Properties

Label 475.2.e.g.201.6
Level $475$
Weight $2$
Character 475.201
Analytic conductor $3.793$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \( x^{12} + 6x^{10} + 29x^{8} + 40x^{6} + 43x^{4} + 7x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.6
Root \(-0.203566 + 0.352587i\) of defining polynomial
Character \(\chi\) \(=\) 475.201
Dual form 475.2.e.g.26.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22810 - 2.12713i) q^{2} +(0.780522 - 1.35190i) q^{3} +(-2.01647 - 3.49262i) q^{4} +(-1.91712 - 3.32055i) q^{6} -4.50527 q^{7} -4.99330 q^{8} +(0.281570 + 0.487693i) q^{9} +O(q^{10})\) \(q+(1.22810 - 2.12713i) q^{2} +(0.780522 - 1.35190i) q^{3} +(-2.01647 - 3.49262i) q^{4} +(-1.91712 - 3.32055i) q^{6} -4.50527 q^{7} -4.99330 q^{8} +(0.281570 + 0.487693i) q^{9} +2.19869 q^{11} -6.29559 q^{12} +(-1.87925 - 3.25495i) q^{13} +(-5.53293 + 9.58332i) q^{14} +(-2.09935 + 3.63617i) q^{16} +(0.332943 - 0.576674i) q^{17} +1.38318 q^{18} +(3.79804 - 2.13891i) q^{19} +(-3.51647 + 6.09070i) q^{21} +(2.70022 - 4.67691i) q^{22} +(-0.244013 - 0.422643i) q^{23} +(-3.89738 + 6.75046i) q^{24} -9.23163 q^{26} +5.56222 q^{27} +(9.08474 + 15.7352i) q^{28} +(-1.79804 - 3.11429i) q^{29} +6.83424 q^{31} +(0.163119 + 0.282531i) q^{32} +(1.71613 - 2.97242i) q^{33} +(-0.817776 - 1.41643i) q^{34} +(1.13555 - 1.96683i) q^{36} +3.01171 q^{37} +(0.114636 - 10.7057i) q^{38} -5.86718 q^{39} +(-0.0362063 + 0.0627112i) q^{41} +(8.63716 + 14.9600i) q^{42} +(0.210271 - 0.364199i) q^{43} +(-4.43359 - 7.67920i) q^{44} -1.19869 q^{46} +(2.51139 + 4.34986i) q^{47} +(3.27717 + 5.67623i) q^{48} +13.2975 q^{49} +(-0.519739 - 0.900215i) q^{51} +(-7.57888 + 13.1270i) q^{52} +(1.30900 + 2.26725i) q^{53} +(6.83097 - 11.8316i) q^{54} +22.4962 q^{56} +(0.0728572 - 6.80405i) q^{57} -8.83269 q^{58} +(-6.26783 + 10.8562i) q^{59} +(-3.53293 - 6.11922i) q^{61} +(8.39315 - 14.5374i) q^{62} +(-1.26855 - 2.19719i) q^{63} -7.59607 q^{64} +(-4.21516 - 7.30087i) q^{66} +(2.86334 + 4.95944i) q^{67} -2.68548 q^{68} -0.761831 q^{69} +(-3.48626 + 6.03838i) q^{71} +(-1.40596 - 2.43520i) q^{72} +(-1.47882 + 2.56139i) q^{73} +(3.69869 - 6.40632i) q^{74} +(-15.1290 - 8.95208i) q^{76} -9.90571 q^{77} +(-7.20549 + 12.4803i) q^{78} +(-5.66849 + 9.81811i) q^{79} +(3.49673 - 6.05651i) q^{81} +(0.0889301 + 0.154031i) q^{82} +15.6999 q^{83} +28.3634 q^{84} +(-0.516467 - 0.894547i) q^{86} -5.61363 q^{87} -10.9787 q^{88} +(0.668486 + 1.15785i) q^{89} +(8.46652 + 14.6644i) q^{91} +(-0.984089 + 1.70449i) q^{92} +(5.33428 - 9.23924i) q^{93} +12.3370 q^{94} +0.509273 q^{96} +(2.19319 - 3.79871i) q^{97} +(16.3307 - 28.2856i) q^{98} +(0.619085 + 1.07229i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 2 q^{4} - 12 q^{6} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 2 q^{4} - 12 q^{6} - 8 q^{9} + 4 q^{11} - 22 q^{14} - 14 q^{16} + 12 q^{19} - 20 q^{21} - 2 q^{24} - 44 q^{26} + 12 q^{29} + 60 q^{31} - 10 q^{34} + 14 q^{36} - 4 q^{39} - 12 q^{41} - 20 q^{44} + 8 q^{46} + 4 q^{49} - 40 q^{51} + 4 q^{54} + 92 q^{56} - 20 q^{59} + 2 q^{61} - 24 q^{64} - 6 q^{66} + 36 q^{69} + 2 q^{71} + 22 q^{74} - 70 q^{76} - 24 q^{79} - 14 q^{81} + 96 q^{84} + 16 q^{86} - 36 q^{89} + 24 q^{91} + 60 q^{94} + 52 q^{96} + 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22810 2.12713i 0.868399 1.50411i 0.00476685 0.999989i \(-0.498483\pi\)
0.863632 0.504123i \(-0.168184\pi\)
\(3\) 0.780522 1.35190i 0.450635 0.780522i −0.547791 0.836615i \(-0.684531\pi\)
0.998426 + 0.0560930i \(0.0178643\pi\)
\(4\) −2.01647 3.49262i −1.00823 1.74631i
\(5\) 0 0
\(6\) −1.91712 3.32055i −0.782662 1.35561i
\(7\) −4.50527 −1.70283 −0.851417 0.524490i \(-0.824256\pi\)
−0.851417 + 0.524490i \(0.824256\pi\)
\(8\) −4.99330 −1.76540
\(9\) 0.281570 + 0.487693i 0.0938566 + 0.162564i
\(10\) 0 0
\(11\) 2.19869 0.662930 0.331465 0.943467i \(-0.392457\pi\)
0.331465 + 0.943467i \(0.392457\pi\)
\(12\) −6.29559 −1.81738
\(13\) −1.87925 3.25495i −0.521209 0.902761i −0.999696 0.0246661i \(-0.992148\pi\)
0.478486 0.878095i \(-0.341186\pi\)
\(14\) −5.53293 + 9.58332i −1.47874 + 2.56125i
\(15\) 0 0
\(16\) −2.09935 + 3.63617i −0.524836 + 0.909043i
\(17\) 0.332943 0.576674i 0.0807506 0.139864i −0.822822 0.568299i \(-0.807602\pi\)
0.903573 + 0.428435i \(0.140935\pi\)
\(18\) 1.38318 0.326020
\(19\) 3.79804 2.13891i 0.871329 0.490699i
\(20\) 0 0
\(21\) −3.51647 + 6.09070i −0.767356 + 1.32910i
\(22\) 2.70022 4.67691i 0.575688 0.997121i
\(23\) −0.244013 0.422643i −0.0508802 0.0881272i 0.839464 0.543416i \(-0.182869\pi\)
−0.890344 + 0.455289i \(0.849536\pi\)
\(24\) −3.89738 + 6.75046i −0.795550 + 1.37793i
\(25\) 0 0
\(26\) −9.23163 −1.81047
\(27\) 5.56222 1.07045
\(28\) 9.08474 + 15.7352i 1.71685 + 2.97368i
\(29\) −1.79804 3.11429i −0.333887 0.578309i 0.649383 0.760461i \(-0.275027\pi\)
−0.983270 + 0.182152i \(0.941694\pi\)
\(30\) 0 0
\(31\) 6.83424 1.22747 0.613733 0.789514i \(-0.289667\pi\)
0.613733 + 0.789514i \(0.289667\pi\)
\(32\) 0.163119 + 0.282531i 0.0288357 + 0.0499449i
\(33\) 1.71613 2.97242i 0.298739 0.517432i
\(34\) −0.817776 1.41643i −0.140247 0.242916i
\(35\) 0 0
\(36\) 1.13555 1.96683i 0.189259 0.327806i
\(37\) 3.01171 0.495123 0.247561 0.968872i \(-0.420371\pi\)
0.247561 + 0.968872i \(0.420371\pi\)
\(38\) 0.114636 10.7057i 0.0185964 1.73670i
\(39\) −5.86718 −0.939500
\(40\) 0 0
\(41\) −0.0362063 + 0.0627112i −0.00565448 + 0.00979384i −0.868839 0.495095i \(-0.835133\pi\)
0.863184 + 0.504889i \(0.168467\pi\)
\(42\) 8.63716 + 14.9600i 1.33274 + 2.30838i
\(43\) 0.210271 0.364199i 0.0320660 0.0555399i −0.849547 0.527513i \(-0.823125\pi\)
0.881613 + 0.471973i \(0.156458\pi\)
\(44\) −4.43359 7.67920i −0.668389 1.15768i
\(45\) 0 0
\(46\) −1.19869 −0.176737
\(47\) 2.51139 + 4.34986i 0.366324 + 0.634492i 0.988988 0.147998i \(-0.0472829\pi\)
−0.622664 + 0.782490i \(0.713950\pi\)
\(48\) 3.27717 + 5.67623i 0.473019 + 0.819293i
\(49\) 13.2975 1.89964
\(50\) 0 0
\(51\) −0.519739 0.900215i −0.0727780 0.126055i
\(52\) −7.57888 + 13.1270i −1.05100 + 1.82039i
\(53\) 1.30900 + 2.26725i 0.179804 + 0.311430i 0.941813 0.336136i \(-0.109120\pi\)
−0.762009 + 0.647566i \(0.775787\pi\)
\(54\) 6.83097 11.8316i 0.929577 1.61008i
\(55\) 0 0
\(56\) 22.4962 3.00618
\(57\) 0.0728572 6.80405i 0.00965017 0.901218i
\(58\) −8.83269 −1.15979
\(59\) −6.26783 + 10.8562i −0.816002 + 1.41336i 0.0926038 + 0.995703i \(0.470481\pi\)
−0.908606 + 0.417654i \(0.862852\pi\)
\(60\) 0 0
\(61\) −3.53293 6.11922i −0.452346 0.783486i 0.546185 0.837664i \(-0.316079\pi\)
−0.998531 + 0.0541782i \(0.982746\pi\)
\(62\) 8.39315 14.5374i 1.06593 1.84625i
\(63\) −1.26855 2.19719i −0.159822 0.276820i
\(64\) −7.59607 −0.949509
\(65\) 0 0
\(66\) −4.21516 7.30087i −0.518850 0.898675i
\(67\) 2.86334 + 4.95944i 0.349812 + 0.605892i 0.986216 0.165464i \(-0.0529121\pi\)
−0.636404 + 0.771356i \(0.719579\pi\)
\(68\) −2.68548 −0.325662
\(69\) −0.761831 −0.0917136
\(70\) 0 0
\(71\) −3.48626 + 6.03838i −0.413743 + 0.716624i −0.995296 0.0968847i \(-0.969112\pi\)
0.581552 + 0.813509i \(0.302446\pi\)
\(72\) −1.40596 2.43520i −0.165694 0.286991i
\(73\) −1.47882 + 2.56139i −0.173083 + 0.299788i −0.939496 0.342560i \(-0.888706\pi\)
0.766413 + 0.642348i \(0.222039\pi\)
\(74\) 3.69869 6.40632i 0.429964 0.744720i
\(75\) 0 0
\(76\) −15.1290 8.95208i −1.73542 1.02687i
\(77\) −9.90571 −1.12886
\(78\) −7.20549 + 12.4803i −0.815861 + 1.41311i
\(79\) −5.66849 + 9.81811i −0.637755 + 1.10462i 0.348170 + 0.937431i \(0.386803\pi\)
−0.985924 + 0.167192i \(0.946530\pi\)
\(80\) 0 0
\(81\) 3.49673 6.05651i 0.388525 0.672946i
\(82\) 0.0889301 + 0.154031i 0.00982068 + 0.0170099i
\(83\) 15.6999 1.72328 0.861642 0.507517i \(-0.169436\pi\)
0.861642 + 0.507517i \(0.169436\pi\)
\(84\) 28.3634 3.09470
\(85\) 0 0
\(86\) −0.516467 0.894547i −0.0556921 0.0964615i
\(87\) −5.61363 −0.601845
\(88\) −10.9787 −1.17034
\(89\) 0.668486 + 1.15785i 0.0708594 + 0.122732i 0.899278 0.437377i \(-0.144092\pi\)
−0.828419 + 0.560109i \(0.810759\pi\)
\(90\) 0 0
\(91\) 8.46652 + 14.6644i 0.887533 + 1.53725i
\(92\) −0.984089 + 1.70449i −0.102598 + 0.177706i
\(93\) 5.33428 9.23924i 0.553139 0.958065i
\(94\) 12.3370 1.27246
\(95\) 0 0
\(96\) 0.509273 0.0519775
\(97\) 2.19319 3.79871i 0.222685 0.385701i −0.732938 0.680296i \(-0.761851\pi\)
0.955622 + 0.294595i \(0.0951847\pi\)
\(98\) 16.3307 28.2856i 1.64965 2.85727i
\(99\) 0.619085 + 1.07229i 0.0622204 + 0.107769i
\(100\) 0 0
\(101\) 5.28430 + 9.15267i 0.525807 + 0.910725i 0.999548 + 0.0300608i \(0.00957008\pi\)
−0.473741 + 0.880664i \(0.657097\pi\)
\(102\) −2.55317 −0.252801
\(103\) −5.75615 −0.567171 −0.283585 0.958947i \(-0.591524\pi\)
−0.283585 + 0.958947i \(0.591524\pi\)
\(104\) 9.38364 + 16.2529i 0.920142 + 1.59373i
\(105\) 0 0
\(106\) 6.43032 0.624568
\(107\) 1.30229 0.125897 0.0629486 0.998017i \(-0.479950\pi\)
0.0629486 + 0.998017i \(0.479950\pi\)
\(108\) −11.2160 19.4267i −1.07926 1.86934i
\(109\) 6.01647 10.4208i 0.576273 0.998134i −0.419629 0.907696i \(-0.637840\pi\)
0.995902 0.0904385i \(-0.0288269\pi\)
\(110\) 0 0
\(111\) 2.35071 4.07155i 0.223120 0.386454i
\(112\) 9.45813 16.3820i 0.893709 1.54795i
\(113\) −7.74626 −0.728707 −0.364353 0.931261i \(-0.618710\pi\)
−0.364353 + 0.931261i \(0.618710\pi\)
\(114\) −14.3836 8.51104i −1.34715 0.797132i
\(115\) 0 0
\(116\) −7.25136 + 12.5597i −0.673272 + 1.16614i
\(117\) 1.05828 1.83299i 0.0978378 0.169460i
\(118\) 15.3951 + 26.6650i 1.41723 + 2.45472i
\(119\) −1.50000 + 2.59808i −0.137505 + 0.238165i
\(120\) 0 0
\(121\) −6.16576 −0.560523
\(122\) −17.3552 −1.57127
\(123\) 0.0565197 + 0.0978950i 0.00509621 + 0.00882689i
\(124\) −13.7810 23.8694i −1.23757 2.14354i
\(125\) 0 0
\(126\) −6.23163 −0.555157
\(127\) −1.96818 3.40898i −0.174647 0.302498i 0.765392 0.643565i \(-0.222545\pi\)
−0.940039 + 0.341066i \(0.889212\pi\)
\(128\) −9.65499 + 16.7229i −0.853389 + 1.47811i
\(129\) −0.328242 0.568531i −0.0289001 0.0500564i
\(130\) 0 0
\(131\) 8.16248 14.1378i 0.713160 1.23523i −0.250505 0.968115i \(-0.580597\pi\)
0.963665 0.267114i \(-0.0860699\pi\)
\(132\) −13.8421 −1.20480
\(133\) −17.1112 + 9.63635i −1.48373 + 0.835578i
\(134\) 14.0659 1.21511
\(135\) 0 0
\(136\) −1.66248 + 2.87951i −0.142557 + 0.246916i
\(137\) −8.21529 14.2293i −0.701879 1.21569i −0.967806 0.251697i \(-0.919011\pi\)
0.265927 0.963993i \(-0.414322\pi\)
\(138\) −0.935605 + 1.62052i −0.0796440 + 0.137947i
\(139\) 1.33424 + 2.31098i 0.113169 + 0.196015i 0.917046 0.398781i \(-0.130567\pi\)
−0.803877 + 0.594795i \(0.797233\pi\)
\(140\) 0 0
\(141\) 7.84079 0.660313
\(142\) 8.56297 + 14.8315i 0.718588 + 1.24463i
\(143\) −4.13188 7.15663i −0.345526 0.598468i
\(144\) −2.36445 −0.197037
\(145\) 0 0
\(146\) 3.63228 + 6.29129i 0.300610 + 0.520671i
\(147\) 10.3790 17.9769i 0.856045 1.48271i
\(148\) −6.07302 10.5188i −0.499199 0.864639i
\(149\) 8.98299 15.5590i 0.735915 1.27464i −0.218405 0.975858i \(-0.570085\pi\)
0.954321 0.298784i \(-0.0965812\pi\)
\(150\) 0 0
\(151\) −12.7344 −1.03631 −0.518154 0.855288i \(-0.673380\pi\)
−0.518154 + 0.855288i \(0.673380\pi\)
\(152\) −18.9647 + 10.6802i −1.53824 + 0.866278i
\(153\) 0.374987 0.0303159
\(154\) −12.1652 + 21.0708i −0.980301 + 1.69793i
\(155\) 0 0
\(156\) 11.8310 + 20.4918i 0.947236 + 1.64066i
\(157\) −10.0270 + 17.3674i −0.800245 + 1.38607i 0.119209 + 0.992869i \(0.461964\pi\)
−0.919454 + 0.393197i \(0.871369\pi\)
\(158\) 13.9230 + 24.1153i 1.10765 + 1.91851i
\(159\) 4.08680 0.324104
\(160\) 0 0
\(161\) 1.09935 + 1.90412i 0.0866406 + 0.150066i
\(162\) −8.58867 14.8760i −0.674790 1.16877i
\(163\) 14.2331 1.11482 0.557412 0.830236i \(-0.311794\pi\)
0.557412 + 0.830236i \(0.311794\pi\)
\(164\) 0.292035 0.0228041
\(165\) 0 0
\(166\) 19.2810 33.3957i 1.49650 2.59201i
\(167\) 2.80815 + 4.86386i 0.217301 + 0.376376i 0.953982 0.299864i \(-0.0969413\pi\)
−0.736681 + 0.676241i \(0.763608\pi\)
\(168\) 17.5588 30.4127i 1.35469 2.34639i
\(169\) −0.563139 + 0.975386i −0.0433184 + 0.0750297i
\(170\) 0 0
\(171\) 2.11254 + 1.25002i 0.161550 + 0.0955918i
\(172\) −1.69601 −0.129320
\(173\) −5.34524 + 9.25824i −0.406391 + 0.703891i −0.994482 0.104904i \(-0.966546\pi\)
0.588091 + 0.808795i \(0.299880\pi\)
\(174\) −6.89411 + 11.9409i −0.522641 + 0.905241i
\(175\) 0 0
\(176\) −4.61581 + 7.99482i −0.347930 + 0.602632i
\(177\) 9.78437 + 16.9470i 0.735438 + 1.27382i
\(178\) 3.28388 0.246137
\(179\) 7.68942 0.574734 0.287367 0.957821i \(-0.407220\pi\)
0.287367 + 0.957821i \(0.407220\pi\)
\(180\) 0 0
\(181\) 3.06314 + 5.30551i 0.227681 + 0.394356i 0.957121 0.289690i \(-0.0935522\pi\)
−0.729439 + 0.684046i \(0.760219\pi\)
\(182\) 41.5910 3.08293
\(183\) −11.0301 −0.815371
\(184\) 1.21843 + 2.11038i 0.0898239 + 0.155580i
\(185\) 0 0
\(186\) −13.1021 22.6935i −0.960691 1.66397i
\(187\) 0.732039 1.26793i 0.0535320 0.0927201i
\(188\) 10.1283 17.5427i 0.738680 1.27943i
\(189\) −25.0593 −1.82280
\(190\) 0 0
\(191\) 5.85517 0.423666 0.211833 0.977306i \(-0.432057\pi\)
0.211833 + 0.977306i \(0.432057\pi\)
\(192\) −5.92891 + 10.2692i −0.427882 + 0.741113i
\(193\) 1.29559 2.24402i 0.0932584 0.161528i −0.815622 0.578585i \(-0.803605\pi\)
0.908880 + 0.417057i \(0.136938\pi\)
\(194\) −5.38692 9.33041i −0.386758 0.669885i
\(195\) 0 0
\(196\) −26.8140 46.4431i −1.91528 3.31737i
\(197\) 19.8628 1.41517 0.707584 0.706629i \(-0.249785\pi\)
0.707584 + 0.706629i \(0.249785\pi\)
\(198\) 3.04120 0.216128
\(199\) 6.38092 + 11.0521i 0.452331 + 0.783460i 0.998530 0.0541948i \(-0.0172592\pi\)
−0.546199 + 0.837655i \(0.683926\pi\)
\(200\) 0 0
\(201\) 8.93959 0.630550
\(202\) 25.9586 1.82644
\(203\) 8.10065 + 14.0307i 0.568554 + 0.984765i
\(204\) −2.09607 + 3.63051i −0.146755 + 0.254186i
\(205\) 0 0
\(206\) −7.06914 + 12.2441i −0.492530 + 0.853088i
\(207\) 0.137413 0.238007i 0.00955089 0.0165426i
\(208\) 15.7808 1.09420
\(209\) 8.35071 4.70279i 0.577631 0.325299i
\(210\) 0 0
\(211\) −6.92759 + 11.9989i −0.476915 + 0.826041i −0.999650 0.0264545i \(-0.991578\pi\)
0.522735 + 0.852495i \(0.324912\pi\)
\(212\) 5.27909 9.14366i 0.362570 0.627989i
\(213\) 5.44221 + 9.42619i 0.372894 + 0.645872i
\(214\) 1.59935 2.77015i 0.109329 0.189363i
\(215\) 0 0
\(216\) −27.7738 −1.88977
\(217\) −30.7901 −2.09017
\(218\) −14.7777 25.5957i −1.00087 1.73356i
\(219\) 2.30850 + 3.99844i 0.155994 + 0.270190i
\(220\) 0 0
\(221\) −2.50273 −0.168352
\(222\) −5.77382 10.0006i −0.387514 0.671193i
\(223\) −10.8480 + 18.7893i −0.726437 + 1.25823i 0.231943 + 0.972729i \(0.425492\pi\)
−0.958380 + 0.285496i \(0.907842\pi\)
\(224\) −0.734898 1.27288i −0.0491024 0.0850479i
\(225\) 0 0
\(226\) −9.51320 + 16.4773i −0.632808 + 1.09606i
\(227\) 8.19628 0.544006 0.272003 0.962296i \(-0.412314\pi\)
0.272003 + 0.962296i \(0.412314\pi\)
\(228\) −23.9109 + 13.4657i −1.58354 + 0.891786i
\(229\) −16.6619 −1.10105 −0.550526 0.834818i \(-0.685573\pi\)
−0.550526 + 0.834818i \(0.685573\pi\)
\(230\) 0 0
\(231\) −7.73163 + 13.3916i −0.508704 + 0.881101i
\(232\) 8.97814 + 15.5506i 0.589444 + 1.02095i
\(233\) −6.10677 + 10.5772i −0.400068 + 0.692937i −0.993734 0.111774i \(-0.964347\pi\)
0.593666 + 0.804711i \(0.297680\pi\)
\(234\) −2.59935 4.50220i −0.169925 0.294318i
\(235\) 0 0
\(236\) 50.5555 3.29088
\(237\) 8.84876 + 15.3265i 0.574789 + 0.995563i
\(238\) 3.68430 + 6.38140i 0.238818 + 0.413645i
\(239\) 2.03948 0.131923 0.0659614 0.997822i \(-0.478989\pi\)
0.0659614 + 0.997822i \(0.478989\pi\)
\(240\) 0 0
\(241\) −8.76183 15.1759i −0.564399 0.977568i −0.997105 0.0760330i \(-0.975775\pi\)
0.432706 0.901535i \(-0.357559\pi\)
\(242\) −7.57218 + 13.1154i −0.486758 + 0.843089i
\(243\) 2.88478 + 4.99659i 0.185059 + 0.320531i
\(244\) −14.2481 + 24.6784i −0.912141 + 1.57987i
\(245\) 0 0
\(246\) 0.277648 0.0177022
\(247\) −14.0995 8.34289i −0.897129 0.530846i
\(248\) −34.1254 −2.16697
\(249\) 12.2541 21.2247i 0.776572 1.34506i
\(250\) 0 0
\(251\) 1.66903 + 2.89084i 0.105348 + 0.182468i 0.913880 0.405984i \(-0.133071\pi\)
−0.808532 + 0.588452i \(0.799738\pi\)
\(252\) −5.11597 + 8.86112i −0.322276 + 0.558198i
\(253\) −0.536509 0.929261i −0.0337301 0.0584222i
\(254\) −9.66849 −0.606655
\(255\) 0 0
\(256\) 16.1185 + 27.9181i 1.00741 + 1.74488i
\(257\) 13.7922 + 23.8889i 0.860337 + 1.49015i 0.871604 + 0.490210i \(0.163080\pi\)
−0.0112676 + 0.999937i \(0.503587\pi\)
\(258\) −1.61246 −0.100387
\(259\) −13.5686 −0.843112
\(260\) 0 0
\(261\) 1.01255 1.75378i 0.0626750 0.108556i
\(262\) −20.0487 34.7254i −1.23861 2.14534i
\(263\) 6.81310 11.8006i 0.420114 0.727658i −0.575837 0.817565i \(-0.695324\pi\)
0.995950 + 0.0899066i \(0.0286569\pi\)
\(264\) −8.56914 + 14.8422i −0.527394 + 0.913473i
\(265\) 0 0
\(266\) −0.516467 + 48.2322i −0.0316666 + 2.95731i
\(267\) 2.08707 0.127727
\(268\) 11.5476 20.0011i 0.705385 1.22176i
\(269\) 1.80404 3.12469i 0.109994 0.190515i −0.805773 0.592224i \(-0.798250\pi\)
0.915768 + 0.401708i \(0.131583\pi\)
\(270\) 0 0
\(271\) −5.28157 + 9.14795i −0.320833 + 0.555698i −0.980660 0.195719i \(-0.937296\pi\)
0.659828 + 0.751417i \(0.270629\pi\)
\(272\) 1.39793 + 2.42128i 0.0847617 + 0.146812i
\(273\) 26.4332 1.59981
\(274\) −40.3568 −2.43804
\(275\) 0 0
\(276\) 1.53621 + 2.66079i 0.0924688 + 0.160161i
\(277\) −6.73487 −0.404659 −0.202330 0.979317i \(-0.564851\pi\)
−0.202330 + 0.979317i \(0.564851\pi\)
\(278\) 6.55434 0.393103
\(279\) 1.92432 + 3.33301i 0.115206 + 0.199542i
\(280\) 0 0
\(281\) −11.7152 20.2912i −0.698868 1.21047i −0.968859 0.247612i \(-0.920354\pi\)
0.269992 0.962863i \(-0.412979\pi\)
\(282\) 9.62928 16.6784i 0.573415 0.993185i
\(283\) 7.34157 12.7160i 0.436411 0.755886i −0.560999 0.827817i \(-0.689583\pi\)
0.997410 + 0.0719306i \(0.0229160\pi\)
\(284\) 28.1197 1.66860
\(285\) 0 0
\(286\) −20.2975 −1.20022
\(287\) 0.163119 0.282531i 0.00962863 0.0166773i
\(288\) −0.0918589 + 0.159104i −0.00541284 + 0.00937531i
\(289\) 8.27830 + 14.3384i 0.486959 + 0.843437i
\(290\) 0 0
\(291\) −3.42367 5.92996i −0.200699 0.347621i
\(292\) 11.9280 0.698031
\(293\) −18.1855 −1.06241 −0.531206 0.847243i \(-0.678261\pi\)
−0.531206 + 0.847243i \(0.678261\pi\)
\(294\) −25.4929 44.1550i −1.48678 2.57517i
\(295\) 0 0
\(296\) −15.0384 −0.874089
\(297\) 12.2296 0.709634
\(298\) −22.0641 38.2161i −1.27814 2.21380i
\(299\) −0.917122 + 1.58850i −0.0530385 + 0.0918654i
\(300\) 0 0
\(301\) −0.947326 + 1.64082i −0.0546030 + 0.0945752i
\(302\) −15.6391 + 27.0877i −0.899928 + 1.55872i
\(303\) 16.4981 0.947788
\(304\) −0.195962 + 18.3006i −0.0112392 + 1.04961i
\(305\) 0 0
\(306\) 0.460522 0.797647i 0.0263263 0.0455985i
\(307\) −14.6901 + 25.4439i −0.838406 + 1.45216i 0.0528200 + 0.998604i \(0.483179\pi\)
−0.891226 + 0.453559i \(0.850154\pi\)
\(308\) 19.9745 + 34.5969i 1.13815 + 1.97134i
\(309\) −4.49281 + 7.78177i −0.255587 + 0.442689i
\(310\) 0 0
\(311\) −0.193232 −0.0109572 −0.00547859 0.999985i \(-0.501744\pi\)
−0.00547859 + 0.999985i \(0.501744\pi\)
\(312\) 29.2966 1.65859
\(313\) 10.6377 + 18.4251i 0.601281 + 1.04145i 0.992627 + 0.121206i \(0.0386761\pi\)
−0.391346 + 0.920243i \(0.627991\pi\)
\(314\) 24.6285 + 42.6578i 1.38986 + 2.40732i
\(315\) 0 0
\(316\) 45.7213 2.57202
\(317\) −9.58506 16.6018i −0.538351 0.932451i −0.998993 0.0448649i \(-0.985714\pi\)
0.460642 0.887586i \(-0.347619\pi\)
\(318\) 5.01901 8.69317i 0.281452 0.487489i
\(319\) −3.95333 6.84736i −0.221344 0.383379i
\(320\) 0 0
\(321\) 1.01647 1.76057i 0.0567337 0.0982656i
\(322\) 5.40043 0.300954
\(323\) 0.0310783 2.90236i 0.00172924 0.161492i
\(324\) −28.2042 −1.56690
\(325\) 0 0
\(326\) 17.4797 30.2758i 0.968112 1.67682i
\(327\) −9.39197 16.2674i −0.519377 0.899588i
\(328\) 0.180789 0.313136i 0.00998240 0.0172900i
\(329\) −11.3145 19.5973i −0.623789 1.08043i
\(330\) 0 0
\(331\) −20.6070 −1.13266 −0.566331 0.824178i \(-0.691638\pi\)
−0.566331 + 0.824178i \(0.691638\pi\)
\(332\) −31.6583 54.8337i −1.73747 3.00939i
\(333\) 0.848007 + 1.46879i 0.0464705 + 0.0804893i
\(334\) 13.7948 0.754816
\(335\) 0 0
\(336\) −14.7646 25.5730i −0.805473 1.39512i
\(337\) 5.10368 8.83982i 0.278015 0.481536i −0.692876 0.721056i \(-0.743657\pi\)
0.970891 + 0.239520i \(0.0769902\pi\)
\(338\) 1.38318 + 2.39575i 0.0752353 + 0.130311i
\(339\) −6.04613 + 10.4722i −0.328381 + 0.568772i
\(340\) 0 0
\(341\) 15.0264 0.813725
\(342\) 5.25339 2.95850i 0.284071 0.159977i
\(343\) −28.3719 −1.53194
\(344\) −1.04994 + 1.81856i −0.0566092 + 0.0980500i
\(345\) 0 0
\(346\) 13.1290 + 22.7401i 0.705820 + 1.22252i
\(347\) −2.72055 + 4.71213i −0.146047 + 0.252960i −0.929763 0.368159i \(-0.879988\pi\)
0.783716 + 0.621119i \(0.213322\pi\)
\(348\) 11.3197 + 19.6063i 0.606800 + 1.05101i
\(349\) −1.55114 −0.0830304 −0.0415152 0.999138i \(-0.513219\pi\)
−0.0415152 + 0.999138i \(0.513219\pi\)
\(350\) 0 0
\(351\) −10.4528 18.1048i −0.557928 0.966360i
\(352\) 0.358649 + 0.621199i 0.0191161 + 0.0331100i
\(353\) −32.9335 −1.75287 −0.876437 0.481517i \(-0.840086\pi\)
−0.876437 + 0.481517i \(0.840086\pi\)
\(354\) 48.0648 2.55461
\(355\) 0 0
\(356\) 2.69596 4.66954i 0.142886 0.247485i
\(357\) 2.34157 + 4.05571i 0.123929 + 0.214651i
\(358\) 9.44339 16.3564i 0.499098 0.864464i
\(359\) 1.74864 3.02873i 0.0922894 0.159850i −0.816185 0.577791i \(-0.803915\pi\)
0.908474 + 0.417941i \(0.137248\pi\)
\(360\) 0 0
\(361\) 9.85017 16.2473i 0.518430 0.855120i
\(362\) 15.0474 0.790873
\(363\) −4.81251 + 8.33551i −0.252591 + 0.437501i
\(364\) 34.1449 59.1408i 1.78968 3.09982i
\(365\) 0 0
\(366\) −13.5461 + 23.4626i −0.708068 + 1.22641i
\(367\) −9.75196 16.8909i −0.509048 0.881697i −0.999945 0.0104794i \(-0.996664\pi\)
0.490897 0.871218i \(-0.336669\pi\)
\(368\) 2.04907 0.106815
\(369\) −0.0407784 −0.00212284
\(370\) 0 0
\(371\) −5.89738 10.2146i −0.306177 0.530314i
\(372\) −43.0256 −2.23077
\(373\) 23.5158 1.21760 0.608802 0.793322i \(-0.291650\pi\)
0.608802 + 0.793322i \(0.291650\pi\)
\(374\) −1.79804 3.11429i −0.0929743 0.161036i
\(375\) 0 0
\(376\) −12.5401 21.7201i −0.646708 1.12013i
\(377\) −6.75791 + 11.7050i −0.348050 + 0.602841i
\(378\) −30.7754 + 53.3046i −1.58292 + 2.74169i
\(379\) −7.05148 −0.362210 −0.181105 0.983464i \(-0.557967\pi\)
−0.181105 + 0.983464i \(0.557967\pi\)
\(380\) 0 0
\(381\) −6.14483 −0.314809
\(382\) 7.19075 12.4547i 0.367911 0.637240i
\(383\) −1.54204 + 2.67090i −0.0787947 + 0.136476i −0.902730 0.430207i \(-0.858440\pi\)
0.823935 + 0.566684i \(0.191774\pi\)
\(384\) 15.0719 + 26.1052i 0.769133 + 1.33218i
\(385\) 0 0
\(386\) −3.18222 5.51177i −0.161971 0.280542i
\(387\) 0.236823 0.0120384
\(388\) −17.6900 −0.898072
\(389\) −4.69542 8.13270i −0.238067 0.412345i 0.722092 0.691797i \(-0.243181\pi\)
−0.960160 + 0.279452i \(0.909847\pi\)
\(390\) 0 0
\(391\) −0.324970 −0.0164344
\(392\) −66.3984 −3.35362
\(393\) −12.7420 22.0698i −0.642749 1.11327i
\(394\) 24.3936 42.2509i 1.22893 2.12857i
\(395\) 0 0
\(396\) 2.49673 4.32446i 0.125465 0.217312i
\(397\) 13.3797 23.1744i 0.671510 1.16309i −0.305966 0.952042i \(-0.598979\pi\)
0.977476 0.211047i \(-0.0676873\pi\)
\(398\) 31.3456 1.57122
\(399\) −0.328242 + 30.6541i −0.0164326 + 1.53462i
\(400\) 0 0
\(401\) 12.5851 21.7980i 0.628468 1.08854i −0.359391 0.933187i \(-0.617016\pi\)
0.987859 0.155352i \(-0.0496511\pi\)
\(402\) 10.9787 19.0157i 0.547569 0.948417i
\(403\) −12.8432 22.2451i −0.639767 1.10811i
\(404\) 21.3112 36.9121i 1.06027 1.83645i
\(405\) 0 0
\(406\) 39.7937 1.97493
\(407\) 6.62183 0.328232
\(408\) 2.59521 + 4.49504i 0.128482 + 0.222538i
\(409\) 14.1608 + 24.5271i 0.700204 + 1.21279i 0.968395 + 0.249423i \(0.0802410\pi\)
−0.268191 + 0.963366i \(0.586426\pi\)
\(410\) 0 0
\(411\) −25.6489 −1.26516
\(412\) 11.6071 + 20.1041i 0.571840 + 0.990457i
\(413\) 28.2383 48.9102i 1.38952 2.40671i
\(414\) −0.337515 0.584593i −0.0165880 0.0287312i
\(415\) 0 0
\(416\) 0.613083 1.06189i 0.0300589 0.0520635i
\(417\) 4.16563 0.203992
\(418\) 0.252049 23.5386i 0.0123281 1.15131i
\(419\) 13.0449 0.637287 0.318643 0.947875i \(-0.396773\pi\)
0.318643 + 0.947875i \(0.396773\pi\)
\(420\) 0 0
\(421\) −1.66248 + 2.87951i −0.0810246 + 0.140339i −0.903690 0.428187i \(-0.859153\pi\)
0.822666 + 0.568525i \(0.192486\pi\)
\(422\) 17.0156 + 29.4718i 0.828305 + 1.43467i
\(423\) −1.41426 + 2.44958i −0.0687638 + 0.119102i
\(424\) −6.53621 11.3210i −0.317426 0.549798i
\(425\) 0 0
\(426\) 26.7344 1.29528
\(427\) 15.9168 + 27.5688i 0.770270 + 1.33415i
\(428\) −2.62603 4.54841i −0.126934 0.219856i
\(429\) −12.9001 −0.622823
\(430\) 0 0
\(431\) −0.0242034 0.0419216i −0.00116584 0.00201929i 0.865442 0.501009i \(-0.167038\pi\)
−0.866608 + 0.498990i \(0.833704\pi\)
\(432\) −11.6770 + 20.2252i −0.561811 + 0.973085i
\(433\) 4.78436 + 8.28676i 0.229922 + 0.398236i 0.957785 0.287486i \(-0.0928196\pi\)
−0.727863 + 0.685723i \(0.759486\pi\)
\(434\) −37.8134 + 65.4948i −1.81510 + 3.14385i
\(435\) 0 0
\(436\) −48.5280 −2.32407
\(437\) −1.83076 1.08329i −0.0875773 0.0518209i
\(438\) 11.3403 0.541861
\(439\) 11.1257 19.2703i 0.531002 0.919723i −0.468343 0.883547i \(-0.655149\pi\)
0.999345 0.0361764i \(-0.0115178\pi\)
\(440\) 0 0
\(441\) 3.74417 + 6.48509i 0.178294 + 0.308814i
\(442\) −3.07361 + 5.32364i −0.146197 + 0.253220i
\(443\) −10.0579 17.4207i −0.477863 0.827684i 0.521815 0.853059i \(-0.325255\pi\)
−0.999678 + 0.0253753i \(0.991922\pi\)
\(444\) −18.9605 −0.899827
\(445\) 0 0
\(446\) 26.6449 + 46.1504i 1.26167 + 2.18528i
\(447\) −14.0229 24.2883i −0.663258 1.14880i
\(448\) 34.2224 1.61686
\(449\) −12.4973 −0.589783 −0.294891 0.955531i \(-0.595283\pi\)
−0.294891 + 0.955531i \(0.595283\pi\)
\(450\) 0 0
\(451\) −0.0796065 + 0.137883i −0.00374852 + 0.00649263i
\(452\) 15.6201 + 27.0548i 0.734707 + 1.27255i
\(453\) −9.93945 + 17.2156i −0.466996 + 0.808861i
\(454\) 10.0659 17.4346i 0.472415 0.818246i
\(455\) 0 0
\(456\) −0.363798 + 33.9746i −0.0170364 + 1.59101i
\(457\) −28.3179 −1.32465 −0.662327 0.749215i \(-0.730431\pi\)
−0.662327 + 0.749215i \(0.730431\pi\)
\(458\) −20.4626 + 35.4422i −0.956153 + 1.65610i
\(459\) 1.85190 3.20759i 0.0864394 0.149717i
\(460\) 0 0
\(461\) −2.65976 + 4.60683i −0.123877 + 0.214562i −0.921293 0.388868i \(-0.872866\pi\)
0.797416 + 0.603430i \(0.206200\pi\)
\(462\) 18.9904 + 32.8924i 0.883515 + 1.53029i
\(463\) −17.9327 −0.833401 −0.416701 0.909044i \(-0.636814\pi\)
−0.416701 + 0.909044i \(0.636814\pi\)
\(464\) 15.0988 0.700944
\(465\) 0 0
\(466\) 14.9995 + 25.9798i 0.694836 + 1.20349i
\(467\) 28.7791 1.33174 0.665868 0.746069i \(-0.268061\pi\)
0.665868 + 0.746069i \(0.268061\pi\)
\(468\) −8.53593 −0.394574
\(469\) −12.9001 22.3436i −0.595672 1.03173i
\(470\) 0 0
\(471\) 15.6527 + 27.1112i 0.721237 + 1.24922i
\(472\) 31.2972 54.2083i 1.44057 2.49514i
\(473\) 0.462320 0.800762i 0.0212575 0.0368191i
\(474\) 43.4687 1.99658
\(475\) 0 0
\(476\) 12.0988 0.554548
\(477\) −0.737147 + 1.27678i −0.0337516 + 0.0584595i
\(478\) 2.50469 4.33824i 0.114562 0.198427i
\(479\) 4.02574 + 6.97279i 0.183941 + 0.318595i 0.943219 0.332171i \(-0.107781\pi\)
−0.759278 + 0.650766i \(0.774448\pi\)
\(480\) 0 0
\(481\) −5.65976 9.80298i −0.258063 0.446978i
\(482\) −43.0417 −1.96049
\(483\) 3.43226 0.156173
\(484\) 12.4330 + 21.5347i 0.565138 + 0.978849i
\(485\) 0 0
\(486\) 14.1712 0.642819
\(487\) 1.09761 0.0497376 0.0248688 0.999691i \(-0.492083\pi\)
0.0248688 + 0.999691i \(0.492083\pi\)
\(488\) 17.6410 + 30.5551i 0.798571 + 1.38316i
\(489\) 11.1093 19.2418i 0.502379 0.870145i
\(490\) 0 0
\(491\) −6.55267 + 11.3496i −0.295718 + 0.512199i −0.975152 0.221538i \(-0.928892\pi\)
0.679434 + 0.733737i \(0.262226\pi\)
\(492\) 0.227940 0.394804i 0.0102763 0.0177991i
\(493\) −2.39458 −0.107846
\(494\) −35.0621 + 19.7456i −1.57752 + 0.888395i
\(495\) 0 0
\(496\) −14.3474 + 24.8505i −0.644219 + 1.11582i
\(497\) 15.7066 27.2046i 0.704536 1.22029i
\(498\) −30.0985 52.1322i −1.34875 2.33610i
\(499\) −12.0703 + 20.9064i −0.540342 + 0.935900i 0.458542 + 0.888673i \(0.348372\pi\)
−0.998884 + 0.0472275i \(0.984961\pi\)
\(500\) 0 0
\(501\) 8.76729 0.391694
\(502\) 8.19895 0.365937
\(503\) 9.48090 + 16.4214i 0.422733 + 0.732194i 0.996206 0.0870300i \(-0.0277376\pi\)
−0.573473 + 0.819224i \(0.694404\pi\)
\(504\) 6.33424 + 10.9712i 0.282150 + 0.488697i
\(505\) 0 0
\(506\) −2.63555 −0.117165
\(507\) 0.879086 + 1.52262i 0.0390416 + 0.0676220i
\(508\) −7.93753 + 13.7482i −0.352171 + 0.609978i
\(509\) −10.9803 19.0184i −0.486692 0.842974i 0.513191 0.858274i \(-0.328463\pi\)
−0.999883 + 0.0152997i \(0.995130\pi\)
\(510\) 0 0
\(511\) 6.66248 11.5398i 0.294731 0.510489i
\(512\) 40.5609 1.79255
\(513\) 21.1255 11.8971i 0.932714 0.525268i
\(514\) 67.7531 2.98846
\(515\) 0 0
\(516\) −1.32378 + 2.29285i −0.0582761 + 0.100937i
\(517\) 5.52177 + 9.56399i 0.242847 + 0.420624i
\(518\) −16.6636 + 28.8622i −0.732157 + 1.26813i
\(519\) 8.34417 + 14.4525i 0.366268 + 0.634395i
\(520\) 0 0
\(521\) 6.56968 0.287823 0.143912 0.989591i \(-0.454032\pi\)
0.143912 + 0.989591i \(0.454032\pi\)
\(522\) −2.48702 4.30764i −0.108854 0.188540i
\(523\) −2.09889 3.63538i −0.0917779 0.158964i 0.816481 0.577372i \(-0.195922\pi\)
−0.908259 + 0.418408i \(0.862588\pi\)
\(524\) −65.8375 −2.87613
\(525\) 0 0
\(526\) −16.7344 28.9848i −0.729653 1.26380i
\(527\) 2.27541 3.94113i 0.0991186 0.171678i
\(528\) 7.20549 + 12.4803i 0.313579 + 0.543134i
\(529\) 11.3809 19.7123i 0.494822 0.857058i
\(530\) 0 0
\(531\) −7.05933 −0.306349
\(532\) 68.1603 + 40.3316i 2.95513 + 1.74860i
\(533\) 0.272162 0.0117887
\(534\) 2.56314 4.43949i 0.110918 0.192115i
\(535\) 0 0
\(536\) −14.2975 24.7640i −0.617558 1.06964i
\(537\) 6.00176 10.3954i 0.258995 0.448593i
\(538\) −4.43108 7.67486i −0.191038 0.330887i
\(539\) 29.2371 1.25933
\(540\) 0 0
\(541\) 2.31505 + 4.00978i 0.0995316 + 0.172394i 0.911491 0.411320i \(-0.134932\pi\)
−0.811959 + 0.583714i \(0.801599\pi\)
\(542\) 12.9726 + 22.4692i 0.557221 + 0.965136i
\(543\) 9.56340 0.410405
\(544\) 0.217238 0.00931400
\(545\) 0 0
\(546\) 32.4627 56.2271i 1.38928 2.40630i
\(547\) 19.0199 + 32.9435i 0.813233 + 1.40856i 0.910590 + 0.413312i \(0.135628\pi\)
−0.0973563 + 0.995250i \(0.531039\pi\)
\(548\) −33.1317 + 57.3858i −1.41532 + 2.45140i
\(549\) 1.98953 3.44597i 0.0849113 0.147071i
\(550\) 0 0
\(551\) −13.4902 7.98236i −0.574701 0.340060i
\(552\) 3.80405 0.161911
\(553\) 25.5381 44.2333i 1.08599 1.88099i
\(554\) −8.27110 + 14.3260i −0.351406 + 0.608652i
\(555\) 0 0
\(556\) 5.38092 9.32002i 0.228202 0.395257i
\(557\) −18.2153 31.5498i −0.771807 1.33681i −0.936572 0.350476i \(-0.886020\pi\)
0.164765 0.986333i \(-0.447313\pi\)
\(558\) 9.45302 0.400178
\(559\) −1.58060 −0.0668523
\(560\) 0 0
\(561\) −1.14275 1.97929i −0.0482468 0.0835659i
\(562\) −57.5496 −2.42758
\(563\) 20.6856 0.871795 0.435897 0.899996i \(-0.356431\pi\)
0.435897 + 0.899996i \(0.356431\pi\)
\(564\) −15.8107 27.3849i −0.665750 1.15311i
\(565\) 0 0
\(566\) −18.0324 31.2330i −0.757958 1.31282i
\(567\) −15.7537 + 27.2862i −0.661594 + 1.14591i
\(568\) 17.4080 30.1515i 0.730422 1.26513i
\(569\) −27.1132 −1.13664 −0.568322 0.822806i \(-0.692407\pi\)
−0.568322 + 0.822806i \(0.692407\pi\)
\(570\) 0 0
\(571\) 46.4687 1.94466 0.972328 0.233622i \(-0.0750578\pi\)
0.972328 + 0.233622i \(0.0750578\pi\)
\(572\) −16.6636 + 28.8622i −0.696741 + 1.20679i
\(573\) 4.57009 7.91564i 0.190918 0.330680i
\(574\) −0.400654 0.693954i −0.0167230 0.0289651i
\(575\) 0 0
\(576\) −2.13882 3.70455i −0.0891177 0.154356i
\(577\) 18.0398 0.751008 0.375504 0.926821i \(-0.377470\pi\)
0.375504 + 0.926821i \(0.377470\pi\)
\(578\) 40.6664 1.69150
\(579\) −2.02247 3.50302i −0.0840509 0.145580i
\(580\) 0 0
\(581\) −70.7322 −2.93447
\(582\) −16.8184 −0.697147
\(583\) 2.87808 + 4.98497i 0.119198 + 0.206457i
\(584\) 7.38419 12.7898i 0.305560 0.529245i
\(585\) 0 0
\(586\) −22.3337 + 38.6831i −0.922597 + 1.59798i
\(587\) −13.0168 + 22.5458i −0.537262 + 0.930565i 0.461788 + 0.886990i \(0.347208\pi\)
−0.999050 + 0.0435750i \(0.986125\pi\)
\(588\) −83.7156 −3.45237
\(589\) 25.9567 14.6178i 1.06953 0.602316i
\(590\) 0 0
\(591\) 15.5034 26.8526i 0.637724 1.10457i
\(592\) −6.32263 + 10.9511i −0.259858 + 0.450088i
\(593\) 9.07803 + 15.7236i 0.372790 + 0.645691i 0.989994 0.141112i \(-0.0450678\pi\)
−0.617203 + 0.786804i \(0.711734\pi\)
\(594\) 15.0192 26.0140i 0.616245 1.06737i
\(595\) 0 0
\(596\) −72.4556 −2.96790
\(597\) 19.9218 0.815345
\(598\) 2.25264 + 3.90168i 0.0921172 + 0.159552i
\(599\) −20.0357 34.7028i −0.818635 1.41792i −0.906688 0.421802i \(-0.861398\pi\)
0.0880531 0.996116i \(-0.471935\pi\)
\(600\) 0 0
\(601\) 15.0473 0.613793 0.306897 0.951743i \(-0.400709\pi\)
0.306897 + 0.951743i \(0.400709\pi\)
\(602\) 2.32683 + 4.03018i 0.0948344 + 0.164258i
\(603\) −1.61246 + 2.79286i −0.0656643 + 0.113734i
\(604\) 25.6784 + 44.4763i 1.04484 + 1.80972i
\(605\) 0 0
\(606\) 20.2613 35.0936i 0.823059 1.42558i
\(607\) −29.3860 −1.19274 −0.596370 0.802709i \(-0.703391\pi\)
−0.596370 + 0.802709i \(0.703391\pi\)
\(608\) 1.22384 + 0.724166i 0.0496333 + 0.0293688i
\(609\) 25.2910 1.02484
\(610\) 0 0
\(611\) 9.43905 16.3489i 0.381863 0.661406i
\(612\) −0.756148 1.30969i −0.0305655 0.0529410i
\(613\) 17.3539 30.0578i 0.700917 1.21402i −0.267229 0.963633i \(-0.586108\pi\)
0.968145 0.250390i \(-0.0805588\pi\)
\(614\) 36.0818 + 62.4955i 1.45614 + 2.52211i
\(615\) 0 0
\(616\) 49.4622 1.99289
\(617\) −5.36376 9.29031i −0.215937 0.374014i 0.737625 0.675210i \(-0.235947\pi\)
−0.953562 + 0.301197i \(0.902614\pi\)
\(618\) 11.0352 + 19.1136i 0.443903 + 0.768862i
\(619\) −36.1437 −1.45274 −0.726370 0.687304i \(-0.758794\pi\)
−0.726370 + 0.687304i \(0.758794\pi\)
\(620\) 0 0
\(621\) −1.35725 2.35083i −0.0544647 0.0943357i
\(622\) −0.237309 + 0.411031i −0.00951521 + 0.0164808i
\(623\) −3.01171 5.21644i −0.120662 0.208992i
\(624\) 12.3172 21.3341i 0.493084 0.854046i
\(625\) 0 0
\(626\) 52.2569 2.08861
\(627\) 0.160191 14.9600i 0.00639739 0.597445i
\(628\) 80.8768 3.22734
\(629\) 1.00273 1.73678i 0.0399814 0.0692499i
\(630\) 0 0
\(631\) 15.7882 + 27.3460i 0.628519 + 1.08863i 0.987849 + 0.155417i \(0.0496720\pi\)
−0.359330 + 0.933211i \(0.616995\pi\)
\(632\) 28.3045 49.0248i 1.12589 1.95010i
\(633\) 10.8143 + 18.7309i 0.429829 + 0.744485i
\(634\) −47.0857 −1.87001
\(635\) 0 0
\(636\) −8.24090 14.2737i −0.326773 0.565987i
\(637\) −24.9893 43.2827i −0.990111 1.71492i
\(638\) −19.4204 −0.768859
\(639\) −3.92650 −0.155330
\(640\) 0 0
\(641\) −9.91331 + 17.1704i −0.391552 + 0.678188i −0.992654 0.120984i \(-0.961395\pi\)
0.601102 + 0.799172i \(0.294728\pi\)
\(642\) −2.49665 4.32432i −0.0985349 0.170667i
\(643\) −6.72843 + 11.6540i −0.265343 + 0.459588i −0.967654 0.252283i \(-0.918819\pi\)
0.702310 + 0.711871i \(0.252152\pi\)
\(644\) 4.43359 7.67920i 0.174708 0.302603i
\(645\) 0 0
\(646\) −6.13555 3.63051i −0.241400 0.142840i
\(647\) 4.19511 0.164927 0.0824634 0.996594i \(-0.473721\pi\)
0.0824634 + 0.996594i \(0.473721\pi\)
\(648\) −17.4602 + 30.2420i −0.685902 + 1.18802i
\(649\) −13.7810 + 23.8694i −0.540953 + 0.936957i
\(650\) 0 0
\(651\) −24.0324 + 41.6253i −0.941904 + 1.63143i
\(652\) −28.7006 49.7109i −1.12400 1.94683i
\(653\) −12.1680 −0.476170 −0.238085 0.971244i \(-0.576520\pi\)
−0.238085 + 0.971244i \(0.576520\pi\)
\(654\) −46.1372 −1.80411
\(655\) 0 0
\(656\) −0.152019 0.263305i −0.00593535 0.0102803i
\(657\) −1.66556 −0.0649798
\(658\) −55.5814 −2.16679
\(659\) −4.12236 7.14013i −0.160584 0.278140i 0.774494 0.632581i \(-0.218004\pi\)
−0.935078 + 0.354441i \(0.884671\pi\)
\(660\) 0 0
\(661\) −10.5599 18.2902i −0.410731 0.711407i 0.584239 0.811582i \(-0.301393\pi\)
−0.994970 + 0.100175i \(0.968060\pi\)
\(662\) −25.3075 + 43.8338i −0.983603 + 1.70365i
\(663\) −1.95344 + 3.38345i −0.0758652 + 0.131402i
\(664\) −78.3941 −3.04228
\(665\) 0 0
\(666\) 4.16576 0.161420
\(667\) −0.877489 + 1.51986i −0.0339765 + 0.0588490i
\(668\) 11.3251 19.6156i 0.438180 0.758951i
\(669\) 16.9342 + 29.3310i 0.654716 + 1.13400i
\(670\) 0 0
\(671\) −7.76783 13.4543i −0.299874 0.519397i
\(672\) −2.29442 −0.0885090
\(673\) −30.2802 −1.16722 −0.583608 0.812036i \(-0.698359\pi\)
−0.583608 + 0.812036i \(0.698359\pi\)
\(674\) −12.5357 21.7124i −0.482856 0.836331i
\(675\) 0 0
\(676\) 4.54221 0.174700
\(677\) 49.9003 1.91783 0.958913 0.283701i \(-0.0915625\pi\)
0.958913 + 0.283701i \(0.0915625\pi\)
\(678\) 14.8505 + 25.7219i 0.570331 + 0.987842i
\(679\) −9.88092 + 17.1142i −0.379195 + 0.656785i
\(680\) 0 0
\(681\) 6.39738 11.0806i 0.245148 0.424609i
\(682\) 18.4539 31.9632i 0.706638 1.22393i
\(683\) 3.11357 0.119137 0.0595687 0.998224i \(-0.481027\pi\)
0.0595687 + 0.998224i \(0.481027\pi\)
\(684\) 0.105997 9.89894i 0.00405290 0.378496i
\(685\) 0 0
\(686\) −34.8436 + 60.3509i −1.33034 + 2.30421i
\(687\) −13.0050 + 22.5254i −0.496172 + 0.859396i
\(688\) 0.882861 + 1.52916i 0.0336588 + 0.0582987i
\(689\) 4.91985 8.52143i 0.187431 0.324641i
\(690\) 0 0
\(691\) −30.2831 −1.15202 −0.576012 0.817441i \(-0.695392\pi\)
−0.576012 + 0.817441i \(0.695392\pi\)
\(692\) 43.1140 1.63895
\(693\) −2.78915 4.83094i −0.105951 0.183512i
\(694\) 6.68222 + 11.5740i 0.253654 + 0.439341i
\(695\) 0 0
\(696\) 28.0305 1.06250
\(697\) 0.0241093 + 0.0417585i 0.000913204 + 0.00158172i
\(698\) −1.90495 + 3.29948i −0.0721035 + 0.124887i
\(699\) 9.53293 + 16.5115i 0.360569 + 0.624523i
\(700\) 0 0
\(701\) −22.2849 + 38.5987i −0.841691 + 1.45785i 0.0467733 + 0.998906i \(0.485106\pi\)
−0.888464 + 0.458946i \(0.848227\pi\)
\(702\) −51.3483 −1.93802
\(703\) 11.4386 6.44177i 0.431415 0.242956i
\(704\) −16.7014 −0.629458
\(705\) 0 0
\(706\) −40.4457 + 70.0540i −1.52219 + 2.63652i
\(707\) −23.8072 41.2353i −0.895363 1.55081i
\(708\) 39.4597 68.3462i 1.48299 2.56861i
\(709\) −4.67176 8.09172i −0.175452 0.303891i 0.764866 0.644190i \(-0.222805\pi\)
−0.940317 + 0.340299i \(0.889472\pi\)
\(710\) 0 0
\(711\) −6.38429 −0.239430
\(712\) −3.33795 5.78150i −0.125095 0.216671i
\(713\) −1.66764 2.88844i −0.0624538 0.108173i
\(714\) 11.5027 0.430479
\(715\) 0 0
\(716\) −15.5055 26.8562i −0.579466 1.00366i
\(717\) 1.59186 2.75718i 0.0594490 0.102969i
\(718\) −4.29500 7.43916i −0.160288 0.277627i
\(719\) −12.6987 + 21.9948i −0.473581 + 0.820267i −0.999543 0.0302417i \(-0.990372\pi\)
0.525961 + 0.850508i \(0.323706\pi\)
\(720\) 0 0
\(721\) 25.9330 0.965797
\(722\) −22.4631 40.9059i −0.835992 1.52236i
\(723\) −27.3552 −1.01735
\(724\) 12.3534 21.3968i 0.459112 0.795205i
\(725\) 0 0
\(726\) 11.8205 + 20.4737i 0.438700 + 0.759851i
\(727\) 15.7189 27.2259i 0.582980 1.00975i −0.412143 0.911119i \(-0.635220\pi\)
0.995124 0.0986328i \(-0.0314469\pi\)
\(728\) −42.2759 73.2240i −1.56685 2.71386i
\(729\) 29.9869 1.11063
\(730\) 0 0
\(731\) −0.140016 0.242515i −0.00517869 0.00896975i
\(732\) 22.2419 + 38.5241i 0.822085 + 1.42389i
\(733\) −25.3946 −0.937971 −0.468985 0.883206i \(-0.655380\pi\)
−0.468985 + 0.883206i \(0.655380\pi\)
\(734\) −47.9056 −1.76823
\(735\) 0 0
\(736\) 0.0796065 0.137883i 0.00293434 0.00508242i
\(737\) 6.29559 + 10.9043i 0.231901 + 0.401664i
\(738\) −0.0500800 + 0.0867411i −0.00184347 + 0.00319299i
\(739\) −17.7541 + 30.7510i −0.653095 + 1.13119i 0.329273 + 0.944235i \(0.393196\pi\)
−0.982368 + 0.186959i \(0.940137\pi\)
\(740\) 0 0
\(741\) −22.2838 + 12.5493i −0.818614 + 0.461011i
\(742\) −28.9703 −1.06353
\(743\) −8.55493 + 14.8176i −0.313850 + 0.543604i −0.979192 0.202934i \(-0.934952\pi\)
0.665342 + 0.746538i \(0.268286\pi\)
\(744\) −26.6357 + 46.1343i −0.976511 + 1.69137i
\(745\) 0 0
\(746\) 28.8798 50.0213i 1.05737 1.83141i
\(747\) 4.42060 + 7.65671i 0.161741 + 0.280144i
\(748\) −5.90453 −0.215891
\(749\) −5.86718 −0.214382
\(750\) 0 0
\(751\) 3.72562 + 6.45297i 0.135950 + 0.235472i 0.925960 0.377622i \(-0.123258\pi\)
−0.790010 + 0.613094i \(0.789925\pi\)
\(752\) −21.0891 −0.769041
\(753\) 5.21086 0.189894
\(754\) 16.5988 + 28.7500i 0.604493 + 1.04701i
\(755\) 0 0
\(756\) 50.5313 + 87.5228i 1.83781 + 3.18317i
\(757\) −26.8838 + 46.5640i −0.977107 + 1.69240i −0.304306 + 0.952574i \(0.598425\pi\)
−0.672801 + 0.739824i \(0.734909\pi\)
\(758\) −8.65994 + 14.9994i −0.314543 + 0.544804i
\(759\) −1.67503 −0.0607997
\(760\) 0 0
\(761\) 23.3939 0.848029 0.424014 0.905655i \(-0.360621\pi\)
0.424014 + 0.905655i \(0.360621\pi\)
\(762\) −7.54647 + 13.0709i −0.273380 + 0.473508i
\(763\) −27.1058 + 46.9487i −0.981297 + 1.69966i
\(764\) −11.8068 20.4499i −0.427154 0.739852i
\(765\) 0 0
\(766\) 3.78757 + 6.56027i 0.136851 + 0.237032i
\(767\) 47.1152 1.70123
\(768\) 50.3235 1.81589
\(769\) 6.62236 + 11.4703i 0.238808 + 0.413628i 0.960373 0.278719i \(-0.0899099\pi\)
−0.721564 + 0.692347i \(0.756577\pi\)
\(770\) 0 0
\(771\) 43.0606 1.55079
\(772\) −10.4500 −0.376105
\(773\) 8.90262 + 15.4198i 0.320205 + 0.554611i 0.980530 0.196369i \(-0.0629149\pi\)
−0.660325 + 0.750980i \(0.729582\pi\)
\(774\) 0.290843 0.503755i 0.0104541 0.0181071i
\(775\) 0 0
\(776\) −10.9512 + 18.9681i −0.393127 + 0.680916i
\(777\) −10.5906 + 18.3434i −0.379935 + 0.658068i
\(778\) −23.0658 −0.826949
\(779\) −0.00337965 + 0.315621i −0.000121088 + 0.0113083i
\(780\) 0 0
\(781\) −7.66521 + 13.2765i −0.274283 + 0.475072i
\(782\) −0.399096 + 0.691255i −0.0142716 + 0.0247192i
\(783\) −10.0011 17.3224i −0.357409 0.619051i
\(784\) −27.9160