Properties

Label 882.3.n.e.325.1
Level $882$
Weight $3$
Character 882.325
Analytic conductor $24.033$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 882.n (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.0327593166\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 325.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 882.325
Dual form 882.3.n.e.19.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.24264 + 0.717439i) q^{5} +2.82843 q^{8} +O(q^{10})\) \(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.24264 + 0.717439i) q^{5} +2.82843 q^{8} +(1.75736 + 1.01461i) q^{10} +(3.00000 - 5.19615i) q^{11} +21.3280i q^{13} +(-2.00000 - 3.46410i) q^{16} +(-7.75736 - 4.47871i) q^{17} +(6.25736 - 3.61269i) q^{19} -2.86976i q^{20} -8.48528 q^{22} +(-18.7279 - 32.4377i) q^{23} +(-11.4706 + 19.8676i) q^{25} +(26.1213 - 15.0812i) q^{26} +33.9411 q^{29} +(-38.2279 - 22.0709i) q^{31} +(-2.82843 + 4.89898i) q^{32} +12.6677i q^{34} +(13.9853 + 24.2232i) q^{37} +(-8.84924 - 5.10911i) q^{38} +(-3.51472 + 2.02922i) q^{40} -54.8313i q^{41} -1.48528 q^{43} +(6.00000 + 10.3923i) q^{44} +(-26.4853 + 45.8739i) q^{46} +(-37.2426 + 21.5020i) q^{47} +32.4437 q^{50} +(-36.9411 - 21.3280i) q^{52} +(-42.7279 + 74.0069i) q^{53} +8.60927i q^{55} +(-24.0000 - 41.5692i) q^{58} +(-35.6985 - 20.6105i) q^{59} +(1.02944 - 0.594346i) q^{61} +62.4259i q^{62} +8.00000 q^{64} +(-15.3015 - 26.5030i) q^{65} +(-2.19848 + 3.80789i) q^{67} +(15.5147 - 8.95743i) q^{68} -137.397 q^{71} +(-68.3528 - 39.4635i) q^{73} +(19.7782 - 34.2568i) q^{74} +14.4508i q^{76} +(-49.1690 - 85.1633i) q^{79} +(4.97056 + 2.86976i) q^{80} +(-67.1543 + 38.7716i) q^{82} +110.401i q^{83} +12.8528 q^{85} +(1.05025 + 1.81909i) q^{86} +(8.48528 - 14.6969i) q^{88} +(-18.0000 + 10.3923i) q^{89} +74.9117 q^{92} +(52.6690 + 30.4085i) q^{94} +(-5.18377 + 8.97855i) q^{95} +10.9867i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{4} + 12q^{5} + O(q^{10}) \) \( 4q - 4q^{4} + 12q^{5} + 24q^{10} + 12q^{11} - 8q^{16} - 48q^{17} + 42q^{19} - 24q^{23} + 22q^{25} + 96q^{26} - 102q^{31} + 22q^{37} + 24q^{38} - 48q^{40} + 28q^{43} + 24q^{44} - 72q^{46} - 132q^{47} + 192q^{50} - 12q^{52} - 120q^{53} - 96q^{58} - 24q^{59} + 72q^{61} + 32q^{64} - 180q^{65} + 110q^{67} + 96q^{68} - 312q^{71} + 66q^{73} + 48q^{74} - 10q^{79} - 48q^{80} - 48q^{82} - 288q^{85} + 24q^{86} - 72q^{89} + 96q^{92} + 24q^{94} + 132q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 1.22474i −0.353553 0.612372i
\(3\) 0 0
\(4\) −1.00000 + 1.73205i −0.250000 + 0.433013i
\(5\) −1.24264 + 0.717439i −0.248528 + 0.143488i −0.619090 0.785320i \(-0.712498\pi\)
0.370562 + 0.928808i \(0.379165\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.82843 0.353553
\(9\) 0 0
\(10\) 1.75736 + 1.01461i 0.175736 + 0.101461i
\(11\) 3.00000 5.19615i 0.272727 0.472377i −0.696832 0.717234i \(-0.745408\pi\)
0.969559 + 0.244857i \(0.0787410\pi\)
\(12\) 0 0
\(13\) 21.3280i 1.64061i 0.571924 + 0.820306i \(0.306197\pi\)
−0.571924 + 0.820306i \(0.693803\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) −7.75736 4.47871i −0.456315 0.263454i 0.254178 0.967157i \(-0.418195\pi\)
−0.710494 + 0.703704i \(0.751528\pi\)
\(18\) 0 0
\(19\) 6.25736 3.61269i 0.329335 0.190141i −0.326211 0.945297i \(-0.605772\pi\)
0.655546 + 0.755156i \(0.272439\pi\)
\(20\) 2.86976i 0.143488i
\(21\) 0 0
\(22\) −8.48528 −0.385695
\(23\) −18.7279 32.4377i −0.814257 1.41034i −0.909860 0.414916i \(-0.863811\pi\)
0.0956024 0.995420i \(-0.469522\pi\)
\(24\) 0 0
\(25\) −11.4706 + 19.8676i −0.458823 + 0.794704i
\(26\) 26.1213 15.0812i 1.00467 0.580044i
\(27\) 0 0
\(28\) 0 0
\(29\) 33.9411 1.17038 0.585192 0.810895i \(-0.301019\pi\)
0.585192 + 0.810895i \(0.301019\pi\)
\(30\) 0 0
\(31\) −38.2279 22.0709i −1.23316 0.711965i −0.265472 0.964119i \(-0.585528\pi\)
−0.967687 + 0.252154i \(0.918861\pi\)
\(32\) −2.82843 + 4.89898i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 12.6677i 0.372580i
\(35\) 0 0
\(36\) 0 0
\(37\) 13.9853 + 24.2232i 0.377981 + 0.654682i 0.990768 0.135566i \(-0.0432853\pi\)
−0.612788 + 0.790248i \(0.709952\pi\)
\(38\) −8.84924 5.10911i −0.232875 0.134450i
\(39\) 0 0
\(40\) −3.51472 + 2.02922i −0.0878680 + 0.0507306i
\(41\) 54.8313i 1.33735i −0.743556 0.668674i \(-0.766862\pi\)
0.743556 0.668674i \(-0.233138\pi\)
\(42\) 0 0
\(43\) −1.48528 −0.0345414 −0.0172707 0.999851i \(-0.505498\pi\)
−0.0172707 + 0.999851i \(0.505498\pi\)
\(44\) 6.00000 + 10.3923i 0.136364 + 0.236189i
\(45\) 0 0
\(46\) −26.4853 + 45.8739i −0.575767 + 0.997258i
\(47\) −37.2426 + 21.5020i −0.792397 + 0.457490i −0.840806 0.541337i \(-0.817918\pi\)
0.0484090 + 0.998828i \(0.484585\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 32.4437 0.648873
\(51\) 0 0
\(52\) −36.9411 21.3280i −0.710406 0.410153i
\(53\) −42.7279 + 74.0069i −0.806187 + 1.39636i 0.109299 + 0.994009i \(0.465139\pi\)
−0.915487 + 0.402348i \(0.868194\pi\)
\(54\) 0 0
\(55\) 8.60927i 0.156532i
\(56\) 0 0
\(57\) 0 0
\(58\) −24.0000 41.5692i −0.413793 0.716711i
\(59\) −35.6985 20.6105i −0.605059 0.349331i 0.165970 0.986131i \(-0.446924\pi\)
−0.771029 + 0.636800i \(0.780258\pi\)
\(60\) 0 0
\(61\) 1.02944 0.594346i 0.0168760 0.00974337i −0.491538 0.870856i \(-0.663565\pi\)
0.508414 + 0.861113i \(0.330232\pi\)
\(62\) 62.4259i 1.00687i
\(63\) 0 0
\(64\) 8.00000 0.125000
\(65\) −15.3015 26.5030i −0.235408 0.407738i
\(66\) 0 0
\(67\) −2.19848 + 3.80789i −0.0328132 + 0.0568341i −0.881966 0.471314i \(-0.843780\pi\)
0.849152 + 0.528148i \(0.177113\pi\)
\(68\) 15.5147 8.95743i 0.228158 0.131727i
\(69\) 0 0
\(70\) 0 0
\(71\) −137.397 −1.93517 −0.967584 0.252548i \(-0.918731\pi\)
−0.967584 + 0.252548i \(0.918731\pi\)
\(72\) 0 0
\(73\) −68.3528 39.4635i −0.936340 0.540596i −0.0475288 0.998870i \(-0.515135\pi\)
−0.888811 + 0.458274i \(0.848468\pi\)
\(74\) 19.7782 34.2568i 0.267273 0.462930i
\(75\) 0 0
\(76\) 14.4508i 0.190141i
\(77\) 0 0
\(78\) 0 0
\(79\) −49.1690 85.1633i −0.622393 1.07802i −0.989039 0.147656i \(-0.952827\pi\)
0.366646 0.930361i \(-0.380506\pi\)
\(80\) 4.97056 + 2.86976i 0.0621320 + 0.0358719i
\(81\) 0 0
\(82\) −67.1543 + 38.7716i −0.818955 + 0.472824i
\(83\) 110.401i 1.33013i 0.746784 + 0.665067i \(0.231597\pi\)
−0.746784 + 0.665067i \(0.768403\pi\)
\(84\) 0 0
\(85\) 12.8528 0.151210
\(86\) 1.05025 + 1.81909i 0.0122122 + 0.0211522i
\(87\) 0 0
\(88\) 8.48528 14.6969i 0.0964237 0.167011i
\(89\) −18.0000 + 10.3923i −0.202247 + 0.116767i −0.597703 0.801717i \(-0.703920\pi\)
0.395456 + 0.918485i \(0.370587\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 74.9117 0.814257
\(93\) 0 0
\(94\) 52.6690 + 30.4085i 0.560309 + 0.323495i
\(95\) −5.18377 + 8.97855i −0.0545660 + 0.0945110i
\(96\) 0 0
\(97\) 10.9867i 0.113264i 0.998395 + 0.0566322i \(0.0180362\pi\)
−0.998395 + 0.0566322i \(0.981964\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −22.9411 39.7352i −0.229411 0.397352i
\(101\) −92.8234 53.5916i −0.919043 0.530610i −0.0357136 0.999362i \(-0.511370\pi\)
−0.883330 + 0.468752i \(0.844704\pi\)
\(102\) 0 0
\(103\) −91.1102 + 52.6025i −0.884565 + 0.510704i −0.872161 0.489219i \(-0.837282\pi\)
−0.0124040 + 0.999923i \(0.503948\pi\)
\(104\) 60.3246i 0.580044i
\(105\) 0 0
\(106\) 120.853 1.14012
\(107\) 59.2721 + 102.662i 0.553945 + 0.959460i 0.997985 + 0.0634534i \(0.0202114\pi\)
−0.444040 + 0.896007i \(0.646455\pi\)
\(108\) 0 0
\(109\) −55.5294 + 96.1798i −0.509444 + 0.882384i 0.490496 + 0.871444i \(0.336816\pi\)
−0.999940 + 0.0109400i \(0.996518\pi\)
\(110\) 10.5442 6.08767i 0.0958560 0.0553425i
\(111\) 0 0
\(112\) 0 0
\(113\) −101.397 −0.897318 −0.448659 0.893703i \(-0.648098\pi\)
−0.448659 + 0.893703i \(0.648098\pi\)
\(114\) 0 0
\(115\) 46.5442 + 26.8723i 0.404732 + 0.233672i
\(116\) −33.9411 + 58.7878i −0.292596 + 0.506791i
\(117\) 0 0
\(118\) 58.2954i 0.494029i
\(119\) 0 0
\(120\) 0 0
\(121\) 42.5000 + 73.6122i 0.351240 + 0.608365i
\(122\) −1.45584 0.840532i −0.0119331 0.00688961i
\(123\) 0 0
\(124\) 76.4558 44.1418i 0.616579 0.355982i
\(125\) 68.7897i 0.550317i
\(126\) 0 0
\(127\) 82.5736 0.650186 0.325093 0.945682i \(-0.394604\pi\)
0.325093 + 0.945682i \(0.394604\pi\)
\(128\) −5.65685 9.79796i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) −21.6396 + 37.4809i −0.166459 + 0.288315i
\(131\) −52.4558 + 30.2854i −0.400426 + 0.231186i −0.686668 0.726971i \(-0.740927\pi\)
0.286242 + 0.958157i \(0.407594\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 6.21825 0.0464049
\(135\) 0 0
\(136\) −21.9411 12.6677i −0.161332 0.0931450i
\(137\) 33.5147 58.0492i 0.244633 0.423717i −0.717395 0.696666i \(-0.754666\pi\)
0.962028 + 0.272949i \(0.0879992\pi\)
\(138\) 0 0
\(139\) 91.5525i 0.658651i −0.944216 0.329326i \(-0.893179\pi\)
0.944216 0.329326i \(-0.106821\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 97.1543 + 168.276i 0.684185 + 1.18504i
\(143\) 110.823 + 63.9839i 0.774989 + 0.447440i
\(144\) 0 0
\(145\) −42.1766 + 24.3507i −0.290873 + 0.167936i
\(146\) 111.620i 0.764518i
\(147\) 0 0
\(148\) −55.9411 −0.377981
\(149\) 40.5442 + 70.2245i 0.272108 + 0.471306i 0.969402 0.245480i \(-0.0789457\pi\)
−0.697293 + 0.716786i \(0.745612\pi\)
\(150\) 0 0
\(151\) 25.6030 44.3457i 0.169556 0.293680i −0.768708 0.639600i \(-0.779100\pi\)
0.938264 + 0.345920i \(0.112433\pi\)
\(152\) 17.6985 10.2182i 0.116437 0.0672252i
\(153\) 0 0
\(154\) 0 0
\(155\) 63.3381 0.408633
\(156\) 0 0
\(157\) −162.000 93.5307i −1.03185 0.595737i −0.114334 0.993442i \(-0.536473\pi\)
−0.917513 + 0.397705i \(0.869807\pi\)
\(158\) −69.5355 + 120.439i −0.440098 + 0.762273i
\(159\) 0 0
\(160\) 8.11689i 0.0507306i
\(161\) 0 0
\(162\) 0 0
\(163\) −41.9706 72.6951i −0.257488 0.445982i 0.708080 0.706132i \(-0.249561\pi\)
−0.965568 + 0.260149i \(0.916228\pi\)
\(164\) 94.9706 + 54.8313i 0.579089 + 0.334337i
\(165\) 0 0
\(166\) 135.213 78.0654i 0.814537 0.470273i
\(167\) 127.620i 0.764190i −0.924123 0.382095i \(-0.875203\pi\)
0.924123 0.382095i \(-0.124797\pi\)
\(168\) 0 0
\(169\) −285.882 −1.69161
\(170\) −9.08831 15.7414i −0.0534607 0.0925966i
\(171\) 0 0
\(172\) 1.48528 2.57258i 0.00863536 0.0149569i
\(173\) −123.816 + 71.4853i −0.715701 + 0.413210i −0.813168 0.582029i \(-0.802259\pi\)
0.0974675 + 0.995239i \(0.468926\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −24.0000 −0.136364
\(177\) 0 0
\(178\) 25.4558 + 14.6969i 0.143010 + 0.0825671i
\(179\) 84.6396 146.600i 0.472847 0.818995i −0.526670 0.850070i \(-0.676560\pi\)
0.999517 + 0.0310748i \(0.00989300\pi\)
\(180\) 0 0
\(181\) 209.969i 1.16005i 0.814600 + 0.580024i \(0.196957\pi\)
−0.814600 + 0.580024i \(0.803043\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −52.9706 91.7477i −0.287883 0.498629i
\(185\) −34.7574 20.0672i −0.187878 0.108471i
\(186\) 0 0
\(187\) −46.5442 + 26.8723i −0.248899 + 0.143702i
\(188\) 86.0082i 0.457490i
\(189\) 0 0
\(190\) 14.6619 0.0771679
\(191\) 33.3015 + 57.6799i 0.174353 + 0.301989i 0.939937 0.341347i \(-0.110883\pi\)
−0.765584 + 0.643336i \(0.777550\pi\)
\(192\) 0 0
\(193\) 4.89697 8.48180i 0.0253729 0.0439472i −0.853060 0.521813i \(-0.825256\pi\)
0.878433 + 0.477865i \(0.158589\pi\)
\(194\) 13.4558 7.76874i 0.0693600 0.0400450i
\(195\) 0 0
\(196\) 0 0
\(197\) 267.161 1.35615 0.678075 0.734993i \(-0.262815\pi\)
0.678075 + 0.734993i \(0.262815\pi\)
\(198\) 0 0
\(199\) 113.397 + 65.4698i 0.569834 + 0.328994i 0.757083 0.653319i \(-0.226624\pi\)
−0.187249 + 0.982312i \(0.559957\pi\)
\(200\) −32.4437 + 56.1941i −0.162218 + 0.280970i
\(201\) 0 0
\(202\) 151.580i 0.750396i
\(203\) 0 0
\(204\) 0 0
\(205\) 39.3381 + 68.1356i 0.191893 + 0.332369i
\(206\) 128.849 + 74.3911i 0.625482 + 0.361122i
\(207\) 0 0
\(208\) 73.8823 42.6559i 0.355203 0.205077i
\(209\) 43.3523i 0.207427i
\(210\) 0 0
\(211\) −23.0883 −0.109423 −0.0547116 0.998502i \(-0.517424\pi\)
−0.0547116 + 0.998502i \(0.517424\pi\)
\(212\) −85.4558 148.014i −0.403094 0.698179i
\(213\) 0 0
\(214\) 83.8234 145.186i 0.391698 0.678441i
\(215\) 1.84567 1.06560i 0.00858452 0.00495627i
\(216\) 0 0
\(217\) 0 0
\(218\) 157.061 0.720463
\(219\) 0 0
\(220\) −14.9117 8.60927i −0.0677804 0.0391330i
\(221\) 95.5219 165.449i 0.432226 0.748637i
\(222\) 0 0
\(223\) 228.631i 1.02525i −0.858613 0.512625i \(-0.828673\pi\)
0.858613 0.512625i \(-0.171327\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 71.6985 + 124.185i 0.317250 + 0.549493i
\(227\) 56.8234 + 32.8070i 0.250323 + 0.144524i 0.619912 0.784671i \(-0.287168\pi\)
−0.369589 + 0.929195i \(0.620502\pi\)
\(228\) 0 0
\(229\) −80.9558 + 46.7399i −0.353519 + 0.204104i −0.666234 0.745743i \(-0.732095\pi\)
0.312715 + 0.949847i \(0.398761\pi\)
\(230\) 76.0063i 0.330462i
\(231\) 0 0
\(232\) 96.0000 0.413793
\(233\) −118.757 205.694i −0.509688 0.882806i −0.999937 0.0112234i \(-0.996427\pi\)
0.490249 0.871583i \(-0.336906\pi\)
\(234\) 0 0
\(235\) 30.8528 53.4386i 0.131289 0.227398i
\(236\) 71.3970 41.2211i 0.302530 0.174666i
\(237\) 0 0
\(238\) 0 0
\(239\) −366.853 −1.53495 −0.767475 0.641079i \(-0.778487\pi\)
−0.767475 + 0.641079i \(0.778487\pi\)
\(240\) 0 0
\(241\) 364.617 + 210.512i 1.51293 + 0.873493i 0.999885 + 0.0151343i \(0.00481759\pi\)
0.513049 + 0.858359i \(0.328516\pi\)
\(242\) 60.1041 104.103i 0.248364 0.430179i
\(243\) 0 0
\(244\) 2.37738i 0.00974337i
\(245\) 0 0
\(246\) 0 0
\(247\) 77.0513 + 133.457i 0.311949 + 0.540311i
\(248\) −108.125 62.4259i −0.435987 0.251717i
\(249\) 0 0
\(250\) −84.2498 + 48.6416i −0.336999 + 0.194567i
\(251\) 146.621i 0.584148i −0.956396 0.292074i \(-0.905655\pi\)
0.956396 0.292074i \(-0.0943454\pi\)
\(252\) 0 0
\(253\) −224.735 −0.888281
\(254\) −58.3883 101.132i −0.229875 0.398156i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) 21.7279 12.5446i 0.0845444 0.0488118i −0.457132 0.889399i \(-0.651123\pi\)
0.541676 + 0.840587i \(0.317790\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 61.2061 0.235408
\(261\) 0 0
\(262\) 74.1838 + 42.8300i 0.283144 + 0.163473i
\(263\) −45.3381 + 78.5279i −0.172388 + 0.298585i −0.939254 0.343222i \(-0.888482\pi\)
0.766866 + 0.641807i \(0.221815\pi\)
\(264\) 0 0
\(265\) 122.619i 0.462712i
\(266\) 0 0
\(267\) 0 0
\(268\) −4.39697 7.61577i −0.0164066 0.0284171i
\(269\) −59.2355 34.1996i −0.220206 0.127136i 0.385839 0.922566i \(-0.373912\pi\)
−0.606046 + 0.795430i \(0.707245\pi\)
\(270\) 0 0
\(271\) 106.971 61.7595i 0.394725 0.227895i −0.289480 0.957184i \(-0.593482\pi\)
0.684206 + 0.729289i \(0.260149\pi\)
\(272\) 35.8297i 0.131727i
\(273\) 0 0
\(274\) −94.7939 −0.345963
\(275\) 68.8234 + 119.206i 0.250267 + 0.433475i
\(276\) 0 0
\(277\) 136.441 236.323i 0.492567 0.853151i −0.507396 0.861713i \(-0.669392\pi\)
0.999963 + 0.00856145i \(0.00272523\pi\)
\(278\) −112.128 + 64.7374i −0.403340 + 0.232868i
\(279\) 0 0
\(280\) 0 0
\(281\) −133.103 −0.473675 −0.236837 0.971549i \(-0.576111\pi\)
−0.236837 + 0.971549i \(0.576111\pi\)
\(282\) 0 0
\(283\) 111.507 + 64.3787i 0.394018 + 0.227486i 0.683900 0.729576i \(-0.260283\pi\)
−0.289882 + 0.957063i \(0.593616\pi\)
\(284\) 137.397 237.979i 0.483792 0.837953i
\(285\) 0 0
\(286\) 180.974i 0.632776i
\(287\) 0 0
\(288\) 0 0
\(289\) −104.382 180.795i −0.361184 0.625589i
\(290\) 59.6468 + 34.4371i 0.205678 + 0.118749i
\(291\) 0 0
\(292\) 136.706 78.9270i 0.468170 0.270298i
\(293\) 308.984i 1.05455i −0.849694 0.527276i \(-0.823213\pi\)
0.849694 0.527276i \(-0.176787\pi\)
\(294\) 0 0
\(295\) 59.1472 0.200499
\(296\) 39.5563 + 68.5136i 0.133636 + 0.231465i
\(297\) 0 0
\(298\) 57.3381 99.3125i 0.192410 0.333263i
\(299\) 691.831 399.429i 2.31381 1.33588i
\(300\) 0 0
\(301\) 0 0
\(302\) −72.4163 −0.239789
\(303\) 0 0
\(304\) −25.0294 14.4508i −0.0823337 0.0475354i
\(305\) −0.852814 + 1.47712i −0.00279611 + 0.00484301i
\(306\) 0 0
\(307\) 606.090i 1.97423i −0.160003 0.987117i \(-0.551150\pi\)
0.160003 0.987117i \(-0.448850\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −44.7868 77.5730i −0.144474 0.250236i
\(311\) −176.044 101.639i −0.566057 0.326813i 0.189516 0.981878i \(-0.439308\pi\)
−0.755573 + 0.655064i \(0.772641\pi\)
\(312\) 0 0
\(313\) 351.294 202.820i 1.12234 0.647986i 0.180346 0.983603i \(-0.442278\pi\)
0.941999 + 0.335617i \(0.108945\pi\)
\(314\) 264.545i 0.842500i
\(315\) 0 0
\(316\) 196.676 0.622393
\(317\) −13.0294 22.5676i −0.0411023 0.0711913i 0.844742 0.535173i \(-0.179754\pi\)
−0.885845 + 0.463982i \(0.846420\pi\)
\(318\) 0 0
\(319\) 101.823 176.363i 0.319196 0.552863i
\(320\) −9.94113 + 5.73951i −0.0310660 + 0.0179360i
\(321\) 0 0
\(322\) 0 0
\(323\) −64.7208 −0.200374
\(324\) 0 0
\(325\) −423.735 244.644i −1.30380 0.752750i
\(326\) −59.3553 + 102.806i −0.182072 + 0.315357i
\(327\) 0 0
\(328\) 155.086i 0.472824i
\(329\) 0 0
\(330\) 0 0
\(331\) 54.3162 + 94.0785i 0.164097 + 0.284225i 0.936334 0.351110i \(-0.114196\pi\)
−0.772237 + 0.635335i \(0.780862\pi\)
\(332\) −191.220 110.401i −0.575965 0.332533i
\(333\) 0 0
\(334\) −156.302 + 90.2407i −0.467969 + 0.270182i
\(335\) 6.30911i 0.0188332i
\(336\) 0 0
\(337\) 441.735 1.31079 0.655393 0.755288i \(-0.272503\pi\)
0.655393 + 0.755288i \(0.272503\pi\)
\(338\) 202.149 + 350.133i 0.598075 + 1.03590i
\(339\) 0 0
\(340\) −12.8528 + 22.2617i −0.0378024 + 0.0654757i
\(341\) −229.368 + 132.425i −0.672632 + 0.388344i
\(342\) 0 0
\(343\) 0 0
\(344\) −4.20101 −0.0122122
\(345\) 0 0
\(346\) 175.103 + 101.096i 0.506077 + 0.292184i
\(347\) 17.0955 29.6102i 0.0492664 0.0853320i −0.840341 0.542059i \(-0.817645\pi\)
0.889607 + 0.456727i \(0.150978\pi\)
\(348\) 0 0
\(349\) 221.787i 0.635493i −0.948176 0.317746i \(-0.897074\pi\)
0.948176 0.317746i \(-0.102926\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 16.9706 + 29.3939i 0.0482118 + 0.0835053i
\(353\) 387.448 + 223.693i 1.09759 + 0.633692i 0.935586 0.353099i \(-0.114872\pi\)
0.162000 + 0.986791i \(0.448206\pi\)
\(354\) 0 0
\(355\) 170.735 98.5739i 0.480944 0.277673i
\(356\) 41.5692i 0.116767i
\(357\) 0 0
\(358\) −239.397 −0.668707
\(359\) 145.882 + 252.675i 0.406357 + 0.703831i 0.994478 0.104941i \(-0.0334655\pi\)
−0.588121 + 0.808773i \(0.700132\pi\)
\(360\) 0 0
\(361\) −154.397 + 267.423i −0.427692 + 0.740785i
\(362\) 257.158 148.470i 0.710381 0.410139i
\(363\) 0 0
\(364\) 0 0
\(365\) 113.251 0.310276
\(366\) 0 0
\(367\) 363.169 + 209.676i 0.989561 + 0.571324i 0.905143 0.425107i \(-0.139763\pi\)
0.0844183 + 0.996430i \(0.473097\pi\)
\(368\) −74.9117 + 129.751i −0.203564 + 0.352584i
\(369\) 0 0
\(370\) 56.7585i 0.153401i
\(371\) 0 0
\(372\) 0 0
\(373\) −15.6909 27.1775i −0.0420668 0.0728618i 0.844225 0.535988i \(-0.180061\pi\)
−0.886292 + 0.463127i \(0.846728\pi\)
\(374\) 65.8234 + 38.0031i 0.175998 + 0.101613i
\(375\) 0 0
\(376\) −105.338 + 60.8170i −0.280155 + 0.161747i
\(377\) 723.895i 1.92015i
\(378\) 0 0
\(379\) 206.779 0.545590 0.272795 0.962072i \(-0.412052\pi\)
0.272795 + 0.962072i \(0.412052\pi\)
\(380\) −10.3675 17.9571i −0.0272830 0.0472555i
\(381\) 0 0
\(382\) 47.0955 81.5717i 0.123287 0.213539i
\(383\) −431.772 + 249.283i −1.12734 + 0.650871i −0.943265 0.332041i \(-0.892263\pi\)
−0.184076 + 0.982912i \(0.558929\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −13.8507 −0.0358827
\(387\) 0 0
\(388\) −19.0294 10.9867i −0.0490449 0.0283161i
\(389\) −324.213 + 561.554i −0.833453 + 1.44358i 0.0618308 + 0.998087i \(0.480306\pi\)
−0.895284 + 0.445496i \(0.853027\pi\)
\(390\) 0 0
\(391\) 335.508i 0.858077i
\(392\) 0 0
\(393\) 0 0
\(394\) −188.912 327.205i −0.479471 0.830469i
\(395\) 122.199 + 70.5516i 0.309364 + 0.178612i
\(396\) 0 0
\(397\) −65.6026 + 37.8757i −0.165246 + 0.0954047i −0.580342 0.814373i \(-0.697081\pi\)
0.415096 + 0.909777i \(0.363748\pi\)
\(398\) 185.176i 0.465268i
\(399\) 0 0
\(400\) 91.7645 0.229411
\(401\) −282.125 488.655i −0.703553 1.21859i −0.967211 0.253974i \(-0.918262\pi\)
0.263658 0.964616i \(-0.415071\pi\)
\(402\) 0 0
\(403\) 470.727 815.324i 1.16806 2.02314i
\(404\) 185.647 107.183i 0.459522 0.265305i
\(405\) 0 0
\(406\) 0 0
\(407\) 167.823 0.412342
\(408\) 0 0
\(409\) 309.559 + 178.724i 0.756868 + 0.436978i 0.828170 0.560477i \(-0.189382\pi\)
−0.0713023 + 0.997455i \(0.522716\pi\)
\(410\) 55.6325 96.3583i 0.135689 0.235020i
\(411\) 0 0
\(412\) 210.410i 0.510704i
\(413\) 0 0
\(414\) 0 0
\(415\) −79.2061 137.189i −0.190858 0.330576i
\(416\) −104.485 60.3246i −0.251167 0.145011i
\(417\) 0 0
\(418\) −53.0955 + 30.6547i −0.127023 + 0.0733365i
\(419\) 502.175i 1.19851i −0.800559 0.599254i \(-0.795464\pi\)
0.800559 0.599254i \(-0.204536\pi\)
\(420\) 0 0
\(421\) 33.7939 0.0802706 0.0401353 0.999194i \(-0.487221\pi\)
0.0401353 + 0.999194i \(0.487221\pi\)
\(422\) 16.3259 + 28.2773i 0.0386870 + 0.0670078i
\(423\) 0 0
\(424\) −120.853 + 209.323i −0.285030 + 0.493687i
\(425\) 177.963 102.747i 0.418735 0.241757i
\(426\) 0 0
\(427\) 0 0
\(428\) −237.088 −0.553945
\(429\) 0 0
\(430\) −2.61017 1.50698i −0.00607017 0.00350461i
\(431\) 251.860 436.234i 0.584362 1.01214i −0.410593 0.911819i \(-0.634678\pi\)
0.994955 0.100326i \(-0.0319884\pi\)
\(432\) 0 0
\(433\) 837.548i 1.93429i 0.254224 + 0.967145i \(0.418180\pi\)
−0.254224 + 0.967145i \(0.581820\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −111.059 192.360i −0.254722 0.441192i
\(437\) −234.375 135.316i −0.536326 0.309648i
\(438\) 0 0
\(439\) 164.558 95.0079i 0.374848 0.216419i −0.300726 0.953711i \(-0.597229\pi\)
0.675575 + 0.737292i \(0.263896\pi\)
\(440\) 24.3507i 0.0553425i
\(441\) 0 0
\(442\) −270.177 −0.611259
\(443\) −84.7279 146.753i −0.191259 0.331271i 0.754408 0.656405i \(-0.227924\pi\)
−0.945668 + 0.325134i \(0.894591\pi\)
\(444\) 0 0
\(445\) 14.9117 25.8278i 0.0335094 0.0580400i
\(446\) −280.014 + 161.666i −0.627835 + 0.362481i
\(447\) 0 0
\(448\) 0 0
\(449\) −18.1035 −0.0403195 −0.0201598 0.999797i \(-0.506417\pi\)
−0.0201598 + 0.999797i \(0.506417\pi\)
\(450\) 0 0
\(451\) −284.912 164.494i −0.631733 0.364731i
\(452\) 101.397 175.625i 0.224330 0.388550i
\(453\) 0 0
\(454\) 92.7922i 0.204388i
\(455\) 0 0
\(456\) 0 0
\(457\) 164.412 + 284.769i 0.359763 + 0.623128i 0.987921 0.154958i \(-0.0495242\pi\)
−0.628158 + 0.778086i \(0.716191\pi\)
\(458\) 114.489 + 66.1002i 0.249976 + 0.144324i
\(459\) 0 0
\(460\) −93.0883 + 53.7446i −0.202366 + 0.116836i
\(461\) 794.331i 1.72306i 0.507706 + 0.861530i \(0.330494\pi\)
−0.507706 + 0.861530i \(0.669506\pi\)
\(462\) 0 0
\(463\) −403.396 −0.871266 −0.435633 0.900124i \(-0.643475\pi\)
−0.435633 + 0.900124i \(0.643475\pi\)
\(464\) −67.8823 117.576i −0.146298 0.253395i
\(465\) 0 0
\(466\) −167.948 + 290.895i −0.360404 + 0.624238i
\(467\) −2.44870 + 1.41376i −0.00524347 + 0.00302732i −0.502619 0.864508i \(-0.667630\pi\)
0.497376 + 0.867535i \(0.334297\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −87.2649 −0.185670
\(471\) 0 0
\(472\) −100.971 58.2954i −0.213921 0.123507i
\(473\) −4.45584 + 7.71775i −0.00942039 + 0.0163166i
\(474\) 0 0
\(475\) 165.758i 0.348965i
\(476\) 0 0
\(477\) 0 0
\(478\) 259.404 + 449.301i 0.542686 + 0.939960i
\(479\) 328.669 + 189.757i 0.686157 + 0.396153i 0.802171 0.597095i \(-0.203678\pi\)
−0.116014 + 0.993248i \(0.537012\pi\)
\(480\) 0 0
\(481\) −516.632 + 298.278i −1.07408 + 0.620120i
\(482\) 595.418i 1.23531i
\(483\) 0 0
\(484\) −170.000 −0.351240
\(485\) −7.88225 13.6525i −0.0162521 0.0281494i
\(486\) 0 0
\(487\) −287.757 + 498.410i −0.590877 + 1.02343i 0.403238 + 0.915095i \(0.367885\pi\)
−0.994115 + 0.108333i \(0.965449\pi\)
\(488\) 2.91169 1.68106i 0.00596657 0.00344480i
\(489\) 0 0
\(490\) 0 0
\(491\) −238.441 −0.485623 −0.242811 0.970074i \(-0.578070\pi\)
−0.242811 + 0.970074i \(0.578070\pi\)
\(492\) 0 0
\(493\) −263.294 152.013i −0.534064 0.308342i
\(494\) 108.967 188.736i 0.220581 0.382057i
\(495\) 0 0
\(496\) 176.567i 0.355982i
\(497\) 0 0
\(498\) 0 0
\(499\) 143.287 + 248.180i 0.287148 + 0.497355i 0.973128 0.230266i \(-0.0739595\pi\)
−0.685980 + 0.727620i \(0.740626\pi\)
\(500\) 119.147 + 68.7897i 0.238294 + 0.137579i
\(501\) 0 0
\(502\) −179.574 + 103.677i −0.357716 + 0.206528i
\(503\) 25.4374i 0.0505714i −0.999680 0.0252857i \(-0.991950\pi\)
0.999680 0.0252857i \(-0.00804954\pi\)
\(504\) 0 0
\(505\) 153.795 0.304544
\(506\) 158.912 + 275.243i 0.314055 + 0.543959i
\(507\) 0 0
\(508\) −82.5736 + 143.022i −0.162546 + 0.281539i
\(509\) −697.889 + 402.926i −1.37110 + 0.791603i −0.991066 0.133370i \(-0.957420\pi\)
−0.380031 + 0.924974i \(0.624087\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 22.6274 0.0441942
\(513\) 0 0
\(514\) −30.7279 17.7408i −0.0597819 0.0345151i
\(515\) 75.4781 130.732i 0.146559 0.253848i
\(516\) 0 0
\(517\) 258.025i 0.499080i
\(518\) 0 0
\(519\) 0 0
\(520\) −43.2792 74.9618i −0.0832293 0.144157i
\(521\) −661.706 382.036i −1.27007 0.733274i −0.295068 0.955476i \(-0.595342\pi\)
−0.975001 + 0.222202i \(0.928676\pi\)
\(522\) 0 0
\(523\) 153.096 88.3900i 0.292726 0.169006i −0.346444 0.938071i \(-0.612611\pi\)
0.639171 + 0.769065i \(0.279278\pi\)
\(524\) 121.142i 0.231186i
\(525\) 0 0
\(526\) 128.235 0.243794
\(527\) 197.698 + 342.424i 0.375139 + 0.649761i
\(528\) 0 0
\(529\) −436.970 + 756.854i −0.826030 + 1.43073i
\(530\) −150.177 + 86.7045i −0.283352 + 0.163593i
\(531\) 0 0
\(532\) 0 0
\(533\) 1169.44 2.19407
\(534\) 0 0
\(535\) −147.308 85.0482i −0.275342 0.158969i
\(536\) −6.21825 + 10.7703i −0.0116012 + 0.0200939i
\(537\) 0 0
\(538\) 96.7312i 0.179798i
\(539\) 0 0
\(540\) 0 0
\(541\) −8.58831 14.8754i −0.0158749 0.0274961i 0.857979 0.513685i \(-0.171720\pi\)
−0.873854 + 0.486189i \(0.838387\pi\)
\(542\) −151.279 87.3411i −0.279113 0.161146i
\(543\) 0 0
\(544\) 43.8823 25.3354i 0.0806659 0.0465725i
\(545\) 159.356i 0.292396i
\(546\) 0 0
\(547\) 212.676 0.388805 0.194402 0.980922i \(-0.437723\pi\)
0.194402 + 0.980922i \(0.437723\pi\)
\(548\) 67.0294 + 116.098i 0.122316 + 0.211858i
\(549\) 0 0
\(550\) 97.3310 168.582i 0.176965 0.306513i
\(551\) 212.382 122.619i 0.385448 0.222538i
\(552\) 0 0
\(553\) 0 0
\(554\) −385.914 −0.696595
\(555\) 0 0
\(556\) 158.574 + 91.5525i 0.285204 + 0.164663i
\(557\) −440.823 + 763.528i −0.791424 + 1.37079i 0.133661 + 0.991027i \(0.457327\pi\)
−0.925085 + 0.379760i \(0.876007\pi\)
\(558\) 0 0
\(559\) 31.6780i 0.0566691i
\(560\) 0 0
\(561\) 0 0
\(562\) 94.1177 + 163.017i 0.167469 + 0.290065i
\(563\) 664.301 + 383.534i 1.17993 + 0.681233i 0.955998 0.293372i \(-0.0947774\pi\)
0.223932 + 0.974605i \(0.428111\pi\)
\(564\) 0 0
\(565\) 126.000 72.7461i 0.223009 0.128754i
\(566\) 182.090i 0.321714i
\(567\) 0 0
\(568\) −388.617 −0.684185
\(569\) −14.6468 25.3689i −0.0257412 0.0445851i 0.852868 0.522127i \(-0.174861\pi\)
−0.878609 + 0.477542i \(0.841528\pi\)
\(570\) 0 0
\(571\) −482.521 + 835.752i −0.845046 + 1.46366i 0.0405347 + 0.999178i \(0.487094\pi\)
−0.885581 + 0.464485i \(0.846239\pi\)
\(572\) −221.647 + 127.968i −0.387494 + 0.223720i
\(573\) 0 0
\(574\) 0 0
\(575\) 859.279 1.49440
\(576\) 0 0
\(577\) −227.883 131.568i −0.394944 0.228021i 0.289356 0.957222i \(-0.406559\pi\)
−0.684300 + 0.729201i \(0.739892\pi\)
\(578\) −147.619 + 255.683i −0.255396 + 0.442359i
\(579\) 0 0
\(580\) 97.4027i 0.167936i
\(581\) 0 0
\(582\) 0 0
\(583\) 256.368 + 444.042i 0.439738 + 0.761649i
\(584\) −193.331 111.620i −0.331046 0.191130i
\(585\) 0 0
\(586\) −378.426 + 218.485i −0.645779 + 0.372841i
\(587\) 436.477i 0.743572i 0.928318 + 0.371786i \(0.121254\pi\)
−0.928318 + 0.371786i \(0.878746\pi\)
\(588\) 0 0
\(589\) −318.941 −0.541496
\(590\) −41.8234 72.4402i −0.0708871 0.122780i
\(591\) 0 0
\(592\) 55.9411 96.8929i 0.0944951 0.163670i
\(593\) 603.603 348.490i 1.01788 0.587673i 0.104391 0.994536i \(-0.466711\pi\)
0.913489 + 0.406863i \(0.133377\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −162.177 −0.272108
\(597\) 0 0
\(598\) −978.396 564.877i −1.63611 0.944611i
\(599\) 199.206 345.035i 0.332564 0.576018i −0.650450 0.759549i \(-0.725419\pi\)
0.983014 + 0.183531i \(0.0587528\pi\)
\(600\) 0 0
\(601\) 36.1691i 0.0601816i −0.999547 0.0300908i \(-0.990420\pi\)
0.999547 0.0300908i \(-0.00957964\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 51.2061 + 88.6915i 0.0847782 + 0.146840i
\(605\) −105.624 60.9823i −0.174586 0.100797i
\(606\) 0 0
\(607\) −27.3457 + 15.7880i −0.0450505 + 0.0260099i −0.522356 0.852727i \(-0.674947\pi\)
0.477306 + 0.878737i \(0.341613\pi\)
\(608\) 40.8729i 0.0672252i
\(609\) 0 0
\(610\) 2.41212 0.00395430
\(611\) −458.595 794.310i −0.750565 1.30002i
\(612\) 0 0
\(613\) 204.632 354.434i 0.333821 0.578195i −0.649436 0.760416i \(-0.724995\pi\)
0.983258 + 0.182220i \(0.0583285\pi\)
\(614\) −742.305 + 428.570i −1.20897 + 0.697997i
\(615\) 0 0
\(616\) 0 0
\(617\) −1227.38 −1.98927 −0.994636 0.103436i \(-0.967016\pi\)
−0.994636 + 0.103436i \(0.967016\pi\)
\(618\) 0 0
\(619\) −412.022 237.881i −0.665625 0.384299i 0.128792 0.991672i \(-0.458890\pi\)
−0.794417 + 0.607373i \(0.792223\pi\)
\(620\) −63.3381 + 109.705i −0.102158 + 0.176943i
\(621\) 0 0
\(622\) 287.478i 0.462184i
\(623\) 0 0
\(624\) 0 0
\(625\) −237.412 411.209i −0.379859 0.657935i
\(626\) −496.805 286.830i −0.793618 0.458195i
\(627\) 0 0
\(628\) 324.000 187.061i 0.515924 0.297869i
\(629\) 250.544i 0.398322i
\(630\) 0 0
\(631\) −54.9420 −0.0870713 −0.0435357 0.999052i \(-0.513862\pi\)
−0.0435357 + 0.999052i \(0.513862\pi\)
\(632\) −139.071 240.878i −0.220049 0.381136i
\(633\) 0 0
\(634\) −18.4264 + 31.9155i −0.0290637 + 0.0503399i
\(635\) −102.609 + 59.2415i −0.161589 + 0.0932937i
\(636\) 0 0
\(637\) 0 0
\(638\) −288.000 −0.451411
\(639\) 0 0
\(640\) 14.0589 + 8.11689i 0.0219670 + 0.0126826i
\(641\) −114.551 + 198.409i −0.178707 + 0.309530i −0.941438 0.337186i \(-0.890525\pi\)
0.762731 + 0.646716i \(0.223858\pi\)
\(642\) 0 0
\(643\) 854.640i 1.32914i 0.747224 + 0.664572i \(0.231386\pi\)
−0.747224 + 0.664572i \(0.768614\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 45.7645 + 79.2664i 0.0708429 + 0.122703i
\(647\) 868.632 + 501.505i 1.34255 + 0.775124i 0.987182 0.159601i \(-0.0510207\pi\)
0.355372 + 0.934725i \(0.384354\pi\)
\(648\) 0 0
\(649\) −214.191 + 123.663i −0.330032 + 0.190544i
\(650\) 691.957i 1.06455i
\(651\) 0 0
\(652\) 167.882 0.257488
\(653\) 635.382 + 1100.51i 0.973020 + 1.68532i 0.686321 + 0.727299i \(0.259224\pi\)
0.286698 + 0.958021i \(0.407442\pi\)
\(654\) 0 0
\(655\) 43.4558 75.2677i 0.0663448 0.114913i
\(656\) −189.941 + 109.663i −0.289544 + 0.167169i
\(657\) 0 0
\(658\) 0 0
\(659\) 783.308 1.18863 0.594315 0.804232i \(-0.297423\pi\)
0.594315 + 0.804232i \(0.297423\pi\)
\(660\) 0 0
\(661\) −72.5589 41.8919i −0.109771 0.0633765i 0.444109 0.895973i \(-0.353520\pi\)
−0.553881 + 0.832596i \(0.686854\pi\)
\(662\) 76.8148 133.047i 0.116034 0.200977i
\(663\) 0 0
\(664\) 312.262i 0.470273i
\(665\) 0 0
\(666\) 0 0
\(667\) −635.647 1100.97i −0.952994 1.65063i
\(668\) 221.044 + 127.620i 0.330904 + 0.191047i
\(669\) 0 0
\(670\) −7.72706 + 4.46122i −0.0115329 + 0.00665853i
\(671\) 7.13215i 0.0106291i
\(672\) 0 0
\(673\) 415.676 0.617647 0.308823 0.951119i \(-0.400065\pi\)
0.308823 + 0.951119i \(0.400065\pi\)
\(674\) −312.354 541.013i −0.463433 0.802690i
\(675\) 0 0
\(676\) 285.882 495.163i 0.422903 0.732489i
\(677\) 685.279 395.646i 1.01223 0.584411i 0.100386 0.994949i \(-0.467992\pi\)
0.911844 + 0.410538i \(0.134659\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 36.3532 0.0534607
\(681\) 0 0
\(682\) 324.375 + 187.278i 0.475623 + 0.274601i
\(683\) −164.080 + 284.195i −0.240235 + 0.416099i −0.960781 0.277308i \(-0.910558\pi\)
0.720546 + 0.693407i \(0.243891\pi\)
\(684\) 0 0
\(685\) 96.1791i 0.140407i
\(686\) 0 0
\(687\) 0 0
\(688\) 2.97056 + 5.14517i 0.00431768 + 0.00747844i
\(689\) −1578.42 911.300i −2.29088 1.32264i
\(690\) 0 0
\(691\) −875.182 + 505.287i −1.26654 + 0.731240i −0.974333 0.225113i \(-0.927725\pi\)
−0.292212 + 0.956353i \(0.594391\pi\)
\(692\) 285.941i 0.413210i
\(693\) 0 0
\(694\) −48.3532 −0.0696733
\(695\) 65.6833 + 113.767i 0.0945084 + 0.163693i
\(696\) 0 0
\(697\) −245.574 + 425.346i −0.352329 + 0.610252i
\(698\) −271.632 + 156.827i −0.389158 + 0.224681i
\(699\) 0 0
\(700\) 0 0
\(701\) 0.103464 0.000147594 7.37972e−5 1.00000i \(-0.499977\pi\)
7.37972e−5 1.00000i \(0.499977\pi\)
\(702\) 0 0
\(703\) 175.022 + 101.049i 0.248964 + 0.143740i
\(704\) 24.0000 41.5692i 0.0340909 0.0590472i
\(705\) 0 0
\(706\) 632.700i 0.896175i
\(707\) 0 0
\(708\) 0 0
\(709\) −602.588 1043.71i −0.849912 1.47209i −0.881286 0.472584i \(-0.843321\pi\)
0.0313734 0.999508i \(-0.490012\pi\)
\(710\) −241.456 139.405i −0.340079 0.196345i
\(711\) 0 0
\(712\) −50.9117 + 29.3939i −0.0715052 + 0.0412835i
\(713\) 1653.37i 2.31889i
\(714\) 0 0
\(715\) −183.618 −0.256809
\(716\) 169.279 + 293.200i 0.236423 + 0.409498i
\(717\) 0 0
\(718\) 206.309 357.337i 0.287338 0.497684i
\(719\) 850.925 491.282i 1.18348 0.683285i 0.226666 0.973973i \(-0.427217\pi\)
0.956818 + 0.290688i \(0.0938840\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 436.701 0.604848
\(723\) 0 0
\(724\) −363.676 209.969i −0.502315 0.290012i
\(725\) −389.324 + 674.329i −0.536998 + 0.930108i
\(726\) 0 0
\(727\) 630.440i 0.867181i 0.901110 + 0.433590i \(0.142753\pi\)
−0.901110 + 0.433590i \(0.857247\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −80.0803 138.703i −0.109699 0.190004i
\(731\) 11.5219 + 6.65215i 0.0157618 + 0.00910007i
\(732\) 0 0
\(733\) −258.486 + 149.237i −0.352641 + 0.203597i −0.665848 0.746088i \(-0.731930\pi\)
0.313207 + 0.949685i \(0.398597\pi\)
\(734\) 593.053i 0.807974i
\(735\) 0 0
\(736\) 211.882 0.287883
\(737\) 13.1909 + 22.8473i 0.0178981 + 0.0310004i
\(738\) 0 0
\(739\) −172.684 + 299.097i −0.233672 + 0.404732i −0.958886 0.283792i \(-0.908408\pi\)
0.725214 + 0.688524i \(0.241741\pi\)
\(740\) 69.5147 40.1343i 0.0939388 0.0542356i
\(741\) 0 0
\(742\) 0 0
\(743\) −683.616 −0.920076 −0.460038 0.887899i \(-0.652164\pi\)
−0.460038 + 0.887899i \(0.652164\pi\)
\(744\) 0 0
\(745\) −100.764 58.1759i −0.135253 0.0780885i
\(746\) −22.1903 + 38.4347i −0.0297457 + 0.0515211i
\(747\) 0 0
\(748\) 107.489i 0.143702i
\(749\) 0 0
\(750\) 0 0
\(751\) 289.169 + 500.855i 0.385045 + 0.666918i 0.991775 0.127990i \(-0.0408525\pi\)
−0.606730 + 0.794908i \(0.707519\pi\)
\(752\) 148.971 + 86.0082i 0.198099 + 0.114373i
\(753\) 0 0
\(754\) 886.587 511.871i 1.17584 0.678874i
\(755\) 73.4744i 0.0973171i
\(756\) 0 0
\(757\) 1204.82 1.59158 0.795788 0.605576i \(-0.207057\pi\)
0.795788 + 0.605576i \(0.207057\pi\)
\(758\) −146.215 253.251i −0.192895 0.334105i
\(759\) 0 0
\(760\) −14.6619 + 25.3952i −0.0192920 + 0.0334147i
\(761\) −202.669 + 117.011i −0.266319 + 0.153760i −0.627214 0.778847i \(-0.715805\pi\)
0.360894 + 0.932607i \(0.382471\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −133.206 −0.174353
\(765\) 0 0
\(766\) 610.617 + 352.540i 0.797151 + 0.460235i
\(767\) 439.581 761.376i 0.573117 0.992668i
\(768\) 0 0
\(769\) 1290.16i 1.67771i −0.544358 0.838853i \(-0.683226\pi\)
0.544358 0.838853i \(-0.316774\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 9.79394 + 16.9636i 0.0126864 + 0.0219736i
\(773\) 345.646 + 199.559i 0.447149 + 0.258161i 0.706625 0.707588i \(-0.250217\pi\)
−0.259477 + 0.965749i \(0.583550\pi\)
\(774\) 0 0
\(775\) 876.992 506.331i 1.13160 0.653331i
\(776\) 31.0749i 0.0400450i
\(777\) 0 0
\(778\) 917.013 1.17868
\(779\) −198.088 343.099i −0.254285 0.440435i
\(780\) 0 0
\(781\) −412.191 + 713.936i −0.527773 + 0.914130i
\(782\) 410.912 237.240i 0.525463 0.303376i
\(783\) 0 0
\(784\) 0 0
\(785\) 268.410 0.341924
\(786\) 0 0
\(787\) 1348.16 + 778.361i 1.71304 + 0.989023i 0.930401 + 0.366544i \(0.119459\pi\)
0.782637 + 0.622478i \(0.213874\pi\)
\(788\) −267.161 + 462.737i −0.339037 + 0.587230i
\(789\) 0 0
\(790\) 199.550i 0.252595i
\(791\) 0