Properties

Label 225.2.k.b.124.1
Level $225$
Weight $2$
Character 225.124
Analytic conductor $1.797$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \( x^{12} - 16x^{8} - 24x^{7} + 96x^{5} + 304x^{4} + 384x^{3} + 288x^{2} + 144x + 36 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 124.1
Root \(-0.180407 - 0.673288i\) of defining polynomial
Character \(\chi\) \(=\) 225.124
Dual form 225.2.k.b.49.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.17731 - 1.25707i) q^{2} +(1.19154 - 1.25707i) q^{3} +(2.16044 + 3.74200i) q^{4} +(-4.17458 + 1.23917i) q^{6} +(0.445256 + 0.257068i) q^{7} -5.83502i q^{8} +(-0.160442 - 2.99571i) q^{9} +O(q^{10})\) \(q+(-2.17731 - 1.25707i) q^{2} +(1.19154 - 1.25707i) q^{3} +(2.16044 + 3.74200i) q^{4} +(-4.17458 + 1.23917i) q^{6} +(0.445256 + 0.257068i) q^{7} -5.83502i q^{8} +(-0.160442 - 2.99571i) q^{9} +(1.66044 - 2.87597i) q^{11} +(7.27821 + 1.74293i) q^{12} +(1.14392 - 0.660442i) q^{13} +(-0.646305 - 1.11943i) q^{14} +(-3.01414 + 5.22064i) q^{16} -3.32088i q^{17} +(-3.41648 + 6.72426i) q^{18} +1.32088 q^{19} +(0.853695 - 0.253408i) q^{21} +(-7.23058 + 4.17458i) q^{22} +(-3.57463 + 2.06382i) q^{23} +(-7.33502 - 6.95269i) q^{24} -3.32088 q^{26} +(-3.95698 - 3.36783i) q^{27} +2.22153i q^{28} +(-0.693252 + 1.20075i) q^{29} +(-4.36783 - 7.56531i) q^{31} +(3.01885 - 1.74293i) q^{32} +(-1.63680 - 5.51414i) q^{33} +(-4.17458 + 7.23058i) q^{34} +(10.8633 - 7.07243i) q^{36} +0.292611i q^{37} +(-2.87597 - 1.66044i) q^{38} +(0.532810 - 2.22493i) q^{39} +(5.67458 + 9.82866i) q^{41} +(-2.17731 - 0.521405i) q^{42} +(8.96263 + 5.17458i) q^{43} +14.3492 q^{44} +10.3774 q^{46} +(4.21174 + 2.43165i) q^{47} +(2.97122 + 10.0096i) q^{48} +(-3.36783 - 5.83326i) q^{49} +(-4.17458 - 3.95698i) q^{51} +(4.94274 + 2.85369i) q^{52} +5.02827i q^{53} +(4.38197 + 12.3070i) q^{54} +(1.50000 - 2.59808i) q^{56} +(1.57389 - 1.66044i) q^{57} +(3.01885 - 1.74293i) q^{58} +(-2.51414 - 4.35461i) q^{59} +(-3.67458 + 6.36456i) q^{61} +21.9627i q^{62} +(0.698664 - 1.37510i) q^{63} +3.29261 q^{64} +(-3.36783 + 14.0635i) q^{66} +(8.18266 - 4.72426i) q^{67} +(12.4267 - 7.17458i) q^{68} +(-1.66498 + 6.95269i) q^{69} +8.99093 q^{71} +(-17.4800 + 0.936184i) q^{72} -6.05655i q^{73} +(0.367832 - 0.637103i) q^{74} +(2.85369 + 4.94274i) q^{76} +(1.47864 - 0.853695i) q^{77} +(-3.95698 + 4.17458i) q^{78} +(-4.02827 + 6.97717i) q^{79} +(-8.94852 + 0.961276i) q^{81} -28.5333i q^{82} +(1.33577 + 0.771205i) q^{83} +(2.79261 + 2.64705i) q^{84} +(-13.0096 - 22.5333i) q^{86} +(0.683382 + 2.30221i) q^{87} +(-16.7813 - 9.68872i) q^{88} +3.00000 q^{89} +0.679116 q^{91} +(-15.4456 - 8.91751i) q^{92} +(-14.7146 - 3.52374i) q^{93} +(-6.11350 - 10.5889i) q^{94} +(1.40611 - 5.87168i) q^{96} +(10.6134 + 6.12763i) q^{97} +16.9344i q^{98} +(-8.88197 - 4.51277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 10 q^{4} - 8 q^{6} + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 10 q^{4} - 8 q^{6} + 14 q^{9} + 4 q^{11} - 18 q^{14} - 10 q^{16} - 16 q^{19} - 30 q^{24} - 8 q^{26} - 14 q^{29} - 16 q^{31} - 8 q^{34} + 20 q^{36} + 28 q^{39} + 26 q^{41} + 88 q^{44} - 12 q^{46} - 4 q^{49} - 8 q^{51} - 10 q^{54} + 18 q^{56} - 4 q^{59} - 2 q^{61} + 60 q^{64} - 4 q^{66} - 78 q^{69} - 40 q^{71} - 32 q^{74} + 24 q^{76} + 4 q^{79} - 38 q^{81} + 54 q^{84} - 56 q^{86} + 36 q^{89} + 40 q^{91} - 62 q^{94} + 26 q^{96} - 44 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.17731 1.25707i −1.53959 0.888882i −0.998863 0.0476826i \(-0.984816\pi\)
−0.540726 0.841199i \(-0.681850\pi\)
\(3\) 1.19154 1.25707i 0.687939 0.725769i
\(4\) 2.16044 + 3.74200i 1.08022 + 1.87100i
\(5\) 0 0
\(6\) −4.17458 + 1.23917i −1.70426 + 0.505889i
\(7\) 0.445256 + 0.257068i 0.168291 + 0.0971627i 0.581780 0.813346i \(-0.302357\pi\)
−0.413489 + 0.910509i \(0.635690\pi\)
\(8\) 5.83502i 2.06299i
\(9\) −0.160442 2.99571i −0.0534807 0.998569i
\(10\) 0 0
\(11\) 1.66044 2.87597i 0.500642 0.867138i −0.499358 0.866396i \(-0.666431\pi\)
1.00000 0.000741679i \(-0.000236084\pi\)
\(12\) 7.27821 + 1.74293i 2.10104 + 0.503141i
\(13\) 1.14392 0.660442i 0.317266 0.183174i −0.332907 0.942960i \(-0.608030\pi\)
0.650173 + 0.759786i \(0.274696\pi\)
\(14\) −0.646305 1.11943i −0.172732 0.299181i
\(15\) 0 0
\(16\) −3.01414 + 5.22064i −0.753534 + 1.30516i
\(17\) 3.32088i 0.805433i −0.915325 0.402716i \(-0.868066\pi\)
0.915325 0.402716i \(-0.131934\pi\)
\(18\) −3.41648 + 6.72426i −0.805271 + 1.58492i
\(19\) 1.32088 0.303032 0.151516 0.988455i \(-0.451585\pi\)
0.151516 + 0.988455i \(0.451585\pi\)
\(20\) 0 0
\(21\) 0.853695 0.253408i 0.186291 0.0552982i
\(22\) −7.23058 + 4.17458i −1.54157 + 0.890023i
\(23\) −3.57463 + 2.06382i −0.745363 + 0.430335i −0.824016 0.566567i \(-0.808271\pi\)
0.0786532 + 0.996902i \(0.474938\pi\)
\(24\) −7.33502 6.95269i −1.49725 1.41921i
\(25\) 0 0
\(26\) −3.32088 −0.651279
\(27\) −3.95698 3.36783i −0.761522 0.648139i
\(28\) 2.22153i 0.419829i
\(29\) −0.693252 + 1.20075i −0.128734 + 0.222973i −0.923186 0.384353i \(-0.874425\pi\)
0.794453 + 0.607326i \(0.207758\pi\)
\(30\) 0 0
\(31\) −4.36783 7.56531i −0.784486 1.35877i −0.929306 0.369311i \(-0.879594\pi\)
0.144820 0.989458i \(-0.453740\pi\)
\(32\) 3.01885 1.74293i 0.533662 0.308110i
\(33\) −1.63680 5.51414i −0.284930 0.959888i
\(34\) −4.17458 + 7.23058i −0.715934 + 1.24003i
\(35\) 0 0
\(36\) 10.8633 7.07243i 1.81055 1.17874i
\(37\) 0.292611i 0.0481049i 0.999711 + 0.0240524i \(0.00765687\pi\)
−0.999711 + 0.0240524i \(0.992343\pi\)
\(38\) −2.87597 1.66044i −0.466544 0.269359i
\(39\) 0.532810 2.22493i 0.0853179 0.356274i
\(40\) 0 0
\(41\) 5.67458 + 9.82866i 0.886220 + 1.53498i 0.844308 + 0.535857i \(0.180012\pi\)
0.0419119 + 0.999121i \(0.486655\pi\)
\(42\) −2.17731 0.521405i −0.335966 0.0804546i
\(43\) 8.96263 + 5.17458i 1.36679 + 0.789116i 0.990517 0.137393i \(-0.0438724\pi\)
0.376272 + 0.926509i \(0.377206\pi\)
\(44\) 14.3492 2.16322
\(45\) 0 0
\(46\) 10.3774 1.53007
\(47\) 4.21174 + 2.43165i 0.614345 + 0.354692i 0.774664 0.632373i \(-0.217919\pi\)
−0.160319 + 0.987065i \(0.551252\pi\)
\(48\) 2.97122 + 10.0096i 0.428859 + 1.44476i
\(49\) −3.36783 5.83326i −0.481119 0.833322i
\(50\) 0 0
\(51\) −4.17458 3.95698i −0.584558 0.554088i
\(52\) 4.94274 + 2.85369i 0.685435 + 0.395736i
\(53\) 5.02827i 0.690687i 0.938476 + 0.345343i \(0.112238\pi\)
−0.938476 + 0.345343i \(0.887762\pi\)
\(54\) 4.38197 + 12.3070i 0.596310 + 1.67477i
\(55\) 0 0
\(56\) 1.50000 2.59808i 0.200446 0.347183i
\(57\) 1.57389 1.66044i 0.208467 0.219931i
\(58\) 3.01885 1.74293i 0.396394 0.228858i
\(59\) −2.51414 4.35461i −0.327313 0.566922i 0.654665 0.755919i \(-0.272810\pi\)
−0.981978 + 0.188997i \(0.939476\pi\)
\(60\) 0 0
\(61\) −3.67458 + 6.36456i −0.470482 + 0.814898i −0.999430 0.0337558i \(-0.989253\pi\)
0.528948 + 0.848654i \(0.322586\pi\)
\(62\) 21.9627i 2.78926i
\(63\) 0.698664 1.37510i 0.0880234 0.173246i
\(64\) 3.29261 0.411576
\(65\) 0 0
\(66\) −3.36783 + 14.0635i −0.414551 + 1.73110i
\(67\) 8.18266 4.72426i 0.999670 0.577160i 0.0915197 0.995803i \(-0.470828\pi\)
0.908151 + 0.418643i \(0.137494\pi\)
\(68\) 12.4267 7.17458i 1.50696 0.870046i
\(69\) −1.66498 + 6.95269i −0.200440 + 0.837005i
\(70\) 0 0
\(71\) 8.99093 1.06703 0.533513 0.845792i \(-0.320871\pi\)
0.533513 + 0.845792i \(0.320871\pi\)
\(72\) −17.4800 + 0.936184i −2.06004 + 0.110330i
\(73\) 6.05655i 0.708865i −0.935082 0.354433i \(-0.884674\pi\)
0.935082 0.354433i \(-0.115326\pi\)
\(74\) 0.367832 0.637103i 0.0427596 0.0740617i
\(75\) 0 0
\(76\) 2.85369 + 4.94274i 0.327341 + 0.566972i
\(77\) 1.47864 0.853695i 0.168507 0.0972875i
\(78\) −3.95698 + 4.17458i −0.448040 + 0.472678i
\(79\) −4.02827 + 6.97717i −0.453216 + 0.784994i −0.998584 0.0532036i \(-0.983057\pi\)
0.545367 + 0.838197i \(0.316390\pi\)
\(80\) 0 0
\(81\) −8.94852 + 0.961276i −0.994280 + 0.106808i
\(82\) 28.5333i 3.15098i
\(83\) 1.33577 + 0.771205i 0.146619 + 0.0846508i 0.571515 0.820592i \(-0.306356\pi\)
−0.424896 + 0.905242i \(0.639689\pi\)
\(84\) 2.79261 + 2.64705i 0.304699 + 0.288817i
\(85\) 0 0
\(86\) −13.0096 22.5333i −1.40286 2.42983i
\(87\) 0.683382 + 2.30221i 0.0732662 + 0.246823i
\(88\) −16.7813 9.68872i −1.78890 1.03282i
\(89\) 3.00000 0.317999 0.159000 0.987279i \(-0.449173\pi\)
0.159000 + 0.987279i \(0.449173\pi\)
\(90\) 0 0
\(91\) 0.679116 0.0711906
\(92\) −15.4456 8.91751i −1.61031 0.929715i
\(93\) −14.7146 3.52374i −1.52583 0.365395i
\(94\) −6.11350 10.5889i −0.630559 1.09216i
\(95\) 0 0
\(96\) 1.40611 5.87168i 0.143510 0.599276i
\(97\) 10.6134 + 6.12763i 1.07762 + 0.622167i 0.930255 0.366915i \(-0.119586\pi\)
0.147370 + 0.989081i \(0.452919\pi\)
\(98\) 16.9344i 1.71063i
\(99\) −8.88197 4.51277i −0.892671 0.453551i
\(100\) 0 0
\(101\) −5.83502 + 10.1066i −0.580606 + 1.00564i 0.414801 + 0.909912i \(0.363851\pi\)
−0.995408 + 0.0957276i \(0.969482\pi\)
\(102\) 4.11514 + 13.8633i 0.407460 + 1.37267i
\(103\) −0.253408 + 0.146305i −0.0249691 + 0.0144159i −0.512433 0.858727i \(-0.671256\pi\)
0.487464 + 0.873143i \(0.337922\pi\)
\(104\) −3.85369 6.67479i −0.377886 0.654517i
\(105\) 0 0
\(106\) 6.32088 10.9481i 0.613939 1.06337i
\(107\) 1.87237i 0.181009i 0.995896 + 0.0905043i \(0.0288479\pi\)
−0.995896 + 0.0905043i \(0.971152\pi\)
\(108\) 4.05358 22.0830i 0.390056 2.12494i
\(109\) −5.54787 −0.531390 −0.265695 0.964057i \(-0.585601\pi\)
−0.265695 + 0.964057i \(0.585601\pi\)
\(110\) 0 0
\(111\) 0.367832 + 0.348659i 0.0349130 + 0.0330932i
\(112\) −2.68412 + 1.54968i −0.253626 + 0.146431i
\(113\) −6.75611 + 3.90064i −0.635561 + 0.366942i −0.782903 0.622144i \(-0.786262\pi\)
0.147341 + 0.989086i \(0.452928\pi\)
\(114\) −5.51414 + 1.63680i −0.516446 + 0.153300i
\(115\) 0 0
\(116\) −5.99093 −0.556244
\(117\) −2.16202 3.32088i −0.199879 0.307016i
\(118\) 12.6418i 1.16377i
\(119\) 0.853695 1.47864i 0.0782581 0.135547i
\(120\) 0 0
\(121\) −0.0141369 0.0244859i −0.00128518 0.00222599i
\(122\) 16.0014 9.23840i 1.44870 0.836405i
\(123\) 19.1168 + 4.57795i 1.72370 + 0.412780i
\(124\) 18.8729 32.6888i 1.69484 2.93554i
\(125\) 0 0
\(126\) −3.24980 + 2.11575i −0.289515 + 0.188486i
\(127\) 17.8916i 1.58762i 0.608166 + 0.793810i \(0.291906\pi\)
−0.608166 + 0.793810i \(0.708094\pi\)
\(128\) −13.2067 7.62490i −1.16732 0.673952i
\(129\) 17.1842 5.10090i 1.51298 0.449109i
\(130\) 0 0
\(131\) 3.00000 + 5.19615i 0.262111 + 0.453990i 0.966803 0.255524i \(-0.0822479\pi\)
−0.704692 + 0.709514i \(0.748915\pi\)
\(132\) 17.0977 18.0379i 1.48816 1.57000i
\(133\) 0.588131 + 0.339558i 0.0509974 + 0.0294434i
\(134\) −23.7549 −2.05211
\(135\) 0 0
\(136\) −19.3774 −1.66160
\(137\) −4.91040 2.83502i −0.419524 0.242212i 0.275350 0.961344i \(-0.411206\pi\)
−0.694874 + 0.719132i \(0.744540\pi\)
\(138\) 12.3652 13.0451i 1.05259 1.11048i
\(139\) 4.00000 + 6.92820i 0.339276 + 0.587643i 0.984297 0.176522i \(-0.0564848\pi\)
−0.645021 + 0.764165i \(0.723151\pi\)
\(140\) 0 0
\(141\) 8.07522 2.39703i 0.680056 0.201866i
\(142\) −19.5760 11.3022i −1.64278 0.948460i
\(143\) 4.38650i 0.366818i
\(144\) 16.1231 + 8.19186i 1.34359 + 0.682655i
\(145\) 0 0
\(146\) −7.61350 + 13.1870i −0.630097 + 1.09136i
\(147\) −11.3457 2.71699i −0.935780 0.224094i
\(148\) −1.09495 + 0.632168i −0.0900042 + 0.0519639i
\(149\) 8.83049 + 15.2948i 0.723422 + 1.25300i 0.959620 + 0.281298i \(0.0907650\pi\)
−0.236199 + 0.971705i \(0.575902\pi\)
\(150\) 0 0
\(151\) −0.632168 + 1.09495i −0.0514451 + 0.0891056i −0.890601 0.454785i \(-0.849716\pi\)
0.839156 + 0.543891i \(0.183049\pi\)
\(152\) 7.70739i 0.625152i
\(153\) −9.94840 + 0.532810i −0.804280 + 0.0430752i
\(154\) −4.29261 −0.345908
\(155\) 0 0
\(156\) 9.47679 2.81306i 0.758750 0.225225i
\(157\) −13.5707 + 7.83502i −1.08306 + 0.625303i −0.931719 0.363179i \(-0.881691\pi\)
−0.151337 + 0.988482i \(0.548358\pi\)
\(158\) 17.5416 10.1276i 1.39553 0.805711i
\(159\) 6.32088 + 5.99141i 0.501279 + 0.475150i
\(160\) 0 0
\(161\) −2.12217 −0.167250
\(162\) 20.6921 + 9.15591i 1.62572 + 0.719356i
\(163\) 15.7074i 1.23030i −0.788411 0.615149i \(-0.789096\pi\)
0.788411 0.615149i \(-0.210904\pi\)
\(164\) −24.5192 + 42.4685i −1.91463 + 3.31623i
\(165\) 0 0
\(166\) −1.93892 3.35830i −0.150489 0.260655i
\(167\) 5.33903 3.08249i 0.413146 0.238530i −0.278994 0.960293i \(-0.590001\pi\)
0.692141 + 0.721763i \(0.256668\pi\)
\(168\) −1.47864 4.98133i −0.114080 0.384318i
\(169\) −5.62763 + 9.74734i −0.432895 + 0.749796i
\(170\) 0 0
\(171\) −0.211926 3.95698i −0.0162064 0.302598i
\(172\) 44.7175i 3.40968i
\(173\) 7.43502 + 4.29261i 0.565274 + 0.326361i 0.755260 0.655426i \(-0.227511\pi\)
−0.189986 + 0.981787i \(0.560844\pi\)
\(174\) 1.40611 5.87168i 0.106597 0.445131i
\(175\) 0 0
\(176\) 10.0096 + 17.3371i 0.754502 + 1.30684i
\(177\) −8.46975 2.02827i −0.636626 0.152454i
\(178\) −6.53192 3.77121i −0.489588 0.282664i
\(179\) 1.06562 0.0796482 0.0398241 0.999207i \(-0.487320\pi\)
0.0398241 + 0.999207i \(0.487320\pi\)
\(180\) 0 0
\(181\) −12.6700 −0.941757 −0.470878 0.882198i \(-0.656063\pi\)
−0.470878 + 0.882198i \(0.656063\pi\)
\(182\) −1.47864 0.853695i −0.109604 0.0632801i
\(183\) 3.62226 + 12.2029i 0.267765 + 0.902061i
\(184\) 12.0424 + 20.8581i 0.887778 + 1.53768i
\(185\) 0 0
\(186\) 27.6086 + 26.1695i 2.02436 + 1.91884i
\(187\) −9.55077 5.51414i −0.698421 0.403234i
\(188\) 21.0137i 1.53258i
\(189\) −0.896105 2.51676i −0.0651821 0.183067i
\(190\) 0 0
\(191\) 8.46719 14.6656i 0.612664 1.06117i −0.378125 0.925754i \(-0.623431\pi\)
0.990789 0.135411i \(-0.0432356\pi\)
\(192\) 3.92329 4.13904i 0.283139 0.298709i
\(193\) −23.1380 + 13.3588i −1.66551 + 0.961585i −0.695502 + 0.718524i \(0.744818\pi\)
−0.970011 + 0.243060i \(0.921849\pi\)
\(194\) −15.4057 26.6835i −1.10607 1.91576i
\(195\) 0 0
\(196\) 14.5520 25.2048i 1.03943 1.80034i
\(197\) 14.2553i 1.01565i −0.861462 0.507823i \(-0.830450\pi\)
0.861462 0.507823i \(-0.169550\pi\)
\(198\) 13.6659 + 20.9909i 0.971194 + 1.49176i
\(199\) 24.6610 1.74817 0.874085 0.485773i \(-0.161462\pi\)
0.874085 + 0.485773i \(0.161462\pi\)
\(200\) 0 0
\(201\) 3.81128 15.9153i 0.268827 1.12258i
\(202\) 25.4093 14.6700i 1.78779 1.03218i
\(203\) −0.617349 + 0.356427i −0.0433294 + 0.0250162i
\(204\) 5.78807 24.1701i 0.405246 1.69224i
\(205\) 0 0
\(206\) 0.735663 0.0512561
\(207\) 6.75611 + 10.3774i 0.469582 + 0.721281i
\(208\) 7.96265i 0.552111i
\(209\) 2.19325 3.79882i 0.151710 0.262770i
\(210\) 0 0
\(211\) 2.68872 + 4.65699i 0.185099 + 0.320601i 0.943610 0.331060i \(-0.107406\pi\)
−0.758511 + 0.651660i \(0.774073\pi\)
\(212\) −18.8158 + 10.8633i −1.29227 + 0.746094i
\(213\) 10.7131 11.3022i 0.734049 0.774415i
\(214\) 2.35369 4.07672i 0.160895 0.278679i
\(215\) 0 0
\(216\) −19.6514 + 23.0891i −1.33711 + 1.57101i
\(217\) 4.49133i 0.304891i
\(218\) 12.0794 + 6.97406i 0.818122 + 0.472343i
\(219\) −7.61350 7.21665i −0.514472 0.487656i
\(220\) 0 0
\(221\) −2.19325 3.79882i −0.147534 0.255537i
\(222\) −0.362594 1.22153i −0.0243357 0.0819835i
\(223\) 7.50375 + 4.33229i 0.502488 + 0.290112i 0.729740 0.683724i \(-0.239641\pi\)
−0.227252 + 0.973836i \(0.572974\pi\)
\(224\) 1.79221 0.119747
\(225\) 0 0
\(226\) 19.6135 1.30467
\(227\) −2.87597 1.66044i −0.190885 0.110207i 0.401512 0.915854i \(-0.368485\pi\)
−0.592397 + 0.805646i \(0.701818\pi\)
\(228\) 9.61367 + 2.30221i 0.636681 + 0.152468i
\(229\) −12.6559 21.9207i −0.836326 1.44856i −0.892946 0.450163i \(-0.851366\pi\)
0.0566206 0.998396i \(-0.481967\pi\)
\(230\) 0 0
\(231\) 0.688716 2.87597i 0.0453142 0.189225i
\(232\) 7.00639 + 4.04514i 0.459992 + 0.265577i
\(233\) 27.6327i 1.81028i −0.425116 0.905139i \(-0.639767\pi\)
0.425116 0.905139i \(-0.360233\pi\)
\(234\) 0.532810 + 9.94840i 0.0348309 + 0.650347i
\(235\) 0 0
\(236\) 10.8633 18.8158i 0.707140 1.22480i
\(237\) 3.97092 + 13.3774i 0.257939 + 0.868958i
\(238\) −3.71751 + 2.14631i −0.240970 + 0.139124i
\(239\) −2.09936 3.63620i −0.135796 0.235206i 0.790105 0.612971i \(-0.210026\pi\)
−0.925901 + 0.377765i \(0.876693\pi\)
\(240\) 0 0
\(241\) −1.80221 + 3.12152i −0.116091 + 0.201075i −0.918215 0.396082i \(-0.870370\pi\)
0.802125 + 0.597157i \(0.203703\pi\)
\(242\) 0.0710844i 0.00456948i
\(243\) −9.45417 + 12.3943i −0.606485 + 0.795095i
\(244\) −31.7549 −2.03290
\(245\) 0 0
\(246\) −35.8684 33.9987i −2.28688 2.16768i
\(247\) 1.51099 0.872368i 0.0961417 0.0555074i
\(248\) −44.1437 + 25.4864i −2.80313 + 1.61839i
\(249\) 2.56108 0.760225i 0.162302 0.0481773i
\(250\) 0 0
\(251\) −6.87783 −0.434125 −0.217062 0.976158i \(-0.569648\pi\)
−0.217062 + 0.976158i \(0.569648\pi\)
\(252\) 6.65504 0.356427i 0.419228 0.0224528i
\(253\) 13.7074i 0.861776i
\(254\) 22.4909 38.9554i 1.41121 2.44428i
\(255\) 0 0
\(256\) 15.8774 + 27.5005i 0.992340 + 1.71878i
\(257\) −15.5885 + 9.00000i −0.972381 + 0.561405i −0.899961 0.435970i \(-0.856405\pi\)
−0.0724199 + 0.997374i \(0.523072\pi\)
\(258\) −43.8274 10.4955i −2.72858 0.653419i
\(259\) −0.0752210 + 0.130287i −0.00467400 + 0.00809561i
\(260\) 0 0
\(261\) 3.70832 + 1.88413i 0.229539 + 0.116625i
\(262\) 15.0848i 0.931943i
\(263\) 5.40059 + 3.11803i 0.333015 + 0.192266i 0.657179 0.753735i \(-0.271750\pi\)
−0.324164 + 0.946001i \(0.605083\pi\)
\(264\) −32.1751 + 9.55077i −1.98024 + 0.587809i
\(265\) 0 0
\(266\) −0.853695 1.47864i −0.0523434 0.0906614i
\(267\) 3.57463 3.77121i 0.218764 0.230794i
\(268\) 35.3563 + 20.4130i 2.15973 + 1.24692i
\(269\) −9.92345 −0.605044 −0.302522 0.953142i \(-0.597828\pi\)
−0.302522 + 0.953142i \(0.597828\pi\)
\(270\) 0 0
\(271\) 6.60442 0.401190 0.200595 0.979674i \(-0.435712\pi\)
0.200595 + 0.979674i \(0.435712\pi\)
\(272\) 17.3371 + 10.0096i 1.05122 + 0.606921i
\(273\) 0.809197 0.853695i 0.0489748 0.0516680i
\(274\) 7.12763 + 12.3454i 0.430596 + 0.745814i
\(275\) 0 0
\(276\) −29.6140 + 8.79054i −1.78255 + 0.529128i
\(277\) −19.6250 11.3305i −1.17915 0.680783i −0.223333 0.974742i \(-0.571694\pi\)
−0.955818 + 0.293959i \(0.905027\pi\)
\(278\) 20.1131i 1.20630i
\(279\) −21.9627 + 14.2985i −1.31487 + 0.856031i
\(280\) 0 0
\(281\) 7.77394 13.4649i 0.463754 0.803246i −0.535390 0.844605i \(-0.679835\pi\)
0.999144 + 0.0413590i \(0.0131687\pi\)
\(282\) −20.5955 4.93205i −1.22644 0.293699i
\(283\) −0.558913 + 0.322689i −0.0332240 + 0.0191819i −0.516520 0.856275i \(-0.672773\pi\)
0.483296 + 0.875457i \(0.339439\pi\)
\(284\) 19.4244 + 33.6440i 1.15262 + 1.99640i
\(285\) 0 0
\(286\) −5.51414 + 9.55077i −0.326058 + 0.564749i
\(287\) 5.83502i 0.344430i
\(288\) −5.70566 8.76394i −0.336209 0.516420i
\(289\) 5.97173 0.351278
\(290\) 0 0
\(291\) 20.3492 6.04039i 1.19289 0.354094i
\(292\) 22.6636 13.0848i 1.32629 0.765731i
\(293\) 1.19289 0.688716i 0.0696895 0.0402352i −0.464750 0.885442i \(-0.653856\pi\)
0.534440 + 0.845207i \(0.320523\pi\)
\(294\) 21.2877 + 20.1781i 1.24152 + 1.17681i
\(295\) 0 0
\(296\) 1.70739 0.0992400
\(297\) −16.2561 + 5.78807i −0.943276 + 0.335858i
\(298\) 44.4021i 2.57214i
\(299\) −2.72606 + 4.72168i −0.157652 + 0.273062i
\(300\) 0 0
\(301\) 2.66044 + 4.60802i 0.153345 + 0.265602i
\(302\) 2.75285 1.58936i 0.158409 0.0914573i
\(303\) 5.75194 + 19.3774i 0.330440 + 1.11320i
\(304\) −3.98133 + 6.89586i −0.228345 + 0.395505i
\(305\) 0 0
\(306\) 22.3305 + 11.3457i 1.27655 + 0.648592i
\(307\) 7.98546i 0.455754i −0.973690 0.227877i \(-0.926822\pi\)
0.973690 0.227877i \(-0.0731785\pi\)
\(308\) 6.38904 + 3.68872i 0.364050 + 0.210184i
\(309\) −0.118031 + 0.492881i −0.00671458 + 0.0280390i
\(310\) 0 0
\(311\) −4.81635 8.34216i −0.273110 0.473040i 0.696547 0.717512i \(-0.254719\pi\)
−0.969657 + 0.244471i \(0.921386\pi\)
\(312\) −12.9825 3.10896i −0.734991 0.176010i
\(313\) −21.2496 12.2685i −1.20110 0.693455i −0.240300 0.970699i \(-0.577246\pi\)
−0.960800 + 0.277244i \(0.910579\pi\)
\(314\) 39.3966 2.22328
\(315\) 0 0
\(316\) −34.8114 −1.95829
\(317\) 17.6229 + 10.1746i 0.989800 + 0.571461i 0.905215 0.424955i \(-0.139710\pi\)
0.0845855 + 0.996416i \(0.473043\pi\)
\(318\) −6.23089 20.9909i −0.349411 1.17711i
\(319\) 2.30221 + 3.98755i 0.128899 + 0.223260i
\(320\) 0 0
\(321\) 2.35369 + 2.23101i 0.131370 + 0.124523i
\(322\) 4.62061 + 2.66771i 0.257497 + 0.148666i
\(323\) 4.38650i 0.244072i
\(324\) −22.9298 31.4085i −1.27388 1.74492i
\(325\) 0 0
\(326\) −19.7453 + 34.1998i −1.09359 + 1.89415i
\(327\) −6.61054 + 6.97406i −0.365564 + 0.385666i
\(328\) 57.3504 33.1113i 3.16665 1.82827i
\(329\) 1.25020 + 2.16541i 0.0689257 + 0.119383i
\(330\) 0 0
\(331\) −8.22153 + 14.2401i −0.451896 + 0.782707i −0.998504 0.0546819i \(-0.982586\pi\)
0.546608 + 0.837389i \(0.315919\pi\)
\(332\) 6.66458i 0.365766i
\(333\) 0.876576 0.0469471i 0.0480360 0.00257269i
\(334\) −15.4996 −0.848100
\(335\) 0 0
\(336\) −1.25020 + 5.22064i −0.0682040 + 0.284809i
\(337\) 4.24096 2.44852i 0.231020 0.133379i −0.380023 0.924977i \(-0.624084\pi\)
0.611042 + 0.791598i \(0.290751\pi\)
\(338\) 24.5062 14.1486i 1.33296 0.769584i
\(339\) −3.14683 + 13.1407i −0.170913 + 0.713704i
\(340\) 0 0
\(341\) −29.0101 −1.57099
\(342\) −4.51277 + 8.88197i −0.244023 + 0.480282i
\(343\) 7.06201i 0.381313i
\(344\) 30.1938 52.2972i 1.62794 2.81967i
\(345\) 0 0
\(346\) −10.7922 18.6927i −0.580193 1.00492i
\(347\) 19.2903 11.1372i 1.03556 0.597878i 0.116984 0.993134i \(-0.462677\pi\)
0.918571 + 0.395256i \(0.129344\pi\)
\(348\) −7.13846 + 7.53101i −0.382662 + 0.403704i
\(349\) −1.47173 + 2.54910i −0.0787797 + 0.136450i −0.902724 0.430221i \(-0.858436\pi\)
0.823944 + 0.566671i \(0.191769\pi\)
\(350\) 0 0
\(351\) −6.75073 1.23917i −0.360327 0.0661420i
\(352\) 11.5761i 0.617011i
\(353\) 16.3069 + 9.41478i 0.867927 + 0.501098i 0.866659 0.498901i \(-0.166263\pi\)
0.00126845 + 0.999999i \(0.499596\pi\)
\(354\) 15.8916 + 15.0632i 0.844627 + 0.800602i
\(355\) 0 0
\(356\) 6.48133 + 11.2260i 0.343510 + 0.594976i
\(357\) −0.841540 2.83502i −0.0445390 0.150045i
\(358\) −2.32018 1.33956i −0.122625 0.0707978i
\(359\) 31.8770 1.68241 0.841203 0.540720i \(-0.181848\pi\)
0.841203 + 0.540720i \(0.181848\pi\)
\(360\) 0 0
\(361\) −17.2553 −0.908172
\(362\) 27.5866 + 15.9271i 1.44992 + 0.837110i
\(363\) −0.0476252 0.0114049i −0.00249968 0.000598604i
\(364\) 1.46719 + 2.54125i 0.0769016 + 0.133198i
\(365\) 0 0
\(366\) 7.45305 31.1228i 0.389577 1.62681i
\(367\) 15.8908 + 9.17458i 0.829495 + 0.478909i 0.853680 0.520798i \(-0.174366\pi\)
−0.0241848 + 0.999708i \(0.507699\pi\)
\(368\) 24.8825i 1.29709i
\(369\) 28.5333 18.5763i 1.48539 0.967044i
\(370\) 0 0
\(371\) −1.29261 + 2.23887i −0.0671090 + 0.116236i
\(372\) −18.6042 62.6747i −0.964582 3.24953i
\(373\) 1.90414 1.09936i 0.0985929 0.0569226i −0.449893 0.893083i \(-0.648538\pi\)
0.548486 + 0.836160i \(0.315205\pi\)
\(374\) 13.8633 + 24.0119i 0.716854 + 1.24163i
\(375\) 0 0
\(376\) 14.1887 24.5756i 0.731727 1.26739i
\(377\) 1.83141i 0.0943226i
\(378\) −1.21265 + 6.60623i −0.0623717 + 0.339788i
\(379\) −15.4713 −0.794709 −0.397354 0.917665i \(-0.630072\pi\)
−0.397354 + 0.917665i \(0.630072\pi\)
\(380\) 0 0
\(381\) 22.4909 + 21.3186i 1.15225 + 1.09219i
\(382\) −36.8713 + 21.2877i −1.88650 + 1.08917i
\(383\) −6.67479 + 3.85369i −0.341066 + 0.196915i −0.660743 0.750612i \(-0.729759\pi\)
0.319677 + 0.947526i \(0.396426\pi\)
\(384\) −25.3214 + 7.51633i −1.29218 + 0.383566i
\(385\) 0 0
\(386\) 67.1715 3.41894
\(387\) 14.0635 27.6796i 0.714890 1.40704i
\(388\) 52.9536i 2.68831i
\(389\) −12.3163 + 21.3325i −0.624464 + 1.08160i 0.364181 + 0.931328i \(0.381349\pi\)
−0.988644 + 0.150274i \(0.951984\pi\)
\(390\) 0 0
\(391\) 6.85369 + 11.8709i 0.346606 + 0.600340i
\(392\) −34.0372 + 19.6514i −1.71914 + 0.992544i
\(393\) 10.1066 + 2.42024i 0.509808 + 0.122085i
\(394\) −17.9198 + 31.0381i −0.902789 + 1.56368i
\(395\) 0 0
\(396\) −2.30221 42.9859i −0.115690 2.16012i
\(397\) 6.77301i 0.339928i −0.985450 0.169964i \(-0.945635\pi\)
0.985450 0.169964i \(-0.0543651\pi\)
\(398\) −53.6945 31.0005i −2.69146 1.55392i
\(399\) 1.12763 0.334723i 0.0564522 0.0167571i
\(400\) 0 0
\(401\) 9.24980 + 16.0211i 0.461913 + 0.800057i 0.999056 0.0434343i \(-0.0138299\pi\)
−0.537143 + 0.843491i \(0.680497\pi\)
\(402\) −28.3050 + 29.8615i −1.41172 + 1.48936i
\(403\) −9.99290 5.76940i −0.497782 0.287394i
\(404\) −50.4249 −2.50873
\(405\) 0 0
\(406\) 1.79221 0.0889459
\(407\) 0.841540 + 0.485863i 0.0417136 + 0.0240833i
\(408\) −23.0891 + 24.3588i −1.14308 + 1.20594i
\(409\) −6.70739 11.6175i −0.331659 0.574450i 0.651178 0.758925i \(-0.274275\pi\)
−0.982837 + 0.184474i \(0.940942\pi\)
\(410\) 0 0
\(411\) −9.41478 + 2.79466i −0.464397 + 0.137850i
\(412\) −1.09495 0.632168i −0.0539442 0.0311447i
\(413\) 2.58522i 0.127210i
\(414\) −1.66498 31.0877i −0.0818292 1.52788i
\(415\) 0 0
\(416\) 2.30221 3.98755i 0.112875 0.195506i
\(417\) 13.4754 + 3.22699i 0.659893 + 0.158026i
\(418\) −9.55077 + 5.51414i −0.467143 + 0.269705i
\(419\) −16.5575 28.6784i −0.808886 1.40103i −0.913636 0.406532i \(-0.866738\pi\)
0.104751 0.994499i \(-0.466596\pi\)
\(420\) 0 0
\(421\) 7.34916 12.7291i 0.358176 0.620379i −0.629480 0.777017i \(-0.716732\pi\)
0.987656 + 0.156637i \(0.0500654\pi\)
\(422\) 13.5196i 0.658124i
\(423\) 6.60876 13.0073i 0.321329 0.632435i
\(424\) 29.3401 1.42488
\(425\) 0 0
\(426\) −37.5333 + 11.1413i −1.81850 + 0.539797i
\(427\) −3.27225 + 1.88924i −0.158355 + 0.0914266i
\(428\) −7.00639 + 4.04514i −0.338667 + 0.195529i
\(429\) −5.51414 5.22672i −0.266225 0.252348i
\(430\) 0 0
\(431\) −32.7549 −1.57775 −0.788873 0.614556i \(-0.789335\pi\)
−0.788873 + 0.614556i \(0.789335\pi\)
\(432\) 29.5091 10.5069i 1.41976 0.505512i
\(433\) 11.8314i 0.568581i 0.958738 + 0.284291i \(0.0917581\pi\)
−0.958738 + 0.284291i \(0.908242\pi\)
\(434\) −5.64591 + 9.77900i −0.271012 + 0.469407i
\(435\) 0 0
\(436\) −11.9859 20.7601i −0.574019 0.994230i
\(437\) −4.72168 + 2.72606i −0.225869 + 0.130405i
\(438\) 7.50509 + 25.2835i 0.358607 + 1.20809i
\(439\) 4.15591 7.19824i 0.198351 0.343553i −0.749643 0.661842i \(-0.769775\pi\)
0.947994 + 0.318289i \(0.103108\pi\)
\(440\) 0 0
\(441\) −16.9344 + 11.0249i −0.806399 + 0.524997i
\(442\) 11.0283i 0.524561i
\(443\) −25.2664 14.5876i −1.20044 0.693076i −0.239789 0.970825i \(-0.577078\pi\)
−0.960654 + 0.277750i \(0.910411\pi\)
\(444\) −0.510000 + 2.12968i −0.0242035 + 0.101070i
\(445\) 0 0
\(446\) −10.8920 18.8654i −0.515750 0.893305i
\(447\) 29.7486 + 7.12397i 1.40706 + 0.336952i
\(448\) 1.46605 + 0.846426i 0.0692645 + 0.0399899i
\(449\) −18.9717 −0.895331 −0.447666 0.894201i \(-0.647744\pi\)
−0.447666 + 0.894201i \(0.647744\pi\)
\(450\) 0 0
\(451\) 37.6892 1.77472
\(452\) −29.1924 16.8542i −1.37309 0.792756i
\(453\) 0.623167 + 2.09936i 0.0292790 + 0.0986365i
\(454\) 4.17458 + 7.23058i 0.195923 + 0.339348i
\(455\) 0 0
\(456\) −9.68872 9.18370i −0.453716 0.430066i
\(457\) 20.1223 + 11.6176i 0.941283 + 0.543450i 0.890362 0.455253i \(-0.150451\pi\)
0.0509206 + 0.998703i \(0.483784\pi\)
\(458\) 63.6374i 2.97358i
\(459\) −11.1842 + 13.1407i −0.522033 + 0.613354i
\(460\) 0 0
\(461\) −2.21285 + 3.83277i −0.103063 + 0.178510i −0.912945 0.408082i \(-0.866198\pi\)
0.809882 + 0.586592i \(0.199531\pi\)
\(462\) −5.11484 + 5.39611i −0.237964 + 0.251050i
\(463\) 16.8950 9.75434i 0.785178 0.453322i −0.0530845 0.998590i \(-0.516905\pi\)
0.838262 + 0.545268i \(0.183572\pi\)
\(464\) −4.17912 7.23844i −0.194011 0.336036i
\(465\) 0 0
\(466\) −34.7362 + 60.1648i −1.60912 + 2.78708i
\(467\) 24.5935i 1.13805i −0.822320 0.569026i \(-0.807321\pi\)
0.822320 0.569026i \(-0.192679\pi\)
\(468\) 7.75581 15.2649i 0.358512 0.705619i
\(469\) 4.85783 0.224314
\(470\) 0 0
\(471\) −6.32088 + 26.3950i −0.291251 + 1.21622i
\(472\) −25.4093 + 14.6700i −1.16956 + 0.675243i
\(473\) 29.7639 17.1842i 1.36854 0.790129i
\(474\) 8.17044 34.1185i 0.375281 1.56711i
\(475\) 0 0
\(476\) 7.37743 0.338144
\(477\) 15.0632 0.806748i 0.689698 0.0369384i
\(478\) 10.5561i 0.482827i
\(479\) 16.3774 28.3665i 0.748304 1.29610i −0.200331 0.979728i \(-0.564202\pi\)
0.948635 0.316372i \(-0.102465\pi\)
\(480\) 0 0
\(481\) 0.193252 + 0.334723i 0.00881155 + 0.0152621i
\(482\) 7.84793 4.53101i 0.357464 0.206382i
\(483\) −2.52866 + 2.66771i −0.115058 + 0.121385i
\(484\) 0.0610840 0.105801i 0.00277655 0.00480912i
\(485\) 0 0
\(486\) 36.1651 15.1017i 1.64048 0.685025i
\(487\) 6.03735i 0.273578i −0.990600 0.136789i \(-0.956322\pi\)
0.990600 0.136789i \(-0.0436783\pi\)
\(488\) 37.1373 + 21.4412i 1.68113 + 0.970600i
\(489\) −19.7453 18.7161i −0.892912 0.846369i
\(490\) 0 0
\(491\) −7.22153 12.5081i −0.325903 0.564480i 0.655792 0.754942i \(-0.272335\pi\)
−0.981695 + 0.190461i \(0.939002\pi\)
\(492\) 24.1701 + 81.4254i 1.08967 + 3.67094i
\(493\) 3.98755 + 2.30221i 0.179590 + 0.103686i
\(494\) −4.38650 −0.197358
\(495\) 0 0
\(496\) 52.6610 2.36455
\(497\) 4.00326 + 2.31128i 0.179571 + 0.103675i
\(498\) −6.53192 1.56422i −0.292702 0.0700942i
\(499\) 10.4859 + 18.1620i 0.469412 + 0.813045i 0.999388 0.0349673i \(-0.0111327\pi\)
−0.529977 + 0.848012i \(0.677799\pi\)
\(500\) 0 0
\(501\) 2.48679 10.3844i 0.111102 0.463943i
\(502\) 14.9751 + 8.64591i 0.668374 + 0.385886i
\(503\) 5.31728i 0.237086i 0.992949 + 0.118543i \(0.0378223\pi\)
−0.992949 + 0.118543i \(0.962178\pi\)
\(504\) −8.02374 4.07672i −0.357406 0.181591i
\(505\) 0 0
\(506\) 17.2311 29.8452i 0.766017 1.32678i
\(507\) 5.54750 + 18.6887i 0.246373 + 0.829995i
\(508\) −66.9502 + 38.6537i −2.97043 + 1.71498i
\(509\) 9.11350 + 15.7850i 0.403949 + 0.699659i 0.994198 0.107561i \(-0.0343041\pi\)
−0.590250 + 0.807221i \(0.700971\pi\)
\(510\) 0 0
\(511\) 1.55695 2.69671i 0.0688753 0.119296i
\(512\) 49.3365i 2.18038i
\(513\) −5.22672 4.44852i −0.230765 0.196407i
\(514\) 45.2545 1.99609
\(515\) 0 0
\(516\) 56.2130 + 53.2829i 2.47464 + 2.34565i
\(517\) 13.9867 8.07522i 0.615134 0.355148i
\(518\) 0.327558 0.189116i 0.0143921 0.00830927i
\(519\) 14.2553 4.23149i 0.625737 0.185742i
\(520\) 0 0
\(521\) 40.1232 1.75783 0.878915 0.476978i \(-0.158268\pi\)
0.878915 + 0.476978i \(0.158268\pi\)
\(522\) −5.70566 8.76394i −0.249730 0.383587i
\(523\) 18.9873i 0.830257i −0.909763 0.415129i \(-0.863737\pi\)
0.909763 0.415129i \(-0.136263\pi\)
\(524\) −12.9627 + 22.4520i −0.566276 + 0.980819i
\(525\) 0 0
\(526\) −7.83916 13.5778i −0.341804 0.592021i
\(527\) −25.1235 + 14.5051i −1.09440 + 0.631851i
\(528\) 33.7209 + 8.07522i 1.46751 + 0.351429i
\(529\) −2.98133 + 5.16381i −0.129623 + 0.224513i
\(530\) 0 0
\(531\) −12.6418 + 8.23028i −0.548606 + 0.357164i
\(532\) 2.93438i 0.127221i
\(533\) 12.9825 + 7.49546i 0.562336 + 0.324665i
\(534\) −12.5237 + 3.71751i −0.541955 + 0.160872i
\(535\) 0 0
\(536\) −27.5661 47.7460i −1.19068 2.06231i
\(537\) 1.26973 1.33956i 0.0547931 0.0578062i
\(538\) 21.6064 + 12.4745i 0.931518 + 0.537812i
\(539\) −22.3684 −0.963473
\(540\) 0 0
\(541\) 16.5279 0.710589 0.355294 0.934754i \(-0.384381\pi\)
0.355294 + 0.934754i \(0.384381\pi\)
\(542\) −14.3799 8.30221i −0.617668 0.356611i
\(543\) −15.0969 + 15.9271i −0.647871 + 0.683498i
\(544\) −5.78807 10.0252i −0.248162 0.429829i
\(545\) 0 0
\(546\) −2.83502 + 0.841540i −0.121328 + 0.0360146i
\(547\) −15.3058 8.83683i −0.654430 0.377835i 0.135721 0.990747i \(-0.456665\pi\)
−0.790151 + 0.612912i \(0.789998\pi\)
\(548\) 24.4996i 1.04657i
\(549\) 19.6559 + 9.98682i 0.838894 + 0.426227i
\(550\) 0 0
\(551\) −0.915706 + 1.58605i −0.0390104 + 0.0675680i
\(552\) 40.5691 + 9.71519i 1.72674 + 0.413506i
\(553\) −3.58722 + 2.07108i −0.152544 + 0.0880715i
\(554\) 28.4864 + 49.3399i 1.21027 + 2.09625i
\(555\) 0 0
\(556\) −17.2835 + 29.9360i −0.732985 + 1.26957i
\(557\) 17.3401i 0.734723i 0.930078 + 0.367362i \(0.119739\pi\)
−0.930078 + 0.367362i \(0.880261\pi\)
\(558\) 65.7937 3.52374i 2.78527 0.149172i
\(559\) 13.6700 0.578181
\(560\) 0 0
\(561\) −18.3118 + 5.43563i −0.773125 + 0.229492i
\(562\) −33.8525 + 19.5447i −1.42798 + 0.824445i
\(563\) −11.2536 + 6.49727i −0.474283 + 0.273827i −0.718031 0.696011i \(-0.754956\pi\)
0.243748 + 0.969839i \(0.421623\pi\)
\(564\) 26.4157 + 25.0388i 1.11230 + 1.05432i
\(565\) 0 0
\(566\) 1.62257 0.0682016
\(567\) −4.23149 1.87237i −0.177706 0.0786321i
\(568\) 52.4623i 2.20127i
\(569\) −8.34009 + 14.4455i −0.349635 + 0.605585i −0.986184 0.165651i \(-0.947028\pi\)
0.636550 + 0.771236i \(0.280361\pi\)
\(570\) 0 0
\(571\) −10.0000 17.3205i −0.418487 0.724841i 0.577301 0.816532i \(-0.304106\pi\)
−0.995788 + 0.0916910i \(0.970773\pi\)
\(572\) 16.4143 9.47679i 0.686316 0.396245i
\(573\) −8.34663 28.1186i −0.348686 1.17467i
\(574\) 7.33502 12.7046i 0.306158 0.530281i
\(575\) 0 0
\(576\) −0.528274 9.86370i −0.0220114 0.410987i
\(577\) 23.5953i 0.982287i −0.871079 0.491144i \(-0.836579\pi\)
0.871079 0.491144i \(-0.163421\pi\)
\(578\) −13.0023 7.50687i −0.540823 0.312245i
\(579\) −10.7771 + 45.0037i −0.447883 + 1.87029i
\(580\) 0 0
\(581\) 0.396505 + 0.686767i 0.0164498 + 0.0284919i
\(582\) −51.8995 12.4285i −2.15130 0.515179i
\(583\) 14.4612 + 8.34916i 0.598920 + 0.345787i
\(584\) −35.3401 −1.46238
\(585\) 0 0
\(586\) −3.46305 −0.143057
\(587\) −24.3592 14.0638i −1.00541 0.580476i −0.0955681 0.995423i \(-0.530467\pi\)
−0.909846 + 0.414947i \(0.863800\pi\)
\(588\) −14.3448 48.3255i −0.591570 1.99291i
\(589\) −5.76940 9.99290i −0.237724 0.411750i
\(590\) 0 0
\(591\) −17.9198 16.9858i −0.737124 0.698702i
\(592\) −1.52761 0.881969i −0.0627846 0.0362487i
\(593\) 9.17872i 0.376925i 0.982080 + 0.188462i \(0.0603503\pi\)
−0.982080 + 0.188462i \(0.939650\pi\)
\(594\) 42.6706 + 7.83265i 1.75079 + 0.321378i
\(595\) 0 0
\(596\) −38.1555 + 66.0873i −1.56291 + 2.70704i
\(597\) 29.3846 31.0005i 1.20263 1.26877i
\(598\) 11.8709 6.85369i 0.485439 0.280268i
\(599\) −15.7357 27.2550i −0.642942 1.11361i −0.984773 0.173846i \(-0.944380\pi\)
0.341831 0.939761i \(-0.388953\pi\)
\(600\) 0 0
\(601\) 14.6327 25.3446i 0.596880 1.03383i −0.396398 0.918079i \(-0.629740\pi\)
0.993279 0.115748i \(-0.0369265\pi\)
\(602\) 13.3774i 0.545223i
\(603\) −15.4653 23.7549i −0.629797 0.967373i
\(604\) −5.46305 −0.222288
\(605\) 0 0
\(606\) 11.8350 49.4212i 0.480765 2.00760i
\(607\) −38.2813 + 22.1017i −1.55379 + 0.897080i −0.555960 + 0.831209i \(0.687649\pi\)
−0.997828 + 0.0658708i \(0.979017\pi\)
\(608\) 3.98755 2.30221i 0.161716 0.0933670i
\(609\) −0.287546 + 1.20075i −0.0116520 + 0.0486568i
\(610\) 0 0
\(611\) 6.42385 0.259881
\(612\) −23.4867 36.0757i −0.949394 1.45828i
\(613\) 35.1715i 1.42056i 0.703918 + 0.710282i \(0.251432\pi\)
−0.703918 + 0.710282i \(0.748568\pi\)
\(614\) −10.0383 + 17.3868i −0.405112 + 0.701674i
\(615\) 0 0
\(616\) −4.98133 8.62791i −0.200703 0.347628i
\(617\) −6.43085 + 3.71285i −0.258896 + 0.149474i −0.623831 0.781559i \(-0.714425\pi\)
0.364935 + 0.931033i \(0.381091\pi\)
\(618\) 0.876576 0.924779i 0.0352610 0.0372001i
\(619\) 4.27394 7.40268i 0.171784 0.297539i −0.767260 0.641337i \(-0.778380\pi\)
0.939044 + 0.343798i \(0.111714\pi\)
\(620\) 0 0
\(621\) 21.0953 + 3.87228i 0.846527 + 0.155389i
\(622\) 24.2179i 0.971050i
\(623\) 1.33577 + 0.771205i 0.0535164 + 0.0308977i
\(624\) 10.0096 + 9.48786i 0.400705 + 0.379818i
\(625\) 0 0
\(626\) 30.8446 + 53.4245i 1.23280 + 2.13527i
\(627\) −2.16202 7.28354i −0.0863429 0.290876i
\(628\) −58.6372 33.8542i −2.33988 1.35093i
\(629\) 0.971726 0.0387453
\(630\) 0 0
\(631\) −2.36836 −0.0942829 −0.0471415 0.998888i \(-0.515011\pi\)
−0.0471415 + 0.998888i \(0.515011\pi\)
\(632\) 40.7120 + 23.5051i 1.61944 + 0.934981i
\(633\) 9.05788 + 2.16912i 0.360019 + 0.0862146i
\(634\) −25.5803 44.3064i −1.01592 1.75963i
\(635\) 0 0
\(636\) −8.76394 + 36.5968i −0.347513 + 1.45116i
\(637\) −7.70506 4.44852i −0.305285 0.176257i
\(638\) 11.5761i 0.458304i
\(639\) −1.44252 26.9342i −0.0570654 1.06550i
\(640\) 0 0
\(641\) 0.0665480 0.115265i 0.00262849 0.00455268i −0.864708 0.502275i \(-0.832497\pi\)
0.867337 + 0.497722i \(0.165830\pi\)
\(642\) −2.32018 7.81635i −0.0915703 0.308487i
\(643\) 19.6124 11.3232i 0.773437 0.446544i −0.0606623 0.998158i \(-0.519321\pi\)
0.834099 + 0.551614i \(0.185988\pi\)
\(644\) −4.58482 7.94114i −0.180667 0.312925i
\(645\) 0 0
\(646\) −5.51414 + 9.55077i −0.216951 + 0.375770i
\(647\) 46.3912i 1.82383i 0.410385 + 0.911913i \(0.365394\pi\)
−0.410385 + 0.911913i \(0.634606\pi\)
\(648\) 5.60907 + 52.2148i 0.220345 + 2.05119i
\(649\) −16.6983 −0.655466
\(650\) 0 0
\(651\) −5.64591 5.35162i −0.221280 0.209746i
\(652\) 58.7770 33.9349i 2.30188 1.32899i
\(653\) −31.5283 + 18.2029i −1.23380 + 0.712333i −0.967819 0.251647i \(-0.919028\pi\)
−0.265977 + 0.963979i \(0.585695\pi\)
\(654\) 23.1600 6.87476i 0.905629 0.268824i
\(655\) 0 0
\(656\) −68.4158 −2.67119
\(657\) −18.1436 + 0.971726i −0.707851 + 0.0379106i
\(658\) 6.28635i 0.245067i
\(659\) 9.57068 16.5769i 0.372821 0.645745i −0.617177 0.786824i \(-0.711724\pi\)
0.989998 + 0.141079i \(0.0450572\pi\)
\(660\) 0 0
\(661\) −19.9536 34.5606i −0.776104 1.34425i −0.934172 0.356824i \(-0.883860\pi\)
0.158067 0.987428i \(-0.449474\pi\)
\(662\) 35.8016 20.6700i 1.39147 0.803364i
\(663\) −7.38874 1.76940i −0.286955 0.0687178i
\(664\) 4.50000 7.79423i 0.174634 0.302475i
\(665\) 0 0
\(666\) −1.96759 0.999697i −0.0762425 0.0387375i
\(667\) 5.72298i 0.221595i
\(668\) 23.0693 + 13.3191i 0.892579 + 0.515331i
\(669\) 14.3870 4.27061i 0.556235 0.165111i
\(670\) 0 0
\(671\) 12.2029 + 21.1360i 0.471086 + 0.815945i
\(672\) 2.13550 2.25293i 0.0823787 0.0869087i
\(673\) 20.4822 + 11.8254i 0.789532 + 0.455836i 0.839798 0.542899i \(-0.182674\pi\)
−0.0502658 + 0.998736i \(0.516007\pi\)
\(674\) −12.3118 −0.474233
\(675\) 0 0
\(676\) −48.6327 −1.87049
\(677\) 12.8199 + 7.40157i 0.492709 + 0.284465i 0.725697 0.688014i \(-0.241517\pi\)
−0.232989 + 0.972479i \(0.574851\pi\)
\(678\) 23.3704 24.6555i 0.897533 0.946889i
\(679\) 3.15044 + 5.45673i 0.120903 + 0.209410i
\(680\) 0 0
\(681\) −5.51414 + 1.63680i −0.211302 + 0.0627223i
\(682\) 63.1639 + 36.4677i 2.41867 + 1.39642i
\(683\) 4.95252i 0.189503i 0.995501 + 0.0947515i \(0.0302057\pi\)
−0.995501 + 0.0947515i \(0.969794\pi\)
\(684\) 14.3492 9.34186i 0.548654 0.357195i
\(685\) 0 0
\(686\) −8.87743 + 15.3762i −0.338942 + 0.587065i
\(687\) −42.6359 10.2101i −1.62666 0.389540i
\(688\) −54.0292 + 31.1938i −2.05984 + 1.18925i
\(689\) 3.32088 + 5.75194i 0.126516 + 0.219131i
\(690\) 0 0
\(691\) 9.60442 16.6353i 0.365369 0.632838i −0.623466 0.781851i \(-0.714276\pi\)
0.988835 + 0.149012i \(0.0476093\pi\)
\(692\) 37.0957i 1.41017i
\(693\) −2.79466 4.29261i −0.106160 0.163063i
\(694\) −56.0011 −2.12577
\(695\) 0 0
\(696\) 13.4335 3.98755i 0.509194 0.151148i
\(697\) 32.6398 18.8446i 1.23632 0.713791i
\(698\) 6.40880 3.70012i 0.242577 0.140052i
\(699\) −34.7362 32.9256i −1.31384 1.24536i
\(700\) 0 0
\(701\) −29.3492 −1.10850 −0.554251 0.832349i \(-0.686995\pi\)
−0.554251 + 0.832349i \(0.686995\pi\)
\(702\) 13.1407 + 11.1842i 0.495963 + 0.422120i
\(703\) 0.386505i 0.0145773i
\(704\) 5.46719 9.46945i 0.206052 0.356893i
\(705\) 0 0
\(706\) −23.6700 40.9977i −0.890834 1.54297i
\(707\) −5.19615 + 3.00000i −0.195421 + 0.112827i
\(708\) −10.7086 36.0757i −0.402455 1.35581i
\(709\) 19.3633 33.5382i 0.727204 1.25955i −0.230857 0.972988i \(-0.574153\pi\)
0.958060 0.286566i \(-0.0925138\pi\)
\(710\) 0 0
\(711\) 21.5479 + 10.9481i 0.808108 + 0.410586i
\(712\) 17.5051i 0.656030i
\(713\) 31.2268 + 18.0288i 1.16945 + 0.675184i
\(714\) −1.73153 + 7.23058i −0.0648008 + 0.270598i
\(715\) 0 0
\(716\) 2.30221 + 3.98755i 0.0860377 + 0.149022i
\(717\) −7.07243 1.69365i −0.264125 0.0632506i
\(718\) −69.4061 40.0716i −2.59021 1.49546i
\(719\) 15.0848 0.562569 0.281284 0.959624i \(-0.409240\pi\)
0.281284 + 0.959624i \(0.409240\pi\)
\(720\) 0 0
\(721\) −0.150442 −0.00560275
\(722\) 37.5700 + 21.6910i 1.39821 + 0.807257i
\(723\) 1.77655 + 5.98494i 0.0660706 + 0.222582i
\(724\) −27.3729 47.4112i −1.01731 1.76203i
\(725\) 0 0
\(726\) 0.0893579 + 0.0847002i 0.00331638 + 0.00314352i
\(727\) −10.6916 6.17277i −0.396528 0.228936i 0.288457 0.957493i \(-0.406858\pi\)
−0.684985 + 0.728557i \(0.740191\pi\)
\(728\) 3.96265i 0.146866i
\(729\) 4.31542 + 26.6529i 0.159830 + 0.987144i
\(730\) 0 0
\(731\) 17.1842 29.7639i 0.635580 1.10086i
\(732\) −37.8373 + 39.9180i −1.39851 + 1.47541i
\(733\) 19.0526 11.0000i 0.703722 0.406294i −0.105010 0.994471i \(-0.533487\pi\)
0.808732 + 0.588177i \(0.200154\pi\)
\(734\) −23.0661 39.9517i −0.851387 1.47465i
\(735\) 0 0
\(736\) −7.19418 + 12.4607i −0.265181 + 0.459307i
\(737\) 31.3774i 1.15580i
\(738\) −85.4775 + 4.57795i −3.14647 + 0.168517i
\(739\) −29.7266 −1.09351 −0.546755 0.837293i \(-0.684137\pi\)
−0.546755 + 0.837293i \(0.684137\pi\)
\(740\) 0 0
\(741\) 0.703781 2.93888i 0.0258540 0.107962i
\(742\) 5.62882 3.24980i 0.206640 0.119304i
\(743\) −41.8851 + 24.1824i −1.53662 + 0.887165i −0.537582 + 0.843212i \(0.680662\pi\)
−0.999034 + 0.0439537i \(0.986005\pi\)
\(744\) −20.5611 + 85.8599i −0.753806 + 3.14778i
\(745\) 0 0
\(746\) −5.52787 −0.202390
\(747\) 2.09599 4.12530i 0.0766883 0.150937i
\(748\) 47.6519i 1.74233i
\(749\) −0.481327 + 0.833682i −0.0175873 + 0.0304621i
\(750\) 0 0
\(751\) 15.9102 + 27.5573i 0.580573 + 1.00558i 0.995411 + 0.0956869i \(0.0305047\pi\)
−0.414838 + 0.909895i \(0.636162\pi\)
\(752\) −25.3895 + 14.6586i −0.925860 + 0.534546i
\(753\) −8.19524 + 8.64591i −0.298651 + 0.315074i
\(754\) 2.30221 3.98755i 0.0838416 0.145218i
\(755\) 0 0
\(756\) 7.48173 8.79054i 0.272108 0.319709i
\(757\) 4.94531i 0.179740i 0.995953 + 0.0898701i \(0.0286452\pi\)
−0.995953 + 0.0898701i \(0.971355\pi\)
\(758\) 33.6858 + 19.4485i 1.22352 + 0.706402i
\(759\) 17.2311 + 16.3330i 0.625450 + 0.592849i
\(760\) 0 0
\(761\) −17.7125 30.6789i −0.642076 1.11211i −0.984969 0.172734i \(-0.944740\pi\)
0.342893 0.939375i \(-0.388593\pi\)
\(762\) −22.1707 74.6898i −0.803160 2.70572i
\(763\) −2.47022 1.42618i −0.0894281 0.0516313i
\(764\) 73.1715 2.64725
\(765\) 0 0
\(766\) 19.3774 0.700135
\(767\) −5.75194 3.32088i −0.207691 0.119910i
\(768\) 53.4887 + 12.8091i 1.93011 + 0.462208i
\(769\) 24.7125 + 42.8032i 0.891154 + 1.54352i 0.838494 + 0.544911i \(0.183437\pi\)
0.0526602 + 0.998612i \(0.483230\pi\)
\(770\) 0 0
\(771\) −7.26073 + 30.3197i −0.261489 + 1.09194i
\(772\) −99.9768 57.7217i −3.59825 2.07745i
\(773\) 12.6599i 0.455345i −0.973738 0.227673i \(-0.926888\pi\)
0.973738 0.227673i \(-0.0731116\pi\)
\(774\) −65.4158 + 42.5882i −2.35132 + 1.53080i
\(775\) 0 0
\(776\) 35.7549 61.9292i 1.28352 2.22313i
\(777\) 0.0741499 + 0.249800i 0.00266011 + 0.00896153i
\(778\) 53.6329 30.9650i 1.92283 1.11015i
\(779\) 7.49546 + 12.9825i 0.268553 + 0.465147i
\(780\)