Properties

Label 405.2.r.a.152.6
Level $405$
Weight $2$
Character 405.152
Analytic conductor $3.234$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.r (of order \(36\), degree \(12\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(16\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 152.6
Character \(\chi\) \(=\) 405.152
Dual form 405.2.r.a.8.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.490069 - 0.343150i) q^{2} +(-0.561625 - 1.54305i) q^{4} +(1.25284 + 1.85213i) q^{5} +(-0.0636379 - 0.136472i) q^{7} +(-0.563947 + 2.10468i) q^{8} +O(q^{10})\) \(q+(-0.490069 - 0.343150i) q^{2} +(-0.561625 - 1.54305i) q^{4} +(1.25284 + 1.85213i) q^{5} +(-0.0636379 - 0.136472i) q^{7} +(-0.563947 + 2.10468i) q^{8} +(0.0215816 - 1.33758i) q^{10} +(3.54970 + 4.23037i) q^{11} +(1.08490 + 1.54940i) q^{13} +(-0.0156434 + 0.0887180i) q^{14} +(-1.51722 + 1.27310i) q^{16} +(-1.18141 - 4.40907i) q^{17} +(6.55178 - 3.78267i) q^{19} +(2.15431 - 2.97340i) q^{20} +(-0.287947 - 3.29125i) q^{22} +(0.883698 + 0.412075i) q^{23} +(-1.86079 + 4.64085i) q^{25} -1.13159i q^{26} +(-0.174843 + 0.174843i) q^{28} +(0.486461 + 2.75886i) q^{29} +(1.70974 - 0.622294i) q^{31} +(5.52167 - 0.483084i) q^{32} +(-0.934001 + 2.56615i) q^{34} +(0.173036 - 0.288843i) q^{35} +(5.71298 - 1.53079i) q^{37} +(-4.50885 - 0.394473i) q^{38} +(-4.60468 + 1.59232i) q^{40} +(0.682276 + 0.120304i) q^{41} +(0.151755 - 1.73456i) q^{43} +(4.53407 - 7.85325i) q^{44} +(-0.291669 - 0.505186i) q^{46} +(-10.0941 + 4.70696i) q^{47} +(4.48494 - 5.34494i) q^{49} +(2.50442 - 1.63581i) q^{50} +(1.78149 - 2.54423i) q^{52} +(-0.204978 - 0.204978i) q^{53} +(-3.38800 + 11.8745i) q^{55} +(0.323118 - 0.0569745i) q^{56} +(0.708303 - 1.51896i) q^{58} +(-0.796564 - 0.668396i) q^{59} +(9.12620 + 3.32167i) q^{61} +(-1.05143 - 0.281730i) q^{62} +(0.558711 + 0.322572i) q^{64} +(-1.51048 + 3.95052i) q^{65} +(-8.96216 + 6.27537i) q^{67} +(-6.13991 + 4.29921i) q^{68} +(-0.183916 + 0.0821758i) q^{70} +(2.53024 + 1.46084i) q^{71} +(-9.95358 - 2.66706i) q^{73} +(-3.32505 - 1.21022i) q^{74} +(-9.51649 - 7.98529i) q^{76} +(0.351431 - 0.753647i) q^{77} +(-11.9179 + 2.10144i) q^{79} +(-4.25878 - 1.21510i) q^{80} +(-0.293080 - 0.293080i) q^{82} +(-4.10306 + 5.85978i) q^{83} +(6.68606 - 7.71197i) q^{85} +(-0.669585 + 0.797981i) q^{86} +(-10.9054 + 5.08528i) q^{88} +(-6.74192 - 11.6773i) q^{89} +(0.142409 - 0.246659i) q^{91} +(0.139546 - 1.59502i) q^{92} +(6.56201 + 1.15706i) q^{94} +(15.2143 + 7.39568i) q^{95} +(3.56471 + 0.311872i) q^{97} +(-4.03205 + 1.08038i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{17}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.490069 0.343150i −0.346531 0.242644i 0.387333 0.921940i \(-0.373396\pi\)
−0.733864 + 0.679296i \(0.762285\pi\)
\(3\) 0 0
\(4\) −0.561625 1.54305i −0.280812 0.771525i
\(5\) 1.25284 + 1.85213i 0.560287 + 0.828299i
\(6\) 0 0
\(7\) −0.0636379 0.136472i −0.0240529 0.0515816i 0.893914 0.448238i \(-0.147948\pi\)
−0.917967 + 0.396656i \(0.870170\pi\)
\(8\) −0.563947 + 2.10468i −0.199385 + 0.744117i
\(9\) 0 0
\(10\) 0.0215816 1.33758i 0.00682471 0.422981i
\(11\) 3.54970 + 4.23037i 1.07027 + 1.27550i 0.959515 + 0.281657i \(0.0908840\pi\)
0.110760 + 0.993847i \(0.464672\pi\)
\(12\) 0 0
\(13\) 1.08490 + 1.54940i 0.300897 + 0.429725i 0.940919 0.338631i \(-0.109964\pi\)
−0.640022 + 0.768356i \(0.721075\pi\)
\(14\) −0.0156434 + 0.0887180i −0.00418087 + 0.0237109i
\(15\) 0 0
\(16\) −1.51722 + 1.27310i −0.379305 + 0.318275i
\(17\) −1.18141 4.40907i −0.286533 1.06936i −0.947712 0.319127i \(-0.896610\pi\)
0.661179 0.750228i \(-0.270056\pi\)
\(18\) 0 0
\(19\) 6.55178 3.78267i 1.50308 0.867804i 0.503087 0.864236i \(-0.332197\pi\)
0.999994 0.00356839i \(-0.00113586\pi\)
\(20\) 2.15431 2.97340i 0.481718 0.664872i
\(21\) 0 0
\(22\) −0.287947 3.29125i −0.0613906 0.701697i
\(23\) 0.883698 + 0.412075i 0.184264 + 0.0859236i 0.512561 0.858651i \(-0.328697\pi\)
−0.328297 + 0.944575i \(0.606475\pi\)
\(24\) 0 0
\(25\) −1.86079 + 4.64085i −0.372158 + 0.928170i
\(26\) 1.13159i 0.221924i
\(27\) 0 0
\(28\) −0.174843 + 0.174843i −0.0330421 + 0.0330421i
\(29\) 0.486461 + 2.75886i 0.0903336 + 0.512307i 0.996078 + 0.0884824i \(0.0282017\pi\)
−0.905744 + 0.423825i \(0.860687\pi\)
\(30\) 0 0
\(31\) 1.70974 0.622294i 0.307078 0.111767i −0.183885 0.982948i \(-0.558867\pi\)
0.490963 + 0.871181i \(0.336645\pi\)
\(32\) 5.52167 0.483084i 0.976103 0.0853979i
\(33\) 0 0
\(34\) −0.934001 + 2.56615i −0.160180 + 0.440090i
\(35\) 0.173036 0.288843i 0.0292484 0.0488234i
\(36\) 0 0
\(37\) 5.71298 1.53079i 0.939209 0.251660i 0.243432 0.969918i \(-0.421727\pi\)
0.695777 + 0.718258i \(0.255060\pi\)
\(38\) −4.50885 0.394473i −0.731431 0.0639920i
\(39\) 0 0
\(40\) −4.60468 + 1.59232i −0.728064 + 0.251768i
\(41\) 0.682276 + 0.120304i 0.106554 + 0.0187883i 0.226671 0.973971i \(-0.427216\pi\)
−0.120117 + 0.992760i \(0.538327\pi\)
\(42\) 0 0
\(43\) 0.151755 1.73456i 0.0231424 0.264518i −0.975805 0.218643i \(-0.929837\pi\)
0.998947 0.0458750i \(-0.0146076\pi\)
\(44\) 4.53407 7.85325i 0.683537 1.18392i
\(45\) 0 0
\(46\) −0.291669 0.505186i −0.0430043 0.0744856i
\(47\) −10.0941 + 4.70696i −1.47238 + 0.686581i −0.982680 0.185311i \(-0.940671\pi\)
−0.489698 + 0.871892i \(0.662893\pi\)
\(48\) 0 0
\(49\) 4.48494 5.34494i 0.640705 0.763563i
\(50\) 2.50442 1.63581i 0.354179 0.231338i
\(51\) 0 0
\(52\) 1.78149 2.54423i 0.247049 0.352822i
\(53\) −0.204978 0.204978i −0.0281559 0.0281559i 0.692889 0.721045i \(-0.256338\pi\)
−0.721045 + 0.692889i \(0.756338\pi\)
\(54\) 0 0
\(55\) −3.38800 + 11.8745i −0.456838 + 1.60116i
\(56\) 0.323118 0.0569745i 0.0431785 0.00761353i
\(57\) 0 0
\(58\) 0.708303 1.51896i 0.0930047 0.199449i
\(59\) −0.796564 0.668396i −0.103704 0.0870178i 0.589462 0.807796i \(-0.299340\pi\)
−0.693165 + 0.720779i \(0.743784\pi\)
\(60\) 0 0
\(61\) 9.12620 + 3.32167i 1.16849 + 0.425296i 0.852123 0.523341i \(-0.175315\pi\)
0.316367 + 0.948637i \(0.397537\pi\)
\(62\) −1.05143 0.281730i −0.133532 0.0357797i
\(63\) 0 0
\(64\) 0.558711 + 0.322572i 0.0698389 + 0.0403215i
\(65\) −1.51048 + 3.95052i −0.187352 + 0.490002i
\(66\) 0 0
\(67\) −8.96216 + 6.27537i −1.09490 + 0.766659i −0.974122 0.226021i \(-0.927428\pi\)
−0.120780 + 0.992679i \(0.538539\pi\)
\(68\) −6.13991 + 4.29921i −0.744573 + 0.521356i
\(69\) 0 0
\(70\) −0.183916 + 0.0821758i −0.0219822 + 0.00982189i
\(71\) 2.53024 + 1.46084i 0.300285 + 0.173369i 0.642571 0.766226i \(-0.277868\pi\)
−0.342286 + 0.939596i \(0.611201\pi\)
\(72\) 0 0
\(73\) −9.95358 2.66706i −1.16498 0.312155i −0.376026 0.926609i \(-0.622710\pi\)
−0.788953 + 0.614454i \(0.789376\pi\)
\(74\) −3.32505 1.21022i −0.386529 0.140685i
\(75\) 0 0
\(76\) −9.51649 7.98529i −1.09162 0.915975i
\(77\) 0.351431 0.753647i 0.0400493 0.0858860i
\(78\) 0 0
\(79\) −11.9179 + 2.10144i −1.34086 + 0.236430i −0.797628 0.603150i \(-0.793912\pi\)
−0.543236 + 0.839580i \(0.682801\pi\)
\(80\) −4.25878 1.21510i −0.476146 0.135853i
\(81\) 0 0
\(82\) −0.293080 0.293080i −0.0323653 0.0323653i
\(83\) −4.10306 + 5.85978i −0.450370 + 0.643194i −0.978567 0.205927i \(-0.933979\pi\)
0.528198 + 0.849121i \(0.322868\pi\)
\(84\) 0 0
\(85\) 6.68606 7.71197i 0.725205 0.836481i
\(86\) −0.669585 + 0.797981i −0.0722033 + 0.0860485i
\(87\) 0 0
\(88\) −10.9054 + 5.08528i −1.16252 + 0.542092i
\(89\) −6.74192 11.6773i −0.714642 1.23780i −0.963097 0.269153i \(-0.913256\pi\)
0.248455 0.968643i \(-0.420077\pi\)
\(90\) 0 0
\(91\) 0.142409 0.246659i 0.0149285 0.0258569i
\(92\) 0.139546 1.59502i 0.0145487 0.166293i
\(93\) 0 0
\(94\) 6.56201 + 1.15706i 0.676819 + 0.119341i
\(95\) 15.2143 + 7.39568i 1.56096 + 0.758781i
\(96\) 0 0
\(97\) 3.56471 + 0.311872i 0.361941 + 0.0316658i 0.266676 0.963786i \(-0.414075\pi\)
0.0952651 + 0.995452i \(0.469630\pi\)
\(98\) −4.03205 + 1.08038i −0.407298 + 0.109135i
\(99\) 0 0
\(100\) 8.20613 + 0.264877i 0.820613 + 0.0264877i
\(101\) 1.31720 3.61898i 0.131067 0.360102i −0.856749 0.515734i \(-0.827519\pi\)
0.987815 + 0.155632i \(0.0497414\pi\)
\(102\) 0 0
\(103\) −12.2709 + 1.07356i −1.20909 + 0.105781i −0.673816 0.738900i \(-0.735346\pi\)
−0.535270 + 0.844681i \(0.679790\pi\)
\(104\) −3.87281 + 1.40959i −0.379760 + 0.138221i
\(105\) 0 0
\(106\) 0.0301151 + 0.170791i 0.00292504 + 0.0165887i
\(107\) −0.874553 + 0.874553i −0.0845462 + 0.0845462i −0.748115 0.663569i \(-0.769041\pi\)
0.663569 + 0.748115i \(0.269041\pi\)
\(108\) 0 0
\(109\) 8.22348i 0.787666i −0.919182 0.393833i \(-0.871149\pi\)
0.919182 0.393833i \(-0.128851\pi\)
\(110\) 5.73508 4.65673i 0.546819 0.444001i
\(111\) 0 0
\(112\) 0.270295 + 0.126041i 0.0255405 + 0.0119097i
\(113\) −0.174058 1.98949i −0.0163740 0.187156i −0.999977 0.00680753i \(-0.997833\pi\)
0.983603 0.180348i \(-0.0577225\pi\)
\(114\) 0 0
\(115\) 0.343914 + 2.15299i 0.0320701 + 0.200767i
\(116\) 3.98385 2.30008i 0.369891 0.213557i
\(117\) 0 0
\(118\) 0.161011 + 0.600901i 0.0148223 + 0.0553174i
\(119\) −0.526532 + 0.441813i −0.0482671 + 0.0405009i
\(120\) 0 0
\(121\) −3.38551 + 19.2002i −0.307774 + 1.74547i
\(122\) −3.33264 4.75950i −0.301723 0.430905i
\(123\) 0 0
\(124\) −1.92046 2.28872i −0.172463 0.205533i
\(125\) −10.9267 + 2.36781i −0.977317 + 0.211783i
\(126\) 0 0
\(127\) −1.72156 + 6.42494i −0.152764 + 0.570121i 0.846523 + 0.532352i \(0.178692\pi\)
−0.999286 + 0.0377691i \(0.987975\pi\)
\(128\) −4.84806 10.3967i −0.428512 0.918948i
\(129\) 0 0
\(130\) 2.09586 1.41771i 0.183819 0.124341i
\(131\) −4.62535 12.7080i −0.404119 1.11031i −0.960233 0.279201i \(-0.909930\pi\)
0.556114 0.831106i \(-0.312292\pi\)
\(132\) 0 0
\(133\) −0.933170 0.653413i −0.0809161 0.0566581i
\(134\) 6.54547 0.565442
\(135\) 0 0
\(136\) 9.94592 0.852856
\(137\) −6.70575 4.69542i −0.572911 0.401156i 0.250907 0.968011i \(-0.419271\pi\)
−0.823818 + 0.566855i \(0.808160\pi\)
\(138\) 0 0
\(139\) 6.24384 + 17.1548i 0.529596 + 1.45505i 0.859548 + 0.511055i \(0.170745\pi\)
−0.329952 + 0.943998i \(0.607033\pi\)
\(140\) −0.542881 0.104782i −0.0458818 0.00885569i
\(141\) 0 0
\(142\) −0.738707 1.58416i −0.0619909 0.132940i
\(143\) −2.70345 + 10.0894i −0.226074 + 0.843720i
\(144\) 0 0
\(145\) −4.50031 + 4.35740i −0.373731 + 0.361862i
\(146\) 3.96274 + 4.72261i 0.327959 + 0.390846i
\(147\) 0 0
\(148\) −5.57064 7.95570i −0.457904 0.653954i
\(149\) 0.725914 4.11686i 0.0594692 0.337266i −0.940528 0.339717i \(-0.889669\pi\)
0.999997 + 0.00245028i \(0.000779950\pi\)
\(150\) 0 0
\(151\) 3.72470 3.12540i 0.303112 0.254341i −0.478526 0.878073i \(-0.658829\pi\)
0.781638 + 0.623732i \(0.214384\pi\)
\(152\) 4.26645 + 15.9226i 0.346055 + 1.29149i
\(153\) 0 0
\(154\) −0.430839 + 0.248745i −0.0347180 + 0.0200445i
\(155\) 3.29460 + 2.38703i 0.264628 + 0.191731i
\(156\) 0 0
\(157\) −1.51739 17.3439i −0.121101 1.38419i −0.777075 0.629407i \(-0.783298\pi\)
0.655974 0.754783i \(-0.272258\pi\)
\(158\) 6.56168 + 3.05976i 0.522019 + 0.243422i
\(159\) 0 0
\(160\) 7.81250 + 9.62164i 0.617633 + 0.760658i
\(161\) 0.146824i 0.0115713i
\(162\) 0 0
\(163\) 2.64439 2.64439i 0.207124 0.207124i −0.595920 0.803044i \(-0.703212\pi\)
0.803044 + 0.595920i \(0.203212\pi\)
\(164\) −0.197548 1.12035i −0.0154259 0.0874848i
\(165\) 0 0
\(166\) 4.02157 1.46373i 0.312134 0.113608i
\(167\) −0.523503 + 0.0458006i −0.0405099 + 0.00354415i −0.107393 0.994217i \(-0.534250\pi\)
0.0668828 + 0.997761i \(0.478695\pi\)
\(168\) 0 0
\(169\) 3.22264 8.85412i 0.247895 0.681086i
\(170\) −5.92299 + 1.48507i −0.454273 + 0.113900i
\(171\) 0 0
\(172\) −2.76175 + 0.740008i −0.210581 + 0.0564251i
\(173\) 17.5306 + 1.53373i 1.33282 + 0.116607i 0.731195 0.682169i \(-0.238963\pi\)
0.601629 + 0.798776i \(0.294519\pi\)
\(174\) 0 0
\(175\) 0.751762 0.0413885i 0.0568279 0.00312867i
\(176\) −10.7714 1.89928i −0.811921 0.143164i
\(177\) 0 0
\(178\) −0.703076 + 8.03619i −0.0526978 + 0.602338i
\(179\) 0.435152 0.753705i 0.0325248 0.0563346i −0.849305 0.527903i \(-0.822979\pi\)
0.881830 + 0.471568i \(0.156312\pi\)
\(180\) 0 0
\(181\) 5.47447 + 9.48206i 0.406914 + 0.704796i 0.994542 0.104335i \(-0.0332715\pi\)
−0.587628 + 0.809131i \(0.699938\pi\)
\(182\) −0.154431 + 0.0720123i −0.0114472 + 0.00533791i
\(183\) 0 0
\(184\) −1.36565 + 1.62751i −0.100677 + 0.119982i
\(185\) 9.99267 + 8.66337i 0.734676 + 0.636943i
\(186\) 0 0
\(187\) 14.4583 20.6486i 1.05730 1.50998i
\(188\) 12.9322 + 12.9322i 0.943177 + 0.943177i
\(189\) 0 0
\(190\) −4.91824 8.84519i −0.356807 0.641698i
\(191\) −14.0251 + 2.47300i −1.01482 + 0.178940i −0.656234 0.754557i \(-0.727852\pi\)
−0.358585 + 0.933497i \(0.616741\pi\)
\(192\) 0 0
\(193\) 5.12102 10.9821i 0.368619 0.790506i −0.631269 0.775564i \(-0.717466\pi\)
0.999888 0.0149426i \(-0.00475655\pi\)
\(194\) −1.63993 1.37607i −0.117740 0.0987960i
\(195\) 0 0
\(196\) −10.7664 3.91864i −0.769026 0.279903i
\(197\) 10.7112 + 2.87005i 0.763138 + 0.204482i 0.619338 0.785124i \(-0.287401\pi\)
0.143800 + 0.989607i \(0.454068\pi\)
\(198\) 0 0
\(199\) 3.29595 + 1.90292i 0.233644 + 0.134894i 0.612252 0.790663i \(-0.290264\pi\)
−0.378608 + 0.925557i \(0.623597\pi\)
\(200\) −8.71811 6.53356i −0.616464 0.461992i
\(201\) 0 0
\(202\) −1.88737 + 1.32155i −0.132795 + 0.0929842i
\(203\) 0.345550 0.241956i 0.0242528 0.0169820i
\(204\) 0 0
\(205\) 0.631964 + 1.41439i 0.0441383 + 0.0987851i
\(206\) 6.38197 + 3.68463i 0.444653 + 0.256720i
\(207\) 0 0
\(208\) −3.61857 0.969592i −0.250902 0.0672291i
\(209\) 39.2589 + 14.2891i 2.71560 + 0.988397i
\(210\) 0 0
\(211\) −0.117333 0.0984540i −0.00807753 0.00677785i 0.638740 0.769423i \(-0.279456\pi\)
−0.646817 + 0.762645i \(0.723900\pi\)
\(212\) −0.201171 + 0.431412i −0.0138165 + 0.0296295i
\(213\) 0 0
\(214\) 0.728694 0.128488i 0.0498125 0.00878329i
\(215\) 3.40276 1.89206i 0.232067 0.129037i
\(216\) 0 0
\(217\) −0.193730 0.193730i −0.0131512 0.0131512i
\(218\) −2.82189 + 4.03007i −0.191122 + 0.272951i
\(219\) 0 0
\(220\) 20.2257 1.44115i 1.36362 0.0971623i
\(221\) 5.54969 6.61386i 0.373312 0.444896i
\(222\) 0 0
\(223\) 24.0272 11.2041i 1.60898 0.750281i 0.609875 0.792498i \(-0.291220\pi\)
0.999108 + 0.0422168i \(0.0134420\pi\)
\(224\) −0.417315 0.722811i −0.0278830 0.0482948i
\(225\) 0 0
\(226\) −0.597394 + 1.03472i −0.0397381 + 0.0688283i
\(227\) 1.41372 16.1589i 0.0938320 1.07250i −0.792630 0.609703i \(-0.791289\pi\)
0.886462 0.462802i \(-0.153156\pi\)
\(228\) 0 0
\(229\) 2.26795 + 0.399901i 0.149871 + 0.0264262i 0.248080 0.968740i \(-0.420200\pi\)
−0.0982095 + 0.995166i \(0.531312\pi\)
\(230\) 0.570257 1.17313i 0.0376016 0.0773537i
\(231\) 0 0
\(232\) −6.08085 0.532006i −0.399228 0.0349279i
\(233\) −5.48640 + 1.47008i −0.359426 + 0.0963080i −0.434013 0.900907i \(-0.642903\pi\)
0.0745868 + 0.997215i \(0.476236\pi\)
\(234\) 0 0
\(235\) −21.3642 12.7986i −1.39365 0.834886i
\(236\) −0.584000 + 1.60453i −0.0380152 + 0.104446i
\(237\) 0 0
\(238\) 0.409645 0.0358393i 0.0265533 0.00232312i
\(239\) −27.4639 + 9.99603i −1.77649 + 0.646589i −0.776628 + 0.629960i \(0.783071\pi\)
−0.999862 + 0.0166299i \(0.994706\pi\)
\(240\) 0 0
\(241\) −1.09121 6.18855i −0.0702909 0.398639i −0.999572 0.0292653i \(-0.990683\pi\)
0.929281 0.369374i \(-0.120428\pi\)
\(242\) 8.24768 8.24768i 0.530181 0.530181i
\(243\) 0 0
\(244\) 15.9477i 1.02095i
\(245\) 15.5184 + 1.61035i 0.991437 + 0.102881i
\(246\) 0 0
\(247\) 12.9689 + 6.04749i 0.825190 + 0.384792i
\(248\) 0.345527 + 3.94939i 0.0219410 + 0.250787i
\(249\) 0 0
\(250\) 6.16737 + 2.58912i 0.390058 + 0.163750i
\(251\) 7.99676 4.61693i 0.504751 0.291418i −0.225923 0.974145i \(-0.572540\pi\)
0.730673 + 0.682727i \(0.239206\pi\)
\(252\) 0 0
\(253\) 1.39363 + 5.20111i 0.0876170 + 0.326991i
\(254\) 3.04840 2.55791i 0.191274 0.160498i
\(255\) 0 0
\(256\) −0.967687 + 5.48803i −0.0604805 + 0.343002i
\(257\) −9.43754 13.4782i −0.588697 0.840747i 0.408713 0.912663i \(-0.365978\pi\)
−0.997411 + 0.0719158i \(0.977089\pi\)
\(258\) 0 0
\(259\) −0.572472 0.682246i −0.0355717 0.0423927i
\(260\) 6.94418 + 0.112043i 0.430660 + 0.00694860i
\(261\) 0 0
\(262\) −2.09402 + 7.81501i −0.129369 + 0.482813i
\(263\) −5.18376 11.1166i −0.319644 0.685480i 0.679179 0.733973i \(-0.262336\pi\)
−0.998824 + 0.0484930i \(0.984558\pi\)
\(264\) 0 0
\(265\) 0.122842 0.636450i 0.00754611 0.0390968i
\(266\) 0.233099 + 0.640435i 0.0142922 + 0.0392676i
\(267\) 0 0
\(268\) 14.7166 + 10.3047i 0.898959 + 0.629458i
\(269\) −18.4528 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(270\) 0 0
\(271\) −13.3622 −0.811695 −0.405848 0.913941i \(-0.633024\pi\)
−0.405848 + 0.913941i \(0.633024\pi\)
\(272\) 7.40563 + 5.18548i 0.449032 + 0.314416i
\(273\) 0 0
\(274\) 1.67505 + 4.60215i 0.101193 + 0.278026i
\(275\) −26.2377 + 8.60180i −1.58220 + 0.518708i
\(276\) 0 0
\(277\) −9.07810 19.4680i −0.545450 1.16972i −0.965063 0.262018i \(-0.915612\pi\)
0.419613 0.907703i \(-0.362166\pi\)
\(278\) 2.82676 10.5496i 0.169538 0.632724i
\(279\) 0 0
\(280\) 0.510339 + 0.527078i 0.0304986 + 0.0314989i
\(281\) −4.46928 5.32628i −0.266615 0.317739i 0.616082 0.787682i \(-0.288719\pi\)
−0.882697 + 0.469943i \(0.844275\pi\)
\(282\) 0 0
\(283\) 13.8553 + 19.7874i 0.823612 + 1.17624i 0.982003 + 0.188864i \(0.0604805\pi\)
−0.158391 + 0.987376i \(0.550631\pi\)
\(284\) 0.833098 4.72473i 0.0494353 0.280361i
\(285\) 0 0
\(286\) 4.78706 4.01682i 0.283065 0.237520i
\(287\) −0.0270006 0.100767i −0.00159379 0.00594811i
\(288\) 0 0
\(289\) −3.32171 + 1.91779i −0.195395 + 0.112811i
\(290\) 3.70071 0.591142i 0.217313 0.0347131i
\(291\) 0 0
\(292\) 1.47478 + 16.8568i 0.0863048 + 0.986468i
\(293\) 14.5847 + 6.80096i 0.852048 + 0.397316i 0.799040 0.601278i \(-0.205341\pi\)
0.0530076 + 0.998594i \(0.483119\pi\)
\(294\) 0 0
\(295\) 0.239992 2.31273i 0.0139729 0.134653i
\(296\) 12.8873i 0.749058i
\(297\) 0 0
\(298\) −1.76845 + 1.76845i −0.102443 + 0.102443i
\(299\) 0.320256 + 1.81626i 0.0185209 + 0.105037i
\(300\) 0 0
\(301\) −0.246377 + 0.0896737i −0.0142009 + 0.00516871i
\(302\) −2.89784 + 0.253528i −0.166752 + 0.0145889i
\(303\) 0 0
\(304\) −5.12477 + 14.0802i −0.293926 + 0.807555i
\(305\) 5.28150 + 21.0645i 0.302418 + 1.20615i
\(306\) 0 0
\(307\) −30.9704 + 8.29849i −1.76757 + 0.473620i −0.988230 0.152978i \(-0.951114\pi\)
−0.779343 + 0.626598i \(0.784447\pi\)
\(308\) −1.36029 0.119010i −0.0775096 0.00678121i
\(309\) 0 0
\(310\) −0.795471 2.30035i −0.0451797 0.130651i
\(311\) 17.6839 + 3.11815i 1.00276 + 0.176814i 0.650840 0.759215i \(-0.274417\pi\)
0.351922 + 0.936029i \(0.385528\pi\)
\(312\) 0 0
\(313\) −0.0467556 + 0.534419i −0.00264278 + 0.0302071i −0.997402 0.0720422i \(-0.977048\pi\)
0.994759 + 0.102249i \(0.0326039\pi\)
\(314\) −5.20792 + 9.02038i −0.293900 + 0.509049i
\(315\) 0 0
\(316\) 9.93599 + 17.2096i 0.558943 + 0.968118i
\(317\) −26.8041 + 12.4989i −1.50547 + 0.702011i −0.988109 0.153758i \(-0.950862\pi\)
−0.517358 + 0.855769i \(0.673085\pi\)
\(318\) 0 0
\(319\) −9.94420 + 11.8510i −0.556768 + 0.663531i
\(320\) 0.102529 + 1.43894i 0.00573155 + 0.0804391i
\(321\) 0 0
\(322\) −0.0503825 + 0.0719537i −0.00280771 + 0.00400982i
\(323\) −24.4183 24.4183i −1.35867 1.35867i
\(324\) 0 0
\(325\) −9.20928 + 2.15175i −0.510839 + 0.119358i
\(326\) −2.20335 + 0.388511i −0.122032 + 0.0215176i
\(327\) 0 0
\(328\) −0.637968 + 1.36813i −0.0352259 + 0.0755422i
\(329\) 1.28474 + 1.07802i 0.0708298 + 0.0594333i
\(330\) 0 0
\(331\) −24.8454 9.04298i −1.36563 0.497047i −0.447837 0.894115i \(-0.647805\pi\)
−0.917789 + 0.397068i \(0.870028\pi\)
\(332\) 11.3463 + 3.04024i 0.622710 + 0.166855i
\(333\) 0 0
\(334\) 0.272269 + 0.157195i 0.0148979 + 0.00860130i
\(335\) −22.8510 8.73707i −1.24848 0.477357i
\(336\) 0 0
\(337\) −14.1961 + 9.94021i −0.773310 + 0.541478i −0.892314 0.451416i \(-0.850919\pi\)
0.119003 + 0.992894i \(0.462030\pi\)
\(338\) −4.61761 + 3.23328i −0.251165 + 0.175867i
\(339\) 0 0
\(340\) −15.6550 5.98570i −0.849013 0.324620i
\(341\) 8.70159 + 5.02387i 0.471218 + 0.272058i
\(342\) 0 0
\(343\) −2.03299 0.544739i −0.109771 0.0294131i
\(344\) 3.56512 + 1.29760i 0.192218 + 0.0699617i
\(345\) 0 0
\(346\) −8.06488 6.76724i −0.433571 0.363809i
\(347\) 3.53574 7.58241i 0.189808 0.407045i −0.788256 0.615347i \(-0.789016\pi\)
0.978065 + 0.208302i \(0.0667937\pi\)
\(348\) 0 0
\(349\) −21.0838 + 3.71764i −1.12859 + 0.199000i −0.706608 0.707605i \(-0.749776\pi\)
−0.421979 + 0.906605i \(0.638665\pi\)
\(350\) −0.382618 0.237684i −0.0204518 0.0127047i
\(351\) 0 0
\(352\) 21.6439 + 21.6439i 1.15362 + 1.15362i
\(353\) 16.6830 23.8257i 0.887944 1.26812i −0.0746612 0.997209i \(-0.523788\pi\)
0.962606 0.270907i \(-0.0873236\pi\)
\(354\) 0 0
\(355\) 0.464325 + 6.51654i 0.0246438 + 0.345862i
\(356\) −14.2323 + 16.9614i −0.754311 + 0.898953i
\(357\) 0 0
\(358\) −0.471889 + 0.220045i −0.0249401 + 0.0116298i
\(359\) 5.32734 + 9.22723i 0.281166 + 0.486995i 0.971672 0.236332i \(-0.0759454\pi\)
−0.690506 + 0.723327i \(0.742612\pi\)
\(360\) 0 0
\(361\) 19.1172 33.1119i 1.00617 1.74273i
\(362\) 0.570901 6.52543i 0.0300059 0.342969i
\(363\) 0 0
\(364\) −0.460587 0.0812140i −0.0241413 0.00425677i
\(365\) −7.53050 21.7767i −0.394164 1.13985i
\(366\) 0 0
\(367\) 21.4206 + 1.87406i 1.11814 + 0.0978249i 0.631209 0.775613i \(-0.282559\pi\)
0.486935 + 0.873438i \(0.338115\pi\)
\(368\) −1.86538 + 0.499826i −0.0972395 + 0.0260552i
\(369\) 0 0
\(370\) −1.92426 7.67463i −0.100038 0.398985i
\(371\) −0.0149294 + 0.0410181i −0.000775094 + 0.00212955i
\(372\) 0 0
\(373\) 10.9407 0.957189i 0.566489 0.0495614i 0.199686 0.979860i \(-0.436008\pi\)
0.366803 + 0.930299i \(0.380452\pi\)
\(374\) −14.1712 + 5.15788i −0.732773 + 0.266708i
\(375\) 0 0
\(376\) −4.21410 23.8994i −0.217326 1.23252i
\(377\) −3.74681 + 3.74681i −0.192970 + 0.192970i
\(378\) 0 0
\(379\) 9.48980i 0.487458i −0.969843 0.243729i \(-0.921629\pi\)
0.969843 0.243729i \(-0.0783708\pi\)
\(380\) 2.86717 27.6301i 0.147083 1.41739i
\(381\) 0 0
\(382\) 7.72187 + 3.60077i 0.395085 + 0.184231i
\(383\) −2.27956 26.0555i −0.116480 1.33137i −0.799364 0.600846i \(-0.794830\pi\)
0.682884 0.730526i \(-0.260725\pi\)
\(384\) 0 0
\(385\) 1.83614 0.293301i 0.0935783 0.0149480i
\(386\) −6.27815 + 3.62469i −0.319549 + 0.184492i
\(387\) 0 0
\(388\) −1.52079 5.67568i −0.0772066 0.288139i
\(389\) −2.90227 + 2.43529i −0.147151 + 0.123474i −0.713391 0.700766i \(-0.752842\pi\)
0.566240 + 0.824240i \(0.308397\pi\)
\(390\) 0 0
\(391\) 0.772861 4.38311i 0.0390852 0.221663i
\(392\) 8.72012 + 12.4536i 0.440433 + 0.629003i
\(393\) 0 0
\(394\) −4.26435 5.08205i −0.214835 0.256030i
\(395\) −18.8233 19.4407i −0.947103 0.978167i
\(396\) 0 0
\(397\) 4.76915 17.7987i 0.239357 0.893292i −0.736779 0.676133i \(-0.763654\pi\)
0.976136 0.217159i \(-0.0696789\pi\)
\(398\) −0.962257 2.06357i −0.0482336 0.103437i
\(399\) 0 0
\(400\) −3.08503 9.41015i −0.154252 0.470508i
\(401\) −3.20835 8.81488i −0.160217 0.440194i 0.833445 0.552603i \(-0.186365\pi\)
−0.993662 + 0.112409i \(0.964143\pi\)
\(402\) 0 0
\(403\) 2.81907 + 1.97394i 0.140428 + 0.0983288i
\(404\) −6.32405 −0.314633
\(405\) 0 0
\(406\) −0.252370 −0.0125249
\(407\) 26.7552 + 18.7342i 1.32621 + 0.928619i
\(408\) 0 0
\(409\) 6.70343 + 18.4175i 0.331464 + 0.910689i 0.987732 + 0.156161i \(0.0499118\pi\)
−0.656268 + 0.754528i \(0.727866\pi\)
\(410\) 0.175641 0.910005i 0.00867429 0.0449420i
\(411\) 0 0
\(412\) 8.54819 + 18.3317i 0.421139 + 0.903136i
\(413\) −0.0405257 + 0.151244i −0.00199414 + 0.00744223i
\(414\) 0 0
\(415\) −15.9936 0.258052i −0.785093 0.0126673i
\(416\) 6.73895 + 8.03117i 0.330404 + 0.393760i
\(417\) 0 0
\(418\) −14.3363 20.4743i −0.701211 1.00143i
\(419\) −4.78282 + 27.1247i −0.233656 + 1.32513i 0.611770 + 0.791035i \(0.290458\pi\)
−0.845426 + 0.534092i \(0.820653\pi\)
\(420\) 0 0
\(421\) −7.89176 + 6.62197i −0.384621 + 0.322735i −0.814513 0.580145i \(-0.802996\pi\)
0.429892 + 0.902880i \(0.358551\pi\)
\(422\) 0.0237167 + 0.0885121i 0.00115451 + 0.00430870i
\(423\) 0 0
\(424\) 0.547009 0.315816i 0.0265651 0.0153374i
\(425\) 22.6601 + 2.72161i 1.09918 + 0.132018i
\(426\) 0 0
\(427\) −0.127458 1.45686i −0.00616814 0.0705022i
\(428\) 1.84065 + 0.858309i 0.0889712 + 0.0414879i
\(429\) 0 0
\(430\) −2.31685 0.240419i −0.111728 0.0115940i
\(431\) 0.427248i 0.0205798i 0.999947 + 0.0102899i \(0.00327543\pi\)
−0.999947 + 0.0102899i \(0.996725\pi\)
\(432\) 0 0
\(433\) −12.7271 + 12.7271i −0.611625 + 0.611625i −0.943369 0.331744i \(-0.892363\pi\)
0.331744 + 0.943369i \(0.392363\pi\)
\(434\) 0.0284626 + 0.161419i 0.00136625 + 0.00774838i
\(435\) 0 0
\(436\) −12.6892 + 4.61851i −0.607705 + 0.221186i
\(437\) 7.34854 0.642914i 0.351528 0.0307547i
\(438\) 0 0
\(439\) −2.87705 + 7.90463i −0.137314 + 0.377267i −0.989222 0.146425i \(-0.953223\pi\)
0.851908 + 0.523692i \(0.175446\pi\)
\(440\) −23.0813 13.8272i −1.10036 0.659188i
\(441\) 0 0
\(442\) −4.98928 + 1.33687i −0.237316 + 0.0635885i
\(443\) 8.73772 + 0.764452i 0.415142 + 0.0363202i 0.292814 0.956170i \(-0.405408\pi\)
0.122328 + 0.992490i \(0.460964\pi\)
\(444\) 0 0
\(445\) 13.1815 27.1168i 0.624861 1.28546i
\(446\) −15.6197 2.75417i −0.739614 0.130414i
\(447\) 0 0
\(448\) 0.00846683 0.0967763i 0.000400020 0.00457225i
\(449\) 12.5244 21.6930i 0.591065 1.02375i −0.403025 0.915189i \(-0.632041\pi\)
0.994089 0.108565i \(-0.0346255\pi\)
\(450\) 0 0
\(451\) 1.91295 + 3.31332i 0.0900772 + 0.156018i
\(452\) −2.97213 + 1.38593i −0.139797 + 0.0651886i
\(453\) 0 0
\(454\) −6.23775 + 7.43386i −0.292752 + 0.348888i
\(455\) 0.635260 0.0452644i 0.0297814 0.00212203i
\(456\) 0 0
\(457\) −19.0426 + 27.1956i −0.890775 + 1.27216i 0.0707647 + 0.997493i \(0.477456\pi\)
−0.961540 + 0.274666i \(0.911433\pi\)
\(458\) −0.974227 0.974227i −0.0455226 0.0455226i
\(459\) 0 0
\(460\) 3.12902 1.73985i 0.145891 0.0811208i
\(461\) −33.1856 + 5.85151i −1.54561 + 0.272532i −0.880438 0.474161i \(-0.842751\pi\)
−0.665169 + 0.746693i \(0.731640\pi\)
\(462\) 0 0
\(463\) 4.31391 9.25121i 0.200484 0.429940i −0.780202 0.625528i \(-0.784884\pi\)
0.980686 + 0.195588i \(0.0626614\pi\)
\(464\) −4.25037 3.56648i −0.197318 0.165570i
\(465\) 0 0
\(466\) 3.19317 + 1.16222i 0.147921 + 0.0538388i
\(467\) 7.55151 + 2.02342i 0.349442 + 0.0936327i 0.429271 0.903176i \(-0.358771\pi\)
−0.0798287 + 0.996809i \(0.525437\pi\)
\(468\) 0 0
\(469\) 1.42675 + 0.823732i 0.0658810 + 0.0380364i
\(470\) 6.07811 + 13.6033i 0.280362 + 0.627474i
\(471\) 0 0
\(472\) 1.85598 1.29957i 0.0854284 0.0598176i
\(473\) 7.87652 5.51520i 0.362163 0.253589i
\(474\) 0 0
\(475\) 5.36333 + 37.4445i 0.246086 + 1.71807i
\(476\) 0.977453 + 0.564332i 0.0448015 + 0.0258661i
\(477\) 0 0
\(478\) 16.8893 + 4.52548i 0.772500 + 0.206991i
\(479\) −12.4057 4.51531i −0.566831 0.206310i 0.0426779 0.999089i \(-0.486411\pi\)
−0.609509 + 0.792779i \(0.708633\pi\)
\(480\) 0 0
\(481\) 8.56981 + 7.19093i 0.390750 + 0.327878i
\(482\) −1.58883 + 3.40726i −0.0723693 + 0.155197i
\(483\) 0 0
\(484\) 31.5283 5.55928i 1.43310 0.252695i
\(485\) 3.88838 + 6.99304i 0.176562 + 0.317537i
\(486\) 0 0
\(487\) 12.1497 + 12.1497i 0.550553 + 0.550553i 0.926601 0.376047i \(-0.122717\pi\)
−0.376047 + 0.926601i \(0.622717\pi\)
\(488\) −12.1377 + 17.3345i −0.549450 + 0.784696i
\(489\) 0 0
\(490\) −7.05252 6.11434i −0.318600 0.276218i
\(491\) 11.2054 13.3541i 0.505693 0.602661i −0.451443 0.892300i \(-0.649091\pi\)
0.957136 + 0.289639i \(0.0935352\pi\)
\(492\) 0 0
\(493\) 11.5893 5.40417i 0.521955 0.243392i
\(494\) −4.28045 7.41396i −0.192587 0.333570i
\(495\) 0 0
\(496\) −1.80181 + 3.12082i −0.0809035 + 0.140129i
\(497\) 0.0383438 0.438272i 0.00171995 0.0196592i
\(498\) 0 0
\(499\) −3.01325 0.531318i −0.134892 0.0237851i 0.105795 0.994388i \(-0.466261\pi\)
−0.240686 + 0.970603i \(0.577373\pi\)
\(500\) 9.79037 + 15.5307i 0.437839 + 0.694553i
\(501\) 0 0
\(502\) −5.50326 0.481473i −0.245623 0.0214892i
\(503\) 6.64016 1.77923i 0.296070 0.0793318i −0.107726 0.994181i \(-0.534357\pi\)
0.403797 + 0.914849i \(0.367690\pi\)
\(504\) 0 0
\(505\) 8.35308 2.09437i 0.371707 0.0931983i
\(506\) 1.10178 3.02713i 0.0489803 0.134572i
\(507\) 0 0
\(508\) 10.8809 0.951954i 0.482761 0.0422361i
\(509\) 28.5486 10.3908i 1.26540 0.460566i 0.379819 0.925061i \(-0.375986\pi\)
0.885576 + 0.464495i \(0.153764\pi\)
\(510\) 0 0
\(511\) 0.269447 + 1.52811i 0.0119196 + 0.0675997i
\(512\) −13.8657 + 13.8657i −0.612783 + 0.612783i
\(513\) 0 0
\(514\) 9.84374i 0.434189i
\(515\) −17.3618 21.3823i −0.765053 0.942216i
\(516\) 0 0
\(517\) −55.7433 25.9935i −2.45159 1.14319i
\(518\) 0.0464382 + 0.530791i 0.00204038 + 0.0233216i
\(519\) 0 0
\(520\) −7.46275 5.40697i −0.327263 0.237111i
\(521\) 1.31724 0.760511i 0.0577095 0.0333186i −0.470868 0.882204i \(-0.656059\pi\)
0.528577 + 0.848885i \(0.322726\pi\)
\(522\) 0 0
\(523\) 3.57368 + 13.3371i 0.156266 + 0.583192i 0.998994 + 0.0448523i \(0.0142817\pi\)
−0.842728 + 0.538340i \(0.819052\pi\)
\(524\) −17.0114 + 14.2743i −0.743148 + 0.623576i
\(525\) 0 0
\(526\) −1.27426 + 7.22671i −0.0555606 + 0.315100i
\(527\) −4.76363 6.80317i −0.207507 0.296351i
\(528\) 0 0
\(529\) −14.1730 16.8907i −0.616217 0.734379i
\(530\) −0.278599 + 0.269751i −0.0121016 + 0.0117173i
\(531\) 0 0
\(532\) −0.484158 + 1.80690i −0.0209909 + 0.0783391i
\(533\) 0.553803 + 1.18763i 0.0239879 + 0.0514421i
\(534\) 0 0
\(535\) −2.71546 0.524114i −0.117400 0.0226594i
\(536\) −8.15346 22.4015i −0.352176 0.967595i
\(537\) 0 0
\(538\) 9.04315 + 6.33208i 0.389878 + 0.272995i
\(539\) 38.5313 1.65966
\(540\) 0 0
\(541\) 0.376014 0.0161661 0.00808305 0.999967i \(-0.497427\pi\)
0.00808305 + 0.999967i \(0.497427\pi\)
\(542\) 6.54839 + 4.58523i 0.281278 + 0.196953i
\(543\) 0 0
\(544\) −8.65328 23.7747i −0.371006 1.01933i
\(545\) 15.2310 10.3027i 0.652423 0.441319i
\(546\) 0 0
\(547\) 5.56415 + 11.9323i 0.237906 + 0.510190i 0.988620 0.150437i \(-0.0480681\pi\)
−0.750714 + 0.660627i \(0.770290\pi\)
\(548\) −3.47915 + 12.9844i −0.148622 + 0.554665i
\(549\) 0 0
\(550\) 15.8100 + 4.78800i 0.674141 + 0.204161i
\(551\) 13.6230 + 16.2353i 0.580361 + 0.691647i
\(552\) 0 0
\(553\) 1.04522 + 1.49272i 0.0444471 + 0.0634770i
\(554\) −2.23156 + 12.6558i −0.0948101 + 0.537695i
\(555\) 0 0
\(556\) 22.9641 19.2691i 0.973893 0.817193i
\(557\) 7.60724 + 28.3906i 0.322329 + 1.20295i 0.916970 + 0.398957i \(0.130628\pi\)
−0.594641 + 0.803991i \(0.702706\pi\)
\(558\) 0 0
\(559\) 2.85217 1.64670i 0.120634 0.0696479i
\(560\) 0.105192 + 0.658531i 0.00444518 + 0.0278280i
\(561\) 0 0
\(562\) 0.362542 + 4.14388i 0.0152929 + 0.174799i
\(563\) −7.92028 3.69329i −0.333800 0.155653i 0.248490 0.968634i \(-0.420066\pi\)
−0.582290 + 0.812981i \(0.697843\pi\)
\(564\) 0 0
\(565\) 3.46674 2.81489i 0.145847 0.118423i
\(566\) 14.4516i 0.607448i
\(567\) 0 0
\(568\) −4.50151 + 4.50151i −0.188879 + 0.188879i
\(569\) 0.230736 + 1.30857i 0.00967296 + 0.0548581i 0.989262 0.146152i \(-0.0466888\pi\)
−0.979589 + 0.201010i \(0.935578\pi\)
\(570\) 0 0
\(571\) −14.3584 + 5.22603i −0.600881 + 0.218703i −0.624508 0.781018i \(-0.714701\pi\)
0.0236277 + 0.999721i \(0.492478\pi\)
\(572\) 17.0868 1.49490i 0.714436 0.0625050i
\(573\) 0 0
\(574\) −0.0213462 + 0.0586482i −0.000890974 + 0.00244793i
\(575\) −3.55675 + 3.33432i −0.148327 + 0.139051i
\(576\) 0 0
\(577\) 33.8078 9.05878i 1.40744 0.377122i 0.526428 0.850220i \(-0.323531\pi\)
0.881010 + 0.473098i \(0.156864\pi\)
\(578\) 2.28596 + 0.199995i 0.0950833 + 0.00831871i
\(579\) 0 0
\(580\) 9.25117 + 4.49699i 0.384134 + 0.186727i
\(581\) 1.06081 + 0.187049i 0.0440097 + 0.00776009i
\(582\) 0 0
\(583\) 0.139522 1.59474i 0.00577840 0.0660475i
\(584\) 11.2266 19.4450i 0.464560 0.804641i
\(585\) 0 0
\(586\) −4.81376 8.33768i −0.198855 0.344426i
\(587\) −28.8395 + 13.4481i −1.19033 + 0.555061i −0.913887 0.405968i \(-0.866934\pi\)
−0.276446 + 0.961030i \(0.589157\pi\)
\(588\) 0 0
\(589\) 8.84789 10.5445i 0.364571 0.434479i
\(590\) −0.911228 + 1.05105i −0.0375146 + 0.0432709i
\(591\) 0 0
\(592\) −6.71900 + 9.59573i −0.276149 + 0.394382i
\(593\) 14.3845 + 14.3845i 0.590702 + 0.590702i 0.937821 0.347119i \(-0.112840\pi\)
−0.347119 + 0.937821i \(0.612840\pi\)
\(594\) 0 0
\(595\) −1.47795 0.421686i −0.0605902 0.0172875i
\(596\) −6.76022 + 1.19201i −0.276909 + 0.0488266i
\(597\) 0 0
\(598\) 0.466302 0.999988i 0.0190685 0.0408925i
\(599\) 30.6931 + 25.7546i 1.25409 + 1.05230i 0.996286 + 0.0861056i \(0.0274423\pi\)
0.257801 + 0.966198i \(0.417002\pi\)
\(600\) 0 0
\(601\) 30.8662 + 11.2344i 1.25906 + 0.458260i 0.883453 0.468519i \(-0.155212\pi\)
0.375606 + 0.926779i \(0.377435\pi\)
\(602\) 0.151513 + 0.0405978i 0.00617521 + 0.00165464i
\(603\) 0 0
\(604\) −6.91453 3.99211i −0.281348 0.162436i
\(605\) −39.8028 + 17.7843i −1.61821 + 0.723036i
\(606\) 0 0
\(607\) 19.8141 13.8740i 0.804231 0.563129i −0.0975958 0.995226i \(-0.531115\pi\)
0.901827 + 0.432097i \(0.142226\pi\)
\(608\) 34.3494 24.0517i 1.39305 0.975426i
\(609\) 0 0
\(610\) 4.63997 12.1354i 0.187867 0.491347i
\(611\) −18.2441 10.5332i −0.738075 0.426128i
\(612\) 0 0
\(613\) 21.4554 + 5.74896i 0.866575 + 0.232198i 0.664606 0.747194i \(-0.268599\pi\)
0.201969 + 0.979392i \(0.435266\pi\)
\(614\) 18.0252 + 6.56065i 0.727440 + 0.264766i
\(615\) 0 0
\(616\) 1.38800 + 1.16467i 0.0559239 + 0.0469258i
\(617\) 4.95167 10.6189i 0.199347 0.427500i −0.781068 0.624446i \(-0.785325\pi\)
0.980414 + 0.196946i \(0.0631024\pi\)
\(618\) 0 0
\(619\) −28.3482 + 4.99855i −1.13941 + 0.200909i −0.711347 0.702841i \(-0.751915\pi\)
−0.428062 + 0.903749i \(0.640803\pi\)
\(620\) 1.83298 6.42434i 0.0736142 0.258008i
\(621\) 0 0
\(622\) −7.59634 7.59634i −0.304585 0.304585i
\(623\) −1.16459 + 1.66321i −0.0466583 + 0.0666349i
\(624\) 0 0
\(625\) −18.0749 17.2713i −0.722997 0.690851i
\(626\) 0.206299 0.245858i 0.00824538 0.00982646i
\(627\) 0 0
\(628\) −25.9103 + 12.0821i −1.03393 + 0.482130i
\(629\) −13.4987 23.3804i −0.538228 0.932239i
\(630\) 0 0
\(631\) −8.26145 + 14.3093i −0.328883 + 0.569643i −0.982291 0.187364i \(-0.940006\pi\)
0.653407 + 0.757007i \(0.273339\pi\)
\(632\) 2.29819 26.2684i 0.0914169 1.04490i
\(633\) 0 0
\(634\) 17.4249 + 3.07247i 0.692029 + 0.122023i
\(635\) −14.0567 + 4.86086i −0.557822 + 0.192898i
\(636\) 0 0
\(637\) 13.1471 + 1.15023i 0.520909 + 0.0455736i
\(638\) 8.94003 2.39547i 0.353939 0.0948377i
\(639\) 0 0
\(640\) 13.1822 22.0047i 0.521073 0.869810i
\(641\) 6.11791 16.8088i 0.241643 0.663909i −0.758285 0.651923i \(-0.773962\pi\)
0.999928 0.0119858i \(-0.00381528\pi\)
\(642\) 0 0
\(643\) 21.1290 1.84855i 0.833247 0.0728997i 0.337456 0.941341i \(-0.390434\pi\)
0.495791 + 0.868442i \(0.334878\pi\)
\(644\) −0.226556 + 0.0824598i −0.00892757 + 0.00324937i
\(645\) 0 0
\(646\) 3.58752 + 20.3458i 0.141149 + 0.800496i
\(647\) 7.44855 7.44855i 0.292833 0.292833i −0.545366 0.838198i \(-0.683609\pi\)
0.838198 + 0.545366i \(0.183609\pi\)
\(648\) 0 0
\(649\) 5.74237i 0.225408i
\(650\) 5.25156 + 2.10566i 0.205983 + 0.0825907i
\(651\) 0 0
\(652\) −5.56558 2.59527i −0.217965 0.101639i
\(653\) 4.00398 + 45.7657i 0.156688 + 1.79095i 0.514838 + 0.857288i \(0.327852\pi\)
−0.358150 + 0.933664i \(0.616592\pi\)
\(654\) 0 0
\(655\) 17.7422 24.4879i 0.693243 0.956821i
\(656\) −1.18832 + 0.686078i −0.0463961 + 0.0267868i
\(657\) 0 0
\(658\) −0.259686 0.969163i −0.0101236 0.0377819i
\(659\) 3.34888 2.81004i 0.130454 0.109464i −0.575226 0.817994i \(-0.695086\pi\)
0.705680 + 0.708531i \(0.250642\pi\)
\(660\) 0 0
\(661\) 6.57135 37.2680i 0.255596 1.44956i −0.538943 0.842342i \(-0.681176\pi\)
0.794539 0.607214i \(-0.207713\pi\)
\(662\) 9.07285 + 12.9574i 0.352626 + 0.503603i
\(663\) 0 0
\(664\) −10.0190 11.9402i −0.388815 0.463371i
\(665\) 0.0410949 2.54698i 0.00159359 0.0987675i
\(666\) 0 0
\(667\) −0.706972 + 2.63846i −0.0273741 + 0.102161i
\(668\) 0.364685 + 0.782069i 0.0141101 + 0.0302592i
\(669\) 0 0
\(670\) 8.20042 + 12.1231i 0.316810 + 0.468355i
\(671\) 18.3434 + 50.3981i 0.708140 + 1.94560i
\(672\) 0 0
\(673\) −35.3130 24.7264i −1.36122 0.953134i −0.999785 0.0207353i \(-0.993399\pi\)
−0.361431 0.932399i \(-0.617712\pi\)
\(674\) 10.3680 0.399362
\(675\) 0 0
\(676\) −15.4723 −0.595088
\(677\) 32.2989 + 22.6160i 1.24135 + 0.869202i 0.994990 0.0999769i \(-0.0318769\pi\)
0.246359 + 0.969179i \(0.420766\pi\)
\(678\) 0 0
\(679\) −0.184289 0.506330i −0.00707236 0.0194312i
\(680\) 12.4606 + 18.4212i 0.477844 + 0.706419i
\(681\) 0 0
\(682\) −2.54044 5.44799i −0.0972785 0.208614i
\(683\) 7.98000 29.7818i 0.305346 1.13957i −0.627301 0.778777i \(-0.715840\pi\)
0.932647 0.360791i \(-0.117493\pi\)
\(684\) 0 0
\(685\) 0.295307 18.3025i 0.0112831 0.699304i
\(686\) 0.809379 + 0.964580i 0.0309022 + 0.0368279i
\(687\) 0 0
\(688\) 1.97802 + 2.82491i 0.0754115 + 0.107699i
\(689\) 0.0952117 0.539972i 0.00362728 0.0205713i
\(690\) 0 0
\(691\) −14.5283 + 12.1907i −0.552681 + 0.463755i −0.875848 0.482587i \(-0.839697\pi\)
0.323166 + 0.946342i \(0.395253\pi\)
\(692\) −7.47898 27.9119i −0.284308 1.06105i
\(693\) 0 0
\(694\) −4.33466 + 2.50262i −0.164541 + 0.0949980i
\(695\) −23.9505 + 33.0566i −0.908493 + 1.25391i
\(696\) 0 0
\(697\) −0.275618 3.15033i −0.0104398 0.119327i
\(698\) 11.6082 + 5.41299i 0.439377 + 0.204885i
\(699\) 0 0
\(700\) −0.486073 1.13676i −0.0183718 0.0429656i
\(701\) 10.8100i 0.408288i 0.978941 + 0.204144i \(0.0654410\pi\)
−0.978941 + 0.204144i \(0.934559\pi\)
\(702\) 0 0
\(703\) 31.6397 31.6397i 1.19331 1.19331i
\(704\) 0.618659 + 3.50859i 0.0233166 + 0.132235i
\(705\) 0 0
\(706\) −16.3516 + 5.95150i −0.615401 + 0.223987i
\(707\) −0.577714 + 0.0505434i −0.0217272 + 0.00190088i
\(708\) 0 0
\(709\) −11.3780 + 31.2608i −0.427310 + 1.17403i 0.520129 + 0.854088i \(0.325884\pi\)
−0.947439 + 0.319937i \(0.896338\pi\)
\(710\) 2.00860 3.35289i 0.0753813 0.125832i
\(711\) 0 0
\(712\) 28.3792 7.60417i 1.06355 0.284978i
\(713\) 1.76732 + 0.154621i 0.0661868 + 0.00579060i
\(714\) 0 0
\(715\) −22.0739 + 7.63327i −0.825518 + 0.285468i
\(716\) −1.40740 0.248162i −0.0525969 0.00927426i
\(717\) 0 0
\(718\) 0.555558 6.35006i 0.0207332 0.236982i
\(719\) −20.7377 + 35.9188i −0.773387 + 1.33955i 0.162310 + 0.986740i \(0.448106\pi\)
−0.935697 + 0.352806i \(0.885228\pi\)
\(720\) 0 0
\(721\) 0.927405 + 1.60631i 0.0345384 + 0.0598222i
\(722\) −20.7311 + 9.66707i −0.771532 + 0.359771i
\(723\) 0 0
\(724\) 11.5567 13.7727i 0.429501 0.511860i
\(725\) −13.7086 2.87606i −0.509126 0.106814i
\(726\) 0 0
\(727\) 7.46713 10.6642i 0.276940 0.395512i −0.656453 0.754367i \(-0.727944\pi\)
0.933393 + 0.358855i \(0.116833\pi\)
\(728\) 0.438827 + 0.438827i 0.0162640 + 0.0162640i
\(729\) 0 0
\(730\) −3.78223 + 13.2562i −0.139986 + 0.490634i
\(731\) −7.82709 + 1.38013i −0.289495 + 0.0510458i
\(732\) 0 0
\(733\) −13.8950 + 29.7979i −0.513223 + 1.10061i 0.463499 + 0.886098i \(0.346594\pi\)
−0.976721 + 0.214512i \(0.931184\pi\)
\(734\) −9.85447 8.26888i −0.363735 0.305210i
\(735\) 0 0
\(736\) 5.07856 + 1.84844i 0.187198 + 0.0681345i
\(737\) −58.3601 15.6375i −2.14972 0.576016i
\(738\) 0 0
\(739\) 13.4399 + 7.75952i 0.494394 + 0.285439i 0.726396 0.687277i \(-0.241194\pi\)
−0.232001 + 0.972715i \(0.574527\pi\)
\(740\) 7.75589 20.2848i 0.285112 0.745683i
\(741\) 0 0
\(742\) 0.0213918 0.0149787i 0.000785317 0.000549885i
\(743\) −25.3533 + 17.7526i −0.930122 + 0.651279i −0.937236 0.348696i \(-0.886625\pi\)
0.00711360 + 0.999975i \(0.497736\pi\)
\(744\) 0 0
\(745\) 8.53442 3.81328i 0.312677 0.139708i
\(746\) −5.69017 3.28522i −0.208332 0.120280i
\(747\) 0 0
\(748\) −39.9821 10.7132i −1.46189 0.391712i
\(749\) 0.175007 + 0.0636972i 0.00639460 + 0.00232745i
\(750\) 0 0
\(751\) 36.7847 + 30.8660i 1.34229 + 1.12632i 0.981030 + 0.193854i \(0.0620989\pi\)
0.361263 + 0.932464i \(0.382346\pi\)
\(752\) 9.32256 19.9923i 0.339959 0.729044i
\(753\) 0 0
\(754\) 3.12191 0.550477i 0.113693 0.0200472i
\(755\) 10.4551 + 2.98302i 0.380500 + 0.108563i
\(756\) 0 0
\(757\) 2.53936 + 2.53936i 0.0922948 + 0.0922948i 0.751747 0.659452i \(-0.229212\pi\)
−0.659452 + 0.751747i \(0.729212\pi\)
\(758\) −3.25643 + 4.65066i −0.118279 + 0.168919i
\(759\) 0 0
\(760\) −24.1456 + 27.8505i −0.875854 + 1.01024i
\(761\) 12.6924 15.1262i 0.460099 0.548324i −0.485254 0.874373i \(-0.661273\pi\)
0.945353 + 0.326049i \(0.105717\pi\)
\(762\) 0 0
\(763\) −1.12227 + 0.523325i −0.0406291 + 0.0189456i
\(764\) 11.6928 + 20.2525i 0.423030 + 0.732710i
\(765\) 0 0
\(766\) −7.82380 + 13.5512i −0.282685 + 0.489625i
\(767\) 0.171420 1.95934i 0.00618961 0.0707475i
\(768\) 0 0
\(769\) −12.6400 2.22877i −0.455810 0.0803717i −0.0589709 0.998260i \(-0.518782\pi\)
−0.396839 + 0.917888i \(0.629893\pi\)
\(770\) −1.00048 0.486334i −0.0360548 0.0175262i
\(771\) 0 0
\(772\) −19.8220 1.73420i −0.713409 0.0624152i
\(773\) 13.0368 3.49320i 0.468901 0.125642i −0.0166290 0.999862i \(-0.505293\pi\)
0.485530 + 0.874220i \(0.338627\pi\)
\(774\) 0 0
\(775\) −0.293490 + 9.09259i −0.0105425 + 0.326616i
\(776\) −2.66670 + 7.32669i −0.0957289 + 0.263013i
\(777\) 0 0
\(778\) 2.25798 0.197548i 0.0809526 0.00708244i
\(779\) 4.92519 1.79262i 0.176463 0.0642274i
\(780\) 0 0
\(781\) 2.80173 + 15.8894i 0.100254 + 0.568567i
\(782\) −1.88282 + 1.88282i −0.0673295 + 0.0673295i
\(783\) 0 0
\(784\) 13.8192i 0.493544i
\(785\) 30.2221 24.5395i 1.07867 0.875851i
\(786\) 0 0
\(787\)