Properties

Label 675.2.k.b.199.6
Level $675$
Weight $2$
Character 675.199
Analytic conductor $5.390$
Analytic rank $0$
Dimension $12$
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.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.38990213644\)
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: \( 2^{6}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.6
Root \(-0.673288 - 0.180407i\) of defining polynomial
Character \(\chi\) \(=\) 675.199
Dual form 675.2.k.b.424.6

$q$-expansion

\(f(q)\) \(=\) \(q+(2.17731 - 1.25707i) q^{2} +(2.16044 - 3.74200i) q^{4} +(0.445256 - 0.257068i) q^{7} -5.83502i q^{8} +O(q^{10})\) \(q+(2.17731 - 1.25707i) q^{2} +(2.16044 - 3.74200i) q^{4} +(0.445256 - 0.257068i) q^{7} -5.83502i q^{8} +(-1.66044 - 2.87597i) q^{11} +(1.14392 + 0.660442i) q^{13} +(0.646305 - 1.11943i) q^{14} +(-3.01414 - 5.22064i) q^{16} -3.32088i q^{17} +1.32088 q^{19} +(-7.23058 - 4.17458i) q^{22} +(3.57463 + 2.06382i) q^{23} +3.32088 q^{26} -2.22153i q^{28} +(0.693252 + 1.20075i) q^{29} +(-4.36783 + 7.56531i) q^{31} +(-3.01885 - 1.74293i) q^{32} +(-4.17458 - 7.23058i) q^{34} -0.292611i q^{37} +(2.87597 - 1.66044i) q^{38} +(-5.67458 + 9.82866i) q^{41} +(8.96263 - 5.17458i) q^{43} -14.3492 q^{44} +10.3774 q^{46} +(-4.21174 + 2.43165i) q^{47} +(-3.36783 + 5.83326i) q^{49} +(4.94274 - 2.85369i) q^{52} +5.02827i q^{53} +(-1.50000 - 2.59808i) q^{56} +(3.01885 + 1.74293i) q^{58} +(2.51414 - 4.35461i) q^{59} +(-3.67458 - 6.36456i) q^{61} +21.9627i q^{62} +3.29261 q^{64} +(8.18266 + 4.72426i) q^{67} +(-12.4267 - 7.17458i) q^{68} -8.99093 q^{71} +6.05655i q^{73} +(-0.367832 - 0.637103i) q^{74} +(2.85369 - 4.94274i) q^{76} +(-1.47864 - 0.853695i) q^{77} +(-4.02827 - 6.97717i) q^{79} +28.5333i q^{82} +(-1.33577 + 0.771205i) q^{83} +(13.0096 - 22.5333i) q^{86} +(-16.7813 + 9.68872i) q^{88} -3.00000 q^{89} +0.679116 q^{91} +(15.4456 - 8.91751i) q^{92} +(-6.11350 + 10.5889i) q^{94} +(10.6134 - 6.12763i) q^{97} +16.9344i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 10 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 10 q^{4} - 4 q^{11} + 18 q^{14} - 10 q^{16} - 16 q^{19} + 8 q^{26} + 14 q^{29} - 16 q^{31} - 8 q^{34} - 26 q^{41} - 88 q^{44} - 12 q^{46} - 4 q^{49} - 18 q^{56} + 4 q^{59} - 2 q^{61} + 60 q^{64} + 40 q^{71} + 32 q^{74} + 24 q^{76} + 4 q^{79} + 56 q^{86} - 36 q^{89} + 40 q^{91} - 62 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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 0.540726 0.841199i \(-0.318150\pi\)
0.998863 0.0476826i \(-0.0151836\pi\)
\(3\) 0 0
\(4\) 2.16044 3.74200i 1.08022 1.87100i
\(5\) 0 0
\(6\) 0 0
\(7\) 0.445256 0.257068i 0.168291 0.0971627i −0.413489 0.910509i \(-0.635690\pi\)
0.581780 + 0.813346i \(0.302357\pi\)
\(8\) 5.83502i 2.06299i
\(9\) 0 0
\(10\) 0 0
\(11\) −1.66044 2.87597i −0.500642 0.867138i −1.00000 0.000741679i \(-0.999764\pi\)
0.499358 0.866396i \(-0.333569\pi\)
\(12\) 0 0
\(13\) 1.14392 + 0.660442i 0.317266 + 0.183174i 0.650173 0.759786i \(-0.274696\pi\)
−0.332907 + 0.942960i \(0.608030\pi\)
\(14\) 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 \(-0.131934\pi\)
\(18\) 0 0
\(19\) 1.32088 0.303032 0.151516 0.988455i \(-0.451585\pi\)
0.151516 + 0.988455i \(0.451585\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −7.23058 4.17458i −1.54157 0.890023i
\(23\) 3.57463 + 2.06382i 0.745363 + 0.430335i 0.824016 0.566567i \(-0.191729\pi\)
−0.0786532 + 0.996902i \(0.525062\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 3.32088 0.651279
\(27\) 0 0
\(28\) 2.22153i 0.419829i
\(29\) 0.693252 + 1.20075i 0.128734 + 0.222973i 0.923186 0.384353i \(-0.125575\pi\)
−0.794453 + 0.607326i \(0.792242\pi\)
\(30\) 0 0
\(31\) −4.36783 + 7.56531i −0.784486 + 1.35877i 0.144820 + 0.989458i \(0.453740\pi\)
−0.929306 + 0.369311i \(0.879594\pi\)
\(32\) −3.01885 1.74293i −0.533662 0.308110i
\(33\) 0 0
\(34\) −4.17458 7.23058i −0.715934 1.24003i
\(35\) 0 0
\(36\) 0 0
\(37\) 0.292611i 0.0481049i −0.999711 0.0240524i \(-0.992343\pi\)
0.999711 0.0240524i \(-0.00765687\pi\)
\(38\) 2.87597 1.66044i 0.466544 0.269359i
\(39\) 0 0
\(40\) 0 0
\(41\) −5.67458 + 9.82866i −0.886220 + 1.53498i −0.0419119 + 0.999121i \(0.513345\pi\)
−0.844308 + 0.535857i \(0.819988\pi\)
\(42\) 0 0
\(43\) 8.96263 5.17458i 1.36679 0.789116i 0.376272 0.926509i \(-0.377206\pi\)
0.990517 + 0.137393i \(0.0438724\pi\)
\(44\) −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 \(-0.782081\pi\)
0.160319 + 0.987065i \(0.448748\pi\)
\(48\) 0 0
\(49\) −3.36783 + 5.83326i −0.481119 + 0.833322i
\(50\) 0 0
\(51\) 0 0
\(52\) 4.94274 2.85369i 0.685435 0.395736i
\(53\) 5.02827i 0.690687i 0.938476 + 0.345343i \(0.112238\pi\)
−0.938476 + 0.345343i \(0.887762\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.50000 2.59808i −0.200446 0.347183i
\(57\) 0 0
\(58\) 3.01885 + 1.74293i 0.396394 + 0.228858i
\(59\) 2.51414 4.35461i 0.327313 0.566922i −0.654665 0.755919i \(-0.727190\pi\)
0.981978 + 0.188997i \(0.0605236\pi\)
\(60\) 0 0
\(61\) −3.67458 6.36456i −0.470482 0.814898i 0.528948 0.848654i \(-0.322586\pi\)
−0.999430 + 0.0337558i \(0.989253\pi\)
\(62\) 21.9627i 2.78926i
\(63\) 0 0
\(64\) 3.29261 0.411576
\(65\) 0 0
\(66\) 0 0
\(67\) 8.18266 + 4.72426i 0.999670 + 0.577160i 0.908151 0.418643i \(-0.137494\pi\)
0.0915197 + 0.995803i \(0.470828\pi\)
\(68\) −12.4267 7.17458i −1.50696 0.870046i
\(69\) 0 0
\(70\) 0 0
\(71\) −8.99093 −1.06703 −0.533513 0.845792i \(-0.679129\pi\)
−0.533513 + 0.845792i \(0.679129\pi\)
\(72\) 0 0
\(73\) 6.05655i 0.708865i 0.935082 + 0.354433i \(0.115326\pi\)
−0.935082 + 0.354433i \(0.884674\pi\)
\(74\) −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
\(78\) 0 0
\(79\) −4.02827 6.97717i −0.453216 0.784994i 0.545367 0.838197i \(-0.316390\pi\)
−0.998584 + 0.0532036i \(0.983057\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 28.5333i 3.15098i
\(83\) −1.33577 + 0.771205i −0.146619 + 0.0846508i −0.571515 0.820592i \(-0.693644\pi\)
0.424896 + 0.905242i \(0.360311\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 13.0096 22.5333i 1.40286 2.42983i
\(87\) 0 0
\(88\) −16.7813 + 9.68872i −1.78890 + 1.03282i
\(89\) −3.00000 −0.317999 −0.159000 0.987279i \(-0.550827\pi\)
−0.159000 + 0.987279i \(0.550827\pi\)
\(90\) 0 0
\(91\) 0.679116 0.0711906
\(92\) 15.4456 8.91751i 1.61031 0.929715i
\(93\) 0 0
\(94\) −6.11350 + 10.5889i −0.630559 + 1.09216i
\(95\) 0 0
\(96\) 0 0
\(97\) 10.6134 6.12763i 1.07762 0.622167i 0.147370 0.989081i \(-0.452919\pi\)
0.930255 + 0.366915i \(0.119586\pi\)
\(98\) 16.9344i 1.71063i
\(99\) 0 0
\(100\) 0 0
\(101\) 5.83502 + 10.1066i 0.580606 + 1.00564i 0.995408 + 0.0957276i \(0.0305178\pi\)
−0.414801 + 0.909912i \(0.636149\pi\)
\(102\) 0 0
\(103\) −0.253408 0.146305i −0.0249691 0.0144159i 0.487464 0.873143i \(-0.337922\pi\)
−0.512433 + 0.858727i \(0.671256\pi\)
\(104\) 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 \(0.971152\pi\)
\(108\) 0 0
\(109\) −5.54787 −0.531390 −0.265695 0.964057i \(-0.585601\pi\)
−0.265695 + 0.964057i \(0.585601\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −2.68412 1.54968i −0.253626 0.146431i
\(113\) 6.75611 + 3.90064i 0.635561 + 0.366942i 0.782903 0.622144i \(-0.213738\pi\)
−0.147341 + 0.989086i \(0.547072\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 5.99093 0.556244
\(117\) 0 0
\(118\) 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
\(123\) 0 0
\(124\) 18.8729 + 32.6888i 1.69484 + 2.93554i
\(125\) 0 0
\(126\) 0 0
\(127\) 17.8916i 1.58762i −0.608166 0.793810i \(-0.708094\pi\)
0.608166 0.793810i \(-0.291906\pi\)
\(128\) 13.2067 7.62490i 1.16732 0.673952i
\(129\) 0 0
\(130\) 0 0
\(131\) −3.00000 + 5.19615i −0.262111 + 0.453990i −0.966803 0.255524i \(-0.917752\pi\)
0.704692 + 0.709514i \(0.251085\pi\)
\(132\) 0 0
\(133\) 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 \(-0.588794\pi\)
0.694874 + 0.719132i \(0.255460\pi\)
\(138\) 0 0
\(139\) 4.00000 6.92820i 0.339276 0.587643i −0.645021 0.764165i \(-0.723151\pi\)
0.984297 + 0.176522i \(0.0564848\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −19.5760 + 11.3022i −1.64278 + 0.948460i
\(143\) 4.38650i 0.366818i
\(144\) 0 0
\(145\) 0 0
\(146\) 7.61350 + 13.1870i 0.630097 + 1.09136i
\(147\) 0 0
\(148\) −1.09495 0.632168i −0.0900042 0.0519639i
\(149\) −8.83049 + 15.2948i −0.723422 + 1.25300i 0.236199 + 0.971705i \(0.424098\pi\)
−0.959620 + 0.281298i \(0.909235\pi\)
\(150\) 0 0
\(151\) −0.632168 1.09495i −0.0514451 0.0891056i 0.839156 0.543891i \(-0.183049\pi\)
−0.890601 + 0.454785i \(0.849716\pi\)
\(152\) 7.70739i 0.625152i
\(153\) 0 0
\(154\) −4.29261 −0.345908
\(155\) 0 0
\(156\) 0 0
\(157\) −13.5707 7.83502i −1.08306 0.625303i −0.151337 0.988482i \(-0.548358\pi\)
−0.931719 + 0.363179i \(0.881691\pi\)
\(158\) −17.5416 10.1276i −1.39553 0.805711i
\(159\) 0 0
\(160\) 0 0
\(161\) 2.12217 0.167250
\(162\) 0 0
\(163\) 15.7074i 1.23030i 0.788411 + 0.615149i \(0.210904\pi\)
−0.788411 + 0.615149i \(0.789096\pi\)
\(164\) 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 \(-0.409999\pi\)
−0.692141 + 0.721763i \(0.743332\pi\)
\(168\) 0 0
\(169\) −5.62763 9.74734i −0.432895 0.749796i
\(170\) 0 0
\(171\) 0 0
\(172\) 44.7175i 3.40968i
\(173\) −7.43502 + 4.29261i −0.565274 + 0.326361i −0.755260 0.655426i \(-0.772489\pi\)
0.189986 + 0.981787i \(0.439156\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −10.0096 + 17.3371i −0.754502 + 1.30684i
\(177\) 0 0
\(178\) −6.53192 + 3.77121i −0.489588 + 0.282664i
\(179\) −1.06562 −0.0796482 −0.0398241 0.999207i \(-0.512680\pi\)
−0.0398241 + 0.999207i \(0.512680\pi\)
\(180\) 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
\(183\) 0 0
\(184\) 12.0424 20.8581i 0.887778 1.53768i
\(185\) 0 0
\(186\) 0 0
\(187\) −9.55077 + 5.51414i −0.698421 + 0.403234i
\(188\) 21.0137i 1.53258i
\(189\) 0 0
\(190\) 0 0
\(191\) −8.46719 14.6656i −0.612664 1.06117i −0.990789 0.135411i \(-0.956764\pi\)
0.378125 0.925754i \(-0.376569\pi\)
\(192\) 0 0
\(193\) −23.1380 13.3588i −1.66551 0.961585i −0.970011 0.243060i \(-0.921849\pi\)
−0.695502 0.718524i \(-0.744818\pi\)
\(194\) 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 \(-0.169550\pi\)
\(198\) 0 0
\(199\) 24.6610 1.74817 0.874085 0.485773i \(-0.161462\pi\)
0.874085 + 0.485773i \(0.161462\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 25.4093 + 14.6700i 1.78779 + 1.03218i
\(203\) 0.617349 + 0.356427i 0.0433294 + 0.0250162i
\(204\) 0 0
\(205\) 0 0
\(206\) −0.735663 −0.0512561
\(207\) 0 0
\(208\) 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 −0.758511 0.651660i \(-0.774073\pi\)
0.943610 + 0.331060i \(0.107406\pi\)
\(212\) 18.8158 + 10.8633i 1.29227 + 0.746094i
\(213\) 0 0
\(214\) 2.35369 + 4.07672i 0.160895 + 0.278679i
\(215\) 0 0
\(216\) 0 0
\(217\) 4.49133i 0.304891i
\(218\) −12.0794 + 6.97406i −0.818122 + 0.472343i
\(219\) 0 0
\(220\) 0 0
\(221\) 2.19325 3.79882i 0.147534 0.255537i
\(222\) 0 0
\(223\) 7.50375 4.33229i 0.502488 0.290112i −0.227252 0.973836i \(-0.572974\pi\)
0.729740 + 0.683724i \(0.239641\pi\)
\(224\) −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 \(-0.631515\pi\)
0.592397 + 0.805646i \(0.298182\pi\)
\(228\) 0 0
\(229\) −12.6559 + 21.9207i −0.836326 + 1.44856i 0.0566206 + 0.998396i \(0.481967\pi\)
−0.892946 + 0.450163i \(0.851366\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 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 0
\(235\) 0 0
\(236\) −10.8633 18.8158i −0.707140 1.22480i
\(237\) 0 0
\(238\) −3.71751 2.14631i −0.240970 0.139124i
\(239\) 2.09936 3.63620i 0.135796 0.235206i −0.790105 0.612971i \(-0.789974\pi\)
0.925901 + 0.377765i \(0.123307\pi\)
\(240\) 0 0
\(241\) −1.80221 3.12152i −0.116091 0.201075i 0.802125 0.597157i \(-0.203703\pi\)
−0.918215 + 0.396082i \(0.870370\pi\)
\(242\) 0.0710844i 0.00456948i
\(243\) 0 0
\(244\) −31.7549 −2.03290
\(245\) 0 0
\(246\) 0 0
\(247\) 1.51099 + 0.872368i 0.0961417 + 0.0555074i
\(248\) 44.1437 + 25.4864i 2.80313 + 1.61839i
\(249\) 0 0
\(250\) 0 0
\(251\) 6.87783 0.434125 0.217062 0.976158i \(-0.430352\pi\)
0.217062 + 0.976158i \(0.430352\pi\)
\(252\) 0 0
\(253\) 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 \(-0.143595\pi\)
0.0724199 + 0.997374i \(0.476928\pi\)
\(258\) 0 0
\(259\) −0.0752210 0.130287i −0.00467400 0.00809561i
\(260\) 0 0
\(261\) 0 0
\(262\) 15.0848i 0.931943i
\(263\) −5.40059 + 3.11803i −0.333015 + 0.192266i −0.657179 0.753735i \(-0.728250\pi\)
0.324164 + 0.946001i \(0.394917\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0.853695 1.47864i 0.0523434 0.0906614i
\(267\) 0 0
\(268\) 35.3563 20.4130i 2.15973 1.24692i
\(269\) 9.92345 0.605044 0.302522 0.953142i \(-0.402172\pi\)
0.302522 + 0.953142i \(0.402172\pi\)
\(270\) 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 0
\(274\) 7.12763 12.3454i 0.430596 0.745814i
\(275\) 0 0
\(276\) 0 0
\(277\) −19.6250 + 11.3305i −1.17915 + 0.680783i −0.955818 0.293959i \(-0.905027\pi\)
−0.223333 + 0.974742i \(0.571694\pi\)
\(278\) 20.1131i 1.20630i
\(279\) 0 0
\(280\) 0 0
\(281\) −7.77394 13.4649i −0.463754 0.803246i 0.535390 0.844605i \(-0.320165\pi\)
−0.999144 + 0.0413590i \(0.986831\pi\)
\(282\) 0 0
\(283\) −0.558913 0.322689i −0.0332240 0.0191819i 0.483296 0.875457i \(-0.339439\pi\)
−0.516520 + 0.856275i \(0.672773\pi\)
\(284\) −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
\(288\) 0 0
\(289\) 5.97173 0.351278
\(290\) 0 0
\(291\) 0 0
\(292\) 22.6636 + 13.0848i 1.32629 + 0.765731i
\(293\) −1.19289 0.688716i −0.0696895 0.0402352i 0.464750 0.885442i \(-0.346144\pi\)
−0.534440 + 0.845207i \(0.679477\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −1.70739 −0.0992400
\(297\) 0 0
\(298\) 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
\(303\) 0 0
\(304\) −3.98133 6.89586i −0.228345 0.395505i
\(305\) 0 0
\(306\) 0 0
\(307\) 7.98546i 0.455754i 0.973690 + 0.227877i \(0.0731785\pi\)
−0.973690 + 0.227877i \(0.926822\pi\)
\(308\) −6.38904 + 3.68872i −0.364050 + 0.210184i
\(309\) 0 0
\(310\) 0 0
\(311\) 4.81635 8.34216i 0.273110 0.473040i −0.696547 0.717512i \(-0.745281\pi\)
0.969657 + 0.244471i \(0.0786143\pi\)
\(312\) 0 0
\(313\) −21.2496 + 12.2685i −1.20110 + 0.693455i −0.960800 0.277244i \(-0.910579\pi\)
−0.240300 + 0.970699i \(0.577246\pi\)
\(314\) −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 \(-0.860290\pi\)
−0.0845855 + 0.996416i \(0.526957\pi\)
\(318\) 0 0
\(319\) 2.30221 3.98755i 0.128899 0.223260i
\(320\) 0 0
\(321\) 0 0
\(322\) 4.62061 2.66771i 0.257497 0.148666i
\(323\) 4.38650i 0.244072i
\(324\) 0 0
\(325\) 0 0
\(326\) 19.7453 + 34.1998i 1.09359 + 1.89415i
\(327\) 0 0
\(328\) 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 0.546608 0.837389i \(-0.315919\pi\)
−0.998504 + 0.0546819i \(0.982586\pi\)
\(332\) 6.66458i 0.365766i
\(333\) 0 0
\(334\) −15.4996 −0.848100
\(335\) 0 0
\(336\) 0 0
\(337\) 4.24096 + 2.44852i 0.231020 + 0.133379i 0.611042 0.791598i \(-0.290751\pi\)
−0.380023 + 0.924977i \(0.624084\pi\)
\(338\) −24.5062 14.1486i −1.33296 0.769584i
\(339\) 0 0
\(340\) 0 0
\(341\) 29.0101 1.57099
\(342\) 0 0
\(343\) 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 \(-0.537323\pi\)
−0.918571 + 0.395256i \(0.870656\pi\)
\(348\) 0 0
\(349\) −1.47173 2.54910i −0.0787797 0.136450i 0.823944 0.566671i \(-0.191769\pi\)
−0.902724 + 0.430221i \(0.858436\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 11.5761i 0.617011i
\(353\) −16.3069 + 9.41478i −0.867927 + 0.501098i −0.866659 0.498901i \(-0.833737\pi\)
−0.00126845 + 0.999999i \(0.500404\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −6.48133 + 11.2260i −0.343510 + 0.594976i
\(357\) 0 0
\(358\) −2.32018 + 1.33956i −0.122625 + 0.0707978i
\(359\) −31.8770 −1.68241 −0.841203 0.540720i \(-0.818152\pi\)
−0.841203 + 0.540720i \(0.818152\pi\)
\(360\) 0 0
\(361\) −17.2553 −0.908172
\(362\) −27.5866 + 15.9271i −1.44992 + 0.837110i
\(363\) 0 0
\(364\) 1.46719 2.54125i 0.0769016 0.133198i
\(365\) 0 0
\(366\) 0 0
\(367\) 15.8908 9.17458i 0.829495 0.478909i −0.0241848 0.999708i \(-0.507699\pi\)
0.853680 + 0.520798i \(0.174366\pi\)
\(368\) 24.8825i 1.29709i
\(369\) 0 0
\(370\) 0 0
\(371\) 1.29261 + 2.23887i 0.0671090 + 0.116236i
\(372\) 0 0
\(373\) 1.90414 + 1.09936i 0.0985929 + 0.0569226i 0.548486 0.836160i \(-0.315205\pi\)
−0.449893 + 0.893083i \(0.648538\pi\)
\(374\) −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
\(378\) 0 0
\(379\) −15.4713 −0.794709 −0.397354 0.917665i \(-0.630072\pi\)
−0.397354 + 0.917665i \(0.630072\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −36.8713 21.2877i −1.88650 1.08917i
\(383\) 6.67479 + 3.85369i 0.341066 + 0.196915i 0.660743 0.750612i \(-0.270241\pi\)
−0.319677 + 0.947526i \(0.603574\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −67.1715 −3.41894
\(387\) 0 0
\(388\) 52.9536i 2.68831i
\(389\) 12.3163 + 21.3325i 0.624464 + 1.08160i 0.988644 + 0.150274i \(0.0480157\pi\)
−0.364181 + 0.931328i \(0.618651\pi\)
\(390\) 0 0
\(391\) 6.85369 11.8709i 0.346606 0.600340i
\(392\) 34.0372 + 19.6514i 1.71914 + 0.992544i
\(393\) 0 0
\(394\) −17.9198 31.0381i −0.902789 1.56368i
\(395\) 0 0
\(396\) 0 0
\(397\) 6.77301i 0.339928i 0.985450 + 0.169964i \(0.0543651\pi\)
−0.985450 + 0.169964i \(0.945635\pi\)
\(398\) 53.6945 31.0005i 2.69146 1.55392i
\(399\) 0 0
\(400\) 0 0
\(401\) −9.24980 + 16.0211i −0.461913 + 0.800057i −0.999056 0.0434343i \(-0.986170\pi\)
0.537143 + 0.843491i \(0.319503\pi\)
\(402\) 0 0
\(403\) −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
\(408\) 0 0
\(409\) −6.70739 + 11.6175i −0.331659 + 0.574450i −0.982837 0.184474i \(-0.940942\pi\)
0.651178 + 0.758925i \(0.274275\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −1.09495 + 0.632168i −0.0539442 + 0.0311447i
\(413\) 2.58522i 0.127210i
\(414\) 0 0
\(415\) 0 0
\(416\) −2.30221 3.98755i −0.112875 0.195506i
\(417\) 0 0
\(418\) −9.55077 5.51414i −0.467143 0.269705i
\(419\) 16.5575 28.6784i 0.808886 1.40103i −0.104751 0.994499i \(-0.533404\pi\)
0.913636 0.406532i \(-0.133262\pi\)
\(420\) 0 0
\(421\) 7.34916 + 12.7291i 0.358176 + 0.620379i 0.987656 0.156637i \(-0.0500654\pi\)
−0.629480 + 0.777017i \(0.716732\pi\)
\(422\) 13.5196i 0.658124i
\(423\) 0 0
\(424\) 29.3401 1.42488
\(425\) 0 0
\(426\) 0 0
\(427\) −3.27225 1.88924i −0.158355 0.0914266i
\(428\) 7.00639 + 4.04514i 0.338667 + 0.195529i
\(429\) 0 0
\(430\) 0 0
\(431\) 32.7549 1.57775 0.788873 0.614556i \(-0.210665\pi\)
0.788873 + 0.614556i \(0.210665\pi\)
\(432\) 0 0
\(433\) 11.8314i 0.568581i −0.958738 0.284291i \(-0.908242\pi\)
0.958738 0.284291i \(-0.0917581\pi\)
\(434\) 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
\(438\) 0 0
\(439\) 4.15591 + 7.19824i 0.198351 + 0.343553i 0.947994 0.318289i \(-0.103108\pi\)
−0.749643 + 0.661842i \(0.769775\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 11.0283i 0.524561i
\(443\) 25.2664 14.5876i 1.20044 0.693076i 0.239789 0.970825i \(-0.422922\pi\)
0.960654 + 0.277750i \(0.0895885\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 10.8920 18.8654i 0.515750 0.893305i
\(447\) 0 0
\(448\) 1.46605 0.846426i 0.0692645 0.0399899i
\(449\) 18.9717 0.895331 0.447666 0.894201i \(-0.352256\pi\)
0.447666 + 0.894201i \(0.352256\pi\)
\(450\) 0 0
\(451\) 37.6892 1.77472
\(452\) 29.1924 16.8542i 1.37309 0.792756i
\(453\) 0 0
\(454\) 4.17458 7.23058i 0.195923 0.339348i
\(455\) 0 0
\(456\) 0 0
\(457\) 20.1223 11.6176i 0.941283 0.543450i 0.0509206 0.998703i \(-0.483784\pi\)
0.890362 + 0.455253i \(0.150451\pi\)
\(458\) 63.6374i 2.97358i
\(459\) 0 0
\(460\) 0 0
\(461\) 2.21285 + 3.83277i 0.103063 + 0.178510i 0.912945 0.408082i \(-0.133802\pi\)
−0.809882 + 0.586592i \(0.800469\pi\)
\(462\) 0 0
\(463\) 16.8950 + 9.75434i 0.785178 + 0.453322i 0.838262 0.545268i \(-0.183572\pi\)
−0.0530845 + 0.998590i \(0.516905\pi\)
\(464\) 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 \(-0.192679\pi\)
\(468\) 0 0
\(469\) 4.85783 0.224314
\(470\) 0 0
\(471\) 0 0
\(472\) −25.4093 14.6700i −1.16956 0.675243i
\(473\) −29.7639 17.1842i −1.36854 0.790129i
\(474\) 0 0
\(475\) 0 0
\(476\) −7.37743 −0.338144
\(477\) 0 0
\(478\) 10.5561i 0.482827i
\(479\) −16.3774 28.3665i −0.748304 1.29610i −0.948635 0.316372i \(-0.897535\pi\)
0.200331 0.979728i \(-0.435798\pi\)
\(480\) 0 0
\(481\) 0.193252 0.334723i 0.00881155 0.0152621i
\(482\) −7.84793 4.53101i −0.357464 0.206382i
\(483\) 0 0
\(484\) 0.0610840 + 0.105801i 0.00277655 + 0.00480912i
\(485\) 0 0
\(486\) 0 0
\(487\) 6.03735i 0.273578i 0.990600 + 0.136789i \(0.0436783\pi\)
−0.990600 + 0.136789i \(0.956322\pi\)
\(488\) −37.1373 + 21.4412i −1.68113 + 0.970600i
\(489\) 0 0
\(490\) 0 0
\(491\) 7.22153 12.5081i 0.325903 0.564480i −0.655792 0.754942i \(-0.727665\pi\)
0.981695 + 0.190461i \(0.0609984\pi\)
\(492\) 0 0
\(493\) 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
\(498\) 0 0
\(499\) 10.4859 18.1620i 0.469412 0.813045i −0.529977 0.848012i \(-0.677799\pi\)
0.999388 + 0.0349673i \(0.0111327\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 14.9751 8.64591i 0.668374 0.385886i
\(503\) 5.31728i 0.237086i 0.992949 + 0.118543i \(0.0378223\pi\)
−0.992949 + 0.118543i \(0.962178\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −17.2311 29.8452i −0.766017 1.32678i
\(507\) 0 0
\(508\) −66.9502 38.6537i −2.97043 1.71498i
\(509\) −9.11350 + 15.7850i −0.403949 + 0.699659i −0.994198 0.107561i \(-0.965696\pi\)
0.590250 + 0.807221i \(0.299029\pi\)
\(510\) 0 0
\(511\) 1.55695 + 2.69671i 0.0688753 + 0.119296i
\(512\) 49.3365i 2.18038i
\(513\) 0 0
\(514\) 45.2545 1.99609
\(515\) 0 0
\(516\) 0 0
\(517\) 13.9867 + 8.07522i 0.615134 + 0.355148i
\(518\) −0.327558 0.189116i −0.0143921 0.00830927i
\(519\) 0 0
\(520\) 0 0
\(521\) −40.1232 −1.75783 −0.878915 0.476978i \(-0.841732\pi\)
−0.878915 + 0.476978i \(0.841732\pi\)
\(522\) 0 0
\(523\) 18.9873i 0.830257i 0.909763 + 0.415129i \(0.136263\pi\)
−0.909763 + 0.415129i \(0.863737\pi\)
\(524\) 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
\(528\) 0 0
\(529\) −2.98133 5.16381i −0.129623 0.224513i
\(530\) 0 0
\(531\) 0 0
\(532\) 2.93438i 0.127221i
\(533\) −12.9825 + 7.49546i −0.562336 + 0.324665i
\(534\) 0 0
\(535\) 0 0
\(536\) 27.5661 47.7460i 1.19068 2.06231i
\(537\) 0 0
\(538\) 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
\(543\) 0 0
\(544\) −5.78807 + 10.0252i −0.248162 + 0.429829i
\(545\) 0 0
\(546\) 0 0
\(547\) −15.3058 + 8.83683i −0.654430 + 0.377835i −0.790151 0.612912i \(-0.789998\pi\)
0.135721 + 0.990747i \(0.456665\pi\)
\(548\) 24.4996i 1.04657i
\(549\) 0 0
\(550\) 0 0
\(551\) 0.915706 + 1.58605i 0.0390104 + 0.0675680i
\(552\) 0 0
\(553\) −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 \(0.880261\pi\)
\(558\) 0 0
\(559\) 13.6700 0.578181
\(560\) 0 0
\(561\) 0 0
\(562\) −33.8525 19.5447i −1.42798 0.824445i
\(563\) 11.2536 + 6.49727i 0.474283 + 0.273827i 0.718031 0.696011i \(-0.245044\pi\)
−0.243748 + 0.969839i \(0.578377\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −1.62257 −0.0682016
\(567\) 0 0
\(568\) 52.4623i 2.20127i
\(569\) 8.34009 + 14.4455i 0.349635 + 0.605585i 0.986184 0.165651i \(-0.0529724\pi\)
−0.636550 + 0.771236i \(0.719639\pi\)
\(570\) 0 0
\(571\) −10.0000 + 17.3205i −0.418487 + 0.724841i −0.995788 0.0916910i \(-0.970773\pi\)
0.577301 + 0.816532i \(0.304106\pi\)
\(572\) −16.4143 9.47679i −0.686316 0.396245i
\(573\) 0 0
\(574\) 7.33502 + 12.7046i 0.306158 + 0.530281i
\(575\) 0 0
\(576\) 0 0
\(577\) 23.5953i 0.982287i 0.871079 + 0.491144i \(0.163421\pi\)
−0.871079 + 0.491144i \(0.836579\pi\)
\(578\) 13.0023 7.50687i 0.540823 0.312245i
\(579\) 0 0
\(580\) 0 0
\(581\) −0.396505 + 0.686767i −0.0164498 + 0.0284919i
\(582\) 0 0
\(583\) 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 \(-0.469533\pi\)
0.909846 + 0.414947i \(0.136200\pi\)
\(588\) 0 0
\(589\) −5.76940 + 9.99290i −0.237724 + 0.411750i
\(590\) 0 0
\(591\) 0 0
\(592\) −1.52761 + 0.881969i −0.0627846 + 0.0362487i
\(593\) 9.17872i 0.376925i 0.982080 + 0.188462i \(0.0603503\pi\)
−0.982080 + 0.188462i \(0.939650\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 38.1555 + 66.0873i 1.56291 + 2.70704i
\(597\) 0 0
\(598\) 11.8709 + 6.85369i 0.485439 + 0.280268i
\(599\) 15.7357 27.2550i 0.642942 1.11361i −0.341831 0.939761i \(-0.611047\pi\)
0.984773 0.173846i \(-0.0556196\pi\)
\(600\) 0 0
\(601\) 14.6327 + 25.3446i 0.596880 + 1.03383i 0.993279 + 0.115748i \(0.0369265\pi\)
−0.396398 + 0.918079i \(0.629740\pi\)
\(602\) 13.3774i 0.545223i
\(603\) 0 0
\(604\) −5.46305 −0.222288
\(605\) 0 0
\(606\) 0 0
\(607\) −38.2813 22.1017i −1.55379 0.897080i −0.997828 0.0658708i \(-0.979017\pi\)
−0.555960 0.831209i \(-0.687649\pi\)
\(608\) −3.98755 2.30221i −0.161716 0.0933670i
\(609\) 0 0
\(610\) 0 0
\(611\) −6.42385 −0.259881
\(612\) 0 0
\(613\) 35.1715i 1.42056i −0.703918 0.710282i \(-0.748568\pi\)
0.703918 0.710282i \(-0.251432\pi\)
\(614\) 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 \(-0.285575\pi\)
−0.364935 + 0.931033i \(0.618909\pi\)
\(618\) 0 0
\(619\) 4.27394 + 7.40268i 0.171784 + 0.297539i 0.939044 0.343798i \(-0.111714\pi\)
−0.767260 + 0.641337i \(0.778380\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 24.2179i 0.971050i
\(623\) −1.33577 + 0.771205i −0.0535164 + 0.0308977i
\(624\) 0 0
\(625\) 0 0
\(626\) −30.8446 + 53.4245i −1.23280 + 2.13527i
\(627\) 0 0
\(628\) −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
\(633\) 0 0
\(634\) −25.5803 + 44.3064i −1.01592 + 1.75963i
\(635\) 0 0
\(636\) 0 0
\(637\) −7.70506 + 4.44852i −0.305285 + 0.176257i
\(638\) 11.5761i 0.458304i
\(639\) 0 0
\(640\) 0 0
\(641\) −0.0665480 0.115265i −0.00262849 0.00455268i 0.864708 0.502275i \(-0.167503\pi\)
−0.867337 + 0.497722i \(0.834170\pi\)
\(642\) 0 0
\(643\) 19.6124 + 11.3232i 0.773437 + 0.446544i 0.834099 0.551614i \(-0.185988\pi\)
−0.0606623 + 0.998158i \(0.519321\pi\)
\(644\) 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 \(0.634606\pi\)
\(648\) 0 0
\(649\) −16.6983 −0.655466
\(650\) 0 0
\(651\) 0 0
\(652\) 58.7770 + 33.9349i 2.30188 + 1.32899i
\(653\) 31.5283 + 18.2029i 1.23380 + 0.712333i 0.967819 0.251647i \(-0.0809721\pi\)
0.265977 + 0.963979i \(0.414305\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 68.4158 2.67119
\(657\) 0 0
\(658\) 6.28635i 0.245067i
\(659\) −9.57068 16.5769i −0.372821 0.645745i 0.617177 0.786824i \(-0.288276\pi\)
−0.989998 + 0.141079i \(0.954943\pi\)
\(660\) 0 0
\(661\) −19.9536 + 34.5606i −0.776104 + 1.34425i 0.158067 + 0.987428i \(0.449474\pi\)
−0.934172 + 0.356824i \(0.883860\pi\)
\(662\) −35.8016 20.6700i −1.39147 0.803364i
\(663\) 0 0
\(664\) 4.50000 + 7.79423i 0.174634 + 0.302475i
\(665\) 0 0
\(666\) 0 0
\(667\) 5.72298i 0.221595i
\(668\) −23.0693 + 13.3191i −0.892579 + 0.515331i
\(669\) 0 0
\(670\) 0 0
\(671\) −12.2029 + 21.1360i −0.471086 + 0.815945i
\(672\) 0 0
\(673\) 20.4822 11.8254i 0.789532 0.455836i −0.0502658 0.998736i \(-0.516007\pi\)
0.839798 + 0.542899i \(0.182674\pi\)
\(674\) 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 \(-0.758483\pi\)
0.232989 + 0.972479i \(0.425149\pi\)
\(678\) 0 0
\(679\) 3.15044 5.45673i 0.120903 0.209410i
\(680\) 0 0
\(681\) 0 0
\(682\) 63.1639 36.4677i 2.41867 1.39642i
\(683\) 4.95252i 0.189503i 0.995501 + 0.0947515i \(0.0302057\pi\)
−0.995501 + 0.0947515i \(0.969794\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 8.87743 + 15.3762i 0.338942 + 0.587065i
\(687\) 0 0
\(688\) −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 0.988835 0.149012i \(-0.0476093\pi\)
−0.623466 + 0.781851i \(0.714276\pi\)
\(692\) 37.0957i 1.41017i
\(693\) 0 0
\(694\) −56.0011 −2.12577
\(695\) 0 0
\(696\) 0 0
\(697\) 32.6398 + 18.8446i 1.23632 + 0.713791i
\(698\) −6.40880 3.70012i −0.242577 0.140052i
\(699\) 0 0
\(700\) 0 0
\(701\) 29.3492 1.10850 0.554251 0.832349i \(-0.313005\pi\)
0.554251 + 0.832349i \(0.313005\pi\)
\(702\) 0 0
\(703\) 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
\(708\) 0 0
\(709\) 19.3633 + 33.5382i 0.727204 + 1.25955i 0.958060 + 0.286566i \(0.0925138\pi\)
−0.230857 + 0.972988i \(0.574153\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 17.5051i 0.656030i
\(713\) −31.2268 + 18.0288i −1.16945 + 0.675184i
\(714\) 0 0
\(715\) 0 0
\(716\) −2.30221 + 3.98755i −0.0860377 + 0.149022i
\(717\) 0 0
\(718\) −69.4061 + 40.0716i −2.59021 + 1.49546i
\(719\) −15.0848 −0.562569 −0.281284 0.959624i \(-0.590760\pi\)
−0.281284 + 0.959624i \(0.590760\pi\)
\(720\) 0 0
\(721\) −0.150442 −0.00560275
\(722\) −37.5700 + 21.6910i −1.39821 + 0.807257i
\(723\) 0 0
\(724\) −27.3729 + 47.4112i −1.01731 + 1.76203i
\(725\) 0 0
\(726\) 0 0
\(727\) −10.6916 + 6.17277i −0.396528 + 0.228936i −0.684985 0.728557i \(-0.740191\pi\)
0.288457 + 0.957493i \(0.406858\pi\)
\(728\) 3.96265i 0.146866i
\(729\) 0 0
\(730\) 0 0
\(731\) −17.1842 29.7639i −0.635580 1.10086i
\(732\) 0 0
\(733\) 19.0526 + 11.0000i 0.703722 + 0.406294i 0.808732 0.588177i \(-0.200154\pi\)
−0.105010 + 0.994471i \(0.533487\pi\)
\(734\) 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
\(738\) 0 0
\(739\) −29.7266 −1.09351 −0.546755 0.837293i \(-0.684137\pi\)
−0.546755 + 0.837293i \(0.684137\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 5.62882 + 3.24980i 0.206640 + 0.119304i
\(743\) 41.8851 + 24.1824i 1.53662 + 0.887165i 0.999034 + 0.0439537i \(0.0139954\pi\)
0.537582 + 0.843212i \(0.319338\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 5.52787 0.202390
\(747\) 0 0
\(748\) 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 −0.414838 0.909895i \(-0.636162\pi\)
0.995411 0.0956869i \(-0.0305047\pi\)
\(752\) 25.3895 + 14.6586i 0.925860 + 0.534546i
\(753\) 0 0
\(754\) 2.30221 + 3.98755i 0.0838416 + 0.145218i
\(755\) 0 0
\(756\) 0 0
\(757\) 4.94531i 0.179740i −0.995953 0.0898701i \(-0.971355\pi\)
0.995953 0.0898701i \(-0.0286452\pi\)
\(758\) −33.6858 + 19.4485i −1.22352 + 0.706402i
\(759\) 0 0
\(760\) 0 0
\(761\) 17.7125 30.6789i 0.642076 1.11211i −0.342893 0.939375i \(-0.611407\pi\)
0.984969 0.172734i \(-0.0552600\pi\)
\(762\) 0 0
\(763\) −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
\(768\) 0 0
\(769\) 24.7125 42.8032i 0.891154 1.54352i 0.0526602 0.998612i \(-0.483230\pi\)
0.838494 0.544911i \(-0.183437\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −99.9768 + 57.7217i −3.59825 + 2.07745i
\(773\) 12.6599i 0.455345i −0.973738 0.227673i \(-0.926888\pi\)
0.973738 0.227673i \(-0.0731116\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −35.7549 61.9292i −1.28352 2.22313i
\(777\) 0 0
\(778\) 53.6329 + 30.9650i 1.92283 + 1.11015i
\(779\) −7.49546 + 12.9825i −0.268553 + 0.465147i
\(780\) 0 0
\(781\) 14.9289 + 25.8576i 0.534199 + 0.925259i
\(782\) 34.4623i 1.23237i
\(783\) 0 0
\(784\) 40.6044 1.45016
\(785\) 0 0
\(786\) 0 0
\(787\) 26.7900 + 15.4672i 0.954959 + 0.551346i 0.894618 0.446832i \(-0.147448\pi\)
0.0603410 + 0.998178i \(0.480781\pi\)
\(788\) −53.3431 30.7977i −1.90027 1.09712i
\(789\) 0 0
\(790\) 0 0
\(791\) 4.01093 0.142612
\(792\) 0 0
\(793\)