Properties

Label 690.3.c.a.91.18
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 91.18
Character \(\chi\) \(=\) 690.91
Dual form 690.3.c.a.91.23

$q$-expansion

\(f(q)\) \(=\) \(q+1.41421 q^{2} -1.73205 q^{3} +2.00000 q^{4} -2.23607i q^{5} -2.44949 q^{6} -7.96402i q^{7} +2.82843 q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+1.41421 q^{2} -1.73205 q^{3} +2.00000 q^{4} -2.23607i q^{5} -2.44949 q^{6} -7.96402i q^{7} +2.82843 q^{8} +3.00000 q^{9} -3.16228i q^{10} -13.6667i q^{11} -3.46410 q^{12} -14.0318 q^{13} -11.2628i q^{14} +3.87298i q^{15} +4.00000 q^{16} +17.2668i q^{17} +4.24264 q^{18} +26.4661i q^{19} -4.47214i q^{20} +13.7941i q^{21} -19.3277i q^{22} +(-11.7666 - 19.7623i) q^{23} -4.89898 q^{24} -5.00000 q^{25} -19.8440 q^{26} -5.19615 q^{27} -15.9280i q^{28} -54.4984 q^{29} +5.47723i q^{30} -22.1628 q^{31} +5.65685 q^{32} +23.6715i q^{33} +24.4189i q^{34} -17.8081 q^{35} +6.00000 q^{36} -32.2493i q^{37} +37.4287i q^{38} +24.3038 q^{39} -6.32456i q^{40} +9.59193 q^{41} +19.5078i q^{42} -65.3706i q^{43} -27.3335i q^{44} -6.70820i q^{45} +(-16.6405 - 27.9481i) q^{46} +82.5547 q^{47} -6.92820 q^{48} -14.4257 q^{49} -7.07107 q^{50} -29.9070i q^{51} -28.0636 q^{52} -21.1000i q^{53} -7.34847 q^{54} -30.5598 q^{55} -22.5257i q^{56} -45.8406i q^{57} -77.0724 q^{58} -105.537 q^{59} +7.74597i q^{60} -33.4803i q^{61} -31.3429 q^{62} -23.8921i q^{63} +8.00000 q^{64} +31.3760i q^{65} +33.4765i q^{66} +34.9712i q^{67} +34.5336i q^{68} +(20.3804 + 34.2292i) q^{69} -25.1845 q^{70} +65.1127 q^{71} +8.48528 q^{72} -126.274 q^{73} -45.6075i q^{74} +8.66025 q^{75} +52.9321i q^{76} -108.842 q^{77} +34.3707 q^{78} -45.0370i q^{79} -8.94427i q^{80} +9.00000 q^{81} +13.5650 q^{82} -10.3487i q^{83} +27.5882i q^{84} +38.6097 q^{85} -92.4480i q^{86} +94.3941 q^{87} -38.6554i q^{88} +20.8576i q^{89} -9.48683i q^{90} +111.750i q^{91} +(-23.5332 - 39.5245i) q^{92} +38.3871 q^{93} +116.750 q^{94} +59.1799 q^{95} -9.79796 q^{96} -146.441i q^{97} -20.4010 q^{98} -41.0002i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 64q^{4} + 96q^{9} + O(q^{10}) \) \( 32q + 64q^{4} + 96q^{9} - 48q^{13} + 128q^{16} - 80q^{23} - 160q^{25} + 120q^{29} + 248q^{31} - 120q^{35} + 192q^{36} - 48q^{39} + 72q^{41} + 160q^{46} + 400q^{47} - 344q^{49} - 96q^{52} - 256q^{58} + 120q^{59} + 160q^{62} + 256q^{64} + 192q^{69} + 104q^{71} + 16q^{73} + 240q^{77} + 192q^{78} + 288q^{81} + 64q^{82} - 120q^{85} + 144q^{87} - 160q^{92} - 192q^{93} + 96q^{94} - 160q^{95} + 64q^{98} + O(q^{100}) \)

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
\(7\) 7.96402i 1.13772i −0.822435 0.568859i \(-0.807385\pi\)
0.822435 0.568859i \(-0.192615\pi\)
\(8\) 2.82843 0.353553
\(9\) 3.00000 0.333333
\(10\) 3.16228i 0.316228i
\(11\) 13.6667i 1.24243i −0.783640 0.621216i \(-0.786639\pi\)
0.783640 0.621216i \(-0.213361\pi\)
\(12\) −3.46410 −0.288675
\(13\) −14.0318 −1.07937 −0.539684 0.841867i \(-0.681456\pi\)
−0.539684 + 0.841867i \(0.681456\pi\)
\(14\) 11.2628i 0.804488i
\(15\) 3.87298i 0.258199i
\(16\) 4.00000 0.250000
\(17\) 17.2668i 1.01569i 0.861447 + 0.507847i \(0.169558\pi\)
−0.861447 + 0.507847i \(0.830442\pi\)
\(18\) 4.24264 0.235702
\(19\) 26.4661i 1.39295i 0.717581 + 0.696475i \(0.245250\pi\)
−0.717581 + 0.696475i \(0.754750\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 13.7941i 0.656862i
\(22\) 19.3277i 0.878532i
\(23\) −11.7666 19.7623i −0.511592 0.859229i
\(24\) −4.89898 −0.204124
\(25\) −5.00000 −0.200000
\(26\) −19.8440 −0.763229
\(27\) −5.19615 −0.192450
\(28\) 15.9280i 0.568859i
\(29\) −54.4984 −1.87926 −0.939628 0.342197i \(-0.888829\pi\)
−0.939628 + 0.342197i \(0.888829\pi\)
\(30\) 5.47723i 0.182574i
\(31\) −22.1628 −0.714929 −0.357465 0.933927i \(-0.616359\pi\)
−0.357465 + 0.933927i \(0.616359\pi\)
\(32\) 5.65685 0.176777
\(33\) 23.6715i 0.717318i
\(34\) 24.4189i 0.718204i
\(35\) −17.8081 −0.508803
\(36\) 6.00000 0.166667
\(37\) 32.2493i 0.871604i −0.900043 0.435802i \(-0.856465\pi\)
0.900043 0.435802i \(-0.143535\pi\)
\(38\) 37.4287i 0.984965i
\(39\) 24.3038 0.623174
\(40\) 6.32456i 0.158114i
\(41\) 9.59193 0.233949 0.116975 0.993135i \(-0.462680\pi\)
0.116975 + 0.993135i \(0.462680\pi\)
\(42\) 19.5078i 0.464471i
\(43\) 65.3706i 1.52025i −0.649778 0.760124i \(-0.725138\pi\)
0.649778 0.760124i \(-0.274862\pi\)
\(44\) 27.3335i 0.621216i
\(45\) 6.70820i 0.149071i
\(46\) −16.6405 27.9481i −0.361750 0.607566i
\(47\) 82.5547 1.75648 0.878242 0.478217i \(-0.158717\pi\)
0.878242 + 0.478217i \(0.158717\pi\)
\(48\) −6.92820 −0.144338
\(49\) −14.4257 −0.294402
\(50\) −7.07107 −0.141421
\(51\) 29.9070i 0.586411i
\(52\) −28.0636 −0.539684
\(53\) 21.1000i 0.398113i −0.979988 0.199056i \(-0.936212\pi\)
0.979988 0.199056i \(-0.0637877\pi\)
\(54\) −7.34847 −0.136083
\(55\) −30.5598 −0.555632
\(56\) 22.5257i 0.402244i
\(57\) 45.8406i 0.804221i
\(58\) −77.0724 −1.32883
\(59\) −105.537 −1.78877 −0.894385 0.447299i \(-0.852386\pi\)
−0.894385 + 0.447299i \(0.852386\pi\)
\(60\) 7.74597i 0.129099i
\(61\) 33.4803i 0.548858i −0.961607 0.274429i \(-0.911511\pi\)
0.961607 0.274429i \(-0.0884888\pi\)
\(62\) −31.3429 −0.505531
\(63\) 23.8921i 0.379239i
\(64\) 8.00000 0.125000
\(65\) 31.3760i 0.482708i
\(66\) 33.4765i 0.507220i
\(67\) 34.9712i 0.521958i 0.965344 + 0.260979i \(0.0840453\pi\)
−0.965344 + 0.260979i \(0.915955\pi\)
\(68\) 34.5336i 0.507847i
\(69\) 20.3804 + 34.2292i 0.295368 + 0.496076i
\(70\) −25.1845 −0.359778
\(71\) 65.1127 0.917080 0.458540 0.888674i \(-0.348373\pi\)
0.458540 + 0.888674i \(0.348373\pi\)
\(72\) 8.48528 0.117851
\(73\) −126.274 −1.72978 −0.864891 0.501959i \(-0.832613\pi\)
−0.864891 + 0.501959i \(0.832613\pi\)
\(74\) 45.6075i 0.616317i
\(75\) 8.66025 0.115470
\(76\) 52.9321i 0.696475i
\(77\) −108.842 −1.41354
\(78\) 34.3707 0.440651
\(79\) 45.0370i 0.570089i −0.958514 0.285045i \(-0.907992\pi\)
0.958514 0.285045i \(-0.0920084\pi\)
\(80\) 8.94427i 0.111803i
\(81\) 9.00000 0.111111
\(82\) 13.5650 0.165427
\(83\) 10.3487i 0.124684i −0.998055 0.0623418i \(-0.980143\pi\)
0.998055 0.0623418i \(-0.0198569\pi\)
\(84\) 27.5882i 0.328431i
\(85\) 38.6097 0.454232
\(86\) 92.4480i 1.07498i
\(87\) 94.3941 1.08499
\(88\) 38.6554i 0.439266i
\(89\) 20.8576i 0.234356i 0.993111 + 0.117178i \(0.0373847\pi\)
−0.993111 + 0.117178i \(0.962615\pi\)
\(90\) 9.48683i 0.105409i
\(91\) 111.750i 1.22802i
\(92\) −23.5332 39.5245i −0.255796 0.429614i
\(93\) 38.3871 0.412764
\(94\) 116.750 1.24202
\(95\) 59.1799 0.622947
\(96\) −9.79796 −0.102062
\(97\) 146.441i 1.50970i −0.655895 0.754852i \(-0.727709\pi\)
0.655895 0.754852i \(-0.272291\pi\)
\(98\) −20.4010 −0.208173
\(99\) 41.0002i 0.414144i
\(100\) −10.0000 −0.100000
\(101\) 110.767 1.09671 0.548354 0.836246i \(-0.315255\pi\)
0.548354 + 0.836246i \(0.315255\pi\)
\(102\) 42.2948i 0.414655i
\(103\) 75.0106i 0.728259i 0.931348 + 0.364129i \(0.118633\pi\)
−0.931348 + 0.364129i \(0.881367\pi\)
\(104\) −39.6879 −0.381615
\(105\) 30.8445 0.293757
\(106\) 29.8399i 0.281508i
\(107\) 1.13721i 0.0106281i −0.999986 0.00531405i \(-0.998308\pi\)
0.999986 0.00531405i \(-0.00169152\pi\)
\(108\) −10.3923 −0.0962250
\(109\) 74.1091i 0.679900i 0.940443 + 0.339950i \(0.110410\pi\)
−0.940443 + 0.339950i \(0.889590\pi\)
\(110\) −43.2180 −0.392891
\(111\) 55.8575i 0.503221i
\(112\) 31.8561i 0.284429i
\(113\) 121.550i 1.07566i 0.843053 + 0.537830i \(0.180756\pi\)
−0.843053 + 0.537830i \(0.819244\pi\)
\(114\) 64.8284i 0.568670i
\(115\) −44.1897 + 26.3110i −0.384259 + 0.228791i
\(116\) −108.997 −0.939628
\(117\) −42.0954 −0.359790
\(118\) −149.252 −1.26485
\(119\) 137.513 1.15557
\(120\) 10.9545i 0.0912871i
\(121\) −65.7799 −0.543635
\(122\) 47.3484i 0.388101i
\(123\) −16.6137 −0.135071
\(124\) −44.3256 −0.357465
\(125\) 11.1803i 0.0894427i
\(126\) 33.7885i 0.268163i
\(127\) −46.6213 −0.367097 −0.183549 0.983011i \(-0.558758\pi\)
−0.183549 + 0.983011i \(0.558758\pi\)
\(128\) 11.3137 0.0883883
\(129\) 113.225i 0.877715i
\(130\) 44.3724i 0.341326i
\(131\) 172.666 1.31806 0.659030 0.752116i \(-0.270967\pi\)
0.659030 + 0.752116i \(0.270967\pi\)
\(132\) 47.3430i 0.358659i
\(133\) 210.776 1.58478
\(134\) 49.4567i 0.369080i
\(135\) 11.6190i 0.0860663i
\(136\) 48.8379i 0.359102i
\(137\) 269.189i 1.96488i −0.186572 0.982441i \(-0.559738\pi\)
0.186572 0.982441i \(-0.440262\pi\)
\(138\) 28.8222 + 48.4074i 0.208857 + 0.350779i
\(139\) −112.626 −0.810260 −0.405130 0.914259i \(-0.632774\pi\)
−0.405130 + 0.914259i \(0.632774\pi\)
\(140\) −35.6162 −0.254401
\(141\) −142.989 −1.01411
\(142\) 92.0832 0.648474
\(143\) 191.769i 1.34104i
\(144\) 12.0000 0.0833333
\(145\) 121.862i 0.840429i
\(146\) −178.579 −1.22314
\(147\) 24.9860 0.169973
\(148\) 64.4987i 0.435802i
\(149\) 53.3780i 0.358241i −0.983827 0.179121i \(-0.942675\pi\)
0.983827 0.179121i \(-0.0573253\pi\)
\(150\) 12.2474 0.0816497
\(151\) 39.7896 0.263507 0.131753 0.991283i \(-0.457939\pi\)
0.131753 + 0.991283i \(0.457939\pi\)
\(152\) 74.8573i 0.492483i
\(153\) 51.8004i 0.338565i
\(154\) −153.926 −0.999521
\(155\) 49.5575i 0.319726i
\(156\) 48.6076 0.311587
\(157\) 263.251i 1.67676i −0.545086 0.838380i \(-0.683503\pi\)
0.545086 0.838380i \(-0.316497\pi\)
\(158\) 63.6920i 0.403114i
\(159\) 36.5462i 0.229850i
\(160\) 12.6491i 0.0790569i
\(161\) −157.387 + 93.7096i −0.977559 + 0.582047i
\(162\) 12.7279 0.0785674
\(163\) 239.678 1.47042 0.735209 0.677840i \(-0.237084\pi\)
0.735209 + 0.677840i \(0.237084\pi\)
\(164\) 19.1839 0.116975
\(165\) 52.9311 0.320794
\(166\) 14.6353i 0.0881646i
\(167\) 316.884 1.89751 0.948753 0.316017i \(-0.102346\pi\)
0.948753 + 0.316017i \(0.102346\pi\)
\(168\) 39.0156i 0.232236i
\(169\) 27.8913 0.165037
\(170\) 54.6024 0.321191
\(171\) 79.3982i 0.464317i
\(172\) 130.741i 0.760124i
\(173\) 115.891 0.669890 0.334945 0.942238i \(-0.391282\pi\)
0.334945 + 0.942238i \(0.391282\pi\)
\(174\) 133.493 0.767203
\(175\) 39.8201i 0.227544i
\(176\) 54.6670i 0.310608i
\(177\) 182.796 1.03275
\(178\) 29.4972i 0.165714i
\(179\) −62.1264 −0.347075 −0.173537 0.984827i \(-0.555520\pi\)
−0.173537 + 0.984827i \(0.555520\pi\)
\(180\) 13.4164i 0.0745356i
\(181\) 34.2525i 0.189240i −0.995513 0.0946202i \(-0.969836\pi\)
0.995513 0.0946202i \(-0.0301637\pi\)
\(182\) 158.038i 0.868339i
\(183\) 57.9897i 0.316883i
\(184\) −33.2810 55.8961i −0.180875 0.303783i
\(185\) −72.1117 −0.389793
\(186\) 54.2876 0.291869
\(187\) 235.981 1.26193
\(188\) 165.109 0.878242
\(189\) 41.3823i 0.218954i
\(190\) 83.6931 0.440490
\(191\) 365.807i 1.91522i 0.288065 + 0.957611i \(0.406988\pi\)
−0.288065 + 0.957611i \(0.593012\pi\)
\(192\) −13.8564 −0.0721688
\(193\) −223.842 −1.15980 −0.579901 0.814687i \(-0.696909\pi\)
−0.579901 + 0.814687i \(0.696909\pi\)
\(194\) 207.099i 1.06752i
\(195\) 54.3449i 0.278692i
\(196\) −28.8513 −0.147201
\(197\) 89.6193 0.454920 0.227460 0.973787i \(-0.426958\pi\)
0.227460 + 0.973787i \(0.426958\pi\)
\(198\) 57.9831i 0.292844i
\(199\) 5.90005i 0.0296485i −0.999890 0.0148243i \(-0.995281\pi\)
0.999890 0.0148243i \(-0.00471888\pi\)
\(200\) −14.1421 −0.0707107
\(201\) 60.5719i 0.301353i
\(202\) 156.649 0.775489
\(203\) 434.027i 2.13806i
\(204\) 59.8139i 0.293205i
\(205\) 21.4482i 0.104625i
\(206\) 106.081i 0.514957i
\(207\) −35.2998 59.2868i −0.170531 0.286410i
\(208\) −56.1272 −0.269842
\(209\) 361.705 1.73065
\(210\) 43.6208 0.207718
\(211\) −231.698 −1.09810 −0.549048 0.835791i \(-0.685009\pi\)
−0.549048 + 0.835791i \(0.685009\pi\)
\(212\) 42.1999i 0.199056i
\(213\) −112.778 −0.529476
\(214\) 1.60825i 0.00751521i
\(215\) −146.173 −0.679875
\(216\) −14.6969 −0.0680414
\(217\) 176.505i 0.813387i
\(218\) 104.806i 0.480762i
\(219\) 218.713 0.998690
\(220\) −61.1195 −0.277816
\(221\) 242.284i 1.09631i
\(222\) 78.9944i 0.355831i
\(223\) 130.000 0.582962 0.291481 0.956577i \(-0.405852\pi\)
0.291481 + 0.956577i \(0.405852\pi\)
\(224\) 45.0513i 0.201122i
\(225\) −15.0000 −0.0666667
\(226\) 171.897i 0.760606i
\(227\) 167.115i 0.736190i −0.929788 0.368095i \(-0.880010\pi\)
0.929788 0.368095i \(-0.119990\pi\)
\(228\) 91.6812i 0.402110i
\(229\) 19.2126i 0.0838976i 0.999120 + 0.0419488i \(0.0133566\pi\)
−0.999120 + 0.0419488i \(0.986643\pi\)
\(230\) −62.4937 + 37.2093i −0.271712 + 0.161780i
\(231\) 188.520 0.816105
\(232\) −154.145 −0.664417
\(233\) 101.698 0.436470 0.218235 0.975896i \(-0.429970\pi\)
0.218235 + 0.975896i \(0.429970\pi\)
\(234\) −59.5319 −0.254410
\(235\) 184.598i 0.785523i
\(236\) −211.075 −0.894385
\(237\) 78.0064i 0.329141i
\(238\) 194.473 0.817113
\(239\) −65.7260 −0.275004 −0.137502 0.990501i \(-0.543907\pi\)
−0.137502 + 0.990501i \(0.543907\pi\)
\(240\) 15.4919i 0.0645497i
\(241\) 191.368i 0.794059i −0.917806 0.397029i \(-0.870041\pi\)
0.917806 0.397029i \(-0.129959\pi\)
\(242\) −93.0268 −0.384408
\(243\) −15.5885 −0.0641500
\(244\) 66.9607i 0.274429i
\(245\) 32.2568i 0.131660i
\(246\) −23.4953 −0.0955094
\(247\) 371.366i 1.50351i
\(248\) −62.6859 −0.252766
\(249\) 17.9245i 0.0719861i
\(250\) 15.8114i 0.0632456i
\(251\) 269.641i 1.07427i 0.843498 + 0.537133i \(0.180493\pi\)
−0.843498 + 0.537133i \(0.819507\pi\)
\(252\) 47.7841i 0.189620i
\(253\) −270.086 + 160.811i −1.06753 + 0.635618i
\(254\) −65.9325 −0.259577
\(255\) −66.8740 −0.262251
\(256\) 16.0000 0.0625000
\(257\) 130.359 0.507234 0.253617 0.967305i \(-0.418380\pi\)
0.253617 + 0.967305i \(0.418380\pi\)
\(258\) 160.125i 0.620638i
\(259\) −256.834 −0.991639
\(260\) 62.7521i 0.241354i
\(261\) −163.495 −0.626419
\(262\) 244.187 0.932010
\(263\) 179.446i 0.682306i −0.940008 0.341153i \(-0.889183\pi\)
0.940008 0.341153i \(-0.110817\pi\)
\(264\) 66.9531i 0.253610i
\(265\) −47.1810 −0.178041
\(266\) 298.083 1.12061
\(267\) 36.1265i 0.135305i
\(268\) 69.9424i 0.260979i
\(269\) 483.252 1.79648 0.898239 0.439508i \(-0.144847\pi\)
0.898239 + 0.439508i \(0.144847\pi\)
\(270\) 16.4317i 0.0608581i
\(271\) 25.8751 0.0954799 0.0477400 0.998860i \(-0.484798\pi\)
0.0477400 + 0.998860i \(0.484798\pi\)
\(272\) 69.0672i 0.253923i
\(273\) 193.556i 0.708996i
\(274\) 380.691i 1.38938i
\(275\) 68.3337i 0.248486i
\(276\) 40.7608 + 68.4585i 0.147684 + 0.248038i
\(277\) −322.130 −1.16293 −0.581463 0.813573i \(-0.697519\pi\)
−0.581463 + 0.813573i \(0.697519\pi\)
\(278\) −159.277 −0.572940
\(279\) −66.4884 −0.238310
\(280\) −50.3689 −0.179889
\(281\) 152.134i 0.541401i 0.962664 + 0.270701i \(0.0872553\pi\)
−0.962664 + 0.270701i \(0.912745\pi\)
\(282\) −202.217 −0.717081
\(283\) 256.411i 0.906047i −0.891499 0.453024i \(-0.850345\pi\)
0.891499 0.453024i \(-0.149655\pi\)
\(284\) 130.225 0.458540
\(285\) −102.503 −0.359658
\(286\) 271.202i 0.948260i
\(287\) 76.3903i 0.266168i
\(288\) 16.9706 0.0589256
\(289\) −9.14209 −0.0316335
\(290\) 172.339i 0.594273i
\(291\) 253.644i 0.871628i
\(292\) −252.548 −0.864891
\(293\) 371.098i 1.26655i −0.773929 0.633273i \(-0.781711\pi\)
0.773929 0.633273i \(-0.218289\pi\)
\(294\) 35.3355 0.120189
\(295\) 235.989i 0.799962i
\(296\) 91.2149i 0.308158i
\(297\) 71.0145i 0.239106i
\(298\) 75.4878i 0.253315i
\(299\) 165.107 + 277.300i 0.552196 + 0.927425i
\(300\) 17.3205 0.0577350
\(301\) −520.613 −1.72961
\(302\) 56.2709 0.186328
\(303\) −191.855 −0.633184
\(304\) 105.864i 0.348238i
\(305\) −74.8643 −0.245457
\(306\) 73.2568i 0.239401i
\(307\) 526.653 1.71548 0.857742 0.514081i \(-0.171867\pi\)
0.857742 + 0.514081i \(0.171867\pi\)
\(308\) −217.685 −0.706768
\(309\) 129.922i 0.420460i
\(310\) 70.0849i 0.226080i
\(311\) 537.154 1.72718 0.863592 0.504192i \(-0.168210\pi\)
0.863592 + 0.504192i \(0.168210\pi\)
\(312\) 68.7415 0.220325
\(313\) 296.354i 0.946819i −0.880842 0.473409i \(-0.843023\pi\)
0.880842 0.473409i \(-0.156977\pi\)
\(314\) 372.294i 1.18565i
\(315\) −53.4243 −0.169601
\(316\) 90.0741i 0.285045i
\(317\) −144.472 −0.455748 −0.227874 0.973691i \(-0.573177\pi\)
−0.227874 + 0.973691i \(0.573177\pi\)
\(318\) 51.6842i 0.162529i
\(319\) 744.816i 2.33485i
\(320\) 17.8885i 0.0559017i
\(321\) 1.96970i 0.00613614i
\(322\) −222.579 + 132.525i −0.691239 + 0.411570i
\(323\) −456.984 −1.41481
\(324\) 18.0000 0.0555556
\(325\) 70.1590 0.215874
\(326\) 338.956 1.03974
\(327\) 128.361i 0.392541i
\(328\) 27.1301 0.0827136
\(329\) 657.468i 1.99838i
\(330\) 74.8558 0.226836
\(331\) −481.196 −1.45376 −0.726882 0.686763i \(-0.759031\pi\)
−0.726882 + 0.686763i \(0.759031\pi\)
\(332\) 20.6975i 0.0623418i
\(333\) 96.7480i 0.290535i
\(334\) 448.141 1.34174
\(335\) 78.1980 0.233427
\(336\) 55.1764i 0.164215i
\(337\) 227.981i 0.676501i 0.941056 + 0.338251i \(0.109835\pi\)
−0.941056 + 0.338251i \(0.890165\pi\)
\(338\) 39.4443 0.116699
\(339\) 210.530i 0.621033i
\(340\) 77.2194 0.227116
\(341\) 302.893i 0.888250i
\(342\) 112.286i 0.328322i
\(343\) 275.351i 0.802772i
\(344\) 184.896i 0.537489i
\(345\) 76.5389 45.5719i 0.221852 0.132092i
\(346\) 163.895 0.473684
\(347\) 284.411 0.819628 0.409814 0.912169i \(-0.365594\pi\)
0.409814 + 0.912169i \(0.365594\pi\)
\(348\) 188.788 0.542495
\(349\) −426.741 −1.22275 −0.611377 0.791340i \(-0.709384\pi\)
−0.611377 + 0.791340i \(0.709384\pi\)
\(350\) 56.3142i 0.160898i
\(351\) 72.9114 0.207725
\(352\) 77.3108i 0.219633i
\(353\) 159.245 0.451118 0.225559 0.974230i \(-0.427579\pi\)
0.225559 + 0.974230i \(0.427579\pi\)
\(354\) 258.513 0.730262
\(355\) 145.596i 0.410131i
\(356\) 41.7153i 0.117178i
\(357\) −238.180 −0.667170
\(358\) −87.8600 −0.245419
\(359\) 660.255i 1.83915i −0.392914 0.919575i \(-0.628533\pi\)
0.392914 0.919575i \(-0.371467\pi\)
\(360\) 18.9737i 0.0527046i
\(361\) −339.453 −0.940312
\(362\) 48.4404i 0.133813i
\(363\) 113.934 0.313868
\(364\) 223.499i 0.614009i
\(365\) 282.358i 0.773582i
\(366\) 82.0098i 0.224070i
\(367\) 153.906i 0.419363i −0.977770 0.209681i \(-0.932757\pi\)
0.977770 0.209681i \(-0.0672427\pi\)
\(368\) −47.0665 79.0490i −0.127898 0.214807i
\(369\) 28.7758 0.0779831
\(370\) −101.981 −0.275625
\(371\) −168.041 −0.452940
\(372\) 76.7742 0.206382
\(373\) 114.077i 0.305836i −0.988239 0.152918i \(-0.951133\pi\)
0.988239 0.152918i \(-0.0488671\pi\)
\(374\) 333.727 0.892319
\(375\) 19.3649i 0.0516398i
\(376\) 233.500 0.621011
\(377\) 764.711 2.02841
\(378\) 58.5234i 0.154824i
\(379\) 568.948i 1.50118i −0.660767 0.750591i \(-0.729769\pi\)
0.660767 0.750591i \(-0.270231\pi\)
\(380\) 118.360 0.311473
\(381\) 80.7505 0.211944
\(382\) 517.330i 1.35427i
\(383\) 598.817i 1.56349i 0.623597 + 0.781746i \(0.285671\pi\)
−0.623597 + 0.781746i \(0.714329\pi\)
\(384\) −19.5959 −0.0510310
\(385\) 243.379i 0.632153i
\(386\) −316.560 −0.820103
\(387\) 196.112i 0.506749i
\(388\) 292.883i 0.754852i
\(389\) 296.143i 0.761293i 0.924721 + 0.380647i \(0.124299\pi\)
−0.924721 + 0.380647i \(0.875701\pi\)
\(390\) 76.8553i 0.197065i
\(391\) 341.231 203.172i 0.872713 0.519621i
\(392\) −40.8020 −0.104087
\(393\) −299.066 −0.760983
\(394\) 126.741 0.321677
\(395\) −100.706 −0.254952
\(396\) 82.0005i 0.207072i
\(397\) −706.135 −1.77868 −0.889338 0.457249i \(-0.848835\pi\)
−0.889338 + 0.457249i \(0.848835\pi\)
\(398\) 8.34394i 0.0209647i
\(399\) −365.075 −0.914976
\(400\) −20.0000 −0.0500000
\(401\) 501.908i 1.25164i 0.779967 + 0.625821i \(0.215236\pi\)
−0.779967 + 0.625821i \(0.784764\pi\)
\(402\) 85.6616i 0.213088i
\(403\) 310.984 0.771672
\(404\) 221.535 0.548354
\(405\) 20.1246i 0.0496904i
\(406\) 613.807i 1.51184i
\(407\) −440.743 −1.08291
\(408\) 84.5897i 0.207328i
\(409\) −351.306 −0.858939 −0.429470 0.903081i \(-0.641299\pi\)
−0.429470 + 0.903081i \(0.641299\pi\)
\(410\) 30.3323i 0.0739813i
\(411\) 466.249i 1.13443i
\(412\) 150.021i 0.364129i
\(413\) 840.502i 2.03511i
\(414\) −49.9215 83.8442i −0.120583 0.202522i
\(415\) −23.1405 −0.0557602
\(416\) −79.3758 −0.190807
\(417\) 195.074 0.467804
\(418\) 511.528 1.22375
\(419\) 497.695i 1.18782i 0.804533 + 0.593908i \(0.202416\pi\)
−0.804533 + 0.593908i \(0.797584\pi\)
\(420\) 61.6891 0.146879
\(421\) 323.572i 0.768581i −0.923212 0.384290i \(-0.874446\pi\)
0.923212 0.384290i \(-0.125554\pi\)
\(422\) −327.671 −0.776470
\(423\) 247.664 0.585495
\(424\) 59.6797i 0.140754i
\(425\) 86.3340i 0.203139i
\(426\) −159.493 −0.374396
\(427\) −266.638 −0.624446
\(428\) 2.27442i 0.00531405i
\(429\) 332.154i 0.774251i
\(430\) −206.720 −0.480744
\(431\) 539.731i 1.25228i −0.779712 0.626138i \(-0.784635\pi\)
0.779712 0.626138i \(-0.215365\pi\)
\(432\) −20.7846 −0.0481125
\(433\) 421.843i 0.974234i 0.873337 + 0.487117i \(0.161951\pi\)
−0.873337 + 0.487117i \(0.838049\pi\)
\(434\) 249.616i 0.575152i
\(435\) 211.072i 0.485222i
\(436\) 148.218i 0.339950i
\(437\) 523.029 311.416i 1.19686 0.712623i
\(438\) 309.307 0.706181
\(439\) 324.408 0.738970 0.369485 0.929237i \(-0.379534\pi\)
0.369485 + 0.929237i \(0.379534\pi\)
\(440\) −86.4361 −0.196446
\(441\) −43.2770 −0.0981338
\(442\) 342.641i 0.775207i
\(443\) 221.797 0.500671 0.250335 0.968159i \(-0.419459\pi\)
0.250335 + 0.968159i \(0.419459\pi\)
\(444\) 111.715i 0.251610i
\(445\) 46.6391 0.104807
\(446\) 183.848 0.412216
\(447\) 92.4533i 0.206831i
\(448\) 63.7122i 0.142215i
\(449\) −523.920 −1.16686 −0.583430 0.812164i \(-0.698290\pi\)
−0.583430 + 0.812164i \(0.698290\pi\)
\(450\) −21.2132 −0.0471405
\(451\) 131.090i 0.290666i
\(452\) 243.099i 0.537830i
\(453\) −68.9175 −0.152136
\(454\) 236.337i 0.520565i
\(455\) 249.880 0.549186
\(456\) 129.657i 0.284335i
\(457\) 379.414i 0.830227i −0.909770 0.415114i \(-0.863742\pi\)
0.909770 0.415114i \(-0.136258\pi\)
\(458\) 27.1707i 0.0593246i
\(459\) 89.7209i 0.195470i
\(460\) −88.3795 + 52.6219i −0.192129 + 0.114395i
\(461\) −449.296 −0.974611 −0.487306 0.873231i \(-0.662020\pi\)
−0.487306 + 0.873231i \(0.662020\pi\)
\(462\) 266.608 0.577074
\(463\) 581.451 1.25583 0.627917 0.778280i \(-0.283908\pi\)
0.627917 + 0.778280i \(0.283908\pi\)
\(464\) −217.994 −0.469814
\(465\) 85.8362i 0.184594i
\(466\) 143.822 0.308631
\(467\) 622.103i 1.33213i 0.745895 + 0.666064i \(0.232022\pi\)
−0.745895 + 0.666064i \(0.767978\pi\)
\(468\) −84.1908 −0.179895
\(469\) 278.511 0.593841
\(470\) 261.061i 0.555449i
\(471\) 455.965i 0.968078i
\(472\) −298.505 −0.632425
\(473\) −893.404 −1.88880
\(474\) 110.318i 0.232738i
\(475\) 132.330i 0.278590i
\(476\) 275.026 0.577786
\(477\) 63.2999i 0.132704i
\(478\) −92.9506 −0.194457
\(479\) 269.556i 0.562747i 0.959598 + 0.281373i \(0.0907900\pi\)
−0.959598 + 0.281373i \(0.909210\pi\)
\(480\) 21.9089i 0.0456435i
\(481\) 452.516i 0.940782i
\(482\) 270.635i 0.561484i
\(483\) 272.602 162.310i 0.564394 0.336045i
\(484\) −131.560 −0.271818
\(485\) −327.453 −0.675160
\(486\) −22.0454 −0.0453609
\(487\) 321.930 0.661048 0.330524 0.943798i \(-0.392775\pi\)
0.330524 + 0.943798i \(0.392775\pi\)
\(488\) 94.6967i 0.194051i
\(489\) −415.135 −0.848946
\(490\) 45.6180i 0.0930979i
\(491\) −420.200 −0.855805 −0.427903 0.903825i \(-0.640747\pi\)
−0.427903 + 0.903825i \(0.640747\pi\)
\(492\) −33.2274 −0.0675354
\(493\) 941.013i 1.90875i
\(494\) 525.192i 1.06314i
\(495\) −91.6793 −0.185211
\(496\) −88.6512 −0.178732
\(497\) 518.559i 1.04338i
\(498\) 25.3491i 0.0509018i
\(499\) −259.403 −0.519845 −0.259922 0.965629i \(-0.583697\pi\)
−0.259922 + 0.965629i \(0.583697\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) −548.859 −1.09553
\(502\) 381.330i 0.759621i
\(503\) 687.217i 1.36624i −0.730307 0.683119i \(-0.760623\pi\)
0.730307 0.683119i \(-0.239377\pi\)
\(504\) 67.5770i 0.134081i
\(505\) 247.684i 0.490463i
\(506\) −381.959 + 227.422i −0.754859 + 0.449450i
\(507\) −48.3092 −0.0952843
\(508\) −93.2427 −0.183549
\(509\) −537.856 −1.05669 −0.528345 0.849030i \(-0.677187\pi\)
−0.528345 + 0.849030i \(0.677187\pi\)
\(510\) −94.5741 −0.185439
\(511\) 1005.65i 1.96800i
\(512\) 22.6274 0.0441942
\(513\) 137.522i 0.268074i
\(514\) 184.356 0.358669
\(515\) 167.729 0.325687
\(516\) 226.451i 0.438858i
\(517\) 1128.25i 2.18231i
\(518\) −363.219 −0.701195
\(519\) −200.729 −0.386761
\(520\) 88.7449i 0.170663i
\(521\) 295.782i 0.567720i −0.958866 0.283860i \(-0.908385\pi\)
0.958866 0.283860i \(-0.0916151\pi\)
\(522\) −231.217 −0.442945
\(523\) 889.701i 1.70115i −0.525855 0.850575i \(-0.676254\pi\)
0.525855 0.850575i \(-0.323746\pi\)
\(524\) 345.332 0.659030
\(525\) 68.9705i 0.131372i
\(526\) 253.776i 0.482463i
\(527\) 382.680i 0.726149i
\(528\) 94.6860i 0.179330i
\(529\) −252.094 + 465.070i −0.476547 + 0.879149i
\(530\) −66.7240 −0.125894
\(531\) −316.612 −0.596256
\(532\) 421.553 0.792392
\(533\) −134.592 −0.252518
\(534\) 51.0906i 0.0956752i
\(535\) −2.54287 −0.00475303
\(536\) 98.9135i 0.184540i
\(537\) 107.606 0.200384
\(538\) 683.422 1.27030
\(539\) 197.152i 0.365774i
\(540\) 23.2379i 0.0430331i
\(541\) 704.031 1.30135 0.650676 0.759356i \(-0.274486\pi\)
0.650676 + 0.759356i \(0.274486\pi\)
\(542\) 36.5929 0.0675145
\(543\) 59.3271i 0.109258i
\(544\) 97.6757i 0.179551i
\(545\) 165.713 0.304061
\(546\) 273.729i 0.501336i
\(547\) 469.176 0.857726 0.428863 0.903370i \(-0.358914\pi\)
0.428863 + 0.903370i \(0.358914\pi\)
\(548\) 538.378i 0.982441i
\(549\) 100.441i 0.182953i
\(550\) 96.6385i 0.175706i
\(551\) 1442.36i 2.61771i
\(552\) 57.6444 + 96.8149i 0.104428 + 0.175389i
\(553\) −358.676 −0.648600
\(554\) −455.561 −0.822313
\(555\) 124.901 0.225047
\(556\) −225.252 −0.405130
\(557\) 280.095i 0.502864i −0.967875 0.251432i \(-0.919099\pi\)
0.967875 0.251432i \(-0.0809015\pi\)
\(558\) −94.0288 −0.168510
\(559\) 917.268i 1.64091i
\(560\) −71.2324 −0.127201
\(561\) −408.731 −0.728575
\(562\) 215.150i 0.382828i
\(563\) 30.3039i 0.0538257i 0.999638 + 0.0269129i \(0.00856767\pi\)
−0.999638 + 0.0269129i \(0.991432\pi\)
\(564\) −285.978 −0.507053
\(565\) 271.793 0.481050
\(566\) 362.620i 0.640672i
\(567\) 71.6762i 0.126413i
\(568\) 184.166 0.324237
\(569\) 253.630i 0.445746i 0.974847 + 0.222873i \(0.0715436\pi\)
−0.974847 + 0.222873i \(0.928456\pi\)
\(570\) −144.961 −0.254317
\(571\) 329.218i 0.576564i 0.957546 + 0.288282i \(0.0930841\pi\)
−0.957546 + 0.288282i \(0.906916\pi\)
\(572\) 383.538i 0.670521i
\(573\) 633.597i 1.10575i
\(574\) 108.032i 0.188209i
\(575\) 58.8331 + 98.8113i 0.102318 + 0.171846i
\(576\) 24.0000 0.0416667
\(577\) 172.230 0.298492 0.149246 0.988800i \(-0.452315\pi\)
0.149246 + 0.988800i \(0.452315\pi\)
\(578\) −12.9289 −0.0223683
\(579\) 387.705 0.669612
\(580\) 243.724i 0.420214i
\(581\) −82.4175 −0.141855
\(582\) 358.707i 0.616334i
\(583\) −288.368 −0.494628
\(584\) −357.157 −0.611570
\(585\) 94.1281i 0.160903i
\(586\) 524.811i 0.895583i
\(587\) −627.853 −1.06960 −0.534798 0.844980i \(-0.679612\pi\)
−0.534798 + 0.844980i \(0.679612\pi\)
\(588\) 49.9720 0.0849864
\(589\) 586.562i 0.995861i
\(590\) 333.739i 0.565659i
\(591\) −155.225 −0.262648
\(592\) 128.997i 0.217901i
\(593\) −916.147 −1.54494 −0.772468 0.635054i \(-0.780978\pi\)
−0.772468 + 0.635054i \(0.780978\pi\)
\(594\) 100.430i 0.169073i
\(595\) 307.489i 0.516788i
\(596\) 106.756i 0.179121i
\(597\) 10.2192i 0.0171176i
\(598\) 233.496 + 392.161i 0.390462 + 0.655788i
\(599\) 767.429 1.28118 0.640592 0.767881i \(-0.278689\pi\)
0.640592 + 0.767881i \(0.278689\pi\)
\(600\) 24.4949 0.0408248
\(601\) −486.951 −0.810234 −0.405117 0.914265i \(-0.632769\pi\)
−0.405117 + 0.914265i \(0.632769\pi\)
\(602\) −736.258 −1.22302
\(603\) 104.914i 0.173986i
\(604\) 79.5791 0.131753
\(605\) 147.088i 0.243121i
\(606\) −271.324 −0.447729
\(607\) −856.769 −1.41148 −0.705740 0.708471i \(-0.749385\pi\)
−0.705740 + 0.708471i \(0.749385\pi\)
\(608\) 149.715i 0.246241i
\(609\) 751.757i 1.23441i
\(610\) −105.874 −0.173564
\(611\) −1158.39 −1.89589
\(612\) 103.601i 0.169282i
\(613\) 996.963i 1.62637i 0.582008 + 0.813183i \(0.302267\pi\)
−0.582008 + 0.813183i \(0.697733\pi\)
\(614\) 744.800 1.21303
\(615\) 37.1494i 0.0604055i
\(616\) −307.852 −0.499760
\(617\) 403.163i 0.653425i 0.945124 + 0.326712i \(0.105941\pi\)
−0.945124 + 0.326712i \(0.894059\pi\)
\(618\) 183.738i 0.297310i
\(619\) 6.17899i 0.00998222i 0.999988 + 0.00499111i \(0.00158873\pi\)
−0.999988 + 0.00499111i \(0.998411\pi\)
\(620\) 99.1151i 0.159863i
\(621\) 61.1411 + 102.688i 0.0984559 + 0.165359i
\(622\) 759.651 1.22130
\(623\) 166.111 0.266630
\(624\) 97.2151 0.155793
\(625\) 25.0000 0.0400000
\(626\) 419.108i 0.669502i
\(627\) −626.491 −0.999189
\(628\) 526.503i 0.838380i
\(629\) 556.843 0.885282
\(630\) −75.5534 −0.119926
\(631\) 478.508i 0.758333i 0.925328 + 0.379166i \(0.123789\pi\)
−0.925328 + 0.379166i \(0.876211\pi\)
\(632\) 127.384i 0.201557i
\(633\) 401.313 0.633985
\(634\) −204.314 −0.322262
\(635\) 104.248i 0.164171i
\(636\) 73.0925i 0.114925i
\(637\) 202.418 0.317768
\(638\) 1053.33i 1.65099i
\(639\) 195.338 0.305693
\(640\) 25.2982i 0.0395285i
\(641\) 431.496i 0.673160i 0.941655 + 0.336580i \(0.109270\pi\)
−0.941655 + 0.336580i \(0.890730\pi\)
\(642\) 2.78558i 0.00433891i
\(643\) 155.797i 0.242297i 0.992634 + 0.121149i \(0.0386578\pi\)
−0.992634 + 0.121149i \(0.961342\pi\)
\(644\) −314.774 + 187.419i −0.488780 + 0.291024i
\(645\) 253.179 0.392526
\(646\) −646.273 −1.00042
\(647\) −797.916 −1.23326 −0.616628 0.787255i \(-0.711502\pi\)
−0.616628 + 0.787255i \(0.711502\pi\)
\(648\) 25.4558 0.0392837
\(649\) 1442.35i 2.22242i
\(650\) 99.2198 0.152646
\(651\) 305.716i 0.469609i
\(652\) 479.356 0.735209
\(653\) 579.230 0.887028 0.443514 0.896267i \(-0.353732\pi\)
0.443514 + 0.896267i \(0.353732\pi\)
\(654\) 181.530i 0.277568i
\(655\) 386.093i 0.589455i
\(656\) 38.3677 0.0584873
\(657\) −378.822 −0.576594
\(658\) 929.800i 1.41307i
\(659\) 991.515i 1.50458i −0.658835 0.752288i \(-0.728950\pi\)
0.658835 0.752288i \(-0.271050\pi\)
\(660\) 105.862 0.160397
\(661\) 985.923i 1.49156i 0.666191 + 0.745781i \(0.267923\pi\)
−0.666191 + 0.745781i \(0.732077\pi\)
\(662\) −680.513 −1.02797
\(663\) 419.648i 0.632954i
\(664\) 29.2706i 0.0440823i
\(665\) 471.310i 0.708737i
\(666\) 136.822i 0.205439i
\(667\) 641.262 + 1077.01i 0.961412 + 1.61471i
\(668\) 633.767 0.948753
\(669\) −225.167 −0.336573
\(670\) 110.589 0.165058
\(671\) −457.567 −0.681918
\(672\) 78.0312i 0.116118i
\(673\) 809.473 1.20278 0.601392 0.798954i \(-0.294613\pi\)
0.601392 + 0.798954i \(0.294613\pi\)
\(674\) 322.414i 0.478358i
\(675\) 25.9808 0.0384900
\(676\) 55.7826 0.0825186
\(677\) 1104.73i 1.63181i −0.578188 0.815903i \(-0.696240\pi\)
0.578188 0.815903i \(-0.303760\pi\)
\(678\) 297.734i 0.439136i
\(679\) −1166.26 −1.71762
\(680\) 109.205 0.160595
\(681\) 289.452i 0.425040i
\(682\) 428.356i 0.628088i
\(683\) −503.585 −0.737313 −0.368657 0.929566i \(-0.620182\pi\)
−0.368657 + 0.929566i \(0.620182\pi\)
\(684\) 158.796i 0.232158i
\(685\) −601.925 −0.878722
\(686\) 389.405i 0.567645i
\(687\) 33.2771i 0.0484383i
\(688\) 261.483i 0.380062i
\(689\) 296.071i 0.429710i
\(690\) 108.242 64.4484i 0.156873 0.0934035i
\(691\) 693.803 1.00406 0.502028 0.864851i \(-0.332587\pi\)
0.502028 + 0.864851i \(0.332587\pi\)
\(692\) 231.782 0.334945
\(693\) −326.527 −0.471179
\(694\) 402.218 0.579565
\(695\) 251.840i 0.362359i
\(696\) 266.987 0.383602
\(697\) 165.622i 0.237621i
\(698\) −603.503 −0.864617
\(699\) −176.145 −0.251996
\(700\) 79.6402i 0.113772i
\(701\) 456.823i 0.651673i −0.945426 0.325836i \(-0.894354\pi\)
0.945426 0.325836i \(-0.105646\pi\)
\(702\) 103.112 0.146884
\(703\) 853.513 1.21410
\(704\) 109.334i 0.155304i
\(705\) 319.733i 0.453522i
\(706\) 225.206 0.318989
\(707\) 882.155i 1.24774i
\(708\) 365.592 0.516373
\(709\) 54.3734i 0.0766903i 0.999265 + 0.0383452i \(0.0122086\pi\)
−0.999265 + 0.0383452i \(0.987791\pi\)
\(710\) 205.904i 0.290006i
\(711\) 135.111i 0.190030i
\(712\) 58.9943i 0.0828572i
\(713\) 260.781 + 437.987i 0.365752 + 0.614287i
\(714\) −336.837 −0.471761
\(715\) 428.808 0.599732
\(716\) −124.253 −0.173537
\(717\) 113.841 0.158774
\(718\) 933.742i 1.30048i
\(719\) 154.273 0.214566 0.107283 0.994229i \(-0.465785\pi\)
0.107283 + 0.994229i \(0.465785\pi\)
\(720\) 26.8328i 0.0372678i
\(721\) 597.386 0.828553
\(722\) −480.059 −0.664901
\(723\) 331.459i 0.458450i
\(724\) 68.5051i 0.0946202i
\(725\) 272.492 0.375851
\(726\) 161.127 0.221938
\(727\) 772.570i 1.06268i 0.847158 + 0.531341i \(0.178312\pi\)
−0.847158 + 0.531341i \(0.821688\pi\)
\(728\) 316.075i 0.434170i
\(729\) 27.0000 0.0370370
\(730\) 399.314i 0.547005i
\(731\) 1128.74 1.54411
\(732\) 115.979i 0.158442i
\(733\) 590.416i 0.805479i −0.915315 0.402739i \(-0.868058\pi\)
0.915315 0.402739i \(-0.131942\pi\)
\(734\) 217.656i 0.296534i
\(735\) 55.8704i 0.0760141i
\(736\) −66.5620 111.792i −0.0904375 0.151892i
\(737\) 477.942 0.648497
\(738\) 40.6951 0.0551424
\(739\) 99.2703 0.134331 0.0671653 0.997742i \(-0.478605\pi\)
0.0671653 + 0.997742i \(0.478605\pi\)
\(740\) −144.223 −0.194897
\(741\) 643.226i 0.868051i
\(742\) −237.645 −0.320277
\(743\) 5.78824i 0.00779036i −0.999992 0.00389518i \(-0.998760\pi\)
0.999992 0.00389518i \(-0.00123988\pi\)
\(744\) 108.575 0.145934
\(745\) −119.357 −0.160210
\(746\) 161.329i 0.216259i
\(747\) 31.0462i 0.0415612i
\(748\) 471.962 0.630965
\(749\) −9.05675 −0.0120918
\(750\) 27.3861i 0.0365148i
\(751\) 4.93292i 0.00656847i −0.999995 0.00328423i \(-0.998955\pi\)
0.999995 0.00328423i \(-0.00104541\pi\)
\(752\) 330.219 0.439121
\(753\) 467.032i 0.620228i
\(754\) 1081.46 1.43430
\(755\) 88.9721i 0.117844i
\(756\) 82.7646i 0.109477i
\(757\) 841.391i 1.11148i −0.831356 0.555740i \(-0.812435\pi\)
0.831356 0.555740i \(-0.187565\pi\)
\(758\) 804.614i 1.06150i
\(759\) 467.802 278.533i 0.616340 0.366974i
\(760\) 167.386 0.220245
\(761\) 122.636 0.161151 0.0805754 0.996749i \(-0.474324\pi\)
0.0805754 + 0.996749i \(0.474324\pi\)
\(762\) 114.198 0.149867
\(763\) 590.207 0.773535
\(764\) 731.615i 0.957611i
\(765\) 115.829 0.151411
\(766\) 846.855i 1.10556i
\(767\) 1480.88 1.93074
\(768\) −27.7128 −0.0360844
\(769\) 495.138i 0.643873i −0.946761 0.321936i \(-0.895666\pi\)
0.946761 0.321936i \(-0.104334\pi\)
\(770\) 344.189i 0.446999i
\(771\) −225.789 −0.292852
\(772\) −447.683 −0.579901
\(773\) 314.784i 0.407224i 0.979052 + 0.203612i \(0.0652680\pi\)
−0.979052 + 0.203612i \(0.934732\pi\)
\(774\) 277.344i 0.358326i
\(775\) 110.814 0.142986
\(776\) 414.199i 0.533761i
\(777\) 444.850 0.572523
\(778\) 418.810i 0.538316i
\(779\) 253.861i 0.325880i
\(780\) 108.690i 0.139346i
\(781\) 889.878i 1.13941i
\(782\) 482.573 287.328i 0.617101 0.367427i
\(783\) 283.182 0.361663
\(784\) −57.7027 −0.0736004
\(785\) −588.648 −0.749870
\(786\) −422.943 −0.538096
\(787\) 870.883i 1.10659i 0.832987 + 0.553293i \(0.186629\pi\)
−0.832987 + 0.553293i \(0.813371\pi\)
\(788\) 179.239 0.227460
\(789\) 310.810i 0.393929i
\(790\) −142.420 −0.180278
\(791\) 968.024 1.22380
\(792\) 115.966i