Properties

Label 720.2.u.a.179.17
Level $720$
Weight $2$
Character 720.179
Analytic conductor $5.749$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 720.u (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.74922894553\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(48\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 179.17
Character \(\chi\) \(=\) 720.179
Dual form 720.2.u.a.539.17

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.612434 - 1.27473i) q^{2} +(-1.24985 + 1.56137i) q^{4} +(-0.263678 - 2.22047i) q^{5} +2.95946i q^{7} +(2.75577 + 0.636981i) q^{8} +O(q^{10})\) \(q+(-0.612434 - 1.27473i) q^{2} +(-1.24985 + 1.56137i) q^{4} +(-0.263678 - 2.22047i) q^{5} +2.95946i q^{7} +(2.75577 + 0.636981i) q^{8} +(-2.66900 + 1.69601i) q^{10} +(1.04021 - 1.04021i) q^{11} +(0.00780247 - 0.00780247i) q^{13} +(3.77249 - 1.81247i) q^{14} +(-0.875749 - 3.90296i) q^{16} -2.00003 q^{17} +(5.10608 - 5.10608i) q^{19} +(3.79653 + 2.36355i) q^{20} +(-1.96305 - 0.688925i) q^{22} +6.49393 q^{23} +(-4.86095 + 1.17098i) q^{25} +(-0.0147245 - 0.00516751i) q^{26} +(-4.62080 - 3.69888i) q^{28} +(5.45997 - 5.45997i) q^{29} -4.99178i q^{31} +(-4.43886 + 3.50664i) q^{32} +(1.22489 + 2.54949i) q^{34} +(6.57137 - 0.780345i) q^{35} +(3.74547 + 3.74547i) q^{37} +(-9.63598 - 3.38171i) q^{38} +(0.687758 - 6.28705i) q^{40} -10.4245 q^{41} +(-3.52161 + 3.52161i) q^{43} +(0.324047 + 2.92427i) q^{44} +(-3.97710 - 8.27798i) q^{46} -10.6419i q^{47} -1.75838 q^{49} +(4.46968 + 5.47923i) q^{50} +(0.00243062 + 0.0219345i) q^{52} +(2.98006 - 2.98006i) q^{53} +(-2.58404 - 2.03548i) q^{55} +(-1.88512 + 8.15557i) q^{56} +(-10.3038 - 3.61610i) q^{58} +(5.47867 - 5.47867i) q^{59} +(-4.67845 - 4.67845i) q^{61} +(-6.36315 + 3.05713i) q^{62} +(7.18851 + 3.51074i) q^{64} +(-0.0193825 - 0.0152678i) q^{65} +(-2.29404 - 2.29404i) q^{67} +(2.49974 - 3.12279i) q^{68} +(-5.01925 - 7.89879i) q^{70} +0.212315i q^{71} +16.4980 q^{73} +(2.48059 - 7.06830i) q^{74} +(1.59064 + 14.3543i) q^{76} +(3.07847 + 3.07847i) q^{77} -4.54833i q^{79} +(-8.43547 + 2.97370i) q^{80} +(6.38432 + 13.2884i) q^{82} +(-4.68359 + 4.68359i) q^{83} +(0.527365 + 4.44100i) q^{85} +(6.64583 + 2.33233i) q^{86} +(3.52918 - 2.20399i) q^{88} +0.123094 q^{89} +(0.0230911 + 0.0230911i) q^{91} +(-8.11644 + 10.1394i) q^{92} +(-13.5655 + 6.51744i) q^{94} +(-12.6842 - 9.99152i) q^{95} +8.29464i q^{97} +(1.07689 + 2.24145i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96q + O(q^{10}) \) \( 96q - 8q^{16} - 16q^{19} + 72q^{34} + 8q^{40} + 8q^{46} - 96q^{49} + 64q^{55} - 32q^{61} + 48q^{64} + 24q^{70} + 40q^{76} - 88q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(271\) \(577\) \(641\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.612434 1.27473i −0.433056 0.901367i
\(3\) 0 0
\(4\) −1.24985 + 1.56137i −0.624925 + 0.780685i
\(5\) −0.263678 2.22047i −0.117921 0.993023i
\(6\) 0 0
\(7\) 2.95946i 1.11857i 0.828976 + 0.559284i \(0.188924\pi\)
−0.828976 + 0.559284i \(0.811076\pi\)
\(8\) 2.75577 + 0.636981i 0.974311 + 0.225207i
\(9\) 0 0
\(10\) −2.66900 + 1.69601i −0.844012 + 0.536324i
\(11\) 1.04021 1.04021i 0.313636 0.313636i −0.532680 0.846317i \(-0.678815\pi\)
0.846317 + 0.532680i \(0.178815\pi\)
\(12\) 0 0
\(13\) 0.00780247 0.00780247i 0.00216402 0.00216402i −0.706024 0.708188i \(-0.749513\pi\)
0.708188 + 0.706024i \(0.249513\pi\)
\(14\) 3.77249 1.81247i 1.00824 0.484403i
\(15\) 0 0
\(16\) −0.875749 3.90296i −0.218937 0.975739i
\(17\) −2.00003 −0.485079 −0.242539 0.970142i \(-0.577980\pi\)
−0.242539 + 0.970142i \(0.577980\pi\)
\(18\) 0 0
\(19\) 5.10608 5.10608i 1.17141 1.17141i 0.189542 0.981873i \(-0.439300\pi\)
0.981873 0.189542i \(-0.0607003\pi\)
\(20\) 3.79653 + 2.36355i 0.848929 + 0.528506i
\(21\) 0 0
\(22\) −1.96305 0.688925i −0.418524 0.146879i
\(23\) 6.49393 1.35408 0.677039 0.735947i \(-0.263263\pi\)
0.677039 + 0.735947i \(0.263263\pi\)
\(24\) 0 0
\(25\) −4.86095 + 1.17098i −0.972189 + 0.234196i
\(26\) −0.0147245 0.00516751i −0.00288771 0.00101343i
\(27\) 0 0
\(28\) −4.62080 3.69888i −0.873250 0.699022i
\(29\) 5.45997 5.45997i 1.01389 1.01389i 0.0139895 0.999902i \(-0.495547\pi\)
0.999902 0.0139895i \(-0.00445315\pi\)
\(30\) 0 0
\(31\) 4.99178i 0.896550i −0.893896 0.448275i \(-0.852039\pi\)
0.893896 0.448275i \(-0.147961\pi\)
\(32\) −4.43886 + 3.50664i −0.784687 + 0.619892i
\(33\) 0 0
\(34\) 1.22489 + 2.54949i 0.210066 + 0.437234i
\(35\) 6.57137 0.780345i 1.11076 0.131902i
\(36\) 0 0
\(37\) 3.74547 + 3.74547i 0.615752 + 0.615752i 0.944439 0.328687i \(-0.106606\pi\)
−0.328687 + 0.944439i \(0.606606\pi\)
\(38\) −9.63598 3.38171i −1.56316 0.548586i
\(39\) 0 0
\(40\) 0.687758 6.28705i 0.108744 0.994070i
\(41\) −10.4245 −1.62803 −0.814017 0.580841i \(-0.802724\pi\)
−0.814017 + 0.580841i \(0.802724\pi\)
\(42\) 0 0
\(43\) −3.52161 + 3.52161i −0.537040 + 0.537040i −0.922658 0.385618i \(-0.873988\pi\)
0.385618 + 0.922658i \(0.373988\pi\)
\(44\) 0.324047 + 2.92427i 0.0488519 + 0.440850i
\(45\) 0 0
\(46\) −3.97710 8.27798i −0.586391 1.22052i
\(47\) 10.6419i 1.55228i −0.630563 0.776138i \(-0.717176\pi\)
0.630563 0.776138i \(-0.282824\pi\)
\(48\) 0 0
\(49\) −1.75838 −0.251197
\(50\) 4.46968 + 5.47923i 0.632109 + 0.774880i
\(51\) 0 0
\(52\) 0.00243062 + 0.0219345i 0.000337066 + 0.00304176i
\(53\) 2.98006 2.98006i 0.409342 0.409342i −0.472167 0.881509i \(-0.656528\pi\)
0.881509 + 0.472167i \(0.156528\pi\)
\(54\) 0 0
\(55\) −2.58404 2.03548i −0.348432 0.274464i
\(56\) −1.88512 + 8.15557i −0.251909 + 1.08983i
\(57\) 0 0
\(58\) −10.3038 3.61610i −1.35296 0.474817i
\(59\) 5.47867 5.47867i 0.713262 0.713262i −0.253954 0.967216i \(-0.581731\pi\)
0.967216 + 0.253954i \(0.0817312\pi\)
\(60\) 0 0
\(61\) −4.67845 4.67845i −0.599014 0.599014i 0.341037 0.940050i \(-0.389222\pi\)
−0.940050 + 0.341037i \(0.889222\pi\)
\(62\) −6.36315 + 3.05713i −0.808120 + 0.388256i
\(63\) 0 0
\(64\) 7.18851 + 3.51074i 0.898564 + 0.438843i
\(65\) −0.0193825 0.0152678i −0.00240410 0.00189374i
\(66\) 0 0
\(67\) −2.29404 2.29404i −0.280261 0.280261i 0.552952 0.833213i \(-0.313501\pi\)
−0.833213 + 0.552952i \(0.813501\pi\)
\(68\) 2.49974 3.12279i 0.303138 0.378693i
\(69\) 0 0
\(70\) −5.01925 7.89879i −0.599916 0.944086i
\(71\) 0.212315i 0.0251971i 0.999921 + 0.0125986i \(0.00401036\pi\)
−0.999921 + 0.0125986i \(0.995990\pi\)
\(72\) 0 0
\(73\) 16.4980 1.93094 0.965472 0.260505i \(-0.0838891\pi\)
0.965472 + 0.260505i \(0.0838891\pi\)
\(74\) 2.48059 7.06830i 0.288363 0.821673i
\(75\) 0 0
\(76\) 1.59064 + 14.3543i 0.182459 + 1.64655i
\(77\) 3.07847 + 3.07847i 0.350824 + 0.350824i
\(78\) 0 0
\(79\) 4.54833i 0.511727i −0.966713 0.255863i \(-0.917640\pi\)
0.966713 0.255863i \(-0.0823597\pi\)
\(80\) −8.43547 + 2.97370i −0.943114 + 0.332469i
\(81\) 0 0
\(82\) 6.38432 + 13.2884i 0.705030 + 1.46746i
\(83\) −4.68359 + 4.68359i −0.514090 + 0.514090i −0.915777 0.401687i \(-0.868424\pi\)
0.401687 + 0.915777i \(0.368424\pi\)
\(84\) 0 0
\(85\) 0.527365 + 4.44100i 0.0572008 + 0.481694i
\(86\) 6.64583 + 2.33233i 0.716639 + 0.251502i
\(87\) 0 0
\(88\) 3.52918 2.20399i 0.376212 0.234946i
\(89\) 0.123094 0.0130479 0.00652395 0.999979i \(-0.497923\pi\)
0.00652395 + 0.999979i \(0.497923\pi\)
\(90\) 0 0
\(91\) 0.0230911 + 0.0230911i 0.00242060 + 0.00242060i
\(92\) −8.11644 + 10.1394i −0.846197 + 1.05711i
\(93\) 0 0
\(94\) −13.5655 + 6.51744i −1.39917 + 0.672223i
\(95\) −12.6842 9.99152i −1.30138 1.02511i
\(96\) 0 0
\(97\) 8.29464i 0.842193i 0.907016 + 0.421096i \(0.138355\pi\)
−0.907016 + 0.421096i \(0.861645\pi\)
\(98\) 1.07689 + 2.24145i 0.108782 + 0.226420i
\(99\) 0 0
\(100\) 4.24713 9.05328i 0.424713 0.905328i
\(101\) −7.95152 7.95152i −0.791205 0.791205i 0.190485 0.981690i \(-0.438994\pi\)
−0.981690 + 0.190485i \(0.938994\pi\)
\(102\) 0 0
\(103\) 6.14632i 0.605615i −0.953052 0.302808i \(-0.902076\pi\)
0.953052 0.302808i \(-0.0979240\pi\)
\(104\) 0.0264718 0.0165318i 0.00259578 0.00162107i
\(105\) 0 0
\(106\) −5.62384 1.97367i −0.546236 0.191699i
\(107\) 5.83941 + 5.83941i 0.564517 + 0.564517i 0.930587 0.366070i \(-0.119297\pi\)
−0.366070 + 0.930587i \(0.619297\pi\)
\(108\) 0 0
\(109\) 10.9696 + 10.9696i 1.05070 + 1.05070i 0.998644 + 0.0520513i \(0.0165759\pi\)
0.0520513 + 0.998644i \(0.483424\pi\)
\(110\) −1.01212 + 4.54054i −0.0965021 + 0.432924i
\(111\) 0 0
\(112\) 11.5506 2.59174i 1.09143 0.244896i
\(113\) −9.95287 −0.936288 −0.468144 0.883652i \(-0.655077\pi\)
−0.468144 + 0.883652i \(0.655077\pi\)
\(114\) 0 0
\(115\) −1.71231 14.4196i −0.159674 1.34463i
\(116\) 1.70089 + 15.3492i 0.157923 + 1.42514i
\(117\) 0 0
\(118\) −10.3391 3.62848i −0.951794 0.334029i
\(119\) 5.91900i 0.542594i
\(120\) 0 0
\(121\) 8.83591i 0.803264i
\(122\) −3.09850 + 8.82897i −0.280525 + 0.799337i
\(123\) 0 0
\(124\) 7.79401 + 6.23897i 0.699923 + 0.560276i
\(125\) 3.88185 + 10.4848i 0.347203 + 0.937790i
\(126\) 0 0
\(127\) 0.542244 0.0481164 0.0240582 0.999711i \(-0.492341\pi\)
0.0240582 + 0.999711i \(0.492341\pi\)
\(128\) 0.0727470 11.3135i 0.00642998 0.999979i
\(129\) 0 0
\(130\) −0.00759176 + 0.0340578i −0.000665841 + 0.00298707i
\(131\) 5.55272 + 5.55272i 0.485143 + 0.485143i 0.906770 0.421626i \(-0.138541\pi\)
−0.421626 + 0.906770i \(0.638541\pi\)
\(132\) 0 0
\(133\) 15.1112 + 15.1112i 1.31031 + 1.31031i
\(134\) −1.51932 + 4.32922i −0.131250 + 0.373987i
\(135\) 0 0
\(136\) −5.51162 1.27398i −0.472617 0.109243i
\(137\) 5.80371i 0.495844i 0.968780 + 0.247922i \(0.0797477\pi\)
−0.968780 + 0.247922i \(0.920252\pi\)
\(138\) 0 0
\(139\) 6.27873 + 6.27873i 0.532555 + 0.532555i 0.921332 0.388777i \(-0.127102\pi\)
−0.388777 + 0.921332i \(0.627102\pi\)
\(140\) −6.99483 + 11.2357i −0.591171 + 0.949586i
\(141\) 0 0
\(142\) 0.270643 0.130029i 0.0227119 0.0109118i
\(143\) 0.0162325i 0.00135743i
\(144\) 0 0
\(145\) −13.5634 10.6840i −1.12638 0.887259i
\(146\) −10.1039 21.0304i −0.836207 1.74049i
\(147\) 0 0
\(148\) −10.5293 + 1.16679i −0.865506 + 0.0959092i
\(149\) −12.6568 12.6568i −1.03689 1.03689i −0.999293 0.0375933i \(-0.988031\pi\)
−0.0375933 0.999293i \(-0.511969\pi\)
\(150\) 0 0
\(151\) 17.1332 1.39428 0.697140 0.716935i \(-0.254456\pi\)
0.697140 + 0.716935i \(0.254456\pi\)
\(152\) 17.3236 10.8187i 1.40513 0.877512i
\(153\) 0 0
\(154\) 2.03884 5.80956i 0.164295 0.468147i
\(155\) −11.0841 + 1.31622i −0.890294 + 0.105722i
\(156\) 0 0
\(157\) −4.80235 + 4.80235i −0.383269 + 0.383269i −0.872279 0.489009i \(-0.837358\pi\)
0.489009 + 0.872279i \(0.337358\pi\)
\(158\) −5.79787 + 2.78555i −0.461254 + 0.221606i
\(159\) 0 0
\(160\) 8.95681 + 8.93171i 0.708098 + 0.706114i
\(161\) 19.2185i 1.51463i
\(162\) 0 0
\(163\) −0.778039 0.778039i −0.0609407 0.0609407i 0.675980 0.736920i \(-0.263721\pi\)
−0.736920 + 0.675980i \(0.763721\pi\)
\(164\) 13.0291 16.2765i 1.01740 1.27098i
\(165\) 0 0
\(166\) 8.83867 + 3.10190i 0.686014 + 0.240754i
\(167\) −5.26638 −0.407525 −0.203763 0.979020i \(-0.565317\pi\)
−0.203763 + 0.979020i \(0.565317\pi\)
\(168\) 0 0
\(169\) 12.9999i 0.999991i
\(170\) 5.33808 3.39206i 0.409412 0.260159i
\(171\) 0 0
\(172\) −1.09705 9.90001i −0.0836492 0.754869i
\(173\) 8.51881 + 8.51881i 0.647673 + 0.647673i 0.952430 0.304757i \(-0.0985752\pi\)
−0.304757 + 0.952430i \(0.598575\pi\)
\(174\) 0 0
\(175\) −3.46546 14.3858i −0.261964 1.08746i
\(176\) −4.97088 3.14894i −0.374694 0.237361i
\(177\) 0 0
\(178\) −0.0753866 0.156911i −0.00565047 0.0117609i
\(179\) 10.2479 + 10.2479i 0.765966 + 0.765966i 0.977394 0.211428i \(-0.0678114\pi\)
−0.211428 + 0.977394i \(0.567811\pi\)
\(180\) 0 0
\(181\) −0.590728 + 0.590728i −0.0439085 + 0.0439085i −0.728720 0.684812i \(-0.759884\pi\)
0.684812 + 0.728720i \(0.259884\pi\)
\(182\) 0.0152930 0.0435765i 0.00113359 0.00323011i
\(183\) 0 0
\(184\) 17.8958 + 4.13651i 1.31929 + 0.304947i
\(185\) 7.32909 9.30429i 0.538846 0.684065i
\(186\) 0 0
\(187\) −2.08046 + 2.08046i −0.152138 + 0.152138i
\(188\) 16.6159 + 13.3007i 1.21184 + 0.970057i
\(189\) 0 0
\(190\) −4.96818 + 22.2881i −0.360430 + 1.61695i
\(191\) 15.2046 1.10017 0.550083 0.835110i \(-0.314596\pi\)
0.550083 + 0.835110i \(0.314596\pi\)
\(192\) 0 0
\(193\) 12.4277i 0.894566i −0.894392 0.447283i \(-0.852392\pi\)
0.894392 0.447283i \(-0.147608\pi\)
\(194\) 10.5734 5.07991i 0.759125 0.364717i
\(195\) 0 0
\(196\) 2.19771 2.74547i 0.156979 0.196105i
\(197\) 7.54210 7.54210i 0.537352 0.537352i −0.385398 0.922750i \(-0.625936\pi\)
0.922750 + 0.385398i \(0.125936\pi\)
\(198\) 0 0
\(199\) 10.0231 0.710517 0.355258 0.934768i \(-0.384393\pi\)
0.355258 + 0.934768i \(0.384393\pi\)
\(200\) −14.1415 + 0.130615i −0.999957 + 0.00923585i
\(201\) 0 0
\(202\) −5.26622 + 15.0058i −0.370530 + 1.05580i
\(203\) 16.1585 + 16.1585i 1.13411 + 1.13411i
\(204\) 0 0
\(205\) 2.74872 + 23.1473i 0.191979 + 1.61668i
\(206\) −7.83488 + 3.76421i −0.545882 + 0.262265i
\(207\) 0 0
\(208\) −0.0372857 0.0236197i −0.00258530 0.00163773i
\(209\) 10.6228i 0.734796i
\(210\) 0 0
\(211\) −15.9950 + 15.9950i −1.10114 + 1.10114i −0.106867 + 0.994273i \(0.534082\pi\)
−0.994273 + 0.106867i \(0.965918\pi\)
\(212\) 0.928345 + 8.37759i 0.0637590 + 0.575375i
\(213\) 0 0
\(214\) 3.86739 11.0199i 0.264370 0.753305i
\(215\) 8.74819 + 6.89104i 0.596621 + 0.469965i
\(216\) 0 0
\(217\) 14.7729 1.00285
\(218\) 7.26507 20.7014i 0.492052 1.40207i
\(219\) 0 0
\(220\) 6.40780 1.49060i 0.432014 0.100496i
\(221\) −0.0156052 + 0.0156052i −0.00104972 + 0.00104972i
\(222\) 0 0
\(223\) 26.9611 1.80545 0.902724 0.430221i \(-0.141564\pi\)
0.902724 + 0.430221i \(0.141564\pi\)
\(224\) −10.3777 13.1366i −0.693392 0.877726i
\(225\) 0 0
\(226\) 6.09547 + 12.6872i 0.405465 + 0.843939i
\(227\) −4.80422 + 4.80422i −0.318867 + 0.318867i −0.848332 0.529465i \(-0.822393\pi\)
0.529465 + 0.848332i \(0.322393\pi\)
\(228\) 0 0
\(229\) −3.77289 + 3.77289i −0.249320 + 0.249320i −0.820691 0.571372i \(-0.806412\pi\)
0.571372 + 0.820691i \(0.306412\pi\)
\(230\) −17.3323 + 11.0137i −1.14286 + 0.726225i
\(231\) 0 0
\(232\) 18.5243 11.5685i 1.21618 0.759511i
\(233\) 12.2685i 0.803737i 0.915697 + 0.401868i \(0.131639\pi\)
−0.915697 + 0.401868i \(0.868361\pi\)
\(234\) 0 0
\(235\) −23.6299 + 2.80603i −1.54145 + 0.183045i
\(236\) 1.70671 + 15.4018i 0.111097 + 1.00257i
\(237\) 0 0
\(238\) −7.54510 + 3.62499i −0.489076 + 0.234974i
\(239\) −12.4166 −0.803164 −0.401582 0.915823i \(-0.631540\pi\)
−0.401582 + 0.915823i \(0.631540\pi\)
\(240\) 0 0
\(241\) −16.6958 −1.07547 −0.537735 0.843114i \(-0.680720\pi\)
−0.537735 + 0.843114i \(0.680720\pi\)
\(242\) 11.2634 5.41141i 0.724036 0.347858i
\(243\) 0 0
\(244\) 13.1521 1.45743i 0.841979 0.0933021i
\(245\) 0.463646 + 3.90442i 0.0296212 + 0.249444i
\(246\) 0 0
\(247\) 0.0796800i 0.00506992i
\(248\) 3.17967 13.7562i 0.201909 0.873518i
\(249\) 0 0
\(250\) 10.9879 11.3695i 0.694935 0.719073i
\(251\) 18.3923 18.3923i 1.16091 1.16091i 0.176634 0.984277i \(-0.443479\pi\)
0.984277 0.176634i \(-0.0565207\pi\)
\(252\) 0 0
\(253\) 6.75507 6.75507i 0.424688 0.424688i
\(254\) −0.332089 0.691212i −0.0208371 0.0433705i
\(255\) 0 0
\(256\) −14.4661 + 6.83602i −0.904133 + 0.427251i
\(257\) −29.8867 −1.86428 −0.932142 0.362094i \(-0.882062\pi\)
−0.932142 + 0.362094i \(0.882062\pi\)
\(258\) 0 0
\(259\) −11.0846 + 11.0846i −0.688761 + 0.688761i
\(260\) 0.0480638 0.0111808i 0.00298079 0.000693401i
\(261\) 0 0
\(262\) 3.67752 10.4789i 0.227198 0.647386i
\(263\) −17.6640 −1.08921 −0.544605 0.838693i \(-0.683320\pi\)
−0.544605 + 0.838693i \(0.683320\pi\)
\(264\) 0 0
\(265\) −7.40289 5.83134i −0.454756 0.358216i
\(266\) 10.0080 28.5173i 0.613632 1.74851i
\(267\) 0 0
\(268\) 6.44905 0.714637i 0.393938 0.0436534i
\(269\) 0.0280978 0.0280978i 0.00171315 0.00171315i −0.706250 0.707963i \(-0.749614\pi\)
0.707963 + 0.706250i \(0.249614\pi\)
\(270\) 0 0
\(271\) 13.7422i 0.834779i −0.908728 0.417390i \(-0.862945\pi\)
0.908728 0.417390i \(-0.137055\pi\)
\(272\) 1.75152 + 7.80603i 0.106202 + 0.473310i
\(273\) 0 0
\(274\) 7.39813 3.55439i 0.446938 0.214728i
\(275\) −3.83836 + 6.27449i −0.231462 + 0.378366i
\(276\) 0 0
\(277\) −23.0188 23.0188i −1.38306 1.38306i −0.839126 0.543937i \(-0.816933\pi\)
−0.543937 0.839126i \(-0.683067\pi\)
\(278\) 4.15835 11.8490i 0.249401 0.710654i
\(279\) 0 0
\(280\) 18.6062 + 2.03539i 1.11194 + 0.121638i
\(281\) −19.3294 −1.15309 −0.576547 0.817064i \(-0.695600\pi\)
−0.576547 + 0.817064i \(0.695600\pi\)
\(282\) 0 0
\(283\) 2.78511 2.78511i 0.165557 0.165557i −0.619466 0.785023i \(-0.712651\pi\)
0.785023 + 0.619466i \(0.212651\pi\)
\(284\) −0.331502 0.265362i −0.0196710 0.0157463i
\(285\) 0 0
\(286\) −0.0206920 + 0.00994132i −0.00122354 + 0.000587842i
\(287\) 30.8509i 1.82107i
\(288\) 0 0
\(289\) −12.9999 −0.764699
\(290\) −5.31252 + 23.8328i −0.311962 + 1.39951i
\(291\) 0 0
\(292\) −20.6200 + 25.7595i −1.20670 + 1.50746i
\(293\) −17.8866 + 17.8866i −1.04495 + 1.04495i −0.0460045 + 0.998941i \(0.514649\pi\)
−0.998941 + 0.0460045i \(0.985351\pi\)
\(294\) 0 0
\(295\) −13.6098 10.7206i −0.792394 0.624178i
\(296\) 7.93585 + 12.7074i 0.461262 + 0.738605i
\(297\) 0 0
\(298\) −8.38250 + 23.8854i −0.485585 + 1.38365i
\(299\) 0.0506687 0.0506687i 0.00293025 0.00293025i
\(300\) 0 0
\(301\) −10.4220 10.4220i −0.600716 0.600716i
\(302\) −10.4929 21.8401i −0.603801 1.25676i
\(303\) 0 0
\(304\) −24.4004 15.4572i −1.39946 0.886529i
\(305\) −9.15473 + 11.6219i −0.524198 + 0.665470i
\(306\) 0 0
\(307\) −23.4113 23.4113i −1.33615 1.33615i −0.899754 0.436397i \(-0.856254\pi\)
−0.436397 0.899754i \(-0.643746\pi\)
\(308\) −8.65425 + 0.959002i −0.493121 + 0.0546442i
\(309\) 0 0
\(310\) 8.46608 + 13.3231i 0.480841 + 0.756699i
\(311\) 24.0385i 1.36310i 0.731772 + 0.681549i \(0.238693\pi\)
−0.731772 + 0.681549i \(0.761307\pi\)
\(312\) 0 0
\(313\) −17.7757 −1.00474 −0.502371 0.864652i \(-0.667539\pi\)
−0.502371 + 0.864652i \(0.667539\pi\)
\(314\) 9.06280 + 3.18056i 0.511444 + 0.179489i
\(315\) 0 0
\(316\) 7.10162 + 5.68473i 0.399497 + 0.319791i
\(317\) 4.69302 + 4.69302i 0.263586 + 0.263586i 0.826509 0.562923i \(-0.190323\pi\)
−0.562923 + 0.826509i \(0.690323\pi\)
\(318\) 0 0
\(319\) 11.3591i 0.635987i
\(320\) 5.90003 16.8876i 0.329822 0.944043i
\(321\) 0 0
\(322\) 24.4983 11.7700i 1.36524 0.655919i
\(323\) −10.2123 + 10.2123i −0.568228 + 0.568228i
\(324\) 0 0
\(325\) −0.0287909 + 0.0470639i −0.00159703 + 0.00261064i
\(326\) −0.515289 + 1.46828i −0.0285392 + 0.0813207i
\(327\) 0 0
\(328\) −28.7275 6.64021i −1.58621 0.366644i
\(329\) 31.4942 1.73633
\(330\) 0 0
\(331\) 20.1568 + 20.1568i 1.10792 + 1.10792i 0.993424 + 0.114494i \(0.0365247\pi\)
0.114494 + 0.993424i \(0.463475\pi\)
\(332\) −1.45903 13.1666i −0.0800745 0.722610i
\(333\) 0 0
\(334\) 3.22531 + 6.71320i 0.176481 + 0.367330i
\(335\) −4.48895 + 5.69873i −0.245258 + 0.311355i
\(336\) 0 0
\(337\) 22.5791i 1.22996i −0.788542 0.614980i \(-0.789164\pi\)
0.788542 0.614980i \(-0.210836\pi\)
\(338\) 16.5713 7.96156i 0.901359 0.433052i
\(339\) 0 0
\(340\) −7.59317 4.72718i −0.411798 0.256367i
\(341\) −5.19252 5.19252i −0.281191 0.281191i
\(342\) 0 0
\(343\) 15.5124i 0.837588i
\(344\) −11.9479 + 7.46154i −0.644189 + 0.402299i
\(345\) 0 0
\(346\) 5.64194 16.0764i 0.303313 0.864270i
\(347\) 8.61782 + 8.61782i 0.462629 + 0.462629i 0.899516 0.436887i \(-0.143919\pi\)
−0.436887 + 0.899516i \(0.643919\pi\)
\(348\) 0 0
\(349\) 11.4945 + 11.4945i 0.615284 + 0.615284i 0.944318 0.329034i \(-0.106723\pi\)
−0.329034 + 0.944318i \(0.606723\pi\)
\(350\) −16.2155 + 13.2278i −0.866756 + 0.707057i
\(351\) 0 0
\(352\) −0.969707 + 8.26502i −0.0516855 + 0.440527i
\(353\) −17.2352 −0.917336 −0.458668 0.888608i \(-0.651673\pi\)
−0.458668 + 0.888608i \(0.651673\pi\)
\(354\) 0 0
\(355\) 0.471438 0.0559829i 0.0250213 0.00297126i
\(356\) −0.153849 + 0.192195i −0.00815396 + 0.0101863i
\(357\) 0 0
\(358\) 6.78711 19.3395i 0.358710 1.02212i
\(359\) 2.27145i 0.119882i −0.998202 0.0599412i \(-0.980909\pi\)
0.998202 0.0599412i \(-0.0190913\pi\)
\(360\) 0 0
\(361\) 33.1441i 1.74442i
\(362\) 1.11480 + 0.391234i 0.0585925 + 0.0205628i
\(363\) 0 0
\(364\) −0.0649140 + 0.00719331i −0.00340242 + 0.000377032i
\(365\) −4.35017 36.6333i −0.227698 1.91747i
\(366\) 0 0
\(367\) −31.1335 −1.62516 −0.812579 0.582852i \(-0.801937\pi\)
−0.812579 + 0.582852i \(0.801937\pi\)
\(368\) −5.68705 25.3455i −0.296458 1.32123i
\(369\) 0 0
\(370\) −16.3490 3.64432i −0.849944 0.189459i
\(371\) 8.81934 + 8.81934i 0.457877 + 0.457877i
\(372\) 0 0
\(373\) 20.3199 + 20.3199i 1.05212 + 1.05212i 0.998565 + 0.0535601i \(0.0170569\pi\)
0.0535601 + 0.998565i \(0.482943\pi\)
\(374\) 3.92616 + 1.37787i 0.203017 + 0.0712480i
\(375\) 0 0
\(376\) 6.77867 29.3265i 0.349583 1.51240i
\(377\) 0.0852026i 0.00438816i
\(378\) 0 0
\(379\) −9.61527 9.61527i −0.493903 0.493903i 0.415630 0.909534i \(-0.363561\pi\)
−0.909534 + 0.415630i \(0.863561\pi\)
\(380\) 31.4538 7.31689i 1.61355 0.375348i
\(381\) 0 0
\(382\) −9.31180 19.3817i −0.476433 0.991653i
\(383\) 1.17749i 0.0601668i 0.999547 + 0.0300834i \(0.00957728\pi\)
−0.999547 + 0.0300834i \(0.990423\pi\)
\(384\) 0 0
\(385\) 6.02391 7.64736i 0.307007 0.389746i
\(386\) −15.8419 + 7.61115i −0.806333 + 0.387397i
\(387\) 0 0
\(388\) −12.9510 10.3671i −0.657487 0.526307i
\(389\) 23.7967 + 23.7967i 1.20654 + 1.20654i 0.972139 + 0.234403i \(0.0753137\pi\)
0.234403 + 0.972139i \(0.424686\pi\)
\(390\) 0 0
\(391\) −12.9881 −0.656834
\(392\) −4.84568 1.12005i −0.244744 0.0565712i
\(393\) 0 0
\(394\) −14.2331 4.99507i −0.717055 0.251648i
\(395\) −10.0994 + 1.19930i −0.508156 + 0.0603431i
\(396\) 0 0
\(397\) −5.88396 + 5.88396i −0.295308 + 0.295308i −0.839173 0.543865i \(-0.816960\pi\)
0.543865 + 0.839173i \(0.316960\pi\)
\(398\) −6.13847 12.7767i −0.307693 0.640436i
\(399\) 0 0
\(400\) 8.82725 + 17.9466i 0.441362 + 0.897329i
\(401\) 15.4433i 0.771202i 0.922666 + 0.385601i \(0.126006\pi\)
−0.922666 + 0.385601i \(0.873994\pi\)
\(402\) 0 0
\(403\) −0.0389482 0.0389482i −0.00194015 0.00194015i
\(404\) 22.3535 2.47705i 1.11213 0.123238i
\(405\) 0 0
\(406\) 10.7017 30.4938i 0.531115 1.51338i
\(407\) 7.79218 0.386244
\(408\) 0 0
\(409\) 8.72546i 0.431446i −0.976455 0.215723i \(-0.930789\pi\)
0.976455 0.215723i \(-0.0692109\pi\)
\(410\) 27.8230 17.6800i 1.37408 0.873154i
\(411\) 0 0
\(412\) 9.59668 + 7.68198i 0.472795 + 0.378464i
\(413\) 16.2139 + 16.2139i 0.797833 + 0.797833i
\(414\) 0 0
\(415\) 11.6347 + 9.16479i 0.571125 + 0.449882i
\(416\) −0.00727361 + 0.0619945i −0.000356618 + 0.00303953i
\(417\) 0 0
\(418\) −13.5412 + 6.50578i −0.662321 + 0.318208i
\(419\) −4.83085 4.83085i −0.236003 0.236003i 0.579190 0.815193i \(-0.303369\pi\)
−0.815193 + 0.579190i \(0.803369\pi\)
\(420\) 0 0
\(421\) 20.2440 20.2440i 0.986633 0.986633i −0.0132784 0.999912i \(-0.504227\pi\)
0.999912 + 0.0132784i \(0.00422678\pi\)
\(422\) 30.1851 + 10.5934i 1.46939 + 0.515676i
\(423\) 0 0
\(424\) 10.1106 6.31410i 0.491013 0.306640i
\(425\) 9.72204 2.34199i 0.471588 0.113603i
\(426\) 0 0
\(427\) 13.8456 13.8456i 0.670038 0.670038i
\(428\) −16.4159 + 1.81909i −0.793491 + 0.0879290i
\(429\) 0 0
\(430\) 3.42650 15.3718i 0.165241 0.741296i
\(431\) 6.63538 0.319615 0.159808 0.987148i \(-0.448913\pi\)
0.159808 + 0.987148i \(0.448913\pi\)
\(432\) 0 0
\(433\) 2.17952i 0.104741i −0.998628 0.0523706i \(-0.983322\pi\)
0.998628 0.0523706i \(-0.0166777\pi\)
\(434\) −9.04745 18.8314i −0.434291 0.903938i
\(435\) 0 0
\(436\) −30.8379 + 3.41724i −1.47687 + 0.163656i
\(437\) 33.1585 33.1585i 1.58619 1.58619i
\(438\) 0 0
\(439\) −18.1795 −0.867661 −0.433830 0.900995i \(-0.642838\pi\)
−0.433830 + 0.900995i \(0.642838\pi\)
\(440\) −5.82446 7.25529i −0.277670 0.345883i
\(441\) 0 0
\(442\) 0.0294495 + 0.0103352i 0.00140077 + 0.000491595i
\(443\) −20.1844 20.1844i −0.958989 0.958989i 0.0402025 0.999192i \(-0.487200\pi\)
−0.999192 + 0.0402025i \(0.987200\pi\)
\(444\) 0 0
\(445\) −0.0324571 0.273325i −0.00153862 0.0129569i
\(446\) −16.5119 34.3680i −0.781860 1.62737i
\(447\) 0 0
\(448\) −10.3899 + 21.2741i −0.490876 + 1.00511i
\(449\) 31.3405i 1.47905i 0.673129 + 0.739525i \(0.264950\pi\)
−0.673129 + 0.739525i \(0.735050\pi\)
\(450\) 0 0
\(451\) −10.8437 + 10.8437i −0.510611 + 0.510611i
\(452\) 12.4396 15.5401i 0.585110 0.730945i
\(453\) 0 0
\(454\) 9.06633 + 3.18180i 0.425504 + 0.149329i
\(455\) 0.0451843 0.0573616i 0.00211827 0.00268915i
\(456\) 0 0
\(457\) −15.6212 −0.730727 −0.365364 0.930865i \(-0.619055\pi\)
−0.365364 + 0.930865i \(0.619055\pi\)
\(458\) 7.12005 + 2.49876i 0.332698 + 0.116759i
\(459\) 0 0
\(460\) 24.6544 + 15.3487i 1.14952 + 0.715638i
\(461\) −9.98698 + 9.98698i −0.465140 + 0.465140i −0.900336 0.435196i \(-0.856679\pi\)
0.435196 + 0.900336i \(0.356679\pi\)
\(462\) 0 0
\(463\) 27.8119 1.29253 0.646264 0.763114i \(-0.276330\pi\)
0.646264 + 0.763114i \(0.276330\pi\)
\(464\) −26.0916 16.5285i −1.21127 0.767315i
\(465\) 0 0
\(466\) 15.6390 7.51365i 0.724462 0.348063i
\(467\) −10.4295 + 10.4295i −0.482620 + 0.482620i −0.905967 0.423348i \(-0.860855\pi\)
0.423348 + 0.905967i \(0.360855\pi\)
\(468\) 0 0
\(469\) 6.78911 6.78911i 0.313492 0.313492i
\(470\) 18.0487 + 28.4032i 0.832524 + 1.31014i
\(471\) 0 0
\(472\) 18.5878 11.6081i 0.855571 0.534308i
\(473\) 7.32645i 0.336871i
\(474\) 0 0
\(475\) −18.8413 + 30.7995i −0.864497 + 1.41318i
\(476\) 9.24175 + 7.39786i 0.423595 + 0.339081i
\(477\) 0 0
\(478\) 7.60435 + 15.8278i 0.347815 + 0.723946i
\(479\) −23.5450 −1.07580 −0.537900 0.843009i \(-0.680782\pi\)
−0.537900 + 0.843009i \(0.680782\pi\)
\(480\) 0 0
\(481\) 0.0584478 0.00266499
\(482\) 10.2251 + 21.2825i 0.465739 + 0.969393i
\(483\) 0 0
\(484\) −13.7961 11.0436i −0.627096 0.501980i
\(485\) 18.4180 2.18712i 0.836317 0.0993119i
\(486\) 0 0
\(487\) 15.4005i 0.697865i 0.937148 + 0.348932i \(0.113456\pi\)
−0.937148 + 0.348932i \(0.886544\pi\)
\(488\) −9.91263 15.8728i −0.448724 0.718527i
\(489\) 0 0
\(490\) 4.69311 2.98222i 0.212013 0.134723i
\(491\) 11.9089 11.9089i 0.537443 0.537443i −0.385334 0.922777i \(-0.625914\pi\)
0.922777 + 0.385334i \(0.125914\pi\)
\(492\) 0 0
\(493\) −10.9201 + 10.9201i −0.491817 + 0.491817i
\(494\) −0.101570 + 0.0487987i −0.00456986 + 0.00219556i
\(495\) 0 0
\(496\) −19.4827 + 4.37154i −0.874798 + 0.196288i
\(497\) −0.628336 −0.0281847
\(498\) 0 0
\(499\) 16.4502 16.4502i 0.736411 0.736411i −0.235471 0.971881i \(-0.575663\pi\)
0.971881 + 0.235471i \(0.0756631\pi\)
\(500\) −21.2224 7.04345i −0.949094 0.314993i
\(501\) 0 0
\(502\) −34.7092 12.1811i −1.54915 0.543667i
\(503\) 11.4298 0.509632 0.254816 0.966990i \(-0.417985\pi\)
0.254816 + 0.966990i \(0.417985\pi\)
\(504\) 0 0
\(505\) −15.5594 + 19.7527i −0.692386 + 0.878985i
\(506\) −12.7479 4.47383i −0.566713 0.198886i
\(507\) 0 0
\(508\) −0.677724 + 0.846643i −0.0300691 + 0.0375637i
\(509\) 26.8748 26.8748i 1.19120 1.19120i 0.214473 0.976730i \(-0.431197\pi\)
0.976730 0.214473i \(-0.0688034\pi\)
\(510\) 0 0
\(511\) 48.8251i 2.15990i
\(512\) 17.5736 + 14.2537i 0.776650 + 0.629932i
\(513\) 0 0
\(514\) 18.3036 + 38.0974i 0.807339 + 1.68040i
\(515\) −13.6477 + 1.62065i −0.601390 + 0.0714145i
\(516\) 0 0
\(517\) −11.0698 11.0698i −0.486850 0.486850i
\(518\) 20.9183 + 7.34121i 0.919098 + 0.322554i
\(519\) 0 0
\(520\) −0.0436883 0.0544207i −0.00191586 0.00238651i
\(521\) −18.0720 −0.791749 −0.395874 0.918305i \(-0.629558\pi\)
−0.395874 + 0.918305i \(0.629558\pi\)
\(522\) 0 0
\(523\) 10.2127 10.2127i 0.446571 0.446571i −0.447642 0.894213i \(-0.647736\pi\)
0.894213 + 0.447642i \(0.147736\pi\)
\(524\) −15.6099 + 1.72978i −0.681922 + 0.0755657i
\(525\) 0 0
\(526\) 10.8180 + 22.5168i 0.471689 + 0.981778i
\(527\) 9.98371i 0.434897i
\(528\) 0 0
\(529\) 19.1711 0.833526
\(530\) −2.89958 + 13.0080i −0.125950 + 0.565030i
\(531\) 0 0
\(532\) −42.4809 + 4.70743i −1.84178 + 0.204093i
\(533\) −0.0813369 + 0.0813369i −0.00352309 + 0.00352309i
\(534\) 0 0
\(535\) 11.4265 14.5059i 0.494010 0.627147i
\(536\) −4.86058 7.78310i −0.209945 0.336179i
\(537\) 0 0
\(538\) −0.0530249 0.0186089i −0.00228607 0.000802287i
\(539\) −1.82909 + 1.82909i −0.0787844 + 0.0787844i
\(540\) 0 0
\(541\) −4.93323 4.93323i −0.212096 0.212096i 0.593061 0.805157i \(-0.297919\pi\)
−0.805157 + 0.593061i \(0.797919\pi\)
\(542\) −17.5175 + 8.41618i −0.752442 + 0.361506i
\(543\) 0 0
\(544\) 8.87785 7.01339i 0.380635 0.300697i
\(545\) 21.4652 27.2500i 0.919466 1.16726i
\(546\) 0 0
\(547\) 25.5794 + 25.5794i 1.09370 + 1.09370i 0.995130 + 0.0985674i \(0.0314260\pi\)
0.0985674 + 0.995130i \(0.468574\pi\)
\(548\) −9.06173 7.25377i −0.387098 0.309865i
\(549\) 0 0
\(550\) 10.3490 + 1.05014i 0.441283 + 0.0447782i
\(551\) 55.7581i 2.37538i
\(552\) 0 0
\(553\) 13.4606 0.572402
\(554\) −15.2451 + 43.4401i −0.647704 + 1.84559i
\(555\) 0 0
\(556\) −17.6509 + 1.95595i −0.748565 + 0.0829506i
\(557\) −4.34156 4.34156i −0.183958 0.183958i 0.609120 0.793078i \(-0.291523\pi\)
−0.793078 + 0.609120i \(0.791523\pi\)
\(558\) 0 0
\(559\) 0.0549545i 0.00232433i
\(560\) −8.80052 24.9644i −0.371890 1.05494i
\(561\) 0 0
\(562\) 11.8380 + 24.6396i 0.499354 + 1.03936i
\(563\) −16.4606 + 16.4606i −0.693731 + 0.693731i −0.963051 0.269320i \(-0.913201\pi\)
0.269320 + 0.963051i \(0.413201\pi\)
\(564\) 0 0
\(565\) 2.62436 + 22.1000i 0.110408 + 0.929755i
\(566\) −5.25594 1.84455i −0.220924 0.0775324i
\(567\) 0 0
\(568\) −0.135240 + 0.585090i −0.00567457 + 0.0245499i
\(569\) −27.5819 −1.15629 −0.578146 0.815933i \(-0.696224\pi\)
−0.578146 + 0.815933i \(0.696224\pi\)
\(570\) 0 0
\(571\) 4.33390 + 4.33390i 0.181368 + 0.181368i 0.791952 0.610584i \(-0.209065\pi\)
−0.610584 + 0.791952i \(0.709065\pi\)
\(572\) 0.0253449 + 0.0202882i 0.00105972 + 0.000848291i
\(573\) 0 0
\(574\) −39.3264 + 18.8941i −1.64145 + 0.788625i
\(575\) −31.5666 + 7.60425i −1.31642 + 0.317119i
\(576\) 0 0
\(577\) 32.4805i 1.35218i 0.736819 + 0.676090i \(0.236327\pi\)
−0.736819 + 0.676090i \(0.763673\pi\)
\(578\) 7.96156 + 16.5713i 0.331157 + 0.689274i
\(579\) 0 0
\(580\) 33.6339 7.82401i 1.39657 0.324874i
\(581\) −13.8609 13.8609i −0.575046 0.575046i
\(582\) 0 0
\(583\) 6.19979i 0.256769i
\(584\) 45.4647 + 10.5089i 1.88134 + 0.434862i
\(585\) 0 0
\(586\) 33.7548 + 11.8461i 1.39440 + 0.489360i
\(587\) 30.2712 + 30.2712i 1.24942 + 1.24942i 0.955975 + 0.293450i \(0.0948033\pi\)
0.293450 + 0.955975i \(0.405197\pi\)
\(588\) 0 0
\(589\) −25.4884 25.4884i −1.05023 1.05023i
\(590\) −5.33072 + 23.9144i −0.219462 + 0.984542i
\(591\) 0 0
\(592\) 11.3383 17.8985i 0.466002 0.735624i
\(593\) 38.4245 1.57790 0.788952 0.614455i \(-0.210624\pi\)
0.788952 + 0.614455i \(0.210624\pi\)
\(594\) 0 0
\(595\) −13.1429 + 1.56071i −0.538808 + 0.0639830i
\(596\) 35.5811 3.94284i 1.45746 0.161505i
\(597\) 0 0
\(598\) −0.0956199 0.0335575i −0.00391019 0.00137227i
\(599\) 20.1491i 0.823269i 0.911349 + 0.411635i \(0.135042\pi\)
−0.911349 + 0.411635i \(0.864958\pi\)
\(600\) 0 0
\(601\) 3.75831i 0.153305i −0.997058 0.0766524i \(-0.975577\pi\)
0.997058 0.0766524i \(-0.0244232\pi\)
\(602\) −6.90243 + 19.6681i −0.281322 + 0.801610i
\(603\) 0 0
\(604\) −21.4139 + 26.7513i −0.871321 + 1.08849i
\(605\) 19.6198 2.32984i 0.797660 0.0947214i
\(606\) 0 0
\(607\) −1.55683 −0.0631899 −0.0315949 0.999501i \(-0.510059\pi\)
−0.0315949 + 0.999501i \(0.510059\pi\)
\(608\) −4.75998 + 40.5703i −0.193043 + 1.64534i
\(609\) 0 0
\(610\) 20.4214 + 4.55210i 0.826840 + 0.184309i
\(611\) −0.0830329 0.0830329i −0.00335915 0.00335915i
\(612\) 0 0
\(613\) −19.5306 19.5306i −0.788832 0.788832i 0.192471 0.981303i \(-0.438350\pi\)
−0.981303 + 0.192471i \(0.938350\pi\)
\(614\) −15.5051 + 44.1808i −0.625734 + 1.78299i
\(615\) 0 0
\(616\) 6.52262 + 10.4445i 0.262804 + 0.420819i
\(617\) 4.07636i 0.164108i −0.996628 0.0820540i \(-0.973852\pi\)
0.996628 0.0820540i \(-0.0261480\pi\)
\(618\) 0 0
\(619\) 5.05003 + 5.05003i 0.202978 + 0.202978i 0.801275 0.598297i \(-0.204156\pi\)
−0.598297 + 0.801275i \(0.704156\pi\)
\(620\) 11.7983 18.9514i 0.473832 0.761107i
\(621\) 0 0
\(622\) 30.6425 14.7220i 1.22865 0.590298i
\(623\) 0.364290i 0.0145950i
\(624\) 0 0
\(625\) 22.2576 11.3841i 0.890305 0.455365i
\(626\) 10.8864 + 22.6592i 0.435110 + 0.905642i
\(627\) 0 0
\(628\) −1.49603 13.5005i −0.0596979 0.538727i
\(629\) −7.49105 7.49105i −0.298688 0.298688i
\(630\) 0 0
\(631\) −0.782254 −0.0311411 −0.0155705 0.999879i \(-0.504956\pi\)
−0.0155705 + 0.999879i \(0.504956\pi\)
\(632\) 2.89720 12.5341i 0.115244 0.498581i
\(633\) 0 0
\(634\) 3.10815 8.85648i 0.123440 0.351736i
\(635\) −0.142978 1.20404i −0.00567391 0.0477807i
\(636\) 0 0
\(637\) −0.0137197 + 0.0137197i −0.000543593 + 0.000543593i
\(638\) −14.4797 + 6.95668i −0.573257 + 0.275418i
\(639\) 0 0
\(640\) −25.1404 + 2.82159i −0.993761 + 0.111533i
\(641\) 2.92420i 0.115499i −0.998331 0.0577495i \(-0.981608\pi\)
0.998331 0.0577495i \(-0.0183925\pi\)
\(642\) 0 0
\(643\) 30.2222 + 30.2222i 1.19185 + 1.19185i 0.976548 + 0.215301i \(0.0690732\pi\)
0.215301 + 0.976548i \(0.430927\pi\)
\(644\) −30.0072 24.0202i −1.18245 0.946530i
\(645\) 0 0
\(646\) 19.2723 + 6.76353i 0.758257 + 0.266108i
\(647\) −48.8394 −1.92007 −0.960037 0.279871i \(-0.909708\pi\)
−0.960037 + 0.279871i \(0.909708\pi\)
\(648\) 0 0
\(649\) 11.3980i 0.447410i
\(650\) 0.0776261 + 0.00787693i 0.00304475 + 0.000308959i
\(651\) 0 0
\(652\) 2.18724 0.242374i 0.0856588 0.00949210i
\(653\) 4.18933 + 4.18933i 0.163941 + 0.163941i 0.784310 0.620369i \(-0.213017\pi\)
−0.620369 + 0.784310i \(0.713017\pi\)
\(654\) 0 0
\(655\) 10.8655 13.7938i 0.424550 0.538967i
\(656\) 9.12925 + 40.6864i 0.356437 + 1.58854i
\(657\) 0 0
\(658\) −19.2881 40.1464i −0.751928 1.56507i
\(659\) −13.0512 13.0512i −0.508402 0.508402i 0.405634 0.914036i \(-0.367051\pi\)
−0.914036 + 0.405634i \(0.867051\pi\)
\(660\) 0 0
\(661\) 8.41832 8.41832i 0.327435 0.327435i −0.524175 0.851610i \(-0.675626\pi\)
0.851610 + 0.524175i \(0.175626\pi\)
\(662\) 13.3497 38.0391i 0.518850 1.47843i
\(663\) 0 0
\(664\) −15.8902 + 9.92352i −0.616660 + 0.385107i
\(665\) 29.5694 37.5384i 1.14665 1.45568i
\(666\) 0 0
\(667\) 35.4567 35.4567i 1.37289 1.37289i
\(668\) 6.58219 8.22277i 0.254673 0.318149i
\(669\) 0 0
\(670\) 10.0135 + 2.23209i 0.386855 + 0.0862330i
\(671\) −9.73317 −0.375745
\(672\) 0 0
\(673\) 8.96622i 0.345622i −0.984955 0.172811i \(-0.944715\pi\)
0.984955 0.172811i \(-0.0552850\pi\)
\(674\) −28.7821 + 13.8282i −1.10865 + 0.532642i
\(675\) 0 0
\(676\) −20.2976 16.2479i −0.780677 0.624919i
\(677\) 16.5376 16.5376i 0.635590 0.635590i −0.313874 0.949464i \(-0.601627\pi\)
0.949464 + 0.313874i \(0.101627\pi\)
\(678\) 0 0
\(679\) −24.5476 −0.942051
\(680\) −1.37554 + 12.5743i −0.0527495 + 0.482202i
\(681\) 0 0
\(682\) −3.43896 + 9.79910i −0.131685 + 0.375227i
\(683\) 3.42707 + 3.42707i 0.131133 + 0.131133i 0.769627 0.638494i \(-0.220442\pi\)
−0.638494 + 0.769627i \(0.720442\pi\)
\(684\) 0 0
\(685\) 12.8869 1.53031i 0.492385 0.0584702i
\(686\) 19.7740 9.50029i 0.754974 0.362723i
\(687\) 0 0
\(688\) 16.8287 + 10.6606i 0.641589 + 0.406433i
\(689\) 0.0465036i 0.00177165i
\(690\) 0 0
\(691\) 18.7477 18.7477i 0.713195 0.713195i −0.254008 0.967202i \(-0.581749\pi\)
0.967202 + 0.254008i \(0.0817489\pi\)
\(692\) −23.9483 + 2.65377i −0.910376 + 0.100881i
\(693\) 0 0
\(694\) 5.70751 16.2632i 0.216654 0.617343i
\(695\) 12.2862 15.5973i 0.466040 0.591639i
\(696\) 0 0
\(697\) 20.8493 0.789725
\(698\) 7.61269 21.6919i 0.288145 0.821050i
\(699\) 0 0
\(700\) 26.7928 + 12.5692i 1.01267 + 0.475070i
\(701\) −28.2156 + 28.2156i −1.06569 + 1.06569i −0.0680026 + 0.997685i \(0.521663\pi\)
−0.997685 + 0.0680026i \(0.978337\pi\)
\(702\) 0 0
\(703\) 38.2493 1.44260
\(704\) 11.1295 3.82567i 0.419459 0.144185i
\(705\) 0 0
\(706\) 10.5554 + 21.9701i 0.397258 + 0.826857i
\(707\) 23.5322 23.5322i 0.885018 0.885018i
\(708\) 0 0
\(709\) 10.7577 10.7577i 0.404013 0.404013i −0.475631 0.879645i \(-0.657780\pi\)
0.879645 + 0.475631i \(0.157780\pi\)
\(710\) −0.360087 0.566668i −0.0135138 0.0212667i
\(711\) 0 0
\(712\) 0.339217 + 0.0784082i 0.0127127 + 0.00293847i
\(713\) 32.4162i 1.21400i
\(714\) 0 0
\(715\) −0.0360437 + 0.00428015i −0.00134796 + 0.000160069i
\(716\) −28.8092 + 3.19242i −1.07665 + 0.119307i
\(717\) 0 0
\(718\) −2.89547 + 1.39111i −0.108058 + 0.0519158i
\(719\) 1.68057 0.0626748 0.0313374 0.999509i \(-0.490023\pi\)
0.0313374 + 0.999509i \(0.490023\pi\)
\(720\) 0 0
\(721\) 18.1898 0.677422
\(722\) −42.2496 + 20.2985i −1.57237 + 0.755433i
\(723\) 0 0
\(724\) −0.184023 1.66067i −0.00683916 0.0617182i
\(725\) −20.1471 + 32.9342i −0.748246 + 1.22314i
\(726\) 0 0
\(727\) 33.3069i 1.23528i 0.786460 + 0.617641i \(0.211912\pi\)
−0.786460 + 0.617641i \(0.788088\pi\)
\(728\) 0.0489250 + 0.0783422i 0.00181328 + 0.00290355i
\(729\) 0 0
\(730\) −44.0332 + 27.9807i −1.62974 + 1.03561i
\(731\) 7.04332 7.04332i 0.260507 0.260507i
\(732\) 0 0
\(733\) 9.28476 9.28476i 0.342941 0.342941i −0.514531 0.857472i \(-0.672034\pi\)
0.857472 + 0.514531i \(0.172034\pi\)
\(734\) 19.0672 + 39.6867i 0.703784 + 1.46486i
\(735\) 0 0
\(736\) −28.8256 + 22.7719i −1.06253 + 0.839382i
\(737\) −4.77258 −0.175800
\(738\) 0 0
\(739\) −24.0117 + 24.0117i −0.883286 + 0.883286i −0.993867 0.110581i \(-0.964729\pi\)
0.110581 + 0.993867i \(0.464729\pi\)
\(740\) 5.36717 + 23.0724i 0.197301 + 0.848158i
\(741\) 0 0
\(742\) 5.84098 16.6435i 0.214429 0.611002i
\(743\) 25.5380 0.936897 0.468448 0.883491i \(-0.344813\pi\)
0.468448 + 0.883491i \(0.344813\pi\)
\(744\) 0 0
\(745\) −24.7667 + 31.4414i −0.907382 + 1.15192i
\(746\) 13.4577 38.3469i 0.492722 1.40398i
\(747\) 0 0
\(748\) −0.648103 5.84863i −0.0236970 0.213847i
\(749\) −17.2815 + 17.2815i −0.631451 + 0.631451i
\(750\) 0 0
\(751\) 38.6627i 1.41082i 0.708799 + 0.705411i \(0.249238\pi\)
−0.708799 + 0.705411i \(0.750762\pi\)
\(752\) −41.5348 + 9.31961i −1.51462 + 0.339851i
\(753\) 0 0
\(754\) −0.108610 + 0.0521809i −0.00395534 + 0.00190032i
\(755\) −4.51766 38.0437i −0.164414 1.38455i
\(756\) 0 0
\(757\) −28.0622 28.0622i −1.01994 1.01994i −0.999797 0.0201412i \(-0.993588\pi\)
−0.0201412 0.999797i \(-0.506412\pi\)
\(758\) −6.36812 + 18.1455i −0.231300 + 0.659076i
\(759\) 0 0
\(760\) −28.5904 35.6139i −1.03708 1.29185i
\(761\) 12.1544 0.440597 0.220299 0.975432i \(-0.429297\pi\)
0.220299 + 0.975432i \(0.429297\pi\)
\(762\) 0 0
\(763\) −32.4640 + 32.4640i −1.17528 + 1.17528i
\(764\) −19.0035 + 23.7400i −0.687521 + 0.858882i
\(765\) 0 0
\(766\) 1.50097 0.721132i 0.0542323 0.0260556i
\(767\) 0.0854944i 0.00308702i
\(768\) 0 0
\(769\) −0.0426731 −0.00153883 −0.000769416 1.00000i \(-0.500245\pi\)
−0.000769416 1.00000i \(0.500245\pi\)
\(770\) −13.4375 2.99533i −0.484255 0.107944i
\(771\) 0 0
\(772\) 19.4042 + 15.5328i 0.698374 + 0.559037i
\(773\) 4.96973 4.96973i 0.178749 0.178749i −0.612061 0.790810i \(-0.709659\pi\)
0.790810 + 0.612061i \(0.209659\pi\)
\(774\) 0 0
\(775\) 5.84526 + 24.2648i 0.209968 + 0.871616i
\(776\) −5.28353 + 22.8581i −0.189667 + 0.820558i
\(777\) 0 0
\(778\) 15.7604 44.9082i 0.565037 1.61004i
\(779\) −53.2283 + 53.2283i −1.90710 + 1.90710i
\(780\) 0 0
\(781\) 0.220853 + 0.220853i 0.00790274 + 0.00790274i
\(782\) 7.95432 + 16.5562i 0.284446 + 0.592049i
\(783\) 0 0
\(784\) 1.53990 + 6.86286i 0.0549963 + 0.245102i
\(785\) 11.9297 + 9.39719i 0.425791 + 0.335400i
\(786\) 0 0
\(787\) 16.8577 + 16.8577i 0.600911 + 0.600911i 0.940554 0.339643i \(-0.110306\pi\)
−0.339643 + 0.940554i \(0.610306\pi\)
\(788\) 2.34951 + 21.2025i 0.0836978 + 0.755308i
\(789\) 0 0
\(790\) 7.71399 + 12.1395i 0.274451 + 0.431904i
\(791\) 29.4551i 1.04730i