Properties

Label 117.4.q.e.82.5
Level $117$
Weight $4$
Character 117.82
Analytic conductor $6.903$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 117.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.90322347067\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
Defining polynomial: \( x^{10} + 70x^{8} + 1645x^{6} + 14700x^{4} + 44100x^{2} + 27648 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 82.5
Root \(5.36472i\) of defining polynomial
Character \(\chi\) \(=\) 117.82
Dual form 117.4.q.e.10.5

$q$-expansion

\(f(q)\) \(=\) \(q+(4.64599 + 2.68236i) q^{2} +(10.3901 + 17.9962i) q^{4} +2.69631i q^{5} +(13.1657 - 7.60123i) q^{7} +68.5626i q^{8} +O(q^{10})\) \(q+(4.64599 + 2.68236i) q^{2} +(10.3901 + 17.9962i) q^{4} +2.69631i q^{5} +(13.1657 - 7.60123i) q^{7} +68.5626i q^{8} +(-7.23249 + 12.5270i) q^{10} +(-57.9240 - 33.4424i) q^{11} +(46.8650 - 0.818689i) q^{13} +81.5570 q^{14} +(-100.789 + 174.571i) q^{16} +(-2.08177 - 3.60573i) q^{17} +(-22.5903 + 13.0425i) q^{19} +(-48.5235 + 28.0150i) q^{20} +(-179.409 - 310.746i) q^{22} +(-23.6621 + 40.9839i) q^{23} +117.730 q^{25} +(219.930 + 121.905i) q^{26} +(273.587 + 157.956i) q^{28} +(128.503 - 222.575i) q^{29} -206.242i q^{31} +(-461.511 + 266.453i) q^{32} -22.3362i q^{34} +(20.4953 + 35.4989i) q^{35} +(-152.149 - 87.8430i) q^{37} -139.939 q^{38} -184.866 q^{40} +(-135.501 - 78.2313i) q^{41} +(25.9922 + 45.0199i) q^{43} -1389.88i q^{44} +(-219.868 + 126.941i) q^{46} +354.222i q^{47} +(-55.9425 + 96.8953i) q^{49} +(546.972 + 315.794i) q^{50} +(501.667 + 834.888i) q^{52} +10.4723 q^{53} +(90.1712 - 156.181i) q^{55} +(521.160 + 902.676i) q^{56} +(1194.05 - 689.386i) q^{58} +(-385.480 + 222.557i) q^{59} +(-59.8481 - 103.660i) q^{61} +(553.216 - 958.199i) q^{62} -1246.28 q^{64} +(2.20744 + 126.363i) q^{65} +(-19.4057 - 11.2039i) q^{67} +(43.2597 - 74.9281i) q^{68} +219.903i q^{70} +(246.997 - 142.604i) q^{71} +740.989i q^{73} +(-471.253 - 816.235i) q^{74} +(-469.432 - 271.027i) q^{76} -1016.81 q^{77} -547.679 q^{79} +(-470.698 - 271.758i) q^{80} +(-419.689 - 726.923i) q^{82} +603.056i q^{83} +(9.72218 - 5.61310i) q^{85} +278.882i q^{86} +(2292.90 - 3971.42i) q^{88} +(186.774 + 107.834i) q^{89} +(610.789 - 367.011i) q^{91} -983.409 q^{92} +(-950.153 + 1645.71i) q^{94} +(-35.1666 - 60.9104i) q^{95} +(-1253.58 + 723.752i) q^{97} +(-519.817 + 300.116i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 30 q^{4} + 30 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 30 q^{4} + 30 q^{7} + 40 q^{10} - 60 q^{11} + 25 q^{13} + 60 q^{14} - 250 q^{16} - 105 q^{17} + 180 q^{19} - 510 q^{20} - 290 q^{22} + 60 q^{23} - 960 q^{25} + 30 q^{26} + 150 q^{28} + 495 q^{29} - 1440 q^{32} - 60 q^{35} - 405 q^{37} + 1380 q^{38} + 2000 q^{40} - 1065 q^{41} - 370 q^{43} - 390 q^{46} + 775 q^{49} + 4320 q^{50} + 2940 q^{52} - 330 q^{53} - 260 q^{55} + 2670 q^{56} + 2040 q^{58} - 780 q^{59} - 1375 q^{61} + 780 q^{62} - 3140 q^{64} - 1605 q^{65} + 1590 q^{67} + 600 q^{68} - 1620 q^{71} - 2190 q^{74} - 5190 q^{76} + 4320 q^{77} + 1100 q^{79} - 8430 q^{80} - 2390 q^{82} + 525 q^{85} + 3170 q^{88} - 2040 q^{89} + 4770 q^{91} + 1740 q^{92} - 3230 q^{94} + 1380 q^{95} - 3750 q^{97} - 180 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.64599 + 2.68236i 1.64260 + 0.948358i 0.979903 + 0.199475i \(0.0639236\pi\)
0.662702 + 0.748883i \(0.269410\pi\)
\(3\) 0 0
\(4\) 10.3901 + 17.9962i 1.29877 + 2.24953i
\(5\) 2.69631i 0.241165i 0.992703 + 0.120583i \(0.0384763\pi\)
−0.992703 + 0.120583i \(0.961524\pi\)
\(6\) 0 0
\(7\) 13.1657 7.60123i 0.710882 0.410428i −0.100505 0.994937i \(-0.532046\pi\)
0.811388 + 0.584509i \(0.198713\pi\)
\(8\) 68.5626i 3.03007i
\(9\) 0 0
\(10\) −7.23249 + 12.5270i −0.228711 + 0.396140i
\(11\) −57.9240 33.4424i −1.58770 0.916661i −0.993685 0.112209i \(-0.964207\pi\)
−0.594018 0.804451i \(-0.702459\pi\)
\(12\) 0 0
\(13\) 46.8650 0.818689i 0.999847 0.0174664i
\(14\) 81.5570 1.55693
\(15\) 0 0
\(16\) −100.789 + 174.571i −1.57482 + 2.72767i
\(17\) −2.08177 3.60573i −0.0297002 0.0514422i 0.850793 0.525501i \(-0.176122\pi\)
−0.880493 + 0.474058i \(0.842789\pi\)
\(18\) 0 0
\(19\) −22.5903 + 13.0425i −0.272766 + 0.157482i −0.630144 0.776478i \(-0.717004\pi\)
0.357378 + 0.933960i \(0.383671\pi\)
\(20\) −48.5235 + 28.0150i −0.542509 + 0.313218i
\(21\) 0 0
\(22\) −179.409 310.746i −1.73865 3.01142i
\(23\) −23.6621 + 40.9839i −0.214517 + 0.371554i −0.953123 0.302583i \(-0.902151\pi\)
0.738606 + 0.674137i \(0.235484\pi\)
\(24\) 0 0
\(25\) 117.730 0.941839
\(26\) 219.930 + 121.905i 1.65892 + 0.919523i
\(27\) 0 0
\(28\) 273.587 + 157.956i 1.84654 + 1.06610i
\(29\) 128.503 222.575i 0.822845 1.42521i −0.0807106 0.996738i \(-0.525719\pi\)
0.903555 0.428471i \(-0.140948\pi\)
\(30\) 0 0
\(31\) 206.242i 1.19491i −0.801903 0.597455i \(-0.796179\pi\)
0.801903 0.597455i \(-0.203821\pi\)
\(32\) −461.511 + 266.453i −2.54951 + 1.47196i
\(33\) 0 0
\(34\) 22.3362i 0.112666i
\(35\) 20.4953 + 35.4989i 0.0989811 + 0.171440i
\(36\) 0 0
\(37\) −152.149 87.8430i −0.676029 0.390305i 0.122328 0.992490i \(-0.460964\pi\)
−0.798357 + 0.602184i \(0.794297\pi\)
\(38\) −139.939 −0.597396
\(39\) 0 0
\(40\) −184.866 −0.730748
\(41\) −135.501 78.2313i −0.516137 0.297992i 0.219216 0.975676i \(-0.429650\pi\)
−0.735353 + 0.677684i \(0.762984\pi\)
\(42\) 0 0
\(43\) 25.9922 + 45.0199i 0.0921809 + 0.159662i 0.908429 0.418040i \(-0.137283\pi\)
−0.816248 + 0.577702i \(0.803950\pi\)
\(44\) 1389.88i 4.76211i
\(45\) 0 0
\(46\) −219.868 + 126.941i −0.704733 + 0.406878i
\(47\) 354.222i 1.09933i 0.835384 + 0.549666i \(0.185245\pi\)
−0.835384 + 0.549666i \(0.814755\pi\)
\(48\) 0 0
\(49\) −55.9425 + 96.8953i −0.163098 + 0.282494i
\(50\) 546.972 + 315.794i 1.54707 + 0.893201i
\(51\) 0 0
\(52\) 501.667 + 834.888i 1.33786 + 2.22650i
\(53\) 10.4723 0.0271412 0.0135706 0.999908i \(-0.495680\pi\)
0.0135706 + 0.999908i \(0.495680\pi\)
\(54\) 0 0
\(55\) 90.1712 156.181i 0.221067 0.382899i
\(56\) 521.160 + 902.676i 1.24362 + 2.15402i
\(57\) 0 0
\(58\) 1194.05 689.386i 2.70322 1.56070i
\(59\) −385.480 + 222.557i −0.850597 + 0.491092i −0.860852 0.508855i \(-0.830069\pi\)
0.0102552 + 0.999947i \(0.496736\pi\)
\(60\) 0 0
\(61\) −59.8481 103.660i −0.125619 0.217579i 0.796356 0.604829i \(-0.206758\pi\)
−0.921975 + 0.387250i \(0.873425\pi\)
\(62\) 553.216 958.199i 1.13320 1.96276i
\(63\) 0 0
\(64\) −1246.28 −2.43413
\(65\) 2.20744 + 126.363i 0.00421230 + 0.241129i
\(66\) 0 0
\(67\) −19.4057 11.2039i −0.0353848 0.0204294i 0.482203 0.876059i \(-0.339837\pi\)
−0.517588 + 0.855630i \(0.673170\pi\)
\(68\) 43.2597 74.9281i 0.0771473 0.133623i
\(69\) 0 0
\(70\) 219.903i 0.375478i
\(71\) 246.997 142.604i 0.412861 0.238365i −0.279157 0.960245i \(-0.590055\pi\)
0.692018 + 0.721880i \(0.256722\pi\)
\(72\) 0 0
\(73\) 740.989i 1.18803i 0.804454 + 0.594015i \(0.202458\pi\)
−0.804454 + 0.594015i \(0.797542\pi\)
\(74\) −471.253 816.235i −0.740299 1.28223i
\(75\) 0 0
\(76\) −469.432 271.027i −0.708520 0.409064i
\(77\) −1016.81 −1.50489
\(78\) 0 0
\(79\) −547.679 −0.779983 −0.389992 0.920818i \(-0.627522\pi\)
−0.389992 + 0.920818i \(0.627522\pi\)
\(80\) −470.698 271.758i −0.657821 0.379793i
\(81\) 0 0
\(82\) −419.689 726.923i −0.565206 0.978966i
\(83\) 603.056i 0.797518i 0.917056 + 0.398759i \(0.130559\pi\)
−0.917056 + 0.398759i \(0.869441\pi\)
\(84\) 0 0
\(85\) 9.72218 5.61310i 0.0124061 0.00716266i
\(86\) 278.882i 0.349682i
\(87\) 0 0
\(88\) 2292.90 3971.42i 2.77754 4.81085i
\(89\) 186.774 + 107.834i 0.222450 + 0.128431i 0.607084 0.794638i \(-0.292339\pi\)
−0.384634 + 0.923069i \(0.625672\pi\)
\(90\) 0 0
\(91\) 610.789 367.011i 0.703605 0.422782i
\(92\) −983.409 −1.11443
\(93\) 0 0
\(94\) −950.153 + 1645.71i −1.04256 + 1.80577i
\(95\) −35.1666 60.9104i −0.0379792 0.0657818i
\(96\) 0 0
\(97\) −1253.58 + 723.752i −1.31218 + 0.757586i −0.982457 0.186492i \(-0.940288\pi\)
−0.329722 + 0.944078i \(0.606955\pi\)
\(98\) −519.817 + 300.116i −0.535810 + 0.309350i
\(99\) 0 0
\(100\) 1223.23 + 2118.70i 1.22323 + 2.11870i
\(101\) 441.725 765.090i 0.435181 0.753756i −0.562129 0.827049i \(-0.690018\pi\)
0.997310 + 0.0732935i \(0.0233510\pi\)
\(102\) 0 0
\(103\) −1251.74 −1.19745 −0.598726 0.800954i \(-0.704326\pi\)
−0.598726 + 0.800954i \(0.704326\pi\)
\(104\) 56.1315 + 3213.19i 0.0529244 + 3.02961i
\(105\) 0 0
\(106\) 48.6543 + 28.0906i 0.0445823 + 0.0257396i
\(107\) −170.807 + 295.846i −0.154323 + 0.267294i −0.932812 0.360363i \(-0.882653\pi\)
0.778490 + 0.627658i \(0.215986\pi\)
\(108\) 0 0
\(109\) 775.177i 0.681179i −0.940212 0.340589i \(-0.889373\pi\)
0.940212 0.340589i \(-0.110627\pi\)
\(110\) 837.869 483.744i 0.726251 0.419301i
\(111\) 0 0
\(112\) 3064.47i 2.58541i
\(113\) 639.524 + 1107.69i 0.532402 + 0.922147i 0.999284 + 0.0378273i \(0.0120437\pi\)
−0.466883 + 0.884319i \(0.654623\pi\)
\(114\) 0 0
\(115\) −110.505 63.8004i −0.0896060 0.0517340i
\(116\) 5340.67 4.27473
\(117\) 0 0
\(118\) −2387.91 −1.86293
\(119\) −54.8160 31.6480i −0.0422267 0.0243796i
\(120\) 0 0
\(121\) 1571.29 + 2721.55i 1.18053 + 2.04474i
\(122\) 642.137i 0.476528i
\(123\) 0 0
\(124\) 3711.58 2142.88i 2.68798 1.55191i
\(125\) 654.476i 0.468305i
\(126\) 0 0
\(127\) −556.910 + 964.597i −0.389117 + 0.673970i −0.992331 0.123609i \(-0.960553\pi\)
0.603214 + 0.797579i \(0.293886\pi\)
\(128\) −2098.10 1211.34i −1.44881 0.836472i
\(129\) 0 0
\(130\) −328.695 + 593.001i −0.221757 + 0.400074i
\(131\) −2100.12 −1.40068 −0.700339 0.713811i \(-0.746968\pi\)
−0.700339 + 0.713811i \(0.746968\pi\)
\(132\) 0 0
\(133\) −198.278 + 343.428i −0.129270 + 0.223902i
\(134\) −60.1057 104.106i −0.0387488 0.0671150i
\(135\) 0 0
\(136\) 247.218 142.732i 0.155874 0.0899936i
\(137\) 1043.58 602.509i 0.650793 0.375736i −0.137967 0.990437i \(-0.544057\pi\)
0.788760 + 0.614701i \(0.210723\pi\)
\(138\) 0 0
\(139\) −161.445 279.631i −0.0985149 0.170633i 0.812555 0.582884i \(-0.198076\pi\)
−0.911070 + 0.412251i \(0.864743\pi\)
\(140\) −425.898 + 737.677i −0.257107 + 0.445322i
\(141\) 0 0
\(142\) 1530.06 0.904223
\(143\) −2741.99 1519.86i −1.60347 0.888789i
\(144\) 0 0
\(145\) 600.131 + 346.486i 0.343711 + 0.198442i
\(146\) −1987.60 + 3442.63i −1.12668 + 1.95146i
\(147\) 0 0
\(148\) 3650.80i 2.02766i
\(149\) 977.620 564.429i 0.537515 0.310335i −0.206556 0.978435i \(-0.566226\pi\)
0.744071 + 0.668100i \(0.232892\pi\)
\(150\) 0 0
\(151\) 2940.44i 1.58470i −0.610066 0.792350i \(-0.708857\pi\)
0.610066 0.792350i \(-0.291143\pi\)
\(152\) −894.228 1548.85i −0.477181 0.826501i
\(153\) 0 0
\(154\) −4724.11 2727.46i −2.47194 1.42718i
\(155\) 556.093 0.288171
\(156\) 0 0
\(157\) 629.388 0.319940 0.159970 0.987122i \(-0.448860\pi\)
0.159970 + 0.987122i \(0.448860\pi\)
\(158\) −2544.51 1469.07i −1.28120 0.739703i
\(159\) 0 0
\(160\) −718.441 1244.38i −0.354986 0.614854i
\(161\) 719.444i 0.352175i
\(162\) 0 0
\(163\) −342.004 + 197.456i −0.164343 + 0.0948832i −0.579915 0.814677i \(-0.696914\pi\)
0.415573 + 0.909560i \(0.363581\pi\)
\(164\) 3251.33i 1.54809i
\(165\) 0 0
\(166\) −1617.61 + 2801.79i −0.756333 + 1.31001i
\(167\) −131.515 75.9299i −0.0609395 0.0351834i 0.469221 0.883081i \(-0.344535\pi\)
−0.530160 + 0.847898i \(0.677868\pi\)
\(168\) 0 0
\(169\) 2195.66 76.7357i 0.999390 0.0349275i
\(170\) 60.2255 0.0271711
\(171\) 0 0
\(172\) −540.126 + 935.525i −0.239443 + 0.414728i
\(173\) −269.407 466.626i −0.118397 0.205069i 0.800736 0.599018i \(-0.204442\pi\)
−0.919132 + 0.393949i \(0.871109\pi\)
\(174\) 0 0
\(175\) 1550.00 894.892i 0.669537 0.386557i
\(176\) 11676.2 6741.24i 5.00070 2.88716i
\(177\) 0 0
\(178\) 578.500 + 1001.99i 0.243598 + 0.421924i
\(179\) 1110.40 1923.27i 0.463659 0.803081i −0.535481 0.844548i \(-0.679870\pi\)
0.999140 + 0.0414660i \(0.0132028\pi\)
\(180\) 0 0
\(181\) 3822.78 1.56986 0.784932 0.619582i \(-0.212698\pi\)
0.784932 + 0.619582i \(0.212698\pi\)
\(182\) 3822.17 66.7698i 1.55669 0.0271940i
\(183\) 0 0
\(184\) −2809.97 1622.33i −1.12583 0.650001i
\(185\) 236.852 410.240i 0.0941282 0.163035i
\(186\) 0 0
\(187\) 278.478i 0.108900i
\(188\) −6374.67 + 3680.42i −2.47298 + 1.42778i
\(189\) 0 0
\(190\) 377.319i 0.144071i
\(191\) 1732.09 + 3000.08i 0.656178 + 1.13653i 0.981597 + 0.190964i \(0.0611612\pi\)
−0.325419 + 0.945570i \(0.605505\pi\)
\(192\) 0 0
\(193\) −4068.07 2348.70i −1.51723 0.875975i −0.999795 0.0202541i \(-0.993552\pi\)
−0.517438 0.855721i \(-0.673114\pi\)
\(194\) −7765.46 −2.87385
\(195\) 0 0
\(196\) −2325.00 −0.847304
\(197\) 2500.98 + 1443.94i 0.904506 + 0.522217i 0.878660 0.477449i \(-0.158438\pi\)
0.0258469 + 0.999666i \(0.491772\pi\)
\(198\) 0 0
\(199\) 31.5046 + 54.5676i 0.0112226 + 0.0194382i 0.871582 0.490249i \(-0.163094\pi\)
−0.860360 + 0.509688i \(0.829761\pi\)
\(200\) 8071.87i 2.85384i
\(201\) 0 0
\(202\) 4104.50 2369.73i 1.42966 0.825415i
\(203\) 3907.14i 1.35087i
\(204\) 0 0
\(205\) 210.936 365.352i 0.0718654 0.124474i
\(206\) −5815.57 3357.62i −1.96694 1.13561i
\(207\) 0 0
\(208\) −4580.55 + 8263.80i −1.52694 + 2.75477i
\(209\) 1744.69 0.577429
\(210\) 0 0
\(211\) 524.848 909.064i 0.171242 0.296600i −0.767612 0.640914i \(-0.778555\pi\)
0.938854 + 0.344315i \(0.111889\pi\)
\(212\) 108.809 + 188.463i 0.0352501 + 0.0610550i
\(213\) 0 0
\(214\) −1587.13 + 916.331i −0.506982 + 0.292706i
\(215\) −121.388 + 70.0832i −0.0385050 + 0.0222309i
\(216\) 0 0
\(217\) −1567.69 2715.33i −0.490424 0.849440i
\(218\) 2079.30 3601.46i 0.646001 1.11891i
\(219\) 0 0
\(220\) 3747.56 1.14846
\(221\) −100.514 167.278i −0.0305942 0.0509156i
\(222\) 0 0
\(223\) 2003.54 + 1156.75i 0.601647 + 0.347361i 0.769689 0.638419i \(-0.220411\pi\)
−0.168042 + 0.985780i \(0.553745\pi\)
\(224\) −4050.75 + 7016.10i −1.20827 + 2.09278i
\(225\) 0 0
\(226\) 6861.74i 2.01963i
\(227\) 3290.43 1899.73i 0.962085 0.555460i 0.0652711 0.997868i \(-0.479209\pi\)
0.896814 + 0.442407i \(0.145875\pi\)
\(228\) 0 0
\(229\) 4321.07i 1.24692i −0.781856 0.623459i \(-0.785727\pi\)
0.781856 0.623459i \(-0.214273\pi\)
\(230\) −342.271 592.832i −0.0981248 0.169957i
\(231\) 0 0
\(232\) 15260.3 + 8810.54i 4.31848 + 2.49328i
\(233\) 5279.77 1.48450 0.742251 0.670122i \(-0.233758\pi\)
0.742251 + 0.670122i \(0.233758\pi\)
\(234\) 0 0
\(235\) −955.094 −0.265121
\(236\) −8010.38 4624.79i −2.20945 1.27563i
\(237\) 0 0
\(238\) −169.783 294.073i −0.0462412 0.0800920i
\(239\) 1547.92i 0.418939i 0.977815 + 0.209469i \(0.0671737\pi\)
−0.977815 + 0.209469i \(0.932826\pi\)
\(240\) 0 0
\(241\) −4259.12 + 2459.00i −1.13840 + 0.657255i −0.946033 0.324069i \(-0.894949\pi\)
−0.192365 + 0.981323i \(0.561616\pi\)
\(242\) 16859.1i 4.47828i
\(243\) 0 0
\(244\) 1243.66 2154.08i 0.326300 0.565168i
\(245\) −261.260 150.839i −0.0681277 0.0393336i
\(246\) 0 0
\(247\) −1048.02 + 629.731i −0.269974 + 0.162222i
\(248\) 14140.5 3.62066
\(249\) 0 0
\(250\) −1755.54 + 3040.69i −0.444121 + 0.769239i
\(251\) −577.890 1000.94i −0.145323 0.251707i 0.784170 0.620546i \(-0.213089\pi\)
−0.929493 + 0.368839i \(0.879756\pi\)
\(252\) 0 0
\(253\) 2741.20 1582.63i 0.681178 0.393278i
\(254\) −5174.80 + 2987.67i −1.27833 + 0.738044i
\(255\) 0 0
\(256\) −1513.40 2621.28i −0.369482 0.639962i
\(257\) −1175.98 + 2036.85i −0.285429 + 0.494378i −0.972713 0.232011i \(-0.925470\pi\)
0.687284 + 0.726389i \(0.258803\pi\)
\(258\) 0 0
\(259\) −2670.86 −0.640769
\(260\) −2251.12 + 1352.65i −0.536956 + 0.322646i
\(261\) 0 0
\(262\) −9757.15 5633.29i −2.30076 1.32834i
\(263\) 2760.94 4782.09i 0.647326 1.12120i −0.336433 0.941707i \(-0.609221\pi\)
0.983759 0.179494i \(-0.0574461\pi\)
\(264\) 0 0
\(265\) 28.2367i 0.00654553i
\(266\) −1842.39 + 1063.71i −0.424678 + 0.245188i
\(267\) 0 0
\(268\) 465.639i 0.106132i
\(269\) 1958.48 + 3392.18i 0.443905 + 0.768866i 0.997975 0.0636038i \(-0.0202594\pi\)
−0.554070 + 0.832470i \(0.686926\pi\)
\(270\) 0 0
\(271\) 2405.41 + 1388.76i 0.539182 + 0.311297i 0.744747 0.667347i \(-0.232570\pi\)
−0.205566 + 0.978643i \(0.565903\pi\)
\(272\) 839.276 0.187090
\(273\) 0 0
\(274\) 6464.58 1.42533
\(275\) −6819.38 3937.17i −1.49536 0.863347i
\(276\) 0 0
\(277\) 3291.54 + 5701.12i 0.713969 + 1.23663i 0.963356 + 0.268227i \(0.0864378\pi\)
−0.249386 + 0.968404i \(0.580229\pi\)
\(278\) 1732.21i 0.373710i
\(279\) 0 0
\(280\) −2433.90 + 1405.21i −0.519476 + 0.299919i
\(281\) 2871.66i 0.609640i −0.952410 0.304820i \(-0.901404\pi\)
0.952410 0.304820i \(-0.0985963\pi\)
\(282\) 0 0
\(283\) 3759.02 6510.81i 0.789578 1.36759i −0.136648 0.990620i \(-0.543633\pi\)
0.926226 0.376969i \(-0.123034\pi\)
\(284\) 5132.66 + 2963.34i 1.07242 + 0.619162i
\(285\) 0 0
\(286\) −8662.43 14416.2i −1.79098 2.98060i
\(287\) −2378.62 −0.489217
\(288\) 0 0
\(289\) 2447.83 4239.77i 0.498236 0.862970i
\(290\) 1858.80 + 3219.54i 0.376388 + 0.651923i
\(291\) 0 0
\(292\) −13335.0 + 7698.97i −2.67251 + 1.54297i
\(293\) −3902.80 + 2253.28i −0.778171 + 0.449278i −0.835782 0.549062i \(-0.814985\pi\)
0.0576104 + 0.998339i \(0.481652\pi\)
\(294\) 0 0
\(295\) −600.083 1039.37i −0.118435 0.205135i
\(296\) 6022.75 10431.7i 1.18265 2.04841i
\(297\) 0 0
\(298\) 6056.02 1.17723
\(299\) −1075.37 + 1940.08i −0.207994 + 0.375244i
\(300\) 0 0
\(301\) 684.413 + 395.146i 0.131060 + 0.0756673i
\(302\) 7887.33 13661.3i 1.50286 2.60304i
\(303\) 0 0
\(304\) 5258.15i 0.992024i
\(305\) 279.500 161.369i 0.0524725 0.0302950i
\(306\) 0 0
\(307\) 9538.89i 1.77333i 0.462409 + 0.886667i \(0.346985\pi\)
−0.462409 + 0.886667i \(0.653015\pi\)
\(308\) −10564.8 18298.8i −1.95450 3.38530i
\(309\) 0 0
\(310\) 2583.60 + 1491.64i 0.473351 + 0.273289i
\(311\) −7466.28 −1.36133 −0.680666 0.732594i \(-0.738309\pi\)
−0.680666 + 0.732594i \(0.738309\pi\)
\(312\) 0 0
\(313\) −1821.65 −0.328964 −0.164482 0.986380i \(-0.552595\pi\)
−0.164482 + 0.986380i \(0.552595\pi\)
\(314\) 2924.13 + 1688.25i 0.525536 + 0.303418i
\(315\) 0 0
\(316\) −5690.46 9856.16i −1.01302 1.75460i
\(317\) 3125.14i 0.553708i 0.960912 + 0.276854i \(0.0892918\pi\)
−0.960912 + 0.276854i \(0.910708\pi\)
\(318\) 0 0
\(319\) −14886.9 + 8594.93i −2.61287 + 1.50854i
\(320\) 3360.35i 0.587029i
\(321\) 0 0
\(322\) −1929.81 + 3342.53i −0.333988 + 0.578484i
\(323\) 94.0554 + 54.3029i 0.0162024 + 0.00935448i
\(324\) 0 0
\(325\) 5517.41 96.3842i 0.941696 0.0164506i
\(326\) −2118.60 −0.359933
\(327\) 0 0
\(328\) 5363.74 9290.27i 0.902936 1.56393i
\(329\) 2692.53 + 4663.59i 0.451197 + 0.781496i
\(330\) 0 0
\(331\) 1345.52 776.836i 0.223433 0.128999i −0.384106 0.923289i \(-0.625490\pi\)
0.607539 + 0.794290i \(0.292157\pi\)
\(332\) −10852.7 + 6265.83i −1.79404 + 1.03579i
\(333\) 0 0
\(334\) −407.343 705.539i −0.0667330 0.115585i
\(335\) 30.2092 52.3238i 0.00492688 0.00853360i
\(336\) 0 0
\(337\) 3190.43 0.515709 0.257855 0.966184i \(-0.416984\pi\)
0.257855 + 0.966184i \(0.416984\pi\)
\(338\) 10406.8 + 5533.04i 1.67473 + 0.890408i
\(339\) 0 0
\(340\) 202.029 + 116.642i 0.0322252 + 0.0186053i
\(341\) −6897.24 + 11946.4i −1.09533 + 1.89716i
\(342\) 0 0
\(343\) 6915.37i 1.08862i
\(344\) −3086.68 + 1782.10i −0.483787 + 0.279315i
\(345\) 0 0
\(346\) 2890.59i 0.449130i
\(347\) −2859.34 4952.53i −0.442356 0.766183i 0.555508 0.831511i \(-0.312524\pi\)
−0.997864 + 0.0653283i \(0.979191\pi\)
\(348\) 0 0
\(349\) 2882.53 + 1664.23i 0.442116 + 0.255256i 0.704495 0.709709i \(-0.251174\pi\)
−0.262379 + 0.964965i \(0.584507\pi\)
\(350\) 9601.70 1.46638
\(351\) 0 0
\(352\) 35643.4 5.39715
\(353\) 10657.7 + 6153.25i 1.60695 + 0.927774i 0.990047 + 0.140737i \(0.0449472\pi\)
0.616905 + 0.787037i \(0.288386\pi\)
\(354\) 0 0
\(355\) 384.504 + 665.981i 0.0574855 + 0.0995679i
\(356\) 4481.64i 0.667210i
\(357\) 0 0
\(358\) 10317.8 5956.98i 1.52322 0.879430i
\(359\) 8539.97i 1.25549i −0.778418 0.627747i \(-0.783977\pi\)
0.778418 0.627747i \(-0.216023\pi\)
\(360\) 0 0
\(361\) −3089.29 + 5350.80i −0.450399 + 0.780114i
\(362\) 17760.6 + 10254.1i 2.57866 + 1.48879i
\(363\) 0 0
\(364\) 12951.0 + 7178.61i 1.86488 + 1.03369i
\(365\) −1997.94 −0.286512
\(366\) 0 0
\(367\) −1248.33 + 2162.17i −0.177553 + 0.307532i −0.941042 0.338290i \(-0.890152\pi\)
0.763489 + 0.645821i \(0.223485\pi\)
\(368\) −4769.74 8261.44i −0.675652 1.17026i
\(369\) 0 0
\(370\) 2200.82 1270.65i 0.309231 0.178535i
\(371\) 137.876 79.6026i 0.0192942 0.0111395i
\(372\) 0 0
\(373\) 571.454 + 989.787i 0.0793264 + 0.137397i 0.902960 0.429726i \(-0.141390\pi\)
−0.823633 + 0.567123i \(0.808056\pi\)
\(374\) −746.978 + 1293.80i −0.103276 + 0.178880i
\(375\) 0 0
\(376\) −24286.4 −3.33105
\(377\) 5840.10 10536.2i 0.797826 1.43936i
\(378\) 0 0
\(379\) −10549.8 6090.91i −1.42983 0.825512i −0.432723 0.901527i \(-0.642447\pi\)
−0.997107 + 0.0760146i \(0.975780\pi\)
\(380\) 730.772 1265.73i 0.0986522 0.170871i
\(381\) 0 0
\(382\) 18584.4i 2.48917i
\(383\) −8816.66 + 5090.30i −1.17627 + 0.679118i −0.955148 0.296129i \(-0.904304\pi\)
−0.221119 + 0.975247i \(0.570971\pi\)
\(384\) 0 0
\(385\) 2741.65i 0.362928i
\(386\) −12600.1 21824.1i −1.66148 2.87776i
\(387\) 0 0
\(388\) −26049.6 15039.8i −3.40843 1.96786i
\(389\) 5845.83 0.761941 0.380971 0.924587i \(-0.375590\pi\)
0.380971 + 0.924587i \(0.375590\pi\)
\(390\) 0 0
\(391\) 197.036 0.0254848
\(392\) −6643.40 3835.57i −0.855975 0.494197i
\(393\) 0 0
\(394\) 7746.36 + 13417.1i 0.990498 + 1.71559i
\(395\) 1476.71i 0.188105i
\(396\) 0 0
\(397\) −2165.86 + 1250.46i −0.273807 + 0.158083i −0.630617 0.776094i \(-0.717198\pi\)
0.356809 + 0.934177i \(0.383865\pi\)
\(398\) 338.027i 0.0425723i
\(399\) 0 0
\(400\) −11865.8 + 20552.2i −1.48323 + 2.56903i
\(401\) −7958.12 4594.62i −0.991046 0.572181i −0.0854594 0.996342i \(-0.527236\pi\)
−0.905587 + 0.424161i \(0.860569\pi\)
\(402\) 0 0
\(403\) −168.848 9665.54i −0.0208708 1.19473i
\(404\) 18358.3 2.26080
\(405\) 0 0
\(406\) 10480.4 18152.5i 1.28111 2.21895i
\(407\) 5875.36 + 10176.4i 0.715555 + 1.23938i
\(408\) 0 0
\(409\) −7979.89 + 4607.19i −0.964744 + 0.556995i −0.897630 0.440750i \(-0.854712\pi\)
−0.0671140 + 0.997745i \(0.521379\pi\)
\(410\) 1960.01 1131.61i 0.236093 0.136308i
\(411\) 0 0
\(412\) −13005.8 22526.6i −1.55521 2.69371i
\(413\) −3383.42 + 5860.25i −0.403116 + 0.698218i
\(414\) 0 0
\(415\) −1626.03 −0.192334
\(416\) −21410.6 + 12865.2i −2.52341 + 1.51627i
\(417\) 0 0
\(418\) 8105.81 + 4679.89i 0.948488 + 0.547610i
\(419\) −3247.20 + 5624.32i −0.378607 + 0.655767i −0.990860 0.134895i \(-0.956930\pi\)
0.612253 + 0.790662i \(0.290263\pi\)
\(420\) 0 0
\(421\) 3059.56i 0.354190i −0.984194 0.177095i \(-0.943330\pi\)
0.984194 0.177095i \(-0.0566699\pi\)
\(422\) 4876.88 2815.67i 0.562566 0.324797i
\(423\) 0 0
\(424\) 718.010i 0.0822398i
\(425\) −245.087 424.502i −0.0279728 0.0484503i
\(426\) 0 0
\(427\) −1575.89 909.839i −0.178601 0.103115i
\(428\) −7098.82 −0.801716
\(429\) 0 0
\(430\) −751.954 −0.0843313
\(431\) −6873.69 3968.53i −0.768199 0.443520i 0.0640325 0.997948i \(-0.479604\pi\)
−0.832232 + 0.554428i \(0.812937\pi\)
\(432\) 0 0
\(433\) 3647.19 + 6317.11i 0.404786 + 0.701111i 0.994297 0.106650i \(-0.0340125\pi\)
−0.589510 + 0.807761i \(0.700679\pi\)
\(434\) 16820.5i 1.86039i
\(435\) 0 0
\(436\) 13950.3 8054.19i 1.53233 0.884692i
\(437\) 1234.45i 0.135130i
\(438\) 0 0
\(439\) 7607.35 13176.3i 0.827059 1.43251i −0.0732765 0.997312i \(-0.523346\pi\)
0.900335 0.435197i \(-0.143321\pi\)
\(440\) 10708.2 + 6182.37i 1.16021 + 0.669848i
\(441\) 0 0
\(442\) −18.2864 1046.79i −0.00196787 0.112649i
\(443\) −1517.05 −0.162703 −0.0813515 0.996685i \(-0.525924\pi\)
−0.0813515 + 0.996685i \(0.525924\pi\)
\(444\) 0 0
\(445\) −290.754 + 503.601i −0.0309732 + 0.0536472i
\(446\) 6205.63 + 10748.5i 0.658845 + 1.14115i
\(447\) 0 0
\(448\) −16408.1 + 9473.24i −1.73038 + 0.999037i
\(449\) 610.761 352.623i 0.0641951 0.0370631i −0.467559 0.883962i \(-0.654866\pi\)
0.531754 + 0.846899i \(0.321533\pi\)
\(450\) 0 0
\(451\) 5232.48 + 9062.93i 0.546315 + 0.946245i
\(452\) −13289.5 + 23018.1i −1.38293 + 2.39531i
\(453\) 0 0
\(454\) 20383.1 2.10710
\(455\) 989.575 + 1646.88i 0.101960 + 0.169685i
\(456\) 0 0
\(457\) −6302.69 3638.86i −0.645137 0.372470i 0.141454 0.989945i \(-0.454822\pi\)
−0.786591 + 0.617475i \(0.788156\pi\)
\(458\) 11590.7 20075.6i 1.18253 2.04820i
\(459\) 0 0
\(460\) 2651.58i 0.268762i
\(461\) 1699.04 980.941i 0.171653 0.0991041i −0.411712 0.911314i \(-0.635069\pi\)
0.583365 + 0.812210i \(0.301736\pi\)
\(462\) 0 0
\(463\) 10374.1i 1.04131i −0.853768 0.520653i \(-0.825689\pi\)
0.853768 0.520653i \(-0.174311\pi\)
\(464\) 25903.4 + 44866.0i 2.59167 + 4.48891i
\(465\) 0 0
\(466\) 24529.7 + 14162.2i 2.43845 + 1.40784i
\(467\) 8788.92 0.870883 0.435442 0.900217i \(-0.356592\pi\)
0.435442 + 0.900217i \(0.356592\pi\)
\(468\) 0 0
\(469\) −340.653 −0.0335392
\(470\) −4437.36 2561.91i −0.435489 0.251430i
\(471\) 0 0
\(472\) −15259.1 26429.5i −1.48804 2.57737i
\(473\) 3476.97i 0.337995i
\(474\) 0 0
\(475\) −2659.55 + 1535.49i −0.256902 + 0.148322i
\(476\) 1315.31i 0.126654i
\(477\) 0 0
\(478\) −4152.07 + 7191.60i −0.397304 + 0.688151i
\(479\) −9648.96 5570.83i −0.920401 0.531394i −0.0366382 0.999329i \(-0.511665\pi\)
−0.883763 + 0.467935i \(0.844998\pi\)
\(480\) 0 0
\(481\) −7202.36 3992.20i −0.682743 0.378438i
\(482\) −26383.8 −2.49325
\(483\) 0 0
\(484\) −32651.8 + 56554.6i −3.06648 + 5.31129i
\(485\) −1951.46 3380.03i −0.182704 0.316452i
\(486\) 0 0
\(487\) 17009.1 9820.23i 1.58266 0.913752i 0.588195 0.808719i \(-0.299839\pi\)
0.994469 0.105033i \(-0.0334948\pi\)
\(488\) 7107.20 4103.34i 0.659278 0.380634i
\(489\) 0 0
\(490\) −809.207 1401.59i −0.0746046 0.129219i
\(491\) 1705.16 2953.42i 0.156726 0.271458i −0.776960 0.629550i \(-0.783239\pi\)
0.933686 + 0.358092i \(0.116573\pi\)
\(492\) 0 0
\(493\) −1070.06 −0.0977546
\(494\) −6558.23 + 114.566i −0.597305 + 0.0104344i
\(495\) 0 0
\(496\) 36003.9 + 20786.9i 3.25932 + 1.88177i
\(497\) 2167.93 3754.96i 0.195664 0.338899i
\(498\) 0 0
\(499\) 5032.44i 0.451469i 0.974189 + 0.225735i \(0.0724782\pi\)
−0.974189 + 0.225735i \(0.927522\pi\)
\(500\) −11778.1 + 6800.09i −1.05347 + 0.608219i
\(501\) 0 0
\(502\) 6200.44i 0.551274i
\(503\) 8594.69 + 14886.4i 0.761866 + 1.31959i 0.941888 + 0.335927i \(0.109050\pi\)
−0.180022 + 0.983663i \(0.557617\pi\)
\(504\) 0 0
\(505\) 2062.92 + 1191.03i 0.181780 + 0.104951i
\(506\) 16980.8 1.49187
\(507\) 0 0
\(508\) −23145.5 −2.02149
\(509\) 805.889 + 465.280i 0.0701776 + 0.0405170i 0.534678 0.845056i \(-0.320433\pi\)
−0.464501 + 0.885573i \(0.653766\pi\)
\(510\) 0 0
\(511\) 5632.43 + 9755.65i 0.487601 + 0.844549i
\(512\) 3143.50i 0.271337i
\(513\) 0 0
\(514\) −10927.1 + 6308.79i −0.937695 + 0.541379i
\(515\) 3375.08i 0.288784i
\(516\) 0 0
\(517\) 11846.1 20518.0i 1.00772 1.74541i
\(518\) −12408.8 7164.21i −1.05253 0.607679i
\(519\) 0 0
\(520\) −8663.76 + 151.348i −0.730637 + 0.0127636i
\(521\) 9869.60 0.829933 0.414966 0.909837i \(-0.363793\pi\)
0.414966 + 0.909837i \(0.363793\pi\)
\(522\) 0 0
\(523\) 10710.3 18550.8i 0.895466 1.55099i 0.0622398 0.998061i \(-0.480176\pi\)
0.833226 0.552932i \(-0.186491\pi\)
\(524\) −21820.6 37794.3i −1.81915 3.15087i
\(525\) 0 0
\(526\) 25654.6 14811.7i 2.12660 1.22779i
\(527\) −743.654 + 429.349i −0.0614688 + 0.0354890i
\(528\) 0 0
\(529\) 4963.71 + 8597.40i 0.407965 + 0.706616i
\(530\) −75.7410 + 131.187i −0.00620750 + 0.0107517i
\(531\) 0 0
\(532\) −8240.54 −0.671565
\(533\) −6414.28 3555.38i −0.521263 0.288931i
\(534\) 0 0
\(535\) −797.693 460.548i −0.0644622 0.0372173i
\(536\) 768.168 1330.51i 0.0619026 0.107218i
\(537\) 0 0
\(538\) 21013.4i 1.68392i
\(539\) 6480.83 3741.71i 0.517902 0.299011i
\(540\) 0 0
\(541\) 7771.50i 0.617602i 0.951127 + 0.308801i \(0.0999277\pi\)
−0.951127 + 0.308801i \(0.900072\pi\)
\(542\) 7450.34 + 12904.4i 0.590442 + 1.02267i
\(543\) 0 0
\(544\) 1921.52 + 1109.39i 0.151442 + 0.0874350i
\(545\) 2090.12 0.164277
\(546\) 0 0
\(547\) −15577.5 −1.21763 −0.608817 0.793310i \(-0.708356\pi\)
−0.608817 + 0.793310i \(0.708356\pi\)
\(548\) 21685.8 + 12520.3i 1.69046 + 0.975986i
\(549\) 0 0
\(550\) −21121.8 36584.1i −1.63752 2.83628i
\(551\) 6704.02i 0.518332i
\(552\) 0 0
\(553\) −7210.58 + 4163.03i −0.554476 + 0.320127i
\(554\) 35316.4i 2.70840i
\(555\) 0 0
\(556\) 3354.87 5810.80i 0.255896 0.443225i
\(557\) −19749.3 11402.3i −1.50234 0.867377i −0.999996 0.00270962i \(-0.999138\pi\)
−0.502345 0.864667i \(-0.667529\pi\)
\(558\) 0 0
\(559\) 1254.98 + 2088.58i 0.0949556 + 0.158028i
\(560\) −8262.78 −0.623511
\(561\) 0 0
\(562\) 7702.83 13341.7i 0.578157 1.00140i
\(563\) 1758.71 + 3046.17i 0.131653 + 0.228030i 0.924314 0.381633i \(-0.124638\pi\)
−0.792661 + 0.609663i \(0.791305\pi\)
\(564\) 0 0
\(565\) −2986.67 + 1724.36i −0.222390 + 0.128397i
\(566\) 34928.7 20166.1i 2.59393 1.49761i
\(567\) 0 0
\(568\) 9777.29 + 16934.8i 0.722264 + 1.25100i
\(569\) 3046.72 5277.08i 0.224473 0.388799i −0.731688 0.681640i \(-0.761267\pi\)
0.956161 + 0.292841i \(0.0946006\pi\)
\(570\) 0 0
\(571\) −10460.2 −0.766630 −0.383315 0.923618i \(-0.625218\pi\)
−0.383315 + 0.923618i \(0.625218\pi\)
\(572\) −1137.88 65137.0i −0.0831771 4.76139i
\(573\) 0 0
\(574\) −11051.0 6380.31i −0.803590 0.463953i
\(575\) −2785.74 + 4825.03i −0.202040 + 0.349944i
\(576\) 0 0
\(577\) 9648.19i 0.696117i 0.937473 + 0.348058i \(0.113159\pi\)
−0.937473 + 0.348058i \(0.886841\pi\)
\(578\) 22745.2 13131.9i 1.63681 0.945012i
\(579\) 0 0
\(580\) 14400.1i 1.03092i
\(581\) 4583.97 + 7939.66i 0.327324 + 0.566941i
\(582\) 0 0
\(583\) −606.599 350.220i −0.0430922 0.0248793i
\(584\) −50804.1 −3.59981
\(585\) 0 0
\(586\) −24176.5 −1.70430
\(587\) −1879.91 1085.37i −0.132184 0.0763166i 0.432450 0.901658i \(-0.357649\pi\)
−0.564634 + 0.825341i \(0.690983\pi\)
\(588\) 0 0
\(589\) 2689.91 + 4659.06i 0.188176 + 0.325931i
\(590\) 6438.56i 0.449274i
\(591\) 0 0
\(592\) 30669.7 17707.2i 2.12925 1.22932i
\(593\) 22885.9i 1.58484i −0.609975 0.792421i \(-0.708820\pi\)
0.609975 0.792421i \(-0.291180\pi\)
\(594\) 0 0
\(595\) 85.3330 147.801i 0.00587951 0.0101836i
\(596\) 20315.2 + 11729.0i 1.39621 + 0.806105i
\(597\) 0 0
\(598\) −10200.2 + 6129.08i −0.697518 + 0.419125i
\(599\) 23978.7 1.63563 0.817815 0.575482i \(-0.195185\pi\)
0.817815 + 0.575482i \(0.195185\pi\)
\(600\) 0 0
\(601\) −6436.62 + 11148.6i −0.436864 + 0.756671i −0.997446 0.0714284i \(-0.977244\pi\)
0.560582 + 0.828099i \(0.310578\pi\)
\(602\) 2119.85 + 3671.69i 0.143519 + 0.248583i
\(603\) 0 0
\(604\) 52916.9 30551.6i 3.56483 2.05816i
\(605\) −7338.16 + 4236.69i −0.493122 + 0.284704i
\(606\) 0 0
\(607\) 3558.57 + 6163.63i 0.237954 + 0.412148i 0.960127 0.279564i \(-0.0901899\pi\)
−0.722173 + 0.691712i \(0.756857\pi\)
\(608\) 6950.43 12038.5i 0.463614 0.803002i
\(609\) 0 0
\(610\) 1731.40 0.114922
\(611\) 289.998 + 16600.6i 0.0192014 + 1.09917i
\(612\) 0 0
\(613\) 150.079 + 86.6484i 0.00988850 + 0.00570913i 0.504936 0.863157i \(-0.331516\pi\)
−0.495048 + 0.868866i \(0.664849\pi\)
\(614\) −25586.8 + 44317.6i −1.68176 + 2.91289i
\(615\) 0 0
\(616\) 69715.5i 4.55993i
\(617\) −5285.14 + 3051.38i −0.344849 + 0.199099i −0.662414 0.749138i \(-0.730468\pi\)
0.317565 + 0.948236i \(0.397135\pi\)
\(618\) 0 0
\(619\) 14867.8i 0.965409i −0.875783 0.482705i \(-0.839654\pi\)
0.875783 0.482705i \(-0.160346\pi\)
\(620\) 5777.88 + 10007.6i 0.374267 + 0.648249i
\(621\) 0 0
\(622\) −34688.3 20027.3i −2.23613 1.29103i
\(623\) 3278.69 0.210847
\(624\) 0 0
\(625\) 12951.6 0.828900
\(626\) −8463.35 4886.32i −0.540357 0.311975i
\(627\) 0 0
\(628\) 6539.43 + 11326.6i 0.415528 + 0.719716i
\(629\) 731.475i 0.0463686i
\(630\) 0 0
\(631\) −14904.8 + 8605.29i −0.940334 + 0.542902i −0.890065 0.455834i \(-0.849341\pi\)
−0.0502690 + 0.998736i \(0.516008\pi\)
\(632\) 37550.3i 2.36340i
\(633\) 0 0
\(634\) −8382.76 + 14519.4i −0.525113 + 0.909523i
\(635\) −2600.86 1501.60i −0.162538 0.0938415i
\(636\) 0 0
\(637\) −2542.42 + 4586.80i −0.158139 + 0.285299i
\(638\) −92218.9 −5.72254
\(639\) 0 0
\(640\) 3266.15 5657.14i 0.201728 0.349403i
\(641\) 6318.01 + 10943.1i 0.389308 + 0.674301i 0.992357 0.123403i \(-0.0393808\pi\)
−0.603049 + 0.797704i \(0.706047\pi\)
\(642\) 0 0
\(643\) 8302.04 4793.19i 0.509177 0.293973i −0.223318 0.974746i \(-0.571689\pi\)
0.732495 + 0.680772i \(0.238356\pi\)
\(644\) −12947.3 + 7475.12i −0.792228 + 0.457393i
\(645\) 0 0
\(646\) 291.320 + 504.581i 0.0177428 + 0.0307314i
\(647\) −2622.16 + 4541.72i −0.159332 + 0.275971i −0.934628 0.355627i \(-0.884267\pi\)
0.775296 + 0.631598i \(0.217601\pi\)
\(648\) 0 0
\(649\) 29771.4 1.80066
\(650\) 25892.4 + 14351.9i 1.56243 + 0.866043i
\(651\) 0 0
\(652\) −7106.94 4103.19i −0.426885 0.246462i
\(653\) 9434.51 16341.1i 0.565392 0.979288i −0.431621 0.902055i \(-0.642058\pi\)
0.997013 0.0772326i \(-0.0246084\pi\)
\(654\) 0 0
\(655\) 5662.59i 0.337795i
\(656\) 27313.8 15769.7i 1.62565 0.938570i
\(657\) 0 0
\(658\) 28889.3i 1.71159i
\(659\) −12149.9 21044.2i −0.718197 1.24395i −0.961713 0.274057i \(-0.911634\pi\)
0.243516 0.969897i \(-0.421699\pi\)
\(660\) 0 0
\(661\) −25907.2 14957.5i −1.52447 0.880151i −0.999580 0.0289779i \(-0.990775\pi\)
−0.524886 0.851173i \(-0.675892\pi\)
\(662\) 8335.03 0.489350
\(663\) 0 0
\(664\) −41347.1 −2.41653
\(665\) −925.988 534.620i −0.0539974 0.0311754i
\(666\) 0 0
\(667\) 6081.32 + 10533.2i 0.353028 + 0.611462i
\(668\) 3155.69i 0.182780i
\(669\) 0 0
\(670\) 280.703 162.064i 0.0161858 0.00934489i
\(671\) 8005.86i 0.460600i
\(672\) 0 0
\(673\) 7746.84 13417.9i 0.443713 0.768533i −0.554249 0.832351i \(-0.686994\pi\)
0.997962 + 0.0638177i \(0.0203276\pi\)
\(674\) 14822.7 + 8557.90i 0.847106 + 0.489077i
\(675\) 0 0
\(676\) 24194.2 + 38716.3i 1.37654 + 2.20279i
\(677\) −11729.7 −0.665891 −0.332945 0.942946i \(-0.608042\pi\)
−0.332945 + 0.942946i \(0.608042\pi\)
\(678\) 0 0
\(679\) −11002.8 + 19057.4i −0.621869 + 1.07711i
\(680\) 384.849 + 666.578i 0.0217034 + 0.0375913i
\(681\) 0 0
\(682\) −64088.9 + 37001.8i −3.59838 + 2.07752i
\(683\) 1011.88 584.210i 0.0566889 0.0327294i −0.471388 0.881926i \(-0.656247\pi\)
0.528077 + 0.849197i \(0.322913\pi\)
\(684\) 0 0
\(685\) 1624.55 + 2813.81i 0.0906145 + 0.156949i
\(686\) −18549.5 + 32128.7i −1.03240 + 1.78816i
\(687\) 0 0
\(688\) −10478.9 −0.580675
\(689\) 490.786 8.57358i 0.0271371 0.000474060i
\(690\) 0 0
\(691\) 28572.7 + 16496.4i 1.57302 + 0.908183i 0.995796 + 0.0915952i \(0.0291966\pi\)
0.577222 + 0.816587i \(0.304137\pi\)
\(692\) 5598.34 9696.62i 0.307539 0.532673i
\(693\) 0 0
\(694\) 30679.2i 1.67805i
\(695\) 753.972 435.306i 0.0411508 0.0237584i
\(696\) 0 0
\(697\) 651.438i 0.0354017i
\(698\) 8928.14 + 15464.0i 0.484147 + 0.838568i
\(699\) 0 0
\(700\) 32209.4 + 18596.1i 1.73914 + 1.00410i
\(701\) −14785.8 −0.796651 −0.398326 0.917244i \(-0.630409\pi\)
−0.398326 + 0.917244i \(0.630409\pi\)
\(702\) 0 0
\(703\) 4582.77 0.245864
\(704\) 72189.3 + 41678.5i 3.86468 + 2.23128i
\(705\) 0 0
\(706\) 33010.5 + 57175.8i 1.75973 + 3.04793i
\(707\) 13430.6i 0.714442i
\(708\) 0 0
\(709\) 10941.4 6317.00i 0.579565 0.334612i −0.181395 0.983410i \(-0.558061\pi\)
0.760961 + 0.648798i \(0.224728\pi\)
\(710\) 4125.52i 0.218067i
\(711\) 0 0
\(712\) −7393.39 + 12805.7i −0.389156 + 0.674038i
\(713\) 8452.62 + 4880.12i 0.443973 + 0.256328i
\(714\) 0 0
\(715\) 4098.01 7393.25i 0.214345 0.386702i
\(716\) 46148.7 2.40874
\(717\) 0 0
\(718\) 22907.3 39676.6i 1.19066 2.06228i
\(719\) 13648.3 + 23639.5i 0.707920 + 1.22615i 0.965627 + 0.259931i \(0.0836998\pi\)
−0.257707 + 0.966223i \(0.582967\pi\)
\(720\) 0 0
\(721\) −16480.1 + 9514.77i −0.851248 + 0.491468i
\(722\) −28705.6 + 16573.2i −1.47966 + 0.854279i
\(723\) 0 0
\(724\) 39719.2 + 68795.7i 2.03889 + 3.53145i
\(725\) 15128.7 26203.7i 0.774987 1.34232i
\(726\) 0 0
\(727\) −4658.21 −0.237639 −0.118819 0.992916i \(-0.537911\pi\)
−0.118819 + 0.992916i \(0.537911\pi\)
\(728\) 25163.2 + 41877.3i 1.28106 + 2.13197i
\(729\) 0 0
\(730\) −9282.39 5359.19i −0.470626 0.271716i
\(731\) 108.220 187.442i 0.00547558 0.00948399i
\(732\) 0 0
\(733\) 166.474i 0.00838864i 0.999991 + 0.00419432i \(0.00133510\pi\)
−0.999991 + 0.00419432i \(0.998665\pi\)
\(734\) −11599.4 + 6696.93i −0.583300 + 0.336769i
\(735\) 0 0
\(736\) 25219.4i 1.26304i
\(737\) 749.370 + 1297.95i 0.0374537 + 0.0648718i
\(738\) 0 0
\(739\) −11031.5 6369.03i −0.549120 0.317035i 0.199647 0.979868i \(-0.436020\pi\)
−0.748767 + 0.662833i \(0.769354\pi\)
\(740\) 9843.70 0.489002
\(741\) 0 0
\(742\) 854.092 0.0422570
\(743\) 26608.2 + 15362.2i 1.31381 + 0.758527i 0.982725 0.185074i \(-0.0592526\pi\)
0.331083 + 0.943602i \(0.392586\pi\)
\(744\) 0 0
\(745\) 1521.88 + 2635.97i 0.0748420 + 0.129630i
\(746\) 6131.38i 0.300919i
\(747\) 0 0
\(748\) −5011.55 + 2893.42i −0.244974 + 0.141436i
\(749\) 5193.37i 0.253353i
\(750\) 0 0
\(751\) −19769.3 + 34241.4i −0.960575 + 1.66376i −0.239514 + 0.970893i \(0.576988\pi\)
−0.721061 + 0.692872i \(0.756345\pi\)
\(752\) −61837.0 35701.6i −2.99862 1.73126i
\(753\) 0 0
\(754\) 55394.8 33285.6i 2.67555 1.60768i
\(755\) 7928.35 0.382175
\(756\) 0 0
\(757\) −11517.6 + 19949.0i −0.552990 + 0.957807i 0.445067 + 0.895497i \(0.353180\pi\)
−0.998057 + 0.0623093i \(0.980153\pi\)
\(758\) −32676.1 56596.6i −1.56576 2.71198i
\(759\) 0 0
\(760\) 4176.18 2411.12i 0.199323 0.115079i
\(761\) −28106.0 + 16227.0i −1.33882 + 0.772968i −0.986632 0.162962i \(-0.947895\pi\)
−0.352187 + 0.935930i \(0.614562\pi\)
\(762\) 0 0
\(763\) −5892.30 10205.8i −0.279575 0.484238i
\(764\) −35993.4 + 62342.4i −1.70444 + 2.95218i
\(765\) 0 0
\(766\) −54616.1 −2.57619
\(767\) −17883.3 + 10745.7i −0.841890 + 0.505874i
\(768\) 0 0
\(769\) −27900.1 16108.1i −1.30833 0.755362i −0.326509 0.945194i \(-0.605873\pi\)
−0.981817 + 0.189831i \(0.939206\pi\)
\(770\) 7354.10 12737.7i 0.344186 0.596148i
\(771\) 0 0
\(772\) 97613.2i 4.55075i
\(773\) 2532.78 1462.30i 0.117849 0.0680404i −0.439917 0.898039i \(-0.644992\pi\)
0.557766 + 0.829998i \(0.311659\pi\)
\(774\) 0 0
\(775\) 24280.9i 1.12541i
\(776\) −49622.3 85948.4i −2.29554 3.97599i
\(777\) 0 0
\(778\) 27159.6 + 15680.6i 1.25157 + 0.722593i
\(779\) 4081.32 0.187713
\(780\) 0 0
\(781\) −19076.1 −0.874001
\(782\) 915.427 + 528.522i 0.0418614 + 0.0241687i
\(783\) 0