Properties

Label 675.2.e.b.226.1
Level $675$
Weight $2$
Character 675.226
Analytic conductor $5.390$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.954288.1
Defining polynomial: \( x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.1
Root \(0.403374 + 1.68443i\) of defining polynomial
Character \(\chi\) \(=\) 675.226
Dual form 675.2.e.b.451.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.25707 - 2.17731i) q^{2} +(-2.16044 + 3.74200i) q^{4} +(-0.257068 - 0.445256i) q^{7} +5.83502 q^{8} +O(q^{10})\) \(q+(-1.25707 - 2.17731i) q^{2} +(-2.16044 + 3.74200i) q^{4} +(-0.257068 - 0.445256i) q^{7} +5.83502 q^{8} +(-1.66044 - 2.87597i) q^{11} +(-0.660442 + 1.14392i) q^{13} +(-0.646305 + 1.11943i) q^{14} +(-3.01414 - 5.22064i) q^{16} -3.32088 q^{17} -1.32088 q^{19} +(-4.17458 + 7.23058i) q^{22} +(-2.06382 + 3.57463i) q^{23} +3.32088 q^{26} +2.22153 q^{28} +(-0.693252 - 1.20075i) q^{29} +(-4.36783 + 7.56531i) q^{31} +(-1.74293 + 3.01885i) q^{32} +(4.17458 + 7.23058i) q^{34} -0.292611 q^{37} +(1.66044 + 2.87597i) q^{38} +(-5.67458 + 9.82866i) q^{41} +(5.17458 + 8.96263i) q^{43} +14.3492 q^{44} +10.3774 q^{46} +(2.43165 + 4.21174i) q^{47} +(3.36783 - 5.83326i) q^{49} +(-2.85369 - 4.94274i) q^{52} -5.02827 q^{53} +(-1.50000 - 2.59808i) q^{56} +(-1.74293 + 3.01885i) q^{58} +(-2.51414 + 4.35461i) q^{59} +(-3.67458 - 6.36456i) q^{61} +21.9627 q^{62} -3.29261 q^{64} +(4.72426 - 8.18266i) q^{67} +(7.17458 - 12.4267i) q^{68} -8.99093 q^{71} -6.05655 q^{73} +(0.367832 + 0.637103i) q^{74} +(2.85369 - 4.94274i) q^{76} +(-0.853695 + 1.47864i) q^{77} +(4.02827 + 6.97717i) q^{79} +28.5333 q^{82} +(-0.771205 - 1.33577i) q^{83} +(13.0096 - 22.5333i) q^{86} +(-9.68872 - 16.7813i) q^{88} +3.00000 q^{89} +0.679116 q^{91} +(-8.91751 - 15.4456i) q^{92} +(6.11350 - 10.5889i) q^{94} +(-6.12763 - 10.6134i) q^{97} -16.9344 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{2} - 5 q^{4} + 5 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - q^{2} - 5 q^{4} + 5 q^{7} + 6 q^{8} - 2 q^{11} + 4 q^{13} - 9 q^{14} - 5 q^{16} - 4 q^{17} + 8 q^{19} - 4 q^{22} - 3 q^{23} + 4 q^{26} - 10 q^{28} - 7 q^{29} - 8 q^{31} - 17 q^{32} + 4 q^{34} - 12 q^{37} + 2 q^{38} - 13 q^{41} + 10 q^{43} + 44 q^{44} - 6 q^{46} - 13 q^{47} + 2 q^{49} - 12 q^{52} - 4 q^{53} - 9 q^{56} - 17 q^{58} - 2 q^{59} - q^{61} + 84 q^{62} - 30 q^{64} + 11 q^{67} + 22 q^{68} + 20 q^{71} + 16 q^{73} - 16 q^{74} + 12 q^{76} - 2 q^{79} + 58 q^{82} + 15 q^{83} + 28 q^{86} - 24 q^{88} + 18 q^{89} + 20 q^{91} - 39 q^{92} + 31 q^{94} - 18 q^{97} - 80 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.25707 2.17731i −0.888882 1.53959i −0.841199 0.540726i \(-0.818150\pi\)
−0.0476826 0.998863i \(-0.515184\pi\)
\(3\) 0 0
\(4\) −2.16044 + 3.74200i −1.08022 + 1.87100i
\(5\) 0 0
\(6\) 0 0
\(7\) −0.257068 0.445256i −0.0971627 0.168291i 0.813346 0.581780i \(-0.197643\pi\)
−0.910509 + 0.413489i \(0.864310\pi\)
\(8\) 5.83502 2.06299
\(9\) 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
\(13\) −0.660442 + 1.14392i −0.183174 + 0.317266i −0.942960 0.332907i \(-0.891970\pi\)
0.759786 + 0.650173i \(0.225304\pi\)
\(14\) −0.646305 + 1.11943i −0.172732 + 0.299181i
\(15\) 0 0
\(16\) −3.01414 5.22064i −0.753534 1.30516i
\(17\) −3.32088 −0.805433 −0.402716 0.915325i \(-0.631934\pi\)
−0.402716 + 0.915325i \(0.631934\pi\)
\(18\) 0 0
\(19\) −1.32088 −0.303032 −0.151516 0.988455i \(-0.548415\pi\)
−0.151516 + 0.988455i \(0.548415\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −4.17458 + 7.23058i −0.890023 + 1.54157i
\(23\) −2.06382 + 3.57463i −0.430335 + 0.745363i −0.996902 0.0786532i \(-0.974938\pi\)
0.566567 + 0.824016i \(0.308271\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 3.32088 0.651279
\(27\) 0 0
\(28\) 2.22153 0.419829
\(29\) −0.693252 1.20075i −0.128734 0.222973i 0.794453 0.607326i \(-0.207758\pi\)
−0.923186 + 0.384353i \(0.874425\pi\)
\(30\) 0 0
\(31\) −4.36783 + 7.56531i −0.784486 + 1.35877i 0.144820 + 0.989458i \(0.453740\pi\)
−0.929306 + 0.369311i \(0.879594\pi\)
\(32\) −1.74293 + 3.01885i −0.308110 + 0.533662i
\(33\) 0 0
\(34\) 4.17458 + 7.23058i 0.715934 + 1.24003i
\(35\) 0 0
\(36\) 0 0
\(37\) −0.292611 −0.0481049 −0.0240524 0.999711i \(-0.507657\pi\)
−0.0240524 + 0.999711i \(0.507657\pi\)
\(38\) 1.66044 + 2.87597i 0.269359 + 0.466544i
\(39\) 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
\(43\) 5.17458 + 8.96263i 0.789116 + 1.36679i 0.926509 + 0.376272i \(0.122794\pi\)
−0.137393 + 0.990517i \(0.543872\pi\)
\(44\) 14.3492 2.16322
\(45\) 0 0
\(46\) 10.3774 1.53007
\(47\) 2.43165 + 4.21174i 0.354692 + 0.614345i 0.987065 0.160319i \(-0.0512523\pi\)
−0.632373 + 0.774664i \(0.717919\pi\)
\(48\) 0 0
\(49\) 3.36783 5.83326i 0.481119 0.833322i
\(50\) 0 0
\(51\) 0 0
\(52\) −2.85369 4.94274i −0.395736 0.685435i
\(53\) −5.02827 −0.690687 −0.345343 0.938476i \(-0.612238\pi\)
−0.345343 + 0.938476i \(0.612238\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.50000 2.59808i −0.200446 0.347183i
\(57\) 0 0
\(58\) −1.74293 + 3.01885i −0.228858 + 0.396394i
\(59\) −2.51414 + 4.35461i −0.327313 + 0.566922i −0.981978 0.188997i \(-0.939476\pi\)
0.654665 + 0.755919i \(0.272810\pi\)
\(60\) 0 0
\(61\) −3.67458 6.36456i −0.470482 0.814898i 0.528948 0.848654i \(-0.322586\pi\)
−0.999430 + 0.0337558i \(0.989253\pi\)
\(62\) 21.9627 2.78926
\(63\) 0 0
\(64\) −3.29261 −0.411576
\(65\) 0 0
\(66\) 0 0
\(67\) 4.72426 8.18266i 0.577160 0.999670i −0.418643 0.908151i \(-0.637494\pi\)
0.995803 0.0915197i \(-0.0291724\pi\)
\(68\) 7.17458 12.4267i 0.870046 1.50696i
\(69\) 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
\(73\) −6.05655 −0.708865 −0.354433 0.935082i \(-0.615326\pi\)
−0.354433 + 0.935082i \(0.615326\pi\)
\(74\) 0.367832 + 0.637103i 0.0427596 + 0.0740617i
\(75\) 0 0
\(76\) 2.85369 4.94274i 0.327341 0.566972i
\(77\) −0.853695 + 1.47864i −0.0972875 + 0.168507i
\(78\) 0 0
\(79\) 4.02827 + 6.97717i 0.453216 + 0.784994i 0.998584 0.0532036i \(-0.0169432\pi\)
−0.545367 + 0.838197i \(0.683610\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 28.5333 3.15098
\(83\) −0.771205 1.33577i −0.0846508 0.146619i 0.820592 0.571515i \(-0.193644\pi\)
−0.905242 + 0.424896i \(0.860311\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 13.0096 22.5333i 1.40286 2.42983i
\(87\) 0 0
\(88\) −9.68872 16.7813i −1.03282 1.78890i
\(89\) 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
\(92\) −8.91751 15.4456i −0.929715 1.61031i
\(93\) 0 0
\(94\) 6.11350 10.5889i 0.630559 1.09216i
\(95\) 0 0
\(96\) 0 0
\(97\) −6.12763 10.6134i −0.622167 1.07762i −0.989081 0.147370i \(-0.952919\pi\)
0.366915 0.930255i \(-0.380414\pi\)
\(98\) −16.9344 −1.71063
\(99\) 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
\(103\) 0.146305 0.253408i 0.0144159 0.0249691i −0.858727 0.512433i \(-0.828744\pi\)
0.873143 + 0.487464i \(0.162078\pi\)
\(104\) −3.85369 + 6.67479i −0.377886 + 0.654517i
\(105\) 0 0
\(106\) 6.32088 + 10.9481i 0.613939 + 1.06337i
\(107\) 1.87237 0.181009 0.0905043 0.995896i \(-0.471152\pi\)
0.0905043 + 0.995896i \(0.471152\pi\)
\(108\) 0 0
\(109\) 5.54787 0.531390 0.265695 0.964057i \(-0.414399\pi\)
0.265695 + 0.964057i \(0.414399\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.54968 + 2.68412i −0.146431 + 0.253626i
\(113\) −3.90064 + 6.75611i −0.366942 + 0.635561i −0.989086 0.147341i \(-0.952928\pi\)
0.622144 + 0.782903i \(0.286262\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 5.99093 0.556244
\(117\) 0 0
\(118\) 12.6418 1.16377
\(119\) 0.853695 + 1.47864i 0.0782581 + 0.135547i
\(120\) 0 0
\(121\) −0.0141369 + 0.0244859i −0.00128518 + 0.00222599i
\(122\) −9.23840 + 16.0014i −0.836405 + 1.44870i
\(123\) 0 0
\(124\) −18.8729 32.6888i −1.69484 2.93554i
\(125\) 0 0
\(126\) 0 0
\(127\) −17.8916 −1.58762 −0.793810 0.608166i \(-0.791906\pi\)
−0.793810 + 0.608166i \(0.791906\pi\)
\(128\) 7.62490 + 13.2067i 0.673952 + 1.16732i
\(129\) 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
\(133\) 0.339558 + 0.588131i 0.0294434 + 0.0509974i
\(134\) −23.7549 −2.05211
\(135\) 0 0
\(136\) −19.3774 −1.66160
\(137\) −2.83502 4.91040i −0.242212 0.419524i 0.719132 0.694874i \(-0.244540\pi\)
−0.961344 + 0.275350i \(0.911206\pi\)
\(138\) 0 0
\(139\) −4.00000 + 6.92820i −0.339276 + 0.587643i −0.984297 0.176522i \(-0.943515\pi\)
0.645021 + 0.764165i \(0.276849\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 11.3022 + 19.5760i 0.948460 + 1.64278i
\(143\) 4.38650 0.366818
\(144\) 0 0
\(145\) 0 0
\(146\) 7.61350 + 13.1870i 0.630097 + 1.09136i
\(147\) 0 0
\(148\) 0.632168 1.09495i 0.0519639 0.0900042i
\(149\) 8.83049 15.2948i 0.723422 1.25300i −0.236199 0.971705i \(-0.575902\pi\)
0.959620 0.281298i \(-0.0907650\pi\)
\(150\) 0 0
\(151\) −0.632168 1.09495i −0.0514451 0.0891056i 0.839156 0.543891i \(-0.183049\pi\)
−0.890601 + 0.454785i \(0.849716\pi\)
\(152\) −7.70739 −0.625152
\(153\) 0 0
\(154\) 4.29261 0.345908
\(155\) 0 0
\(156\) 0 0
\(157\) −7.83502 + 13.5707i −0.625303 + 1.08306i 0.363179 + 0.931719i \(0.381691\pi\)
−0.988482 + 0.151337i \(0.951642\pi\)
\(158\) 10.1276 17.5416i 0.805711 1.39553i
\(159\) 0 0
\(160\) 0 0
\(161\) 2.12217 0.167250
\(162\) 0 0
\(163\) −15.7074 −1.23030 −0.615149 0.788411i \(-0.710904\pi\)
−0.615149 + 0.788411i \(0.710904\pi\)
\(164\) −24.5192 42.4685i −1.91463 3.31623i
\(165\) 0 0
\(166\) −1.93892 + 3.35830i −0.150489 + 0.260655i
\(167\) −3.08249 + 5.33903i −0.238530 + 0.413146i −0.960293 0.278994i \(-0.909999\pi\)
0.721763 + 0.692141i \(0.243332\pi\)
\(168\) 0 0
\(169\) 5.62763 + 9.74734i 0.432895 + 0.749796i
\(170\) 0 0
\(171\) 0 0
\(172\) −44.7175 −3.40968
\(173\) −4.29261 7.43502i −0.326361 0.565274i 0.655426 0.755260i \(-0.272489\pi\)
−0.981787 + 0.189986i \(0.939156\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −10.0096 + 17.3371i −0.754502 + 1.30684i
\(177\) 0 0
\(178\) −3.77121 6.53192i −0.282664 0.489588i
\(179\) 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 \(0.656063\pi\)
\(182\) −0.853695 1.47864i −0.0632801 0.109604i
\(183\) 0 0
\(184\) −12.0424 + 20.8581i −0.887778 + 1.53768i
\(185\) 0 0
\(186\) 0 0
\(187\) 5.51414 + 9.55077i 0.403234 + 0.698421i
\(188\) −21.0137 −1.53258
\(189\) 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
\(193\) 13.3588 23.1380i 0.961585 1.66551i 0.243060 0.970011i \(-0.421849\pi\)
0.718524 0.695502i \(-0.244818\pi\)
\(194\) −15.4057 + 26.6835i −1.10607 + 1.91576i
\(195\) 0 0
\(196\) 14.5520 + 25.2048i 1.03943 + 1.80034i
\(197\) −14.2553 −1.01565 −0.507823 0.861462i \(-0.669550\pi\)
−0.507823 + 0.861462i \(0.669550\pi\)
\(198\) 0 0
\(199\) −24.6610 −1.74817 −0.874085 0.485773i \(-0.838538\pi\)
−0.874085 + 0.485773i \(0.838538\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 14.6700 25.4093i 1.03218 1.78779i
\(203\) −0.356427 + 0.617349i −0.0250162 + 0.0433294i
\(204\) 0 0
\(205\) 0 0
\(206\) −0.735663 −0.0512561
\(207\) 0 0
\(208\) 7.96265 0.552111
\(209\) 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 \(0.107406\pi\)
\(212\) 10.8633 18.8158i 0.746094 1.29227i
\(213\) 0 0
\(214\) −2.35369 4.07672i −0.160895 0.278679i
\(215\) 0 0
\(216\) 0 0
\(217\) 4.49133 0.304891
\(218\) −6.97406 12.0794i −0.472343 0.818122i
\(219\) 0 0
\(220\) 0 0
\(221\) 2.19325 3.79882i 0.147534 0.255537i
\(222\) 0 0
\(223\) 4.33229 + 7.50375i 0.290112 + 0.502488i 0.973836 0.227252i \(-0.0729743\pi\)
−0.683724 + 0.729740i \(0.739641\pi\)
\(224\) 1.79221 0.119747
\(225\) 0 0
\(226\) 19.6135 1.30467
\(227\) −1.66044 2.87597i −0.110207 0.190885i 0.805646 0.592397i \(-0.201818\pi\)
−0.915854 + 0.401512i \(0.868485\pi\)
\(228\) 0 0
\(229\) 12.6559 21.9207i 0.836326 1.44856i −0.0566206 0.998396i \(-0.518033\pi\)
0.892946 0.450163i \(-0.148634\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −4.04514 7.00639i −0.265577 0.459992i
\(233\) 27.6327 1.81028 0.905139 0.425116i \(-0.139767\pi\)
0.905139 + 0.425116i \(0.139767\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −10.8633 18.8158i −0.707140 1.22480i
\(237\) 0 0
\(238\) 2.14631 3.71751i 0.139124 0.240970i
\(239\) −2.09936 + 3.63620i −0.135796 + 0.235206i −0.925901 0.377765i \(-0.876693\pi\)
0.790105 + 0.612971i \(0.210026\pi\)
\(240\) 0 0
\(241\) −1.80221 3.12152i −0.116091 0.201075i 0.802125 0.597157i \(-0.203703\pi\)
−0.918215 + 0.396082i \(0.870370\pi\)
\(242\) 0.0710844 0.00456948
\(243\) 0 0
\(244\) 31.7549 2.03290
\(245\) 0 0
\(246\) 0 0
\(247\) 0.872368 1.51099i 0.0555074 0.0961417i
\(248\) −25.4864 + 44.1437i −1.61839 + 2.80313i
\(249\) 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
\(253\) 13.7074 0.861776
\(254\) 22.4909 + 38.9554i 1.41121 + 2.44428i
\(255\) 0 0
\(256\) 15.8774 27.5005i 0.992340 1.71878i
\(257\) 9.00000 15.5885i 0.561405 0.972381i −0.435970 0.899961i \(-0.643595\pi\)
0.997374 0.0724199i \(-0.0230722\pi\)
\(258\) 0 0
\(259\) 0.0752210 + 0.130287i 0.00467400 + 0.00809561i
\(260\) 0 0
\(261\) 0 0
\(262\) 15.0848 0.931943
\(263\) −3.11803 5.40059i −0.192266 0.333015i 0.753735 0.657179i \(-0.228250\pi\)
−0.946001 + 0.324164i \(0.894917\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0.853695 1.47864i 0.0523434 0.0906614i
\(267\) 0 0
\(268\) 20.4130 + 35.3563i 1.24692 + 2.15973i
\(269\) −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 \(0.435712\pi\)
\(272\) 10.0096 + 17.3371i 0.606921 + 1.05122i
\(273\) 0 0
\(274\) −7.12763 + 12.3454i −0.430596 + 0.745814i
\(275\) 0 0
\(276\) 0 0
\(277\) 11.3305 + 19.6250i 0.680783 + 1.17915i 0.974742 + 0.223333i \(0.0716936\pi\)
−0.293959 + 0.955818i \(0.594973\pi\)
\(278\) 20.1131 1.20630
\(279\) 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
\(283\) 0.322689 0.558913i 0.0191819 0.0332240i −0.856275 0.516520i \(-0.827227\pi\)
0.875457 + 0.483296i \(0.160561\pi\)
\(284\) 19.4244 33.6440i 1.15262 1.99640i
\(285\) 0 0
\(286\) −5.51414 9.55077i −0.326058 0.564749i
\(287\) 5.83502 0.344430
\(288\) 0 0
\(289\) −5.97173 −0.351278
\(290\) 0 0
\(291\) 0 0
\(292\) 13.0848 22.6636i 0.765731 1.32629i
\(293\) 0.688716 1.19289i 0.0402352 0.0696895i −0.845207 0.534440i \(-0.820523\pi\)
0.885442 + 0.464750i \(0.153856\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −1.70739 −0.0992400
\(297\) 0 0
\(298\) −44.4021 −2.57214
\(299\) −2.72606 4.72168i −0.157652 0.273062i
\(300\) 0 0
\(301\) 2.66044 4.60802i 0.153345 0.265602i
\(302\) −1.58936 + 2.75285i −0.0914573 + 0.158409i
\(303\) 0 0
\(304\) 3.98133 + 6.89586i 0.228345 + 0.395505i
\(305\) 0 0
\(306\) 0 0
\(307\) 7.98546 0.455754 0.227877 0.973690i \(-0.426822\pi\)
0.227877 + 0.973690i \(0.426822\pi\)
\(308\) −3.68872 6.38904i −0.210184 0.364050i
\(309\) 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
\(313\) −12.2685 21.2496i −0.693455 1.20110i −0.970699 0.240300i \(-0.922754\pi\)
0.277244 0.960800i \(-0.410579\pi\)
\(314\) 39.3966 2.22328
\(315\) 0 0
\(316\) −34.8114 −1.95829
\(317\) 10.1746 + 17.6229i 0.571461 + 0.989800i 0.996416 + 0.0845855i \(0.0269566\pi\)
−0.424955 + 0.905215i \(0.639710\pi\)
\(318\) 0 0
\(319\) −2.30221 + 3.98755i −0.128899 + 0.223260i
\(320\) 0 0
\(321\) 0 0
\(322\) −2.66771 4.62061i −0.148666 0.257497i
\(323\) 4.38650 0.244072
\(324\) 0 0
\(325\) 0 0
\(326\) 19.7453 + 34.1998i 1.09359 + 1.89415i
\(327\) 0 0
\(328\) −33.1113 + 57.3504i −1.82827 + 3.16665i
\(329\) 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 \(0.982586\pi\)
\(332\) 6.66458 0.365766
\(333\) 0 0
\(334\) 15.4996 0.848100
\(335\) 0 0
\(336\) 0 0
\(337\) 2.44852 4.24096i 0.133379 0.231020i −0.791598 0.611042i \(-0.790751\pi\)
0.924977 + 0.380023i \(0.124084\pi\)
\(338\) 14.1486 24.5062i 0.769584 1.33296i
\(339\) 0 0
\(340\) 0 0
\(341\) 29.0101 1.57099
\(342\) 0 0
\(343\) −7.06201 −0.381313
\(344\) 30.1938 + 52.2972i 1.62794 + 2.81967i
\(345\) 0 0
\(346\) −10.7922 + 18.6927i −0.580193 + 1.00492i
\(347\) −11.1372 + 19.2903i −0.597878 + 1.03556i 0.395256 + 0.918571i \(0.370656\pi\)
−0.993134 + 0.116984i \(0.962677\pi\)
\(348\) 0 0
\(349\) 1.47173 + 2.54910i 0.0787797 + 0.136450i 0.902724 0.430221i \(-0.141564\pi\)
−0.823944 + 0.566671i \(0.808231\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 11.5761 0.617011
\(353\) −9.41478 16.3069i −0.501098 0.867927i −0.999999 0.00126845i \(-0.999596\pi\)
0.498901 0.866659i \(-0.333737\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −6.48133 + 11.2260i −0.343510 + 0.594976i
\(357\) 0 0
\(358\) −1.33956 2.32018i −0.0707978 0.122625i
\(359\) 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
\(362\) 15.9271 + 27.5866i 0.837110 + 1.44992i
\(363\) 0 0
\(364\) −1.46719 + 2.54125i −0.0769016 + 0.133198i
\(365\) 0 0
\(366\) 0 0
\(367\) −9.17458 15.8908i −0.478909 0.829495i 0.520798 0.853680i \(-0.325634\pi\)
−0.999708 + 0.0241848i \(0.992301\pi\)
\(368\) 24.8825 1.29709
\(369\) 0 0
\(370\) 0 0
\(371\) 1.29261 + 2.23887i 0.0671090 + 0.116236i
\(372\) 0 0
\(373\) −1.09936 + 1.90414i −0.0569226 + 0.0985929i −0.893083 0.449893i \(-0.851462\pi\)
0.836160 + 0.548486i \(0.184795\pi\)
\(374\) 13.8633 24.0119i 0.716854 1.24163i
\(375\) 0 0
\(376\) 14.1887 + 24.5756i 0.731727 + 1.26739i
\(377\) 1.83141 0.0943226
\(378\) 0 0
\(379\) 15.4713 0.794709 0.397354 0.917665i \(-0.369928\pi\)
0.397354 + 0.917665i \(0.369928\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −21.2877 + 36.8713i −1.08917 + 1.88650i
\(383\) −3.85369 + 6.67479i −0.196915 + 0.341066i −0.947526 0.319677i \(-0.896426\pi\)
0.750612 + 0.660743i \(0.229759\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −67.1715 −3.41894
\(387\) 0 0
\(388\) 52.9536 2.68831
\(389\) −12.3163 21.3325i −0.624464 1.08160i −0.988644 0.150274i \(-0.951984\pi\)
0.364181 0.931328i \(-0.381349\pi\)
\(390\) 0 0
\(391\) 6.85369 11.8709i 0.346606 0.600340i
\(392\) 19.6514 34.0372i 0.992544 1.71914i
\(393\) 0 0
\(394\) 17.9198 + 31.0381i 0.902789 + 1.56368i
\(395\) 0 0
\(396\) 0 0
\(397\) 6.77301 0.339928 0.169964 0.985450i \(-0.445635\pi\)
0.169964 + 0.985450i \(0.445635\pi\)
\(398\) 31.0005 + 53.6945i 1.55392 + 2.69146i
\(399\) 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
\(403\) −5.76940 9.99290i −0.287394 0.497782i
\(404\) −50.4249 −2.50873
\(405\) 0 0
\(406\) 1.79221 0.0889459
\(407\) 0.485863 + 0.841540i 0.0240833 + 0.0417136i
\(408\) 0 0
\(409\) 6.70739 11.6175i 0.331659 0.574450i −0.651178 0.758925i \(-0.725725\pi\)
0.982837 + 0.184474i \(0.0590583\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0.632168 + 1.09495i 0.0311447 + 0.0539442i
\(413\) 2.58522 0.127210
\(414\) 0 0
\(415\) 0 0
\(416\) −2.30221 3.98755i −0.112875 0.195506i
\(417\) 0 0
\(418\) 5.51414 9.55077i 0.269705 0.467143i
\(419\) −16.5575 + 28.6784i −0.808886 + 1.40103i 0.104751 + 0.994499i \(0.466596\pi\)
−0.913636 + 0.406532i \(0.866738\pi\)
\(420\) 0 0
\(421\) 7.34916 + 12.7291i 0.358176 + 0.620379i 0.987656 0.156637i \(-0.0500654\pi\)
−0.629480 + 0.777017i \(0.716732\pi\)
\(422\) −13.5196 −0.658124
\(423\) 0 0
\(424\) −29.3401 −1.42488
\(425\) 0 0
\(426\) 0 0
\(427\) −1.88924 + 3.27225i −0.0914266 + 0.158355i
\(428\) −4.04514 + 7.00639i −0.195529 + 0.338667i
\(429\) 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
\(433\) 11.8314 0.568581 0.284291 0.958738i \(-0.408242\pi\)
0.284291 + 0.958738i \(0.408242\pi\)
\(434\) −5.64591 9.77900i −0.271012 0.469407i
\(435\) 0 0
\(436\) −11.9859 + 20.7601i −0.574019 + 0.994230i
\(437\) 2.72606 4.72168i 0.130405 0.225869i
\(438\) 0 0
\(439\) −4.15591 7.19824i −0.198351 0.343553i 0.749643 0.661842i \(-0.230225\pi\)
−0.947994 + 0.318289i \(0.896892\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −11.0283 −0.524561
\(443\) 14.5876 + 25.2664i 0.693076 + 1.20044i 0.970825 + 0.239789i \(0.0770781\pi\)
−0.277750 + 0.960654i \(0.589589\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 10.8920 18.8654i 0.515750 0.893305i
\(447\) 0 0
\(448\) 0.846426 + 1.46605i 0.0399899 + 0.0692645i
\(449\) −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
\(452\) −16.8542 29.1924i −0.792756 1.37309i
\(453\) 0 0
\(454\) −4.17458 + 7.23058i −0.195923 + 0.339348i
\(455\) 0 0
\(456\) 0 0
\(457\) −11.6176 20.1223i −0.543450 0.941283i −0.998703 0.0509206i \(-0.983784\pi\)
0.455253 0.890362i \(-0.349549\pi\)
\(458\) −63.6374 −2.97358
\(459\) 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
\(463\) −9.75434 + 16.8950i −0.453322 + 0.785178i −0.998590 0.0530845i \(-0.983095\pi\)
0.545268 + 0.838262i \(0.316428\pi\)
\(464\) −4.17912 + 7.23844i −0.194011 + 0.336036i
\(465\) 0 0
\(466\) −34.7362 60.1648i −1.60912 2.78708i
\(467\) −24.5935 −1.13805 −0.569026 0.822320i \(-0.692679\pi\)
−0.569026 + 0.822320i \(0.692679\pi\)
\(468\) 0 0
\(469\) −4.85783 −0.224314
\(470\) 0 0
\(471\) 0 0
\(472\) −14.6700 + 25.4093i −0.675243 + 1.16956i
\(473\) 17.1842 29.7639i 0.790129 1.36854i
\(474\) 0 0
\(475\) 0 0
\(476\) −7.37743 −0.338144
\(477\) 0 0
\(478\) 10.5561 0.482827
\(479\) 16.3774 + 28.3665i 0.748304 + 1.29610i 0.948635 + 0.316372i \(0.102465\pi\)
−0.200331 + 0.979728i \(0.564202\pi\)
\(480\) 0 0
\(481\) 0.193252 0.334723i 0.00881155 0.0152621i
\(482\) −4.53101 + 7.84793i −0.206382 + 0.357464i
\(483\) 0 0
\(484\) −0.0610840 0.105801i −0.00277655 0.00480912i
\(485\) 0 0
\(486\) 0 0
\(487\) 6.03735 0.273578 0.136789 0.990600i \(-0.456322\pi\)
0.136789 + 0.990600i \(0.456322\pi\)
\(488\) −21.4412 37.1373i −0.970600 1.68113i
\(489\) 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
\(493\) 2.30221 + 3.98755i 0.103686 + 0.179590i
\(494\) −4.38650 −0.197358
\(495\) 0 0
\(496\) 52.6610 2.36455
\(497\) 2.31128 + 4.00326i 0.103675 + 0.179571i
\(498\) 0 0
\(499\) −10.4859 + 18.1620i −0.469412 + 0.813045i −0.999388 0.0349673i \(-0.988867\pi\)
0.529977 + 0.848012i \(0.322201\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −8.64591 14.9751i −0.385886 0.668374i
\(503\) −5.31728 −0.237086 −0.118543 0.992949i \(-0.537822\pi\)
−0.118543 + 0.992949i \(0.537822\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −17.2311 29.8452i −0.766017 1.32678i
\(507\) 0 0
\(508\) 38.6537 66.9502i 1.71498 2.97043i
\(509\) 9.11350 15.7850i 0.403949 0.699659i −0.590250 0.807221i \(-0.700971\pi\)
0.994198 + 0.107561i \(0.0343041\pi\)
\(510\) 0 0
\(511\) 1.55695 + 2.69671i 0.0688753 + 0.119296i
\(512\) −49.3365 −2.18038
\(513\) 0 0
\(514\) −45.2545 −1.99609
\(515\) 0 0
\(516\) 0 0
\(517\) 8.07522 13.9867i 0.355148 0.615134i
\(518\) 0.189116 0.327558i 0.00830927 0.0143921i
\(519\) 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
\(523\) −18.9873 −0.830257 −0.415129 0.909763i \(-0.636263\pi\)
−0.415129 + 0.909763i \(0.636263\pi\)
\(524\) −12.9627 22.4520i −0.566276 0.980819i
\(525\) 0 0
\(526\) −7.83916 + 13.5778i −0.341804 + 0.592021i
\(527\) 14.5051 25.1235i 0.631851 1.09440i
\(528\) 0 0
\(529\) 2.98133 + 5.16381i 0.129623 + 0.224513i
\(530\) 0 0
\(531\) 0 0
\(532\) −2.93438 −0.127221
\(533\) −7.49546 12.9825i −0.324665 0.562336i
\(534\) 0 0
\(535\) 0 0
\(536\) 27.5661 47.7460i 1.19068 2.06231i
\(537\) 0 0
\(538\) 12.4745 + 21.6064i 0.537812 + 0.931518i
\(539\) −22.3684 −0.963473
\(540\) 0 0
\(541\) 16.5279 0.710589 0.355294 0.934754i \(-0.384381\pi\)
0.355294 + 0.934754i \(0.384381\pi\)
\(542\) −8.30221 14.3799i −0.356611 0.617668i
\(543\) 0 0
\(544\) 5.78807 10.0252i 0.248162 0.429829i
\(545\) 0 0
\(546\) 0 0
\(547\) 8.83683 + 15.3058i 0.377835 + 0.654430i 0.990747 0.135721i \(-0.0433352\pi\)
−0.612912 + 0.790151i \(0.710002\pi\)
\(548\) 24.4996 1.04657
\(549\) 0 0
\(550\) 0 0
\(551\) 0.915706 + 1.58605i 0.0390104 + 0.0675680i
\(552\) 0 0
\(553\) 2.07108 3.58722i 0.0880715 0.152544i
\(554\) 28.4864 49.3399i 1.21027 2.09625i
\(555\) 0 0
\(556\) −17.2835 29.9360i −0.732985 1.26957i
\(557\) 17.3401 0.734723 0.367362 0.930078i \(-0.380261\pi\)
0.367362 + 0.930078i \(0.380261\pi\)
\(558\) 0 0
\(559\) −13.6700 −0.578181
\(560\) 0 0
\(561\) 0 0
\(562\) −19.5447 + 33.8525i −0.824445 + 1.42798i
\(563\) −6.49727 + 11.2536i −0.273827 + 0.474283i −0.969839 0.243748i \(-0.921623\pi\)
0.696011 + 0.718031i \(0.254956\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −1.62257 −0.0682016
\(567\) 0 0
\(568\) −52.4623 −2.20127
\(569\) −8.34009 14.4455i −0.349635 0.605585i 0.636550 0.771236i \(-0.280361\pi\)
−0.986184 + 0.165651i \(0.947028\pi\)
\(570\) 0 0
\(571\) −10.0000 + 17.3205i −0.418487 + 0.724841i −0.995788 0.0916910i \(-0.970773\pi\)
0.577301 + 0.816532i \(0.304106\pi\)
\(572\) −9.47679 + 16.4143i −0.396245 + 0.686316i
\(573\) 0 0
\(574\) −7.33502 12.7046i −0.306158 0.530281i
\(575\) 0 0
\(576\) 0 0
\(577\) 23.5953 0.982287 0.491144 0.871079i \(-0.336579\pi\)
0.491144 + 0.871079i \(0.336579\pi\)
\(578\) 7.50687 + 13.0023i 0.312245 + 0.540823i
\(579\) 0 0
\(580\) 0 0
\(581\) −0.396505 + 0.686767i −0.0164498 + 0.0284919i
\(582\) 0 0
\(583\) 8.34916 + 14.4612i 0.345787 + 0.598920i
\(584\) −35.3401 −1.46238
\(585\) 0 0
\(586\) −3.46305 −0.143057
\(587\) −14.0638 24.3592i −0.580476 1.00541i −0.995423 0.0955681i \(-0.969533\pi\)
0.414947 0.909846i \(-0.363800\pi\)
\(588\) 0 0
\(589\) 5.76940 9.99290i 0.237724 0.411750i
\(590\) 0 0
\(591\) 0 0
\(592\) 0.881969 + 1.52761i 0.0362487 + 0.0627846i
\(593\) −9.17872 −0.376925 −0.188462 0.982080i \(-0.560350\pi\)
−0.188462 + 0.982080i \(0.560350\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 38.1555 + 66.0873i 1.56291 + 2.70704i
\(597\) 0 0
\(598\) −6.85369 + 11.8709i −0.280268 + 0.485439i
\(599\) −15.7357 + 27.2550i −0.642942 + 1.11361i 0.341831 + 0.939761i \(0.388953\pi\)
−0.984773 + 0.173846i \(0.944380\pi\)
\(600\) 0 0
\(601\) 14.6327 + 25.3446i 0.596880 + 1.03383i 0.993279 + 0.115748i \(0.0369265\pi\)
−0.396398 + 0.918079i \(0.629740\pi\)
\(602\) −13.3774 −0.545223
\(603\) 0 0
\(604\) 5.46305 0.222288
\(605\) 0 0
\(606\) 0 0
\(607\) −22.1017 + 38.2813i −0.897080 + 1.55379i −0.0658708 + 0.997828i \(0.520983\pi\)
−0.831209 + 0.555960i \(0.812351\pi\)
\(608\) 2.30221 3.98755i 0.0933670 0.161716i
\(609\) 0 0
\(610\) 0 0
\(611\) −6.42385 −0.259881
\(612\) 0 0
\(613\) 35.1715 1.42056 0.710282 0.703918i \(-0.248568\pi\)
0.710282 + 0.703918i \(0.248568\pi\)
\(614\) −10.0383 17.3868i −0.405112 0.701674i
\(615\) 0 0
\(616\) −4.98133 + 8.62791i −0.200703 + 0.347628i
\(617\) 3.71285 6.43085i 0.149474 0.258896i −0.781559 0.623831i \(-0.785575\pi\)
0.931033 + 0.364935i \(0.118909\pi\)
\(618\) 0 0
\(619\) −4.27394 7.40268i −0.171784 0.297539i 0.767260 0.641337i \(-0.221620\pi\)
−0.939044 + 0.343798i \(0.888286\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −24.2179 −0.971050
\(623\) −0.771205 1.33577i −0.0308977 0.0535164i
\(624\) 0 0
\(625\) 0 0
\(626\) −30.8446 + 53.4245i −1.23280 + 2.13527i
\(627\) 0 0
\(628\) −33.8542 58.6372i −1.35093 2.33988i
\(629\) 0.971726 0.0387453
\(630\) 0 0
\(631\) −2.36836 −0.0942829 −0.0471415 0.998888i \(-0.515011\pi\)
−0.0471415 + 0.998888i \(0.515011\pi\)
\(632\) 23.5051 + 40.7120i 0.934981 + 1.61944i
\(633\) 0 0
\(634\) 25.5803 44.3064i 1.01592 1.75963i
\(635\) 0 0
\(636\) 0 0
\(637\) 4.44852 + 7.70506i 0.176257 + 0.305285i
\(638\) 11.5761 0.458304
\(639\) 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
\(643\) −11.3232 + 19.6124i −0.446544 + 0.773437i −0.998158 0.0606623i \(-0.980679\pi\)
0.551614 + 0.834099i \(0.314012\pi\)
\(644\) −4.58482 + 7.94114i −0.180667 + 0.312925i
\(645\) 0 0
\(646\) −5.51414 9.55077i −0.216951 0.375770i
\(647\) 46.3912 1.82383 0.911913 0.410385i \(-0.134606\pi\)
0.911913 + 0.410385i \(0.134606\pi\)
\(648\) 0 0
\(649\) 16.6983 0.655466
\(650\) 0 0
\(651\) 0 0
\(652\) 33.9349 58.7770i 1.32899 2.30188i
\(653\) −18.2029 + 31.5283i −0.712333 + 1.23380i 0.251647 + 0.967819i \(0.419028\pi\)
−0.963979 + 0.265977i \(0.914305\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 68.4158 2.67119
\(657\) 0 0
\(658\) −6.28635 −0.245067
\(659\) 9.57068 + 16.5769i 0.372821 + 0.645745i 0.989998 0.141079i \(-0.0450572\pi\)
−0.617177 + 0.786824i \(0.711724\pi\)
\(660\) 0 0
\(661\) −19.9536 + 34.5606i −0.776104 + 1.34425i 0.158067 + 0.987428i \(0.449474\pi\)
−0.934172 + 0.356824i \(0.883860\pi\)
\(662\) −20.6700 + 35.8016i −0.803364 + 1.39147i
\(663\) 0 0
\(664\) −4.50000 7.79423i −0.174634 0.302475i
\(665\) 0 0
\(666\) 0 0
\(667\) 5.72298 0.221595
\(668\) −13.3191 23.0693i −0.515331 0.892579i
\(669\) 0 0
\(670\) 0 0
\(671\) −12.2029 + 21.1360i −0.471086 + 0.815945i
\(672\) 0 0
\(673\) 11.8254 + 20.4822i 0.455836 + 0.789532i 0.998736 0.0502658i \(-0.0160068\pi\)
−0.542899 + 0.839798i \(0.682674\pi\)
\(674\) −12.3118 −0.474233
\(675\) 0 0
\(676\) −48.6327 −1.87049
\(677\) 7.40157 + 12.8199i 0.284465 + 0.492709i 0.972479 0.232989i \(-0.0748506\pi\)
−0.688014 + 0.725697i \(0.741517\pi\)
\(678\) 0 0
\(679\) −3.15044 + 5.45673i −0.120903 + 0.209410i
\(680\) 0 0
\(681\) 0 0
\(682\) −36.4677 63.1639i −1.39642 2.41867i
\(683\) −4.95252 −0.189503 −0.0947515 0.995501i \(-0.530206\pi\)
−0.0947515 + 0.995501i \(0.530206\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 8.87743 + 15.3762i 0.338942 + 0.587065i
\(687\) 0 0
\(688\) 31.1938 54.0292i 1.18925 2.05984i
\(689\) 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 \(0.714276\pi\)
\(692\) 37.0957 1.41017
\(693\) 0 0
\(694\) 56.0011 2.12577
\(695\) 0 0
\(696\) 0 0
\(697\) 18.8446 32.6398i 0.713791 1.23632i
\(698\) 3.70012 6.40880i 0.140052 0.242577i
\(699\) 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
\(703\) 0.386505 0.0145773
\(704\) 5.46719 + 9.46945i 0.206052 + 0.356893i
\(705\) 0 0
\(706\) −23.6700 + 40.9977i −0.890834 + 1.54297i
\(707\) 3.00000 5.19615i 0.112827 0.195421i
\(708\) 0 0
\(709\) −19.3633 33.5382i −0.727204 1.25955i −0.958060 0.286566i \(-0.907486\pi\)
0.230857 0.972988i \(-0.425847\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 17.5051 0.656030
\(713\) −18.0288 31.2268i −0.675184 1.16945i
\(714\) 0 0
\(715\) 0 0
\(716\) −2.30221 + 3.98755i −0.0860377 + 0.149022i
\(717\) 0 0
\(718\) −40.0716 69.4061i −1.49546 2.59021i
\(719\) 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
\(722\) 21.6910 + 37.5700i 0.807257 + 1.39821i
\(723\) 0 0
\(724\) 27.3729 47.4112i 1.01731 1.76203i
\(725\) 0 0
\(726\) 0 0
\(727\) 6.17277 + 10.6916i 0.228936 + 0.396528i 0.957493 0.288457i \(-0.0931422\pi\)
−0.728557 + 0.684985i \(0.759809\pi\)
\(728\) 3.96265 0.146866
\(729\) 0 0
\(730\) 0 0
\(731\) −17.1842 29.7639i −0.635580 1.10086i
\(732\) 0 0
\(733\) −11.0000 + 19.0526i −0.406294 + 0.703722i −0.994471 0.105010i \(-0.966513\pi\)
0.588177 + 0.808732i \(0.299846\pi\)
\(734\) −23.0661 + 39.9517i −0.851387 + 1.47465i
\(735\) 0 0
\(736\) −7.19418 12.4607i −0.265181 0.459307i
\(737\) −31.3774 −1.15580
\(738\) 0 0
\(739\) 29.7266 1.09351 0.546755 0.837293i \(-0.315863\pi\)
0.546755 + 0.837293i \(0.315863\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 3.24980 5.62882i 0.119304 0.206640i
\(743\) −24.1824 + 41.8851i −0.887165 + 1.53662i −0.0439537 + 0.999034i \(0.513995\pi\)
−0.843212 + 0.537582i \(0.819338\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 5.52787 0.202390
\(747\) 0 0
\(748\) −47.6519 −1.74233
\(749\) −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 \(-0.0305047\pi\)
\(752\) 14.6586 25.3895i 0.534546 0.925860i
\(753\) 0 0
\(754\) −2.30221 3.98755i −0.0838416 0.145218i
\(755\) 0 0
\(756\) 0 0
\(757\) −4.94531 −0.179740 −0.0898701 0.995953i \(-0.528645\pi\)
−0.0898701 + 0.995953i \(0.528645\pi\)
\(758\) −19.4485 33.6858i −0.706402 1.22352i
\(759\) 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
\(763\) −1.42618 2.47022i −0.0516313 0.0894281i
\(764\) 73.1715 2.64725
\(765\) 0 0
\(766\) 19.3774 0.700135
\(767\) −3.32088 5.75194i −0.119910 0.207691i
\(768\) 0 0
\(769\) −24.7125 + 42.8032i −0.891154 + 1.54352i −0.0526602 + 0.998612i \(0.516770\pi\)
−0.838494 + 0.544911i \(0.816563\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 57.7217 + 99.9768i 2.07745 + 3.59825i
\(773\) 12.6599 0.455345 0.227673 0.973738i \(-0.426888\pi\)
0.227673 + 0.973738i \(0.426888\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −35.7549 61.9292i −1.28352 2.22313i
\(777\) 0 0
\(778\) −30.9650 + 53.6329i −1.11015 + 1.92283i
\(779\) 7.49546 12.9825i 0.268553 0.465147i
\(780\) 0 0
\(781\) 14.9289 + 25.8576i 0.534199 + 0.925259i
\(782\) −34.4623 −1.23237
\(783\) 0 0
\(784\) −40.6044 −1.45016
\(785\) 0 0
\(786\) 0 0
\(787\) 15.4672 26.7900i 0.551346 0.954959i −0.446832 0.894618i \(-0.647448\pi\)
0.998178 0.0603410i \(-0.0192188\pi\)
\(788\) 30.7977 53.3431i 1.09712 1.90027i
\(789\) 0 0
\(790\) 0 0
\(791\) 4.01093 0.142612
\(792\) 0 0
\(793\) 9.70739 0.344720
\(794\) −8.51414 14.7469i −0.302155 0.523349i