Properties

Label 230.3.d.a.91.1
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 91.1
Root \(-0.0431371i\) of defining polynomial
Character \(\chi\) \(=\) 230.91
Dual form 230.3.d.a.91.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} -5.41949 q^{3} +2.00000 q^{4} -2.23607i q^{5} +7.66432 q^{6} +8.24199i q^{7} -2.82843 q^{8} +20.3709 q^{9} +O(q^{10})\) \(q-1.41421 q^{2} -5.41949 q^{3} +2.00000 q^{4} -2.23607i q^{5} +7.66432 q^{6} +8.24199i q^{7} -2.82843 q^{8} +20.3709 q^{9} +3.16228i q^{10} +15.8246i q^{11} -10.8390 q^{12} -14.3219 q^{13} -11.6559i q^{14} +12.1184i q^{15} +4.00000 q^{16} -10.1666i q^{17} -28.8088 q^{18} -36.5359i q^{19} -4.47214i q^{20} -44.6674i q^{21} -22.3793i q^{22} +(22.2445 + 5.84663i) q^{23} +15.3286 q^{24} -5.00000 q^{25} +20.2543 q^{26} -61.6245 q^{27} +16.4840i q^{28} +6.46533 q^{29} -17.1379i q^{30} -42.8526 q^{31} -5.65685 q^{32} -85.7611i q^{33} +14.3777i q^{34} +18.4296 q^{35} +40.7418 q^{36} -63.6379i q^{37} +51.6696i q^{38} +77.6175 q^{39} +6.32456i q^{40} -37.0921 q^{41} +63.1692i q^{42} +6.00126i q^{43} +31.6491i q^{44} -45.5507i q^{45} +(-31.4584 - 8.26838i) q^{46} -32.4676 q^{47} -21.6780 q^{48} -18.9303 q^{49} +7.07107 q^{50} +55.0977i q^{51} -28.6438 q^{52} -36.6640i q^{53} +87.1502 q^{54} +35.3848 q^{55} -23.3119i q^{56} +198.006i q^{57} -9.14336 q^{58} +6.65851 q^{59} +24.2367i q^{60} -55.7093i q^{61} +60.6028 q^{62} +167.897i q^{63} +8.00000 q^{64} +32.0248i q^{65} +121.284i q^{66} +4.45984i q^{67} -20.3331i q^{68} +(-120.554 - 31.6858i) q^{69} -26.0634 q^{70} +118.412 q^{71} -57.6176 q^{72} +82.2675 q^{73} +89.9976i q^{74} +27.0975 q^{75} -73.0718i q^{76} -130.426 q^{77} -109.768 q^{78} -133.084i q^{79} -8.94427i q^{80} +150.636 q^{81} +52.4561 q^{82} -67.5614i q^{83} -89.3348i q^{84} -22.7331 q^{85} -8.48707i q^{86} -35.0388 q^{87} -44.7586i q^{88} +104.729i q^{89} +64.4185i q^{90} -118.041i q^{91} +(44.4890 + 11.6933i) q^{92} +232.240 q^{93} +45.9161 q^{94} -81.6968 q^{95} +30.6573 q^{96} -98.6666i q^{97} +26.7715 q^{98} +322.360i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9}+O(q^{10}) \) 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
\(3\) −5.41949 −1.80650 −0.903249 0.429117i \(-0.858825\pi\)
−0.903249 + 0.429117i \(0.858825\pi\)
\(4\) 2.00000 0.500000
\(5\) 2.23607i 0.447214i
\(6\) 7.66432 1.27739
\(7\) 8.24199i 1.17743i 0.808342 + 0.588713i \(0.200365\pi\)
−0.808342 + 0.588713i \(0.799635\pi\)
\(8\) −2.82843 −0.353553
\(9\) 20.3709 2.26343
\(10\) 3.16228i 0.316228i
\(11\) 15.8246i 1.43860i 0.694702 + 0.719298i \(0.255536\pi\)
−0.694702 + 0.719298i \(0.744464\pi\)
\(12\) −10.8390 −0.903249
\(13\) −14.3219 −1.10169 −0.550843 0.834609i \(-0.685694\pi\)
−0.550843 + 0.834609i \(0.685694\pi\)
\(14\) 11.6559i 0.832566i
\(15\) 12.1184i 0.807890i
\(16\) 4.00000 0.250000
\(17\) 10.1666i 0.598034i −0.954248 0.299017i \(-0.903341\pi\)
0.954248 0.299017i \(-0.0966587\pi\)
\(18\) −28.8088 −1.60049
\(19\) 36.5359i 1.92294i −0.274904 0.961472i \(-0.588646\pi\)
0.274904 0.961472i \(-0.411354\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 44.6674i 2.12702i
\(22\) 22.3793i 1.01724i
\(23\) 22.2445 + 5.84663i 0.967151 + 0.254201i
\(24\) 15.3286 0.638693
\(25\) −5.00000 −0.200000
\(26\) 20.2543 0.779010
\(27\) −61.6245 −2.28239
\(28\) 16.4840i 0.588713i
\(29\) 6.46533 0.222942 0.111471 0.993768i \(-0.464444\pi\)
0.111471 + 0.993768i \(0.464444\pi\)
\(30\) 17.1379i 0.571265i
\(31\) −42.8526 −1.38234 −0.691172 0.722691i \(-0.742905\pi\)
−0.691172 + 0.722691i \(0.742905\pi\)
\(32\) −5.65685 −0.176777
\(33\) 85.7611i 2.59882i
\(34\) 14.3777i 0.422874i
\(35\) 18.4296 0.526561
\(36\) 40.7418 1.13172
\(37\) 63.6379i 1.71994i −0.510341 0.859972i \(-0.670481\pi\)
0.510341 0.859972i \(-0.329519\pi\)
\(38\) 51.6696i 1.35973i
\(39\) 77.6175 1.99019
\(40\) 6.32456i 0.158114i
\(41\) −37.0921 −0.904685 −0.452342 0.891844i \(-0.649412\pi\)
−0.452342 + 0.891844i \(0.649412\pi\)
\(42\) 63.1692i 1.50403i
\(43\) 6.00126i 0.139564i 0.997562 + 0.0697821i \(0.0222304\pi\)
−0.997562 + 0.0697821i \(0.977770\pi\)
\(44\) 31.6491i 0.719298i
\(45\) 45.5507i 1.01224i
\(46\) −31.4584 8.26838i −0.683879 0.179747i
\(47\) −32.4676 −0.690800 −0.345400 0.938455i \(-0.612257\pi\)
−0.345400 + 0.938455i \(0.612257\pi\)
\(48\) −21.6780 −0.451624
\(49\) −18.9303 −0.386333
\(50\) 7.07107 0.141421
\(51\) 55.0977i 1.08035i
\(52\) −28.6438 −0.550843
\(53\) 36.6640i 0.691774i −0.938276 0.345887i \(-0.887578\pi\)
0.938276 0.345887i \(-0.112422\pi\)
\(54\) 87.1502 1.61389
\(55\) 35.3848 0.643360
\(56\) 23.3119i 0.416283i
\(57\) 198.006i 3.47379i
\(58\) −9.14336 −0.157644
\(59\) 6.65851 0.112856 0.0564280 0.998407i \(-0.482029\pi\)
0.0564280 + 0.998407i \(0.482029\pi\)
\(60\) 24.2367i 0.403945i
\(61\) 55.7093i 0.913268i −0.889655 0.456634i \(-0.849055\pi\)
0.889655 0.456634i \(-0.150945\pi\)
\(62\) 60.6028 0.977464
\(63\) 167.897i 2.66503i
\(64\) 8.00000 0.125000
\(65\) 32.0248i 0.492689i
\(66\) 121.284i 1.83764i
\(67\) 4.45984i 0.0665648i 0.999446 + 0.0332824i \(0.0105961\pi\)
−0.999446 + 0.0332824i \(0.989404\pi\)
\(68\) 20.3331i 0.299017i
\(69\) −120.554 31.6858i −1.74716 0.459214i
\(70\) −26.0634 −0.372335
\(71\) 118.412 1.66777 0.833886 0.551937i \(-0.186111\pi\)
0.833886 + 0.551937i \(0.186111\pi\)
\(72\) −57.6176 −0.800245
\(73\) 82.2675 1.12695 0.563476 0.826133i \(-0.309464\pi\)
0.563476 + 0.826133i \(0.309464\pi\)
\(74\) 89.9976i 1.21618i
\(75\) 27.0975 0.361300
\(76\) 73.0718i 0.961472i
\(77\) −130.426 −1.69384
\(78\) −109.768 −1.40728
\(79\) 133.084i 1.68461i −0.538999 0.842307i \(-0.681197\pi\)
0.538999 0.842307i \(-0.318803\pi\)
\(80\) 8.94427i 0.111803i
\(81\) 150.636 1.85970
\(82\) 52.4561 0.639709
\(83\) 67.5614i 0.813993i −0.913430 0.406996i \(-0.866576\pi\)
0.913430 0.406996i \(-0.133424\pi\)
\(84\) 89.3348i 1.06351i
\(85\) −22.7331 −0.267449
\(86\) 8.48707i 0.0986868i
\(87\) −35.0388 −0.402745
\(88\) 44.7586i 0.508620i
\(89\) 104.729i 1.17673i 0.808595 + 0.588365i \(0.200228\pi\)
−0.808595 + 0.588365i \(0.799772\pi\)
\(90\) 64.4185i 0.715761i
\(91\) 118.041i 1.29715i
\(92\) 44.4890 + 11.6933i 0.483576 + 0.127101i
\(93\) 232.240 2.49720
\(94\) 45.9161 0.488470
\(95\) −81.6968 −0.859966
\(96\) 30.6573 0.319347
\(97\) 98.6666i 1.01718i −0.861008 0.508591i \(-0.830167\pi\)
0.861008 0.508591i \(-0.169833\pi\)
\(98\) 26.7715 0.273179
\(99\) 322.360i 3.25617i
\(100\) −10.0000 −0.100000
\(101\) −75.6811 −0.749318 −0.374659 0.927163i \(-0.622240\pi\)
−0.374659 + 0.927163i \(0.622240\pi\)
\(102\) 77.9199i 0.763920i
\(103\) 86.8499i 0.843203i 0.906781 + 0.421602i \(0.138532\pi\)
−0.906781 + 0.421602i \(0.861468\pi\)
\(104\) 40.5085 0.389505
\(105\) −99.8793 −0.951231
\(106\) 51.8508i 0.489158i
\(107\) 5.55552i 0.0519208i −0.999663 0.0259604i \(-0.991736\pi\)
0.999663 0.0259604i \(-0.00826438\pi\)
\(108\) −123.249 −1.14119
\(109\) 71.0003i 0.651379i −0.945477 0.325689i \(-0.894404\pi\)
0.945477 0.325689i \(-0.105596\pi\)
\(110\) −50.0416 −0.454924
\(111\) 344.885i 3.10707i
\(112\) 32.9679i 0.294357i
\(113\) 100.763i 0.891707i −0.895106 0.445854i \(-0.852900\pi\)
0.895106 0.445854i \(-0.147100\pi\)
\(114\) 280.023i 2.45634i
\(115\) 13.0735 49.7402i 0.113682 0.432523i
\(116\) 12.9307 0.111471
\(117\) −291.750 −2.49359
\(118\) −9.41655 −0.0798013
\(119\) 83.7927 0.704141
\(120\) 34.2759i 0.285632i
\(121\) −129.417 −1.06956
\(122\) 78.7849i 0.645778i
\(123\) 201.020 1.63431
\(124\) −85.7053 −0.691172
\(125\) 11.1803i 0.0894427i
\(126\) 237.442i 1.88446i
\(127\) −43.9602 −0.346143 −0.173072 0.984909i \(-0.555369\pi\)
−0.173072 + 0.984909i \(0.555369\pi\)
\(128\) −11.3137 −0.0883883
\(129\) 32.5238i 0.252123i
\(130\) 45.2899i 0.348384i
\(131\) −44.4134 −0.339033 −0.169517 0.985527i \(-0.554221\pi\)
−0.169517 + 0.985527i \(0.554221\pi\)
\(132\) 171.522i 1.29941i
\(133\) 301.129 2.26412
\(134\) 6.30717i 0.0470684i
\(135\) 137.797i 1.02072i
\(136\) 28.7554i 0.211437i
\(137\) 44.9295i 0.327953i 0.986464 + 0.163976i \(0.0524321\pi\)
−0.986464 + 0.163976i \(0.947568\pi\)
\(138\) 170.489 + 44.8105i 1.23543 + 0.324713i
\(139\) −139.796 −1.00573 −0.502864 0.864365i \(-0.667720\pi\)
−0.502864 + 0.864365i \(0.667720\pi\)
\(140\) 36.8593 0.263281
\(141\) 175.958 1.24793
\(142\) −167.460 −1.17929
\(143\) 226.638i 1.58488i
\(144\) 81.4836 0.565858
\(145\) 14.4569i 0.0997029i
\(146\) −116.344 −0.796875
\(147\) 102.593 0.697910
\(148\) 127.276i 0.859972i
\(149\) 25.4227i 0.170622i −0.996354 0.0853111i \(-0.972812\pi\)
0.996354 0.0853111i \(-0.0271884\pi\)
\(150\) −38.3216 −0.255477
\(151\) −52.5299 −0.347880 −0.173940 0.984756i \(-0.555650\pi\)
−0.173940 + 0.984756i \(0.555650\pi\)
\(152\) 103.339i 0.679863i
\(153\) 207.102i 1.35361i
\(154\) 184.450 1.19773
\(155\) 95.8214i 0.618203i
\(156\) 155.235 0.995097
\(157\) 74.5874i 0.475079i −0.971378 0.237539i \(-0.923659\pi\)
0.971378 0.237539i \(-0.0763409\pi\)
\(158\) 188.210i 1.19120i
\(159\) 198.700i 1.24969i
\(160\) 12.6491i 0.0790569i
\(161\) −48.1878 + 183.339i −0.299303 + 1.13875i
\(162\) −213.031 −1.31501
\(163\) −18.3238 −0.112416 −0.0562080 0.998419i \(-0.517901\pi\)
−0.0562080 + 0.998419i \(0.517901\pi\)
\(164\) −74.1842 −0.452342
\(165\) −191.768 −1.16223
\(166\) 95.5462i 0.575580i
\(167\) 68.9768 0.413035 0.206517 0.978443i \(-0.433787\pi\)
0.206517 + 0.978443i \(0.433787\pi\)
\(168\) 126.338i 0.752014i
\(169\) 36.1174 0.213712
\(170\) 32.1495 0.189115
\(171\) 744.270i 4.35245i
\(172\) 12.0025i 0.0697821i
\(173\) 118.707 0.686166 0.343083 0.939305i \(-0.388529\pi\)
0.343083 + 0.939305i \(0.388529\pi\)
\(174\) 49.5523 0.284784
\(175\) 41.2099i 0.235485i
\(176\) 63.2982i 0.359649i
\(177\) −36.0857 −0.203874
\(178\) 148.109i 0.832074i
\(179\) −278.892 −1.55806 −0.779029 0.626988i \(-0.784288\pi\)
−0.779029 + 0.626988i \(0.784288\pi\)
\(180\) 91.1014i 0.506119i
\(181\) 66.1123i 0.365261i 0.983182 + 0.182631i \(0.0584613\pi\)
−0.983182 + 0.182631i \(0.941539\pi\)
\(182\) 166.935i 0.917227i
\(183\) 301.916i 1.64982i
\(184\) −62.9169 16.5368i −0.341940 0.0898737i
\(185\) −142.299 −0.769182
\(186\) −328.436 −1.76579
\(187\) 160.882 0.860329
\(188\) −64.9352 −0.345400
\(189\) 507.908i 2.68735i
\(190\) 115.537 0.608088
\(191\) 5.53406i 0.0289741i 0.999895 + 0.0144871i \(0.00461154\pi\)
−0.999895 + 0.0144871i \(0.995388\pi\)
\(192\) −43.3559 −0.225812
\(193\) −72.0460 −0.373295 −0.186648 0.982427i \(-0.559762\pi\)
−0.186648 + 0.982427i \(0.559762\pi\)
\(194\) 139.536i 0.719256i
\(195\) 173.558i 0.890041i
\(196\) −37.8606 −0.193167
\(197\) 191.143 0.970271 0.485136 0.874439i \(-0.338770\pi\)
0.485136 + 0.874439i \(0.338770\pi\)
\(198\) 455.887i 2.30246i
\(199\) 172.543i 0.867051i −0.901141 0.433525i \(-0.857269\pi\)
0.901141 0.433525i \(-0.142731\pi\)
\(200\) 14.1421 0.0707107
\(201\) 24.1701i 0.120249i
\(202\) 107.029 0.529848
\(203\) 53.2871i 0.262498i
\(204\) 110.195i 0.540173i
\(205\) 82.9404i 0.404587i
\(206\) 122.824i 0.596235i
\(207\) 453.140 + 119.101i 2.18908 + 0.575368i
\(208\) −57.2877 −0.275422
\(209\) 578.165 2.76634
\(210\) 141.251 0.672622
\(211\) −334.039 −1.58312 −0.791561 0.611090i \(-0.790731\pi\)
−0.791561 + 0.611090i \(0.790731\pi\)
\(212\) 73.3281i 0.345887i
\(213\) −641.732 −3.01282
\(214\) 7.85670i 0.0367135i
\(215\) 13.4192 0.0624150
\(216\) 174.300 0.806947
\(217\) 353.191i 1.62761i
\(218\) 100.410i 0.460594i
\(219\) −445.848 −2.03584
\(220\) 70.7696 0.321680
\(221\) 145.605i 0.658845i
\(222\) 487.741i 2.19703i
\(223\) −441.580 −1.98018 −0.990089 0.140440i \(-0.955148\pi\)
−0.990089 + 0.140440i \(0.955148\pi\)
\(224\) 46.6237i 0.208142i
\(225\) −101.855 −0.452687
\(226\) 142.500i 0.630532i
\(227\) 54.9222i 0.241948i −0.992656 0.120974i \(-0.961398\pi\)
0.992656 0.120974i \(-0.0386018\pi\)
\(228\) 396.012i 1.73690i
\(229\) 322.300i 1.40743i 0.710485 + 0.703713i \(0.248476\pi\)
−0.710485 + 0.703713i \(0.751524\pi\)
\(230\) −18.4887 + 70.3432i −0.0803855 + 0.305840i
\(231\) 706.841 3.05992
\(232\) −18.2867 −0.0788220
\(233\) 159.208 0.683296 0.341648 0.939828i \(-0.389015\pi\)
0.341648 + 0.939828i \(0.389015\pi\)
\(234\) 412.597 1.76324
\(235\) 72.5998i 0.308935i
\(236\) 13.3170 0.0564280
\(237\) 721.250i 3.04325i
\(238\) −118.501 −0.497903
\(239\) 32.1990 0.134724 0.0673620 0.997729i \(-0.478542\pi\)
0.0673620 + 0.997729i \(0.478542\pi\)
\(240\) 48.4734i 0.201973i
\(241\) 39.8259i 0.165253i 0.996581 + 0.0826263i \(0.0263308\pi\)
−0.996581 + 0.0826263i \(0.973669\pi\)
\(242\) 183.023 0.756292
\(243\) −261.748 −1.07715
\(244\) 111.419i 0.456634i
\(245\) 42.3295i 0.172773i
\(246\) −284.286 −1.15563
\(247\) 523.265i 2.11848i
\(248\) 121.206 0.488732
\(249\) 366.148i 1.47048i
\(250\) 15.8114i 0.0632456i
\(251\) 232.529i 0.926410i 0.886251 + 0.463205i \(0.153301\pi\)
−0.886251 + 0.463205i \(0.846699\pi\)
\(252\) 335.793i 1.33251i
\(253\) −92.5203 + 352.009i −0.365693 + 1.39134i
\(254\) 62.1691 0.244760
\(255\) 123.202 0.483146
\(256\) 16.0000 0.0625000
\(257\) 325.160 1.26521 0.632606 0.774473i \(-0.281985\pi\)
0.632606 + 0.774473i \(0.281985\pi\)
\(258\) 45.9956i 0.178278i
\(259\) 524.503 2.02511
\(260\) 64.0496i 0.246344i
\(261\) 131.705 0.504615
\(262\) 62.8100 0.239733
\(263\) 4.94890i 0.0188171i 0.999956 + 0.00940855i \(0.00299488\pi\)
−0.999956 + 0.00940855i \(0.997005\pi\)
\(264\) 242.569i 0.918822i
\(265\) −81.9833 −0.309371
\(266\) −425.860 −1.60098
\(267\) 567.578i 2.12576i
\(268\) 8.91969i 0.0332824i
\(269\) 235.047 0.873781 0.436891 0.899515i \(-0.356080\pi\)
0.436891 + 0.899515i \(0.356080\pi\)
\(270\) 194.874i 0.721755i
\(271\) −53.5224 −0.197500 −0.0987498 0.995112i \(-0.531484\pi\)
−0.0987498 + 0.995112i \(0.531484\pi\)
\(272\) 40.6663i 0.149508i
\(273\) 639.723i 2.34331i
\(274\) 63.5399i 0.231898i
\(275\) 79.1228i 0.287719i
\(276\) −241.108 63.3715i −0.873578 0.229607i
\(277\) −143.576 −0.518326 −0.259163 0.965834i \(-0.583447\pi\)
−0.259163 + 0.965834i \(0.583447\pi\)
\(278\) 197.702 0.711157
\(279\) −872.947 −3.12884
\(280\) −52.1269 −0.186167
\(281\) 187.330i 0.666656i −0.942811 0.333328i \(-0.891828\pi\)
0.942811 0.333328i \(-0.108172\pi\)
\(282\) −248.842 −0.882419
\(283\) 486.156i 1.71787i −0.512087 0.858934i \(-0.671127\pi\)
0.512087 0.858934i \(-0.328873\pi\)
\(284\) 236.824 0.833886
\(285\) 442.755 1.55353
\(286\) 320.515i 1.12068i
\(287\) 305.712i 1.06520i
\(288\) −115.235 −0.400122
\(289\) 185.641 0.642356
\(290\) 20.4452i 0.0705006i
\(291\) 534.723i 1.83754i
\(292\) 164.535 0.563476
\(293\) 240.733i 0.821616i 0.911722 + 0.410808i \(0.134753\pi\)
−0.911722 + 0.410808i \(0.865247\pi\)
\(294\) −145.088 −0.493497
\(295\) 14.8889i 0.0504708i
\(296\) 179.995i 0.608092i
\(297\) 975.181i 3.28344i
\(298\) 35.9531i 0.120648i
\(299\) −318.584 83.7350i −1.06550 0.280050i
\(300\) 54.1949 0.180650
\(301\) −49.4623 −0.164327
\(302\) 74.2885 0.245988
\(303\) 410.153 1.35364
\(304\) 146.144i 0.480736i
\(305\) −124.570 −0.408426
\(306\) 292.887i 0.957147i
\(307\) 338.091 1.10127 0.550636 0.834745i \(-0.314385\pi\)
0.550636 + 0.834745i \(0.314385\pi\)
\(308\) −260.852 −0.846920
\(309\) 470.683i 1.52324i
\(310\) 135.512i 0.437135i
\(311\) −131.884 −0.424066 −0.212033 0.977263i \(-0.568008\pi\)
−0.212033 + 0.977263i \(0.568008\pi\)
\(312\) −219.536 −0.703640
\(313\) 160.254i 0.511994i −0.966678 0.255997i \(-0.917596\pi\)
0.966678 0.255997i \(-0.0824038\pi\)
\(314\) 105.482i 0.335931i
\(315\) 375.428 1.19184
\(316\) 266.169i 0.842307i
\(317\) −525.687 −1.65832 −0.829160 0.559012i \(-0.811181\pi\)
−0.829160 + 0.559012i \(0.811181\pi\)
\(318\) 281.005i 0.883663i
\(319\) 102.311i 0.320724i
\(320\) 17.8885i 0.0559017i
\(321\) 30.1081i 0.0937948i
\(322\) 68.1479 259.280i 0.211639 0.805218i
\(323\) −371.445 −1.14998
\(324\) 301.271 0.929849
\(325\) 71.6096 0.220337
\(326\) 25.9138 0.0794901
\(327\) 384.786i 1.17671i
\(328\) 104.912 0.319854
\(329\) 267.598i 0.813367i
\(330\) 271.200 0.821819
\(331\) 0.120137 0.000362953 0.000181477 1.00000i \(-0.499942\pi\)
0.000181477 1.00000i \(0.499942\pi\)
\(332\) 135.123i 0.406996i
\(333\) 1296.36i 3.89298i
\(334\) −97.5480 −0.292060
\(335\) 9.97251 0.0297687
\(336\) 178.670i 0.531755i
\(337\) 652.946i 1.93752i 0.247992 + 0.968762i \(0.420229\pi\)
−0.247992 + 0.968762i \(0.579771\pi\)
\(338\) −51.0777 −0.151117
\(339\) 546.084i 1.61087i
\(340\) −45.4663 −0.133724
\(341\) 678.124i 1.98863i
\(342\) 1052.56i 3.07765i
\(343\) 247.834i 0.722548i
\(344\) 16.9741i 0.0493434i
\(345\) −70.8515 + 269.566i −0.205367 + 0.781352i
\(346\) −167.877 −0.485193
\(347\) −468.304 −1.34958 −0.674789 0.738010i \(-0.735766\pi\)
−0.674789 + 0.738010i \(0.735766\pi\)
\(348\) −70.0776 −0.201372
\(349\) 182.288 0.522315 0.261157 0.965296i \(-0.415896\pi\)
0.261157 + 0.965296i \(0.415896\pi\)
\(350\) 58.2796i 0.166513i
\(351\) 882.581 2.51448
\(352\) 89.5172i 0.254310i
\(353\) −301.039 −0.852802 −0.426401 0.904534i \(-0.640219\pi\)
−0.426401 + 0.904534i \(0.640219\pi\)
\(354\) 51.0329 0.144161
\(355\) 264.777i 0.745850i
\(356\) 209.458i 0.588365i
\(357\) −454.114 −1.27203
\(358\) 394.413 1.10171
\(359\) 24.6772i 0.0687388i 0.999409 + 0.0343694i \(0.0109423\pi\)
−0.999409 + 0.0343694i \(0.989058\pi\)
\(360\) 128.837i 0.357880i
\(361\) −973.874 −2.69771
\(362\) 93.4969i 0.258279i
\(363\) 701.372 1.93215
\(364\) 236.082i 0.648577i
\(365\) 183.956i 0.503988i
\(366\) 426.974i 1.16660i
\(367\) 427.508i 1.16487i −0.812877 0.582435i \(-0.802100\pi\)
0.812877 0.582435i \(-0.197900\pi\)
\(368\) 88.9779 + 23.3865i 0.241788 + 0.0635503i
\(369\) −755.599 −2.04769
\(370\) 201.241 0.543894
\(371\) 302.184 0.814513
\(372\) 464.479 1.24860
\(373\) 338.652i 0.907913i −0.891024 0.453957i \(-0.850012\pi\)
0.891024 0.453957i \(-0.149988\pi\)
\(374\) −227.521 −0.608344
\(375\) 60.5918i 0.161578i
\(376\) 91.8323 0.244235
\(377\) −92.5959 −0.245612
\(378\) 718.291i 1.90024i
\(379\) 287.157i 0.757671i −0.925464 0.378835i \(-0.876325\pi\)
0.925464 0.378835i \(-0.123675\pi\)
\(380\) −163.394 −0.429983
\(381\) 238.242 0.625307
\(382\) 7.82634i 0.0204878i
\(383\) 682.661i 1.78240i 0.453606 + 0.891202i \(0.350137\pi\)
−0.453606 + 0.891202i \(0.649863\pi\)
\(384\) 61.3146 0.159673
\(385\) 291.641i 0.757509i
\(386\) 101.888 0.263960
\(387\) 122.251i 0.315894i
\(388\) 197.333i 0.508591i
\(389\) 543.886i 1.39816i −0.715041 0.699082i \(-0.753592\pi\)
0.715041 0.699082i \(-0.246408\pi\)
\(390\) 245.448i 0.629354i
\(391\) 59.4402 226.150i 0.152021 0.578389i
\(392\) 53.5430 0.136589
\(393\) 240.698 0.612463
\(394\) −270.318 −0.686085
\(395\) −297.586 −0.753382
\(396\) 644.721i 1.62808i
\(397\) 99.6609 0.251035 0.125517 0.992091i \(-0.459941\pi\)
0.125517 + 0.992091i \(0.459941\pi\)
\(398\) 244.013i 0.613097i
\(399\) −1631.96 −4.09014
\(400\) −20.0000 −0.0500000
\(401\) 404.668i 1.00915i −0.863369 0.504573i \(-0.831650\pi\)
0.863369 0.504573i \(-0.168350\pi\)
\(402\) 34.1817i 0.0850290i
\(403\) 613.732 1.52291
\(404\) −151.362 −0.374659
\(405\) 336.831i 0.831682i
\(406\) 75.3594i 0.185614i
\(407\) 1007.04 2.47430
\(408\) 155.840i 0.381960i
\(409\) 701.478 1.71510 0.857552 0.514397i \(-0.171984\pi\)
0.857552 + 0.514397i \(0.171984\pi\)
\(410\) 117.295i 0.286087i
\(411\) 243.495i 0.592446i
\(412\) 173.700i 0.421602i
\(413\) 54.8793i 0.132880i
\(414\) −640.837 168.434i −1.54792 0.406847i
\(415\) −151.072 −0.364029
\(416\) 81.0170 0.194752
\(417\) 757.625 1.81685
\(418\) −817.648 −1.95610
\(419\) 685.089i 1.63506i 0.575888 + 0.817529i \(0.304657\pi\)
−0.575888 + 0.817529i \(0.695343\pi\)
\(420\) −199.759 −0.475616
\(421\) 205.326i 0.487711i 0.969812 + 0.243856i \(0.0784123\pi\)
−0.969812 + 0.243856i \(0.921588\pi\)
\(422\) 472.402 1.11944
\(423\) −661.395 −1.56358
\(424\) 103.702i 0.244579i
\(425\) 50.8329i 0.119607i
\(426\) 907.546 2.13039
\(427\) 459.156 1.07531
\(428\) 11.1110i 0.0259604i
\(429\) 1228.26i 2.86308i
\(430\) −18.9777 −0.0441341
\(431\) 355.926i 0.825814i −0.910773 0.412907i \(-0.864513\pi\)
0.910773 0.412907i \(-0.135487\pi\)
\(432\) −246.498 −0.570597
\(433\) 17.2870i 0.0399238i 0.999801 + 0.0199619i \(0.00635449\pi\)
−0.999801 + 0.0199619i \(0.993646\pi\)
\(434\) 499.487i 1.15089i
\(435\) 78.3491i 0.180113i
\(436\) 142.001i 0.325689i
\(437\) 213.612 812.723i 0.488815 1.85978i
\(438\) 630.524 1.43955
\(439\) −458.708 −1.04489 −0.522447 0.852672i \(-0.674981\pi\)
−0.522447 + 0.852672i \(0.674981\pi\)
\(440\) −100.083 −0.227462
\(441\) −385.628 −0.874439
\(442\) 205.916i 0.465874i
\(443\) −196.292 −0.443096 −0.221548 0.975149i \(-0.571111\pi\)
−0.221548 + 0.975149i \(0.571111\pi\)
\(444\) 689.771i 1.55354i
\(445\) 234.181 0.526250
\(446\) 624.488 1.40020
\(447\) 137.778i 0.308228i
\(448\) 65.9359i 0.147178i
\(449\) −344.536 −0.767341 −0.383671 0.923470i \(-0.625340\pi\)
−0.383671 + 0.923470i \(0.625340\pi\)
\(450\) 144.044 0.320098
\(451\) 586.966i 1.30148i
\(452\) 201.526i 0.445854i
\(453\) 284.685 0.628445
\(454\) 77.6717i 0.171083i
\(455\) −263.948 −0.580105
\(456\) 560.046i 1.22817i
\(457\) 122.214i 0.267426i 0.991020 + 0.133713i \(0.0426900\pi\)
−0.991020 + 0.133713i \(0.957310\pi\)
\(458\) 455.802i 0.995200i
\(459\) 626.510i 1.36495i
\(460\) 26.1469 99.4803i 0.0568411 0.216262i
\(461\) 218.326 0.473593 0.236796 0.971559i \(-0.423903\pi\)
0.236796 + 0.971559i \(0.423903\pi\)
\(462\) −999.625 −2.16369
\(463\) −455.380 −0.983542 −0.491771 0.870725i \(-0.663650\pi\)
−0.491771 + 0.870725i \(0.663650\pi\)
\(464\) 25.8613 0.0557356
\(465\) 519.304i 1.11678i
\(466\) −225.154 −0.483163
\(467\) 350.332i 0.750176i −0.926989 0.375088i \(-0.877612\pi\)
0.926989 0.375088i \(-0.122388\pi\)
\(468\) −583.501 −1.24680
\(469\) −36.7580 −0.0783752
\(470\) 102.672i 0.218450i
\(471\) 404.226i 0.858229i
\(472\) −18.8331 −0.0399006
\(473\) −94.9673 −0.200777
\(474\) 1020.00i 2.15190i
\(475\) 182.680i 0.384589i
\(476\) 167.585 0.352070
\(477\) 746.879i 1.56578i
\(478\) −45.5363 −0.0952643
\(479\) 743.178i 1.55152i −0.631028 0.775760i \(-0.717367\pi\)
0.631028 0.775760i \(-0.282633\pi\)
\(480\) 68.5518i 0.142816i
\(481\) 911.417i 1.89484i
\(482\) 56.3223i 0.116851i
\(483\) 261.154 993.603i 0.540691 2.05715i
\(484\) −258.833 −0.534779
\(485\) −220.625 −0.454897
\(486\) 370.167 0.761660
\(487\) −366.770 −0.753122 −0.376561 0.926392i \(-0.622893\pi\)
−0.376561 + 0.926392i \(0.622893\pi\)
\(488\) 157.570i 0.322889i
\(489\) 99.3057 0.203079
\(490\) 59.8629i 0.122169i
\(491\) 127.024 0.258704 0.129352 0.991599i \(-0.458710\pi\)
0.129352 + 0.991599i \(0.458710\pi\)
\(492\) 402.041 0.817156
\(493\) 65.7302i 0.133327i
\(494\) 740.008i 1.49799i
\(495\) 720.820 1.45620
\(496\) −171.411 −0.345586
\(497\) 975.948i 1.96368i
\(498\) 517.812i 1.03978i
\(499\) 523.599 1.04930 0.524648 0.851319i \(-0.324197\pi\)
0.524648 + 0.851319i \(0.324197\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) −373.819 −0.746147
\(502\) 328.845i 0.655071i
\(503\) 646.170i 1.28463i −0.766440 0.642316i \(-0.777974\pi\)
0.766440 0.642316i \(-0.222026\pi\)
\(504\) 474.884i 0.942229i
\(505\) 169.228i 0.335105i
\(506\) 130.844 497.816i 0.258584 0.983826i
\(507\) −195.738 −0.386070
\(508\) −87.9203 −0.173072
\(509\) −605.436 −1.18946 −0.594731 0.803925i \(-0.702741\pi\)
−0.594731 + 0.803925i \(0.702741\pi\)
\(510\) −174.234 −0.341636
\(511\) 678.047i 1.32690i
\(512\) −22.6274 −0.0441942
\(513\) 2251.51i 4.38891i
\(514\) −459.845 −0.894641
\(515\) 194.202 0.377092
\(516\) 65.0476i 0.126061i
\(517\) 513.786i 0.993783i
\(518\) −741.759 −1.43197
\(519\) −643.330 −1.23956
\(520\) 90.5798i 0.174192i
\(521\) 655.952i 1.25902i 0.776990 + 0.629512i \(0.216745\pi\)
−0.776990 + 0.629512i \(0.783255\pi\)
\(522\) −186.258 −0.356817
\(523\) 317.109i 0.606328i 0.952938 + 0.303164i \(0.0980430\pi\)
−0.952938 + 0.303164i \(0.901957\pi\)
\(524\) −88.8267 −0.169517
\(525\) 223.337i 0.425404i
\(526\) 6.99880i 0.0133057i
\(527\) 435.665i 0.826688i
\(528\) 343.044i 0.649705i
\(529\) 460.634 + 260.111i 0.870763 + 0.491702i
\(530\) 115.942 0.218758
\(531\) 135.640 0.255442
\(532\) 602.257 1.13206
\(533\) 531.230 0.996679
\(534\) 802.677i 1.50314i
\(535\) −12.4225 −0.0232197
\(536\) 12.6143i 0.0235342i
\(537\) 1511.46 2.81463
\(538\) −332.407 −0.617856
\(539\) 299.564i 0.555777i
\(540\) 275.593i 0.510358i
\(541\) −222.888 −0.411992 −0.205996 0.978553i \(-0.566043\pi\)
−0.205996 + 0.978553i \(0.566043\pi\)
\(542\) 75.6921 0.139653
\(543\) 358.295i 0.659844i
\(544\) 57.5108i 0.105718i
\(545\) −158.762 −0.291306
\(546\) 904.704i 1.65697i
\(547\) −552.627 −1.01029 −0.505144 0.863035i \(-0.668561\pi\)
−0.505144 + 0.863035i \(0.668561\pi\)
\(548\) 89.8590i 0.163976i
\(549\) 1134.85i 2.06712i
\(550\) 111.897i 0.203448i
\(551\) 236.217i 0.428706i
\(552\) 340.978 + 89.6209i 0.617713 + 0.162357i
\(553\) 1096.88 1.98351
\(554\) 203.048 0.366512
\(555\) 771.187 1.38953
\(556\) −279.592 −0.502864
\(557\) 110.000i 0.197486i −0.995113 0.0987430i \(-0.968518\pi\)
0.995113 0.0987430i \(-0.0314822\pi\)
\(558\) 1234.53 2.21243
\(559\) 85.9496i 0.153756i
\(560\) 73.7186 0.131640
\(561\) −871.896 −1.55418
\(562\) 264.925i 0.471397i
\(563\) 360.367i 0.640084i −0.947403 0.320042i \(-0.896303\pi\)
0.947403 0.320042i \(-0.103697\pi\)
\(564\) 351.916 0.623965
\(565\) −225.313 −0.398784
\(566\) 687.529i 1.21472i
\(567\) 1241.54i 2.18966i
\(568\) −334.919 −0.589646
\(569\) 532.981i 0.936698i −0.883544 0.468349i \(-0.844849\pi\)
0.883544 0.468349i \(-0.155151\pi\)
\(570\) −626.151 −1.09851
\(571\) 582.697i 1.02048i 0.860031 + 0.510242i \(0.170444\pi\)
−0.860031 + 0.510242i \(0.829556\pi\)
\(572\) 453.276i 0.792441i
\(573\) 29.9918i 0.0523417i
\(574\) 432.343i 0.753210i
\(575\) −111.222 29.2332i −0.193430 0.0508403i
\(576\) 162.967 0.282929
\(577\) −869.422 −1.50680 −0.753399 0.657564i \(-0.771587\pi\)
−0.753399 + 0.657564i \(0.771587\pi\)
\(578\) −262.536 −0.454214
\(579\) 390.453 0.674357
\(580\) 28.9138i 0.0498514i
\(581\) 556.840 0.958416
\(582\) 756.212i 1.29933i
\(583\) 580.192 0.995183
\(584\) −232.688 −0.398438
\(585\) 652.374i 1.11517i
\(586\) 340.449i 0.580970i
\(587\) −403.118 −0.686742 −0.343371 0.939200i \(-0.611569\pi\)
−0.343371 + 0.939200i \(0.611569\pi\)
\(588\) 205.185 0.348955
\(589\) 1565.66i 2.65817i
\(590\) 21.0560i 0.0356882i
\(591\) −1035.90 −1.75279
\(592\) 254.552i 0.429986i
\(593\) −668.332 −1.12703 −0.563517 0.826104i \(-0.690552\pi\)
−0.563517 + 0.826104i \(0.690552\pi\)
\(594\) 1379.11i 2.32174i
\(595\) 187.366i 0.314901i
\(596\) 50.8454i 0.0853111i
\(597\) 935.096i 1.56632i
\(598\) 450.545 + 118.419i 0.753420 + 0.198025i
\(599\) 866.946 1.44732 0.723661 0.690155i \(-0.242458\pi\)
0.723661 + 0.690155i \(0.242458\pi\)
\(600\) −76.6432 −0.127739
\(601\) 544.425 0.905866 0.452933 0.891545i \(-0.350378\pi\)
0.452933 + 0.891545i \(0.350378\pi\)
\(602\) 69.9503 0.116196
\(603\) 90.8511i 0.150665i
\(604\) −105.060 −0.173940
\(605\) 289.384i 0.478321i
\(606\) −580.044 −0.957169
\(607\) 23.2820 0.0383559 0.0191779 0.999816i \(-0.493895\pi\)
0.0191779 + 0.999816i \(0.493895\pi\)
\(608\) 206.678i 0.339932i
\(609\) 288.789i 0.474202i
\(610\) 176.168 0.288801
\(611\) 464.999 0.761045
\(612\) 414.205i 0.676805i
\(613\) 559.419i 0.912592i 0.889828 + 0.456296i \(0.150824\pi\)
−0.889828 + 0.456296i \(0.849176\pi\)
\(614\) −478.133 −0.778718
\(615\) 449.495i 0.730886i
\(616\) 368.900 0.598863
\(617\) 1080.07i 1.75052i 0.483649 + 0.875262i \(0.339311\pi\)
−0.483649 + 0.875262i \(0.660689\pi\)
\(618\) 665.646i 1.07710i
\(619\) 729.225i 1.17807i −0.808107 0.589035i \(-0.799508\pi\)
0.808107 0.589035i \(-0.200492\pi\)
\(620\) 191.643i 0.309101i
\(621\) −1370.81 360.296i −2.20742 0.580187i
\(622\) 186.513 0.299860
\(623\) −863.175 −1.38551
\(624\) 310.470 0.497548
\(625\) 25.0000 0.0400000
\(626\) 226.634i 0.362035i
\(627\) −3133.36 −4.99738
\(628\) 149.175i 0.237539i
\(629\) −646.980 −1.02858
\(630\) −530.936 −0.842755
\(631\) 386.633i 0.612731i −0.951914 0.306365i \(-0.900887\pi\)
0.951914 0.306365i \(-0.0991129\pi\)
\(632\) 376.420i 0.595601i
\(633\) 1810.32 2.85991
\(634\) 743.434 1.17261
\(635\) 98.2979i 0.154800i
\(636\) 397.401i 0.624844i
\(637\) 271.118 0.425618
\(638\) 144.690i 0.226786i
\(639\) 2412.15 3.77489
\(640\) 25.2982i 0.0395285i
\(641\) 676.123i 1.05479i 0.849619 + 0.527397i \(0.176832\pi\)
−0.849619 + 0.527397i \(0.823168\pi\)
\(642\) 42.5793i 0.0663229i
\(643\) 1063.72i 1.65430i 0.561980 + 0.827151i \(0.310040\pi\)
−0.561980 + 0.827151i \(0.689960\pi\)
\(644\) −96.3757 + 366.677i −0.149652 + 0.569375i
\(645\) −72.7254 −0.112753
\(646\) 525.303 0.813162
\(647\) −157.776 −0.243857 −0.121929 0.992539i \(-0.538908\pi\)
−0.121929 + 0.992539i \(0.538908\pi\)
\(648\) −426.062 −0.657503
\(649\) 105.368i 0.162354i
\(650\) −101.271 −0.155802
\(651\) 1914.12i 2.94027i
\(652\) −36.6476 −0.0562080
\(653\) 41.1895 0.0630773 0.0315386 0.999503i \(-0.489959\pi\)
0.0315386 + 0.999503i \(0.489959\pi\)
\(654\) 544.169i 0.832063i
\(655\) 99.3113i 0.151620i
\(656\) −148.368 −0.226171
\(657\) 1675.86 2.55078
\(658\) 378.440i 0.575137i
\(659\) 19.2526i 0.0292149i −0.999893 0.0146075i \(-0.995350\pi\)
0.999893 0.0146075i \(-0.00464986\pi\)
\(660\) −383.535 −0.581114
\(661\) 75.8322i 0.114724i 0.998353 + 0.0573618i \(0.0182688\pi\)
−0.998353 + 0.0573618i \(0.981731\pi\)
\(662\) −0.169900 −0.000256647
\(663\) 789.104i 1.19020i
\(664\) 191.092i 0.287790i
\(665\) 673.344i 1.01255i
\(666\) 1833.33i 2.75275i
\(667\) 143.818 + 37.8004i 0.215619 + 0.0566722i
\(668\) 137.954 0.206517
\(669\) 2393.14 3.57719
\(670\) −14.1033 −0.0210497
\(671\) 881.576 1.31382
\(672\) 252.677i 0.376007i
\(673\) 12.6902 0.0188561 0.00942807 0.999956i \(-0.496999\pi\)
0.00942807 + 0.999956i \(0.496999\pi\)
\(674\) 923.405i 1.37004i
\(675\) 308.123 0.456478
\(676\) 72.2347 0.106856
\(677\) 233.185i 0.344439i 0.985059 + 0.172220i \(0.0550939\pi\)
−0.985059 + 0.172220i \(0.944906\pi\)
\(678\) 772.279i 1.13906i
\(679\) 813.209 1.19766
\(680\) 64.2991 0.0945574
\(681\) 297.650i 0.437078i
\(682\) 959.012i 1.40618i
\(683\) 367.020 0.537364 0.268682 0.963229i \(-0.413412\pi\)
0.268682 + 0.963229i \(0.413412\pi\)
\(684\) 1488.54i 2.17623i
\(685\) 100.465 0.146665
\(686\) 350.490i 0.510918i
\(687\) 1746.70i 2.54251i
\(688\) 24.0051i 0.0348911i
\(689\) 525.099i 0.762118i
\(690\) 100.199 381.225i 0.145216 0.552499i
\(691\) −1186.21 −1.71666 −0.858332 0.513095i \(-0.828499\pi\)
−0.858332 + 0.513095i \(0.828499\pi\)
\(692\) 237.413 0.343083
\(693\) −2656.89 −3.83390
\(694\) 662.282 0.954296
\(695\) 312.594i 0.449775i
\(696\) 99.1047 0.142392
\(697\) 377.099i 0.541032i
\(698\) −257.794 −0.369332
\(699\) −862.826 −1.23437
\(700\) 82.4199i 0.117743i
\(701\) 848.508i 1.21043i −0.796064 0.605213i \(-0.793088\pi\)
0.796064 0.605213i \(-0.206912\pi\)
\(702\) −1248.16 −1.77800
\(703\) −2325.07 −3.30736
\(704\) 126.596i 0.179825i
\(705\) 393.454i 0.558091i
\(706\) 425.733 0.603022
\(707\) 623.763i 0.882267i
\(708\) −72.1715 −0.101937
\(709\) 533.757i 0.752831i −0.926451 0.376416i \(-0.877156\pi\)
0.926451 0.376416i \(-0.122844\pi\)
\(710\) 374.451i 0.527396i
\(711\) 2711.05i 3.81301i
\(712\) 296.218i 0.416037i
\(713\) −953.235 250.544i −1.33694 0.351394i
\(714\) 642.214 0.899460
\(715\) −506.778 −0.708780
\(716\) −557.785 −0.779029
\(717\) −174.502 −0.243379
\(718\) 34.8989i 0.0486057i
\(719\) 1210.11 1.68304 0.841520 0.540225i \(-0.181661\pi\)
0.841520 + 0.540225i \(0.181661\pi\)
\(720\) 182.203i 0.253060i
\(721\) −715.816 −0.992810
\(722\) 1377.27 1.90757
\(723\) 215.836i 0.298528i
\(724\) 132.225i 0.182631i
\(725\) −32.3266 −0.0445885
\(726\) −991.890 −1.36624
\(727\) 2.43604i 0.00335081i 0.999999 + 0.00167540i \(0.000533298\pi\)
−0.999999 + 0.00167540i \(0.999467\pi\)
\(728\) 333.870i 0.458613i
\(729\) 62.8190 0.0861715
\(730\) 260.153i 0.356373i
\(731\) 61.0123 0.0834641
\(732\) 603.833i 0.824908i
\(733\) 495.146i 0.675506i −0.941235 0.337753i \(-0.890333\pi\)
0.941235 0.337753i \(-0.109667\pi\)
\(734\) 604.587i 0.823688i
\(735\) 229.404i 0.312115i
\(736\) −125.834 33.0735i −0.170970 0.0449369i
\(737\) −70.5751 −0.0957599
\(738\) 1068.58 1.44794
\(739\) 1235.77 1.67222 0.836112 0.548559i \(-0.184823\pi\)
0.836112 + 0.548559i \(0.184823\pi\)
\(740\) −284.597 −0.384591
\(741\) 2835.83i 3.82703i
\(742\) −427.353 −0.575948
\(743\) 1030.67i 1.38717i −0.720373 0.693587i \(-0.756029\pi\)
0.720373 0.693587i \(-0.243971\pi\)
\(744\) −656.873 −0.882894
\(745\) −56.8469 −0.0763045
\(746\) 478.926i 0.641992i
\(747\) 1376.29i 1.84242i
\(748\) 321.763 0.430164
\(749\) 45.7885 0.0611329
\(750\) 85.6897i 0.114253i
\(751\) 1112.44i 1.48128i −0.671903 0.740639i \(-0.734523\pi\)
0.671903 0.740639i \(-0.265477\pi\)
\(752\) −129.870 −0.172700
\(753\) 1260.19i 1.67356i
\(754\) 130.950 0.173674
\(755\) 117.460i 0.155577i
\(756\) 1015.82i 1.34367i
\(757\) 483.738i 0.639019i 0.947583 + 0.319510i \(0.103518\pi\)
−0.947583 + 0.319510i \(0.896482\pi\)
\(758\) 406.102i 0.535754i
\(759\) 501.413 1907.71i 0.660624 2.51345i
\(760\) 231.073 0.304044
\(761\) 833.341 1.09506 0.547530 0.836786i \(-0.315568\pi\)
0.547530 + 0.836786i \(0.315568\pi\)
\(762\) −336.925 −0.442158
\(763\) 585.183 0.766951
\(764\) 11.0681i 0.0144871i
\(765\) −463.095 −0.605353
\(766\) 965.428i 1.26035i
\(767\) −95.3626 −0.124332
\(768\) −86.7119 −0.112906
\(769\) 356.518i 0.463613i −0.972762 0.231806i \(-0.925536\pi\)
0.972762 0.231806i \(-0.0744636\pi\)
\(770\) 412.442i 0.535640i
\(771\) −1762.20 −2.28560
\(772\) −144.092 −0.186648
\(773\) 286.633i 0.370805i 0.982663 + 0.185403i \(0.0593589\pi\)
−0.982663 + 0.185403i \(0.940641\pi\)
\(774\) 172.889i 0.223371i
\(775\) 214.263 0.276469
\(776\) 279.071i 0.359628i
\(777\) −2842.54 −3.65835
\(778\) 769.171i 0.988651i
\(779\) 1355.19i 1.73966i
\(780\) 347.116i 0.445021i
\(781\) 1873.81i 2.39925i
\(782\) −84.0611 + 319.825i −0.107495 + 0.408983i
\(783\) −398.423 −0.508841
\(784\) −75.7213 −0.0965833
\(785\) −166.782 −0.212462
\(786\) −340.398 −0.433077
\(787\) 930.798i 1.18272i 0.806409 + 0.591359i \(0.201408\pi\)
−0.806409 +