Properties

Label 252.4.x.a.41.15
Level $252$
Weight $4$
Character 252.41
Analytic conductor $14.868$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.x (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.8684813214\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 41.15
Character \(\chi\) \(=\) 252.41
Dual form 252.4.x.a.209.15

$q$-expansion

\(f(q)\) \(=\) \(q+(0.494604 + 5.17256i) q^{3} +(-2.99997 + 5.19610i) q^{5} +(16.2235 + 8.93305i) q^{7} +(-26.5107 + 5.11673i) q^{9} +O(q^{10})\) \(q+(0.494604 + 5.17256i) q^{3} +(-2.99997 + 5.19610i) q^{5} +(16.2235 + 8.93305i) q^{7} +(-26.5107 + 5.11673i) q^{9} +(-39.3810 + 22.7366i) q^{11} +(22.7627 + 13.1421i) q^{13} +(-28.3609 - 12.9475i) q^{15} +19.7249 q^{17} -27.9162i q^{19} +(-38.1826 + 88.3351i) q^{21} +(-60.3466 - 34.8411i) q^{23} +(44.5004 + 77.0769i) q^{25} +(-39.5789 - 134.598i) q^{27} +(-119.031 + 68.7227i) q^{29} +(-138.202 - 79.7908i) q^{31} +(-137.085 - 192.455i) q^{33} +(-95.0869 + 57.4998i) q^{35} -287.829 q^{37} +(-56.7196 + 124.242i) q^{39} +(20.4288 - 35.3837i) q^{41} +(55.4158 + 95.9830i) q^{43} +(52.9443 - 153.102i) q^{45} +(-109.666 - 189.948i) q^{47} +(183.401 + 289.850i) q^{49} +(9.75601 + 102.028i) q^{51} -209.770i q^{53} -272.837i q^{55} +(144.398 - 13.8074i) q^{57} +(-413.880 + 716.860i) q^{59} +(594.209 - 343.066i) q^{61} +(-475.804 - 153.811i) q^{63} +(-136.575 + 78.8515i) q^{65} +(-171.449 + 296.958i) q^{67} +(150.370 - 329.379i) q^{69} +387.476i q^{71} +220.721i q^{73} +(-376.675 + 268.303i) q^{75} +(-842.004 + 17.0742i) q^{77} +(242.301 + 419.677i) q^{79} +(676.638 - 271.297i) q^{81} +(354.323 + 613.706i) q^{83} +(-59.1741 + 102.493i) q^{85} +(-414.346 - 581.706i) q^{87} +140.929 q^{89} +(251.891 + 416.550i) q^{91} +(344.368 - 754.321i) q^{93} +(145.055 + 83.7476i) q^{95} +(1304.31 - 753.041i) q^{97} +(927.683 - 804.267i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 6q^{7} + 60q^{9} + O(q^{10}) \) \( 48q + 6q^{7} + 60q^{9} - 12q^{11} + 192q^{15} - 72q^{21} - 408q^{23} - 600q^{25} - 84q^{29} + 336q^{37} + 36q^{39} + 84q^{43} + 318q^{49} - 1812q^{51} - 852q^{57} - 564q^{63} + 2964q^{65} - 588q^{67} + 2400q^{77} + 204q^{79} + 1980q^{81} - 360q^{85} - 1080q^{91} + 2496q^{93} + 300q^{95} - 4968q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.494604 + 5.17256i 0.0951865 + 0.995459i
\(4\) 0 0
\(5\) −2.99997 + 5.19610i −0.268325 + 0.464753i −0.968430 0.249288i \(-0.919804\pi\)
0.700104 + 0.714041i \(0.253137\pi\)
\(6\) 0 0
\(7\) 16.2235 + 8.93305i 0.875984 + 0.482340i
\(8\) 0 0
\(9\) −26.5107 + 5.11673i −0.981879 + 0.189509i
\(10\) 0 0
\(11\) −39.3810 + 22.7366i −1.07944 + 0.623214i −0.930745 0.365669i \(-0.880840\pi\)
−0.148694 + 0.988883i \(0.547507\pi\)
\(12\) 0 0
\(13\) 22.7627 + 13.1421i 0.485634 + 0.280381i 0.722761 0.691098i \(-0.242873\pi\)
−0.237127 + 0.971479i \(0.576206\pi\)
\(14\) 0 0
\(15\) −28.3609 12.9475i −0.488184 0.222869i
\(16\) 0 0
\(17\) 19.7249 0.281411 0.140706 0.990051i \(-0.455063\pi\)
0.140706 + 0.990051i \(0.455063\pi\)
\(18\) 0 0
\(19\) 27.9162i 0.337074i −0.985695 0.168537i \(-0.946096\pi\)
0.985695 0.168537i \(-0.0539043\pi\)
\(20\) 0 0
\(21\) −38.1826 + 88.3351i −0.396768 + 0.917919i
\(22\) 0 0
\(23\) −60.3466 34.8411i −0.547093 0.315864i 0.200856 0.979621i \(-0.435628\pi\)
−0.747949 + 0.663757i \(0.768961\pi\)
\(24\) 0 0
\(25\) 44.5004 + 77.0769i 0.356003 + 0.616615i
\(26\) 0 0
\(27\) −39.5789 134.598i −0.282110 0.959382i
\(28\) 0 0
\(29\) −119.031 + 68.7227i −0.762191 + 0.440051i −0.830082 0.557641i \(-0.811706\pi\)
0.0678907 + 0.997693i \(0.478373\pi\)
\(30\) 0 0
\(31\) −138.202 79.7908i −0.800702 0.462286i 0.0430146 0.999074i \(-0.486304\pi\)
−0.843717 + 0.536789i \(0.819637\pi\)
\(32\) 0 0
\(33\) −137.085 192.455i −0.723133 1.01522i
\(34\) 0 0
\(35\) −95.0869 + 57.4998i −0.459218 + 0.277693i
\(36\) 0 0
\(37\) −287.829 −1.27889 −0.639443 0.768839i \(-0.720835\pi\)
−0.639443 + 0.768839i \(0.720835\pi\)
\(38\) 0 0
\(39\) −56.7196 + 124.242i −0.232882 + 0.510117i
\(40\) 0 0
\(41\) 20.4288 35.3837i 0.0778157 0.134781i −0.824492 0.565874i \(-0.808539\pi\)
0.902307 + 0.431093i \(0.141872\pi\)
\(42\) 0 0
\(43\) 55.4158 + 95.9830i 0.196531 + 0.340402i 0.947401 0.320048i \(-0.103699\pi\)
−0.750870 + 0.660450i \(0.770366\pi\)
\(44\) 0 0
\(45\) 52.9443 153.102i 0.175388 0.507181i
\(46\) 0 0
\(47\) −109.666 189.948i −0.340351 0.589504i 0.644147 0.764902i \(-0.277212\pi\)
−0.984498 + 0.175397i \(0.943879\pi\)
\(48\) 0 0
\(49\) 183.401 + 289.850i 0.534697 + 0.845044i
\(50\) 0 0
\(51\) 9.75601 + 102.028i 0.0267866 + 0.280133i
\(52\) 0 0
\(53\) 209.770i 0.543664i −0.962345 0.271832i \(-0.912371\pi\)
0.962345 0.271832i \(-0.0876295\pi\)
\(54\) 0 0
\(55\) 272.837i 0.668897i
\(56\) 0 0
\(57\) 144.398 13.8074i 0.335544 0.0320849i
\(58\) 0 0
\(59\) −413.880 + 716.860i −0.913263 + 1.58182i −0.103839 + 0.994594i \(0.533113\pi\)
−0.809425 + 0.587224i \(0.800221\pi\)
\(60\) 0 0
\(61\) 594.209 343.066i 1.24722 0.720085i 0.276668 0.960965i \(-0.410770\pi\)
0.970555 + 0.240881i \(0.0774363\pi\)
\(62\) 0 0
\(63\) −475.804 153.811i −0.951518 0.307593i
\(64\) 0 0
\(65\) −136.575 + 78.8515i −0.260616 + 0.150467i
\(66\) 0 0
\(67\) −171.449 + 296.958i −0.312624 + 0.541480i −0.978930 0.204198i \(-0.934541\pi\)
0.666306 + 0.745679i \(0.267875\pi\)
\(68\) 0 0
\(69\) 150.370 329.379i 0.262354 0.574675i
\(70\) 0 0
\(71\) 387.476i 0.647675i 0.946113 + 0.323838i \(0.104973\pi\)
−0.946113 + 0.323838i \(0.895027\pi\)
\(72\) 0 0
\(73\) 220.721i 0.353882i 0.984221 + 0.176941i \(0.0566202\pi\)
−0.984221 + 0.176941i \(0.943380\pi\)
\(74\) 0 0
\(75\) −376.675 + 268.303i −0.579929 + 0.413080i
\(76\) 0 0
\(77\) −842.004 + 17.0742i −1.24617 + 0.0252699i
\(78\) 0 0
\(79\) 242.301 + 419.677i 0.345076 + 0.597688i 0.985367 0.170443i \(-0.0545200\pi\)
−0.640292 + 0.768132i \(0.721187\pi\)
\(80\) 0 0
\(81\) 676.638 271.297i 0.928173 0.372149i
\(82\) 0 0
\(83\) 354.323 + 613.706i 0.468579 + 0.811602i 0.999355 0.0359099i \(-0.0114329\pi\)
−0.530776 + 0.847512i \(0.678100\pi\)
\(84\) 0 0
\(85\) −59.1741 + 102.493i −0.0755098 + 0.130787i
\(86\) 0 0
\(87\) −414.346 581.706i −0.510604 0.716844i
\(88\) 0 0
\(89\) 140.929 0.167848 0.0839240 0.996472i \(-0.473255\pi\)
0.0839240 + 0.996472i \(0.473255\pi\)
\(90\) 0 0
\(91\) 251.891 + 416.550i 0.290169 + 0.479850i
\(92\) 0 0
\(93\) 344.368 754.321i 0.383970 0.841070i
\(94\) 0 0
\(95\) 145.055 + 83.7476i 0.156656 + 0.0904455i
\(96\) 0 0
\(97\) 1304.31 753.041i 1.36528 0.788245i 0.374960 0.927041i \(-0.377657\pi\)
0.990321 + 0.138796i \(0.0443232\pi\)
\(98\) 0 0
\(99\) 927.683 804.267i 0.941774 0.816484i
\(100\) 0 0
\(101\) 923.516 + 1599.58i 0.909834 + 1.57588i 0.814293 + 0.580454i \(0.197125\pi\)
0.0955414 + 0.995425i \(0.469542\pi\)
\(102\) 0 0
\(103\) 696.481 + 402.114i 0.666275 + 0.384674i 0.794664 0.607050i \(-0.207647\pi\)
−0.128389 + 0.991724i \(0.540981\pi\)
\(104\) 0 0
\(105\) −344.451 463.403i −0.320143 0.430700i
\(106\) 0 0
\(107\) 282.997i 0.255685i −0.991794 0.127843i \(-0.959195\pi\)
0.991794 0.127843i \(-0.0408053\pi\)
\(108\) 0 0
\(109\) 1826.43 1.60496 0.802478 0.596681i \(-0.203514\pi\)
0.802478 + 0.596681i \(0.203514\pi\)
\(110\) 0 0
\(111\) −142.361 1488.81i −0.121733 1.27308i
\(112\) 0 0
\(113\) −815.811 471.008i −0.679159 0.392113i 0.120379 0.992728i \(-0.461589\pi\)
−0.799538 + 0.600615i \(0.794922\pi\)
\(114\) 0 0
\(115\) 362.076 209.044i 0.293598 0.169509i
\(116\) 0 0
\(117\) −670.701 231.935i −0.529968 0.183268i
\(118\) 0 0
\(119\) 320.006 + 176.204i 0.246512 + 0.135736i
\(120\) 0 0
\(121\) 368.410 638.105i 0.276792 0.479418i
\(122\) 0 0
\(123\) 193.129 + 88.1683i 0.141576 + 0.0646331i
\(124\) 0 0
\(125\) −1283.99 −0.918749
\(126\) 0 0
\(127\) 320.551 0.223971 0.111985 0.993710i \(-0.464279\pi\)
0.111985 + 0.993710i \(0.464279\pi\)
\(128\) 0 0
\(129\) −469.069 + 334.115i −0.320149 + 0.228040i
\(130\) 0 0
\(131\) −306.907 + 531.578i −0.204691 + 0.354536i −0.950034 0.312145i \(-0.898952\pi\)
0.745343 + 0.666681i \(0.232286\pi\)
\(132\) 0 0
\(133\) 249.377 452.897i 0.162584 0.295272i
\(134\) 0 0
\(135\) 818.118 + 198.133i 0.521573 + 0.126315i
\(136\) 0 0
\(137\) 1515.86 875.182i 0.945318 0.545780i 0.0536948 0.998557i \(-0.482900\pi\)
0.891623 + 0.452778i \(0.149567\pi\)
\(138\) 0 0
\(139\) 1120.72 + 647.048i 0.683872 + 0.394834i 0.801312 0.598246i \(-0.204135\pi\)
−0.117440 + 0.993080i \(0.537469\pi\)
\(140\) 0 0
\(141\) 928.274 661.204i 0.554431 0.394918i
\(142\) 0 0
\(143\) −1195.23 −0.698950
\(144\) 0 0
\(145\) 824.664i 0.472308i
\(146\) 0 0
\(147\) −1408.56 + 1092.01i −0.790311 + 0.612706i
\(148\) 0 0
\(149\) −2499.23 1442.93i −1.37413 0.793352i −0.382681 0.923880i \(-0.624999\pi\)
−0.991445 + 0.130528i \(0.958333\pi\)
\(150\) 0 0
\(151\) 1540.63 + 2668.45i 0.830297 + 1.43812i 0.897803 + 0.440398i \(0.145163\pi\)
−0.0675056 + 0.997719i \(0.521504\pi\)
\(152\) 0 0
\(153\) −522.922 + 100.927i −0.276312 + 0.0533298i
\(154\) 0 0
\(155\) 829.202 478.740i 0.429697 0.248086i
\(156\) 0 0
\(157\) 1090.13 + 629.388i 0.554153 + 0.319941i 0.750795 0.660535i \(-0.229670\pi\)
−0.196642 + 0.980475i \(0.563004\pi\)
\(158\) 0 0
\(159\) 1085.05 103.753i 0.541195 0.0517495i
\(160\) 0 0
\(161\) −667.793 1104.32i −0.326891 0.540576i
\(162\) 0 0
\(163\) −2906.94 −1.39687 −0.698434 0.715675i \(-0.746119\pi\)
−0.698434 + 0.715675i \(0.746119\pi\)
\(164\) 0 0
\(165\) 1411.27 134.946i 0.665860 0.0636700i
\(166\) 0 0
\(167\) 286.775 496.709i 0.132882 0.230159i −0.791904 0.610645i \(-0.790910\pi\)
0.924786 + 0.380487i \(0.124244\pi\)
\(168\) 0 0
\(169\) −753.072 1304.36i −0.342773 0.593700i
\(170\) 0 0
\(171\) 142.840 + 740.078i 0.0638785 + 0.330966i
\(172\) 0 0
\(173\) 1931.13 + 3344.82i 0.848679 + 1.46995i 0.882388 + 0.470523i \(0.155935\pi\)
−0.0337092 + 0.999432i \(0.510732\pi\)
\(174\) 0 0
\(175\) 33.4177 + 1647.98i 0.0144351 + 0.711860i
\(176\) 0 0
\(177\) −3912.71 1786.25i −1.66157 0.758549i
\(178\) 0 0
\(179\) 2248.26i 0.938787i 0.882989 + 0.469394i \(0.155527\pi\)
−0.882989 + 0.469394i \(0.844473\pi\)
\(180\) 0 0
\(181\) 166.407i 0.0683368i −0.999416 0.0341684i \(-0.989122\pi\)
0.999416 0.0341684i \(-0.0108783\pi\)
\(182\) 0 0
\(183\) 2068.43 + 2903.90i 0.835534 + 1.17302i
\(184\) 0 0
\(185\) 863.478 1495.59i 0.343157 0.594366i
\(186\) 0 0
\(187\) −776.787 + 448.478i −0.303766 + 0.175379i
\(188\) 0 0
\(189\) 560.261 2537.20i 0.215624 0.976476i
\(190\) 0 0
\(191\) −1758.88 + 1015.49i −0.666324 + 0.384703i −0.794682 0.607025i \(-0.792363\pi\)
0.128358 + 0.991728i \(0.459029\pi\)
\(192\) 0 0
\(193\) 251.118 434.949i 0.0936573 0.162219i −0.815390 0.578912i \(-0.803478\pi\)
0.909047 + 0.416693i \(0.136811\pi\)
\(194\) 0 0
\(195\) −475.415 667.441i −0.174591 0.245110i
\(196\) 0 0
\(197\) 3949.11i 1.42823i 0.700026 + 0.714117i \(0.253172\pi\)
−0.700026 + 0.714117i \(0.746828\pi\)
\(198\) 0 0
\(199\) 629.709i 0.224316i −0.993690 0.112158i \(-0.964224\pi\)
0.993690 0.112158i \(-0.0357763\pi\)
\(200\) 0 0
\(201\) −1620.83 739.952i −0.568779 0.259663i
\(202\) 0 0
\(203\) −2545.00 + 51.6076i −0.879922 + 0.0178431i
\(204\) 0 0
\(205\) 122.572 + 212.300i 0.0417599 + 0.0723302i
\(206\) 0 0
\(207\) 1778.10 + 614.886i 0.597038 + 0.206462i
\(208\) 0 0
\(209\) 634.720 + 1099.37i 0.210069 + 0.363851i
\(210\) 0 0
\(211\) −1494.95 + 2589.33i −0.487757 + 0.844820i −0.999901 0.0140797i \(-0.995518\pi\)
0.512144 + 0.858900i \(0.328851\pi\)
\(212\) 0 0
\(213\) −2004.24 + 191.647i −0.644735 + 0.0616500i
\(214\) 0 0
\(215\) −664.983 −0.210937
\(216\) 0 0
\(217\) −1529.33 2529.05i −0.478424 0.791165i
\(218\) 0 0
\(219\) −1141.69 + 109.169i −0.352275 + 0.0336848i
\(220\) 0 0
\(221\) 448.992 + 259.226i 0.136663 + 0.0789023i
\(222\) 0 0
\(223\) −2829.72 + 1633.74i −0.849740 + 0.490598i −0.860563 0.509344i \(-0.829888\pi\)
0.0108230 + 0.999941i \(0.496555\pi\)
\(224\) 0 0
\(225\) −1574.12 1815.67i −0.466406 0.537976i
\(226\) 0 0
\(227\) −2836.86 4913.59i −0.829468 1.43668i −0.898457 0.439063i \(-0.855311\pi\)
0.0689889 0.997617i \(-0.478023\pi\)
\(228\) 0 0
\(229\) −4528.48 2614.52i −1.30677 0.754465i −0.325215 0.945640i \(-0.605437\pi\)
−0.981556 + 0.191175i \(0.938770\pi\)
\(230\) 0 0
\(231\) −504.775 4346.87i −0.143774 1.23811i
\(232\) 0 0
\(233\) 3433.84i 0.965487i 0.875762 + 0.482743i \(0.160360\pi\)
−0.875762 + 0.482743i \(0.839640\pi\)
\(234\) 0 0
\(235\) 1315.98 0.365299
\(236\) 0 0
\(237\) −2050.96 + 1460.89i −0.562128 + 0.400401i
\(238\) 0 0
\(239\) 469.677 + 271.168i 0.127117 + 0.0733908i 0.562210 0.826995i \(-0.309951\pi\)
−0.435093 + 0.900385i \(0.643285\pi\)
\(240\) 0 0
\(241\) 3110.33 1795.75i 0.831343 0.479976i −0.0229693 0.999736i \(-0.507312\pi\)
0.854312 + 0.519760i \(0.173979\pi\)
\(242\) 0 0
\(243\) 1737.97 + 3365.77i 0.458809 + 0.888535i
\(244\) 0 0
\(245\) −2056.29 + 83.4292i −0.536210 + 0.0217555i
\(246\) 0 0
\(247\) 366.876 635.448i 0.0945092 0.163695i
\(248\) 0 0
\(249\) −2999.18 + 2136.30i −0.763315 + 0.543705i
\(250\) 0 0
\(251\) −4334.39 −1.08998 −0.544988 0.838444i \(-0.683466\pi\)
−0.544988 + 0.838444i \(0.683466\pi\)
\(252\) 0 0
\(253\) 3168.68 0.787404
\(254\) 0 0
\(255\) −559.416 255.388i −0.137380 0.0627178i
\(256\) 0 0
\(257\) 3282.88 5686.12i 0.796812 1.38012i −0.124870 0.992173i \(-0.539852\pi\)
0.921682 0.387946i \(-0.126815\pi\)
\(258\) 0 0
\(259\) −4669.58 2571.19i −1.12028 0.616857i
\(260\) 0 0
\(261\) 2803.97 2430.94i 0.664986 0.576519i
\(262\) 0 0
\(263\) 6274.79 3622.75i 1.47118 0.849386i 0.471704 0.881757i \(-0.343639\pi\)
0.999476 + 0.0323711i \(0.0103058\pi\)
\(264\) 0 0
\(265\) 1089.99 + 629.305i 0.252669 + 0.145879i
\(266\) 0 0
\(267\) 69.7041 + 728.965i 0.0159769 + 0.167086i
\(268\) 0 0
\(269\) 3455.87 0.783302 0.391651 0.920114i \(-0.371904\pi\)
0.391651 + 0.920114i \(0.371904\pi\)
\(270\) 0 0
\(271\) 2471.30i 0.553951i −0.960877 0.276975i \(-0.910668\pi\)
0.960877 0.276975i \(-0.0893321\pi\)
\(272\) 0 0
\(273\) −2030.04 + 1508.95i −0.450051 + 0.334527i
\(274\) 0 0
\(275\) −3504.94 2023.58i −0.768567 0.443732i
\(276\) 0 0
\(277\) 2256.85 + 3908.97i 0.489533 + 0.847897i 0.999927 0.0120440i \(-0.00383381\pi\)
−0.510394 + 0.859941i \(0.670500\pi\)
\(278\) 0 0
\(279\) 4072.10 + 1408.17i 0.873800 + 0.302169i
\(280\) 0 0
\(281\) 2090.48 1206.94i 0.443799 0.256228i −0.261409 0.965228i \(-0.584187\pi\)
0.705208 + 0.709001i \(0.250854\pi\)
\(282\) 0 0
\(283\) −3893.62 2247.98i −0.817851 0.472187i 0.0318238 0.999493i \(-0.489868\pi\)
−0.849675 + 0.527307i \(0.823202\pi\)
\(284\) 0 0
\(285\) −361.445 + 791.728i −0.0751233 + 0.164554i
\(286\) 0 0
\(287\) 647.511 391.555i 0.133175 0.0805322i
\(288\) 0 0
\(289\) −4523.93 −0.920808
\(290\) 0 0
\(291\) 4540.27 + 6374.14i 0.914622 + 1.28405i
\(292\) 0 0
\(293\) −1569.64 + 2718.69i −0.312966 + 0.542073i −0.979003 0.203845i \(-0.934656\pi\)
0.666037 + 0.745919i \(0.267989\pi\)
\(294\) 0 0
\(295\) −2483.25 4301.12i −0.490103 0.848884i
\(296\) 0 0
\(297\) 4618.96 + 4400.70i 0.902421 + 0.859779i
\(298\) 0 0
\(299\) −915.768 1586.16i −0.177125 0.306789i
\(300\) 0 0
\(301\) 41.6147 + 2052.21i 0.00796888 + 0.392981i
\(302\) 0 0
\(303\) −7817.13 + 5568.10i −1.48212 + 1.05571i
\(304\) 0 0
\(305\) 4116.75i 0.772868i
\(306\) 0 0
\(307\) 10294.0i 1.91371i 0.290560 + 0.956857i \(0.406158\pi\)
−0.290560 + 0.956857i \(0.593842\pi\)
\(308\) 0 0
\(309\) −1735.47 + 3801.48i −0.319507 + 0.699865i
\(310\) 0 0
\(311\) 3940.59 6825.30i 0.718489 1.24446i −0.243109 0.969999i \(-0.578167\pi\)
0.961598 0.274461i \(-0.0884994\pi\)
\(312\) 0 0
\(313\) −7096.84 + 4097.36i −1.28159 + 0.739925i −0.977139 0.212604i \(-0.931806\pi\)
−0.304449 + 0.952529i \(0.598472\pi\)
\(314\) 0 0
\(315\) 2226.61 2010.90i 0.398271 0.359686i
\(316\) 0 0
\(317\) 7590.80 4382.55i 1.34493 0.776494i 0.357401 0.933951i \(-0.383663\pi\)
0.987526 + 0.157457i \(0.0503295\pi\)
\(318\) 0 0
\(319\) 3125.05 5412.74i 0.548493 0.950017i
\(320\) 0 0
\(321\) 1463.82 139.971i 0.254524 0.0243378i
\(322\) 0 0
\(323\) 550.644i 0.0948564i
\(324\) 0 0
\(325\) 2339.31i 0.399266i
\(326\) 0 0
\(327\) 903.359 + 9447.32i 0.152770 + 1.59767i
\(328\) 0 0
\(329\) −82.3544 4061.26i −0.0138004 0.680561i
\(330\) 0 0
\(331\) −3431.76 5943.98i −0.569869 0.987041i −0.996578 0.0826527i \(-0.973661\pi\)
0.426710 0.904389i \(-0.359673\pi\)
\(332\) 0 0
\(333\) 7630.55 1472.74i 1.25571 0.242360i
\(334\) 0 0
\(335\) −1028.68 1781.73i −0.167770 0.290586i
\(336\) 0 0
\(337\) 2323.81 4024.96i 0.375627 0.650605i −0.614794 0.788688i \(-0.710761\pi\)
0.990421 + 0.138083i \(0.0440941\pi\)
\(338\) 0 0
\(339\) 2032.82 4452.79i 0.325686 0.713399i
\(340\) 0 0
\(341\) 7256.70 1.15241
\(342\) 0 0
\(343\) 386.154 + 6340.70i 0.0607882 + 0.998151i
\(344\) 0 0
\(345\) 1260.38 + 1769.46i 0.196686 + 0.276130i
\(346\) 0 0
\(347\) 8295.04 + 4789.14i 1.28329 + 0.740907i 0.977448 0.211176i \(-0.0677294\pi\)
0.305840 + 0.952083i \(0.401063\pi\)
\(348\) 0 0
\(349\) 755.168 435.997i 0.115826 0.0668721i −0.440968 0.897523i \(-0.645365\pi\)
0.556794 + 0.830651i \(0.312031\pi\)
\(350\) 0 0
\(351\) 867.966 3583.96i 0.131990 0.545007i
\(352\) 0 0
\(353\) 4148.63 + 7185.64i 0.625523 + 1.08344i 0.988440 + 0.151615i \(0.0484475\pi\)
−0.362917 + 0.931821i \(0.618219\pi\)
\(354\) 0 0
\(355\) −2013.36 1162.42i −0.301009 0.173788i
\(356\) 0 0
\(357\) −753.147 + 1742.40i −0.111655 + 0.258313i
\(358\) 0 0
\(359\) 976.696i 0.143588i −0.997419 0.0717939i \(-0.977128\pi\)
0.997419 0.0717939i \(-0.0228724\pi\)
\(360\) 0 0
\(361\) 6079.69 0.886381
\(362\) 0 0
\(363\) 3482.85 + 1590.01i 0.503588 + 0.229901i
\(364\) 0 0
\(365\) −1146.89 662.155i −0.164468 0.0949556i
\(366\) 0 0
\(367\) −6001.51 + 3464.97i −0.853614 + 0.492834i −0.861868 0.507132i \(-0.830706\pi\)
0.00825490 + 0.999966i \(0.497372\pi\)
\(368\) 0 0
\(369\) −360.534 + 1042.58i −0.0508635 + 0.147085i
\(370\) 0 0
\(371\) 1873.89 3403.20i 0.262231 0.476241i
\(372\) 0 0
\(373\) 2259.68 3913.89i 0.313678 0.543307i −0.665477 0.746418i \(-0.731772\pi\)
0.979156 + 0.203111i \(0.0651053\pi\)
\(374\) 0 0
\(375\) −635.067 6641.52i −0.0874525 0.914578i
\(376\) 0 0
\(377\) −3612.63 −0.493528
\(378\) 0 0
\(379\) 2781.32 0.376958 0.188479 0.982077i \(-0.439644\pi\)
0.188479 + 0.982077i \(0.439644\pi\)
\(380\) 0 0
\(381\) 158.546 + 1658.07i 0.0213190 + 0.222954i
\(382\) 0 0
\(383\) 5449.44 9438.71i 0.727033 1.25926i −0.231099 0.972930i \(-0.574232\pi\)
0.958132 0.286327i \(-0.0924345\pi\)
\(384\) 0 0
\(385\) 2437.27 4426.36i 0.322635 0.585943i
\(386\) 0 0
\(387\) −1960.23 2261.03i −0.257479 0.296989i
\(388\) 0 0
\(389\) 1922.09 1109.72i 0.250524 0.144640i −0.369480 0.929239i \(-0.620464\pi\)
0.620004 + 0.784598i \(0.287131\pi\)
\(390\) 0 0
\(391\) −1190.33 687.237i −0.153958 0.0888877i
\(392\) 0 0
\(393\) −2901.41 1324.57i −0.372410 0.170015i
\(394\) 0 0
\(395\) −2907.58 −0.370370
\(396\) 0 0
\(397\) 10873.7i 1.37464i −0.726354 0.687321i \(-0.758786\pi\)
0.726354 0.687321i \(-0.241214\pi\)
\(398\) 0 0
\(399\) 2465.98 + 1065.91i 0.309407 + 0.133740i
\(400\) 0 0
\(401\) −5301.00 3060.53i −0.660147 0.381136i 0.132186 0.991225i \(-0.457800\pi\)
−0.792333 + 0.610089i \(0.791134\pi\)
\(402\) 0 0
\(403\) −2097.23 3632.51i −0.259232 0.449003i
\(404\) 0 0
\(405\) −620.209 + 4329.76i −0.0760949 + 0.531228i
\(406\) 0 0
\(407\) 11335.0 6544.26i 1.38048 0.797020i
\(408\) 0 0
\(409\) −12155.0 7017.69i −1.46950 0.848416i −0.470085 0.882621i \(-0.655777\pi\)
−0.999415 + 0.0342045i \(0.989110\pi\)
\(410\) 0 0
\(411\) 5276.68 + 7408.00i 0.633283 + 0.889075i
\(412\) 0 0
\(413\) −13118.3 + 7932.75i −1.56298 + 0.945145i
\(414\) 0 0
\(415\) −4251.83 −0.502926
\(416\) 0 0
\(417\) −2792.58 + 6117.03i −0.327946 + 0.718350i
\(418\) 0 0
\(419\) 4144.18 7177.94i 0.483190 0.836910i −0.516624 0.856213i \(-0.672811\pi\)
0.999814 + 0.0193028i \(0.00614466\pi\)
\(420\) 0 0
\(421\) 7767.30 + 13453.4i 0.899181 + 1.55743i 0.828544 + 0.559924i \(0.189170\pi\)
0.0706368 + 0.997502i \(0.477497\pi\)
\(422\) 0 0
\(423\) 3879.25 + 4474.52i 0.445899 + 0.514323i
\(424\) 0 0
\(425\) 877.765 + 1520.33i 0.100183 + 0.173522i
\(426\) 0 0
\(427\) 12704.7 257.627i 1.43987 0.0291978i
\(428\) 0 0
\(429\) −591.163 6182.37i −0.0665306 0.695776i
\(430\) 0 0
\(431\) 3167.89i 0.354041i 0.984207 + 0.177021i \(0.0566459\pi\)
−0.984207 + 0.177021i \(0.943354\pi\)
\(432\) 0 0
\(433\) 2187.70i 0.242804i −0.992603 0.121402i \(-0.961261\pi\)
0.992603 0.121402i \(-0.0387391\pi\)
\(434\) 0 0
\(435\) 4265.62 407.882i 0.470163 0.0449573i
\(436\) 0 0
\(437\) −972.630 + 1684.65i −0.106470 + 0.184411i
\(438\) 0 0
\(439\) −1703.79 + 983.684i −0.185234 + 0.106945i −0.589749 0.807586i \(-0.700773\pi\)
0.404516 + 0.914531i \(0.367440\pi\)
\(440\) 0 0
\(441\) −6345.18 6745.72i −0.685151 0.728401i
\(442\) 0 0
\(443\) 2229.21 1287.04i 0.239081 0.138034i −0.375673 0.926752i \(-0.622588\pi\)
0.614754 + 0.788719i \(0.289255\pi\)
\(444\) 0 0
\(445\) −422.783 + 732.282i −0.0450379 + 0.0780079i
\(446\) 0 0
\(447\) 6227.51 13641.1i 0.658952 1.44340i
\(448\) 0 0
\(449\) 9168.11i 0.963630i 0.876273 + 0.481815i \(0.160022\pi\)
−0.876273 + 0.481815i \(0.839978\pi\)
\(450\) 0 0
\(451\) 1857.93i 0.193983i
\(452\) 0 0
\(453\) −13040.7 + 9288.84i −1.35255 + 0.963416i
\(454\) 0 0
\(455\) −2920.10 + 59.2139i −0.300871 + 0.00610108i
\(456\) 0 0
\(457\) 449.418 + 778.415i 0.0460019 + 0.0796777i 0.888110 0.459632i \(-0.152019\pi\)
−0.842108 + 0.539310i \(0.818685\pi\)
\(458\) 0 0
\(459\) −780.690 2654.92i −0.0793889 0.269981i
\(460\) 0 0
\(461\) 750.955 + 1300.69i 0.0758686 + 0.131408i 0.901464 0.432855i \(-0.142494\pi\)
−0.825595 + 0.564263i \(0.809160\pi\)
\(462\) 0 0
\(463\) 515.882 893.534i 0.0517820 0.0896891i −0.838973 0.544174i \(-0.816843\pi\)
0.890755 + 0.454485i \(0.150177\pi\)
\(464\) 0 0
\(465\) 2886.44 + 4052.31i 0.287861 + 0.404132i
\(466\) 0 0
\(467\) 8619.68 0.854114 0.427057 0.904225i \(-0.359550\pi\)
0.427057 + 0.904225i \(0.359550\pi\)
\(468\) 0 0
\(469\) −5434.23 + 3286.12i −0.535031 + 0.323537i
\(470\) 0 0
\(471\) −2716.37 + 5950.07i −0.265740 + 0.582091i
\(472\) 0 0
\(473\) −4364.66 2519.94i −0.424286 0.244962i
\(474\) 0 0
\(475\) 2151.69 1242.28i 0.207845 0.119999i
\(476\) 0 0
\(477\) 1073.34 + 5561.17i 0.103029 + 0.533812i
\(478\) 0 0
\(479\) 2037.51 + 3529.07i 0.194355 + 0.336634i 0.946689 0.322149i \(-0.104405\pi\)
−0.752334 + 0.658782i \(0.771072\pi\)
\(480\) 0 0
\(481\) −6551.77 3782.66i −0.621070 0.358575i
\(482\) 0 0
\(483\) 5381.88 4000.40i 0.507006 0.376862i
\(484\) 0 0
\(485\) 9036.40i 0.846025i
\(486\) 0 0
\(487\) −14817.8 −1.37876 −0.689381 0.724399i \(-0.742117\pi\)
−0.689381 + 0.724399i \(0.742117\pi\)
\(488\) 0 0
\(489\) −1437.78 15036.3i −0.132963 1.39052i
\(490\) 0 0
\(491\) −6217.36 3589.59i −0.571457 0.329931i 0.186274 0.982498i \(-0.440359\pi\)
−0.757731 + 0.652567i \(0.773692\pi\)
\(492\) 0 0
\(493\) −2347.88 + 1355.55i −0.214489 + 0.123835i
\(494\) 0 0
\(495\) 1396.03 + 7233.11i 0.126762 + 0.656776i
\(496\) 0 0
\(497\) −3461.34 + 6286.20i −0.312399 + 0.567353i
\(498\) 0 0
\(499\) −5380.59 + 9319.46i −0.482702 + 0.836065i −0.999803 0.0198598i \(-0.993678\pi\)
0.517100 + 0.855925i \(0.327011\pi\)
\(500\) 0 0
\(501\) 2711.09 + 1237.69i 0.241762 + 0.110371i
\(502\) 0 0
\(503\) −11285.3 −1.00037 −0.500186 0.865918i \(-0.666735\pi\)
−0.500186 + 0.865918i \(0.666735\pi\)
\(504\) 0 0
\(505\) −11082.1 −0.976527
\(506\) 0 0
\(507\) 6374.41 4540.45i 0.558377 0.397729i
\(508\) 0 0
\(509\) 5404.52 9360.91i 0.470631 0.815157i −0.528805 0.848744i \(-0.677360\pi\)
0.999436 + 0.0335864i \(0.0106929\pi\)
\(510\) 0 0
\(511\) −1971.71 + 3580.85i −0.170691 + 0.309995i
\(512\) 0 0
\(513\) −3757.45 + 1104.89i −0.323383 + 0.0950919i
\(514\) 0 0
\(515\) −4178.84 + 2412.66i −0.357557 + 0.206436i
\(516\) 0 0
\(517\) 8637.54 + 4986.89i 0.734775 + 0.424223i
\(518\) 0 0
\(519\) −16346.1 + 11643.3i −1.38250 + 0.984745i
\(520\) 0 0
\(521\) 3085.93 0.259495 0.129747 0.991547i \(-0.458583\pi\)
0.129747 + 0.991547i \(0.458583\pi\)
\(522\) 0 0
\(523\) 2155.94i 0.180254i −0.995930 0.0901268i \(-0.971273\pi\)
0.995930 0.0901268i \(-0.0287272\pi\)
\(524\) 0 0
\(525\) −8507.74 + 987.951i −0.707253 + 0.0821290i
\(526\) 0 0
\(527\) −2726.01 1573.87i −0.225327 0.130092i
\(528\) 0 0
\(529\) −3655.69 6331.85i −0.300460 0.520412i
\(530\) 0 0
\(531\) 7304.27 21122.2i 0.596946 1.72623i
\(532\) 0 0
\(533\) 930.030 536.953i 0.0755799 0.0436361i
\(534\) 0 0
\(535\) 1470.48 + 848.982i 0.118831 + 0.0686069i
\(536\) 0 0
\(537\) −11629.3 + 1112.00i −0.934525 + 0.0893599i
\(538\) 0 0
\(539\) −13812.7 7244.67i −1.10382 0.578942i
\(540\) 0 0
\(541\) 19410.4 1.54255 0.771273 0.636504i \(-0.219620\pi\)
0.771273 + 0.636504i \(0.219620\pi\)
\(542\) 0 0
\(543\) 860.752 82.3057i 0.0680265 0.00650475i
\(544\) 0 0
\(545\) −5479.23 + 9490.31i −0.430651 + 0.745909i
\(546\) 0 0
\(547\) −2279.16 3947.62i −0.178153 0.308570i 0.763095 0.646286i \(-0.223679\pi\)
−0.941248 + 0.337716i \(0.890346\pi\)
\(548\) 0 0
\(549\) −13997.5 + 12135.4i −1.08816 + 0.943396i
\(550\) 0 0
\(551\) 1918.48 + 3322.90i 0.148330 + 0.256915i
\(552\) 0 0
\(553\) 181.957 + 8973.10i 0.0139920 + 0.690009i
\(554\) 0 0
\(555\) 8163.09 + 3726.67i 0.624331 + 0.285024i
\(556\) 0 0
\(557\) 4710.38i 0.358322i 0.983820 + 0.179161i \(0.0573383\pi\)
−0.983820 + 0.179161i \(0.942662\pi\)
\(558\) 0 0
\(559\) 2913.11i 0.220414i
\(560\) 0 0
\(561\) −2703.98 3796.16i −0.203498 0.285693i
\(562\) 0 0
\(563\) −2316.26 + 4011.87i −0.173390 + 0.300320i −0.939603 0.342267i \(-0.888805\pi\)
0.766213 + 0.642587i \(0.222139\pi\)
\(564\) 0 0
\(565\) 4894.81 2826.02i 0.364471 0.210428i
\(566\) 0 0
\(567\) 13400.9 + 1643.07i 0.992567 + 0.121698i
\(568\) 0 0
\(569\) −6667.01 + 3849.20i −0.491205 + 0.283597i −0.725074 0.688671i \(-0.758195\pi\)
0.233869 + 0.972268i \(0.424861\pi\)
\(570\) 0 0
\(571\) −8556.34 + 14820.0i −0.627096 + 1.08616i 0.361036 + 0.932552i \(0.382423\pi\)
−0.988132 + 0.153610i \(0.950910\pi\)
\(572\) 0 0
\(573\) −6122.62 8595.64i −0.446381 0.626680i
\(574\) 0 0
\(575\) 6201.77i 0.449794i
\(576\) 0 0
\(577\) 2389.01i 0.172367i −0.996279 0.0861834i \(-0.972533\pi\)
0.996279 0.0861834i \(-0.0274671\pi\)
\(578\) 0 0
\(579\) 2374.00 + 1083.79i 0.170398 + 0.0777910i
\(580\) 0 0
\(581\) 266.080 + 13121.6i 0.0189998 + 0.936965i
\(582\) 0 0
\(583\) 4769.48 + 8260.97i 0.338819 + 0.586852i
\(584\) 0 0
\(585\) 3217.24 2789.23i 0.227379 0.197129i
\(586\) 0 0
\(587\) −7877.22 13643.7i −0.553880 0.959348i −0.997990 0.0633757i \(-0.979813\pi\)
0.444110 0.895972i \(-0.353520\pi\)
\(588\) 0 0
\(589\) −2227.45 + 3858.06i −0.155824 + 0.269896i
\(590\) 0 0
\(591\) −20427.0 + 1953.24i −1.42175 + 0.135949i
\(592\) 0 0
\(593\) 14439.8 0.999953 0.499976 0.866039i \(-0.333342\pi\)
0.499976 + 0.866039i \(0.333342\pi\)
\(594\) 0 0
\(595\) −1875.58 + 1134.18i −0.129229 + 0.0781458i
\(596\) 0 0
\(597\) 3257.21 311.457i 0.223298 0.0213519i
\(598\) 0 0
\(599\) −13069.6 7545.75i −0.891504 0.514710i −0.0170695 0.999854i \(-0.505434\pi\)
−0.874434 + 0.485145i \(0.838767\pi\)
\(600\) 0 0
\(601\) 21885.4 12635.5i 1.48540 0.857595i 0.485536 0.874217i \(-0.338624\pi\)
0.999862 + 0.0166219i \(0.00529115\pi\)
\(602\) 0 0
\(603\) 3025.78 8749.83i 0.204343 0.590913i
\(604\) 0 0
\(605\) 2210.44 + 3828.59i 0.148541 + 0.257280i
\(606\) 0 0
\(607\) −16922.0 9769.93i −1.13154 0.653293i −0.187216 0.982319i \(-0.559947\pi\)
−0.944321 + 0.329025i \(0.893280\pi\)
\(608\) 0 0
\(609\) −1525.71 13138.6i −0.101519 0.874228i
\(610\) 0 0
\(611\) 5764.97i 0.381711i
\(612\) 0 0
\(613\) 22968.2 1.51334 0.756671 0.653796i \(-0.226825\pi\)
0.756671 + 0.653796i \(0.226825\pi\)
\(614\) 0 0
\(615\) −1037.51 + 739.013i −0.0680268 + 0.0484551i
\(616\) 0 0
\(617\) −24539.5 14167.9i −1.60117 0.924437i −0.991253 0.131974i \(-0.957868\pi\)
−0.609920 0.792463i \(-0.708798\pi\)
\(618\) 0 0
\(619\) 17347.3 10015.5i 1.12641 0.650332i 0.183379 0.983042i \(-0.441297\pi\)
0.943029 + 0.332710i \(0.107963\pi\)
\(620\) 0 0
\(621\) −2301.08 + 9501.48i −0.148694 + 0.613979i
\(622\) 0 0
\(623\) 2286.36 + 1258.93i 0.147032 + 0.0809597i
\(624\) 0 0
\(625\) −1710.61 + 2962.87i −0.109479 + 0.189624i
\(626\) 0 0
\(627\) −5372.61 + 3826.88i −0.342203 + 0.243749i
\(628\) 0 0
\(629\) −5677.39 −0.359893
\(630\) 0 0
\(631\) 7219.42 0.455469 0.227734 0.973723i \(-0.426868\pi\)
0.227734 + 0.973723i \(0.426868\pi\)
\(632\) 0 0
\(633\) −14132.9 6452.03i −0.887412 0.405127i
\(634\) 0 0
\(635\) −961.643 + 1665.61i −0.0600970 + 0.104091i
\(636\) 0 0
\(637\) 365.481 + 9008.04i 0.0227329 + 0.560301i
\(638\) 0 0
\(639\) −1982.61 10272.3i −0.122740 0.635939i
\(640\) 0 0
\(641\) −14946.4 + 8629.29i −0.920976 + 0.531726i −0.883946 0.467588i \(-0.845123\pi\)
−0.0370299 + 0.999314i \(0.511790\pi\)
\(642\) 0 0
\(643\) 21951.3 + 12673.6i 1.34631 + 0.777291i 0.987724 0.156206i \(-0.0499265\pi\)
0.358584 + 0.933498i \(0.383260\pi\)
\(644\) 0 0
\(645\) −328.903 3439.66i −0.0200784 0.209979i
\(646\) 0 0
\(647\) −6799.46 −0.413160 −0.206580 0.978430i \(-0.566233\pi\)
−0.206580 + 0.978430i \(0.566233\pi\)
\(648\) 0 0
\(649\) 37640.9i 2.27663i
\(650\) 0 0
\(651\) 12325.2 9161.45i 0.742033 0.551560i
\(652\) 0 0
\(653\) 19452.8 + 11231.1i 1.16577 + 0.673058i 0.952680 0.303975i \(-0.0983139\pi\)
0.213090 + 0.977033i \(0.431647\pi\)
\(654\) 0 0
\(655\) −1841.42 3189.43i −0.109848 0.190262i
\(656\) 0 0
\(657\) −1129.37 5851.47i −0.0670637 0.347470i
\(658\) 0 0
\(659\) 3236.46 1868.57i 0.191312 0.110454i −0.401285 0.915953i \(-0.631436\pi\)
0.592597 + 0.805499i \(0.298103\pi\)
\(660\) 0 0
\(661\) 10205.8 + 5892.33i 0.600545 + 0.346725i 0.769256 0.638941i \(-0.220627\pi\)
−0.168711 + 0.985666i \(0.553960\pi\)
\(662\) 0 0
\(663\) −1118.79 + 2450.65i −0.0655356 + 0.143553i
\(664\) 0 0
\(665\) 1605.17 + 2654.46i 0.0936030 + 0.154790i
\(666\) 0 0
\(667\) 9577.50 0.555986
\(668\) 0 0
\(669\) −9850.20 13828.8i −0.569254 0.799184i
\(670\) 0 0
\(671\) −15600.4 + 27020.6i −0.897534 + 1.55457i
\(672\) 0 0
\(673\) 5712.35 + 9894.08i 0.327184 + 0.566699i 0.981952 0.189131i \(-0.0605670\pi\)
−0.654768 + 0.755830i \(0.727234\pi\)
\(674\) 0 0
\(675\) 8613.09 9040.26i 0.491138 0.515496i
\(676\) 0 0
\(677\) 15013.5 + 26004.1i 0.852312 + 1.47625i 0.879116 + 0.476607i \(0.158134\pi\)
−0.0268044 + 0.999641i \(0.508533\pi\)
\(678\) 0 0
\(679\) 27887.3 565.500i 1.57617 0.0319615i
\(680\) 0 0
\(681\) 24012.7 17104.1i 1.35120 0.962454i
\(682\) 0 0
\(683\) 18482.4i 1.03545i −0.855548 0.517723i \(-0.826780\pi\)
0.855548 0.517723i \(-0.173220\pi\)
\(684\) 0 0
\(685\) 10502.1i 0.585786i
\(686\) 0 0
\(687\) 11284.0 24717.0i 0.626652 1.37265i
\(688\) 0 0
\(689\) 2756.82 4774.94i 0.152433 0.264022i
\(690\) 0 0
\(691\) −16408.4 + 9473.38i −0.903334 + 0.521540i −0.878280 0.478146i \(-0.841309\pi\)
−0.0250537 + 0.999686i \(0.507976\pi\)
\(692\) 0 0
\(693\) 22234.8 4760.96i 1.21880 0.260972i
\(694\) 0 0
\(695\) −6724.25 + 3882.25i −0.367001 + 0.211888i
\(696\) 0 0
\(697\) 402.956 697.941i 0.0218982 0.0379288i
\(698\) 0 0
\(699\) −17761.7 + 1698.39i −0.961103 + 0.0919013i
\(700\) 0 0
\(701\) 9045.09i 0.487344i 0.969858 + 0.243672i \(0.0783521\pi\)
−0.969858 + 0.243672i \(0.921648\pi\)
\(702\) 0 0
\(703\) 8035.08i 0.431079i
\(704\) 0 0
\(705\) 650.890 + 6807.00i 0.0347715 + 0.363640i
\(706\) 0 0
\(707\) 693.518 + 34200.5i 0.0368917 + 1.81929i
\(708\) 0 0
\(709\) −1866.89 3233.55i −0.0988893 0.171281i 0.812336 0.583190i \(-0.198196\pi\)
−0.911225 + 0.411909i \(0.864862\pi\)
\(710\) 0 0
\(711\) −8570.95 9886.16i −0.452089 0.521463i
\(712\) 0 0
\(713\) 5560.00 + 9630.20i 0.292039 + 0.505826i
\(714\) 0 0
\(715\) 3585.64 6210.51i 0.187546 0.324839i
\(716\) 0 0
\(717\) −1170.33 + 2563.55i −0.0609578 + 0.133525i
\(718\) 0 0
\(719\) 35410.2 1.83669 0.918343 0.395785i \(-0.129527\pi\)
0.918343 + 0.395785i \(0.129527\pi\)
\(720\) 0 0
\(721\) 7707.23 + 12745.4i 0.398103 + 0.658339i
\(722\) 0 0
\(723\) 10827.0 + 15200.2i 0.556929 + 0.781881i
\(724\) 0 0
\(725\) −10593.9 6116.37i −0.542685 0.313319i
\(726\) 0 0
\(727\) −2328.92 + 1344.60i −0.118810 + 0.0685951i −0.558227 0.829688i \(-0.688518\pi\)
0.439417 + 0.898283i \(0.355185\pi\)
\(728\) 0 0
\(729\) −16550.0 + 10654.5i −0.840828 + 0.541302i
\(730\) 0 0
\(731\) 1093.07 + 1893.25i 0.0553060 + 0.0957928i
\(732\) 0 0
\(733\) −10520.4 6073.96i −0.530123 0.306066i 0.210944 0.977498i \(-0.432346\pi\)
−0.741066 + 0.671432i \(0.765680\pi\)
\(734\) 0 0
\(735\) −1448.59 10595.0i −0.0726966 0.531704i
\(736\) 0 0
\(737\) 15592.7i 0.779326i
\(738\) 0 0
\(739\) −33517.3 −1.66841 −0.834204 0.551456i \(-0.814072\pi\)
−0.834204 + 0.551456i \(0.814072\pi\)
\(740\) 0 0
\(741\) 3468.35 + 1583.39i 0.171947 + 0.0784985i
\(742\) 0 0
\(743\) 21381.5 + 12344.6i 1.05573 + 0.609529i 0.924249 0.381790i \(-0.124692\pi\)
0.131485 + 0.991318i \(0.458025\pi\)
\(744\) 0 0
\(745\) 14995.2 8657.49i 0.737426 0.425753i
\(746\) 0 0
\(747\) −12533.5 14456.8i −0.613893 0.708095i
\(748\) 0 0
\(749\) 2528.03 4591.19i 0.123327 0.223976i
\(750\) 0 0
\(751\) −4794.74 + 8304.74i −0.232973 + 0.403521i −0.958682 0.284481i \(-0.908179\pi\)
0.725709 + 0.688002i \(0.241512\pi\)
\(752\) 0 0
\(753\) −2143.80 22419.9i −0.103751 1.08503i
\(754\) 0 0
\(755\) −18487.4 −0.891159
\(756\) 0 0
\(757\) −13621.8 −0.654022 −0.327011 0.945021i \(-0.606041\pi\)
−0.327011 + 0.945021i \(0.606041\pi\)
\(758\) 0 0
\(759\) 1567.24 + 16390.2i 0.0749502 + 0.783829i
\(760\) 0 0
\(761\) −839.906 + 1454.76i −0.0400086 + 0.0692970i −0.885336 0.464951i \(-0.846072\pi\)
0.845328 + 0.534248i \(0.179405\pi\)
\(762\) 0 0
\(763\) 29631.0 + 16315.6i 1.40592 + 0.774134i
\(764\) 0 0
\(765\) 1044.32 3019.93i 0.0493562 0.142727i
\(766\) 0 0
\(767\) −18842.0 + 10878.5i −0.887023 + 0.512123i
\(768\) 0 0
\(769\) 30695.1 + 17721.8i 1.43939 + 0.831034i 0.997807 0.0661849i \(-0.0210827\pi\)
0.441586 + 0.897219i \(0.354416\pi\)
\(770\) 0 0
\(771\) 31035.5 + 14168.5i 1.44970 + 0.661825i
\(772\) 0 0
\(773\) 13901.4 0.646829 0.323415 0.946257i \(-0.395169\pi\)
0.323415 + 0.946257i \(0.395169\pi\)
\(774\) 0 0
\(775\) 14202.9i 0.658300i
\(776\) 0 0
\(777\) 10990.0 25425.4i 0.507420 1.17391i
\(778\) 0 0
\(779\) −987.778 570.294i −0.0454311 0.0262297i
\(780\) 0 0
\(781\) −8809.91 15259.2i −0.403641 0.699126i
\(782\) 0 0
\(783\) 13961.0 + 13301.3i 0.637199 + 0.607090i
\(784\) 0 0
\(785\) −6540.73 + 3776.29i −0.297387 + 0.171696i
\(786\) 0 0
\(787\) −3906.63 2255.49i −0.176946 0.102160i 0.408911 0.912574i \(-0.365909\pi\)
−0.585857 + 0.810415i \(0.699242\pi\)
\(788\) 0 0
\(789\) 21842.4 + 30664.9i 0.985566 + 1.38365i
\(790\) 0 0
\(791\) −9027.72 14929.1i −0.405801 0.671070i
\(792\) 0 0
\(793\) 18034.4 0.807592
\(794\) 0 0
\(795\) −2716.00 + 5949.28i −0.121166 + 0.265408i