Properties

Label 441.2.w.a.251.20
Level $441$
Weight $2$
Character 441.251
Analytic conductor $3.521$
Analytic rank $0$
Dimension $120$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.w (of order \(14\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(20\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 251.20
Character \(\chi\) \(=\) 441.251
Dual form 441.2.w.a.188.20

$q$-expansion

\(f(q)\) \(=\) \(q+(2.13317 + 1.70115i) q^{2} +(1.21148 + 5.30783i) q^{4} +(1.31998 + 0.635668i) q^{5} +(-0.795783 - 2.52324i) q^{7} +(-4.07748 + 8.46697i) q^{8} +O(q^{10})\) \(q+(2.13317 + 1.70115i) q^{2} +(1.21148 + 5.30783i) q^{4} +(1.31998 + 0.635668i) q^{5} +(-0.795783 - 2.52324i) q^{7} +(-4.07748 + 8.46697i) q^{8} +(1.73438 + 3.60147i) q^{10} +(-2.75661 - 2.19832i) q^{11} +(4.51813 + 3.60309i) q^{13} +(2.59486 - 6.73625i) q^{14} +(-13.2912 + 6.40071i) q^{16} +(-0.0162072 + 0.0710083i) q^{17} -4.52011i q^{19} +(-1.77490 + 7.77633i) q^{20} +(-2.14065 - 9.37881i) q^{22} +(-1.76402 + 0.402626i) q^{23} +(-1.77918 - 2.23102i) q^{25} +(3.50857 + 15.3720i) q^{26} +(12.4289 - 7.28073i) q^{28} +(2.61910 + 0.597792i) q^{29} -7.13274i q^{31} +(-20.9170 - 4.77416i) q^{32} +(-0.155368 + 0.123902i) q^{34} +(0.553525 - 3.83647i) q^{35} +(1.33034 - 5.82860i) q^{37} +(7.68938 - 9.64217i) q^{38} +(-10.7644 + 8.58430i) q^{40} +(11.3454 + 5.46367i) q^{41} +(-1.31339 + 0.632493i) q^{43} +(8.32876 - 17.2949i) q^{44} +(-4.44789 - 2.14199i) q^{46} +(-5.84471 + 7.32903i) q^{47} +(-5.73346 + 4.01590i) q^{49} -7.78580i q^{50} +(-13.6510 + 28.3466i) q^{52} +(-9.10665 + 2.07853i) q^{53} +(-2.24126 - 4.65403i) q^{55} +(24.6090 + 3.55058i) q^{56} +(4.57005 + 5.73067i) q^{58} +(-0.107203 + 0.0516262i) q^{59} +(3.20130 + 0.730676i) q^{61} +(12.1339 - 15.2154i) q^{62} +(-18.1023 - 22.6996i) q^{64} +(3.67347 + 7.62804i) q^{65} +5.78127 q^{67} -0.396535 q^{68} +(7.70718 - 7.24224i) q^{70} +(0.0872291 - 0.0199095i) q^{71} +(3.43319 - 2.73788i) q^{73} +(12.7532 - 10.1703i) q^{74} +(23.9920 - 5.47601i) q^{76} +(-3.35323 + 8.70497i) q^{77} -2.89253 q^{79} -21.6128 q^{80} +(14.9073 + 30.9552i) q^{82} +(0.251403 + 0.315250i) q^{83} +(-0.0665309 + 0.0834271i) q^{85} +(-3.87765 - 0.885047i) q^{86} +(29.8532 - 14.3765i) q^{88} +(-6.88377 - 8.63197i) q^{89} +(5.49600 - 14.2676i) q^{91} +(-4.27415 - 8.87536i) q^{92} +(-24.9355 + 5.69137i) q^{94} +(2.87329 - 5.96645i) q^{95} -14.7498i q^{97} +(-19.0621 - 1.18685i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120q + 24q^{4} + O(q^{10}) \) \( 120q + 24q^{4} - 32q^{16} - 44q^{22} - 4q^{25} - 56q^{28} + 112q^{34} - 76q^{37} + 28q^{40} + 8q^{43} - 40q^{46} - 84q^{49} - 140q^{52} + 12q^{58} - 84q^{61} + 24q^{64} + 16q^{67} + 112q^{70} - 84q^{76} - 24q^{79} + 140q^{82} - 96q^{85} - 24q^{88} - 112q^{91} - 112q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{9}{14}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.13317 + 1.70115i 1.50838 + 1.20289i 0.918511 + 0.395396i \(0.129393\pi\)
0.589871 + 0.807498i \(0.299179\pi\)
\(3\) 0 0
\(4\) 1.21148 + 5.30783i 0.605739 + 2.65392i
\(5\) 1.31998 + 0.635668i 0.590313 + 0.284280i 0.705097 0.709111i \(-0.250903\pi\)
−0.114784 + 0.993390i \(0.536618\pi\)
\(6\) 0 0
\(7\) −0.795783 2.52324i −0.300778 0.953694i
\(8\) −4.07748 + 8.46697i −1.44161 + 2.99353i
\(9\) 0 0
\(10\) 1.73438 + 3.60147i 0.548458 + 1.13889i
\(11\) −2.75661 2.19832i −0.831149 0.662819i 0.112542 0.993647i \(-0.464101\pi\)
−0.943691 + 0.330828i \(0.892672\pi\)
\(12\) 0 0
\(13\) 4.51813 + 3.60309i 1.25310 + 0.999317i 0.999487 + 0.0320125i \(0.0101916\pi\)
0.253617 + 0.967305i \(0.418380\pi\)
\(14\) 2.59486 6.73625i 0.693505 1.80034i
\(15\) 0 0
\(16\) −13.2912 + 6.40071i −3.32280 + 1.60018i
\(17\) −0.0162072 + 0.0710083i −0.00393082 + 0.0172220i −0.976855 0.213901i \(-0.931383\pi\)
0.972924 + 0.231123i \(0.0742401\pi\)
\(18\) 0 0
\(19\) 4.52011i 1.03698i −0.855083 0.518492i \(-0.826494\pi\)
0.855083 0.518492i \(-0.173506\pi\)
\(20\) −1.77490 + 7.77633i −0.396879 + 1.73884i
\(21\) 0 0
\(22\) −2.14065 9.37881i −0.456388 1.99957i
\(23\) −1.76402 + 0.402626i −0.367824 + 0.0839533i −0.402438 0.915447i \(-0.631837\pi\)
0.0346140 + 0.999401i \(0.488980\pi\)
\(24\) 0 0
\(25\) −1.77918 2.23102i −0.355836 0.446204i
\(26\) 3.50857 + 15.3720i 0.688086 + 3.01470i
\(27\) 0 0
\(28\) 12.4289 7.28073i 2.34883 1.37593i
\(29\) 2.61910 + 0.597792i 0.486354 + 0.111007i 0.458665 0.888609i \(-0.348328\pi\)
0.0276894 + 0.999617i \(0.491185\pi\)
\(30\) 0 0
\(31\) 7.13274i 1.28108i −0.767926 0.640539i \(-0.778711\pi\)
0.767926 0.640539i \(-0.221289\pi\)
\(32\) −20.9170 4.77416i −3.69763 0.843960i
\(33\) 0 0
\(34\) −0.155368 + 0.123902i −0.0266455 + 0.0212491i
\(35\) 0.553525 3.83647i 0.0935629 0.648483i
\(36\) 0 0
\(37\) 1.33034 5.82860i 0.218706 0.958216i −0.739729 0.672905i \(-0.765046\pi\)
0.958435 0.285310i \(-0.0920967\pi\)
\(38\) 7.68938 9.64217i 1.24738 1.56417i
\(39\) 0 0
\(40\) −10.7644 + 8.58430i −1.70200 + 1.35730i
\(41\) 11.3454 + 5.46367i 1.77186 + 0.853282i 0.964875 + 0.262709i \(0.0846159\pi\)
0.806984 + 0.590573i \(0.201098\pi\)
\(42\) 0 0
\(43\) −1.31339 + 0.632493i −0.200289 + 0.0964543i −0.531340 0.847159i \(-0.678311\pi\)
0.331050 + 0.943613i \(0.392597\pi\)
\(44\) 8.32876 17.2949i 1.25561 2.60730i
\(45\) 0 0
\(46\) −4.44789 2.14199i −0.655805 0.315819i
\(47\) −5.84471 + 7.32903i −0.852538 + 1.06905i 0.144296 + 0.989535i \(0.453908\pi\)
−0.996834 + 0.0795141i \(0.974663\pi\)
\(48\) 0 0
\(49\) −5.73346 + 4.01590i −0.819065 + 0.573700i
\(50\) 7.78580i 1.10108i
\(51\) 0 0
\(52\) −13.6510 + 28.3466i −1.89305 + 3.93096i
\(53\) −9.10665 + 2.07853i −1.25089 + 0.285508i −0.796142 0.605110i \(-0.793129\pi\)
−0.454752 + 0.890618i \(0.650272\pi\)
\(54\) 0 0
\(55\) −2.24126 4.65403i −0.302212 0.627549i
\(56\) 24.6090 + 3.55058i 3.28851 + 0.474466i
\(57\) 0 0
\(58\) 4.57005 + 5.73067i 0.600078 + 0.752474i
\(59\) −0.107203 + 0.0516262i −0.0139566 + 0.00672116i −0.440849 0.897581i \(-0.645323\pi\)
0.426892 + 0.904302i \(0.359608\pi\)
\(60\) 0 0
\(61\) 3.20130 + 0.730676i 0.409885 + 0.0935535i 0.422491 0.906367i \(-0.361156\pi\)
−0.0126066 + 0.999921i \(0.504013\pi\)
\(62\) 12.1339 15.2154i 1.54100 1.93235i
\(63\) 0 0
\(64\) −18.1023 22.6996i −2.26279 2.83745i
\(65\) 3.67347 + 7.62804i 0.455638 + 0.946141i
\(66\) 0 0
\(67\) 5.78127 0.706294 0.353147 0.935568i \(-0.385112\pi\)
0.353147 + 0.935568i \(0.385112\pi\)
\(68\) −0.396535 −0.0480869
\(69\) 0 0
\(70\) 7.70718 7.24224i 0.921184 0.865613i
\(71\) 0.0872291 0.0199095i 0.0103522 0.00236282i −0.217342 0.976096i \(-0.569739\pi\)
0.227694 + 0.973733i \(0.426881\pi\)
\(72\) 0 0
\(73\) 3.43319 2.73788i 0.401824 0.320444i −0.401640 0.915798i \(-0.631560\pi\)
0.803464 + 0.595354i \(0.202988\pi\)
\(74\) 12.7532 10.1703i 1.48252 1.18227i
\(75\) 0 0
\(76\) 23.9920 5.47601i 2.75207 0.628142i
\(77\) −3.35323 + 8.70497i −0.382136 + 0.992024i
\(78\) 0 0
\(79\) −2.89253 −0.325435 −0.162718 0.986673i \(-0.552026\pi\)
−0.162718 + 0.986673i \(0.552026\pi\)
\(80\) −21.6128 −2.41639
\(81\) 0 0
\(82\) 14.9073 + 30.9552i 1.64623 + 3.41843i
\(83\) 0.251403 + 0.315250i 0.0275951 + 0.0346032i 0.795438 0.606036i \(-0.207241\pi\)
−0.767842 + 0.640639i \(0.778670\pi\)
\(84\) 0 0
\(85\) −0.0665309 + 0.0834271i −0.00721629 + 0.00904894i
\(86\) −3.87765 0.885047i −0.418137 0.0954371i
\(87\) 0 0
\(88\) 29.8532 14.3765i 3.18236 1.53254i
\(89\) −6.88377 8.63197i −0.729678 0.914987i 0.269164 0.963094i \(-0.413253\pi\)
−0.998842 + 0.0481072i \(0.984681\pi\)
\(90\) 0 0
\(91\) 5.49600 14.2676i 0.576137 1.49565i
\(92\) −4.27415 8.87536i −0.445611 0.925320i
\(93\) 0 0
\(94\) −24.9355 + 5.69137i −2.57190 + 0.587020i
\(95\) 2.87329 5.96645i 0.294793 0.612144i
\(96\) 0 0
\(97\) 14.7498i 1.49761i −0.662790 0.748805i \(-0.730628\pi\)
0.662790 0.748805i \(-0.269372\pi\)
\(98\) −19.0621 1.18685i −1.92556 0.119890i
\(99\) 0 0
\(100\) 9.68645 12.1464i 0.968645 1.21464i
\(101\) 7.65207 + 3.68504i 0.761409 + 0.366675i 0.773951 0.633246i \(-0.218278\pi\)
−0.0125414 + 0.999921i \(0.503992\pi\)
\(102\) 0 0
\(103\) −1.92234 + 3.99179i −0.189414 + 0.393322i −0.973951 0.226760i \(-0.927187\pi\)
0.784537 + 0.620083i \(0.212901\pi\)
\(104\) −48.9299 + 23.5634i −4.79797 + 2.31058i
\(105\) 0 0
\(106\) −22.9619 11.0579i −2.23026 1.07404i
\(107\) 2.62877 2.09637i 0.254132 0.202664i −0.488134 0.872769i \(-0.662322\pi\)
0.742267 + 0.670105i \(0.233751\pi\)
\(108\) 0 0
\(109\) −7.57622 + 9.50028i −0.725670 + 0.909962i −0.998644 0.0520596i \(-0.983421\pi\)
0.272974 + 0.962022i \(0.411993\pi\)
\(110\) 3.13620 13.7406i 0.299025 1.31011i
\(111\) 0 0
\(112\) 26.7274 + 28.4433i 2.52550 + 2.68764i
\(113\) −11.1377 + 8.88203i −1.04775 + 0.835551i −0.986695 0.162584i \(-0.948017\pi\)
−0.0610528 + 0.998135i \(0.519446\pi\)
\(114\) 0 0
\(115\) −2.58441 0.589874i −0.240997 0.0550060i
\(116\) 14.6259i 1.35799i
\(117\) 0 0
\(118\) −0.316506 0.0722405i −0.0291368 0.00665028i
\(119\) 0.192068 0.0156126i 0.0176069 0.00143121i
\(120\) 0 0
\(121\) 0.318544 + 1.39563i 0.0289585 + 0.126876i
\(122\) 5.58594 + 7.00455i 0.505727 + 0.634162i
\(123\) 0 0
\(124\) 37.8594 8.64116i 3.39988 0.775999i
\(125\) −2.56033 11.2175i −0.229003 1.00333i
\(126\) 0 0
\(127\) −4.26155 + 18.6711i −0.378151 + 1.65679i 0.324974 + 0.945723i \(0.394644\pi\)
−0.703125 + 0.711066i \(0.748213\pi\)
\(128\) 36.3073i 3.20914i
\(129\) 0 0
\(130\) −5.14028 + 22.5210i −0.450832 + 1.97523i
\(131\) −11.8431 + 5.70335i −1.03474 + 0.498304i −0.872585 0.488462i \(-0.837558\pi\)
−0.162153 + 0.986766i \(0.551844\pi\)
\(132\) 0 0
\(133\) −11.4053 + 3.59703i −0.988965 + 0.311902i
\(134\) 12.3324 + 9.83479i 1.06536 + 0.849597i
\(135\) 0 0
\(136\) −0.535141 0.426761i −0.0458880 0.0365944i
\(137\) 1.52964 + 3.17632i 0.130686 + 0.271371i 0.956036 0.293249i \(-0.0947367\pi\)
−0.825350 + 0.564621i \(0.809022\pi\)
\(138\) 0 0
\(139\) 4.97429 10.3292i 0.421914 0.876114i −0.576349 0.817204i \(-0.695523\pi\)
0.998263 0.0589101i \(-0.0187625\pi\)
\(140\) 21.0340 1.70979i 1.77769 0.144503i
\(141\) 0 0
\(142\) 0.219944 + 0.105919i 0.0184573 + 0.00888855i
\(143\) −4.53397 19.8646i −0.379150 1.66116i
\(144\) 0 0
\(145\) 3.07716 + 2.45395i 0.255544 + 0.203789i
\(146\) 11.9811 0.991564
\(147\) 0 0
\(148\) 32.5489 2.67550
\(149\) −9.76826 7.78993i −0.800247 0.638176i 0.135528 0.990774i \(-0.456727\pi\)
−0.935775 + 0.352598i \(0.885298\pi\)
\(150\) 0 0
\(151\) 4.64786 + 20.3636i 0.378237 + 1.65717i 0.702864 + 0.711324i \(0.251904\pi\)
−0.324627 + 0.945842i \(0.605239\pi\)
\(152\) 38.2716 + 18.4306i 3.10424 + 1.49492i
\(153\) 0 0
\(154\) −21.9615 + 12.8649i −1.76971 + 1.03668i
\(155\) 4.53406 9.41507i 0.364184 0.756236i
\(156\) 0 0
\(157\) −5.01362 10.4109i −0.400131 0.830880i −0.999537 0.0304347i \(-0.990311\pi\)
0.599406 0.800445i \(-0.295403\pi\)
\(158\) −6.17027 4.92062i −0.490880 0.391464i
\(159\) 0 0
\(160\) −24.5752 19.5980i −1.94284 1.54936i
\(161\) 2.41970 + 4.13064i 0.190699 + 0.325540i
\(162\) 0 0
\(163\) 8.26562 3.98051i 0.647413 0.311778i −0.0812055 0.996697i \(-0.525877\pi\)
0.728619 + 0.684920i \(0.240163\pi\)
\(164\) −15.2555 + 66.8388i −1.19126 + 5.21923i
\(165\) 0 0
\(166\) 1.10016i 0.0853888i
\(167\) −4.71322 + 20.6500i −0.364720 + 1.59794i 0.376324 + 0.926488i \(0.377188\pi\)
−0.741045 + 0.671456i \(0.765669\pi\)
\(168\) 0 0
\(169\) 4.53849 + 19.8844i 0.349114 + 1.52957i
\(170\) −0.283844 + 0.0647855i −0.0217698 + 0.00496882i
\(171\) 0 0
\(172\) −4.94831 6.20498i −0.377305 0.473126i
\(173\) 1.40176 + 6.14152i 0.106574 + 0.466931i 0.999848 + 0.0174192i \(0.00554499\pi\)
−0.893274 + 0.449512i \(0.851598\pi\)
\(174\) 0 0
\(175\) −4.21355 + 6.26470i −0.318515 + 0.473567i
\(176\) 50.7095 + 11.5741i 3.82237 + 0.872431i
\(177\) 0 0
\(178\) 30.1238i 2.25787i
\(179\) −10.2984 2.35054i −0.769737 0.175687i −0.180420 0.983590i \(-0.557746\pi\)
−0.589316 + 0.807902i \(0.700603\pi\)
\(180\) 0 0
\(181\) −11.4269 + 9.11265i −0.849355 + 0.677338i −0.948168 0.317768i \(-0.897067\pi\)
0.0988136 + 0.995106i \(0.468495\pi\)
\(182\) 35.9952 21.0857i 2.66814 1.56298i
\(183\) 0 0
\(184\) 3.78373 16.5776i 0.278940 1.22212i
\(185\) 5.46107 6.84797i 0.401506 0.503473i
\(186\) 0 0
\(187\) 0.200776 0.160114i 0.0146822 0.0117087i
\(188\) −45.9820 22.1438i −3.35358 1.61500i
\(189\) 0 0
\(190\) 16.2790 7.83957i 1.18101 0.568742i
\(191\) −1.47744 + 3.06794i −0.106904 + 0.221988i −0.947558 0.319585i \(-0.896457\pi\)
0.840654 + 0.541573i \(0.182171\pi\)
\(192\) 0 0
\(193\) −24.4304 11.7651i −1.75854 0.846867i −0.973921 0.226886i \(-0.927146\pi\)
−0.784617 0.619981i \(-0.787140\pi\)
\(194\) 25.0915 31.4638i 1.80147 2.25897i
\(195\) 0 0
\(196\) −28.2617 25.5671i −2.01869 1.82622i
\(197\) 10.1592i 0.723813i −0.932214 0.361906i \(-0.882126\pi\)
0.932214 0.361906i \(-0.117874\pi\)
\(198\) 0 0
\(199\) −0.770780 + 1.60054i −0.0546391 + 0.113459i −0.926501 0.376293i \(-0.877199\pi\)
0.871862 + 0.489752i \(0.162913\pi\)
\(200\) 26.1446 5.96732i 1.84870 0.421954i
\(201\) 0 0
\(202\) 10.0544 + 20.8781i 0.707424 + 1.46898i
\(203\) −0.575863 7.08432i −0.0404176 0.497222i
\(204\) 0 0
\(205\) 11.5026 + 14.4239i 0.803380 + 1.00741i
\(206\) −10.8913 + 5.24498i −0.758834 + 0.365435i
\(207\) 0 0
\(208\) −83.1137 18.9702i −5.76290 1.31534i
\(209\) −9.93666 + 12.4602i −0.687333 + 0.861888i
\(210\) 0 0
\(211\) 1.59686 + 2.00239i 0.109932 + 0.137851i 0.833753 0.552137i \(-0.186187\pi\)
−0.723821 + 0.689987i \(0.757616\pi\)
\(212\) −22.0650 45.8185i −1.51543 3.14683i
\(213\) 0 0
\(214\) 9.17385 0.627112
\(215\) −2.13570 −0.145653
\(216\) 0 0
\(217\) −17.9976 + 5.67612i −1.22176 + 0.385320i
\(218\) −32.3228 + 7.37747i −2.18918 + 0.499665i
\(219\) 0 0
\(220\) 21.9876 17.5345i 1.48240 1.18218i
\(221\) −0.329076 + 0.262429i −0.0221360 + 0.0176529i
\(222\) 0 0
\(223\) 9.80139 2.23710i 0.656350 0.149808i 0.118640 0.992937i \(-0.462147\pi\)
0.537710 + 0.843130i \(0.319290\pi\)
\(224\) 4.59903 + 56.5777i 0.307285 + 3.78025i
\(225\) 0 0
\(226\) −38.8683 −2.58548
\(227\) −8.61559 −0.571837 −0.285918 0.958254i \(-0.592299\pi\)
−0.285918 + 0.958254i \(0.592299\pi\)
\(228\) 0 0
\(229\) −0.485330 1.00780i −0.0320715 0.0665971i 0.884318 0.466886i \(-0.154624\pi\)
−0.916389 + 0.400289i \(0.868910\pi\)
\(230\) −4.50952 5.65476i −0.297349 0.372864i
\(231\) 0 0
\(232\) −15.7408 + 19.7383i −1.03343 + 1.29589i
\(233\) 22.2452 + 5.07733i 1.45733 + 0.332627i 0.876503 0.481397i \(-0.159870\pi\)
0.580831 + 0.814024i \(0.302728\pi\)
\(234\) 0 0
\(235\) −12.3737 + 5.95887i −0.807172 + 0.388714i
\(236\) −0.403898 0.506472i −0.0262915 0.0329685i
\(237\) 0 0
\(238\) 0.436274 + 0.293432i 0.0282795 + 0.0190204i
\(239\) −6.59530 13.6953i −0.426614 0.885874i −0.997878 0.0651074i \(-0.979261\pi\)
0.571264 0.820766i \(-0.306453\pi\)
\(240\) 0 0
\(241\) 4.66449 1.06464i 0.300466 0.0685795i −0.0696299 0.997573i \(-0.522182\pi\)
0.370096 + 0.928993i \(0.379325\pi\)
\(242\) −1.69467 + 3.51902i −0.108937 + 0.226211i
\(243\) 0 0
\(244\) 17.8772i 1.14447i
\(245\) −10.1208 + 1.65633i −0.646596 + 0.105819i
\(246\) 0 0
\(247\) 16.2864 20.4224i 1.03628 1.29945i
\(248\) 60.3927 + 29.0836i 3.83494 + 1.84681i
\(249\) 0 0
\(250\) 13.6211 28.2844i 0.861472 1.78887i
\(251\) 8.64206 4.16179i 0.545482 0.262690i −0.140785 0.990040i \(-0.544963\pi\)
0.686267 + 0.727350i \(0.259248\pi\)
\(252\) 0 0
\(253\) 5.74782 + 2.76800i 0.361362 + 0.174023i
\(254\) −40.8529 + 32.5791i −2.56334 + 2.04419i
\(255\) 0 0
\(256\) 25.5594 32.0504i 1.59746 2.00315i
\(257\) −1.20901 + 5.29704i −0.0754162 + 0.330420i −0.998536 0.0540927i \(-0.982773\pi\)
0.923120 + 0.384513i \(0.125631\pi\)
\(258\) 0 0
\(259\) −15.7656 + 1.28154i −0.979627 + 0.0796309i
\(260\) −36.0380 + 28.7394i −2.23498 + 1.78234i
\(261\) 0 0
\(262\) −34.9657 7.98068i −2.16019 0.493048i
\(263\) 15.2273i 0.938953i −0.882945 0.469476i \(-0.844443\pi\)
0.882945 0.469476i \(-0.155557\pi\)
\(264\) 0 0
\(265\) −13.3418 3.04519i −0.819582 0.187064i
\(266\) −30.4486 11.7290i −1.86692 0.719154i
\(267\) 0 0
\(268\) 7.00388 + 30.6860i 0.427830 + 1.87445i
\(269\) 2.44899 + 3.07094i 0.149318 + 0.187238i 0.850865 0.525385i \(-0.176079\pi\)
−0.701547 + 0.712623i \(0.747507\pi\)
\(270\) 0 0
\(271\) 23.2419 5.30480i 1.41184 0.322244i 0.552444 0.833550i \(-0.313695\pi\)
0.859398 + 0.511307i \(0.170838\pi\)
\(272\) −0.239090 1.04752i −0.0144970 0.0635154i
\(273\) 0 0
\(274\) −2.14042 + 9.37778i −0.129307 + 0.566533i
\(275\) 10.0613i 0.606717i
\(276\) 0 0
\(277\) −0.283943 + 1.24404i −0.0170605 + 0.0747470i −0.982742 0.184984i \(-0.940777\pi\)
0.965681 + 0.259731i \(0.0836339\pi\)
\(278\) 28.1826 13.5720i 1.69028 0.813996i
\(279\) 0 0
\(280\) 30.2263 + 20.3298i 1.80637 + 1.21494i
\(281\) 3.91830 + 3.12474i 0.233746 + 0.186406i 0.733357 0.679844i \(-0.237952\pi\)
−0.499611 + 0.866250i \(0.666524\pi\)
\(282\) 0 0
\(283\) 12.6385 + 10.0788i 0.751279 + 0.599125i 0.922450 0.386116i \(-0.126184\pi\)
−0.171171 + 0.985241i \(0.554755\pi\)
\(284\) 0.211352 + 0.438878i 0.0125415 + 0.0260426i
\(285\) 0 0
\(286\) 24.1209 50.0877i 1.42630 2.96174i
\(287\) 4.75764 32.9751i 0.280835 1.94646i
\(288\) 0 0
\(289\) 15.3117 + 7.37372i 0.900688 + 0.433748i
\(290\) 2.38957 + 10.4694i 0.140321 + 0.614784i
\(291\) 0 0
\(292\) 18.6914 + 14.9059i 1.09383 + 0.872303i
\(293\) 20.4628 1.19545 0.597726 0.801701i \(-0.296071\pi\)
0.597726 + 0.801701i \(0.296071\pi\)
\(294\) 0 0
\(295\) −0.174323 −0.0101495
\(296\) 43.9262 + 35.0299i 2.55316 + 2.03607i
\(297\) 0 0
\(298\) −7.58556 33.2345i −0.439420 1.92522i
\(299\) −9.42077 4.53681i −0.544817 0.262370i
\(300\) 0 0
\(301\) 2.64110 + 2.81066i 0.152231 + 0.162004i
\(302\) −24.7268 + 51.3458i −1.42287 + 2.95462i
\(303\) 0 0
\(304\) 28.9319 + 60.0777i 1.65936 + 3.44569i
\(305\) 3.76118 + 2.99944i 0.215365 + 0.171748i
\(306\) 0 0
\(307\) −2.25444 1.79785i −0.128667 0.102609i 0.557042 0.830485i \(-0.311936\pi\)
−0.685709 + 0.727876i \(0.740508\pi\)
\(308\) −50.2669 7.25249i −2.86422 0.413249i
\(309\) 0 0
\(310\) 25.6884 12.3709i 1.45900 0.702618i
\(311\) 6.09451 26.7018i 0.345588 1.51412i −0.441490 0.897266i \(-0.645550\pi\)
0.787078 0.616854i \(-0.211593\pi\)
\(312\) 0 0
\(313\) 24.6969i 1.39595i 0.716121 + 0.697976i \(0.245916\pi\)
−0.716121 + 0.697976i \(0.754084\pi\)
\(314\) 7.01556 30.7372i 0.395911 1.73460i
\(315\) 0 0
\(316\) −3.50424 15.3531i −0.197129 0.863678i
\(317\) 14.6984 3.35481i 0.825544 0.188425i 0.211180 0.977447i \(-0.432269\pi\)
0.614365 + 0.789022i \(0.289412\pi\)
\(318\) 0 0
\(319\) −5.90569 7.40550i −0.330655 0.414628i
\(320\) −9.46528 41.4701i −0.529125 2.31825i
\(321\) 0 0
\(322\) −1.86520 + 12.9276i −0.103943 + 0.720429i
\(323\) 0.320965 + 0.0732582i 0.0178590 + 0.00407620i
\(324\) 0 0
\(325\) 16.4906i 0.914733i
\(326\) 24.4034 + 5.56993i 1.35158 + 0.308490i
\(327\) 0 0
\(328\) −92.5216 + 73.7835i −5.10865 + 4.07401i
\(329\) 23.1440 + 8.91526i 1.27597 + 0.491514i
\(330\) 0 0
\(331\) −3.13342 + 13.7284i −0.172228 + 0.754582i 0.812850 + 0.582474i \(0.197915\pi\)
−0.985078 + 0.172108i \(0.944942\pi\)
\(332\) −1.36872 + 1.71633i −0.0751185 + 0.0941956i
\(333\) 0 0
\(334\) −45.1828 + 36.0321i −2.47229 + 1.97159i
\(335\) 7.63115 + 3.67497i 0.416934 + 0.200785i
\(336\) 0 0
\(337\) −1.80007 + 0.866866i −0.0980558 + 0.0472212i −0.482269 0.876023i \(-0.660187\pi\)
0.384213 + 0.923245i \(0.374473\pi\)
\(338\) −24.1450 + 50.1375i −1.31331 + 2.72712i
\(339\) 0 0
\(340\) −0.523418 0.252065i −0.0283863 0.0136701i
\(341\) −15.6801 + 19.6622i −0.849123 + 1.06477i
\(342\) 0 0
\(343\) 14.6957 + 11.2711i 0.793491 + 0.608582i
\(344\) 13.6994i 0.738621i
\(345\) 0 0
\(346\) −7.45744 + 15.4855i −0.400915 + 0.832508i
\(347\) −20.7078 + 4.72642i −1.11165 + 0.253728i −0.738641 0.674099i \(-0.764532\pi\)
−0.373012 + 0.927826i \(0.621675\pi\)
\(348\) 0 0
\(349\) −6.81637 14.1543i −0.364872 0.757664i 0.635018 0.772497i \(-0.280993\pi\)
−0.999890 + 0.0148331i \(0.995278\pi\)
\(350\) −19.6454 + 6.19581i −1.05009 + 0.331180i
\(351\) 0 0
\(352\) 47.1648 + 59.1427i 2.51389 + 3.15232i
\(353\) 13.6112 6.55479i 0.724449 0.348876i −0.0350491 0.999386i \(-0.511159\pi\)
0.759498 + 0.650509i \(0.225444\pi\)
\(354\) 0 0
\(355\) 0.127796 + 0.0291687i 0.00678273 + 0.00154811i
\(356\) 37.4775 46.9953i 1.98631 2.49075i
\(357\) 0 0
\(358\) −17.9696 22.5332i −0.949723 1.19091i
\(359\) 0.547033 + 1.13592i 0.0288713 + 0.0599518i 0.914906 0.403668i \(-0.132265\pi\)
−0.886034 + 0.463619i \(0.846550\pi\)
\(360\) 0 0
\(361\) −1.43137 −0.0753354
\(362\) −39.8775 −2.09592
\(363\) 0 0
\(364\) 82.3883 + 11.8870i 4.31832 + 0.623046i
\(365\) 6.27211 1.43157i 0.328297 0.0749318i
\(366\) 0 0
\(367\) 6.88746 5.49257i 0.359523 0.286710i −0.427024 0.904240i \(-0.640438\pi\)
0.786547 + 0.617530i \(0.211867\pi\)
\(368\) 20.8689 16.6424i 1.08786 0.867543i
\(369\) 0 0
\(370\) 23.2988 5.31781i 1.21125 0.276460i
\(371\) 12.4915 + 21.3242i 0.648529 + 1.10710i
\(372\) 0 0
\(373\) 22.5978 1.17007 0.585036 0.811008i \(-0.301081\pi\)
0.585036 + 0.811008i \(0.301081\pi\)
\(374\) 0.700667 0.0362306
\(375\) 0 0
\(376\) −38.2230 79.3709i −1.97120 4.09324i
\(377\) 9.67953 + 12.1377i 0.498521 + 0.625126i
\(378\) 0 0
\(379\) 0.280801 0.352114i 0.0144238 0.0180869i −0.774567 0.632492i \(-0.782032\pi\)
0.788991 + 0.614405i \(0.210604\pi\)
\(380\) 35.1498 + 8.02272i 1.80315 + 0.411557i
\(381\) 0 0
\(382\) −8.37066 + 4.03110i −0.428280 + 0.206249i
\(383\) 11.2565 + 14.1152i 0.575180 + 0.721253i 0.981282 0.192575i \(-0.0616838\pi\)
−0.406102 + 0.913828i \(0.633112\pi\)
\(384\) 0 0
\(385\) −9.95966 + 9.35884i −0.507592 + 0.476971i
\(386\) −32.1001 66.6566i −1.63385 3.39273i
\(387\) 0 0
\(388\) 78.2893 17.8690i 3.97453 0.907162i
\(389\) −0.724287 + 1.50400i −0.0367228 + 0.0762557i −0.918523 0.395367i \(-0.870617\pi\)
0.881800 + 0.471623i \(0.156332\pi\)
\(390\) 0 0
\(391\) 0.131786i 0.00666468i
\(392\) −10.6245 64.9198i −0.536617 3.27894i
\(393\) 0 0
\(394\) 17.2823 21.6713i 0.870670 1.09179i
\(395\) −3.81808 1.83869i −0.192108 0.0925145i
\(396\) 0 0
\(397\) −3.34201 + 6.93975i −0.167731 + 0.348296i −0.967843 0.251553i \(-0.919059\pi\)
0.800113 + 0.599849i \(0.204773\pi\)
\(398\) −4.36697 + 2.10302i −0.218896 + 0.105415i
\(399\) 0 0
\(400\) 37.9275 + 18.2649i 1.89638 + 0.913247i
\(401\) 0.0933946 0.0744797i 0.00466390 0.00371934i −0.621155 0.783688i \(-0.713336\pi\)
0.625819 + 0.779968i \(0.284765\pi\)
\(402\) 0 0
\(403\) 25.6999 32.2267i 1.28020 1.60532i
\(404\) −10.2893 + 45.0803i −0.511911 + 2.24283i
\(405\) 0 0
\(406\) 10.8231 16.0917i 0.537140 0.798618i
\(407\) −16.4804 + 13.1427i −0.816901 + 0.651457i
\(408\) 0 0
\(409\) −8.45967 1.93086i −0.418304 0.0954751i 0.00818811 0.999966i \(-0.497394\pi\)
−0.426492 + 0.904491i \(0.640251\pi\)
\(410\) 50.3363i 2.48593i
\(411\) 0 0
\(412\) −23.5166 5.36752i −1.15858 0.264438i
\(413\) 0.215576 + 0.229415i 0.0106078 + 0.0112888i
\(414\) 0 0
\(415\) 0.131453 + 0.575932i 0.00645276 + 0.0282714i
\(416\) −77.3038 96.9360i −3.79013 4.75268i
\(417\) 0 0
\(418\) −42.3932 + 9.67598i −2.07352 + 0.473267i
\(419\) 4.97988 + 21.8183i 0.243283 + 1.06589i 0.938007 + 0.346616i \(0.112669\pi\)
−0.694724 + 0.719276i \(0.744473\pi\)
\(420\) 0 0
\(421\) −3.38186 + 14.8169i −0.164822 + 0.722131i 0.823192 + 0.567764i \(0.192191\pi\)
−0.988013 + 0.154368i \(0.950666\pi\)
\(422\) 6.98795i 0.340168i
\(423\) 0 0
\(424\) 19.5333 85.5809i 0.948620 4.15618i
\(425\) 0.187256 0.0901780i 0.00908327 0.00437427i
\(426\) 0 0
\(427\) −0.703872 8.65910i −0.0340628 0.419043i
\(428\) 14.3119 + 11.4134i 0.691791 + 0.551685i
\(429\) 0 0
\(430\) −4.55581 3.63314i −0.219701 0.175206i
\(431\) −10.0936 20.9597i −0.486193 1.00959i −0.989372 0.145408i \(-0.953550\pi\)
0.503178 0.864183i \(-0.332164\pi\)
\(432\) 0 0
\(433\) 4.12640 8.56856i 0.198302 0.411779i −0.777977 0.628292i \(-0.783754\pi\)
0.976280 + 0.216513i \(0.0694685\pi\)
\(434\) −48.0479 18.5085i −2.30637 0.888435i
\(435\) 0 0
\(436\) −59.6044 28.7039i −2.85453 1.37467i
\(437\) 1.81991 + 7.97356i 0.0870583 + 0.381427i
\(438\) 0 0
\(439\) 1.45640 + 1.16144i 0.0695101 + 0.0554325i 0.657629 0.753342i \(-0.271560\pi\)
−0.588118 + 0.808775i \(0.700131\pi\)
\(440\) 48.5443 2.31426
\(441\) 0 0
\(442\) −1.14841 −0.0546241
\(443\) 21.6172 + 17.2392i 1.02707 + 0.819057i 0.983667 0.180000i \(-0.0576099\pi\)
0.0433990 + 0.999058i \(0.486181\pi\)
\(444\) 0 0
\(445\) −3.59936 15.7698i −0.170626 0.747561i
\(446\) 24.7137 + 11.9015i 1.17023 + 0.563552i
\(447\) 0 0
\(448\) −42.8710 + 63.7405i −2.02546 + 3.01146i
\(449\) 1.12501 2.33611i 0.0530926 0.110248i −0.872735 0.488195i \(-0.837656\pi\)
0.925827 + 0.377947i \(0.123370\pi\)
\(450\) 0 0
\(451\) −19.2640 40.0021i −0.907107 1.88363i
\(452\) −60.6374 48.3567i −2.85214 2.27451i
\(453\) 0 0
\(454\) −18.3785 14.6564i −0.862548 0.687859i
\(455\) 16.3241 15.3393i 0.765284 0.719117i
\(456\) 0 0
\(457\) −17.3537 + 8.35711i −0.811773 + 0.390929i −0.793248 0.608899i \(-0.791611\pi\)
−0.0185252 + 0.999828i \(0.505897\pi\)
\(458\) 0.679121 2.97542i 0.0317333 0.139032i
\(459\) 0 0
\(460\) 14.4322i 0.672906i
\(461\) 2.93845 12.8742i 0.136857 0.599610i −0.859258 0.511543i \(-0.829074\pi\)
0.996115 0.0880666i \(-0.0280688\pi\)
\(462\) 0 0
\(463\) 5.06271 + 22.1812i 0.235284 + 1.03085i 0.945182 + 0.326543i \(0.105884\pi\)
−0.709898 + 0.704304i \(0.751259\pi\)
\(464\) −38.6372 + 8.81870i −1.79369 + 0.409398i
\(465\) 0 0
\(466\) 38.8157 + 48.6733i 1.79810 + 2.25475i
\(467\) −2.10430 9.21953i −0.0973753 0.426629i 0.902617 0.430444i \(-0.141643\pi\)
−0.999993 + 0.00381464i \(0.998786\pi\)
\(468\) 0 0
\(469\) −4.60063 14.5875i −0.212438 0.673589i
\(470\) −36.5322 8.33824i −1.68511 0.384614i
\(471\) 0 0
\(472\) 1.11819i 0.0514689i
\(473\) 5.01092 + 1.14371i 0.230402 + 0.0525878i
\(474\) 0 0
\(475\) −10.0844 + 8.04208i −0.462706 + 0.368996i
\(476\) 0.315556 + 1.00055i 0.0144635 + 0.0458602i
\(477\) 0 0
\(478\) 9.22879 40.4340i 0.422115 1.84941i
\(479\) 17.2516 21.6328i 0.788246 0.988429i −0.211693 0.977336i \(-0.567898\pi\)
0.999938 0.0110924i \(-0.00353089\pi\)
\(480\) 0 0
\(481\) 27.0116 21.5410i 1.23162 0.982187i
\(482\) 11.7613 + 5.66393i 0.535712 + 0.257985i
\(483\) 0 0
\(484\) −7.02187 + 3.38156i −0.319176 + 0.153707i
\(485\) 9.37595 19.4694i 0.425740 0.884058i
\(486\) 0 0
\(487\) 35.6076 + 17.1477i 1.61353 + 0.777037i 0.999921 0.0125691i \(-0.00400099\pi\)
0.613614 + 0.789606i \(0.289715\pi\)
\(488\) −19.2399 + 24.1260i −0.870947 + 1.09213i
\(489\) 0 0
\(490\) −24.4071 13.6838i −1.10260 0.618171i
\(491\) 8.27699i 0.373535i −0.982404 0.186768i \(-0.940199\pi\)
0.982404 0.186768i \(-0.0598012\pi\)
\(492\) 0 0
\(493\) −0.0848964 + 0.176289i −0.00382354 + 0.00793966i
\(494\) 69.4832 15.8591i 3.12620 0.713534i
\(495\) 0 0
\(496\) 45.6546 + 94.8027i 2.04995 + 4.25677i
\(497\) −0.119652 0.204256i −0.00536711 0.00916214i
\(498\) 0 0
\(499\) −3.45628 4.33403i −0.154724 0.194018i 0.698428 0.715681i \(-0.253883\pi\)
−0.853152 + 0.521663i \(0.825312\pi\)
\(500\) 56.4390 27.1796i 2.52403 1.21551i
\(501\) 0 0
\(502\) 25.5148 + 5.82359i 1.13878 + 0.259920i
\(503\) 14.2223 17.8342i 0.634141 0.795187i −0.356116 0.934442i \(-0.615899\pi\)
0.990257 + 0.139255i \(0.0444706\pi\)
\(504\) 0 0
\(505\) 7.75810 + 9.72835i 0.345231 + 0.432906i
\(506\) 7.55231 + 15.6825i 0.335741 + 0.697173i
\(507\) 0 0
\(508\) −104.266 −4.62604
\(509\) 10.5120 0.465936 0.232968 0.972484i \(-0.425156\pi\)
0.232968 + 0.972484i \(0.425156\pi\)
\(510\) 0 0
\(511\) −9.64038 6.48399i −0.426465 0.286835i
\(512\) 38.2512 8.73059i 1.69048 0.385841i
\(513\) 0 0
\(514\) −11.5901 + 9.24278i −0.511217 + 0.407682i
\(515\) −5.07490 + 4.04710i −0.223627 + 0.178337i
\(516\) 0 0
\(517\) 32.2231 7.35472i 1.41717 0.323460i
\(518\) −35.8108 24.0859i −1.57344 1.05827i
\(519\) 0 0
\(520\) −79.5649 −3.48915
\(521\) −10.3652 −0.454108 −0.227054 0.973882i \(-0.572909\pi\)
−0.227054 + 0.973882i \(0.572909\pi\)
\(522\) 0 0
\(523\) −15.5673 32.3258i −0.680710 1.41351i −0.899142 0.437657i \(-0.855808\pi\)
0.218432 0.975852i \(-0.429906\pi\)
\(524\) −44.6201 55.9518i −1.94924 2.44427i
\(525\) 0 0
\(526\) 25.9038 32.4824i 1.12946 1.41630i
\(527\) 0.506484 + 0.115602i 0.0220628 + 0.00503569i
\(528\) 0 0
\(529\) −17.7726 + 8.55884i −0.772723 + 0.372124i
\(530\) −23.2801 29.1924i −1.01122 1.26804i
\(531\) 0 0
\(532\) −32.9097 56.1798i −1.42682 2.43570i
\(533\) 31.5741 + 65.5642i 1.36762 + 2.83990i
\(534\) 0 0
\(535\) 4.80251 1.09614i 0.207631 0.0473904i
\(536\) −23.5730 + 48.9498i −1.01820 + 2.11431i
\(537\) 0 0
\(538\) 10.7169i 0.462040i
\(539\) 24.6332 + 1.53372i 1.06103 + 0.0660621i
\(540\) 0 0
\(541\) 3.39539 4.25769i 0.145979 0.183052i −0.703466 0.710729i \(-0.748365\pi\)
0.849445 + 0.527677i \(0.176937\pi\)
\(542\) 58.6032 + 28.2218i 2.51722 + 1.21223i
\(543\) 0 0
\(544\) 0.678010 1.40790i 0.0290694 0.0603633i
\(545\) −16.0395 + 7.72421i −0.687056 + 0.330869i
\(546\) 0 0
\(547\) −6.43439 3.09864i −0.275115 0.132488i 0.291240 0.956650i \(-0.405932\pi\)
−0.566354 + 0.824162i \(0.691647\pi\)
\(548\) −15.0063 + 11.9671i −0.641036 + 0.511209i
\(549\) 0 0
\(550\) −17.1157 + 21.4624i −0.729816 + 0.915160i
\(551\) 2.70208 11.8386i 0.115113 0.504341i
\(552\) 0 0
\(553\) 2.30183 + 7.29854i 0.0978836 + 0.310366i
\(554\) −2.72199 + 2.17072i −0.115646 + 0.0922250i
\(555\) 0 0
\(556\) 60.8521 + 13.8891i 2.58070 + 0.589029i
\(557\) 38.5139i 1.63189i −0.578131 0.815944i \(-0.696218\pi\)
0.578131 0.815944i \(-0.303782\pi\)
\(558\) 0 0
\(559\) −8.21298 1.87456i −0.347372 0.0792854i
\(560\) 17.1991 + 54.5343i 0.726796 + 2.30450i
\(561\) 0 0
\(562\) 3.04276 + 13.3312i 0.128351 + 0.562343i
\(563\) 22.1754 + 27.8071i 0.934582 + 1.17193i 0.984888 + 0.173195i \(0.0554090\pi\)
−0.0503056 + 0.998734i \(0.516020\pi\)
\(564\) 0 0
\(565\) −20.3476 + 4.64420i −0.856028 + 0.195383i
\(566\) 9.81443 + 42.9998i 0.412531 + 1.80742i
\(567\) 0 0
\(568\) −0.187102 + 0.819747i −0.00785062 + 0.0343958i
\(569\) 17.9670i 0.753215i −0.926373 0.376607i \(-0.877091\pi\)
0.926373 0.376607i \(-0.122909\pi\)
\(570\) 0 0
\(571\) −1.78530 + 7.82192i −0.0747125 + 0.327337i −0.998448 0.0556944i \(-0.982263\pi\)
0.923735 + 0.383031i \(0.125120\pi\)
\(572\) 99.9453 48.1311i 4.17892 2.01246i
\(573\) 0 0
\(574\) 66.2445 62.2482i 2.76499 2.59819i
\(575\) 4.03677 + 3.21922i 0.168345 + 0.134251i
\(576\) 0 0
\(577\) 24.0467 + 19.1766i 1.00108 + 0.798334i 0.979502 0.201433i \(-0.0645599\pi\)
0.0215767 + 0.999767i \(0.493131\pi\)
\(578\) 20.1187 + 41.7769i 0.836827 + 1.73769i
\(579\) 0 0
\(580\) −9.29725 + 19.3059i −0.386047 + 0.801636i
\(581\) 0.595388 0.885221i 0.0247008 0.0367252i
\(582\) 0 0
\(583\) 29.6728 + 14.2896i 1.22892 + 0.591817i
\(584\) 9.18277 + 40.2323i 0.379986 + 1.66483i
\(585\) 0 0
\(586\) 43.6508 + 34.8103i 1.80320 + 1.43800i
\(587\) −40.1365 −1.65661 −0.828305 0.560277i \(-0.810694\pi\)
−0.828305 + 0.560277i \(0.810694\pi\)
\(588\) 0 0
\(589\) −32.2408 −1.32846
\(590\) −0.371861 0.296549i −0.0153093 0.0122087i
\(591\) 0 0
\(592\) 19.6253 + 85.9842i 0.806596 + 3.53393i
\(593\) −5.84985 2.81714i −0.240224 0.115686i 0.309899 0.950770i \(-0.399705\pi\)
−0.550123 + 0.835084i \(0.685419\pi\)
\(594\) 0 0
\(595\) 0.263451 + 0.101483i 0.0108004 + 0.00416041i
\(596\) 29.5136 61.2856i 1.20892 2.51036i
\(597\) 0 0
\(598\) −12.3784 25.7039i −0.506189 1.05111i
\(599\) −17.3733 13.8548i −0.709855 0.566090i 0.200613 0.979671i \(-0.435707\pi\)
−0.910468 + 0.413580i \(0.864278\pi\)
\(600\) 0 0
\(601\) 1.77391 + 1.41465i 0.0723593 + 0.0577046i 0.659001 0.752142i \(-0.270979\pi\)
−0.586642 + 0.809846i \(0.699551\pi\)
\(602\) 0.852580 + 10.4885i 0.0347486 + 0.427480i
\(603\) 0 0
\(604\) −102.456 + 49.3401i −4.16887 + 2.00762i
\(605\) −0.466688 + 2.04469i −0.0189736 + 0.0831286i
\(606\) 0 0
\(607\) 11.1437i 0.452309i 0.974091 + 0.226155i \(0.0726154\pi\)
−0.974091 + 0.226155i \(0.927385\pi\)
\(608\) −21.5797 + 94.5469i −0.875173 + 3.83438i
\(609\) 0 0
\(610\) 2.92075 + 12.7967i 0.118258 + 0.518122i
\(611\) −52.8143 + 12.0545i −2.13664 + 0.487674i
\(612\) 0 0
\(613\) 13.0330 + 16.3429i 0.526399 + 0.660084i 0.971954 0.235171i \(-0.0755650\pi\)
−0.445555 + 0.895255i \(0.646994\pi\)
\(614\) −1.75069 7.67026i −0.0706520 0.309547i
\(615\) 0 0
\(616\) −60.0320 63.8860i −2.41876 2.57404i
\(617\) 38.9482 + 8.88967i 1.56799 + 0.357884i 0.916267 0.400569i \(-0.131187\pi\)
0.651728 + 0.758453i \(0.274045\pi\)
\(618\) 0 0
\(619\) 30.9056i 1.24220i 0.783730 + 0.621101i \(0.213315\pi\)
−0.783730 + 0.621101i \(0.786685\pi\)
\(620\) 55.4665 + 12.6599i 2.22759 + 0.508433i
\(621\) 0 0
\(622\) 58.4244 46.5919i 2.34260 1.86816i
\(623\) −16.3025 + 24.2386i −0.653147 + 0.971097i
\(624\) 0 0
\(625\) 0.576143 2.52425i 0.0230457 0.100970i
\(626\) −42.0131 + 52.6828i −1.67918 + 2.10563i
\(627\) 0 0
\(628\) 49.1854 39.2241i 1.96271 1.56521i
\(629\) 0.392318 + 0.188930i 0.0156427 + 0.00753314i
\(630\) 0 0
\(631\) 37.0455 17.8402i 1.47476 0.710207i 0.488068 0.872806i \(-0.337702\pi\)
0.986692 + 0.162599i \(0.0519877\pi\)
\(632\) 11.7942 24.4910i 0.469149 0.974199i
\(633\) 0 0
\(634\) 37.0613 + 17.8478i 1.47189 + 0.708825i
\(635\) −17.4938 + 21.9365i −0.694219 + 0.870523i
\(636\) 0 0
\(637\) −40.3742 2.51380i −1.59968 0.0996002i
\(638\) 25.8437i 1.02316i
\(639\) 0 0
\(640\) 23.0794 47.9248i 0.912293 1.89440i
\(641\) −9.56366 + 2.18284i −0.377742 + 0.0862171i −0.407176 0.913350i \(-0.633487\pi\)
0.0294344 + 0.999567i \(0.490629\pi\)
\(642\) 0 0
\(643\) 5.92252 + 12.2982i 0.233561 + 0.484995i 0.984502 0.175375i \(-0.0561138\pi\)
−0.750940 + 0.660370i \(0.770399\pi\)
\(644\) −18.9933 + 17.8475i −0.748442 + 0.703292i
\(645\) 0 0
\(646\) 0.560051 + 0.702282i 0.0220349 + 0.0276309i
\(647\) 11.6891 5.62917i 0.459546 0.221306i −0.189764 0.981830i \(-0.560772\pi\)
0.649310 + 0.760524i \(0.275058\pi\)
\(648\) 0 0
\(649\) 0.409008 + 0.0933534i 0.0160550 + 0.00366444i
\(650\) 28.0529 35.1773i 1.10033 1.37977i
\(651\) 0 0
\(652\) 31.1415 + 39.0502i 1.21960 + 1.52932i
\(653\) −1.93538 4.01886i −0.0757374 0.157270i 0.859662 0.510863i \(-0.170674\pi\)
−0.935399 + 0.353593i \(0.884960\pi\)
\(654\) 0 0
\(655\) −19.2581 −0.752476
\(656\) −185.766 −7.25294
\(657\) 0 0
\(658\) 34.2040 + 58.3892i 1.33341 + 2.27625i
\(659\) −30.2786 + 6.91089i −1.17949 + 0.269210i −0.766935 0.641724i \(-0.778219\pi\)
−0.412551 + 0.910934i \(0.635362\pi\)
\(660\) 0 0
\(661\) 12.1178 9.66364i 0.471329 0.375872i −0.358827 0.933404i \(-0.616823\pi\)
0.830155 + 0.557532i \(0.188252\pi\)
\(662\) −30.0382 + 23.9547i −1.16747 + 0.931025i
\(663\) 0 0
\(664\) −3.69431 + 0.843201i −0.143367 + 0.0327225i
\(665\) −17.3413 2.50199i −0.672466 0.0970232i
\(666\) 0 0
\(667\) −4.86083 −0.188212
\(668\) −115.317 −4.46174
\(669\) 0 0
\(670\) 10.0269 + 20.8211i 0.387373 + 0.804388i
\(671\) −7.21848 9.05168i −0.278666 0.349436i
\(672\) 0 0
\(673\) 4.35420 5.46000i 0.167842 0.210467i −0.690796 0.723050i \(-0.742740\pi\)
0.858638 + 0.512582i \(0.171311\pi\)
\(674\) −5.31452 1.21300i −0.204708 0.0467232i
\(675\) 0 0
\(676\) −100.045 + 48.1791i −3.84788 + 1.85304i
\(677\) 16.8312 + 21.1057i 0.646877 + 0.811158i 0.991844 0.127457i \(-0.0406814\pi\)
−0.344967 + 0.938615i \(0.612110\pi\)
\(678\) 0 0
\(679\) −37.2171 + 11.7376i −1.42826 + 0.450448i
\(680\) −0.435097 0.903487i −0.0166852 0.0346472i
\(681\) 0 0
\(682\) −66.8966 + 15.2687i −2.56160 + 0.584669i
\(683\) −1.44083 + 2.99191i −0.0551318 + 0.114482i −0.926715 0.375766i \(-0.877380\pi\)
0.871583 + 0.490248i \(0.163094\pi\)
\(684\) 0 0
\(685\) 5.16502i 0.197345i
\(686\) 12.1746 + 49.0427i 0.464828 + 1.87246i
\(687\) 0 0
\(688\) 13.4081 16.8132i 0.511178 0.640997i
\(689\) −48.6342 23.4210i −1.85281 0.892268i
\(690\) 0 0
\(691\) 13.0674 27.1348i 0.497109 1.03226i −0.489928 0.871763i \(-0.662977\pi\)
0.987037 0.160495i \(-0.0513090\pi\)
\(692\) −30.9000 + 14.8806i −1.17464 + 0.565677i
\(693\) 0 0
\(694\) −52.2137 25.1448i −1.98200 0.954483i
\(695\) 13.1319 10.4724i 0.498122 0.397239i
\(696\) 0 0
\(697\) −0.571844 + 0.717069i −0.0216601 + 0.0271609i
\(698\) 9.53813 41.7893i 0.361024 1.58175i
\(699\) 0 0
\(700\) −38.3566 14.7753i −1.44974 0.558454i
\(701\) 38.2616 30.5126i 1.44512 1.15244i 0.484427 0.874831i \(-0.339028\pi\)
0.960693 0.277614i \(-0.0895435\pi\)
\(702\) 0 0
\(703\) −26.3459 6.01328i −0.993654 0.226795i
\(704\) 102.369i 3.85817i
\(705\) 0 0
\(706\) 40.1857 + 9.17211i 1.51241 + 0.345197i
\(707\) 3.20885 22.2405i 0.120681 0.836439i
\(708\) 0 0
\(709\) −4.52772 19.8372i −0.170042 0.745003i −0.985980 0.166864i \(-0.946636\pi\)
0.815938 0.578140i \(-0.196221\pi\)
\(710\) 0.222991 + 0.279622i 0.00836872 + 0.0104940i
\(711\) 0 0
\(712\) 101.155 23.0880i 3.79095 0.865259i
\(713\) 2.87183 + 12.5823i 0.107551 + 0.471211i
\(714\) 0 0
\(715\) 6.64257 29.1030i 0.248418 1.08839i
\(716\) 57.5097i 2.14924i
\(717\) 0 0
\(718\) −0.765462 + 3.35371i −0.0285668 + 0.125159i
\(719\) −17.1150 + 8.24217i −0.638283 + 0.307381i −0.724893 0.688861i \(-0.758111\pi\)
0.0866100 + 0.996242i \(0.472397\pi\)
\(720\) 0 0
\(721\) 11.6020 + 1.67393i 0.432081 + 0.0623405i
\(722\) −3.05336 2.43498i −0.113634 0.0906205i
\(723\) 0 0
\(724\) −62.2119 49.6123i −2.31209 1.84383i
\(725\) −3.32616 6.90684i −0.123530 0.256513i
\(726\) 0 0
\(727\) −3.14524 + 6.53117i −0.116651 + 0.242228i −0.951117 0.308832i \(-0.900062\pi\)
0.834466 + 0.551059i \(0.185776\pi\)
\(728\) 98.3936 + 104.710i 3.64671 + 3.88082i
\(729\) 0 0
\(730\) 15.8148 + 7.61602i 0.585333 + 0.281881i
\(731\) −0.0236260 0.103512i −0.000873839 0.00382854i
\(732\) 0 0
\(733\) 11.1482 + 8.89042i 0.411770 + 0.328375i 0.807368 0.590048i \(-0.200891\pi\)
−0.395598 + 0.918424i \(0.629463\pi\)
\(734\) 24.0358 0.887179
\(735\) 0 0
\(736\) 38.8201 1.43093
\(737\) −15.9367 12.7091i −0.587036 0.468145i
\(738\) 0 0
\(739\) −11.0300 48.3255i −0.405744 1.77768i −0.603430 0.797416i \(-0.706200\pi\)
0.197686 0.980265i \(-0.436657\pi\)
\(740\) 42.9639 + 20.6903i 1.57938 + 0.760591i
\(741\) 0 0
\(742\) −9.62895 + 66.7381i −0.353490 + 2.45003i
\(743\) 11.8289 24.5630i 0.433962 0.901131i −0.563234 0.826297i \(-0.690443\pi\)
0.997196 0.0748335i \(-0.0238425\pi\)
\(744\) 0 0
\(745\) −7.94209 16.4919i −0.290976 0.604217i
\(746\) 48.2051 + 38.4423i 1.76491 + 1.40747i
\(747\) 0 0
\(748\) 1.09309 + 0.871712i 0.0399674 + 0.0318730i
\(749\) −7.38157 4.96475i −0.269717 0.181408i
\(750\) 0 0
\(751\) 20.0306 9.64622i 0.730926 0.351996i −0.0311220 0.999516i \(-0.509908\pi\)
0.762048 + 0.647520i \(0.224194\pi\)
\(752\) 30.7722 134.822i 1.12215 4.91645i
\(753\) 0 0
\(754\) 42.3582i 1.54260i
\(755\) −6.80942 + 29.8340i −0.247820 + 1.08577i
\(756\) 0 0
\(757\) 8.60933 + 37.7200i 0.312912 + 1.37096i 0.849713 + 0.527246i \(0.176775\pi\)
−0.536801 + 0.843709i \(0.680367\pi\)
\(758\) 1.19800 0.273435i 0.0435132 0.00993159i
\(759\) 0 0
\(760\) 38.8020 + 48.6561i 1.40750 + 1.76494i
\(761\) −0.614011 2.69016i −0.0222579 0.0975181i 0.962579 0.271002i \(-0.0873548\pi\)
−0.984837 + 0.173483i \(0.944498\pi\)
\(762\) 0 0
\(763\) 30.0005 + 11.5564i 1.08609 + 0.418371i
\(764\) −18.0740 4.12527i −0.653894 0.149247i
\(765\) 0 0
\(766\) 49.2591i 1.77980i
\(767\) −0.670371 0.153008i −0.0242057 0.00552479i
\(768\) 0 0
\(769\) −7.05593 + 5.62692i −0.254443 + 0.202912i −0.742402 0.669955i \(-0.766313\pi\)
0.487958 + 0.872867i \(0.337742\pi\)
\(770\) −37.1665 + 3.02115i −1.33939 + 0.108875i
\(771\) 0 0
\(772\) 32.8501 143.926i 1.18230 5.18000i
\(773\) −30.1925 + 37.8602i −1.08595 + 1.36174i −0.158683 + 0.987330i \(0.550725\pi\)
−0.927265 + 0.374406i \(0.877847\pi\)
\(774\) 0 0
\(775\) −15.9133 + 12.6904i −0.571622 + 0.455853i
\(776\) 124.886 + 60.1418i 4.48314 + 2.15897i
\(777\) 0 0
\(778\) −4.10355 + 1.97617i −0.147119 + 0.0708490i
\(779\) 24.6964 51.2826i 0.884840 1.83739i
\(780\) 0 0
\(781\) −0.284224 0.136875i −0.0101703 0.00489777i
\(782\) 0.224187 0.281121i 0.00801690 0.0100529i
\(783\) 0 0
\(784\) 50.4999 90.0743i 1.80357 3.21694i
\(785\) 16.9292i 0.604228i
\(786\) 0 0
\(787\) −13.1796 + 27.3678i −0.469803 + 0.975555i 0.522606 + 0.852574i \(0.324960\pi\)
−0.992409 + 0.122981i \(0.960755\pi\)
\(788\) 53.9234 12.3077i 1.92094 0.438442i
\(789\) 0 0
\(790\)