Properties

Label 225.2.e.b.76.3
Level $225$
Weight $2$
Character 225.76
Analytic conductor $1.797$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.79663404548\)
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: \( 1 \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 76.3
Root \(0.403374 + 1.68443i\) of defining polynomial
Character \(\chi\) \(=\) 225.76
Dual form 225.2.e.b.151.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.25707 + 2.17731i) q^{2} +(-1.25707 + 1.19154i) q^{3} +(-2.16044 + 3.74200i) q^{4} +(-4.17458 - 1.23917i) q^{6} +(-0.257068 - 0.445256i) q^{7} -5.83502 q^{8} +(0.160442 - 2.99571i) q^{9} +O(q^{10})\) \(q+(1.25707 + 2.17731i) q^{2} +(-1.25707 + 1.19154i) q^{3} +(-2.16044 + 3.74200i) q^{4} +(-4.17458 - 1.23917i) q^{6} +(-0.257068 - 0.445256i) q^{7} -5.83502 q^{8} +(0.160442 - 2.99571i) q^{9} +(1.66044 + 2.87597i) q^{11} +(-1.74293 - 7.27821i) q^{12} +(-0.660442 + 1.14392i) q^{13} +(0.646305 - 1.11943i) q^{14} +(-3.01414 - 5.22064i) q^{16} +3.32088 q^{17} +(6.72426 - 3.41648i) q^{18} -1.32088 q^{19} +(0.853695 + 0.253408i) q^{21} +(-4.17458 + 7.23058i) q^{22} +(2.06382 - 3.57463i) q^{23} +(7.33502 - 6.95269i) q^{24} -3.32088 q^{26} +(3.36783 + 3.95698i) q^{27} +2.22153 q^{28} +(0.693252 + 1.20075i) q^{29} +(-4.36783 + 7.56531i) q^{31} +(1.74293 - 3.01885i) q^{32} +(-5.51414 - 1.63680i) q^{33} +(4.17458 + 7.23058i) q^{34} +(10.8633 + 7.07243i) q^{36} -0.292611 q^{37} +(-1.66044 - 2.87597i) q^{38} +(-0.532810 - 2.22493i) q^{39} +(5.67458 - 9.82866i) q^{41} +(0.521405 + 2.17731i) q^{42} +(5.17458 + 8.96263i) q^{43} -14.3492 q^{44} +10.3774 q^{46} +(-2.43165 - 4.21174i) q^{47} +(10.0096 + 2.97122i) q^{48} +(3.36783 - 5.83326i) q^{49} +(-4.17458 + 3.95698i) q^{51} +(-2.85369 - 4.94274i) q^{52} +5.02827 q^{53} +(-4.38197 + 12.3070i) q^{54} +(1.50000 + 2.59808i) q^{56} +(1.66044 - 1.57389i) q^{57} +(-1.74293 + 3.01885i) q^{58} +(2.51414 - 4.35461i) q^{59} +(-3.67458 - 6.36456i) q^{61} -21.9627 q^{62} +(-1.37510 + 0.698664i) q^{63} -3.29261 q^{64} +(-3.36783 - 14.0635i) q^{66} +(4.72426 - 8.18266i) q^{67} +(-7.17458 + 12.4267i) q^{68} +(1.66498 + 6.95269i) q^{69} +8.99093 q^{71} +(-0.936184 + 17.4800i) q^{72} -6.05655 q^{73} +(-0.367832 - 0.637103i) q^{74} +(2.85369 - 4.94274i) q^{76} +(0.853695 - 1.47864i) q^{77} +(4.17458 - 3.95698i) q^{78} +(4.02827 + 6.97717i) q^{79} +(-8.94852 - 0.961276i) q^{81} +28.5333 q^{82} +(0.771205 + 1.33577i) q^{83} +(-2.79261 + 2.64705i) q^{84} +(-13.0096 + 22.5333i) q^{86} +(-2.30221 - 0.683382i) q^{87} +(-9.68872 - 16.7813i) q^{88} -3.00000 q^{89} +0.679116 q^{91} +(8.91751 + 15.4456i) q^{92} +(-3.52374 - 14.7146i) q^{93} +(6.11350 - 10.5889i) q^{94} +(1.40611 + 5.87168i) q^{96} +(-6.12763 - 10.6134i) q^{97} +16.9344 q^{98} +(8.88197 - 4.51277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{2} - q^{3} - 5 q^{4} - 4 q^{6} + 5 q^{7} - 6 q^{8} - 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + q^{2} - q^{3} - 5 q^{4} - 4 q^{6} + 5 q^{7} - 6 q^{8} - 7 q^{9} + 2 q^{11} - 17 q^{12} + 4 q^{13} + 9 q^{14} - 5 q^{16} + 4 q^{17} + 23 q^{18} + 8 q^{19} - 4 q^{22} + 3 q^{23} + 15 q^{24} - 4 q^{26} + 2 q^{27} - 10 q^{28} + 7 q^{29} - 8 q^{31} + 17 q^{32} - 20 q^{33} + 4 q^{34} + 10 q^{36} - 12 q^{37} - 2 q^{38} - 14 q^{39} + 13 q^{41} + 33 q^{42} + 10 q^{43} - 44 q^{44} - 6 q^{46} + 13 q^{47} + 10 q^{48} + 2 q^{49} - 4 q^{51} - 12 q^{52} + 4 q^{53} + 5 q^{54} + 9 q^{56} + 2 q^{57} - 17 q^{58} + 2 q^{59} - q^{61} - 84 q^{62} - 33 q^{63} - 30 q^{64} - 2 q^{66} + 11 q^{67} - 22 q^{68} + 39 q^{69} - 20 q^{71} - 15 q^{72} + 16 q^{73} + 16 q^{74} + 12 q^{76} + 4 q^{78} - 2 q^{79} - 19 q^{81} + 58 q^{82} - 15 q^{83} - 27 q^{84} - 28 q^{86} + 26 q^{87} - 24 q^{88} - 18 q^{89} + 20 q^{91} + 39 q^{92} + 42 q^{93} + 31 q^{94} + 13 q^{96} - 18 q^{97} + 80 q^{98} + 22 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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 \(0.484816\pi\)
\(3\) −1.25707 + 1.19154i −0.725769 + 0.687939i
\(4\) −2.16044 + 3.74200i −1.08022 + 1.87100i
\(5\) 0 0
\(6\) −4.17458 1.23917i −1.70426 0.505889i
\(7\) −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
\(9\) 0.160442 2.99571i 0.0534807 0.998569i
\(10\) 0 0
\(11\) 1.66044 + 2.87597i 0.500642 + 0.867138i 1.00000 0.000741679i \(0.000236084\pi\)
−0.499358 + 0.866396i \(0.666431\pi\)
\(12\) −1.74293 7.27821i −0.503141 2.10104i
\(13\) −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 \(-0.368066\pi\)
0.402716 + 0.915325i \(0.368066\pi\)
\(18\) 6.72426 3.41648i 1.58492 0.805271i
\(19\) −1.32088 −0.303032 −0.151516 0.988455i \(-0.548415\pi\)
−0.151516 + 0.988455i \(0.548415\pi\)
\(20\) 0 0
\(21\) 0.853695 + 0.253408i 0.186291 + 0.0552982i
\(22\) −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 \(0.0250620\pi\)
\(24\) 7.33502 6.95269i 1.49725 1.41921i
\(25\) 0 0
\(26\) −3.32088 −0.651279
\(27\) 3.36783 + 3.95698i 0.648139 + 0.761522i
\(28\) 2.22153 0.419829
\(29\) 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 \(0.879594\pi\)
\(32\) 1.74293 3.01885i 0.308110 0.533662i
\(33\) −5.51414 1.63680i −0.959888 0.284930i
\(34\) 4.17458 + 7.23058i 0.715934 + 1.24003i
\(35\) 0 0
\(36\) 10.8633 + 7.07243i 1.81055 + 1.17874i
\(37\) −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
\(39\) −0.532810 2.22493i −0.0853179 0.356274i
\(40\) 0 0
\(41\) 5.67458 9.82866i 0.886220 1.53498i 0.0419119 0.999121i \(-0.486655\pi\)
0.844308 0.535857i \(-0.180012\pi\)
\(42\) 0.521405 + 2.17731i 0.0804546 + 0.335966i
\(43\) 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 0.632373 0.774664i \(-0.282081\pi\)
−0.987065 + 0.160319i \(0.948748\pi\)
\(48\) 10.0096 + 2.97122i 1.44476 + 0.428859i
\(49\) 3.36783 5.83326i 0.481119 0.833322i
\(50\) 0 0
\(51\) −4.17458 + 3.95698i −0.584558 + 0.554088i
\(52\) −2.85369 4.94274i −0.395736 0.685435i
\(53\) 5.02827 0.690687 0.345343 0.938476i \(-0.387762\pi\)
0.345343 + 0.938476i \(0.387762\pi\)
\(54\) −4.38197 + 12.3070i −0.596310 + 1.67477i
\(55\) 0 0
\(56\) 1.50000 + 2.59808i 0.200446 + 0.347183i
\(57\) 1.66044 1.57389i 0.219931 0.208467i
\(58\) −1.74293 + 3.01885i −0.228858 + 0.396394i
\(59\) 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 \(0.989253\pi\)
\(62\) −21.9627 −2.78926
\(63\) −1.37510 + 0.698664i −0.173246 + 0.0880234i
\(64\) −3.29261 −0.411576
\(65\) 0 0
\(66\) −3.36783 14.0635i −0.414551 1.73110i
\(67\) 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
\(69\) 1.66498 + 6.95269i 0.200440 + 0.837005i
\(70\) 0 0
\(71\) 8.99093 1.06703 0.533513 0.845792i \(-0.320871\pi\)
0.533513 + 0.845792i \(0.320871\pi\)
\(72\) −0.936184 + 17.4800i −0.110330 + 2.06004i
\(73\) −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
\(78\) 4.17458 3.95698i 0.472678 0.448040i
\(79\) 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
\(81\) −8.94852 0.961276i −0.994280 0.106808i
\(82\) 28.5333 3.15098
\(83\) 0.771205 + 1.33577i 0.0846508 + 0.146619i 0.905242 0.424896i \(-0.139689\pi\)
−0.820592 + 0.571515i \(0.806356\pi\)
\(84\) −2.79261 + 2.64705i −0.304699 + 0.288817i
\(85\) 0 0
\(86\) −13.0096 + 22.5333i −1.40286 + 2.42983i
\(87\) −2.30221 0.683382i −0.246823 0.0732662i
\(88\) −9.68872 16.7813i −1.03282 1.78890i
\(89\) −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
\(92\) 8.91751 + 15.4456i 0.929715 + 1.61031i
\(93\) −3.52374 14.7146i −0.365395 1.52583i
\(94\) 6.11350 10.5889i 0.630559 1.09216i
\(95\) 0 0
\(96\) 1.40611 + 5.87168i 0.143510 + 0.599276i
\(97\) −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
\(99\) 8.88197 4.51277i 0.892671 0.453551i
\(100\) 0 0
\(101\) −5.83502 10.1066i −0.580606 1.00564i −0.995408 0.0957276i \(-0.969482\pi\)
0.414801 0.909912i \(-0.363851\pi\)
\(102\) −13.8633 4.11514i −1.37267 0.407460i
\(103\) 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 \(-0.528848\pi\)
−0.0905043 + 0.995896i \(0.528848\pi\)
\(108\) −22.0830 + 4.05358i −2.12494 + 0.390056i
\(109\) 5.54787 0.531390 0.265695 0.964057i \(-0.414399\pi\)
0.265695 + 0.964057i \(0.414399\pi\)
\(110\) 0 0
\(111\) 0.367832 0.348659i 0.0349130 0.0330932i
\(112\) −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 \(0.0470716\pi\)
\(114\) 5.51414 + 1.63680i 0.516446 + 0.153300i
\(115\) 0 0
\(116\) −5.99093 −0.556244
\(117\) 3.32088 + 2.16202i 0.307016 + 0.199879i
\(118\) 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
\(123\) 4.57795 + 19.1168i 0.412780 + 1.72370i
\(124\) −18.8729 32.6888i −1.69484 2.93554i
\(125\) 0 0
\(126\) −3.24980 2.11575i −0.289515 0.188486i
\(127\) −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
\(129\) −17.1842 5.10090i −1.51298 0.449109i
\(130\) 0 0
\(131\) 3.00000 5.19615i 0.262111 0.453990i −0.704692 0.709514i \(-0.748915\pi\)
0.966803 + 0.255524i \(0.0822479\pi\)
\(132\) 18.0379 17.0977i 1.57000 1.48816i
\(133\) 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 \(0.755460\pi\)
\(138\) −13.0451 + 12.3652i −1.11048 + 1.05259i
\(139\) −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
\(141\) 8.07522 + 2.39703i 0.680056 + 0.201866i
\(142\) 11.3022 + 19.5760i 0.948460 + 1.64278i
\(143\) −4.38650 −0.366818
\(144\) −16.1231 + 8.19186i −1.34359 + 0.682655i
\(145\) 0 0
\(146\) −7.61350 13.1870i −0.630097 1.09136i
\(147\) 2.71699 + 11.3457i 0.224094 + 0.935780i
\(148\) 0.632168 1.09495i 0.0519639 0.0900042i
\(149\) −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 \(0.849716\pi\)
\(152\) 7.70739 0.625152
\(153\) 0.532810 9.94840i 0.0430752 0.804280i
\(154\) 4.29261 0.345908
\(155\) 0 0
\(156\) 9.47679 + 2.81306i 0.758750 + 0.225225i
\(157\) −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
\(159\) −6.32088 + 5.99141i −0.501279 + 0.475150i
\(160\) 0 0
\(161\) −2.12217 −0.167250
\(162\) −9.15591 20.6921i −0.719356 1.62572i
\(163\) −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 −0.721763 0.692141i \(-0.756668\pi\)
0.960293 + 0.278994i \(0.0900011\pi\)
\(168\) −4.98133 1.47864i −0.384318 0.114080i
\(169\) 5.62763 + 9.74734i 0.432895 + 0.749796i
\(170\) 0 0
\(171\) −0.211926 + 3.95698i −0.0162064 + 0.302598i
\(172\) −44.7175 −3.40968
\(173\) 4.29261 + 7.43502i 0.326361 + 0.565274i 0.981787 0.189986i \(-0.0608441\pi\)
−0.655426 + 0.755260i \(0.727511\pi\)
\(174\) −1.40611 5.87168i −0.106597 0.445131i
\(175\) 0 0
\(176\) 10.0096 17.3371i 0.754502 1.30684i
\(177\) 2.02827 + 8.46975i 0.152454 + 0.636626i
\(178\) −3.77121 6.53192i −0.282664 0.489588i
\(179\) −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 \(0.656063\pi\)
\(182\) 0.853695 + 1.47864i 0.0632801 + 0.109604i
\(183\) 12.2029 + 3.62226i 0.902061 + 0.267765i
\(184\) −12.0424 + 20.8581i −0.887778 + 1.53768i
\(185\) 0 0
\(186\) 27.6086 26.1695i 2.02436 1.91884i
\(187\) 5.51414 + 9.55077i 0.403234 + 0.698421i
\(188\) 21.0137 1.53258
\(189\) 0.896105 2.51676i 0.0651821 0.183067i
\(190\) 0 0
\(191\) 8.46719 + 14.6656i 0.612664 + 1.06117i 0.990789 + 0.135411i \(0.0432356\pi\)
−0.378125 + 0.925754i \(0.623431\pi\)
\(192\) 4.13904 3.92329i 0.298709 0.283139i
\(193\) 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 \(-0.330450\pi\)
0.507823 + 0.861462i \(0.330450\pi\)
\(198\) 20.9909 + 13.6659i 1.49176 + 0.971194i
\(199\) −24.6610 −1.74817 −0.874085 0.485773i \(-0.838538\pi\)
−0.874085 + 0.485773i \(0.838538\pi\)
\(200\) 0 0
\(201\) 3.81128 + 15.9153i 0.268827 + 1.12258i
\(202\) 14.6700 25.4093i 1.03218 1.78779i
\(203\) 0.356427 0.617349i 0.0250162 0.0433294i
\(204\) −5.78807 24.1701i −0.405246 1.69224i
\(205\) 0 0
\(206\) 0.735663 0.0512561
\(207\) −10.3774 6.75611i −0.721281 0.469582i
\(208\) 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
\(213\) −11.3022 + 10.7131i −0.774415 + 0.734049i
\(214\) −2.35369 4.07672i −0.160895 0.278679i
\(215\) 0 0
\(216\) −19.6514 23.0891i −1.33711 1.57101i
\(217\) 4.49133 0.304891
\(218\) 6.97406 + 12.0794i 0.472343 + 0.818122i
\(219\) 7.61350 7.21665i 0.514472 0.487656i
\(220\) 0 0
\(221\) −2.19325 + 3.79882i −0.147534 + 0.255537i
\(222\) 1.22153 + 0.362594i 0.0819835 + 0.0243357i
\(223\) 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 0.915854 0.401512i \(-0.131515\pi\)
−0.805646 + 0.592397i \(0.798182\pi\)
\(228\) 2.30221 + 9.61367i 0.152468 + 0.636681i
\(229\) 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
\(231\) 0.688716 + 2.87597i 0.0453142 + 0.189225i
\(232\) −4.04514 7.00639i −0.265577 0.459992i
\(233\) −27.6327 −1.81028 −0.905139 0.425116i \(-0.860233\pi\)
−0.905139 + 0.425116i \(0.860233\pi\)
\(234\) −0.532810 + 9.94840i −0.0348309 + 0.650347i
\(235\) 0 0
\(236\) 10.8633 + 18.8158i 0.707140 + 1.22480i
\(237\) −13.3774 3.97092i −0.868958 0.257939i
\(238\) 2.14631 3.71751i 0.139124 0.240970i
\(239\) 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 \(0.870370\pi\)
\(242\) −0.0710844 −0.00456948
\(243\) 12.3943 9.45417i 0.795095 0.606485i
\(244\) 31.7549 2.03290
\(245\) 0 0
\(246\) −35.8684 + 33.9987i −2.28688 + 2.16768i
\(247\) 0.872368 1.51099i 0.0555074 0.0961417i
\(248\) 25.4864 44.1437i 1.61839 2.80313i
\(249\) −2.56108 0.760225i −0.162302 0.0481773i
\(250\) 0 0
\(251\) −6.87783 −0.434125 −0.217062 0.976158i \(-0.569648\pi\)
−0.217062 + 0.976158i \(0.569648\pi\)
\(252\) 0.356427 6.65504i 0.0224528 0.419228i
\(253\) 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 \(0.976928\pi\)
\(258\) −10.4955 43.8274i −0.653419 2.72858i
\(259\) 0.0752210 + 0.130287i 0.00467400 + 0.00809561i
\(260\) 0 0
\(261\) 3.70832 1.88413i 0.229539 0.116625i
\(262\) 15.0848 0.931943
\(263\) 3.11803 + 5.40059i 0.192266 + 0.333015i 0.946001 0.324164i \(-0.105083\pi\)
−0.753735 + 0.657179i \(0.771750\pi\)
\(264\) 32.1751 + 9.55077i 1.98024 + 0.587809i
\(265\) 0 0
\(266\) −0.853695 + 1.47864i −0.0523434 + 0.0906614i
\(267\) 3.77121 3.57463i 0.230794 0.218764i
\(268\) 20.4130 + 35.3563i 1.24692 + 2.15973i
\(269\) 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 \(0.435712\pi\)
\(272\) −10.0096 17.3371i −0.606921 1.05122i
\(273\) −0.853695 + 0.809197i −0.0516680 + 0.0489748i
\(274\) −7.12763 + 12.3454i −0.430596 + 0.745814i
\(275\) 0 0
\(276\) −29.6140 8.79054i −1.78255 0.529128i
\(277\) 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
\(279\) 21.9627 + 14.2985i 1.31487 + 0.856031i
\(280\) 0 0
\(281\) 7.77394 + 13.4649i 0.463754 + 0.803246i 0.999144 0.0413590i \(-0.0131687\pi\)
−0.535390 + 0.844605i \(0.679835\pi\)
\(282\) 4.93205 + 20.5955i 0.293699 + 1.22644i
\(283\) 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
\(288\) −8.76394 5.70566i −0.516420 0.336209i
\(289\) −5.97173 −0.351278
\(290\) 0 0
\(291\) 20.3492 + 6.04039i 1.19289 + 0.354094i
\(292\) 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 \(0.179477\pi\)
\(294\) −21.2877 + 20.1781i −1.24152 + 1.17681i
\(295\) 0 0
\(296\) 1.70739 0.0992400
\(297\) −5.78807 + 16.2561i −0.335858 + 0.943276i
\(298\) −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
\(303\) 19.3774 + 5.75194i 1.11320 + 0.330440i
\(304\) 3.98133 + 6.89586i 0.228345 + 0.395505i
\(305\) 0 0
\(306\) 22.3305 11.3457i 1.27655 0.648592i
\(307\) 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
\(309\) 0.118031 + 0.492881i 0.00671458 + 0.0280390i
\(310\) 0 0
\(311\) −4.81635 + 8.34216i −0.273110 + 0.473040i −0.969657 0.244471i \(-0.921386\pi\)
0.696547 + 0.717512i \(0.254719\pi\)
\(312\) 3.10896 + 12.9825i 0.176010 + 0.734991i
\(313\) −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 \(-0.973043\pi\)
0.424955 0.905215i \(-0.360290\pi\)
\(318\) −20.9909 6.23089i −1.17711 0.349411i
\(319\) −2.30221 + 3.98755i −0.128899 + 0.223260i
\(320\) 0 0
\(321\) 2.35369 2.23101i 0.131370 0.124523i
\(322\) −2.66771 4.62061i −0.148666 0.257497i
\(323\) −4.38650 −0.244072
\(324\) 22.9298 31.4085i 1.27388 1.74492i
\(325\) 0 0
\(326\) −19.7453 34.1998i −1.09359 1.89415i
\(327\) −6.97406 + 6.61054i −0.385666 + 0.365564i
\(328\) −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
\(333\) −0.0469471 + 0.876576i −0.00257269 + 0.0480360i
\(334\) 15.4996 0.848100
\(335\) 0 0
\(336\) −1.25020 5.22064i −0.0682040 0.284809i
\(337\) 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
\(339\) 3.14683 + 13.1407i 0.170913 + 0.713704i
\(340\) 0 0
\(341\) −29.0101 −1.57099
\(342\) −8.88197 + 4.51277i −0.480282 + 0.244023i
\(343\) −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 \(-0.0373226\pi\)
\(348\) 7.53101 7.13846i 0.403704 0.382662i
\(349\) 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
\(351\) −6.75073 + 1.23917i −0.360327 + 0.0661420i
\(352\) 11.5761 0.617011
\(353\) 9.41478 + 16.3069i 0.501098 + 0.867927i 0.999999 + 0.00126845i \(0.000403761\pi\)
−0.498901 + 0.866659i \(0.666263\pi\)
\(354\) −15.8916 + 15.0632i −0.844627 + 0.800602i
\(355\) 0 0
\(356\) 6.48133 11.2260i 0.343510 0.594976i
\(357\) 2.83502 + 0.841540i 0.150045 + 0.0445390i
\(358\) −1.33956 2.32018i −0.0707978 0.122625i
\(359\) −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
\(362\) −15.9271 27.5866i −0.837110 1.44992i
\(363\) −0.0114049 0.0476252i −0.000598604 0.00249968i
\(364\) −1.46719 + 2.54125i −0.0769016 + 0.133198i
\(365\) 0 0
\(366\) 7.45305 + 31.1228i 0.389577 + 1.62681i
\(367\) −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
\(369\) −28.5333 18.5763i −1.48539 0.967044i
\(370\) 0 0
\(371\) −1.29261 2.23887i −0.0671090 0.116236i
\(372\) 62.6747 + 18.6042i 3.24953 + 0.964582i
\(373\) −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
\(378\) 6.60623 1.21265i 0.339788 0.0623717i
\(379\) 15.4713 0.794709 0.397354 0.917665i \(-0.369928\pi\)
0.397354 + 0.917665i \(0.369928\pi\)
\(380\) 0 0
\(381\) 22.4909 21.3186i 1.15225 1.09219i
\(382\) −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 \(0.103574\pi\)
\(384\) 25.3214 + 7.51633i 1.29218 + 0.383566i
\(385\) 0 0
\(386\) 67.1715 3.41894
\(387\) 27.6796 14.0635i 1.40704 0.714890i
\(388\) 52.9536 2.68831
\(389\) 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
\(392\) −19.6514 + 34.0372i −0.992544 + 1.71914i
\(393\) 2.42024 + 10.1066i 0.122085 + 0.509808i
\(394\) 17.9198 + 31.0381i 0.902789 + 1.56368i
\(395\) 0 0
\(396\) −2.30221 + 42.9859i −0.115690 + 2.16012i
\(397\) 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
\(399\) −1.12763 0.334723i −0.0564522 0.0167571i
\(400\) 0 0
\(401\) 9.24980 16.0211i 0.461913 0.800057i −0.537143 0.843491i \(-0.680497\pi\)
0.999056 + 0.0434343i \(0.0138299\pi\)
\(402\) −29.8615 + 28.3050i −1.48936 + 1.41172i
\(403\) −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
\(408\) 24.3588 23.0891i 1.20594 1.14308i
\(409\) 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
\(411\) −9.41478 2.79466i −0.464397 0.137850i
\(412\) 0.632168 + 1.09495i 0.0311447 + 0.0539442i
\(413\) −2.58522 −0.127210
\(414\) 1.66498 31.0877i 0.0818292 1.52788i
\(415\) 0 0
\(416\) 2.30221 + 3.98755i 0.112875 + 0.195506i
\(417\) −3.22699 13.4754i −0.158026 0.659893i
\(418\) 5.51414 9.55077i 0.269705 0.467143i
\(419\) 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 \(0.716732\pi\)
\(422\) 13.5196 0.658124
\(423\) −13.0073 + 6.60876i −0.632435 + 0.321329i
\(424\) −29.3401 −1.42488
\(425\) 0 0
\(426\) −37.5333 11.1413i −1.81850 0.539797i
\(427\) −1.88924 + 3.27225i −0.0914266 + 0.158355i
\(428\) 4.04514 7.00639i 0.195529 0.338667i
\(429\) 5.51414 5.22672i 0.266225 0.252348i
\(430\) 0 0
\(431\) −32.7549 −1.57775 −0.788873 0.614556i \(-0.789335\pi\)
−0.788873 + 0.614556i \(0.789335\pi\)
\(432\) 10.5069 29.5091i 0.505512 1.41976i
\(433\) 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
\(438\) 25.2835 + 7.50509i 1.20809 + 0.358607i
\(439\) −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
\(441\) −16.9344 11.0249i −0.806399 0.524997i
\(442\) −11.0283 −0.524561
\(443\) −14.5876 25.2664i −0.693076 1.20044i −0.970825 0.239789i \(-0.922922\pi\)
0.277750 0.960654i \(-0.410411\pi\)
\(444\) 0.510000 + 2.12968i 0.0242035 + 0.101070i
\(445\) 0 0
\(446\) −10.8920 + 18.8654i −0.515750 + 0.893305i
\(447\) −7.12397 29.7486i −0.336952 1.40706i
\(448\) 0.846426 + 1.46605i 0.0399899 + 0.0692645i
\(449\) 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
\(452\) 16.8542 + 29.1924i 0.792756 + 1.37309i
\(453\) 2.09936 + 0.623167i 0.0986365 + 0.0292790i
\(454\) −4.17458 + 7.23058i −0.195923 + 0.339348i
\(455\) 0 0
\(456\) −9.68872 + 9.18370i −0.453716 + 0.430066i
\(457\) −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
\(459\) 11.1842 + 13.1407i 0.522033 + 0.613354i
\(460\) 0 0
\(461\) −2.21285 3.83277i −0.103063 0.178510i 0.809882 0.586592i \(-0.199531\pi\)
−0.912945 + 0.408082i \(0.866198\pi\)
\(462\) −5.39611 + 5.11484i −0.251050 + 0.237964i
\(463\) −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 \(-0.307321\pi\)
0.569026 + 0.822320i \(0.307321\pi\)
\(468\) −15.2649 + 7.75581i −0.705619 + 0.358512i
\(469\) −4.85783 −0.224314
\(470\) 0 0
\(471\) −6.32088 26.3950i −0.291251 1.21622i
\(472\) −14.6700 + 25.4093i −0.675243 + 1.16956i
\(473\) −17.1842 + 29.7639i −0.790129 + 1.36854i
\(474\) −8.17044 34.1185i −0.375281 1.56711i
\(475\) 0 0
\(476\) 7.37743 0.338144
\(477\) 0.806748 15.0632i 0.0369384 0.689698i
\(478\) 10.5561 0.482827
\(479\) −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
\(482\) 4.53101 7.84793i 0.206382 0.357464i
\(483\) 2.66771 2.52866i 0.121385 0.115058i
\(484\) −0.0610840 0.105801i −0.00277655 0.00480912i
\(485\) 0 0
\(486\) 36.1651 + 15.1017i 1.64048 + 0.685025i
\(487\) 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
\(489\) 19.7453 18.7161i 0.892912 0.846369i
\(490\) 0 0
\(491\) −7.22153 + 12.5081i −0.325903 + 0.564480i −0.981695 0.190461i \(-0.939002\pi\)
0.655792 + 0.754942i \(0.272335\pi\)
\(492\) −81.4254 24.1701i −3.67094 1.08967i
\(493\) 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
\(498\) −1.56422 6.53192i −0.0700942 0.292702i
\(499\) −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
\(501\) 2.48679 + 10.3844i 0.111102 + 0.463943i
\(502\) −8.64591 14.9751i −0.385886 0.668374i
\(503\) 5.31728 0.237086 0.118543 0.992949i \(-0.462178\pi\)
0.118543 + 0.992949i \(0.462178\pi\)
\(504\) 8.02374 4.07672i 0.357406 0.181591i
\(505\) 0 0
\(506\) 17.2311 + 29.8452i 0.766017 + 1.32678i
\(507\) −18.6887 5.54750i −0.829995 0.246373i
\(508\) 38.6537 66.9502i 1.71498 2.97043i
\(509\) −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
\(512\) 49.3365 2.18038
\(513\) −4.44852 5.22672i −0.196407 0.230765i
\(514\) −45.2545 −1.99609
\(515\) 0 0
\(516\) 56.2130 53.2829i 2.47464 2.34565i
\(517\) 8.07522 13.9867i 0.355148 0.615134i
\(518\) −0.189116 + 0.327558i −0.00830927 + 0.0143921i
\(519\) −14.2553 4.23149i −0.625737 0.185742i
\(520\) 0 0
\(521\) 40.1232 1.75783 0.878915 0.476978i \(-0.158268\pi\)
0.878915 + 0.476978i \(0.158268\pi\)
\(522\) 8.76394 + 5.70566i 0.383587 + 0.249730i
\(523\) −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
\(528\) 8.07522 + 33.7209i 0.351429 + 1.46751i
\(529\) 2.98133 + 5.16381i 0.129623 + 0.224513i
\(530\) 0 0
\(531\) −12.6418 8.23028i −0.548606 0.357164i
\(532\) −2.93438 −0.127221
\(533\) 7.49546 + 12.9825i 0.324665 + 0.562336i
\(534\) 12.5237 + 3.71751i 0.541955 + 0.160872i
\(535\) 0 0
\(536\) −27.5661 + 47.7460i −1.19068 + 2.06231i
\(537\) 1.33956 1.26973i 0.0578062 0.0547931i
\(538\) 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
\(543\) 15.9271 15.0969i 0.683498 0.647871i
\(544\) 5.78807 10.0252i 0.248162 0.429829i
\(545\) 0 0
\(546\) −2.83502 0.841540i −0.121328 0.0360146i
\(547\) 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
\(549\) −19.6559 + 9.98682i −0.838894 + 0.426227i
\(550\) 0 0
\(551\) −0.915706 1.58605i −0.0390104 0.0675680i
\(552\) −9.71519 40.5691i −0.413506 1.72674i
\(553\) 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 \(0.619739\pi\)
\(558\) −3.52374 + 65.7937i −0.149172 + 2.78527i
\(559\) −13.6700 −0.578181
\(560\) 0 0
\(561\) −18.3118 5.43563i −0.773125 0.229492i
\(562\) −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 \(0.0783770\pi\)
\(564\) −26.4157 + 25.0388i −1.11230 + 1.05432i
\(565\) 0 0
\(566\) 1.62257 0.0682016
\(567\) 1.87237 + 4.23149i 0.0786321 + 0.177706i
\(568\) −52.4623 −2.20127
\(569\) 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 \(0.304106\pi\)
\(572\) 9.47679 16.4143i 0.396245 0.686316i
\(573\) −28.1186 8.34663i −1.17467 0.348686i
\(574\) −7.33502 12.7046i −0.306158 0.530281i
\(575\) 0 0
\(576\) −0.528274 + 9.86370i −0.0220114 + 0.410987i
\(577\) 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
\(579\) 10.7771 + 45.0037i 0.447883 + 1.87029i
\(580\) 0 0
\(581\) 0.396505 0.686767i 0.0164498 0.0284919i
\(582\) 12.4285 + 51.8995i 0.515179 + 2.15130i
\(583\) 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 \(0.636200\pi\)
\(588\) −48.3255 14.3448i −1.99291 0.591570i
\(589\) 5.76940 9.99290i 0.237724 0.411750i
\(590\) 0 0
\(591\) −17.9198 + 16.9858i −0.737124 + 0.698702i
\(592\) 0.881969 + 1.52761i 0.0362487 + 0.0627846i
\(593\) 9.17872 0.376925 0.188462 0.982080i \(-0.439650\pi\)
0.188462 + 0.982080i \(0.439650\pi\)
\(594\) −42.6706 + 7.83265i −1.75079 + 0.321378i
\(595\) 0 0
\(596\) −38.1555 66.0873i −1.56291 2.70704i
\(597\) 31.0005 29.3846i 1.26877 1.20263i
\(598\) −6.85369 + 11.8709i −0.280268 + 0.485439i
\(599\) 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 \(0.629740\pi\)
\(602\) 13.3774 0.545223
\(603\) −23.7549 15.4653i −0.967373 0.629797i
\(604\) 5.46305 0.222288
\(605\) 0 0
\(606\) 11.8350 + 49.4212i 0.480765 + 2.00760i
\(607\) −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
\(609\) 0.287546 + 1.20075i 0.0116520 + 0.0486568i
\(610\) 0 0
\(611\) 6.42385 0.259881
\(612\) 36.0757 + 23.4867i 1.45828 + 0.949394i
\(613\) 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 −0.931033 0.364935i \(-0.881091\pi\)
0.781559 + 0.623831i \(0.214425\pi\)
\(618\) −0.924779 + 0.876576i −0.0372001 + 0.0352610i
\(619\) −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
\(621\) 21.0953 3.87228i 0.846527 0.155389i
\(622\) −24.2179 −0.971050
\(623\) 0.771205 + 1.33577i 0.0308977 + 0.0535164i
\(624\) −10.0096 + 9.48786i −0.400705 + 0.379818i
\(625\) 0 0
\(626\) 30.8446 53.4245i 1.23280 2.13527i
\(627\) 7.28354 + 2.16202i 0.290876 + 0.0863429i
\(628\) −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
\(633\) 2.16912 + 9.05788i 0.0862146 + 0.360019i
\(634\) 25.5803 44.3064i 1.01592 1.75963i
\(635\) 0 0
\(636\) −8.76394 36.5968i −0.347513 1.45116i
\(637\) 4.44852 + 7.70506i 0.176257 + 0.305285i
\(638\) −11.5761 −0.458304
\(639\) 1.44252 26.9342i 0.0570654 1.06550i
\(640\) 0 0
\(641\) 0.0665480 + 0.115265i 0.00262849 + 0.00455268i 0.867337 0.497722i \(-0.165830\pi\)
−0.864708 + 0.502275i \(0.832497\pi\)
\(642\) 7.81635 + 2.32018i 0.308487 + 0.0915703i
\(643\) −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 \(-0.865394\pi\)
−0.911913 + 0.410385i \(0.865394\pi\)
\(648\) 52.2148 + 5.60907i 2.05119 + 0.220345i
\(649\) 16.6983 0.655466
\(650\) 0 0
\(651\) −5.64591 + 5.35162i −0.221280 + 0.209746i
\(652\) 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 \(-0.0856946\pi\)
\(654\) −23.1600 6.87476i −0.905629 0.268824i
\(655\) 0 0
\(656\) −68.4158 −2.67119
\(657\) −0.971726 + 18.1436i −0.0379106 + 0.707851i
\(658\) −6.28635 −0.245067
\(659\) −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 \(0.883860\pi\)
\(662\) 20.6700 35.8016i 0.803364 1.39147i
\(663\) −1.76940 7.38874i −0.0687178 0.286955i
\(664\) −4.50000 7.79423i −0.174634 0.302475i
\(665\) 0 0
\(666\) −1.96759 + 0.999697i −0.0762425 + 0.0387375i
\(667\) 5.72298 0.221595
\(668\) 13.3191 + 23.0693i 0.515331 + 0.892579i
\(669\) −14.3870 4.27061i −0.556235 0.165111i
\(670\) 0 0
\(671\) 12.2029 21.1360i 0.471086 0.815945i
\(672\) 2.25293 2.13550i 0.0869087 0.0823787i
\(673\) 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 0.688014 0.725697i \(-0.258483\pi\)
−0.972479 + 0.232989i \(0.925149\pi\)
\(678\) −24.6555 + 23.3704i −0.946889 + 0.897533i
\(679\) −3.15044 + 5.45673i −0.120903 + 0.209410i
\(680\) 0 0
\(681\) −5.51414 1.63680i −0.211302 0.0627223i
\(682\) −36.4677 63.1639i −1.39642 2.41867i
\(683\) 4.95252 0.189503 0.0947515 0.995501i \(-0.469794\pi\)
0.0947515 + 0.995501i \(0.469794\pi\)
\(684\) −14.3492 9.34186i −0.548654 0.357195i
\(685\) 0 0
\(686\) −8.87743 15.3762i −0.338942 0.587065i
\(687\) 10.2101 + 42.6359i 0.389540 + 1.62666i
\(688\) 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
\(693\) −4.29261 2.79466i −0.163063 0.106160i
\(694\) 56.0011 2.12577
\(695\) 0 0
\(696\) 13.4335 + 3.98755i 0.509194 + 0.151148i
\(697\) 18.8446 32.6398i 0.713791 1.23632i
\(698\) −3.70012 + 6.40880i −0.140052 + 0.242577i
\(699\) 34.7362 32.9256i 1.31384 1.24536i
\(700\) 0 0
\(701\) −29.3492 −1.10850 −0.554251 0.832349i \(-0.686995\pi\)
−0.554251 + 0.832349i \(0.686995\pi\)
\(702\) −11.1842 13.1407i −0.422120 0.495963i
\(703\) 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
\(708\) −36.0757 10.7086i −1.35581 0.402455i
\(709\) −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
\(711\) 21.5479 10.9481i 0.808108 0.410586i
\(712\) 17.5051 0.656030
\(713\) 18.0288 + 31.2268i 0.675184 + 1.16945i
\(714\) 1.73153 + 7.23058i 0.0648008 + 0.270598i
\(715\) 0 0
\(716\) 2.30221 3.98755i 0.0860377 0.149022i
\(717\) 1.69365 + 7.07243i 0.0632506 + 0.264125i
\(718\) −40.0716 69.4061i −1.49546 2.59021i
\(719\) −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
\(722\) −21.6910 37.5700i −0.807257 1.39821i
\(723\) 5.98494 + 1.77655i 0.222582 + 0.0660706i
\(724\) 27.3729 47.4112i 1.01731 1.76203i
\(725\) 0 0
\(726\) 0.0893579 0.0847002i 0.00331638 0.00314352i
\(727\) 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
\(729\) −4.31542 + 26.6529i −0.159830 + 0.987144i
\(730\) 0 0
\(731\) 17.1842 + 29.7639i 0.635580 + 1.10086i
\(732\) −39.9180 + 37.8373i −1.47541 + 1.39851i
\(733\) −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
\(738\) 4.57795 85.4775i 0.168517 3.14647i
\(739\) 29.7266 1.09351 0.546755 0.837293i \(-0.315863\pi\)
0.546755 + 0.837293i \(0.315863\pi\)
\(740\) 0 0
\(741\) 0.703781 + 2.93888i 0.0258540 + 0.107962i
\(742\) 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 \(-0.180662\pi\)
\(744\) 20.5611 + 85.8599i 0.753806 + 3.14778i
\(745\) 0 0
\(746\) −5.52787 −0.202390
\(747\) 4.12530 2.09599i 0.150937 0.0766883i
\(748\) −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
\(753\) 8.64591 8.19524i 0.315074 0.298651i
\(754\) −2.30221 3.98755i −0.0838416 0.145218i
\(755\) 0 0
\(756\) 7.48173 + 8.79054i 0.272108 + 0.319709i
\(757\) −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
\(759\) −17.2311 + 16.3330i −0.625450 + 0.592849i
\(760\) 0 0
\(761\) −17.7125 + 30.6789i −0.642076 + 1.11211i 0.342893 + 0.939375i \(0.388593\pi\)
−0.984969 + 0.172734i \(0.944740\pi\)
\(762\) 74.6898 + 22.1707i 2.70572 + 0.803160i
\(763\) −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
\(768\) 12.8091 + 53.4887i 0.462208 + 1.93011i
\(769\) −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
\(771\) −7.26073 30.3197i −0.261489 1.09194i
\(772\) 57.7217 + 99.9768i 2.07745 + 3.59825i
\(773\) −12.6599 −0.455345 −0.227673 0.973738i \(-0.573112\pi\)
−0.227673 + 0.973738i \(0.573112\pi\)
\(774\) 65.4158 + 42.5882i 2.35132 + 1.53080i
\(775\) 0 0
\(776\) 35.7549 + 61.9292i 1.28352 + 2.22313i
\(777\) −0.249800 0.0741499i −0.00896153 0.00266011i
\(778\) −30.9650 + 53.6329i −1.11015 + 1.92283i
\(779\) −7.49546 + 12.9825i −0.268553 + 0.465147i
\(780\) 0 0