Properties

Label 3330.2.d.p.1999.1
Level $3330$
Weight $2$
Character 3330.1999
Analytic conductor $26.590$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3330.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(26.5901838731\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \(x^{10} - 2 x^{9} + 2 x^{8} - 4 x^{7} + 51 x^{6} - 124 x^{5} + 154 x^{4} - 46 x^{3} + x^{2} + 4 x + 8\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 370)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1999.1
Root \(1.24331 + 1.24331i\) of defining polynomial
Character \(\chi\) \(=\) 3330.1999
Dual form 3330.2.d.p.1999.6

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000 q^{4} +(-2.07757 + 0.826871i) q^{5} +4.67211i q^{7} +1.00000i q^{8} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000 q^{4} +(-2.07757 + 0.826871i) q^{5} +4.67211i q^{7} +1.00000i q^{8} +(0.826871 + 2.07757i) q^{10} -0.0451320 q^{11} -5.26514i q^{13} +4.67211 q^{14} +1.00000 q^{16} -3.60861i q^{17} +6.22000 q^{19} +(2.07757 - 0.826871i) q^{20} +0.0451320i q^{22} -2.20164i q^{23} +(3.63257 - 3.43576i) q^{25} -5.26514 q^{26} -4.67211i q^{28} -4.20386 q^{29} -3.01051 q^{31} -1.00000i q^{32} -3.60861 q^{34} +(-3.86323 - 9.70662i) q^{35} +1.00000i q^{37} -6.22000i q^{38} +(-0.826871 - 2.07757i) q^{40} +7.38299 q^{41} +5.54789i q^{43} +0.0451320 q^{44} -2.20164 q^{46} +4.28072i q^{47} -14.8286 q^{49} +(-3.43576 - 3.63257i) q^{50} +5.26514i q^{52} +6.10215i q^{53} +(0.0937647 - 0.0373183i) q^{55} -4.67211 q^{56} +4.20386i q^{58} +13.5275 q^{59} -4.27299 q^{61} +3.01051i q^{62} -1.00000 q^{64} +(4.35359 + 10.9387i) q^{65} +12.3751i q^{67} +3.60861i q^{68} +(-9.70662 + 3.86323i) q^{70} +4.49354 q^{71} -7.03811i q^{73} +1.00000 q^{74} -6.22000 q^{76} -0.210861i q^{77} +8.72499 q^{79} +(-2.07757 + 0.826871i) q^{80} -7.38299i q^{82} -0.880231i q^{83} +(2.98386 + 7.49713i) q^{85} +5.54789 q^{86} -0.0451320i q^{88} +9.97602 q^{89} +24.5993 q^{91} +2.20164i q^{92} +4.28072 q^{94} +(-12.9225 + 5.14314i) q^{95} +0.240408i q^{97} +14.8286i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 10q^{4} - 6q^{5} + O(q^{10}) \) \( 10q - 10q^{4} - 6q^{5} + 2q^{10} - 6q^{11} - 2q^{14} + 10q^{16} - 8q^{19} + 6q^{20} + 4q^{25} + 12q^{26} + 22q^{29} + 46q^{31} - 18q^{34} - 32q^{35} - 2q^{40} + 14q^{41} + 6q^{44} + 12q^{46} - 60q^{49} - 8q^{50} + 42q^{55} + 2q^{56} + 40q^{59} - 18q^{61} - 10q^{64} - 4q^{65} - 6q^{70} - 12q^{71} + 10q^{74} + 8q^{76} - 40q^{79} - 6q^{80} + 36q^{85} + 34q^{86} + 24q^{89} + 32q^{91} - 24q^{94} - 12q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3330\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) −2.07757 + 0.826871i −0.929116 + 0.369788i
\(6\) 0 0
\(7\) 4.67211i 1.76589i 0.469475 + 0.882946i \(0.344443\pi\)
−0.469475 + 0.882946i \(0.655557\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0.826871 + 2.07757i 0.261480 + 0.656984i
\(11\) −0.0451320 −0.0136078 −0.00680390 0.999977i \(-0.502166\pi\)
−0.00680390 + 0.999977i \(0.502166\pi\)
\(12\) 0 0
\(13\) 5.26514i 1.46029i −0.683294 0.730143i \(-0.739453\pi\)
0.683294 0.730143i \(-0.260547\pi\)
\(14\) 4.67211 1.24867
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 3.60861i 0.875217i −0.899166 0.437608i \(-0.855826\pi\)
0.899166 0.437608i \(-0.144174\pi\)
\(18\) 0 0
\(19\) 6.22000 1.42697 0.713483 0.700672i \(-0.247116\pi\)
0.713483 + 0.700672i \(0.247116\pi\)
\(20\) 2.07757 0.826871i 0.464558 0.184894i
\(21\) 0 0
\(22\) 0.0451320i 0.00962217i
\(23\) 2.20164i 0.459073i −0.973300 0.229536i \(-0.926279\pi\)
0.973300 0.229536i \(-0.0737210\pi\)
\(24\) 0 0
\(25\) 3.63257 3.43576i 0.726514 0.687152i
\(26\) −5.26514 −1.03258
\(27\) 0 0
\(28\) 4.67211i 0.882946i
\(29\) −4.20386 −0.780637 −0.390319 0.920680i \(-0.627635\pi\)
−0.390319 + 0.920680i \(0.627635\pi\)
\(30\) 0 0
\(31\) −3.01051 −0.540704 −0.270352 0.962762i \(-0.587140\pi\)
−0.270352 + 0.962762i \(0.587140\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) −3.60861 −0.618872
\(35\) −3.86323 9.70662i −0.653006 1.64072i
\(36\) 0 0
\(37\) 1.00000i 0.164399i
\(38\) 6.22000i 1.00902i
\(39\) 0 0
\(40\) −0.826871 2.07757i −0.130740 0.328492i
\(41\) 7.38299 1.15303 0.576515 0.817087i \(-0.304412\pi\)
0.576515 + 0.817087i \(0.304412\pi\)
\(42\) 0 0
\(43\) 5.54789i 0.846046i 0.906119 + 0.423023i \(0.139031\pi\)
−0.906119 + 0.423023i \(0.860969\pi\)
\(44\) 0.0451320 0.00680390
\(45\) 0 0
\(46\) −2.20164 −0.324613
\(47\) 4.28072i 0.624407i 0.950015 + 0.312204i \(0.101067\pi\)
−0.950015 + 0.312204i \(0.898933\pi\)
\(48\) 0 0
\(49\) −14.8286 −2.11837
\(50\) −3.43576 3.63257i −0.485890 0.513723i
\(51\) 0 0
\(52\) 5.26514i 0.730143i
\(53\) 6.10215i 0.838194i 0.907941 + 0.419097i \(0.137653\pi\)
−0.907941 + 0.419097i \(0.862347\pi\)
\(54\) 0 0
\(55\) 0.0937647 0.0373183i 0.0126432 0.00503200i
\(56\) −4.67211 −0.624337
\(57\) 0 0
\(58\) 4.20386i 0.551994i
\(59\) 13.5275 1.76113 0.880565 0.473926i \(-0.157164\pi\)
0.880565 + 0.473926i \(0.157164\pi\)
\(60\) 0 0
\(61\) −4.27299 −0.547100 −0.273550 0.961858i \(-0.588198\pi\)
−0.273550 + 0.961858i \(0.588198\pi\)
\(62\) 3.01051i 0.382335i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 4.35359 + 10.9387i 0.539996 + 1.35678i
\(66\) 0 0
\(67\) 12.3751i 1.51186i 0.654650 + 0.755932i \(0.272816\pi\)
−0.654650 + 0.755932i \(0.727184\pi\)
\(68\) 3.60861i 0.437608i
\(69\) 0 0
\(70\) −9.70662 + 3.86323i −1.16016 + 0.461745i
\(71\) 4.49354 0.533285 0.266642 0.963796i \(-0.414086\pi\)
0.266642 + 0.963796i \(0.414086\pi\)
\(72\) 0 0
\(73\) 7.03811i 0.823748i −0.911241 0.411874i \(-0.864874\pi\)
0.911241 0.411874i \(-0.135126\pi\)
\(74\) 1.00000 0.116248
\(75\) 0 0
\(76\) −6.22000 −0.713483
\(77\) 0.210861i 0.0240299i
\(78\) 0 0
\(79\) 8.72499 0.981638 0.490819 0.871262i \(-0.336698\pi\)
0.490819 + 0.871262i \(0.336698\pi\)
\(80\) −2.07757 + 0.826871i −0.232279 + 0.0924470i
\(81\) 0 0
\(82\) 7.38299i 0.815315i
\(83\) 0.880231i 0.0966179i −0.998832 0.0483090i \(-0.984617\pi\)
0.998832 0.0483090i \(-0.0153832\pi\)
\(84\) 0 0
\(85\) 2.98386 + 7.49713i 0.323645 + 0.813178i
\(86\) 5.54789 0.598245
\(87\) 0 0
\(88\) 0.0451320i 0.00481108i
\(89\) 9.97602 1.05746 0.528728 0.848791i \(-0.322669\pi\)
0.528728 + 0.848791i \(0.322669\pi\)
\(90\) 0 0
\(91\) 24.5993 2.57871
\(92\) 2.20164i 0.229536i
\(93\) 0 0
\(94\) 4.28072 0.441523
\(95\) −12.9225 + 5.14314i −1.32582 + 0.527675i
\(96\) 0 0
\(97\) 0.240408i 0.0244097i 0.999926 + 0.0122049i \(0.00388502\pi\)
−0.999926 + 0.0122049i \(0.996115\pi\)
\(98\) 14.8286i 1.49792i
\(99\) 0 0
\(100\) −3.63257 + 3.43576i −0.363257 + 0.343576i
\(101\) 5.61775 0.558987 0.279494 0.960148i \(-0.409833\pi\)
0.279494 + 0.960148i \(0.409833\pi\)
\(102\) 0 0
\(103\) 12.5663i 1.23819i 0.785316 + 0.619095i \(0.212501\pi\)
−0.785316 + 0.619095i \(0.787499\pi\)
\(104\) 5.26514 0.516289
\(105\) 0 0
\(106\) 6.10215 0.592693
\(107\) 17.9395i 1.73427i 0.498070 + 0.867137i \(0.334042\pi\)
−0.498070 + 0.867137i \(0.665958\pi\)
\(108\) 0 0
\(109\) −3.09936 −0.296865 −0.148433 0.988923i \(-0.547423\pi\)
−0.148433 + 0.988923i \(0.547423\pi\)
\(110\) −0.0373183 0.0937647i −0.00355816 0.00894011i
\(111\) 0 0
\(112\) 4.67211i 0.441473i
\(113\) 4.36184i 0.410328i 0.978728 + 0.205164i \(0.0657727\pi\)
−0.978728 + 0.205164i \(0.934227\pi\)
\(114\) 0 0
\(115\) 1.82047 + 4.57405i 0.169760 + 0.426532i
\(116\) 4.20386 0.390319
\(117\) 0 0
\(118\) 13.5275i 1.24531i
\(119\) 16.8598 1.54554
\(120\) 0 0
\(121\) −10.9980 −0.999815
\(122\) 4.27299i 0.386858i
\(123\) 0 0
\(124\) 3.01051 0.270352
\(125\) −4.70597 + 10.1417i −0.420915 + 0.907100i
\(126\) 0 0
\(127\) 17.6572i 1.56683i 0.621502 + 0.783413i \(0.286523\pi\)
−0.621502 + 0.783413i \(0.713477\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) 10.9387 4.35359i 0.959385 0.381835i
\(131\) 10.3103 0.900812 0.450406 0.892824i \(-0.351279\pi\)
0.450406 + 0.892824i \(0.351279\pi\)
\(132\) 0 0
\(133\) 29.0605i 2.51987i
\(134\) 12.3751 1.06905
\(135\) 0 0
\(136\) 3.60861 0.309436
\(137\) 3.21863i 0.274986i −0.990503 0.137493i \(-0.956095\pi\)
0.990503 0.137493i \(-0.0439045\pi\)
\(138\) 0 0
\(139\) −20.9400 −1.77611 −0.888055 0.459737i \(-0.847944\pi\)
−0.888055 + 0.459737i \(0.847944\pi\)
\(140\) 3.86323 + 9.70662i 0.326503 + 0.820359i
\(141\) 0 0
\(142\) 4.49354i 0.377089i
\(143\) 0.237626i 0.0198713i
\(144\) 0 0
\(145\) 8.73380 3.47605i 0.725303 0.288670i
\(146\) −7.03811 −0.582478
\(147\) 0 0
\(148\) 1.00000i 0.0821995i
\(149\) −21.9832 −1.80093 −0.900467 0.434924i \(-0.856775\pi\)
−0.900467 + 0.434924i \(0.856775\pi\)
\(150\) 0 0
\(151\) 14.1877 1.15458 0.577290 0.816539i \(-0.304110\pi\)
0.577290 + 0.816539i \(0.304110\pi\)
\(152\) 6.22000i 0.504509i
\(153\) 0 0
\(154\) −0.210861 −0.0169917
\(155\) 6.25454 2.48931i 0.502377 0.199946i
\(156\) 0 0
\(157\) 19.9316i 1.59072i −0.606139 0.795359i \(-0.707283\pi\)
0.606139 0.795359i \(-0.292717\pi\)
\(158\) 8.72499i 0.694123i
\(159\) 0 0
\(160\) 0.826871 + 2.07757i 0.0653699 + 0.164246i
\(161\) 10.2863 0.810673
\(162\) 0 0
\(163\) 8.65087i 0.677588i −0.940861 0.338794i \(-0.889981\pi\)
0.940861 0.338794i \(-0.110019\pi\)
\(164\) −7.38299 −0.576515
\(165\) 0 0
\(166\) −0.880231 −0.0683192
\(167\) 11.9640i 0.925803i 0.886410 + 0.462901i \(0.153192\pi\)
−0.886410 + 0.462901i \(0.846808\pi\)
\(168\) 0 0
\(169\) −14.7216 −1.13243
\(170\) 7.49713 2.98386i 0.575004 0.228851i
\(171\) 0 0
\(172\) 5.54789i 0.423023i
\(173\) 5.33508i 0.405619i −0.979218 0.202809i \(-0.934993\pi\)
0.979218 0.202809i \(-0.0650071\pi\)
\(174\) 0 0
\(175\) 16.0523 + 16.9718i 1.21344 + 1.28294i
\(176\) −0.0451320 −0.00340195
\(177\) 0 0
\(178\) 9.97602i 0.747734i
\(179\) −5.27905 −0.394575 −0.197288 0.980346i \(-0.563213\pi\)
−0.197288 + 0.980346i \(0.563213\pi\)
\(180\) 0 0
\(181\) 17.7448 1.31896 0.659478 0.751723i \(-0.270777\pi\)
0.659478 + 0.751723i \(0.270777\pi\)
\(182\) 24.5993i 1.82342i
\(183\) 0 0
\(184\) 2.20164 0.162307
\(185\) −0.826871 2.07757i −0.0607928 0.152746i
\(186\) 0 0
\(187\) 0.162864i 0.0119098i
\(188\) 4.28072i 0.312204i
\(189\) 0 0
\(190\) 5.14314 + 12.9225i 0.373123 + 0.937495i
\(191\) 3.11649 0.225501 0.112751 0.993623i \(-0.464034\pi\)
0.112751 + 0.993623i \(0.464034\pi\)
\(192\) 0 0
\(193\) 8.78278i 0.632198i 0.948726 + 0.316099i \(0.102373\pi\)
−0.948726 + 0.316099i \(0.897627\pi\)
\(194\) 0.240408 0.0172603
\(195\) 0 0
\(196\) 14.8286 1.05919
\(197\) 7.00278i 0.498928i −0.968384 0.249464i \(-0.919746\pi\)
0.968384 0.249464i \(-0.0802544\pi\)
\(198\) 0 0
\(199\) −17.3202 −1.22780 −0.613900 0.789384i \(-0.710400\pi\)
−0.613900 + 0.789384i \(0.710400\pi\)
\(200\) 3.43576 + 3.63257i 0.242945 + 0.256861i
\(201\) 0 0
\(202\) 5.61775i 0.395264i
\(203\) 19.6409i 1.37852i
\(204\) 0 0
\(205\) −15.3387 + 6.10478i −1.07130 + 0.426377i
\(206\) 12.5663 0.875533
\(207\) 0 0
\(208\) 5.26514i 0.365071i
\(209\) −0.280721 −0.0194179
\(210\) 0 0
\(211\) 6.77438 0.466368 0.233184 0.972433i \(-0.425086\pi\)
0.233184 + 0.972433i \(0.425086\pi\)
\(212\) 6.10215i 0.419097i
\(213\) 0 0
\(214\) 17.9395 1.22632
\(215\) −4.58739 11.5261i −0.312858 0.786075i
\(216\) 0 0
\(217\) 14.0654i 0.954825i
\(218\) 3.09936i 0.209915i
\(219\) 0 0
\(220\) −0.0937647 + 0.0373183i −0.00632161 + 0.00251600i
\(221\) −18.9998 −1.27807
\(222\) 0 0
\(223\) 10.2559i 0.686784i 0.939192 + 0.343392i \(0.111576\pi\)
−0.939192 + 0.343392i \(0.888424\pi\)
\(224\) 4.67211 0.312168
\(225\) 0 0
\(226\) 4.36184 0.290145
\(227\) 11.2744i 0.748306i 0.927367 + 0.374153i \(0.122066\pi\)
−0.927367 + 0.374153i \(0.877934\pi\)
\(228\) 0 0
\(229\) 9.40494 0.621496 0.310748 0.950492i \(-0.399421\pi\)
0.310748 + 0.950492i \(0.399421\pi\)
\(230\) 4.57405 1.82047i 0.301604 0.120038i
\(231\) 0 0
\(232\) 4.20386i 0.275997i
\(233\) 3.22867i 0.211517i −0.994392 0.105759i \(-0.966273\pi\)
0.994392 0.105759i \(-0.0337271\pi\)
\(234\) 0 0
\(235\) −3.53961 8.89348i −0.230898 0.580147i
\(236\) −13.5275 −0.880565
\(237\) 0 0
\(238\) 16.8598i 1.09286i
\(239\) −17.8612 −1.15534 −0.577672 0.816269i \(-0.696039\pi\)
−0.577672 + 0.816269i \(0.696039\pi\)
\(240\) 0 0
\(241\) 26.6840 1.71887 0.859434 0.511248i \(-0.170816\pi\)
0.859434 + 0.511248i \(0.170816\pi\)
\(242\) 10.9980i 0.706976i
\(243\) 0 0
\(244\) 4.27299 0.273550
\(245\) 30.8074 12.2614i 1.96821 0.783349i
\(246\) 0 0
\(247\) 32.7492i 2.08378i
\(248\) 3.01051i 0.191168i
\(249\) 0 0
\(250\) 10.1417 + 4.70597i 0.641417 + 0.297632i
\(251\) 30.1552 1.90338 0.951690 0.307060i \(-0.0993453\pi\)
0.951690 + 0.307060i \(0.0993453\pi\)
\(252\) 0 0
\(253\) 0.0993641i 0.00624697i
\(254\) 17.6572 1.10791
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 3.15376i 0.196726i 0.995151 + 0.0983632i \(0.0313607\pi\)
−0.995151 + 0.0983632i \(0.968639\pi\)
\(258\) 0 0
\(259\) −4.67211 −0.290311
\(260\) −4.35359 10.9387i −0.269998 0.678388i
\(261\) 0 0
\(262\) 10.3103i 0.636970i
\(263\) 14.0332i 0.865322i 0.901557 + 0.432661i \(0.142425\pi\)
−0.901557 + 0.432661i \(0.857575\pi\)
\(264\) 0 0
\(265\) −5.04569 12.6776i −0.309954 0.778780i
\(266\) 29.0605 1.78182
\(267\) 0 0
\(268\) 12.3751i 0.755932i
\(269\) −30.1257 −1.83679 −0.918397 0.395660i \(-0.870516\pi\)
−0.918397 + 0.395660i \(0.870516\pi\)
\(270\) 0 0
\(271\) 14.8802 0.903910 0.451955 0.892041i \(-0.350727\pi\)
0.451955 + 0.892041i \(0.350727\pi\)
\(272\) 3.60861i 0.218804i
\(273\) 0 0
\(274\) −3.21863 −0.194445
\(275\) −0.163945 + 0.155063i −0.00988625 + 0.00935063i
\(276\) 0 0
\(277\) 0.147278i 0.00884908i 0.999990 + 0.00442454i \(0.00140838\pi\)
−0.999990 + 0.00442454i \(0.998592\pi\)
\(278\) 20.9400i 1.25590i
\(279\) 0 0
\(280\) 9.70662 3.86323i 0.580082 0.230872i
\(281\) 25.5247 1.52268 0.761339 0.648354i \(-0.224542\pi\)
0.761339 + 0.648354i \(0.224542\pi\)
\(282\) 0 0
\(283\) 0.0562691i 0.00334485i −0.999999 0.00167242i \(-0.999468\pi\)
0.999999 0.00167242i \(-0.000532349\pi\)
\(284\) −4.49354 −0.266642
\(285\) 0 0
\(286\) 0.237626 0.0140511
\(287\) 34.4942i 2.03613i
\(288\) 0 0
\(289\) 3.97793 0.233996
\(290\) −3.47605 8.73380i −0.204121 0.512866i
\(291\) 0 0
\(292\) 7.03811i 0.411874i
\(293\) 13.7033i 0.800557i 0.916394 + 0.400278i \(0.131087\pi\)
−0.916394 + 0.400278i \(0.868913\pi\)
\(294\) 0 0
\(295\) −28.1043 + 11.1855i −1.63629 + 0.651245i
\(296\) −1.00000 −0.0581238
\(297\) 0 0
\(298\) 21.9832i 1.27345i
\(299\) −11.5919 −0.670377
\(300\) 0 0
\(301\) −25.9204 −1.49403
\(302\) 14.1877i 0.816411i
\(303\) 0 0
\(304\) 6.22000 0.356742
\(305\) 8.87742 3.53321i 0.508320 0.202311i
\(306\) 0 0
\(307\) 17.5823i 1.00348i −0.865020 0.501738i \(-0.832694\pi\)
0.865020 0.501738i \(-0.167306\pi\)
\(308\) 0.210861i 0.0120149i
\(309\) 0 0
\(310\) −2.48931 6.25454i −0.141383 0.355234i
\(311\) −0.353133 −0.0200244 −0.0100122 0.999950i \(-0.503187\pi\)
−0.0100122 + 0.999950i \(0.503187\pi\)
\(312\) 0 0
\(313\) 18.8717i 1.06669i 0.845897 + 0.533346i \(0.179066\pi\)
−0.845897 + 0.533346i \(0.820934\pi\)
\(314\) −19.9316 −1.12481
\(315\) 0 0
\(316\) −8.72499 −0.490819
\(317\) 15.1979i 0.853601i −0.904346 0.426800i \(-0.859641\pi\)
0.904346 0.426800i \(-0.140359\pi\)
\(318\) 0 0
\(319\) 0.189728 0.0106228
\(320\) 2.07757 0.826871i 0.116140 0.0462235i
\(321\) 0 0
\(322\) 10.2863i 0.573232i
\(323\) 22.4456i 1.24890i
\(324\) 0 0
\(325\) −18.0897 19.1260i −1.00344 1.06092i
\(326\) −8.65087 −0.479127
\(327\) 0 0
\(328\) 7.38299i 0.407658i
\(329\) −20.0000 −1.10264
\(330\) 0 0
\(331\) −23.0210 −1.26535 −0.632674 0.774418i \(-0.718043\pi\)
−0.632674 + 0.774418i \(0.718043\pi\)
\(332\) 0.880231i 0.0483090i
\(333\) 0 0
\(334\) 11.9640 0.654641
\(335\) −10.2326 25.7102i −0.559069 1.40470i
\(336\) 0 0
\(337\) 34.0776i 1.85633i 0.372173 + 0.928163i \(0.378613\pi\)
−0.372173 + 0.928163i \(0.621387\pi\)
\(338\) 14.7216i 0.800752i
\(339\) 0 0
\(340\) −2.98386 7.49713i −0.161822 0.406589i
\(341\) 0.135870 0.00735779
\(342\) 0 0
\(343\) 36.5761i 1.97493i
\(344\) −5.54789 −0.299122
\(345\) 0 0
\(346\) −5.33508 −0.286816
\(347\) 13.8449i 0.743236i −0.928386 0.371618i \(-0.878803\pi\)
0.928386 0.371618i \(-0.121197\pi\)
\(348\) 0 0
\(349\) −11.3765 −0.608970 −0.304485 0.952517i \(-0.598484\pi\)
−0.304485 + 0.952517i \(0.598484\pi\)
\(350\) 16.9718 16.0523i 0.907179 0.858029i
\(351\) 0 0
\(352\) 0.0451320i 0.00240554i
\(353\) 19.2631i 1.02527i 0.858606 + 0.512636i \(0.171331\pi\)
−0.858606 + 0.512636i \(0.828669\pi\)
\(354\) 0 0
\(355\) −9.33562 + 3.71558i −0.495483 + 0.197202i
\(356\) −9.97602 −0.528728
\(357\) 0 0
\(358\) 5.27905i 0.279007i
\(359\) 14.6645 0.773961 0.386980 0.922088i \(-0.373518\pi\)
0.386980 + 0.922088i \(0.373518\pi\)
\(360\) 0 0
\(361\) 19.6884 1.03623
\(362\) 17.7448i 0.932643i
\(363\) 0 0
\(364\) −24.5993 −1.28935
\(365\) 5.81961 + 14.6221i 0.304612 + 0.765357i
\(366\) 0 0
\(367\) 0.868349i 0.0453275i 0.999743 + 0.0226637i \(0.00721471\pi\)
−0.999743 + 0.0226637i \(0.992785\pi\)
\(368\) 2.20164i 0.114768i
\(369\) 0 0
\(370\) −2.07757 + 0.826871i −0.108008 + 0.0429870i
\(371\) −28.5099 −1.48016
\(372\) 0 0
\(373\) 32.4555i 1.68048i −0.542214 0.840240i \(-0.682414\pi\)
0.542214 0.840240i \(-0.317586\pi\)
\(374\) 0.162864 0.00842148
\(375\) 0 0
\(376\) −4.28072 −0.220761
\(377\) 22.1339i 1.13995i
\(378\) 0 0
\(379\) 30.2511 1.55389 0.776947 0.629566i \(-0.216767\pi\)
0.776947 + 0.629566i \(0.216767\pi\)
\(380\) 12.9225 5.14314i 0.662909 0.263838i
\(381\) 0 0
\(382\) 3.11649i 0.159453i
\(383\) 14.4935i 0.740585i 0.928915 + 0.370293i \(0.120743\pi\)
−0.928915 + 0.370293i \(0.879257\pi\)
\(384\) 0 0
\(385\) 0.174355 + 0.438079i 0.00888597 + 0.0223266i
\(386\) 8.78278 0.447032
\(387\) 0 0
\(388\) 0.240408i 0.0122049i
\(389\) 36.9033 1.87107 0.935537 0.353229i \(-0.114916\pi\)
0.935537 + 0.353229i \(0.114916\pi\)
\(390\) 0 0
\(391\) −7.94485 −0.401788
\(392\) 14.8286i 0.748958i
\(393\) 0 0
\(394\) −7.00278 −0.352795
\(395\) −18.1267 + 7.21444i −0.912056 + 0.362998i
\(396\) 0 0
\(397\) 22.9365i 1.15115i 0.817749 + 0.575575i \(0.195222\pi\)
−0.817749 + 0.575575i \(0.804778\pi\)
\(398\) 17.3202i 0.868185i
\(399\) 0 0
\(400\) 3.63257 3.43576i 0.181628 0.171788i
\(401\) −27.4332 −1.36995 −0.684973 0.728568i \(-0.740186\pi\)
−0.684973 + 0.728568i \(0.740186\pi\)
\(402\) 0 0
\(403\) 15.8508i 0.789582i
\(404\) −5.61775 −0.279494
\(405\) 0 0
\(406\) −19.6409 −0.974761
\(407\) 0.0451320i 0.00223711i
\(408\) 0 0
\(409\) 21.3920 1.05777 0.528883 0.848695i \(-0.322611\pi\)
0.528883 + 0.848695i \(0.322611\pi\)
\(410\) 6.10478 + 15.3387i 0.301494 + 0.757522i
\(411\) 0 0
\(412\) 12.5663i 0.619095i
\(413\) 63.2019i 3.10996i
\(414\) 0 0
\(415\) 0.727838 + 1.82874i 0.0357282 + 0.0897693i
\(416\) −5.26514 −0.258144
\(417\) 0 0
\(418\) 0.280721i 0.0137305i
\(419\) 23.0891 1.12797 0.563987 0.825784i \(-0.309267\pi\)
0.563987 + 0.825784i \(0.309267\pi\)
\(420\) 0 0
\(421\) −1.83757 −0.0895576 −0.0447788 0.998997i \(-0.514258\pi\)
−0.0447788 + 0.998997i \(0.514258\pi\)
\(422\) 6.77438i 0.329772i
\(423\) 0 0
\(424\) −6.10215 −0.296346
\(425\) −12.3983 13.1085i −0.601407 0.635857i
\(426\) 0 0
\(427\) 19.9639i 0.966120i
\(428\) 17.9395i 0.867137i
\(429\) 0 0
\(430\) −11.5261 + 4.58739i −0.555839 + 0.221224i
\(431\) 15.9796 0.769710 0.384855 0.922977i \(-0.374251\pi\)
0.384855 + 0.922977i \(0.374251\pi\)
\(432\) 0 0
\(433\) 25.2525i 1.21356i 0.794870 + 0.606779i \(0.207539\pi\)
−0.794870 + 0.606779i \(0.792461\pi\)
\(434\) −14.0654 −0.675163
\(435\) 0 0
\(436\) 3.09936 0.148433
\(437\) 13.6942i 0.655082i
\(438\) 0 0
\(439\) 9.30792 0.444243 0.222121 0.975019i \(-0.428702\pi\)
0.222121 + 0.975019i \(0.428702\pi\)
\(440\) 0.0373183 + 0.0937647i 0.00177908 + 0.00447005i
\(441\) 0 0
\(442\) 18.9998i 0.903729i
\(443\) 9.52445i 0.452520i −0.974067 0.226260i \(-0.927350\pi\)
0.974067 0.226260i \(-0.0726500\pi\)
\(444\) 0 0
\(445\) −20.7258 + 8.24888i −0.982499 + 0.391035i
\(446\) 10.2559 0.485629
\(447\) 0 0
\(448\) 4.67211i 0.220736i
\(449\) 5.43278 0.256389 0.128194 0.991749i \(-0.459082\pi\)
0.128194 + 0.991749i \(0.459082\pi\)
\(450\) 0 0
\(451\) −0.333209 −0.0156902
\(452\) 4.36184i 0.205164i
\(453\) 0 0
\(454\) 11.2744 0.529132
\(455\) −51.1067 + 20.3404i −2.39592 + 0.953575i
\(456\) 0 0
\(457\) 7.54789i 0.353076i 0.984294 + 0.176538i \(0.0564898\pi\)
−0.984294 + 0.176538i \(0.943510\pi\)
\(458\) 9.40494i 0.439464i
\(459\) 0 0
\(460\) −1.82047 4.57405i −0.0848798 0.213266i
\(461\) 35.4323 1.65025 0.825124 0.564952i \(-0.191105\pi\)
0.825124 + 0.564952i \(0.191105\pi\)
\(462\) 0 0
\(463\) 20.9124i 0.971883i −0.873991 0.485942i \(-0.838477\pi\)
0.873991 0.485942i \(-0.161523\pi\)
\(464\) −4.20386 −0.195159
\(465\) 0 0
\(466\) −3.22867 −0.149565
\(467\) 6.62523i 0.306579i −0.988181 0.153289i \(-0.951013\pi\)
0.988181 0.153289i \(-0.0489867\pi\)
\(468\) 0 0
\(469\) −57.8180 −2.66979
\(470\) −8.89348 + 3.53961i −0.410226 + 0.163270i
\(471\) 0 0
\(472\) 13.5275i 0.622653i
\(473\) 0.250387i 0.0115128i
\(474\) 0 0
\(475\) 22.5946 21.3704i 1.03671 0.980543i
\(476\) −16.8598 −0.772769
\(477\) 0 0
\(478\) 17.8612i 0.816952i
\(479\) −29.4581 −1.34597 −0.672987 0.739655i \(-0.734989\pi\)
−0.672987 + 0.739655i \(0.734989\pi\)
\(480\) 0 0
\(481\) 5.26514 0.240070
\(482\) 26.6840i 1.21542i
\(483\) 0 0
\(484\) 10.9980 0.499907
\(485\) −0.198786 0.499463i −0.00902642 0.0226795i
\(486\) 0 0
\(487\) 8.80654i 0.399063i 0.979891 + 0.199531i \(0.0639419\pi\)
−0.979891 + 0.199531i \(0.936058\pi\)
\(488\) 4.27299i 0.193429i
\(489\) 0 0
\(490\) −12.2614 30.8074i −0.553912 1.39174i
\(491\) −5.14258 −0.232082 −0.116041 0.993244i \(-0.537020\pi\)
−0.116041 + 0.993244i \(0.537020\pi\)
\(492\) 0 0
\(493\) 15.1701i 0.683227i
\(494\) −32.7492 −1.47345
\(495\) 0 0
\(496\) −3.01051 −0.135176
\(497\) 20.9943i 0.941723i
\(498\) 0 0
\(499\) 12.9692 0.580579 0.290290 0.956939i \(-0.406248\pi\)
0.290290 + 0.956939i \(0.406248\pi\)
\(500\) 4.70597 10.1417i 0.210457 0.453550i
\(501\) 0 0
\(502\) 30.1552i 1.34589i
\(503\) 17.2091i 0.767314i 0.923476 + 0.383657i \(0.125336\pi\)
−0.923476 + 0.383657i \(0.874664\pi\)
\(504\) 0 0
\(505\) −11.6713 + 4.64516i −0.519364 + 0.206707i
\(506\) 0.0993641 0.00441727
\(507\) 0 0
\(508\) 17.6572i 0.783413i
\(509\) −12.1085 −0.536698 −0.268349 0.963322i \(-0.586478\pi\)
−0.268349 + 0.963322i \(0.586478\pi\)
\(510\) 0 0
\(511\) 32.8828 1.45465
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 3.15376 0.139107
\(515\) −10.3907 26.1072i −0.457868 1.15042i
\(516\) 0 0
\(517\) 0.193197i 0.00849681i
\(518\) 4.67211i 0.205281i
\(519\) 0 0
\(520\) −10.9387 + 4.35359i −0.479692 + 0.190918i
\(521\) 18.7936 0.823362 0.411681 0.911328i \(-0.364942\pi\)
0.411681 + 0.911328i \(0.364942\pi\)
\(522\) 0 0
\(523\) 42.9985i 1.88019i 0.340909 + 0.940096i \(0.389265\pi\)
−0.340909 + 0.940096i \(0.610735\pi\)
\(524\) −10.3103 −0.450406
\(525\) 0 0
\(526\) 14.0332 0.611875
\(527\) 10.8638i 0.473233i
\(528\) 0 0
\(529\) 18.1528 0.789252
\(530\) −12.6776 + 5.04569i −0.550680 + 0.219171i
\(531\) 0 0
\(532\) 29.0605i 1.25993i
\(533\) 38.8725i 1.68375i
\(534\) 0 0
\(535\) −14.8336 37.2704i −0.641314 1.61134i
\(536\) −12.3751 −0.534525
\(537\) 0 0
\(538\) 30.1257i 1.29881i
\(539\) 0.669244 0.0288264
\(540\) 0 0
\(541\) 30.1751 1.29733 0.648664 0.761075i \(-0.275328\pi\)
0.648664 + 0.761075i \(0.275328\pi\)
\(542\) 14.8802i 0.639161i
\(543\) 0 0
\(544\) −3.60861 −0.154718
\(545\) 6.43914 2.56278i 0.275822 0.109777i
\(546\) 0 0
\(547\) 31.6736i 1.35426i −0.735862 0.677132i \(-0.763223\pi\)
0.735862 0.677132i \(-0.236777\pi\)
\(548\) 3.21863i 0.137493i
\(549\) 0 0
\(550\) 0.155063 + 0.163945i 0.00661189 + 0.00699063i
\(551\) −26.1480 −1.11394
\(552\) 0 0
\(553\) 40.7641i 1.73347i
\(554\) 0.147278 0.00625724
\(555\) 0 0
\(556\) 20.9400 0.888055
\(557\) 0.708971i 0.0300401i 0.999887 + 0.0150200i \(0.00478120\pi\)
−0.999887 + 0.0150200i \(0.995219\pi\)
\(558\) 0 0
\(559\) 29.2104 1.23547
\(560\) −3.86323 9.70662i −0.163251 0.410180i
\(561\) 0 0
\(562\) 25.5247i 1.07670i
\(563\) 29.9399i 1.26182i −0.775857 0.630908i \(-0.782682\pi\)
0.775857 0.630908i \(-0.217318\pi\)
\(564\) 0 0
\(565\) −3.60668 9.06202i −0.151734 0.381242i
\(566\) −0.0562691 −0.00236517
\(567\) 0 0
\(568\) 4.49354i 0.188545i
\(569\) 21.1453 0.886456 0.443228 0.896409i \(-0.353833\pi\)
0.443228 + 0.896409i \(0.353833\pi\)
\(570\) 0 0
\(571\) −19.5326 −0.817416 −0.408708 0.912665i \(-0.634020\pi\)
−0.408708 + 0.912665i \(0.634020\pi\)
\(572\) 0.237626i 0.00993564i
\(573\) 0 0
\(574\) 34.4942 1.43976
\(575\) −7.56429 7.99759i −0.315453 0.333523i
\(576\) 0 0
\(577\) 1.08303i 0.0450873i 0.999746 + 0.0225436i \(0.00717647\pi\)
−0.999746 + 0.0225436i \(0.992824\pi\)
\(578\) 3.97793i 0.165460i
\(579\) 0 0
\(580\) −8.73380 + 3.47605i −0.362651 + 0.144335i
\(581\) 4.11254 0.170617
\(582\) 0 0
\(583\) 0.275402i 0.0114060i
\(584\) 7.03811 0.291239
\(585\) 0 0
\(586\) 13.7033 0.566079
\(587\) 1.16839i 0.0482244i −0.999709 0.0241122i \(-0.992324\pi\)
0.999709 0.0241122i \(-0.00767590\pi\)
\(588\) 0 0
\(589\) −18.7254 −0.771566
\(590\) 11.1855 + 28.1043i 0.460499 + 1.15703i
\(591\) 0 0
\(592\) 1.00000i 0.0410997i
\(593\) 6.01305i 0.246926i −0.992349 0.123463i \(-0.960600\pi\)
0.992349 0.123463i \(-0.0394001\pi\)
\(594\) 0 0
\(595\) −35.0274 + 13.9409i −1.43598 + 0.571521i
\(596\) 21.9832 0.900467
\(597\) 0 0
\(598\) 11.5919i 0.474028i
\(599\) −11.9208 −0.487072 −0.243536 0.969892i \(-0.578307\pi\)
−0.243536 + 0.969892i \(0.578307\pi\)
\(600\) 0 0
\(601\) 21.7772 0.888309 0.444155 0.895950i \(-0.353504\pi\)
0.444155 + 0.895950i \(0.353504\pi\)
\(602\) 25.9204i 1.05644i
\(603\) 0 0
\(604\) −14.1877 −0.577290
\(605\) 22.8490 9.09390i 0.928944 0.369720i
\(606\) 0 0
\(607\) 5.16486i 0.209635i 0.994491 + 0.104818i \(0.0334259\pi\)
−0.994491 + 0.104818i \(0.966574\pi\)
\(608\) 6.22000i 0.252254i
\(609\) 0 0
\(610\) −3.53321 8.87742i −0.143056 0.359436i
\(611\) 22.5386 0.911813
\(612\) 0 0
\(613\) 39.5817i 1.59869i 0.600873 + 0.799344i \(0.294820\pi\)
−0.600873 + 0.799344i \(0.705180\pi\)
\(614\) −17.5823 −0.709565
\(615\) 0 0
\(616\) 0.210861 0.00849585
\(617\) 44.9917i 1.81130i −0.424027 0.905650i \(-0.639384\pi\)
0.424027 0.905650i \(-0.360616\pi\)
\(618\) 0 0
\(619\) −30.0465 −1.20767 −0.603836 0.797108i \(-0.706362\pi\)
−0.603836 + 0.797108i \(0.706362\pi\)
\(620\) −6.25454 + 2.48931i −0.251188 + 0.0999729i
\(621\) 0 0
\(622\) 0.353133i 0.0141594i
\(623\) 46.6091i 1.86735i
\(624\) 0 0
\(625\) 1.39110 24.9613i 0.0556438 0.998451i
\(626\) 18.8717 0.754265
\(627\) 0 0
\(628\) 19.9316i 0.795359i
\(629\) 3.60861 0.143885
\(630\) 0 0
\(631\) 5.01448 0.199623 0.0998116 0.995006i \(-0.468176\pi\)
0.0998116 + 0.995006i \(0.468176\pi\)
\(632\) 8.72499i 0.347061i
\(633\) 0 0
\(634\) −15.1979 −0.603587
\(635\) −14.6003 36.6841i −0.579393 1.45576i
\(636\) 0 0
\(637\) 78.0747i 3.09343i
\(638\) 0.189728i 0.00751142i
\(639\) 0 0
\(640\) −0.826871 2.07757i −0.0326850 0.0821230i
\(641\) −18.9133 −0.747031 −0.373515 0.927624i \(-0.621848\pi\)
−0.373515 + 0.927624i \(0.621848\pi\)
\(642\) 0 0
\(643\) 22.9344i 0.904444i −0.891906 0.452222i \(-0.850632\pi\)
0.891906 0.452222i \(-0.149368\pi\)
\(644\) −10.2863 −0.405336
\(645\) 0 0
\(646\) −22.4456 −0.883109
\(647\) 10.4741i 0.411779i −0.978575 0.205889i \(-0.933991\pi\)
0.978575 0.205889i \(-0.0660087\pi\)
\(648\) 0 0
\(649\) −0.610522 −0.0239651
\(650\) −19.1260 + 18.0897i −0.750182 + 0.709538i
\(651\) 0 0
\(652\) 8.65087i 0.338794i
\(653\) 44.7251i 1.75023i −0.483916 0.875115i \(-0.660786\pi\)
0.483916 0.875115i \(-0.339214\pi\)
\(654\) 0 0
\(655\) −21.4203 + 8.52526i −0.836959 + 0.333110i
\(656\) 7.38299 0.288257
\(657\) 0 0
\(658\) 20.0000i 0.779681i
\(659\) 15.1056 0.588431 0.294215 0.955739i \(-0.404942\pi\)
0.294215 + 0.955739i \(0.404942\pi\)
\(660\) 0 0
\(661\) 34.9654 1.36000 0.679998 0.733214i \(-0.261981\pi\)
0.679998 + 0.733214i \(0.261981\pi\)
\(662\) 23.0210i 0.894736i
\(663\) 0 0
\(664\) 0.880231 0.0341596
\(665\) −24.0293 60.3752i −0.931817 2.34125i
\(666\) 0 0
\(667\) 9.25537i 0.358369i
\(668\) 11.9640i 0.462901i
\(669\) 0 0
\(670\) −25.7102 + 10.2326i −0.993271 + 0.395322i
\(671\) 0.192848 0.00744483
\(672\) 0 0
\(673\) 35.2496i 1.35877i −0.733782 0.679385i \(-0.762246\pi\)
0.733782 0.679385i \(-0.237754\pi\)
\(674\) 34.0776 1.31262
\(675\) 0 0
\(676\) 14.7216 0.566217
\(677\) 23.2835i 0.894858i 0.894320 + 0.447429i \(0.147660\pi\)
−0.894320 + 0.447429i \(0.852340\pi\)
\(678\) 0 0
\(679\) −1.12321 −0.0431049
\(680\) −7.49713 + 2.98386i −0.287502 + 0.114426i
\(681\) 0 0
\(682\) 0.135870i 0.00520274i
\(683\) 11.8131i 0.452017i −0.974125 0.226008i \(-0.927432\pi\)
0.974125 0.226008i \(-0.0725676\pi\)
\(684\) 0 0
\(685\) 2.66140 + 6.68693i 0.101687 + 0.255494i
\(686\) −36.5761 −1.39648
\(687\) 0 0
\(688\) 5.54789i 0.211511i
\(689\) 32.1286 1.22400
\(690\) 0 0
\(691\) 14.1858 0.539652 0.269826 0.962909i \(-0.413034\pi\)
0.269826 + 0.962909i \(0.413034\pi\)
\(692\) 5.33508i 0.202809i
\(693\) 0 0
\(694\) −13.8449 −0.525547
\(695\) 43.5043 17.3147i 1.65021 0.656784i
\(696\) 0 0
\(697\) 26.6423i 1.00915i
\(698\) 11.3765i 0.430607i
\(699\) 0 0
\(700\) −16.0523 16.9718i −0.606718 0.641472i
\(701\) −19.2184 −0.725870 −0.362935 0.931815i \(-0.618225\pi\)
−0.362935 + 0.931815i \(0.618225\pi\)
\(702\) 0 0
\(703\) 6.22000i 0.234592i
\(704\) 0.0451320 0.00170097
\(705\) 0 0
\(706\) 19.2631 0.724976
\(707\) 26.2468i 0.987111i
\(708\) 0 0
\(709\) −4.52525 −0.169949 −0.0849746 0.996383i \(-0.527081\pi\)
−0.0849746 + 0.996383i \(0.527081\pi\)
\(710\) 3.71558 + 9.33562i 0.139443 + 0.350360i
\(711\) 0 0
\(712\) 9.97602i 0.373867i
\(713\) 6.62805i 0.248222i
\(714\) 0 0
\(715\) −0.196486 0.493684i −0.00734816 0.0184627i
\(716\) 5.27905 0.197288
\(717\) 0 0
\(718\) 14.6645i 0.547273i
\(719\) 0.915477 0.0341415 0.0170708 0.999854i \(-0.494566\pi\)
0.0170708 + 0.999854i \(0.494566\pi\)
\(720\) 0 0
\(721\) −58.7110 −2.18651
\(722\) 19.6884i 0.732728i
\(723\) 0 0
\(724\) −17.7448 −0.659478
\(725\) −15.2708 + 14.4435i −0.567143 + 0.536417i
\(726\) 0 0
\(727\) 11.7429i 0.435521i −0.976002 0.217760i \(-0.930125\pi\)
0.976002 0.217760i \(-0.0698752\pi\)
\(728\) 24.5993i 0.911710i
\(729\) 0 0
\(730\) 14.6221 5.81961i 0.541189 0.215393i
\(731\) 20.0202 0.740473
\(732\) 0 0
\(733\) 27.6776i 1.02230i −0.859493 0.511148i \(-0.829220\pi\)
0.859493 0.511148i \(-0.170780\pi\)
\(734\) 0.868349 0.0320514
\(735\) 0 0
\(736\) −2.20164 −0.0811534
\(737\) 0.558514i 0.0205731i
\(738\) 0 0
\(739\) 6.52187 0.239911 0.119956 0.992779i \(-0.461725\pi\)
0.119956 + 0.992779i \(0.461725\pi\)
\(740\) 0.826871 + 2.07757i 0.0303964 + 0.0763729i
\(741\) 0 0
\(742\) 28.5099i 1.04663i
\(743\) 43.0091i 1.57785i 0.614489 + 0.788925i \(0.289362\pi\)
−0.614489 + 0.788925i \(0.710638\pi\)
\(744\) 0 0
\(745\) 45.6716 18.1773i 1.67328 0.665964i
\(746\) −32.4555 −1.18828
\(747\) 0 0
\(748\) 0.162864i 0.00595489i
\(749\) −83.8152 −3.06254
\(750\) 0 0
\(751\) −29.7068 −1.08402 −0.542008 0.840373i \(-0.682336\pi\)
−0.542008 + 0.840373i \(0.682336\pi\)
\(752\) 4.28072i 0.156102i
\(753\) 0 0
\(754\) 22.1339 0.806069
\(755\) −29.4759 + 11.7314i −1.07274 + 0.426950i
\(756\) 0 0
\(757\) 32.7918i 1.19184i 0.803044 + 0.595920i \(0.203212\pi\)
−0.803044 + 0.595920i \(0.796788\pi\)
\(758\) 30.2511i 1.09877i
\(759\) 0 0
\(760\) −5.14314 12.9225i −0.186561 0.468747i
\(761\) −22.9411 −0.831616 −0.415808 0.909452i \(-0.636501\pi\)
−0.415808 + 0.909452i \(0.636501\pi\)
\(762\) 0 0
\(763\) 14.4806i 0.524232i
\(764\) −3.11649 −0.112751
\(765\) 0 0
\(766\) 14.4935 0.523673
\(767\) 71.2241i 2.57175i
\(768\) 0 0
\(769\) −10.8123 −0.389902 −0.194951 0.980813i \(-0.562455\pi\)
−0.194951 + 0.980813i \(0.562455\pi\)
\(770\) 0.438079 0.174355i 0.0157873 0.00628333i
\(771\) 0 0
\(772\) 8.78278i 0.316099i
\(773\) 37.9989i 1.36673i −0.730079 0.683363i \(-0.760517\pi\)
0.730079 0.683363i \(-0.239483\pi\)
\(774\) 0 0
\(775\) −10.9359 + 10.3434i −0.392829 + 0.371546i
\(776\) −0.240408 −0.00863014
\(777\) 0 0
\(778\) 36.9033i 1.32305i
\(779\) 45.9222 1.64533
\(780\) 0 0
\(781\) −0.202802 −0.00725683
\(782\) 7.94485i 0.284107i
\(783\) 0 0
\(784\) −14.8286 −0.529593
\(785\) 16.4809 + 41.4093i 0.588228 + 1.47796i
\(786\) 0 0
\(787\) 31.7730i 1.13258i 0.824205 + 0.566292i \(0.191623\pi\)
−0.824205 + 0.566292i \(0.808377\pi\)
\(788\) 7.00278i 0.249464i
\(789\) 0 0
\(790\) 7.21444 + 18.1267i 0.256678 + 0.644921i
\(791\) −20.3790 −0.724594
\(792\) 0 0
\(793\) 22.4979i 0.798923i
\(794\) 22.9365 0.813986
\(795\) 0 0
\(796\) 17.3202 0.613900
\(797\) 9.02551i 0.319700i −0.987141 0.159850i \(-0.948899\pi\)