Properties

Label 144.3.o.a.31.1
Level $144$
Weight $3$
Character 144.31
Analytic conductor $3.924$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 144.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.92371580679\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.856615824.2
Defining polynomial: \(x^{8} + 11 x^{6} + 36 x^{4} + 32 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.1
Root \(1.07834i\) of defining polynomial
Character \(\chi\) \(=\) 144.31
Dual form 144.3.o.a.79.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.64956 - 1.40707i) q^{3} +(-3.01729 + 5.22611i) q^{5} +(10.2332 - 5.90815i) q^{7} +(5.04032 + 7.45622i) q^{9} +O(q^{10})\) \(q+(-2.64956 - 1.40707i) q^{3} +(-3.01729 + 5.22611i) q^{5} +(10.2332 - 5.90815i) q^{7} +(5.04032 + 7.45622i) q^{9} +(5.28454 - 3.05103i) q^{11} +(7.44868 - 12.9015i) q^{13} +(15.3480 - 9.60134i) q^{15} +26.6919 q^{17} +9.45610i q^{19} +(-35.4267 + 1.25516i) q^{21} +(-17.2673 - 9.96931i) q^{23} +(-5.70813 - 9.88677i) q^{25} +(-2.86322 - 26.8478i) q^{27} +(22.3114 + 38.6445i) q^{29} +(5.42359 + 3.13131i) q^{31} +(-18.2947 + 0.648178i) q^{33} +71.3065i q^{35} -6.65707 q^{37} +(-37.8890 + 23.7024i) q^{39} +(8.82853 - 15.2915i) q^{41} +(20.2696 - 11.7027i) q^{43} +(-54.1751 + 3.84365i) q^{45} +(-36.4261 + 21.0306i) q^{47} +(45.3125 - 78.4835i) q^{49} +(-70.7216 - 37.5572i) q^{51} -51.6192 q^{53} +36.8234i q^{55} +(13.3054 - 25.0545i) q^{57} +(-32.9024 - 18.9962i) q^{59} +(-45.3815 - 78.6031i) q^{61} +(95.6311 + 46.5221i) q^{63} +(44.9497 + 77.8552i) q^{65} +(53.4577 + 30.8638i) q^{67} +(31.7233 + 50.7106i) q^{69} -39.5232i q^{71} +35.0355 q^{73} +(1.21267 + 34.2273i) q^{75} +(36.0519 - 62.4437i) q^{77} +(-77.9605 + 45.0105i) q^{79} +(-30.1903 + 75.1634i) q^{81} +(102.357 - 59.0957i) q^{83} +(-80.5372 + 139.494i) q^{85} +(-4.73997 - 133.785i) q^{87} -14.4499 q^{89} -176.032i q^{91} +(-9.96416 - 15.9280i) q^{93} +(-49.4186 - 28.5318i) q^{95} +(67.5561 + 117.011i) q^{97} +(49.3849 + 24.0245i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 3q^{3} + 3q^{5} + 3q^{7} - 3q^{9} + O(q^{10}) \) \( 8q - 3q^{3} + 3q^{5} + 3q^{7} - 3q^{9} + 18q^{11} + 5q^{13} - 21q^{15} + 6q^{17} - 33q^{21} - 81q^{23} - 23q^{25} + 108q^{27} + 69q^{29} + 45q^{31} + 72q^{33} - 20q^{37} - 141q^{39} + 54q^{41} - 117q^{45} + 207q^{47} + 41q^{49} - 141q^{51} - 252q^{53} - 273q^{57} - 306q^{59} + 7q^{61} + 441q^{63} + 93q^{65} + 12q^{67} + 189q^{69} + 74q^{73} - 387q^{75} + 207q^{77} + 33q^{79} + 117q^{81} + 549q^{83} - 30q^{85} - 87q^{87} - 168q^{89} - 27q^{93} - 684q^{95} - 10q^{97} + 585q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.64956 1.40707i −0.883186 0.469023i
\(4\) 0 0
\(5\) −3.01729 + 5.22611i −0.603459 + 1.04522i 0.388834 + 0.921308i \(0.372878\pi\)
−0.992293 + 0.123914i \(0.960455\pi\)
\(6\) 0 0
\(7\) 10.2332 5.90815i 1.46189 0.844021i 0.462789 0.886468i \(-0.346849\pi\)
0.999099 + 0.0424471i \(0.0135154\pi\)
\(8\) 0 0
\(9\) 5.04032 + 7.45622i 0.560036 + 0.828469i
\(10\) 0 0
\(11\) 5.28454 3.05103i 0.480413 0.277366i −0.240176 0.970729i \(-0.577205\pi\)
0.720588 + 0.693363i \(0.243872\pi\)
\(12\) 0 0
\(13\) 7.44868 12.9015i 0.572975 0.992422i −0.423283 0.905997i \(-0.639123\pi\)
0.996258 0.0864245i \(-0.0275441\pi\)
\(14\) 0 0
\(15\) 15.3480 9.60134i 1.02320 0.640089i
\(16\) 0 0
\(17\) 26.6919 1.57011 0.785055 0.619427i \(-0.212635\pi\)
0.785055 + 0.619427i \(0.212635\pi\)
\(18\) 0 0
\(19\) 9.45610i 0.497689i 0.968543 + 0.248845i \(0.0800509\pi\)
−0.968543 + 0.248845i \(0.919949\pi\)
\(20\) 0 0
\(21\) −35.4267 + 1.25516i −1.68698 + 0.0597695i
\(22\) 0 0
\(23\) −17.2673 9.96931i −0.750754 0.433448i 0.0752122 0.997168i \(-0.476037\pi\)
−0.825966 + 0.563719i \(0.809370\pi\)
\(24\) 0 0
\(25\) −5.70813 9.88677i −0.228325 0.395471i
\(26\) 0 0
\(27\) −2.86322 26.8478i −0.106045 0.994361i
\(28\) 0 0
\(29\) 22.3114 + 38.6445i 0.769360 + 1.33257i 0.937910 + 0.346877i \(0.112758\pi\)
−0.168551 + 0.985693i \(0.553909\pi\)
\(30\) 0 0
\(31\) 5.42359 + 3.13131i 0.174955 + 0.101010i 0.584920 0.811091i \(-0.301126\pi\)
−0.409965 + 0.912101i \(0.634459\pi\)
\(32\) 0 0
\(33\) −18.2947 + 0.648178i −0.554385 + 0.0196418i
\(34\) 0 0
\(35\) 71.3065i 2.03733i
\(36\) 0 0
\(37\) −6.65707 −0.179921 −0.0899604 0.995945i \(-0.528674\pi\)
−0.0899604 + 0.995945i \(0.528674\pi\)
\(38\) 0 0
\(39\) −37.8890 + 23.7024i −0.971512 + 0.607755i
\(40\) 0 0
\(41\) 8.82853 15.2915i 0.215330 0.372963i −0.738045 0.674752i \(-0.764251\pi\)
0.953375 + 0.301789i \(0.0975839\pi\)
\(42\) 0 0
\(43\) 20.2696 11.7027i 0.471386 0.272155i −0.245433 0.969413i \(-0.578930\pi\)
0.716820 + 0.697258i \(0.245597\pi\)
\(44\) 0 0
\(45\) −54.1751 + 3.84365i −1.20389 + 0.0854145i
\(46\) 0 0
\(47\) −36.4261 + 21.0306i −0.775023 + 0.447460i −0.834664 0.550760i \(-0.814338\pi\)
0.0596404 + 0.998220i \(0.481005\pi\)
\(48\) 0 0
\(49\) 45.3125 78.4835i 0.924744 1.60170i
\(50\) 0 0
\(51\) −70.7216 37.5572i −1.38670 0.736417i
\(52\) 0 0
\(53\) −51.6192 −0.973948 −0.486974 0.873416i \(-0.661899\pi\)
−0.486974 + 0.873416i \(0.661899\pi\)
\(54\) 0 0
\(55\) 36.8234i 0.669517i
\(56\) 0 0
\(57\) 13.3054 25.0545i 0.233428 0.439552i
\(58\) 0 0
\(59\) −32.9024 18.9962i −0.557668 0.321970i 0.194541 0.980894i \(-0.437678\pi\)
−0.752209 + 0.658925i \(0.771012\pi\)
\(60\) 0 0
\(61\) −45.3815 78.6031i −0.743960 1.28858i −0.950679 0.310176i \(-0.899612\pi\)
0.206720 0.978400i \(-0.433721\pi\)
\(62\) 0 0
\(63\) 95.6311 + 46.5221i 1.51795 + 0.738446i
\(64\) 0 0
\(65\) 44.9497 + 77.8552i 0.691534 + 1.19777i
\(66\) 0 0
\(67\) 53.4577 + 30.8638i 0.797876 + 0.460654i 0.842728 0.538340i \(-0.180948\pi\)
−0.0448520 + 0.998994i \(0.514282\pi\)
\(68\) 0 0
\(69\) 31.7233 + 50.7106i 0.459759 + 0.734936i
\(70\) 0 0
\(71\) 39.5232i 0.556665i −0.960485 0.278333i \(-0.910218\pi\)
0.960485 0.278333i \(-0.0897817\pi\)
\(72\) 0 0
\(73\) 35.0355 0.479938 0.239969 0.970780i \(-0.422863\pi\)
0.239969 + 0.970780i \(0.422863\pi\)
\(74\) 0 0
\(75\) 1.21267 + 34.2273i 0.0161689 + 0.456364i
\(76\) 0 0
\(77\) 36.0519 62.4437i 0.468206 0.810957i
\(78\) 0 0
\(79\) −77.9605 + 45.0105i −0.986842 + 0.569753i −0.904329 0.426837i \(-0.859628\pi\)
−0.0825131 + 0.996590i \(0.526295\pi\)
\(80\) 0 0
\(81\) −30.1903 + 75.1634i −0.372720 + 0.927944i
\(82\) 0 0
\(83\) 102.357 59.0957i 1.23321 0.711996i 0.265515 0.964107i \(-0.414458\pi\)
0.967698 + 0.252111i \(0.0811247\pi\)
\(84\) 0 0
\(85\) −80.5372 + 139.494i −0.947496 + 1.64111i
\(86\) 0 0
\(87\) −4.73997 133.785i −0.0544824 1.53775i
\(88\) 0 0
\(89\) −14.4499 −0.162359 −0.0811794 0.996700i \(-0.525869\pi\)
−0.0811794 + 0.996700i \(0.525869\pi\)
\(90\) 0 0
\(91\) 176.032i 1.93441i
\(92\) 0 0
\(93\) −9.96416 15.9280i −0.107141 0.171268i
\(94\) 0 0
\(95\) −49.4186 28.5318i −0.520196 0.300335i
\(96\) 0 0
\(97\) 67.5561 + 117.011i 0.696455 + 1.20629i 0.969688 + 0.244347i \(0.0785736\pi\)
−0.273233 + 0.961948i \(0.588093\pi\)
\(98\) 0 0
\(99\) 49.3849 + 24.0245i 0.498838 + 0.242672i
\(100\) 0 0
\(101\) −11.7439 20.3411i −0.116277 0.201397i 0.802013 0.597307i \(-0.203763\pi\)
−0.918289 + 0.395910i \(0.870429\pi\)
\(102\) 0 0
\(103\) −27.2852 15.7531i −0.264905 0.152943i 0.361665 0.932308i \(-0.382208\pi\)
−0.626570 + 0.779365i \(0.715542\pi\)
\(104\) 0 0
\(105\) 100.333 188.931i 0.955553 1.79934i
\(106\) 0 0
\(107\) 208.386i 1.94753i 0.227558 + 0.973765i \(0.426926\pi\)
−0.227558 + 0.973765i \(0.573074\pi\)
\(108\) 0 0
\(109\) 64.5228 0.591952 0.295976 0.955195i \(-0.404355\pi\)
0.295976 + 0.955195i \(0.404355\pi\)
\(110\) 0 0
\(111\) 17.6383 + 9.36695i 0.158904 + 0.0843869i
\(112\) 0 0
\(113\) 1.79115 3.10236i 0.0158509 0.0274545i −0.857991 0.513664i \(-0.828288\pi\)
0.873842 + 0.486210i \(0.161621\pi\)
\(114\) 0 0
\(115\) 104.201 60.1607i 0.906098 0.523136i
\(116\) 0 0
\(117\) 133.740 9.48868i 1.14308 0.0810998i
\(118\) 0 0
\(119\) 273.143 157.699i 2.29532 1.32521i
\(120\) 0 0
\(121\) −41.8824 + 72.5425i −0.346136 + 0.599525i
\(122\) 0 0
\(123\) −44.9079 + 28.0933i −0.365104 + 0.228401i
\(124\) 0 0
\(125\) −81.9723 −0.655778
\(126\) 0 0
\(127\) 92.5083i 0.728412i 0.931319 + 0.364206i \(0.118660\pi\)
−0.931319 + 0.364206i \(0.881340\pi\)
\(128\) 0 0
\(129\) −70.1720 + 2.48618i −0.543969 + 0.0192727i
\(130\) 0 0
\(131\) −105.265 60.7749i −0.803552 0.463931i 0.0411598 0.999153i \(-0.486895\pi\)
−0.844712 + 0.535222i \(0.820228\pi\)
\(132\) 0 0
\(133\) 55.8680 + 96.7663i 0.420060 + 0.727566i
\(134\) 0 0
\(135\) 148.948 + 66.0441i 1.10332 + 0.489215i
\(136\) 0 0
\(137\) −128.420 222.430i −0.937372 1.62358i −0.770348 0.637623i \(-0.779918\pi\)
−0.167024 0.985953i \(-0.553416\pi\)
\(138\) 0 0
\(139\) −111.156 64.1761i −0.799685 0.461698i 0.0436761 0.999046i \(-0.486093\pi\)
−0.843361 + 0.537348i \(0.819426\pi\)
\(140\) 0 0
\(141\) 126.105 4.46786i 0.894358 0.0316870i
\(142\) 0 0
\(143\) 90.9045i 0.635696i
\(144\) 0 0
\(145\) −269.281 −1.85711
\(146\) 0 0
\(147\) −230.490 + 144.189i −1.56796 + 0.980877i
\(148\) 0 0
\(149\) 10.8586 18.8076i 0.0728762 0.126225i −0.827285 0.561783i \(-0.810116\pi\)
0.900161 + 0.435558i \(0.143449\pi\)
\(150\) 0 0
\(151\) −242.937 + 140.260i −1.60886 + 0.928874i −0.619230 + 0.785209i \(0.712555\pi\)
−0.989626 + 0.143665i \(0.954111\pi\)
\(152\) 0 0
\(153\) 134.536 + 199.020i 0.879317 + 1.30079i
\(154\) 0 0
\(155\) −32.7291 + 18.8962i −0.211156 + 0.121911i
\(156\) 0 0
\(157\) 52.5346 90.9926i 0.334615 0.579571i −0.648796 0.760963i \(-0.724727\pi\)
0.983411 + 0.181392i \(0.0580603\pi\)
\(158\) 0 0
\(159\) 136.768 + 72.6318i 0.860177 + 0.456804i
\(160\) 0 0
\(161\) −235.601 −1.46336
\(162\) 0 0
\(163\) 145.690i 0.893804i 0.894583 + 0.446902i \(0.147473\pi\)
−0.894583 + 0.446902i \(0.852527\pi\)
\(164\) 0 0
\(165\) 51.8131 97.5658i 0.314019 0.591308i
\(166\) 0 0
\(167\) −212.778 122.847i −1.27412 0.735613i −0.298359 0.954454i \(-0.596439\pi\)
−0.975761 + 0.218840i \(0.929773\pi\)
\(168\) 0 0
\(169\) −26.4655 45.8396i −0.156601 0.271241i
\(170\) 0 0
\(171\) −70.5067 + 47.6618i −0.412320 + 0.278724i
\(172\) 0 0
\(173\) 21.9101 + 37.9494i 0.126648 + 0.219361i 0.922376 0.386294i \(-0.126245\pi\)
−0.795728 + 0.605654i \(0.792911\pi\)
\(174\) 0 0
\(175\) −116.825 67.4490i −0.667572 0.385423i
\(176\) 0 0
\(177\) 60.4479 + 96.6275i 0.341514 + 0.545918i
\(178\) 0 0
\(179\) 57.0637i 0.318791i 0.987215 + 0.159396i \(0.0509546\pi\)
−0.987215 + 0.159396i \(0.949045\pi\)
\(180\) 0 0
\(181\) 92.7281 0.512310 0.256155 0.966636i \(-0.417544\pi\)
0.256155 + 0.966636i \(0.417544\pi\)
\(182\) 0 0
\(183\) 9.64111 + 272.118i 0.0526837 + 1.48699i
\(184\) 0 0
\(185\) 20.0863 34.7905i 0.108575 0.188057i
\(186\) 0 0
\(187\) 141.054 81.4377i 0.754300 0.435495i
\(188\) 0 0
\(189\) −187.921 257.823i −0.994288 1.36414i
\(190\) 0 0
\(191\) −77.4667 + 44.7254i −0.405585 + 0.234164i −0.688891 0.724865i \(-0.741902\pi\)
0.283306 + 0.959030i \(0.408569\pi\)
\(192\) 0 0
\(193\) −115.213 + 199.555i −0.596959 + 1.03396i 0.396308 + 0.918118i \(0.370291\pi\)
−0.993267 + 0.115846i \(0.963042\pi\)
\(194\) 0 0
\(195\) −9.54937 269.529i −0.0489711 1.38220i
\(196\) 0 0
\(197\) −95.9308 −0.486958 −0.243479 0.969906i \(-0.578289\pi\)
−0.243479 + 0.969906i \(0.578289\pi\)
\(198\) 0 0
\(199\) 50.1566i 0.252043i 0.992028 + 0.126021i \(0.0402208\pi\)
−0.992028 + 0.126021i \(0.959779\pi\)
\(200\) 0 0
\(201\) −98.2118 156.994i −0.488616 0.781065i
\(202\) 0 0
\(203\) 456.635 + 263.639i 2.24944 + 1.29871i
\(204\) 0 0
\(205\) 53.2766 + 92.2777i 0.259886 + 0.450135i
\(206\) 0 0
\(207\) −12.6996 178.998i −0.0613509 0.864722i
\(208\) 0 0
\(209\) 28.8508 + 49.9711i 0.138042 + 0.239096i
\(210\) 0 0
\(211\) −2.28029 1.31653i −0.0108071 0.00623946i 0.494587 0.869128i \(-0.335319\pi\)
−0.505394 + 0.862889i \(0.668653\pi\)
\(212\) 0 0
\(213\) −55.6119 + 104.719i −0.261089 + 0.491639i
\(214\) 0 0
\(215\) 141.242i 0.656938i
\(216\) 0 0
\(217\) 74.0010 0.341019
\(218\) 0 0
\(219\) −92.8286 49.2973i −0.423875 0.225102i
\(220\) 0 0
\(221\) 198.819 344.365i 0.899633 1.55821i
\(222\) 0 0
\(223\) 152.757 88.1940i 0.685007 0.395489i −0.116732 0.993163i \(-0.537242\pi\)
0.801739 + 0.597675i \(0.203909\pi\)
\(224\) 0 0
\(225\) 44.9471 92.3936i 0.199765 0.410638i
\(226\) 0 0
\(227\) −1.85772 + 1.07256i −0.00818380 + 0.00472492i −0.504086 0.863653i \(-0.668171\pi\)
0.495903 + 0.868378i \(0.334837\pi\)
\(228\) 0 0
\(229\) 63.6447 110.236i 0.277925 0.481379i −0.692944 0.720991i \(-0.743687\pi\)
0.970869 + 0.239612i \(0.0770201\pi\)
\(230\) 0 0
\(231\) −183.384 + 114.721i −0.793870 + 0.496627i
\(232\) 0 0
\(233\) 262.526 1.12672 0.563360 0.826211i \(-0.309508\pi\)
0.563360 + 0.826211i \(0.309508\pi\)
\(234\) 0 0
\(235\) 253.822i 1.08009i
\(236\) 0 0
\(237\) 269.894 9.56229i 1.13879 0.0403472i
\(238\) 0 0
\(239\) −270.558 156.207i −1.13204 0.653584i −0.187594 0.982247i \(-0.560069\pi\)
−0.944447 + 0.328662i \(0.893402\pi\)
\(240\) 0 0
\(241\) −14.7110 25.4801i −0.0610413 0.105727i 0.833890 0.551931i \(-0.186109\pi\)
−0.894931 + 0.446204i \(0.852775\pi\)
\(242\) 0 0
\(243\) 185.751 156.670i 0.764408 0.644733i
\(244\) 0 0
\(245\) 273.442 + 473.616i 1.11609 + 1.93312i
\(246\) 0 0
\(247\) 121.998 + 70.4354i 0.493918 + 0.285164i
\(248\) 0 0
\(249\) −354.352 + 12.5546i −1.42310 + 0.0504202i
\(250\) 0 0
\(251\) 195.326i 0.778192i −0.921197 0.389096i \(-0.872787\pi\)
0.921197 0.389096i \(-0.127213\pi\)
\(252\) 0 0
\(253\) −121.667 −0.480896
\(254\) 0 0
\(255\) 409.666 256.278i 1.60653 1.00501i
\(256\) 0 0
\(257\) −218.673 + 378.753i −0.850867 + 1.47375i 0.0295596 + 0.999563i \(0.490590\pi\)
−0.880427 + 0.474182i \(0.842744\pi\)
\(258\) 0 0
\(259\) −68.1232 + 39.3310i −0.263024 + 0.151857i
\(260\) 0 0
\(261\) −175.685 + 361.140i −0.673124 + 1.38368i
\(262\) 0 0
\(263\) 64.8138 37.4203i 0.246440 0.142282i −0.371693 0.928356i \(-0.621223\pi\)
0.618133 + 0.786073i \(0.287889\pi\)
\(264\) 0 0
\(265\) 155.750 269.768i 0.587738 1.01799i
\(266\) 0 0
\(267\) 38.2859 + 20.3320i 0.143393 + 0.0761499i
\(268\) 0 0
\(269\) 40.6759 0.151212 0.0756058 0.997138i \(-0.475911\pi\)
0.0756058 + 0.997138i \(0.475911\pi\)
\(270\) 0 0
\(271\) 130.442i 0.481337i 0.970607 + 0.240668i \(0.0773666\pi\)
−0.970607 + 0.240668i \(0.922633\pi\)
\(272\) 0 0
\(273\) −247.688 + 466.406i −0.907283 + 1.70845i
\(274\) 0 0
\(275\) −60.3297 34.8314i −0.219381 0.126659i
\(276\) 0 0
\(277\) −114.408 198.160i −0.413025 0.715379i 0.582194 0.813050i \(-0.302194\pi\)
−0.995219 + 0.0976702i \(0.968861\pi\)
\(278\) 0 0
\(279\) 3.98890 + 56.2223i 0.0142971 + 0.201514i
\(280\) 0 0
\(281\) 23.9532 + 41.4882i 0.0852429 + 0.147645i 0.905495 0.424358i \(-0.139500\pi\)
−0.820252 + 0.572003i \(0.806167\pi\)
\(282\) 0 0
\(283\) 307.250 + 177.391i 1.08569 + 0.626824i 0.932426 0.361361i \(-0.117688\pi\)
0.153265 + 0.988185i \(0.451021\pi\)
\(284\) 0 0
\(285\) 90.7912 + 145.132i 0.318566 + 0.509235i
\(286\) 0 0
\(287\) 208.641i 0.726973i
\(288\) 0 0
\(289\) 423.455 1.46524
\(290\) 0 0
\(291\) −14.3520 405.082i −0.0493196 1.39204i
\(292\) 0 0
\(293\) −27.9478 + 48.4071i −0.0953851 + 0.165212i −0.909769 0.415114i \(-0.863742\pi\)
0.814384 + 0.580326i \(0.197075\pi\)
\(294\) 0 0
\(295\) 198.552 114.634i 0.673059 0.388591i
\(296\) 0 0
\(297\) −97.0441 133.142i −0.326748 0.448290i
\(298\) 0 0
\(299\) −257.238 + 148.516i −0.860327 + 0.496710i
\(300\) 0 0
\(301\) 138.282 239.512i 0.459409 0.795720i
\(302\) 0 0
\(303\) 2.49495 + 70.4194i 0.00823415 + 0.232407i
\(304\) 0 0
\(305\) 547.718 1.79580
\(306\) 0 0
\(307\) 57.3939i 0.186951i −0.995622 0.0934754i \(-0.970202\pi\)
0.995622 0.0934754i \(-0.0297976\pi\)
\(308\) 0 0
\(309\) 50.1280 + 80.1309i 0.162226 + 0.259323i
\(310\) 0 0
\(311\) 215.498 + 124.418i 0.692920 + 0.400058i 0.804705 0.593675i \(-0.202323\pi\)
−0.111785 + 0.993732i \(0.535657\pi\)
\(312\) 0 0
\(313\) −307.856 533.222i −0.983565 1.70358i −0.648147 0.761515i \(-0.724456\pi\)
−0.335417 0.942070i \(-0.608877\pi\)
\(314\) 0 0
\(315\) −531.677 + 359.408i −1.68786 + 1.14098i
\(316\) 0 0
\(317\) −128.314 222.246i −0.404775 0.701090i 0.589521 0.807753i \(-0.299317\pi\)
−0.994295 + 0.106663i \(0.965983\pi\)
\(318\) 0 0
\(319\) 235.811 + 136.146i 0.739220 + 0.426789i
\(320\) 0 0
\(321\) 293.213 552.130i 0.913435 1.72003i
\(322\) 0 0
\(323\) 252.401i 0.781427i
\(324\) 0 0
\(325\) −170.072 −0.523299
\(326\) 0 0
\(327\) −170.957 90.7879i −0.522804 0.277639i
\(328\) 0 0
\(329\) −248.504 + 430.422i −0.755331 + 1.30827i
\(330\) 0 0
\(331\) −125.743 + 72.5978i −0.379889 + 0.219329i −0.677770 0.735274i \(-0.737053\pi\)
0.297881 + 0.954603i \(0.403720\pi\)
\(332\) 0 0
\(333\) −33.5538 49.6365i −0.100762 0.149059i
\(334\) 0 0
\(335\) −322.595 + 186.250i −0.962971 + 0.555971i
\(336\) 0 0
\(337\) 21.8136 37.7823i 0.0647288 0.112114i −0.831845 0.555008i \(-0.812715\pi\)
0.896574 + 0.442895i \(0.146048\pi\)
\(338\) 0 0
\(339\) −9.11098 + 5.69962i −0.0268761 + 0.0168130i
\(340\) 0 0
\(341\) 38.2149 0.112067
\(342\) 0 0
\(343\) 491.852i 1.43397i
\(344\) 0 0
\(345\) −360.738 + 12.7809i −1.04562 + 0.0370460i
\(346\) 0 0
\(347\) 156.116 + 90.1337i 0.449902 + 0.259751i 0.707789 0.706424i \(-0.249693\pi\)
−0.257887 + 0.966175i \(0.583026\pi\)
\(348\) 0 0
\(349\) 46.5629 + 80.6493i 0.133418 + 0.231087i 0.924992 0.379987i \(-0.124071\pi\)
−0.791574 + 0.611073i \(0.790738\pi\)
\(350\) 0 0
\(351\) −367.703 163.040i −1.04759 0.464503i
\(352\) 0 0
\(353\) −215.455 373.178i −0.610353 1.05716i −0.991181 0.132516i \(-0.957694\pi\)
0.380828 0.924646i \(-0.375639\pi\)
\(354\) 0 0
\(355\) 206.553 + 119.253i 0.581838 + 0.335925i
\(356\) 0 0
\(357\) −945.603 + 33.5026i −2.64875 + 0.0938447i
\(358\) 0 0
\(359\) 316.054i 0.880374i 0.897906 + 0.440187i \(0.145088\pi\)
−0.897906 + 0.440187i \(0.854912\pi\)
\(360\) 0 0
\(361\) 271.582 0.752305
\(362\) 0 0
\(363\) 213.042 133.274i 0.586893 0.367146i
\(364\) 0 0
\(365\) −105.712 + 183.099i −0.289623 + 0.501642i
\(366\) 0 0
\(367\) −453.751 + 261.973i −1.23638 + 0.713824i −0.968352 0.249588i \(-0.919705\pi\)
−0.268027 + 0.963411i \(0.586372\pi\)
\(368\) 0 0
\(369\) 158.515 11.2464i 0.429580 0.0304782i
\(370\) 0 0
\(371\) −528.231 + 304.974i −1.42380 + 0.822033i
\(372\) 0 0
\(373\) −163.567 + 283.306i −0.438518 + 0.759535i −0.997575 0.0695940i \(-0.977830\pi\)
0.559058 + 0.829129i \(0.311163\pi\)
\(374\) 0 0
\(375\) 217.190 + 115.341i 0.579174 + 0.307575i
\(376\) 0 0
\(377\) 664.763 1.76330
\(378\) 0 0
\(379\) 443.580i 1.17040i 0.810890 + 0.585198i \(0.198983\pi\)
−0.810890 + 0.585198i \(0.801017\pi\)
\(380\) 0 0
\(381\) 130.165 245.106i 0.341641 0.643323i
\(382\) 0 0
\(383\) 393.008 + 226.903i 1.02613 + 0.592436i 0.915873 0.401467i \(-0.131500\pi\)
0.110256 + 0.993903i \(0.464833\pi\)
\(384\) 0 0
\(385\) 217.558 + 376.822i 0.565086 + 0.978758i
\(386\) 0 0
\(387\) 189.423 + 92.1495i 0.489465 + 0.238112i
\(388\) 0 0
\(389\) 82.4361 + 142.783i 0.211918 + 0.367053i 0.952315 0.305117i \(-0.0986957\pi\)
−0.740397 + 0.672170i \(0.765362\pi\)
\(390\) 0 0
\(391\) −460.897 266.099i −1.17877 0.680561i
\(392\) 0 0
\(393\) 193.392 + 309.142i 0.492092 + 0.786621i
\(394\) 0 0
\(395\) 543.240i 1.37529i
\(396\) 0 0
\(397\) −395.775 −0.996914 −0.498457 0.866915i \(-0.666100\pi\)
−0.498457 + 0.866915i \(0.666100\pi\)
\(398\) 0 0
\(399\) −11.8689 334.998i −0.0297467 0.839594i
\(400\) 0 0
\(401\) 173.838 301.097i 0.433512 0.750864i −0.563661 0.826006i \(-0.690608\pi\)
0.997173 + 0.0751418i \(0.0239409\pi\)
\(402\) 0 0
\(403\) 80.7971 46.6483i 0.200489 0.115752i
\(404\) 0 0
\(405\) −301.719 384.568i −0.744985 0.949551i
\(406\) 0 0
\(407\) −35.1795 + 20.3109i −0.0864362 + 0.0499040i
\(408\) 0 0
\(409\) −32.7989 + 56.8094i −0.0801930 + 0.138898i −0.903333 0.428941i \(-0.858887\pi\)
0.823140 + 0.567839i \(0.192220\pi\)
\(410\) 0 0
\(411\) 27.2823 + 770.037i 0.0663802 + 1.87357i
\(412\) 0 0
\(413\) −448.930 −1.08700
\(414\) 0 0
\(415\) 713.236i 1.71864i
\(416\) 0 0
\(417\) 204.215 + 326.442i 0.489724 + 0.782836i
\(418\) 0 0
\(419\) −595.923 344.056i −1.42225 0.821137i −0.425760 0.904836i \(-0.639993\pi\)
−0.996491 + 0.0836989i \(0.973327\pi\)
\(420\) 0 0
\(421\) −146.855 254.360i −0.348823 0.604180i 0.637217 0.770684i \(-0.280085\pi\)
−0.986041 + 0.166504i \(0.946752\pi\)
\(422\) 0 0
\(423\) −340.408 165.600i −0.804747 0.391489i
\(424\) 0 0
\(425\) −152.361 263.896i −0.358496 0.620932i
\(426\) 0 0
\(427\) −928.798 536.242i −2.17517 1.25584i
\(428\) 0 0
\(429\) −127.909 + 240.857i −0.298156 + 0.561438i
\(430\) 0 0
\(431\) 555.264i 1.28832i −0.764893 0.644158i \(-0.777208\pi\)
0.764893 0.644158i \(-0.222792\pi\)
\(432\) 0 0
\(433\) −559.107 −1.29124 −0.645620 0.763659i \(-0.723401\pi\)
−0.645620 + 0.763659i \(0.723401\pi\)
\(434\) 0 0
\(435\) 713.475 + 378.896i 1.64017 + 0.871026i
\(436\) 0 0
\(437\) 94.2707 163.282i 0.215722 0.373642i
\(438\) 0 0
\(439\) 518.563 299.393i 1.18124 0.681988i 0.224937 0.974373i \(-0.427782\pi\)
0.956301 + 0.292385i \(0.0944490\pi\)
\(440\) 0 0
\(441\) 813.579 57.7224i 1.84485 0.130890i
\(442\) 0 0
\(443\) 528.448 305.100i 1.19289 0.688713i 0.233926 0.972254i \(-0.424843\pi\)
0.958960 + 0.283542i \(0.0915094\pi\)
\(444\) 0 0
\(445\) 43.5997 75.5169i 0.0979768 0.169701i
\(446\) 0 0
\(447\) −55.2339 + 34.5530i −0.123566 + 0.0772998i
\(448\) 0 0
\(449\) −342.989 −0.763896 −0.381948 0.924184i \(-0.624747\pi\)
−0.381948 + 0.924184i \(0.624747\pi\)
\(450\) 0 0
\(451\) 107.744i 0.238901i
\(452\) 0 0
\(453\) 841.032 29.7976i 1.85658 0.0657784i
\(454\) 0 0
\(455\) 919.960 + 531.139i 2.02189 + 1.16734i
\(456\) 0 0
\(457\) 140.770 + 243.821i 0.308030 + 0.533524i 0.977931 0.208926i \(-0.0669968\pi\)
−0.669901 + 0.742450i \(0.733663\pi\)
\(458\) 0 0
\(459\) −76.4247 716.616i −0.166503 1.56126i
\(460\) 0 0
\(461\) 49.0643 + 84.9819i 0.106430 + 0.184343i 0.914322 0.404989i \(-0.132725\pi\)
−0.807891 + 0.589331i \(0.799391\pi\)
\(462\) 0 0
\(463\) 625.293 + 361.013i 1.35052 + 0.779726i 0.988323 0.152374i \(-0.0486918\pi\)
0.362202 + 0.932100i \(0.382025\pi\)
\(464\) 0 0
\(465\) 113.306 4.01441i 0.243669 0.00863314i
\(466\) 0 0
\(467\) 723.722i 1.54972i −0.632130 0.774862i \(-0.717819\pi\)
0.632130 0.774862i \(-0.282181\pi\)
\(468\) 0 0
\(469\) 729.392 1.55521
\(470\) 0 0
\(471\) −267.226 + 167.171i −0.567359 + 0.354927i
\(472\) 0 0
\(473\) 71.4104 123.686i 0.150973 0.261494i
\(474\) 0 0
\(475\) 93.4903 53.9766i 0.196822 0.113635i
\(476\) 0 0
\(477\) −260.178 384.884i −0.545446 0.806885i
\(478\) 0 0
\(479\) −303.671 + 175.325i −0.633969 + 0.366022i −0.782288 0.622917i \(-0.785947\pi\)
0.148318 + 0.988940i \(0.452614\pi\)
\(480\) 0 0
\(481\) −49.5863 + 85.8861i −0.103090 + 0.178557i
\(482\) 0 0
\(483\) 624.238 + 331.506i 1.29242 + 0.686348i
\(484\) 0 0
\(485\) −815.347 −1.68113
\(486\) 0 0
\(487\) 693.565i 1.42416i −0.702099 0.712079i \(-0.747754\pi\)
0.702099 0.712079i \(-0.252246\pi\)
\(488\) 0 0
\(489\) 204.996 386.015i 0.419214 0.789396i
\(490\) 0 0
\(491\) 450.850 + 260.298i 0.918228 + 0.530139i 0.883069 0.469243i \(-0.155473\pi\)
0.0351585 + 0.999382i \(0.488806\pi\)
\(492\) 0 0
\(493\) 595.534 + 1031.49i 1.20798 + 2.09228i
\(494\) 0 0
\(495\) −274.563 + 185.602i −0.554674 + 0.374953i
\(496\) 0 0
\(497\) −233.509 404.450i −0.469837 0.813782i
\(498\) 0 0
\(499\) 359.858 + 207.764i 0.721158 + 0.416361i 0.815179 0.579209i \(-0.196639\pi\)
−0.0940208 + 0.995570i \(0.529972\pi\)
\(500\) 0 0
\(501\) 390.913 + 624.884i 0.780266 + 1.24727i
\(502\) 0 0
\(503\) 153.470i 0.305109i −0.988295 0.152555i \(-0.951250\pi\)
0.988295 0.152555i \(-0.0487500\pi\)
\(504\) 0 0
\(505\) 141.740 0.280673
\(506\) 0 0
\(507\) 5.62249 + 158.694i 0.0110897 + 0.313005i
\(508\) 0 0
\(509\) −290.604 + 503.341i −0.570932 + 0.988883i 0.425539 + 0.904940i \(0.360085\pi\)
−0.996471 + 0.0839427i \(0.973249\pi\)
\(510\) 0 0
\(511\) 358.526 206.995i 0.701616 0.405078i
\(512\) 0 0
\(513\) 253.875 27.0749i 0.494883 0.0527776i
\(514\) 0 0
\(515\) 164.655 95.0635i 0.319718 0.184589i
\(516\) 0 0
\(517\) −128.330 + 222.274i −0.248221 + 0.429931i
\(518\) 0 0
\(519\) −4.65470 131.378i −0.00896860 0.253137i
\(520\) 0 0
\(521\) −119.457 −0.229284 −0.114642 0.993407i \(-0.536572\pi\)
−0.114642 + 0.993407i \(0.536572\pi\)
\(522\) 0 0
\(523\) 291.527i 0.557413i −0.960376 0.278706i \(-0.910094\pi\)
0.960376 0.278706i \(-0.0899056\pi\)
\(524\) 0 0
\(525\) 214.630 + 343.091i 0.408818 + 0.653506i
\(526\) 0 0
\(527\) 144.766 + 83.5805i 0.274698 + 0.158597i
\(528\) 0 0
\(529\) −65.7259 113.841i −0.124246 0.215200i
\(530\) 0 0
\(531\) −24.1988 341.074i −0.0455721 0.642325i
\(532\) 0 0
\(533\) −131.522 227.802i −0.246758 0.427397i
\(534\) 0 0
\(535\) −1089.05 628.761i −2.03560 1.17525i
\(536\) 0 0
\(537\) 80.2924 151.193i 0.149520 0.281552i
\(538\) 0 0
\(539\) 552.999i 1.02597i
\(540\) 0 0
\(541\) −918.712 −1.69817 −0.849087 0.528254i \(-0.822847\pi\)
−0.849087 + 0.528254i \(0.822847\pi\)
\(542\) 0 0
\(543\) −245.688 130.475i −0.452465 0.240285i
\(544\) 0 0
\(545\) −194.684 + 337.203i −0.357219 + 0.618721i
\(546\) 0 0
\(547\) −865.726 + 499.827i −1.58268 + 0.913761i −0.588214 + 0.808705i \(0.700169\pi\)
−0.994466 + 0.105056i \(0.966498\pi\)
\(548\) 0 0
\(549\) 357.344 734.559i 0.650901 1.33800i
\(550\) 0 0
\(551\) −365.427 + 210.979i −0.663206 + 0.382902i
\(552\) 0 0
\(553\) −531.858 + 921.205i −0.961768 + 1.66583i
\(554\) 0 0
\(555\) −102.173 + 63.9168i −0.184095 + 0.115165i
\(556\) 0 0
\(557\) 730.122 1.31081 0.655406 0.755277i \(-0.272497\pi\)
0.655406 + 0.755277i \(0.272497\pi\)
\(558\) 0 0
\(559\) 348.678i 0.623752i
\(560\) 0 0
\(561\) −488.320 + 17.3011i −0.870445 + 0.0308397i
\(562\) 0 0
\(563\) −335.889 193.926i −0.596606 0.344451i 0.171099 0.985254i \(-0.445268\pi\)
−0.767705 + 0.640803i \(0.778601\pi\)
\(564\) 0 0
\(565\) 10.8088 + 18.7215i 0.0191307 + 0.0331353i
\(566\) 0 0
\(567\) 135.133 + 947.533i 0.238329 + 1.67113i
\(568\) 0 0
\(569\) −278.389 482.184i −0.489260 0.847423i 0.510664 0.859780i \(-0.329400\pi\)
−0.999924 + 0.0123576i \(0.996066\pi\)
\(570\) 0 0
\(571\) 28.0470 + 16.1930i 0.0491191 + 0.0283589i 0.524358 0.851498i \(-0.324305\pi\)
−0.475239 + 0.879857i \(0.657639\pi\)
\(572\) 0 0
\(573\) 268.184 9.50172i 0.468035 0.0165824i
\(574\) 0 0
\(575\) 227.624i 0.395869i
\(576\) 0 0
\(577\) 221.536 0.383945 0.191972 0.981400i \(-0.438512\pi\)
0.191972 + 0.981400i \(0.438512\pi\)
\(578\) 0 0
\(579\) 586.051 366.620i 1.01218 0.633195i
\(580\) 0 0
\(581\) 698.292 1209.48i 1.20188 2.08172i
\(582\) 0 0
\(583\) −272.784 + 157.492i −0.467897 + 0.270140i
\(584\) 0 0
\(585\) −353.944 + 727.570i −0.605033 + 1.24371i
\(586\) 0 0
\(587\) 653.747 377.441i 1.11371 0.643000i 0.173921 0.984760i \(-0.444356\pi\)
0.939787 + 0.341759i \(0.111023\pi\)
\(588\) 0 0
\(589\) −29.6100 + 51.2860i −0.0502716 + 0.0870730i
\(590\) 0 0
\(591\) 254.174 + 134.981i 0.430075 + 0.228395i
\(592\) 0 0
\(593\) 697.420 1.17609 0.588044 0.808829i \(-0.299898\pi\)
0.588044 + 0.808829i \(0.299898\pi\)
\(594\) 0 0
\(595\) 1903.30i 3.19883i
\(596\) 0 0
\(597\) 70.5737 132.893i 0.118214 0.222601i
\(598\) 0 0
\(599\) 80.7777 + 46.6370i 0.134854 + 0.0778581i 0.565909 0.824467i \(-0.308525\pi\)
−0.431055 + 0.902326i \(0.641859\pi\)
\(600\) 0 0
\(601\) 215.014 + 372.414i 0.357760 + 0.619658i 0.987586 0.157078i \(-0.0502074\pi\)
−0.629827 + 0.776736i \(0.716874\pi\)
\(602\) 0 0
\(603\) 39.3166 + 554.156i 0.0652017 + 0.918998i
\(604\) 0 0
\(605\) −252.743 437.764i −0.417757 0.723577i
\(606\) 0 0
\(607\) 474.182 + 273.769i 0.781189 + 0.451019i 0.836851 0.547430i \(-0.184394\pi\)
−0.0556627 + 0.998450i \(0.517727\pi\)
\(608\) 0 0
\(609\) −838.925 1341.04i −1.37755 2.20204i
\(610\) 0 0
\(611\) 626.601i 1.02553i
\(612\) 0 0
\(613\) −6.42863 −0.0104872 −0.00524358 0.999986i \(-0.501669\pi\)
−0.00524358 + 0.999986i \(0.501669\pi\)
\(614\) 0 0
\(615\) −11.3184 319.459i −0.0184039 0.519446i
\(616\) 0 0
\(617\) −517.155 + 895.739i −0.838177 + 1.45177i 0.0532398 + 0.998582i \(0.483045\pi\)
−0.891417 + 0.453184i \(0.850288\pi\)
\(618\) 0 0
\(619\) −641.544 + 370.395i −1.03642 + 0.598377i −0.918817 0.394684i \(-0.870854\pi\)
−0.117602 + 0.993061i \(0.537521\pi\)
\(620\) 0 0
\(621\) −218.213 + 492.134i −0.351390 + 0.792486i
\(622\) 0 0
\(623\) −147.869 + 85.3724i −0.237350 + 0.137034i
\(624\) 0 0
\(625\) 390.038 675.565i 0.624060 1.08090i
\(626\) 0 0
\(627\) −6.12923 172.996i −0.00977549 0.275911i
\(628\) 0 0
\(629\) −177.689 −0.282495
\(630\) 0 0
\(631\) 693.165i 1.09852i −0.835652 0.549259i \(-0.814910\pi\)
0.835652 0.549259i \(-0.185090\pi\)
\(632\) 0 0
\(633\) 4.18932 + 6.69674i 0.00661820 + 0.0105794i
\(634\) 0 0
\(635\) −483.458 279.125i −0.761351 0.439566i
\(636\) 0 0
\(637\) −675.036 1169.20i −1.05971 1.83547i
\(638\) 0 0
\(639\) 294.694 199.210i 0.461180 0.311752i
\(640\) 0 0
\(641\) 115.145 + 199.438i 0.179634 + 0.311135i 0.941755 0.336299i \(-0.109175\pi\)
−0.762121 + 0.647434i \(0.775842\pi\)
\(642\) 0 0
\(643\) −662.916 382.735i −1.03097 0.595233i −0.113710 0.993514i \(-0.536274\pi\)
−0.917263 + 0.398281i \(0.869607\pi\)
\(644\) 0 0
\(645\) 198.737 374.228i 0.308119 0.580198i
\(646\) 0 0
\(647\) 339.078i 0.524078i 0.965057 + 0.262039i \(0.0843949\pi\)
−0.965057 + 0.262039i \(0.915605\pi\)
\(648\) 0 0
\(649\) −231.832 −0.357214
\(650\) 0 0
\(651\) −196.070 104.124i −0.301183 0.159945i
\(652\) 0 0
\(653\) 73.8243 127.867i 0.113054 0.195815i −0.803946 0.594702i \(-0.797270\pi\)
0.917000 + 0.398887i \(0.130603\pi\)
\(654\) 0 0
\(655\) 635.233 366.752i 0.969821 0.559926i
\(656\) 0 0
\(657\) 176.590 + 261.232i 0.268783 + 0.397614i
\(658\) 0 0
\(659\) −795.428 + 459.241i −1.20702 + 0.696875i −0.962108 0.272669i \(-0.912094\pi\)
−0.244915 + 0.969544i \(0.578760\pi\)
\(660\) 0 0
\(661\) −103.150 + 178.662i −0.156052 + 0.270290i −0.933442 0.358729i \(-0.883210\pi\)
0.777389 + 0.629020i \(0.216543\pi\)
\(662\) 0 0
\(663\) −1011.33 + 632.662i −1.52538 + 0.954242i
\(664\) 0 0
\(665\) −674.281 −1.01396
\(666\) 0 0
\(667\) 889.718i 1.33391i
\(668\) 0 0
\(669\) −528.832 + 18.7364i −0.790482 + 0.0280066i
\(670\) 0 0
\(671\) −479.641 276.921i −0.714815 0.412699i
\(672\) 0 0
\(673\) −333.272 577.245i −0.495204 0.857719i 0.504780 0.863248i \(-0.331573\pi\)
−0.999985 + 0.00552878i \(0.998240\pi\)
\(674\) 0 0
\(675\) −249.094 + 181.559i −0.369028 + 0.268976i
\(676\) 0 0
\(677\) 235.497 + 407.893i 0.347854 + 0.602500i 0.985868 0.167524i \(-0.0535773\pi\)
−0.638014 + 0.770025i \(0.720244\pi\)
\(678\) 0 0
\(679\) 1382.63 + 798.263i 2.03628 + 1.17565i
\(680\) 0 0
\(681\) 6.43130 0.227860i 0.00944391 0.000334596i
\(682\) 0 0
\(683\) 909.494i 1.33162i 0.746123 + 0.665808i \(0.231913\pi\)
−0.746123 + 0.665808i \(0.768087\pi\)
\(684\) 0 0
\(685\) 1549.92 2.26266
\(686\) 0 0
\(687\) −323.740 + 202.524i −0.471237 + 0.294795i
\(688\) 0 0
\(689\) −384.495 + 665.965i −0.558048 + 0.966567i
\(690\) 0 0
\(691\) −366.787 + 211.764i −0.530805 + 0.306461i −0.741344 0.671125i \(-0.765811\pi\)
0.210539 + 0.977585i \(0.432478\pi\)
\(692\) 0 0
\(693\) 647.307 45.9256i 0.934065 0.0662707i
\(694\) 0 0
\(695\) 670.782 387.276i 0.965154 0.557232i
\(696\) 0 0
\(697\) 235.650 408.158i 0.338092 0.585592i
\(698\) 0 0
\(699\) −695.578 369.392i −0.995104 0.528457i
\(700\) 0 0
\(701\) −66.5738 −0.0949697 −0.0474849 0.998872i \(-0.515121\pi\)
−0.0474849 + 0.998872i \(0.515121\pi\)
\(702\) 0 0
\(703\) 62.9499i 0.0895446i
\(704\) 0 0
\(705\) −357.145 + 672.517i −0.506589 + 0.953924i
\(706\) 0 0
\(707\) −240.356 138.770i −0.339967 0.196280i
\(708\) 0 0
\(709\) −48.3932 83.8194i −0.0682555 0.118222i 0.829878 0.557945i \(-0.188410\pi\)
−0.898133 + 0.439723i \(0.855077\pi\)
\(710\) 0 0
\(711\) −728.554 354.423i −1.02469 0.498485i
\(712\) 0 0
\(713\) −62.4340 108.139i −0.0875652 0.151667i
\(714\) 0 0
\(715\) 475.077 + 274.286i 0.664443 + 0.383616i
\(716\) 0 0
\(717\) 497.065 + 794.572i 0.693257 + 1.10819i
\(718\) 0 0
\(719\) 1184.39i 1.64727i 0.567120 + 0.823635i \(0.308058\pi\)
−0.567120 + 0.823635i \(0.691942\pi\)
\(720\) 0 0
\(721\) −372.287 −0.516348
\(722\) 0 0
\(723\) 3.12528 + 88.2104i 0.00432266 + 0.122006i
\(724\) 0 0
\(725\) 254.713 441.176i 0.351329 0.608519i
\(726\) 0 0
\(727\) 687.700 397.044i 0.945942 0.546140i 0.0541243 0.998534i \(-0.482763\pi\)
0.891818 + 0.452394i \(0.149430\pi\)
\(728\) 0 0
\(729\) −712.604 + 153.742i −0.977509 + 0.210895i
\(730\) 0 0
\(731\) 541.034 312.366i 0.740128 0.427313i
\(732\) 0 0
\(733\) −64.4932 + 111.706i −0.0879853 + 0.152395i −0.906659 0.421863i \(-0.861376\pi\)
0.818674 + 0.574258i \(0.194710\pi\)
\(734\) 0 0
\(735\) −58.0916 1639.62i −0.0790361 2.23078i
\(736\) 0 0
\(737\) 376.666 0.511080
\(738\) 0 0
\(739\) 17.7228i 0.0239822i 0.999928 + 0.0119911i \(0.00381697\pi\)
−0.999928 + 0.0119911i \(0.996183\pi\)
\(740\) 0 0
\(741\) −224.133 358.282i −0.302473 0.483511i
\(742\) 0 0
\(743\) 39.9367 + 23.0575i 0.0537507 + 0.0310330i 0.526635 0.850092i \(-0.323454\pi\)
−0.472884 + 0.881125i \(0.656787\pi\)
\(744\) 0 0
\(745\) 65.5269 + 113.496i 0.0879556 + 0.152343i
\(746\) 0 0
\(747\) 956.541 + 465.333i 1.28051 + 0.622935i
\(748\) 0 0
\(749\) 1231.17 + 2132.45i 1.64376 + 2.84707i
\(750\) 0 0
\(751\) −205.122 118.427i −0.273132 0.157693i 0.357178 0.934036i \(-0.383739\pi\)
−0.630310 + 0.776343i \(0.717072\pi\)
\(752\) 0 0
\(753\) −274.837 + 517.528i −0.364990 + 0.687288i
\(754\) 0 0
\(755\) 1692.82i 2.24215i
\(756\) 0 0
\(757\) 193.736 0.255925 0.127963 0.991779i \(-0.459156\pi\)
0.127963 + 0.991779i \(0.459156\pi\)
\(758\) 0 0
\(759\) 322.363 + 171.193i 0.424720 + 0.225551i
\(760\) 0 0
\(761\) −41.0648 + 71.1263i −0.0539616 + 0.0934642i −0.891744 0.452539i \(-0.850518\pi\)
0.837783 + 0.546004i \(0.183852\pi\)
\(762\) 0 0
\(763\) 660.276 381.210i 0.865368 0.499620i
\(764\) 0 0
\(765\) −1446.03 + 102.594i −1.89024 + 0.134110i
\(766\) 0 0
\(767\) −490.159 + 282.993i −0.639060 + 0.368961i
\(768\) 0 0
\(769\) 659.227 1141.82i 0.857253 1.48481i −0.0172867 0.999851i \(-0.505503\pi\)
0.874539 0.484955i \(-0.161164\pi\)
\(770\) 0 0
\(771\) 1112.32 695.839i 1.44269 0.902515i
\(772\) 0 0
\(773\) −1.74554 −0.00225814 −0.00112907 0.999999i \(-0.500359\pi\)
−0.00112907 + 0.999999i \(0.500359\pi\)
\(774\) 0 0
\(775\) 71.4958i 0.0922526i
\(776\) 0 0
\(777\) 235.838 8.35569i 0.303523 0.0107538i
\(778\) 0 0
\(779\) 144.598 + 83.4835i 0.185620 + 0.107167i
\(780\) 0 0
\(781\) −120.587 208.862i −0.154400 0.267429i
\(782\) 0 0
\(783\) 973.637 709.660i 1.24347 0.906335i
\(784\) 0 0
\(785\) 317.025 + 549.103i 0.403853 + 0.699494i
\(786\) 0 0
\(787\) 1026.21 + 592.484i 1.30395 + 0.752838i 0.981080 0.193603i \(-0.0620175\pi\)
0.322875 + 0.946442i \(0.395351\pi\)
\(788\) 0 0
\(789\) −224.381 + 7.94977i −0.284386 + 0.0100758i
\(790\) 0 0
\(791\) 42.3295i 0.0535139i
\(792\) 0 0
\(793\) −1352.13 −1.70508
\(794\) 0 0
\(795\) −792.251