Properties

Label 144.3.o.a.79.1
Level $144$
Weight $3$
Character 144.79
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 79.1
Root \(-1.07834i\) of defining polynomial
Character \(\chi\) \(=\) 144.79
Dual form 144.3.o.a.31.1

$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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 −0.992293 0.123914i \(-0.960455\pi\)
0.388834 0.921308i \(-0.372878\pi\)
\(6\) 0 0
\(7\) 10.2332 + 5.90815i 1.46189 + 0.844021i 0.999099 0.0424471i \(-0.0135154\pi\)
0.462789 + 0.886468i \(0.346849\pi\)
\(8\) 0 0
\(9\) 5.04032 7.45622i 0.560036 0.828469i
\(10\) 0 0
\(11\) 5.28454 + 3.05103i 0.480413 + 0.277366i 0.720588 0.693363i \(-0.243872\pi\)
−0.240176 + 0.970729i \(0.577205\pi\)
\(12\) 0 0
\(13\) 7.44868 + 12.9015i 0.572975 + 0.992422i 0.996258 + 0.0864245i \(0.0275441\pi\)
−0.423283 + 0.905997i \(0.639123\pi\)
\(14\) 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 \(-0.919949\pi\)
0.968543 0.248845i \(-0.0800509\pi\)
\(20\) 0 0
\(21\) −35.4267 1.25516i −1.68698 0.0597695i
\(22\) 0 0
\(23\) −17.2673 + 9.96931i −0.750754 + 0.433448i −0.825966 0.563719i \(-0.809370\pi\)
0.0752122 + 0.997168i \(0.476037\pi\)
\(24\) 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 −0.168551 0.985693i \(-0.553909\pi\)
0.937910 0.346877i \(-0.112758\pi\)
\(30\) 0 0
\(31\) 5.42359 3.13131i 0.174955 0.101010i −0.409965 0.912101i \(-0.634459\pi\)
0.584920 + 0.811091i \(0.301126\pi\)
\(32\) 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 0.953375 0.301789i \(-0.0975839\pi\)
−0.738045 + 0.674752i \(0.764251\pi\)
\(42\) 0 0
\(43\) 20.2696 + 11.7027i 0.471386 + 0.272155i 0.716820 0.697258i \(-0.245597\pi\)
−0.245433 + 0.969413i \(0.578930\pi\)
\(44\) 0 0
\(45\) −54.1751 3.84365i −1.20389 0.0854145i
\(46\) 0 0
\(47\) −36.4261 21.0306i −0.775023 0.447460i 0.0596404 0.998220i \(-0.481005\pi\)
−0.834664 + 0.550760i \(0.814338\pi\)
\(48\) 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 −0.752209 0.658925i \(-0.771012\pi\)
0.194541 + 0.980894i \(0.437678\pi\)
\(60\) 0 0
\(61\) −45.3815 + 78.6031i −0.743960 + 1.28858i 0.206720 + 0.978400i \(0.433721\pi\)
−0.950679 + 0.310176i \(0.899612\pi\)
\(62\) 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 −0.0448520 0.998994i \(-0.514282\pi\)
0.842728 + 0.538340i \(0.180948\pi\)
\(68\) 0 0
\(69\) 31.7233 50.7106i 0.459759 0.734936i
\(70\) 0 0
\(71\) 39.5232i 0.556665i 0.960485 + 0.278333i \(0.0897817\pi\)
−0.960485 + 0.278333i \(0.910218\pi\)
\(72\) 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 −0.0825131 0.996590i \(-0.526295\pi\)
−0.904329 + 0.426837i \(0.859628\pi\)
\(80\) 0 0
\(81\) −30.1903 75.1634i −0.372720 0.927944i
\(82\) 0 0
\(83\) 102.357 + 59.0957i 1.23321 + 0.711996i 0.967698 0.252111i \(-0.0811247\pi\)
0.265515 + 0.964107i \(0.414458\pi\)
\(84\) 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 −0.273233 0.961948i \(-0.588093\pi\)
0.969688 0.244347i \(-0.0785736\pi\)
\(98\) 0 0
\(99\) 49.3849 24.0245i 0.498838 0.242672i
\(100\) 0 0
\(101\) −11.7439 + 20.3411i −0.116277 + 0.201397i −0.918289 0.395910i \(-0.870429\pi\)
0.802013 + 0.597307i \(0.203763\pi\)
\(102\) 0 0
\(103\) −27.2852 + 15.7531i −0.264905 + 0.152943i −0.626570 0.779365i \(-0.715542\pi\)
0.361665 + 0.932308i \(0.382208\pi\)
\(104\) 0 0
\(105\) 100.333 + 188.931i 0.955553 + 1.79934i
\(106\) 0 0
\(107\) 208.386i 1.94753i −0.227558 0.973765i \(-0.573074\pi\)
0.227558 0.973765i \(-0.426926\pi\)
\(108\) 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 0.873842 0.486210i \(-0.161621\pi\)
−0.857991 + 0.513664i \(0.828288\pi\)
\(114\) 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 \(-0.881340\pi\)
0.931319 0.364206i \(-0.118660\pi\)
\(128\) 0 0
\(129\) −70.1720 2.48618i −0.543969 0.0192727i
\(130\) 0 0
\(131\) −105.265 + 60.7749i −0.803552 + 0.463931i −0.844712 0.535222i \(-0.820228\pi\)
0.0411598 + 0.999153i \(0.486895\pi\)
\(132\) 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 −0.167024 + 0.985953i \(0.553416\pi\)
−0.770348 + 0.637623i \(0.779918\pi\)
\(138\) 0 0
\(139\) −111.156 + 64.1761i −0.799685 + 0.461698i −0.843361 0.537348i \(-0.819426\pi\)
0.0436761 + 0.999046i \(0.486093\pi\)
\(140\) 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 0.900161 0.435558i \(-0.143449\pi\)
−0.827285 + 0.561783i \(0.810116\pi\)
\(150\) 0 0
\(151\) −242.937 140.260i −1.60886 0.928874i −0.989626 0.143665i \(-0.954111\pi\)
−0.619230 0.785209i \(-0.712555\pi\)
\(152\) 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 0.983411 0.181392i \(-0.0580603\pi\)
−0.648796 + 0.760963i \(0.724727\pi\)
\(158\) 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 \(-0.852527\pi\)
0.894583 0.446902i \(-0.147473\pi\)
\(164\) 0 0
\(165\) 51.8131 + 97.5658i 0.314019 + 0.591308i
\(166\) 0 0
\(167\) −212.778 + 122.847i −1.27412 + 0.735613i −0.975761 0.218840i \(-0.929773\pi\)
−0.298359 + 0.954454i \(0.596439\pi\)
\(168\) 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 −0.795728 0.605654i \(-0.792911\pi\)
0.922376 + 0.386294i \(0.126245\pi\)
\(174\) 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 \(-0.949045\pi\)
0.987215 0.159396i \(-0.0509546\pi\)
\(180\) 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 0.283306 0.959030i \(-0.408569\pi\)
−0.688891 + 0.724865i \(0.741902\pi\)
\(192\) 0 0
\(193\) −115.213 199.555i −0.596959 1.03396i −0.993267 0.115846i \(-0.963042\pi\)
0.396308 0.918118i \(-0.370291\pi\)
\(194\) 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 \(-0.959779\pi\)
0.992028 0.126021i \(-0.0402208\pi\)
\(200\) 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 −0.505394 0.862889i \(-0.668653\pi\)
0.494587 + 0.869128i \(0.335319\pi\)
\(212\) 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 0.801739 0.597675i \(-0.203909\pi\)
−0.116732 + 0.993163i \(0.537242\pi\)
\(224\) 0 0
\(225\) 44.9471 + 92.3936i 0.199765 + 0.410638i
\(226\) 0 0
\(227\) −1.85772 1.07256i −0.00818380 0.00472492i 0.495903 0.868378i \(-0.334837\pi\)
−0.504086 + 0.863653i \(0.668171\pi\)
\(228\) 0 0
\(229\) 63.6447 + 110.236i 0.277925 + 0.481379i 0.970869 0.239612i \(-0.0770201\pi\)
−0.692944 + 0.720991i \(0.743687\pi\)
\(230\) 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 −0.944447 0.328662i \(-0.893402\pi\)
−0.187594 + 0.982247i \(0.560069\pi\)
\(240\) 0 0
\(241\) −14.7110 + 25.4801i −0.0610413 + 0.105727i −0.894931 0.446204i \(-0.852775\pi\)
0.833890 + 0.551931i \(0.186109\pi\)
\(242\) 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 \(0.127213\pi\)
−0.921197 + 0.389096i \(0.872787\pi\)
\(252\) 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 −0.880427 0.474182i \(-0.842744\pi\)
0.0295596 0.999563i \(-0.490590\pi\)
\(258\) 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 0.618133 0.786073i \(-0.287889\pi\)
−0.371693 + 0.928356i \(0.621223\pi\)
\(264\) 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 \(-0.922633\pi\)
0.970607 0.240668i \(-0.0773666\pi\)
\(272\) 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 −0.995219 0.0976702i \(-0.968861\pi\)
0.582194 + 0.813050i \(0.302194\pi\)
\(278\) 0 0
\(279\) 3.98890 56.2223i 0.0142971 0.201514i
\(280\) 0 0
\(281\) 23.9532 41.4882i 0.0852429 0.147645i −0.820252 0.572003i \(-0.806167\pi\)
0.905495 + 0.424358i \(0.139500\pi\)
\(282\) 0 0
\(283\) 307.250 177.391i 1.08569 0.626824i 0.153265 0.988185i \(-0.451021\pi\)
0.932426 + 0.361361i \(0.117688\pi\)
\(284\) 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 0.814384 0.580326i \(-0.197075\pi\)
−0.909769 + 0.415114i \(0.863742\pi\)
\(294\) 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 \(0.0297976\pi\)
−0.995622 + 0.0934754i \(0.970202\pi\)
\(308\) 0 0
\(309\) 50.1280 80.1309i 0.162226 0.259323i
\(310\) 0 0
\(311\) 215.498 124.418i 0.692920 0.400058i −0.111785 0.993732i \(-0.535657\pi\)
0.804705 + 0.593675i \(0.202323\pi\)
\(312\) 0 0
\(313\) −307.856 + 533.222i −0.983565 + 1.70358i −0.335417 + 0.942070i \(0.608877\pi\)
−0.648147 + 0.761515i \(0.724456\pi\)
\(314\) 0 0
\(315\) −531.677 359.408i −1.68786 1.14098i
\(316\) 0 0
\(317\) −128.314 + 222.246i −0.404775 + 0.701090i −0.994295 0.106663i \(-0.965983\pi\)
0.589521 + 0.807753i \(0.299317\pi\)
\(318\) 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 0.297881 0.954603i \(-0.403720\pi\)
−0.677770 + 0.735274i \(0.737053\pi\)
\(332\) 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 0.896574 0.442895i \(-0.146048\pi\)
−0.831845 + 0.555008i \(0.812715\pi\)
\(338\) 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 −0.257887 0.966175i \(-0.583026\pi\)
0.707789 + 0.706424i \(0.249693\pi\)
\(348\) 0 0
\(349\) 46.5629 80.6493i 0.133418 0.231087i −0.791574 0.611073i \(-0.790738\pi\)
0.924992 + 0.379987i \(0.124071\pi\)
\(350\) 0 0
\(351\) −367.703 + 163.040i −1.04759 + 0.464503i
\(352\) 0 0
\(353\) −215.455 + 373.178i −0.610353 + 1.05716i 0.380828 + 0.924646i \(0.375639\pi\)
−0.991181 + 0.132516i \(0.957694\pi\)
\(354\) 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 \(-0.854912\pi\)
0.897906 0.440187i \(-0.145088\pi\)
\(360\) 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 −0.268027 0.963411i \(-0.586372\pi\)
−0.968352 + 0.249588i \(0.919705\pi\)
\(368\) 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 0.559058 0.829129i \(-0.311163\pi\)
−0.997575 + 0.0695940i \(0.977830\pi\)
\(374\) 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 \(-0.801017\pi\)
0.810890 0.585198i \(-0.198983\pi\)
\(380\) 0 0
\(381\) 130.165 + 245.106i 0.341641 + 0.643323i
\(382\) 0 0
\(383\) 393.008 226.903i 1.02613 0.592436i 0.110256 0.993903i \(-0.464833\pi\)
0.915873 + 0.401467i \(0.131500\pi\)
\(384\) 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 −0.740397 0.672170i \(-0.765362\pi\)
0.952315 + 0.305117i \(0.0986957\pi\)
\(390\) 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 0.997173 0.0751418i \(-0.0239409\pi\)
−0.563661 + 0.826006i \(0.690608\pi\)
\(402\) 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 0.823140 0.567839i \(-0.192220\pi\)
−0.903333 + 0.428941i \(0.858887\pi\)
\(410\) 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 −0.996491 0.0836989i \(-0.973327\pi\)
−0.425760 + 0.904836i \(0.639993\pi\)
\(420\) 0 0
\(421\) −146.855 + 254.360i −0.348823 + 0.604180i −0.986041 0.166504i \(-0.946752\pi\)
0.637217 + 0.770684i \(0.280085\pi\)
\(422\) 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 \(0.222792\pi\)
−0.764893 + 0.644158i \(0.777208\pi\)
\(432\) 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 0.956301 0.292385i \(-0.0944490\pi\)
0.224937 + 0.974373i \(0.427782\pi\)
\(440\) 0 0
\(441\) 813.579 + 57.7224i 1.84485 + 0.130890i
\(442\) 0 0
\(443\) 528.448 + 305.100i 1.19289 + 0.688713i 0.958960 0.283542i \(-0.0915094\pi\)
0.233926 + 0.972254i \(0.424843\pi\)
\(444\) 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 −0.669901 0.742450i \(-0.733663\pi\)
0.977931 + 0.208926i \(0.0669968\pi\)
\(458\) 0 0
\(459\) −76.4247 + 716.616i −0.166503 + 1.56126i
\(460\) 0 0
\(461\) 49.0643 84.9819i 0.106430 0.184343i −0.807891 0.589331i \(-0.799391\pi\)
0.914322 + 0.404989i \(0.132725\pi\)
\(462\) 0 0
\(463\) 625.293 361.013i 1.35052 0.779726i 0.362202 0.932100i \(-0.382025\pi\)
0.988323 + 0.152374i \(0.0486918\pi\)
\(464\) 0 0
\(465\) 113.306 + 4.01441i 0.243669 + 0.00863314i
\(466\) 0 0
\(467\) 723.722i 1.54972i 0.632130 + 0.774862i \(0.282181\pi\)
−0.632130 + 0.774862i \(0.717819\pi\)
\(468\) 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 0.148318 0.988940i \(-0.452614\pi\)
−0.782288 + 0.622917i \(0.785947\pi\)
\(480\) 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 \(0.252246\pi\)
−0.702099 + 0.712079i \(0.747754\pi\)
\(488\) 0 0
\(489\) 204.996 + 386.015i 0.419214 + 0.789396i
\(490\) 0 0
\(491\) 450.850 260.298i 0.918228 0.530139i 0.0351585 0.999382i \(-0.488806\pi\)
0.883069 + 0.469243i \(0.155473\pi\)
\(492\) 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 −0.0940208 0.995570i \(-0.529972\pi\)
0.815179 + 0.579209i \(0.196639\pi\)
\(500\) 0 0
\(501\) 390.913 624.884i 0.780266 1.24727i
\(502\) 0 0
\(503\) 153.470i 0.305109i 0.988295 + 0.152555i \(0.0487500\pi\)
−0.988295 + 0.152555i \(0.951250\pi\)
\(504\) 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 −0.996471 0.0839427i \(-0.973249\pi\)
0.425539 0.904940i \(-0.360085\pi\)
\(510\) 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 \(0.0899056\pi\)
−0.960376 + 0.278706i \(0.910094\pi\)
\(524\) 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 −0.994466 0.105056i \(-0.966498\pi\)
−0.588214 0.808705i \(-0.700169\pi\)
\(548\) 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 −0.767705 0.640803i \(-0.778601\pi\)
0.171099 + 0.985254i \(0.445268\pi\)
\(564\) 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 −0.999924 0.0123576i \(-0.996066\pi\)
0.510664 + 0.859780i \(0.329400\pi\)
\(570\) 0 0
\(571\) 28.0470 16.1930i 0.0491191 0.0283589i −0.475239 0.879857i \(-0.657639\pi\)
0.524358 + 0.851498i \(0.324305\pi\)
\(572\) 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 0.939787 0.341759i \(-0.111023\pi\)
0.173921 + 0.984760i \(0.444356\pi\)
\(588\) 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 −0.431055 0.902326i \(-0.641859\pi\)
0.565909 + 0.824467i \(0.308525\pi\)
\(600\) 0 0
\(601\) 215.014 372.414i 0.357760 0.619658i −0.629827 0.776736i \(-0.716874\pi\)
0.987586 + 0.157078i \(0.0502074\pi\)
\(602\) 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 −0.0556627 0.998450i \(-0.517727\pi\)
0.836851 + 0.547430i \(0.184394\pi\)
\(608\) 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 −0.891417 0.453184i \(-0.850288\pi\)
0.0532398 0.998582i \(-0.483045\pi\)
\(618\) 0 0
\(619\) −641.544 370.395i −1.03642 0.598377i −0.117602 0.993061i \(-0.537521\pi\)
−0.918817 + 0.394684i \(0.870854\pi\)
\(620\) 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 \(0.185090\pi\)
−0.835652 + 0.549259i \(0.814910\pi\)
\(632\) 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 −0.762121 0.647434i \(-0.775842\pi\)
0.941755 + 0.336299i \(0.109175\pi\)
\(642\) 0 0
\(643\) −662.916 + 382.735i −1.03097 + 0.595233i −0.917263 0.398281i \(-0.869607\pi\)
−0.113710 + 0.993514i \(0.536274\pi\)
\(644\) 0 0
\(645\) 198.737 + 374.228i 0.308119 + 0.580198i
\(646\) 0 0
\(647\) 339.078i 0.524078i −0.965057 0.262039i \(-0.915605\pi\)
0.965057 0.262039i \(-0.0843949\pi\)
\(648\) 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 0.917000 0.398887i \(-0.130603\pi\)
−0.803946 + 0.594702i \(0.797270\pi\)
\(654\) 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 −0.244915 0.969544i \(-0.578760\pi\)
−0.962108 + 0.272669i \(0.912094\pi\)
\(660\) 0 0
\(661\) −103.150 178.662i −0.156052 0.270290i 0.777389 0.629020i \(-0.216543\pi\)
−0.933442 + 0.358729i \(0.883210\pi\)
\(662\) 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 −0.999985 0.00552878i \(-0.998240\pi\)
0.504780 + 0.863248i \(0.331573\pi\)
\(674\) 0 0
\(675\) −249.094 181.559i −0.369028 0.268976i
\(676\) 0 0
\(677\) 235.497 407.893i 0.347854 0.602500i −0.638014 0.770025i \(-0.720244\pi\)
0.985868 + 0.167524i \(0.0535773\pi\)
\(678\) 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 \(-0.768087\pi\)
0.746123 0.665808i \(-0.231913\pi\)
\(684\) 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 0.210539 0.977585i \(-0.432478\pi\)
−0.741344 + 0.671125i \(0.765811\pi\)
\(692\) 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 −0.898133 0.439723i \(-0.855077\pi\)
0.829878 + 0.557945i \(0.188410\pi\)
\(710\) 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 \(-0.691942\pi\)
0.567120 0.823635i \(-0.308058\pi\)
\(720\) 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 0.891818 0.452394i \(-0.149430\pi\)
0.0541243 + 0.998534i \(0.482763\pi\)
\(728\) 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 0.818674 0.574258i \(-0.194710\pi\)
−0.906659 + 0.421863i \(0.861376\pi\)
\(734\) 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 \(-0.996183\pi\)
0.999928 0.0119911i \(-0.00381697\pi\)
\(740\) 0 0
\(741\) −224.133 + 358.282i −0.302473 + 0.483511i
\(742\) 0 0
\(743\) 39.9367 23.0575i 0.0537507 0.0310330i −0.472884 0.881125i \(-0.656787\pi\)
0.526635 + 0.850092i \(0.323454\pi\)
\(744\) 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 −0.630310 0.776343i \(-0.717072\pi\)
0.357178 + 0.934036i \(0.383739\pi\)
\(752\) 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 0.837783 0.546004i \(-0.183852\pi\)
−0.891744 + 0.452539i \(0.850518\pi\)
\(762\) 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 0.874539 + 0.484955i \(0.161164\pi\)
−0.0172867 + 0.999851i \(0.505503\pi\)
\(770\) 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 0.322875 0.946442i \(-0.395351\pi\)
0.981080 + 0.193603i \(0.0620175\pi\)
\(788\) 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