Properties

Label 324.3.o.a.29.2
Level $324$
Weight $3$
Character 324.29
Analytic conductor $8.828$
Analytic rank $0$
Dimension $324$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 324.o (of order \(54\), degree \(18\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.82836056527\)
Analytic rank: \(0\)
Dimension: \(324\)
Relative dimension: \(18\) over \(\Q(\zeta_{54})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label 29.2
Character \(\chi\) \(=\) 324.29
Dual form 324.3.o.a.257.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.97121 + 0.414613i) q^{3} +(-0.778741 + 0.734705i) q^{5} +(1.20130 - 0.140411i) q^{7} +(8.65619 - 2.46381i) q^{9} +O(q^{10})\) \(q+(-2.97121 + 0.414613i) q^{3} +(-0.778741 + 0.734705i) q^{5} +(1.20130 - 0.140411i) q^{7} +(8.65619 - 2.46381i) q^{9} +(5.77404 - 1.72863i) q^{11} +(-0.360819 - 6.19502i) q^{13} +(2.00919 - 2.50584i) q^{15} +(-8.28376 + 22.7594i) q^{17} +(-34.1830 + 12.4416i) q^{19} +(-3.51109 + 0.915264i) q^{21} +(-0.0387925 + 0.331891i) q^{23} +(-1.38697 + 23.8134i) q^{25} +(-24.6978 + 10.9095i) q^{27} +(8.38751 + 16.7009i) q^{29} +(-12.6693 + 17.0178i) q^{31} +(-16.4392 + 7.53013i) q^{33} +(-0.832338 + 0.991941i) q^{35} +(27.8439 - 23.3638i) q^{37} +(3.64061 + 18.2571i) q^{39} +(23.2739 + 35.3863i) q^{41} +(-39.9262 - 9.46267i) q^{43} +(-4.93076 + 8.27841i) q^{45} +(-73.5059 + 54.7231i) q^{47} +(-46.2558 + 10.9628i) q^{49} +(15.1764 - 71.0576i) q^{51} +(37.1563 - 21.4522i) q^{53} +(-3.22645 + 5.58837i) q^{55} +(96.4064 - 51.1393i) q^{57} +(38.6036 + 11.5572i) q^{59} +(-24.0027 + 55.6445i) q^{61} +(10.0527 - 4.17519i) q^{63} +(4.83249 + 4.55922i) q^{65} +(-32.8598 - 16.5028i) q^{67} +(-0.0223457 - 1.00220i) q^{69} +(28.4416 - 5.01502i) q^{71} +(4.09057 - 23.1988i) q^{73} +(-5.75236 - 71.3297i) q^{75} +(6.69361 - 2.88734i) q^{77} +(-24.3817 - 16.0361i) q^{79} +(68.8593 - 42.6544i) q^{81} +(18.8759 - 28.6995i) q^{83} +(-10.2706 - 23.8098i) q^{85} +(-31.8455 - 46.1443i) q^{87} +(41.3193 + 7.28571i) q^{89} +(-1.30330 - 7.39139i) q^{91} +(30.5874 - 55.8164i) q^{93} +(17.4788 - 34.8032i) q^{95} +(44.3589 - 47.0177i) q^{97} +(45.7222 - 29.1895i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 324 q + O(q^{10}) \) \( 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(1\) \(e\left(\frac{37}{54}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.97121 + 0.414613i −0.990404 + 0.138204i
\(4\) 0 0
\(5\) −0.778741 + 0.734705i −0.155748 + 0.146941i −0.760171 0.649722i \(-0.774885\pi\)
0.604423 + 0.796663i \(0.293404\pi\)
\(6\) 0 0
\(7\) 1.20130 0.140411i 0.171614 0.0200588i −0.0298521 0.999554i \(-0.509504\pi\)
0.201466 + 0.979496i \(0.435430\pi\)
\(8\) 0 0
\(9\) 8.65619 2.46381i 0.961799 0.273756i
\(10\) 0 0
\(11\) 5.77404 1.72863i 0.524913 0.157149i −0.0133736 0.999911i \(-0.504257\pi\)
0.538286 + 0.842762i \(0.319072\pi\)
\(12\) 0 0
\(13\) −0.360819 6.19502i −0.0277553 0.476540i −0.983334 0.181806i \(-0.941806\pi\)
0.955579 0.294734i \(-0.0952312\pi\)
\(14\) 0 0
\(15\) 2.00919 2.50584i 0.133946 0.167056i
\(16\) 0 0
\(17\) −8.28376 + 22.7594i −0.487280 + 1.33879i 0.415854 + 0.909431i \(0.363483\pi\)
−0.903134 + 0.429359i \(0.858740\pi\)
\(18\) 0 0
\(19\) −34.1830 + 12.4416i −1.79910 + 0.654820i −0.800656 + 0.599125i \(0.795515\pi\)
−0.998448 + 0.0556954i \(0.982262\pi\)
\(20\) 0 0
\(21\) −3.51109 + 0.915264i −0.167195 + 0.0435840i
\(22\) 0 0
\(23\) −0.0387925 + 0.331891i −0.00168663 + 0.0144300i −0.994055 0.108875i \(-0.965275\pi\)
0.992369 + 0.123305i \(0.0393493\pi\)
\(24\) 0 0
\(25\) −1.38697 + 23.8134i −0.0554789 + 0.952537i
\(26\) 0 0
\(27\) −24.6978 + 10.9095i −0.914735 + 0.404054i
\(28\) 0 0
\(29\) 8.38751 + 16.7009i 0.289224 + 0.575893i 0.990583 0.136916i \(-0.0437190\pi\)
−0.701358 + 0.712809i \(0.747423\pi\)
\(30\) 0 0
\(31\) −12.6693 + 17.0178i −0.408687 + 0.548962i −0.958042 0.286627i \(-0.907466\pi\)
0.549355 + 0.835589i \(0.314873\pi\)
\(32\) 0 0
\(33\) −16.4392 + 7.53013i −0.498157 + 0.228186i
\(34\) 0 0
\(35\) −0.832338 + 0.991941i −0.0237811 + 0.0283412i
\(36\) 0 0
\(37\) 27.8439 23.3638i 0.752539 0.631455i −0.183634 0.982995i \(-0.558786\pi\)
0.936173 + 0.351539i \(0.114342\pi\)
\(38\) 0 0
\(39\) 3.64061 + 18.2571i 0.0933489 + 0.468131i
\(40\) 0 0
\(41\) 23.2739 + 35.3863i 0.567657 + 0.863081i 0.999239 0.0389929i \(-0.0124150\pi\)
−0.431582 + 0.902074i \(0.642045\pi\)
\(42\) 0 0
\(43\) −39.9262 9.46267i −0.928515 0.220062i −0.261583 0.965181i \(-0.584245\pi\)
−0.666932 + 0.745119i \(0.732393\pi\)
\(44\) 0 0
\(45\) −4.93076 + 8.27841i −0.109573 + 0.183965i
\(46\) 0 0
\(47\) −73.5059 + 54.7231i −1.56396 + 1.16432i −0.648985 + 0.760801i \(0.724806\pi\)
−0.914970 + 0.403521i \(0.867786\pi\)
\(48\) 0 0
\(49\) −46.2558 + 10.9628i −0.943996 + 0.223731i
\(50\) 0 0
\(51\) 15.1764 71.0576i 0.297577 1.39329i
\(52\) 0 0
\(53\) 37.1563 21.4522i 0.701062 0.404758i −0.106681 0.994293i \(-0.534022\pi\)
0.807743 + 0.589535i \(0.200689\pi\)
\(54\) 0 0
\(55\) −3.22645 + 5.58837i −0.0586627 + 0.101607i
\(56\) 0 0
\(57\) 96.4064 51.1393i 1.69134 0.897180i
\(58\) 0 0
\(59\) 38.6036 + 11.5572i 0.654298 + 0.195884i 0.596711 0.802456i \(-0.296474\pi\)
0.0575876 + 0.998340i \(0.481659\pi\)
\(60\) 0 0
\(61\) −24.0027 + 55.6445i −0.393486 + 0.912204i 0.600183 + 0.799863i \(0.295094\pi\)
−0.993670 + 0.112342i \(0.964165\pi\)
\(62\) 0 0
\(63\) 10.0527 4.17519i 0.159567 0.0662728i
\(64\) 0 0
\(65\) 4.83249 + 4.55922i 0.0743461 + 0.0701419i
\(66\) 0 0
\(67\) −32.8598 16.5028i −0.490445 0.246311i 0.186348 0.982484i \(-0.440335\pi\)
−0.676794 + 0.736173i \(0.736631\pi\)
\(68\) 0 0
\(69\) −0.0223457 1.00220i −0.000323850 0.0145247i
\(70\) 0 0
\(71\) 28.4416 5.01502i 0.400586 0.0706340i 0.0302740 0.999542i \(-0.490362\pi\)
0.370312 + 0.928908i \(0.379251\pi\)
\(72\) 0 0
\(73\) 4.09057 23.1988i 0.0560352 0.317792i −0.943887 0.330269i \(-0.892861\pi\)
0.999922 + 0.0124771i \(0.00397170\pi\)
\(74\) 0 0
\(75\) −5.75236 71.3297i −0.0766982 0.951063i
\(76\) 0 0
\(77\) 6.69361 2.88734i 0.0869300 0.0374979i
\(78\) 0 0
\(79\) −24.3817 16.0361i −0.308630 0.202989i 0.385740 0.922608i \(-0.373946\pi\)
−0.694369 + 0.719619i \(0.744317\pi\)
\(80\) 0 0
\(81\) 68.8593 42.6544i 0.850115 0.526597i
\(82\) 0 0
\(83\) 18.8759 28.6995i 0.227421 0.345777i −0.703694 0.710504i \(-0.748467\pi\)
0.931115 + 0.364727i \(0.118838\pi\)
\(84\) 0 0
\(85\) −10.2706 23.8098i −0.120830 0.280116i
\(86\) 0 0
\(87\) −31.8455 46.1443i −0.366040 0.530395i
\(88\) 0 0
\(89\) 41.3193 + 7.28571i 0.464262 + 0.0818619i 0.400886 0.916128i \(-0.368702\pi\)
0.0633757 + 0.997990i \(0.479813\pi\)
\(90\) 0 0
\(91\) −1.30330 7.39139i −0.0143220 0.0812240i
\(92\) 0 0
\(93\) 30.5874 55.8164i 0.328896 0.600177i
\(94\) 0 0
\(95\) 17.4788 34.8032i 0.183987 0.366349i
\(96\) 0 0
\(97\) 44.3589 47.0177i 0.457308 0.484718i −0.457155 0.889387i \(-0.651132\pi\)
0.914463 + 0.404669i \(0.132613\pi\)
\(98\) 0 0
\(99\) 45.7222 29.1895i 0.461840 0.294844i
\(100\) 0 0
\(101\) 150.506 + 64.9217i 1.49015 + 0.642789i 0.976560 0.215244i \(-0.0690548\pi\)
0.513593 + 0.858034i \(0.328314\pi\)
\(102\) 0 0
\(103\) 2.83290 9.46253i 0.0275038 0.0918692i −0.943136 0.332408i \(-0.892139\pi\)
0.970640 + 0.240539i \(0.0773241\pi\)
\(104\) 0 0
\(105\) 2.06178 3.29237i 0.0196360 0.0313559i
\(106\) 0 0
\(107\) −34.7426 20.0586i −0.324697 0.187464i 0.328787 0.944404i \(-0.393360\pi\)
−0.653484 + 0.756940i \(0.726693\pi\)
\(108\) 0 0
\(109\) −44.3700 76.8512i −0.407065 0.705057i 0.587495 0.809228i \(-0.300114\pi\)
−0.994559 + 0.104171i \(0.966781\pi\)
\(110\) 0 0
\(111\) −73.0433 + 80.9634i −0.658048 + 0.729400i
\(112\) 0 0
\(113\) 34.3857 + 145.085i 0.304298 + 1.28394i 0.883376 + 0.468664i \(0.155265\pi\)
−0.579078 + 0.815272i \(0.696587\pi\)
\(114\) 0 0
\(115\) −0.213633 0.286958i −0.00185767 0.00249529i
\(116\) 0 0
\(117\) −18.3866 52.7363i −0.157151 0.450738i
\(118\) 0 0
\(119\) −6.75556 + 28.5039i −0.0567694 + 0.239529i
\(120\) 0 0
\(121\) −70.7427 + 46.5282i −0.584650 + 0.384530i
\(122\) 0 0
\(123\) −83.8234 95.4905i −0.681491 0.776346i
\(124\) 0 0
\(125\) −33.6203 40.0671i −0.268962 0.320537i
\(126\) 0 0
\(127\) −54.3795 45.6298i −0.428185 0.359290i 0.403081 0.915164i \(-0.367939\pi\)
−0.831266 + 0.555874i \(0.812384\pi\)
\(128\) 0 0
\(129\) 122.552 + 11.5617i 0.950019 + 0.0896255i
\(130\) 0 0
\(131\) 114.940 + 85.5695i 0.877403 + 0.653202i 0.938631 0.344922i \(-0.112095\pi\)
−0.0612287 + 0.998124i \(0.519502\pi\)
\(132\) 0 0
\(133\) −39.3169 + 19.7457i −0.295616 + 0.148464i
\(134\) 0 0
\(135\) 11.2180 26.6413i 0.0830963 0.197343i
\(136\) 0 0
\(137\) −150.380 8.75864i −1.09766 0.0639317i −0.500262 0.865874i \(-0.666763\pi\)
−0.597402 + 0.801942i \(0.703800\pi\)
\(138\) 0 0
\(139\) −91.9529 10.7477i −0.661531 0.0773219i −0.221299 0.975206i \(-0.571030\pi\)
−0.440232 + 0.897884i \(0.645104\pi\)
\(140\) 0 0
\(141\) 195.713 193.070i 1.38803 1.36929i
\(142\) 0 0
\(143\) −12.7923 35.1466i −0.0894567 0.245780i
\(144\) 0 0
\(145\) −18.8019 6.84334i −0.129668 0.0471955i
\(146\) 0 0
\(147\) 132.890 51.7511i 0.904017 0.352049i
\(148\) 0 0
\(149\) 59.2658 3.45184i 0.397757 0.0231667i 0.141899 0.989881i \(-0.454679\pi\)
0.255858 + 0.966714i \(0.417642\pi\)
\(150\) 0 0
\(151\) 77.5199 + 258.934i 0.513377 + 1.71480i 0.684019 + 0.729464i \(0.260230\pi\)
−0.170643 + 0.985333i \(0.554584\pi\)
\(152\) 0 0
\(153\) −15.6309 + 217.420i −0.102163 + 1.42104i
\(154\) 0 0
\(155\) −2.63697 22.5607i −0.0170127 0.145553i
\(156\) 0 0
\(157\) −148.884 157.808i −0.948305 1.00514i −0.999979 0.00648054i \(-0.997937\pi\)
0.0516740 0.998664i \(-0.483544\pi\)
\(158\) 0 0
\(159\) −101.505 + 79.1444i −0.638395 + 0.497764i
\(160\) 0 0
\(161\) 0.404146i 0.00251022i
\(162\) 0 0
\(163\) 89.0345 0.546224 0.273112 0.961982i \(-0.411947\pi\)
0.273112 + 0.961982i \(0.411947\pi\)
\(164\) 0 0
\(165\) 7.26945 17.9420i 0.0440573 0.108739i
\(166\) 0 0
\(167\) 69.4702 65.5418i 0.415989 0.392466i −0.449592 0.893234i \(-0.648431\pi\)
0.865581 + 0.500768i \(0.166949\pi\)
\(168\) 0 0
\(169\) 129.609 15.1491i 0.766918 0.0896399i
\(170\) 0 0
\(171\) −265.241 + 191.917i −1.55112 + 1.12232i
\(172\) 0 0
\(173\) −261.821 + 78.3839i −1.51341 + 0.453086i −0.932588 0.360942i \(-0.882455\pi\)
−0.580825 + 0.814028i \(0.697270\pi\)
\(174\) 0 0
\(175\) 1.67751 + 28.8017i 0.00958576 + 0.164581i
\(176\) 0 0
\(177\) −119.491 18.3332i −0.675092 0.103577i
\(178\) 0 0
\(179\) 94.6285 259.990i 0.528651 1.45246i −0.332009 0.943276i \(-0.607726\pi\)
0.860660 0.509180i \(-0.170051\pi\)
\(180\) 0 0
\(181\) 228.647 83.2208i 1.26324 0.459783i 0.378388 0.925647i \(-0.376479\pi\)
0.884856 + 0.465864i \(0.154256\pi\)
\(182\) 0 0
\(183\) 48.2461 175.283i 0.263640 0.957832i
\(184\) 0 0
\(185\) −4.51771 + 38.6515i −0.0244200 + 0.208927i
\(186\) 0 0
\(187\) −8.48801 + 145.733i −0.0453904 + 0.779323i
\(188\) 0 0
\(189\) −28.1376 + 16.5733i −0.148876 + 0.0876896i
\(190\) 0 0
\(191\) 72.9716 + 145.298i 0.382050 + 0.760725i 0.999668 0.0257533i \(-0.00819845\pi\)
−0.617618 + 0.786478i \(0.711902\pi\)
\(192\) 0 0
\(193\) −30.1128 + 40.4485i −0.156025 + 0.209578i −0.873261 0.487252i \(-0.837999\pi\)
0.717237 + 0.696830i \(0.245407\pi\)
\(194\) 0 0
\(195\) −16.2487 11.5428i −0.0833265 0.0591938i
\(196\) 0 0
\(197\) −21.5514 + 25.6840i −0.109398 + 0.130376i −0.817965 0.575268i \(-0.804898\pi\)
0.708567 + 0.705644i \(0.249342\pi\)
\(198\) 0 0
\(199\) 125.777 105.539i 0.632045 0.530349i −0.269519 0.962995i \(-0.586865\pi\)
0.901564 + 0.432647i \(0.142420\pi\)
\(200\) 0 0
\(201\) 104.476 + 35.4093i 0.519780 + 0.176166i
\(202\) 0 0
\(203\) 12.4209 + 18.8850i 0.0611866 + 0.0930296i
\(204\) 0 0
\(205\) −44.1229 10.4573i −0.215233 0.0510113i
\(206\) 0 0
\(207\) 0.481920 + 2.96849i 0.00232812 + 0.0143405i
\(208\) 0 0
\(209\) −175.867 + 130.928i −0.841468 + 0.626450i
\(210\) 0 0
\(211\) −243.815 + 57.7853i −1.15552 + 0.273864i −0.763323 0.646017i \(-0.776434\pi\)
−0.392199 + 0.919880i \(0.628286\pi\)
\(212\) 0 0
\(213\) −82.4266 + 26.6929i −0.386980 + 0.125319i
\(214\) 0 0
\(215\) 38.0444 21.9650i 0.176951 0.102163i
\(216\) 0 0
\(217\) −12.8301 + 22.2224i −0.0591248 + 0.102407i
\(218\) 0 0
\(219\) −2.53543 + 70.6245i −0.0115773 + 0.322486i
\(220\) 0 0
\(221\) 143.984 + 43.1060i 0.651512 + 0.195050i
\(222\) 0 0
\(223\) −33.7256 + 78.1847i −0.151236 + 0.350604i −0.976945 0.213492i \(-0.931516\pi\)
0.825709 + 0.564096i \(0.190775\pi\)
\(224\) 0 0
\(225\) 46.6657 + 209.551i 0.207403 + 0.931337i
\(226\) 0 0
\(227\) −76.3324 72.0159i −0.336266 0.317251i 0.499524 0.866300i \(-0.333508\pi\)
−0.835790 + 0.549049i \(0.814990\pi\)
\(228\) 0 0
\(229\) −96.3716 48.3996i −0.420837 0.211352i 0.225762 0.974182i \(-0.427513\pi\)
−0.646599 + 0.762830i \(0.723809\pi\)
\(230\) 0 0
\(231\) −18.6910 + 11.3542i −0.0809134 + 0.0491522i
\(232\) 0 0
\(233\) 181.840 32.0634i 0.780431 0.137611i 0.230781 0.973006i \(-0.425872\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(234\) 0 0
\(235\) 17.0368 96.6203i 0.0724969 0.411150i
\(236\) 0 0
\(237\) 79.0921 + 37.5377i 0.333722 + 0.158387i
\(238\) 0 0
\(239\) −128.718 + 55.5236i −0.538569 + 0.232316i −0.647949 0.761684i \(-0.724373\pi\)
0.109379 + 0.994000i \(0.465114\pi\)
\(240\) 0 0
\(241\) 78.3341 + 51.5212i 0.325038 + 0.213781i 0.701532 0.712638i \(-0.252500\pi\)
−0.376494 + 0.926419i \(0.622870\pi\)
\(242\) 0 0
\(243\) −186.911 + 155.285i −0.769179 + 0.639033i
\(244\) 0 0
\(245\) 27.9669 42.5216i 0.114150 0.173557i
\(246\) 0 0
\(247\) 89.4097 + 207.275i 0.361983 + 0.839170i
\(248\) 0 0
\(249\) −44.1852 + 93.0984i −0.177451 + 0.373889i
\(250\) 0 0
\(251\) −438.833 77.3781i −1.74834 0.308279i −0.794203 0.607652i \(-0.792111\pi\)
−0.954136 + 0.299373i \(0.903223\pi\)
\(252\) 0 0
\(253\) 0.349729 + 1.98341i 0.00138233 + 0.00783957i
\(254\) 0 0
\(255\) 40.3879 + 66.4857i 0.158384 + 0.260728i
\(256\) 0 0
\(257\) 10.1176 20.1458i 0.0393682 0.0783885i −0.873089 0.487562i \(-0.837886\pi\)
0.912457 + 0.409173i \(0.134183\pi\)
\(258\) 0 0
\(259\) 30.1683 31.9765i 0.116480 0.123461i
\(260\) 0 0
\(261\) 113.752 + 123.901i 0.435830 + 0.474717i
\(262\) 0 0
\(263\) −298.996 128.974i −1.13687 0.490397i −0.257376 0.966311i \(-0.582858\pi\)
−0.879492 + 0.475914i \(0.842117\pi\)
\(264\) 0 0
\(265\) −13.1741 + 44.0046i −0.0497136 + 0.166055i
\(266\) 0 0
\(267\) −125.789 4.51585i −0.471121 0.0169133i
\(268\) 0 0
\(269\) −262.094 151.320i −0.974327 0.562528i −0.0737745 0.997275i \(-0.523505\pi\)
−0.900553 + 0.434747i \(0.856838\pi\)
\(270\) 0 0
\(271\) 110.665 + 191.678i 0.408360 + 0.707300i 0.994706 0.102761i \(-0.0327676\pi\)
−0.586346 + 0.810060i \(0.699434\pi\)
\(272\) 0 0
\(273\) 6.93695 + 21.4210i 0.0254101 + 0.0784652i
\(274\) 0 0
\(275\) 33.1562 + 139.897i 0.120568 + 0.508717i
\(276\) 0 0
\(277\) 234.429 + 314.893i 0.846315 + 1.13680i 0.989129 + 0.147049i \(0.0469776\pi\)
−0.142814 + 0.989750i \(0.545615\pi\)
\(278\) 0 0
\(279\) −67.7393 + 178.524i −0.242793 + 0.639872i
\(280\) 0 0
\(281\) 17.3731 73.3029i 0.0618260 0.260864i −0.933350 0.358967i \(-0.883129\pi\)
0.995176 + 0.0981024i \(0.0312773\pi\)
\(282\) 0 0
\(283\) 327.917 215.674i 1.15872 0.762100i 0.183428 0.983033i \(-0.441281\pi\)
0.975289 + 0.220933i \(0.0709103\pi\)
\(284\) 0 0
\(285\) −37.5034 + 110.654i −0.131591 + 0.388261i
\(286\) 0 0
\(287\) 32.9275 + 39.2415i 0.114730 + 0.136730i
\(288\) 0 0
\(289\) −227.984 191.301i −0.788873 0.661943i
\(290\) 0 0
\(291\) −112.306 + 158.091i −0.385930 + 0.543269i
\(292\) 0 0
\(293\) −170.905 127.234i −0.583294 0.434246i 0.264641 0.964347i \(-0.414747\pi\)
−0.847935 + 0.530101i \(0.822154\pi\)
\(294\) 0 0
\(295\) −38.5533 + 19.3622i −0.130689 + 0.0656346i
\(296\) 0 0
\(297\) −123.748 + 105.685i −0.416660 + 0.355843i
\(298\) 0 0
\(299\) 2.07007 + 0.120568i 0.00692331 + 0.000403237i
\(300\) 0 0
\(301\) −49.2918 5.76138i −0.163760 0.0191408i
\(302\) 0 0
\(303\) −474.101 130.495i −1.56469 0.430675i
\(304\) 0 0
\(305\) −22.1904 60.9675i −0.0727553 0.199893i
\(306\) 0 0
\(307\) 309.152 + 112.522i 1.00701 + 0.366522i 0.792284 0.610152i \(-0.208892\pi\)
0.214726 + 0.976674i \(0.431114\pi\)
\(308\) 0 0
\(309\) −4.49384 + 29.2897i −0.0145432 + 0.0947888i
\(310\) 0 0
\(311\) 396.037 23.0665i 1.27343 0.0741688i 0.591931 0.805988i \(-0.298366\pi\)
0.681498 + 0.731820i \(0.261329\pi\)
\(312\) 0 0
\(313\) −86.6535 289.443i −0.276848 0.924738i −0.977447 0.211182i \(-0.932269\pi\)
0.700599 0.713556i \(-0.252916\pi\)
\(314\) 0 0
\(315\) −4.76092 + 10.6372i −0.0151140 + 0.0337687i
\(316\) 0 0
\(317\) 48.3177 + 413.385i 0.152422 + 1.30405i 0.825467 + 0.564451i \(0.190912\pi\)
−0.673045 + 0.739602i \(0.735014\pi\)
\(318\) 0 0
\(319\) 77.2996 + 81.9328i 0.242318 + 0.256843i
\(320\) 0 0
\(321\) 111.544 + 45.1937i 0.347490 + 0.140790i
\(322\) 0 0
\(323\) 881.048i 2.72770i
\(324\) 0 0
\(325\) 148.025 0.455462
\(326\) 0 0
\(327\) 163.696 + 209.945i 0.500600 + 0.642033i
\(328\) 0 0
\(329\) −80.6186 + 76.0597i −0.245041 + 0.231184i
\(330\) 0 0
\(331\) 481.426 56.2707i 1.45446 0.170002i 0.648158 0.761506i \(-0.275540\pi\)
0.806302 + 0.591504i \(0.201465\pi\)
\(332\) 0 0
\(333\) 183.459 270.844i 0.550926 0.813345i
\(334\) 0 0
\(335\) 37.7140 11.2908i 0.112579 0.0337040i
\(336\) 0 0
\(337\) −27.0241 463.986i −0.0801902 1.37681i −0.763086 0.646297i \(-0.776317\pi\)
0.682896 0.730516i \(-0.260720\pi\)
\(338\) 0 0
\(339\) −162.321 416.821i −0.478824 1.22956i
\(340\) 0 0
\(341\) −43.7355 + 120.162i −0.128257 + 0.352382i
\(342\) 0 0
\(343\) −109.718 + 39.9340i −0.319877 + 0.116426i
\(344\) 0 0
\(345\) 0.753724 + 0.764039i 0.00218471 + 0.00221461i
\(346\) 0 0
\(347\) 37.1225 317.603i 0.106981 0.915284i −0.828034 0.560677i \(-0.810541\pi\)
0.935016 0.354606i \(-0.115385\pi\)
\(348\) 0 0
\(349\) −17.5818 + 301.868i −0.0503776 + 0.864951i 0.874580 + 0.484881i \(0.161137\pi\)
−0.924958 + 0.380070i \(0.875900\pi\)
\(350\) 0 0
\(351\) 76.4958 + 149.067i 0.217937 + 0.424693i
\(352\) 0 0
\(353\) −80.0934 159.479i −0.226894 0.451782i 0.751164 0.660115i \(-0.229493\pi\)
−0.978058 + 0.208333i \(0.933196\pi\)
\(354\) 0 0
\(355\) −18.4641 + 24.8016i −0.0520115 + 0.0698635i
\(356\) 0 0
\(357\) 8.25408 87.4921i 0.0231207 0.245076i
\(358\) 0 0
\(359\) 189.196 225.475i 0.527009 0.628065i −0.435214 0.900327i \(-0.643327\pi\)
0.962223 + 0.272262i \(0.0877716\pi\)
\(360\) 0 0
\(361\) 737.140 618.534i 2.04194 1.71339i
\(362\) 0 0
\(363\) 190.900 167.576i 0.525896 0.461641i
\(364\) 0 0
\(365\) 13.8588 + 21.0712i 0.0379692 + 0.0577294i
\(366\) 0 0
\(367\) 194.178 + 46.0211i 0.529096 + 0.125398i 0.486477 0.873693i \(-0.338282\pi\)
0.0426191 + 0.999091i \(0.486430\pi\)
\(368\) 0 0
\(369\) 288.649 + 248.968i 0.782246 + 0.674710i
\(370\) 0 0
\(371\) 41.6235 30.9876i 0.112193 0.0835244i
\(372\) 0 0
\(373\) −390.052 + 92.4440i −1.04572 + 0.247839i −0.717351 0.696712i \(-0.754646\pi\)
−0.328365 + 0.944551i \(0.606497\pi\)
\(374\) 0 0
\(375\) 116.505 + 105.108i 0.310681 + 0.280289i
\(376\) 0 0
\(377\) 100.436 57.9868i 0.266409 0.153811i
\(378\) 0 0
\(379\) 106.140 183.841i 0.280054 0.485068i −0.691344 0.722526i \(-0.742981\pi\)
0.971398 + 0.237458i \(0.0763143\pi\)
\(380\) 0 0
\(381\) 180.492 + 113.029i 0.473731 + 0.296665i
\(382\) 0 0
\(383\) 415.047 + 124.257i 1.08367 + 0.324430i 0.778358 0.627821i \(-0.216053\pi\)
0.305315 + 0.952251i \(0.401238\pi\)
\(384\) 0 0
\(385\) −3.09125 + 7.16632i −0.00802921 + 0.0186138i
\(386\) 0 0
\(387\) −368.923 + 16.4596i −0.953289 + 0.0425313i
\(388\) 0 0
\(389\) −506.880 478.217i −1.30303 1.22935i −0.956645 0.291258i \(-0.905926\pi\)
−0.346389 0.938091i \(-0.612592\pi\)
\(390\) 0 0
\(391\) −7.23230 3.63220i −0.0184969 0.00928951i
\(392\) 0 0
\(393\) −376.989 206.589i −0.959258 0.525673i
\(394\) 0 0
\(395\) 30.7689 5.42539i 0.0778959 0.0137352i
\(396\) 0 0
\(397\) 102.876 583.438i 0.259133 1.46962i −0.526103 0.850421i \(-0.676347\pi\)
0.785236 0.619196i \(-0.212541\pi\)
\(398\) 0 0
\(399\) 108.632 74.9699i 0.272261 0.187895i
\(400\) 0 0
\(401\) −265.409 + 114.486i −0.661868 + 0.285502i −0.700395 0.713756i \(-0.746993\pi\)
0.0385269 + 0.999258i \(0.487733\pi\)
\(402\) 0 0
\(403\) 109.997 + 72.3463i 0.272946 + 0.179519i
\(404\) 0 0
\(405\) −22.2852 + 83.8080i −0.0550253 + 0.206933i
\(406\) 0 0
\(407\) 120.385 183.036i 0.295785 0.449719i
\(408\) 0 0
\(409\) −42.3672 98.2183i −0.103587 0.240143i 0.858538 0.512750i \(-0.171373\pi\)
−0.962125 + 0.272607i \(0.912114\pi\)
\(410\) 0 0
\(411\) 450.442 36.3258i 1.09597 0.0883838i
\(412\) 0 0
\(413\) 47.9971 + 8.46318i 0.116216 + 0.0204920i
\(414\) 0 0
\(415\) 6.38616 + 36.2177i 0.0153883 + 0.0872716i
\(416\) 0 0
\(417\) 277.668 6.19104i 0.665869 0.0148466i
\(418\) 0 0
\(419\) 258.406 514.528i 0.616720 1.22799i −0.340939 0.940085i \(-0.610745\pi\)
0.957659 0.287905i \(-0.0929586\pi\)
\(420\) 0 0
\(421\) −45.7837 + 48.5279i −0.108750 + 0.115268i −0.779462 0.626450i \(-0.784507\pi\)
0.670712 + 0.741718i \(0.265989\pi\)
\(422\) 0 0
\(423\) −501.454 + 654.798i −1.18547 + 1.54799i
\(424\) 0 0
\(425\) −530.490 228.831i −1.24821 0.538426i
\(426\) 0 0
\(427\) −21.0212 + 70.2157i −0.0492300 + 0.164440i
\(428\) 0 0
\(429\) 52.5809 + 99.1241i 0.122566 + 0.231058i
\(430\) 0 0
\(431\) 108.057 + 62.3866i 0.250712 + 0.144749i 0.620090 0.784531i \(-0.287096\pi\)
−0.369378 + 0.929279i \(0.620429\pi\)
\(432\) 0 0
\(433\) 46.4896 + 80.5223i 0.107366 + 0.185964i 0.914702 0.404128i \(-0.132425\pi\)
−0.807336 + 0.590092i \(0.799092\pi\)
\(434\) 0 0
\(435\) 58.7018 + 12.5375i 0.134947 + 0.0288218i
\(436\) 0 0
\(437\) −2.80321 11.8277i −0.00641466 0.0270656i
\(438\) 0 0
\(439\) 409.665 + 550.276i 0.933178 + 1.25348i 0.967190 + 0.254054i \(0.0817642\pi\)
−0.0340117 + 0.999421i \(0.510828\pi\)
\(440\) 0 0
\(441\) −373.389 + 208.862i −0.846687 + 0.473609i
\(442\) 0 0
\(443\) −129.689 + 547.203i −0.292753 + 1.23522i 0.605537 + 0.795817i \(0.292958\pi\)
−0.898290 + 0.439403i \(0.855190\pi\)
\(444\) 0 0
\(445\) −37.5299 + 24.6838i −0.0843369 + 0.0554692i
\(446\) 0 0
\(447\) −174.660 + 34.8285i −0.390738 + 0.0779161i
\(448\) 0 0
\(449\) 8.81629 + 10.5068i 0.0196354 + 0.0234006i 0.775773 0.631012i \(-0.217360\pi\)
−0.756137 + 0.654413i \(0.772916\pi\)
\(450\) 0 0
\(451\) 195.555 + 164.090i 0.433602 + 0.363836i
\(452\) 0 0
\(453\) −337.685 737.208i −0.745443 1.62739i
\(454\) 0 0
\(455\) 6.44542 + 4.79844i 0.0141658 + 0.0105460i
\(456\) 0 0
\(457\) −426.168 + 214.030i −0.932534 + 0.468336i −0.849133 0.528180i \(-0.822875\pi\)
−0.0834016 + 0.996516i \(0.526578\pi\)
\(458\) 0 0
\(459\) −43.7022 652.480i −0.0952117 1.42153i
\(460\) 0 0
\(461\) 319.978 + 18.6366i 0.694096 + 0.0404265i 0.401566 0.915830i \(-0.368466\pi\)
0.292530 + 0.956256i \(0.405503\pi\)
\(462\) 0 0
\(463\) 431.949 + 50.4875i 0.932934 + 0.109044i 0.568961 0.822365i \(-0.307346\pi\)
0.363974 + 0.931409i \(0.381420\pi\)
\(464\) 0 0
\(465\) 17.1889 + 65.9392i 0.0369655 + 0.141805i
\(466\) 0 0
\(467\) 18.2564 + 50.1589i 0.0390929 + 0.107407i 0.957703 0.287758i \(-0.0929098\pi\)
−0.918610 + 0.395165i \(0.870688\pi\)
\(468\) 0 0
\(469\) −41.7916 15.2109i −0.0891078 0.0324326i
\(470\) 0 0
\(471\) 507.795 + 407.151i 1.07812 + 0.864439i
\(472\) 0 0
\(473\) −246.893 + 14.3799i −0.521972 + 0.0304014i
\(474\) 0 0
\(475\) −248.866 831.269i −0.523928 1.75004i
\(476\) 0 0
\(477\) 268.778 277.240i 0.563475 0.581216i
\(478\) 0 0
\(479\) 99.2174 + 848.859i 0.207134 + 1.77215i 0.552337 + 0.833621i \(0.313736\pi\)
−0.345203 + 0.938528i \(0.612190\pi\)
\(480\) 0 0
\(481\) −154.786 164.064i −0.321801 0.341089i
\(482\) 0 0
\(483\) −0.167564 1.20080i −0.000346924 0.00248614i
\(484\) 0 0
\(485\) 69.2053i 0.142691i
\(486\) 0 0
\(487\) −465.553 −0.955962 −0.477981 0.878370i \(-0.658631\pi\)
−0.477981 + 0.878370i \(0.658631\pi\)
\(488\) 0 0
\(489\) −264.540 + 36.9149i −0.540982 + 0.0754905i
\(490\) 0 0
\(491\) 229.030 216.079i 0.466456 0.440078i −0.416780 0.909007i \(-0.636841\pi\)
0.883236 + 0.468929i \(0.155360\pi\)
\(492\) 0 0
\(493\) −449.583 + 52.5487i −0.911933 + 0.106590i
\(494\) 0 0
\(495\) −14.1601 + 56.3234i −0.0286062 + 0.113785i
\(496\) 0 0
\(497\) 33.4626 10.0180i 0.0673291 0.0201570i
\(498\) 0 0
\(499\) 8.24337 + 141.533i 0.0165198 + 0.283634i 0.996444 + 0.0842616i \(0.0268532\pi\)
−0.979924 + 0.199372i \(0.936110\pi\)
\(500\) 0 0
\(501\) −179.236 + 223.542i −0.357757 + 0.446191i
\(502\) 0 0
\(503\) 35.0652 96.3409i 0.0697122 0.191533i −0.899944 0.436006i \(-0.856393\pi\)
0.969656 + 0.244473i \(0.0786150\pi\)
\(504\) 0 0
\(505\) −164.903 + 60.0198i −0.326541 + 0.118851i
\(506\) 0 0
\(507\) −378.815 + 98.7490i −0.747170 + 0.194771i
\(508\) 0 0
\(509\) −113.919 + 974.639i −0.223809 + 1.91481i 0.152476 + 0.988307i \(0.451275\pi\)
−0.376285 + 0.926504i \(0.622799\pi\)
\(510\) 0 0
\(511\) 1.65661 28.4430i 0.00324191 0.0556614i
\(512\) 0 0
\(513\) 708.515 680.198i 1.38112 1.32592i
\(514\) 0 0
\(515\) 4.74607 + 9.45021i 0.00921567 + 0.0183499i
\(516\) 0 0
\(517\) −329.830 + 443.038i −0.637969 + 0.856941i
\(518\) 0 0
\(519\) 745.425 341.450i 1.43627 0.657899i
\(520\) 0 0
\(521\) −576.849 + 687.462i −1.10720 + 1.31950i −0.164302 + 0.986410i \(0.552537\pi\)
−0.942894 + 0.333094i \(0.891907\pi\)
\(522\) 0 0
\(523\) −572.084 + 480.036i −1.09385 + 0.917850i −0.996996 0.0774481i \(-0.975323\pi\)
−0.0968552 + 0.995298i \(0.530878\pi\)
\(524\) 0 0
\(525\) −16.9258 84.8804i −0.0322396 0.161677i
\(526\) 0 0
\(527\) −282.367 429.318i −0.535800 0.814645i
\(528\) 0 0
\(529\) 514.632 + 121.970i 0.972839 + 0.230567i
\(530\) 0 0
\(531\) 362.635 + 4.92919i 0.682928 + 0.00928284i
\(532\) 0 0
\(533\) 210.821 156.951i 0.395537 0.294466i
\(534\) 0 0
\(535\) 41.7927 9.90504i 0.0781171 0.0185141i
\(536\) 0 0
\(537\) −173.366 + 811.718i −0.322842 + 1.51158i
\(538\) 0 0
\(539\) −248.132 + 143.259i −0.460357 + 0.265787i
\(540\) 0 0
\(541\) −401.428 + 695.295i −0.742012 + 1.28520i 0.209566 + 0.977795i \(0.432795\pi\)
−0.951578 + 0.307408i \(0.900538\pi\)
\(542\) 0 0
\(543\) −644.855 + 342.067i −1.18758 + 0.629957i
\(544\) 0 0
\(545\) 91.0157 + 27.2483i 0.167001 + 0.0499969i
\(546\) 0 0
\(547\) 30.5581 70.8416i 0.0558649 0.129509i −0.887998 0.459848i \(-0.847904\pi\)
0.943862 + 0.330339i \(0.107163\pi\)
\(548\) 0 0
\(549\) −70.6746 + 540.807i −0.128733 + 0.985077i
\(550\) 0 0
\(551\) −494.496 466.533i −0.897451 0.846702i
\(552\) 0 0
\(553\) −31.5413 15.8407i −0.0570368 0.0286449i
\(554\) 0 0
\(555\) −2.60234 116.715i −0.00468890 0.210297i
\(556\) 0 0
\(557\) 771.582 136.051i 1.38525 0.244256i 0.569179 0.822214i \(-0.307261\pi\)
0.816067 + 0.577958i \(0.196150\pi\)
\(558\) 0 0
\(559\) −44.2154 + 250.758i −0.0790972 + 0.448583i
\(560\) 0 0
\(561\) −35.2033 436.524i −0.0627511 0.778118i
\(562\) 0 0
\(563\) 148.337 63.9865i 0.263477 0.113653i −0.260244 0.965543i \(-0.583803\pi\)
0.523720 + 0.851890i \(0.324544\pi\)
\(564\) 0 0
\(565\) −133.372 87.7202i −0.236057 0.155257i
\(566\) 0 0
\(567\) 76.7312 60.9091i 0.135328 0.107423i
\(568\) 0 0
\(569\) 201.744 306.737i 0.354559 0.539081i −0.613535 0.789668i \(-0.710253\pi\)
0.968094 + 0.250586i \(0.0806234\pi\)
\(570\) 0 0
\(571\) 242.246 + 561.588i 0.424248 + 0.983517i 0.987556 + 0.157270i \(0.0502693\pi\)
−0.563308 + 0.826247i \(0.690471\pi\)
\(572\) 0 0
\(573\) −277.057 401.457i −0.483520 0.700624i
\(574\) 0 0
\(575\) −7.84965 1.38411i −0.0136516 0.00240714i
\(576\) 0 0
\(577\) −44.5737 252.790i −0.0772508 0.438111i −0.998761 0.0497578i \(-0.984155\pi\)
0.921510 0.388354i \(-0.126956\pi\)
\(578\) 0 0
\(579\) 72.7010 132.666i 0.125563 0.229130i
\(580\) 0 0
\(581\) 18.6459 37.1269i 0.0320927 0.0639018i
\(582\) 0 0
\(583\) 177.459 188.095i 0.304389 0.322634i
\(584\) 0 0
\(585\) 53.0640 + 27.5592i 0.0907078 + 0.0471097i
\(586\) 0 0
\(587\) 771.561 + 332.819i 1.31441 + 0.566983i 0.933815 0.357757i \(-0.116458\pi\)
0.380599 + 0.924740i \(0.375718\pi\)
\(588\) 0 0
\(589\) 221.346 739.346i 0.375799 1.25526i
\(590\) 0 0
\(591\) 53.3849 85.2481i 0.0903299 0.144244i
\(592\) 0 0
\(593\) −599.640 346.203i −1.01120 0.583815i −0.0996558 0.995022i \(-0.531774\pi\)
−0.911542 + 0.411207i \(0.865108\pi\)
\(594\) 0 0
\(595\) −15.6811 27.1605i −0.0263549 0.0456479i
\(596\) 0 0
\(597\) −329.952 + 365.729i −0.552683 + 0.612611i
\(598\) 0 0
\(599\) 244.171 + 1030.24i 0.407631 + 1.71993i 0.659090 + 0.752064i \(0.270942\pi\)
−0.251459 + 0.967868i \(0.580910\pi\)
\(600\) 0 0
\(601\) −158.278 212.604i −0.263357 0.353750i 0.650700 0.759335i \(-0.274475\pi\)
−0.914058 + 0.405585i \(0.867068\pi\)
\(602\) 0 0
\(603\) −325.101 61.8914i −0.539139 0.102639i
\(604\) 0 0
\(605\) 20.9058 88.2084i 0.0345550 0.145799i
\(606\) 0 0
\(607\) 58.2652 38.3216i 0.0959887 0.0631328i −0.500607 0.865675i \(-0.666890\pi\)
0.596596 + 0.802542i \(0.296520\pi\)
\(608\) 0 0
\(609\) −44.7350 50.9615i −0.0734565 0.0836806i
\(610\) 0 0
\(611\) 365.533 + 435.626i 0.598254 + 0.712971i
\(612\) 0 0
\(613\) −797.070 668.821i −1.30028 1.09106i −0.990097 0.140384i \(-0.955166\pi\)
−0.310180 0.950678i \(-0.600389\pi\)
\(614\) 0 0
\(615\) 135.434 + 12.7770i 0.220218 + 0.0207755i
\(616\) 0 0
\(617\) −82.5136 61.4291i −0.133733 0.0995609i 0.528213 0.849112i \(-0.322862\pi\)
−0.661947 + 0.749551i \(0.730270\pi\)
\(618\) 0 0
\(619\) −902.223 + 453.114i −1.45755 + 0.732009i −0.988508 0.151167i \(-0.951697\pi\)
−0.469042 + 0.883176i \(0.655401\pi\)
\(620\) 0 0
\(621\) −2.66266 8.62020i −0.00428770 0.0138812i
\(622\) 0 0
\(623\) 50.6597 + 2.95059i 0.0813157 + 0.00473610i
\(624\) 0 0
\(625\) −536.693 62.7304i −0.858709 0.100369i
\(626\) 0 0
\(627\) 468.253 461.932i 0.746815 0.736733i
\(628\) 0 0
\(629\) 301.095 + 827.253i 0.478689 + 1.31519i
\(630\) 0 0
\(631\) 721.784 + 262.708i 1.14387 + 0.416336i 0.843311 0.537426i \(-0.180603\pi\)
0.300562 + 0.953762i \(0.402826\pi\)
\(632\) 0 0
\(633\) 700.468 272.781i 1.10658 0.430934i
\(634\) 0 0
\(635\) 75.8720 4.41904i 0.119483 0.00695912i
\(636\) 0 0
\(637\) 84.6049 + 282.600i 0.132818 + 0.443642i
\(638\) 0 0
\(639\) 233.840 113.485i 0.365946 0.177599i
\(640\) 0 0
\(641\) 60.7427 + 519.687i 0.0947625 + 0.810745i 0.954131 + 0.299388i \(0.0967826\pi\)
−0.859369 + 0.511356i \(0.829143\pi\)
\(642\) 0 0
\(643\) −438.664 464.957i −0.682215 0.723106i 0.290044 0.957013i \(-0.406330\pi\)
−0.972259 + 0.233908i \(0.924849\pi\)
\(644\) 0 0
\(645\) −103.931 + 81.0362i −0.161133 + 0.125638i
\(646\) 0 0
\(647\) 60.2187i 0.0930738i −0.998917 0.0465369i \(-0.985181\pi\)
0.998917 0.0465369i \(-0.0148185\pi\)
\(648\) 0 0
\(649\) 242.877 0.374233
\(650\) 0 0
\(651\) 28.9072 71.3468i 0.0444043 0.109596i
\(652\) 0 0
\(653\) −578.261 + 545.561i −0.885546 + 0.835469i −0.987222 0.159348i \(-0.949061\pi\)
0.101677 + 0.994817i \(0.467579\pi\)
\(654\) 0 0
\(655\) −152.377 + 17.8103i −0.232636 + 0.0271913i
\(656\) 0 0
\(657\) −21.7486 210.892i −0.0331028 0.320992i
\(658\) 0 0
\(659\) −45.9575 + 13.7588i −0.0697382 + 0.0208782i −0.321482 0.946916i \(-0.604181\pi\)
0.251744 + 0.967794i \(0.418996\pi\)
\(660\) 0 0
\(661\) −0.623298 10.7016i −0.000942962 0.0161900i 0.997804 0.0662379i \(-0.0210996\pi\)
−0.998747 + 0.0500479i \(0.984063\pi\)
\(662\) 0 0
\(663\) −445.679 68.3793i −0.672216 0.103136i
\(664\) 0 0
\(665\) 16.1104 44.2631i 0.0242262 0.0665610i
\(666\) 0 0
\(667\) −5.86825 + 2.13587i −0.00879798 + 0.00320220i
\(668\) 0 0
\(669\) 67.7894 246.286i 0.101330 0.368141i
\(670\) 0 0
\(671\) −42.4035 + 362.785i −0.0631945 + 0.540664i
\(672\) 0 0
\(673\) −4.39869 + 75.5226i −0.00653594 + 0.112218i −0.999998 0.00194400i \(-0.999381\pi\)
0.993462 + 0.114162i \(0.0364182\pi\)
\(674\) 0 0
\(675\) −225.536 603.271i −0.334128 0.893735i
\(676\) 0 0
\(677\) 487.570 + 970.833i 0.720193 + 1.43402i 0.893458 + 0.449146i \(0.148272\pi\)
−0.173266 + 0.984875i \(0.555432\pi\)
\(678\) 0 0
\(679\) 46.6863 62.7106i 0.0687575 0.0923573i
\(680\) 0 0
\(681\) 256.658 + 182.326i 0.376885 + 0.267733i
\(682\) 0 0
\(683\) −398.492 + 474.905i −0.583444 + 0.695321i −0.974332 0.225117i \(-0.927724\pi\)
0.390888 + 0.920438i \(0.372168\pi\)
\(684\) 0 0
\(685\) 123.542 103.664i 0.180353 0.151335i
\(686\) 0 0
\(687\) 306.407 + 103.849i 0.446008 + 0.151162i
\(688\) 0 0
\(689\) −146.303 222.443i −0.212342 0.322850i
\(690\) 0 0
\(691\) −630.545 149.442i −0.912511 0.216269i −0.252563 0.967580i \(-0.581274\pi\)
−0.659948 + 0.751311i \(0.729422\pi\)
\(692\) 0 0
\(693\) 50.8273 41.4851i 0.0733439 0.0598631i
\(694\) 0 0
\(695\) 79.5039 59.1885i 0.114394 0.0851633i
\(696\) 0 0
\(697\) −998.168 + 236.570i −1.43209 + 0.339412i
\(698\) 0 0
\(699\) −526.993 + 170.661i −0.753924 + 0.244150i
\(700\) 0 0
\(701\) 921.497 532.027i 1.31455 0.758954i 0.331701 0.943385i \(-0.392377\pi\)
0.982846 + 0.184431i \(0.0590442\pi\)
\(702\) 0 0
\(703\) −661.105 + 1145.07i −0.940406 + 1.62883i
\(704\) 0 0
\(705\) −10.5598 + 294.143i −0.0149784 + 0.417224i
\(706\) 0 0
\(707\) 189.917 + 56.8575i 0.268624 + 0.0804208i
\(708\) 0 0
\(709\) 160.548 372.193i 0.226444 0.524955i −0.766680 0.642030i \(-0.778092\pi\)
0.993123 + 0.117075i \(0.0373517\pi\)
\(710\) 0 0
\(711\) −250.563 78.7399i −0.352409 0.110745i
\(712\) 0 0
\(713\) −5.15659 4.86499i −0.00723225 0.00682327i
\(714\) 0 0
\(715\) 35.7843 + 17.9715i 0.0500479 + 0.0251350i
\(716\) 0 0
\(717\) 359.428 218.340i 0.501294 0.304519i
\(718\) 0 0
\(719\) −160.541 + 28.3078i −0.223284 + 0.0393710i −0.284171 0.958774i \(-0.591718\pi\)
0.0608866 + 0.998145i \(0.480607\pi\)
\(720\) 0 0
\(721\) 2.07450 11.7651i 0.00287725 0.0163177i
\(722\) 0 0
\(723\) −254.109 120.602i −0.351464 0.166808i
\(724\) 0 0
\(725\) −409.339 + 176.572i −0.564605 + 0.243547i
\(726\) 0 0
\(727\) −604.538 397.611i −0.831552 0.546920i 0.0608578 0.998146i \(-0.480616\pi\)
−0.892410 + 0.451226i \(0.850987\pi\)
\(728\) 0 0
\(729\) 490.967 538.880i 0.673481 0.739205i
\(730\) 0 0
\(731\) 546.104 830.310i 0.747064 1.13586i
\(732\) 0 0
\(733\) 442.571 + 1025.99i 0.603780 + 1.39972i 0.896295 + 0.443459i \(0.146249\pi\)
−0.292515 + 0.956261i \(0.594492\pi\)
\(734\) 0 0
\(735\) −65.4655 + 137.936i −0.0890687 + 0.187668i
\(736\) 0 0
\(737\) −218.261 38.4854i −0.296149 0.0522190i
\(738\) 0 0
\(739\) −121.724 690.330i −0.164714 0.934140i −0.949359 0.314194i \(-0.898266\pi\)
0.784645 0.619946i \(-0.212845\pi\)
\(740\) 0 0
\(741\) −351.594 578.787i −0.474486 0.781090i
\(742\) 0 0
\(743\) 410.024 816.424i 0.551849 1.09882i −0.428864 0.903369i \(-0.641086\pi\)
0.980713 0.195452i \(-0.0626175\pi\)
\(744\) 0 0
\(745\) −43.6166 + 46.2309i −0.0585458 + 0.0620549i
\(746\) 0 0
\(747\) 92.6838 294.935i 0.124075 0.394826i
\(748\) 0 0
\(749\) −44.5526 19.2181i −0.0594827 0.0256583i
\(750\) 0 0
\(751\) −364.595 + 1217.83i −0.485480 + 1.62162i 0.267490 + 0.963561i \(0.413806\pi\)
−0.752970 + 0.658055i \(0.771379\pi\)
\(752\) 0 0
\(753\) 1335.95 + 47.9608i 1.77417 + 0.0636929i
\(754\) 0 0
\(755\) −250.608 144.689i −0.331931 0.191641i
\(756\) 0 0
\(757\) 480.896 + 832.936i 0.635265 + 1.10031i 0.986459 + 0.164008i \(0.0524424\pi\)
−0.351194 + 0.936303i \(0.614224\pi\)
\(758\) 0 0
\(759\) −1.86147 5.74813i −0.00245252 0.00757329i
\(760\) 0 0
\(761\) −30.8440 130.141i −0.0405309 0.171013i 0.949015 0.315230i \(-0.102082\pi\)
−0.989546 + 0.144217i \(0.953934\pi\)
\(762\) 0 0
\(763\) −64.0923 86.0909i −0.0840004 0.112832i
\(764\) 0 0
\(765\) −147.567 180.798i −0.192898 0.236337i
\(766\) 0 0
\(767\) 57.6679 243.320i 0.0751864 0.317236i
\(768\) 0 0
\(769\) 1056.66 694.974i 1.37407 0.903737i 0.374343 0.927290i \(-0.377868\pi\)
0.999723 + 0.0235536i \(0.00749804\pi\)
\(770\) 0 0
\(771\) −21.7089 + 64.0524i −0.0281568 + 0.0830771i
\(772\) 0 0
\(773\) 811.830 + 967.501i 1.05023 + 1.25162i 0.966916 + 0.255095i \(0.0821067\pi\)
0.0833162 + 0.996523i \(0.473449\pi\)
\(774\) 0 0
\(775\) −387.681 325.303i −0.500233 0.419745i
\(776\) 0 0
\(777\) −76.3784 + 107.517i −0.0982991 + 0.138375i
\(778\) 0 0
\(779\) −1235.83 920.044i −1.58644 1.18106i
\(780\) 0 0
\(781\) 155.554 78.1220i 0.199172 0.100028i
\(782\) 0 0
\(783\) −389.351 320.973i −0.497256 0.409927i
\(784\) 0 0
\(785\) 231.884 + 13.5057i 0.295394 + 0.0172047i
\(786\) 0 0
\(787\) 1286.56 + 150.377i 1.63476 + 0.191076i 0.883336 0.468740i \(-0.155292\pi\)
0.751427 + 0.659817i \(0.229366\pi\)
\(788\) 0 0
\(789\) 941.855 + 259.242i 1.19373 + 0.328571i
\(790\) 0 0
\(791\) 61.6790 + 169.462i 0.0779759 + 0.214237i
\(792\) 0 0
\(793\) 353.379 + 128.619i 0.445623 + 0.162194i
\(794\) 0 0
\(795\) 20.8982 136.209i 0.0262870 0.171332i