Properties

Label 720.2.u.a.179.18
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 179.18
Character \(\chi\) \(=\) 720.179
Dual form 720.2.u.a.539.18

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.612434 - 1.27473i) q^{2} +(-1.24985 + 1.56137i) q^{4} +(2.22047 + 0.263678i) q^{5} -2.95946i q^{7} +(2.75577 + 0.636981i) q^{8} +O(q^{10})\) \(q+(-0.612434 - 1.27473i) q^{2} +(-1.24985 + 1.56137i) q^{4} +(2.22047 + 0.263678i) q^{5} -2.95946i q^{7} +(2.75577 + 0.636981i) q^{8} +(-1.02377 - 2.99197i) q^{10} +(-1.04021 + 1.04021i) q^{11} +(-0.00780247 + 0.00780247i) q^{13} +(-3.77249 + 1.81247i) q^{14} +(-0.875749 - 3.90296i) q^{16} -2.00003 q^{17} +(5.10608 - 5.10608i) q^{19} +(-3.18695 + 3.13741i) q^{20} +(1.96305 + 0.688925i) q^{22} +6.49393 q^{23} +(4.86095 + 1.17098i) q^{25} +(0.0147245 + 0.00516751i) q^{26} +(4.62080 + 3.69888i) q^{28} +(-5.45997 + 5.45997i) q^{29} -4.99178i q^{31} +(-4.43886 + 3.50664i) q^{32} +(1.22489 + 2.54949i) q^{34} +(0.780345 - 6.57137i) q^{35} +(-3.74547 - 3.74547i) q^{37} +(-9.63598 - 3.38171i) q^{38} +(5.95113 + 2.14103i) q^{40} +10.4245 q^{41} +(3.52161 - 3.52161i) q^{43} +(-0.324047 - 2.92427i) q^{44} +(-3.97710 - 8.27798i) q^{46} -10.6419i q^{47} -1.75838 q^{49} +(-1.48433 - 6.91352i) q^{50} +(-0.00243062 - 0.0219345i) q^{52} +(2.98006 - 2.98006i) q^{53} +(-2.58404 + 2.03548i) q^{55} +(1.88512 - 8.15557i) q^{56} +(10.3038 + 3.61610i) q^{58} +(-5.47867 + 5.47867i) q^{59} +(-4.67845 - 4.67845i) q^{61} +(-6.36315 + 3.05713i) q^{62} +(7.18851 + 3.51074i) q^{64} +(-0.0193825 + 0.0152678i) q^{65} +(2.29404 + 2.29404i) q^{67} +(2.49974 - 3.12279i) q^{68} +(-8.85461 + 3.02980i) q^{70} -0.212315i q^{71} -16.4980 q^{73} +(-2.48059 + 7.06830i) q^{74} +(1.59064 + 14.3543i) q^{76} +(3.07847 + 3.07847i) q^{77} -4.54833i q^{79} +(-0.915447 - 8.89730i) q^{80} +(-6.38432 - 13.2884i) q^{82} +(-4.68359 + 4.68359i) q^{83} +(-4.44100 - 0.527365i) q^{85} +(-6.64583 - 2.33233i) q^{86} +(-3.52918 + 2.20399i) q^{88} -0.123094 q^{89} +(0.0230911 + 0.0230911i) q^{91} +(-8.11644 + 10.1394i) q^{92} +(-13.5655 + 6.51744i) q^{94} +(12.6842 - 9.99152i) q^{95} -8.29464i q^{97} +(1.07689 + 2.24145i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96q + O(q^{10}) \) \( 96q - 8q^{16} - 16q^{19} + 72q^{34} + 8q^{40} + 8q^{46} - 96q^{49} + 64q^{55} - 32q^{61} + 48q^{64} + 24q^{70} + 40q^{76} - 88q^{94} + O(q^{100}) \)

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
\(5\) 2.22047 + 0.263678i 0.993023 + 0.117921i
\(6\) 0 0
\(7\) 2.95946i 1.11857i −0.828976 0.559284i \(-0.811076\pi\)
0.828976 0.559284i \(-0.188924\pi\)
\(8\) 2.75577 + 0.636981i 0.974311 + 0.225207i
\(9\) 0 0
\(10\) −1.02377 2.99197i −0.323745 0.946144i
\(11\) −1.04021 + 1.04021i −0.313636 + 0.313636i −0.846317 0.532680i \(-0.821185\pi\)
0.532680 + 0.846317i \(0.321185\pi\)
\(12\) 0 0
\(13\) −0.00780247 + 0.00780247i −0.00216402 + 0.00216402i −0.708188 0.706024i \(-0.750487\pi\)
0.706024 + 0.708188i \(0.250487\pi\)
\(14\) −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 \(-0.0607003\pi\)
\(20\) −3.18695 + 3.13741i −0.712624 + 0.701546i
\(21\) 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 \(0.504453\pi\)
−0.999902 + 0.0139895i \(0.995547\pi\)
\(30\) 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
\(35\) 0.780345 6.57137i 0.131902 1.11076i
\(36\) 0 0
\(37\) −3.74547 3.74547i −0.615752 0.615752i 0.328687 0.944439i \(-0.393394\pi\)
−0.944439 + 0.328687i \(0.893394\pi\)
\(38\) −9.63598 3.38171i −1.56316 0.548586i
\(39\) 0 0
\(40\) 5.95113 + 2.14103i 0.940957 + 0.338527i
\(41\) 10.4245 1.62803 0.814017 0.580841i \(-0.197276\pi\)
0.814017 + 0.580841i \(0.197276\pi\)
\(42\) 0 0
\(43\) 3.52161 3.52161i 0.537040 0.537040i −0.385618 0.922658i \(-0.626012\pi\)
0.922658 + 0.385618i \(0.126012\pi\)
\(44\) −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
\(50\) −1.48433 6.91352i −0.209916 0.977719i
\(51\) 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 −0.967216 0.253954i \(-0.918269\pi\)
0.253954 + 0.967216i \(0.418269\pi\)
\(60\) 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 0.833213 0.552952i \(-0.186499\pi\)
−0.552952 + 0.833213i \(0.686499\pi\)
\(68\) 2.49974 3.12279i 0.303138 0.378693i
\(69\) 0 0
\(70\) −8.85461 + 3.02980i −1.05833 + 0.362131i
\(71\) 0.212315i 0.0251971i −0.999921 0.0125986i \(-0.995990\pi\)
0.999921 0.0125986i \(-0.00401036\pi\)
\(72\) 0 0
\(73\) −16.4980 −1.93094 −0.965472 0.260505i \(-0.916111\pi\)
−0.965472 + 0.260505i \(0.916111\pi\)
\(74\) −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 \(-0.0823597\pi\)
\(80\) −0.915447 8.89730i −0.102350 0.994748i
\(81\) 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
\(85\) −4.44100 0.527365i −0.481694 0.0572008i
\(86\) −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 \(-0.502077\pi\)
−0.00652395 + 0.999979i \(0.502077\pi\)
\(90\) 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 \(-0.861645\pi\)
0.907016 0.421096i \(-0.138355\pi\)
\(98\) 1.07689 + 2.24145i 0.108782 + 0.226420i
\(99\) 0 0
\(100\) −7.90379 + 6.12619i −0.790379 + 0.612619i
\(101\) 7.95152 + 7.95152i 0.791205 + 0.791205i 0.981690 0.190485i \(-0.0610060\pi\)
−0.190485 + 0.981690i \(0.561006\pi\)
\(102\) 0 0
\(103\) 6.14632i 0.605615i 0.953052 + 0.302808i \(0.0979240\pi\)
−0.953052 + 0.302808i \(0.902076\pi\)
\(104\) −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 \(0.483424\pi\)
\(110\) 4.17723 + 2.04735i 0.398283 + 0.195207i
\(111\) 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
\(115\) 14.4196 + 1.71231i 1.34463 + 0.159674i
\(116\) −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
\(125\) 10.4848 + 3.88185i 0.937790 + 0.347203i
\(126\) 0 0
\(127\) −0.542244 −0.0481164 −0.0240582 0.999711i \(-0.507659\pi\)
−0.0240582 + 0.999711i \(0.507659\pi\)
\(128\) 0.0727470 11.3135i 0.00642998 0.999979i
\(129\) 0 0
\(130\) 0.0313327 + 0.0153568i 0.00274806 + 0.00134688i
\(131\) −5.55272 5.55272i −0.485143 0.485143i 0.421626 0.906770i \(-0.361459\pi\)
−0.906770 + 0.421626i \(0.861459\pi\)
\(132\) 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 \(0.627102\pi\)
\(140\) 9.28503 + 9.43164i 0.784728 + 0.797119i
\(141\) 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 \(0.0119691\pi\)
0.0375933 + 0.999293i \(0.488031\pi\)
\(150\) 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
\(155\) 1.31622 11.0841i 0.105722 0.890294i
\(156\) 0 0
\(157\) 4.80235 4.80235i 0.383269 0.383269i −0.489009 0.872279i \(-0.662642\pi\)
0.872279 + 0.489009i \(0.162642\pi\)
\(158\) −5.79787 + 2.78555i −0.461254 + 0.221606i
\(159\) 0 0
\(160\) −10.7810 + 6.61595i −0.852310 + 0.523037i
\(161\) 19.2185i 1.51463i
\(162\) 0 0
\(163\) 0.778039 + 0.778039i 0.0609407 + 0.0609407i 0.736920 0.675980i \(-0.236279\pi\)
−0.675980 + 0.736920i \(0.736279\pi\)
\(164\) −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
\(170\) 2.04757 + 5.98403i 0.157042 + 0.458954i
\(171\) 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 0.211428 0.977394i \(-0.432189\pi\)
−0.977394 + 0.211428i \(0.932189\pi\)
\(180\) 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
\(190\) −20.5047 10.0498i −1.48757 0.729088i
\(191\) −15.2046 −1.10017 −0.550083 0.835110i \(-0.685404\pi\)
−0.550083 + 0.835110i \(0.685404\pi\)
\(192\) 0 0
\(193\) 12.4277i 0.894566i 0.894392 + 0.447283i \(0.147608\pi\)
−0.894392 + 0.447283i \(0.852392\pi\)
\(194\) −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 \(0.384393\pi\)
\(200\) 12.6498 + 6.32327i 0.894472 + 0.447123i
\(201\) 0 0
\(202\) 5.26622 15.0058i 0.370530 1.05580i
\(203\) 16.1585 + 16.1585i 1.13411 + 1.13411i
\(204\) 0 0
\(205\) 23.1473 + 2.74872i 1.61668 + 0.191979i
\(206\) 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
\(220\) 0.0515320 6.57869i 0.00347428 0.443535i
\(221\) 0.0156052 0.0156052i 0.00104972 0.00104972i
\(222\) 0 0
\(223\) −26.9611 −1.80545 −0.902724 0.430221i \(-0.858436\pi\)
−0.902724 + 0.430221i \(0.858436\pi\)
\(224\) 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 \(0.306412\pi\)
\(230\) −6.64829 19.4296i −0.438376 1.28115i
\(231\) 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
\(235\) 2.80603 23.6299i 0.183045 1.54145i
\(236\) −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 \(-0.368460\pi\)
0.401582 + 0.915823i \(0.368460\pi\)
\(240\) 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
\(245\) −3.90442 0.463646i −0.249444 0.0296212i
\(246\) 0 0
\(247\) 0.0796800i 0.00506992i
\(248\) 3.17967 13.7562i 0.201909 0.873518i
\(249\) 0 0
\(250\) −1.47296 15.7426i −0.0931583 0.995651i
\(251\) −18.3923 + 18.3923i −1.16091 + 1.16091i −0.176634 + 0.984277i \(0.556521\pi\)
−0.984277 + 0.176634i \(0.943479\pi\)
\(252\) 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
\(260\) 0.000386533 0.0493456i 2.39717e−5 0.00306029i
\(261\) 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 −0.707963 0.706250i \(-0.750386\pi\)
0.706250 + 0.707963i \(0.250386\pi\)
\(270\) 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
\(275\) −6.27449 + 3.83836i −0.378366 + 0.231462i
\(276\) 0 0
\(277\) 23.0188 + 23.0188i 1.38306 + 1.38306i 0.839126 + 0.543937i \(0.183067\pi\)
0.543937 + 0.839126i \(0.316933\pi\)
\(278\) 4.15835 11.8490i 0.249401 0.710654i
\(279\) 0 0
\(280\) 6.33629 17.6121i 0.378666 1.05253i
\(281\) 19.3294 1.15309 0.576547 0.817064i \(-0.304400\pi\)
0.576547 + 0.817064i \(0.304400\pi\)
\(282\) 0 0
\(283\) −2.78511 + 2.78511i −0.165557 + 0.165557i −0.785023 0.619466i \(-0.787349\pi\)
0.619466 + 0.785023i \(0.287349\pi\)
\(284\) 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
\(290\) 21.9258 + 10.7463i 1.28753 + 0.631046i
\(291\) 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 \(0.143746\pi\)
0.436397 + 0.899754i \(0.356254\pi\)
\(308\) −8.65425 + 0.959002i −0.493121 + 0.0546442i
\(309\) 0 0
\(310\) −14.9353 + 5.11044i −0.848265 + 0.290253i
\(311\) 24.0385i 1.36310i −0.731772 0.681549i \(-0.761307\pi\)
0.731772 0.681549i \(-0.238693\pi\)
\(312\) 0 0
\(313\) 17.7757 1.00474 0.502371 0.864652i \(-0.332461\pi\)
0.502371 + 0.864652i \(0.332461\pi\)
\(314\) −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
\(320\) 15.0361 + 9.69094i 0.840546 + 0.541740i
\(321\) 0 0
\(322\) −24.4983 + 11.7700i −1.36524 + 0.655919i
\(323\) −10.2123 + 10.2123i −0.568228 + 0.568228i
\(324\) 0 0
\(325\) −0.0470639 + 0.0287909i −0.00261064 + 0.00159703i
\(326\) 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 \(0.210836\pi\)
−0.788542 + 0.614980i \(0.789164\pi\)
\(338\) 16.5713 7.96156i 0.901359 0.433052i
\(339\) 0 0
\(340\) 6.37400 6.27492i 0.345679 0.340305i
\(341\) 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 \(0.606723\pi\)
\(350\) −20.4603 + 4.39281i −1.09365 + 0.234806i
\(351\) 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
\(355\) 0.0559829 0.471438i 0.00297126 0.0250213i
\(356\) 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 \(0.0190913\pi\)
−0.998202 + 0.0599412i \(0.980909\pi\)
\(360\) 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
\(365\) −36.6333 4.35017i −1.91747 0.227698i
\(366\) 0 0
\(367\) 31.1335 1.62516 0.812579 0.582852i \(-0.198063\pi\)
0.812579 + 0.582852i \(0.198063\pi\)
\(368\) −5.68705 25.3455i −0.296458 1.32123i
\(369\) 0 0
\(370\) −7.37184 + 15.0408i −0.383244 + 0.781936i
\(371\) −8.81934 8.81934i −0.457877 0.457877i
\(372\) 0 0
\(373\) −20.3199 20.3199i −1.05212 1.05212i −0.998565 0.0535601i \(-0.982943\pi\)
−0.0535601 0.998565i \(-0.517057\pi\)
\(374\) −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 \(0.863561\pi\)
\(380\) −0.252954 + 32.2927i −0.0129763 + 1.65658i
\(381\) 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 \(-0.924686\pi\)
−0.234403 0.972139i \(-0.575314\pi\)
\(390\) 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
\(395\) 1.19930 10.0994i 0.0603431 0.508156i
\(396\) 0 0
\(397\) 5.88396 5.88396i 0.295308 0.295308i −0.543865 0.839173i \(-0.683040\pi\)
0.839173 + 0.543865i \(0.183040\pi\)
\(398\) −6.13847 12.7767i −0.307693 0.640436i
\(399\) 0 0
\(400\) 0.313307 19.9975i 0.0156654 0.999877i
\(401\) 15.4433i 0.771202i −0.922666 0.385601i \(-0.873994\pi\)
0.922666 0.385601i \(-0.126006\pi\)
\(402\) 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 \(-0.0692109\pi\)
\(410\) −10.6723 31.1898i −0.527068 1.54036i
\(411\) 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 0.815193 0.579190i \(-0.196631\pi\)
−0.579190 + 0.815193i \(0.696631\pi\)
\(420\) 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
\(430\) −14.1419 6.93123i −0.681982 0.334254i
\(431\) −6.63538 −0.319615 −0.159808 0.987148i \(-0.551087\pi\)
−0.159808 + 0.987148i \(0.551087\pi\)
\(432\) 0 0
\(433\) 2.17952i 0.104741i 0.998628 + 0.0523706i \(0.0166777\pi\)
−0.998628 + 0.0523706i \(0.983322\pi\)
\(434\) 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 \(0.642838\pi\)
\(440\) −8.41758 + 3.96332i −0.401293 + 0.188944i
\(441\) 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
\(445\) −0.273325 0.0324571i −0.0129569 0.00153862i
\(446\) 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 \(-0.735050\pi\)
0.673129 0.739525i \(-0.264950\pi\)
\(450\) 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 \(-0.380945\pi\)
0.365364 + 0.930865i \(0.380945\pi\)
\(458\) 7.12005 + 2.49876i 0.332698 + 0.116759i
\(459\) 0 0
\(460\) −20.6958 + 20.3741i −0.964948 + 0.949948i
\(461\) 9.98698 9.98698i 0.465140 0.465140i −0.435196 0.900336i \(-0.643321\pi\)
0.900336 + 0.435196i \(0.143321\pi\)
\(462\) 0 0
\(463\) −27.8119 −1.29253 −0.646264 0.763114i \(-0.723670\pi\)
−0.646264 + 0.763114i \(0.723670\pi\)
\(464\) 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
\(470\) −31.8402 + 10.8948i −1.46868 + 0.502542i
\(471\) 0 0
\(472\) −18.5878 + 11.6081i −0.855571 + 0.534308i
\(473\) 7.32645i 0.336871i
\(474\) 0 0
\(475\) 30.7995 18.8413i 1.41318 0.864497i
\(476\) −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 \(-0.319218\pi\)
0.537900 + 0.843009i \(0.319218\pi\)
\(480\) 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
\(485\) 2.18712 18.4180i 0.0993119 0.836317i
\(486\) 0 0
\(487\) 15.4005i 0.697865i −0.937148 0.348932i \(-0.886544\pi\)
0.937148 0.348932i \(-0.113456\pi\)
\(488\) −9.91263 15.8728i −0.448724 0.718527i
\(489\) 0 0
\(490\) 1.80017 + 5.26101i 0.0813236 + 0.237668i
\(491\) −11.9089 + 11.9089i −0.537443 + 0.537443i −0.922777 0.385334i \(-0.874086\pi\)
0.385334 + 0.922777i \(0.374086\pi\)
\(492\) 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 \(0.0756631\pi\)
\(500\) −19.1654 + 11.5189i −0.857105 + 0.515143i
\(501\) 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 \(0.568803\pi\)
−0.976730 + 0.214473i \(0.931197\pi\)
\(510\) 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
\(515\) −1.62065 + 13.6477i −0.0714145 + 0.601390i
\(516\) 0 0
\(517\) 11.0698 + 11.0698i 0.486850 + 0.486850i
\(518\) 20.9183 + 7.34121i 0.919098 + 0.322554i
\(519\) 0 0
\(520\) −0.0631389 + 0.0297282i −0.00276882 + 0.00130367i
\(521\) 18.0720 0.791749 0.395874 0.918305i \(-0.370442\pi\)
0.395874 + 0.918305i \(0.370442\pi\)
\(522\) 0 0
\(523\) −10.2127 + 10.2127i −0.446571 + 0.446571i −0.894213 0.447642i \(-0.852264\pi\)
0.447642 + 0.894213i \(0.352264\pi\)
\(524\) 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
\(530\) −11.9671 5.86535i −0.519819 0.254774i
\(531\) 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 \(-0.968574\pi\)
−0.0985674 0.995130i \(-0.531426\pi\)
\(548\) −9.06173 7.25377i −0.387098 0.309865i
\(549\) 0 0
\(550\) 8.73556 + 5.64752i 0.372486 + 0.240811i
\(551\) 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
\(560\) −26.3312 + 2.70922i −1.11269 + 0.114486i
\(561\) 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
\(565\) −22.1000 2.62436i −0.929755 0.110408i
\(566\) 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 \(-0.303776\pi\)
0.578146 + 0.815933i \(0.303776\pi\)
\(570\) 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 \(-0.763673\pi\)
0.736819 0.676090i \(-0.236327\pi\)
\(578\) 7.96156 + 16.5713i 0.331157 + 0.689274i
\(579\) 0 0
\(580\) 0.270486 34.5308i 0.0112313 1.43382i
\(581\) 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
\(590\) 22.0009 + 10.7831i 0.905764 + 0.443934i
\(591\) 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
\(595\) −1.56071 + 13.1429i −0.0639830 + 0.538808i
\(596\) −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 \(-0.864958\pi\)
0.911349 0.411635i \(-0.135042\pi\)
\(600\) 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
\(605\) −2.32984 + 19.6198i −0.0947214 + 0.797660i
\(606\) 0 0
\(607\) 1.55683 0.0631899 0.0315949 0.999501i \(-0.489941\pi\)
0.0315949 + 0.999501i \(0.489941\pi\)
\(608\) −4.75998 + 40.5703i −0.193043 + 1.64534i
\(609\) 0 0
\(610\) −9.20812 + 18.7874i −0.372826 + 0.760681i
\(611\) 0.0830329 + 0.0830329i 0.00335915 + 0.00335915i
\(612\) 0 0
\(613\) 19.5306 + 19.5306i 0.788832 + 0.788832i 0.981303 0.192471i \(-0.0616501\pi\)
−0.192471 + 0.981303i \(0.561650\pi\)
\(614\) 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 \(0.704156\pi\)
\(620\) 15.6613 + 15.9085i 0.628971 + 0.638903i
\(621\) 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
\(635\) −1.20404 0.142978i −0.0477807 0.00567391i
\(636\) 0 0
\(637\) 0.0137197 0.0137197i 0.000543593 0.000543593i
\(638\) −14.4797 + 6.95668i −0.573257 + 0.275418i
\(639\) 0 0
\(640\) 3.14465 25.1020i 0.124303 0.992244i
\(641\) 2.92420i 0.115499i 0.998331 + 0.0577495i \(0.0183925\pi\)
−0.998331 + 0.0577495i \(0.981608\pi\)
\(642\) 0 0
\(643\) −30.2222 30.2222i −1.19185 1.19185i −0.976548 0.215301i \(-0.930927\pi\)
−0.215301 0.976548i \(-0.569073\pi\)
\(644\) 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
\(650\) 0.0655240 + 0.0423611i 0.00257006 + 0.00166154i
\(651\) 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 0.914036 0.405634i \(-0.132949\pi\)
−0.405634 + 0.914036i \(0.632949\pi\)
\(660\) 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
\(670\) 4.51513 9.21227i 0.174435 0.355901i
\(671\) 9.73317 0.375745
\(672\) 0 0
\(673\) 8.96622i 0.345622i 0.984955 + 0.172811i \(0.0552850\pi\)
−0.984955 + 0.172811i \(0.944715\pi\)
\(674\) 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
\(680\) −11.9024 4.28213i −0.456438 0.164212i
\(681\) 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
\(685\) −1.53031 + 12.8869i −0.0584702 + 0.492385i
\(686\) −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
\(700\) 18.1302 + 23.3909i 0.685256 + 0.884093i
\(701\) 28.2156 28.2156i 1.06569 1.06569i 0.0680026 0.997685i \(-0.478337\pi\)
0.997685 0.0680026i \(-0.0216626\pi\)
\(702\) 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 \(0.157780\pi\)
\(710\) −0.635240 + 0.217362i −0.0238401 + 0.00815744i
\(711\) 0 0
\(712\) −0.339217 0.0784082i −0.0127127 0.00293847i
\(713\) 32.4162i 1.21400i
\(714\) 0 0
\(715\) 0.00428015 0.0360437i 0.000160069 0.00134796i
\(716\) 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 \(-0.509977\pi\)
−0.0313374 + 0.999509i \(0.509977\pi\)
\(720\) 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
\(725\) −32.9342 + 20.1471i −1.22314 + 0.748246i
\(726\) 0 0
\(727\) 33.3069i 1.23528i −0.786460 0.617641i \(-0.788088\pi\)
0.786460 0.617641i \(-0.211912\pi\)
\(728\) 0.0489250 + 0.0783422i 0.00181328 + 0.00290355i
\(729\) 0 0
\(730\) 16.8902 + 49.3615i 0.625133 + 1.82695i
\(731\) −7.04332 + 7.04332i −0.260507 + 0.260507i
\(732\) 0 0
\(733\) −9.28476 + 9.28476i −0.342941 + 0.342941i −0.857472 0.514531i \(-0.827966\pi\)
0.514531 + 0.857472i \(0.327966\pi\)
\(734\) −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 \(0.464729\pi\)
\(740\) 23.6877 + 0.185550i 0.870777 + 0.00682094i
\(741\) 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
\(755\) 38.0437 + 4.51766i 1.38455 + 0.164414i
\(756\) 0 0
\(757\) 28.0622 + 28.0622i 1.01994 + 1.01994i 0.999797 + 0.0201412i \(0.00641158\pi\)
0.0201412 + 0.999797i \(0.493588\pi\)
\(758\) −6.36812 + 18.1455i −0.231300 + 0.659076i
\(759\) 0 0
\(760\) 41.3192 19.4547i 1.49881 0.705695i
\(761\) −12.1544 −0.440597 −0.220299 0.975432i \(-0.570703\pi\)
−0.220299 + 0.975432i \(0.570703\pi\)
\(762\) 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 \(0.500245\pi\)
\(770\) 6.05904 12.3623i 0.218353 0.445507i
\(771\) 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 0.339643 0.940554i \(-0.389694\pi\)
−0.940554 + 0.339643i \(0.889694\pi\)
\(788\) 2.34951 + 21.2025i 0.0836978 + 0.755308i
\(789\) 0 0
\(790\) −13.6085 + 4.65644i −0.484167 + 0.165669i
\(791\) 29.4551i 1.04730i