Properties

Label 690.3.c.a.91.2
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 91.2
Character \(\chi\) \(=\) 690.91
Dual form 690.3.c.a.91.7

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} -1.73205 q^{3} +2.00000 q^{4} -2.23607i q^{5} +2.44949 q^{6} -8.87387i q^{7} -2.82843 q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-1.41421 q^{2} -1.73205 q^{3} +2.00000 q^{4} -2.23607i q^{5} +2.44949 q^{6} -8.87387i q^{7} -2.82843 q^{8} +3.00000 q^{9} +3.16228i q^{10} +6.26975i q^{11} -3.46410 q^{12} +22.5219 q^{13} +12.5496i q^{14} +3.87298i q^{15} +4.00000 q^{16} +9.43891i q^{17} -4.24264 q^{18} -10.5287i q^{19} -4.47214i q^{20} +15.3700i q^{21} -8.86676i q^{22} +(22.7674 - 3.26244i) q^{23} +4.89898 q^{24} -5.00000 q^{25} -31.8508 q^{26} -5.19615 q^{27} -17.7477i q^{28} -7.04808 q^{29} -5.47723i q^{30} -18.9154 q^{31} -5.65685 q^{32} -10.8595i q^{33} -13.3486i q^{34} -19.8426 q^{35} +6.00000 q^{36} +39.6300i q^{37} +14.8899i q^{38} -39.0091 q^{39} +6.32456i q^{40} -2.96787 q^{41} -21.7365i q^{42} -73.5577i q^{43} +12.5395i q^{44} -6.70820i q^{45} +(-32.1980 + 4.61379i) q^{46} +64.8976 q^{47} -6.92820 q^{48} -29.7456 q^{49} +7.07107 q^{50} -16.3487i q^{51} +45.0438 q^{52} +14.0544i q^{53} +7.34847 q^{54} +14.0196 q^{55} +25.0991i q^{56} +18.2363i q^{57} +9.96748 q^{58} +19.3254 q^{59} +7.74597i q^{60} -55.1446i q^{61} +26.7504 q^{62} -26.6216i q^{63} +8.00000 q^{64} -50.3605i q^{65} +15.3577i q^{66} -41.0130i q^{67} +18.8778i q^{68} +(-39.4344 + 5.65071i) q^{69} +28.0616 q^{70} -33.4246 q^{71} -8.48528 q^{72} +40.7761 q^{73} -56.0452i q^{74} +8.66025 q^{75} -21.0575i q^{76} +55.6369 q^{77} +55.1672 q^{78} -49.8081i q^{79} -8.94427i q^{80} +9.00000 q^{81} +4.19721 q^{82} -36.6835i q^{83} +30.7400i q^{84} +21.1060 q^{85} +104.026i q^{86} +12.2076 q^{87} -17.7335i q^{88} -129.178i q^{89} +9.48683i q^{90} -199.857i q^{91} +(45.5349 - 6.52488i) q^{92} +32.7624 q^{93} -91.7790 q^{94} -23.5430 q^{95} +9.79796 q^{96} -101.382i q^{97} +42.0666 q^{98} +18.8092i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 64q^{4} + 96q^{9} + O(q^{10}) \) \( 32q + 64q^{4} + 96q^{9} - 48q^{13} + 128q^{16} - 80q^{23} - 160q^{25} + 120q^{29} + 248q^{31} - 120q^{35} + 192q^{36} - 48q^{39} + 72q^{41} + 160q^{46} + 400q^{47} - 344q^{49} - 96q^{52} - 256q^{58} + 120q^{59} + 160q^{62} + 256q^{64} + 192q^{69} + 104q^{71} + 16q^{73} + 240q^{77} + 192q^{78} + 288q^{81} + 64q^{82} - 120q^{85} + 144q^{87} - 160q^{92} - 192q^{93} + 96q^{94} - 160q^{95} + 64q^{98} + O(q^{100}) \)

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
\(7\) 8.87387i 1.26770i −0.773458 0.633848i \(-0.781474\pi\)
0.773458 0.633848i \(-0.218526\pi\)
\(8\) −2.82843 −0.353553
\(9\) 3.00000 0.333333
\(10\) 3.16228i 0.316228i
\(11\) 6.26975i 0.569977i 0.958531 + 0.284989i \(0.0919898\pi\)
−0.958531 + 0.284989i \(0.908010\pi\)
\(12\) −3.46410 −0.288675
\(13\) 22.5219 1.73245 0.866227 0.499650i \(-0.166538\pi\)
0.866227 + 0.499650i \(0.166538\pi\)
\(14\) 12.5496i 0.896396i
\(15\) 3.87298i 0.258199i
\(16\) 4.00000 0.250000
\(17\) 9.43891i 0.555230i 0.960692 + 0.277615i \(0.0895440\pi\)
−0.960692 + 0.277615i \(0.910456\pi\)
\(18\) −4.24264 −0.235702
\(19\) 10.5287i 0.554145i −0.960849 0.277072i \(-0.910636\pi\)
0.960849 0.277072i \(-0.0893642\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 15.3700i 0.731905i
\(22\) 8.86676i 0.403035i
\(23\) 22.7674 3.26244i 0.989889 0.141845i
\(24\) 4.89898 0.204124
\(25\) −5.00000 −0.200000
\(26\) −31.8508 −1.22503
\(27\) −5.19615 −0.192450
\(28\) 17.7477i 0.633848i
\(29\) −7.04808 −0.243037 −0.121519 0.992589i \(-0.538776\pi\)
−0.121519 + 0.992589i \(0.538776\pi\)
\(30\) 5.47723i 0.182574i
\(31\) −18.9154 −0.610174 −0.305087 0.952324i \(-0.598686\pi\)
−0.305087 + 0.952324i \(0.598686\pi\)
\(32\) −5.65685 −0.176777
\(33\) 10.8595i 0.329076i
\(34\) 13.3486i 0.392607i
\(35\) −19.8426 −0.566931
\(36\) 6.00000 0.166667
\(37\) 39.6300i 1.07108i 0.844510 + 0.535540i \(0.179892\pi\)
−0.844510 + 0.535540i \(0.820108\pi\)
\(38\) 14.8899i 0.391839i
\(39\) −39.0091 −1.00023
\(40\) 6.32456i 0.158114i
\(41\) −2.96787 −0.0723872 −0.0361936 0.999345i \(-0.511523\pi\)
−0.0361936 + 0.999345i \(0.511523\pi\)
\(42\) 21.7365i 0.517535i
\(43\) 73.5577i 1.71064i −0.518097 0.855322i \(-0.673359\pi\)
0.518097 0.855322i \(-0.326641\pi\)
\(44\) 12.5395i 0.284989i
\(45\) 6.70820i 0.149071i
\(46\) −32.1980 + 4.61379i −0.699957 + 0.100300i
\(47\) 64.8976 1.38080 0.690400 0.723428i \(-0.257435\pi\)
0.690400 + 0.723428i \(0.257435\pi\)
\(48\) −6.92820 −0.144338
\(49\) −29.7456 −0.607053
\(50\) 7.07107 0.141421
\(51\) 16.3487i 0.320562i
\(52\) 45.0438 0.866227
\(53\) 14.0544i 0.265177i 0.991171 + 0.132589i \(0.0423290\pi\)
−0.991171 + 0.132589i \(0.957671\pi\)
\(54\) 7.34847 0.136083
\(55\) 14.0196 0.254901
\(56\) 25.0991i 0.448198i
\(57\) 18.2363i 0.319936i
\(58\) 9.96748 0.171853
\(59\) 19.3254 0.327548 0.163774 0.986498i \(-0.447633\pi\)
0.163774 + 0.986498i \(0.447633\pi\)
\(60\) 7.74597i 0.129099i
\(61\) 55.1446i 0.904010i −0.892015 0.452005i \(-0.850709\pi\)
0.892015 0.452005i \(-0.149291\pi\)
\(62\) 26.7504 0.431458
\(63\) 26.6216i 0.422565i
\(64\) 8.00000 0.125000
\(65\) 50.3605i 0.774777i
\(66\) 15.3577i 0.232692i
\(67\) 41.0130i 0.612134i −0.952010 0.306067i \(-0.900987\pi\)
0.952010 0.306067i \(-0.0990132\pi\)
\(68\) 18.8778i 0.277615i
\(69\) −39.4344 + 5.65071i −0.571513 + 0.0818944i
\(70\) 28.0616 0.400881
\(71\) −33.4246 −0.470769 −0.235384 0.971902i \(-0.575635\pi\)
−0.235384 + 0.971902i \(0.575635\pi\)
\(72\) −8.48528 −0.117851
\(73\) 40.7761 0.558576 0.279288 0.960207i \(-0.409902\pi\)
0.279288 + 0.960207i \(0.409902\pi\)
\(74\) 56.0452i 0.757368i
\(75\) 8.66025 0.115470
\(76\) 21.0575i 0.277072i
\(77\) 55.6369 0.722558
\(78\) 55.1672 0.707272
\(79\) 49.8081i 0.630482i −0.949012 0.315241i \(-0.897915\pi\)
0.949012 0.315241i \(-0.102085\pi\)
\(80\) 8.94427i 0.111803i
\(81\) 9.00000 0.111111
\(82\) 4.19721 0.0511855
\(83\) 36.6835i 0.441969i −0.975277 0.220985i \(-0.929073\pi\)
0.975277 0.220985i \(-0.0709271\pi\)
\(84\) 30.7400i 0.365952i
\(85\) 21.1060 0.248306
\(86\) 104.026i 1.20961i
\(87\) 12.2076 0.140318
\(88\) 17.7335i 0.201517i
\(89\) 129.178i 1.45144i −0.687992 0.725718i \(-0.741508\pi\)
0.687992 0.725718i \(-0.258492\pi\)
\(90\) 9.48683i 0.105409i
\(91\) 199.857i 2.19623i
\(92\) 45.5349 6.52488i 0.494944 0.0709226i
\(93\) 32.7624 0.352284
\(94\) −91.7790 −0.976372
\(95\) −23.5430 −0.247821
\(96\) 9.79796 0.102062
\(97\) 101.382i 1.04518i −0.852585 0.522588i \(-0.824967\pi\)
0.852585 0.522588i \(-0.175033\pi\)
\(98\) 42.0666 0.429252
\(99\) 18.8092i 0.189992i
\(100\) −10.0000 −0.100000
\(101\) −162.334 −1.60726 −0.803632 0.595127i \(-0.797102\pi\)
−0.803632 + 0.595127i \(0.797102\pi\)
\(102\) 23.1205i 0.226672i
\(103\) 131.572i 1.27740i −0.769456 0.638699i \(-0.779473\pi\)
0.769456 0.638699i \(-0.220527\pi\)
\(104\) −63.7016 −0.612515
\(105\) 34.3684 0.327318
\(106\) 19.8759i 0.187509i
\(107\) 15.7264i 0.146976i 0.997296 + 0.0734878i \(0.0234130\pi\)
−0.997296 + 0.0734878i \(0.976587\pi\)
\(108\) −10.3923 −0.0962250
\(109\) 99.8298i 0.915870i −0.888986 0.457935i \(-0.848589\pi\)
0.888986 0.457935i \(-0.151411\pi\)
\(110\) −19.8267 −0.180243
\(111\) 68.6411i 0.618388i
\(112\) 35.4955i 0.316924i
\(113\) 139.012i 1.23020i 0.788450 + 0.615099i \(0.210884\pi\)
−0.788450 + 0.615099i \(0.789116\pi\)
\(114\) 25.7901i 0.226229i
\(115\) −7.29504 50.9096i −0.0634351 0.442692i
\(116\) −14.0962 −0.121519
\(117\) 67.5657 0.577485
\(118\) −27.3302 −0.231612
\(119\) 83.7597 0.703863
\(120\) 10.9545i 0.0912871i
\(121\) 81.6903 0.675126
\(122\) 77.9863i 0.639232i
\(123\) 5.14051 0.0417928
\(124\) −37.8308 −0.305087
\(125\) 11.1803i 0.0894427i
\(126\) 37.6487i 0.298799i
\(127\) −9.57946 −0.0754288 −0.0377144 0.999289i \(-0.512008\pi\)
−0.0377144 + 0.999289i \(0.512008\pi\)
\(128\) −11.3137 −0.0883883
\(129\) 127.406i 0.987641i
\(130\) 71.2205i 0.547850i
\(131\) −50.3313 −0.384209 −0.192104 0.981375i \(-0.561531\pi\)
−0.192104 + 0.981375i \(0.561531\pi\)
\(132\) 21.7190i 0.164538i
\(133\) −93.4308 −0.702487
\(134\) 58.0011i 0.432844i
\(135\) 11.6190i 0.0860663i
\(136\) 26.6973i 0.196303i
\(137\) 56.8530i 0.414985i −0.978237 0.207493i \(-0.933470\pi\)
0.978237 0.207493i \(-0.0665303\pi\)
\(138\) 55.7686 7.99132i 0.404120 0.0579081i
\(139\) 106.054 0.762976 0.381488 0.924374i \(-0.375412\pi\)
0.381488 + 0.924374i \(0.375412\pi\)
\(140\) −39.6852 −0.283465
\(141\) −112.406 −0.797205
\(142\) 47.2695 0.332884
\(143\) 141.207i 0.987459i
\(144\) 12.0000 0.0833333
\(145\) 15.7600i 0.108689i
\(146\) −57.6660 −0.394973
\(147\) 51.5209 0.350482
\(148\) 79.2599i 0.535540i
\(149\) 50.9174i 0.341728i 0.985295 + 0.170864i \(0.0546558\pi\)
−0.985295 + 0.170864i \(0.945344\pi\)
\(150\) −12.2474 −0.0816497
\(151\) −214.536 −1.42077 −0.710383 0.703815i \(-0.751478\pi\)
−0.710383 + 0.703815i \(0.751478\pi\)
\(152\) 29.7798i 0.195920i
\(153\) 28.3167i 0.185077i
\(154\) −78.6825 −0.510925
\(155\) 42.2961i 0.272878i
\(156\) −78.0182 −0.500117
\(157\) 33.5167i 0.213482i 0.994287 + 0.106741i \(0.0340416\pi\)
−0.994287 + 0.106741i \(0.965958\pi\)
\(158\) 70.4393i 0.445818i
\(159\) 24.3429i 0.153100i
\(160\) 12.6491i 0.0790569i
\(161\) −28.9505 202.035i −0.179817 1.25488i
\(162\) −12.7279 −0.0785674
\(163\) 173.861 1.06663 0.533317 0.845915i \(-0.320945\pi\)
0.533317 + 0.845915i \(0.320945\pi\)
\(164\) −5.93575 −0.0361936
\(165\) −24.2826 −0.147167
\(166\) 51.8782i 0.312519i
\(167\) 73.4751 0.439971 0.219985 0.975503i \(-0.429399\pi\)
0.219985 + 0.975503i \(0.429399\pi\)
\(168\) 43.4729i 0.258767i
\(169\) 338.237 2.00140
\(170\) −29.8485 −0.175579
\(171\) 31.5862i 0.184715i
\(172\) 147.115i 0.855322i
\(173\) 85.3858 0.493559 0.246780 0.969072i \(-0.420628\pi\)
0.246780 + 0.969072i \(0.420628\pi\)
\(174\) −17.2642 −0.0992195
\(175\) 44.3694i 0.253539i
\(176\) 25.0790i 0.142494i
\(177\) −33.4725 −0.189110
\(178\) 182.685i 1.02632i
\(179\) 49.1221 0.274425 0.137213 0.990542i \(-0.456186\pi\)
0.137213 + 0.990542i \(0.456186\pi\)
\(180\) 13.4164i 0.0745356i
\(181\) 6.70433i 0.0370405i −0.999828 0.0185203i \(-0.994104\pi\)
0.999828 0.0185203i \(-0.00589552\pi\)
\(182\) 282.640i 1.55297i
\(183\) 95.5133i 0.521931i
\(184\) −64.3961 + 9.22758i −0.349979 + 0.0501499i
\(185\) 88.6153 0.479002
\(186\) −46.3331 −0.249103
\(187\) −59.1796 −0.316468
\(188\) 129.795 0.690400
\(189\) 46.1100i 0.243968i
\(190\) 33.2948 0.175236
\(191\) 155.274i 0.812954i −0.913661 0.406477i \(-0.866757\pi\)
0.913661 0.406477i \(-0.133243\pi\)
\(192\) −13.8564 −0.0721688
\(193\) −29.0926 −0.150739 −0.0753695 0.997156i \(-0.524014\pi\)
−0.0753695 + 0.997156i \(0.524014\pi\)
\(194\) 143.376i 0.739051i
\(195\) 87.2270i 0.447318i
\(196\) −59.4912 −0.303527
\(197\) −323.403 −1.64164 −0.820820 0.571187i \(-0.806483\pi\)
−0.820820 + 0.571187i \(0.806483\pi\)
\(198\) 26.6003i 0.134345i
\(199\) 317.291i 1.59443i 0.603697 + 0.797214i \(0.293694\pi\)
−0.603697 + 0.797214i \(0.706306\pi\)
\(200\) 14.1421 0.0707107
\(201\) 71.0366i 0.353416i
\(202\) 229.574 1.13651
\(203\) 62.5437i 0.308097i
\(204\) 32.6973i 0.160281i
\(205\) 6.63637i 0.0323725i
\(206\) 186.071i 0.903257i
\(207\) 68.3023 9.78732i 0.329963 0.0472818i
\(208\) 90.0876 0.433114
\(209\) 66.0126 0.315850
\(210\) −48.6042 −0.231449
\(211\) −254.286 −1.20515 −0.602573 0.798064i \(-0.705858\pi\)
−0.602573 + 0.798064i \(0.705858\pi\)
\(212\) 28.1088i 0.132589i
\(213\) 57.8931 0.271799
\(214\) 22.2405i 0.103927i
\(215\) −164.480 −0.765023
\(216\) 14.6969 0.0680414
\(217\) 167.853i 0.773516i
\(218\) 141.181i 0.647618i
\(219\) −70.6262 −0.322494
\(220\) 28.0392 0.127451
\(221\) 212.582i 0.961911i
\(222\) 97.0732i 0.437267i
\(223\) 82.8200 0.371390 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(224\) 50.1982i 0.224099i
\(225\) −15.0000 −0.0666667
\(226\) 196.593i 0.869882i
\(227\) 89.4993i 0.394270i −0.980376 0.197135i \(-0.936836\pi\)
0.980376 0.197135i \(-0.0631637\pi\)
\(228\) 36.4727i 0.159968i
\(229\) 32.1076i 0.140208i 0.997540 + 0.0701040i \(0.0223331\pi\)
−0.997540 + 0.0701040i \(0.977667\pi\)
\(230\) 10.3167 + 71.9970i 0.0448554 + 0.313030i
\(231\) −96.3660 −0.417169
\(232\) 19.9350 0.0859266
\(233\) −167.955 −0.720837 −0.360418 0.932791i \(-0.617366\pi\)
−0.360418 + 0.932791i \(0.617366\pi\)
\(234\) −95.5524 −0.408344
\(235\) 145.115i 0.617512i
\(236\) 38.6507 0.163774
\(237\) 86.2702i 0.364009i
\(238\) −118.454 −0.497706
\(239\) 96.4681 0.403632 0.201816 0.979423i \(-0.435316\pi\)
0.201816 + 0.979423i \(0.435316\pi\)
\(240\) 15.4919i 0.0645497i
\(241\) 428.477i 1.77791i 0.457991 + 0.888957i \(0.348569\pi\)
−0.457991 + 0.888957i \(0.651431\pi\)
\(242\) −115.527 −0.477386
\(243\) −15.5885 −0.0641500
\(244\) 110.289i 0.452005i
\(245\) 66.5132i 0.271482i
\(246\) −7.26978 −0.0295519
\(247\) 237.128i 0.960031i
\(248\) 53.5008 0.215729
\(249\) 63.5376i 0.255171i
\(250\) 15.8114i 0.0632456i
\(251\) 62.3046i 0.248226i 0.992268 + 0.124113i \(0.0396085\pi\)
−0.992268 + 0.124113i \(0.960392\pi\)
\(252\) 53.2432i 0.211283i
\(253\) 20.4547 + 142.746i 0.0808485 + 0.564214i
\(254\) 13.5474 0.0533362
\(255\) −36.5567 −0.143360
\(256\) 16.0000 0.0625000
\(257\) −89.4115 −0.347905 −0.173952 0.984754i \(-0.555654\pi\)
−0.173952 + 0.984754i \(0.555654\pi\)
\(258\) 180.179i 0.698368i
\(259\) 351.671 1.35780
\(260\) 100.721i 0.387389i
\(261\) −21.1442 −0.0810124
\(262\) 71.1792 0.271676
\(263\) 373.027i 1.41835i −0.705030 0.709177i \(-0.749067\pi\)
0.705030 0.709177i \(-0.250933\pi\)
\(264\) 30.7154i 0.116346i
\(265\) 31.4266 0.118591
\(266\) 132.131 0.496733
\(267\) 223.743i 0.837987i
\(268\) 82.0260i 0.306067i
\(269\) −329.332 −1.22428 −0.612141 0.790748i \(-0.709692\pi\)
−0.612141 + 0.790748i \(0.709692\pi\)
\(270\) 16.4317i 0.0608581i
\(271\) −474.870 −1.75229 −0.876144 0.482049i \(-0.839893\pi\)
−0.876144 + 0.482049i \(0.839893\pi\)
\(272\) 37.7556i 0.138808i
\(273\) 346.162i 1.26799i
\(274\) 80.4023i 0.293439i
\(275\) 31.3487i 0.113995i
\(276\) −78.8687 + 11.3014i −0.285756 + 0.0409472i
\(277\) −65.9751 −0.238177 −0.119089 0.992884i \(-0.537997\pi\)
−0.119089 + 0.992884i \(0.537997\pi\)
\(278\) −149.983 −0.539506
\(279\) −56.7462 −0.203391
\(280\) 56.1233 0.200440
\(281\) 414.508i 1.47512i 0.675284 + 0.737558i \(0.264021\pi\)
−0.675284 + 0.737558i \(0.735979\pi\)
\(282\) 158.966 0.563709
\(283\) 447.429i 1.58102i −0.612448 0.790511i \(-0.709815\pi\)
0.612448 0.790511i \(-0.290185\pi\)
\(284\) −66.8492 −0.235384
\(285\) 40.7777 0.143080
\(286\) 199.696i 0.698239i
\(287\) 26.3365i 0.0917649i
\(288\) −16.9706 −0.0589256
\(289\) 199.907 0.691720
\(290\) 22.2880i 0.0768551i
\(291\) 175.599i 0.603433i
\(292\) 81.5521 0.279288
\(293\) 346.420i 1.18232i 0.806554 + 0.591160i \(0.201330\pi\)
−0.806554 + 0.591160i \(0.798670\pi\)
\(294\) −72.8616 −0.247828
\(295\) 43.2128i 0.146484i
\(296\) 112.090i 0.378684i
\(297\) 32.5786i 0.109692i
\(298\) 72.0081i 0.241638i
\(299\) 512.766 73.4764i 1.71494 0.245740i
\(300\) 17.3205 0.0577350
\(301\) −652.742 −2.16858
\(302\) 303.399 1.00463
\(303\) 281.170 0.927954
\(304\) 42.1150i 0.138536i
\(305\) −123.307 −0.404286
\(306\) 40.0459i 0.130869i
\(307\) 531.509 1.73130 0.865650 0.500649i \(-0.166905\pi\)
0.865650 + 0.500649i \(0.166905\pi\)
\(308\) 111.274 0.361279
\(309\) 227.890i 0.737507i
\(310\) 59.8158i 0.192954i
\(311\) 423.951 1.36319 0.681594 0.731731i \(-0.261287\pi\)
0.681594 + 0.731731i \(0.261287\pi\)
\(312\) 110.334 0.353636
\(313\) 3.36548i 0.0107523i −0.999986 0.00537616i \(-0.998289\pi\)
0.999986 0.00537616i \(-0.00171129\pi\)
\(314\) 47.3998i 0.150955i
\(315\) −59.5277 −0.188977
\(316\) 99.6162i 0.315241i
\(317\) 162.592 0.512910 0.256455 0.966556i \(-0.417445\pi\)
0.256455 + 0.966556i \(0.417445\pi\)
\(318\) 34.4261i 0.108258i
\(319\) 44.1897i 0.138526i
\(320\) 17.8885i 0.0559017i
\(321\) 27.2389i 0.0848564i
\(322\) 40.9422 + 285.721i 0.127150 + 0.887333i
\(323\) 99.3799 0.307678
\(324\) 18.0000 0.0555556
\(325\) −112.610 −0.346491
\(326\) −245.877 −0.754225
\(327\) 172.910i 0.528778i
\(328\) 8.39442 0.0255927
\(329\) 575.893i 1.75043i
\(330\) 34.3408 0.104063
\(331\) −610.713 −1.84505 −0.922527 0.385933i \(-0.873880\pi\)
−0.922527 + 0.385933i \(0.873880\pi\)
\(332\) 73.3669i 0.220985i
\(333\) 118.890i 0.357027i
\(334\) −103.910 −0.311106
\(335\) −91.7079 −0.273755
\(336\) 61.4800i 0.182976i
\(337\) 103.172i 0.306148i 0.988215 + 0.153074i \(0.0489174\pi\)
−0.988215 + 0.153074i \(0.951083\pi\)
\(338\) −478.339 −1.41520
\(339\) 240.777i 0.710256i
\(340\) 42.2121 0.124153
\(341\) 118.595i 0.347785i
\(342\) 44.6697i 0.130613i
\(343\) 170.861i 0.498137i
\(344\) 208.053i 0.604804i
\(345\) 12.6354 + 88.1779i 0.0366243 + 0.255588i
\(346\) −120.754 −0.348999
\(347\) 589.976 1.70022 0.850109 0.526606i \(-0.176536\pi\)
0.850109 + 0.526606i \(0.176536\pi\)
\(348\) 24.4153 0.0701588
\(349\) 90.7968 0.260163 0.130081 0.991503i \(-0.458476\pi\)
0.130081 + 0.991503i \(0.458476\pi\)
\(350\) 62.7478i 0.179279i
\(351\) −117.027 −0.333411
\(352\) 35.4670i 0.100759i
\(353\) −41.1499 −0.116572 −0.0582859 0.998300i \(-0.518564\pi\)
−0.0582859 + 0.998300i \(0.518564\pi\)
\(354\) 47.3373 0.133721
\(355\) 74.7397i 0.210534i
\(356\) 258.356i 0.725718i
\(357\) −145.076 −0.406375
\(358\) −69.4692 −0.194048
\(359\) 227.208i 0.632892i −0.948610 0.316446i \(-0.897510\pi\)
0.948610 0.316446i \(-0.102490\pi\)
\(360\) 18.9737i 0.0527046i
\(361\) 250.145 0.692924
\(362\) 9.48136i 0.0261916i
\(363\) −141.492 −0.389784
\(364\) 399.713i 1.09811i
\(365\) 91.1780i 0.249803i
\(366\) 135.076i 0.369061i
\(367\) 47.5374i 0.129530i −0.997901 0.0647648i \(-0.979370\pi\)
0.997901 0.0647648i \(-0.0206297\pi\)
\(368\) 91.0698 13.0498i 0.247472 0.0354613i
\(369\) −8.90362 −0.0241291
\(370\) −125.321 −0.338705
\(371\) 124.717 0.336164
\(372\) 65.5249 0.176142
\(373\) 436.640i 1.17062i 0.810811 + 0.585308i \(0.199026\pi\)
−0.810811 + 0.585308i \(0.800974\pi\)
\(374\) 83.6926 0.223777
\(375\) 19.3649i 0.0516398i
\(376\) −183.558 −0.488186
\(377\) −158.736 −0.421051
\(378\) 65.2094i 0.172512i
\(379\) 430.461i 1.13578i 0.823104 + 0.567891i \(0.192240\pi\)
−0.823104 + 0.567891i \(0.807760\pi\)
\(380\) −47.0860 −0.123911
\(381\) 16.5921 0.0435489
\(382\) 219.591i 0.574846i
\(383\) 625.629i 1.63350i −0.576994 0.816748i \(-0.695774\pi\)
0.576994 0.816748i \(-0.304226\pi\)
\(384\) 19.5959 0.0510310
\(385\) 124.408i 0.323138i
\(386\) 41.1432 0.106589
\(387\) 220.673i 0.570215i
\(388\) 202.764i 0.522588i
\(389\) 499.976i 1.28529i 0.766166 + 0.642643i \(0.222162\pi\)
−0.766166 + 0.642643i \(0.777838\pi\)
\(390\) 123.358i 0.316302i
\(391\) 30.7939 + 214.900i 0.0787567 + 0.549616i
\(392\) 84.1333 0.214626
\(393\) 87.1764 0.221823
\(394\) 457.361 1.16081
\(395\) −111.374 −0.281960
\(396\) 37.6185i 0.0949962i
\(397\) 212.359 0.534909 0.267455 0.963570i \(-0.413817\pi\)
0.267455 + 0.963570i \(0.413817\pi\)
\(398\) 448.718i 1.12743i
\(399\) 161.827 0.405581
\(400\) −20.0000 −0.0500000
\(401\) 109.048i 0.271940i −0.990713 0.135970i \(-0.956585\pi\)
0.990713 0.135970i \(-0.0434150\pi\)
\(402\) 100.461i 0.249903i
\(403\) −426.011 −1.05710
\(404\) −324.667 −0.803632
\(405\) 20.1246i 0.0496904i
\(406\) 88.4502i 0.217858i
\(407\) −248.470 −0.610491
\(408\) 46.2410i 0.113336i
\(409\) 43.2954 0.105857 0.0529283 0.998598i \(-0.483145\pi\)
0.0529283 + 0.998598i \(0.483145\pi\)
\(410\) 9.38524i 0.0228908i
\(411\) 98.4723i 0.239592i
\(412\) 263.144i 0.638699i
\(413\) 171.491i 0.415232i
\(414\) −96.5941 + 13.8414i −0.233319 + 0.0334332i
\(415\) −82.0267 −0.197655
\(416\) −127.403 −0.306258
\(417\) −183.690 −0.440504
\(418\) −93.3559 −0.223339
\(419\) 705.421i 1.68358i 0.539804 + 0.841791i \(0.318498\pi\)
−0.539804 + 0.841791i \(0.681502\pi\)
\(420\) 68.7367 0.163659
\(421\) 519.578i 1.23415i −0.786904 0.617076i \(-0.788317\pi\)
0.786904 0.617076i \(-0.211683\pi\)
\(422\) 359.614 0.852166
\(423\) 194.693 0.460266
\(424\) 39.7519i 0.0937544i
\(425\) 47.1946i 0.111046i
\(426\) −81.8732 −0.192191
\(427\) −489.347 −1.14601
\(428\) 31.4528i 0.0734878i
\(429\) 244.577i 0.570110i
\(430\) 232.610 0.540953
\(431\) 482.538i 1.11958i −0.828635 0.559789i \(-0.810882\pi\)
0.828635 0.559789i \(-0.189118\pi\)
\(432\) −20.7846 −0.0481125
\(433\) 431.177i 0.995789i −0.867238 0.497894i \(-0.834107\pi\)
0.867238 0.497894i \(-0.165893\pi\)
\(434\) 237.380i 0.546958i
\(435\) 27.2971i 0.0627519i
\(436\) 199.660i 0.457935i
\(437\) −34.3494 239.713i −0.0786028 0.548542i
\(438\) 99.8805 0.228038
\(439\) 354.292 0.807044 0.403522 0.914970i \(-0.367786\pi\)
0.403522 + 0.914970i \(0.367786\pi\)
\(440\) −39.6534 −0.0901213
\(441\) −89.2368 −0.202351
\(442\) 300.637i 0.680174i
\(443\) −602.448 −1.35993 −0.679964 0.733246i \(-0.738004\pi\)
−0.679964 + 0.733246i \(0.738004\pi\)
\(444\) 137.282i 0.309194i
\(445\) −288.850 −0.649102
\(446\) −117.125 −0.262612
\(447\) 88.1916i 0.197297i
\(448\) 70.9910i 0.158462i
\(449\) 780.691 1.73873 0.869366 0.494169i \(-0.164528\pi\)
0.869366 + 0.494169i \(0.164528\pi\)
\(450\) 21.2132 0.0471405
\(451\) 18.6078i 0.0412590i
\(452\) 278.025i 0.615099i
\(453\) 371.587 0.820280
\(454\) 126.571i 0.278791i
\(455\) −446.893 −0.982182
\(456\) 51.5801i 0.113114i
\(457\) 504.211i 1.10331i 0.834073 + 0.551654i \(0.186003\pi\)
−0.834073 + 0.551654i \(0.813997\pi\)
\(458\) 45.4070i 0.0991420i
\(459\) 49.0460i 0.106854i
\(460\) −14.5901 101.819i −0.0317176 0.221346i
\(461\) 533.437 1.15713 0.578565 0.815636i \(-0.303613\pi\)
0.578565 + 0.815636i \(0.303613\pi\)
\(462\) 136.282 0.294983
\(463\) 614.183 1.32653 0.663265 0.748385i \(-0.269170\pi\)
0.663265 + 0.748385i \(0.269170\pi\)
\(464\) −28.1923 −0.0607593
\(465\) 73.2590i 0.157546i
\(466\) 237.524 0.509709
\(467\) 725.648i 1.55385i −0.629593 0.776925i \(-0.716778\pi\)
0.629593 0.776925i \(-0.283222\pi\)
\(468\) 135.131 0.288742
\(469\) −363.944 −0.776000
\(470\) 205.224i 0.436647i
\(471\) 58.0527i 0.123254i
\(472\) −54.6604 −0.115806
\(473\) 461.188 0.975028
\(474\) 122.004i 0.257393i
\(475\) 52.6437i 0.110829i
\(476\) 167.519 0.351931
\(477\) 42.1632i 0.0883925i
\(478\) −136.426 −0.285411
\(479\) 344.695i 0.719613i 0.933027 + 0.359807i \(0.117157\pi\)
−0.933027 + 0.359807i \(0.882843\pi\)
\(480\) 21.9089i 0.0456435i
\(481\) 892.542i 1.85560i
\(482\) 605.958i 1.25717i
\(483\) 50.1437 + 349.936i 0.103817 + 0.724504i
\(484\) 163.381 0.337563
\(485\) −226.697 −0.467417
\(486\) 22.0454 0.0453609
\(487\) −358.665 −0.736479 −0.368239 0.929731i \(-0.620039\pi\)
−0.368239 + 0.929731i \(0.620039\pi\)
\(488\) 155.973i 0.319616i
\(489\) −301.137 −0.615822
\(490\) 94.0639i 0.191967i
\(491\) −614.809 −1.25216 −0.626079 0.779760i \(-0.715341\pi\)
−0.626079 + 0.779760i \(0.715341\pi\)
\(492\) 10.2810 0.0208964
\(493\) 66.5262i 0.134941i
\(494\) 335.349i 0.678844i
\(495\) 42.0587 0.0849672
\(496\) −75.6616 −0.152544
\(497\) 296.606i 0.596792i
\(498\) 89.8557i 0.180433i
\(499\) 800.923 1.60506 0.802528 0.596614i \(-0.203488\pi\)
0.802528 + 0.596614i \(0.203488\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) −127.263 −0.254017
\(502\) 88.1121i 0.175522i
\(503\) 167.203i 0.332412i −0.986091 0.166206i \(-0.946848\pi\)
0.986091 0.166206i \(-0.0531517\pi\)
\(504\) 75.2973i 0.149399i
\(505\) 362.989i 0.718790i
\(506\) −28.9273 201.873i −0.0571685 0.398959i
\(507\) −585.843 −1.15551
\(508\) −19.1589 −0.0377144
\(509\) 458.839 0.901451 0.450726 0.892663i \(-0.351165\pi\)
0.450726 + 0.892663i \(0.351165\pi\)
\(510\) 51.6990 0.101371
\(511\) 361.841i 0.708105i
\(512\) −22.6274 −0.0441942
\(513\) 54.7090i 0.106645i
\(514\) 126.447 0.246006
\(515\) −294.204 −0.571270
\(516\) 254.811i 0.493820i
\(517\) 406.891i 0.787024i
\(518\) −497.338 −0.960112
\(519\) −147.893 −0.284957
\(520\) 142.441i 0.273925i
\(521\) 993.025i 1.90600i −0.302974 0.952999i \(-0.597980\pi\)
0.302974 0.952999i \(-0.402020\pi\)
\(522\) 29.9025 0.0572844
\(523\) 742.227i 1.41917i 0.704619 + 0.709586i \(0.251118\pi\)
−0.704619 + 0.709586i \(0.748882\pi\)
\(524\) −100.663 −0.192104
\(525\) 76.8500i 0.146381i
\(526\) 527.540i 1.00293i
\(527\) 178.541i 0.338787i
\(528\) 43.4381i 0.0822691i
\(529\) 507.713 148.555i 0.959760 0.280822i
\(530\) −44.4439 −0.0838565
\(531\) 57.9761 0.109183
\(532\) −186.862 −0.351244
\(533\) −66.8422 −0.125407
\(534\) 316.420i 0.592546i
\(535\) 35.1653 0.0657295
\(536\) 116.002i 0.216422i
\(537\) −85.0820 −0.158440
\(538\) 465.746 0.865698
\(539\) 186.497i 0.346006i
\(540\) 23.2379i 0.0430331i
\(541\) 718.623 1.32832 0.664162 0.747589i \(-0.268788\pi\)
0.664162 + 0.747589i \(0.268788\pi\)
\(542\) 671.568 1.23906
\(543\) 11.6122i 0.0213853i
\(544\) 53.3945i 0.0981517i
\(545\) −223.226 −0.409589
\(546\) 489.547i 0.896606i
\(547\) −59.5405 −0.108849 −0.0544245 0.998518i \(-0.517332\pi\)
−0.0544245 + 0.998518i \(0.517332\pi\)
\(548\) 113.706i 0.207493i
\(549\) 165.434i 0.301337i
\(550\) 44.3338i 0.0806069i
\(551\) 74.2074i 0.134678i
\(552\) 111.537 15.9826i 0.202060 0.0289540i
\(553\) −441.991 −0.799260
\(554\) 93.3028 0.168417
\(555\) −153.486 −0.276552
\(556\) 212.107 0.381488
\(557\) 426.547i 0.765793i 0.923791 + 0.382896i \(0.125073\pi\)
−0.923791 + 0.382896i \(0.874927\pi\)
\(558\) 80.2513 0.143819
\(559\) 1656.66i 2.96361i
\(560\) −79.3703 −0.141733
\(561\) 102.502 0.182713
\(562\) 586.202i 1.04306i
\(563\) 664.896i 1.18099i −0.807042 0.590494i \(-0.798933\pi\)
0.807042 0.590494i \(-0.201067\pi\)
\(564\) −224.812 −0.398602
\(565\) 310.841 0.550162
\(566\) 632.760i 1.11795i
\(567\) 79.8649i 0.140855i
\(568\) 94.5390 0.166442
\(569\) 532.599i 0.936026i −0.883722 0.468013i \(-0.844970\pi\)
0.883722 0.468013i \(-0.155030\pi\)
\(570\) −57.6683 −0.101173
\(571\) 61.1738i 0.107135i 0.998564 + 0.0535673i \(0.0170592\pi\)
−0.998564 + 0.0535673i \(0.982941\pi\)
\(572\) 282.413i 0.493730i
\(573\) 268.943i 0.469359i
\(574\) 37.2455i 0.0648876i
\(575\) −113.837 + 16.3122i −0.197978 + 0.0283691i
\(576\) 24.0000 0.0416667
\(577\) 753.571 1.30602 0.653008 0.757351i \(-0.273507\pi\)
0.653008 + 0.757351i \(0.273507\pi\)
\(578\) −282.711 −0.489120
\(579\) 50.3899 0.0870292
\(580\) 31.5200i 0.0543447i
\(581\) −325.524 −0.560283
\(582\) 248.334i 0.426691i
\(583\) −88.1176 −0.151145
\(584\) −115.332 −0.197486
\(585\) 151.082i 0.258259i
\(586\) 489.912i 0.836027i
\(587\) 38.5168 0.0656164 0.0328082 0.999462i \(-0.489555\pi\)
0.0328082 + 0.999462i \(0.489555\pi\)
\(588\) 103.042 0.175241
\(589\) 199.156i 0.338125i
\(590\) 61.1122i 0.103580i
\(591\) 560.150 0.947801
\(592\) 158.520i 0.267770i
\(593\) 499.235 0.841880 0.420940 0.907089i \(-0.361700\pi\)
0.420940 + 0.907089i \(0.361700\pi\)
\(594\) 46.0730i 0.0775641i
\(595\) 187.292i 0.314777i
\(596\) 101.835i 0.170864i
\(597\) 549.565i 0.920544i
\(598\) −725.161 + 103.911i −1.21264 + 0.173765i
\(599\) −649.431 −1.08419 −0.542096 0.840317i \(-0.682369\pi\)
−0.542096 + 0.840317i \(0.682369\pi\)
\(600\) −24.4949 −0.0408248
\(601\) −552.930 −0.920017 −0.460009 0.887914i \(-0.652154\pi\)
−0.460009 + 0.887914i \(0.652154\pi\)
\(602\) 923.116 1.53342
\(603\) 123.039i 0.204045i
\(604\) −429.072 −0.710383
\(605\) 182.665i 0.301926i
\(606\) −397.635 −0.656163
\(607\) 483.183 0.796017 0.398009 0.917382i \(-0.369701\pi\)
0.398009 + 0.917382i \(0.369701\pi\)
\(608\) 59.5596i 0.0979599i
\(609\) 108.329i 0.177880i
\(610\) 174.383 0.285873
\(611\) 1461.62 2.39217
\(612\) 56.6335i 0.0925383i
\(613\) 562.528i 0.917664i 0.888523 + 0.458832i \(0.151732\pi\)
−0.888523 + 0.458832i \(0.848268\pi\)
\(614\) −751.668 −1.22421
\(615\) 11.4945i 0.0186903i
\(616\) −157.365 −0.255463
\(617\) 1185.68i 1.92169i −0.277090 0.960844i \(-0.589370\pi\)
0.277090 0.960844i \(-0.410630\pi\)
\(618\) 322.284i 0.521496i
\(619\) 1214.46i 1.96197i 0.194072 + 0.980987i \(0.437830\pi\)
−0.194072 + 0.980987i \(0.562170\pi\)
\(620\) 84.5922i 0.136439i
\(621\) −118.303 + 16.9521i −0.190504 + 0.0272981i
\(622\) −599.558 −0.963919
\(623\) −1146.31 −1.83998
\(624\) −156.036 −0.250058
\(625\) 25.0000 0.0400000
\(626\) 4.75951i 0.00760305i
\(627\) −114.337 −0.182356
\(628\) 67.0335i 0.106741i
\(629\) −374.064 −0.594696
\(630\) 84.1849 0.133627
\(631\) 578.694i 0.917106i −0.888667 0.458553i \(-0.848368\pi\)
0.888667 0.458553i \(-0.151632\pi\)
\(632\) 140.879i 0.222909i
\(633\) 440.436 0.695791
\(634\) −229.940 −0.362682
\(635\) 21.4203i 0.0337328i
\(636\) 48.6859i 0.0765501i
\(637\) −669.928 −1.05169
\(638\) 62.4936i 0.0979524i
\(639\) −100.274 −0.156923
\(640\) 25.2982i 0.0395285i
\(641\) 742.212i 1.15790i 0.815364 + 0.578949i \(0.196537\pi\)
−0.815364 + 0.578949i \(0.803463\pi\)
\(642\) 38.5216i 0.0600025i
\(643\) 1108.65i 1.72418i 0.506759 + 0.862088i \(0.330843\pi\)
−0.506759 + 0.862088i \(0.669157\pi\)
\(644\) −57.9010 404.071i −0.0899083 0.627439i
\(645\) 284.888 0.441686
\(646\) −140.544 −0.217561
\(647\) 313.155 0.484011 0.242005 0.970275i \(-0.422195\pi\)
0.242005 + 0.970275i \(0.422195\pi\)
\(648\) −25.4558 −0.0392837
\(649\) 121.165i 0.186695i
\(650\) 159.254 0.245006
\(651\) 290.730i 0.446589i
\(652\) 347.723 0.533317
\(653\) −328.562 −0.503158 −0.251579 0.967837i \(-0.580950\pi\)
−0.251579 + 0.967837i \(0.580950\pi\)
\(654\) 244.532i 0.373902i
\(655\) 112.544i 0.171823i
\(656\) −11.8715 −0.0180968
\(657\) 122.328 0.186192
\(658\) 814.435i 1.23774i
\(659\) 216.986i 0.329266i 0.986355 + 0.164633i \(0.0526440\pi\)
−0.986355 + 0.164633i \(0.947356\pi\)
\(660\) −48.5653 −0.0735837
\(661\) 867.631i 1.31260i 0.754498 + 0.656302i \(0.227880\pi\)
−0.754498 + 0.656302i \(0.772120\pi\)
\(662\) 863.678 1.30465
\(663\) 368.203i 0.555360i
\(664\) 103.756i 0.156260i
\(665\) 208.918i 0.314162i
\(666\) 168.136i 0.252456i
\(667\) −160.467 + 22.9939i −0.240580 + 0.0344737i
\(668\) 146.950 0.219985
\(669\) −143.448 −0.214422
\(670\) 129.695 0.193574
\(671\) 345.743 0.515265
\(672\) 86.9458i 0.129384i
\(673\) −445.497 −0.661957 −0.330978 0.943638i \(-0.607379\pi\)
−0.330978 + 0.943638i \(0.607379\pi\)
\(674\) 145.907i 0.216480i
\(675\) 25.9808 0.0384900
\(676\) 676.473 1.00070
\(677\) 568.893i 0.840314i 0.907451 + 0.420157i \(0.138025\pi\)
−0.907451 + 0.420157i \(0.861975\pi\)
\(678\) 340.510i 0.502227i
\(679\) −899.652 −1.32497
\(680\) −59.6969 −0.0877896
\(681\) 155.017i 0.227632i
\(682\) 167.718i 0.245921i
\(683\) −452.155 −0.662013 −0.331007 0.943628i \(-0.607388\pi\)
−0.331007 + 0.943628i \(0.607388\pi\)
\(684\) 63.1725i 0.0923574i
\(685\) −127.127 −0.185587
\(686\) 241.634i 0.352236i
\(687\) 55.6120i 0.0809491i
\(688\) 294.231i 0.427661i
\(689\) 316.532i 0.459408i
\(690\) −17.8691 124.702i −0.0258973 0.180728i
\(691\) 271.476 0.392874 0.196437 0.980516i \(-0.437063\pi\)
0.196437 + 0.980516i \(0.437063\pi\)
\(692\) 170.772 0.246780
\(693\) 166.911 0.240853
\(694\) −834.352 −1.20224
\(695\) 237.143i 0.341213i
\(696\) −34.5284 −0.0496097
\(697\) 28.0135i 0.0401915i
\(698\) −128.406 −0.183963
\(699\) 290.907 0.416175
\(700\) 88.7387i 0.126770i
\(701\) 629.831i 0.898474i −0.893413 0.449237i \(-0.851696\pi\)
0.893413 0.449237i \(-0.148304\pi\)
\(702\) 165.502 0.235757
\(703\) 417.254 0.593533
\(704\) 50.1580i 0.0712471i
\(705\) 251.347i 0.356521i
\(706\) 58.1947 0.0824288
\(707\) 1440.53i 2.03752i
\(708\) −66.9450 −0.0945551
\(709\) 525.929i 0.741790i 0.928675 + 0.370895i \(0.120949\pi\)
−0.928675 + 0.370895i \(0.879051\pi\)
\(710\) 105.698i 0.148870i
\(711\) 149.424i 0.210161i
\(712\) 365.370i 0.513160i
\(713\) −430.655 + 61.7104i −0.604005 + 0.0865503i
\(714\) 205.168 0.287351
\(715\) 315.748 0.441605
\(716\) 98.2443 0.137213
\(717\) −167.088 −0.233037
\(718\) 321.321i 0.447522i
\(719\) −632.328 −0.879455 −0.439727 0.898131i \(-0.644925\pi\)
−0.439727 + 0.898131i \(0.644925\pi\)
\(720\) 26.8328i 0.0372678i
\(721\) −1167.55 −1.61935
\(722\) −353.759 −0.489971
\(723\) 742.144i 1.02648i
\(724\) 13.4087i 0.0185203i
\(725\) 35.2404 0.0486074
\(726\) 200.099 0.275619
\(727\) 1047.57i 1.44095i 0.693481 + 0.720475i \(0.256076\pi\)
−0.693481 + 0.720475i \(0.743924\pi\)
\(728\) 565.280i 0.776483i
\(729\) 27.0000 0.0370370
\(730\) 128.945i 0.176637i
\(731\) 694.304 0.949801
\(732\) 191.027i 0.260965i
\(733\) 1084.08i 1.47896i 0.673180 + 0.739479i \(0.264928\pi\)
−0.673180 + 0.739479i \(0.735072\pi\)
\(734\) 67.2280i 0.0915913i
\(735\) 115.204i 0.156740i
\(736\) −128.792 + 18.4552i −0.174989 + 0.0250749i
\(737\) 257.141 0.348903
\(738\) 12.5916 0.0170618
\(739\) −219.665 −0.297246 −0.148623 0.988894i \(-0.547484\pi\)
−0.148623 + 0.988894i \(0.547484\pi\)
\(740\) 177.231 0.239501
\(741\) 410.717i 0.554274i
\(742\) −176.376 −0.237704
\(743\) 498.194i 0.670517i 0.942126 + 0.335259i \(0.108824\pi\)
−0.942126 + 0.335259i \(0.891176\pi\)
\(744\) −92.6662 −0.124551
\(745\) 113.855 0.152825
\(746\) 617.502i 0.827750i
\(747\) 110.050i 0.147323i
\(748\) −118.359 −0.158234
\(749\) 139.554 0.186320
\(750\) 27.3861i 0.0365148i
\(751\) 102.191i 0.136074i 0.997683 + 0.0680368i \(0.0216735\pi\)
−0.997683 + 0.0680368i \(0.978326\pi\)
\(752\) 259.590 0.345200
\(753\) 107.915i 0.143313i
\(754\) 224.487 0.297728
\(755\) 479.717i 0.635386i
\(756\) 92.2200i 0.121984i
\(757\) 657.156i 0.868106i 0.900887 + 0.434053i \(0.142917\pi\)
−0.900887 + 0.434053i \(0.857083\pi\)
\(758\) 608.764i 0.803119i
\(759\) −35.4285 247.244i −0.0466779 0.325749i
\(760\) 66.5897 0.0876180
\(761\) 26.7073 0.0350950 0.0175475 0.999846i \(-0.494414\pi\)
0.0175475 + 0.999846i \(0.494414\pi\)
\(762\) −23.4648 −0.0307937
\(763\) −885.877 −1.16104
\(764\) 310.549i 0.406477i
\(765\) 63.3181 0.0827688
\(766\) 884.773i 1.15506i
\(767\) 435.244 0.567463
\(768\) −27.7128 −0.0360844
\(769\) 614.585i 0.799200i 0.916690 + 0.399600i \(0.130851\pi\)
−0.916690 + 0.399600i \(0.869149\pi\)
\(770\) 175.939i 0.228493i
\(771\) 154.865 0.200863
\(772\) −58.1853 −0.0753695
\(773\) 537.714i 0.695619i 0.937565 + 0.347810i \(0.113074\pi\)
−0.937565 + 0.347810i \(0.886926\pi\)
\(774\) 312.079i 0.403203i
\(775\) 94.5770 0.122035
\(776\) 286.752i 0.369526i
\(777\) −609.112 −0.783928
\(778\) 707.073i 0.908834i
\(779\) 31.2480i 0.0401130i
\(780\) 174.454i 0.223659i
\(781\) 209.564i 0.268327i
\(782\) −43.5491 303.914i −0.0556894 0.388637i
\(783\) 36.6229 0.0467725
\(784\) −118.982 −0.151763
\(785\) 74.9457 0.0954722
\(786\) −123.286 −0.156852
\(787\) 974.561i 1.23832i −0.785263 0.619162i \(-0.787473\pi\)
0.785263 0.619162i \(-0.212527\pi\)
\(788\) −646.806 −0.820820
\(789\) 646.102i 0.818887i
\(790\) 157.507 0.199376
\(791\) 1233.58 1.55952
\(792\) 53.2006i