Properties

Label 690.3.c.a.91.6
Level $690$
Weight $3$
Character 690.91
Analytic conductor $18.801$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 91.6
Character \(\chi\) \(=\) 690.91
Dual form 690.3.c.a.91.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} -1.73205 q^{3} +2.00000 q^{4} +2.23607i q^{5} +2.44949 q^{6} -1.52229i q^{7} -2.82843 q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-1.41421 q^{2} -1.73205 q^{3} +2.00000 q^{4} +2.23607i q^{5} +2.44949 q^{6} -1.52229i q^{7} -2.82843 q^{8} +3.00000 q^{9} -3.16228i q^{10} +2.20036i q^{11} -3.46410 q^{12} -1.82994 q^{13} +2.15284i q^{14} -3.87298i q^{15} +4.00000 q^{16} -23.2496i q^{17} -4.24264 q^{18} +2.85690i q^{19} +4.47214i q^{20} +2.63668i q^{21} -3.11178i q^{22} +(-14.5452 + 17.8168i) q^{23} +4.89898 q^{24} -5.00000 q^{25} +2.58793 q^{26} -5.19615 q^{27} -3.04458i q^{28} -7.23088 q^{29} +5.47723i q^{30} +49.9104 q^{31} -5.65685 q^{32} -3.81114i q^{33} +32.8800i q^{34} +3.40394 q^{35} +6.00000 q^{36} +9.68006i q^{37} -4.04027i q^{38} +3.16955 q^{39} -6.32456i q^{40} -62.1103 q^{41} -3.72883i q^{42} -76.6308i q^{43} +4.40073i q^{44} +6.70820i q^{45} +(20.5700 - 25.1967i) q^{46} +17.1464 q^{47} -6.92820 q^{48} +46.6826 q^{49} +7.07107 q^{50} +40.2696i q^{51} -3.65988 q^{52} +33.9334i q^{53} +7.34847 q^{54} -4.92016 q^{55} +4.30569i q^{56} -4.94830i q^{57} +10.2260 q^{58} +35.2164 q^{59} -7.74597i q^{60} +8.54346i q^{61} -70.5840 q^{62} -4.56687i q^{63} +8.00000 q^{64} -4.09187i q^{65} +5.38977i q^{66} -78.9586i q^{67} -46.4993i q^{68} +(25.1930 - 30.8596i) q^{69} -4.81390 q^{70} +111.407 q^{71} -8.48528 q^{72} +134.217 q^{73} -13.6897i q^{74} +8.66025 q^{75} +5.71380i q^{76} +3.34959 q^{77} -4.48242 q^{78} -72.4039i q^{79} +8.94427i q^{80} +9.00000 q^{81} +87.8373 q^{82} -119.919i q^{83} +5.27337i q^{84} +51.9878 q^{85} +108.372i q^{86} +12.5243 q^{87} -6.22357i q^{88} +73.9324i q^{89} -9.48683i q^{90} +2.78570i q^{91} +(-29.0904 + 35.6335i) q^{92} -86.4474 q^{93} -24.2486 q^{94} -6.38822 q^{95} +9.79796 q^{96} -178.439i q^{97} -66.0192 q^{98} +6.60109i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 64q^{4} + 96q^{9} + O(q^{10}) \) \( 32q + 64q^{4} + 96q^{9} - 48q^{13} + 128q^{16} - 80q^{23} - 160q^{25} + 120q^{29} + 248q^{31} - 120q^{35} + 192q^{36} - 48q^{39} + 72q^{41} + 160q^{46} + 400q^{47} - 344q^{49} - 96q^{52} - 256q^{58} + 120q^{59} + 160q^{62} + 256q^{64} + 192q^{69} + 104q^{71} + 16q^{73} + 240q^{77} + 192q^{78} + 288q^{81} + 64q^{82} - 120q^{85} + 144q^{87} - 160q^{92} - 192q^{93} + 96q^{94} - 160q^{95} + 64q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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
\(3\) −1.73205 −0.577350
\(4\) 2.00000 0.500000
\(5\) 2.23607i 0.447214i
\(6\) 2.44949 0.408248
\(7\) 1.52229i 0.217470i −0.994071 0.108735i \(-0.965320\pi\)
0.994071 0.108735i \(-0.0346800\pi\)
\(8\) −2.82843 −0.353553
\(9\) 3.00000 0.333333
\(10\) 3.16228i 0.316228i
\(11\) 2.20036i 0.200033i 0.994986 + 0.100016i \(0.0318896\pi\)
−0.994986 + 0.100016i \(0.968110\pi\)
\(12\) −3.46410 −0.288675
\(13\) −1.82994 −0.140765 −0.0703824 0.997520i \(-0.522422\pi\)
−0.0703824 + 0.997520i \(0.522422\pi\)
\(14\) 2.15284i 0.153774i
\(15\) 3.87298i 0.258199i
\(16\) 4.00000 0.250000
\(17\) 23.2496i 1.36763i −0.729657 0.683813i \(-0.760320\pi\)
0.729657 0.683813i \(-0.239680\pi\)
\(18\) −4.24264 −0.235702
\(19\) 2.85690i 0.150363i 0.997170 + 0.0751816i \(0.0239536\pi\)
−0.997170 + 0.0751816i \(0.976046\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 2.63668i 0.125556i
\(22\) 3.11178i 0.141445i
\(23\) −14.5452 + 17.8168i −0.632400 + 0.774642i
\(24\) 4.89898 0.204124
\(25\) −5.00000 −0.200000
\(26\) 2.58793 0.0995357
\(27\) −5.19615 −0.192450
\(28\) 3.04458i 0.108735i
\(29\) −7.23088 −0.249341 −0.124670 0.992198i \(-0.539787\pi\)
−0.124670 + 0.992198i \(0.539787\pi\)
\(30\) 5.47723i 0.182574i
\(31\) 49.9104 1.61001 0.805007 0.593266i \(-0.202162\pi\)
0.805007 + 0.593266i \(0.202162\pi\)
\(32\) −5.65685 −0.176777
\(33\) 3.81114i 0.115489i
\(34\) 32.8800i 0.967058i
\(35\) 3.40394 0.0972555
\(36\) 6.00000 0.166667
\(37\) 9.68006i 0.261623i 0.991407 + 0.130812i \(0.0417583\pi\)
−0.991407 + 0.130812i \(0.958242\pi\)
\(38\) 4.04027i 0.106323i
\(39\) 3.16955 0.0812706
\(40\) 6.32456i 0.158114i
\(41\) −62.1103 −1.51489 −0.757443 0.652901i \(-0.773552\pi\)
−0.757443 + 0.652901i \(0.773552\pi\)
\(42\) 3.72883i 0.0887817i
\(43\) 76.6308i 1.78211i −0.453893 0.891056i \(-0.649965\pi\)
0.453893 0.891056i \(-0.350035\pi\)
\(44\) 4.40073i 0.100016i
\(45\) 6.70820i 0.149071i
\(46\) 20.5700 25.1967i 0.447174 0.547755i
\(47\) 17.1464 0.364817 0.182408 0.983223i \(-0.441611\pi\)
0.182408 + 0.983223i \(0.441611\pi\)
\(48\) −6.92820 −0.144338
\(49\) 46.6826 0.952707
\(50\) 7.07107 0.141421
\(51\) 40.2696i 0.789599i
\(52\) −3.65988 −0.0703824
\(53\) 33.9334i 0.640253i 0.947375 + 0.320127i \(0.103725\pi\)
−0.947375 + 0.320127i \(0.896275\pi\)
\(54\) 7.34847 0.136083
\(55\) −4.92016 −0.0894575
\(56\) 4.30569i 0.0768872i
\(57\) 4.94830i 0.0868122i
\(58\) 10.2260 0.176311
\(59\) 35.2164 0.596889 0.298444 0.954427i \(-0.403532\pi\)
0.298444 + 0.954427i \(0.403532\pi\)
\(60\) 7.74597i 0.129099i
\(61\) 8.54346i 0.140057i 0.997545 + 0.0700284i \(0.0223090\pi\)
−0.997545 + 0.0700284i \(0.977691\pi\)
\(62\) −70.5840 −1.13845
\(63\) 4.56687i 0.0724900i
\(64\) 8.00000 0.125000
\(65\) 4.09187i 0.0629519i
\(66\) 5.38977i 0.0816631i
\(67\) 78.9586i 1.17849i −0.807956 0.589243i \(-0.799426\pi\)
0.807956 0.589243i \(-0.200574\pi\)
\(68\) 46.4993i 0.683813i
\(69\) 25.1930 30.8596i 0.365116 0.447240i
\(70\) −4.81390 −0.0687700
\(71\) 111.407 1.56911 0.784554 0.620061i \(-0.212892\pi\)
0.784554 + 0.620061i \(0.212892\pi\)
\(72\) −8.48528 −0.117851
\(73\) 134.217 1.83858 0.919291 0.393578i \(-0.128763\pi\)
0.919291 + 0.393578i \(0.128763\pi\)
\(74\) 13.6897i 0.184996i
\(75\) 8.66025 0.115470
\(76\) 5.71380i 0.0751816i
\(77\) 3.34959 0.0435012
\(78\) −4.48242 −0.0574670
\(79\) 72.4039i 0.916505i −0.888822 0.458252i \(-0.848476\pi\)
0.888822 0.458252i \(-0.151524\pi\)
\(80\) 8.94427i 0.111803i
\(81\) 9.00000 0.111111
\(82\) 87.8373 1.07119
\(83\) 119.919i 1.44481i −0.691472 0.722403i \(-0.743037\pi\)
0.691472 0.722403i \(-0.256963\pi\)
\(84\) 5.27337i 0.0627782i
\(85\) 51.9878 0.611621
\(86\) 108.372i 1.26014i
\(87\) 12.5243 0.143957
\(88\) 6.22357i 0.0707223i
\(89\) 73.9324i 0.830701i 0.909661 + 0.415351i \(0.136341\pi\)
−0.909661 + 0.415351i \(0.863659\pi\)
\(90\) 9.48683i 0.105409i
\(91\) 2.78570i 0.0306121i
\(92\) −29.0904 + 35.6335i −0.316200 + 0.387321i
\(93\) −86.4474 −0.929542
\(94\) −24.2486 −0.257964
\(95\) −6.38822 −0.0672445
\(96\) 9.79796 0.102062
\(97\) 178.439i 1.83958i −0.392408 0.919791i \(-0.628358\pi\)
0.392408 0.919791i \(-0.371642\pi\)
\(98\) −66.0192 −0.673665
\(99\) 6.60109i 0.0666777i
\(100\) −10.0000 −0.100000
\(101\) 147.269 1.45811 0.729053 0.684457i \(-0.239961\pi\)
0.729053 + 0.684457i \(0.239961\pi\)
\(102\) 56.9498i 0.558331i
\(103\) 58.9552i 0.572380i −0.958173 0.286190i \(-0.907611\pi\)
0.958173 0.286190i \(-0.0923889\pi\)
\(104\) 5.17586 0.0497679
\(105\) −5.89580 −0.0561505
\(106\) 47.9891i 0.452727i
\(107\) 111.196i 1.03922i −0.854404 0.519609i \(-0.826078\pi\)
0.854404 0.519609i \(-0.173922\pi\)
\(108\) −10.3923 −0.0962250
\(109\) 52.7876i 0.484290i −0.970240 0.242145i \(-0.922149\pi\)
0.970240 0.242145i \(-0.0778509\pi\)
\(110\) 6.95816 0.0632560
\(111\) 16.7664i 0.151048i
\(112\) 6.08916i 0.0543675i
\(113\) 25.4121i 0.224886i 0.993658 + 0.112443i \(0.0358676\pi\)
−0.993658 + 0.112443i \(0.964132\pi\)
\(114\) 6.99795i 0.0613855i
\(115\) −39.8395 32.5240i −0.346431 0.282818i
\(116\) −14.4618 −0.124670
\(117\) −5.48983 −0.0469216
\(118\) −49.8035 −0.422064
\(119\) −35.3927 −0.297418
\(120\) 10.9545i 0.0912871i
\(121\) 116.158 0.959987
\(122\) 12.0823i 0.0990350i
\(123\) 107.578 0.874620
\(124\) 99.8208 0.805007
\(125\) 11.1803i 0.0894427i
\(126\) 6.45853i 0.0512582i
\(127\) 100.861 0.794177 0.397089 0.917780i \(-0.370021\pi\)
0.397089 + 0.917780i \(0.370021\pi\)
\(128\) −11.3137 −0.0883883
\(129\) 132.728i 1.02890i
\(130\) 5.78678i 0.0445137i
\(131\) −28.6539 −0.218732 −0.109366 0.994002i \(-0.534882\pi\)
−0.109366 + 0.994002i \(0.534882\pi\)
\(132\) 7.62228i 0.0577445i
\(133\) 4.34903 0.0326995
\(134\) 111.664i 0.833316i
\(135\) 11.6190i 0.0860663i
\(136\) 65.7599i 0.483529i
\(137\) 159.048i 1.16094i 0.814282 + 0.580469i \(0.197131\pi\)
−0.814282 + 0.580469i \(0.802869\pi\)
\(138\) −35.6283 + 43.6420i −0.258176 + 0.316246i
\(139\) 119.112 0.856918 0.428459 0.903561i \(-0.359057\pi\)
0.428459 + 0.903561i \(0.359057\pi\)
\(140\) 6.80789 0.0486278
\(141\) −29.6984 −0.210627
\(142\) −157.553 −1.10953
\(143\) 4.02654i 0.0281576i
\(144\) 12.0000 0.0833333
\(145\) 16.1687i 0.111509i
\(146\) −189.811 −1.30007
\(147\) −80.8567 −0.550046
\(148\) 19.3601i 0.130812i
\(149\) 245.833i 1.64989i −0.565214 0.824945i \(-0.691206\pi\)
0.565214 0.824945i \(-0.308794\pi\)
\(150\) −12.2474 −0.0816497
\(151\) 209.449 1.38708 0.693541 0.720417i \(-0.256050\pi\)
0.693541 + 0.720417i \(0.256050\pi\)
\(152\) 8.08053i 0.0531614i
\(153\) 69.7489i 0.455875i
\(154\) −4.73704 −0.0307600
\(155\) 111.603i 0.720020i
\(156\) 6.33911 0.0406353
\(157\) 211.566i 1.34755i 0.738935 + 0.673777i \(0.235329\pi\)
−0.738935 + 0.673777i \(0.764671\pi\)
\(158\) 102.395i 0.648067i
\(159\) 58.7744i 0.369650i
\(160\) 12.6491i 0.0790569i
\(161\) 27.1223 + 22.1420i 0.168461 + 0.137528i
\(162\) −12.7279 −0.0785674
\(163\) −14.1494 −0.0868061 −0.0434030 0.999058i \(-0.513820\pi\)
−0.0434030 + 0.999058i \(0.513820\pi\)
\(164\) −124.221 −0.757443
\(165\) 8.52197 0.0516483
\(166\) 169.591i 1.02163i
\(167\) 52.0666 0.311776 0.155888 0.987775i \(-0.450176\pi\)
0.155888 + 0.987775i \(0.450176\pi\)
\(168\) 7.45767i 0.0443909i
\(169\) −165.651 −0.980185
\(170\) −73.5218 −0.432481
\(171\) 8.57070i 0.0501211i
\(172\) 153.262i 0.891056i
\(173\) −219.256 −1.26738 −0.633688 0.773589i \(-0.718460\pi\)
−0.633688 + 0.773589i \(0.718460\pi\)
\(174\) −17.7120 −0.101793
\(175\) 7.61145i 0.0434940i
\(176\) 8.80145i 0.0500082i
\(177\) −60.9966 −0.344614
\(178\) 104.556i 0.587395i
\(179\) −84.3515 −0.471237 −0.235619 0.971846i \(-0.575712\pi\)
−0.235619 + 0.971846i \(0.575712\pi\)
\(180\) 13.4164i 0.0745356i
\(181\) 272.635i 1.50627i 0.657867 + 0.753134i \(0.271459\pi\)
−0.657867 + 0.753134i \(0.728541\pi\)
\(182\) 3.93958i 0.0216460i
\(183\) 14.7977i 0.0808618i
\(184\) 41.1400 50.3934i 0.223587 0.273877i
\(185\) −21.6453 −0.117001
\(186\) 122.255 0.657285
\(187\) 51.1577 0.273570
\(188\) 34.2928 0.182408
\(189\) 7.91005i 0.0418521i
\(190\) 9.03431 0.0475490
\(191\) 235.645i 1.23375i 0.787063 + 0.616873i \(0.211601\pi\)
−0.787063 + 0.616873i \(0.788399\pi\)
\(192\) −13.8564 −0.0721688
\(193\) −340.126 −1.76231 −0.881155 0.472828i \(-0.843233\pi\)
−0.881155 + 0.472828i \(0.843233\pi\)
\(194\) 252.352i 1.30078i
\(195\) 7.08734i 0.0363453i
\(196\) 93.3653 0.476353
\(197\) −221.673 −1.12524 −0.562621 0.826715i \(-0.690207\pi\)
−0.562621 + 0.826715i \(0.690207\pi\)
\(198\) 9.33535i 0.0471482i
\(199\) 198.065i 0.995303i −0.867377 0.497651i \(-0.834196\pi\)
0.867377 0.497651i \(-0.165804\pi\)
\(200\) 14.1421 0.0707107
\(201\) 136.760i 0.680400i
\(202\) −208.269 −1.03104
\(203\) 11.0075i 0.0542241i
\(204\) 80.5391i 0.394800i
\(205\) 138.883i 0.677478i
\(206\) 83.3752i 0.404734i
\(207\) −43.6356 + 53.4503i −0.210800 + 0.258214i
\(208\) −7.31977 −0.0351912
\(209\) −6.28622 −0.0300776
\(210\) 8.33792 0.0397044
\(211\) −105.845 −0.501636 −0.250818 0.968034i \(-0.580700\pi\)
−0.250818 + 0.968034i \(0.580700\pi\)
\(212\) 67.8668i 0.320127i
\(213\) −192.962 −0.905925
\(214\) 157.255i 0.734838i
\(215\) 171.352 0.796985
\(216\) 14.6969 0.0680414
\(217\) 75.9781i 0.350130i
\(218\) 74.6529i 0.342445i
\(219\) −232.470 −1.06151
\(220\) −9.84032 −0.0447287
\(221\) 42.5455i 0.192514i
\(222\) 23.7112i 0.106807i
\(223\) 230.988 1.03582 0.517910 0.855435i \(-0.326710\pi\)
0.517910 + 0.855435i \(0.326710\pi\)
\(224\) 8.61137i 0.0384436i
\(225\) −15.0000 −0.0666667
\(226\) 35.9382i 0.159019i
\(227\) 146.750i 0.646475i −0.946318 0.323237i \(-0.895229\pi\)
0.946318 0.323237i \(-0.104771\pi\)
\(228\) 9.89659i 0.0434061i
\(229\) 203.857i 0.890203i −0.895480 0.445102i \(-0.853168\pi\)
0.895480 0.445102i \(-0.146832\pi\)
\(230\) 56.3416 + 45.9959i 0.244963 + 0.199982i
\(231\) −5.80166 −0.0251154
\(232\) 20.4520 0.0881553
\(233\) 296.931 1.27438 0.637191 0.770706i \(-0.280096\pi\)
0.637191 + 0.770706i \(0.280096\pi\)
\(234\) 7.76379 0.0331786
\(235\) 38.3405i 0.163151i
\(236\) 70.4328 0.298444
\(237\) 125.407i 0.529144i
\(238\) 50.0528 0.210306
\(239\) −266.458 −1.11488 −0.557442 0.830216i \(-0.688217\pi\)
−0.557442 + 0.830216i \(0.688217\pi\)
\(240\) 15.4919i 0.0645497i
\(241\) 327.615i 1.35940i 0.733490 + 0.679700i \(0.237890\pi\)
−0.733490 + 0.679700i \(0.762110\pi\)
\(242\) −164.273 −0.678813
\(243\) −15.5885 −0.0641500
\(244\) 17.0869i 0.0700284i
\(245\) 104.386i 0.426063i
\(246\) −152.139 −0.618450
\(247\) 5.22796i 0.0211658i
\(248\) −141.168 −0.569226
\(249\) 207.706i 0.834160i
\(250\) 15.8114i 0.0632456i
\(251\) 5.89337i 0.0234796i 0.999931 + 0.0117398i \(0.00373698\pi\)
−0.999931 + 0.0117398i \(0.996263\pi\)
\(252\) 9.13374i 0.0362450i
\(253\) −39.2034 32.0047i −0.154954 0.126501i
\(254\) −142.638 −0.561568
\(255\) −90.0455 −0.353120
\(256\) 16.0000 0.0625000
\(257\) −45.2730 −0.176160 −0.0880798 0.996113i \(-0.528073\pi\)
−0.0880798 + 0.996113i \(0.528073\pi\)
\(258\) 187.706i 0.727544i
\(259\) 14.7359 0.0568952
\(260\) 8.18375i 0.0314760i
\(261\) −21.6926 −0.0831136
\(262\) 40.5228 0.154667
\(263\) 211.508i 0.804215i −0.915593 0.402107i \(-0.868278\pi\)
0.915593 0.402107i \(-0.131722\pi\)
\(264\) 10.7795i 0.0408316i
\(265\) −75.8774 −0.286330
\(266\) −6.15046 −0.0231220
\(267\) 128.055i 0.479606i
\(268\) 157.917i 0.589243i
\(269\) −133.758 −0.497242 −0.248621 0.968601i \(-0.579977\pi\)
−0.248621 + 0.968601i \(0.579977\pi\)
\(270\) 16.4317i 0.0608581i
\(271\) 186.815 0.689353 0.344676 0.938722i \(-0.387989\pi\)
0.344676 + 0.938722i \(0.387989\pi\)
\(272\) 92.9986i 0.341907i
\(273\) 4.82498i 0.0176739i
\(274\) 224.929i 0.820907i
\(275\) 11.0018i 0.0400066i
\(276\) 50.3860 61.7191i 0.182558 0.223620i
\(277\) −128.144 −0.462615 −0.231308 0.972881i \(-0.574300\pi\)
−0.231308 + 0.972881i \(0.574300\pi\)
\(278\) −168.449 −0.605933
\(279\) 149.731 0.536671
\(280\) −9.62781 −0.0343850
\(281\) 183.268i 0.652200i −0.945335 0.326100i \(-0.894265\pi\)
0.945335 0.326100i \(-0.105735\pi\)
\(282\) 41.9999 0.148936
\(283\) 436.731i 1.54322i 0.636097 + 0.771609i \(0.280548\pi\)
−0.636097 + 0.771609i \(0.719452\pi\)
\(284\) 222.813 0.784554
\(285\) 11.0647 0.0388236
\(286\) 5.69438i 0.0199104i
\(287\) 94.5499i 0.329442i
\(288\) −16.9706 −0.0589256
\(289\) −251.546 −0.870401
\(290\) 22.8661i 0.0788485i
\(291\) 309.066i 1.06208i
\(292\) 268.433 0.919291
\(293\) 34.4017i 0.117412i −0.998275 0.0587060i \(-0.981303\pi\)
0.998275 0.0587060i \(-0.0186974\pi\)
\(294\) 114.349 0.388941
\(295\) 78.7463i 0.266937i
\(296\) 27.3793i 0.0924978i
\(297\) 11.4334i 0.0384964i
\(298\) 347.661i 1.16665i
\(299\) 26.6169 32.6037i 0.0890196 0.109042i
\(300\) 17.3205 0.0577350
\(301\) −116.654 −0.387556
\(302\) −296.206 −0.980815
\(303\) −255.077 −0.841838
\(304\) 11.4276i 0.0375908i
\(305\) −19.1038 −0.0626353
\(306\) 98.6399i 0.322353i
\(307\) −263.872 −0.859518 −0.429759 0.902944i \(-0.641401\pi\)
−0.429759 + 0.902944i \(0.641401\pi\)
\(308\) 6.69918 0.0217506
\(309\) 102.113i 0.330464i
\(310\) 157.831i 0.509131i
\(311\) 12.9685 0.0416992 0.0208496 0.999783i \(-0.493363\pi\)
0.0208496 + 0.999783i \(0.493363\pi\)
\(312\) −8.96485 −0.0287335
\(313\) 71.7752i 0.229314i −0.993405 0.114657i \(-0.963423\pi\)
0.993405 0.114657i \(-0.0365769\pi\)
\(314\) 299.199i 0.952864i
\(315\) 10.2118 0.0324185
\(316\) 144.808i 0.458252i
\(317\) 193.888 0.611633 0.305816 0.952090i \(-0.401071\pi\)
0.305816 + 0.952090i \(0.401071\pi\)
\(318\) 83.1196i 0.261382i
\(319\) 15.9106i 0.0498764i
\(320\) 17.8885i 0.0559017i
\(321\) 192.598i 0.599993i
\(322\) −38.3567 31.3135i −0.119120 0.0972469i
\(323\) 66.4219 0.205641
\(324\) 18.0000 0.0555556
\(325\) 9.14971 0.0281530
\(326\) 20.0103 0.0613812
\(327\) 91.4308i 0.279605i
\(328\) 175.675 0.535593
\(329\) 26.1018i 0.0793367i
\(330\) −12.0519 −0.0365209
\(331\) 393.325 1.18829 0.594147 0.804356i \(-0.297490\pi\)
0.594147 + 0.804356i \(0.297490\pi\)
\(332\) 239.838i 0.722403i
\(333\) 29.0402i 0.0872078i
\(334\) −73.6333 −0.220459
\(335\) 176.557 0.527035
\(336\) 10.5467i 0.0313891i
\(337\) 39.3542i 0.116778i −0.998294 0.0583891i \(-0.981404\pi\)
0.998294 0.0583891i \(-0.0185964\pi\)
\(338\) 234.266 0.693096
\(339\) 44.0151i 0.129838i
\(340\) 103.976 0.305811
\(341\) 109.821i 0.322056i
\(342\) 12.1208i 0.0354409i
\(343\) 145.657i 0.424655i
\(344\) 216.745i 0.630072i
\(345\) 69.0041 + 56.3333i 0.200012 + 0.163285i
\(346\) 310.075 0.896170
\(347\) 309.497 0.891922 0.445961 0.895052i \(-0.352862\pi\)
0.445961 + 0.895052i \(0.352862\pi\)
\(348\) 25.0485 0.0719785
\(349\) −328.191 −0.940375 −0.470188 0.882567i \(-0.655814\pi\)
−0.470188 + 0.882567i \(0.655814\pi\)
\(350\) 10.7642i 0.0307549i
\(351\) 9.50866 0.0270902
\(352\) 12.4471i 0.0353612i
\(353\) −111.495 −0.315851 −0.157925 0.987451i \(-0.550481\pi\)
−0.157925 + 0.987451i \(0.550481\pi\)
\(354\) 86.2623 0.243679
\(355\) 249.113i 0.701726i
\(356\) 147.865i 0.415351i
\(357\) 61.3020 0.171714
\(358\) 119.291 0.333215
\(359\) 516.911i 1.43986i −0.694045 0.719932i \(-0.744173\pi\)
0.694045 0.719932i \(-0.255827\pi\)
\(360\) 18.9737i 0.0527046i
\(361\) 352.838 0.977391
\(362\) 385.564i 1.06509i
\(363\) −201.192 −0.554249
\(364\) 5.57140i 0.0153061i
\(365\) 300.117i 0.822239i
\(366\) 20.9271i 0.0571779i
\(367\) 32.4661i 0.0884635i −0.999021 0.0442318i \(-0.985916\pi\)
0.999021 0.0442318i \(-0.0140840\pi\)
\(368\) −58.1808 + 71.2671i −0.158100 + 0.193661i
\(369\) −186.331 −0.504962
\(370\) 30.6110 0.0827325
\(371\) 51.6565 0.139236
\(372\) −172.895 −0.464771
\(373\) 153.444i 0.411377i 0.978617 + 0.205689i \(0.0659434\pi\)
−0.978617 + 0.205689i \(0.934057\pi\)
\(374\) −72.3478 −0.193443
\(375\) 19.3649i 0.0516398i
\(376\) −48.4973 −0.128982
\(377\) 13.2321 0.0350984
\(378\) 11.1865i 0.0295939i
\(379\) 597.537i 1.57662i −0.615281 0.788308i \(-0.710958\pi\)
0.615281 0.788308i \(-0.289042\pi\)
\(380\) −12.7764 −0.0336222
\(381\) −174.696 −0.458518
\(382\) 333.253i 0.872390i
\(383\) 309.730i 0.808694i 0.914606 + 0.404347i \(0.132501\pi\)
−0.914606 + 0.404347i \(0.867499\pi\)
\(384\) 19.5959 0.0510310
\(385\) 7.48991i 0.0194543i
\(386\) 481.010 1.24614
\(387\) 229.892i 0.594037i
\(388\) 356.879i 0.919791i
\(389\) 295.042i 0.758461i −0.925302 0.379231i \(-0.876189\pi\)
0.925302 0.379231i \(-0.123811\pi\)
\(390\) 10.0230i 0.0257000i
\(391\) 414.234 + 338.171i 1.05942 + 0.864886i
\(392\) −132.038 −0.336833
\(393\) 49.6301 0.126285
\(394\) 313.492 0.795666
\(395\) 161.900 0.409873
\(396\) 13.2022i 0.0333388i
\(397\) 45.4461 0.114474 0.0572368 0.998361i \(-0.481771\pi\)
0.0572368 + 0.998361i \(0.481771\pi\)
\(398\) 280.107i 0.703785i
\(399\) −7.53274 −0.0188791
\(400\) −20.0000 −0.0500000
\(401\) 51.4990i 0.128427i 0.997936 + 0.0642133i \(0.0204538\pi\)
−0.997936 + 0.0642133i \(0.979546\pi\)
\(402\) 193.408i 0.481115i
\(403\) −91.3332 −0.226633
\(404\) 294.537 0.729053
\(405\) 20.1246i 0.0496904i
\(406\) 15.5669i 0.0383422i
\(407\) −21.2996 −0.0523333
\(408\) 113.900i 0.279166i
\(409\) −507.527 −1.24090 −0.620449 0.784247i \(-0.713050\pi\)
−0.620449 + 0.784247i \(0.713050\pi\)
\(410\) 196.410i 0.479049i
\(411\) 275.480i 0.670268i
\(412\) 117.910i 0.286190i
\(413\) 53.6096i 0.129805i
\(414\) 61.7100 75.5902i 0.149058 0.182585i
\(415\) 268.147 0.646137
\(416\) 10.3517 0.0248839
\(417\) −206.307 −0.494742
\(418\) 8.89005 0.0212681
\(419\) 471.677i 1.12572i −0.826552 0.562861i \(-0.809701\pi\)
0.826552 0.562861i \(-0.190299\pi\)
\(420\) −11.7916 −0.0280753
\(421\) 760.247i 1.80581i 0.429838 + 0.902906i \(0.358570\pi\)
−0.429838 + 0.902906i \(0.641430\pi\)
\(422\) 149.688 0.354711
\(423\) 51.4391 0.121606
\(424\) 95.9782i 0.226364i
\(425\) 116.248i 0.273525i
\(426\) 272.889 0.640585
\(427\) 13.0056 0.0304581
\(428\) 222.393i 0.519609i
\(429\) 6.97417i 0.0162568i
\(430\) −242.328 −0.563553
\(431\) 601.309i 1.39515i −0.716512 0.697575i \(-0.754262\pi\)
0.716512 0.697575i \(-0.245738\pi\)
\(432\) −20.7846 −0.0481125
\(433\) 466.438i 1.07722i −0.842554 0.538612i \(-0.818949\pi\)
0.842554 0.538612i \(-0.181051\pi\)
\(434\) 107.449i 0.247579i
\(435\) 28.0051i 0.0643795i
\(436\) 105.575i 0.242145i
\(437\) −50.9007 41.5542i −0.116478 0.0950896i
\(438\) 328.762 0.750598
\(439\) −294.320 −0.670432 −0.335216 0.942141i \(-0.608809\pi\)
−0.335216 + 0.942141i \(0.608809\pi\)
\(440\) 13.9163 0.0316280
\(441\) 140.048 0.317569
\(442\) 60.1684i 0.136128i
\(443\) 642.170 1.44959 0.724797 0.688962i \(-0.241934\pi\)
0.724797 + 0.688962i \(0.241934\pi\)
\(444\) 33.5327i 0.0755241i
\(445\) −165.318 −0.371501
\(446\) −326.666 −0.732435
\(447\) 425.796i 0.952564i
\(448\) 12.1783i 0.0271837i
\(449\) 663.924 1.47867 0.739337 0.673336i \(-0.235139\pi\)
0.739337 + 0.673336i \(0.235139\pi\)
\(450\) 21.2132 0.0471405
\(451\) 136.665i 0.303027i
\(452\) 50.8243i 0.112443i
\(453\) −362.777 −0.800832
\(454\) 207.536i 0.457127i
\(455\) −6.22902 −0.0136902
\(456\) 13.9959i 0.0306928i
\(457\) 22.1190i 0.0484005i 0.999707 + 0.0242002i \(0.00770393\pi\)
−0.999707 + 0.0242002i \(0.992296\pi\)
\(458\) 288.297i 0.629469i
\(459\) 120.809i 0.263200i
\(460\) −79.6790 65.0481i −0.173215 0.141409i
\(461\) −332.992 −0.722325 −0.361162 0.932503i \(-0.617620\pi\)
−0.361162 + 0.932503i \(0.617620\pi\)
\(462\) 8.20479 0.0177593
\(463\) −58.4021 −0.126139 −0.0630693 0.998009i \(-0.520089\pi\)
−0.0630693 + 0.998009i \(0.520089\pi\)
\(464\) −28.9235 −0.0623352
\(465\) 193.302i 0.415704i
\(466\) −419.924 −0.901124
\(467\) 609.288i 1.30469i 0.757924 + 0.652343i \(0.226214\pi\)
−0.757924 + 0.652343i \(0.773786\pi\)
\(468\) −10.9797 −0.0234608
\(469\) −120.198 −0.256285
\(470\) 54.2216i 0.115365i
\(471\) 366.443i 0.778010i
\(472\) −99.6071 −0.211032
\(473\) 168.616 0.356481
\(474\) 177.353i 0.374161i
\(475\) 14.2845i 0.0300726i
\(476\) −70.7854 −0.148709
\(477\) 101.800i 0.213418i
\(478\) 376.828 0.788343
\(479\) 200.294i 0.418150i 0.977900 + 0.209075i \(0.0670453\pi\)
−0.977900 + 0.209075i \(0.932955\pi\)
\(480\) 21.9089i 0.0456435i
\(481\) 17.7140i 0.0368273i
\(482\) 463.318i 0.961241i
\(483\) −46.9772 38.3511i −0.0972613 0.0794018i
\(484\) 232.317 0.479993
\(485\) 399.003 0.822686
\(486\) 22.0454 0.0453609
\(487\) 136.133 0.279534 0.139767 0.990184i \(-0.455365\pi\)
0.139767 + 0.990184i \(0.455365\pi\)
\(488\) 24.1646i 0.0495175i
\(489\) 24.5075 0.0501175
\(490\) 147.623i 0.301272i
\(491\) −217.319 −0.442604 −0.221302 0.975205i \(-0.571031\pi\)
−0.221302 + 0.975205i \(0.571031\pi\)
\(492\) 215.156 0.437310
\(493\) 168.115i 0.341005i
\(494\) 7.39345i 0.0149665i
\(495\) −14.7605 −0.0298192
\(496\) 199.642 0.402503
\(497\) 169.593i 0.341234i
\(498\) 293.740i 0.589840i
\(499\) −620.672 −1.24383 −0.621916 0.783084i \(-0.713646\pi\)
−0.621916 + 0.783084i \(0.713646\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) −90.1821 −0.180004
\(502\) 8.33449i 0.0166026i
\(503\) 165.943i 0.329906i −0.986301 0.164953i \(-0.947253\pi\)
0.986301 0.164953i \(-0.0527473\pi\)
\(504\) 12.9171i 0.0256291i
\(505\) 329.303i 0.652085i
\(506\) 55.4419 + 45.2615i 0.109569 + 0.0894496i
\(507\) 286.916 0.565910
\(508\) 201.721 0.397089
\(509\) −376.623 −0.739928 −0.369964 0.929046i \(-0.620630\pi\)
−0.369964 + 0.929046i \(0.620630\pi\)
\(510\) 127.344 0.249693
\(511\) 204.316i 0.399836i
\(512\) −22.6274 −0.0441942
\(513\) 14.8449i 0.0289374i
\(514\) 64.0257 0.124564
\(515\) 131.828 0.255976
\(516\) 265.457i 0.514452i
\(517\) 37.7283i 0.0729754i
\(518\) −20.8397 −0.0402310
\(519\) 379.762 0.731720
\(520\) 11.5736i 0.0222569i
\(521\) 675.726i 1.29698i −0.761223 0.648490i \(-0.775401\pi\)
0.761223 0.648490i \(-0.224599\pi\)
\(522\) 30.6780 0.0587702
\(523\) 53.9295i 0.103116i −0.998670 0.0515578i \(-0.983581\pi\)
0.998670 0.0515578i \(-0.0164186\pi\)
\(524\) −57.3079 −0.109366
\(525\) 13.1834i 0.0251113i
\(526\) 299.118i 0.568666i
\(527\) 1160.40i 2.20190i
\(528\) 15.2446i 0.0288723i
\(529\) −105.875 518.297i −0.200141 0.979767i
\(530\) 107.307 0.202466
\(531\) 105.649 0.198963
\(532\) 8.69806 0.0163497
\(533\) 113.658 0.213243
\(534\) 181.097i 0.339132i
\(535\) 248.643 0.464752
\(536\) 223.329i 0.416658i
\(537\) 146.101 0.272069
\(538\) 189.163 0.351604
\(539\) 102.719i 0.190573i
\(540\) 23.2379i 0.0430331i
\(541\) 32.6654 0.0603797 0.0301899 0.999544i \(-0.490389\pi\)
0.0301899 + 0.999544i \(0.490389\pi\)
\(542\) −264.196 −0.487446
\(543\) 472.217i 0.869645i
\(544\) 131.520i 0.241764i
\(545\) 118.037 0.216581
\(546\) 6.82355i 0.0124973i
\(547\) 125.227 0.228934 0.114467 0.993427i \(-0.463484\pi\)
0.114467 + 0.993427i \(0.463484\pi\)
\(548\) 318.097i 0.580469i
\(549\) 25.6304i 0.0466856i
\(550\) 15.5589i 0.0282889i
\(551\) 20.6579i 0.0374917i
\(552\) −71.2566 + 87.2840i −0.129088 + 0.158123i
\(553\) −110.220 −0.199312
\(554\) 181.224 0.327118
\(555\) 37.4907 0.0675508
\(556\) 238.223 0.428459
\(557\) 18.9083i 0.0339466i −0.999856 0.0169733i \(-0.994597\pi\)
0.999856 0.0169733i \(-0.00540303\pi\)
\(558\) −211.752 −0.379484
\(559\) 140.230i 0.250859i
\(560\) 13.6158 0.0243139
\(561\) −88.6077 −0.157946
\(562\) 259.181i 0.461175i
\(563\) 663.769i 1.17899i 0.807774 + 0.589493i \(0.200672\pi\)
−0.807774 + 0.589493i \(0.799328\pi\)
\(564\) −59.3968 −0.105313
\(565\) −56.8233 −0.100572
\(566\) 617.630i 1.09122i
\(567\) 13.7006i 0.0241633i
\(568\) −315.105 −0.554763
\(569\) 491.805i 0.864332i 0.901794 + 0.432166i \(0.142251\pi\)
−0.901794 + 0.432166i \(0.857749\pi\)
\(570\) −15.6479 −0.0274524
\(571\) 880.062i 1.54126i 0.637280 + 0.770632i \(0.280060\pi\)
−0.637280 + 0.770632i \(0.719940\pi\)
\(572\) 8.05307i 0.0140788i
\(573\) 408.150i 0.712303i
\(574\) 133.714i 0.232951i
\(575\) 72.7260 89.0839i 0.126480 0.154928i
\(576\) 24.0000 0.0416667
\(577\) −4.02697 −0.00697914 −0.00348957 0.999994i \(-0.501111\pi\)
−0.00348957 + 0.999994i \(0.501111\pi\)
\(578\) 355.740 0.615467
\(579\) 589.115 1.01747
\(580\) 32.3375i 0.0557543i
\(581\) −182.551 −0.314202
\(582\) 437.086i 0.751006i
\(583\) −74.6658 −0.128072
\(584\) −379.622 −0.650037
\(585\) 12.2756i 0.0209840i
\(586\) 48.6513i 0.0830228i
\(587\) −313.115 −0.533415 −0.266708 0.963778i \(-0.585936\pi\)
−0.266708 + 0.963778i \(0.585936\pi\)
\(588\) −161.713 −0.275023
\(589\) 142.589i 0.242087i
\(590\) 111.364i 0.188753i
\(591\) 383.948 0.649659
\(592\) 38.7202i 0.0654058i
\(593\) 643.656 1.08542 0.542712 0.839919i \(-0.317398\pi\)
0.542712 + 0.839919i \(0.317398\pi\)
\(594\) 16.1693i 0.0272210i
\(595\) 79.1405i 0.133009i
\(596\) 491.667i 0.824945i
\(597\) 343.059i 0.574638i
\(598\) −37.6419 + 46.1085i −0.0629464 + 0.0771046i
\(599\) 482.724 0.805884 0.402942 0.915226i \(-0.367988\pi\)
0.402942 + 0.915226i \(0.367988\pi\)
\(600\) −24.4949 −0.0408248
\(601\) −510.476 −0.849377 −0.424689 0.905340i \(-0.639616\pi\)
−0.424689 + 0.905340i \(0.639616\pi\)
\(602\) 164.974 0.274043
\(603\) 236.876i 0.392829i
\(604\) 418.899 0.693541
\(605\) 259.738i 0.429319i
\(606\) 360.733 0.595269
\(607\) −719.184 −1.18482 −0.592409 0.805638i \(-0.701823\pi\)
−0.592409 + 0.805638i \(0.701823\pi\)
\(608\) 16.1611i 0.0265807i
\(609\) 19.0655i 0.0313063i
\(610\) 27.0168 0.0442898
\(611\) −31.3769 −0.0513533
\(612\) 139.498i 0.227938i
\(613\) 672.054i 1.09634i 0.836368 + 0.548168i \(0.184675\pi\)
−0.836368 + 0.548168i \(0.815325\pi\)
\(614\) 373.171 0.607771
\(615\) 240.552i 0.391142i
\(616\) −9.47407 −0.0153800
\(617\) 295.731i 0.479305i 0.970859 + 0.239653i \(0.0770336\pi\)
−0.970859 + 0.239653i \(0.922966\pi\)
\(618\) 144.410i 0.233673i
\(619\) 823.442i 1.33028i −0.746720 0.665139i \(-0.768372\pi\)
0.746720 0.665139i \(-0.231628\pi\)
\(620\) 223.206i 0.360010i
\(621\) 75.5790 92.5787i 0.121705 0.149080i
\(622\) −18.3402 −0.0294858
\(623\) 112.547 0.180653
\(624\) 12.6782 0.0203176
\(625\) 25.0000 0.0400000
\(626\) 101.505i 0.162149i
\(627\) 10.8880 0.0173653
\(628\) 423.132i 0.673777i
\(629\) 225.058 0.357803
\(630\) −14.4417 −0.0229233
\(631\) 471.460i 0.747163i 0.927597 + 0.373582i \(0.121870\pi\)
−0.927597 + 0.373582i \(0.878130\pi\)
\(632\) 204.789i 0.324033i
\(633\) 183.329 0.289620
\(634\) −274.199 −0.432490
\(635\) 225.531i 0.355167i
\(636\) 117.549i 0.184825i
\(637\) −85.4265 −0.134108
\(638\) 22.5009i 0.0352679i
\(639\) 334.220 0.523036
\(640\) 25.2982i 0.0395285i
\(641\) 1114.03i 1.73796i −0.494850 0.868979i \(-0.664777\pi\)
0.494850 0.868979i \(-0.335223\pi\)
\(642\) 272.374i 0.424259i
\(643\) 182.160i 0.283298i −0.989917 0.141649i \(-0.954760\pi\)
0.989917 0.141649i \(-0.0452404\pi\)
\(644\) 54.2446 + 44.2840i 0.0842307 + 0.0687640i
\(645\) −296.790 −0.460139
\(646\) −93.9348 −0.145410
\(647\) 231.496 0.357799 0.178899 0.983867i \(-0.442746\pi\)
0.178899 + 0.983867i \(0.442746\pi\)
\(648\) −25.4558 −0.0392837
\(649\) 77.4889i 0.119397i
\(650\) −12.9396 −0.0199071
\(651\) 131.598i 0.202147i
\(652\) −28.2988 −0.0434030
\(653\) 961.708 1.47275 0.736377 0.676572i \(-0.236535\pi\)
0.736377 + 0.676572i \(0.236535\pi\)
\(654\) 129.303i 0.197710i
\(655\) 64.0722i 0.0978201i
\(656\) −248.441 −0.378721
\(657\) 402.650 0.612861
\(658\) 36.9135i 0.0560995i
\(659\) 482.196i 0.731709i 0.930672 + 0.365854i \(0.119223\pi\)
−0.930672 + 0.365854i \(0.880777\pi\)
\(660\) 17.0439 0.0258241
\(661\) 514.781i 0.778792i −0.921070 0.389396i \(-0.872684\pi\)
0.921070 0.389396i \(-0.127316\pi\)
\(662\) −556.246 −0.840251
\(663\) 73.6910i 0.111148i
\(664\) 339.182i 0.510816i
\(665\) 9.72473i 0.0146236i
\(666\) 41.0690i 0.0616652i
\(667\) 105.175 128.831i 0.157683 0.193150i
\(668\) 104.133 0.155888
\(669\) −400.083 −0.598031
\(670\) −249.689 −0.372670
\(671\) −18.7987 −0.0280160
\(672\) 14.9153i 0.0221954i
\(673\) −1100.79 −1.63565 −0.817824 0.575468i \(-0.804820\pi\)
−0.817824 + 0.575468i \(0.804820\pi\)
\(674\) 55.6553i 0.0825746i
\(675\) 25.9808 0.0384900
\(676\) −331.303 −0.490093
\(677\) 155.504i 0.229695i −0.993383 0.114848i \(-0.963362\pi\)
0.993383 0.114848i \(-0.0366380\pi\)
\(678\) 62.2468i 0.0918094i
\(679\) −271.637 −0.400054
\(680\) −147.044 −0.216241
\(681\) 254.178i 0.373242i
\(682\) 155.310i 0.227728i
\(683\) −1077.79 −1.57803 −0.789014 0.614376i \(-0.789408\pi\)
−0.789014 + 0.614376i \(0.789408\pi\)
\(684\) 17.1414i 0.0250605i
\(685\) −355.643 −0.519187
\(686\) 205.990i 0.300276i
\(687\) 353.090i 0.513959i
\(688\) 306.523i 0.445528i
\(689\) 62.0962i 0.0901251i
\(690\) −97.5865 79.6673i −0.141430 0.115460i
\(691\) −884.748 −1.28039 −0.640194 0.768214i \(-0.721146\pi\)
−0.640194 + 0.768214i \(0.721146\pi\)
\(692\) −438.512 −0.633688
\(693\) 10.0488 0.0145004
\(694\) −437.695 −0.630684
\(695\) 266.342i 0.383225i
\(696\) −35.4239 −0.0508965
\(697\) 1444.04i 2.07180i
\(698\) 464.132 0.664946
\(699\) −514.299 −0.735765
\(700\) 15.2229i 0.0217470i
\(701\) 666.703i 0.951074i −0.879696 0.475537i \(-0.842254\pi\)
0.879696 0.475537i \(-0.157746\pi\)
\(702\) −13.4473 −0.0191557
\(703\) −27.6550 −0.0393385
\(704\) 17.6029i 0.0250041i
\(705\) 66.4076i 0.0941952i
\(706\) 157.678 0.223340
\(707\) 224.186i 0.317094i
\(708\) −121.993 −0.172307
\(709\) 967.418i 1.36448i 0.731127 + 0.682241i \(0.238995\pi\)
−0.731127 + 0.682241i \(0.761005\pi\)
\(710\) 352.299i 0.496195i
\(711\) 217.212i 0.305502i
\(712\) 209.112i 0.293697i
\(713\) −725.957 + 889.242i −1.01817 + 1.24718i
\(714\) −86.6941 −0.121420
\(715\) 9.00361 0.0125925
\(716\) −168.703 −0.235619
\(717\) 461.518 0.643679
\(718\) 731.023i 1.01814i
\(719\) −216.266 −0.300787 −0.150393 0.988626i \(-0.548054\pi\)
−0.150393 + 0.988626i \(0.548054\pi\)
\(720\) 26.8328i 0.0372678i
\(721\) −89.7469 −0.124476
\(722\) −498.988 −0.691120
\(723\) 567.447i 0.784850i
\(724\) 545.269i 0.753134i
\(725\) 36.1544 0.0498681
\(726\) 284.529 0.391913
\(727\) 113.587i 0.156240i −0.996944 0.0781200i \(-0.975108\pi\)
0.996944 0.0781200i \(-0.0248917\pi\)
\(728\) 7.87916i 0.0108230i
\(729\) 27.0000 0.0370370
\(730\) 424.430i 0.581411i
\(731\) −1781.64 −2.43726
\(732\) 29.5954i 0.0404309i
\(733\) 104.468i 0.142522i −0.997458 0.0712608i \(-0.977298\pi\)
0.997458 0.0712608i \(-0.0227023\pi\)
\(734\) 45.9140i 0.0625531i
\(735\) 180.801i 0.245988i
\(736\) 82.2800 100.787i 0.111794 0.136939i
\(737\) 173.738 0.235736
\(738\) 263.512 0.357062
\(739\) 828.795 1.12151 0.560755 0.827982i \(-0.310511\pi\)
0.560755 + 0.827982i \(0.310511\pi\)
\(740\) −43.2905 −0.0585007
\(741\) 9.05510i 0.0122201i
\(742\) −73.0533 −0.0984546
\(743\) 1067.78i 1.43712i 0.695465 + 0.718560i \(0.255198\pi\)
−0.695465 + 0.718560i \(0.744802\pi\)
\(744\) 244.510 0.328643
\(745\) 549.700 0.737853
\(746\) 217.002i 0.290888i
\(747\) 359.757i 0.481602i
\(748\) 102.315 0.136785
\(749\) −169.273 −0.225999
\(750\) 27.3861i 0.0365148i
\(751\) 116.437i 0.155043i −0.996991 0.0775213i \(-0.975299\pi\)
0.996991 0.0775213i \(-0.0247006\pi\)
\(752\) 68.5855 0.0912042
\(753\) 10.2076i 0.0135559i
\(754\) −18.7130 −0.0248183
\(755\) 468.343i 0.620322i
\(756\) 15.8201i 0.0209261i
\(757\) 893.537i 1.18037i 0.807269 + 0.590183i \(0.200944\pi\)
−0.807269 + 0.590183i \(0.799056\pi\)
\(758\) 845.045i 1.11484i
\(759\) 67.9022 + 55.4338i 0.0894627 + 0.0730353i
\(760\) 18.0686 0.0237745
\(761\) −80.0115 −0.105140 −0.0525700 0.998617i \(-0.516741\pi\)
−0.0525700 + 0.998617i \(0.516741\pi\)
\(762\) 247.057 0.324221
\(763\) −80.3580 −0.105318
\(764\) 471.291i 0.616873i
\(765\) 155.963 0.203874
\(766\) 438.024i 0.571833i
\(767\) −64.4440 −0.0840209
\(768\) −27.7128 −0.0360844
\(769\) 890.267i 1.15769i 0.815436 + 0.578847i \(0.196497\pi\)
−0.815436 + 0.578847i \(0.803503\pi\)
\(770\) 10.5923i 0.0137563i
\(771\) 78.4151 0.101706
\(772\) −680.251 −0.881155
\(773\) 619.222i 0.801063i −0.916283 0.400531i \(-0.868826\pi\)
0.916283 0.400531i \(-0.131174\pi\)
\(774\) 325.117i 0.420048i
\(775\) −249.552 −0.322003
\(776\) 504.703i 0.650391i
\(777\) −25.5233 −0.0328485
\(778\) 417.252i 0.536313i
\(779\) 177.443i 0.227783i
\(780\) 14.1747i 0.0181727i
\(781\) 245.135i 0.313873i
\(782\) −585.815 478.245i −0.749124 0.611567i
\(783\) 37.5728 0.0479856
\(784\) 186.731 0.238177
\(785\) −473.076 −0.602644
\(786\) −70.1875 −0.0892971
\(787\) 375.043i 0.476548i −0.971198 0.238274i \(-0.923418\pi\)
0.971198 0.238274i \(-0.0765816\pi\)
\(788\) −443.345 −0.562621
\(789\) 366.343i 0.464314i
\(790\) −228.961 −0.289824
\(791\) 38.6846 0.0489060
\(792\)