.0373781i \(0.0119006\pi\)
−0.999301 + 0.0373781i \(0.988099\pi\)
\(570\) −352.909 −0.619139
\(571\) 459.356i 0.804476i −0.915535 0.402238i \(-0.868232\pi\)
0.915535 0.402238i \(-0.131768\pi\)
\(572\) 451.921i 0.790071i
\(573\) 123.748i 0.215965i
\(574\) 72.7186i 0.126687i
\(575\) −100.140 + 56.5418i −0.174157 + 0.0983336i
\(576\) 43.1430 0.0749010
\(577\) 831.608 1.44126 0.720630 0.693319i \(-0.243852\pi\)
0.720630 + 0.693319i \(0.243852\pi\)
\(578\) 404.944 0.700596
\(579\) −1201.68 −2.07544
\(580\) 225.053i 0.388022i
\(581\) −727.287 −1.25179
\(582\) 770.616i 1.32408i
\(583\) 229.959 0.394441
\(584\) 136.102 0.233052
\(585\) 241.897i 0.413499i
\(586\) 409.115i 0.698149i
\(587\) −166.970 −0.284447 −0.142223 0.989835i \(-0.545425\pi\)
−0.142223 + 0.989835i \(0.545425\pi\)
\(588\) 10.8920 0.0185238
\(589\) 327.452i 0.555945i
\(590\) 208.359i 0.353151i
\(591\) 739.585 1.25141
\(592\) 162.171i 0.273938i
\(593\) 900.895 1.51922 0.759608 0.650381i \(-0.225391\pi\)
0.759608 + 0.650381i \(0.225391\pi\)
\(594\) 218.000i 0.367004i
\(595\) 25.9049i 0.0435376i
\(596\) 364.881i 0.612217i
\(597\) 281.050i 0.470771i
\(598\) 568.169 320.804i 0.950116 0.536462i
\(599\) −129.221 −0.215727 −0.107864 0.994166i \(-0.534401\pi\)
−0.107864 + 0.994166i \(0.534401\pi\)
\(600\) 53.6524 0.0894206
\(601\) 580.916 0.966582 0.483291 0.875460i \(-0.339441\pi\)
0.483291 + 0.875460i \(0.339441\pi\)
\(602\) 720.136 1.19624
\(603\) 670.024i 1.11115i
\(604\) 59.5217 0.0985458
\(605\) 13.1615i 0.0217545i
\(606\) −553.150 −0.912789
\(607\) −1063.36 −1.75183 −0.875915 0.482466i \(-0.839741\pi\)
−0.875915 + 0.482466i \(0.839741\pi\)
\(608\) 166.404i 0.273691i
\(609\) 1355.85i 2.22635i
\(610\) −119.307 −0.195585
\(611\) −128.516 −0.210337
\(612\) 17.5946i 0.0287493i
\(613\) 442.412i 0.721715i 0.932621 + 0.360858i \(0.117516\pi\)
−0.932621 + 0.360858i \(0.882484\pi\)
\(614\) −797.298 −1.29853
\(615\) 61.4216i 0.0998725i
\(616\) −226.266 −0.367316
\(617\) 936.724i 1.51819i −0.650979 0.759095i \(-0.725642\pi\)
0.650979 0.759095i \(-0.274358\pi\)
\(618\) 530.427i 0.858296i
\(619\) 401.856i 0.649202i 0.945851 + 0.324601i \(0.105230\pi\)
−0.945851 + 0.324601i \(0.894770\pi\)
\(620\) 49.7821i 0.0802937i
\(621\) 274.077 154.752i 0.441348 0.249197i
\(622\) 108.814 0.174941
\(623\) 68.4524 0.109875
\(624\) −304.410 −0.487837
\(625\) 25.0000 0.0400000
\(626\) 617.691i 0.986726i
\(627\) 1257.10 2.00495
\(628\) 128.219i 0.204170i
\(629\) −66.1367 −0.105146
\(630\) 121.112 0.192242
\(631\) 1033.92i 1.63854i 0.573411 + 0.819268i \(0.305620\pi\)
−0.573411 + 0.819268i \(0.694380\pi\)
\(632\) 285.746i 0.452130i
\(633\) 18.0212 0.0284694
\(634\) 135.308 0.213420
\(635\) 66.9722i 0.105468i
\(636\) 154.899i 0.243552i
\(637\) −28.7958 −0.0452053
\(638\) 801.662i 1.25652i
\(639\) 234.944 0.367674
\(640\) 25.2982i 0.0395285i
\(641\) 188.175i 0.293564i −0.989169 0.146782i \(-0.953108\pi\)
0.989169 0.146782i \(-0.0468916\pi\)
\(642\) 120.983i 0.188446i
\(643\) 1055.82i 1.64203i 0.570909 + 0.821013i \(0.306591\pi\)
−0.570909 + 0.821013i \(0.693409\pi\)
\(644\) −160.619 284.470i −0.249409 0.441723i
\(645\) 608.261 0.943041
\(646\) −67.8629 −0.105051
\(647\) −443.636 −0.685681 −0.342841 0.939394i \(-0.611389\pi\)
−0.342841 + 0.939394i \(0.611389\pi\)
\(648\) −284.123 −0.438462
\(649\) 742.197i 1.14360i
\(650\) −141.844 −0.218221
\(651\) 299.916i 0.460701i
\(652\) −150.666 −0.231082
\(653\) 117.465 0.179886 0.0899429 0.995947i \(-0.471332\pi\)
0.0899429 + 0.995947i \(0.471332\pi\)
\(654\) 162.239i 0.248072i
\(655\) 260.471i 0.397666i
\(656\) −28.9616 −0.0441487
\(657\) 259.502 0.394980
\(658\) 64.3451i 0.0977888i
\(659\) 664.743i 1.00871i −0.863495 0.504357i \(-0.831730\pi\)
0.863495 0.504357i \(-0.168270\pi\)
\(660\) −191.115 −0.289569
\(661\) 426.231i 0.644828i −0.946599 0.322414i \(-0.895506\pi\)
0.946599 0.322414i \(-0.104494\pi\)
\(662\) 728.514 1.10047
\(663\) 124.144i 0.187246i
\(664\) 289.656i 0.436229i
\(665\) 467.135i 0.702459i
\(666\) 309.207i 0.464275i
\(667\) −1007.88 + 569.075i −1.51106 + 0.853185i
\(668\) 544.918 0.815745
\(669\) −804.198 −1.20209
\(670\) −392.889 −0.586402
\(671\) 424.983 0.633358
\(672\) 152.411i 0.226802i
\(673\) −824.444 −1.22503 −0.612514 0.790460i \(-0.709842\pi\)
−0.612514 + 0.790460i \(0.709842\pi\)
\(674\) 356.089i 0.528322i
\(675\) −68.4235 −0.101368
\(676\) 466.786 0.690512
\(677\) 530.039i 0.782924i 0.920194 + 0.391462i \(0.128031\pi\)
−0.920194 + 0.391462i \(0.871969\pi\)
\(678\) 1145.14i 1.68899i
\(679\) −1020.04 −1.50227
\(680\) 10.3171 0.0151722
\(681\) 1479.36i 2.17233i
\(682\) 177.329i 0.260013i
\(683\) 414.954 0.607546 0.303773 0.952744i \(-0.401754\pi\)
0.303773 + 0.952744i \(0.401754\pi\)
\(684\) 317.278i 0.463857i
\(685\) −212.026 −0.309527
\(686\) 477.712i 0.696373i
\(687\) 591.833i 0.861475i
\(688\) 286.808i 0.416872i
\(689\) 409.515i 0.594361i
\(690\) −135.667 240.277i −0.196619 0.348227i
\(691\) −363.154 −0.525548 −0.262774 0.964857i \(-0.584637\pi\)
−0.262774 + 0.964857i \(0.584637\pi\)
\(692\) 523.630 0.756691
\(693\) −431.415 −0.622532
\(694\) −237.445 −0.342139
\(695\) 199.630i 0.287238i
\(696\) 539.993 0.775852
\(697\) 11.8111i 0.0169456i
\(698\) 186.250 0.266834
\(699\) 176.399 0.252360
\(700\) 71.0180i 0.101454i
\(701\) 928.839i 1.32502i −0.749053 0.662510i \(-0.769491\pi\)
0.749053 0.662510i \(-0.230509\pi\)
\(702\) 388.218 0.553017
\(703\) −1192.63 −1.69648
\(704\) 90.1149i 0.128004i
\(705\) 54.3489i 0.0770906i
\(706\) 329.064 0.466096
\(707\) 732.188i 1.03563i
\(708\) 499.938 0.706127
\(709\) 44.8088i 0.0632000i 0.999501 + 0.0316000i \(0.0100603\pi\)
−0.999501 + 0.0316000i \(0.989940\pi\)
\(710\) 137.767i 0.194037i
\(711\) 544.823i 0.766277i
\(712\) 27.2625i 0.0382900i
\(713\) 222.944 125.880i 0.312684 0.176550i
\(714\) 62.1563 0.0870536
\(715\) 505.263 0.706661
\(716\) −368.812 −0.515101
\(717\) 1725.17 2.40609
\(718\) 291.133i 0.405478i
\(719\) 1308.36 1.81969 0.909844 0.414950i \(-0.136201\pi\)
0.909844 + 0.414950i \(0.136201\pi\)
\(720\) 48.2353i 0.0669935i
\(721\) −702.110 −0.973800
\(722\) −713.223 −0.987843
\(723\) 566.630i 0.783721i
\(724\) 383.734i 0.530019i
\(725\) 251.617 0.347057
\(726\) 31.5797 0.0434982
\(727\) 515.858i 0.709570i 0.934948 + 0.354785i \(0.115446\pi\)
−0.934948 + 0.354785i \(0.884554\pi\)
\(728\) 402.938i 0.553487i
\(729\) −74.4769 −0.102163
\(730\) 152.167i 0.208448i
\(731\) 116.966 0.160008
\(732\) 286.265i 0.391073i
\(733\) 405.638i 0.553394i −0.960957 0.276697i \(-0.910760\pi\)
0.960957 0.276697i \(-0.0892398\pi\)
\(734\) 224.019i 0.305203i
\(735\) 12.1776i 0.0165682i
\(736\) 113.295 63.9698i 0.153934 0.0869155i
\(737\) 1399.51 1.89893
\(738\) −55.2201 −0.0748240
\(739\) 601.397 0.813798 0.406899 0.913473i \(-0.366610\pi\)
0.406899 + 0.913473i \(0.366610\pi\)
\(740\) 181.313 0.245018
\(741\) 2238.66i 3.02114i
\(742\) 205.035 0.276327
\(743\) 775.124i 1.04324i 0.853179 + 0.521618i \(0.174671\pi\)
−0.853179 + 0.521618i \(0.825329\pi\)
\(744\) −119.447 −0.160548
\(745\) −407.950 −0.547583
\(746\) 94.8990i 0.127210i
\(747\) 552.278i 0.739328i
\(748\) −36.7506 −0.0491319
\(749\) −160.141 −0.213806
\(750\) 59.9852i 0.0799802i
\(751\) 533.250i 0.710054i −0.934856 0.355027i \(-0.884472\pi\)
0.934856 0.355027i \(-0.115528\pi\)
\(752\) −25.6267 −0.0340780
\(753\) 1382.89i 1.83650i
\(754\) −1427.61 −1.89338
\(755\) 66.5473i 0.0881421i
\(756\) 194.372i 0.257106i
\(757\) 794.660i 1.04975i 0.851180 + 0.524875i \(0.175888\pi\)
−0.851180 + 0.524875i \(0.824112\pi\)
\(758\) 14.8537i 0.0195959i
\(759\) 483.260 + 855.890i 0.636706 + 1.12766i
\(760\) 186.046 0.244797
\(761\) −1322.01 −1.73720 −0.868599 0.495515i \(-0.834979\pi\)
−0.868599 + 0.495515i \(0.834979\pi\)
\(762\) 160.694 0.210884
\(763\) 214.751 0.281456
\(764\) 65.2371i 0.0853888i
\(765\) 19.6713 0.0257141
\(766\) 510.500i 0.666449i
\(767\) −1321.71 −1.72323
\(768\) −60.7007 −0.0790374
\(769\) 1443.85i 1.87757i −0.344500 0.938786i \(-0.611952\pi\)
0.344500 0.938786i \(-0.388048\pi\)
\(770\) 252.973i 0.328537i
\(771\) −226.523 −0.293804
\(772\) 633.497 0.820592
\(773\) 64.8298i 0.0838678i −0.999120 0.0419339i \(-0.986648\pi\)
0.999120 0.0419339i \(-0.0133519\pi\)
\(774\) 546.848i 0.706522i
\(775\) −55.6580 −0.0718168
\(776\) 406.251i 0.523519i
\(777\) 1092.34 1.40584
\(778\) 66.7905i 0.0858490i
\(779\) 212.986i 0.273410i
\(780\) 340.341i 0.436334i
\(781\) 490.739i 0.628347i
\(782\) −26.0881 46.2041i −0.0333608 0.0590845i
\(783\) −688.659 −0.879514
\(784\) −5.74200 −0.00732398
\(785\) −143.353 −0.182615
\(786\) 624.976 0.795135
\(787\) 1247.04i 1.58455i 0.610163 + 0.792276i \(0.291104\pi\)
−0.610163