Properties

Label 720.2.u.a.179.5
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 179.5
Character \(\chi\) \(=\) 720.179
Dual form 720.2.u.a.539.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.31018 - 0.532382i) q^{2} +(1.43314 + 1.39503i) q^{4} +(-1.50698 - 1.65197i) q^{5} -4.30751i q^{7} +(-1.13498 - 2.59072i) q^{8} +O(q^{10})\) \(q+(-1.31018 - 0.532382i) q^{2} +(1.43314 + 1.39503i) q^{4} +(-1.50698 - 1.65197i) q^{5} -4.30751i q^{7} +(-1.13498 - 2.59072i) q^{8} +(1.09494 + 2.96667i) q^{10} +(-4.26649 + 4.26649i) q^{11} +(-2.10930 + 2.10930i) q^{13} +(-2.29324 + 5.64362i) q^{14} +(0.107775 + 3.99855i) q^{16} -3.59142 q^{17} +(0.954870 - 0.954870i) q^{19} +(0.144830 - 4.46979i) q^{20} +(7.86127 - 3.31847i) q^{22} +6.53188 q^{23} +(-0.457999 + 4.97898i) q^{25} +(3.88652 - 1.64061i) q^{26} +(6.00912 - 6.17327i) q^{28} +(1.84857 - 1.84857i) q^{29} +7.64329i q^{31} +(1.98755 - 5.29619i) q^{32} +(4.70541 + 1.91201i) q^{34} +(-7.11588 + 6.49135i) q^{35} +(-1.90965 - 1.90965i) q^{37} +(-1.75941 + 0.742695i) q^{38} +(-2.56939 + 5.77912i) q^{40} +7.67058 q^{41} +(-5.43308 + 5.43308i) q^{43} +(-12.0664 + 0.162586i) q^{44} +(-8.55794 - 3.47746i) q^{46} +3.24864i q^{47} -11.5547 q^{49} +(3.25078 - 6.27953i) q^{50} +(-5.96546 + 0.0803806i) q^{52} +(-6.08323 + 6.08323i) q^{53} +(13.4776 + 0.618574i) q^{55} +(-11.1596 + 4.88894i) q^{56} +(-3.40610 + 1.43781i) q^{58} +(-2.97848 + 2.97848i) q^{59} +(-0.157020 - 0.157020i) q^{61} +(4.06915 - 10.0141i) q^{62} +(-5.42364 + 5.88082i) q^{64} +(6.66318 + 0.305816i) q^{65} +(-0.305394 - 0.305394i) q^{67} +(-5.14701 - 5.01014i) q^{68} +(12.7790 - 4.71647i) q^{70} -1.61808i q^{71} -6.90696 q^{73} +(1.48532 + 3.51865i) q^{74} +(2.70053 - 0.0363879i) q^{76} +(18.3780 + 18.3780i) q^{77} -5.39306i q^{79} +(6.44306 - 6.20379i) q^{80} +(-10.0498 - 4.08368i) q^{82} +(-5.82210 + 5.82210i) q^{83} +(5.41221 + 5.93291i) q^{85} +(10.0108 - 4.22584i) q^{86} +(15.8957 + 6.21090i) q^{88} -7.74878 q^{89} +(9.08585 + 9.08585i) q^{91} +(9.36110 + 9.11218i) q^{92} +(1.72952 - 4.25630i) q^{94} +(-3.01639 - 0.138441i) q^{95} -9.34141i q^{97} +(15.1387 + 6.15150i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96q + O(q^{10}) \) \( 96q - 8q^{16} - 16q^{19} + 72q^{34} + 8q^{40} + 8q^{46} - 96q^{49} + 64q^{55} - 32q^{61} + 48q^{64} + 24q^{70} + 40q^{76} - 88q^{94} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.31018 0.532382i −0.926437 0.376451i
\(3\) 0 0
\(4\) 1.43314 + 1.39503i 0.716570 + 0.697516i
\(5\) −1.50698 1.65197i −0.673944 0.738783i
\(6\) 0 0
\(7\) 4.30751i 1.62809i −0.580804 0.814044i \(-0.697262\pi\)
0.580804 0.814044i \(-0.302738\pi\)
\(8\) −1.13498 2.59072i −0.401276 0.915957i
\(9\) 0 0
\(10\) 1.09494 + 2.96667i 0.346251 + 0.938142i
\(11\) −4.26649 + 4.26649i −1.28640 + 1.28640i −0.349435 + 0.936961i \(0.613626\pi\)
−0.936961 + 0.349435i \(0.886374\pi\)
\(12\) 0 0
\(13\) −2.10930 + 2.10930i −0.585015 + 0.585015i −0.936277 0.351262i \(-0.885753\pi\)
0.351262 + 0.936277i \(0.385753\pi\)
\(14\) −2.29324 + 5.64362i −0.612895 + 1.50832i
\(15\) 0 0
\(16\) 0.107775 + 3.99855i 0.0269438 + 0.999637i
\(17\) −3.59142 −0.871048 −0.435524 0.900177i \(-0.643437\pi\)
−0.435524 + 0.900177i \(0.643437\pi\)
\(18\) 0 0
\(19\) 0.954870 0.954870i 0.219062 0.219062i −0.589041 0.808103i \(-0.700494\pi\)
0.808103 + 0.589041i \(0.200494\pi\)
\(20\) 0.144830 4.46979i 0.0323850 0.999475i
\(21\) 0 0
\(22\) 7.86127 3.31847i 1.67603 0.707499i
\(23\) 6.53188 1.36199 0.680996 0.732287i \(-0.261547\pi\)
0.680996 + 0.732287i \(0.261547\pi\)
\(24\) 0 0
\(25\) −0.457999 + 4.97898i −0.0915997 + 0.995796i
\(26\) 3.88652 1.64061i 0.762209 0.321750i
\(27\) 0 0
\(28\) 6.00912 6.17327i 1.13562 1.16664i
\(29\) 1.84857 1.84857i 0.343270 0.343270i −0.514325 0.857595i \(-0.671958\pi\)
0.857595 + 0.514325i \(0.171958\pi\)
\(30\) 0 0
\(31\) 7.64329i 1.37278i 0.727236 + 0.686388i \(0.240805\pi\)
−0.727236 + 0.686388i \(0.759195\pi\)
\(32\) 1.98755 5.29619i 0.351352 0.936243i
\(33\) 0 0
\(34\) 4.70541 + 1.91201i 0.806970 + 0.327907i
\(35\) −7.11588 + 6.49135i −1.20280 + 1.09724i
\(36\) 0 0
\(37\) −1.90965 1.90965i −0.313945 0.313945i 0.532491 0.846436i \(-0.321256\pi\)
−0.846436 + 0.532491i \(0.821256\pi\)
\(38\) −1.75941 + 0.742695i −0.285413 + 0.120481i
\(39\) 0 0
\(40\) −2.56939 + 5.77912i −0.406256 + 0.913759i
\(41\) 7.67058 1.19794 0.598972 0.800770i \(-0.295576\pi\)
0.598972 + 0.800770i \(0.295576\pi\)
\(42\) 0 0
\(43\) −5.43308 + 5.43308i −0.828537 + 0.828537i −0.987314 0.158777i \(-0.949245\pi\)
0.158777 + 0.987314i \(0.449245\pi\)
\(44\) −12.0664 + 0.162586i −1.81907 + 0.0245108i
\(45\) 0 0
\(46\) −8.55794 3.47746i −1.26180 0.512723i
\(47\) 3.24864i 0.473863i 0.971526 + 0.236932i \(0.0761417\pi\)
−0.971526 + 0.236932i \(0.923858\pi\)
\(48\) 0 0
\(49\) −11.5547 −1.65067
\(50\) 3.25078 6.27953i 0.459730 0.888059i
\(51\) 0 0
\(52\) −5.96546 + 0.0803806i −0.827261 + 0.0111468i
\(53\) −6.08323 + 6.08323i −0.835596 + 0.835596i −0.988276 0.152680i \(-0.951210\pi\)
0.152680 + 0.988276i \(0.451210\pi\)
\(54\) 0 0
\(55\) 13.4776 + 0.618574i 1.81732 + 0.0834085i
\(56\) −11.1596 + 4.88894i −1.49126 + 0.653312i
\(57\) 0 0
\(58\) −3.40610 + 1.43781i −0.447243 + 0.188794i
\(59\) −2.97848 + 2.97848i −0.387765 + 0.387765i −0.873889 0.486125i \(-0.838410\pi\)
0.486125 + 0.873889i \(0.338410\pi\)
\(60\) 0 0
\(61\) −0.157020 0.157020i −0.0201044 0.0201044i 0.696983 0.717088i \(-0.254525\pi\)
−0.717088 + 0.696983i \(0.754525\pi\)
\(62\) 4.06915 10.0141i 0.516782 1.27179i
\(63\) 0 0
\(64\) −5.42364 + 5.88082i −0.677955 + 0.735103i
\(65\) 6.66318 + 0.305816i 0.826466 + 0.0379318i
\(66\) 0 0
\(67\) −0.305394 0.305394i −0.0373098 0.0373098i 0.688206 0.725516i \(-0.258399\pi\)
−0.725516 + 0.688206i \(0.758399\pi\)
\(68\) −5.14701 5.01014i −0.624166 0.607569i
\(69\) 0 0
\(70\) 12.7790 4.71647i 1.52738 0.563726i
\(71\) 1.61808i 0.192030i −0.995380 0.0960152i \(-0.969390\pi\)
0.995380 0.0960152i \(-0.0306097\pi\)
\(72\) 0 0
\(73\) −6.90696 −0.808399 −0.404199 0.914671i \(-0.632450\pi\)
−0.404199 + 0.914671i \(0.632450\pi\)
\(74\) 1.48532 + 3.51865i 0.172665 + 0.409035i
\(75\) 0 0
\(76\) 2.70053 0.0363879i 0.309773 0.00417398i
\(77\) 18.3780 + 18.3780i 2.09436 + 2.09436i
\(78\) 0 0
\(79\) 5.39306i 0.606767i −0.952869 0.303383i \(-0.901884\pi\)
0.952869 0.303383i \(-0.0981163\pi\)
\(80\) 6.44306 6.20379i 0.720356 0.693605i
\(81\) 0 0
\(82\) −10.0498 4.08368i −1.10982 0.450967i
\(83\) −5.82210 + 5.82210i −0.639059 + 0.639059i −0.950323 0.311265i \(-0.899247\pi\)
0.311265 + 0.950323i \(0.399247\pi\)
\(84\) 0 0
\(85\) 5.41221 + 5.93291i 0.587037 + 0.643515i
\(86\) 10.0108 4.22584i 1.07949 0.455684i
\(87\) 0 0
\(88\) 15.8957 + 6.21090i 1.69448 + 0.662084i
\(89\) −7.74878 −0.821369 −0.410684 0.911778i \(-0.634710\pi\)
−0.410684 + 0.911778i \(0.634710\pi\)
\(90\) 0 0
\(91\) 9.08585 + 9.08585i 0.952455 + 0.952455i
\(92\) 9.36110 + 9.11218i 0.975962 + 0.950011i
\(93\) 0 0
\(94\) 1.72952 4.25630i 0.178386 0.439004i
\(95\) −3.01639 0.138441i −0.309475 0.0142038i
\(96\) 0 0
\(97\) 9.34141i 0.948476i −0.880397 0.474238i \(-0.842724\pi\)
0.880397 0.474238i \(-0.157276\pi\)
\(98\) 15.1387 + 6.15150i 1.52924 + 0.621396i
\(99\) 0 0
\(100\) −7.60221 + 6.49665i −0.760221 + 0.649665i
\(101\) −7.91178 7.91178i −0.787251 0.787251i 0.193792 0.981043i \(-0.437921\pi\)
−0.981043 + 0.193792i \(0.937921\pi\)
\(102\) 0 0
\(103\) 16.1744i 1.59371i 0.604172 + 0.796854i \(0.293504\pi\)
−0.604172 + 0.796854i \(0.706496\pi\)
\(104\) 7.85862 + 3.07059i 0.770601 + 0.301096i
\(105\) 0 0
\(106\) 11.2087 4.73152i 1.08869 0.459566i
\(107\) 5.26603 + 5.26603i 0.509086 + 0.509086i 0.914246 0.405160i \(-0.132784\pi\)
−0.405160 + 0.914246i \(0.632784\pi\)
\(108\) 0 0
\(109\) −11.9434 11.9434i −1.14397 1.14397i −0.987718 0.156248i \(-0.950060\pi\)
−0.156248 0.987718i \(-0.549940\pi\)
\(110\) −17.3288 7.98570i −1.65224 0.761406i
\(111\) 0 0
\(112\) 17.2238 0.464243i 1.62750 0.0438668i
\(113\) −18.0886 −1.70163 −0.850815 0.525466i \(-0.823891\pi\)
−0.850815 + 0.525466i \(0.823891\pi\)
\(114\) 0 0
\(115\) −9.84344 10.7905i −0.917906 1.00622i
\(116\) 5.22806 0.0704446i 0.485413 0.00654062i
\(117\) 0 0
\(118\) 5.48802 2.31665i 0.505214 0.213265i
\(119\) 15.4701i 1.41814i
\(120\) 0 0
\(121\) 25.4059i 2.30963i
\(122\) 0.122130 + 0.289319i 0.0110571 + 0.0261937i
\(123\) 0 0
\(124\) −10.6626 + 10.9539i −0.957532 + 0.983689i
\(125\) 8.91531 6.74664i 0.797410 0.603438i
\(126\) 0 0
\(127\) −7.28333 −0.646291 −0.323145 0.946349i \(-0.604740\pi\)
−0.323145 + 0.946349i \(0.604740\pi\)
\(128\) 10.2368 4.81748i 0.904813 0.425810i
\(129\) 0 0
\(130\) −8.56715 3.94803i −0.751389 0.346265i
\(131\) 9.89718 + 9.89718i 0.864721 + 0.864721i 0.991882 0.127161i \(-0.0405865\pi\)
−0.127161 + 0.991882i \(0.540587\pi\)
\(132\) 0 0
\(133\) −4.11312 4.11312i −0.356652 0.356652i
\(134\) 0.237535 + 0.562707i 0.0205199 + 0.0486105i
\(135\) 0 0
\(136\) 4.07619 + 9.30436i 0.349530 + 0.797842i
\(137\) 17.7974i 1.52054i −0.649608 0.760269i \(-0.725067\pi\)
0.649608 0.760269i \(-0.274933\pi\)
\(138\) 0 0
\(139\) 4.98268 + 4.98268i 0.422625 + 0.422625i 0.886107 0.463481i \(-0.153400\pi\)
−0.463481 + 0.886107i \(0.653400\pi\)
\(140\) −19.2537 0.623857i −1.62723 0.0527256i
\(141\) 0 0
\(142\) −0.861435 + 2.11997i −0.0722900 + 0.177904i
\(143\) 17.9986i 1.50512i
\(144\) 0 0
\(145\) −5.83953 0.268013i −0.484947 0.0222573i
\(146\) 9.04936 + 3.67714i 0.748930 + 0.304322i
\(147\) 0 0
\(148\) −0.0727725 5.40082i −0.00598186 0.443945i
\(149\) 9.78188 + 9.78188i 0.801363 + 0.801363i 0.983309 0.181946i \(-0.0582395\pi\)
−0.181946 + 0.983309i \(0.558240\pi\)
\(150\) 0 0
\(151\) −12.0108 −0.977422 −0.488711 0.872446i \(-0.662533\pi\)
−0.488711 + 0.872446i \(0.662533\pi\)
\(152\) −3.55756 1.39004i −0.288556 0.112747i
\(153\) 0 0
\(154\) −14.2943 33.8625i −1.15187 2.72872i
\(155\) 12.6265 11.5183i 1.01418 0.925173i
\(156\) 0 0
\(157\) −8.81467 + 8.81467i −0.703488 + 0.703488i −0.965157 0.261670i \(-0.915727\pi\)
0.261670 + 0.965157i \(0.415727\pi\)
\(158\) −2.87117 + 7.06588i −0.228418 + 0.562131i
\(159\) 0 0
\(160\) −11.7443 + 4.69791i −0.928472 + 0.371402i
\(161\) 28.1362i 2.21744i
\(162\) 0 0
\(163\) −8.90000 8.90000i −0.697102 0.697102i 0.266682 0.963784i \(-0.414073\pi\)
−0.963784 + 0.266682i \(0.914073\pi\)
\(164\) 10.9930 + 10.7007i 0.858410 + 0.835584i
\(165\) 0 0
\(166\) 10.7276 4.52841i 0.832621 0.351473i
\(167\) 4.24306 0.328338 0.164169 0.986432i \(-0.447506\pi\)
0.164169 + 0.986432i \(0.447506\pi\)
\(168\) 0 0
\(169\) 4.10170i 0.315515i
\(170\) −3.93239 10.6545i −0.301601 0.817166i
\(171\) 0 0
\(172\) −15.3657 + 0.207042i −1.17162 + 0.0157868i
\(173\) −4.03165 4.03165i −0.306521 0.306521i 0.537037 0.843558i \(-0.319543\pi\)
−0.843558 + 0.537037i \(0.819543\pi\)
\(174\) 0 0
\(175\) 21.4470 + 1.97284i 1.62124 + 0.149132i
\(176\) −17.5196 16.5999i −1.32059 1.25127i
\(177\) 0 0
\(178\) 10.1523 + 4.12531i 0.760946 + 0.309205i
\(179\) 0.833880 + 0.833880i 0.0623272 + 0.0623272i 0.737583 0.675256i \(-0.235967\pi\)
−0.675256 + 0.737583i \(0.735967\pi\)
\(180\) 0 0
\(181\) −10.5947 + 10.5947i −0.787501 + 0.787501i −0.981084 0.193583i \(-0.937989\pi\)
0.193583 + 0.981084i \(0.437989\pi\)
\(182\) −7.06695 16.7412i −0.523837 1.24094i
\(183\) 0 0
\(184\) −7.41355 16.9223i −0.546534 1.24753i
\(185\) −0.276870 + 6.03250i −0.0203559 + 0.443518i
\(186\) 0 0
\(187\) 15.3228 15.3228i 1.12051 1.12051i
\(188\) −4.53196 + 4.65575i −0.330527 + 0.339556i
\(189\) 0 0
\(190\) 3.87831 + 1.78725i 0.281362 + 0.129661i
\(191\) 3.83158 0.277244 0.138622 0.990345i \(-0.455733\pi\)
0.138622 + 0.990345i \(0.455733\pi\)
\(192\) 0 0
\(193\) 5.03272i 0.362263i −0.983459 0.181132i \(-0.942024\pi\)
0.983459 0.181132i \(-0.0579760\pi\)
\(194\) −4.97320 + 12.2389i −0.357055 + 0.878703i
\(195\) 0 0
\(196\) −16.5595 16.1191i −1.18282 1.15137i
\(197\) 7.01759 7.01759i 0.499982 0.499982i −0.411450 0.911432i \(-0.634978\pi\)
0.911432 + 0.411450i \(0.134978\pi\)
\(198\) 0 0
\(199\) 13.7542 0.975009 0.487504 0.873121i \(-0.337907\pi\)
0.487504 + 0.873121i \(0.337907\pi\)
\(200\) 13.4190 4.46449i 0.948863 0.315687i
\(201\) 0 0
\(202\) 6.15376 + 14.5779i 0.432977 + 1.02570i
\(203\) −7.96273 7.96273i −0.558874 0.558874i
\(204\) 0 0
\(205\) −11.5594 12.6716i −0.807346 0.885020i
\(206\) 8.61094 21.1913i 0.599953 1.47647i
\(207\) 0 0
\(208\) −8.66147 8.20681i −0.600565 0.569040i
\(209\) 8.14789i 0.563601i
\(210\) 0 0
\(211\) 12.8000 12.8000i 0.881190 0.881190i −0.112466 0.993656i \(-0.535875\pi\)
0.993656 + 0.112466i \(0.0358748\pi\)
\(212\) −17.2044 + 0.231818i −1.18160 + 0.0159213i
\(213\) 0 0
\(214\) −4.09590 9.70298i −0.279990 0.663282i
\(215\) 17.1628 + 0.787712i 1.17050 + 0.0537215i
\(216\) 0 0
\(217\) 32.9236 2.23500
\(218\) 9.28951 + 22.0064i 0.629165 + 1.49046i
\(219\) 0 0
\(220\) 18.4524 + 19.6882i 1.24406 + 1.32738i
\(221\) 7.57539 7.57539i 0.509576 0.509576i
\(222\) 0 0
\(223\) 12.7040 0.850723 0.425362 0.905023i \(-0.360147\pi\)
0.425362 + 0.905023i \(0.360147\pi\)
\(224\) −22.8134 8.56140i −1.52429 0.572033i
\(225\) 0 0
\(226\) 23.6993 + 9.63002i 1.57645 + 0.640580i
\(227\) −13.3440 + 13.3440i −0.885675 + 0.885675i −0.994104 0.108429i \(-0.965418\pi\)
0.108429 + 0.994104i \(0.465418\pi\)
\(228\) 0 0
\(229\) −1.09552 + 1.09552i −0.0723941 + 0.0723941i −0.742377 0.669983i \(-0.766302\pi\)
0.669983 + 0.742377i \(0.266302\pi\)
\(230\) 7.15203 + 19.3779i 0.471591 + 1.27774i
\(231\) 0 0
\(232\) −6.88720 2.69103i −0.452167 0.176675i
\(233\) 17.1156i 1.12128i −0.828060 0.560640i \(-0.810555\pi\)
0.828060 0.560640i \(-0.189445\pi\)
\(234\) 0 0
\(235\) 5.36665 4.89565i 0.350082 0.319357i
\(236\) −8.42364 + 0.113503i −0.548332 + 0.00738841i
\(237\) 0 0
\(238\) 8.23600 20.2686i 0.533861 1.31382i
\(239\) −17.8555 −1.15498 −0.577488 0.816399i \(-0.695967\pi\)
−0.577488 + 0.816399i \(0.695967\pi\)
\(240\) 0 0
\(241\) 5.11525 0.329502 0.164751 0.986335i \(-0.447318\pi\)
0.164751 + 0.986335i \(0.447318\pi\)
\(242\) −13.5256 + 33.2863i −0.869461 + 2.13972i
\(243\) 0 0
\(244\) −0.00598368 0.444080i −0.000383066 0.0284293i
\(245\) 17.4127 + 19.0880i 1.11246 + 1.21949i
\(246\) 0 0
\(247\) 4.02822i 0.256309i
\(248\) 19.8016 8.67498i 1.25740 0.550862i
\(249\) 0 0
\(250\) −15.2724 + 4.09296i −0.965914 + 0.258862i
\(251\) −4.02622 + 4.02622i −0.254133 + 0.254133i −0.822663 0.568530i \(-0.807512\pi\)
0.568530 + 0.822663i \(0.307512\pi\)
\(252\) 0 0
\(253\) −27.8682 + 27.8682i −1.75206 + 1.75206i
\(254\) 9.54246 + 3.87751i 0.598747 + 0.243297i
\(255\) 0 0
\(256\) −15.9768 + 0.861887i −0.998548 + 0.0538680i
\(257\) −29.1773 −1.82003 −0.910016 0.414573i \(-0.863931\pi\)
−0.910016 + 0.414573i \(0.863931\pi\)
\(258\) 0 0
\(259\) −8.22585 + 8.22585i −0.511130 + 0.511130i
\(260\) 9.12264 + 9.73362i 0.565762 + 0.603654i
\(261\) 0 0
\(262\) −7.69800 18.2362i −0.475584 1.12663i
\(263\) 1.92706 0.118828 0.0594139 0.998233i \(-0.481077\pi\)
0.0594139 + 0.998233i \(0.481077\pi\)
\(264\) 0 0
\(265\) 19.2166 + 0.881973i 1.18047 + 0.0541792i
\(266\) 3.19917 + 7.57867i 0.196154 + 0.464678i
\(267\) 0 0
\(268\) −0.0116379 0.863706i −0.000710895 0.0527592i
\(269\) −9.93701 + 9.93701i −0.605870 + 0.605870i −0.941864 0.335994i \(-0.890928\pi\)
0.335994 + 0.941864i \(0.390928\pi\)
\(270\) 0 0
\(271\) 15.0777i 0.915907i −0.888976 0.457954i \(-0.848583\pi\)
0.888976 0.457954i \(-0.151417\pi\)
\(272\) −0.387066 14.3605i −0.0234693 0.870731i
\(273\) 0 0
\(274\) −9.47504 + 23.3178i −0.572408 + 1.40868i
\(275\) −19.2887 23.1968i −1.16315 1.39882i
\(276\) 0 0
\(277\) −4.33837 4.33837i −0.260667 0.260667i 0.564658 0.825325i \(-0.309008\pi\)
−0.825325 + 0.564658i \(0.809008\pi\)
\(278\) −3.87551 9.18089i −0.232438 0.550633i
\(279\) 0 0
\(280\) 24.8936 + 11.0677i 1.48768 + 0.661420i
\(281\) −2.93138 −0.174871 −0.0874357 0.996170i \(-0.527867\pi\)
−0.0874357 + 0.996170i \(0.527867\pi\)
\(282\) 0 0
\(283\) −12.3064 + 12.3064i −0.731542 + 0.731542i −0.970925 0.239383i \(-0.923055\pi\)
0.239383 + 0.970925i \(0.423055\pi\)
\(284\) 2.25727 2.31893i 0.133944 0.137603i
\(285\) 0 0
\(286\) −9.58215 + 23.5814i −0.566604 + 1.39440i
\(287\) 33.0411i 1.95036i
\(288\) 0 0
\(289\) −4.10170 −0.241276
\(290\) 7.50815 + 3.46001i 0.440894 + 0.203179i
\(291\) 0 0
\(292\) −9.89863 9.63543i −0.579274 0.563871i
\(293\) 15.2191 15.2191i 0.889109 0.889109i −0.105328 0.994437i \(-0.533589\pi\)
0.994437 + 0.105328i \(0.0335894\pi\)
\(294\) 0 0
\(295\) 9.40886 + 0.431832i 0.547805 + 0.0251422i
\(296\) −2.77996 + 7.11479i −0.161582 + 0.413539i
\(297\) 0 0
\(298\) −7.60832 18.0237i −0.440738 1.04409i
\(299\) −13.7777 + 13.7777i −0.796786 + 0.796786i
\(300\) 0 0
\(301\) 23.4031 + 23.4031i 1.34893 + 1.34893i
\(302\) 15.7363 + 6.39432i 0.905520 + 0.367952i
\(303\) 0 0
\(304\) 3.92100 + 3.71518i 0.224885 + 0.213080i
\(305\) −0.0227655 + 0.496019i −0.00130355 + 0.0284020i
\(306\) 0 0
\(307\) 3.79402 + 3.79402i 0.216536 + 0.216536i 0.807037 0.590501i \(-0.201070\pi\)
−0.590501 + 0.807037i \(0.701070\pi\)
\(308\) 0.700342 + 51.9760i 0.0399057 + 2.96161i
\(309\) 0 0
\(310\) −22.6751 + 8.36895i −1.28786 + 0.475325i
\(311\) 18.1916i 1.03155i 0.856724 + 0.515775i \(0.172496\pi\)
−0.856724 + 0.515775i \(0.827504\pi\)
\(312\) 0 0
\(313\) 16.7785 0.948377 0.474188 0.880423i \(-0.342742\pi\)
0.474188 + 0.880423i \(0.342742\pi\)
\(314\) 16.2416 6.85603i 0.916565 0.386908i
\(315\) 0 0
\(316\) 7.52349 7.72901i 0.423229 0.434791i
\(317\) −0.103425 0.103425i −0.00580894 0.00580894i 0.704196 0.710005i \(-0.251307\pi\)
−0.710005 + 0.704196i \(0.751307\pi\)
\(318\) 0 0
\(319\) 15.7738i 0.883163i
\(320\) 17.8883 + 0.0973777i 0.999985 + 0.00544358i
\(321\) 0 0
\(322\) −14.9792 + 36.8634i −0.834758 + 2.05432i
\(323\) −3.42934 + 3.42934i −0.190814 + 0.190814i
\(324\) 0 0
\(325\) −9.53611 11.4682i −0.528968 0.636143i
\(326\) 6.92240 + 16.3988i 0.383396 + 0.908246i
\(327\) 0 0
\(328\) −8.70595 19.8723i −0.480706 1.09726i
\(329\) 13.9936 0.771490
\(330\) 0 0
\(331\) 2.18428 + 2.18428i 0.120059 + 0.120059i 0.764583 0.644525i \(-0.222945\pi\)
−0.644525 + 0.764583i \(0.722945\pi\)
\(332\) −16.4659 + 0.221867i −0.903683 + 0.0121765i
\(333\) 0 0
\(334\) −5.55917 2.25893i −0.304184 0.123603i
\(335\) −0.0442773 + 0.964725i −0.00241913 + 0.0527085i
\(336\) 0 0
\(337\) 20.9206i 1.13962i 0.821778 + 0.569808i \(0.192982\pi\)
−0.821778 + 0.569808i \(0.807018\pi\)
\(338\) 2.18367 5.37396i 0.118776 0.292305i
\(339\) 0 0
\(340\) −0.520145 + 16.0529i −0.0282088 + 0.870591i
\(341\) −32.6100 32.6100i −1.76593 1.76593i
\(342\) 0 0
\(343\) 19.6193i 1.05934i
\(344\) 20.2420 + 7.90915i 1.09138 + 0.426433i
\(345\) 0 0
\(346\) 3.13581 + 7.42857i 0.168582 + 0.399362i
\(347\) 4.34853 + 4.34853i 0.233441 + 0.233441i 0.814127 0.580686i \(-0.197216\pi\)
−0.580686 + 0.814127i \(0.697216\pi\)
\(348\) 0 0
\(349\) 3.70979 + 3.70979i 0.198580 + 0.198580i 0.799391 0.600811i \(-0.205155\pi\)
−0.600811 + 0.799391i \(0.705155\pi\)
\(350\) −27.0491 14.0028i −1.44584 0.748480i
\(351\) 0 0
\(352\) 14.1163 + 31.0760i 0.752401 + 1.65636i
\(353\) 16.3398 0.869681 0.434840 0.900508i \(-0.356805\pi\)
0.434840 + 0.900508i \(0.356805\pi\)
\(354\) 0 0
\(355\) −2.67301 + 2.43842i −0.141869 + 0.129418i
\(356\) −11.1051 10.8098i −0.588568 0.572917i
\(357\) 0 0
\(358\) −0.648590 1.53648i −0.0342790 0.0812053i
\(359\) 24.6929i 1.30324i −0.758545 0.651621i \(-0.774089\pi\)
0.758545 0.651621i \(-0.225911\pi\)
\(360\) 0 0
\(361\) 17.1764i 0.904024i
\(362\) 19.5215 8.24056i 1.02603 0.433114i
\(363\) 0 0
\(364\) 0.346241 + 25.6963i 0.0181479 + 1.34685i
\(365\) 10.4087 + 11.4101i 0.544815 + 0.597231i
\(366\) 0 0
\(367\) 6.68177 0.348786 0.174393 0.984676i \(-0.444204\pi\)
0.174393 + 0.984676i \(0.444204\pi\)
\(368\) 0.703974 + 26.1180i 0.0366972 + 1.36150i
\(369\) 0 0
\(370\) 3.57434 7.75626i 0.185821 0.403229i
\(371\) 26.2036 + 26.2036i 1.36042 + 1.36042i
\(372\) 0 0
\(373\) 18.9638 + 18.9638i 0.981911 + 0.981911i 0.999839 0.0179284i \(-0.00570709\pi\)
−0.0179284 + 0.999839i \(0.505707\pi\)
\(374\) −28.2331 + 11.9180i −1.45990 + 0.616265i
\(375\) 0 0
\(376\) 8.41631 3.68714i 0.434038 0.190150i
\(377\) 7.79837i 0.401636i
\(378\) 0 0
\(379\) −17.4207 17.4207i −0.894843 0.894843i 0.100131 0.994974i \(-0.468074\pi\)
−0.994974 + 0.100131i \(0.968074\pi\)
\(380\) −4.12977 4.40636i −0.211853 0.226042i
\(381\) 0 0
\(382\) −5.02006 2.03986i −0.256849 0.104369i
\(383\) 10.4542i 0.534182i −0.963671 0.267091i \(-0.913938\pi\)
0.963671 0.267091i \(-0.0860625\pi\)
\(384\) 0 0
\(385\) 2.66452 58.0551i 0.135796 2.95876i
\(386\) −2.67933 + 6.59376i −0.136374 + 0.335614i
\(387\) 0 0
\(388\) 13.0316 13.3875i 0.661577 0.679649i
\(389\) −6.71454 6.71454i −0.340441 0.340441i 0.516092 0.856533i \(-0.327386\pi\)
−0.856533 + 0.516092i \(0.827386\pi\)
\(390\) 0 0
\(391\) −23.4587 −1.18636
\(392\) 13.1143 + 29.9349i 0.662373 + 1.51194i
\(393\) 0 0
\(394\) −12.9303 + 5.45826i −0.651421 + 0.274983i
\(395\) −8.90917 + 8.12726i −0.448269 + 0.408927i
\(396\) 0 0
\(397\) 25.8345 25.8345i 1.29660 1.29660i 0.365968 0.930628i \(-0.380738\pi\)
0.930628 0.365968i \(-0.119262\pi\)
\(398\) −18.0205 7.32248i −0.903284 0.367043i
\(399\) 0 0
\(400\) −19.9580 1.29472i −0.997902 0.0647360i
\(401\) 18.5375i 0.925717i 0.886432 + 0.462858i \(0.153176\pi\)
−0.886432 + 0.462858i \(0.846824\pi\)
\(402\) 0 0
\(403\) −16.1220 16.1220i −0.803094 0.803094i
\(404\) −0.301500 22.3759i −0.0150002 1.11324i
\(405\) 0 0
\(406\) 6.19339 + 14.6718i 0.307373 + 0.728150i
\(407\) 16.2950 0.807715
\(408\) 0 0
\(409\) 6.45252i 0.319057i 0.987193 + 0.159528i \(0.0509973\pi\)
−0.987193 + 0.159528i \(0.949003\pi\)
\(410\) 8.39883 + 22.7560i 0.414789 + 1.12384i
\(411\) 0 0
\(412\) −22.5638 + 23.1801i −1.11164 + 1.14200i
\(413\) 12.8298 + 12.8298i 0.631315 + 0.631315i
\(414\) 0 0
\(415\) 18.3917 + 0.844113i 0.902815 + 0.0414359i
\(416\) 6.97892 + 15.3636i 0.342170 + 0.753263i
\(417\) 0 0
\(418\) 4.33779 10.6752i 0.212168 0.522141i
\(419\) −12.0000 12.0000i −0.586236 0.586236i 0.350374 0.936610i \(-0.386055\pi\)
−0.936610 + 0.350374i \(0.886055\pi\)
\(420\) 0 0
\(421\) 23.9012 23.9012i 1.16487 1.16487i 0.181478 0.983395i \(-0.441912\pi\)
0.983395 0.181478i \(-0.0580882\pi\)
\(422\) −23.5848 + 9.95582i −1.14809 + 0.484642i
\(423\) 0 0
\(424\) 22.6643 + 8.85560i 1.10067 + 0.430066i
\(425\) 1.64487 17.8816i 0.0797877 0.867386i
\(426\) 0 0
\(427\) −0.676366 + 0.676366i −0.0327317 + 0.0327317i
\(428\) 0.200676 + 14.8932i 0.00970005 + 0.719891i
\(429\) 0 0
\(430\) −22.0670 10.1692i −1.06417 0.490404i
\(431\) 12.5590 0.604944 0.302472 0.953158i \(-0.402188\pi\)
0.302472 + 0.953158i \(0.402188\pi\)
\(432\) 0 0
\(433\) 4.64837i 0.223386i 0.993743 + 0.111693i \(0.0356274\pi\)
−0.993743 + 0.111693i \(0.964373\pi\)
\(434\) −43.1358 17.5279i −2.07058 0.841367i
\(435\) 0 0
\(436\) −0.455134 33.7778i −0.0217970 1.61767i
\(437\) 6.23710 6.23710i 0.298361 0.298361i
\(438\) 0 0
\(439\) 7.09686 0.338715 0.169357 0.985555i \(-0.445831\pi\)
0.169357 + 0.985555i \(0.445831\pi\)
\(440\) −13.6943 35.6188i −0.652850 1.69806i
\(441\) 0 0
\(442\) −13.9581 + 5.89212i −0.663920 + 0.280259i
\(443\) −16.7044 16.7044i −0.793649 0.793649i 0.188436 0.982085i \(-0.439658\pi\)
−0.982085 + 0.188436i \(0.939658\pi\)
\(444\) 0 0
\(445\) 11.6773 + 12.8007i 0.553556 + 0.606813i
\(446\) −16.6445 6.76338i −0.788141 0.320255i
\(447\) 0 0
\(448\) 25.3317 + 23.3624i 1.19681 + 1.10377i
\(449\) 22.3540i 1.05495i 0.849571 + 0.527475i \(0.176861\pi\)
−0.849571 + 0.527475i \(0.823139\pi\)
\(450\) 0 0
\(451\) −32.7265 + 32.7265i −1.54103 + 1.54103i
\(452\) −25.9234 25.2341i −1.21934 1.18691i
\(453\) 0 0
\(454\) 24.5872 10.3790i 1.15393 0.487109i
\(455\) 1.31731 28.7018i 0.0617562 1.34556i
\(456\) 0 0
\(457\) −28.9883 −1.35602 −0.678008 0.735055i \(-0.737156\pi\)
−0.678008 + 0.735055i \(0.737156\pi\)
\(458\) 2.01856 0.852093i 0.0943213 0.0398157i
\(459\) 0 0
\(460\) 0.946013 29.1961i 0.0441081 1.36128i
\(461\) −3.75610 + 3.75610i −0.174939 + 0.174939i −0.789146 0.614206i \(-0.789476\pi\)
0.614206 + 0.789146i \(0.289476\pi\)
\(462\) 0 0
\(463\) −18.4896 −0.859286 −0.429643 0.902999i \(-0.641361\pi\)
−0.429643 + 0.902999i \(0.641361\pi\)
\(464\) 7.59081 + 7.19235i 0.352395 + 0.333897i
\(465\) 0 0
\(466\) −9.11203 + 22.4245i −0.422107 + 1.03879i
\(467\) −17.8623 + 17.8623i −0.826570 + 0.826570i −0.987041 0.160471i \(-0.948699\pi\)
0.160471 + 0.987041i \(0.448699\pi\)
\(468\) 0 0
\(469\) −1.31549 + 1.31549i −0.0607436 + 0.0607436i
\(470\) −9.63763 + 3.55707i −0.444551 + 0.164075i
\(471\) 0 0
\(472\) 11.0969 + 4.33588i 0.510776 + 0.199575i
\(473\) 46.3604i 2.13165i
\(474\) 0 0
\(475\) 4.31695 + 5.19161i 0.198075 + 0.238207i
\(476\) −21.5813 + 22.1708i −0.989176 + 1.01620i
\(477\) 0 0
\(478\) 23.3939 + 9.50594i 1.07001 + 0.434792i
\(479\) 21.2617 0.971474 0.485737 0.874105i \(-0.338551\pi\)
0.485737 + 0.874105i \(0.338551\pi\)
\(480\) 0 0
\(481\) 8.05606 0.367325
\(482\) −6.70190 2.72327i −0.305263 0.124041i
\(483\) 0 0
\(484\) 35.4420 36.4102i 1.61100 1.65501i
\(485\) −15.4317 + 14.0773i −0.700718 + 0.639219i
\(486\) 0 0
\(487\) 38.2041i 1.73119i 0.500744 + 0.865595i \(0.333060\pi\)
−0.500744 + 0.865595i \(0.666940\pi\)
\(488\) −0.228580 + 0.585010i −0.0103473 + 0.0264821i
\(489\) 0 0
\(490\) −12.6517 34.2789i −0.571545 1.54856i
\(491\) −11.2555 + 11.2555i −0.507953 + 0.507953i −0.913898 0.405945i \(-0.866943\pi\)
0.405945 + 0.913898i \(0.366943\pi\)
\(492\) 0 0
\(493\) −6.63898 + 6.63898i −0.299005 + 0.299005i
\(494\) 2.14455 5.27769i 0.0964879 0.237454i
\(495\) 0 0
\(496\) −30.5621 + 0.823756i −1.37228 + 0.0369877i
\(497\) −6.96989 −0.312642
\(498\) 0 0
\(499\) 19.2924 19.2924i 0.863646 0.863646i −0.128114 0.991759i \(-0.540892\pi\)
0.991759 + 0.128114i \(0.0408923\pi\)
\(500\) 22.1887 + 2.76826i 0.992307 + 0.123800i
\(501\) 0 0
\(502\) 7.41856 3.13159i 0.331107 0.139770i
\(503\) −27.8587 −1.24216 −0.621078 0.783748i \(-0.713305\pi\)
−0.621078 + 0.783748i \(0.713305\pi\)
\(504\) 0 0
\(505\) −1.14708 + 24.9929i −0.0510445 + 1.11217i
\(506\) 51.3489 21.6758i 2.28274 0.963608i
\(507\) 0 0
\(508\) −10.4380 10.1605i −0.463112 0.450798i
\(509\) 0.475925 0.475925i 0.0210950 0.0210950i −0.696481 0.717576i \(-0.745252\pi\)
0.717576 + 0.696481i \(0.245252\pi\)
\(510\) 0 0
\(511\) 29.7518i 1.31614i
\(512\) 21.3913 + 7.37652i 0.945370 + 0.325999i
\(513\) 0 0
\(514\) 38.2275 + 15.5335i 1.68614 + 0.685153i
\(515\) 26.7196 24.3745i 1.17740 1.07407i
\(516\) 0 0
\(517\) −13.8603 13.8603i −0.609575 0.609575i
\(518\) 15.1566 6.39805i 0.665945 0.281114i
\(519\) 0 0
\(520\) −6.77029 17.6095i −0.296897 0.772229i
\(521\) −28.2023 −1.23557 −0.617783 0.786348i \(-0.711969\pi\)
−0.617783 + 0.786348i \(0.711969\pi\)
\(522\) 0 0
\(523\) 10.5066 10.5066i 0.459420 0.459420i −0.439045 0.898465i \(-0.644683\pi\)
0.898465 + 0.439045i \(0.144683\pi\)
\(524\) 0.377159 + 27.9909i 0.0164763 + 1.22279i
\(525\) 0 0
\(526\) −2.52480 1.02593i −0.110086 0.0447328i
\(527\) 27.4503i 1.19575i
\(528\) 0 0
\(529\) 19.6655 0.855022
\(530\) −24.7077 11.3861i −1.07323 0.494582i
\(531\) 0 0
\(532\) −0.156741 11.6326i −0.00679560 0.504337i
\(533\) −16.1796 + 16.1796i −0.700815 + 0.700815i
\(534\) 0 0
\(535\) 0.763491 16.6351i 0.0330086 0.719199i
\(536\) −0.444574 + 1.13781i −0.0192027 + 0.0491457i
\(537\) 0 0
\(538\) 18.3095 7.72898i 0.789380 0.333220i
\(539\) 49.2979 49.2979i 2.12341 2.12341i
\(540\) 0 0
\(541\) −12.4368 12.4368i −0.534698 0.534698i 0.387269 0.921967i \(-0.373419\pi\)
−0.921967 + 0.387269i \(0.873419\pi\)
\(542\) −8.02711 + 19.7545i −0.344794 + 0.848530i
\(543\) 0 0
\(544\) −7.13813 + 19.0209i −0.306045 + 0.815512i
\(545\) −1.73160 + 37.7285i −0.0741736 + 1.61611i
\(546\) 0 0
\(547\) 5.78283 + 5.78283i 0.247256 + 0.247256i 0.819844 0.572588i \(-0.194060\pi\)
−0.572588 + 0.819844i \(0.694060\pi\)
\(548\) 24.8280 25.5062i 1.06060 1.08957i
\(549\) 0 0
\(550\) 12.9221 + 40.6610i 0.551001 + 1.73379i
\(551\) 3.53028i 0.150395i
\(552\) 0 0
\(553\) −23.2307 −0.987870
\(554\) 3.37437 + 7.99371i 0.143363 + 0.339620i
\(555\) 0 0
\(556\) 0.189878 + 14.0919i 0.00805264 + 0.597628i
\(557\) 12.9551 + 12.9551i 0.548924 + 0.548924i 0.926130 0.377205i \(-0.123115\pi\)
−0.377205 + 0.926130i \(0.623115\pi\)
\(558\) 0 0
\(559\) 22.9200i 0.969413i
\(560\) −26.7229 27.7536i −1.12925 1.17280i
\(561\) 0 0
\(562\) 3.84063 + 1.56061i 0.162007 + 0.0658305i
\(563\) −14.1388 + 14.1388i −0.595881 + 0.595881i −0.939214 0.343333i \(-0.888444\pi\)
0.343333 + 0.939214i \(0.388444\pi\)
\(564\) 0 0
\(565\) 27.2592 + 29.8817i 1.14680 + 1.25713i
\(566\) 22.6754 9.57192i 0.953117 0.402338i
\(567\) 0 0
\(568\) −4.19198 + 1.83648i −0.175892 + 0.0770572i
\(569\) 1.34936 0.0565679 0.0282840 0.999600i \(-0.490996\pi\)
0.0282840 + 0.999600i \(0.490996\pi\)
\(570\) 0 0
\(571\) −32.6417 32.6417i −1.36601 1.36601i −0.866045 0.499967i \(-0.833346\pi\)
−0.499967 0.866045i \(-0.666654\pi\)
\(572\) 25.1087 25.7945i 1.04985 1.07852i
\(573\) 0 0
\(574\) −17.5905 + 43.2898i −0.734213 + 1.80688i
\(575\) −2.99159 + 32.5221i −0.124758 + 1.35627i
\(576\) 0 0
\(577\) 40.3389i 1.67933i 0.543104 + 0.839665i \(0.317249\pi\)
−0.543104 + 0.839665i \(0.682751\pi\)
\(578\) 5.37396 + 2.18367i 0.223527 + 0.0908286i
\(579\) 0 0
\(580\) −7.99498 8.53043i −0.331973 0.354207i
\(581\) 25.0788 + 25.0788i 1.04044 + 1.04044i
\(582\) 0 0
\(583\) 51.9081i 2.14981i
\(584\) 7.83926 + 17.8940i 0.324391 + 0.740459i
\(585\) 0 0
\(586\) −28.0421 + 11.8374i −1.15841 + 0.488997i
\(587\) 9.96452 + 9.96452i 0.411280 + 0.411280i 0.882184 0.470905i \(-0.156072\pi\)
−0.470905 + 0.882184i \(0.656072\pi\)
\(588\) 0 0
\(589\) 7.29835 + 7.29835i 0.300723 + 0.300723i
\(590\) −12.0974 5.57489i −0.498042 0.229514i
\(591\) 0 0
\(592\) 7.43002 7.84165i 0.305372 0.322290i
\(593\) −19.4892 −0.800324 −0.400162 0.916444i \(-0.631046\pi\)
−0.400162 + 0.916444i \(0.631046\pi\)
\(594\) 0 0
\(595\) 25.5561 23.3132i 1.04770 0.955748i
\(596\) 0.372765 + 27.6648i 0.0152690 + 1.13320i
\(597\) 0 0
\(598\) 25.3863 10.7163i 1.03812 0.438221i
\(599\) 16.4963i 0.674020i −0.941501 0.337010i \(-0.890584\pi\)
0.941501 0.337010i \(-0.109416\pi\)
\(600\) 0 0
\(601\) 8.09948i 0.330385i −0.986261 0.165192i \(-0.947176\pi\)
0.986261 0.165192i \(-0.0528245\pi\)
\(602\) −18.2029 43.1216i −0.741893 1.75751i
\(603\) 0 0
\(604\) −17.2131 16.7554i −0.700391 0.681768i
\(605\) −41.9697 + 38.2863i −1.70631 + 1.55656i
\(606\) 0 0
\(607\) 0.975144 0.0395799 0.0197899 0.999804i \(-0.493700\pi\)
0.0197899 + 0.999804i \(0.493700\pi\)
\(608\) −3.15932 6.95503i −0.128127 0.282064i
\(609\) 0 0
\(610\) 0.293898 0.637754i 0.0118996 0.0258219i
\(611\) −6.85236 6.85236i −0.277217 0.277217i
\(612\) 0 0
\(613\) 7.41162 + 7.41162i 0.299353 + 0.299353i 0.840760 0.541408i \(-0.182108\pi\)
−0.541408 + 0.840760i \(0.682108\pi\)
\(614\) −2.95098 6.99072i −0.119092 0.282122i
\(615\) 0 0
\(616\) 26.7535 68.4708i 1.07793 2.75877i
\(617\) 15.5875i 0.627531i 0.949501 + 0.313765i \(0.101591\pi\)
−0.949501 + 0.313765i \(0.898409\pi\)
\(618\) 0 0
\(619\) −3.34655 3.34655i −0.134509 0.134509i 0.636647 0.771156i \(-0.280321\pi\)
−0.771156 + 0.636647i \(0.780321\pi\)
\(620\) 34.1639 + 1.10698i 1.37206 + 0.0444573i
\(621\) 0 0
\(622\) 9.68486 23.8342i 0.388328 0.955665i
\(623\) 33.3780i 1.33726i
\(624\) 0 0
\(625\) −24.5805 4.56073i −0.983219 0.182429i
\(626\) −21.9828 8.93257i −0.878611 0.357017i
\(627\) 0 0
\(628\) −24.9294 + 0.335907i −0.994791 + 0.0134041i
\(629\) 6.85837 + 6.85837i 0.273461 + 0.273461i
\(630\) 0 0
\(631\) −17.5464 −0.698510 −0.349255 0.937028i \(-0.613565\pi\)
−0.349255 + 0.937028i \(0.613565\pi\)
\(632\) −13.9719 + 6.12102i −0.555773 + 0.243481i
\(633\) 0 0
\(634\) 0.0804439 + 0.190567i 0.00319483 + 0.00756840i
\(635\) 10.9759 + 12.0318i 0.435564 + 0.477468i
\(636\) 0 0
\(637\) 24.3723 24.3723i 0.965666 0.965666i
\(638\) 8.39768 20.6665i 0.332467 0.818194i
\(639\) 0 0
\(640\) −23.3850 9.65098i −0.924374 0.381488i
\(641\) 30.7369i 1.21403i −0.794689 0.607016i \(-0.792366\pi\)
0.794689 0.607016i \(-0.207634\pi\)
\(642\) 0 0
\(643\) 2.00487 + 2.00487i 0.0790643 + 0.0790643i 0.745533 0.666469i \(-0.232195\pi\)
−0.666469 + 0.745533i \(0.732195\pi\)
\(644\) 39.2509 40.3231i 1.54670 1.58895i
\(645\) 0 0
\(646\) 6.31877 2.66733i 0.248609 0.104945i
\(647\) 41.0262 1.61291 0.806453 0.591298i \(-0.201384\pi\)
0.806453 + 0.591298i \(0.201384\pi\)
\(648\) 0 0
\(649\) 25.4153i 0.997637i
\(650\) 6.38854 + 20.1023i 0.250579 + 0.788476i
\(651\) 0 0
\(652\) −0.339159 25.1707i −0.0132825 0.985762i
\(653\) −10.2034 10.2034i −0.399291 0.399291i 0.478692 0.877983i \(-0.341111\pi\)
−0.877983 + 0.478692i \(0.841111\pi\)
\(654\) 0 0
\(655\) 1.43494 31.2647i 0.0560676 1.22161i
\(656\) 0.826697 + 30.6712i 0.0322771 + 1.19751i
\(657\) 0 0
\(658\) −18.3341 7.44992i −0.714737 0.290428i
\(659\) −14.6544 14.6544i −0.570853 0.570853i 0.361514 0.932367i \(-0.382260\pi\)
−0.932367 + 0.361514i \(0.882260\pi\)
\(660\) 0 0
\(661\) 31.9191 31.9191i 1.24151 1.24151i 0.282131 0.959376i \(-0.408959\pi\)
0.959376 0.282131i \(-0.0910414\pi\)
\(662\) −1.69892 4.02466i −0.0660306 0.156423i
\(663\) 0 0
\(664\) 21.6914 + 8.47546i 0.841789 + 0.328912i
\(665\) −0.596337 + 12.9931i −0.0231250 + 0.503852i
\(666\) 0 0
\(667\) 12.0746 12.0746i 0.467531 0.467531i
\(668\) 6.08089 + 5.91920i 0.235277 + 0.229021i
\(669\) 0 0
\(670\) 0.571613 1.24039i 0.0220833 0.0479204i
\(671\) 1.33985 0.0517243
\(672\) 0 0
\(673\) 3.74068i 0.144193i −0.997398 0.0720963i \(-0.977031\pi\)
0.997398 0.0720963i \(-0.0229689\pi\)
\(674\) 11.1377 27.4097i 0.429009 1.05578i
\(675\) 0 0
\(676\) −5.72199 + 5.87830i −0.220077 + 0.226088i
\(677\) −14.8520 + 14.8520i −0.570808 + 0.570808i −0.932354 0.361546i \(-0.882249\pi\)
0.361546 + 0.932354i \(0.382249\pi\)
\(678\) 0 0
\(679\) −40.2382 −1.54420
\(680\) 9.22776 20.7553i 0.353868 0.795928i
\(681\) 0 0
\(682\) 25.3640 + 60.0860i 0.971237 + 2.30081i
\(683\) 0.704118 + 0.704118i 0.0269423 + 0.0269423i 0.720450 0.693507i \(-0.243935\pi\)
−0.693507 + 0.720450i \(0.743935\pi\)
\(684\) 0 0
\(685\) −29.4008 + 26.8205i −1.12335 + 1.02476i
\(686\) 10.4450 25.7049i 0.398791 0.981416i
\(687\) 0 0
\(688\) −22.3100 21.1389i −0.850560 0.805913i
\(689\) 25.6627i 0.977672i
\(690\) 0 0
\(691\) −27.9600 + 27.9600i −1.06365 + 1.06365i −0.0658160 + 0.997832i \(0.520965\pi\)
−0.997832 + 0.0658160i \(0.979035\pi\)
\(692\) −0.153637 11.4022i −0.00584040 0.433447i
\(693\) 0 0
\(694\) −3.38227 8.01243i −0.128389 0.304148i
\(695\) 0.722410 15.7400i 0.0274026 0.597054i
\(696\) 0 0
\(697\) −27.5483 −1.04347
\(698\) −2.88546 6.83551i −0.109216 0.258728i
\(699\) 0 0
\(700\) 27.9844 + 32.7466i 1.05771 + 1.23771i
\(701\) 3.89364 3.89364i 0.147061 0.147061i −0.629743 0.776804i \(-0.716840\pi\)
0.776804 + 0.629743i \(0.216840\pi\)
\(702\) 0 0
\(703\) −3.64694 −0.137547
\(704\) −1.95056 48.2304i −0.0735146 1.81775i
\(705\) 0 0
\(706\) −21.4081 8.69902i −0.805704 0.327392i
\(707\) −34.0801 + 34.0801i −1.28171 + 1.28171i
\(708\) 0 0
\(709\) −24.4875 + 24.4875i −0.919648 + 0.919648i −0.997004 0.0773555i \(-0.975352\pi\)
0.0773555 + 0.997004i \(0.475352\pi\)
\(710\) 4.80029 1.77170i 0.180152 0.0664907i
\(711\) 0 0
\(712\) 8.79470 + 20.0749i 0.329595 + 0.752338i
\(713\) 49.9251i 1.86971i
\(714\) 0 0
\(715\) −29.7332 + 27.1236i −1.11196 + 1.01437i
\(716\) 0.0317773 + 2.35836i 0.00118757 + 0.0881359i
\(717\) 0 0
\(718\) −13.1461 + 32.3521i −0.490606 + 1.20737i
\(719\) 16.1711 0.603079 0.301540 0.953454i \(-0.402499\pi\)
0.301540 + 0.953454i \(0.402499\pi\)
\(720\) 0 0
\(721\) 69.6714 2.59470
\(722\) 9.14443 22.5042i 0.340320 0.837520i
\(723\) 0 0
\(724\) −29.9637 + 0.403741i −1.11359 + 0.0150049i
\(725\) 8.35734 + 10.0506i 0.310384 + 0.373271i
\(726\) 0 0
\(727\) 37.5868i 1.39402i −0.717063 0.697008i \(-0.754514\pi\)
0.717063 0.697008i \(-0.245486\pi\)
\(728\) 13.2266 33.8511i 0.490211 1.25461i
\(729\) 0 0
\(730\) −7.56271 20.4906i −0.279909 0.758393i
\(731\) 19.5125 19.5125i 0.721695 0.721695i
\(732\) 0 0
\(733\) −10.5565 + 10.5565i −0.389913 + 0.389913i −0.874656 0.484744i \(-0.838913\pi\)
0.484744 + 0.874656i \(0.338913\pi\)
\(734\) −8.75432 3.55726i −0.323128 0.131301i
\(735\) 0 0
\(736\) 12.9824 34.5941i 0.478539 1.27516i
\(737\) 2.60592 0.0959903
\(738\) 0 0
\(739\) −5.50334 + 5.50334i −0.202444 + 0.202444i −0.801046 0.598603i \(-0.795723\pi\)
0.598603 + 0.801046i \(0.295723\pi\)
\(740\) −8.81232 + 8.25917i −0.323947 + 0.303613i
\(741\) 0 0
\(742\) −20.3811 48.2817i −0.748214 1.77248i
\(743\) 5.53668 0.203121 0.101561 0.994829i \(-0.467616\pi\)
0.101561 + 0.994829i \(0.467616\pi\)
\(744\) 0 0
\(745\) 1.41822 30.9005i 0.0519595 1.13211i
\(746\) −14.7500 34.9421i −0.540037 1.27932i
\(747\) 0 0
\(748\) 43.3354 0.583915i 1.58450 0.0213501i
\(749\) 22.6835 22.6835i 0.828837 0.828837i
\(750\) 0 0
\(751\) 30.2295i 1.10309i −0.834145 0.551546i \(-0.814038\pi\)
0.834145 0.551546i \(-0.185962\pi\)
\(752\) −12.9898 + 0.350123i −0.473691 + 0.0127677i
\(753\) 0 0
\(754\) 4.15171 10.2173i 0.151196 0.372091i
\(755\) 18.1000 + 19.8414i 0.658728 + 0.722103i
\(756\) 0 0
\(757\) −25.8317 25.8317i −0.938870 0.938870i 0.0593667 0.998236i \(-0.481092\pi\)
−0.998236 + 0.0593667i \(0.981092\pi\)
\(758\) 13.5498 + 32.0988i 0.492151 + 1.16588i
\(759\) 0 0
\(760\) 3.06488 + 7.97174i 0.111175 + 0.289165i
\(761\) 6.93351 0.251340 0.125670 0.992072i \(-0.459892\pi\)
0.125670 + 0.992072i \(0.459892\pi\)
\(762\) 0 0
\(763\) −51.4462 + 51.4462i −1.86248 + 1.86248i
\(764\) 5.49119 + 5.34518i 0.198664 + 0.193382i
\(765\) 0 0
\(766\) −5.56560 + 13.6968i −0.201093 + 0.494886i
\(767\) 12.5650i 0.453696i
\(768\) 0 0
\(769\) 18.4481 0.665257 0.332629 0.943058i \(-0.392064\pi\)
0.332629 + 0.943058i \(0.392064\pi\)
\(770\) −34.3985 + 74.6441i −1.23964 + 2.68999i
\(771\) 0 0
\(772\) 7.02080 7.21259i 0.252684 0.259587i
\(773\) 8.74138 8.74138i 0.314405 0.314405i −0.532208 0.846614i \(-0.678638\pi\)
0.846614 + 0.532208i \(0.178638\pi\)
\(774\) 0 0
\(775\) −38.0558 3.50062i −1.36700 0.125746i
\(776\) −24.2010 + 10.6023i −0.868763 + 0.380601i
\(777\) 0 0
\(778\) 5.22255 + 12.3719i 0.187237 + 0.443556i
\(779\) 7.32440 7.32440i 0.262424 0.262424i
\(780\) 0 0
\(781\) 6.90351 + 6.90351i 0.247027 + 0.247027i
\(782\) 30.7352 + 12.4890i 1.09909 + 0.446606i
\(783\) 0 0
\(784\) −1.24531 46.2019i −0.0444752 1.65007i
\(785\) 27.8451 + 1.27799i 0.993836 + 0.0456134i
\(786\) 0 0
\(787\) 16.3355 + 16.3355i 0.582299 + 0.582299i 0.935534 0.353235i \(-0.114919\pi\)
−0.353235 + 0.935534i \(0.614919\pi\)
\(788\) 19.8469 0.267424i 0.707018 0.00952659i
\(789\) 0 0
\(790\) 15.9994 5.90509i 0.569234 0.210094i
\(791\) 77.9168i 2.77040i