Properties

Label 675.2.r.a.46.9
Level $675$
Weight $2$
Character 675.46
Analytic conductor $5.390$
Analytic rank $0$
Dimension $224$
CM no
Inner twists $4$

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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 46.9
Character \(\chi\) \(=\) 675.46
Dual form 675.2.r.a.631.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.797750 - 0.885991i) q^{2} +(0.0604816 - 0.575444i) q^{4} +(-1.30610 - 1.81497i) q^{5} +(0.157578 - 0.272934i) q^{7} +(-2.48714 + 1.80701i) q^{8} +O(q^{10})\) \(q+(-0.797750 - 0.885991i) q^{2} +(0.0604816 - 0.575444i) q^{4} +(-1.30610 - 1.81497i) q^{5} +(0.157578 - 0.272934i) q^{7} +(-2.48714 + 1.80701i) q^{8} +(-0.566103 + 2.60508i) q^{10} +(-1.93450 - 2.14848i) q^{11} +(4.36810 - 4.85127i) q^{13} +(-0.367525 + 0.0781199i) q^{14} +(2.45317 + 0.521438i) q^{16} +(-0.794350 + 0.577129i) q^{17} +(-5.88399 + 4.27497i) q^{19} +(-1.12341 + 0.641816i) q^{20} +(-0.360286 + 3.42790i) q^{22} +(-1.28104 + 0.272294i) q^{23} +(-1.58820 + 4.74106i) q^{25} -7.78284 q^{26} +(-0.147528 - 0.107185i) q^{28} +(3.94048 - 1.75442i) q^{29} +(-7.91741 - 3.52506i) q^{31} +(1.57924 + 2.73533i) q^{32} +(1.14502 + 0.243382i) q^{34} +(-0.701179 + 0.0704794i) q^{35} +(0.00738727 + 0.0227357i) q^{37} +(8.48155 + 1.80281i) q^{38} +(6.52812 + 2.15393i) q^{40} +(-3.06561 + 3.40470i) q^{41} +(-1.34599 + 2.33132i) q^{43} +(-1.35333 + 0.983252i) q^{44} +(1.26320 + 0.917772i) q^{46} +(4.76261 - 2.12045i) q^{47} +(3.45034 + 5.97616i) q^{49} +(5.46752 - 2.37504i) q^{50} +(-2.52745 - 2.80701i) q^{52} +(3.44104 + 2.50006i) q^{53} +(-1.37277 + 6.31717i) q^{55} +(0.101275 + 0.963571i) q^{56} +(-4.69792 - 2.09165i) q^{58} +(-3.46632 + 3.84974i) q^{59} +(-4.95936 - 5.50792i) q^{61} +(3.19295 + 9.82688i) q^{62} +(2.71365 - 8.35176i) q^{64} +(-14.5101 - 1.59172i) q^{65} +(-2.27694 - 1.01376i) q^{67} +(0.284062 + 0.492010i) q^{68} +(0.621810 + 0.565014i) q^{70} +(-9.63629 - 7.00118i) q^{71} +(-0.283594 + 0.872814i) q^{73} +(0.0142504 - 0.0246825i) q^{74} +(2.10413 + 3.64447i) q^{76} +(-0.891228 + 0.189436i) q^{77} +(-10.3980 + 4.62948i) q^{79} +(-2.25770 - 5.13348i) q^{80} +5.46212 q^{82} +(-1.03926 - 9.88793i) q^{83} +(2.08497 + 0.687930i) q^{85} +(3.13929 - 0.667278i) q^{86} +(8.69369 + 1.84790i) q^{88} +(-3.78718 + 11.6557i) q^{89} +(-0.635757 - 1.95666i) q^{91} +(0.0792106 + 0.753639i) q^{92} +(-5.67808 - 2.52804i) q^{94} +(15.4440 + 5.09571i) q^{95} +(-6.75362 + 3.00691i) q^{97} +(2.54232 - 7.82445i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 224 q + 3 q^{2} + 23 q^{4} + 8 q^{5} - 8 q^{7} + 20 q^{8}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.797750 0.885991i −0.564095 0.626491i 0.391853 0.920028i \(-0.371834\pi\)
−0.955948 + 0.293537i \(0.905168\pi\)
\(3\) 0 0
\(4\) 0.0604816 0.575444i 0.0302408 0.287722i
\(5\) −1.30610 1.81497i −0.584106 0.811678i
\(6\) 0 0
\(7\) 0.157578 0.272934i 0.0595591 0.103159i −0.834708 0.550692i \(-0.814364\pi\)
0.894268 + 0.447533i \(0.147697\pi\)
\(8\) −2.48714 + 1.80701i −0.879336 + 0.638875i
\(9\) 0 0
\(10\) −0.566103 + 2.60508i −0.179017 + 0.823800i
\(11\) −1.93450 2.14848i −0.583273 0.647790i 0.377210 0.926128i \(-0.376883\pi\)
−0.960483 + 0.278337i \(0.910217\pi\)
\(12\) 0 0
\(13\) 4.36810 4.85127i 1.21149 1.34550i 0.290039 0.957015i \(-0.406332\pi\)
0.921455 0.388486i \(-0.127002\pi\)
\(14\) −0.367525 + 0.0781199i −0.0982253 + 0.0208784i
\(15\) 0 0
\(16\) 2.45317 + 0.521438i 0.613293 + 0.130359i
\(17\) −0.794350 + 0.577129i −0.192658 + 0.139974i −0.679933 0.733274i \(-0.737991\pi\)
0.487275 + 0.873249i \(0.337991\pi\)
\(18\) 0 0
\(19\) −5.88399 + 4.27497i −1.34988 + 0.980746i −0.350863 + 0.936427i \(0.614112\pi\)
−0.999017 + 0.0443190i \(0.985888\pi\)
\(20\) −1.12341 + 0.641816i −0.251201 + 0.143514i
\(21\) 0 0
\(22\) −0.360286 + 3.42790i −0.0768133 + 0.730830i
\(23\) −1.28104 + 0.272294i −0.267116 + 0.0567773i −0.339523 0.940598i \(-0.610266\pi\)
0.0724063 + 0.997375i \(0.476932\pi\)
\(24\) 0 0
\(25\) −1.58820 + 4.74106i −0.317641 + 0.948211i
\(26\) −7.78284 −1.52634
\(27\) 0 0
\(28\) −0.147528 0.107185i −0.0278801 0.0202561i
\(29\) 3.94048 1.75442i 0.731729 0.325787i −0.00682892 0.999977i \(-0.502174\pi\)
0.738558 + 0.674190i \(0.235507\pi\)
\(30\) 0 0
\(31\) −7.91741 3.52506i −1.42201 0.633120i −0.455614 0.890178i \(-0.650580\pi\)
−0.966396 + 0.257058i \(0.917247\pi\)
\(32\) 1.57924 + 2.73533i 0.279173 + 0.483542i
\(33\) 0 0
\(34\) 1.14502 + 0.243382i 0.196370 + 0.0417397i
\(35\) −0.701179 + 0.0704794i −0.118521 + 0.0119132i
\(36\) 0 0
\(37\) 0.00738727 + 0.0227357i 0.00121446 + 0.00373772i 0.951662 0.307148i \(-0.0993745\pi\)
−0.950447 + 0.310885i \(0.899375\pi\)
\(38\) 8.48155 + 1.80281i 1.37589 + 0.292454i
\(39\) 0 0
\(40\) 6.52812 + 2.15393i 1.03219 + 0.340567i
\(41\) −3.06561 + 3.40470i −0.478767 + 0.531725i −0.933344 0.358983i \(-0.883124\pi\)
0.454577 + 0.890707i \(0.349790\pi\)
\(42\) 0 0
\(43\) −1.34599 + 2.33132i −0.205261 + 0.355523i −0.950216 0.311592i \(-0.899138\pi\)
0.744955 + 0.667115i \(0.232471\pi\)
\(44\) −1.35333 + 0.983252i −0.204022 + 0.148231i
\(45\) 0 0
\(46\) 1.26320 + 0.917772i 0.186249 + 0.135318i
\(47\) 4.76261 2.12045i 0.694698 0.309300i −0.0288398 0.999584i \(-0.509181\pi\)
0.723538 + 0.690284i \(0.242515\pi\)
\(48\) 0 0
\(49\) 3.45034 + 5.97616i 0.492905 + 0.853737i
\(50\) 5.46752 2.37504i 0.773225 0.335882i
\(51\) 0 0
\(52\) −2.52745 2.80701i −0.350494 0.389263i
\(53\) 3.44104 + 2.50006i 0.472663 + 0.343410i 0.798478 0.602024i \(-0.205639\pi\)
−0.325815 + 0.945433i \(0.605639\pi\)
\(54\) 0 0
\(55\) −1.37277 + 6.31717i −0.185104 + 0.851808i
\(56\) 0.101275 + 0.963571i 0.0135335 + 0.128763i
\(57\) 0 0
\(58\) −4.69792 2.09165i −0.616867 0.274647i
\(59\) −3.46632 + 3.84974i −0.451276 + 0.501193i −0.925256 0.379342i \(-0.876150\pi\)
0.473980 + 0.880536i \(0.342817\pi\)
\(60\) 0 0
\(61\) −4.95936 5.50792i −0.634980 0.705217i 0.336674 0.941621i \(-0.390698\pi\)
−0.971655 + 0.236404i \(0.924031\pi\)
\(62\) 3.19295 + 9.82688i 0.405505 + 1.24801i
\(63\) 0 0
\(64\) 2.71365 8.35176i 0.339207 1.04397i
\(65\) −14.5101 1.59172i −1.79975 0.197428i
\(66\) 0 0
\(67\) −2.27694 1.01376i −0.278173 0.123851i 0.262908 0.964821i \(-0.415318\pi\)
−0.541081 + 0.840970i \(0.681985\pi\)
\(68\) 0.284062 + 0.492010i 0.0344476 + 0.0596649i
\(69\) 0 0
\(70\) 0.621810 + 0.565014i 0.0743205 + 0.0675321i
\(71\) −9.63629 7.00118i −1.14362 0.830887i −0.155999 0.987757i \(-0.549860\pi\)
−0.987619 + 0.156870i \(0.949860\pi\)
\(72\) 0 0
\(73\) −0.283594 + 0.872814i −0.0331922 + 0.102155i −0.966280 0.257493i \(-0.917103\pi\)
0.933088 + 0.359649i \(0.117103\pi\)
\(74\) 0.0142504 0.0246825i 0.00165658 0.00286928i
\(75\) 0 0
\(76\) 2.10413 + 3.64447i 0.241361 + 0.418049i
\(77\) −0.891228 + 0.189436i −0.101565 + 0.0215883i
\(78\) 0 0
\(79\) −10.3980 + 4.62948i −1.16986 + 0.520857i −0.897361 0.441298i \(-0.854518\pi\)
−0.272503 + 0.962155i \(0.587851\pi\)
\(80\) −2.25770 5.13348i −0.252418 0.573940i
\(81\) 0 0
\(82\) 5.46212 0.603191
\(83\) −1.03926 9.88793i −0.114074 1.08534i −0.890453 0.455075i \(-0.849612\pi\)
0.776379 0.630266i \(-0.217054\pi\)
\(84\) 0 0
\(85\) 2.08497 + 0.687930i 0.226147 + 0.0746165i
\(86\) 3.13929 0.667278i 0.338519 0.0719544i
\(87\) 0 0
\(88\) 8.69369 + 1.84790i 0.926750 + 0.196987i
\(89\) −3.78718 + 11.6557i −0.401440 + 1.23551i 0.522391 + 0.852706i \(0.325040\pi\)
−0.923831 + 0.382800i \(0.874960\pi\)
\(90\) 0 0
\(91\) −0.635757 1.95666i −0.0666455 0.205114i
\(92\) 0.0792106 + 0.753639i 0.00825828 + 0.0785723i
\(93\) 0 0
\(94\) −5.67808 2.52804i −0.585649 0.260748i
\(95\) 15.4440 + 5.09571i 1.58452 + 0.522809i
\(96\) 0 0
\(97\) −6.75362 + 3.00691i −0.685726 + 0.305305i −0.719867 0.694112i \(-0.755797\pi\)
0.0341407 + 0.999417i \(0.489131\pi\)
\(98\) 2.54232 7.82445i 0.256813 0.790389i
\(99\) 0 0
\(100\) 2.63216 + 1.20067i 0.263216 + 0.120067i
\(101\) 5.77262 9.99848i 0.574397 0.994885i −0.421709 0.906731i \(-0.638570\pi\)
0.996107 0.0881544i \(-0.0280969\pi\)
\(102\) 0 0
\(103\) 1.71092 16.2783i 0.168582 1.60395i −0.503851 0.863790i \(-0.668084\pi\)
0.672433 0.740158i \(-0.265249\pi\)
\(104\) −2.09778 + 19.9590i −0.205704 + 1.95714i
\(105\) 0 0
\(106\) −0.530057 5.04315i −0.0514837 0.489834i
\(107\) 10.1611 0.982314 0.491157 0.871071i \(-0.336574\pi\)
0.491157 + 0.871071i \(0.336574\pi\)
\(108\) 0 0
\(109\) 3.42411 + 10.5383i 0.327970 + 1.00939i 0.970082 + 0.242777i \(0.0780584\pi\)
−0.642112 + 0.766611i \(0.721942\pi\)
\(110\) 6.69209 3.82327i 0.638065 0.364534i
\(111\) 0 0
\(112\) 0.528885 0.587387i 0.0499750 0.0555028i
\(113\) 9.81486 10.9005i 0.923305 1.02543i −0.0762934 0.997085i \(-0.524309\pi\)
0.999598 0.0283484i \(-0.00902478\pi\)
\(114\) 0 0
\(115\) 2.16738 + 1.96941i 0.202109 + 0.183648i
\(116\) −0.771242 2.37364i −0.0716080 0.220387i
\(117\) 0 0
\(118\) 6.17609 0.568555
\(119\) 0.0323456 + 0.307748i 0.00296512 + 0.0282112i
\(120\) 0 0
\(121\) 0.276140 2.62729i 0.0251036 0.238845i
\(122\) −0.923645 + 8.78789i −0.0836229 + 0.795618i
\(123\) 0 0
\(124\) −2.50733 + 4.34283i −0.225165 + 0.389998i
\(125\) 10.6792 3.30976i 0.955178 0.296034i
\(126\) 0 0
\(127\) 4.75644 14.6388i 0.422066 1.29899i −0.483710 0.875228i \(-0.660711\pi\)
0.905776 0.423757i \(-0.139289\pi\)
\(128\) −3.79357 + 1.68900i −0.335307 + 0.149288i
\(129\) 0 0
\(130\) 10.1652 + 14.1256i 0.891544 + 1.23890i
\(131\) −3.04960 1.35777i −0.266445 0.118629i 0.269166 0.963094i \(-0.413252\pi\)
−0.535611 + 0.844465i \(0.679919\pi\)
\(132\) 0 0
\(133\) 0.239594 + 2.27959i 0.0207754 + 0.197665i
\(134\) 0.918249 + 2.82608i 0.0793247 + 0.244136i
\(135\) 0 0
\(136\) 0.932779 2.87080i 0.0799851 0.246169i
\(137\) −8.26092 1.75591i −0.705778 0.150018i −0.158979 0.987282i \(-0.550820\pi\)
−0.546799 + 0.837264i \(0.684154\pi\)
\(138\) 0 0
\(139\) 1.39912 0.297391i 0.118671 0.0252244i −0.148193 0.988958i \(-0.547346\pi\)
0.266864 + 0.963734i \(0.414012\pi\)
\(140\) −0.00185147 + 0.407752i −0.000156477 + 0.0344613i
\(141\) 0 0
\(142\) 1.48437 + 14.1229i 0.124566 + 1.18516i
\(143\) −18.8729 −1.57823
\(144\) 0 0
\(145\) −8.33087 4.86040i −0.691841 0.403634i
\(146\) 0.999543 0.445025i 0.0827228 0.0368305i
\(147\) 0 0
\(148\) 0.0135299 0.00287587i 0.00111215 0.000236395i
\(149\) −10.3534 17.9326i −0.848181 1.46909i −0.882830 0.469693i \(-0.844365\pi\)
0.0346486 0.999400i \(-0.488969\pi\)
\(150\) 0 0
\(151\) 10.6562 18.4570i 0.867186 1.50201i 0.00232675 0.999997i \(-0.499259\pi\)
0.864860 0.502014i \(-0.167407\pi\)
\(152\) 6.90938 21.2649i 0.560425 1.72481i
\(153\) 0 0
\(154\) 0.878816 + 0.638497i 0.0708170 + 0.0514516i
\(155\) 3.94307 + 18.9739i 0.316715 + 1.52402i
\(156\) 0 0
\(157\) −6.98186 12.0929i −0.557213 0.965122i −0.997728 0.0673760i \(-0.978537\pi\)
0.440514 0.897746i \(-0.354796\pi\)
\(158\) 12.3967 + 5.51935i 0.986226 + 0.439096i
\(159\) 0 0
\(160\) 2.90188 6.43889i 0.229414 0.509039i
\(161\) −0.127547 + 0.392548i −0.0100521 + 0.0309371i
\(162\) 0 0
\(163\) −0.190245 0.585515i −0.0149012 0.0458611i 0.943329 0.331858i \(-0.107675\pi\)
−0.958231 + 0.285997i \(0.907675\pi\)
\(164\) 1.77380 + 1.97001i 0.138511 + 0.153832i
\(165\) 0 0
\(166\) −7.93155 + 8.80888i −0.615608 + 0.683702i
\(167\) 4.93325 + 2.19642i 0.381746 + 0.169964i 0.588633 0.808401i \(-0.299666\pi\)
−0.206887 + 0.978365i \(0.566333\pi\)
\(168\) 0 0
\(169\) −3.09563 29.4529i −0.238125 2.26561i
\(170\) −1.05378 2.39606i −0.0808216 0.183769i
\(171\) 0 0
\(172\) 1.26014 + 0.915544i 0.0960846 + 0.0698096i
\(173\) 0.243366 + 0.270286i 0.0185028 + 0.0205494i 0.752325 0.658792i \(-0.228932\pi\)
−0.733822 + 0.679341i \(0.762266\pi\)
\(174\) 0 0
\(175\) 1.04373 + 1.18056i 0.0788984 + 0.0892422i
\(176\) −3.62536 6.27931i −0.273272 0.473321i
\(177\) 0 0
\(178\) 13.3481 5.94296i 1.00048 0.445444i
\(179\) −12.2855 8.92591i −0.918259 0.667154i 0.0248313 0.999692i \(-0.492095\pi\)
−0.943090 + 0.332538i \(0.892095\pi\)
\(180\) 0 0
\(181\) 0.0462635 0.0336124i 0.00343874 0.00249839i −0.586065 0.810264i \(-0.699324\pi\)
0.589503 + 0.807766i \(0.299324\pi\)
\(182\) −1.22641 + 2.12420i −0.0909074 + 0.157456i
\(183\) 0 0
\(184\) 2.69410 2.99210i 0.198611 0.220580i
\(185\) 0.0316160 0.0431027i 0.00232445 0.00316898i
\(186\) 0 0
\(187\) 2.77662 + 0.590188i 0.203046 + 0.0431588i
\(188\) −0.932151 2.86887i −0.0679841 0.209234i
\(189\) 0 0
\(190\) −7.80571 17.7484i −0.566286 1.28760i
\(191\) 2.34418 + 0.498271i 0.169619 + 0.0360536i 0.291938 0.956437i \(-0.405700\pi\)
−0.122319 + 0.992491i \(0.539033\pi\)
\(192\) 0 0
\(193\) 2.94773 + 5.10562i 0.212182 + 0.367511i 0.952397 0.304860i \(-0.0986095\pi\)
−0.740215 + 0.672370i \(0.765276\pi\)
\(194\) 8.05179 + 3.58489i 0.578085 + 0.257380i
\(195\) 0 0
\(196\) 3.64763 1.62403i 0.260545 0.116002i
\(197\) 12.8434 + 9.33130i 0.915057 + 0.664828i 0.942289 0.334801i \(-0.108669\pi\)
−0.0272318 + 0.999629i \(0.508669\pi\)
\(198\) 0 0
\(199\) 4.61006 0.326798 0.163399 0.986560i \(-0.447754\pi\)
0.163399 + 0.986560i \(0.447754\pi\)
\(200\) −4.61706 14.6616i −0.326475 1.03673i
\(201\) 0 0
\(202\) −13.4637 + 2.86179i −0.947301 + 0.201355i
\(203\) 0.142096 1.35195i 0.00997316 0.0948882i
\(204\) 0 0
\(205\) 10.1834 + 1.11709i 0.711240 + 0.0780211i
\(206\) −15.7873 + 11.4702i −1.09995 + 0.799164i
\(207\) 0 0
\(208\) 13.2453 9.62331i 0.918400 0.667256i
\(209\) 20.5673 + 4.37170i 1.42267 + 0.302397i
\(210\) 0 0
\(211\) −0.144843 + 0.0307873i −0.00997140 + 0.00211949i −0.212895 0.977075i \(-0.568289\pi\)
0.202923 + 0.979195i \(0.434956\pi\)
\(212\) 1.64676 1.82892i 0.113100 0.125611i
\(213\) 0 0
\(214\) −8.10605 9.00268i −0.554118 0.615410i
\(215\) 5.98927 0.602015i 0.408465 0.0410571i
\(216\) 0 0
\(217\) −2.20972 + 1.60546i −0.150006 + 0.108986i
\(218\) 6.60528 11.4407i 0.447366 0.774861i
\(219\) 0 0
\(220\) 3.55215 + 1.17202i 0.239486 + 0.0790178i
\(221\) −0.669994 + 6.37456i −0.0450686 + 0.428800i
\(222\) 0 0
\(223\) −1.10187 1.22375i −0.0737867 0.0819485i 0.705121 0.709087i \(-0.250893\pi\)
−0.778908 + 0.627139i \(0.784226\pi\)
\(224\) 0.995419 0.0665092
\(225\) 0 0
\(226\) −17.4876 −1.16326
\(227\) 2.45055 + 2.72161i 0.162648 + 0.180639i 0.818960 0.573851i \(-0.194551\pi\)
−0.656312 + 0.754490i \(0.727884\pi\)
\(228\) 0 0
\(229\) 0.0884967 0.841990i 0.00584803 0.0556403i −0.991209 0.132308i \(-0.957761\pi\)
0.997057 + 0.0766674i \(0.0244280\pi\)
\(230\) 0.0158532 3.49138i 0.00104533 0.230214i
\(231\) 0 0
\(232\) −6.63027 + 11.4840i −0.435299 + 0.753960i
\(233\) −9.04329 + 6.57033i −0.592445 + 0.430437i −0.843189 0.537617i \(-0.819325\pi\)
0.250744 + 0.968053i \(0.419325\pi\)
\(234\) 0 0
\(235\) −10.0690 5.87446i −0.656829 0.383207i
\(236\) 2.00566 + 2.22751i 0.130557 + 0.144999i
\(237\) 0 0
\(238\) 0.246858 0.274164i 0.0160015 0.0177714i
\(239\) −15.9775 + 3.39613i −1.03350 + 0.219677i −0.693280 0.720669i \(-0.743835\pi\)
−0.340220 + 0.940346i \(0.610502\pi\)
\(240\) 0 0
\(241\) −2.04979 0.435696i −0.132038 0.0280656i 0.141418 0.989950i \(-0.454834\pi\)
−0.273457 + 0.961884i \(0.588167\pi\)
\(242\) −2.54805 + 1.85127i −0.163795 + 0.119004i
\(243\) 0 0
\(244\) −3.46945 + 2.52070i −0.222109 + 0.161372i
\(245\) 6.34004 14.0677i 0.405050 0.898753i
\(246\) 0 0
\(247\) −4.96285 + 47.2184i −0.315779 + 3.00443i
\(248\) 26.0615 5.53955i 1.65491 0.351762i
\(249\) 0 0
\(250\) −11.4518 6.82133i −0.724273 0.431419i
\(251\) 15.8673 1.00154 0.500769 0.865581i \(-0.333051\pi\)
0.500769 + 0.865581i \(0.333051\pi\)
\(252\) 0 0
\(253\) 3.06320 + 2.22554i 0.192582 + 0.139919i
\(254\) −16.7643 + 7.46396i −1.05189 + 0.468330i
\(255\) 0 0
\(256\) −11.5220 5.12990i −0.720122 0.320619i
\(257\) 1.09760 + 1.90109i 0.0684661 + 0.118587i 0.898226 0.439533i \(-0.144856\pi\)
−0.829760 + 0.558120i \(0.811523\pi\)
\(258\) 0 0
\(259\) 0.00736942 + 0.00156642i 0.000457913 + 9.73325e-5i
\(260\) −1.79354 + 8.25347i −0.111230 + 0.511858i
\(261\) 0 0
\(262\) 1.22985 + 3.78508i 0.0759801 + 0.233843i
\(263\) −29.0145 6.16721i −1.78911 0.380287i −0.810454 0.585802i \(-0.800780\pi\)
−0.978654 + 0.205515i \(0.934113\pi\)
\(264\) 0 0
\(265\) 0.0431849 9.51070i 0.00265283 0.584237i
\(266\) 1.82856 2.03082i 0.112116 0.124517i
\(267\) 0 0
\(268\) −0.721076 + 1.24894i −0.0440467 + 0.0762912i
\(269\) 20.4742 14.8754i 1.24833 0.906968i 0.250210 0.968192i \(-0.419500\pi\)
0.998124 + 0.0612238i \(0.0195003\pi\)
\(270\) 0 0
\(271\) −15.2201 11.0580i −0.924555 0.671728i 0.0200987 0.999798i \(-0.493602\pi\)
−0.944654 + 0.328070i \(0.893602\pi\)
\(272\) −2.24961 + 1.00159i −0.136403 + 0.0607305i
\(273\) 0 0
\(274\) 5.03443 + 8.71989i 0.304141 + 0.526788i
\(275\) 13.2584 5.75934i 0.799513 0.347301i
\(276\) 0 0
\(277\) 15.1456 + 16.8209i 0.910012 + 1.01067i 0.999892 + 0.0147182i \(0.00468511\pi\)
−0.0898796 + 0.995953i \(0.528648\pi\)
\(278\) −1.37963 1.00236i −0.0827447 0.0601176i
\(279\) 0 0
\(280\) 1.61657 1.44233i 0.0966087 0.0861958i
\(281\) −0.0980168 0.932568i −0.00584719 0.0556323i 0.991209 0.132304i \(-0.0422374\pi\)
−0.997056 + 0.0766714i \(0.975571\pi\)
\(282\) 0 0
\(283\) 10.5924 + 4.71605i 0.629653 + 0.280340i 0.696648 0.717414i \(-0.254674\pi\)
−0.0669940 + 0.997753i \(0.521341\pi\)
\(284\) −4.61161 + 5.12171i −0.273648 + 0.303917i
\(285\) 0 0
\(286\) 15.0559 + 16.7213i 0.890273 + 0.988748i
\(287\) 0.446185 + 1.37322i 0.0263375 + 0.0810583i
\(288\) 0 0
\(289\) −4.95538 + 15.2511i −0.291493 + 0.897122i
\(290\) 2.33968 + 11.2585i 0.137391 + 0.661120i
\(291\) 0 0
\(292\) 0.485103 + 0.215982i 0.0283885 + 0.0126394i
\(293\) −11.8547 20.5330i −0.692561 1.19955i −0.970996 0.239096i \(-0.923149\pi\)
0.278435 0.960455i \(-0.410184\pi\)
\(294\) 0 0
\(295\) 11.5145 + 1.26311i 0.670400 + 0.0735411i
\(296\) −0.0594568 0.0431979i −0.00345586 0.00251083i
\(297\) 0 0
\(298\) −7.62869 + 23.4787i −0.441918 + 1.36008i
\(299\) −4.27476 + 7.40411i −0.247216 + 0.428190i
\(300\) 0 0
\(301\) 0.424198 + 0.734732i 0.0244504 + 0.0423493i
\(302\) −24.8537 + 5.28282i −1.43017 + 0.303992i
\(303\) 0 0
\(304\) −16.6636 + 7.41911i −0.955722 + 0.425515i
\(305\) −3.51928 + 16.1950i −0.201513 + 0.927321i
\(306\) 0 0
\(307\) −12.6269 −0.720652 −0.360326 0.932826i \(-0.617335\pi\)
−0.360326 + 0.932826i \(0.617335\pi\)
\(308\) 0.0551071 + 0.524309i 0.00314002 + 0.0298753i
\(309\) 0 0
\(310\) 13.6651 18.6300i 0.776128 1.05811i
\(311\) −13.8540 + 2.94477i −0.785590 + 0.166982i −0.583207 0.812324i \(-0.698202\pi\)
−0.202384 + 0.979306i \(0.564869\pi\)
\(312\) 0 0
\(313\) −2.73979 0.582360i −0.154862 0.0329169i 0.129828 0.991537i \(-0.458557\pi\)
−0.284690 + 0.958620i \(0.591891\pi\)
\(314\) −5.14446 + 15.8330i −0.290319 + 0.893509i
\(315\) 0 0
\(316\) 2.03512 + 6.26345i 0.114484 + 0.352347i
\(317\) 3.11752 + 29.6613i 0.175098 + 1.66594i 0.630902 + 0.775862i \(0.282685\pi\)
−0.455805 + 0.890080i \(0.650649\pi\)
\(318\) 0 0
\(319\) −11.3922 5.07212i −0.637839 0.283984i
\(320\) −18.7025 + 5.98305i −1.04550 + 0.334463i
\(321\) 0 0
\(322\) 0.449545 0.200150i 0.0250522 0.0111539i
\(323\) 2.20674 6.79164i 0.122786 0.377897i
\(324\) 0 0
\(325\) 16.0627 + 28.4142i 0.890998 + 1.57614i
\(326\) −0.366993 + 0.635650i −0.0203259 + 0.0352054i
\(327\) 0 0
\(328\) 1.47225 14.0075i 0.0812916 0.773437i
\(329\) 0.171742 1.63402i 0.00946844 0.0900862i
\(330\) 0 0
\(331\) 2.12974 + 20.2631i 0.117061 + 1.11376i 0.882519 + 0.470277i \(0.155846\pi\)
−0.765458 + 0.643486i \(0.777487\pi\)
\(332\) −5.75281 −0.315726
\(333\) 0 0
\(334\) −1.98949 6.12301i −0.108860 0.335036i
\(335\) 1.13398 + 5.45665i 0.0619557 + 0.298129i
\(336\) 0 0
\(337\) 17.7807 19.7475i 0.968576 1.07571i −0.0285223 0.999593i \(-0.509080\pi\)
0.997099 0.0761198i \(-0.0242532\pi\)
\(338\) −23.6255 + 26.2388i −1.28506 + 1.42720i
\(339\) 0 0
\(340\) 0.521967 1.15818i 0.0283077 0.0628109i
\(341\) 7.74271 + 23.8296i 0.419291 + 1.29045i
\(342\) 0 0
\(343\) 4.38089 0.236546
\(344\) −0.865065 8.23054i −0.0466412 0.443761i
\(345\) 0 0
\(346\) 0.0453252 0.431241i 0.00243670 0.0231837i
\(347\) 2.14059 20.3664i 0.114913 1.09332i −0.773347 0.633983i \(-0.781419\pi\)
0.888260 0.459341i \(-0.151914\pi\)
\(348\) 0 0
\(349\) 2.88806 5.00227i 0.154594 0.267766i −0.778317 0.627872i \(-0.783926\pi\)
0.932911 + 0.360106i \(0.117260\pi\)
\(350\) 0.213335 1.86653i 0.0114032 0.0997701i
\(351\) 0 0
\(352\) 2.82175 8.68445i 0.150400 0.462883i
\(353\) −12.6340 + 5.62502i −0.672440 + 0.299390i −0.714408 0.699729i \(-0.753304\pi\)
0.0419678 + 0.999119i \(0.486637\pi\)
\(354\) 0 0
\(355\) −0.120935 + 26.6338i −0.00641857 + 1.41357i
\(356\) 6.47817 + 2.88427i 0.343342 + 0.152866i
\(357\) 0 0
\(358\) 1.89245 + 18.0055i 0.100019 + 0.951618i
\(359\) −0.158269 0.487102i −0.00835313 0.0257083i 0.946793 0.321843i \(-0.104302\pi\)
−0.955146 + 0.296135i \(0.904302\pi\)
\(360\) 0 0
\(361\) 10.4747 32.2377i 0.551299 1.69672i
\(362\) −0.0666870 0.0141748i −0.00350499 0.000745008i
\(363\) 0 0
\(364\) −1.16440 + 0.247501i −0.0610311 + 0.0129726i
\(365\) 1.95453 0.625268i 0.102305 0.0327280i
\(366\) 0 0
\(367\) 2.04367 + 19.4442i 0.106679 + 1.01498i 0.908633 + 0.417595i \(0.137127\pi\)
−0.801955 + 0.597385i \(0.796207\pi\)
\(368\) −3.28461 −0.171222
\(369\) 0 0
\(370\) −0.0634103 + 0.00637373i −0.00329655 + 0.000331354i
\(371\) 1.22458 0.545220i 0.0635773 0.0283064i
\(372\) 0 0
\(373\) −24.2570 + 5.15599i −1.25598 + 0.266967i −0.787394 0.616450i \(-0.788570\pi\)
−0.468587 + 0.883417i \(0.655237\pi\)
\(374\) −1.69214 2.93088i −0.0874987 0.151552i
\(375\) 0 0
\(376\) −8.01359 + 13.8800i −0.413270 + 0.715804i
\(377\) 8.70129 26.7798i 0.448139 1.37923i
\(378\) 0 0
\(379\) 15.1691 + 11.0210i 0.779184 + 0.566110i 0.904734 0.425977i \(-0.140070\pi\)
−0.125550 + 0.992087i \(0.540070\pi\)
\(380\) 3.86637 8.57897i 0.198341 0.440092i
\(381\) 0 0
\(382\) −1.42861 2.47442i −0.0730938 0.126602i
\(383\) −5.00833 2.22985i −0.255914 0.113940i 0.274770 0.961510i \(-0.411398\pi\)
−0.530684 + 0.847570i \(0.678065\pi\)
\(384\) 0 0
\(385\) 1.50785 + 1.37013i 0.0768473 + 0.0698280i
\(386\) 2.17198 6.68468i 0.110551 0.340241i
\(387\) 0 0
\(388\) 1.32184 + 4.06819i 0.0671061 + 0.206531i
\(389\) 1.04925 + 1.16531i 0.0531990 + 0.0590835i 0.769157 0.639060i \(-0.220676\pi\)
−0.715958 + 0.698143i \(0.754010\pi\)
\(390\) 0 0
\(391\) 0.860448 0.955625i 0.0435148 0.0483280i
\(392\) −19.3805 8.62874i −0.978861 0.435817i
\(393\) 0 0
\(394\) −1.97840 18.8232i −0.0996704 0.948300i
\(395\) 21.9831 + 12.8254i 1.10609 + 0.645317i
\(396\) 0 0
\(397\) 7.83333 + 5.69125i 0.393143 + 0.285635i 0.766742 0.641955i \(-0.221876\pi\)
−0.373599 + 0.927590i \(0.621876\pi\)
\(398\) −3.67768 4.08447i −0.184345 0.204736i
\(399\) 0 0
\(400\) −6.36831 + 10.8025i −0.318415 + 0.540124i
\(401\) 0.505309 + 0.875221i 0.0252339 + 0.0437064i 0.878367 0.477988i \(-0.158634\pi\)
−0.853133 + 0.521694i \(0.825300\pi\)
\(402\) 0 0
\(403\) −51.6851 + 23.0117i −2.57462 + 1.14629i
\(404\) −5.40443 3.92655i −0.268880 0.195353i
\(405\) 0 0
\(406\) −1.31117 + 0.952622i −0.0650724 + 0.0472779i
\(407\) 0.0345565 0.0598535i 0.00171290 0.00296683i
\(408\) 0 0
\(409\) 5.36444 5.95782i 0.265255 0.294595i −0.595773 0.803153i \(-0.703154\pi\)
0.861028 + 0.508557i \(0.169821\pi\)
\(410\) −7.13408 9.91357i −0.352327 0.489596i
\(411\) 0 0
\(412\) −9.26377 1.96908i −0.456393 0.0970094i
\(413\) 0.504507 + 1.55271i 0.0248251 + 0.0764040i
\(414\) 0 0
\(415\) −16.5889 + 14.8009i −0.814316 + 0.726546i
\(416\) 20.1681 + 4.28687i 0.988823 + 0.210181i
\(417\) 0 0
\(418\) −12.5342 21.7099i −0.613070 1.06187i
\(419\) −22.8670 10.1810i −1.11713 0.497377i −0.236711 0.971580i \(-0.576069\pi\)
−0.880415 + 0.474204i \(0.842736\pi\)
\(420\) 0 0
\(421\) 30.1379 13.4182i 1.46883 0.653965i 0.492512 0.870305i \(-0.336079\pi\)
0.976318 + 0.216340i \(0.0694120\pi\)
\(422\) 0.142826 + 0.103769i 0.00695265 + 0.00505140i
\(423\) 0 0
\(424\) −13.0760 −0.635026
\(425\) −1.47461 4.68265i −0.0715291 0.227142i
\(426\) 0 0
\(427\) −2.28479 + 0.485646i −0.110569 + 0.0235021i
\(428\) 0.614562 5.84717i 0.0297060 0.282633i
\(429\) 0 0
\(430\) −5.31132 4.82618i −0.256135 0.232739i
\(431\) −4.71468 + 3.42542i −0.227098 + 0.164997i −0.695516 0.718511i \(-0.744824\pi\)
0.468418 + 0.883507i \(0.344824\pi\)
\(432\) 0 0
\(433\) −1.68629 + 1.22516i −0.0810381 + 0.0588776i −0.627567 0.778563i \(-0.715949\pi\)
0.546529 + 0.837440i \(0.315949\pi\)
\(434\) 3.18523 + 0.677041i 0.152896 + 0.0324990i
\(435\) 0 0
\(436\) 6.27131 1.33301i 0.300341 0.0638395i
\(437\) 6.37361 7.07861i 0.304891 0.338616i
\(438\) 0 0
\(439\) 15.2474 + 16.9340i 0.727721 + 0.808216i 0.987528 0.157445i \(-0.0503256\pi\)
−0.259807 + 0.965661i \(0.583659\pi\)
\(440\) −8.00095 18.1923i −0.381430 0.867284i
\(441\) 0 0
\(442\) 6.18230 4.49170i 0.294062 0.213648i
\(443\) −4.50211 + 7.79787i −0.213901 + 0.370488i −0.952932 0.303184i \(-0.901950\pi\)
0.739031 + 0.673672i \(0.235284\pi\)
\(444\) 0 0
\(445\) 26.1012 8.34996i 1.23732 0.395826i
\(446\) −0.205216 + 1.95250i −0.00971724 + 0.0924534i
\(447\) 0 0
\(448\) −1.85187 2.05671i −0.0874925 0.0971702i
\(449\) 2.14345 0.101156 0.0505779 0.998720i \(-0.483894\pi\)
0.0505779 + 0.998720i \(0.483894\pi\)
\(450\) 0 0
\(451\) 13.2453 0.623698
\(452\) −5.67902 6.30719i −0.267118 0.296665i
\(453\) 0 0
\(454\) 0.456397 4.34233i 0.0214198 0.203795i
\(455\) −2.72091 + 3.70947i −0.127558 + 0.173903i
\(456\) 0 0
\(457\) 9.78295 16.9446i 0.457627 0.792634i −0.541208 0.840889i \(-0.682033\pi\)
0.998835 + 0.0482552i \(0.0153661\pi\)
\(458\) −0.816594 + 0.593290i −0.0381569 + 0.0277226i
\(459\) 0 0
\(460\) 1.26437 1.12809i 0.0589516 0.0525976i
\(461\) 2.55207 + 2.83436i 0.118862 + 0.132009i 0.799639 0.600482i \(-0.205024\pi\)
−0.680777 + 0.732491i \(0.738358\pi\)
\(462\) 0 0
\(463\) 6.05576 6.72560i 0.281435 0.312565i −0.585808 0.810450i \(-0.699223\pi\)
0.867243 + 0.497884i \(0.165890\pi\)
\(464\) 10.5815 2.24917i 0.491234 0.104415i
\(465\) 0 0
\(466\) 13.0355 + 2.77079i 0.603860 + 0.128354i
\(467\) −24.8972 + 18.0889i −1.15211 + 0.837053i −0.988759 0.149515i \(-0.952229\pi\)
−0.163346 + 0.986569i \(0.552229\pi\)
\(468\) 0 0
\(469\) −0.635487 + 0.461708i −0.0293441 + 0.0213197i
\(470\) 2.82782 + 13.6074i 0.130438 + 0.627662i
\(471\) 0 0
\(472\) 1.66469 15.8385i 0.0766238 0.729027i
\(473\) 7.61260 1.61811i 0.350028 0.0744007i
\(474\) 0 0
\(475\) −10.9229 34.6859i −0.501177 1.59150i
\(476\) 0.179048 0.00820666
\(477\) 0 0
\(478\) 15.7550 + 11.4467i 0.720617 + 0.523559i
\(479\) −11.2505 + 5.00905i −0.514049 + 0.228870i −0.647331 0.762209i \(-0.724115\pi\)
0.133282 + 0.991078i \(0.457448\pi\)
\(480\) 0 0
\(481\) 0.142565 + 0.0634742i 0.00650042 + 0.00289417i
\(482\) 1.24920 + 2.16367i 0.0568993 + 0.0985524i
\(483\) 0 0
\(484\) −1.49516 0.317806i −0.0679618 0.0144457i
\(485\) 14.2783 + 8.33027i 0.648346 + 0.378258i
\(486\) 0 0
\(487\) 1.53444 + 4.72251i 0.0695320 + 0.213997i 0.979784 0.200056i \(-0.0641125\pi\)
−0.910252 + 0.414054i \(0.864113\pi\)
\(488\) 22.2875 + 4.73735i 1.00891 + 0.214450i
\(489\) 0 0
\(490\) −17.5216 + 5.60530i −0.791547 + 0.253221i
\(491\) 12.7546 14.1654i 0.575605 0.639274i −0.383090 0.923711i \(-0.625140\pi\)
0.958695 + 0.284437i \(0.0918066\pi\)
\(492\) 0 0
\(493\) −2.11760 + 3.66778i −0.0953718 + 0.165189i
\(494\) 45.7942 33.2714i 2.06038 1.49695i
\(495\) 0 0
\(496\) −17.5847 12.7760i −0.789576 0.573660i
\(497\) −3.42933 + 1.52684i −0.153827 + 0.0684880i
\(498\) 0 0
\(499\) −2.50922 4.34610i −0.112328 0.194558i 0.804380 0.594115i \(-0.202497\pi\)
−0.916709 + 0.399557i \(0.869164\pi\)
\(500\) −1.25868 6.34547i −0.0562900 0.283778i
\(501\) 0 0
\(502\) −12.6582 14.0583i −0.564962 0.627453i
\(503\) 5.48055 + 3.98186i 0.244366 + 0.177542i 0.703226 0.710966i \(-0.251742\pi\)
−0.458860 + 0.888508i \(0.651742\pi\)
\(504\) 0 0
\(505\) −25.6865 + 2.58190i −1.14304 + 0.114893i
\(506\) −0.471854 4.48939i −0.0209765 0.199578i
\(507\) 0 0
\(508\) −8.13615 3.62245i −0.360983 0.160720i
\(509\) 6.65406 7.39008i 0.294936 0.327559i −0.577405 0.816458i \(-0.695935\pi\)
0.872341 + 0.488899i \(0.162601\pi\)
\(510\) 0 0
\(511\) 0.193532 + 0.214939i 0.00856136 + 0.00950835i
\(512\) 7.21302 + 22.1994i 0.318774 + 0.981084i
\(513\) 0 0
\(514\) 0.808743 2.48906i 0.0356721 0.109788i
\(515\) −31.7792 + 18.1558i −1.40036 + 0.800041i
\(516\) 0 0
\(517\) −13.7690 6.13035i −0.605560 0.269613i
\(518\) −0.00449112 0.00777885i −0.000197329 0.000341783i
\(519\) 0 0
\(520\) 38.9648 22.2611i 1.70872 0.976212i
\(521\) −15.4969 11.2591i −0.678930 0.493272i 0.194072 0.980987i \(-0.437830\pi\)
−0.873003 + 0.487715i \(0.837830\pi\)
\(522\) 0 0
\(523\) 0.0808887 0.248950i 0.00353702 0.0108858i −0.949272 0.314455i \(-0.898178\pi\)
0.952809 + 0.303569i \(0.0981783\pi\)
\(524\) −0.965764 + 1.67275i −0.0421896 + 0.0730745i
\(525\) 0 0
\(526\) 17.6822 + 30.6265i 0.770980 + 1.33538i
\(527\) 8.32361 1.76924i 0.362582 0.0770692i
\(528\) 0 0
\(529\) −19.4446 + 8.65730i −0.845418 + 0.376404i
\(530\) −8.46084 + 7.54890i −0.367516 + 0.327903i
\(531\) 0 0
\(532\) 1.32626 0.0575009
\(533\) 3.12624 + 29.7442i 0.135412 + 1.28836i
\(534\) 0 0
\(535\) −13.2715 18.4421i −0.573775 0.797322i
\(536\) 7.49495 1.59310i 0.323733 0.0688115i
\(537\) 0 0
\(538\) −29.5128 6.27313i −1.27239 0.270454i
\(539\) 6.16497 18.9738i 0.265544 0.817261i
\(540\) 0 0
\(541\) 6.23922 + 19.2023i 0.268245 + 0.825573i 0.990928 + 0.134394i \(0.0429087\pi\)
−0.722683 + 0.691180i \(0.757091\pi\)
\(542\) 2.34450 + 22.3064i 0.100705 + 0.958143i
\(543\) 0 0
\(544\) −2.83311 1.26138i −0.121468 0.0540813i
\(545\) 14.6545 19.9787i 0.627729 0.855795i
\(546\) 0 0
\(547\) −6.86422 + 3.05615i −0.293493 + 0.130671i −0.548201 0.836346i \(-0.684687\pi\)
0.254708 + 0.967018i \(0.418021\pi\)
\(548\) −1.51006 + 4.64750i −0.0645067 + 0.198531i
\(549\) 0 0
\(550\) −15.6796 7.15234i −0.668582 0.304977i
\(551\) −15.6857 + 27.1684i −0.668233 + 1.15741i
\(552\) 0 0
\(553\) −0.374956 + 3.56747i −0.0159447 + 0.151704i
\(554\) 2.82076 26.8378i 0.119843 1.14023i
\(555\) 0 0
\(556\) −0.0865112 0.823099i −0.00366889 0.0349072i
\(557\) −17.2753 −0.731980 −0.365990 0.930619i \(-0.619270\pi\)
−0.365990 + 0.930619i \(0.619270\pi\)
\(558\) 0 0
\(559\) 5.43045 + 16.7132i 0.229684 + 0.706894i
\(560\) −1.75686 0.192723i −0.0742411 0.00814404i
\(561\) 0 0
\(562\) −0.748054 + 0.830798i −0.0315548 + 0.0350451i
\(563\) −1.80844 + 2.00848i −0.0762167 + 0.0846473i −0.780047 0.625721i \(-0.784805\pi\)
0.703830 + 0.710368i \(0.251472\pi\)
\(564\) 0 0
\(565\) −32.6033 3.57649i −1.37163 0.150464i
\(566\) −4.27172 13.1470i −0.179554 0.552610i
\(567\) 0 0
\(568\) 36.6180 1.53646
\(569\) −4.46837 42.5137i −0.187324 1.78227i −0.535201 0.844725i \(-0.679764\pi\)
0.347877 0.937540i \(-0.386903\pi\)
\(570\) 0 0
\(571\) −3.16839 + 30.1452i −0.132593 + 1.26154i 0.702601 + 0.711584i \(0.252022\pi\)
−0.835194 + 0.549955i \(0.814645\pi\)
\(572\) −1.14147 + 10.8603i −0.0477271 + 0.454093i
\(573\) 0 0
\(574\) 0.860713 1.49080i 0.0359255 0.0622247i
\(575\) 0.743598 6.50596i 0.0310102 0.271317i
\(576\) 0 0
\(577\) 11.8163 36.3667i 0.491917 1.51396i −0.329790 0.944054i \(-0.606978\pi\)
0.821707 0.569910i \(-0.193022\pi\)
\(578\) 17.4655 7.77613i 0.726468 0.323444i
\(579\) 0 0
\(580\) −3.30075 + 4.49999i −0.137056 + 0.186852i
\(581\) −2.86252 1.27448i −0.118757 0.0528741i
\(582\) 0 0
\(583\) −1.28536 12.2294i −0.0532340 0.506488i
\(584\) −0.871846 2.68327i −0.0360773 0.111034i
\(585\) 0 0
\(586\) −8.73494 + 26.8834i −0.360837 + 1.11054i
\(587\) 18.3047 + 3.89078i 0.755515 + 0.160590i 0.569539 0.821964i \(-0.307122\pi\)
0.185976 + 0.982554i \(0.440455\pi\)
\(588\) 0 0
\(589\) 61.6556 13.1053i 2.54047 0.539994i
\(590\) −8.06659 11.2094i −0.332096 0.461484i
\(591\) 0 0
\(592\) 0.00626701 + 0.0596266i 0.000257572 + 0.00245064i
\(593\) 42.4830 1.74457 0.872284 0.489000i \(-0.162638\pi\)
0.872284 + 0.489000i \(0.162638\pi\)
\(594\) 0 0
\(595\) 0.516306 0.460656i 0.0211665 0.0188851i
\(596\) −10.9454 + 4.87320i −0.448340 + 0.199614i
\(597\) 0 0
\(598\) 9.97017 2.11922i 0.407710 0.0866615i
\(599\) 22.9566 + 39.7621i 0.937983 + 1.62463i 0.769226 + 0.638977i \(0.220642\pi\)
0.168757 + 0.985658i \(0.446025\pi\)
\(600\) 0 0
\(601\) 13.8303 23.9548i 0.564150 0.977136i −0.432978 0.901404i \(-0.642537\pi\)
0.997128 0.0757320i \(-0.0241293\pi\)
\(602\) 0.312563 0.961968i 0.0127391 0.0392069i
\(603\) 0 0
\(604\) −9.97648 7.24834i −0.405937 0.294931i
\(605\) −5.12911 + 2.93032i −0.208528 + 0.119135i
\(606\) 0 0
\(607\) −7.77177 13.4611i −0.315446 0.546369i 0.664086 0.747656i \(-0.268821\pi\)
−0.979532 + 0.201287i \(0.935488\pi\)
\(608\) −20.9857 9.34344i −0.851083 0.378926i
\(609\) 0 0
\(610\) 17.1561 9.80148i 0.694630 0.396850i
\(611\) 10.5167 32.3671i 0.425460 1.30943i
\(612\) 0 0
\(613\) −12.9646 39.9011i −0.523637 1.61159i −0.766996 0.641652i \(-0.778249\pi\)
0.243359 0.969936i \(-0.421751\pi\)
\(614\) 10.0731 + 11.1873i 0.406516 + 0.451482i
\(615\) 0 0
\(616\) 1.87429 2.08161i 0.0755174 0.0838706i
\(617\) 8.46425 + 3.76852i 0.340758 + 0.151715i 0.569979 0.821659i \(-0.306951\pi\)
−0.229221 + 0.973374i \(0.573618\pi\)
\(618\) 0 0
\(619\) −1.08260 10.3002i −0.0435132 0.414001i −0.994497 0.104761i \(-0.966592\pi\)
0.950984 0.309240i \(-0.100074\pi\)
\(620\) 11.1569 1.12144i 0.448073 0.0450383i
\(621\) 0 0
\(622\) 13.6611 + 9.92537i 0.547760 + 0.397971i
\(623\) 2.58447 + 2.87034i 0.103545 + 0.114998i
\(624\) 0 0
\(625\) −19.9552 15.0595i −0.798208 0.602381i
\(626\) 1.66970 + 2.89201i 0.0667347 + 0.115588i
\(627\) 0 0
\(628\) −7.38109 + 3.28627i −0.294537 + 0.131136i
\(629\) −0.0189895 0.0137967i −0.000757161 0.000550110i
\(630\) 0 0
\(631\) 29.6450 21.5383i 1.18015 0.857428i 0.187960 0.982177i \(-0.439813\pi\)
0.992188 + 0.124749i \(0.0398126\pi\)
\(632\) 17.4957 30.3034i 0.695941 1.20541i
\(633\) 0 0
\(634\) 23.7926 26.4244i 0.944925 1.04945i
\(635\) −32.7814 + 10.4870i −1.30089 + 0.416163i
\(636\) 0 0
\(637\) 44.0634 + 9.36597i 1.74586 + 0.371093i
\(638\) 4.59425 + 14.1397i 0.181888 + 0.559794i
\(639\) 0 0
\(640\) 8.02026 + 4.67918i 0.317029 + 0.184961i
\(641\) −25.7650 5.47651i −1.01766 0.216309i −0.331261 0.943539i \(-0.607474\pi\)
−0.686394 + 0.727230i \(0.740807\pi\)
\(642\) 0 0
\(643\) 24.3415 + 42.1606i 0.959934 + 1.66265i 0.722651 + 0.691213i \(0.242923\pi\)
0.237282 + 0.971441i \(0.423743\pi\)
\(644\) 0.218175 + 0.0971380i 0.00859732 + 0.00382777i
\(645\) 0 0
\(646\) −7.77776 + 3.46288i −0.306012 + 0.136245i
\(647\) −10.6167 7.71348i −0.417386 0.303248i 0.359199 0.933261i \(-0.383050\pi\)
−0.776585 + 0.630012i \(0.783050\pi\)
\(648\) 0 0
\(649\) 14.9767 0.587885
\(650\) 12.3607 36.8989i 0.484828 1.44729i
\(651\) 0 0
\(652\) −0.348437 + 0.0740627i −0.0136459 + 0.00290052i
\(653\) −5.05266 + 48.0729i −0.197726 + 1.88124i 0.224109 + 0.974564i \(0.428053\pi\)
−0.421835 + 0.906673i \(0.638614\pi\)
\(654\) 0 0
\(655\) 1.51878 + 7.30830i 0.0593435 + 0.285559i
\(656\) −9.29580 + 6.75379i −0.362940 + 0.263691i
\(657\) 0 0
\(658\) −1.58473 + 1.15137i −0.0617792 + 0.0448853i
\(659\) 29.3437 + 6.23721i 1.14307 + 0.242967i 0.740263 0.672318i \(-0.234701\pi\)
0.402807 + 0.915285i \(0.368034\pi\)
\(660\) 0 0
\(661\) −11.7271 + 2.49266i −0.456130 + 0.0969533i −0.430246 0.902712i \(-0.641573\pi\)
−0.0258835 + 0.999665i \(0.508240\pi\)
\(662\) 16.2540 18.0519i 0.631729 0.701606i
\(663\) 0 0
\(664\) 20.4524 + 22.7147i 0.793707 + 0.881501i
\(665\) 3.82444 3.41222i 0.148305 0.132320i
\(666\) 0 0
\(667\) −4.57022 + 3.32046i −0.176959 + 0.128569i
\(668\) 1.56229 2.70596i 0.0604468 0.104697i
\(669\) 0 0
\(670\) 3.92992 5.35774i 0.151826 0.206987i
\(671\) −2.23978 + 21.3101i −0.0864659 + 0.822668i
\(672\) 0 0
\(673\) −17.3708 19.2922i −0.669593 0.743659i 0.308637 0.951180i \(-0.400127\pi\)
−0.978231 + 0.207521i \(0.933460\pi\)
\(674\) −31.6806 −1.22029
\(675\) 0 0
\(676\) −17.1357 −0.659067
\(677\) −26.3010 29.2103i −1.01083 1.12264i −0.992430 0.122810i \(-0.960809\pi\)
−0.0184004 0.999831i \(-0.505857\pi\)
\(678\) 0 0
\(679\) −0.243539 + 2.31712i −0.00934616 + 0.0889227i
\(680\) −6.42871 + 2.05659i −0.246530 + 0.0788666i
\(681\) 0 0
\(682\) 14.9361 25.8700i 0.571932 0.990615i
\(683\) 26.3578 19.1501i 1.00855 0.732757i 0.0446482 0.999003i \(-0.485783\pi\)
0.963905 + 0.266246i \(0.0857833\pi\)
\(684\) 0 0
\(685\) 7.60267 + 17.2867i 0.290483 + 0.660491i
\(686\) −3.49486 3.88143i −0.133434 0.148194i
\(687\) 0 0
\(688\) −4.51758 + 5.01729i −0.172231 + 0.191282i
\(689\) 27.1593 5.77288i 1.03469 0.219929i
\(690\) 0 0
\(691\) −32.6488 6.93971i −1.24202 0.263999i −0.460375 0.887725i \(-0.652285\pi\)
−0.781643 + 0.623726i \(0.785618\pi\)
\(692\) 0.170254 0.123696i 0.00647207 0.00470223i
\(693\) 0 0
\(694\) −19.7521 + 14.3507i −0.749779 + 0.544746i
\(695\) −2.36714 2.15092i −0.0897907 0.0815892i
\(696\) 0 0
\(697\) 0.470212 4.47377i 0.0178106 0.169456i
\(698\) −6.73592 + 1.43176i −0.254958 + 0.0541931i
\(699\) 0 0
\(700\) 0.742475 0.529205i 0.0280629 0.0200021i
\(701\) 47.0156 1.77575 0.887877 0.460081i \(-0.152180\pi\)
0.887877 + 0.460081i \(0.152180\pi\)
\(702\) 0 0
\(703\) −0.140661 0.102196i −0.00530513 0.00385441i
\(704\) −23.1931 + 10.3262i −0.874124 + 0.389185i
\(705\) 0 0
\(706\) 15.0625 + 6.70626i 0.566885 + 0.252393i
\(707\) −1.81928 3.15109i −0.0684211 0.118509i
\(708\) 0 0
\(709\) 2.86671 + 0.609338i 0.107661 + 0.0228842i 0.261427 0.965223i \(-0.415807\pi\)
−0.153766 + 0.988107i \(0.549140\pi\)
\(710\) 23.6938 21.1400i 0.889212 0.793369i
\(711\) 0 0
\(712\) −11.6428 35.8329i −0.436333 1.34289i
\(713\) 11.1024 + 2.35989i 0.415789 + 0.0883786i
\(714\) 0 0
\(715\) 24.6499 + 34.2537i 0.921855 + 1.28102i
\(716\) −5.87941 + 6.52975i −0.219724 + 0.244028i
\(717\) 0 0
\(718\) −0.305309 + 0.528811i −0.0113940 + 0.0197351i
\(719\) −13.9385 + 10.1269i −0.519820 + 0.377671i −0.816536 0.577295i \(-0.804108\pi\)
0.296716 + 0.954966i \(0.404108\pi\)
\(720\) 0 0
\(721\) −4.17330 3.03208i −0.155422 0.112920i
\(722\) −36.9185 + 16.4372i −1.37397 + 0.611729i
\(723\) 0 0
\(724\) −0.0165440 0.0286550i −0.000614851 0.00106495i
\(725\) 2.05949 + 21.4684i 0.0764875 + 0.797317i
\(726\) 0 0
\(727\) −0.116229 0.129085i −0.00431069 0.00478751i 0.740986 0.671521i \(-0.234359\pi\)
−0.745296 + 0.666733i \(0.767692\pi\)
\(728\) 5.11692 + 3.71766i 0.189646 + 0.137786i
\(729\) 0 0
\(730\) −2.11321 1.23289i −0.0782134 0.0456313i
\(731\) −0.276287 2.62869i −0.0102188 0.0972257i
\(732\) 0 0
\(733\) −48.4219 21.5588i −1.78851 0.796294i −0.977401 0.211392i \(-0.932200\pi\)
−0.811104 0.584902i \(-0.801133\pi\)
\(734\) 15.5971 17.3223i 0.575698 0.639378i
\(735\) 0 0
\(736\) −2.76790 3.07406i −0.102026 0.113311i
\(737\) 2.22670 + 6.85308i 0.0820216 + 0.252436i
\(738\) 0 0
\(739\) −1.32714 + 4.08451i −0.0488195 + 0.150251i −0.972494 0.232926i \(-0.925170\pi\)
0.923675 + 0.383177i \(0.125170\pi\)
\(740\) −0.0228910 0.0208002i −0.000841491 0.000764629i
\(741\) 0 0
\(742\) −1.45997 0.650022i −0.0535973 0.0238631i
\(743\) 15.1680 + 26.2718i 0.556461 + 0.963820i 0.997788 + 0.0664731i \(0.0211746\pi\)
−0.441327 + 0.897346i \(0.645492\pi\)
\(744\) 0 0
\(745\) −19.0245 + 42.2127i −0.697002 + 1.54656i
\(746\) 23.9192 + 17.3783i 0.875745 + 0.636266i
\(747\) 0 0
\(748\) 0.507554 1.56209i 0.0185580 0.0571157i
\(749\) 1.60118 2.77332i 0.0585057 0.101335i
\(750\) 0 0
\(751\) 13.8299 + 23.9541i 0.504661 + 0.874099i 0.999985 + 0.00539081i \(0.00171596\pi\)
−0.495324 + 0.868708i \(0.664951\pi\)
\(752\) 12.7892 2.71843i 0.466374 0.0991308i
\(753\) 0 0
\(754\) −30.6681 + 13.6543i −1.11687 + 0.497262i
\(755\) −47.4169 + 4.76614i −1.72568 + 0.173457i
\(756\) 0 0
\(757\) 31.2908 1.13729 0.568643 0.822585i \(-0.307469\pi\)
0.568643 + 0.822585i \(0.307469\pi\)
\(758\) −2.33664 22.2317i −0.0848707 0.807491i
\(759\) 0 0
\(760\) −47.6194 + 15.2338i −1.72734 + 0.552587i
\(761\) −18.0350 + 3.83346i −0.653769 + 0.138963i −0.522843 0.852429i \(-0.675128\pi\)
−0.130926 + 0.991392i \(0.541795\pi\)
\(762\) 0 0
\(763\) 3.41583 + 0.726057i 0.123661 + 0.0262850i
\(764\) 0.428507 1.31881i 0.0155028 0.0477128i
\(765\) 0 0
\(766\) 2.01977 + 6.21620i 0.0729771 + 0.224601i
\(767\) 3.53488 + 33.6321i 0.127637 + 1.21438i
\(768\) 0 0
\(769\) −15.0205 6.68758i −0.541655 0.241160i 0.117625 0.993058i \(-0.462472\pi\)
−0.659280 + 0.751898i \(0.729139\pi\)
\(770\) 0.0110291 2.42896i 0.000397461 0.0875337i
\(771\) 0 0
\(772\) 3.11629 1.38746i 0.112158 0.0499358i
\(773\) −11.8001 + 36.3171i −0.424421 + 1.30623i 0.479126 + 0.877746i \(0.340954\pi\)
−0.903547 + 0.428489i \(0.859046\pi\)
\(774\) 0 0
\(775\) 29.2870 31.9384i 1.05202 1.14726i
\(776\) 11.3637 19.6825i 0.407932 0.706559i
\(777\) 0 0
\(778\) 0.195415 1.85925i 0.00700597 0.0666573i
\(779\) 3.48301 33.1386i 0.124792 1.18731i
\(780\) 0 0
\(781\) 3.59952 + 34.2471i 0.128801 + 1.22546i
\(782\) −1.53310 −0.0548235
\(783\) 0 0
\(784\) 5.34808 + 16.4597i 0.191003 + 0.587846i
\(785\) −12.8293 + 28.4664i −0.457896 + 1.01601i
\(786\) 0 0
\(787\) −8.48025