Properties

Label 324.3.o.a.5.17
Level $324$
Weight $3$
Character 324.5
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 5.17
Character \(\chi\) \(=\) 324.5
Dual form 324.3.o.a.65.17

$q$-expansion

\(f(q)\) \(=\) \(q+(2.94286 + 0.582717i) q^{3} +(5.13522 - 3.82303i) q^{5} +(3.31229 - 2.17853i) q^{7} +(8.32088 + 3.42971i) q^{9} +O(q^{10})\) \(q+(2.94286 + 0.582717i) q^{3} +(5.13522 - 3.82303i) q^{5} +(3.31229 - 2.17853i) q^{7} +(8.32088 + 3.42971i) q^{9} +(-0.480652 + 4.11224i) q^{11} +(-0.145678 - 0.486597i) q^{13} +(17.3400 - 8.25827i) q^{15} +(-19.6534 - 3.46543i) q^{17} +(-2.04833 - 11.6166i) q^{19} +(11.0171 - 4.48098i) q^{21} +(8.81970 - 13.4097i) q^{23} +(4.58486 - 15.3145i) q^{25} +(22.4887 + 14.9419i) q^{27} +(-10.8795 + 10.2643i) q^{29} +(-1.57896 + 27.1097i) q^{31} +(-3.81077 + 11.8217i) q^{33} +(8.68077 - 23.8502i) q^{35} +(11.6418 - 4.23727i) q^{37} +(-0.145161 - 1.51688i) q^{39} +(1.01794 - 4.29502i) q^{41} +(21.3640 + 49.5273i) q^{43} +(55.8415 - 14.1987i) q^{45} +(25.7996 - 1.50266i) q^{47} +(-13.1826 + 30.5607i) q^{49} +(-55.8180 - 21.6507i) q^{51} +(-5.12718 - 2.96018i) q^{53} +(13.2530 + 22.9548i) q^{55} +(0.741268 - 35.3798i) q^{57} +(-8.92774 - 76.3817i) q^{59} +(-13.5091 - 6.78452i) q^{61} +(35.0329 - 6.76707i) q^{63} +(-2.60836 - 1.94185i) q^{65} +(-68.4316 + 72.5333i) q^{67} +(33.7692 - 34.3235i) q^{69} +(5.41579 - 6.45429i) q^{71} +(-24.0192 + 20.1545i) q^{73} +(22.4166 - 42.3968i) q^{75} +(7.36658 + 14.6681i) q^{77} +(50.9936 - 12.0857i) q^{79} +(57.4741 + 57.0765i) q^{81} +(-14.7516 - 62.2420i) q^{83} +(-114.173 + 57.3399i) q^{85} +(-37.9982 + 23.8668i) q^{87} +(-108.213 - 128.963i) q^{89} +(-1.54259 - 1.29439i) q^{91} +(-20.4439 + 78.8599i) q^{93} +(-54.9294 - 51.8232i) q^{95} +(-42.4611 + 57.0351i) q^{97} +(-18.1033 + 32.5690i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 324 q + O(q^{10}) \) \( 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(163\) \(245\)
\(\chi(n)\) \(1\) \(e\left(\frac{23}{54}\right)\)

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
\(3\) 2.94286 + 0.582717i 0.980954 + 0.194239i
\(4\) 0 0
\(5\) 5.13522 3.82303i 1.02704 0.764606i 0.0547818 0.998498i \(-0.482554\pi\)
0.972263 + 0.233892i \(0.0751463\pi\)
\(6\) 0 0
\(7\) 3.31229 2.17853i 0.473185 0.311218i −0.290424 0.956898i \(-0.593796\pi\)
0.763608 + 0.645680i \(0.223426\pi\)
\(8\) 0 0
\(9\) 8.32088 + 3.42971i 0.924542 + 0.381079i
\(10\) 0 0
\(11\) −0.480652 + 4.11224i −0.0436956 + 0.373840i 0.953643 + 0.300939i \(0.0972999\pi\)
−0.997339 + 0.0729015i \(0.976774\pi\)
\(12\) 0 0
\(13\) −0.145678 0.486597i −0.0112060 0.0374305i 0.952204 0.305464i \(-0.0988115\pi\)
−0.963410 + 0.268033i \(0.913626\pi\)
\(14\) 0 0
\(15\) 17.3400 8.25827i 1.15600 0.550552i
\(16\) 0 0
\(17\) −19.6534 3.46543i −1.15608 0.203849i −0.437454 0.899241i \(-0.644120\pi\)
−0.718631 + 0.695392i \(0.755231\pi\)
\(18\) 0 0
\(19\) −2.04833 11.6166i −0.107807 0.611402i −0.990062 0.140631i \(-0.955087\pi\)
0.882255 0.470771i \(-0.156024\pi\)
\(20\) 0 0
\(21\) 11.0171 4.48098i 0.524623 0.213380i
\(22\) 0 0
\(23\) 8.81970 13.4097i 0.383465 0.583030i −0.591248 0.806490i \(-0.701365\pi\)
0.974713 + 0.223459i \(0.0717350\pi\)
\(24\) 0 0
\(25\) 4.58486 15.3145i 0.183394 0.612580i
\(26\) 0 0
\(27\) 22.4887 + 14.9419i 0.832913 + 0.553403i
\(28\) 0 0
\(29\) −10.8795 + 10.2643i −0.375157 + 0.353942i −0.850608 0.525800i \(-0.823766\pi\)
0.475452 + 0.879742i \(0.342285\pi\)
\(30\) 0 0
\(31\) −1.57896 + 27.1097i −0.0509341 + 0.874505i 0.871990 + 0.489524i \(0.162829\pi\)
−0.922924 + 0.384982i \(0.874208\pi\)
\(32\) 0 0
\(33\) −3.81077 + 11.8217i −0.115478 + 0.358233i
\(34\) 0 0
\(35\) 8.68077 23.8502i 0.248022 0.681435i
\(36\) 0 0
\(37\) 11.6418 4.23727i 0.314644 0.114521i −0.179871 0.983690i \(-0.557568\pi\)
0.494515 + 0.869169i \(0.335346\pi\)
\(38\) 0 0
\(39\) −0.145161 1.51688i −0.00372207 0.0388943i
\(40\) 0 0
\(41\) 1.01794 4.29502i 0.0248278 0.104757i −0.959220 0.282660i \(-0.908783\pi\)
0.984048 + 0.177903i \(0.0569314\pi\)
\(42\) 0 0
\(43\) 21.3640 + 49.5273i 0.496837 + 1.15180i 0.963584 + 0.267407i \(0.0861667\pi\)
−0.466747 + 0.884391i \(0.654574\pi\)
\(44\) 0 0
\(45\) 55.8415 14.1987i 1.24092 0.315526i
\(46\) 0 0
\(47\) 25.7996 1.50266i 0.548929 0.0319715i 0.218560 0.975823i \(-0.429864\pi\)
0.330369 + 0.943852i \(0.392827\pi\)
\(48\) 0 0
\(49\) −13.1826 + 30.5607i −0.269033 + 0.623689i
\(50\) 0 0
\(51\) −55.8180 21.6507i −1.09447 0.424523i
\(52\) 0 0
\(53\) −5.12718 2.96018i −0.0967393 0.0558524i 0.450850 0.892600i \(-0.351121\pi\)
−0.547589 + 0.836747i \(0.684454\pi\)
\(54\) 0 0
\(55\) 13.2530 + 22.9548i 0.240963 + 0.417360i
\(56\) 0 0
\(57\) 0.741268 35.3798i 0.0130047 0.620698i
\(58\) 0 0
\(59\) −8.92774 76.3817i −0.151318 1.29460i −0.828999 0.559249i \(-0.811089\pi\)
0.677682 0.735355i \(-0.262985\pi\)
\(60\) 0 0
\(61\) −13.5091 6.78452i −0.221460 0.111222i 0.334610 0.942357i \(-0.391395\pi\)
−0.556071 + 0.831135i \(0.687692\pi\)
\(62\) 0 0
\(63\) 35.0329 6.76707i 0.556078 0.107414i
\(64\) 0 0
\(65\) −2.60836 1.94185i −0.0401286 0.0298747i
\(66\) 0 0
\(67\) −68.4316 + 72.5333i −1.02137 + 1.08259i −0.0248087 + 0.999692i \(0.507898\pi\)
−0.996558 + 0.0828936i \(0.973584\pi\)
\(68\) 0 0
\(69\) 33.7692 34.3235i 0.489409 0.497442i
\(70\) 0 0
\(71\) 5.41579 6.45429i 0.0762788 0.0909055i −0.726555 0.687108i \(-0.758880\pi\)
0.802834 + 0.596202i \(0.203324\pi\)
\(72\) 0 0
\(73\) −24.0192 + 20.1545i −0.329031 + 0.276089i −0.792305 0.610126i \(-0.791119\pi\)
0.463274 + 0.886215i \(0.346675\pi\)
\(74\) 0 0
\(75\) 22.4166 42.3968i 0.298888 0.565290i
\(76\) 0 0
\(77\) 7.36658 + 14.6681i 0.0956698 + 0.190494i
\(78\) 0 0
\(79\) 50.9936 12.0857i 0.645488 0.152983i 0.105183 0.994453i \(-0.466457\pi\)
0.540305 + 0.841469i \(0.318309\pi\)
\(80\) 0 0
\(81\) 57.4741 + 57.0765i 0.709557 + 0.704648i
\(82\) 0 0
\(83\) −14.7516 62.2420i −0.177730 0.749904i −0.986767 0.162145i \(-0.948159\pi\)
0.809036 0.587758i \(-0.199989\pi\)
\(84\) 0 0
\(85\) −114.173 + 57.3399i −1.34321 + 0.674588i
\(86\) 0 0
\(87\) −37.9982 + 23.8668i −0.436761 + 0.274331i
\(88\) 0 0
\(89\) −108.213 128.963i −1.21587 1.44902i −0.856751 0.515730i \(-0.827521\pi\)
−0.359122 0.933291i \(-0.616924\pi\)
\(90\) 0 0
\(91\) −1.54259 1.29439i −0.0169516 0.0142240i
\(92\) 0 0
\(93\) −20.4439 + 78.8599i −0.219827 + 0.847956i
\(94\) 0 0
\(95\) −54.9294 51.8232i −0.578204 0.545508i
\(96\) 0 0
\(97\) −42.4611 + 57.0351i −0.437743 + 0.587991i −0.965175 0.261607i \(-0.915748\pi\)
0.527432 + 0.849597i \(0.323155\pi\)
\(98\) 0 0
\(99\) −18.1033 + 32.5690i −0.182861 + 0.328980i
\(100\) 0 0
\(101\) −74.6109 + 148.563i −0.738722 + 1.47092i 0.138261 + 0.990396i \(0.455849\pi\)
−0.876983 + 0.480521i \(0.840448\pi\)
\(102\) 0 0
\(103\) 20.3945 2.38378i 0.198005 0.0231435i −0.0165122 0.999864i \(-0.505256\pi\)
0.214517 + 0.976720i \(0.431182\pi\)
\(104\) 0 0
\(105\) 39.4443 65.1295i 0.375660 0.620281i
\(106\) 0 0
\(107\) 87.2888 50.3962i 0.815783 0.470992i −0.0331773 0.999449i \(-0.510563\pi\)
0.848960 + 0.528457i \(0.177229\pi\)
\(108\) 0 0
\(109\) −107.068 + 185.447i −0.982273 + 1.70135i −0.328797 + 0.944401i \(0.606643\pi\)
−0.653477 + 0.756947i \(0.726690\pi\)
\(110\) 0 0
\(111\) 36.7294 5.68583i 0.330895 0.0512237i
\(112\) 0 0
\(113\) −113.758 49.0703i −1.00671 0.434250i −0.172089 0.985081i \(-0.555052\pi\)
−0.834617 + 0.550831i \(0.814311\pi\)
\(114\) 0 0
\(115\) −5.97459 102.580i −0.0519530 0.891998i
\(116\) 0 0
\(117\) 0.456722 4.54855i 0.00390360 0.0388765i
\(118\) 0 0
\(119\) −72.6475 + 31.3371i −0.610483 + 0.263337i
\(120\) 0 0
\(121\) 101.059 + 23.9514i 0.835198 + 0.197945i
\(122\) 0 0
\(123\) 5.49843 12.0465i 0.0447027 0.0979388i
\(124\) 0 0
\(125\) 19.7371 + 54.2273i 0.157897 + 0.433819i
\(126\) 0 0
\(127\) −12.1409 4.41892i −0.0955974 0.0347946i 0.293779 0.955873i \(-0.405087\pi\)
−0.389376 + 0.921079i \(0.627309\pi\)
\(128\) 0 0
\(129\) 34.0109 + 158.201i 0.263650 + 1.22637i
\(130\) 0 0
\(131\) −95.9762 5.58998i −0.732643 0.0426716i −0.312233 0.950006i \(-0.601077\pi\)
−0.420410 + 0.907334i \(0.638114\pi\)
\(132\) 0 0
\(133\) −32.0918 34.0154i −0.241292 0.255755i
\(134\) 0 0
\(135\) 172.608 9.24492i 1.27857 0.0684809i
\(136\) 0 0
\(137\) −53.9684 16.1571i −0.393930 0.117935i 0.0837109 0.996490i \(-0.473323\pi\)
−0.477641 + 0.878555i \(0.658508\pi\)
\(138\) 0 0
\(139\) −166.507 109.514i −1.19790 0.787868i −0.215834 0.976430i \(-0.569247\pi\)
−0.982061 + 0.188562i \(0.939617\pi\)
\(140\) 0 0
\(141\) 76.8004 + 10.6118i 0.544684 + 0.0752608i
\(142\) 0 0
\(143\) 2.07102 0.365177i 0.0144827 0.00255369i
\(144\) 0 0
\(145\) −16.6281 + 94.3024i −0.114676 + 0.650361i
\(146\) 0 0
\(147\) −56.6029 + 82.2543i −0.385054 + 0.559553i
\(148\) 0 0
\(149\) −261.088 + 78.1647i −1.75227 + 0.524595i −0.992135 0.125169i \(-0.960053\pi\)
−0.760135 + 0.649765i \(0.774867\pi\)
\(150\) 0 0
\(151\) −142.117 16.6110i −0.941169 0.110007i −0.368349 0.929688i \(-0.620077\pi\)
−0.572820 + 0.819681i \(0.694151\pi\)
\(152\) 0 0
\(153\) −151.648 96.2411i −0.991167 0.629027i
\(154\) 0 0
\(155\) 95.5328 + 145.251i 0.616341 + 0.937100i
\(156\) 0 0
\(157\) −94.2629 126.617i −0.600400 0.806478i 0.393197 0.919454i \(-0.371369\pi\)
−0.993598 + 0.112976i \(0.963962\pi\)
\(158\) 0 0
\(159\) −13.3636 11.6991i −0.0840481 0.0735792i
\(160\) 0 0
\(161\) 63.6308i 0.395222i
\(162\) 0 0
\(163\) 293.050 1.79785 0.898925 0.438102i \(-0.144349\pi\)
0.898925 + 0.438102i \(0.144349\pi\)
\(164\) 0 0
\(165\) 25.6255 + 75.2756i 0.155306 + 0.456216i
\(166\) 0 0
\(167\) 1.80830 1.34623i 0.0108282 0.00806126i −0.591731 0.806136i \(-0.701555\pi\)
0.602559 + 0.798074i \(0.294148\pi\)
\(168\) 0 0
\(169\) 140.982 92.7252i 0.834212 0.548670i
\(170\) 0 0
\(171\) 22.7978 103.686i 0.133321 0.606350i
\(172\) 0 0
\(173\) 0.815873 6.98024i 0.00471603 0.0403482i −0.990675 0.136243i \(-0.956497\pi\)
0.995391 + 0.0958949i \(0.0305713\pi\)
\(174\) 0 0
\(175\) −18.1767 60.7143i −0.103867 0.346939i
\(176\) 0 0
\(177\) 18.2358 229.983i 0.103027 1.29934i
\(178\) 0 0
\(179\) 282.326 + 49.7817i 1.57724 + 0.278110i 0.892627 0.450796i \(-0.148860\pi\)
0.684614 + 0.728906i \(0.259971\pi\)
\(180\) 0 0
\(181\) 37.9341 + 215.135i 0.209580 + 1.18859i 0.890067 + 0.455829i \(0.150657\pi\)
−0.680487 + 0.732760i \(0.738232\pi\)
\(182\) 0 0
\(183\) −35.8019 27.8379i −0.195639 0.152120i
\(184\) 0 0
\(185\) 43.5841 66.2663i 0.235590 0.358196i
\(186\) 0 0
\(187\) 23.6972 79.1540i 0.126723 0.423283i
\(188\) 0 0
\(189\) 107.040 + 0.499714i 0.566351 + 0.00264399i
\(190\) 0 0
\(191\) 199.702 188.409i 1.04556 0.986437i 0.0456403 0.998958i \(-0.485467\pi\)
0.999922 + 0.0125212i \(0.00398572\pi\)
\(192\) 0 0
\(193\) −15.9478 + 273.813i −0.0826312 + 1.41872i 0.661127 + 0.750274i \(0.270078\pi\)
−0.743758 + 0.668449i \(0.766959\pi\)
\(194\) 0 0
\(195\) −6.54450 7.23454i −0.0335615 0.0371002i
\(196\) 0 0
\(197\) 76.5284 210.260i 0.388469 1.06731i −0.579222 0.815170i \(-0.696643\pi\)
0.967691 0.252140i \(-0.0811343\pi\)
\(198\) 0 0
\(199\) 285.813 104.027i 1.43625 0.522751i 0.497532 0.867446i \(-0.334240\pi\)
0.938715 + 0.344695i \(0.112018\pi\)
\(200\) 0 0
\(201\) −243.651 + 173.579i −1.21219 + 0.863578i
\(202\) 0 0
\(203\) −13.6751 + 57.6998i −0.0673651 + 0.284236i
\(204\) 0 0
\(205\) −11.1926 25.9475i −0.0545983 0.126573i
\(206\) 0 0
\(207\) 119.379 81.3315i 0.576710 0.392906i
\(208\) 0 0
\(209\) 48.7550 2.83965i 0.233277 0.0135869i
\(210\) 0 0
\(211\) 102.122 236.746i 0.483991 1.12202i −0.484908 0.874565i \(-0.661147\pi\)
0.968900 0.247453i \(-0.0795937\pi\)
\(212\) 0 0
\(213\) 19.6990 15.8382i 0.0924834 0.0743578i
\(214\) 0 0
\(215\) 299.053 + 172.658i 1.39095 + 0.803063i
\(216\) 0 0
\(217\) 53.8292 + 93.2350i 0.248061 + 0.429654i
\(218\) 0 0
\(219\) −82.4297 + 45.3156i −0.376391 + 0.206920i
\(220\) 0 0
\(221\) 1.17680 + 10.0681i 0.00532487 + 0.0455572i
\(222\) 0 0
\(223\) −41.3364 20.7599i −0.185365 0.0930937i 0.353696 0.935360i \(-0.384925\pi\)
−0.539061 + 0.842267i \(0.681221\pi\)
\(224\) 0 0
\(225\) 90.6743 111.705i 0.402997 0.496468i
\(226\) 0 0
\(227\) 15.6789 + 11.6725i 0.0690698 + 0.0514206i 0.631140 0.775669i \(-0.282587\pi\)
−0.562070 + 0.827090i \(0.689995\pi\)
\(228\) 0 0
\(229\) −56.5030 + 59.8896i −0.246738 + 0.261527i −0.838892 0.544298i \(-0.816796\pi\)
0.592154 + 0.805825i \(0.298278\pi\)
\(230\) 0 0
\(231\) 13.1315 + 47.4587i 0.0568463 + 0.205449i
\(232\) 0 0
\(233\) 129.196 153.970i 0.554491 0.660817i −0.413880 0.910331i \(-0.635827\pi\)
0.968371 + 0.249515i \(0.0802711\pi\)
\(234\) 0 0
\(235\) 126.742 106.349i 0.539329 0.452550i
\(236\) 0 0
\(237\) 157.110 5.85173i 0.662910 0.0246908i
\(238\) 0 0
\(239\) −24.7626 49.3063i −0.103609 0.206303i 0.835855 0.548951i \(-0.184972\pi\)
−0.939464 + 0.342648i \(0.888676\pi\)
\(240\) 0 0
\(241\) 157.284 37.2771i 0.652632 0.154677i 0.109055 0.994036i \(-0.465218\pi\)
0.543577 + 0.839359i \(0.317070\pi\)
\(242\) 0 0
\(243\) 135.879 + 201.459i 0.559173 + 0.829051i
\(244\) 0 0
\(245\) 49.1390 + 207.334i 0.200567 + 0.846260i
\(246\) 0 0
\(247\) −5.35423 + 2.68899i −0.0216770 + 0.0108866i
\(248\) 0 0
\(249\) −7.14254 191.766i −0.0286849 0.770143i
\(250\) 0 0
\(251\) 111.884 + 133.339i 0.445755 + 0.531230i 0.941399 0.337296i \(-0.109512\pi\)
−0.495644 + 0.868526i \(0.665068\pi\)
\(252\) 0 0
\(253\) 50.9047 + 42.7141i 0.201204 + 0.168831i
\(254\) 0 0
\(255\) −369.409 + 102.213i −1.44866 + 0.400835i
\(256\) 0 0
\(257\) −60.6402 57.2111i −0.235954 0.222611i 0.559178 0.829048i \(-0.311117\pi\)
−0.795132 + 0.606437i \(0.792598\pi\)
\(258\) 0 0
\(259\) 29.3301 39.3971i 0.113243 0.152112i
\(260\) 0 0
\(261\) −125.731 + 48.0945i −0.481728 + 0.184270i
\(262\) 0 0
\(263\) −184.811 + 367.990i −0.702705 + 1.39920i 0.204650 + 0.978835i \(0.434394\pi\)
−0.907355 + 0.420365i \(0.861902\pi\)
\(264\) 0 0
\(265\) −37.6461 + 4.40019i −0.142061 + 0.0166045i
\(266\) 0 0
\(267\) −243.306 442.577i −0.911259 1.65759i
\(268\) 0 0
\(269\) 106.187 61.3070i 0.394747 0.227907i −0.289468 0.957188i \(-0.593478\pi\)
0.684215 + 0.729281i \(0.260145\pi\)
\(270\) 0 0
\(271\) −183.075 + 317.095i −0.675553 + 1.17009i 0.300753 + 0.953702i \(0.402762\pi\)
−0.976307 + 0.216391i \(0.930571\pi\)
\(272\) 0 0
\(273\) −3.78537 4.70810i −0.0138658 0.0172458i
\(274\) 0 0
\(275\) 60.7732 + 26.2150i 0.220993 + 0.0953272i
\(276\) 0 0
\(277\) −19.7624 339.308i −0.0713445 1.22494i −0.824026 0.566552i \(-0.808277\pi\)
0.752681 0.658385i \(-0.228760\pi\)
\(278\) 0 0
\(279\) −106.117 + 220.161i −0.380347 + 0.789107i
\(280\) 0 0
\(281\) 223.848 96.5584i 0.796610 0.343624i 0.0414302 0.999141i \(-0.486809\pi\)
0.755180 + 0.655517i \(0.227549\pi\)
\(282\) 0 0
\(283\) −323.938 76.7746i −1.14466 0.271288i −0.385822 0.922573i \(-0.626082\pi\)
−0.758834 + 0.651285i \(0.774230\pi\)
\(284\) 0 0
\(285\) −131.451 184.517i −0.461233 0.647428i
\(286\) 0 0
\(287\) −5.98511 16.4440i −0.0208541 0.0572960i
\(288\) 0 0
\(289\) 102.677 + 37.3714i 0.355284 + 0.129313i
\(290\) 0 0
\(291\) −158.192 + 143.104i −0.543617 + 0.491765i
\(292\) 0 0
\(293\) 95.7610 + 5.57744i 0.326829 + 0.0190356i 0.220775 0.975325i \(-0.429141\pi\)
0.106054 + 0.994360i \(0.466178\pi\)
\(294\) 0 0
\(295\) −337.855 358.106i −1.14527 1.21392i
\(296\) 0 0
\(297\) −72.2539 + 85.2970i −0.243279 + 0.287195i
\(298\) 0 0
\(299\) −7.80995 2.33814i −0.0261202 0.00781988i
\(300\) 0 0
\(301\) 178.660 + 117.507i 0.593556 + 0.390388i
\(302\) 0 0
\(303\) −306.140 + 393.722i −1.01036 + 1.29941i
\(304\) 0 0
\(305\) −95.3096 + 16.8056i −0.312490 + 0.0551005i
\(306\) 0 0
\(307\) 77.2135 437.900i 0.251510 1.42638i −0.553365 0.832939i \(-0.686656\pi\)
0.804875 0.593445i \(-0.202232\pi\)
\(308\) 0 0
\(309\) 61.4074 + 4.86911i 0.198729 + 0.0157576i
\(310\) 0 0
\(311\) −278.336 + 83.3283i −0.894970 + 0.267937i −0.701077 0.713086i \(-0.747297\pi\)
−0.193894 + 0.981023i \(0.562112\pi\)
\(312\) 0 0
\(313\) 246.796 + 28.8463i 0.788486 + 0.0921608i 0.500799 0.865564i \(-0.333040\pi\)
0.287687 + 0.957725i \(0.407114\pi\)
\(314\) 0 0
\(315\) 154.031 168.682i 0.488988 0.535500i
\(316\) 0 0
\(317\) 9.91703 + 15.0781i 0.0312840 + 0.0475650i 0.850791 0.525504i \(-0.176123\pi\)
−0.819507 + 0.573069i \(0.805753\pi\)
\(318\) 0 0
\(319\) −36.9801 49.6729i −0.115925 0.155714i
\(320\) 0 0
\(321\) 286.246 97.4444i 0.891731 0.303565i
\(322\) 0 0
\(323\) 235.405i 0.728809i
\(324\) 0 0
\(325\) −8.11989 −0.0249843
\(326\) 0 0
\(327\) −423.149 + 483.354i −1.29403 + 1.47815i
\(328\) 0 0
\(329\) 82.1824 61.1825i 0.249794 0.185965i
\(330\) 0 0
\(331\) 332.686 218.811i 1.00509 0.661060i 0.0635591 0.997978i \(-0.479755\pi\)
0.941534 + 0.336918i \(0.109384\pi\)
\(332\) 0 0
\(333\) 111.403 + 4.67022i 0.334543 + 0.0140247i
\(334\) 0 0
\(335\) −74.1145 + 634.090i −0.221237 + 1.89281i
\(336\) 0 0
\(337\) −41.3165 138.007i −0.122601 0.409516i 0.874551 0.484933i \(-0.161156\pi\)
−0.997152 + 0.0754177i \(0.975971\pi\)
\(338\) 0 0
\(339\) −306.179 210.696i −0.903184 0.621521i
\(340\) 0 0
\(341\) −110.723 19.5234i −0.324700 0.0572533i
\(342\) 0 0
\(343\) 56.6458 + 321.254i 0.165148 + 0.936601i
\(344\) 0 0
\(345\) 42.1926 305.360i 0.122297 0.885100i
\(346\) 0 0
\(347\) 91.7987 139.573i 0.264550 0.402228i −0.678646 0.734465i \(-0.737433\pi\)
0.943196 + 0.332237i \(0.107803\pi\)
\(348\) 0 0
\(349\) 129.783 433.504i 0.371870 1.24213i −0.543463 0.839433i \(-0.682887\pi\)
0.915333 0.402698i \(-0.131928\pi\)
\(350\) 0 0
\(351\) 3.99458 13.1196i 0.0113806 0.0373778i
\(352\) 0 0
\(353\) −298.495 + 281.616i −0.845596 + 0.797779i −0.981202 0.192984i \(-0.938183\pi\)
0.135606 + 0.990763i \(0.456702\pi\)
\(354\) 0 0
\(355\) 3.13634 53.8490i 0.00883477 0.151687i
\(356\) 0 0
\(357\) −232.052 + 49.8877i −0.650006 + 0.139742i
\(358\) 0 0
\(359\) −51.9954 + 142.856i −0.144834 + 0.397928i −0.990804 0.135302i \(-0.956800\pi\)
0.845971 + 0.533230i \(0.179022\pi\)
\(360\) 0 0
\(361\) 208.478 75.8799i 0.577502 0.210194i
\(362\) 0 0
\(363\) 283.446 + 129.374i 0.780842 + 0.356403i
\(364\) 0 0
\(365\) −46.2927 + 195.324i −0.126829 + 0.535135i
\(366\) 0 0
\(367\) −27.7762 64.3924i −0.0756843 0.175456i 0.876173 0.481996i \(-0.160088\pi\)
−0.951858 + 0.306540i \(0.900829\pi\)
\(368\) 0 0
\(369\) 23.2008 32.2471i 0.0628748 0.0873905i
\(370\) 0 0
\(371\) −23.4316 + 1.36473i −0.0631578 + 0.00367853i
\(372\) 0 0
\(373\) −67.6896 + 156.922i −0.181474 + 0.420703i −0.984534 0.175195i \(-0.943944\pi\)
0.803060 + 0.595898i \(0.203204\pi\)
\(374\) 0 0
\(375\) 26.4845 + 171.085i 0.0706253 + 0.456226i
\(376\) 0 0
\(377\) 6.57949 + 3.79867i 0.0174522 + 0.0100760i
\(378\) 0 0
\(379\) −334.436 579.260i −0.882417 1.52839i −0.848646 0.528961i \(-0.822582\pi\)
−0.0337710 0.999430i \(-0.510752\pi\)
\(380\) 0 0
\(381\) −33.1540 20.0790i −0.0870182 0.0527007i
\(382\) 0 0
\(383\) 50.0181 + 427.932i 0.130595 + 1.11732i 0.886531 + 0.462669i \(0.153108\pi\)
−0.755935 + 0.654646i \(0.772818\pi\)
\(384\) 0 0
\(385\) 93.9055 + 47.1611i 0.243910 + 0.122496i
\(386\) 0 0
\(387\) 7.90286 + 485.383i 0.0204208 + 1.25422i
\(388\) 0 0
\(389\) 427.571 + 318.315i 1.09915 + 0.818290i 0.984547 0.175121i \(-0.0560316\pi\)
0.114607 + 0.993411i \(0.463439\pi\)
\(390\) 0 0
\(391\) −219.808 + 232.983i −0.562168 + 0.595863i
\(392\) 0 0
\(393\) −279.188 72.3775i −0.710401 0.184167i
\(394\) 0 0
\(395\) 215.659 257.013i 0.545973 0.650665i
\(396\) 0 0
\(397\) 564.141 473.370i 1.42101 1.19237i 0.470212 0.882553i \(-0.344177\pi\)
0.950797 0.309815i \(-0.100267\pi\)
\(398\) 0 0
\(399\) −74.6206 118.803i −0.187019 0.297752i
\(400\) 0 0
\(401\) −195.937 390.142i −0.488621 0.972924i −0.993933 0.109987i \(-0.964919\pi\)
0.505312 0.862936i \(-0.331377\pi\)
\(402\) 0 0
\(403\) 13.4215 3.18095i 0.0333040 0.00789318i
\(404\) 0 0
\(405\) 513.348 + 73.3748i 1.26752 + 0.181172i
\(406\) 0 0
\(407\) 11.8290 + 49.9106i 0.0290640 + 0.122630i
\(408\) 0 0
\(409\) −200.565 + 100.727i −0.490378 + 0.246277i −0.676765 0.736199i \(-0.736619\pi\)
0.186387 + 0.982476i \(0.440322\pi\)
\(410\) 0 0
\(411\) −149.407 78.9964i −0.363520 0.192205i
\(412\) 0 0
\(413\) −195.971 233.549i −0.474506 0.565494i
\(414\) 0 0
\(415\) −313.706 263.231i −0.755918 0.634291i
\(416\) 0 0
\(417\) −426.193 419.310i −1.02205 1.00554i
\(418\) 0 0
\(419\) −102.084 96.3112i −0.243637 0.229860i 0.554731 0.832030i \(-0.312821\pi\)
−0.798368 + 0.602170i \(0.794303\pi\)
\(420\) 0 0
\(421\) 30.6961 41.2320i 0.0729123 0.0979382i −0.764171 0.645014i \(-0.776852\pi\)
0.837083 + 0.547076i \(0.184259\pi\)
\(422\) 0 0
\(423\) 219.829 + 75.9819i 0.519691 + 0.179626i
\(424\) 0 0
\(425\) −143.179 + 285.094i −0.336893 + 0.670809i
\(426\) 0 0
\(427\) −59.5263 + 6.95763i −0.139406 + 0.0162942i
\(428\) 0 0
\(429\) 6.30753 + 0.132154i 0.0147029 + 0.000308051i
\(430\) 0 0
\(431\) −109.124 + 63.0028i −0.253188 + 0.146178i −0.621223 0.783634i \(-0.713364\pi\)
0.368035 + 0.929812i \(0.380031\pi\)
\(432\) 0 0
\(433\) −295.692 + 512.153i −0.682891 + 1.18280i 0.291203 + 0.956661i \(0.405944\pi\)
−0.974095 + 0.226141i \(0.927389\pi\)
\(434\) 0 0
\(435\) −103.886 + 267.829i −0.238818 + 0.615700i
\(436\) 0 0
\(437\) −173.841 74.9878i −0.397806 0.171597i
\(438\) 0 0
\(439\) 29.9433 + 514.106i 0.0682079 + 1.17108i 0.842658 + 0.538449i \(0.180990\pi\)
−0.774450 + 0.632635i \(0.781973\pi\)
\(440\) 0 0
\(441\) −214.506 + 209.080i −0.486407 + 0.474104i
\(442\) 0 0
\(443\) 344.399 148.559i 0.777424 0.335348i 0.0298740 0.999554i \(-0.490489\pi\)
0.747550 + 0.664206i \(0.231230\pi\)
\(444\) 0 0
\(445\) −1048.73 248.552i −2.35669 0.558545i
\(446\) 0 0
\(447\) −813.895 + 77.8874i −1.82079 + 0.174245i
\(448\) 0 0
\(449\) −195.608 537.429i −0.435653 1.19695i −0.942293 0.334789i \(-0.891335\pi\)
0.506640 0.862158i \(-0.330887\pi\)
\(450\) 0 0
\(451\) 17.1729 + 6.25042i 0.0380773 + 0.0138590i
\(452\) 0 0
\(453\) −408.550 131.698i −0.901876 0.290723i
\(454\) 0 0
\(455\) −12.8700 0.749594i −0.0282858 0.00164746i
\(456\) 0 0
\(457\) 127.422 + 135.059i 0.278823 + 0.295535i 0.851617 0.524164i \(-0.175622\pi\)
−0.572795 + 0.819699i \(0.694141\pi\)
\(458\) 0 0
\(459\) −390.199 371.592i −0.850108 0.809570i
\(460\) 0 0
\(461\) −171.978 51.4870i −0.373055 0.111685i 0.0947866 0.995498i \(-0.469783\pi\)
−0.467842 + 0.883812i \(0.654968\pi\)
\(462\) 0 0
\(463\) 415.868 + 273.521i 0.898203 + 0.590757i 0.912471 0.409141i \(-0.134172\pi\)
−0.0142686 + 0.999898i \(0.504542\pi\)
\(464\) 0 0
\(465\) 196.500 + 483.121i 0.422581 + 1.03897i
\(466\) 0 0
\(467\) −51.2883 + 9.04351i −0.109825 + 0.0193651i −0.228291 0.973593i \(-0.573314\pi\)
0.118466 + 0.992958i \(0.462202\pi\)
\(468\) 0 0
\(469\) −68.6497 + 389.332i −0.146375 + 0.830131i
\(470\) 0 0
\(471\) −203.621 427.545i −0.432316 0.907739i
\(472\) 0 0
\(473\) −213.937 + 64.0485i −0.452298 + 0.135409i
\(474\) 0 0
\(475\) −187.294 21.8916i −0.394304 0.0460875i
\(476\) 0 0
\(477\) −32.5101 42.2161i −0.0681554 0.0885033i
\(478\) 0 0
\(479\) −0.741567 1.12750i −0.00154816 0.00235386i 0.834713 0.550685i \(-0.185634\pi\)
−0.836261 + 0.548332i \(0.815263\pi\)
\(480\) 0 0
\(481\) −3.75779 5.04759i −0.00781246 0.0104940i
\(482\) 0 0
\(483\) 37.0787 187.257i 0.0767676 0.387695i
\(484\) 0 0
\(485\) 455.218i 0.938594i
\(486\) 0 0
\(487\) 168.122 0.345220 0.172610 0.984990i \(-0.444780\pi\)
0.172610 + 0.984990i \(0.444780\pi\)
\(488\) 0 0
\(489\) 862.405 + 170.765i 1.76361 + 0.349213i
\(490\) 0 0
\(491\) 437.109 325.415i 0.890241 0.662760i −0.0516545 0.998665i \(-0.516449\pi\)
0.941896 + 0.335905i \(0.109042\pi\)
\(492\) 0 0
\(493\) 249.391 164.027i 0.505863 0.332712i
\(494\) 0 0
\(495\) 31.5480 + 236.458i 0.0637333 + 0.477693i
\(496\) 0 0
\(497\) 3.87783 33.1770i 0.00780248 0.0667544i
\(498\) 0 0
\(499\) 117.013 + 390.852i 0.234496 + 0.783270i 0.991528 + 0.129893i \(0.0414632\pi\)
−0.757033 + 0.653377i \(0.773352\pi\)
\(500\) 0 0
\(501\) 6.10606 2.90804i 0.0121877 0.00580448i
\(502\) 0 0
\(503\) 664.772 + 117.217i 1.32161 + 0.233036i 0.789559 0.613674i \(-0.210309\pi\)
0.532054 + 0.846710i \(0.321420\pi\)
\(504\) 0 0
\(505\) 184.816 + 1048.14i 0.365972 + 2.07553i
\(506\) 0 0
\(507\) 468.923 190.725i 0.924897 0.376184i
\(508\) 0 0
\(509\) 331.048 503.335i 0.650390 0.988870i −0.348284 0.937389i \(-0.613236\pi\)
0.998674 0.0514806i \(-0.0163940\pi\)
\(510\) 0 0
\(511\) −35.6515 + 119.084i −0.0697681 + 0.233042i
\(512\) 0 0
\(513\) 127.510 291.849i 0.248558 0.568906i
\(514\) 0 0
\(515\) 95.6172 90.2102i 0.185664 0.175165i
\(516\) 0 0
\(517\) −6.22136 + 106.817i −0.0120336 + 0.206609i
\(518\) 0 0
\(519\) 6.46850 20.0665i 0.0124634 0.0386637i
\(520\) 0 0
\(521\) 67.7865 186.242i 0.130108 0.357470i −0.857484 0.514511i \(-0.827973\pi\)
0.987592 + 0.157041i \(0.0501956\pi\)
\(522\) 0 0
\(523\) −56.8108 + 20.6774i −0.108625 + 0.0395362i −0.395761 0.918354i \(-0.629519\pi\)
0.287136 + 0.957890i \(0.407297\pi\)
\(524\) 0 0
\(525\) −18.1122 189.266i −0.0344994 0.360506i
\(526\) 0 0
\(527\) 124.979 527.326i 0.237151 1.00062i
\(528\) 0 0
\(529\) 107.493 + 249.197i 0.203201 + 0.471073i
\(530\) 0 0
\(531\) 187.681 666.182i 0.353447 1.25458i
\(532\) 0 0
\(533\) −2.23823 + 0.130362i −0.00419931 + 0.000244582i
\(534\) 0 0
\(535\) 255.581 592.503i 0.477721 1.10748i
\(536\) 0 0
\(537\) 801.838 + 311.017i 1.49318 + 0.579175i
\(538\) 0 0
\(539\) −119.337 68.8992i −0.221404 0.127828i
\(540\) 0 0
\(541\) −438.908 760.211i −0.811290 1.40520i −0.911961 0.410277i \(-0.865432\pi\)
0.100671 0.994920i \(-0.467901\pi\)
\(542\) 0 0
\(543\) −13.7279 + 655.217i −0.0252817 + 1.20666i
\(544\) 0 0
\(545\) 159.152 + 1361.63i 0.292022 + 2.49841i
\(546\) 0 0
\(547\) 857.245 + 430.525i 1.56718 + 0.787065i 0.999349 0.0360826i \(-0.0114880\pi\)
0.567827 + 0.823148i \(0.307784\pi\)
\(548\) 0 0
\(549\) −89.1386 102.785i −0.162365 0.187223i
\(550\) 0 0
\(551\) 141.522 + 105.359i 0.256845 + 0.191214i
\(552\) 0 0
\(553\) 142.577 151.122i 0.257824 0.273277i
\(554\) 0 0
\(555\) 166.876 169.616i 0.300678 0.305614i
\(556\) 0 0
\(557\) 405.425 483.167i 0.727872 0.867445i −0.267498 0.963558i \(-0.586197\pi\)
0.995370 + 0.0961139i \(0.0306413\pi\)
\(558\) 0 0
\(559\) 20.9876 17.6107i 0.0375449 0.0315039i
\(560\) 0 0
\(561\) 115.862 219.131i 0.206527 0.390607i
\(562\) 0 0
\(563\) −348.907 694.732i −0.619729 1.23398i −0.956318 0.292330i \(-0.905570\pi\)
0.336589 0.941652i \(-0.390727\pi\)
\(564\) 0 0
\(565\) −771.769 + 182.913i −1.36596 + 0.323739i
\(566\) 0 0
\(567\) 314.714 + 63.8448i 0.555051 + 0.112601i
\(568\) 0 0
\(569\) −121.231 511.512i −0.213059 0.898967i −0.969536 0.244947i \(-0.921229\pi\)
0.756477 0.654020i \(-0.226919\pi\)
\(570\) 0 0
\(571\) 322.100 161.765i 0.564098 0.283301i −0.143810 0.989605i \(-0.545935\pi\)
0.707908 + 0.706305i \(0.249639\pi\)
\(572\) 0 0
\(573\) 697.486 438.093i 1.21725 0.764560i
\(574\) 0 0
\(575\) −164.926 196.551i −0.286827 0.341827i
\(576\) 0 0
\(577\) −185.271 155.461i −0.321094 0.269430i 0.467965 0.883747i \(-0.344987\pi\)
−0.789059 + 0.614317i \(0.789432\pi\)
\(578\) 0 0
\(579\) −206.488 + 796.502i −0.356629 + 1.37565i
\(580\) 0 0
\(581\) −184.458 174.027i −0.317483 0.299530i
\(582\) 0 0
\(583\) 14.6374 19.6614i 0.0251070 0.0337245i
\(584\) 0 0
\(585\) −15.0439 25.1039i −0.0257160 0.0429126i
\(586\) 0 0
\(587\) −83.9334 + 167.125i −0.142987 + 0.284711i −0.953715 0.300713i \(-0.902775\pi\)
0.810728 + 0.585424i \(0.199072\pi\)
\(588\) 0 0
\(589\) 318.158 37.1873i 0.540166 0.0631363i
\(590\) 0 0
\(591\) 347.735 574.172i 0.588384 0.971526i
\(592\) 0 0
\(593\) −381.562 + 220.295i −0.643444 + 0.371493i −0.785940 0.618303i \(-0.787821\pi\)
0.142496 + 0.989795i \(0.454487\pi\)
\(594\) 0 0
\(595\) −253.258 + 438.656i −0.425644 + 0.737237i
\(596\) 0 0
\(597\) 901.727 139.590i 1.51043 0.233820i
\(598\) 0 0
\(599\) 741.144 + 319.698i 1.23730 + 0.533720i 0.911337 0.411662i \(-0.135052\pi\)
0.325965 + 0.945382i \(0.394311\pi\)
\(600\) 0 0
\(601\) −18.2648 313.595i −0.0303907 0.521789i −0.978810 0.204770i \(-0.934355\pi\)
0.948419 0.317019i \(-0.102682\pi\)
\(602\) 0 0
\(603\) −818.179 + 368.840i −1.35685 + 0.611675i
\(604\) 0 0
\(605\) 610.527 263.356i 1.00914 0.435299i
\(606\) 0 0
\(607\) −32.7866 7.77056i −0.0540141 0.0128016i 0.203520 0.979071i \(-0.434762\pi\)
−0.257534 + 0.966269i \(0.582910\pi\)
\(608\) 0 0
\(609\) −73.8666 + 161.834i −0.121292 + 0.265737i
\(610\) 0 0
\(611\) −4.48962 12.3351i −0.00734798 0.0201884i
\(612\) 0 0
\(613\) 774.586 + 281.926i 1.26360 + 0.459912i 0.884975 0.465639i \(-0.154175\pi\)
0.378623 + 0.925551i \(0.376398\pi\)
\(614\) 0 0
\(615\) −17.8184 82.8820i −0.0289730 0.134768i
\(616\) 0 0
\(617\) −825.427 48.0757i −1.33781 0.0779184i −0.625741 0.780031i \(-0.715203\pi\)
−0.712066 + 0.702112i \(0.752240\pi\)
\(618\) 0 0
\(619\) −724.278 767.690i −1.17008 1.24021i −0.965226 0.261417i \(-0.915810\pi\)
−0.204852 0.978793i \(-0.565671\pi\)
\(620\) 0 0
\(621\) 398.709 169.783i 0.642044 0.273403i
\(622\) 0 0
\(623\) −639.381 191.418i −1.02629 0.307252i
\(624\) 0 0
\(625\) 642.571 + 422.626i 1.02811 + 0.676201i
\(626\) 0 0
\(627\) 145.134 + 20.0536i 0.231474 + 0.0319835i
\(628\) 0 0
\(629\) −243.486 + 42.9331i −0.387099 + 0.0682561i
\(630\) 0 0
\(631\) 18.2014 103.225i 0.0288453 0.163590i −0.966982 0.254843i \(-0.917976\pi\)
0.995828 + 0.0912533i \(0.0290873\pi\)
\(632\) 0 0
\(633\) 438.487 637.202i 0.692713 1.00664i
\(634\) 0 0
\(635\) −79.2397 + 23.7228i −0.124787 + 0.0373588i
\(636\) 0 0
\(637\) 16.7912 + 1.96261i 0.0263598 + 0.00308101i
\(638\) 0 0
\(639\) 67.2005 35.1308i 0.105165 0.0549777i
\(640\) 0 0
\(641\) −473.763 720.322i −0.739101 1.12375i −0.987885 0.155189i \(-0.950401\pi\)
0.248784 0.968559i \(-0.419969\pi\)
\(642\) 0 0
\(643\) 338.275 + 454.382i 0.526088 + 0.706659i 0.983155 0.182773i \(-0.0585074\pi\)
−0.457067 + 0.889432i \(0.651100\pi\)
\(644\) 0 0
\(645\) 779.462 + 682.374i 1.20847 + 1.05794i
\(646\) 0 0
\(647\) 99.8467i 0.154323i −0.997019 0.0771613i \(-0.975414\pi\)
0.997019 0.0771613i \(-0.0245856\pi\)
\(648\) 0 0
\(649\) 318.391 0.490587
\(650\) 0 0
\(651\) 104.082 + 305.745i 0.159881 + 0.469654i
\(652\) 0 0
\(653\) −358.868 + 267.167i −0.549568 + 0.409138i −0.835810 0.549019i \(-0.815001\pi\)
0.286242 + 0.958157i \(0.407594\pi\)
\(654\) 0 0
\(655\) −514.230 + 338.214i −0.785084 + 0.516358i
\(656\) 0 0
\(657\) −268.985 + 85.3244i −0.409415 + 0.129870i
\(658\) 0 0
\(659\) 92.8145 794.079i 0.140841 1.20498i −0.719219 0.694784i \(-0.755500\pi\)
0.860060 0.510192i \(-0.170426\pi\)
\(660\) 0 0
\(661\) −273.529 913.651i −0.413811 1.38223i −0.870311 0.492502i \(-0.836082\pi\)
0.456500 0.889723i \(-0.349103\pi\)
\(662\) 0 0
\(663\) −2.40372 + 30.3149i −0.00362553 + 0.0457238i
\(664\) 0 0
\(665\) −294.841 51.9884i −0.443369 0.0781780i
\(666\) 0 0
\(667\) 41.6871 + 236.419i 0.0624995 + 0.354452i
\(668\) 0 0
\(669\) −109.550 85.1809i −0.163752 0.127326i
\(670\) 0 0
\(671\) 34.3927 52.2916i 0.0512560 0.0779309i
\(672\) 0 0
\(673\) −23.9476 + 79.9905i −0.0355833 + 0.118857i −0.973936 0.226823i \(-0.927166\pi\)
0.938353 + 0.345679i \(0.112351\pi\)
\(674\) 0 0
\(675\) 331.935 275.896i 0.491755 0.408735i
\(676\) 0 0
\(677\) 442.155 417.152i 0.653109 0.616177i −0.286641 0.958038i \(-0.592539\pi\)
0.939751 + 0.341861i \(0.111057\pi\)
\(678\) 0 0
\(679\) −16.3908 + 281.420i −0.0241397 + 0.414462i
\(680\) 0 0
\(681\) 39.3390 + 43.4868i 0.0577665 + 0.0638573i
\(682\) 0 0
\(683\) −394.613 + 1084.19i −0.577764 + 1.58739i 0.214177 + 0.976795i \(0.431293\pi\)
−0.791941 + 0.610598i \(0.790929\pi\)
\(684\) 0 0
\(685\) −338.909 + 123.353i −0.494757 + 0.180077i
\(686\) 0 0
\(687\) −201.179 + 143.322i −0.292837 + 0.208620i
\(688\) 0 0
\(689\) −0.693499 + 2.92610i −0.00100653 + 0.00424688i
\(690\) 0 0
\(691\) 124.496 + 288.613i 0.180167 + 0.417675i 0.984236 0.176862i \(-0.0565947\pi\)
−0.804068 + 0.594537i \(0.797335\pi\)
\(692\) 0 0
\(693\) 10.9892 + 147.316i 0.0158574 + 0.212578i
\(694\) 0 0
\(695\) −1273.73 + 74.1861i −1.83270 + 0.106743i
\(696\) 0 0
\(697\) −34.8901 + 80.8843i −0.0500575 + 0.116046i
\(698\) 0 0
\(699\) 469.928 377.828i 0.672287 0.540527i
\(700\) 0 0
\(701\) 332.684 + 192.075i 0.474585 + 0.274002i 0.718157 0.695881i \(-0.244986\pi\)
−0.243572 + 0.969883i \(0.578319\pi\)
\(702\) 0 0
\(703\) −73.0691 126.559i −0.103939 0.180028i
\(704\) 0 0
\(705\) 434.956 239.117i 0.616960 0.339173i
\(706\) 0 0
\(707\) 76.5147 + 654.625i 0.108224 + 0.925919i
\(708\) 0 0
\(709\) 330.680 + 166.074i 0.466404 + 0.234237i 0.666450 0.745550i \(-0.267813\pi\)
−0.200046 + 0.979786i \(0.564109\pi\)
\(710\) 0 0
\(711\) 465.762 + 74.3296i 0.655080 + 0.104542i
\(712\) 0 0
\(713\) 349.606 + 260.272i 0.490332 + 0.365038i
\(714\) 0 0
\(715\) 9.23908 9.79286i 0.0129218 0.0136963i
\(716\) 0 0
\(717\) −44.1412 159.531i −0.0615637 0.222498i
\(718\) 0 0
\(719\) 552.176 658.057i 0.767977 0.915239i −0.230347 0.973109i \(-0.573986\pi\)
0.998324 + 0.0578691i \(0.0184306\pi\)
\(720\) 0 0
\(721\) 62.3595 52.3258i 0.0864903 0.0725740i
\(722\) 0 0
\(723\) 484.588 18.0490i 0.670246 0.0249641i
\(724\) 0 0
\(725\) 107.312 + 213.675i 0.148016 + 0.294724i
\(726\) 0 0
\(727\) −1152.88 + 273.237i −1.58580 + 0.375842i −0.926578 0.376103i \(-0.877264\pi\)
−0.659226 + 0.751945i \(0.729116\pi\)
\(728\) 0 0
\(729\) 282.480 + 672.046i 0.387489 + 0.921874i
\(730\) 0 0
\(731\) −248.242 1047.42i −0.339593 1.43286i
\(732\) 0 0
\(733\) −492.368 + 247.277i −0.671717 + 0.337349i −0.751755 0.659443i \(-0.770792\pi\)
0.0800379 + 0.996792i \(0.474496\pi\)
\(734\) 0 0
\(735\) 23.7924 + 638.789i 0.0323707 + 0.869100i
\(736\) 0 0
\(737\) −265.382 316.271i −0.360085 0.429132i
\(738\) 0 0
\(739\) −983.763 825.475i −1.33121 1.11702i −0.983794 0.179305i \(-0.942615\pi\)
−0.347415 0.937712i \(-0.612940\pi\)
\(740\) 0 0
\(741\) −17.3237 + 4.79334i −0.0233788 + 0.00646874i
\(742\) 0 0
\(743\) 357.739 + 337.510i 0.481480 + 0.454253i 0.888305 0.459253i \(-0.151883\pi\)
−0.406826 + 0.913506i \(0.633364\pi\)
\(744\) 0 0
\(745\) −1041.92 + 1399.54i −1.39855 + 1.87858i
\(746\) 0 0
\(747\) 90.7256 568.502i 0.121453 0.761047i
\(748\) 0 0
\(749\) 179.336 357.088i 0.239434 0.476753i
\(750\) 0 0
\(751\) 904.358 105.704i 1.20420 0.140751i 0.509772 0.860309i \(-0.329730\pi\)
0.694432 + 0.719558i \(0.255656\pi\)
\(752\) 0 0
\(753\) 251.562 + 457.595i 0.334080 + 0.607695i
\(754\) 0 0
\(755\) −793.304 + 458.015i −1.05073 + 0.606642i
\(756\) 0 0
\(757\) −339.653 + 588.297i −0.448683 + 0.777142i −0.998301 0.0582742i \(-0.981440\pi\)
0.549617 + 0.835417i \(0.314774\pi\)
\(758\) 0 0
\(759\) 124.915 + 155.365i 0.164579 + 0.204697i
\(760\) 0 0
\(761\) −574.668 247.887i −0.755148 0.325739i −0.0165300 0.999863i \(-0.505262\pi\)
−0.738618 + 0.674124i \(0.764521\pi\)
\(762\) 0 0
\(763\) 49.3615 + 847.505i 0.0646940 + 1.11075i
\(764\) 0 0
\(765\) −1146.68 + 85.5376i −1.49893 + 0.111814i
\(766\) 0 0
\(767\) −35.8665 + 15.4713i −0.0467621 + 0.0201712i
\(768\) 0 0
\(769\) −533.194 126.369i −0.693360 0.164329i −0.131198 0.991356i \(-0.541882\pi\)
−0.562162 + 0.827027i \(0.690030\pi\)
\(770\) 0 0
\(771\) −145.118 203.700i −0.188220 0.264203i
\(772\) 0 0
\(773\) 59.2640 + 162.826i 0.0766675 + 0.210642i 0.972106 0.234544i \(-0.0753597\pi\)
−0.895438 + 0.445186i \(0.853137\pi\)
\(774\) 0 0
\(775\) 407.931 + 148.475i 0.526363 + 0.191581i
\(776\) 0 0
\(777\) 109.272 98.8492i 0.140633 0.127219i
\(778\) 0 0
\(779\) −51.9788 3.02742i −0.0667250 0.00388629i
\(780\) 0 0
\(781\) 23.9385 + 25.3733i 0.0306511 + 0.0324882i
\(782\) 0 0
\(783\) −398.035 + 68.2698i −0.508346 + 0.0871901i
\(784\) 0 0
\(785\) −968.121 289.837i −1.23328 0.369219i
\(786\) 0 0
\(787\) 265.276 + 174.475i 0.337073 + 0.221696i 0.706749 0.707464i \(-0.250161\pi\)
−0.369676 + 0.929161i \(0.620531\pi\)
\(788\) 0 0
\(789\) −758.308 + 975.250i −0.961100 + 1.23606i
\(790\) 0 0
\(791\) −483.700 + 85.2894i −0.611504 + 0.107825i
\(792\) 0 0
\(793\) −1.33335 + 7.56183i −0.00168141 + 0.00953572i
\(794\) 0 0
\(795\) −113.351 8.98784i −0.142580 0.0113055i