Properties

Label 441.2.w.a.251.15
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 251.15
Character \(\chi\) \(=\) 441.251
Dual form 441.2.w.a.188.15

$q$-expansion

\(f(q)\) \(=\) \(q+(1.16155 + 0.926303i) q^{2} +(0.0461133 + 0.202036i) q^{4} +(-2.75921 - 1.32877i) q^{5} +(-2.64574 + 0.00862187i) q^{7} +(1.15564 - 2.39971i) q^{8} +O(q^{10})\) \(q+(1.16155 + 0.926303i) q^{2} +(0.0461133 + 0.202036i) q^{4} +(-2.75921 - 1.32877i) q^{5} +(-2.64574 + 0.00862187i) q^{7} +(1.15564 - 2.39971i) q^{8} +(-1.97412 - 4.09929i) q^{10} +(-4.38394 - 3.49607i) q^{11} +(-0.126413 - 0.100811i) q^{13} +(-3.08114 - 2.44074i) q^{14} +(3.93860 - 1.89673i) q^{16} +(0.351332 - 1.53929i) q^{17} +5.64561i q^{19} +(0.141222 - 0.618733i) q^{20} +(-1.85373 - 8.12172i) q^{22} +(4.97667 - 1.13589i) q^{23} +(2.73018 + 3.42354i) q^{25} +(-0.0534533 - 0.234194i) q^{26} +(-0.123746 - 0.534136i) q^{28} +(-3.45359 - 0.788260i) q^{29} -0.856946i q^{31} +(1.13844 + 0.259840i) q^{32} +(1.83393 - 1.46251i) q^{34} +(7.31161 + 3.49178i) q^{35} +(0.520922 - 2.28231i) q^{37} +(-5.22954 + 6.55764i) q^{38} +(-6.37730 + 5.08572i) q^{40} +(-10.3963 - 5.00660i) q^{41} +(10.9288 - 5.26303i) q^{43} +(0.504174 - 1.04693i) q^{44} +(6.83282 + 3.29051i) q^{46} +(-6.32346 + 7.92937i) q^{47} +(6.99985 - 0.0456224i) q^{49} +6.50558i q^{50} +(0.0145381 - 0.0301888i) q^{52} +(6.39600 - 1.45985i) q^{53} +(7.45075 + 15.4716i) q^{55} +(-3.03682 + 6.35895i) q^{56} +(-3.28135 - 4.11468i) q^{58} +(8.14279 - 3.92136i) q^{59} +(-0.616348 - 0.140677i) q^{61} +(0.793792 - 0.995384i) q^{62} +(-4.36954 - 5.47923i) q^{64} +(0.214847 + 0.446134i) q^{65} -10.8925 q^{67} +0.327192 q^{68} +(5.25833 + 10.8286i) q^{70} +(4.40071 - 1.00443i) q^{71} +(5.53256 - 4.41207i) q^{73} +(2.71918 - 2.16848i) q^{74} +(-1.14061 + 0.260338i) q^{76} +(11.6289 + 9.21190i) q^{77} -9.69282 q^{79} -13.3877 q^{80} +(-7.43819 - 15.4456i) q^{82} +(-4.61146 - 5.78259i) q^{83} +(-3.01475 + 3.78038i) q^{85} +(17.5695 + 4.01012i) q^{86} +(-13.4558 + 6.47997i) q^{88} +(-1.71125 - 2.14584i) q^{89} +(0.335326 + 0.265630i) q^{91} +(0.458982 + 0.953086i) q^{92} +(-14.6900 + 3.35290i) q^{94} +(7.50169 - 15.5774i) q^{95} -6.81046i q^{97} +(8.17292 + 6.43099i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q + 24 q^{4} + O(q^{10}) \) \( 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.16155 + 0.926303i 0.821338 + 0.654995i 0.941221 0.337793i \(-0.109680\pi\)
−0.119882 + 0.992788i \(0.538252\pi\)
\(3\) 0 0
\(4\) 0.0461133 + 0.202036i 0.0230567 + 0.101018i
\(5\) −2.75921 1.32877i −1.23396 0.594242i −0.300792 0.953690i \(-0.597251\pi\)
−0.933165 + 0.359448i \(0.882965\pi\)
\(6\) 0 0
\(7\) −2.64574 + 0.00862187i −0.999995 + 0.00325876i
\(8\) 1.15564 2.39971i 0.408579 0.848424i
\(9\) 0 0
\(10\) −1.97412 4.09929i −0.624270 1.29631i
\(11\) −4.38394 3.49607i −1.32181 1.05411i −0.994002 0.109361i \(-0.965120\pi\)
−0.327805 0.944745i \(-0.606309\pi\)
\(12\) 0 0
\(13\) −0.126413 0.100811i −0.0350608 0.0279600i 0.605803 0.795615i \(-0.292852\pi\)
−0.640863 + 0.767655i \(0.721424\pi\)
\(14\) −3.08114 2.44074i −0.823468 0.652315i
\(15\) 0 0
\(16\) 3.93860 1.89673i 0.984650 0.474183i
\(17\) 0.351332 1.53929i 0.0852105 0.373331i −0.914286 0.405070i \(-0.867247\pi\)
0.999496 + 0.0317384i \(0.0101043\pi\)
\(18\) 0 0
\(19\) 5.64561i 1.29519i 0.761984 + 0.647595i \(0.224225\pi\)
−0.761984 + 0.647595i \(0.775775\pi\)
\(20\) 0.141222 0.618733i 0.0315781 0.138353i
\(21\) 0 0
\(22\) −1.85373 8.12172i −0.395216 1.73156i
\(23\) 4.97667 1.13589i 1.03771 0.236850i 0.330463 0.943819i \(-0.392795\pi\)
0.707245 + 0.706969i \(0.249938\pi\)
\(24\) 0 0
\(25\) 2.73018 + 3.42354i 0.546036 + 0.684707i
\(26\) −0.0534533 0.234194i −0.0104831 0.0459293i
\(27\) 0 0
\(28\) −0.123746 0.534136i −0.0233857 0.100942i
\(29\) −3.45359 0.788260i −0.641316 0.146376i −0.110518 0.993874i \(-0.535251\pi\)
−0.530799 + 0.847498i \(0.678108\pi\)
\(30\) 0 0
\(31\) 0.856946i 0.153912i −0.997034 0.0769561i \(-0.975480\pi\)
0.997034 0.0769561i \(-0.0245201\pi\)
\(32\) 1.13844 + 0.259840i 0.201249 + 0.0459337i
\(33\) 0 0
\(34\) 1.83393 1.46251i 0.314517 0.250819i
\(35\) 7.31161 + 3.49178i 1.23589 + 0.590218i
\(36\) 0 0
\(37\) 0.520922 2.28231i 0.0856390 0.375209i −0.913888 0.405967i \(-0.866935\pi\)
0.999527 + 0.0307578i \(0.00979205\pi\)
\(38\) −5.22954 + 6.55764i −0.848344 + 1.06379i
\(39\) 0 0
\(40\) −6.37730 + 5.08572i −1.00834 + 0.804123i
\(41\) −10.3963 5.00660i −1.62363 0.781900i −1.00000 0.000182349i \(-0.999942\pi\)
−0.623632 0.781718i \(-0.714344\pi\)
\(42\) 0 0
\(43\) 10.9288 5.26303i 1.66662 0.802604i 0.668352 0.743845i \(-0.267000\pi\)
0.998272 0.0587591i \(-0.0187144\pi\)
\(44\) 0.504174 1.04693i 0.0760071 0.157830i
\(45\) 0 0
\(46\) 6.83282 + 3.29051i 1.00745 + 0.485160i
\(47\) −6.32346 + 7.92937i −0.922372 + 1.15662i 0.0649500 + 0.997889i \(0.479311\pi\)
−0.987322 + 0.158730i \(0.949260\pi\)
\(48\) 0 0
\(49\) 6.99985 0.0456224i 0.999979 0.00651749i
\(50\) 6.50558i 0.920027i
\(51\) 0 0
\(52\) 0.0145381 0.0301888i 0.00201608 0.00418643i
\(53\) 6.39600 1.45985i 0.878558 0.200525i 0.240626 0.970618i \(-0.422647\pi\)
0.637932 + 0.770093i \(0.279790\pi\)
\(54\) 0 0
\(55\) 7.45075 + 15.4716i 1.00466 + 2.08620i
\(56\) −3.03682 + 6.35895i −0.405812 + 0.849751i
\(57\) 0 0
\(58\) −3.28135 4.11468i −0.430862 0.540284i
\(59\) 8.14279 3.92136i 1.06010 0.510518i 0.179198 0.983813i \(-0.442650\pi\)
0.880904 + 0.473295i \(0.156936\pi\)
\(60\) 0 0
\(61\) −0.616348 0.140677i −0.0789153 0.0180119i 0.182881 0.983135i \(-0.441458\pi\)
−0.261796 + 0.965123i \(0.584315\pi\)
\(62\) 0.793792 0.995384i 0.100812 0.126414i
\(63\) 0 0
\(64\) −4.36954 5.47923i −0.546192 0.684903i
\(65\) 0.214847 + 0.446134i 0.0266484 + 0.0553361i
\(66\) 0 0
\(67\) −10.8925 −1.33073 −0.665367 0.746516i \(-0.731725\pi\)
−0.665367 + 0.746516i \(0.731725\pi\)
\(68\) 0.327192 0.0396778
\(69\) 0 0
\(70\) 5.25833 + 10.8286i 0.628491 + 1.29427i
\(71\) 4.40071 1.00443i 0.522268 0.119204i 0.0467436 0.998907i \(-0.485116\pi\)
0.475524 + 0.879703i \(0.342258\pi\)
\(72\) 0 0
\(73\) 5.53256 4.41207i 0.647537 0.516394i −0.243747 0.969839i \(-0.578377\pi\)
0.891284 + 0.453445i \(0.149805\pi\)
\(74\) 2.71918 2.16848i 0.316099 0.252080i
\(75\) 0 0
\(76\) −1.14061 + 0.260338i −0.130837 + 0.0298628i
\(77\) 11.6289 + 9.21190i 1.32524 + 1.04979i
\(78\) 0 0
\(79\) −9.69282 −1.09053 −0.545263 0.838265i \(-0.683570\pi\)
−0.545263 + 0.838265i \(0.683570\pi\)
\(80\) −13.3877 −1.49680
\(81\) 0 0
\(82\) −7.43819 15.4456i −0.821410 1.70568i
\(83\) −4.61146 5.78259i −0.506173 0.634721i 0.461436 0.887173i \(-0.347334\pi\)
−0.967609 + 0.252452i \(0.918763\pi\)
\(84\) 0 0
\(85\) −3.01475 + 3.78038i −0.326995 + 0.410039i
\(86\) 17.5695 + 4.01012i 1.89456 + 0.432422i
\(87\) 0 0
\(88\) −13.4558 + 6.47997i −1.43439 + 0.690767i
\(89\) −1.71125 2.14584i −0.181392 0.227459i 0.682819 0.730587i \(-0.260754\pi\)
−0.864212 + 0.503129i \(0.832182\pi\)
\(90\) 0 0
\(91\) 0.335326 + 0.265630i 0.0351517 + 0.0278456i
\(92\) 0.458982 + 0.953086i 0.0478522 + 0.0993660i
\(93\) 0 0
\(94\) −14.6900 + 3.35290i −1.51516 + 0.345825i
\(95\) 7.50169 15.5774i 0.769657 1.59821i
\(96\) 0 0
\(97\) 6.81046i 0.691497i −0.938327 0.345749i \(-0.887625\pi\)
0.938327 0.345749i \(-0.112375\pi\)
\(98\) 8.17292 + 6.43099i 0.825590 + 0.649628i
\(99\) 0 0
\(100\) −0.565779 + 0.709464i −0.0565779 + 0.0709464i
\(101\) 0.859158 + 0.413749i 0.0854894 + 0.0411695i 0.476140 0.879370i \(-0.342036\pi\)
−0.390650 + 0.920539i \(0.627750\pi\)
\(102\) 0 0
\(103\) −6.04953 + 12.5620i −0.596078 + 1.23777i 0.356734 + 0.934206i \(0.383890\pi\)
−0.952812 + 0.303562i \(0.901824\pi\)
\(104\) −0.388006 + 0.186854i −0.0380471 + 0.0183225i
\(105\) 0 0
\(106\) 8.78152 + 4.22896i 0.852936 + 0.410753i
\(107\) 6.41385 5.11488i 0.620051 0.494474i −0.262350 0.964973i \(-0.584497\pi\)
0.882401 + 0.470499i \(0.155926\pi\)
\(108\) 0 0
\(109\) 6.71224 8.41689i 0.642916 0.806191i −0.348448 0.937328i \(-0.613291\pi\)
0.991364 + 0.131137i \(0.0418627\pi\)
\(110\) −5.67703 + 24.8727i −0.541284 + 2.37152i
\(111\) 0 0
\(112\) −10.4042 + 5.05221i −0.983100 + 0.477389i
\(113\) −10.4348 + 8.32149i −0.981625 + 0.782820i −0.976135 0.217165i \(-0.930319\pi\)
−0.00549020 + 0.999985i \(0.501748\pi\)
\(114\) 0 0
\(115\) −15.2410 3.47867i −1.42123 0.324387i
\(116\) 0.734099i 0.0681593i
\(117\) 0 0
\(118\) 13.0906 + 2.98785i 1.20509 + 0.275054i
\(119\) −0.916260 + 4.07557i −0.0839934 + 0.373607i
\(120\) 0 0
\(121\) 4.54865 + 19.9290i 0.413514 + 1.81172i
\(122\) −0.585608 0.734329i −0.0530184 0.0664830i
\(123\) 0 0
\(124\) 0.173134 0.0395166i 0.0155479 0.00354870i
\(125\) 0.423282 + 1.85452i 0.0378595 + 0.165873i
\(126\) 0 0
\(127\) −1.30691 + 5.72596i −0.115970 + 0.508097i 0.883261 + 0.468882i \(0.155343\pi\)
−0.999231 + 0.0392151i \(0.987514\pi\)
\(128\) 12.7473i 1.12672i
\(129\) 0 0
\(130\) −0.163701 + 0.717219i −0.0143575 + 0.0629042i
\(131\) 13.5262 6.51387i 1.18179 0.569120i 0.263357 0.964698i \(-0.415170\pi\)
0.918432 + 0.395579i \(0.129456\pi\)
\(132\) 0 0
\(133\) −0.0486757 14.9368i −0.00422072 1.29518i
\(134\) −12.6522 10.0898i −1.09298 0.871625i
\(135\) 0 0
\(136\) −3.28782 2.62195i −0.281928 0.224830i
\(137\) −5.11747 10.6265i −0.437215 0.907886i −0.996862 0.0791550i \(-0.974778\pi\)
0.559648 0.828731i \(-0.310936\pi\)
\(138\) 0 0
\(139\) 7.48155 15.5356i 0.634577 1.31771i −0.297246 0.954801i \(-0.596068\pi\)
0.931823 0.362912i \(-0.118217\pi\)
\(140\) −0.368301 + 1.63822i −0.0311271 + 0.138455i
\(141\) 0 0
\(142\) 6.04204 + 2.90969i 0.507037 + 0.244176i
\(143\) 0.201745 + 0.883902i 0.0168707 + 0.0739156i
\(144\) 0 0
\(145\) 8.48178 + 6.76400i 0.704374 + 0.561719i
\(146\) 10.5133 0.870083
\(147\) 0 0
\(148\) 0.485129 0.0398773
\(149\) 7.35855 + 5.86825i 0.602836 + 0.480746i 0.876710 0.481020i \(-0.159734\pi\)
−0.273874 + 0.961766i \(0.588305\pi\)
\(150\) 0 0
\(151\) 1.36982 + 6.00156i 0.111474 + 0.488400i 0.999586 + 0.0287726i \(0.00915988\pi\)
−0.888112 + 0.459627i \(0.847983\pi\)
\(152\) 13.5478 + 6.52427i 1.09887 + 0.529188i
\(153\) 0 0
\(154\) 4.97450 + 21.4719i 0.400857 + 1.73026i
\(155\) −1.13868 + 2.36450i −0.0914611 + 0.189921i
\(156\) 0 0
\(157\) −8.06690 16.7511i −0.643808 1.33688i −0.926000 0.377524i \(-0.876776\pi\)
0.282191 0.959358i \(-0.408939\pi\)
\(158\) −11.2587 8.97849i −0.895692 0.714290i
\(159\) 0 0
\(160\) −2.79592 2.22967i −0.221037 0.176271i
\(161\) −13.1572 + 3.04818i −1.03693 + 0.240230i
\(162\) 0 0
\(163\) −6.64838 + 3.20169i −0.520742 + 0.250776i −0.675742 0.737139i \(-0.736177\pi\)
0.155000 + 0.987914i \(0.450462\pi\)
\(164\) 0.532104 2.33130i 0.0415503 0.182044i
\(165\) 0 0
\(166\) 10.9884i 0.852862i
\(167\) −2.94816 + 12.9167i −0.228136 + 0.999528i 0.723023 + 0.690824i \(0.242752\pi\)
−0.951158 + 0.308703i \(0.900105\pi\)
\(168\) 0 0
\(169\) −2.88695 12.6486i −0.222073 0.972967i
\(170\) −7.00355 + 1.59851i −0.537148 + 0.122600i
\(171\) 0 0
\(172\) 1.56728 + 1.96531i 0.119504 + 0.149853i
\(173\) −0.268273 1.17538i −0.0203964 0.0893625i 0.963705 0.266968i \(-0.0860219\pi\)
−0.984102 + 0.177606i \(0.943165\pi\)
\(174\) 0 0
\(175\) −7.25285 9.03424i −0.548264 0.682924i
\(176\) −23.8977 5.45449i −1.80136 0.411148i
\(177\) 0 0
\(178\) 4.07763i 0.305632i
\(179\) 17.1681 + 3.91850i 1.28320 + 0.292882i 0.809143 0.587612i \(-0.199932\pi\)
0.474057 + 0.880494i \(0.342789\pi\)
\(180\) 0 0
\(181\) −1.88800 + 1.50563i −0.140334 + 0.111913i −0.691141 0.722720i \(-0.742892\pi\)
0.550807 + 0.834633i \(0.314320\pi\)
\(182\) 0.143443 + 0.619156i 0.0106327 + 0.0458949i
\(183\) 0 0
\(184\) 3.02542 13.2552i 0.223037 0.977188i
\(185\) −4.46998 + 5.60518i −0.328640 + 0.412101i
\(186\) 0 0
\(187\) −6.92167 + 5.51985i −0.506163 + 0.403651i
\(188\) −1.89361 0.911916i −0.138106 0.0665083i
\(189\) 0 0
\(190\) 23.1430 11.1451i 1.67897 0.808549i
\(191\) −3.51849 + 7.30622i −0.254589 + 0.528659i −0.988616 0.150461i \(-0.951924\pi\)
0.734027 + 0.679120i \(0.237639\pi\)
\(192\) 0 0
\(193\) 0.856581 + 0.412508i 0.0616580 + 0.0296930i 0.464459 0.885595i \(-0.346249\pi\)
−0.402801 + 0.915288i \(0.631963\pi\)
\(194\) 6.30855 7.91067i 0.452928 0.567953i
\(195\) 0 0
\(196\) 0.332004 + 1.41212i 0.0237146 + 0.100865i
\(197\) 14.5833i 1.03902i −0.854465 0.519509i \(-0.826115\pi\)
0.854465 0.519509i \(-0.173885\pi\)
\(198\) 0 0
\(199\) −1.27445 + 2.64642i −0.0903433 + 0.187600i −0.941244 0.337726i \(-0.890342\pi\)
0.850901 + 0.525326i \(0.176057\pi\)
\(200\) 11.3706 2.59526i 0.804021 0.183513i
\(201\) 0 0
\(202\) 0.614696 + 1.27643i 0.0432499 + 0.0898093i
\(203\) 9.14410 + 2.05575i 0.641790 + 0.144286i
\(204\) 0 0
\(205\) 22.0330 + 27.6286i 1.53885 + 1.92966i
\(206\) −18.6630 + 8.98763i −1.30031 + 0.626198i
\(207\) 0 0
\(208\) −0.689104 0.157283i −0.0477808 0.0109056i
\(209\) 19.7375 24.7500i 1.36527 1.71199i
\(210\) 0 0
\(211\) 7.50330 + 9.40884i 0.516548 + 0.647731i 0.969872 0.243615i \(-0.0783332\pi\)
−0.453324 + 0.891346i \(0.649762\pi\)
\(212\) 0.589882 + 1.22490i 0.0405132 + 0.0841266i
\(213\) 0 0
\(214\) 12.1879 0.833150
\(215\) −37.1482 −2.53348
\(216\) 0 0
\(217\) 0.00738848 + 2.26726i 0.000501563 + 0.153911i
\(218\) 15.5932 3.55904i 1.05610 0.241049i
\(219\) 0 0
\(220\) −2.78224 + 2.21877i −0.187579 + 0.149589i
\(221\) −0.199590 + 0.159168i −0.0134259 + 0.0107068i
\(222\) 0 0
\(223\) 28.5534 6.51713i 1.91208 0.436420i 0.912450 0.409188i \(-0.134188\pi\)
0.999629 0.0272313i \(-0.00866905\pi\)
\(224\) −3.01424 0.677654i −0.201397 0.0452777i
\(225\) 0 0
\(226\) −19.8288 −1.31899
\(227\) −0.395985 −0.0262824 −0.0131412 0.999914i \(-0.504183\pi\)
−0.0131412 + 0.999914i \(0.504183\pi\)
\(228\) 0 0
\(229\) −9.94649 20.6541i −0.657282 1.36486i −0.916887 0.399146i \(-0.869307\pi\)
0.259605 0.965715i \(-0.416408\pi\)
\(230\) −14.4809 18.1585i −0.954841 1.19733i
\(231\) 0 0
\(232\) −5.88270 + 7.37667i −0.386218 + 0.484302i
\(233\) 5.08467 + 1.16054i 0.333108 + 0.0760297i 0.385804 0.922581i \(-0.373924\pi\)
−0.0526958 + 0.998611i \(0.516781\pi\)
\(234\) 0 0
\(235\) 27.9841 13.4764i 1.82548 0.879104i
\(236\) 1.16775 + 1.46431i 0.0760138 + 0.0953183i
\(237\) 0 0
\(238\) −4.83950 + 3.88524i −0.313698 + 0.251843i
\(239\) 2.07368 + 4.30604i 0.134135 + 0.278535i 0.957208 0.289401i \(-0.0934563\pi\)
−0.823072 + 0.567936i \(0.807742\pi\)
\(240\) 0 0
\(241\) 21.2200 4.84332i 1.36690 0.311986i 0.524762 0.851249i \(-0.324154\pi\)
0.842137 + 0.539264i \(0.181297\pi\)
\(242\) −13.1768 + 27.3619i −0.847035 + 1.75889i
\(243\) 0 0
\(244\) 0.131011i 0.00838714i
\(245\) −19.3747 9.17528i −1.23780 0.586187i
\(246\) 0 0
\(247\) 0.569141 0.713680i 0.0362136 0.0454104i
\(248\) −2.05642 0.990319i −0.130583 0.0628853i
\(249\) 0 0
\(250\) −1.22619 + 2.54620i −0.0775509 + 0.161036i
\(251\) −13.1197 + 6.31813i −0.828110 + 0.398797i −0.799406 0.600791i \(-0.794852\pi\)
−0.0287041 + 0.999588i \(0.509138\pi\)
\(252\) 0 0
\(253\) −25.7886 12.4191i −1.62132 0.780784i
\(254\) −6.82202 + 5.44038i −0.428051 + 0.341360i
\(255\) 0 0
\(256\) 3.06882 3.84817i 0.191801 0.240511i
\(257\) −2.56465 + 11.2365i −0.159978 + 0.700911i 0.829772 + 0.558103i \(0.188470\pi\)
−0.989750 + 0.142809i \(0.954387\pi\)
\(258\) 0 0
\(259\) −1.35854 + 6.04287i −0.0844158 + 0.375486i
\(260\) −0.0802276 + 0.0639794i −0.00497551 + 0.00396783i
\(261\) 0 0
\(262\) 21.7451 + 4.96319i 1.34342 + 0.306627i
\(263\) 0.202684i 0.0124980i −0.999980 0.00624902i \(-0.998011\pi\)
0.999980 0.00624902i \(-0.00198914\pi\)
\(264\) 0 0
\(265\) −19.5877 4.47077i −1.20326 0.274637i
\(266\) 13.7795 17.3949i 0.844873 1.06655i
\(267\) 0 0
\(268\) −0.502291 2.20068i −0.0306823 0.134428i
\(269\) −10.0208 12.5657i −0.610978 0.766143i 0.376066 0.926593i \(-0.377277\pi\)
−0.987044 + 0.160451i \(0.948705\pi\)
\(270\) 0 0
\(271\) 10.5944 2.41809i 0.643562 0.146889i 0.111730 0.993739i \(-0.464361\pi\)
0.531832 + 0.846850i \(0.321504\pi\)
\(272\) −1.53585 6.72901i −0.0931248 0.408006i
\(273\) 0 0
\(274\) 3.89921 17.0835i 0.235560 1.03205i
\(275\) 24.5535i 1.48063i
\(276\) 0 0
\(277\) 1.59759 6.99950i 0.0959899 0.420559i −0.903986 0.427563i \(-0.859372\pi\)
0.999975 + 0.00700363i \(0.00222934\pi\)
\(278\) 23.0809 11.1152i 1.38430 0.666643i
\(279\) 0 0
\(280\) 16.8288 13.5105i 1.00571 0.807405i
\(281\) 4.28527 + 3.41739i 0.255638 + 0.203864i 0.742920 0.669380i \(-0.233440\pi\)
−0.487282 + 0.873245i \(0.662012\pi\)
\(282\) 0 0
\(283\) 13.3207 + 10.6229i 0.791834 + 0.631467i 0.933553 0.358440i \(-0.116691\pi\)
−0.141718 + 0.989907i \(0.545263\pi\)
\(284\) 0.405862 + 0.842782i 0.0240835 + 0.0500099i
\(285\) 0 0
\(286\) −0.584425 + 1.21357i −0.0345578 + 0.0717599i
\(287\) 27.5491 + 13.1565i 1.62617 + 0.776605i
\(288\) 0 0
\(289\) 13.0705 + 6.29442i 0.768853 + 0.370260i
\(290\) 3.58648 + 15.7134i 0.210606 + 0.922723i
\(291\) 0 0
\(292\) 1.14652 + 0.914320i 0.0670950 + 0.0535065i
\(293\) −26.8491 −1.56854 −0.784270 0.620420i \(-0.786962\pi\)
−0.784270 + 0.620420i \(0.786962\pi\)
\(294\) 0 0
\(295\) −27.6783 −1.61149
\(296\) −4.87487 3.88758i −0.283346 0.225961i
\(297\) 0 0
\(298\) 3.11153 + 13.6325i 0.180246 + 0.789710i
\(299\) −0.743629 0.358113i −0.0430052 0.0207102i
\(300\) 0 0
\(301\) −28.8693 + 14.0188i −1.66400 + 0.808031i
\(302\) −3.96816 + 8.23996i −0.228342 + 0.474157i
\(303\) 0 0
\(304\) 10.7082 + 22.2358i 0.614157 + 1.27531i
\(305\) 1.51371 + 1.20714i 0.0866746 + 0.0691207i
\(306\) 0 0
\(307\) −19.9681 15.9241i −1.13964 0.908834i −0.142920 0.989734i \(-0.545649\pi\)
−0.996722 + 0.0809003i \(0.974220\pi\)
\(308\) −1.32488 + 2.77424i −0.0754923 + 0.158077i
\(309\) 0 0
\(310\) −3.51287 + 1.69171i −0.199518 + 0.0960827i
\(311\) −4.68552 + 20.5286i −0.265691 + 1.16407i 0.649280 + 0.760550i \(0.275071\pi\)
−0.914971 + 0.403520i \(0.867787\pi\)
\(312\) 0 0
\(313\) 24.0859i 1.36142i −0.732555 0.680708i \(-0.761672\pi\)
0.732555 0.680708i \(-0.238328\pi\)
\(314\) 6.14650 26.9296i 0.346867 1.51972i
\(315\) 0 0
\(316\) −0.446968 1.95829i −0.0251439 0.110163i
\(317\) −17.9501 + 4.09700i −1.00818 + 0.230110i −0.694557 0.719438i \(-0.744400\pi\)
−0.313622 + 0.949548i \(0.601542\pi\)
\(318\) 0 0
\(319\) 12.3845 + 15.5297i 0.693401 + 0.869497i
\(320\) 4.77587 + 20.9244i 0.266979 + 1.16971i
\(321\) 0 0
\(322\) −18.1062 8.64693i −1.00902 0.481874i
\(323\) 8.69020 + 1.98348i 0.483535 + 0.110364i
\(324\) 0 0
\(325\) 0.708014i 0.0392735i
\(326\) −10.6882 2.43950i −0.591962 0.135111i
\(327\) 0 0
\(328\) −24.0287 + 19.1623i −1.32677 + 1.05806i
\(329\) 16.6619 21.0336i 0.918598 1.15962i
\(330\) 0 0
\(331\) 3.71516 16.2772i 0.204203 0.894674i −0.764140 0.645051i \(-0.776836\pi\)
0.968343 0.249623i \(-0.0803067\pi\)
\(332\) 0.955639 1.19833i 0.0524475 0.0657671i
\(333\) 0 0
\(334\) −15.3893 + 12.2725i −0.842063 + 0.671523i
\(335\) 30.0548 + 14.4736i 1.64207 + 0.790778i
\(336\) 0 0
\(337\) −30.9969 + 14.9273i −1.68851 + 0.813144i −0.692749 + 0.721179i \(0.743601\pi\)
−0.995762 + 0.0919653i \(0.970685\pi\)
\(338\) 8.36308 17.3661i 0.454892 0.944592i
\(339\) 0 0
\(340\) −0.902791 0.434761i −0.0489607 0.0235782i
\(341\) −2.99595 + 3.75680i −0.162240 + 0.203442i
\(342\) 0 0
\(343\) −18.5194 + 0.181057i −0.999952 + 0.00977615i
\(344\) 32.3080i 1.74193i
\(345\) 0 0
\(346\) 0.777147 1.61376i 0.0417797 0.0867564i
\(347\) 12.3329 2.81490i 0.662064 0.151112i 0.121731 0.992563i \(-0.461155\pi\)
0.540333 + 0.841451i \(0.318298\pi\)
\(348\) 0 0
\(349\) −1.27642 2.65052i −0.0683254 0.141879i 0.864009 0.503476i \(-0.167946\pi\)
−0.932334 + 0.361597i \(0.882232\pi\)
\(350\) −0.0560903 17.2120i −0.00299815 0.920022i
\(351\) 0 0
\(352\) −4.08241 5.11918i −0.217593 0.272853i
\(353\) 18.8308 9.06845i 1.00226 0.482665i 0.140557 0.990073i \(-0.455111\pi\)
0.861706 + 0.507408i \(0.169396\pi\)
\(354\) 0 0
\(355\) −13.4771 3.07607i −0.715292 0.163261i
\(356\) 0.354625 0.444686i 0.0187951 0.0235683i
\(357\) 0 0
\(358\) 16.3118 + 20.4543i 0.862105 + 1.08105i
\(359\) 11.4770 + 23.8322i 0.605732 + 1.25781i 0.948017 + 0.318219i \(0.103085\pi\)
−0.342286 + 0.939596i \(0.611201\pi\)
\(360\) 0 0
\(361\) −12.8729 −0.677519
\(362\) −3.58768 −0.188564
\(363\) 0 0
\(364\) −0.0382038 + 0.0799969i −0.00200242 + 0.00419298i
\(365\) −21.1281 + 4.82236i −1.10590 + 0.252414i
\(366\) 0 0
\(367\) 4.39923 3.50827i 0.229638 0.183130i −0.501911 0.864919i \(-0.667369\pi\)
0.731548 + 0.681789i \(0.238798\pi\)
\(368\) 17.4466 13.9132i 0.909469 0.725278i
\(369\) 0 0
\(370\) −10.3842 + 2.37013i −0.539849 + 0.123217i
\(371\) −16.9095 + 3.91751i −0.877900 + 0.203387i
\(372\) 0 0
\(373\) −16.4267 −0.850540 −0.425270 0.905067i \(-0.639821\pi\)
−0.425270 + 0.905067i \(0.639821\pi\)
\(374\) −13.1529 −0.680121
\(375\) 0 0
\(376\) 11.7205 + 24.3379i 0.604440 + 1.25513i
\(377\) 0.357115 + 0.447808i 0.0183924 + 0.0230633i
\(378\) 0 0
\(379\) 9.13137 11.4504i 0.469047 0.588166i −0.489891 0.871784i \(-0.662963\pi\)
0.958937 + 0.283618i \(0.0915347\pi\)
\(380\) 3.49312 + 0.797282i 0.179193 + 0.0408997i
\(381\) 0 0
\(382\) −10.8547 + 5.22733i −0.555373 + 0.267454i
\(383\) −10.1270 12.6989i −0.517466 0.648881i 0.452603 0.891712i \(-0.350495\pi\)
−0.970069 + 0.242831i \(0.921924\pi\)
\(384\) 0 0
\(385\) −19.8461 40.8697i −1.01145 2.08291i
\(386\) 0.612852 + 1.27260i 0.0311934 + 0.0647737i
\(387\) 0 0
\(388\) 1.37596 0.314053i 0.0698535 0.0159436i
\(389\) −2.22663 + 4.62365i −0.112895 + 0.234429i −0.949759 0.312982i \(-0.898672\pi\)
0.836864 + 0.547410i \(0.184386\pi\)
\(390\) 0 0
\(391\) 8.05959i 0.407591i
\(392\) 7.97981 16.8503i 0.403041 0.851069i
\(393\) 0 0
\(394\) 13.5086 16.9392i 0.680553 0.853386i
\(395\) 26.7445 + 12.8795i 1.34566 + 0.648037i
\(396\) 0 0
\(397\) 2.39913 4.98184i 0.120409 0.250031i −0.832049 0.554702i \(-0.812832\pi\)
0.952458 + 0.304671i \(0.0985465\pi\)
\(398\) −3.93172 + 1.89342i −0.197079 + 0.0949085i
\(399\) 0 0
\(400\) 17.2466 + 8.30553i 0.862331 + 0.415277i
\(401\) −16.6316 + 13.2632i −0.830541 + 0.662335i −0.943539 0.331261i \(-0.892526\pi\)
0.112998 + 0.993595i \(0.463955\pi\)
\(402\) 0 0
\(403\) −0.0863899 + 0.108330i −0.00430339 + 0.00539628i
\(404\) −0.0439734 + 0.192660i −0.00218776 + 0.00958519i
\(405\) 0 0
\(406\) 8.71706 + 10.8581i 0.432620 + 0.538877i
\(407\) −10.2628 + 8.18431i −0.508708 + 0.405681i
\(408\) 0 0
\(409\) 16.8749 + 3.85158i 0.834408 + 0.190448i 0.618321 0.785926i \(-0.287813\pi\)
0.216087 + 0.976374i \(0.430670\pi\)
\(410\) 52.5012i 2.59285i
\(411\) 0 0
\(412\) −2.81693 0.642946i −0.138780 0.0316757i
\(413\) −21.5099 + 10.4451i −1.05843 + 0.513970i
\(414\) 0 0
\(415\) 5.04028 + 22.0829i 0.247418 + 1.08401i
\(416\) −0.117719 0.147614i −0.00577163 0.00723740i
\(417\) 0 0
\(418\) 45.8520 10.4654i 2.24269 0.511880i
\(419\) 5.31551 + 23.2888i 0.259679 + 1.13773i 0.921595 + 0.388152i \(0.126886\pi\)
−0.661916 + 0.749578i \(0.730256\pi\)
\(420\) 0 0
\(421\) −7.28529 + 31.9189i −0.355063 + 1.55563i 0.410248 + 0.911974i \(0.365442\pi\)
−0.765312 + 0.643660i \(0.777415\pi\)
\(422\) 17.8791i 0.870343i
\(423\) 0 0
\(424\) 3.88826 17.0356i 0.188830 0.827320i
\(425\) 6.22900 2.99973i 0.302151 0.145508i
\(426\) 0 0
\(427\) 1.63191 + 0.366881i 0.0789735 + 0.0177546i
\(428\) 1.32915 + 1.05996i 0.0642470 + 0.0512353i
\(429\) 0 0
\(430\) −43.1494 34.4105i −2.08085 1.65942i
\(431\) 5.17869 + 10.7537i 0.249449 + 0.517986i 0.987666 0.156578i \(-0.0500461\pi\)
−0.738217 + 0.674564i \(0.764332\pi\)
\(432\) 0 0
\(433\) −2.55898 + 5.31377i −0.122977 + 0.255364i −0.953364 0.301823i \(-0.902405\pi\)
0.830387 + 0.557186i \(0.188119\pi\)
\(434\) −2.09158 + 2.64037i −0.100399 + 0.126742i
\(435\) 0 0
\(436\) 2.01003 + 0.967982i 0.0962632 + 0.0463579i
\(437\) 6.41280 + 28.0963i 0.306766 + 1.34403i
\(438\) 0 0
\(439\) 30.0294 + 23.9476i 1.43322 + 1.14296i 0.965914 + 0.258864i \(0.0833481\pi\)
0.467310 + 0.884094i \(0.345223\pi\)
\(440\) 45.7377 2.18046
\(441\) 0 0
\(442\) −0.379272 −0.0180401
\(443\) 20.7453 + 16.5438i 0.985640 + 0.786022i 0.976847 0.213940i \(-0.0686295\pi\)
0.00879328 + 0.999961i \(0.497201\pi\)
\(444\) 0 0
\(445\) 1.87038 + 8.19468i 0.0886646 + 0.388465i
\(446\) 39.2030 + 18.8792i 1.85632 + 0.893955i
\(447\) 0 0
\(448\) 11.6079 + 14.4589i 0.548421 + 0.683120i
\(449\) 4.72913 9.82014i 0.223181 0.463441i −0.759070 0.651009i \(-0.774346\pi\)
0.982252 + 0.187568i \(0.0600604\pi\)
\(450\) 0 0
\(451\) 28.0734 + 58.2950i 1.32192 + 2.74500i
\(452\) −2.16242 1.72447i −0.101712 0.0811124i
\(453\) 0 0
\(454\) −0.459955 0.366802i −0.0215868 0.0172149i
\(455\) −0.572274 1.17850i −0.0268286 0.0552489i
\(456\) 0 0
\(457\) −5.20275 + 2.50551i −0.243374 + 0.117203i −0.551595 0.834112i \(-0.685981\pi\)
0.308221 + 0.951315i \(0.400266\pi\)
\(458\) 7.57864 33.2042i 0.354126 1.55153i
\(459\) 0 0
\(460\) 3.23964i 0.151049i
\(461\) 0.522508 2.28926i 0.0243356 0.106621i −0.961301 0.275499i \(-0.911157\pi\)
0.985637 + 0.168877i \(0.0540142\pi\)
\(462\) 0 0
\(463\) 4.73786 + 20.7579i 0.220187 + 0.964702i 0.957337 + 0.288973i \(0.0933139\pi\)
−0.737150 + 0.675729i \(0.763829\pi\)
\(464\) −15.0975 + 3.44589i −0.700882 + 0.159972i
\(465\) 0 0
\(466\) 4.83107 + 6.05797i 0.223795 + 0.280630i
\(467\) −5.44149 23.8407i −0.251802 1.10322i −0.929774 0.368130i \(-0.879998\pi\)
0.677972 0.735087i \(-0.262859\pi\)
\(468\) 0 0
\(469\) 28.8188 0.0939140i 1.33073 0.00433655i
\(470\) 44.9881 + 10.2682i 2.07515 + 0.473638i
\(471\) 0 0
\(472\) 24.0720i 1.10800i
\(473\) −66.3111 15.1351i −3.04899 0.695911i
\(474\) 0 0
\(475\) −19.3279 + 15.4135i −0.886826 + 0.707221i
\(476\) −0.865663 + 0.00282100i −0.0396776 + 0.000129301i
\(477\) 0 0
\(478\) −1.58002 + 6.92253i −0.0722686 + 0.316629i
\(479\) −13.9399 + 17.4801i −0.636930 + 0.798685i −0.990615 0.136680i \(-0.956357\pi\)
0.353686 + 0.935364i \(0.384928\pi\)
\(480\) 0 0
\(481\) −0.295934 + 0.235999i −0.0134934 + 0.0107606i
\(482\) 29.1344 + 14.0304i 1.32704 + 0.639067i
\(483\) 0 0
\(484\) −3.81661 + 1.83798i −0.173482 + 0.0835446i
\(485\) −9.04951 + 18.7915i −0.410917 + 0.853278i
\(486\) 0 0
\(487\) −35.9295 17.3027i −1.62812 0.784062i −0.999982 0.00596062i \(-0.998103\pi\)
−0.628139 0.778101i \(-0.716183\pi\)
\(488\) −1.04986 + 1.31648i −0.0475249 + 0.0595943i
\(489\) 0 0
\(490\) −14.0055 28.6044i −0.632705 1.29221i
\(491\) 0.0942791i 0.00425476i 0.999998 + 0.00212738i \(0.000677166\pi\)
−0.999998 + 0.00212738i \(0.999323\pi\)
\(492\) 0 0
\(493\) −2.42672 + 5.03913i −0.109294 + 0.226951i
\(494\) 1.32217 0.301776i 0.0594872 0.0135776i
\(495\) 0 0
\(496\) −1.62540 3.37517i −0.0729825 0.151550i
\(497\) −11.6345 + 2.69541i −0.521876 + 0.120905i
\(498\) 0 0
\(499\) 6.29351 + 7.89181i 0.281736 + 0.353286i 0.902483 0.430725i \(-0.141742\pi\)
−0.620747 + 0.784011i \(0.713171\pi\)
\(500\) −0.355161 + 0.171036i −0.0158833 + 0.00764898i
\(501\) 0 0
\(502\) −21.0917 4.81404i −0.941369 0.214861i
\(503\) −18.8923 + 23.6903i −0.842368 + 1.05630i 0.155288 + 0.987869i \(0.450369\pi\)
−0.997656 + 0.0684268i \(0.978202\pi\)
\(504\) 0 0
\(505\) −1.82082 2.28324i −0.0810256 0.101603i
\(506\) −18.4508 38.3135i −0.820238 1.70324i
\(507\) 0 0
\(508\) −1.21711 −0.0540007
\(509\) 19.1471 0.848679 0.424340 0.905503i \(-0.360506\pi\)
0.424340 + 0.905503i \(0.360506\pi\)
\(510\) 0 0
\(511\) −14.5997 + 11.7209i −0.645851 + 0.518501i
\(512\) −17.7263 + 4.04591i −0.783399 + 0.178806i
\(513\) 0 0
\(514\) −13.3873 + 10.6760i −0.590490 + 0.470900i
\(515\) 33.3838 26.6227i 1.47107 1.17314i
\(516\) 0 0
\(517\) 55.4434 12.6546i 2.43840 0.556548i
\(518\) −7.17555 + 5.76066i −0.315276 + 0.253109i
\(519\) 0 0
\(520\) 1.31887 0.0578365
\(521\) 6.27022 0.274703 0.137352 0.990522i \(-0.456141\pi\)
0.137352 + 0.990522i \(0.456141\pi\)
\(522\) 0 0
\(523\) −12.3641 25.6744i −0.540645 1.12266i −0.975059 0.221948i \(-0.928759\pi\)
0.434413 0.900714i \(-0.356956\pi\)
\(524\) 1.93977 + 2.43240i 0.0847393 + 0.106260i
\(525\) 0 0
\(526\) 0.187747 0.235428i 0.00818617 0.0102651i
\(527\) −1.31908 0.301073i −0.0574602 0.0131149i
\(528\) 0 0
\(529\) 2.75473 1.32661i 0.119771 0.0576787i
\(530\) −18.6108 23.3372i −0.808400 1.01370i
\(531\) 0 0
\(532\) 3.01552 0.698619i 0.130739 0.0302890i
\(533\) 0.809512 + 1.68097i 0.0350639 + 0.0728108i
\(534\) 0 0
\(535\) −24.4937 + 5.59052i −1.05895 + 0.241699i
\(536\) −12.5878 + 26.1389i −0.543711 + 1.12903i
\(537\) 0 0
\(538\) 23.8779i 1.02945i
\(539\) −30.8464 24.2720i −1.32865 1.04547i
\(540\) 0 0
\(541\) −5.53360 + 6.93892i −0.237908 + 0.298327i −0.886424 0.462873i \(-0.846818\pi\)
0.648516 + 0.761201i \(0.275390\pi\)
\(542\) 14.5457 + 7.00486i 0.624793 + 0.300885i
\(543\) 0 0
\(544\) 0.799937 1.66109i 0.0342970 0.0712185i
\(545\) −29.7046 + 14.3050i −1.27240 + 0.612757i
\(546\) 0 0
\(547\) −6.39834 3.08128i −0.273573 0.131746i 0.292067 0.956398i \(-0.405657\pi\)
−0.565641 + 0.824652i \(0.691371\pi\)
\(548\) 1.91095 1.52394i 0.0816319 0.0650993i
\(549\) 0 0
\(550\) 22.7440 28.5200i 0.969807 1.21610i
\(551\) 4.45021 19.4976i 0.189585 0.830627i
\(552\) 0 0
\(553\) 25.6446 0.0835702i 1.09052 0.00355377i
\(554\) 8.33934 6.65040i 0.354305 0.282549i
\(555\) 0 0
\(556\) 3.48375 + 0.795142i 0.147744 + 0.0337215i
\(557\) 8.93590i 0.378626i 0.981917 + 0.189313i \(0.0606261\pi\)
−0.981917 + 0.189313i \(0.939374\pi\)
\(558\) 0 0
\(559\) −1.91212 0.436428i −0.0808740 0.0184590i
\(560\) 35.4205 0.115427i 1.49679 0.00487770i
\(561\) 0 0
\(562\) 1.81201 + 7.93892i 0.0764349 + 0.334883i
\(563\) −14.6444 18.3635i −0.617189 0.773930i 0.370757 0.928730i \(-0.379098\pi\)
−0.987946 + 0.154800i \(0.950527\pi\)
\(564\) 0 0
\(565\) 39.8492 9.09532i 1.67647 0.382643i
\(566\) 5.63260 + 24.6780i 0.236756 + 1.03730i
\(567\) 0 0
\(568\) 2.67528 11.7212i 0.112252 0.491809i
\(569\) 22.9316i 0.961342i −0.876901 0.480671i \(-0.840393\pi\)
0.876901 0.480671i \(-0.159607\pi\)
\(570\) 0 0
\(571\) 3.34250 14.6444i 0.139879 0.612851i −0.855581 0.517669i \(-0.826800\pi\)
0.995460 0.0951815i \(-0.0303431\pi\)
\(572\) −0.169277 + 0.0815193i −0.00707781 + 0.00340849i
\(573\) 0 0
\(574\) 19.8127 + 40.8008i 0.826964 + 1.70299i
\(575\) 17.4760 + 13.9366i 0.728799 + 0.581198i
\(576\) 0 0
\(577\) 5.54341 + 4.42072i 0.230775 + 0.184037i 0.732050 0.681251i \(-0.238564\pi\)
−0.501274 + 0.865288i \(0.667135\pi\)
\(578\) 9.35147 + 19.4185i 0.388970 + 0.807704i
\(579\) 0 0
\(580\) −0.975445 + 2.02553i −0.0405032 + 0.0841057i
\(581\) 12.2506 + 15.2594i 0.508239 + 0.633068i
\(582\) 0 0
\(583\) −33.1434 15.9610i −1.37266 0.661038i
\(584\) −4.19404 18.3753i −0.173550 0.760374i
\(585\) 0 0
\(586\) −31.1865 24.8704i −1.28830 1.02739i
\(587\) −16.8193 −0.694206 −0.347103 0.937827i \(-0.612835\pi\)
−0.347103 + 0.937827i \(0.612835\pi\)
\(588\) 0 0
\(589\) 4.83798 0.199346
\(590\) −32.1496 25.6385i −1.32358 1.05552i
\(591\) 0 0
\(592\) −2.27722 9.97714i −0.0935931 0.410058i
\(593\) 9.27765 + 4.46788i 0.380987 + 0.183474i 0.614568 0.788864i \(-0.289330\pi\)
−0.233581 + 0.972337i \(0.575044\pi\)
\(594\) 0 0
\(595\) 7.94364 10.0279i 0.325657 0.411103i
\(596\) −0.846268 + 1.75729i −0.0346645 + 0.0719816i
\(597\) 0 0
\(598\) −0.532040 1.10479i −0.0217567 0.0451783i
\(599\) −17.7390 14.1464i −0.724798 0.578007i 0.190065 0.981771i \(-0.439130\pi\)
−0.914863 + 0.403765i \(0.867701\pi\)
\(600\) 0 0
\(601\) −7.17003 5.71790i −0.292471 0.233238i 0.466251 0.884653i \(-0.345604\pi\)
−0.758722 + 0.651414i \(0.774176\pi\)
\(602\) −46.5188 10.4582i −1.89596 0.426246i
\(603\) 0 0
\(604\) −1.14936 + 0.553504i −0.0467669 + 0.0225217i
\(605\) 13.9302 61.0323i 0.566344 2.48132i
\(606\) 0 0
\(607\) 26.9406i 1.09348i 0.837301 + 0.546742i \(0.184132\pi\)
−0.837301 + 0.546742i \(0.815868\pi\)
\(608\) −1.46696 + 6.42716i −0.0594929 + 0.260656i
\(609\) 0 0
\(610\) 0.640064 + 2.80430i 0.0259154 + 0.113543i
\(611\) 1.59874 0.364902i 0.0646782 0.0147624i
\(612\) 0 0
\(613\) 2.23951 + 2.80826i 0.0904532 + 0.113425i 0.824998 0.565135i \(-0.191176\pi\)
−0.734545 + 0.678560i \(0.762604\pi\)
\(614\) −8.44344 36.9931i −0.340749 1.49292i
\(615\) 0 0
\(616\) 35.5446 17.2603i 1.43213 0.695438i
\(617\) 14.0559 + 3.20816i 0.565868 + 0.129156i 0.495878 0.868392i \(-0.334846\pi\)
0.0699898 + 0.997548i \(0.477703\pi\)
\(618\) 0 0
\(619\) 0.980947i 0.0394276i −0.999806 0.0197138i \(-0.993725\pi\)
0.999806 0.0197138i \(-0.00627550\pi\)
\(620\) −0.530221 0.121019i −0.0212942 0.00486026i
\(621\) 0 0
\(622\) −24.4582 + 19.5047i −0.980683 + 0.782069i
\(623\) 4.54602 + 5.66258i 0.182133 + 0.226866i
\(624\) 0 0
\(625\) 6.16825 27.0249i 0.246730 1.08099i
\(626\) 22.3109 27.9769i 0.891721 1.11818i
\(627\) 0 0
\(628\) 3.01232 2.40225i 0.120205 0.0958602i
\(629\) −3.33010 1.60369i −0.132780 0.0639434i
\(630\) 0 0
\(631\) −13.1070 + 6.31199i −0.521781 + 0.251276i −0.676186 0.736731i \(-0.736368\pi\)
0.154405 + 0.988008i \(0.450654\pi\)
\(632\) −11.2014 + 23.2599i −0.445567 + 0.925229i
\(633\) 0 0
\(634\) −24.6450 11.8684i −0.978777 0.471354i
\(635\) 11.2145 14.0625i 0.445034 0.558055i
\(636\) 0 0
\(637\) −0.889474 0.699897i −0.0352423 0.0277309i
\(638\) 29.5103i 1.16833i
\(639\) 0 0
\(640\) −16.9382 + 35.1726i −0.669542 + 1.39032i
\(641\) 15.3622 3.50631i 0.606769 0.138491i 0.0919120 0.995767i \(-0.470702\pi\)
0.514857 + 0.857276i \(0.327845\pi\)
\(642\) 0 0
\(643\) 7.33780 + 15.2371i 0.289375 + 0.600892i 0.994085 0.108602i \(-0.0346375\pi\)
−0.704711 + 0.709495i \(0.748923\pi\)
\(644\) −1.22256 2.51766i −0.0481757 0.0992096i
\(645\) 0 0
\(646\) 8.25677 + 10.3537i 0.324858 + 0.407360i
\(647\) 29.3155 14.1176i 1.15251 0.555020i 0.242724 0.970096i \(-0.421959\pi\)
0.909787 + 0.415076i \(0.136245\pi\)
\(648\) 0 0
\(649\) −49.4069 11.2768i −1.93939 0.442653i
\(650\) 0.655836 0.822392i 0.0257240 0.0322569i
\(651\) 0 0
\(652\) −0.953435 1.19557i −0.0373394 0.0468221i
\(653\) −16.6651 34.6055i −0.652157 1.35422i −0.920443 0.390878i \(-0.872171\pi\)
0.268286 0.963339i \(-0.413543\pi\)
\(654\) 0 0
\(655\) −45.9770 −1.79647
\(656\) −50.4431 −1.96947
\(657\) 0 0
\(658\) 38.8370 8.99755i 1.51402 0.350761i
\(659\) 14.1684 3.23384i 0.551922 0.125973i 0.0625406 0.998042i \(-0.480080\pi\)
0.489381 + 0.872070i \(0.337223\pi\)
\(660\) 0 0
\(661\) 28.9366 23.0762i 1.12550 0.897558i 0.129927 0.991524i \(-0.458526\pi\)
0.995575 + 0.0939653i \(0.0299543\pi\)
\(662\) 19.3929 15.4653i 0.753727 0.601078i
\(663\) 0 0
\(664\) −19.2057 + 4.38357i −0.745325 + 0.170115i
\(665\) −19.7132 + 41.2784i −0.764445 + 1.60071i
\(666\) 0 0
\(667\) −18.0828 −0.700168
\(668\) −2.74559 −0.106230
\(669\) 0 0
\(670\) 21.5031 + 44.6517i 0.830737 + 1.72504i
\(671\) 2.21021 + 2.77152i 0.0853243 + 0.106993i
\(672\) 0 0
\(673\) 10.8518 13.6078i 0.418308 0.524542i −0.527375 0.849633i \(-0.676824\pi\)
0.945683 + 0.325091i \(0.105395\pi\)
\(674\) −49.8317 11.3738i −1.91944 0.438101i
\(675\) 0 0
\(676\) 2.42234 1.16654i 0.0931668 0.0448668i
\(677\) 1.30490 + 1.63630i 0.0501514 + 0.0628879i 0.806275 0.591541i \(-0.201480\pi\)
−0.756123 + 0.654429i \(0.772909\pi\)
\(678\) 0 0
\(679\) 0.0587189 + 18.0187i 0.00225342 + 0.691494i
\(680\) 5.58783 + 11.6033i 0.214284 + 0.444964i
\(681\) 0 0
\(682\) −6.95988 + 1.58855i −0.266507 + 0.0608286i
\(683\) −1.08682 + 2.25680i −0.0415860 + 0.0863542i −0.920727 0.390208i \(-0.872403\pi\)
0.879141 + 0.476562i \(0.158117\pi\)
\(684\) 0 0
\(685\) 36.1208i 1.38010i
\(686\) −21.6789 16.9443i −0.827702 0.646935i
\(687\) 0 0
\(688\) 33.0616 41.4579i 1.26046 1.58057i
\(689\) −0.955709 0.460245i −0.0364096 0.0175339i
\(690\) 0 0
\(691\) 18.1168 37.6199i 0.689195 1.43113i −0.202863 0.979207i \(-0.565025\pi\)
0.892058 0.451921i \(-0.149261\pi\)
\(692\) 0.225098 0.108401i 0.00855694 0.00412080i
\(693\) 0 0
\(694\) 16.9327 + 8.15435i 0.642756 + 0.309535i
\(695\) −41.2864 + 32.9248i −1.56608 + 1.24891i
\(696\) 0 0
\(697\) −11.3591 + 14.2439i −0.430258 + 0.539527i
\(698\) 0.972560 4.26107i 0.0368120 0.161284i
\(699\) 0 0
\(700\) 1.49079 1.88193i 0.0563464 0.0711304i
\(701\) 24.0216 19.1566i 0.907282 0.723533i −0.0541625 0.998532i \(-0.517249\pi\)
0.961445 + 0.274999i \(0.0886775\pi\)
\(702\) 0 0
\(703\) 12.8850 + 2.94092i 0.485967 + 0.110919i
\(704\) 39.2968i 1.48105i
\(705\) 0 0
\(706\) 30.2730 + 6.90962i 1.13934 + 0.260047i
\(707\) −2.27667 1.08726i −0.0856231 0.0408907i
\(708\) 0 0
\(709\) −9.65247 42.2902i −0.362506 1.58824i −0.746811 0.665036i \(-0.768416\pi\)
0.384305 0.923206i \(-0.374441\pi\)
\(710\) −12.8050 16.0569i −0.480562 0.602605i
\(711\) 0 0
\(712\) −7.12697 + 1.62668i −0.267095 + 0.0609626i
\(713\) −0.973400 4.26474i −0.0364541 0.159716i
\(714\) 0 0
\(715\) 0.617842 2.70694i 0.0231060 0.101234i
\(716\) 3.64925i 0.136379i
\(717\) 0 0
\(718\) −8.74478 + 38.3134i −0.326352 + 1.42984i
\(719\) 5.29463 2.54976i 0.197457 0.0950900i −0.332543 0.943088i \(-0.607907\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(720\) 0 0
\(721\) 15.8972 33.2878i 0.592041 1.23970i
\(722\) −14.9524 11.9242i −0.556472 0.443772i
\(723\) 0 0
\(724\) −0.391254 0.312014i −0.0145408 0.0115959i
\(725\) −6.73029 13.9756i −0.249957 0.519041i
\(726\) 0 0
\(727\) 21.0355 43.6807i 0.780163 1.62003i −0.00441016 0.999990i \(-0.501404\pi\)
0.784574 0.620036i \(-0.212882\pi\)
\(728\) 1.02495 0.497711i 0.0379872 0.0184464i
\(729\) 0 0
\(730\) −29.0083 13.9697i −1.07364 0.517040i
\(731\) −4.26167 18.6716i −0.157623 0.690594i
\(732\) 0 0
\(733\) 20.5255 + 16.3685i 0.758125 + 0.604585i 0.924369 0.381500i \(-0.124592\pi\)
−0.166244 + 0.986085i \(0.553164\pi\)
\(734\) 8.35963 0.308560
\(735\) 0 0
\(736\) 5.96077 0.219717
\(737\) 47.7522 + 38.0811i 1.75897 + 1.40273i
\(738\) 0 0
\(739\) 5.33449 + 23.3719i 0.196232 + 0.859751i 0.973154 + 0.230154i \(0.0739228\pi\)
−0.776922 + 0.629597i \(0.783220\pi\)
\(740\) −1.33857 0.644623i −0.0492069 0.0236968i
\(741\) 0 0
\(742\) −23.2701 11.1130i −0.854270 0.407971i
\(743\) 1.67693 3.48217i 0.0615205 0.127749i −0.867942 0.496666i \(-0.834557\pi\)
0.929462 + 0.368918i \(0.120272\pi\)
\(744\) 0 0
\(745\) −12.5063 25.9695i −0.458194 0.951450i
\(746\) −19.0803 15.2161i −0.698581 0.557100i
\(747\) 0 0
\(748\) −1.43439 1.14389i −0.0524464 0.0418246i
\(749\) −16.9253 + 13.5879i −0.618436 + 0.496492i
\(750\) 0 0
\(751\) 5.76201 2.77484i 0.210259 0.101255i −0.325791 0.945442i \(-0.605630\pi\)
0.536049 + 0.844187i \(0.319916\pi\)
\(752\) −9.86572 + 43.2246i −0.359766 + 1.57624i
\(753\) 0 0
\(754\) 0.850948i 0.0309897i
\(755\) 4.19506 18.3797i 0.152674 0.668907i
\(756\) 0 0
\(757\) 0.101990 + 0.446847i 0.00370689 + 0.0162409i 0.976748 0.214393i \(-0.0687772\pi\)
−0.973041 + 0.230634i \(0.925920\pi\)
\(758\) 21.2130 4.84174i 0.770492 0.175860i
\(759\) 0 0
\(760\) −28.7120 36.0037i −1.04149 1.30599i
\(761\) −8.93457 39.1449i −0.323878 1.41900i −0.830589 0.556886i \(-0.811996\pi\)
0.506711 0.862116i \(-0.330861\pi\)
\(762\) 0 0
\(763\) −17.6863 + 22.3267i −0.640286 + 0.808282i
\(764\) −1.63837 0.373946i −0.0592740 0.0135289i
\(765\) 0 0
\(766\) 24.1310i 0.871889i
\(767\) −1.42468 0.325173i −0.0514421 0.0117413i
\(768\) 0 0
\(769\) −2.13350 + 1.70141i −0.0769358 + 0.0613543i −0.661203 0.750207i \(-0.729954\pi\)
0.584267 + 0.811562i \(0.301382\pi\)
\(770\) 14.8055 65.8556i 0.533553 2.37327i
\(771\) 0 0
\(772\) −0.0438415 + 0.192082i −0.00157789 + 0.00691318i
\(773\) 14.4004 18.0575i 0.517946 0.649483i −0.452226 0.891904i \(-0.649370\pi\)
0.970171 + 0.242420i \(0.0779413\pi\)
\(774\) 0 0
\(775\) 2.93379 2.33962i 0.105385 0.0840415i
\(776\) −16.3431 7.87042i −0.586683 0.282532i
\(777\) 0 0
\(778\) −6.86925 + 3.30806i −0.246274 + 0.118600i
\(779\) 28.2653 58.6935i 1.01271 2.10291i
\(780\) 0 0
\(781\) −22.8040 10.9818i −0.815991 0.392961i
\(782\) 7.46563 9.36160i 0.266970 0.334770i
\(783\) 0 0
\(784\) 27.4831 13.4565i 0.981539 0.480590i
\(785\) 56.9388i 2.03223i
\(786\) 0 0
\(787\) −7.42263 + 15.4133i −0.264588 + 0.549423i −0.990361 0.138512i \(-0.955768\pi\)
0.725773 + 0.687935i \(0.241482\pi\)
\(788\) 2.94635 0.672485i 0.104959 0.0239563i
\(789\)