Properties

Label 405.4.e.c.271.1
Level $405$
Weight $4$
Character 405.271
Analytic conductor $23.896$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.8957735523\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 5)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 271.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 405.271
Dual form 405.4.e.c.136.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.00000 - 3.46410i) q^{2} +(-4.00000 + 6.92820i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-3.00000 - 5.19615i) q^{7} +O(q^{10})\) \(q+(-2.00000 - 3.46410i) q^{2} +(-4.00000 + 6.92820i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-3.00000 - 5.19615i) q^{7} +20.0000 q^{10} +(16.0000 + 27.7128i) q^{11} +(19.0000 - 32.9090i) q^{13} +(-12.0000 + 20.7846i) q^{14} +(32.0000 + 55.4256i) q^{16} -26.0000 q^{17} +100.000 q^{19} +(-20.0000 - 34.6410i) q^{20} +(64.0000 - 110.851i) q^{22} +(-39.0000 + 67.5500i) q^{23} +(-12.5000 - 21.6506i) q^{25} -152.000 q^{26} +48.0000 q^{28} +(-25.0000 - 43.3013i) q^{29} +(54.0000 - 93.5307i) q^{31} +(128.000 - 221.703i) q^{32} +(52.0000 + 90.0666i) q^{34} +30.0000 q^{35} +266.000 q^{37} +(-200.000 - 346.410i) q^{38} +(11.0000 - 19.0526i) q^{41} +(-221.000 - 382.783i) q^{43} -256.000 q^{44} +312.000 q^{46} +(-257.000 - 445.137i) q^{47} +(153.500 - 265.870i) q^{49} +(-50.0000 + 86.6025i) q^{50} +(152.000 + 263.272i) q^{52} -2.00000 q^{53} -160.000 q^{55} +(-100.000 + 173.205i) q^{58} +(250.000 - 433.013i) q^{59} +(259.000 + 448.601i) q^{61} -432.000 q^{62} -512.000 q^{64} +(95.0000 + 164.545i) q^{65} +(-63.0000 + 109.119i) q^{67} +(104.000 - 180.133i) q^{68} +(-60.0000 - 103.923i) q^{70} -412.000 q^{71} -878.000 q^{73} +(-532.000 - 921.451i) q^{74} +(-400.000 + 692.820i) q^{76} +(96.0000 - 166.277i) q^{77} +(-300.000 - 519.615i) q^{79} -320.000 q^{80} -88.0000 q^{82} +(141.000 + 244.219i) q^{83} +(65.0000 - 112.583i) q^{85} +(-884.000 + 1531.13i) q^{86} +150.000 q^{89} -228.000 q^{91} +(-312.000 - 540.400i) q^{92} +(-1028.00 + 1780.55i) q^{94} +(-250.000 + 433.013i) q^{95} +(-193.000 - 334.286i) q^{97} -1228.00 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 4 q^{2} - 8 q^{4} - 5 q^{5} - 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 4 q^{2} - 8 q^{4} - 5 q^{5} - 6 q^{7} + 40 q^{10} + 32 q^{11} + 38 q^{13} - 24 q^{14} + 64 q^{16} - 52 q^{17} + 200 q^{19} - 40 q^{20} + 128 q^{22} - 78 q^{23} - 25 q^{25} - 304 q^{26} + 96 q^{28} - 50 q^{29} + 108 q^{31} + 256 q^{32} + 104 q^{34} + 60 q^{35} + 532 q^{37} - 400 q^{38} + 22 q^{41} - 442 q^{43} - 512 q^{44} + 624 q^{46} - 514 q^{47} + 307 q^{49} - 100 q^{50} + 304 q^{52} - 4 q^{53} - 320 q^{55} - 200 q^{58} + 500 q^{59} + 518 q^{61} - 864 q^{62} - 1024 q^{64} + 190 q^{65} - 126 q^{67} + 208 q^{68} - 120 q^{70} - 824 q^{71} - 1756 q^{73} - 1064 q^{74} - 800 q^{76} + 192 q^{77} - 600 q^{79} - 640 q^{80} - 176 q^{82} + 282 q^{83} + 130 q^{85} - 1768 q^{86} + 300 q^{89} - 456 q^{91} - 624 q^{92} - 2056 q^{94} - 500 q^{95} - 386 q^{97} - 2456 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 3.46410i −0.707107 1.22474i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(3\) 0 0
\(4\) −4.00000 + 6.92820i −0.500000 + 0.866025i
\(5\) −2.50000 + 4.33013i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) −3.00000 5.19615i −0.161985 0.280566i 0.773596 0.633680i \(-0.218456\pi\)
−0.935580 + 0.353114i \(0.885123\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 20.0000 0.632456
\(11\) 16.0000 + 27.7128i 0.438562 + 0.759612i 0.997579 0.0695447i \(-0.0221546\pi\)
−0.559017 + 0.829156i \(0.688821\pi\)
\(12\) 0 0
\(13\) 19.0000 32.9090i 0.405358 0.702100i −0.589005 0.808129i \(-0.700480\pi\)
0.994363 + 0.106029i \(0.0338136\pi\)
\(14\) −12.0000 + 20.7846i −0.229081 + 0.396780i
\(15\) 0 0
\(16\) 32.0000 + 55.4256i 0.500000 + 0.866025i
\(17\) −26.0000 −0.370937 −0.185468 0.982650i \(-0.559380\pi\)
−0.185468 + 0.982650i \(0.559380\pi\)
\(18\) 0 0
\(19\) 100.000 1.20745 0.603726 0.797192i \(-0.293682\pi\)
0.603726 + 0.797192i \(0.293682\pi\)
\(20\) −20.0000 34.6410i −0.223607 0.387298i
\(21\) 0 0
\(22\) 64.0000 110.851i 0.620220 1.07425i
\(23\) −39.0000 + 67.5500i −0.353568 + 0.612398i −0.986872 0.161506i \(-0.948365\pi\)
0.633304 + 0.773903i \(0.281698\pi\)
\(24\) 0 0
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) −152.000 −1.14653
\(27\) 0 0
\(28\) 48.0000 0.323970
\(29\) −25.0000 43.3013i −0.160082 0.277270i 0.774816 0.632187i \(-0.217843\pi\)
−0.934898 + 0.354917i \(0.884509\pi\)
\(30\) 0 0
\(31\) 54.0000 93.5307i 0.312861 0.541891i −0.666120 0.745845i \(-0.732046\pi\)
0.978980 + 0.203954i \(0.0653793\pi\)
\(32\) 128.000 221.703i 0.707107 1.22474i
\(33\) 0 0
\(34\) 52.0000 + 90.0666i 0.262292 + 0.454303i
\(35\) 30.0000 0.144884
\(36\) 0 0
\(37\) 266.000 1.18190 0.590948 0.806710i \(-0.298754\pi\)
0.590948 + 0.806710i \(0.298754\pi\)
\(38\) −200.000 346.410i −0.853797 1.47882i
\(39\) 0 0
\(40\) 0 0
\(41\) 11.0000 19.0526i 0.0419003 0.0725734i −0.844315 0.535848i \(-0.819992\pi\)
0.886215 + 0.463274i \(0.153325\pi\)
\(42\) 0 0
\(43\) −221.000 382.783i −0.783772 1.35753i −0.929730 0.368242i \(-0.879960\pi\)
0.145958 0.989291i \(-0.453373\pi\)
\(44\) −256.000 −0.877124
\(45\) 0 0
\(46\) 312.000 1.00004
\(47\) −257.000 445.137i −0.797602 1.38149i −0.921174 0.389152i \(-0.872768\pi\)
0.123571 0.992336i \(-0.460565\pi\)
\(48\) 0 0
\(49\) 153.500 265.870i 0.447522 0.775131i
\(50\) −50.0000 + 86.6025i −0.141421 + 0.244949i
\(51\) 0 0
\(52\) 152.000 + 263.272i 0.405358 + 0.702100i
\(53\) −2.00000 −0.00518342 −0.00259171 0.999997i \(-0.500825\pi\)
−0.00259171 + 0.999997i \(0.500825\pi\)
\(54\) 0 0
\(55\) −160.000 −0.392262
\(56\) 0 0
\(57\) 0 0
\(58\) −100.000 + 173.205i −0.226390 + 0.392120i
\(59\) 250.000 433.013i 0.551648 0.955482i −0.446508 0.894780i \(-0.647333\pi\)
0.998156 0.0607026i \(-0.0193341\pi\)
\(60\) 0 0
\(61\) 259.000 + 448.601i 0.543632 + 0.941598i 0.998692 + 0.0511373i \(0.0162846\pi\)
−0.455060 + 0.890461i \(0.650382\pi\)
\(62\) −432.000 −0.884904
\(63\) 0 0
\(64\) −512.000 −1.00000
\(65\) 95.0000 + 164.545i 0.181282 + 0.313989i
\(66\) 0 0
\(67\) −63.0000 + 109.119i −0.114876 + 0.198971i −0.917730 0.397205i \(-0.869980\pi\)
0.802854 + 0.596175i \(0.203314\pi\)
\(68\) 104.000 180.133i 0.185468 0.321241i
\(69\) 0 0
\(70\) −60.0000 103.923i −0.102448 0.177445i
\(71\) −412.000 −0.688668 −0.344334 0.938847i \(-0.611895\pi\)
−0.344334 + 0.938847i \(0.611895\pi\)
\(72\) 0 0
\(73\) −878.000 −1.40770 −0.703850 0.710348i \(-0.748537\pi\)
−0.703850 + 0.710348i \(0.748537\pi\)
\(74\) −532.000 921.451i −0.835726 1.44752i
\(75\) 0 0
\(76\) −400.000 + 692.820i −0.603726 + 1.04568i
\(77\) 96.0000 166.277i 0.142081 0.246091i
\(78\) 0 0
\(79\) −300.000 519.615i −0.427249 0.740016i 0.569379 0.822075i \(-0.307184\pi\)
−0.996627 + 0.0820590i \(0.973850\pi\)
\(80\) −320.000 −0.447214
\(81\) 0 0
\(82\) −88.0000 −0.118512
\(83\) 141.000 + 244.219i 0.186467 + 0.322970i 0.944070 0.329745i \(-0.106963\pi\)
−0.757603 + 0.652716i \(0.773630\pi\)
\(84\) 0 0
\(85\) 65.0000 112.583i 0.0829440 0.143663i
\(86\) −884.000 + 1531.13i −1.10842 + 1.91984i
\(87\) 0 0
\(88\) 0 0
\(89\) 150.000 0.178651 0.0893257 0.996002i \(-0.471529\pi\)
0.0893257 + 0.996002i \(0.471529\pi\)
\(90\) 0 0
\(91\) −228.000 −0.262647
\(92\) −312.000 540.400i −0.353568 0.612398i
\(93\) 0 0
\(94\) −1028.00 + 1780.55i −1.12798 + 1.95372i
\(95\) −250.000 + 433.013i −0.269994 + 0.467644i
\(96\) 0 0
\(97\) −193.000 334.286i −0.202022 0.349913i 0.747157 0.664647i \(-0.231418\pi\)
−0.949180 + 0.314734i \(0.898085\pi\)
\(98\) −1228.00 −1.26578
\(99\) 0 0
\(100\) 200.000 0.200000
\(101\) 351.000 + 607.950i 0.345800 + 0.598943i 0.985499 0.169682i \(-0.0542742\pi\)
−0.639699 + 0.768626i \(0.720941\pi\)
\(102\) 0 0
\(103\) 299.000 517.883i 0.286032 0.495423i −0.686827 0.726821i \(-0.740997\pi\)
0.972859 + 0.231399i \(0.0743301\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 4.00000 + 6.92820i 0.00366523 + 0.00634836i
\(107\) 1194.00 1.07877 0.539385 0.842059i \(-0.318657\pi\)
0.539385 + 0.842059i \(0.318657\pi\)
\(108\) 0 0
\(109\) −550.000 −0.483307 −0.241653 0.970363i \(-0.577690\pi\)
−0.241653 + 0.970363i \(0.577690\pi\)
\(110\) 320.000 + 554.256i 0.277371 + 0.480421i
\(111\) 0 0
\(112\) 192.000 332.554i 0.161985 0.280566i
\(113\) 781.000 1352.73i 0.650180 1.12614i −0.332899 0.942962i \(-0.608027\pi\)
0.983079 0.183182i \(-0.0586397\pi\)
\(114\) 0 0
\(115\) −195.000 337.750i −0.158120 0.273873i
\(116\) 400.000 0.320164
\(117\) 0 0
\(118\) −2000.00 −1.56030
\(119\) 78.0000 + 135.100i 0.0600861 + 0.104072i
\(120\) 0 0
\(121\) 153.500 265.870i 0.115327 0.199752i
\(122\) 1036.00 1794.40i 0.768812 1.33162i
\(123\) 0 0
\(124\) 432.000 + 748.246i 0.312861 + 0.541891i
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 1846.00 1.28981 0.644906 0.764262i \(-0.276897\pi\)
0.644906 + 0.764262i \(0.276897\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 380.000 658.179i 0.256371 0.444047i
\(131\) −1104.00 + 1912.18i −0.736312 + 1.27533i 0.217833 + 0.975986i \(0.430101\pi\)
−0.954145 + 0.299344i \(0.903232\pi\)
\(132\) 0 0
\(133\) −300.000 519.615i −0.195589 0.338770i
\(134\) 504.000 0.324918
\(135\) 0 0
\(136\) 0 0
\(137\) −1167.00 2021.30i −0.727763 1.26052i −0.957827 0.287347i \(-0.907227\pi\)
0.230064 0.973176i \(-0.426107\pi\)
\(138\) 0 0
\(139\) 350.000 606.218i 0.213573 0.369919i −0.739257 0.673423i \(-0.764823\pi\)
0.952830 + 0.303504i \(0.0981566\pi\)
\(140\) −120.000 + 207.846i −0.0724418 + 0.125473i
\(141\) 0 0
\(142\) 824.000 + 1427.21i 0.486962 + 0.843442i
\(143\) 1216.00 0.711098
\(144\) 0 0
\(145\) 250.000 0.143182
\(146\) 1756.00 + 3041.48i 0.995394 + 1.72407i
\(147\) 0 0
\(148\) −1064.00 + 1842.90i −0.590948 + 1.02355i
\(149\) 1025.00 1775.35i 0.563566 0.976124i −0.433616 0.901098i \(-0.642763\pi\)
0.997182 0.0750264i \(-0.0239041\pi\)
\(150\) 0 0
\(151\) −926.000 1603.88i −0.499052 0.864383i 0.500948 0.865478i \(-0.332985\pi\)
−0.999999 + 0.00109462i \(0.999652\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −768.000 −0.401865
\(155\) 270.000 + 467.654i 0.139916 + 0.242341i
\(156\) 0 0
\(157\) 1247.00 2159.87i 0.633894 1.09794i −0.352854 0.935678i \(-0.614789\pi\)
0.986748 0.162259i \(-0.0518780\pi\)
\(158\) −1200.00 + 2078.46i −0.604221 + 1.04654i
\(159\) 0 0
\(160\) 640.000 + 1108.51i 0.316228 + 0.547723i
\(161\) 468.000 0.229090
\(162\) 0 0
\(163\) 2762.00 1.32722 0.663609 0.748080i \(-0.269024\pi\)
0.663609 + 0.748080i \(0.269024\pi\)
\(164\) 88.0000 + 152.420i 0.0419003 + 0.0725734i
\(165\) 0 0
\(166\) 564.000 976.877i 0.263704 0.456749i
\(167\) 1563.00 2707.20i 0.724243 1.25443i −0.235042 0.971985i \(-0.575523\pi\)
0.959285 0.282440i \(-0.0911439\pi\)
\(168\) 0 0
\(169\) 376.500 + 652.117i 0.171370 + 0.296822i
\(170\) −520.000 −0.234601
\(171\) 0 0
\(172\) 3536.00 1.56754
\(173\) −39.0000 67.5500i −0.0171394 0.0296863i 0.857328 0.514770i \(-0.172123\pi\)
−0.874468 + 0.485083i \(0.838789\pi\)
\(174\) 0 0
\(175\) −75.0000 + 129.904i −0.0323970 + 0.0561132i
\(176\) −1024.00 + 1773.62i −0.438562 + 0.759612i
\(177\) 0 0
\(178\) −300.000 519.615i −0.126326 0.218802i
\(179\) 1300.00 0.542830 0.271415 0.962462i \(-0.412508\pi\)
0.271415 + 0.962462i \(0.412508\pi\)
\(180\) 0 0
\(181\) 1742.00 0.715369 0.357685 0.933842i \(-0.383566\pi\)
0.357685 + 0.933842i \(0.383566\pi\)
\(182\) 456.000 + 789.815i 0.185720 + 0.321676i
\(183\) 0 0
\(184\) 0 0
\(185\) −665.000 + 1151.81i −0.264280 + 0.457746i
\(186\) 0 0
\(187\) −416.000 720.533i −0.162679 0.281768i
\(188\) 4112.00 1.59520
\(189\) 0 0
\(190\) 2000.00 0.763659
\(191\) 1886.00 + 3266.65i 0.714483 + 1.23752i 0.963159 + 0.268933i \(0.0866712\pi\)
−0.248676 + 0.968587i \(0.579996\pi\)
\(192\) 0 0
\(193\) 179.000 310.037i 0.0667601 0.115632i −0.830713 0.556700i \(-0.812067\pi\)
0.897473 + 0.441069i \(0.145400\pi\)
\(194\) −772.000 + 1337.14i −0.285703 + 0.494852i
\(195\) 0 0
\(196\) 1228.00 + 2126.96i 0.447522 + 0.775131i
\(197\) 2214.00 0.800716 0.400358 0.916359i \(-0.368886\pi\)
0.400358 + 0.916359i \(0.368886\pi\)
\(198\) 0 0
\(199\) −2600.00 −0.926176 −0.463088 0.886312i \(-0.653259\pi\)
−0.463088 + 0.886312i \(0.653259\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 1404.00 2431.80i 0.489035 0.847034i
\(203\) −150.000 + 259.808i −0.0518618 + 0.0898272i
\(204\) 0 0
\(205\) 55.0000 + 95.2628i 0.0187384 + 0.0324558i
\(206\) −2392.00 −0.809022
\(207\) 0 0
\(208\) 2432.00 0.810716
\(209\) 1600.00 + 2771.28i 0.529542 + 0.917194i
\(210\) 0 0
\(211\) 584.000 1011.52i 0.190541 0.330027i −0.754888 0.655853i \(-0.772309\pi\)
0.945430 + 0.325826i \(0.105642\pi\)
\(212\) 8.00000 13.8564i 0.00259171 0.00448897i
\(213\) 0 0
\(214\) −2388.00 4136.14i −0.762805 1.32122i
\(215\) 2210.00 0.701027
\(216\) 0 0
\(217\) −648.000 −0.202715
\(218\) 1100.00 + 1905.26i 0.341750 + 0.591928i
\(219\) 0 0
\(220\) 640.000 1108.51i 0.196131 0.339709i
\(221\) −494.000 + 855.633i −0.150362 + 0.260435i
\(222\) 0 0
\(223\) 3239.00 + 5610.11i 0.972643 + 1.68467i 0.687502 + 0.726182i \(0.258707\pi\)
0.285141 + 0.958486i \(0.407959\pi\)
\(224\) −1536.00 −0.458162
\(225\) 0 0
\(226\) −6248.00 −1.83899
\(227\) 323.000 + 559.452i 0.0944417 + 0.163578i 0.909375 0.415976i \(-0.136560\pi\)
−0.814934 + 0.579554i \(0.803227\pi\)
\(228\) 0 0
\(229\) −1875.00 + 3247.60i −0.541063 + 0.937149i 0.457780 + 0.889065i \(0.348645\pi\)
−0.998843 + 0.0480836i \(0.984689\pi\)
\(230\) −780.000 + 1351.00i −0.223616 + 0.387314i
\(231\) 0 0
\(232\) 0 0
\(233\) −1482.00 −0.416691 −0.208346 0.978055i \(-0.566808\pi\)
−0.208346 + 0.978055i \(0.566808\pi\)
\(234\) 0 0
\(235\) 2570.00 0.713397
\(236\) 2000.00 + 3464.10i 0.551648 + 0.955482i
\(237\) 0 0
\(238\) 312.000 540.400i 0.0849746 0.147180i
\(239\) 700.000 1212.44i 0.189453 0.328142i −0.755615 0.655016i \(-0.772662\pi\)
0.945068 + 0.326874i \(0.105995\pi\)
\(240\) 0 0
\(241\) −1511.00 2617.13i −0.403867 0.699519i 0.590321 0.807168i \(-0.299001\pi\)
−0.994189 + 0.107649i \(0.965668\pi\)
\(242\) −1228.00 −0.326194
\(243\) 0 0
\(244\) −4144.00 −1.08726
\(245\) 767.500 + 1329.35i 0.200138 + 0.346649i
\(246\) 0 0
\(247\) 1900.00 3290.90i 0.489450 0.847752i
\(248\) 0 0
\(249\) 0 0
\(250\) −250.000 433.013i −0.0632456 0.109545i
\(251\) 1248.00 0.313837 0.156918 0.987612i \(-0.449844\pi\)
0.156918 + 0.987612i \(0.449844\pi\)
\(252\) 0 0
\(253\) −2496.00 −0.620246
\(254\) −3692.00 6394.73i −0.912034 1.57969i
\(255\) 0 0
\(256\) −2048.00 + 3547.24i −0.500000 + 0.866025i
\(257\) 1053.00 1823.85i 0.255581 0.442679i −0.709472 0.704734i \(-0.751067\pi\)
0.965053 + 0.262054i \(0.0843999\pi\)
\(258\) 0 0
\(259\) −798.000 1382.18i −0.191449 0.331600i
\(260\) −1520.00 −0.362563
\(261\) 0 0
\(262\) 8832.00 2.08261
\(263\) −1819.00 3150.60i −0.426480 0.738686i 0.570077 0.821591i \(-0.306913\pi\)
−0.996557 + 0.0829055i \(0.973580\pi\)
\(264\) 0 0
\(265\) 5.00000 8.66025i 0.00115905 0.00200753i
\(266\) −1200.00 + 2078.46i −0.276604 + 0.479093i
\(267\) 0 0
\(268\) −504.000 872.954i −0.114876 0.198971i
\(269\) 6550.00 1.48461 0.742306 0.670061i \(-0.233732\pi\)
0.742306 + 0.670061i \(0.233732\pi\)
\(270\) 0 0
\(271\) −4388.00 −0.983587 −0.491793 0.870712i \(-0.663658\pi\)
−0.491793 + 0.870712i \(0.663658\pi\)
\(272\) −832.000 1441.07i −0.185468 0.321241i
\(273\) 0 0
\(274\) −4668.00 + 8085.21i −1.02921 + 1.78265i
\(275\) 400.000 692.820i 0.0877124 0.151922i
\(276\) 0 0
\(277\) −273.000 472.850i −0.0592165 0.102566i 0.834897 0.550406i \(-0.185527\pi\)
−0.894114 + 0.447840i \(0.852194\pi\)
\(278\) −2800.00 −0.604075
\(279\) 0 0
\(280\) 0 0
\(281\) −3429.00 5939.20i −0.727961 1.26087i −0.957744 0.287623i \(-0.907135\pi\)
0.229783 0.973242i \(-0.426198\pi\)
\(282\) 0 0
\(283\) −4641.00 + 8038.45i −0.974837 + 1.68847i −0.294364 + 0.955693i \(0.595108\pi\)
−0.680473 + 0.732774i \(0.738225\pi\)
\(284\) 1648.00 2854.42i 0.344334 0.596404i
\(285\) 0 0
\(286\) −2432.00 4212.35i −0.502822 0.870914i
\(287\) −132.000 −0.0271488
\(288\) 0 0
\(289\) −4237.00 −0.862406
\(290\) −500.000 866.025i −0.101245 0.175361i
\(291\) 0 0
\(292\) 3512.00 6082.96i 0.703850 1.21910i
\(293\) 2421.00 4193.30i 0.482718 0.836092i −0.517085 0.855934i \(-0.672983\pi\)
0.999803 + 0.0198420i \(0.00631633\pi\)
\(294\) 0 0
\(295\) 1250.00 + 2165.06i 0.246704 + 0.427305i
\(296\) 0 0
\(297\) 0 0
\(298\) −8200.00 −1.59400
\(299\) 1482.00 + 2566.90i 0.286643 + 0.496480i
\(300\) 0 0
\(301\) −1326.00 + 2296.70i −0.253918 + 0.439799i
\(302\) −3704.00 + 6415.52i −0.705766 + 1.22242i
\(303\) 0 0
\(304\) 3200.00 + 5542.56i 0.603726 + 1.04568i
\(305\) −2590.00 −0.486239
\(306\) 0 0
\(307\) −2594.00 −0.482239 −0.241120 0.970495i \(-0.577515\pi\)
−0.241120 + 0.970495i \(0.577515\pi\)
\(308\) 768.000 + 1330.22i 0.142081 + 0.246091i
\(309\) 0 0
\(310\) 1080.00 1870.61i 0.197871 0.342722i
\(311\) 3666.00 6349.70i 0.668424 1.15774i −0.309921 0.950762i \(-0.600303\pi\)
0.978345 0.206982i \(-0.0663640\pi\)
\(312\) 0 0
\(313\) −781.000 1352.73i −0.141037 0.244284i 0.786850 0.617144i \(-0.211710\pi\)
−0.927888 + 0.372860i \(0.878377\pi\)
\(314\) −9976.00 −1.79292
\(315\) 0 0
\(316\) 4800.00 0.854497
\(317\) 713.000 + 1234.95i 0.126328 + 0.218807i 0.922251 0.386591i \(-0.126347\pi\)
−0.795923 + 0.605398i \(0.793014\pi\)
\(318\) 0 0
\(319\) 800.000 1385.64i 0.140412 0.243201i
\(320\) 1280.00 2217.03i 0.223607 0.387298i
\(321\) 0 0
\(322\) −936.000 1621.20i −0.161991 0.280577i
\(323\) −2600.00 −0.447888
\(324\) 0 0
\(325\) −950.000 −0.162143
\(326\) −5524.00 9567.85i −0.938485 1.62550i
\(327\) 0 0
\(328\) 0 0
\(329\) −1542.00 + 2670.82i −0.258399 + 0.447560i
\(330\) 0 0
\(331\) 2004.00 + 3471.03i 0.332779 + 0.576390i 0.983056 0.183308i \(-0.0586804\pi\)
−0.650277 + 0.759697i \(0.725347\pi\)
\(332\) −2256.00 −0.372934
\(333\) 0 0
\(334\) −12504.0 −2.04847
\(335\) −315.000 545.596i −0.0513740 0.0889824i
\(336\) 0 0
\(337\) −4433.00 + 7678.18i −0.716561 + 1.24112i 0.245794 + 0.969322i \(0.420951\pi\)
−0.962355 + 0.271797i \(0.912382\pi\)
\(338\) 1506.00 2608.47i 0.242354 0.419769i
\(339\) 0 0
\(340\) 520.000 + 900.666i 0.0829440 + 0.143663i
\(341\) 3456.00 0.548835
\(342\) 0 0
\(343\) −3900.00 −0.613936
\(344\) 0 0
\(345\) 0 0
\(346\) −156.000 + 270.200i −0.0242388 + 0.0419828i
\(347\) −857.000 + 1484.37i −0.132583 + 0.229640i −0.924671 0.380766i \(-0.875660\pi\)
0.792089 + 0.610406i \(0.208994\pi\)
\(348\) 0 0
\(349\) −575.000 995.929i −0.0881921 0.152753i 0.818555 0.574428i \(-0.194776\pi\)
−0.906747 + 0.421675i \(0.861442\pi\)
\(350\) 600.000 0.0916324
\(351\) 0 0
\(352\) 8192.00 1.24044
\(353\) −2199.00 3808.78i −0.331561 0.574280i 0.651257 0.758857i \(-0.274242\pi\)
−0.982818 + 0.184577i \(0.940909\pi\)
\(354\) 0 0
\(355\) 1030.00 1784.01i 0.153991 0.266720i
\(356\) −600.000 + 1039.23i −0.0893257 + 0.154717i
\(357\) 0 0
\(358\) −2600.00 4503.33i −0.383839 0.664828i
\(359\) −1800.00 −0.264625 −0.132312 0.991208i \(-0.542240\pi\)
−0.132312 + 0.991208i \(0.542240\pi\)
\(360\) 0 0
\(361\) 3141.00 0.457938
\(362\) −3484.00 6034.47i −0.505842 0.876145i
\(363\) 0 0
\(364\) 912.000 1579.63i 0.131324 0.227459i
\(365\) 2195.00 3801.85i 0.314771 0.545200i
\(366\) 0 0
\(367\) 2937.00 + 5087.03i 0.417739 + 0.723545i 0.995712 0.0925111i \(-0.0294894\pi\)
−0.577973 + 0.816056i \(0.696156\pi\)
\(368\) −4992.00 −0.707136
\(369\) 0 0
\(370\) 5320.00 0.747496
\(371\) 6.00000 + 10.3923i 0.000839635 + 0.00145429i
\(372\) 0 0
\(373\) 1039.00 1799.60i 0.144229 0.249812i −0.784856 0.619678i \(-0.787263\pi\)
0.929085 + 0.369866i \(0.120597\pi\)
\(374\) −1664.00 + 2882.13i −0.230063 + 0.398480i
\(375\) 0 0
\(376\) 0 0
\(377\) −1900.00 −0.259562
\(378\) 0 0
\(379\) 7900.00 1.07070 0.535351 0.844630i \(-0.320179\pi\)
0.535351 + 0.844630i \(0.320179\pi\)
\(380\) −2000.00 3464.10i −0.269994 0.467644i
\(381\) 0 0
\(382\) 7544.00 13066.6i 1.01043 1.75012i
\(383\) −3759.00 + 6510.78i −0.501504 + 0.868630i 0.498495 + 0.866893i \(0.333886\pi\)
−0.999998 + 0.00173723i \(0.999447\pi\)
\(384\) 0 0
\(385\) 480.000 + 831.384i 0.0635404 + 0.110055i
\(386\) −1432.00 −0.188826
\(387\) 0 0
\(388\) 3088.00 0.404045
\(389\) −975.000 1688.75i −0.127081 0.220111i 0.795464 0.606001i \(-0.207227\pi\)
−0.922544 + 0.385891i \(0.873894\pi\)
\(390\) 0 0
\(391\) 1014.00 1756.30i 0.131151 0.227161i
\(392\) 0 0
\(393\) 0 0
\(394\) −4428.00 7669.52i −0.566191 0.980672i
\(395\) 3000.00 0.382143
\(396\) 0 0
\(397\) 13786.0 1.74282 0.871410 0.490555i \(-0.163206\pi\)
0.871410 + 0.490555i \(0.163206\pi\)
\(398\) 5200.00 + 9006.66i 0.654906 + 1.13433i
\(399\) 0 0
\(400\) 800.000 1385.64i 0.100000 0.173205i
\(401\) 3201.00 5544.29i 0.398629 0.690446i −0.594928 0.803779i \(-0.702819\pi\)
0.993557 + 0.113333i \(0.0361527\pi\)
\(402\) 0 0
\(403\) −2052.00 3554.17i −0.253641 0.439319i
\(404\) −5616.00 −0.691600
\(405\) 0 0
\(406\) 1200.00 0.146687
\(407\) 4256.00 + 7371.61i 0.518334 + 0.897781i
\(408\) 0 0
\(409\) −5575.00 + 9656.18i −0.674000 + 1.16740i 0.302760 + 0.953067i \(0.402092\pi\)
−0.976760 + 0.214335i \(0.931241\pi\)
\(410\) 220.000 381.051i 0.0265001 0.0458995i
\(411\) 0 0
\(412\) 2392.00 + 4143.07i 0.286032 + 0.495423i
\(413\) −3000.00 −0.357434
\(414\) 0 0
\(415\) −1410.00 −0.166781
\(416\) −4864.00 8424.70i −0.573263 0.992920i
\(417\) 0 0
\(418\) 6400.00 11085.1i 0.748886 1.29711i
\(419\) −6850.00 + 11864.5i −0.798674 + 1.38334i 0.121806 + 0.992554i \(0.461131\pi\)
−0.920480 + 0.390790i \(0.872202\pi\)
\(420\) 0 0
\(421\) 2719.00 + 4709.45i 0.314765 + 0.545189i 0.979387 0.201991i \(-0.0647410\pi\)
−0.664623 + 0.747179i \(0.731408\pi\)
\(422\) −4672.00 −0.538932
\(423\) 0 0
\(424\) 0 0
\(425\) 325.000 + 562.917i 0.0370937 + 0.0642481i
\(426\) 0 0
\(427\) 1554.00 2691.61i 0.176120 0.305049i
\(428\) −4776.00 + 8272.27i −0.539385 + 0.934242i
\(429\) 0 0
\(430\) −4420.00 7655.66i −0.495701 0.858579i
\(431\) −7692.00 −0.859653 −0.429827 0.902911i \(-0.641425\pi\)
−0.429827 + 0.902911i \(0.641425\pi\)
\(432\) 0 0
\(433\) −1118.00 −0.124082 −0.0620412 0.998074i \(-0.519761\pi\)
−0.0620412 + 0.998074i \(0.519761\pi\)
\(434\) 1296.00 + 2244.74i 0.143341 + 0.248274i
\(435\) 0 0
\(436\) 2200.00 3810.51i 0.241653 0.418556i
\(437\) −3900.00 + 6755.00i −0.426916 + 0.739440i
\(438\) 0 0
\(439\) 1300.00 + 2251.67i 0.141334 + 0.244798i 0.927999 0.372582i \(-0.121528\pi\)
−0.786665 + 0.617380i \(0.788194\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 3952.00 0.425288
\(443\) −5979.00 10355.9i −0.641243 1.11067i −0.985155 0.171664i \(-0.945086\pi\)
0.343912 0.939002i \(-0.388248\pi\)
\(444\) 0 0
\(445\) −375.000 + 649.519i −0.0399477 + 0.0691914i
\(446\) 12956.0 22440.5i 1.37553 2.38248i
\(447\) 0 0
\(448\) 1536.00 + 2660.43i 0.161985 + 0.280566i
\(449\) 17050.0 1.79207 0.896035 0.443984i \(-0.146435\pi\)
0.896035 + 0.443984i \(0.146435\pi\)
\(450\) 0 0
\(451\) 704.000 0.0735035
\(452\) 6248.00 + 10821.9i 0.650180 + 1.12614i
\(453\) 0 0
\(454\) 1292.00 2237.81i 0.133561 0.231334i
\(455\) 570.000 987.269i 0.0587297 0.101723i
\(456\) 0 0
\(457\) 4747.00 + 8222.05i 0.485898 + 0.841600i 0.999869 0.0162080i \(-0.00515939\pi\)
−0.513971 + 0.857808i \(0.671826\pi\)
\(458\) 15000.0 1.53036
\(459\) 0 0
\(460\) 3120.00 0.316241
\(461\) −5709.00 9888.28i −0.576778 0.999009i −0.995846 0.0910539i \(-0.970976\pi\)
0.419068 0.907955i \(-0.362357\pi\)
\(462\) 0 0
\(463\) −3981.00 + 6895.29i −0.399596 + 0.692120i −0.993676 0.112286i \(-0.964183\pi\)
0.594080 + 0.804406i \(0.297516\pi\)
\(464\) 1600.00 2771.28i 0.160082 0.277270i
\(465\) 0 0
\(466\) 2964.00 + 5133.80i 0.294645 + 0.510340i
\(467\) −6526.00 −0.646654 −0.323327 0.946287i \(-0.604801\pi\)
−0.323327 + 0.946287i \(0.604801\pi\)
\(468\) 0 0
\(469\) 756.000 0.0744325
\(470\) −5140.00 8902.74i −0.504448 0.873729i
\(471\) 0 0
\(472\) 0 0
\(473\) 7072.00 12249.1i 0.687465 1.19072i
\(474\) 0 0
\(475\) −1250.00 2165.06i −0.120745 0.209137i
\(476\) −1248.00 −0.120172
\(477\) 0 0
\(478\) −5600.00 −0.535854
\(479\) 8700.00 + 15068.8i 0.829881 + 1.43740i 0.898131 + 0.439728i \(0.144925\pi\)
−0.0682495 + 0.997668i \(0.521741\pi\)
\(480\) 0 0
\(481\) 5054.00 8753.78i 0.479091 0.829809i
\(482\) −6044.00 + 10468.5i −0.571155 + 0.989269i
\(483\) 0 0
\(484\) 1228.00 + 2126.96i 0.115327 + 0.199752i
\(485\) 1930.00 0.180694
\(486\) 0 0
\(487\) 1166.00 0.108494 0.0542469 0.998528i \(-0.482724\pi\)
0.0542469 + 0.998528i \(0.482724\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 3070.00 5317.40i 0.283038 0.490236i
\(491\) 3536.00 6124.53i 0.325005 0.562925i −0.656508 0.754319i \(-0.727967\pi\)
0.981513 + 0.191394i \(0.0613007\pi\)
\(492\) 0 0
\(493\) 650.000 + 1125.83i 0.0593804 + 0.102850i
\(494\) −15200.0 −1.38437
\(495\) 0 0
\(496\) 6912.00 0.625722
\(497\) 1236.00 + 2140.81i 0.111554 + 0.193217i
\(498\) 0 0
\(499\) −50.0000 + 86.6025i −0.00448559 + 0.00776926i −0.868259 0.496110i \(-0.834761\pi\)
0.863774 + 0.503880i \(0.168094\pi\)
\(500\) −500.000 + 866.025i −0.0447214 + 0.0774597i
\(501\) 0 0
\(502\) −2496.00 4323.20i −0.221916 0.384370i
\(503\) −2602.00 −0.230651 −0.115325 0.993328i \(-0.536791\pi\)
−0.115325 + 0.993328i \(0.536791\pi\)
\(504\) 0 0
\(505\) −3510.00 −0.309293
\(506\) 4992.00 + 8646.40i 0.438580 + 0.759643i
\(507\) 0 0
\(508\) −7384.00 + 12789.5i −0.644906 + 1.11701i
\(509\) 5575.00 9656.18i 0.485476 0.840870i −0.514384 0.857560i \(-0.671979\pi\)
0.999861 + 0.0166899i \(0.00531281\pi\)
\(510\) 0 0
\(511\) 2634.00 + 4562.22i 0.228026 + 0.394953i
\(512\) 16384.0 1.41421
\(513\) 0 0
\(514\) −8424.00 −0.722892
\(515\) 1495.00 + 2589.42i 0.127918 + 0.221560i
\(516\) 0 0
\(517\) 8224.00 14244.4i 0.699596 1.21174i
\(518\) −3192.00 + 5528.71i −0.270750 + 0.468953i
\(519\) 0 0
\(520\) 0 0
\(521\) 3638.00 0.305919 0.152959 0.988232i \(-0.451120\pi\)
0.152959 + 0.988232i \(0.451120\pi\)
\(522\) 0 0
\(523\) −2078.00 −0.173737 −0.0868686 0.996220i \(-0.527686\pi\)
−0.0868686 + 0.996220i \(0.527686\pi\)
\(524\) −8832.00 15297.5i −0.736312 1.27533i
\(525\) 0 0
\(526\) −7276.00 + 12602.4i −0.603134 + 1.04466i
\(527\) −1404.00 + 2431.80i −0.116052 + 0.201007i
\(528\) 0 0
\(529\) 3041.50 + 5268.03i 0.249979 + 0.432977i
\(530\) −40.0000 −0.00327828
\(531\) 0 0
\(532\) 4800.00 0.391177
\(533\) −418.000 723.997i −0.0339692 0.0588364i
\(534\) 0 0
\(535\) −2985.00 + 5170.17i −0.241220 + 0.417806i
\(536\) 0 0
\(537\) 0 0
\(538\) −13100.0 22689.9i −1.04978 1.81827i
\(539\) 9824.00 0.785064
\(540\) 0 0
\(541\) 5622.00 0.446781 0.223391 0.974729i \(-0.428287\pi\)
0.223391 + 0.974729i \(0.428287\pi\)
\(542\) 8776.00 + 15200.5i 0.695501 + 1.20464i
\(543\) 0 0
\(544\) −3328.00 + 5764.27i −0.262292 + 0.454303i
\(545\) 1375.00 2381.57i 0.108071 0.187184i
\(546\) 0 0
\(547\) −8243.00 14277.3i −0.644324 1.11600i −0.984457 0.175625i \(-0.943805\pi\)
0.340133 0.940377i \(-0.389528\pi\)
\(548\) 18672.0 1.45553
\(549\) 0 0
\(550\) −3200.00 −0.248088
\(551\) −2500.00 4330.13i −0.193291 0.334791i
\(552\) 0 0
\(553\) −1800.00 + 3117.69i −0.138416 + 0.239743i
\(554\) −1092.00 + 1891.40i −0.0837448 + 0.145050i
\(555\) 0 0
\(556\) 2800.00 + 4849.74i 0.213573 + 0.369919i
\(557\) −11706.0 −0.890483 −0.445242 0.895410i \(-0.646882\pi\)
−0.445242 + 0.895410i \(0.646882\pi\)
\(558\) 0 0
\(559\) −16796.0 −1.27083
\(560\) 960.000 + 1662.77i 0.0724418 + 0.125473i
\(561\) 0 0
\(562\) −13716.0 + 23756.8i −1.02949 + 1.78313i
\(563\) −12519.0 + 21683.5i −0.937146 + 1.62318i −0.166383 + 0.986061i \(0.553209\pi\)
−0.770763 + 0.637123i \(0.780125\pi\)
\(564\) 0 0
\(565\) 3905.00 + 6763.66i 0.290769 + 0.503627i
\(566\) 37128.0 2.75725
\(567\) 0 0
\(568\) 0 0
\(569\) 8775.00 + 15198.7i 0.646515 + 1.11980i 0.983949 + 0.178448i \(0.0571076\pi\)
−0.337434 + 0.941349i \(0.609559\pi\)
\(570\) 0 0
\(571\) −5356.00 + 9276.86i −0.392542 + 0.679903i −0.992784 0.119915i \(-0.961738\pi\)
0.600242 + 0.799819i \(0.295071\pi\)
\(572\) −4864.00 + 8424.70i −0.355549 + 0.615829i
\(573\) 0 0
\(574\) 264.000 + 457.261i 0.0191971 + 0.0332504i
\(575\) 1950.00 0.141427
\(576\) 0 0
\(577\) −13654.0 −0.985136 −0.492568 0.870274i \(-0.663942\pi\)
−0.492568 + 0.870274i \(0.663942\pi\)
\(578\) 8474.00 + 14677.4i 0.609813 + 1.05623i
\(579\) 0 0
\(580\) −1000.00 + 1732.05i −0.0715909 + 0.123999i
\(581\) 846.000 1465.31i 0.0604096 0.104633i
\(582\) 0 0
\(583\) −32.0000 55.4256i −0.00227325 0.00393738i
\(584\) 0 0
\(585\) 0 0
\(586\) −19368.0 −1.36533
\(587\) 7083.00 + 12268.1i 0.498035 + 0.862622i 0.999997 0.00226720i \(-0.000721674\pi\)
−0.501962 + 0.864890i \(0.667388\pi\)
\(588\) 0 0
\(589\) 5400.00 9353.07i 0.377764 0.654307i
\(590\) 5000.00 8660.25i 0.348893 0.604300i
\(591\) 0 0
\(592\) 8512.00 + 14743.2i 0.590948 + 1.02355i
\(593\) −17842.0 −1.23555 −0.617777 0.786354i \(-0.711966\pi\)
−0.617777 + 0.786354i \(0.711966\pi\)
\(594\) 0 0
\(595\) −780.000 −0.0537427
\(596\) 8200.00 + 14202.8i 0.563566 + 0.976124i
\(597\) 0 0
\(598\) 5928.00 10267.6i 0.405374 0.702129i
\(599\) −8800.00 + 15242.0i −0.600264 + 1.03969i 0.392517 + 0.919745i \(0.371605\pi\)
−0.992781 + 0.119943i \(0.961729\pi\)
\(600\) 0 0
\(601\) −13651.0 23644.2i −0.926516 1.60477i −0.789105 0.614258i \(-0.789455\pi\)
−0.137410 0.990514i \(-0.543878\pi\)
\(602\) 10608.0 0.718189
\(603\) 0 0
\(604\) 14816.0 0.998103
\(605\) 767.500 + 1329.35i 0.0515757 + 0.0893318i
\(606\) 0 0
\(607\) 1897.00 3285.70i 0.126848 0.219708i −0.795606 0.605815i \(-0.792847\pi\)
0.922454 + 0.386107i \(0.126181\pi\)
\(608\) 12800.0 22170.3i 0.853797 1.47882i
\(609\) 0 0
\(610\) 5180.00 + 8972.02i 0.343823 + 0.595519i
\(611\) −19532.0 −1.29326
\(612\) 0 0
\(613\) −13238.0 −0.872231 −0.436116 0.899891i \(-0.643646\pi\)
−0.436116 + 0.899891i \(0.643646\pi\)
\(614\) 5188.00 + 8985.88i 0.340995 + 0.590620i
\(615\) 0 0
\(616\) 0 0
\(617\) −5787.00 + 10023.4i −0.377595 + 0.654013i −0.990712 0.135979i \(-0.956582\pi\)
0.613117 + 0.789992i \(0.289915\pi\)
\(618\) 0 0
\(619\) −4150.00 7188.01i −0.269471 0.466738i 0.699254 0.714873i \(-0.253516\pi\)
−0.968725 + 0.248135i \(0.920182\pi\)
\(620\) −4320.00 −0.279831
\(621\) 0 0
\(622\) −29328.0 −1.89059
\(623\) −450.000 779.423i −0.0289388 0.0501235i
\(624\) 0 0
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) −3124.00 + 5410.93i −0.199457 + 0.345470i
\(627\) 0 0
\(628\) 9976.00 + 17278.9i 0.633894 + 1.09794i
\(629\) −6916.00 −0.438409
\(630\) 0 0
\(631\) −7508.00 −0.473675 −0.236837 0.971549i \(-0.576111\pi\)
−0.236837 + 0.971549i \(0.576111\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 2852.00 4939.81i 0.178655 0.309440i
\(635\) −4615.00 + 7993.41i −0.288411 + 0.499542i
\(636\) 0 0
\(637\) −5833.00 10103.1i −0.362813 0.628411i
\(638\) −6400.00 −0.397145
\(639\) 0 0
\(640\) 0 0
\(641\) −13689.0 23710.0i −0.843499 1.46098i −0.886918 0.461927i \(-0.847158\pi\)
0.0434190 0.999057i \(-0.486175\pi\)
\(642\) 0 0
\(643\) −921.000 + 1595.22i −0.0564863 + 0.0978372i −0.892886 0.450283i \(-0.851323\pi\)
0.836400 + 0.548120i \(0.184656\pi\)
\(644\) −1872.00 + 3242.40i −0.114545 + 0.198398i
\(645\) 0 0
\(646\) 5200.00 + 9006.66i 0.316705 + 0.548549i
\(647\) 10114.0 0.614563 0.307282 0.951619i \(-0.400581\pi\)
0.307282 + 0.951619i \(0.400581\pi\)
\(648\) 0 0
\(649\) 16000.0 0.967727
\(650\) 1900.00 + 3290.90i 0.114653 + 0.198584i
\(651\) 0 0
\(652\) −11048.0 + 19135.7i −0.663609 + 1.14940i
\(653\) 5201.00 9008.40i 0.311686 0.539856i −0.667042 0.745020i \(-0.732440\pi\)
0.978727 + 0.205165i \(0.0657730\pi\)
\(654\) 0 0
\(655\) −5520.00 9560.92i −0.329289 0.570345i
\(656\) 1408.00 0.0838006
\(657\) 0 0
\(658\) 12336.0 0.730862
\(659\) 3550.00 + 6148.78i 0.209846 + 0.363464i 0.951666 0.307135i \(-0.0993705\pi\)
−0.741820 + 0.670599i \(0.766037\pi\)
\(660\) 0 0
\(661\) 3559.00 6164.37i 0.209424 0.362732i −0.742109 0.670279i \(-0.766175\pi\)
0.951533 + 0.307546i \(0.0995079\pi\)
\(662\) 8016.00 13884.1i 0.470620 0.815138i
\(663\) 0 0
\(664\) 0 0
\(665\) 3000.00 0.174940
\(666\) 0 0
\(667\) 3900.00 0.226400
\(668\) 12504.0 + 21657.6i 0.724243 + 1.25443i
\(669\) 0 0
\(670\) −1260.00 + 2182.38i −0.0726538 + 0.125840i
\(671\) −8288.00 + 14355.2i −0.476833 + 0.825898i
\(672\) 0 0
\(673\) 15639.0 + 27087.5i 0.895749 + 1.55148i 0.832875 + 0.553462i \(0.186693\pi\)
0.0628744 + 0.998021i \(0.479973\pi\)
\(674\) 35464.0 2.02674
\(675\) 0 0
\(676\) −6024.00 −0.342740
\(677\) −15027.0 26027.5i −0.853079 1.47758i −0.878416 0.477897i \(-0.841399\pi\)
0.0253367 0.999679i \(-0.491934\pi\)
\(678\) 0 0
\(679\) −1158.00 + 2005.71i −0.0654491 + 0.113361i
\(680\) 0 0
\(681\) 0 0
\(682\) −6912.00 11971.9i −0.388085 0.672183i
\(683\) 4518.00 0.253113 0.126557 0.991959i \(-0.459607\pi\)
0.126557 + 0.991959i \(0.459607\pi\)
\(684\) 0 0
\(685\) 11670.0 0.650931
\(686\) 7800.00 + 13510.0i 0.434119 + 0.751916i
\(687\) 0 0
\(688\) 14144.0 24498.1i 0.783772 1.35753i
\(689\) −38.0000 + 65.8179i −0.00210114 + 0.00363928i
\(690\) 0 0
\(691\) −14636.0 25350.3i −0.805759 1.39562i −0.915777 0.401686i \(-0.868424\pi\)
0.110018 0.993930i \(-0.464909\pi\)
\(692\) 624.000 0.0342788
\(693\) 0 0
\(694\) 6856.00 0.375000
\(695\) 1750.00 + 3031.09i 0.0955126 + 0.165433i
\(696\) 0 0
\(697\) −286.000 + 495.367i −0.0155424 + 0.0269202i
\(698\) −2300.00 + 3983.72i −0.124722 + 0.216026i
\(699\) 0 0
\(700\) −600.000 1039.23i −0.0323970 0.0561132i
\(701\) 5798.00 0.312393 0.156196 0.987726i \(-0.450077\pi\)
0.156196 + 0.987726i \(0.450077\pi\)
\(702\) 0 0
\(703\) 26600.0 1.42708
\(704\) −8192.00 14189.0i −0.438562 0.759612i
\(705\) 0 0
\(706\) −8796.00 + 15235.1i −0.468898 + 0.812155i
\(707\) 2106.00 3647.70i 0.112029 0.194039i
\(708\) 0 0
\(709\) −4475.00 7750.93i −0.237041 0.410567i 0.722823 0.691033i \(-0.242844\pi\)
−0.959864 + 0.280466i \(0.909511\pi\)
\(710\) −8240.00 −0.435552
\(711\) 0 0
\(712\) 0 0
\(713\) 4212.00 + 7295.40i 0.221235 + 0.383190i
\(714\) 0 0
\(715\) −3040.00 + 5265.43i −0.159006 + 0.275407i
\(716\) −5200.00 + 9006.66i −0.271415 + 0.470105i
\(717\) 0 0
\(718\) 3600.00 + 6235.38i 0.187118 + 0.324098i
\(719\) −7800.00 −0.404577 −0.202289 0.979326i \(-0.564838\pi\)
−0.202289 + 0.979326i \(0.564838\pi\)
\(720\) 0 0
\(721\) −3588.00 −0.185332
\(722\) −6282.00 10880.7i −0.323811 0.560858i
\(723\) 0 0
\(724\) −6968.00 + 12068.9i −0.357685 + 0.619528i
\(725\) −625.000 + 1082.53i −0.0320164 + 0.0554541i
\(726\) 0 0
\(727\) 4277.00 + 7407.98i 0.218191 + 0.377919i 0.954255 0.298994i \(-0.0966510\pi\)
−0.736064 + 0.676912i \(0.763318\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −17560.0 −0.890308
\(731\) 5746.00 + 9952.36i 0.290730 + 0.503559i
\(732\) 0 0
\(733\) −1441.00 + 2495.89i −0.0726119 + 0.125768i −0.900045 0.435796i \(-0.856467\pi\)
0.827433 + 0.561564i \(0.189800\pi\)
\(734\) 11748.0 20348.1i 0.590772 1.02325i
\(735\) 0 0
\(736\) 9984.00 + 17292.8i 0.500021 + 0.866061i
\(737\) −4032.00 −0.201521
\(738\) 0 0
\(739\) 18700.0 0.930840 0.465420 0.885090i \(-0.345903\pi\)
0.465420 + 0.885090i \(0.345903\pi\)
\(740\) −5320.00 9214.51i −0.264280 0.457746i
\(741\) 0 0
\(742\) 24.0000 41.5692i 0.00118742 0.00205668i
\(743\) 6121.00 10601.9i 0.302231 0.523480i −0.674410 0.738357i \(-0.735602\pi\)
0.976641 + 0.214878i \(0.0689352\pi\)
\(744\) 0 0
\(745\) 5125.00 + 8876.76i 0.252034 + 0.436536i
\(746\) −8312.00 −0.407941
\(747\) 0 0
\(748\) 6656.00 0.325358
\(749\) −3582.00 6204.21i −0.174744 0.302666i
\(750\) 0 0
\(751\) 15574.0 26975.0i 0.756729 1.31069i −0.187781 0.982211i \(-0.560130\pi\)
0.944510 0.328482i \(-0.106537\pi\)
\(752\) 16448.0 28488.8i 0.797602 1.38149i
\(753\) 0 0
\(754\) 3800.00 + 6581.79i 0.183538 + 0.317898i
\(755\) 9260.00 0.446365
\(756\) 0 0
\(757\) −7694.00 −0.369410 −0.184705 0.982794i \(-0.559133\pi\)
−0.184705 + 0.982794i \(0.559133\pi\)
\(758\) −15800.0 27366.4i −0.757100 1.31134i
\(759\) 0 0
\(760\) 0 0
\(761\) −2259.00 + 3912.70i −0.107607 + 0.186380i −0.914800 0.403907i \(-0.867652\pi\)
0.807194 + 0.590287i \(0.200985\pi\)
\(762\) 0 0
\(763\) 1650.00 + 2857.88i 0.0782883 + 0.135599i
\(764\) −30176.0 −1.42897
\(765\) 0 0
\(766\) 30072.0 1.41847
\(767\) −9500.00 16454.5i −0.447230 0.774624i
\(768\) 0 0
\(769\) 19775.0 34251.3i 0.927314 1.60616i 0.139518 0.990220i \(-0.455445\pi\)
0.787796 0.615936i \(-0.211222\pi\)
\(770\) 1920.00 3325.54i 0.0898597 0.155642i
\(771\) 0 0
\(772\) 1432.00 + 2480.30i 0.0667601 + 0.115632i
\(773\) −22122.0 −1.02933 −0.514666 0.857391i \(-0.672084\pi\)
−0.514666 + 0.857391i \(0.672084\pi\)
\(774\) 0 0
\(775\) −2700.00 −0.125144
\(776\) 0 0
\(777\) 0 0
\(778\) −3900.00 + 6755.00i −0.179720 + 0.311283i
\(779\) 1100.00 1905.26i 0.0505925 0.0876289i
\(780\) 0 0
\(781\) −6592.00 11417.7i −0.302023 0.523120i
\(782\) −8112.00 −0.370952
\(783\) 0 0
\(784\) 19648.0 0.895044
\(785\) 6235.00 + 10799.3i 0.283486 + 0.491013i
\(786\) 0 0
\(787\) 8317.00