Properties

Label 300.2.o.a.109.6
Level $300$
Weight $2$
Character 300.109
Analytic conductor $2.396$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.o (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 109.6
Character \(\chi\) \(=\) 300.109
Dual form 300.2.o.a.289.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.951057 - 0.309017i) q^{3} +(2.23394 - 0.0974182i) q^{5} -1.31873i q^{7} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(0.951057 - 0.309017i) q^{3} +(2.23394 - 0.0974182i) q^{5} -1.31873i q^{7} +(0.809017 - 0.587785i) q^{9} +(-1.25737 - 0.913532i) q^{11} +(1.42727 + 1.96447i) q^{13} +(2.09450 - 0.782977i) q^{15} +(-1.25004 - 0.406161i) q^{17} +(0.315522 - 0.971077i) q^{19} +(-0.407508 - 1.25418i) q^{21} +(-2.94350 + 4.05137i) q^{23} +(4.98102 - 0.435254i) q^{25} +(0.587785 - 0.809017i) q^{27} +(1.82443 + 5.61503i) q^{29} +(2.73547 - 8.41891i) q^{31} +(-1.47813 - 0.480272i) q^{33} +(-0.128468 - 2.94596i) q^{35} +(-2.95370 - 4.06542i) q^{37} +(1.96447 + 1.42727i) q^{39} +(-6.43499 + 4.67529i) q^{41} +6.84831i q^{43} +(1.75004 - 1.39189i) q^{45} +(-7.37336 + 2.39575i) q^{47} +5.26096 q^{49} -1.31436 q^{51} +(-3.75685 + 1.22067i) q^{53} +(-2.89789 - 1.91829i) q^{55} -1.02105i q^{57} +(-6.35355 + 4.61613i) q^{59} +(2.83287 + 2.05820i) q^{61} +(-0.775127 - 1.06687i) q^{63} +(3.37982 + 4.24947i) q^{65} +(-7.92426 - 2.57475i) q^{67} +(-1.54749 + 4.76268i) q^{69} +(-4.00454 - 12.3247i) q^{71} +(-7.47339 + 10.2862i) q^{73} +(4.60273 - 1.95317i) q^{75} +(-1.20470 + 1.65812i) q^{77} +(0.386585 + 1.18979i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-7.80521 - 2.53607i) q^{83} +(-2.83208 - 0.785565i) q^{85} +(3.47028 + 4.77643i) q^{87} +(7.74667 + 5.62829i) q^{89} +(2.59059 - 1.88218i) q^{91} -8.85217i q^{93} +(0.610258 - 2.20007i) q^{95} +(-15.4769 + 5.02874i) q^{97} -1.55419 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 2q^{5} + 6q^{9} + O(q^{10}) \) \( 24q - 2q^{5} + 6q^{9} - 6q^{11} + 4q^{15} + 10q^{17} + 10q^{19} - 4q^{21} + 40q^{23} - 4q^{25} + 4q^{29} + 6q^{31} + 10q^{33} - 6q^{35} - 10q^{41} + 2q^{45} - 40q^{47} - 56q^{49} + 16q^{51} - 60q^{53} - 62q^{55} - 36q^{59} - 12q^{61} - 10q^{63} + 20q^{67} + 4q^{69} + 40q^{71} + 60q^{73} + 8q^{75} - 40q^{77} + 8q^{79} - 6q^{81} - 50q^{83} + 34q^{85} - 20q^{87} - 30q^{91} - 60q^{95} - 40q^{97} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.951057 0.309017i 0.549093 0.178411i
\(4\) 0 0
\(5\) 2.23394 0.0974182i 0.999051 0.0435667i
\(6\) 0 0
\(7\) 1.31873i 0.498431i −0.968448 0.249216i \(-0.919827\pi\)
0.968448 0.249216i \(-0.0801728\pi\)
\(8\) 0 0
\(9\) 0.809017 0.587785i 0.269672 0.195928i
\(10\) 0 0
\(11\) −1.25737 0.913532i −0.379111 0.275440i 0.381868 0.924217i \(-0.375281\pi\)
−0.760979 + 0.648777i \(0.775281\pi\)
\(12\) 0 0
\(13\) 1.42727 + 1.96447i 0.395854 + 0.544846i 0.959697 0.281036i \(-0.0906780\pi\)
−0.563844 + 0.825882i \(0.690678\pi\)
\(14\) 0 0
\(15\) 2.09450 0.782977i 0.540799 0.202164i
\(16\) 0 0
\(17\) −1.25004 0.406161i −0.303178 0.0985085i 0.153477 0.988152i \(-0.450953\pi\)
−0.456655 + 0.889644i \(0.650953\pi\)
\(18\) 0 0
\(19\) 0.315522 0.971077i 0.0723857 0.222780i −0.908318 0.418280i \(-0.862633\pi\)
0.980704 + 0.195500i \(0.0626330\pi\)
\(20\) 0 0
\(21\) −0.407508 1.25418i −0.0889256 0.273685i
\(22\) 0 0
\(23\) −2.94350 + 4.05137i −0.613761 + 0.844770i −0.996880 0.0789291i \(-0.974850\pi\)
0.383119 + 0.923699i \(0.374850\pi\)
\(24\) 0 0
\(25\) 4.98102 0.435254i 0.996204 0.0870507i
\(26\) 0 0
\(27\) 0.587785 0.809017i 0.113119 0.155695i
\(28\) 0 0
\(29\) 1.82443 + 5.61503i 0.338789 + 1.04268i 0.964825 + 0.262891i \(0.0846760\pi\)
−0.626037 + 0.779794i \(0.715324\pi\)
\(30\) 0 0
\(31\) 2.73547 8.41891i 0.491305 1.51208i −0.331332 0.943514i \(-0.607498\pi\)
0.822637 0.568567i \(-0.192502\pi\)
\(32\) 0 0
\(33\) −1.47813 0.480272i −0.257309 0.0836047i
\(34\) 0 0
\(35\) −0.128468 2.94596i −0.0217150 0.497958i
\(36\) 0 0
\(37\) −2.95370 4.06542i −0.485586 0.668352i 0.493981 0.869473i \(-0.335541\pi\)
−0.979566 + 0.201121i \(0.935541\pi\)
\(38\) 0 0
\(39\) 1.96447 + 1.42727i 0.314567 + 0.228546i
\(40\) 0 0
\(41\) −6.43499 + 4.67529i −1.00498 + 0.730158i −0.963150 0.268967i \(-0.913318\pi\)
−0.0418271 + 0.999125i \(0.513318\pi\)
\(42\) 0 0
\(43\) 6.84831i 1.04436i 0.852836 + 0.522179i \(0.174881\pi\)
−0.852836 + 0.522179i \(0.825119\pi\)
\(44\) 0 0
\(45\) 1.75004 1.39189i 0.260880 0.207491i
\(46\) 0 0
\(47\) −7.37336 + 2.39575i −1.07552 + 0.349456i −0.792633 0.609698i \(-0.791291\pi\)
−0.282882 + 0.959155i \(0.591291\pi\)
\(48\) 0 0
\(49\) 5.26096 0.751566
\(50\) 0 0
\(51\) −1.31436 −0.184048
\(52\) 0 0
\(53\) −3.75685 + 1.22067i −0.516043 + 0.167673i −0.555449 0.831551i \(-0.687454\pi\)
0.0394057 + 0.999223i \(0.487454\pi\)
\(54\) 0 0
\(55\) −2.89789 1.91829i −0.390751 0.258662i
\(56\) 0 0
\(57\) 1.02105i 0.135241i
\(58\) 0 0
\(59\) −6.35355 + 4.61613i −0.827162 + 0.600969i −0.918755 0.394828i \(-0.870804\pi\)
0.0915928 + 0.995797i \(0.470804\pi\)
\(60\) 0 0
\(61\) 2.83287 + 2.05820i 0.362711 + 0.263525i 0.754182 0.656665i \(-0.228034\pi\)
−0.391471 + 0.920191i \(0.628034\pi\)
\(62\) 0 0
\(63\) −0.775127 1.06687i −0.0976568 0.134413i
\(64\) 0 0
\(65\) 3.37982 + 4.24947i 0.419215 + 0.527082i
\(66\) 0 0
\(67\) −7.92426 2.57475i −0.968102 0.314555i −0.218052 0.975937i \(-0.569970\pi\)
−0.750050 + 0.661382i \(0.769970\pi\)
\(68\) 0 0
\(69\) −1.54749 + 4.76268i −0.186296 + 0.573359i
\(70\) 0 0
\(71\) −4.00454 12.3247i −0.475252 1.46267i −0.845618 0.533788i \(-0.820768\pi\)
0.370366 0.928886i \(-0.379232\pi\)
\(72\) 0 0
\(73\) −7.47339 + 10.2862i −0.874694 + 1.20391i 0.103168 + 0.994664i \(0.467102\pi\)
−0.977862 + 0.209249i \(0.932898\pi\)
\(74\) 0 0
\(75\) 4.60273 1.95317i 0.531477 0.225533i
\(76\) 0 0
\(77\) −1.20470 + 1.65812i −0.137288 + 0.188961i
\(78\) 0 0
\(79\) 0.386585 + 1.18979i 0.0434942 + 0.133861i 0.970446 0.241320i \(-0.0775804\pi\)
−0.926951 + 0.375182i \(0.877580\pi\)
\(80\) 0 0
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) 0 0
\(83\) −7.80521 2.53607i −0.856734 0.278370i −0.152470 0.988308i \(-0.548723\pi\)
−0.704264 + 0.709939i \(0.748723\pi\)
\(84\) 0 0
\(85\) −2.83208 0.785565i −0.307182 0.0852065i
\(86\) 0 0
\(87\) 3.47028 + 4.77643i 0.372053 + 0.512087i
\(88\) 0 0
\(89\) 7.74667 + 5.62829i 0.821146 + 0.596597i 0.917040 0.398794i \(-0.130571\pi\)
−0.0958948 + 0.995391i \(0.530571\pi\)
\(90\) 0 0
\(91\) 2.59059 1.88218i 0.271568 0.197306i
\(92\) 0 0
\(93\) 8.85217i 0.917927i
\(94\) 0 0
\(95\) 0.610258 2.20007i 0.0626112 0.225722i
\(96\) 0 0
\(97\) −15.4769 + 5.02874i −1.57144 + 0.510591i −0.959833 0.280573i \(-0.909476\pi\)
−0.611604 + 0.791164i \(0.709476\pi\)
\(98\) 0 0
\(99\) −1.55419 −0.156202
\(100\) 0 0
\(101\) 5.63722 0.560925 0.280462 0.959865i \(-0.409512\pi\)
0.280462 + 0.959865i \(0.409512\pi\)
\(102\) 0 0
\(103\) 8.00179 2.59994i 0.788439 0.256179i 0.113000 0.993595i \(-0.463954\pi\)
0.675439 + 0.737415i \(0.263954\pi\)
\(104\) 0 0
\(105\) −1.03253 2.76208i −0.100765 0.269551i
\(106\) 0 0
\(107\) 2.06196i 0.199337i −0.995021 0.0996687i \(-0.968222\pi\)
0.995021 0.0996687i \(-0.0317783\pi\)
\(108\) 0 0
\(109\) 11.3052 8.21372i 1.08284 0.786731i 0.104666 0.994507i \(-0.466623\pi\)
0.978176 + 0.207776i \(0.0666226\pi\)
\(110\) 0 0
\(111\) −4.06542 2.95370i −0.385873 0.280353i
\(112\) 0 0
\(113\) 3.50093 + 4.81862i 0.329340 + 0.453297i 0.941290 0.337599i \(-0.109615\pi\)
−0.611950 + 0.790896i \(0.709615\pi\)
\(114\) 0 0
\(115\) −6.18093 + 9.33730i −0.576375 + 0.870707i
\(116\) 0 0
\(117\) 2.30937 + 0.750360i 0.213502 + 0.0693708i
\(118\) 0 0
\(119\) −0.535615 + 1.64845i −0.0490997 + 0.151113i
\(120\) 0 0
\(121\) −2.65275 8.16433i −0.241159 0.742211i
\(122\) 0 0
\(123\) −4.67529 + 6.43499i −0.421557 + 0.580224i
\(124\) 0 0
\(125\) 11.0849 1.45757i 0.991465 0.130369i
\(126\) 0 0
\(127\) −1.42406 + 1.96004i −0.126364 + 0.173926i −0.867512 0.497417i \(-0.834282\pi\)
0.741147 + 0.671342i \(0.234282\pi\)
\(128\) 0 0
\(129\) 2.11624 + 6.51313i 0.186325 + 0.573449i
\(130\) 0 0
\(131\) 3.37948 10.4010i 0.295267 0.908737i −0.687865 0.725839i \(-0.741452\pi\)
0.983132 0.182899i \(-0.0585481\pi\)
\(132\) 0 0
\(133\) −1.28058 0.416087i −0.111041 0.0360793i
\(134\) 0 0
\(135\) 1.23427 1.86456i 0.106229 0.160476i
\(136\) 0 0
\(137\) 2.19602 + 3.02256i 0.187618 + 0.258235i 0.892456 0.451134i \(-0.148980\pi\)
−0.704838 + 0.709368i \(0.748980\pi\)
\(138\) 0 0
\(139\) −1.73765 1.26247i −0.147385 0.107082i 0.511649 0.859194i \(-0.329035\pi\)
−0.659034 + 0.752113i \(0.729035\pi\)
\(140\) 0 0
\(141\) −6.27216 + 4.55699i −0.528211 + 0.383768i
\(142\) 0 0
\(143\) 3.77392i 0.315591i
\(144\) 0 0
\(145\) 4.62269 + 12.3659i 0.383894 + 1.02693i
\(146\) 0 0
\(147\) 5.00347 1.62573i 0.412680 0.134088i
\(148\) 0 0
\(149\) 7.85344 0.643379 0.321690 0.946845i \(-0.395749\pi\)
0.321690 + 0.946845i \(0.395749\pi\)
\(150\) 0 0
\(151\) 22.5124 1.83203 0.916016 0.401141i \(-0.131386\pi\)
0.916016 + 0.401141i \(0.131386\pi\)
\(152\) 0 0
\(153\) −1.25004 + 0.406161i −0.101059 + 0.0328362i
\(154\) 0 0
\(155\) 5.29073 19.0739i 0.424962 1.53205i
\(156\) 0 0
\(157\) 19.4083i 1.54895i −0.632602 0.774477i \(-0.718013\pi\)
0.632602 0.774477i \(-0.281987\pi\)
\(158\) 0 0
\(159\) −3.19577 + 2.32186i −0.253441 + 0.184136i
\(160\) 0 0
\(161\) 5.34265 + 3.88166i 0.421060 + 0.305918i
\(162\) 0 0
\(163\) 8.89817 + 12.2473i 0.696959 + 0.959281i 0.999980 + 0.00629741i \(0.00200454\pi\)
−0.303022 + 0.952984i \(0.597995\pi\)
\(164\) 0 0
\(165\) −3.34884 0.928906i −0.260707 0.0723152i
\(166\) 0 0
\(167\) 17.9807 + 5.84227i 1.39139 + 0.452089i 0.906395 0.422431i \(-0.138823\pi\)
0.484990 + 0.874519i \(0.338823\pi\)
\(168\) 0 0
\(169\) 2.19518 6.75608i 0.168860 0.519698i
\(170\) 0 0
\(171\) −0.315522 0.971077i −0.0241286 0.0742601i
\(172\) 0 0
\(173\) 14.1479 19.4729i 1.07564 1.48050i 0.211415 0.977396i \(-0.432193\pi\)
0.864228 0.503100i \(-0.167807\pi\)
\(174\) 0 0
\(175\) −0.573980 6.56860i −0.0433888 0.496539i
\(176\) 0 0
\(177\) −4.61613 + 6.35355i −0.346969 + 0.477562i
\(178\) 0 0
\(179\) −0.461162 1.41931i −0.0344689 0.106084i 0.932342 0.361578i \(-0.117762\pi\)
−0.966811 + 0.255494i \(0.917762\pi\)
\(180\) 0 0
\(181\) −0.809018 + 2.48990i −0.0601338 + 0.185073i −0.976611 0.215014i \(-0.931020\pi\)
0.916477 + 0.400087i \(0.131020\pi\)
\(182\) 0 0
\(183\) 3.33023 + 1.08206i 0.246178 + 0.0799881i
\(184\) 0 0
\(185\) −6.99446 8.79419i −0.514243 0.646562i
\(186\) 0 0
\(187\) 1.20071 + 1.65264i 0.0878050 + 0.120853i
\(188\) 0 0
\(189\) −1.06687 0.775127i −0.0776035 0.0563822i
\(190\) 0 0
\(191\) −16.6599 + 12.1041i −1.20547 + 0.875824i −0.994811 0.101736i \(-0.967560\pi\)
−0.210657 + 0.977560i \(0.567560\pi\)
\(192\) 0 0
\(193\) 5.15953i 0.371391i −0.982607 0.185696i \(-0.940546\pi\)
0.982607 0.185696i \(-0.0594539\pi\)
\(194\) 0 0
\(195\) 4.52756 + 2.99707i 0.324225 + 0.214625i
\(196\) 0 0
\(197\) 9.99630 3.24799i 0.712207 0.231410i 0.0695657 0.997577i \(-0.477839\pi\)
0.642641 + 0.766167i \(0.277839\pi\)
\(198\) 0 0
\(199\) −3.65216 −0.258895 −0.129447 0.991586i \(-0.541320\pi\)
−0.129447 + 0.991586i \(0.541320\pi\)
\(200\) 0 0
\(201\) −8.33206 −0.587698
\(202\) 0 0
\(203\) 7.40468 2.40593i 0.519707 0.168863i
\(204\) 0 0
\(205\) −13.9200 + 11.0712i −0.972212 + 0.773249i
\(206\) 0 0
\(207\) 5.00777i 0.348064i
\(208\) 0 0
\(209\) −1.28384 + 0.932763i −0.0888049 + 0.0645206i
\(210\) 0 0
\(211\) 21.3259 + 15.4941i 1.46813 + 1.06666i 0.981150 + 0.193249i \(0.0619026\pi\)
0.486983 + 0.873411i \(0.338097\pi\)
\(212\) 0 0
\(213\) −7.61709 10.4840i −0.521914 0.718354i
\(214\) 0 0
\(215\) 0.667150 + 15.2988i 0.0454993 + 1.04337i
\(216\) 0 0
\(217\) −11.1022 3.60733i −0.753669 0.244882i
\(218\) 0 0
\(219\) −3.92899 + 12.0922i −0.265497 + 0.817115i
\(220\) 0 0
\(221\) −0.986247 3.03536i −0.0663422 0.204180i
\(222\) 0 0
\(223\) −10.8706 + 14.9621i −0.727950 + 1.00194i 0.271272 + 0.962503i \(0.412556\pi\)
−0.999222 + 0.0394348i \(0.987444\pi\)
\(224\) 0 0
\(225\) 3.77389 3.27990i 0.251593 0.218660i
\(226\) 0 0
\(227\) 10.9690 15.0976i 0.728039 1.00206i −0.271179 0.962529i \(-0.587414\pi\)
0.999218 0.0395311i \(-0.0125864\pi\)
\(228\) 0 0
\(229\) −8.63423 26.5734i −0.570566 1.75602i −0.650803 0.759247i \(-0.725568\pi\)
0.0802368 0.996776i \(-0.474432\pi\)
\(230\) 0 0
\(231\) −0.633347 + 1.94924i −0.0416712 + 0.128251i
\(232\) 0 0
\(233\) −23.5456 7.65043i −1.54252 0.501196i −0.590452 0.807073i \(-0.701050\pi\)
−0.952071 + 0.305877i \(0.901050\pi\)
\(234\) 0 0
\(235\) −16.2383 + 6.07028i −1.05927 + 0.395981i
\(236\) 0 0
\(237\) 0.735329 + 1.01209i 0.0477647 + 0.0657425i
\(238\) 0 0
\(239\) −9.47102 6.88110i −0.612629 0.445101i 0.237710 0.971336i \(-0.423603\pi\)
−0.850339 + 0.526235i \(0.823603\pi\)
\(240\) 0 0
\(241\) −24.1221 + 17.5257i −1.55384 + 1.12893i −0.612998 + 0.790084i \(0.710037\pi\)
−0.940842 + 0.338846i \(0.889963\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) 11.7527 0.512514i 0.750853 0.0327433i
\(246\) 0 0
\(247\) 2.35799 0.766156i 0.150035 0.0487493i
\(248\) 0 0
\(249\) −8.20689 −0.520090
\(250\) 0 0
\(251\) −2.87297 −0.181340 −0.0906700 0.995881i \(-0.528901\pi\)
−0.0906700 + 0.995881i \(0.528901\pi\)
\(252\) 0 0
\(253\) 7.40212 2.40510i 0.465367 0.151207i
\(254\) 0 0
\(255\) −2.93622 + 0.128043i −0.183873 + 0.00801837i
\(256\) 0 0
\(257\) 8.11716i 0.506334i 0.967423 + 0.253167i \(0.0814723\pi\)
−0.967423 + 0.253167i \(0.918528\pi\)
\(258\) 0 0
\(259\) −5.36118 + 3.89512i −0.333127 + 0.242031i
\(260\) 0 0
\(261\) 4.77643 + 3.47028i 0.295654 + 0.214805i
\(262\) 0 0
\(263\) 13.1117 + 18.0467i 0.808501 + 1.11281i 0.991553 + 0.129703i \(0.0414025\pi\)
−0.183051 + 0.983103i \(0.558597\pi\)
\(264\) 0 0
\(265\) −8.27368 + 3.09291i −0.508248 + 0.189996i
\(266\) 0 0
\(267\) 9.10676 + 2.95897i 0.557325 + 0.181086i
\(268\) 0 0
\(269\) 2.53369 7.79789i 0.154482 0.475446i −0.843626 0.536931i \(-0.819584\pi\)
0.998108 + 0.0614851i \(0.0195837\pi\)
\(270\) 0 0
\(271\) −2.93158 9.02246i −0.178081 0.548075i 0.821680 0.569949i \(-0.193037\pi\)
−0.999761 + 0.0218733i \(0.993037\pi\)
\(272\) 0 0
\(273\) 1.88218 2.59059i 0.113915 0.156790i
\(274\) 0 0
\(275\) −6.66060 4.00305i −0.401649 0.241393i
\(276\) 0 0
\(277\) 0.270190 0.371885i 0.0162341 0.0223444i −0.800823 0.598901i \(-0.795604\pi\)
0.817057 + 0.576557i \(0.195604\pi\)
\(278\) 0 0
\(279\) −2.73547 8.41891i −0.163768 0.504027i
\(280\) 0 0
\(281\) −4.71493 + 14.5111i −0.281269 + 0.865658i 0.706223 + 0.707990i \(0.250398\pi\)
−0.987492 + 0.157668i \(0.949602\pi\)
\(282\) 0 0
\(283\) 10.1502 + 3.29800i 0.603366 + 0.196046i 0.594741 0.803917i \(-0.297255\pi\)
0.00862506 + 0.999963i \(0.497255\pi\)
\(284\) 0 0
\(285\) −0.0994689 2.28097i −0.00589203 0.135113i
\(286\) 0 0
\(287\) 6.16543 + 8.48598i 0.363934 + 0.500912i
\(288\) 0 0
\(289\) −12.3557 8.97692i −0.726804 0.528054i
\(290\) 0 0
\(291\) −13.1654 + 9.56522i −0.771770 + 0.560723i
\(292\) 0 0
\(293\) 30.8334i 1.80130i −0.434541 0.900652i \(-0.643089\pi\)
0.434541 0.900652i \(-0.356911\pi\)
\(294\) 0 0
\(295\) −13.7438 + 10.9311i −0.800195 + 0.636435i
\(296\) 0 0
\(297\) −1.47813 + 0.480272i −0.0857696 + 0.0278682i
\(298\) 0 0
\(299\) −12.1600 −0.703229
\(300\) 0 0
\(301\) 9.03104 0.520541
\(302\) 0 0
\(303\) 5.36132 1.74200i 0.308000 0.100075i
\(304\) 0 0
\(305\) 6.52897 + 4.32193i 0.373848 + 0.247473i
\(306\) 0 0
\(307\) 17.8634i 1.01952i 0.860318 + 0.509758i \(0.170265\pi\)
−0.860318 + 0.509758i \(0.829735\pi\)
\(308\) 0 0
\(309\) 6.80673 4.94538i 0.387221 0.281333i
\(310\) 0 0
\(311\) 9.75942 + 7.09063i 0.553406 + 0.402073i 0.829040 0.559190i \(-0.188888\pi\)
−0.275634 + 0.961263i \(0.588888\pi\)
\(312\) 0 0
\(313\) 11.0264 + 15.1766i 0.623250 + 0.857830i 0.997584 0.0694641i \(-0.0221289\pi\)
−0.374335 + 0.927294i \(0.622129\pi\)
\(314\) 0 0
\(315\) −1.83552 2.30782i −0.103420 0.130031i
\(316\) 0 0
\(317\) −10.1912 3.31133i −0.572395 0.185983i 0.00849553 0.999964i \(-0.497296\pi\)
−0.580891 + 0.813981i \(0.697296\pi\)
\(318\) 0 0
\(319\) 2.83552 8.72685i 0.158759 0.488610i
\(320\) 0 0
\(321\) −0.637181 1.96104i −0.0355640 0.109455i
\(322\) 0 0
\(323\) −0.788827 + 1.08573i −0.0438915 + 0.0604115i
\(324\) 0 0
\(325\) 7.96430 + 9.16383i 0.441780 + 0.508318i
\(326\) 0 0
\(327\) 8.21372 11.3052i 0.454219 0.625179i
\(328\) 0 0
\(329\) 3.15934 + 9.72344i 0.174180 + 0.536071i
\(330\) 0 0
\(331\) 0.671547 2.06681i 0.0369116 0.113602i −0.930903 0.365266i \(-0.880978\pi\)
0.967815 + 0.251664i \(0.0809779\pi\)
\(332\) 0 0
\(333\) −4.77919 1.55285i −0.261898 0.0850959i
\(334\) 0 0
\(335\) −17.9532 4.97988i −0.980887 0.272080i
\(336\) 0 0
\(337\) −5.91844 8.14603i −0.322398 0.443743i 0.616800 0.787120i \(-0.288429\pi\)
−0.939197 + 0.343378i \(0.888429\pi\)
\(338\) 0 0
\(339\) 4.81862 + 3.50093i 0.261711 + 0.190144i
\(340\) 0 0
\(341\) −11.1304 + 8.08674i −0.602747 + 0.437922i
\(342\) 0 0
\(343\) 16.1688i 0.873035i
\(344\) 0 0
\(345\) −2.99303 + 10.7903i −0.161139 + 0.580931i
\(346\) 0 0
\(347\) 13.9570 4.53489i 0.749249 0.243446i 0.0905912 0.995888i \(-0.471124\pi\)
0.658658 + 0.752442i \(0.271124\pi\)
\(348\) 0 0
\(349\) −18.5685 −0.993949 −0.496974 0.867765i \(-0.665556\pi\)
−0.496974 + 0.867765i \(0.665556\pi\)
\(350\) 0 0
\(351\) 2.42822 0.129609
\(352\) 0 0
\(353\) 17.5663 5.70763i 0.934959 0.303787i 0.198370 0.980127i \(-0.436435\pi\)
0.736589 + 0.676340i \(0.236435\pi\)
\(354\) 0 0
\(355\) −10.1466 27.1426i −0.538524 1.44058i
\(356\) 0 0
\(357\) 1.73329i 0.0917352i
\(358\) 0 0
\(359\) −19.9550 + 14.4981i −1.05318 + 0.765182i −0.972815 0.231583i \(-0.925609\pi\)
−0.0803676 + 0.996765i \(0.525609\pi\)
\(360\) 0 0
\(361\) 14.5279 + 10.5551i 0.764626 + 0.555533i
\(362\) 0 0
\(363\) −5.04583 6.94499i −0.264837 0.364517i
\(364\) 0 0
\(365\) −15.6931 + 23.7069i −0.821413 + 1.24088i
\(366\) 0 0
\(367\) 12.4469 + 4.04423i 0.649721 + 0.211107i 0.615291 0.788300i \(-0.289038\pi\)
0.0344301 + 0.999407i \(0.489038\pi\)
\(368\) 0 0
\(369\) −2.45795 + 7.56478i −0.127956 + 0.393807i
\(370\) 0 0
\(371\) 1.60973 + 4.95425i 0.0835733 + 0.257212i
\(372\) 0 0
\(373\) −0.174079 + 0.239599i −0.00901348 + 0.0124060i −0.813500 0.581565i \(-0.802441\pi\)
0.804486 + 0.593971i \(0.202441\pi\)
\(374\) 0 0
\(375\) 10.0920 4.81166i 0.521147 0.248473i
\(376\) 0 0
\(377\) −8.42659 + 11.5982i −0.433992 + 0.597338i
\(378\) 0 0
\(379\) −2.41901 7.44495i −0.124256 0.382421i 0.869509 0.493918i \(-0.164436\pi\)
−0.993765 + 0.111496i \(0.964436\pi\)
\(380\) 0 0
\(381\) −0.748670 + 2.30417i −0.0383555 + 0.118046i
\(382\) 0 0
\(383\) −19.8293 6.44294i −1.01323 0.329219i −0.245090 0.969500i \(-0.578818\pi\)
−0.768140 + 0.640282i \(0.778818\pi\)
\(384\) 0 0
\(385\) −2.52970 + 3.82152i −0.128925 + 0.194763i
\(386\) 0 0
\(387\) 4.02534 + 5.54040i 0.204619 + 0.281634i
\(388\) 0 0
\(389\) −22.6010 16.4206i −1.14592 0.832558i −0.157985 0.987441i \(-0.550500\pi\)
−0.987933 + 0.154883i \(0.950500\pi\)
\(390\) 0 0
\(391\) 5.32498 3.86883i 0.269296 0.195655i
\(392\) 0 0
\(393\) 10.9362i 0.551660i
\(394\) 0 0
\(395\) 0.979517 + 2.62026i 0.0492848 + 0.131839i
\(396\) 0 0
\(397\) 30.6358 9.95418i 1.53757 0.499586i 0.586863 0.809686i \(-0.300363\pi\)
0.950704 + 0.310100i \(0.100363\pi\)
\(398\) 0 0
\(399\) −1.34649 −0.0674086
\(400\) 0 0
\(401\) −10.3441 −0.516562 −0.258281 0.966070i \(-0.583156\pi\)
−0.258281 + 0.966070i \(0.583156\pi\)
\(402\) 0 0
\(403\) 20.4429 6.64232i 1.01834 0.330877i
\(404\) 0 0
\(405\) 0.597677 2.15471i 0.0296988 0.107068i
\(406\) 0 0
\(407\) 7.81004i 0.387129i
\(408\) 0 0
\(409\) 29.7399 21.6073i 1.47054 1.06841i 0.490087 0.871673i \(-0.336965\pi\)
0.980456 0.196739i \(-0.0630351\pi\)
\(410\) 0 0
\(411\) 3.02256 + 2.19602i 0.149092 + 0.108322i
\(412\) 0 0
\(413\) 6.08740 + 8.37859i 0.299542 + 0.412284i
\(414\) 0 0
\(415\) −17.6835 4.90507i −0.868048 0.240780i
\(416\) 0 0
\(417\) −2.04272 0.663721i −0.100033 0.0325026i
\(418\) 0 0
\(419\) 8.74262 26.9070i 0.427105 1.31449i −0.473859 0.880601i \(-0.657139\pi\)
0.900964 0.433894i \(-0.142861\pi\)
\(420\) 0 0
\(421\) 0.392142 + 1.20689i 0.0191118 + 0.0588202i 0.960158 0.279459i \(-0.0901551\pi\)
−0.941046 + 0.338279i \(0.890155\pi\)
\(422\) 0 0
\(423\) −4.55699 + 6.27216i −0.221568 + 0.304963i
\(424\) 0 0
\(425\) −6.40323 1.47901i −0.310602 0.0717427i
\(426\) 0 0
\(427\) 2.71420 3.73577i 0.131349 0.180787i
\(428\) 0 0
\(429\) −1.16621 3.58921i −0.0563049 0.173289i
\(430\) 0 0
\(431\) 2.24011 6.89434i 0.107902 0.332089i −0.882498 0.470315i \(-0.844140\pi\)
0.990401 + 0.138226i \(0.0441402\pi\)
\(432\) 0 0
\(433\) 3.64988 + 1.18592i 0.175402 + 0.0569916i 0.395401 0.918508i \(-0.370606\pi\)
−0.219999 + 0.975500i \(0.570606\pi\)
\(434\) 0 0
\(435\) 8.21772 + 10.3322i 0.394010 + 0.495392i
\(436\) 0 0
\(437\) 3.00546 + 4.13666i 0.143771 + 0.197883i
\(438\) 0 0
\(439\) 25.5358 + 18.5528i 1.21876 + 0.885479i 0.995996 0.0893940i \(-0.0284930\pi\)
0.222761 + 0.974873i \(0.428493\pi\)
\(440\) 0 0
\(441\) 4.25621 3.09232i 0.202677 0.147253i
\(442\) 0 0
\(443\) 2.65284i 0.126040i 0.998012 + 0.0630200i \(0.0200732\pi\)
−0.998012 + 0.0630200i \(0.979927\pi\)
\(444\) 0 0
\(445\) 17.8539 + 11.8186i 0.846358 + 0.560256i
\(446\) 0 0
\(447\) 7.46907 2.42685i 0.353275 0.114786i
\(448\) 0 0
\(449\) 27.3646 1.29142 0.645709 0.763584i \(-0.276562\pi\)
0.645709 + 0.763584i \(0.276562\pi\)
\(450\) 0 0
\(451\) 12.3622 0.582113
\(452\) 0 0
\(453\) 21.4106 6.95671i 1.00596 0.326855i
\(454\) 0 0
\(455\) 5.60389 4.45705i 0.262714 0.208950i
\(456\) 0 0
\(457\) 1.66698i 0.0779781i −0.999240 0.0389891i \(-0.987586\pi\)
0.999240 0.0389891i \(-0.0124138\pi\)
\(458\) 0 0
\(459\) −1.06334 + 0.772564i −0.0496326 + 0.0360602i
\(460\) 0 0
\(461\) 27.8272 + 20.2176i 1.29604 + 0.941630i 0.999909 0.0135170i \(-0.00430273\pi\)
0.296133 + 0.955147i \(0.404303\pi\)
\(462\) 0 0
\(463\) −20.7939 28.6204i −0.966377 1.33010i −0.943856 0.330357i \(-0.892831\pi\)
−0.0225205 0.999746i \(-0.507169\pi\)
\(464\) 0 0
\(465\) −0.862362 19.7753i −0.0399911 0.917055i
\(466\) 0 0
\(467\) 22.9613 + 7.46057i 1.06252 + 0.345234i 0.787571 0.616224i \(-0.211338\pi\)
0.274951 + 0.961458i \(0.411338\pi\)
\(468\) 0 0
\(469\) −3.39538 + 10.4499i −0.156784 + 0.482532i
\(470\) 0 0
\(471\) −5.99751 18.4584i −0.276351 0.850520i
\(472\) 0 0
\(473\) 6.25615 8.61086i 0.287658 0.395928i
\(474\) 0 0
\(475\) 1.14896 4.97428i 0.0527177 0.228236i
\(476\) 0 0
\(477\) −2.32186 + 3.19577i −0.106311 + 0.146324i
\(478\) 0 0
\(479\) 7.03656 + 21.6563i 0.321509 + 0.989502i 0.972992 + 0.230839i \(0.0741470\pi\)
−0.651483 + 0.758663i \(0.725853\pi\)
\(480\) 0 0
\(481\) 3.77067 11.6049i 0.171928 0.529139i
\(482\) 0 0
\(483\) 6.28066 + 2.04071i 0.285780 + 0.0928555i
\(484\) 0 0
\(485\) −34.0846 + 12.7416i −1.54770 + 0.578568i
\(486\) 0 0
\(487\) −5.49973 7.56973i −0.249217 0.343017i 0.666020 0.745934i \(-0.267996\pi\)
−0.915237 + 0.402917i \(0.867996\pi\)
\(488\) 0 0
\(489\) 12.2473 + 8.89817i 0.553841 + 0.402389i
\(490\) 0 0
\(491\) −14.7363 + 10.7066i −0.665042 + 0.483181i −0.868362 0.495931i \(-0.834827\pi\)
0.203320 + 0.979112i \(0.434827\pi\)
\(492\) 0 0
\(493\) 7.76000i 0.349493i
\(494\) 0 0
\(495\) −3.47198 + 0.151407i −0.156054 + 0.00680523i
\(496\) 0 0
\(497\) −16.2529 + 5.28089i −0.729043 + 0.236880i
\(498\) 0 0
\(499\) −6.14936 −0.275283 −0.137642 0.990482i \(-0.543952\pi\)
−0.137642 + 0.990482i \(0.543952\pi\)
\(500\) 0 0
\(501\) 18.9060 0.844657
\(502\) 0 0
\(503\) −15.0653 + 4.89502i −0.671730 + 0.218258i −0.624971 0.780648i \(-0.714889\pi\)
−0.0467590 + 0.998906i \(0.514889\pi\)
\(504\) 0 0
\(505\) 12.5932 0.549168i 0.560392 0.0244377i
\(506\) 0 0
\(507\) 7.10376i 0.315489i
\(508\) 0 0
\(509\) −4.09898 + 2.97808i −0.181684 + 0.132001i −0.674910 0.737900i \(-0.735818\pi\)
0.493226 + 0.869901i \(0.335818\pi\)
\(510\) 0 0
\(511\) 13.5647 + 9.85535i 0.600068 + 0.435975i
\(512\) 0 0
\(513\) −0.600159 0.826047i −0.0264976 0.0364709i
\(514\) 0 0
\(515\) 17.6223 6.58764i 0.776530 0.290286i
\(516\) 0 0
\(517\) 11.4596 + 3.72346i 0.503994 + 0.163758i
\(518\) 0 0
\(519\) 7.43798 22.8918i 0.326491 1.00484i
\(520\) 0 0
\(521\) −11.2578 34.6481i −0.493215 1.51796i −0.819720 0.572764i \(-0.805871\pi\)
0.326505 0.945195i \(-0.394129\pi\)
\(522\) 0 0
\(523\) −6.80572 + 9.36727i −0.297593 + 0.409602i −0.931462 0.363839i \(-0.881466\pi\)
0.633869 + 0.773441i \(0.281466\pi\)
\(524\) 0 0
\(525\) −2.57570 6.06974i −0.112413 0.264905i
\(526\) 0 0
\(527\) −6.83887 + 9.41289i −0.297906 + 0.410032i
\(528\) 0 0
\(529\) −0.642075 1.97610i −0.0279163 0.0859175i
\(530\) 0 0
\(531\) −2.42684 + 7.46905i −0.105316 + 0.324129i
\(532\) 0 0
\(533\) −18.3689 5.96843i −0.795647 0.258521i
\(534\) 0 0
\(535\) −0.200873 4.60631i −0.00868448 0.199148i
\(536\) 0 0
\(537\) −0.877183 1.20734i −0.0378532 0.0521005i
\(538\) 0 0
\(539\) −6.61498 4.80606i −0.284927 0.207012i
\(540\) 0 0
\(541\) −17.2715 + 12.5485i −0.742559 + 0.539500i −0.893511 0.449041i \(-0.851766\pi\)
0.150953 + 0.988541i \(0.451766\pi\)
\(542\) 0 0
\(543\) 2.61804i 0.112351i
\(544\) 0 0
\(545\) 24.4550 19.4503i 1.04754 0.833160i
\(546\) 0 0
\(547\) −24.1049 + 7.83217i −1.03065 + 0.334879i −0.775048 0.631902i \(-0.782274\pi\)
−0.255604 + 0.966781i \(0.582274\pi\)
\(548\) 0 0
\(549\) 3.50161 0.149445
\(550\) 0 0
\(551\) 6.02827 0.256813
\(552\) 0 0
\(553\) 1.56900 0.509800i 0.0667207 0.0216789i
\(554\) 0 0
\(555\) −9.36968 6.20236i −0.397721 0.263276i
\(556\) 0 0
\(557\) 0.953134i 0.0403856i 0.999796 + 0.0201928i \(0.00642800\pi\)
−0.999796 + 0.0201928i \(0.993572\pi\)
\(558\) 0 0
\(559\) −13.4533 + 9.77439i −0.569014 + 0.413413i
\(560\) 0 0
\(561\) 1.65264 + 1.20071i 0.0697746 + 0.0506942i
\(562\) 0 0
\(563\) 17.9315 + 24.6806i 0.755723 + 1.04016i 0.997558 + 0.0698461i \(0.0222508\pi\)
−0.241835 + 0.970317i \(0.577749\pi\)
\(564\) 0 0
\(565\) 8.29030 + 10.4235i 0.348776 + 0.438519i
\(566\) 0 0
\(567\) −1.25418 0.407508i −0.0526707 0.0171137i
\(568\) 0 0
\(569\) −9.81510 + 30.2078i −0.411471 + 1.26638i 0.503899 + 0.863762i \(0.331898\pi\)
−0.915370 + 0.402614i \(0.868102\pi\)
\(570\) 0 0
\(571\) −8.65796 26.6465i −0.362324 1.11512i −0.951640 0.307217i \(-0.900602\pi\)
0.589315 0.807903i \(-0.299398\pi\)
\(572\) 0 0
\(573\) −12.1041 + 16.6599i −0.505657 + 0.695977i
\(574\) 0 0
\(575\) −12.8982 + 21.4611i −0.537893 + 0.894991i
\(576\) 0 0
\(577\) −3.33187 + 4.58593i −0.138708 + 0.190915i −0.872719 0.488222i \(-0.837646\pi\)
0.734012 + 0.679137i \(0.237646\pi\)
\(578\) 0 0
\(579\) −1.59438 4.90701i −0.0662603 0.203928i
\(580\) 0 0
\(581\) −3.34438 + 10.2929i −0.138748 + 0.427023i
\(582\) 0 0
\(583\) 5.83888 + 1.89717i 0.241822 + 0.0785726i
\(584\) 0 0
\(585\) 5.23211 + 1.45129i 0.216321 + 0.0600034i
\(586\) 0 0
\(587\) −19.9949 27.5206i −0.825278 1.13590i −0.988784 0.149355i \(-0.952280\pi\)
0.163506 0.986542i \(-0.447720\pi\)
\(588\) 0 0
\(589\) −7.31231 5.31270i −0.301298 0.218906i
\(590\) 0 0
\(591\) 8.50336 6.17805i 0.349781 0.254131i
\(592\) 0 0
\(593\) 22.9225i 0.941313i 0.882316 + 0.470657i \(0.155983\pi\)
−0.882316 + 0.470657i \(0.844017\pi\)
\(594\) 0 0
\(595\) −1.03594 + 3.73473i −0.0424696 + 0.153109i
\(596\) 0 0
\(597\) −3.47341 + 1.12858i −0.142157 + 0.0461896i
\(598\) 0 0
\(599\) 17.7017 0.723270 0.361635 0.932320i \(-0.382219\pi\)
0.361635 + 0.932320i \(0.382219\pi\)
\(600\) 0 0
\(601\) −28.8773 −1.17793 −0.588964 0.808159i \(-0.700464\pi\)
−0.588964 + 0.808159i \(0.700464\pi\)
\(602\) 0 0
\(603\) −7.92426 + 2.57475i −0.322701 + 0.104852i
\(604\) 0 0
\(605\) −6.72145 17.9802i −0.273266 0.731000i
\(606\) 0 0
\(607\) 11.5926i 0.470528i 0.971932 + 0.235264i \(0.0755954\pi\)
−0.971932 + 0.235264i \(0.924405\pi\)
\(608\) 0 0
\(609\) 6.29880 4.57634i 0.255240 0.185443i
\(610\) 0 0
\(611\) −15.2302 11.0654i −0.616146 0.447657i
\(612\) 0 0
\(613\) −7.48123 10.2970i −0.302164 0.415893i 0.630754 0.775983i \(-0.282746\pi\)
−0.932917 + 0.360090i \(0.882746\pi\)
\(614\) 0 0
\(615\) −9.81746 + 14.8309i −0.395878 + 0.598038i
\(616\) 0 0
\(617\) −40.7643 13.2451i −1.64111 0.533229i −0.664323 0.747446i \(-0.731280\pi\)
−0.976786 + 0.214217i \(0.931280\pi\)
\(618\) 0 0
\(619\) −4.30448 + 13.2478i −0.173012 + 0.532475i −0.999537 0.0304242i \(-0.990314\pi\)
0.826525 + 0.562899i \(0.190314\pi\)
\(620\) 0 0
\(621\) 1.54749 + 4.76268i 0.0620985 + 0.191120i
\(622\) 0 0
\(623\) 7.42216 10.2157i 0.297363 0.409285i
\(624\) 0 0
\(625\) 24.6211 4.33601i 0.984844 0.173441i
\(626\) 0 0
\(627\) −0.932763 + 1.28384i −0.0372510 + 0.0512715i
\(628\) 0 0
\(629\) 2.04102 + 6.28160i 0.0813806 + 0.250464i
\(630\) 0 0
\(631\) −2.66089 + 8.18939i −0.105928 + 0.326014i −0.989947 0.141437i \(-0.954828\pi\)
0.884019 + 0.467451i \(0.154828\pi\)
\(632\) 0 0
\(633\) 25.0701 + 8.14575i 0.996445 + 0.323765i
\(634\) 0 0
\(635\) −2.99032 + 4.51736i −0.118667 + 0.179266i
\(636\) 0 0
\(637\) 7.50882 + 10.3350i 0.297510 + 0.409488i
\(638\) 0 0
\(639\) −10.4840 7.61709i −0.414742 0.301327i
\(640\) 0 0
\(641\) 17.0591 12.3942i 0.673794 0.489540i −0.197499 0.980303i \(-0.563282\pi\)
0.871293 + 0.490763i \(0.163282\pi\)
\(642\) 0 0
\(643\) 12.2412i 0.482747i −0.970432 0.241374i \(-0.922402\pi\)
0.970432 0.241374i \(-0.0775979\pi\)
\(644\) 0 0
\(645\) 5.36207 + 14.3438i 0.211131 + 0.564787i
\(646\) 0 0
\(647\) 10.7461 3.49162i 0.422472 0.137270i −0.0900623 0.995936i \(-0.528707\pi\)
0.512535 + 0.858667i \(0.328707\pi\)
\(648\) 0 0
\(649\) 12.2057 0.479117
\(650\) 0 0
\(651\) −11.6736 −0.457524
\(652\) 0 0
\(653\) −20.2319 + 6.57373i −0.791734 + 0.257250i −0.676842 0.736128i \(-0.736652\pi\)
−0.114892 + 0.993378i \(0.536652\pi\)
\(654\) 0 0
\(655\) 6.53633 23.5644i 0.255396 0.920738i
\(656\) 0 0
\(657\) 12.7145i 0.496039i
\(658\) 0 0
\(659\) −14.9986 + 10.8971i −0.584263 + 0.424492i −0.840258 0.542186i \(-0.817597\pi\)
0.255995 + 0.966678i \(0.417597\pi\)
\(660\) 0 0
\(661\) −16.0800 11.6828i −0.625441 0.454409i 0.229377 0.973338i \(-0.426331\pi\)
−0.854818 + 0.518928i \(0.826331\pi\)
\(662\) 0 0
\(663\) −1.87595 2.58203i −0.0728560 0.100278i
\(664\) 0 0
\(665\) −2.90129 0.804763i −0.112507 0.0312074i
\(666\) 0 0
\(667\) −28.1188 9.13635i −1.08876 0.353761i
\(668\) 0 0
\(669\) −5.71502 + 17.5890i −0.220955 + 0.680031i
\(670\) 0 0
\(671\) −1.68173 5.17583i −0.0649224 0.199811i
\(672\) 0 0
\(673\) −25.6055 + 35.2430i −0.987021 + 1.35852i −0.0540603 + 0.998538i \(0.517216\pi\)
−0.932960 + 0.359980i \(0.882784\pi\)
\(674\) 0 0
\(675\) 2.57564 4.28557i 0.0991365 0.164951i
\(676\) 0 0
\(677\) −2.73904 + 3.76996i −0.105270 + 0.144891i −0.858402 0.512978i \(-0.828542\pi\)
0.753132 + 0.657870i \(0.228542\pi\)
\(678\) 0 0
\(679\) 6.63152 + 20.4097i 0.254494 + 0.783253i
\(680\) 0 0
\(681\) 5.76675 17.7482i 0.220982 0.680114i
\(682\) 0 0
\(683\) −37.0242 12.0299i −1.41669 0.460311i −0.502141 0.864786i \(-0.667454\pi\)
−0.914549 + 0.404475i \(0.867454\pi\)
\(684\) 0 0
\(685\) 5.20024 + 6.53830i 0.198691 + 0.249816i
\(686\) 0 0
\(687\) −16.4233 22.6047i −0.626588 0.862424i
\(688\) 0 0
\(689\) −7.76002 5.63798i −0.295633 0.214790i
\(690\) 0 0
\(691\) 7.81060 5.67473i 0.297129 0.215877i −0.429225 0.903198i \(-0.641213\pi\)
0.726354 + 0.687321i \(0.241213\pi\)
\(692\) 0 0
\(693\) 2.04956i 0.0778562i
\(694\) 0 0
\(695\) −4.00479 2.65102i −0.151910 0.100559i
\(696\) 0 0
\(697\) 9.94289 3.23064i 0.376614 0.122369i
\(698\) 0 0
\(699\) −24.7573 −0.936407
\(700\) 0 0
\(701\) 18.6430 0.704135 0.352068 0.935975i \(-0.385479\pi\)
0.352068 + 0.935975i \(0.385479\pi\)
\(702\) 0 0
\(703\) −4.87980 + 1.58554i −0.184045 + 0.0597999i
\(704\) 0 0
\(705\) −13.5677 + 10.7911i −0.510990 + 0.406416i
\(706\) 0 0
\(707\) 7.43395i 0.279582i
\(708\) 0 0
\(709\) −9.85935 + 7.16324i −0.370276 + 0.269021i −0.757325 0.653038i \(-0.773494\pi\)
0.387050 + 0.922059i \(0.373494\pi\)
\(710\) 0 0
\(711\) 1.01209 + 0.735329i 0.0379565 + 0.0275770i
\(712\) 0 0
\(713\) 26.0563 + 35.8634i 0.975817 + 1.34310i
\(714\) 0 0
\(715\) −0.367649 8.43073i −0.0137493 0.315291i
\(716\) 0 0
\(717\) −11.1338 3.61761i −0.415801 0.135102i
\(718\) 0 0
\(719\) 13.2311 40.7210i 0.493435 1.51864i −0.325947 0.945388i \(-0.605683\pi\)
0.819382 0.573248i \(-0.194317\pi\)
\(720\) 0 0
\(721\) −3.42860 10.5522i −0.127688 0.392983i
\(722\) 0 0
\(723\) −17.5257 + 24.1221i −0.651788 + 0.897110i
\(724\) 0 0
\(725\) 11.5315 + 27.1745i 0.428269 + 1.00923i
\(726\) 0 0
\(727\) 0.631037 0.868548i 0.0234039 0.0322126i −0.797155 0.603775i \(-0.793663\pi\)
0.820559 + 0.571562i \(0.193663\pi\)
\(728\) 0 0
\(729\) −0.309017 0.951057i −0.0114451 0.0352243i
\(730\) 0 0
\(731\) 2.78152 8.56063i 0.102878 0.316626i
\(732\) 0 0
\(733\) 0.773538 + 0.251338i 0.0285713 + 0.00928337i 0.323268 0.946308i \(-0.395219\pi\)
−0.294696 + 0.955591i \(0.595219\pi\)
\(734\) 0 0
\(735\) 11.0191 4.11921i 0.406446 0.151940i
\(736\) 0 0
\(737\) 7.61160 + 10.4765i 0.280377 + 0.385906i
\(738\) 0 0
\(739\) 30.6000 + 22.2322i 1.12564 + 0.817824i 0.985054 0.172244i \(-0.0551018\pi\)
0.140585 + 0.990069i \(0.455102\pi\)
\(740\) 0 0
\(741\) 2.00582 1.45732i 0.0736857 0.0535358i
\(742\) 0 0
\(743\) 45.7517i 1.67847i 0.543772 + 0.839233i \(0.316996\pi\)
−0.543772 + 0.839233i \(0.683004\pi\)
\(744\) 0 0
\(745\) 17.5442 0.765068i 0.642768 0.0280299i
\(746\) 0 0
\(747\) −7.80521 + 2.53607i −0.285578 + 0.0927899i
\(748\) 0 0
\(749\) −2.71916 −0.0993560
\(750\) 0 0
\(751\) −39.1925 −1.43016 −0.715078 0.699045i \(-0.753609\pi\)
−0.715078 + 0.699045i \(0.753609\pi\)
\(752\) 0 0
\(753\) −2.73235 + 0.887796i −0.0995725 + 0.0323531i
\(754\) 0 0
\(755\) 50.2915 2.19312i 1.83029 0.0798157i
\(756\) 0 0
\(757\) 4.48615i 0.163052i −0.996671 0.0815259i \(-0.974021\pi\)
0.996671 0.0815259i \(-0.0259793\pi\)
\(758\) 0 0
\(759\) 6.29662 4.57476i 0.228553 0.166053i
\(760\) 0 0
\(761\) −17.2776 12.5529i −0.626312 0.455043i 0.228808 0.973471i \(-0.426517\pi\)
−0.855121 + 0.518429i \(0.826517\pi\)
\(762\) 0 0
\(763\) −10.8316 14.9085i −0.392131 0.539723i
\(764\) 0 0
\(765\) −2.75294 + 1.02912i −0.0995328 + 0.0372078i
\(766\) 0 0
\(767\) −18.1365 5.89290i −0.654870 0.212780i
\(768\) 0 0
\(769\) −7.94179 + 24.4423i −0.286388 + 0.881413i 0.699591 + 0.714544i \(0.253366\pi\)
−0.985979 + 0.166869i \(0.946634\pi\)
\(770\) 0 0
\(771\) 2.50834 + 7.71988i 0.0903357 + 0.278025i
\(772\) 0 0
\(773\) 17.4223 23.9797i 0.626636 0.862490i −0.371179 0.928561i \(-0.621046\pi\)
0.997815 + 0.0660712i \(0.0210465\pi\)
\(774\) 0 0
\(775\) 9.96107 43.1254i 0.357812 1.54911i
\(776\) 0 0
\(777\) −3.89512 + 5.36118i −0.139737 + 0.192331i
\(778\) 0 0
\(779\) 2.50969 + 7.72403i 0.0899189 + 0.276742i
\(780\) 0 0
\(781\) −6.22383 + 19.1550i −0.222706 + 0.685420i
\(782\) 0 0
\(783\) 5.61503 + 1.82443i 0.200665 + 0.0651999i
\(784\) 0 0
\(785\) −1.89073 43.3572i −0.0674829 1.54748i
\(786\) 0 0
\(787\) −4.72360 6.50148i −0.168378 0.231753i 0.716486 0.697601i \(-0.245749\pi\)
−0.884865 + 0.465848i \(0.845749\pi\)
\(788\) 0 0
\(789\) 18.0467 + 13.1117i 0.642479 + 0.466789i
\(790\) 0 0
\(791\) 6.35443 4.61676i 0.225938 0.164153i
\(792\) 0 0
\(793\) 8.50268i 0.301939i
\(794\) 0 0
\(795\) −6.91298 + 5.49824i −0.245178 + 0.195002i
\(796\) 0 0
\(797\) 15.6232 5.07628i 0.553401