Properties

Label 475.2.e.g.201.1
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 201.1
Root \(0.203566 - 0.352587i\) of defining polynomial
Character \(\chi\) \(=\) 475.201
Dual form 475.2.e.g.26.1

$q$-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 \(0.501517\pi\)
−0.863632 + 0.504123i \(0.831816\pi\)
\(3\) −0.780522 + 1.35190i −0.450635 + 0.780522i −0.998426 0.0560930i \(-0.982136\pi\)
0.547791 + 0.836615i \(0.315469\pi\)
\(4\) −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 \(-0.175744\pi\)
0.851417 + 0.524490i \(0.175744\pi\)
\(8\) 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 \(0.00785227\pi\)
−0.478486 + 0.878095i \(0.658814\pi\)
\(14\) −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 −0.903573 0.428435i \(-0.859065\pi\)
0.822822 + 0.568299i \(0.192398\pi\)
\(18\) −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 0.890344 0.455289i \(-0.150464\pi\)
−0.839464 + 0.543416i \(0.817131\pi\)
\(24\) −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 \(-0.579629\pi\)
−0.247561 + 0.968872i \(0.579629\pi\)
\(38\) −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 −0.881613 0.471973i \(-0.843542\pi\)
0.849547 + 0.527513i \(0.176875\pi\)
\(44\) −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 0.622664 0.782490i \(-0.286050\pi\)
−0.988988 + 0.147998i \(0.952717\pi\)
\(48\) −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 0.762009 0.647566i \(-0.224213\pi\)
−0.941813 + 0.336136i \(0.890880\pi\)
\(54\) 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 0.636404 0.771356i \(-0.280421\pi\)
−0.986216 + 0.165464i \(0.947088\pi\)
\(68\) 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 −0.766413 0.642348i \(-0.777961\pi\)
0.939496 + 0.342560i \(0.111294\pi\)
\(74\) 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 \(-0.830564\pi\)
−0.861642 + 0.507517i \(0.830564\pi\)
\(84\) 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 −0.955622 0.294595i \(-0.904815\pi\)
0.732938 + 0.680296i \(0.238149\pi\)
\(98\) −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 \(-0.408476\pi\)
0.283585 + 0.958947i \(0.408476\pi\)
\(104\) 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 \(-0.520050\pi\)
−0.0629486 + 0.998017i \(0.520050\pi\)
\(108\) 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 \(-0.381290\pi\)
0.364353 + 0.931261i \(0.381290\pi\)
\(114\) −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 0.940039 0.341066i \(-0.110788\pi\)
−0.765392 + 0.643565i \(0.777455\pi\)
\(128\) 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 \(0.0809887\pi\)
−0.265927 + 0.963993i \(0.585678\pi\)
\(138\) 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 \(-0.538036\pi\)
0.919454 0.393197i \(-0.128631\pi\)
\(158\) −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 \(-0.688206\pi\)
−0.557412 + 0.830236i \(0.688206\pi\)
\(164\) 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 0.736681 0.676241i \(-0.236392\pi\)
−0.953982 + 0.299864i \(0.903059\pi\)
\(168\) −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 −0.588091 0.808795i \(-0.700120\pi\)
0.994482 + 0.104904i \(0.0334536\pi\)
\(174\) −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 −0.908880 0.417057i \(-0.863062\pi\)
0.815622 + 0.578585i \(0.196395\pi\)
\(194\) −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 \(-0.750215\pi\)
−0.707584 + 0.706629i \(0.750215\pi\)
\(198\) −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 \(-0.574508\pi\)
0.958380 0.285496i \(-0.0921584\pi\)
\(224\) −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 \(-0.587686\pi\)
−0.272003 + 0.962296i \(0.587686\pi\)
\(228\) 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 −0.593666 0.804711i \(-0.702320\pi\)
0.993734 + 0.111774i \(0.0356533\pi\)
\(234\) −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 \(-0.836920\pi\)
0.0112676 0.999937i \(-0.496413\pi\)
\(258\) 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 −0.995950 0.0899066i \(-0.971343\pi\)
0.575837 + 0.817565i \(0.304676\pi\)
\(264\) −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 \(-0.435149\pi\)
0.202330 + 0.979317i \(0.435149\pi\)
\(278\) −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 −0.997410 0.0719306i \(-0.977084\pi\)
0.560999 + 0.827817i \(0.310417\pi\)
\(284\) 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 \(-0.321739\pi\)
0.531206 + 0.847243i \(0.321739\pi\)
\(294\) −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 \(-0.516821\pi\)
0.891226 0.453559i \(-0.149846\pi\)
\(308\) −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 \(-0.961324\pi\)
0.391346 0.920243i \(-0.372009\pi\)
\(314\) 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 \(0.0142857\pi\)
−0.460642 + 0.887586i \(0.652381\pi\)
\(318\) −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 −0.970891 0.239520i \(-0.923010\pi\)
0.692876 + 0.721056i \(0.256343\pi\)
\(338\) −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 −0.783716 0.621119i \(-0.786678\pi\)
0.929763 + 0.368159i \(0.120012\pi\)
\(348\) −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 \(-0.159914\pi\)
0.876437 + 0.481517i \(0.159914\pi\)
\(354\) 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 \(0.00333575\pi\)
−0.490897 + 0.871218i \(0.663331\pi\)
\(368\) −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 \(-0.708350\pi\)
−0.608802 + 0.793322i \(0.708350\pi\)
\(374\) −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 −0.823935 0.566684i \(-0.808226\pi\)
0.902730 + 0.430207i \(0.141560\pi\)
\(384\) 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 \(0.401021\pi\)
−0.977476 + 0.211047i \(0.932313\pi\)
\(398\) −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 0.727863 0.685723i \(-0.240514\pi\)
−0.957785 + 0.287486i \(0.907180\pi\)
\(434\) −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 0.999678 0.0253753i \(-0.00807806\pi\)
−0.521815 + 0.853059i \(0.674745\pi\)
\(444\) −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 \(-0.269569\pi\)
0.662327 + 0.749215i \(0.269569\pi\)
\(458\) 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 \(-0.363186\pi\)
0.416701 + 0.909044i \(0.363186\pi\)
\(464\) 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 \(-0.731939\pi\)
−0.665868 + 0.746069i \(0.731939\pi\)
\(468\) 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 \(-0.507917\pi\)
−0.0248688 + 0.999691i \(0.507917\pi\)
\(488\) −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 0.573473 0.819224i \(-0.305596\pi\)
−0.996206 + 0.0870300i \(0.972262\pi\)
\(504\) 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 0.908259 0.418408i \(-0.137412\pi\)
−0.816481 + 0.577372i \(0.804078\pi\)
\(524\) −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 \(-0.864372\pi\)
0.0973563 0.995250i \(-0.468961\pi\)
\(548\) 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 \(0.113980\pi\)
−0.164765 + 0.986333i \(0.552687\pi\)
\(558\) −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 \(-0.643569\pi\)
−0.435897 + 0.899996i \(0.643569\pi\)
\(564\) −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 \(-0.622530\pi\)
−0.375504 + 0.926821i \(0.622530\pi\)
\(578\) −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 \(-0.652792\pi\)
0.999050 0.0435750i \(-0.0138747\pi\)
\(588\) 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 0.617203 0.786804i \(-0.288266\pi\)
−0.989994 + 0.141112i \(0.954932\pi\)
\(594\) 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 \(-0.296609\pi\)
0.596370 + 0.802709i \(0.296609\pi\)
\(608\) −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 \(0.413892\pi\)
−0.968145 + 0.250390i \(0.919441\pi\)
\(614\) 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 0.953562 0.301197i \(-0.0973861\pi\)
−0.737625 + 0.675210i \(0.764053\pi\)
\(618\) −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 −0.702310 0.711871i \(-0.747848\pi\)
0.967654 + 0.252283i \(0.0811814\pi\)
\(644\) 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 \(-0.526279\pi\)
−0.0824634 + 0.996594i \(0.526279\pi\)
\(648\) 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 \(-0.423480\pi\)
0.238085 + 0.971244i \(0.423480\pi\)
\(654\) −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 \(-0.301641\pi\)
0.583608 + 0.812036i \(0.301641\pi\)
\(674\) −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 \(-0.908438\pi\)
−0.958913 + 0.283701i \(0.908438\pi\)
\(678\) −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 \(-0.518973\pi\)
−0.0595687 + 0.998224i \(0.518973\pi\)
\(684\) 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 \(0.364780\pi\)
−0.995124 + 0.0986328i \(0.968553\pi\)
\(728\) 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 \(-0.344620\pi\)
0.468985 + 0.883206i \(0.344620\pi\)
\(734\) −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 −0.665342 0.746538i \(-0.731714\pi\)
0.979192 + 0.202934i \(0.0650477\pi\)
\(744\) −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 \(-0.401575\pi\)
0.672801 0.739824i \(-0.265091\pi\)
\(758\) 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 0.660325 0.750980i \(-0.270418\pi\)
−0.980530 + 0.196369i \(0.937085\pi\)
\(774\) 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