Properties

Label 230.3.d.a.91.4
Level $230$
Weight $3$
Character 230.91
Analytic conductor $6.267$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 230.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.26704608029\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \( x^{16} + 78x^{14} + 2165x^{12} + 28310x^{10} + 184804x^{8} + 569634x^{6} + 696037x^{4} + 285578x^{2} + 529 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 91.4
Root \(-2.98291i\) of defining polynomial
Character \(\chi\) \(=\) 230.91
Dual form 230.3.d.a.91.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} -0.278523 q^{3} +2.00000 q^{4} +2.23607i q^{5} +0.393890 q^{6} -8.51262i q^{7} -2.82843 q^{8} -8.92243 q^{9} +O(q^{10})\) \(q-1.41421 q^{2} -0.278523 q^{3} +2.00000 q^{4} +2.23607i q^{5} +0.393890 q^{6} -8.51262i q^{7} -2.82843 q^{8} -8.92243 q^{9} -3.16228i q^{10} +7.57553i q^{11} -0.557045 q^{12} -2.64076 q^{13} +12.0387i q^{14} -0.622795i q^{15} +4.00000 q^{16} -7.56057i q^{17} +12.6182 q^{18} -24.2676i q^{19} +4.47214i q^{20} +2.37096i q^{21} -10.7134i q^{22} +(-15.7366 - 16.7738i) q^{23} +0.787781 q^{24} -5.00000 q^{25} +3.73460 q^{26} +4.99180 q^{27} -17.0252i q^{28} -31.8513 q^{29} +0.880766i q^{30} -56.5071 q^{31} -5.65685 q^{32} -2.10995i q^{33} +10.6923i q^{34} +19.0348 q^{35} -17.8449 q^{36} -39.9378i q^{37} +34.3195i q^{38} +0.735511 q^{39} -6.32456i q^{40} -42.5710 q^{41} -3.35304i q^{42} -20.5721i q^{43} +15.1511i q^{44} -19.9511i q^{45} +(22.2549 + 23.7217i) q^{46} +84.3049 q^{47} -1.11409 q^{48} -23.4647 q^{49} +7.07107 q^{50} +2.10579i q^{51} -5.28152 q^{52} -11.9189i q^{53} -7.05947 q^{54} -16.9394 q^{55} +24.0773i q^{56} +6.75907i q^{57} +45.0446 q^{58} +67.6561 q^{59} -1.24559i q^{60} +35.1621i q^{61} +79.9131 q^{62} +75.9532i q^{63} +8.00000 q^{64} -5.90492i q^{65} +2.98393i q^{66} -44.0660i q^{67} -15.1211i q^{68} +(4.38299 + 4.67188i) q^{69} -26.9193 q^{70} +8.86597 q^{71} +25.2364 q^{72} -87.4150 q^{73} +56.4805i q^{74} +1.39261 q^{75} -48.5352i q^{76} +64.4876 q^{77} -1.04017 q^{78} +154.217i q^{79} +8.94427i q^{80} +78.9115 q^{81} +60.2046 q^{82} +141.642i q^{83} +4.74191i q^{84} +16.9059 q^{85} +29.0933i q^{86} +8.87131 q^{87} -21.4268i q^{88} +63.7252i q^{89} +28.2152i q^{90} +22.4798i q^{91} +(-31.4732 - 33.5476i) q^{92} +15.7385 q^{93} -119.225 q^{94} +54.2639 q^{95} +1.57556 q^{96} -143.322i q^{97} +33.1841 q^{98} -67.5921i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9} + 24 q^{13} + 64 q^{16} - 32 q^{18} + 4 q^{23} - 16 q^{24} - 80 q^{25} + 96 q^{26} - 96 q^{27} - 108 q^{29} - 116 q^{31} + 60 q^{35} + 128 q^{36} + 248 q^{39} - 156 q^{41} - 124 q^{46} - 128 q^{47} - 28 q^{49} + 48 q^{52} + 224 q^{54} + 160 q^{58} + 204 q^{59} + 64 q^{62} + 128 q^{64} - 268 q^{69} - 120 q^{70} + 236 q^{71} - 64 q^{72} - 112 q^{73} - 936 q^{77} - 432 q^{78} - 136 q^{81} - 64 q^{82} + 60 q^{85} - 152 q^{87} + 8 q^{92} + 856 q^{93} - 216 q^{94} - 160 q^{95} - 32 q^{96} + 256 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 −0.707107
\(3\) −0.278523 −0.0928408 −0.0464204 0.998922i \(-0.514781\pi\)
−0.0464204 + 0.998922i \(0.514781\pi\)
\(4\) 2.00000 0.500000
\(5\) 2.23607i 0.447214i
\(6\) 0.393890 0.0656484
\(7\) 8.51262i 1.21609i −0.793903 0.608044i \(-0.791954\pi\)
0.793903 0.608044i \(-0.208046\pi\)
\(8\) −2.82843 −0.353553
\(9\) −8.92243 −0.991381
\(10\) 3.16228i 0.316228i
\(11\) 7.57553i 0.688684i 0.938844 + 0.344342i \(0.111898\pi\)
−0.938844 + 0.344342i \(0.888102\pi\)
\(12\) −0.557045 −0.0464204
\(13\) −2.64076 −0.203135 −0.101568 0.994829i \(-0.532386\pi\)
−0.101568 + 0.994829i \(0.532386\pi\)
\(14\) 12.0387i 0.859904i
\(15\) 0.622795i 0.0415197i
\(16\) 4.00000 0.250000
\(17\) 7.56057i 0.444739i −0.974962 0.222370i \(-0.928621\pi\)
0.974962 0.222370i \(-0.0713792\pi\)
\(18\) 12.6182 0.701012
\(19\) 24.2676i 1.27724i −0.769522 0.638620i \(-0.779505\pi\)
0.769522 0.638620i \(-0.220495\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 2.37096i 0.112903i
\(22\) 10.7134i 0.486973i
\(23\) −15.7366 16.7738i −0.684199 0.729295i
\(24\) 0.787781 0.0328242
\(25\) −5.00000 −0.200000
\(26\) 3.73460 0.143638
\(27\) 4.99180 0.184881
\(28\) 17.0252i 0.608044i
\(29\) −31.8513 −1.09832 −0.549161 0.835717i \(-0.685053\pi\)
−0.549161 + 0.835717i \(0.685053\pi\)
\(30\) 0.880766i 0.0293589i
\(31\) −56.5071 −1.82281 −0.911405 0.411511i \(-0.865001\pi\)
−0.911405 + 0.411511i \(0.865001\pi\)
\(32\) −5.65685 −0.176777
\(33\) 2.10995i 0.0639380i
\(34\) 10.6923i 0.314478i
\(35\) 19.0348 0.543851
\(36\) −17.8449 −0.495690
\(37\) 39.9378i 1.07940i −0.841858 0.539700i \(-0.818538\pi\)
0.841858 0.539700i \(-0.181462\pi\)
\(38\) 34.3195i 0.903146i
\(39\) 0.735511 0.0188593
\(40\) 6.32456i 0.158114i
\(41\) −42.5710 −1.03832 −0.519159 0.854678i \(-0.673755\pi\)
−0.519159 + 0.854678i \(0.673755\pi\)
\(42\) 3.35304i 0.0798342i
\(43\) 20.5721i 0.478420i −0.970968 0.239210i \(-0.923112\pi\)
0.970968 0.239210i \(-0.0768884\pi\)
\(44\) 15.1511i 0.344342i
\(45\) 19.9511i 0.443359i
\(46\) 22.2549 + 23.7217i 0.483802 + 0.515690i
\(47\) 84.3049 1.79372 0.896860 0.442314i \(-0.145842\pi\)
0.896860 + 0.442314i \(0.145842\pi\)
\(48\) −1.11409 −0.0232102
\(49\) −23.4647 −0.478871
\(50\) 7.07107 0.141421
\(51\) 2.10579i 0.0412900i
\(52\) −5.28152 −0.101568
\(53\) 11.9189i 0.224885i −0.993658 0.112443i \(-0.964133\pi\)
0.993658 0.112443i \(-0.0358674\pi\)
\(54\) −7.05947 −0.130731
\(55\) −16.9394 −0.307989
\(56\) 24.0773i 0.429952i
\(57\) 6.75907i 0.118580i
\(58\) 45.0446 0.776631
\(59\) 67.6561 1.14671 0.573357 0.819306i \(-0.305641\pi\)
0.573357 + 0.819306i \(0.305641\pi\)
\(60\) 1.24559i 0.0207598i
\(61\) 35.1621i 0.576428i 0.957566 + 0.288214i \(0.0930614\pi\)
−0.957566 + 0.288214i \(0.906939\pi\)
\(62\) 79.9131 1.28892
\(63\) 75.9532i 1.20561i
\(64\) 8.00000 0.125000
\(65\) 5.90492i 0.0908449i
\(66\) 2.98393i 0.0452110i
\(67\) 44.0660i 0.657701i −0.944382 0.328850i \(-0.893339\pi\)
0.944382 0.328850i \(-0.106661\pi\)
\(68\) 15.1211i 0.222370i
\(69\) 4.38299 + 4.67188i 0.0635216 + 0.0677084i
\(70\) −26.9193 −0.384561
\(71\) 8.86597 0.124873 0.0624364 0.998049i \(-0.480113\pi\)
0.0624364 + 0.998049i \(0.480113\pi\)
\(72\) 25.2364 0.350506
\(73\) −87.4150 −1.19747 −0.598733 0.800949i \(-0.704329\pi\)
−0.598733 + 0.800949i \(0.704329\pi\)
\(74\) 56.4805i 0.763250i
\(75\) 1.39261 0.0185682
\(76\) 48.5352i 0.638620i
\(77\) 64.4876 0.837501
\(78\) −1.04017 −0.0133355
\(79\) 154.217i 1.95211i 0.217517 + 0.976057i \(0.430204\pi\)
−0.217517 + 0.976057i \(0.569796\pi\)
\(80\) 8.94427i 0.111803i
\(81\) 78.9115 0.974216
\(82\) 60.2046 0.734202
\(83\) 141.642i 1.70653i 0.521476 + 0.853266i \(0.325382\pi\)
−0.521476 + 0.853266i \(0.674618\pi\)
\(84\) 4.74191i 0.0564513i
\(85\) 16.9059 0.198893
\(86\) 29.0933i 0.338294i
\(87\) 8.87131 0.101969
\(88\) 21.4268i 0.243487i
\(89\) 63.7252i 0.716013i 0.933719 + 0.358007i \(0.116543\pi\)
−0.933719 + 0.358007i \(0.883457\pi\)
\(90\) 28.2152i 0.313502i
\(91\) 22.4798i 0.247030i
\(92\) −31.4732 33.5476i −0.342100 0.364648i
\(93\) 15.7385 0.169231
\(94\) −119.225 −1.26835
\(95\) 54.2639 0.571199
\(96\) 1.57556 0.0164121
\(97\) 143.322i 1.47755i −0.673952 0.738775i \(-0.735404\pi\)
0.673952 0.738775i \(-0.264596\pi\)
\(98\) 33.1841 0.338613
\(99\) 67.5921i 0.682748i
\(100\) −10.0000 −0.100000
\(101\) 27.7102 0.274359 0.137179 0.990546i \(-0.456196\pi\)
0.137179 + 0.990546i \(0.456196\pi\)
\(102\) 2.97803i 0.0291964i
\(103\) 133.542i 1.29652i 0.761418 + 0.648261i \(0.224503\pi\)
−0.761418 + 0.648261i \(0.775497\pi\)
\(104\) 7.46919 0.0718192
\(105\) −5.30162 −0.0504916
\(106\) 16.8559i 0.159018i
\(107\) 50.3091i 0.470179i −0.971974 0.235089i \(-0.924462\pi\)
0.971974 0.235089i \(-0.0755383\pi\)
\(108\) 9.98360 0.0924407
\(109\) 128.819i 1.18182i −0.806737 0.590911i \(-0.798768\pi\)
0.806737 0.590911i \(-0.201232\pi\)
\(110\) 23.9559 0.217781
\(111\) 11.1236i 0.100212i
\(112\) 34.0505i 0.304022i
\(113\) 86.3028i 0.763742i −0.924216 0.381871i \(-0.875280\pi\)
0.924216 0.381871i \(-0.124720\pi\)
\(114\) 9.55876i 0.0838488i
\(115\) 37.5073 35.1881i 0.326151 0.305983i
\(116\) −63.7027 −0.549161
\(117\) 23.5620 0.201384
\(118\) −95.6802 −0.810849
\(119\) −64.3602 −0.540842
\(120\) 1.76153i 0.0146794i
\(121\) 63.6114 0.525714
\(122\) 49.7267i 0.407596i
\(123\) 11.8570 0.0963983
\(124\) −113.014 −0.911405
\(125\) 11.1803i 0.0894427i
\(126\) 107.414i 0.852492i
\(127\) −11.0135 −0.0867206 −0.0433603 0.999059i \(-0.513806\pi\)
−0.0433603 + 0.999059i \(0.513806\pi\)
\(128\) −11.3137 −0.0883883
\(129\) 5.72978i 0.0444169i
\(130\) 8.35081i 0.0642370i
\(131\) 3.63941 0.0277818 0.0138909 0.999904i \(-0.495578\pi\)
0.0138909 + 0.999904i \(0.495578\pi\)
\(132\) 4.21991i 0.0319690i
\(133\) −206.581 −1.55324
\(134\) 62.3187i 0.465065i
\(135\) 11.1620i 0.0826815i
\(136\) 21.3845i 0.157239i
\(137\) 9.69785i 0.0707873i 0.999373 + 0.0353936i \(0.0112685\pi\)
−0.999373 + 0.0353936i \(0.988732\pi\)
\(138\) −6.19849 6.60703i −0.0449166 0.0478771i
\(139\) 8.05485 0.0579486 0.0289743 0.999580i \(-0.490776\pi\)
0.0289743 + 0.999580i \(0.490776\pi\)
\(140\) 38.0696 0.271926
\(141\) −23.4808 −0.166531
\(142\) −12.5384 −0.0882984
\(143\) 20.0051i 0.139896i
\(144\) −35.6897 −0.247845
\(145\) 71.2217i 0.491184i
\(146\) 123.624 0.846737
\(147\) 6.53544 0.0444588
\(148\) 79.8755i 0.539700i
\(149\) 144.062i 0.966859i 0.875383 + 0.483430i \(0.160609\pi\)
−0.875383 + 0.483430i \(0.839391\pi\)
\(150\) −1.96945 −0.0131297
\(151\) −109.956 −0.728188 −0.364094 0.931362i \(-0.618621\pi\)
−0.364094 + 0.931362i \(0.618621\pi\)
\(152\) 68.6391i 0.451573i
\(153\) 67.4586i 0.440906i
\(154\) −91.1992 −0.592202
\(155\) 126.354i 0.815185i
\(156\) 1.47102 0.00942963
\(157\) 24.8208i 0.158094i −0.996871 0.0790471i \(-0.974812\pi\)
0.996871 0.0790471i \(-0.0251877\pi\)
\(158\) 218.096i 1.38035i
\(159\) 3.31969i 0.0208785i
\(160\) 12.6491i 0.0790569i
\(161\) −142.789 + 133.960i −0.886887 + 0.832047i
\(162\) −111.598 −0.688875
\(163\) 108.964 0.668489 0.334244 0.942486i \(-0.391519\pi\)
0.334244 + 0.942486i \(0.391519\pi\)
\(164\) −85.1421 −0.519159
\(165\) 4.71800 0.0285940
\(166\) 200.312i 1.20670i
\(167\) 72.1383 0.431966 0.215983 0.976397i \(-0.430704\pi\)
0.215983 + 0.976397i \(0.430704\pi\)
\(168\) 6.70608i 0.0399171i
\(169\) −162.026 −0.958736
\(170\) −23.9086 −0.140639
\(171\) 216.526i 1.26623i
\(172\) 41.1441i 0.239210i
\(173\) −150.077 −0.867497 −0.433748 0.901034i \(-0.642809\pi\)
−0.433748 + 0.901034i \(0.642809\pi\)
\(174\) −12.5459 −0.0721031
\(175\) 42.5631i 0.243218i
\(176\) 30.3021i 0.172171i
\(177\) −18.8437 −0.106462
\(178\) 90.1210i 0.506298i
\(179\) 207.058 1.15675 0.578375 0.815771i \(-0.303687\pi\)
0.578375 + 0.815771i \(0.303687\pi\)
\(180\) 39.9023i 0.221679i
\(181\) 331.138i 1.82949i −0.404031 0.914746i \(-0.632391\pi\)
0.404031 0.914746i \(-0.367609\pi\)
\(182\) 31.7912i 0.174677i
\(183\) 9.79343i 0.0535160i
\(184\) 44.5098 + 47.4434i 0.241901 + 0.257845i
\(185\) 89.3036 0.482722
\(186\) −22.2576 −0.119665
\(187\) 57.2753 0.306285
\(188\) 168.610 0.896860
\(189\) 42.4933i 0.224832i
\(190\) −76.7408 −0.403899
\(191\) 172.749i 0.904447i −0.891905 0.452223i \(-0.850631\pi\)
0.891905 0.452223i \(-0.149369\pi\)
\(192\) −2.22818 −0.0116051
\(193\) 136.450 0.706996 0.353498 0.935435i \(-0.384992\pi\)
0.353498 + 0.935435i \(0.384992\pi\)
\(194\) 202.689i 1.04479i
\(195\) 1.64465i 0.00843412i
\(196\) −46.9293 −0.239435
\(197\) −271.090 −1.37609 −0.688046 0.725667i \(-0.741531\pi\)
−0.688046 + 0.725667i \(0.741531\pi\)
\(198\) 95.5896i 0.482776i
\(199\) 257.292i 1.29292i −0.762946 0.646462i \(-0.776248\pi\)
0.762946 0.646462i \(-0.223752\pi\)
\(200\) 14.1421 0.0707107
\(201\) 12.2734i 0.0610615i
\(202\) −39.1882 −0.194001
\(203\) 271.138i 1.33566i
\(204\) 4.21158i 0.0206450i
\(205\) 95.1918i 0.464350i
\(206\) 188.857i 0.916780i
\(207\) 140.408 + 149.663i 0.678302 + 0.723009i
\(208\) −10.5630 −0.0507838
\(209\) 183.840 0.879615
\(210\) 7.49762 0.0357030
\(211\) 54.1944 0.256846 0.128423 0.991720i \(-0.459009\pi\)
0.128423 + 0.991720i \(0.459009\pi\)
\(212\) 23.8378i 0.112443i
\(213\) −2.46937 −0.0115933
\(214\) 71.1478i 0.332467i
\(215\) 46.0005 0.213956
\(216\) −14.1189 −0.0653655
\(217\) 481.023i 2.21670i
\(218\) 182.177i 0.835674i
\(219\) 24.3471 0.111174
\(220\) −33.8788 −0.153994
\(221\) 19.9656i 0.0903423i
\(222\) 15.7311i 0.0708608i
\(223\) 104.611 0.469105 0.234553 0.972103i \(-0.424637\pi\)
0.234553 + 0.972103i \(0.424637\pi\)
\(224\) 48.1546i 0.214976i
\(225\) 44.6121 0.198276
\(226\) 122.051i 0.540047i
\(227\) 200.484i 0.883190i −0.897215 0.441595i \(-0.854413\pi\)
0.897215 0.441595i \(-0.145587\pi\)
\(228\) 13.5181i 0.0592901i
\(229\) 22.0718i 0.0963834i −0.998838 0.0481917i \(-0.984654\pi\)
0.998838 0.0481917i \(-0.0153458\pi\)
\(230\) −53.0434 + 49.7634i −0.230623 + 0.216363i
\(231\) −17.9612 −0.0777543
\(232\) 90.0892 0.388315
\(233\) −338.632 −1.45335 −0.726677 0.686979i \(-0.758936\pi\)
−0.726677 + 0.686979i \(0.758936\pi\)
\(234\) −33.3217 −0.142400
\(235\) 188.511i 0.802176i
\(236\) 135.312 0.573357
\(237\) 42.9529i 0.181236i
\(238\) 91.0191 0.382433
\(239\) 149.374 0.624997 0.312499 0.949918i \(-0.398834\pi\)
0.312499 + 0.949918i \(0.398834\pi\)
\(240\) 2.49118i 0.0103799i
\(241\) 133.030i 0.551991i −0.961159 0.275995i \(-0.910993\pi\)
0.961159 0.275995i \(-0.0890074\pi\)
\(242\) −89.9601 −0.371736
\(243\) −66.9048 −0.275328
\(244\) 70.3242i 0.288214i
\(245\) 52.4686i 0.214158i
\(246\) −16.7683 −0.0681639
\(247\) 64.0848i 0.259453i
\(248\) 159.826 0.644461
\(249\) 39.4505i 0.158436i
\(250\) 15.8114i 0.0632456i
\(251\) 376.920i 1.50167i 0.660489 + 0.750836i \(0.270349\pi\)
−0.660489 + 0.750836i \(0.729651\pi\)
\(252\) 151.906i 0.602803i
\(253\) 127.070 119.213i 0.502254 0.471197i
\(254\) 15.5755 0.0613208
\(255\) −4.70869 −0.0184654
\(256\) 16.0000 0.0625000
\(257\) 226.085 0.879708 0.439854 0.898069i \(-0.355030\pi\)
0.439854 + 0.898069i \(0.355030\pi\)
\(258\) 8.10314i 0.0314075i
\(259\) −339.975 −1.31264
\(260\) 11.8098i 0.0454224i
\(261\) 284.191 1.08885
\(262\) −5.14690 −0.0196447
\(263\) 2.43654i 0.00926441i 0.999989 + 0.00463221i \(0.00147448\pi\)
−0.999989 + 0.00463221i \(0.998526\pi\)
\(264\) 5.96785i 0.0226055i
\(265\) 26.6515 0.100572
\(266\) 292.149 1.09830
\(267\) 17.7489i 0.0664753i
\(268\) 88.1319i 0.328850i
\(269\) −311.337 −1.15739 −0.578694 0.815545i \(-0.696437\pi\)
−0.578694 + 0.815545i \(0.696437\pi\)
\(270\) 15.7855i 0.0584647i
\(271\) 260.751 0.962182 0.481091 0.876671i \(-0.340241\pi\)
0.481091 + 0.876671i \(0.340241\pi\)
\(272\) 30.2423i 0.111185i
\(273\) 6.26112i 0.0229345i
\(274\) 13.7148i 0.0500541i
\(275\) 37.8776i 0.137737i
\(276\) 8.76599 + 9.34376i 0.0317608 + 0.0338542i
\(277\) −182.267 −0.658004 −0.329002 0.944329i \(-0.606712\pi\)
−0.329002 + 0.944329i \(0.606712\pi\)
\(278\) −11.3913 −0.0409758
\(279\) 504.180 1.80710
\(280\) −53.8385 −0.192280
\(281\) 4.60502i 0.0163880i −0.999966 0.00819398i \(-0.997392\pi\)
0.999966 0.00819398i \(-0.00260825\pi\)
\(282\) 33.2069 0.117755
\(283\) 332.897i 1.17631i −0.808747 0.588157i \(-0.799854\pi\)
0.808747 0.588157i \(-0.200146\pi\)
\(284\) 17.7319 0.0624364
\(285\) −15.1137 −0.0530306
\(286\) 28.2915i 0.0989215i
\(287\) 362.391i 1.26269i
\(288\) 50.4729 0.175253
\(289\) 231.838 0.802207
\(290\) 100.723i 0.347320i
\(291\) 39.9185i 0.137177i
\(292\) −174.830 −0.598733
\(293\) 336.114i 1.14715i −0.819154 0.573574i \(-0.805557\pi\)
0.819154 0.573574i \(-0.194443\pi\)
\(294\) −9.24251 −0.0314371
\(295\) 151.284i 0.512826i
\(296\) 112.961i 0.381625i
\(297\) 37.8155i 0.127325i
\(298\) 203.734i 0.683673i
\(299\) 41.5565 + 44.2955i 0.138985 + 0.148146i
\(300\) 2.78523 0.00928408
\(301\) −175.122 −0.581801
\(302\) 155.502 0.514907
\(303\) −7.71792 −0.0254717
\(304\) 97.0703i 0.319310i
\(305\) −78.6248 −0.257786
\(306\) 95.4009i 0.311768i
\(307\) −457.934 −1.49164 −0.745821 0.666147i \(-0.767943\pi\)
−0.745821 + 0.666147i \(0.767943\pi\)
\(308\) 128.975 0.418750
\(309\) 37.1944i 0.120370i
\(310\) 178.691i 0.576423i
\(311\) −455.620 −1.46502 −0.732508 0.680758i \(-0.761650\pi\)
−0.732508 + 0.680758i \(0.761650\pi\)
\(312\) −2.08034 −0.00666775
\(313\) 589.353i 1.88292i 0.337130 + 0.941458i \(0.390544\pi\)
−0.337130 + 0.941458i \(0.609456\pi\)
\(314\) 35.1019i 0.111789i
\(315\) −169.837 −0.539164
\(316\) 308.434i 0.976057i
\(317\) −386.251 −1.21846 −0.609229 0.792994i \(-0.708521\pi\)
−0.609229 + 0.792994i \(0.708521\pi\)
\(318\) 4.69475i 0.0147634i
\(319\) 241.291i 0.756397i
\(320\) 17.8885i 0.0559017i
\(321\) 14.0122i 0.0436518i
\(322\) 201.934 189.447i 0.627124 0.588346i
\(323\) −183.477 −0.568039
\(324\) 157.823 0.487108
\(325\) 13.2038 0.0406271
\(326\) −154.098 −0.472693
\(327\) 35.8789i 0.109721i
\(328\) 120.409 0.367101
\(329\) 717.655i 2.18132i
\(330\) −6.67226 −0.0202190
\(331\) 220.712 0.666803 0.333402 0.942785i \(-0.391804\pi\)
0.333402 + 0.942785i \(0.391804\pi\)
\(332\) 283.284i 0.853266i
\(333\) 356.342i 1.07010i
\(334\) −102.019 −0.305446
\(335\) 98.5345 0.294133
\(336\) 9.48382i 0.0282257i
\(337\) 193.563i 0.574371i −0.957875 0.287185i \(-0.907280\pi\)
0.957875 0.287185i \(-0.0927196\pi\)
\(338\) 229.140 0.677929
\(339\) 24.0373i 0.0709064i
\(340\) 33.8119 0.0994467
\(341\) 428.071i 1.25534i
\(342\) 306.213i 0.895361i
\(343\) 217.373i 0.633739i
\(344\) 58.1866i 0.169147i
\(345\) −10.4466 + 9.80067i −0.0302801 + 0.0284077i
\(346\) 212.241 0.613413
\(347\) −262.429 −0.756278 −0.378139 0.925749i \(-0.623436\pi\)
−0.378139 + 0.925749i \(0.623436\pi\)
\(348\) 17.7426 0.0509846
\(349\) 229.831 0.658543 0.329271 0.944235i \(-0.393197\pi\)
0.329271 + 0.944235i \(0.393197\pi\)
\(350\) 60.1933i 0.171981i
\(351\) −13.1821 −0.0375560
\(352\) 42.8536i 0.121743i
\(353\) 367.482 1.04103 0.520513 0.853854i \(-0.325741\pi\)
0.520513 + 0.853854i \(0.325741\pi\)
\(354\) 26.6491 0.0752799
\(355\) 19.8249i 0.0558448i
\(356\) 127.450i 0.358007i
\(357\) 17.9258 0.0502123
\(358\) −292.824 −0.817945
\(359\) 239.971i 0.668442i −0.942495 0.334221i \(-0.891527\pi\)
0.942495 0.334221i \(-0.108473\pi\)
\(360\) 56.4304i 0.156751i
\(361\) −227.915 −0.631344
\(362\) 468.300i 1.29365i
\(363\) −17.7172 −0.0488077
\(364\) 44.9595i 0.123515i
\(365\) 195.466i 0.535523i
\(366\) 13.8500i 0.0378416i
\(367\) 389.113i 1.06025i −0.847918 0.530127i \(-0.822144\pi\)
0.847918 0.530127i \(-0.177856\pi\)
\(368\) −62.9463 67.0952i −0.171050 0.182324i
\(369\) 379.837 1.02937
\(370\) −126.294 −0.341336
\(371\) −101.461 −0.273480
\(372\) 31.4770 0.0846156
\(373\) 546.309i 1.46463i 0.680964 + 0.732317i \(0.261561\pi\)
−0.680964 + 0.732317i \(0.738439\pi\)
\(374\) −80.9995 −0.216576
\(375\) 3.11398i 0.00830394i
\(376\) −238.450 −0.634176
\(377\) 84.1117 0.223108
\(378\) 60.0946i 0.158980i
\(379\) 295.837i 0.780573i 0.920693 + 0.390287i \(0.127624\pi\)
−0.920693 + 0.390287i \(0.872376\pi\)
\(380\) 108.528 0.285600
\(381\) 3.06751 0.00805122
\(382\) 244.304i 0.639541i
\(383\) 566.033i 1.47789i −0.673765 0.738946i \(-0.735324\pi\)
0.673765 0.738946i \(-0.264676\pi\)
\(384\) 3.15112 0.00820605
\(385\) 144.199i 0.374542i
\(386\) −192.970 −0.499921
\(387\) 183.553i 0.474296i
\(388\) 286.645i 0.738775i
\(389\) 196.043i 0.503966i −0.967732 0.251983i \(-0.918917\pi\)
0.967732 0.251983i \(-0.0810826\pi\)
\(390\) 2.32589i 0.00596382i
\(391\) −126.819 + 118.978i −0.324346 + 0.304290i
\(392\) 66.3681 0.169306
\(393\) −1.01366 −0.00257928
\(394\) 383.380 0.973045
\(395\) −344.840 −0.873012
\(396\) 135.184i 0.341374i
\(397\) −298.788 −0.752616 −0.376308 0.926495i \(-0.622806\pi\)
−0.376308 + 0.926495i \(0.622806\pi\)
\(398\) 363.866i 0.914236i
\(399\) 57.5374 0.144204
\(400\) −20.0000 −0.0500000
\(401\) 785.114i 1.95789i 0.204121 + 0.978946i \(0.434567\pi\)
−0.204121 + 0.978946i \(0.565433\pi\)
\(402\) 17.3572i 0.0431770i
\(403\) 149.222 0.370277
\(404\) 55.4204 0.137179
\(405\) 176.451i 0.435683i
\(406\) 383.447i 0.944452i
\(407\) 302.550 0.743365
\(408\) 5.95607i 0.0145982i
\(409\) 358.186 0.875761 0.437881 0.899033i \(-0.355729\pi\)
0.437881 + 0.899033i \(0.355729\pi\)
\(410\) 134.621i 0.328345i
\(411\) 2.70107i 0.00657195i
\(412\) 267.084i 0.648261i
\(413\) 575.930i 1.39450i
\(414\) −198.568 211.655i −0.479632 0.511245i
\(415\) −316.722 −0.763184
\(416\) 14.9384 0.0359096
\(417\) −2.24346 −0.00537999
\(418\) −259.988 −0.621982
\(419\) 195.271i 0.466042i −0.972472 0.233021i \(-0.925139\pi\)
0.972472 0.233021i \(-0.0748610\pi\)
\(420\) −10.6032 −0.0252458
\(421\) 768.042i 1.82433i −0.409826 0.912164i \(-0.634410\pi\)
0.409826 0.912164i \(-0.365590\pi\)
\(422\) −76.6425 −0.181617
\(423\) −752.204 −1.77826
\(424\) 33.7118i 0.0795089i
\(425\) 37.8028i 0.0889479i
\(426\) 3.49222 0.00819770
\(427\) 299.321 0.700987
\(428\) 100.618i 0.235089i
\(429\) 5.57188i 0.0129881i
\(430\) −65.0546 −0.151290
\(431\) 333.122i 0.772905i 0.922309 + 0.386453i \(0.126300\pi\)
−0.922309 + 0.386453i \(0.873700\pi\)
\(432\) 19.9672 0.0462204
\(433\) 7.49741i 0.0173150i −0.999963 0.00865752i \(-0.997244\pi\)
0.999963 0.00865752i \(-0.00275581\pi\)
\(434\) 680.270i 1.56744i
\(435\) 19.8369i 0.0456020i
\(436\) 257.637i 0.590911i
\(437\) −407.059 + 381.889i −0.931485 + 0.873887i
\(438\) −34.4319 −0.0786117
\(439\) −303.939 −0.692344 −0.346172 0.938171i \(-0.612519\pi\)
−0.346172 + 0.938171i \(0.612519\pi\)
\(440\) 47.9118 0.108891
\(441\) 209.362 0.474743
\(442\) 28.2357i 0.0638816i
\(443\) 637.145 1.43825 0.719125 0.694881i \(-0.244543\pi\)
0.719125 + 0.694881i \(0.244543\pi\)
\(444\) 22.2471i 0.0501062i
\(445\) −142.494 −0.320211
\(446\) −147.942 −0.331708
\(447\) 40.1245i 0.0897640i
\(448\) 68.1009i 0.152011i
\(449\) 88.9331 0.198069 0.0990346 0.995084i \(-0.468425\pi\)
0.0990346 + 0.995084i \(0.468425\pi\)
\(450\) −63.0911 −0.140202
\(451\) 322.498i 0.715073i
\(452\) 172.606i 0.381871i
\(453\) 30.6253 0.0676056
\(454\) 283.527i 0.624509i
\(455\) −50.2663 −0.110475
\(456\) 19.1175i 0.0419244i
\(457\) 377.669i 0.826410i 0.910638 + 0.413205i \(0.135591\pi\)
−0.910638 + 0.413205i \(0.864409\pi\)
\(458\) 31.2142i 0.0681534i
\(459\) 37.7408i 0.0822240i
\(460\) 75.0147 70.3761i 0.163075 0.152992i
\(461\) −585.070 −1.26913 −0.634566 0.772869i \(-0.718821\pi\)
−0.634566 + 0.772869i \(0.718821\pi\)
\(462\) 25.4010 0.0549806
\(463\) −225.877 −0.487854 −0.243927 0.969794i \(-0.578436\pi\)
−0.243927 + 0.969794i \(0.578436\pi\)
\(464\) −127.405 −0.274580
\(465\) 35.1924i 0.0756825i
\(466\) 478.897 1.02768
\(467\) 702.984i 1.50532i −0.658410 0.752659i \(-0.728771\pi\)
0.658410 0.752659i \(-0.271229\pi\)
\(468\) 47.1240 0.100692
\(469\) −375.117 −0.799822
\(470\) 266.595i 0.567224i
\(471\) 6.91315i 0.0146776i
\(472\) −191.360 −0.405424
\(473\) 155.844 0.329480
\(474\) 60.7446i 0.128153i
\(475\) 121.338i 0.255448i
\(476\) −128.720 −0.270421
\(477\) 106.346i 0.222947i
\(478\) −211.247 −0.441940
\(479\) 291.706i 0.608989i −0.952514 0.304494i \(-0.901512\pi\)
0.952514 0.304494i \(-0.0984875\pi\)
\(480\) 3.52306i 0.00733971i
\(481\) 105.466i 0.219264i
\(482\) 188.132i 0.390316i
\(483\) 39.7699 37.3107i 0.0823394 0.0772479i
\(484\) 127.223 0.262857
\(485\) 320.479 0.660781
\(486\) 94.6177 0.194687
\(487\) 205.957 0.422909 0.211454 0.977388i \(-0.432180\pi\)
0.211454 + 0.977388i \(0.432180\pi\)
\(488\) 99.4534i 0.203798i
\(489\) −30.3488 −0.0620630
\(490\) 74.2018i 0.151432i
\(491\) −192.478 −0.392012 −0.196006 0.980603i \(-0.562797\pi\)
−0.196006 + 0.980603i \(0.562797\pi\)
\(492\) 23.7140 0.0481992
\(493\) 240.814i 0.488467i
\(494\) 90.6296i 0.183461i
\(495\) 151.140 0.305334
\(496\) −226.028 −0.455703
\(497\) 75.4726i 0.151856i
\(498\) 55.7915i 0.112031i
\(499\) 887.386 1.77833 0.889164 0.457589i \(-0.151287\pi\)
0.889164 + 0.457589i \(0.151287\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) −20.0921 −0.0401041
\(502\) 533.045i 1.06184i
\(503\) 330.810i 0.657673i −0.944387 0.328837i \(-0.893343\pi\)
0.944387 0.328837i \(-0.106657\pi\)
\(504\) 214.828i 0.426246i
\(505\) 61.9619i 0.122697i
\(506\) −179.704 + 168.592i −0.355147 + 0.333187i
\(507\) 45.1280 0.0890099
\(508\) −22.0270 −0.0433603
\(509\) −407.928 −0.801430 −0.400715 0.916203i \(-0.631238\pi\)
−0.400715 + 0.916203i \(0.631238\pi\)
\(510\) 6.65909 0.0130570
\(511\) 744.131i 1.45622i
\(512\) −22.6274 −0.0441942
\(513\) 121.139i 0.236138i
\(514\) −319.733 −0.622048
\(515\) −298.609 −0.579822
\(516\) 11.4596i 0.0222085i
\(517\) 638.654i 1.23531i
\(518\) 480.797 0.928180
\(519\) 41.7998 0.0805391
\(520\) 16.7016i 0.0321185i
\(521\) 458.780i 0.880576i −0.897857 0.440288i \(-0.854876\pi\)
0.897857 0.440288i \(-0.145124\pi\)
\(522\) −401.907 −0.769937
\(523\) 404.987i 0.774354i −0.922005 0.387177i \(-0.873450\pi\)
0.922005 0.387177i \(-0.126550\pi\)
\(524\) 7.27882 0.0138909
\(525\) 11.8548i 0.0225805i
\(526\) 3.44579i 0.00655093i
\(527\) 427.226i 0.810675i
\(528\) 8.43982i 0.0159845i
\(529\) −33.7199 + 527.924i −0.0637427 + 0.997966i
\(530\) −37.6909 −0.0711149
\(531\) −603.656 −1.13683
\(532\) −413.161 −0.776619
\(533\) 112.420 0.210919
\(534\) 25.1007i 0.0470051i
\(535\) 112.495 0.210270
\(536\) 124.637i 0.232532i
\(537\) −57.6703 −0.107394
\(538\) 440.298 0.818397
\(539\) 177.757i 0.329791i
\(540\) 22.3240i 0.0413408i
\(541\) 1047.51 1.93625 0.968123 0.250477i \(-0.0805875\pi\)
0.968123 + 0.250477i \(0.0805875\pi\)
\(542\) −368.758 −0.680366
\(543\) 92.2294i 0.169851i
\(544\) 42.7690i 0.0786195i
\(545\) 288.047 0.528527
\(546\) 8.85457i 0.0162172i
\(547\) 123.784 0.226296 0.113148 0.993578i \(-0.463907\pi\)
0.113148 + 0.993578i \(0.463907\pi\)
\(548\) 19.3957i 0.0353936i
\(549\) 313.731i 0.571459i
\(550\) 53.5671i 0.0973946i
\(551\) 772.955i 1.40282i
\(552\) −12.3970 13.2141i −0.0224583 0.0239385i
\(553\) 1312.79 2.37394
\(554\) 257.765 0.465279
\(555\) −24.8731 −0.0448163
\(556\) 16.1097 0.0289743
\(557\) 246.292i 0.442176i 0.975254 + 0.221088i \(0.0709608\pi\)
−0.975254 + 0.221088i \(0.929039\pi\)
\(558\) −713.019 −1.27781
\(559\) 54.3259i 0.0971840i
\(560\) 76.1392 0.135963
\(561\) −15.9525 −0.0284357
\(562\) 6.51248i 0.0115880i
\(563\) 574.776i 1.02092i 0.859902 + 0.510458i \(0.170524\pi\)
−0.859902 + 0.510458i \(0.829476\pi\)
\(564\) −46.9616 −0.0832653
\(565\) 192.979 0.341556
\(566\) 470.787i 0.831780i
\(567\) 671.743i 1.18473i
\(568\) −25.0768 −0.0441492
\(569\) 794.332i 1.39601i 0.716091 + 0.698007i \(0.245930\pi\)
−0.716091 + 0.698007i \(0.754070\pi\)
\(570\) 21.3740 0.0374983
\(571\) 416.688i 0.729751i −0.931056 0.364876i \(-0.881111\pi\)
0.931056 0.364876i \(-0.118889\pi\)
\(572\) 40.0103i 0.0699480i
\(573\) 48.1146i 0.0839696i
\(574\) 512.498i 0.892854i
\(575\) 78.6829 + 83.8689i 0.136840 + 0.145859i
\(576\) −71.3794 −0.123923
\(577\) −282.647 −0.489856 −0.244928 0.969541i \(-0.578764\pi\)
−0.244928 + 0.969541i \(0.578764\pi\)
\(578\) −327.868 −0.567246
\(579\) −38.0044 −0.0656381
\(580\) 142.443i 0.245592i
\(581\) 1205.75 2.07529
\(582\) 56.4533i 0.0969988i
\(583\) 90.2920 0.154875
\(584\) 247.247 0.423368
\(585\) 52.6862i 0.0900618i
\(586\) 475.337i 0.811156i
\(587\) −168.123 −0.286410 −0.143205 0.989693i \(-0.545741\pi\)
−0.143205 + 0.989693i \(0.545741\pi\)
\(588\) 13.0709 0.0222294
\(589\) 1371.29i 2.32817i
\(590\) 213.947i 0.362623i
\(591\) 75.5048 0.127758
\(592\) 159.751i 0.269850i
\(593\) −419.364 −0.707191 −0.353595 0.935398i \(-0.615041\pi\)
−0.353595 + 0.935398i \(0.615041\pi\)
\(594\) 53.4792i 0.0900323i
\(595\) 143.914i 0.241872i
\(596\) 288.124i 0.483430i
\(597\) 71.6616i 0.120036i
\(598\) −58.7698 62.6433i −0.0982773 0.104755i
\(599\) −519.774 −0.867736 −0.433868 0.900977i \(-0.642852\pi\)
−0.433868 + 0.900977i \(0.642852\pi\)
\(600\) −3.93890 −0.00656484
\(601\) 1089.19 1.81230 0.906151 0.422955i \(-0.139007\pi\)
0.906151 + 0.422955i \(0.139007\pi\)
\(602\) 247.660 0.411395
\(603\) 393.175i 0.652032i
\(604\) −219.913 −0.364094
\(605\) 142.239i 0.235107i
\(606\) 10.9148 0.0180112
\(607\) 890.673 1.46734 0.733668 0.679508i \(-0.237807\pi\)
0.733668 + 0.679508i \(0.237807\pi\)
\(608\) 137.278i 0.225786i
\(609\) 75.5181i 0.124003i
\(610\) 111.192 0.182282
\(611\) −222.629 −0.364368
\(612\) 134.917i 0.220453i
\(613\) 629.354i 1.02668i −0.858186 0.513339i \(-0.828408\pi\)
0.858186 0.513339i \(-0.171592\pi\)
\(614\) 647.616 1.05475
\(615\) 26.5131i 0.0431107i
\(616\) −182.398 −0.296101
\(617\) 157.187i 0.254760i 0.991854 + 0.127380i \(0.0406568\pi\)
−0.991854 + 0.127380i \(0.959343\pi\)
\(618\) 52.6008i 0.0851146i
\(619\) 462.293i 0.746838i 0.927663 + 0.373419i \(0.121815\pi\)
−0.927663 + 0.373419i \(0.878185\pi\)
\(620\) 252.707i 0.407593i
\(621\) −78.5539 83.7314i −0.126496 0.134833i
\(622\) 644.344 1.03592
\(623\) 542.468 0.870735
\(624\) 2.94204 0.00471481
\(625\) 25.0000 0.0400000
\(626\) 833.471i 1.33142i
\(627\) −51.2035 −0.0816642
\(628\) 49.6416i 0.0790471i
\(629\) −301.952 −0.480051
\(630\) 240.185 0.381246
\(631\) 411.630i 0.652345i 0.945310 + 0.326173i \(0.105759\pi\)
−0.945310 + 0.326173i \(0.894241\pi\)
\(632\) 436.191i 0.690176i
\(633\) −15.0944 −0.0238458
\(634\) 546.242 0.861581
\(635\) 24.6270i 0.0387827i
\(636\) 6.63937i 0.0104393i
\(637\) 61.9645 0.0972756
\(638\) 341.236i 0.534853i
\(639\) −79.1060 −0.123797
\(640\) 25.2982i 0.0395285i
\(641\) 251.089i 0.391715i −0.980632 0.195857i \(-0.937251\pi\)
0.980632 0.195857i \(-0.0627490\pi\)
\(642\) 19.8163i 0.0308665i
\(643\) 102.907i 0.160042i 0.996793 + 0.0800211i \(0.0254988\pi\)
−0.996793 + 0.0800211i \(0.974501\pi\)
\(644\) −285.578 + 267.919i −0.443444 + 0.416023i
\(645\) −12.8122 −0.0198639
\(646\) 259.475 0.401664
\(647\) −437.368 −0.675993 −0.337997 0.941147i \(-0.609749\pi\)
−0.337997 + 0.941147i \(0.609749\pi\)
\(648\) −223.195 −0.344437
\(649\) 512.530i 0.789723i
\(650\) −18.6730 −0.0287277
\(651\) 133.976i 0.205800i
\(652\) 217.927 0.334244
\(653\) −94.4001 −0.144564 −0.0722819 0.997384i \(-0.523028\pi\)
−0.0722819 + 0.997384i \(0.523028\pi\)
\(654\) 50.7404i 0.0775847i
\(655\) 8.13797i 0.0124244i
\(656\) −170.284 −0.259580
\(657\) 779.954 1.18714
\(658\) 1014.92i 1.54243i
\(659\) 759.727i 1.15285i −0.817151 0.576424i \(-0.804448\pi\)
0.817151 0.576424i \(-0.195552\pi\)
\(660\) 9.43600 0.0142970
\(661\) 581.754i 0.880112i −0.897970 0.440056i \(-0.854959\pi\)
0.897970 0.440056i \(-0.145041\pi\)
\(662\) −312.134 −0.471501
\(663\) 5.56088i 0.00838745i
\(664\) 400.625i 0.603350i
\(665\) 461.928i 0.694629i
\(666\) 503.943i 0.756672i
\(667\) 501.231 + 534.267i 0.751471 + 0.801001i
\(668\) 144.277 0.215983
\(669\) −29.1364 −0.0435521
\(670\) −139.349 −0.207983
\(671\) −266.371 −0.396977
\(672\) 13.4122i 0.0199586i
\(673\) −831.173 −1.23503 −0.617513 0.786560i \(-0.711860\pi\)
−0.617513 + 0.786560i \(0.711860\pi\)
\(674\) 273.739i 0.406142i
\(675\) −24.9590 −0.0369763
\(676\) −324.053 −0.479368
\(677\) 106.706i 0.157616i −0.996890 0.0788079i \(-0.974889\pi\)
0.996890 0.0788079i \(-0.0251114\pi\)
\(678\) 33.9938i 0.0501384i
\(679\) −1220.05 −1.79683
\(680\) −47.8172 −0.0703195
\(681\) 55.8393i 0.0819961i
\(682\) 605.384i 0.887660i
\(683\) 380.675 0.557357 0.278678 0.960385i \(-0.410104\pi\)
0.278678 + 0.960385i \(0.410104\pi\)
\(684\) 433.051i 0.633116i
\(685\) −21.6851 −0.0316570
\(686\) 307.411i 0.448121i
\(687\) 6.14749i 0.00894832i
\(688\) 82.2883i 0.119605i
\(689\) 31.4750i 0.0456821i
\(690\) 14.7738 13.8602i 0.0214113 0.0200873i
\(691\) −318.845 −0.461425 −0.230713 0.973022i \(-0.574106\pi\)
−0.230713 + 0.973022i \(0.574106\pi\)
\(692\) −300.154 −0.433748
\(693\) −575.385 −0.830282
\(694\) 371.130 0.534769
\(695\) 18.0112i 0.0259154i
\(696\) −25.0919 −0.0360515
\(697\) 321.861i 0.461781i
\(698\) −325.031 −0.465660
\(699\) 94.3165 0.134931
\(700\) 85.1262i 0.121609i
\(701\) 112.754i 0.160848i −0.996761 0.0804239i \(-0.974373\pi\)
0.996761 0.0804239i \(-0.0256274\pi\)
\(702\) 18.6424 0.0265561
\(703\) −969.193 −1.37865
\(704\) 60.6042i 0.0860855i
\(705\) 52.5047i 0.0744747i
\(706\) −519.698 −0.736116
\(707\) 235.887i 0.333644i
\(708\) −37.6875 −0.0532309
\(709\) 465.481i 0.656531i 0.944585 + 0.328266i \(0.106464\pi\)
−0.944585 + 0.328266i \(0.893536\pi\)
\(710\) 28.0367i 0.0394883i
\(711\) 1375.99i 1.93529i
\(712\) 180.242i 0.253149i
\(713\) 889.229 + 947.838i 1.24717 + 1.32937i
\(714\) −25.3509 −0.0355054
\(715\) 44.7328 0.0625634
\(716\) 414.116 0.578375
\(717\) −41.6041 −0.0580253
\(718\) 339.370i 0.472660i
\(719\) −347.913 −0.483885 −0.241943 0.970291i \(-0.577785\pi\)
−0.241943 + 0.970291i \(0.577785\pi\)
\(720\) 79.8046i 0.110840i
\(721\) 1136.79 1.57669
\(722\) 322.321 0.446428
\(723\) 37.0518i 0.0512473i
\(724\) 662.276i 0.914746i
\(725\) 159.257 0.219664
\(726\) 25.0559 0.0345123
\(727\) 88.3077i 0.121469i −0.998154 0.0607343i \(-0.980656\pi\)
0.998154 0.0607343i \(-0.0193442\pi\)
\(728\) 63.5824i 0.0873385i
\(729\) −691.569 −0.948654
\(730\) 276.431i 0.378672i
\(731\) −155.536 −0.212772
\(732\) 19.5869i 0.0267580i
\(733\) 510.848i 0.696928i 0.937322 + 0.348464i \(0.113297\pi\)
−0.937322 + 0.348464i \(0.886703\pi\)
\(734\) 550.289i 0.749712i
\(735\) 14.6137i 0.0198826i
\(736\) 89.0196 + 94.8869i 0.120950 + 0.128922i
\(737\) 333.823 0.452948
\(738\) −537.171 −0.727873
\(739\) −416.763 −0.563955 −0.281978 0.959421i \(-0.590990\pi\)
−0.281978 + 0.959421i \(0.590990\pi\)
\(740\) 178.607 0.241361
\(741\) 17.8491i 0.0240878i
\(742\) 143.488 0.193380
\(743\) 633.469i 0.852583i −0.904586 0.426291i \(-0.859820\pi\)
0.904586 0.426291i \(-0.140180\pi\)
\(744\) −44.5152 −0.0598323
\(745\) −322.132 −0.432393
\(746\) 772.597i 1.03565i
\(747\) 1263.79i 1.69182i
\(748\) 114.551 0.153142
\(749\) −428.262 −0.571779
\(750\) 4.40383i 0.00587177i
\(751\) 1282.52i 1.70775i −0.520475 0.853877i \(-0.674245\pi\)
0.520475 0.853877i \(-0.325755\pi\)
\(752\) 337.219 0.448430
\(753\) 104.981i 0.139416i
\(754\) −118.952 −0.157761
\(755\) 245.870i 0.325655i
\(756\) 84.9866i 0.112416i
\(757\) 1233.64i 1.62964i −0.579716 0.814819i \(-0.696836\pi\)
0.579716 0.814819i \(-0.303164\pi\)
\(758\) 418.377i 0.551949i
\(759\) −35.3919 + 33.2035i −0.0466297 + 0.0437463i
\(760\) −153.482 −0.201950
\(761\) −262.559 −0.345018 −0.172509 0.985008i \(-0.555187\pi\)
−0.172509 + 0.985008i \(0.555187\pi\)
\(762\) −4.33812 −0.00569307
\(763\) −1096.58 −1.43720
\(764\) 345.499i 0.452223i
\(765\) −150.842 −0.197179
\(766\) 800.491i 1.04503i
\(767\) −178.663 −0.232938
\(768\) −4.45636 −0.00580255
\(769\) 801.510i 1.04228i 0.853473 + 0.521138i \(0.174492\pi\)
−0.853473 + 0.521138i \(0.825508\pi\)
\(770\) 203.928i 0.264841i
\(771\) −62.9698 −0.0816729
\(772\) 272.900 0.353498
\(773\) 1143.79i 1.47967i −0.672786 0.739837i \(-0.734903\pi\)
0.672786 0.739837i \(-0.265097\pi\)
\(774\) 259.583i 0.335378i
\(775\) 282.536 0.364562
\(776\) 405.377i 0.522393i
\(777\) 94.6907 0.121867
\(778\) 277.246i 0.356357i
\(779\) 1033.10i 1.32618i
\(780\) 3.28930i 0.00421706i
\(781\) 67.1644i 0.0859979i
\(782\) 179.350 168.260i 0.229347 0.215166i
\(783\) −158.995 −0.203059
\(784\) −93.8587 −0.119718
\(785\) 55.5010 0.0707019
\(786\) 1.43353 0.00182383
\(787\) 111.467i 0.141635i &minu