Properties

Label 135.2.e.b.91.3
Level $135$
Weight $2$
Character 135.91
Analytic conductor $1.078$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 135 = 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 135.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.07798042729\)
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 91.3
Root \(0.403374 + 1.68443i\) of defining polynomial
Character \(\chi\) \(=\) 135.91
Dual form 135.2.e.b.46.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.25707 + 2.17731i) q^{2} +(-2.16044 + 3.74200i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.257068 + 0.445256i) q^{7} -5.83502 q^{8} +O(q^{10})\) \(q+(1.25707 + 2.17731i) q^{2} +(-2.16044 + 3.74200i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.257068 + 0.445256i) q^{7} -5.83502 q^{8} +2.51414 q^{10} +(-1.66044 - 2.87597i) q^{11} +(0.660442 - 1.14392i) q^{13} +(-0.646305 + 1.11943i) q^{14} +(-3.01414 - 5.22064i) q^{16} +3.32088 q^{17} -1.32088 q^{19} +(2.16044 + 3.74200i) q^{20} +(4.17458 - 7.23058i) q^{22} +(2.06382 - 3.57463i) q^{23} +(-0.500000 - 0.866025i) q^{25} +3.32088 q^{26} -2.22153 q^{28} +(-0.693252 - 1.20075i) q^{29} +(-4.36783 + 7.56531i) q^{31} +(1.74293 - 3.01885i) q^{32} +(4.17458 + 7.23058i) q^{34} +0.514137 q^{35} +0.292611 q^{37} +(-1.66044 - 2.87597i) q^{38} +(-2.91751 + 5.05328i) q^{40} +(-5.67458 + 9.82866i) q^{41} +(-5.17458 - 8.96263i) q^{43} +14.3492 q^{44} +10.3774 q^{46} +(-2.43165 - 4.21174i) q^{47} +(3.36783 - 5.83326i) q^{49} +(1.25707 - 2.17731i) q^{50} +(2.85369 + 4.94274i) q^{52} +5.02827 q^{53} -3.32088 q^{55} +(-1.50000 - 2.59808i) q^{56} +(1.74293 - 3.01885i) q^{58} +(-2.51414 + 4.35461i) q^{59} +(-3.67458 - 6.36456i) q^{61} -21.9627 q^{62} -3.29261 q^{64} +(-0.660442 - 1.14392i) q^{65} +(-4.72426 + 8.18266i) q^{67} +(-7.17458 + 12.4267i) q^{68} +(0.646305 + 1.11943i) q^{70} -8.99093 q^{71} +6.05655 q^{73} +(0.367832 + 0.637103i) q^{74} +(2.85369 - 4.94274i) q^{76} +(0.853695 - 1.47864i) q^{77} +(4.02827 + 6.97717i) q^{79} -6.02827 q^{80} -28.5333 q^{82} +(0.771205 + 1.33577i) q^{83} +(1.66044 - 2.87597i) q^{85} +(13.0096 - 22.5333i) q^{86} +(9.68872 + 16.7813i) q^{88} +3.00000 q^{89} +0.679116 q^{91} +(8.91751 + 15.4456i) q^{92} +(6.11350 - 10.5889i) q^{94} +(-0.660442 + 1.14392i) q^{95} +(6.12763 + 10.6134i) q^{97} +16.9344 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{2} - 5 q^{4} + 3 q^{5} - 5 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + q^{2} - 5 q^{4} + 3 q^{5} - 5 q^{7} - 6 q^{8} + 2 q^{10} - 2 q^{11} - 4 q^{13} - 9 q^{14} - 5 q^{16} + 4 q^{17} + 8 q^{19} + 5 q^{20} + 4 q^{22} + 3 q^{23} - 3 q^{25} + 4 q^{26} + 10 q^{28} - 7 q^{29} - 8 q^{31} + 17 q^{32} + 4 q^{34} - 10 q^{35} + 12 q^{37} - 2 q^{38} - 3 q^{40} - 13 q^{41} - 10 q^{43} + 44 q^{44} - 6 q^{46} + 13 q^{47} + 2 q^{49} + q^{50} + 12 q^{52} + 4 q^{53} - 4 q^{55} - 9 q^{56} + 17 q^{58} - 2 q^{59} - q^{61} - 84 q^{62} - 30 q^{64} + 4 q^{65} - 11 q^{67} - 22 q^{68} + 9 q^{70} + 20 q^{71} - 16 q^{73} - 16 q^{74} + 12 q^{76} - 2 q^{79} - 10 q^{80} - 58 q^{82} - 15 q^{83} + 2 q^{85} + 28 q^{86} + 24 q^{88} + 18 q^{89} + 20 q^{91} + 39 q^{92} + 31 q^{94} + 4 q^{95} + 18 q^{97} + 80 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/135\mathbb{Z}\right)^\times\).

\(n\) \(56\) \(82\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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 \(0.181850\pi\)
0.0476826 + 0.998863i \(0.484816\pi\)
\(3\) 0 0
\(4\) −2.16044 + 3.74200i −1.08022 + 1.87100i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) 0.257068 + 0.445256i 0.0971627 + 0.168291i 0.910509 0.413489i \(-0.135690\pi\)
−0.813346 + 0.581780i \(0.802357\pi\)
\(8\) −5.83502 −2.06299
\(9\) 0 0
\(10\) 2.51414 0.795040
\(11\) −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 −0.759786 0.650173i \(-0.774696\pi\)
0.942960 + 0.332907i \(0.108030\pi\)
\(14\) −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 \(-0.368066\pi\)
0.402716 + 0.915325i \(0.368066\pi\)
\(18\) 0 0
\(19\) −1.32088 −0.303032 −0.151516 0.988455i \(-0.548415\pi\)
−0.151516 + 0.988455i \(0.548415\pi\)
\(20\) 2.16044 + 3.74200i 0.483090 + 0.836736i
\(21\) 0 0
\(22\) 4.17458 7.23058i 0.890023 1.54157i
\(23\) 2.06382 3.57463i 0.430335 0.745363i −0.566567 0.824016i \(-0.691729\pi\)
0.996902 + 0.0786532i \(0.0250620\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 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
\(35\) 0.514137 0.0869050
\(36\) 0 0
\(37\) 0.292611 0.0481049 0.0240524 0.999711i \(-0.492343\pi\)
0.0240524 + 0.999711i \(0.492343\pi\)
\(38\) −1.66044 2.87597i −0.269359 0.466544i
\(39\) 0 0
\(40\) −2.91751 + 5.05328i −0.461299 + 0.798993i
\(41\) −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 \(-0.877206\pi\)
0.137393 0.990517i \(-0.456128\pi\)
\(44\) 14.3492 2.16322
\(45\) 0 0
\(46\) 10.3774 1.53007
\(47\) −2.43165 4.21174i −0.354692 0.614345i 0.632373 0.774664i \(-0.282081\pi\)
−0.987065 + 0.160319i \(0.948748\pi\)
\(48\) 0 0
\(49\) 3.36783 5.83326i 0.481119 0.833322i
\(50\) 1.25707 2.17731i 0.177776 0.307918i
\(51\) 0 0
\(52\) 2.85369 + 4.94274i 0.395736 + 0.685435i
\(53\) 5.02827 0.690687 0.345343 0.938476i \(-0.387762\pi\)
0.345343 + 0.938476i \(0.387762\pi\)
\(54\) 0 0
\(55\) −3.32088 −0.447788
\(56\) −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
\(65\) −0.660442 1.14392i −0.0819178 0.141886i
\(66\) 0 0
\(67\) −4.72426 + 8.18266i −0.577160 + 0.999670i 0.418643 + 0.908151i \(0.362506\pi\)
−0.995803 + 0.0915197i \(0.970828\pi\)
\(68\) −7.17458 + 12.4267i −0.870046 + 1.50696i
\(69\) 0 0
\(70\) 0.646305 + 1.11943i 0.0772483 + 0.133798i
\(71\) −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 \(-0.384674\pi\)
0.354433 + 0.935082i \(0.384674\pi\)
\(74\) 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 \(0.683610\pi\)
\(80\) −6.02827 −0.673982
\(81\) 0 0
\(82\) −28.5333 −3.15098
\(83\) 0.771205 + 1.33577i 0.0846508 + 0.146619i 0.905242 0.424896i \(-0.139689\pi\)
−0.820592 + 0.571515i \(0.806356\pi\)
\(84\) 0 0
\(85\) 1.66044 2.87597i 0.180100 0.311943i
\(86\) 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
\(95\) −0.660442 + 1.14392i −0.0677599 + 0.117364i
\(96\) 0 0
\(97\) 6.12763 + 10.6134i 0.622167 + 1.07762i 0.989081 + 0.147370i \(0.0470808\pi\)
−0.366915 + 0.930255i \(0.619586\pi\)
\(98\) 16.9344 1.71063
\(99\) 0 0
\(100\) 4.32088 0.432088
\(101\) 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 −0.873143 0.487464i \(-0.837922\pi\)
0.858727 + 0.512433i \(0.171256\pi\)
\(104\) −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 \(-0.528848\pi\)
−0.0905043 + 0.995896i \(0.528848\pi\)
\(108\) 0 0
\(109\) 5.54787 0.531390 0.265695 0.964057i \(-0.414399\pi\)
0.265695 + 0.964057i \(0.414399\pi\)
\(110\) −4.17458 7.23058i −0.398031 0.689409i
\(111\) 0 0
\(112\) 1.54968 2.68412i 0.146431 0.253626i
\(113\) 3.90064 6.75611i 0.366942 0.635561i −0.622144 0.782903i \(-0.713738\pi\)
0.989086 + 0.147341i \(0.0470716\pi\)
\(114\) 0 0
\(115\) −2.06382 3.57463i −0.192452 0.333336i
\(116\) 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
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 17.8916 1.58762 0.793810 0.608166i \(-0.208094\pi\)
0.793810 + 0.608166i \(0.208094\pi\)
\(128\) −7.62490 13.2067i −0.673952 1.16732i
\(129\) 0 0
\(130\) 1.66044 2.87597i 0.145630 0.252239i
\(131\) −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 0.961344 0.275350i \(-0.0887936\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(138\) 0 0
\(139\) −4.00000 + 6.92820i −0.339276 + 0.587643i −0.984297 0.176522i \(-0.943515\pi\)
0.645021 + 0.764165i \(0.276849\pi\)
\(140\) −1.11076 + 1.92390i −0.0938766 + 0.162599i
\(141\) 0 0
\(142\) −11.3022 19.5760i −0.948460 1.64278i
\(143\) −4.38650 −0.366818
\(144\) 0 0
\(145\) −1.38650 −0.115143
\(146\) 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
\(155\) 4.36783 + 7.56531i 0.350833 + 0.607660i
\(156\) 0 0
\(157\) 7.83502 13.5707i 0.625303 1.08306i −0.363179 0.931719i \(-0.618309\pi\)
0.988482 0.151337i \(-0.0483579\pi\)
\(158\) −10.1276 + 17.5416i −0.805711 + 1.39553i
\(159\) 0 0
\(160\) −1.74293 3.01885i −0.137791 0.238661i
\(161\) 2.12217 0.167250
\(162\) 0 0
\(163\) 15.7074 1.23030 0.615149 0.788411i \(-0.289096\pi\)
0.615149 + 0.788411i \(0.289096\pi\)
\(164\) −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 −0.721763 0.692141i \(-0.756668\pi\)
0.960293 + 0.278994i \(0.0900011\pi\)
\(168\) 0 0
\(169\) 5.62763 + 9.74734i 0.432895 + 0.749796i
\(170\) 8.34916 0.640351
\(171\) 0 0
\(172\) 44.7175 3.40968
\(173\) 4.29261 + 7.43502i 0.326361 + 0.565274i 0.981787 0.189986i \(-0.0608441\pi\)
−0.655426 + 0.755260i \(0.727511\pi\)
\(174\) 0 0
\(175\) 0.257068 0.445256i 0.0194325 0.0336582i
\(176\) −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
\(185\) 0.146305 0.253408i 0.0107566 0.0186309i
\(186\) 0 0
\(187\) −5.51414 9.55077i −0.403234 0.698421i
\(188\) 21.0137 1.53258
\(189\) 0 0
\(190\) −3.32088 −0.240922
\(191\) −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 \(0.578151\pi\)
−0.718524 + 0.695502i \(0.755182\pi\)
\(194\) −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 \(-0.330450\pi\)
0.507823 + 0.861462i \(0.330450\pi\)
\(198\) 0 0
\(199\) −24.6610 −1.74817 −0.874085 0.485773i \(-0.838538\pi\)
−0.874085 + 0.485773i \(0.838538\pi\)
\(200\) 2.91751 + 5.05328i 0.206299 + 0.357321i
\(201\) 0 0
\(202\) −14.6700 + 25.4093i −1.03218 + 1.78779i
\(203\) 0.356427 0.617349i 0.0250162 0.0433294i
\(204\) 0 0
\(205\) 5.67458 + 9.82866i 0.396330 + 0.686463i
\(206\) −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
\(215\) −10.3492 −0.705807
\(216\) 0 0
\(217\) −4.49133 −0.304891
\(218\) 6.97406 + 12.0794i 0.472343 + 0.818122i
\(219\) 0 0
\(220\) 7.17458 12.4267i 0.483710 0.837810i
\(221\) 2.19325 3.79882i 0.147534 0.255537i
\(222\) 0 0
\(223\) −4.33229 7.50375i −0.290112 0.502488i 0.683724 0.729740i \(-0.260359\pi\)
−0.973836 + 0.227252i \(0.927026\pi\)
\(224\) 1.79221 0.119747
\(225\) 0 0
\(226\) 19.6135 1.30467
\(227\) 1.66044 + 2.87597i 0.110207 + 0.190885i 0.915854 0.401512i \(-0.131515\pi\)
−0.805646 + 0.592397i \(0.798182\pi\)
\(228\) 0 0
\(229\) 12.6559 21.9207i 0.836326 1.44856i −0.0566206 0.998396i \(-0.518033\pi\)
0.892946 0.450163i \(-0.148634\pi\)
\(230\) 5.18872 8.98712i 0.342134 0.592593i
\(231\) 0 0
\(232\) 4.04514 + 7.00639i 0.265577 + 0.459992i
\(233\) −27.6327 −1.81028 −0.905139 0.425116i \(-0.860233\pi\)
−0.905139 + 0.425116i \(0.860233\pi\)
\(234\) 0 0
\(235\) −4.86330 −0.317246
\(236\) −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
\(245\) −3.36783 5.83326i −0.215163 0.372673i
\(246\) 0 0
\(247\) −0.872368 + 1.51099i −0.0555074 + 0.0961417i
\(248\) 25.4864 44.1437i 1.61839 2.80313i
\(249\) 0 0
\(250\) −1.25707 2.17731i −0.0795040 0.137705i
\(251\) 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 \(0.356405\pi\)
−0.997374 + 0.0724199i \(0.976928\pi\)
\(258\) 0 0
\(259\) 0.0752210 + 0.130287i 0.00467400 + 0.00809561i
\(260\) 5.70739 0.353957
\(261\) 0 0
\(262\) −15.0848 −0.931943
\(263\) 3.11803 + 5.40059i 0.192266 + 0.333015i 0.946001 0.324164i \(-0.105083\pi\)
−0.753735 + 0.657179i \(0.771750\pi\)
\(264\) 0 0
\(265\) 2.51414 4.35461i 0.154442 0.267502i
\(266\) 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
\(275\) −1.66044 + 2.87597i −0.100128 + 0.173428i
\(276\) 0 0
\(277\) −11.3305 19.6250i −0.680783 1.17915i −0.974742 0.223333i \(-0.928306\pi\)
0.293959 0.955818i \(-0.405027\pi\)
\(278\) −20.1131 −1.20630
\(279\) 0 0
\(280\) −3.00000 −0.179284
\(281\) −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 −0.875457 0.483296i \(-0.839439\pi\)
0.856275 + 0.516520i \(0.172773\pi\)
\(284\) 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
\(290\) −1.74293 3.01885i −0.102348 0.177273i
\(291\) 0 0
\(292\) −13.0848 + 22.6636i −0.765731 + 1.32629i
\(293\) −0.688716 + 1.19289i −0.0402352 + 0.0696895i −0.885442 0.464750i \(-0.846144\pi\)
0.845207 + 0.534440i \(0.179477\pi\)
\(294\) 0 0
\(295\) 2.51414 + 4.35461i 0.146379 + 0.253535i
\(296\) −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
\(305\) −7.34916 −0.420812
\(306\) 0 0
\(307\) −7.98546 −0.455754 −0.227877 0.973690i \(-0.573178\pi\)
−0.227877 + 0.973690i \(0.573178\pi\)
\(308\) 3.68872 + 6.38904i 0.210184 + 0.364050i
\(309\) 0 0
\(310\) −10.9813 + 19.0202i −0.623697 + 1.08028i
\(311\) 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 \(0.0772458\pi\)
−0.277244 + 0.960800i \(0.589421\pi\)
\(314\) 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 \(-0.973043\pi\)
0.424955 0.905215i \(-0.360290\pi\)
\(318\) 0 0
\(319\) −2.30221 + 3.98755i −0.128899 + 0.223260i
\(320\) −1.64631 + 2.85148i −0.0920313 + 0.159403i
\(321\) 0 0
\(322\) 2.66771 + 4.62061i 0.148666 + 0.257497i
\(323\) −4.38650 −0.244072
\(324\) 0 0
\(325\) −1.32088 −0.0732695
\(326\) 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
\(335\) 4.72426 + 8.18266i 0.258114 + 0.447066i
\(336\) 0 0
\(337\) −2.44852 + 4.24096i −0.133379 + 0.231020i −0.924977 0.380023i \(-0.875916\pi\)
0.791598 + 0.611042i \(0.209249\pi\)
\(338\) −14.1486 + 24.5062i −0.769584 + 1.33296i
\(339\) 0 0
\(340\) 7.17458 + 12.4267i 0.389096 + 0.673934i
\(341\) 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 \(-0.629344\pi\)
0.993134 0.116984i \(-0.0373226\pi\)
\(348\) 0 0
\(349\) 1.47173 + 2.54910i 0.0787797 + 0.136450i 0.902724 0.430221i \(-0.141564\pi\)
−0.823944 + 0.566671i \(0.808231\pi\)
\(350\) 1.29261 0.0690929
\(351\) 0 0
\(352\) −11.5761 −0.617011
\(353\) 9.41478 + 16.3069i 0.501098 + 0.867927i 0.999999 + 0.00126845i \(0.000403761\pi\)
−0.498901 + 0.866659i \(0.666263\pi\)
\(354\) 0 0
\(355\) −4.49546 + 7.78637i −0.238594 + 0.413258i
\(356\) −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
\(365\) 3.02827 5.24512i 0.158507 0.274542i
\(366\) 0 0
\(367\) 9.17458 + 15.8908i 0.478909 + 0.829495i 0.999708 0.0241848i \(-0.00769900\pi\)
−0.520798 + 0.853680i \(0.674366\pi\)
\(368\) −24.8825 −1.29709
\(369\) 0 0
\(370\) 0.735663 0.0382453
\(371\) 1.29261 + 2.23887i 0.0671090 + 0.116236i
\(372\) 0 0
\(373\) 1.09936 1.90414i 0.0569226 0.0985929i −0.836160 0.548486i \(-0.815205\pi\)
0.893083 + 0.449893i \(0.148538\pi\)
\(374\) 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 \(0.369928\pi\)
\(380\) −2.85369 4.94274i −0.146391 0.253557i
\(381\) 0 0
\(382\) 21.2877 36.8713i 1.08917 1.88650i
\(383\) 3.85369 6.67479i 0.196915 0.341066i −0.750612 0.660743i \(-0.770241\pi\)
0.947526 + 0.319677i \(0.103574\pi\)
\(384\) 0 0
\(385\) −0.853695 1.47864i −0.0435083 0.0753586i
\(386\) −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
\(395\) 8.05655 0.405369
\(396\) 0 0
\(397\) −6.77301 −0.339928 −0.169964 0.985450i \(-0.554365\pi\)
−0.169964 + 0.985450i \(0.554365\pi\)
\(398\) −31.0005 53.6945i −1.55392 2.69146i
\(399\) 0 0
\(400\) −3.01414 + 5.22064i −0.150707 + 0.261032i
\(401\) −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 \(0.0590583\pi\)
\(410\) −14.2667 + 24.7106i −0.704581 + 1.22037i
\(411\) 0 0
\(412\) −0.632168 1.09495i −0.0311447 0.0539442i
\(413\) −2.58522 −0.127210
\(414\) 0 0
\(415\) 1.54241 0.0757140
\(416\) −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
\(425\) −1.66044 2.87597i −0.0805433 0.139505i
\(426\) 0 0
\(427\) 1.88924 3.27225i 0.0914266 0.158355i
\(428\) 4.04514 7.00639i 0.195529 0.338667i
\(429\) 0 0
\(430\) −13.0096 22.5333i −0.627379 1.08665i
\(431\) 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 \(-0.591758\pi\)
−0.284291 + 0.958738i \(0.591758\pi\)
\(434\) −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 \(0.896892\pi\)
\(440\) 19.3774 0.923783
\(441\) 0 0
\(442\) 11.0283 0.524561
\(443\) −14.5876 25.2664i −0.693076 1.20044i −0.970825 0.239789i \(-0.922922\pi\)
0.277750 0.960654i \(-0.410411\pi\)
\(444\) 0 0
\(445\) 1.50000 2.59808i 0.0711068 0.123161i
\(446\) 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
\(455\) 0.339558 0.588131i 0.0159187 0.0275720i
\(456\) 0 0
\(457\) 11.6176 + 20.1223i 0.543450 + 0.941283i 0.998703 + 0.0509206i \(0.0162155\pi\)
−0.455253 + 0.890362i \(0.650451\pi\)
\(458\) 63.6374 2.97358
\(459\) 0 0
\(460\) 17.8350 0.831562
\(461\) 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 −0.545268 0.838262i \(-0.683572\pi\)
0.998590 + 0.0530845i \(0.0169053\pi\)
\(464\) −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 \(-0.307321\pi\)
0.569026 + 0.822320i \(0.307321\pi\)
\(468\) 0 0
\(469\) −4.85783 −0.224314
\(470\) −6.11350 10.5889i −0.281995 0.488429i
\(471\) 0 0
\(472\) 14.6700 25.4093i 0.675243 1.16956i
\(473\) −17.1842 + 29.7639i −0.790129 + 1.36854i
\(474\) 0 0
\(475\) 0.660442 + 1.14392i 0.0303032 + 0.0524866i
\(476\) −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
\(485\) 12.2553 0.556483
\(486\) 0 0
\(487\) −6.03735 −0.273578 −0.136789 0.990600i \(-0.543678\pi\)
−0.136789 + 0.990600i \(0.543678\pi\)
\(488\) 21.4412 + 37.1373i 0.970600 + 1.68113i
\(489\) 0 0
\(490\) 8.46719 14.6656i 0.382509 0.662524i
\(491\) 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 \(0.322201\pi\)
\(500\) 2.16044 3.74200i 0.0966179 0.167347i
\(501\) 0 0
\(502\) 8.64591 + 14.9751i 0.385886 + 0.668374i
\(503\) 5.31728 0.237086 0.118543 0.992949i \(-0.462178\pi\)
0.118543 + 0.992949i \(0.462178\pi\)
\(504\) 0 0
\(505\) 11.6700 0.519310
\(506\) −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
\(515\) 0.146305 + 0.253408i 0.00644698 + 0.0111665i
\(516\) 0 0
\(517\) −8.07522 + 13.9867i −0.355148 + 0.615134i
\(518\) −0.189116 + 0.327558i −0.00830927 + 0.0143921i
\(519\) 0 0
\(520\) 3.85369 + 6.67479i 0.168996 + 0.292709i
\(521\) −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 \(-0.363737\pi\)
0.415129 + 0.909763i \(0.363737\pi\)
\(524\) −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
\(530\) 12.6418 0.549123
\(531\) 0 0
\(532\) 2.93438 0.127221
\(533\) 7.49546 + 12.9825i 0.324665 + 0.562336i
\(534\) 0 0
\(535\) −0.936184 + 1.62152i −0.0404748 + 0.0701043i
\(536\) 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
\(545\) 2.77394 4.80460i 0.118822 0.205806i
\(546\) 0 0
\(547\) −8.83683 15.3058i −0.377835 0.654430i 0.612912 0.790151i \(-0.289998\pi\)
−0.990747 + 0.135721i \(0.956665\pi\)
\(548\) −24.4996 −1.04657
\(549\) 0 0
\(550\) −8.34916 −0.356009
\(551\) 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 \(-0.619739\pi\)
−0.367362 + 0.930078i \(0.619739\pi\)
\(558\) 0 0
\(559\) −13.6700 −0.578181
\(560\) −1.54968 2.68412i −0.0654859 0.113425i
\(561\) 0 0
\(562\) 19.5447 33.8525i 0.824445 1.42798i
\(563\) 6.49727 11.2536i 0.273827 0.474283i −0.696011 0.718031i \(-0.745044\pi\)
0.969839 + 0.243748i \(0.0783770\pi\)
\(564\) 0 0
\(565\) −3.90064 6.75611i −0.164101 0.284232i
\(566\) −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
\(575\) −4.12763 −0.172134
\(576\) 0 0
\(577\) −23.5953 −0.982287 −0.491144 0.871079i \(-0.663421\pi\)
−0.491144 + 0.871079i \(0.663421\pi\)
\(578\) −7.50687 13.0023i −0.312245 0.540823i
\(579\) 0 0
\(580\) 2.99546 5.18830i 0.124380 0.215432i
\(581\) −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 \(0.0304668\pi\)
−0.414947 + 0.909846i \(0.636200\pi\)
\(588\) 0 0
\(589\) 5.76940 9.99290i 0.237724 0.411750i
\(590\) −6.32088 + 10.9481i −0.260227 + 0.450726i
\(591\) 0 0
\(592\) −0.881969 1.52761i −0.0362487 0.0627846i
\(593\) 9.17872 0.376925 0.188462 0.982080i \(-0.439650\pi\)
0.188462 + 0.982080i \(0.439650\pi\)
\(594\) 0 0
\(595\) 1.70739 0.0699961
\(596\) 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
\(605\) 0.0141369 + 0.0244859i 0.000574748 + 0.000995493i
\(606\) 0 0
\(607\) 22.1017 38.2813i 0.897080 1.55379i 0.0658708 0.997828i \(-0.479017\pi\)
0.831209 0.555960i \(-0.187649\pi\)
\(608\) −2.30221 + 3.98755i −0.0933670 + 0.161716i
\(609\) 0 0
\(610\) −9.23840 16.0014i −0.374052 0.647877i
\(611\) −6.42385 −0.259881
\(612\) 0 0
\(613\) −35.1715 −1.42056 −0.710282 0.703918i \(-0.751432\pi\)
−0.710282 + 0.703918i \(0.751432\pi\)
\(614\) −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 −0.931033 0.364935i \(-0.881091\pi\)
0.781559 + 0.623831i \(0.214425\pi\)
\(618\) 0 0
\(619\) −4.27394 7.40268i −0.171784 0.297539i 0.767260 0.641337i \(-0.221620\pi\)
−0.939044 + 0.343798i \(0.888286\pi\)
\(620\) −37.7458 −1.51591
\(621\) 0 0
\(622\) 24.2179 0.971050
\(623\) 0.771205 + 1.33577i 0.0308977 + 0.0535164i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −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
\(635\) 8.94578 15.4946i 0.355003 0.614883i
\(636\) 0 0
\(637\) −4.44852 7.70506i −0.176257 0.305285i
\(638\) −11.5761 −0.458304
\(639\) 0 0
\(640\) −15.2498 −0.602801
\(641\) −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 −0.551614 0.834099i \(-0.685988\pi\)
0.998158 + 0.0606623i \(0.0193213\pi\)
\(644\) −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 \(-0.865394\pi\)
−0.911913 + 0.410385i \(0.865394\pi\)
\(648\) 0 0
\(649\) 16.6983 0.655466
\(650\) −1.66044 2.87597i −0.0651279 0.112805i
\(651\) 0 0
\(652\) −33.9349 + 58.7770i −1.32899 + 2.30188i
\(653\) 18.2029 31.5283i 0.712333 1.23380i −0.251647 0.967819i \(-0.580972\pi\)
0.963979 0.265977i \(-0.0856946\pi\)
\(654\) 0 0
\(655\) 3.00000 + 5.19615i 0.117220 + 0.203030i
\(656\) 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
\(665\) −0.679116 −0.0263350
\(666\) 0 0
\(667\) −5.72298 −0.221595
\(668\) 13.3191 + 23.0693i 0.515331 + 0.892579i
\(669\) 0 0
\(670\) −11.8774 + 20.5723i −0.458865 + 0.794778i
\(671\) −12.2029 + 21.1360i −0.471086 + 0.815945i
\(672\) 0 0
\(673\) −11.8254 20.4822i −0.455836 0.789532i 0.542899 0.839798i \(-0.317326\pi\)
−0.998736 + 0.0502658i \(0.983993\pi\)
\(674\) −12.3118 −0.474233
\(675\) 0 0
\(676\) −48.6327 −1.87049
\(677\) −7.40157 12.8199i −0.284465 0.492709i 0.688014 0.725697i \(-0.258483\pi\)
−0.972479 + 0.232989i \(0.925149\pi\)
\(678\) 0 0
\(679\) −3.15044 + 5.45673i −0.120903 + 0.209410i
\(680\) −9.68872 + 16.7813i −0.371545 + 0.643535i
\(681\) 0 0
\(682\) 36.4677 + 63.1639i 1.39642 + 2.41867i
\(683\) 4.95252 0.189503 0.0947515 0.995501i \(-0.469794\pi\)
0.0947515 + 0.995501i \(0.469794\pi\)
\(684\) 0 0
\(685\) 5.67004 0.216641
\(686\) 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
\(695\) 4.00000 + 6.92820i 0.151729 + 0.262802i
\(696\) 0 0
\(697\) −18.8446 + 32.6398i −0.713791 + 1.23632i
\(698\) −3.70012 + 6.40880i −0.140052 + 0.242577i
\(699\) 0 0
\(700\) 1.11076 + 1.92390i 0.0419829 + 0.0727165i
\(701\) 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 \(-0.425847\pi\)
\(710\) −22.6044 −0.848329
\(711\) 0 0
\(712\) −17.5051 −0.656030
\(713\) 18.0288 + 31.2268i 0.675184 + 1.16945i
\(714\) 0 0
\(715\) −2.19325 + 3.79882i −0.0820230 + 0.142068i
\(716\) −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
\(725\) −0.693252 + 1.20075i −0.0257467 + 0.0445947i
\(726\) 0 0
\(727\) −6.17277 10.6916i −0.228936 0.396528i 0.728557 0.684985i \(-0.240191\pi\)
−0.957493 + 0.288457i \(0.906858\pi\)
\(728\) −3.96265 −0.146866
\(729\) 0 0
\(730\) 15.2270 0.563576
\(731\) −17.1842 29.7639i −0.635580 1.10086i
\(732\) 0 0
\(733\) 11.0000 19.0526i 0.406294 0.703722i −0.588177 0.808732i \(-0.700154\pi\)
0.994471 + 0.105010i \(0.0334875\pi\)
\(734\) −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 \(0.315863\pi\)
\(740\) 0.632168 + 1.09495i 0.0232390 + 0.0402511i
\(741\) 0 0
\(742\) −3.24980 + 5.62882i −0.119304 + 0.206640i
\(743\) 24.1824 41.8851i 0.887165 1.53662i 0.0439537 0.999034i \(-0.486005\pi\)
0.843212 0.537582i \(-0.180662\pi\)
\(744\) 0 0
\(745\) −8.83049 15.2948i −0.323524 0.560360i
\(746\) 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
\(755\) −1.26434 −0.0460139
\(756\) 0 0
\(757\) 4.94531 0.179740 0.0898701 0.995953i \(-0.471355\pi\)
0.0898701 + 0.995953i \(0.471355\pi\)
\(758\) 19.4485 + 33.6858i 0.706402 + 1.22352i
\(759\) 0 0
\(760\) 3.85369 6.67479i 0.139788 0.242120i
\(761\) 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 \(0.816563\pi\)
\(770\) 2.14631 3.71751i 0.0773475 0.133970i
\(771\) 0 0
\(772\) −57.7217 99.9768i −2.07745 3.59825i
\(773\) −12.6599 −0.455345 −0.227673 0.973738i \(-0.573112\pi\)
−0.227673 + 0.973738i \(0.573112\pi\)
\(774\) 0 0
\(775\) 8.73566 0.313794
\(776\) −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
\(785\) −7.83502 13.5707i −0.279644 0.484357i
\(786\) 0 0
\(787\) −15.4672 + 26.7900i −0.551346 + 0.954959i 0.446832 + 0.894618i \(0.352552\pi\)
−0.998178 + 0.0603410i \(0.980781\pi\)
\(788\) −30.7977 + 53.3431i −1.09712 + 1.90027i