Properties

Label 675.2.r.a.46.1
Level $675$
Weight $2$
Character 675.46
Analytic conductor $5.390$
Analytic rank $0$
Dimension $224$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.r (of order \(15\), degree \(8\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(224\)
Relative dimension: \(28\) over \(\Q(\zeta_{15})\)
Twist minimal: no (minimal twist has level 225)
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 46.1
Character \(\chi\) \(=\) 675.46
Dual form 675.2.r.a.631.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.77417 - 1.97042i) q^{2} +(-0.525803 + 5.00268i) q^{4} +(1.61775 + 1.54366i) q^{5} +(1.02644 - 1.77785i) q^{7} +(6.50010 - 4.72260i) q^{8} +O(q^{10})\) \(q+(-1.77417 - 1.97042i) q^{2} +(-0.525803 + 5.00268i) q^{4} +(1.61775 + 1.54366i) q^{5} +(1.02644 - 1.77785i) q^{7} +(6.50010 - 4.72260i) q^{8} +(0.171493 - 5.92636i) q^{10} +(3.84053 + 4.26534i) q^{11} +(-1.39743 + 1.55200i) q^{13} +(-5.32421 + 1.13169i) q^{14} +(-10.9972 - 2.33752i) q^{16} +(0.0247468 - 0.0179796i) q^{17} +(-5.30003 + 3.85070i) q^{19} +(-8.57307 + 7.28142i) q^{20} +(1.59074 - 15.1349i) q^{22} +(-3.94065 + 0.837611i) q^{23} +(0.234221 + 4.99451i) q^{25} +5.53738 q^{26} +(8.35433 + 6.06978i) q^{28} +(-2.99836 + 1.33495i) q^{29} +(2.93669 + 1.30750i) q^{31} +(6.87040 + 11.8999i) q^{32} +(-0.0793325 - 0.0168626i) q^{34} +(4.40493 - 1.29164i) q^{35} +(1.37908 + 4.24438i) q^{37} +(16.9906 + 3.61147i) q^{38} +(17.8056 + 2.39397i) q^{40} +(-1.29130 + 1.43413i) q^{41} +(0.309512 - 0.536091i) q^{43} +(-23.3575 + 16.9702i) q^{44} +(8.64184 + 6.27867i) q^{46} +(2.37044 - 1.05539i) q^{47} +(1.39282 + 2.41244i) q^{49} +(9.42573 - 9.32264i) q^{50} +(-7.02940 - 7.80695i) q^{52} +(2.83942 + 2.06296i) q^{53} +(-0.371228 + 12.8287i) q^{55} +(-1.72410 - 16.4037i) q^{56} +(7.95002 + 3.53958i) q^{58} +(5.43616 - 6.03746i) q^{59} +(-5.51851 - 6.12893i) q^{61} +(-2.63388 - 8.10625i) q^{62} +(4.31002 - 13.2649i) q^{64} +(-4.65646 + 0.353593i) q^{65} +(-0.642929 - 0.286250i) q^{67} +(0.0769343 + 0.133254i) q^{68} +(-10.3602 - 6.38797i) q^{70} +(-3.81216 - 2.76970i) q^{71} +(2.55263 - 7.85620i) q^{73} +(5.91647 - 10.2476i) q^{74} +(-16.4770 - 28.5391i) q^{76} +(11.5252 - 2.44977i) q^{77} +(10.9723 - 4.88520i) q^{79} +(-14.1823 - 20.7574i) q^{80} +5.11682 q^{82} +(1.37616 + 13.0933i) q^{83} +(0.0677885 + 0.00911420i) q^{85} +(-1.60545 + 0.341249i) q^{86} +(45.1073 + 9.58785i) q^{88} +(-1.99904 + 6.15242i) q^{89} +(1.32485 + 4.07747i) q^{91} +(-2.11830 - 20.1543i) q^{92} +(-6.28513 - 2.79832i) q^{94} +(-14.5183 - 1.95199i) q^{95} +(-9.33612 + 4.15671i) q^{97} +(2.28241 - 7.02454i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8} - 20 q^{10} + 11 q^{11} - 3 q^{13} - q^{14} + 23 q^{16} + 24 q^{17} - 12 q^{19} - q^{20} - 11 q^{22} - q^{23} - 16 q^{25} + 136 q^{26} + 4 q^{28} + 15 q^{29} + 3 q^{31} - 12 q^{32} + q^{34} - 14 q^{35} - 24 q^{37} - 55 q^{38} + q^{40} + 19 q^{41} - 8 q^{43} - 4 q^{44} - 20 q^{46} + 10 q^{47} - 72 q^{49} + 3 q^{50} - 25 q^{52} + 12 q^{53} - 20 q^{55} + 60 q^{56} - 23 q^{58} + 30 q^{59} - 3 q^{61} + 44 q^{62} - 44 q^{64} - 51 q^{65} - 12 q^{67} + 156 q^{68} - 16 q^{70} - 42 q^{71} - 12 q^{73} - 90 q^{74} - 8 q^{76} - 31 q^{77} - 15 q^{79} - 298 q^{80} + 8 q^{82} - 59 q^{83} - 11 q^{85} - 9 q^{86} - 23 q^{88} - 106 q^{89} + 30 q^{91} - 11 q^{92} + 25 q^{94} - 7 q^{95} - 21 q^{97} - 146 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.77417 1.97042i −1.25453 1.39330i −0.886003 0.463679i \(-0.846529\pi\)
−0.368527 0.929617i \(-0.620138\pi\)
\(3\) 0 0
\(4\) −0.525803 + 5.00268i −0.262902 + 2.50134i
\(5\) 1.61775 + 1.54366i 0.723479 + 0.690346i
\(6\) 0 0
\(7\) 1.02644 1.77785i 0.387959 0.671966i −0.604215 0.796821i \(-0.706513\pi\)
0.992175 + 0.124855i \(0.0398467\pi\)
\(8\) 6.50010 4.72260i 2.29813 1.66969i
\(9\) 0 0
\(10\) 0.171493 5.92636i 0.0542308 1.87408i
\(11\) 3.84053 + 4.26534i 1.15796 + 1.28605i 0.951519 + 0.307590i \(0.0995226\pi\)
0.206445 + 0.978458i \(0.433811\pi\)
\(12\) 0 0
\(13\) −1.39743 + 1.55200i −0.387577 + 0.430448i −0.905085 0.425230i \(-0.860193\pi\)
0.517508 + 0.855678i \(0.326860\pi\)
\(14\) −5.32421 + 1.13169i −1.42295 + 0.302458i
\(15\) 0 0
\(16\) −10.9972 2.33752i −2.74929 0.584379i
\(17\) 0.0247468 0.0179796i 0.00600198 0.00436070i −0.584780 0.811192i \(-0.698819\pi\)
0.590782 + 0.806831i \(0.298819\pi\)
\(18\) 0 0
\(19\) −5.30003 + 3.85070i −1.21591 + 0.883410i −0.995754 0.0920546i \(-0.970657\pi\)
−0.220156 + 0.975465i \(0.570657\pi\)
\(20\) −8.57307 + 7.28142i −1.91700 + 1.62818i
\(21\) 0 0
\(22\) 1.59074 15.1349i 0.339147 3.22677i
\(23\) −3.94065 + 0.837611i −0.821683 + 0.174654i −0.599524 0.800357i \(-0.704644\pi\)
−0.222158 + 0.975011i \(0.571310\pi\)
\(24\) 0 0
\(25\) 0.234221 + 4.99451i 0.0468442 + 0.998902i
\(26\) 5.53738 1.08597
\(27\) 0 0
\(28\) 8.35433 + 6.06978i 1.57882 + 1.14708i
\(29\) −2.99836 + 1.33495i −0.556781 + 0.247895i −0.665781 0.746147i \(-0.731902\pi\)
0.109000 + 0.994042i \(0.465235\pi\)
\(30\) 0 0
\(31\) 2.93669 + 1.30750i 0.527446 + 0.234834i 0.653143 0.757235i \(-0.273450\pi\)
−0.125697 + 0.992069i \(0.540117\pi\)
\(32\) 6.87040 + 11.8999i 1.21453 + 2.10362i
\(33\) 0 0
\(34\) −0.0793325 0.0168626i −0.0136054 0.00289192i
\(35\) 4.40493 1.29164i 0.744569 0.218327i
\(36\) 0 0
\(37\) 1.37908 + 4.24438i 0.226720 + 0.697771i 0.998112 + 0.0614120i \(0.0195604\pi\)
−0.771393 + 0.636359i \(0.780440\pi\)
\(38\) 16.9906 + 3.61147i 2.75625 + 0.585858i
\(39\) 0 0
\(40\) 17.8056 + 2.39397i 2.81531 + 0.378520i
\(41\) −1.29130 + 1.43413i −0.201667 + 0.223974i −0.835492 0.549503i \(-0.814817\pi\)
0.633825 + 0.773476i \(0.281484\pi\)
\(42\) 0 0
\(43\) 0.309512 0.536091i 0.0472002 0.0817531i −0.841460 0.540319i \(-0.818303\pi\)
0.888660 + 0.458566i \(0.151637\pi\)
\(44\) −23.3575 + 16.9702i −3.52128 + 2.55836i
\(45\) 0 0
\(46\) 8.64184 + 6.27867i 1.27417 + 0.925739i
\(47\) 2.37044 1.05539i 0.345764 0.153944i −0.226505 0.974010i \(-0.572730\pi\)
0.572269 + 0.820066i \(0.306063\pi\)
\(48\) 0 0
\(49\) 1.39282 + 2.41244i 0.198975 + 0.344635i
\(50\) 9.42573 9.32264i 1.33300 1.31842i
\(51\) 0 0
\(52\) −7.02940 7.80695i −0.974803 1.08263i
\(53\) 2.83942 + 2.06296i 0.390024 + 0.283369i 0.765465 0.643477i \(-0.222509\pi\)
−0.375441 + 0.926846i \(0.622509\pi\)
\(54\) 0 0
\(55\) −0.371228 + 12.8287i −0.0500564 + 1.72983i
\(56\) −1.72410 16.4037i −0.230392 2.19204i
\(57\) 0 0
\(58\) 7.95002 + 3.53958i 1.04389 + 0.464769i
\(59\) 5.43616 6.03746i 0.707727 0.786011i −0.276859 0.960911i \(-0.589293\pi\)
0.984586 + 0.174900i \(0.0559601\pi\)
\(60\) 0 0
\(61\) −5.51851 6.12893i −0.706573 0.784729i 0.277835 0.960629i \(-0.410383\pi\)
−0.984408 + 0.175900i \(0.943716\pi\)
\(62\) −2.63388 8.10625i −0.334503 1.02949i
\(63\) 0 0
\(64\) 4.31002 13.2649i 0.538753 1.65811i
\(65\) −4.65646 + 0.353593i −0.577562 + 0.0438578i
\(66\) 0 0
\(67\) −0.642929 0.286250i −0.0785463 0.0349710i 0.367087 0.930186i \(-0.380355\pi\)
−0.445634 + 0.895215i \(0.647022\pi\)
\(68\) 0.0769343 + 0.133254i 0.00932966 + 0.0161594i
\(69\) 0 0
\(70\) −10.3602 6.38797i −1.23828 0.763509i
\(71\) −3.81216 2.76970i −0.452421 0.328703i 0.338130 0.941099i \(-0.390206\pi\)
−0.790551 + 0.612397i \(0.790206\pi\)
\(72\) 0 0
\(73\) 2.55263 7.85620i 0.298763 0.919499i −0.683168 0.730261i \(-0.739398\pi\)
0.981931 0.189237i \(-0.0606016\pi\)
\(74\) 5.91647 10.2476i 0.687776 1.19126i
\(75\) 0 0
\(76\) −16.4770 28.5391i −1.89005 3.27366i
\(77\) 11.5252 2.44977i 1.31342 0.279177i
\(78\) 0 0
\(79\) 10.9723 4.88520i 1.23448 0.549628i 0.317389 0.948295i \(-0.397194\pi\)
0.917095 + 0.398668i \(0.130527\pi\)
\(80\) −14.1823 20.7574i −1.58563 2.32075i
\(81\) 0 0
\(82\) 5.11682 0.565058
\(83\) 1.37616 + 13.0933i 0.151053 + 1.43717i 0.763064 + 0.646323i \(0.223694\pi\)
−0.612011 + 0.790849i \(0.709639\pi\)
\(84\) 0 0
\(85\) 0.0677885 + 0.00911420i 0.00735270 + 0.000988573i
\(86\) −1.60545 + 0.341249i −0.173120 + 0.0367979i
\(87\) 0 0
\(88\) 45.1073 + 9.58785i 4.80845 + 1.02207i
\(89\) −1.99904 + 6.15242i −0.211898 + 0.652155i 0.787461 + 0.616364i \(0.211395\pi\)
−0.999359 + 0.0357910i \(0.988605\pi\)
\(90\) 0 0
\(91\) 1.32485 + 4.07747i 0.138882 + 0.427435i
\(92\) −2.11830 20.1543i −0.220848 2.10123i
\(93\) 0 0
\(94\) −6.28513 2.79832i −0.648262 0.288625i
\(95\) −14.5183 1.95199i −1.48954 0.200270i
\(96\) 0 0
\(97\) −9.33612 + 4.15671i −0.947940 + 0.422050i −0.821681 0.569947i \(-0.806964\pi\)
−0.126258 + 0.991997i \(0.540297\pi\)
\(98\) 2.28241 7.02454i 0.230558 0.709585i
\(99\) 0 0
\(100\) −25.1091 1.45440i −2.51091 0.145440i
\(101\) 1.06922 1.85194i 0.106391 0.184275i −0.807915 0.589300i \(-0.799404\pi\)
0.914306 + 0.405025i \(0.132737\pi\)
\(102\) 0 0
\(103\) 0.126240 1.20110i 0.0124388 0.118348i −0.986541 0.163517i \(-0.947716\pi\)
0.998979 + 0.0451695i \(0.0143828\pi\)
\(104\) −1.75394 + 16.6877i −0.171988 + 1.63636i
\(105\) 0 0
\(106\) −0.972728 9.25489i −0.0944797 0.898914i
\(107\) 11.1600 1.07887 0.539437 0.842026i \(-0.318637\pi\)
0.539437 + 0.842026i \(0.318637\pi\)
\(108\) 0 0
\(109\) 2.86190 + 8.80802i 0.274120 + 0.843655i 0.989451 + 0.144869i \(0.0462761\pi\)
−0.715331 + 0.698786i \(0.753724\pi\)
\(110\) 25.9366 22.0289i 2.47296 2.10037i
\(111\) 0 0
\(112\) −15.4437 + 17.1520i −1.45929 + 1.62071i
\(113\) 5.84918 6.49617i 0.550244 0.611108i −0.402300 0.915508i \(-0.631789\pi\)
0.952544 + 0.304400i \(0.0984559\pi\)
\(114\) 0 0
\(115\) −7.66797 4.72799i −0.715042 0.440887i
\(116\) −5.10181 15.7018i −0.473691 1.45787i
\(117\) 0 0
\(118\) −21.5410 −1.98301
\(119\) −0.00656389 0.0624513i −0.000601711 0.00572490i
\(120\) 0 0
\(121\) −2.29365 + 21.8226i −0.208513 + 1.98387i
\(122\) −2.28576 + 21.7476i −0.206943 + 1.96893i
\(123\) 0 0
\(124\) −8.08513 + 14.0039i −0.726066 + 1.25758i
\(125\) −7.33092 + 8.44142i −0.655698 + 0.755024i
\(126\) 0 0
\(127\) −0.411180 + 1.26548i −0.0364863 + 0.112293i −0.967641 0.252331i \(-0.918803\pi\)
0.931155 + 0.364625i \(0.118803\pi\)
\(128\) −8.67841 + 3.86388i −0.767070 + 0.341522i
\(129\) 0 0
\(130\) 8.95808 + 8.54783i 0.785676 + 0.749694i
\(131\) 15.5424 + 6.91991i 1.35794 + 0.604596i 0.951095 0.308900i \(-0.0999608\pi\)
0.406849 + 0.913495i \(0.366627\pi\)
\(132\) 0 0
\(133\) 1.40579 + 13.3752i 0.121897 + 1.15978i
\(134\) 0.576634 + 1.77470i 0.0498136 + 0.153310i
\(135\) 0 0
\(136\) 0.0759462 0.233738i 0.00651233 0.0200429i
\(137\) 4.86487 + 1.03406i 0.415634 + 0.0883456i 0.410982 0.911644i \(-0.365186\pi\)
0.00465171 + 0.999989i \(0.498519\pi\)
\(138\) 0 0
\(139\) 12.9544 2.75355i 1.09878 0.233553i 0.377370 0.926062i \(-0.376828\pi\)
0.721409 + 0.692510i \(0.243495\pi\)
\(140\) 4.14553 + 22.7156i 0.350361 + 1.91982i
\(141\) 0 0
\(142\) 1.30597 + 12.4255i 0.109595 + 1.04272i
\(143\) −11.9867 −1.00238
\(144\) 0 0
\(145\) −6.91131 2.46883i −0.573953 0.205025i
\(146\) −20.0088 + 8.90850i −1.65594 + 0.737273i
\(147\) 0 0
\(148\) −21.9584 + 4.66740i −1.80497 + 0.383658i
\(149\) −7.12203 12.3357i −0.583459 1.01058i −0.995066 0.0992193i \(-0.968365\pi\)
0.411606 0.911362i \(-0.364968\pi\)
\(150\) 0 0
\(151\) 9.46978 16.4021i 0.770640 1.33479i −0.166573 0.986029i \(-0.553270\pi\)
0.937213 0.348758i \(-0.113397\pi\)
\(152\) −16.2654 + 50.0598i −1.31930 + 4.06038i
\(153\) 0 0
\(154\) −25.2748 18.3632i −2.03670 1.47975i
\(155\) 2.73249 + 6.64847i 0.219479 + 0.534018i
\(156\) 0 0
\(157\) 4.74777 + 8.22338i 0.378913 + 0.656297i 0.990904 0.134567i \(-0.0429645\pi\)
−0.611991 + 0.790865i \(0.709631\pi\)
\(158\) −29.0927 12.9529i −2.31449 1.03048i
\(159\) 0 0
\(160\) −7.25481 + 29.8566i −0.573543 + 2.36037i
\(161\) −2.55571 + 7.86566i −0.201418 + 0.619901i
\(162\) 0 0
\(163\) −2.92027 8.98768i −0.228733 0.703969i −0.997891 0.0649101i \(-0.979324\pi\)
0.769158 0.639059i \(-0.220676\pi\)
\(164\) −6.49553 7.21402i −0.507216 0.563320i
\(165\) 0 0
\(166\) 23.3577 25.9413i 1.81291 2.01344i
\(167\) 13.5729 + 6.04304i 1.05030 + 0.467624i 0.857967 0.513705i \(-0.171727\pi\)
0.192335 + 0.981329i \(0.438394\pi\)
\(168\) 0 0
\(169\) 0.902967 + 8.59116i 0.0694590 + 0.660858i
\(170\) −0.102310 0.149742i −0.00784680 0.0114847i
\(171\) 0 0
\(172\) 2.51915 + 1.83027i 0.192083 + 0.139557i
\(173\) −4.44318 4.93465i −0.337809 0.375175i 0.550175 0.835049i \(-0.314561\pi\)
−0.887984 + 0.459875i \(0.847894\pi\)
\(174\) 0 0
\(175\) 9.11992 + 4.71018i 0.689401 + 0.356056i
\(176\) −32.2646 55.8839i −2.43203 4.21241i
\(177\) 0 0
\(178\) 15.6695 6.97651i 1.17448 0.522911i
\(179\) 3.95088 + 2.87048i 0.295303 + 0.214550i 0.725564 0.688154i \(-0.241579\pi\)
−0.430262 + 0.902704i \(0.641579\pi\)
\(180\) 0 0
\(181\) 8.58407 6.23669i 0.638049 0.463570i −0.221131 0.975244i \(-0.570975\pi\)
0.859179 + 0.511675i \(0.170975\pi\)
\(182\) 5.68381 9.84464i 0.421312 0.729734i
\(183\) 0 0
\(184\) −21.6589 + 24.0547i −1.59672 + 1.77333i
\(185\) −4.32087 + 8.99517i −0.317677 + 0.661338i
\(186\) 0 0
\(187\) 0.171730 + 0.0365023i 0.0125581 + 0.00266932i
\(188\) 4.03339 + 12.4135i 0.294165 + 0.905347i
\(189\) 0 0
\(190\) 21.9117 + 32.0703i 1.58964 + 2.32662i
\(191\) −23.3711 4.96768i −1.69107 0.359448i −0.741006 0.671498i \(-0.765651\pi\)
−0.950066 + 0.312050i \(0.898984\pi\)
\(192\) 0 0
\(193\) −12.8260 22.2154i −0.923239 1.59910i −0.794369 0.607435i \(-0.792198\pi\)
−0.128870 0.991662i \(-0.541135\pi\)
\(194\) 24.7544 + 11.0213i 1.77726 + 0.791287i
\(195\) 0 0
\(196\) −12.8010 + 5.69939i −0.914360 + 0.407099i
\(197\) −12.4362 9.03540i −0.886039 0.643745i 0.0488029 0.998808i \(-0.484459\pi\)
−0.934842 + 0.355063i \(0.884459\pi\)
\(198\) 0 0
\(199\) −3.19201 −0.226275 −0.113138 0.993579i \(-0.536090\pi\)
−0.113138 + 0.993579i \(0.536090\pi\)
\(200\) 25.1095 + 31.3587i 1.77551 + 2.21739i
\(201\) 0 0
\(202\) −5.54607 + 1.17885i −0.390220 + 0.0829439i
\(203\) −0.704293 + 6.70090i −0.0494317 + 0.470311i
\(204\) 0 0
\(205\) −4.30281 + 0.326738i −0.300521 + 0.0228204i
\(206\) −2.59063 + 1.88221i −0.180498 + 0.131140i
\(207\) 0 0
\(208\) 18.9956 13.8011i 1.31711 0.956934i
\(209\) −36.7794 7.81771i −2.54409 0.540762i
\(210\) 0 0
\(211\) 26.0148 5.52961i 1.79093 0.380674i 0.811805 0.583928i \(-0.198485\pi\)
0.979126 + 0.203254i \(0.0651517\pi\)
\(212\) −11.8133 + 13.1200i −0.811341 + 0.901085i
\(213\) 0 0
\(214\) −19.7997 21.9898i −1.35348 1.50319i
\(215\) 1.32826 0.389478i 0.0905863 0.0265622i
\(216\) 0 0
\(217\) 5.33890 3.87893i 0.362428 0.263319i
\(218\) 12.2780 21.2661i 0.831570 1.44032i
\(219\) 0 0
\(220\) −63.9829 8.60252i −4.31372 0.579982i
\(221\) −0.00667752 + 0.0635323i −0.000449178 + 0.00427365i
\(222\) 0 0
\(223\) −11.4373 12.7024i −0.765898 0.850616i 0.226458 0.974021i \(-0.427285\pi\)
−0.992356 + 0.123405i \(0.960619\pi\)
\(224\) 28.2083 1.88475
\(225\) 0 0
\(226\) −23.1776 −1.54175
\(227\) 8.24685 + 9.15906i 0.547363 + 0.607908i 0.951823 0.306648i \(-0.0992073\pi\)
−0.404460 + 0.914556i \(0.632541\pi\)
\(228\) 0 0
\(229\) −2.14725 + 20.4298i −0.141895 + 1.35004i 0.659412 + 0.751782i \(0.270805\pi\)
−0.801306 + 0.598254i \(0.795861\pi\)
\(230\) 4.28820 + 23.4974i 0.282755 + 1.54937i
\(231\) 0 0
\(232\) −13.1852 + 22.8374i −0.865648 + 1.49935i
\(233\) 6.68678 4.85823i 0.438065 0.318273i −0.346800 0.937939i \(-0.612732\pi\)
0.784866 + 0.619666i \(0.212732\pi\)
\(234\) 0 0
\(235\) 5.46394 + 1.95181i 0.356428 + 0.127322i
\(236\) 27.3452 + 30.3699i 1.78002 + 1.97691i
\(237\) 0 0
\(238\) −0.111410 + 0.123733i −0.00722162 + 0.00802042i
\(239\) −17.6630 + 3.75440i −1.14253 + 0.242852i −0.740033 0.672571i \(-0.765190\pi\)
−0.402495 + 0.915422i \(0.631857\pi\)
\(240\) 0 0
\(241\) −12.6786 2.69491i −0.816698 0.173595i −0.219422 0.975630i \(-0.570417\pi\)
−0.597276 + 0.802035i \(0.703750\pi\)
\(242\) 47.0690 34.1976i 3.02571 2.19831i
\(243\) 0 0
\(244\) 33.5627 24.3848i 2.14863 1.56107i
\(245\) −1.47075 + 6.05277i −0.0939630 + 0.386698i
\(246\) 0 0
\(247\) 1.43013 13.6067i 0.0909967 0.865776i
\(248\) 25.2636 5.36994i 1.60424 0.340992i
\(249\) 0 0
\(250\) 29.6395 0.531557i 1.87456 0.0336186i
\(251\) 8.02701 0.506661 0.253330 0.967380i \(-0.418474\pi\)
0.253330 + 0.967380i \(0.418474\pi\)
\(252\) 0 0
\(253\) −18.7069 13.5914i −1.17609 0.854481i
\(254\) 3.22303 1.43499i 0.202231 0.0900391i
\(255\) 0 0
\(256\) −2.47295 1.10103i −0.154559 0.0688143i
\(257\) −6.92454 11.9937i −0.431941 0.748144i 0.565100 0.825023i \(-0.308838\pi\)
−0.997040 + 0.0768792i \(0.975504\pi\)
\(258\) 0 0
\(259\) 8.96143 + 1.90481i 0.556836 + 0.118359i
\(260\) 0.679467 23.4807i 0.0421388 1.45621i
\(261\) 0 0
\(262\) −13.9397 42.9021i −0.861200 2.65050i
\(263\) −15.3140 3.25510i −0.944304 0.200718i −0.290066 0.957007i \(-0.593677\pi\)
−0.654238 + 0.756289i \(0.727011\pi\)
\(264\) 0 0
\(265\) 1.40896 + 7.72045i 0.0865515 + 0.474263i
\(266\) 23.8606 26.4999i 1.46299 1.62481i
\(267\) 0 0
\(268\) 1.77007 3.06586i 0.108124 0.187277i
\(269\) 5.63335 4.09287i 0.343472 0.249547i −0.402654 0.915352i \(-0.631912\pi\)
0.746125 + 0.665806i \(0.231912\pi\)
\(270\) 0 0
\(271\) 14.6785 + 10.6646i 0.891658 + 0.647828i 0.936310 0.351175i \(-0.114218\pi\)
−0.0446517 + 0.999003i \(0.514218\pi\)
\(272\) −0.314172 + 0.139878i −0.0190495 + 0.00848137i
\(273\) 0 0
\(274\) −6.59358 11.4204i −0.398333 0.689933i
\(275\) −20.4038 + 20.1806i −1.23039 + 1.21694i
\(276\) 0 0
\(277\) −10.5077 11.6700i −0.631348 0.701183i 0.339574 0.940579i \(-0.389717\pi\)
−0.970922 + 0.239396i \(0.923050\pi\)
\(278\) −28.4090 20.6404i −1.70386 1.23793i
\(279\) 0 0
\(280\) 22.5326 29.1985i 1.34658 1.74494i
\(281\) −2.01464 19.1680i −0.120183 1.14347i −0.873845 0.486204i \(-0.838381\pi\)
0.753662 0.657262i \(-0.228286\pi\)
\(282\) 0 0
\(283\) 5.77953 + 2.57321i 0.343558 + 0.152962i 0.571260 0.820769i \(-0.306455\pi\)
−0.227703 + 0.973731i \(0.573121\pi\)
\(284\) 15.8604 17.6147i 0.941140 1.04524i
\(285\) 0 0
\(286\) 21.2665 + 23.6188i 1.25751 + 1.39661i
\(287\) 1.22423 + 3.76779i 0.0722640 + 0.222406i
\(288\) 0 0
\(289\) −5.25300 + 16.1671i −0.309000 + 0.951004i
\(290\) 7.39723 + 17.9983i 0.434380 + 1.05690i
\(291\) 0 0
\(292\) 37.9599 + 16.9008i 2.22143 + 0.989047i
\(293\) −11.3054 19.5815i −0.660467 1.14396i −0.980493 0.196554i \(-0.937025\pi\)
0.320026 0.947409i \(-0.396309\pi\)
\(294\) 0 0
\(295\) 18.1141 1.37552i 1.05465 0.0800856i
\(296\) 29.0086 + 21.0760i 1.68609 + 1.22502i
\(297\) 0 0
\(298\) −11.6708 + 35.9191i −0.676072 + 2.08074i
\(299\) 4.20681 7.28640i 0.243286 0.421384i
\(300\) 0 0
\(301\) −0.635394 1.10053i −0.0366235 0.0634338i
\(302\) −49.1201 + 10.4408i −2.82655 + 0.600801i
\(303\) 0 0
\(304\) 67.2863 29.9578i 3.85913 1.71820i
\(305\) 0.533423 18.4338i 0.0305437 1.05551i
\(306\) 0 0
\(307\) 1.98814 0.113469 0.0567346 0.998389i \(-0.481931\pi\)
0.0567346 + 0.998389i \(0.481931\pi\)
\(308\) 6.19539 + 58.9452i 0.353015 + 3.35872i
\(309\) 0 0
\(310\) 8.25234 17.1797i 0.468702 0.975741i
\(311\) 8.61147 1.83042i 0.488312 0.103794i 0.0428252 0.999083i \(-0.486364\pi\)
0.445486 + 0.895289i \(0.353031\pi\)
\(312\) 0 0
\(313\) −32.1133 6.82590i −1.81515 0.385822i −0.830035 0.557711i \(-0.811680\pi\)
−0.985116 + 0.171888i \(0.945013\pi\)
\(314\) 7.78014 23.9448i 0.439059 1.35128i
\(315\) 0 0
\(316\) 18.6698 + 57.4598i 1.05026 + 3.23237i
\(317\) 1.63358 + 15.5425i 0.0917512 + 0.872954i 0.939498 + 0.342554i \(0.111292\pi\)
−0.847747 + 0.530401i \(0.822042\pi\)
\(318\) 0 0
\(319\) −17.2093 7.66208i −0.963537 0.428994i
\(320\) 27.4490 14.8060i 1.53445 0.827683i
\(321\) 0 0
\(322\) 20.0329 8.91923i 1.11639 0.497049i
\(323\) −0.0619248 + 0.190585i −0.00344559 + 0.0106044i
\(324\) 0 0
\(325\) −8.07880 6.61596i −0.448131 0.366988i
\(326\) −12.5284 + 21.6999i −0.693885 + 1.20184i
\(327\) 0 0
\(328\) −1.62073 + 15.4203i −0.0894901 + 0.851441i
\(329\) 0.556800 5.29760i 0.0306974 0.292066i
\(330\) 0 0
\(331\) 2.25995 + 21.5019i 0.124218 + 1.18185i 0.862033 + 0.506852i \(0.169191\pi\)
−0.737815 + 0.675002i \(0.764143\pi\)
\(332\) −66.2251 −3.63457
\(333\) 0 0
\(334\) −12.1733 37.4657i −0.666095 2.05003i
\(335\) −0.598224 1.45555i −0.0326845 0.0795249i
\(336\) 0 0
\(337\) 9.52716 10.5810i 0.518977 0.576383i −0.425500 0.904958i \(-0.639902\pi\)
0.944478 + 0.328576i \(0.106569\pi\)
\(338\) 15.3262 17.0214i 0.833633 0.925843i
\(339\) 0 0
\(340\) −0.0812389 + 0.334332i −0.00440580 + 0.0181317i
\(341\) 5.70153 + 17.5475i 0.308755 + 0.950250i
\(342\) 0 0
\(343\) 20.0888 1.08470
\(344\) −0.519881 4.94634i −0.0280301 0.266689i
\(345\) 0 0
\(346\) −1.84036 + 17.5099i −0.0989384 + 0.941336i
\(347\) 1.98457 18.8819i 0.106537 1.01363i −0.802425 0.596753i \(-0.796457\pi\)
0.908962 0.416879i \(-0.136876\pi\)
\(348\) 0 0
\(349\) −1.26140 + 2.18481i −0.0675211 + 0.116950i −0.897810 0.440384i \(-0.854842\pi\)
0.830288 + 0.557334i \(0.188176\pi\)
\(350\) −6.89930 26.3267i −0.368783 1.40722i
\(351\) 0 0
\(352\) −24.3711 + 75.0065i −1.29898 + 3.99786i
\(353\) −4.05214 + 1.80413i −0.215674 + 0.0960241i −0.511730 0.859146i \(-0.670995\pi\)
0.296056 + 0.955171i \(0.404328\pi\)
\(354\) 0 0
\(355\) −1.89165 10.3654i −0.100398 0.550136i
\(356\) −29.7275 13.2355i −1.57555 0.701482i
\(357\) 0 0
\(358\) −1.35349 12.8776i −0.0715343 0.680603i
\(359\) 10.5484 + 32.4646i 0.556722 + 1.71341i 0.691352 + 0.722518i \(0.257015\pi\)
−0.134630 + 0.990896i \(0.542985\pi\)
\(360\) 0 0
\(361\) 7.39111 22.7475i 0.389006 1.19724i
\(362\) −27.5185 5.84924i −1.44634 0.307429i
\(363\) 0 0
\(364\) −21.0949 + 4.48386i −1.10567 + 0.235018i
\(365\) 16.2568 8.76895i 0.850921 0.458988i
\(366\) 0 0
\(367\) −1.13659 10.8139i −0.0593296 0.564483i −0.983297 0.182011i \(-0.941739\pi\)
0.923967 0.382472i \(-0.124927\pi\)
\(368\) 45.2939 2.36111
\(369\) 0 0
\(370\) 25.3902 7.44506i 1.31997 0.387050i
\(371\) 6.58214 2.93056i 0.341728 0.152147i
\(372\) 0 0
\(373\) 23.8047 5.05984i 1.23256 0.261989i 0.454824 0.890581i \(-0.349702\pi\)
0.777735 + 0.628593i \(0.216369\pi\)
\(374\) −0.232754 0.403141i −0.0120354 0.0208459i
\(375\) 0 0
\(376\) 10.4239 18.0548i 0.537573 0.931104i
\(377\) 2.11814 6.51896i 0.109090 0.335744i
\(378\) 0 0
\(379\) −4.12810 2.99924i −0.212046 0.154061i 0.476693 0.879070i \(-0.341835\pi\)
−0.688739 + 0.725009i \(0.741835\pi\)
\(380\) 17.3989 71.6040i 0.892547 3.67321i
\(381\) 0 0
\(382\) 31.6759 + 54.8643i 1.62068 + 2.80710i
\(383\) 18.7507 + 8.34835i 0.958116 + 0.426581i 0.825384 0.564571i \(-0.190958\pi\)
0.132732 + 0.991152i \(0.457625\pi\)
\(384\) 0 0
\(385\) 22.4266 + 13.8280i 1.14296 + 0.704738i
\(386\) −21.0179 + 64.6866i −1.06979 + 3.29246i
\(387\) 0 0
\(388\) −15.8857 48.8913i −0.806476 2.48208i
\(389\) 7.98747 + 8.87098i 0.404981 + 0.449777i 0.910791 0.412868i \(-0.135473\pi\)
−0.505810 + 0.862645i \(0.668806\pi\)
\(390\) 0 0
\(391\) −0.0824586 + 0.0915796i −0.00417011 + 0.00463138i
\(392\) 20.4465 + 9.10336i 1.03270 + 0.459789i
\(393\) 0 0
\(394\) 4.26038 + 40.5348i 0.214635 + 2.04211i
\(395\) 25.2916 + 9.03455i 1.27256 + 0.454577i
\(396\) 0 0
\(397\) −11.3426 8.24087i −0.569268 0.413597i 0.265571 0.964091i \(-0.414439\pi\)
−0.834839 + 0.550494i \(0.814439\pi\)
\(398\) 5.66317 + 6.28959i 0.283869 + 0.315269i
\(399\) 0 0
\(400\) 9.09899 55.4729i 0.454949 2.77364i
\(401\) 0.970609 + 1.68114i 0.0484699 + 0.0839523i 0.889242 0.457436i \(-0.151232\pi\)
−0.840773 + 0.541388i \(0.817899\pi\)
\(402\) 0 0
\(403\) −6.13306 + 2.73062i −0.305510 + 0.136022i
\(404\) 8.70247 + 6.32271i 0.432964 + 0.314567i
\(405\) 0 0
\(406\) 14.4531 10.5008i 0.717296 0.521146i
\(407\) −12.8073 + 22.1829i −0.634835 + 1.09957i
\(408\) 0 0
\(409\) 7.32900 8.13967i 0.362396 0.402481i −0.534181 0.845370i \(-0.679380\pi\)
0.896576 + 0.442889i \(0.146047\pi\)
\(410\) 8.27773 + 7.89864i 0.408808 + 0.390086i
\(411\) 0 0
\(412\) 5.94233 + 1.26308i 0.292757 + 0.0622275i
\(413\) −5.15382 15.8618i −0.253603 0.780509i
\(414\) 0 0
\(415\) −17.9853 + 23.3059i −0.882863 + 1.14404i
\(416\) −28.0696 5.96637i −1.37622 0.292525i
\(417\) 0 0
\(418\) 49.8489 + 86.3409i 2.43819 + 4.22307i
\(419\) −15.2038 6.76918i −0.742755 0.330696i 0.000233416 1.00000i \(-0.499926\pi\)
−0.742989 + 0.669304i \(0.766592\pi\)
\(420\) 0 0
\(421\) 7.03341 3.13148i 0.342787 0.152619i −0.228120 0.973633i \(-0.573258\pi\)
0.570908 + 0.821014i \(0.306591\pi\)
\(422\) −57.0504 41.4495i −2.77717 2.01773i
\(423\) 0 0
\(424\) 28.1990 1.36946
\(425\) 0.0955956 + 0.119387i 0.00463707 + 0.00579112i
\(426\) 0 0
\(427\) −16.5608 + 3.52010i −0.801432 + 0.170350i
\(428\) −5.86794 + 55.8297i −0.283638 + 2.69863i
\(429\) 0 0
\(430\) −3.12399 1.92622i −0.150652 0.0928904i
\(431\) 26.1475 18.9973i 1.25948 0.915066i 0.260748 0.965407i \(-0.416031\pi\)
0.998732 + 0.0503406i \(0.0160307\pi\)
\(432\) 0 0
\(433\) −25.4573 + 18.4958i −1.22340 + 0.888852i −0.996378 0.0850377i \(-0.972899\pi\)
−0.227022 + 0.973890i \(0.572899\pi\)
\(434\) −17.1153 3.63796i −0.821558 0.174628i
\(435\) 0 0
\(436\) −45.5685 + 9.68589i −2.18234 + 0.463870i
\(437\) 17.6602 19.6136i 0.844801 0.938246i
\(438\) 0 0
\(439\) −12.1190 13.4595i −0.578409 0.642389i 0.380943 0.924598i \(-0.375599\pi\)
−0.959353 + 0.282210i \(0.908933\pi\)
\(440\) 58.1719 + 85.1411i 2.77324 + 4.05894i
\(441\) 0 0
\(442\) 0.137032 0.0995598i 0.00651797 0.00473558i
\(443\) 19.3559 33.5254i 0.919626 1.59284i 0.119642 0.992817i \(-0.461825\pi\)
0.799984 0.600022i \(-0.204841\pi\)
\(444\) 0 0
\(445\) −12.7312 + 6.86722i −0.603517 + 0.325538i
\(446\) −4.73731 + 45.0725i −0.224318 + 2.13425i
\(447\) 0 0
\(448\) −19.1590 21.2783i −0.905179 1.00530i
\(449\) 4.76841 0.225035 0.112518 0.993650i \(-0.464109\pi\)
0.112518 + 0.993650i \(0.464109\pi\)
\(450\) 0 0
\(451\) −11.0763 −0.521564
\(452\) 29.4228 + 32.6773i 1.38393 + 1.53701i
\(453\) 0 0
\(454\) 3.41584 32.4995i 0.160313 1.52528i
\(455\) −4.15096 + 8.64144i −0.194600 + 0.405117i
\(456\) 0 0
\(457\) 2.37786 4.11857i 0.111232 0.192659i −0.805035 0.593227i \(-0.797854\pi\)
0.916267 + 0.400568i \(0.131187\pi\)
\(458\) 44.0648 32.0149i 2.05901 1.49596i
\(459\) 0 0
\(460\) 27.6845 35.8744i 1.29079 1.67265i
\(461\) −5.92471 6.58006i −0.275941 0.306464i 0.589205 0.807984i \(-0.299441\pi\)
−0.865146 + 0.501520i \(0.832774\pi\)
\(462\) 0 0
\(463\) 1.03602 1.15062i 0.0481481 0.0534739i −0.718590 0.695434i \(-0.755212\pi\)
0.766738 + 0.641960i \(0.221879\pi\)
\(464\) 36.0939 7.67199i 1.67562 0.356163i
\(465\) 0 0
\(466\) −21.4362 4.55641i −0.993015 0.211072i
\(467\) −27.9575 + 20.3123i −1.29372 + 0.939942i −0.999873 0.0159111i \(-0.994935\pi\)
−0.293846 + 0.955853i \(0.594935\pi\)
\(468\) 0 0
\(469\) −1.16884 + 0.849213i −0.0539721 + 0.0392130i
\(470\) −5.84810 14.2291i −0.269753 0.656339i
\(471\) 0 0
\(472\) 6.82304 64.9169i 0.314056 2.98804i
\(473\) 3.47530 0.738698i 0.159794 0.0339654i
\(474\) 0 0
\(475\) −20.4737 25.5691i −0.939399 1.17319i
\(476\) 0.315875 0.0144781
\(477\) 0 0
\(478\) 38.7350 + 28.1427i 1.77170 + 1.28722i
\(479\) 22.3481 9.95002i 1.02111 0.454628i 0.173268 0.984875i \(-0.444567\pi\)
0.847843 + 0.530247i \(0.177901\pi\)
\(480\) 0 0
\(481\) −8.51445 3.79088i −0.388226 0.172849i
\(482\) 17.1839 + 29.7633i 0.782704 + 1.35568i
\(483\) 0 0
\(484\) −107.966 22.9488i −4.90753 1.04313i
\(485\) −21.5200 7.68730i −0.977175 0.349062i
\(486\) 0 0
\(487\) 1.67643 + 5.15952i 0.0759663 + 0.233800i 0.981828 0.189774i \(-0.0607754\pi\)
−0.905862 + 0.423574i \(0.860775\pi\)
\(488\) −64.8153 13.7769i −2.93405 0.623652i
\(489\) 0 0
\(490\) 14.5359 7.84067i 0.656664 0.354205i
\(491\) −14.7320 + 16.3615i −0.664845 + 0.738385i −0.977373 0.211523i \(-0.932158\pi\)
0.312528 + 0.949909i \(0.398824\pi\)
\(492\) 0 0
\(493\) −0.0501978 + 0.0869451i −0.00226080 + 0.00391581i
\(494\) −29.3482 + 21.3227i −1.32044 + 0.959356i
\(495\) 0 0
\(496\) −29.2390 21.2433i −1.31287 0.953854i
\(497\) −8.83709 + 3.93453i −0.396398 + 0.176488i
\(498\) 0 0
\(499\) −20.3177 35.1912i −0.909544 1.57538i −0.814699 0.579884i \(-0.803098\pi\)
−0.0948451 0.995492i \(-0.530236\pi\)
\(500\) −38.3751 41.1128i −1.71619 1.83862i
\(501\) 0 0
\(502\) −14.2413 15.8166i −0.635621 0.705928i
\(503\) −32.8363 23.8569i −1.46410 1.06373i −0.982272 0.187461i \(-0.939974\pi\)
−0.481825 0.876268i \(-0.660026\pi\)
\(504\) 0 0
\(505\) 4.58849 1.34546i 0.204185 0.0598723i
\(506\) 6.40861 + 60.9738i 0.284897 + 2.71062i
\(507\) 0 0
\(508\) −6.11460 2.72240i −0.271292 0.120787i
\(509\) 29.6993 32.9844i 1.31640 1.46201i 0.524414 0.851463i \(-0.324284\pi\)
0.791983 0.610543i \(-0.209049\pi\)
\(510\) 0 0
\(511\) −11.3470 12.6022i −0.501963 0.557487i
\(512\) 8.08909 + 24.8957i 0.357491 + 1.10024i
\(513\) 0 0
\(514\) −11.3472 + 34.9231i −0.500503 + 1.54039i
\(515\) 2.05831 1.74820i 0.0907000 0.0770349i
\(516\) 0 0
\(517\) 13.6053 + 6.05749i 0.598362 + 0.266408i
\(518\) −12.1459 21.0372i −0.533658 0.924323i
\(519\) 0 0
\(520\) −28.5975 + 24.2889i −1.25408 + 1.06514i
\(521\) 7.98161 + 5.79898i 0.349681 + 0.254058i 0.748735 0.662869i \(-0.230662\pi\)
−0.399054 + 0.916927i \(0.630662\pi\)
\(522\) 0 0
\(523\) −2.46257 + 7.57903i −0.107681 + 0.331408i −0.990350 0.138587i \(-0.955744\pi\)
0.882669 + 0.469994i \(0.155744\pi\)
\(524\) −42.7904 + 74.1151i −1.86931 + 3.23773i
\(525\) 0 0
\(526\) 20.7558 + 35.9502i 0.904998 + 1.56750i
\(527\) 0.0961821 0.0204441i 0.00418976 0.000890561i
\(528\) 0 0
\(529\) −6.18440 + 2.75347i −0.268887 + 0.119716i
\(530\) 12.7128 16.4736i 0.552208 0.715569i
\(531\) 0 0
\(532\) −67.6511 −2.93305
\(533\) −0.421278 4.00819i −0.0182476 0.173614i
\(534\) 0 0
\(535\) 18.0540 + 17.2272i 0.780543 + 0.744797i
\(536\) −5.53094 + 1.17564i −0.238900 + 0.0507798i
\(537\) 0 0
\(538\) −18.0592 3.83860i −0.778588 0.165494i
\(539\) −4.94071 + 15.2059i −0.212811 + 0.654966i
\(540\) 0 0
\(541\) −3.72498 11.4643i −0.160149 0.492889i 0.838497 0.544906i \(-0.183435\pi\)
−0.998646 + 0.0520177i \(0.983435\pi\)
\(542\) −5.02858 47.8437i −0.215996 2.05506i
\(543\) 0 0
\(544\) 0.383976 + 0.170957i 0.0164628 + 0.00732972i
\(545\) −8.96676 + 18.6670i −0.384094 + 0.799605i
\(546\) 0 0
\(547\) 1.14311 0.508944i 0.0488757 0.0217609i −0.382153 0.924099i \(-0.624817\pi\)
0.431029 + 0.902338i \(0.358151\pi\)
\(548\) −7.73103 + 23.7937i −0.330253 + 1.01642i
\(549\) 0 0
\(550\) 75.9640 + 4.40007i 3.23912 + 0.187620i
\(551\) 10.7509 18.6211i 0.458003 0.793284i
\(552\) 0 0
\(553\) 2.57732 24.5216i 0.109599 1.04276i
\(554\) −4.35229 + 41.4092i −0.184911 + 1.75931i
\(555\) 0 0
\(556\) 6.96364 + 66.2547i 0.295324 + 2.80982i
\(557\) 44.8687 1.90115 0.950574 0.310498i \(-0.100496\pi\)
0.950574 + 0.310498i \(0.100496\pi\)
\(558\) 0 0
\(559\) 0.399493 + 1.22951i 0.0168967 + 0.0520028i
\(560\) −51.4609 + 3.90774i −2.17462 + 0.165132i
\(561\) 0 0
\(562\) −34.1946 + 37.9770i −1.44241 + 1.60196i
\(563\) −26.2271 + 29.1282i −1.10534 + 1.22761i −0.133732 + 0.991018i \(0.542696\pi\)
−0.971610 + 0.236589i \(0.923971\pi\)
\(564\) 0 0
\(565\) 19.4904 1.48002i 0.819966 0.0622650i
\(566\) −5.18358 15.9534i −0.217882 0.670573i
\(567\) 0 0
\(568\) −37.8596 −1.58855
\(569\) −2.71156 25.7988i −0.113675 1.08154i −0.891487 0.453046i \(-0.850337\pi\)
0.777813 0.628496i \(-0.216329\pi\)
\(570\) 0 0
\(571\) −1.13569 + 10.8054i −0.0475272 + 0.452191i 0.944717 + 0.327887i \(0.106337\pi\)
−0.992244 + 0.124304i \(0.960330\pi\)
\(572\) 6.30264 59.9656i 0.263527 2.50729i
\(573\) 0 0
\(574\) 5.25213 9.09696i 0.219220 0.379700i
\(575\) −5.10644 19.4854i −0.212953 0.812599i
\(576\) 0 0
\(577\) −1.77776 + 5.47137i −0.0740090 + 0.227776i −0.981217 0.192905i \(-0.938209\pi\)
0.907208 + 0.420681i \(0.138209\pi\)
\(578\) 41.1756 18.3326i 1.71268 0.762534i
\(579\) 0 0
\(580\) 15.9847 33.2770i 0.663730 1.38175i
\(581\) 24.6905 + 10.9929i 1.02433 + 0.456062i
\(582\) 0 0
\(583\) 2.10565 + 20.0339i 0.0872072 + 0.829721i
\(584\) −20.5093 63.1211i −0.848680 2.61197i
\(585\) 0 0
\(586\) −18.5260 + 57.0173i −0.765304 + 2.35536i
\(587\) 6.76644 + 1.43825i 0.279281 + 0.0593630i 0.345423 0.938447i \(-0.387736\pi\)
−0.0661417 + 0.997810i \(0.521069\pi\)
\(588\) 0 0
\(589\) −20.5993 + 4.37852i −0.848781 + 0.180414i
\(590\) −34.8480 33.2520i −1.43467 1.36896i
\(591\) 0 0
\(592\) −5.24467 49.8997i −0.215555 2.05086i
\(593\) −18.6586 −0.766219 −0.383109 0.923703i \(-0.625147\pi\)
−0.383109 + 0.923703i \(0.625147\pi\)
\(594\) 0 0
\(595\) 0.0857849 0.111163i 0.00351684 0.00455723i
\(596\) 65.4565 29.1431i 2.68120 1.19375i
\(597\) 0 0
\(598\) −21.8209 + 4.63817i −0.892322 + 0.189669i
\(599\) 3.61776 + 6.26614i 0.147818 + 0.256027i 0.930421 0.366494i \(-0.119442\pi\)
−0.782603 + 0.622521i \(0.786108\pi\)
\(600\) 0 0
\(601\) 3.28224 5.68501i 0.133886 0.231897i −0.791286 0.611447i \(-0.790588\pi\)
0.925171 + 0.379550i \(0.123921\pi\)
\(602\) −1.04122 + 3.20453i −0.0424368 + 0.130607i
\(603\) 0 0
\(604\) 77.0755 + 55.9986i 3.13616 + 2.27855i
\(605\) −37.3972 + 31.7629i −1.52041 + 1.29134i
\(606\) 0 0
\(607\) −8.23189 14.2580i −0.334122 0.578716i 0.649194 0.760623i \(-0.275106\pi\)
−0.983316 + 0.181907i \(0.941773\pi\)
\(608\) −82.2362 36.6139i −3.33512 1.48489i
\(609\) 0 0
\(610\) −37.2686 + 31.6536i −1.50896 + 1.28162i
\(611\) −1.67456 + 5.15376i −0.0677454 + 0.208499i
\(612\) 0 0
\(613\) 5.27406 + 16.2319i 0.213017 + 0.655599i 0.999288 + 0.0377179i \(0.0120088\pi\)
−0.786271 + 0.617881i \(0.787991\pi\)
\(614\) −3.52730 3.91747i −0.142350 0.158096i
\(615\) 0 0
\(616\) 63.3459 70.3528i 2.55228 2.83459i
\(617\) 2.05173 + 0.913488i 0.0825994 + 0.0367756i 0.447621 0.894224i \(-0.352272\pi\)
−0.365021 + 0.930999i \(0.618938\pi\)
\(618\) 0 0
\(619\) 1.09152 + 10.3851i 0.0438717 + 0.417412i 0.994312 + 0.106505i \(0.0339660\pi\)
−0.950440 + 0.310907i \(0.899367\pi\)
\(620\) −34.6969 + 10.1740i −1.39346 + 0.408599i
\(621\) 0 0
\(622\) −18.8849 13.7207i −0.757217 0.550150i
\(623\) 8.88620 + 9.86912i 0.356018 + 0.395398i
\(624\) 0 0
\(625\) −24.8903 + 2.33964i −0.995611 + 0.0935856i
\(626\) 43.5247 + 75.3870i 1.73960 + 3.01307i
\(627\) 0 0
\(628\) −43.6354 + 19.4277i −1.74124 + 0.775251i
\(629\) 0.110440 + 0.0802394i 0.00440353 + 0.00319936i
\(630\) 0 0
\(631\) 3.19101 2.31840i 0.127032 0.0922941i −0.522455 0.852667i \(-0.674984\pi\)
0.649487 + 0.760373i \(0.274984\pi\)
\(632\) 48.2504 83.5722i 1.91930 3.32432i
\(633\) 0 0
\(634\) 27.7270 30.7939i 1.10118 1.22298i
\(635\) −2.61866 + 1.41251i −0.103918 + 0.0560537i
\(636\) 0 0
\(637\) −5.69049 1.20955i −0.225465 0.0479242i
\(638\) 15.4348 + 47.5034i 0.611070 + 1.88068i
\(639\) 0 0
\(640\) −20.0040 7.14574i −0.790727 0.282460i
\(641\) 12.9263 + 2.74756i 0.510557 + 0.108522i 0.455985 0.889988i \(-0.349287\pi\)
0.0545722 + 0.998510i \(0.482620\pi\)
\(642\) 0 0
\(643\) −7.49326 12.9787i −0.295505 0.511831i 0.679597 0.733586i \(-0.262155\pi\)
−0.975102 + 0.221755i \(0.928821\pi\)
\(644\) −38.0056 16.9212i −1.49763 0.666789i
\(645\) 0 0
\(646\) 0.485397 0.216113i 0.0190977 0.00850284i
\(647\) 40.6013 + 29.4986i 1.59620 + 1.15971i 0.894334 + 0.447400i \(0.147650\pi\)
0.701867 + 0.712308i \(0.252350\pi\)
\(648\) 0 0
\(649\) 46.6296 1.83037
\(650\) 1.29697 + 27.6565i 0.0508714 + 1.08478i
\(651\) 0 0
\(652\) 46.4980 9.88345i 1.82100 0.387066i
\(653\) 0.734841 6.99155i 0.0287566 0.273600i −0.970690 0.240335i \(-0.922743\pi\)
0.999447 0.0332654i \(-0.0105906\pi\)
\(654\) 0 0
\(655\) 14.4617 + 35.1868i 0.565064 + 1.37486i
\(656\) 17.5529 12.7529i 0.685325 0.497918i
\(657\) 0 0
\(658\) −11.4263 + 8.30172i −0.445445 + 0.323635i
\(659\) 34.6451 + 7.36404i 1.34958 + 0.286862i 0.825306 0.564686i \(-0.191003\pi\)
0.524276 + 0.851549i \(0.324336\pi\)
\(660\) 0 0
\(661\) 5.03987 1.07126i 0.196028 0.0416671i −0.108851 0.994058i \(-0.534717\pi\)
0.304879 + 0.952391i \(0.401384\pi\)
\(662\) 38.3583 42.6012i 1.49084 1.65574i
\(663\) 0 0
\(664\) 70.7794 + 78.6085i 2.74677 + 3.05060i
\(665\) −18.3726 + 23.8078i −0.712457 + 0.923226i
\(666\) 0 0
\(667\) 10.6973 7.77205i 0.414201 0.300935i
\(668\) −37.3681 + 64.7234i −1.44581 + 2.50422i
\(669\) 0 0
\(670\) −1.80668 + 3.76114i −0.0697982 + 0.145306i
\(671\) 4.94796 47.0767i 0.191014 1.81737i
\(672\) 0 0
\(673\) 13.1777 + 14.6353i 0.507962 + 0.564149i 0.941511 0.336981i \(-0.109406\pi\)
−0.433550 + 0.901130i \(0.642739\pi\)
\(674\) −37.7518 −1.45414
\(675\) 0 0
\(676\) −43.4536 −1.67129
\(677\) 5.89101 + 6.54263i 0.226410 + 0.251454i 0.845637 0.533758i \(-0.179221\pi\)
−0.619227 + 0.785212i \(0.712554\pi\)
\(678\) 0 0
\(679\) −2.19299 + 20.8649i −0.0841592 + 0.800721i
\(680\) 0.483675 0.260895i 0.0185481 0.0100049i
\(681\) 0 0
\(682\) 24.4604 42.3667i 0.936638 1.62230i
\(683\) 22.8601 16.6088i 0.874716 0.635519i −0.0571320 0.998367i \(-0.518196\pi\)
0.931848 + 0.362848i \(0.118196\pi\)
\(684\) 0 0
\(685\) 6.27389 + 9.18255i 0.239713 + 0.350847i
\(686\) −35.6411 39.5834i −1.36078 1.51130i
\(687\) 0 0
\(688\) −4.65687 + 5.17198i −0.177542 + 0.197180i
\(689\) −7.16960 + 1.52395i −0.273140 + 0.0580577i
\(690\) 0 0
\(691\) 49.4141 + 10.5033i 1.87980 + 0.399564i 0.997472 0.0710668i \(-0.0226403\pi\)
0.882330 + 0.470631i \(0.155974\pi\)
\(692\) 27.0227 19.6332i 1.02725 0.746341i
\(693\) 0 0
\(694\) −40.7262 + 29.5893i −1.54594 + 1.12319i
\(695\) 25.2075 + 15.5427i 0.956176 + 0.589567i
\(696\) 0 0
\(697\) −0.00617037 + 0.0587072i −0.000233719 + 0.00222369i
\(698\) 6.54293 1.39074i 0.247653 0.0526404i
\(699\) 0 0
\(700\) −28.3588 + 43.1475i −1.07186 + 1.63082i
\(701\) −30.7464 −1.16128 −0.580638 0.814162i \(-0.697197\pi\)
−0.580638 + 0.814162i \(0.697197\pi\)
\(702\) 0 0
\(703\) −23.6530 17.1849i −0.892089 0.648140i
\(704\) 73.1320 32.5605i 2.75627 1.22717i
\(705\) 0 0
\(706\) 10.7441 + 4.78358i 0.404359 + 0.180032i
\(707\) −2.19498 3.80182i −0.0825509 0.142982i
\(708\) 0 0
\(709\) 25.9024 + 5.50573i 0.972787 + 0.206772i 0.666778 0.745257i \(-0.267673\pi\)
0.306009 + 0.952029i \(0.401006\pi\)
\(710\) −17.0680 + 22.1173i −0.640551 + 0.830047i
\(711\) 0 0
\(712\) 16.0614 + 49.4320i 0.601927 + 1.85254i
\(713\) −12.6677 2.69259i −0.474408 0.100838i
\(714\) 0 0
\(715\) −19.3914 18.5034i −0.725199 0.691987i
\(716\) −16.4375 + 18.2557i −0.614298 + 0.682247i
\(717\) 0 0
\(718\) 45.2541 78.3825i 1.68887 2.92521i
\(719\) −2.59090 + 1.88240i −0.0966244 + 0.0702017i −0.635048 0.772472i \(-0.719020\pi\)
0.538424 + 0.842674i \(0.319020\pi\)
\(720\) 0 0
\(721\) −2.00579 1.45730i −0.0746997 0.0542725i
\(722\) −57.9352 + 25.7944i −2.15613 + 0.959969i
\(723\) 0 0
\(724\) 26.6867 + 46.2227i 0.991802 + 1.71785i
\(725\) −7.36972 14.6627i −0.273705 0.544557i
\(726\) 0 0
\(727\) 27.4745 + 30.5136i 1.01897 + 1.13169i 0.991240 + 0.132070i \(0.0421625\pi\)
0.0277340 + 0.999615i \(0.491171\pi\)
\(728\) 27.8679 + 20.2472i 1.03285 + 0.750411i
\(729\) 0 0
\(730\) −46.1209 16.4751i −1.70701 0.609772i
\(731\) −0.00197926 0.0188314i −7.32057e−5 0.000696506i
\(732\) 0 0
\(733\) −38.0712 16.9504i −1.40619 0.626077i −0.443401 0.896323i \(-0.646228\pi\)
−0.962791 + 0.270246i \(0.912895\pi\)
\(734\) −19.2915 + 21.4254i −0.712062 + 0.790825i
\(735\) 0 0
\(736\) −37.0413 41.1386i −1.36536 1.51639i
\(737\) −1.24823 3.84166i −0.0459792 0.141509i
\(738\) 0 0
\(739\) 7.60793 23.4148i 0.279862 0.861327i −0.708030 0.706183i \(-0.750416\pi\)
0.987892 0.155144i \(-0.0495842\pi\)
\(740\) −42.7281 26.3456i −1.57071 0.968485i
\(741\) 0 0
\(742\) −17.4523 7.77026i −0.640694 0.285255i
\(743\) 1.29297 + 2.23949i 0.0474346 + 0.0821591i 0.888768 0.458358i \(-0.151562\pi\)
−0.841333 + 0.540517i \(0.818229\pi\)
\(744\) 0 0
\(745\) 7.52051 30.9501i 0.275530 1.13392i
\(746\) −52.2036 37.9281i −1.91131 1.38865i
\(747\) 0 0
\(748\) −0.272906 + 0.839918i −0.00997843 + 0.0307104i
\(749\) 11.4551 19.8408i 0.418559 0.724966i
\(750\) 0 0
\(751\) −1.67267 2.89715i −0.0610367 0.105719i 0.833892 0.551927i \(-0.186107\pi\)
−0.894929 + 0.446208i \(0.852774\pi\)
\(752\) −28.5351 + 6.06532i −1.04057 + 0.221180i
\(753\) 0 0
\(754\) −16.6030 + 7.39215i −0.604647 + 0.269206i
\(755\) 40.6391 11.9164i 1.47901 0.433683i
\(756\) 0 0
\(757\) −12.7280 −0.462606 −0.231303 0.972882i \(-0.574299\pi\)
−0.231303 + 0.972882i \(0.574299\pi\)
\(758\) 1.41421 + 13.4553i 0.0513662 + 0.488717i
\(759\) 0 0
\(760\) −103.589 + 55.8759i −3.75756 + 2.02683i
\(761\) −21.8602 + 4.64654i −0.792433 + 0.168437i −0.586307 0.810089i \(-0.699419\pi\)
−0.206126 + 0.978526i \(0.566086\pi\)
\(762\) 0 0
\(763\) 18.5969 + 3.95290i 0.673255 + 0.143105i
\(764\) 37.1403 114.306i 1.34369 4.13545i
\(765\) 0 0
\(766\) −16.8172 51.7582i −0.607632 1.87010i
\(767\) 1.77351 + 16.8739i 0.0640379 + 0.609280i
\(768\) 0 0
\(769\) 32.4894 + 14.4652i 1.17160 + 0.521628i 0.897905 0.440189i \(-0.145089\pi\)
0.273691 + 0.961818i \(0.411755\pi\)
\(770\) −12.5417 68.7229i −0.451972 2.47660i
\(771\) 0 0
\(772\) 117.880 52.4837i 4.24261 1.88893i
\(773\) −5.00935 + 15.4172i −0.180174 + 0.554518i −0.999832 0.0183350i \(-0.994163\pi\)
0.819658 + 0.572853i \(0.194163\pi\)
\(774\) 0 0
\(775\) −5.84249 + 14.9736i −0.209868 + 0.537867i
\(776\) −41.0552 + 71.1097i −1.47380 + 2.55269i
\(777\) 0 0
\(778\) 3.30840 31.4773i 0.118612 1.12852i
\(779\) 1.32151 12.5733i 0.0473480 0.450486i
\(780\) 0 0
\(781\) −2.82702 26.8973i −0.101159 0.962461i
\(782\) 0.326746 0.0116844
\(783\) 0 0
\(784\) −9.67798 29.7857i −0.345642 1.06378i
\(785\) −5.01341 + 20.6323i −0.178936 + 0.736399i
\(786\) 0 0
\(787\) −15.0507 + 16.7155i −0.536499