Properties

Label 690.3.c.a.91.12
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 91.12
Character \(\chi\) \(=\) 690.91
Dual form 690.3.c.a.91.13

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} +1.73205 q^{3} +2.00000 q^{4} -2.23607i q^{5} -2.44949 q^{6} +12.3097i q^{7} -2.82843 q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-1.41421 q^{2} +1.73205 q^{3} +2.00000 q^{4} -2.23607i q^{5} -2.44949 q^{6} +12.3097i q^{7} -2.82843 q^{8} +3.00000 q^{9} +3.16228i q^{10} -16.3902i q^{11} +3.46410 q^{12} -0.736671 q^{13} -17.4085i q^{14} -3.87298i q^{15} +4.00000 q^{16} -27.6301i q^{17} -4.24264 q^{18} -16.9936i q^{19} -4.47214i q^{20} +21.3210i q^{21} +23.1793i q^{22} +(-11.5510 + 19.8890i) q^{23} -4.89898 q^{24} -5.00000 q^{25} +1.04181 q^{26} +5.19615 q^{27} +24.6194i q^{28} +45.7427 q^{29} +5.47723i q^{30} +55.8779 q^{31} -5.65685 q^{32} -28.3887i q^{33} +39.0749i q^{34} +27.5253 q^{35} +6.00000 q^{36} +4.22262i q^{37} +24.0326i q^{38} -1.27595 q^{39} +6.32456i q^{40} +23.5007 q^{41} -30.1525i q^{42} +8.31673i q^{43} -32.7805i q^{44} -6.70820i q^{45} +(16.3356 - 28.1273i) q^{46} +19.7428 q^{47} +6.92820 q^{48} -102.528 q^{49} +7.07107 q^{50} -47.8568i q^{51} -1.47334 q^{52} +28.0875i q^{53} -7.34847 q^{54} -36.6497 q^{55} -34.8171i q^{56} -29.4338i q^{57} -64.6899 q^{58} +61.9670 q^{59} -7.74597i q^{60} -56.2784i q^{61} -79.0233 q^{62} +36.9291i q^{63} +8.00000 q^{64} +1.64725i q^{65} +40.1477i q^{66} -63.8492i q^{67} -55.2603i q^{68} +(-20.0070 + 34.4488i) q^{69} -38.9266 q^{70} +22.3876 q^{71} -8.48528 q^{72} +93.7225 q^{73} -5.97168i q^{74} -8.66025 q^{75} -33.9872i q^{76} +201.759 q^{77} +1.80447 q^{78} +29.5036i q^{79} -8.94427i q^{80} +9.00000 q^{81} -33.2350 q^{82} +119.769i q^{83} +42.6420i q^{84} -61.7829 q^{85} -11.7616i q^{86} +79.2287 q^{87} +46.3586i q^{88} -151.467i q^{89} +9.48683i q^{90} -9.06819i q^{91} +(-23.1021 + 39.7781i) q^{92} +96.7834 q^{93} -27.9206 q^{94} -37.9989 q^{95} -9.79796 q^{96} -89.5915i q^{97} +144.997 q^{98} -49.1707i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 64q^{4} + 96q^{9} + O(q^{10}) \) \( 32q + 64q^{4} + 96q^{9} - 48q^{13} + 128q^{16} - 80q^{23} - 160q^{25} + 120q^{29} + 248q^{31} - 120q^{35} + 192q^{36} - 48q^{39} + 72q^{41} + 160q^{46} + 400q^{47} - 344q^{49} - 96q^{52} - 256q^{58} + 120q^{59} + 160q^{62} + 256q^{64} + 192q^{69} + 104q^{71} + 16q^{73} + 240q^{77} + 192q^{78} + 288q^{81} + 64q^{82} - 120q^{85} + 144q^{87} - 160q^{92} - 192q^{93} + 96q^{94} - 160q^{95} + 64q^{98} + O(q^{100}) \)

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
\(7\) 12.3097i 1.75853i 0.476336 + 0.879263i \(0.341965\pi\)
−0.476336 + 0.879263i \(0.658035\pi\)
\(8\) −2.82843 −0.353553
\(9\) 3.00000 0.333333
\(10\) 3.16228i 0.316228i
\(11\) 16.3902i 1.49002i −0.667053 0.745011i \(-0.732444\pi\)
0.667053 0.745011i \(-0.267556\pi\)
\(12\) 3.46410 0.288675
\(13\) −0.736671 −0.0566670 −0.0283335 0.999599i \(-0.509020\pi\)
−0.0283335 + 0.999599i \(0.509020\pi\)
\(14\) 17.4085i 1.24347i
\(15\) 3.87298i 0.258199i
\(16\) 4.00000 0.250000
\(17\) 27.6301i 1.62530i −0.582750 0.812651i \(-0.698023\pi\)
0.582750 0.812651i \(-0.301977\pi\)
\(18\) −4.24264 −0.235702
\(19\) 16.9936i 0.894401i −0.894434 0.447200i \(-0.852421\pi\)
0.894434 0.447200i \(-0.147579\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 21.3210i 1.01529i
\(22\) 23.1793i 1.05360i
\(23\) −11.5510 + 19.8890i −0.502219 + 0.864741i
\(24\) −4.89898 −0.204124
\(25\) −5.00000 −0.200000
\(26\) 1.04181 0.0400696
\(27\) 5.19615 0.192450
\(28\) 24.6194i 0.879263i
\(29\) 45.7427 1.57733 0.788667 0.614821i \(-0.210772\pi\)
0.788667 + 0.614821i \(0.210772\pi\)
\(30\) 5.47723i 0.182574i
\(31\) 55.8779 1.80251 0.901256 0.433286i \(-0.142646\pi\)
0.901256 + 0.433286i \(0.142646\pi\)
\(32\) −5.65685 −0.176777
\(33\) 28.3887i 0.860264i
\(34\) 39.0749i 1.14926i
\(35\) 27.5253 0.786437
\(36\) 6.00000 0.166667
\(37\) 4.22262i 0.114125i 0.998371 + 0.0570624i \(0.0181734\pi\)
−0.998371 + 0.0570624i \(0.981827\pi\)
\(38\) 24.0326i 0.632437i
\(39\) −1.27595 −0.0327167
\(40\) 6.32456i 0.158114i
\(41\) 23.5007 0.573188 0.286594 0.958052i \(-0.407477\pi\)
0.286594 + 0.958052i \(0.407477\pi\)
\(42\) 30.1525i 0.717916i
\(43\) 8.31673i 0.193412i 0.995313 + 0.0967061i \(0.0308307\pi\)
−0.995313 + 0.0967061i \(0.969169\pi\)
\(44\) 32.7805i 0.745011i
\(45\) 6.70820i 0.149071i
\(46\) 16.3356 28.1273i 0.355122 0.611464i
\(47\) 19.7428 0.420061 0.210030 0.977695i \(-0.432644\pi\)
0.210030 + 0.977695i \(0.432644\pi\)
\(48\) 6.92820 0.144338
\(49\) −102.528 −2.09242
\(50\) 7.07107 0.141421
\(51\) 47.8568i 0.938369i
\(52\) −1.47334 −0.0283335
\(53\) 28.0875i 0.529953i 0.964255 + 0.264976i \(0.0853642\pi\)
−0.964255 + 0.264976i \(0.914636\pi\)
\(54\) −7.34847 −0.136083
\(55\) −36.6497 −0.666358
\(56\) 34.8171i 0.621733i
\(57\) 29.4338i 0.516383i
\(58\) −64.6899 −1.11534
\(59\) 61.9670 1.05029 0.525144 0.851014i \(-0.324012\pi\)
0.525144 + 0.851014i \(0.324012\pi\)
\(60\) 7.74597i 0.129099i
\(61\) 56.2784i 0.922596i −0.887245 0.461298i \(-0.847384\pi\)
0.887245 0.461298i \(-0.152616\pi\)
\(62\) −79.0233 −1.27457
\(63\) 36.9291i 0.586176i
\(64\) 8.00000 0.125000
\(65\) 1.64725i 0.0253422i
\(66\) 40.1477i 0.608299i
\(67\) 63.8492i 0.952973i −0.879182 0.476486i \(-0.841910\pi\)
0.879182 0.476486i \(-0.158090\pi\)
\(68\) 55.2603i 0.812651i
\(69\) −20.0070 + 34.4488i −0.289956 + 0.499258i
\(70\) −38.9266 −0.556095
\(71\) 22.3876 0.315318 0.157659 0.987494i \(-0.449605\pi\)
0.157659 + 0.987494i \(0.449605\pi\)
\(72\) −8.48528 −0.117851
\(73\) 93.7225 1.28387 0.641935 0.766759i \(-0.278132\pi\)
0.641935 + 0.766759i \(0.278132\pi\)
\(74\) 5.97168i 0.0806984i
\(75\) −8.66025 −0.115470
\(76\) 33.9872i 0.447200i
\(77\) 201.759 2.62024
\(78\) 1.80447 0.0231342
\(79\) 29.5036i 0.373463i 0.982411 + 0.186732i \(0.0597894\pi\)
−0.982411 + 0.186732i \(0.940211\pi\)
\(80\) 8.94427i 0.111803i
\(81\) 9.00000 0.111111
\(82\) −33.2350 −0.405305
\(83\) 119.769i 1.44300i 0.692412 + 0.721502i \(0.256548\pi\)
−0.692412 + 0.721502i \(0.743452\pi\)
\(84\) 42.6420i 0.507643i
\(85\) −61.7829 −0.726858
\(86\) 11.7616i 0.136763i
\(87\) 79.2287 0.910674
\(88\) 46.3586i 0.526802i
\(89\) 151.467i 1.70188i −0.525261 0.850941i \(-0.676032\pi\)
0.525261 0.850941i \(-0.323968\pi\)
\(90\) 9.48683i 0.105409i
\(91\) 9.06819i 0.0996504i
\(92\) −23.1021 + 39.7781i −0.251109 + 0.432370i
\(93\) 96.7834 1.04068
\(94\) −27.9206 −0.297028
\(95\) −37.9989 −0.399988
\(96\) −9.79796 −0.102062
\(97\) 89.5915i 0.923624i −0.886978 0.461812i \(-0.847200\pi\)
0.886978 0.461812i \(-0.152800\pi\)
\(98\) 144.997 1.47956
\(99\) 49.1707i 0.496674i
\(100\) −10.0000 −0.100000
\(101\) −139.120 −1.37743 −0.688715 0.725032i \(-0.741825\pi\)
−0.688715 + 0.725032i \(0.741825\pi\)
\(102\) 67.6798i 0.663527i
\(103\) 100.537i 0.976083i 0.872820 + 0.488042i \(0.162289\pi\)
−0.872820 + 0.488042i \(0.837711\pi\)
\(104\) 2.08362 0.0200348
\(105\) 47.6752 0.454050
\(106\) 39.7217i 0.374733i
\(107\) 114.130i 1.06664i −0.845914 0.533319i \(-0.820945\pi\)
0.845914 0.533319i \(-0.179055\pi\)
\(108\) 10.3923 0.0962250
\(109\) 42.6647i 0.391420i 0.980662 + 0.195710i \(0.0627011\pi\)
−0.980662 + 0.195710i \(0.937299\pi\)
\(110\) 51.8305 0.471186
\(111\) 7.31379i 0.0658900i
\(112\) 49.2387i 0.439632i
\(113\) 113.101i 1.00090i −0.865767 0.500448i \(-0.833169\pi\)
0.865767 0.500448i \(-0.166831\pi\)
\(114\) 41.6257i 0.365138i
\(115\) 44.4732 + 25.8289i 0.386724 + 0.224599i
\(116\) 91.4854 0.788667
\(117\) −2.21001 −0.0188890
\(118\) −87.6345 −0.742665
\(119\) 340.119 2.85814
\(120\) 10.9545i 0.0912871i
\(121\) −147.640 −1.22016
\(122\) 79.5896i 0.652374i
\(123\) 40.7044 0.330930
\(124\) 111.756 0.901256
\(125\) 11.1803i 0.0894427i
\(126\) 52.2256i 0.414489i
\(127\) 56.8211 0.447410 0.223705 0.974657i \(-0.428185\pi\)
0.223705 + 0.974657i \(0.428185\pi\)
\(128\) −11.3137 −0.0883883
\(129\) 14.4050i 0.111667i
\(130\) 2.32956i 0.0179197i
\(131\) −41.8455 −0.319431 −0.159716 0.987163i \(-0.551058\pi\)
−0.159716 + 0.987163i \(0.551058\pi\)
\(132\) 56.7774i 0.430132i
\(133\) 209.186 1.57283
\(134\) 90.2964i 0.673853i
\(135\) 11.6190i 0.0860663i
\(136\) 78.1499i 0.574631i
\(137\) 42.0689i 0.307072i −0.988143 0.153536i \(-0.950934\pi\)
0.988143 0.153536i \(-0.0490661\pi\)
\(138\) 28.2941 48.7180i 0.205030 0.353029i
\(139\) 232.680 1.67395 0.836977 0.547237i \(-0.184321\pi\)
0.836977 + 0.547237i \(0.184321\pi\)
\(140\) 55.0506 0.393219
\(141\) 34.1956 0.242522
\(142\) −31.6608 −0.222964
\(143\) 12.0742i 0.0844350i
\(144\) 12.0000 0.0833333
\(145\) 102.284i 0.705405i
\(146\) −132.544 −0.907833
\(147\) −177.584 −1.20806
\(148\) 8.44523i 0.0570624i
\(149\) 69.9994i 0.469795i 0.972020 + 0.234897i \(0.0754754\pi\)
−0.972020 + 0.234897i \(0.924525\pi\)
\(150\) 12.2474 0.0816497
\(151\) −243.908 −1.61528 −0.807641 0.589675i \(-0.799256\pi\)
−0.807641 + 0.589675i \(0.799256\pi\)
\(152\) 48.0652i 0.316218i
\(153\) 82.8904i 0.541768i
\(154\) −285.330 −1.85279
\(155\) 124.947i 0.806108i
\(156\) −2.55190 −0.0163583
\(157\) 54.9962i 0.350294i 0.984542 + 0.175147i \(0.0560401\pi\)
−0.984542 + 0.175147i \(0.943960\pi\)
\(158\) 41.7244i 0.264078i
\(159\) 48.6490i 0.305968i
\(160\) 12.6491i 0.0790569i
\(161\) −244.828 142.190i −1.52067 0.883165i
\(162\) −12.7279 −0.0785674
\(163\) −61.4656 −0.377090 −0.188545 0.982065i \(-0.560377\pi\)
−0.188545 + 0.982065i \(0.560377\pi\)
\(164\) 47.0014 0.286594
\(165\) −63.4791 −0.384722
\(166\) 169.380i 1.02036i
\(167\) 203.105 1.21620 0.608099 0.793862i \(-0.291933\pi\)
0.608099 + 0.793862i \(0.291933\pi\)
\(168\) 60.3049i 0.358958i
\(169\) −168.457 −0.996789
\(170\) 87.3742 0.513966
\(171\) 50.9808i 0.298134i
\(172\) 16.6335i 0.0967061i
\(173\) 157.267 0.909059 0.454530 0.890732i \(-0.349807\pi\)
0.454530 + 0.890732i \(0.349807\pi\)
\(174\) −112.046 −0.643944
\(175\) 61.5484i 0.351705i
\(176\) 65.5609i 0.372505i
\(177\) 107.330 0.606384
\(178\) 214.207i 1.20341i
\(179\) −142.176 −0.794280 −0.397140 0.917758i \(-0.629997\pi\)
−0.397140 + 0.917758i \(0.629997\pi\)
\(180\) 13.4164i 0.0745356i
\(181\) 104.944i 0.579803i 0.957057 + 0.289901i \(0.0936225\pi\)
−0.957057 + 0.289901i \(0.906377\pi\)
\(182\) 12.8244i 0.0704635i
\(183\) 97.4770i 0.532661i
\(184\) 32.6713 56.2547i 0.177561 0.305732i
\(185\) 9.44206 0.0510381
\(186\) −136.872 −0.735873
\(187\) −452.865 −2.42174
\(188\) 39.4857 0.210030
\(189\) 63.9630i 0.338429i
\(190\) 53.7385 0.282834
\(191\) 225.646i 1.18139i −0.806894 0.590697i \(-0.798853\pi\)
0.806894 0.590697i \(-0.201147\pi\)
\(192\) 13.8564 0.0721688
\(193\) 156.066 0.808634 0.404317 0.914619i \(-0.367509\pi\)
0.404317 + 0.914619i \(0.367509\pi\)
\(194\) 126.701i 0.653100i
\(195\) 2.85311i 0.0146314i
\(196\) −205.057 −1.04621
\(197\) −318.292 −1.61569 −0.807847 0.589393i \(-0.799367\pi\)
−0.807847 + 0.589393i \(0.799367\pi\)
\(198\) 69.5379i 0.351201i
\(199\) 50.9274i 0.255917i 0.991780 + 0.127958i \(0.0408424\pi\)
−0.991780 + 0.127958i \(0.959158\pi\)
\(200\) 14.1421 0.0707107
\(201\) 110.590i 0.550199i
\(202\) 196.746 0.973990
\(203\) 563.078i 2.77378i
\(204\) 95.7136i 0.469185i
\(205\) 52.5492i 0.256338i
\(206\) 142.180i 0.690195i
\(207\) −34.6531 + 59.6671i −0.167406 + 0.288247i
\(208\) −2.94668 −0.0141667
\(209\) −278.529 −1.33268
\(210\) −67.4229 −0.321062
\(211\) 61.4496 0.291230 0.145615 0.989341i \(-0.453484\pi\)
0.145615 + 0.989341i \(0.453484\pi\)
\(212\) 56.1750i 0.264976i
\(213\) 38.7764 0.182049
\(214\) 161.405i 0.754227i
\(215\) 18.5968 0.0864966
\(216\) −14.6969 −0.0680414
\(217\) 687.839i 3.16977i
\(218\) 60.3371i 0.276775i
\(219\) 162.332 0.741243
\(220\) −73.2993 −0.333179
\(221\) 20.3543i 0.0921010i
\(222\) 10.3433i 0.0465912i
\(223\) −245.051 −1.09888 −0.549441 0.835533i \(-0.685159\pi\)
−0.549441 + 0.835533i \(0.685159\pi\)
\(224\) 69.6341i 0.310867i
\(225\) −15.0000 −0.0666667
\(226\) 159.949i 0.707740i
\(227\) 319.342i 1.40679i 0.710797 + 0.703397i \(0.248334\pi\)
−0.710797 + 0.703397i \(0.751666\pi\)
\(228\) 58.8676i 0.258191i
\(229\) 393.219i 1.71711i 0.512717 + 0.858557i \(0.328639\pi\)
−0.512717 + 0.858557i \(0.671361\pi\)
\(230\) −62.8946 36.5276i −0.273455 0.158816i
\(231\) 349.456 1.51280
\(232\) −129.380 −0.557672
\(233\) −226.065 −0.970235 −0.485117 0.874449i \(-0.661223\pi\)
−0.485117 + 0.874449i \(0.661223\pi\)
\(234\) 3.12543 0.0133565
\(235\) 44.1463i 0.187857i
\(236\) 123.934 0.525144
\(237\) 51.1017i 0.215619i
\(238\) −481.000 −2.02101
\(239\) −119.938 −0.501831 −0.250915 0.968009i \(-0.580732\pi\)
−0.250915 + 0.968009i \(0.580732\pi\)
\(240\) 15.4919i 0.0645497i
\(241\) 239.516i 0.993844i −0.867795 0.496922i \(-0.834464\pi\)
0.867795 0.496922i \(-0.165536\pi\)
\(242\) 208.794 0.862785
\(243\) 15.5885 0.0641500
\(244\) 112.557i 0.461298i
\(245\) 229.260i 0.935757i
\(246\) −57.5648 −0.234003
\(247\) 12.5187i 0.0506830i
\(248\) −158.047 −0.637285
\(249\) 207.447i 0.833119i
\(250\) 15.8114i 0.0632456i
\(251\) 186.568i 0.743301i −0.928373 0.371650i \(-0.878792\pi\)
0.928373 0.371650i \(-0.121208\pi\)
\(252\) 73.8581i 0.293088i
\(253\) 325.986 + 189.324i 1.28848 + 0.748317i
\(254\) −80.3571 −0.316367
\(255\) −107.011 −0.419651
\(256\) 16.0000 0.0625000
\(257\) −252.617 −0.982944 −0.491472 0.870893i \(-0.663541\pi\)
−0.491472 + 0.870893i \(0.663541\pi\)
\(258\) 20.3717i 0.0789602i
\(259\) −51.9791 −0.200691
\(260\) 3.29449i 0.0126711i
\(261\) 137.228 0.525778
\(262\) 59.1785 0.225872
\(263\) 257.480i 0.979010i −0.872001 0.489505i \(-0.837178\pi\)
0.872001 0.489505i \(-0.162822\pi\)
\(264\) 80.2954i 0.304149i
\(265\) 62.8055 0.237002
\(266\) −295.834 −1.11216
\(267\) 262.349i 0.982582i
\(268\) 127.698i 0.476486i
\(269\) 334.855 1.24481 0.622406 0.782694i \(-0.286155\pi\)
0.622406 + 0.782694i \(0.286155\pi\)
\(270\) 16.4317i 0.0608581i
\(271\) −324.994 −1.19924 −0.599620 0.800285i \(-0.704682\pi\)
−0.599620 + 0.800285i \(0.704682\pi\)
\(272\) 110.521i 0.406326i
\(273\) 15.7066i 0.0575332i
\(274\) 59.4944i 0.217133i
\(275\) 81.9512i 0.298004i
\(276\) −40.0140 + 68.8976i −0.144978 + 0.249629i
\(277\) 139.848 0.504865 0.252433 0.967614i \(-0.418769\pi\)
0.252433 + 0.967614i \(0.418769\pi\)
\(278\) −329.059 −1.18366
\(279\) 167.634 0.600838
\(280\) −77.8533 −0.278047
\(281\) 180.786i 0.643367i −0.946847 0.321683i \(-0.895751\pi\)
0.946847 0.321683i \(-0.104249\pi\)
\(282\) −48.3599 −0.171489
\(283\) 313.878i 1.10911i 0.832148 + 0.554554i \(0.187111\pi\)
−0.832148 + 0.554554i \(0.812889\pi\)
\(284\) 44.7752 0.157659
\(285\) −65.8160 −0.230933
\(286\) 17.0755i 0.0597046i
\(287\) 289.286i 1.00797i
\(288\) −16.9706 −0.0589256
\(289\) −474.425 −1.64161
\(290\) 144.651i 0.498797i
\(291\) 155.177i 0.533254i
\(292\) 187.445 0.641935
\(293\) 358.632i 1.22400i 0.790858 + 0.612000i \(0.209635\pi\)
−0.790858 + 0.612000i \(0.790365\pi\)
\(294\) 251.142 0.854225
\(295\) 138.562i 0.469703i
\(296\) 11.9434i 0.0403492i
\(297\) 85.1661i 0.286755i
\(298\) 98.9941i 0.332195i
\(299\) 8.50931 14.6517i 0.0284592 0.0490022i
\(300\) −17.3205 −0.0577350
\(301\) −102.376 −0.340121
\(302\) 344.937 1.14218
\(303\) −240.964 −0.795259
\(304\) 67.9745i 0.223600i
\(305\) −125.842 −0.412598
\(306\) 117.225i 0.383088i
\(307\) 238.617 0.777255 0.388627 0.921395i \(-0.372949\pi\)
0.388627 + 0.921395i \(0.372949\pi\)
\(308\) 403.517 1.31012
\(309\) 174.134i 0.563542i
\(310\) 176.701i 0.570005i
\(311\) −48.3746 −0.155545 −0.0777727 0.996971i \(-0.524781\pi\)
−0.0777727 + 0.996971i \(0.524781\pi\)
\(312\) 3.60893 0.0115671
\(313\) 156.768i 0.500857i 0.968135 + 0.250429i \(0.0805716\pi\)
−0.968135 + 0.250429i \(0.919428\pi\)
\(314\) 77.7764i 0.247696i
\(315\) 82.5759 0.262146
\(316\) 59.0072i 0.186732i
\(317\) −469.006 −1.47951 −0.739757 0.672874i \(-0.765059\pi\)
−0.739757 + 0.672874i \(0.765059\pi\)
\(318\) 68.8000i 0.216352i
\(319\) 749.733i 2.35026i
\(320\) 17.8885i 0.0559017i
\(321\) 197.679i 0.615824i
\(322\) 346.239 + 201.086i 1.07528 + 0.624492i
\(323\) −469.536 −1.45367
\(324\) 18.0000 0.0555556
\(325\) 3.68335 0.0113334
\(326\) 86.9255 0.266643
\(327\) 73.8975i 0.225986i
\(328\) −66.4701 −0.202653
\(329\) 243.028i 0.738688i
\(330\) 89.7730 0.272039
\(331\) 59.9419 0.181093 0.0905467 0.995892i \(-0.471139\pi\)
0.0905467 + 0.995892i \(0.471139\pi\)
\(332\) 239.539i 0.721502i
\(333\) 12.6678i 0.0380416i
\(334\) −287.234 −0.859981
\(335\) −142.771 −0.426182
\(336\) 85.2840i 0.253821i
\(337\) 88.6746i 0.263129i −0.991308 0.131565i \(-0.958000\pi\)
0.991308 0.131565i \(-0.0420001\pi\)
\(338\) 238.235 0.704836
\(339\) 195.897i 0.577867i
\(340\) −123.566 −0.363429
\(341\) 915.852i 2.68578i
\(342\) 72.0978i 0.210812i
\(343\) 658.918i 1.92104i
\(344\) 23.5233i 0.0683816i
\(345\) 77.0299 + 44.7370i 0.223275 + 0.129672i
\(346\) −222.410 −0.642802
\(347\) 560.347 1.61483 0.807417 0.589981i \(-0.200865\pi\)
0.807417 + 0.589981i \(0.200865\pi\)
\(348\) 158.457 0.455337
\(349\) −204.499 −0.585958 −0.292979 0.956119i \(-0.594647\pi\)
−0.292979 + 0.956119i \(0.594647\pi\)
\(350\) 87.0426i 0.248693i
\(351\) −3.82785 −0.0109056
\(352\) 92.7172i 0.263401i
\(353\) 37.1800 0.105326 0.0526629 0.998612i \(-0.483229\pi\)
0.0526629 + 0.998612i \(0.483229\pi\)
\(354\) −151.787 −0.428778
\(355\) 50.0602i 0.141015i
\(356\) 302.935i 0.850941i
\(357\) 589.103 1.65015
\(358\) 201.068 0.561641
\(359\) 165.775i 0.461770i −0.972981 0.230885i \(-0.925838\pi\)
0.972981 0.230885i \(-0.0741620\pi\)
\(360\) 18.9737i 0.0527046i
\(361\) 72.2170 0.200047
\(362\) 148.414i 0.409982i
\(363\) −255.719 −0.704461
\(364\) 18.1364i 0.0498252i
\(365\) 209.570i 0.574164i
\(366\) 137.853i 0.376648i
\(367\) 607.172i 1.65442i −0.561893 0.827210i \(-0.689927\pi\)
0.561893 0.827210i \(-0.310073\pi\)
\(368\) −46.2041 + 79.5561i −0.125555 + 0.216185i
\(369\) 70.5021 0.191063
\(370\) −13.3531 −0.0360894
\(371\) −345.748 −0.931936
\(372\) 193.567 0.520341
\(373\) 105.223i 0.282099i −0.990003 0.141050i \(-0.954952\pi\)
0.990003 0.141050i \(-0.0450477\pi\)
\(374\) 640.447 1.71243
\(375\) 19.3649i 0.0516398i
\(376\) −55.8412 −0.148514
\(377\) −33.6973 −0.0893827
\(378\) 90.4574i 0.239305i
\(379\) 490.558i 1.29435i 0.762342 + 0.647175i \(0.224050\pi\)
−0.762342 + 0.647175i \(0.775950\pi\)
\(380\) −75.9978 −0.199994
\(381\) 98.4170 0.258312
\(382\) 319.112i 0.835372i
\(383\) 504.773i 1.31795i −0.752167 0.658973i \(-0.770991\pi\)
0.752167 0.658973i \(-0.229009\pi\)
\(384\) −19.5959 −0.0510310
\(385\) 451.146i 1.17181i
\(386\) −220.711 −0.571790
\(387\) 24.9502i 0.0644708i
\(388\) 179.183i 0.461812i
\(389\) 763.205i 1.96197i 0.194090 + 0.980984i \(0.437825\pi\)
−0.194090 + 0.980984i \(0.562175\pi\)
\(390\) 4.03491i 0.0103459i
\(391\) 549.537 + 319.157i 1.40547 + 0.816258i
\(392\) 289.994 0.739781
\(393\) −72.4786 −0.184424
\(394\) 450.132 1.14247
\(395\) 65.9720 0.167018
\(396\) 98.3414i 0.248337i
\(397\) −753.911 −1.89902 −0.949510 0.313737i \(-0.898419\pi\)
−0.949510 + 0.313737i \(0.898419\pi\)
\(398\) 72.0222i 0.180960i
\(399\) 362.321 0.908073
\(400\) −20.0000 −0.0500000
\(401\) 701.572i 1.74956i 0.484523 + 0.874778i \(0.338993\pi\)
−0.484523 + 0.874778i \(0.661007\pi\)
\(402\) 156.398i 0.389049i
\(403\) −41.1636 −0.102143
\(404\) −278.241 −0.688715
\(405\) 20.1246i 0.0496904i
\(406\) 796.313i 1.96136i
\(407\) 69.2097 0.170048
\(408\) 135.360i 0.331764i
\(409\) 214.043 0.523333 0.261666 0.965158i \(-0.415728\pi\)
0.261666 + 0.965158i \(0.415728\pi\)
\(410\) 74.3158i 0.181258i
\(411\) 72.8655i 0.177288i
\(412\) 201.073i 0.488042i
\(413\) 762.794i 1.84696i
\(414\) 49.0069 84.3820i 0.118374 0.203821i
\(415\) 267.813 0.645331
\(416\) 4.16724 0.0100174
\(417\) 403.013 0.966458
\(418\) 393.900 0.942344
\(419\) 210.362i 0.502057i −0.967980 0.251029i \(-0.919231\pi\)
0.967980 0.251029i \(-0.0807688\pi\)
\(420\) 95.3504 0.227025
\(421\) 176.903i 0.420196i 0.977680 + 0.210098i \(0.0673783\pi\)
−0.977680 + 0.210098i \(0.932622\pi\)
\(422\) −86.9029 −0.205931
\(423\) 59.2285 0.140020
\(424\) 79.4434i 0.187367i
\(425\) 138.151i 0.325061i
\(426\) −54.8382 −0.128728
\(427\) 692.769 1.62241
\(428\) 228.261i 0.533319i
\(429\) 20.9131i 0.0487486i
\(430\) −26.2998 −0.0611623
\(431\) 3.50520i 0.00813272i 0.999992 + 0.00406636i \(0.00129437\pi\)
−0.999992 + 0.00406636i \(0.998706\pi\)
\(432\) 20.7846 0.0481125
\(433\) 456.481i 1.05423i 0.849794 + 0.527114i \(0.176726\pi\)
−0.849794 + 0.527114i \(0.823274\pi\)
\(434\) 972.752i 2.24136i
\(435\) 177.161i 0.407266i
\(436\) 85.3295i 0.195710i
\(437\) 337.987 + 196.294i 0.773425 + 0.449185i
\(438\) −229.572 −0.524138
\(439\) 412.180 0.938907 0.469453 0.882957i \(-0.344451\pi\)
0.469453 + 0.882957i \(0.344451\pi\)
\(440\) 103.661 0.235593
\(441\) −307.585 −0.697472
\(442\) 28.7854i 0.0651252i
\(443\) 695.794 1.57064 0.785321 0.619089i \(-0.212498\pi\)
0.785321 + 0.619089i \(0.212498\pi\)
\(444\) 14.6276i 0.0329450i
\(445\) −338.692 −0.761105
\(446\) 346.554 0.777027
\(447\) 121.243i 0.271236i
\(448\) 98.4775i 0.219816i
\(449\) −220.418 −0.490908 −0.245454 0.969408i \(-0.578937\pi\)
−0.245454 + 0.969408i \(0.578937\pi\)
\(450\) 21.2132 0.0471405
\(451\) 385.182i 0.854062i
\(452\) 226.202i 0.500448i
\(453\) −422.460 −0.932583
\(454\) 451.618i 0.994754i
\(455\) −20.2771 −0.0445650
\(456\) 83.2514i 0.182569i
\(457\) 192.452i 0.421120i 0.977581 + 0.210560i \(0.0675287\pi\)
−0.977581 + 0.210560i \(0.932471\pi\)
\(458\) 556.096i 1.21418i
\(459\) 143.570i 0.312790i
\(460\) 88.9465 + 51.6578i 0.193362 + 0.112300i
\(461\) −426.613 −0.925408 −0.462704 0.886513i \(-0.653121\pi\)
−0.462704 + 0.886513i \(0.653121\pi\)
\(462\) −494.206 −1.06971
\(463\) 157.129 0.339371 0.169686 0.985498i \(-0.445725\pi\)
0.169686 + 0.985498i \(0.445725\pi\)
\(464\) 182.971 0.394333
\(465\) 216.414i 0.465407i
\(466\) 319.704 0.686060
\(467\) 418.986i 0.897187i 0.893736 + 0.448594i \(0.148075\pi\)
−0.893736 + 0.448594i \(0.851925\pi\)
\(468\) −4.42002 −0.00944450
\(469\) 785.963 1.67583
\(470\) 62.4324i 0.132835i
\(471\) 95.2563i 0.202243i
\(472\) −175.269 −0.371333
\(473\) 136.313 0.288188
\(474\) 72.2687i 0.152466i
\(475\) 84.9681i 0.178880i
\(476\) 680.237 1.42907
\(477\) 84.2625i 0.176651i
\(478\) 169.617 0.354848
\(479\) 393.407i 0.821308i 0.911791 + 0.410654i \(0.134700\pi\)
−0.911791 + 0.410654i \(0.865300\pi\)
\(480\) 21.9089i 0.0456435i
\(481\) 3.11068i 0.00646711i
\(482\) 338.727i 0.702754i
\(483\) −424.054 246.280i −0.877959 0.509896i
\(484\) −295.279 −0.610081
\(485\) −200.333 −0.413057
\(486\) −22.0454 −0.0453609
\(487\) −130.137 −0.267221 −0.133611 0.991034i \(-0.542657\pi\)
−0.133611 + 0.991034i \(0.542657\pi\)
\(488\) 159.179i 0.326187i
\(489\) −106.462 −0.217713
\(490\) 324.223i 0.661680i
\(491\) 779.481 1.58754 0.793769 0.608219i \(-0.208116\pi\)
0.793769 + 0.608219i \(0.208116\pi\)
\(492\) 81.4089 0.165465
\(493\) 1263.88i 2.56365i
\(494\) 17.7041i 0.0358383i
\(495\) −109.949 −0.222119
\(496\) 223.512 0.450628
\(497\) 275.584i 0.554495i
\(498\) 293.374i 0.589104i
\(499\) 181.903 0.364535 0.182267 0.983249i \(-0.441656\pi\)
0.182267 + 0.983249i \(0.441656\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) 351.788 0.702172
\(502\) 263.848i 0.525593i
\(503\) 306.185i 0.608719i 0.952557 + 0.304359i \(0.0984423\pi\)
−0.952557 + 0.304359i \(0.901558\pi\)
\(504\) 104.451i 0.207244i
\(505\) 311.083i 0.616005i
\(506\) −461.014 267.745i −0.911094 0.529140i
\(507\) −291.777 −0.575496
\(508\) 113.642 0.223705
\(509\) −736.428 −1.44681 −0.723406 0.690422i \(-0.757425\pi\)
−0.723406 + 0.690422i \(0.757425\pi\)
\(510\) 151.337 0.296738
\(511\) 1153.70i 2.25772i
\(512\) −22.6274 −0.0441942
\(513\) 88.3014i 0.172128i
\(514\) 357.254 0.695046
\(515\) 224.807 0.436518
\(516\) 28.8100i 0.0558333i
\(517\) 323.590i 0.625899i
\(518\) 73.5095 0.141910
\(519\) 272.395 0.524846
\(520\) 4.65911i 0.00895984i
\(521\) 638.384i 1.22531i −0.790352 0.612653i \(-0.790102\pi\)
0.790352 0.612653i \(-0.209898\pi\)
\(522\) −194.070 −0.371781
\(523\) 545.787i 1.04357i 0.853077 + 0.521785i \(0.174734\pi\)
−0.853077 + 0.521785i \(0.825266\pi\)
\(524\) −83.6910 −0.159716
\(525\) 106.605i 0.203057i
\(526\) 364.131i 0.692265i
\(527\) 1543.91i 2.92963i
\(528\) 113.555i 0.215066i
\(529\) −262.147 459.478i −0.495552 0.868578i
\(530\) −88.8205 −0.167586
\(531\) 185.901 0.350096
\(532\) 418.372 0.786414
\(533\) −17.3123 −0.0324808
\(534\) 371.018i 0.694790i
\(535\) −255.203 −0.477015
\(536\) 180.593i 0.336927i
\(537\) −246.256 −0.458578
\(538\) −473.556 −0.880215
\(539\) 1680.46i 3.11774i
\(540\) 23.2379i 0.0430331i
\(541\) 500.231 0.924641 0.462320 0.886713i \(-0.347017\pi\)
0.462320 + 0.886713i \(0.347017\pi\)
\(542\) 459.611 0.847991
\(543\) 181.769i 0.334749i
\(544\) 156.300i 0.287316i
\(545\) 95.4013 0.175048
\(546\) 22.2124i 0.0406821i
\(547\) 698.533 1.27702 0.638512 0.769612i \(-0.279550\pi\)
0.638512 + 0.769612i \(0.279550\pi\)
\(548\) 84.1378i 0.153536i
\(549\) 168.835i 0.307532i
\(550\) 115.896i 0.210721i
\(551\) 777.334i 1.41077i
\(552\) 56.5883 97.4360i 0.102515 0.176514i
\(553\) −363.180 −0.656745
\(554\) −197.775 −0.356994
\(555\) 16.3541 0.0294669
\(556\) 465.359 0.836977
\(557\) 299.862i 0.538352i 0.963091 + 0.269176i \(0.0867514\pi\)
−0.963091 + 0.269176i \(0.913249\pi\)
\(558\) −237.070 −0.424856
\(559\) 6.12669i 0.0109601i
\(560\) 110.101 0.196609
\(561\) −784.384 −1.39819
\(562\) 255.670i 0.454929i
\(563\) 721.083i 1.28079i −0.768047 0.640394i \(-0.778771\pi\)
0.768047 0.640394i \(-0.221229\pi\)
\(564\) 68.3912 0.121261
\(565\) −252.902 −0.447614
\(566\) 443.890i 0.784258i
\(567\) 110.787i 0.195392i
\(568\) −63.3217 −0.111482
\(569\) 295.012i 0.518474i 0.965814 + 0.259237i \(0.0834711\pi\)
−0.965814 + 0.259237i \(0.916529\pi\)
\(570\) 93.0779 0.163295
\(571\) 240.613i 0.421389i 0.977552 + 0.210694i \(0.0675725\pi\)
−0.977552 + 0.210694i \(0.932428\pi\)
\(572\) 24.1484i 0.0422175i
\(573\) 390.831i 0.682078i
\(574\) 409.113i 0.712740i
\(575\) 57.7552 99.4452i 0.100444 0.172948i
\(576\) 24.0000 0.0416667
\(577\) −781.267 −1.35402 −0.677008 0.735976i \(-0.736724\pi\)
−0.677008 + 0.735976i \(0.736724\pi\)
\(578\) 670.939 1.16079
\(579\) 270.315 0.466865
\(580\) 204.568i 0.352703i
\(581\) −1474.32 −2.53756
\(582\) 219.453i 0.377068i
\(583\) 460.361 0.789641
\(584\) −265.087 −0.453917
\(585\) 4.94174i 0.00844741i
\(586\) 507.182i 0.865499i
\(587\) −825.864 −1.40692 −0.703462 0.710733i \(-0.748363\pi\)
−0.703462 + 0.710733i \(0.748363\pi\)
\(588\) −355.169 −0.604029
\(589\) 949.568i 1.61217i
\(590\) 195.957i 0.332130i
\(591\) −551.297 −0.932821
\(592\) 16.8905i 0.0285312i
\(593\) −257.273 −0.433849 −0.216925 0.976188i \(-0.569603\pi\)
−0.216925 + 0.976188i \(0.569603\pi\)
\(594\) 120.443i 0.202766i
\(595\) 760.528i 1.27820i
\(596\) 139.999i 0.234897i
\(597\) 88.2088i 0.147754i
\(598\) −12.0340 + 20.7206i −0.0201237 + 0.0346498i
\(599\) −1081.22 −1.80505 −0.902523 0.430641i \(-0.858288\pi\)
−0.902523 + 0.430641i \(0.858288\pi\)
\(600\) 24.4949 0.0408248
\(601\) 481.001 0.800334 0.400167 0.916442i \(-0.368952\pi\)
0.400167 + 0.916442i \(0.368952\pi\)
\(602\) 144.782 0.240502
\(603\) 191.547i 0.317658i
\(604\) −487.815 −0.807641
\(605\) 330.132i 0.545673i
\(606\) 340.774 0.562333
\(607\) 878.744 1.44768 0.723842 0.689966i \(-0.242375\pi\)
0.723842 + 0.689966i \(0.242375\pi\)
\(608\) 96.1304i 0.158109i
\(609\) 975.280i 1.60144i
\(610\) 177.968 0.291751
\(611\) −14.5440 −0.0238036
\(612\) 165.781i 0.270884i
\(613\) 249.513i 0.407036i −0.979071 0.203518i \(-0.934762\pi\)
0.979071 0.203518i \(-0.0652375\pi\)
\(614\) −337.456 −0.549602
\(615\) 91.0179i 0.147997i
\(616\) −570.660 −0.926395
\(617\) 399.806i 0.647984i 0.946060 + 0.323992i \(0.105025\pi\)
−0.946060 + 0.323992i \(0.894975\pi\)
\(618\) 246.263i 0.398484i
\(619\) 38.5190i 0.0622278i −0.999516 0.0311139i \(-0.990095\pi\)
0.999516 0.0311139i \(-0.00990547\pi\)
\(620\) 249.894i 0.403054i
\(621\) −60.0209 + 103.346i −0.0966521 + 0.166419i
\(622\) 68.4120 0.109987
\(623\) 1864.52 2.99280
\(624\) −5.10380 −0.00817917
\(625\) 25.0000 0.0400000
\(626\) 221.704i 0.354160i
\(627\) −482.427 −0.769421
\(628\) 109.992i 0.175147i
\(629\) 116.672 0.185487
\(630\) −116.780 −0.185365
\(631\) 950.121i 1.50574i 0.658170 + 0.752870i \(0.271331\pi\)
−0.658170 + 0.752870i \(0.728669\pi\)
\(632\) 83.4487i 0.132039i
\(633\) 106.434 0.168142
\(634\) 663.274 1.04617
\(635\) 127.056i 0.200088i
\(636\) 97.2979i 0.152984i
\(637\) 75.5297 0.118571
\(638\) 1060.28i 1.66189i
\(639\) 67.1628 0.105106
\(640\) 25.2982i 0.0395285i
\(641\) 423.980i 0.661435i −0.943730 0.330717i \(-0.892709\pi\)
0.943730 0.330717i \(-0.107291\pi\)
\(642\) 279.561i 0.435453i
\(643\) 311.699i 0.484758i 0.970182 + 0.242379i \(0.0779278\pi\)
−0.970182 + 0.242379i \(0.922072\pi\)
\(644\) −489.656 284.379i −0.760335 0.441583i
\(645\) 32.2106 0.0499388
\(646\) 664.024 1.02790
\(647\) −1127.57 −1.74277 −0.871387 0.490597i \(-0.836779\pi\)
−0.871387 + 0.490597i \(0.836779\pi\)
\(648\) −25.4558 −0.0392837
\(649\) 1015.65i 1.56495i
\(650\) −5.20905 −0.00801392
\(651\) 1191.37i 1.83007i
\(652\) −122.931 −0.188545
\(653\) −483.611 −0.740599 −0.370299 0.928912i \(-0.620745\pi\)
−0.370299 + 0.928912i \(0.620745\pi\)
\(654\) 104.507i 0.159796i
\(655\) 93.5694i 0.142854i
\(656\) 94.0029 0.143297
\(657\) 281.168 0.427957
\(658\) 343.694i 0.522331i
\(659\) 375.574i 0.569915i 0.958540 + 0.284958i \(0.0919795\pi\)
−0.958540 + 0.284958i \(0.908021\pi\)
\(660\) −126.958 −0.192361
\(661\) 249.264i 0.377101i 0.982064 + 0.188550i \(0.0603789\pi\)
−0.982064 + 0.188550i \(0.939621\pi\)
\(662\) −84.7707 −0.128052
\(663\) 35.2547i 0.0531745i
\(664\) 338.759i 0.510179i
\(665\) 467.754i 0.703390i
\(666\) 17.9150i 0.0268995i
\(667\) −528.375 + 909.778i −0.792167 + 1.36398i
\(668\) 406.210 0.608099
\(669\) −424.440 −0.634440
\(670\) 201.909 0.301356
\(671\) −922.415 −1.37469
\(672\) 120.610i 0.179479i
\(673\) −393.290 −0.584384 −0.292192 0.956360i \(-0.594385\pi\)
−0.292192 + 0.956360i \(0.594385\pi\)
\(674\) 125.405i 0.186061i
\(675\) −25.9808 −0.0384900
\(676\) −336.915 −0.498394
\(677\) 78.7429i 0.116311i 0.998308 + 0.0581557i \(0.0185220\pi\)
−0.998308 + 0.0581557i \(0.981478\pi\)
\(678\) 277.040i 0.408614i
\(679\) 1102.84 1.62422
\(680\) 174.748 0.256983
\(681\) 553.117i 0.812213i
\(682\) 1295.21i 1.89913i
\(683\) 773.666 1.13275 0.566374 0.824149i \(-0.308346\pi\)
0.566374 + 0.824149i \(0.308346\pi\)
\(684\) 101.962i 0.149067i
\(685\) −94.0689 −0.137327
\(686\) 931.851i 1.35838i
\(687\) 681.076i 0.991377i
\(688\) 33.2669i 0.0483531i
\(689\) 20.6912i 0.0300308i
\(690\) −108.937 63.2676i −0.157879 0.0916922i
\(691\) 780.457 1.12946 0.564730 0.825276i \(-0.308980\pi\)
0.564730 + 0.825276i \(0.308980\pi\)
\(692\) 314.535 0.454530
\(693\) 605.276 0.873414
\(694\) −792.451 −1.14186
\(695\) 520.288i 0.748615i
\(696\) −224.092 −0.321972
\(697\) 649.328i 0.931604i
\(698\) 289.206 0.414335
\(699\) −391.556 −0.560165
\(700\) 123.097i 0.175853i
\(701\) 690.190i 0.984579i 0.870431 + 0.492290i \(0.163840\pi\)
−0.870431 + 0.492290i \(0.836160\pi\)
\(702\) 5.41340 0.00771140
\(703\) 71.7575 0.102073
\(704\) 131.122i 0.186253i
\(705\) 76.4637i 0.108459i
\(706\) −52.5805 −0.0744766
\(707\) 1712.53i 2.42225i
\(708\) 214.660 0.303192
\(709\) 691.256i 0.974973i 0.873131 + 0.487486i \(0.162086\pi\)
−0.873131 + 0.487486i \(0.837914\pi\)
\(710\) 70.7958i 0.0997123i
\(711\) 88.5107i 0.124488i
\(712\) 428.415i 0.601706i
\(713\) −645.447 + 1111.36i −0.905256 + 1.55871i
\(714\) −833.117 −1.16683
\(715\) 26.9987 0.0377605
\(716\) −284.352 −0.397140
\(717\) −207.738 −0.289732
\(718\) 234.442i 0.326520i
\(719\) 591.124 0.822148 0.411074 0.911602i \(-0.365154\pi\)
0.411074 + 0.911602i \(0.365154\pi\)
\(720\) 26.8328i 0.0372678i
\(721\) −1237.57 −1.71647
\(722\) −102.130 −0.141455
\(723\) 414.855i 0.573796i
\(724\) 209.889i 0.289901i
\(725\) −228.713 −0.315467
\(726\) 361.642 0.498129
\(727\) 380.059i 0.522777i 0.965234 + 0.261389i \(0.0841804\pi\)
−0.965234 + 0.261389i \(0.915820\pi\)
\(728\) 25.6487i 0.0352317i
\(729\) 27.0000 0.0370370
\(730\) 296.377i 0.405995i
\(731\) 229.792 0.314354
\(732\) 194.954i 0.266331i
\(733\) 438.730i 0.598540i −0.954169 0.299270i \(-0.903257\pi\)
0.954169 0.299270i \(-0.0967431\pi\)
\(734\) 858.671i 1.16985i
\(735\) 397.091i 0.540260i
\(736\) 65.3425 112.509i 0.0887806 0.152866i
\(737\) −1046.50 −1.41995
\(738\) −99.7051 −0.135102
\(739\) −515.703 −0.697839 −0.348920 0.937153i \(-0.613451\pi\)
−0.348920 + 0.937153i \(0.613451\pi\)
\(740\) 18.8841 0.0255191
\(741\) 21.6830i 0.0292618i
\(742\) 488.962 0.658978
\(743\) 413.330i 0.556298i 0.960538 + 0.278149i \(0.0897209\pi\)
−0.960538 + 0.278149i \(0.910279\pi\)
\(744\) −273.745 −0.367936
\(745\) 156.523 0.210099
\(746\) 148.808i 0.199474i
\(747\) 359.308i 0.481002i
\(748\) −905.729 −1.21087
\(749\) 1404.91 1.87571
\(750\) 27.3861i 0.0365148i
\(751\) 863.045i 1.14919i −0.818436 0.574597i \(-0.805159\pi\)
0.818436 0.574597i \(-0.194841\pi\)
\(752\) 78.9714 0.105015
\(753\) 323.146i 0.429145i
\(754\) 47.6552 0.0632031
\(755\) 545.394i 0.722376i
\(756\) 127.926i 0.169214i
\(757\) 1048.70i 1.38534i −0.721254 0.692671i \(-0.756434\pi\)
0.721254 0.692671i \(-0.243566\pi\)
\(758\) 693.754i 0.915243i
\(759\) 564.624 + 327.919i 0.743905 + 0.432041i
\(760\) 107.477 0.141417
\(761\) −113.408 −0.149025 −0.0745126 0.997220i \(-0.523740\pi\)
−0.0745126 + 0.997220i \(0.523740\pi\)
\(762\) −139.183 −0.182654
\(763\) −525.190 −0.688322
\(764\) 451.292i 0.590697i
\(765\) −185.349 −0.242286
\(766\) 713.857i 0.931929i
\(767\) −45.6492 −0.0595166
\(768\) 27.7128 0.0360844
\(769\) 1143.62i 1.48716i 0.668648 + 0.743579i \(0.266873\pi\)
−0.668648 + 0.743579i \(0.733127\pi\)
\(770\) 638.017i 0.828593i
\(771\) −437.545 −0.567503
\(772\) 312.133 0.404317
\(773\) 149.788i 0.193775i 0.995295 + 0.0968877i \(0.0308888\pi\)
−0.995295 + 0.0968877i \(0.969111\pi\)
\(774\) 35.2849i 0.0455877i
\(775\) −279.389 −0.360503
\(776\) 253.403i 0.326550i
\(777\) −90.0304 −0.115869
\(778\) 1079.34i 1.38732i
\(779\) 399.362i 0.512660i
\(780\) 5.70623i 0.00731568i
\(781\) 366.938i 0.469831i
\(782\) −777.163 451.356i −0.993814 0.577181i
\(783\) 237.686 0.303558
\(784\) −410.114 −0.523104
\(785\) 122.975 0.156656
\(786\) 102.500 0.130407
\(787\) 923.698i 1.17370i −0.809697 0.586848i \(-0.800369\pi\)
0.809697 0.586848i \(-0.199631\pi\)
\(788\) −636.583 −0.807847
\(789\) 445.968i 0.565232i
\(790\) −93.2985 −0.118099
\(791\) 1392.24 1.76010
\(792\) 139.076i 0.175601i