Properties

Label 720.2.u.a.179.6
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 179.6
Character \(\chi\) \(=\) 720.179
Dual form 720.2.u.a.539.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.31018 - 0.532382i) q^{2} +(1.43314 + 1.39503i) q^{4} +(1.65197 + 1.50698i) q^{5} +4.30751i q^{7} +(-1.13498 - 2.59072i) q^{8} +O(q^{10})\) \(q+(-1.31018 - 0.532382i) q^{2} +(1.43314 + 1.39503i) q^{4} +(1.65197 + 1.50698i) q^{5} +4.30751i q^{7} +(-1.13498 - 2.59072i) q^{8} +(-1.36208 - 2.85390i) q^{10} +(4.26649 - 4.26649i) q^{11} +(2.10930 - 2.10930i) q^{13} +(2.29324 - 5.64362i) q^{14} +(0.107775 + 3.99855i) q^{16} -3.59142 q^{17} +(0.954870 - 0.954870i) q^{19} +(0.265210 + 4.46427i) q^{20} +(-7.86127 + 3.31847i) q^{22} +6.53188 q^{23} +(0.457999 + 4.97898i) q^{25} +(-3.88652 + 1.64061i) q^{26} +(-6.00912 + 6.17327i) q^{28} +(-1.84857 + 1.84857i) q^{29} +7.64329i q^{31} +(1.98755 - 5.29619i) q^{32} +(4.70541 + 1.91201i) q^{34} +(-6.49135 + 7.11588i) q^{35} +(1.90965 + 1.90965i) q^{37} +(-1.75941 + 0.742695i) q^{38} +(2.02922 - 5.99018i) q^{40} -7.67058 q^{41} +(5.43308 - 5.43308i) q^{43} +(12.0664 - 0.162586i) q^{44} +(-8.55794 - 3.47746i) q^{46} +3.24864i q^{47} -11.5547 q^{49} +(2.05066 - 6.76719i) q^{50} +(5.96546 - 0.0803806i) q^{52} +(-6.08323 + 6.08323i) q^{53} +(13.4776 - 0.618574i) q^{55} +(11.1596 - 4.88894i) q^{56} +(3.40610 - 1.43781i) q^{58} +(2.97848 - 2.97848i) q^{59} +(-0.157020 - 0.157020i) q^{61} +(4.06915 - 10.0141i) q^{62} +(-5.42364 + 5.88082i) q^{64} +(6.66318 - 0.305816i) q^{65} +(0.305394 + 0.305394i) q^{67} +(-5.14701 - 5.01014i) q^{68} +(12.2932 - 5.86719i) q^{70} +1.61808i q^{71} +6.90696 q^{73} +(-1.48532 - 3.51865i) q^{74} +(2.70053 - 0.0363879i) q^{76} +(18.3780 + 18.3780i) q^{77} -5.39306i q^{79} +(-5.84771 + 6.76789i) q^{80} +(10.0498 + 4.08368i) q^{82} +(-5.82210 + 5.82210i) q^{83} +(-5.93291 - 5.41221i) q^{85} +(-10.0108 + 4.22584i) q^{86} +(-15.8957 - 6.21090i) q^{88} +7.74878 q^{89} +(9.08585 + 9.08585i) q^{91} +(9.36110 + 9.11218i) q^{92} +(1.72952 - 4.25630i) q^{94} +(3.01639 - 0.138441i) q^{95} +9.34141i q^{97} +(15.1387 + 6.15150i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96q + O(q^{10}) \) \( 96q - 8q^{16} - 16q^{19} + 72q^{34} + 8q^{40} + 8q^{46} - 96q^{49} + 64q^{55} - 32q^{61} + 48q^{64} + 24q^{70} + 40q^{76} - 88q^{94} + O(q^{100}) \)

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
\(5\) 1.65197 + 1.50698i 0.738783 + 0.673944i
\(6\) 0 0
\(7\) 4.30751i 1.62809i 0.580804 + 0.814044i \(0.302738\pi\)
−0.580804 + 0.814044i \(0.697262\pi\)
\(8\) −1.13498 2.59072i −0.401276 0.915957i
\(9\) 0 0
\(10\) −1.36208 2.85390i −0.430729 0.902481i
\(11\) 4.26649 4.26649i 1.28640 1.28640i 0.349435 0.936961i \(-0.386374\pi\)
0.936961 0.349435i \(-0.113626\pi\)
\(12\) 0 0
\(13\) 2.10930 2.10930i 0.585015 0.585015i −0.351262 0.936277i \(-0.614247\pi\)
0.936277 + 0.351262i \(0.114247\pi\)
\(14\) 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 \(0.200494\pi\)
\(20\) 0.265210 + 4.46427i 0.0593028 + 0.998240i
\(21\) 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 −0.857595 0.514325i \(-0.828042\pi\)
0.514325 + 0.857595i \(0.328042\pi\)
\(30\) 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
\(35\) −6.49135 + 7.11588i −1.09724 + 1.20280i
\(36\) 0 0
\(37\) 1.90965 + 1.90965i 0.313945 + 0.313945i 0.846436 0.532491i \(-0.178744\pi\)
−0.532491 + 0.846436i \(0.678744\pi\)
\(38\) −1.75941 + 0.742695i −0.285413 + 0.120481i
\(39\) 0 0
\(40\) 2.02922 5.99018i 0.320848 0.947131i
\(41\) −7.67058 −1.19794 −0.598972 0.800770i \(-0.704424\pi\)
−0.598972 + 0.800770i \(0.704424\pi\)
\(42\) 0 0
\(43\) 5.43308 5.43308i 0.828537 0.828537i −0.158777 0.987314i \(-0.550755\pi\)
0.987314 + 0.158777i \(0.0507552\pi\)
\(44\) 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
\(50\) 2.05066 6.76719i 0.290007 0.957025i
\(51\) 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 −0.486125 0.873889i \(-0.661590\pi\)
0.873889 + 0.486125i \(0.161590\pi\)
\(60\) 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 0.725516 0.688206i \(-0.241601\pi\)
−0.688206 + 0.725516i \(0.741601\pi\)
\(68\) −5.14701 5.01014i −0.624166 0.607569i
\(69\) 0 0
\(70\) 12.2932 5.86719i 1.46932 0.701264i
\(71\) 1.61808i 0.192030i 0.995380 + 0.0960152i \(0.0306097\pi\)
−0.995380 + 0.0960152i \(0.969390\pi\)
\(72\) 0 0
\(73\) 6.90696 0.808399 0.404199 0.914671i \(-0.367550\pi\)
0.404199 + 0.914671i \(0.367550\pi\)
\(74\) −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 \(-0.0981163\pi\)
\(80\) −5.84771 + 6.76789i −0.653793 + 0.756673i
\(81\) 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
\(85\) −5.93291 5.41221i −0.643515 0.587037i
\(86\) −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 \(-0.365290\pi\)
0.410684 + 0.911778i \(0.365290\pi\)
\(90\) 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 \(0.157276\pi\)
−0.880397 + 0.474238i \(0.842724\pi\)
\(98\) 15.1387 + 6.15150i 1.52924 + 0.621396i
\(99\) 0 0
\(100\) −6.28946 + 7.77449i −0.628946 + 0.777449i
\(101\) 7.91178 + 7.91178i 0.787251 + 0.787251i 0.981043 0.193792i \(-0.0620786\pi\)
−0.193792 + 0.981043i \(0.562079\pi\)
\(102\) 0 0
\(103\) 16.1744i 1.59371i −0.604172 0.796854i \(-0.706496\pi\)
0.604172 0.796854i \(-0.293504\pi\)
\(104\) −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 \(-0.549940\pi\)
\(110\) −17.9874 6.36481i −1.71504 0.606861i
\(111\) 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
\(115\) 10.7905 + 9.84344i 1.00622 + 0.917906i
\(116\) −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
\(125\) −6.74664 + 8.91531i −0.603438 + 0.797410i
\(126\) 0 0
\(127\) 7.28333 0.646291 0.323145 0.946349i \(-0.395260\pi\)
0.323145 + 0.946349i \(0.395260\pi\)
\(128\) 10.2368 4.81748i 0.904813 0.425810i
\(129\) 0 0
\(130\) −8.89277 3.14668i −0.779948 0.275982i
\(131\) −9.89718 9.89718i −0.864721 0.864721i 0.127161 0.991882i \(-0.459413\pi\)
−0.991882 + 0.127161i \(0.959413\pi\)
\(132\) 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 \(0.653400\pi\)
\(140\) −19.2299 + 1.14240i −1.62522 + 0.0965502i
\(141\) 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 0.181946 0.983309i \(-0.441760\pi\)
−0.983309 + 0.181946i \(0.941760\pi\)
\(150\) 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
\(155\) −11.5183 + 12.6265i −0.925173 + 1.01418i
\(156\) 0 0
\(157\) 8.81467 8.81467i 0.703488 0.703488i −0.261670 0.965157i \(-0.584273\pi\)
0.965157 + 0.261670i \(0.0842732\pi\)
\(158\) −2.87117 + 7.06588i −0.228418 + 0.562131i
\(159\) 0 0
\(160\) 11.2646 5.75394i 0.890548 0.454889i
\(161\) 28.1362i 2.21744i
\(162\) 0 0
\(163\) 8.90000 + 8.90000i 0.697102 + 0.697102i 0.963784 0.266682i \(-0.0859275\pi\)
−0.266682 + 0.963784i \(0.585927\pi\)
\(164\) −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
\(170\) 4.89182 + 10.2495i 0.375185 + 0.786104i
\(171\) 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 0.675256 0.737583i \(-0.264033\pi\)
−0.737583 + 0.675256i \(0.764033\pi\)
\(180\) 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
\(190\) −4.02571 1.42449i −0.292056 0.103343i
\(191\) −3.83158 −0.277244 −0.138622 0.990345i \(-0.544267\pi\)
−0.138622 + 0.990345i \(0.544267\pi\)
\(192\) 0 0
\(193\) 5.03272i 0.362263i 0.983459 + 0.181132i \(0.0579760\pi\)
−0.983459 + 0.181132i \(0.942024\pi\)
\(194\) 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 \(0.337907\pi\)
\(200\) 12.3793 6.83759i 0.875350 0.483490i
\(201\) 0 0
\(202\) −6.15376 14.5779i −0.432977 1.02570i
\(203\) −7.96273 7.96273i −0.558874 0.558874i
\(204\) 0 0
\(205\) −12.6716 11.5594i −0.885020 0.807346i
\(206\) −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
\(220\) 20.1783 + 17.9152i 1.36042 + 1.20784i
\(221\) −7.57539 + 7.57539i −0.509576 + 0.509576i
\(222\) 0 0
\(223\) −12.7040 −0.850723 −0.425362 0.905023i \(-0.639853\pi\)
−0.425362 + 0.905023i \(0.639853\pi\)
\(224\) 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 \(0.266302\pi\)
\(230\) −8.89697 18.6413i −0.586649 1.22917i
\(231\) 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
\(235\) −4.89565 + 5.36665i −0.319357 + 0.350082i
\(236\) 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 \(-0.304033\pi\)
0.577488 + 0.816399i \(0.304033\pi\)
\(240\) 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
\(245\) −19.0880 17.4127i −1.21949 1.11246i
\(246\) 0 0
\(247\) 4.02822i 0.256309i
\(248\) 19.8016 8.67498i 1.25740 0.550862i
\(249\) 0 0
\(250\) 13.5857 8.08887i 0.859233 0.511585i
\(251\) 4.02622 4.02622i 0.254133 0.254133i −0.568530 0.822663i \(-0.692488\pi\)
0.822663 + 0.568530i \(0.192488\pi\)
\(252\) 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
\(260\) 9.97589 + 8.85707i 0.618678 + 0.549292i
\(261\) 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 −0.335994 0.941864i \(-0.609072\pi\)
0.941864 + 0.335994i \(0.109072\pi\)
\(270\) 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
\(275\) 23.1968 + 19.2887i 1.39882 + 1.16315i
\(276\) 0 0
\(277\) 4.33837 + 4.33837i 0.260667 + 0.260667i 0.825325 0.564658i \(-0.190992\pi\)
−0.564658 + 0.825325i \(0.690992\pi\)
\(278\) −3.87551 9.18089i −0.232438 0.550633i
\(279\) 0 0
\(280\) 25.8028 + 8.74090i 1.54201 + 0.522369i
\(281\) 2.93138 0.174871 0.0874357 0.996170i \(-0.472133\pi\)
0.0874357 + 0.996170i \(0.472133\pi\)
\(282\) 0 0
\(283\) 12.3064 12.3064i 0.731542 0.731542i −0.239383 0.970925i \(-0.576945\pi\)
0.970925 + 0.239383i \(0.0769452\pi\)
\(284\) −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
\(290\) 7.79352 + 2.75772i 0.457651 + 0.161939i
\(291\) 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 0.590501 0.807037i \(-0.298930\pi\)
−0.807037 + 0.590501i \(0.798930\pi\)
\(308\) 0.700342 + 51.9760i 0.0399057 + 2.96161i
\(309\) 0 0
\(310\) 21.8132 10.4108i 1.23890 0.591294i
\(311\) 18.1916i 1.03155i −0.856724 0.515775i \(-0.827504\pi\)
0.856724 0.515775i \(-0.172496\pi\)
\(312\) 0 0
\(313\) −16.7785 −0.948377 −0.474188 0.880423i \(-0.657258\pi\)
−0.474188 + 0.880423i \(0.657258\pi\)
\(314\) −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
\(320\) −17.8220 + 1.54159i −0.996280 + 0.0861777i
\(321\) 0 0
\(322\) 14.9792 36.8634i 0.834758 2.05432i
\(323\) −3.42934 + 3.42934i −0.190814 + 0.190814i
\(324\) 0 0
\(325\) 11.4682 + 9.53611i 0.636143 + 0.528968i
\(326\) −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 \(-0.807018\pi\)
0.821778 0.569808i \(-0.192982\pi\)
\(338\) 2.18367 5.37396i 0.118776 0.292305i
\(339\) 0 0
\(340\) −0.952482 16.0331i −0.0516556 0.869515i
\(341\) 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 \(0.705155\pi\)
\(350\) 29.1497 + 8.83324i 1.55812 + 0.472157i
\(351\) 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
\(355\) −2.43842 + 2.67301i −0.129418 + 0.141869i
\(356\) 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 \(0.225911\pi\)
−0.758545 + 0.651621i \(0.774089\pi\)
\(360\) 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
\(365\) 11.4101 + 10.4087i 0.597231 + 0.544815i
\(366\) 0 0
\(367\) −6.68177 −0.348786 −0.174393 0.984676i \(-0.555796\pi\)
−0.174393 + 0.984676i \(0.555796\pi\)
\(368\) 0.703974 + 26.1180i 0.0366972 + 1.36150i
\(369\) 0 0
\(370\) 2.84885 8.05106i 0.148104 0.418555i
\(371\) −26.2036 26.2036i −1.36042 1.36042i
\(372\) 0 0
\(373\) −18.9638 18.9638i −0.981911 0.981911i 0.0179284 0.999839i \(-0.494293\pi\)
−0.999839 + 0.0179284i \(0.994293\pi\)
\(374\) 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 \(0.968074\pi\)
\(380\) 4.51603 + 4.00955i 0.231668 + 0.205686i
\(381\) 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 0.856533 0.516092i \(-0.172614\pi\)
−0.516092 + 0.856533i \(0.672614\pi\)
\(390\) 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
\(395\) 8.12726 8.90917i 0.408927 0.448269i
\(396\) 0 0
\(397\) −25.8345 + 25.8345i −1.29660 + 1.29660i −0.365968 + 0.930628i \(0.619262\pi\)
−0.930628 + 0.365968i \(0.880738\pi\)
\(398\) −18.0205 7.32248i −0.903284 0.367043i
\(399\) 0 0
\(400\) −19.8593 + 2.36794i −0.992966 + 0.118397i
\(401\) 18.5375i 0.925717i −0.886432 0.462858i \(-0.846824\pi\)
0.886432 0.462858i \(-0.153176\pi\)
\(402\) 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 \(0.949003\pi\)
\(410\) 10.4480 + 21.8910i 0.515988 + 1.08112i
\(411\) 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 0.936610 0.350374i \(-0.113945\pi\)
−0.350374 + 0.936610i \(0.613945\pi\)
\(420\) 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
\(430\) −22.9058 8.10515i −1.10461 0.390865i
\(431\) −12.5590 −0.604944 −0.302472 0.953158i \(-0.597812\pi\)
−0.302472 + 0.953158i \(0.597812\pi\)
\(432\) 0 0
\(433\) 4.64837i 0.223386i −0.993743 0.111693i \(-0.964373\pi\)
0.993743 0.111693i \(-0.0356274\pi\)
\(434\) 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 \(0.445831\pi\)
\(440\) −16.8994 34.2147i −0.805647 1.63112i
\(441\) 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
\(445\) 12.8007 + 11.6773i 0.606813 + 0.553556i
\(446\) 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 \(-0.823139\pi\)
0.849571 0.527475i \(-0.176861\pi\)
\(450\) 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 \(-0.262844\pi\)
0.678008 + 0.735055i \(0.262844\pi\)
\(458\) 2.01856 0.852093i 0.0943213 0.0398157i
\(459\) 0 0
\(460\) 1.73232 + 29.1601i 0.0807700 + 1.35959i
\(461\) 3.75610 3.75610i 0.174939 0.174939i −0.614206 0.789146i \(-0.710524\pi\)
0.789146 + 0.614206i \(0.210524\pi\)
\(462\) 0 0
\(463\) 18.4896 0.859286 0.429643 0.902999i \(-0.358639\pi\)
0.429643 + 0.902999i \(0.358639\pi\)
\(464\) −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
\(470\) 9.27129 4.42492i 0.427653 0.204106i
\(471\) 0 0
\(472\) −11.0969 4.33588i −0.510776 0.199575i
\(473\) 46.3604i 2.13165i
\(474\) 0 0
\(475\) 5.19161 + 4.31695i 0.238207 + 0.198075i
\(476\) 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 \(-0.661449\pi\)
−0.485737 + 0.874105i \(0.661449\pi\)
\(480\) 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
\(485\) −14.0773 + 15.4317i −0.639219 + 0.700718i
\(486\) 0 0
\(487\) 38.2041i 1.73119i −0.500744 0.865595i \(-0.666940\pi\)
0.500744 0.865595i \(-0.333060\pi\)
\(488\) −0.228580 + 0.585010i −0.0103473 + 0.0264821i
\(489\) 0 0
\(490\) 15.7384 + 32.9759i 0.710990 + 1.48970i
\(491\) 11.2555 11.2555i 0.507953 0.507953i −0.405945 0.913898i \(-0.633057\pi\)
0.913898 + 0.405945i \(0.133057\pi\)
\(492\) 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 \(0.0408923\pi\)
\(500\) −22.1060 + 3.36510i −0.988611 + 0.150492i
\(501\) 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 −0.717576 0.696481i \(-0.754748\pi\)
0.696481 + 0.717576i \(0.254748\pi\)
\(510\) 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
\(515\) 24.3745 26.7196i 1.07407 1.17740i
\(516\) 0 0
\(517\) 13.8603 + 13.8603i 0.609575 + 0.609575i
\(518\) 15.1566 6.39805i 0.665945 0.281114i
\(519\) 0 0
\(520\) −8.35486 16.9153i −0.366385 0.741786i
\(521\) 28.2023 1.23557 0.617783 0.786348i \(-0.288031\pi\)
0.617783 + 0.786348i \(0.288031\pi\)
\(522\) 0 0
\(523\) −10.5066 + 10.5066i −0.459420 + 0.459420i −0.898465 0.439045i \(-0.855317\pi\)
0.439045 + 0.898465i \(0.355317\pi\)
\(524\) −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
\(530\) 25.6468 + 9.07505i 1.11403 + 0.394195i
\(531\) 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 0.572588 0.819844i \(-0.305940\pi\)
−0.819844 + 0.572588i \(0.805940\pi\)
\(548\) 24.8280 25.5062i 1.06060 1.08957i
\(549\) 0 0
\(550\) −20.1230 37.6213i −0.858049 1.60418i
\(551\) 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
\(560\) −29.1528 25.1891i −1.23193 1.06443i
\(561\) 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
\(565\) −29.8817 27.2592i −1.25713 1.14680i
\(566\) −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 \(-0.509004\pi\)
−0.0282840 + 0.999600i \(0.509004\pi\)
\(570\) 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 \(-0.682751\pi\)
0.543104 0.839665i \(-0.317249\pi\)
\(578\) 5.37396 + 2.18367i 0.223527 + 0.0908286i
\(579\) 0 0
\(580\) −8.74275 7.76223i −0.363023 0.322309i
\(581\) −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
\(590\) −12.5572 4.44333i −0.516972 0.182929i
\(591\) 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
\(595\) 23.3132 25.5561i 0.955748 1.04770i
\(596\) −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 \(0.109416\pi\)
−0.941501 + 0.337010i \(0.890584\pi\)
\(600\) 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
\(605\) 38.2863 41.9697i 1.55656 1.70631i
\(606\) 0 0
\(607\) −0.975144 −0.0395799 −0.0197899 0.999804i \(-0.506300\pi\)
−0.0197899 + 0.999804i \(0.506300\pi\)
\(608\) −3.15932 6.95503i −0.128127 0.282064i
\(609\) 0 0
\(610\) −0.234245 + 0.661994i −0.00948429 + 0.0268033i
\(611\) 6.85236 + 6.85236i 0.277217 + 0.277217i
\(612\) 0 0
\(613\) −7.41162 7.41162i −0.299353 0.299353i 0.541408 0.840760i \(-0.317892\pi\)
−0.840760 + 0.541408i \(0.817892\pi\)
\(614\) 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 \(0.780321\pi\)
\(620\) −34.1217 + 2.02708i −1.37036 + 0.0814095i
\(621\) 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
\(635\) 12.0318 + 10.9759i 0.477468 + 0.435564i
\(636\) 0 0
\(637\) −24.3723 + 24.3723i −0.965666 + 0.965666i
\(638\) 8.39768 20.6665i 0.332467 0.818194i
\(639\) 0 0
\(640\) 24.1707 + 7.46834i 0.955432 + 0.295212i
\(641\) 30.7369i 1.21403i 0.794689 + 0.607016i \(0.207634\pi\)
−0.794689 + 0.607016i \(0.792366\pi\)
\(642\) 0 0
\(643\) −2.00487 2.00487i −0.0790643 0.0790643i 0.666469 0.745533i \(-0.267805\pi\)
−0.745533 + 0.666469i \(0.767805\pi\)
\(644\) −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
\(650\) −9.94858 18.5995i −0.390215 0.729532i
\(651\) 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 0.932367 0.361514i \(-0.117740\pi\)
−0.361514 + 0.932367i \(0.617740\pi\)
\(660\) 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
\(670\) 0.455591 1.28753i 0.0176010 0.0497418i
\(671\) −1.33985 −0.0517243
\(672\) 0 0
\(673\) 3.74068i 0.144193i 0.997398 + 0.0720963i \(0.0229689\pi\)
−0.997398 + 0.0720963i \(0.977031\pi\)
\(674\) −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
\(680\) −7.28779 + 21.5133i −0.279474 + 0.824996i
\(681\) 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
\(685\) 26.8205 29.4008i 1.02476 1.12335i
\(686\) −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
\(700\) −33.4887 27.0919i −1.26576 1.02398i
\(701\) −3.89364 + 3.89364i −0.147061 + 0.147061i −0.776804 0.629743i \(-0.783160\pi\)
0.629743 + 0.776804i \(0.283160\pi\)
\(702\) 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 \(0.475352\pi\)
\(710\) 4.61783 2.20396i 0.173304 0.0827130i
\(711\) 0 0
\(712\) −8.79470 20.0749i −0.329595 0.752338i
\(713\) 49.9251i 1.86971i
\(714\) 0 0
\(715\) 27.1236 29.7332i 1.01437 1.11196i
\(716\) −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 \(-0.597501\pi\)
−0.301540 + 0.953454i \(0.597501\pi\)
\(720\) 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
\(725\) −10.0506 8.35734i −0.373271 0.310384i
\(726\) 0 0
\(727\) 37.5868i 1.39402i 0.717063 + 0.697008i \(0.245486\pi\)
−0.717063 + 0.697008i \(0.754514\pi\)
\(728\) 13.2266 33.8511i 0.490211 1.25461i
\(729\) 0 0
\(730\) −9.40786 19.7118i −0.348200 0.729565i
\(731\) −19.5125 + 19.5125i −0.721695 + 0.721695i
\(732\) 0 0
\(733\) 10.5565 10.5565i 0.389913 0.389913i −0.484744 0.874656i \(-0.661087\pi\)
0.874656 + 0.484744i \(0.161087\pi\)
\(734\) 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 \(0.295723\pi\)
\(740\) −8.01874 + 9.03165i −0.294775 + 0.332010i
\(741\) 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
\(755\) −19.8414 18.1000i −0.722103 0.658728i
\(756\) 0 0
\(757\) 25.8317 + 25.8317i 0.938870 + 0.938870i 0.998236 0.0593667i \(-0.0189081\pi\)
−0.0593667 + 0.998236i \(0.518908\pi\)
\(758\) 13.5498 + 32.0988i 0.492151 + 1.16588i
\(759\) 0 0
\(760\) −3.78220 7.65749i −0.137195 0.277766i
\(761\) −6.93351 −0.251340 −0.125670 0.992072i \(-0.540108\pi\)
−0.125670 + 0.992072i \(0.540108\pi\)
\(762\) 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 \(0.392064\pi\)
\(770\) 27.4165 77.4812i 0.988022 2.79223i
\(771\) 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 0.353235 0.935534i \(-0.385081\pi\)
−0.935534 + 0.353235i \(0.885081\pi\)
\(788\) 19.8469 0.267424i 0.707018 0.00952659i
\(789\) 0 0
\(790\) −15.3912 + 7.34580i −0.547596 + 0.261352i
\(791\) 77.9168i 2.77040i